For nest-cam v350 release
diff --git a/CMakeLists.txt b/CMakeLists.txt
new file mode 100644
index 0000000..a57caee
--- /dev/null
+++ b/CMakeLists.txt
@@ -0,0 +1,684 @@
+# cmake_minimum_require must be the first command of the file
+cmake_minimum_required(VERSION 3.10.0)
+
+# NOTE Remove setting the policy once the minimum required CMake version is
+# increased to at least 3.15. Retain enabling the export to package registry.
+if (POLICY CMP0090)
+ # The export command does not populate package registry by default
+ cmake_policy (SET CMP0090 NEW)
+
+ # Unless otherwise specified, always export to package registry to ensure
+ # backwards compatibility.
+ if (NOT DEFINED CMAKE_EXPORT_PACKAGE_REGISTRY)
+ set (CMAKE_EXPORT_PACKAGE_REGISTRY ON)
+ endif (NOT DEFINED CMAKE_EXPORT_PACKAGE_REGISTRY)
+endif (POLICY CMP0090)
+
+project(Eigen3)
+
+# Remove this block after bumping CMake to v3.21.0
+# PROJECT_IS_TOP_LEVEL is defined then by default
+if(CMAKE_VERSION VERSION_LESS 3.21.0)
+ if(CMAKE_SOURCE_DIR STREQUAL CMAKE_CURRENT_SOURCE_DIR)
+ set(PROJECT_IS_TOP_LEVEL TRUE)
+ else()
+ set(PROJECT_IS_TOP_LEVEL FALSE)
+ endif()
+endif()
+
+set(CMAKE_CXX_STANDARD 14 CACHE STRING "Default C++ standard")
+set(CMAKE_CXX_STANDARD_REQUIRED ON CACHE BOOL "Require C++ standard")
+set(CMAKE_CXX_EXTENSIONS OFF CACHE BOOL "Allow C++ extensions")
+
+# guard against in-source builds
+
+if(${CMAKE_SOURCE_DIR} STREQUAL ${CMAKE_BINARY_DIR})
+ message(FATAL_ERROR "In-source builds not allowed. Please make a new directory (called a build directory) and run CMake from there. You may need to remove CMakeCache.txt. ")
+endif()
+
+
+# Alias Eigen_*_DIR to Eigen3_*_DIR:
+
+set(Eigen_SOURCE_DIR ${Eigen3_SOURCE_DIR})
+set(Eigen_BINARY_DIR ${Eigen3_BINARY_DIR})
+
+# guard against bad build-type strings
+
+if (NOT CMAKE_BUILD_TYPE)
+ set(CMAKE_BUILD_TYPE "Release")
+endif()
+
+
+#############################################################################
+# retrieve version information #
+#############################################################################
+
+# automatically parse the version number
+file(READ "${PROJECT_SOURCE_DIR}/Eigen/src/Core/util/Macros.h" _eigen_version_header)
+string(REGEX MATCH "define[ \t]+EIGEN_WORLD_VERSION[ \t]+([0-9]+)" _eigen_world_version_match "${_eigen_version_header}")
+set(EIGEN_WORLD_VERSION "${CMAKE_MATCH_1}")
+string(REGEX MATCH "define[ \t]+EIGEN_MAJOR_VERSION[ \t]+([0-9]+)" _eigen_major_version_match "${_eigen_version_header}")
+set(EIGEN_MAJOR_VERSION "${CMAKE_MATCH_1}")
+string(REGEX MATCH "define[ \t]+EIGEN_MINOR_VERSION[ \t]+([0-9]+)" _eigen_minor_version_match "${_eigen_version_header}")
+set(EIGEN_MINOR_VERSION "${CMAKE_MATCH_1}")
+set(EIGEN_VERSION_NUMBER ${EIGEN_WORLD_VERSION}.${EIGEN_MAJOR_VERSION}.${EIGEN_MINOR_VERSION})
+
+# if we are not in a git clone
+if(IS_DIRECTORY ${CMAKE_SOURCE_DIR}/.git)
+ # if the git program is absent or this will leave the EIGEN_GIT_REVNUM string empty,
+ # but won't stop CMake.
+ execute_process(COMMAND git ls-remote --refs -q ${CMAKE_SOURCE_DIR} HEAD OUTPUT_VARIABLE EIGEN_GIT_OUTPUT)
+endif()
+
+# extract the git rev number from the git output...
+if(EIGEN_GIT_OUTPUT)
+string(REGEX MATCH "^([0-9;a-f]+).*" EIGEN_GIT_CHANGESET_MATCH "${EIGEN_GIT_OUTPUT}")
+set(EIGEN_GIT_REVNUM "${CMAKE_MATCH_1}")
+endif()
+#...and show it next to the version number
+if(EIGEN_GIT_REVNUM)
+ set(EIGEN_VERSION "${EIGEN_VERSION_NUMBER} (git rev ${EIGEN_GIT_REVNUM})")
+else()
+ set(EIGEN_VERSION "${EIGEN_VERSION_NUMBER}")
+endif()
+
+include(CheckCXXCompilerFlag)
+include(GNUInstallDirs)
+include(CMakeDependentOption)
+
+set(CMAKE_MODULE_PATH ${PROJECT_SOURCE_DIR}/cmake)
+
+macro(ei_add_cxx_compiler_flag FLAG)
+ string(REGEX REPLACE "-" "" SFLAG1 ${FLAG})
+ string(REGEX REPLACE "\\+" "p" SFLAG ${SFLAG1})
+ check_cxx_compiler_flag(${FLAG} COMPILER_SUPPORT_${SFLAG})
+ if(COMPILER_SUPPORT_${SFLAG})
+ set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} ${FLAG}")
+ endif()
+endmacro()
+
+# Determine if we should build shared libraries on this platform.
+get_cmake_property(EIGEN_BUILD_SHARED_LIBS TARGET_SUPPORTS_SHARED_LIBS)
+
+#############################################################################
+# find how to link to the standard libraries #
+#############################################################################
+
+find_package(StandardMathLibrary)
+
+
+set(EIGEN_TEST_CUSTOM_LINKER_FLAGS "" CACHE STRING "Additional linker flags when linking unit tests.")
+set(EIGEN_TEST_CUSTOM_CXX_FLAGS "" CACHE STRING "Additional compiler flags when compiling unit tests.")
+# convert space separated argument into CMake lists for downstream consumption
+separate_arguments(EIGEN_TEST_CUSTOM_CXX_FLAGS NATIVE_COMMAND ${EIGEN_TEST_CUSTOM_CXX_FLAGS})
+
+set(EIGEN_STANDARD_LIBRARIES_TO_LINK_TO "")
+
+if(NOT STANDARD_MATH_LIBRARY_FOUND)
+
+ message(FATAL_ERROR
+ "Can't link to the standard math library. Please report to the Eigen developers, telling them about your platform.")
+
+else()
+ if(EIGEN_STANDARD_LIBRARIES_TO_LINK_TO)
+ set(EIGEN_STANDARD_LIBRARIES_TO_LINK_TO "${EIGEN_STANDARD_LIBRARIES_TO_LINK_TO} ${STANDARD_MATH_LIBRARY}")
+ else()
+ set(EIGEN_STANDARD_LIBRARIES_TO_LINK_TO "${STANDARD_MATH_LIBRARY}")
+ endif()
+endif()
+
+if(EIGEN_STANDARD_LIBRARIES_TO_LINK_TO)
+ message(STATUS "Standard libraries to link to explicitly: ${EIGEN_STANDARD_LIBRARIES_TO_LINK_TO}")
+else()
+ message(STATUS "Standard libraries to link to explicitly: none")
+endif()
+
+option(EIGEN_BUILD_BTL "Build benchmark suite" OFF)
+option(EIGEN_BUILD_SPBENCH "Build sparse benchmark suite" OFF)
+
+# Disable pkgconfig only for native Windows builds
+if(NOT WIN32 OR NOT CMAKE_HOST_SYSTEM_NAME MATCHES Windows)
+ option(EIGEN_BUILD_PKGCONFIG "Build pkg-config .pc file for Eigen" ON)
+endif()
+
+set(CMAKE_INCLUDE_CURRENT_DIR OFF)
+
+option(EIGEN_SPLIT_LARGE_TESTS "Split large tests into smaller executables" ON)
+
+option(EIGEN_DEFAULT_TO_ROW_MAJOR "Use row-major as default matrix storage order" OFF)
+if(EIGEN_DEFAULT_TO_ROW_MAJOR)
+ add_definitions("-DEIGEN_DEFAULT_TO_ROW_MAJOR")
+endif()
+
+set(EIGEN_TEST_MAX_SIZE "320" CACHE STRING "Maximal matrix/vector size, default is 320")
+
+if(NOT MSVC)
+ # We assume that other compilers are partly compatible with GNUCC
+
+ # clang outputs some warnings for unknown flags that are not caught by check_cxx_compiler_flag
+ # adding -Werror turns such warnings into errors
+ check_cxx_compiler_flag("-Werror" COMPILER_SUPPORT_WERROR)
+ if(COMPILER_SUPPORT_WERROR)
+ set(CMAKE_REQUIRED_FLAGS "-Werror")
+ endif()
+ ei_add_cxx_compiler_flag("-pedantic")
+ ei_add_cxx_compiler_flag("-Wall")
+ ei_add_cxx_compiler_flag("-Wextra")
+ #ei_add_cxx_compiler_flag("-Weverything") # clang
+
+ ei_add_cxx_compiler_flag("-Wundef")
+ ei_add_cxx_compiler_flag("-Wcast-align")
+ ei_add_cxx_compiler_flag("-Wchar-subscripts")
+ ei_add_cxx_compiler_flag("-Wnon-virtual-dtor")
+ ei_add_cxx_compiler_flag("-Wunused-local-typedefs")
+ ei_add_cxx_compiler_flag("-Wpointer-arith")
+ ei_add_cxx_compiler_flag("-Wwrite-strings")
+ ei_add_cxx_compiler_flag("-Wformat-security")
+ ei_add_cxx_compiler_flag("-Wshorten-64-to-32")
+ ei_add_cxx_compiler_flag("-Wlogical-op")
+ ei_add_cxx_compiler_flag("-Wenum-conversion")
+ ei_add_cxx_compiler_flag("-Wc++11-extensions")
+ ei_add_cxx_compiler_flag("-Wdouble-promotion")
+# ei_add_cxx_compiler_flag("-Wconversion")
+
+ ei_add_cxx_compiler_flag("-Wshadow")
+
+ ei_add_cxx_compiler_flag("-Wno-psabi")
+ ei_add_cxx_compiler_flag("-Wno-variadic-macros")
+ ei_add_cxx_compiler_flag("-Wno-long-long")
+
+ ei_add_cxx_compiler_flag("-fno-check-new")
+ ei_add_cxx_compiler_flag("-fno-common")
+ ei_add_cxx_compiler_flag("-fstrict-aliasing")
+ ei_add_cxx_compiler_flag("-wd981") # disable ICC's "operands are evaluated in unspecified order" remark
+ ei_add_cxx_compiler_flag("-wd2304") # disable ICC's "warning #2304: non-explicit constructor with single argument may cause implicit type conversion" produced by -Wnon-virtual-dtor
+
+ if(ANDROID_NDK)
+ ei_add_cxx_compiler_flag("-pie")
+ ei_add_cxx_compiler_flag("-fPIE")
+ endif()
+
+ set(CMAKE_REQUIRED_FLAGS "")
+
+ option(EIGEN_TEST_SSE2 "Enable/Disable SSE2 in tests/examples" OFF)
+ if(EIGEN_TEST_SSE2)
+ set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -msse2")
+ message(STATUS "Enabling SSE2 in tests/examples")
+ endif()
+
+ option(EIGEN_TEST_SSE3 "Enable/Disable SSE3 in tests/examples" OFF)
+ if(EIGEN_TEST_SSE3)
+ set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -msse3")
+ message(STATUS "Enabling SSE3 in tests/examples")
+ endif()
+
+ option(EIGEN_TEST_SSSE3 "Enable/Disable SSSE3 in tests/examples" OFF)
+ if(EIGEN_TEST_SSSE3)
+ set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -mssse3")
+ message(STATUS "Enabling SSSE3 in tests/examples")
+ endif()
+
+ option(EIGEN_TEST_SSE4_1 "Enable/Disable SSE4.1 in tests/examples" OFF)
+ if(EIGEN_TEST_SSE4_1)
+ set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -msse4.1")
+ message(STATUS "Enabling SSE4.1 in tests/examples")
+ endif()
+
+ option(EIGEN_TEST_SSE4_2 "Enable/Disable SSE4.2 in tests/examples" OFF)
+ if(EIGEN_TEST_SSE4_2)
+ set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -msse4.2")
+ message(STATUS "Enabling SSE4.2 in tests/examples")
+ endif()
+
+ option(EIGEN_TEST_AVX "Enable/Disable AVX in tests/examples" OFF)
+ if(EIGEN_TEST_AVX)
+ set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -mavx")
+ message(STATUS "Enabling AVX in tests/examples")
+ endif()
+
+ option(EIGEN_TEST_FMA "Enable/Disable FMA in tests/examples" OFF)
+ if(EIGEN_TEST_FMA AND NOT EIGEN_TEST_NEON)
+ set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -mfma")
+ message(STATUS "Enabling FMA in tests/examples")
+ endif()
+
+ option(EIGEN_TEST_AVX2 "Enable/Disable AVX2 in tests/examples" OFF)
+ if(EIGEN_TEST_AVX2)
+ set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -mavx2 -mfma")
+ message(STATUS "Enabling AVX2 in tests/examples")
+ endif()
+
+ option(EIGEN_TEST_AVX512 "Enable/Disable AVX512 in tests/examples" OFF)
+ if(EIGEN_TEST_AVX512)
+ set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -mavx512f -mfma")
+ message(STATUS "Enabling AVX512 in tests/examples")
+ endif()
+
+ option(EIGEN_TEST_AVX512DQ "Enable/Disable AVX512DQ in tests/examples" OFF)
+ if(EIGEN_TEST_AVX512DQ)
+ set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -mavx512dq -mfma")
+ message(STATUS "Enabling AVX512DQ in tests/examples")
+ endif()
+
+ option(EIGEN_TEST_AVX512FP16 "Enable/Disable AVX512-FP16 in tests/examples" OFF)
+ if(EIGEN_TEST_AVX512FP16)
+ set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -mavx512f -mfma -mavx512vl -mavx512fp16")
+ message(STATUS "Enabling AVX512-FP16 in tests/examples")
+ endif()
+
+ option(EIGEN_TEST_F16C "Enable/Disable F16C in tests/examples" OFF)
+ if(EIGEN_TEST_F16C)
+ set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -mf16c")
+ message(STATUS "Enabling F16C in tests/examples")
+ endif()
+
+ option(EIGEN_TEST_ALTIVEC "Enable/Disable AltiVec in tests/examples" OFF)
+ if(EIGEN_TEST_ALTIVEC)
+ set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -maltivec -mabi=altivec")
+ message(STATUS "Enabling AltiVec in tests/examples")
+ endif()
+
+ option(EIGEN_TEST_VSX "Enable/Disable VSX in tests/examples" OFF)
+ if(EIGEN_TEST_VSX)
+ set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -m64 -mvsx")
+ message(STATUS "Enabling VSX in tests/examples")
+ endif()
+
+ option(EIGEN_TEST_MSA "Enable/Disable MSA in tests/examples" OFF)
+ if(EIGEN_TEST_MSA)
+ set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -mmsa")
+ message(STATUS "Enabling MSA in tests/examples")
+ endif()
+
+ option(EIGEN_TEST_NEON "Enable/Disable Neon in tests/examples" OFF)
+ if(EIGEN_TEST_NEON)
+ if(EIGEN_TEST_FMA)
+ set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -mfpu=neon-vfpv4")
+ else()
+ set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -mfpu=neon")
+ endif()
+ set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -mfloat-abi=hard")
+ message(STATUS "Enabling NEON in tests/examples")
+ endif()
+
+ option(EIGEN_TEST_NEON64 "Enable/Disable Neon in tests/examples" OFF)
+ if(EIGEN_TEST_NEON64)
+ set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS}")
+ message(STATUS "Enabling NEON in tests/examples")
+ endif()
+
+ option(EIGEN_TEST_Z13 "Enable/Disable S390X(zEC13) ZVECTOR in tests/examples" OFF)
+ if(EIGEN_TEST_Z13)
+ set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -march=z13 -mzvector")
+ message(STATUS "Enabling S390X(zEC13) ZVECTOR in tests/examples")
+ endif()
+
+ option(EIGEN_TEST_Z14 "Enable/Disable S390X(zEC14) ZVECTOR in tests/examples" OFF)
+ if(EIGEN_TEST_Z14)
+ set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -march=z14 -mzvector")
+ message(STATUS "Enabling S390X(zEC13) ZVECTOR in tests/examples")
+ endif()
+
+ check_cxx_compiler_flag("-fopenmp" COMPILER_SUPPORT_OPENMP)
+ if(COMPILER_SUPPORT_OPENMP)
+ option(EIGEN_TEST_OPENMP "Enable/Disable OpenMP in tests/examples" OFF)
+ if(EIGEN_TEST_OPENMP)
+ set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -fopenmp")
+ message(STATUS "Enabling OpenMP in tests/examples")
+ endif()
+ endif()
+
+else()
+
+ # C4127 - conditional expression is constant
+ # C4714 - marked as __forceinline not inlined (I failed to deactivate it selectively)
+ # We can disable this warning in the unit tests since it is clear that it occurs
+ # because we are oftentimes returning objects that have a destructor or may
+ # throw exceptions - in particular in the unit tests we are throwing extra many
+ # exceptions to cover indexing errors.
+ # C4505 - unreferenced local function has been removed (impossible to deactivate selectively)
+ set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} /EHsc /wd4127 /wd4505 /wd4714")
+
+ # replace all /Wx by /W4
+ string(REGEX REPLACE "/W[0-9]" "/W4" CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS}")
+
+ check_cxx_compiler_flag("/openmp" COMPILER_SUPPORT_OPENMP)
+ if(COMPILER_SUPPORT_OPENMP)
+ option(EIGEN_TEST_OPENMP "Enable/Disable OpenMP in tests/examples" OFF)
+ if(EIGEN_TEST_OPENMP)
+ set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} /openmp")
+ message(STATUS "Enabling OpenMP in tests/examples")
+ endif()
+ endif()
+
+ option(EIGEN_TEST_SSE2 "Enable/Disable SSE2 in tests/examples" OFF)
+ if(EIGEN_TEST_SSE2)
+ if(NOT CMAKE_CL_64)
+ # arch is not supported on 64 bit systems, SSE is enabled automatically.
+ set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} /arch:SSE2")
+ endif()
+ message(STATUS "Enabling SSE2 in tests/examples")
+ endif()
+
+ option(EIGEN_TEST_AVX "Enable/Disable AVX in tests/examples" OFF)
+ if(EIGEN_TEST_AVX)
+ set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} /arch:AVX")
+ message(STATUS "Enabling AVX in tests/examples")
+ endif()
+
+ option(EIGEN_TEST_FMA "Enable/Disable FMA/AVX2 in tests/examples" OFF)
+ option(EIGEN_TEST_AVX2 "Enable/Disable FMA/AVX2 in tests/examples" OFF)
+ if((EIGEN_TEST_FMA AND NOT EIGEN_TEST_NEON) OR EIGEN_TEST_AVX2)
+ set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} /arch:AVX2")
+ message(STATUS "Enabling FMA/AVX2 in tests/examples")
+ endif()
+
+ option(EIGEN_TEST_AVX512 "Enable/Disable AVX512 in tests/examples" OFF)
+ option(EIGEN_TEST_AVX512DQ "Enable/Disable AVX512DQ in tests/examples" OFF)
+ if(EIGEN_TEST_AVX512 OR EIGEN_TEST_AVX512DQ)
+ set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} /arch:AVX512")
+ message(STATUS "Enabling AVX512 in tests/examples")
+ endif()
+
+endif()
+
+option(EIGEN_TEST_NO_EXPLICIT_VECTORIZATION "Disable explicit vectorization in tests/examples" OFF)
+option(EIGEN_TEST_X87 "Force using X87 instructions. Implies no vectorization." OFF)
+option(EIGEN_TEST_32BIT "Force generating 32bit code." OFF)
+
+if(EIGEN_TEST_X87)
+ set(EIGEN_TEST_NO_EXPLICIT_VECTORIZATION ON)
+ if(CMAKE_COMPILER_IS_GNUCXX)
+ set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -mfpmath=387")
+ message(STATUS "Forcing use of x87 instructions in tests/examples")
+ else()
+ message(STATUS "EIGEN_TEST_X87 ignored on your compiler")
+ endif()
+endif()
+
+if(EIGEN_TEST_32BIT)
+ if(CMAKE_COMPILER_IS_GNUCXX)
+ set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -m32")
+ message(STATUS "Forcing generation of 32-bit code in tests/examples")
+ else()
+ message(STATUS "EIGEN_TEST_32BIT ignored on your compiler")
+ endif()
+endif()
+
+if(EIGEN_TEST_NO_EXPLICIT_VECTORIZATION)
+ add_definitions(-DEIGEN_DONT_VECTORIZE=1)
+ message(STATUS "Disabling vectorization in tests/examples")
+endif()
+
+option(EIGEN_TEST_NO_EXPLICIT_ALIGNMENT "Disable explicit alignment (hence vectorization) in tests/examples" OFF)
+if(EIGEN_TEST_NO_EXPLICIT_ALIGNMENT)
+ add_definitions(-DEIGEN_DONT_ALIGN=1)
+ message(STATUS "Disabling alignment in tests/examples")
+endif()
+
+option(EIGEN_TEST_NO_EXCEPTIONS "Disables C++ exceptions" OFF)
+if(EIGEN_TEST_NO_EXCEPTIONS)
+ ei_add_cxx_compiler_flag("-fno-exceptions")
+ message(STATUS "Disabling exceptions in tests/examples")
+endif()
+
+set(EIGEN_CUDA_CXX_FLAGS "" CACHE STRING "Additional flags to pass to the cuda compiler.")
+set(EIGEN_CUDA_COMPUTE_ARCH 30 CACHE STRING "The CUDA compute architecture(s) to target when compiling CUDA code")
+
+include_directories(${CMAKE_CURRENT_SOURCE_DIR})
+
+# Backward compatibility support for EIGEN_INCLUDE_INSTALL_DIR
+if(EIGEN_INCLUDE_INSTALL_DIR)
+ message(WARNING "EIGEN_INCLUDE_INSTALL_DIR is deprecated. Use INCLUDE_INSTALL_DIR instead.")
+endif()
+
+if(EIGEN_INCLUDE_INSTALL_DIR AND NOT INCLUDE_INSTALL_DIR)
+ set(INCLUDE_INSTALL_DIR ${EIGEN_INCLUDE_INSTALL_DIR}
+ CACHE PATH "The directory relative to CMAKE_INSTALL_PREFIX where Eigen header files are installed")
+else()
+ set(INCLUDE_INSTALL_DIR
+ "${CMAKE_INSTALL_INCLUDEDIR}/eigen3"
+ CACHE PATH "The directory relative to CMAKE_INSTALL_PREFIX where Eigen header files are installed"
+ )
+endif()
+set(CMAKEPACKAGE_INSTALL_DIR
+ "${CMAKE_INSTALL_DATADIR}/eigen3/cmake"
+ CACHE PATH "The directory relative to CMAKE_INSTALL_PREFIX where Eigen3Config.cmake is installed"
+ )
+set(PKGCONFIG_INSTALL_DIR
+ "${CMAKE_INSTALL_DATADIR}/pkgconfig"
+ CACHE PATH "The directory relative to CMAKE_INSTALL_PREFIX where eigen3.pc is installed"
+ )
+
+foreach(var INCLUDE_INSTALL_DIR CMAKEPACKAGE_INSTALL_DIR PKGCONFIG_INSTALL_DIR)
+ # If an absolute path is specified, make it relative to "{CMAKE_INSTALL_PREFIX}".
+ if(IS_ABSOLUTE "${${var}}")
+ file(RELATIVE_PATH "${var}" "${CMAKE_INSTALL_PREFIX}" "${${var}}")
+ endif()
+endforeach()
+
+install(FILES
+ signature_of_eigen3_matrix_library
+ DESTINATION ${INCLUDE_INSTALL_DIR} COMPONENT Devel
+ )
+
+if(EIGEN_BUILD_PKGCONFIG)
+ configure_file(eigen3.pc.in eigen3.pc @ONLY)
+ install(FILES ${CMAKE_CURRENT_BINARY_DIR}/eigen3.pc
+ DESTINATION ${PKGCONFIG_INSTALL_DIR}
+ )
+endif()
+
+install(DIRECTORY Eigen DESTINATION ${INCLUDE_INSTALL_DIR} COMPONENT Devel)
+
+
+option(EIGEN_BUILD_DOC "Enable creation of Eigen documentation" ON)
+if(EIGEN_BUILD_DOC)
+ add_subdirectory(doc EXCLUDE_FROM_ALL)
+endif()
+
+
+cmake_dependent_option(BUILD_TESTING "Enable creation of tests." ON "PROJECT_IS_TOP_LEVEL" OFF)
+option(EIGEN_BUILD_TESTING "Enable creation of Eigen tests." ${BUILD_TESTING})
+if(EIGEN_BUILD_TESTING)
+ include(EigenConfigureTesting)
+
+ if(EIGEN_LEAVE_TEST_IN_ALL_TARGET)
+ add_subdirectory(test) # can't do EXCLUDE_FROM_ALL here, breaks CTest
+ else()
+ add_subdirectory(test EXCLUDE_FROM_ALL)
+ endif()
+
+ add_subdirectory(failtest)
+endif()
+
+include(CMakeDetermineFortranCompiler)
+option(EIGEN_BUILD_BLAS "Toggles the building of the Eigen Blas library" ${CMAKE_Fortran_COMPILER})
+option(EIGEN_BUILD_LAPACK "Toggles the building of the included Eigen LAPACK library" ${CMAKE_Fortran_COMPILER})
+if(EIGEN_LEAVE_TEST_IN_ALL_TARGET)
+ add_subdirectory(blas)
+ add_subdirectory(lapack)
+else()
+ add_subdirectory(blas EXCLUDE_FROM_ALL)
+ add_subdirectory(lapack EXCLUDE_FROM_ALL)
+endif()
+
+# add SYCL
+option(EIGEN_TEST_SYCL "Add Sycl support." OFF)
+option(EIGEN_SYCL_TRISYCL "Use the triSYCL Sycl implementation (ComputeCPP by default)." OFF)
+if(EIGEN_TEST_SYCL)
+ set (CMAKE_MODULE_PATH "${CMAKE_ROOT}/Modules" "cmake/Modules/" "${CMAKE_MODULE_PATH}")
+ find_package(Threads REQUIRED)
+ if(EIGEN_SYCL_TRISYCL)
+ message(STATUS "Using triSYCL")
+ include(FindTriSYCL)
+ else()
+ message(STATUS "Using ComputeCPP SYCL")
+ include(FindComputeCpp)
+ set(COMPUTECPP_DRIVER_DEFAULT_VALUE OFF)
+ if (NOT MSVC)
+ set(COMPUTECPP_DRIVER_DEFAULT_VALUE ON)
+ endif()
+ option(COMPUTECPP_USE_COMPILER_DRIVER
+ "Use ComputeCpp driver instead of a 2 steps compilation"
+ ${COMPUTECPP_DRIVER_DEFAULT_VALUE}
+ )
+ endif(EIGEN_SYCL_TRISYCL)
+ option(EIGEN_DONT_VECTORIZE_SYCL "Don't use vectorisation in the SYCL tests." OFF)
+ if(EIGEN_DONT_VECTORIZE_SYCL)
+ message(STATUS "Disabling SYCL vectorization in tests/examples")
+ # When disabling SYCL vectorization, also disable Eigen default vectorization
+ add_definitions(-DEIGEN_DONT_VECTORIZE=1)
+ add_definitions(-DEIGEN_DONT_VECTORIZE_SYCL=1)
+ endif()
+endif()
+
+add_subdirectory(unsupported)
+
+add_subdirectory(demos EXCLUDE_FROM_ALL)
+
+# must be after test and unsupported, for configuring buildtests.in
+add_subdirectory(scripts EXCLUDE_FROM_ALL)
+
+# TODO: consider also replacing EIGEN_BUILD_BTL by a custom target "make btl"?
+if(EIGEN_BUILD_BTL)
+ add_subdirectory(bench/btl EXCLUDE_FROM_ALL)
+endif()
+
+find_package(CLANG_FORMAT 9 EXACT)
+if(CLANG_FORMAT_FOUND)
+set(FORMAT_SOURCES)
+list(APPEND FORMAT_SUBDIRS blas bench demos "doc" Eigen include lapack scripts share unsupported test failtest)
+foreach(DIR ${FORMAT_SUBDIRS})
+ set(ABS_DIR ${CMAKE_CURRENT_SOURCE_DIR}/${DIR})
+ file(GLOB_RECURSE ${DIR}_SOURCES ${ABS_DIR}/*.cc ${ABS_DIR}/*.h ${ABS_DIR}/*.cpp ${ABS_DIR}/*.hpp ${ABS_DIR}/*.c)
+ list(APPEND FORMAT_SOURCES ${${DIR}_SOURCES})
+ endforeach()
+ file(GLOB FORMAT_SOURCES_WITHOUTENDING LIST_DIRECTORIES false ${CMAKE_CURRENT_SOURCE_DIR}/Eigen/* ${CMAKE_CURRENT_SOURCE_DIR}/Eigen/CXX11/* ${CMAKE_CURRENT_SOURCE_DIR}/unsupported/Eigen/* ${CMAKE_CURRENT_SOURCE_DIR}/unsupported/Eigen/CXX11/*)
+ list(FILTER FORMAT_SOURCES_WITHOUTENDING EXCLUDE REGEX ".*.txt$")
+ list (APPEND FORMAT_SOURCES ${FORMAT_SOURCES_WITHOUTENDING})
+ add_custom_target(format
+ COMMAND ${CLANG_FORMAT_EXECUTABLE} -i -style=file ${FORMAT_SOURCES}
+ DEPENDS ${FORMAT_SOURCES})
+endif()
+
+if(NOT WIN32 AND EIGEN_BUILD_SPBENCH)
+ add_subdirectory(bench/spbench EXCLUDE_FROM_ALL)
+endif()
+
+configure_file(scripts/cdashtesting.cmake.in cdashtesting.cmake @ONLY)
+
+if(EIGEN_BUILD_TESTING)
+ ei_testing_print_summary()
+endif()
+
+message(STATUS "")
+message(STATUS "Configured Eigen ${EIGEN_VERSION_NUMBER}")
+message(STATUS "")
+
+if(PROJECT_IS_TOP_LEVEL)
+ string(TOLOWER "${CMAKE_GENERATOR}" cmake_generator_tolower)
+ if(cmake_generator_tolower MATCHES "makefile")
+ message(STATUS "Available targets (use: make TARGET):")
+ else()
+ message(STATUS "Available targets (use: cmake --build . --target TARGET):")
+ endif()
+ message(STATUS "---------+--------------------------------------------------------------")
+ message(STATUS "Target | Description")
+ message(STATUS "---------+--------------------------------------------------------------")
+ message(STATUS "install | Install Eigen. Headers will be installed to:")
+ message(STATUS " | <CMAKE_INSTALL_PREFIX>/<INCLUDE_INSTALL_DIR>")
+ message(STATUS " | Using the following values:")
+ message(STATUS " | CMAKE_INSTALL_PREFIX: ${CMAKE_INSTALL_PREFIX}")
+ message(STATUS " | INCLUDE_INSTALL_DIR: ${INCLUDE_INSTALL_DIR}")
+ message(STATUS " | Change the install location of Eigen headers using:")
+ message(STATUS " | cmake . -DCMAKE_INSTALL_PREFIX=yourprefix")
+ message(STATUS " | Or:")
+ message(STATUS " | cmake . -DINCLUDE_INSTALL_DIR=yourdir")
+ message(STATUS "doc | Generate the API documentation, requires Doxygen & LaTeX")
+ if(EIGEN_BUILD_TESTING)
+ message(STATUS "check | Build and run the unit-tests. Read this page:")
+ message(STATUS " | http://eigen.tuxfamily.org/index.php?title=Tests")
+ endif()
+ if(CLANG_FORMAT_FOUND)
+ message(STATUS "format | Formats the source code according to .clang-format file")
+ endif()
+ message(STATUS "blas | Build BLAS library (not the same thing as Eigen)")
+ message(STATUS "uninstall| Remove files installed by the install target")
+ message(STATUS "---------+--------------------------------------------------------------")
+ message(STATUS "")
+endif()
+
+set ( EIGEN_VERSION_STRING ${EIGEN_VERSION_NUMBER} )
+set ( EIGEN_VERSION_MAJOR ${EIGEN_WORLD_VERSION} )
+set ( EIGEN_VERSION_MINOR ${EIGEN_MAJOR_VERSION} )
+set ( EIGEN_VERSION_PATCH ${EIGEN_MINOR_VERSION} )
+
+include (CMakePackageConfigHelpers)
+
+# Imported target support
+add_library (eigen INTERFACE)
+add_library (Eigen3::Eigen ALIAS eigen)
+target_include_directories (eigen INTERFACE
+ $<BUILD_INTERFACE:${CMAKE_CURRENT_SOURCE_DIR}>
+ $<INSTALL_INTERFACE:${INCLUDE_INSTALL_DIR}>
+)
+
+# Export as title case Eigen
+set_target_properties (eigen PROPERTIES EXPORT_NAME Eigen)
+
+install (TARGETS eigen EXPORT Eigen3Targets)
+
+option(EIGEN_BUILD_CMAKE_PACKAGE "Enables the creation of EigenConfig.cmake and related files" ON)
+if(EIGEN_BUILD_CMAKE_PACKAGE)
+configure_package_config_file (
+ ${CMAKE_CURRENT_SOURCE_DIR}/cmake/Eigen3Config.cmake.in
+ ${CMAKE_CURRENT_BINARY_DIR}/Eigen3Config.cmake
+ INSTALL_DESTINATION ${CMAKEPACKAGE_INSTALL_DIR}
+ NO_SET_AND_CHECK_MACRO # Eigen does not provide legacy style defines
+ NO_CHECK_REQUIRED_COMPONENTS_MACRO # Eigen does not provide components
+)
+
+# NOTE Remove the first code path once the minimum required CMake version is
+# bumped to 3.14 or above.
+if (CMAKE_VERSION VERSION_LESS 3.14)
+ # Remove CMAKE_SIZEOF_VOID_P from Eigen3ConfigVersion.cmake since Eigen does
+ # not depend on architecture specific settings or libraries. More
+ # specifically, an Eigen3Config.cmake generated from a 64 bit target can be
+ # used for 32 bit targets as well (and vice versa).
+ set (_Eigen3_CMAKE_SIZEOF_VOID_P ${CMAKE_SIZEOF_VOID_P})
+ unset (CMAKE_SIZEOF_VOID_P)
+ write_basic_package_version_file (Eigen3ConfigVersion.cmake
+ VERSION ${EIGEN_VERSION_NUMBER}
+ COMPATIBILITY SameMajorVersion)
+ set (CMAKE_SIZEOF_VOID_P ${_Eigen3_CMAKE_SIZEOF_VOID_P})
+else (CMAKE_VERSION VERSION_LESS 3.14)
+ write_basic_package_version_file (Eigen3ConfigVersion.cmake
+ VERSION ${EIGEN_VERSION_NUMBER}
+ COMPATIBILITY SameMajorVersion
+ ARCH_INDEPENDENT)
+endif (CMAKE_VERSION VERSION_LESS 3.14)
+
+# The Eigen target will be located in the Eigen3 namespace. Other CMake
+# targets can refer to it using Eigen3::Eigen.
+export (TARGETS eigen NAMESPACE Eigen3:: FILE Eigen3Targets.cmake)
+# Export Eigen3 package to CMake registry such that it can be easily found by
+# CMake even if it has not been installed to a standard directory.
+export (PACKAGE Eigen3)
+
+install (EXPORT Eigen3Targets NAMESPACE Eigen3:: DESTINATION ${CMAKEPACKAGE_INSTALL_DIR})
+
+install (FILES ${CMAKE_CURRENT_BINARY_DIR}/Eigen3Config.cmake
+ ${CMAKE_CURRENT_BINARY_DIR}/Eigen3ConfigVersion.cmake
+ DESTINATION ${CMAKEPACKAGE_INSTALL_DIR})
+
+# Add uninstall target
+if(NOT TARGET uninstall)
+ add_custom_target ( uninstall
+ COMMAND ${CMAKE_COMMAND} -P ${CMAKE_CURRENT_SOURCE_DIR}/cmake/EigenUninstall.cmake)
+endif()
+endif()
+
+if (EIGEN_SPLIT_TESTSUITE)
+ ei_split_testsuite("${EIGEN_SPLIT_TESTSUITE}")
+endif()
diff --git a/COPYING.APACHE b/COPYING.APACHE
new file mode 100644
index 0000000..61e948d
--- /dev/null
+++ b/COPYING.APACHE
@@ -0,0 +1,203 @@
+/*
+ Apache License
+ Version 2.0, January 2004
+ http://www.apache.org/licenses/
+
+ TERMS AND CONDITIONS FOR USE, REPRODUCTION, AND DISTRIBUTION
+
+ 1. Definitions.
+
+ "License" shall mean the terms and conditions for use, reproduction,
+ and distribution as defined by Sections 1 through 9 of this document.
+
+ "Licensor" shall mean the copyright owner or entity authorized by
+ the copyright owner that is granting the License.
+
+ "Legal Entity" shall mean the union of the acting entity and all
+ other entities that control, are controlled by, or are under common
+ control with that entity. For the purposes of this definition,
+ "control" means (i) the power, direct or indirect, to cause the
+ direction or management of such entity, whether by contract or
+ otherwise, or (ii) ownership of fifty percent (50%) or more of the
+ outstanding shares, or (iii) beneficial ownership of such entity.
+
+ "You" (or "Your") shall mean an individual or Legal Entity
+ exercising permissions granted by this License.
+
+ "Source" form shall mean the preferred form for making modifications,
+ including but not limited to software source code, documentation
+ source, and configuration files.
+
+ "Object" form shall mean any form resulting from mechanical
+ transformation or translation of a Source form, including but
+ not limited to compiled object code, generated documentation,
+ and conversions to other media types.
+
+ "Work" shall mean the work of authorship, whether in Source or
+ Object form, made available under the License, as indicated by a
+ copyright notice that is included in or attached to the work
+ (an example is provided in the Appendix below).
+
+ "Derivative Works" shall mean any work, whether in Source or Object
+ form, that is based on (or derived from) the Work and for which the
+ editorial revisions, annotations, elaborations, or other modifications
+ represent, as a whole, an original work of authorship. For the purposes
+ of this License, Derivative Works shall not include works that remain
+ separable from, or merely link (or bind by name) to the interfaces of,
+ the Work and Derivative Works thereof.
+
+ "Contribution" shall mean any work of authorship, including
+ the original version of the Work and any modifications or additions
+ to that Work or Derivative Works thereof, that is intentionally
+ submitted to Licensor for inclusion in the Work by the copyright owner
+ or by an individual or Legal Entity authorized to submit on behalf of
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+ means any form of electronic, verbal, or written communication sent
+ to the Licensor or its representatives, including but not limited to
+ communication on electronic mailing lists, source code control systems,
+ and issue tracking systems that are managed by, or on behalf of, the
+ Licensor for the purpose of discussing and improving the Work, but
+ excluding communication that is conspicuously marked or otherwise
+ designated in writing by the copyright owner as "Not a Contribution."
+
+ "Contributor" shall mean Licensor and any individual or Legal Entity
+ on behalf of whom a Contribution has been received by Licensor and
+ subsequently incorporated within the Work.
+
+ 2. Grant of Copyright License. Subject to the terms and conditions of
+ this License, each Contributor hereby grants to You a perpetual,
+ worldwide, non-exclusive, no-charge, royalty-free, irrevocable
+ copyright license to reproduce, prepare Derivative Works of,
+ publicly display, publicly perform, sublicense, and distribute the
+ Work and such Derivative Works in Source or Object form.
+
+ 3. Grant of Patent License. Subject to the terms and conditions of
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+ worldwide, non-exclusive, no-charge, royalty-free, irrevocable
+ (except as stated in this section) patent license to make, have made,
+ use, offer to sell, sell, import, and otherwise transfer the Work,
+ where such license applies only to those patent claims licensable
+ by such Contributor that are necessarily infringed by their
+ Contribution(s) alone or by combination of their Contribution(s)
+ with the Work to which such Contribution(s) was submitted. If You
+ institute patent litigation against any entity (including a
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+ or a Contribution incorporated within the Work constitutes direct
+ or contributory patent infringement, then any patent licenses
+ granted to You under this License for that Work shall terminate
+ as of the date such litigation is filed.
+
+ 4. Redistribution. You may reproduce and distribute copies of the
+ Work or Derivative Works thereof in any medium, with or without
+ modifications, and in Source or Object form, provided that You
+ meet the following conditions:
+
+ (a) You must give any other recipients of the Work or
+ Derivative Works a copy of this License; and
+
+ (b) You must cause any modified files to carry prominent notices
+ stating that You changed the files; and
+
+ (c) You must retain, in the Source form of any Derivative Works
+ that You distribute, all copyright, patent, trademark, and
+ attribution notices from the Source form of the Work,
+ excluding those notices that do not pertain to any part of
+ the Derivative Works; and
+
+ (d) If the Work includes a "NOTICE" text file as part of its
+ distribution, then any Derivative Works that You distribute must
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+ within a display generated by the Derivative Works, if and
+ wherever such third-party notices normally appear. The contents
+ of the NOTICE file are for informational purposes only and
+ do not modify the License. You may add Your own attribution
+ notices within Derivative Works that You distribute, alongside
+ or as an addendum to the NOTICE text from the Work, provided
+ that such additional attribution notices cannot be construed
+ as modifying the License.
+
+ You may add Your own copyright statement to Your modifications and
+ may provide additional or different license terms and conditions
+ for use, reproduction, or distribution of Your modifications, or
+ for any such Derivative Works as a whole, provided Your use,
+ reproduction, and distribution of the Work otherwise complies with
+ the conditions stated in this License.
+
+ 5. Submission of Contributions. Unless You explicitly state otherwise,
+ any Contribution intentionally submitted for inclusion in the Work
+ by You to the Licensor shall be under the terms and conditions of
+ this License, without any additional terms or conditions.
+ Notwithstanding the above, nothing herein shall supersede or modify
+ the terms of any separate license agreement you may have executed
+ with Licensor regarding such Contributions.
+
+ 6. Trademarks. This License does not grant permission to use the trade
+ names, trademarks, service marks, or product names of the Licensor,
+ except as required for reasonable and customary use in describing the
+ origin of the Work and reproducing the content of the NOTICE file.
+
+ 7. Disclaimer of Warranty. Unless required by applicable law or
+ agreed to in writing, Licensor provides the Work (and each
+ Contributor provides its Contributions) on an "AS IS" BASIS,
+ WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or
+ implied, including, without limitation, any warranties or conditions
+ of TITLE, NON-INFRINGEMENT, MERCHANTABILITY, or FITNESS FOR A
+ PARTICULAR PURPOSE. You are solely responsible for determining the
+ appropriateness of using or redistributing the Work and assume any
+ risks associated with Your exercise of permissions under this License.
+
+ 8. Limitation of Liability. In no event and under no legal theory,
+ whether in tort (including negligence), contract, or otherwise,
+ unless required by applicable law (such as deliberate and grossly
+ negligent acts) or agreed to in writing, shall any Contributor be
+ liable to You for damages, including any direct, indirect, special,
+ incidental, or consequential damages of any character arising as a
+ result of this License or out of the use or inability to use the
+ Work (including but not limited to damages for loss of goodwill,
+ work stoppage, computer failure or malfunction, or any and all
+ other commercial damages or losses), even if such Contributor
+ has been advised of the possibility of such damages.
+
+ 9. Accepting Warranty or Additional Liability. While redistributing
+ the Work or Derivative Works thereof, You may choose to offer,
+ and charge a fee for, acceptance of support, warranty, indemnity,
+ or other liability obligations and/or rights consistent with this
+ License. However, in accepting such obligations, You may act only
+ on Your own behalf and on Your sole responsibility, not on behalf
+ of any other Contributor, and only if You agree to indemnify,
+ defend, and hold each Contributor harmless for any liability
+ incurred by, or claims asserted against, such Contributor by reason
+ of your accepting any such warranty or additional liability.
+
+ END OF TERMS AND CONDITIONS
+
+ APPENDIX: How to apply the Apache License to your work.
+
+ To apply the Apache License to your work, attach the following
+ boilerplate notice, with the fields enclosed by brackets "[]"
+ replaced with your own identifying information. (Don't include
+ the brackets!) The text should be enclosed in the appropriate
+ comment syntax for the file format. We also recommend that a
+ file or class name and description of purpose be included on the
+ same "printed page" as the copyright notice for easier
+ identification within third-party archives.
+
+ Copyright [yyyy] [name of copyright owner]
+
+ Licensed under the Apache License, Version 2.0 (the "License");
+ you may not use this file except in compliance with the License.
+ You may obtain a copy of the License at
+
+ http://www.apache.org/licenses/LICENSE-2.0
+
+ Unless required by applicable law or agreed to in writing, software
+ distributed under the License is distributed on an "AS IS" BASIS,
+ WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ See the License for the specific language governing permissions and
+ limitations under the License.
+*/
\ No newline at end of file
diff --git a/COPYING.BSD b/COPYING.BSD
new file mode 100644
index 0000000..8964ddf
--- /dev/null
+++ b/COPYING.BSD
@@ -0,0 +1,26 @@
+/*
+ Copyright (c) 2011, Intel Corporation. All rights reserved.
+
+ Redistribution and use in source and binary forms, with or without modification,
+ are permitted provided that the following conditions are met:
+
+ * Redistributions of source code must retain the above copyright notice, this
+ list of conditions and the following disclaimer.
+ * Redistributions in binary form must reproduce the above copyright notice,
+ this list of conditions and the following disclaimer in the documentation
+ and/or other materials provided with the distribution.
+ * Neither the name of Intel Corporation nor the names of its contributors may
+ be used to endorse or promote products derived from this software without
+ specific prior written permission.
+
+ THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
+ ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
+ WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
+ DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR
+ ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
+ (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
+ LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON
+ ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
+ (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
+ SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+*/
diff --git a/COPYING.MINPACK b/COPYING.MINPACK
new file mode 100644
index 0000000..132cc3f
--- /dev/null
+++ b/COPYING.MINPACK
@@ -0,0 +1,51 @@
+Minpack Copyright Notice (1999) University of Chicago. All rights reserved
+
+Redistribution and use in source and binary forms, with or
+without modification, are permitted provided that the
+following conditions are met:
+
+1. Redistributions of source code must retain the above
+copyright notice, this list of conditions and the following
+disclaimer.
+
+2. Redistributions in binary form must reproduce the above
+copyright notice, this list of conditions and the following
+disclaimer in the documentation and/or other materials
+provided with the distribution.
+
+3. The end-user documentation included with the
+redistribution, if any, must include the following
+acknowledgment:
+
+ "This product includes software developed by the
+ University of Chicago, as Operator of Argonne National
+ Laboratory.
+
+Alternately, this acknowledgment may appear in the software
+itself, if and wherever such third-party acknowledgments
+normally appear.
+
+4. WARRANTY DISCLAIMER. THE SOFTWARE IS SUPPLIED "AS IS"
+WITHOUT WARRANTY OF ANY KIND. THE COPYRIGHT HOLDER, THE
+UNITED STATES, THE UNITED STATES DEPARTMENT OF ENERGY, AND
+THEIR EMPLOYEES: (1) DISCLAIM ANY WARRANTIES, EXPRESS OR
+IMPLIED, INCLUDING BUT NOT LIMITED TO ANY IMPLIED WARRANTIES
+OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE, TITLE
+OR NON-INFRINGEMENT, (2) DO NOT ASSUME ANY LEGAL LIABILITY
+OR RESPONSIBILITY FOR THE ACCURACY, COMPLETENESS, OR
+USEFULNESS OF THE SOFTWARE, (3) DO NOT REPRESENT THAT USE OF
+THE SOFTWARE WOULD NOT INFRINGE PRIVATELY OWNED RIGHTS, (4)
+DO NOT WARRANT THAT THE SOFTWARE WILL FUNCTION
+UNINTERRUPTED, THAT IT IS ERROR-FREE OR THAT ANY ERRORS WILL
+BE CORRECTED.
+
+5. LIMITATION OF LIABILITY. IN NO EVENT WILL THE COPYRIGHT
+HOLDER, THE UNITED STATES, THE UNITED STATES DEPARTMENT OF
+ENERGY, OR THEIR EMPLOYEES: BE LIABLE FOR ANY INDIRECT,
+INCIDENTAL, CONSEQUENTIAL, SPECIAL OR PUNITIVE DAMAGES OF
+ANY KIND OR NATURE, INCLUDING BUT NOT LIMITED TO LOSS OF
+PROFITS OR LOSS OF DATA, FOR ANY REASON WHATSOEVER, WHETHER
+SUCH LIABILITY IS ASSERTED ON THE BASIS OF CONTRACT, TORT
+(INCLUDING NEGLIGENCE OR STRICT LIABILITY), OR OTHERWISE,
+EVEN IF ANY OF SAID PARTIES HAS BEEN WARNED OF THE
+POSSIBILITY OF SUCH LOSS OR DAMAGES.
diff --git a/COPYING.MPL2 b/COPYING.MPL2
new file mode 100644
index 0000000..ee6256c
--- /dev/null
+++ b/COPYING.MPL2
@@ -0,0 +1,373 @@
+Mozilla Public License Version 2.0
+==================================
+
+1. Definitions
+--------------
+
+1.1. "Contributor"
+ means each individual or legal entity that creates, contributes to
+ the creation of, or owns Covered Software.
+
+1.2. "Contributor Version"
+ means the combination of the Contributions of others (if any) used
+ by a Contributor and that particular Contributor's Contribution.
+
+1.3. "Contribution"
+ means Covered Software of a particular Contributor.
+
+1.4. "Covered Software"
+ means Source Code Form to which the initial Contributor has attached
+ the notice in Exhibit A, the Executable Form of such Source Code
+ Form, and Modifications of such Source Code Form, in each case
+ including portions thereof.
+
+1.5. "Incompatible With Secondary Licenses"
+ means
+
+ (a) that the initial Contributor has attached the notice described
+ in Exhibit B to the Covered Software; or
+
+ (b) that the Covered Software was made available under the terms of
+ version 1.1 or earlier of the License, but not also under the
+ terms of a Secondary License.
+
+1.6. "Executable Form"
+ means any form of the work other than Source Code Form.
+
+1.7. "Larger Work"
+ means a work that combines Covered Software with other material, in
+ a separate file or files, that is not Covered Software.
+
+1.8. "License"
+ means this document.
+
+1.9. "Licensable"
+ means having the right to grant, to the maximum extent possible,
+ whether at the time of the initial grant or subsequently, any and
+ all of the rights conveyed by this License.
+
+1.10. "Modifications"
+ means any of the following:
+
+ (a) any file in Source Code Form that results from an addition to,
+ deletion from, or modification of the contents of Covered
+ Software; or
+
+ (b) any new file in Source Code Form that contains any Covered
+ Software.
+
+1.11. "Patent Claims" of a Contributor
+ means any patent claim(s), including without limitation, method,
+ process, and apparatus claims, in any patent Licensable by such
+ Contributor that would be infringed, but for the grant of the
+ License, by the making, using, selling, offering for sale, having
+ made, import, or transfer of either its Contributions or its
+ Contributor Version.
+
+1.12. "Secondary License"
+ means either the GNU General Public License, Version 2.0, the GNU
+ Lesser General Public License, Version 2.1, the GNU Affero General
+ Public License, Version 3.0, or any later versions of those
+ licenses.
+
+1.13. "Source Code Form"
+ means the form of the work preferred for making modifications.
+
+1.14. "You" (or "Your")
+ means an individual or a legal entity exercising rights under this
+ License. For legal entities, "You" includes any entity that
+ controls, is controlled by, or is under common control with You. For
+ purposes of this definition, "control" means (a) the power, direct
+ or indirect, to cause the direction or management of such entity,
+ whether by contract or otherwise, or (b) ownership of more than
+ fifty percent (50%) of the outstanding shares or beneficial
+ ownership of such entity.
+
+2. License Grants and Conditions
+--------------------------------
+
+2.1. Grants
+
+Each Contributor hereby grants You a world-wide, royalty-free,
+non-exclusive license:
+
+(a) under intellectual property rights (other than patent or trademark)
+ Licensable by such Contributor to use, reproduce, make available,
+ modify, display, perform, distribute, and otherwise exploit its
+ Contributions, either on an unmodified basis, with Modifications, or
+ as part of a Larger Work; and
+
+(b) under Patent Claims of such Contributor to make, use, sell, offer
+ for sale, have made, import, and otherwise transfer either its
+ Contributions or its Contributor Version.
+
+2.2. Effective Date
+
+The licenses granted in Section 2.1 with respect to any Contribution
+become effective for each Contribution on the date the Contributor first
+distributes such Contribution.
+
+2.3. Limitations on Grant Scope
+
+The licenses granted in this Section 2 are the only rights granted under
+this License. No additional rights or licenses will be implied from the
+distribution or licensing of Covered Software under this License.
+Notwithstanding Section 2.1(b) above, no patent license is granted by a
+Contributor:
+
+(a) for any code that a Contributor has removed from Covered Software;
+ or
+
+(b) for infringements caused by: (i) Your and any other third party's
+ modifications of Covered Software, or (ii) the combination of its
+ Contributions with other software (except as part of its Contributor
+ Version); or
+
+(c) under Patent Claims infringed by Covered Software in the absence of
+ its Contributions.
+
+This License does not grant any rights in the trademarks, service marks,
+or logos of any Contributor (except as may be necessary to comply with
+the notice requirements in Section 3.4).
+
+2.4. Subsequent Licenses
+
+No Contributor makes additional grants as a result of Your choice to
+distribute the Covered Software under a subsequent version of this
+License (see Section 10.2) or under the terms of a Secondary License (if
+permitted under the terms of Section 3.3).
+
+2.5. Representation
+
+Each Contributor represents that the Contributor believes its
+Contributions are its original creation(s) or it has sufficient rights
+to grant the rights to its Contributions conveyed by this License.
+
+2.6. Fair Use
+
+This License is not intended to limit any rights You have under
+applicable copyright doctrines of fair use, fair dealing, or other
+equivalents.
+
+2.7. Conditions
+
+Sections 3.1, 3.2, 3.3, and 3.4 are conditions of the licenses granted
+in Section 2.1.
+
+3. Responsibilities
+-------------------
+
+3.1. Distribution of Source Form
+
+All distribution of Covered Software in Source Code Form, including any
+Modifications that You create or to which You contribute, must be under
+the terms of this License. You must inform recipients that the Source
+Code Form of the Covered Software is governed by the terms of this
+License, and how they can obtain a copy of this License. You may not
+attempt to alter or restrict the recipients' rights in the Source Code
+Form.
+
+3.2. Distribution of Executable Form
+
+If You distribute Covered Software in Executable Form then:
+
+(a) such Covered Software must also be made available in Source Code
+ Form, as described in Section 3.1, and You must inform recipients of
+ the Executable Form how they can obtain a copy of such Source Code
+ Form by reasonable means in a timely manner, at a charge no more
+ than the cost of distribution to the recipient; and
+
+(b) You may distribute such Executable Form under the terms of this
+ License, or sublicense it under different terms, provided that the
+ license for the Executable Form does not attempt to limit or alter
+ the recipients' rights in the Source Code Form under this License.
+
+3.3. Distribution of a Larger Work
+
+You may create and distribute a Larger Work under terms of Your choice,
+provided that You also comply with the requirements of this License for
+the Covered Software. If the Larger Work is a combination of Covered
+Software with a work governed by one or more Secondary Licenses, and the
+Covered Software is not Incompatible With Secondary Licenses, this
+License permits You to additionally distribute such Covered Software
+under the terms of such Secondary License(s), so that the recipient of
+the Larger Work may, at their option, further distribute the Covered
+Software under the terms of either this License or such Secondary
+License(s).
+
+3.4. Notices
+
+You may not remove or alter the substance of any license notices
+(including copyright notices, patent notices, disclaimers of warranty,
+or limitations of liability) contained within the Source Code Form of
+the Covered Software, except that You may alter any license notices to
+the extent required to remedy known factual inaccuracies.
+
+3.5. Application of Additional Terms
+
+You may choose to offer, and to charge a fee for, warranty, support,
+indemnity or liability obligations to one or more recipients of Covered
+Software. However, You may do so only on Your own behalf, and not on
+behalf of any Contributor. You must make it absolutely clear that any
+such warranty, support, indemnity, or liability obligation is offered by
+You alone, and You hereby agree to indemnify every Contributor for any
+liability incurred by such Contributor as a result of warranty, support,
+indemnity or liability terms You offer. You may include additional
+disclaimers of warranty and limitations of liability specific to any
+jurisdiction.
+
+4. Inability to Comply Due to Statute or Regulation
+---------------------------------------------------
+
+If it is impossible for You to comply with any of the terms of this
+License with respect to some or all of the Covered Software due to
+statute, judicial order, or regulation then You must: (a) comply with
+the terms of this License to the maximum extent possible; and (b)
+describe the limitations and the code they affect. Such description must
+be placed in a text file included with all distributions of the Covered
+Software under this License. Except to the extent prohibited by statute
+or regulation, such description must be sufficiently detailed for a
+recipient of ordinary skill to be able to understand it.
+
+5. Termination
+--------------
+
+5.1. The rights granted under this License will terminate automatically
+if You fail to comply with any of its terms. However, if You become
+compliant, then the rights granted under this License from a particular
+Contributor are reinstated (a) provisionally, unless and until such
+Contributor explicitly and finally terminates Your grants, and (b) on an
+ongoing basis, if such Contributor fails to notify You of the
+non-compliance by some reasonable means prior to 60 days after You have
+come back into compliance. Moreover, Your grants from a particular
+Contributor are reinstated on an ongoing basis if such Contributor
+notifies You of the non-compliance by some reasonable means, this is the
+first time You have received notice of non-compliance with this License
+from such Contributor, and You become compliant prior to 30 days after
+Your receipt of the notice.
+
+5.2. If You initiate litigation against any entity by asserting a patent
+infringement claim (excluding declaratory judgment actions,
+counter-claims, and cross-claims) alleging that a Contributor Version
+directly or indirectly infringes any patent, then the rights granted to
+You by any and all Contributors for the Covered Software under Section
+2.1 of this License shall terminate.
+
+5.3. In the event of termination under Sections 5.1 or 5.2 above, all
+end user license agreements (excluding distributors and resellers) which
+have been validly granted by You or Your distributors under this License
+prior to termination shall survive termination.
+
+************************************************************************
+* *
+* 6. Disclaimer of Warranty *
+* ------------------------- *
+* *
+* Covered Software is provided under this License on an "as is" *
+* basis, without warranty of any kind, either expressed, implied, or *
+* statutory, including, without limitation, warranties that the *
+* Covered Software is free of defects, merchantable, fit for a *
+* particular purpose or non-infringing. The entire risk as to the *
+* quality and performance of the Covered Software is with You. *
+* Should any Covered Software prove defective in any respect, You *
+* (not any Contributor) assume the cost of any necessary servicing, *
+* repair, or correction. This disclaimer of warranty constitutes an *
+* essential part of this License. No use of any Covered Software is *
+* authorized under this License except under this disclaimer. *
+* *
+************************************************************************
+
+************************************************************************
+* *
+* 7. Limitation of Liability *
+* -------------------------- *
+* *
+* Under no circumstances and under no legal theory, whether tort *
+* (including negligence), contract, or otherwise, shall any *
+* Contributor, or anyone who distributes Covered Software as *
+* permitted above, be liable to You for any direct, indirect, *
+* special, incidental, or consequential damages of any character *
+* including, without limitation, damages for lost profits, loss of *
+* goodwill, work stoppage, computer failure or malfunction, or any *
+* and all other commercial damages or losses, even if such party *
+* shall have been informed of the possibility of such damages. This *
+* limitation of liability shall not apply to liability for death or *
+* personal injury resulting from such party's negligence to the *
+* extent applicable law prohibits such limitation. Some *
+* jurisdictions do not allow the exclusion or limitation of *
+* incidental or consequential damages, so this exclusion and *
+* limitation may not apply to You. *
+* *
+************************************************************************
+
+8. Litigation
+-------------
+
+Any litigation relating to this License may be brought only in the
+courts of a jurisdiction where the defendant maintains its principal
+place of business and such litigation shall be governed by laws of that
+jurisdiction, without reference to its conflict-of-law provisions.
+Nothing in this Section shall prevent a party's ability to bring
+cross-claims or counter-claims.
+
+9. Miscellaneous
+----------------
+
+This License represents the complete agreement concerning the subject
+matter hereof. If any provision of this License is held to be
+unenforceable, such provision shall be reformed only to the extent
+necessary to make it enforceable. Any law or regulation which provides
+that the language of a contract shall be construed against the drafter
+shall not be used to construe this License against a Contributor.
+
+10. Versions of the License
+---------------------------
+
+10.1. New Versions
+
+Mozilla Foundation is the license steward. Except as provided in Section
+10.3, no one other than the license steward has the right to modify or
+publish new versions of this License. Each version will be given a
+distinguishing version number.
+
+10.2. Effect of New Versions
+
+You may distribute the Covered Software under the terms of the version
+of the License under which You originally received the Covered Software,
+or under the terms of any subsequent version published by the license
+steward.
+
+10.3. Modified Versions
+
+If you create software not governed by this License, and you want to
+create a new license for such software, you may create and use a
+modified version of this License if you rename the license and remove
+any references to the name of the license steward (except to note that
+such modified license differs from this License).
+
+10.4. Distributing Source Code Form that is Incompatible With Secondary
+Licenses
+
+If You choose to distribute Source Code Form that is Incompatible With
+Secondary Licenses under the terms of this version of the License, the
+notice described in Exhibit B of this License must be attached.
+
+Exhibit A - Source Code Form License Notice
+-------------------------------------------
+
+ This Source Code Form is subject to the terms of the Mozilla Public
+ License, v. 2.0. If a copy of the MPL was not distributed with this
+ file, You can obtain one at https://mozilla.org/MPL/2.0/.
+
+If it is not possible or desirable to put the notice in a particular
+file, then You may include the notice in a location (such as a LICENSE
+file in a relevant directory) where a recipient would be likely to look
+for such a notice.
+
+You may add additional accurate notices of copyright ownership.
+
+Exhibit B - "Incompatible With Secondary Licenses" Notice
+---------------------------------------------------------
+
+ This Source Code Form is "Incompatible With Secondary Licenses", as
+ defined by the Mozilla Public License, v. 2.0.
diff --git a/COPYING.README b/COPYING.README
new file mode 100644
index 0000000..de5b632
--- /dev/null
+++ b/COPYING.README
@@ -0,0 +1,18 @@
+Eigen is primarily MPL2 licensed. See COPYING.MPL2 and these links:
+ http://www.mozilla.org/MPL/2.0/
+ http://www.mozilla.org/MPL/2.0/FAQ.html
+
+Some files contain third-party code under BSD or LGPL licenses, whence the other
+COPYING.* files here.
+
+All the LGPL code is either LGPL 2.1-only, or LGPL 2.1-or-later.
+For this reason, the COPYING.LGPL file contains the LGPL 2.1 text.
+
+If you want to guarantee that the Eigen code that you are #including is licensed
+under the MPL2 and possibly more permissive licenses (like BSD), #define this
+preprocessor symbol:
+ EIGEN_MPL2_ONLY
+For example, with most compilers, you could add this to your project CXXFLAGS:
+ -DEIGEN_MPL2_ONLY
+This will cause a compilation error to be generated if you #include any code that is
+LGPL licensed.
diff --git a/CTestConfig.cmake b/CTestConfig.cmake
new file mode 100644
index 0000000..0ea24b8
--- /dev/null
+++ b/CTestConfig.cmake
@@ -0,0 +1,17 @@
+## This file should be placed in the root directory of your project.
+## Then modify the CMakeLists.txt file in the root directory of your
+## project to incorporate the testing dashboard.
+## # The following are required to uses Dart and the Cdash dashboard
+## enable_testing()
+## include(CTest)
+set(CTEST_PROJECT_NAME "Eigen")
+set(CTEST_NIGHTLY_START_TIME "00:00:00 UTC")
+
+set(CTEST_DROP_METHOD "http")
+set(CTEST_DROP_SITE "my.cdash.org")
+set(CTEST_DROP_LOCATION "/submit.php?project=Eigen")
+set(CTEST_DROP_SITE_CDASH TRUE)
+#set(CTEST_PROJECT_SUBPROJECTS
+#Official
+#Unsupported
+#)
diff --git a/CTestCustom.cmake.in b/CTestCustom.cmake.in
new file mode 100644
index 0000000..89e487f
--- /dev/null
+++ b/CTestCustom.cmake.in
@@ -0,0 +1,4 @@
+
+set(CTEST_CUSTOM_MAXIMUM_NUMBER_OF_WARNINGS "2000")
+set(CTEST_CUSTOM_MAXIMUM_NUMBER_OF_ERRORS "2000")
+list(APPEND CTEST_CUSTOM_ERROR_EXCEPTION @EIGEN_CTEST_ERROR_EXCEPTION@)
diff --git a/Eigen/AccelerateSupport b/Eigen/AccelerateSupport
new file mode 100644
index 0000000..8cee7ac
--- /dev/null
+++ b/Eigen/AccelerateSupport
@@ -0,0 +1,50 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_ACCELERATESUPPORT_MODULE_H
+#define EIGEN_ACCELERATESUPPORT_MODULE_H
+
+#include "SparseCore"
+
+#include "src/Core/util/DisableStupidWarnings.h"
+
+/** \ingroup Support_modules
+ * \defgroup AccelerateSupport_Module AccelerateSupport module
+ *
+ * This module provides an interface to the Apple Accelerate library.
+ * It provides the seven following main factorization classes:
+ * - class AccelerateLLT: a Cholesky (LL^T) factorization.
+ * - class AccelerateLDLT: the default LDL^T factorization.
+ * - class AccelerateLDLTUnpivoted: a Cholesky-like LDL^T factorization with only 1x1 pivots and no pivoting
+ * - class AccelerateLDLTSBK: an LDL^T factorization with Supernode Bunch-Kaufman and static pivoting
+ * - class AccelerateLDLTTPP: an LDL^T factorization with full threshold partial pivoting
+ * - class AccelerateQR: a QR factorization
+ * - class AccelerateCholeskyAtA: a QR factorization without storing Q (equivalent to A^TA = R^T R)
+ *
+ * \code
+ * #include <Eigen/AccelerateSupport>
+ * \endcode
+ *
+ * In order to use this module, the Accelerate headers must be accessible from
+ * the include paths, and your binary must be linked to the Accelerate framework.
+ * The Accelerate library is only available on Apple hardware.
+ *
+ * Note that many of the algorithms can be influenced by the UpLo template
+ * argument. All matrices are assumed to be symmetric. For example, the following
+ * creates an LDLT factorization where your matrix is symmetric (implicit) and
+ * uses the lower triangle:
+ *
+ * \code
+ * AccelerateLDLT<SparseMatrix<float>, Lower> ldlt;
+ * \endcode
+ */
+
+#include "src/AccelerateSupport/AccelerateSupport.h"
+
+#include "src/Core/util/ReenableStupidWarnings.h"
+
+#endif // EIGEN_ACCELERATESUPPORT_MODULE_H
diff --git a/Eigen/Cholesky b/Eigen/Cholesky
new file mode 100644
index 0000000..2c686f1
--- /dev/null
+++ b/Eigen/Cholesky
@@ -0,0 +1,41 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_CHOLESKY_MODULE_H
+#define EIGEN_CHOLESKY_MODULE_H
+
+#include "Core"
+#include "Jacobi"
+
+#include "src/Core/util/DisableStupidWarnings.h"
+
+/** \defgroup Cholesky_Module Cholesky module
+ *
+ *
+ *
+ * This module provides two variants of the Cholesky decomposition for selfadjoint (hermitian) matrices.
+ * Those decompositions are also accessible via the following methods:
+ * - MatrixBase::llt()
+ * - MatrixBase::ldlt()
+ * - SelfAdjointView::llt()
+ * - SelfAdjointView::ldlt()
+ *
+ * \code
+ * #include <Eigen/Cholesky>
+ * \endcode
+ */
+
+#include "src/Cholesky/LLT.h"
+#include "src/Cholesky/LDLT.h"
+#ifdef EIGEN_USE_LAPACKE
+#include "src/misc/lapacke_helpers.h"
+#include "src/Cholesky/LLT_LAPACKE.h"
+#endif
+
+#include "src/Core/util/ReenableStupidWarnings.h"
+
+#endif // EIGEN_CHOLESKY_MODULE_H
diff --git a/Eigen/CholmodSupport b/Eigen/CholmodSupport
new file mode 100644
index 0000000..bed8924
--- /dev/null
+++ b/Eigen/CholmodSupport
@@ -0,0 +1,48 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_CHOLMODSUPPORT_MODULE_H
+#define EIGEN_CHOLMODSUPPORT_MODULE_H
+
+#include "SparseCore"
+
+#include "src/Core/util/DisableStupidWarnings.h"
+
+extern "C" {
+ #include <cholmod.h>
+}
+
+/** \ingroup Support_modules
+ * \defgroup CholmodSupport_Module CholmodSupport module
+ *
+ * This module provides an interface to the Cholmod library which is part of the <a href="http://www.suitesparse.com">suitesparse</a> package.
+ * It provides the two following main factorization classes:
+ * - class CholmodSupernodalLLT: a supernodal LLT Cholesky factorization.
+ * - class CholmodDecomposiiton: a general L(D)LT Cholesky factorization with automatic or explicit runtime selection of the underlying factorization method (supernodal or simplicial).
+ *
+ * For the sake of completeness, this module also propose the two following classes:
+ * - class CholmodSimplicialLLT
+ * - class CholmodSimplicialLDLT
+ * Note that these classes does not bring any particular advantage compared to the built-in
+ * SimplicialLLT and SimplicialLDLT factorization classes.
+ *
+ * \code
+ * #include <Eigen/CholmodSupport>
+ * \endcode
+ *
+ * In order to use this module, the cholmod headers must be accessible from the include paths, and your binary must be linked to the cholmod library and its dependencies.
+ * The dependencies depend on how cholmod has been compiled.
+ * For a cmake based project, you can use our FindCholmod.cmake module to help you in this task.
+ *
+ */
+
+#include "src/CholmodSupport/CholmodSupport.h"
+
+#include "src/Core/util/ReenableStupidWarnings.h"
+
+#endif // EIGEN_CHOLMODSUPPORT_MODULE_H
+
diff --git a/Eigen/Core b/Eigen/Core
new file mode 100644
index 0000000..48c2121
--- /dev/null
+++ b/Eigen/Core
@@ -0,0 +1,400 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2007-2011 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_CORE_MODULE_H
+#define EIGEN_CORE_MODULE_H
+
+// first thing Eigen does: stop the compiler from reporting useless warnings.
+#include "src/Core/util/DisableStupidWarnings.h"
+
+// then include this file where all our macros are defined. It's really important to do it first because
+// it's where we do all the compiler/OS/arch detections and define most defaults.
+#include "src/Core/util/Macros.h"
+
+// This detects SSE/AVX/NEON/etc. and configure alignment settings
+#include "src/Core/util/ConfigureVectorization.h"
+
+// We need cuda_runtime.h/hip_runtime.h to ensure that
+// the EIGEN_USING_STD macro works properly on the device side
+#if defined(EIGEN_CUDACC)
+ #include <cuda_runtime.h>
+#elif defined(EIGEN_HIPCC)
+ #include <hip/hip_runtime.h>
+#endif
+
+
+#ifdef EIGEN_EXCEPTIONS
+ #include <new>
+#endif
+
+// Disable the ipa-cp-clone optimization flag with MinGW 6.x or newer (enabled by default with -O3)
+// See http://eigen.tuxfamily.org/bz/show_bug.cgi?id=556 for details.
+#if EIGEN_COMP_MINGW && EIGEN_GNUC_AT_MOST(5,5)
+ #pragma GCC optimize ("-fno-ipa-cp-clone")
+#endif
+
+// Prevent ICC from specializing std::complex operators that silently fail
+// on device. This allows us to use our own device-compatible specializations
+// instead.
+#if defined(EIGEN_COMP_ICC) && defined(EIGEN_GPU_COMPILE_PHASE) \
+ && !defined(_OVERRIDE_COMPLEX_SPECIALIZATION_)
+#define _OVERRIDE_COMPLEX_SPECIALIZATION_ 1
+#endif
+#include <complex>
+
+// this include file manages BLAS and MKL related macros
+// and inclusion of their respective header files
+#include "src/Core/util/MKL_support.h"
+
+
+#if defined(EIGEN_HAS_CUDA_FP16) || defined(EIGEN_HAS_HIP_FP16)
+ #define EIGEN_HAS_GPU_FP16
+#endif
+
+#if defined(EIGEN_HAS_CUDA_BF16) || defined(EIGEN_HAS_HIP_BF16)
+ #define EIGEN_HAS_GPU_BF16
+#endif
+
+#if (defined _OPENMP) && (!defined EIGEN_DONT_PARALLELIZE)
+ #define EIGEN_HAS_OPENMP
+#endif
+
+#ifdef EIGEN_HAS_OPENMP
+#include <atomic>
+#include <omp.h>
+#endif
+
+// MSVC for windows mobile does not have the errno.h file
+#if !(EIGEN_COMP_MSVC && EIGEN_OS_WINCE) && !EIGEN_COMP_ARM
+#define EIGEN_HAS_ERRNO
+#endif
+
+#ifdef EIGEN_HAS_ERRNO
+#include <cerrno>
+#endif
+#include <cstddef>
+#include <cstdlib>
+#include <cmath>
+#include <cassert>
+#include <functional>
+#ifndef EIGEN_NO_IO
+ #include <sstream>
+ #include <iosfwd>
+#endif
+#include <cstring>
+#include <string>
+#include <limits>
+#include <climits> // for CHAR_BIT
+// for min/max:
+#include <algorithm>
+
+#include <array>
+
+// for std::is_nothrow_move_assignable
+#include <type_traits>
+
+// for outputting debug info
+#ifdef EIGEN_DEBUG_ASSIGN
+#include <iostream>
+#endif
+
+// required for __cpuid, needs to be included after cmath
+// also required for _BitScanReverse on Windows on ARM
+#if EIGEN_COMP_MSVC && (EIGEN_ARCH_i386_OR_x86_64 || EIGEN_ARCH_ARM64) && !EIGEN_OS_WINCE
+ #include <intrin.h>
+#endif
+
+#if defined(EIGEN_USE_SYCL)
+ #undef min
+ #undef max
+ #undef isnan
+ #undef isinf
+ #undef isfinite
+ #include <CL/sycl.hpp>
+ #include <map>
+ #include <memory>
+ #include <utility>
+ #include <thread>
+ #ifndef EIGEN_SYCL_LOCAL_THREAD_DIM0
+ #define EIGEN_SYCL_LOCAL_THREAD_DIM0 16
+ #endif
+ #ifndef EIGEN_SYCL_LOCAL_THREAD_DIM1
+ #define EIGEN_SYCL_LOCAL_THREAD_DIM1 16
+ #endif
+#endif
+
+
+#if defined EIGEN2_SUPPORT_STAGE40_FULL_EIGEN3_STRICTNESS || defined EIGEN2_SUPPORT_STAGE30_FULL_EIGEN3_API || defined EIGEN2_SUPPORT_STAGE20_RESOLVE_API_CONFLICTS || defined EIGEN2_SUPPORT_STAGE10_FULL_EIGEN2_API || defined EIGEN2_SUPPORT
+// This will generate an error message:
+#error Eigen2-support is only available up to version 3.2. Please go to "http://eigen.tuxfamily.org/index.php?title=Eigen2" for further information
+#endif
+
+namespace Eigen {
+
+// we use size_t frequently and we'll never remember to prepend it with std:: every time just to
+// ensure QNX/QCC support
+using std::size_t;
+// gcc 4.6.0 wants std:: for ptrdiff_t
+using std::ptrdiff_t;
+
+}
+
+/** \defgroup Core_Module Core module
+ * This is the main module of Eigen providing dense matrix and vector support
+ * (both fixed and dynamic size) with all the features corresponding to a BLAS library
+ * and much more...
+ *
+ * \code
+ * #include <Eigen/Core>
+ * \endcode
+ */
+
+#include "src/Core/util/Constants.h"
+#include "src/Core/util/Meta.h"
+#include "src/Core/util/ForwardDeclarations.h"
+#include "src/Core/util/StaticAssert.h"
+#include "src/Core/util/XprHelper.h"
+#include "src/Core/util/Memory.h"
+#include "src/Core/util/IntegralConstant.h"
+#include "src/Core/util/Serializer.h"
+#include "src/Core/util/SymbolicIndex.h"
+
+#include "src/Core/NumTraits.h"
+#include "src/Core/MathFunctions.h"
+#include "src/Core/GenericPacketMath.h"
+#include "src/Core/MathFunctionsImpl.h"
+#include "src/Core/arch/Default/ConjHelper.h"
+// Generic half float support
+#include "src/Core/arch/Default/Half.h"
+#include "src/Core/arch/Default/BFloat16.h"
+#include "src/Core/arch/Default/TypeCasting.h"
+#include "src/Core/arch/Default/GenericPacketMathFunctionsFwd.h"
+
+#ifndef EIGEN_GPU_COMPILE_PHASE
+ #include <csignal>
+#endif
+
+#if defined EIGEN_VECTORIZE_AVX512
+ #if defined EIGEN_VECTORIZE_AVX512FP16
+ #include "src/Core/arch/AVX512/PacketMathFP16.h"
+ #endif
+ #include "src/Core/arch/SSE/PacketMath.h"
+ #include "src/Core/arch/SSE/TypeCasting.h"
+ #include "src/Core/arch/SSE/Complex.h"
+ #include "src/Core/arch/AVX/PacketMath.h"
+ #include "src/Core/arch/AVX/TypeCasting.h"
+ #include "src/Core/arch/AVX/Complex.h"
+ #include "src/Core/arch/AVX512/PacketMath.h"
+ #include "src/Core/arch/AVX512/TypeCasting.h"
+ #include "src/Core/arch/AVX512/Complex.h"
+ #include "src/Core/arch/SSE/MathFunctions.h"
+ #include "src/Core/arch/AVX/MathFunctions.h"
+ #include "src/Core/arch/AVX512/MathFunctions.h"
+ #include "src/Core/arch/AVX512/TrsmKernel.h"
+#elif defined EIGEN_VECTORIZE_AVX
+ // Use AVX for floats and doubles, SSE for integers
+ #include "src/Core/arch/SSE/PacketMath.h"
+ #include "src/Core/arch/SSE/TypeCasting.h"
+ #include "src/Core/arch/SSE/Complex.h"
+ #include "src/Core/arch/AVX/PacketMath.h"
+ #include "src/Core/arch/AVX/TypeCasting.h"
+ #include "src/Core/arch/AVX/Complex.h"
+ #include "src/Core/arch/SSE/MathFunctions.h"
+ #include "src/Core/arch/AVX/MathFunctions.h"
+#elif defined EIGEN_VECTORIZE_SSE
+ #include "src/Core/arch/SSE/PacketMath.h"
+ #include "src/Core/arch/SSE/TypeCasting.h"
+ #include "src/Core/arch/SSE/MathFunctions.h"
+ #include "src/Core/arch/SSE/Complex.h"
+#elif defined(EIGEN_VECTORIZE_ALTIVEC) || defined(EIGEN_VECTORIZE_VSX)
+ #include "src/Core/arch/AltiVec/PacketMath.h"
+ #include "src/Core/arch/AltiVec/MathFunctions.h"
+ #include "src/Core/arch/AltiVec/Complex.h"
+#elif defined EIGEN_VECTORIZE_NEON
+ #include "src/Core/arch/NEON/PacketMath.h"
+ #include "src/Core/arch/NEON/TypeCasting.h"
+ #include "src/Core/arch/NEON/MathFunctions.h"
+ #include "src/Core/arch/NEON/Complex.h"
+#elif defined EIGEN_VECTORIZE_SVE
+ #include "src/Core/arch/SVE/PacketMath.h"
+ #include "src/Core/arch/SVE/TypeCasting.h"
+ #include "src/Core/arch/SVE/MathFunctions.h"
+#elif defined EIGEN_VECTORIZE_ZVECTOR
+ #include "src/Core/arch/ZVector/PacketMath.h"
+ #include "src/Core/arch/ZVector/MathFunctions.h"
+ #include "src/Core/arch/ZVector/Complex.h"
+#elif defined EIGEN_VECTORIZE_MSA
+ #include "src/Core/arch/MSA/PacketMath.h"
+ #include "src/Core/arch/MSA/MathFunctions.h"
+ #include "src/Core/arch/MSA/Complex.h"
+#endif
+
+#if defined EIGEN_VECTORIZE_GPU
+ #include "src/Core/arch/GPU/PacketMath.h"
+ #include "src/Core/arch/GPU/MathFunctions.h"
+ #include "src/Core/arch/GPU/TypeCasting.h"
+#endif
+
+#if defined(EIGEN_USE_SYCL)
+ #include "src/Core/arch/SYCL/SyclMemoryModel.h"
+ #include "src/Core/arch/SYCL/InteropHeaders.h"
+#if !defined(EIGEN_DONT_VECTORIZE_SYCL)
+ #include "src/Core/arch/SYCL/PacketMath.h"
+ #include "src/Core/arch/SYCL/MathFunctions.h"
+ #include "src/Core/arch/SYCL/TypeCasting.h"
+#endif
+#endif
+
+#include "src/Core/arch/Default/Settings.h"
+// This file provides generic implementations valid for scalar as well
+#include "src/Core/arch/Default/GenericPacketMathFunctions.h"
+
+#include "src/Core/functors/TernaryFunctors.h"
+#include "src/Core/functors/BinaryFunctors.h"
+#include "src/Core/functors/UnaryFunctors.h"
+#include "src/Core/functors/NullaryFunctors.h"
+#include "src/Core/functors/StlFunctors.h"
+#include "src/Core/functors/AssignmentFunctors.h"
+
+// Specialized functors for GPU.
+#ifdef EIGEN_GPUCC
+#include "src/Core/arch/GPU/Complex.h"
+#endif
+
+// Specializations of vectorized activation functions for NEON.
+#ifdef EIGEN_VECTORIZE_NEON
+#include "src/Core/arch/NEON/UnaryFunctors.h"
+#endif
+
+#include "src/Core/util/IndexedViewHelper.h"
+#include "src/Core/util/ReshapedHelper.h"
+#include "src/Core/ArithmeticSequence.h"
+#ifndef EIGEN_NO_IO
+ #include "src/Core/IO.h"
+#endif
+#include "src/Core/DenseCoeffsBase.h"
+#include "src/Core/DenseBase.h"
+#include "src/Core/MatrixBase.h"
+#include "src/Core/EigenBase.h"
+
+#include "src/Core/Product.h"
+#include "src/Core/CoreEvaluators.h"
+#include "src/Core/AssignEvaluator.h"
+
+#ifndef EIGEN_PARSED_BY_DOXYGEN // work around Doxygen bug triggered by Assign.h r814874
+ // at least confirmed with Doxygen 1.5.5 and 1.5.6
+ #include "src/Core/Assign.h"
+#endif
+
+#include "src/Core/ArrayBase.h"
+#include "src/Core/util/BlasUtil.h"
+#include "src/Core/DenseStorage.h"
+#include "src/Core/NestByValue.h"
+
+// #include "src/Core/ForceAlignedAccess.h"
+
+#include "src/Core/ReturnByValue.h"
+#include "src/Core/NoAlias.h"
+#include "src/Core/PlainObjectBase.h"
+#include "src/Core/Matrix.h"
+#include "src/Core/Array.h"
+#include "src/Core/CwiseTernaryOp.h"
+#include "src/Core/CwiseBinaryOp.h"
+#include "src/Core/CwiseUnaryOp.h"
+#include "src/Core/CwiseNullaryOp.h"
+#include "src/Core/CwiseUnaryView.h"
+#include "src/Core/SelfCwiseBinaryOp.h"
+#include "src/Core/Dot.h"
+#include "src/Core/StableNorm.h"
+#include "src/Core/Stride.h"
+#include "src/Core/MapBase.h"
+#include "src/Core/Map.h"
+#include "src/Core/Ref.h"
+#include "src/Core/Block.h"
+#include "src/Core/VectorBlock.h"
+#include "src/Core/IndexedView.h"
+#include "src/Core/Reshaped.h"
+#include "src/Core/Transpose.h"
+#include "src/Core/DiagonalMatrix.h"
+#include "src/Core/Diagonal.h"
+#include "src/Core/DiagonalProduct.h"
+#include "src/Core/SkewSymmetricMatrix3.h"
+#include "src/Core/Redux.h"
+#include "src/Core/Visitor.h"
+#include "src/Core/Fuzzy.h"
+#include "src/Core/Swap.h"
+#include "src/Core/CommaInitializer.h"
+#include "src/Core/GeneralProduct.h"
+#include "src/Core/Solve.h"
+#include "src/Core/Inverse.h"
+#include "src/Core/SolverBase.h"
+#include "src/Core/PermutationMatrix.h"
+#include "src/Core/Transpositions.h"
+#include "src/Core/TriangularMatrix.h"
+#include "src/Core/SelfAdjointView.h"
+#include "src/Core/products/GeneralBlockPanelKernel.h"
+#include "src/Core/products/Parallelizer.h"
+#include "src/Core/ProductEvaluators.h"
+#include "src/Core/products/GeneralMatrixVector.h"
+#include "src/Core/products/GeneralMatrixMatrix.h"
+#include "src/Core/SolveTriangular.h"
+#include "src/Core/products/GeneralMatrixMatrixTriangular.h"
+#include "src/Core/products/SelfadjointMatrixVector.h"
+#include "src/Core/products/SelfadjointMatrixMatrix.h"
+#include "src/Core/products/SelfadjointProduct.h"
+#include "src/Core/products/SelfadjointRank2Update.h"
+#include "src/Core/products/TriangularMatrixVector.h"
+#include "src/Core/products/TriangularMatrixMatrix.h"
+#include "src/Core/products/TriangularSolverMatrix.h"
+#include "src/Core/products/TriangularSolverVector.h"
+#include "src/Core/BandMatrix.h"
+#include "src/Core/CoreIterators.h"
+#include "src/Core/ConditionEstimator.h"
+
+#if defined(EIGEN_VECTORIZE_VSX)
+ #include "src/Core/arch/AltiVec/MatrixProduct.h"
+#elif defined EIGEN_VECTORIZE_NEON
+ #include "src/Core/arch/NEON/GeneralBlockPanelKernel.h"
+#endif
+
+#if defined(EIGEN_VECTORIZE_AVX512)
+ #include "src/Core/arch/AVX512/GemmKernel.h"
+#endif
+
+#include "src/Core/BooleanRedux.h"
+#include "src/Core/Select.h"
+#include "src/Core/VectorwiseOp.h"
+#include "src/Core/PartialReduxEvaluator.h"
+#include "src/Core/Random.h"
+#include "src/Core/Replicate.h"
+#include "src/Core/Reverse.h"
+#include "src/Core/ArrayWrapper.h"
+#include "src/Core/StlIterators.h"
+
+#ifdef EIGEN_USE_BLAS
+#include "src/Core/products/GeneralMatrixMatrix_BLAS.h"
+#include "src/Core/products/GeneralMatrixVector_BLAS.h"
+#include "src/Core/products/GeneralMatrixMatrixTriangular_BLAS.h"
+#include "src/Core/products/SelfadjointMatrixMatrix_BLAS.h"
+#include "src/Core/products/SelfadjointMatrixVector_BLAS.h"
+#include "src/Core/products/TriangularMatrixMatrix_BLAS.h"
+#include "src/Core/products/TriangularMatrixVector_BLAS.h"
+#include "src/Core/products/TriangularSolverMatrix_BLAS.h"
+#endif // EIGEN_USE_BLAS
+
+#ifdef EIGEN_USE_MKL_VML
+#include "src/Core/Assign_MKL.h"
+#endif
+
+#include "src/Core/GlobalFunctions.h"
+
+#include "src/Core/util/ReenableStupidWarnings.h"
+
+#endif // EIGEN_CORE_MODULE_H
diff --git a/Eigen/Dense b/Eigen/Dense
new file mode 100644
index 0000000..5768910
--- /dev/null
+++ b/Eigen/Dense
@@ -0,0 +1,7 @@
+#include "Core"
+#include "LU"
+#include "Cholesky"
+#include "QR"
+#include "SVD"
+#include "Geometry"
+#include "Eigenvalues"
diff --git a/Eigen/Eigen b/Eigen/Eigen
new file mode 100644
index 0000000..654c8dc
--- /dev/null
+++ b/Eigen/Eigen
@@ -0,0 +1,2 @@
+#include "Dense"
+#include "Sparse"
diff --git a/Eigen/Eigenvalues b/Eigen/Eigenvalues
new file mode 100644
index 0000000..5467a2e
--- /dev/null
+++ b/Eigen/Eigenvalues
@@ -0,0 +1,60 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_EIGENVALUES_MODULE_H
+#define EIGEN_EIGENVALUES_MODULE_H
+
+#include "Core"
+
+#include "Cholesky"
+#include "Jacobi"
+#include "Householder"
+#include "LU"
+#include "Geometry"
+
+#include "src/Core/util/DisableStupidWarnings.h"
+
+/** \defgroup Eigenvalues_Module Eigenvalues module
+ *
+ *
+ *
+ * This module mainly provides various eigenvalue solvers.
+ * This module also provides some MatrixBase methods, including:
+ * - MatrixBase::eigenvalues(),
+ * - MatrixBase::operatorNorm()
+ *
+ * \code
+ * #include <Eigen/Eigenvalues>
+ * \endcode
+ */
+
+#include "src/misc/RealSvd2x2.h"
+#include "src/Eigenvalues/Tridiagonalization.h"
+#include "src/Eigenvalues/RealSchur.h"
+#include "src/Eigenvalues/EigenSolver.h"
+#include "src/Eigenvalues/SelfAdjointEigenSolver.h"
+#include "src/Eigenvalues/GeneralizedSelfAdjointEigenSolver.h"
+#include "src/Eigenvalues/HessenbergDecomposition.h"
+#include "src/Eigenvalues/ComplexSchur.h"
+#include "src/Eigenvalues/ComplexEigenSolver.h"
+#include "src/Eigenvalues/RealQZ.h"
+#include "src/Eigenvalues/GeneralizedEigenSolver.h"
+#include "src/Eigenvalues/MatrixBaseEigenvalues.h"
+#ifdef EIGEN_USE_LAPACKE
+#ifdef EIGEN_USE_MKL
+#include "mkl_lapacke.h"
+#else
+#include "src/misc/lapacke.h"
+#endif
+#include "src/Eigenvalues/RealSchur_LAPACKE.h"
+#include "src/Eigenvalues/ComplexSchur_LAPACKE.h"
+#include "src/Eigenvalues/SelfAdjointEigenSolver_LAPACKE.h"
+#endif
+
+#include "src/Core/util/ReenableStupidWarnings.h"
+
+#endif // EIGEN_EIGENVALUES_MODULE_H
diff --git a/Eigen/Geometry b/Eigen/Geometry
new file mode 100644
index 0000000..bc78110
--- /dev/null
+++ b/Eigen/Geometry
@@ -0,0 +1,59 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_GEOMETRY_MODULE_H
+#define EIGEN_GEOMETRY_MODULE_H
+
+#include "Core"
+
+#include "SVD"
+#include "LU"
+#include <limits>
+
+#include "src/Core/util/DisableStupidWarnings.h"
+
+/** \defgroup Geometry_Module Geometry module
+ *
+ * This module provides support for:
+ * - fixed-size homogeneous transformations
+ * - translation, scaling, 2D and 3D rotations
+ * - \link Quaternion quaternions \endlink
+ * - cross products (\ref MatrixBase::cross, \ref MatrixBase::cross3)
+ * - orthognal vector generation (\ref MatrixBase::unitOrthogonal)
+ * - some linear components: \link ParametrizedLine parametrized-lines \endlink and \link Hyperplane hyperplanes \endlink
+ * - \link AlignedBox axis aligned bounding boxes \endlink
+ * - \link umeyama least-square transformation fitting \endlink
+ *
+ * \code
+ * #include <Eigen/Geometry>
+ * \endcode
+ */
+
+#include "src/Geometry/OrthoMethods.h"
+#include "src/Geometry/EulerAngles.h"
+
+#include "src/Geometry/Homogeneous.h"
+#include "src/Geometry/RotationBase.h"
+#include "src/Geometry/Rotation2D.h"
+#include "src/Geometry/Quaternion.h"
+#include "src/Geometry/AngleAxis.h"
+#include "src/Geometry/Transform.h"
+#include "src/Geometry/Translation.h"
+#include "src/Geometry/Scaling.h"
+#include "src/Geometry/Hyperplane.h"
+#include "src/Geometry/ParametrizedLine.h"
+#include "src/Geometry/AlignedBox.h"
+#include "src/Geometry/Umeyama.h"
+
+// Use the SSE optimized version whenever possible.
+#if (defined EIGEN_VECTORIZE_SSE) || (defined EIGEN_VECTORIZE_NEON)
+#include "src/Geometry/arch/Geometry_SIMD.h"
+#endif
+
+#include "src/Core/util/ReenableStupidWarnings.h"
+
+#endif // EIGEN_GEOMETRY_MODULE_H
diff --git a/Eigen/Householder b/Eigen/Householder
new file mode 100644
index 0000000..f2fa799
--- /dev/null
+++ b/Eigen/Householder
@@ -0,0 +1,29 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_HOUSEHOLDER_MODULE_H
+#define EIGEN_HOUSEHOLDER_MODULE_H
+
+#include "Core"
+
+#include "src/Core/util/DisableStupidWarnings.h"
+
+/** \defgroup Householder_Module Householder module
+ * This module provides Householder transformations.
+ *
+ * \code
+ * #include <Eigen/Householder>
+ * \endcode
+ */
+
+#include "src/Householder/Householder.h"
+#include "src/Householder/HouseholderSequence.h"
+#include "src/Householder/BlockHouseholder.h"
+
+#include "src/Core/util/ReenableStupidWarnings.h"
+
+#endif // EIGEN_HOUSEHOLDER_MODULE_H
diff --git a/Eigen/IterativeLinearSolvers b/Eigen/IterativeLinearSolvers
new file mode 100644
index 0000000..26a0560
--- /dev/null
+++ b/Eigen/IterativeLinearSolvers
@@ -0,0 +1,48 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_ITERATIVELINEARSOLVERS_MODULE_H
+#define EIGEN_ITERATIVELINEARSOLVERS_MODULE_H
+
+#include "SparseCore"
+#include "OrderingMethods"
+
+#include "src/Core/util/DisableStupidWarnings.h"
+
+/**
+ * \defgroup IterativeLinearSolvers_Module IterativeLinearSolvers module
+ *
+ * This module currently provides iterative methods to solve problems of the form \c A \c x = \c b, where \c A is a squared matrix, usually very large and sparse.
+ * Those solvers are accessible via the following classes:
+ * - ConjugateGradient for selfadjoint (hermitian) matrices,
+ * - LeastSquaresConjugateGradient for rectangular least-square problems,
+ * - BiCGSTAB for general square matrices.
+ *
+ * These iterative solvers are associated with some preconditioners:
+ * - IdentityPreconditioner - not really useful
+ * - DiagonalPreconditioner - also called Jacobi preconditioner, work very well on diagonal dominant matrices.
+ * - IncompleteLUT - incomplete LU factorization with dual thresholding
+ *
+ * Such problems can also be solved using the direct sparse decomposition modules: SparseCholesky, CholmodSupport, UmfPackSupport, SuperLUSupport, AccelerateSupport.
+ *
+ \code
+ #include <Eigen/IterativeLinearSolvers>
+ \endcode
+ */
+
+#include "src/IterativeLinearSolvers/SolveWithGuess.h"
+#include "src/IterativeLinearSolvers/IterativeSolverBase.h"
+#include "src/IterativeLinearSolvers/BasicPreconditioners.h"
+#include "src/IterativeLinearSolvers/ConjugateGradient.h"
+#include "src/IterativeLinearSolvers/LeastSquareConjugateGradient.h"
+#include "src/IterativeLinearSolvers/BiCGSTAB.h"
+#include "src/IterativeLinearSolvers/IncompleteLUT.h"
+#include "src/IterativeLinearSolvers/IncompleteCholesky.h"
+
+#include "src/Core/util/ReenableStupidWarnings.h"
+
+#endif // EIGEN_ITERATIVELINEARSOLVERS_MODULE_H
diff --git a/Eigen/Jacobi b/Eigen/Jacobi
new file mode 100644
index 0000000..43edc7a
--- /dev/null
+++ b/Eigen/Jacobi
@@ -0,0 +1,32 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_JACOBI_MODULE_H
+#define EIGEN_JACOBI_MODULE_H
+
+#include "Core"
+
+#include "src/Core/util/DisableStupidWarnings.h"
+
+/** \defgroup Jacobi_Module Jacobi module
+ * This module provides Jacobi and Givens rotations.
+ *
+ * \code
+ * #include <Eigen/Jacobi>
+ * \endcode
+ *
+ * In addition to listed classes, it defines the two following MatrixBase methods to apply a Jacobi or Givens rotation:
+ * - MatrixBase::applyOnTheLeft()
+ * - MatrixBase::applyOnTheRight().
+ */
+
+#include "src/Jacobi/Jacobi.h"
+
+#include "src/Core/util/ReenableStupidWarnings.h"
+
+#endif // EIGEN_JACOBI_MODULE_H
+
diff --git a/Eigen/KLUSupport b/Eigen/KLUSupport
new file mode 100644
index 0000000..b23d905
--- /dev/null
+++ b/Eigen/KLUSupport
@@ -0,0 +1,41 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_KLUSUPPORT_MODULE_H
+#define EIGEN_KLUSUPPORT_MODULE_H
+
+#include <Eigen/SparseCore>
+
+#include <Eigen/src/Core/util/DisableStupidWarnings.h>
+
+extern "C" {
+#include <btf.h>
+#include <klu.h>
+ }
+
+/** \ingroup Support_modules
+ * \defgroup KLUSupport_Module KLUSupport module
+ *
+ * This module provides an interface to the KLU library which is part of the <a href="http://www.suitesparse.com">suitesparse</a> package.
+ * It provides the following factorization class:
+ * - class KLU: a sparse LU factorization, well-suited for circuit simulation.
+ *
+ * \code
+ * #include <Eigen/KLUSupport>
+ * \endcode
+ *
+ * In order to use this module, the klu and btf headers must be accessible from the include paths, and your binary must be linked to the klu library and its dependencies.
+ * The dependencies depend on how umfpack has been compiled.
+ * For a cmake based project, you can use our FindKLU.cmake module to help you in this task.
+ *
+ */
+
+#include "src/KLUSupport/KLUSupport.h"
+
+#include <Eigen/src/Core/util/ReenableStupidWarnings.h>
+
+#endif // EIGEN_KLUSUPPORT_MODULE_H
diff --git a/Eigen/LU b/Eigen/LU
new file mode 100644
index 0000000..b7f9a8a
--- /dev/null
+++ b/Eigen/LU
@@ -0,0 +1,43 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_LU_MODULE_H
+#define EIGEN_LU_MODULE_H
+
+#include "Core"
+
+#include "src/Core/util/DisableStupidWarnings.h"
+
+/** \defgroup LU_Module LU module
+ * This module includes %LU decomposition and related notions such as matrix inversion and determinant.
+ * This module defines the following MatrixBase methods:
+ * - MatrixBase::inverse()
+ * - MatrixBase::determinant()
+ *
+ * \code
+ * #include <Eigen/LU>
+ * \endcode
+ */
+
+#include "src/misc/Kernel.h"
+#include "src/misc/Image.h"
+#include "src/LU/FullPivLU.h"
+#include "src/LU/PartialPivLU.h"
+#ifdef EIGEN_USE_LAPACKE
+#include "src/misc/lapacke_helpers.h"
+#include "src/LU/PartialPivLU_LAPACKE.h"
+#endif
+#include "src/LU/Determinant.h"
+#include "src/LU/InverseImpl.h"
+
+#if defined EIGEN_VECTORIZE_SSE || defined EIGEN_VECTORIZE_NEON
+ #include "src/LU/arch/InverseSize4.h"
+#endif
+
+#include "src/Core/util/ReenableStupidWarnings.h"
+
+#endif // EIGEN_LU_MODULE_H
diff --git a/Eigen/MetisSupport b/Eigen/MetisSupport
new file mode 100644
index 0000000..85c41bf
--- /dev/null
+++ b/Eigen/MetisSupport
@@ -0,0 +1,35 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_METISSUPPORT_MODULE_H
+#define EIGEN_METISSUPPORT_MODULE_H
+
+#include "SparseCore"
+
+#include "src/Core/util/DisableStupidWarnings.h"
+
+extern "C" {
+#include <metis.h>
+}
+
+
+/** \ingroup Support_modules
+ * \defgroup MetisSupport_Module MetisSupport module
+ *
+ * \code
+ * #include <Eigen/MetisSupport>
+ * \endcode
+ * This module defines an interface to the METIS reordering package (http://glaros.dtc.umn.edu/gkhome/views/metis).
+ * It can be used just as any other built-in method as explained in \link OrderingMethods_Module here. \endlink
+ */
+
+
+#include "src/MetisSupport/MetisSupport.h"
+
+#include "src/Core/util/ReenableStupidWarnings.h"
+
+#endif // EIGEN_METISSUPPORT_MODULE_H
diff --git a/Eigen/OrderingMethods b/Eigen/OrderingMethods
new file mode 100644
index 0000000..29691a6
--- /dev/null
+++ b/Eigen/OrderingMethods
@@ -0,0 +1,70 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_ORDERINGMETHODS_MODULE_H
+#define EIGEN_ORDERINGMETHODS_MODULE_H
+
+#include "SparseCore"
+
+#include "src/Core/util/DisableStupidWarnings.h"
+
+/**
+ * \defgroup OrderingMethods_Module OrderingMethods module
+ *
+ * This module is currently for internal use only
+ *
+ * It defines various built-in and external ordering methods for sparse matrices.
+ * They are typically used to reduce the number of elements during
+ * the sparse matrix decomposition (LLT, LU, QR).
+ * Precisely, in a preprocessing step, a permutation matrix P is computed using
+ * those ordering methods and applied to the columns of the matrix.
+ * Using for instance the sparse Cholesky decomposition, it is expected that
+ * the nonzeros elements in LLT(A*P) will be much smaller than that in LLT(A).
+ *
+ *
+ * Usage :
+ * \code
+ * #include <Eigen/OrderingMethods>
+ * \endcode
+ *
+ * A simple usage is as a template parameter in the sparse decomposition classes :
+ *
+ * \code
+ * SparseLU<MatrixType, COLAMDOrdering<int> > solver;
+ * \endcode
+ *
+ * \code
+ * SparseQR<MatrixType, COLAMDOrdering<int> > solver;
+ * \endcode
+ *
+ * It is possible as well to call directly a particular ordering method for your own purpose,
+ * \code
+ * AMDOrdering<int> ordering;
+ * PermutationMatrix<Dynamic, Dynamic, int> perm;
+ * SparseMatrix<double> A;
+ * //Fill the matrix ...
+ *
+ * ordering(A, perm); // Call AMD
+ * \endcode
+ *
+ * \note Some of these methods (like AMD or METIS), need the sparsity pattern
+ * of the input matrix to be symmetric. When the matrix is structurally unsymmetric,
+ * Eigen computes internally the pattern of \f$A^T*A\f$ before calling the method.
+ * If your matrix is already symmetric (at leat in structure), you can avoid that
+ * by calling the method with a SelfAdjointView type.
+ *
+ * \code
+ * // Call the ordering on the pattern of the lower triangular matrix A
+ * ordering(A.selfadjointView<Lower>(), perm);
+ * \endcode
+ */
+
+#include "src/OrderingMethods/Amd.h"
+#include "src/OrderingMethods/Ordering.h"
+#include "src/Core/util/ReenableStupidWarnings.h"
+
+#endif // EIGEN_ORDERINGMETHODS_MODULE_H
diff --git a/Eigen/PaStiXSupport b/Eigen/PaStiXSupport
new file mode 100644
index 0000000..234619a
--- /dev/null
+++ b/Eigen/PaStiXSupport
@@ -0,0 +1,49 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_PASTIXSUPPORT_MODULE_H
+#define EIGEN_PASTIXSUPPORT_MODULE_H
+
+#include "SparseCore"
+
+#include "src/Core/util/DisableStupidWarnings.h"
+
+extern "C" {
+#include <pastix_nompi.h>
+#include <pastix.h>
+}
+
+#ifdef complex
+#undef complex
+#endif
+
+/** \ingroup Support_modules
+ * \defgroup PaStiXSupport_Module PaStiXSupport module
+ *
+ * This module provides an interface to the <a href="http://pastix.gforge.inria.fr/">PaSTiX</a> library.
+ * PaSTiX is a general \b supernodal, \b parallel and \b opensource sparse solver.
+ * It provides the two following main factorization classes:
+ * - class PastixLLT : a supernodal, parallel LLt Cholesky factorization.
+ * - class PastixLDLT: a supernodal, parallel LDLt Cholesky factorization.
+ * - class PastixLU : a supernodal, parallel LU factorization (optimized for a symmetric pattern).
+ *
+ * \code
+ * #include <Eigen/PaStiXSupport>
+ * \endcode
+ *
+ * In order to use this module, the PaSTiX headers must be accessible from the include paths, and your binary must be linked to the PaSTiX library and its dependencies.
+ * This wrapper resuires PaStiX version 5.x compiled without MPI support.
+ * The dependencies depend on how PaSTiX has been compiled.
+ * For a cmake based project, you can use our FindPaSTiX.cmake module to help you in this task.
+ *
+ */
+
+#include "src/PaStiXSupport/PaStiXSupport.h"
+
+#include "src/Core/util/ReenableStupidWarnings.h"
+
+#endif // EIGEN_PASTIXSUPPORT_MODULE_H
diff --git a/Eigen/PardisoSupport b/Eigen/PardisoSupport
new file mode 100644
index 0000000..340edf5
--- /dev/null
+++ b/Eigen/PardisoSupport
@@ -0,0 +1,35 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_PARDISOSUPPORT_MODULE_H
+#define EIGEN_PARDISOSUPPORT_MODULE_H
+
+#include "SparseCore"
+
+#include "src/Core/util/DisableStupidWarnings.h"
+
+#include <mkl_pardiso.h>
+
+/** \ingroup Support_modules
+ * \defgroup PardisoSupport_Module PardisoSupport module
+ *
+ * This module brings support for the Intel(R) MKL PARDISO direct sparse solvers.
+ *
+ * \code
+ * #include <Eigen/PardisoSupport>
+ * \endcode
+ *
+ * In order to use this module, the MKL headers must be accessible from the include paths, and your binary must be linked to the MKL library and its dependencies.
+ * See this \ref TopicUsingIntelMKL "page" for more information on MKL-Eigen integration.
+ *
+ */
+
+#include "src/PardisoSupport/PardisoSupport.h"
+
+#include "src/Core/util/ReenableStupidWarnings.h"
+
+#endif // EIGEN_PARDISOSUPPORT_MODULE_H
diff --git a/Eigen/QR b/Eigen/QR
new file mode 100644
index 0000000..1f6c22e
--- /dev/null
+++ b/Eigen/QR
@@ -0,0 +1,46 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_QR_MODULE_H
+#define EIGEN_QR_MODULE_H
+
+#include "Core"
+
+#include "Cholesky"
+#include "Jacobi"
+#include "Householder"
+
+#include "src/Core/util/DisableStupidWarnings.h"
+
+/** \defgroup QR_Module QR module
+ *
+ *
+ *
+ * This module provides various QR decompositions
+ * This module also provides some MatrixBase methods, including:
+ * - MatrixBase::householderQr()
+ * - MatrixBase::colPivHouseholderQr()
+ * - MatrixBase::fullPivHouseholderQr()
+ *
+ * \code
+ * #include <Eigen/QR>
+ * \endcode
+ */
+
+#include "src/QR/HouseholderQR.h"
+#include "src/QR/FullPivHouseholderQR.h"
+#include "src/QR/ColPivHouseholderQR.h"
+#include "src/QR/CompleteOrthogonalDecomposition.h"
+#ifdef EIGEN_USE_LAPACKE
+#include "src/misc/lapacke_helpers.h"
+#include "src/QR/HouseholderQR_LAPACKE.h"
+#include "src/QR/ColPivHouseholderQR_LAPACKE.h"
+#endif
+
+#include "src/Core/util/ReenableStupidWarnings.h"
+
+#endif // EIGEN_QR_MODULE_H
diff --git a/Eigen/QtAlignedMalloc b/Eigen/QtAlignedMalloc
new file mode 100644
index 0000000..6fe8237
--- /dev/null
+++ b/Eigen/QtAlignedMalloc
@@ -0,0 +1,39 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_QTMALLOC_MODULE_H
+#define EIGEN_QTMALLOC_MODULE_H
+
+#include "Core"
+
+#if (!EIGEN_MALLOC_ALREADY_ALIGNED)
+
+#include "src/Core/util/DisableStupidWarnings.h"
+
+void *qMalloc(std::size_t size)
+{
+ return Eigen::internal::aligned_malloc(size);
+}
+
+void qFree(void *ptr)
+{
+ Eigen::internal::aligned_free(ptr);
+}
+
+void *qRealloc(void *ptr, std::size_t size)
+{
+ void* newPtr = Eigen::internal::aligned_malloc(size);
+ std::memcpy(newPtr, ptr, size);
+ Eigen::internal::aligned_free(ptr);
+ return newPtr;
+}
+
+#include "src/Core/util/ReenableStupidWarnings.h"
+
+#endif
+
+#endif // EIGEN_QTMALLOC_MODULE_H
diff --git a/Eigen/SPQRSupport b/Eigen/SPQRSupport
new file mode 100644
index 0000000..33c3370
--- /dev/null
+++ b/Eigen/SPQRSupport
@@ -0,0 +1,34 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_SPQRSUPPORT_MODULE_H
+#define EIGEN_SPQRSUPPORT_MODULE_H
+
+#include "SparseCore"
+
+#include "src/Core/util/DisableStupidWarnings.h"
+
+#include "SuiteSparseQR.hpp"
+
+/** \ingroup Support_modules
+ * \defgroup SPQRSupport_Module SuiteSparseQR module
+ *
+ * This module provides an interface to the SPQR library, which is part of the <a href="http://www.suitesparse.com">suitesparse</a> package.
+ *
+ * \code
+ * #include <Eigen/SPQRSupport>
+ * \endcode
+ *
+ * In order to use this module, the SPQR headers must be accessible from the include paths, and your binary must be linked to the SPQR library and its dependencies (Cholmod, AMD, COLAMD,...).
+ * For a cmake based project, you can use our FindSPQR.cmake and FindCholmod.Cmake modules
+ *
+ */
+
+#include "Eigen/CholmodSupport"
+#include "src/SPQRSupport/SuiteSparseQRSupport.h"
+
+#endif
diff --git a/Eigen/SVD b/Eigen/SVD
new file mode 100644
index 0000000..3451794
--- /dev/null
+++ b/Eigen/SVD
@@ -0,0 +1,50 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_SVD_MODULE_H
+#define EIGEN_SVD_MODULE_H
+
+#include "QR"
+#include "Householder"
+#include "Jacobi"
+
+#include "src/Core/util/DisableStupidWarnings.h"
+
+/** \defgroup SVD_Module SVD module
+ *
+ *
+ *
+ * This module provides SVD decomposition for matrices (both real and complex).
+ * Two decomposition algorithms are provided:
+ * - JacobiSVD implementing two-sided Jacobi iterations is numerically very accurate, fast for small matrices, but very slow for larger ones.
+ * - BDCSVD implementing a recursive divide & conquer strategy on top of an upper-bidiagonalization which remains fast for large problems.
+ * These decompositions are accessible via the respective classes and following MatrixBase methods:
+ * - MatrixBase::jacobiSvd()
+ * - MatrixBase::bdcSvd()
+ *
+ * \code
+ * #include <Eigen/SVD>
+ * \endcode
+ */
+
+#include "src/misc/RealSvd2x2.h"
+#include "src/SVD/UpperBidiagonalization.h"
+#include "src/SVD/SVDBase.h"
+#include "src/SVD/JacobiSVD.h"
+#include "src/SVD/BDCSVD.h"
+#if defined(EIGEN_USE_LAPACKE) && !defined(EIGEN_USE_LAPACKE_STRICT)
+#ifdef EIGEN_USE_MKL
+#include "mkl_lapacke.h"
+#else
+#include "src/misc/lapacke.h"
+#endif
+#include "src/SVD/JacobiSVD_LAPACKE.h"
+#endif
+
+#include "src/Core/util/ReenableStupidWarnings.h"
+
+#endif // EIGEN_SVD_MODULE_H
diff --git a/Eigen/Sparse b/Eigen/Sparse
new file mode 100644
index 0000000..a2ef7a6
--- /dev/null
+++ b/Eigen/Sparse
@@ -0,0 +1,34 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_SPARSE_MODULE_H
+#define EIGEN_SPARSE_MODULE_H
+
+/** \defgroup Sparse_Module Sparse meta-module
+ *
+ * Meta-module including all related modules:
+ * - \ref SparseCore_Module
+ * - \ref OrderingMethods_Module
+ * - \ref SparseCholesky_Module
+ * - \ref SparseLU_Module
+ * - \ref SparseQR_Module
+ * - \ref IterativeLinearSolvers_Module
+ *
+ \code
+ #include <Eigen/Sparse>
+ \endcode
+ */
+
+#include "SparseCore"
+#include "OrderingMethods"
+#include "SparseCholesky"
+#include "SparseLU"
+#include "SparseQR"
+#include "IterativeLinearSolvers"
+
+#endif // EIGEN_SPARSE_MODULE_H
+
diff --git a/Eigen/SparseCholesky b/Eigen/SparseCholesky
new file mode 100644
index 0000000..d2b1f12
--- /dev/null
+++ b/Eigen/SparseCholesky
@@ -0,0 +1,37 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2013 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_SPARSECHOLESKY_MODULE_H
+#define EIGEN_SPARSECHOLESKY_MODULE_H
+
+#include "SparseCore"
+#include "OrderingMethods"
+
+#include "src/Core/util/DisableStupidWarnings.h"
+
+/**
+ * \defgroup SparseCholesky_Module SparseCholesky module
+ *
+ * This module currently provides two variants of the direct sparse Cholesky decomposition for selfadjoint (hermitian) matrices.
+ * Those decompositions are accessible via the following classes:
+ * - SimplicialLLt,
+ * - SimplicialLDLt
+ *
+ * Such problems can also be solved using the ConjugateGradient solver from the IterativeLinearSolvers module.
+ *
+ * \code
+ * #include <Eigen/SparseCholesky>
+ * \endcode
+ */
+
+#include "src/SparseCholesky/SimplicialCholesky.h"
+#include "src/SparseCholesky/SimplicialCholesky_impl.h"
+#include "src/Core/util/ReenableStupidWarnings.h"
+
+#endif // EIGEN_SPARSECHOLESKY_MODULE_H
diff --git a/Eigen/SparseCore b/Eigen/SparseCore
new file mode 100644
index 0000000..b2db46b
--- /dev/null
+++ b/Eigen/SparseCore
@@ -0,0 +1,68 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_SPARSECORE_MODULE_H
+#define EIGEN_SPARSECORE_MODULE_H
+
+#include "Core"
+
+#include "src/Core/util/DisableStupidWarnings.h"
+
+#include <vector>
+#include <map>
+#include <cstdlib>
+#include <cstring>
+#include <algorithm>
+
+/**
+ * \defgroup SparseCore_Module SparseCore module
+ *
+ * This module provides a sparse matrix representation, and basic associated matrix manipulations
+ * and operations.
+ *
+ * See the \ref TutorialSparse "Sparse tutorial"
+ *
+ * \code
+ * #include <Eigen/SparseCore>
+ * \endcode
+ *
+ * This module depends on: Core.
+ */
+
+#include "src/SparseCore/SparseUtil.h"
+#include "src/SparseCore/SparseMatrixBase.h"
+#include "src/SparseCore/SparseAssign.h"
+#include "src/SparseCore/CompressedStorage.h"
+#include "src/SparseCore/AmbiVector.h"
+#include "src/SparseCore/SparseCompressedBase.h"
+#include "src/SparseCore/SparseMatrix.h"
+#include "src/SparseCore/SparseMap.h"
+#include "src/SparseCore/SparseVector.h"
+#include "src/SparseCore/SparseRef.h"
+#include "src/SparseCore/SparseCwiseUnaryOp.h"
+#include "src/SparseCore/SparseCwiseBinaryOp.h"
+#include "src/SparseCore/SparseTranspose.h"
+#include "src/SparseCore/SparseBlock.h"
+#include "src/SparseCore/SparseDot.h"
+#include "src/SparseCore/SparseRedux.h"
+#include "src/SparseCore/SparseView.h"
+#include "src/SparseCore/SparseDiagonalProduct.h"
+#include "src/SparseCore/ConservativeSparseSparseProduct.h"
+#include "src/SparseCore/SparseSparseProductWithPruning.h"
+#include "src/SparseCore/SparseProduct.h"
+#include "src/SparseCore/SparseDenseProduct.h"
+#include "src/SparseCore/SparseSelfAdjointView.h"
+#include "src/SparseCore/SparseTriangularView.h"
+#include "src/SparseCore/TriangularSolver.h"
+#include "src/SparseCore/SparsePermutation.h"
+#include "src/SparseCore/SparseFuzzy.h"
+#include "src/SparseCore/SparseSolverBase.h"
+
+#include "src/Core/util/ReenableStupidWarnings.h"
+
+#endif // EIGEN_SPARSECORE_MODULE_H
+
diff --git a/Eigen/SparseLU b/Eigen/SparseLU
new file mode 100644
index 0000000..37c4a5c
--- /dev/null
+++ b/Eigen/SparseLU
@@ -0,0 +1,50 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2012 Désiré Nuentsa-Wakam <desire.nuentsa_wakam@inria.fr>
+// Copyright (C) 2012 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_SPARSELU_MODULE_H
+#define EIGEN_SPARSELU_MODULE_H
+
+#include "SparseCore"
+
+/**
+ * \defgroup SparseLU_Module SparseLU module
+ * This module defines a supernodal factorization of general sparse matrices.
+ * The code is fully optimized for supernode-panel updates with specialized kernels.
+ * Please, see the documentation of the SparseLU class for more details.
+ */
+
+// Ordering interface
+#include "OrderingMethods"
+
+#include "src/Core/util/DisableStupidWarnings.h"
+
+#include "src/SparseLU/SparseLU_gemm_kernel.h"
+
+#include "src/SparseLU/SparseLU_Structs.h"
+#include "src/SparseLU/SparseLU_SupernodalMatrix.h"
+#include "src/SparseLU/SparseLUImpl.h"
+#include "src/SparseCore/SparseColEtree.h"
+#include "src/SparseLU/SparseLU_Memory.h"
+#include "src/SparseLU/SparseLU_heap_relax_snode.h"
+#include "src/SparseLU/SparseLU_relax_snode.h"
+#include "src/SparseLU/SparseLU_pivotL.h"
+#include "src/SparseLU/SparseLU_panel_dfs.h"
+#include "src/SparseLU/SparseLU_kernel_bmod.h"
+#include "src/SparseLU/SparseLU_panel_bmod.h"
+#include "src/SparseLU/SparseLU_column_dfs.h"
+#include "src/SparseLU/SparseLU_column_bmod.h"
+#include "src/SparseLU/SparseLU_copy_to_ucol.h"
+#include "src/SparseLU/SparseLU_pruneL.h"
+#include "src/SparseLU/SparseLU_Utils.h"
+#include "src/SparseLU/SparseLU.h"
+
+#include "src/Core/util/ReenableStupidWarnings.h"
+
+#endif // EIGEN_SPARSELU_MODULE_H
diff --git a/Eigen/SparseQR b/Eigen/SparseQR
new file mode 100644
index 0000000..f5fc5fa
--- /dev/null
+++ b/Eigen/SparseQR
@@ -0,0 +1,36 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_SPARSEQR_MODULE_H
+#define EIGEN_SPARSEQR_MODULE_H
+
+#include "SparseCore"
+#include "OrderingMethods"
+#include "src/Core/util/DisableStupidWarnings.h"
+
+/** \defgroup SparseQR_Module SparseQR module
+ * \brief Provides QR decomposition for sparse matrices
+ *
+ * This module provides a simplicial version of the left-looking Sparse QR decomposition.
+ * The columns of the input matrix should be reordered to limit the fill-in during the
+ * decomposition. Built-in methods (COLAMD, AMD) or external methods (METIS) can be used to this end.
+ * See the \link OrderingMethods_Module OrderingMethods\endlink module for the list
+ * of built-in and external ordering methods.
+ *
+ * \code
+ * #include <Eigen/SparseQR>
+ * \endcode
+ *
+ *
+ */
+
+#include "src/SparseCore/SparseColEtree.h"
+#include "src/SparseQR/SparseQR.h"
+
+#include "src/Core/util/ReenableStupidWarnings.h"
+
+#endif
diff --git a/Eigen/StdDeque b/Eigen/StdDeque
new file mode 100644
index 0000000..bc68397
--- /dev/null
+++ b/Eigen/StdDeque
@@ -0,0 +1,27 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2009 Hauke Heibel <hauke.heibel@googlemail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_STDDEQUE_MODULE_H
+#define EIGEN_STDDEQUE_MODULE_H
+
+#include "Core"
+#include <deque>
+
+#if EIGEN_COMP_MSVC && EIGEN_OS_WIN64 && (EIGEN_MAX_STATIC_ALIGN_BYTES<=16) /* MSVC auto aligns up to 16 bytes in 64 bit builds */
+
+#define EIGEN_DEFINE_STL_DEQUE_SPECIALIZATION(...)
+
+#else
+
+#include "src/StlSupport/StdDeque.h"
+
+#endif
+
+#endif // EIGEN_STDDEQUE_MODULE_H
diff --git a/Eigen/StdList b/Eigen/StdList
new file mode 100644
index 0000000..4c6262c
--- /dev/null
+++ b/Eigen/StdList
@@ -0,0 +1,26 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009 Hauke Heibel <hauke.heibel@googlemail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_STDLIST_MODULE_H
+#define EIGEN_STDLIST_MODULE_H
+
+#include "Core"
+#include <list>
+
+#if EIGEN_COMP_MSVC && EIGEN_OS_WIN64 && (EIGEN_MAX_STATIC_ALIGN_BYTES<=16) /* MSVC auto aligns up to 16 bytes in 64 bit builds */
+
+#define EIGEN_DEFINE_STL_LIST_SPECIALIZATION(...)
+
+#else
+
+#include "src/StlSupport/StdList.h"
+
+#endif
+
+#endif // EIGEN_STDLIST_MODULE_H
diff --git a/Eigen/StdVector b/Eigen/StdVector
new file mode 100644
index 0000000..0c4697a
--- /dev/null
+++ b/Eigen/StdVector
@@ -0,0 +1,27 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2009 Hauke Heibel <hauke.heibel@googlemail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_STDVECTOR_MODULE_H
+#define EIGEN_STDVECTOR_MODULE_H
+
+#include "Core"
+#include <vector>
+
+#if EIGEN_COMP_MSVC && EIGEN_OS_WIN64 && (EIGEN_MAX_STATIC_ALIGN_BYTES<=16) /* MSVC auto aligns up to 16 bytes in 64 bit builds */
+
+#define EIGEN_DEFINE_STL_VECTOR_SPECIALIZATION(...)
+
+#else
+
+#include "src/StlSupport/StdVector.h"
+
+#endif
+
+#endif // EIGEN_STDVECTOR_MODULE_H
diff --git a/Eigen/SuperLUSupport b/Eigen/SuperLUSupport
new file mode 100644
index 0000000..59312a8
--- /dev/null
+++ b/Eigen/SuperLUSupport
@@ -0,0 +1,64 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_SUPERLUSUPPORT_MODULE_H
+#define EIGEN_SUPERLUSUPPORT_MODULE_H
+
+#include "SparseCore"
+
+#include "src/Core/util/DisableStupidWarnings.h"
+
+#ifdef EMPTY
+#define EIGEN_EMPTY_WAS_ALREADY_DEFINED
+#endif
+
+typedef int int_t;
+#include <slu_Cnames.h>
+#include <supermatrix.h>
+#include <slu_util.h>
+
+// slu_util.h defines a preprocessor token named EMPTY which is really polluting,
+// so we remove it in favor of a SUPERLU_EMPTY token.
+// If EMPTY was already defined then we don't undef it.
+
+#if defined(EIGEN_EMPTY_WAS_ALREADY_DEFINED)
+# undef EIGEN_EMPTY_WAS_ALREADY_DEFINED
+#elif defined(EMPTY)
+# undef EMPTY
+#endif
+
+#define SUPERLU_EMPTY (-1)
+
+namespace Eigen { struct SluMatrix; }
+
+/** \ingroup Support_modules
+ * \defgroup SuperLUSupport_Module SuperLUSupport module
+ *
+ * This module provides an interface to the <a href="http://crd-legacy.lbl.gov/~xiaoye/SuperLU/">SuperLU</a> library.
+ * It provides the following factorization class:
+ * - class SuperLU: a supernodal sequential LU factorization.
+ * - class SuperILU: a supernodal sequential incomplete LU factorization (to be used as a preconditioner for iterative methods).
+ *
+ * \warning This wrapper requires at least versions 4.0 of SuperLU. The 3.x versions are not supported.
+ *
+ * \warning When including this module, you have to use SUPERLU_EMPTY instead of EMPTY which is no longer defined because it is too polluting.
+ *
+ * \code
+ * #include <Eigen/SuperLUSupport>
+ * \endcode
+ *
+ * In order to use this module, the superlu headers must be accessible from the include paths, and your binary must be linked to the superlu library and its dependencies.
+ * The dependencies depend on how superlu has been compiled.
+ * For a cmake based project, you can use our FindSuperLU.cmake module to help you in this task.
+ *
+ */
+
+#include "src/SuperLUSupport/SuperLUSupport.h"
+
+#include "src/Core/util/ReenableStupidWarnings.h"
+
+#endif // EIGEN_SUPERLUSUPPORT_MODULE_H
diff --git a/Eigen/UmfPackSupport b/Eigen/UmfPackSupport
new file mode 100644
index 0000000..00eec80
--- /dev/null
+++ b/Eigen/UmfPackSupport
@@ -0,0 +1,40 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_UMFPACKSUPPORT_MODULE_H
+#define EIGEN_UMFPACKSUPPORT_MODULE_H
+
+#include "SparseCore"
+
+#include "src/Core/util/DisableStupidWarnings.h"
+
+extern "C" {
+#include <umfpack.h>
+}
+
+/** \ingroup Support_modules
+ * \defgroup UmfPackSupport_Module UmfPackSupport module
+ *
+ * This module provides an interface to the UmfPack library which is part of the <a href="http://www.suitesparse.com">suitesparse</a> package.
+ * It provides the following factorization class:
+ * - class UmfPackLU: a multifrontal sequential LU factorization.
+ *
+ * \code
+ * #include <Eigen/UmfPackSupport>
+ * \endcode
+ *
+ * In order to use this module, the umfpack headers must be accessible from the include paths, and your binary must be linked to the umfpack library and its dependencies.
+ * The dependencies depend on how umfpack has been compiled.
+ * For a cmake based project, you can use our FindUmfPack.cmake module to help you in this task.
+ *
+ */
+
+#include "src/UmfPackSupport/UmfPackSupport.h"
+
+#include "src/Core/util/ReenableStupidWarnings.h"
+
+#endif // EIGEN_UMFPACKSUPPORT_MODULE_H
diff --git a/Eigen/src/AccelerateSupport/AccelerateSupport.h b/Eigen/src/AccelerateSupport/AccelerateSupport.h
new file mode 100644
index 0000000..0417688
--- /dev/null
+++ b/Eigen/src/AccelerateSupport/AccelerateSupport.h
@@ -0,0 +1,421 @@
+#ifndef EIGEN_ACCELERATESUPPORT_H
+#define EIGEN_ACCELERATESUPPORT_H
+
+#include <Accelerate/Accelerate.h>
+
+#include <Eigen/Sparse>
+
+namespace Eigen {
+
+template <typename MatrixType_, int UpLo_, SparseFactorization_t Solver_, bool EnforceSquare_>
+class AccelerateImpl;
+
+/** \ingroup AccelerateSupport_Module
+ * \class AccelerateLLT
+ * \brief A direct Cholesky (LLT) factorization and solver based on Accelerate
+ *
+ * \warning Only single and double precision real scalar types are supported by Accelerate
+ *
+ * \tparam MatrixType_ the type of the sparse matrix A, it must be a SparseMatrix<>
+ * \tparam UpLo_ additional information about the matrix structure. Default is Lower.
+ *
+ * \sa \ref TutorialSparseSolverConcept, class AccelerateLLT
+ */
+template <typename MatrixType, int UpLo = Lower>
+using AccelerateLLT = AccelerateImpl<MatrixType, UpLo | Symmetric, SparseFactorizationCholesky, true>;
+
+/** \ingroup AccelerateSupport_Module
+ * \class AccelerateLDLT
+ * \brief The default Cholesky (LDLT) factorization and solver based on Accelerate
+ *
+ * \warning Only single and double precision real scalar types are supported by Accelerate
+ *
+ * \tparam MatrixType_ the type of the sparse matrix A, it must be a SparseMatrix<>
+ * \tparam UpLo_ additional information about the matrix structure. Default is Lower.
+ *
+ * \sa \ref TutorialSparseSolverConcept, class AccelerateLDLT
+ */
+template <typename MatrixType, int UpLo = Lower>
+using AccelerateLDLT = AccelerateImpl<MatrixType, UpLo | Symmetric, SparseFactorizationLDLT, true>;
+
+/** \ingroup AccelerateSupport_Module
+ * \class AccelerateLDLTUnpivoted
+ * \brief A direct Cholesky-like LDL^T factorization and solver based on Accelerate with only 1x1 pivots and no pivoting
+ *
+ * \warning Only single and double precision real scalar types are supported by Accelerate
+ *
+ * \tparam MatrixType_ the type of the sparse matrix A, it must be a SparseMatrix<>
+ * \tparam UpLo_ additional information about the matrix structure. Default is Lower.
+ *
+ * \sa \ref TutorialSparseSolverConcept, class AccelerateLDLTUnpivoted
+ */
+template <typename MatrixType, int UpLo = Lower>
+using AccelerateLDLTUnpivoted = AccelerateImpl<MatrixType, UpLo | Symmetric, SparseFactorizationLDLTUnpivoted, true>;
+
+/** \ingroup AccelerateSupport_Module
+ * \class AccelerateLDLTSBK
+ * \brief A direct Cholesky (LDLT) factorization and solver based on Accelerate with Supernode Bunch-Kaufman and static pivoting
+ *
+ * \warning Only single and double precision real scalar types are supported by Accelerate
+ *
+ * \tparam MatrixType_ the type of the sparse matrix A, it must be a SparseMatrix<>
+ * \tparam UpLo_ additional information about the matrix structure. Default is Lower.
+ *
+ * \sa \ref TutorialSparseSolverConcept, class AccelerateLDLTSBK
+ */
+template <typename MatrixType, int UpLo = Lower>
+using AccelerateLDLTSBK = AccelerateImpl<MatrixType, UpLo | Symmetric, SparseFactorizationLDLTSBK, true>;
+
+/** \ingroup AccelerateSupport_Module
+ * \class AccelerateLDLTTPP
+ * \brief A direct Cholesky (LDLT) factorization and solver based on Accelerate with full threshold partial pivoting
+ *
+ * \warning Only single and double precision real scalar types are supported by Accelerate
+ *
+ * \tparam MatrixType_ the type of the sparse matrix A, it must be a SparseMatrix<>
+ * \tparam UpLo_ additional information about the matrix structure. Default is Lower.
+ *
+ * \sa \ref TutorialSparseSolverConcept, class AccelerateLDLTTPP
+ */
+template <typename MatrixType, int UpLo = Lower>
+using AccelerateLDLTTPP = AccelerateImpl<MatrixType, UpLo | Symmetric, SparseFactorizationLDLTTPP, true>;
+
+/** \ingroup AccelerateSupport_Module
+ * \class AccelerateQR
+ * \brief A QR factorization and solver based on Accelerate
+ *
+ * \warning Only single and double precision real scalar types are supported by Accelerate
+ *
+ * \tparam MatrixType_ the type of the sparse matrix A, it must be a SparseMatrix<>
+ *
+ * \sa \ref TutorialSparseSolverConcept, class AccelerateQR
+ */
+template <typename MatrixType>
+using AccelerateQR = AccelerateImpl<MatrixType, 0, SparseFactorizationQR, false>;
+
+/** \ingroup AccelerateSupport_Module
+ * \class AccelerateCholeskyAtA
+ * \brief A QR factorization and solver based on Accelerate without storing Q (equivalent to A^TA = R^T R)
+ *
+ * \warning Only single and double precision real scalar types are supported by Accelerate
+ *
+ * \tparam MatrixType_ the type of the sparse matrix A, it must be a SparseMatrix<>
+ *
+ * \sa \ref TutorialSparseSolverConcept, class AccelerateCholeskyAtA
+ */
+template <typename MatrixType>
+using AccelerateCholeskyAtA = AccelerateImpl<MatrixType, 0, SparseFactorizationCholeskyAtA, false>;
+
+namespace internal {
+template <typename T>
+struct AccelFactorizationDeleter {
+ void operator()(T* sym) {
+ if (sym) {
+ SparseCleanup(*sym);
+ delete sym;
+ sym = nullptr;
+ }
+ }
+};
+
+template <typename DenseVecT, typename DenseMatT, typename SparseMatT, typename NumFactT>
+struct SparseTypesTraitBase {
+ typedef DenseVecT AccelDenseVector;
+ typedef DenseMatT AccelDenseMatrix;
+ typedef SparseMatT AccelSparseMatrix;
+
+ typedef SparseOpaqueSymbolicFactorization SymbolicFactorization;
+ typedef NumFactT NumericFactorization;
+
+ typedef AccelFactorizationDeleter<SymbolicFactorization> SymbolicFactorizationDeleter;
+ typedef AccelFactorizationDeleter<NumericFactorization> NumericFactorizationDeleter;
+};
+
+template <typename Scalar>
+struct SparseTypesTrait {};
+
+template <>
+struct SparseTypesTrait<double> : SparseTypesTraitBase<DenseVector_Double, DenseMatrix_Double, SparseMatrix_Double,
+ SparseOpaqueFactorization_Double> {};
+
+template <>
+struct SparseTypesTrait<float>
+ : SparseTypesTraitBase<DenseVector_Float, DenseMatrix_Float, SparseMatrix_Float, SparseOpaqueFactorization_Float> {
+};
+
+} // end namespace internal
+
+template <typename MatrixType_, int UpLo_, SparseFactorization_t Solver_, bool EnforceSquare_>
+class AccelerateImpl : public SparseSolverBase<AccelerateImpl<MatrixType_, UpLo_, Solver_, EnforceSquare_> > {
+ protected:
+ using Base = SparseSolverBase<AccelerateImpl>;
+ using Base::derived;
+ using Base::m_isInitialized;
+
+ public:
+ using Base::_solve_impl;
+
+ typedef MatrixType_ MatrixType;
+ typedef typename MatrixType::Scalar Scalar;
+ typedef typename MatrixType::StorageIndex StorageIndex;
+ enum { ColsAtCompileTime = Dynamic, MaxColsAtCompileTime = Dynamic };
+ enum { UpLo = UpLo_ };
+
+ using AccelDenseVector = typename internal::SparseTypesTrait<Scalar>::AccelDenseVector;
+ using AccelDenseMatrix = typename internal::SparseTypesTrait<Scalar>::AccelDenseMatrix;
+ using AccelSparseMatrix = typename internal::SparseTypesTrait<Scalar>::AccelSparseMatrix;
+ using SymbolicFactorization = typename internal::SparseTypesTrait<Scalar>::SymbolicFactorization;
+ using NumericFactorization = typename internal::SparseTypesTrait<Scalar>::NumericFactorization;
+ using SymbolicFactorizationDeleter = typename internal::SparseTypesTrait<Scalar>::SymbolicFactorizationDeleter;
+ using NumericFactorizationDeleter = typename internal::SparseTypesTrait<Scalar>::NumericFactorizationDeleter;
+
+ AccelerateImpl() {
+ m_isInitialized = false;
+
+ auto check_flag_set = [](int value, int flag) { return ((value & flag) == flag); };
+
+ if (check_flag_set(UpLo_, Symmetric)) {
+ m_sparseKind = SparseSymmetric;
+ m_triType = (UpLo_ & Lower) ? SparseLowerTriangle : SparseUpperTriangle;
+ } else if (check_flag_set(UpLo_, UnitLower)) {
+ m_sparseKind = SparseUnitTriangular;
+ m_triType = SparseLowerTriangle;
+ } else if (check_flag_set(UpLo_, UnitUpper)) {
+ m_sparseKind = SparseUnitTriangular;
+ m_triType = SparseUpperTriangle;
+ } else if (check_flag_set(UpLo_, StrictlyLower)) {
+ m_sparseKind = SparseTriangular;
+ m_triType = SparseLowerTriangle;
+ } else if (check_flag_set(UpLo_, StrictlyUpper)) {
+ m_sparseKind = SparseTriangular;
+ m_triType = SparseUpperTriangle;
+ } else if (check_flag_set(UpLo_, Lower)) {
+ m_sparseKind = SparseTriangular;
+ m_triType = SparseLowerTriangle;
+ } else if (check_flag_set(UpLo_, Upper)) {
+ m_sparseKind = SparseTriangular;
+ m_triType = SparseUpperTriangle;
+ } else {
+ m_sparseKind = SparseOrdinary;
+ m_triType = (UpLo_ & Lower) ? SparseLowerTriangle : SparseUpperTriangle;
+ }
+
+ m_order = SparseOrderDefault;
+ }
+
+ explicit AccelerateImpl(const MatrixType& matrix) : AccelerateImpl() { compute(matrix); }
+
+ ~AccelerateImpl() {}
+
+ inline Index cols() const { return m_nCols; }
+ inline Index rows() const { return m_nRows; }
+
+ ComputationInfo info() const {
+ eigen_assert(m_isInitialized && "Decomposition is not initialized.");
+ return m_info;
+ }
+
+ void analyzePattern(const MatrixType& matrix);
+
+ void factorize(const MatrixType& matrix);
+
+ void compute(const MatrixType& matrix);
+
+ template <typename Rhs, typename Dest>
+ void _solve_impl(const MatrixBase<Rhs>& b, MatrixBase<Dest>& dest) const;
+
+ /** Sets the ordering algorithm to use. */
+ void setOrder(SparseOrder_t order) { m_order = order; }
+
+ private:
+ template <typename T>
+ void buildAccelSparseMatrix(const SparseMatrix<T>& a, AccelSparseMatrix& A, std::vector<long>& columnStarts) {
+ const Index nColumnsStarts = a.cols() + 1;
+
+ columnStarts.resize(nColumnsStarts);
+
+ for (Index i = 0; i < nColumnsStarts; i++) columnStarts[i] = a.outerIndexPtr()[i];
+
+ SparseAttributes_t attributes{};
+ attributes.transpose = false;
+ attributes.triangle = m_triType;
+ attributes.kind = m_sparseKind;
+
+ SparseMatrixStructure structure{};
+ structure.attributes = attributes;
+ structure.rowCount = static_cast<int>(a.rows());
+ structure.columnCount = static_cast<int>(a.cols());
+ structure.blockSize = 1;
+ structure.columnStarts = columnStarts.data();
+ structure.rowIndices = const_cast<int*>(a.innerIndexPtr());
+
+ A.structure = structure;
+ A.data = const_cast<T*>(a.valuePtr());
+ }
+
+ void doAnalysis(AccelSparseMatrix& A) {
+ m_numericFactorization.reset(nullptr);
+
+ SparseSymbolicFactorOptions opts{};
+ opts.control = SparseDefaultControl;
+ opts.orderMethod = m_order;
+ opts.order = nullptr;
+ opts.ignoreRowsAndColumns = nullptr;
+ opts.malloc = malloc;
+ opts.free = free;
+ opts.reportError = nullptr;
+
+ m_symbolicFactorization.reset(new SymbolicFactorization(SparseFactor(Solver_, A.structure, opts)));
+
+ SparseStatus_t status = m_symbolicFactorization->status;
+
+ updateInfoStatus(status);
+
+ if (status != SparseStatusOK) m_symbolicFactorization.reset(nullptr);
+ }
+
+ void doFactorization(AccelSparseMatrix& A) {
+ SparseStatus_t status = SparseStatusReleased;
+
+ if (m_symbolicFactorization) {
+ m_numericFactorization.reset(new NumericFactorization(SparseFactor(*m_symbolicFactorization, A)));
+
+ status = m_numericFactorization->status;
+
+ if (status != SparseStatusOK) m_numericFactorization.reset(nullptr);
+ }
+
+ updateInfoStatus(status);
+ }
+
+ protected:
+ void updateInfoStatus(SparseStatus_t status) const {
+ switch (status) {
+ case SparseStatusOK:
+ m_info = Success;
+ break;
+ case SparseFactorizationFailed:
+ case SparseMatrixIsSingular:
+ m_info = NumericalIssue;
+ break;
+ case SparseInternalError:
+ case SparseParameterError:
+ case SparseStatusReleased:
+ default:
+ m_info = InvalidInput;
+ break;
+ }
+ }
+
+ mutable ComputationInfo m_info;
+ Index m_nRows, m_nCols;
+ std::unique_ptr<SymbolicFactorization, SymbolicFactorizationDeleter> m_symbolicFactorization;
+ std::unique_ptr<NumericFactorization, NumericFactorizationDeleter> m_numericFactorization;
+ SparseKind_t m_sparseKind;
+ SparseTriangle_t m_triType;
+ SparseOrder_t m_order;
+};
+
+/** Computes the symbolic and numeric decomposition of matrix \a a */
+template <typename MatrixType_, int UpLo_, SparseFactorization_t Solver_, bool EnforceSquare_>
+void AccelerateImpl<MatrixType_, UpLo_, Solver_, EnforceSquare_>::compute(const MatrixType& a) {
+ if (EnforceSquare_) eigen_assert(a.rows() == a.cols());
+
+ m_nRows = a.rows();
+ m_nCols = a.cols();
+
+ AccelSparseMatrix A{};
+ std::vector<long> columnStarts;
+
+ buildAccelSparseMatrix(a, A, columnStarts);
+
+ doAnalysis(A);
+
+ if (m_symbolicFactorization) doFactorization(A);
+
+ m_isInitialized = true;
+}
+
+/** Performs a symbolic decomposition on the sparsity pattern of matrix \a a.
+ *
+ * This function is particularly useful when solving for several problems having the same structure.
+ *
+ * \sa factorize()
+ */
+template <typename MatrixType_, int UpLo_, SparseFactorization_t Solver_, bool EnforceSquare_>
+void AccelerateImpl<MatrixType_, UpLo_, Solver_, EnforceSquare_>::analyzePattern(const MatrixType& a) {
+ if (EnforceSquare_) eigen_assert(a.rows() == a.cols());
+
+ m_nRows = a.rows();
+ m_nCols = a.cols();
+
+ AccelSparseMatrix A{};
+ std::vector<long> columnStarts;
+
+ buildAccelSparseMatrix(a, A, columnStarts);
+
+ doAnalysis(A);
+
+ m_isInitialized = true;
+}
+
+/** Performs a numeric decomposition of matrix \a a.
+ *
+ * The given matrix must have the same sparsity pattern as the matrix on which the symbolic decomposition has been performed.
+ *
+ * \sa analyzePattern()
+ */
+template <typename MatrixType_, int UpLo_, SparseFactorization_t Solver_, bool EnforceSquare_>
+void AccelerateImpl<MatrixType_, UpLo_, Solver_, EnforceSquare_>::factorize(const MatrixType& a) {
+ eigen_assert(m_symbolicFactorization && "You must first call analyzePattern()");
+ eigen_assert(m_nRows == a.rows() && m_nCols == a.cols());
+
+ if (EnforceSquare_) eigen_assert(a.rows() == a.cols());
+
+ AccelSparseMatrix A{};
+ std::vector<long> columnStarts;
+
+ buildAccelSparseMatrix(a, A, columnStarts);
+
+ doFactorization(A);
+}
+
+template <typename MatrixType_, int UpLo_, SparseFactorization_t Solver_, bool EnforceSquare_>
+template <typename Rhs, typename Dest>
+void AccelerateImpl<MatrixType_, UpLo_, Solver_, EnforceSquare_>::_solve_impl(const MatrixBase<Rhs>& b,
+ MatrixBase<Dest>& x) const {
+ if (!m_numericFactorization) {
+ m_info = InvalidInput;
+ return;
+ }
+
+ eigen_assert(m_nRows == b.rows());
+ eigen_assert(((b.cols() == 1) || b.outerStride() == b.rows()));
+
+ SparseStatus_t status = SparseStatusOK;
+
+ Scalar* b_ptr = const_cast<Scalar*>(b.derived().data());
+ Scalar* x_ptr = const_cast<Scalar*>(x.derived().data());
+
+ AccelDenseMatrix xmat{};
+ xmat.attributes = SparseAttributes_t();
+ xmat.columnCount = static_cast<int>(x.cols());
+ xmat.rowCount = static_cast<int>(x.rows());
+ xmat.columnStride = xmat.rowCount;
+ xmat.data = x_ptr;
+
+ AccelDenseMatrix bmat{};
+ bmat.attributes = SparseAttributes_t();
+ bmat.columnCount = static_cast<int>(b.cols());
+ bmat.rowCount = static_cast<int>(b.rows());
+ bmat.columnStride = bmat.rowCount;
+ bmat.data = b_ptr;
+
+ SparseSolve(*m_numericFactorization, bmat, xmat);
+
+ updateInfoStatus(status);
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_ACCELERATESUPPORT_H
diff --git a/Eigen/src/AccelerateSupport/InternalHeaderCheck.h b/Eigen/src/AccelerateSupport/InternalHeaderCheck.h
new file mode 100644
index 0000000..69bcff5
--- /dev/null
+++ b/Eigen/src/AccelerateSupport/InternalHeaderCheck.h
@@ -0,0 +1,3 @@
+#ifndef EIGEN_ACCELERATESUPPORT_MODULE_H
+#error "Please include Eigen/AccelerateSupport instead of including headers inside the src directory directly."
+#endif
diff --git a/Eigen/src/Cholesky/InternalHeaderCheck.h b/Eigen/src/Cholesky/InternalHeaderCheck.h
new file mode 100644
index 0000000..5de2b21
--- /dev/null
+++ b/Eigen/src/Cholesky/InternalHeaderCheck.h
@@ -0,0 +1,3 @@
+#ifndef EIGEN_CHOLESKY_MODULE_H
+#error "Please include Eigen/Cholesky instead of including headers inside the src directory directly."
+#endif
diff --git a/Eigen/src/Cholesky/LDLT.h b/Eigen/src/Cholesky/LDLT.h
new file mode 100644
index 0000000..1d0369b
--- /dev/null
+++ b/Eigen/src/Cholesky/LDLT.h
@@ -0,0 +1,685 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2011 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2009 Keir Mierle <mierle@gmail.com>
+// Copyright (C) 2009 Benoit Jacob <jacob.benoit.1@gmail.com>
+// Copyright (C) 2011 Timothy E. Holy <tim.holy@gmail.com >
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_LDLT_H
+#define EIGEN_LDLT_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+ template<typename MatrixType_, int UpLo_> struct traits<LDLT<MatrixType_, UpLo_> >
+ : traits<MatrixType_>
+ {
+ typedef MatrixXpr XprKind;
+ typedef SolverStorage StorageKind;
+ typedef int StorageIndex;
+ enum { Flags = 0 };
+ };
+
+ template<typename MatrixType, int UpLo> struct LDLT_Traits;
+
+ // PositiveSemiDef means positive semi-definite and non-zero; same for NegativeSemiDef
+ enum SignMatrix { PositiveSemiDef, NegativeSemiDef, ZeroSign, Indefinite };
+}
+
+/** \ingroup Cholesky_Module
+ *
+ * \class LDLT
+ *
+ * \brief Robust Cholesky decomposition of a matrix with pivoting
+ *
+ * \tparam MatrixType_ the type of the matrix of which to compute the LDL^T Cholesky decomposition
+ * \tparam UpLo_ the triangular part that will be used for the decomposition: Lower (default) or Upper.
+ * The other triangular part won't be read.
+ *
+ * Perform a robust Cholesky decomposition of a positive semidefinite or negative semidefinite
+ * matrix \f$ A \f$ such that \f$ A = P^TLDL^*P \f$, where P is a permutation matrix, L
+ * is lower triangular with a unit diagonal and D is a diagonal matrix.
+ *
+ * The decomposition uses pivoting to ensure stability, so that D will have
+ * zeros in the bottom right rank(A) - n submatrix. Avoiding the square root
+ * on D also stabilizes the computation.
+ *
+ * Remember that Cholesky decompositions are not rank-revealing. Also, do not use a Cholesky
+ * decomposition to determine whether a system of equations has a solution.
+ *
+ * This class supports the \link InplaceDecomposition inplace decomposition \endlink mechanism.
+ *
+ * \sa MatrixBase::ldlt(), SelfAdjointView::ldlt(), class LLT
+ */
+template<typename MatrixType_, int UpLo_> class LDLT
+ : public SolverBase<LDLT<MatrixType_, UpLo_> >
+{
+ public:
+ typedef MatrixType_ MatrixType;
+ typedef SolverBase<LDLT> Base;
+ friend class SolverBase<LDLT>;
+
+ EIGEN_GENERIC_PUBLIC_INTERFACE(LDLT)
+ enum {
+ MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime,
+ MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime,
+ UpLo = UpLo_
+ };
+ typedef Matrix<Scalar, RowsAtCompileTime, 1, 0, MaxRowsAtCompileTime, 1> TmpMatrixType;
+
+ typedef Transpositions<RowsAtCompileTime, MaxRowsAtCompileTime> TranspositionType;
+ typedef PermutationMatrix<RowsAtCompileTime, MaxRowsAtCompileTime> PermutationType;
+
+ typedef internal::LDLT_Traits<MatrixType,UpLo> Traits;
+
+ /** \brief Default Constructor.
+ *
+ * The default constructor is useful in cases in which the user intends to
+ * perform decompositions via LDLT::compute(const MatrixType&).
+ */
+ LDLT()
+ : m_matrix(),
+ m_transpositions(),
+ m_sign(internal::ZeroSign),
+ m_isInitialized(false)
+ {}
+
+ /** \brief Default Constructor with memory preallocation
+ *
+ * Like the default constructor but with preallocation of the internal data
+ * according to the specified problem \a size.
+ * \sa LDLT()
+ */
+ explicit LDLT(Index size)
+ : m_matrix(size, size),
+ m_transpositions(size),
+ m_temporary(size),
+ m_sign(internal::ZeroSign),
+ m_isInitialized(false)
+ {}
+
+ /** \brief Constructor with decomposition
+ *
+ * This calculates the decomposition for the input \a matrix.
+ *
+ * \sa LDLT(Index size)
+ */
+ template<typename InputType>
+ explicit LDLT(const EigenBase<InputType>& matrix)
+ : m_matrix(matrix.rows(), matrix.cols()),
+ m_transpositions(matrix.rows()),
+ m_temporary(matrix.rows()),
+ m_sign(internal::ZeroSign),
+ m_isInitialized(false)
+ {
+ compute(matrix.derived());
+ }
+
+ /** \brief Constructs a LDLT factorization from a given matrix
+ *
+ * This overloaded constructor is provided for \link InplaceDecomposition inplace decomposition \endlink when \c MatrixType is a Eigen::Ref.
+ *
+ * \sa LDLT(const EigenBase&)
+ */
+ template<typename InputType>
+ explicit LDLT(EigenBase<InputType>& matrix)
+ : m_matrix(matrix.derived()),
+ m_transpositions(matrix.rows()),
+ m_temporary(matrix.rows()),
+ m_sign(internal::ZeroSign),
+ m_isInitialized(false)
+ {
+ compute(matrix.derived());
+ }
+
+ /** Clear any existing decomposition
+ * \sa rankUpdate(w,sigma)
+ */
+ void setZero()
+ {
+ m_isInitialized = false;
+ }
+
+ /** \returns a view of the upper triangular matrix U */
+ inline typename Traits::MatrixU matrixU() const
+ {
+ eigen_assert(m_isInitialized && "LDLT is not initialized.");
+ return Traits::getU(m_matrix);
+ }
+
+ /** \returns a view of the lower triangular matrix L */
+ inline typename Traits::MatrixL matrixL() const
+ {
+ eigen_assert(m_isInitialized && "LDLT is not initialized.");
+ return Traits::getL(m_matrix);
+ }
+
+ /** \returns the permutation matrix P as a transposition sequence.
+ */
+ inline const TranspositionType& transpositionsP() const
+ {
+ eigen_assert(m_isInitialized && "LDLT is not initialized.");
+ return m_transpositions;
+ }
+
+ /** \returns the coefficients of the diagonal matrix D */
+ inline Diagonal<const MatrixType> vectorD() const
+ {
+ eigen_assert(m_isInitialized && "LDLT is not initialized.");
+ return m_matrix.diagonal();
+ }
+
+ /** \returns true if the matrix is positive (semidefinite) */
+ inline bool isPositive() const
+ {
+ eigen_assert(m_isInitialized && "LDLT is not initialized.");
+ return m_sign == internal::PositiveSemiDef || m_sign == internal::ZeroSign;
+ }
+
+ /** \returns true if the matrix is negative (semidefinite) */
+ inline bool isNegative(void) const
+ {
+ eigen_assert(m_isInitialized && "LDLT is not initialized.");
+ return m_sign == internal::NegativeSemiDef || m_sign == internal::ZeroSign;
+ }
+
+ #ifdef EIGEN_PARSED_BY_DOXYGEN
+ /** \returns a solution x of \f$ A x = b \f$ using the current decomposition of A.
+ *
+ * This function also supports in-place solves using the syntax <tt>x = decompositionObject.solve(x)</tt> .
+ *
+ * \note_about_checking_solutions
+ *
+ * More precisely, this method solves \f$ A x = b \f$ using the decomposition \f$ A = P^T L D L^* P \f$
+ * by solving the systems \f$ P^T y_1 = b \f$, \f$ L y_2 = y_1 \f$, \f$ D y_3 = y_2 \f$,
+ * \f$ L^* y_4 = y_3 \f$ and \f$ P x = y_4 \f$ in succession. If the matrix \f$ A \f$ is singular, then
+ * \f$ D \f$ will also be singular (all the other matrices are invertible). In that case, the
+ * least-square solution of \f$ D y_3 = y_2 \f$ is computed. This does not mean that this function
+ * computes the least-square solution of \f$ A x = b \f$ if \f$ A \f$ is singular.
+ *
+ * \sa MatrixBase::ldlt(), SelfAdjointView::ldlt()
+ */
+ template<typename Rhs>
+ inline const Solve<LDLT, Rhs>
+ solve(const MatrixBase<Rhs>& b) const;
+ #endif
+
+ template<typename Derived>
+ bool solveInPlace(MatrixBase<Derived> &bAndX) const;
+
+ template<typename InputType>
+ LDLT& compute(const EigenBase<InputType>& matrix);
+
+ /** \returns an estimate of the reciprocal condition number of the matrix of
+ * which \c *this is the LDLT decomposition.
+ */
+ RealScalar rcond() const
+ {
+ eigen_assert(m_isInitialized && "LDLT is not initialized.");
+ return internal::rcond_estimate_helper(m_l1_norm, *this);
+ }
+
+ template <typename Derived>
+ LDLT& rankUpdate(const MatrixBase<Derived>& w, const RealScalar& alpha=1);
+
+ /** \returns the internal LDLT decomposition matrix
+ *
+ * TODO: document the storage layout
+ */
+ inline const MatrixType& matrixLDLT() const
+ {
+ eigen_assert(m_isInitialized && "LDLT is not initialized.");
+ return m_matrix;
+ }
+
+ MatrixType reconstructedMatrix() const;
+
+ /** \returns the adjoint of \c *this, that is, a const reference to the decomposition itself as the underlying matrix is self-adjoint.
+ *
+ * This method is provided for compatibility with other matrix decompositions, thus enabling generic code such as:
+ * \code x = decomposition.adjoint().solve(b) \endcode
+ */
+ const LDLT& adjoint() const { return *this; }
+
+ EIGEN_DEVICE_FUNC inline EIGEN_CONSTEXPR Index rows() const EIGEN_NOEXCEPT { return m_matrix.rows(); }
+ EIGEN_DEVICE_FUNC inline EIGEN_CONSTEXPR Index cols() const EIGEN_NOEXCEPT { return m_matrix.cols(); }
+
+ /** \brief Reports whether previous computation was successful.
+ *
+ * \returns \c Success if computation was successful,
+ * \c NumericalIssue if the factorization failed because of a zero pivot.
+ */
+ ComputationInfo info() const
+ {
+ eigen_assert(m_isInitialized && "LDLT is not initialized.");
+ return m_info;
+ }
+
+ #ifndef EIGEN_PARSED_BY_DOXYGEN
+ template<typename RhsType, typename DstType>
+ void _solve_impl(const RhsType &rhs, DstType &dst) const;
+
+ template<bool Conjugate, typename RhsType, typename DstType>
+ void _solve_impl_transposed(const RhsType &rhs, DstType &dst) const;
+ #endif
+
+ protected:
+
+ EIGEN_STATIC_ASSERT_NON_INTEGER(Scalar)
+
+ /** \internal
+ * Used to compute and store the Cholesky decomposition A = L D L^* = U^* D U.
+ * The strict upper part is used during the decomposition, the strict lower
+ * part correspond to the coefficients of L (its diagonal is equal to 1 and
+ * is not stored), and the diagonal entries correspond to D.
+ */
+ MatrixType m_matrix;
+ RealScalar m_l1_norm;
+ TranspositionType m_transpositions;
+ TmpMatrixType m_temporary;
+ internal::SignMatrix m_sign;
+ bool m_isInitialized;
+ ComputationInfo m_info;
+};
+
+namespace internal {
+
+template<int UpLo> struct ldlt_inplace;
+
+template<> struct ldlt_inplace<Lower>
+{
+ template<typename MatrixType, typename TranspositionType, typename Workspace>
+ static bool unblocked(MatrixType& mat, TranspositionType& transpositions, Workspace& temp, SignMatrix& sign)
+ {
+ using std::abs;
+ typedef typename MatrixType::Scalar Scalar;
+ typedef typename MatrixType::RealScalar RealScalar;
+ typedef typename TranspositionType::StorageIndex IndexType;
+ eigen_assert(mat.rows()==mat.cols());
+ const Index size = mat.rows();
+ bool found_zero_pivot = false;
+ bool ret = true;
+
+ if (size <= 1)
+ {
+ transpositions.setIdentity();
+ if(size==0) sign = ZeroSign;
+ else if (numext::real(mat.coeff(0,0)) > static_cast<RealScalar>(0) ) sign = PositiveSemiDef;
+ else if (numext::real(mat.coeff(0,0)) < static_cast<RealScalar>(0)) sign = NegativeSemiDef;
+ else sign = ZeroSign;
+ return true;
+ }
+
+ for (Index k = 0; k < size; ++k)
+ {
+ // Find largest diagonal element
+ Index index_of_biggest_in_corner;
+ mat.diagonal().tail(size-k).cwiseAbs().maxCoeff(&index_of_biggest_in_corner);
+ index_of_biggest_in_corner += k;
+
+ transpositions.coeffRef(k) = IndexType(index_of_biggest_in_corner);
+ if(k != index_of_biggest_in_corner)
+ {
+ // apply the transposition while taking care to consider only
+ // the lower triangular part
+ Index s = size-index_of_biggest_in_corner-1; // trailing size after the biggest element
+ mat.row(k).head(k).swap(mat.row(index_of_biggest_in_corner).head(k));
+ mat.col(k).tail(s).swap(mat.col(index_of_biggest_in_corner).tail(s));
+ std::swap(mat.coeffRef(k,k),mat.coeffRef(index_of_biggest_in_corner,index_of_biggest_in_corner));
+ for(Index i=k+1;i<index_of_biggest_in_corner;++i)
+ {
+ Scalar tmp = mat.coeffRef(i,k);
+ mat.coeffRef(i,k) = numext::conj(mat.coeffRef(index_of_biggest_in_corner,i));
+ mat.coeffRef(index_of_biggest_in_corner,i) = numext::conj(tmp);
+ }
+ if(NumTraits<Scalar>::IsComplex)
+ mat.coeffRef(index_of_biggest_in_corner,k) = numext::conj(mat.coeff(index_of_biggest_in_corner,k));
+ }
+
+ // partition the matrix:
+ // A00 | - | -
+ // lu = A10 | A11 | -
+ // A20 | A21 | A22
+ Index rs = size - k - 1;
+ Block<MatrixType,Dynamic,1> A21(mat,k+1,k,rs,1);
+ Block<MatrixType,1,Dynamic> A10(mat,k,0,1,k);
+ Block<MatrixType,Dynamic,Dynamic> A20(mat,k+1,0,rs,k);
+
+ if(k>0)
+ {
+ temp.head(k) = mat.diagonal().real().head(k).asDiagonal() * A10.adjoint();
+ mat.coeffRef(k,k) -= (A10 * temp.head(k)).value();
+ if(rs>0)
+ A21.noalias() -= A20 * temp.head(k);
+ }
+
+ // In some previous versions of Eigen (e.g., 3.2.1), the scaling was omitted if the pivot
+ // was smaller than the cutoff value. However, since LDLT is not rank-revealing
+ // we should only make sure that we do not introduce INF or NaN values.
+ // Remark that LAPACK also uses 0 as the cutoff value.
+ RealScalar realAkk = numext::real(mat.coeffRef(k,k));
+ bool pivot_is_valid = (abs(realAkk) > RealScalar(0));
+
+ if(k==0 && !pivot_is_valid)
+ {
+ // The entire diagonal is zero, there is nothing more to do
+ // except filling the transpositions, and checking whether the matrix is zero.
+ sign = ZeroSign;
+ for(Index j = 0; j<size; ++j)
+ {
+ transpositions.coeffRef(j) = IndexType(j);
+ ret = ret && (mat.col(j).tail(size-j-1).array()==Scalar(0)).all();
+ }
+ return ret;
+ }
+
+ if((rs>0) && pivot_is_valid)
+ A21 /= realAkk;
+ else if(rs>0)
+ ret = ret && (A21.array()==Scalar(0)).all();
+
+ if(found_zero_pivot && pivot_is_valid) ret = false; // factorization failed
+ else if(!pivot_is_valid) found_zero_pivot = true;
+
+ if (sign == PositiveSemiDef) {
+ if (realAkk < static_cast<RealScalar>(0)) sign = Indefinite;
+ } else if (sign == NegativeSemiDef) {
+ if (realAkk > static_cast<RealScalar>(0)) sign = Indefinite;
+ } else if (sign == ZeroSign) {
+ if (realAkk > static_cast<RealScalar>(0)) sign = PositiveSemiDef;
+ else if (realAkk < static_cast<RealScalar>(0)) sign = NegativeSemiDef;
+ }
+ }
+
+ return ret;
+ }
+
+ // Reference for the algorithm: Davis and Hager, "Multiple Rank
+ // Modifications of a Sparse Cholesky Factorization" (Algorithm 1)
+ // Trivial rearrangements of their computations (Timothy E. Holy)
+ // allow their algorithm to work for rank-1 updates even if the
+ // original matrix is not of full rank.
+ // Here only rank-1 updates are implemented, to reduce the
+ // requirement for intermediate storage and improve accuracy
+ template<typename MatrixType, typename WDerived>
+ static bool updateInPlace(MatrixType& mat, MatrixBase<WDerived>& w, const typename MatrixType::RealScalar& sigma=1)
+ {
+ using numext::isfinite;
+ typedef typename MatrixType::Scalar Scalar;
+ typedef typename MatrixType::RealScalar RealScalar;
+
+ const Index size = mat.rows();
+ eigen_assert(mat.cols() == size && w.size()==size);
+
+ RealScalar alpha = 1;
+
+ // Apply the update
+ for (Index j = 0; j < size; j++)
+ {
+ // Check for termination due to an original decomposition of low-rank
+ if (!(isfinite)(alpha))
+ break;
+
+ // Update the diagonal terms
+ RealScalar dj = numext::real(mat.coeff(j,j));
+ Scalar wj = w.coeff(j);
+ RealScalar swj2 = sigma*numext::abs2(wj);
+ RealScalar gamma = dj*alpha + swj2;
+
+ mat.coeffRef(j,j) += swj2/alpha;
+ alpha += swj2/dj;
+
+
+ // Update the terms of L
+ Index rs = size-j-1;
+ w.tail(rs) -= wj * mat.col(j).tail(rs);
+ if(!numext::is_exactly_zero(gamma))
+ mat.col(j).tail(rs) += (sigma*numext::conj(wj)/gamma)*w.tail(rs);
+ }
+ return true;
+ }
+
+ template<typename MatrixType, typename TranspositionType, typename Workspace, typename WType>
+ static bool update(MatrixType& mat, const TranspositionType& transpositions, Workspace& tmp, const WType& w, const typename MatrixType::RealScalar& sigma=1)
+ {
+ // Apply the permutation to the input w
+ tmp = transpositions * w;
+
+ return ldlt_inplace<Lower>::updateInPlace(mat,tmp,sigma);
+ }
+};
+
+template<> struct ldlt_inplace<Upper>
+{
+ template<typename MatrixType, typename TranspositionType, typename Workspace>
+ static EIGEN_STRONG_INLINE bool unblocked(MatrixType& mat, TranspositionType& transpositions, Workspace& temp, SignMatrix& sign)
+ {
+ Transpose<MatrixType> matt(mat);
+ return ldlt_inplace<Lower>::unblocked(matt, transpositions, temp, sign);
+ }
+
+ template<typename MatrixType, typename TranspositionType, typename Workspace, typename WType>
+ static EIGEN_STRONG_INLINE bool update(MatrixType& mat, TranspositionType& transpositions, Workspace& tmp, WType& w, const typename MatrixType::RealScalar& sigma=1)
+ {
+ Transpose<MatrixType> matt(mat);
+ return ldlt_inplace<Lower>::update(matt, transpositions, tmp, w.conjugate(), sigma);
+ }
+};
+
+template<typename MatrixType> struct LDLT_Traits<MatrixType,Lower>
+{
+ typedef const TriangularView<const MatrixType, UnitLower> MatrixL;
+ typedef const TriangularView<const typename MatrixType::AdjointReturnType, UnitUpper> MatrixU;
+ static inline MatrixL getL(const MatrixType& m) { return MatrixL(m); }
+ static inline MatrixU getU(const MatrixType& m) { return MatrixU(m.adjoint()); }
+};
+
+template<typename MatrixType> struct LDLT_Traits<MatrixType,Upper>
+{
+ typedef const TriangularView<const typename MatrixType::AdjointReturnType, UnitLower> MatrixL;
+ typedef const TriangularView<const MatrixType, UnitUpper> MatrixU;
+ static inline MatrixL getL(const MatrixType& m) { return MatrixL(m.adjoint()); }
+ static inline MatrixU getU(const MatrixType& m) { return MatrixU(m); }
+};
+
+} // end namespace internal
+
+/** Compute / recompute the LDLT decomposition A = L D L^* = U^* D U of \a matrix
+ */
+template<typename MatrixType, int UpLo_>
+template<typename InputType>
+LDLT<MatrixType,UpLo_>& LDLT<MatrixType,UpLo_>::compute(const EigenBase<InputType>& a)
+{
+ eigen_assert(a.rows()==a.cols());
+ const Index size = a.rows();
+
+ m_matrix = a.derived();
+
+ // Compute matrix L1 norm = max abs column sum.
+ m_l1_norm = RealScalar(0);
+ // TODO move this code to SelfAdjointView
+ for (Index col = 0; col < size; ++col) {
+ RealScalar abs_col_sum;
+ if (UpLo_ == Lower)
+ abs_col_sum = m_matrix.col(col).tail(size - col).template lpNorm<1>() + m_matrix.row(col).head(col).template lpNorm<1>();
+ else
+ abs_col_sum = m_matrix.col(col).head(col).template lpNorm<1>() + m_matrix.row(col).tail(size - col).template lpNorm<1>();
+ if (abs_col_sum > m_l1_norm)
+ m_l1_norm = abs_col_sum;
+ }
+
+ m_transpositions.resize(size);
+ m_isInitialized = false;
+ m_temporary.resize(size);
+ m_sign = internal::ZeroSign;
+
+ m_info = internal::ldlt_inplace<UpLo>::unblocked(m_matrix, m_transpositions, m_temporary, m_sign) ? Success : NumericalIssue;
+
+ m_isInitialized = true;
+ return *this;
+}
+
+/** Update the LDLT decomposition: given A = L D L^T, efficiently compute the decomposition of A + sigma w w^T.
+ * \param w a vector to be incorporated into the decomposition.
+ * \param sigma a scalar, +1 for updates and -1 for "downdates," which correspond to removing previously-added column vectors. Optional; default value is +1.
+ * \sa setZero()
+ */
+template<typename MatrixType, int UpLo_>
+template<typename Derived>
+LDLT<MatrixType,UpLo_>& LDLT<MatrixType,UpLo_>::rankUpdate(const MatrixBase<Derived>& w, const typename LDLT<MatrixType,UpLo_>::RealScalar& sigma)
+{
+ typedef typename TranspositionType::StorageIndex IndexType;
+ const Index size = w.rows();
+ if (m_isInitialized)
+ {
+ eigen_assert(m_matrix.rows()==size);
+ }
+ else
+ {
+ m_matrix.resize(size,size);
+ m_matrix.setZero();
+ m_transpositions.resize(size);
+ for (Index i = 0; i < size; i++)
+ m_transpositions.coeffRef(i) = IndexType(i);
+ m_temporary.resize(size);
+ m_sign = sigma>=0 ? internal::PositiveSemiDef : internal::NegativeSemiDef;
+ m_isInitialized = true;
+ }
+
+ internal::ldlt_inplace<UpLo>::update(m_matrix, m_transpositions, m_temporary, w, sigma);
+
+ return *this;
+}
+
+#ifndef EIGEN_PARSED_BY_DOXYGEN
+template<typename MatrixType_, int UpLo_>
+template<typename RhsType, typename DstType>
+void LDLT<MatrixType_,UpLo_>::_solve_impl(const RhsType &rhs, DstType &dst) const
+{
+ _solve_impl_transposed<true>(rhs, dst);
+}
+
+template<typename MatrixType_,int UpLo_>
+template<bool Conjugate, typename RhsType, typename DstType>
+void LDLT<MatrixType_,UpLo_>::_solve_impl_transposed(const RhsType &rhs, DstType &dst) const
+{
+ // dst = P b
+ dst = m_transpositions * rhs;
+
+ // dst = L^-1 (P b)
+ // dst = L^-*T (P b)
+ matrixL().template conjugateIf<!Conjugate>().solveInPlace(dst);
+
+ // dst = D^-* (L^-1 P b)
+ // dst = D^-1 (L^-*T P b)
+ // more precisely, use pseudo-inverse of D (see bug 241)
+ using std::abs;
+ const typename Diagonal<const MatrixType>::RealReturnType vecD(vectorD());
+ // In some previous versions, tolerance was set to the max of 1/highest (or rather numeric_limits::min())
+ // and the maximal diagonal entry * epsilon as motivated by LAPACK's xGELSS:
+ // RealScalar tolerance = numext::maxi(vecD.array().abs().maxCoeff() * NumTraits<RealScalar>::epsilon(),RealScalar(1) / NumTraits<RealScalar>::highest());
+ // However, LDLT is not rank revealing, and so adjusting the tolerance wrt to the highest
+ // diagonal element is not well justified and leads to numerical issues in some cases.
+ // Moreover, Lapack's xSYTRS routines use 0 for the tolerance.
+ // Using numeric_limits::min() gives us more robustness to denormals.
+ RealScalar tolerance = (std::numeric_limits<RealScalar>::min)();
+ for (Index i = 0; i < vecD.size(); ++i)
+ {
+ if(abs(vecD(i)) > tolerance)
+ dst.row(i) /= vecD(i);
+ else
+ dst.row(i).setZero();
+ }
+
+ // dst = L^-* (D^-* L^-1 P b)
+ // dst = L^-T (D^-1 L^-*T P b)
+ matrixL().transpose().template conjugateIf<Conjugate>().solveInPlace(dst);
+
+ // dst = P^T (L^-* D^-* L^-1 P b) = A^-1 b
+ // dst = P^-T (L^-T D^-1 L^-*T P b) = A^-1 b
+ dst = m_transpositions.transpose() * dst;
+}
+#endif
+
+/** \internal use x = ldlt_object.solve(x);
+ *
+ * This is the \em in-place version of solve().
+ *
+ * \param bAndX represents both the right-hand side matrix b and result x.
+ *
+ * \returns true always! If you need to check for existence of solutions, use another decomposition like LU, QR, or SVD.
+ *
+ * This version avoids a copy when the right hand side matrix b is not
+ * needed anymore.
+ *
+ * \sa LDLT::solve(), MatrixBase::ldlt()
+ */
+template<typename MatrixType,int UpLo_>
+template<typename Derived>
+bool LDLT<MatrixType,UpLo_>::solveInPlace(MatrixBase<Derived> &bAndX) const
+{
+ eigen_assert(m_isInitialized && "LDLT is not initialized.");
+ eigen_assert(m_matrix.rows() == bAndX.rows());
+
+ bAndX = this->solve(bAndX);
+
+ return true;
+}
+
+/** \returns the matrix represented by the decomposition,
+ * i.e., it returns the product: P^T L D L^* P.
+ * This function is provided for debug purpose. */
+template<typename MatrixType, int UpLo_>
+MatrixType LDLT<MatrixType,UpLo_>::reconstructedMatrix() const
+{
+ eigen_assert(m_isInitialized && "LDLT is not initialized.");
+ const Index size = m_matrix.rows();
+ MatrixType res(size,size);
+
+ // P
+ res.setIdentity();
+ res = transpositionsP() * res;
+ // L^* P
+ res = matrixU() * res;
+ // D(L^*P)
+ res = vectorD().real().asDiagonal() * res;
+ // L(DL^*P)
+ res = matrixL() * res;
+ // P^T (LDL^*P)
+ res = transpositionsP().transpose() * res;
+
+ return res;
+}
+
+/** \cholesky_module
+ * \returns the Cholesky decomposition with full pivoting without square root of \c *this
+ * \sa MatrixBase::ldlt()
+ */
+template<typename MatrixType, unsigned int UpLo>
+inline const LDLT<typename SelfAdjointView<MatrixType, UpLo>::PlainObject, UpLo>
+SelfAdjointView<MatrixType, UpLo>::ldlt() const
+{
+ return LDLT<PlainObject,UpLo>(m_matrix);
+}
+
+/** \cholesky_module
+ * \returns the Cholesky decomposition with full pivoting without square root of \c *this
+ * \sa SelfAdjointView::ldlt()
+ */
+template<typename Derived>
+inline const LDLT<typename MatrixBase<Derived>::PlainObject>
+MatrixBase<Derived>::ldlt() const
+{
+ return LDLT<PlainObject>(derived());
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_LDLT_H
diff --git a/Eigen/src/Cholesky/LLT.h b/Eigen/src/Cholesky/LLT.h
new file mode 100644
index 0000000..1443eac
--- /dev/null
+++ b/Eigen/src/Cholesky/LLT.h
@@ -0,0 +1,555 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_LLT_H
+#define EIGEN_LLT_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal{
+
+template<typename MatrixType_, int UpLo_> struct traits<LLT<MatrixType_, UpLo_> >
+ : traits<MatrixType_>
+{
+ typedef MatrixXpr XprKind;
+ typedef SolverStorage StorageKind;
+ typedef int StorageIndex;
+ enum { Flags = 0 };
+};
+
+template<typename MatrixType, int UpLo> struct LLT_Traits;
+}
+
+/** \ingroup Cholesky_Module
+ *
+ * \class LLT
+ *
+ * \brief Standard Cholesky decomposition (LL^T) of a matrix and associated features
+ *
+ * \tparam MatrixType_ the type of the matrix of which we are computing the LL^T Cholesky decomposition
+ * \tparam UpLo_ the triangular part that will be used for the decomposition: Lower (default) or Upper.
+ * The other triangular part won't be read.
+ *
+ * This class performs a LL^T Cholesky decomposition of a symmetric, positive definite
+ * matrix A such that A = LL^* = U^*U, where L is lower triangular.
+ *
+ * While the Cholesky decomposition is particularly useful to solve selfadjoint problems like D^*D x = b,
+ * for that purpose, we recommend the Cholesky decomposition without square root which is more stable
+ * and even faster. Nevertheless, this standard Cholesky decomposition remains useful in many other
+ * situations like generalised eigen problems with hermitian matrices.
+ *
+ * Remember that Cholesky decompositions are not rank-revealing. This LLT decomposition is only stable on positive definite matrices,
+ * use LDLT instead for the semidefinite case. Also, do not use a Cholesky decomposition to determine whether a system of equations
+ * has a solution.
+ *
+ * Example: \include LLT_example.cpp
+ * Output: \verbinclude LLT_example.out
+ *
+ * \b Performance: for best performance, it is recommended to use a column-major storage format
+ * with the Lower triangular part (the default), or, equivalently, a row-major storage format
+ * with the Upper triangular part. Otherwise, you might get a 20% slowdown for the full factorization
+ * step, and rank-updates can be up to 3 times slower.
+ *
+ * This class supports the \link InplaceDecomposition inplace decomposition \endlink mechanism.
+ *
+ * Note that during the decomposition, only the lower (or upper, as defined by UpLo_) triangular part of A is considered.
+ * Therefore, the strict lower part does not have to store correct values.
+ *
+ * \sa MatrixBase::llt(), SelfAdjointView::llt(), class LDLT
+ */
+template<typename MatrixType_, int UpLo_> class LLT
+ : public SolverBase<LLT<MatrixType_, UpLo_> >
+{
+ public:
+ typedef MatrixType_ MatrixType;
+ typedef SolverBase<LLT> Base;
+ friend class SolverBase<LLT>;
+
+ EIGEN_GENERIC_PUBLIC_INTERFACE(LLT)
+ enum {
+ MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime
+ };
+
+ enum {
+ PacketSize = internal::packet_traits<Scalar>::size,
+ AlignmentMask = int(PacketSize)-1,
+ UpLo = UpLo_
+ };
+
+ typedef internal::LLT_Traits<MatrixType,UpLo> Traits;
+
+ /**
+ * \brief Default Constructor.
+ *
+ * The default constructor is useful in cases in which the user intends to
+ * perform decompositions via LLT::compute(const MatrixType&).
+ */
+ LLT() : m_matrix(), m_isInitialized(false) {}
+
+ /** \brief Default Constructor with memory preallocation
+ *
+ * Like the default constructor but with preallocation of the internal data
+ * according to the specified problem \a size.
+ * \sa LLT()
+ */
+ explicit LLT(Index size) : m_matrix(size, size),
+ m_isInitialized(false) {}
+
+ template<typename InputType>
+ explicit LLT(const EigenBase<InputType>& matrix)
+ : m_matrix(matrix.rows(), matrix.cols()),
+ m_isInitialized(false)
+ {
+ compute(matrix.derived());
+ }
+
+ /** \brief Constructs a LLT factorization from a given matrix
+ *
+ * This overloaded constructor is provided for \link InplaceDecomposition inplace decomposition \endlink when
+ * \c MatrixType is a Eigen::Ref.
+ *
+ * \sa LLT(const EigenBase&)
+ */
+ template<typename InputType>
+ explicit LLT(EigenBase<InputType>& matrix)
+ : m_matrix(matrix.derived()),
+ m_isInitialized(false)
+ {
+ compute(matrix.derived());
+ }
+
+ /** \returns a view of the upper triangular matrix U */
+ inline typename Traits::MatrixU matrixU() const
+ {
+ eigen_assert(m_isInitialized && "LLT is not initialized.");
+ return Traits::getU(m_matrix);
+ }
+
+ /** \returns a view of the lower triangular matrix L */
+ inline typename Traits::MatrixL matrixL() const
+ {
+ eigen_assert(m_isInitialized && "LLT is not initialized.");
+ return Traits::getL(m_matrix);
+ }
+
+ #ifdef EIGEN_PARSED_BY_DOXYGEN
+ /** \returns the solution x of \f$ A x = b \f$ using the current decomposition of A.
+ *
+ * Since this LLT class assumes anyway that the matrix A is invertible, the solution
+ * theoretically exists and is unique regardless of b.
+ *
+ * Example: \include LLT_solve.cpp
+ * Output: \verbinclude LLT_solve.out
+ *
+ * \sa solveInPlace(), MatrixBase::llt(), SelfAdjointView::llt()
+ */
+ template<typename Rhs>
+ inline const Solve<LLT, Rhs>
+ solve(const MatrixBase<Rhs>& b) const;
+ #endif
+
+ template<typename Derived>
+ void solveInPlace(const MatrixBase<Derived> &bAndX) const;
+
+ template<typename InputType>
+ LLT& compute(const EigenBase<InputType>& matrix);
+
+ /** \returns an estimate of the reciprocal condition number of the matrix of
+ * which \c *this is the Cholesky decomposition.
+ */
+ RealScalar rcond() const
+ {
+ eigen_assert(m_isInitialized && "LLT is not initialized.");
+ eigen_assert(m_info == Success && "LLT failed because matrix appears to be negative");
+ return internal::rcond_estimate_helper(m_l1_norm, *this);
+ }
+
+ /** \returns the LLT decomposition matrix
+ *
+ * TODO: document the storage layout
+ */
+ inline const MatrixType& matrixLLT() const
+ {
+ eigen_assert(m_isInitialized && "LLT is not initialized.");
+ return m_matrix;
+ }
+
+ MatrixType reconstructedMatrix() const;
+
+
+ /** \brief Reports whether previous computation was successful.
+ *
+ * \returns \c Success if computation was successful,
+ * \c NumericalIssue if the matrix.appears not to be positive definite.
+ */
+ ComputationInfo info() const
+ {
+ eigen_assert(m_isInitialized && "LLT is not initialized.");
+ return m_info;
+ }
+
+ /** \returns the adjoint of \c *this, that is, a const reference to the decomposition itself as the underlying matrix is self-adjoint.
+ *
+ * This method is provided for compatibility with other matrix decompositions, thus enabling generic code such as:
+ * \code x = decomposition.adjoint().solve(b) \endcode
+ */
+ const LLT& adjoint() const EIGEN_NOEXCEPT { return *this; }
+
+ inline EIGEN_CONSTEXPR Index rows() const EIGEN_NOEXCEPT { return m_matrix.rows(); }
+ inline EIGEN_CONSTEXPR Index cols() const EIGEN_NOEXCEPT { return m_matrix.cols(); }
+
+ template<typename VectorType>
+ LLT & rankUpdate(const VectorType& vec, const RealScalar& sigma = 1);
+
+ #ifndef EIGEN_PARSED_BY_DOXYGEN
+ template<typename RhsType, typename DstType>
+ void _solve_impl(const RhsType &rhs, DstType &dst) const;
+
+ template<bool Conjugate, typename RhsType, typename DstType>
+ void _solve_impl_transposed(const RhsType &rhs, DstType &dst) const;
+ #endif
+
+ protected:
+
+ EIGEN_STATIC_ASSERT_NON_INTEGER(Scalar)
+
+ /** \internal
+ * Used to compute and store L
+ * The strict upper part is not used and even not initialized.
+ */
+ MatrixType m_matrix;
+ RealScalar m_l1_norm;
+ bool m_isInitialized;
+ ComputationInfo m_info;
+};
+
+namespace internal {
+
+template<typename Scalar, int UpLo> struct llt_inplace;
+
+template<typename MatrixType, typename VectorType>
+static Index llt_rank_update_lower(MatrixType& mat, const VectorType& vec, const typename MatrixType::RealScalar& sigma)
+{
+ using std::sqrt;
+ typedef typename MatrixType::Scalar Scalar;
+ typedef typename MatrixType::RealScalar RealScalar;
+ typedef typename MatrixType::ColXpr ColXpr;
+ typedef internal::remove_all_t<ColXpr> ColXprCleaned;
+ typedef typename ColXprCleaned::SegmentReturnType ColXprSegment;
+ typedef Matrix<Scalar,Dynamic,1> TempVectorType;
+ typedef typename TempVectorType::SegmentReturnType TempVecSegment;
+
+ Index n = mat.cols();
+ eigen_assert(mat.rows()==n && vec.size()==n);
+
+ TempVectorType temp;
+
+ if(sigma>0)
+ {
+ // This version is based on Givens rotations.
+ // It is faster than the other one below, but only works for updates,
+ // i.e., for sigma > 0
+ temp = sqrt(sigma) * vec;
+
+ for(Index i=0; i<n; ++i)
+ {
+ JacobiRotation<Scalar> g;
+ g.makeGivens(mat(i,i), -temp(i), &mat(i,i));
+
+ Index rs = n-i-1;
+ if(rs>0)
+ {
+ ColXprSegment x(mat.col(i).tail(rs));
+ TempVecSegment y(temp.tail(rs));
+ apply_rotation_in_the_plane(x, y, g);
+ }
+ }
+ }
+ else
+ {
+ temp = vec;
+ RealScalar beta = 1;
+ for(Index j=0; j<n; ++j)
+ {
+ RealScalar Ljj = numext::real(mat.coeff(j,j));
+ RealScalar dj = numext::abs2(Ljj);
+ Scalar wj = temp.coeff(j);
+ RealScalar swj2 = sigma*numext::abs2(wj);
+ RealScalar gamma = dj*beta + swj2;
+
+ RealScalar x = dj + swj2/beta;
+ if (x<=RealScalar(0))
+ return j;
+ RealScalar nLjj = sqrt(x);
+ mat.coeffRef(j,j) = nLjj;
+ beta += swj2/dj;
+
+ // Update the terms of L
+ Index rs = n-j-1;
+ if(rs)
+ {
+ temp.tail(rs) -= (wj/Ljj) * mat.col(j).tail(rs);
+ if(!numext::is_exactly_zero(gamma))
+ mat.col(j).tail(rs) = (nLjj/Ljj) * mat.col(j).tail(rs) + (nLjj * sigma*numext::conj(wj)/gamma)*temp.tail(rs);
+ }
+ }
+ }
+ return -1;
+}
+
+template<typename Scalar> struct llt_inplace<Scalar, Lower>
+{
+ typedef typename NumTraits<Scalar>::Real RealScalar;
+ template<typename MatrixType>
+ static Index unblocked(MatrixType& mat)
+ {
+ using std::sqrt;
+
+ eigen_assert(mat.rows()==mat.cols());
+ const Index size = mat.rows();
+ for(Index k = 0; k < size; ++k)
+ {
+ Index rs = size-k-1; // remaining size
+
+ Block<MatrixType,Dynamic,1> A21(mat,k+1,k,rs,1);
+ Block<MatrixType,1,Dynamic> A10(mat,k,0,1,k);
+ Block<MatrixType,Dynamic,Dynamic> A20(mat,k+1,0,rs,k);
+
+ RealScalar x = numext::real(mat.coeff(k,k));
+ if (k>0) x -= A10.squaredNorm();
+ if (x<=RealScalar(0))
+ return k;
+ mat.coeffRef(k,k) = x = sqrt(x);
+ if (k>0 && rs>0) A21.noalias() -= A20 * A10.adjoint();
+ if (rs>0) A21 /= x;
+ }
+ return -1;
+ }
+
+ template<typename MatrixType>
+ static Index blocked(MatrixType& m)
+ {
+ eigen_assert(m.rows()==m.cols());
+ Index size = m.rows();
+ if(size<32)
+ return unblocked(m);
+
+ Index blockSize = size/8;
+ blockSize = (blockSize/16)*16;
+ blockSize = (std::min)((std::max)(blockSize,Index(8)), Index(128));
+
+ for (Index k=0; k<size; k+=blockSize)
+ {
+ // partition the matrix:
+ // A00 | - | -
+ // lu = A10 | A11 | -
+ // A20 | A21 | A22
+ Index bs = (std::min)(blockSize, size-k);
+ Index rs = size - k - bs;
+ Block<MatrixType,Dynamic,Dynamic> A11(m,k, k, bs,bs);
+ Block<MatrixType,Dynamic,Dynamic> A21(m,k+bs,k, rs,bs);
+ Block<MatrixType,Dynamic,Dynamic> A22(m,k+bs,k+bs,rs,rs);
+
+ Index ret;
+ if((ret=unblocked(A11))>=0) return k+ret;
+ if(rs>0) A11.adjoint().template triangularView<Upper>().template solveInPlace<OnTheRight>(A21);
+ if(rs>0) A22.template selfadjointView<Lower>().rankUpdate(A21,typename NumTraits<RealScalar>::Literal(-1)); // bottleneck
+ }
+ return -1;
+ }
+
+ template<typename MatrixType, typename VectorType>
+ static Index rankUpdate(MatrixType& mat, const VectorType& vec, const RealScalar& sigma)
+ {
+ return Eigen::internal::llt_rank_update_lower(mat, vec, sigma);
+ }
+};
+
+template<typename Scalar> struct llt_inplace<Scalar, Upper>
+{
+ typedef typename NumTraits<Scalar>::Real RealScalar;
+
+ template<typename MatrixType>
+ static EIGEN_STRONG_INLINE Index unblocked(MatrixType& mat)
+ {
+ Transpose<MatrixType> matt(mat);
+ return llt_inplace<Scalar, Lower>::unblocked(matt);
+ }
+ template<typename MatrixType>
+ static EIGEN_STRONG_INLINE Index blocked(MatrixType& mat)
+ {
+ Transpose<MatrixType> matt(mat);
+ return llt_inplace<Scalar, Lower>::blocked(matt);
+ }
+ template<typename MatrixType, typename VectorType>
+ static Index rankUpdate(MatrixType& mat, const VectorType& vec, const RealScalar& sigma)
+ {
+ Transpose<MatrixType> matt(mat);
+ return llt_inplace<Scalar, Lower>::rankUpdate(matt, vec.conjugate(), sigma);
+ }
+};
+
+template<typename MatrixType> struct LLT_Traits<MatrixType,Lower>
+{
+ typedef const TriangularView<const MatrixType, Lower> MatrixL;
+ typedef const TriangularView<const typename MatrixType::AdjointReturnType, Upper> MatrixU;
+ static inline MatrixL getL(const MatrixType& m) { return MatrixL(m); }
+ static inline MatrixU getU(const MatrixType& m) { return MatrixU(m.adjoint()); }
+ static bool inplace_decomposition(MatrixType& m)
+ { return llt_inplace<typename MatrixType::Scalar, Lower>::blocked(m)==-1; }
+};
+
+template<typename MatrixType> struct LLT_Traits<MatrixType,Upper>
+{
+ typedef const TriangularView<const typename MatrixType::AdjointReturnType, Lower> MatrixL;
+ typedef const TriangularView<const MatrixType, Upper> MatrixU;
+ static inline MatrixL getL(const MatrixType& m) { return MatrixL(m.adjoint()); }
+ static inline MatrixU getU(const MatrixType& m) { return MatrixU(m); }
+ static bool inplace_decomposition(MatrixType& m)
+ { return llt_inplace<typename MatrixType::Scalar, Upper>::blocked(m)==-1; }
+};
+
+} // end namespace internal
+
+/** Computes / recomputes the Cholesky decomposition A = LL^* = U^*U of \a matrix
+ *
+ * \returns a reference to *this
+ *
+ * Example: \include TutorialLinAlgComputeTwice.cpp
+ * Output: \verbinclude TutorialLinAlgComputeTwice.out
+ */
+template<typename MatrixType, int UpLo_>
+template<typename InputType>
+LLT<MatrixType,UpLo_>& LLT<MatrixType,UpLo_>::compute(const EigenBase<InputType>& a)
+{
+ eigen_assert(a.rows()==a.cols());
+ const Index size = a.rows();
+ m_matrix.resize(size, size);
+ if (!internal::is_same_dense(m_matrix, a.derived()))
+ m_matrix = a.derived();
+
+ // Compute matrix L1 norm = max abs column sum.
+ m_l1_norm = RealScalar(0);
+ // TODO move this code to SelfAdjointView
+ for (Index col = 0; col < size; ++col) {
+ RealScalar abs_col_sum;
+ if (UpLo_ == Lower)
+ abs_col_sum = m_matrix.col(col).tail(size - col).template lpNorm<1>() + m_matrix.row(col).head(col).template lpNorm<1>();
+ else
+ abs_col_sum = m_matrix.col(col).head(col).template lpNorm<1>() + m_matrix.row(col).tail(size - col).template lpNorm<1>();
+ if (abs_col_sum > m_l1_norm)
+ m_l1_norm = abs_col_sum;
+ }
+
+ m_isInitialized = true;
+ bool ok = Traits::inplace_decomposition(m_matrix);
+ m_info = ok ? Success : NumericalIssue;
+
+ return *this;
+}
+
+/** Performs a rank one update (or dowdate) of the current decomposition.
+ * If A = LL^* before the rank one update,
+ * then after it we have LL^* = A + sigma * v v^* where \a v must be a vector
+ * of same dimension.
+ */
+template<typename MatrixType_, int UpLo_>
+template<typename VectorType>
+LLT<MatrixType_,UpLo_> & LLT<MatrixType_,UpLo_>::rankUpdate(const VectorType& v, const RealScalar& sigma)
+{
+ EIGEN_STATIC_ASSERT_VECTOR_ONLY(VectorType);
+ eigen_assert(v.size()==m_matrix.cols());
+ eigen_assert(m_isInitialized);
+ if(internal::llt_inplace<typename MatrixType::Scalar, UpLo>::rankUpdate(m_matrix,v,sigma)>=0)
+ m_info = NumericalIssue;
+ else
+ m_info = Success;
+
+ return *this;
+}
+
+#ifndef EIGEN_PARSED_BY_DOXYGEN
+template<typename MatrixType_,int UpLo_>
+template<typename RhsType, typename DstType>
+void LLT<MatrixType_,UpLo_>::_solve_impl(const RhsType &rhs, DstType &dst) const
+{
+ _solve_impl_transposed<true>(rhs, dst);
+}
+
+template<typename MatrixType_,int UpLo_>
+template<bool Conjugate, typename RhsType, typename DstType>
+void LLT<MatrixType_,UpLo_>::_solve_impl_transposed(const RhsType &rhs, DstType &dst) const
+{
+ dst = rhs;
+
+ matrixL().template conjugateIf<!Conjugate>().solveInPlace(dst);
+ matrixU().template conjugateIf<!Conjugate>().solveInPlace(dst);
+}
+#endif
+
+/** \internal use x = llt_object.solve(x);
+ *
+ * This is the \em in-place version of solve().
+ *
+ * \param bAndX represents both the right-hand side matrix b and result x.
+ *
+ * This version avoids a copy when the right hand side matrix b is not needed anymore.
+ *
+ * \warning The parameter is only marked 'const' to make the C++ compiler accept a temporary expression here.
+ * This function will const_cast it, so constness isn't honored here.
+ *
+ * \sa LLT::solve(), MatrixBase::llt()
+ */
+template<typename MatrixType, int UpLo_>
+template<typename Derived>
+void LLT<MatrixType,UpLo_>::solveInPlace(const MatrixBase<Derived> &bAndX) const
+{
+ eigen_assert(m_isInitialized && "LLT is not initialized.");
+ eigen_assert(m_matrix.rows()==bAndX.rows());
+ matrixL().solveInPlace(bAndX);
+ matrixU().solveInPlace(bAndX);
+}
+
+/** \returns the matrix represented by the decomposition,
+ * i.e., it returns the product: L L^*.
+ * This function is provided for debug purpose. */
+template<typename MatrixType, int UpLo_>
+MatrixType LLT<MatrixType,UpLo_>::reconstructedMatrix() const
+{
+ eigen_assert(m_isInitialized && "LLT is not initialized.");
+ return matrixL() * matrixL().adjoint().toDenseMatrix();
+}
+
+/** \cholesky_module
+ * \returns the LLT decomposition of \c *this
+ * \sa SelfAdjointView::llt()
+ */
+template<typename Derived>
+inline const LLT<typename MatrixBase<Derived>::PlainObject>
+MatrixBase<Derived>::llt() const
+{
+ return LLT<PlainObject>(derived());
+}
+
+/** \cholesky_module
+ * \returns the LLT decomposition of \c *this
+ * \sa SelfAdjointView::llt()
+ */
+template<typename MatrixType, unsigned int UpLo>
+inline const LLT<typename SelfAdjointView<MatrixType, UpLo>::PlainObject, UpLo>
+SelfAdjointView<MatrixType, UpLo>::llt() const
+{
+ return LLT<PlainObject,UpLo>(m_matrix);
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_LLT_H
diff --git a/Eigen/src/Cholesky/LLT_LAPACKE.h b/Eigen/src/Cholesky/LLT_LAPACKE.h
new file mode 100644
index 0000000..62bc679
--- /dev/null
+++ b/Eigen/src/Cholesky/LLT_LAPACKE.h
@@ -0,0 +1,121 @@
+/*
+ Copyright (c) 2011, Intel Corporation. All rights reserved.
+
+ Redistribution and use in source and binary forms, with or without modification,
+ are permitted provided that the following conditions are met:
+
+ * Redistributions of source code must retain the above copyright notice, this
+ list of conditions and the following disclaimer.
+ * Redistributions in binary form must reproduce the above copyright notice,
+ this list of conditions and the following disclaimer in the documentation
+ and/or other materials provided with the distribution.
+ * Neither the name of Intel Corporation nor the names of its contributors may
+ be used to endorse or promote products derived from this software without
+ specific prior written permission.
+
+ THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
+ ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
+ WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
+ DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR
+ ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
+ (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
+ LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON
+ ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
+ (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
+ SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+
+ ********************************************************************************
+ * Content : Eigen bindings to LAPACKe
+ * LLt decomposition based on LAPACKE_?potrf function.
+ ********************************************************************************
+*/
+
+#ifndef EIGEN_LLT_LAPACKE_H
+#define EIGEN_LLT_LAPACKE_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+
+namespace lapacke_helpers {
+ // -------------------------------------------------------------------------------------------------------------------
+ // Dispatch for rank update handling upper and lower parts
+ // -------------------------------------------------------------------------------------------------------------------
+
+ template<UpLoType Mode>
+ struct rank_update {};
+
+ template<>
+ struct rank_update<Lower> {
+ template<typename MatrixType, typename VectorType>
+ static Index run(MatrixType &mat, const VectorType &vec, const typename MatrixType::RealScalar &sigma) {
+ return Eigen::internal::llt_rank_update_lower(mat, vec, sigma);
+ }
+ };
+
+ template<>
+ struct rank_update<Upper> {
+ template<typename MatrixType, typename VectorType>
+ static Index run(MatrixType &mat, const VectorType &vec, const typename MatrixType::RealScalar &sigma) {
+ Transpose<MatrixType> matt(mat);
+ return Eigen::internal::llt_rank_update_lower(matt, vec.conjugate(), sigma);
+ }
+ };
+
+ // -------------------------------------------------------------------------------------------------------------------
+ // Generic lapacke llt implementation that hands of to the dispatches
+ // -------------------------------------------------------------------------------------------------------------------
+
+ template<typename Scalar, UpLoType Mode>
+ struct lapacke_llt {
+ template<typename MatrixType>
+ static Index blocked(MatrixType& m)
+ {
+ eigen_assert(m.rows() == m.cols());
+ if(m.rows() == 0) {
+ return -1;
+ }
+ /* Set up parameters for ?potrf */
+ lapack_int size = to_lapack(m.rows());
+ lapack_int matrix_order = lapack_storage_of(m);
+ Scalar* a = &(m.coeffRef(0,0));
+ lapack_int lda = to_lapack(m.outerStride());
+
+ lapack_int info = potrf(matrix_order, translate_mode<Mode>, size, to_lapack(a), lda );
+ info = (info==0) ? -1 : info>0 ? info-1 : size;
+ return info;
+ }
+
+ template<typename MatrixType, typename VectorType>
+ static Index rankUpdate(MatrixType& mat, const VectorType& vec, const typename MatrixType::RealScalar& sigma)
+ {
+ return rank_update<Mode>::run(mat, vec, sigma);
+ }
+ };
+}
+// end namespace lapacke_helpers
+
+/*
+ * Here, we just put the generic implementation from lapacke_llt into a full specialization of the llt_inplace
+ * type. By being a full specialization, the versions defined here thus get precedence over the generic implementation
+ * in LLT.h for double, float and complex double, complex float types.
+ */
+
+#define EIGEN_LAPACKE_LLT(EIGTYPE) \
+template<> struct llt_inplace<EIGTYPE, Lower> : public lapacke_helpers::lapacke_llt<EIGTYPE, Lower> {}; \
+template<> struct llt_inplace<EIGTYPE, Upper> : public lapacke_helpers::lapacke_llt<EIGTYPE, Upper> {};
+
+EIGEN_LAPACKE_LLT(double)
+EIGEN_LAPACKE_LLT(float)
+EIGEN_LAPACKE_LLT(std::complex<double>)
+EIGEN_LAPACKE_LLT(std::complex<float>)
+
+#undef EIGEN_LAPACKE_LLT
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_LLT_LAPACKE_H
diff --git a/Eigen/src/CholmodSupport/CholmodSupport.h b/Eigen/src/CholmodSupport/CholmodSupport.h
new file mode 100644
index 0000000..91c1cfc
--- /dev/null
+++ b/Eigen/src/CholmodSupport/CholmodSupport.h
@@ -0,0 +1,684 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2010 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_CHOLMODSUPPORT_H
+#define EIGEN_CHOLMODSUPPORT_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+
+template<typename Scalar> struct cholmod_configure_matrix;
+
+template<> struct cholmod_configure_matrix<double> {
+ template<typename CholmodType>
+ static void run(CholmodType& mat) {
+ mat.xtype = CHOLMOD_REAL;
+ mat.dtype = CHOLMOD_DOUBLE;
+ }
+};
+
+template<> struct cholmod_configure_matrix<std::complex<double> > {
+ template<typename CholmodType>
+ static void run(CholmodType& mat) {
+ mat.xtype = CHOLMOD_COMPLEX;
+ mat.dtype = CHOLMOD_DOUBLE;
+ }
+};
+
+// Other scalar types are not yet supported by Cholmod
+// template<> struct cholmod_configure_matrix<float> {
+// template<typename CholmodType>
+// static void run(CholmodType& mat) {
+// mat.xtype = CHOLMOD_REAL;
+// mat.dtype = CHOLMOD_SINGLE;
+// }
+// };
+//
+// template<> struct cholmod_configure_matrix<std::complex<float> > {
+// template<typename CholmodType>
+// static void run(CholmodType& mat) {
+// mat.xtype = CHOLMOD_COMPLEX;
+// mat.dtype = CHOLMOD_SINGLE;
+// }
+// };
+
+} // namespace internal
+
+/** Wraps the Eigen sparse matrix \a mat into a Cholmod sparse matrix object.
+ * Note that the data are shared.
+ */
+template<typename Scalar_, int Options_, typename StorageIndex_>
+cholmod_sparse viewAsCholmod(Ref<SparseMatrix<Scalar_,Options_,StorageIndex_> > mat)
+{
+ cholmod_sparse res;
+ res.nzmax = mat.nonZeros();
+ res.nrow = mat.rows();
+ res.ncol = mat.cols();
+ res.p = mat.outerIndexPtr();
+ res.i = mat.innerIndexPtr();
+ res.x = mat.valuePtr();
+ res.z = 0;
+ res.sorted = 1;
+ if(mat.isCompressed())
+ {
+ res.packed = 1;
+ res.nz = 0;
+ }
+ else
+ {
+ res.packed = 0;
+ res.nz = mat.innerNonZeroPtr();
+ }
+
+ res.dtype = 0;
+ res.stype = -1;
+
+ if (internal::is_same<StorageIndex_,int>::value)
+ {
+ res.itype = CHOLMOD_INT;
+ }
+ else if (internal::is_same<StorageIndex_,SuiteSparse_long>::value)
+ {
+ res.itype = CHOLMOD_LONG;
+ }
+ else
+ {
+ eigen_assert(false && "Index type not supported yet");
+ }
+
+ // setup res.xtype
+ internal::cholmod_configure_matrix<Scalar_>::run(res);
+
+ res.stype = 0;
+
+ return res;
+}
+
+template<typename Scalar_, int Options_, typename Index_>
+const cholmod_sparse viewAsCholmod(const SparseMatrix<Scalar_,Options_,Index_>& mat)
+{
+ cholmod_sparse res = viewAsCholmod(Ref<SparseMatrix<Scalar_,Options_,Index_> >(mat.const_cast_derived()));
+ return res;
+}
+
+template<typename Scalar_, int Options_, typename Index_>
+const cholmod_sparse viewAsCholmod(const SparseVector<Scalar_,Options_,Index_>& mat)
+{
+ cholmod_sparse res = viewAsCholmod(Ref<SparseMatrix<Scalar_,Options_,Index_> >(mat.const_cast_derived()));
+ return res;
+}
+
+/** Returns a view of the Eigen sparse matrix \a mat as Cholmod sparse matrix.
+ * The data are not copied but shared. */
+template<typename Scalar_, int Options_, typename Index_, unsigned int UpLo>
+cholmod_sparse viewAsCholmod(const SparseSelfAdjointView<const SparseMatrix<Scalar_,Options_,Index_>, UpLo>& mat)
+{
+ cholmod_sparse res = viewAsCholmod(Ref<SparseMatrix<Scalar_,Options_,Index_> >(mat.matrix().const_cast_derived()));
+
+ if(UpLo==Upper) res.stype = 1;
+ if(UpLo==Lower) res.stype = -1;
+ // swap stype for rowmajor matrices (only works for real matrices)
+ EIGEN_STATIC_ASSERT((Options_ & RowMajorBit) == 0 || NumTraits<Scalar_>::IsComplex == 0, THIS_METHOD_IS_ONLY_FOR_COLUMN_MAJOR_MATRICES);
+ if(Options_ & RowMajorBit) res.stype *=-1;
+
+ return res;
+}
+
+/** Returns a view of the Eigen \b dense matrix \a mat as Cholmod dense matrix.
+ * The data are not copied but shared. */
+template<typename Derived>
+cholmod_dense viewAsCholmod(MatrixBase<Derived>& mat)
+{
+ EIGEN_STATIC_ASSERT((internal::traits<Derived>::Flags&RowMajorBit)==0,THIS_METHOD_IS_ONLY_FOR_COLUMN_MAJOR_MATRICES);
+ typedef typename Derived::Scalar Scalar;
+
+ cholmod_dense res;
+ res.nrow = mat.rows();
+ res.ncol = mat.cols();
+ res.nzmax = res.nrow * res.ncol;
+ res.d = Derived::IsVectorAtCompileTime ? mat.derived().size() : mat.derived().outerStride();
+ res.x = (void*)(mat.derived().data());
+ res.z = 0;
+
+ internal::cholmod_configure_matrix<Scalar>::run(res);
+
+ return res;
+}
+
+/** Returns a view of the Cholmod sparse matrix \a cm as an Eigen sparse matrix.
+ * The data are not copied but shared. */
+template<typename Scalar, int Flags, typename StorageIndex>
+Map<SparseMatrix<Scalar,Flags,StorageIndex> > viewAsEigen(cholmod_sparse& cm)
+{
+ return Map<SparseMatrix<Scalar,Flags,StorageIndex> >
+ (cm.nrow, cm.ncol, static_cast<StorageIndex*>(cm.p)[cm.ncol],
+ static_cast<StorageIndex*>(cm.p), static_cast<StorageIndex*>(cm.i),static_cast<Scalar*>(cm.x) );
+}
+
+namespace internal {
+
+// template specializations for int and long that call the correct cholmod method
+
+#define EIGEN_CHOLMOD_SPECIALIZE0(ret, name) \
+ template<typename StorageIndex_> inline ret cm_ ## name (cholmod_common &Common) { return cholmod_ ## name (&Common); } \
+ template<> inline ret cm_ ## name<SuiteSparse_long> (cholmod_common &Common) { return cholmod_l_ ## name (&Common); }
+
+#define EIGEN_CHOLMOD_SPECIALIZE1(ret, name, t1, a1) \
+ template<typename StorageIndex_> inline ret cm_ ## name (t1& a1, cholmod_common &Common) { return cholmod_ ## name (&a1, &Common); } \
+ template<> inline ret cm_ ## name<SuiteSparse_long> (t1& a1, cholmod_common &Common) { return cholmod_l_ ## name (&a1, &Common); }
+
+EIGEN_CHOLMOD_SPECIALIZE0(int, start)
+EIGEN_CHOLMOD_SPECIALIZE0(int, finish)
+
+EIGEN_CHOLMOD_SPECIALIZE1(int, free_factor, cholmod_factor*, L)
+EIGEN_CHOLMOD_SPECIALIZE1(int, free_dense, cholmod_dense*, X)
+EIGEN_CHOLMOD_SPECIALIZE1(int, free_sparse, cholmod_sparse*, A)
+
+EIGEN_CHOLMOD_SPECIALIZE1(cholmod_factor*, analyze, cholmod_sparse, A)
+
+template<typename StorageIndex_> inline cholmod_dense* cm_solve (int sys, cholmod_factor& L, cholmod_dense& B, cholmod_common &Common) { return cholmod_solve (sys, &L, &B, &Common); }
+template<> inline cholmod_dense* cm_solve<SuiteSparse_long> (int sys, cholmod_factor& L, cholmod_dense& B, cholmod_common &Common) { return cholmod_l_solve (sys, &L, &B, &Common); }
+
+template<typename StorageIndex_> inline cholmod_sparse* cm_spsolve (int sys, cholmod_factor& L, cholmod_sparse& B, cholmod_common &Common) { return cholmod_spsolve (sys, &L, &B, &Common); }
+template<> inline cholmod_sparse* cm_spsolve<SuiteSparse_long> (int sys, cholmod_factor& L, cholmod_sparse& B, cholmod_common &Common) { return cholmod_l_spsolve (sys, &L, &B, &Common); }
+
+template<typename StorageIndex_>
+inline int cm_factorize_p (cholmod_sparse* A, double beta[2], StorageIndex_* fset, std::size_t fsize, cholmod_factor* L, cholmod_common &Common) { return cholmod_factorize_p (A, beta, fset, fsize, L, &Common); }
+template<>
+inline int cm_factorize_p<SuiteSparse_long> (cholmod_sparse* A, double beta[2], SuiteSparse_long* fset, std::size_t fsize, cholmod_factor* L, cholmod_common &Common) { return cholmod_l_factorize_p (A, beta, fset, fsize, L, &Common); }
+
+#undef EIGEN_CHOLMOD_SPECIALIZE0
+#undef EIGEN_CHOLMOD_SPECIALIZE1
+
+} // namespace internal
+
+
+enum CholmodMode {
+ CholmodAuto, CholmodSimplicialLLt, CholmodSupernodalLLt, CholmodLDLt
+};
+
+
+/** \ingroup CholmodSupport_Module
+ * \class CholmodBase
+ * \brief The base class for the direct Cholesky factorization of Cholmod
+ * \sa class CholmodSupernodalLLT, class CholmodSimplicialLDLT, class CholmodSimplicialLLT
+ */
+template<typename MatrixType_, int UpLo_, typename Derived>
+class CholmodBase : public SparseSolverBase<Derived>
+{
+ protected:
+ typedef SparseSolverBase<Derived> Base;
+ using Base::derived;
+ using Base::m_isInitialized;
+ public:
+ typedef MatrixType_ MatrixType;
+ enum { UpLo = UpLo_ };
+ typedef typename MatrixType::Scalar Scalar;
+ typedef typename MatrixType::RealScalar RealScalar;
+ typedef MatrixType CholMatrixType;
+ typedef typename MatrixType::StorageIndex StorageIndex;
+ enum {
+ ColsAtCompileTime = MatrixType::ColsAtCompileTime,
+ MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime
+ };
+
+ public:
+
+ CholmodBase()
+ : m_cholmodFactor(0), m_info(Success), m_factorizationIsOk(false), m_analysisIsOk(false)
+ {
+ EIGEN_STATIC_ASSERT((internal::is_same<double,RealScalar>::value), CHOLMOD_SUPPORTS_DOUBLE_PRECISION_ONLY);
+ m_shiftOffset[0] = m_shiftOffset[1] = 0.0;
+ internal::cm_start<StorageIndex>(m_cholmod);
+ }
+
+ explicit CholmodBase(const MatrixType& matrix)
+ : m_cholmodFactor(0), m_info(Success), m_factorizationIsOk(false), m_analysisIsOk(false)
+ {
+ EIGEN_STATIC_ASSERT((internal::is_same<double,RealScalar>::value), CHOLMOD_SUPPORTS_DOUBLE_PRECISION_ONLY);
+ m_shiftOffset[0] = m_shiftOffset[1] = 0.0;
+ internal::cm_start<StorageIndex>(m_cholmod);
+ compute(matrix);
+ }
+
+ ~CholmodBase()
+ {
+ if(m_cholmodFactor)
+ internal::cm_free_factor<StorageIndex>(m_cholmodFactor, m_cholmod);
+ internal::cm_finish<StorageIndex>(m_cholmod);
+ }
+
+ inline StorageIndex cols() const { return internal::convert_index<StorageIndex, Index>(m_cholmodFactor->n); }
+ inline StorageIndex rows() const { return internal::convert_index<StorageIndex, Index>(m_cholmodFactor->n); }
+
+ /** \brief Reports whether previous computation was successful.
+ *
+ * \returns \c Success if computation was successful,
+ * \c NumericalIssue if the matrix.appears to be negative.
+ */
+ ComputationInfo info() const
+ {
+ eigen_assert(m_isInitialized && "Decomposition is not initialized.");
+ return m_info;
+ }
+
+ /** Computes the sparse Cholesky decomposition of \a matrix */
+ Derived& compute(const MatrixType& matrix)
+ {
+ analyzePattern(matrix);
+ factorize(matrix);
+ return derived();
+ }
+
+ /** Performs a symbolic decomposition on the sparsity pattern of \a matrix.
+ *
+ * This function is particularly useful when solving for several problems having the same structure.
+ *
+ * \sa factorize()
+ */
+ void analyzePattern(const MatrixType& matrix)
+ {
+ if(m_cholmodFactor)
+ {
+ internal::cm_free_factor<StorageIndex>(m_cholmodFactor, m_cholmod);
+ m_cholmodFactor = 0;
+ }
+ cholmod_sparse A = viewAsCholmod(matrix.template selfadjointView<UpLo>());
+ m_cholmodFactor = internal::cm_analyze<StorageIndex>(A, m_cholmod);
+
+ this->m_isInitialized = true;
+ this->m_info = Success;
+ m_analysisIsOk = true;
+ m_factorizationIsOk = false;
+ }
+
+ /** Performs a numeric decomposition of \a matrix
+ *
+ * The given matrix must have the same sparsity pattern as the matrix on which the symbolic decomposition has been performed.
+ *
+ * \sa analyzePattern()
+ */
+ void factorize(const MatrixType& matrix)
+ {
+ eigen_assert(m_analysisIsOk && "You must first call analyzePattern()");
+ cholmod_sparse A = viewAsCholmod(matrix.template selfadjointView<UpLo>());
+ internal::cm_factorize_p<StorageIndex>(&A, m_shiftOffset, 0, 0, m_cholmodFactor, m_cholmod);
+
+ // If the factorization failed, minor is the column at which it did. On success minor == n.
+ this->m_info = (m_cholmodFactor->minor == m_cholmodFactor->n ? Success : NumericalIssue);
+ m_factorizationIsOk = true;
+ }
+
+ /** Returns a reference to the Cholmod's configuration structure to get a full control over the performed operations.
+ * See the Cholmod user guide for details. */
+ cholmod_common& cholmod() { return m_cholmod; }
+
+ #ifndef EIGEN_PARSED_BY_DOXYGEN
+ /** \internal */
+ template<typename Rhs,typename Dest>
+ void _solve_impl(const MatrixBase<Rhs> &b, MatrixBase<Dest> &dest) const
+ {
+ eigen_assert(m_factorizationIsOk && "The decomposition is not in a valid state for solving, you must first call either compute() or symbolic()/numeric()");
+ const Index size = m_cholmodFactor->n;
+ EIGEN_UNUSED_VARIABLE(size);
+ eigen_assert(size==b.rows());
+
+ // Cholmod needs column-major storage without inner-stride, which corresponds to the default behavior of Ref.
+ Ref<const Matrix<typename Rhs::Scalar,Dynamic,Dynamic,ColMajor> > b_ref(b.derived());
+
+ cholmod_dense b_cd = viewAsCholmod(b_ref);
+ cholmod_dense* x_cd = internal::cm_solve<StorageIndex>(CHOLMOD_A, *m_cholmodFactor, b_cd, m_cholmod);
+ if(!x_cd)
+ {
+ this->m_info = NumericalIssue;
+ return;
+ }
+ // TODO optimize this copy by swapping when possible (be careful with alignment, etc.)
+ // NOTE Actually, the copy can be avoided by calling cholmod_solve2 instead of cholmod_solve
+ dest = Matrix<Scalar,Dest::RowsAtCompileTime,Dest::ColsAtCompileTime>::Map(reinterpret_cast<Scalar*>(x_cd->x),b.rows(),b.cols());
+ internal::cm_free_dense<StorageIndex>(x_cd, m_cholmod);
+ }
+
+ /** \internal */
+ template<typename RhsDerived, typename DestDerived>
+ void _solve_impl(const SparseMatrixBase<RhsDerived> &b, SparseMatrixBase<DestDerived> &dest) const
+ {
+ eigen_assert(m_factorizationIsOk && "The decomposition is not in a valid state for solving, you must first call either compute() or symbolic()/numeric()");
+ const Index size = m_cholmodFactor->n;
+ EIGEN_UNUSED_VARIABLE(size);
+ eigen_assert(size==b.rows());
+
+ // note: cs stands for Cholmod Sparse
+ Ref<SparseMatrix<typename RhsDerived::Scalar,ColMajor,typename RhsDerived::StorageIndex> > b_ref(b.const_cast_derived());
+ cholmod_sparse b_cs = viewAsCholmod(b_ref);
+ cholmod_sparse* x_cs = internal::cm_spsolve<StorageIndex>(CHOLMOD_A, *m_cholmodFactor, b_cs, m_cholmod);
+ if(!x_cs)
+ {
+ this->m_info = NumericalIssue;
+ return;
+ }
+ // TODO optimize this copy by swapping when possible (be careful with alignment, etc.)
+ // NOTE cholmod_spsolve in fact just calls the dense solver for blocks of 4 columns at a time (similar to Eigen's sparse solver)
+ dest.derived() = viewAsEigen<typename DestDerived::Scalar,ColMajor,typename DestDerived::StorageIndex>(*x_cs);
+ internal::cm_free_sparse<StorageIndex>(x_cs, m_cholmod);
+ }
+ #endif // EIGEN_PARSED_BY_DOXYGEN
+
+
+ /** Sets the shift parameter that will be used to adjust the diagonal coefficients during the numerical factorization.
+ *
+ * During the numerical factorization, an offset term is added to the diagonal coefficients:\n
+ * \c d_ii = \a offset + \c d_ii
+ *
+ * The default is \a offset=0.
+ *
+ * \returns a reference to \c *this.
+ */
+ Derived& setShift(const RealScalar& offset)
+ {
+ m_shiftOffset[0] = double(offset);
+ return derived();
+ }
+
+ /** \returns the determinant of the underlying matrix from the current factorization */
+ Scalar determinant() const
+ {
+ using std::exp;
+ return exp(logDeterminant());
+ }
+
+ /** \returns the log determinant of the underlying matrix from the current factorization */
+ Scalar logDeterminant() const
+ {
+ using std::log;
+ using numext::real;
+ eigen_assert(m_factorizationIsOk && "The decomposition is not in a valid state for solving, you must first call either compute() or symbolic()/numeric()");
+
+ RealScalar logDet = 0;
+ Scalar *x = static_cast<Scalar*>(m_cholmodFactor->x);
+ if (m_cholmodFactor->is_super)
+ {
+ // Supernodal factorization stored as a packed list of dense column-major blocs,
+ // as described by the following structure:
+
+ // super[k] == index of the first column of the j-th super node
+ StorageIndex *super = static_cast<StorageIndex*>(m_cholmodFactor->super);
+ // pi[k] == offset to the description of row indices
+ StorageIndex *pi = static_cast<StorageIndex*>(m_cholmodFactor->pi);
+ // px[k] == offset to the respective dense block
+ StorageIndex *px = static_cast<StorageIndex*>(m_cholmodFactor->px);
+
+ Index nb_super_nodes = m_cholmodFactor->nsuper;
+ for (Index k=0; k < nb_super_nodes; ++k)
+ {
+ StorageIndex ncols = super[k + 1] - super[k];
+ StorageIndex nrows = pi[k + 1] - pi[k];
+
+ Map<const Array<Scalar,1,Dynamic>, 0, InnerStride<> > sk(x + px[k], ncols, InnerStride<>(nrows+1));
+ logDet += sk.real().log().sum();
+ }
+ }
+ else
+ {
+ // Simplicial factorization stored as standard CSC matrix.
+ StorageIndex *p = static_cast<StorageIndex*>(m_cholmodFactor->p);
+ Index size = m_cholmodFactor->n;
+ for (Index k=0; k<size; ++k)
+ logDet += log(real( x[p[k]] ));
+ }
+ if (m_cholmodFactor->is_ll)
+ logDet *= 2.0;
+ return logDet;
+ }
+
+ template<typename Stream>
+ void dumpMemory(Stream& /*s*/)
+ {}
+
+ protected:
+ mutable cholmod_common m_cholmod;
+ cholmod_factor* m_cholmodFactor;
+ double m_shiftOffset[2];
+ mutable ComputationInfo m_info;
+ int m_factorizationIsOk;
+ int m_analysisIsOk;
+};
+
+/** \ingroup CholmodSupport_Module
+ * \class CholmodSimplicialLLT
+ * \brief A simplicial direct Cholesky (LLT) factorization and solver based on Cholmod
+ *
+ * This class allows to solve for A.X = B sparse linear problems via a simplicial LL^T Cholesky factorization
+ * using the Cholmod library.
+ * This simplicial variant is equivalent to Eigen's built-in SimplicialLLT class. Therefore, it has little practical interest.
+ * The sparse matrix A must be selfadjoint and positive definite. The vectors or matrices
+ * X and B can be either dense or sparse.
+ *
+ * \tparam MatrixType_ the type of the sparse matrix A, it must be a SparseMatrix<>
+ * \tparam UpLo_ the triangular part that will be used for the computations. It can be Lower
+ * or Upper. Default is Lower.
+ *
+ * \implsparsesolverconcept
+ *
+ * This class supports all kind of SparseMatrix<>: row or column major; upper, lower, or both; compressed or non compressed.
+ *
+ * \warning Only double precision real and complex scalar types are supported by Cholmod.
+ *
+ * \sa \ref TutorialSparseSolverConcept, class CholmodSupernodalLLT, class SimplicialLLT
+ */
+template<typename MatrixType_, int UpLo_ = Lower>
+class CholmodSimplicialLLT : public CholmodBase<MatrixType_, UpLo_, CholmodSimplicialLLT<MatrixType_, UpLo_> >
+{
+ typedef CholmodBase<MatrixType_, UpLo_, CholmodSimplicialLLT> Base;
+ using Base::m_cholmod;
+
+ public:
+
+ typedef MatrixType_ MatrixType;
+
+ CholmodSimplicialLLT() : Base() { init(); }
+
+ CholmodSimplicialLLT(const MatrixType& matrix) : Base()
+ {
+ init();
+ this->compute(matrix);
+ }
+
+ ~CholmodSimplicialLLT() {}
+ protected:
+ void init()
+ {
+ m_cholmod.final_asis = 0;
+ m_cholmod.supernodal = CHOLMOD_SIMPLICIAL;
+ m_cholmod.final_ll = 1;
+ }
+};
+
+
+/** \ingroup CholmodSupport_Module
+ * \class CholmodSimplicialLDLT
+ * \brief A simplicial direct Cholesky (LDLT) factorization and solver based on Cholmod
+ *
+ * This class allows to solve for A.X = B sparse linear problems via a simplicial LDL^T Cholesky factorization
+ * using the Cholmod library.
+ * This simplicial variant is equivalent to Eigen's built-in SimplicialLDLT class. Therefore, it has little practical interest.
+ * The sparse matrix A must be selfadjoint and positive definite. The vectors or matrices
+ * X and B can be either dense or sparse.
+ *
+ * \tparam MatrixType_ the type of the sparse matrix A, it must be a SparseMatrix<>
+ * \tparam UpLo_ the triangular part that will be used for the computations. It can be Lower
+ * or Upper. Default is Lower.
+ *
+ * \implsparsesolverconcept
+ *
+ * This class supports all kind of SparseMatrix<>: row or column major; upper, lower, or both; compressed or non compressed.
+ *
+ * \warning Only double precision real and complex scalar types are supported by Cholmod.
+ *
+ * \sa \ref TutorialSparseSolverConcept, class CholmodSupernodalLLT, class SimplicialLDLT
+ */
+template<typename MatrixType_, int UpLo_ = Lower>
+class CholmodSimplicialLDLT : public CholmodBase<MatrixType_, UpLo_, CholmodSimplicialLDLT<MatrixType_, UpLo_> >
+{
+ typedef CholmodBase<MatrixType_, UpLo_, CholmodSimplicialLDLT> Base;
+ using Base::m_cholmod;
+
+ public:
+
+ typedef MatrixType_ MatrixType;
+
+ CholmodSimplicialLDLT() : Base() { init(); }
+
+ CholmodSimplicialLDLT(const MatrixType& matrix) : Base()
+ {
+ init();
+ this->compute(matrix);
+ }
+
+ ~CholmodSimplicialLDLT() {}
+ protected:
+ void init()
+ {
+ m_cholmod.final_asis = 1;
+ m_cholmod.supernodal = CHOLMOD_SIMPLICIAL;
+ }
+};
+
+/** \ingroup CholmodSupport_Module
+ * \class CholmodSupernodalLLT
+ * \brief A supernodal Cholesky (LLT) factorization and solver based on Cholmod
+ *
+ * This class allows to solve for A.X = B sparse linear problems via a supernodal LL^T Cholesky factorization
+ * using the Cholmod library.
+ * This supernodal variant performs best on dense enough problems, e.g., 3D FEM, or very high order 2D FEM.
+ * The sparse matrix A must be selfadjoint and positive definite. The vectors or matrices
+ * X and B can be either dense or sparse.
+ *
+ * \tparam MatrixType_ the type of the sparse matrix A, it must be a SparseMatrix<>
+ * \tparam UpLo_ the triangular part that will be used for the computations. It can be Lower
+ * or Upper. Default is Lower.
+ *
+ * \implsparsesolverconcept
+ *
+ * This class supports all kind of SparseMatrix<>: row or column major; upper, lower, or both; compressed or non compressed.
+ *
+ * \warning Only double precision real and complex scalar types are supported by Cholmod.
+ *
+ * \sa \ref TutorialSparseSolverConcept
+ */
+template<typename MatrixType_, int UpLo_ = Lower>
+class CholmodSupernodalLLT : public CholmodBase<MatrixType_, UpLo_, CholmodSupernodalLLT<MatrixType_, UpLo_> >
+{
+ typedef CholmodBase<MatrixType_, UpLo_, CholmodSupernodalLLT> Base;
+ using Base::m_cholmod;
+
+ public:
+
+ typedef MatrixType_ MatrixType;
+
+ CholmodSupernodalLLT() : Base() { init(); }
+
+ CholmodSupernodalLLT(const MatrixType& matrix) : Base()
+ {
+ init();
+ this->compute(matrix);
+ }
+
+ ~CholmodSupernodalLLT() {}
+ protected:
+ void init()
+ {
+ m_cholmod.final_asis = 1;
+ m_cholmod.supernodal = CHOLMOD_SUPERNODAL;
+ }
+};
+
+/** \ingroup CholmodSupport_Module
+ * \class CholmodDecomposition
+ * \brief A general Cholesky factorization and solver based on Cholmod
+ *
+ * This class allows to solve for A.X = B sparse linear problems via a LL^T or LDL^T Cholesky factorization
+ * using the Cholmod library. The sparse matrix A must be selfadjoint and positive definite. The vectors or matrices
+ * X and B can be either dense or sparse.
+ *
+ * This variant permits to change the underlying Cholesky method at runtime.
+ * On the other hand, it does not provide access to the result of the factorization.
+ * The default is to let Cholmod automatically choose between a simplicial and supernodal factorization.
+ *
+ * \tparam MatrixType_ the type of the sparse matrix A, it must be a SparseMatrix<>
+ * \tparam UpLo_ the triangular part that will be used for the computations. It can be Lower
+ * or Upper. Default is Lower.
+ *
+ * \implsparsesolverconcept
+ *
+ * This class supports all kind of SparseMatrix<>: row or column major; upper, lower, or both; compressed or non compressed.
+ *
+ * \warning Only double precision real and complex scalar types are supported by Cholmod.
+ *
+ * \sa \ref TutorialSparseSolverConcept
+ */
+template<typename MatrixType_, int UpLo_ = Lower>
+class CholmodDecomposition : public CholmodBase<MatrixType_, UpLo_, CholmodDecomposition<MatrixType_, UpLo_> >
+{
+ typedef CholmodBase<MatrixType_, UpLo_, CholmodDecomposition> Base;
+ using Base::m_cholmod;
+
+ public:
+
+ typedef MatrixType_ MatrixType;
+
+ CholmodDecomposition() : Base() { init(); }
+
+ CholmodDecomposition(const MatrixType& matrix) : Base()
+ {
+ init();
+ this->compute(matrix);
+ }
+
+ ~CholmodDecomposition() {}
+
+ void setMode(CholmodMode mode)
+ {
+ switch(mode)
+ {
+ case CholmodAuto:
+ m_cholmod.final_asis = 1;
+ m_cholmod.supernodal = CHOLMOD_AUTO;
+ break;
+ case CholmodSimplicialLLt:
+ m_cholmod.final_asis = 0;
+ m_cholmod.supernodal = CHOLMOD_SIMPLICIAL;
+ m_cholmod.final_ll = 1;
+ break;
+ case CholmodSupernodalLLt:
+ m_cholmod.final_asis = 1;
+ m_cholmod.supernodal = CHOLMOD_SUPERNODAL;
+ break;
+ case CholmodLDLt:
+ m_cholmod.final_asis = 1;
+ m_cholmod.supernodal = CHOLMOD_SIMPLICIAL;
+ break;
+ default:
+ break;
+ }
+ }
+ protected:
+ void init()
+ {
+ m_cholmod.final_asis = 1;
+ m_cholmod.supernodal = CHOLMOD_AUTO;
+ }
+};
+
+} // end namespace Eigen
+
+#endif // EIGEN_CHOLMODSUPPORT_H
diff --git a/Eigen/src/CholmodSupport/InternalHeaderCheck.h b/Eigen/src/CholmodSupport/InternalHeaderCheck.h
new file mode 100644
index 0000000..0fb3abc
--- /dev/null
+++ b/Eigen/src/CholmodSupport/InternalHeaderCheck.h
@@ -0,0 +1,3 @@
+#ifndef EIGEN_CHOLMODSUPPORT_MODULE_H
+#error "Please include Eigen/CholmodSupport instead of including headers inside the src directory directly."
+#endif
diff --git a/Eigen/src/Core/ArithmeticSequence.h b/Eigen/src/Core/ArithmeticSequence.h
new file mode 100644
index 0000000..81005c5
--- /dev/null
+++ b/Eigen/src/Core/ArithmeticSequence.h
@@ -0,0 +1,258 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2017 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_ARITHMETIC_SEQUENCE_H
+#define EIGEN_ARITHMETIC_SEQUENCE_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+
+// Helper to cleanup the type of the increment:
+template<typename T> struct cleanup_seq_incr {
+ typedef typename cleanup_index_type<T,DynamicIndex>::type type;
+};
+
+} // namespace internal
+
+//--------------------------------------------------------------------------------
+// seq(first,last,incr) and seqN(first,size,incr)
+//--------------------------------------------------------------------------------
+
+template<typename FirstType=Index,typename SizeType=Index,typename IncrType=internal::FixedInt<1> >
+class ArithmeticSequence;
+
+template<typename FirstType,typename SizeType,typename IncrType>
+ArithmeticSequence<typename internal::cleanup_index_type<FirstType>::type,
+ typename internal::cleanup_index_type<SizeType>::type,
+ typename internal::cleanup_seq_incr<IncrType>::type >
+seqN(FirstType first, SizeType size, IncrType incr);
+
+/** \class ArithmeticSequence
+ * \ingroup Core_Module
+ *
+ * This class represents an arithmetic progression \f$ a_0, a_1, a_2, ..., a_{n-1}\f$ defined by
+ * its \em first value \f$ a_0 \f$, its \em size (aka length) \em n, and the \em increment (aka stride)
+ * that is equal to \f$ a_{i+1}-a_{i}\f$ for any \em i.
+ *
+ * It is internally used as the return type of the Eigen::seq and Eigen::seqN functions, and as the input arguments
+ * of DenseBase::operator()(const RowIndices&, const ColIndices&), and most of the time this is the
+ * only way it is used.
+ *
+ * \tparam FirstType type of the first element, usually an Index,
+ * but internally it can be a symbolic expression
+ * \tparam SizeType type representing the size of the sequence, usually an Index
+ * or a compile time integral constant. Internally, it can also be a symbolic expression
+ * \tparam IncrType type of the increment, can be a runtime Index, or a compile time integral constant (default is compile-time 1)
+ *
+ * \sa Eigen::seq, Eigen::seqN, DenseBase::operator()(const RowIndices&, const ColIndices&), class IndexedView
+ */
+template<typename FirstType,typename SizeType,typename IncrType>
+class ArithmeticSequence
+{
+public:
+ ArithmeticSequence(FirstType first, SizeType size) : m_first(first), m_size(size) {}
+ ArithmeticSequence(FirstType first, SizeType size, IncrType incr) : m_first(first), m_size(size), m_incr(incr) {}
+
+ enum {
+ SizeAtCompileTime = internal::get_fixed_value<SizeType>::value,
+ IncrAtCompileTime = internal::get_fixed_value<IncrType,DynamicIndex>::value
+ };
+
+ /** \returns the size, i.e., number of elements, of the sequence */
+ Index size() const { return m_size; }
+
+ /** \returns the first element \f$ a_0 \f$ in the sequence */
+ Index first() const { return m_first; }
+
+ /** \returns the value \f$ a_i \f$ at index \a i in the sequence. */
+ Index operator[](Index i) const { return m_first + i * m_incr; }
+
+ const FirstType& firstObject() const { return m_first; }
+ const SizeType& sizeObject() const { return m_size; }
+ const IncrType& incrObject() const { return m_incr; }
+
+protected:
+ FirstType m_first;
+ SizeType m_size;
+ IncrType m_incr;
+
+public:
+ auto reverse() const -> decltype(Eigen::seqN(m_first+(m_size+fix<-1>())*m_incr,m_size,-m_incr)) {
+ return seqN(m_first+(m_size+fix<-1>())*m_incr,m_size,-m_incr);
+ }
+};
+
+/** \returns an ArithmeticSequence starting at \a first, of length \a size, and increment \a incr
+ *
+ * \sa seqN(FirstType,SizeType), seq(FirstType,LastType,IncrType) */
+template<typename FirstType,typename SizeType,typename IncrType>
+ArithmeticSequence<typename internal::cleanup_index_type<FirstType>::type,typename internal::cleanup_index_type<SizeType>::type,typename internal::cleanup_seq_incr<IncrType>::type >
+seqN(FirstType first, SizeType size, IncrType incr) {
+ return ArithmeticSequence<typename internal::cleanup_index_type<FirstType>::type,typename internal::cleanup_index_type<SizeType>::type,typename internal::cleanup_seq_incr<IncrType>::type>(first,size,incr);
+}
+
+/** \returns an ArithmeticSequence starting at \a first, of length \a size, and unit increment
+ *
+ * \sa seqN(FirstType,SizeType,IncrType), seq(FirstType,LastType) */
+template<typename FirstType,typename SizeType>
+ArithmeticSequence<typename internal::cleanup_index_type<FirstType>::type,typename internal::cleanup_index_type<SizeType>::type >
+seqN(FirstType first, SizeType size) {
+ return ArithmeticSequence<typename internal::cleanup_index_type<FirstType>::type,typename internal::cleanup_index_type<SizeType>::type>(first,size);
+}
+
+#ifdef EIGEN_PARSED_BY_DOXYGEN
+
+/** \returns an ArithmeticSequence starting at \a f, up (or down) to \a l, and with positive (or negative) increment \a incr
+ *
+ * It is essentially an alias to:
+ * \code
+ * seqN(f, (l-f+incr)/incr, incr);
+ * \endcode
+ *
+ * \sa seqN(FirstType,SizeType,IncrType), seq(FirstType,LastType)
+ */
+template<typename FirstType,typename LastType, typename IncrType>
+auto seq(FirstType f, LastType l, IncrType incr);
+
+/** \returns an ArithmeticSequence starting at \a f, up (or down) to \a l, and unit increment
+ *
+ * It is essentially an alias to:
+ * \code
+ * seqN(f,l-f+1);
+ * \endcode
+ *
+ * \sa seqN(FirstType,SizeType), seq(FirstType,LastType,IncrType)
+ */
+template<typename FirstType,typename LastType>
+auto seq(FirstType f, LastType l);
+
+#else // EIGEN_PARSED_BY_DOXYGEN
+
+template<typename FirstType,typename LastType>
+auto seq(FirstType f, LastType l) -> decltype(seqN(typename internal::cleanup_index_type<FirstType>::type(f),
+ ( typename internal::cleanup_index_type<LastType>::type(l)
+ - typename internal::cleanup_index_type<FirstType>::type(f)+fix<1>())))
+{
+ return seqN(typename internal::cleanup_index_type<FirstType>::type(f),
+ (typename internal::cleanup_index_type<LastType>::type(l)
+ -typename internal::cleanup_index_type<FirstType>::type(f)+fix<1>()));
+}
+
+template<typename FirstType,typename LastType, typename IncrType>
+auto seq(FirstType f, LastType l, IncrType incr)
+ -> decltype(seqN(typename internal::cleanup_index_type<FirstType>::type(f),
+ ( typename internal::cleanup_index_type<LastType>::type(l)
+ - typename internal::cleanup_index_type<FirstType>::type(f)+typename internal::cleanup_seq_incr<IncrType>::type(incr)
+ ) / typename internal::cleanup_seq_incr<IncrType>::type(incr),
+ typename internal::cleanup_seq_incr<IncrType>::type(incr)))
+{
+ typedef typename internal::cleanup_seq_incr<IncrType>::type CleanedIncrType;
+ return seqN(typename internal::cleanup_index_type<FirstType>::type(f),
+ ( typename internal::cleanup_index_type<LastType>::type(l)
+ -typename internal::cleanup_index_type<FirstType>::type(f)+CleanedIncrType(incr)) / CleanedIncrType(incr),
+ CleanedIncrType(incr));
+}
+
+
+#endif // EIGEN_PARSED_BY_DOXYGEN
+
+namespace placeholders {
+
+/** \cpp11
+ * \returns a symbolic ArithmeticSequence representing the last \a size elements with increment \a incr.
+ *
+ * It is a shortcut for: \code seqN(last-(size-fix<1>)*incr, size, incr) \endcode
+ *
+ * \sa lastN(SizeType), seqN(FirstType,SizeType), seq(FirstType,LastType,IncrType) */
+template<typename SizeType,typename IncrType>
+auto lastN(SizeType size, IncrType incr)
+-> decltype(seqN(Eigen::placeholders::last-(size-fix<1>())*incr, size, incr))
+{
+ return seqN(Eigen::placeholders::last-(size-fix<1>())*incr, size, incr);
+}
+
+/** \cpp11
+ * \returns a symbolic ArithmeticSequence representing the last \a size elements with a unit increment.
+ *
+ * It is a shortcut for: \code seq(last+fix<1>-size, last) \endcode
+ *
+ * \sa lastN(SizeType,IncrType, seqN(FirstType,SizeType), seq(FirstType,LastType) */
+template<typename SizeType>
+auto lastN(SizeType size)
+-> decltype(seqN(Eigen::placeholders::last+fix<1>()-size, size))
+{
+ return seqN(Eigen::placeholders::last+fix<1>()-size, size);
+}
+
+} // namespace placeholders
+
+namespace internal {
+
+// Convert a symbolic span into a usable one (i.e., remove last/end "keywords")
+template<typename T>
+struct make_size_type {
+ typedef std::conditional_t<symbolic::is_symbolic<T>::value, Index, T> type;
+};
+
+template<typename FirstType,typename SizeType,typename IncrType,int XprSize>
+struct IndexedViewCompatibleType<ArithmeticSequence<FirstType,SizeType,IncrType>, XprSize> {
+ typedef ArithmeticSequence<Index,typename make_size_type<SizeType>::type,IncrType> type;
+};
+
+template<typename FirstType,typename SizeType,typename IncrType>
+ArithmeticSequence<Index,typename make_size_type<SizeType>::type,IncrType>
+makeIndexedViewCompatible(const ArithmeticSequence<FirstType,SizeType,IncrType>& ids, Index size,SpecializedType) {
+ return ArithmeticSequence<Index,typename make_size_type<SizeType>::type,IncrType>(
+ eval_expr_given_size(ids.firstObject(),size),eval_expr_given_size(ids.sizeObject(),size),ids.incrObject());
+}
+
+template<typename FirstType,typename SizeType,typename IncrType>
+struct get_compile_time_incr<ArithmeticSequence<FirstType,SizeType,IncrType> > {
+ enum { value = get_fixed_value<IncrType,DynamicIndex>::value };
+};
+
+} // end namespace internal
+
+/** \namespace Eigen::indexing
+ * \ingroup Core_Module
+ *
+ * The sole purpose of this namespace is to be able to import all functions
+ * and symbols that are expected to be used within operator() for indexing
+ * and slicing. If you already imported the whole Eigen namespace:
+ * \code using namespace Eigen; \endcode
+ * then you are already all set. Otherwise, if you don't want/cannot import
+ * the whole Eigen namespace, the following line:
+ * \code using namespace Eigen::indexing; \endcode
+ * is equivalent to:
+ * \code
+ using Eigen::fix;
+ using Eigen::seq;
+ using Eigen::seqN;
+ using Eigen::placeholders::all;
+ using Eigen::placeholders::last;
+ using Eigen::placeholders::lastN; // c++11 only
+ using Eigen::placeholders::lastp1;
+ \endcode
+ */
+namespace indexing {
+ using Eigen::fix;
+ using Eigen::seq;
+ using Eigen::seqN;
+ using Eigen::placeholders::all;
+ using Eigen::placeholders::last;
+ using Eigen::placeholders::lastN;
+ using Eigen::placeholders::lastp1;
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_ARITHMETIC_SEQUENCE_H
diff --git a/Eigen/src/Core/Array.h b/Eigen/src/Core/Array.h
new file mode 100644
index 0000000..7be8971
--- /dev/null
+++ b/Eigen/src/Core/Array.h
@@ -0,0 +1,404 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_ARRAY_H
+#define EIGEN_ARRAY_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+template<typename Scalar_, int Rows_, int Cols_, int Options_, int MaxRows_, int MaxCols_>
+struct traits<Array<Scalar_, Rows_, Cols_, Options_, MaxRows_, MaxCols_> > : traits<Matrix<Scalar_, Rows_, Cols_, Options_, MaxRows_, MaxCols_> >
+{
+ typedef ArrayXpr XprKind;
+ typedef ArrayBase<Array<Scalar_, Rows_, Cols_, Options_, MaxRows_, MaxCols_> > XprBase;
+};
+}
+
+/** \class Array
+ * \ingroup Core_Module
+ *
+ * \brief General-purpose arrays with easy API for coefficient-wise operations
+ *
+ * The %Array class is very similar to the Matrix class. It provides
+ * general-purpose one- and two-dimensional arrays. The difference between the
+ * %Array and the %Matrix class is primarily in the API: the API for the
+ * %Array class provides easy access to coefficient-wise operations, while the
+ * API for the %Matrix class provides easy access to linear-algebra
+ * operations.
+ *
+ * See documentation of class Matrix for detailed information on the template parameters
+ * storage layout.
+ *
+ * This class can be extended with the help of the plugin mechanism described on the page
+ * \ref TopicCustomizing_Plugins by defining the preprocessor symbol \c EIGEN_ARRAY_PLUGIN.
+ *
+ * \sa \blank \ref TutorialArrayClass, \ref TopicClassHierarchy
+ */
+template<typename Scalar_, int Rows_, int Cols_, int Options_, int MaxRows_, int MaxCols_>
+class Array
+ : public PlainObjectBase<Array<Scalar_, Rows_, Cols_, Options_, MaxRows_, MaxCols_> >
+{
+ public:
+
+ typedef PlainObjectBase<Array> Base;
+ EIGEN_DENSE_PUBLIC_INTERFACE(Array)
+
+ enum { Options = Options_ };
+ typedef typename Base::PlainObject PlainObject;
+
+ protected:
+ template <typename Derived, typename OtherDerived, bool IsVector>
+ friend struct internal::conservative_resize_like_impl;
+
+ using Base::m_storage;
+
+ public:
+
+ using Base::base;
+ using Base::coeff;
+ using Base::coeffRef;
+
+ /**
+ * The usage of
+ * using Base::operator=;
+ * fails on MSVC. Since the code below is working with GCC and MSVC, we skipped
+ * the usage of 'using'. This should be done only for operator=.
+ */
+ template<typename OtherDerived>
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE Array& operator=(const EigenBase<OtherDerived> &other)
+ {
+ return Base::operator=(other);
+ }
+
+ /** Set all the entries to \a value.
+ * \sa DenseBase::setConstant(), DenseBase::fill()
+ */
+ /* This overload is needed because the usage of
+ * using Base::operator=;
+ * fails on MSVC. Since the code below is working with GCC and MSVC, we skipped
+ * the usage of 'using'. This should be done only for operator=.
+ */
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE Array& operator=(const Scalar &value)
+ {
+ Base::setConstant(value);
+ return *this;
+ }
+
+ /** Copies the value of the expression \a other into \c *this with automatic resizing.
+ *
+ * *this might be resized to match the dimensions of \a other. If *this was a null matrix (not already initialized),
+ * it will be initialized.
+ *
+ * Note that copying a row-vector into a vector (and conversely) is allowed.
+ * The resizing, if any, is then done in the appropriate way so that row-vectors
+ * remain row-vectors and vectors remain vectors.
+ */
+ template<typename OtherDerived>
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE Array& operator=(const DenseBase<OtherDerived>& other)
+ {
+ return Base::_set(other);
+ }
+
+ /** This is a special case of the templated operator=. Its purpose is to
+ * prevent a default operator= from hiding the templated operator=.
+ */
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE Array& operator=(const Array& other)
+ {
+ return Base::_set(other);
+ }
+
+ /** Default constructor.
+ *
+ * For fixed-size matrices, does nothing.
+ *
+ * For dynamic-size matrices, creates an empty matrix of size 0. Does not allocate any array. Such a matrix
+ * is called a null matrix. This constructor is the unique way to create null matrices: resizing
+ * a matrix to 0 is not supported.
+ *
+ * \sa resize(Index,Index)
+ */
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE Array() : Base()
+ {
+ EIGEN_INITIALIZE_COEFFS_IF_THAT_OPTION_IS_ENABLED
+ }
+
+#ifndef EIGEN_PARSED_BY_DOXYGEN
+ // FIXME is it still needed ??
+ /** \internal */
+ EIGEN_DEVICE_FUNC
+ Array(internal::constructor_without_unaligned_array_assert)
+ : Base(internal::constructor_without_unaligned_array_assert())
+ {
+ EIGEN_INITIALIZE_COEFFS_IF_THAT_OPTION_IS_ENABLED
+ }
+#endif
+
+ EIGEN_DEVICE_FUNC
+ Array(Array&& other) EIGEN_NOEXCEPT_IF(std::is_nothrow_move_constructible<Scalar>::value)
+ : Base(std::move(other))
+ {
+ }
+ EIGEN_DEVICE_FUNC
+ Array& operator=(Array&& other) EIGEN_NOEXCEPT_IF(std::is_nothrow_move_assignable<Scalar>::value)
+ {
+ Base::operator=(std::move(other));
+ return *this;
+ }
+
+ /** \copydoc PlainObjectBase(const Scalar& a0, const Scalar& a1, const Scalar& a2, const Scalar& a3, const ArgTypes&... args)
+ *
+ * Example: \include Array_variadic_ctor_cxx11.cpp
+ * Output: \verbinclude Array_variadic_ctor_cxx11.out
+ *
+ * \sa Array(const std::initializer_list<std::initializer_list<Scalar>>&)
+ * \sa Array(const Scalar&), Array(const Scalar&,const Scalar&)
+ */
+ template <typename... ArgTypes>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ Array(const Scalar& a0, const Scalar& a1, const Scalar& a2, const Scalar& a3, const ArgTypes&... args)
+ : Base(a0, a1, a2, a3, args...) {}
+
+ /** \brief Constructs an array and initializes it from the coefficients given as initializer-lists grouped by row. \cpp11
+ *
+ * In the general case, the constructor takes a list of rows, each row being represented as a list of coefficients:
+ *
+ * Example: \include Array_initializer_list_23_cxx11.cpp
+ * Output: \verbinclude Array_initializer_list_23_cxx11.out
+ *
+ * Each of the inner initializer lists must contain the exact same number of elements, otherwise an assertion is triggered.
+ *
+ * In the case of a compile-time column 1D array, implicit transposition from a single row is allowed.
+ * Therefore <code> Array<int,Dynamic,1>{{1,2,3,4,5}}</code> is legal and the more verbose syntax
+ * <code>Array<int,Dynamic,1>{{1},{2},{3},{4},{5}}</code> can be avoided:
+ *
+ * Example: \include Array_initializer_list_vector_cxx11.cpp
+ * Output: \verbinclude Array_initializer_list_vector_cxx11.out
+ *
+ * In the case of fixed-sized arrays, the initializer list sizes must exactly match the array sizes,
+ * and implicit transposition is allowed for compile-time 1D arrays only.
+ *
+ * \sa Array(const Scalar& a0, const Scalar& a1, const Scalar& a2, const Scalar& a3, const ArgTypes&... args)
+ */
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE Array(const std::initializer_list<std::initializer_list<Scalar>>& list) : Base(list) {}
+
+ #ifndef EIGEN_PARSED_BY_DOXYGEN
+ template<typename T>
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE explicit Array(const T& x)
+ {
+ Base::template _init1<T>(x);
+ }
+
+ template<typename T0, typename T1>
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE Array(const T0& val0, const T1& val1)
+ {
+ this->template _init2<T0,T1>(val0, val1);
+ }
+
+ #else
+ /** \brief Constructs a fixed-sized array initialized with coefficients starting at \a data */
+ EIGEN_DEVICE_FUNC explicit Array(const Scalar *data);
+ /** Constructs a vector or row-vector with given dimension. \only_for_vectors
+ *
+ * Note that this is only useful for dynamic-size vectors. For fixed-size vectors,
+ * it is redundant to pass the dimension here, so it makes more sense to use the default
+ * constructor Array() instead.
+ */
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE explicit Array(Index dim);
+ /** constructs an initialized 1x1 Array with the given coefficient
+ * \sa const Scalar& a0, const Scalar& a1, const Scalar& a2, const Scalar& a3, const ArgTypes&... args */
+ Array(const Scalar& value);
+ /** constructs an uninitialized array with \a rows rows and \a cols columns.
+ *
+ * This is useful for dynamic-size arrays. For fixed-size arrays,
+ * it is redundant to pass these parameters, so one should use the default constructor
+ * Array() instead. */
+ Array(Index rows, Index cols);
+ /** constructs an initialized 2D vector with given coefficients
+ * \sa Array(const Scalar& a0, const Scalar& a1, const Scalar& a2, const Scalar& a3, const ArgTypes&... args) */
+ Array(const Scalar& val0, const Scalar& val1);
+ #endif // end EIGEN_PARSED_BY_DOXYGEN
+
+ /** constructs an initialized 3D vector with given coefficients
+ * \sa Array(const Scalar& a0, const Scalar& a1, const Scalar& a2, const Scalar& a3, const ArgTypes&... args)
+ */
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE Array(const Scalar& val0, const Scalar& val1, const Scalar& val2)
+ {
+ EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(Array, 3)
+ m_storage.data()[0] = val0;
+ m_storage.data()[1] = val1;
+ m_storage.data()[2] = val2;
+ }
+ /** constructs an initialized 4D vector with given coefficients
+ * \sa Array(const Scalar& a0, const Scalar& a1, const Scalar& a2, const Scalar& a3, const ArgTypes&... args)
+ */
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE Array(const Scalar& val0, const Scalar& val1, const Scalar& val2, const Scalar& val3)
+ {
+ EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(Array, 4)
+ m_storage.data()[0] = val0;
+ m_storage.data()[1] = val1;
+ m_storage.data()[2] = val2;
+ m_storage.data()[3] = val3;
+ }
+
+ /** Copy constructor */
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE Array(const Array& other)
+ : Base(other)
+ { }
+
+ private:
+ struct PrivateType {};
+ public:
+
+ /** \sa MatrixBase::operator=(const EigenBase<OtherDerived>&) */
+ template<typename OtherDerived>
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE Array(const EigenBase<OtherDerived> &other,
+ std::enable_if_t<internal::is_convertible<typename OtherDerived::Scalar,Scalar>::value,
+ PrivateType> = PrivateType())
+ : Base(other.derived())
+ { }
+
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
+ inline Index innerStride() const EIGEN_NOEXCEPT{ return 1; }
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
+ inline Index outerStride() const EIGEN_NOEXCEPT { return this->innerSize(); }
+
+ #ifdef EIGEN_ARRAY_PLUGIN
+ #include EIGEN_ARRAY_PLUGIN
+ #endif
+
+ private:
+
+ template<typename MatrixType, typename OtherDerived, bool SwapPointers>
+ friend struct internal::matrix_swap_impl;
+};
+
+/** \defgroup arraytypedefs Global array typedefs
+ * \ingroup Core_Module
+ *
+ * %Eigen defines several typedef shortcuts for most common 1D and 2D array types.
+ *
+ * The general patterns are the following:
+ *
+ * \c ArrayRowsColsType where \c Rows and \c Cols can be \c 2,\c 3,\c 4 for fixed size square matrices or \c X for dynamic size,
+ * and where \c Type can be \c i for integer, \c f for float, \c d for double, \c cf for complex float, \c cd
+ * for complex double.
+ *
+ * For example, \c Array33d is a fixed-size 3x3 array type of doubles, and \c ArrayXXf is a dynamic-size matrix of floats.
+ *
+ * There are also \c ArraySizeType which are self-explanatory. For example, \c Array4cf is
+ * a fixed-size 1D array of 4 complex floats.
+ *
+ * With \cpp11, template alias are also defined for common sizes.
+ * They follow the same pattern as above except that the scalar type suffix is replaced by a
+ * template parameter, i.e.:
+ * - `ArrayRowsCols<Type>` where `Rows` and `Cols` can be \c 2,\c 3,\c 4, or \c X for fixed or dynamic size.
+ * - `ArraySize<Type>` where `Size` can be \c 2,\c 3,\c 4 or \c X for fixed or dynamic size 1D arrays.
+ *
+ * \sa class Array
+ */
+
+#define EIGEN_MAKE_ARRAY_TYPEDEFS(Type, TypeSuffix, Size, SizeSuffix) \
+/** \ingroup arraytypedefs */ \
+typedef Array<Type, Size, Size> Array##SizeSuffix##SizeSuffix##TypeSuffix; \
+/** \ingroup arraytypedefs */ \
+typedef Array<Type, Size, 1> Array##SizeSuffix##TypeSuffix;
+
+#define EIGEN_MAKE_ARRAY_FIXED_TYPEDEFS(Type, TypeSuffix, Size) \
+/** \ingroup arraytypedefs */ \
+typedef Array<Type, Size, Dynamic> Array##Size##X##TypeSuffix; \
+/** \ingroup arraytypedefs */ \
+typedef Array<Type, Dynamic, Size> Array##X##Size##TypeSuffix;
+
+#define EIGEN_MAKE_ARRAY_TYPEDEFS_ALL_SIZES(Type, TypeSuffix) \
+EIGEN_MAKE_ARRAY_TYPEDEFS(Type, TypeSuffix, 2, 2) \
+EIGEN_MAKE_ARRAY_TYPEDEFS(Type, TypeSuffix, 3, 3) \
+EIGEN_MAKE_ARRAY_TYPEDEFS(Type, TypeSuffix, 4, 4) \
+EIGEN_MAKE_ARRAY_TYPEDEFS(Type, TypeSuffix, Dynamic, X) \
+EIGEN_MAKE_ARRAY_FIXED_TYPEDEFS(Type, TypeSuffix, 2) \
+EIGEN_MAKE_ARRAY_FIXED_TYPEDEFS(Type, TypeSuffix, 3) \
+EIGEN_MAKE_ARRAY_FIXED_TYPEDEFS(Type, TypeSuffix, 4)
+
+EIGEN_MAKE_ARRAY_TYPEDEFS_ALL_SIZES(int, i)
+EIGEN_MAKE_ARRAY_TYPEDEFS_ALL_SIZES(float, f)
+EIGEN_MAKE_ARRAY_TYPEDEFS_ALL_SIZES(double, d)
+EIGEN_MAKE_ARRAY_TYPEDEFS_ALL_SIZES(std::complex<float>, cf)
+EIGEN_MAKE_ARRAY_TYPEDEFS_ALL_SIZES(std::complex<double>, cd)
+
+#undef EIGEN_MAKE_ARRAY_TYPEDEFS_ALL_SIZES
+#undef EIGEN_MAKE_ARRAY_TYPEDEFS
+#undef EIGEN_MAKE_ARRAY_FIXED_TYPEDEFS
+
+#define EIGEN_MAKE_ARRAY_TYPEDEFS(Size, SizeSuffix) \
+/** \ingroup arraytypedefs */ \
+/** \brief \cpp11 */ \
+template <typename Type> \
+using Array##SizeSuffix##SizeSuffix = Array<Type, Size, Size>; \
+/** \ingroup arraytypedefs */ \
+/** \brief \cpp11 */ \
+template <typename Type> \
+using Array##SizeSuffix = Array<Type, Size, 1>;
+
+#define EIGEN_MAKE_ARRAY_FIXED_TYPEDEFS(Size) \
+/** \ingroup arraytypedefs */ \
+/** \brief \cpp11 */ \
+template <typename Type> \
+using Array##Size##X = Array<Type, Size, Dynamic>; \
+/** \ingroup arraytypedefs */ \
+/** \brief \cpp11 */ \
+template <typename Type> \
+using Array##X##Size = Array<Type, Dynamic, Size>;
+
+EIGEN_MAKE_ARRAY_TYPEDEFS(2, 2)
+EIGEN_MAKE_ARRAY_TYPEDEFS(3, 3)
+EIGEN_MAKE_ARRAY_TYPEDEFS(4, 4)
+EIGEN_MAKE_ARRAY_TYPEDEFS(Dynamic, X)
+EIGEN_MAKE_ARRAY_FIXED_TYPEDEFS(2)
+EIGEN_MAKE_ARRAY_FIXED_TYPEDEFS(3)
+EIGEN_MAKE_ARRAY_FIXED_TYPEDEFS(4)
+
+#undef EIGEN_MAKE_ARRAY_TYPEDEFS
+#undef EIGEN_MAKE_ARRAY_FIXED_TYPEDEFS
+
+#define EIGEN_USING_ARRAY_TYPEDEFS_FOR_TYPE_AND_SIZE(TypeSuffix, SizeSuffix) \
+using Eigen::Matrix##SizeSuffix##TypeSuffix; \
+using Eigen::Vector##SizeSuffix##TypeSuffix; \
+using Eigen::RowVector##SizeSuffix##TypeSuffix;
+
+#define EIGEN_USING_ARRAY_TYPEDEFS_FOR_TYPE(TypeSuffix) \
+EIGEN_USING_ARRAY_TYPEDEFS_FOR_TYPE_AND_SIZE(TypeSuffix, 2) \
+EIGEN_USING_ARRAY_TYPEDEFS_FOR_TYPE_AND_SIZE(TypeSuffix, 3) \
+EIGEN_USING_ARRAY_TYPEDEFS_FOR_TYPE_AND_SIZE(TypeSuffix, 4) \
+EIGEN_USING_ARRAY_TYPEDEFS_FOR_TYPE_AND_SIZE(TypeSuffix, X) \
+
+#define EIGEN_USING_ARRAY_TYPEDEFS \
+EIGEN_USING_ARRAY_TYPEDEFS_FOR_TYPE(i) \
+EIGEN_USING_ARRAY_TYPEDEFS_FOR_TYPE(f) \
+EIGEN_USING_ARRAY_TYPEDEFS_FOR_TYPE(d) \
+EIGEN_USING_ARRAY_TYPEDEFS_FOR_TYPE(cf) \
+EIGEN_USING_ARRAY_TYPEDEFS_FOR_TYPE(cd)
+
+} // end namespace Eigen
+
+#endif // EIGEN_ARRAY_H
diff --git a/Eigen/src/Core/ArrayBase.h b/Eigen/src/Core/ArrayBase.h
new file mode 100644
index 0000000..28397e5
--- /dev/null
+++ b/Eigen/src/Core/ArrayBase.h
@@ -0,0 +1,228 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_ARRAYBASE_H
+#define EIGEN_ARRAYBASE_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+template<typename ExpressionType> class MatrixWrapper;
+
+/** \class ArrayBase
+ * \ingroup Core_Module
+ *
+ * \brief Base class for all 1D and 2D array, and related expressions
+ *
+ * An array is similar to a dense vector or matrix. While matrices are mathematical
+ * objects with well defined linear algebra operators, an array is just a collection
+ * of scalar values arranged in a one or two dimensional fashion. As the main consequence,
+ * all operations applied to an array are performed coefficient wise. Furthermore,
+ * arrays support scalar math functions of the c++ standard library (e.g., std::sin(x)), and convenient
+ * constructors allowing to easily write generic code working for both scalar values
+ * and arrays.
+ *
+ * This class is the base that is inherited by all array expression types.
+ *
+ * \tparam Derived is the derived type, e.g., an array or an expression type.
+ *
+ * This class can be extended with the help of the plugin mechanism described on the page
+ * \ref TopicCustomizing_Plugins by defining the preprocessor symbol \c EIGEN_ARRAYBASE_PLUGIN.
+ *
+ * \sa class MatrixBase, \ref TopicClassHierarchy
+ */
+template<typename Derived> class ArrayBase
+ : public DenseBase<Derived>
+{
+ public:
+#ifndef EIGEN_PARSED_BY_DOXYGEN
+ /** The base class for a given storage type. */
+ typedef ArrayBase StorageBaseType;
+
+ typedef ArrayBase Eigen_BaseClassForSpecializationOfGlobalMathFuncImpl;
+
+ typedef typename internal::traits<Derived>::StorageKind StorageKind;
+ typedef typename internal::traits<Derived>::Scalar Scalar;
+ typedef typename internal::packet_traits<Scalar>::type PacketScalar;
+ typedef typename NumTraits<Scalar>::Real RealScalar;
+
+ typedef DenseBase<Derived> Base;
+ using Base::RowsAtCompileTime;
+ using Base::ColsAtCompileTime;
+ using Base::SizeAtCompileTime;
+ using Base::MaxRowsAtCompileTime;
+ using Base::MaxColsAtCompileTime;
+ using Base::MaxSizeAtCompileTime;
+ using Base::IsVectorAtCompileTime;
+ using Base::Flags;
+
+ using Base::derived;
+ using Base::const_cast_derived;
+ using Base::rows;
+ using Base::cols;
+ using Base::size;
+ using Base::coeff;
+ using Base::coeffRef;
+ using Base::lazyAssign;
+ using Base::operator-;
+ using Base::operator=;
+ using Base::operator+=;
+ using Base::operator-=;
+ using Base::operator*=;
+ using Base::operator/=;
+
+ typedef typename Base::CoeffReturnType CoeffReturnType;
+
+#endif // not EIGEN_PARSED_BY_DOXYGEN
+
+#ifndef EIGEN_PARSED_BY_DOXYGEN
+ typedef typename Base::PlainObject PlainObject;
+
+ /** \internal Represents a matrix with all coefficients equal to one another*/
+ typedef CwiseNullaryOp<internal::scalar_constant_op<Scalar>,PlainObject> ConstantReturnType;
+#endif // not EIGEN_PARSED_BY_DOXYGEN
+
+#define EIGEN_CURRENT_STORAGE_BASE_CLASS Eigen::ArrayBase
+#define EIGEN_DOC_UNARY_ADDONS(X,Y)
+# include "../plugins/MatrixCwiseUnaryOps.h"
+# include "../plugins/ArrayCwiseUnaryOps.h"
+# include "../plugins/CommonCwiseBinaryOps.h"
+# include "../plugins/MatrixCwiseBinaryOps.h"
+# include "../plugins/ArrayCwiseBinaryOps.h"
+# ifdef EIGEN_ARRAYBASE_PLUGIN
+# include EIGEN_ARRAYBASE_PLUGIN
+# endif
+#undef EIGEN_CURRENT_STORAGE_BASE_CLASS
+#undef EIGEN_DOC_UNARY_ADDONS
+
+ /** Special case of the template operator=, in order to prevent the compiler
+ * from generating a default operator= (issue hit with g++ 4.1)
+ */
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ Derived& operator=(const ArrayBase& other)
+ {
+ internal::call_assignment(derived(), other.derived());
+ return derived();
+ }
+
+ /** Set all the entries to \a value.
+ * \sa DenseBase::setConstant(), DenseBase::fill() */
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ Derived& operator=(const Scalar &value)
+ { Base::setConstant(value); return derived(); }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ Derived& operator+=(const Scalar& scalar);
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ Derived& operator-=(const Scalar& scalar);
+
+ template<typename OtherDerived>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ Derived& operator+=(const ArrayBase<OtherDerived>& other);
+ template<typename OtherDerived>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ Derived& operator-=(const ArrayBase<OtherDerived>& other);
+
+ template<typename OtherDerived>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ Derived& operator*=(const ArrayBase<OtherDerived>& other);
+
+ template<typename OtherDerived>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ Derived& operator/=(const ArrayBase<OtherDerived>& other);
+
+ public:
+ EIGEN_DEVICE_FUNC
+ ArrayBase<Derived>& array() { return *this; }
+ EIGEN_DEVICE_FUNC
+ const ArrayBase<Derived>& array() const { return *this; }
+
+ /** \returns an \link Eigen::MatrixBase Matrix \endlink expression of this array
+ * \sa MatrixBase::array() */
+ EIGEN_DEVICE_FUNC
+ MatrixWrapper<Derived> matrix() { return MatrixWrapper<Derived>(derived()); }
+ EIGEN_DEVICE_FUNC
+ const MatrixWrapper<const Derived> matrix() const { return MatrixWrapper<const Derived>(derived()); }
+
+// template<typename Dest>
+// inline void evalTo(Dest& dst) const { dst = matrix(); }
+
+ protected:
+ EIGEN_DEFAULT_COPY_CONSTRUCTOR(ArrayBase)
+ EIGEN_DEFAULT_EMPTY_CONSTRUCTOR_AND_DESTRUCTOR(ArrayBase)
+
+ private:
+ explicit ArrayBase(Index);
+ ArrayBase(Index,Index);
+ template<typename OtherDerived> explicit ArrayBase(const ArrayBase<OtherDerived>&);
+ protected:
+ // mixing arrays and matrices is not legal
+ template<typename OtherDerived> Derived& operator+=(const MatrixBase<OtherDerived>& )
+ {EIGEN_STATIC_ASSERT(std::ptrdiff_t(sizeof(typename OtherDerived::Scalar))==-1,YOU_CANNOT_MIX_ARRAYS_AND_MATRICES); return *this;}
+ // mixing arrays and matrices is not legal
+ template<typename OtherDerived> Derived& operator-=(const MatrixBase<OtherDerived>& )
+ {EIGEN_STATIC_ASSERT(std::ptrdiff_t(sizeof(typename OtherDerived::Scalar))==-1,YOU_CANNOT_MIX_ARRAYS_AND_MATRICES); return *this;}
+};
+
+/** replaces \c *this by \c *this - \a other.
+ *
+ * \returns a reference to \c *this
+ */
+template<typename Derived>
+template<typename OtherDerived>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived &
+ArrayBase<Derived>::operator-=(const ArrayBase<OtherDerived> &other)
+{
+ call_assignment(derived(), other.derived(), internal::sub_assign_op<Scalar,typename OtherDerived::Scalar>());
+ return derived();
+}
+
+/** replaces \c *this by \c *this + \a other.
+ *
+ * \returns a reference to \c *this
+ */
+template<typename Derived>
+template<typename OtherDerived>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived &
+ArrayBase<Derived>::operator+=(const ArrayBase<OtherDerived>& other)
+{
+ call_assignment(derived(), other.derived(), internal::add_assign_op<Scalar,typename OtherDerived::Scalar>());
+ return derived();
+}
+
+/** replaces \c *this by \c *this * \a other coefficient wise.
+ *
+ * \returns a reference to \c *this
+ */
+template<typename Derived>
+template<typename OtherDerived>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived &
+ArrayBase<Derived>::operator*=(const ArrayBase<OtherDerived>& other)
+{
+ call_assignment(derived(), other.derived(), internal::mul_assign_op<Scalar,typename OtherDerived::Scalar>());
+ return derived();
+}
+
+/** replaces \c *this by \c *this / \a other coefficient wise.
+ *
+ * \returns a reference to \c *this
+ */
+template<typename Derived>
+template<typename OtherDerived>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived &
+ArrayBase<Derived>::operator/=(const ArrayBase<OtherDerived>& other)
+{
+ call_assignment(derived(), other.derived(), internal::div_assign_op<Scalar,typename OtherDerived::Scalar>());
+ return derived();
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_ARRAYBASE_H
diff --git a/Eigen/src/Core/ArrayWrapper.h b/Eigen/src/Core/ArrayWrapper.h
new file mode 100644
index 0000000..e65b8fb
--- /dev/null
+++ b/Eigen/src/Core/ArrayWrapper.h
@@ -0,0 +1,211 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009-2010 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_ARRAYWRAPPER_H
+#define EIGEN_ARRAYWRAPPER_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+/** \class ArrayWrapper
+ * \ingroup Core_Module
+ *
+ * \brief Expression of a mathematical vector or matrix as an array object
+ *
+ * This class is the return type of MatrixBase::array(), and most of the time
+ * this is the only way it is use.
+ *
+ * \sa MatrixBase::array(), class MatrixWrapper
+ */
+
+namespace internal {
+template<typename ExpressionType>
+struct traits<ArrayWrapper<ExpressionType> >
+ : public traits<remove_all_t<typename ExpressionType::Nested> >
+{
+ typedef ArrayXpr XprKind;
+ // Let's remove NestByRefBit
+ enum {
+ Flags0 = traits<remove_all_t<typename ExpressionType::Nested> >::Flags,
+ LvalueBitFlag = is_lvalue<ExpressionType>::value ? LvalueBit : 0,
+ Flags = (Flags0 & ~(NestByRefBit | LvalueBit)) | LvalueBitFlag
+ };
+};
+}
+
+template<typename ExpressionType>
+class ArrayWrapper : public ArrayBase<ArrayWrapper<ExpressionType> >
+{
+ public:
+ typedef ArrayBase<ArrayWrapper> Base;
+ EIGEN_DENSE_PUBLIC_INTERFACE(ArrayWrapper)
+ EIGEN_INHERIT_ASSIGNMENT_OPERATORS(ArrayWrapper)
+ typedef internal::remove_all_t<ExpressionType> NestedExpression;
+
+ typedef std::conditional_t<
+ internal::is_lvalue<ExpressionType>::value,
+ Scalar,
+ const Scalar
+ > ScalarWithConstIfNotLvalue;
+
+ typedef typename internal::ref_selector<ExpressionType>::non_const_type NestedExpressionType;
+
+ using Base::coeffRef;
+
+ EIGEN_DEVICE_FUNC
+ explicit EIGEN_STRONG_INLINE ArrayWrapper(ExpressionType& matrix) : m_expression(matrix) {}
+
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
+ inline Index rows() const EIGEN_NOEXCEPT { return m_expression.rows(); }
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
+ inline Index cols() const EIGEN_NOEXCEPT { return m_expression.cols(); }
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
+ inline Index outerStride() const EIGEN_NOEXCEPT { return m_expression.outerStride(); }
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
+ inline Index innerStride() const EIGEN_NOEXCEPT { return m_expression.innerStride(); }
+
+ EIGEN_DEVICE_FUNC
+ inline ScalarWithConstIfNotLvalue* data() { return m_expression.data(); }
+ EIGEN_DEVICE_FUNC
+ inline const Scalar* data() const { return m_expression.data(); }
+
+ EIGEN_DEVICE_FUNC
+ inline const Scalar& coeffRef(Index rowId, Index colId) const
+ {
+ return m_expression.coeffRef(rowId, colId);
+ }
+
+ EIGEN_DEVICE_FUNC
+ inline const Scalar& coeffRef(Index index) const
+ {
+ return m_expression.coeffRef(index);
+ }
+
+ template<typename Dest>
+ EIGEN_DEVICE_FUNC
+ inline void evalTo(Dest& dst) const { dst = m_expression; }
+
+ EIGEN_DEVICE_FUNC
+ const internal::remove_all_t<NestedExpressionType>&
+ nestedExpression() const
+ {
+ return m_expression;
+ }
+
+ /** Forwards the resizing request to the nested expression
+ * \sa DenseBase::resize(Index) */
+ EIGEN_DEVICE_FUNC
+ void resize(Index newSize) { m_expression.resize(newSize); }
+ /** Forwards the resizing request to the nested expression
+ * \sa DenseBase::resize(Index,Index)*/
+ EIGEN_DEVICE_FUNC
+ void resize(Index rows, Index cols) { m_expression.resize(rows,cols); }
+
+ protected:
+ NestedExpressionType m_expression;
+};
+
+/** \class MatrixWrapper
+ * \ingroup Core_Module
+ *
+ * \brief Expression of an array as a mathematical vector or matrix
+ *
+ * This class is the return type of ArrayBase::matrix(), and most of the time
+ * this is the only way it is use.
+ *
+ * \sa MatrixBase::matrix(), class ArrayWrapper
+ */
+
+namespace internal {
+template<typename ExpressionType>
+struct traits<MatrixWrapper<ExpressionType> >
+ : public traits<remove_all_t<typename ExpressionType::Nested> >
+{
+ typedef MatrixXpr XprKind;
+ // Let's remove NestByRefBit
+ enum {
+ Flags0 = traits<remove_all_t<typename ExpressionType::Nested> >::Flags,
+ LvalueBitFlag = is_lvalue<ExpressionType>::value ? LvalueBit : 0,
+ Flags = (Flags0 & ~(NestByRefBit | LvalueBit)) | LvalueBitFlag
+ };
+};
+}
+
+template<typename ExpressionType>
+class MatrixWrapper : public MatrixBase<MatrixWrapper<ExpressionType> >
+{
+ public:
+ typedef MatrixBase<MatrixWrapper<ExpressionType> > Base;
+ EIGEN_DENSE_PUBLIC_INTERFACE(MatrixWrapper)
+ EIGEN_INHERIT_ASSIGNMENT_OPERATORS(MatrixWrapper)
+ typedef internal::remove_all_t<ExpressionType> NestedExpression;
+
+ typedef std::conditional_t<
+ internal::is_lvalue<ExpressionType>::value,
+ Scalar,
+ const Scalar
+ > ScalarWithConstIfNotLvalue;
+
+ typedef typename internal::ref_selector<ExpressionType>::non_const_type NestedExpressionType;
+
+ using Base::coeffRef;
+
+ EIGEN_DEVICE_FUNC
+ explicit inline MatrixWrapper(ExpressionType& matrix) : m_expression(matrix) {}
+
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
+ inline Index rows() const EIGEN_NOEXCEPT { return m_expression.rows(); }
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
+ inline Index cols() const EIGEN_NOEXCEPT { return m_expression.cols(); }
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
+ inline Index outerStride() const EIGEN_NOEXCEPT { return m_expression.outerStride(); }
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
+ inline Index innerStride() const EIGEN_NOEXCEPT { return m_expression.innerStride(); }
+
+ EIGEN_DEVICE_FUNC
+ inline ScalarWithConstIfNotLvalue* data() { return m_expression.data(); }
+ EIGEN_DEVICE_FUNC
+ inline const Scalar* data() const { return m_expression.data(); }
+
+ EIGEN_DEVICE_FUNC
+ inline const Scalar& coeffRef(Index rowId, Index colId) const
+ {
+ return m_expression.derived().coeffRef(rowId, colId);
+ }
+
+ EIGEN_DEVICE_FUNC
+ inline const Scalar& coeffRef(Index index) const
+ {
+ return m_expression.coeffRef(index);
+ }
+
+ EIGEN_DEVICE_FUNC
+ const internal::remove_all_t<NestedExpressionType>&
+ nestedExpression() const
+ {
+ return m_expression;
+ }
+
+ /** Forwards the resizing request to the nested expression
+ * \sa DenseBase::resize(Index) */
+ EIGEN_DEVICE_FUNC
+ void resize(Index newSize) { m_expression.resize(newSize); }
+ /** Forwards the resizing request to the nested expression
+ * \sa DenseBase::resize(Index,Index)*/
+ EIGEN_DEVICE_FUNC
+ void resize(Index rows, Index cols) { m_expression.resize(rows,cols); }
+
+ protected:
+ NestedExpressionType m_expression;
+};
+
+} // end namespace Eigen
+
+#endif // EIGEN_ARRAYWRAPPER_H
diff --git a/Eigen/src/Core/Assign.h b/Eigen/src/Core/Assign.h
new file mode 100644
index 0000000..dc716d3
--- /dev/null
+++ b/Eigen/src/Core/Assign.h
@@ -0,0 +1,92 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2007 Michael Olbrich <michael.olbrich@gmx.net>
+// Copyright (C) 2006-2010 Benoit Jacob <jacob.benoit.1@gmail.com>
+// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_ASSIGN_H
+#define EIGEN_ASSIGN_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+template<typename Derived>
+template<typename OtherDerived>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& DenseBase<Derived>
+ ::lazyAssign(const DenseBase<OtherDerived>& other)
+{
+ enum{
+ SameType = internal::is_same<typename Derived::Scalar,typename OtherDerived::Scalar>::value
+ };
+
+ EIGEN_STATIC_ASSERT_LVALUE(Derived)
+ EIGEN_STATIC_ASSERT_SAME_MATRIX_SIZE(Derived,OtherDerived)
+ EIGEN_STATIC_ASSERT(SameType,YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY)
+
+ eigen_assert(rows() == other.rows() && cols() == other.cols());
+ internal::call_assignment_no_alias(derived(),other.derived());
+
+ return derived();
+}
+
+template<typename Derived>
+template<typename OtherDerived>
+EIGEN_DEVICE_FUNC
+EIGEN_STRONG_INLINE Derived& DenseBase<Derived>::operator=(const DenseBase<OtherDerived>& other)
+{
+ internal::call_assignment(derived(), other.derived());
+ return derived();
+}
+
+template<typename Derived>
+EIGEN_DEVICE_FUNC
+EIGEN_STRONG_INLINE Derived& DenseBase<Derived>::operator=(const DenseBase& other)
+{
+ internal::call_assignment(derived(), other.derived());
+ return derived();
+}
+
+template<typename Derived>
+EIGEN_DEVICE_FUNC
+EIGEN_STRONG_INLINE Derived& MatrixBase<Derived>::operator=(const MatrixBase& other)
+{
+ internal::call_assignment(derived(), other.derived());
+ return derived();
+}
+
+template<typename Derived>
+template <typename OtherDerived>
+EIGEN_DEVICE_FUNC
+EIGEN_STRONG_INLINE Derived& MatrixBase<Derived>::operator=(const DenseBase<OtherDerived>& other)
+{
+ internal::call_assignment(derived(), other.derived());
+ return derived();
+}
+
+template<typename Derived>
+template <typename OtherDerived>
+EIGEN_DEVICE_FUNC
+EIGEN_STRONG_INLINE Derived& MatrixBase<Derived>::operator=(const EigenBase<OtherDerived>& other)
+{
+ internal::call_assignment(derived(), other.derived());
+ return derived();
+}
+
+template<typename Derived>
+template<typename OtherDerived>
+EIGEN_DEVICE_FUNC
+EIGEN_STRONG_INLINE Derived& MatrixBase<Derived>::operator=(const ReturnByValue<OtherDerived>& other)
+{
+ other.derived().evalTo(derived());
+ return derived();
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_ASSIGN_H
diff --git a/Eigen/src/Core/AssignEvaluator.h b/Eigen/src/Core/AssignEvaluator.h
new file mode 100644
index 0000000..8fb1f81
--- /dev/null
+++ b/Eigen/src/Core/AssignEvaluator.h
@@ -0,0 +1,1011 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2011 Benoit Jacob <jacob.benoit.1@gmail.com>
+// Copyright (C) 2011-2014 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2011-2012 Jitse Niesen <jitse@maths.leeds.ac.uk>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_ASSIGN_EVALUATOR_H
+#define EIGEN_ASSIGN_EVALUATOR_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+// This implementation is based on Assign.h
+
+namespace internal {
+
+/***************************************************************************
+* Part 1 : the logic deciding a strategy for traversal and unrolling *
+***************************************************************************/
+
+// copy_using_evaluator_traits is based on assign_traits
+
+template <typename DstEvaluator, typename SrcEvaluator, typename AssignFunc, int MaxPacketSize = -1>
+struct copy_using_evaluator_traits
+{
+ typedef typename DstEvaluator::XprType Dst;
+ typedef typename Dst::Scalar DstScalar;
+
+ enum {
+ DstFlags = DstEvaluator::Flags,
+ SrcFlags = SrcEvaluator::Flags
+ };
+
+public:
+ enum {
+ DstAlignment = DstEvaluator::Alignment,
+ SrcAlignment = SrcEvaluator::Alignment,
+ DstHasDirectAccess = (DstFlags & DirectAccessBit) == DirectAccessBit,
+ JointAlignment = plain_enum_min(DstAlignment, SrcAlignment)
+ };
+
+private:
+ enum {
+ InnerSize = int(Dst::IsVectorAtCompileTime) ? int(Dst::SizeAtCompileTime)
+ : int(DstFlags)&RowMajorBit ? int(Dst::ColsAtCompileTime)
+ : int(Dst::RowsAtCompileTime),
+ InnerMaxSize = int(Dst::IsVectorAtCompileTime) ? int(Dst::MaxSizeAtCompileTime)
+ : int(DstFlags)&RowMajorBit ? int(Dst::MaxColsAtCompileTime)
+ : int(Dst::MaxRowsAtCompileTime),
+ RestrictedInnerSize = min_size_prefer_fixed(InnerSize, MaxPacketSize),
+ RestrictedLinearSize = min_size_prefer_fixed(Dst::SizeAtCompileTime, MaxPacketSize),
+ OuterStride = int(outer_stride_at_compile_time<Dst>::ret),
+ MaxSizeAtCompileTime = Dst::SizeAtCompileTime
+ };
+
+ // TODO distinguish between linear traversal and inner-traversals
+ typedef typename find_best_packet<DstScalar,RestrictedLinearSize>::type LinearPacketType;
+ typedef typename find_best_packet<DstScalar,RestrictedInnerSize>::type InnerPacketType;
+
+ enum {
+ LinearPacketSize = unpacket_traits<LinearPacketType>::size,
+ InnerPacketSize = unpacket_traits<InnerPacketType>::size
+ };
+
+public:
+ enum {
+ LinearRequiredAlignment = unpacket_traits<LinearPacketType>::alignment,
+ InnerRequiredAlignment = unpacket_traits<InnerPacketType>::alignment
+ };
+
+private:
+ enum {
+ DstIsRowMajor = DstFlags&RowMajorBit,
+ SrcIsRowMajor = SrcFlags&RowMajorBit,
+ StorageOrdersAgree = (int(DstIsRowMajor) == int(SrcIsRowMajor)),
+ MightVectorize = bool(StorageOrdersAgree)
+ && (int(DstFlags) & int(SrcFlags) & ActualPacketAccessBit)
+ && bool(functor_traits<AssignFunc>::PacketAccess),
+ MayInnerVectorize = MightVectorize
+ && int(InnerSize)!=Dynamic && int(InnerSize)%int(InnerPacketSize)==0
+ && int(OuterStride)!=Dynamic && int(OuterStride)%int(InnerPacketSize)==0
+ && (EIGEN_UNALIGNED_VECTORIZE || int(JointAlignment)>=int(InnerRequiredAlignment)),
+ MayLinearize = bool(StorageOrdersAgree) && (int(DstFlags) & int(SrcFlags) & LinearAccessBit),
+ MayLinearVectorize = bool(MightVectorize) && bool(MayLinearize) && bool(DstHasDirectAccess)
+ && (EIGEN_UNALIGNED_VECTORIZE || (int(DstAlignment)>=int(LinearRequiredAlignment)) || MaxSizeAtCompileTime == Dynamic),
+ /* If the destination isn't aligned, we have to do runtime checks and we don't unroll,
+ so it's only good for large enough sizes. */
+ MaySliceVectorize = bool(MightVectorize) && bool(DstHasDirectAccess)
+ && (int(InnerMaxSize)==Dynamic || int(InnerMaxSize)>=(EIGEN_UNALIGNED_VECTORIZE?InnerPacketSize:(3*InnerPacketSize)))
+ /* slice vectorization can be slow, so we only want it if the slices are big, which is
+ indicated by InnerMaxSize rather than InnerSize, think of the case of a dynamic block
+ in a fixed-size matrix
+ However, with EIGEN_UNALIGNED_VECTORIZE and unrolling, slice vectorization is still worth it */
+ };
+
+public:
+ enum {
+ Traversal = int(Dst::SizeAtCompileTime) == 0 ? int(AllAtOnceTraversal) // If compile-size is zero, traversing will fail at compile-time.
+ : (int(MayLinearVectorize) && (LinearPacketSize>InnerPacketSize)) ? int(LinearVectorizedTraversal)
+ : int(MayInnerVectorize) ? int(InnerVectorizedTraversal)
+ : int(MayLinearVectorize) ? int(LinearVectorizedTraversal)
+ : int(MaySliceVectorize) ? int(SliceVectorizedTraversal)
+ : int(MayLinearize) ? int(LinearTraversal)
+ : int(DefaultTraversal),
+ Vectorized = int(Traversal) == InnerVectorizedTraversal
+ || int(Traversal) == LinearVectorizedTraversal
+ || int(Traversal) == SliceVectorizedTraversal
+ };
+
+ typedef std::conditional_t<int(Traversal)==LinearVectorizedTraversal, LinearPacketType, InnerPacketType> PacketType;
+
+private:
+ enum {
+ ActualPacketSize = int(Traversal)==LinearVectorizedTraversal ? LinearPacketSize
+ : Vectorized ? InnerPacketSize
+ : 1,
+ UnrollingLimit = EIGEN_UNROLLING_LIMIT * ActualPacketSize,
+ MayUnrollCompletely = int(Dst::SizeAtCompileTime) != Dynamic
+ && int(Dst::SizeAtCompileTime) * (int(DstEvaluator::CoeffReadCost)+int(SrcEvaluator::CoeffReadCost)) <= int(UnrollingLimit),
+ MayUnrollInner = int(InnerSize) != Dynamic
+ && int(InnerSize) * (int(DstEvaluator::CoeffReadCost)+int(SrcEvaluator::CoeffReadCost)) <= int(UnrollingLimit)
+ };
+
+public:
+ enum {
+ Unrolling = (int(Traversal) == int(InnerVectorizedTraversal) || int(Traversal) == int(DefaultTraversal))
+ ? (
+ int(MayUnrollCompletely) ? int(CompleteUnrolling)
+ : int(MayUnrollInner) ? int(InnerUnrolling)
+ : int(NoUnrolling)
+ )
+ : int(Traversal) == int(LinearVectorizedTraversal)
+ ? ( bool(MayUnrollCompletely) && ( EIGEN_UNALIGNED_VECTORIZE || (int(DstAlignment)>=int(LinearRequiredAlignment)))
+ ? int(CompleteUnrolling)
+ : int(NoUnrolling) )
+ : int(Traversal) == int(LinearTraversal)
+ ? ( bool(MayUnrollCompletely) ? int(CompleteUnrolling)
+ : int(NoUnrolling) )
+#if EIGEN_UNALIGNED_VECTORIZE
+ : int(Traversal) == int(SliceVectorizedTraversal)
+ ? ( bool(MayUnrollInner) ? int(InnerUnrolling)
+ : int(NoUnrolling) )
+#endif
+ : int(NoUnrolling)
+ };
+
+#ifdef EIGEN_DEBUG_ASSIGN
+ static void debug()
+ {
+ std::cerr << "DstXpr: " << typeid(typename DstEvaluator::XprType).name() << std::endl;
+ std::cerr << "SrcXpr: " << typeid(typename SrcEvaluator::XprType).name() << std::endl;
+ std::cerr.setf(std::ios::hex, std::ios::basefield);
+ std::cerr << "DstFlags" << " = " << DstFlags << " (" << demangle_flags(DstFlags) << " )" << std::endl;
+ std::cerr << "SrcFlags" << " = " << SrcFlags << " (" << demangle_flags(SrcFlags) << " )" << std::endl;
+ std::cerr.unsetf(std::ios::hex);
+ EIGEN_DEBUG_VAR(DstAlignment)
+ EIGEN_DEBUG_VAR(SrcAlignment)
+ EIGEN_DEBUG_VAR(LinearRequiredAlignment)
+ EIGEN_DEBUG_VAR(InnerRequiredAlignment)
+ EIGEN_DEBUG_VAR(JointAlignment)
+ EIGEN_DEBUG_VAR(InnerSize)
+ EIGEN_DEBUG_VAR(InnerMaxSize)
+ EIGEN_DEBUG_VAR(LinearPacketSize)
+ EIGEN_DEBUG_VAR(InnerPacketSize)
+ EIGEN_DEBUG_VAR(ActualPacketSize)
+ EIGEN_DEBUG_VAR(StorageOrdersAgree)
+ EIGEN_DEBUG_VAR(MightVectorize)
+ EIGEN_DEBUG_VAR(MayLinearize)
+ EIGEN_DEBUG_VAR(MayInnerVectorize)
+ EIGEN_DEBUG_VAR(MayLinearVectorize)
+ EIGEN_DEBUG_VAR(MaySliceVectorize)
+ std::cerr << "Traversal" << " = " << Traversal << " (" << demangle_traversal(Traversal) << ")" << std::endl;
+ EIGEN_DEBUG_VAR(SrcEvaluator::CoeffReadCost)
+ EIGEN_DEBUG_VAR(DstEvaluator::CoeffReadCost)
+ EIGEN_DEBUG_VAR(Dst::SizeAtCompileTime)
+ EIGEN_DEBUG_VAR(UnrollingLimit)
+ EIGEN_DEBUG_VAR(MayUnrollCompletely)
+ EIGEN_DEBUG_VAR(MayUnrollInner)
+ std::cerr << "Unrolling" << " = " << Unrolling << " (" << demangle_unrolling(Unrolling) << ")" << std::endl;
+ std::cerr << std::endl;
+ }
+#endif
+};
+
+/***************************************************************************
+* Part 2 : meta-unrollers
+***************************************************************************/
+
+/************************
+*** Default traversal ***
+************************/
+
+template<typename Kernel, int Index, int Stop>
+struct copy_using_evaluator_DefaultTraversal_CompleteUnrolling
+{
+ // FIXME: this is not very clean, perhaps this information should be provided by the kernel?
+ typedef typename Kernel::DstEvaluatorType DstEvaluatorType;
+ typedef typename DstEvaluatorType::XprType DstXprType;
+
+ enum {
+ outer = Index / DstXprType::InnerSizeAtCompileTime,
+ inner = Index % DstXprType::InnerSizeAtCompileTime
+ };
+
+ EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE void run(Kernel &kernel)
+ {
+ kernel.assignCoeffByOuterInner(outer, inner);
+ copy_using_evaluator_DefaultTraversal_CompleteUnrolling<Kernel, Index+1, Stop>::run(kernel);
+ }
+};
+
+template<typename Kernel, int Stop>
+struct copy_using_evaluator_DefaultTraversal_CompleteUnrolling<Kernel, Stop, Stop>
+{
+ EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE EIGEN_CONSTEXPR void run(Kernel&) { }
+};
+
+template<typename Kernel, int Index_, int Stop>
+struct copy_using_evaluator_DefaultTraversal_InnerUnrolling
+{
+ EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE void run(Kernel &kernel, Index outer)
+ {
+ kernel.assignCoeffByOuterInner(outer, Index_);
+ copy_using_evaluator_DefaultTraversal_InnerUnrolling<Kernel, Index_+1, Stop>::run(kernel, outer);
+ }
+};
+
+template<typename Kernel, int Stop>
+struct copy_using_evaluator_DefaultTraversal_InnerUnrolling<Kernel, Stop, Stop>
+{
+ EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE void run(Kernel&, Index) { }
+};
+
+/***********************
+*** Linear traversal ***
+***********************/
+
+template<typename Kernel, int Index, int Stop>
+struct copy_using_evaluator_LinearTraversal_CompleteUnrolling
+{
+ EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE void run(Kernel& kernel)
+ {
+ kernel.assignCoeff(Index);
+ copy_using_evaluator_LinearTraversal_CompleteUnrolling<Kernel, Index+1, Stop>::run(kernel);
+ }
+};
+
+template<typename Kernel, int Stop>
+struct copy_using_evaluator_LinearTraversal_CompleteUnrolling<Kernel, Stop, Stop>
+{
+ EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE void run(Kernel&) { }
+};
+
+/**************************
+*** Inner vectorization ***
+**************************/
+
+template<typename Kernel, int Index, int Stop>
+struct copy_using_evaluator_innervec_CompleteUnrolling
+{
+ // FIXME: this is not very clean, perhaps this information should be provided by the kernel?
+ typedef typename Kernel::DstEvaluatorType DstEvaluatorType;
+ typedef typename DstEvaluatorType::XprType DstXprType;
+ typedef typename Kernel::PacketType PacketType;
+
+ enum {
+ outer = Index / DstXprType::InnerSizeAtCompileTime,
+ inner = Index % DstXprType::InnerSizeAtCompileTime,
+ SrcAlignment = Kernel::AssignmentTraits::SrcAlignment,
+ DstAlignment = Kernel::AssignmentTraits::DstAlignment
+ };
+
+ EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE void run(Kernel &kernel)
+ {
+ kernel.template assignPacketByOuterInner<DstAlignment, SrcAlignment, PacketType>(outer, inner);
+ enum { NextIndex = Index + unpacket_traits<PacketType>::size };
+ copy_using_evaluator_innervec_CompleteUnrolling<Kernel, NextIndex, Stop>::run(kernel);
+ }
+};
+
+template<typename Kernel, int Stop>
+struct copy_using_evaluator_innervec_CompleteUnrolling<Kernel, Stop, Stop>
+{
+ EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE EIGEN_CONSTEXPR void run(Kernel&) { }
+};
+
+template<typename Kernel, int Index_, int Stop, int SrcAlignment, int DstAlignment>
+struct copy_using_evaluator_innervec_InnerUnrolling
+{
+ typedef typename Kernel::PacketType PacketType;
+ EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE void run(Kernel &kernel, Index outer)
+ {
+ kernel.template assignPacketByOuterInner<DstAlignment, SrcAlignment, PacketType>(outer, Index_);
+ enum { NextIndex = Index_ + unpacket_traits<PacketType>::size };
+ copy_using_evaluator_innervec_InnerUnrolling<Kernel, NextIndex, Stop, SrcAlignment, DstAlignment>::run(kernel, outer);
+ }
+};
+
+template<typename Kernel, int Stop, int SrcAlignment, int DstAlignment>
+struct copy_using_evaluator_innervec_InnerUnrolling<Kernel, Stop, Stop, SrcAlignment, DstAlignment>
+{
+ EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE void run(Kernel &, Index) { }
+};
+
+/***************************************************************************
+* Part 3 : implementation of all cases
+***************************************************************************/
+
+// dense_assignment_loop is based on assign_impl
+
+template<typename Kernel,
+ int Traversal = Kernel::AssignmentTraits::Traversal,
+ int Unrolling = Kernel::AssignmentTraits::Unrolling>
+struct dense_assignment_loop;
+
+/************************
+***** Special Cases *****
+************************/
+
+// Zero-sized assignment is a no-op.
+template<typename Kernel, int Unrolling>
+struct dense_assignment_loop<Kernel, AllAtOnceTraversal, Unrolling>
+{
+ EIGEN_DEVICE_FUNC static void EIGEN_STRONG_INLINE EIGEN_CONSTEXPR run(Kernel& /*kernel*/)
+ {
+ EIGEN_STATIC_ASSERT(int(Kernel::DstEvaluatorType::XprType::SizeAtCompileTime) == 0,
+ EIGEN_INTERNAL_ERROR_PLEASE_FILE_A_BUG_REPORT)
+ }
+};
+
+/************************
+*** Default traversal ***
+************************/
+
+template<typename Kernel>
+struct dense_assignment_loop<Kernel, DefaultTraversal, NoUnrolling>
+{
+ EIGEN_DEVICE_FUNC static void EIGEN_STRONG_INLINE run(Kernel &kernel)
+ {
+ for(Index outer = 0; outer < kernel.outerSize(); ++outer) {
+ for(Index inner = 0; inner < kernel.innerSize(); ++inner) {
+ kernel.assignCoeffByOuterInner(outer, inner);
+ }
+ }
+ }
+};
+
+template<typename Kernel>
+struct dense_assignment_loop<Kernel, DefaultTraversal, CompleteUnrolling>
+{
+ EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE void run(Kernel &kernel)
+ {
+ typedef typename Kernel::DstEvaluatorType::XprType DstXprType;
+ copy_using_evaluator_DefaultTraversal_CompleteUnrolling<Kernel, 0, DstXprType::SizeAtCompileTime>::run(kernel);
+ }
+};
+
+template<typename Kernel>
+struct dense_assignment_loop<Kernel, DefaultTraversal, InnerUnrolling>
+{
+ EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE void run(Kernel &kernel)
+ {
+ typedef typename Kernel::DstEvaluatorType::XprType DstXprType;
+
+ const Index outerSize = kernel.outerSize();
+ for(Index outer = 0; outer < outerSize; ++outer)
+ copy_using_evaluator_DefaultTraversal_InnerUnrolling<Kernel, 0, DstXprType::InnerSizeAtCompileTime>::run(kernel, outer);
+ }
+};
+
+/***************************
+*** Linear vectorization ***
+***************************/
+
+
+// The goal of unaligned_dense_assignment_loop is simply to factorize the handling
+// of the non vectorizable beginning and ending parts
+
+template <bool IsAligned = false>
+struct unaligned_dense_assignment_loop
+{
+ // if IsAligned = true, then do nothing
+ template <typename Kernel>
+ EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE EIGEN_CONSTEXPR void run(Kernel&, Index, Index) {}
+};
+
+template <>
+struct unaligned_dense_assignment_loop<false>
+{
+ // MSVC must not inline this functions. If it does, it fails to optimize the
+ // packet access path.
+ // FIXME check which version exhibits this issue
+#if EIGEN_COMP_MSVC
+ template <typename Kernel>
+ static EIGEN_DONT_INLINE void run(Kernel &kernel,
+ Index start,
+ Index end)
+#else
+ template <typename Kernel>
+ EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE EIGEN_CONSTEXPR void run(Kernel &kernel,
+ Index start,
+ Index end)
+#endif
+ {
+ for (Index index = start; index < end; ++index)
+ kernel.assignCoeff(index);
+ }
+};
+
+template<typename Kernel>
+struct dense_assignment_loop<Kernel, LinearVectorizedTraversal, NoUnrolling>
+{
+ EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE EIGEN_CONSTEXPR void run(Kernel &kernel)
+ {
+ const Index size = kernel.size();
+ typedef typename Kernel::Scalar Scalar;
+ typedef typename Kernel::PacketType PacketType;
+ enum {
+ requestedAlignment = Kernel::AssignmentTraits::LinearRequiredAlignment,
+ packetSize = unpacket_traits<PacketType>::size,
+ dstIsAligned = int(Kernel::AssignmentTraits::DstAlignment)>=int(requestedAlignment),
+ dstAlignment = packet_traits<Scalar>::AlignedOnScalar ? int(requestedAlignment)
+ : int(Kernel::AssignmentTraits::DstAlignment),
+ srcAlignment = Kernel::AssignmentTraits::JointAlignment
+ };
+ const Index alignedStart = dstIsAligned ? 0 : internal::first_aligned<requestedAlignment>(kernel.dstDataPtr(), size);
+ const Index alignedEnd = alignedStart + ((size-alignedStart)/packetSize)*packetSize;
+
+ unaligned_dense_assignment_loop<dstIsAligned!=0>::run(kernel, 0, alignedStart);
+
+ for(Index index = alignedStart; index < alignedEnd; index += packetSize)
+ kernel.template assignPacket<dstAlignment, srcAlignment, PacketType>(index);
+
+ unaligned_dense_assignment_loop<>::run(kernel, alignedEnd, size);
+ }
+};
+
+template<typename Kernel>
+struct dense_assignment_loop<Kernel, LinearVectorizedTraversal, CompleteUnrolling>
+{
+ EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE EIGEN_CONSTEXPR void run(Kernel &kernel)
+ {
+ typedef typename Kernel::DstEvaluatorType::XprType DstXprType;
+ typedef typename Kernel::PacketType PacketType;
+
+ enum { size = DstXprType::SizeAtCompileTime,
+ packetSize =unpacket_traits<PacketType>::size,
+ alignedSize = (int(size)/packetSize)*packetSize };
+
+ copy_using_evaluator_innervec_CompleteUnrolling<Kernel, 0, alignedSize>::run(kernel);
+ copy_using_evaluator_DefaultTraversal_CompleteUnrolling<Kernel, alignedSize, size>::run(kernel);
+ }
+};
+
+/**************************
+*** Inner vectorization ***
+**************************/
+
+template<typename Kernel>
+struct dense_assignment_loop<Kernel, InnerVectorizedTraversal, NoUnrolling>
+{
+ typedef typename Kernel::PacketType PacketType;
+ enum {
+ SrcAlignment = Kernel::AssignmentTraits::SrcAlignment,
+ DstAlignment = Kernel::AssignmentTraits::DstAlignment
+ };
+ EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE EIGEN_CONSTEXPR void run(Kernel &kernel)
+ {
+ const Index innerSize = kernel.innerSize();
+ const Index outerSize = kernel.outerSize();
+ const Index packetSize = unpacket_traits<PacketType>::size;
+ for(Index outer = 0; outer < outerSize; ++outer)
+ for(Index inner = 0; inner < innerSize; inner+=packetSize)
+ kernel.template assignPacketByOuterInner<DstAlignment, SrcAlignment, PacketType>(outer, inner);
+ }
+};
+
+template<typename Kernel>
+struct dense_assignment_loop<Kernel, InnerVectorizedTraversal, CompleteUnrolling>
+{
+ EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE void run(Kernel &kernel)
+ {
+ typedef typename Kernel::DstEvaluatorType::XprType DstXprType;
+ copy_using_evaluator_innervec_CompleteUnrolling<Kernel, 0, DstXprType::SizeAtCompileTime>::run(kernel);
+ }
+};
+
+template<typename Kernel>
+struct dense_assignment_loop<Kernel, InnerVectorizedTraversal, InnerUnrolling>
+{
+ EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE void run(Kernel &kernel)
+ {
+ typedef typename Kernel::DstEvaluatorType::XprType DstXprType;
+ typedef typename Kernel::AssignmentTraits Traits;
+ const Index outerSize = kernel.outerSize();
+ for(Index outer = 0; outer < outerSize; ++outer)
+ copy_using_evaluator_innervec_InnerUnrolling<Kernel, 0, DstXprType::InnerSizeAtCompileTime,
+ Traits::SrcAlignment, Traits::DstAlignment>::run(kernel, outer);
+ }
+};
+
+/***********************
+*** Linear traversal ***
+***********************/
+
+template<typename Kernel>
+struct dense_assignment_loop<Kernel, LinearTraversal, NoUnrolling>
+{
+ EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE EIGEN_CONSTEXPR void run(Kernel &kernel)
+ {
+ const Index size = kernel.size();
+ for(Index i = 0; i < size; ++i)
+ kernel.assignCoeff(i);
+ }
+};
+
+template<typename Kernel>
+struct dense_assignment_loop<Kernel, LinearTraversal, CompleteUnrolling>
+{
+ EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE EIGEN_CONSTEXPR void run(Kernel &kernel)
+ {
+ typedef typename Kernel::DstEvaluatorType::XprType DstXprType;
+ copy_using_evaluator_LinearTraversal_CompleteUnrolling<Kernel, 0, DstXprType::SizeAtCompileTime>::run(kernel);
+ }
+};
+
+/**************************
+*** Slice vectorization ***
+***************************/
+
+template<typename Kernel>
+struct dense_assignment_loop<Kernel, SliceVectorizedTraversal, NoUnrolling>
+{
+ EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE EIGEN_CONSTEXPR void run(Kernel &kernel)
+ {
+ typedef typename Kernel::Scalar Scalar;
+ typedef typename Kernel::PacketType PacketType;
+ enum {
+ packetSize = unpacket_traits<PacketType>::size,
+ requestedAlignment = int(Kernel::AssignmentTraits::InnerRequiredAlignment),
+ alignable = packet_traits<Scalar>::AlignedOnScalar || int(Kernel::AssignmentTraits::DstAlignment)>=sizeof(Scalar),
+ dstIsAligned = int(Kernel::AssignmentTraits::DstAlignment)>=int(requestedAlignment),
+ dstAlignment = alignable ? int(requestedAlignment)
+ : int(Kernel::AssignmentTraits::DstAlignment)
+ };
+ const Scalar *dst_ptr = kernel.dstDataPtr();
+ if((!bool(dstIsAligned)) && (UIntPtr(dst_ptr) % sizeof(Scalar))>0)
+ {
+ // the pointer is not aligned-on scalar, so alignment is not possible
+ return dense_assignment_loop<Kernel,DefaultTraversal,NoUnrolling>::run(kernel);
+ }
+ const Index packetAlignedMask = packetSize - 1;
+ const Index innerSize = kernel.innerSize();
+ const Index outerSize = kernel.outerSize();
+ const Index alignedStep = alignable ? (packetSize - kernel.outerStride() % packetSize) & packetAlignedMask : 0;
+ Index alignedStart = ((!alignable) || bool(dstIsAligned)) ? 0 : internal::first_aligned<requestedAlignment>(dst_ptr, innerSize);
+
+ for(Index outer = 0; outer < outerSize; ++outer)
+ {
+ const Index alignedEnd = alignedStart + ((innerSize-alignedStart) & ~packetAlignedMask);
+ // do the non-vectorizable part of the assignment
+ for(Index inner = 0; inner<alignedStart ; ++inner)
+ kernel.assignCoeffByOuterInner(outer, inner);
+
+ // do the vectorizable part of the assignment
+ for(Index inner = alignedStart; inner<alignedEnd; inner+=packetSize)
+ kernel.template assignPacketByOuterInner<dstAlignment, Unaligned, PacketType>(outer, inner);
+
+ // do the non-vectorizable part of the assignment
+ for(Index inner = alignedEnd; inner<innerSize ; ++inner)
+ kernel.assignCoeffByOuterInner(outer, inner);
+
+ alignedStart = numext::mini((alignedStart+alignedStep)%packetSize, innerSize);
+ }
+ }
+};
+
+#if EIGEN_UNALIGNED_VECTORIZE
+template<typename Kernel>
+struct dense_assignment_loop<Kernel, SliceVectorizedTraversal, InnerUnrolling>
+{
+ EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE EIGEN_CONSTEXPR void run(Kernel &kernel)
+ {
+ typedef typename Kernel::DstEvaluatorType::XprType DstXprType;
+ typedef typename Kernel::PacketType PacketType;
+
+ enum { innerSize = DstXprType::InnerSizeAtCompileTime,
+ packetSize =unpacket_traits<PacketType>::size,
+ vectorizableSize = (int(innerSize) / int(packetSize)) * int(packetSize),
+ size = DstXprType::SizeAtCompileTime };
+
+ for(Index outer = 0; outer < kernel.outerSize(); ++outer)
+ {
+ copy_using_evaluator_innervec_InnerUnrolling<Kernel, 0, vectorizableSize, 0, 0>::run(kernel, outer);
+ copy_using_evaluator_DefaultTraversal_InnerUnrolling<Kernel, vectorizableSize, innerSize>::run(kernel, outer);
+ }
+ }
+};
+#endif
+
+
+/***************************************************************************
+* Part 4 : Generic dense assignment kernel
+***************************************************************************/
+
+// This class generalize the assignment of a coefficient (or packet) from one dense evaluator
+// to another dense writable evaluator.
+// It is parametrized by the two evaluators, and the actual assignment functor.
+// This abstraction level permits to keep the evaluation loops as simple and as generic as possible.
+// One can customize the assignment using this generic dense_assignment_kernel with different
+// functors, or by completely overloading it, by-passing a functor.
+template<typename DstEvaluatorTypeT, typename SrcEvaluatorTypeT, typename Functor, int Version = Specialized>
+class generic_dense_assignment_kernel
+{
+protected:
+ typedef typename DstEvaluatorTypeT::XprType DstXprType;
+ typedef typename SrcEvaluatorTypeT::XprType SrcXprType;
+public:
+
+ typedef DstEvaluatorTypeT DstEvaluatorType;
+ typedef SrcEvaluatorTypeT SrcEvaluatorType;
+ typedef typename DstEvaluatorType::Scalar Scalar;
+ typedef copy_using_evaluator_traits<DstEvaluatorTypeT, SrcEvaluatorTypeT, Functor> AssignmentTraits;
+ typedef typename AssignmentTraits::PacketType PacketType;
+
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ generic_dense_assignment_kernel(DstEvaluatorType &dst, const SrcEvaluatorType &src, const Functor &func, DstXprType& dstExpr)
+ : m_dst(dst), m_src(src), m_functor(func), m_dstExpr(dstExpr)
+ {
+ #ifdef EIGEN_DEBUG_ASSIGN
+ AssignmentTraits::debug();
+ #endif
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR Index size() const EIGEN_NOEXCEPT { return m_dstExpr.size(); }
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR Index innerSize() const EIGEN_NOEXCEPT { return m_dstExpr.innerSize(); }
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR Index outerSize() const EIGEN_NOEXCEPT { return m_dstExpr.outerSize(); }
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR Index rows() const EIGEN_NOEXCEPT { return m_dstExpr.rows(); }
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR Index cols() const EIGEN_NOEXCEPT { return m_dstExpr.cols(); }
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR Index outerStride() const EIGEN_NOEXCEPT { return m_dstExpr.outerStride(); }
+
+ EIGEN_DEVICE_FUNC DstEvaluatorType& dstEvaluator() EIGEN_NOEXCEPT { return m_dst; }
+ EIGEN_DEVICE_FUNC const SrcEvaluatorType& srcEvaluator() const EIGEN_NOEXCEPT { return m_src; }
+
+ /// Assign src(row,col) to dst(row,col) through the assignment functor.
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void assignCoeff(Index row, Index col)
+ {
+ m_functor.assignCoeff(m_dst.coeffRef(row,col), m_src.coeff(row,col));
+ }
+
+ /// \sa assignCoeff(Index,Index)
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void assignCoeff(Index index)
+ {
+ m_functor.assignCoeff(m_dst.coeffRef(index), m_src.coeff(index));
+ }
+
+ /// \sa assignCoeff(Index,Index)
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void assignCoeffByOuterInner(Index outer, Index inner)
+ {
+ Index row = rowIndexByOuterInner(outer, inner);
+ Index col = colIndexByOuterInner(outer, inner);
+ assignCoeff(row, col);
+ }
+
+
+ template<int StoreMode, int LoadMode, typename PacketType>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void assignPacket(Index row, Index col)
+ {
+ m_functor.template assignPacket<StoreMode>(&m_dst.coeffRef(row,col), m_src.template packet<LoadMode,PacketType>(row,col));
+ }
+
+ template<int StoreMode, int LoadMode, typename PacketType>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void assignPacket(Index index)
+ {
+ m_functor.template assignPacket<StoreMode>(&m_dst.coeffRef(index), m_src.template packet<LoadMode,PacketType>(index));
+ }
+
+ template<int StoreMode, int LoadMode, typename PacketType>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void assignPacketByOuterInner(Index outer, Index inner)
+ {
+ Index row = rowIndexByOuterInner(outer, inner);
+ Index col = colIndexByOuterInner(outer, inner);
+ assignPacket<StoreMode,LoadMode,PacketType>(row, col);
+ }
+
+ EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE Index rowIndexByOuterInner(Index outer, Index inner)
+ {
+ typedef typename DstEvaluatorType::ExpressionTraits Traits;
+ return int(Traits::RowsAtCompileTime) == 1 ? 0
+ : int(Traits::ColsAtCompileTime) == 1 ? inner
+ : int(DstEvaluatorType::Flags)&RowMajorBit ? outer
+ : inner;
+ }
+
+ EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE Index colIndexByOuterInner(Index outer, Index inner)
+ {
+ typedef typename DstEvaluatorType::ExpressionTraits Traits;
+ return int(Traits::ColsAtCompileTime) == 1 ? 0
+ : int(Traits::RowsAtCompileTime) == 1 ? inner
+ : int(DstEvaluatorType::Flags)&RowMajorBit ? inner
+ : outer;
+ }
+
+ EIGEN_DEVICE_FUNC const Scalar* dstDataPtr() const
+ {
+ return m_dstExpr.data();
+ }
+
+protected:
+ DstEvaluatorType& m_dst;
+ const SrcEvaluatorType& m_src;
+ const Functor &m_functor;
+ // TODO find a way to avoid the needs of the original expression
+ DstXprType& m_dstExpr;
+};
+
+// Special kernel used when computing small products whose operands have dynamic dimensions. It ensures that the
+// PacketSize used is no larger than 4, thereby increasing the chance that vectorized instructions will be used
+// when computing the product.
+
+template<typename DstEvaluatorTypeT, typename SrcEvaluatorTypeT, typename Functor>
+class restricted_packet_dense_assignment_kernel : public generic_dense_assignment_kernel<DstEvaluatorTypeT, SrcEvaluatorTypeT, Functor, BuiltIn>
+{
+protected:
+ typedef generic_dense_assignment_kernel<DstEvaluatorTypeT, SrcEvaluatorTypeT, Functor, BuiltIn> Base;
+ public:
+ typedef typename Base::Scalar Scalar;
+ typedef typename Base::DstXprType DstXprType;
+ typedef copy_using_evaluator_traits<DstEvaluatorTypeT, SrcEvaluatorTypeT, Functor, 4> AssignmentTraits;
+ typedef typename AssignmentTraits::PacketType PacketType;
+
+ EIGEN_DEVICE_FUNC restricted_packet_dense_assignment_kernel(DstEvaluatorTypeT &dst, const SrcEvaluatorTypeT &src, const Functor &func, DstXprType& dstExpr)
+ : Base(dst, src, func, dstExpr)
+ {
+ }
+ };
+
+/***************************************************************************
+* Part 5 : Entry point for dense rectangular assignment
+***************************************************************************/
+
+template<typename DstXprType,typename SrcXprType, typename Functor>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+void resize_if_allowed(DstXprType &dst, const SrcXprType& src, const Functor &/*func*/)
+{
+ EIGEN_ONLY_USED_FOR_DEBUG(dst);
+ EIGEN_ONLY_USED_FOR_DEBUG(src);
+ eigen_assert(dst.rows() == src.rows() && dst.cols() == src.cols());
+}
+
+template<typename DstXprType,typename SrcXprType, typename T1, typename T2>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+void resize_if_allowed(DstXprType &dst, const SrcXprType& src, const internal::assign_op<T1,T2> &/*func*/)
+{
+ Index dstRows = src.rows();
+ Index dstCols = src.cols();
+ if(((dst.rows()!=dstRows) || (dst.cols()!=dstCols)))
+ dst.resize(dstRows, dstCols);
+ eigen_assert(dst.rows() == dstRows && dst.cols() == dstCols);
+}
+
+template<typename DstXprType, typename SrcXprType, typename Functor>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE EIGEN_CONSTEXPR void call_dense_assignment_loop(DstXprType& dst, const SrcXprType& src, const Functor &func)
+{
+ typedef evaluator<DstXprType> DstEvaluatorType;
+ typedef evaluator<SrcXprType> SrcEvaluatorType;
+
+ SrcEvaluatorType srcEvaluator(src);
+
+ // NOTE To properly handle A = (A*A.transpose())/s with A rectangular,
+ // we need to resize the destination after the source evaluator has been created.
+ resize_if_allowed(dst, src, func);
+
+ DstEvaluatorType dstEvaluator(dst);
+
+ typedef generic_dense_assignment_kernel<DstEvaluatorType,SrcEvaluatorType,Functor> Kernel;
+ Kernel kernel(dstEvaluator, srcEvaluator, func, dst.const_cast_derived());
+
+ dense_assignment_loop<Kernel>::run(kernel);
+}
+
+// Specialization for filling the destination with a constant value.
+#ifndef EIGEN_GPU_COMPILE_PHASE
+template<typename DstXprType>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void call_dense_assignment_loop(DstXprType& dst, const Eigen::CwiseNullaryOp<Eigen::internal::scalar_constant_op<typename DstXprType::Scalar>, DstXprType>& src, const internal::assign_op<typename DstXprType::Scalar,typename DstXprType::Scalar>& func)
+{
+ resize_if_allowed(dst, src, func);
+ std::fill_n(dst.data(), dst.size(), src.functor()());
+}
+#endif
+
+template<typename DstXprType, typename SrcXprType>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void call_dense_assignment_loop(DstXprType& dst, const SrcXprType& src)
+{
+ call_dense_assignment_loop(dst, src, internal::assign_op<typename DstXprType::Scalar,typename SrcXprType::Scalar>());
+}
+
+/***************************************************************************
+* Part 6 : Generic assignment
+***************************************************************************/
+
+// Based on the respective shapes of the destination and source,
+// the class AssignmentKind determine the kind of assignment mechanism.
+// AssignmentKind must define a Kind typedef.
+template<typename DstShape, typename SrcShape> struct AssignmentKind;
+
+// Assignment kind defined in this file:
+struct Dense2Dense {};
+struct EigenBase2EigenBase {};
+
+template<typename,typename> struct AssignmentKind { typedef EigenBase2EigenBase Kind; };
+template<> struct AssignmentKind<DenseShape,DenseShape> { typedef Dense2Dense Kind; };
+
+// This is the main assignment class
+template< typename DstXprType, typename SrcXprType, typename Functor,
+ typename Kind = typename AssignmentKind< typename evaluator_traits<DstXprType>::Shape , typename evaluator_traits<SrcXprType>::Shape >::Kind,
+ typename EnableIf = void>
+struct Assignment;
+
+
+// The only purpose of this call_assignment() function is to deal with noalias() / "assume-aliasing" and automatic transposition.
+// Indeed, I (Gael) think that this concept of "assume-aliasing" was a mistake, and it makes thing quite complicated.
+// So this intermediate function removes everything related to "assume-aliasing" such that Assignment
+// does not has to bother about these annoying details.
+
+template<typename Dst, typename Src>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+void call_assignment(Dst& dst, const Src& src)
+{
+ call_assignment(dst, src, internal::assign_op<typename Dst::Scalar,typename Src::Scalar>());
+}
+template<typename Dst, typename Src>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+void call_assignment(const Dst& dst, const Src& src)
+{
+ call_assignment(dst, src, internal::assign_op<typename Dst::Scalar,typename Src::Scalar>());
+}
+
+// Deal with "assume-aliasing"
+template<typename Dst, typename Src, typename Func>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE EIGEN_CONSTEXPR
+void call_assignment(Dst& dst, const Src& src, const Func& func, std::enable_if_t< evaluator_assume_aliasing<Src>::value, void*> = 0)
+{
+ typename plain_matrix_type<Src>::type tmp(src);
+ call_assignment_no_alias(dst, tmp, func);
+}
+
+template<typename Dst, typename Src, typename Func>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+void call_assignment(Dst& dst, const Src& src, const Func& func, std::enable_if_t<!evaluator_assume_aliasing<Src>::value, void*> = 0)
+{
+ call_assignment_no_alias(dst, src, func);
+}
+
+// by-pass "assume-aliasing"
+// When there is no aliasing, we require that 'dst' has been properly resized
+template<typename Dst, template <typename> class StorageBase, typename Src, typename Func>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE EIGEN_CONSTEXPR
+void call_assignment(NoAlias<Dst,StorageBase>& dst, const Src& src, const Func& func)
+{
+ call_assignment_no_alias(dst.expression(), src, func);
+}
+
+
+template<typename Dst, typename Src, typename Func>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE EIGEN_CONSTEXPR
+void call_assignment_no_alias(Dst& dst, const Src& src, const Func& func)
+{
+ enum {
+ NeedToTranspose = ( (int(Dst::RowsAtCompileTime) == 1 && int(Src::ColsAtCompileTime) == 1)
+ || (int(Dst::ColsAtCompileTime) == 1 && int(Src::RowsAtCompileTime) == 1)
+ ) && int(Dst::SizeAtCompileTime) != 1
+ };
+
+ typedef std::conditional_t<NeedToTranspose, Transpose<Dst>, Dst> ActualDstTypeCleaned;
+ typedef std::conditional_t<NeedToTranspose, Transpose<Dst>, Dst&> ActualDstType;
+ ActualDstType actualDst(dst);
+
+ // TODO check whether this is the right place to perform these checks:
+ EIGEN_STATIC_ASSERT_LVALUE(Dst)
+ EIGEN_STATIC_ASSERT_SAME_MATRIX_SIZE(ActualDstTypeCleaned,Src)
+ EIGEN_CHECK_BINARY_COMPATIBILIY(Func,typename ActualDstTypeCleaned::Scalar,typename Src::Scalar);
+
+ Assignment<ActualDstTypeCleaned,Src,Func>::run(actualDst, src, func);
+}
+
+template<typename Dst, typename Src, typename Func>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+void call_restricted_packet_assignment_no_alias(Dst& dst, const Src& src, const Func& func)
+{
+ typedef evaluator<Dst> DstEvaluatorType;
+ typedef evaluator<Src> SrcEvaluatorType;
+ typedef restricted_packet_dense_assignment_kernel<DstEvaluatorType,SrcEvaluatorType,Func> Kernel;
+
+ EIGEN_STATIC_ASSERT_LVALUE(Dst)
+ EIGEN_CHECK_BINARY_COMPATIBILIY(Func,typename Dst::Scalar,typename Src::Scalar);
+
+ SrcEvaluatorType srcEvaluator(src);
+ resize_if_allowed(dst, src, func);
+
+ DstEvaluatorType dstEvaluator(dst);
+ Kernel kernel(dstEvaluator, srcEvaluator, func, dst.const_cast_derived());
+
+ dense_assignment_loop<Kernel>::run(kernel);
+}
+
+template<typename Dst, typename Src>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE EIGEN_CONSTEXPR
+void call_assignment_no_alias(Dst& dst, const Src& src)
+{
+ call_assignment_no_alias(dst, src, internal::assign_op<typename Dst::Scalar,typename Src::Scalar>());
+}
+
+template<typename Dst, typename Src, typename Func>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE EIGEN_CONSTEXPR
+void call_assignment_no_alias_no_transpose(Dst& dst, const Src& src, const Func& func)
+{
+ // TODO check whether this is the right place to perform these checks:
+ EIGEN_STATIC_ASSERT_LVALUE(Dst)
+ EIGEN_STATIC_ASSERT_SAME_MATRIX_SIZE(Dst,Src)
+ EIGEN_CHECK_BINARY_COMPATIBILIY(Func,typename Dst::Scalar,typename Src::Scalar);
+
+ Assignment<Dst,Src,Func>::run(dst, src, func);
+}
+template<typename Dst, typename Src>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE EIGEN_CONSTEXPR
+void call_assignment_no_alias_no_transpose(Dst& dst, const Src& src)
+{
+ call_assignment_no_alias_no_transpose(dst, src, internal::assign_op<typename Dst::Scalar,typename Src::Scalar>());
+}
+
+// forward declaration
+template<typename Dst, typename Src> void check_for_aliasing(const Dst &dst, const Src &src);
+
+// Generic Dense to Dense assignment
+// Note that the last template argument "Weak" is needed to make it possible to perform
+// both partial specialization+SFINAE without ambiguous specialization
+template< typename DstXprType, typename SrcXprType, typename Functor, typename Weak>
+struct Assignment<DstXprType, SrcXprType, Functor, Dense2Dense, Weak>
+{
+ EIGEN_DEVICE_FUNC
+ static EIGEN_STRONG_INLINE void run(DstXprType &dst, const SrcXprType &src, const Functor &func)
+ {
+#ifndef EIGEN_NO_DEBUG
+ internal::check_for_aliasing(dst, src);
+#endif
+
+ call_dense_assignment_loop(dst, src, func);
+ }
+};
+
+// Generic assignment through evalTo.
+// TODO: not sure we have to keep that one, but it helps porting current code to new evaluator mechanism.
+// Note that the last template argument "Weak" is needed to make it possible to perform
+// both partial specialization+SFINAE without ambiguous specialization
+template< typename DstXprType, typename SrcXprType, typename Functor, typename Weak>
+struct Assignment<DstXprType, SrcXprType, Functor, EigenBase2EigenBase, Weak>
+{
+ EIGEN_DEVICE_FUNC
+ static EIGEN_STRONG_INLINE void run(DstXprType &dst, const SrcXprType &src, const internal::assign_op<typename DstXprType::Scalar,typename SrcXprType::Scalar> &/*func*/)
+ {
+ Index dstRows = src.rows();
+ Index dstCols = src.cols();
+ if((dst.rows()!=dstRows) || (dst.cols()!=dstCols))
+ dst.resize(dstRows, dstCols);
+
+ eigen_assert(dst.rows() == src.rows() && dst.cols() == src.cols());
+ src.evalTo(dst);
+ }
+
+ // NOTE The following two functions are templated to avoid their instantiation if not needed
+ // This is needed because some expressions supports evalTo only and/or have 'void' as scalar type.
+ template<typename SrcScalarType>
+ EIGEN_DEVICE_FUNC
+ static EIGEN_STRONG_INLINE void run(DstXprType &dst, const SrcXprType &src, const internal::add_assign_op<typename DstXprType::Scalar,SrcScalarType> &/*func*/)
+ {
+ Index dstRows = src.rows();
+ Index dstCols = src.cols();
+ if((dst.rows()!=dstRows) || (dst.cols()!=dstCols))
+ dst.resize(dstRows, dstCols);
+
+ eigen_assert(dst.rows() == src.rows() && dst.cols() == src.cols());
+ src.addTo(dst);
+ }
+
+ template<typename SrcScalarType>
+ EIGEN_DEVICE_FUNC
+ static EIGEN_STRONG_INLINE void run(DstXprType &dst, const SrcXprType &src, const internal::sub_assign_op<typename DstXprType::Scalar,SrcScalarType> &/*func*/)
+ {
+ Index dstRows = src.rows();
+ Index dstCols = src.cols();
+ if((dst.rows()!=dstRows) || (dst.cols()!=dstCols))
+ dst.resize(dstRows, dstCols);
+
+ eigen_assert(dst.rows() == src.rows() && dst.cols() == src.cols());
+ src.subTo(dst);
+ }
+};
+
+} // namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_ASSIGN_EVALUATOR_H
diff --git a/Eigen/src/Core/Assign_MKL.h b/Eigen/src/Core/Assign_MKL.h
new file mode 100644
index 0000000..f9b86c8
--- /dev/null
+++ b/Eigen/src/Core/Assign_MKL.h
@@ -0,0 +1,180 @@
+/*
+ Copyright (c) 2011, Intel Corporation. All rights reserved.
+ Copyright (C) 2015 Gael Guennebaud <gael.guennebaud@inria.fr>
+
+ Redistribution and use in source and binary forms, with or without modification,
+ are permitted provided that the following conditions are met:
+
+ * Redistributions of source code must retain the above copyright notice, this
+ list of conditions and the following disclaimer.
+ * Redistributions in binary form must reproduce the above copyright notice,
+ this list of conditions and the following disclaimer in the documentation
+ and/or other materials provided with the distribution.
+ * Neither the name of Intel Corporation nor the names of its contributors may
+ be used to endorse or promote products derived from this software without
+ specific prior written permission.
+
+ THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
+ ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
+ WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
+ DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR
+ ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
+ (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
+ LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON
+ ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
+ (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
+ SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+
+ ********************************************************************************
+ * Content : Eigen bindings to Intel(R) MKL
+ * MKL VML support for coefficient-wise unary Eigen expressions like a=b.sin()
+ ********************************************************************************
+*/
+
+#ifndef EIGEN_ASSIGN_VML_H
+#define EIGEN_ASSIGN_VML_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+
+template<typename Dst, typename Src>
+class vml_assign_traits
+{
+ private:
+ enum {
+ DstHasDirectAccess = Dst::Flags & DirectAccessBit,
+ SrcHasDirectAccess = Src::Flags & DirectAccessBit,
+ StorageOrdersAgree = (int(Dst::IsRowMajor) == int(Src::IsRowMajor)),
+ InnerSize = int(Dst::IsVectorAtCompileTime) ? int(Dst::SizeAtCompileTime)
+ : int(Dst::Flags)&RowMajorBit ? int(Dst::ColsAtCompileTime)
+ : int(Dst::RowsAtCompileTime),
+ InnerMaxSize = int(Dst::IsVectorAtCompileTime) ? int(Dst::MaxSizeAtCompileTime)
+ : int(Dst::Flags)&RowMajorBit ? int(Dst::MaxColsAtCompileTime)
+ : int(Dst::MaxRowsAtCompileTime),
+ MaxSizeAtCompileTime = Dst::SizeAtCompileTime,
+
+ MightEnableVml = StorageOrdersAgree && DstHasDirectAccess && SrcHasDirectAccess && Src::InnerStrideAtCompileTime==1 && Dst::InnerStrideAtCompileTime==1,
+ MightLinearize = MightEnableVml && (int(Dst::Flags) & int(Src::Flags) & LinearAccessBit),
+ VmlSize = MightLinearize ? MaxSizeAtCompileTime : InnerMaxSize,
+ LargeEnough = VmlSize==Dynamic || VmlSize>=EIGEN_MKL_VML_THRESHOLD
+ };
+ public:
+ enum {
+ EnableVml = MightEnableVml && LargeEnough,
+ Traversal = MightLinearize ? LinearTraversal : DefaultTraversal
+ };
+};
+
+#define EIGEN_PP_EXPAND(ARG) ARG
+#if !defined (EIGEN_FAST_MATH) || (EIGEN_FAST_MATH != 1)
+#define EIGEN_VMLMODE_EXPAND_xLA , VML_HA
+#else
+#define EIGEN_VMLMODE_EXPAND_xLA , VML_LA
+#endif
+
+#define EIGEN_VMLMODE_EXPAND_x_
+
+#define EIGEN_VMLMODE_PREFIX_xLA vm
+#define EIGEN_VMLMODE_PREFIX_x_ v
+#define EIGEN_VMLMODE_PREFIX(VMLMODE) EIGEN_CAT(EIGEN_VMLMODE_PREFIX_x,VMLMODE)
+
+#define EIGEN_MKL_VML_DECLARE_UNARY_CALL(EIGENOP, VMLOP, EIGENTYPE, VMLTYPE, VMLMODE) \
+ template< typename DstXprType, typename SrcXprNested> \
+ struct Assignment<DstXprType, CwiseUnaryOp<scalar_##EIGENOP##_op<EIGENTYPE>, SrcXprNested>, assign_op<EIGENTYPE,EIGENTYPE>, \
+ Dense2Dense, std::enable_if_t<vml_assign_traits<DstXprType,SrcXprNested>::EnableVml>> { \
+ typedef CwiseUnaryOp<scalar_##EIGENOP##_op<EIGENTYPE>, SrcXprNested> SrcXprType; \
+ static void run(DstXprType &dst, const SrcXprType &src, const assign_op<EIGENTYPE,EIGENTYPE> &func) { \
+ resize_if_allowed(dst, src, func); \
+ eigen_assert(dst.rows() == src.rows() && dst.cols() == src.cols()); \
+ if(vml_assign_traits<DstXprType,SrcXprNested>::Traversal==LinearTraversal) { \
+ VMLOP(dst.size(), (const VMLTYPE*)src.nestedExpression().data(), \
+ (VMLTYPE*)dst.data() EIGEN_PP_EXPAND(EIGEN_VMLMODE_EXPAND_x##VMLMODE) ); \
+ } else { \
+ const Index outerSize = dst.outerSize(); \
+ for(Index outer = 0; outer < outerSize; ++outer) { \
+ const EIGENTYPE *src_ptr = src.IsRowMajor ? &(src.nestedExpression().coeffRef(outer,0)) : \
+ &(src.nestedExpression().coeffRef(0, outer)); \
+ EIGENTYPE *dst_ptr = dst.IsRowMajor ? &(dst.coeffRef(outer,0)) : &(dst.coeffRef(0, outer)); \
+ VMLOP( dst.innerSize(), (const VMLTYPE*)src_ptr, \
+ (VMLTYPE*)dst_ptr EIGEN_PP_EXPAND(EIGEN_VMLMODE_EXPAND_x##VMLMODE)); \
+ } \
+ } \
+ } \
+ }; \
+
+
+#define EIGEN_MKL_VML_DECLARE_UNARY_CALLS_REAL(EIGENOP, VMLOP, VMLMODE) \
+ EIGEN_MKL_VML_DECLARE_UNARY_CALL(EIGENOP, EIGEN_CAT(EIGEN_VMLMODE_PREFIX(VMLMODE),s##VMLOP), float, float, VMLMODE) \
+ EIGEN_MKL_VML_DECLARE_UNARY_CALL(EIGENOP, EIGEN_CAT(EIGEN_VMLMODE_PREFIX(VMLMODE),d##VMLOP), double, double, VMLMODE)
+
+#define EIGEN_MKL_VML_DECLARE_UNARY_CALLS_CPLX(EIGENOP, VMLOP, VMLMODE) \
+ EIGEN_MKL_VML_DECLARE_UNARY_CALL(EIGENOP, EIGEN_CAT(EIGEN_VMLMODE_PREFIX(VMLMODE),c##VMLOP), scomplex, MKL_Complex8, VMLMODE) \
+ EIGEN_MKL_VML_DECLARE_UNARY_CALL(EIGENOP, EIGEN_CAT(EIGEN_VMLMODE_PREFIX(VMLMODE),z##VMLOP), dcomplex, MKL_Complex16, VMLMODE)
+
+#define EIGEN_MKL_VML_DECLARE_UNARY_CALLS(EIGENOP, VMLOP, VMLMODE) \
+ EIGEN_MKL_VML_DECLARE_UNARY_CALLS_REAL(EIGENOP, VMLOP, VMLMODE) \
+ EIGEN_MKL_VML_DECLARE_UNARY_CALLS_CPLX(EIGENOP, VMLOP, VMLMODE)
+
+
+EIGEN_MKL_VML_DECLARE_UNARY_CALLS(sin, Sin, LA)
+EIGEN_MKL_VML_DECLARE_UNARY_CALLS(asin, Asin, LA)
+EIGEN_MKL_VML_DECLARE_UNARY_CALLS(sinh, Sinh, LA)
+EIGEN_MKL_VML_DECLARE_UNARY_CALLS(cos, Cos, LA)
+EIGEN_MKL_VML_DECLARE_UNARY_CALLS(acos, Acos, LA)
+EIGEN_MKL_VML_DECLARE_UNARY_CALLS(cosh, Cosh, LA)
+EIGEN_MKL_VML_DECLARE_UNARY_CALLS(tan, Tan, LA)
+EIGEN_MKL_VML_DECLARE_UNARY_CALLS(atan, Atan, LA)
+EIGEN_MKL_VML_DECLARE_UNARY_CALLS(tanh, Tanh, LA)
+// EIGEN_MKL_VML_DECLARE_UNARY_CALLS(abs, Abs, _)
+EIGEN_MKL_VML_DECLARE_UNARY_CALLS(exp, Exp, LA)
+EIGEN_MKL_VML_DECLARE_UNARY_CALLS(log, Ln, LA)
+EIGEN_MKL_VML_DECLARE_UNARY_CALLS(log10, Log10, LA)
+EIGEN_MKL_VML_DECLARE_UNARY_CALLS(sqrt, Sqrt, _)
+
+EIGEN_MKL_VML_DECLARE_UNARY_CALLS_REAL(square, Sqr, _)
+EIGEN_MKL_VML_DECLARE_UNARY_CALLS_CPLX(arg, Arg, _)
+EIGEN_MKL_VML_DECLARE_UNARY_CALLS_REAL(round, Round, _)
+EIGEN_MKL_VML_DECLARE_UNARY_CALLS_REAL(floor, Floor, _)
+EIGEN_MKL_VML_DECLARE_UNARY_CALLS_REAL(ceil, Ceil, _)
+
+#define EIGEN_MKL_VML_DECLARE_POW_CALL(EIGENOP, VMLOP, EIGENTYPE, VMLTYPE, VMLMODE) \
+ template< typename DstXprType, typename SrcXprNested, typename Plain> \
+ struct Assignment<DstXprType, CwiseBinaryOp<scalar_##EIGENOP##_op<EIGENTYPE,EIGENTYPE>, SrcXprNested, \
+ const CwiseNullaryOp<internal::scalar_constant_op<EIGENTYPE>,Plain> >, assign_op<EIGENTYPE,EIGENTYPE>, \
+ Dense2Dense, std::enable_if_t<vml_assign_traits<DstXprType,SrcXprNested>::EnableVml>> { \
+ typedef CwiseBinaryOp<scalar_##EIGENOP##_op<EIGENTYPE,EIGENTYPE>, SrcXprNested, \
+ const CwiseNullaryOp<internal::scalar_constant_op<EIGENTYPE>,Plain> > SrcXprType; \
+ static void run(DstXprType &dst, const SrcXprType &src, const assign_op<EIGENTYPE,EIGENTYPE> &func) { \
+ resize_if_allowed(dst, src, func); \
+ eigen_assert(dst.rows() == src.rows() && dst.cols() == src.cols()); \
+ VMLTYPE exponent = reinterpret_cast<const VMLTYPE&>(src.rhs().functor().m_other); \
+ if(vml_assign_traits<DstXprType,SrcXprNested>::Traversal==LinearTraversal) \
+ { \
+ VMLOP( dst.size(), (const VMLTYPE*)src.lhs().data(), exponent, \
+ (VMLTYPE*)dst.data() EIGEN_PP_EXPAND(EIGEN_VMLMODE_EXPAND_x##VMLMODE) ); \
+ } else { \
+ const Index outerSize = dst.outerSize(); \
+ for(Index outer = 0; outer < outerSize; ++outer) { \
+ const EIGENTYPE *src_ptr = src.IsRowMajor ? &(src.lhs().coeffRef(outer,0)) : \
+ &(src.lhs().coeffRef(0, outer)); \
+ EIGENTYPE *dst_ptr = dst.IsRowMajor ? &(dst.coeffRef(outer,0)) : &(dst.coeffRef(0, outer)); \
+ VMLOP( dst.innerSize(), (const VMLTYPE*)src_ptr, exponent, \
+ (VMLTYPE*)dst_ptr EIGEN_PP_EXPAND(EIGEN_VMLMODE_EXPAND_x##VMLMODE)); \
+ } \
+ } \
+ } \
+ };
+
+EIGEN_MKL_VML_DECLARE_POW_CALL(pow, vmsPowx, float, float, LA)
+EIGEN_MKL_VML_DECLARE_POW_CALL(pow, vmdPowx, double, double, LA)
+EIGEN_MKL_VML_DECLARE_POW_CALL(pow, vmcPowx, scomplex, MKL_Complex8, LA)
+EIGEN_MKL_VML_DECLARE_POW_CALL(pow, vmzPowx, dcomplex, MKL_Complex16, LA)
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_ASSIGN_VML_H
diff --git a/Eigen/src/Core/BandMatrix.h b/Eigen/src/Core/BandMatrix.h
new file mode 100644
index 0000000..dcb0d13
--- /dev/null
+++ b/Eigen/src/Core/BandMatrix.h
@@ -0,0 +1,355 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_BANDMATRIX_H
+#define EIGEN_BANDMATRIX_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+
+template<typename Derived>
+class BandMatrixBase : public EigenBase<Derived>
+{
+ public:
+
+ enum {
+ Flags = internal::traits<Derived>::Flags,
+ CoeffReadCost = internal::traits<Derived>::CoeffReadCost,
+ RowsAtCompileTime = internal::traits<Derived>::RowsAtCompileTime,
+ ColsAtCompileTime = internal::traits<Derived>::ColsAtCompileTime,
+ MaxRowsAtCompileTime = internal::traits<Derived>::MaxRowsAtCompileTime,
+ MaxColsAtCompileTime = internal::traits<Derived>::MaxColsAtCompileTime,
+ Supers = internal::traits<Derived>::Supers,
+ Subs = internal::traits<Derived>::Subs,
+ Options = internal::traits<Derived>::Options
+ };
+ typedef typename internal::traits<Derived>::Scalar Scalar;
+ typedef Matrix<Scalar,RowsAtCompileTime,ColsAtCompileTime> DenseMatrixType;
+ typedef typename DenseMatrixType::StorageIndex StorageIndex;
+ typedef typename internal::traits<Derived>::CoefficientsType CoefficientsType;
+ typedef EigenBase<Derived> Base;
+
+ protected:
+ enum {
+ DataRowsAtCompileTime = ((Supers!=Dynamic) && (Subs!=Dynamic))
+ ? 1 + Supers + Subs
+ : Dynamic,
+ SizeAtCompileTime = min_size_prefer_dynamic(RowsAtCompileTime,ColsAtCompileTime)
+ };
+
+ public:
+
+ using Base::derived;
+ using Base::rows;
+ using Base::cols;
+
+ /** \returns the number of super diagonals */
+ inline Index supers() const { return derived().supers(); }
+
+ /** \returns the number of sub diagonals */
+ inline Index subs() const { return derived().subs(); }
+
+ /** \returns an expression of the underlying coefficient matrix */
+ inline const CoefficientsType& coeffs() const { return derived().coeffs(); }
+
+ /** \returns an expression of the underlying coefficient matrix */
+ inline CoefficientsType& coeffs() { return derived().coeffs(); }
+
+ /** \returns a vector expression of the \a i -th column,
+ * only the meaningful part is returned.
+ * \warning the internal storage must be column major. */
+ inline Block<CoefficientsType,Dynamic,1> col(Index i)
+ {
+ EIGEN_STATIC_ASSERT((int(Options) & int(RowMajor)) == 0, THIS_METHOD_IS_ONLY_FOR_COLUMN_MAJOR_MATRICES);
+ Index start = 0;
+ Index len = coeffs().rows();
+ if (i<=supers())
+ {
+ start = supers()-i;
+ len = (std::min)(rows(),std::max<Index>(0,coeffs().rows() - (supers()-i)));
+ }
+ else if (i>=rows()-subs())
+ len = std::max<Index>(0,coeffs().rows() - (i + 1 - rows() + subs()));
+ return Block<CoefficientsType,Dynamic,1>(coeffs(), start, i, len, 1);
+ }
+
+ /** \returns a vector expression of the main diagonal */
+ inline Block<CoefficientsType,1,SizeAtCompileTime> diagonal()
+ { return Block<CoefficientsType,1,SizeAtCompileTime>(coeffs(),supers(),0,1,(std::min)(rows(),cols())); }
+
+ /** \returns a vector expression of the main diagonal (const version) */
+ inline const Block<const CoefficientsType,1,SizeAtCompileTime> diagonal() const
+ { return Block<const CoefficientsType,1,SizeAtCompileTime>(coeffs(),supers(),0,1,(std::min)(rows(),cols())); }
+
+ template<int Index> struct DiagonalIntReturnType {
+ enum {
+ ReturnOpposite = (int(Options) & int(SelfAdjoint)) && (((Index) > 0 && Supers == 0) || ((Index) < 0 && Subs == 0)),
+ Conjugate = ReturnOpposite && NumTraits<Scalar>::IsComplex,
+ ActualIndex = ReturnOpposite ? -Index : Index,
+ DiagonalSize = (RowsAtCompileTime==Dynamic || ColsAtCompileTime==Dynamic)
+ ? Dynamic
+ : (ActualIndex<0
+ ? min_size_prefer_dynamic(ColsAtCompileTime, RowsAtCompileTime + ActualIndex)
+ : min_size_prefer_dynamic(RowsAtCompileTime, ColsAtCompileTime - ActualIndex))
+ };
+ typedef Block<CoefficientsType,1, DiagonalSize> BuildType;
+ typedef std::conditional_t<Conjugate,
+ CwiseUnaryOp<internal::scalar_conjugate_op<Scalar>,BuildType >,
+ BuildType> Type;
+ };
+
+ /** \returns a vector expression of the \a N -th sub or super diagonal */
+ template<int N> inline typename DiagonalIntReturnType<N>::Type diagonal()
+ {
+ return typename DiagonalIntReturnType<N>::BuildType(coeffs(), supers()-N, (std::max)(0,N), 1, diagonalLength(N));
+ }
+
+ /** \returns a vector expression of the \a N -th sub or super diagonal */
+ template<int N> inline const typename DiagonalIntReturnType<N>::Type diagonal() const
+ {
+ return typename DiagonalIntReturnType<N>::BuildType(coeffs(), supers()-N, (std::max)(0,N), 1, diagonalLength(N));
+ }
+
+ /** \returns a vector expression of the \a i -th sub or super diagonal */
+ inline Block<CoefficientsType,1,Dynamic> diagonal(Index i)
+ {
+ eigen_assert((i<0 && -i<=subs()) || (i>=0 && i<=supers()));
+ return Block<CoefficientsType,1,Dynamic>(coeffs(), supers()-i, std::max<Index>(0,i), 1, diagonalLength(i));
+ }
+
+ /** \returns a vector expression of the \a i -th sub or super diagonal */
+ inline const Block<const CoefficientsType,1,Dynamic> diagonal(Index i) const
+ {
+ eigen_assert((i<0 && -i<=subs()) || (i>=0 && i<=supers()));
+ return Block<const CoefficientsType,1,Dynamic>(coeffs(), supers()-i, std::max<Index>(0,i), 1, diagonalLength(i));
+ }
+
+ template<typename Dest> inline void evalTo(Dest& dst) const
+ {
+ dst.resize(rows(),cols());
+ dst.setZero();
+ dst.diagonal() = diagonal();
+ for (Index i=1; i<=supers();++i)
+ dst.diagonal(i) = diagonal(i);
+ for (Index i=1; i<=subs();++i)
+ dst.diagonal(-i) = diagonal(-i);
+ }
+
+ DenseMatrixType toDenseMatrix() const
+ {
+ DenseMatrixType res(rows(),cols());
+ evalTo(res);
+ return res;
+ }
+
+ protected:
+
+ inline Index diagonalLength(Index i) const
+ { return i<0 ? (std::min)(cols(),rows()+i) : (std::min)(rows(),cols()-i); }
+};
+
+/**
+ * \class BandMatrix
+ * \ingroup Core_Module
+ *
+ * \brief Represents a rectangular matrix with a banded storage
+ *
+ * \tparam Scalar_ Numeric type, i.e. float, double, int
+ * \tparam Rows_ Number of rows, or \b Dynamic
+ * \tparam Cols_ Number of columns, or \b Dynamic
+ * \tparam Supers_ Number of super diagonal
+ * \tparam Subs_ Number of sub diagonal
+ * \tparam Options_ A combination of either \b #RowMajor or \b #ColMajor, and of \b #SelfAdjoint
+ * The former controls \ref TopicStorageOrders "storage order", and defaults to
+ * column-major. The latter controls whether the matrix represents a selfadjoint
+ * matrix in which case either Supers of Subs have to be null.
+ *
+ * \sa class TridiagonalMatrix
+ */
+
+template<typename Scalar_, int Rows_, int Cols_, int Supers_, int Subs_, int Options_>
+struct traits<BandMatrix<Scalar_,Rows_,Cols_,Supers_,Subs_,Options_> >
+{
+ typedef Scalar_ Scalar;
+ typedef Dense StorageKind;
+ typedef Eigen::Index StorageIndex;
+ enum {
+ CoeffReadCost = NumTraits<Scalar>::ReadCost,
+ RowsAtCompileTime = Rows_,
+ ColsAtCompileTime = Cols_,
+ MaxRowsAtCompileTime = Rows_,
+ MaxColsAtCompileTime = Cols_,
+ Flags = LvalueBit,
+ Supers = Supers_,
+ Subs = Subs_,
+ Options = Options_,
+ DataRowsAtCompileTime = ((Supers!=Dynamic) && (Subs!=Dynamic)) ? 1 + Supers + Subs : Dynamic
+ };
+ typedef Matrix<Scalar, DataRowsAtCompileTime, ColsAtCompileTime, int(Options) & int(RowMajor) ? RowMajor : ColMajor> CoefficientsType;
+};
+
+template<typename Scalar_, int Rows, int Cols, int Supers, int Subs, int Options>
+class BandMatrix : public BandMatrixBase<BandMatrix<Scalar_,Rows,Cols,Supers,Subs,Options> >
+{
+ public:
+
+ typedef typename internal::traits<BandMatrix>::Scalar Scalar;
+ typedef typename internal::traits<BandMatrix>::StorageIndex StorageIndex;
+ typedef typename internal::traits<BandMatrix>::CoefficientsType CoefficientsType;
+
+ explicit inline BandMatrix(Index rows=Rows, Index cols=Cols, Index supers=Supers, Index subs=Subs)
+ : m_coeffs(1+supers+subs,cols),
+ m_rows(rows), m_supers(supers), m_subs(subs)
+ {
+ }
+
+ /** \returns the number of columns */
+ inline EIGEN_CONSTEXPR Index rows() const { return m_rows.value(); }
+
+ /** \returns the number of rows */
+ inline EIGEN_CONSTEXPR Index cols() const { return m_coeffs.cols(); }
+
+ /** \returns the number of super diagonals */
+ inline EIGEN_CONSTEXPR Index supers() const { return m_supers.value(); }
+
+ /** \returns the number of sub diagonals */
+ inline EIGEN_CONSTEXPR Index subs() const { return m_subs.value(); }
+
+ inline const CoefficientsType& coeffs() const { return m_coeffs; }
+ inline CoefficientsType& coeffs() { return m_coeffs; }
+
+ protected:
+
+ CoefficientsType m_coeffs;
+ internal::variable_if_dynamic<Index, Rows> m_rows;
+ internal::variable_if_dynamic<Index, Supers> m_supers;
+ internal::variable_if_dynamic<Index, Subs> m_subs;
+};
+
+template<typename CoefficientsType_,int Rows_, int Cols_, int Supers_, int Subs_,int Options_>
+class BandMatrixWrapper;
+
+template<typename CoefficientsType_,int Rows_, int Cols_, int Supers_, int Subs_,int Options_>
+struct traits<BandMatrixWrapper<CoefficientsType_,Rows_,Cols_,Supers_,Subs_,Options_> >
+{
+ typedef typename CoefficientsType_::Scalar Scalar;
+ typedef typename CoefficientsType_::StorageKind StorageKind;
+ typedef typename CoefficientsType_::StorageIndex StorageIndex;
+ enum {
+ CoeffReadCost = internal::traits<CoefficientsType_>::CoeffReadCost,
+ RowsAtCompileTime = Rows_,
+ ColsAtCompileTime = Cols_,
+ MaxRowsAtCompileTime = Rows_,
+ MaxColsAtCompileTime = Cols_,
+ Flags = LvalueBit,
+ Supers = Supers_,
+ Subs = Subs_,
+ Options = Options_,
+ DataRowsAtCompileTime = ((Supers!=Dynamic) && (Subs!=Dynamic)) ? 1 + Supers + Subs : Dynamic
+ };
+ typedef CoefficientsType_ CoefficientsType;
+};
+
+template<typename CoefficientsType_,int Rows_, int Cols_, int Supers_, int Subs_,int Options_>
+class BandMatrixWrapper : public BandMatrixBase<BandMatrixWrapper<CoefficientsType_,Rows_,Cols_,Supers_,Subs_,Options_> >
+{
+ public:
+
+ typedef typename internal::traits<BandMatrixWrapper>::Scalar Scalar;
+ typedef typename internal::traits<BandMatrixWrapper>::CoefficientsType CoefficientsType;
+ typedef typename internal::traits<BandMatrixWrapper>::StorageIndex StorageIndex;
+
+ explicit inline BandMatrixWrapper(const CoefficientsType& coeffs, Index rows=Rows_, Index cols=Cols_, Index supers=Supers_, Index subs=Subs_)
+ : m_coeffs(coeffs),
+ m_rows(rows), m_supers(supers), m_subs(subs)
+ {
+ EIGEN_UNUSED_VARIABLE(cols);
+ // eigen_assert(coeffs.cols()==cols() && (supers()+subs()+1)==coeffs.rows());
+ }
+
+ /** \returns the number of columns */
+ inline EIGEN_CONSTEXPR Index rows() const { return m_rows.value(); }
+
+ /** \returns the number of rows */
+ inline EIGEN_CONSTEXPR Index cols() const { return m_coeffs.cols(); }
+
+ /** \returns the number of super diagonals */
+ inline EIGEN_CONSTEXPR Index supers() const { return m_supers.value(); }
+
+ /** \returns the number of sub diagonals */
+ inline EIGEN_CONSTEXPR Index subs() const { return m_subs.value(); }
+
+ inline const CoefficientsType& coeffs() const { return m_coeffs; }
+
+ protected:
+
+ const CoefficientsType& m_coeffs;
+ internal::variable_if_dynamic<Index, Rows_> m_rows;
+ internal::variable_if_dynamic<Index, Supers_> m_supers;
+ internal::variable_if_dynamic<Index, Subs_> m_subs;
+};
+
+/**
+ * \class TridiagonalMatrix
+ * \ingroup Core_Module
+ *
+ * \brief Represents a tridiagonal matrix with a compact banded storage
+ *
+ * \tparam Scalar Numeric type, i.e. float, double, int
+ * \tparam Size Number of rows and cols, or \b Dynamic
+ * \tparam Options Can be 0 or \b SelfAdjoint
+ *
+ * \sa class BandMatrix
+ */
+template<typename Scalar, int Size, int Options>
+class TridiagonalMatrix : public BandMatrix<Scalar,Size,Size,Options&SelfAdjoint?0:1,1,Options|RowMajor>
+{
+ typedef BandMatrix<Scalar,Size,Size,Options&SelfAdjoint?0:1,1,Options|RowMajor> Base;
+ typedef typename Base::StorageIndex StorageIndex;
+ public:
+ explicit TridiagonalMatrix(Index size = Size) : Base(size,size,Options&SelfAdjoint?0:1,1) {}
+
+ inline typename Base::template DiagonalIntReturnType<1>::Type super()
+ { return Base::template diagonal<1>(); }
+ inline const typename Base::template DiagonalIntReturnType<1>::Type super() const
+ { return Base::template diagonal<1>(); }
+ inline typename Base::template DiagonalIntReturnType<-1>::Type sub()
+ { return Base::template diagonal<-1>(); }
+ inline const typename Base::template DiagonalIntReturnType<-1>::Type sub() const
+ { return Base::template diagonal<-1>(); }
+ protected:
+};
+
+
+struct BandShape {};
+
+template<typename Scalar_, int Rows_, int Cols_, int Supers_, int Subs_, int Options_>
+struct evaluator_traits<BandMatrix<Scalar_,Rows_,Cols_,Supers_,Subs_,Options_> >
+ : public evaluator_traits_base<BandMatrix<Scalar_,Rows_,Cols_,Supers_,Subs_,Options_> >
+{
+ typedef BandShape Shape;
+};
+
+template<typename CoefficientsType_,int Rows_, int Cols_, int Supers_, int Subs_,int Options_>
+struct evaluator_traits<BandMatrixWrapper<CoefficientsType_,Rows_,Cols_,Supers_,Subs_,Options_> >
+ : public evaluator_traits_base<BandMatrixWrapper<CoefficientsType_,Rows_,Cols_,Supers_,Subs_,Options_> >
+{
+ typedef BandShape Shape;
+};
+
+template<> struct AssignmentKind<DenseShape,BandShape> { typedef EigenBase2EigenBase Kind; };
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_BANDMATRIX_H
diff --git a/Eigen/src/Core/Block.h b/Eigen/src/Core/Block.h
new file mode 100644
index 0000000..19c4b68
--- /dev/null
+++ b/Eigen/src/Core/Block.h
@@ -0,0 +1,450 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2006-2010 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_BLOCK_H
+#define EIGEN_BLOCK_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+template<typename XprType, int BlockRows, int BlockCols, bool InnerPanel>
+struct traits<Block<XprType, BlockRows, BlockCols, InnerPanel> > : traits<XprType>
+{
+ typedef typename traits<XprType>::Scalar Scalar;
+ typedef typename traits<XprType>::StorageKind StorageKind;
+ typedef typename traits<XprType>::XprKind XprKind;
+ typedef typename ref_selector<XprType>::type XprTypeNested;
+ typedef std::remove_reference_t<XprTypeNested> XprTypeNested_;
+ enum{
+ MatrixRows = traits<XprType>::RowsAtCompileTime,
+ MatrixCols = traits<XprType>::ColsAtCompileTime,
+ RowsAtCompileTime = MatrixRows == 0 ? 0 : BlockRows,
+ ColsAtCompileTime = MatrixCols == 0 ? 0 : BlockCols,
+ MaxRowsAtCompileTime = BlockRows==0 ? 0
+ : RowsAtCompileTime != Dynamic ? int(RowsAtCompileTime)
+ : int(traits<XprType>::MaxRowsAtCompileTime),
+ MaxColsAtCompileTime = BlockCols==0 ? 0
+ : ColsAtCompileTime != Dynamic ? int(ColsAtCompileTime)
+ : int(traits<XprType>::MaxColsAtCompileTime),
+
+ XprTypeIsRowMajor = (int(traits<XprType>::Flags)&RowMajorBit) != 0,
+ IsRowMajor = (MaxRowsAtCompileTime==1&&MaxColsAtCompileTime!=1) ? 1
+ : (MaxColsAtCompileTime==1&&MaxRowsAtCompileTime!=1) ? 0
+ : XprTypeIsRowMajor,
+ HasSameStorageOrderAsXprType = (IsRowMajor == XprTypeIsRowMajor),
+ InnerSize = IsRowMajor ? int(ColsAtCompileTime) : int(RowsAtCompileTime),
+ InnerStrideAtCompileTime = HasSameStorageOrderAsXprType
+ ? int(inner_stride_at_compile_time<XprType>::ret)
+ : int(outer_stride_at_compile_time<XprType>::ret),
+ OuterStrideAtCompileTime = HasSameStorageOrderAsXprType
+ ? int(outer_stride_at_compile_time<XprType>::ret)
+ : int(inner_stride_at_compile_time<XprType>::ret),
+
+ // FIXME, this traits is rather specialized for dense object and it needs to be cleaned further
+ FlagsLvalueBit = is_lvalue<XprType>::value ? LvalueBit : 0,
+ FlagsRowMajorBit = IsRowMajor ? RowMajorBit : 0,
+ Flags = (traits<XprType>::Flags & (DirectAccessBit | (InnerPanel?CompressedAccessBit:0))) | FlagsLvalueBit | FlagsRowMajorBit,
+ // FIXME DirectAccessBit should not be handled by expressions
+ //
+ // Alignment is needed by MapBase's assertions
+ // We can sefely set it to false here. Internal alignment errors will be detected by an eigen_internal_assert in the respective evaluator
+ Alignment = 0
+ };
+};
+
+template<typename XprType, int BlockRows=Dynamic, int BlockCols=Dynamic, bool InnerPanel = false,
+ bool HasDirectAccess = internal::has_direct_access<XprType>::ret> class BlockImpl_dense;
+
+} // end namespace internal
+
+template<typename XprType, int BlockRows, int BlockCols, bool InnerPanel, typename StorageKind> class BlockImpl;
+
+/** \class Block
+ * \ingroup Core_Module
+ *
+ * \brief Expression of a fixed-size or dynamic-size block
+ *
+ * \tparam XprType the type of the expression in which we are taking a block
+ * \tparam BlockRows the number of rows of the block we are taking at compile time (optional)
+ * \tparam BlockCols the number of columns of the block we are taking at compile time (optional)
+ * \tparam InnerPanel is true, if the block maps to a set of rows of a row major matrix or
+ * to set of columns of a column major matrix (optional). The parameter allows to determine
+ * at compile time whether aligned access is possible on the block expression.
+ *
+ * This class represents an expression of either a fixed-size or dynamic-size block. It is the return
+ * type of DenseBase::block(Index,Index,Index,Index) and DenseBase::block<int,int>(Index,Index) and
+ * most of the time this is the only way it is used.
+ *
+ * However, if you want to directly maniputate block expressions,
+ * for instance if you want to write a function returning such an expression, you
+ * will need to use this class.
+ *
+ * Here is an example illustrating the dynamic case:
+ * \include class_Block.cpp
+ * Output: \verbinclude class_Block.out
+ *
+ * \note Even though this expression has dynamic size, in the case where \a XprType
+ * has fixed size, this expression inherits a fixed maximal size which means that evaluating
+ * it does not cause a dynamic memory allocation.
+ *
+ * Here is an example illustrating the fixed-size case:
+ * \include class_FixedBlock.cpp
+ * Output: \verbinclude class_FixedBlock.out
+ *
+ * \sa DenseBase::block(Index,Index,Index,Index), DenseBase::block(Index,Index), class VectorBlock
+ */
+template<typename XprType, int BlockRows, int BlockCols, bool InnerPanel> class Block
+ : public BlockImpl<XprType, BlockRows, BlockCols, InnerPanel, typename internal::traits<XprType>::StorageKind>
+{
+ typedef BlockImpl<XprType, BlockRows, BlockCols, InnerPanel, typename internal::traits<XprType>::StorageKind> Impl;
+ public:
+ //typedef typename Impl::Base Base;
+ typedef Impl Base;
+ EIGEN_GENERIC_PUBLIC_INTERFACE(Block)
+ EIGEN_INHERIT_ASSIGNMENT_OPERATORS(Block)
+
+ typedef internal::remove_all_t<XprType> NestedExpression;
+
+ /** Column or Row constructor
+ */
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ Block(XprType& xpr, Index i) : Impl(xpr,i)
+ {
+ eigen_assert( (i>=0) && (
+ ((BlockRows==1) && (BlockCols==XprType::ColsAtCompileTime) && i<xpr.rows())
+ ||((BlockRows==XprType::RowsAtCompileTime) && (BlockCols==1) && i<xpr.cols())));
+ }
+
+ /** Fixed-size constructor
+ */
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ Block(XprType& xpr, Index startRow, Index startCol)
+ : Impl(xpr, startRow, startCol)
+ {
+ EIGEN_STATIC_ASSERT(RowsAtCompileTime!=Dynamic && ColsAtCompileTime!=Dynamic,THIS_METHOD_IS_ONLY_FOR_FIXED_SIZE)
+ eigen_assert(startRow >= 0 && BlockRows >= 0 && startRow + BlockRows <= xpr.rows()
+ && startCol >= 0 && BlockCols >= 0 && startCol + BlockCols <= xpr.cols());
+ }
+
+ /** Dynamic-size constructor
+ */
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ Block(XprType& xpr,
+ Index startRow, Index startCol,
+ Index blockRows, Index blockCols)
+ : Impl(xpr, startRow, startCol, blockRows, blockCols)
+ {
+ eigen_assert((RowsAtCompileTime==Dynamic || RowsAtCompileTime==blockRows)
+ && (ColsAtCompileTime==Dynamic || ColsAtCompileTime==blockCols));
+ eigen_assert(startRow >= 0 && blockRows >= 0 && startRow <= xpr.rows() - blockRows
+ && startCol >= 0 && blockCols >= 0 && startCol <= xpr.cols() - blockCols);
+ }
+};
+
+// The generic default implementation for dense block simplu forward to the internal::BlockImpl_dense
+// that must be specialized for direct and non-direct access...
+template<typename XprType, int BlockRows, int BlockCols, bool InnerPanel>
+class BlockImpl<XprType, BlockRows, BlockCols, InnerPanel, Dense>
+ : public internal::BlockImpl_dense<XprType, BlockRows, BlockCols, InnerPanel>
+{
+ typedef internal::BlockImpl_dense<XprType, BlockRows, BlockCols, InnerPanel> Impl;
+ typedef typename XprType::StorageIndex StorageIndex;
+ public:
+ typedef Impl Base;
+ EIGEN_INHERIT_ASSIGNMENT_OPERATORS(BlockImpl)
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE BlockImpl(XprType& xpr, Index i) : Impl(xpr,i) {}
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE BlockImpl(XprType& xpr, Index startRow, Index startCol) : Impl(xpr, startRow, startCol) {}
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE BlockImpl(XprType& xpr, Index startRow, Index startCol, Index blockRows, Index blockCols)
+ : Impl(xpr, startRow, startCol, blockRows, blockCols) {}
+};
+
+namespace internal {
+
+/** \internal Internal implementation of dense Blocks in the general case. */
+template<typename XprType, int BlockRows, int BlockCols, bool InnerPanel, bool HasDirectAccess> class BlockImpl_dense
+ : public internal::dense_xpr_base<Block<XprType, BlockRows, BlockCols, InnerPanel> >::type
+{
+ typedef Block<XprType, BlockRows, BlockCols, InnerPanel> BlockType;
+ typedef typename internal::ref_selector<XprType>::non_const_type XprTypeNested;
+ public:
+
+ typedef typename internal::dense_xpr_base<BlockType>::type Base;
+ EIGEN_DENSE_PUBLIC_INTERFACE(BlockType)
+ EIGEN_INHERIT_ASSIGNMENT_OPERATORS(BlockImpl_dense)
+
+ // class InnerIterator; // FIXME apparently never used
+
+ /** Column or Row constructor
+ */
+ EIGEN_DEVICE_FUNC
+ inline BlockImpl_dense(XprType& xpr, Index i)
+ : m_xpr(xpr),
+ // It is a row if and only if BlockRows==1 and BlockCols==XprType::ColsAtCompileTime,
+ // and it is a column if and only if BlockRows==XprType::RowsAtCompileTime and BlockCols==1,
+ // all other cases are invalid.
+ // The case a 1x1 matrix seems ambiguous, but the result is the same anyway.
+ m_startRow( (BlockRows==1) && (BlockCols==XprType::ColsAtCompileTime) ? i : 0),
+ m_startCol( (BlockRows==XprType::RowsAtCompileTime) && (BlockCols==1) ? i : 0),
+ m_blockRows(BlockRows==1 ? 1 : xpr.rows()),
+ m_blockCols(BlockCols==1 ? 1 : xpr.cols())
+ {}
+
+ /** Fixed-size constructor
+ */
+ EIGEN_DEVICE_FUNC
+ inline BlockImpl_dense(XprType& xpr, Index startRow, Index startCol)
+ : m_xpr(xpr), m_startRow(startRow), m_startCol(startCol),
+ m_blockRows(BlockRows), m_blockCols(BlockCols)
+ {}
+
+ /** Dynamic-size constructor
+ */
+ EIGEN_DEVICE_FUNC
+ inline BlockImpl_dense(XprType& xpr,
+ Index startRow, Index startCol,
+ Index blockRows, Index blockCols)
+ : m_xpr(xpr), m_startRow(startRow), m_startCol(startCol),
+ m_blockRows(blockRows), m_blockCols(blockCols)
+ {}
+
+ EIGEN_DEVICE_FUNC inline Index rows() const { return m_blockRows.value(); }
+ EIGEN_DEVICE_FUNC inline Index cols() const { return m_blockCols.value(); }
+
+ EIGEN_DEVICE_FUNC
+ inline Scalar& coeffRef(Index rowId, Index colId)
+ {
+ EIGEN_STATIC_ASSERT_LVALUE(XprType)
+ return m_xpr.coeffRef(rowId + m_startRow.value(), colId + m_startCol.value());
+ }
+
+ EIGEN_DEVICE_FUNC
+ inline const Scalar& coeffRef(Index rowId, Index colId) const
+ {
+ return m_xpr.derived().coeffRef(rowId + m_startRow.value(), colId + m_startCol.value());
+ }
+
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE const CoeffReturnType coeff(Index rowId, Index colId) const
+ {
+ return m_xpr.coeff(rowId + m_startRow.value(), colId + m_startCol.value());
+ }
+
+ EIGEN_DEVICE_FUNC
+ inline Scalar& coeffRef(Index index)
+ {
+ EIGEN_STATIC_ASSERT_LVALUE(XprType)
+ return m_xpr.coeffRef(m_startRow.value() + (RowsAtCompileTime == 1 ? 0 : index),
+ m_startCol.value() + (RowsAtCompileTime == 1 ? index : 0));
+ }
+
+ EIGEN_DEVICE_FUNC
+ inline const Scalar& coeffRef(Index index) const
+ {
+ return m_xpr.coeffRef(m_startRow.value() + (RowsAtCompileTime == 1 ? 0 : index),
+ m_startCol.value() + (RowsAtCompileTime == 1 ? index : 0));
+ }
+
+ EIGEN_DEVICE_FUNC
+ inline const CoeffReturnType coeff(Index index) const
+ {
+ return m_xpr.coeff(m_startRow.value() + (RowsAtCompileTime == 1 ? 0 : index),
+ m_startCol.value() + (RowsAtCompileTime == 1 ? index : 0));
+ }
+
+ template<int LoadMode>
+ EIGEN_DEVICE_FUNC inline PacketScalar packet(Index rowId, Index colId) const
+ {
+ return m_xpr.template packet<Unaligned>(rowId + m_startRow.value(), colId + m_startCol.value());
+ }
+
+ template<int LoadMode>
+ EIGEN_DEVICE_FUNC inline void writePacket(Index rowId, Index colId, const PacketScalar& val)
+ {
+ m_xpr.template writePacket<Unaligned>(rowId + m_startRow.value(), colId + m_startCol.value(), val);
+ }
+
+ template<int LoadMode>
+ EIGEN_DEVICE_FUNC inline PacketScalar packet(Index index) const
+ {
+ return m_xpr.template packet<Unaligned>
+ (m_startRow.value() + (RowsAtCompileTime == 1 ? 0 : index),
+ m_startCol.value() + (RowsAtCompileTime == 1 ? index : 0));
+ }
+
+ template<int LoadMode>
+ EIGEN_DEVICE_FUNC inline void writePacket(Index index, const PacketScalar& val)
+ {
+ m_xpr.template writePacket<Unaligned>
+ (m_startRow.value() + (RowsAtCompileTime == 1 ? 0 : index),
+ m_startCol.value() + (RowsAtCompileTime == 1 ? index : 0), val);
+ }
+
+ #ifdef EIGEN_PARSED_BY_DOXYGEN
+ /** \sa MapBase::data() */
+ EIGEN_DEVICE_FUNC inline const Scalar* data() const;
+ EIGEN_DEVICE_FUNC inline Index innerStride() const;
+ EIGEN_DEVICE_FUNC inline Index outerStride() const;
+ #endif
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ const internal::remove_all_t<XprTypeNested>& nestedExpression() const
+ {
+ return m_xpr;
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ XprType& nestedExpression() { return m_xpr; }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE EIGEN_CONSTEXPR
+ StorageIndex startRow() const EIGEN_NOEXCEPT
+ {
+ return m_startRow.value();
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE EIGEN_CONSTEXPR
+ StorageIndex startCol() const EIGEN_NOEXCEPT
+ {
+ return m_startCol.value();
+ }
+
+ protected:
+
+ XprTypeNested m_xpr;
+ const internal::variable_if_dynamic<StorageIndex, (XprType::RowsAtCompileTime == 1 && BlockRows==1) ? 0 : Dynamic> m_startRow;
+ const internal::variable_if_dynamic<StorageIndex, (XprType::ColsAtCompileTime == 1 && BlockCols==1) ? 0 : Dynamic> m_startCol;
+ const internal::variable_if_dynamic<StorageIndex, RowsAtCompileTime> m_blockRows;
+ const internal::variable_if_dynamic<StorageIndex, ColsAtCompileTime> m_blockCols;
+};
+
+/** \internal Internal implementation of dense Blocks in the direct access case.*/
+template<typename XprType, int BlockRows, int BlockCols, bool InnerPanel>
+class BlockImpl_dense<XprType,BlockRows,BlockCols, InnerPanel,true>
+ : public MapBase<Block<XprType, BlockRows, BlockCols, InnerPanel> >
+{
+ typedef Block<XprType, BlockRows, BlockCols, InnerPanel> BlockType;
+ typedef typename internal::ref_selector<XprType>::non_const_type XprTypeNested;
+ enum {
+ XprTypeIsRowMajor = (int(traits<XprType>::Flags)&RowMajorBit) != 0
+ };
+ public:
+
+ typedef MapBase<BlockType> Base;
+ EIGEN_DENSE_PUBLIC_INTERFACE(BlockType)
+ EIGEN_INHERIT_ASSIGNMENT_OPERATORS(BlockImpl_dense)
+
+ /** Column or Row constructor
+ */
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ BlockImpl_dense(XprType& xpr, Index i)
+ : Base(xpr.data() + i * ( ((BlockRows==1) && (BlockCols==XprType::ColsAtCompileTime) && (!XprTypeIsRowMajor))
+ || ((BlockRows==XprType::RowsAtCompileTime) && (BlockCols==1) && ( XprTypeIsRowMajor)) ? xpr.innerStride() : xpr.outerStride()),
+ BlockRows==1 ? 1 : xpr.rows(),
+ BlockCols==1 ? 1 : xpr.cols()),
+ m_xpr(xpr),
+ m_startRow( (BlockRows==1) && (BlockCols==XprType::ColsAtCompileTime) ? i : 0),
+ m_startCol( (BlockRows==XprType::RowsAtCompileTime) && (BlockCols==1) ? i : 0)
+ {
+ init();
+ }
+
+ /** Fixed-size constructor
+ */
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ BlockImpl_dense(XprType& xpr, Index startRow, Index startCol)
+ : Base(xpr.data()+xpr.innerStride()*(XprTypeIsRowMajor?startCol:startRow) + xpr.outerStride()*(XprTypeIsRowMajor?startRow:startCol)),
+ m_xpr(xpr), m_startRow(startRow), m_startCol(startCol)
+ {
+ init();
+ }
+
+ /** Dynamic-size constructor
+ */
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ BlockImpl_dense(XprType& xpr,
+ Index startRow, Index startCol,
+ Index blockRows, Index blockCols)
+ : Base(xpr.data()+xpr.innerStride()*(XprTypeIsRowMajor?startCol:startRow) + xpr.outerStride()*(XprTypeIsRowMajor?startRow:startCol), blockRows, blockCols),
+ m_xpr(xpr), m_startRow(startRow), m_startCol(startCol)
+ {
+ init();
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ const internal::remove_all_t<XprTypeNested>& nestedExpression() const EIGEN_NOEXCEPT
+ {
+ return m_xpr;
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ XprType& nestedExpression() { return m_xpr; }
+
+ /** \sa MapBase::innerStride() */
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE EIGEN_CONSTEXPR
+ Index innerStride() const EIGEN_NOEXCEPT
+ {
+ return internal::traits<BlockType>::HasSameStorageOrderAsXprType
+ ? m_xpr.innerStride()
+ : m_xpr.outerStride();
+ }
+
+ /** \sa MapBase::outerStride() */
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE EIGEN_CONSTEXPR
+ Index outerStride() const EIGEN_NOEXCEPT
+ {
+ return internal::traits<BlockType>::HasSameStorageOrderAsXprType
+ ? m_xpr.outerStride()
+ : m_xpr.innerStride();
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE EIGEN_CONSTEXPR
+ StorageIndex startRow() const EIGEN_NOEXCEPT { return m_startRow.value(); }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE EIGEN_CONSTEXPR
+ StorageIndex startCol() const EIGEN_NOEXCEPT { return m_startCol.value(); }
+
+ #ifndef __SUNPRO_CC
+ // FIXME sunstudio is not friendly with the above friend...
+ // META-FIXME there is no 'friend' keyword around here. Is this obsolete?
+ protected:
+ #endif
+
+ #ifndef EIGEN_PARSED_BY_DOXYGEN
+ /** \internal used by allowAligned() */
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ BlockImpl_dense(XprType& xpr, const Scalar* data, Index blockRows, Index blockCols)
+ : Base(data, blockRows, blockCols), m_xpr(xpr)
+ {
+ init();
+ }
+ #endif
+
+ protected:
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ void init()
+ {
+ m_outerStride = internal::traits<BlockType>::HasSameStorageOrderAsXprType
+ ? m_xpr.outerStride()
+ : m_xpr.innerStride();
+ }
+
+ XprTypeNested m_xpr;
+ const internal::variable_if_dynamic<StorageIndex, (XprType::RowsAtCompileTime == 1 && BlockRows==1) ? 0 : Dynamic> m_startRow;
+ const internal::variable_if_dynamic<StorageIndex, (XprType::ColsAtCompileTime == 1 && BlockCols==1) ? 0 : Dynamic> m_startCol;
+ Index m_outerStride;
+};
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_BLOCK_H
diff --git a/Eigen/src/Core/BooleanRedux.h b/Eigen/src/Core/BooleanRedux.h
new file mode 100644
index 0000000..20e5bd9
--- /dev/null
+++ b/Eigen/src/Core/BooleanRedux.h
@@ -0,0 +1,166 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_ALLANDANY_H
+#define EIGEN_ALLANDANY_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+
+template<typename Derived, int UnrollCount, int InnerSize>
+struct all_unroller
+{
+ enum {
+ IsRowMajor = (int(Derived::Flags) & int(RowMajor)),
+ i = (UnrollCount-1) / InnerSize,
+ j = (UnrollCount-1) % InnerSize
+ };
+
+ EIGEN_DEVICE_FUNC static inline bool run(const Derived &mat)
+ {
+ return all_unroller<Derived, UnrollCount-1, InnerSize>::run(mat) && mat.coeff(IsRowMajor ? i : j, IsRowMajor ? j : i);
+ }
+};
+
+template<typename Derived, int InnerSize>
+struct all_unroller<Derived, 0, InnerSize>
+{
+ EIGEN_DEVICE_FUNC static inline bool run(const Derived &/*mat*/) { return true; }
+};
+
+template<typename Derived, int InnerSize>
+struct all_unroller<Derived, Dynamic, InnerSize>
+{
+ EIGEN_DEVICE_FUNC static inline bool run(const Derived &) { return false; }
+};
+
+template<typename Derived, int UnrollCount, int InnerSize>
+struct any_unroller
+{
+ enum {
+ IsRowMajor = (int(Derived::Flags) & int(RowMajor)),
+ i = (UnrollCount-1) / InnerSize,
+ j = (UnrollCount-1) % InnerSize
+ };
+
+ EIGEN_DEVICE_FUNC static inline bool run(const Derived &mat)
+ {
+ return any_unroller<Derived, UnrollCount-1, InnerSize>::run(mat) || mat.coeff(IsRowMajor ? i : j, IsRowMajor ? j : i);
+ }
+};
+
+template<typename Derived, int InnerSize>
+struct any_unroller<Derived, 0, InnerSize>
+{
+ EIGEN_DEVICE_FUNC static inline bool run(const Derived & /*mat*/) { return false; }
+};
+
+template<typename Derived, int InnerSize>
+struct any_unroller<Derived, Dynamic, InnerSize>
+{
+ EIGEN_DEVICE_FUNC static inline bool run(const Derived &) { return false; }
+};
+
+} // end namespace internal
+
+/** \returns true if all coefficients are true
+ *
+ * Example: \include MatrixBase_all.cpp
+ * Output: \verbinclude MatrixBase_all.out
+ *
+ * \sa any(), Cwise::operator<()
+ */
+template<typename Derived>
+EIGEN_DEVICE_FUNC inline bool DenseBase<Derived>::all() const
+{
+ typedef internal::evaluator<Derived> Evaluator;
+ enum {
+ unroll = SizeAtCompileTime != Dynamic
+ && SizeAtCompileTime * (int(Evaluator::CoeffReadCost) + int(NumTraits<Scalar>::AddCost)) <= EIGEN_UNROLLING_LIMIT,
+ };
+ Evaluator evaluator(derived());
+ if(unroll)
+ return internal::all_unroller<Evaluator, unroll ? int(SizeAtCompileTime) : Dynamic, InnerSizeAtCompileTime>::run(evaluator);
+ else
+ {
+ for(Index i = 0; i < derived().outerSize(); ++i)
+ for(Index j = 0; j < derived().innerSize(); ++j)
+ if (!evaluator.coeff(IsRowMajor ? i : j, IsRowMajor ? j : i)) return false;
+ return true;
+ }
+}
+
+/** \returns true if at least one coefficient is true
+ *
+ * \sa all()
+ */
+template<typename Derived>
+EIGEN_DEVICE_FUNC inline bool DenseBase<Derived>::any() const
+{
+ typedef internal::evaluator<Derived> Evaluator;
+ enum {
+ unroll = SizeAtCompileTime != Dynamic
+ && SizeAtCompileTime * (int(Evaluator::CoeffReadCost) + int(NumTraits<Scalar>::AddCost)) <= EIGEN_UNROLLING_LIMIT,
+ };
+ Evaluator evaluator(derived());
+ if(unroll)
+ return internal::any_unroller<Evaluator, unroll ? int(SizeAtCompileTime) : Dynamic, InnerSizeAtCompileTime>::run(evaluator);
+ else
+ {
+ for(Index i = 0; i < derived().outerSize(); ++i)
+ for(Index j = 0; j < derived().innerSize(); ++j)
+ if (evaluator.coeff(IsRowMajor ? i : j, IsRowMajor ? j : i)) return true;
+ return false;
+ }
+}
+
+/** \returns the number of coefficients which evaluate to true
+ *
+ * \sa all(), any()
+ */
+template<typename Derived>
+EIGEN_DEVICE_FUNC inline Eigen::Index DenseBase<Derived>::count() const
+{
+ return derived().template cast<bool>().template cast<Index>().sum();
+}
+
+/** \returns true is \c *this contains at least one Not A Number (NaN).
+ *
+ * \sa allFinite()
+ */
+template<typename Derived>
+EIGEN_DEVICE_FUNC inline bool DenseBase<Derived>::hasNaN() const
+{
+#if EIGEN_COMP_MSVC || (defined __FAST_MATH__)
+ return derived().array().isNaN().any();
+#else
+ return !((derived().array()==derived().array()).all());
+#endif
+}
+
+/** \returns true if \c *this contains only finite numbers, i.e., no NaN and no +/-INF values.
+ *
+ * \sa hasNaN()
+ */
+template<typename Derived>
+EIGEN_DEVICE_FUNC inline bool DenseBase<Derived>::allFinite() const
+{
+#if EIGEN_COMP_MSVC || (defined __FAST_MATH__)
+ return derived().array().isFinite().all();
+#else
+ return !((derived()-derived()).hasNaN());
+#endif
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_ALLANDANY_H
diff --git a/Eigen/src/Core/CommaInitializer.h b/Eigen/src/Core/CommaInitializer.h
new file mode 100644
index 0000000..7c2eea8
--- /dev/null
+++ b/Eigen/src/Core/CommaInitializer.h
@@ -0,0 +1,166 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_COMMAINITIALIZER_H
+#define EIGEN_COMMAINITIALIZER_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+/** \class CommaInitializer
+ * \ingroup Core_Module
+ *
+ * \brief Helper class used by the comma initializer operator
+ *
+ * This class is internally used to implement the comma initializer feature. It is
+ * the return type of MatrixBase::operator<<, and most of the time this is the only
+ * way it is used.
+ *
+ * \sa \blank \ref MatrixBaseCommaInitRef "MatrixBase::operator<<", CommaInitializer::finished()
+ */
+template<typename XprType>
+struct CommaInitializer
+{
+ typedef typename XprType::Scalar Scalar;
+
+ EIGEN_DEVICE_FUNC
+ inline CommaInitializer(XprType& xpr, const Scalar& s)
+ : m_xpr(xpr), m_row(0), m_col(1), m_currentBlockRows(1)
+ {
+ eigen_assert(m_xpr.rows() > 0 && m_xpr.cols() > 0
+ && "Cannot comma-initialize a 0x0 matrix (operator<<)");
+ m_xpr.coeffRef(0,0) = s;
+ }
+
+ template<typename OtherDerived>
+ EIGEN_DEVICE_FUNC
+ inline CommaInitializer(XprType& xpr, const DenseBase<OtherDerived>& other)
+ : m_xpr(xpr), m_row(0), m_col(other.cols()), m_currentBlockRows(other.rows())
+ {
+ eigen_assert(m_xpr.rows() >= other.rows() && m_xpr.cols() >= other.cols()
+ && "Cannot comma-initialize a 0x0 matrix (operator<<)");
+ m_xpr.template block<OtherDerived::RowsAtCompileTime, OtherDerived::ColsAtCompileTime>(0, 0, other.rows(), other.cols()) = other;
+ }
+
+ /* Copy/Move constructor which transfers ownership. This is crucial in
+ * absence of return value optimization to avoid assertions during destruction. */
+ // FIXME in C++11 mode this could be replaced by a proper RValue constructor
+ EIGEN_DEVICE_FUNC
+ inline CommaInitializer(const CommaInitializer& o)
+ : m_xpr(o.m_xpr), m_row(o.m_row), m_col(o.m_col), m_currentBlockRows(o.m_currentBlockRows) {
+ // Mark original object as finished. In absence of R-value references we need to const_cast:
+ const_cast<CommaInitializer&>(o).m_row = m_xpr.rows();
+ const_cast<CommaInitializer&>(o).m_col = m_xpr.cols();
+ const_cast<CommaInitializer&>(o).m_currentBlockRows = 0;
+ }
+
+ /* inserts a scalar value in the target matrix */
+ EIGEN_DEVICE_FUNC
+ CommaInitializer& operator,(const Scalar& s)
+ {
+ if (m_col==m_xpr.cols())
+ {
+ m_row+=m_currentBlockRows;
+ m_col = 0;
+ m_currentBlockRows = 1;
+ eigen_assert(m_row<m_xpr.rows()
+ && "Too many rows passed to comma initializer (operator<<)");
+ }
+ eigen_assert(m_col<m_xpr.cols()
+ && "Too many coefficients passed to comma initializer (operator<<)");
+ eigen_assert(m_currentBlockRows==1);
+ m_xpr.coeffRef(m_row, m_col++) = s;
+ return *this;
+ }
+
+ /* inserts a matrix expression in the target matrix */
+ template<typename OtherDerived>
+ EIGEN_DEVICE_FUNC
+ CommaInitializer& operator,(const DenseBase<OtherDerived>& other)
+ {
+ if (m_col==m_xpr.cols() && (other.cols()!=0 || other.rows()!=m_currentBlockRows))
+ {
+ m_row+=m_currentBlockRows;
+ m_col = 0;
+ m_currentBlockRows = other.rows();
+ eigen_assert(m_row+m_currentBlockRows<=m_xpr.rows()
+ && "Too many rows passed to comma initializer (operator<<)");
+ }
+ eigen_assert((m_col + other.cols() <= m_xpr.cols())
+ && "Too many coefficients passed to comma initializer (operator<<)");
+ eigen_assert(m_currentBlockRows==other.rows());
+ m_xpr.template block<OtherDerived::RowsAtCompileTime, OtherDerived::ColsAtCompileTime>
+ (m_row, m_col, other.rows(), other.cols()) = other;
+ m_col += other.cols();
+ return *this;
+ }
+
+ EIGEN_DEVICE_FUNC
+ inline ~CommaInitializer()
+#if defined VERIFY_RAISES_ASSERT && (!defined EIGEN_NO_ASSERTION_CHECKING) && defined EIGEN_EXCEPTIONS
+ EIGEN_EXCEPTION_SPEC(Eigen::eigen_assert_exception)
+#endif
+ {
+ finished();
+ }
+
+ /** \returns the built matrix once all its coefficients have been set.
+ * Calling finished is 100% optional. Its purpose is to write expressions
+ * like this:
+ * \code
+ * quaternion.fromRotationMatrix((Matrix3f() << axis0, axis1, axis2).finished());
+ * \endcode
+ */
+ EIGEN_DEVICE_FUNC
+ inline XprType& finished() {
+ eigen_assert(((m_row+m_currentBlockRows) == m_xpr.rows() || m_xpr.cols() == 0)
+ && m_col == m_xpr.cols()
+ && "Too few coefficients passed to comma initializer (operator<<)");
+ return m_xpr;
+ }
+
+ XprType& m_xpr; // target expression
+ Index m_row; // current row id
+ Index m_col; // current col id
+ Index m_currentBlockRows; // current block height
+};
+
+/** \anchor MatrixBaseCommaInitRef
+ * Convenient operator to set the coefficients of a matrix.
+ *
+ * The coefficients must be provided in a row major order and exactly match
+ * the size of the matrix. Otherwise an assertion is raised.
+ *
+ * Example: \include MatrixBase_set.cpp
+ * Output: \verbinclude MatrixBase_set.out
+ *
+ * \note According the c++ standard, the argument expressions of this comma initializer are evaluated in arbitrary order.
+ *
+ * \sa CommaInitializer::finished(), class CommaInitializer
+ */
+template<typename Derived>
+EIGEN_DEVICE_FUNC inline CommaInitializer<Derived> DenseBase<Derived>::operator<< (const Scalar& s)
+{
+ return CommaInitializer<Derived>(*static_cast<Derived*>(this), s);
+}
+
+/** \sa operator<<(const Scalar&) */
+template<typename Derived>
+template<typename OtherDerived>
+EIGEN_DEVICE_FUNC inline CommaInitializer<Derived>
+DenseBase<Derived>::operator<<(const DenseBase<OtherDerived>& other)
+{
+ return CommaInitializer<Derived>(*static_cast<Derived *>(this), other);
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_COMMAINITIALIZER_H
diff --git a/Eigen/src/Core/ConditionEstimator.h b/Eigen/src/Core/ConditionEstimator.h
new file mode 100644
index 0000000..694be8b
--- /dev/null
+++ b/Eigen/src/Core/ConditionEstimator.h
@@ -0,0 +1,177 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2016 Rasmus Munk Larsen (rmlarsen@google.com)
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_CONDITIONESTIMATOR_H
+#define EIGEN_CONDITIONESTIMATOR_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+
+template <typename Vector, typename RealVector, bool IsComplex>
+struct rcond_compute_sign {
+ static inline Vector run(const Vector& v) {
+ const RealVector v_abs = v.cwiseAbs();
+ return (v_abs.array() == static_cast<typename Vector::RealScalar>(0))
+ .select(Vector::Ones(v.size()), v.cwiseQuotient(v_abs));
+ }
+};
+
+// Partial specialization to avoid elementwise division for real vectors.
+template <typename Vector>
+struct rcond_compute_sign<Vector, Vector, false> {
+ static inline Vector run(const Vector& v) {
+ return (v.array() < static_cast<typename Vector::RealScalar>(0))
+ .select(-Vector::Ones(v.size()), Vector::Ones(v.size()));
+ }
+};
+
+/**
+ * \returns an estimate of ||inv(matrix)||_1 given a decomposition of
+ * \a matrix that implements .solve() and .adjoint().solve() methods.
+ *
+ * This function implements Algorithms 4.1 and 5.1 from
+ * http://www.maths.manchester.ac.uk/~higham/narep/narep135.pdf
+ * which also forms the basis for the condition number estimators in
+ * LAPACK. Since at most 10 calls to the solve method of dec are
+ * performed, the total cost is O(dims^2), as opposed to O(dims^3)
+ * needed to compute the inverse matrix explicitly.
+ *
+ * The most common usage is in estimating the condition number
+ * ||matrix||_1 * ||inv(matrix)||_1. The first term ||matrix||_1 can be
+ * computed directly in O(n^2) operations.
+ *
+ * Supports the following decompositions: FullPivLU, PartialPivLU, LDLT, and
+ * LLT.
+ *
+ * \sa FullPivLU, PartialPivLU, LDLT, LLT.
+ */
+template <typename Decomposition>
+typename Decomposition::RealScalar rcond_invmatrix_L1_norm_estimate(const Decomposition& dec)
+{
+ typedef typename Decomposition::MatrixType MatrixType;
+ typedef typename Decomposition::Scalar Scalar;
+ typedef typename Decomposition::RealScalar RealScalar;
+ typedef typename internal::plain_col_type<MatrixType>::type Vector;
+ typedef typename internal::plain_col_type<MatrixType, RealScalar>::type RealVector;
+ const bool is_complex = (NumTraits<Scalar>::IsComplex != 0);
+
+ eigen_assert(dec.rows() == dec.cols());
+ const Index n = dec.rows();
+ if (n == 0)
+ return 0;
+
+ // Disable Index to float conversion warning
+#ifdef __INTEL_COMPILER
+ #pragma warning push
+ #pragma warning ( disable : 2259 )
+#endif
+ Vector v = dec.solve(Vector::Ones(n) / Scalar(n));
+#ifdef __INTEL_COMPILER
+ #pragma warning pop
+#endif
+
+ // lower_bound is a lower bound on
+ // ||inv(matrix)||_1 = sup_v ||inv(matrix) v||_1 / ||v||_1
+ // and is the objective maximized by the ("super-") gradient ascent
+ // algorithm below.
+ RealScalar lower_bound = v.template lpNorm<1>();
+ if (n == 1)
+ return lower_bound;
+
+ // Gradient ascent algorithm follows: We know that the optimum is achieved at
+ // one of the simplices v = e_i, so in each iteration we follow a
+ // super-gradient to move towards the optimal one.
+ RealScalar old_lower_bound = lower_bound;
+ Vector sign_vector(n);
+ Vector old_sign_vector;
+ Index v_max_abs_index = -1;
+ Index old_v_max_abs_index = v_max_abs_index;
+ for (int k = 0; k < 4; ++k)
+ {
+ sign_vector = internal::rcond_compute_sign<Vector, RealVector, is_complex>::run(v);
+ if (k > 0 && !is_complex && sign_vector == old_sign_vector) {
+ // Break if the solution stagnated.
+ break;
+ }
+ // v_max_abs_index = argmax |real( inv(matrix)^T * sign_vector )|
+ v = dec.adjoint().solve(sign_vector);
+ v.real().cwiseAbs().maxCoeff(&v_max_abs_index);
+ if (v_max_abs_index == old_v_max_abs_index) {
+ // Break if the solution stagnated.
+ break;
+ }
+ // Move to the new simplex e_j, where j = v_max_abs_index.
+ v = dec.solve(Vector::Unit(n, v_max_abs_index)); // v = inv(matrix) * e_j.
+ lower_bound = v.template lpNorm<1>();
+ if (lower_bound <= old_lower_bound) {
+ // Break if the gradient step did not increase the lower_bound.
+ break;
+ }
+ if (!is_complex) {
+ old_sign_vector = sign_vector;
+ }
+ old_v_max_abs_index = v_max_abs_index;
+ old_lower_bound = lower_bound;
+ }
+ // The following calculates an independent estimate of ||matrix||_1 by
+ // multiplying matrix by a vector with entries of slowly increasing
+ // magnitude and alternating sign:
+ // v_i = (-1)^{i} (1 + (i / (dim-1))), i = 0,...,dim-1.
+ // This improvement to Hager's algorithm above is due to Higham. It was
+ // added to make the algorithm more robust in certain corner cases where
+ // large elements in the matrix might otherwise escape detection due to
+ // exact cancellation (especially when op and op_adjoint correspond to a
+ // sequence of backsubstitutions and permutations), which could cause
+ // Hager's algorithm to vastly underestimate ||matrix||_1.
+ Scalar alternating_sign(RealScalar(1));
+ for (Index i = 0; i < n; ++i) {
+ // The static_cast is needed when Scalar is a complex and RealScalar implements expression templates
+ v[i] = alternating_sign * static_cast<RealScalar>(RealScalar(1) + (RealScalar(i) / (RealScalar(n - 1))));
+ alternating_sign = -alternating_sign;
+ }
+ v = dec.solve(v);
+ const RealScalar alternate_lower_bound = (2 * v.template lpNorm<1>()) / (3 * RealScalar(n));
+ return numext::maxi(lower_bound, alternate_lower_bound);
+}
+
+/** \brief Reciprocal condition number estimator.
+ *
+ * Computing a decomposition of a dense matrix takes O(n^3) operations, while
+ * this method estimates the condition number quickly and reliably in O(n^2)
+ * operations.
+ *
+ * \returns an estimate of the reciprocal condition number
+ * (1 / (||matrix||_1 * ||inv(matrix)||_1)) of matrix, given ||matrix||_1 and
+ * its decomposition. Supports the following decompositions: FullPivLU,
+ * PartialPivLU, LDLT, and LLT.
+ *
+ * \sa FullPivLU, PartialPivLU, LDLT, LLT.
+ */
+template <typename Decomposition>
+typename Decomposition::RealScalar
+rcond_estimate_helper(typename Decomposition::RealScalar matrix_norm, const Decomposition& dec)
+{
+ typedef typename Decomposition::RealScalar RealScalar;
+ eigen_assert(dec.rows() == dec.cols());
+ if (dec.rows() == 0) return NumTraits<RealScalar>::infinity();
+ if (numext::is_exactly_zero(matrix_norm)) return RealScalar(0);
+ if (dec.rows() == 1) return RealScalar(1);
+ const RealScalar inverse_matrix_norm = rcond_invmatrix_L1_norm_estimate(dec);
+ return (numext::is_exactly_zero(inverse_matrix_norm) ? RealScalar(0)
+ : (RealScalar(1) / inverse_matrix_norm) / matrix_norm);
+}
+
+} // namespace internal
+
+} // namespace Eigen
+
+#endif
diff --git a/Eigen/src/Core/CoreEvaluators.h b/Eigen/src/Core/CoreEvaluators.h
new file mode 100644
index 0000000..1729507
--- /dev/null
+++ b/Eigen/src/Core/CoreEvaluators.h
@@ -0,0 +1,1744 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2011 Benoit Jacob <jacob.benoit.1@gmail.com>
+// Copyright (C) 2011-2014 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2011-2012 Jitse Niesen <jitse@maths.leeds.ac.uk>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+
+#ifndef EIGEN_COREEVALUATORS_H
+#define EIGEN_COREEVALUATORS_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+
+// This class returns the evaluator kind from the expression storage kind.
+// Default assumes index based accessors
+template<typename StorageKind>
+struct storage_kind_to_evaluator_kind {
+ typedef IndexBased Kind;
+};
+
+// This class returns the evaluator shape from the expression storage kind.
+// It can be Dense, Sparse, Triangular, Diagonal, SelfAdjoint, Band, etc.
+template<typename StorageKind> struct storage_kind_to_shape;
+
+template<> struct storage_kind_to_shape<Dense> { typedef DenseShape Shape; };
+template<> struct storage_kind_to_shape<SolverStorage> { typedef SolverShape Shape; };
+template<> struct storage_kind_to_shape<PermutationStorage> { typedef PermutationShape Shape; };
+template<> struct storage_kind_to_shape<TranspositionsStorage> { typedef TranspositionsShape Shape; };
+
+// Evaluators have to be specialized with respect to various criteria such as:
+// - storage/structure/shape
+// - scalar type
+// - etc.
+// Therefore, we need specialization of evaluator providing additional template arguments for each kind of evaluators.
+// We currently distinguish the following kind of evaluators:
+// - unary_evaluator for expressions taking only one arguments (CwiseUnaryOp, CwiseUnaryView, Transpose, MatrixWrapper, ArrayWrapper, Reverse, Replicate)
+// - binary_evaluator for expression taking two arguments (CwiseBinaryOp)
+// - ternary_evaluator for expression taking three arguments (CwiseTernaryOp)
+// - product_evaluator for linear algebra products (Product); special case of binary_evaluator because it requires additional tags for dispatching.
+// - mapbase_evaluator for Map, Block, Ref
+// - block_evaluator for Block (special dispatching to a mapbase_evaluator or unary_evaluator)
+
+template< typename T,
+ typename Arg1Kind = typename evaluator_traits<typename T::Arg1>::Kind,
+ typename Arg2Kind = typename evaluator_traits<typename T::Arg2>::Kind,
+ typename Arg3Kind = typename evaluator_traits<typename T::Arg3>::Kind,
+ typename Arg1Scalar = typename traits<typename T::Arg1>::Scalar,
+ typename Arg2Scalar = typename traits<typename T::Arg2>::Scalar,
+ typename Arg3Scalar = typename traits<typename T::Arg3>::Scalar> struct ternary_evaluator;
+
+template< typename T,
+ typename LhsKind = typename evaluator_traits<typename T::Lhs>::Kind,
+ typename RhsKind = typename evaluator_traits<typename T::Rhs>::Kind,
+ typename LhsScalar = typename traits<typename T::Lhs>::Scalar,
+ typename RhsScalar = typename traits<typename T::Rhs>::Scalar> struct binary_evaluator;
+
+template< typename T,
+ typename Kind = typename evaluator_traits<typename T::NestedExpression>::Kind,
+ typename Scalar = typename T::Scalar> struct unary_evaluator;
+
+// evaluator_traits<T> contains traits for evaluator<T>
+
+template<typename T>
+struct evaluator_traits_base
+{
+ // by default, get evaluator kind and shape from storage
+ typedef typename storage_kind_to_evaluator_kind<typename traits<T>::StorageKind>::Kind Kind;
+ typedef typename storage_kind_to_shape<typename traits<T>::StorageKind>::Shape Shape;
+};
+
+// Default evaluator traits
+template<typename T>
+struct evaluator_traits : public evaluator_traits_base<T>
+{
+};
+
+template<typename T, typename Shape = typename evaluator_traits<T>::Shape >
+struct evaluator_assume_aliasing {
+ static const bool value = false;
+};
+
+// By default, we assume a unary expression:
+template<typename T>
+struct evaluator : public unary_evaluator<T>
+{
+ typedef unary_evaluator<T> Base;
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ explicit evaluator(const T& xpr) : Base(xpr) {}
+};
+
+
+// TODO: Think about const-correctness
+template<typename T>
+struct evaluator<const T>
+ : evaluator<T>
+{
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ explicit evaluator(const T& xpr) : evaluator<T>(xpr) {}
+};
+
+// ---------- base class for all evaluators ----------
+
+template<typename ExpressionType>
+struct evaluator_base
+{
+ // TODO that's not very nice to have to propagate all these traits. They are currently only needed to handle outer,inner indices.
+ typedef traits<ExpressionType> ExpressionTraits;
+
+ enum {
+ Alignment = 0
+ };
+ // noncopyable:
+ // Don't make this class inherit noncopyable as this kills EBO (Empty Base Optimization)
+ // and make complex evaluator much larger than then should do.
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE evaluator_base() {}
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE ~evaluator_base() {}
+private:
+ EIGEN_DEVICE_FUNC evaluator_base(const evaluator_base&);
+ EIGEN_DEVICE_FUNC const evaluator_base& operator=(const evaluator_base&);
+};
+
+// -------------------- Matrix and Array --------------------
+//
+// evaluator<PlainObjectBase> is a common base class for the
+// Matrix and Array evaluators.
+// Here we directly specialize evaluator. This is not really a unary expression, and it is, by definition, dense,
+// so no need for more sophisticated dispatching.
+
+// this helper permits to completely eliminate m_outerStride if it is known at compiletime.
+template<typename Scalar,int OuterStride> class plainobjectbase_evaluator_data {
+public:
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ plainobjectbase_evaluator_data(const Scalar* ptr, Index outerStride) : data(ptr)
+ {
+#ifndef EIGEN_INTERNAL_DEBUGGING
+ EIGEN_UNUSED_VARIABLE(outerStride);
+#endif
+ eigen_internal_assert(outerStride==OuterStride);
+ }
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE EIGEN_CONSTEXPR
+ Index outerStride() const EIGEN_NOEXCEPT { return OuterStride; }
+ const Scalar *data;
+};
+
+template<typename Scalar> class plainobjectbase_evaluator_data<Scalar,Dynamic> {
+public:
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ plainobjectbase_evaluator_data(const Scalar* ptr, Index outerStride) : data(ptr), m_outerStride(outerStride) {}
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ Index outerStride() const { return m_outerStride; }
+ const Scalar *data;
+protected:
+ Index m_outerStride;
+};
+
+template<typename Derived>
+struct evaluator<PlainObjectBase<Derived> >
+ : evaluator_base<Derived>
+{
+ typedef PlainObjectBase<Derived> PlainObjectType;
+ typedef typename PlainObjectType::Scalar Scalar;
+ typedef typename PlainObjectType::CoeffReturnType CoeffReturnType;
+
+ enum {
+ IsRowMajor = PlainObjectType::IsRowMajor,
+ IsVectorAtCompileTime = PlainObjectType::IsVectorAtCompileTime,
+ RowsAtCompileTime = PlainObjectType::RowsAtCompileTime,
+ ColsAtCompileTime = PlainObjectType::ColsAtCompileTime,
+
+ CoeffReadCost = NumTraits<Scalar>::ReadCost,
+ Flags = traits<Derived>::EvaluatorFlags,
+ Alignment = traits<Derived>::Alignment
+ };
+ enum {
+ // We do not need to know the outer stride for vectors
+ OuterStrideAtCompileTime = IsVectorAtCompileTime ? 0
+ : int(IsRowMajor) ? ColsAtCompileTime
+ : RowsAtCompileTime
+ };
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ evaluator()
+ : m_d(0,OuterStrideAtCompileTime)
+ {
+ EIGEN_INTERNAL_CHECK_COST_VALUE(CoeffReadCost);
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ explicit evaluator(const PlainObjectType& m)
+ : m_d(m.data(),IsVectorAtCompileTime ? 0 : m.outerStride())
+ {
+ EIGEN_INTERNAL_CHECK_COST_VALUE(CoeffReadCost);
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ CoeffReturnType coeff(Index row, Index col) const
+ {
+ if (IsRowMajor)
+ return m_d.data[row * m_d.outerStride() + col];
+ else
+ return m_d.data[row + col * m_d.outerStride()];
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ CoeffReturnType coeff(Index index) const
+ {
+ return m_d.data[index];
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ Scalar& coeffRef(Index row, Index col)
+ {
+ if (IsRowMajor)
+ return const_cast<Scalar*>(m_d.data)[row * m_d.outerStride() + col];
+ else
+ return const_cast<Scalar*>(m_d.data)[row + col * m_d.outerStride()];
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ Scalar& coeffRef(Index index)
+ {
+ return const_cast<Scalar*>(m_d.data)[index];
+ }
+
+ template<int LoadMode, typename PacketType>
+ EIGEN_STRONG_INLINE
+ PacketType packet(Index row, Index col) const
+ {
+ if (IsRowMajor)
+ return ploadt<PacketType, LoadMode>(m_d.data + row * m_d.outerStride() + col);
+ else
+ return ploadt<PacketType, LoadMode>(m_d.data + row + col * m_d.outerStride());
+ }
+
+ template<int LoadMode, typename PacketType>
+ EIGEN_STRONG_INLINE
+ PacketType packet(Index index) const
+ {
+ return ploadt<PacketType, LoadMode>(m_d.data + index);
+ }
+
+ template<int StoreMode,typename PacketType>
+ EIGEN_STRONG_INLINE
+ void writePacket(Index row, Index col, const PacketType& x)
+ {
+ if (IsRowMajor)
+ return pstoret<Scalar, PacketType, StoreMode>
+ (const_cast<Scalar*>(m_d.data) + row * m_d.outerStride() + col, x);
+ else
+ return pstoret<Scalar, PacketType, StoreMode>
+ (const_cast<Scalar*>(m_d.data) + row + col * m_d.outerStride(), x);
+ }
+
+ template<int StoreMode, typename PacketType>
+ EIGEN_STRONG_INLINE
+ void writePacket(Index index, const PacketType& x)
+ {
+ return pstoret<Scalar, PacketType, StoreMode>(const_cast<Scalar*>(m_d.data) + index, x);
+ }
+
+protected:
+
+ plainobjectbase_evaluator_data<Scalar,OuterStrideAtCompileTime> m_d;
+};
+
+template<typename Scalar, int Rows, int Cols, int Options, int MaxRows, int MaxCols>
+struct evaluator<Matrix<Scalar, Rows, Cols, Options, MaxRows, MaxCols> >
+ : evaluator<PlainObjectBase<Matrix<Scalar, Rows, Cols, Options, MaxRows, MaxCols> > >
+{
+ typedef Matrix<Scalar, Rows, Cols, Options, MaxRows, MaxCols> XprType;
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ evaluator() {}
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ explicit evaluator(const XprType& m)
+ : evaluator<PlainObjectBase<XprType> >(m)
+ { }
+};
+
+template<typename Scalar, int Rows, int Cols, int Options, int MaxRows, int MaxCols>
+struct evaluator<Array<Scalar, Rows, Cols, Options, MaxRows, MaxCols> >
+ : evaluator<PlainObjectBase<Array<Scalar, Rows, Cols, Options, MaxRows, MaxCols> > >
+{
+ typedef Array<Scalar, Rows, Cols, Options, MaxRows, MaxCols> XprType;
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ evaluator() {}
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ explicit evaluator(const XprType& m)
+ : evaluator<PlainObjectBase<XprType> >(m)
+ { }
+};
+
+// -------------------- Transpose --------------------
+
+template<typename ArgType>
+struct unary_evaluator<Transpose<ArgType>, IndexBased>
+ : evaluator_base<Transpose<ArgType> >
+{
+ typedef Transpose<ArgType> XprType;
+
+ enum {
+ CoeffReadCost = evaluator<ArgType>::CoeffReadCost,
+ Flags = evaluator<ArgType>::Flags ^ RowMajorBit,
+ Alignment = evaluator<ArgType>::Alignment
+ };
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ explicit unary_evaluator(const XprType& t) : m_argImpl(t.nestedExpression()) {}
+
+ typedef typename XprType::Scalar Scalar;
+ typedef typename XprType::CoeffReturnType CoeffReturnType;
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ CoeffReturnType coeff(Index row, Index col) const
+ {
+ return m_argImpl.coeff(col, row);
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ CoeffReturnType coeff(Index index) const
+ {
+ return m_argImpl.coeff(index);
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ Scalar& coeffRef(Index row, Index col)
+ {
+ return m_argImpl.coeffRef(col, row);
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ typename XprType::Scalar& coeffRef(Index index)
+ {
+ return m_argImpl.coeffRef(index);
+ }
+
+ template<int LoadMode, typename PacketType>
+ EIGEN_STRONG_INLINE
+ PacketType packet(Index row, Index col) const
+ {
+ return m_argImpl.template packet<LoadMode,PacketType>(col, row);
+ }
+
+ template<int LoadMode, typename PacketType>
+ EIGEN_STRONG_INLINE
+ PacketType packet(Index index) const
+ {
+ return m_argImpl.template packet<LoadMode,PacketType>(index);
+ }
+
+ template<int StoreMode, typename PacketType>
+ EIGEN_STRONG_INLINE
+ void writePacket(Index row, Index col, const PacketType& x)
+ {
+ m_argImpl.template writePacket<StoreMode,PacketType>(col, row, x);
+ }
+
+ template<int StoreMode, typename PacketType>
+ EIGEN_STRONG_INLINE
+ void writePacket(Index index, const PacketType& x)
+ {
+ m_argImpl.template writePacket<StoreMode,PacketType>(index, x);
+ }
+
+protected:
+ evaluator<ArgType> m_argImpl;
+};
+
+// -------------------- CwiseNullaryOp --------------------
+// Like Matrix and Array, this is not really a unary expression, so we directly specialize evaluator.
+// Likewise, there is not need to more sophisticated dispatching here.
+
+template<typename Scalar,typename NullaryOp,
+ bool has_nullary = has_nullary_operator<NullaryOp>::value,
+ bool has_unary = has_unary_operator<NullaryOp>::value,
+ bool has_binary = has_binary_operator<NullaryOp>::value>
+struct nullary_wrapper
+{
+ template <typename IndexType>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar operator()(const NullaryOp& op, IndexType i, IndexType j) const { return op(i,j); }
+ template <typename IndexType>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar operator()(const NullaryOp& op, IndexType i) const { return op(i); }
+
+ template <typename T, typename IndexType> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE T packetOp(const NullaryOp& op, IndexType i, IndexType j) const { return op.template packetOp<T>(i,j); }
+ template <typename T, typename IndexType> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE T packetOp(const NullaryOp& op, IndexType i) const { return op.template packetOp<T>(i); }
+};
+
+template<typename Scalar,typename NullaryOp>
+struct nullary_wrapper<Scalar,NullaryOp,true,false,false>
+{
+ template <typename IndexType>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar operator()(const NullaryOp& op, IndexType=0, IndexType=0) const { return op(); }
+ template <typename T, typename IndexType> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE T packetOp(const NullaryOp& op, IndexType=0, IndexType=0) const { return op.template packetOp<T>(); }
+};
+
+template<typename Scalar,typename NullaryOp>
+struct nullary_wrapper<Scalar,NullaryOp,false,false,true>
+{
+ template <typename IndexType>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar operator()(const NullaryOp& op, IndexType i, IndexType j=0) const { return op(i,j); }
+ template <typename T, typename IndexType> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE T packetOp(const NullaryOp& op, IndexType i, IndexType j=0) const { return op.template packetOp<T>(i,j); }
+};
+
+// We need the following specialization for vector-only functors assigned to a runtime vector,
+// for instance, using linspace and assigning a RowVectorXd to a MatrixXd or even a row of a MatrixXd.
+// In this case, i==0 and j is used for the actual iteration.
+template<typename Scalar,typename NullaryOp>
+struct nullary_wrapper<Scalar,NullaryOp,false,true,false>
+{
+ template <typename IndexType>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar operator()(const NullaryOp& op, IndexType i, IndexType j) const {
+ eigen_assert(i==0 || j==0);
+ return op(i+j);
+ }
+ template <typename T, typename IndexType> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE T packetOp(const NullaryOp& op, IndexType i, IndexType j) const {
+ eigen_assert(i==0 || j==0);
+ return op.template packetOp<T>(i+j);
+ }
+
+ template <typename IndexType>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar operator()(const NullaryOp& op, IndexType i) const { return op(i); }
+ template <typename T, typename IndexType>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE T packetOp(const NullaryOp& op, IndexType i) const { return op.template packetOp<T>(i); }
+};
+
+template<typename Scalar,typename NullaryOp>
+struct nullary_wrapper<Scalar,NullaryOp,false,false,false> {};
+
+#if 0 && EIGEN_COMP_MSVC>0
+// Disable this ugly workaround. This is now handled in traits<Ref>::match,
+// but this piece of code might still become handly if some other weird compilation
+// erros pop up again.
+
+// MSVC exhibits a weird compilation error when
+// compiling:
+// Eigen::MatrixXf A = MatrixXf::Random(3,3);
+// Ref<const MatrixXf> R = 2.f*A;
+// and that has_*ary_operator<scalar_constant_op<float>> have not been instantiated yet.
+// The "problem" is that evaluator<2.f*A> is instantiated by traits<Ref>::match<2.f*A>
+// and at that time has_*ary_operator<T> returns true regardless of T.
+// Then nullary_wrapper is badly instantiated as nullary_wrapper<.,.,true,true,true>.
+// The trick is thus to defer the proper instantiation of nullary_wrapper when coeff(),
+// and packet() are really instantiated as implemented below:
+
+// This is a simple wrapper around Index to enforce the re-instantiation of
+// has_*ary_operator when needed.
+template<typename T> struct nullary_wrapper_workaround_msvc {
+ nullary_wrapper_workaround_msvc(const T&);
+ operator T()const;
+};
+
+template<typename Scalar,typename NullaryOp>
+struct nullary_wrapper<Scalar,NullaryOp,true,true,true>
+{
+ template <typename IndexType>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar operator()(const NullaryOp& op, IndexType i, IndexType j) const {
+ return nullary_wrapper<Scalar,NullaryOp,
+ has_nullary_operator<NullaryOp,nullary_wrapper_workaround_msvc<IndexType> >::value,
+ has_unary_operator<NullaryOp,nullary_wrapper_workaround_msvc<IndexType> >::value,
+ has_binary_operator<NullaryOp,nullary_wrapper_workaround_msvc<IndexType> >::value>().operator()(op,i,j);
+ }
+ template <typename IndexType>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar operator()(const NullaryOp& op, IndexType i) const {
+ return nullary_wrapper<Scalar,NullaryOp,
+ has_nullary_operator<NullaryOp,nullary_wrapper_workaround_msvc<IndexType> >::value,
+ has_unary_operator<NullaryOp,nullary_wrapper_workaround_msvc<IndexType> >::value,
+ has_binary_operator<NullaryOp,nullary_wrapper_workaround_msvc<IndexType> >::value>().operator()(op,i);
+ }
+
+ template <typename T, typename IndexType>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE T packetOp(const NullaryOp& op, IndexType i, IndexType j) const {
+ return nullary_wrapper<Scalar,NullaryOp,
+ has_nullary_operator<NullaryOp,nullary_wrapper_workaround_msvc<IndexType> >::value,
+ has_unary_operator<NullaryOp,nullary_wrapper_workaround_msvc<IndexType> >::value,
+ has_binary_operator<NullaryOp,nullary_wrapper_workaround_msvc<IndexType> >::value>().template packetOp<T>(op,i,j);
+ }
+ template <typename T, typename IndexType>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE T packetOp(const NullaryOp& op, IndexType i) const {
+ return nullary_wrapper<Scalar,NullaryOp,
+ has_nullary_operator<NullaryOp,nullary_wrapper_workaround_msvc<IndexType> >::value,
+ has_unary_operator<NullaryOp,nullary_wrapper_workaround_msvc<IndexType> >::value,
+ has_binary_operator<NullaryOp,nullary_wrapper_workaround_msvc<IndexType> >::value>().template packetOp<T>(op,i);
+ }
+};
+#endif // MSVC workaround
+
+template<typename NullaryOp, typename PlainObjectType>
+struct evaluator<CwiseNullaryOp<NullaryOp,PlainObjectType> >
+ : evaluator_base<CwiseNullaryOp<NullaryOp,PlainObjectType> >
+{
+ typedef CwiseNullaryOp<NullaryOp,PlainObjectType> XprType;
+ typedef internal::remove_all_t<PlainObjectType> PlainObjectTypeCleaned;
+
+ enum {
+ CoeffReadCost = internal::functor_traits<NullaryOp>::Cost,
+
+ Flags = (evaluator<PlainObjectTypeCleaned>::Flags
+ & ( HereditaryBits
+ | (functor_has_linear_access<NullaryOp>::ret ? LinearAccessBit : 0)
+ | (functor_traits<NullaryOp>::PacketAccess ? PacketAccessBit : 0)))
+ | (functor_traits<NullaryOp>::IsRepeatable ? 0 : EvalBeforeNestingBit),
+ Alignment = AlignedMax
+ };
+
+ EIGEN_DEVICE_FUNC explicit evaluator(const XprType& n)
+ : m_functor(n.functor()), m_wrapper()
+ {
+ EIGEN_INTERNAL_CHECK_COST_VALUE(CoeffReadCost);
+ }
+
+ typedef typename XprType::CoeffReturnType CoeffReturnType;
+
+ template <typename IndexType>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ CoeffReturnType coeff(IndexType row, IndexType col) const
+ {
+ return m_wrapper(m_functor, row, col);
+ }
+
+ template <typename IndexType>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ CoeffReturnType coeff(IndexType index) const
+ {
+ return m_wrapper(m_functor,index);
+ }
+
+ template<int LoadMode, typename PacketType, typename IndexType>
+ EIGEN_STRONG_INLINE
+ PacketType packet(IndexType row, IndexType col) const
+ {
+ return m_wrapper.template packetOp<PacketType>(m_functor, row, col);
+ }
+
+ template<int LoadMode, typename PacketType, typename IndexType>
+ EIGEN_STRONG_INLINE
+ PacketType packet(IndexType index) const
+ {
+ return m_wrapper.template packetOp<PacketType>(m_functor, index);
+ }
+
+protected:
+ const NullaryOp m_functor;
+ const internal::nullary_wrapper<CoeffReturnType,NullaryOp> m_wrapper;
+};
+
+// -------------------- CwiseUnaryOp --------------------
+
+template<typename UnaryOp, typename ArgType>
+struct unary_evaluator<CwiseUnaryOp<UnaryOp, ArgType>, IndexBased >
+ : evaluator_base<CwiseUnaryOp<UnaryOp, ArgType> >
+{
+ typedef CwiseUnaryOp<UnaryOp, ArgType> XprType;
+
+ enum {
+ CoeffReadCost = int(evaluator<ArgType>::CoeffReadCost) + int(functor_traits<UnaryOp>::Cost),
+
+ Flags = evaluator<ArgType>::Flags
+ & (HereditaryBits | LinearAccessBit | (functor_traits<UnaryOp>::PacketAccess ? PacketAccessBit : 0)),
+ Alignment = evaluator<ArgType>::Alignment
+ };
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ explicit unary_evaluator(const XprType& op) : m_d(op)
+ {
+ EIGEN_INTERNAL_CHECK_COST_VALUE(functor_traits<UnaryOp>::Cost);
+ EIGEN_INTERNAL_CHECK_COST_VALUE(CoeffReadCost);
+ }
+
+ typedef typename XprType::CoeffReturnType CoeffReturnType;
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ CoeffReturnType coeff(Index row, Index col) const
+ {
+ return m_d.func()(m_d.argImpl.coeff(row, col));
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ CoeffReturnType coeff(Index index) const
+ {
+ return m_d.func()(m_d.argImpl.coeff(index));
+ }
+
+ template<int LoadMode, typename PacketType>
+ EIGEN_STRONG_INLINE
+ PacketType packet(Index row, Index col) const
+ {
+ return m_d.func().packetOp(m_d.argImpl.template packet<LoadMode, PacketType>(row, col));
+ }
+
+ template<int LoadMode, typename PacketType>
+ EIGEN_STRONG_INLINE
+ PacketType packet(Index index) const
+ {
+ return m_d.func().packetOp(m_d.argImpl.template packet<LoadMode, PacketType>(index));
+ }
+
+protected:
+
+ // this helper permits to completely eliminate the functor if it is empty
+ struct Data
+ {
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ Data(const XprType& xpr) : op(xpr.functor()), argImpl(xpr.nestedExpression()) {}
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ const UnaryOp& func() const { return op; }
+ UnaryOp op;
+ evaluator<ArgType> argImpl;
+ };
+
+ Data m_d;
+};
+
+// -------------------- CwiseTernaryOp --------------------
+
+// this is a ternary expression
+template<typename TernaryOp, typename Arg1, typename Arg2, typename Arg3>
+struct evaluator<CwiseTernaryOp<TernaryOp, Arg1, Arg2, Arg3> >
+ : public ternary_evaluator<CwiseTernaryOp<TernaryOp, Arg1, Arg2, Arg3> >
+{
+ typedef CwiseTernaryOp<TernaryOp, Arg1, Arg2, Arg3> XprType;
+ typedef ternary_evaluator<CwiseTernaryOp<TernaryOp, Arg1, Arg2, Arg3> > Base;
+
+ EIGEN_DEVICE_FUNC explicit evaluator(const XprType& xpr) : Base(xpr) {}
+};
+
+template<typename TernaryOp, typename Arg1, typename Arg2, typename Arg3>
+struct ternary_evaluator<CwiseTernaryOp<TernaryOp, Arg1, Arg2, Arg3>, IndexBased, IndexBased>
+ : evaluator_base<CwiseTernaryOp<TernaryOp, Arg1, Arg2, Arg3> >
+{
+ typedef CwiseTernaryOp<TernaryOp, Arg1, Arg2, Arg3> XprType;
+
+ enum {
+ CoeffReadCost = int(evaluator<Arg1>::CoeffReadCost) + int(evaluator<Arg2>::CoeffReadCost) + int(evaluator<Arg3>::CoeffReadCost) + int(functor_traits<TernaryOp>::Cost),
+
+ Arg1Flags = evaluator<Arg1>::Flags,
+ Arg2Flags = evaluator<Arg2>::Flags,
+ Arg3Flags = evaluator<Arg3>::Flags,
+ SameType = is_same<typename Arg1::Scalar,typename Arg2::Scalar>::value && is_same<typename Arg1::Scalar,typename Arg3::Scalar>::value,
+ StorageOrdersAgree = (int(Arg1Flags)&RowMajorBit)==(int(Arg2Flags)&RowMajorBit) && (int(Arg1Flags)&RowMajorBit)==(int(Arg3Flags)&RowMajorBit),
+ Flags0 = (int(Arg1Flags) | int(Arg2Flags) | int(Arg3Flags)) & (
+ HereditaryBits
+ | (int(Arg1Flags) & int(Arg2Flags) & int(Arg3Flags) &
+ ( (StorageOrdersAgree ? LinearAccessBit : 0)
+ | (functor_traits<TernaryOp>::PacketAccess && StorageOrdersAgree && SameType ? PacketAccessBit : 0)
+ )
+ )
+ ),
+ Flags = (Flags0 & ~RowMajorBit) | (Arg1Flags & RowMajorBit),
+ Alignment = plain_enum_min(
+ plain_enum_min(evaluator<Arg1>::Alignment, evaluator<Arg2>::Alignment),
+ evaluator<Arg3>::Alignment)
+ };
+
+ EIGEN_DEVICE_FUNC explicit ternary_evaluator(const XprType& xpr) : m_d(xpr)
+ {
+ EIGEN_INTERNAL_CHECK_COST_VALUE(functor_traits<TernaryOp>::Cost);
+ EIGEN_INTERNAL_CHECK_COST_VALUE(CoeffReadCost);
+ }
+
+ typedef typename XprType::CoeffReturnType CoeffReturnType;
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ CoeffReturnType coeff(Index row, Index col) const
+ {
+ return m_d.func()(m_d.arg1Impl.coeff(row, col), m_d.arg2Impl.coeff(row, col), m_d.arg3Impl.coeff(row, col));
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ CoeffReturnType coeff(Index index) const
+ {
+ return m_d.func()(m_d.arg1Impl.coeff(index), m_d.arg2Impl.coeff(index), m_d.arg3Impl.coeff(index));
+ }
+
+ template<int LoadMode, typename PacketType>
+ EIGEN_STRONG_INLINE
+ PacketType packet(Index row, Index col) const
+ {
+ return m_d.func().packetOp(m_d.arg1Impl.template packet<LoadMode,PacketType>(row, col),
+ m_d.arg2Impl.template packet<LoadMode,PacketType>(row, col),
+ m_d.arg3Impl.template packet<LoadMode,PacketType>(row, col));
+ }
+
+ template<int LoadMode, typename PacketType>
+ EIGEN_STRONG_INLINE
+ PacketType packet(Index index) const
+ {
+ return m_d.func().packetOp(m_d.arg1Impl.template packet<LoadMode,PacketType>(index),
+ m_d.arg2Impl.template packet<LoadMode,PacketType>(index),
+ m_d.arg3Impl.template packet<LoadMode,PacketType>(index));
+ }
+
+protected:
+ // this helper permits to completely eliminate the functor if it is empty
+ struct Data
+ {
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ Data(const XprType& xpr) : op(xpr.functor()), arg1Impl(xpr.arg1()), arg2Impl(xpr.arg2()), arg3Impl(xpr.arg3()) {}
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ const TernaryOp& func() const { return op; }
+ TernaryOp op;
+ evaluator<Arg1> arg1Impl;
+ evaluator<Arg2> arg2Impl;
+ evaluator<Arg3> arg3Impl;
+ };
+
+ Data m_d;
+};
+
+// -------------------- CwiseBinaryOp --------------------
+
+// this is a binary expression
+template<typename BinaryOp, typename Lhs, typename Rhs>
+struct evaluator<CwiseBinaryOp<BinaryOp, Lhs, Rhs> >
+ : public binary_evaluator<CwiseBinaryOp<BinaryOp, Lhs, Rhs> >
+{
+ typedef CwiseBinaryOp<BinaryOp, Lhs, Rhs> XprType;
+ typedef binary_evaluator<CwiseBinaryOp<BinaryOp, Lhs, Rhs> > Base;
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ explicit evaluator(const XprType& xpr) : Base(xpr) {}
+};
+
+template<typename BinaryOp, typename Lhs, typename Rhs>
+struct binary_evaluator<CwiseBinaryOp<BinaryOp, Lhs, Rhs>, IndexBased, IndexBased>
+ : evaluator_base<CwiseBinaryOp<BinaryOp, Lhs, Rhs> >
+{
+ typedef CwiseBinaryOp<BinaryOp, Lhs, Rhs> XprType;
+
+ enum {
+ CoeffReadCost = int(evaluator<Lhs>::CoeffReadCost) + int(evaluator<Rhs>::CoeffReadCost) + int(functor_traits<BinaryOp>::Cost),
+
+ LhsFlags = evaluator<Lhs>::Flags,
+ RhsFlags = evaluator<Rhs>::Flags,
+ SameType = is_same<typename Lhs::Scalar,typename Rhs::Scalar>::value,
+ StorageOrdersAgree = (int(LhsFlags)&RowMajorBit)==(int(RhsFlags)&RowMajorBit),
+ Flags0 = (int(LhsFlags) | int(RhsFlags)) & (
+ HereditaryBits
+ | (int(LhsFlags) & int(RhsFlags) &
+ ( (StorageOrdersAgree ? LinearAccessBit : 0)
+ | (functor_traits<BinaryOp>::PacketAccess && StorageOrdersAgree && SameType ? PacketAccessBit : 0)
+ )
+ )
+ ),
+ Flags = (Flags0 & ~RowMajorBit) | (LhsFlags & RowMajorBit),
+ Alignment = plain_enum_min(evaluator<Lhs>::Alignment, evaluator<Rhs>::Alignment)
+ };
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ explicit binary_evaluator(const XprType& xpr) : m_d(xpr)
+ {
+ EIGEN_INTERNAL_CHECK_COST_VALUE(functor_traits<BinaryOp>::Cost);
+ EIGEN_INTERNAL_CHECK_COST_VALUE(CoeffReadCost);
+ }
+
+ typedef typename XprType::CoeffReturnType CoeffReturnType;
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ CoeffReturnType coeff(Index row, Index col) const
+ {
+ return m_d.func()(m_d.lhsImpl.coeff(row, col), m_d.rhsImpl.coeff(row, col));
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ CoeffReturnType coeff(Index index) const
+ {
+ return m_d.func()(m_d.lhsImpl.coeff(index), m_d.rhsImpl.coeff(index));
+ }
+
+ template<int LoadMode, typename PacketType>
+ EIGEN_STRONG_INLINE
+ PacketType packet(Index row, Index col) const
+ {
+ return m_d.func().packetOp(m_d.lhsImpl.template packet<LoadMode,PacketType>(row, col),
+ m_d.rhsImpl.template packet<LoadMode,PacketType>(row, col));
+ }
+
+ template<int LoadMode, typename PacketType>
+ EIGEN_STRONG_INLINE
+ PacketType packet(Index index) const
+ {
+ return m_d.func().packetOp(m_d.lhsImpl.template packet<LoadMode,PacketType>(index),
+ m_d.rhsImpl.template packet<LoadMode,PacketType>(index));
+ }
+
+protected:
+
+ // this helper permits to completely eliminate the functor if it is empty
+ struct Data
+ {
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ Data(const XprType& xpr) : op(xpr.functor()), lhsImpl(xpr.lhs()), rhsImpl(xpr.rhs()) {}
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ const BinaryOp& func() const { return op; }
+ BinaryOp op;
+ evaluator<Lhs> lhsImpl;
+ evaluator<Rhs> rhsImpl;
+ };
+
+ Data m_d;
+};
+
+// -------------------- CwiseUnaryView --------------------
+
+template<typename UnaryOp, typename ArgType, typename StrideType>
+struct unary_evaluator<CwiseUnaryView<UnaryOp, ArgType, StrideType>, IndexBased>
+ : evaluator_base<CwiseUnaryView<UnaryOp, ArgType, StrideType> >
+{
+ typedef CwiseUnaryView<UnaryOp, ArgType, StrideType> XprType;
+
+ enum {
+ CoeffReadCost = int(evaluator<ArgType>::CoeffReadCost) + int(functor_traits<UnaryOp>::Cost),
+
+ Flags = (evaluator<ArgType>::Flags & (HereditaryBits | LinearAccessBit | DirectAccessBit)),
+
+ Alignment = 0 // FIXME it is not very clear why alignment is necessarily lost...
+ };
+
+ EIGEN_DEVICE_FUNC explicit unary_evaluator(const XprType& op) : m_d(op)
+ {
+ EIGEN_INTERNAL_CHECK_COST_VALUE(functor_traits<UnaryOp>::Cost);
+ EIGEN_INTERNAL_CHECK_COST_VALUE(CoeffReadCost);
+ }
+
+ typedef typename XprType::Scalar Scalar;
+ typedef typename XprType::CoeffReturnType CoeffReturnType;
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ CoeffReturnType coeff(Index row, Index col) const
+ {
+ return m_d.func()(m_d.argImpl.coeff(row, col));
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ CoeffReturnType coeff(Index index) const
+ {
+ return m_d.func()(m_d.argImpl.coeff(index));
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ Scalar& coeffRef(Index row, Index col)
+ {
+ return m_d.func()(m_d.argImpl.coeffRef(row, col));
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ Scalar& coeffRef(Index index)
+ {
+ return m_d.func()(m_d.argImpl.coeffRef(index));
+ }
+
+protected:
+
+ // this helper permits to completely eliminate the functor if it is empty
+ struct Data
+ {
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ Data(const XprType& xpr) : op(xpr.functor()), argImpl(xpr.nestedExpression()) {}
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ const UnaryOp& func() const { return op; }
+ UnaryOp op;
+ evaluator<ArgType> argImpl;
+ };
+
+ Data m_d;
+};
+
+// -------------------- Map --------------------
+
+// FIXME perhaps the PlainObjectType could be provided by Derived::PlainObject ?
+// but that might complicate template specialization
+template<typename Derived, typename PlainObjectType>
+struct mapbase_evaluator;
+
+template<typename Derived, typename PlainObjectType>
+struct mapbase_evaluator : evaluator_base<Derived>
+{
+ typedef Derived XprType;
+ typedef typename XprType::PointerType PointerType;
+ typedef typename XprType::Scalar Scalar;
+ typedef typename XprType::CoeffReturnType CoeffReturnType;
+
+ enum {
+ IsRowMajor = XprType::RowsAtCompileTime,
+ ColsAtCompileTime = XprType::ColsAtCompileTime,
+ CoeffReadCost = NumTraits<Scalar>::ReadCost
+ };
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ explicit mapbase_evaluator(const XprType& map)
+ : m_data(const_cast<PointerType>(map.data())),
+ m_innerStride(map.innerStride()),
+ m_outerStride(map.outerStride())
+ {
+ EIGEN_STATIC_ASSERT(check_implication((evaluator<Derived>::Flags & PacketAccessBit) != 0,
+ internal::inner_stride_at_compile_time<Derived>::ret == 1),
+ PACKET_ACCESS_REQUIRES_TO_HAVE_INNER_STRIDE_FIXED_TO_1);
+ EIGEN_INTERNAL_CHECK_COST_VALUE(CoeffReadCost);
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ CoeffReturnType coeff(Index row, Index col) const
+ {
+ return m_data[col * colStride() + row * rowStride()];
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ CoeffReturnType coeff(Index index) const
+ {
+ return m_data[index * m_innerStride.value()];
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ Scalar& coeffRef(Index row, Index col)
+ {
+ return m_data[col * colStride() + row * rowStride()];
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ Scalar& coeffRef(Index index)
+ {
+ return m_data[index * m_innerStride.value()];
+ }
+
+ template<int LoadMode, typename PacketType>
+ EIGEN_STRONG_INLINE
+ PacketType packet(Index row, Index col) const
+ {
+ PointerType ptr = m_data + row * rowStride() + col * colStride();
+ return internal::ploadt<PacketType, LoadMode>(ptr);
+ }
+
+ template<int LoadMode, typename PacketType>
+ EIGEN_STRONG_INLINE
+ PacketType packet(Index index) const
+ {
+ return internal::ploadt<PacketType, LoadMode>(m_data + index * m_innerStride.value());
+ }
+
+ template<int StoreMode, typename PacketType>
+ EIGEN_STRONG_INLINE
+ void writePacket(Index row, Index col, const PacketType& x)
+ {
+ PointerType ptr = m_data + row * rowStride() + col * colStride();
+ return internal::pstoret<Scalar, PacketType, StoreMode>(ptr, x);
+ }
+
+ template<int StoreMode, typename PacketType>
+ EIGEN_STRONG_INLINE
+ void writePacket(Index index, const PacketType& x)
+ {
+ internal::pstoret<Scalar, PacketType, StoreMode>(m_data + index * m_innerStride.value(), x);
+ }
+protected:
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE EIGEN_CONSTEXPR
+ Index rowStride() const EIGEN_NOEXCEPT {
+ return XprType::IsRowMajor ? m_outerStride.value() : m_innerStride.value();
+ }
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE EIGEN_CONSTEXPR
+ Index colStride() const EIGEN_NOEXCEPT {
+ return XprType::IsRowMajor ? m_innerStride.value() : m_outerStride.value();
+ }
+
+ PointerType m_data;
+ const internal::variable_if_dynamic<Index, XprType::InnerStrideAtCompileTime> m_innerStride;
+ const internal::variable_if_dynamic<Index, XprType::OuterStrideAtCompileTime> m_outerStride;
+};
+
+template<typename PlainObjectType, int MapOptions, typename StrideType>
+struct evaluator<Map<PlainObjectType, MapOptions, StrideType> >
+ : public mapbase_evaluator<Map<PlainObjectType, MapOptions, StrideType>, PlainObjectType>
+{
+ typedef Map<PlainObjectType, MapOptions, StrideType> XprType;
+ typedef typename XprType::Scalar Scalar;
+ // TODO: should check for smaller packet types once we can handle multi-sized packet types
+ typedef typename packet_traits<Scalar>::type PacketScalar;
+
+ enum {
+ InnerStrideAtCompileTime = StrideType::InnerStrideAtCompileTime == 0
+ ? int(PlainObjectType::InnerStrideAtCompileTime)
+ : int(StrideType::InnerStrideAtCompileTime),
+ OuterStrideAtCompileTime = StrideType::OuterStrideAtCompileTime == 0
+ ? int(PlainObjectType::OuterStrideAtCompileTime)
+ : int(StrideType::OuterStrideAtCompileTime),
+ HasNoInnerStride = InnerStrideAtCompileTime == 1,
+ HasNoOuterStride = StrideType::OuterStrideAtCompileTime == 0,
+ HasNoStride = HasNoInnerStride && HasNoOuterStride,
+ IsDynamicSize = PlainObjectType::SizeAtCompileTime==Dynamic,
+
+ PacketAccessMask = bool(HasNoInnerStride) ? ~int(0) : ~int(PacketAccessBit),
+ LinearAccessMask = bool(HasNoStride) || bool(PlainObjectType::IsVectorAtCompileTime) ? ~int(0) : ~int(LinearAccessBit),
+ Flags = int( evaluator<PlainObjectType>::Flags) & (LinearAccessMask&PacketAccessMask),
+
+ Alignment = int(MapOptions)&int(AlignedMask)
+ };
+
+ EIGEN_DEVICE_FUNC explicit evaluator(const XprType& map)
+ : mapbase_evaluator<XprType, PlainObjectType>(map)
+ { }
+};
+
+// -------------------- Ref --------------------
+
+template<typename PlainObjectType, int RefOptions, typename StrideType>
+struct evaluator<Ref<PlainObjectType, RefOptions, StrideType> >
+ : public mapbase_evaluator<Ref<PlainObjectType, RefOptions, StrideType>, PlainObjectType>
+{
+ typedef Ref<PlainObjectType, RefOptions, StrideType> XprType;
+
+ enum {
+ Flags = evaluator<Map<PlainObjectType, RefOptions, StrideType> >::Flags,
+ Alignment = evaluator<Map<PlainObjectType, RefOptions, StrideType> >::Alignment
+ };
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ explicit evaluator(const XprType& ref)
+ : mapbase_evaluator<XprType, PlainObjectType>(ref)
+ { }
+};
+
+// -------------------- Block --------------------
+
+template<typename ArgType, int BlockRows, int BlockCols, bool InnerPanel,
+ bool HasDirectAccess = internal::has_direct_access<ArgType>::ret> struct block_evaluator;
+
+template<typename ArgType, int BlockRows, int BlockCols, bool InnerPanel>
+struct evaluator<Block<ArgType, BlockRows, BlockCols, InnerPanel> >
+ : block_evaluator<ArgType, BlockRows, BlockCols, InnerPanel>
+{
+ typedef Block<ArgType, BlockRows, BlockCols, InnerPanel> XprType;
+ typedef typename XprType::Scalar Scalar;
+ // TODO: should check for smaller packet types once we can handle multi-sized packet types
+ typedef typename packet_traits<Scalar>::type PacketScalar;
+
+ enum {
+ CoeffReadCost = evaluator<ArgType>::CoeffReadCost,
+
+ RowsAtCompileTime = traits<XprType>::RowsAtCompileTime,
+ ColsAtCompileTime = traits<XprType>::ColsAtCompileTime,
+ MaxRowsAtCompileTime = traits<XprType>::MaxRowsAtCompileTime,
+ MaxColsAtCompileTime = traits<XprType>::MaxColsAtCompileTime,
+
+ ArgTypeIsRowMajor = (int(evaluator<ArgType>::Flags)&RowMajorBit) != 0,
+ IsRowMajor = (MaxRowsAtCompileTime==1 && MaxColsAtCompileTime!=1) ? 1
+ : (MaxColsAtCompileTime==1 && MaxRowsAtCompileTime!=1) ? 0
+ : ArgTypeIsRowMajor,
+ HasSameStorageOrderAsArgType = (IsRowMajor == ArgTypeIsRowMajor),
+ InnerSize = IsRowMajor ? int(ColsAtCompileTime) : int(RowsAtCompileTime),
+ InnerStrideAtCompileTime = HasSameStorageOrderAsArgType
+ ? int(inner_stride_at_compile_time<ArgType>::ret)
+ : int(outer_stride_at_compile_time<ArgType>::ret),
+ OuterStrideAtCompileTime = HasSameStorageOrderAsArgType
+ ? int(outer_stride_at_compile_time<ArgType>::ret)
+ : int(inner_stride_at_compile_time<ArgType>::ret),
+ MaskPacketAccessBit = (InnerStrideAtCompileTime == 1 || HasSameStorageOrderAsArgType) ? PacketAccessBit : 0,
+
+ FlagsLinearAccessBit = (RowsAtCompileTime == 1 || ColsAtCompileTime == 1 || (InnerPanel && (evaluator<ArgType>::Flags&LinearAccessBit))) ? LinearAccessBit : 0,
+ FlagsRowMajorBit = XprType::Flags&RowMajorBit,
+ Flags0 = evaluator<ArgType>::Flags & ( (HereditaryBits & ~RowMajorBit) |
+ DirectAccessBit |
+ MaskPacketAccessBit),
+ Flags = Flags0 | FlagsLinearAccessBit | FlagsRowMajorBit,
+
+ PacketAlignment = unpacket_traits<PacketScalar>::alignment,
+ Alignment0 = (InnerPanel && (OuterStrideAtCompileTime!=Dynamic)
+ && (OuterStrideAtCompileTime!=0)
+ && (((OuterStrideAtCompileTime * int(sizeof(Scalar))) % int(PacketAlignment)) == 0)) ? int(PacketAlignment) : 0,
+ Alignment = plain_enum_min(evaluator<ArgType>::Alignment, Alignment0)
+ };
+ typedef block_evaluator<ArgType, BlockRows, BlockCols, InnerPanel> block_evaluator_type;
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ explicit evaluator(const XprType& block) : block_evaluator_type(block)
+ {
+ EIGEN_INTERNAL_CHECK_COST_VALUE(CoeffReadCost);
+ }
+};
+
+// no direct-access => dispatch to a unary evaluator
+template<typename ArgType, int BlockRows, int BlockCols, bool InnerPanel>
+struct block_evaluator<ArgType, BlockRows, BlockCols, InnerPanel, /*HasDirectAccess*/ false>
+ : unary_evaluator<Block<ArgType, BlockRows, BlockCols, InnerPanel> >
+{
+ typedef Block<ArgType, BlockRows, BlockCols, InnerPanel> XprType;
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ explicit block_evaluator(const XprType& block)
+ : unary_evaluator<XprType>(block)
+ {}
+};
+
+template<typename ArgType, int BlockRows, int BlockCols, bool InnerPanel>
+struct unary_evaluator<Block<ArgType, BlockRows, BlockCols, InnerPanel>, IndexBased>
+ : evaluator_base<Block<ArgType, BlockRows, BlockCols, InnerPanel> >
+{
+ typedef Block<ArgType, BlockRows, BlockCols, InnerPanel> XprType;
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ explicit unary_evaluator(const XprType& block)
+ : m_argImpl(block.nestedExpression()),
+ m_startRow(block.startRow()),
+ m_startCol(block.startCol()),
+ m_linear_offset(ForwardLinearAccess?(ArgType::IsRowMajor ? block.startRow()*block.nestedExpression().cols() + block.startCol() : block.startCol()*block.nestedExpression().rows() + block.startRow()):0)
+ { }
+
+ typedef typename XprType::Scalar Scalar;
+ typedef typename XprType::CoeffReturnType CoeffReturnType;
+
+ enum {
+ RowsAtCompileTime = XprType::RowsAtCompileTime,
+ ForwardLinearAccess = (InnerPanel || int(XprType::IsRowMajor)==int(ArgType::IsRowMajor)) && bool(evaluator<ArgType>::Flags&LinearAccessBit)
+ };
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ CoeffReturnType coeff(Index row, Index col) const
+ {
+ return m_argImpl.coeff(m_startRow.value() + row, m_startCol.value() + col);
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ CoeffReturnType coeff(Index index) const
+ {
+ return linear_coeff_impl(index, bool_constant<ForwardLinearAccess>());
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ Scalar& coeffRef(Index row, Index col)
+ {
+ return m_argImpl.coeffRef(m_startRow.value() + row, m_startCol.value() + col);
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ Scalar& coeffRef(Index index)
+ {
+ return linear_coeffRef_impl(index, bool_constant<ForwardLinearAccess>());
+ }
+
+ template<int LoadMode, typename PacketType>
+ EIGEN_STRONG_INLINE
+ PacketType packet(Index row, Index col) const
+ {
+ return m_argImpl.template packet<LoadMode,PacketType>(m_startRow.value() + row, m_startCol.value() + col);
+ }
+
+ template<int LoadMode, typename PacketType>
+ EIGEN_STRONG_INLINE
+ PacketType packet(Index index) const
+ {
+ if (ForwardLinearAccess)
+ return m_argImpl.template packet<LoadMode,PacketType>(m_linear_offset.value() + index);
+ else
+ return packet<LoadMode,PacketType>(RowsAtCompileTime == 1 ? 0 : index,
+ RowsAtCompileTime == 1 ? index : 0);
+ }
+
+ template<int StoreMode, typename PacketType>
+ EIGEN_STRONG_INLINE
+ void writePacket(Index row, Index col, const PacketType& x)
+ {
+ return m_argImpl.template writePacket<StoreMode,PacketType>(m_startRow.value() + row, m_startCol.value() + col, x);
+ }
+
+ template<int StoreMode, typename PacketType>
+ EIGEN_STRONG_INLINE
+ void writePacket(Index index, const PacketType& x)
+ {
+ if (ForwardLinearAccess)
+ return m_argImpl.template writePacket<StoreMode,PacketType>(m_linear_offset.value() + index, x);
+ else
+ return writePacket<StoreMode,PacketType>(RowsAtCompileTime == 1 ? 0 : index,
+ RowsAtCompileTime == 1 ? index : 0,
+ x);
+ }
+
+protected:
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ CoeffReturnType linear_coeff_impl(Index index, internal::true_type /* ForwardLinearAccess */) const
+ {
+ return m_argImpl.coeff(m_linear_offset.value() + index);
+ }
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ CoeffReturnType linear_coeff_impl(Index index, internal::false_type /* not ForwardLinearAccess */) const
+ {
+ return coeff(RowsAtCompileTime == 1 ? 0 : index, RowsAtCompileTime == 1 ? index : 0);
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ Scalar& linear_coeffRef_impl(Index index, internal::true_type /* ForwardLinearAccess */)
+ {
+ return m_argImpl.coeffRef(m_linear_offset.value() + index);
+ }
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ Scalar& linear_coeffRef_impl(Index index, internal::false_type /* not ForwardLinearAccess */)
+ {
+ return coeffRef(RowsAtCompileTime == 1 ? 0 : index, RowsAtCompileTime == 1 ? index : 0);
+ }
+
+ evaluator<ArgType> m_argImpl;
+ const variable_if_dynamic<Index, (ArgType::RowsAtCompileTime == 1 && BlockRows==1) ? 0 : Dynamic> m_startRow;
+ const variable_if_dynamic<Index, (ArgType::ColsAtCompileTime == 1 && BlockCols==1) ? 0 : Dynamic> m_startCol;
+ const variable_if_dynamic<Index, ForwardLinearAccess ? Dynamic : 0> m_linear_offset;
+};
+
+// TODO: This evaluator does not actually use the child evaluator;
+// all action is via the data() as returned by the Block expression.
+
+template<typename ArgType, int BlockRows, int BlockCols, bool InnerPanel>
+struct block_evaluator<ArgType, BlockRows, BlockCols, InnerPanel, /* HasDirectAccess */ true>
+ : mapbase_evaluator<Block<ArgType, BlockRows, BlockCols, InnerPanel>,
+ typename Block<ArgType, BlockRows, BlockCols, InnerPanel>::PlainObject>
+{
+ typedef Block<ArgType, BlockRows, BlockCols, InnerPanel> XprType;
+ typedef typename XprType::Scalar Scalar;
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ explicit block_evaluator(const XprType& block)
+ : mapbase_evaluator<XprType, typename XprType::PlainObject>(block)
+ {
+ eigen_internal_assert((internal::is_constant_evaluated() || (internal::UIntPtr(block.data()) % plain_enum_max(1,evaluator<XprType>::Alignment)) == 0) \
+ && "data is not aligned");
+ }
+};
+
+
+// -------------------- Select --------------------
+// NOTE shall we introduce a ternary_evaluator?
+
+// TODO enable vectorization for Select
+template<typename ConditionMatrixType, typename ThenMatrixType, typename ElseMatrixType>
+struct evaluator<Select<ConditionMatrixType, ThenMatrixType, ElseMatrixType> >
+ : evaluator_base<Select<ConditionMatrixType, ThenMatrixType, ElseMatrixType> >
+{
+ typedef Select<ConditionMatrixType, ThenMatrixType, ElseMatrixType> XprType;
+ enum {
+ CoeffReadCost = evaluator<ConditionMatrixType>::CoeffReadCost
+ + plain_enum_max(evaluator<ThenMatrixType>::CoeffReadCost,
+ evaluator<ElseMatrixType>::CoeffReadCost),
+
+ Flags = (unsigned int)evaluator<ThenMatrixType>::Flags & evaluator<ElseMatrixType>::Flags & HereditaryBits,
+
+ Alignment = plain_enum_min(evaluator<ThenMatrixType>::Alignment, evaluator<ElseMatrixType>::Alignment)
+ };
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ explicit evaluator(const XprType& select)
+ : m_conditionImpl(select.conditionMatrix()),
+ m_thenImpl(select.thenMatrix()),
+ m_elseImpl(select.elseMatrix())
+ {
+ EIGEN_INTERNAL_CHECK_COST_VALUE(CoeffReadCost);
+ }
+
+ typedef typename XprType::CoeffReturnType CoeffReturnType;
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ CoeffReturnType coeff(Index row, Index col) const
+ {
+ if (m_conditionImpl.coeff(row, col))
+ return m_thenImpl.coeff(row, col);
+ else
+ return m_elseImpl.coeff(row, col);
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ CoeffReturnType coeff(Index index) const
+ {
+ if (m_conditionImpl.coeff(index))
+ return m_thenImpl.coeff(index);
+ else
+ return m_elseImpl.coeff(index);
+ }
+
+protected:
+ evaluator<ConditionMatrixType> m_conditionImpl;
+ evaluator<ThenMatrixType> m_thenImpl;
+ evaluator<ElseMatrixType> m_elseImpl;
+};
+
+
+// -------------------- Replicate --------------------
+
+template<typename ArgType, int RowFactor, int ColFactor>
+struct unary_evaluator<Replicate<ArgType, RowFactor, ColFactor> >
+ : evaluator_base<Replicate<ArgType, RowFactor, ColFactor> >
+{
+ typedef Replicate<ArgType, RowFactor, ColFactor> XprType;
+ typedef typename XprType::CoeffReturnType CoeffReturnType;
+ enum {
+ Factor = (RowFactor==Dynamic || ColFactor==Dynamic) ? Dynamic : RowFactor*ColFactor
+ };
+ typedef typename internal::nested_eval<ArgType,Factor>::type ArgTypeNested;
+ typedef internal::remove_all_t<ArgTypeNested> ArgTypeNestedCleaned;
+
+ enum {
+ CoeffReadCost = evaluator<ArgTypeNestedCleaned>::CoeffReadCost,
+ LinearAccessMask = XprType::IsVectorAtCompileTime ? LinearAccessBit : 0,
+ Flags = (evaluator<ArgTypeNestedCleaned>::Flags & (HereditaryBits|LinearAccessMask) & ~RowMajorBit) | (traits<XprType>::Flags & RowMajorBit),
+
+ Alignment = evaluator<ArgTypeNestedCleaned>::Alignment
+ };
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ explicit unary_evaluator(const XprType& replicate)
+ : m_arg(replicate.nestedExpression()),
+ m_argImpl(m_arg),
+ m_rows(replicate.nestedExpression().rows()),
+ m_cols(replicate.nestedExpression().cols())
+ {}
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ CoeffReturnType coeff(Index row, Index col) const
+ {
+ // try to avoid using modulo; this is a pure optimization strategy
+ const Index actual_row = internal::traits<XprType>::RowsAtCompileTime==1 ? 0
+ : RowFactor==1 ? row
+ : row % m_rows.value();
+ const Index actual_col = internal::traits<XprType>::ColsAtCompileTime==1 ? 0
+ : ColFactor==1 ? col
+ : col % m_cols.value();
+
+ return m_argImpl.coeff(actual_row, actual_col);
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ CoeffReturnType coeff(Index index) const
+ {
+ // try to avoid using modulo; this is a pure optimization strategy
+ const Index actual_index = internal::traits<XprType>::RowsAtCompileTime==1
+ ? (ColFactor==1 ? index : index%m_cols.value())
+ : (RowFactor==1 ? index : index%m_rows.value());
+
+ return m_argImpl.coeff(actual_index);
+ }
+
+ template<int LoadMode, typename PacketType>
+ EIGEN_STRONG_INLINE
+ PacketType packet(Index row, Index col) const
+ {
+ const Index actual_row = internal::traits<XprType>::RowsAtCompileTime==1 ? 0
+ : RowFactor==1 ? row
+ : row % m_rows.value();
+ const Index actual_col = internal::traits<XprType>::ColsAtCompileTime==1 ? 0
+ : ColFactor==1 ? col
+ : col % m_cols.value();
+
+ return m_argImpl.template packet<LoadMode,PacketType>(actual_row, actual_col);
+ }
+
+ template<int LoadMode, typename PacketType>
+ EIGEN_STRONG_INLINE
+ PacketType packet(Index index) const
+ {
+ const Index actual_index = internal::traits<XprType>::RowsAtCompileTime==1
+ ? (ColFactor==1 ? index : index%m_cols.value())
+ : (RowFactor==1 ? index : index%m_rows.value());
+
+ return m_argImpl.template packet<LoadMode,PacketType>(actual_index);
+ }
+
+protected:
+ const ArgTypeNested m_arg;
+ evaluator<ArgTypeNestedCleaned> m_argImpl;
+ const variable_if_dynamic<Index, ArgType::RowsAtCompileTime> m_rows;
+ const variable_if_dynamic<Index, ArgType::ColsAtCompileTime> m_cols;
+};
+
+// -------------------- MatrixWrapper and ArrayWrapper --------------------
+//
+// evaluator_wrapper_base<T> is a common base class for the
+// MatrixWrapper and ArrayWrapper evaluators.
+
+template<typename XprType>
+struct evaluator_wrapper_base
+ : evaluator_base<XprType>
+{
+ typedef remove_all_t<typename XprType::NestedExpressionType> ArgType;
+ enum {
+ CoeffReadCost = evaluator<ArgType>::CoeffReadCost,
+ Flags = evaluator<ArgType>::Flags,
+ Alignment = evaluator<ArgType>::Alignment
+ };
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ explicit evaluator_wrapper_base(const ArgType& arg) : m_argImpl(arg) {}
+
+ typedef typename ArgType::Scalar Scalar;
+ typedef typename ArgType::CoeffReturnType CoeffReturnType;
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ CoeffReturnType coeff(Index row, Index col) const
+ {
+ return m_argImpl.coeff(row, col);
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ CoeffReturnType coeff(Index index) const
+ {
+ return m_argImpl.coeff(index);
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ Scalar& coeffRef(Index row, Index col)
+ {
+ return m_argImpl.coeffRef(row, col);
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ Scalar& coeffRef(Index index)
+ {
+ return m_argImpl.coeffRef(index);
+ }
+
+ template<int LoadMode, typename PacketType>
+ EIGEN_STRONG_INLINE
+ PacketType packet(Index row, Index col) const
+ {
+ return m_argImpl.template packet<LoadMode,PacketType>(row, col);
+ }
+
+ template<int LoadMode, typename PacketType>
+ EIGEN_STRONG_INLINE
+ PacketType packet(Index index) const
+ {
+ return m_argImpl.template packet<LoadMode,PacketType>(index);
+ }
+
+ template<int StoreMode, typename PacketType>
+ EIGEN_STRONG_INLINE
+ void writePacket(Index row, Index col, const PacketType& x)
+ {
+ m_argImpl.template writePacket<StoreMode>(row, col, x);
+ }
+
+ template<int StoreMode, typename PacketType>
+ EIGEN_STRONG_INLINE
+ void writePacket(Index index, const PacketType& x)
+ {
+ m_argImpl.template writePacket<StoreMode>(index, x);
+ }
+
+protected:
+ evaluator<ArgType> m_argImpl;
+};
+
+template<typename TArgType>
+struct unary_evaluator<MatrixWrapper<TArgType> >
+ : evaluator_wrapper_base<MatrixWrapper<TArgType> >
+{
+ typedef MatrixWrapper<TArgType> XprType;
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ explicit unary_evaluator(const XprType& wrapper)
+ : evaluator_wrapper_base<MatrixWrapper<TArgType> >(wrapper.nestedExpression())
+ { }
+};
+
+template<typename TArgType>
+struct unary_evaluator<ArrayWrapper<TArgType> >
+ : evaluator_wrapper_base<ArrayWrapper<TArgType> >
+{
+ typedef ArrayWrapper<TArgType> XprType;
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ explicit unary_evaluator(const XprType& wrapper)
+ : evaluator_wrapper_base<ArrayWrapper<TArgType> >(wrapper.nestedExpression())
+ { }
+};
+
+
+// -------------------- Reverse --------------------
+
+// defined in Reverse.h:
+template<typename PacketType, bool ReversePacket> struct reverse_packet_cond;
+
+template<typename ArgType, int Direction>
+struct unary_evaluator<Reverse<ArgType, Direction> >
+ : evaluator_base<Reverse<ArgType, Direction> >
+{
+ typedef Reverse<ArgType, Direction> XprType;
+ typedef typename XprType::Scalar Scalar;
+ typedef typename XprType::CoeffReturnType CoeffReturnType;
+
+ enum {
+ IsRowMajor = XprType::IsRowMajor,
+ IsColMajor = !IsRowMajor,
+ ReverseRow = (Direction == Vertical) || (Direction == BothDirections),
+ ReverseCol = (Direction == Horizontal) || (Direction == BothDirections),
+ ReversePacket = (Direction == BothDirections)
+ || ((Direction == Vertical) && IsColMajor)
+ || ((Direction == Horizontal) && IsRowMajor),
+
+ CoeffReadCost = evaluator<ArgType>::CoeffReadCost,
+
+ // let's enable LinearAccess only with vectorization because of the product overhead
+ // FIXME enable DirectAccess with negative strides?
+ Flags0 = evaluator<ArgType>::Flags,
+ LinearAccess = ( (Direction==BothDirections) && (int(Flags0)&PacketAccessBit) )
+ || ((ReverseRow && XprType::ColsAtCompileTime==1) || (ReverseCol && XprType::RowsAtCompileTime==1))
+ ? LinearAccessBit : 0,
+
+ Flags = int(Flags0) & (HereditaryBits | PacketAccessBit | LinearAccess),
+
+ Alignment = 0 // FIXME in some rare cases, Alignment could be preserved, like a Vector4f.
+ };
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ explicit unary_evaluator(const XprType& reverse)
+ : m_argImpl(reverse.nestedExpression()),
+ m_rows(ReverseRow ? reverse.nestedExpression().rows() : 1),
+ m_cols(ReverseCol ? reverse.nestedExpression().cols() : 1)
+ { }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ CoeffReturnType coeff(Index row, Index col) const
+ {
+ return m_argImpl.coeff(ReverseRow ? m_rows.value() - row - 1 : row,
+ ReverseCol ? m_cols.value() - col - 1 : col);
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ CoeffReturnType coeff(Index index) const
+ {
+ return m_argImpl.coeff(m_rows.value() * m_cols.value() - index - 1);
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ Scalar& coeffRef(Index row, Index col)
+ {
+ return m_argImpl.coeffRef(ReverseRow ? m_rows.value() - row - 1 : row,
+ ReverseCol ? m_cols.value() - col - 1 : col);
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ Scalar& coeffRef(Index index)
+ {
+ return m_argImpl.coeffRef(m_rows.value() * m_cols.value() - index - 1);
+ }
+
+ template<int LoadMode, typename PacketType>
+ EIGEN_STRONG_INLINE
+ PacketType packet(Index row, Index col) const
+ {
+ enum {
+ PacketSize = unpacket_traits<PacketType>::size,
+ OffsetRow = ReverseRow && IsColMajor ? PacketSize : 1,
+ OffsetCol = ReverseCol && IsRowMajor ? PacketSize : 1
+ };
+ typedef internal::reverse_packet_cond<PacketType,ReversePacket> reverse_packet;
+ return reverse_packet::run(m_argImpl.template packet<LoadMode,PacketType>(
+ ReverseRow ? m_rows.value() - row - OffsetRow : row,
+ ReverseCol ? m_cols.value() - col - OffsetCol : col));
+ }
+
+ template<int LoadMode, typename PacketType>
+ EIGEN_STRONG_INLINE
+ PacketType packet(Index index) const
+ {
+ enum { PacketSize = unpacket_traits<PacketType>::size };
+ return preverse(m_argImpl.template packet<LoadMode,PacketType>(m_rows.value() * m_cols.value() - index - PacketSize));
+ }
+
+ template<int LoadMode, typename PacketType>
+ EIGEN_STRONG_INLINE
+ void writePacket(Index row, Index col, const PacketType& x)
+ {
+ // FIXME we could factorize some code with packet(i,j)
+ enum {
+ PacketSize = unpacket_traits<PacketType>::size,
+ OffsetRow = ReverseRow && IsColMajor ? PacketSize : 1,
+ OffsetCol = ReverseCol && IsRowMajor ? PacketSize : 1
+ };
+ typedef internal::reverse_packet_cond<PacketType,ReversePacket> reverse_packet;
+ m_argImpl.template writePacket<LoadMode>(
+ ReverseRow ? m_rows.value() - row - OffsetRow : row,
+ ReverseCol ? m_cols.value() - col - OffsetCol : col,
+ reverse_packet::run(x));
+ }
+
+ template<int LoadMode, typename PacketType>
+ EIGEN_STRONG_INLINE
+ void writePacket(Index index, const PacketType& x)
+ {
+ enum { PacketSize = unpacket_traits<PacketType>::size };
+ m_argImpl.template writePacket<LoadMode>
+ (m_rows.value() * m_cols.value() - index - PacketSize, preverse(x));
+ }
+
+protected:
+ evaluator<ArgType> m_argImpl;
+
+ // If we do not reverse rows, then we do not need to know the number of rows; same for columns
+ // Nonetheless, in this case it is important to set to 1 such that the coeff(index) method works fine for vectors.
+ const variable_if_dynamic<Index, ReverseRow ? ArgType::RowsAtCompileTime : 1> m_rows;
+ const variable_if_dynamic<Index, ReverseCol ? ArgType::ColsAtCompileTime : 1> m_cols;
+};
+
+
+// -------------------- Diagonal --------------------
+
+template<typename ArgType, int DiagIndex>
+struct evaluator<Diagonal<ArgType, DiagIndex> >
+ : evaluator_base<Diagonal<ArgType, DiagIndex> >
+{
+ typedef Diagonal<ArgType, DiagIndex> XprType;
+
+ enum {
+ CoeffReadCost = evaluator<ArgType>::CoeffReadCost,
+
+ Flags = (unsigned int)(evaluator<ArgType>::Flags & (HereditaryBits | DirectAccessBit) & ~RowMajorBit) | LinearAccessBit,
+
+ Alignment = 0
+ };
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ explicit evaluator(const XprType& diagonal)
+ : m_argImpl(diagonal.nestedExpression()),
+ m_index(diagonal.index())
+ { }
+
+ typedef typename XprType::Scalar Scalar;
+ typedef typename XprType::CoeffReturnType CoeffReturnType;
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ CoeffReturnType coeff(Index row, Index) const
+ {
+ return m_argImpl.coeff(row + rowOffset(), row + colOffset());
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ CoeffReturnType coeff(Index index) const
+ {
+ return m_argImpl.coeff(index + rowOffset(), index + colOffset());
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ Scalar& coeffRef(Index row, Index)
+ {
+ return m_argImpl.coeffRef(row + rowOffset(), row + colOffset());
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ Scalar& coeffRef(Index index)
+ {
+ return m_argImpl.coeffRef(index + rowOffset(), index + colOffset());
+ }
+
+protected:
+ evaluator<ArgType> m_argImpl;
+ const internal::variable_if_dynamicindex<Index, XprType::DiagIndex> m_index;
+
+private:
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE EIGEN_CONSTEXPR
+ Index rowOffset() const { return m_index.value() > 0 ? 0 : -m_index.value(); }
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE EIGEN_CONSTEXPR
+ Index colOffset() const { return m_index.value() > 0 ? m_index.value() : 0; }
+};
+
+
+//----------------------------------------------------------------------
+// deprecated code
+//----------------------------------------------------------------------
+
+// -------------------- EvalToTemp --------------------
+
+// expression class for evaluating nested expression to a temporary
+
+template<typename ArgType> class EvalToTemp;
+
+template<typename ArgType>
+struct traits<EvalToTemp<ArgType> >
+ : public traits<ArgType>
+{ };
+
+template<typename ArgType>
+class EvalToTemp
+ : public dense_xpr_base<EvalToTemp<ArgType> >::type
+{
+ public:
+
+ typedef typename dense_xpr_base<EvalToTemp>::type Base;
+ EIGEN_GENERIC_PUBLIC_INTERFACE(EvalToTemp)
+
+ explicit EvalToTemp(const ArgType& arg)
+ : m_arg(arg)
+ { }
+
+ const ArgType& arg() const
+ {
+ return m_arg;
+ }
+
+ EIGEN_CONSTEXPR Index rows() const EIGEN_NOEXCEPT
+ {
+ return m_arg.rows();
+ }
+
+ EIGEN_CONSTEXPR Index cols() const EIGEN_NOEXCEPT
+ {
+ return m_arg.cols();
+ }
+
+ private:
+ const ArgType& m_arg;
+};
+
+template<typename ArgType>
+struct evaluator<EvalToTemp<ArgType> >
+ : public evaluator<typename ArgType::PlainObject>
+{
+ typedef EvalToTemp<ArgType> XprType;
+ typedef typename ArgType::PlainObject PlainObject;
+ typedef evaluator<PlainObject> Base;
+
+ EIGEN_DEVICE_FUNC explicit evaluator(const XprType& xpr)
+ : m_result(xpr.arg())
+ {
+ internal::construct_at<Base>(this, m_result);
+ }
+
+ // This constructor is used when nesting an EvalTo evaluator in another evaluator
+ EIGEN_DEVICE_FUNC evaluator(const ArgType& arg)
+ : m_result(arg)
+ {
+ internal::construct_at<Base>(this, m_result);
+ }
+
+protected:
+ PlainObject m_result;
+};
+
+} // namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_COREEVALUATORS_H
diff --git a/Eigen/src/Core/CoreIterators.h b/Eigen/src/Core/CoreIterators.h
new file mode 100644
index 0000000..f74568a
--- /dev/null
+++ b/Eigen/src/Core/CoreIterators.h
@@ -0,0 +1,134 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2014 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_COREITERATORS_H
+#define EIGEN_COREITERATORS_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+/* This file contains the respective InnerIterator definition of the expressions defined in Eigen/Core
+ */
+
+namespace internal {
+
+template<typename XprType, typename EvaluatorKind>
+class inner_iterator_selector;
+
+}
+
+/** \class InnerIterator
+ * \brief An InnerIterator allows to loop over the element of any matrix expression.
+ *
+ * \warning To be used with care because an evaluator is constructed every time an InnerIterator iterator is constructed.
+ *
+ * TODO: add a usage example
+ */
+template<typename XprType>
+class InnerIterator
+{
+protected:
+ typedef internal::inner_iterator_selector<XprType, typename internal::evaluator_traits<XprType>::Kind> IteratorType;
+ typedef internal::evaluator<XprType> EvaluatorType;
+ typedef typename internal::traits<XprType>::Scalar Scalar;
+public:
+ /** Construct an iterator over the \a outerId -th row or column of \a xpr */
+ InnerIterator(const XprType &xpr, const Index &outerId)
+ : m_eval(xpr), m_iter(m_eval, outerId, xpr.innerSize())
+ {}
+
+ /// \returns the value of the current coefficient.
+ EIGEN_STRONG_INLINE Scalar value() const { return m_iter.value(); }
+ /** Increment the iterator \c *this to the next non-zero coefficient.
+ * Explicit zeros are not skipped over. To skip explicit zeros, see class SparseView
+ */
+ EIGEN_STRONG_INLINE InnerIterator& operator++() { m_iter.operator++(); return *this; }
+ EIGEN_STRONG_INLINE InnerIterator& operator+=(Index i) { m_iter.operator+=(i); return *this; }
+ EIGEN_STRONG_INLINE InnerIterator operator+(Index i)
+ { InnerIterator result(*this); result+=i; return result; }
+
+
+ /// \returns the column or row index of the current coefficient.
+ EIGEN_STRONG_INLINE Index index() const { return m_iter.index(); }
+ /// \returns the row index of the current coefficient.
+ EIGEN_STRONG_INLINE Index row() const { return m_iter.row(); }
+ /// \returns the column index of the current coefficient.
+ EIGEN_STRONG_INLINE Index col() const { return m_iter.col(); }
+ /// \returns \c true if the iterator \c *this still references a valid coefficient.
+ EIGEN_STRONG_INLINE operator bool() const { return m_iter; }
+
+protected:
+ EvaluatorType m_eval;
+ IteratorType m_iter;
+private:
+ // If you get here, then you're not using the right InnerIterator type, e.g.:
+ // SparseMatrix<double,RowMajor> A;
+ // SparseMatrix<double>::InnerIterator it(A,0);
+ template<typename T> InnerIterator(const EigenBase<T>&,Index outer);
+};
+
+namespace internal {
+
+// Generic inner iterator implementation for dense objects
+template<typename XprType>
+class inner_iterator_selector<XprType, IndexBased>
+{
+protected:
+ typedef evaluator<XprType> EvaluatorType;
+ typedef typename traits<XprType>::Scalar Scalar;
+ enum { IsRowMajor = (XprType::Flags&RowMajorBit)==RowMajorBit };
+
+public:
+ EIGEN_STRONG_INLINE inner_iterator_selector(const EvaluatorType &eval, const Index &outerId, const Index &innerSize)
+ : m_eval(eval), m_inner(0), m_outer(outerId), m_end(innerSize)
+ {}
+
+ EIGEN_STRONG_INLINE Scalar value() const
+ {
+ return (IsRowMajor) ? m_eval.coeff(m_outer, m_inner)
+ : m_eval.coeff(m_inner, m_outer);
+ }
+
+ EIGEN_STRONG_INLINE inner_iterator_selector& operator++() { m_inner++; return *this; }
+
+ EIGEN_STRONG_INLINE Index index() const { return m_inner; }
+ inline Index row() const { return IsRowMajor ? m_outer : index(); }
+ inline Index col() const { return IsRowMajor ? index() : m_outer; }
+
+ EIGEN_STRONG_INLINE operator bool() const { return m_inner < m_end && m_inner>=0; }
+
+protected:
+ const EvaluatorType& m_eval;
+ Index m_inner;
+ const Index m_outer;
+ const Index m_end;
+};
+
+// For iterator-based evaluator, inner-iterator is already implemented as
+// evaluator<>::InnerIterator
+template<typename XprType>
+class inner_iterator_selector<XprType, IteratorBased>
+ : public evaluator<XprType>::InnerIterator
+{
+protected:
+ typedef typename evaluator<XprType>::InnerIterator Base;
+ typedef evaluator<XprType> EvaluatorType;
+
+public:
+ EIGEN_STRONG_INLINE inner_iterator_selector(const EvaluatorType &eval, const Index &outerId, const Index &/*innerSize*/)
+ : Base(eval, outerId)
+ {}
+};
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_COREITERATORS_H
diff --git a/Eigen/src/Core/CwiseBinaryOp.h b/Eigen/src/Core/CwiseBinaryOp.h
new file mode 100644
index 0000000..21a061a
--- /dev/null
+++ b/Eigen/src/Core/CwiseBinaryOp.h
@@ -0,0 +1,185 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2014 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_CWISE_BINARY_OP_H
+#define EIGEN_CWISE_BINARY_OP_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+template<typename BinaryOp, typename Lhs, typename Rhs>
+struct traits<CwiseBinaryOp<BinaryOp, Lhs, Rhs> >
+{
+ // we must not inherit from traits<Lhs> since it has
+ // the potential to cause problems with MSVC
+ typedef remove_all_t<Lhs> Ancestor;
+ typedef typename traits<Ancestor>::XprKind XprKind;
+ enum {
+ RowsAtCompileTime = traits<Ancestor>::RowsAtCompileTime,
+ ColsAtCompileTime = traits<Ancestor>::ColsAtCompileTime,
+ MaxRowsAtCompileTime = traits<Ancestor>::MaxRowsAtCompileTime,
+ MaxColsAtCompileTime = traits<Ancestor>::MaxColsAtCompileTime
+ };
+
+ // even though we require Lhs and Rhs to have the same scalar type (see CwiseBinaryOp constructor),
+ // we still want to handle the case when the result type is different.
+ typedef typename result_of<
+ BinaryOp(
+ const typename Lhs::Scalar&,
+ const typename Rhs::Scalar&
+ )
+ >::type Scalar;
+ typedef typename cwise_promote_storage_type<typename traits<Lhs>::StorageKind,
+ typename traits<Rhs>::StorageKind,
+ BinaryOp>::ret StorageKind;
+ typedef typename promote_index_type<typename traits<Lhs>::StorageIndex,
+ typename traits<Rhs>::StorageIndex>::type StorageIndex;
+ typedef typename Lhs::Nested LhsNested;
+ typedef typename Rhs::Nested RhsNested;
+ typedef std::remove_reference_t<LhsNested> LhsNested_;
+ typedef std::remove_reference_t<RhsNested> RhsNested_;
+ enum {
+ Flags = cwise_promote_storage_order<typename traits<Lhs>::StorageKind,typename traits<Rhs>::StorageKind,LhsNested_::Flags & RowMajorBit,RhsNested_::Flags & RowMajorBit>::value
+ };
+};
+} // end namespace internal
+
+template<typename BinaryOp, typename Lhs, typename Rhs, typename StorageKind>
+class CwiseBinaryOpImpl;
+
+/** \class CwiseBinaryOp
+ * \ingroup Core_Module
+ *
+ * \brief Generic expression where a coefficient-wise binary operator is applied to two expressions
+ *
+ * \tparam BinaryOp template functor implementing the operator
+ * \tparam LhsType the type of the left-hand side
+ * \tparam RhsType the type of the right-hand side
+ *
+ * This class represents an expression where a coefficient-wise binary operator is applied to two expressions.
+ * It is the return type of binary operators, by which we mean only those binary operators where
+ * both the left-hand side and the right-hand side are Eigen expressions.
+ * For example, the return type of matrix1+matrix2 is a CwiseBinaryOp.
+ *
+ * Most of the time, this is the only way that it is used, so you typically don't have to name
+ * CwiseBinaryOp types explicitly.
+ *
+ * \sa MatrixBase::binaryExpr(const MatrixBase<OtherDerived> &,const CustomBinaryOp &) const, class CwiseUnaryOp, class CwiseNullaryOp
+ */
+template<typename BinaryOp, typename LhsType, typename RhsType>
+class CwiseBinaryOp :
+ public CwiseBinaryOpImpl<
+ BinaryOp, LhsType, RhsType,
+ typename internal::cwise_promote_storage_type<typename internal::traits<LhsType>::StorageKind,
+ typename internal::traits<RhsType>::StorageKind,
+ BinaryOp>::ret>,
+ internal::no_assignment_operator
+{
+ public:
+
+ typedef internal::remove_all_t<BinaryOp> Functor;
+ typedef internal::remove_all_t<LhsType> Lhs;
+ typedef internal::remove_all_t<RhsType> Rhs;
+
+ typedef typename CwiseBinaryOpImpl<
+ BinaryOp, LhsType, RhsType,
+ typename internal::cwise_promote_storage_type<typename internal::traits<LhsType>::StorageKind,
+ typename internal::traits<Rhs>::StorageKind,
+ BinaryOp>::ret>::Base Base;
+ EIGEN_GENERIC_PUBLIC_INTERFACE(CwiseBinaryOp)
+
+ EIGEN_CHECK_BINARY_COMPATIBILIY(BinaryOp,typename Lhs::Scalar,typename Rhs::Scalar)
+ EIGEN_STATIC_ASSERT_SAME_MATRIX_SIZE(Lhs, Rhs)
+
+ typedef typename internal::ref_selector<LhsType>::type LhsNested;
+ typedef typename internal::ref_selector<RhsType>::type RhsNested;
+ typedef std::remove_reference_t<LhsNested> LhsNested_;
+ typedef std::remove_reference_t<RhsNested> RhsNested_;
+
+#if EIGEN_COMP_MSVC
+ //Required for Visual Studio or the Copy constructor will probably not get inlined!
+ EIGEN_STRONG_INLINE
+ CwiseBinaryOp(const CwiseBinaryOp<BinaryOp,LhsType,RhsType>&) = default;
+#endif
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ CwiseBinaryOp(const Lhs& aLhs, const Rhs& aRhs, const BinaryOp& func = BinaryOp())
+ : m_lhs(aLhs), m_rhs(aRhs), m_functor(func)
+ {
+ eigen_assert(aLhs.rows() == aRhs.rows() && aLhs.cols() == aRhs.cols());
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE EIGEN_CONSTEXPR
+ Index rows() const EIGEN_NOEXCEPT {
+ // return the fixed size type if available to enable compile time optimizations
+ return internal::traits<internal::remove_all_t<LhsNested>>::RowsAtCompileTime==Dynamic ? m_rhs.rows() : m_lhs.rows();
+ }
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE EIGEN_CONSTEXPR
+ Index cols() const EIGEN_NOEXCEPT {
+ // return the fixed size type if available to enable compile time optimizations
+ return internal::traits<internal::remove_all_t<LhsNested>>::ColsAtCompileTime==Dynamic ? m_rhs.cols() : m_lhs.cols();
+ }
+
+ /** \returns the left hand side nested expression */
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ const LhsNested_& lhs() const { return m_lhs; }
+ /** \returns the right hand side nested expression */
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ const RhsNested_& rhs() const { return m_rhs; }
+ /** \returns the functor representing the binary operation */
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ const BinaryOp& functor() const { return m_functor; }
+
+ protected:
+ LhsNested m_lhs;
+ RhsNested m_rhs;
+ const BinaryOp m_functor;
+};
+
+// Generic API dispatcher
+template<typename BinaryOp, typename Lhs, typename Rhs, typename StorageKind>
+class CwiseBinaryOpImpl
+ : public internal::generic_xpr_base<CwiseBinaryOp<BinaryOp, Lhs, Rhs> >::type
+{
+public:
+ typedef typename internal::generic_xpr_base<CwiseBinaryOp<BinaryOp, Lhs, Rhs> >::type Base;
+};
+
+/** replaces \c *this by \c *this - \a other.
+ *
+ * \returns a reference to \c *this
+ */
+template<typename Derived>
+template<typename OtherDerived>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived &
+MatrixBase<Derived>::operator-=(const MatrixBase<OtherDerived> &other)
+{
+ call_assignment(derived(), other.derived(), internal::sub_assign_op<Scalar,typename OtherDerived::Scalar>());
+ return derived();
+}
+
+/** replaces \c *this by \c *this + \a other.
+ *
+ * \returns a reference to \c *this
+ */
+template<typename Derived>
+template<typename OtherDerived>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived &
+MatrixBase<Derived>::operator+=(const MatrixBase<OtherDerived>& other)
+{
+ call_assignment(derived(), other.derived(), internal::add_assign_op<Scalar,typename OtherDerived::Scalar>());
+ return derived();
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_CWISE_BINARY_OP_H
diff --git a/Eigen/src/Core/CwiseNullaryOp.h b/Eigen/src/Core/CwiseNullaryOp.h
new file mode 100644
index 0000000..a62f54d
--- /dev/null
+++ b/Eigen/src/Core/CwiseNullaryOp.h
@@ -0,0 +1,1003 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2010 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_CWISE_NULLARY_OP_H
+#define EIGEN_CWISE_NULLARY_OP_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+template<typename NullaryOp, typename PlainObjectType>
+struct traits<CwiseNullaryOp<NullaryOp, PlainObjectType> > : traits<PlainObjectType>
+{
+ enum {
+ Flags = traits<PlainObjectType>::Flags & RowMajorBit
+ };
+};
+
+} // namespace internal
+
+/** \class CwiseNullaryOp
+ * \ingroup Core_Module
+ *
+ * \brief Generic expression of a matrix where all coefficients are defined by a functor
+ *
+ * \tparam NullaryOp template functor implementing the operator
+ * \tparam PlainObjectType the underlying plain matrix/array type
+ *
+ * This class represents an expression of a generic nullary operator.
+ * It is the return type of the Ones(), Zero(), Constant(), Identity() and Random() methods,
+ * and most of the time this is the only way it is used.
+ *
+ * However, if you want to write a function returning such an expression, you
+ * will need to use this class.
+ *
+ * The functor NullaryOp must expose one of the following method:
+ <table class="manual">
+ <tr ><td>\c operator()() </td><td>if the procedural generation does not depend on the coefficient entries (e.g., random numbers)</td></tr>
+ <tr class="alt"><td>\c operator()(Index i)</td><td>if the procedural generation makes sense for vectors only and that it depends on the coefficient index \c i (e.g., linspace) </td></tr>
+ <tr ><td>\c operator()(Index i,Index j)</td><td>if the procedural generation depends on the matrix coordinates \c i, \c j (e.g., to generate a checkerboard with 0 and 1)</td></tr>
+ </table>
+ * It is also possible to expose the last two operators if the generation makes sense for matrices but can be optimized for vectors.
+ *
+ * See DenseBase::NullaryExpr(Index,const CustomNullaryOp&) for an example binding
+ * C++11 random number generators.
+ *
+ * A nullary expression can also be used to implement custom sophisticated matrix manipulations
+ * that cannot be covered by the existing set of natively supported matrix manipulations.
+ * See this \ref TopicCustomizing_NullaryExpr "page" for some examples and additional explanations
+ * on the behavior of CwiseNullaryOp.
+ *
+ * \sa class CwiseUnaryOp, class CwiseBinaryOp, DenseBase::NullaryExpr
+ */
+template<typename NullaryOp, typename PlainObjectType>
+class CwiseNullaryOp : public internal::dense_xpr_base< CwiseNullaryOp<NullaryOp, PlainObjectType> >::type, internal::no_assignment_operator
+{
+ public:
+
+ typedef typename internal::dense_xpr_base<CwiseNullaryOp>::type Base;
+ EIGEN_DENSE_PUBLIC_INTERFACE(CwiseNullaryOp)
+
+ EIGEN_DEVICE_FUNC
+ CwiseNullaryOp(Index rows, Index cols, const NullaryOp& func = NullaryOp())
+ : m_rows(rows), m_cols(cols), m_functor(func)
+ {
+ eigen_assert(rows >= 0
+ && (RowsAtCompileTime == Dynamic || RowsAtCompileTime == rows)
+ && cols >= 0
+ && (ColsAtCompileTime == Dynamic || ColsAtCompileTime == cols));
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE EIGEN_CONSTEXPR
+ Index rows() const { return m_rows.value(); }
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE EIGEN_CONSTEXPR
+ Index cols() const { return m_cols.value(); }
+
+ /** \returns the functor representing the nullary operation */
+ EIGEN_DEVICE_FUNC
+ const NullaryOp& functor() const { return m_functor; }
+
+ protected:
+ const internal::variable_if_dynamic<Index, RowsAtCompileTime> m_rows;
+ const internal::variable_if_dynamic<Index, ColsAtCompileTime> m_cols;
+ const NullaryOp m_functor;
+};
+
+
+/** \returns an expression of a matrix defined by a custom functor \a func
+ *
+ * The parameters \a rows and \a cols are the number of rows and of columns of
+ * the returned matrix. Must be compatible with this MatrixBase type.
+ *
+ * This variant is meant to be used for dynamic-size matrix types. For fixed-size types,
+ * it is redundant to pass \a rows and \a cols as arguments, so Zero() should be used
+ * instead.
+ *
+ * The template parameter \a CustomNullaryOp is the type of the functor.
+ *
+ * \sa class CwiseNullaryOp
+ */
+template<typename Derived>
+template<typename CustomNullaryOp>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+#ifndef EIGEN_PARSED_BY_DOXYGEN
+const CwiseNullaryOp<CustomNullaryOp,typename DenseBase<Derived>::PlainObject>
+#else
+const CwiseNullaryOp<CustomNullaryOp,PlainObject>
+#endif
+DenseBase<Derived>::NullaryExpr(Index rows, Index cols, const CustomNullaryOp& func)
+{
+ return CwiseNullaryOp<CustomNullaryOp, PlainObject>(rows, cols, func);
+}
+
+/** \returns an expression of a matrix defined by a custom functor \a func
+ *
+ * The parameter \a size is the size of the returned vector.
+ * Must be compatible with this MatrixBase type.
+ *
+ * \only_for_vectors
+ *
+ * This variant is meant to be used for dynamic-size vector types. For fixed-size types,
+ * it is redundant to pass \a size as argument, so Zero() should be used
+ * instead.
+ *
+ * The template parameter \a CustomNullaryOp is the type of the functor.
+ *
+ * Here is an example with C++11 random generators: \include random_cpp11.cpp
+ * Output: \verbinclude random_cpp11.out
+ *
+ * \sa class CwiseNullaryOp
+ */
+template<typename Derived>
+template<typename CustomNullaryOp>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+#ifndef EIGEN_PARSED_BY_DOXYGEN
+const CwiseNullaryOp<CustomNullaryOp, typename DenseBase<Derived>::PlainObject>
+#else
+const CwiseNullaryOp<CustomNullaryOp, PlainObject>
+#endif
+DenseBase<Derived>::NullaryExpr(Index size, const CustomNullaryOp& func)
+{
+ EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
+ if(RowsAtCompileTime == 1) return CwiseNullaryOp<CustomNullaryOp, PlainObject>(1, size, func);
+ else return CwiseNullaryOp<CustomNullaryOp, PlainObject>(size, 1, func);
+}
+
+/** \returns an expression of a matrix defined by a custom functor \a func
+ *
+ * This variant is only for fixed-size DenseBase types. For dynamic-size types, you
+ * need to use the variants taking size arguments.
+ *
+ * The template parameter \a CustomNullaryOp is the type of the functor.
+ *
+ * \sa class CwiseNullaryOp
+ */
+template<typename Derived>
+template<typename CustomNullaryOp>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+#ifndef EIGEN_PARSED_BY_DOXYGEN
+const CwiseNullaryOp<CustomNullaryOp, typename DenseBase<Derived>::PlainObject>
+#else
+const CwiseNullaryOp<CustomNullaryOp, PlainObject>
+#endif
+DenseBase<Derived>::NullaryExpr(const CustomNullaryOp& func)
+{
+ return CwiseNullaryOp<CustomNullaryOp, PlainObject>(RowsAtCompileTime, ColsAtCompileTime, func);
+}
+
+/** \returns an expression of a constant matrix of value \a value
+ *
+ * The parameters \a rows and \a cols are the number of rows and of columns of
+ * the returned matrix. Must be compatible with this DenseBase type.
+ *
+ * This variant is meant to be used for dynamic-size matrix types. For fixed-size types,
+ * it is redundant to pass \a rows and \a cols as arguments, so Zero() should be used
+ * instead.
+ *
+ * The template parameter \a CustomNullaryOp is the type of the functor.
+ *
+ * \sa class CwiseNullaryOp
+ */
+template<typename Derived>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename DenseBase<Derived>::ConstantReturnType
+DenseBase<Derived>::Constant(Index rows, Index cols, const Scalar& value)
+{
+ return DenseBase<Derived>::NullaryExpr(rows, cols, internal::scalar_constant_op<Scalar>(value));
+}
+
+/** \returns an expression of a constant matrix of value \a value
+ *
+ * The parameter \a size is the size of the returned vector.
+ * Must be compatible with this DenseBase type.
+ *
+ * \only_for_vectors
+ *
+ * This variant is meant to be used for dynamic-size vector types. For fixed-size types,
+ * it is redundant to pass \a size as argument, so Zero() should be used
+ * instead.
+ *
+ * The template parameter \a CustomNullaryOp is the type of the functor.
+ *
+ * \sa class CwiseNullaryOp
+ */
+template<typename Derived>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename DenseBase<Derived>::ConstantReturnType
+DenseBase<Derived>::Constant(Index size, const Scalar& value)
+{
+ return DenseBase<Derived>::NullaryExpr(size, internal::scalar_constant_op<Scalar>(value));
+}
+
+/** \returns an expression of a constant matrix of value \a value
+ *
+ * This variant is only for fixed-size DenseBase types. For dynamic-size types, you
+ * need to use the variants taking size arguments.
+ *
+ * The template parameter \a CustomNullaryOp is the type of the functor.
+ *
+ * \sa class CwiseNullaryOp
+ */
+template<typename Derived>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename DenseBase<Derived>::ConstantReturnType
+DenseBase<Derived>::Constant(const Scalar& value)
+{
+ EIGEN_STATIC_ASSERT_FIXED_SIZE(Derived)
+ return DenseBase<Derived>::NullaryExpr(RowsAtCompileTime, ColsAtCompileTime, internal::scalar_constant_op<Scalar>(value));
+}
+
+/** \deprecated because of accuracy loss. In Eigen 3.3, it is an alias for LinSpaced(Index,const Scalar&,const Scalar&)
+ *
+ * \only_for_vectors
+ *
+ * Example: \include DenseBase_LinSpaced_seq_deprecated.cpp
+ * Output: \verbinclude DenseBase_LinSpaced_seq_deprecated.out
+ *
+ * \sa LinSpaced(Index,const Scalar&, const Scalar&), setLinSpaced(Index,const Scalar&,const Scalar&)
+ */
+template<typename Derived>
+EIGEN_DEPRECATED EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename DenseBase<Derived>::RandomAccessLinSpacedReturnType
+DenseBase<Derived>::LinSpaced(Sequential_t, Index size, const Scalar& low, const Scalar& high)
+{
+ EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
+ return DenseBase<Derived>::NullaryExpr(size, internal::linspaced_op<Scalar>(low,high,size));
+}
+
+/** \deprecated because of accuracy loss. In Eigen 3.3, it is an alias for LinSpaced(const Scalar&,const Scalar&)
+ *
+ * \sa LinSpaced(const Scalar&, const Scalar&)
+ */
+template<typename Derived>
+EIGEN_DEPRECATED EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename DenseBase<Derived>::RandomAccessLinSpacedReturnType
+DenseBase<Derived>::LinSpaced(Sequential_t, const Scalar& low, const Scalar& high)
+{
+ EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
+ EIGEN_STATIC_ASSERT_FIXED_SIZE(Derived)
+ return DenseBase<Derived>::NullaryExpr(Derived::SizeAtCompileTime, internal::linspaced_op<Scalar>(low,high,Derived::SizeAtCompileTime));
+}
+
+/**
+ * \brief Sets a linearly spaced vector.
+ *
+ * The function generates 'size' equally spaced values in the closed interval [low,high].
+ * When size is set to 1, a vector of length 1 containing 'high' is returned.
+ *
+ * \only_for_vectors
+ *
+ * Example: \include DenseBase_LinSpaced.cpp
+ * Output: \verbinclude DenseBase_LinSpaced.out
+ *
+ * For integer scalar types, an even spacing is possible if and only if the length of the range,
+ * i.e., \c high-low is a scalar multiple of \c size-1, or if \c size is a scalar multiple of the
+ * number of values \c high-low+1 (meaning each value can be repeated the same number of time).
+ * If one of these two considions is not satisfied, then \c high is lowered to the largest value
+ * satisfying one of this constraint.
+ * Here are some examples:
+ *
+ * Example: \include DenseBase_LinSpacedInt.cpp
+ * Output: \verbinclude DenseBase_LinSpacedInt.out
+ *
+ * \sa setLinSpaced(Index,const Scalar&,const Scalar&), CwiseNullaryOp
+ */
+template<typename Derived>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename DenseBase<Derived>::RandomAccessLinSpacedReturnType
+DenseBase<Derived>::LinSpaced(Index size, const Scalar& low, const Scalar& high)
+{
+ EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
+ return DenseBase<Derived>::NullaryExpr(size, internal::linspaced_op<Scalar>(low,high,size));
+}
+
+/**
+ * \copydoc DenseBase::LinSpaced(Index, const Scalar&, const Scalar&)
+ * Special version for fixed size types which does not require the size parameter.
+ */
+template<typename Derived>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename DenseBase<Derived>::RandomAccessLinSpacedReturnType
+DenseBase<Derived>::LinSpaced(const Scalar& low, const Scalar& high)
+{
+ EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
+ EIGEN_STATIC_ASSERT_FIXED_SIZE(Derived)
+ return DenseBase<Derived>::NullaryExpr(Derived::SizeAtCompileTime, internal::linspaced_op<Scalar>(low,high,Derived::SizeAtCompileTime));
+}
+
+/** \returns true if all coefficients in this matrix are approximately equal to \a val, to within precision \a prec */
+template<typename Derived>
+EIGEN_DEVICE_FUNC bool DenseBase<Derived>::isApproxToConstant
+(const Scalar& val, const RealScalar& prec) const
+{
+ typename internal::nested_eval<Derived,1>::type self(derived());
+ for(Index j = 0; j < cols(); ++j)
+ for(Index i = 0; i < rows(); ++i)
+ if(!internal::isApprox(self.coeff(i, j), val, prec))
+ return false;
+ return true;
+}
+
+/** This is just an alias for isApproxToConstant().
+ *
+ * \returns true if all coefficients in this matrix are approximately equal to \a value, to within precision \a prec */
+template<typename Derived>
+EIGEN_DEVICE_FUNC bool DenseBase<Derived>::isConstant
+(const Scalar& val, const RealScalar& prec) const
+{
+ return isApproxToConstant(val, prec);
+}
+
+/** Alias for setConstant(): sets all coefficients in this expression to \a val.
+ *
+ * \sa setConstant(), Constant(), class CwiseNullaryOp
+ */
+template<typename Derived>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void DenseBase<Derived>::fill(const Scalar& val)
+{
+ setConstant(val);
+}
+
+/** Sets all coefficients in this expression to value \a val.
+ *
+ * \sa fill(), setConstant(Index,const Scalar&), setConstant(Index,Index,const Scalar&), setZero(), setOnes(), Constant(), class CwiseNullaryOp, setZero(), setOnes()
+ */
+template<typename Derived>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& DenseBase<Derived>::setConstant(const Scalar& val)
+{
+ return derived() = Constant(rows(), cols(), val);
+}
+
+/** Resizes to the given \a size, and sets all coefficients in this expression to the given value \a val.
+ *
+ * \only_for_vectors
+ *
+ * Example: \include Matrix_setConstant_int.cpp
+ * Output: \verbinclude Matrix_setConstant_int.out
+ *
+ * \sa MatrixBase::setConstant(const Scalar&), setConstant(Index,Index,const Scalar&), class CwiseNullaryOp, MatrixBase::Constant(const Scalar&)
+ */
+template<typename Derived>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived&
+PlainObjectBase<Derived>::setConstant(Index size, const Scalar& val)
+{
+ resize(size);
+ return setConstant(val);
+}
+
+/** Resizes to the given size, and sets all coefficients in this expression to the given value \a val.
+ *
+ * \param rows the new number of rows
+ * \param cols the new number of columns
+ * \param val the value to which all coefficients are set
+ *
+ * Example: \include Matrix_setConstant_int_int.cpp
+ * Output: \verbinclude Matrix_setConstant_int_int.out
+ *
+ * \sa MatrixBase::setConstant(const Scalar&), setConstant(Index,const Scalar&), class CwiseNullaryOp, MatrixBase::Constant(const Scalar&)
+ */
+template<typename Derived>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived&
+PlainObjectBase<Derived>::setConstant(Index rows, Index cols, const Scalar& val)
+{
+ resize(rows, cols);
+ return setConstant(val);
+}
+
+/** Resizes to the given size, changing only the number of columns, and sets all
+ * coefficients in this expression to the given value \a val. For the parameter
+ * of type NoChange_t, just pass the special value \c NoChange.
+ *
+ * \sa MatrixBase::setConstant(const Scalar&), setConstant(Index,const Scalar&), class CwiseNullaryOp, MatrixBase::Constant(const Scalar&)
+ */
+template<typename Derived>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived&
+PlainObjectBase<Derived>::setConstant(NoChange_t, Index cols, const Scalar& val)
+{
+ return setConstant(rows(), cols, val);
+}
+
+/** Resizes to the given size, changing only the number of rows, and sets all
+ * coefficients in this expression to the given value \a val. For the parameter
+ * of type NoChange_t, just pass the special value \c NoChange.
+ *
+ * \sa MatrixBase::setConstant(const Scalar&), setConstant(Index,const Scalar&), class CwiseNullaryOp, MatrixBase::Constant(const Scalar&)
+ */
+template<typename Derived>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived&
+PlainObjectBase<Derived>::setConstant(Index rows, NoChange_t, const Scalar& val)
+{
+ return setConstant(rows, cols(), val);
+}
+
+
+/**
+ * \brief Sets a linearly spaced vector.
+ *
+ * The function generates 'size' equally spaced values in the closed interval [low,high].
+ * When size is set to 1, a vector of length 1 containing 'high' is returned.
+ *
+ * \only_for_vectors
+ *
+ * Example: \include DenseBase_setLinSpaced.cpp
+ * Output: \verbinclude DenseBase_setLinSpaced.out
+ *
+ * For integer scalar types, do not miss the explanations on the definition
+ * of \link LinSpaced(Index,const Scalar&,const Scalar&) even spacing \endlink.
+ *
+ * \sa LinSpaced(Index,const Scalar&,const Scalar&), CwiseNullaryOp
+ */
+template<typename Derived>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& DenseBase<Derived>::setLinSpaced(Index newSize, const Scalar& low, const Scalar& high)
+{
+ EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
+ return derived() = Derived::NullaryExpr(newSize, internal::linspaced_op<Scalar>(low,high,newSize));
+}
+
+/**
+ * \brief Sets a linearly spaced vector.
+ *
+ * The function fills \c *this with equally spaced values in the closed interval [low,high].
+ * When size is set to 1, a vector of length 1 containing 'high' is returned.
+ *
+ * \only_for_vectors
+ *
+ * For integer scalar types, do not miss the explanations on the definition
+ * of \link LinSpaced(Index,const Scalar&,const Scalar&) even spacing \endlink.
+ *
+ * \sa LinSpaced(Index,const Scalar&,const Scalar&), setLinSpaced(Index, const Scalar&, const Scalar&), CwiseNullaryOp
+ */
+template<typename Derived>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& DenseBase<Derived>::setLinSpaced(const Scalar& low, const Scalar& high)
+{
+ EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
+ return setLinSpaced(size(), low, high);
+}
+
+// zero:
+
+/** \returns an expression of a zero matrix.
+ *
+ * The parameters \a rows and \a cols are the number of rows and of columns of
+ * the returned matrix. Must be compatible with this MatrixBase type.
+ *
+ * This variant is meant to be used for dynamic-size matrix types. For fixed-size types,
+ * it is redundant to pass \a rows and \a cols as arguments, so Zero() should be used
+ * instead.
+ *
+ * Example: \include MatrixBase_zero_int_int.cpp
+ * Output: \verbinclude MatrixBase_zero_int_int.out
+ *
+ * \sa Zero(), Zero(Index)
+ */
+template<typename Derived>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename DenseBase<Derived>::ConstantReturnType
+DenseBase<Derived>::Zero(Index rows, Index cols)
+{
+ return Constant(rows, cols, Scalar(0));
+}
+
+/** \returns an expression of a zero vector.
+ *
+ * The parameter \a size is the size of the returned vector.
+ * Must be compatible with this MatrixBase type.
+ *
+ * \only_for_vectors
+ *
+ * This variant is meant to be used for dynamic-size vector types. For fixed-size types,
+ * it is redundant to pass \a size as argument, so Zero() should be used
+ * instead.
+ *
+ * Example: \include MatrixBase_zero_int.cpp
+ * Output: \verbinclude MatrixBase_zero_int.out
+ *
+ * \sa Zero(), Zero(Index,Index)
+ */
+template<typename Derived>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename DenseBase<Derived>::ConstantReturnType
+DenseBase<Derived>::Zero(Index size)
+{
+ return Constant(size, Scalar(0));
+}
+
+/** \returns an expression of a fixed-size zero matrix or vector.
+ *
+ * This variant is only for fixed-size MatrixBase types. For dynamic-size types, you
+ * need to use the variants taking size arguments.
+ *
+ * Example: \include MatrixBase_zero.cpp
+ * Output: \verbinclude MatrixBase_zero.out
+ *
+ * \sa Zero(Index), Zero(Index,Index)
+ */
+template<typename Derived>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename DenseBase<Derived>::ConstantReturnType
+DenseBase<Derived>::Zero()
+{
+ return Constant(Scalar(0));
+}
+
+/** \returns true if *this is approximately equal to the zero matrix,
+ * within the precision given by \a prec.
+ *
+ * Example: \include MatrixBase_isZero.cpp
+ * Output: \verbinclude MatrixBase_isZero.out
+ *
+ * \sa class CwiseNullaryOp, Zero()
+ */
+template<typename Derived>
+EIGEN_DEVICE_FUNC bool DenseBase<Derived>::isZero(const RealScalar& prec) const
+{
+ typename internal::nested_eval<Derived,1>::type self(derived());
+ for(Index j = 0; j < cols(); ++j)
+ for(Index i = 0; i < rows(); ++i)
+ if(!internal::isMuchSmallerThan(self.coeff(i, j), static_cast<Scalar>(1), prec))
+ return false;
+ return true;
+}
+
+/** Sets all coefficients in this expression to zero.
+ *
+ * Example: \include MatrixBase_setZero.cpp
+ * Output: \verbinclude MatrixBase_setZero.out
+ *
+ * \sa class CwiseNullaryOp, Zero()
+ */
+template<typename Derived>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& DenseBase<Derived>::setZero()
+{
+ return setConstant(Scalar(0));
+}
+
+/** Resizes to the given \a size, and sets all coefficients in this expression to zero.
+ *
+ * \only_for_vectors
+ *
+ * Example: \include Matrix_setZero_int.cpp
+ * Output: \verbinclude Matrix_setZero_int.out
+ *
+ * \sa DenseBase::setZero(), setZero(Index,Index), class CwiseNullaryOp, DenseBase::Zero()
+ */
+template<typename Derived>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived&
+PlainObjectBase<Derived>::setZero(Index newSize)
+{
+ resize(newSize);
+ return setConstant(Scalar(0));
+}
+
+/** Resizes to the given size, and sets all coefficients in this expression to zero.
+ *
+ * \param rows the new number of rows
+ * \param cols the new number of columns
+ *
+ * Example: \include Matrix_setZero_int_int.cpp
+ * Output: \verbinclude Matrix_setZero_int_int.out
+ *
+ * \sa DenseBase::setZero(), setZero(Index), class CwiseNullaryOp, DenseBase::Zero()
+ */
+template<typename Derived>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived&
+PlainObjectBase<Derived>::setZero(Index rows, Index cols)
+{
+ resize(rows, cols);
+ return setConstant(Scalar(0));
+}
+
+/** Resizes to the given size, changing only the number of columns, and sets all
+ * coefficients in this expression to zero. For the parameter of type NoChange_t,
+ * just pass the special value \c NoChange.
+ *
+ * \sa DenseBase::setZero(), setZero(Index), setZero(Index, Index), setZero(Index, NoChange_t), class CwiseNullaryOp, DenseBase::Zero()
+ */
+template<typename Derived>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived&
+PlainObjectBase<Derived>::setZero(NoChange_t, Index cols)
+{
+ return setZero(rows(), cols);
+}
+
+/** Resizes to the given size, changing only the number of rows, and sets all
+ * coefficients in this expression to zero. For the parameter of type NoChange_t,
+ * just pass the special value \c NoChange.
+ *
+ * \sa DenseBase::setZero(), setZero(Index), setZero(Index, Index), setZero(NoChange_t, Index), class CwiseNullaryOp, DenseBase::Zero()
+ */
+template<typename Derived>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived&
+PlainObjectBase<Derived>::setZero(Index rows, NoChange_t)
+{
+ return setZero(rows, cols());
+}
+
+// ones:
+
+/** \returns an expression of a matrix where all coefficients equal one.
+ *
+ * The parameters \a rows and \a cols are the number of rows and of columns of
+ * the returned matrix. Must be compatible with this MatrixBase type.
+ *
+ * This variant is meant to be used for dynamic-size matrix types. For fixed-size types,
+ * it is redundant to pass \a rows and \a cols as arguments, so Ones() should be used
+ * instead.
+ *
+ * Example: \include MatrixBase_ones_int_int.cpp
+ * Output: \verbinclude MatrixBase_ones_int_int.out
+ *
+ * \sa Ones(), Ones(Index), isOnes(), class Ones
+ */
+template<typename Derived>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename DenseBase<Derived>::ConstantReturnType
+DenseBase<Derived>::Ones(Index rows, Index cols)
+{
+ return Constant(rows, cols, Scalar(1));
+}
+
+/** \returns an expression of a vector where all coefficients equal one.
+ *
+ * The parameter \a newSize is the size of the returned vector.
+ * Must be compatible with this MatrixBase type.
+ *
+ * \only_for_vectors
+ *
+ * This variant is meant to be used for dynamic-size vector types. For fixed-size types,
+ * it is redundant to pass \a size as argument, so Ones() should be used
+ * instead.
+ *
+ * Example: \include MatrixBase_ones_int.cpp
+ * Output: \verbinclude MatrixBase_ones_int.out
+ *
+ * \sa Ones(), Ones(Index,Index), isOnes(), class Ones
+ */
+template<typename Derived>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename DenseBase<Derived>::ConstantReturnType
+DenseBase<Derived>::Ones(Index newSize)
+{
+ return Constant(newSize, Scalar(1));
+}
+
+/** \returns an expression of a fixed-size matrix or vector where all coefficients equal one.
+ *
+ * This variant is only for fixed-size MatrixBase types. For dynamic-size types, you
+ * need to use the variants taking size arguments.
+ *
+ * Example: \include MatrixBase_ones.cpp
+ * Output: \verbinclude MatrixBase_ones.out
+ *
+ * \sa Ones(Index), Ones(Index,Index), isOnes(), class Ones
+ */
+template<typename Derived>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename DenseBase<Derived>::ConstantReturnType
+DenseBase<Derived>::Ones()
+{
+ return Constant(Scalar(1));
+}
+
+/** \returns true if *this is approximately equal to the matrix where all coefficients
+ * are equal to 1, within the precision given by \a prec.
+ *
+ * Example: \include MatrixBase_isOnes.cpp
+ * Output: \verbinclude MatrixBase_isOnes.out
+ *
+ * \sa class CwiseNullaryOp, Ones()
+ */
+template<typename Derived>
+EIGEN_DEVICE_FUNC bool DenseBase<Derived>::isOnes
+(const RealScalar& prec) const
+{
+ return isApproxToConstant(Scalar(1), prec);
+}
+
+/** Sets all coefficients in this expression to one.
+ *
+ * Example: \include MatrixBase_setOnes.cpp
+ * Output: \verbinclude MatrixBase_setOnes.out
+ *
+ * \sa class CwiseNullaryOp, Ones()
+ */
+template<typename Derived>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& DenseBase<Derived>::setOnes()
+{
+ return setConstant(Scalar(1));
+}
+
+/** Resizes to the given \a newSize, and sets all coefficients in this expression to one.
+ *
+ * \only_for_vectors
+ *
+ * Example: \include Matrix_setOnes_int.cpp
+ * Output: \verbinclude Matrix_setOnes_int.out
+ *
+ * \sa MatrixBase::setOnes(), setOnes(Index,Index), class CwiseNullaryOp, MatrixBase::Ones()
+ */
+template<typename Derived>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived&
+PlainObjectBase<Derived>::setOnes(Index newSize)
+{
+ resize(newSize);
+ return setConstant(Scalar(1));
+}
+
+/** Resizes to the given size, and sets all coefficients in this expression to one.
+ *
+ * \param rows the new number of rows
+ * \param cols the new number of columns
+ *
+ * Example: \include Matrix_setOnes_int_int.cpp
+ * Output: \verbinclude Matrix_setOnes_int_int.out
+ *
+ * \sa MatrixBase::setOnes(), setOnes(Index), class CwiseNullaryOp, MatrixBase::Ones()
+ */
+template<typename Derived>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived&
+PlainObjectBase<Derived>::setOnes(Index rows, Index cols)
+{
+ resize(rows, cols);
+ return setConstant(Scalar(1));
+}
+
+/** Resizes to the given size, changing only the number of rows, and sets all
+ * coefficients in this expression to one. For the parameter of type NoChange_t,
+ * just pass the special value \c NoChange.
+ *
+ * \sa MatrixBase::setOnes(), setOnes(Index), setOnes(Index, Index), setOnes(NoChange_t, Index), class CwiseNullaryOp, MatrixBase::Ones()
+ */
+template<typename Derived>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived&
+PlainObjectBase<Derived>::setOnes(Index rows, NoChange_t)
+{
+ return setOnes(rows, cols());
+}
+
+/** Resizes to the given size, changing only the number of columns, and sets all
+ * coefficients in this expression to one. For the parameter of type NoChange_t,
+ * just pass the special value \c NoChange.
+ *
+ * \sa MatrixBase::setOnes(), setOnes(Index), setOnes(Index, Index), setOnes(Index, NoChange_t) class CwiseNullaryOp, MatrixBase::Ones()
+ */
+template<typename Derived>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived&
+PlainObjectBase<Derived>::setOnes(NoChange_t, Index cols)
+{
+ return setOnes(rows(), cols);
+}
+
+// Identity:
+
+/** \returns an expression of the identity matrix (not necessarily square).
+ *
+ * The parameters \a rows and \a cols are the number of rows and of columns of
+ * the returned matrix. Must be compatible with this MatrixBase type.
+ *
+ * This variant is meant to be used for dynamic-size matrix types. For fixed-size types,
+ * it is redundant to pass \a rows and \a cols as arguments, so Identity() should be used
+ * instead.
+ *
+ * Example: \include MatrixBase_identity_int_int.cpp
+ * Output: \verbinclude MatrixBase_identity_int_int.out
+ *
+ * \sa Identity(), setIdentity(), isIdentity()
+ */
+template<typename Derived>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename MatrixBase<Derived>::IdentityReturnType
+MatrixBase<Derived>::Identity(Index rows, Index cols)
+{
+ return DenseBase<Derived>::NullaryExpr(rows, cols, internal::scalar_identity_op<Scalar>());
+}
+
+/** \returns an expression of the identity matrix (not necessarily square).
+ *
+ * This variant is only for fixed-size MatrixBase types. For dynamic-size types, you
+ * need to use the variant taking size arguments.
+ *
+ * Example: \include MatrixBase_identity.cpp
+ * Output: \verbinclude MatrixBase_identity.out
+ *
+ * \sa Identity(Index,Index), setIdentity(), isIdentity()
+ */
+template<typename Derived>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename MatrixBase<Derived>::IdentityReturnType
+MatrixBase<Derived>::Identity()
+{
+ EIGEN_STATIC_ASSERT_FIXED_SIZE(Derived)
+ return MatrixBase<Derived>::NullaryExpr(RowsAtCompileTime, ColsAtCompileTime, internal::scalar_identity_op<Scalar>());
+}
+
+/** \returns true if *this is approximately equal to the identity matrix
+ * (not necessarily square),
+ * within the precision given by \a prec.
+ *
+ * Example: \include MatrixBase_isIdentity.cpp
+ * Output: \verbinclude MatrixBase_isIdentity.out
+ *
+ * \sa class CwiseNullaryOp, Identity(), Identity(Index,Index), setIdentity()
+ */
+template<typename Derived>
+bool MatrixBase<Derived>::isIdentity
+(const RealScalar& prec) const
+{
+ typename internal::nested_eval<Derived,1>::type self(derived());
+ for(Index j = 0; j < cols(); ++j)
+ {
+ for(Index i = 0; i < rows(); ++i)
+ {
+ if(i == j)
+ {
+ if(!internal::isApprox(self.coeff(i, j), static_cast<Scalar>(1), prec))
+ return false;
+ }
+ else
+ {
+ if(!internal::isMuchSmallerThan(self.coeff(i, j), static_cast<RealScalar>(1), prec))
+ return false;
+ }
+ }
+ }
+ return true;
+}
+
+namespace internal {
+
+template<typename Derived, bool Big = (Derived::SizeAtCompileTime>=16)>
+struct setIdentity_impl
+{
+ EIGEN_DEVICE_FUNC
+ static EIGEN_STRONG_INLINE Derived& run(Derived& m)
+ {
+ return m = Derived::Identity(m.rows(), m.cols());
+ }
+};
+
+template<typename Derived>
+struct setIdentity_impl<Derived, true>
+{
+ EIGEN_DEVICE_FUNC
+ static EIGEN_STRONG_INLINE Derived& run(Derived& m)
+ {
+ m.setZero();
+ const Index size = numext::mini(m.rows(), m.cols());
+ for(Index i = 0; i < size; ++i) m.coeffRef(i,i) = typename Derived::Scalar(1);
+ return m;
+ }
+};
+
+} // end namespace internal
+
+/** Writes the identity expression (not necessarily square) into *this.
+ *
+ * Example: \include MatrixBase_setIdentity.cpp
+ * Output: \verbinclude MatrixBase_setIdentity.out
+ *
+ * \sa class CwiseNullaryOp, Identity(), Identity(Index,Index), isIdentity()
+ */
+template<typename Derived>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& MatrixBase<Derived>::setIdentity()
+{
+ return internal::setIdentity_impl<Derived>::run(derived());
+}
+
+/** \brief Resizes to the given size, and writes the identity expression (not necessarily square) into *this.
+ *
+ * \param rows the new number of rows
+ * \param cols the new number of columns
+ *
+ * Example: \include Matrix_setIdentity_int_int.cpp
+ * Output: \verbinclude Matrix_setIdentity_int_int.out
+ *
+ * \sa MatrixBase::setIdentity(), class CwiseNullaryOp, MatrixBase::Identity()
+ */
+template<typename Derived>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& MatrixBase<Derived>::setIdentity(Index rows, Index cols)
+{
+ derived().resize(rows, cols);
+ return setIdentity();
+}
+
+/** \returns an expression of the i-th unit (basis) vector.
+ *
+ * \only_for_vectors
+ *
+ * \sa MatrixBase::Unit(Index), MatrixBase::UnitX(), MatrixBase::UnitY(), MatrixBase::UnitZ(), MatrixBase::UnitW()
+ */
+template<typename Derived>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename MatrixBase<Derived>::BasisReturnType MatrixBase<Derived>::Unit(Index newSize, Index i)
+{
+ EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
+ return BasisReturnType(SquareMatrixType::Identity(newSize,newSize), i);
+}
+
+/** \returns an expression of the i-th unit (basis) vector.
+ *
+ * \only_for_vectors
+ *
+ * This variant is for fixed-size vector only.
+ *
+ * \sa MatrixBase::Unit(Index,Index), MatrixBase::UnitX(), MatrixBase::UnitY(), MatrixBase::UnitZ(), MatrixBase::UnitW()
+ */
+template<typename Derived>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename MatrixBase<Derived>::BasisReturnType MatrixBase<Derived>::Unit(Index i)
+{
+ EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
+ return BasisReturnType(SquareMatrixType::Identity(),i);
+}
+
+/** \returns an expression of the X axis unit vector (1{,0}^*)
+ *
+ * \only_for_vectors
+ *
+ * \sa MatrixBase::Unit(Index,Index), MatrixBase::Unit(Index), MatrixBase::UnitY(), MatrixBase::UnitZ(), MatrixBase::UnitW()
+ */
+template<typename Derived>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename MatrixBase<Derived>::BasisReturnType MatrixBase<Derived>::UnitX()
+{ return Derived::Unit(0); }
+
+/** \returns an expression of the Y axis unit vector (0,1{,0}^*)
+ *
+ * \only_for_vectors
+ *
+ * \sa MatrixBase::Unit(Index,Index), MatrixBase::Unit(Index), MatrixBase::UnitY(), MatrixBase::UnitZ(), MatrixBase::UnitW()
+ */
+template<typename Derived>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename MatrixBase<Derived>::BasisReturnType MatrixBase<Derived>::UnitY()
+{ return Derived::Unit(1); }
+
+/** \returns an expression of the Z axis unit vector (0,0,1{,0}^*)
+ *
+ * \only_for_vectors
+ *
+ * \sa MatrixBase::Unit(Index,Index), MatrixBase::Unit(Index), MatrixBase::UnitY(), MatrixBase::UnitZ(), MatrixBase::UnitW()
+ */
+template<typename Derived>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename MatrixBase<Derived>::BasisReturnType MatrixBase<Derived>::UnitZ()
+{ return Derived::Unit(2); }
+
+/** \returns an expression of the W axis unit vector (0,0,0,1)
+ *
+ * \only_for_vectors
+ *
+ * \sa MatrixBase::Unit(Index,Index), MatrixBase::Unit(Index), MatrixBase::UnitY(), MatrixBase::UnitZ(), MatrixBase::UnitW()
+ */
+template<typename Derived>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename MatrixBase<Derived>::BasisReturnType MatrixBase<Derived>::UnitW()
+{ return Derived::Unit(3); }
+
+/** \brief Set the coefficients of \c *this to the i-th unit (basis) vector
+ *
+ * \param i index of the unique coefficient to be set to 1
+ *
+ * \only_for_vectors
+ *
+ * \sa MatrixBase::setIdentity(), class CwiseNullaryOp, MatrixBase::Unit(Index,Index)
+ */
+template<typename Derived>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& MatrixBase<Derived>::setUnit(Index i)
+{
+ EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived);
+ eigen_assert(i<size());
+ derived().setZero();
+ derived().coeffRef(i) = Scalar(1);
+ return derived();
+}
+
+/** \brief Resizes to the given \a newSize, and writes the i-th unit (basis) vector into *this.
+ *
+ * \param newSize the new size of the vector
+ * \param i index of the unique coefficient to be set to 1
+ *
+ * \only_for_vectors
+ *
+ * \sa MatrixBase::setIdentity(), class CwiseNullaryOp, MatrixBase::Unit(Index,Index)
+ */
+template<typename Derived>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& MatrixBase<Derived>::setUnit(Index newSize, Index i)
+{
+ EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived);
+ eigen_assert(i<newSize);
+ derived().resize(newSize);
+ return setUnit(i);
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_CWISE_NULLARY_OP_H
diff --git a/Eigen/src/Core/CwiseTernaryOp.h b/Eigen/src/Core/CwiseTernaryOp.h
new file mode 100644
index 0000000..8d24a48
--- /dev/null
+++ b/Eigen/src/Core/CwiseTernaryOp.h
@@ -0,0 +1,199 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2014 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+// Copyright (C) 2016 Eugene Brevdo <ebrevdo@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_CWISE_TERNARY_OP_H
+#define EIGEN_CWISE_TERNARY_OP_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+template <typename TernaryOp, typename Arg1, typename Arg2, typename Arg3>
+struct traits<CwiseTernaryOp<TernaryOp, Arg1, Arg2, Arg3> > {
+ // we must not inherit from traits<Arg1> since it has
+ // the potential to cause problems with MSVC
+ typedef remove_all_t<Arg1> Ancestor;
+ typedef typename traits<Ancestor>::XprKind XprKind;
+ enum {
+ RowsAtCompileTime = traits<Ancestor>::RowsAtCompileTime,
+ ColsAtCompileTime = traits<Ancestor>::ColsAtCompileTime,
+ MaxRowsAtCompileTime = traits<Ancestor>::MaxRowsAtCompileTime,
+ MaxColsAtCompileTime = traits<Ancestor>::MaxColsAtCompileTime
+ };
+
+ // even though we require Arg1, Arg2, and Arg3 to have the same scalar type
+ // (see CwiseTernaryOp constructor),
+ // we still want to handle the case when the result type is different.
+ typedef typename result_of<TernaryOp(
+ const typename Arg1::Scalar&, const typename Arg2::Scalar&,
+ const typename Arg3::Scalar&)>::type Scalar;
+
+ typedef typename internal::traits<Arg1>::StorageKind StorageKind;
+ typedef typename internal::traits<Arg1>::StorageIndex StorageIndex;
+
+ typedef typename Arg1::Nested Arg1Nested;
+ typedef typename Arg2::Nested Arg2Nested;
+ typedef typename Arg3::Nested Arg3Nested;
+ typedef std::remove_reference_t<Arg1Nested> Arg1Nested_;
+ typedef std::remove_reference_t<Arg2Nested> Arg2Nested_;
+ typedef std::remove_reference_t<Arg3Nested> Arg3Nested_;
+ enum { Flags = Arg1Nested_::Flags & RowMajorBit };
+};
+} // end namespace internal
+
+template <typename TernaryOp, typename Arg1, typename Arg2, typename Arg3,
+ typename StorageKind>
+class CwiseTernaryOpImpl;
+
+/** \class CwiseTernaryOp
+ * \ingroup Core_Module
+ *
+ * \brief Generic expression where a coefficient-wise ternary operator is
+ * applied to two expressions
+ *
+ * \tparam TernaryOp template functor implementing the operator
+ * \tparam Arg1Type the type of the first argument
+ * \tparam Arg2Type the type of the second argument
+ * \tparam Arg3Type the type of the third argument
+ *
+ * This class represents an expression where a coefficient-wise ternary
+ * operator is applied to three expressions.
+ * It is the return type of ternary operators, by which we mean only those
+ * ternary operators where
+ * all three arguments are Eigen expressions.
+ * For example, the return type of betainc(matrix1, matrix2, matrix3) is a
+ * CwiseTernaryOp.
+ *
+ * Most of the time, this is the only way that it is used, so you typically
+ * don't have to name
+ * CwiseTernaryOp types explicitly.
+ *
+ * \sa MatrixBase::ternaryExpr(const MatrixBase<Argument2> &, const
+ * MatrixBase<Argument3> &, const CustomTernaryOp &) const, class CwiseBinaryOp,
+ * class CwiseUnaryOp, class CwiseNullaryOp
+ */
+template <typename TernaryOp, typename Arg1Type, typename Arg2Type,
+ typename Arg3Type>
+class CwiseTernaryOp : public CwiseTernaryOpImpl<
+ TernaryOp, Arg1Type, Arg2Type, Arg3Type,
+ typename internal::traits<Arg1Type>::StorageKind>,
+ internal::no_assignment_operator
+{
+ public:
+ typedef internal::remove_all_t<Arg1Type> Arg1;
+ typedef internal::remove_all_t<Arg2Type> Arg2;
+ typedef internal::remove_all_t<Arg3Type> Arg3;
+
+ // require the sizes to match
+ EIGEN_STATIC_ASSERT_SAME_MATRIX_SIZE(Arg1, Arg2)
+ EIGEN_STATIC_ASSERT_SAME_MATRIX_SIZE(Arg1, Arg3)
+
+ // The index types should match
+ EIGEN_STATIC_ASSERT((internal::is_same<
+ typename internal::traits<Arg1Type>::StorageKind,
+ typename internal::traits<Arg2Type>::StorageKind>::value),
+ STORAGE_KIND_MUST_MATCH)
+ EIGEN_STATIC_ASSERT((internal::is_same<
+ typename internal::traits<Arg1Type>::StorageKind,
+ typename internal::traits<Arg3Type>::StorageKind>::value),
+ STORAGE_KIND_MUST_MATCH)
+
+ typedef typename CwiseTernaryOpImpl<
+ TernaryOp, Arg1Type, Arg2Type, Arg3Type,
+ typename internal::traits<Arg1Type>::StorageKind>::Base Base;
+ EIGEN_GENERIC_PUBLIC_INTERFACE(CwiseTernaryOp)
+
+ typedef typename internal::ref_selector<Arg1Type>::type Arg1Nested;
+ typedef typename internal::ref_selector<Arg2Type>::type Arg2Nested;
+ typedef typename internal::ref_selector<Arg3Type>::type Arg3Nested;
+ typedef std::remove_reference_t<Arg1Nested> Arg1Nested_;
+ typedef std::remove_reference_t<Arg2Nested> Arg2Nested_;
+ typedef std::remove_reference_t<Arg3Nested> Arg3Nested_;
+
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE CwiseTernaryOp(const Arg1& a1, const Arg2& a2,
+ const Arg3& a3,
+ const TernaryOp& func = TernaryOp())
+ : m_arg1(a1), m_arg2(a2), m_arg3(a3), m_functor(func) {
+ eigen_assert(a1.rows() == a2.rows() && a1.cols() == a2.cols() &&
+ a1.rows() == a3.rows() && a1.cols() == a3.cols());
+ }
+
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE Index rows() const {
+ // return the fixed size type if available to enable compile time
+ // optimizations
+ if (internal::traits<internal::remove_all_t<Arg1Nested>>::
+ RowsAtCompileTime == Dynamic &&
+ internal::traits<internal::remove_all_t<Arg2Nested>>::
+ RowsAtCompileTime == Dynamic)
+ return m_arg3.rows();
+ else if (internal::traits<internal::remove_all_t<Arg1Nested>>::
+ RowsAtCompileTime == Dynamic &&
+ internal::traits<internal::remove_all_t<Arg3Nested>>::
+ RowsAtCompileTime == Dynamic)
+ return m_arg2.rows();
+ else
+ return m_arg1.rows();
+ }
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE Index cols() const {
+ // return the fixed size type if available to enable compile time
+ // optimizations
+ if (internal::traits<internal::remove_all_t<Arg1Nested>>::
+ ColsAtCompileTime == Dynamic &&
+ internal::traits<internal::remove_all_t<Arg2Nested>>::
+ ColsAtCompileTime == Dynamic)
+ return m_arg3.cols();
+ else if (internal::traits<internal::remove_all_t<Arg1Nested>>::
+ ColsAtCompileTime == Dynamic &&
+ internal::traits<internal::remove_all_t<Arg3Nested>>::
+ ColsAtCompileTime == Dynamic)
+ return m_arg2.cols();
+ else
+ return m_arg1.cols();
+ }
+
+ /** \returns the first argument nested expression */
+ EIGEN_DEVICE_FUNC
+ const Arg1Nested_& arg1() const { return m_arg1; }
+ /** \returns the first argument nested expression */
+ EIGEN_DEVICE_FUNC
+ const Arg2Nested_& arg2() const { return m_arg2; }
+ /** \returns the third argument nested expression */
+ EIGEN_DEVICE_FUNC
+ const Arg3Nested_& arg3() const { return m_arg3; }
+ /** \returns the functor representing the ternary operation */
+ EIGEN_DEVICE_FUNC
+ const TernaryOp& functor() const { return m_functor; }
+
+ protected:
+ Arg1Nested m_arg1;
+ Arg2Nested m_arg2;
+ Arg3Nested m_arg3;
+ const TernaryOp m_functor;
+};
+
+// Generic API dispatcher
+template <typename TernaryOp, typename Arg1, typename Arg2, typename Arg3,
+ typename StorageKind>
+class CwiseTernaryOpImpl
+ : public internal::generic_xpr_base<
+ CwiseTernaryOp<TernaryOp, Arg1, Arg2, Arg3> >::type {
+ public:
+ typedef typename internal::generic_xpr_base<
+ CwiseTernaryOp<TernaryOp, Arg1, Arg2, Arg3> >::type Base;
+};
+
+} // end namespace Eigen
+
+#endif // EIGEN_CWISE_TERNARY_OP_H
diff --git a/Eigen/src/Core/CwiseUnaryOp.h b/Eigen/src/Core/CwiseUnaryOp.h
new file mode 100644
index 0000000..ff7d0b9
--- /dev/null
+++ b/Eigen/src/Core/CwiseUnaryOp.h
@@ -0,0 +1,105 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2014 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_CWISE_UNARY_OP_H
+#define EIGEN_CWISE_UNARY_OP_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+template<typename UnaryOp, typename XprType>
+struct traits<CwiseUnaryOp<UnaryOp, XprType> >
+ : traits<XprType>
+{
+ typedef typename result_of<
+ UnaryOp(const typename XprType::Scalar&)
+ >::type Scalar;
+ typedef typename XprType::Nested XprTypeNested;
+ typedef std::remove_reference_t<XprTypeNested> XprTypeNested_;
+ enum {
+ Flags = XprTypeNested_::Flags & RowMajorBit
+ };
+};
+}
+
+template<typename UnaryOp, typename XprType, typename StorageKind>
+class CwiseUnaryOpImpl;
+
+/** \class CwiseUnaryOp
+ * \ingroup Core_Module
+ *
+ * \brief Generic expression where a coefficient-wise unary operator is applied to an expression
+ *
+ * \tparam UnaryOp template functor implementing the operator
+ * \tparam XprType the type of the expression to which we are applying the unary operator
+ *
+ * This class represents an expression where a unary operator is applied to an expression.
+ * It is the return type of all operations taking exactly 1 input expression, regardless of the
+ * presence of other inputs such as scalars. For example, the operator* in the expression 3*matrix
+ * is considered unary, because only the right-hand side is an expression, and its
+ * return type is a specialization of CwiseUnaryOp.
+ *
+ * Most of the time, this is the only way that it is used, so you typically don't have to name
+ * CwiseUnaryOp types explicitly.
+ *
+ * \sa MatrixBase::unaryExpr(const CustomUnaryOp &) const, class CwiseBinaryOp, class CwiseNullaryOp
+ */
+template<typename UnaryOp, typename XprType>
+class CwiseUnaryOp : public CwiseUnaryOpImpl<UnaryOp, XprType, typename internal::traits<XprType>::StorageKind>, internal::no_assignment_operator
+{
+ public:
+
+ typedef typename CwiseUnaryOpImpl<UnaryOp, XprType,typename internal::traits<XprType>::StorageKind>::Base Base;
+ EIGEN_GENERIC_PUBLIC_INTERFACE(CwiseUnaryOp)
+ typedef typename internal::ref_selector<XprType>::type XprTypeNested;
+ typedef internal::remove_all_t<XprType> NestedExpression;
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ explicit CwiseUnaryOp(const XprType& xpr, const UnaryOp& func = UnaryOp())
+ : m_xpr(xpr), m_functor(func) {}
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE EIGEN_CONSTEXPR
+ Index rows() const EIGEN_NOEXCEPT { return m_xpr.rows(); }
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE EIGEN_CONSTEXPR
+ Index cols() const EIGEN_NOEXCEPT { return m_xpr.cols(); }
+
+ /** \returns the functor representing the unary operation */
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ const UnaryOp& functor() const { return m_functor; }
+
+ /** \returns the nested expression */
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ const internal::remove_all_t<XprTypeNested>&
+ nestedExpression() const { return m_xpr; }
+
+ /** \returns the nested expression */
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ internal::remove_all_t<XprTypeNested>&
+ nestedExpression() { return m_xpr; }
+
+ protected:
+ XprTypeNested m_xpr;
+ const UnaryOp m_functor;
+};
+
+// Generic API dispatcher
+template<typename UnaryOp, typename XprType, typename StorageKind>
+class CwiseUnaryOpImpl
+ : public internal::generic_xpr_base<CwiseUnaryOp<UnaryOp, XprType> >::type
+{
+public:
+ typedef typename internal::generic_xpr_base<CwiseUnaryOp<UnaryOp, XprType> >::type Base;
+};
+
+} // end namespace Eigen
+
+#endif // EIGEN_CWISE_UNARY_OP_H
diff --git a/Eigen/src/Core/CwiseUnaryView.h b/Eigen/src/Core/CwiseUnaryView.h
new file mode 100644
index 0000000..b4539a6
--- /dev/null
+++ b/Eigen/src/Core/CwiseUnaryView.h
@@ -0,0 +1,143 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009-2010 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_CWISE_UNARY_VIEW_H
+#define EIGEN_CWISE_UNARY_VIEW_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+template<typename ViewOp, typename MatrixType, typename StrideType>
+struct traits<CwiseUnaryView<ViewOp, MatrixType, StrideType> >
+ : traits<MatrixType>
+{
+ typedef typename result_of<
+ ViewOp(const typename traits<MatrixType>::Scalar&)
+ >::type Scalar;
+ typedef typename MatrixType::Nested MatrixTypeNested;
+ typedef remove_all_t<MatrixTypeNested> MatrixTypeNested_;
+ enum {
+ FlagsLvalueBit = is_lvalue<MatrixType>::value ? LvalueBit : 0,
+ Flags = traits<MatrixTypeNested_>::Flags & (RowMajorBit | FlagsLvalueBit | DirectAccessBit), // FIXME DirectAccessBit should not be handled by expressions
+ MatrixTypeInnerStride = inner_stride_at_compile_time<MatrixType>::ret,
+ // need to cast the sizeof's from size_t to int explicitly, otherwise:
+ // "error: no integral type can represent all of the enumerator values
+ InnerStrideAtCompileTime = StrideType::InnerStrideAtCompileTime == 0
+ ? (MatrixTypeInnerStride == Dynamic
+ ? int(Dynamic)
+ : int(MatrixTypeInnerStride) * int(sizeof(typename traits<MatrixType>::Scalar) / sizeof(Scalar)))
+ : int(StrideType::InnerStrideAtCompileTime),
+
+ OuterStrideAtCompileTime = StrideType::OuterStrideAtCompileTime == 0
+ ? (outer_stride_at_compile_time<MatrixType>::ret == Dynamic
+ ? int(Dynamic)
+ : outer_stride_at_compile_time<MatrixType>::ret * int(sizeof(typename traits<MatrixType>::Scalar) / sizeof(Scalar)))
+ : int(StrideType::OuterStrideAtCompileTime)
+ };
+};
+}
+
+template<typename ViewOp, typename MatrixType, typename StrideType, typename StorageKind>
+class CwiseUnaryViewImpl;
+
+/** \class CwiseUnaryView
+ * \ingroup Core_Module
+ *
+ * \brief Generic lvalue expression of a coefficient-wise unary operator of a matrix or a vector
+ *
+ * \tparam ViewOp template functor implementing the view
+ * \tparam MatrixType the type of the matrix we are applying the unary operator
+ *
+ * This class represents a lvalue expression of a generic unary view operator of a matrix or a vector.
+ * It is the return type of real() and imag(), and most of the time this is the only way it is used.
+ *
+ * \sa MatrixBase::unaryViewExpr(const CustomUnaryOp &) const, class CwiseUnaryOp
+ */
+template<typename ViewOp, typename MatrixType, typename StrideType>
+class CwiseUnaryView : public CwiseUnaryViewImpl<ViewOp, MatrixType, StrideType, typename internal::traits<MatrixType>::StorageKind>
+{
+ public:
+
+ typedef typename CwiseUnaryViewImpl<ViewOp, MatrixType, StrideType, typename internal::traits<MatrixType>::StorageKind>::Base Base;
+ EIGEN_GENERIC_PUBLIC_INTERFACE(CwiseUnaryView)
+ typedef typename internal::ref_selector<MatrixType>::non_const_type MatrixTypeNested;
+ typedef internal::remove_all_t<MatrixType> NestedExpression;
+
+ explicit EIGEN_DEVICE_FUNC inline CwiseUnaryView(MatrixType& mat, const ViewOp& func = ViewOp())
+ : m_matrix(mat), m_functor(func) {}
+
+ EIGEN_INHERIT_ASSIGNMENT_OPERATORS(CwiseUnaryView)
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE EIGEN_CONSTEXPR
+ Index rows() const EIGEN_NOEXCEPT { return m_matrix.rows(); }
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE EIGEN_CONSTEXPR
+ Index cols() const EIGEN_NOEXCEPT { return m_matrix.cols(); }
+
+ /** \returns the functor representing unary operation */
+ EIGEN_DEVICE_FUNC const ViewOp& functor() const { return m_functor; }
+
+ /** \returns the nested expression */
+ EIGEN_DEVICE_FUNC const internal::remove_all_t<MatrixTypeNested>&
+ nestedExpression() const { return m_matrix; }
+
+ /** \returns the nested expression */
+ EIGEN_DEVICE_FUNC std::remove_reference_t<MatrixTypeNested>&
+ nestedExpression() { return m_matrix; }
+
+ protected:
+ MatrixTypeNested m_matrix;
+ ViewOp m_functor;
+};
+
+// Generic API dispatcher
+template<typename ViewOp, typename XprType, typename StrideType, typename StorageKind>
+class CwiseUnaryViewImpl
+ : public internal::generic_xpr_base<CwiseUnaryView<ViewOp, XprType, StrideType> >::type
+{
+public:
+ typedef typename internal::generic_xpr_base<CwiseUnaryView<ViewOp, XprType, StrideType> >::type Base;
+};
+
+template<typename ViewOp, typename MatrixType, typename StrideType>
+class CwiseUnaryViewImpl<ViewOp,MatrixType,StrideType,Dense>
+ : public internal::dense_xpr_base< CwiseUnaryView<ViewOp, MatrixType, StrideType> >::type
+{
+ public:
+
+ typedef CwiseUnaryView<ViewOp, MatrixType,StrideType> Derived;
+ typedef typename internal::dense_xpr_base< CwiseUnaryView<ViewOp, MatrixType,StrideType> >::type Base;
+
+ EIGEN_DENSE_PUBLIC_INTERFACE(Derived)
+ EIGEN_INHERIT_ASSIGNMENT_OPERATORS(CwiseUnaryViewImpl)
+
+ EIGEN_DEVICE_FUNC inline Scalar* data() { return &(this->coeffRef(0)); }
+ EIGEN_DEVICE_FUNC inline const Scalar* data() const { return &(this->coeff(0)); }
+
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR inline Index innerStride() const
+ {
+ return StrideType::InnerStrideAtCompileTime != 0
+ ? int(StrideType::InnerStrideAtCompileTime)
+ : derived().nestedExpression().innerStride() * sizeof(typename internal::traits<MatrixType>::Scalar) / sizeof(Scalar);
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR inline Index outerStride() const
+ {
+ return StrideType::OuterStrideAtCompileTime != 0
+ ? int(StrideType::OuterStrideAtCompileTime)
+ : derived().nestedExpression().outerStride() * sizeof(typename internal::traits<MatrixType>::Scalar) / sizeof(Scalar);
+ }
+ protected:
+ EIGEN_DEFAULT_EMPTY_CONSTRUCTOR_AND_DESTRUCTOR(CwiseUnaryViewImpl)
+};
+
+} // end namespace Eigen
+
+#endif // EIGEN_CWISE_UNARY_VIEW_H
diff --git a/Eigen/src/Core/DenseBase.h b/Eigen/src/Core/DenseBase.h
new file mode 100644
index 0000000..6e17779
--- /dev/null
+++ b/Eigen/src/Core/DenseBase.h
@@ -0,0 +1,684 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2007-2010 Benoit Jacob <jacob.benoit.1@gmail.com>
+// Copyright (C) 2008-2010 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_DENSEBASE_H
+#define EIGEN_DENSEBASE_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+// The index type defined by EIGEN_DEFAULT_DENSE_INDEX_TYPE must be a signed type.
+EIGEN_STATIC_ASSERT(NumTraits<DenseIndex>::IsSigned,THE_INDEX_TYPE_MUST_BE_A_SIGNED_TYPE)
+
+/** \class DenseBase
+ * \ingroup Core_Module
+ *
+ * \brief Base class for all dense matrices, vectors, and arrays
+ *
+ * This class is the base that is inherited by all dense objects (matrix, vector, arrays,
+ * and related expression types). The common Eigen API for dense objects is contained in this class.
+ *
+ * \tparam Derived is the derived type, e.g., a matrix type or an expression.
+ *
+ * This class can be extended with the help of the plugin mechanism described on the page
+ * \ref TopicCustomizing_Plugins by defining the preprocessor symbol \c EIGEN_DENSEBASE_PLUGIN.
+ *
+ * \sa \blank \ref TopicClassHierarchy
+ */
+template<typename Derived> class DenseBase
+#ifndef EIGEN_PARSED_BY_DOXYGEN
+ : public DenseCoeffsBase<Derived, internal::accessors_level<Derived>::value>
+#else
+ : public DenseCoeffsBase<Derived,DirectWriteAccessors>
+#endif // not EIGEN_PARSED_BY_DOXYGEN
+{
+ public:
+
+ /** Inner iterator type to iterate over the coefficients of a row or column.
+ * \sa class InnerIterator
+ */
+ typedef Eigen::InnerIterator<Derived> InnerIterator;
+
+ typedef typename internal::traits<Derived>::StorageKind StorageKind;
+
+ /**
+ * \brief The type used to store indices
+ * \details This typedef is relevant for types that store multiple indices such as
+ * PermutationMatrix or Transpositions, otherwise it defaults to Eigen::Index
+ * \sa \blank \ref TopicPreprocessorDirectives, Eigen::Index, SparseMatrixBase.
+ */
+ typedef typename internal::traits<Derived>::StorageIndex StorageIndex;
+
+ /** The numeric type of the expression' coefficients, e.g. float, double, int or std::complex<float>, etc. */
+ typedef typename internal::traits<Derived>::Scalar Scalar;
+
+ /** The numeric type of the expression' coefficients, e.g. float, double, int or std::complex<float>, etc.
+ *
+ * It is an alias for the Scalar type */
+ typedef Scalar value_type;
+
+ typedef typename NumTraits<Scalar>::Real RealScalar;
+ typedef DenseCoeffsBase<Derived, internal::accessors_level<Derived>::value> Base;
+
+ using Base::derived;
+ using Base::const_cast_derived;
+ using Base::rows;
+ using Base::cols;
+ using Base::size;
+ using Base::rowIndexByOuterInner;
+ using Base::colIndexByOuterInner;
+ using Base::coeff;
+ using Base::coeffByOuterInner;
+ using Base::operator();
+ using Base::operator[];
+ using Base::x;
+ using Base::y;
+ using Base::z;
+ using Base::w;
+ using Base::stride;
+ using Base::innerStride;
+ using Base::outerStride;
+ using Base::rowStride;
+ using Base::colStride;
+ typedef typename Base::CoeffReturnType CoeffReturnType;
+
+ enum {
+
+ RowsAtCompileTime = internal::traits<Derived>::RowsAtCompileTime,
+ /**< The number of rows at compile-time. This is just a copy of the value provided
+ * by the \a Derived type. If a value is not known at compile-time,
+ * it is set to the \a Dynamic constant.
+ * \sa MatrixBase::rows(), MatrixBase::cols(), ColsAtCompileTime, SizeAtCompileTime */
+
+ ColsAtCompileTime = internal::traits<Derived>::ColsAtCompileTime,
+ /**< The number of columns at compile-time. This is just a copy of the value provided
+ * by the \a Derived type. If a value is not known at compile-time,
+ * it is set to the \a Dynamic constant.
+ * \sa MatrixBase::rows(), MatrixBase::cols(), RowsAtCompileTime, SizeAtCompileTime */
+
+
+ SizeAtCompileTime = (internal::size_of_xpr_at_compile_time<Derived>::ret),
+ /**< This is equal to the number of coefficients, i.e. the number of
+ * rows times the number of columns, or to \a Dynamic if this is not
+ * known at compile-time. \sa RowsAtCompileTime, ColsAtCompileTime */
+
+ MaxRowsAtCompileTime = internal::traits<Derived>::MaxRowsAtCompileTime,
+ /**< This value is equal to the maximum possible number of rows that this expression
+ * might have. If this expression might have an arbitrarily high number of rows,
+ * this value is set to \a Dynamic.
+ *
+ * This value is useful to know when evaluating an expression, in order to determine
+ * whether it is possible to avoid doing a dynamic memory allocation.
+ *
+ * \sa RowsAtCompileTime, MaxColsAtCompileTime, MaxSizeAtCompileTime
+ */
+
+ MaxColsAtCompileTime = internal::traits<Derived>::MaxColsAtCompileTime,
+ /**< This value is equal to the maximum possible number of columns that this expression
+ * might have. If this expression might have an arbitrarily high number of columns,
+ * this value is set to \a Dynamic.
+ *
+ * This value is useful to know when evaluating an expression, in order to determine
+ * whether it is possible to avoid doing a dynamic memory allocation.
+ *
+ * \sa ColsAtCompileTime, MaxRowsAtCompileTime, MaxSizeAtCompileTime
+ */
+
+ MaxSizeAtCompileTime = internal::size_at_compile_time(internal::traits<Derived>::MaxRowsAtCompileTime,
+ internal::traits<Derived>::MaxColsAtCompileTime),
+ /**< This value is equal to the maximum possible number of coefficients that this expression
+ * might have. If this expression might have an arbitrarily high number of coefficients,
+ * this value is set to \a Dynamic.
+ *
+ * This value is useful to know when evaluating an expression, in order to determine
+ * whether it is possible to avoid doing a dynamic memory allocation.
+ *
+ * \sa SizeAtCompileTime, MaxRowsAtCompileTime, MaxColsAtCompileTime
+ */
+
+ IsVectorAtCompileTime = internal::traits<Derived>::RowsAtCompileTime == 1
+ || internal::traits<Derived>::ColsAtCompileTime == 1,
+ /**< This is set to true if either the number of rows or the number of
+ * columns is known at compile-time to be equal to 1. Indeed, in that case,
+ * we are dealing with a column-vector (if there is only one column) or with
+ * a row-vector (if there is only one row). */
+
+ NumDimensions = int(MaxSizeAtCompileTime) == 1 ? 0 : bool(IsVectorAtCompileTime) ? 1 : 2,
+ /**< This value is equal to Tensor::NumDimensions, i.e. 0 for scalars, 1 for vectors,
+ * and 2 for matrices.
+ */
+
+ Flags = internal::traits<Derived>::Flags,
+ /**< This stores expression \ref flags flags which may or may not be inherited by new expressions
+ * constructed from this one. See the \ref flags "list of flags".
+ */
+
+ IsRowMajor = int(Flags) & RowMajorBit, /**< True if this expression has row-major storage order. */
+
+ InnerSizeAtCompileTime = int(IsVectorAtCompileTime) ? int(SizeAtCompileTime)
+ : int(IsRowMajor) ? int(ColsAtCompileTime) : int(RowsAtCompileTime),
+
+ InnerStrideAtCompileTime = internal::inner_stride_at_compile_time<Derived>::ret,
+ OuterStrideAtCompileTime = internal::outer_stride_at_compile_time<Derived>::ret
+ };
+
+ typedef typename internal::find_best_packet<Scalar,SizeAtCompileTime>::type PacketScalar;
+
+ enum { IsPlainObjectBase = 0 };
+
+ /** The plain matrix type corresponding to this expression.
+ * \sa PlainObject */
+ typedef Matrix<typename internal::traits<Derived>::Scalar,
+ internal::traits<Derived>::RowsAtCompileTime,
+ internal::traits<Derived>::ColsAtCompileTime,
+ AutoAlign | (internal::traits<Derived>::Flags&RowMajorBit ? RowMajor : ColMajor),
+ internal::traits<Derived>::MaxRowsAtCompileTime,
+ internal::traits<Derived>::MaxColsAtCompileTime
+ > PlainMatrix;
+
+ /** The plain array type corresponding to this expression.
+ * \sa PlainObject */
+ typedef Array<typename internal::traits<Derived>::Scalar,
+ internal::traits<Derived>::RowsAtCompileTime,
+ internal::traits<Derived>::ColsAtCompileTime,
+ AutoAlign | (internal::traits<Derived>::Flags&RowMajorBit ? RowMajor : ColMajor),
+ internal::traits<Derived>::MaxRowsAtCompileTime,
+ internal::traits<Derived>::MaxColsAtCompileTime
+ > PlainArray;
+
+ /** \brief The plain matrix or array type corresponding to this expression.
+ *
+ * This is not necessarily exactly the return type of eval(). In the case of plain matrices,
+ * the return type of eval() is a const reference to a matrix, not a matrix! It is however guaranteed
+ * that the return type of eval() is either PlainObject or const PlainObject&.
+ */
+ typedef std::conditional_t<internal::is_same<typename internal::traits<Derived>::XprKind,MatrixXpr >::value,
+ PlainMatrix, PlainArray> PlainObject;
+
+ /** \returns the outer size.
+ *
+ * \note For a vector, this returns just 1. For a matrix (non-vector), this is the major dimension
+ * with respect to the \ref TopicStorageOrders "storage order", i.e., the number of columns for a
+ * column-major matrix, and the number of rows for a row-major matrix. */
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
+ Index outerSize() const
+ {
+ return IsVectorAtCompileTime ? 1
+ : int(IsRowMajor) ? this->rows() : this->cols();
+ }
+
+ /** \returns the inner size.
+ *
+ * \note For a vector, this is just the size. For a matrix (non-vector), this is the minor dimension
+ * with respect to the \ref TopicStorageOrders "storage order", i.e., the number of rows for a
+ * column-major matrix, and the number of columns for a row-major matrix. */
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
+ Index innerSize() const
+ {
+ return IsVectorAtCompileTime ? this->size()
+ : int(IsRowMajor) ? this->cols() : this->rows();
+ }
+
+ /** Only plain matrices/arrays, not expressions, may be resized; therefore the only useful resize methods are
+ * Matrix::resize() and Array::resize(). The present method only asserts that the new size equals the old size, and does
+ * nothing else.
+ */
+ EIGEN_DEVICE_FUNC
+ void resize(Index newSize)
+ {
+ EIGEN_ONLY_USED_FOR_DEBUG(newSize);
+ eigen_assert(newSize == this->size()
+ && "DenseBase::resize() does not actually allow to resize.");
+ }
+ /** Only plain matrices/arrays, not expressions, may be resized; therefore the only useful resize methods are
+ * Matrix::resize() and Array::resize(). The present method only asserts that the new size equals the old size, and does
+ * nothing else.
+ */
+ EIGEN_DEVICE_FUNC
+ void resize(Index rows, Index cols)
+ {
+ EIGEN_ONLY_USED_FOR_DEBUG(rows);
+ EIGEN_ONLY_USED_FOR_DEBUG(cols);
+ eigen_assert(rows == this->rows() && cols == this->cols()
+ && "DenseBase::resize() does not actually allow to resize.");
+ }
+
+#ifndef EIGEN_PARSED_BY_DOXYGEN
+ /** \internal Represents a matrix with all coefficients equal to one another*/
+ typedef CwiseNullaryOp<internal::scalar_constant_op<Scalar>,PlainObject> ConstantReturnType;
+ /** \internal \deprecated Represents a vector with linearly spaced coefficients that allows sequential access only. */
+ EIGEN_DEPRECATED typedef CwiseNullaryOp<internal::linspaced_op<Scalar>,PlainObject> SequentialLinSpacedReturnType;
+ /** \internal Represents a vector with linearly spaced coefficients that allows random access. */
+ typedef CwiseNullaryOp<internal::linspaced_op<Scalar>,PlainObject> RandomAccessLinSpacedReturnType;
+ /** \internal the return type of MatrixBase::eigenvalues() */
+ typedef Matrix<typename NumTraits<typename internal::traits<Derived>::Scalar>::Real, internal::traits<Derived>::ColsAtCompileTime, 1> EigenvaluesReturnType;
+
+#endif // not EIGEN_PARSED_BY_DOXYGEN
+
+ /** Copies \a other into *this. \returns a reference to *this. */
+ template<typename OtherDerived>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ Derived& operator=(const DenseBase<OtherDerived>& other);
+
+ /** Special case of the template operator=, in order to prevent the compiler
+ * from generating a default operator= (issue hit with g++ 4.1)
+ */
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ Derived& operator=(const DenseBase& other);
+
+ template<typename OtherDerived>
+ EIGEN_DEVICE_FUNC
+ Derived& operator=(const EigenBase<OtherDerived> &other);
+
+ template<typename OtherDerived>
+ EIGEN_DEVICE_FUNC
+ Derived& operator+=(const EigenBase<OtherDerived> &other);
+
+ template<typename OtherDerived>
+ EIGEN_DEVICE_FUNC
+ Derived& operator-=(const EigenBase<OtherDerived> &other);
+
+ template<typename OtherDerived>
+ EIGEN_DEVICE_FUNC
+ Derived& operator=(const ReturnByValue<OtherDerived>& func);
+
+ /** \internal
+ * Copies \a other into *this without evaluating other. \returns a reference to *this. */
+ template<typename OtherDerived>
+ /** \deprecated */
+ EIGEN_DEPRECATED EIGEN_DEVICE_FUNC
+ Derived& lazyAssign(const DenseBase<OtherDerived>& other);
+
+ EIGEN_DEVICE_FUNC
+ CommaInitializer<Derived> operator<< (const Scalar& s);
+
+ template<unsigned int Added,unsigned int Removed>
+ /** \deprecated it now returns \c *this */
+ EIGEN_DEPRECATED
+ const Derived& flagged() const
+ { return derived(); }
+
+ template<typename OtherDerived>
+ EIGEN_DEVICE_FUNC
+ CommaInitializer<Derived> operator<< (const DenseBase<OtherDerived>& other);
+
+ typedef Transpose<Derived> TransposeReturnType;
+ EIGEN_DEVICE_FUNC
+ TransposeReturnType transpose();
+ typedef Transpose<const Derived> ConstTransposeReturnType;
+ EIGEN_DEVICE_FUNC
+ const ConstTransposeReturnType transpose() const;
+ EIGEN_DEVICE_FUNC
+ void transposeInPlace();
+
+ EIGEN_DEVICE_FUNC static const ConstantReturnType
+ Constant(Index rows, Index cols, const Scalar& value);
+ EIGEN_DEVICE_FUNC static const ConstantReturnType
+ Constant(Index size, const Scalar& value);
+ EIGEN_DEVICE_FUNC static const ConstantReturnType
+ Constant(const Scalar& value);
+
+ EIGEN_DEPRECATED EIGEN_DEVICE_FUNC static const RandomAccessLinSpacedReturnType
+ LinSpaced(Sequential_t, Index size, const Scalar& low, const Scalar& high);
+ EIGEN_DEPRECATED EIGEN_DEVICE_FUNC static const RandomAccessLinSpacedReturnType
+ LinSpaced(Sequential_t, const Scalar& low, const Scalar& high);
+
+ EIGEN_DEVICE_FUNC static const RandomAccessLinSpacedReturnType
+ LinSpaced(Index size, const Scalar& low, const Scalar& high);
+ EIGEN_DEVICE_FUNC static const RandomAccessLinSpacedReturnType
+ LinSpaced(const Scalar& low, const Scalar& high);
+
+ template<typename CustomNullaryOp> EIGEN_DEVICE_FUNC
+ static const CwiseNullaryOp<CustomNullaryOp, PlainObject>
+ NullaryExpr(Index rows, Index cols, const CustomNullaryOp& func);
+ template<typename CustomNullaryOp> EIGEN_DEVICE_FUNC
+ static const CwiseNullaryOp<CustomNullaryOp, PlainObject>
+ NullaryExpr(Index size, const CustomNullaryOp& func);
+ template<typename CustomNullaryOp> EIGEN_DEVICE_FUNC
+ static const CwiseNullaryOp<CustomNullaryOp, PlainObject>
+ NullaryExpr(const CustomNullaryOp& func);
+
+ EIGEN_DEVICE_FUNC static const ConstantReturnType Zero(Index rows, Index cols);
+ EIGEN_DEVICE_FUNC static const ConstantReturnType Zero(Index size);
+ EIGEN_DEVICE_FUNC static const ConstantReturnType Zero();
+ EIGEN_DEVICE_FUNC static const ConstantReturnType Ones(Index rows, Index cols);
+ EIGEN_DEVICE_FUNC static const ConstantReturnType Ones(Index size);
+ EIGEN_DEVICE_FUNC static const ConstantReturnType Ones();
+
+ EIGEN_DEVICE_FUNC void fill(const Scalar& value);
+ EIGEN_DEVICE_FUNC Derived& setConstant(const Scalar& value);
+ EIGEN_DEVICE_FUNC Derived& setLinSpaced(Index size, const Scalar& low, const Scalar& high);
+ EIGEN_DEVICE_FUNC Derived& setLinSpaced(const Scalar& low, const Scalar& high);
+ EIGEN_DEVICE_FUNC Derived& setZero();
+ EIGEN_DEVICE_FUNC Derived& setOnes();
+ EIGEN_DEVICE_FUNC Derived& setRandom();
+
+ template<typename OtherDerived> EIGEN_DEVICE_FUNC
+ bool isApprox(const DenseBase<OtherDerived>& other,
+ const RealScalar& prec = NumTraits<Scalar>::dummy_precision()) const;
+ EIGEN_DEVICE_FUNC
+ bool isMuchSmallerThan(const RealScalar& other,
+ const RealScalar& prec = NumTraits<Scalar>::dummy_precision()) const;
+ template<typename OtherDerived> EIGEN_DEVICE_FUNC
+ bool isMuchSmallerThan(const DenseBase<OtherDerived>& other,
+ const RealScalar& prec = NumTraits<Scalar>::dummy_precision()) const;
+
+ EIGEN_DEVICE_FUNC bool isApproxToConstant(const Scalar& value, const RealScalar& prec = NumTraits<Scalar>::dummy_precision()) const;
+ EIGEN_DEVICE_FUNC bool isConstant(const Scalar& value, const RealScalar& prec = NumTraits<Scalar>::dummy_precision()) const;
+ EIGEN_DEVICE_FUNC bool isZero(const RealScalar& prec = NumTraits<Scalar>::dummy_precision()) const;
+ EIGEN_DEVICE_FUNC bool isOnes(const RealScalar& prec = NumTraits<Scalar>::dummy_precision()) const;
+
+ EIGEN_DEVICE_FUNC inline bool hasNaN() const;
+ EIGEN_DEVICE_FUNC inline bool allFinite() const;
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ Derived& operator*=(const Scalar& other);
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ Derived& operator/=(const Scalar& other);
+
+ typedef internal::add_const_on_value_type_t<typename internal::eval<Derived>::type> EvalReturnType;
+ /** \returns the matrix or vector obtained by evaluating this expression.
+ *
+ * Notice that in the case of a plain matrix or vector (not an expression) this function just returns
+ * a const reference, in order to avoid a useless copy.
+ *
+ * \warning Be careful with eval() and the auto C++ keyword, as detailed in this \link TopicPitfalls_auto_keyword page \endlink.
+ */
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE EvalReturnType eval() const
+ {
+ // Even though MSVC does not honor strong inlining when the return type
+ // is a dynamic matrix, we desperately need strong inlining for fixed
+ // size types on MSVC.
+ return typename internal::eval<Derived>::type(derived());
+ }
+
+ /** swaps *this with the expression \a other.
+ *
+ */
+ template<typename OtherDerived>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ void swap(const DenseBase<OtherDerived>& other)
+ {
+ EIGEN_STATIC_ASSERT(!OtherDerived::IsPlainObjectBase,THIS_EXPRESSION_IS_NOT_A_LVALUE__IT_IS_READ_ONLY);
+ eigen_assert(rows()==other.rows() && cols()==other.cols());
+ call_assignment(derived(), other.const_cast_derived(), internal::swap_assign_op<Scalar>());
+ }
+
+ /** swaps *this with the matrix or array \a other.
+ *
+ */
+ template<typename OtherDerived>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ void swap(PlainObjectBase<OtherDerived>& other)
+ {
+ eigen_assert(rows()==other.rows() && cols()==other.cols());
+ call_assignment(derived(), other.derived(), internal::swap_assign_op<Scalar>());
+ }
+
+ EIGEN_DEVICE_FUNC inline const NestByValue<Derived> nestByValue() const;
+ EIGEN_DEVICE_FUNC inline const ForceAlignedAccess<Derived> forceAlignedAccess() const;
+ EIGEN_DEVICE_FUNC inline ForceAlignedAccess<Derived> forceAlignedAccess();
+ template<bool Enable> EIGEN_DEVICE_FUNC
+ inline const std::conditional_t<Enable,ForceAlignedAccess<Derived>,Derived&> forceAlignedAccessIf() const;
+ template<bool Enable> EIGEN_DEVICE_FUNC
+ inline std::conditional_t<Enable,ForceAlignedAccess<Derived>,Derived&> forceAlignedAccessIf();
+
+ EIGEN_DEVICE_FUNC Scalar sum() const;
+ EIGEN_DEVICE_FUNC Scalar mean() const;
+ EIGEN_DEVICE_FUNC Scalar trace() const;
+
+ EIGEN_DEVICE_FUNC Scalar prod() const;
+
+ template<int NaNPropagation>
+ EIGEN_DEVICE_FUNC typename internal::traits<Derived>::Scalar minCoeff() const;
+ template<int NaNPropagation>
+ EIGEN_DEVICE_FUNC typename internal::traits<Derived>::Scalar maxCoeff() const;
+
+
+ // By default, the fastest version with undefined NaN propagation semantics is
+ // used.
+ // TODO(rmlarsen): Replace with default template argument when we move to
+ // c++11 or beyond.
+ EIGEN_DEVICE_FUNC inline typename internal::traits<Derived>::Scalar minCoeff() const {
+ return minCoeff<PropagateFast>();
+ }
+ EIGEN_DEVICE_FUNC inline typename internal::traits<Derived>::Scalar maxCoeff() const {
+ return maxCoeff<PropagateFast>();
+ }
+
+ template<int NaNPropagation, typename IndexType>
+ EIGEN_DEVICE_FUNC
+ typename internal::traits<Derived>::Scalar minCoeff(IndexType* row, IndexType* col) const;
+ template<int NaNPropagation, typename IndexType>
+ EIGEN_DEVICE_FUNC
+ typename internal::traits<Derived>::Scalar maxCoeff(IndexType* row, IndexType* col) const;
+ template<int NaNPropagation, typename IndexType>
+ EIGEN_DEVICE_FUNC
+ typename internal::traits<Derived>::Scalar minCoeff(IndexType* index) const;
+ template<int NaNPropagation, typename IndexType>
+ EIGEN_DEVICE_FUNC
+ typename internal::traits<Derived>::Scalar maxCoeff(IndexType* index) const;
+
+ // TODO(rmlarsen): Replace these methods with a default template argument.
+ template<typename IndexType>
+ EIGEN_DEVICE_FUNC inline
+ typename internal::traits<Derived>::Scalar minCoeff(IndexType* row, IndexType* col) const {
+ return minCoeff<PropagateFast>(row, col);
+ }
+ template<typename IndexType>
+ EIGEN_DEVICE_FUNC inline
+ typename internal::traits<Derived>::Scalar maxCoeff(IndexType* row, IndexType* col) const {
+ return maxCoeff<PropagateFast>(row, col);
+ }
+ template<typename IndexType>
+ EIGEN_DEVICE_FUNC inline
+ typename internal::traits<Derived>::Scalar minCoeff(IndexType* index) const {
+ return minCoeff<PropagateFast>(index);
+ }
+ template<typename IndexType>
+ EIGEN_DEVICE_FUNC inline
+ typename internal::traits<Derived>::Scalar maxCoeff(IndexType* index) const {
+ return maxCoeff<PropagateFast>(index);
+ }
+
+ template<typename BinaryOp>
+ EIGEN_DEVICE_FUNC
+ Scalar redux(const BinaryOp& func) const;
+
+ template<typename Visitor>
+ EIGEN_DEVICE_FUNC
+ void visit(Visitor& func) const;
+
+ /** \returns a WithFormat proxy object allowing to print a matrix the with given
+ * format \a fmt.
+ *
+ * See class IOFormat for some examples.
+ *
+ * \sa class IOFormat, class WithFormat
+ */
+ inline const WithFormat<Derived> format(const IOFormat& fmt) const
+ {
+ return WithFormat<Derived>(derived(), fmt);
+ }
+
+ /** \returns the unique coefficient of a 1x1 expression */
+ EIGEN_DEVICE_FUNC
+ CoeffReturnType value() const
+ {
+ EIGEN_STATIC_ASSERT_SIZE_1x1(Derived)
+ eigen_assert(this->rows() == 1 && this->cols() == 1);
+ return derived().coeff(0,0);
+ }
+
+ EIGEN_DEVICE_FUNC bool all() const;
+ EIGEN_DEVICE_FUNC bool any() const;
+ EIGEN_DEVICE_FUNC Index count() const;
+
+ typedef VectorwiseOp<Derived, Horizontal> RowwiseReturnType;
+ typedef const VectorwiseOp<const Derived, Horizontal> ConstRowwiseReturnType;
+ typedef VectorwiseOp<Derived, Vertical> ColwiseReturnType;
+ typedef const VectorwiseOp<const Derived, Vertical> ConstColwiseReturnType;
+
+ /** \returns a VectorwiseOp wrapper of *this for broadcasting and partial reductions
+ *
+ * Example: \include MatrixBase_rowwise.cpp
+ * Output: \verbinclude MatrixBase_rowwise.out
+ *
+ * \sa colwise(), class VectorwiseOp, \ref TutorialReductionsVisitorsBroadcasting
+ */
+ //Code moved here due to a CUDA compiler bug
+ EIGEN_DEVICE_FUNC inline ConstRowwiseReturnType rowwise() const {
+ return ConstRowwiseReturnType(derived());
+ }
+ EIGEN_DEVICE_FUNC RowwiseReturnType rowwise();
+
+ /** \returns a VectorwiseOp wrapper of *this broadcasting and partial reductions
+ *
+ * Example: \include MatrixBase_colwise.cpp
+ * Output: \verbinclude MatrixBase_colwise.out
+ *
+ * \sa rowwise(), class VectorwiseOp, \ref TutorialReductionsVisitorsBroadcasting
+ */
+ EIGEN_DEVICE_FUNC inline ConstColwiseReturnType colwise() const {
+ return ConstColwiseReturnType(derived());
+ }
+ EIGEN_DEVICE_FUNC ColwiseReturnType colwise();
+
+ typedef CwiseNullaryOp<internal::scalar_random_op<Scalar>,PlainObject> RandomReturnType;
+ static const RandomReturnType Random(Index rows, Index cols);
+ static const RandomReturnType Random(Index size);
+ static const RandomReturnType Random();
+
+ template<typename ThenDerived,typename ElseDerived>
+ inline EIGEN_DEVICE_FUNC const Select<Derived,ThenDerived,ElseDerived>
+ select(const DenseBase<ThenDerived>& thenMatrix,
+ const DenseBase<ElseDerived>& elseMatrix) const;
+
+ template<typename ThenDerived>
+ inline EIGEN_DEVICE_FUNC const Select<Derived,ThenDerived, typename ThenDerived::ConstantReturnType>
+ select(const DenseBase<ThenDerived>& thenMatrix, const typename ThenDerived::Scalar& elseScalar) const;
+
+ template<typename ElseDerived>
+ inline EIGEN_DEVICE_FUNC const Select<Derived, typename ElseDerived::ConstantReturnType, ElseDerived >
+ select(const typename ElseDerived::Scalar& thenScalar, const DenseBase<ElseDerived>& elseMatrix) const;
+
+ template<int p> RealScalar lpNorm() const;
+
+ template<int RowFactor, int ColFactor>
+ EIGEN_DEVICE_FUNC
+ const Replicate<Derived,RowFactor,ColFactor> replicate() const;
+ /**
+ * \return an expression of the replication of \c *this
+ *
+ * Example: \include MatrixBase_replicate_int_int.cpp
+ * Output: \verbinclude MatrixBase_replicate_int_int.out
+ *
+ * \sa VectorwiseOp::replicate(), DenseBase::replicate<int,int>(), class Replicate
+ */
+ //Code moved here due to a CUDA compiler bug
+ EIGEN_DEVICE_FUNC
+ const Replicate<Derived, Dynamic, Dynamic> replicate(Index rowFactor, Index colFactor) const
+ {
+ return Replicate<Derived, Dynamic, Dynamic>(derived(), rowFactor, colFactor);
+ }
+
+ typedef Reverse<Derived, BothDirections> ReverseReturnType;
+ typedef const Reverse<const Derived, BothDirections> ConstReverseReturnType;
+ EIGEN_DEVICE_FUNC ReverseReturnType reverse();
+ /** This is the const version of reverse(). */
+ //Code moved here due to a CUDA compiler bug
+ EIGEN_DEVICE_FUNC ConstReverseReturnType reverse() const
+ {
+ return ConstReverseReturnType(derived());
+ }
+ EIGEN_DEVICE_FUNC void reverseInPlace();
+
+ #ifdef EIGEN_PARSED_BY_DOXYGEN
+ /** STL-like <a href="https://en.cppreference.com/w/cpp/named_req/RandomAccessIterator">RandomAccessIterator</a>
+ * iterator type as returned by the begin() and end() methods.
+ */
+ typedef random_access_iterator_type iterator;
+ /** This is the const version of iterator (aka read-only) */
+ typedef random_access_iterator_type const_iterator;
+ #else
+ typedef std::conditional_t< (Flags&DirectAccessBit)==DirectAccessBit,
+ internal::pointer_based_stl_iterator<Derived>,
+ internal::generic_randaccess_stl_iterator<Derived>
+ > iterator_type;
+
+ typedef std::conditional_t< (Flags&DirectAccessBit)==DirectAccessBit,
+ internal::pointer_based_stl_iterator<const Derived>,
+ internal::generic_randaccess_stl_iterator<const Derived>
+ > const_iterator_type;
+
+ // Stl-style iterators are supported only for vectors.
+
+ typedef std::conditional_t<IsVectorAtCompileTime, iterator_type, void> iterator;
+
+ typedef std::conditional_t<IsVectorAtCompileTime, const_iterator_type, void> const_iterator;
+ #endif
+
+ inline iterator begin();
+ inline const_iterator begin() const;
+ inline const_iterator cbegin() const;
+ inline iterator end();
+ inline const_iterator end() const;
+ inline const_iterator cend() const;
+
+#define EIGEN_CURRENT_STORAGE_BASE_CLASS Eigen::DenseBase
+#define EIGEN_DOC_BLOCK_ADDONS_NOT_INNER_PANEL
+#define EIGEN_DOC_BLOCK_ADDONS_INNER_PANEL_IF(COND)
+#define EIGEN_DOC_UNARY_ADDONS(X,Y)
+# include "../plugins/CommonCwiseUnaryOps.h"
+# include "../plugins/BlockMethods.h"
+# include "../plugins/IndexedViewMethods.h"
+# include "../plugins/ReshapedMethods.h"
+# ifdef EIGEN_DENSEBASE_PLUGIN
+# include EIGEN_DENSEBASE_PLUGIN
+# endif
+#undef EIGEN_CURRENT_STORAGE_BASE_CLASS
+#undef EIGEN_DOC_BLOCK_ADDONS_NOT_INNER_PANEL
+#undef EIGEN_DOC_BLOCK_ADDONS_INNER_PANEL_IF
+#undef EIGEN_DOC_UNARY_ADDONS
+
+ // disable the use of evalTo for dense objects with a nice compilation error
+ template<typename Dest>
+ EIGEN_DEVICE_FUNC
+ inline void evalTo(Dest& ) const
+ {
+ EIGEN_STATIC_ASSERT((internal::is_same<Dest,void>::value),THE_EVAL_EVALTO_FUNCTION_SHOULD_NEVER_BE_CALLED_FOR_DENSE_OBJECTS);
+ }
+
+ protected:
+ EIGEN_DEFAULT_COPY_CONSTRUCTOR(DenseBase)
+ /** Default constructor. Do nothing. */
+ EIGEN_DEVICE_FUNC DenseBase()
+ {
+ /* Just checks for self-consistency of the flags.
+ * Only do it when debugging Eigen, as this borders on paranoia and could slow compilation down
+ */
+#ifdef EIGEN_INTERNAL_DEBUGGING
+ EIGEN_STATIC_ASSERT((internal::check_implication(MaxRowsAtCompileTime==1 && MaxColsAtCompileTime!=1, int(IsRowMajor))
+ && internal::check_implication(MaxColsAtCompileTime==1 && MaxRowsAtCompileTime!=1, int(!IsRowMajor))),
+ INVALID_STORAGE_ORDER_FOR_THIS_VECTOR_EXPRESSION)
+#endif
+ }
+
+ private:
+ EIGEN_DEVICE_FUNC explicit DenseBase(int);
+ EIGEN_DEVICE_FUNC DenseBase(int,int);
+ template<typename OtherDerived> EIGEN_DEVICE_FUNC explicit DenseBase(const DenseBase<OtherDerived>&);
+};
+
+} // end namespace Eigen
+
+#endif // EIGEN_DENSEBASE_H
diff --git a/Eigen/src/Core/DenseCoeffsBase.h b/Eigen/src/Core/DenseCoeffsBase.h
new file mode 100644
index 0000000..7f0bcf4
--- /dev/null
+++ b/Eigen/src/Core/DenseCoeffsBase.h
@@ -0,0 +1,687 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2006-2010 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_DENSECOEFFSBASE_H
+#define EIGEN_DENSECOEFFSBASE_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+template<typename T> struct add_const_on_value_type_if_arithmetic
+{
+ typedef std::conditional_t<is_arithmetic<T>::value, T, add_const_on_value_type_t<T>> type;
+};
+}
+
+/** \brief Base class providing read-only coefficient access to matrices and arrays.
+ * \ingroup Core_Module
+ * \tparam Derived Type of the derived class
+ *
+ * \note #ReadOnlyAccessors Constant indicating read-only access
+ *
+ * This class defines the \c operator() \c const function and friends, which can be used to read specific
+ * entries of a matrix or array.
+ *
+ * \sa DenseCoeffsBase<Derived, WriteAccessors>, DenseCoeffsBase<Derived, DirectAccessors>,
+ * \ref TopicClassHierarchy
+ */
+template<typename Derived>
+class DenseCoeffsBase<Derived,ReadOnlyAccessors> : public EigenBase<Derived>
+{
+ public:
+ typedef typename internal::traits<Derived>::StorageKind StorageKind;
+ typedef typename internal::traits<Derived>::Scalar Scalar;
+ typedef typename internal::packet_traits<Scalar>::type PacketScalar;
+
+ // Explanation for this CoeffReturnType typedef.
+ // - This is the return type of the coeff() method.
+ // - The LvalueBit means exactly that we can offer a coeffRef() method, which means exactly that we can get references
+ // to coeffs, which means exactly that we can have coeff() return a const reference (as opposed to returning a value).
+ // - The is_arithmetic check is required since "const int", "const double", etc. will cause warnings on some systems
+ // while the declaration of "const T", where T is a non arithmetic type does not. Always returning "const Scalar&" is
+ // not possible, since the underlying expressions might not offer a valid address the reference could be referring to.
+ typedef std::conditional_t<bool(internal::traits<Derived>::Flags&LvalueBit),
+ const Scalar&,
+ std::conditional_t<internal::is_arithmetic<Scalar>::value, Scalar, const Scalar>
+ > CoeffReturnType;
+
+ typedef typename internal::add_const_on_value_type_if_arithmetic<
+ typename internal::packet_traits<Scalar>::type
+ >::type PacketReturnType;
+
+ typedef EigenBase<Derived> Base;
+ using Base::rows;
+ using Base::cols;
+ using Base::size;
+ using Base::derived;
+
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE Index rowIndexByOuterInner(Index outer, Index inner) const
+ {
+ return int(Derived::RowsAtCompileTime) == 1 ? 0
+ : int(Derived::ColsAtCompileTime) == 1 ? inner
+ : int(Derived::Flags)&RowMajorBit ? outer
+ : inner;
+ }
+
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE Index colIndexByOuterInner(Index outer, Index inner) const
+ {
+ return int(Derived::ColsAtCompileTime) == 1 ? 0
+ : int(Derived::RowsAtCompileTime) == 1 ? inner
+ : int(Derived::Flags)&RowMajorBit ? inner
+ : outer;
+ }
+
+ /** Short version: don't use this function, use
+ * \link operator()(Index,Index) const \endlink instead.
+ *
+ * Long version: this function is similar to
+ * \link operator()(Index,Index) const \endlink, but without the assertion.
+ * Use this for limiting the performance cost of debugging code when doing
+ * repeated coefficient access. Only use this when it is guaranteed that the
+ * parameters \a row and \a col are in range.
+ *
+ * If EIGEN_INTERNAL_DEBUGGING is defined, an assertion will be made, making this
+ * function equivalent to \link operator()(Index,Index) const \endlink.
+ *
+ * \sa operator()(Index,Index) const, coeffRef(Index,Index), coeff(Index) const
+ */
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE CoeffReturnType coeff(Index row, Index col) const
+ {
+ eigen_internal_assert(row >= 0 && row < rows()
+ && col >= 0 && col < cols());
+ return internal::evaluator<Derived>(derived()).coeff(row,col);
+ }
+
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE CoeffReturnType coeffByOuterInner(Index outer, Index inner) const
+ {
+ return coeff(rowIndexByOuterInner(outer, inner),
+ colIndexByOuterInner(outer, inner));
+ }
+
+ /** \returns the coefficient at given the given row and column.
+ *
+ * \sa operator()(Index,Index), operator[](Index)
+ */
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE CoeffReturnType operator()(Index row, Index col) const
+ {
+ eigen_assert(row >= 0 && row < rows()
+ && col >= 0 && col < cols());
+ return coeff(row, col);
+ }
+
+ /** Short version: don't use this function, use
+ * \link operator[](Index) const \endlink instead.
+ *
+ * Long version: this function is similar to
+ * \link operator[](Index) const \endlink, but without the assertion.
+ * Use this for limiting the performance cost of debugging code when doing
+ * repeated coefficient access. Only use this when it is guaranteed that the
+ * parameter \a index is in range.
+ *
+ * If EIGEN_INTERNAL_DEBUGGING is defined, an assertion will be made, making this
+ * function equivalent to \link operator[](Index) const \endlink.
+ *
+ * \sa operator[](Index) const, coeffRef(Index), coeff(Index,Index) const
+ */
+
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE CoeffReturnType
+ coeff(Index index) const
+ {
+ EIGEN_STATIC_ASSERT(internal::evaluator<Derived>::Flags & LinearAccessBit,
+ THIS_COEFFICIENT_ACCESSOR_TAKING_ONE_ACCESS_IS_ONLY_FOR_EXPRESSIONS_ALLOWING_LINEAR_ACCESS)
+ eigen_internal_assert(index >= 0 && index < size());
+ return internal::evaluator<Derived>(derived()).coeff(index);
+ }
+
+
+ /** \returns the coefficient at given index.
+ *
+ * This method is allowed only for vector expressions, and for matrix expressions having the LinearAccessBit.
+ *
+ * \sa operator[](Index), operator()(Index,Index) const, x() const, y() const,
+ * z() const, w() const
+ */
+
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE CoeffReturnType
+ operator[](Index index) const
+ {
+ EIGEN_STATIC_ASSERT(Derived::IsVectorAtCompileTime,
+ THE_BRACKET_OPERATOR_IS_ONLY_FOR_VECTORS__USE_THE_PARENTHESIS_OPERATOR_INSTEAD)
+ eigen_assert(index >= 0 && index < size());
+ return coeff(index);
+ }
+
+ /** \returns the coefficient at given index.
+ *
+ * This is synonymous to operator[](Index) const.
+ *
+ * This method is allowed only for vector expressions, and for matrix expressions having the LinearAccessBit.
+ *
+ * \sa operator[](Index), operator()(Index,Index) const, x() const, y() const,
+ * z() const, w() const
+ */
+
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE CoeffReturnType
+ operator()(Index index) const
+ {
+ eigen_assert(index >= 0 && index < size());
+ return coeff(index);
+ }
+
+ /** equivalent to operator[](0). */
+
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE CoeffReturnType
+ x() const { return (*this)[0]; }
+
+ /** equivalent to operator[](1). */
+
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE CoeffReturnType
+ y() const
+ {
+ EIGEN_STATIC_ASSERT(Derived::SizeAtCompileTime==-1 || Derived::SizeAtCompileTime>=2, OUT_OF_RANGE_ACCESS);
+ return (*this)[1];
+ }
+
+ /** equivalent to operator[](2). */
+
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE CoeffReturnType
+ z() const
+ {
+ EIGEN_STATIC_ASSERT(Derived::SizeAtCompileTime==-1 || Derived::SizeAtCompileTime>=3, OUT_OF_RANGE_ACCESS);
+ return (*this)[2];
+ }
+
+ /** equivalent to operator[](3). */
+
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE CoeffReturnType
+ w() const
+ {
+ EIGEN_STATIC_ASSERT(Derived::SizeAtCompileTime==-1 || Derived::SizeAtCompileTime>=4, OUT_OF_RANGE_ACCESS);
+ return (*this)[3];
+ }
+
+ /** \internal
+ * \returns the packet of coefficients starting at the given row and column. It is your responsibility
+ * to ensure that a packet really starts there. This method is only available on expressions having the
+ * PacketAccessBit.
+ *
+ * The \a LoadMode parameter may have the value \a #Aligned or \a #Unaligned. Its effect is to select
+ * the appropriate vectorization instruction. Aligned access is faster, but is only possible for packets
+ * starting at an address which is a multiple of the packet size.
+ */
+
+ template<int LoadMode>
+ EIGEN_STRONG_INLINE PacketReturnType packet(Index row, Index col) const
+ {
+ typedef typename internal::packet_traits<Scalar>::type DefaultPacketType;
+ eigen_internal_assert(row >= 0 && row < rows() && col >= 0 && col < cols());
+ return internal::evaluator<Derived>(derived()).template packet<LoadMode,DefaultPacketType>(row,col);
+ }
+
+
+ /** \internal */
+ template<int LoadMode>
+ EIGEN_STRONG_INLINE PacketReturnType packetByOuterInner(Index outer, Index inner) const
+ {
+ return packet<LoadMode>(rowIndexByOuterInner(outer, inner),
+ colIndexByOuterInner(outer, inner));
+ }
+
+ /** \internal
+ * \returns the packet of coefficients starting at the given index. It is your responsibility
+ * to ensure that a packet really starts there. This method is only available on expressions having the
+ * PacketAccessBit and the LinearAccessBit.
+ *
+ * The \a LoadMode parameter may have the value \a #Aligned or \a #Unaligned. Its effect is to select
+ * the appropriate vectorization instruction. Aligned access is faster, but is only possible for packets
+ * starting at an address which is a multiple of the packet size.
+ */
+
+ template<int LoadMode>
+ EIGEN_STRONG_INLINE PacketReturnType packet(Index index) const
+ {
+ EIGEN_STATIC_ASSERT(internal::evaluator<Derived>::Flags & LinearAccessBit,
+ THIS_COEFFICIENT_ACCESSOR_TAKING_ONE_ACCESS_IS_ONLY_FOR_EXPRESSIONS_ALLOWING_LINEAR_ACCESS)
+ typedef typename internal::packet_traits<Scalar>::type DefaultPacketType;
+ eigen_internal_assert(index >= 0 && index < size());
+ return internal::evaluator<Derived>(derived()).template packet<LoadMode,DefaultPacketType>(index);
+ }
+
+ protected:
+ // explanation: DenseBase is doing "using ..." on the methods from DenseCoeffsBase.
+ // But some methods are only available in the DirectAccess case.
+ // So we add dummy methods here with these names, so that "using... " doesn't fail.
+ // It's not private so that the child class DenseBase can access them, and it's not public
+ // either since it's an implementation detail, so has to be protected.
+ void coeffRef();
+ void coeffRefByOuterInner();
+ void writePacket();
+ void writePacketByOuterInner();
+ void copyCoeff();
+ void copyCoeffByOuterInner();
+ void copyPacket();
+ void copyPacketByOuterInner();
+ void stride();
+ void innerStride();
+ void outerStride();
+ void rowStride();
+ void colStride();
+};
+
+/** \brief Base class providing read/write coefficient access to matrices and arrays.
+ * \ingroup Core_Module
+ * \tparam Derived Type of the derived class
+ *
+ * \note #WriteAccessors Constant indicating read/write access
+ *
+ * This class defines the non-const \c operator() function and friends, which can be used to write specific
+ * entries of a matrix or array. This class inherits DenseCoeffsBase<Derived, ReadOnlyAccessors> which
+ * defines the const variant for reading specific entries.
+ *
+ * \sa DenseCoeffsBase<Derived, DirectAccessors>, \ref TopicClassHierarchy
+ */
+template<typename Derived>
+class DenseCoeffsBase<Derived, WriteAccessors> : public DenseCoeffsBase<Derived, ReadOnlyAccessors>
+{
+ public:
+
+ typedef DenseCoeffsBase<Derived, ReadOnlyAccessors> Base;
+
+ typedef typename internal::traits<Derived>::StorageKind StorageKind;
+ typedef typename internal::traits<Derived>::Scalar Scalar;
+ typedef typename internal::packet_traits<Scalar>::type PacketScalar;
+ typedef typename NumTraits<Scalar>::Real RealScalar;
+
+ using Base::coeff;
+ using Base::rows;
+ using Base::cols;
+ using Base::size;
+ using Base::derived;
+ using Base::rowIndexByOuterInner;
+ using Base::colIndexByOuterInner;
+ using Base::operator[];
+ using Base::operator();
+ using Base::x;
+ using Base::y;
+ using Base::z;
+ using Base::w;
+
+ /** Short version: don't use this function, use
+ * \link operator()(Index,Index) \endlink instead.
+ *
+ * Long version: this function is similar to
+ * \link operator()(Index,Index) \endlink, but without the assertion.
+ * Use this for limiting the performance cost of debugging code when doing
+ * repeated coefficient access. Only use this when it is guaranteed that the
+ * parameters \a row and \a col are in range.
+ *
+ * If EIGEN_INTERNAL_DEBUGGING is defined, an assertion will be made, making this
+ * function equivalent to \link operator()(Index,Index) \endlink.
+ *
+ * \sa operator()(Index,Index), coeff(Index, Index) const, coeffRef(Index)
+ */
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE Scalar& coeffRef(Index row, Index col)
+ {
+ eigen_internal_assert(row >= 0 && row < rows()
+ && col >= 0 && col < cols());
+ return internal::evaluator<Derived>(derived()).coeffRef(row,col);
+ }
+
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE Scalar&
+ coeffRefByOuterInner(Index outer, Index inner)
+ {
+ return coeffRef(rowIndexByOuterInner(outer, inner),
+ colIndexByOuterInner(outer, inner));
+ }
+
+ /** \returns a reference to the coefficient at given the given row and column.
+ *
+ * \sa operator[](Index)
+ */
+
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE Scalar&
+ operator()(Index row, Index col)
+ {
+ eigen_assert(row >= 0 && row < rows()
+ && col >= 0 && col < cols());
+ return coeffRef(row, col);
+ }
+
+
+ /** Short version: don't use this function, use
+ * \link operator[](Index) \endlink instead.
+ *
+ * Long version: this function is similar to
+ * \link operator[](Index) \endlink, but without the assertion.
+ * Use this for limiting the performance cost of debugging code when doing
+ * repeated coefficient access. Only use this when it is guaranteed that the
+ * parameters \a row and \a col are in range.
+ *
+ * If EIGEN_INTERNAL_DEBUGGING is defined, an assertion will be made, making this
+ * function equivalent to \link operator[](Index) \endlink.
+ *
+ * \sa operator[](Index), coeff(Index) const, coeffRef(Index,Index)
+ */
+
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE Scalar&
+ coeffRef(Index index)
+ {
+ EIGEN_STATIC_ASSERT(internal::evaluator<Derived>::Flags & LinearAccessBit,
+ THIS_COEFFICIENT_ACCESSOR_TAKING_ONE_ACCESS_IS_ONLY_FOR_EXPRESSIONS_ALLOWING_LINEAR_ACCESS)
+ eigen_internal_assert(index >= 0 && index < size());
+ return internal::evaluator<Derived>(derived()).coeffRef(index);
+ }
+
+ /** \returns a reference to the coefficient at given index.
+ *
+ * This method is allowed only for vector expressions, and for matrix expressions having the LinearAccessBit.
+ *
+ * \sa operator[](Index) const, operator()(Index,Index), x(), y(), z(), w()
+ */
+
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE Scalar&
+ operator[](Index index)
+ {
+ EIGEN_STATIC_ASSERT(Derived::IsVectorAtCompileTime,
+ THE_BRACKET_OPERATOR_IS_ONLY_FOR_VECTORS__USE_THE_PARENTHESIS_OPERATOR_INSTEAD)
+ eigen_assert(index >= 0 && index < size());
+ return coeffRef(index);
+ }
+
+ /** \returns a reference to the coefficient at given index.
+ *
+ * This is synonymous to operator[](Index).
+ *
+ * This method is allowed only for vector expressions, and for matrix expressions having the LinearAccessBit.
+ *
+ * \sa operator[](Index) const, operator()(Index,Index), x(), y(), z(), w()
+ */
+
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE Scalar&
+ operator()(Index index)
+ {
+ eigen_assert(index >= 0 && index < size());
+ return coeffRef(index);
+ }
+
+ /** equivalent to operator[](0). */
+
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE Scalar&
+ x() { return (*this)[0]; }
+
+ /** equivalent to operator[](1). */
+
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE Scalar&
+ y()
+ {
+ EIGEN_STATIC_ASSERT(Derived::SizeAtCompileTime==-1 || Derived::SizeAtCompileTime>=2, OUT_OF_RANGE_ACCESS);
+ return (*this)[1];
+ }
+
+ /** equivalent to operator[](2). */
+
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE Scalar&
+ z()
+ {
+ EIGEN_STATIC_ASSERT(Derived::SizeAtCompileTime==-1 || Derived::SizeAtCompileTime>=3, OUT_OF_RANGE_ACCESS);
+ return (*this)[2];
+ }
+
+ /** equivalent to operator[](3). */
+
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE Scalar&
+ w()
+ {
+ EIGEN_STATIC_ASSERT(Derived::SizeAtCompileTime==-1 || Derived::SizeAtCompileTime>=4, OUT_OF_RANGE_ACCESS);
+ return (*this)[3];
+ }
+};
+
+/** \brief Base class providing direct read-only coefficient access to matrices and arrays.
+ * \ingroup Core_Module
+ * \tparam Derived Type of the derived class
+ *
+ * \note #DirectAccessors Constant indicating direct access
+ *
+ * This class defines functions to work with strides which can be used to access entries directly. This class
+ * inherits DenseCoeffsBase<Derived, ReadOnlyAccessors> which defines functions to access entries read-only using
+ * \c operator() .
+ *
+ * \sa \blank \ref TopicClassHierarchy
+ */
+template<typename Derived>
+class DenseCoeffsBase<Derived, DirectAccessors> : public DenseCoeffsBase<Derived, ReadOnlyAccessors>
+{
+ public:
+
+ typedef DenseCoeffsBase<Derived, ReadOnlyAccessors> Base;
+ typedef typename internal::traits<Derived>::Scalar Scalar;
+ typedef typename NumTraits<Scalar>::Real RealScalar;
+
+ using Base::rows;
+ using Base::cols;
+ using Base::size;
+ using Base::derived;
+
+ /** \returns the pointer increment between two consecutive elements within a slice in the inner direction.
+ *
+ * \sa outerStride(), rowStride(), colStride()
+ */
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
+ inline Index innerStride() const
+ {
+ return derived().innerStride();
+ }
+
+ /** \returns the pointer increment between two consecutive inner slices (for example, between two consecutive columns
+ * in a column-major matrix).
+ *
+ * \sa innerStride(), rowStride(), colStride()
+ */
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
+ inline Index outerStride() const
+ {
+ return derived().outerStride();
+ }
+
+ // FIXME shall we remove it ?
+ EIGEN_CONSTEXPR inline Index stride() const
+ {
+ return Derived::IsVectorAtCompileTime ? innerStride() : outerStride();
+ }
+
+ /** \returns the pointer increment between two consecutive rows.
+ *
+ * \sa innerStride(), outerStride(), colStride()
+ */
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
+ inline Index rowStride() const
+ {
+ return Derived::IsRowMajor ? outerStride() : innerStride();
+ }
+
+ /** \returns the pointer increment between two consecutive columns.
+ *
+ * \sa innerStride(), outerStride(), rowStride()
+ */
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
+ inline Index colStride() const
+ {
+ return Derived::IsRowMajor ? innerStride() : outerStride();
+ }
+};
+
+/** \brief Base class providing direct read/write coefficient access to matrices and arrays.
+ * \ingroup Core_Module
+ * \tparam Derived Type of the derived class
+ *
+ * \note #DirectWriteAccessors Constant indicating direct access
+ *
+ * This class defines functions to work with strides which can be used to access entries directly. This class
+ * inherits DenseCoeffsBase<Derived, WriteAccessors> which defines functions to access entries read/write using
+ * \c operator().
+ *
+ * \sa \blank \ref TopicClassHierarchy
+ */
+template<typename Derived>
+class DenseCoeffsBase<Derived, DirectWriteAccessors>
+ : public DenseCoeffsBase<Derived, WriteAccessors>
+{
+ public:
+
+ typedef DenseCoeffsBase<Derived, WriteAccessors> Base;
+ typedef typename internal::traits<Derived>::Scalar Scalar;
+ typedef typename NumTraits<Scalar>::Real RealScalar;
+
+ using Base::rows;
+ using Base::cols;
+ using Base::size;
+ using Base::derived;
+
+ /** \returns the pointer increment between two consecutive elements within a slice in the inner direction.
+ *
+ * \sa outerStride(), rowStride(), colStride()
+ */
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
+ inline Index innerStride() const EIGEN_NOEXCEPT
+ {
+ return derived().innerStride();
+ }
+
+ /** \returns the pointer increment between two consecutive inner slices (for example, between two consecutive columns
+ * in a column-major matrix).
+ *
+ * \sa innerStride(), rowStride(), colStride()
+ */
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
+ inline Index outerStride() const EIGEN_NOEXCEPT
+ {
+ return derived().outerStride();
+ }
+
+ // FIXME shall we remove it ?
+ EIGEN_CONSTEXPR inline Index stride() const EIGEN_NOEXCEPT
+ {
+ return Derived::IsVectorAtCompileTime ? innerStride() : outerStride();
+ }
+
+ /** \returns the pointer increment between two consecutive rows.
+ *
+ * \sa innerStride(), outerStride(), colStride()
+ */
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
+ inline Index rowStride() const EIGEN_NOEXCEPT
+ {
+ return Derived::IsRowMajor ? outerStride() : innerStride();
+ }
+
+ /** \returns the pointer increment between two consecutive columns.
+ *
+ * \sa innerStride(), outerStride(), rowStride()
+ */
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
+ inline Index colStride() const EIGEN_NOEXCEPT
+ {
+ return Derived::IsRowMajor ? innerStride() : outerStride();
+ }
+};
+
+namespace internal {
+
+template<int Alignment, typename Derived, bool JustReturnZero>
+struct first_aligned_impl
+{
+ static EIGEN_CONSTEXPR inline Index run(const Derived&) EIGEN_NOEXCEPT
+ { return 0; }
+};
+
+template<int Alignment, typename Derived>
+struct first_aligned_impl<Alignment, Derived, false>
+{
+ static inline Index run(const Derived& m)
+ {
+ return internal::first_aligned<Alignment>(m.data(), m.size());
+ }
+};
+
+/** \internal \returns the index of the first element of the array stored by \a m that is properly aligned with respect to \a Alignment for vectorization.
+ *
+ * \tparam Alignment requested alignment in Bytes.
+ *
+ * There is also the variant first_aligned(const Scalar*, Integer) defined in Memory.h. See it for more
+ * documentation.
+ */
+template<int Alignment, typename Derived>
+static inline Index first_aligned(const DenseBase<Derived>& m)
+{
+ enum { ReturnZero = (int(evaluator<Derived>::Alignment) >= Alignment) || !(Derived::Flags & DirectAccessBit) };
+ return first_aligned_impl<Alignment, Derived, ReturnZero>::run(m.derived());
+}
+
+template<typename Derived>
+static inline Index first_default_aligned(const DenseBase<Derived>& m)
+{
+ typedef typename Derived::Scalar Scalar;
+ typedef typename packet_traits<Scalar>::type DefaultPacketType;
+ return internal::first_aligned<int(unpacket_traits<DefaultPacketType>::alignment),Derived>(m);
+}
+
+template<typename Derived, bool HasDirectAccess = has_direct_access<Derived>::ret>
+struct inner_stride_at_compile_time
+{
+ enum { ret = traits<Derived>::InnerStrideAtCompileTime };
+};
+
+template<typename Derived>
+struct inner_stride_at_compile_time<Derived, false>
+{
+ enum { ret = 0 };
+};
+
+template<typename Derived, bool HasDirectAccess = has_direct_access<Derived>::ret>
+struct outer_stride_at_compile_time
+{
+ enum { ret = traits<Derived>::OuterStrideAtCompileTime };
+};
+
+template<typename Derived>
+struct outer_stride_at_compile_time<Derived, false>
+{
+ enum { ret = 0 };
+};
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_DENSECOEFFSBASE_H
diff --git a/Eigen/src/Core/DenseStorage.h b/Eigen/src/Core/DenseStorage.h
new file mode 100644
index 0000000..5e2763e
--- /dev/null
+++ b/Eigen/src/Core/DenseStorage.h
@@ -0,0 +1,625 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2006-2009 Benoit Jacob <jacob.benoit.1@gmail.com>
+// Copyright (C) 2010-2013 Hauke Heibel <hauke.heibel@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_MATRIXSTORAGE_H
+#define EIGEN_MATRIXSTORAGE_H
+
+#ifdef EIGEN_DENSE_STORAGE_CTOR_PLUGIN
+ #define EIGEN_INTERNAL_DENSE_STORAGE_CTOR_PLUGIN(X) X; EIGEN_DENSE_STORAGE_CTOR_PLUGIN;
+#else
+ #define EIGEN_INTERNAL_DENSE_STORAGE_CTOR_PLUGIN(X)
+#endif
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+
+struct constructor_without_unaligned_array_assert {};
+
+template<typename T, int Size>
+EIGEN_DEVICE_FUNC
+void check_static_allocation_size()
+{
+ // if EIGEN_STACK_ALLOCATION_LIMIT is defined to 0, then no limit
+ #if EIGEN_STACK_ALLOCATION_LIMIT
+ EIGEN_STATIC_ASSERT(Size * sizeof(T) <= EIGEN_STACK_ALLOCATION_LIMIT, OBJECT_ALLOCATED_ON_STACK_IS_TOO_BIG);
+ #endif
+}
+
+/** \internal
+ * Static array. If the MatrixOrArrayOptions require auto-alignment, the array will be automatically aligned:
+ * to 16 bytes boundary if the total size is a multiple of 16 bytes.
+ */
+template <typename T, int Size, int MatrixOrArrayOptions,
+ int Alignment = (MatrixOrArrayOptions&DontAlign) ? 0
+ : compute_default_alignment<T,Size>::value >
+struct plain_array
+{
+ T array[Size];
+
+ EIGEN_DEVICE_FUNC
+ plain_array()
+ {
+ check_static_allocation_size<T,Size>();
+ }
+
+ EIGEN_DEVICE_FUNC
+ plain_array(constructor_without_unaligned_array_assert)
+ {
+ check_static_allocation_size<T,Size>();
+ }
+};
+
+#if defined(EIGEN_DISABLE_UNALIGNED_ARRAY_ASSERT)
+ #define EIGEN_MAKE_UNALIGNED_ARRAY_ASSERT(sizemask)
+#elif EIGEN_COMP_GNUC
+ // GCC 4.7 is too aggressive in its optimizations and remove the alignment test based on the fact the array is declared to be aligned.
+ // See this bug report: http://gcc.gnu.org/bugzilla/show_bug.cgi?id=53900
+ // Hiding the origin of the array pointer behind a function argument seems to do the trick even if the function is inlined:
+ template<typename PtrType>
+ EIGEN_ALWAYS_INLINE PtrType eigen_unaligned_array_assert_workaround_gcc47(PtrType array) { return array; }
+ #define EIGEN_MAKE_UNALIGNED_ARRAY_ASSERT(sizemask) \
+ eigen_assert((internal::is_constant_evaluated() \
+ || (internal::UIntPtr(eigen_unaligned_array_assert_workaround_gcc47(array)) & (sizemask)) == 0) \
+ && "this assertion is explained here: " \
+ "http://eigen.tuxfamily.org/dox-devel/group__TopicUnalignedArrayAssert.html" \
+ " **** READ THIS WEB PAGE !!! ****");
+#else
+ #define EIGEN_MAKE_UNALIGNED_ARRAY_ASSERT(sizemask) \
+ eigen_assert((internal::is_constant_evaluated() || (internal::UIntPtr(array) & (sizemask)) == 0) \
+ && "this assertion is explained here: " \
+ "http://eigen.tuxfamily.org/dox-devel/group__TopicUnalignedArrayAssert.html" \
+ " **** READ THIS WEB PAGE !!! ****");
+#endif
+
+template <typename T, int Size, int MatrixOrArrayOptions>
+struct plain_array<T, Size, MatrixOrArrayOptions, 8>
+{
+ EIGEN_ALIGN_TO_BOUNDARY(8) T array[Size];
+
+ EIGEN_DEVICE_FUNC
+ plain_array()
+ {
+ EIGEN_MAKE_UNALIGNED_ARRAY_ASSERT(7);
+ check_static_allocation_size<T,Size>();
+ }
+
+ EIGEN_DEVICE_FUNC
+ plain_array(constructor_without_unaligned_array_assert)
+ {
+ check_static_allocation_size<T,Size>();
+ }
+};
+
+template <typename T, int Size, int MatrixOrArrayOptions>
+struct plain_array<T, Size, MatrixOrArrayOptions, 16>
+{
+ EIGEN_ALIGN_TO_BOUNDARY(16) T array[Size];
+
+ EIGEN_DEVICE_FUNC
+ plain_array()
+ {
+ EIGEN_MAKE_UNALIGNED_ARRAY_ASSERT(15);
+ check_static_allocation_size<T,Size>();
+ }
+
+ EIGEN_DEVICE_FUNC
+ plain_array(constructor_without_unaligned_array_assert)
+ {
+ check_static_allocation_size<T,Size>();
+ }
+};
+
+template <typename T, int Size, int MatrixOrArrayOptions>
+struct plain_array<T, Size, MatrixOrArrayOptions, 32>
+{
+ EIGEN_ALIGN_TO_BOUNDARY(32) T array[Size];
+
+ EIGEN_DEVICE_FUNC
+ plain_array()
+ {
+ EIGEN_MAKE_UNALIGNED_ARRAY_ASSERT(31);
+ check_static_allocation_size<T,Size>();
+ }
+
+ EIGEN_DEVICE_FUNC
+ plain_array(constructor_without_unaligned_array_assert)
+ {
+ check_static_allocation_size<T,Size>();
+ }
+};
+
+template <typename T, int Size, int MatrixOrArrayOptions>
+struct plain_array<T, Size, MatrixOrArrayOptions, 64>
+{
+ EIGEN_ALIGN_TO_BOUNDARY(64) T array[Size];
+
+ EIGEN_DEVICE_FUNC
+ plain_array()
+ {
+ EIGEN_MAKE_UNALIGNED_ARRAY_ASSERT(63);
+ check_static_allocation_size<T,Size>();
+ }
+
+ EIGEN_DEVICE_FUNC
+ plain_array(constructor_without_unaligned_array_assert)
+ {
+ check_static_allocation_size<T,Size>();
+ }
+};
+
+template <typename T, int MatrixOrArrayOptions, int Alignment>
+struct plain_array<T, 0, MatrixOrArrayOptions, Alignment>
+{
+ T array[1];
+ EIGEN_DEVICE_FUNC plain_array() {}
+ EIGEN_DEVICE_FUNC plain_array(constructor_without_unaligned_array_assert) {}
+};
+
+struct plain_array_helper {
+ template<typename T, int Size, int MatrixOrArrayOptions, int Alignment>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ static void copy(const plain_array<T, Size, MatrixOrArrayOptions, Alignment>& src, const Eigen::Index size,
+ plain_array<T, Size, MatrixOrArrayOptions, Alignment>& dst) {
+ smart_copy(src.array, src.array + size, dst.array);
+ }
+
+ template<typename T, int Size, int MatrixOrArrayOptions, int Alignment>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ static void swap(plain_array<T, Size, MatrixOrArrayOptions, Alignment>& a, const Eigen::Index a_size,
+ plain_array<T, Size, MatrixOrArrayOptions, Alignment>& b, const Eigen::Index b_size) {
+ if (a_size < b_size) {
+ std::swap_ranges(b.array, b.array + a_size, a.array);
+ smart_move(b.array + a_size, b.array + b_size, a.array + a_size);
+ } else if (a_size > b_size) {
+ std::swap_ranges(a.array, a.array + b_size, b.array);
+ smart_move(a.array + b_size, a.array + a_size, b.array + b_size);
+ } else {
+ std::swap_ranges(a.array, a.array + a_size, b.array);
+ }
+ }
+};
+
+} // end namespace internal
+
+/** \internal
+ *
+ * \class DenseStorage
+ * \ingroup Core_Module
+ *
+ * \brief Stores the data of a matrix
+ *
+ * This class stores the data of fixed-size, dynamic-size or mixed matrices
+ * in a way as compact as possible.
+ *
+ * \sa Matrix
+ */
+template<typename T, int Size, int Rows_, int Cols_, int Options_> class DenseStorage;
+
+// purely fixed-size matrix
+template<typename T, int Size, int Rows_, int Cols_, int Options_> class DenseStorage
+{
+ internal::plain_array<T,Size,Options_> m_data;
+ public:
+ EIGEN_DEVICE_FUNC DenseStorage() {
+ EIGEN_INTERNAL_DENSE_STORAGE_CTOR_PLUGIN(Index size = Size)
+ }
+ EIGEN_DEVICE_FUNC
+ explicit DenseStorage(internal::constructor_without_unaligned_array_assert)
+ : m_data(internal::constructor_without_unaligned_array_assert()) {}
+#if defined(EIGEN_DENSE_STORAGE_CTOR_PLUGIN)
+ EIGEN_DEVICE_FUNC
+ DenseStorage(const DenseStorage& other) : m_data(other.m_data) {
+ EIGEN_INTERNAL_DENSE_STORAGE_CTOR_PLUGIN(Index size = Size)
+ }
+#else
+ EIGEN_DEVICE_FUNC DenseStorage(const DenseStorage&) = default;
+#endif
+ EIGEN_DEVICE_FUNC DenseStorage& operator=(const DenseStorage&) = default;
+ EIGEN_DEVICE_FUNC DenseStorage(DenseStorage&&) = default;
+ EIGEN_DEVICE_FUNC DenseStorage& operator=(DenseStorage&&) = default;
+ EIGEN_DEVICE_FUNC DenseStorage(Index size, Index rows, Index cols) {
+ EIGEN_INTERNAL_DENSE_STORAGE_CTOR_PLUGIN({})
+ eigen_internal_assert(size==rows*cols && rows==Rows_ && cols==Cols_);
+ EIGEN_UNUSED_VARIABLE(size);
+ EIGEN_UNUSED_VARIABLE(rows);
+ EIGEN_UNUSED_VARIABLE(cols);
+ }
+ EIGEN_DEVICE_FUNC void swap(DenseStorage& other) {
+ numext::swap(m_data, other.m_data);
+ }
+ EIGEN_DEVICE_FUNC static EIGEN_CONSTEXPR Index rows(void) EIGEN_NOEXCEPT {return Rows_;}
+ EIGEN_DEVICE_FUNC static EIGEN_CONSTEXPR Index cols(void) EIGEN_NOEXCEPT {return Cols_;}
+ EIGEN_DEVICE_FUNC void conservativeResize(Index,Index,Index) {}
+ EIGEN_DEVICE_FUNC void resize(Index,Index,Index) {}
+ EIGEN_DEVICE_FUNC const T *data() const { return m_data.array; }
+ EIGEN_DEVICE_FUNC T *data() { return m_data.array; }
+};
+
+// null matrix
+template<typename T, int Rows_, int Cols_, int Options_> class DenseStorage<T, 0, Rows_, Cols_, Options_>
+{
+ public:
+ EIGEN_DEVICE_FUNC DenseStorage() {}
+ EIGEN_DEVICE_FUNC explicit DenseStorage(internal::constructor_without_unaligned_array_assert) {}
+ EIGEN_DEVICE_FUNC DenseStorage(const DenseStorage&) {}
+ EIGEN_DEVICE_FUNC DenseStorage& operator=(const DenseStorage&) { return *this; }
+ EIGEN_DEVICE_FUNC DenseStorage(Index,Index,Index) {}
+ EIGEN_DEVICE_FUNC void swap(DenseStorage& ) {}
+ EIGEN_DEVICE_FUNC static EIGEN_CONSTEXPR Index rows(void) EIGEN_NOEXCEPT {return Rows_;}
+ EIGEN_DEVICE_FUNC static EIGEN_CONSTEXPR Index cols(void) EIGEN_NOEXCEPT {return Cols_;}
+ EIGEN_DEVICE_FUNC void conservativeResize(Index,Index,Index) {}
+ EIGEN_DEVICE_FUNC void resize(Index,Index,Index) {}
+ EIGEN_DEVICE_FUNC const T *data() const { return 0; }
+ EIGEN_DEVICE_FUNC T *data() { return 0; }
+};
+
+// more specializations for null matrices; these are necessary to resolve ambiguities
+template<typename T, int Options_> class DenseStorage<T, 0, Dynamic, Dynamic, Options_>
+: public DenseStorage<T, 0, 0, 0, Options_> { };
+
+template<typename T, int Rows_, int Options_> class DenseStorage<T, 0, Rows_, Dynamic, Options_>
+: public DenseStorage<T, 0, 0, 0, Options_> { };
+
+template<typename T, int Cols_, int Options_> class DenseStorage<T, 0, Dynamic, Cols_, Options_>
+: public DenseStorage<T, 0, 0, 0, Options_> { };
+
+// dynamic-size matrix with fixed-size storage
+template<typename T, int Size, int Options_> class DenseStorage<T, Size, Dynamic, Dynamic, Options_>
+{
+ internal::plain_array<T,Size,Options_> m_data;
+ Index m_rows;
+ Index m_cols;
+ public:
+ EIGEN_DEVICE_FUNC DenseStorage() : m_rows(0), m_cols(0) {}
+ EIGEN_DEVICE_FUNC explicit DenseStorage(internal::constructor_without_unaligned_array_assert)
+ : m_data(internal::constructor_without_unaligned_array_assert()), m_rows(0), m_cols(0) {}
+ EIGEN_DEVICE_FUNC DenseStorage(const DenseStorage& other)
+ : m_data(internal::constructor_without_unaligned_array_assert()), m_rows(other.m_rows), m_cols(other.m_cols)
+ {
+ internal::plain_array_helper::copy(other.m_data, m_rows * m_cols, m_data);
+ }
+ EIGEN_DEVICE_FUNC DenseStorage& operator=(const DenseStorage& other)
+ {
+ if (this != &other)
+ {
+ m_rows = other.m_rows;
+ m_cols = other.m_cols;
+ internal::plain_array_helper::copy(other.m_data, m_rows * m_cols, m_data);
+ }
+ return *this;
+ }
+ EIGEN_DEVICE_FUNC DenseStorage(Index, Index rows, Index cols) : m_rows(rows), m_cols(cols) {}
+ EIGEN_DEVICE_FUNC void swap(DenseStorage& other)
+ {
+ internal::plain_array_helper::swap(m_data, m_rows * m_cols, other.m_data, other.m_rows * other.m_cols);
+ numext::swap(m_rows,other.m_rows);
+ numext::swap(m_cols,other.m_cols);
+ }
+ EIGEN_DEVICE_FUNC Index rows() const {return m_rows;}
+ EIGEN_DEVICE_FUNC Index cols() const {return m_cols;}
+ EIGEN_DEVICE_FUNC void conservativeResize(Index, Index rows, Index cols) { m_rows = rows; m_cols = cols; }
+ EIGEN_DEVICE_FUNC void resize(Index, Index rows, Index cols) { m_rows = rows; m_cols = cols; }
+ EIGEN_DEVICE_FUNC const T *data() const { return m_data.array; }
+ EIGEN_DEVICE_FUNC T *data() { return m_data.array; }
+};
+
+// dynamic-size matrix with fixed-size storage and fixed width
+template<typename T, int Size, int Cols_, int Options_> class DenseStorage<T, Size, Dynamic, Cols_, Options_>
+{
+ internal::plain_array<T,Size,Options_> m_data;
+ Index m_rows;
+ public:
+ EIGEN_DEVICE_FUNC DenseStorage() : m_rows(0) {}
+ EIGEN_DEVICE_FUNC explicit DenseStorage(internal::constructor_without_unaligned_array_assert)
+ : m_data(internal::constructor_without_unaligned_array_assert()), m_rows(0) {}
+ EIGEN_DEVICE_FUNC DenseStorage(const DenseStorage& other)
+ : m_data(internal::constructor_without_unaligned_array_assert()), m_rows(other.m_rows)
+ {
+ internal::plain_array_helper::copy(other.m_data, m_rows * Cols_, m_data);
+ }
+
+ EIGEN_DEVICE_FUNC DenseStorage& operator=(const DenseStorage& other)
+ {
+ if (this != &other)
+ {
+ m_rows = other.m_rows;
+ internal::plain_array_helper::copy(other.m_data, m_rows * Cols_, m_data);
+ }
+ return *this;
+ }
+ EIGEN_DEVICE_FUNC DenseStorage(Index, Index rows, Index) : m_rows(rows) {}
+ EIGEN_DEVICE_FUNC void swap(DenseStorage& other)
+ {
+ internal::plain_array_helper::swap(m_data, m_rows * Cols_, other.m_data, other.m_rows * Cols_);
+ numext::swap(m_rows, other.m_rows);
+ }
+ EIGEN_DEVICE_FUNC Index rows(void) const EIGEN_NOEXCEPT {return m_rows;}
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR Index cols(void) const EIGEN_NOEXCEPT {return Cols_;}
+ EIGEN_DEVICE_FUNC void conservativeResize(Index, Index rows, Index) { m_rows = rows; }
+ EIGEN_DEVICE_FUNC void resize(Index, Index rows, Index) { m_rows = rows; }
+ EIGEN_DEVICE_FUNC const T *data() const { return m_data.array; }
+ EIGEN_DEVICE_FUNC T *data() { return m_data.array; }
+};
+
+// dynamic-size matrix with fixed-size storage and fixed height
+template<typename T, int Size, int Rows_, int Options_> class DenseStorage<T, Size, Rows_, Dynamic, Options_>
+{
+ internal::plain_array<T,Size,Options_> m_data;
+ Index m_cols;
+ public:
+ EIGEN_DEVICE_FUNC DenseStorage() : m_cols(0) {}
+ EIGEN_DEVICE_FUNC explicit DenseStorage(internal::constructor_without_unaligned_array_assert)
+ : m_data(internal::constructor_without_unaligned_array_assert()), m_cols(0) {}
+ EIGEN_DEVICE_FUNC DenseStorage(const DenseStorage& other)
+ : m_data(internal::constructor_without_unaligned_array_assert()), m_cols(other.m_cols)
+ {
+ internal::plain_array_helper::copy(other.m_data, Rows_ * m_cols, m_data);
+ }
+ EIGEN_DEVICE_FUNC DenseStorage& operator=(const DenseStorage& other)
+ {
+ if (this != &other)
+ {
+ m_cols = other.m_cols;
+ internal::plain_array_helper::copy(other.m_data, Rows_ * m_cols, m_data);
+ }
+ return *this;
+ }
+ EIGEN_DEVICE_FUNC DenseStorage(Index, Index, Index cols) : m_cols(cols) {}
+ EIGEN_DEVICE_FUNC void swap(DenseStorage& other) {
+ internal::plain_array_helper::swap(m_data, Rows_ * m_cols, other.m_data, Rows_ * other.m_cols);
+ numext::swap(m_cols, other.m_cols);
+ }
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR Index rows(void) const EIGEN_NOEXCEPT {return Rows_;}
+ EIGEN_DEVICE_FUNC Index cols(void) const EIGEN_NOEXCEPT {return m_cols;}
+ EIGEN_DEVICE_FUNC void conservativeResize(Index, Index, Index cols) { m_cols = cols; }
+ EIGEN_DEVICE_FUNC void resize(Index, Index, Index cols) { m_cols = cols; }
+ EIGEN_DEVICE_FUNC const T *data() const { return m_data.array; }
+ EIGEN_DEVICE_FUNC T *data() { return m_data.array; }
+};
+
+// purely dynamic matrix.
+template<typename T, int Options_> class DenseStorage<T, Dynamic, Dynamic, Dynamic, Options_>
+{
+ T *m_data;
+ Index m_rows;
+ Index m_cols;
+ public:
+ EIGEN_DEVICE_FUNC DenseStorage() : m_data(0), m_rows(0), m_cols(0) {}
+ EIGEN_DEVICE_FUNC explicit DenseStorage(internal::constructor_without_unaligned_array_assert)
+ : m_data(0), m_rows(0), m_cols(0) {}
+ EIGEN_DEVICE_FUNC DenseStorage(Index size, Index rows, Index cols)
+ : m_data(internal::conditional_aligned_new_auto<T,(Options_&DontAlign)==0>(size)), m_rows(rows), m_cols(cols)
+ {
+ EIGEN_INTERNAL_DENSE_STORAGE_CTOR_PLUGIN({})
+ eigen_internal_assert(size==rows*cols && rows>=0 && cols >=0);
+ }
+ EIGEN_DEVICE_FUNC DenseStorage(const DenseStorage& other)
+ : m_data(internal::conditional_aligned_new_auto<T,(Options_&DontAlign)==0>(other.m_rows*other.m_cols))
+ , m_rows(other.m_rows)
+ , m_cols(other.m_cols)
+ {
+ EIGEN_INTERNAL_DENSE_STORAGE_CTOR_PLUGIN(Index size = m_rows*m_cols)
+ internal::smart_copy(other.m_data, other.m_data+other.m_rows*other.m_cols, m_data);
+ }
+ EIGEN_DEVICE_FUNC DenseStorage& operator=(const DenseStorage& other)
+ {
+ if (this != &other)
+ {
+ DenseStorage tmp(other);
+ this->swap(tmp);
+ }
+ return *this;
+ }
+ EIGEN_DEVICE_FUNC
+ DenseStorage(DenseStorage&& other) EIGEN_NOEXCEPT
+ : m_data(std::move(other.m_data))
+ , m_rows(std::move(other.m_rows))
+ , m_cols(std::move(other.m_cols))
+ {
+ other.m_data = nullptr;
+ other.m_rows = 0;
+ other.m_cols = 0;
+ }
+ EIGEN_DEVICE_FUNC
+ DenseStorage& operator=(DenseStorage&& other) EIGEN_NOEXCEPT
+ {
+ numext::swap(m_data, other.m_data);
+ numext::swap(m_rows, other.m_rows);
+ numext::swap(m_cols, other.m_cols);
+ return *this;
+ }
+ EIGEN_DEVICE_FUNC ~DenseStorage() { internal::conditional_aligned_delete_auto<T,(Options_&DontAlign)==0>(m_data, m_rows*m_cols); }
+ EIGEN_DEVICE_FUNC void swap(DenseStorage& other)
+ {
+ numext::swap(m_data,other.m_data);
+ numext::swap(m_rows,other.m_rows);
+ numext::swap(m_cols,other.m_cols);
+ }
+ EIGEN_DEVICE_FUNC Index rows(void) const EIGEN_NOEXCEPT {return m_rows;}
+ EIGEN_DEVICE_FUNC Index cols(void) const EIGEN_NOEXCEPT {return m_cols;}
+ void conservativeResize(Index size, Index rows, Index cols)
+ {
+ m_data = internal::conditional_aligned_realloc_new_auto<T,(Options_&DontAlign)==0>(m_data, size, m_rows*m_cols);
+ m_rows = rows;
+ m_cols = cols;
+ }
+ EIGEN_DEVICE_FUNC void resize(Index size, Index rows, Index cols)
+ {
+ if(size != m_rows*m_cols)
+ {
+ internal::conditional_aligned_delete_auto<T,(Options_&DontAlign)==0>(m_data, m_rows*m_cols);
+ if (size>0) // >0 and not simply !=0 to let the compiler knows that size cannot be negative
+ m_data = internal::conditional_aligned_new_auto<T,(Options_&DontAlign)==0>(size);
+ else
+ m_data = 0;
+ EIGEN_INTERNAL_DENSE_STORAGE_CTOR_PLUGIN({})
+ }
+ m_rows = rows;
+ m_cols = cols;
+ }
+ EIGEN_DEVICE_FUNC const T *data() const { return m_data; }
+ EIGEN_DEVICE_FUNC T *data() { return m_data; }
+};
+
+// matrix with dynamic width and fixed height (so that matrix has dynamic size).
+template<typename T, int Rows_, int Options_> class DenseStorage<T, Dynamic, Rows_, Dynamic, Options_>
+{
+ T *m_data;
+ Index m_cols;
+ public:
+ EIGEN_DEVICE_FUNC DenseStorage() : m_data(0), m_cols(0) {}
+ explicit DenseStorage(internal::constructor_without_unaligned_array_assert) : m_data(0), m_cols(0) {}
+ EIGEN_DEVICE_FUNC DenseStorage(Index size, Index rows, Index cols) : m_data(internal::conditional_aligned_new_auto<T,(Options_&DontAlign)==0>(size)), m_cols(cols)
+ {
+ EIGEN_INTERNAL_DENSE_STORAGE_CTOR_PLUGIN({})
+ eigen_internal_assert(size==rows*cols && rows==Rows_ && cols >=0);
+ EIGEN_UNUSED_VARIABLE(rows);
+ }
+ EIGEN_DEVICE_FUNC DenseStorage(const DenseStorage& other)
+ : m_data(internal::conditional_aligned_new_auto<T,(Options_&DontAlign)==0>(Rows_*other.m_cols))
+ , m_cols(other.m_cols)
+ {
+ EIGEN_INTERNAL_DENSE_STORAGE_CTOR_PLUGIN(Index size = m_cols*Rows_)
+ internal::smart_copy(other.m_data, other.m_data+Rows_*m_cols, m_data);
+ }
+ EIGEN_DEVICE_FUNC DenseStorage& operator=(const DenseStorage& other)
+ {
+ if (this != &other)
+ {
+ DenseStorage tmp(other);
+ this->swap(tmp);
+ }
+ return *this;
+ }
+ EIGEN_DEVICE_FUNC
+ DenseStorage(DenseStorage&& other) EIGEN_NOEXCEPT
+ : m_data(std::move(other.m_data))
+ , m_cols(std::move(other.m_cols))
+ {
+ other.m_data = nullptr;
+ other.m_cols = 0;
+ }
+ EIGEN_DEVICE_FUNC
+ DenseStorage& operator=(DenseStorage&& other) EIGEN_NOEXCEPT
+ {
+ numext::swap(m_data, other.m_data);
+ numext::swap(m_cols, other.m_cols);
+ return *this;
+ }
+ EIGEN_DEVICE_FUNC ~DenseStorage() { internal::conditional_aligned_delete_auto<T,(Options_&DontAlign)==0>(m_data, Rows_*m_cols); }
+ EIGEN_DEVICE_FUNC void swap(DenseStorage& other) {
+ numext::swap(m_data,other.m_data);
+ numext::swap(m_cols,other.m_cols);
+ }
+ EIGEN_DEVICE_FUNC static EIGEN_CONSTEXPR Index rows(void) EIGEN_NOEXCEPT {return Rows_;}
+ EIGEN_DEVICE_FUNC Index cols(void) const EIGEN_NOEXCEPT {return m_cols;}
+ EIGEN_DEVICE_FUNC void conservativeResize(Index size, Index, Index cols)
+ {
+ m_data = internal::conditional_aligned_realloc_new_auto<T,(Options_&DontAlign)==0>(m_data, size, Rows_*m_cols);
+ m_cols = cols;
+ }
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void resize(Index size, Index, Index cols)
+ {
+ if(size != Rows_*m_cols)
+ {
+ internal::conditional_aligned_delete_auto<T,(Options_&DontAlign)==0>(m_data, Rows_*m_cols);
+ if (size>0) // >0 and not simply !=0 to let the compiler knows that size cannot be negative
+ m_data = internal::conditional_aligned_new_auto<T,(Options_&DontAlign)==0>(size);
+ else
+ m_data = 0;
+ EIGEN_INTERNAL_DENSE_STORAGE_CTOR_PLUGIN({})
+ }
+ m_cols = cols;
+ }
+ EIGEN_DEVICE_FUNC const T *data() const { return m_data; }
+ EIGEN_DEVICE_FUNC T *data() { return m_data; }
+};
+
+// matrix with dynamic height and fixed width (so that matrix has dynamic size).
+template<typename T, int Cols_, int Options_> class DenseStorage<T, Dynamic, Dynamic, Cols_, Options_>
+{
+ T *m_data;
+ Index m_rows;
+ public:
+ EIGEN_DEVICE_FUNC DenseStorage() : m_data(0), m_rows(0) {}
+ explicit DenseStorage(internal::constructor_without_unaligned_array_assert) : m_data(0), m_rows(0) {}
+ EIGEN_DEVICE_FUNC DenseStorage(Index size, Index rows, Index cols) : m_data(internal::conditional_aligned_new_auto<T,(Options_&DontAlign)==0>(size)), m_rows(rows)
+ {
+ EIGEN_INTERNAL_DENSE_STORAGE_CTOR_PLUGIN({})
+ eigen_internal_assert(size==rows*cols && rows>=0 && cols == Cols_);
+ EIGEN_UNUSED_VARIABLE(cols);
+ }
+ EIGEN_DEVICE_FUNC DenseStorage(const DenseStorage& other)
+ : m_data(internal::conditional_aligned_new_auto<T,(Options_&DontAlign)==0>(other.m_rows*Cols_))
+ , m_rows(other.m_rows)
+ {
+ EIGEN_INTERNAL_DENSE_STORAGE_CTOR_PLUGIN(Index size = m_rows*Cols_)
+ internal::smart_copy(other.m_data, other.m_data+other.m_rows*Cols_, m_data);
+ }
+ EIGEN_DEVICE_FUNC DenseStorage& operator=(const DenseStorage& other)
+ {
+ if (this != &other)
+ {
+ DenseStorage tmp(other);
+ this->swap(tmp);
+ }
+ return *this;
+ }
+ EIGEN_DEVICE_FUNC
+ DenseStorage(DenseStorage&& other) EIGEN_NOEXCEPT
+ : m_data(std::move(other.m_data))
+ , m_rows(std::move(other.m_rows))
+ {
+ other.m_data = nullptr;
+ other.m_rows = 0;
+ }
+ EIGEN_DEVICE_FUNC
+ DenseStorage& operator=(DenseStorage&& other) EIGEN_NOEXCEPT
+ {
+ numext::swap(m_data, other.m_data);
+ numext::swap(m_rows, other.m_rows);
+ return *this;
+ }
+ EIGEN_DEVICE_FUNC ~DenseStorage() { internal::conditional_aligned_delete_auto<T,(Options_&DontAlign)==0>(m_data, Cols_*m_rows); }
+ EIGEN_DEVICE_FUNC void swap(DenseStorage& other) {
+ numext::swap(m_data,other.m_data);
+ numext::swap(m_rows,other.m_rows);
+ }
+ EIGEN_DEVICE_FUNC Index rows(void) const EIGEN_NOEXCEPT {return m_rows;}
+ EIGEN_DEVICE_FUNC static EIGEN_CONSTEXPR Index cols(void) {return Cols_;}
+ void conservativeResize(Index size, Index rows, Index)
+ {
+ m_data = internal::conditional_aligned_realloc_new_auto<T,(Options_&DontAlign)==0>(m_data, size, m_rows*Cols_);
+ m_rows = rows;
+ }
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void resize(Index size, Index rows, Index)
+ {
+ if(size != m_rows*Cols_)
+ {
+ internal::conditional_aligned_delete_auto<T,(Options_&DontAlign)==0>(m_data, Cols_*m_rows);
+ if (size>0) // >0 and not simply !=0 to let the compiler knows that size cannot be negative
+ m_data = internal::conditional_aligned_new_auto<T,(Options_&DontAlign)==0>(size);
+ else
+ m_data = 0;
+ EIGEN_INTERNAL_DENSE_STORAGE_CTOR_PLUGIN({})
+ }
+ m_rows = rows;
+ }
+ EIGEN_DEVICE_FUNC const T *data() const { return m_data; }
+ EIGEN_DEVICE_FUNC T *data() { return m_data; }
+};
+
+} // end namespace Eigen
+
+#endif // EIGEN_MATRIX_H
diff --git a/Eigen/src/Core/Diagonal.h b/Eigen/src/Core/Diagonal.h
new file mode 100644
index 0000000..4af17dd
--- /dev/null
+++ b/Eigen/src/Core/Diagonal.h
@@ -0,0 +1,261 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2007-2009 Benoit Jacob <jacob.benoit.1@gmail.com>
+// Copyright (C) 2009-2010 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_DIAGONAL_H
+#define EIGEN_DIAGONAL_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+/** \class Diagonal
+ * \ingroup Core_Module
+ *
+ * \brief Expression of a diagonal/subdiagonal/superdiagonal in a matrix
+ *
+ * \tparam MatrixType the type of the object in which we are taking a sub/main/super diagonal
+ * \tparam DiagIndex the index of the sub/super diagonal. The default is 0 and it means the main diagonal.
+ * A positive value means a superdiagonal, a negative value means a subdiagonal.
+ * You can also use DynamicIndex so the index can be set at runtime.
+ *
+ * The matrix is not required to be square.
+ *
+ * This class represents an expression of the main diagonal, or any sub/super diagonal
+ * of a square matrix. It is the return type of MatrixBase::diagonal() and MatrixBase::diagonal(Index) and most of the
+ * time this is the only way it is used.
+ *
+ * \sa MatrixBase::diagonal(), MatrixBase::diagonal(Index)
+ */
+
+namespace internal {
+template<typename MatrixType, int DiagIndex>
+struct traits<Diagonal<MatrixType,DiagIndex> >
+ : traits<MatrixType>
+{
+ typedef typename ref_selector<MatrixType>::type MatrixTypeNested;
+ typedef std::remove_reference_t<MatrixTypeNested> MatrixTypeNested_;
+ typedef typename MatrixType::StorageKind StorageKind;
+ enum {
+ RowsAtCompileTime = (int(DiagIndex) == DynamicIndex || int(MatrixType::SizeAtCompileTime) == Dynamic) ? Dynamic
+ : (plain_enum_min(MatrixType::RowsAtCompileTime - plain_enum_max(-DiagIndex, 0),
+ MatrixType::ColsAtCompileTime - plain_enum_max( DiagIndex, 0))),
+ ColsAtCompileTime = 1,
+ MaxRowsAtCompileTime = int(MatrixType::MaxSizeAtCompileTime) == Dynamic ? Dynamic
+ : DiagIndex == DynamicIndex ? min_size_prefer_fixed(MatrixType::MaxRowsAtCompileTime,
+ MatrixType::MaxColsAtCompileTime)
+ : (plain_enum_min(MatrixType::MaxRowsAtCompileTime - plain_enum_max(-DiagIndex, 0),
+ MatrixType::MaxColsAtCompileTime - plain_enum_max( DiagIndex, 0))),
+ MaxColsAtCompileTime = 1,
+ MaskLvalueBit = is_lvalue<MatrixType>::value ? LvalueBit : 0,
+ Flags = (unsigned int)MatrixTypeNested_::Flags & (RowMajorBit | MaskLvalueBit | DirectAccessBit) & ~RowMajorBit, // FIXME DirectAccessBit should not be handled by expressions
+ MatrixTypeOuterStride = outer_stride_at_compile_time<MatrixType>::ret,
+ InnerStrideAtCompileTime = MatrixTypeOuterStride == Dynamic ? Dynamic : MatrixTypeOuterStride+1,
+ OuterStrideAtCompileTime = 0
+ };
+};
+}
+
+template<typename MatrixType, int DiagIndex_> class Diagonal
+ : public internal::dense_xpr_base< Diagonal<MatrixType,DiagIndex_> >::type
+{
+ public:
+
+ enum { DiagIndex = DiagIndex_ };
+ typedef typename internal::dense_xpr_base<Diagonal>::type Base;
+ EIGEN_DENSE_PUBLIC_INTERFACE(Diagonal)
+
+ EIGEN_DEVICE_FUNC
+ explicit inline Diagonal(MatrixType& matrix, Index a_index = DiagIndex) : m_matrix(matrix), m_index(a_index)
+ {
+ eigen_assert( a_index <= m_matrix.cols() && -a_index <= m_matrix.rows() );
+ }
+
+ EIGEN_INHERIT_ASSIGNMENT_OPERATORS(Diagonal)
+
+ EIGEN_DEVICE_FUNC
+ inline Index rows() const
+ {
+ return m_index.value()<0 ? numext::mini<Index>(m_matrix.cols(),m_matrix.rows()+m_index.value())
+ : numext::mini<Index>(m_matrix.rows(),m_matrix.cols()-m_index.value());
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
+ inline Index cols() const EIGEN_NOEXCEPT { return 1; }
+
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
+ inline Index innerStride() const EIGEN_NOEXCEPT {
+ return m_matrix.outerStride() + 1;
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
+ inline Index outerStride() const EIGEN_NOEXCEPT { return 0; }
+
+ typedef std::conditional_t<
+ internal::is_lvalue<MatrixType>::value,
+ Scalar,
+ const Scalar
+ > ScalarWithConstIfNotLvalue;
+
+ EIGEN_DEVICE_FUNC
+ inline ScalarWithConstIfNotLvalue* data() { return &(m_matrix.coeffRef(rowOffset(), colOffset())); }
+ EIGEN_DEVICE_FUNC
+ inline const Scalar* data() const { return &(m_matrix.coeffRef(rowOffset(), colOffset())); }
+
+ EIGEN_DEVICE_FUNC
+ inline Scalar& coeffRef(Index row, Index)
+ {
+ EIGEN_STATIC_ASSERT_LVALUE(MatrixType)
+ return m_matrix.coeffRef(row+rowOffset(), row+colOffset());
+ }
+
+ EIGEN_DEVICE_FUNC
+ inline const Scalar& coeffRef(Index row, Index) const
+ {
+ return m_matrix.coeffRef(row+rowOffset(), row+colOffset());
+ }
+
+ EIGEN_DEVICE_FUNC
+ inline CoeffReturnType coeff(Index row, Index) const
+ {
+ return m_matrix.coeff(row+rowOffset(), row+colOffset());
+ }
+
+ EIGEN_DEVICE_FUNC
+ inline Scalar& coeffRef(Index idx)
+ {
+ EIGEN_STATIC_ASSERT_LVALUE(MatrixType)
+ return m_matrix.coeffRef(idx+rowOffset(), idx+colOffset());
+ }
+
+ EIGEN_DEVICE_FUNC
+ inline const Scalar& coeffRef(Index idx) const
+ {
+ return m_matrix.coeffRef(idx+rowOffset(), idx+colOffset());
+ }
+
+ EIGEN_DEVICE_FUNC
+ inline CoeffReturnType coeff(Index idx) const
+ {
+ return m_matrix.coeff(idx+rowOffset(), idx+colOffset());
+ }
+
+ EIGEN_DEVICE_FUNC
+ inline const internal::remove_all_t<typename MatrixType::Nested>&
+ nestedExpression() const
+ {
+ return m_matrix;
+ }
+
+ EIGEN_DEVICE_FUNC
+ inline Index index() const
+ {
+ return m_index.value();
+ }
+
+ protected:
+ typename internal::ref_selector<MatrixType>::non_const_type m_matrix;
+ const internal::variable_if_dynamicindex<Index, DiagIndex> m_index;
+
+ private:
+ // some compilers may fail to optimize std::max etc in case of compile-time constants...
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE EIGEN_CONSTEXPR
+ Index absDiagIndex() const EIGEN_NOEXCEPT { return m_index.value()>0 ? m_index.value() : -m_index.value(); }
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE EIGEN_CONSTEXPR
+ Index rowOffset() const EIGEN_NOEXCEPT { return m_index.value()>0 ? 0 : -m_index.value(); }
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE EIGEN_CONSTEXPR
+ Index colOffset() const EIGEN_NOEXCEPT { return m_index.value()>0 ? m_index.value() : 0; }
+ // trigger a compile-time error if someone try to call packet
+ template<int LoadMode> typename MatrixType::PacketReturnType packet(Index) const;
+ template<int LoadMode> typename MatrixType::PacketReturnType packet(Index,Index) const;
+};
+
+/** \returns an expression of the main diagonal of the matrix \c *this
+ *
+ * \c *this is not required to be square.
+ *
+ * Example: \include MatrixBase_diagonal.cpp
+ * Output: \verbinclude MatrixBase_diagonal.out
+ *
+ * \sa class Diagonal */
+template<typename Derived>
+EIGEN_DEVICE_FUNC inline typename MatrixBase<Derived>::DiagonalReturnType
+MatrixBase<Derived>::diagonal()
+{
+ return DiagonalReturnType(derived());
+}
+
+/** This is the const version of diagonal(). */
+template<typename Derived>
+EIGEN_DEVICE_FUNC inline
+const typename MatrixBase<Derived>::ConstDiagonalReturnType
+MatrixBase<Derived>::diagonal() const
+{
+ return ConstDiagonalReturnType(derived());
+}
+
+/** \returns an expression of the \a DiagIndex-th sub or super diagonal of the matrix \c *this
+ *
+ * \c *this is not required to be square.
+ *
+ * The template parameter \a DiagIndex represent a super diagonal if \a DiagIndex > 0
+ * and a sub diagonal otherwise. \a DiagIndex == 0 is equivalent to the main diagonal.
+ *
+ * Example: \include MatrixBase_diagonal_int.cpp
+ * Output: \verbinclude MatrixBase_diagonal_int.out
+ *
+ * \sa MatrixBase::diagonal(), class Diagonal */
+template<typename Derived>
+EIGEN_DEVICE_FUNC inline Diagonal<Derived, DynamicIndex>
+MatrixBase<Derived>::diagonal(Index index)
+{
+ return Diagonal<Derived, DynamicIndex>(derived(), index);
+}
+
+/** This is the const version of diagonal(Index). */
+template<typename Derived>
+EIGEN_DEVICE_FUNC inline const Diagonal<const Derived, DynamicIndex>
+MatrixBase<Derived>::diagonal(Index index) const
+{
+ return Diagonal<const Derived, DynamicIndex>(derived(), index);
+}
+
+/** \returns an expression of the \a DiagIndex-th sub or super diagonal of the matrix \c *this
+ *
+ * \c *this is not required to be square.
+ *
+ * The template parameter \a DiagIndex represent a super diagonal if \a DiagIndex > 0
+ * and a sub diagonal otherwise. \a DiagIndex == 0 is equivalent to the main diagonal.
+ *
+ * Example: \include MatrixBase_diagonal_template_int.cpp
+ * Output: \verbinclude MatrixBase_diagonal_template_int.out
+ *
+ * \sa MatrixBase::diagonal(), class Diagonal */
+template<typename Derived>
+template<int Index_>
+EIGEN_DEVICE_FUNC
+inline Diagonal<Derived, Index_>
+MatrixBase<Derived>::diagonal()
+{
+ return Diagonal<Derived, Index_>(derived());
+}
+
+/** This is the const version of diagonal<int>(). */
+template<typename Derived>
+template<int Index_>
+EIGEN_DEVICE_FUNC
+inline const Diagonal<const Derived, Index_>
+MatrixBase<Derived>::diagonal() const
+{
+ return Diagonal<const Derived, Index_>(derived());
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_DIAGONAL_H
diff --git a/Eigen/src/Core/DiagonalMatrix.h b/Eigen/src/Core/DiagonalMatrix.h
new file mode 100644
index 0000000..405cc71
--- /dev/null
+++ b/Eigen/src/Core/DiagonalMatrix.h
@@ -0,0 +1,443 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2007-2009 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_DIAGONALMATRIX_H
+#define EIGEN_DIAGONALMATRIX_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+/** \class DiagonalBase
+ * \ingroup Core_Module
+ *
+ * \brief Base class for diagonal matrices and expressions
+ *
+ * This is the base class that is inherited by diagonal matrix and related expression
+ * types, which internally use a vector for storing the diagonal entries. Diagonal
+ * types always represent square matrices.
+ *
+ * \tparam Derived is the derived type, a DiagonalMatrix or DiagonalWrapper.
+ *
+ * \sa class DiagonalMatrix, class DiagonalWrapper
+ */
+template<typename Derived>
+class DiagonalBase : public EigenBase<Derived>
+{
+ public:
+ typedef typename internal::traits<Derived>::DiagonalVectorType DiagonalVectorType;
+ typedef typename DiagonalVectorType::Scalar Scalar;
+ typedef typename DiagonalVectorType::RealScalar RealScalar;
+ typedef typename internal::traits<Derived>::StorageKind StorageKind;
+ typedef typename internal::traits<Derived>::StorageIndex StorageIndex;
+
+ enum {
+ RowsAtCompileTime = DiagonalVectorType::SizeAtCompileTime,
+ ColsAtCompileTime = DiagonalVectorType::SizeAtCompileTime,
+ MaxRowsAtCompileTime = DiagonalVectorType::MaxSizeAtCompileTime,
+ MaxColsAtCompileTime = DiagonalVectorType::MaxSizeAtCompileTime,
+ IsVectorAtCompileTime = 0,
+ Flags = NoPreferredStorageOrderBit
+ };
+
+ typedef Matrix<Scalar, RowsAtCompileTime, ColsAtCompileTime, 0, MaxRowsAtCompileTime, MaxColsAtCompileTime> DenseMatrixType;
+ typedef DenseMatrixType DenseType;
+ typedef DiagonalMatrix<Scalar,DiagonalVectorType::SizeAtCompileTime,DiagonalVectorType::MaxSizeAtCompileTime> PlainObject;
+
+ /** \returns a reference to the derived object. */
+ EIGEN_DEVICE_FUNC
+ inline const Derived& derived() const { return *static_cast<const Derived*>(this); }
+ /** \returns a const reference to the derived object. */
+ EIGEN_DEVICE_FUNC
+ inline Derived& derived() { return *static_cast<Derived*>(this); }
+
+ /**
+ * Constructs a dense matrix from \c *this. Note, this directly returns a dense matrix type,
+ * not an expression.
+ * \returns A dense matrix, with its diagonal entries set from the the derived object. */
+ EIGEN_DEVICE_FUNC
+ DenseMatrixType toDenseMatrix() const { return derived(); }
+
+ /** \returns a reference to the derived object's vector of diagonal coefficients. */
+ EIGEN_DEVICE_FUNC
+ inline const DiagonalVectorType& diagonal() const { return derived().diagonal(); }
+ /** \returns a const reference to the derived object's vector of diagonal coefficients. */
+ EIGEN_DEVICE_FUNC
+ inline DiagonalVectorType& diagonal() { return derived().diagonal(); }
+
+ /** \returns the number of rows. */
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
+ inline Index rows() const { return diagonal().size(); }
+ /** \returns the number of columns. */
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
+ inline Index cols() const { return diagonal().size(); }
+
+ /** \returns the diagonal matrix product of \c *this by the dense matrix, \a matrix */
+ template<typename MatrixDerived>
+ EIGEN_DEVICE_FUNC
+ const Product<Derived,MatrixDerived,LazyProduct>
+ operator*(const MatrixBase<MatrixDerived> &matrix) const
+ {
+ return Product<Derived, MatrixDerived, LazyProduct>(derived(),matrix.derived());
+ }
+
+ template <typename OtherDerived>
+ using DiagonalProductReturnType = DiagonalWrapper<const EIGEN_CWISE_BINARY_RETURN_TYPE(
+ DiagonalVectorType, typename OtherDerived::DiagonalVectorType, product)>;
+
+ /** \returns the diagonal matrix product of \c *this by the diagonal matrix \a other */
+ template <typename OtherDerived>
+ EIGEN_DEVICE_FUNC const DiagonalProductReturnType<OtherDerived> operator*(
+ const DiagonalBase<OtherDerived>& other) const {
+ return diagonal().cwiseProduct(other.diagonal()).asDiagonal();
+ }
+
+ using DiagonalInverseReturnType =
+ DiagonalWrapper<const CwiseUnaryOp<internal::scalar_inverse_op<Scalar>, const DiagonalVectorType>>;
+
+ /** \returns the inverse \c *this. Computed as the coefficient-wise inverse of the diagonal. */
+ EIGEN_DEVICE_FUNC
+ inline const DiagonalInverseReturnType inverse() const { return diagonal().cwiseInverse().asDiagonal(); }
+
+ using DiagonalScaleReturnType =
+ DiagonalWrapper<const EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(DiagonalVectorType, Scalar, product)>;
+
+ /** \returns the product of \c *this by the scalar \a scalar */
+ EIGEN_DEVICE_FUNC
+ inline const DiagonalScaleReturnType operator*(const Scalar& scalar) const {
+ return (diagonal() * scalar).asDiagonal();
+ }
+
+ using ScaleDiagonalReturnType =
+ DiagonalWrapper<const EIGEN_SCALAR_BINARYOP_EXPR_RETURN_TYPE(Scalar, DiagonalVectorType, product)>;
+
+ /** \returns the product of a scalar and the diagonal matrix \a other */
+ EIGEN_DEVICE_FUNC
+ friend inline const ScaleDiagonalReturnType operator*(const Scalar& scalar, const DiagonalBase& other) {
+ return (scalar * other.diagonal()).asDiagonal();
+ }
+
+ template <typename OtherDerived>
+ using DiagonalSumReturnType = DiagonalWrapper<const EIGEN_CWISE_BINARY_RETURN_TYPE(
+ DiagonalVectorType, typename OtherDerived::DiagonalVectorType, sum)>;
+
+ /** \returns the sum of \c *this and the diagonal matrix \a other */
+ template <typename OtherDerived>
+ EIGEN_DEVICE_FUNC inline const DiagonalSumReturnType<OtherDerived> operator+(
+ const DiagonalBase<OtherDerived>& other) const {
+ return (diagonal() + other.diagonal()).asDiagonal();
+ }
+
+ template <typename OtherDerived>
+ using DiagonalDifferenceReturnType = DiagonalWrapper<const EIGEN_CWISE_BINARY_RETURN_TYPE(
+ DiagonalVectorType, typename OtherDerived::DiagonalVectorType, difference)>;
+
+ /** \returns the difference of \c *this and the diagonal matrix \a other */
+ template <typename OtherDerived>
+ EIGEN_DEVICE_FUNC inline const DiagonalDifferenceReturnType<OtherDerived> operator-(
+ const DiagonalBase<OtherDerived>& other) const {
+ return (diagonal() - other.diagonal()).asDiagonal();
+ }
+};
+
+/** \class DiagonalMatrix
+ * \ingroup Core_Module
+ *
+ * \brief Represents a diagonal matrix with its storage
+ *
+ * \tparam Scalar_ the type of coefficients
+ * \tparam SizeAtCompileTime the dimension of the matrix, or Dynamic
+ * \tparam MaxSizeAtCompileTime the dimension of the matrix, or Dynamic. This parameter is optional and defaults
+ * to SizeAtCompileTime. Most of the time, you do not need to specify it.
+ *
+ * \sa class DiagonalBase, class DiagonalWrapper
+ */
+
+namespace internal {
+template<typename Scalar_, int SizeAtCompileTime, int MaxSizeAtCompileTime>
+struct traits<DiagonalMatrix<Scalar_,SizeAtCompileTime,MaxSizeAtCompileTime> >
+ : traits<Matrix<Scalar_,SizeAtCompileTime,SizeAtCompileTime,0,MaxSizeAtCompileTime,MaxSizeAtCompileTime> >
+{
+ typedef Matrix<Scalar_,SizeAtCompileTime,1,0,MaxSizeAtCompileTime,1> DiagonalVectorType;
+ typedef DiagonalShape StorageKind;
+ enum {
+ Flags = LvalueBit | NoPreferredStorageOrderBit | NestByRefBit
+ };
+};
+}
+template<typename Scalar_, int SizeAtCompileTime, int MaxSizeAtCompileTime>
+class DiagonalMatrix
+ : public DiagonalBase<DiagonalMatrix<Scalar_,SizeAtCompileTime,MaxSizeAtCompileTime> >
+{
+ public:
+ #ifndef EIGEN_PARSED_BY_DOXYGEN
+ typedef typename internal::traits<DiagonalMatrix>::DiagonalVectorType DiagonalVectorType;
+ typedef const DiagonalMatrix& Nested;
+ typedef Scalar_ Scalar;
+ typedef typename internal::traits<DiagonalMatrix>::StorageKind StorageKind;
+ typedef typename internal::traits<DiagonalMatrix>::StorageIndex StorageIndex;
+ #endif
+
+ protected:
+
+ DiagonalVectorType m_diagonal;
+
+ public:
+
+ /** const version of diagonal(). */
+ EIGEN_DEVICE_FUNC
+ inline const DiagonalVectorType& diagonal() const { return m_diagonal; }
+ /** \returns a reference to the stored vector of diagonal coefficients. */
+ EIGEN_DEVICE_FUNC
+ inline DiagonalVectorType& diagonal() { return m_diagonal; }
+
+ /** Default constructor without initialization */
+ EIGEN_DEVICE_FUNC
+ inline DiagonalMatrix() {}
+
+ /** Constructs a diagonal matrix with given dimension */
+ EIGEN_DEVICE_FUNC
+ explicit inline DiagonalMatrix(Index dim) : m_diagonal(dim) {}
+
+ /** 2D constructor. */
+ EIGEN_DEVICE_FUNC
+ inline DiagonalMatrix(const Scalar& x, const Scalar& y) : m_diagonal(x,y) {}
+
+ /** 3D constructor. */
+ EIGEN_DEVICE_FUNC
+ inline DiagonalMatrix(const Scalar& x, const Scalar& y, const Scalar& z) : m_diagonal(x,y,z) {}
+
+ /** \brief Construct a diagonal matrix with fixed size from an arbitrary number of coefficients.
+ *
+ * \warning To construct a diagonal matrix of fixed size, the number of values passed to this
+ * constructor must match the fixed dimension of \c *this.
+ *
+ * \sa DiagonalMatrix(const Scalar&, const Scalar&)
+ * \sa DiagonalMatrix(const Scalar&, const Scalar&, const Scalar&)
+ */
+ template <typename... ArgTypes>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ DiagonalMatrix(const Scalar& a0, const Scalar& a1, const Scalar& a2, const ArgTypes&... args)
+ : m_diagonal(a0, a1, a2, args...) {}
+
+ /** \brief Constructs a DiagonalMatrix and initializes it by elements given by an initializer list of initializer
+ * lists \cpp11
+ */
+ EIGEN_DEVICE_FUNC
+ explicit EIGEN_STRONG_INLINE DiagonalMatrix(const std::initializer_list<std::initializer_list<Scalar>>& list)
+ : m_diagonal(list) {}
+
+ /** \brief Constructs a DiagonalMatrix from an r-value diagonal vector type */
+ EIGEN_DEVICE_FUNC
+ explicit inline DiagonalMatrix(DiagonalVectorType&& diag) : m_diagonal(std::move(diag)) {}
+
+ /** Copy constructor. */
+ template<typename OtherDerived>
+ EIGEN_DEVICE_FUNC
+ inline DiagonalMatrix(const DiagonalBase<OtherDerived>& other) : m_diagonal(other.diagonal()) {}
+
+ #ifndef EIGEN_PARSED_BY_DOXYGEN
+ /** copy constructor. prevent a default copy constructor from hiding the other templated constructor */
+ inline DiagonalMatrix(const DiagonalMatrix& other) : m_diagonal(other.diagonal()) {}
+ #endif
+
+ /** generic constructor from expression of the diagonal coefficients */
+ template<typename OtherDerived>
+ EIGEN_DEVICE_FUNC
+ explicit inline DiagonalMatrix(const MatrixBase<OtherDerived>& other) : m_diagonal(other)
+ {}
+
+ /** Copy operator. */
+ template<typename OtherDerived>
+ EIGEN_DEVICE_FUNC
+ DiagonalMatrix& operator=(const DiagonalBase<OtherDerived>& other)
+ {
+ m_diagonal = other.diagonal();
+ return *this;
+ }
+
+ #ifndef EIGEN_PARSED_BY_DOXYGEN
+ /** This is a special case of the templated operator=. Its purpose is to
+ * prevent a default operator= from hiding the templated operator=.
+ */
+ EIGEN_DEVICE_FUNC
+ DiagonalMatrix& operator=(const DiagonalMatrix& other)
+ {
+ m_diagonal = other.diagonal();
+ return *this;
+ }
+ #endif
+
+ typedef DiagonalWrapper<const CwiseNullaryOp<internal::scalar_constant_op<Scalar>, DiagonalVectorType>>
+ InitializeReturnType;
+
+ /** Initializes a diagonal matrix of size SizeAtCompileTime with coefficients set to zero */
+ EIGEN_DEVICE_FUNC
+ static const InitializeReturnType Zero() { return DiagonalVectorType::Zero().asDiagonal(); }
+ /** Initializes a diagonal matrix of size dim with coefficients set to zero */
+ EIGEN_DEVICE_FUNC
+ static const InitializeReturnType Zero(Index size) { return DiagonalVectorType::Zero(size).asDiagonal(); }
+ /** Initializes a identity matrix of size SizeAtCompileTime */
+ EIGEN_DEVICE_FUNC
+ static const InitializeReturnType Identity() { return DiagonalVectorType::Ones().asDiagonal(); }
+ /** Initializes a identity matrix of size dim */
+ EIGEN_DEVICE_FUNC
+ static const InitializeReturnType Identity(Index size) { return DiagonalVectorType::Ones(size).asDiagonal(); }
+
+ /** Resizes to given size. */
+ EIGEN_DEVICE_FUNC
+ inline void resize(Index size) { m_diagonal.resize(size); }
+ /** Sets all coefficients to zero. */
+ EIGEN_DEVICE_FUNC
+ inline void setZero() { m_diagonal.setZero(); }
+ /** Resizes and sets all coefficients to zero. */
+ EIGEN_DEVICE_FUNC
+ inline void setZero(Index size) { m_diagonal.setZero(size); }
+ /** Sets this matrix to be the identity matrix of the current size. */
+ EIGEN_DEVICE_FUNC
+ inline void setIdentity() { m_diagonal.setOnes(); }
+ /** Sets this matrix to be the identity matrix of the given size. */
+ EIGEN_DEVICE_FUNC
+ inline void setIdentity(Index size) { m_diagonal.setOnes(size); }
+};
+
+/** \class DiagonalWrapper
+ * \ingroup Core_Module
+ *
+ * \brief Expression of a diagonal matrix
+ *
+ * \tparam DiagonalVectorType_ the type of the vector of diagonal coefficients
+ *
+ * This class is an expression of a diagonal matrix, but not storing its own vector of diagonal coefficients,
+ * instead wrapping an existing vector expression. It is the return type of MatrixBase::asDiagonal()
+ * and most of the time this is the only way that it is used.
+ *
+ * \sa class DiagonalMatrix, class DiagonalBase, MatrixBase::asDiagonal()
+ */
+
+namespace internal {
+template<typename DiagonalVectorType_>
+struct traits<DiagonalWrapper<DiagonalVectorType_> >
+{
+ typedef DiagonalVectorType_ DiagonalVectorType;
+ typedef typename DiagonalVectorType::Scalar Scalar;
+ typedef typename DiagonalVectorType::StorageIndex StorageIndex;
+ typedef DiagonalShape StorageKind;
+ typedef typename traits<DiagonalVectorType>::XprKind XprKind;
+ enum {
+ RowsAtCompileTime = DiagonalVectorType::SizeAtCompileTime,
+ ColsAtCompileTime = DiagonalVectorType::SizeAtCompileTime,
+ MaxRowsAtCompileTime = DiagonalVectorType::MaxSizeAtCompileTime,
+ MaxColsAtCompileTime = DiagonalVectorType::MaxSizeAtCompileTime,
+ Flags = (traits<DiagonalVectorType>::Flags & LvalueBit) | NoPreferredStorageOrderBit
+ };
+};
+}
+
+template<typename DiagonalVectorType_>
+class DiagonalWrapper
+ : public DiagonalBase<DiagonalWrapper<DiagonalVectorType_> >, internal::no_assignment_operator
+{
+ public:
+ #ifndef EIGEN_PARSED_BY_DOXYGEN
+ typedef DiagonalVectorType_ DiagonalVectorType;
+ typedef DiagonalWrapper Nested;
+ #endif
+
+ /** Constructor from expression of diagonal coefficients to wrap. */
+ EIGEN_DEVICE_FUNC
+ explicit inline DiagonalWrapper(DiagonalVectorType& a_diagonal) : m_diagonal(a_diagonal) {}
+
+ /** \returns a const reference to the wrapped expression of diagonal coefficients. */
+ EIGEN_DEVICE_FUNC
+ const DiagonalVectorType& diagonal() const { return m_diagonal; }
+
+ protected:
+ typename DiagonalVectorType::Nested m_diagonal;
+};
+
+/** \returns a pseudo-expression of a diagonal matrix with *this as vector of diagonal coefficients
+ *
+ * \only_for_vectors
+ *
+ * Example: \include MatrixBase_asDiagonal.cpp
+ * Output: \verbinclude MatrixBase_asDiagonal.out
+ *
+ * \sa class DiagonalWrapper, class DiagonalMatrix, diagonal(), isDiagonal()
+ **/
+template<typename Derived>
+EIGEN_DEVICE_FUNC inline const DiagonalWrapper<const Derived>
+MatrixBase<Derived>::asDiagonal() const
+{
+ return DiagonalWrapper<const Derived>(derived());
+}
+
+/** \returns true if *this is approximately equal to a diagonal matrix,
+ * within the precision given by \a prec.
+ *
+ * Example: \include MatrixBase_isDiagonal.cpp
+ * Output: \verbinclude MatrixBase_isDiagonal.out
+ *
+ * \sa asDiagonal()
+ */
+template<typename Derived>
+bool MatrixBase<Derived>::isDiagonal(const RealScalar& prec) const
+{
+ if(cols() != rows()) return false;
+ RealScalar maxAbsOnDiagonal = static_cast<RealScalar>(-1);
+ for(Index j = 0; j < cols(); ++j)
+ {
+ RealScalar absOnDiagonal = numext::abs(coeff(j,j));
+ if(absOnDiagonal > maxAbsOnDiagonal) maxAbsOnDiagonal = absOnDiagonal;
+ }
+ for(Index j = 0; j < cols(); ++j)
+ for(Index i = 0; i < j; ++i)
+ {
+ if(!internal::isMuchSmallerThan(coeff(i, j), maxAbsOnDiagonal, prec)) return false;
+ if(!internal::isMuchSmallerThan(coeff(j, i), maxAbsOnDiagonal, prec)) return false;
+ }
+ return true;
+}
+
+namespace internal {
+
+template<> struct storage_kind_to_shape<DiagonalShape> { typedef DiagonalShape Shape; };
+
+struct Diagonal2Dense {};
+
+template<> struct AssignmentKind<DenseShape,DiagonalShape> { typedef Diagonal2Dense Kind; };
+
+// Diagonal matrix to Dense assignment
+template< typename DstXprType, typename SrcXprType, typename Functor>
+struct Assignment<DstXprType, SrcXprType, Functor, Diagonal2Dense>
+{
+ static void run(DstXprType &dst, const SrcXprType &src, const internal::assign_op<typename DstXprType::Scalar,typename SrcXprType::Scalar> &/*func*/)
+ {
+ Index dstRows = src.rows();
+ Index dstCols = src.cols();
+ if((dst.rows()!=dstRows) || (dst.cols()!=dstCols))
+ dst.resize(dstRows, dstCols);
+
+ dst.setZero();
+ dst.diagonal() = src.diagonal();
+ }
+
+ static void run(DstXprType &dst, const SrcXprType &src, const internal::add_assign_op<typename DstXprType::Scalar,typename SrcXprType::Scalar> &/*func*/)
+ { dst.diagonal() += src.diagonal(); }
+
+ static void run(DstXprType &dst, const SrcXprType &src, const internal::sub_assign_op<typename DstXprType::Scalar,typename SrcXprType::Scalar> &/*func*/)
+ { dst.diagonal() -= src.diagonal(); }
+};
+
+} // namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_DIAGONALMATRIX_H
diff --git a/Eigen/src/Core/DiagonalProduct.h b/Eigen/src/Core/DiagonalProduct.h
new file mode 100644
index 0000000..3cd34ba
--- /dev/null
+++ b/Eigen/src/Core/DiagonalProduct.h
@@ -0,0 +1,30 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2007-2009 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_DIAGONALPRODUCT_H
+#define EIGEN_DIAGONALPRODUCT_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+/** \returns the diagonal matrix product of \c *this by the diagonal matrix \a diagonal.
+ */
+template<typename Derived>
+template<typename DiagonalDerived>
+EIGEN_DEVICE_FUNC inline const Product<Derived, DiagonalDerived, LazyProduct>
+MatrixBase<Derived>::operator*(const DiagonalBase<DiagonalDerived> &a_diagonal) const
+{
+ return Product<Derived, DiagonalDerived, LazyProduct>(derived(),a_diagonal.derived());
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_DIAGONALPRODUCT_H
diff --git a/Eigen/src/Core/Dot.h b/Eigen/src/Core/Dot.h
new file mode 100644
index 0000000..0c13192
--- /dev/null
+++ b/Eigen/src/Core/Dot.h
@@ -0,0 +1,315 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2006-2008, 2010 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_DOT_H
+#define EIGEN_DOT_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+
+// helper function for dot(). The problem is that if we put that in the body of dot(), then upon calling dot
+// with mismatched types, the compiler emits errors about failing to instantiate cwiseProduct BEFORE
+// looking at the static assertions. Thus this is a trick to get better compile errors.
+template<typename T, typename U,
+ bool NeedToTranspose = T::IsVectorAtCompileTime && U::IsVectorAtCompileTime &&
+ ((int(T::RowsAtCompileTime) == 1 && int(U::ColsAtCompileTime) == 1) ||
+ (int(T::ColsAtCompileTime) == 1 && int(U::RowsAtCompileTime) == 1))>
+struct dot_nocheck
+{
+ typedef scalar_conj_product_op<typename traits<T>::Scalar,typename traits<U>::Scalar> conj_prod;
+ typedef typename conj_prod::result_type ResScalar;
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE
+ static ResScalar run(const MatrixBase<T>& a, const MatrixBase<U>& b)
+ {
+ return a.template binaryExpr<conj_prod>(b).sum();
+ }
+};
+
+template<typename T, typename U>
+struct dot_nocheck<T, U, true>
+{
+ typedef scalar_conj_product_op<typename traits<T>::Scalar,typename traits<U>::Scalar> conj_prod;
+ typedef typename conj_prod::result_type ResScalar;
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE
+ static ResScalar run(const MatrixBase<T>& a, const MatrixBase<U>& b)
+ {
+ return a.transpose().template binaryExpr<conj_prod>(b).sum();
+ }
+};
+
+} // end namespace internal
+
+/** \fn MatrixBase::dot
+ * \returns the dot product of *this with other.
+ *
+ * \only_for_vectors
+ *
+ * \note If the scalar type is complex numbers, then this function returns the hermitian
+ * (sesquilinear) dot product, conjugate-linear in the first variable and linear in the
+ * second variable.
+ *
+ * \sa squaredNorm(), norm()
+ */
+template<typename Derived>
+template<typename OtherDerived>
+EIGEN_DEVICE_FUNC
+EIGEN_STRONG_INLINE
+typename ScalarBinaryOpTraits<typename internal::traits<Derived>::Scalar,typename internal::traits<OtherDerived>::Scalar>::ReturnType
+MatrixBase<Derived>::dot(const MatrixBase<OtherDerived>& other) const
+{
+ EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
+ EIGEN_STATIC_ASSERT_VECTOR_ONLY(OtherDerived)
+ EIGEN_STATIC_ASSERT_SAME_VECTOR_SIZE(Derived,OtherDerived)
+#if !(defined(EIGEN_NO_STATIC_ASSERT) && defined(EIGEN_NO_DEBUG))
+ typedef internal::scalar_conj_product_op<Scalar,typename OtherDerived::Scalar> func;
+ EIGEN_CHECK_BINARY_COMPATIBILIY(func,Scalar,typename OtherDerived::Scalar);
+#endif
+
+ eigen_assert(size() == other.size());
+
+ return internal::dot_nocheck<Derived,OtherDerived>::run(*this, other);
+}
+
+//---------- implementation of L2 norm and related functions ----------
+
+/** \returns, for vectors, the squared \em l2 norm of \c *this, and for matrices the squared Frobenius norm.
+ * In both cases, it consists in the sum of the square of all the matrix entries.
+ * For vectors, this is also equals to the dot product of \c *this with itself.
+ *
+ * \sa dot(), norm(), lpNorm()
+ */
+template<typename Derived>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE typename NumTraits<typename internal::traits<Derived>::Scalar>::Real MatrixBase<Derived>::squaredNorm() const
+{
+ return numext::real((*this).cwiseAbs2().sum());
+}
+
+/** \returns, for vectors, the \em l2 norm of \c *this, and for matrices the Frobenius norm.
+ * In both cases, it consists in the square root of the sum of the square of all the matrix entries.
+ * For vectors, this is also equals to the square root of the dot product of \c *this with itself.
+ *
+ * \sa lpNorm(), dot(), squaredNorm()
+ */
+template<typename Derived>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE typename NumTraits<typename internal::traits<Derived>::Scalar>::Real MatrixBase<Derived>::norm() const
+{
+ return numext::sqrt(squaredNorm());
+}
+
+/** \returns an expression of the quotient of \c *this by its own norm.
+ *
+ * \warning If the input vector is too small (i.e., this->norm()==0),
+ * then this function returns a copy of the input.
+ *
+ * \only_for_vectors
+ *
+ * \sa norm(), normalize()
+ */
+template<typename Derived>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename MatrixBase<Derived>::PlainObject
+MatrixBase<Derived>::normalized() const
+{
+ typedef typename internal::nested_eval<Derived,2>::type Nested_;
+ Nested_ n(derived());
+ RealScalar z = n.squaredNorm();
+ // NOTE: after extensive benchmarking, this conditional does not impact performance, at least on recent x86 CPU
+ if(z>RealScalar(0))
+ return n / numext::sqrt(z);
+ else
+ return n;
+}
+
+/** Normalizes the vector, i.e. divides it by its own norm.
+ *
+ * \only_for_vectors
+ *
+ * \warning If the input vector is too small (i.e., this->norm()==0), then \c *this is left unchanged.
+ *
+ * \sa norm(), normalized()
+ */
+template<typename Derived>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void MatrixBase<Derived>::normalize()
+{
+ RealScalar z = squaredNorm();
+ // NOTE: after extensive benchmarking, this conditional does not impact performance, at least on recent x86 CPU
+ if(z>RealScalar(0))
+ derived() /= numext::sqrt(z);
+}
+
+/** \returns an expression of the quotient of \c *this by its own norm while avoiding underflow and overflow.
+ *
+ * \only_for_vectors
+ *
+ * This method is analogue to the normalized() method, but it reduces the risk of
+ * underflow and overflow when computing the norm.
+ *
+ * \warning If the input vector is too small (i.e., this->norm()==0),
+ * then this function returns a copy of the input.
+ *
+ * \sa stableNorm(), stableNormalize(), normalized()
+ */
+template<typename Derived>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename MatrixBase<Derived>::PlainObject
+MatrixBase<Derived>::stableNormalized() const
+{
+ typedef typename internal::nested_eval<Derived,3>::type Nested_;
+ Nested_ n(derived());
+ RealScalar w = n.cwiseAbs().maxCoeff();
+ RealScalar z = (n/w).squaredNorm();
+ if(z>RealScalar(0))
+ return n / (numext::sqrt(z)*w);
+ else
+ return n;
+}
+
+/** Normalizes the vector while avoid underflow and overflow
+ *
+ * \only_for_vectors
+ *
+ * This method is analogue to the normalize() method, but it reduces the risk of
+ * underflow and overflow when computing the norm.
+ *
+ * \warning If the input vector is too small (i.e., this->norm()==0), then \c *this is left unchanged.
+ *
+ * \sa stableNorm(), stableNormalized(), normalize()
+ */
+template<typename Derived>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void MatrixBase<Derived>::stableNormalize()
+{
+ RealScalar w = cwiseAbs().maxCoeff();
+ RealScalar z = (derived()/w).squaredNorm();
+ if(z>RealScalar(0))
+ derived() /= numext::sqrt(z)*w;
+}
+
+//---------- implementation of other norms ----------
+
+namespace internal {
+
+template<typename Derived, int p>
+struct lpNorm_selector
+{
+ typedef typename NumTraits<typename traits<Derived>::Scalar>::Real RealScalar;
+ EIGEN_DEVICE_FUNC
+ static inline RealScalar run(const MatrixBase<Derived>& m)
+ {
+ EIGEN_USING_STD(pow)
+ return pow(m.cwiseAbs().array().pow(p).sum(), RealScalar(1)/p);
+ }
+};
+
+template<typename Derived>
+struct lpNorm_selector<Derived, 1>
+{
+ EIGEN_DEVICE_FUNC
+ static inline typename NumTraits<typename traits<Derived>::Scalar>::Real run(const MatrixBase<Derived>& m)
+ {
+ return m.cwiseAbs().sum();
+ }
+};
+
+template<typename Derived>
+struct lpNorm_selector<Derived, 2>
+{
+ EIGEN_DEVICE_FUNC
+ static inline typename NumTraits<typename traits<Derived>::Scalar>::Real run(const MatrixBase<Derived>& m)
+ {
+ return m.norm();
+ }
+};
+
+template<typename Derived>
+struct lpNorm_selector<Derived, Infinity>
+{
+ typedef typename NumTraits<typename traits<Derived>::Scalar>::Real RealScalar;
+ EIGEN_DEVICE_FUNC
+ static inline RealScalar run(const MatrixBase<Derived>& m)
+ {
+ if(Derived::SizeAtCompileTime==0 || (Derived::SizeAtCompileTime==Dynamic && m.size()==0))
+ return RealScalar(0);
+ return m.cwiseAbs().maxCoeff();
+ }
+};
+
+} // end namespace internal
+
+/** \returns the \b coefficient-wise \f$ \ell^p \f$ norm of \c *this, that is, returns the p-th root of the sum of the p-th powers of the absolute values
+ * of the coefficients of \c *this. If \a p is the special value \a Eigen::Infinity, this function returns the \f$ \ell^\infty \f$
+ * norm, that is the maximum of the absolute values of the coefficients of \c *this.
+ *
+ * In all cases, if \c *this is empty, then the value 0 is returned.
+ *
+ * \note For matrices, this function does not compute the <a href="https://en.wikipedia.org/wiki/Operator_norm">operator-norm</a>. That is, if \c *this is a matrix, then its coefficients are interpreted as a 1D vector. Nonetheless, you can easily compute the 1-norm and \f$\infty\f$-norm matrix operator norms using \link TutorialReductionsVisitorsBroadcastingReductionsNorm partial reductions \endlink.
+ *
+ * \sa norm()
+ */
+template<typename Derived>
+template<int p>
+#ifndef EIGEN_PARSED_BY_DOXYGEN
+EIGEN_DEVICE_FUNC inline typename NumTraits<typename internal::traits<Derived>::Scalar>::Real
+#else
+EIGEN_DEVICE_FUNC MatrixBase<Derived>::RealScalar
+#endif
+MatrixBase<Derived>::lpNorm() const
+{
+ return internal::lpNorm_selector<Derived, p>::run(*this);
+}
+
+//---------- implementation of isOrthogonal / isUnitary ----------
+
+/** \returns true if *this is approximately orthogonal to \a other,
+ * within the precision given by \a prec.
+ *
+ * Example: \include MatrixBase_isOrthogonal.cpp
+ * Output: \verbinclude MatrixBase_isOrthogonal.out
+ */
+template<typename Derived>
+template<typename OtherDerived>
+bool MatrixBase<Derived>::isOrthogonal
+(const MatrixBase<OtherDerived>& other, const RealScalar& prec) const
+{
+ typename internal::nested_eval<Derived,2>::type nested(derived());
+ typename internal::nested_eval<OtherDerived,2>::type otherNested(other.derived());
+ return numext::abs2(nested.dot(otherNested)) <= prec * prec * nested.squaredNorm() * otherNested.squaredNorm();
+}
+
+/** \returns true if *this is approximately an unitary matrix,
+ * within the precision given by \a prec. In the case where the \a Scalar
+ * type is real numbers, a unitary matrix is an orthogonal matrix, whence the name.
+ *
+ * \note This can be used to check whether a family of vectors forms an orthonormal basis.
+ * Indeed, \c m.isUnitary() returns true if and only if the columns (equivalently, the rows) of m form an
+ * orthonormal basis.
+ *
+ * Example: \include MatrixBase_isUnitary.cpp
+ * Output: \verbinclude MatrixBase_isUnitary.out
+ */
+template<typename Derived>
+bool MatrixBase<Derived>::isUnitary(const RealScalar& prec) const
+{
+ typename internal::nested_eval<Derived,1>::type self(derived());
+ for(Index i = 0; i < cols(); ++i)
+ {
+ if(!internal::isApprox(self.col(i).squaredNorm(), static_cast<RealScalar>(1), prec))
+ return false;
+ for(Index j = 0; j < i; ++j)
+ if(!internal::isMuchSmallerThan(self.col(i).dot(self.col(j)), static_cast<Scalar>(1), prec))
+ return false;
+ }
+ return true;
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_DOT_H
diff --git a/Eigen/src/Core/EigenBase.h b/Eigen/src/Core/EigenBase.h
new file mode 100644
index 0000000..105488d
--- /dev/null
+++ b/Eigen/src/Core/EigenBase.h
@@ -0,0 +1,162 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009 Benoit Jacob <jacob.benoit.1@gmail.com>
+// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_EIGENBASE_H
+#define EIGEN_EIGENBASE_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+/** \class EigenBase
+ * \ingroup Core_Module
+ *
+ * Common base class for all classes T such that MatrixBase has an operator=(T) and a constructor MatrixBase(T).
+ *
+ * In other words, an EigenBase object is an object that can be copied into a MatrixBase.
+ *
+ * Besides MatrixBase-derived classes, this also includes special matrix classes such as diagonal matrices, etc.
+ *
+ * Notice that this class is trivial, it is only used to disambiguate overloaded functions.
+ *
+ * \sa \blank \ref TopicClassHierarchy
+ */
+template<typename Derived> struct EigenBase
+{
+// typedef typename internal::plain_matrix_type<Derived>::type PlainObject;
+
+ /** \brief The interface type of indices
+ * \details To change this, \c \#define the preprocessor symbol \c EIGEN_DEFAULT_DENSE_INDEX_TYPE.
+ * \sa StorageIndex, \ref TopicPreprocessorDirectives.
+ * DEPRECATED: Since Eigen 3.3, its usage is deprecated. Use Eigen::Index instead.
+ * Deprecation is not marked with a doxygen comment because there are too many existing usages to add the deprecation attribute.
+ */
+ typedef Eigen::Index Index;
+
+ // FIXME is it needed?
+ typedef typename internal::traits<Derived>::StorageKind StorageKind;
+
+ /** \returns a reference to the derived object */
+ EIGEN_DEVICE_FUNC
+ Derived& derived() { return *static_cast<Derived*>(this); }
+ /** \returns a const reference to the derived object */
+ EIGEN_DEVICE_FUNC
+ const Derived& derived() const { return *static_cast<const Derived*>(this); }
+
+ EIGEN_DEVICE_FUNC
+ inline Derived& const_cast_derived() const
+ { return *static_cast<Derived*>(const_cast<EigenBase*>(this)); }
+ EIGEN_DEVICE_FUNC
+ inline const Derived& const_derived() const
+ { return *static_cast<const Derived*>(this); }
+
+ /** \returns the number of rows. \sa cols(), RowsAtCompileTime */
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
+ inline Index rows() const EIGEN_NOEXCEPT { return derived().rows(); }
+ /** \returns the number of columns. \sa rows(), ColsAtCompileTime*/
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
+ inline Index cols() const EIGEN_NOEXCEPT { return derived().cols(); }
+ /** \returns the number of coefficients, which is rows()*cols().
+ * \sa rows(), cols(), SizeAtCompileTime. */
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
+ inline Index size() const EIGEN_NOEXCEPT { return rows() * cols(); }
+
+ /** \internal Don't use it, but do the equivalent: \code dst = *this; \endcode */
+ template<typename Dest>
+ EIGEN_DEVICE_FUNC
+ inline void evalTo(Dest& dst) const
+ { derived().evalTo(dst); }
+
+ /** \internal Don't use it, but do the equivalent: \code dst += *this; \endcode */
+ template<typename Dest>
+ EIGEN_DEVICE_FUNC
+ inline void addTo(Dest& dst) const
+ {
+ // This is the default implementation,
+ // derived class can reimplement it in a more optimized way.
+ typename Dest::PlainObject res(rows(),cols());
+ evalTo(res);
+ dst += res;
+ }
+
+ /** \internal Don't use it, but do the equivalent: \code dst -= *this; \endcode */
+ template<typename Dest>
+ EIGEN_DEVICE_FUNC
+ inline void subTo(Dest& dst) const
+ {
+ // This is the default implementation,
+ // derived class can reimplement it in a more optimized way.
+ typename Dest::PlainObject res(rows(),cols());
+ evalTo(res);
+ dst -= res;
+ }
+
+ /** \internal Don't use it, but do the equivalent: \code dst.applyOnTheRight(*this); \endcode */
+ template<typename Dest>
+ EIGEN_DEVICE_FUNC inline void applyThisOnTheRight(Dest& dst) const
+ {
+ // This is the default implementation,
+ // derived class can reimplement it in a more optimized way.
+ dst = dst * this->derived();
+ }
+
+ /** \internal Don't use it, but do the equivalent: \code dst.applyOnTheLeft(*this); \endcode */
+ template<typename Dest>
+ EIGEN_DEVICE_FUNC inline void applyThisOnTheLeft(Dest& dst) const
+ {
+ // This is the default implementation,
+ // derived class can reimplement it in a more optimized way.
+ dst = this->derived() * dst;
+ }
+
+};
+
+/***************************************************************************
+* Implementation of matrix base methods
+***************************************************************************/
+
+/** \brief Copies the generic expression \a other into *this.
+ *
+ * \details The expression must provide a (templated) evalTo(Derived& dst) const
+ * function which does the actual job. In practice, this allows any user to write
+ * its own special matrix without having to modify MatrixBase
+ *
+ * \returns a reference to *this.
+ */
+template<typename Derived>
+template<typename OtherDerived>
+EIGEN_DEVICE_FUNC
+Derived& DenseBase<Derived>::operator=(const EigenBase<OtherDerived> &other)
+{
+ call_assignment(derived(), other.derived());
+ return derived();
+}
+
+template<typename Derived>
+template<typename OtherDerived>
+EIGEN_DEVICE_FUNC
+Derived& DenseBase<Derived>::operator+=(const EigenBase<OtherDerived> &other)
+{
+ call_assignment(derived(), other.derived(), internal::add_assign_op<Scalar,typename OtherDerived::Scalar>());
+ return derived();
+}
+
+template<typename Derived>
+template<typename OtherDerived>
+EIGEN_DEVICE_FUNC
+Derived& DenseBase<Derived>::operator-=(const EigenBase<OtherDerived> &other)
+{
+ call_assignment(derived(), other.derived(), internal::sub_assign_op<Scalar,typename OtherDerived::Scalar>());
+ return derived();
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_EIGENBASE_H
diff --git a/Eigen/src/Core/ForceAlignedAccess.h b/Eigen/src/Core/ForceAlignedAccess.h
new file mode 100644
index 0000000..b00785e
--- /dev/null
+++ b/Eigen/src/Core/ForceAlignedAccess.h
@@ -0,0 +1,152 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009-2010 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_FORCEALIGNEDACCESS_H
+#define EIGEN_FORCEALIGNEDACCESS_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+/** \class ForceAlignedAccess
+ * \ingroup Core_Module
+ *
+ * \brief Enforce aligned packet loads and stores regardless of what is requested
+ *
+ * \param ExpressionType the type of the object of which we are forcing aligned packet access
+ *
+ * This class is the return type of MatrixBase::forceAlignedAccess()
+ * and most of the time this is the only way it is used.
+ *
+ * \sa MatrixBase::forceAlignedAccess()
+ */
+
+namespace internal {
+template<typename ExpressionType>
+struct traits<ForceAlignedAccess<ExpressionType> > : public traits<ExpressionType>
+{};
+}
+
+template<typename ExpressionType> class ForceAlignedAccess
+ : public internal::dense_xpr_base< ForceAlignedAccess<ExpressionType> >::type
+{
+ public:
+
+ typedef typename internal::dense_xpr_base<ForceAlignedAccess>::type Base;
+ EIGEN_DENSE_PUBLIC_INTERFACE(ForceAlignedAccess)
+
+ EIGEN_DEVICE_FUNC explicit inline ForceAlignedAccess(const ExpressionType& matrix) : m_expression(matrix) {}
+
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
+ inline Index rows() const EIGEN_NOEXCEPT { return m_expression.rows(); }
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
+ inline Index cols() const EIGEN_NOEXCEPT { return m_expression.cols(); }
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
+ inline Index outerStride() const EIGEN_NOEXCEPT { return m_expression.outerStride(); }
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
+ inline Index innerStride() const EIGEN_NOEXCEPT { return m_expression.innerStride(); }
+
+ EIGEN_DEVICE_FUNC inline const CoeffReturnType coeff(Index row, Index col) const
+ {
+ return m_expression.coeff(row, col);
+ }
+
+ EIGEN_DEVICE_FUNC inline Scalar& coeffRef(Index row, Index col)
+ {
+ return m_expression.const_cast_derived().coeffRef(row, col);
+ }
+
+ EIGEN_DEVICE_FUNC inline const CoeffReturnType coeff(Index index) const
+ {
+ return m_expression.coeff(index);
+ }
+
+ EIGEN_DEVICE_FUNC inline Scalar& coeffRef(Index index)
+ {
+ return m_expression.const_cast_derived().coeffRef(index);
+ }
+
+ template<int LoadMode>
+ inline const PacketScalar packet(Index row, Index col) const
+ {
+ return m_expression.template packet<Aligned>(row, col);
+ }
+
+ template<int LoadMode>
+ inline void writePacket(Index row, Index col, const PacketScalar& x)
+ {
+ m_expression.const_cast_derived().template writePacket<Aligned>(row, col, x);
+ }
+
+ template<int LoadMode>
+ inline const PacketScalar packet(Index index) const
+ {
+ return m_expression.template packet<Aligned>(index);
+ }
+
+ template<int LoadMode>
+ inline void writePacket(Index index, const PacketScalar& x)
+ {
+ m_expression.const_cast_derived().template writePacket<Aligned>(index, x);
+ }
+
+ EIGEN_DEVICE_FUNC operator const ExpressionType&() const { return m_expression; }
+
+ protected:
+ const ExpressionType& m_expression;
+
+ private:
+ ForceAlignedAccess& operator=(const ForceAlignedAccess&);
+};
+
+/** \returns an expression of *this with forced aligned access
+ * \sa forceAlignedAccessIf(),class ForceAlignedAccess
+ */
+template<typename Derived>
+inline const ForceAlignedAccess<Derived>
+MatrixBase<Derived>::forceAlignedAccess() const
+{
+ return ForceAlignedAccess<Derived>(derived());
+}
+
+/** \returns an expression of *this with forced aligned access
+ * \sa forceAlignedAccessIf(), class ForceAlignedAccess
+ */
+template<typename Derived>
+inline ForceAlignedAccess<Derived>
+MatrixBase<Derived>::forceAlignedAccess()
+{
+ return ForceAlignedAccess<Derived>(derived());
+}
+
+/** \returns an expression of *this with forced aligned access if \a Enable is true.
+ * \sa forceAlignedAccess(), class ForceAlignedAccess
+ */
+template<typename Derived>
+template<bool Enable>
+inline add_const_on_value_type_t<std::conditional_t<Enable,ForceAlignedAccess<Derived>,Derived&>>
+MatrixBase<Derived>::forceAlignedAccessIf() const
+{
+ return derived(); // FIXME This should not work but apparently is never used
+}
+
+/** \returns an expression of *this with forced aligned access if \a Enable is true.
+ * \sa forceAlignedAccess(), class ForceAlignedAccess
+ */
+template<typename Derived>
+template<bool Enable>
+inline std::conditional_t<Enable,ForceAlignedAccess<Derived>,Derived&>
+MatrixBase<Derived>::forceAlignedAccessIf()
+{
+ return derived(); // FIXME This should not work but apparently is never used
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_FORCEALIGNEDACCESS_H
diff --git a/Eigen/src/Core/Fuzzy.h b/Eigen/src/Core/Fuzzy.h
new file mode 100644
index 0000000..b16b2da
--- /dev/null
+++ b/Eigen/src/Core/Fuzzy.h
@@ -0,0 +1,157 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_FUZZY_H
+#define EIGEN_FUZZY_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal
+{
+
+template<typename Derived, typename OtherDerived, bool is_integer = NumTraits<typename Derived::Scalar>::IsInteger>
+struct isApprox_selector
+{
+ EIGEN_DEVICE_FUNC
+ static bool run(const Derived& x, const OtherDerived& y, const typename Derived::RealScalar& prec)
+ {
+ typename internal::nested_eval<Derived,2>::type nested(x);
+ typename internal::nested_eval<OtherDerived,2>::type otherNested(y);
+ return (nested - otherNested).cwiseAbs2().sum() <= prec * prec * numext::mini(nested.cwiseAbs2().sum(), otherNested.cwiseAbs2().sum());
+ }
+};
+
+template<typename Derived, typename OtherDerived>
+struct isApprox_selector<Derived, OtherDerived, true>
+{
+ EIGEN_DEVICE_FUNC
+ static bool run(const Derived& x, const OtherDerived& y, const typename Derived::RealScalar&)
+ {
+ return x.matrix() == y.matrix();
+ }
+};
+
+template<typename Derived, typename OtherDerived, bool is_integer = NumTraits<typename Derived::Scalar>::IsInteger>
+struct isMuchSmallerThan_object_selector
+{
+ EIGEN_DEVICE_FUNC
+ static bool run(const Derived& x, const OtherDerived& y, const typename Derived::RealScalar& prec)
+ {
+ return x.cwiseAbs2().sum() <= numext::abs2(prec) * y.cwiseAbs2().sum();
+ }
+};
+
+template<typename Derived, typename OtherDerived>
+struct isMuchSmallerThan_object_selector<Derived, OtherDerived, true>
+{
+ EIGEN_DEVICE_FUNC
+ static bool run(const Derived& x, const OtherDerived&, const typename Derived::RealScalar&)
+ {
+ return x.matrix() == Derived::Zero(x.rows(), x.cols()).matrix();
+ }
+};
+
+template<typename Derived, bool is_integer = NumTraits<typename Derived::Scalar>::IsInteger>
+struct isMuchSmallerThan_scalar_selector
+{
+ EIGEN_DEVICE_FUNC
+ static bool run(const Derived& x, const typename Derived::RealScalar& y, const typename Derived::RealScalar& prec)
+ {
+ return x.cwiseAbs2().sum() <= numext::abs2(prec * y);
+ }
+};
+
+template<typename Derived>
+struct isMuchSmallerThan_scalar_selector<Derived, true>
+{
+ EIGEN_DEVICE_FUNC
+ static bool run(const Derived& x, const typename Derived::RealScalar&, const typename Derived::RealScalar&)
+ {
+ return x.matrix() == Derived::Zero(x.rows(), x.cols()).matrix();
+ }
+};
+
+} // end namespace internal
+
+
+/** \returns \c true if \c *this is approximately equal to \a other, within the precision
+ * determined by \a prec.
+ *
+ * \note The fuzzy compares are done multiplicatively. Two vectors \f$ v \f$ and \f$ w \f$
+ * are considered to be approximately equal within precision \f$ p \f$ if
+ * \f[ \Vert v - w \Vert \leqslant p\,\min(\Vert v\Vert, \Vert w\Vert). \f]
+ * For matrices, the comparison is done using the Hilbert-Schmidt norm (aka Frobenius norm
+ * L2 norm).
+ *
+ * \note Because of the multiplicativeness of this comparison, one can't use this function
+ * to check whether \c *this is approximately equal to the zero matrix or vector.
+ * Indeed, \c isApprox(zero) returns false unless \c *this itself is exactly the zero matrix
+ * or vector. If you want to test whether \c *this is zero, use internal::isMuchSmallerThan(const
+ * RealScalar&, RealScalar) instead.
+ *
+ * \sa internal::isMuchSmallerThan(const RealScalar&, RealScalar) const
+ */
+template<typename Derived>
+template<typename OtherDerived>
+EIGEN_DEVICE_FUNC bool DenseBase<Derived>::isApprox(
+ const DenseBase<OtherDerived>& other,
+ const RealScalar& prec
+) const
+{
+ return internal::isApprox_selector<Derived, OtherDerived>::run(derived(), other.derived(), prec);
+}
+
+/** \returns \c true if the norm of \c *this is much smaller than \a other,
+ * within the precision determined by \a prec.
+ *
+ * \note The fuzzy compares are done multiplicatively. A vector \f$ v \f$ is
+ * considered to be much smaller than \f$ x \f$ within precision \f$ p \f$ if
+ * \f[ \Vert v \Vert \leqslant p\,\vert x\vert. \f]
+ *
+ * For matrices, the comparison is done using the Hilbert-Schmidt norm. For this reason,
+ * the value of the reference scalar \a other should come from the Hilbert-Schmidt norm
+ * of a reference matrix of same dimensions.
+ *
+ * \sa isApprox(), isMuchSmallerThan(const DenseBase<OtherDerived>&, RealScalar) const
+ */
+template<typename Derived>
+EIGEN_DEVICE_FUNC bool DenseBase<Derived>::isMuchSmallerThan(
+ const typename NumTraits<Scalar>::Real& other,
+ const RealScalar& prec
+) const
+{
+ return internal::isMuchSmallerThan_scalar_selector<Derived>::run(derived(), other, prec);
+}
+
+/** \returns \c true if the norm of \c *this is much smaller than the norm of \a other,
+ * within the precision determined by \a prec.
+ *
+ * \note The fuzzy compares are done multiplicatively. A vector \f$ v \f$ is
+ * considered to be much smaller than a vector \f$ w \f$ within precision \f$ p \f$ if
+ * \f[ \Vert v \Vert \leqslant p\,\Vert w\Vert. \f]
+ * For matrices, the comparison is done using the Hilbert-Schmidt norm.
+ *
+ * \sa isApprox(), isMuchSmallerThan(const RealScalar&, RealScalar) const
+ */
+template<typename Derived>
+template<typename OtherDerived>
+EIGEN_DEVICE_FUNC bool DenseBase<Derived>::isMuchSmallerThan(
+ const DenseBase<OtherDerived>& other,
+ const RealScalar& prec
+) const
+{
+ return internal::isMuchSmallerThan_object_selector<Derived, OtherDerived>::run(derived(), other.derived(), prec);
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_FUZZY_H
diff --git a/Eigen/src/Core/GeneralProduct.h b/Eigen/src/Core/GeneralProduct.h
new file mode 100644
index 0000000..661a3c4
--- /dev/null
+++ b/Eigen/src/Core/GeneralProduct.h
@@ -0,0 +1,467 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+// Copyright (C) 2008-2011 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_GENERAL_PRODUCT_H
+#define EIGEN_GENERAL_PRODUCT_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+enum {
+ Large = 2,
+ Small = 3
+};
+
+// Define the threshold value to fallback from the generic matrix-matrix product
+// implementation (heavy) to the lightweight coeff-based product one.
+// See generic_product_impl<Lhs,Rhs,DenseShape,DenseShape,GemmProduct>
+// in products/GeneralMatrixMatrix.h for more details.
+// TODO This threshold should also be used in the compile-time selector below.
+#ifndef EIGEN_GEMM_TO_COEFFBASED_THRESHOLD
+// This default value has been obtained on a Haswell architecture.
+#define EIGEN_GEMM_TO_COEFFBASED_THRESHOLD 20
+#endif
+
+namespace internal {
+
+template<int Rows, int Cols, int Depth> struct product_type_selector;
+
+template<int Size, int MaxSize> struct product_size_category
+{
+ enum {
+ #ifndef EIGEN_GPU_COMPILE_PHASE
+ is_large = MaxSize == Dynamic ||
+ Size >= EIGEN_CACHEFRIENDLY_PRODUCT_THRESHOLD ||
+ (Size==Dynamic && MaxSize>=EIGEN_CACHEFRIENDLY_PRODUCT_THRESHOLD),
+ #else
+ is_large = 0,
+ #endif
+ value = is_large ? Large
+ : Size == 1 ? 1
+ : Small
+ };
+};
+
+template<typename Lhs, typename Rhs> struct product_type
+{
+ typedef remove_all_t<Lhs> Lhs_;
+ typedef remove_all_t<Rhs> Rhs_;
+ enum {
+ MaxRows = traits<Lhs_>::MaxRowsAtCompileTime,
+ Rows = traits<Lhs_>::RowsAtCompileTime,
+ MaxCols = traits<Rhs_>::MaxColsAtCompileTime,
+ Cols = traits<Rhs_>::ColsAtCompileTime,
+ MaxDepth = min_size_prefer_fixed(traits<Lhs_>::MaxColsAtCompileTime,
+ traits<Rhs_>::MaxRowsAtCompileTime),
+ Depth = min_size_prefer_fixed(traits<Lhs_>::ColsAtCompileTime,
+ traits<Rhs_>::RowsAtCompileTime)
+ };
+
+ // the splitting into different lines of code here, introducing the _select enums and the typedef below,
+ // is to work around an internal compiler error with gcc 4.1 and 4.2.
+private:
+ enum {
+ rows_select = product_size_category<Rows,MaxRows>::value,
+ cols_select = product_size_category<Cols,MaxCols>::value,
+ depth_select = product_size_category<Depth,MaxDepth>::value
+ };
+ typedef product_type_selector<rows_select, cols_select, depth_select> selector;
+
+public:
+ enum {
+ value = selector::ret,
+ ret = selector::ret
+ };
+#ifdef EIGEN_DEBUG_PRODUCT
+ static void debug()
+ {
+ EIGEN_DEBUG_VAR(Rows);
+ EIGEN_DEBUG_VAR(Cols);
+ EIGEN_DEBUG_VAR(Depth);
+ EIGEN_DEBUG_VAR(rows_select);
+ EIGEN_DEBUG_VAR(cols_select);
+ EIGEN_DEBUG_VAR(depth_select);
+ EIGEN_DEBUG_VAR(value);
+ }
+#endif
+};
+
+/* The following allows to select the kind of product at compile time
+ * based on the three dimensions of the product.
+ * This is a compile time mapping from {1,Small,Large}^3 -> {product types} */
+// FIXME I'm not sure the current mapping is the ideal one.
+template<int M, int N> struct product_type_selector<M,N,1> { enum { ret = OuterProduct }; };
+template<int M> struct product_type_selector<M, 1, 1> { enum { ret = LazyCoeffBasedProductMode }; };
+template<int N> struct product_type_selector<1, N, 1> { enum { ret = LazyCoeffBasedProductMode }; };
+template<int Depth> struct product_type_selector<1, 1, Depth> { enum { ret = InnerProduct }; };
+template<> struct product_type_selector<1, 1, 1> { enum { ret = InnerProduct }; };
+template<> struct product_type_selector<Small,1, Small> { enum { ret = CoeffBasedProductMode }; };
+template<> struct product_type_selector<1, Small,Small> { enum { ret = CoeffBasedProductMode }; };
+template<> struct product_type_selector<Small,Small,Small> { enum { ret = CoeffBasedProductMode }; };
+template<> struct product_type_selector<Small, Small, 1> { enum { ret = LazyCoeffBasedProductMode }; };
+template<> struct product_type_selector<Small, Large, 1> { enum { ret = LazyCoeffBasedProductMode }; };
+template<> struct product_type_selector<Large, Small, 1> { enum { ret = LazyCoeffBasedProductMode }; };
+template<> struct product_type_selector<1, Large,Small> { enum { ret = CoeffBasedProductMode }; };
+template<> struct product_type_selector<1, Large,Large> { enum { ret = GemvProduct }; };
+template<> struct product_type_selector<1, Small,Large> { enum { ret = CoeffBasedProductMode }; };
+template<> struct product_type_selector<Large,1, Small> { enum { ret = CoeffBasedProductMode }; };
+template<> struct product_type_selector<Large,1, Large> { enum { ret = GemvProduct }; };
+template<> struct product_type_selector<Small,1, Large> { enum { ret = CoeffBasedProductMode }; };
+template<> struct product_type_selector<Small,Small,Large> { enum { ret = GemmProduct }; };
+template<> struct product_type_selector<Large,Small,Large> { enum { ret = GemmProduct }; };
+template<> struct product_type_selector<Small,Large,Large> { enum { ret = GemmProduct }; };
+template<> struct product_type_selector<Large,Large,Large> { enum { ret = GemmProduct }; };
+template<> struct product_type_selector<Large,Small,Small> { enum { ret = CoeffBasedProductMode }; };
+template<> struct product_type_selector<Small,Large,Small> { enum { ret = CoeffBasedProductMode }; };
+template<> struct product_type_selector<Large,Large,Small> { enum { ret = GemmProduct }; };
+
+} // end namespace internal
+
+/***********************************************************************
+* Implementation of Inner Vector Vector Product
+***********************************************************************/
+
+// FIXME : maybe the "inner product" could return a Scalar
+// instead of a 1x1 matrix ??
+// Pro: more natural for the user
+// Cons: this could be a problem if in a meta unrolled algorithm a matrix-matrix
+// product ends up to a row-vector times col-vector product... To tackle this use
+// case, we could have a specialization for Block<MatrixType,1,1> with: operator=(Scalar x);
+
+/***********************************************************************
+* Implementation of Outer Vector Vector Product
+***********************************************************************/
+
+/***********************************************************************
+* Implementation of General Matrix Vector Product
+***********************************************************************/
+
+/* According to the shape/flags of the matrix we have to distinghish 3 different cases:
+ * 1 - the matrix is col-major, BLAS compatible and M is large => call fast BLAS-like colmajor routine
+ * 2 - the matrix is row-major, BLAS compatible and N is large => call fast BLAS-like rowmajor routine
+ * 3 - all other cases are handled using a simple loop along the outer-storage direction.
+ * Therefore we need a lower level meta selector.
+ * Furthermore, if the matrix is the rhs, then the product has to be transposed.
+ */
+namespace internal {
+
+template<int Side, int StorageOrder, bool BlasCompatible>
+struct gemv_dense_selector;
+
+} // end namespace internal
+
+namespace internal {
+
+template<typename Scalar,int Size,int MaxSize,bool Cond> struct gemv_static_vector_if;
+
+template<typename Scalar,int Size,int MaxSize>
+struct gemv_static_vector_if<Scalar,Size,MaxSize,false>
+{
+ EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Scalar* data() { eigen_internal_assert(false && "should never be called"); return 0; }
+};
+
+template<typename Scalar,int Size>
+struct gemv_static_vector_if<Scalar,Size,Dynamic,true>
+{
+ EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Scalar* data() { return 0; }
+};
+
+template<typename Scalar,int Size,int MaxSize>
+struct gemv_static_vector_if<Scalar,Size,MaxSize,true>
+{
+ enum {
+ ForceAlignment = internal::packet_traits<Scalar>::Vectorizable,
+ PacketSize = internal::packet_traits<Scalar>::size
+ };
+ #if EIGEN_MAX_STATIC_ALIGN_BYTES!=0
+ internal::plain_array<Scalar, internal::min_size_prefer_fixed(Size, MaxSize), 0,
+ internal::plain_enum_min(AlignedMax, PacketSize)> m_data;
+ EIGEN_STRONG_INLINE Scalar* data() { return m_data.array; }
+ #else
+ // Some architectures cannot align on the stack,
+ // => let's manually enforce alignment by allocating more data and return the address of the first aligned element.
+ internal::plain_array<Scalar, internal::min_size_prefer_fixed(Size, MaxSize)+(ForceAlignment?EIGEN_MAX_ALIGN_BYTES:0),0> m_data;
+ EIGEN_STRONG_INLINE Scalar* data() {
+ return ForceAlignment
+ ? reinterpret_cast<Scalar*>((internal::UIntPtr(m_data.array) & ~(std::size_t(EIGEN_MAX_ALIGN_BYTES-1))) + EIGEN_MAX_ALIGN_BYTES)
+ : m_data.array;
+ }
+ #endif
+};
+
+// The vector is on the left => transposition
+template<int StorageOrder, bool BlasCompatible>
+struct gemv_dense_selector<OnTheLeft,StorageOrder,BlasCompatible>
+{
+ template<typename Lhs, typename Rhs, typename Dest>
+ static void run(const Lhs &lhs, const Rhs &rhs, Dest& dest, const typename Dest::Scalar& alpha)
+ {
+ Transpose<Dest> destT(dest);
+ enum { OtherStorageOrder = StorageOrder == RowMajor ? ColMajor : RowMajor };
+ gemv_dense_selector<OnTheRight,OtherStorageOrder,BlasCompatible>
+ ::run(rhs.transpose(), lhs.transpose(), destT, alpha);
+ }
+};
+
+template<> struct gemv_dense_selector<OnTheRight,ColMajor,true>
+{
+ template<typename Lhs, typename Rhs, typename Dest>
+ static inline void run(const Lhs &lhs, const Rhs &rhs, Dest& dest, const typename Dest::Scalar& alpha)
+ {
+ typedef typename Lhs::Scalar LhsScalar;
+ typedef typename Rhs::Scalar RhsScalar;
+ typedef typename Dest::Scalar ResScalar;
+
+ typedef internal::blas_traits<Lhs> LhsBlasTraits;
+ typedef typename LhsBlasTraits::DirectLinearAccessType ActualLhsType;
+ typedef internal::blas_traits<Rhs> RhsBlasTraits;
+ typedef typename RhsBlasTraits::DirectLinearAccessType ActualRhsType;
+
+ typedef Map<Matrix<ResScalar,Dynamic,1>, plain_enum_min(AlignedMax, internal::packet_traits<ResScalar>::size)> MappedDest;
+
+ ActualLhsType actualLhs = LhsBlasTraits::extract(lhs);
+ ActualRhsType actualRhs = RhsBlasTraits::extract(rhs);
+
+ ResScalar actualAlpha = combine_scalar_factors(alpha, lhs, rhs);
+
+ // make sure Dest is a compile-time vector type (bug 1166)
+ typedef std::conditional_t<Dest::IsVectorAtCompileTime, Dest, typename Dest::ColXpr> ActualDest;
+
+ enum {
+ // FIXME find a way to allow an inner stride on the result if packet_traits<Scalar>::size==1
+ // on, the other hand it is good for the cache to pack the vector anyways...
+ EvalToDestAtCompileTime = (ActualDest::InnerStrideAtCompileTime==1),
+ ComplexByReal = (NumTraits<LhsScalar>::IsComplex) && (!NumTraits<RhsScalar>::IsComplex),
+ MightCannotUseDest = ((!EvalToDestAtCompileTime) || ComplexByReal) && (ActualDest::MaxSizeAtCompileTime!=0)
+ };
+
+ typedef const_blas_data_mapper<LhsScalar,Index,ColMajor> LhsMapper;
+ typedef const_blas_data_mapper<RhsScalar,Index,RowMajor> RhsMapper;
+ RhsScalar compatibleAlpha = get_factor<ResScalar,RhsScalar>::run(actualAlpha);
+
+ if(!MightCannotUseDest)
+ {
+ // shortcut if we are sure to be able to use dest directly,
+ // this ease the compiler to generate cleaner and more optimzized code for most common cases
+ general_matrix_vector_product
+ <Index,LhsScalar,LhsMapper,ColMajor,LhsBlasTraits::NeedToConjugate,RhsScalar,RhsMapper,RhsBlasTraits::NeedToConjugate>::run(
+ actualLhs.rows(), actualLhs.cols(),
+ LhsMapper(actualLhs.data(), actualLhs.outerStride()),
+ RhsMapper(actualRhs.data(), actualRhs.innerStride()),
+ dest.data(), 1,
+ compatibleAlpha);
+ }
+ else
+ {
+ gemv_static_vector_if<ResScalar,ActualDest::SizeAtCompileTime,ActualDest::MaxSizeAtCompileTime,MightCannotUseDest> static_dest;
+
+ const bool alphaIsCompatible = (!ComplexByReal) || (numext::is_exactly_zero(numext::imag(actualAlpha)));
+ const bool evalToDest = EvalToDestAtCompileTime && alphaIsCompatible;
+
+ ei_declare_aligned_stack_constructed_variable(ResScalar,actualDestPtr,dest.size(),
+ evalToDest ? dest.data() : static_dest.data());
+
+ if(!evalToDest)
+ {
+ #ifdef EIGEN_DENSE_STORAGE_CTOR_PLUGIN
+ Index size = dest.size();
+ EIGEN_DENSE_STORAGE_CTOR_PLUGIN
+ #endif
+ if(!alphaIsCompatible)
+ {
+ MappedDest(actualDestPtr, dest.size()).setZero();
+ compatibleAlpha = RhsScalar(1);
+ }
+ else
+ MappedDest(actualDestPtr, dest.size()) = dest;
+ }
+
+ general_matrix_vector_product
+ <Index,LhsScalar,LhsMapper,ColMajor,LhsBlasTraits::NeedToConjugate,RhsScalar,RhsMapper,RhsBlasTraits::NeedToConjugate>::run(
+ actualLhs.rows(), actualLhs.cols(),
+ LhsMapper(actualLhs.data(), actualLhs.outerStride()),
+ RhsMapper(actualRhs.data(), actualRhs.innerStride()),
+ actualDestPtr, 1,
+ compatibleAlpha);
+
+ if (!evalToDest)
+ {
+ if(!alphaIsCompatible)
+ dest.matrix() += actualAlpha * MappedDest(actualDestPtr, dest.size());
+ else
+ dest = MappedDest(actualDestPtr, dest.size());
+ }
+ }
+ }
+};
+
+template<> struct gemv_dense_selector<OnTheRight,RowMajor,true>
+{
+ template<typename Lhs, typename Rhs, typename Dest>
+ static void run(const Lhs &lhs, const Rhs &rhs, Dest& dest, const typename Dest::Scalar& alpha)
+ {
+ typedef typename Lhs::Scalar LhsScalar;
+ typedef typename Rhs::Scalar RhsScalar;
+ typedef typename Dest::Scalar ResScalar;
+
+ typedef internal::blas_traits<Lhs> LhsBlasTraits;
+ typedef typename LhsBlasTraits::DirectLinearAccessType ActualLhsType;
+ typedef internal::blas_traits<Rhs> RhsBlasTraits;
+ typedef typename RhsBlasTraits::DirectLinearAccessType ActualRhsType;
+ typedef internal::remove_all_t<ActualRhsType> ActualRhsTypeCleaned;
+
+ std::add_const_t<ActualLhsType> actualLhs = LhsBlasTraits::extract(lhs);
+ std::add_const_t<ActualRhsType> actualRhs = RhsBlasTraits::extract(rhs);
+
+ ResScalar actualAlpha = combine_scalar_factors(alpha, lhs, rhs);
+
+ enum {
+ // FIXME find a way to allow an inner stride on the result if packet_traits<Scalar>::size==1
+ // on, the other hand it is good for the cache to pack the vector anyways...
+ DirectlyUseRhs = ActualRhsTypeCleaned::InnerStrideAtCompileTime==1 || ActualRhsTypeCleaned::MaxSizeAtCompileTime==0
+ };
+
+ gemv_static_vector_if<RhsScalar,ActualRhsTypeCleaned::SizeAtCompileTime,ActualRhsTypeCleaned::MaxSizeAtCompileTime,!DirectlyUseRhs> static_rhs;
+
+ ei_declare_aligned_stack_constructed_variable(RhsScalar,actualRhsPtr,actualRhs.size(),
+ DirectlyUseRhs ? const_cast<RhsScalar*>(actualRhs.data()) : static_rhs.data());
+
+ if(!DirectlyUseRhs)
+ {
+ #ifdef EIGEN_DENSE_STORAGE_CTOR_PLUGIN
+ Index size = actualRhs.size();
+ EIGEN_DENSE_STORAGE_CTOR_PLUGIN
+ #endif
+ Map<typename ActualRhsTypeCleaned::PlainObject>(actualRhsPtr, actualRhs.size()) = actualRhs;
+ }
+
+ typedef const_blas_data_mapper<LhsScalar,Index,RowMajor> LhsMapper;
+ typedef const_blas_data_mapper<RhsScalar,Index,ColMajor> RhsMapper;
+ general_matrix_vector_product
+ <Index,LhsScalar,LhsMapper,RowMajor,LhsBlasTraits::NeedToConjugate,RhsScalar,RhsMapper,RhsBlasTraits::NeedToConjugate>::run(
+ actualLhs.rows(), actualLhs.cols(),
+ LhsMapper(actualLhs.data(), actualLhs.outerStride()),
+ RhsMapper(actualRhsPtr, 1),
+ dest.data(), dest.col(0).innerStride(), //NOTE if dest is not a vector at compile-time, then dest.innerStride() might be wrong. (bug 1166)
+ actualAlpha);
+ }
+};
+
+template<> struct gemv_dense_selector<OnTheRight,ColMajor,false>
+{
+ template<typename Lhs, typename Rhs, typename Dest>
+ static void run(const Lhs &lhs, const Rhs &rhs, Dest& dest, const typename Dest::Scalar& alpha)
+ {
+ EIGEN_STATIC_ASSERT((!nested_eval<Lhs,1>::Evaluate),EIGEN_INTERNAL_COMPILATION_ERROR_OR_YOU_MADE_A_PROGRAMMING_MISTAKE);
+ // TODO if rhs is large enough it might be beneficial to make sure that dest is sequentially stored in memory, otherwise use a temp
+ typename nested_eval<Rhs,1>::type actual_rhs(rhs);
+ const Index size = rhs.rows();
+ for(Index k=0; k<size; ++k)
+ dest += (alpha*actual_rhs.coeff(k)) * lhs.col(k);
+ }
+};
+
+template<> struct gemv_dense_selector<OnTheRight,RowMajor,false>
+{
+ template<typename Lhs, typename Rhs, typename Dest>
+ static void run(const Lhs &lhs, const Rhs &rhs, Dest& dest, const typename Dest::Scalar& alpha)
+ {
+ EIGEN_STATIC_ASSERT((!nested_eval<Lhs,1>::Evaluate),EIGEN_INTERNAL_COMPILATION_ERROR_OR_YOU_MADE_A_PROGRAMMING_MISTAKE);
+ typename nested_eval<Rhs,Lhs::RowsAtCompileTime>::type actual_rhs(rhs);
+ const Index rows = dest.rows();
+ for(Index i=0; i<rows; ++i)
+ dest.coeffRef(i) += alpha * (lhs.row(i).cwiseProduct(actual_rhs.transpose())).sum();
+ }
+};
+
+} // end namespace internal
+
+/***************************************************************************
+* Implementation of matrix base methods
+***************************************************************************/
+
+/** \returns the matrix product of \c *this and \a other.
+ *
+ * \note If instead of the matrix product you want the coefficient-wise product, see Cwise::operator*().
+ *
+ * \sa lazyProduct(), operator*=(const MatrixBase&), Cwise::operator*()
+ */
+template<typename Derived>
+template<typename OtherDerived>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+const Product<Derived, OtherDerived>
+MatrixBase<Derived>::operator*(const MatrixBase<OtherDerived> &other) const
+{
+ // A note regarding the function declaration: In MSVC, this function will sometimes
+ // not be inlined since DenseStorage is an unwindable object for dynamic
+ // matrices and product types are holding a member to store the result.
+ // Thus it does not help tagging this function with EIGEN_STRONG_INLINE.
+ enum {
+ ProductIsValid = Derived::ColsAtCompileTime==Dynamic
+ || OtherDerived::RowsAtCompileTime==Dynamic
+ || int(Derived::ColsAtCompileTime)==int(OtherDerived::RowsAtCompileTime),
+ AreVectors = Derived::IsVectorAtCompileTime && OtherDerived::IsVectorAtCompileTime,
+ SameSizes = EIGEN_PREDICATE_SAME_MATRIX_SIZE(Derived,OtherDerived)
+ };
+ // note to the lost user:
+ // * for a dot product use: v1.dot(v2)
+ // * for a coeff-wise product use: v1.cwiseProduct(v2)
+ EIGEN_STATIC_ASSERT(ProductIsValid || !(AreVectors && SameSizes),
+ INVALID_VECTOR_VECTOR_PRODUCT__IF_YOU_WANTED_A_DOT_OR_COEFF_WISE_PRODUCT_YOU_MUST_USE_THE_EXPLICIT_FUNCTIONS)
+ EIGEN_STATIC_ASSERT(ProductIsValid || !(SameSizes && !AreVectors),
+ INVALID_MATRIX_PRODUCT__IF_YOU_WANTED_A_COEFF_WISE_PRODUCT_YOU_MUST_USE_THE_EXPLICIT_FUNCTION)
+ EIGEN_STATIC_ASSERT(ProductIsValid || SameSizes, INVALID_MATRIX_PRODUCT)
+#ifdef EIGEN_DEBUG_PRODUCT
+ internal::product_type<Derived,OtherDerived>::debug();
+#endif
+
+ return Product<Derived, OtherDerived>(derived(), other.derived());
+}
+
+/** \returns an expression of the matrix product of \c *this and \a other without implicit evaluation.
+ *
+ * The returned product will behave like any other expressions: the coefficients of the product will be
+ * computed once at a time as requested. This might be useful in some extremely rare cases when only
+ * a small and no coherent fraction of the result's coefficients have to be computed.
+ *
+ * \warning This version of the matrix product can be much much slower. So use it only if you know
+ * what you are doing and that you measured a true speed improvement.
+ *
+ * \sa operator*(const MatrixBase&)
+ */
+template<typename Derived>
+template<typename OtherDerived>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+const Product<Derived,OtherDerived,LazyProduct>
+MatrixBase<Derived>::lazyProduct(const MatrixBase<OtherDerived> &other) const
+{
+ enum {
+ ProductIsValid = Derived::ColsAtCompileTime==Dynamic
+ || OtherDerived::RowsAtCompileTime==Dynamic
+ || int(Derived::ColsAtCompileTime)==int(OtherDerived::RowsAtCompileTime),
+ AreVectors = Derived::IsVectorAtCompileTime && OtherDerived::IsVectorAtCompileTime,
+ SameSizes = EIGEN_PREDICATE_SAME_MATRIX_SIZE(Derived,OtherDerived)
+ };
+ // note to the lost user:
+ // * for a dot product use: v1.dot(v2)
+ // * for a coeff-wise product use: v1.cwiseProduct(v2)
+ EIGEN_STATIC_ASSERT(ProductIsValid || !(AreVectors && SameSizes),
+ INVALID_VECTOR_VECTOR_PRODUCT__IF_YOU_WANTED_A_DOT_OR_COEFF_WISE_PRODUCT_YOU_MUST_USE_THE_EXPLICIT_FUNCTIONS)
+ EIGEN_STATIC_ASSERT(ProductIsValid || !(SameSizes && !AreVectors),
+ INVALID_MATRIX_PRODUCT__IF_YOU_WANTED_A_COEFF_WISE_PRODUCT_YOU_MUST_USE_THE_EXPLICIT_FUNCTION)
+ EIGEN_STATIC_ASSERT(ProductIsValid || SameSizes, INVALID_MATRIX_PRODUCT)
+
+ return Product<Derived,OtherDerived,LazyProduct>(derived(), other.derived());
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_PRODUCT_H
diff --git a/Eigen/src/Core/GenericPacketMath.h b/Eigen/src/Core/GenericPacketMath.h
new file mode 100644
index 0000000..b67c4ed
--- /dev/null
+++ b/Eigen/src/Core/GenericPacketMath.h
@@ -0,0 +1,1198 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_GENERIC_PACKET_MATH_H
+#define EIGEN_GENERIC_PACKET_MATH_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+
+/** \internal
+ * \file GenericPacketMath.h
+ *
+ * Default implementation for types not supported by the vectorization.
+ * In practice these functions are provided to make easier the writing
+ * of generic vectorized code.
+ */
+
+#ifndef EIGEN_DEBUG_ALIGNED_LOAD
+#define EIGEN_DEBUG_ALIGNED_LOAD
+#endif
+
+#ifndef EIGEN_DEBUG_UNALIGNED_LOAD
+#define EIGEN_DEBUG_UNALIGNED_LOAD
+#endif
+
+#ifndef EIGEN_DEBUG_ALIGNED_STORE
+#define EIGEN_DEBUG_ALIGNED_STORE
+#endif
+
+#ifndef EIGEN_DEBUG_UNALIGNED_STORE
+#define EIGEN_DEBUG_UNALIGNED_STORE
+#endif
+
+struct default_packet_traits
+{
+ enum {
+ HasHalfPacket = 0,
+
+ HasAdd = 1,
+ HasSub = 1,
+ HasShift = 1,
+ HasMul = 1,
+ HasNegate = 1,
+ HasAbs = 1,
+ HasArg = 0,
+ HasAbs2 = 1,
+ HasAbsDiff = 0,
+ HasMin = 1,
+ HasMax = 1,
+ HasConj = 1,
+ HasSetLinear = 1,
+ HasSign = 1,
+ HasBlend = 0,
+ // This flag is used to indicate whether packet comparison is supported.
+ // pcmp_eq, pcmp_lt and pcmp_le should be defined for it to be true.
+ HasCmp = 0,
+
+ HasDiv = 0,
+ HasReciprocal = 0,
+ HasSqrt = 0,
+ HasRsqrt = 0,
+ HasExp = 0,
+ HasExpm1 = 0,
+ HasLog = 0,
+ HasLog1p = 0,
+ HasLog10 = 0,
+ HasPow = 0,
+
+ HasSin = 0,
+ HasCos = 0,
+ HasTan = 0,
+ HasASin = 0,
+ HasACos = 0,
+ HasATan = 0,
+ HasSinh = 0,
+ HasCosh = 0,
+ HasTanh = 0,
+ HasLGamma = 0,
+ HasDiGamma = 0,
+ HasZeta = 0,
+ HasPolygamma = 0,
+ HasErf = 0,
+ HasErfc = 0,
+ HasNdtri = 0,
+ HasBessel = 0,
+ HasIGamma = 0,
+ HasIGammaDerA = 0,
+ HasGammaSampleDerAlpha = 0,
+ HasIGammac = 0,
+ HasBetaInc = 0,
+
+ HasRound = 0,
+ HasRint = 0,
+ HasFloor = 0,
+ HasCeil = 0
+ };
+};
+
+template<typename T> struct packet_traits : default_packet_traits
+{
+ typedef T type;
+ typedef T half;
+ enum {
+ Vectorizable = 0,
+ size = 1,
+ AlignedOnScalar = 0,
+ HasHalfPacket = 0
+ };
+ enum {
+ HasAdd = 0,
+ HasSub = 0,
+ HasMul = 0,
+ HasNegate = 0,
+ HasAbs = 0,
+ HasAbs2 = 0,
+ HasMin = 0,
+ HasMax = 0,
+ HasConj = 0,
+ HasSetLinear = 0
+ };
+};
+
+template<typename T> struct packet_traits<const T> : packet_traits<T> { };
+
+template<typename T> struct unpacket_traits
+{
+ typedef T type;
+ typedef T half;
+ enum
+ {
+ size = 1,
+ alignment = 1,
+ vectorizable = false,
+ masked_load_available=false,
+ masked_store_available=false
+ };
+};
+
+template<typename T> struct unpacket_traits<const T> : unpacket_traits<T> { };
+
+template <typename Src, typename Tgt> struct type_casting_traits {
+ enum {
+ VectorizedCast = 0,
+ SrcCoeffRatio = 1,
+ TgtCoeffRatio = 1
+ };
+};
+
+/** \internal Wrapper to ensure that multiple packet types can map to the same
+ same underlying vector type. */
+template<typename T, int unique_id = 0>
+struct eigen_packet_wrapper
+{
+ EIGEN_ALWAYS_INLINE operator T&() { return m_val; }
+ EIGEN_ALWAYS_INLINE operator const T&() const { return m_val; }
+ EIGEN_ALWAYS_INLINE eigen_packet_wrapper() = default;
+ EIGEN_ALWAYS_INLINE eigen_packet_wrapper(const T &v) : m_val(v) {}
+ EIGEN_ALWAYS_INLINE eigen_packet_wrapper& operator=(const T &v) {
+ m_val = v;
+ return *this;
+ }
+
+ T m_val;
+};
+
+
+/** \internal A convenience utility for determining if the type is a scalar.
+ * This is used to enable some generic packet implementations.
+ */
+template<typename Packet>
+struct is_scalar {
+ using Scalar = typename unpacket_traits<Packet>::type;
+ enum {
+ value = internal::is_same<Packet, Scalar>::value
+ };
+};
+
+/** \internal \returns static_cast<TgtType>(a) (coeff-wise) */
+template <typename SrcPacket, typename TgtPacket>
+EIGEN_DEVICE_FUNC inline TgtPacket
+pcast(const SrcPacket& a) {
+ return static_cast<TgtPacket>(a);
+}
+template <typename SrcPacket, typename TgtPacket>
+EIGEN_DEVICE_FUNC inline TgtPacket
+pcast(const SrcPacket& a, const SrcPacket& /*b*/) {
+ return static_cast<TgtPacket>(a);
+}
+template <typename SrcPacket, typename TgtPacket>
+EIGEN_DEVICE_FUNC inline TgtPacket
+pcast(const SrcPacket& a, const SrcPacket& /*b*/, const SrcPacket& /*c*/, const SrcPacket& /*d*/) {
+ return static_cast<TgtPacket>(a);
+}
+template <typename SrcPacket, typename TgtPacket>
+EIGEN_DEVICE_FUNC inline TgtPacket
+pcast(const SrcPacket& a, const SrcPacket& /*b*/, const SrcPacket& /*c*/, const SrcPacket& /*d*/,
+ const SrcPacket& /*e*/, const SrcPacket& /*f*/, const SrcPacket& /*g*/, const SrcPacket& /*h*/) {
+ return static_cast<TgtPacket>(a);
+}
+
+/** \internal \returns reinterpret_cast<Target>(a) */
+template <typename Target, typename Packet>
+EIGEN_DEVICE_FUNC inline Target
+preinterpret(const Packet& a); /* { return reinterpret_cast<const Target&>(a); } */
+
+/** \internal \returns a + b (coeff-wise) */
+template<typename Packet> EIGEN_DEVICE_FUNC inline Packet
+padd(const Packet& a, const Packet& b) { return a+b; }
+// Avoid compiler warning for boolean algebra.
+template<> EIGEN_DEVICE_FUNC inline bool
+padd(const bool& a, const bool& b) { return a || b; }
+
+/** \internal \returns a packet version of \a *from, (un-aligned masked add)
+ * There is no generic implementation. We only have implementations for specialized
+ * cases. Generic case should not be called.
+ */
+template<typename Packet> EIGEN_DEVICE_FUNC inline
+std::enable_if_t<unpacket_traits<Packet>::masked_fpops_available, Packet>
+padd(const Packet& a, const Packet& b, typename unpacket_traits<Packet>::mask_t umask);
+
+
+/** \internal \returns a - b (coeff-wise) */
+template<typename Packet> EIGEN_DEVICE_FUNC inline Packet
+psub(const Packet& a, const Packet& b) { return a-b; }
+
+/** \internal \returns -a (coeff-wise) */
+template<typename Packet> EIGEN_DEVICE_FUNC inline Packet
+pnegate(const Packet& a) { return -a; }
+
+template<> EIGEN_DEVICE_FUNC inline bool
+pnegate(const bool& a) { return !a; }
+
+/** \internal \returns conj(a) (coeff-wise) */
+template<typename Packet> EIGEN_DEVICE_FUNC inline Packet
+pconj(const Packet& a) { return numext::conj(a); }
+
+/** \internal \returns a * b (coeff-wise) */
+template<typename Packet> EIGEN_DEVICE_FUNC inline Packet
+pmul(const Packet& a, const Packet& b) { return a*b; }
+// Avoid compiler warning for boolean algebra.
+template<> EIGEN_DEVICE_FUNC inline bool
+pmul(const bool& a, const bool& b) { return a && b; }
+
+/** \internal \returns a / b (coeff-wise) */
+template<typename Packet> EIGEN_DEVICE_FUNC inline Packet
+pdiv(const Packet& a, const Packet& b) { return a/b; }
+
+// In the generic case, memset to all one bits.
+template<typename Packet, typename EnableIf = void>
+struct ptrue_impl {
+ static EIGEN_DEVICE_FUNC inline Packet run(const Packet& /*a*/){
+ Packet b;
+ memset(static_cast<void*>(&b), 0xff, sizeof(Packet));
+ return b;
+ }
+};
+
+// For non-trivial scalars, set to Scalar(1) (i.e. a non-zero value).
+// Although this is technically not a valid bitmask, the scalar path for pselect
+// uses a comparison to zero, so this should still work in most cases. We don't
+// have another option, since the scalar type requires initialization.
+template<typename T>
+struct ptrue_impl<T,
+ std::enable_if_t<is_scalar<T>::value && NumTraits<T>::RequireInitialization> > {
+ static EIGEN_DEVICE_FUNC inline T run(const T& /*a*/){
+ return T(1);
+ }
+};
+
+/** \internal \returns one bits. */
+template<typename Packet> EIGEN_DEVICE_FUNC inline Packet
+ptrue(const Packet& a) {
+ return ptrue_impl<Packet>::run(a);
+}
+
+// In the general case, memset to zero.
+template<typename Packet, typename EnableIf = void>
+struct pzero_impl {
+ static EIGEN_DEVICE_FUNC inline Packet run(const Packet& /*a*/) {
+ Packet b;
+ memset(static_cast<void*>(&b), 0x00, sizeof(Packet));
+ return b;
+ }
+};
+
+// For scalars, explicitly set to Scalar(0), since the underlying representation
+// for zero may not consist of all-zero bits.
+template<typename T>
+struct pzero_impl<T,
+ std::enable_if_t<is_scalar<T>::value>> {
+ static EIGEN_DEVICE_FUNC inline T run(const T& /*a*/) {
+ return T(0);
+ }
+};
+
+/** \internal \returns packet of zeros */
+template<typename Packet> EIGEN_DEVICE_FUNC inline Packet
+pzero(const Packet& a) {
+ return pzero_impl<Packet>::run(a);
+}
+
+/** \internal \returns a <= b as a bit mask */
+template<typename Packet> EIGEN_DEVICE_FUNC inline Packet
+pcmp_le(const Packet& a, const Packet& b) { return a<=b ? ptrue(a) : pzero(a); }
+
+/** \internal \returns a < b as a bit mask */
+template<typename Packet> EIGEN_DEVICE_FUNC inline Packet
+pcmp_lt(const Packet& a, const Packet& b) { return a<b ? ptrue(a) : pzero(a); }
+
+/** \internal \returns a == b as a bit mask */
+template<typename Packet> EIGEN_DEVICE_FUNC inline Packet
+pcmp_eq(const Packet& a, const Packet& b) { return a==b ? ptrue(a) : pzero(a); }
+
+/** \internal \returns a < b or a==NaN or b==NaN as a bit mask */
+template<typename Packet> EIGEN_DEVICE_FUNC inline Packet
+pcmp_lt_or_nan(const Packet& a, const Packet& b) { return a>=b ? pzero(a) : ptrue(a); }
+
+template<typename T>
+struct bit_and {
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR EIGEN_ALWAYS_INLINE T operator()(const T& a, const T& b) const {
+ return a & b;
+ }
+};
+
+template<typename T>
+struct bit_or {
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR EIGEN_ALWAYS_INLINE T operator()(const T& a, const T& b) const {
+ return a | b;
+ }
+};
+
+template<typename T>
+struct bit_xor {
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR EIGEN_ALWAYS_INLINE T operator()(const T& a, const T& b) const {
+ return a ^ b;
+ }
+};
+
+template<typename T>
+struct bit_not {
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR EIGEN_ALWAYS_INLINE T operator()(const T& a) const {
+ return ~a;
+ }
+};
+
+// Use operators &, |, ^, ~.
+template<typename T>
+struct operator_bitwise_helper {
+ EIGEN_DEVICE_FUNC static inline T bitwise_and(const T& a, const T& b) { return bit_and<T>()(a, b); }
+ EIGEN_DEVICE_FUNC static inline T bitwise_or(const T& a, const T& b) { return bit_or<T>()(a, b); }
+ EIGEN_DEVICE_FUNC static inline T bitwise_xor(const T& a, const T& b) { return bit_xor<T>()(a, b); }
+ EIGEN_DEVICE_FUNC static inline T bitwise_not(const T& a) { return bit_not<T>()(a); }
+};
+
+// Apply binary operations byte-by-byte
+template<typename T>
+struct bytewise_bitwise_helper {
+ EIGEN_DEVICE_FUNC static inline T bitwise_and(const T& a, const T& b) {
+ return binary(a, b, bit_and<unsigned char>());
+ }
+ EIGEN_DEVICE_FUNC static inline T bitwise_or(const T& a, const T& b) {
+ return binary(a, b, bit_or<unsigned char>());
+ }
+ EIGEN_DEVICE_FUNC static inline T bitwise_xor(const T& a, const T& b) {
+ return binary(a, b, bit_xor<unsigned char>());
+ }
+ EIGEN_DEVICE_FUNC static inline T bitwise_not(const T& a) {
+ return unary(a,bit_not<unsigned char>());
+ }
+
+ private:
+ template<typename Op>
+ EIGEN_DEVICE_FUNC static inline T unary(const T& a, Op op) {
+ const unsigned char* a_ptr = reinterpret_cast<const unsigned char*>(&a);
+ T c;
+ unsigned char* c_ptr = reinterpret_cast<unsigned char*>(&c);
+ for (size_t i = 0; i < sizeof(T); ++i) {
+ *c_ptr++ = op(*a_ptr++);
+ }
+ return c;
+ }
+
+ template<typename Op>
+ EIGEN_DEVICE_FUNC static inline T binary(const T& a, const T& b, Op op) {
+ const unsigned char* a_ptr = reinterpret_cast<const unsigned char*>(&a);
+ const unsigned char* b_ptr = reinterpret_cast<const unsigned char*>(&b);
+ T c;
+ unsigned char* c_ptr = reinterpret_cast<unsigned char*>(&c);
+ for (size_t i = 0; i < sizeof(T); ++i) {
+ *c_ptr++ = op(*a_ptr++, *b_ptr++);
+ }
+ return c;
+ }
+};
+
+// In the general case, use byte-by-byte manipulation.
+template<typename T, typename EnableIf = void>
+struct bitwise_helper : public bytewise_bitwise_helper<T> {};
+
+// For integers or non-trivial scalars, use binary operators.
+template<typename T>
+struct bitwise_helper<T,
+ typename std::enable_if_t<
+ is_scalar<T>::value && (NumTraits<T>::IsInteger || NumTraits<T>::RequireInitialization)>
+ > : public operator_bitwise_helper<T> {};
+
+/** \internal \returns the bitwise and of \a a and \a b */
+template<typename Packet> EIGEN_DEVICE_FUNC inline Packet
+pand(const Packet& a, const Packet& b) {
+ return bitwise_helper<Packet>::bitwise_and(a, b);
+}
+
+/** \internal \returns the bitwise or of \a a and \a b */
+template<typename Packet> EIGEN_DEVICE_FUNC inline Packet
+por(const Packet& a, const Packet& b) {
+ return bitwise_helper<Packet>::bitwise_or(a, b);
+}
+
+/** \internal \returns the bitwise xor of \a a and \a b */
+template<typename Packet> EIGEN_DEVICE_FUNC inline Packet
+pxor(const Packet& a, const Packet& b) {
+ return bitwise_helper<Packet>::bitwise_xor(a, b);
+}
+
+/** \internal \returns the bitwise not of \a a */
+template<typename Packet> EIGEN_DEVICE_FUNC inline Packet
+pnot(const Packet& a) {
+ return bitwise_helper<Packet>::bitwise_not(a);
+}
+
+/** \internal \returns the bitwise and of \a a and not \a b */
+template<typename Packet> EIGEN_DEVICE_FUNC inline Packet
+pandnot(const Packet& a, const Packet& b) { return pand(a, pnot(b)); }
+
+// In the general case, use bitwise select.
+template<typename Packet, typename EnableIf = void>
+struct pselect_impl {
+ static EIGEN_DEVICE_FUNC inline Packet run(const Packet& mask, const Packet& a, const Packet& b) {
+ return por(pand(a,mask),pandnot(b,mask));
+ }
+};
+
+// For scalars, use ternary select.
+template<typename Packet>
+struct pselect_impl<Packet,
+ std::enable_if_t<is_scalar<Packet>::value> > {
+ static EIGEN_DEVICE_FUNC inline Packet run(const Packet& mask, const Packet& a, const Packet& b) {
+ return numext::equal_strict(mask, Packet(0)) ? b : a;
+ }
+};
+
+/** \internal \returns \a or \b for each field in packet according to \mask */
+template<typename Packet> EIGEN_DEVICE_FUNC inline Packet
+pselect(const Packet& mask, const Packet& a, const Packet& b) {
+ return pselect_impl<Packet>::run(mask, a, b);
+}
+
+template<> EIGEN_DEVICE_FUNC inline bool pselect<bool>(
+ const bool& cond, const bool& a, const bool& b) {
+ return cond ? a : b;
+}
+
+/** \internal \returns the min or of \a a and \a b (coeff-wise)
+ If either \a a or \a b are NaN, the result is implementation defined. */
+template<int NaNPropagation>
+struct pminmax_impl {
+ template <typename Packet, typename Op>
+ static EIGEN_DEVICE_FUNC inline Packet run(const Packet& a, const Packet& b, Op op) {
+ return op(a,b);
+ }
+};
+
+/** \internal \returns the min or max of \a a and \a b (coeff-wise)
+ If either \a a or \a b are NaN, NaN is returned. */
+template<>
+struct pminmax_impl<PropagateNaN> {
+ template <typename Packet, typename Op>
+ static EIGEN_DEVICE_FUNC inline Packet run(const Packet& a, const Packet& b, Op op) {
+ Packet not_nan_mask_a = pcmp_eq(a, a);
+ Packet not_nan_mask_b = pcmp_eq(b, b);
+ return pselect(not_nan_mask_a,
+ pselect(not_nan_mask_b, op(a, b), b),
+ a);
+ }
+};
+
+/** \internal \returns the min or max of \a a and \a b (coeff-wise)
+ If both \a a and \a b are NaN, NaN is returned.
+ Equivalent to std::fmin(a, b). */
+template<>
+struct pminmax_impl<PropagateNumbers> {
+ template <typename Packet, typename Op>
+ static EIGEN_DEVICE_FUNC inline Packet run(const Packet& a, const Packet& b, Op op) {
+ Packet not_nan_mask_a = pcmp_eq(a, a);
+ Packet not_nan_mask_b = pcmp_eq(b, b);
+ return pselect(not_nan_mask_a,
+ pselect(not_nan_mask_b, op(a, b), a),
+ b);
+ }
+};
+
+
+#ifndef SYCL_DEVICE_ONLY
+#define EIGEN_BINARY_OP_NAN_PROPAGATION(Type, Func) Func
+#else
+#define EIGEN_BINARY_OP_NAN_PROPAGATION(Type, Func) \
+[](const Type& a, const Type& b) { \
+ return Func(a, b);}
+#endif
+
+/** \internal \returns the min of \a a and \a b (coeff-wise).
+ If \a a or \b b is NaN, the return value is implementation defined. */
+template<typename Packet> EIGEN_DEVICE_FUNC inline Packet
+pmin(const Packet& a, const Packet& b) { return numext::mini(a,b); }
+
+/** \internal \returns the min of \a a and \a b (coeff-wise).
+ NaNPropagation determines the NaN propagation semantics. */
+template <int NaNPropagation, typename Packet>
+EIGEN_DEVICE_FUNC inline Packet pmin(const Packet& a, const Packet& b) {
+ return pminmax_impl<NaNPropagation>::run(a, b, EIGEN_BINARY_OP_NAN_PROPAGATION(Packet, (pmin<Packet>)));
+}
+
+/** \internal \returns the max of \a a and \a b (coeff-wise)
+ If \a a or \b b is NaN, the return value is implementation defined. */
+template<typename Packet> EIGEN_DEVICE_FUNC inline Packet
+pmax(const Packet& a, const Packet& b) { return numext::maxi(a, b); }
+
+/** \internal \returns the max of \a a and \a b (coeff-wise).
+ NaNPropagation determines the NaN propagation semantics. */
+template <int NaNPropagation, typename Packet>
+EIGEN_DEVICE_FUNC inline Packet pmax(const Packet& a, const Packet& b) {
+ return pminmax_impl<NaNPropagation>::run(a, b, EIGEN_BINARY_OP_NAN_PROPAGATION(Packet,(pmax<Packet>)));
+}
+
+/** \internal \returns the absolute value of \a a */
+template<typename Packet> EIGEN_DEVICE_FUNC inline Packet
+pabs(const Packet& a) { return numext::abs(a); }
+template<> EIGEN_DEVICE_FUNC inline unsigned int
+pabs(const unsigned int& a) { return a; }
+template<> EIGEN_DEVICE_FUNC inline unsigned long
+pabs(const unsigned long& a) { return a; }
+template<> EIGEN_DEVICE_FUNC inline unsigned long long
+pabs(const unsigned long long& a) { return a; }
+
+/** \internal \returns the addsub value of \a a,b */
+template<typename Packet> EIGEN_DEVICE_FUNC inline Packet
+paddsub(const Packet& a, const Packet& b) {
+ return pselect(peven_mask(a), padd(a, b), psub(a, b));
+ }
+
+/** \internal \returns the phase angle of \a a */
+template<typename Packet> EIGEN_DEVICE_FUNC inline Packet
+parg(const Packet& a) { using numext::arg; return arg(a); }
+
+
+/** \internal \returns \a a logically shifted by N bits to the right */
+template<int N> EIGEN_DEVICE_FUNC inline int
+parithmetic_shift_right(const int& a) { return a >> N; }
+template<int N> EIGEN_DEVICE_FUNC inline long int
+parithmetic_shift_right(const long int& a) { return a >> N; }
+
+/** \internal \returns \a a arithmetically shifted by N bits to the right */
+template<int N> EIGEN_DEVICE_FUNC inline int
+plogical_shift_right(const int& a) { return static_cast<int>(static_cast<unsigned int>(a) >> N); }
+template<int N> EIGEN_DEVICE_FUNC inline long int
+plogical_shift_right(const long int& a) { return static_cast<long>(static_cast<unsigned long>(a) >> N); }
+
+/** \internal \returns \a a shifted by N bits to the left */
+template<int N> EIGEN_DEVICE_FUNC inline int
+plogical_shift_left(const int& a) { return a << N; }
+template<int N> EIGEN_DEVICE_FUNC inline long int
+plogical_shift_left(const long int& a) { return a << N; }
+
+/** \internal \returns the significant and exponent of the underlying floating point numbers
+ * See https://en.cppreference.com/w/cpp/numeric/math/frexp
+ */
+template <typename Packet>
+EIGEN_DEVICE_FUNC inline Packet pfrexp(const Packet& a, Packet& exponent) {
+ int exp;
+ EIGEN_USING_STD(frexp);
+ Packet result = static_cast<Packet>(frexp(a, &exp));
+ exponent = static_cast<Packet>(exp);
+ return result;
+}
+
+/** \internal \returns a * 2^((int)exponent)
+ * See https://en.cppreference.com/w/cpp/numeric/math/ldexp
+ */
+template<typename Packet> EIGEN_DEVICE_FUNC inline Packet
+pldexp(const Packet &a, const Packet &exponent) {
+ EIGEN_USING_STD(ldexp)
+ return static_cast<Packet>(ldexp(a, static_cast<int>(exponent)));
+}
+
+/** \internal \returns the min of \a a and \a b (coeff-wise) */
+template<typename Packet> EIGEN_DEVICE_FUNC inline Packet
+pabsdiff(const Packet& a, const Packet& b) { return pselect(pcmp_lt(a, b), psub(b, a), psub(a, b)); }
+
+/** \internal \returns a packet version of \a *from, from must be properly aligned */
+template<typename Packet> EIGEN_DEVICE_FUNC inline Packet
+pload(const typename unpacket_traits<Packet>::type* from) { return *from; }
+
+/** \internal \returns n elements of a packet version of \a *from, from must be properly aligned
+ * offset indicates the starting element in which to load and
+ * offset + n <= unpacket_traits::size
+ * All elements before offset and after the last element loaded will initialized with zero */
+template<typename Packet> EIGEN_DEVICE_FUNC inline Packet
+pload_partial(const typename unpacket_traits<Packet>::type* from, const Index n, const Index offset = 0)
+{
+ const Index packet_size = unpacket_traits<Packet>::size;
+ eigen_assert(n + offset <= packet_size && "number of elements plus offset will read past end of packet");
+ typedef typename unpacket_traits<Packet>::type Scalar;
+ EIGEN_ALIGN_MAX Scalar elements[packet_size] = { Scalar(0) };
+ for (Index i = offset; i < numext::mini(n+offset,packet_size); i++) {
+ elements[i] = from[i-offset];
+ }
+ return pload<Packet>(elements);
+}
+
+/** \internal \returns a packet version of \a *from, (un-aligned load) */
+template<typename Packet> EIGEN_DEVICE_FUNC inline Packet
+ploadu(const typename unpacket_traits<Packet>::type* from) { return *from; }
+
+/** \internal \returns n elements of a packet version of \a *from, (un-aligned load)
+ * All elements after the last element loaded will initialized with zero */
+template<typename Packet> EIGEN_DEVICE_FUNC inline Packet
+ploadu_partial(const typename unpacket_traits<Packet>::type* from, const Index n)
+{
+ const Index packet_size = unpacket_traits<Packet>::size;
+ eigen_assert(n <= packet_size && "number of elements will read past end of packet");
+ typedef typename unpacket_traits<Packet>::type Scalar;
+ EIGEN_ALIGN_MAX Scalar elements[packet_size] = { Scalar(0) };
+ for (Index i = 0; i < numext::mini(n,packet_size); i++) {
+ elements[i] = from[i];
+ }
+ return pload<Packet>(elements);
+}
+
+/** \internal \returns a packet version of \a *from, (un-aligned masked load)
+ * There is no generic implementation. We only have implementations for specialized
+ * cases. Generic case should not be called.
+ */
+template<typename Packet> EIGEN_DEVICE_FUNC inline
+std::enable_if_t<unpacket_traits<Packet>::masked_load_available, Packet>
+ploadu(const typename unpacket_traits<Packet>::type* from, typename unpacket_traits<Packet>::mask_t umask);
+
+/** \internal \returns a packet with constant coefficients \a a, e.g.: (a,a,a,a) */
+template<typename Packet> EIGEN_DEVICE_FUNC inline Packet
+pset1(const typename unpacket_traits<Packet>::type& a) { return a; }
+
+/** \internal \returns a packet with constant coefficients set from bits */
+template<typename Packet,typename BitsType> EIGEN_DEVICE_FUNC inline Packet
+pset1frombits(BitsType a);
+
+/** \internal \returns a packet with constant coefficients \a a[0], e.g.: (a[0],a[0],a[0],a[0]) */
+template<typename Packet> EIGEN_DEVICE_FUNC inline Packet
+pload1(const typename unpacket_traits<Packet>::type *a) { return pset1<Packet>(*a); }
+
+/** \internal \returns a packet with elements of \a *from duplicated.
+ * For instance, for a packet of 8 elements, 4 scalars will be read from \a *from and
+ * duplicated to form: {from[0],from[0],from[1],from[1],from[2],from[2],from[3],from[3]}
+ * Currently, this function is only used for scalar * complex products.
+ */
+template<typename Packet> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet
+ploaddup(const typename unpacket_traits<Packet>::type* from) { return *from; }
+
+/** \internal \returns a packet with elements of \a *from quadrupled.
+ * For instance, for a packet of 8 elements, 2 scalars will be read from \a *from and
+ * replicated to form: {from[0],from[0],from[0],from[0],from[1],from[1],from[1],from[1]}
+ * Currently, this function is only used in matrix products.
+ * For packet-size smaller or equal to 4, this function is equivalent to pload1
+ */
+template<typename Packet> EIGEN_DEVICE_FUNC inline Packet
+ploadquad(const typename unpacket_traits<Packet>::type* from)
+{ return pload1<Packet>(from); }
+
+/** \internal equivalent to
+ * \code
+ * a0 = pload1(a+0);
+ * a1 = pload1(a+1);
+ * a2 = pload1(a+2);
+ * a3 = pload1(a+3);
+ * \endcode
+ * \sa pset1, pload1, ploaddup, pbroadcast2
+ */
+template<typename Packet> EIGEN_DEVICE_FUNC
+inline void pbroadcast4(const typename unpacket_traits<Packet>::type *a,
+ Packet& a0, Packet& a1, Packet& a2, Packet& a3)
+{
+ a0 = pload1<Packet>(a+0);
+ a1 = pload1<Packet>(a+1);
+ a2 = pload1<Packet>(a+2);
+ a3 = pload1<Packet>(a+3);
+}
+
+/** \internal equivalent to
+ * \code
+ * a0 = pload1(a+0);
+ * a1 = pload1(a+1);
+ * \endcode
+ * \sa pset1, pload1, ploaddup, pbroadcast4
+ */
+template<typename Packet> EIGEN_DEVICE_FUNC
+inline void pbroadcast2(const typename unpacket_traits<Packet>::type *a,
+ Packet& a0, Packet& a1)
+{
+ a0 = pload1<Packet>(a+0);
+ a1 = pload1<Packet>(a+1);
+}
+
+/** \internal \brief Returns a packet with coefficients (a,a+1,...,a+packet_size-1). */
+template<typename Packet> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet
+plset(const typename unpacket_traits<Packet>::type& a) { return a; }
+
+/** \internal \returns a packet with constant coefficients \a a, e.g.: (x, 0, x, 0),
+ where x is the value of all 1-bits. */
+template<typename Packet> EIGEN_DEVICE_FUNC inline Packet
+peven_mask(const Packet& /*a*/) {
+ typedef typename unpacket_traits<Packet>::type Scalar;
+ const size_t n = unpacket_traits<Packet>::size;
+ EIGEN_ALIGN_TO_BOUNDARY(sizeof(Packet)) Scalar elements[n];
+ for(size_t i = 0; i < n; ++i) {
+ memset(elements+i, ((i & 1) == 0 ? 0xff : 0), sizeof(Scalar));
+ }
+ return ploadu<Packet>(elements);
+}
+
+
+/** \internal copy the packet \a from to \a *to, \a to must be properly aligned */
+template<typename Scalar, typename Packet> EIGEN_DEVICE_FUNC inline void pstore(Scalar* to, const Packet& from)
+{ (*to) = from; }
+
+/** \internal copy n elements of the packet \a from to \a *to, \a to must be properly aligned
+ * offset indicates the starting element in which to store and
+ * offset + n <= unpacket_traits::size */
+template<typename Scalar, typename Packet> EIGEN_DEVICE_FUNC inline void pstore_partial(Scalar* to, const Packet& from, const Index n, const Index offset = 0)
+{
+ const Index packet_size = unpacket_traits<Packet>::size;
+ eigen_assert(n + offset <= packet_size && "number of elements plus offset will write past end of packet");
+ EIGEN_ALIGN_MAX Scalar elements[packet_size];
+ pstore<Scalar>(elements, from);
+ for (Index i = 0; i < numext::mini(n,packet_size-offset); i++) {
+ to[i] = elements[i + offset];
+ }
+}
+
+/** \internal copy the packet \a from to \a *to, (un-aligned store) */
+template<typename Scalar, typename Packet> EIGEN_DEVICE_FUNC inline void pstoreu(Scalar* to, const Packet& from)
+{ (*to) = from; }
+
+/** \internal copy n elements of the packet \a from to \a *to, (un-aligned store) */
+template<typename Scalar, typename Packet> EIGEN_DEVICE_FUNC inline void pstoreu_partial(Scalar* to, const Packet& from, const Index n)
+{
+ const Index packet_size = unpacket_traits<Packet>::size;
+ eigen_assert(n <= packet_size && "number of elements will write past end of packet");
+ EIGEN_ALIGN_MAX Scalar elements[packet_size];
+ pstore<Scalar>(elements, from);
+ for (Index i = 0; i < numext::mini(n,packet_size); i++) {
+ to[i] = elements[i];
+ }
+}
+
+/** \internal copy the packet \a from to \a *to, (un-aligned store with a mask)
+ * There is no generic implementation. We only have implementations for specialized
+ * cases. Generic case should not be called.
+ */
+template<typename Scalar, typename Packet>
+EIGEN_DEVICE_FUNC inline
+std::enable_if_t<unpacket_traits<Packet>::masked_store_available, void>
+pstoreu(Scalar* to, const Packet& from, typename unpacket_traits<Packet>::mask_t umask);
+
+template<typename Scalar, typename Packet> EIGEN_DEVICE_FUNC inline Packet pgather(const Scalar* from, Index /*stride*/)
+{ return ploadu<Packet>(from); }
+
+template<typename Scalar, typename Packet> EIGEN_DEVICE_FUNC inline Packet pgather_partial(const Scalar* from, Index stride, const Index n)
+{
+ const Index packet_size = unpacket_traits<Packet>::size;
+ EIGEN_ALIGN_MAX Scalar elements[packet_size] = { Scalar(0) };
+ for (Index i = 0; i < numext::mini(n,packet_size); i++) {
+ elements[i] = from[i*stride];
+ }
+ return pload<Packet>(elements);
+}
+
+template<typename Scalar, typename Packet> EIGEN_DEVICE_FUNC inline void pscatter(Scalar* to, const Packet& from, Index /*stride*/)
+{ pstore(to, from); }
+
+template<typename Scalar, typename Packet> EIGEN_DEVICE_FUNC inline void pscatter_partial(Scalar* to, const Packet& from, Index stride, const Index n)
+{
+ const Index packet_size = unpacket_traits<Packet>::size;
+ EIGEN_ALIGN_MAX Scalar elements[packet_size];
+ pstore<Scalar>(elements, from);
+ for (Index i = 0; i < numext::mini(n,packet_size); i++) {
+ to[i*stride] = elements[i];
+ }
+}
+
+/** \internal tries to do cache prefetching of \a addr */
+template<typename Scalar> EIGEN_DEVICE_FUNC inline void prefetch(const Scalar* addr)
+{
+#if defined(EIGEN_HIP_DEVICE_COMPILE)
+ // do nothing
+#elif defined(EIGEN_CUDA_ARCH)
+#if defined(__LP64__) || EIGEN_OS_WIN64
+ // 64-bit pointer operand constraint for inlined asm
+ asm(" prefetch.L1 [ %1 ];" : "=l"(addr) : "l"(addr));
+#else
+ // 32-bit pointer operand constraint for inlined asm
+ asm(" prefetch.L1 [ %1 ];" : "=r"(addr) : "r"(addr));
+#endif
+#elif (!EIGEN_COMP_MSVC) && (EIGEN_COMP_GNUC || EIGEN_COMP_CLANG || EIGEN_COMP_ICC)
+ __builtin_prefetch(addr);
+#endif
+}
+
+/** \internal \returns the reversed elements of \a a*/
+template<typename Packet> EIGEN_DEVICE_FUNC inline Packet preverse(const Packet& a)
+{ return a; }
+
+/** \internal \returns \a a with real and imaginary part flipped (for complex type only) */
+template<typename Packet> EIGEN_DEVICE_FUNC inline Packet pcplxflip(const Packet& a)
+{
+ return Packet(numext::imag(a),numext::real(a));
+}
+
+/**************************
+* Special math functions
+***************************/
+
+/** \internal \returns the sine of \a a (coeff-wise) */
+template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+Packet psin(const Packet& a) { EIGEN_USING_STD(sin); return sin(a); }
+
+/** \internal \returns the cosine of \a a (coeff-wise) */
+template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+Packet pcos(const Packet& a) { EIGEN_USING_STD(cos); return cos(a); }
+
+/** \internal \returns the tan of \a a (coeff-wise) */
+template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+Packet ptan(const Packet& a) { EIGEN_USING_STD(tan); return tan(a); }
+
+/** \internal \returns the arc sine of \a a (coeff-wise) */
+template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+Packet pasin(const Packet& a) { EIGEN_USING_STD(asin); return asin(a); }
+
+/** \internal \returns the arc cosine of \a a (coeff-wise) */
+template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+Packet pacos(const Packet& a) { EIGEN_USING_STD(acos); return acos(a); }
+
+/** \internal \returns the arc tangent of \a a (coeff-wise) */
+template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+Packet patan(const Packet& a) { EIGEN_USING_STD(atan); return atan(a); }
+
+/** \internal \returns the hyperbolic sine of \a a (coeff-wise) */
+template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+Packet psinh(const Packet& a) { EIGEN_USING_STD(sinh); return sinh(a); }
+
+/** \internal \returns the hyperbolic cosine of \a a (coeff-wise) */
+template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+Packet pcosh(const Packet& a) { EIGEN_USING_STD(cosh); return cosh(a); }
+
+/** \internal \returns the hyperbolic tan of \a a (coeff-wise) */
+template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+Packet ptanh(const Packet& a) { EIGEN_USING_STD(tanh); return tanh(a); }
+
+/** \internal \returns the exp of \a a (coeff-wise) */
+template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+Packet pexp(const Packet& a) { EIGEN_USING_STD(exp); return exp(a); }
+
+/** \internal \returns the expm1 of \a a (coeff-wise) */
+template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+Packet pexpm1(const Packet& a) { return numext::expm1(a); }
+
+/** \internal \returns the log of \a a (coeff-wise) */
+template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+Packet plog(const Packet& a) { EIGEN_USING_STD(log); return log(a); }
+
+/** \internal \returns the log1p of \a a (coeff-wise) */
+template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+Packet plog1p(const Packet& a) { return numext::log1p(a); }
+
+/** \internal \returns the log10 of \a a (coeff-wise) */
+template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+Packet plog10(const Packet& a) { EIGEN_USING_STD(log10); return log10(a); }
+
+/** \internal \returns the log10 of \a a (coeff-wise) */
+template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+Packet plog2(const Packet& a) {
+ typedef typename internal::unpacket_traits<Packet>::type Scalar;
+ return pmul(pset1<Packet>(Scalar(EIGEN_LOG2E)), plog(a));
+}
+
+/** \internal \returns the square-root of \a a (coeff-wise) */
+template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+Packet psqrt(const Packet& a) { return numext::sqrt(a); }
+
+/** \internal \returns the rounded value of \a a (coeff-wise) */
+template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+Packet pround(const Packet& a) { using numext::round; return round(a); }
+
+/** \internal \returns the floor of \a a (coeff-wise) */
+template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+Packet pfloor(const Packet& a) { using numext::floor; return floor(a); }
+
+/** \internal \returns the rounded value of \a a (coeff-wise) with current
+ * rounding mode */
+template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+Packet print(const Packet& a) { using numext::rint; return rint(a); }
+
+/** \internal \returns the ceil of \a a (coeff-wise) */
+template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+Packet pceil(const Packet& a) { using numext::ceil; return ceil(a); }
+
+template<typename Packet, typename EnableIf = void>
+struct psign_impl {
+ static EIGEN_DEVICE_FUNC inline Packet run(const Packet& a) {
+ return numext::sign(a);
+ }
+};
+
+/** \internal \returns the sign of \a a (coeff-wise) */
+template<typename Packet> EIGEN_DEVICE_FUNC inline Packet
+psign(const Packet& a) {
+ return psign_impl<Packet>::run(a);
+}
+
+template<> EIGEN_DEVICE_FUNC inline bool
+psign(const bool& a) {
+ return a;
+}
+
+/** \internal \returns the first element of a packet */
+template<typename Packet>
+EIGEN_DEVICE_FUNC inline typename unpacket_traits<Packet>::type
+pfirst(const Packet& a)
+{ return a; }
+
+/** \internal \returns the sum of the elements of upper and lower half of \a a if \a a is larger than 4.
+ * For a packet {a0, a1, a2, a3, a4, a5, a6, a7}, it returns a half packet {a0+a4, a1+a5, a2+a6, a3+a7}
+ * For packet-size smaller or equal to 4, this boils down to a noop.
+ */
+template<typename Packet>
+EIGEN_DEVICE_FUNC inline std::conditional_t<(unpacket_traits<Packet>::size%8)==0,typename unpacket_traits<Packet>::half,Packet>
+predux_half_dowto4(const Packet& a)
+{ return a; }
+
+// Slow generic implementation of Packet reduction.
+template <typename Packet, typename Op>
+EIGEN_DEVICE_FUNC inline typename unpacket_traits<Packet>::type
+predux_helper(const Packet& a, Op op) {
+ typedef typename unpacket_traits<Packet>::type Scalar;
+ const size_t n = unpacket_traits<Packet>::size;
+ EIGEN_ALIGN_TO_BOUNDARY(sizeof(Packet)) Scalar elements[n];
+ pstoreu<Scalar>(elements, a);
+ for(size_t k = n / 2; k > 0; k /= 2) {
+ for(size_t i = 0; i < k; ++i) {
+ elements[i] = op(elements[i], elements[i + k]);
+ }
+ }
+ return elements[0];
+}
+
+/** \internal \returns the sum of the elements of \a a*/
+template<typename Packet>
+EIGEN_DEVICE_FUNC inline typename unpacket_traits<Packet>::type
+predux(const Packet& a)
+{
+ return a;
+}
+
+/** \internal \returns the product of the elements of \a a */
+template <typename Packet>
+EIGEN_DEVICE_FUNC inline typename unpacket_traits<Packet>::type predux_mul(
+ const Packet& a) {
+ typedef typename unpacket_traits<Packet>::type Scalar;
+ return predux_helper(a, EIGEN_BINARY_OP_NAN_PROPAGATION(Scalar, (pmul<Scalar>)));
+}
+
+/** \internal \returns the min of the elements of \a a */
+template <typename Packet>
+EIGEN_DEVICE_FUNC inline typename unpacket_traits<Packet>::type predux_min(
+ const Packet &a) {
+ typedef typename unpacket_traits<Packet>::type Scalar;
+ return predux_helper(a, EIGEN_BINARY_OP_NAN_PROPAGATION(Scalar, (pmin<PropagateFast, Scalar>)));
+}
+
+template <int NaNPropagation, typename Packet>
+EIGEN_DEVICE_FUNC inline typename unpacket_traits<Packet>::type predux_min(
+ const Packet& a) {
+ typedef typename unpacket_traits<Packet>::type Scalar;
+ return predux_helper(a, EIGEN_BINARY_OP_NAN_PROPAGATION(Scalar, (pmin<NaNPropagation, Scalar>)));
+}
+
+/** \internal \returns the min of the elements of \a a */
+template <typename Packet>
+EIGEN_DEVICE_FUNC inline typename unpacket_traits<Packet>::type predux_max(
+ const Packet &a) {
+ typedef typename unpacket_traits<Packet>::type Scalar;
+ return predux_helper(a, EIGEN_BINARY_OP_NAN_PROPAGATION(Scalar, (pmax<PropagateFast, Scalar>)));
+}
+
+template <int NaNPropagation, typename Packet>
+EIGEN_DEVICE_FUNC inline typename unpacket_traits<Packet>::type predux_max(
+ const Packet& a) {
+ typedef typename unpacket_traits<Packet>::type Scalar;
+ return predux_helper(a, EIGEN_BINARY_OP_NAN_PROPAGATION(Scalar, (pmax<NaNPropagation, Scalar>)));
+}
+
+#undef EIGEN_BINARY_OP_NAN_PROPAGATION
+
+/** \internal \returns true if all coeffs of \a a means "true"
+ * It is supposed to be called on values returned by pcmp_*.
+ */
+// not needed yet
+// template<typename Packet> EIGEN_DEVICE_FUNC inline bool predux_all(const Packet& a)
+// { return bool(a); }
+
+/** \internal \returns true if any coeffs of \a a means "true"
+ * It is supposed to be called on values returned by pcmp_*.
+ */
+template<typename Packet> EIGEN_DEVICE_FUNC inline bool predux_any(const Packet& a)
+{
+ // Dirty but generic implementation where "true" is assumed to be non 0 and all the sames.
+ // It is expected that "true" is either:
+ // - Scalar(1)
+ // - bits full of ones (NaN for floats),
+ // - or first bit equals to 1 (1 for ints, smallest denormal for floats).
+ // For all these cases, taking the sum is just fine, and this boils down to a no-op for scalars.
+ typedef typename unpacket_traits<Packet>::type Scalar;
+ return numext::not_equal_strict(predux(a), Scalar(0));
+}
+
+/***************************************************************************
+* The following functions might not have to be overwritten for vectorized types
+***************************************************************************/
+
+// FMA instructions.
+/** \internal \returns a * b + c (coeff-wise) */
+template <typename Packet>
+EIGEN_DEVICE_FUNC inline Packet pmadd(const Packet& a, const Packet& b,
+ const Packet& c) {
+ return padd(pmul(a, b), c);
+}
+
+/** \internal \returns a * b - c (coeff-wise) */
+template <typename Packet>
+EIGEN_DEVICE_FUNC inline Packet pmsub(const Packet& a, const Packet& b,
+ const Packet& c) {
+ return psub(pmul(a, b), c);
+}
+
+/** \internal \returns -(a * b) + c (coeff-wise) */
+template <typename Packet>
+EIGEN_DEVICE_FUNC inline Packet pnmadd(const Packet& a, const Packet& b,
+ const Packet& c) {
+ return padd(pnegate(pmul(a, b)), c);
+}
+
+/** \internal \returns -(a * b) - c (coeff-wise) */
+template <typename Packet>
+EIGEN_DEVICE_FUNC inline Packet pnmsub(const Packet& a, const Packet& b,
+ const Packet& c) {
+ return psub(pnegate(pmul(a, b)), c);
+}
+
+/** \internal copy a packet with constant coefficient \a a (e.g., [a,a,a,a]) to \a *to. \a to must be 16 bytes aligned */
+// NOTE: this function must really be templated on the packet type (think about different packet types for the same scalar type)
+template<typename Packet>
+inline void pstore1(typename unpacket_traits<Packet>::type* to, const typename unpacket_traits<Packet>::type& a)
+{
+ pstore(to, pset1<Packet>(a));
+}
+
+/** \internal \returns a packet version of \a *from.
+ * The pointer \a from must be aligned on a \a Alignment bytes boundary. */
+template<typename Packet, int Alignment>
+EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE Packet ploadt(const typename unpacket_traits<Packet>::type* from)
+{
+ if(Alignment >= unpacket_traits<Packet>::alignment)
+ return pload<Packet>(from);
+ else
+ return ploadu<Packet>(from);
+}
+
+/** \internal \returns n elements of a packet version of \a *from.
+ * The pointer \a from must be aligned on a \a Alignment bytes boundary. */
+template<typename Packet, int Alignment>
+EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE Packet ploadt_partial(const typename unpacket_traits<Packet>::type* from, const Index n, const Index offset = 0)
+{
+ if(Alignment >= unpacket_traits<Packet>::alignment)
+ return pload_partial<Packet>(from, n, offset);
+ else
+ return ploadu_partial<Packet>(from, n);
+}
+
+/** \internal copy the packet \a from to \a *to.
+ * The pointer \a from must be aligned on a \a Alignment bytes boundary. */
+template<typename Scalar, typename Packet, int Alignment>
+EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE void pstoret(Scalar* to, const Packet& from)
+{
+ if(Alignment >= unpacket_traits<Packet>::alignment)
+ pstore(to, from);
+ else
+ pstoreu(to, from);
+}
+
+/** \internal copy n elements of the packet \a from to \a *to.
+ * The pointer \a from must be aligned on a \a Alignment bytes boundary. */
+template<typename Scalar, typename Packet, int Alignment>
+EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE void pstoret_partial(Scalar* to, const Packet& from, const Index n, const Index offset = 0)
+{
+ if(Alignment >= unpacket_traits<Packet>::alignment)
+ pstore_partial(to, from, n, offset);
+ else
+ pstoreu_partial(to, from, n);
+}
+
+/** \internal \returns a packet version of \a *from.
+ * Unlike ploadt, ploadt_ro takes advantage of the read-only memory path on the
+ * hardware if available to speedup the loading of data that won't be modified
+ * by the current computation.
+ */
+template<typename Packet, int LoadMode>
+EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE Packet ploadt_ro(const typename unpacket_traits<Packet>::type* from)
+{
+ return ploadt<Packet, LoadMode>(from);
+}
+
+/***************************************************************************
+* Fast complex products (GCC generates a function call which is very slow)
+***************************************************************************/
+
+// Eigen+CUDA does not support complexes.
+#if !defined(EIGEN_GPUCC)
+
+template<> inline std::complex<float> pmul(const std::complex<float>& a, const std::complex<float>& b)
+{ return std::complex<float>(a.real()*b.real() - a.imag()*b.imag(), a.imag()*b.real() + a.real()*b.imag()); }
+
+template<> inline std::complex<double> pmul(const std::complex<double>& a, const std::complex<double>& b)
+{ return std::complex<double>(a.real()*b.real() - a.imag()*b.imag(), a.imag()*b.real() + a.real()*b.imag()); }
+
+#endif
+
+
+/***************************************************************************
+ * PacketBlock, that is a collection of N packets where the number of words
+ * in the packet is a multiple of N.
+***************************************************************************/
+template <typename Packet,int N=unpacket_traits<Packet>::size> struct PacketBlock {
+ Packet packet[N];
+};
+
+template<typename Packet> EIGEN_DEVICE_FUNC inline void
+ptranspose(PacketBlock<Packet,1>& /*kernel*/) {
+ // Nothing to do in the scalar case, i.e. a 1x1 matrix.
+}
+
+/***************************************************************************
+ * Selector, i.e. vector of N boolean values used to select (i.e. blend)
+ * words from 2 packets.
+***************************************************************************/
+template <size_t N> struct Selector {
+ bool select[N];
+};
+
+template<typename Packet> EIGEN_DEVICE_FUNC inline Packet
+pblend(const Selector<unpacket_traits<Packet>::size>& ifPacket, const Packet& thenPacket, const Packet& elsePacket) {
+ return ifPacket.select[0] ? thenPacket : elsePacket;
+}
+
+/** \internal \returns 1 / a (coeff-wise) */
+template <typename Packet>
+EIGEN_DEVICE_FUNC inline Packet preciprocal(const Packet& a) {
+ using Scalar = typename unpacket_traits<Packet>::type;
+ return pdiv(pset1<Packet>(Scalar(1)), a);
+}
+
+/** \internal \returns the reciprocal square-root of \a a (coeff-wise) */
+template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+Packet prsqrt(const Packet& a) {
+ return preciprocal<Packet>(psqrt(a));
+}
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_GENERIC_PACKET_MATH_H
diff --git a/Eigen/src/Core/GlobalFunctions.h b/Eigen/src/Core/GlobalFunctions.h
new file mode 100644
index 0000000..18792cb
--- /dev/null
+++ b/Eigen/src/Core/GlobalFunctions.h
@@ -0,0 +1,212 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2010-2016 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2010 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_GLOBAL_FUNCTIONS_H
+#define EIGEN_GLOBAL_FUNCTIONS_H
+
+#ifdef EIGEN_PARSED_BY_DOXYGEN
+
+#define EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(NAME,FUNCTOR,DOC_OP,DOC_DETAILS) \
+ /** \returns an expression of the coefficient-wise DOC_OP of \a x
+
+ DOC_DETAILS
+
+ \sa <a href="group__CoeffwiseMathFunctions.html#cwisetable_##NAME">Math functions</a>, class CwiseUnaryOp
+ */ \
+ template<typename Derived> \
+ inline const Eigen::CwiseUnaryOp<Eigen::internal::FUNCTOR<typename Derived::Scalar>, const Derived> \
+ NAME(const Eigen::ArrayBase<Derived>& x);
+
+#else
+
+#define EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(NAME,FUNCTOR,DOC_OP,DOC_DETAILS) \
+ template<typename Derived> \
+ inline const Eigen::CwiseUnaryOp<Eigen::internal::FUNCTOR<typename Derived::Scalar>, const Derived> \
+ (NAME)(const Eigen::ArrayBase<Derived>& x) { \
+ return Eigen::CwiseUnaryOp<Eigen::internal::FUNCTOR<typename Derived::Scalar>, const Derived>(x.derived()); \
+ }
+
+#endif // EIGEN_PARSED_BY_DOXYGEN
+
+#define EIGEN_ARRAY_DECLARE_GLOBAL_EIGEN_UNARY(NAME,FUNCTOR) \
+ \
+ template<typename Derived> \
+ struct NAME##_retval<ArrayBase<Derived> > \
+ { \
+ typedef const Eigen::CwiseUnaryOp<Eigen::internal::FUNCTOR<typename Derived::Scalar>, const Derived> type; \
+ }; \
+ template<typename Derived> \
+ struct NAME##_impl<ArrayBase<Derived> > \
+ { \
+ static inline typename NAME##_retval<ArrayBase<Derived> >::type run(const Eigen::ArrayBase<Derived>& x) \
+ { \
+ return typename NAME##_retval<ArrayBase<Derived> >::type(x.derived()); \
+ } \
+ };
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen
+{
+ EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(real,scalar_real_op,real part,\sa ArrayBase::real)
+ EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(imag,scalar_imag_op,imaginary part,\sa ArrayBase::imag)
+ EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(conj,scalar_conjugate_op,complex conjugate,\sa ArrayBase::conjugate)
+ EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(inverse,scalar_inverse_op,inverse,\sa ArrayBase::inverse)
+ EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(sin,scalar_sin_op,sine,\sa ArrayBase::sin)
+ EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(cos,scalar_cos_op,cosine,\sa ArrayBase::cos)
+ EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(tan,scalar_tan_op,tangent,\sa ArrayBase::tan)
+ EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(atan,scalar_atan_op,arc-tangent,\sa ArrayBase::atan)
+ EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(asin,scalar_asin_op,arc-sine,\sa ArrayBase::asin)
+ EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(acos,scalar_acos_op,arc-consine,\sa ArrayBase::acos)
+ EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(sinh,scalar_sinh_op,hyperbolic sine,\sa ArrayBase::sinh)
+ EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(cosh,scalar_cosh_op,hyperbolic cosine,\sa ArrayBase::cosh)
+ EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(tanh,scalar_tanh_op,hyperbolic tangent,\sa ArrayBase::tanh)
+ EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(asinh,scalar_asinh_op,inverse hyperbolic sine,\sa ArrayBase::asinh)
+ EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(acosh,scalar_acosh_op,inverse hyperbolic cosine,\sa ArrayBase::acosh)
+ EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(atanh,scalar_atanh_op,inverse hyperbolic tangent,\sa ArrayBase::atanh)
+ EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(logistic,scalar_logistic_op,logistic function,\sa ArrayBase::logistic)
+ EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(lgamma,scalar_lgamma_op,natural logarithm of the gamma function,\sa ArrayBase::lgamma)
+ EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(digamma,scalar_digamma_op,derivative of lgamma,\sa ArrayBase::digamma)
+ EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(erf,scalar_erf_op,error function,\sa ArrayBase::erf)
+ EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(erfc,scalar_erfc_op,complement error function,\sa ArrayBase::erfc)
+ EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(ndtri,scalar_ndtri_op,inverse normal distribution function,\sa ArrayBase::ndtri)
+ EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(exp,scalar_exp_op,exponential,\sa ArrayBase::exp)
+ EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(expm1,scalar_expm1_op,exponential of a value minus 1,\sa ArrayBase::expm1)
+ EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(log,scalar_log_op,natural logarithm,\sa Eigen::log10 DOXCOMMA ArrayBase::log)
+ EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(log1p,scalar_log1p_op,natural logarithm of 1 plus the value,\sa ArrayBase::log1p)
+ EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(log10,scalar_log10_op,base 10 logarithm,\sa Eigen::log DOXCOMMA ArrayBase::log10)
+ EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(log2,scalar_log2_op,base 2 logarithm,\sa Eigen::log DOXCOMMA ArrayBase::log2)
+ EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(abs,scalar_abs_op,absolute value,\sa ArrayBase::abs DOXCOMMA MatrixBase::cwiseAbs)
+ EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(abs2,scalar_abs2_op,squared absolute value,\sa ArrayBase::abs2 DOXCOMMA MatrixBase::cwiseAbs2)
+ EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(arg,scalar_arg_op,complex argument,\sa ArrayBase::arg DOXCOMMA MatrixBase::cwiseArg)
+ EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(sqrt,scalar_sqrt_op,square root,\sa ArrayBase::sqrt DOXCOMMA MatrixBase::cwiseSqrt)
+ EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(rsqrt,scalar_rsqrt_op,reciprocal square root,\sa ArrayBase::rsqrt)
+ EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(square,scalar_square_op,square (power 2),\sa Eigen::abs2 DOXCOMMA Eigen::pow DOXCOMMA ArrayBase::square)
+ EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(cube,scalar_cube_op,cube (power 3),\sa Eigen::pow DOXCOMMA ArrayBase::cube)
+ EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(rint,scalar_rint_op,nearest integer,\sa Eigen::floor DOXCOMMA Eigen::ceil DOXCOMMA ArrayBase::round)
+ EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(round,scalar_round_op,nearest integer,\sa Eigen::floor DOXCOMMA Eigen::ceil DOXCOMMA ArrayBase::round)
+ EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(floor,scalar_floor_op,nearest integer not greater than the giben value,\sa Eigen::ceil DOXCOMMA ArrayBase::floor)
+ EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(ceil,scalar_ceil_op,nearest integer not less than the giben value,\sa Eigen::floor DOXCOMMA ArrayBase::ceil)
+ EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(isnan,scalar_isnan_op,not-a-number test,\sa Eigen::isinf DOXCOMMA Eigen::isfinite DOXCOMMA ArrayBase::isnan)
+ EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(isinf,scalar_isinf_op,infinite value test,\sa Eigen::isnan DOXCOMMA Eigen::isfinite DOXCOMMA ArrayBase::isinf)
+ EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(isfinite,scalar_isfinite_op,finite value test,\sa Eigen::isinf DOXCOMMA Eigen::isnan DOXCOMMA ArrayBase::isfinite)
+ EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(sign,scalar_sign_op,sign (or 0),\sa ArrayBase::sign)
+
+ template <typename Derived, typename ScalarExponent>
+ using GlobalUnaryPowReturnType = std::enable_if_t<
+ !internal::is_arithmetic<typename NumTraits<Derived>::Real>::value &&
+ internal::is_arithmetic<typename NumTraits<ScalarExponent>::Real>::value,
+ CwiseUnaryOp<internal::scalar_unary_pow_op<typename Derived::Scalar, ScalarExponent>, const Derived> >;
+
+ /** \returns an expression of the coefficient-wise power of \a x to the given constant \a exponent.
+ *
+ * \tparam ScalarExponent is the scalar type of \a exponent. It must be compatible with the scalar type of the given
+ * expression (\c Derived::Scalar).
+ *
+ * \sa ArrayBase::pow()
+ *
+ * \relates ArrayBase
+ */
+#ifdef EIGEN_PARSED_BY_DOXYGEN
+ template <typename Derived, typename ScalarExponent>
+ EIGEN_DEVICE_FUNC inline const GlobalUnaryPowReturnType<Derived, ScalarExponent> pow(
+ const Eigen::ArrayBase<Derived>& x, const ScalarExponent& exponent);
+#else
+ template <typename Derived, typename ScalarExponent>
+ EIGEN_DEVICE_FUNC inline const GlobalUnaryPowReturnType<Derived, ScalarExponent> pow(
+ const Eigen::ArrayBase<Derived>& x, const ScalarExponent& exponent) {
+ return GlobalUnaryPowReturnType<Derived, ScalarExponent>(
+ x.derived(), internal::scalar_unary_pow_op<typename Derived::Scalar, ScalarExponent>(exponent));
+ }
+#endif
+
+ /** \returns an expression of the coefficient-wise power of \a x to the given array of \a exponents.
+ *
+ * This function computes the coefficient-wise power.
+ *
+ * Example: \include Cwise_array_power_array.cpp
+ * Output: \verbinclude Cwise_array_power_array.out
+ *
+ * \sa ArrayBase::pow()
+ *
+ * \relates ArrayBase
+ */
+ template<typename Derived,typename ExponentDerived>
+ inline const Eigen::CwiseBinaryOp<Eigen::internal::scalar_pow_op<typename Derived::Scalar, typename ExponentDerived::Scalar>, const Derived, const ExponentDerived>
+ pow(const Eigen::ArrayBase<Derived>& x, const Eigen::ArrayBase<ExponentDerived>& exponents)
+ {
+ return Eigen::CwiseBinaryOp<Eigen::internal::scalar_pow_op<typename Derived::Scalar, typename ExponentDerived::Scalar>, const Derived, const ExponentDerived>(
+ x.derived(),
+ exponents.derived()
+ );
+ }
+
+ /** \returns an expression of the coefficient-wise power of the scalar \a x to the given array of \a exponents.
+ *
+ * This function computes the coefficient-wise power between a scalar and an array of exponents.
+ *
+ * \tparam Scalar is the scalar type of \a x. It must be compatible with the scalar type of the given array expression (\c Derived::Scalar).
+ *
+ * Example: \include Cwise_scalar_power_array.cpp
+ * Output: \verbinclude Cwise_scalar_power_array.out
+ *
+ * \sa ArrayBase::pow()
+ *
+ * \relates ArrayBase
+ */
+#ifdef EIGEN_PARSED_BY_DOXYGEN
+ template<typename Scalar,typename Derived>
+ inline const CwiseBinaryOp<internal::scalar_pow_op<Scalar,Derived::Scalar>,Constant<Scalar>,Derived>
+ pow(const Scalar& x,const Eigen::ArrayBase<Derived>& x);
+#else
+ template <typename Scalar, typename Derived>
+ EIGEN_DEVICE_FUNC inline
+ const EIGEN_SCALAR_BINARYOP_EXPR_RETURN_TYPE(typename internal::promote_scalar_arg<typename Derived::Scalar
+ EIGEN_COMMA Scalar EIGEN_COMMA
+ EIGEN_SCALAR_BINARY_SUPPORTED(pow,Scalar,typename Derived::Scalar)>::type,Derived,pow)
+ pow(const Scalar& x, const Eigen::ArrayBase<Derived>& exponents) {
+ typedef typename internal::promote_scalar_arg<typename Derived::Scalar,Scalar,
+ EIGEN_SCALAR_BINARY_SUPPORTED(pow,Scalar,typename Derived::Scalar)>::type PromotedScalar;
+ return EIGEN_SCALAR_BINARYOP_EXPR_RETURN_TYPE(PromotedScalar,Derived,pow)(
+ typename internal::plain_constant_type<Derived,PromotedScalar>::type(exponents.derived().rows(), exponents.derived().cols(), internal::scalar_constant_op<PromotedScalar>(x)), exponents.derived());
+ }
+#endif
+
+ /** \returns an expression of the coefficient-wise atan2(\a x, \a y). \a x and \a y must be of the same type.
+ *
+ * This function computes the coefficient-wise atan2().
+ *
+ * \sa ArrayBase::atan2()
+ *
+ * \relates ArrayBase
+ */
+ template <typename LhsDerived, typename RhsDerived>
+ inline const std::enable_if_t<
+ std::is_same<typename LhsDerived::Scalar, typename RhsDerived::Scalar>::value,
+ Eigen::CwiseBinaryOp<Eigen::internal::scalar_atan2_op<typename LhsDerived::Scalar, typename RhsDerived::Scalar>, const LhsDerived, const RhsDerived>
+ >
+ atan2(const Eigen::ArrayBase<LhsDerived>& x, const Eigen::ArrayBase<RhsDerived>& exponents) {
+ return Eigen::CwiseBinaryOp<Eigen::internal::scalar_atan2_op<typename LhsDerived::Scalar, typename RhsDerived::Scalar>, const LhsDerived, const RhsDerived>(
+ x.derived(),
+ exponents.derived()
+ );
+ }
+
+ namespace internal
+ {
+ EIGEN_ARRAY_DECLARE_GLOBAL_EIGEN_UNARY(real,scalar_real_op)
+ EIGEN_ARRAY_DECLARE_GLOBAL_EIGEN_UNARY(imag,scalar_imag_op)
+ EIGEN_ARRAY_DECLARE_GLOBAL_EIGEN_UNARY(abs2,scalar_abs2_op)
+ }
+}
+
+// TODO: cleanly disable those functions that are not supported on Array (numext::real_ref, internal::random, internal::isApprox...)
+
+#endif // EIGEN_GLOBAL_FUNCTIONS_H
diff --git a/Eigen/src/Core/IO.h b/Eigen/src/Core/IO.h
new file mode 100644
index 0000000..897d7b0
--- /dev/null
+++ b/Eigen/src/Core/IO.h
@@ -0,0 +1,258 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_IO_H
+#define EIGEN_IO_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+enum { DontAlignCols = 1 };
+enum { StreamPrecision = -1,
+ FullPrecision = -2 };
+
+namespace internal {
+template<typename Derived>
+std::ostream & print_matrix(std::ostream & s, const Derived& _m, const IOFormat& fmt);
+}
+
+/** \class IOFormat
+ * \ingroup Core_Module
+ *
+ * \brief Stores a set of parameters controlling the way matrices are printed
+ *
+ * List of available parameters:
+ * - \b precision number of digits for floating point values, or one of the special constants \c StreamPrecision and \c FullPrecision.
+ * The default is the special value \c StreamPrecision which means to use the
+ * stream's own precision setting, as set for instance using \c cout.precision(3). The other special value
+ * \c FullPrecision means that the number of digits will be computed to match the full precision of each floating-point
+ * type.
+ * - \b flags an OR-ed combination of flags, the default value is 0, the only currently available flag is \c DontAlignCols which
+ * allows to disable the alignment of columns, resulting in faster code.
+ * - \b coeffSeparator string printed between two coefficients of the same row
+ * - \b rowSeparator string printed between two rows
+ * - \b rowPrefix string printed at the beginning of each row
+ * - \b rowSuffix string printed at the end of each row
+ * - \b matPrefix string printed at the beginning of the matrix
+ * - \b matSuffix string printed at the end of the matrix
+ * - \b fill character printed to fill the empty space in aligned columns
+ *
+ * Example: \include IOFormat.cpp
+ * Output: \verbinclude IOFormat.out
+ *
+ * \sa DenseBase::format(), class WithFormat
+ */
+struct IOFormat
+{
+ /** Default constructor, see class IOFormat for the meaning of the parameters */
+ IOFormat(int _precision = StreamPrecision, int _flags = 0,
+ const std::string& _coeffSeparator = " ",
+ const std::string& _rowSeparator = "\n", const std::string& _rowPrefix="", const std::string& _rowSuffix="",
+ const std::string& _matPrefix="", const std::string& _matSuffix="", const char _fill=' ')
+ : matPrefix(_matPrefix), matSuffix(_matSuffix), rowPrefix(_rowPrefix), rowSuffix(_rowSuffix), rowSeparator(_rowSeparator),
+ rowSpacer(""), coeffSeparator(_coeffSeparator), fill(_fill), precision(_precision), flags(_flags)
+ {
+ // TODO check if rowPrefix, rowSuffix or rowSeparator contains a newline
+ // don't add rowSpacer if columns are not to be aligned
+ if((flags & DontAlignCols))
+ return;
+ int i = int(matSuffix.length())-1;
+ while (i>=0 && matSuffix[i]!='\n')
+ {
+ rowSpacer += ' ';
+ i--;
+ }
+ }
+ std::string matPrefix, matSuffix;
+ std::string rowPrefix, rowSuffix, rowSeparator, rowSpacer;
+ std::string coeffSeparator;
+ char fill;
+ int precision;
+ int flags;
+};
+
+/** \class WithFormat
+ * \ingroup Core_Module
+ *
+ * \brief Pseudo expression providing matrix output with given format
+ *
+ * \tparam ExpressionType the type of the object on which IO stream operations are performed
+ *
+ * This class represents an expression with stream operators controlled by a given IOFormat.
+ * It is the return type of DenseBase::format()
+ * and most of the time this is the only way it is used.
+ *
+ * See class IOFormat for some examples.
+ *
+ * \sa DenseBase::format(), class IOFormat
+ */
+template<typename ExpressionType>
+class WithFormat
+{
+ public:
+
+ WithFormat(const ExpressionType& matrix, const IOFormat& format)
+ : m_matrix(matrix), m_format(format)
+ {}
+
+ friend std::ostream & operator << (std::ostream & s, const WithFormat& wf)
+ {
+ return internal::print_matrix(s, wf.m_matrix.eval(), wf.m_format);
+ }
+
+ protected:
+ typename ExpressionType::Nested m_matrix;
+ IOFormat m_format;
+};
+
+namespace internal {
+
+// NOTE: This helper is kept for backward compatibility with previous code specializing
+// this internal::significant_decimals_impl structure. In the future we should directly
+// call digits10() which has been introduced in July 2016 in 3.3.
+template<typename Scalar>
+struct significant_decimals_impl
+{
+ static inline int run()
+ {
+ return NumTraits<Scalar>::digits10();
+ }
+};
+
+/** \internal
+ * print the matrix \a _m to the output stream \a s using the output format \a fmt */
+template<typename Derived>
+std::ostream & print_matrix(std::ostream & s, const Derived& _m, const IOFormat& fmt)
+{
+ using internal::is_same;
+
+ if(_m.size() == 0)
+ {
+ s << fmt.matPrefix << fmt.matSuffix;
+ return s;
+ }
+
+ typename Derived::Nested m = _m;
+ typedef typename Derived::Scalar Scalar;
+ typedef std::conditional_t<
+ is_same<Scalar, char>::value ||
+ is_same<Scalar, unsigned char>::value ||
+ is_same<Scalar, numext::int8_t>::value ||
+ is_same<Scalar, numext::uint8_t>::value,
+ int,
+ std::conditional_t<
+ is_same<Scalar, std::complex<char> >::value ||
+ is_same<Scalar, std::complex<unsigned char> >::value ||
+ is_same<Scalar, std::complex<numext::int8_t> >::value ||
+ is_same<Scalar, std::complex<numext::uint8_t> >::value,
+ std::complex<int>,
+ const Scalar&
+ >
+ > PrintType;
+
+ Index width = 0;
+
+ std::streamsize explicit_precision;
+ if(fmt.precision == StreamPrecision)
+ {
+ explicit_precision = 0;
+ }
+ else if(fmt.precision == FullPrecision)
+ {
+ if (NumTraits<Scalar>::IsInteger)
+ {
+ explicit_precision = 0;
+ }
+ else
+ {
+ explicit_precision = significant_decimals_impl<Scalar>::run();
+ }
+ }
+ else
+ {
+ explicit_precision = fmt.precision;
+ }
+
+ std::streamsize old_precision = 0;
+ if(explicit_precision) old_precision = s.precision(explicit_precision);
+
+ bool align_cols = !(fmt.flags & DontAlignCols);
+ if(align_cols)
+ {
+ // compute the largest width
+ for(Index j = 0; j < m.cols(); ++j)
+ for(Index i = 0; i < m.rows(); ++i)
+ {
+ std::stringstream sstr;
+ sstr.copyfmt(s);
+ sstr << static_cast<PrintType>(m.coeff(i,j));
+ width = std::max<Index>(width, Index(sstr.str().length()));
+ }
+ }
+ std::streamsize old_width = s.width();
+ char old_fill_character = s.fill();
+ s << fmt.matPrefix;
+ for(Index i = 0; i < m.rows(); ++i)
+ {
+ if (i)
+ s << fmt.rowSpacer;
+ s << fmt.rowPrefix;
+ if(width) {
+ s.fill(fmt.fill);
+ s.width(width);
+ }
+ s << static_cast<PrintType>(m.coeff(i, 0));
+ for(Index j = 1; j < m.cols(); ++j)
+ {
+ s << fmt.coeffSeparator;
+ if(width) {
+ s.fill(fmt.fill);
+ s.width(width);
+ }
+ s << static_cast<PrintType>(m.coeff(i, j));
+ }
+ s << fmt.rowSuffix;
+ if( i < m.rows() - 1)
+ s << fmt.rowSeparator;
+ }
+ s << fmt.matSuffix;
+ if(explicit_precision) s.precision(old_precision);
+ if(width) {
+ s.fill(old_fill_character);
+ s.width(old_width);
+ }
+ return s;
+}
+
+} // end namespace internal
+
+/** \relates DenseBase
+ *
+ * Outputs the matrix, to the given stream.
+ *
+ * If you wish to print the matrix with a format different than the default, use DenseBase::format().
+ *
+ * It is also possible to change the default format by defining EIGEN_DEFAULT_IO_FORMAT before including Eigen headers.
+ * If not defined, this will automatically be defined to Eigen::IOFormat(), that is the Eigen::IOFormat with default parameters.
+ *
+ * \sa DenseBase::format()
+ */
+template<typename Derived>
+std::ostream & operator <<
+(std::ostream & s,
+ const DenseBase<Derived> & m)
+{
+ return internal::print_matrix(s, m.eval(), EIGEN_DEFAULT_IO_FORMAT);
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_IO_H
diff --git a/Eigen/src/Core/IndexedView.h b/Eigen/src/Core/IndexedView.h
new file mode 100644
index 0000000..f967301
--- /dev/null
+++ b/Eigen/src/Core/IndexedView.h
@@ -0,0 +1,249 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2017 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_INDEXED_VIEW_H
+#define EIGEN_INDEXED_VIEW_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+
+template<typename XprType, typename RowIndices, typename ColIndices>
+struct traits<IndexedView<XprType, RowIndices, ColIndices> >
+ : traits<XprType>
+{
+ enum {
+ RowsAtCompileTime = int(array_size<RowIndices>::value),
+ ColsAtCompileTime = int(array_size<ColIndices>::value),
+ MaxRowsAtCompileTime = RowsAtCompileTime,
+ MaxColsAtCompileTime = ColsAtCompileTime,
+
+ XprTypeIsRowMajor = (int(traits<XprType>::Flags)&RowMajorBit) != 0,
+ IsRowMajor = (MaxRowsAtCompileTime==1&&MaxColsAtCompileTime!=1) ? 1
+ : (MaxColsAtCompileTime==1&&MaxRowsAtCompileTime!=1) ? 0
+ : XprTypeIsRowMajor,
+
+ RowIncr = int(get_compile_time_incr<RowIndices>::value),
+ ColIncr = int(get_compile_time_incr<ColIndices>::value),
+ InnerIncr = IsRowMajor ? ColIncr : RowIncr,
+ OuterIncr = IsRowMajor ? RowIncr : ColIncr,
+
+ HasSameStorageOrderAsXprType = (IsRowMajor == XprTypeIsRowMajor),
+ XprInnerStride = HasSameStorageOrderAsXprType ? int(inner_stride_at_compile_time<XprType>::ret) : int(outer_stride_at_compile_time<XprType>::ret),
+ XprOuterstride = HasSameStorageOrderAsXprType ? int(outer_stride_at_compile_time<XprType>::ret) : int(inner_stride_at_compile_time<XprType>::ret),
+
+ InnerSize = XprTypeIsRowMajor ? ColsAtCompileTime : RowsAtCompileTime,
+ IsBlockAlike = InnerIncr==1 && OuterIncr==1,
+ IsInnerPannel = HasSameStorageOrderAsXprType && is_same<AllRange<InnerSize>,std::conditional_t<XprTypeIsRowMajor,ColIndices,RowIndices>>::value,
+
+ InnerStrideAtCompileTime = InnerIncr<0 || InnerIncr==DynamicIndex || XprInnerStride==Dynamic || InnerIncr==UndefinedIncr ? Dynamic : XprInnerStride * InnerIncr,
+ OuterStrideAtCompileTime = OuterIncr<0 || OuterIncr==DynamicIndex || XprOuterstride==Dynamic || OuterIncr==UndefinedIncr ? Dynamic : XprOuterstride * OuterIncr,
+
+ ReturnAsScalar = is_same<RowIndices,SingleRange>::value && is_same<ColIndices,SingleRange>::value,
+ ReturnAsBlock = (!ReturnAsScalar) && IsBlockAlike,
+ ReturnAsIndexedView = (!ReturnAsScalar) && (!ReturnAsBlock),
+
+ // FIXME we deal with compile-time strides if and only if we have DirectAccessBit flag,
+ // but this is too strict regarding negative strides...
+ DirectAccessMask = (int(InnerIncr)!=UndefinedIncr && int(OuterIncr)!=UndefinedIncr && InnerIncr>=0 && OuterIncr>=0) ? DirectAccessBit : 0,
+ FlagsRowMajorBit = IsRowMajor ? RowMajorBit : 0,
+ FlagsLvalueBit = is_lvalue<XprType>::value ? LvalueBit : 0,
+ FlagsLinearAccessBit = (RowsAtCompileTime == 1 || ColsAtCompileTime == 1) ? LinearAccessBit : 0,
+ Flags = (traits<XprType>::Flags & (HereditaryBits | DirectAccessMask )) | FlagsLvalueBit | FlagsRowMajorBit | FlagsLinearAccessBit
+ };
+
+ typedef Block<XprType,RowsAtCompileTime,ColsAtCompileTime,IsInnerPannel> BlockType;
+};
+
+}
+
+template<typename XprType, typename RowIndices, typename ColIndices, typename StorageKind>
+class IndexedViewImpl;
+
+
+/** \class IndexedView
+ * \ingroup Core_Module
+ *
+ * \brief Expression of a non-sequential sub-matrix defined by arbitrary sequences of row and column indices
+ *
+ * \tparam XprType the type of the expression in which we are taking the intersections of sub-rows and sub-columns
+ * \tparam RowIndices the type of the object defining the sequence of row indices
+ * \tparam ColIndices the type of the object defining the sequence of column indices
+ *
+ * This class represents an expression of a sub-matrix (or sub-vector) defined as the intersection
+ * of sub-sets of rows and columns, that are themself defined by generic sequences of row indices \f$ \{r_0,r_1,..r_{m-1}\} \f$
+ * and column indices \f$ \{c_0,c_1,..c_{n-1} \}\f$. Let \f$ A \f$ be the nested matrix, then the resulting matrix \f$ B \f$ has \c m
+ * rows and \c n columns, and its entries are given by: \f$ B(i,j) = A(r_i,c_j) \f$.
+ *
+ * The \c RowIndices and \c ColIndices types must be compatible with the following API:
+ * \code
+ * <integral type> operator[](Index) const;
+ * Index size() const;
+ * \endcode
+ *
+ * Typical supported types thus include:
+ * - std::vector<int>
+ * - std::valarray<int>
+ * - std::array<int>
+ * - Plain C arrays: int[N]
+ * - Eigen::ArrayXi
+ * - decltype(ArrayXi::LinSpaced(...))
+ * - Any view/expressions of the previous types
+ * - Eigen::ArithmeticSequence
+ * - Eigen::internal::AllRange (helper for Eigen::placeholders::all)
+ * - Eigen::internal::SingleRange (helper for single index)
+ * - etc.
+ *
+ * In typical usages of %Eigen, this class should never be used directly. It is the return type of
+ * DenseBase::operator()(const RowIndices&, const ColIndices&).
+ *
+ * \sa class Block
+ */
+template<typename XprType, typename RowIndices, typename ColIndices>
+class IndexedView : public IndexedViewImpl<XprType, RowIndices, ColIndices, typename internal::traits<XprType>::StorageKind>
+{
+public:
+ typedef typename IndexedViewImpl<XprType, RowIndices, ColIndices, typename internal::traits<XprType>::StorageKind>::Base Base;
+ EIGEN_GENERIC_PUBLIC_INTERFACE(IndexedView)
+ EIGEN_INHERIT_ASSIGNMENT_OPERATORS(IndexedView)
+
+ typedef typename internal::ref_selector<XprType>::non_const_type MatrixTypeNested;
+ typedef internal::remove_all_t<XprType> NestedExpression;
+
+ template<typename T0, typename T1>
+ IndexedView(XprType& xpr, const T0& rowIndices, const T1& colIndices)
+ : m_xpr(xpr), m_rowIndices(rowIndices), m_colIndices(colIndices)
+ {}
+
+ /** \returns number of rows */
+ Index rows() const { return internal::index_list_size(m_rowIndices); }
+
+ /** \returns number of columns */
+ Index cols() const { return internal::index_list_size(m_colIndices); }
+
+ /** \returns the nested expression */
+ const internal::remove_all_t<XprType>&
+ nestedExpression() const { return m_xpr; }
+
+ /** \returns the nested expression */
+ std::remove_reference_t<XprType>&
+ nestedExpression() { return m_xpr; }
+
+ /** \returns a const reference to the object storing/generating the row indices */
+ const RowIndices& rowIndices() const { return m_rowIndices; }
+
+ /** \returns a const reference to the object storing/generating the column indices */
+ const ColIndices& colIndices() const { return m_colIndices; }
+
+protected:
+ MatrixTypeNested m_xpr;
+ RowIndices m_rowIndices;
+ ColIndices m_colIndices;
+};
+
+
+// Generic API dispatcher
+template<typename XprType, typename RowIndices, typename ColIndices, typename StorageKind>
+class IndexedViewImpl
+ : public internal::generic_xpr_base<IndexedView<XprType, RowIndices, ColIndices> >::type
+{
+public:
+ typedef typename internal::generic_xpr_base<IndexedView<XprType, RowIndices, ColIndices> >::type Base;
+};
+
+namespace internal {
+
+
+template<typename ArgType, typename RowIndices, typename ColIndices>
+struct unary_evaluator<IndexedView<ArgType, RowIndices, ColIndices>, IndexBased>
+ : evaluator_base<IndexedView<ArgType, RowIndices, ColIndices> >
+{
+ typedef IndexedView<ArgType, RowIndices, ColIndices> XprType;
+
+ enum {
+ CoeffReadCost = evaluator<ArgType>::CoeffReadCost /* TODO + cost of row/col index */,
+
+ FlagsLinearAccessBit = (traits<XprType>::RowsAtCompileTime == 1 || traits<XprType>::ColsAtCompileTime == 1) ? LinearAccessBit : 0,
+
+ FlagsRowMajorBit = traits<XprType>::FlagsRowMajorBit,
+
+ Flags = (evaluator<ArgType>::Flags & (HereditaryBits & ~RowMajorBit /*| LinearAccessBit | DirectAccessBit*/)) | FlagsLinearAccessBit | FlagsRowMajorBit,
+
+ Alignment = 0
+ };
+
+ EIGEN_DEVICE_FUNC explicit unary_evaluator(const XprType& xpr) : m_argImpl(xpr.nestedExpression()), m_xpr(xpr)
+ {
+ EIGEN_INTERNAL_CHECK_COST_VALUE(CoeffReadCost);
+ }
+
+ typedef typename XprType::Scalar Scalar;
+ typedef typename XprType::CoeffReturnType CoeffReturnType;
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ CoeffReturnType coeff(Index row, Index col) const
+ {
+ eigen_assert(m_xpr.rowIndices()[row] >= 0 && m_xpr.rowIndices()[row] < m_xpr.nestedExpression().rows()
+ && m_xpr.colIndices()[col] >= 0 && m_xpr.colIndices()[col] < m_xpr.nestedExpression().cols());
+ return m_argImpl.coeff(m_xpr.rowIndices()[row], m_xpr.colIndices()[col]);
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ Scalar& coeffRef(Index row, Index col)
+ {
+ eigen_assert(m_xpr.rowIndices()[row] >= 0 && m_xpr.rowIndices()[row] < m_xpr.nestedExpression().rows()
+ && m_xpr.colIndices()[col] >= 0 && m_xpr.colIndices()[col] < m_xpr.nestedExpression().cols());
+ return m_argImpl.coeffRef(m_xpr.rowIndices()[row], m_xpr.colIndices()[col]);
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ Scalar& coeffRef(Index index)
+ {
+ EIGEN_STATIC_ASSERT_LVALUE(XprType)
+ Index row = XprType::RowsAtCompileTime == 1 ? 0 : index;
+ Index col = XprType::RowsAtCompileTime == 1 ? index : 0;
+ eigen_assert(m_xpr.rowIndices()[row] >= 0 && m_xpr.rowIndices()[row] < m_xpr.nestedExpression().rows()
+ && m_xpr.colIndices()[col] >= 0 && m_xpr.colIndices()[col] < m_xpr.nestedExpression().cols());
+ return m_argImpl.coeffRef( m_xpr.rowIndices()[row], m_xpr.colIndices()[col]);
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ const Scalar& coeffRef(Index index) const
+ {
+ Index row = XprType::RowsAtCompileTime == 1 ? 0 : index;
+ Index col = XprType::RowsAtCompileTime == 1 ? index : 0;
+ eigen_assert(m_xpr.rowIndices()[row] >= 0 && m_xpr.rowIndices()[row] < m_xpr.nestedExpression().rows()
+ && m_xpr.colIndices()[col] >= 0 && m_xpr.colIndices()[col] < m_xpr.nestedExpression().cols());
+ return m_argImpl.coeffRef( m_xpr.rowIndices()[row], m_xpr.colIndices()[col]);
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ const CoeffReturnType coeff(Index index) const
+ {
+ Index row = XprType::RowsAtCompileTime == 1 ? 0 : index;
+ Index col = XprType::RowsAtCompileTime == 1 ? index : 0;
+ eigen_assert(m_xpr.rowIndices()[row] >= 0 && m_xpr.rowIndices()[row] < m_xpr.nestedExpression().rows()
+ && m_xpr.colIndices()[col] >= 0 && m_xpr.colIndices()[col] < m_xpr.nestedExpression().cols());
+ return m_argImpl.coeff( m_xpr.rowIndices()[row], m_xpr.colIndices()[col]);
+ }
+
+protected:
+
+ evaluator<ArgType> m_argImpl;
+ const XprType& m_xpr;
+
+};
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_INDEXED_VIEW_H
diff --git a/Eigen/src/Core/InternalHeaderCheck.h b/Eigen/src/Core/InternalHeaderCheck.h
new file mode 100644
index 0000000..1cea572
--- /dev/null
+++ b/Eigen/src/Core/InternalHeaderCheck.h
@@ -0,0 +1,3 @@
+#ifndef EIGEN_CORE_MODULE_H
+#error "Please include Eigen/Core instead of including headers inside the src directory directly."
+#endif
diff --git a/Eigen/src/Core/Inverse.h b/Eigen/src/Core/Inverse.h
new file mode 100644
index 0000000..9c70733
--- /dev/null
+++ b/Eigen/src/Core/Inverse.h
@@ -0,0 +1,119 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2014-2019 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_INVERSE_H
+#define EIGEN_INVERSE_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+template<typename XprType,typename StorageKind> class InverseImpl;
+
+namespace internal {
+
+template<typename XprType>
+struct traits<Inverse<XprType> >
+ : traits<typename XprType::PlainObject>
+{
+ typedef typename XprType::PlainObject PlainObject;
+ typedef traits<PlainObject> BaseTraits;
+ enum {
+ Flags = BaseTraits::Flags & RowMajorBit
+ };
+};
+
+} // end namespace internal
+
+/** \class Inverse
+ *
+ * \brief Expression of the inverse of another expression
+ *
+ * \tparam XprType the type of the expression we are taking the inverse
+ *
+ * This class represents an abstract expression of A.inverse()
+ * and most of the time this is the only way it is used.
+ *
+ */
+template<typename XprType>
+class Inverse : public InverseImpl<XprType,typename internal::traits<XprType>::StorageKind>
+{
+public:
+ typedef typename XprType::StorageIndex StorageIndex;
+ typedef typename XprType::Scalar Scalar;
+ typedef typename internal::ref_selector<XprType>::type XprTypeNested;
+ typedef internal::remove_all_t<XprTypeNested> XprTypeNestedCleaned;
+ typedef typename internal::ref_selector<Inverse>::type Nested;
+ typedef internal::remove_all_t<XprType> NestedExpression;
+
+ explicit EIGEN_DEVICE_FUNC Inverse(const XprType &xpr)
+ : m_xpr(xpr)
+ {}
+
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR Index rows() const EIGEN_NOEXCEPT { return m_xpr.cols(); }
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR Index cols() const EIGEN_NOEXCEPT { return m_xpr.rows(); }
+
+ EIGEN_DEVICE_FUNC const XprTypeNestedCleaned& nestedExpression() const { return m_xpr; }
+
+protected:
+ XprTypeNested m_xpr;
+};
+
+// Generic API dispatcher
+template<typename XprType, typename StorageKind>
+class InverseImpl
+ : public internal::generic_xpr_base<Inverse<XprType> >::type
+{
+public:
+ typedef typename internal::generic_xpr_base<Inverse<XprType> >::type Base;
+ typedef typename XprType::Scalar Scalar;
+private:
+
+ Scalar coeff(Index row, Index col) const;
+ Scalar coeff(Index i) const;
+};
+
+namespace internal {
+
+/** \internal
+ * \brief Default evaluator for Inverse expression.
+ *
+ * This default evaluator for Inverse expression simply evaluate the inverse into a temporary
+ * by a call to internal::call_assignment_no_alias.
+ * Therefore, inverse implementers only have to specialize Assignment<Dst,Inverse<...>, ...> for
+ * there own nested expression.
+ *
+ * \sa class Inverse
+ */
+template<typename ArgType>
+struct unary_evaluator<Inverse<ArgType> >
+ : public evaluator<typename Inverse<ArgType>::PlainObject>
+{
+ typedef Inverse<ArgType> InverseType;
+ typedef typename InverseType::PlainObject PlainObject;
+ typedef evaluator<PlainObject> Base;
+
+ enum { Flags = Base::Flags | EvalBeforeNestingBit };
+
+ unary_evaluator(const InverseType& inv_xpr)
+ : m_result(inv_xpr.rows(), inv_xpr.cols())
+ {
+ internal::construct_at<Base>(this, m_result);
+ internal::call_assignment_no_alias(m_result, inv_xpr);
+ }
+
+protected:
+ PlainObject m_result;
+};
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_INVERSE_H
diff --git a/Eigen/src/Core/Map.h b/Eigen/src/Core/Map.h
new file mode 100644
index 0000000..56d1ff8
--- /dev/null
+++ b/Eigen/src/Core/Map.h
@@ -0,0 +1,170 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2007-2010 Benoit Jacob <jacob.benoit.1@gmail.com>
+// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_MAP_H
+#define EIGEN_MAP_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+template<typename PlainObjectType, int MapOptions, typename StrideType>
+struct traits<Map<PlainObjectType, MapOptions, StrideType> >
+ : public traits<PlainObjectType>
+{
+ typedef traits<PlainObjectType> TraitsBase;
+ enum {
+ PlainObjectTypeInnerSize = ((traits<PlainObjectType>::Flags&RowMajorBit)==RowMajorBit)
+ ? PlainObjectType::ColsAtCompileTime
+ : PlainObjectType::RowsAtCompileTime,
+
+ InnerStrideAtCompileTime = StrideType::InnerStrideAtCompileTime == 0
+ ? int(PlainObjectType::InnerStrideAtCompileTime)
+ : int(StrideType::InnerStrideAtCompileTime),
+ OuterStrideAtCompileTime = StrideType::OuterStrideAtCompileTime == 0
+ ? (InnerStrideAtCompileTime==Dynamic || PlainObjectTypeInnerSize==Dynamic
+ ? Dynamic
+ : int(InnerStrideAtCompileTime) * int(PlainObjectTypeInnerSize))
+ : int(StrideType::OuterStrideAtCompileTime),
+ Alignment = int(MapOptions)&int(AlignedMask),
+ Flags0 = TraitsBase::Flags & (~NestByRefBit),
+ Flags = is_lvalue<PlainObjectType>::value ? int(Flags0) : (int(Flags0) & ~LvalueBit)
+ };
+private:
+ enum { Options }; // Expressions don't have Options
+};
+}
+
+/** \class Map
+ * \ingroup Core_Module
+ *
+ * \brief A matrix or vector expression mapping an existing array of data.
+ *
+ * \tparam PlainObjectType the equivalent matrix type of the mapped data
+ * \tparam MapOptions specifies the pointer alignment in bytes. It can be: \c #Aligned128, \c #Aligned64, \c #Aligned32, \c #Aligned16, \c #Aligned8 or \c #Unaligned.
+ * The default is \c #Unaligned.
+ * \tparam StrideType optionally specifies strides. By default, Map assumes the memory layout
+ * of an ordinary, contiguous array. This can be overridden by specifying strides.
+ * The type passed here must be a specialization of the Stride template, see examples below.
+ *
+ * This class represents a matrix or vector expression mapping an existing array of data.
+ * It can be used to let Eigen interface without any overhead with non-Eigen data structures,
+ * such as plain C arrays or structures from other libraries. By default, it assumes that the
+ * data is laid out contiguously in memory. You can however override this by explicitly specifying
+ * inner and outer strides.
+ *
+ * Here's an example of simply mapping a contiguous array as a \ref TopicStorageOrders "column-major" matrix:
+ * \include Map_simple.cpp
+ * Output: \verbinclude Map_simple.out
+ *
+ * If you need to map non-contiguous arrays, you can do so by specifying strides:
+ *
+ * Here's an example of mapping an array as a vector, specifying an inner stride, that is, the pointer
+ * increment between two consecutive coefficients. Here, we're specifying the inner stride as a compile-time
+ * fixed value.
+ * \include Map_inner_stride.cpp
+ * Output: \verbinclude Map_inner_stride.out
+ *
+ * Here's an example of mapping an array while specifying an outer stride. Here, since we're mapping
+ * as a column-major matrix, 'outer stride' means the pointer increment between two consecutive columns.
+ * Here, we're specifying the outer stride as a runtime parameter. Note that here \c OuterStride<> is
+ * a short version of \c OuterStride<Dynamic> because the default template parameter of OuterStride
+ * is \c Dynamic
+ * \include Map_outer_stride.cpp
+ * Output: \verbinclude Map_outer_stride.out
+ *
+ * For more details and for an example of specifying both an inner and an outer stride, see class Stride.
+ *
+ * \b Tip: to change the array of data mapped by a Map object, you can use the C++
+ * placement new syntax:
+ *
+ * Example: \include Map_placement_new.cpp
+ * Output: \verbinclude Map_placement_new.out
+ *
+ * This class is the return type of PlainObjectBase::Map() but can also be used directly.
+ *
+ * \sa PlainObjectBase::Map(), \ref TopicStorageOrders
+ */
+template<typename PlainObjectType, int MapOptions, typename StrideType> class Map
+ : public MapBase<Map<PlainObjectType, MapOptions, StrideType> >
+{
+ public:
+
+ typedef MapBase<Map> Base;
+ EIGEN_DENSE_PUBLIC_INTERFACE(Map)
+
+ typedef typename Base::PointerType PointerType;
+ typedef PointerType PointerArgType;
+ EIGEN_DEVICE_FUNC
+ inline PointerType cast_to_pointer_type(PointerArgType ptr) { return ptr; }
+
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
+ inline Index innerStride() const
+ {
+ return StrideType::InnerStrideAtCompileTime != 0 ? m_stride.inner() : 1;
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
+ inline Index outerStride() const
+ {
+ return StrideType::OuterStrideAtCompileTime != 0 ? m_stride.outer()
+ : internal::traits<Map>::OuterStrideAtCompileTime != Dynamic ? Index(internal::traits<Map>::OuterStrideAtCompileTime)
+ : IsVectorAtCompileTime ? (this->size() * innerStride())
+ : int(Flags)&RowMajorBit ? (this->cols() * innerStride())
+ : (this->rows() * innerStride());
+ }
+
+ /** Constructor in the fixed-size case.
+ *
+ * \param dataPtr pointer to the array to map
+ * \param stride optional Stride object, passing the strides.
+ */
+ EIGEN_DEVICE_FUNC
+ explicit inline Map(PointerArgType dataPtr, const StrideType& stride = StrideType())
+ : Base(cast_to_pointer_type(dataPtr)), m_stride(stride)
+ {
+ }
+
+ /** Constructor in the dynamic-size vector case.
+ *
+ * \param dataPtr pointer to the array to map
+ * \param size the size of the vector expression
+ * \param stride optional Stride object, passing the strides.
+ */
+ EIGEN_DEVICE_FUNC
+ inline Map(PointerArgType dataPtr, Index size, const StrideType& stride = StrideType())
+ : Base(cast_to_pointer_type(dataPtr), size), m_stride(stride)
+ {
+ }
+
+ /** Constructor in the dynamic-size matrix case.
+ *
+ * \param dataPtr pointer to the array to map
+ * \param rows the number of rows of the matrix expression
+ * \param cols the number of columns of the matrix expression
+ * \param stride optional Stride object, passing the strides.
+ */
+ EIGEN_DEVICE_FUNC
+ inline Map(PointerArgType dataPtr, Index rows, Index cols, const StrideType& stride = StrideType())
+ : Base(cast_to_pointer_type(dataPtr), rows, cols), m_stride(stride)
+ {
+ }
+
+ EIGEN_INHERIT_ASSIGNMENT_OPERATORS(Map)
+
+ protected:
+ StrideType m_stride;
+};
+
+
+} // end namespace Eigen
+
+#endif // EIGEN_MAP_H
diff --git a/Eigen/src/Core/MapBase.h b/Eigen/src/Core/MapBase.h
new file mode 100644
index 0000000..bf8c163
--- /dev/null
+++ b/Eigen/src/Core/MapBase.h
@@ -0,0 +1,312 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2007-2010 Benoit Jacob <jacob.benoit.1@gmail.com>
+// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_MAPBASE_H
+#define EIGEN_MAPBASE_H
+
+#define EIGEN_STATIC_ASSERT_INDEX_BASED_ACCESS(Derived) \
+ EIGEN_STATIC_ASSERT((int(internal::evaluator<Derived>::Flags) & LinearAccessBit) || Derived::IsVectorAtCompileTime, \
+ YOU_ARE_TRYING_TO_USE_AN_INDEX_BASED_ACCESSOR_ON_AN_EXPRESSION_THAT_DOES_NOT_SUPPORT_THAT)
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+/** \ingroup Core_Module
+ *
+ * \brief Base class for dense Map and Block expression with direct access
+ *
+ * This base class provides the const low-level accessors (e.g. coeff, coeffRef) of dense
+ * Map and Block objects with direct access.
+ * Typical users do not have to directly deal with this class.
+ *
+ * This class can be extended by through the macro plugin \c EIGEN_MAPBASE_PLUGIN.
+ * See \link TopicCustomizing_Plugins customizing Eigen \endlink for details.
+ *
+ * The \c Derived class has to provide the following two methods describing the memory layout:
+ * \code Index innerStride() const; \endcode
+ * \code Index outerStride() const; \endcode
+ *
+ * \sa class Map, class Block
+ */
+template<typename Derived> class MapBase<Derived, ReadOnlyAccessors>
+ : public internal::dense_xpr_base<Derived>::type
+{
+ public:
+
+ typedef typename internal::dense_xpr_base<Derived>::type Base;
+ enum {
+ RowsAtCompileTime = internal::traits<Derived>::RowsAtCompileTime,
+ ColsAtCompileTime = internal::traits<Derived>::ColsAtCompileTime,
+ InnerStrideAtCompileTime = internal::traits<Derived>::InnerStrideAtCompileTime,
+ SizeAtCompileTime = Base::SizeAtCompileTime
+ };
+
+ typedef typename internal::traits<Derived>::StorageKind StorageKind;
+ typedef typename internal::traits<Derived>::Scalar Scalar;
+ typedef typename internal::packet_traits<Scalar>::type PacketScalar;
+ typedef typename NumTraits<Scalar>::Real RealScalar;
+ typedef std::conditional_t<
+ bool(internal::is_lvalue<Derived>::value),
+ Scalar *,
+ const Scalar *>
+ PointerType;
+
+ using Base::derived;
+// using Base::RowsAtCompileTime;
+// using Base::ColsAtCompileTime;
+// using Base::SizeAtCompileTime;
+ using Base::MaxRowsAtCompileTime;
+ using Base::MaxColsAtCompileTime;
+ using Base::MaxSizeAtCompileTime;
+ using Base::IsVectorAtCompileTime;
+ using Base::Flags;
+ using Base::IsRowMajor;
+
+ using Base::rows;
+ using Base::cols;
+ using Base::size;
+ using Base::coeff;
+ using Base::coeffRef;
+ using Base::lazyAssign;
+ using Base::eval;
+
+ using Base::innerStride;
+ using Base::outerStride;
+ using Base::rowStride;
+ using Base::colStride;
+
+ // bug 217 - compile error on ICC 11.1
+ using Base::operator=;
+
+ typedef typename Base::CoeffReturnType CoeffReturnType;
+
+ /** \copydoc DenseBase::rows() */
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
+ inline Index rows() const EIGEN_NOEXCEPT { return m_rows.value(); }
+ /** \copydoc DenseBase::cols() */
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
+ inline Index cols() const EIGEN_NOEXCEPT { return m_cols.value(); }
+
+ /** Returns a pointer to the first coefficient of the matrix or vector.
+ *
+ * \note When addressing this data, make sure to honor the strides returned by innerStride() and outerStride().
+ *
+ * \sa innerStride(), outerStride()
+ */
+ EIGEN_DEVICE_FUNC inline const Scalar* data() const { return m_data; }
+
+ /** \copydoc PlainObjectBase::coeff(Index,Index) const */
+ EIGEN_DEVICE_FUNC
+ inline const Scalar& coeff(Index rowId, Index colId) const
+ {
+ return m_data[colId * colStride() + rowId * rowStride()];
+ }
+
+ /** \copydoc PlainObjectBase::coeff(Index) const */
+ EIGEN_DEVICE_FUNC
+ inline const Scalar& coeff(Index index) const
+ {
+ EIGEN_STATIC_ASSERT_INDEX_BASED_ACCESS(Derived)
+ return m_data[index * innerStride()];
+ }
+
+ /** \copydoc PlainObjectBase::coeffRef(Index,Index) const */
+ EIGEN_DEVICE_FUNC
+ inline const Scalar& coeffRef(Index rowId, Index colId) const
+ {
+ return this->m_data[colId * colStride() + rowId * rowStride()];
+ }
+
+ /** \copydoc PlainObjectBase::coeffRef(Index) const */
+ EIGEN_DEVICE_FUNC
+ inline const Scalar& coeffRef(Index index) const
+ {
+ EIGEN_STATIC_ASSERT_INDEX_BASED_ACCESS(Derived)
+ return this->m_data[index * innerStride()];
+ }
+
+ /** \internal */
+ template<int LoadMode>
+ inline PacketScalar packet(Index rowId, Index colId) const
+ {
+ return internal::ploadt<PacketScalar, LoadMode>
+ (m_data + (colId * colStride() + rowId * rowStride()));
+ }
+
+ /** \internal */
+ template<int LoadMode>
+ inline PacketScalar packet(Index index) const
+ {
+ EIGEN_STATIC_ASSERT_INDEX_BASED_ACCESS(Derived)
+ return internal::ploadt<PacketScalar, LoadMode>(m_data + index * innerStride());
+ }
+
+ /** \internal Constructor for fixed size matrices or vectors */
+ EIGEN_DEVICE_FUNC
+ explicit inline MapBase(PointerType dataPtr) : m_data(dataPtr), m_rows(RowsAtCompileTime), m_cols(ColsAtCompileTime)
+ {
+ EIGEN_STATIC_ASSERT_FIXED_SIZE(Derived)
+ checkSanity<Derived>();
+ }
+
+ /** \internal Constructor for dynamically sized vectors */
+ EIGEN_DEVICE_FUNC
+ inline MapBase(PointerType dataPtr, Index vecSize)
+ : m_data(dataPtr),
+ m_rows(RowsAtCompileTime == Dynamic ? vecSize : Index(RowsAtCompileTime)),
+ m_cols(ColsAtCompileTime == Dynamic ? vecSize : Index(ColsAtCompileTime))
+ {
+ EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
+ eigen_assert(vecSize >= 0);
+ eigen_assert(dataPtr == 0 || SizeAtCompileTime == Dynamic || SizeAtCompileTime == vecSize);
+ checkSanity<Derived>();
+ }
+
+ /** \internal Constructor for dynamically sized matrices */
+ EIGEN_DEVICE_FUNC
+ inline MapBase(PointerType dataPtr, Index rows, Index cols)
+ : m_data(dataPtr), m_rows(rows), m_cols(cols)
+ {
+ eigen_assert( (dataPtr == 0)
+ || ( rows >= 0 && (RowsAtCompileTime == Dynamic || RowsAtCompileTime == rows)
+ && cols >= 0 && (ColsAtCompileTime == Dynamic || ColsAtCompileTime == cols)));
+ checkSanity<Derived>();
+ }
+
+ #ifdef EIGEN_MAPBASE_PLUGIN
+ #include EIGEN_MAPBASE_PLUGIN
+ #endif
+
+ protected:
+ EIGEN_DEFAULT_COPY_CONSTRUCTOR(MapBase)
+ EIGEN_DEFAULT_EMPTY_CONSTRUCTOR_AND_DESTRUCTOR(MapBase)
+
+ template<typename T>
+ EIGEN_DEVICE_FUNC
+ void checkSanity(std::enable_if_t<(internal::traits<T>::Alignment>0),void*> = 0) const
+ {
+#if EIGEN_MAX_ALIGN_BYTES>0
+ // innerStride() is not set yet when this function is called, so we optimistically assume the lowest plausible value:
+ const Index minInnerStride = InnerStrideAtCompileTime == Dynamic ? 1 : Index(InnerStrideAtCompileTime);
+ EIGEN_ONLY_USED_FOR_DEBUG(minInnerStride);
+ eigen_assert(( ((internal::UIntPtr(m_data) % internal::traits<Derived>::Alignment) == 0)
+ || (cols() * rows() * minInnerStride * sizeof(Scalar)) < internal::traits<Derived>::Alignment ) && "data is not aligned");
+#endif
+ }
+
+ template<typename T>
+ EIGEN_DEVICE_FUNC
+ void checkSanity(std::enable_if_t<internal::traits<T>::Alignment==0,void*> = 0) const
+ {}
+
+ PointerType m_data;
+ const internal::variable_if_dynamic<Index, RowsAtCompileTime> m_rows;
+ const internal::variable_if_dynamic<Index, ColsAtCompileTime> m_cols;
+};
+
+/** \ingroup Core_Module
+ *
+ * \brief Base class for non-const dense Map and Block expression with direct access
+ *
+ * This base class provides the non-const low-level accessors (e.g. coeff and coeffRef) of
+ * dense Map and Block objects with direct access.
+ * It inherits MapBase<Derived, ReadOnlyAccessors> which defines the const variant for reading specific entries.
+ *
+ * \sa class Map, class Block
+ */
+template<typename Derived> class MapBase<Derived, WriteAccessors>
+ : public MapBase<Derived, ReadOnlyAccessors>
+{
+ typedef MapBase<Derived, ReadOnlyAccessors> ReadOnlyMapBase;
+ public:
+
+ typedef MapBase<Derived, ReadOnlyAccessors> Base;
+
+ typedef typename Base::Scalar Scalar;
+ typedef typename Base::PacketScalar PacketScalar;
+ typedef typename Base::StorageIndex StorageIndex;
+ typedef typename Base::PointerType PointerType;
+
+ using Base::derived;
+ using Base::rows;
+ using Base::cols;
+ using Base::size;
+ using Base::coeff;
+ using Base::coeffRef;
+
+ using Base::innerStride;
+ using Base::outerStride;
+ using Base::rowStride;
+ using Base::colStride;
+
+ typedef std::conditional_t<
+ internal::is_lvalue<Derived>::value,
+ Scalar,
+ const Scalar
+ > ScalarWithConstIfNotLvalue;
+
+ EIGEN_DEVICE_FUNC
+ inline const Scalar* data() const { return this->m_data; }
+ EIGEN_DEVICE_FUNC
+ inline ScalarWithConstIfNotLvalue* data() { return this->m_data; } // no const-cast here so non-const-correct code will give a compile error
+
+ EIGEN_DEVICE_FUNC
+ inline ScalarWithConstIfNotLvalue& coeffRef(Index row, Index col)
+ {
+ return this->m_data[col * colStride() + row * rowStride()];
+ }
+
+ EIGEN_DEVICE_FUNC
+ inline ScalarWithConstIfNotLvalue& coeffRef(Index index)
+ {
+ EIGEN_STATIC_ASSERT_INDEX_BASED_ACCESS(Derived)
+ return this->m_data[index * innerStride()];
+ }
+
+ template<int StoreMode>
+ inline void writePacket(Index row, Index col, const PacketScalar& val)
+ {
+ internal::pstoret<Scalar, PacketScalar, StoreMode>
+ (this->m_data + (col * colStride() + row * rowStride()), val);
+ }
+
+ template<int StoreMode>
+ inline void writePacket(Index index, const PacketScalar& val)
+ {
+ EIGEN_STATIC_ASSERT_INDEX_BASED_ACCESS(Derived)
+ internal::pstoret<Scalar, PacketScalar, StoreMode>
+ (this->m_data + index * innerStride(), val);
+ }
+
+ EIGEN_DEVICE_FUNC explicit inline MapBase(PointerType dataPtr) : Base(dataPtr) {}
+ EIGEN_DEVICE_FUNC inline MapBase(PointerType dataPtr, Index vecSize) : Base(dataPtr, vecSize) {}
+ EIGEN_DEVICE_FUNC inline MapBase(PointerType dataPtr, Index rows, Index cols) : Base(dataPtr, rows, cols) {}
+
+ EIGEN_DEVICE_FUNC
+ Derived& operator=(const MapBase& other)
+ {
+ ReadOnlyMapBase::Base::operator=(other);
+ return derived();
+ }
+
+ // In theory we could simply refer to Base:Base::operator=, but MSVC does not like Base::Base,
+ // see bugs 821 and 920.
+ using ReadOnlyMapBase::Base::operator=;
+ protected:
+ EIGEN_DEFAULT_COPY_CONSTRUCTOR(MapBase)
+ EIGEN_DEFAULT_EMPTY_CONSTRUCTOR_AND_DESTRUCTOR(MapBase)
+};
+
+#undef EIGEN_STATIC_ASSERT_INDEX_BASED_ACCESS
+
+} // end namespace Eigen
+
+#endif // EIGEN_MAPBASE_H
diff --git a/Eigen/src/Core/MathFunctions.h b/Eigen/src/Core/MathFunctions.h
new file mode 100644
index 0000000..0eee333
--- /dev/null
+++ b/Eigen/src/Core/MathFunctions.h
@@ -0,0 +1,2042 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2006-2010 Benoit Jacob <jacob.benoit.1@gmail.com>
+// Copyright (c) 2021, NVIDIA CORPORATION. All rights reserved.
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_MATHFUNCTIONS_H
+#define EIGEN_MATHFUNCTIONS_H
+
+// TODO this should better be moved to NumTraits
+// Source: WolframAlpha
+#define EIGEN_PI 3.141592653589793238462643383279502884197169399375105820974944592307816406L
+#define EIGEN_LOG2E 1.442695040888963407359924681001892137426645954152985934135449406931109219L
+#define EIGEN_LN2 0.693147180559945309417232121458176568075500134360255254120680009493393621L
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+
+/** \internal \class global_math_functions_filtering_base
+ *
+ * What it does:
+ * Defines a typedef 'type' as follows:
+ * - if type T has a member typedef Eigen_BaseClassForSpecializationOfGlobalMathFuncImpl, then
+ * global_math_functions_filtering_base<T>::type is a typedef for it.
+ * - otherwise, global_math_functions_filtering_base<T>::type is a typedef for T.
+ *
+ * How it's used:
+ * To allow to defined the global math functions (like sin...) in certain cases, like the Array expressions.
+ * When you do sin(array1+array2), the object array1+array2 has a complicated expression type, all what you want to know
+ * is that it inherits ArrayBase. So we implement a partial specialization of sin_impl for ArrayBase<Derived>.
+ * So we must make sure to use sin_impl<ArrayBase<Derived> > and not sin_impl<Derived>, otherwise our partial specialization
+ * won't be used. How does sin know that? That's exactly what global_math_functions_filtering_base tells it.
+ *
+ * How it's implemented:
+ * SFINAE in the style of enable_if. Highly susceptible of breaking compilers. With GCC, it sure does work, but if you replace
+ * the typename dummy by an integer template parameter, it doesn't work anymore!
+ */
+
+template<typename T, typename dummy = void>
+struct global_math_functions_filtering_base
+{
+ typedef T type;
+};
+
+template<typename T> struct always_void { typedef void type; };
+
+template<typename T>
+struct global_math_functions_filtering_base
+ <T,
+ typename always_void<typename T::Eigen_BaseClassForSpecializationOfGlobalMathFuncImpl>::type
+ >
+{
+ typedef typename T::Eigen_BaseClassForSpecializationOfGlobalMathFuncImpl type;
+};
+
+#define EIGEN_MATHFUNC_IMPL(func, scalar) Eigen::internal::func##_impl<typename Eigen::internal::global_math_functions_filtering_base<scalar>::type>
+#define EIGEN_MATHFUNC_RETVAL(func, scalar) typename Eigen::internal::func##_retval<typename Eigen::internal::global_math_functions_filtering_base<scalar>::type>::type
+
+/****************************************************************************
+* Implementation of real *
+****************************************************************************/
+
+template<typename Scalar, bool IsComplex = NumTraits<Scalar>::IsComplex>
+struct real_default_impl
+{
+ typedef typename NumTraits<Scalar>::Real RealScalar;
+ EIGEN_DEVICE_FUNC
+ static inline RealScalar run(const Scalar& x)
+ {
+ return x;
+ }
+};
+
+template<typename Scalar>
+struct real_default_impl<Scalar,true>
+{
+ typedef typename NumTraits<Scalar>::Real RealScalar;
+ EIGEN_DEVICE_FUNC
+ static inline RealScalar run(const Scalar& x)
+ {
+ using std::real;
+ return real(x);
+ }
+};
+
+template<typename Scalar> struct real_impl : real_default_impl<Scalar> {};
+
+#if defined(EIGEN_GPU_COMPILE_PHASE)
+template<typename T>
+struct real_impl<std::complex<T> >
+{
+ typedef T RealScalar;
+ EIGEN_DEVICE_FUNC
+ static inline T run(const std::complex<T>& x)
+ {
+ return x.real();
+ }
+};
+#endif
+
+template<typename Scalar>
+struct real_retval
+{
+ typedef typename NumTraits<Scalar>::Real type;
+};
+
+/****************************************************************************
+* Implementation of imag *
+****************************************************************************/
+
+template<typename Scalar, bool IsComplex = NumTraits<Scalar>::IsComplex>
+struct imag_default_impl
+{
+ typedef typename NumTraits<Scalar>::Real RealScalar;
+ EIGEN_DEVICE_FUNC
+ static inline RealScalar run(const Scalar&)
+ {
+ return RealScalar(0);
+ }
+};
+
+template<typename Scalar>
+struct imag_default_impl<Scalar,true>
+{
+ typedef typename NumTraits<Scalar>::Real RealScalar;
+ EIGEN_DEVICE_FUNC
+ static inline RealScalar run(const Scalar& x)
+ {
+ using std::imag;
+ return imag(x);
+ }
+};
+
+template<typename Scalar> struct imag_impl : imag_default_impl<Scalar> {};
+
+#if defined(EIGEN_GPU_COMPILE_PHASE)
+template<typename T>
+struct imag_impl<std::complex<T> >
+{
+ typedef T RealScalar;
+ EIGEN_DEVICE_FUNC
+ static inline T run(const std::complex<T>& x)
+ {
+ return x.imag();
+ }
+};
+#endif
+
+template<typename Scalar>
+struct imag_retval
+{
+ typedef typename NumTraits<Scalar>::Real type;
+};
+
+/****************************************************************************
+* Implementation of real_ref *
+****************************************************************************/
+
+template<typename Scalar>
+struct real_ref_impl
+{
+ typedef typename NumTraits<Scalar>::Real RealScalar;
+ EIGEN_DEVICE_FUNC
+ static inline RealScalar& run(Scalar& x)
+ {
+ return reinterpret_cast<RealScalar*>(&x)[0];
+ }
+ EIGEN_DEVICE_FUNC
+ static inline const RealScalar& run(const Scalar& x)
+ {
+ return reinterpret_cast<const RealScalar*>(&x)[0];
+ }
+};
+
+template<typename Scalar>
+struct real_ref_retval
+{
+ typedef typename NumTraits<Scalar>::Real & type;
+};
+
+/****************************************************************************
+* Implementation of imag_ref *
+****************************************************************************/
+
+template<typename Scalar, bool IsComplex>
+struct imag_ref_default_impl
+{
+ typedef typename NumTraits<Scalar>::Real RealScalar;
+ EIGEN_DEVICE_FUNC
+ static inline RealScalar& run(Scalar& x)
+ {
+ return reinterpret_cast<RealScalar*>(&x)[1];
+ }
+ EIGEN_DEVICE_FUNC
+ static inline const RealScalar& run(const Scalar& x)
+ {
+ return reinterpret_cast<RealScalar*>(&x)[1];
+ }
+};
+
+template<typename Scalar>
+struct imag_ref_default_impl<Scalar, false>
+{
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
+ static inline Scalar run(Scalar&)
+ {
+ return Scalar(0);
+ }
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
+ static inline const Scalar run(const Scalar&)
+ {
+ return Scalar(0);
+ }
+};
+
+template<typename Scalar>
+struct imag_ref_impl : imag_ref_default_impl<Scalar, NumTraits<Scalar>::IsComplex> {};
+
+template<typename Scalar>
+struct imag_ref_retval
+{
+ typedef typename NumTraits<Scalar>::Real & type;
+};
+
+
+/****************************************************************************
+* Implementation of sign *
+****************************************************************************/
+template<typename Scalar, bool IsComplex = (NumTraits<Scalar>::IsComplex!=0),
+ bool IsInteger = (NumTraits<Scalar>::IsInteger!=0)>
+struct sign_impl
+{
+ EIGEN_DEVICE_FUNC
+ static inline Scalar run(const Scalar& a)
+ {
+ return Scalar( (a>Scalar(0)) - (a<Scalar(0)) );
+ }
+};
+
+template<typename Scalar>
+struct sign_impl<Scalar, false, false>
+{
+ EIGEN_DEVICE_FUNC
+ static inline Scalar run(const Scalar& a)
+ {
+ return (std::isnan)(a) ? a : Scalar( (a>Scalar(0)) - (a<Scalar(0)) );
+ }
+};
+
+template<typename Scalar, bool IsInteger>
+struct sign_impl<Scalar, true, IsInteger>
+{
+ EIGEN_DEVICE_FUNC
+ static inline Scalar run(const Scalar& a)
+ {
+ using real_type = typename NumTraits<Scalar>::Real;
+ real_type aa = std::abs(a);
+ if (aa==real_type(0))
+ return Scalar(0);
+ aa = real_type(1)/aa;
+ return Scalar(a.real()*aa, a.imag()*aa );
+ }
+};
+
+// The sign function for bool is the identity.
+template<>
+struct sign_impl<bool, false, true>
+{
+ EIGEN_DEVICE_FUNC
+ static inline bool run(const bool& a)
+ {
+ return a;
+ }
+};
+
+template<typename Scalar>
+struct sign_retval
+{
+ typedef Scalar type;
+};
+
+/****************************************************************************
+* Implementation of conj *
+****************************************************************************/
+
+template<typename Scalar, bool IsComplex = NumTraits<Scalar>::IsComplex>
+struct conj_default_impl
+{
+ EIGEN_DEVICE_FUNC
+ static inline Scalar run(const Scalar& x)
+ {
+ return x;
+ }
+};
+
+template<typename Scalar>
+struct conj_default_impl<Scalar,true>
+{
+ EIGEN_DEVICE_FUNC
+ static inline Scalar run(const Scalar& x)
+ {
+ using std::conj;
+ return conj(x);
+ }
+};
+
+template<typename Scalar, bool IsComplex = NumTraits<Scalar>::IsComplex>
+struct conj_impl : conj_default_impl<Scalar, IsComplex> {};
+
+template<typename Scalar>
+struct conj_retval
+{
+ typedef Scalar type;
+};
+
+/****************************************************************************
+* Implementation of abs2 *
+****************************************************************************/
+
+template<typename Scalar,bool IsComplex>
+struct abs2_impl_default
+{
+ typedef typename NumTraits<Scalar>::Real RealScalar;
+ EIGEN_DEVICE_FUNC
+ static inline RealScalar run(const Scalar& x)
+ {
+ return x*x;
+ }
+};
+
+template<typename Scalar>
+struct abs2_impl_default<Scalar, true> // IsComplex
+{
+ typedef typename NumTraits<Scalar>::Real RealScalar;
+ EIGEN_DEVICE_FUNC
+ static inline RealScalar run(const Scalar& x)
+ {
+ return x.real()*x.real() + x.imag()*x.imag();
+ }
+};
+
+template<typename Scalar>
+struct abs2_impl
+{
+ typedef typename NumTraits<Scalar>::Real RealScalar;
+ EIGEN_DEVICE_FUNC
+ static inline RealScalar run(const Scalar& x)
+ {
+ return abs2_impl_default<Scalar,NumTraits<Scalar>::IsComplex>::run(x);
+ }
+};
+
+template<typename Scalar>
+struct abs2_retval
+{
+ typedef typename NumTraits<Scalar>::Real type;
+};
+
+/****************************************************************************
+* Implementation of sqrt/rsqrt *
+****************************************************************************/
+
+template<typename Scalar>
+struct sqrt_impl
+{
+ EIGEN_DEVICE_FUNC
+ static EIGEN_ALWAYS_INLINE Scalar run(const Scalar& x)
+ {
+ EIGEN_USING_STD(sqrt);
+ return sqrt(x);
+ }
+};
+
+// Complex sqrt defined in MathFunctionsImpl.h.
+template<typename T> EIGEN_DEVICE_FUNC std::complex<T> complex_sqrt(const std::complex<T>& a_x);
+
+// Custom implementation is faster than `std::sqrt`, works on
+// GPU, and correctly handles special cases (unlike MSVC).
+template<typename T>
+struct sqrt_impl<std::complex<T> >
+{
+ EIGEN_DEVICE_FUNC
+ static EIGEN_ALWAYS_INLINE std::complex<T> run(const std::complex<T>& x)
+ {
+ return complex_sqrt<T>(x);
+ }
+};
+
+template<typename Scalar>
+struct sqrt_retval
+{
+ typedef Scalar type;
+};
+
+// Default implementation relies on numext::sqrt, at bottom of file.
+template<typename T>
+struct rsqrt_impl;
+
+// Complex rsqrt defined in MathFunctionsImpl.h.
+template<typename T> EIGEN_DEVICE_FUNC std::complex<T> complex_rsqrt(const std::complex<T>& a_x);
+
+template<typename T>
+struct rsqrt_impl<std::complex<T> >
+{
+ EIGEN_DEVICE_FUNC
+ static EIGEN_ALWAYS_INLINE std::complex<T> run(const std::complex<T>& x)
+ {
+ return complex_rsqrt<T>(x);
+ }
+};
+
+template<typename Scalar>
+struct rsqrt_retval
+{
+ typedef Scalar type;
+};
+
+/****************************************************************************
+* Implementation of norm1 *
+****************************************************************************/
+
+template<typename Scalar, bool IsComplex>
+struct norm1_default_impl;
+
+template<typename Scalar>
+struct norm1_default_impl<Scalar,true>
+{
+ typedef typename NumTraits<Scalar>::Real RealScalar;
+ EIGEN_DEVICE_FUNC
+ static inline RealScalar run(const Scalar& x)
+ {
+ EIGEN_USING_STD(abs);
+ return abs(x.real()) + abs(x.imag());
+ }
+};
+
+template<typename Scalar>
+struct norm1_default_impl<Scalar, false>
+{
+ EIGEN_DEVICE_FUNC
+ static inline Scalar run(const Scalar& x)
+ {
+ EIGEN_USING_STD(abs);
+ return abs(x);
+ }
+};
+
+template<typename Scalar>
+struct norm1_impl : norm1_default_impl<Scalar, NumTraits<Scalar>::IsComplex> {};
+
+template<typename Scalar>
+struct norm1_retval
+{
+ typedef typename NumTraits<Scalar>::Real type;
+};
+
+/****************************************************************************
+* Implementation of hypot *
+****************************************************************************/
+
+template<typename Scalar> struct hypot_impl;
+
+template<typename Scalar>
+struct hypot_retval
+{
+ typedef typename NumTraits<Scalar>::Real type;
+};
+
+/****************************************************************************
+* Implementation of cast *
+****************************************************************************/
+
+template<typename OldType, typename NewType, typename EnableIf = void>
+struct cast_impl
+{
+ EIGEN_DEVICE_FUNC
+ static inline NewType run(const OldType& x)
+ {
+ return static_cast<NewType>(x);
+ }
+};
+
+// Casting from S -> Complex<T> leads to an implicit conversion from S to T,
+// generating warnings on clang. Here we explicitly cast the real component.
+template<typename OldType, typename NewType>
+struct cast_impl<OldType, NewType,
+ typename std::enable_if_t<
+ !NumTraits<OldType>::IsComplex && NumTraits<NewType>::IsComplex
+ >>
+{
+ EIGEN_DEVICE_FUNC
+ static inline NewType run(const OldType& x)
+ {
+ typedef typename NumTraits<NewType>::Real NewReal;
+ return static_cast<NewType>(static_cast<NewReal>(x));
+ }
+};
+
+// here, for once, we're plainly returning NewType: we don't want cast to do weird things.
+
+template<typename OldType, typename NewType>
+EIGEN_DEVICE_FUNC
+inline NewType cast(const OldType& x)
+{
+ return cast_impl<OldType, NewType>::run(x);
+}
+
+/****************************************************************************
+* Implementation of round *
+****************************************************************************/
+
+template<typename Scalar>
+struct round_impl
+{
+ EIGEN_STATIC_ASSERT((!NumTraits<Scalar>::IsComplex), NUMERIC_TYPE_MUST_BE_REAL)
+
+ EIGEN_DEVICE_FUNC
+ static inline Scalar run(const Scalar& x)
+ {
+ EIGEN_USING_STD(round);
+ return Scalar(round(x));
+ }
+};
+
+template<typename Scalar>
+struct round_retval
+{
+ typedef Scalar type;
+};
+
+/****************************************************************************
+* Implementation of rint *
+****************************************************************************/
+
+template<typename Scalar>
+struct rint_impl {
+ EIGEN_STATIC_ASSERT((!NumTraits<Scalar>::IsComplex), NUMERIC_TYPE_MUST_BE_REAL)
+
+ EIGEN_DEVICE_FUNC
+ static inline Scalar run(const Scalar& x)
+ {
+ EIGEN_USING_STD(rint);
+ return rint(x);
+ }
+};
+
+template<typename Scalar>
+struct rint_retval
+{
+ typedef Scalar type;
+};
+
+/****************************************************************************
+* Implementation of arg *
+****************************************************************************/
+
+// Visual Studio 2017 has a bug where arg(float) returns 0 for negative inputs.
+// This seems to be fixed in VS 2019.
+#if (!EIGEN_COMP_MSVC || EIGEN_COMP_MSVC >= 1920)
+// std::arg is only defined for types of std::complex, or integer types or float/double/long double
+template<typename Scalar,
+ bool HasStdImpl = NumTraits<Scalar>::IsComplex || is_integral<Scalar>::value
+ || is_same<Scalar, float>::value || is_same<Scalar, double>::value
+ || is_same<Scalar, long double>::value >
+struct arg_default_impl;
+
+template<typename Scalar>
+struct arg_default_impl<Scalar, true> {
+ typedef typename NumTraits<Scalar>::Real RealScalar;
+ EIGEN_DEVICE_FUNC
+ static inline RealScalar run(const Scalar& x)
+ {
+ #if defined(EIGEN_HIP_DEVICE_COMPILE)
+ // HIP does not seem to have a native device side implementation for the math routine "arg"
+ using std::arg;
+ #else
+ EIGEN_USING_STD(arg);
+ #endif
+ return static_cast<RealScalar>(arg(x));
+ }
+};
+
+// Must be non-complex floating-point type (e.g. half/bfloat16).
+template<typename Scalar>
+struct arg_default_impl<Scalar, false> {
+ typedef typename NumTraits<Scalar>::Real RealScalar;
+ EIGEN_DEVICE_FUNC
+ static inline RealScalar run(const Scalar& x)
+ {
+ return (x < Scalar(0)) ? RealScalar(EIGEN_PI) : RealScalar(0);
+ }
+};
+#else
+template<typename Scalar, bool IsComplex = NumTraits<Scalar>::IsComplex>
+struct arg_default_impl
+{
+ typedef typename NumTraits<Scalar>::Real RealScalar;
+ EIGEN_DEVICE_FUNC
+ static inline RealScalar run(const Scalar& x)
+ {
+ return (x < RealScalar(0)) ? RealScalar(EIGEN_PI) : RealScalar(0);
+ }
+};
+
+template<typename Scalar>
+struct arg_default_impl<Scalar,true>
+{
+ typedef typename NumTraits<Scalar>::Real RealScalar;
+ EIGEN_DEVICE_FUNC
+ static inline RealScalar run(const Scalar& x)
+ {
+ EIGEN_USING_STD(arg);
+ return arg(x);
+ }
+};
+#endif
+template<typename Scalar> struct arg_impl : arg_default_impl<Scalar> {};
+
+template<typename Scalar>
+struct arg_retval
+{
+ typedef typename NumTraits<Scalar>::Real type;
+};
+
+/****************************************************************************
+* Implementation of expm1 *
+****************************************************************************/
+
+// This implementation is based on GSL Math's expm1.
+namespace std_fallback {
+ // fallback expm1 implementation in case there is no expm1(Scalar) function in namespace of Scalar,
+ // or that there is no suitable std::expm1 function available. Implementation
+ // attributed to Kahan. See: http://www.plunk.org/~hatch/rightway.php.
+ template<typename Scalar>
+ EIGEN_DEVICE_FUNC inline Scalar expm1(const Scalar& x) {
+ EIGEN_STATIC_ASSERT_NON_INTEGER(Scalar)
+ typedef typename NumTraits<Scalar>::Real RealScalar;
+
+ EIGEN_USING_STD(exp);
+ Scalar u = exp(x);
+ if (numext::equal_strict(u, Scalar(1))) {
+ return x;
+ }
+ Scalar um1 = u - RealScalar(1);
+ if (numext::equal_strict(um1, Scalar(-1))) {
+ return RealScalar(-1);
+ }
+
+ EIGEN_USING_STD(log);
+ Scalar logu = log(u);
+ return numext::equal_strict(u, logu) ? u : (u - RealScalar(1)) * x / logu;
+ }
+}
+
+template<typename Scalar>
+struct expm1_impl {
+ EIGEN_DEVICE_FUNC static inline Scalar run(const Scalar& x)
+ {
+ EIGEN_STATIC_ASSERT_NON_INTEGER(Scalar)
+ using std::expm1;
+ return expm1(x);
+ }
+};
+
+template<typename Scalar>
+struct expm1_retval
+{
+ typedef Scalar type;
+};
+
+/****************************************************************************
+* Implementation of log *
+****************************************************************************/
+
+// Complex log defined in MathFunctionsImpl.h.
+template<typename T> EIGEN_DEVICE_FUNC std::complex<T> complex_log(const std::complex<T>& z);
+
+template<typename Scalar>
+struct log_impl {
+ EIGEN_DEVICE_FUNC static inline Scalar run(const Scalar& x)
+ {
+ EIGEN_USING_STD(log);
+ return static_cast<Scalar>(log(x));
+ }
+};
+
+template<typename Scalar>
+struct log_impl<std::complex<Scalar> > {
+ EIGEN_DEVICE_FUNC static inline std::complex<Scalar> run(const std::complex<Scalar>& z)
+ {
+ return complex_log(z);
+ }
+};
+
+/****************************************************************************
+* Implementation of log1p *
+****************************************************************************/
+
+namespace std_fallback {
+ // fallback log1p implementation in case there is no log1p(Scalar) function in namespace of Scalar,
+ // or that there is no suitable std::log1p function available
+ template<typename Scalar>
+ EIGEN_DEVICE_FUNC inline Scalar log1p(const Scalar& x) {
+ EIGEN_STATIC_ASSERT_NON_INTEGER(Scalar)
+ typedef typename NumTraits<Scalar>::Real RealScalar;
+ EIGEN_USING_STD(log);
+ Scalar x1p = RealScalar(1) + x;
+ Scalar log_1p = log_impl<Scalar>::run(x1p);
+ const bool is_small = numext::equal_strict(x1p, Scalar(1));
+ const bool is_inf = numext::equal_strict(x1p, log_1p);
+ return (is_small || is_inf) ? x : x * (log_1p / (x1p - RealScalar(1)));
+ }
+}
+
+template<typename Scalar>
+struct log1p_impl {
+ EIGEN_STATIC_ASSERT_NON_INTEGER(Scalar)
+
+ EIGEN_DEVICE_FUNC static inline Scalar run(const Scalar& x)
+ {
+ using std::log1p;
+ return log1p(x);
+ }
+};
+
+// Specialization for complex types that are not supported by std::log1p.
+template <typename RealScalar>
+struct log1p_impl<std::complex<RealScalar> > {
+ EIGEN_STATIC_ASSERT_NON_INTEGER(RealScalar)
+
+ EIGEN_DEVICE_FUNC static inline std::complex<RealScalar> run(
+ const std::complex<RealScalar>& x) {
+ return std_fallback::log1p(x);
+ }
+};
+
+template<typename Scalar>
+struct log1p_retval
+{
+ typedef Scalar type;
+};
+
+/****************************************************************************
+* Implementation of pow *
+****************************************************************************/
+
+template<typename ScalarX,typename ScalarY, bool IsInteger = NumTraits<ScalarX>::IsInteger&&NumTraits<ScalarY>::IsInteger>
+struct pow_impl
+{
+ //typedef Scalar retval;
+ typedef typename ScalarBinaryOpTraits<ScalarX,ScalarY,internal::scalar_pow_op<ScalarX,ScalarY> >::ReturnType result_type;
+ static EIGEN_DEVICE_FUNC inline result_type run(const ScalarX& x, const ScalarY& y)
+ {
+ EIGEN_USING_STD(pow);
+ return pow(x, y);
+ }
+};
+
+template<typename ScalarX,typename ScalarY>
+struct pow_impl<ScalarX,ScalarY, true>
+{
+ typedef ScalarX result_type;
+ static EIGEN_DEVICE_FUNC inline ScalarX run(ScalarX x, ScalarY y)
+ {
+ ScalarX res(1);
+ eigen_assert(!NumTraits<ScalarY>::IsSigned || y >= 0);
+ if(y & 1) res *= x;
+ y >>= 1;
+ while(y)
+ {
+ x *= x;
+ if(y&1) res *= x;
+ y >>= 1;
+ }
+ return res;
+ }
+};
+
+/****************************************************************************
+* Implementation of random *
+****************************************************************************/
+
+template<typename Scalar,
+ bool IsComplex,
+ bool IsInteger>
+struct random_default_impl {};
+
+template<typename Scalar>
+struct random_impl : random_default_impl<Scalar, NumTraits<Scalar>::IsComplex, NumTraits<Scalar>::IsInteger> {};
+
+template<typename Scalar>
+struct random_retval
+{
+ typedef Scalar type;
+};
+
+template<typename Scalar> inline EIGEN_MATHFUNC_RETVAL(random, Scalar) random(const Scalar& x, const Scalar& y);
+template<typename Scalar> inline EIGEN_MATHFUNC_RETVAL(random, Scalar) random();
+
+template<typename Scalar>
+struct random_default_impl<Scalar, false, false>
+{
+ static inline Scalar run(const Scalar& x, const Scalar& y)
+ {
+ return x + (y-x) * Scalar(std::rand()) / Scalar(RAND_MAX);
+ }
+ static inline Scalar run()
+ {
+ return run(Scalar(NumTraits<Scalar>::IsSigned ? -1 : 0), Scalar(1));
+ }
+};
+
+enum {
+ meta_floor_log2_terminate,
+ meta_floor_log2_move_up,
+ meta_floor_log2_move_down,
+ meta_floor_log2_bogus
+};
+
+template<unsigned int n, int lower, int upper> struct meta_floor_log2_selector
+{
+ enum { middle = (lower + upper) / 2,
+ value = (upper <= lower + 1) ? int(meta_floor_log2_terminate)
+ : (n < (1 << middle)) ? int(meta_floor_log2_move_down)
+ : (n==0) ? int(meta_floor_log2_bogus)
+ : int(meta_floor_log2_move_up)
+ };
+};
+
+template<unsigned int n,
+ int lower = 0,
+ int upper = sizeof(unsigned int) * CHAR_BIT - 1,
+ int selector = meta_floor_log2_selector<n, lower, upper>::value>
+struct meta_floor_log2 {};
+
+template<unsigned int n, int lower, int upper>
+struct meta_floor_log2<n, lower, upper, meta_floor_log2_move_down>
+{
+ enum { value = meta_floor_log2<n, lower, meta_floor_log2_selector<n, lower, upper>::middle>::value };
+};
+
+template<unsigned int n, int lower, int upper>
+struct meta_floor_log2<n, lower, upper, meta_floor_log2_move_up>
+{
+ enum { value = meta_floor_log2<n, meta_floor_log2_selector<n, lower, upper>::middle, upper>::value };
+};
+
+template<unsigned int n, int lower, int upper>
+struct meta_floor_log2<n, lower, upper, meta_floor_log2_terminate>
+{
+ enum { value = (n >= ((unsigned int)(1) << (lower+1))) ? lower+1 : lower };
+};
+
+template<unsigned int n, int lower, int upper>
+struct meta_floor_log2<n, lower, upper, meta_floor_log2_bogus>
+{
+ // no value, error at compile time
+};
+
+template<typename Scalar>
+struct random_default_impl<Scalar, false, true>
+{
+ static inline Scalar run(const Scalar& x, const Scalar& y)
+ {
+ if (y <= x)
+ return x;
+ // ScalarU is the unsigned counterpart of Scalar, possibly Scalar itself.
+ typedef typename make_unsigned<Scalar>::type ScalarU;
+ // ScalarX is the widest of ScalarU and unsigned int.
+ // We'll deal only with ScalarX and unsigned int below thus avoiding signed
+ // types and arithmetic and signed overflows (which are undefined behavior).
+ typedef std::conditional_t<(ScalarU(-1) > unsigned(-1)), ScalarU, unsigned> ScalarX;
+ // The following difference doesn't overflow, provided our integer types are two's
+ // complement and have the same number of padding bits in signed and unsigned variants.
+ // This is the case in most modern implementations of C++.
+ ScalarX range = ScalarX(y) - ScalarX(x);
+ ScalarX offset = 0;
+ ScalarX divisor = 1;
+ ScalarX multiplier = 1;
+ const unsigned rand_max = RAND_MAX;
+ if (range <= rand_max) divisor = (rand_max + 1) / (range + 1);
+ else multiplier = 1 + range / (rand_max + 1);
+ // Rejection sampling.
+ do {
+ offset = (unsigned(std::rand()) * multiplier) / divisor;
+ } while (offset > range);
+ return Scalar(ScalarX(x) + offset);
+ }
+
+ static inline Scalar run()
+ {
+#ifdef EIGEN_MAKING_DOCS
+ return run(Scalar(NumTraits<Scalar>::IsSigned ? -10 : 0), Scalar(10));
+#else
+ enum { rand_bits = meta_floor_log2<(unsigned int)(RAND_MAX)+1>::value,
+ scalar_bits = sizeof(Scalar) * CHAR_BIT,
+ shift = plain_enum_max(0, int(rand_bits) - int(scalar_bits)),
+ offset = NumTraits<Scalar>::IsSigned ? (1 << (plain_enum_min(rand_bits, scalar_bits)-1)) : 0
+ };
+ return Scalar((std::rand() >> shift) - offset);
+#endif
+ }
+};
+
+template<typename Scalar>
+struct random_default_impl<Scalar, true, false>
+{
+ static inline Scalar run(const Scalar& x, const Scalar& y)
+ {
+ return Scalar(random(x.real(), y.real()),
+ random(x.imag(), y.imag()));
+ }
+ static inline Scalar run()
+ {
+ typedef typename NumTraits<Scalar>::Real RealScalar;
+ return Scalar(random<RealScalar>(), random<RealScalar>());
+ }
+};
+
+template<typename Scalar>
+inline EIGEN_MATHFUNC_RETVAL(random, Scalar) random(const Scalar& x, const Scalar& y)
+{
+ return EIGEN_MATHFUNC_IMPL(random, Scalar)::run(x, y);
+}
+
+template<typename Scalar>
+inline EIGEN_MATHFUNC_RETVAL(random, Scalar) random()
+{
+ return EIGEN_MATHFUNC_IMPL(random, Scalar)::run();
+}
+
+// Implementation of is* functions
+
+// std::is* do not work with fast-math and gcc, std::is* are available on MSVC 2013 and newer, as well as in clang.
+#if (!(EIGEN_COMP_GNUC_STRICT && __FINITE_MATH_ONLY__)) || (EIGEN_COMP_MSVC) || (EIGEN_COMP_CLANG)
+#define EIGEN_USE_STD_FPCLASSIFY 1
+#else
+#define EIGEN_USE_STD_FPCLASSIFY 0
+#endif
+
+template<typename T>
+EIGEN_DEVICE_FUNC
+std::enable_if_t<internal::is_integral<T>::value,bool>
+isnan_impl(const T&) { return false; }
+
+template<typename T>
+EIGEN_DEVICE_FUNC
+std::enable_if_t<internal::is_integral<T>::value,bool>
+isinf_impl(const T&) { return false; }
+
+template<typename T>
+EIGEN_DEVICE_FUNC
+std::enable_if_t<internal::is_integral<T>::value,bool>
+isfinite_impl(const T&) { return true; }
+
+template<typename T>
+EIGEN_DEVICE_FUNC
+std::enable_if_t<(!internal::is_integral<T>::value)&&(!NumTraits<T>::IsComplex),bool>
+isfinite_impl(const T& x)
+{
+ #if defined(EIGEN_GPU_COMPILE_PHASE)
+ return (::isfinite)(x);
+ #elif EIGEN_USE_STD_FPCLASSIFY
+ using std::isfinite;
+ return isfinite EIGEN_NOT_A_MACRO (x);
+ #else
+ return x<=NumTraits<T>::highest() && x>=NumTraits<T>::lowest();
+ #endif
+}
+
+template<typename T>
+EIGEN_DEVICE_FUNC
+std::enable_if_t<(!internal::is_integral<T>::value)&&(!NumTraits<T>::IsComplex),bool>
+isinf_impl(const T& x)
+{
+ #if defined(EIGEN_GPU_COMPILE_PHASE)
+ return (::isinf)(x);
+ #elif EIGEN_USE_STD_FPCLASSIFY
+ using std::isinf;
+ return isinf EIGEN_NOT_A_MACRO (x);
+ #else
+ return x>NumTraits<T>::highest() || x<NumTraits<T>::lowest();
+ #endif
+}
+
+template<typename T>
+EIGEN_DEVICE_FUNC
+std::enable_if_t<(!internal::is_integral<T>::value)&&(!NumTraits<T>::IsComplex),bool>
+isnan_impl(const T& x)
+{
+ #if defined(EIGEN_GPU_COMPILE_PHASE)
+ return (::isnan)(x);
+ #elif EIGEN_USE_STD_FPCLASSIFY
+ using std::isnan;
+ return isnan EIGEN_NOT_A_MACRO (x);
+ #else
+ return x != x;
+ #endif
+}
+
+#if (!EIGEN_USE_STD_FPCLASSIFY)
+
+#if EIGEN_COMP_MSVC
+
+template<typename T> EIGEN_DEVICE_FUNC bool isinf_msvc_helper(T x)
+{
+ return _fpclass(x)==_FPCLASS_NINF || _fpclass(x)==_FPCLASS_PINF;
+}
+
+//MSVC defines a _isnan builtin function, but for double only
+EIGEN_DEVICE_FUNC inline bool isnan_impl(const long double& x) { return _isnan(x)!=0; }
+EIGEN_DEVICE_FUNC inline bool isnan_impl(const double& x) { return _isnan(x)!=0; }
+EIGEN_DEVICE_FUNC inline bool isnan_impl(const float& x) { return _isnan(x)!=0; }
+
+EIGEN_DEVICE_FUNC inline bool isinf_impl(const long double& x) { return isinf_msvc_helper(x); }
+EIGEN_DEVICE_FUNC inline bool isinf_impl(const double& x) { return isinf_msvc_helper(x); }
+EIGEN_DEVICE_FUNC inline bool isinf_impl(const float& x) { return isinf_msvc_helper(x); }
+
+#elif (defined __FINITE_MATH_ONLY__ && __FINITE_MATH_ONLY__ && EIGEN_COMP_GNUC)
+
+#if EIGEN_COMP_GNUC
+ #define EIGEN_TMP_NOOPT_ATTRIB EIGEN_DEVICE_FUNC inline __attribute__((optimize("no-finite-math-only")))
+#else
+ // NOTE the inline qualifier and noinline attribute are both needed: the former is to avoid linking issue (duplicate symbol),
+ // while the second prevent too aggressive optimizations in fast-math mode:
+ #define EIGEN_TMP_NOOPT_ATTRIB EIGEN_DEVICE_FUNC inline __attribute__((noinline,optimize("no-finite-math-only")))
+#endif
+
+template<> EIGEN_TMP_NOOPT_ATTRIB bool isnan_impl(const long double& x) { return __builtin_isnan(x); }
+template<> EIGEN_TMP_NOOPT_ATTRIB bool isnan_impl(const double& x) { return __builtin_isnan(x); }
+template<> EIGEN_TMP_NOOPT_ATTRIB bool isnan_impl(const float& x) { return __builtin_isnan(x); }
+template<> EIGEN_TMP_NOOPT_ATTRIB bool isinf_impl(const double& x) { return __builtin_isinf(x); }
+template<> EIGEN_TMP_NOOPT_ATTRIB bool isinf_impl(const float& x) { return __builtin_isinf(x); }
+template<> EIGEN_TMP_NOOPT_ATTRIB bool isinf_impl(const long double& x) { return __builtin_isinf(x); }
+
+#undef EIGEN_TMP_NOOPT_ATTRIB
+
+#endif
+
+#endif
+
+// The following overload are defined at the end of this file
+template<typename T> EIGEN_DEVICE_FUNC bool isfinite_impl(const std::complex<T>& x);
+template<typename T> EIGEN_DEVICE_FUNC bool isnan_impl(const std::complex<T>& x);
+template<typename T> EIGEN_DEVICE_FUNC bool isinf_impl(const std::complex<T>& x);
+
+template<typename T> T generic_fast_tanh_float(const T& a_x);
+} // end namespace internal
+
+/****************************************************************************
+* Generic math functions *
+****************************************************************************/
+
+namespace numext {
+
+#if (!defined(EIGEN_GPUCC) || defined(EIGEN_CONSTEXPR_ARE_DEVICE_FUNC))
+template<typename T>
+EIGEN_DEVICE_FUNC
+EIGEN_ALWAYS_INLINE T mini(const T& x, const T& y)
+{
+ EIGEN_USING_STD(min)
+ return min EIGEN_NOT_A_MACRO (x,y);
+}
+
+template<typename T>
+EIGEN_DEVICE_FUNC
+EIGEN_ALWAYS_INLINE T maxi(const T& x, const T& y)
+{
+ EIGEN_USING_STD(max)
+ return max EIGEN_NOT_A_MACRO (x,y);
+}
+#else
+template<typename T>
+EIGEN_DEVICE_FUNC
+EIGEN_ALWAYS_INLINE T mini(const T& x, const T& y)
+{
+ return y < x ? y : x;
+}
+template<>
+EIGEN_DEVICE_FUNC
+EIGEN_ALWAYS_INLINE float mini(const float& x, const float& y)
+{
+ return fminf(x, y);
+}
+template<>
+EIGEN_DEVICE_FUNC
+EIGEN_ALWAYS_INLINE double mini(const double& x, const double& y)
+{
+ return fmin(x, y);
+}
+template<>
+EIGEN_DEVICE_FUNC
+EIGEN_ALWAYS_INLINE long double mini(const long double& x, const long double& y)
+{
+#if defined(EIGEN_HIPCC)
+ // no "fminl" on HIP yet
+ return (x < y) ? x : y;
+#else
+ return fminl(x, y);
+#endif
+}
+
+template<typename T>
+EIGEN_DEVICE_FUNC
+EIGEN_ALWAYS_INLINE T maxi(const T& x, const T& y)
+{
+ return x < y ? y : x;
+}
+template<>
+EIGEN_DEVICE_FUNC
+EIGEN_ALWAYS_INLINE float maxi(const float& x, const float& y)
+{
+ return fmaxf(x, y);
+}
+template<>
+EIGEN_DEVICE_FUNC
+EIGEN_ALWAYS_INLINE double maxi(const double& x, const double& y)
+{
+ return fmax(x, y);
+}
+template<>
+EIGEN_DEVICE_FUNC
+EIGEN_ALWAYS_INLINE long double maxi(const long double& x, const long double& y)
+{
+#if defined(EIGEN_HIPCC)
+ // no "fmaxl" on HIP yet
+ return (x > y) ? x : y;
+#else
+ return fmaxl(x, y);
+#endif
+}
+#endif
+
+#if defined(SYCL_DEVICE_ONLY)
+
+
+#define SYCL_SPECIALIZE_SIGNED_INTEGER_TYPES_BINARY(NAME, FUNC) \
+ SYCL_SPECIALIZE_BINARY_FUNC(NAME, FUNC, cl::sycl::cl_char) \
+ SYCL_SPECIALIZE_BINARY_FUNC(NAME, FUNC, cl::sycl::cl_short) \
+ SYCL_SPECIALIZE_BINARY_FUNC(NAME, FUNC, cl::sycl::cl_int) \
+ SYCL_SPECIALIZE_BINARY_FUNC(NAME, FUNC, cl::sycl::cl_long)
+#define SYCL_SPECIALIZE_SIGNED_INTEGER_TYPES_UNARY(NAME, FUNC) \
+ SYCL_SPECIALIZE_UNARY_FUNC(NAME, FUNC, cl::sycl::cl_char) \
+ SYCL_SPECIALIZE_UNARY_FUNC(NAME, FUNC, cl::sycl::cl_short) \
+ SYCL_SPECIALIZE_UNARY_FUNC(NAME, FUNC, cl::sycl::cl_int) \
+ SYCL_SPECIALIZE_UNARY_FUNC(NAME, FUNC, cl::sycl::cl_long)
+#define SYCL_SPECIALIZE_UNSIGNED_INTEGER_TYPES_BINARY(NAME, FUNC) \
+ SYCL_SPECIALIZE_BINARY_FUNC(NAME, FUNC, cl::sycl::cl_uchar) \
+ SYCL_SPECIALIZE_BINARY_FUNC(NAME, FUNC, cl::sycl::cl_ushort) \
+ SYCL_SPECIALIZE_BINARY_FUNC(NAME, FUNC, cl::sycl::cl_uint) \
+ SYCL_SPECIALIZE_BINARY_FUNC(NAME, FUNC, cl::sycl::cl_ulong)
+#define SYCL_SPECIALIZE_UNSIGNED_INTEGER_TYPES_UNARY(NAME, FUNC) \
+ SYCL_SPECIALIZE_UNARY_FUNC(NAME, FUNC, cl::sycl::cl_uchar) \
+ SYCL_SPECIALIZE_UNARY_FUNC(NAME, FUNC, cl::sycl::cl_ushort) \
+ SYCL_SPECIALIZE_UNARY_FUNC(NAME, FUNC, cl::sycl::cl_uint) \
+ SYCL_SPECIALIZE_UNARY_FUNC(NAME, FUNC, cl::sycl::cl_ulong)
+#define SYCL_SPECIALIZE_INTEGER_TYPES_BINARY(NAME, FUNC) \
+ SYCL_SPECIALIZE_SIGNED_INTEGER_TYPES_BINARY(NAME, FUNC) \
+ SYCL_SPECIALIZE_UNSIGNED_INTEGER_TYPES_BINARY(NAME, FUNC)
+#define SYCL_SPECIALIZE_INTEGER_TYPES_UNARY(NAME, FUNC) \
+ SYCL_SPECIALIZE_SIGNED_INTEGER_TYPES_UNARY(NAME, FUNC) \
+ SYCL_SPECIALIZE_UNSIGNED_INTEGER_TYPES_UNARY(NAME, FUNC)
+#define SYCL_SPECIALIZE_FLOATING_TYPES_BINARY(NAME, FUNC) \
+ SYCL_SPECIALIZE_BINARY_FUNC(NAME, FUNC, cl::sycl::cl_float) \
+ SYCL_SPECIALIZE_BINARY_FUNC(NAME, FUNC,cl::sycl::cl_double)
+#define SYCL_SPECIALIZE_FLOATING_TYPES_UNARY(NAME, FUNC) \
+ SYCL_SPECIALIZE_UNARY_FUNC(NAME, FUNC, cl::sycl::cl_float) \
+ SYCL_SPECIALIZE_UNARY_FUNC(NAME, FUNC,cl::sycl::cl_double)
+#define SYCL_SPECIALIZE_FLOATING_TYPES_UNARY_FUNC_RET_TYPE(NAME, FUNC, RET_TYPE) \
+ SYCL_SPECIALIZE_GEN_UNARY_FUNC(NAME, FUNC, RET_TYPE, cl::sycl::cl_float) \
+ SYCL_SPECIALIZE_GEN_UNARY_FUNC(NAME, FUNC, RET_TYPE, cl::sycl::cl_double)
+
+#define SYCL_SPECIALIZE_GEN_UNARY_FUNC(NAME, FUNC, RET_TYPE, ARG_TYPE) \
+template<> \
+ EIGEN_DEVICE_FUNC \
+ EIGEN_ALWAYS_INLINE RET_TYPE NAME(const ARG_TYPE& x) { \
+ return cl::sycl::FUNC(x); \
+ }
+
+#define SYCL_SPECIALIZE_UNARY_FUNC(NAME, FUNC, TYPE) \
+ SYCL_SPECIALIZE_GEN_UNARY_FUNC(NAME, FUNC, TYPE, TYPE)
+
+#define SYCL_SPECIALIZE_GEN1_BINARY_FUNC(NAME, FUNC, RET_TYPE, ARG_TYPE1, ARG_TYPE2) \
+ template<> \
+ EIGEN_DEVICE_FUNC \
+ EIGEN_ALWAYS_INLINE RET_TYPE NAME(const ARG_TYPE1& x, const ARG_TYPE2& y) { \
+ return cl::sycl::FUNC(x, y); \
+ }
+
+#define SYCL_SPECIALIZE_GEN2_BINARY_FUNC(NAME, FUNC, RET_TYPE, ARG_TYPE) \
+ SYCL_SPECIALIZE_GEN1_BINARY_FUNC(NAME, FUNC, RET_TYPE, ARG_TYPE, ARG_TYPE)
+
+#define SYCL_SPECIALIZE_BINARY_FUNC(NAME, FUNC, TYPE) \
+ SYCL_SPECIALIZE_GEN2_BINARY_FUNC(NAME, FUNC, TYPE, TYPE)
+
+SYCL_SPECIALIZE_INTEGER_TYPES_BINARY(mini, min)
+SYCL_SPECIALIZE_FLOATING_TYPES_BINARY(mini, fmin)
+SYCL_SPECIALIZE_INTEGER_TYPES_BINARY(maxi, max)
+SYCL_SPECIALIZE_FLOATING_TYPES_BINARY(maxi, fmax)
+
+#endif
+
+
+template<typename Scalar>
+EIGEN_DEVICE_FUNC
+inline EIGEN_MATHFUNC_RETVAL(real, Scalar) real(const Scalar& x)
+{
+ return EIGEN_MATHFUNC_IMPL(real, Scalar)::run(x);
+}
+
+template<typename Scalar>
+EIGEN_DEVICE_FUNC
+inline internal::add_const_on_value_type_t< EIGEN_MATHFUNC_RETVAL(real_ref, Scalar) > real_ref(const Scalar& x)
+{
+ return internal::real_ref_impl<Scalar>::run(x);
+}
+
+template<typename Scalar>
+EIGEN_DEVICE_FUNC
+inline EIGEN_MATHFUNC_RETVAL(real_ref, Scalar) real_ref(Scalar& x)
+{
+ return EIGEN_MATHFUNC_IMPL(real_ref, Scalar)::run(x);
+}
+
+template<typename Scalar>
+EIGEN_DEVICE_FUNC
+inline EIGEN_MATHFUNC_RETVAL(imag, Scalar) imag(const Scalar& x)
+{
+ return EIGEN_MATHFUNC_IMPL(imag, Scalar)::run(x);
+}
+
+template<typename Scalar>
+EIGEN_DEVICE_FUNC
+inline EIGEN_MATHFUNC_RETVAL(arg, Scalar) arg(const Scalar& x)
+{
+ return EIGEN_MATHFUNC_IMPL(arg, Scalar)::run(x);
+}
+
+template<typename Scalar>
+EIGEN_DEVICE_FUNC
+inline internal::add_const_on_value_type_t< EIGEN_MATHFUNC_RETVAL(imag_ref, Scalar) > imag_ref(const Scalar& x)
+{
+ return internal::imag_ref_impl<Scalar>::run(x);
+}
+
+template<typename Scalar>
+EIGEN_DEVICE_FUNC
+inline EIGEN_MATHFUNC_RETVAL(imag_ref, Scalar) imag_ref(Scalar& x)
+{
+ return EIGEN_MATHFUNC_IMPL(imag_ref, Scalar)::run(x);
+}
+
+template<typename Scalar>
+EIGEN_DEVICE_FUNC
+inline EIGEN_MATHFUNC_RETVAL(conj, Scalar) conj(const Scalar& x)
+{
+ return EIGEN_MATHFUNC_IMPL(conj, Scalar)::run(x);
+}
+
+template<typename Scalar>
+EIGEN_DEVICE_FUNC
+inline EIGEN_MATHFUNC_RETVAL(sign, Scalar) sign(const Scalar& x)
+{
+ return EIGEN_MATHFUNC_IMPL(sign, Scalar)::run(x);
+}
+
+template<typename Scalar>
+EIGEN_DEVICE_FUNC
+inline EIGEN_MATHFUNC_RETVAL(abs2, Scalar) abs2(const Scalar& x)
+{
+ return EIGEN_MATHFUNC_IMPL(abs2, Scalar)::run(x);
+}
+
+EIGEN_DEVICE_FUNC
+inline bool abs2(bool x) { return x; }
+
+template<typename T>
+EIGEN_DEVICE_FUNC
+EIGEN_ALWAYS_INLINE T absdiff(const T& x, const T& y)
+{
+ return x > y ? x - y : y - x;
+}
+template<>
+EIGEN_DEVICE_FUNC
+EIGEN_ALWAYS_INLINE float absdiff(const float& x, const float& y)
+{
+ return fabsf(x - y);
+}
+template<>
+EIGEN_DEVICE_FUNC
+EIGEN_ALWAYS_INLINE double absdiff(const double& x, const double& y)
+{
+ return fabs(x - y);
+}
+
+#if !defined(EIGEN_GPUCC)
+// HIP and CUDA do not support long double.
+template<>
+EIGEN_DEVICE_FUNC
+EIGEN_ALWAYS_INLINE long double absdiff(const long double& x, const long double& y) {
+ return fabsl(x - y);
+}
+#endif
+
+template<typename Scalar>
+EIGEN_DEVICE_FUNC
+inline EIGEN_MATHFUNC_RETVAL(norm1, Scalar) norm1(const Scalar& x)
+{
+ return EIGEN_MATHFUNC_IMPL(norm1, Scalar)::run(x);
+}
+
+template<typename Scalar>
+EIGEN_DEVICE_FUNC
+inline EIGEN_MATHFUNC_RETVAL(hypot, Scalar) hypot(const Scalar& x, const Scalar& y)
+{
+ return EIGEN_MATHFUNC_IMPL(hypot, Scalar)::run(x, y);
+}
+
+#if defined(SYCL_DEVICE_ONLY)
+ SYCL_SPECIALIZE_FLOATING_TYPES_BINARY(hypot, hypot)
+#endif
+
+template<typename Scalar>
+EIGEN_DEVICE_FUNC
+inline EIGEN_MATHFUNC_RETVAL(log1p, Scalar) log1p(const Scalar& x)
+{
+ return EIGEN_MATHFUNC_IMPL(log1p, Scalar)::run(x);
+}
+
+#if defined(SYCL_DEVICE_ONLY)
+SYCL_SPECIALIZE_FLOATING_TYPES_UNARY(log1p, log1p)
+#endif
+
+#if defined(EIGEN_GPUCC)
+template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
+float log1p(const float &x) { return ::log1pf(x); }
+
+template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
+double log1p(const double &x) { return ::log1p(x); }
+#endif
+
+template<typename ScalarX,typename ScalarY>
+EIGEN_DEVICE_FUNC
+inline typename internal::pow_impl<ScalarX,ScalarY>::result_type pow(const ScalarX& x, const ScalarY& y)
+{
+ return internal::pow_impl<ScalarX,ScalarY>::run(x, y);
+}
+
+#if defined(SYCL_DEVICE_ONLY)
+SYCL_SPECIALIZE_FLOATING_TYPES_BINARY(pow, pow)
+#endif
+
+template<typename T> EIGEN_DEVICE_FUNC bool (isnan) (const T &x) { return internal::isnan_impl(x); }
+template<typename T> EIGEN_DEVICE_FUNC bool (isinf) (const T &x) { return internal::isinf_impl(x); }
+template<typename T> EIGEN_DEVICE_FUNC bool (isfinite)(const T &x) { return internal::isfinite_impl(x); }
+
+#if defined(SYCL_DEVICE_ONLY)
+SYCL_SPECIALIZE_FLOATING_TYPES_UNARY_FUNC_RET_TYPE(isnan, isnan, bool)
+SYCL_SPECIALIZE_FLOATING_TYPES_UNARY_FUNC_RET_TYPE(isinf, isinf, bool)
+SYCL_SPECIALIZE_FLOATING_TYPES_UNARY_FUNC_RET_TYPE(isfinite, isfinite, bool)
+#endif
+
+template<typename Scalar>
+EIGEN_DEVICE_FUNC
+inline EIGEN_MATHFUNC_RETVAL(rint, Scalar) rint(const Scalar& x)
+{
+ return EIGEN_MATHFUNC_IMPL(rint, Scalar)::run(x);
+}
+
+template<typename Scalar>
+EIGEN_DEVICE_FUNC
+inline EIGEN_MATHFUNC_RETVAL(round, Scalar) round(const Scalar& x)
+{
+ return EIGEN_MATHFUNC_IMPL(round, Scalar)::run(x);
+}
+
+#if defined(SYCL_DEVICE_ONLY)
+SYCL_SPECIALIZE_FLOATING_TYPES_UNARY(round, round)
+#endif
+
+template<typename T>
+EIGEN_DEVICE_FUNC
+T (floor)(const T& x)
+{
+ EIGEN_USING_STD(floor)
+ return floor(x);
+}
+
+#if defined(SYCL_DEVICE_ONLY)
+SYCL_SPECIALIZE_FLOATING_TYPES_UNARY(floor, floor)
+#endif
+
+#if defined(EIGEN_GPUCC)
+template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
+float floor(const float &x) { return ::floorf(x); }
+
+template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
+double floor(const double &x) { return ::floor(x); }
+#endif
+
+template<typename T>
+EIGEN_DEVICE_FUNC
+T (ceil)(const T& x)
+{
+ EIGEN_USING_STD(ceil);
+ return ceil(x);
+}
+
+#if defined(SYCL_DEVICE_ONLY)
+SYCL_SPECIALIZE_FLOATING_TYPES_UNARY(ceil, ceil)
+#endif
+
+#if defined(EIGEN_GPUCC)
+template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
+float ceil(const float &x) { return ::ceilf(x); }
+
+template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
+double ceil(const double &x) { return ::ceil(x); }
+#endif
+
+
+/** Log base 2 for 32 bits positive integers.
+ * Conveniently returns 0 for x==0. */
+inline int log2(int x)
+{
+ eigen_assert(x>=0);
+ unsigned int v(x);
+ static const int table[32] = { 0, 9, 1, 10, 13, 21, 2, 29, 11, 14, 16, 18, 22, 25, 3, 30, 8, 12, 20, 28, 15, 17, 24, 7, 19, 27, 23, 6, 26, 5, 4, 31 };
+ v |= v >> 1;
+ v |= v >> 2;
+ v |= v >> 4;
+ v |= v >> 8;
+ v |= v >> 16;
+ return table[(v * 0x07C4ACDDU) >> 27];
+}
+
+/** \returns the square root of \a x.
+ *
+ * It is essentially equivalent to
+ * \code using std::sqrt; return sqrt(x); \endcode
+ * but slightly faster for float/double and some compilers (e.g., gcc), thanks to
+ * specializations when SSE is enabled.
+ *
+ * It's usage is justified in performance critical functions, like norm/normalize.
+ */
+template<typename Scalar>
+EIGEN_DEVICE_FUNC
+EIGEN_ALWAYS_INLINE EIGEN_MATHFUNC_RETVAL(sqrt, Scalar) sqrt(const Scalar& x)
+{
+ return EIGEN_MATHFUNC_IMPL(sqrt, Scalar)::run(x);
+}
+
+// Boolean specialization, avoids implicit float to bool conversion (-Wimplicit-conversion-floating-point-to-bool).
+template<>
+EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_DEVICE_FUNC
+bool sqrt<bool>(const bool &x) { return x; }
+
+#if defined(SYCL_DEVICE_ONLY)
+SYCL_SPECIALIZE_FLOATING_TYPES_UNARY(sqrt, sqrt)
+#endif
+
+/** \returns the reciprocal square root of \a x. **/
+template<typename T>
+EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
+T rsqrt(const T& x)
+{
+ return internal::rsqrt_impl<T>::run(x);
+}
+
+template<typename T>
+EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
+T log(const T &x) {
+ return internal::log_impl<T>::run(x);
+}
+
+#if defined(SYCL_DEVICE_ONLY)
+SYCL_SPECIALIZE_FLOATING_TYPES_UNARY(log, log)
+#endif
+
+
+#if defined(EIGEN_GPUCC)
+template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
+float log(const float &x) { return ::logf(x); }
+
+template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
+double log(const double &x) { return ::log(x); }
+#endif
+
+template<typename T>
+EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
+std::enable_if_t<NumTraits<T>::IsSigned || NumTraits<T>::IsComplex,typename NumTraits<T>::Real>
+abs(const T &x) {
+ EIGEN_USING_STD(abs);
+ return abs(x);
+}
+
+template<typename T>
+EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
+std::enable_if_t<!(NumTraits<T>::IsSigned || NumTraits<T>::IsComplex),typename NumTraits<T>::Real>
+abs(const T &x) {
+ return x;
+}
+
+#if defined(SYCL_DEVICE_ONLY)
+SYCL_SPECIALIZE_INTEGER_TYPES_UNARY(abs, abs)
+SYCL_SPECIALIZE_FLOATING_TYPES_UNARY(abs, fabs)
+#endif
+
+#if defined(EIGEN_GPUCC)
+template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
+float abs(const float &x) { return ::fabsf(x); }
+
+template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
+double abs(const double &x) { return ::fabs(x); }
+
+template <> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
+float abs(const std::complex<float>& x) {
+ return ::hypotf(x.real(), x.imag());
+}
+
+template <> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
+double abs(const std::complex<double>& x) {
+ return ::hypot(x.real(), x.imag());
+}
+#endif
+
+template<typename T>
+EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
+T exp(const T &x) {
+ EIGEN_USING_STD(exp);
+ return exp(x);
+}
+
+#if defined(SYCL_DEVICE_ONLY)
+SYCL_SPECIALIZE_FLOATING_TYPES_UNARY(exp, exp)
+#endif
+
+#if defined(EIGEN_GPUCC)
+template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
+float exp(const float &x) { return ::expf(x); }
+
+template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
+double exp(const double &x) { return ::exp(x); }
+
+template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
+std::complex<float> exp(const std::complex<float>& x) {
+ float com = ::expf(x.real());
+ float res_real = com * ::cosf(x.imag());
+ float res_imag = com * ::sinf(x.imag());
+ return std::complex<float>(res_real, res_imag);
+}
+
+template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
+std::complex<double> exp(const std::complex<double>& x) {
+ double com = ::exp(x.real());
+ double res_real = com * ::cos(x.imag());
+ double res_imag = com * ::sin(x.imag());
+ return std::complex<double>(res_real, res_imag);
+}
+#endif
+
+template<typename Scalar>
+EIGEN_DEVICE_FUNC
+inline EIGEN_MATHFUNC_RETVAL(expm1, Scalar) expm1(const Scalar& x)
+{
+ return EIGEN_MATHFUNC_IMPL(expm1, Scalar)::run(x);
+}
+
+#if defined(SYCL_DEVICE_ONLY)
+SYCL_SPECIALIZE_FLOATING_TYPES_UNARY(expm1, expm1)
+#endif
+
+#if defined(EIGEN_GPUCC)
+template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
+float expm1(const float &x) { return ::expm1f(x); }
+
+template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
+double expm1(const double &x) { return ::expm1(x); }
+#endif
+
+template<typename T>
+EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
+T cos(const T &x) {
+ EIGEN_USING_STD(cos);
+ return cos(x);
+}
+
+#if defined(SYCL_DEVICE_ONLY)
+SYCL_SPECIALIZE_FLOATING_TYPES_UNARY(cos,cos)
+#endif
+
+#if defined(EIGEN_GPUCC)
+template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
+float cos(const float &x) { return ::cosf(x); }
+
+template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
+double cos(const double &x) { return ::cos(x); }
+#endif
+
+template<typename T>
+EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
+T sin(const T &x) {
+ EIGEN_USING_STD(sin);
+ return sin(x);
+}
+
+#if defined(SYCL_DEVICE_ONLY)
+SYCL_SPECIALIZE_FLOATING_TYPES_UNARY(sin, sin)
+#endif
+
+#if defined(EIGEN_GPUCC)
+template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
+float sin(const float &x) { return ::sinf(x); }
+
+template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
+double sin(const double &x) { return ::sin(x); }
+#endif
+
+template<typename T>
+EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
+T tan(const T &x) {
+ EIGEN_USING_STD(tan);
+ return tan(x);
+}
+
+#if defined(SYCL_DEVICE_ONLY)
+SYCL_SPECIALIZE_FLOATING_TYPES_UNARY(tan, tan)
+#endif
+
+#if defined(EIGEN_GPUCC)
+template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
+float tan(const float &x) { return ::tanf(x); }
+
+template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
+double tan(const double &x) { return ::tan(x); }
+#endif
+
+template<typename T>
+EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
+T acos(const T &x) {
+ EIGEN_USING_STD(acos);
+ return acos(x);
+}
+
+template<typename T>
+EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
+T acosh(const T &x) {
+ EIGEN_USING_STD(acosh);
+ return static_cast<T>(acosh(x));
+}
+
+#if defined(SYCL_DEVICE_ONLY)
+SYCL_SPECIALIZE_FLOATING_TYPES_UNARY(acos, acos)
+SYCL_SPECIALIZE_FLOATING_TYPES_UNARY(acosh, acosh)
+#endif
+
+#if defined(EIGEN_GPUCC)
+template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
+float acos(const float &x) { return ::acosf(x); }
+
+template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
+double acos(const double &x) { return ::acos(x); }
+#endif
+
+template<typename T>
+EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
+T asin(const T &x) {
+ EIGEN_USING_STD(asin);
+ return asin(x);
+}
+
+template<typename T>
+EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
+T asinh(const T &x) {
+ EIGEN_USING_STD(asinh);
+ return static_cast<T>(asinh(x));
+}
+
+#if defined(SYCL_DEVICE_ONLY)
+SYCL_SPECIALIZE_FLOATING_TYPES_UNARY(asin, asin)
+SYCL_SPECIALIZE_FLOATING_TYPES_UNARY(asinh, asinh)
+#endif
+
+#if defined(EIGEN_GPUCC)
+template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
+float asin(const float &x) { return ::asinf(x); }
+
+template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
+double asin(const double &x) { return ::asin(x); }
+#endif
+
+template<typename T>
+EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
+T atan(const T &x) {
+ EIGEN_USING_STD(atan);
+ return static_cast<T>(atan(x));
+}
+
+template<typename T>
+EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
+T atanh(const T &x) {
+ EIGEN_USING_STD(atanh);
+ return static_cast<T>(atanh(x));
+}
+
+#if defined(SYCL_DEVICE_ONLY)
+SYCL_SPECIALIZE_FLOATING_TYPES_UNARY(atan, atan)
+SYCL_SPECIALIZE_FLOATING_TYPES_UNARY(atanh, atanh)
+#endif
+
+#if defined(EIGEN_GPUCC)
+template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
+float atan(const float &x) { return ::atanf(x); }
+
+template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
+double atan(const double &x) { return ::atan(x); }
+#endif
+
+
+template<typename T>
+EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
+T cosh(const T &x) {
+ EIGEN_USING_STD(cosh);
+ return static_cast<T>(cosh(x));
+}
+
+#if defined(SYCL_DEVICE_ONLY)
+SYCL_SPECIALIZE_FLOATING_TYPES_UNARY(cosh, cosh)
+#endif
+
+#if defined(EIGEN_GPUCC)
+template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
+float cosh(const float &x) { return ::coshf(x); }
+
+template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
+double cosh(const double &x) { return ::cosh(x); }
+#endif
+
+template<typename T>
+EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
+T sinh(const T &x) {
+ EIGEN_USING_STD(sinh);
+ return static_cast<T>(sinh(x));
+}
+
+#if defined(SYCL_DEVICE_ONLY)
+SYCL_SPECIALIZE_FLOATING_TYPES_UNARY(sinh, sinh)
+#endif
+
+#if defined(EIGEN_GPUCC)
+template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
+float sinh(const float &x) { return ::sinhf(x); }
+
+template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
+double sinh(const double &x) { return ::sinh(x); }
+#endif
+
+template<typename T>
+EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
+T tanh(const T &x) {
+ EIGEN_USING_STD(tanh);
+ return tanh(x);
+}
+
+#if (!defined(EIGEN_GPUCC)) && EIGEN_FAST_MATH && !defined(SYCL_DEVICE_ONLY)
+EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
+float tanh(float x) { return internal::generic_fast_tanh_float(x); }
+#endif
+
+#if defined(SYCL_DEVICE_ONLY)
+SYCL_SPECIALIZE_FLOATING_TYPES_UNARY(tanh, tanh)
+#endif
+
+#if defined(EIGEN_GPUCC)
+template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
+float tanh(const float &x) { return ::tanhf(x); }
+
+template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
+double tanh(const double &x) { return ::tanh(x); }
+#endif
+
+template <typename T>
+EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
+T fmod(const T& a, const T& b) {
+ EIGEN_USING_STD(fmod);
+ return fmod(a, b);
+}
+
+#if defined(SYCL_DEVICE_ONLY)
+SYCL_SPECIALIZE_FLOATING_TYPES_BINARY(fmod, fmod)
+#endif
+
+#if defined(EIGEN_GPUCC)
+template <>
+EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
+float fmod(const float& a, const float& b) {
+ return ::fmodf(a, b);
+}
+
+template <>
+EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
+double fmod(const double& a, const double& b) {
+ return ::fmod(a, b);
+}
+#endif
+
+#if defined(SYCL_DEVICE_ONLY)
+#undef SYCL_SPECIALIZE_SIGNED_INTEGER_TYPES_BINARY
+#undef SYCL_SPECIALIZE_SIGNED_INTEGER_TYPES_UNARY
+#undef SYCL_SPECIALIZE_UNSIGNED_INTEGER_TYPES_BINARY
+#undef SYCL_SPECIALIZE_UNSIGNED_INTEGER_TYPES_UNARY
+#undef SYCL_SPECIALIZE_INTEGER_TYPES_BINARY
+#undef SYCL_SPECIALIZE_UNSIGNED_INTEGER_TYPES_UNARY
+#undef SYCL_SPECIALIZE_FLOATING_TYPES_BINARY
+#undef SYCL_SPECIALIZE_FLOATING_TYPES_UNARY
+#undef SYCL_SPECIALIZE_FLOATING_TYPES_UNARY_FUNC_RET_TYPE
+#undef SYCL_SPECIALIZE_GEN_UNARY_FUNC
+#undef SYCL_SPECIALIZE_UNARY_FUNC
+#undef SYCL_SPECIALIZE_GEN1_BINARY_FUNC
+#undef SYCL_SPECIALIZE_GEN2_BINARY_FUNC
+#undef SYCL_SPECIALIZE_BINARY_FUNC
+#endif
+
+} // end namespace numext
+
+namespace internal {
+
+template<typename T>
+EIGEN_DEVICE_FUNC bool isfinite_impl(const std::complex<T>& x)
+{
+ return (numext::isfinite)(numext::real(x)) && (numext::isfinite)(numext::imag(x));
+}
+
+template<typename T>
+EIGEN_DEVICE_FUNC bool isnan_impl(const std::complex<T>& x)
+{
+ return (numext::isnan)(numext::real(x)) || (numext::isnan)(numext::imag(x));
+}
+
+template<typename T>
+EIGEN_DEVICE_FUNC bool isinf_impl(const std::complex<T>& x)
+{
+ return ((numext::isinf)(numext::real(x)) || (numext::isinf)(numext::imag(x))) && (!(numext::isnan)(x));
+}
+
+/****************************************************************************
+* Implementation of fuzzy comparisons *
+****************************************************************************/
+
+template<typename Scalar,
+ bool IsComplex,
+ bool IsInteger>
+struct scalar_fuzzy_default_impl {};
+
+template<typename Scalar>
+struct scalar_fuzzy_default_impl<Scalar, false, false>
+{
+ typedef typename NumTraits<Scalar>::Real RealScalar;
+ template<typename OtherScalar> EIGEN_DEVICE_FUNC
+ static inline bool isMuchSmallerThan(const Scalar& x, const OtherScalar& y, const RealScalar& prec)
+ {
+ return numext::abs(x) <= numext::abs(y) * prec;
+ }
+ EIGEN_DEVICE_FUNC
+ static inline bool isApprox(const Scalar& x, const Scalar& y, const RealScalar& prec)
+ {
+ return numext::abs(x - y) <= numext::mini(numext::abs(x), numext::abs(y)) * prec;
+ }
+ EIGEN_DEVICE_FUNC
+ static inline bool isApproxOrLessThan(const Scalar& x, const Scalar& y, const RealScalar& prec)
+ {
+ return x <= y || isApprox(x, y, prec);
+ }
+};
+
+template<typename Scalar>
+struct scalar_fuzzy_default_impl<Scalar, false, true>
+{
+ typedef typename NumTraits<Scalar>::Real RealScalar;
+ template<typename OtherScalar> EIGEN_DEVICE_FUNC
+ static inline bool isMuchSmallerThan(const Scalar& x, const Scalar&, const RealScalar&)
+ {
+ return x == Scalar(0);
+ }
+ EIGEN_DEVICE_FUNC
+ static inline bool isApprox(const Scalar& x, const Scalar& y, const RealScalar&)
+ {
+ return x == y;
+ }
+ EIGEN_DEVICE_FUNC
+ static inline bool isApproxOrLessThan(const Scalar& x, const Scalar& y, const RealScalar&)
+ {
+ return x <= y;
+ }
+};
+
+template<typename Scalar>
+struct scalar_fuzzy_default_impl<Scalar, true, false>
+{
+ typedef typename NumTraits<Scalar>::Real RealScalar;
+ template<typename OtherScalar> EIGEN_DEVICE_FUNC
+ static inline bool isMuchSmallerThan(const Scalar& x, const OtherScalar& y, const RealScalar& prec)
+ {
+ return numext::abs2(x) <= numext::abs2(y) * prec * prec;
+ }
+ EIGEN_DEVICE_FUNC
+ static inline bool isApprox(const Scalar& x, const Scalar& y, const RealScalar& prec)
+ {
+ return numext::abs2(x - y) <= numext::mini(numext::abs2(x), numext::abs2(y)) * prec * prec;
+ }
+};
+
+template<typename Scalar>
+struct scalar_fuzzy_impl : scalar_fuzzy_default_impl<Scalar, NumTraits<Scalar>::IsComplex, NumTraits<Scalar>::IsInteger> {};
+
+template<typename Scalar, typename OtherScalar> EIGEN_DEVICE_FUNC
+inline bool isMuchSmallerThan(const Scalar& x, const OtherScalar& y,
+ const typename NumTraits<Scalar>::Real &precision = NumTraits<Scalar>::dummy_precision())
+{
+ return scalar_fuzzy_impl<Scalar>::template isMuchSmallerThan<OtherScalar>(x, y, precision);
+}
+
+template<typename Scalar> EIGEN_DEVICE_FUNC
+inline bool isApprox(const Scalar& x, const Scalar& y,
+ const typename NumTraits<Scalar>::Real &precision = NumTraits<Scalar>::dummy_precision())
+{
+ return scalar_fuzzy_impl<Scalar>::isApprox(x, y, precision);
+}
+
+template<typename Scalar> EIGEN_DEVICE_FUNC
+inline bool isApproxOrLessThan(const Scalar& x, const Scalar& y,
+ const typename NumTraits<Scalar>::Real &precision = NumTraits<Scalar>::dummy_precision())
+{
+ return scalar_fuzzy_impl<Scalar>::isApproxOrLessThan(x, y, precision);
+}
+
+/******************************************
+*** The special case of the bool type ***
+******************************************/
+
+template<> struct random_impl<bool>
+{
+ static inline bool run()
+ {
+ return random<int>(0,1)==0 ? false : true;
+ }
+
+ static inline bool run(const bool& a, const bool& b)
+ {
+ return random<int>(a, b)==0 ? false : true;
+ }
+};
+
+template<> struct scalar_fuzzy_impl<bool>
+{
+ typedef bool RealScalar;
+
+ template<typename OtherScalar> EIGEN_DEVICE_FUNC
+ static inline bool isMuchSmallerThan(const bool& x, const bool&, const bool&)
+ {
+ return !x;
+ }
+
+ EIGEN_DEVICE_FUNC
+ static inline bool isApprox(bool x, bool y, bool)
+ {
+ return x == y;
+ }
+
+ EIGEN_DEVICE_FUNC
+ static inline bool isApproxOrLessThan(const bool& x, const bool& y, const bool&)
+ {
+ return (!x) || y;
+ }
+
+};
+
+} // end namespace internal
+
+// Default implementations that rely on other numext implementations
+namespace internal {
+
+// Specialization for complex types that are not supported by std::expm1.
+template <typename RealScalar>
+struct expm1_impl<std::complex<RealScalar> > {
+ EIGEN_STATIC_ASSERT_NON_INTEGER(RealScalar)
+
+ EIGEN_DEVICE_FUNC static inline std::complex<RealScalar> run(
+ const std::complex<RealScalar>& x) {
+ RealScalar xr = x.real();
+ RealScalar xi = x.imag();
+ // expm1(z) = exp(z) - 1
+ // = exp(x + i * y) - 1
+ // = exp(x) * (cos(y) + i * sin(y)) - 1
+ // = exp(x) * cos(y) - 1 + i * exp(x) * sin(y)
+ // Imag(expm1(z)) = exp(x) * sin(y)
+ // Real(expm1(z)) = exp(x) * cos(y) - 1
+ // = exp(x) * cos(y) - 1.
+ // = expm1(x) + exp(x) * (cos(y) - 1)
+ // = expm1(x) + exp(x) * (2 * sin(y / 2) ** 2)
+ RealScalar erm1 = numext::expm1<RealScalar>(xr);
+ RealScalar er = erm1 + RealScalar(1.);
+ RealScalar sin2 = numext::sin(xi / RealScalar(2.));
+ sin2 = sin2 * sin2;
+ RealScalar s = numext::sin(xi);
+ RealScalar real_part = erm1 - RealScalar(2.) * er * sin2;
+ return std::complex<RealScalar>(real_part, er * s);
+ }
+};
+
+template<typename T>
+struct rsqrt_impl {
+ EIGEN_DEVICE_FUNC
+ static EIGEN_ALWAYS_INLINE T run(const T& x) {
+ return T(1)/numext::sqrt(x);
+ }
+};
+
+#if defined(EIGEN_GPU_COMPILE_PHASE)
+template<typename T>
+struct conj_impl<std::complex<T>, true>
+{
+ EIGEN_DEVICE_FUNC
+ static inline std::complex<T> run(const std::complex<T>& x)
+ {
+ return std::complex<T>(numext::real(x), -numext::imag(x));
+ }
+};
+#endif
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_MATHFUNCTIONS_H
diff --git a/Eigen/src/Core/MathFunctionsImpl.h b/Eigen/src/Core/MathFunctionsImpl.h
new file mode 100644
index 0000000..642e5d6
--- /dev/null
+++ b/Eigen/src/Core/MathFunctionsImpl.h
@@ -0,0 +1,335 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2014 Pedro Gonnet (pedro.gonnet@gmail.com)
+// Copyright (C) 2016 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_MATHFUNCTIONSIMPL_H
+#define EIGEN_MATHFUNCTIONSIMPL_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+
+/** \internal Fast reciprocal using Newton-Raphson's method.
+
+ Preconditions:
+ 1. The starting guess provided in approx_a_recip must have at least half
+ the leading mantissa bits in the correct result, such that a single
+ Newton-Raphson step is sufficient to get within 1-2 ulps of the currect
+ result.
+ 2. If a is zero, approx_a_recip must be infinite with the same sign as a.
+ 3. If a is infinite, approx_a_recip must be zero with the same sign as a.
+
+ If the preconditions are satisfied, which they are for for the _*_rcp_ps
+ instructions on x86, the result has a maximum relative error of 2 ulps,
+ and correctly handles reciprocals of zero, infinity, and NaN.
+*/
+template <typename Packet, int Steps>
+struct generic_reciprocal_newton_step {
+ static_assert(Steps > 0, "Steps must be at least 1.");
+ EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE Packet
+ run(const Packet& a, const Packet& approx_a_recip) {
+ using Scalar = typename unpacket_traits<Packet>::type;
+ const Packet two = pset1<Packet>(Scalar(2));
+ // Refine the approximation using one Newton-Raphson step:
+ // x_{i} = x_{i-1} * (2 - a * x_{i-1})
+ const Packet x =
+ generic_reciprocal_newton_step<Packet,Steps - 1>::run(a, approx_a_recip);
+ const Packet tmp = pnmadd(a, x, two);
+ // If tmp is NaN, it means that a is either +/-0 or +/-Inf.
+ // In this case return the approximation directly.
+ const Packet is_not_nan = pcmp_eq(tmp, tmp);
+ return pselect(is_not_nan, pmul(x, tmp), x);
+ }
+};
+
+template<typename Packet>
+struct generic_reciprocal_newton_step<Packet, 0> {
+ EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE Packet
+ run(const Packet& /*unused*/, const Packet& approx_rsqrt) {
+ return approx_rsqrt;
+ }
+};
+
+
+/** \internal Fast reciprocal sqrt using Newton-Raphson's method.
+
+ Preconditions:
+ 1. The starting guess provided in approx_a_recip must have at least half
+ the leading mantissa bits in the correct result, such that a single
+ Newton-Raphson step is sufficient to get within 1-2 ulps of the currect
+ result.
+ 2. If a is zero, approx_a_recip must be infinite with the same sign as a.
+ 3. If a is infinite, approx_a_recip must be zero with the same sign as a.
+
+ If the preconditions are satisfied, which they are for for the _*_rcp_ps
+ instructions on x86, the result has a maximum relative error of 2 ulps,
+ and correctly handles zero, infinity, and NaN. Positive denormals are
+ treated as zero.
+*/
+template <typename Packet, int Steps>
+struct generic_rsqrt_newton_step {
+ static_assert(Steps > 0, "Steps must be at least 1.");
+
+ EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE Packet
+ run(const Packet& a, const Packet& approx_rsqrt) {
+ using Scalar = typename unpacket_traits<Packet>::type;
+ const Packet one_point_five = pset1<Packet>(Scalar(1.5));
+ const Packet minus_half = pset1<Packet>(Scalar(-0.5));
+
+ // Refine the approximation using one Newton-Raphson step:
+ // x_{n+1} = x_n * (1.5 + (-0.5 * x_n) * (a * x_n)).
+ // The approximation is expressed this way to avoid over/under-flows.
+ Packet x_newton = pmul(approx_rsqrt, pmadd(pmul(minus_half, approx_rsqrt), pmul(a, approx_rsqrt), one_point_five));
+ for (int step = 1; step < Steps; ++step) {
+ x_newton = pmul(x_newton, pmadd(pmul(minus_half, x_newton), pmul(a, x_newton), one_point_five));
+ }
+
+ // If approx_rsqrt is 0 or +/-inf, we should return it as is. Note:
+ // on intel, approx_rsqrt can be inf for small denormal values.
+ const Packet return_approx = por(pcmp_eq(approx_rsqrt, pzero(a)),
+ pcmp_eq(pabs(approx_rsqrt), pset1<Packet>(NumTraits<Scalar>::infinity())));
+ return pselect(return_approx, approx_rsqrt, x_newton);
+ }
+};
+
+template<typename Packet>
+struct generic_rsqrt_newton_step<Packet, 0> {
+ EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE Packet
+ run(const Packet& /*unused*/, const Packet& approx_rsqrt) {
+ return approx_rsqrt;
+ }
+};
+
+
+/** \internal Fast sqrt using Newton-Raphson's method.
+
+ Preconditions:
+ 1. The starting guess for the reciprocal sqrt provided in approx_rsqrt must
+ have at least half the leading mantissa bits in the correct result, such
+ that a single Newton-Raphson step is sufficient to get within 1-2 ulps of
+ the currect result.
+ 2. If a is zero, approx_rsqrt must be infinite.
+ 3. If a is infinite, approx_rsqrt must be zero.
+
+ If the preconditions are satisfied, which they are for for the _*_rsqrt_ps
+ instructions on x86, the result has a maximum relative error of 2 ulps,
+ and correctly handles zero and infinity, and NaN. Positive denormal inputs
+ are treated as zero.
+*/
+template <typename Packet, int Steps=1>
+struct generic_sqrt_newton_step {
+ static_assert(Steps > 0, "Steps must be at least 1.");
+
+ EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE Packet
+ run(const Packet& a, const Packet& approx_rsqrt) {
+ using Scalar = typename unpacket_traits<Packet>::type;
+ const Packet one_point_five = pset1<Packet>(Scalar(1.5));
+ const Packet minus_half = pset1<Packet>(Scalar(-0.5));
+ // If a is inf or zero, return a directly.
+ const Packet inf_mask = pcmp_eq(a, pset1<Packet>(NumTraits<Scalar>::infinity()));
+ const Packet return_a = por(pcmp_eq(a, pzero(a)), inf_mask);
+ // Do a single step of Newton's iteration for reciprocal square root:
+ // x_{n+1} = x_n * (1.5 + (-0.5 * x_n) * (a * x_n))).
+ // The Newton's step is computed this way to avoid over/under-flows.
+ Packet rsqrt = pmul(approx_rsqrt, pmadd(pmul(minus_half, approx_rsqrt), pmul(a, approx_rsqrt), one_point_five));
+ for (int step = 1; step < Steps; ++step) {
+ rsqrt = pmul(rsqrt, pmadd(pmul(minus_half, rsqrt), pmul(a, rsqrt), one_point_five));
+ }
+
+ // Return sqrt(x) = x * rsqrt(x) for non-zero finite positive arguments.
+ // Return a itself for 0 or +inf, NaN for negative arguments.
+ return pselect(return_a, a, pmul(a, rsqrt));
+ }
+};
+
+/** \internal \returns the hyperbolic tan of \a a (coeff-wise)
+ Doesn't do anything fancy, just a 13/6-degree rational interpolant which
+ is accurate up to a couple of ulps in the (approximate) range [-8, 8],
+ outside of which tanh(x) = +/-1 in single precision. The input is clamped
+ to the range [-c, c]. The value c is chosen as the smallest value where
+ the approximation evaluates to exactly 1. In the reange [-0.0004, 0.0004]
+ the approximation tanh(x) ~= x is used for better accuracy as x tends to zero.
+
+ This implementation works on both scalars and packets.
+*/
+template<typename T>
+T generic_fast_tanh_float(const T& a_x)
+{
+ // Clamp the inputs to the range [-c, c]
+#ifdef EIGEN_VECTORIZE_FMA
+ const T plus_clamp = pset1<T>(7.99881172180175781f);
+ const T minus_clamp = pset1<T>(-7.99881172180175781f);
+#else
+ const T plus_clamp = pset1<T>(7.90531110763549805f);
+ const T minus_clamp = pset1<T>(-7.90531110763549805f);
+#endif
+ const T tiny = pset1<T>(0.0004f);
+ const T x = pmax(pmin(a_x, plus_clamp), minus_clamp);
+ const T tiny_mask = pcmp_lt(pabs(a_x), tiny);
+ // The monomial coefficients of the numerator polynomial (odd).
+ const T alpha_1 = pset1<T>(4.89352455891786e-03f);
+ const T alpha_3 = pset1<T>(6.37261928875436e-04f);
+ const T alpha_5 = pset1<T>(1.48572235717979e-05f);
+ const T alpha_7 = pset1<T>(5.12229709037114e-08f);
+ const T alpha_9 = pset1<T>(-8.60467152213735e-11f);
+ const T alpha_11 = pset1<T>(2.00018790482477e-13f);
+ const T alpha_13 = pset1<T>(-2.76076847742355e-16f);
+
+ // The monomial coefficients of the denominator polynomial (even).
+ const T beta_0 = pset1<T>(4.89352518554385e-03f);
+ const T beta_2 = pset1<T>(2.26843463243900e-03f);
+ const T beta_4 = pset1<T>(1.18534705686654e-04f);
+ const T beta_6 = pset1<T>(1.19825839466702e-06f);
+
+ // Since the polynomials are odd/even, we need x^2.
+ const T x2 = pmul(x, x);
+
+ // Evaluate the numerator polynomial p.
+ T p = pmadd(x2, alpha_13, alpha_11);
+ p = pmadd(x2, p, alpha_9);
+ p = pmadd(x2, p, alpha_7);
+ p = pmadd(x2, p, alpha_5);
+ p = pmadd(x2, p, alpha_3);
+ p = pmadd(x2, p, alpha_1);
+ p = pmul(x, p);
+
+ // Evaluate the denominator polynomial q.
+ T q = pmadd(x2, beta_6, beta_4);
+ q = pmadd(x2, q, beta_2);
+ q = pmadd(x2, q, beta_0);
+
+ // Divide the numerator by the denominator.
+ return pselect(tiny_mask, x, pdiv(p, q));
+}
+
+template<typename RealScalar>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+RealScalar positive_real_hypot(const RealScalar& x, const RealScalar& y)
+{
+ // IEEE IEC 6059 special cases.
+ if ((numext::isinf)(x) || (numext::isinf)(y))
+ return NumTraits<RealScalar>::infinity();
+ if ((numext::isnan)(x) || (numext::isnan)(y))
+ return NumTraits<RealScalar>::quiet_NaN();
+
+ EIGEN_USING_STD(sqrt);
+ RealScalar p, qp;
+ p = numext::maxi(x,y);
+ if(numext::is_exactly_zero(p)) return RealScalar(0);
+ qp = numext::mini(y,x) / p;
+ return p * sqrt(RealScalar(1) + qp*qp);
+}
+
+template<typename Scalar>
+struct hypot_impl
+{
+ typedef typename NumTraits<Scalar>::Real RealScalar;
+ static EIGEN_DEVICE_FUNC
+ inline RealScalar run(const Scalar& x, const Scalar& y)
+ {
+ EIGEN_USING_STD(abs);
+ return positive_real_hypot<RealScalar>(abs(x), abs(y));
+ }
+};
+
+// Generic complex sqrt implementation that correctly handles corner cases
+// according to https://en.cppreference.com/w/cpp/numeric/complex/sqrt
+template<typename T>
+EIGEN_DEVICE_FUNC std::complex<T> complex_sqrt(const std::complex<T>& z) {
+ // Computes the principal sqrt of the input.
+ //
+ // For a complex square root of the number x + i*y. We want to find real
+ // numbers u and v such that
+ // (u + i*v)^2 = x + i*y <=>
+ // u^2 - v^2 + i*2*u*v = x + i*v.
+ // By equating the real and imaginary parts we get:
+ // u^2 - v^2 = x
+ // 2*u*v = y.
+ //
+ // For x >= 0, this has the numerically stable solution
+ // u = sqrt(0.5 * (x + sqrt(x^2 + y^2)))
+ // v = y / (2 * u)
+ // and for x < 0,
+ // v = sign(y) * sqrt(0.5 * (-x + sqrt(x^2 + y^2)))
+ // u = y / (2 * v)
+ //
+ // Letting w = sqrt(0.5 * (|x| + |z|)),
+ // if x == 0: u = w, v = sign(y) * w
+ // if x > 0: u = w, v = y / (2 * w)
+ // if x < 0: u = |y| / (2 * w), v = sign(y) * w
+
+ const T x = numext::real(z);
+ const T y = numext::imag(z);
+ const T zero = T(0);
+ const T w = numext::sqrt(T(0.5) * (numext::abs(x) + numext::hypot(x, y)));
+
+ return
+ (numext::isinf)(y) ? std::complex<T>(NumTraits<T>::infinity(), y)
+ : numext::is_exactly_zero(x) ? std::complex<T>(w, y < zero ? -w : w)
+ : x > zero ? std::complex<T>(w, y / (2 * w))
+ : std::complex<T>(numext::abs(y) / (2 * w), y < zero ? -w : w );
+}
+
+// Generic complex rsqrt implementation.
+template<typename T>
+EIGEN_DEVICE_FUNC std::complex<T> complex_rsqrt(const std::complex<T>& z) {
+ // Computes the principal reciprocal sqrt of the input.
+ //
+ // For a complex reciprocal square root of the number z = x + i*y. We want to
+ // find real numbers u and v such that
+ // (u + i*v)^2 = 1 / (x + i*y) <=>
+ // u^2 - v^2 + i*2*u*v = x/|z|^2 - i*v/|z|^2.
+ // By equating the real and imaginary parts we get:
+ // u^2 - v^2 = x/|z|^2
+ // 2*u*v = y/|z|^2.
+ //
+ // For x >= 0, this has the numerically stable solution
+ // u = sqrt(0.5 * (x + |z|)) / |z|
+ // v = -y / (2 * u * |z|)
+ // and for x < 0,
+ // v = -sign(y) * sqrt(0.5 * (-x + |z|)) / |z|
+ // u = -y / (2 * v * |z|)
+ //
+ // Letting w = sqrt(0.5 * (|x| + |z|)),
+ // if x == 0: u = w / |z|, v = -sign(y) * w / |z|
+ // if x > 0: u = w / |z|, v = -y / (2 * w * |z|)
+ // if x < 0: u = |y| / (2 * w * |z|), v = -sign(y) * w / |z|
+
+ const T x = numext::real(z);
+ const T y = numext::imag(z);
+ const T zero = T(0);
+
+ const T abs_z = numext::hypot(x, y);
+ const T w = numext::sqrt(T(0.5) * (numext::abs(x) + abs_z));
+ const T woz = w / abs_z;
+ // Corner cases consistent with 1/sqrt(z) on gcc/clang.
+ return
+ numext::is_exactly_zero(abs_z) ? std::complex<T>(NumTraits<T>::infinity(), NumTraits<T>::quiet_NaN())
+ : ((numext::isinf)(x) || (numext::isinf)(y)) ? std::complex<T>(zero, zero)
+ : numext::is_exactly_zero(x) ? std::complex<T>(woz, y < zero ? woz : -woz)
+ : x > zero ? std::complex<T>(woz, -y / (2 * w * abs_z))
+ : std::complex<T>(numext::abs(y) / (2 * w * abs_z), y < zero ? woz : -woz );
+}
+
+template<typename T>
+EIGEN_DEVICE_FUNC std::complex<T> complex_log(const std::complex<T>& z) {
+ // Computes complex log.
+ T a = numext::abs(z);
+ EIGEN_USING_STD(atan2);
+ T b = atan2(z.imag(), z.real());
+ return std::complex<T>(numext::log(a), b);
+}
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_MATHFUNCTIONSIMPL_H
diff --git a/Eigen/src/Core/Matrix.h b/Eigen/src/Core/Matrix.h
new file mode 100644
index 0000000..23acd8a
--- /dev/null
+++ b/Eigen/src/Core/Matrix.h
@@ -0,0 +1,556 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2006-2010 Benoit Jacob <jacob.benoit.1@gmail.com>
+// Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_MATRIX_H
+#define EIGEN_MATRIX_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+template<typename Scalar_, int Rows_, int Cols_, int Options_, int MaxRows_, int MaxCols_>
+struct traits<Matrix<Scalar_, Rows_, Cols_, Options_, MaxRows_, MaxCols_> >
+{
+private:
+ constexpr static int size = internal::size_at_compile_time(Rows_,Cols_);
+ typedef typename find_best_packet<Scalar_,size>::type PacketScalar;
+ enum {
+ row_major_bit = Options_&RowMajor ? RowMajorBit : 0,
+ is_dynamic_size_storage = MaxRows_==Dynamic || MaxCols_==Dynamic,
+ max_size = is_dynamic_size_storage ? Dynamic : MaxRows_*MaxCols_,
+ default_alignment = compute_default_alignment<Scalar_,max_size>::value,
+ actual_alignment = ((Options_&DontAlign)==0) ? default_alignment : 0,
+ required_alignment = unpacket_traits<PacketScalar>::alignment,
+ packet_access_bit = (packet_traits<Scalar_>::Vectorizable && (EIGEN_UNALIGNED_VECTORIZE || (actual_alignment>=required_alignment))) ? PacketAccessBit : 0
+ };
+
+public:
+ typedef Scalar_ Scalar;
+ typedef Dense StorageKind;
+ typedef Eigen::Index StorageIndex;
+ typedef MatrixXpr XprKind;
+ enum {
+ RowsAtCompileTime = Rows_,
+ ColsAtCompileTime = Cols_,
+ MaxRowsAtCompileTime = MaxRows_,
+ MaxColsAtCompileTime = MaxCols_,
+ Flags = compute_matrix_flags(Options_),
+ Options = Options_,
+ InnerStrideAtCompileTime = 1,
+ OuterStrideAtCompileTime = (Options&RowMajor) ? ColsAtCompileTime : RowsAtCompileTime,
+
+ // FIXME, the following flag in only used to define NeedsToAlign in PlainObjectBase
+ EvaluatorFlags = LinearAccessBit | DirectAccessBit | packet_access_bit | row_major_bit,
+ Alignment = actual_alignment
+ };
+};
+}
+
+/** \class Matrix
+ * \ingroup Core_Module
+ *
+ * \brief The matrix class, also used for vectors and row-vectors
+ *
+ * The %Matrix class is the work-horse for all \em dense (\ref dense "note") matrices and vectors within Eigen.
+ * Vectors are matrices with one column, and row-vectors are matrices with one row.
+ *
+ * The %Matrix class encompasses \em both fixed-size and dynamic-size objects (\ref fixedsize "note").
+ *
+ * The first three template parameters are required:
+ * \tparam Scalar_ Numeric type, e.g. float, double, int or std::complex<float>.
+ * User defined scalar types are supported as well (see \ref user_defined_scalars "here").
+ * \tparam Rows_ Number of rows, or \b Dynamic
+ * \tparam Cols_ Number of columns, or \b Dynamic
+ *
+ * The remaining template parameters are optional -- in most cases you don't have to worry about them.
+ * \tparam Options_ A combination of either \b #RowMajor or \b #ColMajor, and of either
+ * \b #AutoAlign or \b #DontAlign.
+ * The former controls \ref TopicStorageOrders "storage order", and defaults to column-major. The latter controls alignment, which is required
+ * for vectorization. It defaults to aligning matrices except for fixed sizes that aren't a multiple of the packet size.
+ * \tparam MaxRows_ Maximum number of rows. Defaults to \a Rows_ (\ref maxrows "note").
+ * \tparam MaxCols_ Maximum number of columns. Defaults to \a Cols_ (\ref maxrows "note").
+ *
+ * Eigen provides a number of typedefs covering the usual cases. Here are some examples:
+ *
+ * \li \c Matrix2d is a 2x2 square matrix of doubles (\c Matrix<double, 2, 2>)
+ * \li \c Vector4f is a vector of 4 floats (\c Matrix<float, 4, 1>)
+ * \li \c RowVector3i is a row-vector of 3 ints (\c Matrix<int, 1, 3>)
+ *
+ * \li \c MatrixXf is a dynamic-size matrix of floats (\c Matrix<float, Dynamic, Dynamic>)
+ * \li \c VectorXf is a dynamic-size vector of floats (\c Matrix<float, Dynamic, 1>)
+ *
+ * \li \c Matrix2Xf is a partially fixed-size (dynamic-size) matrix of floats (\c Matrix<float, 2, Dynamic>)
+ * \li \c MatrixX3d is a partially dynamic-size (fixed-size) matrix of double (\c Matrix<double, Dynamic, 3>)
+ *
+ * See \link matrixtypedefs this page \endlink for a complete list of predefined \em %Matrix and \em Vector typedefs.
+ *
+ * You can access elements of vectors and matrices using normal subscripting:
+ *
+ * \code
+ * Eigen::VectorXd v(10);
+ * v[0] = 0.1;
+ * v[1] = 0.2;
+ * v(0) = 0.3;
+ * v(1) = 0.4;
+ *
+ * Eigen::MatrixXi m(10, 10);
+ * m(0, 1) = 1;
+ * m(0, 2) = 2;
+ * m(0, 3) = 3;
+ * \endcode
+ *
+ * This class can be extended with the help of the plugin mechanism described on the page
+ * \ref TopicCustomizing_Plugins by defining the preprocessor symbol \c EIGEN_MATRIX_PLUGIN.
+ *
+ * <i><b>Some notes:</b></i>
+ *
+ * <dl>
+ * <dt><b>\anchor dense Dense versus sparse:</b></dt>
+ * <dd>This %Matrix class handles dense, not sparse matrices and vectors. For sparse matrices and vectors, see the Sparse module.
+ *
+ * Dense matrices and vectors are plain usual arrays of coefficients. All the coefficients are stored, in an ordinary contiguous array.
+ * This is unlike Sparse matrices and vectors where the coefficients are stored as a list of nonzero coefficients.</dd>
+ *
+ * <dt><b>\anchor fixedsize Fixed-size versus dynamic-size:</b></dt>
+ * <dd>Fixed-size means that the numbers of rows and columns are known are compile-time. In this case, Eigen allocates the array
+ * of coefficients as a fixed-size array, as a class member. This makes sense for very small matrices, typically up to 4x4, sometimes up
+ * to 16x16. Larger matrices should be declared as dynamic-size even if one happens to know their size at compile-time.
+ *
+ * Dynamic-size means that the numbers of rows or columns are not necessarily known at compile-time. In this case they are runtime
+ * variables, and the array of coefficients is allocated dynamically on the heap.
+ *
+ * Note that \em dense matrices, be they Fixed-size or Dynamic-size, <em>do not</em> expand dynamically in the sense of a std::map.
+ * If you want this behavior, see the Sparse module.</dd>
+ *
+ * <dt><b>\anchor maxrows MaxRows_ and MaxCols_:</b></dt>
+ * <dd>In most cases, one just leaves these parameters to the default values.
+ * These parameters mean the maximum size of rows and columns that the matrix may have. They are useful in cases
+ * when the exact numbers of rows and columns are not known are compile-time, but it is known at compile-time that they cannot
+ * exceed a certain value. This happens when taking dynamic-size blocks inside fixed-size matrices: in this case MaxRows_ and MaxCols_
+ * are the dimensions of the original matrix, while Rows_ and Cols_ are Dynamic.</dd>
+ * </dl>
+ *
+ * <i><b>ABI and storage layout</b></i>
+ *
+ * The table below summarizes the ABI of some possible Matrix instances which is fixed thorough the lifetime of Eigen 3.
+ * <table class="manual">
+ * <tr><th>Matrix type</th><th>Equivalent C structure</th></tr>
+ * <tr><td>\code Matrix<T,Dynamic,Dynamic> \endcode</td><td>\code
+ * struct {
+ * T *data; // with (size_t(data)%EIGEN_MAX_ALIGN_BYTES)==0
+ * Eigen::Index rows, cols;
+ * };
+ * \endcode</td></tr>
+ * <tr class="alt"><td>\code
+ * Matrix<T,Dynamic,1>
+ * Matrix<T,1,Dynamic> \endcode</td><td>\code
+ * struct {
+ * T *data; // with (size_t(data)%EIGEN_MAX_ALIGN_BYTES)==0
+ * Eigen::Index size;
+ * };
+ * \endcode</td></tr>
+ * <tr><td>\code Matrix<T,Rows,Cols> \endcode</td><td>\code
+ * struct {
+ * T data[Rows*Cols]; // with (size_t(data)%A(Rows*Cols*sizeof(T)))==0
+ * };
+ * \endcode</td></tr>
+ * <tr class="alt"><td>\code Matrix<T,Dynamic,Dynamic,0,MaxRows,MaxCols> \endcode</td><td>\code
+ * struct {
+ * T data[MaxRows*MaxCols]; // with (size_t(data)%A(MaxRows*MaxCols*sizeof(T)))==0
+ * Eigen::Index rows, cols;
+ * };
+ * \endcode</td></tr>
+ * </table>
+ * Note that in this table Rows, Cols, MaxRows and MaxCols are all positive integers. A(S) is defined to the largest possible power-of-two
+ * smaller to EIGEN_MAX_STATIC_ALIGN_BYTES.
+ *
+ * \see MatrixBase for the majority of the API methods for matrices, \ref TopicClassHierarchy,
+ * \ref TopicStorageOrders
+ */
+
+template<typename Scalar_, int Rows_, int Cols_, int Options_, int MaxRows_, int MaxCols_>
+class Matrix
+ : public PlainObjectBase<Matrix<Scalar_, Rows_, Cols_, Options_, MaxRows_, MaxCols_> >
+{
+ public:
+
+ /** \brief Base class typedef.
+ * \sa PlainObjectBase
+ */
+ typedef PlainObjectBase<Matrix> Base;
+
+ enum { Options = Options_ };
+
+ EIGEN_DENSE_PUBLIC_INTERFACE(Matrix)
+
+ typedef typename Base::PlainObject PlainObject;
+
+ using Base::base;
+ using Base::coeffRef;
+
+ /**
+ * \brief Assigns matrices to each other.
+ *
+ * \note This is a special case of the templated operator=. Its purpose is
+ * to prevent a default operator= from hiding the templated operator=.
+ *
+ * \callgraph
+ */
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE Matrix& operator=(const Matrix& other)
+ {
+ return Base::_set(other);
+ }
+
+ /** \internal
+ * \brief Copies the value of the expression \a other into \c *this with automatic resizing.
+ *
+ * *this might be resized to match the dimensions of \a other. If *this was a null matrix (not already initialized),
+ * it will be initialized.
+ *
+ * Note that copying a row-vector into a vector (and conversely) is allowed.
+ * The resizing, if any, is then done in the appropriate way so that row-vectors
+ * remain row-vectors and vectors remain vectors.
+ */
+ template<typename OtherDerived>
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE Matrix& operator=(const DenseBase<OtherDerived>& other)
+ {
+ return Base::_set(other);
+ }
+
+ /* Here, doxygen failed to copy the brief information when using \copydoc */
+
+ /**
+ * \brief Copies the generic expression \a other into *this.
+ * \copydetails DenseBase::operator=(const EigenBase<OtherDerived> &other)
+ */
+ template<typename OtherDerived>
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE Matrix& operator=(const EigenBase<OtherDerived> &other)
+ {
+ return Base::operator=(other);
+ }
+
+ template<typename OtherDerived>
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE Matrix& operator=(const ReturnByValue<OtherDerived>& func)
+ {
+ return Base::operator=(func);
+ }
+
+ /** \brief Default constructor.
+ *
+ * For fixed-size matrices, does nothing.
+ *
+ * For dynamic-size matrices, creates an empty matrix of size 0. Does not allocate any array. Such a matrix
+ * is called a null matrix. This constructor is the unique way to create null matrices: resizing
+ * a matrix to 0 is not supported.
+ *
+ * \sa resize(Index,Index)
+ */
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ Matrix() : Base()
+ {
+ EIGEN_INITIALIZE_COEFFS_IF_THAT_OPTION_IS_ENABLED
+ }
+
+ // FIXME is it still needed
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ explicit Matrix(internal::constructor_without_unaligned_array_assert)
+ : Base(internal::constructor_without_unaligned_array_assert())
+ { EIGEN_INITIALIZE_COEFFS_IF_THAT_OPTION_IS_ENABLED }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ Matrix(Matrix&& other) EIGEN_NOEXCEPT_IF(std::is_nothrow_move_constructible<Scalar>::value)
+ : Base(std::move(other)) {}
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ Matrix& operator=(Matrix&& other) EIGEN_NOEXCEPT_IF(std::is_nothrow_move_assignable<Scalar>::value)
+ {
+ Base::operator=(std::move(other));
+ return *this;
+ }
+
+ /** \copydoc PlainObjectBase(const Scalar&, const Scalar&, const Scalar&, const Scalar&, const ArgTypes&... args)
+ *
+ * Example: \include Matrix_variadic_ctor_cxx11.cpp
+ * Output: \verbinclude Matrix_variadic_ctor_cxx11.out
+ *
+ * \sa Matrix(const std::initializer_list<std::initializer_list<Scalar>>&)
+ */
+ template <typename... ArgTypes>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ Matrix(const Scalar& a0, const Scalar& a1, const Scalar& a2, const Scalar& a3, const ArgTypes&... args)
+ : Base(a0, a1, a2, a3, args...) {}
+
+ /** \brief Constructs a Matrix and initializes it from the coefficients given as initializer-lists grouped by row. \cpp11
+ *
+ * In the general case, the constructor takes a list of rows, each row being represented as a list of coefficients:
+ *
+ * Example: \include Matrix_initializer_list_23_cxx11.cpp
+ * Output: \verbinclude Matrix_initializer_list_23_cxx11.out
+ *
+ * Each of the inner initializer lists must contain the exact same number of elements, otherwise an assertion is triggered.
+ *
+ * In the case of a compile-time column vector, implicit transposition from a single row is allowed.
+ * Therefore <code>VectorXd{{1,2,3,4,5}}</code> is legal and the more verbose syntax
+ * <code>RowVectorXd{{1},{2},{3},{4},{5}}</code> can be avoided:
+ *
+ * Example: \include Matrix_initializer_list_vector_cxx11.cpp
+ * Output: \verbinclude Matrix_initializer_list_vector_cxx11.out
+ *
+ * In the case of fixed-sized matrices, the initializer list sizes must exactly match the matrix sizes,
+ * and implicit transposition is allowed for compile-time vectors only.
+ *
+ * \sa Matrix(const Scalar& a0, const Scalar& a1, const Scalar& a2, const Scalar& a3, const ArgTypes&... args)
+ */
+ EIGEN_DEVICE_FUNC
+ explicit EIGEN_STRONG_INLINE Matrix(const std::initializer_list<std::initializer_list<Scalar>>& list) : Base(list) {}
+
+#ifndef EIGEN_PARSED_BY_DOXYGEN
+
+ // This constructor is for both 1x1 matrices and dynamic vectors
+ template<typename T>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ explicit Matrix(const T& x)
+ {
+ Base::template _init1<T>(x);
+ }
+
+ template<typename T0, typename T1>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ Matrix(const T0& x, const T1& y)
+ {
+ Base::template _init2<T0,T1>(x, y);
+ }
+
+
+#else
+ /** \brief Constructs a fixed-sized matrix initialized with coefficients starting at \a data */
+ EIGEN_DEVICE_FUNC
+ explicit Matrix(const Scalar *data);
+
+ /** \brief Constructs a vector or row-vector with given dimension. \only_for_vectors
+ *
+ * This is useful for dynamic-size vectors. For fixed-size vectors,
+ * it is redundant to pass these parameters, so one should use the default constructor
+ * Matrix() instead.
+ *
+ * \warning This constructor is disabled for fixed-size \c 1x1 matrices. For instance,
+ * calling Matrix<double,1,1>(1) will call the initialization constructor: Matrix(const Scalar&).
+ * For fixed-size \c 1x1 matrices it is therefore recommended to use the default
+ * constructor Matrix() instead, especially when using one of the non standard
+ * \c EIGEN_INITIALIZE_MATRICES_BY_{ZERO,\c NAN} macros (see \ref TopicPreprocessorDirectives).
+ */
+ EIGEN_STRONG_INLINE explicit Matrix(Index dim);
+ /** \brief Constructs an initialized 1x1 matrix with the given coefficient
+ * \sa Matrix(const Scalar&, const Scalar&, const Scalar&, const Scalar&, const ArgTypes&...) */
+ Matrix(const Scalar& x);
+ /** \brief Constructs an uninitialized matrix with \a rows rows and \a cols columns.
+ *
+ * This is useful for dynamic-size matrices. For fixed-size matrices,
+ * it is redundant to pass these parameters, so one should use the default constructor
+ * Matrix() instead.
+ *
+ * \warning This constructor is disabled for fixed-size \c 1x2 and \c 2x1 vectors. For instance,
+ * calling Matrix2f(2,1) will call the initialization constructor: Matrix(const Scalar& x, const Scalar& y).
+ * For fixed-size \c 1x2 or \c 2x1 vectors it is therefore recommended to use the default
+ * constructor Matrix() instead, especially when using one of the non standard
+ * \c EIGEN_INITIALIZE_MATRICES_BY_{ZERO,\c NAN} macros (see \ref TopicPreprocessorDirectives).
+ */
+ EIGEN_DEVICE_FUNC
+ Matrix(Index rows, Index cols);
+
+ /** \brief Constructs an initialized 2D vector with given coefficients
+ * \sa Matrix(const Scalar&, const Scalar&, const Scalar&, const Scalar&, const ArgTypes&...) */
+ Matrix(const Scalar& x, const Scalar& y);
+ #endif // end EIGEN_PARSED_BY_DOXYGEN
+
+ /** \brief Constructs an initialized 3D vector with given coefficients
+ * \sa Matrix(const Scalar&, const Scalar&, const Scalar&, const Scalar&, const ArgTypes&...)
+ */
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE Matrix(const Scalar& x, const Scalar& y, const Scalar& z)
+ {
+ EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(Matrix, 3)
+ m_storage.data()[0] = x;
+ m_storage.data()[1] = y;
+ m_storage.data()[2] = z;
+ }
+ /** \brief Constructs an initialized 4D vector with given coefficients
+ * \sa Matrix(const Scalar&, const Scalar&, const Scalar&, const Scalar&, const ArgTypes&...)
+ */
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE Matrix(const Scalar& x, const Scalar& y, const Scalar& z, const Scalar& w)
+ {
+ EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(Matrix, 4)
+ m_storage.data()[0] = x;
+ m_storage.data()[1] = y;
+ m_storage.data()[2] = z;
+ m_storage.data()[3] = w;
+ }
+
+
+ /** \brief Copy constructor */
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE Matrix(const Matrix& other) : Base(other)
+ { }
+
+ /** \brief Copy constructor for generic expressions.
+ * \sa MatrixBase::operator=(const EigenBase<OtherDerived>&)
+ */
+ template<typename OtherDerived>
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE Matrix(const EigenBase<OtherDerived> &other)
+ : Base(other.derived())
+ { }
+
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
+ inline Index innerStride() const EIGEN_NOEXCEPT { return 1; }
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
+ inline Index outerStride() const EIGEN_NOEXCEPT { return this->innerSize(); }
+
+ /////////// Geometry module ///////////
+
+ template<typename OtherDerived>
+ EIGEN_DEVICE_FUNC
+ explicit Matrix(const RotationBase<OtherDerived,ColsAtCompileTime>& r);
+ template<typename OtherDerived>
+ EIGEN_DEVICE_FUNC
+ Matrix& operator=(const RotationBase<OtherDerived,ColsAtCompileTime>& r);
+
+ // allow to extend Matrix outside Eigen
+ #ifdef EIGEN_MATRIX_PLUGIN
+ #include EIGEN_MATRIX_PLUGIN
+ #endif
+
+ protected:
+ template <typename Derived, typename OtherDerived, bool IsVector>
+ friend struct internal::conservative_resize_like_impl;
+
+ using Base::m_storage;
+};
+
+/** \defgroup matrixtypedefs Global matrix typedefs
+ *
+ * \ingroup Core_Module
+ *
+ * %Eigen defines several typedef shortcuts for most common matrix and vector types.
+ *
+ * The general patterns are the following:
+ *
+ * \c MatrixSizeType where \c Size can be \c 2,\c 3,\c 4 for fixed size square matrices or \c X for dynamic size,
+ * and where \c Type can be \c i for integer, \c f for float, \c d for double, \c cf for complex float, \c cd
+ * for complex double.
+ *
+ * For example, \c Matrix3d is a fixed-size 3x3 matrix type of doubles, and \c MatrixXf is a dynamic-size matrix of floats.
+ *
+ * There are also \c VectorSizeType and \c RowVectorSizeType which are self-explanatory. For example, \c Vector4cf is
+ * a fixed-size vector of 4 complex floats.
+ *
+ * With \cpp11, template alias are also defined for common sizes.
+ * They follow the same pattern as above except that the scalar type suffix is replaced by a
+ * template parameter, i.e.:
+ * - `MatrixSize<Type>` where `Size` can be \c 2,\c 3,\c 4 for fixed size square matrices or \c X for dynamic size.
+ * - `MatrixXSize<Type>` and `MatrixSizeX<Type>` where `Size` can be \c 2,\c 3,\c 4 for hybrid dynamic/fixed matrices.
+ * - `VectorSize<Type>` and `RowVectorSize<Type>` for column and row vectors.
+ *
+ * With \cpp11, you can also use fully generic column and row vector types: `Vector<Type,Size>` and `RowVector<Type,Size>`.
+ *
+ * \sa class Matrix
+ */
+
+#define EIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, Size, SizeSuffix) \
+/** \ingroup matrixtypedefs */ \
+/** \brief `Size`×`Size` matrix of type `Type`. */ \
+typedef Matrix<Type, Size, Size> Matrix##SizeSuffix##TypeSuffix; \
+/** \ingroup matrixtypedefs */ \
+/** \brief `Size`×`1` vector of type `Type`. */ \
+typedef Matrix<Type, Size, 1> Vector##SizeSuffix##TypeSuffix; \
+/** \ingroup matrixtypedefs */ \
+/** \brief `1`×`Size` vector of type `Type`. */ \
+typedef Matrix<Type, 1, Size> RowVector##SizeSuffix##TypeSuffix;
+
+#define EIGEN_MAKE_FIXED_TYPEDEFS(Type, TypeSuffix, Size) \
+/** \ingroup matrixtypedefs */ \
+/** \brief `Size`×`Dynamic` matrix of type `Type`. */ \
+typedef Matrix<Type, Size, Dynamic> Matrix##Size##X##TypeSuffix; \
+/** \ingroup matrixtypedefs */ \
+/** \brief `Dynamic`×`Size` matrix of type `Type`. */ \
+typedef Matrix<Type, Dynamic, Size> Matrix##X##Size##TypeSuffix;
+
+#define EIGEN_MAKE_TYPEDEFS_ALL_SIZES(Type, TypeSuffix) \
+EIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, 2, 2) \
+EIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, 3, 3) \
+EIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, 4, 4) \
+EIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, Dynamic, X) \
+EIGEN_MAKE_FIXED_TYPEDEFS(Type, TypeSuffix, 2) \
+EIGEN_MAKE_FIXED_TYPEDEFS(Type, TypeSuffix, 3) \
+EIGEN_MAKE_FIXED_TYPEDEFS(Type, TypeSuffix, 4)
+
+EIGEN_MAKE_TYPEDEFS_ALL_SIZES(int, i)
+EIGEN_MAKE_TYPEDEFS_ALL_SIZES(float, f)
+EIGEN_MAKE_TYPEDEFS_ALL_SIZES(double, d)
+EIGEN_MAKE_TYPEDEFS_ALL_SIZES(std::complex<float>, cf)
+EIGEN_MAKE_TYPEDEFS_ALL_SIZES(std::complex<double>, cd)
+
+#undef EIGEN_MAKE_TYPEDEFS_ALL_SIZES
+#undef EIGEN_MAKE_TYPEDEFS
+#undef EIGEN_MAKE_FIXED_TYPEDEFS
+
+#define EIGEN_MAKE_TYPEDEFS(Size, SizeSuffix) \
+/** \ingroup matrixtypedefs */ \
+/** \brief \cpp11 `Size`×`Size` matrix of type `Type`.*/ \
+template <typename Type> \
+using Matrix##SizeSuffix = Matrix<Type, Size, Size>; \
+/** \ingroup matrixtypedefs */ \
+/** \brief \cpp11 `Size`×`1` vector of type `Type`.*/ \
+template <typename Type> \
+using Vector##SizeSuffix = Matrix<Type, Size, 1>; \
+/** \ingroup matrixtypedefs */ \
+/** \brief \cpp11 `1`×`Size` vector of type `Type`.*/ \
+template <typename Type> \
+using RowVector##SizeSuffix = Matrix<Type, 1, Size>;
+
+#define EIGEN_MAKE_FIXED_TYPEDEFS(Size) \
+/** \ingroup matrixtypedefs */ \
+/** \brief \cpp11 `Size`×`Dynamic` matrix of type `Type` */ \
+template <typename Type> \
+using Matrix##Size##X = Matrix<Type, Size, Dynamic>; \
+/** \ingroup matrixtypedefs */ \
+/** \brief \cpp11 `Dynamic`×`Size` matrix of type `Type`. */ \
+template <typename Type> \
+using Matrix##X##Size = Matrix<Type, Dynamic, Size>;
+
+EIGEN_MAKE_TYPEDEFS(2, 2)
+EIGEN_MAKE_TYPEDEFS(3, 3)
+EIGEN_MAKE_TYPEDEFS(4, 4)
+EIGEN_MAKE_TYPEDEFS(Dynamic, X)
+EIGEN_MAKE_FIXED_TYPEDEFS(2)
+EIGEN_MAKE_FIXED_TYPEDEFS(3)
+EIGEN_MAKE_FIXED_TYPEDEFS(4)
+
+/** \ingroup matrixtypedefs
+ * \brief \cpp11 `Size`×`1` vector of type `Type`. */
+template <typename Type, int Size>
+using Vector = Matrix<Type, Size, 1>;
+
+/** \ingroup matrixtypedefs
+ * \brief \cpp11 `1`×`Size` vector of type `Type`. */
+template <typename Type, int Size>
+using RowVector = Matrix<Type, 1, Size>;
+
+#undef EIGEN_MAKE_TYPEDEFS
+#undef EIGEN_MAKE_FIXED_TYPEDEFS
+
+} // end namespace Eigen
+
+#endif // EIGEN_MATRIX_H
diff --git a/Eigen/src/Core/MatrixBase.h b/Eigen/src/Core/MatrixBase.h
new file mode 100644
index 0000000..d87c6b3
--- /dev/null
+++ b/Eigen/src/Core/MatrixBase.h
@@ -0,0 +1,559 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2006-2009 Benoit Jacob <jacob.benoit.1@gmail.com>
+// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_MATRIXBASE_H
+#define EIGEN_MATRIXBASE_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+/** \class MatrixBase
+ * \ingroup Core_Module
+ *
+ * \brief Base class for all dense matrices, vectors, and expressions
+ *
+ * This class is the base that is inherited by all matrix, vector, and related expression
+ * types. Most of the Eigen API is contained in this class, and its base classes. Other important
+ * classes for the Eigen API are Matrix, and VectorwiseOp.
+ *
+ * Note that some methods are defined in other modules such as the \ref LU_Module LU module
+ * for all functions related to matrix inversions.
+ *
+ * \tparam Derived is the derived type, e.g. a matrix type, or an expression, etc.
+ *
+ * When writing a function taking Eigen objects as argument, if you want your function
+ * to take as argument any matrix, vector, or expression, just let it take a
+ * MatrixBase argument. As an example, here is a function printFirstRow which, given
+ * a matrix, vector, or expression \a x, prints the first row of \a x.
+ *
+ * \code
+ template<typename Derived>
+ void printFirstRow(const Eigen::MatrixBase<Derived>& x)
+ {
+ cout << x.row(0) << endl;
+ }
+ * \endcode
+ *
+ * This class can be extended with the help of the plugin mechanism described on the page
+ * \ref TopicCustomizing_Plugins by defining the preprocessor symbol \c EIGEN_MATRIXBASE_PLUGIN.
+ *
+ * \sa \blank \ref TopicClassHierarchy
+ */
+template<typename Derived> class MatrixBase
+ : public DenseBase<Derived>
+{
+ public:
+#ifndef EIGEN_PARSED_BY_DOXYGEN
+ typedef MatrixBase StorageBaseType;
+ typedef typename internal::traits<Derived>::StorageKind StorageKind;
+ typedef typename internal::traits<Derived>::StorageIndex StorageIndex;
+ typedef typename internal::traits<Derived>::Scalar Scalar;
+ typedef typename internal::packet_traits<Scalar>::type PacketScalar;
+ typedef typename NumTraits<Scalar>::Real RealScalar;
+
+ typedef DenseBase<Derived> Base;
+ using Base::RowsAtCompileTime;
+ using Base::ColsAtCompileTime;
+ using Base::SizeAtCompileTime;
+ using Base::MaxRowsAtCompileTime;
+ using Base::MaxColsAtCompileTime;
+ using Base::MaxSizeAtCompileTime;
+ using Base::IsVectorAtCompileTime;
+ using Base::Flags;
+
+ using Base::derived;
+ using Base::const_cast_derived;
+ using Base::rows;
+ using Base::cols;
+ using Base::size;
+ using Base::coeff;
+ using Base::coeffRef;
+ using Base::lazyAssign;
+ using Base::eval;
+ using Base::operator-;
+ using Base::operator+=;
+ using Base::operator-=;
+ using Base::operator*=;
+ using Base::operator/=;
+
+ typedef typename Base::CoeffReturnType CoeffReturnType;
+ typedef typename Base::ConstTransposeReturnType ConstTransposeReturnType;
+ typedef typename Base::RowXpr RowXpr;
+ typedef typename Base::ColXpr ColXpr;
+#endif // not EIGEN_PARSED_BY_DOXYGEN
+
+
+
+#ifndef EIGEN_PARSED_BY_DOXYGEN
+ /** type of the equivalent square matrix */
+ typedef Matrix<Scalar, internal::max_size_prefer_dynamic(RowsAtCompileTime, ColsAtCompileTime),
+ internal::max_size_prefer_dynamic(RowsAtCompileTime, ColsAtCompileTime)> SquareMatrixType;
+#endif // not EIGEN_PARSED_BY_DOXYGEN
+
+ /** \returns the size of the main diagonal, which is min(rows(),cols()).
+ * \sa rows(), cols(), SizeAtCompileTime. */
+ EIGEN_DEVICE_FUNC
+ inline Index diagonalSize() const { return (numext::mini)(rows(),cols()); }
+
+ typedef typename Base::PlainObject PlainObject;
+
+#ifndef EIGEN_PARSED_BY_DOXYGEN
+ /** \internal Represents a matrix with all coefficients equal to one another*/
+ typedef CwiseNullaryOp<internal::scalar_constant_op<Scalar>,PlainObject> ConstantReturnType;
+ /** \internal the return type of MatrixBase::adjoint() */
+ typedef std::conditional_t<NumTraits<Scalar>::IsComplex,
+ CwiseUnaryOp<internal::scalar_conjugate_op<Scalar>, ConstTransposeReturnType>,
+ ConstTransposeReturnType
+ > AdjointReturnType;
+ /** \internal Return type of eigenvalues() */
+ typedef Matrix<std::complex<RealScalar>, internal::traits<Derived>::ColsAtCompileTime, 1, ColMajor> EigenvaluesReturnType;
+ /** \internal the return type of identity */
+ typedef CwiseNullaryOp<internal::scalar_identity_op<Scalar>,PlainObject> IdentityReturnType;
+ /** \internal the return type of unit vectors */
+ typedef Block<const CwiseNullaryOp<internal::scalar_identity_op<Scalar>, SquareMatrixType>,
+ internal::traits<Derived>::RowsAtCompileTime,
+ internal::traits<Derived>::ColsAtCompileTime> BasisReturnType;
+#endif // not EIGEN_PARSED_BY_DOXYGEN
+
+#define EIGEN_CURRENT_STORAGE_BASE_CLASS Eigen::MatrixBase
+#define EIGEN_DOC_UNARY_ADDONS(X,Y)
+# include "../plugins/CommonCwiseBinaryOps.h"
+# include "../plugins/MatrixCwiseUnaryOps.h"
+# include "../plugins/MatrixCwiseBinaryOps.h"
+# ifdef EIGEN_MATRIXBASE_PLUGIN
+# include EIGEN_MATRIXBASE_PLUGIN
+# endif
+#undef EIGEN_CURRENT_STORAGE_BASE_CLASS
+#undef EIGEN_DOC_UNARY_ADDONS
+
+ /** Special case of the template operator=, in order to prevent the compiler
+ * from generating a default operator= (issue hit with g++ 4.1)
+ */
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ Derived& operator=(const MatrixBase& other);
+
+ // We cannot inherit here via Base::operator= since it is causing
+ // trouble with MSVC.
+
+ template <typename OtherDerived>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ Derived& operator=(const DenseBase<OtherDerived>& other);
+
+ template <typename OtherDerived>
+ EIGEN_DEVICE_FUNC
+ Derived& operator=(const EigenBase<OtherDerived>& other);
+
+ template<typename OtherDerived>
+ EIGEN_DEVICE_FUNC
+ Derived& operator=(const ReturnByValue<OtherDerived>& other);
+
+ template<typename OtherDerived>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ Derived& operator+=(const MatrixBase<OtherDerived>& other);
+ template<typename OtherDerived>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ Derived& operator-=(const MatrixBase<OtherDerived>& other);
+
+ template<typename OtherDerived>
+ EIGEN_DEVICE_FUNC
+ const Product<Derived,OtherDerived>
+ operator*(const MatrixBase<OtherDerived> &other) const;
+
+ template<typename OtherDerived>
+ EIGEN_DEVICE_FUNC
+ const Product<Derived,OtherDerived,LazyProduct>
+ lazyProduct(const MatrixBase<OtherDerived> &other) const;
+
+ template<typename OtherDerived>
+ Derived& operator*=(const EigenBase<OtherDerived>& other);
+
+ template<typename OtherDerived>
+ void applyOnTheLeft(const EigenBase<OtherDerived>& other);
+
+ template<typename OtherDerived>
+ void applyOnTheRight(const EigenBase<OtherDerived>& other);
+
+ template<typename DiagonalDerived>
+ EIGEN_DEVICE_FUNC
+ const Product<Derived, DiagonalDerived, LazyProduct>
+ operator*(const DiagonalBase<DiagonalDerived> &diagonal) const;
+
+ template<typename SkewDerived>
+ EIGEN_DEVICE_FUNC
+ const Product<Derived, SkewDerived, LazyProduct>
+ operator*(const SkewSymmetricBase<SkewDerived> &skew) const;
+
+ template<typename OtherDerived>
+ EIGEN_DEVICE_FUNC
+ typename ScalarBinaryOpTraits<typename internal::traits<Derived>::Scalar,typename internal::traits<OtherDerived>::Scalar>::ReturnType
+ dot(const MatrixBase<OtherDerived>& other) const;
+
+ EIGEN_DEVICE_FUNC RealScalar squaredNorm() const;
+ EIGEN_DEVICE_FUNC RealScalar norm() const;
+ RealScalar stableNorm() const;
+ RealScalar blueNorm() const;
+ RealScalar hypotNorm() const;
+ EIGEN_DEVICE_FUNC const PlainObject normalized() const;
+ EIGEN_DEVICE_FUNC const PlainObject stableNormalized() const;
+ EIGEN_DEVICE_FUNC void normalize();
+ EIGEN_DEVICE_FUNC void stableNormalize();
+
+ EIGEN_DEVICE_FUNC const AdjointReturnType adjoint() const;
+ EIGEN_DEVICE_FUNC void adjointInPlace();
+
+ typedef Diagonal<Derived> DiagonalReturnType;
+ EIGEN_DEVICE_FUNC
+ DiagonalReturnType diagonal();
+
+ typedef Diagonal<const Derived> ConstDiagonalReturnType;
+ EIGEN_DEVICE_FUNC
+ const ConstDiagonalReturnType diagonal() const;
+
+ template<int Index>
+ EIGEN_DEVICE_FUNC
+ Diagonal<Derived, Index> diagonal();
+
+ template<int Index>
+ EIGEN_DEVICE_FUNC
+ const Diagonal<const Derived, Index> diagonal() const;
+
+ EIGEN_DEVICE_FUNC
+ Diagonal<Derived, DynamicIndex> diagonal(Index index);
+ EIGEN_DEVICE_FUNC
+ const Diagonal<const Derived, DynamicIndex> diagonal(Index index) const;
+
+ template<unsigned int Mode> struct TriangularViewReturnType { typedef TriangularView<Derived, Mode> Type; };
+ template<unsigned int Mode> struct ConstTriangularViewReturnType { typedef const TriangularView<const Derived, Mode> Type; };
+
+ template<unsigned int Mode>
+ EIGEN_DEVICE_FUNC
+ typename TriangularViewReturnType<Mode>::Type triangularView();
+ template<unsigned int Mode>
+ EIGEN_DEVICE_FUNC
+ typename ConstTriangularViewReturnType<Mode>::Type triangularView() const;
+
+ template<unsigned int UpLo> struct SelfAdjointViewReturnType { typedef SelfAdjointView<Derived, UpLo> Type; };
+ template<unsigned int UpLo> struct ConstSelfAdjointViewReturnType { typedef const SelfAdjointView<const Derived, UpLo> Type; };
+
+ template<unsigned int UpLo>
+ EIGEN_DEVICE_FUNC
+ typename SelfAdjointViewReturnType<UpLo>::Type selfadjointView();
+ template<unsigned int UpLo>
+ EIGEN_DEVICE_FUNC
+ typename ConstSelfAdjointViewReturnType<UpLo>::Type selfadjointView() const;
+
+ const SparseView<Derived> sparseView(const Scalar& m_reference = Scalar(0),
+ const typename NumTraits<Scalar>::Real& m_epsilon = NumTraits<Scalar>::dummy_precision()) const;
+ EIGEN_DEVICE_FUNC static const IdentityReturnType Identity();
+ EIGEN_DEVICE_FUNC static const IdentityReturnType Identity(Index rows, Index cols);
+ EIGEN_DEVICE_FUNC static const BasisReturnType Unit(Index size, Index i);
+ EIGEN_DEVICE_FUNC static const BasisReturnType Unit(Index i);
+ EIGEN_DEVICE_FUNC static const BasisReturnType UnitX();
+ EIGEN_DEVICE_FUNC static const BasisReturnType UnitY();
+ EIGEN_DEVICE_FUNC static const BasisReturnType UnitZ();
+ EIGEN_DEVICE_FUNC static const BasisReturnType UnitW();
+
+ EIGEN_DEVICE_FUNC
+ const DiagonalWrapper<const Derived> asDiagonal() const;
+ const PermutationWrapper<const Derived> asPermutation() const;
+ EIGEN_DEVICE_FUNC
+ const SkewSymmetricWrapper<const Derived> asSkewSymmetric() const;
+
+ EIGEN_DEVICE_FUNC
+ Derived& setIdentity();
+ EIGEN_DEVICE_FUNC
+ Derived& setIdentity(Index rows, Index cols);
+ EIGEN_DEVICE_FUNC Derived& setUnit(Index i);
+ EIGEN_DEVICE_FUNC Derived& setUnit(Index newSize, Index i);
+
+ bool isIdentity(const RealScalar& prec = NumTraits<Scalar>::dummy_precision()) const;
+ bool isDiagonal(const RealScalar& prec = NumTraits<Scalar>::dummy_precision()) const;
+
+ bool isUpperTriangular(const RealScalar& prec = NumTraits<Scalar>::dummy_precision()) const;
+ bool isLowerTriangular(const RealScalar& prec = NumTraits<Scalar>::dummy_precision()) const;
+
+ bool isSkewSymmetric(const RealScalar& prec = NumTraits<Scalar>::dummy_precision()) const;
+
+ template<typename OtherDerived>
+ bool isOrthogonal(const MatrixBase<OtherDerived>& other,
+ const RealScalar& prec = NumTraits<Scalar>::dummy_precision()) const;
+ bool isUnitary(const RealScalar& prec = NumTraits<Scalar>::dummy_precision()) const;
+
+ /** \returns true if each coefficients of \c *this and \a other are all exactly equal.
+ * \warning When using floating point scalar values you probably should rather use a
+ * fuzzy comparison such as isApprox()
+ * \sa isApprox(), operator!= */
+ template<typename OtherDerived>
+ EIGEN_DEVICE_FUNC inline bool operator==(const MatrixBase<OtherDerived>& other) const
+ { return cwiseEqual(other).all(); }
+
+ /** \returns true if at least one pair of coefficients of \c *this and \a other are not exactly equal to each other.
+ * \warning When using floating point scalar values you probably should rather use a
+ * fuzzy comparison such as isApprox()
+ * \sa isApprox(), operator== */
+ template<typename OtherDerived>
+ EIGEN_DEVICE_FUNC inline bool operator!=(const MatrixBase<OtherDerived>& other) const
+ { return cwiseNotEqual(other).any(); }
+
+ NoAlias<Derived,Eigen::MatrixBase > EIGEN_DEVICE_FUNC noalias();
+
+ // TODO forceAlignedAccess is temporarily disabled
+ // Need to find a nicer workaround.
+ inline const Derived& forceAlignedAccess() const { return derived(); }
+ inline Derived& forceAlignedAccess() { return derived(); }
+ template<bool Enable> inline const Derived& forceAlignedAccessIf() const { return derived(); }
+ template<bool Enable> inline Derived& forceAlignedAccessIf() { return derived(); }
+
+ EIGEN_DEVICE_FUNC Scalar trace() const;
+
+ template<int p> EIGEN_DEVICE_FUNC RealScalar lpNorm() const;
+
+ EIGEN_DEVICE_FUNC MatrixBase<Derived>& matrix() { return *this; }
+ EIGEN_DEVICE_FUNC const MatrixBase<Derived>& matrix() const { return *this; }
+
+ /** \returns an \link Eigen::ArrayBase Array \endlink expression of this matrix
+ * \sa ArrayBase::matrix() */
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE ArrayWrapper<Derived> array() { return ArrayWrapper<Derived>(derived()); }
+ /** \returns a const \link Eigen::ArrayBase Array \endlink expression of this matrix
+ * \sa ArrayBase::matrix() */
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const ArrayWrapper<const Derived> array() const { return ArrayWrapper<const Derived>(derived()); }
+
+/////////// LU module ///////////
+
+ inline const FullPivLU<PlainObject> fullPivLu() const;
+ inline const PartialPivLU<PlainObject> partialPivLu() const;
+
+ inline const PartialPivLU<PlainObject> lu() const;
+
+ EIGEN_DEVICE_FUNC
+ inline const Inverse<Derived> inverse() const;
+
+ template<typename ResultType>
+ inline void computeInverseAndDetWithCheck(
+ ResultType& inverse,
+ typename ResultType::Scalar& determinant,
+ bool& invertible,
+ const RealScalar& absDeterminantThreshold = NumTraits<Scalar>::dummy_precision()
+ ) const;
+
+ template<typename ResultType>
+ inline void computeInverseWithCheck(
+ ResultType& inverse,
+ bool& invertible,
+ const RealScalar& absDeterminantThreshold = NumTraits<Scalar>::dummy_precision()
+ ) const;
+
+ EIGEN_DEVICE_FUNC
+ Scalar determinant() const;
+
+/////////// Cholesky module ///////////
+
+ inline const LLT<PlainObject> llt() const;
+ inline const LDLT<PlainObject> ldlt() const;
+
+/////////// QR module ///////////
+
+ inline const HouseholderQR<PlainObject> householderQr() const;
+ inline const ColPivHouseholderQR<PlainObject> colPivHouseholderQr() const;
+ inline const FullPivHouseholderQR<PlainObject> fullPivHouseholderQr() const;
+ inline const CompleteOrthogonalDecomposition<PlainObject> completeOrthogonalDecomposition() const;
+
+/////////// Eigenvalues module ///////////
+
+ inline EigenvaluesReturnType eigenvalues() const;
+ inline RealScalar operatorNorm() const;
+
+/////////// SVD module ///////////
+
+ template<int Options = 0>
+ inline JacobiSVD<PlainObject, Options> jacobiSvd() const;
+ template<int Options = 0>
+ EIGEN_DEPRECATED
+ inline JacobiSVD<PlainObject, Options> jacobiSvd(unsigned int computationOptions) const;
+
+ template<int Options = 0>
+ inline BDCSVD<PlainObject, Options> bdcSvd() const;
+ template<int Options = 0>
+ EIGEN_DEPRECATED
+ inline BDCSVD<PlainObject, Options> bdcSvd(unsigned int computationOptions) const;
+
+/////////// Geometry module ///////////
+
+ #ifndef EIGEN_PARSED_BY_DOXYGEN
+ /// \internal helper struct to form the return type of the cross product
+ template<typename OtherDerived> struct cross_product_return_type {
+ typedef typename ScalarBinaryOpTraits<typename internal::traits<Derived>::Scalar,typename internal::traits<OtherDerived>::Scalar>::ReturnType Scalar;
+ typedef Matrix<Scalar,MatrixBase::RowsAtCompileTime,MatrixBase::ColsAtCompileTime> type;
+ };
+ #endif // EIGEN_PARSED_BY_DOXYGEN
+ template<typename OtherDerived>
+ EIGEN_DEVICE_FUNC
+#ifndef EIGEN_PARSED_BY_DOXYGEN
+ inline typename cross_product_return_type<OtherDerived>::type
+#else
+ inline PlainObject
+#endif
+ cross(const MatrixBase<OtherDerived>& other) const;
+
+ template<typename OtherDerived>
+ EIGEN_DEVICE_FUNC
+ inline PlainObject cross3(const MatrixBase<OtherDerived>& other) const;
+
+ EIGEN_DEVICE_FUNC
+ inline PlainObject unitOrthogonal(void) const;
+
+ EIGEN_DEVICE_FUNC
+ inline Matrix<Scalar,3,1> eulerAngles(Index a0, Index a1, Index a2) const;
+
+ // put this as separate enum value to work around possible GCC 4.3 bug (?)
+ enum { HomogeneousReturnTypeDirection = ColsAtCompileTime==1&&RowsAtCompileTime==1 ? ((internal::traits<Derived>::Flags&RowMajorBit)==RowMajorBit ? Horizontal : Vertical)
+ : ColsAtCompileTime==1 ? Vertical : Horizontal };
+ typedef Homogeneous<Derived, HomogeneousReturnTypeDirection> HomogeneousReturnType;
+ EIGEN_DEVICE_FUNC
+ inline HomogeneousReturnType homogeneous() const;
+
+ enum {
+ SizeMinusOne = SizeAtCompileTime==Dynamic ? Dynamic : SizeAtCompileTime-1
+ };
+ typedef Block<const Derived,
+ internal::traits<Derived>::ColsAtCompileTime==1 ? SizeMinusOne : 1,
+ internal::traits<Derived>::ColsAtCompileTime==1 ? 1 : SizeMinusOne> ConstStartMinusOne;
+ typedef EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(ConstStartMinusOne,Scalar,quotient) HNormalizedReturnType;
+ EIGEN_DEVICE_FUNC
+ inline const HNormalizedReturnType hnormalized() const;
+
+////////// Householder module ///////////
+
+ EIGEN_DEVICE_FUNC
+ void makeHouseholderInPlace(Scalar& tau, RealScalar& beta);
+ template<typename EssentialPart>
+ EIGEN_DEVICE_FUNC
+ void makeHouseholder(EssentialPart& essential,
+ Scalar& tau, RealScalar& beta) const;
+ template<typename EssentialPart>
+ EIGEN_DEVICE_FUNC
+ void applyHouseholderOnTheLeft(const EssentialPart& essential,
+ const Scalar& tau,
+ Scalar* workspace);
+ template<typename EssentialPart>
+ EIGEN_DEVICE_FUNC
+ void applyHouseholderOnTheRight(const EssentialPart& essential,
+ const Scalar& tau,
+ Scalar* workspace);
+
+///////// Jacobi module /////////
+
+ template<typename OtherScalar>
+ EIGEN_DEVICE_FUNC
+ void applyOnTheLeft(Index p, Index q, const JacobiRotation<OtherScalar>& j);
+ template<typename OtherScalar>
+ EIGEN_DEVICE_FUNC
+ void applyOnTheRight(Index p, Index q, const JacobiRotation<OtherScalar>& j);
+
+///////// SparseCore module /////////
+
+ template<typename OtherDerived>
+ EIGEN_STRONG_INLINE const typename SparseMatrixBase<OtherDerived>::template CwiseProductDenseReturnType<Derived>::Type
+ cwiseProduct(const SparseMatrixBase<OtherDerived> &other) const
+ {
+ return other.cwiseProduct(derived());
+ }
+
+///////// MatrixFunctions module /////////
+
+ typedef typename internal::stem_function<Scalar>::type StemFunction;
+#define EIGEN_MATRIX_FUNCTION(ReturnType, Name, Description) \
+ /** \returns an expression of the matrix Description of \c *this. \brief This function requires the <a href="unsupported/group__MatrixFunctions__Module.html"> unsupported MatrixFunctions module</a>. To compute the coefficient-wise Description use ArrayBase::##Name . */ \
+ const ReturnType<Derived> Name() const;
+#define EIGEN_MATRIX_FUNCTION_1(ReturnType, Name, Description, Argument) \
+ /** \returns an expression of the matrix Description of \c *this. \brief This function requires the <a href="unsupported/group__MatrixFunctions__Module.html"> unsupported MatrixFunctions module</a>. To compute the coefficient-wise Description use ArrayBase::##Name . */ \
+ const ReturnType<Derived> Name(Argument) const;
+
+ EIGEN_MATRIX_FUNCTION(MatrixExponentialReturnValue, exp, exponential)
+ /** \brief Helper function for the <a href="unsupported/group__MatrixFunctions__Module.html"> unsupported MatrixFunctions module</a>.*/
+ const MatrixFunctionReturnValue<Derived> matrixFunction(StemFunction f) const;
+ EIGEN_MATRIX_FUNCTION(MatrixFunctionReturnValue, cosh, hyperbolic cosine)
+ EIGEN_MATRIX_FUNCTION(MatrixFunctionReturnValue, sinh, hyperbolic sine)
+ EIGEN_MATRIX_FUNCTION(MatrixFunctionReturnValue, atanh, inverse hyperbolic cosine)
+ EIGEN_MATRIX_FUNCTION(MatrixFunctionReturnValue, acosh, inverse hyperbolic cosine)
+ EIGEN_MATRIX_FUNCTION(MatrixFunctionReturnValue, asinh, inverse hyperbolic sine)
+ EIGEN_MATRIX_FUNCTION(MatrixFunctionReturnValue, cos, cosine)
+ EIGEN_MATRIX_FUNCTION(MatrixFunctionReturnValue, sin, sine)
+ EIGEN_MATRIX_FUNCTION(MatrixSquareRootReturnValue, sqrt, square root)
+ EIGEN_MATRIX_FUNCTION(MatrixLogarithmReturnValue, log, logarithm)
+ EIGEN_MATRIX_FUNCTION_1(MatrixPowerReturnValue, pow, power to \c p, const RealScalar& p)
+ EIGEN_MATRIX_FUNCTION_1(MatrixComplexPowerReturnValue, pow, power to \c p, const std::complex<RealScalar>& p)
+
+ protected:
+ EIGEN_DEFAULT_COPY_CONSTRUCTOR(MatrixBase)
+ EIGEN_DEFAULT_EMPTY_CONSTRUCTOR_AND_DESTRUCTOR(MatrixBase)
+
+ private:
+ EIGEN_DEVICE_FUNC explicit MatrixBase(int);
+ EIGEN_DEVICE_FUNC MatrixBase(int,int);
+ template<typename OtherDerived> EIGEN_DEVICE_FUNC explicit MatrixBase(const MatrixBase<OtherDerived>&);
+ protected:
+ // mixing arrays and matrices is not legal
+ template<typename OtherDerived> Derived& operator+=(const ArrayBase<OtherDerived>& )
+ {EIGEN_STATIC_ASSERT(std::ptrdiff_t(sizeof(typename OtherDerived::Scalar))==-1,YOU_CANNOT_MIX_ARRAYS_AND_MATRICES); return *this;}
+ // mixing arrays and matrices is not legal
+ template<typename OtherDerived> Derived& operator-=(const ArrayBase<OtherDerived>& )
+ {EIGEN_STATIC_ASSERT(std::ptrdiff_t(sizeof(typename OtherDerived::Scalar))==-1,YOU_CANNOT_MIX_ARRAYS_AND_MATRICES); return *this;}
+};
+
+
+/***************************************************************************
+* Implementation of matrix base methods
+***************************************************************************/
+
+/** replaces \c *this by \c *this * \a other.
+ *
+ * \returns a reference to \c *this
+ *
+ * Example: \include MatrixBase_applyOnTheRight.cpp
+ * Output: \verbinclude MatrixBase_applyOnTheRight.out
+ */
+template<typename Derived>
+template<typename OtherDerived>
+inline Derived&
+MatrixBase<Derived>::operator*=(const EigenBase<OtherDerived> &other)
+{
+ other.derived().applyThisOnTheRight(derived());
+ return derived();
+}
+
+/** replaces \c *this by \c *this * \a other. It is equivalent to MatrixBase::operator*=().
+ *
+ * Example: \include MatrixBase_applyOnTheRight.cpp
+ * Output: \verbinclude MatrixBase_applyOnTheRight.out
+ */
+template<typename Derived>
+template<typename OtherDerived>
+inline void MatrixBase<Derived>::applyOnTheRight(const EigenBase<OtherDerived> &other)
+{
+ other.derived().applyThisOnTheRight(derived());
+}
+
+/** replaces \c *this by \a other * \c *this.
+ *
+ * Example: \include MatrixBase_applyOnTheLeft.cpp
+ * Output: \verbinclude MatrixBase_applyOnTheLeft.out
+ */
+template<typename Derived>
+template<typename OtherDerived>
+inline void MatrixBase<Derived>::applyOnTheLeft(const EigenBase<OtherDerived> &other)
+{
+ other.derived().applyThisOnTheLeft(derived());
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_MATRIXBASE_H
diff --git a/Eigen/src/Core/NestByValue.h b/Eigen/src/Core/NestByValue.h
new file mode 100644
index 0000000..5f1dc84
--- /dev/null
+++ b/Eigen/src/Core/NestByValue.h
@@ -0,0 +1,87 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_NESTBYVALUE_H
+#define EIGEN_NESTBYVALUE_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+template<typename ExpressionType>
+struct traits<NestByValue<ExpressionType> > : public traits<ExpressionType>
+{
+ enum {
+ Flags = traits<ExpressionType>::Flags & ~NestByRefBit
+ };
+};
+}
+
+/** \class NestByValue
+ * \ingroup Core_Module
+ *
+ * \brief Expression which must be nested by value
+ *
+ * \tparam ExpressionType the type of the object of which we are requiring nesting-by-value
+ *
+ * This class is the return type of MatrixBase::nestByValue()
+ * and most of the time this is the only way it is used.
+ *
+ * \sa MatrixBase::nestByValue()
+ */
+template<typename ExpressionType> class NestByValue
+ : public internal::dense_xpr_base< NestByValue<ExpressionType> >::type
+{
+ public:
+
+ typedef typename internal::dense_xpr_base<NestByValue>::type Base;
+ EIGEN_DENSE_PUBLIC_INTERFACE(NestByValue)
+
+ EIGEN_DEVICE_FUNC explicit inline NestByValue(const ExpressionType& matrix) : m_expression(matrix) {}
+
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR inline Index rows() const EIGEN_NOEXCEPT { return m_expression.rows(); }
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR inline Index cols() const EIGEN_NOEXCEPT { return m_expression.cols(); }
+
+ EIGEN_DEVICE_FUNC operator const ExpressionType&() const { return m_expression; }
+
+ EIGEN_DEVICE_FUNC const ExpressionType& nestedExpression() const { return m_expression; }
+
+ protected:
+ const ExpressionType m_expression;
+};
+
+/** \returns an expression of the temporary version of *this.
+ */
+template<typename Derived>
+EIGEN_DEVICE_FUNC inline const NestByValue<Derived>
+DenseBase<Derived>::nestByValue() const
+{
+ return NestByValue<Derived>(derived());
+}
+
+namespace internal {
+
+// Evaluator of Solve -> eval into a temporary
+template<typename ArgType>
+struct evaluator<NestByValue<ArgType> >
+ : public evaluator<ArgType>
+{
+ typedef evaluator<ArgType> Base;
+
+ EIGEN_DEVICE_FUNC explicit evaluator(const NestByValue<ArgType>& xpr)
+ : Base(xpr.nestedExpression())
+ {}
+};
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_NESTBYVALUE_H
diff --git a/Eigen/src/Core/NoAlias.h b/Eigen/src/Core/NoAlias.h
new file mode 100644
index 0000000..09c0aac
--- /dev/null
+++ b/Eigen/src/Core/NoAlias.h
@@ -0,0 +1,111 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_NOALIAS_H
+#define EIGEN_NOALIAS_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+/** \class NoAlias
+ * \ingroup Core_Module
+ *
+ * \brief Pseudo expression providing an operator = assuming no aliasing
+ *
+ * \tparam ExpressionType the type of the object on which to do the lazy assignment
+ *
+ * This class represents an expression with special assignment operators
+ * assuming no aliasing between the target expression and the source expression.
+ * More precisely it alloas to bypass the EvalBeforeAssignBit flag of the source expression.
+ * It is the return type of MatrixBase::noalias()
+ * and most of the time this is the only way it is used.
+ *
+ * \sa MatrixBase::noalias()
+ */
+template<typename ExpressionType, template <typename> class StorageBase>
+class NoAlias
+{
+ public:
+ typedef typename ExpressionType::Scalar Scalar;
+
+ EIGEN_DEVICE_FUNC
+ explicit NoAlias(ExpressionType& expression) : m_expression(expression) {}
+
+ template<typename OtherDerived>
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE ExpressionType& operator=(const StorageBase<OtherDerived>& other)
+ {
+ call_assignment_no_alias(m_expression, other.derived(), internal::assign_op<Scalar,typename OtherDerived::Scalar>());
+ return m_expression;
+ }
+
+ template<typename OtherDerived>
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE ExpressionType& operator+=(const StorageBase<OtherDerived>& other)
+ {
+ call_assignment_no_alias(m_expression, other.derived(), internal::add_assign_op<Scalar,typename OtherDerived::Scalar>());
+ return m_expression;
+ }
+
+ template<typename OtherDerived>
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE ExpressionType& operator-=(const StorageBase<OtherDerived>& other)
+ {
+ call_assignment_no_alias(m_expression, other.derived(), internal::sub_assign_op<Scalar,typename OtherDerived::Scalar>());
+ return m_expression;
+ }
+
+ EIGEN_DEVICE_FUNC
+ ExpressionType& expression() const
+ {
+ return m_expression;
+ }
+
+ protected:
+ ExpressionType& m_expression;
+};
+
+/** \returns a pseudo expression of \c *this with an operator= assuming
+ * no aliasing between \c *this and the source expression.
+ *
+ * More precisely, noalias() allows to bypass the EvalBeforeAssignBit flag.
+ * Currently, even though several expressions may alias, only product
+ * expressions have this flag. Therefore, noalias() is only useful when
+ * the source expression contains a matrix product.
+ *
+ * Here are some examples where noalias is useful:
+ * \code
+ * D.noalias() = A * B;
+ * D.noalias() += A.transpose() * B;
+ * D.noalias() -= 2 * A * B.adjoint();
+ * \endcode
+ *
+ * On the other hand the following example will lead to a \b wrong result:
+ * \code
+ * A.noalias() = A * B;
+ * \endcode
+ * because the result matrix A is also an operand of the matrix product. Therefore,
+ * there is no alternative than evaluating A * B in a temporary, that is the default
+ * behavior when you write:
+ * \code
+ * A = A * B;
+ * \endcode
+ *
+ * \sa class NoAlias
+ */
+template<typename Derived>
+NoAlias<Derived,MatrixBase> EIGEN_DEVICE_FUNC MatrixBase<Derived>::noalias()
+{
+ return NoAlias<Derived, Eigen::MatrixBase >(derived());
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_NOALIAS_H
diff --git a/Eigen/src/Core/NumTraits.h b/Eigen/src/Core/NumTraits.h
new file mode 100644
index 0000000..4f1f992
--- /dev/null
+++ b/Eigen/src/Core/NumTraits.h
@@ -0,0 +1,333 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2006-2010 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_NUMTRAITS_H
+#define EIGEN_NUMTRAITS_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+
+// default implementation of digits10(), based on numeric_limits if specialized,
+// 0 for integer types, and log10(epsilon()) otherwise.
+template< typename T,
+ bool use_numeric_limits = std::numeric_limits<T>::is_specialized,
+ bool is_integer = NumTraits<T>::IsInteger>
+struct default_digits10_impl
+{
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
+ static int run() { return std::numeric_limits<T>::digits10; }
+};
+
+template<typename T>
+struct default_digits10_impl<T,false,false> // Floating point
+{
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
+ static int run() {
+ using std::log10;
+ using std::ceil;
+ typedef typename NumTraits<T>::Real Real;
+ return int(ceil(-log10(NumTraits<Real>::epsilon())));
+ }
+};
+
+template<typename T>
+struct default_digits10_impl<T,false,true> // Integer
+{
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
+ static int run() { return 0; }
+};
+
+
+// default implementation of digits(), based on numeric_limits if specialized,
+// 0 for integer types, and log2(epsilon()) otherwise.
+template< typename T,
+ bool use_numeric_limits = std::numeric_limits<T>::is_specialized,
+ bool is_integer = NumTraits<T>::IsInteger>
+struct default_digits_impl
+{
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
+ static int run() { return std::numeric_limits<T>::digits; }
+};
+
+template<typename T>
+struct default_digits_impl<T,false,false> // Floating point
+{
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
+ static int run() {
+ using std::log2;
+ using std::ceil;
+ typedef typename NumTraits<T>::Real Real;
+ return int(ceil(-log2(NumTraits<Real>::epsilon())));
+ }
+};
+
+template<typename T>
+struct default_digits_impl<T,false,true> // Integer
+{
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
+ static int run() { return 0; }
+};
+
+} // end namespace internal
+
+namespace numext {
+/** \internal bit-wise cast without changing the underlying bit representation. */
+
+// TODO: Replace by std::bit_cast (available in C++20)
+template <typename Tgt, typename Src>
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Tgt bit_cast(const Src& src) {
+ // The behaviour of memcpy is not specified for non-trivially copyable types
+ EIGEN_STATIC_ASSERT(std::is_trivially_copyable<Src>::value, THIS_TYPE_IS_NOT_SUPPORTED);
+ EIGEN_STATIC_ASSERT(std::is_trivially_copyable<Tgt>::value && std::is_default_constructible<Tgt>::value,
+ THIS_TYPE_IS_NOT_SUPPORTED);
+ EIGEN_STATIC_ASSERT(sizeof(Src) == sizeof(Tgt), THIS_TYPE_IS_NOT_SUPPORTED);
+
+ Tgt tgt;
+ // Load src into registers first. This allows the memcpy to be elided by CUDA.
+ const Src staged = src;
+ EIGEN_USING_STD(memcpy)
+ memcpy(&tgt, &staged, sizeof(Tgt));
+ return tgt;
+}
+} // namespace numext
+
+/** \class NumTraits
+ * \ingroup Core_Module
+ *
+ * \brief Holds information about the various numeric (i.e. scalar) types allowed by Eigen.
+ *
+ * \tparam T the numeric type at hand
+ *
+ * This class stores enums, typedefs and static methods giving information about a numeric type.
+ *
+ * The provided data consists of:
+ * \li A typedef \c Real, giving the "real part" type of \a T. If \a T is already real,
+ * then \c Real is just a typedef to \a T. If \a T is \c std::complex<U> then \c Real
+ * is a typedef to \a U.
+ * \li A typedef \c NonInteger, giving the type that should be used for operations producing non-integral values,
+ * such as quotients, square roots, etc. If \a T is a floating-point type, then this typedef just gives
+ * \a T again. Note however that many Eigen functions such as internal::sqrt simply refuse to
+ * take integers. Outside of a few cases, Eigen doesn't do automatic type promotion. Thus, this typedef is
+ * only intended as a helper for code that needs to explicitly promote types.
+ * \li A typedef \c Literal giving the type to use for numeric literals such as "2" or "0.5". For instance, for \c std::complex<U>, Literal is defined as \c U.
+ * Of course, this type must be fully compatible with \a T. In doubt, just use \a T here.
+ * \li A typedef \a Nested giving the type to use to nest a value inside of the expression tree. If you don't know what
+ * this means, just use \a T here.
+ * \li An enum value \a IsComplex. It is equal to 1 if \a T is a \c std::complex
+ * type, and to 0 otherwise.
+ * \li An enum value \a IsInteger. It is equal to \c 1 if \a T is an integer type such as \c int,
+ * and to \c 0 otherwise.
+ * \li Enum values ReadCost, AddCost and MulCost representing a rough estimate of the number of CPU cycles needed
+ * to by move / add / mul instructions respectively, assuming the data is already stored in CPU registers.
+ * Stay vague here. No need to do architecture-specific stuff. If you don't know what this means, just use \c Eigen::HugeCost.
+ * \li An enum value \a IsSigned. It is equal to \c 1 if \a T is a signed type and to 0 if \a T is unsigned.
+ * \li An enum value \a RequireInitialization. It is equal to \c 1 if the constructor of the numeric type \a T must
+ * be called, and to 0 if it is safe not to call it. Default is 0 if \a T is an arithmetic type, and 1 otherwise.
+ * \li An epsilon() function which, unlike <a href="http://en.cppreference.com/w/cpp/types/numeric_limits/epsilon">std::numeric_limits::epsilon()</a>,
+ * it returns a \a Real instead of a \a T.
+ * \li A dummy_precision() function returning a weak epsilon value. It is mainly used as a default
+ * value by the fuzzy comparison operators.
+ * \li highest() and lowest() functions returning the highest and lowest possible values respectively.
+ * \li digits() function returning the number of radix digits (non-sign digits for integers, mantissa for floating-point). This is
+ * the analogue of <a href="http://en.cppreference.com/w/cpp/types/numeric_limits/digits">std::numeric_limits<T>::digits</a>
+ * which is used as the default implementation if specialized.
+ * \li digits10() function returning the number of decimal digits that can be represented without change. This is
+ * the analogue of <a href="http://en.cppreference.com/w/cpp/types/numeric_limits/digits10">std::numeric_limits<T>::digits10</a>
+ * which is used as the default implementation if specialized.
+ * \li min_exponent() and max_exponent() functions returning the highest and lowest possible values, respectively,
+ * such that the radix raised to the power exponent-1 is a normalized floating-point number. These are equivalent to
+ * <a href="http://en.cppreference.com/w/cpp/types/numeric_limits/min_exponent">std::numeric_limits<T>::min_exponent</a>/
+ * <a href="http://en.cppreference.com/w/cpp/types/numeric_limits/max_exponent">std::numeric_limits<T>::max_exponent</a>.
+ * \li infinity() function returning a representation of positive infinity, if available.
+ * \li quiet_NaN function returning a non-signaling "not-a-number", if available.
+ */
+
+template<typename T> struct GenericNumTraits
+{
+ enum {
+ IsInteger = std::numeric_limits<T>::is_integer,
+ IsSigned = std::numeric_limits<T>::is_signed,
+ IsComplex = 0,
+ RequireInitialization = internal::is_arithmetic<T>::value ? 0 : 1,
+ ReadCost = 1,
+ AddCost = 1,
+ MulCost = 1
+ };
+
+ typedef T Real;
+ typedef std::conditional_t<IsInteger, std::conditional_t<sizeof(T)<=2, float, double>, T> NonInteger;
+ typedef T Nested;
+ typedef T Literal;
+
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
+ static inline Real epsilon()
+ {
+ return numext::numeric_limits<T>::epsilon();
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
+ static inline int digits10()
+ {
+ return internal::default_digits10_impl<T>::run();
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
+ static inline int digits()
+ {
+ return internal::default_digits_impl<T>::run();
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
+ static inline int min_exponent()
+ {
+ return numext::numeric_limits<T>::min_exponent;
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
+ static inline int max_exponent()
+ {
+ return numext::numeric_limits<T>::max_exponent;
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
+ static inline Real dummy_precision()
+ {
+ // make sure to override this for floating-point types
+ return Real(0);
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
+ static inline T highest() {
+ return (numext::numeric_limits<T>::max)();
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
+ static inline T lowest() {
+ return IsInteger ? (numext::numeric_limits<T>::min)()
+ : static_cast<T>(-(numext::numeric_limits<T>::max)());
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
+ static inline T infinity() {
+ return numext::numeric_limits<T>::infinity();
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
+ static inline T quiet_NaN() {
+ return numext::numeric_limits<T>::quiet_NaN();
+ }
+};
+
+template<typename T> struct NumTraits : GenericNumTraits<T>
+{};
+
+template<> struct NumTraits<float>
+ : GenericNumTraits<float>
+{
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
+ static inline float dummy_precision() { return 1e-5f; }
+};
+
+template<> struct NumTraits<double> : GenericNumTraits<double>
+{
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
+ static inline double dummy_precision() { return 1e-12; }
+};
+
+template<> struct NumTraits<long double>
+ : GenericNumTraits<long double>
+{
+ EIGEN_CONSTEXPR
+ static inline long double dummy_precision() { return 1e-15l; }
+};
+
+template<typename Real_> struct NumTraits<std::complex<Real_> >
+ : GenericNumTraits<std::complex<Real_> >
+{
+ typedef Real_ Real;
+ typedef typename NumTraits<Real_>::Literal Literal;
+ enum {
+ IsComplex = 1,
+ RequireInitialization = NumTraits<Real_>::RequireInitialization,
+ ReadCost = 2 * NumTraits<Real_>::ReadCost,
+ AddCost = 2 * NumTraits<Real>::AddCost,
+ MulCost = 4 * NumTraits<Real>::MulCost + 2 * NumTraits<Real>::AddCost
+ };
+
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
+ static inline Real epsilon() { return NumTraits<Real>::epsilon(); }
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
+ static inline Real dummy_precision() { return NumTraits<Real>::dummy_precision(); }
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
+ static inline int digits10() { return NumTraits<Real>::digits10(); }
+};
+
+template<typename Scalar, int Rows, int Cols, int Options, int MaxRows, int MaxCols>
+struct NumTraits<Array<Scalar, Rows, Cols, Options, MaxRows, MaxCols> >
+{
+ typedef Array<Scalar, Rows, Cols, Options, MaxRows, MaxCols> ArrayType;
+ typedef typename NumTraits<Scalar>::Real RealScalar;
+ typedef Array<RealScalar, Rows, Cols, Options, MaxRows, MaxCols> Real;
+ typedef typename NumTraits<Scalar>::NonInteger NonIntegerScalar;
+ typedef Array<NonIntegerScalar, Rows, Cols, Options, MaxRows, MaxCols> NonInteger;
+ typedef ArrayType & Nested;
+ typedef typename NumTraits<Scalar>::Literal Literal;
+
+ enum {
+ IsComplex = NumTraits<Scalar>::IsComplex,
+ IsInteger = NumTraits<Scalar>::IsInteger,
+ IsSigned = NumTraits<Scalar>::IsSigned,
+ RequireInitialization = 1,
+ ReadCost = ArrayType::SizeAtCompileTime==Dynamic ? HugeCost : ArrayType::SizeAtCompileTime * int(NumTraits<Scalar>::ReadCost),
+ AddCost = ArrayType::SizeAtCompileTime==Dynamic ? HugeCost : ArrayType::SizeAtCompileTime * int(NumTraits<Scalar>::AddCost),
+ MulCost = ArrayType::SizeAtCompileTime==Dynamic ? HugeCost : ArrayType::SizeAtCompileTime * int(NumTraits<Scalar>::MulCost)
+ };
+
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
+ static inline RealScalar epsilon() { return NumTraits<RealScalar>::epsilon(); }
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
+ static inline RealScalar dummy_precision() { return NumTraits<RealScalar>::dummy_precision(); }
+
+ EIGEN_CONSTEXPR
+ static inline int digits10() { return NumTraits<Scalar>::digits10(); }
+};
+
+template<> struct NumTraits<std::string>
+ : GenericNumTraits<std::string>
+{
+ enum {
+ RequireInitialization = 1,
+ ReadCost = HugeCost,
+ AddCost = HugeCost,
+ MulCost = HugeCost
+ };
+
+ EIGEN_CONSTEXPR
+ static inline int digits10() { return 0; }
+
+private:
+ static inline std::string epsilon();
+ static inline std::string dummy_precision();
+ static inline std::string lowest();
+ static inline std::string highest();
+ static inline std::string infinity();
+ static inline std::string quiet_NaN();
+};
+
+// Empty specialization for void to allow template specialization based on NumTraits<T>::Real with T==void and SFINAE.
+template<> struct NumTraits<void> {};
+
+template<> struct NumTraits<bool> : GenericNumTraits<bool> {};
+
+} // end namespace Eigen
+
+#endif // EIGEN_NUMTRAITS_H
diff --git a/Eigen/src/Core/PartialReduxEvaluator.h b/Eigen/src/Core/PartialReduxEvaluator.h
new file mode 100644
index 0000000..693fc35
--- /dev/null
+++ b/Eigen/src/Core/PartialReduxEvaluator.h
@@ -0,0 +1,239 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2011-2018 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_PARTIALREDUX_H
+#define EIGEN_PARTIALREDUX_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+
+
+/***************************************************************************
+*
+* This file provides evaluators for partial reductions.
+* There are two modes:
+*
+* - scalar path: simply calls the respective function on the column or row.
+* -> nothing special here, all the tricky part is handled by the return
+* types of VectorwiseOp's members. They embed the functor calling the
+* respective DenseBase's member function.
+*
+* - vectorized path: implements a packet-wise reductions followed by
+* some (optional) processing of the outcome, e.g., division by n for mean.
+*
+* For the vectorized path let's observe that the packet-size and outer-unrolling
+* are both decided by the assignment logic. So all we have to do is to decide
+* on the inner unrolling.
+*
+* For the unrolling, we can reuse "internal::redux_vec_unroller" from Redux.h,
+* but be need to be careful to specify correct increment.
+*
+***************************************************************************/
+
+
+/* logic deciding a strategy for unrolling of vectorized paths */
+template<typename Func, typename Evaluator>
+struct packetwise_redux_traits
+{
+ enum {
+ OuterSize = int(Evaluator::IsRowMajor) ? Evaluator::RowsAtCompileTime : Evaluator::ColsAtCompileTime,
+ Cost = OuterSize == Dynamic ? HugeCost
+ : OuterSize * Evaluator::CoeffReadCost + (OuterSize-1) * functor_traits<Func>::Cost,
+ Unrolling = Cost <= EIGEN_UNROLLING_LIMIT ? CompleteUnrolling : NoUnrolling
+ };
+
+};
+
+/* Value to be returned when size==0 , by default let's return 0 */
+template<typename PacketType,typename Func>
+EIGEN_DEVICE_FUNC
+PacketType packetwise_redux_empty_value(const Func& ) {
+ const typename unpacket_traits<PacketType>::type zero(0);
+ return pset1<PacketType>(zero);
+}
+
+/* For products the default is 1 */
+template<typename PacketType,typename Scalar>
+EIGEN_DEVICE_FUNC
+PacketType packetwise_redux_empty_value(const scalar_product_op<Scalar,Scalar>& ) {
+ return pset1<PacketType>(Scalar(1));
+}
+
+/* Perform the actual reduction */
+template<typename Func, typename Evaluator,
+ int Unrolling = packetwise_redux_traits<Func, Evaluator>::Unrolling
+>
+struct packetwise_redux_impl;
+
+/* Perform the actual reduction with unrolling */
+template<typename Func, typename Evaluator>
+struct packetwise_redux_impl<Func, Evaluator, CompleteUnrolling>
+{
+ typedef redux_novec_unroller<Func,Evaluator, 0, Evaluator::SizeAtCompileTime> Base;
+ typedef typename Evaluator::Scalar Scalar;
+
+ template<typename PacketType>
+ EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE
+ PacketType run(const Evaluator &eval, const Func& func, Index /*size*/)
+ {
+ return redux_vec_unroller<Func, Evaluator, 0, packetwise_redux_traits<Func, Evaluator>::OuterSize>::template run<PacketType>(eval,func);
+ }
+};
+
+/* Add a specialization of redux_vec_unroller for size==0 at compiletime.
+ * This specialization is not required for general reductions, which is
+ * why it is defined here.
+ */
+template<typename Func, typename Evaluator, int Start>
+struct redux_vec_unroller<Func, Evaluator, Start, 0>
+{
+ template<typename PacketType>
+ EIGEN_DEVICE_FUNC
+ static EIGEN_STRONG_INLINE PacketType run(const Evaluator &, const Func& f)
+ {
+ return packetwise_redux_empty_value<PacketType>(f);
+ }
+};
+
+/* Perform the actual reduction for dynamic sizes */
+template<typename Func, typename Evaluator>
+struct packetwise_redux_impl<Func, Evaluator, NoUnrolling>
+{
+ typedef typename Evaluator::Scalar Scalar;
+ typedef typename redux_traits<Func, Evaluator>::PacketType PacketScalar;
+
+ template<typename PacketType>
+ EIGEN_DEVICE_FUNC
+ static PacketType run(const Evaluator &eval, const Func& func, Index size)
+ {
+ if(size==0)
+ return packetwise_redux_empty_value<PacketType>(func);
+
+ const Index size4 = (size-1)&(~3);
+ PacketType p = eval.template packetByOuterInner<Unaligned,PacketType>(0,0);
+ Index i = 1;
+ // This loop is optimized for instruction pipelining:
+ // - each iteration generates two independent instructions
+ // - thanks to branch prediction and out-of-order execution we have independent instructions across loops
+ for(; i<size4; i+=4)
+ p = func.packetOp(p,
+ func.packetOp(
+ func.packetOp(eval.template packetByOuterInner<Unaligned,PacketType>(i+0,0),eval.template packetByOuterInner<Unaligned,PacketType>(i+1,0)),
+ func.packetOp(eval.template packetByOuterInner<Unaligned,PacketType>(i+2,0),eval.template packetByOuterInner<Unaligned,PacketType>(i+3,0))));
+ for(; i<size; ++i)
+ p = func.packetOp(p, eval.template packetByOuterInner<Unaligned,PacketType>(i,0));
+ return p;
+ }
+};
+
+template< typename ArgType, typename MemberOp, int Direction>
+struct evaluator<PartialReduxExpr<ArgType, MemberOp, Direction> >
+ : evaluator_base<PartialReduxExpr<ArgType, MemberOp, Direction> >
+{
+ typedef PartialReduxExpr<ArgType, MemberOp, Direction> XprType;
+ typedef typename internal::nested_eval<ArgType,1>::type ArgTypeNested;
+ typedef add_const_on_value_type_t<ArgTypeNested> ConstArgTypeNested;
+ typedef internal::remove_all_t<ArgTypeNested> ArgTypeNestedCleaned;
+ typedef typename ArgType::Scalar InputScalar;
+ typedef typename XprType::Scalar Scalar;
+ enum {
+ TraversalSize = Direction==int(Vertical) ? int(ArgType::RowsAtCompileTime) : int(ArgType::ColsAtCompileTime)
+ };
+ typedef typename MemberOp::template Cost<int(TraversalSize)> CostOpType;
+ enum {
+ CoeffReadCost = TraversalSize==Dynamic ? HugeCost
+ : TraversalSize==0 ? 1
+ : int(TraversalSize) * int(evaluator<ArgType>::CoeffReadCost) + int(CostOpType::value),
+
+ ArgFlags_ = evaluator<ArgType>::Flags,
+
+ Vectorizable_ = bool(int(ArgFlags_)&PacketAccessBit)
+ && bool(MemberOp::Vectorizable)
+ && (Direction==int(Vertical) ? bool(ArgFlags_&RowMajorBit) : (ArgFlags_&RowMajorBit)==0)
+ && (TraversalSize!=0),
+
+ Flags = (traits<XprType>::Flags&RowMajorBit)
+ | (evaluator<ArgType>::Flags&(HereditaryBits&(~RowMajorBit)))
+ | (Vectorizable_ ? PacketAccessBit : 0)
+ | LinearAccessBit,
+
+ Alignment = 0 // FIXME this will need to be improved once PartialReduxExpr is vectorized
+ };
+
+ EIGEN_DEVICE_FUNC explicit evaluator(const XprType xpr)
+ : m_arg(xpr.nestedExpression()), m_functor(xpr.functor())
+ {
+ EIGEN_INTERNAL_CHECK_COST_VALUE(TraversalSize==Dynamic ? HugeCost : (TraversalSize==0 ? 1 : int(CostOpType::value)));
+ EIGEN_INTERNAL_CHECK_COST_VALUE(CoeffReadCost);
+ }
+
+ typedef typename XprType::CoeffReturnType CoeffReturnType;
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ const Scalar coeff(Index i, Index j) const
+ {
+ return coeff(Direction==Vertical ? j : i);
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ const Scalar coeff(Index index) const
+ {
+ return m_functor(m_arg.template subVector<DirectionType(Direction)>(index));
+ }
+
+ template<int LoadMode,typename PacketType>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ PacketType packet(Index i, Index j) const
+ {
+ return packet<LoadMode,PacketType>(Direction==Vertical ? j : i);
+ }
+
+ template<int LoadMode,typename PacketType>
+ EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC
+ PacketType packet(Index idx) const
+ {
+ enum { PacketSize = internal::unpacket_traits<PacketType>::size };
+ typedef Block<const ArgTypeNestedCleaned,
+ Direction==Vertical ? int(ArgType::RowsAtCompileTime) : int(PacketSize),
+ Direction==Vertical ? int(PacketSize) : int(ArgType::ColsAtCompileTime),
+ true /* InnerPanel */> PanelType;
+
+ PanelType panel(m_arg,
+ Direction==Vertical ? 0 : idx,
+ Direction==Vertical ? idx : 0,
+ Direction==Vertical ? m_arg.rows() : Index(PacketSize),
+ Direction==Vertical ? Index(PacketSize) : m_arg.cols());
+
+ // FIXME
+ // See bug 1612, currently if PacketSize==1 (i.e. complex<double> with 128bits registers) then the storage-order of panel get reversed
+ // and methods like packetByOuterInner do not make sense anymore in this context.
+ // So let's just by pass "vectorization" in this case:
+ if(PacketSize==1)
+ return internal::pset1<PacketType>(coeff(idx));
+
+ typedef typename internal::redux_evaluator<PanelType> PanelEvaluator;
+ PanelEvaluator panel_eval(panel);
+ typedef typename MemberOp::BinaryOp BinaryOp;
+ PacketType p = internal::packetwise_redux_impl<BinaryOp,PanelEvaluator>::template run<PacketType>(panel_eval,m_functor.binaryFunc(),m_arg.outerSize());
+ return p;
+ }
+
+protected:
+ ConstArgTypeNested m_arg;
+ const MemberOp m_functor;
+};
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_PARTIALREDUX_H
diff --git a/Eigen/src/Core/PermutationMatrix.h b/Eigen/src/Core/PermutationMatrix.h
new file mode 100644
index 0000000..73a7300
--- /dev/null
+++ b/Eigen/src/Core/PermutationMatrix.h
@@ -0,0 +1,607 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009 Benoit Jacob <jacob.benoit.1@gmail.com>
+// Copyright (C) 2009-2015 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_PERMUTATIONMATRIX_H
+#define EIGEN_PERMUTATIONMATRIX_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+
+enum PermPermProduct_t {PermPermProduct};
+
+} // end namespace internal
+
+/** \class PermutationBase
+ * \ingroup Core_Module
+ *
+ * \brief Base class for permutations
+ *
+ * \tparam Derived the derived class
+ *
+ * This class is the base class for all expressions representing a permutation matrix,
+ * internally stored as a vector of integers.
+ * The convention followed here is that if \f$ \sigma \f$ is a permutation, the corresponding permutation matrix
+ * \f$ P_\sigma \f$ is such that if \f$ (e_1,\ldots,e_p) \f$ is the canonical basis, we have:
+ * \f[ P_\sigma(e_i) = e_{\sigma(i)}. \f]
+ * This convention ensures that for any two permutations \f$ \sigma, \tau \f$, we have:
+ * \f[ P_{\sigma\circ\tau} = P_\sigma P_\tau. \f]
+ *
+ * Permutation matrices are square and invertible.
+ *
+ * Notice that in addition to the member functions and operators listed here, there also are non-member
+ * operator* to multiply any kind of permutation object with any kind of matrix expression (MatrixBase)
+ * on either side.
+ *
+ * \sa class PermutationMatrix, class PermutationWrapper
+ */
+template<typename Derived>
+class PermutationBase : public EigenBase<Derived>
+{
+ typedef internal::traits<Derived> Traits;
+ typedef EigenBase<Derived> Base;
+ public:
+
+ #ifndef EIGEN_PARSED_BY_DOXYGEN
+ typedef typename Traits::IndicesType IndicesType;
+ enum {
+ Flags = Traits::Flags,
+ RowsAtCompileTime = Traits::RowsAtCompileTime,
+ ColsAtCompileTime = Traits::ColsAtCompileTime,
+ MaxRowsAtCompileTime = Traits::MaxRowsAtCompileTime,
+ MaxColsAtCompileTime = Traits::MaxColsAtCompileTime
+ };
+ typedef typename Traits::StorageIndex StorageIndex;
+ typedef Matrix<StorageIndex,RowsAtCompileTime,ColsAtCompileTime,0,MaxRowsAtCompileTime,MaxColsAtCompileTime>
+ DenseMatrixType;
+ typedef PermutationMatrix<IndicesType::SizeAtCompileTime,IndicesType::MaxSizeAtCompileTime,StorageIndex>
+ PlainPermutationType;
+ typedef PlainPermutationType PlainObject;
+ using Base::derived;
+ typedef Inverse<Derived> InverseReturnType;
+ typedef void Scalar;
+ #endif
+
+ /** Copies the other permutation into *this */
+ template<typename OtherDerived>
+ Derived& operator=(const PermutationBase<OtherDerived>& other)
+ {
+ indices() = other.indices();
+ return derived();
+ }
+
+ /** Assignment from the Transpositions \a tr */
+ template<typename OtherDerived>
+ Derived& operator=(const TranspositionsBase<OtherDerived>& tr)
+ {
+ setIdentity(tr.size());
+ for(Index k=size()-1; k>=0; --k)
+ applyTranspositionOnTheRight(k,tr.coeff(k));
+ return derived();
+ }
+
+ /** \returns the number of rows */
+ inline EIGEN_DEVICE_FUNC Index rows() const { return Index(indices().size()); }
+
+ /** \returns the number of columns */
+ inline EIGEN_DEVICE_FUNC Index cols() const { return Index(indices().size()); }
+
+ /** \returns the size of a side of the respective square matrix, i.e., the number of indices */
+ inline EIGEN_DEVICE_FUNC Index size() const { return Index(indices().size()); }
+
+ #ifndef EIGEN_PARSED_BY_DOXYGEN
+ template<typename DenseDerived>
+ void evalTo(MatrixBase<DenseDerived>& other) const
+ {
+ other.setZero();
+ for (Index i=0; i<rows(); ++i)
+ other.coeffRef(indices().coeff(i),i) = typename DenseDerived::Scalar(1);
+ }
+ #endif
+
+ /** \returns a Matrix object initialized from this permutation matrix. Notice that it
+ * is inefficient to return this Matrix object by value. For efficiency, favor using
+ * the Matrix constructor taking EigenBase objects.
+ */
+ DenseMatrixType toDenseMatrix() const
+ {
+ return derived();
+ }
+
+ /** const version of indices(). */
+ const IndicesType& indices() const { return derived().indices(); }
+ /** \returns a reference to the stored array representing the permutation. */
+ IndicesType& indices() { return derived().indices(); }
+
+ /** Resizes to given size.
+ */
+ inline void resize(Index newSize)
+ {
+ indices().resize(newSize);
+ }
+
+ /** Sets *this to be the identity permutation matrix */
+ void setIdentity()
+ {
+ StorageIndex n = StorageIndex(size());
+ for(StorageIndex i = 0; i < n; ++i)
+ indices().coeffRef(i) = i;
+ }
+
+ /** Sets *this to be the identity permutation matrix of given size.
+ */
+ void setIdentity(Index newSize)
+ {
+ resize(newSize);
+ setIdentity();
+ }
+
+ /** Multiplies *this by the transposition \f$(ij)\f$ on the left.
+ *
+ * \returns a reference to *this.
+ *
+ * \warning This is much slower than applyTranspositionOnTheRight(Index,Index):
+ * this has linear complexity and requires a lot of branching.
+ *
+ * \sa applyTranspositionOnTheRight(Index,Index)
+ */
+ Derived& applyTranspositionOnTheLeft(Index i, Index j)
+ {
+ eigen_assert(i>=0 && j>=0 && i<size() && j<size());
+ for(Index k = 0; k < size(); ++k)
+ {
+ if(indices().coeff(k) == i) indices().coeffRef(k) = StorageIndex(j);
+ else if(indices().coeff(k) == j) indices().coeffRef(k) = StorageIndex(i);
+ }
+ return derived();
+ }
+
+ /** Multiplies *this by the transposition \f$(ij)\f$ on the right.
+ *
+ * \returns a reference to *this.
+ *
+ * This is a fast operation, it only consists in swapping two indices.
+ *
+ * \sa applyTranspositionOnTheLeft(Index,Index)
+ */
+ Derived& applyTranspositionOnTheRight(Index i, Index j)
+ {
+ eigen_assert(i>=0 && j>=0 && i<size() && j<size());
+ std::swap(indices().coeffRef(i), indices().coeffRef(j));
+ return derived();
+ }
+
+ /** \returns the inverse permutation matrix.
+ *
+ * \note \blank \note_try_to_help_rvo
+ */
+ inline InverseReturnType inverse() const
+ { return InverseReturnType(derived()); }
+ /** \returns the tranpose permutation matrix.
+ *
+ * \note \blank \note_try_to_help_rvo
+ */
+ inline InverseReturnType transpose() const
+ { return InverseReturnType(derived()); }
+
+ /**** multiplication helpers to hopefully get RVO ****/
+
+
+#ifndef EIGEN_PARSED_BY_DOXYGEN
+ protected:
+ template<typename OtherDerived>
+ void assignTranspose(const PermutationBase<OtherDerived>& other)
+ {
+ for (Index i=0; i<rows();++i) indices().coeffRef(other.indices().coeff(i)) = i;
+ }
+ template<typename Lhs,typename Rhs>
+ void assignProduct(const Lhs& lhs, const Rhs& rhs)
+ {
+ eigen_assert(lhs.cols() == rhs.rows());
+ for (Index i=0; i<rows();++i) indices().coeffRef(i) = lhs.indices().coeff(rhs.indices().coeff(i));
+ }
+#endif
+
+ public:
+
+ /** \returns the product permutation matrix.
+ *
+ * \note \blank \note_try_to_help_rvo
+ */
+ template<typename Other>
+ inline PlainPermutationType operator*(const PermutationBase<Other>& other) const
+ { return PlainPermutationType(internal::PermPermProduct, derived(), other.derived()); }
+
+ /** \returns the product of a permutation with another inverse permutation.
+ *
+ * \note \blank \note_try_to_help_rvo
+ */
+ template<typename Other>
+ inline PlainPermutationType operator*(const InverseImpl<Other,PermutationStorage>& other) const
+ { return PlainPermutationType(internal::PermPermProduct, *this, other.eval()); }
+
+ /** \returns the product of an inverse permutation with another permutation.
+ *
+ * \note \blank \note_try_to_help_rvo
+ */
+ template<typename Other> friend
+ inline PlainPermutationType operator*(const InverseImpl<Other, PermutationStorage>& other, const PermutationBase& perm)
+ { return PlainPermutationType(internal::PermPermProduct, other.eval(), perm); }
+
+ /** \returns the determinant of the permutation matrix, which is either 1 or -1 depending on the parity of the permutation.
+ *
+ * This function is O(\c n) procedure allocating a buffer of \c n booleans.
+ */
+ Index determinant() const
+ {
+ Index res = 1;
+ Index n = size();
+ Matrix<bool,RowsAtCompileTime,1,0,MaxRowsAtCompileTime> mask(n);
+ mask.fill(false);
+ Index r = 0;
+ while(r < n)
+ {
+ // search for the next seed
+ while(r<n && mask[r]) r++;
+ if(r>=n)
+ break;
+ // we got one, let's follow it until we are back to the seed
+ Index k0 = r++;
+ mask.coeffRef(k0) = true;
+ for(Index k=indices().coeff(k0); k!=k0; k=indices().coeff(k))
+ {
+ mask.coeffRef(k) = true;
+ res = -res;
+ }
+ }
+ return res;
+ }
+
+ protected:
+
+};
+
+namespace internal {
+template<int SizeAtCompileTime, int MaxSizeAtCompileTime, typename StorageIndex_>
+struct traits<PermutationMatrix<SizeAtCompileTime, MaxSizeAtCompileTime, StorageIndex_> >
+ : traits<Matrix<StorageIndex_,SizeAtCompileTime,SizeAtCompileTime,0,MaxSizeAtCompileTime,MaxSizeAtCompileTime> >
+{
+ typedef PermutationStorage StorageKind;
+ typedef Matrix<StorageIndex_, SizeAtCompileTime, 1, 0, MaxSizeAtCompileTime, 1> IndicesType;
+ typedef StorageIndex_ StorageIndex;
+ typedef void Scalar;
+};
+}
+
+/** \class PermutationMatrix
+ * \ingroup Core_Module
+ *
+ * \brief Permutation matrix
+ *
+ * \tparam SizeAtCompileTime the number of rows/cols, or Dynamic
+ * \tparam MaxSizeAtCompileTime the maximum number of rows/cols, or Dynamic. This optional parameter defaults to SizeAtCompileTime. Most of the time, you should not have to specify it.
+ * \tparam StorageIndex_ the integer type of the indices
+ *
+ * This class represents a permutation matrix, internally stored as a vector of integers.
+ *
+ * \sa class PermutationBase, class PermutationWrapper, class DiagonalMatrix
+ */
+template<int SizeAtCompileTime, int MaxSizeAtCompileTime, typename StorageIndex_>
+class PermutationMatrix : public PermutationBase<PermutationMatrix<SizeAtCompileTime, MaxSizeAtCompileTime, StorageIndex_> >
+{
+ typedef PermutationBase<PermutationMatrix> Base;
+ typedef internal::traits<PermutationMatrix> Traits;
+ public:
+
+ typedef const PermutationMatrix& Nested;
+
+ #ifndef EIGEN_PARSED_BY_DOXYGEN
+ typedef typename Traits::IndicesType IndicesType;
+ typedef typename Traits::StorageIndex StorageIndex;
+ #endif
+
+ inline PermutationMatrix()
+ {}
+
+ /** Constructs an uninitialized permutation matrix of given size.
+ */
+ explicit inline PermutationMatrix(Index size) : m_indices(size)
+ {
+ eigen_internal_assert(size <= NumTraits<StorageIndex>::highest());
+ }
+
+ /** Copy constructor. */
+ template<typename OtherDerived>
+ inline PermutationMatrix(const PermutationBase<OtherDerived>& other)
+ : m_indices(other.indices()) {}
+
+ /** Generic constructor from expression of the indices. The indices
+ * array has the meaning that the permutations sends each integer i to indices[i].
+ *
+ * \warning It is your responsibility to check that the indices array that you passes actually
+ * describes a permutation, i.e., each value between 0 and n-1 occurs exactly once, where n is the
+ * array's size.
+ */
+ template<typename Other>
+ explicit inline PermutationMatrix(const MatrixBase<Other>& indices) : m_indices(indices)
+ {}
+
+ /** Convert the Transpositions \a tr to a permutation matrix */
+ template<typename Other>
+ explicit PermutationMatrix(const TranspositionsBase<Other>& tr)
+ : m_indices(tr.size())
+ {
+ *this = tr;
+ }
+
+ /** Copies the other permutation into *this */
+ template<typename Other>
+ PermutationMatrix& operator=(const PermutationBase<Other>& other)
+ {
+ m_indices = other.indices();
+ return *this;
+ }
+
+ /** Assignment from the Transpositions \a tr */
+ template<typename Other>
+ PermutationMatrix& operator=(const TranspositionsBase<Other>& tr)
+ {
+ return Base::operator=(tr.derived());
+ }
+
+ /** const version of indices(). */
+ const IndicesType& indices() const { return m_indices; }
+ /** \returns a reference to the stored array representing the permutation. */
+ IndicesType& indices() { return m_indices; }
+
+
+ /**** multiplication helpers to hopefully get RVO ****/
+
+#ifndef EIGEN_PARSED_BY_DOXYGEN
+ template<typename Other>
+ PermutationMatrix(const InverseImpl<Other,PermutationStorage>& other)
+ : m_indices(other.derived().nestedExpression().size())
+ {
+ eigen_internal_assert(m_indices.size() <= NumTraits<StorageIndex>::highest());
+ StorageIndex end = StorageIndex(m_indices.size());
+ for (StorageIndex i=0; i<end;++i)
+ m_indices.coeffRef(other.derived().nestedExpression().indices().coeff(i)) = i;
+ }
+ template<typename Lhs,typename Rhs>
+ PermutationMatrix(internal::PermPermProduct_t, const Lhs& lhs, const Rhs& rhs)
+ : m_indices(lhs.indices().size())
+ {
+ Base::assignProduct(lhs,rhs);
+ }
+#endif
+
+ protected:
+
+ IndicesType m_indices;
+};
+
+
+namespace internal {
+template<int SizeAtCompileTime, int MaxSizeAtCompileTime, typename StorageIndex_, int PacketAccess_>
+struct traits<Map<PermutationMatrix<SizeAtCompileTime, MaxSizeAtCompileTime, StorageIndex_>,PacketAccess_> >
+ : traits<Matrix<StorageIndex_,SizeAtCompileTime,SizeAtCompileTime,0,MaxSizeAtCompileTime,MaxSizeAtCompileTime> >
+{
+ typedef PermutationStorage StorageKind;
+ typedef Map<const Matrix<StorageIndex_, SizeAtCompileTime, 1, 0, MaxSizeAtCompileTime, 1>, PacketAccess_> IndicesType;
+ typedef StorageIndex_ StorageIndex;
+ typedef void Scalar;
+};
+}
+
+template<int SizeAtCompileTime, int MaxSizeAtCompileTime, typename StorageIndex_, int PacketAccess_>
+class Map<PermutationMatrix<SizeAtCompileTime, MaxSizeAtCompileTime, StorageIndex_>,PacketAccess_>
+ : public PermutationBase<Map<PermutationMatrix<SizeAtCompileTime, MaxSizeAtCompileTime, StorageIndex_>,PacketAccess_> >
+{
+ typedef PermutationBase<Map> Base;
+ typedef internal::traits<Map> Traits;
+ public:
+
+ #ifndef EIGEN_PARSED_BY_DOXYGEN
+ typedef typename Traits::IndicesType IndicesType;
+ typedef typename IndicesType::Scalar StorageIndex;
+ #endif
+
+ inline Map(const StorageIndex* indicesPtr)
+ : m_indices(indicesPtr)
+ {}
+
+ inline Map(const StorageIndex* indicesPtr, Index size)
+ : m_indices(indicesPtr,size)
+ {}
+
+ /** Copies the other permutation into *this */
+ template<typename Other>
+ Map& operator=(const PermutationBase<Other>& other)
+ { return Base::operator=(other.derived()); }
+
+ /** Assignment from the Transpositions \a tr */
+ template<typename Other>
+ Map& operator=(const TranspositionsBase<Other>& tr)
+ { return Base::operator=(tr.derived()); }
+
+ #ifndef EIGEN_PARSED_BY_DOXYGEN
+ /** This is a special case of the templated operator=. Its purpose is to
+ * prevent a default operator= from hiding the templated operator=.
+ */
+ Map& operator=(const Map& other)
+ {
+ m_indices = other.m_indices;
+ return *this;
+ }
+ #endif
+
+ /** const version of indices(). */
+ const IndicesType& indices() const { return m_indices; }
+ /** \returns a reference to the stored array representing the permutation. */
+ IndicesType& indices() { return m_indices; }
+
+ protected:
+
+ IndicesType m_indices;
+};
+
+template<typename IndicesType_> class TranspositionsWrapper;
+namespace internal {
+template<typename IndicesType_>
+struct traits<PermutationWrapper<IndicesType_> >
+{
+ typedef PermutationStorage StorageKind;
+ typedef void Scalar;
+ typedef typename IndicesType_::Scalar StorageIndex;
+ typedef IndicesType_ IndicesType;
+ enum {
+ RowsAtCompileTime = IndicesType_::SizeAtCompileTime,
+ ColsAtCompileTime = IndicesType_::SizeAtCompileTime,
+ MaxRowsAtCompileTime = IndicesType::MaxSizeAtCompileTime,
+ MaxColsAtCompileTime = IndicesType::MaxSizeAtCompileTime,
+ Flags = 0
+ };
+};
+}
+
+/** \class PermutationWrapper
+ * \ingroup Core_Module
+ *
+ * \brief Class to view a vector of integers as a permutation matrix
+ *
+ * \tparam IndicesType_ the type of the vector of integer (can be any compatible expression)
+ *
+ * This class allows to view any vector expression of integers as a permutation matrix.
+ *
+ * \sa class PermutationBase, class PermutationMatrix
+ */
+template<typename IndicesType_>
+class PermutationWrapper : public PermutationBase<PermutationWrapper<IndicesType_> >
+{
+ typedef PermutationBase<PermutationWrapper> Base;
+ typedef internal::traits<PermutationWrapper> Traits;
+ public:
+
+ #ifndef EIGEN_PARSED_BY_DOXYGEN
+ typedef typename Traits::IndicesType IndicesType;
+ #endif
+
+ inline PermutationWrapper(const IndicesType& indices)
+ : m_indices(indices)
+ {}
+
+ /** const version of indices(). */
+ const internal::remove_all_t<typename IndicesType::Nested>&
+ indices() const { return m_indices; }
+
+ protected:
+
+ typename IndicesType::Nested m_indices;
+};
+
+
+/** \returns the matrix with the permutation applied to the columns.
+ */
+template<typename MatrixDerived, typename PermutationDerived>
+EIGEN_DEVICE_FUNC
+const Product<MatrixDerived, PermutationDerived, AliasFreeProduct>
+operator*(const MatrixBase<MatrixDerived> &matrix,
+ const PermutationBase<PermutationDerived>& permutation)
+{
+ return Product<MatrixDerived, PermutationDerived, AliasFreeProduct>
+ (matrix.derived(), permutation.derived());
+}
+
+/** \returns the matrix with the permutation applied to the rows.
+ */
+template<typename PermutationDerived, typename MatrixDerived>
+EIGEN_DEVICE_FUNC
+const Product<PermutationDerived, MatrixDerived, AliasFreeProduct>
+operator*(const PermutationBase<PermutationDerived> &permutation,
+ const MatrixBase<MatrixDerived>& matrix)
+{
+ return Product<PermutationDerived, MatrixDerived, AliasFreeProduct>
+ (permutation.derived(), matrix.derived());
+}
+
+
+template<typename PermutationType>
+class InverseImpl<PermutationType, PermutationStorage>
+ : public EigenBase<Inverse<PermutationType> >
+{
+ typedef typename PermutationType::PlainPermutationType PlainPermutationType;
+ typedef internal::traits<PermutationType> PermTraits;
+ protected:
+ InverseImpl() {}
+ public:
+ typedef Inverse<PermutationType> InverseType;
+ using EigenBase<Inverse<PermutationType> >::derived;
+
+ #ifndef EIGEN_PARSED_BY_DOXYGEN
+ typedef typename PermutationType::DenseMatrixType DenseMatrixType;
+ enum {
+ RowsAtCompileTime = PermTraits::RowsAtCompileTime,
+ ColsAtCompileTime = PermTraits::ColsAtCompileTime,
+ MaxRowsAtCompileTime = PermTraits::MaxRowsAtCompileTime,
+ MaxColsAtCompileTime = PermTraits::MaxColsAtCompileTime
+ };
+ #endif
+
+ #ifndef EIGEN_PARSED_BY_DOXYGEN
+ template<typename DenseDerived>
+ void evalTo(MatrixBase<DenseDerived>& other) const
+ {
+ other.setZero();
+ for (Index i=0; i<derived().rows();++i)
+ other.coeffRef(i, derived().nestedExpression().indices().coeff(i)) = typename DenseDerived::Scalar(1);
+ }
+ #endif
+
+ /** \return the equivalent permutation matrix */
+ PlainPermutationType eval() const { return derived(); }
+
+ DenseMatrixType toDenseMatrix() const { return derived(); }
+
+ /** \returns the matrix with the inverse permutation applied to the columns.
+ */
+ template<typename OtherDerived> friend
+ const Product<OtherDerived, InverseType, AliasFreeProduct>
+ operator*(const MatrixBase<OtherDerived>& matrix, const InverseType& trPerm)
+ {
+ return Product<OtherDerived, InverseType, AliasFreeProduct>(matrix.derived(), trPerm.derived());
+ }
+
+ /** \returns the matrix with the inverse permutation applied to the rows.
+ */
+ template<typename OtherDerived>
+ const Product<InverseType, OtherDerived, AliasFreeProduct>
+ operator*(const MatrixBase<OtherDerived>& matrix) const
+ {
+ return Product<InverseType, OtherDerived, AliasFreeProduct>(derived(), matrix.derived());
+ }
+};
+
+template<typename Derived>
+const PermutationWrapper<const Derived> MatrixBase<Derived>::asPermutation() const
+{
+ return derived();
+}
+
+namespace internal {
+
+template<> struct AssignmentKind<DenseShape,PermutationShape> { typedef EigenBase2EigenBase Kind; };
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_PERMUTATIONMATRIX_H
diff --git a/Eigen/src/Core/PlainObjectBase.h b/Eigen/src/Core/PlainObjectBase.h
new file mode 100644
index 0000000..222eaf5
--- /dev/null
+++ b/Eigen/src/Core/PlainObjectBase.h
@@ -0,0 +1,1107 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_DENSESTORAGEBASE_H
+#define EIGEN_DENSESTORAGEBASE_H
+
+#if defined(EIGEN_INITIALIZE_MATRICES_BY_ZERO)
+# define EIGEN_INITIALIZE_COEFFS
+# define EIGEN_INITIALIZE_COEFFS_IF_THAT_OPTION_IS_ENABLED for(Index i=0;i<base().size();++i) coeffRef(i)=Scalar(0);
+#elif defined(EIGEN_INITIALIZE_MATRICES_BY_NAN)
+# define EIGEN_INITIALIZE_COEFFS
+# define EIGEN_INITIALIZE_COEFFS_IF_THAT_OPTION_IS_ENABLED for(Index i=0;i<base().size();++i) coeffRef(i)=std::numeric_limits<Scalar>::quiet_NaN();
+#else
+# undef EIGEN_INITIALIZE_COEFFS
+# define EIGEN_INITIALIZE_COEFFS_IF_THAT_OPTION_IS_ENABLED
+#endif
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+
+template<int MaxSizeAtCompileTime> struct check_rows_cols_for_overflow {
+ template<typename Index>
+ EIGEN_DEVICE_FUNC
+ static EIGEN_ALWAYS_INLINE void run(Index, Index)
+ {
+ }
+};
+
+template<> struct check_rows_cols_for_overflow<Dynamic> {
+ template<typename Index>
+ EIGEN_DEVICE_FUNC
+ static EIGEN_ALWAYS_INLINE void run(Index rows, Index cols)
+ {
+ // http://hg.mozilla.org/mozilla-central/file/6c8a909977d3/xpcom/ds/CheckedInt.h#l242
+ // we assume Index is signed
+ Index max_index = (std::size_t(1) << (8 * sizeof(Index) - 1)) - 1; // assume Index is signed
+ bool error = (rows == 0 || cols == 0) ? false
+ : (rows > max_index / cols);
+ if (error)
+ throw_std_bad_alloc();
+ }
+};
+
+template <typename Derived,
+ typename OtherDerived = Derived,
+ bool IsVector = bool(Derived::IsVectorAtCompileTime) && bool(OtherDerived::IsVectorAtCompileTime)>
+struct conservative_resize_like_impl;
+
+template<typename MatrixTypeA, typename MatrixTypeB, bool SwapPointers> struct matrix_swap_impl;
+
+} // end namespace internal
+
+#ifdef EIGEN_PARSED_BY_DOXYGEN
+namespace doxygen {
+
+// This is a workaround to doxygen not being able to understand the inheritance logic
+// when it is hidden by the dense_xpr_base helper struct.
+// Moreover, doxygen fails to include members that are not documented in the declaration body of
+// MatrixBase if we inherits MatrixBase<Matrix<Scalar_, Rows_, Cols_, Options_, MaxRows_, MaxCols_> >,
+// this is why we simply inherits MatrixBase, though this does not make sense.
+
+/** This class is just a workaround for Doxygen and it does not not actually exist. */
+template<typename Derived> struct dense_xpr_base_dispatcher;
+/** This class is just a workaround for Doxygen and it does not not actually exist. */
+template<typename Scalar_, int Rows_, int Cols_, int Options_, int MaxRows_, int MaxCols_>
+struct dense_xpr_base_dispatcher<Matrix<Scalar_, Rows_, Cols_, Options_, MaxRows_, MaxCols_> >
+ : public MatrixBase {};
+/** This class is just a workaround for Doxygen and it does not not actually exist. */
+template<typename Scalar_, int Rows_, int Cols_, int Options_, int MaxRows_, int MaxCols_>
+struct dense_xpr_base_dispatcher<Array<Scalar_, Rows_, Cols_, Options_, MaxRows_, MaxCols_> >
+ : public ArrayBase {};
+
+} // namespace doxygen
+
+/** \class PlainObjectBase
+ * \ingroup Core_Module
+ * \brief %Dense storage base class for matrices and arrays.
+ *
+ * This class can be extended with the help of the plugin mechanism described on the page
+ * \ref TopicCustomizing_Plugins by defining the preprocessor symbol \c EIGEN_PLAINOBJECTBASE_PLUGIN.
+ *
+ * \tparam Derived is the derived type, e.g., a Matrix or Array
+ *
+ * \sa \ref TopicClassHierarchy
+ */
+template<typename Derived>
+class PlainObjectBase : public doxygen::dense_xpr_base_dispatcher<Derived>
+#else
+template<typename Derived>
+class PlainObjectBase : public internal::dense_xpr_base<Derived>::type
+#endif
+{
+ public:
+ enum { Options = internal::traits<Derived>::Options };
+ typedef typename internal::dense_xpr_base<Derived>::type Base;
+
+ typedef typename internal::traits<Derived>::StorageKind StorageKind;
+ typedef typename internal::traits<Derived>::Scalar Scalar;
+
+ typedef typename internal::packet_traits<Scalar>::type PacketScalar;
+ typedef typename NumTraits<Scalar>::Real RealScalar;
+ typedef Derived DenseType;
+
+ using Base::RowsAtCompileTime;
+ using Base::ColsAtCompileTime;
+ using Base::SizeAtCompileTime;
+ using Base::MaxRowsAtCompileTime;
+ using Base::MaxColsAtCompileTime;
+ using Base::MaxSizeAtCompileTime;
+ using Base::IsVectorAtCompileTime;
+ using Base::Flags;
+
+ typedef Eigen::Map<Derived, Unaligned> MapType;
+ typedef const Eigen::Map<const Derived, Unaligned> ConstMapType;
+ typedef Eigen::Map<Derived, AlignedMax> AlignedMapType;
+ typedef const Eigen::Map<const Derived, AlignedMax> ConstAlignedMapType;
+ template<typename StrideType> struct StridedMapType { typedef Eigen::Map<Derived, Unaligned, StrideType> type; };
+ template<typename StrideType> struct StridedConstMapType { typedef Eigen::Map<const Derived, Unaligned, StrideType> type; };
+ template<typename StrideType> struct StridedAlignedMapType { typedef Eigen::Map<Derived, AlignedMax, StrideType> type; };
+ template<typename StrideType> struct StridedConstAlignedMapType { typedef Eigen::Map<const Derived, AlignedMax, StrideType> type; };
+
+ protected:
+ DenseStorage<Scalar, Base::MaxSizeAtCompileTime, Base::RowsAtCompileTime, Base::ColsAtCompileTime, Options> m_storage;
+
+ public:
+ enum { NeedsToAlign = (SizeAtCompileTime != Dynamic) && (internal::traits<Derived>::Alignment>0) };
+ EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF(NeedsToAlign)
+
+ EIGEN_STATIC_ASSERT(internal::check_implication(MaxRowsAtCompileTime==1 && MaxColsAtCompileTime!=1, (int(Options)&RowMajor)==RowMajor), INVALID_MATRIX_TEMPLATE_PARAMETERS)
+ EIGEN_STATIC_ASSERT(internal::check_implication(MaxColsAtCompileTime==1 && MaxRowsAtCompileTime!=1, (int(Options)&RowMajor)==0), INVALID_MATRIX_TEMPLATE_PARAMETERS)
+ EIGEN_STATIC_ASSERT((RowsAtCompileTime == Dynamic) || (RowsAtCompileTime >= 0), INVALID_MATRIX_TEMPLATE_PARAMETERS)
+ EIGEN_STATIC_ASSERT((ColsAtCompileTime == Dynamic) || (ColsAtCompileTime >= 0), INVALID_MATRIX_TEMPLATE_PARAMETERS)
+ EIGEN_STATIC_ASSERT((MaxRowsAtCompileTime == Dynamic) || (MaxRowsAtCompileTime >= 0), INVALID_MATRIX_TEMPLATE_PARAMETERS)
+ EIGEN_STATIC_ASSERT((MaxColsAtCompileTime == Dynamic) || (MaxColsAtCompileTime >= 0), INVALID_MATRIX_TEMPLATE_PARAMETERS)
+ EIGEN_STATIC_ASSERT((MaxRowsAtCompileTime == RowsAtCompileTime || RowsAtCompileTime==Dynamic), INVALID_MATRIX_TEMPLATE_PARAMETERS)
+ EIGEN_STATIC_ASSERT((MaxColsAtCompileTime == ColsAtCompileTime || ColsAtCompileTime==Dynamic), INVALID_MATRIX_TEMPLATE_PARAMETERS)
+ EIGEN_STATIC_ASSERT(((Options & (DontAlign|RowMajor)) == Options), INVALID_MATRIX_TEMPLATE_PARAMETERS)
+
+ EIGEN_DEVICE_FUNC
+ Base& base() { return *static_cast<Base*>(this); }
+ EIGEN_DEVICE_FUNC
+ const Base& base() const { return *static_cast<const Base*>(this); }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE EIGEN_CONSTEXPR
+ Index rows() const EIGEN_NOEXCEPT { return m_storage.rows(); }
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE EIGEN_CONSTEXPR
+ Index cols() const EIGEN_NOEXCEPT { return m_storage.cols(); }
+
+ /** This is an overloaded version of DenseCoeffsBase<Derived,ReadOnlyAccessors>::coeff(Index,Index) const
+ * provided to by-pass the creation of an evaluator of the expression, thus saving compilation efforts.
+ *
+ * See DenseCoeffsBase<Derived,ReadOnlyAccessors>::coeff(Index) const for details. */
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE const Scalar& coeff(Index rowId, Index colId) const
+ {
+ if(Flags & RowMajorBit)
+ return m_storage.data()[colId + rowId * m_storage.cols()];
+ else // column-major
+ return m_storage.data()[rowId + colId * m_storage.rows()];
+ }
+
+ /** This is an overloaded version of DenseCoeffsBase<Derived,ReadOnlyAccessors>::coeff(Index) const
+ * provided to by-pass the creation of an evaluator of the expression, thus saving compilation efforts.
+ *
+ * See DenseCoeffsBase<Derived,ReadOnlyAccessors>::coeff(Index) const for details. */
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE const Scalar& coeff(Index index) const
+ {
+ return m_storage.data()[index];
+ }
+
+ /** This is an overloaded version of DenseCoeffsBase<Derived,WriteAccessors>::coeffRef(Index,Index) const
+ * provided to by-pass the creation of an evaluator of the expression, thus saving compilation efforts.
+ *
+ * See DenseCoeffsBase<Derived,WriteAccessors>::coeffRef(Index,Index) const for details. */
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE Scalar& coeffRef(Index rowId, Index colId)
+ {
+ if(Flags & RowMajorBit)
+ return m_storage.data()[colId + rowId * m_storage.cols()];
+ else // column-major
+ return m_storage.data()[rowId + colId * m_storage.rows()];
+ }
+
+ /** This is an overloaded version of DenseCoeffsBase<Derived,WriteAccessors>::coeffRef(Index) const
+ * provided to by-pass the creation of an evaluator of the expression, thus saving compilation efforts.
+ *
+ * See DenseCoeffsBase<Derived,WriteAccessors>::coeffRef(Index) const for details. */
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE Scalar& coeffRef(Index index)
+ {
+ return m_storage.data()[index];
+ }
+
+ /** This is the const version of coeffRef(Index,Index) which is thus synonym of coeff(Index,Index).
+ * It is provided for convenience. */
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE const Scalar& coeffRef(Index rowId, Index colId) const
+ {
+ if(Flags & RowMajorBit)
+ return m_storage.data()[colId + rowId * m_storage.cols()];
+ else // column-major
+ return m_storage.data()[rowId + colId * m_storage.rows()];
+ }
+
+ /** This is the const version of coeffRef(Index) which is thus synonym of coeff(Index).
+ * It is provided for convenience. */
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE const Scalar& coeffRef(Index index) const
+ {
+ return m_storage.data()[index];
+ }
+
+ /** \internal */
+ template<int LoadMode>
+ EIGEN_STRONG_INLINE PacketScalar packet(Index rowId, Index colId) const
+ {
+ return internal::ploadt<PacketScalar, LoadMode>
+ (m_storage.data() + (Flags & RowMajorBit
+ ? colId + rowId * m_storage.cols()
+ : rowId + colId * m_storage.rows()));
+ }
+
+ /** \internal */
+ template<int LoadMode>
+ EIGEN_STRONG_INLINE PacketScalar packet(Index index) const
+ {
+ return internal::ploadt<PacketScalar, LoadMode>(m_storage.data() + index);
+ }
+
+ /** \internal */
+ template<int StoreMode>
+ EIGEN_STRONG_INLINE void writePacket(Index rowId, Index colId, const PacketScalar& val)
+ {
+ internal::pstoret<Scalar, PacketScalar, StoreMode>
+ (m_storage.data() + (Flags & RowMajorBit
+ ? colId + rowId * m_storage.cols()
+ : rowId + colId * m_storage.rows()), val);
+ }
+
+ /** \internal */
+ template<int StoreMode>
+ EIGEN_STRONG_INLINE void writePacket(Index index, const PacketScalar& val)
+ {
+ internal::pstoret<Scalar, PacketScalar, StoreMode>(m_storage.data() + index, val);
+ }
+
+ /** \returns a const pointer to the data array of this matrix */
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar *data() const
+ { return m_storage.data(); }
+
+ /** \returns a pointer to the data array of this matrix */
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar *data()
+ { return m_storage.data(); }
+
+ /** Resizes \c *this to a \a rows x \a cols matrix.
+ *
+ * This method is intended for dynamic-size matrices, although it is legal to call it on any
+ * matrix as long as fixed dimensions are left unchanged. If you only want to change the number
+ * of rows and/or of columns, you can use resize(NoChange_t, Index), resize(Index, NoChange_t).
+ *
+ * If the current number of coefficients of \c *this exactly matches the
+ * product \a rows * \a cols, then no memory allocation is performed and
+ * the current values are left unchanged. In all other cases, including
+ * shrinking, the data is reallocated and all previous values are lost.
+ *
+ * Example: \include Matrix_resize_int_int.cpp
+ * Output: \verbinclude Matrix_resize_int_int.out
+ *
+ * \sa resize(Index) for vectors, resize(NoChange_t, Index), resize(Index, NoChange_t)
+ */
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE void resize(Index rows, Index cols)
+ {
+ eigen_assert(internal::check_implication(RowsAtCompileTime!=Dynamic, rows==RowsAtCompileTime)
+ && internal::check_implication(ColsAtCompileTime!=Dynamic, cols==ColsAtCompileTime)
+ && internal::check_implication(RowsAtCompileTime==Dynamic && MaxRowsAtCompileTime!=Dynamic, rows<=MaxRowsAtCompileTime)
+ && internal::check_implication(ColsAtCompileTime==Dynamic && MaxColsAtCompileTime!=Dynamic, cols<=MaxColsAtCompileTime)
+ && rows>=0 && cols>=0 && "Invalid sizes when resizing a matrix or array.");
+ internal::check_rows_cols_for_overflow<MaxSizeAtCompileTime>::run(rows, cols);
+ #ifdef EIGEN_INITIALIZE_COEFFS
+ Index size = rows*cols;
+ bool size_changed = size != this->size();
+ m_storage.resize(size, rows, cols);
+ if(size_changed) EIGEN_INITIALIZE_COEFFS_IF_THAT_OPTION_IS_ENABLED
+ #else
+ m_storage.resize(rows*cols, rows, cols);
+ #endif
+ }
+
+ /** Resizes \c *this to a vector of length \a size
+ *
+ * \only_for_vectors. This method does not work for
+ * partially dynamic matrices when the static dimension is anything other
+ * than 1. For example it will not work with Matrix<double, 2, Dynamic>.
+ *
+ * Example: \include Matrix_resize_int.cpp
+ * Output: \verbinclude Matrix_resize_int.out
+ *
+ * \sa resize(Index,Index), resize(NoChange_t, Index), resize(Index, NoChange_t)
+ */
+ EIGEN_DEVICE_FUNC
+ inline void resize(Index size)
+ {
+ EIGEN_STATIC_ASSERT_VECTOR_ONLY(PlainObjectBase)
+ eigen_assert(((SizeAtCompileTime == Dynamic && (MaxSizeAtCompileTime==Dynamic || size<=MaxSizeAtCompileTime)) || SizeAtCompileTime == size) && size>=0);
+ #ifdef EIGEN_INITIALIZE_COEFFS
+ bool size_changed = size != this->size();
+ #endif
+ if(RowsAtCompileTime == 1)
+ m_storage.resize(size, 1, size);
+ else
+ m_storage.resize(size, size, 1);
+ #ifdef EIGEN_INITIALIZE_COEFFS
+ if(size_changed) EIGEN_INITIALIZE_COEFFS_IF_THAT_OPTION_IS_ENABLED
+ #endif
+ }
+
+ /** Resizes the matrix, changing only the number of columns. For the parameter of type NoChange_t, just pass the special value \c NoChange
+ * as in the example below.
+ *
+ * Example: \include Matrix_resize_NoChange_int.cpp
+ * Output: \verbinclude Matrix_resize_NoChange_int.out
+ *
+ * \sa resize(Index,Index)
+ */
+ EIGEN_DEVICE_FUNC
+ inline void resize(NoChange_t, Index cols)
+ {
+ resize(rows(), cols);
+ }
+
+ /** Resizes the matrix, changing only the number of rows. For the parameter of type NoChange_t, just pass the special value \c NoChange
+ * as in the example below.
+ *
+ * Example: \include Matrix_resize_int_NoChange.cpp
+ * Output: \verbinclude Matrix_resize_int_NoChange.out
+ *
+ * \sa resize(Index,Index)
+ */
+ EIGEN_DEVICE_FUNC
+ inline void resize(Index rows, NoChange_t)
+ {
+ resize(rows, cols());
+ }
+
+ /** Resizes \c *this to have the same dimensions as \a other.
+ * Takes care of doing all the checking that's needed.
+ *
+ * Note that copying a row-vector into a vector (and conversely) is allowed.
+ * The resizing, if any, is then done in the appropriate way so that row-vectors
+ * remain row-vectors and vectors remain vectors.
+ */
+ template<typename OtherDerived>
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE void resizeLike(const EigenBase<OtherDerived>& _other)
+ {
+ const OtherDerived& other = _other.derived();
+ internal::check_rows_cols_for_overflow<MaxSizeAtCompileTime>::run(other.rows(), other.cols());
+ const Index othersize = other.rows()*other.cols();
+ if(RowsAtCompileTime == 1)
+ {
+ eigen_assert(other.rows() == 1 || other.cols() == 1);
+ resize(1, othersize);
+ }
+ else if(ColsAtCompileTime == 1)
+ {
+ eigen_assert(other.rows() == 1 || other.cols() == 1);
+ resize(othersize, 1);
+ }
+ else resize(other.rows(), other.cols());
+ }
+
+ /** Resizes the matrix to \a rows x \a cols while leaving old values untouched.
+ *
+ * The method is intended for matrices of dynamic size. If you only want to change the number
+ * of rows and/or of columns, you can use conservativeResize(NoChange_t, Index) or
+ * conservativeResize(Index, NoChange_t).
+ *
+ * Matrices are resized relative to the top-left element. In case values need to be
+ * appended to the matrix they will be uninitialized.
+ */
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE void conservativeResize(Index rows, Index cols)
+ {
+ internal::conservative_resize_like_impl<Derived>::run(*this, rows, cols);
+ }
+
+ /** Resizes the matrix to \a rows x \a cols while leaving old values untouched.
+ *
+ * As opposed to conservativeResize(Index rows, Index cols), this version leaves
+ * the number of columns unchanged.
+ *
+ * In case the matrix is growing, new rows will be uninitialized.
+ */
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE void conservativeResize(Index rows, NoChange_t)
+ {
+ // Note: see the comment in conservativeResize(Index,Index)
+ conservativeResize(rows, cols());
+ }
+
+ /** Resizes the matrix to \a rows x \a cols while leaving old values untouched.
+ *
+ * As opposed to conservativeResize(Index rows, Index cols), this version leaves
+ * the number of rows unchanged.
+ *
+ * In case the matrix is growing, new columns will be uninitialized.
+ */
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE void conservativeResize(NoChange_t, Index cols)
+ {
+ // Note: see the comment in conservativeResize(Index,Index)
+ conservativeResize(rows(), cols);
+ }
+
+ /** Resizes the vector to \a size while retaining old values.
+ *
+ * \only_for_vectors. This method does not work for
+ * partially dynamic matrices when the static dimension is anything other
+ * than 1. For example it will not work with Matrix<double, 2, Dynamic>.
+ *
+ * When values are appended, they will be uninitialized.
+ */
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE void conservativeResize(Index size)
+ {
+ internal::conservative_resize_like_impl<Derived>::run(*this, size);
+ }
+
+ /** Resizes the matrix to \a rows x \a cols of \c other, while leaving old values untouched.
+ *
+ * The method is intended for matrices of dynamic size. If you only want to change the number
+ * of rows and/or of columns, you can use conservativeResize(NoChange_t, Index) or
+ * conservativeResize(Index, NoChange_t).
+ *
+ * Matrices are resized relative to the top-left element. In case values need to be
+ * appended to the matrix they will copied from \c other.
+ */
+ template<typename OtherDerived>
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE void conservativeResizeLike(const DenseBase<OtherDerived>& other)
+ {
+ internal::conservative_resize_like_impl<Derived,OtherDerived>::run(*this, other);
+ }
+
+ /** This is a special case of the templated operator=. Its purpose is to
+ * prevent a default operator= from hiding the templated operator=.
+ */
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE Derived& operator=(const PlainObjectBase& other)
+ {
+ return _set(other);
+ }
+
+ /** \sa MatrixBase::lazyAssign() */
+ template<typename OtherDerived>
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE Derived& lazyAssign(const DenseBase<OtherDerived>& other)
+ {
+ _resize_to_match(other);
+ return Base::lazyAssign(other.derived());
+ }
+
+ template<typename OtherDerived>
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE Derived& operator=(const ReturnByValue<OtherDerived>& func)
+ {
+ resize(func.rows(), func.cols());
+ return Base::operator=(func);
+ }
+
+ // Prevent user from trying to instantiate PlainObjectBase objects
+ // by making all its constructor protected. See bug 1074.
+ protected:
+
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE PlainObjectBase() : m_storage()
+ {
+// EIGEN_INITIALIZE_COEFFS_IF_THAT_OPTION_IS_ENABLED
+ }
+
+#ifndef EIGEN_PARSED_BY_DOXYGEN
+ // FIXME is it still needed ?
+ /** \internal */
+ EIGEN_DEVICE_FUNC
+ explicit PlainObjectBase(internal::constructor_without_unaligned_array_assert)
+ : m_storage(internal::constructor_without_unaligned_array_assert())
+ {
+ // EIGEN_INITIALIZE_COEFFS_IF_THAT_OPTION_IS_ENABLED
+ }
+#endif
+
+ EIGEN_DEVICE_FUNC
+ PlainObjectBase(PlainObjectBase&& other) EIGEN_NOEXCEPT
+ : m_storage( std::move(other.m_storage) )
+ {
+ }
+
+ EIGEN_DEVICE_FUNC
+ PlainObjectBase& operator=(PlainObjectBase&& other) EIGEN_NOEXCEPT
+ {
+ m_storage = std::move(other.m_storage);
+ return *this;
+ }
+
+ /** Copy constructor */
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE PlainObjectBase(const PlainObjectBase& other)
+ : Base(), m_storage(other.m_storage) { }
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE PlainObjectBase(Index size, Index rows, Index cols)
+ : m_storage(size, rows, cols)
+ {
+// EIGEN_INITIALIZE_COEFFS_IF_THAT_OPTION_IS_ENABLED
+ }
+
+ /** \brief Construct a row of column vector with fixed size from an arbitrary number of coefficients.
+ *
+ * \only_for_vectors
+ *
+ * This constructor is for 1D array or vectors with more than 4 coefficients.
+ *
+ * \warning To construct a column (resp. row) vector of fixed length, the number of values passed to this
+ * constructor must match the the fixed number of rows (resp. columns) of \c *this.
+ */
+ template <typename... ArgTypes>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ PlainObjectBase(const Scalar& a0, const Scalar& a1, const Scalar& a2, const Scalar& a3, const ArgTypes&... args)
+ : m_storage()
+ {
+ EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(PlainObjectBase, sizeof...(args) + 4);
+ m_storage.data()[0] = a0;
+ m_storage.data()[1] = a1;
+ m_storage.data()[2] = a2;
+ m_storage.data()[3] = a3;
+ Index i = 4;
+ auto x = {(m_storage.data()[i++] = args, 0)...};
+ static_cast<void>(x);
+ }
+
+ /** \brief Constructs a Matrix or Array and initializes it by elements given by an initializer list of initializer
+ * lists
+ */
+ EIGEN_DEVICE_FUNC
+ explicit EIGEN_STRONG_INLINE PlainObjectBase(const std::initializer_list<std::initializer_list<Scalar>>& list)
+ : m_storage()
+ {
+ size_t list_size = 0;
+ if (list.begin() != list.end()) {
+ list_size = list.begin()->size();
+ }
+
+ // This is to allow syntax like VectorXi {{1, 2, 3, 4}}
+ if (ColsAtCompileTime == 1 && list.size() == 1) {
+ eigen_assert(list_size == static_cast<size_t>(RowsAtCompileTime) || RowsAtCompileTime == Dynamic);
+ resize(list_size, ColsAtCompileTime);
+ std::copy(list.begin()->begin(), list.begin()->end(), m_storage.data());
+ } else {
+ eigen_assert(list.size() == static_cast<size_t>(RowsAtCompileTime) || RowsAtCompileTime == Dynamic);
+ eigen_assert(list_size == static_cast<size_t>(ColsAtCompileTime) || ColsAtCompileTime == Dynamic);
+ resize(list.size(), list_size);
+
+ Index row_index = 0;
+ for (const std::initializer_list<Scalar>& row : list) {
+ eigen_assert(list_size == row.size());
+ Index col_index = 0;
+ for (const Scalar& e : row) {
+ coeffRef(row_index, col_index) = e;
+ ++col_index;
+ }
+ ++row_index;
+ }
+ }
+ }
+
+ /** \sa PlainObjectBase::operator=(const EigenBase<OtherDerived>&) */
+ template<typename OtherDerived>
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE PlainObjectBase(const DenseBase<OtherDerived> &other)
+ : m_storage()
+ {
+ resizeLike(other);
+ _set_noalias(other);
+ }
+
+ /** \sa PlainObjectBase::operator=(const EigenBase<OtherDerived>&) */
+ template<typename OtherDerived>
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE PlainObjectBase(const EigenBase<OtherDerived> &other)
+ : m_storage()
+ {
+ resizeLike(other);
+ *this = other.derived();
+ }
+ /** \brief Copy constructor with in-place evaluation */
+ template<typename OtherDerived>
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE PlainObjectBase(const ReturnByValue<OtherDerived>& other)
+ {
+ // FIXME this does not automatically transpose vectors if necessary
+ resize(other.rows(), other.cols());
+ other.evalTo(this->derived());
+ }
+
+ public:
+
+ /** \brief Copies the generic expression \a other into *this.
+ * \copydetails DenseBase::operator=(const EigenBase<OtherDerived> &other)
+ */
+ template<typename OtherDerived>
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE Derived& operator=(const EigenBase<OtherDerived> &other)
+ {
+ _resize_to_match(other);
+ Base::operator=(other.derived());
+ return this->derived();
+ }
+
+ /** \name Map
+ * These are convenience functions returning Map objects. The Map() static functions return unaligned Map objects,
+ * while the AlignedMap() functions return aligned Map objects and thus should be called only with 16-byte-aligned
+ * \a data pointers.
+ *
+ * Here is an example using strides:
+ * \include Matrix_Map_stride.cpp
+ * Output: \verbinclude Matrix_Map_stride.out
+ *
+ * \see class Map
+ */
+ ///@{
+ static inline ConstMapType Map(const Scalar* data)
+ { return ConstMapType(data); }
+ static inline MapType Map(Scalar* data)
+ { return MapType(data); }
+ static inline ConstMapType Map(const Scalar* data, Index size)
+ { return ConstMapType(data, size); }
+ static inline MapType Map(Scalar* data, Index size)
+ { return MapType(data, size); }
+ static inline ConstMapType Map(const Scalar* data, Index rows, Index cols)
+ { return ConstMapType(data, rows, cols); }
+ static inline MapType Map(Scalar* data, Index rows, Index cols)
+ { return MapType(data, rows, cols); }
+
+ static inline ConstAlignedMapType MapAligned(const Scalar* data)
+ { return ConstAlignedMapType(data); }
+ static inline AlignedMapType MapAligned(Scalar* data)
+ { return AlignedMapType(data); }
+ static inline ConstAlignedMapType MapAligned(const Scalar* data, Index size)
+ { return ConstAlignedMapType(data, size); }
+ static inline AlignedMapType MapAligned(Scalar* data, Index size)
+ { return AlignedMapType(data, size); }
+ static inline ConstAlignedMapType MapAligned(const Scalar* data, Index rows, Index cols)
+ { return ConstAlignedMapType(data, rows, cols); }
+ static inline AlignedMapType MapAligned(Scalar* data, Index rows, Index cols)
+ { return AlignedMapType(data, rows, cols); }
+
+ template<int Outer, int Inner>
+ static inline typename StridedConstMapType<Stride<Outer, Inner> >::type Map(const Scalar* data, const Stride<Outer, Inner>& stride)
+ { return typename StridedConstMapType<Stride<Outer, Inner> >::type(data, stride); }
+ template<int Outer, int Inner>
+ static inline typename StridedMapType<Stride<Outer, Inner> >::type Map(Scalar* data, const Stride<Outer, Inner>& stride)
+ { return typename StridedMapType<Stride<Outer, Inner> >::type(data, stride); }
+ template<int Outer, int Inner>
+ static inline typename StridedConstMapType<Stride<Outer, Inner> >::type Map(const Scalar* data, Index size, const Stride<Outer, Inner>& stride)
+ { return typename StridedConstMapType<Stride<Outer, Inner> >::type(data, size, stride); }
+ template<int Outer, int Inner>
+ static inline typename StridedMapType<Stride<Outer, Inner> >::type Map(Scalar* data, Index size, const Stride<Outer, Inner>& stride)
+ { return typename StridedMapType<Stride<Outer, Inner> >::type(data, size, stride); }
+ template<int Outer, int Inner>
+ static inline typename StridedConstMapType<Stride<Outer, Inner> >::type Map(const Scalar* data, Index rows, Index cols, const Stride<Outer, Inner>& stride)
+ { return typename StridedConstMapType<Stride<Outer, Inner> >::type(data, rows, cols, stride); }
+ template<int Outer, int Inner>
+ static inline typename StridedMapType<Stride<Outer, Inner> >::type Map(Scalar* data, Index rows, Index cols, const Stride<Outer, Inner>& stride)
+ { return typename StridedMapType<Stride<Outer, Inner> >::type(data, rows, cols, stride); }
+
+ template<int Outer, int Inner>
+ static inline typename StridedConstAlignedMapType<Stride<Outer, Inner> >::type MapAligned(const Scalar* data, const Stride<Outer, Inner>& stride)
+ { return typename StridedConstAlignedMapType<Stride<Outer, Inner> >::type(data, stride); }
+ template<int Outer, int Inner>
+ static inline typename StridedAlignedMapType<Stride<Outer, Inner> >::type MapAligned(Scalar* data, const Stride<Outer, Inner>& stride)
+ { return typename StridedAlignedMapType<Stride<Outer, Inner> >::type(data, stride); }
+ template<int Outer, int Inner>
+ static inline typename StridedConstAlignedMapType<Stride<Outer, Inner> >::type MapAligned(const Scalar* data, Index size, const Stride<Outer, Inner>& stride)
+ { return typename StridedConstAlignedMapType<Stride<Outer, Inner> >::type(data, size, stride); }
+ template<int Outer, int Inner>
+ static inline typename StridedAlignedMapType<Stride<Outer, Inner> >::type MapAligned(Scalar* data, Index size, const Stride<Outer, Inner>& stride)
+ { return typename StridedAlignedMapType<Stride<Outer, Inner> >::type(data, size, stride); }
+ template<int Outer, int Inner>
+ static inline typename StridedConstAlignedMapType<Stride<Outer, Inner> >::type MapAligned(const Scalar* data, Index rows, Index cols, const Stride<Outer, Inner>& stride)
+ { return typename StridedConstAlignedMapType<Stride<Outer, Inner> >::type(data, rows, cols, stride); }
+ template<int Outer, int Inner>
+ static inline typename StridedAlignedMapType<Stride<Outer, Inner> >::type MapAligned(Scalar* data, Index rows, Index cols, const Stride<Outer, Inner>& stride)
+ { return typename StridedAlignedMapType<Stride<Outer, Inner> >::type(data, rows, cols, stride); }
+ ///@}
+
+ using Base::setConstant;
+ EIGEN_DEVICE_FUNC Derived& setConstant(Index size, const Scalar& val);
+ EIGEN_DEVICE_FUNC Derived& setConstant(Index rows, Index cols, const Scalar& val);
+ EIGEN_DEVICE_FUNC Derived& setConstant(NoChange_t, Index cols, const Scalar& val);
+ EIGEN_DEVICE_FUNC Derived& setConstant(Index rows, NoChange_t, const Scalar& val);
+
+ using Base::setZero;
+ EIGEN_DEVICE_FUNC Derived& setZero(Index size);
+ EIGEN_DEVICE_FUNC Derived& setZero(Index rows, Index cols);
+ EIGEN_DEVICE_FUNC Derived& setZero(NoChange_t, Index cols);
+ EIGEN_DEVICE_FUNC Derived& setZero(Index rows, NoChange_t);
+
+ using Base::setOnes;
+ EIGEN_DEVICE_FUNC Derived& setOnes(Index size);
+ EIGEN_DEVICE_FUNC Derived& setOnes(Index rows, Index cols);
+ EIGEN_DEVICE_FUNC Derived& setOnes(NoChange_t, Index cols);
+ EIGEN_DEVICE_FUNC Derived& setOnes(Index rows, NoChange_t);
+
+ using Base::setRandom;
+ Derived& setRandom(Index size);
+ Derived& setRandom(Index rows, Index cols);
+ Derived& setRandom(NoChange_t, Index cols);
+ Derived& setRandom(Index rows, NoChange_t);
+
+ #ifdef EIGEN_PLAINOBJECTBASE_PLUGIN
+ #include EIGEN_PLAINOBJECTBASE_PLUGIN
+ #endif
+
+ protected:
+ /** \internal Resizes *this in preparation for assigning \a other to it.
+ * Takes care of doing all the checking that's needed.
+ *
+ * Note that copying a row-vector into a vector (and conversely) is allowed.
+ * The resizing, if any, is then done in the appropriate way so that row-vectors
+ * remain row-vectors and vectors remain vectors.
+ */
+ template<typename OtherDerived>
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE void _resize_to_match(const EigenBase<OtherDerived>& other)
+ {
+ #ifdef EIGEN_NO_AUTOMATIC_RESIZING
+ eigen_assert((this->size()==0 || (IsVectorAtCompileTime ? (this->size() == other.size())
+ : (rows() == other.rows() && cols() == other.cols())))
+ && "Size mismatch. Automatic resizing is disabled because EIGEN_NO_AUTOMATIC_RESIZING is defined");
+ EIGEN_ONLY_USED_FOR_DEBUG(other);
+ #else
+ resizeLike(other);
+ #endif
+ }
+
+ /**
+ * \brief Copies the value of the expression \a other into \c *this with automatic resizing.
+ *
+ * *this might be resized to match the dimensions of \a other. If *this was a null matrix (not already initialized),
+ * it will be initialized.
+ *
+ * Note that copying a row-vector into a vector (and conversely) is allowed.
+ * The resizing, if any, is then done in the appropriate way so that row-vectors
+ * remain row-vectors and vectors remain vectors.
+ *
+ * \sa operator=(const MatrixBase<OtherDerived>&), _set_noalias()
+ *
+ * \internal
+ */
+ // aliasing is dealt once in internal::call_assignment
+ // so at this stage we have to assume aliasing... and resising has to be done later.
+ template<typename OtherDerived>
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE Derived& _set(const DenseBase<OtherDerived>& other)
+ {
+ internal::call_assignment(this->derived(), other.derived());
+ return this->derived();
+ }
+
+ /** \internal Like _set() but additionally makes the assumption that no aliasing effect can happen (which
+ * is the case when creating a new matrix) so one can enforce lazy evaluation.
+ *
+ * \sa operator=(const MatrixBase<OtherDerived>&), _set()
+ */
+ template<typename OtherDerived>
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE Derived& _set_noalias(const DenseBase<OtherDerived>& other)
+ {
+ // I don't think we need this resize call since the lazyAssign will anyways resize
+ // and lazyAssign will be called by the assign selector.
+ //_resize_to_match(other);
+ // the 'false' below means to enforce lazy evaluation. We don't use lazyAssign() because
+ // it wouldn't allow to copy a row-vector into a column-vector.
+ internal::call_assignment_no_alias(this->derived(), other.derived(), internal::assign_op<Scalar,typename OtherDerived::Scalar>());
+ return this->derived();
+ }
+
+ template<typename T0, typename T1>
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE void _init2(Index rows, Index cols, std::enable_if_t<Base::SizeAtCompileTime!=2,T0>* = 0)
+ {
+ const bool t0_is_integer_alike = internal::is_valid_index_type<T0>::value;
+ const bool t1_is_integer_alike = internal::is_valid_index_type<T1>::value;
+ EIGEN_STATIC_ASSERT(t0_is_integer_alike &&
+ t1_is_integer_alike,
+ FLOATING_POINT_ARGUMENT_PASSED__INTEGER_WAS_EXPECTED)
+ resize(rows,cols);
+ }
+
+ template<typename T0, typename T1>
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE void _init2(const T0& val0, const T1& val1, std::enable_if_t<Base::SizeAtCompileTime==2,T0>* = 0)
+ {
+ EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(PlainObjectBase, 2)
+ m_storage.data()[0] = Scalar(val0);
+ m_storage.data()[1] = Scalar(val1);
+ }
+
+ template<typename T0, typename T1>
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE void _init2(const Index& val0, const Index& val1,
+ std::enable_if_t< (!internal::is_same<Index,Scalar>::value)
+ && (internal::is_same<T0,Index>::value)
+ && (internal::is_same<T1,Index>::value)
+ && Base::SizeAtCompileTime==2,T1>* = 0)
+ {
+ EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(PlainObjectBase, 2)
+ m_storage.data()[0] = Scalar(val0);
+ m_storage.data()[1] = Scalar(val1);
+ }
+
+ // The argument is convertible to the Index type and we either have a non 1x1 Matrix, or a dynamic-sized Array,
+ // then the argument is meant to be the size of the object.
+ template<typename T>
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE void _init1(Index size, std::enable_if_t< (Base::SizeAtCompileTime!=1 || !internal::is_convertible<T, Scalar>::value)
+ && ((!internal::is_same<typename internal::traits<Derived>::XprKind,ArrayXpr>::value || Base::SizeAtCompileTime==Dynamic)),T>* = 0)
+ {
+ // NOTE MSVC 2008 complains if we directly put bool(NumTraits<T>::IsInteger) as the EIGEN_STATIC_ASSERT argument.
+ const bool is_integer_alike = internal::is_valid_index_type<T>::value;
+ EIGEN_UNUSED_VARIABLE(is_integer_alike);
+ EIGEN_STATIC_ASSERT(is_integer_alike,
+ FLOATING_POINT_ARGUMENT_PASSED__INTEGER_WAS_EXPECTED)
+ resize(size);
+ }
+
+ // We have a 1x1 matrix/array => the argument is interpreted as the value of the unique coefficient (case where scalar type can be implicitly converted)
+ template<typename T>
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE void _init1(const Scalar& val0, std::enable_if_t<Base::SizeAtCompileTime==1 && internal::is_convertible<T, Scalar>::value,T>* = 0)
+ {
+ EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(PlainObjectBase, 1)
+ m_storage.data()[0] = val0;
+ }
+
+ // We have a 1x1 matrix/array => the argument is interpreted as the value of the unique coefficient (case where scalar type match the index type)
+ template<typename T>
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE void _init1(const Index& val0,
+ std::enable_if_t< (!internal::is_same<Index,Scalar>::value)
+ && (internal::is_same<Index,T>::value)
+ && Base::SizeAtCompileTime==1
+ && internal::is_convertible<T, Scalar>::value,T*>* = 0)
+ {
+ EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(PlainObjectBase, 1)
+ m_storage.data()[0] = Scalar(val0);
+ }
+
+ // Initialize a fixed size matrix from a pointer to raw data
+ template<typename T>
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE void _init1(const Scalar* data){
+ this->_set_noalias(ConstMapType(data));
+ }
+
+ // Initialize an arbitrary matrix from a dense expression
+ template<typename T, typename OtherDerived>
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE void _init1(const DenseBase<OtherDerived>& other){
+ this->_set_noalias(other);
+ }
+
+ // Initialize an arbitrary matrix from an object convertible to the Derived type.
+ template<typename T>
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE void _init1(const Derived& other){
+ this->_set_noalias(other);
+ }
+
+ // Initialize an arbitrary matrix from a generic Eigen expression
+ template<typename T, typename OtherDerived>
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE void _init1(const EigenBase<OtherDerived>& other){
+ this->derived() = other;
+ }
+
+ template<typename T, typename OtherDerived>
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE void _init1(const ReturnByValue<OtherDerived>& other)
+ {
+ resize(other.rows(), other.cols());
+ other.evalTo(this->derived());
+ }
+
+ template<typename T, typename OtherDerived, int ColsAtCompileTime>
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE void _init1(const RotationBase<OtherDerived,ColsAtCompileTime>& r)
+ {
+ this->derived() = r;
+ }
+
+ // For fixed-size Array<Scalar,...>
+ template<typename T>
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE void _init1(const Scalar& val0,
+ std::enable_if_t< Base::SizeAtCompileTime!=Dynamic
+ && Base::SizeAtCompileTime!=1
+ && internal::is_convertible<T, Scalar>::value
+ && internal::is_same<typename internal::traits<Derived>::XprKind,ArrayXpr>::value,T>* = 0)
+ {
+ Base::setConstant(val0);
+ }
+
+ // For fixed-size Array<Index,...>
+ template<typename T>
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE void _init1(const Index& val0,
+ std::enable_if_t< (!internal::is_same<Index,Scalar>::value)
+ && (internal::is_same<Index,T>::value)
+ && Base::SizeAtCompileTime!=Dynamic
+ && Base::SizeAtCompileTime!=1
+ && internal::is_convertible<T, Scalar>::value
+ && internal::is_same<typename internal::traits<Derived>::XprKind,ArrayXpr>::value,T*>* = 0)
+ {
+ Base::setConstant(val0);
+ }
+
+ template<typename MatrixTypeA, typename MatrixTypeB, bool SwapPointers>
+ friend struct internal::matrix_swap_impl;
+
+ public:
+
+#ifndef EIGEN_PARSED_BY_DOXYGEN
+ /** \internal
+ * \brief Override DenseBase::swap() since for dynamic-sized matrices
+ * of same type it is enough to swap the data pointers.
+ */
+ template<typename OtherDerived>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ void swap(DenseBase<OtherDerived> & other)
+ {
+ enum { SwapPointers = internal::is_same<Derived, OtherDerived>::value && Base::SizeAtCompileTime==Dynamic };
+ internal::matrix_swap_impl<Derived, OtherDerived, bool(SwapPointers)>::run(this->derived(), other.derived());
+ }
+
+ /** \internal
+ * \brief const version forwarded to DenseBase::swap
+ */
+ template<typename OtherDerived>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ void swap(DenseBase<OtherDerived> const & other)
+ { Base::swap(other.derived()); }
+
+ enum { IsPlainObjectBase = 1 };
+#endif
+ public:
+ // These apparently need to be down here for nvcc+icc to prevent duplicate
+ // Map symbol.
+ template<typename PlainObjectType, int MapOptions, typename StrideType> friend class Eigen::Map;
+ friend class Eigen::Map<Derived, Unaligned>;
+ friend class Eigen::Map<const Derived, Unaligned>;
+#if EIGEN_MAX_ALIGN_BYTES>0
+ // for EIGEN_MAX_ALIGN_BYTES==0, AlignedMax==Unaligned, and many compilers generate warnings for friend-ing a class twice.
+ friend class Eigen::Map<Derived, AlignedMax>;
+ friend class Eigen::Map<const Derived, AlignedMax>;
+#endif
+};
+
+namespace internal {
+
+template <typename Derived, typename OtherDerived, bool IsVector>
+struct conservative_resize_like_impl
+{
+ static constexpr bool IsRelocatable = std::is_trivially_copyable<typename Derived::Scalar>::value;
+ static void run(DenseBase<Derived>& _this, Index rows, Index cols)
+ {
+ if (_this.rows() == rows && _this.cols() == cols) return;
+ EIGEN_STATIC_ASSERT_DYNAMIC_SIZE(Derived)
+
+ if ( IsRelocatable
+ && (( Derived::IsRowMajor && _this.cols() == cols) || // row-major and we change only the number of rows
+ (!Derived::IsRowMajor && _this.rows() == rows) )) // column-major and we change only the number of columns
+ {
+ internal::check_rows_cols_for_overflow<Derived::MaxSizeAtCompileTime>::run(rows, cols);
+ _this.derived().m_storage.conservativeResize(rows*cols,rows,cols);
+ }
+ else
+ {
+ // The storage order does not allow us to use reallocation.
+ Derived tmp(rows,cols);
+ const Index common_rows = numext::mini(rows, _this.rows());
+ const Index common_cols = numext::mini(cols, _this.cols());
+ tmp.block(0,0,common_rows,common_cols) = _this.block(0,0,common_rows,common_cols);
+ _this.derived().swap(tmp);
+ }
+ }
+
+ static void run(DenseBase<Derived>& _this, const DenseBase<OtherDerived>& other)
+ {
+ if (_this.rows() == other.rows() && _this.cols() == other.cols()) return;
+
+ // Note: Here is space for improvement. Basically, for conservativeResize(Index,Index),
+ // neither RowsAtCompileTime or ColsAtCompileTime must be Dynamic. If only one of the
+ // dimensions is dynamic, one could use either conservativeResize(Index rows, NoChange_t) or
+ // conservativeResize(NoChange_t, Index cols). For these methods new static asserts like
+ // EIGEN_STATIC_ASSERT_DYNAMIC_ROWS and EIGEN_STATIC_ASSERT_DYNAMIC_COLS would be good.
+ EIGEN_STATIC_ASSERT_DYNAMIC_SIZE(Derived)
+ EIGEN_STATIC_ASSERT_DYNAMIC_SIZE(OtherDerived)
+
+ if ( IsRelocatable &&
+ (( Derived::IsRowMajor && _this.cols() == other.cols()) || // row-major and we change only the number of rows
+ (!Derived::IsRowMajor && _this.rows() == other.rows()) )) // column-major and we change only the number of columns
+ {
+ const Index new_rows = other.rows() - _this.rows();
+ const Index new_cols = other.cols() - _this.cols();
+ _this.derived().m_storage.conservativeResize(other.size(),other.rows(),other.cols());
+ if (new_rows>0)
+ _this.bottomRightCorner(new_rows, other.cols()) = other.bottomRows(new_rows);
+ else if (new_cols>0)
+ _this.bottomRightCorner(other.rows(), new_cols) = other.rightCols(new_cols);
+ }
+ else
+ {
+ // The storage order does not allow us to use reallocation.
+ Derived tmp(other);
+ const Index common_rows = numext::mini(tmp.rows(), _this.rows());
+ const Index common_cols = numext::mini(tmp.cols(), _this.cols());
+ tmp.block(0,0,common_rows,common_cols) = _this.block(0,0,common_rows,common_cols);
+ _this.derived().swap(tmp);
+ }
+ }
+};
+
+// Here, the specialization for vectors inherits from the general matrix case
+// to allow calling .conservativeResize(rows,cols) on vectors.
+template <typename Derived, typename OtherDerived>
+struct conservative_resize_like_impl<Derived,OtherDerived,true>
+ : conservative_resize_like_impl<Derived,OtherDerived,false>
+{
+ typedef conservative_resize_like_impl<Derived,OtherDerived,false> Base;
+ using Base::run;
+ using Base::IsRelocatable;
+
+ static void run(DenseBase<Derived>& _this, Index size)
+ {
+ const Index new_rows = Derived::RowsAtCompileTime==1 ? 1 : size;
+ const Index new_cols = Derived::RowsAtCompileTime==1 ? size : 1;
+ if(IsRelocatable)
+ _this.derived().m_storage.conservativeResize(size,new_rows,new_cols);
+ else
+ Base::run(_this.derived(), new_rows, new_cols);
+ }
+
+ static void run(DenseBase<Derived>& _this, const DenseBase<OtherDerived>& other)
+ {
+ if (_this.rows() == other.rows() && _this.cols() == other.cols()) return;
+
+ const Index num_new_elements = other.size() - _this.size();
+
+ const Index new_rows = Derived::RowsAtCompileTime==1 ? 1 : other.rows();
+ const Index new_cols = Derived::RowsAtCompileTime==1 ? other.cols() : 1;
+ if(IsRelocatable)
+ _this.derived().m_storage.conservativeResize(other.size(),new_rows,new_cols);
+ else
+ Base::run(_this.derived(), new_rows, new_cols);
+
+ if (num_new_elements > 0)
+ _this.tail(num_new_elements) = other.tail(num_new_elements);
+ }
+};
+
+template<typename MatrixTypeA, typename MatrixTypeB, bool SwapPointers>
+struct matrix_swap_impl
+{
+ EIGEN_DEVICE_FUNC
+ static EIGEN_STRONG_INLINE void run(MatrixTypeA& a, MatrixTypeB& b)
+ {
+ a.base().swap(b);
+ }
+};
+
+template<typename MatrixTypeA, typename MatrixTypeB>
+struct matrix_swap_impl<MatrixTypeA, MatrixTypeB, true>
+{
+ EIGEN_DEVICE_FUNC
+ static inline void run(MatrixTypeA& a, MatrixTypeB& b)
+ {
+ static_cast<typename MatrixTypeA::Base&>(a).m_storage.swap(static_cast<typename MatrixTypeB::Base&>(b).m_storage);
+ }
+};
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_DENSESTORAGEBASE_H
diff --git a/Eigen/src/Core/Product.h b/Eigen/src/Core/Product.h
new file mode 100644
index 0000000..85842d1
--- /dev/null
+++ b/Eigen/src/Core/Product.h
@@ -0,0 +1,193 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2011 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_PRODUCT_H
+#define EIGEN_PRODUCT_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+template<typename Lhs, typename Rhs, int Option, typename StorageKind> class ProductImpl;
+
+namespace internal {
+
+template<typename Lhs, typename Rhs, int Option>
+struct traits<Product<Lhs, Rhs, Option> >
+{
+ typedef remove_all_t<Lhs> LhsCleaned;
+ typedef remove_all_t<Rhs> RhsCleaned;
+ typedef traits<LhsCleaned> LhsTraits;
+ typedef traits<RhsCleaned> RhsTraits;
+
+ typedef MatrixXpr XprKind;
+
+ typedef typename ScalarBinaryOpTraits<typename traits<LhsCleaned>::Scalar, typename traits<RhsCleaned>::Scalar>::ReturnType Scalar;
+ typedef typename product_promote_storage_type<typename LhsTraits::StorageKind,
+ typename RhsTraits::StorageKind,
+ internal::product_type<Lhs,Rhs>::ret>::ret StorageKind;
+ typedef typename promote_index_type<typename LhsTraits::StorageIndex,
+ typename RhsTraits::StorageIndex>::type StorageIndex;
+
+ enum {
+ RowsAtCompileTime = LhsTraits::RowsAtCompileTime,
+ ColsAtCompileTime = RhsTraits::ColsAtCompileTime,
+ MaxRowsAtCompileTime = LhsTraits::MaxRowsAtCompileTime,
+ MaxColsAtCompileTime = RhsTraits::MaxColsAtCompileTime,
+
+ // FIXME: only needed by GeneralMatrixMatrixTriangular
+ InnerSize = min_size_prefer_fixed(LhsTraits::ColsAtCompileTime, RhsTraits::RowsAtCompileTime),
+
+ // The storage order is somewhat arbitrary here. The correct one will be determined through the evaluator.
+ Flags = (MaxRowsAtCompileTime==1 && MaxColsAtCompileTime!=1) ? RowMajorBit
+ : (MaxColsAtCompileTime==1 && MaxRowsAtCompileTime!=1) ? 0
+ : ( ((LhsTraits::Flags&NoPreferredStorageOrderBit) && (RhsTraits::Flags&RowMajorBit))
+ || ((RhsTraits::Flags&NoPreferredStorageOrderBit) && (LhsTraits::Flags&RowMajorBit)) ) ? RowMajorBit
+ : NoPreferredStorageOrderBit
+ };
+};
+
+} // end namespace internal
+
+/** \class Product
+ * \ingroup Core_Module
+ *
+ * \brief Expression of the product of two arbitrary matrices or vectors
+ *
+ * \tparam Lhs_ the type of the left-hand side expression
+ * \tparam Rhs_ the type of the right-hand side expression
+ *
+ * This class represents an expression of the product of two arbitrary matrices.
+ *
+ * The other template parameters are:
+ * \tparam Option can be DefaultProduct, AliasFreeProduct, or LazyProduct
+ *
+ */
+template<typename Lhs_, typename Rhs_, int Option>
+class Product : public ProductImpl<Lhs_,Rhs_,Option,
+ typename internal::product_promote_storage_type<typename internal::traits<Lhs_>::StorageKind,
+ typename internal::traits<Rhs_>::StorageKind,
+ internal::product_type<Lhs_,Rhs_>::ret>::ret>
+{
+ public:
+
+ typedef Lhs_ Lhs;
+ typedef Rhs_ Rhs;
+
+ typedef typename ProductImpl<
+ Lhs, Rhs, Option,
+ typename internal::product_promote_storage_type<typename internal::traits<Lhs>::StorageKind,
+ typename internal::traits<Rhs>::StorageKind,
+ internal::product_type<Lhs,Rhs>::ret>::ret>::Base Base;
+ EIGEN_GENERIC_PUBLIC_INTERFACE(Product)
+
+ typedef typename internal::ref_selector<Lhs>::type LhsNested;
+ typedef typename internal::ref_selector<Rhs>::type RhsNested;
+ typedef internal::remove_all_t<LhsNested> LhsNestedCleaned;
+ typedef internal::remove_all_t<RhsNested> RhsNestedCleaned;
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ Product(const Lhs& lhs, const Rhs& rhs) : m_lhs(lhs), m_rhs(rhs)
+ {
+ eigen_assert(lhs.cols() == rhs.rows()
+ && "invalid matrix product"
+ && "if you wanted a coeff-wise or a dot product use the respective explicit functions");
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE EIGEN_CONSTEXPR
+ Index rows() const EIGEN_NOEXCEPT { return m_lhs.rows(); }
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE EIGEN_CONSTEXPR
+ Index cols() const EIGEN_NOEXCEPT { return m_rhs.cols(); }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ const LhsNestedCleaned& lhs() const { return m_lhs; }
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ const RhsNestedCleaned& rhs() const { return m_rhs; }
+
+ protected:
+
+ LhsNested m_lhs;
+ RhsNested m_rhs;
+};
+
+namespace internal {
+
+template<typename Lhs, typename Rhs, int Option, int ProductTag = internal::product_type<Lhs,Rhs>::ret>
+class dense_product_base
+ : public internal::dense_xpr_base<Product<Lhs,Rhs,Option> >::type
+{};
+
+/** Conversion to scalar for inner-products */
+template<typename Lhs, typename Rhs, int Option>
+class dense_product_base<Lhs, Rhs, Option, InnerProduct>
+ : public internal::dense_xpr_base<Product<Lhs,Rhs,Option> >::type
+{
+ typedef Product<Lhs,Rhs,Option> ProductXpr;
+ typedef typename internal::dense_xpr_base<ProductXpr>::type Base;
+public:
+ using Base::derived;
+ typedef typename Base::Scalar Scalar;
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE operator const Scalar() const
+ {
+ return internal::evaluator<ProductXpr>(derived()).coeff(0,0);
+ }
+};
+
+} // namespace internal
+
+// Generic API dispatcher
+template<typename Lhs, typename Rhs, int Option, typename StorageKind>
+class ProductImpl : public internal::generic_xpr_base<Product<Lhs,Rhs,Option>, MatrixXpr, StorageKind>::type
+{
+ public:
+ typedef typename internal::generic_xpr_base<Product<Lhs,Rhs,Option>, MatrixXpr, StorageKind>::type Base;
+};
+
+template<typename Lhs, typename Rhs, int Option>
+class ProductImpl<Lhs,Rhs,Option,Dense>
+ : public internal::dense_product_base<Lhs,Rhs,Option>
+{
+ typedef Product<Lhs, Rhs, Option> Derived;
+
+ public:
+
+ typedef typename internal::dense_product_base<Lhs, Rhs, Option> Base;
+ EIGEN_DENSE_PUBLIC_INTERFACE(Derived)
+ protected:
+ enum {
+ IsOneByOne = (RowsAtCompileTime == 1 || RowsAtCompileTime == Dynamic) &&
+ (ColsAtCompileTime == 1 || ColsAtCompileTime == Dynamic),
+ EnableCoeff = IsOneByOne || Option==LazyProduct
+ };
+
+ public:
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar coeff(Index row, Index col) const
+ {
+ EIGEN_STATIC_ASSERT(EnableCoeff, THIS_METHOD_IS_ONLY_FOR_INNER_OR_LAZY_PRODUCTS);
+ eigen_assert( (Option==LazyProduct) || (this->rows() == 1 && this->cols() == 1) );
+
+ return internal::evaluator<Derived>(derived()).coeff(row,col);
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar coeff(Index i) const
+ {
+ EIGEN_STATIC_ASSERT(EnableCoeff, THIS_METHOD_IS_ONLY_FOR_INNER_OR_LAZY_PRODUCTS);
+ eigen_assert( (Option==LazyProduct) || (this->rows() == 1 && this->cols() == 1) );
+
+ return internal::evaluator<Derived>(derived()).coeff(i);
+ }
+
+
+};
+
+} // end namespace Eigen
+
+#endif // EIGEN_PRODUCT_H
diff --git a/Eigen/src/Core/ProductEvaluators.h b/Eigen/src/Core/ProductEvaluators.h
new file mode 100644
index 0000000..9da2406
--- /dev/null
+++ b/Eigen/src/Core/ProductEvaluators.h
@@ -0,0 +1,1215 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+// Copyright (C) 2008-2010 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2011 Jitse Niesen <jitse@maths.leeds.ac.uk>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+
+#ifndef EIGEN_PRODUCTEVALUATORS_H
+#define EIGEN_PRODUCTEVALUATORS_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+
+/** \internal
+ * Evaluator of a product expression.
+ * Since products require special treatments to handle all possible cases,
+ * we simply defer the evaluation logic to a product_evaluator class
+ * which offers more partial specialization possibilities.
+ *
+ * \sa class product_evaluator
+ */
+template<typename Lhs, typename Rhs, int Options>
+struct evaluator<Product<Lhs, Rhs, Options> >
+ : public product_evaluator<Product<Lhs, Rhs, Options> >
+{
+ typedef Product<Lhs, Rhs, Options> XprType;
+ typedef product_evaluator<XprType> Base;
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE explicit evaluator(const XprType& xpr) : Base(xpr) {}
+};
+
+// Catch "scalar * ( A * B )" and transform it to "(A*scalar) * B"
+// TODO we should apply that rule only if that's really helpful
+template<typename Lhs, typename Rhs, typename Scalar1, typename Scalar2, typename Plain1>
+struct evaluator_assume_aliasing<CwiseBinaryOp<internal::scalar_product_op<Scalar1,Scalar2>,
+ const CwiseNullaryOp<internal::scalar_constant_op<Scalar1>, Plain1>,
+ const Product<Lhs, Rhs, DefaultProduct> > >
+{
+ static const bool value = true;
+};
+template<typename Lhs, typename Rhs, typename Scalar1, typename Scalar2, typename Plain1>
+struct evaluator<CwiseBinaryOp<internal::scalar_product_op<Scalar1,Scalar2>,
+ const CwiseNullaryOp<internal::scalar_constant_op<Scalar1>, Plain1>,
+ const Product<Lhs, Rhs, DefaultProduct> > >
+ : public evaluator<Product<EIGEN_SCALAR_BINARYOP_EXPR_RETURN_TYPE(Scalar1,Lhs,product), Rhs, DefaultProduct> >
+{
+ typedef CwiseBinaryOp<internal::scalar_product_op<Scalar1,Scalar2>,
+ const CwiseNullaryOp<internal::scalar_constant_op<Scalar1>, Plain1>,
+ const Product<Lhs, Rhs, DefaultProduct> > XprType;
+ typedef evaluator<Product<EIGEN_SCALAR_BINARYOP_EXPR_RETURN_TYPE(Scalar1,Lhs,product), Rhs, DefaultProduct> > Base;
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE explicit evaluator(const XprType& xpr)
+ : Base(xpr.lhs().functor().m_other * xpr.rhs().lhs() * xpr.rhs().rhs())
+ {}
+};
+
+
+template<typename Lhs, typename Rhs, int DiagIndex>
+struct evaluator<Diagonal<const Product<Lhs, Rhs, DefaultProduct>, DiagIndex> >
+ : public evaluator<Diagonal<const Product<Lhs, Rhs, LazyProduct>, DiagIndex> >
+{
+ typedef Diagonal<const Product<Lhs, Rhs, DefaultProduct>, DiagIndex> XprType;
+ typedef evaluator<Diagonal<const Product<Lhs, Rhs, LazyProduct>, DiagIndex> > Base;
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE explicit evaluator(const XprType& xpr)
+ : Base(Diagonal<const Product<Lhs, Rhs, LazyProduct>, DiagIndex>(
+ Product<Lhs, Rhs, LazyProduct>(xpr.nestedExpression().lhs(), xpr.nestedExpression().rhs()),
+ xpr.index() ))
+ {}
+};
+
+
+// Helper class to perform a matrix product with the destination at hand.
+// Depending on the sizes of the factors, there are different evaluation strategies
+// as controlled by internal::product_type.
+template< typename Lhs, typename Rhs,
+ typename LhsShape = typename evaluator_traits<Lhs>::Shape,
+ typename RhsShape = typename evaluator_traits<Rhs>::Shape,
+ int ProductType = internal::product_type<Lhs,Rhs>::value>
+struct generic_product_impl;
+
+template<typename Lhs, typename Rhs>
+struct evaluator_assume_aliasing<Product<Lhs, Rhs, DefaultProduct> > {
+ static const bool value = true;
+};
+
+// This is the default evaluator implementation for products:
+// It creates a temporary and call generic_product_impl
+template<typename Lhs, typename Rhs, int Options, int ProductTag, typename LhsShape, typename RhsShape>
+struct product_evaluator<Product<Lhs, Rhs, Options>, ProductTag, LhsShape, RhsShape>
+ : public evaluator<typename Product<Lhs, Rhs, Options>::PlainObject>
+{
+ typedef Product<Lhs, Rhs, Options> XprType;
+ typedef typename XprType::PlainObject PlainObject;
+ typedef evaluator<PlainObject> Base;
+ enum {
+ Flags = Base::Flags | EvalBeforeNestingBit
+ };
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ explicit product_evaluator(const XprType& xpr)
+ : m_result(xpr.rows(), xpr.cols())
+ {
+ internal::construct_at<Base>(this, m_result);
+
+// FIXME shall we handle nested_eval here?,
+// if so, then we must take care at removing the call to nested_eval in the specializations (e.g., in permutation_matrix_product, transposition_matrix_product, etc.)
+// typedef typename internal::nested_eval<Lhs,Rhs::ColsAtCompileTime>::type LhsNested;
+// typedef typename internal::nested_eval<Rhs,Lhs::RowsAtCompileTime>::type RhsNested;
+// typedef internal::remove_all_t<LhsNested> LhsNestedCleaned;
+// typedef internal::remove_all_t<RhsNested> RhsNestedCleaned;
+//
+// const LhsNested lhs(xpr.lhs());
+// const RhsNested rhs(xpr.rhs());
+//
+// generic_product_impl<LhsNestedCleaned, RhsNestedCleaned>::evalTo(m_result, lhs, rhs);
+
+ generic_product_impl<Lhs, Rhs, LhsShape, RhsShape, ProductTag>::evalTo(m_result, xpr.lhs(), xpr.rhs());
+ }
+
+protected:
+ PlainObject m_result;
+};
+
+// The following three shortcuts are enabled only if the scalar types match exactly.
+// TODO: we could enable them for different scalar types when the product is not vectorized.
+
+// Dense = Product
+template< typename DstXprType, typename Lhs, typename Rhs, int Options, typename Scalar>
+struct Assignment<DstXprType, Product<Lhs,Rhs,Options>, internal::assign_op<Scalar,Scalar>, Dense2Dense,
+ std::enable_if_t<(Options==DefaultProduct || Options==AliasFreeProduct)>>
+{
+ typedef Product<Lhs,Rhs,Options> SrcXprType;
+ static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ void run(DstXprType &dst, const SrcXprType &src, const internal::assign_op<Scalar,Scalar> &)
+ {
+ Index dstRows = src.rows();
+ Index dstCols = src.cols();
+ if((dst.rows()!=dstRows) || (dst.cols()!=dstCols))
+ dst.resize(dstRows, dstCols);
+ // FIXME shall we handle nested_eval here?
+ generic_product_impl<Lhs, Rhs>::evalTo(dst, src.lhs(), src.rhs());
+ }
+};
+
+// Dense += Product
+template< typename DstXprType, typename Lhs, typename Rhs, int Options, typename Scalar>
+struct Assignment<DstXprType, Product<Lhs,Rhs,Options>, internal::add_assign_op<Scalar,Scalar>, Dense2Dense,
+ std::enable_if_t<(Options==DefaultProduct || Options==AliasFreeProduct)>>
+{
+ typedef Product<Lhs,Rhs,Options> SrcXprType;
+ static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ void run(DstXprType &dst, const SrcXprType &src, const internal::add_assign_op<Scalar,Scalar> &)
+ {
+ eigen_assert(dst.rows() == src.rows() && dst.cols() == src.cols());
+ // FIXME shall we handle nested_eval here?
+ generic_product_impl<Lhs, Rhs>::addTo(dst, src.lhs(), src.rhs());
+ }
+};
+
+// Dense -= Product
+template< typename DstXprType, typename Lhs, typename Rhs, int Options, typename Scalar>
+struct Assignment<DstXprType, Product<Lhs,Rhs,Options>, internal::sub_assign_op<Scalar,Scalar>, Dense2Dense,
+ std::enable_if_t<(Options==DefaultProduct || Options==AliasFreeProduct)>>
+{
+ typedef Product<Lhs,Rhs,Options> SrcXprType;
+ static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ void run(DstXprType &dst, const SrcXprType &src, const internal::sub_assign_op<Scalar,Scalar> &)
+ {
+ eigen_assert(dst.rows() == src.rows() && dst.cols() == src.cols());
+ // FIXME shall we handle nested_eval here?
+ generic_product_impl<Lhs, Rhs>::subTo(dst, src.lhs(), src.rhs());
+ }
+};
+
+
+// Dense ?= scalar * Product
+// TODO we should apply that rule if that's really helpful
+// for instance, this is not good for inner products
+template< typename DstXprType, typename Lhs, typename Rhs, typename AssignFunc, typename Scalar, typename ScalarBis, typename Plain>
+struct Assignment<DstXprType, CwiseBinaryOp<internal::scalar_product_op<ScalarBis,Scalar>, const CwiseNullaryOp<internal::scalar_constant_op<ScalarBis>,Plain>,
+ const Product<Lhs,Rhs,DefaultProduct> >, AssignFunc, Dense2Dense>
+{
+ typedef CwiseBinaryOp<internal::scalar_product_op<ScalarBis,Scalar>,
+ const CwiseNullaryOp<internal::scalar_constant_op<ScalarBis>,Plain>,
+ const Product<Lhs,Rhs,DefaultProduct> > SrcXprType;
+ static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ void run(DstXprType &dst, const SrcXprType &src, const AssignFunc& func)
+ {
+ call_assignment_no_alias(dst, (src.lhs().functor().m_other * src.rhs().lhs())*src.rhs().rhs(), func);
+ }
+};
+
+//----------------------------------------
+// Catch "Dense ?= xpr + Product<>" expression to save one temporary
+// FIXME we could probably enable these rules for any product, i.e., not only Dense and DefaultProduct
+
+template<typename OtherXpr, typename Lhs, typename Rhs>
+struct evaluator_assume_aliasing<CwiseBinaryOp<internal::scalar_sum_op<typename OtherXpr::Scalar,typename Product<Lhs,Rhs,DefaultProduct>::Scalar>, const OtherXpr,
+ const Product<Lhs,Rhs,DefaultProduct> >, DenseShape > {
+ static const bool value = true;
+};
+
+template<typename OtherXpr, typename Lhs, typename Rhs>
+struct evaluator_assume_aliasing<CwiseBinaryOp<internal::scalar_difference_op<typename OtherXpr::Scalar,typename Product<Lhs,Rhs,DefaultProduct>::Scalar>, const OtherXpr,
+ const Product<Lhs,Rhs,DefaultProduct> >, DenseShape > {
+ static const bool value = true;
+};
+
+template<typename DstXprType, typename OtherXpr, typename ProductType, typename Func1, typename Func2>
+struct assignment_from_xpr_op_product
+{
+ template<typename SrcXprType, typename InitialFunc>
+ static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ void run(DstXprType &dst, const SrcXprType &src, const InitialFunc& /*func*/)
+ {
+ call_assignment_no_alias(dst, src.lhs(), Func1());
+ call_assignment_no_alias(dst, src.rhs(), Func2());
+ }
+};
+
+#define EIGEN_CATCH_ASSIGN_XPR_OP_PRODUCT(ASSIGN_OP,BINOP,ASSIGN_OP2) \
+ template< typename DstXprType, typename OtherXpr, typename Lhs, typename Rhs, typename DstScalar, typename SrcScalar, typename OtherScalar,typename ProdScalar> \
+ struct Assignment<DstXprType, CwiseBinaryOp<internal::BINOP<OtherScalar,ProdScalar>, const OtherXpr, \
+ const Product<Lhs,Rhs,DefaultProduct> >, internal::ASSIGN_OP<DstScalar,SrcScalar>, Dense2Dense> \
+ : assignment_from_xpr_op_product<DstXprType, OtherXpr, Product<Lhs,Rhs,DefaultProduct>, internal::ASSIGN_OP<DstScalar,OtherScalar>, internal::ASSIGN_OP2<DstScalar,ProdScalar> > \
+ {}
+
+EIGEN_CATCH_ASSIGN_XPR_OP_PRODUCT(assign_op, scalar_sum_op,add_assign_op);
+EIGEN_CATCH_ASSIGN_XPR_OP_PRODUCT(add_assign_op,scalar_sum_op,add_assign_op);
+EIGEN_CATCH_ASSIGN_XPR_OP_PRODUCT(sub_assign_op,scalar_sum_op,sub_assign_op);
+
+EIGEN_CATCH_ASSIGN_XPR_OP_PRODUCT(assign_op, scalar_difference_op,sub_assign_op);
+EIGEN_CATCH_ASSIGN_XPR_OP_PRODUCT(add_assign_op,scalar_difference_op,sub_assign_op);
+EIGEN_CATCH_ASSIGN_XPR_OP_PRODUCT(sub_assign_op,scalar_difference_op,add_assign_op);
+
+//----------------------------------------
+
+template<typename Lhs, typename Rhs>
+struct generic_product_impl<Lhs,Rhs,DenseShape,DenseShape,InnerProduct>
+{
+ template<typename Dst>
+ static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void evalTo(Dst& dst, const Lhs& lhs, const Rhs& rhs)
+ {
+ dst.coeffRef(0,0) = (lhs.transpose().cwiseProduct(rhs)).sum();
+ }
+
+ template<typename Dst>
+ static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void addTo(Dst& dst, const Lhs& lhs, const Rhs& rhs)
+ {
+ dst.coeffRef(0,0) += (lhs.transpose().cwiseProduct(rhs)).sum();
+ }
+
+ template<typename Dst>
+ static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void subTo(Dst& dst, const Lhs& lhs, const Rhs& rhs)
+ { dst.coeffRef(0,0) -= (lhs.transpose().cwiseProduct(rhs)).sum(); }
+};
+
+
+/***********************************************************************
+* Implementation of outer dense * dense vector product
+***********************************************************************/
+
+// Column major result
+template<typename Dst, typename Lhs, typename Rhs, typename Func>
+void EIGEN_DEVICE_FUNC outer_product_selector_run(Dst& dst, const Lhs &lhs, const Rhs &rhs, const Func& func, const false_type&)
+{
+ evaluator<Rhs> rhsEval(rhs);
+ ei_declare_local_nested_eval(Lhs,lhs,Rhs::SizeAtCompileTime,actual_lhs);
+ // FIXME if cols is large enough, then it might be useful to make sure that lhs is sequentially stored
+ // FIXME not very good if rhs is real and lhs complex while alpha is real too
+ const Index cols = dst.cols();
+ for (Index j=0; j<cols; ++j)
+ func(dst.col(j), rhsEval.coeff(Index(0),j) * actual_lhs);
+}
+
+// Row major result
+template<typename Dst, typename Lhs, typename Rhs, typename Func>
+void EIGEN_DEVICE_FUNC outer_product_selector_run(Dst& dst, const Lhs &lhs, const Rhs &rhs, const Func& func, const true_type&)
+{
+ evaluator<Lhs> lhsEval(lhs);
+ ei_declare_local_nested_eval(Rhs,rhs,Lhs::SizeAtCompileTime,actual_rhs);
+ // FIXME if rows is large enough, then it might be useful to make sure that rhs is sequentially stored
+ // FIXME not very good if lhs is real and rhs complex while alpha is real too
+ const Index rows = dst.rows();
+ for (Index i=0; i<rows; ++i)
+ func(dst.row(i), lhsEval.coeff(i,Index(0)) * actual_rhs);
+}
+
+template<typename Lhs, typename Rhs>
+struct generic_product_impl<Lhs,Rhs,DenseShape,DenseShape,OuterProduct>
+{
+ template<typename T> struct is_row_major : std::conditional_t<(int(T::Flags)&RowMajorBit), internal::true_type, internal::false_type> {};
+ typedef typename Product<Lhs,Rhs>::Scalar Scalar;
+
+ // TODO it would be nice to be able to exploit our *_assign_op functors for that purpose
+ struct set { template<typename Dst, typename Src> EIGEN_DEVICE_FUNC void operator()(const Dst& dst, const Src& src) const { dst.const_cast_derived() = src; } };
+ struct add { template<typename Dst, typename Src> EIGEN_DEVICE_FUNC void operator()(const Dst& dst, const Src& src) const { dst.const_cast_derived() += src; } };
+ struct sub { template<typename Dst, typename Src> EIGEN_DEVICE_FUNC void operator()(const Dst& dst, const Src& src) const { dst.const_cast_derived() -= src; } };
+ struct adds {
+ Scalar m_scale;
+ explicit adds(const Scalar& s) : m_scale(s) {}
+ template<typename Dst, typename Src> void EIGEN_DEVICE_FUNC operator()(const Dst& dst, const Src& src) const {
+ dst.const_cast_derived() += m_scale * src;
+ }
+ };
+
+ template<typename Dst>
+ static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void evalTo(Dst& dst, const Lhs& lhs, const Rhs& rhs)
+ {
+ internal::outer_product_selector_run(dst, lhs, rhs, set(), is_row_major<Dst>());
+ }
+
+ template<typename Dst>
+ static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void addTo(Dst& dst, const Lhs& lhs, const Rhs& rhs)
+ {
+ internal::outer_product_selector_run(dst, lhs, rhs, add(), is_row_major<Dst>());
+ }
+
+ template<typename Dst>
+ static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void subTo(Dst& dst, const Lhs& lhs, const Rhs& rhs)
+ {
+ internal::outer_product_selector_run(dst, lhs, rhs, sub(), is_row_major<Dst>());
+ }
+
+ template<typename Dst>
+ static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void scaleAndAddTo(Dst& dst, const Lhs& lhs, const Rhs& rhs, const Scalar& alpha)
+ {
+ internal::outer_product_selector_run(dst, lhs, rhs, adds(alpha), is_row_major<Dst>());
+ }
+
+};
+
+
+// This base class provides default implementations for evalTo, addTo, subTo, in terms of scaleAndAddTo
+template<typename Lhs, typename Rhs, typename Derived>
+struct generic_product_impl_base
+{
+ typedef typename Product<Lhs,Rhs>::Scalar Scalar;
+
+ template<typename Dst>
+ static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void evalTo(Dst& dst, const Lhs& lhs, const Rhs& rhs)
+ { dst.setZero(); scaleAndAddTo(dst, lhs, rhs, Scalar(1)); }
+
+ template<typename Dst>
+ static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void addTo(Dst& dst, const Lhs& lhs, const Rhs& rhs)
+ { scaleAndAddTo(dst,lhs, rhs, Scalar(1)); }
+
+ template<typename Dst>
+ static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void subTo(Dst& dst, const Lhs& lhs, const Rhs& rhs)
+ { scaleAndAddTo(dst, lhs, rhs, Scalar(-1)); }
+
+ template<typename Dst>
+ static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void scaleAndAddTo(Dst& dst, const Lhs& lhs, const Rhs& rhs, const Scalar& alpha)
+ { Derived::scaleAndAddTo(dst,lhs,rhs,alpha); }
+
+};
+
+template<typename Lhs, typename Rhs>
+struct generic_product_impl<Lhs,Rhs,DenseShape,DenseShape,GemvProduct>
+ : generic_product_impl_base<Lhs,Rhs,generic_product_impl<Lhs,Rhs,DenseShape,DenseShape,GemvProduct> >
+{
+ typedef typename nested_eval<Lhs,1>::type LhsNested;
+ typedef typename nested_eval<Rhs,1>::type RhsNested;
+ typedef typename Product<Lhs,Rhs>::Scalar Scalar;
+ enum { Side = Lhs::IsVectorAtCompileTime ? OnTheLeft : OnTheRight };
+ typedef internal::remove_all_t<std::conditional_t<int(Side)==OnTheRight,LhsNested,RhsNested>> MatrixType;
+
+ template<typename Dest>
+ static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void scaleAndAddTo(Dest& dst, const Lhs& lhs, const Rhs& rhs, const Scalar& alpha)
+ {
+ // Fallback to inner product if both the lhs and rhs is a runtime vector.
+ if (lhs.rows() == 1 && rhs.cols() == 1) {
+ dst.coeffRef(0,0) += alpha * lhs.row(0).conjugate().dot(rhs.col(0));
+ return;
+ }
+ LhsNested actual_lhs(lhs);
+ RhsNested actual_rhs(rhs);
+ internal::gemv_dense_selector<Side,
+ (int(MatrixType::Flags)&RowMajorBit) ? RowMajor : ColMajor,
+ bool(internal::blas_traits<MatrixType>::HasUsableDirectAccess)
+ >::run(actual_lhs, actual_rhs, dst, alpha);
+ }
+};
+
+template<typename Lhs, typename Rhs>
+struct generic_product_impl<Lhs,Rhs,DenseShape,DenseShape,CoeffBasedProductMode>
+{
+ typedef typename Product<Lhs,Rhs>::Scalar Scalar;
+
+ template<typename Dst>
+ static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void evalTo(Dst& dst, const Lhs& lhs, const Rhs& rhs)
+ {
+ // Same as: dst.noalias() = lhs.lazyProduct(rhs);
+ // but easier on the compiler side
+ call_assignment_no_alias(dst, lhs.lazyProduct(rhs), internal::assign_op<typename Dst::Scalar,Scalar>());
+ }
+
+ template<typename Dst>
+ static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void addTo(Dst& dst, const Lhs& lhs, const Rhs& rhs)
+ {
+ // dst.noalias() += lhs.lazyProduct(rhs);
+ call_assignment_no_alias(dst, lhs.lazyProduct(rhs), internal::add_assign_op<typename Dst::Scalar,Scalar>());
+ }
+
+ template<typename Dst>
+ static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void subTo(Dst& dst, const Lhs& lhs, const Rhs& rhs)
+ {
+ // dst.noalias() -= lhs.lazyProduct(rhs);
+ call_assignment_no_alias(dst, lhs.lazyProduct(rhs), internal::sub_assign_op<typename Dst::Scalar,Scalar>());
+ }
+
+ // This is a special evaluation path called from generic_product_impl<...,GemmProduct> in file GeneralMatrixMatrix.h
+ // This variant tries to extract scalar multiples from both the LHS and RHS and factor them out. For instance:
+ // dst {,+,-}= (s1*A)*(B*s2)
+ // will be rewritten as:
+ // dst {,+,-}= (s1*s2) * (A.lazyProduct(B))
+ // There are at least four benefits of doing so:
+ // 1 - huge performance gain for heap-allocated matrix types as it save costly allocations.
+ // 2 - it is faster than simply by-passing the heap allocation through stack allocation.
+ // 3 - it makes this fallback consistent with the heavy GEMM routine.
+ // 4 - it fully by-passes huge stack allocation attempts when multiplying huge fixed-size matrices.
+ // (see https://stackoverflow.com/questions/54738495)
+ // For small fixed sizes matrices, however, the gains are less obvious, it is sometimes x2 faster, but sometimes x3 slower,
+ // and the behavior depends also a lot on the compiler... This is why this re-writing strategy is currently
+ // enabled only when falling back from the main GEMM.
+ template<typename Dst, typename Func>
+ static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ void eval_dynamic(Dst& dst, const Lhs& lhs, const Rhs& rhs, const Func &func)
+ {
+ enum {
+ HasScalarFactor = blas_traits<Lhs>::HasScalarFactor || blas_traits<Rhs>::HasScalarFactor,
+ ConjLhs = blas_traits<Lhs>::NeedToConjugate,
+ ConjRhs = blas_traits<Rhs>::NeedToConjugate
+ };
+ // FIXME: in c++11 this should be auto, and extractScalarFactor should also return auto
+ // this is important for real*complex_mat
+ Scalar actualAlpha = combine_scalar_factors<Scalar>(lhs, rhs);
+
+ eval_dynamic_impl(dst,
+ blas_traits<Lhs>::extract(lhs).template conjugateIf<ConjLhs>(),
+ blas_traits<Rhs>::extract(rhs).template conjugateIf<ConjRhs>(),
+ func,
+ actualAlpha,
+ std::conditional_t<HasScalarFactor,true_type,false_type>());
+ }
+
+protected:
+
+ template<typename Dst, typename LhsT, typename RhsT, typename Func, typename Scalar>
+ static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ void eval_dynamic_impl(Dst& dst, const LhsT& lhs, const RhsT& rhs, const Func &func, const Scalar& s /* == 1 */, false_type)
+ {
+ EIGEN_UNUSED_VARIABLE(s);
+ eigen_internal_assert(numext::is_exactly_one(s));
+ call_restricted_packet_assignment_no_alias(dst, lhs.lazyProduct(rhs), func);
+ }
+
+ template<typename Dst, typename LhsT, typename RhsT, typename Func, typename Scalar>
+ static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ void eval_dynamic_impl(Dst& dst, const LhsT& lhs, const RhsT& rhs, const Func &func, const Scalar& s, true_type)
+ {
+ call_restricted_packet_assignment_no_alias(dst, s * lhs.lazyProduct(rhs), func);
+ }
+};
+
+// This specialization enforces the use of a coefficient-based evaluation strategy
+template<typename Lhs, typename Rhs>
+struct generic_product_impl<Lhs,Rhs,DenseShape,DenseShape,LazyCoeffBasedProductMode>
+ : generic_product_impl<Lhs,Rhs,DenseShape,DenseShape,CoeffBasedProductMode> {};
+
+// Case 2: Evaluate coeff by coeff
+//
+// This is mostly taken from CoeffBasedProduct.h
+// The main difference is that we add an extra argument to the etor_product_*_impl::run() function
+// for the inner dimension of the product, because evaluator object do not know their size.
+
+template<int Traversal, int UnrollingIndex, typename Lhs, typename Rhs, typename RetScalar>
+struct etor_product_coeff_impl;
+
+template<int StorageOrder, int UnrollingIndex, typename Lhs, typename Rhs, typename Packet, int LoadMode>
+struct etor_product_packet_impl;
+
+template<typename Lhs, typename Rhs, int ProductTag>
+struct product_evaluator<Product<Lhs, Rhs, LazyProduct>, ProductTag, DenseShape, DenseShape>
+ : evaluator_base<Product<Lhs, Rhs, LazyProduct> >
+{
+ typedef Product<Lhs, Rhs, LazyProduct> XprType;
+ typedef typename XprType::Scalar Scalar;
+ typedef typename XprType::CoeffReturnType CoeffReturnType;
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ explicit product_evaluator(const XprType& xpr)
+ : m_lhs(xpr.lhs()),
+ m_rhs(xpr.rhs()),
+ m_lhsImpl(m_lhs), // FIXME the creation of the evaluator objects should result in a no-op, but check that!
+ m_rhsImpl(m_rhs), // Moreover, they are only useful for the packet path, so we could completely disable them when not needed,
+ // or perhaps declare them on the fly on the packet method... We have experiment to check what's best.
+ m_innerDim(xpr.lhs().cols())
+ {
+ EIGEN_INTERNAL_CHECK_COST_VALUE(NumTraits<Scalar>::MulCost);
+ EIGEN_INTERNAL_CHECK_COST_VALUE(NumTraits<Scalar>::AddCost);
+ EIGEN_INTERNAL_CHECK_COST_VALUE(CoeffReadCost);
+#if 0
+ std::cerr << "LhsOuterStrideBytes= " << LhsOuterStrideBytes << "\n";
+ std::cerr << "RhsOuterStrideBytes= " << RhsOuterStrideBytes << "\n";
+ std::cerr << "LhsAlignment= " << LhsAlignment << "\n";
+ std::cerr << "RhsAlignment= " << RhsAlignment << "\n";
+ std::cerr << "CanVectorizeLhs= " << CanVectorizeLhs << "\n";
+ std::cerr << "CanVectorizeRhs= " << CanVectorizeRhs << "\n";
+ std::cerr << "CanVectorizeInner= " << CanVectorizeInner << "\n";
+ std::cerr << "EvalToRowMajor= " << EvalToRowMajor << "\n";
+ std::cerr << "Alignment= " << Alignment << "\n";
+ std::cerr << "Flags= " << Flags << "\n";
+#endif
+ }
+
+ // Everything below here is taken from CoeffBasedProduct.h
+
+ typedef typename internal::nested_eval<Lhs,Rhs::ColsAtCompileTime>::type LhsNested;
+ typedef typename internal::nested_eval<Rhs,Lhs::RowsAtCompileTime>::type RhsNested;
+
+ typedef internal::remove_all_t<LhsNested> LhsNestedCleaned;
+ typedef internal::remove_all_t<RhsNested> RhsNestedCleaned;
+
+ typedef evaluator<LhsNestedCleaned> LhsEtorType;
+ typedef evaluator<RhsNestedCleaned> RhsEtorType;
+
+ enum {
+ RowsAtCompileTime = LhsNestedCleaned::RowsAtCompileTime,
+ ColsAtCompileTime = RhsNestedCleaned::ColsAtCompileTime,
+ InnerSize = min_size_prefer_fixed(LhsNestedCleaned::ColsAtCompileTime, RhsNestedCleaned::RowsAtCompileTime),
+ MaxRowsAtCompileTime = LhsNestedCleaned::MaxRowsAtCompileTime,
+ MaxColsAtCompileTime = RhsNestedCleaned::MaxColsAtCompileTime
+ };
+
+ typedef typename find_best_packet<Scalar,RowsAtCompileTime>::type LhsVecPacketType;
+ typedef typename find_best_packet<Scalar,ColsAtCompileTime>::type RhsVecPacketType;
+
+ enum {
+
+ LhsCoeffReadCost = LhsEtorType::CoeffReadCost,
+ RhsCoeffReadCost = RhsEtorType::CoeffReadCost,
+ CoeffReadCost = InnerSize==0 ? NumTraits<Scalar>::ReadCost
+ : InnerSize == Dynamic ? HugeCost
+ : InnerSize * (NumTraits<Scalar>::MulCost + int(LhsCoeffReadCost) + int(RhsCoeffReadCost))
+ + (InnerSize - 1) * NumTraits<Scalar>::AddCost,
+
+ Unroll = CoeffReadCost <= EIGEN_UNROLLING_LIMIT,
+
+ LhsFlags = LhsEtorType::Flags,
+ RhsFlags = RhsEtorType::Flags,
+
+ LhsRowMajor = LhsFlags & RowMajorBit,
+ RhsRowMajor = RhsFlags & RowMajorBit,
+
+ LhsVecPacketSize = unpacket_traits<LhsVecPacketType>::size,
+ RhsVecPacketSize = unpacket_traits<RhsVecPacketType>::size,
+
+ // Here, we don't care about alignment larger than the usable packet size.
+ LhsAlignment = plain_enum_min(LhsEtorType::Alignment, LhsVecPacketSize*int(sizeof(typename LhsNestedCleaned::Scalar))),
+ RhsAlignment = plain_enum_min(RhsEtorType::Alignment, RhsVecPacketSize*int(sizeof(typename RhsNestedCleaned::Scalar))),
+
+ SameType = is_same<typename LhsNestedCleaned::Scalar,typename RhsNestedCleaned::Scalar>::value,
+
+ CanVectorizeRhs = bool(RhsRowMajor) && (RhsFlags & PacketAccessBit) && (ColsAtCompileTime!=1),
+ CanVectorizeLhs = (!LhsRowMajor) && (LhsFlags & PacketAccessBit) && (RowsAtCompileTime!=1),
+
+ EvalToRowMajor = (MaxRowsAtCompileTime==1&&MaxColsAtCompileTime!=1) ? 1
+ : (MaxColsAtCompileTime==1&&MaxRowsAtCompileTime!=1) ? 0
+ : (bool(RhsRowMajor) && !CanVectorizeLhs),
+
+ Flags = ((int(LhsFlags) | int(RhsFlags)) & HereditaryBits & ~RowMajorBit)
+ | (EvalToRowMajor ? RowMajorBit : 0)
+ // TODO enable vectorization for mixed types
+ | (SameType && (CanVectorizeLhs || CanVectorizeRhs) ? PacketAccessBit : 0)
+ | (XprType::IsVectorAtCompileTime ? LinearAccessBit : 0),
+
+ LhsOuterStrideBytes = int(LhsNestedCleaned::OuterStrideAtCompileTime) * int(sizeof(typename LhsNestedCleaned::Scalar)),
+ RhsOuterStrideBytes = int(RhsNestedCleaned::OuterStrideAtCompileTime) * int(sizeof(typename RhsNestedCleaned::Scalar)),
+
+ Alignment = bool(CanVectorizeLhs) ? (LhsOuterStrideBytes<=0 || (int(LhsOuterStrideBytes) % plain_enum_max(1, LhsAlignment))!=0 ? 0 : LhsAlignment)
+ : bool(CanVectorizeRhs) ? (RhsOuterStrideBytes<=0 || (int(RhsOuterStrideBytes) % plain_enum_max(1, RhsAlignment))!=0 ? 0 : RhsAlignment)
+ : 0,
+
+ /* CanVectorizeInner deserves special explanation. It does not affect the product flags. It is not used outside
+ * of Product. If the Product itself is not a packet-access expression, there is still a chance that the inner
+ * loop of the product might be vectorized. This is the meaning of CanVectorizeInner. Since it doesn't affect
+ * the Flags, it is safe to make this value depend on ActualPacketAccessBit, that doesn't affect the ABI.
+ */
+ CanVectorizeInner = SameType
+ && LhsRowMajor
+ && (!RhsRowMajor)
+ && (int(LhsFlags) & int(RhsFlags) & ActualPacketAccessBit)
+ && (int(InnerSize) % packet_traits<Scalar>::size == 0)
+ };
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const CoeffReturnType coeff(Index row, Index col) const
+ {
+ return (m_lhs.row(row).transpose().cwiseProduct( m_rhs.col(col) )).sum();
+ }
+
+ /* Allow index-based non-packet access. It is impossible though to allow index-based packed access,
+ * which is why we don't set the LinearAccessBit.
+ * TODO: this seems possible when the result is a vector
+ */
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ const CoeffReturnType coeff(Index index) const
+ {
+ const Index row = (RowsAtCompileTime == 1 || MaxRowsAtCompileTime==1) ? 0 : index;
+ const Index col = (RowsAtCompileTime == 1 || MaxRowsAtCompileTime==1) ? index : 0;
+ return (m_lhs.row(row).transpose().cwiseProduct( m_rhs.col(col) )).sum();
+ }
+
+ template<int LoadMode, typename PacketType>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ const PacketType packet(Index row, Index col) const
+ {
+ PacketType res;
+ typedef etor_product_packet_impl<bool(int(Flags)&RowMajorBit) ? RowMajor : ColMajor,
+ Unroll ? int(InnerSize) : Dynamic,
+ LhsEtorType, RhsEtorType, PacketType, LoadMode> PacketImpl;
+ PacketImpl::run(row, col, m_lhsImpl, m_rhsImpl, m_innerDim, res);
+ return res;
+ }
+
+ template<int LoadMode, typename PacketType>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ const PacketType packet(Index index) const
+ {
+ const Index row = (RowsAtCompileTime == 1 || MaxRowsAtCompileTime==1) ? 0 : index;
+ const Index col = (RowsAtCompileTime == 1 || MaxRowsAtCompileTime==1) ? index : 0;
+ return packet<LoadMode,PacketType>(row,col);
+ }
+
+protected:
+ add_const_on_value_type_t<LhsNested> m_lhs;
+ add_const_on_value_type_t<RhsNested> m_rhs;
+
+ LhsEtorType m_lhsImpl;
+ RhsEtorType m_rhsImpl;
+
+ // TODO: Get rid of m_innerDim if known at compile time
+ Index m_innerDim;
+};
+
+template<typename Lhs, typename Rhs>
+struct product_evaluator<Product<Lhs, Rhs, DefaultProduct>, LazyCoeffBasedProductMode, DenseShape, DenseShape>
+ : product_evaluator<Product<Lhs, Rhs, LazyProduct>, CoeffBasedProductMode, DenseShape, DenseShape>
+{
+ typedef Product<Lhs, Rhs, DefaultProduct> XprType;
+ typedef Product<Lhs, Rhs, LazyProduct> BaseProduct;
+ typedef product_evaluator<BaseProduct, CoeffBasedProductMode, DenseShape, DenseShape> Base;
+ enum {
+ Flags = Base::Flags | EvalBeforeNestingBit
+ };
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ explicit product_evaluator(const XprType& xpr)
+ : Base(BaseProduct(xpr.lhs(),xpr.rhs()))
+ {}
+};
+
+/****************************************
+*** Coeff based product, Packet path ***
+****************************************/
+
+template<int UnrollingIndex, typename Lhs, typename Rhs, typename Packet, int LoadMode>
+struct etor_product_packet_impl<RowMajor, UnrollingIndex, Lhs, Rhs, Packet, LoadMode>
+{
+ static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void run(Index row, Index col, const Lhs& lhs, const Rhs& rhs, Index innerDim, Packet &res)
+ {
+ etor_product_packet_impl<RowMajor, UnrollingIndex-1, Lhs, Rhs, Packet, LoadMode>::run(row, col, lhs, rhs, innerDim, res);
+ res = pmadd(pset1<Packet>(lhs.coeff(row, Index(UnrollingIndex-1))), rhs.template packet<LoadMode,Packet>(Index(UnrollingIndex-1), col), res);
+ }
+};
+
+template<int UnrollingIndex, typename Lhs, typename Rhs, typename Packet, int LoadMode>
+struct etor_product_packet_impl<ColMajor, UnrollingIndex, Lhs, Rhs, Packet, LoadMode>
+{
+ static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void run(Index row, Index col, const Lhs& lhs, const Rhs& rhs, Index innerDim, Packet &res)
+ {
+ etor_product_packet_impl<ColMajor, UnrollingIndex-1, Lhs, Rhs, Packet, LoadMode>::run(row, col, lhs, rhs, innerDim, res);
+ res = pmadd(lhs.template packet<LoadMode,Packet>(row, Index(UnrollingIndex-1)), pset1<Packet>(rhs.coeff(Index(UnrollingIndex-1), col)), res);
+ }
+};
+
+template<typename Lhs, typename Rhs, typename Packet, int LoadMode>
+struct etor_product_packet_impl<RowMajor, 1, Lhs, Rhs, Packet, LoadMode>
+{
+ static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void run(Index row, Index col, const Lhs& lhs, const Rhs& rhs, Index /*innerDim*/, Packet &res)
+ {
+ res = pmul(pset1<Packet>(lhs.coeff(row, Index(0))),rhs.template packet<LoadMode,Packet>(Index(0), col));
+ }
+};
+
+template<typename Lhs, typename Rhs, typename Packet, int LoadMode>
+struct etor_product_packet_impl<ColMajor, 1, Lhs, Rhs, Packet, LoadMode>
+{
+ static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void run(Index row, Index col, const Lhs& lhs, const Rhs& rhs, Index /*innerDim*/, Packet &res)
+ {
+ res = pmul(lhs.template packet<LoadMode,Packet>(row, Index(0)), pset1<Packet>(rhs.coeff(Index(0), col)));
+ }
+};
+
+template<typename Lhs, typename Rhs, typename Packet, int LoadMode>
+struct etor_product_packet_impl<RowMajor, 0, Lhs, Rhs, Packet, LoadMode>
+{
+ static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void run(Index /*row*/, Index /*col*/, const Lhs& /*lhs*/, const Rhs& /*rhs*/, Index /*innerDim*/, Packet &res)
+ {
+ res = pset1<Packet>(typename unpacket_traits<Packet>::type(0));
+ }
+};
+
+template<typename Lhs, typename Rhs, typename Packet, int LoadMode>
+struct etor_product_packet_impl<ColMajor, 0, Lhs, Rhs, Packet, LoadMode>
+{
+ static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void run(Index /*row*/, Index /*col*/, const Lhs& /*lhs*/, const Rhs& /*rhs*/, Index /*innerDim*/, Packet &res)
+ {
+ res = pset1<Packet>(typename unpacket_traits<Packet>::type(0));
+ }
+};
+
+template<typename Lhs, typename Rhs, typename Packet, int LoadMode>
+struct etor_product_packet_impl<RowMajor, Dynamic, Lhs, Rhs, Packet, LoadMode>
+{
+ static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void run(Index row, Index col, const Lhs& lhs, const Rhs& rhs, Index innerDim, Packet& res)
+ {
+ res = pset1<Packet>(typename unpacket_traits<Packet>::type(0));
+ for(Index i = 0; i < innerDim; ++i)
+ res = pmadd(pset1<Packet>(lhs.coeff(row, i)), rhs.template packet<LoadMode,Packet>(i, col), res);
+ }
+};
+
+template<typename Lhs, typename Rhs, typename Packet, int LoadMode>
+struct etor_product_packet_impl<ColMajor, Dynamic, Lhs, Rhs, Packet, LoadMode>
+{
+ static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void run(Index row, Index col, const Lhs& lhs, const Rhs& rhs, Index innerDim, Packet& res)
+ {
+ res = pset1<Packet>(typename unpacket_traits<Packet>::type(0));
+ for(Index i = 0; i < innerDim; ++i)
+ res = pmadd(lhs.template packet<LoadMode,Packet>(row, i), pset1<Packet>(rhs.coeff(i, col)), res);
+ }
+};
+
+
+/***************************************************************************
+* Triangular products
+***************************************************************************/
+template<int Mode, bool LhsIsTriangular,
+ typename Lhs, bool LhsIsVector,
+ typename Rhs, bool RhsIsVector>
+struct triangular_product_impl;
+
+template<typename Lhs, typename Rhs, int ProductTag>
+struct generic_product_impl<Lhs,Rhs,TriangularShape,DenseShape,ProductTag>
+ : generic_product_impl_base<Lhs,Rhs,generic_product_impl<Lhs,Rhs,TriangularShape,DenseShape,ProductTag> >
+{
+ typedef typename Product<Lhs,Rhs>::Scalar Scalar;
+
+ template<typename Dest>
+ static void scaleAndAddTo(Dest& dst, const Lhs& lhs, const Rhs& rhs, const Scalar& alpha)
+ {
+ triangular_product_impl<Lhs::Mode,true,typename Lhs::MatrixType,false,Rhs, Rhs::ColsAtCompileTime==1>
+ ::run(dst, lhs.nestedExpression(), rhs, alpha);
+ }
+};
+
+template<typename Lhs, typename Rhs, int ProductTag>
+struct generic_product_impl<Lhs,Rhs,DenseShape,TriangularShape,ProductTag>
+: generic_product_impl_base<Lhs,Rhs,generic_product_impl<Lhs,Rhs,DenseShape,TriangularShape,ProductTag> >
+{
+ typedef typename Product<Lhs,Rhs>::Scalar Scalar;
+
+ template<typename Dest>
+ static void scaleAndAddTo(Dest& dst, const Lhs& lhs, const Rhs& rhs, const Scalar& alpha)
+ {
+ triangular_product_impl<Rhs::Mode,false,Lhs,Lhs::RowsAtCompileTime==1, typename Rhs::MatrixType, false>::run(dst, lhs, rhs.nestedExpression(), alpha);
+ }
+};
+
+
+/***************************************************************************
+* SelfAdjoint products
+***************************************************************************/
+template <typename Lhs, int LhsMode, bool LhsIsVector,
+ typename Rhs, int RhsMode, bool RhsIsVector>
+struct selfadjoint_product_impl;
+
+template<typename Lhs, typename Rhs, int ProductTag>
+struct generic_product_impl<Lhs,Rhs,SelfAdjointShape,DenseShape,ProductTag>
+ : generic_product_impl_base<Lhs,Rhs,generic_product_impl<Lhs,Rhs,SelfAdjointShape,DenseShape,ProductTag> >
+{
+ typedef typename Product<Lhs,Rhs>::Scalar Scalar;
+
+ template<typename Dest>
+ static EIGEN_DEVICE_FUNC
+ void scaleAndAddTo(Dest& dst, const Lhs& lhs, const Rhs& rhs, const Scalar& alpha)
+ {
+ selfadjoint_product_impl<typename Lhs::MatrixType,Lhs::Mode,false,Rhs,0,Rhs::IsVectorAtCompileTime>::run(dst, lhs.nestedExpression(), rhs, alpha);
+ }
+};
+
+template<typename Lhs, typename Rhs, int ProductTag>
+struct generic_product_impl<Lhs,Rhs,DenseShape,SelfAdjointShape,ProductTag>
+: generic_product_impl_base<Lhs,Rhs,generic_product_impl<Lhs,Rhs,DenseShape,SelfAdjointShape,ProductTag> >
+{
+ typedef typename Product<Lhs,Rhs>::Scalar Scalar;
+
+ template<typename Dest>
+ static void scaleAndAddTo(Dest& dst, const Lhs& lhs, const Rhs& rhs, const Scalar& alpha)
+ {
+ selfadjoint_product_impl<Lhs,0,Lhs::IsVectorAtCompileTime,typename Rhs::MatrixType,Rhs::Mode,false>::run(dst, lhs, rhs.nestedExpression(), alpha);
+ }
+};
+
+
+/***************************************************************************
+* Diagonal products
+***************************************************************************/
+
+template<typename MatrixType, typename DiagonalType, typename Derived, int ProductOrder>
+struct diagonal_product_evaluator_base
+ : evaluator_base<Derived>
+{
+ typedef typename ScalarBinaryOpTraits<typename MatrixType::Scalar, typename DiagonalType::Scalar>::ReturnType Scalar;
+public:
+ enum {
+ CoeffReadCost = int(NumTraits<Scalar>::MulCost) + int(evaluator<MatrixType>::CoeffReadCost) + int(evaluator<DiagonalType>::CoeffReadCost),
+
+ MatrixFlags = evaluator<MatrixType>::Flags,
+ DiagFlags = evaluator<DiagonalType>::Flags,
+
+ StorageOrder_ = (Derived::MaxRowsAtCompileTime==1 && Derived::MaxColsAtCompileTime!=1) ? RowMajor
+ : (Derived::MaxColsAtCompileTime==1 && Derived::MaxRowsAtCompileTime!=1) ? ColMajor
+ : MatrixFlags & RowMajorBit ? RowMajor : ColMajor,
+ SameStorageOrder_ = StorageOrder_ == (MatrixFlags & RowMajorBit ? RowMajor : ColMajor),
+
+ ScalarAccessOnDiag_ = !((int(StorageOrder_) == ColMajor && int(ProductOrder) == OnTheLeft)
+ ||(int(StorageOrder_) == RowMajor && int(ProductOrder) == OnTheRight)),
+ SameTypes_ = is_same<typename MatrixType::Scalar, typename DiagonalType::Scalar>::value,
+ // FIXME currently we need same types, but in the future the next rule should be the one
+ //Vectorizable_ = bool(int(MatrixFlags)&PacketAccessBit) && ((!_PacketOnDiag) || (SameTypes_ && bool(int(DiagFlags)&PacketAccessBit))),
+ Vectorizable_ = bool(int(MatrixFlags)&PacketAccessBit)
+ && SameTypes_
+ && (SameStorageOrder_ || (MatrixFlags&LinearAccessBit)==LinearAccessBit)
+ && (ScalarAccessOnDiag_ || (bool(int(DiagFlags)&PacketAccessBit))),
+ LinearAccessMask_ = (MatrixType::RowsAtCompileTime==1 || MatrixType::ColsAtCompileTime==1) ? LinearAccessBit : 0,
+ Flags = ((HereditaryBits|LinearAccessMask_) & (unsigned int)(MatrixFlags)) | (Vectorizable_ ? PacketAccessBit : 0),
+ Alignment = evaluator<MatrixType>::Alignment,
+
+ AsScalarProduct = (DiagonalType::SizeAtCompileTime==1)
+ || (DiagonalType::SizeAtCompileTime==Dynamic && MatrixType::RowsAtCompileTime==1 && ProductOrder==OnTheLeft)
+ || (DiagonalType::SizeAtCompileTime==Dynamic && MatrixType::ColsAtCompileTime==1 && ProductOrder==OnTheRight)
+ };
+
+ EIGEN_DEVICE_FUNC diagonal_product_evaluator_base(const MatrixType &mat, const DiagonalType &diag)
+ : m_diagImpl(diag), m_matImpl(mat)
+ {
+ EIGEN_INTERNAL_CHECK_COST_VALUE(NumTraits<Scalar>::MulCost);
+ EIGEN_INTERNAL_CHECK_COST_VALUE(CoeffReadCost);
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar coeff(Index idx) const
+ {
+ if(AsScalarProduct)
+ return m_diagImpl.coeff(0) * m_matImpl.coeff(idx);
+ else
+ return m_diagImpl.coeff(idx) * m_matImpl.coeff(idx);
+ }
+
+protected:
+ template<int LoadMode,typename PacketType>
+ EIGEN_STRONG_INLINE PacketType packet_impl(Index row, Index col, Index id, internal::true_type) const
+ {
+ return internal::pmul(m_matImpl.template packet<LoadMode,PacketType>(row, col),
+ internal::pset1<PacketType>(m_diagImpl.coeff(id)));
+ }
+
+ template<int LoadMode,typename PacketType>
+ EIGEN_STRONG_INLINE PacketType packet_impl(Index row, Index col, Index id, internal::false_type) const
+ {
+ enum {
+ InnerSize = (MatrixType::Flags & RowMajorBit) ? MatrixType::ColsAtCompileTime : MatrixType::RowsAtCompileTime,
+ DiagonalPacketLoadMode = plain_enum_min(LoadMode,((InnerSize%16) == 0) ? int(Aligned16) : int(evaluator<DiagonalType>::Alignment)) // FIXME hardcoded 16!!
+ };
+ return internal::pmul(m_matImpl.template packet<LoadMode,PacketType>(row, col),
+ m_diagImpl.template packet<DiagonalPacketLoadMode,PacketType>(id));
+ }
+
+ evaluator<DiagonalType> m_diagImpl;
+ evaluator<MatrixType> m_matImpl;
+};
+
+// diagonal * dense
+template<typename Lhs, typename Rhs, int ProductKind, int ProductTag>
+struct product_evaluator<Product<Lhs, Rhs, ProductKind>, ProductTag, DiagonalShape, DenseShape>
+ : diagonal_product_evaluator_base<Rhs, typename Lhs::DiagonalVectorType, Product<Lhs, Rhs, LazyProduct>, OnTheLeft>
+{
+ typedef diagonal_product_evaluator_base<Rhs, typename Lhs::DiagonalVectorType, Product<Lhs, Rhs, LazyProduct>, OnTheLeft> Base;
+ using Base::m_diagImpl;
+ using Base::m_matImpl;
+ using Base::coeff;
+ typedef typename Base::Scalar Scalar;
+
+ typedef Product<Lhs, Rhs, ProductKind> XprType;
+ typedef typename XprType::PlainObject PlainObject;
+ typedef typename Lhs::DiagonalVectorType DiagonalType;
+
+
+ enum { StorageOrder = Base::StorageOrder_ };
+
+ EIGEN_DEVICE_FUNC explicit product_evaluator(const XprType& xpr)
+ : Base(xpr.rhs(), xpr.lhs().diagonal())
+ {
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar coeff(Index row, Index col) const
+ {
+ return m_diagImpl.coeff(row) * m_matImpl.coeff(row, col);
+ }
+
+#ifndef EIGEN_GPUCC
+ template<int LoadMode,typename PacketType>
+ EIGEN_STRONG_INLINE PacketType packet(Index row, Index col) const
+ {
+ // FIXME: NVCC used to complain about the template keyword, but we have to check whether this is still the case.
+ // See also similar calls below.
+ return this->template packet_impl<LoadMode,PacketType>(row,col, row,
+ std::conditional_t<int(StorageOrder)==RowMajor, internal::true_type, internal::false_type>());
+ }
+
+ template<int LoadMode,typename PacketType>
+ EIGEN_STRONG_INLINE PacketType packet(Index idx) const
+ {
+ return packet<LoadMode,PacketType>(int(StorageOrder)==ColMajor?idx:0,int(StorageOrder)==ColMajor?0:idx);
+ }
+#endif
+};
+
+// dense * diagonal
+template<typename Lhs, typename Rhs, int ProductKind, int ProductTag>
+struct product_evaluator<Product<Lhs, Rhs, ProductKind>, ProductTag, DenseShape, DiagonalShape>
+ : diagonal_product_evaluator_base<Lhs, typename Rhs::DiagonalVectorType, Product<Lhs, Rhs, LazyProduct>, OnTheRight>
+{
+ typedef diagonal_product_evaluator_base<Lhs, typename Rhs::DiagonalVectorType, Product<Lhs, Rhs, LazyProduct>, OnTheRight> Base;
+ using Base::m_diagImpl;
+ using Base::m_matImpl;
+ using Base::coeff;
+ typedef typename Base::Scalar Scalar;
+
+ typedef Product<Lhs, Rhs, ProductKind> XprType;
+ typedef typename XprType::PlainObject PlainObject;
+
+ enum { StorageOrder = Base::StorageOrder_ };
+
+ EIGEN_DEVICE_FUNC explicit product_evaluator(const XprType& xpr)
+ : Base(xpr.lhs(), xpr.rhs().diagonal())
+ {
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar coeff(Index row, Index col) const
+ {
+ return m_matImpl.coeff(row, col) * m_diagImpl.coeff(col);
+ }
+
+#ifndef EIGEN_GPUCC
+ template<int LoadMode,typename PacketType>
+ EIGEN_STRONG_INLINE PacketType packet(Index row, Index col) const
+ {
+ return this->template packet_impl<LoadMode,PacketType>(row,col, col,
+ std::conditional_t<int(StorageOrder)==ColMajor, internal::true_type, internal::false_type>());
+ }
+
+ template<int LoadMode,typename PacketType>
+ EIGEN_STRONG_INLINE PacketType packet(Index idx) const
+ {
+ return packet<LoadMode,PacketType>(int(StorageOrder)==ColMajor?idx:0,int(StorageOrder)==ColMajor?0:idx);
+ }
+#endif
+};
+
+/***************************************************************************
+* Products with permutation matrices
+***************************************************************************/
+
+/** \internal
+ * \class permutation_matrix_product
+ * Internal helper class implementing the product between a permutation matrix and a matrix.
+ * This class is specialized for DenseShape below and for SparseShape in SparseCore/SparsePermutation.h
+ */
+template<typename ExpressionType, int Side, bool Transposed, typename ExpressionShape>
+struct permutation_matrix_product;
+
+template<typename ExpressionType, int Side, bool Transposed>
+struct permutation_matrix_product<ExpressionType, Side, Transposed, DenseShape>
+{
+ typedef typename nested_eval<ExpressionType, 1>::type MatrixType;
+ typedef remove_all_t<MatrixType> MatrixTypeCleaned;
+
+ template<typename Dest, typename PermutationType>
+ static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void run(Dest& dst, const PermutationType& perm, const ExpressionType& xpr)
+ {
+ MatrixType mat(xpr);
+ const Index n = Side==OnTheLeft ? mat.rows() : mat.cols();
+ // FIXME we need an is_same for expression that is not sensitive to constness. For instance
+ // is_same_xpr<Block<const Matrix>, Block<Matrix> >::value should be true.
+ //if(is_same<MatrixTypeCleaned,Dest>::value && extract_data(dst) == extract_data(mat))
+ if(is_same_dense(dst, mat))
+ {
+ // apply the permutation inplace
+ Matrix<bool,PermutationType::RowsAtCompileTime,1,0,PermutationType::MaxRowsAtCompileTime> mask(perm.size());
+ mask.fill(false);
+ Index r = 0;
+ while(r < perm.size())
+ {
+ // search for the next seed
+ while(r<perm.size() && mask[r]) r++;
+ if(r>=perm.size())
+ break;
+ // we got one, let's follow it until we are back to the seed
+ Index k0 = r++;
+ Index kPrev = k0;
+ mask.coeffRef(k0) = true;
+ for(Index k=perm.indices().coeff(k0); k!=k0; k=perm.indices().coeff(k))
+ {
+ Block<Dest, Side==OnTheLeft ? 1 : Dest::RowsAtCompileTime, Side==OnTheRight ? 1 : Dest::ColsAtCompileTime>(dst, k)
+ .swap(Block<Dest, Side==OnTheLeft ? 1 : Dest::RowsAtCompileTime, Side==OnTheRight ? 1 : Dest::ColsAtCompileTime>
+ (dst,((Side==OnTheLeft) ^ Transposed) ? k0 : kPrev));
+
+ mask.coeffRef(k) = true;
+ kPrev = k;
+ }
+ }
+ }
+ else
+ {
+ for(Index i = 0; i < n; ++i)
+ {
+ Block<Dest, Side==OnTheLeft ? 1 : Dest::RowsAtCompileTime, Side==OnTheRight ? 1 : Dest::ColsAtCompileTime>
+ (dst, ((Side==OnTheLeft) ^ Transposed) ? perm.indices().coeff(i) : i)
+
+ =
+
+ Block<const MatrixTypeCleaned,Side==OnTheLeft ? 1 : MatrixTypeCleaned::RowsAtCompileTime,Side==OnTheRight ? 1 : MatrixTypeCleaned::ColsAtCompileTime>
+ (mat, ((Side==OnTheRight) ^ Transposed) ? perm.indices().coeff(i) : i);
+ }
+ }
+ }
+};
+
+template<typename Lhs, typename Rhs, int ProductTag, typename MatrixShape>
+struct generic_product_impl<Lhs, Rhs, PermutationShape, MatrixShape, ProductTag>
+{
+ template<typename Dest>
+ static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void evalTo(Dest& dst, const Lhs& lhs, const Rhs& rhs)
+ {
+ permutation_matrix_product<Rhs, OnTheLeft, false, MatrixShape>::run(dst, lhs, rhs);
+ }
+};
+
+template<typename Lhs, typename Rhs, int ProductTag, typename MatrixShape>
+struct generic_product_impl<Lhs, Rhs, MatrixShape, PermutationShape, ProductTag>
+{
+ template<typename Dest>
+ static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void evalTo(Dest& dst, const Lhs& lhs, const Rhs& rhs)
+ {
+ permutation_matrix_product<Lhs, OnTheRight, false, MatrixShape>::run(dst, rhs, lhs);
+ }
+};
+
+template<typename Lhs, typename Rhs, int ProductTag, typename MatrixShape>
+struct generic_product_impl<Inverse<Lhs>, Rhs, PermutationShape, MatrixShape, ProductTag>
+{
+ template<typename Dest>
+ static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void evalTo(Dest& dst, const Inverse<Lhs>& lhs, const Rhs& rhs)
+ {
+ permutation_matrix_product<Rhs, OnTheLeft, true, MatrixShape>::run(dst, lhs.nestedExpression(), rhs);
+ }
+};
+
+template<typename Lhs, typename Rhs, int ProductTag, typename MatrixShape>
+struct generic_product_impl<Lhs, Inverse<Rhs>, MatrixShape, PermutationShape, ProductTag>
+{
+ template<typename Dest>
+ static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void evalTo(Dest& dst, const Lhs& lhs, const Inverse<Rhs>& rhs)
+ {
+ permutation_matrix_product<Lhs, OnTheRight, true, MatrixShape>::run(dst, rhs.nestedExpression(), lhs);
+ }
+};
+
+
+/***************************************************************************
+* Products with transpositions matrices
+***************************************************************************/
+
+// FIXME could we unify Transpositions and Permutation into a single "shape"??
+
+/** \internal
+ * \class transposition_matrix_product
+ * Internal helper class implementing the product between a permutation matrix and a matrix.
+ */
+template<typename ExpressionType, int Side, bool Transposed, typename ExpressionShape>
+struct transposition_matrix_product
+{
+ typedef typename nested_eval<ExpressionType, 1>::type MatrixType;
+ typedef remove_all_t<MatrixType> MatrixTypeCleaned;
+
+ template<typename Dest, typename TranspositionType>
+ static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void run(Dest& dst, const TranspositionType& tr, const ExpressionType& xpr)
+ {
+ MatrixType mat(xpr);
+ typedef typename TranspositionType::StorageIndex StorageIndex;
+ const Index size = tr.size();
+ StorageIndex j = 0;
+
+ if(!is_same_dense(dst,mat))
+ dst = mat;
+
+ for(Index k=(Transposed?size-1:0) ; Transposed?k>=0:k<size ; Transposed?--k:++k)
+ if(Index(j=tr.coeff(k))!=k)
+ {
+ if(Side==OnTheLeft) dst.row(k).swap(dst.row(j));
+ else if(Side==OnTheRight) dst.col(k).swap(dst.col(j));
+ }
+ }
+};
+
+template<typename Lhs, typename Rhs, int ProductTag, typename MatrixShape>
+struct generic_product_impl<Lhs, Rhs, TranspositionsShape, MatrixShape, ProductTag>
+{
+ template<typename Dest>
+ static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void evalTo(Dest& dst, const Lhs& lhs, const Rhs& rhs)
+ {
+ transposition_matrix_product<Rhs, OnTheLeft, false, MatrixShape>::run(dst, lhs, rhs);
+ }
+};
+
+template<typename Lhs, typename Rhs, int ProductTag, typename MatrixShape>
+struct generic_product_impl<Lhs, Rhs, MatrixShape, TranspositionsShape, ProductTag>
+{
+ template<typename Dest>
+ static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void evalTo(Dest& dst, const Lhs& lhs, const Rhs& rhs)
+ {
+ transposition_matrix_product<Lhs, OnTheRight, false, MatrixShape>::run(dst, rhs, lhs);
+ }
+};
+
+
+template<typename Lhs, typename Rhs, int ProductTag, typename MatrixShape>
+struct generic_product_impl<Transpose<Lhs>, Rhs, TranspositionsShape, MatrixShape, ProductTag>
+{
+ template<typename Dest>
+ static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void evalTo(Dest& dst, const Transpose<Lhs>& lhs, const Rhs& rhs)
+ {
+ transposition_matrix_product<Rhs, OnTheLeft, true, MatrixShape>::run(dst, lhs.nestedExpression(), rhs);
+ }
+};
+
+template<typename Lhs, typename Rhs, int ProductTag, typename MatrixShape>
+struct generic_product_impl<Lhs, Transpose<Rhs>, MatrixShape, TranspositionsShape, ProductTag>
+{
+ template<typename Dest>
+ static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void evalTo(Dest& dst, const Lhs& lhs, const Transpose<Rhs>& rhs)
+ {
+ transposition_matrix_product<Lhs, OnTheRight, true, MatrixShape>::run(dst, rhs.nestedExpression(), lhs);
+ }
+};
+
+/***************************************************************************
+* skew symmetric products
+* for now we just call the generic implementation
+***************************************************************************/
+template<typename Lhs, typename Rhs, int ProductTag, typename MatrixShape>
+struct generic_product_impl<Lhs, Rhs, SkewSymmetricShape, MatrixShape, ProductTag>
+{
+ template<typename Dest>
+ static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void evalTo(Dest& dst, const Lhs& lhs, const Rhs& rhs)
+ {
+ generic_product_impl<typename Lhs::DenseMatrixType , Rhs, DenseShape, MatrixShape, ProductTag>::evalTo(dst, lhs, rhs);
+ }
+};
+
+template<typename Lhs, typename Rhs, int ProductTag, typename MatrixShape>
+struct generic_product_impl<Lhs, Rhs, MatrixShape, SkewSymmetricShape, ProductTag>
+{
+ template<typename Dest>
+ static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void evalTo(Dest& dst, const Lhs& lhs, const Rhs& rhs)
+ {
+ generic_product_impl<Lhs, typename Rhs::DenseMatrixType, MatrixShape, DenseShape, ProductTag>::evalTo(dst, lhs, rhs);
+ }
+};
+
+template<typename Lhs, typename Rhs, int ProductTag>
+struct generic_product_impl<Lhs, Rhs, SkewSymmetricShape, SkewSymmetricShape, ProductTag>
+{
+ template<typename Dest>
+ static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void evalTo(Dest& dst, const Lhs& lhs, const Rhs& rhs)
+ {
+ generic_product_impl<typename Lhs::DenseMatrixType, typename Rhs::DenseMatrixType, DenseShape, DenseShape, ProductTag>::evalTo(dst, lhs, rhs);
+ }
+};
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_PRODUCT_EVALUATORS_H
diff --git a/Eigen/src/Core/Random.h b/Eigen/src/Core/Random.h
new file mode 100644
index 0000000..fab6889
--- /dev/null
+++ b/Eigen/src/Core/Random.h
@@ -0,0 +1,219 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_RANDOM_H
+#define EIGEN_RANDOM_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+
+template<typename Scalar> struct scalar_random_op {
+ inline const Scalar operator() () const { return random<Scalar>(); }
+};
+
+template<typename Scalar>
+struct functor_traits<scalar_random_op<Scalar> >
+{ enum { Cost = 5 * NumTraits<Scalar>::MulCost, PacketAccess = false, IsRepeatable = false }; };
+
+} // end namespace internal
+
+/** \returns a random matrix expression
+ *
+ * Numbers are uniformly spread through their whole definition range for integer types,
+ * and in the [-1:1] range for floating point scalar types.
+ *
+ * The parameters \a rows and \a cols are the number of rows and of columns of
+ * the returned matrix. Must be compatible with this MatrixBase type.
+ *
+ * \not_reentrant
+ *
+ * This variant is meant to be used for dynamic-size matrix types. For fixed-size types,
+ * it is redundant to pass \a rows and \a cols as arguments, so Random() should be used
+ * instead.
+ *
+ *
+ * Example: \include MatrixBase_random_int_int.cpp
+ * Output: \verbinclude MatrixBase_random_int_int.out
+ *
+ * This expression has the "evaluate before nesting" flag so that it will be evaluated into
+ * a temporary matrix whenever it is nested in a larger expression. This prevents unexpected
+ * behavior with expressions involving random matrices.
+ *
+ * See DenseBase::NullaryExpr(Index, const CustomNullaryOp&) for an example using C++11 random generators.
+ *
+ * \sa DenseBase::setRandom(), DenseBase::Random(Index), DenseBase::Random()
+ */
+template<typename Derived>
+inline const typename DenseBase<Derived>::RandomReturnType
+DenseBase<Derived>::Random(Index rows, Index cols)
+{
+ return NullaryExpr(rows, cols, internal::scalar_random_op<Scalar>());
+}
+
+/** \returns a random vector expression
+ *
+ * Numbers are uniformly spread through their whole definition range for integer types,
+ * and in the [-1:1] range for floating point scalar types.
+ *
+ * The parameter \a size is the size of the returned vector.
+ * Must be compatible with this MatrixBase type.
+ *
+ * \only_for_vectors
+ * \not_reentrant
+ *
+ * This variant is meant to be used for dynamic-size vector types. For fixed-size types,
+ * it is redundant to pass \a size as argument, so Random() should be used
+ * instead.
+ *
+ * Example: \include MatrixBase_random_int.cpp
+ * Output: \verbinclude MatrixBase_random_int.out
+ *
+ * This expression has the "evaluate before nesting" flag so that it will be evaluated into
+ * a temporary vector whenever it is nested in a larger expression. This prevents unexpected
+ * behavior with expressions involving random matrices.
+ *
+ * \sa DenseBase::setRandom(), DenseBase::Random(Index,Index), DenseBase::Random()
+ */
+template<typename Derived>
+inline const typename DenseBase<Derived>::RandomReturnType
+DenseBase<Derived>::Random(Index size)
+{
+ return NullaryExpr(size, internal::scalar_random_op<Scalar>());
+}
+
+/** \returns a fixed-size random matrix or vector expression
+ *
+ * Numbers are uniformly spread through their whole definition range for integer types,
+ * and in the [-1:1] range for floating point scalar types.
+ *
+ * This variant is only for fixed-size MatrixBase types. For dynamic-size types, you
+ * need to use the variants taking size arguments.
+ *
+ * Example: \include MatrixBase_random.cpp
+ * Output: \verbinclude MatrixBase_random.out
+ *
+ * This expression has the "evaluate before nesting" flag so that it will be evaluated into
+ * a temporary matrix whenever it is nested in a larger expression. This prevents unexpected
+ * behavior with expressions involving random matrices.
+ *
+ * \not_reentrant
+ *
+ * \sa DenseBase::setRandom(), DenseBase::Random(Index,Index), DenseBase::Random(Index)
+ */
+template<typename Derived>
+inline const typename DenseBase<Derived>::RandomReturnType
+DenseBase<Derived>::Random()
+{
+ return NullaryExpr(RowsAtCompileTime, ColsAtCompileTime, internal::scalar_random_op<Scalar>());
+}
+
+/** Sets all coefficients in this expression to random values.
+ *
+ * Numbers are uniformly spread through their whole definition range for integer types,
+ * and in the [-1:1] range for floating point scalar types.
+ *
+ * \not_reentrant
+ *
+ * Example: \include MatrixBase_setRandom.cpp
+ * Output: \verbinclude MatrixBase_setRandom.out
+ *
+ * \sa class CwiseNullaryOp, setRandom(Index), setRandom(Index,Index)
+ */
+template<typename Derived>
+EIGEN_DEVICE_FUNC inline Derived& DenseBase<Derived>::setRandom()
+{
+ return *this = Random(rows(), cols());
+}
+
+/** Resizes to the given \a newSize, and sets all coefficients in this expression to random values.
+ *
+ * Numbers are uniformly spread through their whole definition range for integer types,
+ * and in the [-1:1] range for floating point scalar types.
+ *
+ * \only_for_vectors
+ * \not_reentrant
+ *
+ * Example: \include Matrix_setRandom_int.cpp
+ * Output: \verbinclude Matrix_setRandom_int.out
+ *
+ * \sa DenseBase::setRandom(), setRandom(Index,Index), class CwiseNullaryOp, DenseBase::Random()
+ */
+template<typename Derived>
+EIGEN_STRONG_INLINE Derived&
+PlainObjectBase<Derived>::setRandom(Index newSize)
+{
+ resize(newSize);
+ return setRandom();
+}
+
+/** Resizes to the given size, and sets all coefficients in this expression to random values.
+ *
+ * Numbers are uniformly spread through their whole definition range for integer types,
+ * and in the [-1:1] range for floating point scalar types.
+ *
+ * \not_reentrant
+ *
+ * \param rows the new number of rows
+ * \param cols the new number of columns
+ *
+ * Example: \include Matrix_setRandom_int_int.cpp
+ * Output: \verbinclude Matrix_setRandom_int_int.out
+ *
+ * \sa DenseBase::setRandom(), setRandom(Index), class CwiseNullaryOp, DenseBase::Random()
+ */
+template<typename Derived>
+EIGEN_STRONG_INLINE Derived&
+PlainObjectBase<Derived>::setRandom(Index rows, Index cols)
+{
+ resize(rows, cols);
+ return setRandom();
+}
+
+/** Resizes to the given size, changing only the number of columns, and sets all
+ * coefficients in this expression to random values. For the parameter of type
+ * NoChange_t, just pass the special value \c NoChange.
+ *
+ * Numbers are uniformly spread through their whole definition range for integer types,
+ * and in the [-1:1] range for floating point scalar types.
+ *
+ * \not_reentrant
+ *
+ * \sa DenseBase::setRandom(), setRandom(Index), setRandom(Index, NoChange_t), class CwiseNullaryOp, DenseBase::Random()
+ */
+template<typename Derived>
+EIGEN_STRONG_INLINE Derived&
+PlainObjectBase<Derived>::setRandom(NoChange_t, Index cols)
+{
+ return setRandom(rows(), cols);
+}
+
+/** Resizes to the given size, changing only the number of rows, and sets all
+ * coefficients in this expression to random values. For the parameter of type
+ * NoChange_t, just pass the special value \c NoChange.
+ *
+ * Numbers are uniformly spread through their whole definition range for integer types,
+ * and in the [-1:1] range for floating point scalar types.
+ *
+ * \not_reentrant
+ *
+ * \sa DenseBase::setRandom(), setRandom(Index), setRandom(NoChange_t, Index), class CwiseNullaryOp, DenseBase::Random()
+ */
+template<typename Derived>
+EIGEN_STRONG_INLINE Derived&
+PlainObjectBase<Derived>::setRandom(Index rows, NoChange_t)
+{
+ return setRandom(rows, cols());
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_RANDOM_H
diff --git a/Eigen/src/Core/Redux.h b/Eigen/src/Core/Redux.h
new file mode 100644
index 0000000..796e6c4
--- /dev/null
+++ b/Eigen/src/Core/Redux.h
@@ -0,0 +1,516 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_REDUX_H
+#define EIGEN_REDUX_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+
+// TODO
+// * implement other kind of vectorization
+// * factorize code
+
+/***************************************************************************
+* Part 1 : the logic deciding a strategy for vectorization and unrolling
+***************************************************************************/
+
+template<typename Func, typename Evaluator>
+struct redux_traits
+{
+public:
+ typedef typename find_best_packet<typename Evaluator::Scalar,Evaluator::SizeAtCompileTime>::type PacketType;
+ enum {
+ PacketSize = unpacket_traits<PacketType>::size,
+ InnerMaxSize = int(Evaluator::IsRowMajor)
+ ? Evaluator::MaxColsAtCompileTime
+ : Evaluator::MaxRowsAtCompileTime,
+ OuterMaxSize = int(Evaluator::IsRowMajor)
+ ? Evaluator::MaxRowsAtCompileTime
+ : Evaluator::MaxColsAtCompileTime,
+ SliceVectorizedWork = int(InnerMaxSize)==Dynamic ? Dynamic
+ : int(OuterMaxSize)==Dynamic ? (int(InnerMaxSize)>=int(PacketSize) ? Dynamic : 0)
+ : (int(InnerMaxSize)/int(PacketSize)) * int(OuterMaxSize)
+ };
+
+ enum {
+ MightVectorize = (int(Evaluator::Flags)&ActualPacketAccessBit)
+ && (functor_traits<Func>::PacketAccess),
+ MayLinearVectorize = bool(MightVectorize) && (int(Evaluator::Flags)&LinearAccessBit),
+ MaySliceVectorize = bool(MightVectorize) && (int(SliceVectorizedWork)==Dynamic || int(SliceVectorizedWork)>=3)
+ };
+
+public:
+ enum {
+ Traversal = int(MayLinearVectorize) ? int(LinearVectorizedTraversal)
+ : int(MaySliceVectorize) ? int(SliceVectorizedTraversal)
+ : int(DefaultTraversal)
+ };
+
+public:
+ enum {
+ Cost = Evaluator::SizeAtCompileTime == Dynamic ? HugeCost
+ : int(Evaluator::SizeAtCompileTime) * int(Evaluator::CoeffReadCost) + (Evaluator::SizeAtCompileTime-1) * functor_traits<Func>::Cost,
+ UnrollingLimit = EIGEN_UNROLLING_LIMIT * (int(Traversal) == int(DefaultTraversal) ? 1 : int(PacketSize))
+ };
+
+public:
+ enum {
+ Unrolling = Cost <= UnrollingLimit ? CompleteUnrolling : NoUnrolling
+ };
+
+#ifdef EIGEN_DEBUG_ASSIGN
+ static void debug()
+ {
+ std::cerr << "Xpr: " << typeid(typename Evaluator::XprType).name() << std::endl;
+ std::cerr.setf(std::ios::hex, std::ios::basefield);
+ EIGEN_DEBUG_VAR(Evaluator::Flags)
+ std::cerr.unsetf(std::ios::hex);
+ EIGEN_DEBUG_VAR(InnerMaxSize)
+ EIGEN_DEBUG_VAR(OuterMaxSize)
+ EIGEN_DEBUG_VAR(SliceVectorizedWork)
+ EIGEN_DEBUG_VAR(PacketSize)
+ EIGEN_DEBUG_VAR(MightVectorize)
+ EIGEN_DEBUG_VAR(MayLinearVectorize)
+ EIGEN_DEBUG_VAR(MaySliceVectorize)
+ std::cerr << "Traversal" << " = " << Traversal << " (" << demangle_traversal(Traversal) << ")" << std::endl;
+ EIGEN_DEBUG_VAR(UnrollingLimit)
+ std::cerr << "Unrolling" << " = " << Unrolling << " (" << demangle_unrolling(Unrolling) << ")" << std::endl;
+ std::cerr << std::endl;
+ }
+#endif
+};
+
+/***************************************************************************
+* Part 2 : unrollers
+***************************************************************************/
+
+/*** no vectorization ***/
+
+template<typename Func, typename Evaluator, int Start, int Length>
+struct redux_novec_unroller
+{
+ enum {
+ HalfLength = Length/2
+ };
+
+ typedef typename Evaluator::Scalar Scalar;
+
+ EIGEN_DEVICE_FUNC
+ static EIGEN_STRONG_INLINE Scalar run(const Evaluator &eval, const Func& func)
+ {
+ return func(redux_novec_unroller<Func, Evaluator, Start, HalfLength>::run(eval,func),
+ redux_novec_unroller<Func, Evaluator, Start+HalfLength, Length-HalfLength>::run(eval,func));
+ }
+};
+
+template<typename Func, typename Evaluator, int Start>
+struct redux_novec_unroller<Func, Evaluator, Start, 1>
+{
+ enum {
+ outer = Start / Evaluator::InnerSizeAtCompileTime,
+ inner = Start % Evaluator::InnerSizeAtCompileTime
+ };
+
+ typedef typename Evaluator::Scalar Scalar;
+
+ EIGEN_DEVICE_FUNC
+ static EIGEN_STRONG_INLINE Scalar run(const Evaluator &eval, const Func&)
+ {
+ return eval.coeffByOuterInner(outer, inner);
+ }
+};
+
+// This is actually dead code and will never be called. It is required
+// to prevent false warnings regarding failed inlining though
+// for 0 length run() will never be called at all.
+template<typename Func, typename Evaluator, int Start>
+struct redux_novec_unroller<Func, Evaluator, Start, 0>
+{
+ typedef typename Evaluator::Scalar Scalar;
+ EIGEN_DEVICE_FUNC
+ static EIGEN_STRONG_INLINE Scalar run(const Evaluator&, const Func&) { return Scalar(); }
+};
+
+/*** vectorization ***/
+
+template<typename Func, typename Evaluator, int Start, int Length>
+struct redux_vec_unroller
+{
+ template<typename PacketType>
+ EIGEN_DEVICE_FUNC
+ static EIGEN_STRONG_INLINE PacketType run(const Evaluator &eval, const Func& func)
+ {
+ enum {
+ PacketSize = unpacket_traits<PacketType>::size,
+ HalfLength = Length/2
+ };
+
+ return func.packetOp(
+ redux_vec_unroller<Func, Evaluator, Start, HalfLength>::template run<PacketType>(eval,func),
+ redux_vec_unroller<Func, Evaluator, Start+HalfLength, Length-HalfLength>::template run<PacketType>(eval,func) );
+ }
+};
+
+template<typename Func, typename Evaluator, int Start>
+struct redux_vec_unroller<Func, Evaluator, Start, 1>
+{
+ template<typename PacketType>
+ EIGEN_DEVICE_FUNC
+ static EIGEN_STRONG_INLINE PacketType run(const Evaluator &eval, const Func&)
+ {
+ enum {
+ PacketSize = unpacket_traits<PacketType>::size,
+ index = Start * PacketSize,
+ outer = index / int(Evaluator::InnerSizeAtCompileTime),
+ inner = index % int(Evaluator::InnerSizeAtCompileTime),
+ alignment = Evaluator::Alignment
+ };
+ return eval.template packetByOuterInner<alignment,PacketType>(outer, inner);
+ }
+};
+
+/***************************************************************************
+* Part 3 : implementation of all cases
+***************************************************************************/
+
+template<typename Func, typename Evaluator,
+ int Traversal = redux_traits<Func, Evaluator>::Traversal,
+ int Unrolling = redux_traits<Func, Evaluator>::Unrolling
+>
+struct redux_impl;
+
+template<typename Func, typename Evaluator>
+struct redux_impl<Func, Evaluator, DefaultTraversal, NoUnrolling>
+{
+ typedef typename Evaluator::Scalar Scalar;
+
+ template<typename XprType>
+ EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE
+ Scalar run(const Evaluator &eval, const Func& func, const XprType& xpr)
+ {
+ eigen_assert(xpr.rows()>0 && xpr.cols()>0 && "you are using an empty matrix");
+ Scalar res = eval.coeffByOuterInner(0, 0);
+ for(Index i = 1; i < xpr.innerSize(); ++i)
+ res = func(res, eval.coeffByOuterInner(0, i));
+ for(Index i = 1; i < xpr.outerSize(); ++i)
+ for(Index j = 0; j < xpr.innerSize(); ++j)
+ res = func(res, eval.coeffByOuterInner(i, j));
+ return res;
+ }
+};
+
+template<typename Func, typename Evaluator>
+struct redux_impl<Func,Evaluator, DefaultTraversal, CompleteUnrolling>
+ : redux_novec_unroller<Func,Evaluator, 0, Evaluator::SizeAtCompileTime>
+{
+ typedef redux_novec_unroller<Func,Evaluator, 0, Evaluator::SizeAtCompileTime> Base;
+ typedef typename Evaluator::Scalar Scalar;
+ template<typename XprType>
+ EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE
+ Scalar run(const Evaluator &eval, const Func& func, const XprType& /*xpr*/)
+ {
+ return Base::run(eval,func);
+ }
+};
+
+template<typename Func, typename Evaluator>
+struct redux_impl<Func, Evaluator, LinearVectorizedTraversal, NoUnrolling>
+{
+ typedef typename Evaluator::Scalar Scalar;
+ typedef typename redux_traits<Func, Evaluator>::PacketType PacketScalar;
+
+ template<typename XprType>
+ static Scalar run(const Evaluator &eval, const Func& func, const XprType& xpr)
+ {
+ const Index size = xpr.size();
+
+ const Index packetSize = redux_traits<Func, Evaluator>::PacketSize;
+ const int packetAlignment = unpacket_traits<PacketScalar>::alignment;
+ enum {
+ alignment0 = (bool(Evaluator::Flags & DirectAccessBit) && bool(packet_traits<Scalar>::AlignedOnScalar)) ? int(packetAlignment) : int(Unaligned),
+ alignment = plain_enum_max(alignment0, Evaluator::Alignment)
+ };
+ const Index alignedStart = internal::first_default_aligned(xpr);
+ const Index alignedSize2 = ((size-alignedStart)/(2*packetSize))*(2*packetSize);
+ const Index alignedSize = ((size-alignedStart)/(packetSize))*(packetSize);
+ const Index alignedEnd2 = alignedStart + alignedSize2;
+ const Index alignedEnd = alignedStart + alignedSize;
+ Scalar res;
+ if(alignedSize)
+ {
+ PacketScalar packet_res0 = eval.template packet<alignment,PacketScalar>(alignedStart);
+ if(alignedSize>packetSize) // we have at least two packets to partly unroll the loop
+ {
+ PacketScalar packet_res1 = eval.template packet<alignment,PacketScalar>(alignedStart+packetSize);
+ for(Index index = alignedStart + 2*packetSize; index < alignedEnd2; index += 2*packetSize)
+ {
+ packet_res0 = func.packetOp(packet_res0, eval.template packet<alignment,PacketScalar>(index));
+ packet_res1 = func.packetOp(packet_res1, eval.template packet<alignment,PacketScalar>(index+packetSize));
+ }
+
+ packet_res0 = func.packetOp(packet_res0,packet_res1);
+ if(alignedEnd>alignedEnd2)
+ packet_res0 = func.packetOp(packet_res0, eval.template packet<alignment,PacketScalar>(alignedEnd2));
+ }
+ res = func.predux(packet_res0);
+
+ for(Index index = 0; index < alignedStart; ++index)
+ res = func(res,eval.coeff(index));
+
+ for(Index index = alignedEnd; index < size; ++index)
+ res = func(res,eval.coeff(index));
+ }
+ else // too small to vectorize anything.
+ // since this is dynamic-size hence inefficient anyway for such small sizes, don't try to optimize.
+ {
+ res = eval.coeff(0);
+ for(Index index = 1; index < size; ++index)
+ res = func(res,eval.coeff(index));
+ }
+
+ return res;
+ }
+};
+
+// NOTE: for SliceVectorizedTraversal we simply bypass unrolling
+template<typename Func, typename Evaluator, int Unrolling>
+struct redux_impl<Func, Evaluator, SliceVectorizedTraversal, Unrolling>
+{
+ typedef typename Evaluator::Scalar Scalar;
+ typedef typename redux_traits<Func, Evaluator>::PacketType PacketType;
+
+ template<typename XprType>
+ EIGEN_DEVICE_FUNC static Scalar run(const Evaluator &eval, const Func& func, const XprType& xpr)
+ {
+ eigen_assert(xpr.rows()>0 && xpr.cols()>0 && "you are using an empty matrix");
+ const Index innerSize = xpr.innerSize();
+ const Index outerSize = xpr.outerSize();
+ enum {
+ packetSize = redux_traits<Func, Evaluator>::PacketSize
+ };
+ const Index packetedInnerSize = ((innerSize)/packetSize)*packetSize;
+ Scalar res;
+ if(packetedInnerSize)
+ {
+ PacketType packet_res = eval.template packet<Unaligned,PacketType>(0,0);
+ for(Index j=0; j<outerSize; ++j)
+ for(Index i=(j==0?packetSize:0); i<packetedInnerSize; i+=Index(packetSize))
+ packet_res = func.packetOp(packet_res, eval.template packetByOuterInner<Unaligned,PacketType>(j,i));
+
+ res = func.predux(packet_res);
+ for(Index j=0; j<outerSize; ++j)
+ for(Index i=packetedInnerSize; i<innerSize; ++i)
+ res = func(res, eval.coeffByOuterInner(j,i));
+ }
+ else // too small to vectorize anything.
+ // since this is dynamic-size hence inefficient anyway for such small sizes, don't try to optimize.
+ {
+ res = redux_impl<Func, Evaluator, DefaultTraversal, NoUnrolling>::run(eval, func, xpr);
+ }
+
+ return res;
+ }
+};
+
+template<typename Func, typename Evaluator>
+struct redux_impl<Func, Evaluator, LinearVectorizedTraversal, CompleteUnrolling>
+{
+ typedef typename Evaluator::Scalar Scalar;
+
+ typedef typename redux_traits<Func, Evaluator>::PacketType PacketType;
+ enum {
+ PacketSize = redux_traits<Func, Evaluator>::PacketSize,
+ Size = Evaluator::SizeAtCompileTime,
+ VectorizedSize = (int(Size) / int(PacketSize)) * int(PacketSize)
+ };
+
+ template<typename XprType>
+ EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE
+ Scalar run(const Evaluator &eval, const Func& func, const XprType &xpr)
+ {
+ EIGEN_ONLY_USED_FOR_DEBUG(xpr)
+ eigen_assert(xpr.rows()>0 && xpr.cols()>0 && "you are using an empty matrix");
+ if (VectorizedSize > 0) {
+ Scalar res = func.predux(redux_vec_unroller<Func, Evaluator, 0, Size / PacketSize>::template run<PacketType>(eval,func));
+ if (VectorizedSize != Size)
+ res = func(res,redux_novec_unroller<Func, Evaluator, VectorizedSize, Size-VectorizedSize>::run(eval,func));
+ return res;
+ }
+ else {
+ return redux_novec_unroller<Func, Evaluator, 0, Size>::run(eval,func);
+ }
+ }
+};
+
+// evaluator adaptor
+template<typename XprType_>
+class redux_evaluator : public internal::evaluator<XprType_>
+{
+ typedef internal::evaluator<XprType_> Base;
+public:
+ typedef XprType_ XprType;
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ explicit redux_evaluator(const XprType &xpr) : Base(xpr) {}
+
+ typedef typename XprType::Scalar Scalar;
+ typedef typename XprType::CoeffReturnType CoeffReturnType;
+ typedef typename XprType::PacketScalar PacketScalar;
+
+ enum {
+ MaxRowsAtCompileTime = XprType::MaxRowsAtCompileTime,
+ MaxColsAtCompileTime = XprType::MaxColsAtCompileTime,
+ // TODO we should not remove DirectAccessBit and rather find an elegant way to query the alignment offset at runtime from the evaluator
+ Flags = Base::Flags & ~DirectAccessBit,
+ IsRowMajor = XprType::IsRowMajor,
+ SizeAtCompileTime = XprType::SizeAtCompileTime,
+ InnerSizeAtCompileTime = XprType::InnerSizeAtCompileTime
+ };
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ CoeffReturnType coeffByOuterInner(Index outer, Index inner) const
+ { return Base::coeff(IsRowMajor ? outer : inner, IsRowMajor ? inner : outer); }
+
+ template<int LoadMode, typename PacketType>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ PacketType packetByOuterInner(Index outer, Index inner) const
+ { return Base::template packet<LoadMode,PacketType>(IsRowMajor ? outer : inner, IsRowMajor ? inner : outer); }
+
+};
+
+} // end namespace internal
+
+/***************************************************************************
+* Part 4 : public API
+***************************************************************************/
+
+
+/** \returns the result of a full redux operation on the whole matrix or vector using \a func
+ *
+ * The template parameter \a BinaryOp is the type of the functor \a func which must be
+ * an associative operator. Both current C++98 and C++11 functor styles are handled.
+ *
+ * \warning the matrix must be not empty, otherwise an assertion is triggered.
+ *
+ * \sa DenseBase::sum(), DenseBase::minCoeff(), DenseBase::maxCoeff(), MatrixBase::colwise(), MatrixBase::rowwise()
+ */
+template<typename Derived>
+template<typename Func>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE typename internal::traits<Derived>::Scalar
+DenseBase<Derived>::redux(const Func& func) const
+{
+ eigen_assert(this->rows()>0 && this->cols()>0 && "you are using an empty matrix");
+
+ typedef typename internal::redux_evaluator<Derived> ThisEvaluator;
+ ThisEvaluator thisEval(derived());
+
+ // The initial expression is passed to the reducer as an additional argument instead of
+ // passing it as a member of redux_evaluator to help
+ return internal::redux_impl<Func, ThisEvaluator>::run(thisEval, func, derived());
+}
+
+/** \returns the minimum of all coefficients of \c *this.
+ * In case \c *this contains NaN, NaNPropagation determines the behavior:
+ * NaNPropagation == PropagateFast : undefined
+ * NaNPropagation == PropagateNaN : result is NaN
+ * NaNPropagation == PropagateNumbers : result is minimum of elements that are not NaN
+ * \warning the matrix must be not empty, otherwise an assertion is triggered.
+ */
+template<typename Derived>
+template<int NaNPropagation>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE typename internal::traits<Derived>::Scalar
+DenseBase<Derived>::minCoeff() const
+{
+ return derived().redux(Eigen::internal::scalar_min_op<Scalar,Scalar, NaNPropagation>());
+}
+
+/** \returns the maximum of all coefficients of \c *this.
+ * In case \c *this contains NaN, NaNPropagation determines the behavior:
+ * NaNPropagation == PropagateFast : undefined
+ * NaNPropagation == PropagateNaN : result is NaN
+ * NaNPropagation == PropagateNumbers : result is maximum of elements that are not NaN
+ * \warning the matrix must be not empty, otherwise an assertion is triggered.
+ */
+template<typename Derived>
+template<int NaNPropagation>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE typename internal::traits<Derived>::Scalar
+DenseBase<Derived>::maxCoeff() const
+{
+ return derived().redux(Eigen::internal::scalar_max_op<Scalar,Scalar, NaNPropagation>());
+}
+
+/** \returns the sum of all coefficients of \c *this
+ *
+ * If \c *this is empty, then the value 0 is returned.
+ *
+ * \sa trace(), prod(), mean()
+ */
+template<typename Derived>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE typename internal::traits<Derived>::Scalar
+DenseBase<Derived>::sum() const
+{
+ if(SizeAtCompileTime==0 || (SizeAtCompileTime==Dynamic && size()==0))
+ return Scalar(0);
+ return derived().redux(Eigen::internal::scalar_sum_op<Scalar,Scalar>());
+}
+
+/** \returns the mean of all coefficients of *this
+*
+* \sa trace(), prod(), sum()
+*/
+template<typename Derived>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE typename internal::traits<Derived>::Scalar
+DenseBase<Derived>::mean() const
+{
+#ifdef __INTEL_COMPILER
+ #pragma warning push
+ #pragma warning ( disable : 2259 )
+#endif
+ return Scalar(derived().redux(Eigen::internal::scalar_sum_op<Scalar,Scalar>())) / Scalar(this->size());
+#ifdef __INTEL_COMPILER
+ #pragma warning pop
+#endif
+}
+
+/** \returns the product of all coefficients of *this
+ *
+ * Example: \include MatrixBase_prod.cpp
+ * Output: \verbinclude MatrixBase_prod.out
+ *
+ * \sa sum(), mean(), trace()
+ */
+template<typename Derived>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE typename internal::traits<Derived>::Scalar
+DenseBase<Derived>::prod() const
+{
+ if(SizeAtCompileTime==0 || (SizeAtCompileTime==Dynamic && size()==0))
+ return Scalar(1);
+ return derived().redux(Eigen::internal::scalar_product_op<Scalar>());
+}
+
+/** \returns the trace of \c *this, i.e. the sum of the coefficients on the main diagonal.
+ *
+ * \c *this can be any matrix, not necessarily square.
+ *
+ * \sa diagonal(), sum()
+ */
+template<typename Derived>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE typename internal::traits<Derived>::Scalar
+MatrixBase<Derived>::trace() const
+{
+ return derived().diagonal().sum();
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_REDUX_H
diff --git a/Eigen/src/Core/Ref.h b/Eigen/src/Core/Ref.h
new file mode 100644
index 0000000..81de5f9
--- /dev/null
+++ b/Eigen/src/Core/Ref.h
@@ -0,0 +1,383 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2012 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_REF_H
+#define EIGEN_REF_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+
+template<typename PlainObjectType_, int Options_, typename StrideType_>
+struct traits<Ref<PlainObjectType_, Options_, StrideType_> >
+ : public traits<Map<PlainObjectType_, Options_, StrideType_> >
+{
+ typedef PlainObjectType_ PlainObjectType;
+ typedef StrideType_ StrideType;
+ enum {
+ Options = Options_,
+ Flags = traits<Map<PlainObjectType_, Options_, StrideType_> >::Flags | NestByRefBit,
+ Alignment = traits<Map<PlainObjectType_, Options_, StrideType_> >::Alignment
+ };
+
+ template<typename Derived> struct match {
+ enum {
+ IsVectorAtCompileTime = PlainObjectType::IsVectorAtCompileTime || Derived::IsVectorAtCompileTime,
+ HasDirectAccess = internal::has_direct_access<Derived>::ret,
+ StorageOrderMatch = IsVectorAtCompileTime || ((PlainObjectType::Flags&RowMajorBit)==(Derived::Flags&RowMajorBit)),
+ InnerStrideMatch = int(StrideType::InnerStrideAtCompileTime)==int(Dynamic)
+ || int(StrideType::InnerStrideAtCompileTime)==int(Derived::InnerStrideAtCompileTime)
+ || (int(StrideType::InnerStrideAtCompileTime)==0 && int(Derived::InnerStrideAtCompileTime)==1),
+ OuterStrideMatch = IsVectorAtCompileTime
+ || int(StrideType::OuterStrideAtCompileTime)==int(Dynamic) || int(StrideType::OuterStrideAtCompileTime)==int(Derived::OuterStrideAtCompileTime),
+ // NOTE, this indirection of evaluator<Derived>::Alignment is needed
+ // to workaround a very strange bug in MSVC related to the instantiation
+ // of has_*ary_operator in evaluator<CwiseNullaryOp>.
+ // This line is surprisingly very sensitive. For instance, simply adding parenthesis
+ // as "DerivedAlignment = (int(evaluator<Derived>::Alignment))," will make MSVC fail...
+ DerivedAlignment = int(evaluator<Derived>::Alignment),
+ AlignmentMatch = (int(traits<PlainObjectType>::Alignment)==int(Unaligned)) || (DerivedAlignment >= int(Alignment)), // FIXME the first condition is not very clear, it should be replaced by the required alignment
+ ScalarTypeMatch = internal::is_same<typename PlainObjectType::Scalar, typename Derived::Scalar>::value,
+ MatchAtCompileTime = HasDirectAccess && StorageOrderMatch && InnerStrideMatch && OuterStrideMatch && AlignmentMatch && ScalarTypeMatch
+ };
+ typedef std::conditional_t<MatchAtCompileTime,internal::true_type,internal::false_type> type;
+ };
+
+};
+
+template<typename Derived>
+struct traits<RefBase<Derived> > : public traits<Derived> {};
+
+}
+
+template<typename Derived> class RefBase
+ : public MapBase<Derived>
+{
+ typedef typename internal::traits<Derived>::PlainObjectType PlainObjectType;
+ typedef typename internal::traits<Derived>::StrideType StrideType;
+
+public:
+
+ typedef MapBase<Derived> Base;
+ EIGEN_DENSE_PUBLIC_INTERFACE(RefBase)
+
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR inline Index innerStride() const
+ {
+ return StrideType::InnerStrideAtCompileTime != 0 ? m_stride.inner() : 1;
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR inline Index outerStride() const
+ {
+ return StrideType::OuterStrideAtCompileTime != 0 ? m_stride.outer()
+ : IsVectorAtCompileTime ? this->size()
+ : int(Flags)&RowMajorBit ? this->cols()
+ : this->rows();
+ }
+
+ EIGEN_DEVICE_FUNC RefBase()
+ : Base(0,RowsAtCompileTime==Dynamic?0:RowsAtCompileTime,ColsAtCompileTime==Dynamic?0:ColsAtCompileTime),
+ // Stride<> does not allow default ctor for Dynamic strides, so let' initialize it with dummy values:
+ m_stride(StrideType::OuterStrideAtCompileTime==Dynamic?0:StrideType::OuterStrideAtCompileTime,
+ StrideType::InnerStrideAtCompileTime==Dynamic?0:StrideType::InnerStrideAtCompileTime)
+ {}
+
+ EIGEN_INHERIT_ASSIGNMENT_OPERATORS(RefBase)
+
+protected:
+
+ typedef Stride<StrideType::OuterStrideAtCompileTime,StrideType::InnerStrideAtCompileTime> StrideBase;
+
+ // Resolves inner stride if default 0.
+ static EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR Index resolveInnerStride(Index inner) {
+ return inner == 0 ? 1 : inner;
+ }
+
+ // Resolves outer stride if default 0.
+ static EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR Index resolveOuterStride(Index inner, Index outer, Index rows, Index cols, bool isVectorAtCompileTime, bool isRowMajor) {
+ return outer == 0 ? isVectorAtCompileTime ? inner * rows * cols : isRowMajor ? inner * cols : inner * rows : outer;
+ }
+
+ // Returns true if construction is valid, false if there is a stride mismatch,
+ // and fails if there is a size mismatch.
+ template<typename Expression>
+ EIGEN_DEVICE_FUNC bool construct(Expression& expr)
+ {
+ // Check matrix sizes. If this is a compile-time vector, we do allow
+ // implicitly transposing.
+ EIGEN_STATIC_ASSERT(
+ EIGEN_PREDICATE_SAME_MATRIX_SIZE(PlainObjectType, Expression)
+ // If it is a vector, the transpose sizes might match.
+ || ( PlainObjectType::IsVectorAtCompileTime
+ && ((int(PlainObjectType::RowsAtCompileTime)==Eigen::Dynamic
+ || int(Expression::ColsAtCompileTime)==Eigen::Dynamic
+ || int(PlainObjectType::RowsAtCompileTime)==int(Expression::ColsAtCompileTime))
+ && (int(PlainObjectType::ColsAtCompileTime)==Eigen::Dynamic
+ || int(Expression::RowsAtCompileTime)==Eigen::Dynamic
+ || int(PlainObjectType::ColsAtCompileTime)==int(Expression::RowsAtCompileTime)))),
+ YOU_MIXED_MATRICES_OF_DIFFERENT_SIZES
+ )
+
+ // Determine runtime rows and columns.
+ Index rows = expr.rows();
+ Index cols = expr.cols();
+ if(PlainObjectType::RowsAtCompileTime==1)
+ {
+ eigen_assert(expr.rows()==1 || expr.cols()==1);
+ rows = 1;
+ cols = expr.size();
+ }
+ else if(PlainObjectType::ColsAtCompileTime==1)
+ {
+ eigen_assert(expr.rows()==1 || expr.cols()==1);
+ rows = expr.size();
+ cols = 1;
+ }
+ // Verify that the sizes are valid.
+ eigen_assert(
+ (PlainObjectType::RowsAtCompileTime == Dynamic) || (PlainObjectType::RowsAtCompileTime == rows));
+ eigen_assert(
+ (PlainObjectType::ColsAtCompileTime == Dynamic) || (PlainObjectType::ColsAtCompileTime == cols));
+
+
+ // If this is a vector, we might be transposing, which means that stride should swap.
+ const bool transpose = PlainObjectType::IsVectorAtCompileTime && (rows != expr.rows());
+ // If the storage format differs, we also need to swap the stride.
+ const bool row_major = ((PlainObjectType::Flags)&RowMajorBit) != 0;
+ const bool expr_row_major = (Expression::Flags&RowMajorBit) != 0;
+ const bool storage_differs = (row_major != expr_row_major);
+
+ const bool swap_stride = (transpose != storage_differs);
+
+ // Determine expr's actual strides, resolving any defaults if zero.
+ const Index expr_inner_actual = resolveInnerStride(expr.innerStride());
+ const Index expr_outer_actual = resolveOuterStride(expr_inner_actual,
+ expr.outerStride(),
+ expr.rows(),
+ expr.cols(),
+ Expression::IsVectorAtCompileTime != 0,
+ expr_row_major);
+
+ // If this is a column-major row vector or row-major column vector, the inner-stride
+ // is arbitrary, so set it to either the compile-time inner stride or 1.
+ const bool row_vector = (rows == 1);
+ const bool col_vector = (cols == 1);
+ const Index inner_stride =
+ ( (!row_major && row_vector) || (row_major && col_vector) ) ?
+ ( StrideType::InnerStrideAtCompileTime > 0 ? Index(StrideType::InnerStrideAtCompileTime) : 1)
+ : swap_stride ? expr_outer_actual : expr_inner_actual;
+
+ // If this is a column-major column vector or row-major row vector, the outer-stride
+ // is arbitrary, so set it to either the compile-time outer stride or vector size.
+ const Index outer_stride =
+ ( (!row_major && col_vector) || (row_major && row_vector) ) ?
+ ( StrideType::OuterStrideAtCompileTime > 0 ? Index(StrideType::OuterStrideAtCompileTime) : rows * cols * inner_stride)
+ : swap_stride ? expr_inner_actual : expr_outer_actual;
+
+ // Check if given inner/outer strides are compatible with compile-time strides.
+ const bool inner_valid = (StrideType::InnerStrideAtCompileTime == Dynamic)
+ || (resolveInnerStride(Index(StrideType::InnerStrideAtCompileTime)) == inner_stride);
+ if (!inner_valid) {
+ return false;
+ }
+
+ const bool outer_valid = (StrideType::OuterStrideAtCompileTime == Dynamic)
+ || (resolveOuterStride(
+ inner_stride,
+ Index(StrideType::OuterStrideAtCompileTime),
+ rows, cols, PlainObjectType::IsVectorAtCompileTime != 0,
+ row_major)
+ == outer_stride);
+ if (!outer_valid) {
+ return false;
+ }
+
+ internal::construct_at<Base>(this, expr.data(), rows, cols);
+ internal::construct_at(&m_stride,
+ (StrideType::OuterStrideAtCompileTime == 0) ? 0 : outer_stride,
+ (StrideType::InnerStrideAtCompileTime == 0) ? 0 : inner_stride );
+ return true;
+ }
+
+ StrideBase m_stride;
+};
+
+/** \class Ref
+ * \ingroup Core_Module
+ *
+ * \brief A matrix or vector expression mapping an existing expression
+ *
+ * \tparam PlainObjectType the equivalent matrix type of the mapped data
+ * \tparam Options specifies the pointer alignment in bytes. It can be: \c #Aligned128, , \c #Aligned64, \c #Aligned32, \c #Aligned16, \c #Aligned8 or \c #Unaligned.
+ * The default is \c #Unaligned.
+ * \tparam StrideType optionally specifies strides. By default, Ref implies a contiguous storage along the inner dimension (inner stride==1),
+ * but accepts a variable outer stride (leading dimension).
+ * This can be overridden by specifying strides.
+ * The type passed here must be a specialization of the Stride template, see examples below.
+ *
+ * This class provides a way to write non-template functions taking Eigen objects as parameters while limiting the number of copies.
+ * A Ref<> object can represent either a const expression or a l-value:
+ * \code
+ * // in-out argument:
+ * void foo1(Ref<VectorXf> x);
+ *
+ * // read-only const argument:
+ * void foo2(const Ref<const VectorXf>& x);
+ * \endcode
+ *
+ * In the in-out case, the input argument must satisfy the constraints of the actual Ref<> type, otherwise a compilation issue will be triggered.
+ * By default, a Ref<VectorXf> can reference any dense vector expression of float having a contiguous memory layout.
+ * Likewise, a Ref<MatrixXf> can reference any column-major dense matrix expression of float whose column's elements are contiguously stored with
+ * the possibility to have a constant space in-between each column, i.e. the inner stride must be equal to 1, but the outer stride (or leading dimension)
+ * can be greater than the number of rows.
+ *
+ * In the const case, if the input expression does not match the above requirement, then it is evaluated into a temporary before being passed to the function.
+ * Here are some examples:
+ * \code
+ * MatrixXf A;
+ * VectorXf a;
+ * foo1(a.head()); // OK
+ * foo1(A.col()); // OK
+ * foo1(A.row()); // Compilation error because here innerstride!=1
+ * foo2(A.row()); // Compilation error because A.row() is a 1xN object while foo2 is expecting a Nx1 object
+ * foo2(A.row().transpose()); // The row is copied into a contiguous temporary
+ * foo2(2*a); // The expression is evaluated into a temporary
+ * foo2(A.col().segment(2,4)); // No temporary
+ * \endcode
+ *
+ * The range of inputs that can be referenced without temporary can be enlarged using the last two template parameters.
+ * Here is an example accepting an innerstride!=1:
+ * \code
+ * // in-out argument:
+ * void foo3(Ref<VectorXf,0,InnerStride<> > x);
+ * foo3(A.row()); // OK
+ * \endcode
+ * The downside here is that the function foo3 might be significantly slower than foo1 because it won't be able to exploit vectorization, and will involve more
+ * expensive address computations even if the input is contiguously stored in memory. To overcome this issue, one might propose to overload internally calling a
+ * template function, e.g.:
+ * \code
+ * // in the .h:
+ * void foo(const Ref<MatrixXf>& A);
+ * void foo(const Ref<MatrixXf,0,Stride<> >& A);
+ *
+ * // in the .cpp:
+ * template<typename TypeOfA> void foo_impl(const TypeOfA& A) {
+ * ... // crazy code goes here
+ * }
+ * void foo(const Ref<MatrixXf>& A) { foo_impl(A); }
+ * void foo(const Ref<MatrixXf,0,Stride<> >& A) { foo_impl(A); }
+ * \endcode
+ *
+ * See also the following stackoverflow questions for further references:
+ * - <a href="http://stackoverflow.com/questions/21132538/correct-usage-of-the-eigenref-class">Correct usage of the Eigen::Ref<> class</a>
+ *
+ * \sa PlainObjectBase::Map(), \ref TopicStorageOrders
+ */
+template<typename PlainObjectType, int Options, typename StrideType> class Ref
+ : public RefBase<Ref<PlainObjectType, Options, StrideType> >
+{
+ private:
+ typedef internal::traits<Ref> Traits;
+ template<typename Derived>
+ EIGEN_DEVICE_FUNC inline Ref(const PlainObjectBase<Derived>& expr,
+ std::enable_if_t<bool(Traits::template match<Derived>::MatchAtCompileTime),Derived>* = 0);
+ public:
+
+ typedef RefBase<Ref> Base;
+ EIGEN_DENSE_PUBLIC_INTERFACE(Ref)
+
+
+ #ifndef EIGEN_PARSED_BY_DOXYGEN
+ template<typename Derived>
+ EIGEN_DEVICE_FUNC inline Ref(PlainObjectBase<Derived>& expr,
+ std::enable_if_t<bool(Traits::template match<Derived>::MatchAtCompileTime),Derived>* = 0)
+ {
+ EIGEN_STATIC_ASSERT(bool(Traits::template match<Derived>::MatchAtCompileTime), STORAGE_LAYOUT_DOES_NOT_MATCH);
+ // Construction must pass since we will not create temporary storage in the non-const case.
+ const bool success = Base::construct(expr.derived());
+ EIGEN_UNUSED_VARIABLE(success)
+ eigen_assert(success);
+ }
+ template<typename Derived>
+ EIGEN_DEVICE_FUNC inline Ref(const DenseBase<Derived>& expr,
+ std::enable_if_t<bool(Traits::template match<Derived>::MatchAtCompileTime),Derived>* = 0)
+ #else
+ /** Implicit constructor from any dense expression */
+ template<typename Derived>
+ inline Ref(DenseBase<Derived>& expr)
+ #endif
+ {
+ EIGEN_STATIC_ASSERT(bool(internal::is_lvalue<Derived>::value), THIS_EXPRESSION_IS_NOT_A_LVALUE__IT_IS_READ_ONLY);
+ EIGEN_STATIC_ASSERT(bool(Traits::template match<Derived>::MatchAtCompileTime), STORAGE_LAYOUT_DOES_NOT_MATCH);
+ EIGEN_STATIC_ASSERT(!Derived::IsPlainObjectBase,THIS_EXPRESSION_IS_NOT_A_LVALUE__IT_IS_READ_ONLY);
+ // Construction must pass since we will not create temporary storage in the non-const case.
+ const bool success = Base::construct(expr.const_cast_derived());
+ EIGEN_UNUSED_VARIABLE(success)
+ eigen_assert(success);
+ }
+
+ EIGEN_INHERIT_ASSIGNMENT_OPERATORS(Ref)
+
+};
+
+// this is the const ref version
+template<typename TPlainObjectType, int Options, typename StrideType> class Ref<const TPlainObjectType, Options, StrideType>
+ : public RefBase<Ref<const TPlainObjectType, Options, StrideType> >
+{
+ typedef internal::traits<Ref> Traits;
+ public:
+
+ typedef RefBase<Ref> Base;
+ EIGEN_DENSE_PUBLIC_INTERFACE(Ref)
+
+ template<typename Derived>
+ EIGEN_DEVICE_FUNC inline Ref(const DenseBase<Derived>& expr,
+ std::enable_if_t<bool(Traits::template match<Derived>::ScalarTypeMatch),Derived>* = 0)
+ {
+// std::cout << match_helper<Derived>::HasDirectAccess << "," << match_helper<Derived>::OuterStrideMatch << "," << match_helper<Derived>::InnerStrideMatch << "\n";
+// std::cout << int(StrideType::OuterStrideAtCompileTime) << " - " << int(Derived::OuterStrideAtCompileTime) << "\n";
+// std::cout << int(StrideType::InnerStrideAtCompileTime) << " - " << int(Derived::InnerStrideAtCompileTime) << "\n";
+ construct(expr.derived(), typename Traits::template match<Derived>::type());
+ }
+
+ EIGEN_DEVICE_FUNC inline Ref(const Ref& other) : Base(other) {
+ // copy constructor shall not copy the m_object, to avoid unnecessary malloc and copy
+ }
+
+ template<typename OtherRef>
+ EIGEN_DEVICE_FUNC inline Ref(const RefBase<OtherRef>& other) {
+ construct(other.derived(), typename Traits::template match<OtherRef>::type());
+ }
+
+ protected:
+
+ template<typename Expression>
+ EIGEN_DEVICE_FUNC void construct(const Expression& expr,internal::true_type)
+ {
+ // Check if we can use the underlying expr's storage directly, otherwise call the copy version.
+ if (!Base::construct(expr)) {
+ construct(expr, internal::false_type());
+ }
+ }
+
+ template<typename Expression>
+ EIGEN_DEVICE_FUNC void construct(const Expression& expr, internal::false_type)
+ {
+ internal::call_assignment_no_alias(m_object,expr,internal::assign_op<Scalar,Scalar>());
+ Base::construct(m_object);
+ }
+
+ protected:
+ TPlainObjectType m_object;
+};
+
+} // end namespace Eigen
+
+#endif // EIGEN_REF_H
diff --git a/Eigen/src/Core/Replicate.h b/Eigen/src/Core/Replicate.h
new file mode 100644
index 0000000..4f91bbe
--- /dev/null
+++ b/Eigen/src/Core/Replicate.h
@@ -0,0 +1,144 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009-2010 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_REPLICATE_H
+#define EIGEN_REPLICATE_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+template<typename MatrixType,int RowFactor,int ColFactor>
+struct traits<Replicate<MatrixType,RowFactor,ColFactor> >
+ : traits<MatrixType>
+{
+ typedef typename MatrixType::Scalar Scalar;
+ typedef typename traits<MatrixType>::StorageKind StorageKind;
+ typedef typename traits<MatrixType>::XprKind XprKind;
+ typedef typename ref_selector<MatrixType>::type MatrixTypeNested;
+ typedef std::remove_reference_t<MatrixTypeNested> MatrixTypeNested_;
+ enum {
+ RowsAtCompileTime = RowFactor==Dynamic || int(MatrixType::RowsAtCompileTime)==Dynamic
+ ? Dynamic
+ : RowFactor * MatrixType::RowsAtCompileTime,
+ ColsAtCompileTime = ColFactor==Dynamic || int(MatrixType::ColsAtCompileTime)==Dynamic
+ ? Dynamic
+ : ColFactor * MatrixType::ColsAtCompileTime,
+ //FIXME we don't propagate the max sizes !!!
+ MaxRowsAtCompileTime = RowsAtCompileTime,
+ MaxColsAtCompileTime = ColsAtCompileTime,
+ IsRowMajor = MaxRowsAtCompileTime==1 && MaxColsAtCompileTime!=1 ? 1
+ : MaxColsAtCompileTime==1 && MaxRowsAtCompileTime!=1 ? 0
+ : (MatrixType::Flags & RowMajorBit) ? 1 : 0,
+
+ // FIXME enable DirectAccess with negative strides?
+ Flags = IsRowMajor ? RowMajorBit : 0
+ };
+};
+}
+
+/**
+ * \class Replicate
+ * \ingroup Core_Module
+ *
+ * \brief Expression of the multiple replication of a matrix or vector
+ *
+ * \tparam MatrixType the type of the object we are replicating
+ * \tparam RowFactor number of repetitions at compile time along the vertical direction, can be Dynamic.
+ * \tparam ColFactor number of repetitions at compile time along the horizontal direction, can be Dynamic.
+ *
+ * This class represents an expression of the multiple replication of a matrix or vector.
+ * It is the return type of DenseBase::replicate() and most of the time
+ * this is the only way it is used.
+ *
+ * \sa DenseBase::replicate()
+ */
+template<typename MatrixType,int RowFactor,int ColFactor> class Replicate
+ : public internal::dense_xpr_base< Replicate<MatrixType,RowFactor,ColFactor> >::type
+{
+ typedef typename internal::traits<Replicate>::MatrixTypeNested MatrixTypeNested;
+ typedef typename internal::traits<Replicate>::MatrixTypeNested_ MatrixTypeNested_;
+ public:
+
+ typedef typename internal::dense_xpr_base<Replicate>::type Base;
+ EIGEN_DENSE_PUBLIC_INTERFACE(Replicate)
+ typedef internal::remove_all_t<MatrixType> NestedExpression;
+
+ template<typename OriginalMatrixType>
+ EIGEN_DEVICE_FUNC
+ inline explicit Replicate(const OriginalMatrixType& matrix)
+ : m_matrix(matrix), m_rowFactor(RowFactor), m_colFactor(ColFactor)
+ {
+ EIGEN_STATIC_ASSERT((internal::is_same<std::remove_const_t<MatrixType>,OriginalMatrixType>::value),
+ THE_MATRIX_OR_EXPRESSION_THAT_YOU_PASSED_DOES_NOT_HAVE_THE_EXPECTED_TYPE)
+ eigen_assert(RowFactor!=Dynamic && ColFactor!=Dynamic);
+ }
+
+ template<typename OriginalMatrixType>
+ EIGEN_DEVICE_FUNC
+ inline Replicate(const OriginalMatrixType& matrix, Index rowFactor, Index colFactor)
+ : m_matrix(matrix), m_rowFactor(rowFactor), m_colFactor(colFactor)
+ {
+ EIGEN_STATIC_ASSERT((internal::is_same<std::remove_const_t<MatrixType>,OriginalMatrixType>::value),
+ THE_MATRIX_OR_EXPRESSION_THAT_YOU_PASSED_DOES_NOT_HAVE_THE_EXPECTED_TYPE)
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
+ inline Index rows() const { return m_matrix.rows() * m_rowFactor.value(); }
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
+ inline Index cols() const { return m_matrix.cols() * m_colFactor.value(); }
+
+ EIGEN_DEVICE_FUNC
+ const MatrixTypeNested_& nestedExpression() const
+ {
+ return m_matrix;
+ }
+
+ protected:
+ MatrixTypeNested m_matrix;
+ const internal::variable_if_dynamic<Index, RowFactor> m_rowFactor;
+ const internal::variable_if_dynamic<Index, ColFactor> m_colFactor;
+};
+
+/**
+ * \return an expression of the replication of \c *this
+ *
+ * Example: \include MatrixBase_replicate.cpp
+ * Output: \verbinclude MatrixBase_replicate.out
+ *
+ * \sa VectorwiseOp::replicate(), DenseBase::replicate(Index,Index), class Replicate
+ */
+template<typename Derived>
+template<int RowFactor, int ColFactor>
+EIGEN_DEVICE_FUNC const Replicate<Derived,RowFactor,ColFactor>
+DenseBase<Derived>::replicate() const
+{
+ return Replicate<Derived,RowFactor,ColFactor>(derived());
+}
+
+/**
+ * \return an expression of the replication of each column (or row) of \c *this
+ *
+ * Example: \include DirectionWise_replicate_int.cpp
+ * Output: \verbinclude DirectionWise_replicate_int.out
+ *
+ * \sa VectorwiseOp::replicate(), DenseBase::replicate(), class Replicate
+ */
+template<typename ExpressionType, int Direction>
+EIGEN_DEVICE_FUNC const typename VectorwiseOp<ExpressionType,Direction>::ReplicateReturnType
+VectorwiseOp<ExpressionType,Direction>::replicate(Index factor) const
+{
+ return typename VectorwiseOp<ExpressionType,Direction>::ReplicateReturnType
+ (_expression(),Direction==Vertical?factor:1,Direction==Horizontal?factor:1);
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_REPLICATE_H
diff --git a/Eigen/src/Core/Reshaped.h b/Eigen/src/Core/Reshaped.h
new file mode 100644
index 0000000..c90e61f
--- /dev/null
+++ b/Eigen/src/Core/Reshaped.h
@@ -0,0 +1,455 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2017 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2014 yoco <peter.xiau@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_RESHAPED_H
+#define EIGEN_RESHAPED_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+/** \class Reshaped
+ * \ingroup Core_Module
+ *
+ * \brief Expression of a fixed-size or dynamic-size reshape
+ *
+ * \tparam XprType the type of the expression in which we are taking a reshape
+ * \tparam Rows the number of rows of the reshape we are taking at compile time (optional)
+ * \tparam Cols the number of columns of the reshape we are taking at compile time (optional)
+ * \tparam Order can be ColMajor or RowMajor, default is ColMajor.
+ *
+ * This class represents an expression of either a fixed-size or dynamic-size reshape.
+ * It is the return type of DenseBase::reshaped(NRowsType,NColsType) and
+ * most of the time this is the only way it is used.
+ *
+ * If you want to directly manipulate reshaped expressions,
+ * for instance if you want to write a function returning such an expression,
+ * it is advised to use the \em auto keyword for such use cases.
+ *
+ * Here is an example illustrating the dynamic case:
+ * \include class_Reshaped.cpp
+ * Output: \verbinclude class_Reshaped.out
+ *
+ * Here is an example illustrating the fixed-size case:
+ * \include class_FixedReshaped.cpp
+ * Output: \verbinclude class_FixedReshaped.out
+ *
+ * \sa DenseBase::reshaped(NRowsType,NColsType)
+ */
+
+namespace internal {
+
+template<typename XprType, int Rows, int Cols, int Order>
+struct traits<Reshaped<XprType, Rows, Cols, Order> > : traits<XprType>
+{
+ typedef typename traits<XprType>::Scalar Scalar;
+ typedef typename traits<XprType>::StorageKind StorageKind;
+ typedef typename traits<XprType>::XprKind XprKind;
+ enum{
+ MatrixRows = traits<XprType>::RowsAtCompileTime,
+ MatrixCols = traits<XprType>::ColsAtCompileTime,
+ RowsAtCompileTime = Rows,
+ ColsAtCompileTime = Cols,
+ MaxRowsAtCompileTime = Rows,
+ MaxColsAtCompileTime = Cols,
+ XpxStorageOrder = ((int(traits<XprType>::Flags) & RowMajorBit) == RowMajorBit) ? RowMajor : ColMajor,
+ ReshapedStorageOrder = (RowsAtCompileTime == 1 && ColsAtCompileTime != 1) ? RowMajor
+ : (ColsAtCompileTime == 1 && RowsAtCompileTime != 1) ? ColMajor
+ : XpxStorageOrder,
+ HasSameStorageOrderAsXprType = (ReshapedStorageOrder == XpxStorageOrder),
+ InnerSize = (ReshapedStorageOrder==int(RowMajor)) ? int(ColsAtCompileTime) : int(RowsAtCompileTime),
+ InnerStrideAtCompileTime = HasSameStorageOrderAsXprType
+ ? int(inner_stride_at_compile_time<XprType>::ret)
+ : Dynamic,
+ OuterStrideAtCompileTime = Dynamic,
+
+ HasDirectAccess = internal::has_direct_access<XprType>::ret
+ && (Order==int(XpxStorageOrder))
+ && ((evaluator<XprType>::Flags&LinearAccessBit)==LinearAccessBit),
+
+ MaskPacketAccessBit = (InnerSize == Dynamic || (InnerSize % packet_traits<Scalar>::size) == 0)
+ && (InnerStrideAtCompileTime == 1)
+ ? PacketAccessBit : 0,
+ //MaskAlignedBit = ((OuterStrideAtCompileTime!=Dynamic) && (((OuterStrideAtCompileTime * int(sizeof(Scalar))) % 16) == 0)) ? AlignedBit : 0,
+ FlagsLinearAccessBit = (RowsAtCompileTime == 1 || ColsAtCompileTime == 1) ? LinearAccessBit : 0,
+ FlagsLvalueBit = is_lvalue<XprType>::value ? LvalueBit : 0,
+ FlagsRowMajorBit = (ReshapedStorageOrder==int(RowMajor)) ? RowMajorBit : 0,
+ FlagsDirectAccessBit = HasDirectAccess ? DirectAccessBit : 0,
+ Flags0 = traits<XprType>::Flags & ( (HereditaryBits & ~RowMajorBit) | MaskPacketAccessBit),
+
+ Flags = (Flags0 | FlagsLinearAccessBit | FlagsLvalueBit | FlagsRowMajorBit | FlagsDirectAccessBit)
+ };
+};
+
+template<typename XprType, int Rows, int Cols, int Order, bool HasDirectAccess> class ReshapedImpl_dense;
+
+} // end namespace internal
+
+template<typename XprType, int Rows, int Cols, int Order, typename StorageKind> class ReshapedImpl;
+
+template<typename XprType, int Rows, int Cols, int Order> class Reshaped
+ : public ReshapedImpl<XprType, Rows, Cols, Order, typename internal::traits<XprType>::StorageKind>
+{
+ typedef ReshapedImpl<XprType, Rows, Cols, Order, typename internal::traits<XprType>::StorageKind> Impl;
+ public:
+ //typedef typename Impl::Base Base;
+ typedef Impl Base;
+ EIGEN_GENERIC_PUBLIC_INTERFACE(Reshaped)
+ EIGEN_INHERIT_ASSIGNMENT_OPERATORS(Reshaped)
+
+ /** Fixed-size constructor
+ */
+ EIGEN_DEVICE_FUNC
+ inline Reshaped(XprType& xpr)
+ : Impl(xpr)
+ {
+ EIGEN_STATIC_ASSERT(RowsAtCompileTime!=Dynamic && ColsAtCompileTime!=Dynamic,THIS_METHOD_IS_ONLY_FOR_FIXED_SIZE)
+ eigen_assert(Rows * Cols == xpr.rows() * xpr.cols());
+ }
+
+ /** Dynamic-size constructor
+ */
+ EIGEN_DEVICE_FUNC
+ inline Reshaped(XprType& xpr,
+ Index reshapeRows, Index reshapeCols)
+ : Impl(xpr, reshapeRows, reshapeCols)
+ {
+ eigen_assert((RowsAtCompileTime==Dynamic || RowsAtCompileTime==reshapeRows)
+ && (ColsAtCompileTime==Dynamic || ColsAtCompileTime==reshapeCols));
+ eigen_assert(reshapeRows * reshapeCols == xpr.rows() * xpr.cols());
+ }
+};
+
+// The generic default implementation for dense reshape simply forward to the internal::ReshapedImpl_dense
+// that must be specialized for direct and non-direct access...
+template<typename XprType, int Rows, int Cols, int Order>
+class ReshapedImpl<XprType, Rows, Cols, Order, Dense>
+ : public internal::ReshapedImpl_dense<XprType, Rows, Cols, Order,internal::traits<Reshaped<XprType,Rows,Cols,Order> >::HasDirectAccess>
+{
+ typedef internal::ReshapedImpl_dense<XprType, Rows, Cols, Order,internal::traits<Reshaped<XprType,Rows,Cols,Order> >::HasDirectAccess> Impl;
+ public:
+ typedef Impl Base;
+ EIGEN_INHERIT_ASSIGNMENT_OPERATORS(ReshapedImpl)
+ EIGEN_DEVICE_FUNC inline ReshapedImpl(XprType& xpr) : Impl(xpr) {}
+ EIGEN_DEVICE_FUNC inline ReshapedImpl(XprType& xpr, Index reshapeRows, Index reshapeCols)
+ : Impl(xpr, reshapeRows, reshapeCols) {}
+};
+
+namespace internal {
+
+/** \internal Internal implementation of dense Reshaped in the general case. */
+template<typename XprType, int Rows, int Cols, int Order>
+class ReshapedImpl_dense<XprType,Rows,Cols,Order,false>
+ : public internal::dense_xpr_base<Reshaped<XprType, Rows, Cols, Order> >::type
+{
+ typedef Reshaped<XprType, Rows, Cols, Order> ReshapedType;
+ public:
+
+ typedef typename internal::dense_xpr_base<ReshapedType>::type Base;
+ EIGEN_DENSE_PUBLIC_INTERFACE(ReshapedType)
+ EIGEN_INHERIT_ASSIGNMENT_OPERATORS(ReshapedImpl_dense)
+
+ typedef typename internal::ref_selector<XprType>::non_const_type MatrixTypeNested;
+ typedef internal::remove_all_t<XprType> NestedExpression;
+
+ class InnerIterator;
+
+ /** Fixed-size constructor
+ */
+ EIGEN_DEVICE_FUNC
+ inline ReshapedImpl_dense(XprType& xpr)
+ : m_xpr(xpr), m_rows(Rows), m_cols(Cols)
+ {}
+
+ /** Dynamic-size constructor
+ */
+ EIGEN_DEVICE_FUNC
+ inline ReshapedImpl_dense(XprType& xpr, Index nRows, Index nCols)
+ : m_xpr(xpr), m_rows(nRows), m_cols(nCols)
+ {}
+
+ EIGEN_DEVICE_FUNC Index rows() const { return m_rows; }
+ EIGEN_DEVICE_FUNC Index cols() const { return m_cols; }
+
+ #ifdef EIGEN_PARSED_BY_DOXYGEN
+ /** \sa MapBase::data() */
+ EIGEN_DEVICE_FUNC inline const Scalar* data() const;
+ EIGEN_DEVICE_FUNC inline Index innerStride() const;
+ EIGEN_DEVICE_FUNC inline Index outerStride() const;
+ #endif
+
+ /** \returns the nested expression */
+ EIGEN_DEVICE_FUNC
+ const internal::remove_all_t<XprType>&
+ nestedExpression() const { return m_xpr; }
+
+ /** \returns the nested expression */
+ EIGEN_DEVICE_FUNC
+ std::remove_reference_t<XprType>&
+ nestedExpression() { return m_xpr; }
+
+ protected:
+
+ MatrixTypeNested m_xpr;
+ const internal::variable_if_dynamic<Index, Rows> m_rows;
+ const internal::variable_if_dynamic<Index, Cols> m_cols;
+};
+
+
+/** \internal Internal implementation of dense Reshaped in the direct access case. */
+template<typename XprType, int Rows, int Cols, int Order>
+class ReshapedImpl_dense<XprType, Rows, Cols, Order, true>
+ : public MapBase<Reshaped<XprType, Rows, Cols, Order> >
+{
+ typedef Reshaped<XprType, Rows, Cols, Order> ReshapedType;
+ typedef typename internal::ref_selector<XprType>::non_const_type XprTypeNested;
+ public:
+
+ typedef MapBase<ReshapedType> Base;
+ EIGEN_DENSE_PUBLIC_INTERFACE(ReshapedType)
+ EIGEN_INHERIT_ASSIGNMENT_OPERATORS(ReshapedImpl_dense)
+
+ /** Fixed-size constructor
+ */
+ EIGEN_DEVICE_FUNC
+ inline ReshapedImpl_dense(XprType& xpr)
+ : Base(xpr.data()), m_xpr(xpr)
+ {}
+
+ /** Dynamic-size constructor
+ */
+ EIGEN_DEVICE_FUNC
+ inline ReshapedImpl_dense(XprType& xpr, Index nRows, Index nCols)
+ : Base(xpr.data(), nRows, nCols),
+ m_xpr(xpr)
+ {}
+
+ EIGEN_DEVICE_FUNC
+ const internal::remove_all_t<XprTypeNested>& nestedExpression() const
+ {
+ return m_xpr;
+ }
+
+ EIGEN_DEVICE_FUNC
+ XprType& nestedExpression() { return m_xpr; }
+
+ /** \sa MapBase::innerStride() */
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
+ inline Index innerStride() const
+ {
+ return m_xpr.innerStride();
+ }
+
+ /** \sa MapBase::outerStride() */
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
+ inline Index outerStride() const
+ {
+ return ((Flags&RowMajorBit)==RowMajorBit) ? this->cols() : this->rows();
+ }
+
+ protected:
+
+ XprTypeNested m_xpr;
+};
+
+// Evaluators
+template<typename ArgType, int Rows, int Cols, int Order, bool HasDirectAccess> struct reshaped_evaluator;
+
+template<typename ArgType, int Rows, int Cols, int Order>
+struct evaluator<Reshaped<ArgType, Rows, Cols, Order> >
+ : reshaped_evaluator<ArgType, Rows, Cols, Order, traits<Reshaped<ArgType,Rows,Cols,Order> >::HasDirectAccess>
+{
+ typedef Reshaped<ArgType, Rows, Cols, Order> XprType;
+ typedef typename XprType::Scalar Scalar;
+ // TODO: should check for smaller packet types
+ typedef typename packet_traits<Scalar>::type PacketScalar;
+
+ enum {
+ CoeffReadCost = evaluator<ArgType>::CoeffReadCost,
+ HasDirectAccess = traits<XprType>::HasDirectAccess,
+
+// RowsAtCompileTime = traits<XprType>::RowsAtCompileTime,
+// ColsAtCompileTime = traits<XprType>::ColsAtCompileTime,
+// MaxRowsAtCompileTime = traits<XprType>::MaxRowsAtCompileTime,
+// MaxColsAtCompileTime = traits<XprType>::MaxColsAtCompileTime,
+//
+// InnerStrideAtCompileTime = traits<XprType>::HasSameStorageOrderAsXprType
+// ? int(inner_stride_at_compile_time<ArgType>::ret)
+// : Dynamic,
+// OuterStrideAtCompileTime = Dynamic,
+
+ FlagsLinearAccessBit = (traits<XprType>::RowsAtCompileTime == 1 || traits<XprType>::ColsAtCompileTime == 1 || HasDirectAccess) ? LinearAccessBit : 0,
+ FlagsRowMajorBit = (traits<XprType>::ReshapedStorageOrder==int(RowMajor)) ? RowMajorBit : 0,
+ FlagsDirectAccessBit = HasDirectAccess ? DirectAccessBit : 0,
+ Flags0 = evaluator<ArgType>::Flags & (HereditaryBits & ~RowMajorBit),
+ Flags = Flags0 | FlagsLinearAccessBit | FlagsRowMajorBit | FlagsDirectAccessBit,
+
+ PacketAlignment = unpacket_traits<PacketScalar>::alignment,
+ Alignment = evaluator<ArgType>::Alignment
+ };
+ typedef reshaped_evaluator<ArgType, Rows, Cols, Order, HasDirectAccess> reshaped_evaluator_type;
+ EIGEN_DEVICE_FUNC explicit evaluator(const XprType& xpr) : reshaped_evaluator_type(xpr)
+ {
+ EIGEN_INTERNAL_CHECK_COST_VALUE(CoeffReadCost);
+ }
+};
+
+template<typename ArgType, int Rows, int Cols, int Order>
+struct reshaped_evaluator<ArgType, Rows, Cols, Order, /* HasDirectAccess */ false>
+ : evaluator_base<Reshaped<ArgType, Rows, Cols, Order> >
+{
+ typedef Reshaped<ArgType, Rows, Cols, Order> XprType;
+
+ enum {
+ CoeffReadCost = evaluator<ArgType>::CoeffReadCost /* TODO + cost of index computations */,
+
+ Flags = (evaluator<ArgType>::Flags & (HereditaryBits /*| LinearAccessBit | DirectAccessBit*/)),
+
+ Alignment = 0
+ };
+
+ EIGEN_DEVICE_FUNC explicit reshaped_evaluator(const XprType& xpr) : m_argImpl(xpr.nestedExpression()), m_xpr(xpr)
+ {
+ EIGEN_INTERNAL_CHECK_COST_VALUE(CoeffReadCost);
+ }
+
+ typedef typename XprType::Scalar Scalar;
+ typedef typename XprType::CoeffReturnType CoeffReturnType;
+
+ typedef std::pair<Index, Index> RowCol;
+
+ EIGEN_DEVICE_FUNC inline RowCol index_remap(Index rowId, Index colId) const
+ {
+ if(Order==ColMajor)
+ {
+ const Index nth_elem_idx = colId * m_xpr.rows() + rowId;
+ return RowCol(nth_elem_idx % m_xpr.nestedExpression().rows(),
+ nth_elem_idx / m_xpr.nestedExpression().rows());
+ }
+ else
+ {
+ const Index nth_elem_idx = colId + rowId * m_xpr.cols();
+ return RowCol(nth_elem_idx / m_xpr.nestedExpression().cols(),
+ nth_elem_idx % m_xpr.nestedExpression().cols());
+ }
+ }
+
+ EIGEN_DEVICE_FUNC
+ inline Scalar& coeffRef(Index rowId, Index colId)
+ {
+ EIGEN_STATIC_ASSERT_LVALUE(XprType)
+ const RowCol row_col = index_remap(rowId, colId);
+ return m_argImpl.coeffRef(row_col.first, row_col.second);
+ }
+
+ EIGEN_DEVICE_FUNC
+ inline const Scalar& coeffRef(Index rowId, Index colId) const
+ {
+ const RowCol row_col = index_remap(rowId, colId);
+ return m_argImpl.coeffRef(row_col.first, row_col.second);
+ }
+
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE const CoeffReturnType coeff(Index rowId, Index colId) const
+ {
+ const RowCol row_col = index_remap(rowId, colId);
+ return m_argImpl.coeff(row_col.first, row_col.second);
+ }
+
+ EIGEN_DEVICE_FUNC
+ inline Scalar& coeffRef(Index index)
+ {
+ EIGEN_STATIC_ASSERT_LVALUE(XprType)
+ const RowCol row_col = index_remap(Rows == 1 ? 0 : index,
+ Rows == 1 ? index : 0);
+ return m_argImpl.coeffRef(row_col.first, row_col.second);
+
+ }
+
+ EIGEN_DEVICE_FUNC
+ inline const Scalar& coeffRef(Index index) const
+ {
+ const RowCol row_col = index_remap(Rows == 1 ? 0 : index,
+ Rows == 1 ? index : 0);
+ return m_argImpl.coeffRef(row_col.first, row_col.second);
+ }
+
+ EIGEN_DEVICE_FUNC
+ inline const CoeffReturnType coeff(Index index) const
+ {
+ const RowCol row_col = index_remap(Rows == 1 ? 0 : index,
+ Rows == 1 ? index : 0);
+ return m_argImpl.coeff(row_col.first, row_col.second);
+ }
+#if 0
+ EIGEN_DEVICE_FUNC
+ template<int LoadMode>
+ inline PacketScalar packet(Index rowId, Index colId) const
+ {
+ const RowCol row_col = index_remap(rowId, colId);
+ return m_argImpl.template packet<Unaligned>(row_col.first, row_col.second);
+
+ }
+
+ template<int LoadMode>
+ EIGEN_DEVICE_FUNC
+ inline void writePacket(Index rowId, Index colId, const PacketScalar& val)
+ {
+ const RowCol row_col = index_remap(rowId, colId);
+ m_argImpl.const_cast_derived().template writePacket<Unaligned>
+ (row_col.first, row_col.second, val);
+ }
+
+ template<int LoadMode>
+ EIGEN_DEVICE_FUNC
+ inline PacketScalar packet(Index index) const
+ {
+ const RowCol row_col = index_remap(RowsAtCompileTime == 1 ? 0 : index,
+ RowsAtCompileTime == 1 ? index : 0);
+ return m_argImpl.template packet<Unaligned>(row_col.first, row_col.second);
+ }
+
+ template<int LoadMode>
+ EIGEN_DEVICE_FUNC
+ inline void writePacket(Index index, const PacketScalar& val)
+ {
+ const RowCol row_col = index_remap(RowsAtCompileTime == 1 ? 0 : index,
+ RowsAtCompileTime == 1 ? index : 0);
+ return m_argImpl.template packet<Unaligned>(row_col.first, row_col.second, val);
+ }
+#endif
+protected:
+
+ evaluator<ArgType> m_argImpl;
+ const XprType& m_xpr;
+
+};
+
+template<typename ArgType, int Rows, int Cols, int Order>
+struct reshaped_evaluator<ArgType, Rows, Cols, Order, /* HasDirectAccess */ true>
+: mapbase_evaluator<Reshaped<ArgType, Rows, Cols, Order>,
+ typename Reshaped<ArgType, Rows, Cols, Order>::PlainObject>
+{
+ typedef Reshaped<ArgType, Rows, Cols, Order> XprType;
+ typedef typename XprType::Scalar Scalar;
+
+ EIGEN_DEVICE_FUNC explicit reshaped_evaluator(const XprType& xpr)
+ : mapbase_evaluator<XprType, typename XprType::PlainObject>(xpr)
+ {
+ // TODO: for the 3.4 release, this should be turned to an internal assertion, but let's keep it as is for the beta lifetime
+ eigen_assert(((internal::UIntPtr(xpr.data()) % plain_enum_max(1, evaluator<XprType>::Alignment)) == 0) && "data is not aligned");
+ }
+};
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_RESHAPED_H
diff --git a/Eigen/src/Core/ReturnByValue.h b/Eigen/src/Core/ReturnByValue.h
new file mode 100644
index 0000000..9025282
--- /dev/null
+++ b/Eigen/src/Core/ReturnByValue.h
@@ -0,0 +1,121 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009-2010 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2009-2010 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_RETURNBYVALUE_H
+#define EIGEN_RETURNBYVALUE_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+
+template<typename Derived>
+struct traits<ReturnByValue<Derived> >
+ : public traits<typename traits<Derived>::ReturnType>
+{
+ enum {
+ // We're disabling the DirectAccess because e.g. the constructor of
+ // the Block-with-DirectAccess expression requires to have a coeffRef method.
+ // Also, we don't want to have to implement the stride stuff.
+ Flags = (traits<typename traits<Derived>::ReturnType>::Flags
+ | EvalBeforeNestingBit) & ~DirectAccessBit
+ };
+};
+
+/* The ReturnByValue object doesn't even have a coeff() method.
+ * So the only way that nesting it in an expression can work, is by evaluating it into a plain matrix.
+ * So internal::nested always gives the plain return matrix type.
+ *
+ * FIXME: I don't understand why we need this specialization: isn't this taken care of by the EvalBeforeNestingBit ??
+ * Answer: EvalBeforeNestingBit should be deprecated since we have the evaluators
+ */
+template<typename Derived,int n,typename PlainObject>
+struct nested_eval<ReturnByValue<Derived>, n, PlainObject>
+{
+ typedef typename traits<Derived>::ReturnType type;
+};
+
+} // end namespace internal
+
+/** \class ReturnByValue
+ * \ingroup Core_Module
+ *
+ */
+template<typename Derived> class ReturnByValue
+ : public internal::dense_xpr_base< ReturnByValue<Derived> >::type, internal::no_assignment_operator
+{
+ public:
+ typedef typename internal::traits<Derived>::ReturnType ReturnType;
+
+ typedef typename internal::dense_xpr_base<ReturnByValue>::type Base;
+ EIGEN_DENSE_PUBLIC_INTERFACE(ReturnByValue)
+
+ template<typename Dest>
+ EIGEN_DEVICE_FUNC
+ inline void evalTo(Dest& dst) const
+ { static_cast<const Derived*>(this)->evalTo(dst); }
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
+ inline Index rows() const EIGEN_NOEXCEPT { return static_cast<const Derived*>(this)->rows(); }
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
+ inline Index cols() const EIGEN_NOEXCEPT { return static_cast<const Derived*>(this)->cols(); }
+
+#ifndef EIGEN_PARSED_BY_DOXYGEN
+#define Unusable YOU_ARE_TRYING_TO_ACCESS_A_SINGLE_COEFFICIENT_IN_A_SPECIAL_EXPRESSION_WHERE_THAT_IS_NOT_ALLOWED_BECAUSE_THAT_WOULD_BE_INEFFICIENT
+ class Unusable{
+ Unusable(const Unusable&) {}
+ Unusable& operator=(const Unusable&) {return *this;}
+ };
+ const Unusable& coeff(Index) const { return *reinterpret_cast<const Unusable*>(this); }
+ const Unusable& coeff(Index,Index) const { return *reinterpret_cast<const Unusable*>(this); }
+ Unusable& coeffRef(Index) { return *reinterpret_cast<Unusable*>(this); }
+ Unusable& coeffRef(Index,Index) { return *reinterpret_cast<Unusable*>(this); }
+#undef Unusable
+#endif
+};
+
+template<typename Derived>
+template<typename OtherDerived>
+EIGEN_DEVICE_FUNC Derived& DenseBase<Derived>::operator=(const ReturnByValue<OtherDerived>& other)
+{
+ other.evalTo(derived());
+ return derived();
+}
+
+namespace internal {
+
+// Expression is evaluated in a temporary; default implementation of Assignment is bypassed so that
+// when a ReturnByValue expression is assigned, the evaluator is not constructed.
+// TODO: Finalize port to new regime; ReturnByValue should not exist in the expression world
+
+template<typename Derived>
+struct evaluator<ReturnByValue<Derived> >
+ : public evaluator<typename internal::traits<Derived>::ReturnType>
+{
+ typedef ReturnByValue<Derived> XprType;
+ typedef typename internal::traits<Derived>::ReturnType PlainObject;
+ typedef evaluator<PlainObject> Base;
+
+ EIGEN_DEVICE_FUNC explicit evaluator(const XprType& xpr)
+ : m_result(xpr.rows(), xpr.cols())
+ {
+ internal::construct_at<Base>(this, m_result);
+ xpr.evalTo(m_result);
+ }
+
+protected:
+ PlainObject m_result;
+};
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_RETURNBYVALUE_H
diff --git a/Eigen/src/Core/Reverse.h b/Eigen/src/Core/Reverse.h
new file mode 100644
index 0000000..97e1d68
--- /dev/null
+++ b/Eigen/src/Core/Reverse.h
@@ -0,0 +1,219 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+// Copyright (C) 2009 Ricard Marxer <email@ricardmarxer.com>
+// Copyright (C) 2009-2010 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_REVERSE_H
+#define EIGEN_REVERSE_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+
+template<typename MatrixType, int Direction>
+struct traits<Reverse<MatrixType, Direction> >
+ : traits<MatrixType>
+{
+ typedef typename MatrixType::Scalar Scalar;
+ typedef typename traits<MatrixType>::StorageKind StorageKind;
+ typedef typename traits<MatrixType>::XprKind XprKind;
+ typedef typename ref_selector<MatrixType>::type MatrixTypeNested;
+ typedef std::remove_reference_t<MatrixTypeNested> MatrixTypeNested_;
+ enum {
+ RowsAtCompileTime = MatrixType::RowsAtCompileTime,
+ ColsAtCompileTime = MatrixType::ColsAtCompileTime,
+ MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime,
+ MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime,
+ Flags = MatrixTypeNested_::Flags & (RowMajorBit | LvalueBit)
+ };
+};
+
+template<typename PacketType, bool ReversePacket> struct reverse_packet_cond
+{
+ static inline PacketType run(const PacketType& x) { return preverse(x); }
+};
+
+template<typename PacketType> struct reverse_packet_cond<PacketType,false>
+{
+ static inline PacketType run(const PacketType& x) { return x; }
+};
+
+} // end namespace internal
+
+/** \class Reverse
+ * \ingroup Core_Module
+ *
+ * \brief Expression of the reverse of a vector or matrix
+ *
+ * \tparam MatrixType the type of the object of which we are taking the reverse
+ * \tparam Direction defines the direction of the reverse operation, can be Vertical, Horizontal, or BothDirections
+ *
+ * This class represents an expression of the reverse of a vector.
+ * It is the return type of MatrixBase::reverse() and VectorwiseOp::reverse()
+ * and most of the time this is the only way it is used.
+ *
+ * \sa MatrixBase::reverse(), VectorwiseOp::reverse()
+ */
+template<typename MatrixType, int Direction> class Reverse
+ : public internal::dense_xpr_base< Reverse<MatrixType, Direction> >::type
+{
+ public:
+
+ typedef typename internal::dense_xpr_base<Reverse>::type Base;
+ EIGEN_DENSE_PUBLIC_INTERFACE(Reverse)
+ typedef internal::remove_all_t<MatrixType> NestedExpression;
+ using Base::IsRowMajor;
+
+ protected:
+ enum {
+ PacketSize = internal::packet_traits<Scalar>::size,
+ IsColMajor = !IsRowMajor,
+ ReverseRow = (Direction == Vertical) || (Direction == BothDirections),
+ ReverseCol = (Direction == Horizontal) || (Direction == BothDirections),
+ OffsetRow = ReverseRow && IsColMajor ? PacketSize : 1,
+ OffsetCol = ReverseCol && IsRowMajor ? PacketSize : 1,
+ ReversePacket = (Direction == BothDirections)
+ || ((Direction == Vertical) && IsColMajor)
+ || ((Direction == Horizontal) && IsRowMajor)
+ };
+ typedef internal::reverse_packet_cond<PacketScalar,ReversePacket> reverse_packet;
+ public:
+
+ EIGEN_DEVICE_FUNC explicit inline Reverse(const MatrixType& matrix) : m_matrix(matrix) { }
+
+ EIGEN_INHERIT_ASSIGNMENT_OPERATORS(Reverse)
+
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
+ inline Index rows() const EIGEN_NOEXCEPT { return m_matrix.rows(); }
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
+ inline Index cols() const EIGEN_NOEXCEPT { return m_matrix.cols(); }
+
+ EIGEN_DEVICE_FUNC inline Index innerStride() const
+ {
+ return -m_matrix.innerStride();
+ }
+
+ EIGEN_DEVICE_FUNC const internal::remove_all_t<typename MatrixType::Nested>&
+ nestedExpression() const
+ {
+ return m_matrix;
+ }
+
+ protected:
+ typename MatrixType::Nested m_matrix;
+};
+
+/** \returns an expression of the reverse of *this.
+ *
+ * Example: \include MatrixBase_reverse.cpp
+ * Output: \verbinclude MatrixBase_reverse.out
+ *
+ */
+template<typename Derived>
+EIGEN_DEVICE_FUNC inline typename DenseBase<Derived>::ReverseReturnType
+DenseBase<Derived>::reverse()
+{
+ return ReverseReturnType(derived());
+}
+
+
+//reverse const overload moved DenseBase.h due to a CUDA compiler bug
+
+/** This is the "in place" version of reverse: it reverses \c *this.
+ *
+ * In most cases it is probably better to simply use the reversed expression
+ * of a matrix. However, when reversing the matrix data itself is really needed,
+ * then this "in-place" version is probably the right choice because it provides
+ * the following additional benefits:
+ * - less error prone: doing the same operation with .reverse() requires special care:
+ * \code m = m.reverse().eval(); \endcode
+ * - this API enables reverse operations without the need for a temporary
+ * - it allows future optimizations (cache friendliness, etc.)
+ *
+ * \sa VectorwiseOp::reverseInPlace(), reverse() */
+template<typename Derived>
+EIGEN_DEVICE_FUNC inline void DenseBase<Derived>::reverseInPlace()
+{
+ if(cols()>rows())
+ {
+ Index half = cols()/2;
+ leftCols(half).swap(rightCols(half).reverse());
+ if((cols()%2)==1)
+ {
+ Index half2 = rows()/2;
+ col(half).head(half2).swap(col(half).tail(half2).reverse());
+ }
+ }
+ else
+ {
+ Index half = rows()/2;
+ topRows(half).swap(bottomRows(half).reverse());
+ if((rows()%2)==1)
+ {
+ Index half2 = cols()/2;
+ row(half).head(half2).swap(row(half).tail(half2).reverse());
+ }
+ }
+}
+
+namespace internal {
+
+template<int Direction>
+struct vectorwise_reverse_inplace_impl;
+
+template<>
+struct vectorwise_reverse_inplace_impl<Vertical>
+{
+ template<typename ExpressionType>
+ static void run(ExpressionType &xpr)
+ {
+ constexpr Index HalfAtCompileTime = ExpressionType::RowsAtCompileTime==Dynamic?Dynamic:ExpressionType::RowsAtCompileTime/2;
+ Index half = xpr.rows()/2;
+ xpr.template topRows<HalfAtCompileTime>(half)
+ .swap(xpr.template bottomRows<HalfAtCompileTime>(half).colwise().reverse());
+ }
+};
+
+template<>
+struct vectorwise_reverse_inplace_impl<Horizontal>
+{
+ template<typename ExpressionType>
+ static void run(ExpressionType &xpr)
+ {
+ constexpr Index HalfAtCompileTime = ExpressionType::ColsAtCompileTime==Dynamic?Dynamic:ExpressionType::ColsAtCompileTime/2;
+ Index half = xpr.cols()/2;
+ xpr.template leftCols<HalfAtCompileTime>(half)
+ .swap(xpr.template rightCols<HalfAtCompileTime>(half).rowwise().reverse());
+ }
+};
+
+} // end namespace internal
+
+/** This is the "in place" version of VectorwiseOp::reverse: it reverses each column or row of \c *this.
+ *
+ * In most cases it is probably better to simply use the reversed expression
+ * of a matrix. However, when reversing the matrix data itself is really needed,
+ * then this "in-place" version is probably the right choice because it provides
+ * the following additional benefits:
+ * - less error prone: doing the same operation with .reverse() requires special care:
+ * \code m = m.reverse().eval(); \endcode
+ * - this API enables reverse operations without the need for a temporary
+ *
+ * \sa DenseBase::reverseInPlace(), reverse() */
+template<typename ExpressionType, int Direction>
+EIGEN_DEVICE_FUNC void VectorwiseOp<ExpressionType,Direction>::reverseInPlace()
+{
+ internal::vectorwise_reverse_inplace_impl<Direction>::run(m_matrix);
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_REVERSE_H
diff --git a/Eigen/src/Core/Select.h b/Eigen/src/Core/Select.h
new file mode 100644
index 0000000..d9ed2b2
--- /dev/null
+++ b/Eigen/src/Core/Select.h
@@ -0,0 +1,166 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2010 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_SELECT_H
+#define EIGEN_SELECT_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+/** \class Select
+ * \ingroup Core_Module
+ *
+ * \brief Expression of a coefficient wise version of the C++ ternary operator ?:
+ *
+ * \tparam ConditionMatrixType the type of the \em condition expression which must be a boolean matrix
+ * \tparam ThenMatrixType the type of the \em then expression
+ * \tparam ElseMatrixType the type of the \em else expression
+ *
+ * This class represents an expression of a coefficient wise version of the C++ ternary operator ?:.
+ * It is the return type of DenseBase::select() and most of the time this is the only way it is used.
+ *
+ * \sa DenseBase::select(const DenseBase<ThenDerived>&, const DenseBase<ElseDerived>&) const
+ */
+
+namespace internal {
+template<typename ConditionMatrixType, typename ThenMatrixType, typename ElseMatrixType>
+struct traits<Select<ConditionMatrixType, ThenMatrixType, ElseMatrixType> >
+ : traits<ThenMatrixType>
+{
+ typedef typename traits<ThenMatrixType>::Scalar Scalar;
+ typedef Dense StorageKind;
+ typedef typename traits<ThenMatrixType>::XprKind XprKind;
+ typedef typename ConditionMatrixType::Nested ConditionMatrixNested;
+ typedef typename ThenMatrixType::Nested ThenMatrixNested;
+ typedef typename ElseMatrixType::Nested ElseMatrixNested;
+ enum {
+ RowsAtCompileTime = ConditionMatrixType::RowsAtCompileTime,
+ ColsAtCompileTime = ConditionMatrixType::ColsAtCompileTime,
+ MaxRowsAtCompileTime = ConditionMatrixType::MaxRowsAtCompileTime,
+ MaxColsAtCompileTime = ConditionMatrixType::MaxColsAtCompileTime,
+ Flags = (unsigned int)ThenMatrixType::Flags & ElseMatrixType::Flags & RowMajorBit
+ };
+};
+}
+
+template<typename ConditionMatrixType, typename ThenMatrixType, typename ElseMatrixType>
+class Select : public internal::dense_xpr_base< Select<ConditionMatrixType, ThenMatrixType, ElseMatrixType> >::type,
+ internal::no_assignment_operator
+{
+ public:
+
+ typedef typename internal::dense_xpr_base<Select>::type Base;
+ EIGEN_DENSE_PUBLIC_INTERFACE(Select)
+
+ inline EIGEN_DEVICE_FUNC
+ Select(const ConditionMatrixType& a_conditionMatrix,
+ const ThenMatrixType& a_thenMatrix,
+ const ElseMatrixType& a_elseMatrix)
+ : m_condition(a_conditionMatrix), m_then(a_thenMatrix), m_else(a_elseMatrix)
+ {
+ eigen_assert(m_condition.rows() == m_then.rows() && m_condition.rows() == m_else.rows());
+ eigen_assert(m_condition.cols() == m_then.cols() && m_condition.cols() == m_else.cols());
+ }
+
+ inline EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
+ Index rows() const EIGEN_NOEXCEPT { return m_condition.rows(); }
+ inline EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
+ Index cols() const EIGEN_NOEXCEPT { return m_condition.cols(); }
+
+ inline EIGEN_DEVICE_FUNC
+ const Scalar coeff(Index i, Index j) const
+ {
+ if (m_condition.coeff(i,j))
+ return m_then.coeff(i,j);
+ else
+ return m_else.coeff(i,j);
+ }
+
+ inline EIGEN_DEVICE_FUNC
+ const Scalar coeff(Index i) const
+ {
+ if (m_condition.coeff(i))
+ return m_then.coeff(i);
+ else
+ return m_else.coeff(i);
+ }
+
+ inline EIGEN_DEVICE_FUNC const ConditionMatrixType& conditionMatrix() const
+ {
+ return m_condition;
+ }
+
+ inline EIGEN_DEVICE_FUNC const ThenMatrixType& thenMatrix() const
+ {
+ return m_then;
+ }
+
+ inline EIGEN_DEVICE_FUNC const ElseMatrixType& elseMatrix() const
+ {
+ return m_else;
+ }
+
+ protected:
+ typename ConditionMatrixType::Nested m_condition;
+ typename ThenMatrixType::Nested m_then;
+ typename ElseMatrixType::Nested m_else;
+};
+
+
+/** \returns a matrix where each coefficient (i,j) is equal to \a thenMatrix(i,j)
+ * if \c *this(i,j), and \a elseMatrix(i,j) otherwise.
+ *
+ * Example: \include MatrixBase_select.cpp
+ * Output: \verbinclude MatrixBase_select.out
+ *
+ * \sa class Select
+ */
+template<typename Derived>
+template<typename ThenDerived,typename ElseDerived>
+inline EIGEN_DEVICE_FUNC const Select<Derived,ThenDerived,ElseDerived>
+DenseBase<Derived>::select(const DenseBase<ThenDerived>& thenMatrix,
+ const DenseBase<ElseDerived>& elseMatrix) const
+{
+ return Select<Derived,ThenDerived,ElseDerived>(derived(), thenMatrix.derived(), elseMatrix.derived());
+}
+
+/** Version of DenseBase::select(const DenseBase&, const DenseBase&) with
+ * the \em else expression being a scalar value.
+ *
+ * \sa DenseBase::select(const DenseBase<ThenDerived>&, const DenseBase<ElseDerived>&) const, class Select
+ */
+template<typename Derived>
+template<typename ThenDerived>
+inline EIGEN_DEVICE_FUNC const Select<Derived,ThenDerived, typename ThenDerived::ConstantReturnType>
+DenseBase<Derived>::select(const DenseBase<ThenDerived>& thenMatrix,
+ const typename ThenDerived::Scalar& elseScalar) const
+{
+ return Select<Derived,ThenDerived,typename ThenDerived::ConstantReturnType>(
+ derived(), thenMatrix.derived(), ThenDerived::Constant(rows(),cols(),elseScalar));
+}
+
+/** Version of DenseBase::select(const DenseBase&, const DenseBase&) with
+ * the \em then expression being a scalar value.
+ *
+ * \sa DenseBase::select(const DenseBase<ThenDerived>&, const DenseBase<ElseDerived>&) const, class Select
+ */
+template<typename Derived>
+template<typename ElseDerived>
+inline EIGEN_DEVICE_FUNC const Select<Derived, typename ElseDerived::ConstantReturnType, ElseDerived >
+DenseBase<Derived>::select(const typename ElseDerived::Scalar& thenScalar,
+ const DenseBase<ElseDerived>& elseMatrix) const
+{
+ return Select<Derived,typename ElseDerived::ConstantReturnType,ElseDerived>(
+ derived(), ElseDerived::Constant(rows(),cols(),thenScalar), elseMatrix.derived());
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_SELECT_H
diff --git a/Eigen/src/Core/SelfAdjointView.h b/Eigen/src/Core/SelfAdjointView.h
new file mode 100644
index 0000000..7a930db
--- /dev/null
+++ b/Eigen/src/Core/SelfAdjointView.h
@@ -0,0 +1,365 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_SELFADJOINTMATRIX_H
+#define EIGEN_SELFADJOINTMATRIX_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+/** \class SelfAdjointView
+ * \ingroup Core_Module
+ *
+ *
+ * \brief Expression of a selfadjoint matrix from a triangular part of a dense matrix
+ *
+ * \tparam MatrixType the type of the dense matrix storing the coefficients
+ * \tparam TriangularPart can be either \c #Lower or \c #Upper
+ *
+ * This class is an expression of a sefladjoint matrix from a triangular part of a matrix
+ * with given dense storage of the coefficients. It is the return type of MatrixBase::selfadjointView()
+ * and most of the time this is the only way that it is used.
+ *
+ * \sa class TriangularBase, MatrixBase::selfadjointView()
+ */
+
+namespace internal {
+template<typename MatrixType, unsigned int UpLo>
+struct traits<SelfAdjointView<MatrixType, UpLo> > : traits<MatrixType>
+{
+ typedef typename ref_selector<MatrixType>::non_const_type MatrixTypeNested;
+ typedef remove_all_t<MatrixTypeNested> MatrixTypeNestedCleaned;
+ typedef MatrixType ExpressionType;
+ typedef typename MatrixType::PlainObject FullMatrixType;
+ enum {
+ Mode = UpLo | SelfAdjoint,
+ FlagsLvalueBit = is_lvalue<MatrixType>::value ? LvalueBit : 0,
+ Flags = MatrixTypeNestedCleaned::Flags & (HereditaryBits|FlagsLvalueBit)
+ & (~(PacketAccessBit | DirectAccessBit | LinearAccessBit)) // FIXME these flags should be preserved
+ };
+};
+}
+
+
+template<typename MatrixType_, unsigned int UpLo> class SelfAdjointView
+ : public TriangularBase<SelfAdjointView<MatrixType_, UpLo> >
+{
+ public:
+ EIGEN_STATIC_ASSERT(UpLo==Lower || UpLo==Upper,SELFADJOINTVIEW_ACCEPTS_UPPER_AND_LOWER_MODE_ONLY)
+
+ typedef MatrixType_ MatrixType;
+ typedef TriangularBase<SelfAdjointView> Base;
+ typedef typename internal::traits<SelfAdjointView>::MatrixTypeNested MatrixTypeNested;
+ typedef typename internal::traits<SelfAdjointView>::MatrixTypeNestedCleaned MatrixTypeNestedCleaned;
+ typedef MatrixTypeNestedCleaned NestedExpression;
+
+ /** \brief The type of coefficients in this matrix */
+ typedef typename internal::traits<SelfAdjointView>::Scalar Scalar;
+ typedef typename MatrixType::StorageIndex StorageIndex;
+ typedef internal::remove_all_t<typename MatrixType::ConjugateReturnType> MatrixConjugateReturnType;
+ typedef SelfAdjointView<std::add_const_t<MatrixType>, UpLo> ConstSelfAdjointView;
+
+ enum {
+ Mode = internal::traits<SelfAdjointView>::Mode,
+ Flags = internal::traits<SelfAdjointView>::Flags,
+ TransposeMode = ((int(Mode) & int(Upper)) ? Lower : 0) | ((int(Mode) & int(Lower)) ? Upper : 0)
+ };
+ typedef typename MatrixType::PlainObject PlainObject;
+
+ EIGEN_DEVICE_FUNC
+ explicit inline SelfAdjointView(MatrixType& matrix) : m_matrix(matrix) { }
+
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
+ inline Index rows() const EIGEN_NOEXCEPT { return m_matrix.rows(); }
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
+ inline Index cols() const EIGEN_NOEXCEPT { return m_matrix.cols(); }
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
+ inline Index outerStride() const EIGEN_NOEXCEPT { return m_matrix.outerStride(); }
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
+ inline Index innerStride() const EIGEN_NOEXCEPT { return m_matrix.innerStride(); }
+
+ /** \sa MatrixBase::coeff()
+ * \warning the coordinates must fit into the referenced triangular part
+ */
+ EIGEN_DEVICE_FUNC
+ inline Scalar coeff(Index row, Index col) const
+ {
+ Base::check_coordinates_internal(row, col);
+ return m_matrix.coeff(row, col);
+ }
+
+ /** \sa MatrixBase::coeffRef()
+ * \warning the coordinates must fit into the referenced triangular part
+ */
+ EIGEN_DEVICE_FUNC
+ inline Scalar& coeffRef(Index row, Index col)
+ {
+ EIGEN_STATIC_ASSERT_LVALUE(SelfAdjointView);
+ Base::check_coordinates_internal(row, col);
+ return m_matrix.coeffRef(row, col);
+ }
+
+ /** \internal */
+ EIGEN_DEVICE_FUNC
+ const MatrixTypeNestedCleaned& _expression() const { return m_matrix; }
+
+ EIGEN_DEVICE_FUNC
+ const MatrixTypeNestedCleaned& nestedExpression() const { return m_matrix; }
+ EIGEN_DEVICE_FUNC
+ MatrixTypeNestedCleaned& nestedExpression() { return m_matrix; }
+
+ /** Efficient triangular matrix times vector/matrix product */
+ template<typename OtherDerived>
+ EIGEN_DEVICE_FUNC
+ const Product<SelfAdjointView,OtherDerived>
+ operator*(const MatrixBase<OtherDerived>& rhs) const
+ {
+ return Product<SelfAdjointView,OtherDerived>(*this, rhs.derived());
+ }
+
+ /** Efficient vector/matrix times triangular matrix product */
+ template<typename OtherDerived> friend
+ EIGEN_DEVICE_FUNC
+ const Product<OtherDerived,SelfAdjointView>
+ operator*(const MatrixBase<OtherDerived>& lhs, const SelfAdjointView& rhs)
+ {
+ return Product<OtherDerived,SelfAdjointView>(lhs.derived(),rhs);
+ }
+
+ friend EIGEN_DEVICE_FUNC
+ const SelfAdjointView<const EIGEN_SCALAR_BINARYOP_EXPR_RETURN_TYPE(Scalar,MatrixType,product),UpLo>
+ operator*(const Scalar& s, const SelfAdjointView& mat)
+ {
+ return (s*mat.nestedExpression()).template selfadjointView<UpLo>();
+ }
+
+ /** Perform a symmetric rank 2 update of the selfadjoint matrix \c *this:
+ * \f$ this = this + \alpha u v^* + conj(\alpha) v u^* \f$
+ * \returns a reference to \c *this
+ *
+ * The vectors \a u and \c v \b must be column vectors, however they can be
+ * a adjoint expression without any overhead. Only the meaningful triangular
+ * part of the matrix is updated, the rest is left unchanged.
+ *
+ * \sa rankUpdate(const MatrixBase<DerivedU>&, Scalar)
+ */
+ template<typename DerivedU, typename DerivedV>
+ EIGEN_DEVICE_FUNC
+ SelfAdjointView& rankUpdate(const MatrixBase<DerivedU>& u, const MatrixBase<DerivedV>& v, const Scalar& alpha = Scalar(1));
+
+ /** Perform a symmetric rank K update of the selfadjoint matrix \c *this:
+ * \f$ this = this + \alpha ( u u^* ) \f$ where \a u is a vector or matrix.
+ *
+ * \returns a reference to \c *this
+ *
+ * Note that to perform \f$ this = this + \alpha ( u^* u ) \f$ you can simply
+ * call this function with u.adjoint().
+ *
+ * \sa rankUpdate(const MatrixBase<DerivedU>&, const MatrixBase<DerivedV>&, Scalar)
+ */
+ template<typename DerivedU>
+ EIGEN_DEVICE_FUNC
+ SelfAdjointView& rankUpdate(const MatrixBase<DerivedU>& u, const Scalar& alpha = Scalar(1));
+
+ /** \returns an expression of a triangular view extracted from the current selfadjoint view of a given triangular part
+ *
+ * The parameter \a TriMode can have the following values: \c #Upper, \c #StrictlyUpper, \c #UnitUpper,
+ * \c #Lower, \c #StrictlyLower, \c #UnitLower.
+ *
+ * If \c TriMode references the same triangular part than \c *this, then this method simply return a \c TriangularView of the nested expression,
+ * otherwise, the nested expression is first transposed, thus returning a \c TriangularView<Transpose<MatrixType>> object.
+ *
+ * \sa MatrixBase::triangularView(), class TriangularView
+ */
+ template<unsigned int TriMode>
+ EIGEN_DEVICE_FUNC
+ std::conditional_t<(TriMode&(Upper|Lower))==(UpLo&(Upper|Lower)),
+ TriangularView<MatrixType,TriMode>,
+ TriangularView<typename MatrixType::AdjointReturnType,TriMode> >
+ triangularView() const
+ {
+ std::conditional_t<(TriMode&(Upper|Lower))==(UpLo&(Upper|Lower)), MatrixType&, typename MatrixType::ConstTransposeReturnType> tmp1(m_matrix);
+ std::conditional_t<(TriMode&(Upper|Lower))==(UpLo&(Upper|Lower)), MatrixType&, typename MatrixType::AdjointReturnType> tmp2(tmp1);
+ return std::conditional_t<(TriMode&(Upper|Lower))==(UpLo&(Upper|Lower)),
+ TriangularView<MatrixType,TriMode>,
+ TriangularView<typename MatrixType::AdjointReturnType,TriMode> >(tmp2);
+ }
+
+ typedef SelfAdjointView<const MatrixConjugateReturnType,UpLo> ConjugateReturnType;
+ /** \sa MatrixBase::conjugate() const */
+ EIGEN_DEVICE_FUNC
+ inline const ConjugateReturnType conjugate() const
+ { return ConjugateReturnType(m_matrix.conjugate()); }
+
+ /** \returns an expression of the complex conjugate of \c *this if Cond==true,
+ * returns \c *this otherwise.
+ */
+ template<bool Cond>
+ EIGEN_DEVICE_FUNC
+ inline std::conditional_t<Cond,ConjugateReturnType,ConstSelfAdjointView>
+ conjugateIf() const
+ {
+ typedef std::conditional_t<Cond,ConjugateReturnType,ConstSelfAdjointView> ReturnType;
+ return ReturnType(m_matrix.template conjugateIf<Cond>());
+ }
+
+ typedef SelfAdjointView<const typename MatrixType::AdjointReturnType,TransposeMode> AdjointReturnType;
+ /** \sa MatrixBase::adjoint() const */
+ EIGEN_DEVICE_FUNC
+ inline const AdjointReturnType adjoint() const
+ { return AdjointReturnType(m_matrix.adjoint()); }
+
+ typedef SelfAdjointView<typename MatrixType::TransposeReturnType,TransposeMode> TransposeReturnType;
+ /** \sa MatrixBase::transpose() */
+ template<class Dummy=int>
+ EIGEN_DEVICE_FUNC
+ inline TransposeReturnType transpose(std::enable_if_t<Eigen::internal::is_lvalue<MatrixType>::value, Dummy*> = nullptr)
+ {
+ typename MatrixType::TransposeReturnType tmp(m_matrix);
+ return TransposeReturnType(tmp);
+ }
+
+ typedef SelfAdjointView<const typename MatrixType::ConstTransposeReturnType,TransposeMode> ConstTransposeReturnType;
+ /** \sa MatrixBase::transpose() const */
+ EIGEN_DEVICE_FUNC
+ inline const ConstTransposeReturnType transpose() const
+ {
+ return ConstTransposeReturnType(m_matrix.transpose());
+ }
+
+ /** \returns a const expression of the main diagonal of the matrix \c *this
+ *
+ * This method simply returns the diagonal of the nested expression, thus by-passing the SelfAdjointView decorator.
+ *
+ * \sa MatrixBase::diagonal(), class Diagonal */
+ EIGEN_DEVICE_FUNC
+ typename MatrixType::ConstDiagonalReturnType diagonal() const
+ {
+ return typename MatrixType::ConstDiagonalReturnType(m_matrix);
+ }
+
+/////////// Cholesky module ///////////
+
+ const LLT<PlainObject, UpLo> llt() const;
+ const LDLT<PlainObject, UpLo> ldlt() const;
+
+/////////// Eigenvalue module ///////////
+
+ /** Real part of #Scalar */
+ typedef typename NumTraits<Scalar>::Real RealScalar;
+ /** Return type of eigenvalues() */
+ typedef Matrix<RealScalar, internal::traits<MatrixType>::ColsAtCompileTime, 1> EigenvaluesReturnType;
+
+ EIGEN_DEVICE_FUNC
+ EigenvaluesReturnType eigenvalues() const;
+ EIGEN_DEVICE_FUNC
+ RealScalar operatorNorm() const;
+
+ protected:
+ MatrixTypeNested m_matrix;
+};
+
+
+// template<typename OtherDerived, typename MatrixType, unsigned int UpLo>
+// internal::selfadjoint_matrix_product_returntype<OtherDerived,SelfAdjointView<MatrixType,UpLo> >
+// operator*(const MatrixBase<OtherDerived>& lhs, const SelfAdjointView<MatrixType,UpLo>& rhs)
+// {
+// return internal::matrix_selfadjoint_product_returntype<OtherDerived,SelfAdjointView<MatrixType,UpLo> >(lhs.derived(),rhs);
+// }
+
+// selfadjoint to dense matrix
+
+namespace internal {
+
+// TODO currently a selfadjoint expression has the form SelfAdjointView<.,.>
+// in the future selfadjoint-ness should be defined by the expression traits
+// such that Transpose<SelfAdjointView<.,.> > is valid. (currently TriangularBase::transpose() is overloaded to make it work)
+template<typename MatrixType, unsigned int Mode>
+struct evaluator_traits<SelfAdjointView<MatrixType,Mode> >
+{
+ typedef typename storage_kind_to_evaluator_kind<typename MatrixType::StorageKind>::Kind Kind;
+ typedef SelfAdjointShape Shape;
+};
+
+template<int UpLo, int SetOpposite, typename DstEvaluatorTypeT, typename SrcEvaluatorTypeT, typename Functor, int Version>
+class triangular_dense_assignment_kernel<UpLo,SelfAdjoint,SetOpposite,DstEvaluatorTypeT,SrcEvaluatorTypeT,Functor,Version>
+ : public generic_dense_assignment_kernel<DstEvaluatorTypeT, SrcEvaluatorTypeT, Functor, Version>
+{
+protected:
+ typedef generic_dense_assignment_kernel<DstEvaluatorTypeT, SrcEvaluatorTypeT, Functor, Version> Base;
+ typedef typename Base::DstXprType DstXprType;
+ typedef typename Base::SrcXprType SrcXprType;
+ using Base::m_dst;
+ using Base::m_src;
+ using Base::m_functor;
+public:
+
+ typedef typename Base::DstEvaluatorType DstEvaluatorType;
+ typedef typename Base::SrcEvaluatorType SrcEvaluatorType;
+ typedef typename Base::Scalar Scalar;
+ typedef typename Base::AssignmentTraits AssignmentTraits;
+
+
+ EIGEN_DEVICE_FUNC triangular_dense_assignment_kernel(DstEvaluatorType &dst, const SrcEvaluatorType &src, const Functor &func, DstXprType& dstExpr)
+ : Base(dst, src, func, dstExpr)
+ {}
+
+ EIGEN_DEVICE_FUNC void assignCoeff(Index row, Index col)
+ {
+ eigen_internal_assert(row!=col);
+ Scalar tmp = m_src.coeff(row,col);
+ m_functor.assignCoeff(m_dst.coeffRef(row,col), tmp);
+ m_functor.assignCoeff(m_dst.coeffRef(col,row), numext::conj(tmp));
+ }
+
+ EIGEN_DEVICE_FUNC void assignDiagonalCoeff(Index id)
+ {
+ Base::assignCoeff(id,id);
+ }
+
+ EIGEN_DEVICE_FUNC void assignOppositeCoeff(Index, Index)
+ { eigen_internal_assert(false && "should never be called"); }
+};
+
+} // end namespace internal
+
+/***************************************************************************
+* Implementation of MatrixBase methods
+***************************************************************************/
+
+/** This is the const version of MatrixBase::selfadjointView() */
+template<typename Derived>
+template<unsigned int UpLo>
+EIGEN_DEVICE_FUNC typename MatrixBase<Derived>::template ConstSelfAdjointViewReturnType<UpLo>::Type
+MatrixBase<Derived>::selfadjointView() const
+{
+ return typename ConstSelfAdjointViewReturnType<UpLo>::Type(derived());
+}
+
+/** \returns an expression of a symmetric/self-adjoint view extracted from the upper or lower triangular part of the current matrix
+ *
+ * The parameter \a UpLo can be either \c #Upper or \c #Lower
+ *
+ * Example: \include MatrixBase_selfadjointView.cpp
+ * Output: \verbinclude MatrixBase_selfadjointView.out
+ *
+ * \sa class SelfAdjointView
+ */
+template<typename Derived>
+template<unsigned int UpLo>
+EIGEN_DEVICE_FUNC typename MatrixBase<Derived>::template SelfAdjointViewReturnType<UpLo>::Type
+MatrixBase<Derived>::selfadjointView()
+{
+ return typename SelfAdjointViewReturnType<UpLo>::Type(derived());
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_SELFADJOINTMATRIX_H
diff --git a/Eigen/src/Core/SelfCwiseBinaryOp.h b/Eigen/src/Core/SelfCwiseBinaryOp.h
new file mode 100644
index 0000000..14dbec0
--- /dev/null
+++ b/Eigen/src/Core/SelfCwiseBinaryOp.h
@@ -0,0 +1,49 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009-2010 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_SELFCWISEBINARYOP_H
+#define EIGEN_SELFCWISEBINARYOP_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+// TODO generalize the scalar type of 'other'
+
+template<typename Derived>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& DenseBase<Derived>::operator*=(const Scalar& other)
+{
+ internal::call_assignment(this->derived(), PlainObject::Constant(rows(),cols(),other), internal::mul_assign_op<Scalar,Scalar>());
+ return derived();
+}
+
+template<typename Derived>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& ArrayBase<Derived>::operator+=(const Scalar& other)
+{
+ internal::call_assignment(this->derived(), PlainObject::Constant(rows(),cols(),other), internal::add_assign_op<Scalar,Scalar>());
+ return derived();
+}
+
+template<typename Derived>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& ArrayBase<Derived>::operator-=(const Scalar& other)
+{
+ internal::call_assignment(this->derived(), PlainObject::Constant(rows(),cols(),other), internal::sub_assign_op<Scalar,Scalar>());
+ return derived();
+}
+
+template<typename Derived>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& DenseBase<Derived>::operator/=(const Scalar& other)
+{
+ internal::call_assignment(this->derived(), PlainObject::Constant(rows(),cols(),other), internal::div_assign_op<Scalar,Scalar>());
+ return derived();
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_SELFCWISEBINARYOP_H
diff --git a/Eigen/src/Core/SkewSymmetricMatrix3.h b/Eigen/src/Core/SkewSymmetricMatrix3.h
new file mode 100644
index 0000000..7f6b5fd
--- /dev/null
+++ b/Eigen/src/Core/SkewSymmetricMatrix3.h
@@ -0,0 +1,412 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2007-2009 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_SKEWSYMMETRICMATRIX3_H
+#define EIGEN_SKEWSYMMETRICMATRIX3_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+/** \class SkewSymmetricBase
+ * \ingroup Core_Module
+ *
+ * \brief Base class for skew symmetric matrices and expressions
+ *
+ * This is the base class that is inherited by SkewSymmetricMatrix3 and related expression
+ * types, which internally use a three vector for storing the entries. SkewSymmetric
+ * types always represent square three times three matrices.
+ *
+ * This implementations follows class DiagonalMatrix
+ *
+ * \tparam Derived is the derived type, a SkewSymmetricMatrix3 or SkewSymmetricWrapper.
+ *
+ * \sa class SkewSymmetricMatrix3, class SkewSymmetricWrapper
+ */
+template<typename Derived>
+class SkewSymmetricBase : public EigenBase<Derived>
+{
+ public:
+ typedef typename internal::traits<Derived>::SkewSymmetricVectorType SkewSymmetricVectorType;
+ typedef typename SkewSymmetricVectorType::Scalar Scalar;
+ typedef typename SkewSymmetricVectorType::RealScalar RealScalar;
+ typedef typename internal::traits<Derived>::StorageKind StorageKind;
+ typedef typename internal::traits<Derived>::StorageIndex StorageIndex;
+
+ enum {
+ RowsAtCompileTime = SkewSymmetricVectorType::SizeAtCompileTime,
+ ColsAtCompileTime = SkewSymmetricVectorType::SizeAtCompileTime,
+ MaxRowsAtCompileTime = SkewSymmetricVectorType::MaxSizeAtCompileTime,
+ MaxColsAtCompileTime = SkewSymmetricVectorType::MaxSizeAtCompileTime,
+ IsVectorAtCompileTime = 0,
+ Flags = NoPreferredStorageOrderBit
+ };
+
+ typedef Matrix<Scalar, RowsAtCompileTime, ColsAtCompileTime, 0, MaxRowsAtCompileTime, MaxColsAtCompileTime> DenseMatrixType;
+ typedef DenseMatrixType DenseType;
+ typedef SkewSymmetricMatrix3<Scalar> PlainObject;
+
+ /** \returns a reference to the derived object. */
+ EIGEN_DEVICE_FUNC
+ inline const Derived& derived() const { return *static_cast<const Derived*>(this); }
+ /** \returns a const reference to the derived object. */
+ EIGEN_DEVICE_FUNC
+ inline Derived& derived() { return *static_cast<Derived*>(this); }
+
+ /**
+ * Constructs a dense matrix from \c *this. Note, this directly returns a dense matrix type,
+ * not an expression.
+ * \returns A dense matrix, with its entries set from the the derived object. */
+ EIGEN_DEVICE_FUNC
+ DenseMatrixType toDenseMatrix() const { return derived(); }
+
+ /** Determinant vanishes */
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
+ inline Scalar determinant() const { return 0; }
+
+ /** A.transpose() = -A */
+ EIGEN_DEVICE_FUNC
+ PlainObject transpose() const { return (-vector()).asSkewSymmetric(); }
+
+ /** \returns the exponential of this matrix using Rodrigues’ formula */
+ EIGEN_DEVICE_FUNC
+ DenseMatrixType exponential() const {
+ DenseMatrixType retVal = DenseMatrixType::Identity();
+ const SkewSymmetricVectorType& v = vector();
+ if (v.isZero()) {
+ return retVal;
+ }
+ const Scalar norm2 = v.squaredNorm();
+ const Scalar norm = numext::sqrt(norm2);
+ retVal += ((((1 - numext::cos(norm))/norm2)*derived())*derived()) + (numext::sin(norm)/norm)*derived().toDenseMatrix();
+ return retVal;
+ }
+
+ /** \returns a reference to the derived object's vector of coefficients. */
+ EIGEN_DEVICE_FUNC
+ inline const SkewSymmetricVectorType& vector() const { return derived().vector(); }
+ /** \returns a const reference to the derived object's vector of coefficients. */
+ EIGEN_DEVICE_FUNC
+ inline SkewSymmetricVectorType& vector() { return derived().vector(); }
+
+ /** \returns the number of rows. */
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
+ inline Index rows() const { return 3; }
+ /** \returns the number of columns. */
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
+ inline Index cols() const { return 3; }
+
+ /** \returns the matrix product of \c *this by the dense matrix, \a matrix */
+ template<typename MatrixDerived>
+ EIGEN_DEVICE_FUNC
+ Product<Derived,MatrixDerived,LazyProduct>
+ operator*(const MatrixBase<MatrixDerived> &matrix) const
+ {
+ return Product<Derived, MatrixDerived, LazyProduct>(derived(), matrix.derived());
+ }
+
+ /** \returns the matrix product of \c *this by the skew symmetric matrix, \a matrix */
+ template<typename MatrixDerived>
+ EIGEN_DEVICE_FUNC
+ Product<Derived,MatrixDerived,LazyProduct>
+ operator*(const SkewSymmetricBase<MatrixDerived> &matrix) const
+ {
+ return Product<Derived, MatrixDerived, LazyProduct>(derived(), matrix.derived());
+ }
+
+ template <typename OtherDerived>
+ using SkewSymmetricProductReturnType = SkewSymmetricWrapper<const EIGEN_CWISE_BINARY_RETURN_TYPE(
+ SkewSymmetricVectorType, typename OtherDerived::SkewSymmetricVectorType, product)>;
+
+ /** \returns the wedge product of \c *this by the skew symmetric matrix \a other
+ * A wedge B = AB - BA */
+ template <typename OtherDerived>
+ EIGEN_DEVICE_FUNC SkewSymmetricProductReturnType<OtherDerived> wedge(
+ const SkewSymmetricBase<OtherDerived>& other) const {
+ return vector().cross(other.vector()).asSkewSymmetric();
+ }
+
+ using SkewSymmetricScaleReturnType =
+ SkewSymmetricWrapper<const EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(SkewSymmetricVectorType, Scalar, product)>;
+
+ /** \returns the product of \c *this by the scalar \a scalar */
+ EIGEN_DEVICE_FUNC
+ inline SkewSymmetricScaleReturnType operator*(const Scalar& scalar) const {
+ return (vector() * scalar).asSkewSymmetric();
+ }
+
+ using ScaleSkewSymmetricReturnType =
+ SkewSymmetricWrapper<const EIGEN_SCALAR_BINARYOP_EXPR_RETURN_TYPE(Scalar, SkewSymmetricVectorType, product)>;
+
+ /** \returns the product of a scalar and the skew symmetric matrix \a other */
+ EIGEN_DEVICE_FUNC
+ friend inline ScaleSkewSymmetricReturnType operator*(const Scalar& scalar, const SkewSymmetricBase& other) {
+ return (scalar * other.vector()).asSkewSymmetric();
+ }
+
+ template <typename OtherDerived>
+ using SkewSymmetricSumReturnType = SkewSymmetricWrapper<const EIGEN_CWISE_BINARY_RETURN_TYPE(
+ SkewSymmetricVectorType, typename OtherDerived::SkewSymmetricVectorType, sum)>;
+
+ /** \returns the sum of \c *this and the skew symmetric matrix \a other */
+ template <typename OtherDerived>
+ EIGEN_DEVICE_FUNC inline SkewSymmetricSumReturnType<OtherDerived> operator+(
+ const SkewSymmetricBase<OtherDerived>& other) const {
+ return (vector() + other.vector()).asSkewSymmetric();
+ }
+
+ template <typename OtherDerived>
+ using SkewSymmetricDifferenceReturnType = SkewSymmetricWrapper<const EIGEN_CWISE_BINARY_RETURN_TYPE(
+ SkewSymmetricVectorType, typename OtherDerived::SkewSymmetricVectorType, difference)>;
+
+ /** \returns the difference of \c *this and the skew symmetric matrix \a other */
+ template <typename OtherDerived>
+ EIGEN_DEVICE_FUNC inline SkewSymmetricDifferenceReturnType<OtherDerived> operator-(
+ const SkewSymmetricBase<OtherDerived>& other) const {
+ return (vector() - other.vector()).asSkewSymmetric();
+ }
+};
+
+/** \class SkewSymmetricMatrix3
+ * \ingroup Core_Module
+ *
+ * \brief Represents a 3x3 skew symmetric matrix with its storage
+ *
+ * \tparam Scalar_ the type of coefficients
+ *
+ * \sa class SkewSymmetricBase, class SkewSymmetricWrapper
+ */
+
+namespace internal {
+template<typename Scalar_>
+struct traits<SkewSymmetricMatrix3<Scalar_> >
+ : traits<Matrix<Scalar_,3,3,0,3,3> >
+{
+ typedef Matrix<Scalar_,3,1,0,3,1> SkewSymmetricVectorType;
+ typedef SkewSymmetricShape StorageKind;
+ enum {
+ Flags = LvalueBit | NoPreferredStorageOrderBit | NestByRefBit
+ };
+};
+}
+template<typename Scalar_>
+class SkewSymmetricMatrix3
+ : public SkewSymmetricBase<SkewSymmetricMatrix3<Scalar_> >
+{
+ public:
+ #ifndef EIGEN_PARSED_BY_DOXYGEN
+ typedef typename internal::traits<SkewSymmetricMatrix3>::SkewSymmetricVectorType SkewSymmetricVectorType;
+ typedef const SkewSymmetricMatrix3& Nested;
+ typedef Scalar_ Scalar;
+ typedef typename internal::traits<SkewSymmetricMatrix3>::StorageKind StorageKind;
+ typedef typename internal::traits<SkewSymmetricMatrix3>::StorageIndex StorageIndex;
+ #endif
+
+ protected:
+
+ SkewSymmetricVectorType m_vector;
+
+ public:
+
+ /** const version of vector(). */
+ EIGEN_DEVICE_FUNC
+ inline const SkewSymmetricVectorType& vector() const { return m_vector; }
+ /** \returns a reference to the stored vector of coefficients. */
+ EIGEN_DEVICE_FUNC
+ inline SkewSymmetricVectorType& vector() { return m_vector; }
+
+ /** Default constructor without initialization */
+ EIGEN_DEVICE_FUNC
+ inline SkewSymmetricMatrix3() {}
+
+ /** Constructor from three scalars */
+ EIGEN_DEVICE_FUNC
+ inline SkewSymmetricMatrix3(const Scalar& x, const Scalar& y, const Scalar& z) : m_vector(x,y,z) {}
+
+ /** \brief Constructs a SkewSymmetricMatrix3 from an r-value vector type */
+ EIGEN_DEVICE_FUNC
+ explicit inline SkewSymmetricMatrix3(SkewSymmetricVectorType&& vec) : m_vector(std::move(vec)) {}
+
+ /** generic constructor from expression of the coefficients */
+ template<typename OtherDerived>
+ EIGEN_DEVICE_FUNC
+ explicit inline SkewSymmetricMatrix3(const MatrixBase<OtherDerived>& other) : m_vector(other)
+ {}
+
+ /** Copy constructor. */
+ template<typename OtherDerived>
+ EIGEN_DEVICE_FUNC
+ inline SkewSymmetricMatrix3(const SkewSymmetricBase<OtherDerived>& other) : m_vector(other.vector()) {}
+
+ #ifndef EIGEN_PARSED_BY_DOXYGEN
+ /** copy constructor. prevent a default copy constructor from hiding the other templated constructor */
+ inline SkewSymmetricMatrix3(const SkewSymmetricMatrix3& other) : m_vector(other.vector()) {}
+ #endif
+
+ /** Copy operator. */
+ template<typename OtherDerived>
+ EIGEN_DEVICE_FUNC
+ SkewSymmetricMatrix3& operator=(const SkewSymmetricBase<OtherDerived>& other)
+ {
+ m_vector = other.vector();
+ return *this;
+ }
+
+ #ifndef EIGEN_PARSED_BY_DOXYGEN
+ /** This is a special case of the templated operator=. Its purpose is to
+ * prevent a default operator= from hiding the templated operator=.
+ */
+ EIGEN_DEVICE_FUNC
+ SkewSymmetricMatrix3& operator=(const SkewSymmetricMatrix3& other)
+ {
+ m_vector = other.vector();
+ return *this;
+ }
+ #endif
+
+ typedef SkewSymmetricWrapper<const CwiseNullaryOp<internal::scalar_constant_op<Scalar>, SkewSymmetricVectorType>>
+ InitializeReturnType;
+
+ /** Initializes a skew symmetric matrix with coefficients set to zero */
+ EIGEN_DEVICE_FUNC
+ static InitializeReturnType Zero() { return SkewSymmetricVectorType::Zero().asSkewSymmetric(); }
+
+ /** Sets all coefficients to zero. */
+ EIGEN_DEVICE_FUNC
+ inline void setZero() { m_vector.setZero(); }
+};
+
+/** \class SkewSymmetricWrapper
+ * \ingroup Core_Module
+ *
+ * \brief Expression of a skew symmetric matrix
+ *
+ * \tparam SkewSymmetricVectorType_ the type of the vector of coefficients
+ *
+ * This class is an expression of a skew symmetric matrix, but not storing its own vector of coefficients,
+ * instead wrapping an existing vector expression. It is the return type of MatrixBase::asSkewSymmetric()
+ * and most of the time this is the only way that it is used.
+ *
+ * \sa class SkewSymmetricMatrix3, class SkewSymmetricBase, MatrixBase::asSkewSymmetric()
+ */
+
+namespace internal {
+template<typename SkewSymmetricVectorType_>
+struct traits<SkewSymmetricWrapper<SkewSymmetricVectorType_> >
+{
+ typedef SkewSymmetricVectorType_ SkewSymmetricVectorType;
+ typedef typename SkewSymmetricVectorType::Scalar Scalar;
+ typedef typename SkewSymmetricVectorType::StorageIndex StorageIndex;
+ typedef SkewSymmetricShape StorageKind;
+ typedef typename traits<SkewSymmetricVectorType>::XprKind XprKind;
+ enum {
+ RowsAtCompileTime = SkewSymmetricVectorType::SizeAtCompileTime,
+ ColsAtCompileTime = SkewSymmetricVectorType::SizeAtCompileTime,
+ MaxRowsAtCompileTime = SkewSymmetricVectorType::MaxSizeAtCompileTime,
+ MaxColsAtCompileTime = SkewSymmetricVectorType::MaxSizeAtCompileTime,
+ Flags = (traits<SkewSymmetricVectorType>::Flags & LvalueBit) | NoPreferredStorageOrderBit
+ };
+};
+}
+
+template<typename SkewSymmetricVectorType_>
+class SkewSymmetricWrapper
+ : public SkewSymmetricBase<SkewSymmetricWrapper<SkewSymmetricVectorType_> >, internal::no_assignment_operator
+{
+ public:
+ #ifndef EIGEN_PARSED_BY_DOXYGEN
+ typedef SkewSymmetricVectorType_ SkewSymmetricVectorType;
+ typedef SkewSymmetricWrapper Nested;
+ #endif
+
+ /** Constructor from expression of coefficients to wrap. */
+ EIGEN_DEVICE_FUNC
+ explicit inline SkewSymmetricWrapper(SkewSymmetricVectorType& a_vector) : m_vector(a_vector) {}
+
+ /** \returns a const reference to the wrapped expression of coefficients. */
+ EIGEN_DEVICE_FUNC
+ const SkewSymmetricVectorType& vector() const { return m_vector; }
+
+ protected:
+ typename SkewSymmetricVectorType::Nested m_vector;
+};
+
+/** \returns a pseudo-expression of a skew symmetric matrix with *this as vector of coefficients
+ *
+ * \only_for_vectors
+ *
+ * \sa class SkewSymmetricWrapper, class SkewSymmetricMatrix3, vector(), isSkewSymmetric()
+ **/
+template<typename Derived>
+EIGEN_DEVICE_FUNC inline const SkewSymmetricWrapper<const Derived>
+MatrixBase<Derived>::asSkewSymmetric() const
+{
+ return SkewSymmetricWrapper<const Derived>(derived());
+}
+
+/** \returns true if *this is approximately equal to a skew symmetric matrix,
+ * within the precision given by \a prec.
+ */
+template<typename Derived>
+bool MatrixBase<Derived>::isSkewSymmetric(const RealScalar& prec) const
+{
+ if(cols() != rows()) return false;
+ return (this->transpose() + *this).isZero(prec);
+}
+
+/** \returns the matrix product of \c *this by the skew symmetric matrix \skew.
+ */
+template<typename Derived>
+template<typename SkewDerived>
+EIGEN_DEVICE_FUNC inline const Product<Derived, SkewDerived, LazyProduct>
+MatrixBase<Derived>::operator*(const SkewSymmetricBase<SkewDerived> &skew) const
+{
+ return Product<Derived, SkewDerived, LazyProduct>(derived(), skew.derived());
+}
+
+namespace internal {
+
+template<> struct storage_kind_to_shape<SkewSymmetricShape> { typedef SkewSymmetricShape Shape; };
+
+struct SkewSymmetric2Dense {};
+
+template<> struct AssignmentKind<DenseShape,SkewSymmetricShape> { typedef SkewSymmetric2Dense Kind; };
+
+// SkewSymmetric matrix to Dense assignment
+template< typename DstXprType, typename SrcXprType, typename Functor>
+struct Assignment<DstXprType, SrcXprType, Functor, SkewSymmetric2Dense>
+{
+ static void run(DstXprType &dst, const SrcXprType &src, const internal::assign_op<typename DstXprType::Scalar,typename SrcXprType::Scalar> &/*func*/)
+ {
+ if((dst.rows()!=3) || (dst.cols()!=3)) {
+ dst.resize(3, 3);
+ }
+ dst.diagonal().setZero();
+ const typename SrcXprType::SkewSymmetricVectorType v = src.vector();
+ dst(0, 1) = -v(2);
+ dst(1, 0) = v(2);
+ dst(0, 2) = v(1);
+ dst(2, 0) = -v(1);
+ dst(1, 2) = -v(0);
+ dst(2, 1) = v(0);
+ }
+
+ static void run(DstXprType &dst, const SrcXprType &src, const internal::add_assign_op<typename DstXprType::Scalar,typename SrcXprType::Scalar> &/*func*/)
+ { dst.vector() += src.vector(); }
+
+ static void run(DstXprType &dst, const SrcXprType &src, const internal::sub_assign_op<typename DstXprType::Scalar,typename SrcXprType::Scalar> &/*func*/)
+ { dst.vector() -= src.vector(); }
+};
+
+} // namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_SKEWSYMMETRICMATRIX3_H
diff --git a/Eigen/src/Core/Solve.h b/Eigen/src/Core/Solve.h
new file mode 100644
index 0000000..f77eac9
--- /dev/null
+++ b/Eigen/src/Core/Solve.h
@@ -0,0 +1,190 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2014 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_SOLVE_H
+#define EIGEN_SOLVE_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+template<typename Decomposition, typename RhsType, typename StorageKind> class SolveImpl;
+
+/** \class Solve
+ * \ingroup Core_Module
+ *
+ * \brief Pseudo expression representing a solving operation
+ *
+ * \tparam Decomposition the type of the matrix or decomposition object
+ * \tparam Rhstype the type of the right-hand side
+ *
+ * This class represents an expression of A.solve(B)
+ * and most of the time this is the only way it is used.
+ *
+ */
+namespace internal {
+
+// this solve_traits class permits to determine the evaluation type with respect to storage kind (Dense vs Sparse)
+template<typename Decomposition, typename RhsType,typename StorageKind> struct solve_traits;
+
+template<typename Decomposition, typename RhsType>
+struct solve_traits<Decomposition,RhsType,Dense>
+{
+ typedef typename make_proper_matrix_type<typename RhsType::Scalar,
+ Decomposition::ColsAtCompileTime,
+ RhsType::ColsAtCompileTime,
+ RhsType::PlainObject::Options,
+ Decomposition::MaxColsAtCompileTime,
+ RhsType::MaxColsAtCompileTime>::type PlainObject;
+};
+
+template<typename Decomposition, typename RhsType>
+struct traits<Solve<Decomposition, RhsType> >
+ : traits<typename solve_traits<Decomposition,RhsType,typename internal::traits<RhsType>::StorageKind>::PlainObject>
+{
+ typedef typename solve_traits<Decomposition,RhsType,typename internal::traits<RhsType>::StorageKind>::PlainObject PlainObject;
+ typedef typename promote_index_type<typename Decomposition::StorageIndex, typename RhsType::StorageIndex>::type StorageIndex;
+ typedef traits<PlainObject> BaseTraits;
+ enum {
+ Flags = BaseTraits::Flags & RowMajorBit,
+ CoeffReadCost = HugeCost
+ };
+};
+
+}
+
+
+template<typename Decomposition, typename RhsType>
+class Solve : public SolveImpl<Decomposition,RhsType,typename internal::traits<RhsType>::StorageKind>
+{
+public:
+ typedef typename internal::traits<Solve>::PlainObject PlainObject;
+ typedef typename internal::traits<Solve>::StorageIndex StorageIndex;
+
+ Solve(const Decomposition &dec, const RhsType &rhs)
+ : m_dec(dec), m_rhs(rhs)
+ {}
+
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR Index rows() const EIGEN_NOEXCEPT { return m_dec.cols(); }
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR Index cols() const EIGEN_NOEXCEPT { return m_rhs.cols(); }
+
+ EIGEN_DEVICE_FUNC const Decomposition& dec() const { return m_dec; }
+ EIGEN_DEVICE_FUNC const RhsType& rhs() const { return m_rhs; }
+
+protected:
+ const Decomposition &m_dec;
+ const typename internal::ref_selector<RhsType>::type m_rhs;
+};
+
+
+// Specialization of the Solve expression for dense results
+template<typename Decomposition, typename RhsType>
+class SolveImpl<Decomposition,RhsType,Dense>
+ : public MatrixBase<Solve<Decomposition,RhsType> >
+{
+ typedef Solve<Decomposition,RhsType> Derived;
+
+public:
+
+ typedef MatrixBase<Solve<Decomposition,RhsType> > Base;
+ EIGEN_DENSE_PUBLIC_INTERFACE(Derived)
+
+private:
+
+ Scalar coeff(Index row, Index col) const;
+ Scalar coeff(Index i) const;
+};
+
+// Generic API dispatcher
+template<typename Decomposition, typename RhsType, typename StorageKind>
+class SolveImpl : public internal::generic_xpr_base<Solve<Decomposition,RhsType>, MatrixXpr, StorageKind>::type
+{
+ public:
+ typedef typename internal::generic_xpr_base<Solve<Decomposition,RhsType>, MatrixXpr, StorageKind>::type Base;
+};
+
+namespace internal {
+
+// Evaluator of Solve -> eval into a temporary
+template<typename Decomposition, typename RhsType>
+struct evaluator<Solve<Decomposition,RhsType> >
+ : public evaluator<typename Solve<Decomposition,RhsType>::PlainObject>
+{
+ typedef Solve<Decomposition,RhsType> SolveType;
+ typedef typename SolveType::PlainObject PlainObject;
+ typedef evaluator<PlainObject> Base;
+
+ enum { Flags = Base::Flags | EvalBeforeNestingBit };
+
+ EIGEN_DEVICE_FUNC explicit evaluator(const SolveType& solve)
+ : m_result(solve.rows(), solve.cols())
+ {
+ internal::construct_at<Base>(this, m_result);
+ solve.dec()._solve_impl(solve.rhs(), m_result);
+ }
+
+protected:
+ PlainObject m_result;
+};
+
+// Specialization for "dst = dec.solve(rhs)"
+// NOTE we need to specialize it for Dense2Dense to avoid ambiguous specialization error and a Sparse2Sparse specialization must exist somewhere
+template<typename DstXprType, typename DecType, typename RhsType, typename Scalar>
+struct Assignment<DstXprType, Solve<DecType,RhsType>, internal::assign_op<Scalar,Scalar>, Dense2Dense>
+{
+ typedef Solve<DecType,RhsType> SrcXprType;
+ static void run(DstXprType &dst, const SrcXprType &src, const internal::assign_op<Scalar,Scalar> &)
+ {
+ Index dstRows = src.rows();
+ Index dstCols = src.cols();
+ if((dst.rows()!=dstRows) || (dst.cols()!=dstCols))
+ dst.resize(dstRows, dstCols);
+
+ src.dec()._solve_impl(src.rhs(), dst);
+ }
+};
+
+// Specialization for "dst = dec.transpose().solve(rhs)"
+template<typename DstXprType, typename DecType, typename RhsType, typename Scalar>
+struct Assignment<DstXprType, Solve<Transpose<const DecType>,RhsType>, internal::assign_op<Scalar,Scalar>, Dense2Dense>
+{
+ typedef Solve<Transpose<const DecType>,RhsType> SrcXprType;
+ static void run(DstXprType &dst, const SrcXprType &src, const internal::assign_op<Scalar,Scalar> &)
+ {
+ Index dstRows = src.rows();
+ Index dstCols = src.cols();
+ if((dst.rows()!=dstRows) || (dst.cols()!=dstCols))
+ dst.resize(dstRows, dstCols);
+
+ src.dec().nestedExpression().template _solve_impl_transposed<false>(src.rhs(), dst);
+ }
+};
+
+// Specialization for "dst = dec.adjoint().solve(rhs)"
+template<typename DstXprType, typename DecType, typename RhsType, typename Scalar>
+struct Assignment<DstXprType, Solve<CwiseUnaryOp<internal::scalar_conjugate_op<typename DecType::Scalar>, const Transpose<const DecType> >,RhsType>,
+ internal::assign_op<Scalar,Scalar>, Dense2Dense>
+{
+ typedef Solve<CwiseUnaryOp<internal::scalar_conjugate_op<typename DecType::Scalar>, const Transpose<const DecType> >,RhsType> SrcXprType;
+ static void run(DstXprType &dst, const SrcXprType &src, const internal::assign_op<Scalar,Scalar> &)
+ {
+ Index dstRows = src.rows();
+ Index dstCols = src.cols();
+ if((dst.rows()!=dstRows) || (dst.cols()!=dstCols))
+ dst.resize(dstRows, dstCols);
+
+ src.dec().nestedExpression().nestedExpression().template _solve_impl_transposed<true>(src.rhs(), dst);
+ }
+};
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_SOLVE_H
diff --git a/Eigen/src/Core/SolveTriangular.h b/Eigen/src/Core/SolveTriangular.h
new file mode 100644
index 0000000..71d6f85
--- /dev/null
+++ b/Eigen/src/Core/SolveTriangular.h
@@ -0,0 +1,237 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_SOLVETRIANGULAR_H
+#define EIGEN_SOLVETRIANGULAR_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+
+// Forward declarations:
+// The following two routines are implemented in the products/TriangularSolver*.h files
+template<typename LhsScalar, typename RhsScalar, typename Index, int Side, int Mode, bool Conjugate, int StorageOrder>
+struct triangular_solve_vector;
+
+template <typename Scalar, typename Index, int Side, int Mode, bool Conjugate, int TriStorageOrder, int OtherStorageOrder, int OtherInnerStride>
+struct triangular_solve_matrix;
+
+// small helper struct extracting some traits on the underlying solver operation
+template<typename Lhs, typename Rhs, int Side>
+class trsolve_traits
+{
+ private:
+ enum {
+ RhsIsVectorAtCompileTime = (Side==OnTheLeft ? Rhs::ColsAtCompileTime : Rhs::RowsAtCompileTime)==1
+ };
+ public:
+ enum {
+ Unrolling = (RhsIsVectorAtCompileTime && Rhs::SizeAtCompileTime != Dynamic && Rhs::SizeAtCompileTime <= 8)
+ ? CompleteUnrolling : NoUnrolling,
+ RhsVectors = RhsIsVectorAtCompileTime ? 1 : Dynamic
+ };
+};
+
+template<typename Lhs, typename Rhs,
+ int Side, // can be OnTheLeft/OnTheRight
+ int Mode, // can be Upper/Lower | UnitDiag
+ int Unrolling = trsolve_traits<Lhs,Rhs,Side>::Unrolling,
+ int RhsVectors = trsolve_traits<Lhs,Rhs,Side>::RhsVectors
+ >
+struct triangular_solver_selector;
+
+template<typename Lhs, typename Rhs, int Side, int Mode>
+struct triangular_solver_selector<Lhs,Rhs,Side,Mode,NoUnrolling,1>
+{
+ typedef typename Lhs::Scalar LhsScalar;
+ typedef typename Rhs::Scalar RhsScalar;
+ typedef blas_traits<Lhs> LhsProductTraits;
+ typedef typename LhsProductTraits::ExtractType ActualLhsType;
+ typedef Map<Matrix<RhsScalar,Dynamic,1>, Aligned> MappedRhs;
+ static EIGEN_DEVICE_FUNC void run(const Lhs& lhs, Rhs& rhs)
+ {
+ ActualLhsType actualLhs = LhsProductTraits::extract(lhs);
+
+ // FIXME find a way to allow an inner stride if packet_traits<Scalar>::size==1
+
+ bool useRhsDirectly = Rhs::InnerStrideAtCompileTime==1 || rhs.innerStride()==1;
+
+ ei_declare_aligned_stack_constructed_variable(RhsScalar,actualRhs,rhs.size(),
+ (useRhsDirectly ? rhs.data() : 0));
+
+ if(!useRhsDirectly)
+ MappedRhs(actualRhs,rhs.size()) = rhs;
+
+ triangular_solve_vector<LhsScalar, RhsScalar, Index, Side, Mode, LhsProductTraits::NeedToConjugate,
+ (int(Lhs::Flags) & RowMajorBit) ? RowMajor : ColMajor>
+ ::run(actualLhs.cols(), actualLhs.data(), actualLhs.outerStride(), actualRhs);
+
+ if(!useRhsDirectly)
+ rhs = MappedRhs(actualRhs, rhs.size());
+ }
+};
+
+// the rhs is a matrix
+template<typename Lhs, typename Rhs, int Side, int Mode>
+struct triangular_solver_selector<Lhs,Rhs,Side,Mode,NoUnrolling,Dynamic>
+{
+ typedef typename Rhs::Scalar Scalar;
+ typedef blas_traits<Lhs> LhsProductTraits;
+ typedef typename LhsProductTraits::DirectLinearAccessType ActualLhsType;
+
+ static EIGEN_DEVICE_FUNC void run(const Lhs& lhs, Rhs& rhs)
+ {
+ add_const_on_value_type_t<ActualLhsType> actualLhs = LhsProductTraits::extract(lhs);
+
+ const Index size = lhs.rows();
+ const Index othersize = Side==OnTheLeft? rhs.cols() : rhs.rows();
+
+ typedef internal::gemm_blocking_space<(Rhs::Flags&RowMajorBit) ? RowMajor : ColMajor,Scalar,Scalar,
+ Rhs::MaxRowsAtCompileTime, Rhs::MaxColsAtCompileTime, Lhs::MaxRowsAtCompileTime,4> BlockingType;
+
+ BlockingType blocking(rhs.rows(), rhs.cols(), size, 1, false);
+
+ triangular_solve_matrix<Scalar,Index,Side,Mode,LhsProductTraits::NeedToConjugate,(int(Lhs::Flags) & RowMajorBit) ? RowMajor : ColMajor,
+ (Rhs::Flags&RowMajorBit) ? RowMajor : ColMajor, Rhs::InnerStrideAtCompileTime>
+ ::run(size, othersize, &actualLhs.coeffRef(0,0), actualLhs.outerStride(), &rhs.coeffRef(0,0), rhs.innerStride(), rhs.outerStride(), blocking);
+ }
+};
+
+/***************************************************************************
+* meta-unrolling implementation
+***************************************************************************/
+
+template<typename Lhs, typename Rhs, int Mode, int LoopIndex, int Size,
+ bool Stop = LoopIndex==Size>
+struct triangular_solver_unroller;
+
+template<typename Lhs, typename Rhs, int Mode, int LoopIndex, int Size>
+struct triangular_solver_unroller<Lhs,Rhs,Mode,LoopIndex,Size,false> {
+ enum {
+ IsLower = ((Mode&Lower)==Lower),
+ DiagIndex = IsLower ? LoopIndex : Size - LoopIndex - 1,
+ StartIndex = IsLower ? 0 : DiagIndex+1
+ };
+ static EIGEN_DEVICE_FUNC void run(const Lhs& lhs, Rhs& rhs)
+ {
+ if (LoopIndex>0)
+ rhs.coeffRef(DiagIndex) -= lhs.row(DiagIndex).template segment<LoopIndex>(StartIndex).transpose()
+ .cwiseProduct(rhs.template segment<LoopIndex>(StartIndex)).sum();
+
+ if(!(Mode & UnitDiag))
+ rhs.coeffRef(DiagIndex) /= lhs.coeff(DiagIndex,DiagIndex);
+
+ triangular_solver_unroller<Lhs,Rhs,Mode,LoopIndex+1,Size>::run(lhs,rhs);
+ }
+};
+
+template<typename Lhs, typename Rhs, int Mode, int LoopIndex, int Size>
+struct triangular_solver_unroller<Lhs,Rhs,Mode,LoopIndex,Size,true> {
+ static EIGEN_DEVICE_FUNC void run(const Lhs&, Rhs&) {}
+};
+
+template<typename Lhs, typename Rhs, int Mode>
+struct triangular_solver_selector<Lhs,Rhs,OnTheLeft,Mode,CompleteUnrolling,1> {
+ static EIGEN_DEVICE_FUNC void run(const Lhs& lhs, Rhs& rhs)
+ { triangular_solver_unroller<Lhs,Rhs,Mode,0,Rhs::SizeAtCompileTime>::run(lhs,rhs); }
+};
+
+template<typename Lhs, typename Rhs, int Mode>
+struct triangular_solver_selector<Lhs,Rhs,OnTheRight,Mode,CompleteUnrolling,1> {
+ static EIGEN_DEVICE_FUNC void run(const Lhs& lhs, Rhs& rhs)
+ {
+ Transpose<const Lhs> trLhs(lhs);
+ Transpose<Rhs> trRhs(rhs);
+
+ triangular_solver_unroller<Transpose<const Lhs>,Transpose<Rhs>,
+ ((Mode&Upper)==Upper ? Lower : Upper) | (Mode&UnitDiag),
+ 0,Rhs::SizeAtCompileTime>::run(trLhs,trRhs);
+ }
+};
+
+} // end namespace internal
+
+/***************************************************************************
+* TriangularView methods
+***************************************************************************/
+
+#ifndef EIGEN_PARSED_BY_DOXYGEN
+template<typename MatrixType, unsigned int Mode>
+template<int Side, typename OtherDerived>
+EIGEN_DEVICE_FUNC void TriangularViewImpl<MatrixType,Mode,Dense>::solveInPlace(const MatrixBase<OtherDerived>& _other) const
+{
+ OtherDerived& other = _other.const_cast_derived();
+ eigen_assert( derived().cols() == derived().rows() && ((Side==OnTheLeft && derived().cols() == other.rows()) || (Side==OnTheRight && derived().cols() == other.cols())) );
+ eigen_assert((!(int(Mode) & int(ZeroDiag))) && bool(int(Mode) & (int(Upper) | int(Lower))));
+ // If solving for a 0x0 matrix, nothing to do, simply return.
+ if (derived().cols() == 0)
+ return;
+
+ enum { copy = (internal::traits<OtherDerived>::Flags & RowMajorBit) && OtherDerived::IsVectorAtCompileTime && OtherDerived::SizeAtCompileTime!=1};
+ typedef std::conditional_t<copy,
+ typename internal::plain_matrix_type_column_major<OtherDerived>::type, OtherDerived&> OtherCopy;
+ OtherCopy otherCopy(other);
+
+ internal::triangular_solver_selector<MatrixType, std::remove_reference_t<OtherCopy>,
+ Side, Mode>::run(derived().nestedExpression(), otherCopy);
+
+ if (copy)
+ other = otherCopy;
+}
+
+template<typename Derived, unsigned int Mode>
+template<int Side, typename Other>
+const internal::triangular_solve_retval<Side,TriangularView<Derived,Mode>,Other>
+TriangularViewImpl<Derived,Mode,Dense>::solve(const MatrixBase<Other>& other) const
+{
+ return internal::triangular_solve_retval<Side,TriangularViewType,Other>(derived(), other.derived());
+}
+#endif
+
+namespace internal {
+
+
+template<int Side, typename TriangularType, typename Rhs>
+struct traits<triangular_solve_retval<Side, TriangularType, Rhs> >
+{
+ typedef typename internal::plain_matrix_type_column_major<Rhs>::type ReturnType;
+};
+
+template<int Side, typename TriangularType, typename Rhs> struct triangular_solve_retval
+ : public ReturnByValue<triangular_solve_retval<Side, TriangularType, Rhs> >
+{
+ typedef remove_all_t<typename Rhs::Nested> RhsNestedCleaned;
+ typedef ReturnByValue<triangular_solve_retval> Base;
+
+ triangular_solve_retval(const TriangularType& tri, const Rhs& rhs)
+ : m_triangularMatrix(tri), m_rhs(rhs)
+ {}
+
+ inline EIGEN_CONSTEXPR Index rows() const EIGEN_NOEXCEPT { return m_rhs.rows(); }
+ inline EIGEN_CONSTEXPR Index cols() const EIGEN_NOEXCEPT { return m_rhs.cols(); }
+
+ template<typename Dest> inline void evalTo(Dest& dst) const
+ {
+ if(!is_same_dense(dst,m_rhs))
+ dst = m_rhs;
+ m_triangularMatrix.template solveInPlace<Side>(dst);
+ }
+
+ protected:
+ const TriangularType& m_triangularMatrix;
+ typename Rhs::Nested m_rhs;
+};
+
+} // namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_SOLVETRIANGULAR_H
diff --git a/Eigen/src/Core/SolverBase.h b/Eigen/src/Core/SolverBase.h
new file mode 100644
index 0000000..7396e04
--- /dev/null
+++ b/Eigen/src/Core/SolverBase.h
@@ -0,0 +1,169 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2015 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_SOLVERBASE_H
+#define EIGEN_SOLVERBASE_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+
+template<typename Derived>
+struct solve_assertion {
+ template<bool Transpose_, typename Rhs>
+ static void run(const Derived& solver, const Rhs& b) { solver.template _check_solve_assertion<Transpose_>(b); }
+};
+
+template<typename Derived>
+struct solve_assertion<Transpose<Derived> >
+{
+ typedef Transpose<Derived> type;
+
+ template<bool Transpose_, typename Rhs>
+ static void run(const type& transpose, const Rhs& b)
+ {
+ internal::solve_assertion<internal::remove_all_t<Derived>>::template run<true>(transpose.nestedExpression(), b);
+ }
+};
+
+template<typename Scalar, typename Derived>
+struct solve_assertion<CwiseUnaryOp<Eigen::internal::scalar_conjugate_op<Scalar>, const Transpose<Derived> > >
+{
+ typedef CwiseUnaryOp<Eigen::internal::scalar_conjugate_op<Scalar>, const Transpose<Derived> > type;
+
+ template<bool Transpose_, typename Rhs>
+ static void run(const type& adjoint, const Rhs& b)
+ {
+ internal::solve_assertion<internal::remove_all_t<Transpose<Derived> >>::template run<true>(adjoint.nestedExpression(), b);
+ }
+};
+} // end namespace internal
+
+/** \class SolverBase
+ * \brief A base class for matrix decomposition and solvers
+ *
+ * \tparam Derived the actual type of the decomposition/solver.
+ *
+ * Any matrix decomposition inheriting this base class provide the following API:
+ *
+ * \code
+ * MatrixType A, b, x;
+ * DecompositionType dec(A);
+ * x = dec.solve(b); // solve A * x = b
+ * x = dec.transpose().solve(b); // solve A^T * x = b
+ * x = dec.adjoint().solve(b); // solve A' * x = b
+ * \endcode
+ *
+ * \warning Currently, any other usage of transpose() and adjoint() are not supported and will produce compilation errors.
+ *
+ * \sa class PartialPivLU, class FullPivLU, class HouseholderQR, class ColPivHouseholderQR, class FullPivHouseholderQR, class CompleteOrthogonalDecomposition, class LLT, class LDLT, class SVDBase
+ */
+template<typename Derived>
+class SolverBase : public EigenBase<Derived>
+{
+ public:
+
+ typedef EigenBase<Derived> Base;
+ typedef typename internal::traits<Derived>::Scalar Scalar;
+ typedef Scalar CoeffReturnType;
+
+ template<typename Derived_>
+ friend struct internal::solve_assertion;
+
+ enum {
+ RowsAtCompileTime = internal::traits<Derived>::RowsAtCompileTime,
+ ColsAtCompileTime = internal::traits<Derived>::ColsAtCompileTime,
+ SizeAtCompileTime = (internal::size_of_xpr_at_compile_time<Derived>::ret),
+ MaxRowsAtCompileTime = internal::traits<Derived>::MaxRowsAtCompileTime,
+ MaxColsAtCompileTime = internal::traits<Derived>::MaxColsAtCompileTime,
+ MaxSizeAtCompileTime = internal::size_at_compile_time(internal::traits<Derived>::MaxRowsAtCompileTime,
+ internal::traits<Derived>::MaxColsAtCompileTime),
+ IsVectorAtCompileTime = internal::traits<Derived>::MaxRowsAtCompileTime == 1
+ || internal::traits<Derived>::MaxColsAtCompileTime == 1,
+ NumDimensions = int(MaxSizeAtCompileTime) == 1 ? 0 : bool(IsVectorAtCompileTime) ? 1 : 2
+ };
+
+ /** Default constructor */
+ SolverBase()
+ {}
+
+ ~SolverBase()
+ {}
+
+ using Base::derived;
+
+ /** \returns an expression of the solution x of \f$ A x = b \f$ using the current decomposition of A.
+ */
+ template<typename Rhs>
+ inline const Solve<Derived, Rhs>
+ solve(const MatrixBase<Rhs>& b) const
+ {
+ internal::solve_assertion<internal::remove_all_t<Derived>>::template run<false>(derived(), b);
+ return Solve<Derived, Rhs>(derived(), b.derived());
+ }
+
+ /** \internal the return type of transpose() */
+ typedef Transpose<const Derived> ConstTransposeReturnType;
+ /** \returns an expression of the transposed of the factored matrix.
+ *
+ * A typical usage is to solve for the transposed problem A^T x = b:
+ * \code x = dec.transpose().solve(b); \endcode
+ *
+ * \sa adjoint(), solve()
+ */
+ inline const ConstTransposeReturnType transpose() const
+ {
+ return ConstTransposeReturnType(derived());
+ }
+
+ /** \internal the return type of adjoint() */
+ typedef std::conditional_t<NumTraits<Scalar>::IsComplex,
+ CwiseUnaryOp<internal::scalar_conjugate_op<Scalar>, const ConstTransposeReturnType>,
+ const ConstTransposeReturnType
+ > AdjointReturnType;
+ /** \returns an expression of the adjoint of the factored matrix
+ *
+ * A typical usage is to solve for the adjoint problem A' x = b:
+ * \code x = dec.adjoint().solve(b); \endcode
+ *
+ * For real scalar types, this function is equivalent to transpose().
+ *
+ * \sa transpose(), solve()
+ */
+ inline const AdjointReturnType adjoint() const
+ {
+ return AdjointReturnType(derived().transpose());
+ }
+
+ protected:
+
+ template<bool Transpose_, typename Rhs>
+ void _check_solve_assertion(const Rhs& b) const {
+ EIGEN_ONLY_USED_FOR_DEBUG(b);
+ eigen_assert(derived().m_isInitialized && "Solver is not initialized.");
+ eigen_assert((Transpose_?derived().cols():derived().rows())==b.rows() && "SolverBase::solve(): invalid number of rows of the right hand side matrix b");
+ }
+};
+
+namespace internal {
+
+template<typename Derived>
+struct generic_xpr_base<Derived, MatrixXpr, SolverStorage>
+{
+ typedef SolverBase<Derived> type;
+
+};
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_SOLVERBASE_H
diff --git a/Eigen/src/Core/StableNorm.h b/Eigen/src/Core/StableNorm.h
new file mode 100644
index 0000000..a3bc918
--- /dev/null
+++ b/Eigen/src/Core/StableNorm.h
@@ -0,0 +1,253 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_STABLENORM_H
+#define EIGEN_STABLENORM_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+
+template<typename ExpressionType, typename Scalar>
+inline void stable_norm_kernel(const ExpressionType& bl, Scalar& ssq, Scalar& scale, Scalar& invScale)
+{
+ Scalar maxCoeff = bl.cwiseAbs().maxCoeff();
+
+ if(maxCoeff>scale)
+ {
+ ssq = ssq * numext::abs2(scale/maxCoeff);
+ Scalar tmp = Scalar(1)/maxCoeff;
+ if(tmp > NumTraits<Scalar>::highest())
+ {
+ invScale = NumTraits<Scalar>::highest();
+ scale = Scalar(1)/invScale;
+ }
+ else if(maxCoeff>NumTraits<Scalar>::highest()) // we got a INF
+ {
+ invScale = Scalar(1);
+ scale = maxCoeff;
+ }
+ else
+ {
+ scale = maxCoeff;
+ invScale = tmp;
+ }
+ }
+ else if(maxCoeff!=maxCoeff) // we got a NaN
+ {
+ scale = maxCoeff;
+ }
+
+ // TODO if the maxCoeff is much much smaller than the current scale,
+ // then we can neglect this sub vector
+ if(scale>Scalar(0)) // if scale==0, then bl is 0
+ ssq += (bl*invScale).squaredNorm();
+}
+
+template<typename VectorType, typename RealScalar>
+void stable_norm_impl_inner_step(const VectorType &vec, RealScalar& ssq, RealScalar& scale, RealScalar& invScale)
+{
+ typedef typename VectorType::Scalar Scalar;
+ const Index blockSize = 4096;
+
+ typedef typename internal::nested_eval<VectorType,2>::type VectorTypeCopy;
+ typedef internal::remove_all_t<VectorTypeCopy> VectorTypeCopyClean;
+ const VectorTypeCopy copy(vec);
+
+ enum {
+ CanAlign = ( (int(VectorTypeCopyClean::Flags)&DirectAccessBit)
+ || (int(internal::evaluator<VectorTypeCopyClean>::Alignment)>0) // FIXME Alignment)>0 might not be enough
+ ) && (blockSize*sizeof(Scalar)*2<EIGEN_STACK_ALLOCATION_LIMIT)
+ && (EIGEN_MAX_STATIC_ALIGN_BYTES>0) // if we cannot allocate on the stack, then let's not bother about this optimization
+ };
+ typedef std::conditional_t<CanAlign, Ref<const Matrix<Scalar,Dynamic,1,0,blockSize,1>, internal::evaluator<VectorTypeCopyClean>::Alignment>,
+ typename VectorTypeCopyClean::ConstSegmentReturnType> SegmentWrapper;
+ Index n = vec.size();
+
+ Index bi = internal::first_default_aligned(copy);
+ if (bi>0)
+ internal::stable_norm_kernel(copy.head(bi), ssq, scale, invScale);
+ for (; bi<n; bi+=blockSize)
+ internal::stable_norm_kernel(SegmentWrapper(copy.segment(bi,numext::mini(blockSize, n - bi))), ssq, scale, invScale);
+}
+
+template<typename VectorType>
+typename VectorType::RealScalar
+stable_norm_impl(const VectorType &vec, std::enable_if_t<VectorType::IsVectorAtCompileTime>* = 0 )
+{
+ using std::sqrt;
+ using std::abs;
+
+ Index n = vec.size();
+
+ if(n==1)
+ return abs(vec.coeff(0));
+
+ typedef typename VectorType::RealScalar RealScalar;
+ RealScalar scale(0);
+ RealScalar invScale(1);
+ RealScalar ssq(0); // sum of squares
+
+ stable_norm_impl_inner_step(vec, ssq, scale, invScale);
+
+ return scale * sqrt(ssq);
+}
+
+template<typename MatrixType>
+typename MatrixType::RealScalar
+stable_norm_impl(const MatrixType &mat, std::enable_if_t<!MatrixType::IsVectorAtCompileTime>* = 0 )
+{
+ using std::sqrt;
+
+ typedef typename MatrixType::RealScalar RealScalar;
+ RealScalar scale(0);
+ RealScalar invScale(1);
+ RealScalar ssq(0); // sum of squares
+
+ for(Index j=0; j<mat.outerSize(); ++j)
+ stable_norm_impl_inner_step(mat.innerVector(j), ssq, scale, invScale);
+ return scale * sqrt(ssq);
+}
+
+template<typename Derived>
+inline typename NumTraits<typename traits<Derived>::Scalar>::Real
+blueNorm_impl(const EigenBase<Derived>& _vec)
+{
+ typedef typename Derived::RealScalar RealScalar;
+ using std::pow;
+ using std::sqrt;
+ using std::abs;
+
+ // This program calculates the machine-dependent constants
+ // bl, b2, slm, s2m, relerr overfl
+ // from the "basic" machine-dependent numbers
+ // nbig, ibeta, it, iemin, iemax, rbig.
+ // The following define the basic machine-dependent constants.
+ // For portability, the PORT subprograms "ilmaeh" and "rlmach"
+ // are used. For any specific computer, each of the assignment
+ // statements can be replaced
+ static const int ibeta = std::numeric_limits<RealScalar>::radix; // base for floating-point numbers
+ static const int it = NumTraits<RealScalar>::digits(); // number of base-beta digits in mantissa
+ static const int iemin = NumTraits<RealScalar>::min_exponent(); // minimum exponent
+ static const int iemax = NumTraits<RealScalar>::max_exponent(); // maximum exponent
+ static const RealScalar rbig = NumTraits<RealScalar>::highest(); // largest floating-point number
+ static const RealScalar b1 = RealScalar(pow(RealScalar(ibeta),RealScalar(-((1-iemin)/2)))); // lower boundary of midrange
+ static const RealScalar b2 = RealScalar(pow(RealScalar(ibeta),RealScalar((iemax + 1 - it)/2))); // upper boundary of midrange
+ static const RealScalar s1m = RealScalar(pow(RealScalar(ibeta),RealScalar((2-iemin)/2))); // scaling factor for lower range
+ static const RealScalar s2m = RealScalar(pow(RealScalar(ibeta),RealScalar(- ((iemax+it)/2)))); // scaling factor for upper range
+ static const RealScalar eps = RealScalar(pow(double(ibeta), 1-it));
+ static const RealScalar relerr = sqrt(eps); // tolerance for neglecting asml
+
+ const Derived& vec(_vec.derived());
+ Index n = vec.size();
+ RealScalar ab2 = b2 / RealScalar(n);
+ RealScalar asml = RealScalar(0);
+ RealScalar amed = RealScalar(0);
+ RealScalar abig = RealScalar(0);
+
+ for(Index j=0; j<vec.outerSize(); ++j)
+ {
+ for(typename Derived::InnerIterator iter(vec, j); iter; ++iter)
+ {
+ RealScalar ax = abs(iter.value());
+ if(ax > ab2) abig += numext::abs2(ax*s2m);
+ else if(ax < b1) asml += numext::abs2(ax*s1m);
+ else amed += numext::abs2(ax);
+ }
+ }
+ if(amed!=amed)
+ return amed; // we got a NaN
+ if(abig > RealScalar(0))
+ {
+ abig = sqrt(abig);
+ if(abig > rbig) // overflow, or *this contains INF values
+ return abig; // return INF
+ if(amed > RealScalar(0))
+ {
+ abig = abig/s2m;
+ amed = sqrt(amed);
+ }
+ else
+ return abig/s2m;
+ }
+ else if(asml > RealScalar(0))
+ {
+ if (amed > RealScalar(0))
+ {
+ abig = sqrt(amed);
+ amed = sqrt(asml) / s1m;
+ }
+ else
+ return sqrt(asml)/s1m;
+ }
+ else
+ return sqrt(amed);
+ asml = numext::mini(abig, amed);
+ abig = numext::maxi(abig, amed);
+ if(asml <= abig*relerr)
+ return abig;
+ else
+ return abig * sqrt(RealScalar(1) + numext::abs2(asml/abig));
+}
+
+} // end namespace internal
+
+/** \returns the \em l2 norm of \c *this avoiding underflow and overflow.
+ * This version use a blockwise two passes algorithm:
+ * 1 - find the absolute largest coefficient \c s
+ * 2 - compute \f$ s \Vert \frac{*this}{s} \Vert \f$ in a standard way
+ *
+ * For architecture/scalar types supporting vectorization, this version
+ * is faster than blueNorm(). Otherwise the blueNorm() is much faster.
+ *
+ * \sa norm(), blueNorm(), hypotNorm()
+ */
+template<typename Derived>
+inline typename NumTraits<typename internal::traits<Derived>::Scalar>::Real
+MatrixBase<Derived>::stableNorm() const
+{
+ return internal::stable_norm_impl(derived());
+}
+
+/** \returns the \em l2 norm of \c *this using the Blue's algorithm.
+ * A Portable Fortran Program to Find the Euclidean Norm of a Vector,
+ * ACM TOMS, Vol 4, Issue 1, 1978.
+ *
+ * For architecture/scalar types without vectorization, this version
+ * is much faster than stableNorm(). Otherwise the stableNorm() is faster.
+ *
+ * \sa norm(), stableNorm(), hypotNorm()
+ */
+template<typename Derived>
+inline typename NumTraits<typename internal::traits<Derived>::Scalar>::Real
+MatrixBase<Derived>::blueNorm() const
+{
+ return internal::blueNorm_impl(*this);
+}
+
+/** \returns the \em l2 norm of \c *this avoiding undeflow and overflow.
+ * This version use a concatenation of hypot() calls, and it is very slow.
+ *
+ * \sa norm(), stableNorm()
+ */
+template<typename Derived>
+inline typename NumTraits<typename internal::traits<Derived>::Scalar>::Real
+MatrixBase<Derived>::hypotNorm() const
+{
+ if(size()==1)
+ return numext::abs(coeff(0,0));
+ else
+ return this->cwiseAbs().redux(internal::scalar_hypot_op<RealScalar>());
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_STABLENORM_H
diff --git a/Eigen/src/Core/StlIterators.h b/Eigen/src/Core/StlIterators.h
new file mode 100644
index 0000000..d5d3971
--- /dev/null
+++ b/Eigen/src/Core/StlIterators.h
@@ -0,0 +1,465 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2018 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_STLITERATORS_H
+#define EIGEN_STLITERATORS_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+
+template<typename IteratorType>
+struct indexed_based_stl_iterator_traits;
+
+template<typename Derived>
+class indexed_based_stl_iterator_base
+{
+protected:
+ typedef indexed_based_stl_iterator_traits<Derived> traits;
+ typedef typename traits::XprType XprType;
+ typedef indexed_based_stl_iterator_base<typename traits::non_const_iterator> non_const_iterator;
+ typedef indexed_based_stl_iterator_base<typename traits::const_iterator> const_iterator;
+ typedef std::conditional_t<internal::is_const<XprType>::value,non_const_iterator,const_iterator> other_iterator;
+ // NOTE: in C++03 we cannot declare friend classes through typedefs because we need to write friend class:
+ friend class indexed_based_stl_iterator_base<typename traits::const_iterator>;
+ friend class indexed_based_stl_iterator_base<typename traits::non_const_iterator>;
+public:
+ typedef Index difference_type;
+ typedef std::random_access_iterator_tag iterator_category;
+
+ indexed_based_stl_iterator_base() EIGEN_NO_THROW : mp_xpr(0), m_index(0) {}
+ indexed_based_stl_iterator_base(XprType& xpr, Index index) EIGEN_NO_THROW : mp_xpr(&xpr), m_index(index) {}
+
+ indexed_based_stl_iterator_base(const non_const_iterator& other) EIGEN_NO_THROW
+ : mp_xpr(other.mp_xpr), m_index(other.m_index)
+ {}
+
+ indexed_based_stl_iterator_base& operator=(const non_const_iterator& other)
+ {
+ mp_xpr = other.mp_xpr;
+ m_index = other.m_index;
+ return *this;
+ }
+
+ Derived& operator++() { ++m_index; return derived(); }
+ Derived& operator--() { --m_index; return derived(); }
+
+ Derived operator++(int) { Derived prev(derived()); operator++(); return prev;}
+ Derived operator--(int) { Derived prev(derived()); operator--(); return prev;}
+
+ friend Derived operator+(const indexed_based_stl_iterator_base& a, Index b) { Derived ret(a.derived()); ret += b; return ret; }
+ friend Derived operator-(const indexed_based_stl_iterator_base& a, Index b) { Derived ret(a.derived()); ret -= b; return ret; }
+ friend Derived operator+(Index a, const indexed_based_stl_iterator_base& b) { Derived ret(b.derived()); ret += a; return ret; }
+ friend Derived operator-(Index a, const indexed_based_stl_iterator_base& b) { Derived ret(b.derived()); ret -= a; return ret; }
+
+ Derived& operator+=(Index b) { m_index += b; return derived(); }
+ Derived& operator-=(Index b) { m_index -= b; return derived(); }
+
+ difference_type operator-(const indexed_based_stl_iterator_base& other) const
+ {
+ eigen_assert(mp_xpr == other.mp_xpr);
+ return m_index - other.m_index;
+ }
+
+ difference_type operator-(const other_iterator& other) const
+ {
+ eigen_assert(mp_xpr == other.mp_xpr);
+ return m_index - other.m_index;
+ }
+
+ bool operator==(const indexed_based_stl_iterator_base& other) const { eigen_assert(mp_xpr == other.mp_xpr); return m_index == other.m_index; }
+ bool operator!=(const indexed_based_stl_iterator_base& other) const { eigen_assert(mp_xpr == other.mp_xpr); return m_index != other.m_index; }
+ bool operator< (const indexed_based_stl_iterator_base& other) const { eigen_assert(mp_xpr == other.mp_xpr); return m_index < other.m_index; }
+ bool operator<=(const indexed_based_stl_iterator_base& other) const { eigen_assert(mp_xpr == other.mp_xpr); return m_index <= other.m_index; }
+ bool operator> (const indexed_based_stl_iterator_base& other) const { eigen_assert(mp_xpr == other.mp_xpr); return m_index > other.m_index; }
+ bool operator>=(const indexed_based_stl_iterator_base& other) const { eigen_assert(mp_xpr == other.mp_xpr); return m_index >= other.m_index; }
+
+ bool operator==(const other_iterator& other) const { eigen_assert(mp_xpr == other.mp_xpr); return m_index == other.m_index; }
+ bool operator!=(const other_iterator& other) const { eigen_assert(mp_xpr == other.mp_xpr); return m_index != other.m_index; }
+ bool operator< (const other_iterator& other) const { eigen_assert(mp_xpr == other.mp_xpr); return m_index < other.m_index; }
+ bool operator<=(const other_iterator& other) const { eigen_assert(mp_xpr == other.mp_xpr); return m_index <= other.m_index; }
+ bool operator> (const other_iterator& other) const { eigen_assert(mp_xpr == other.mp_xpr); return m_index > other.m_index; }
+ bool operator>=(const other_iterator& other) const { eigen_assert(mp_xpr == other.mp_xpr); return m_index >= other.m_index; }
+
+protected:
+
+ Derived& derived() { return static_cast<Derived&>(*this); }
+ const Derived& derived() const { return static_cast<const Derived&>(*this); }
+
+ XprType *mp_xpr;
+ Index m_index;
+};
+
+template<typename Derived>
+class indexed_based_stl_reverse_iterator_base
+{
+protected:
+ typedef indexed_based_stl_iterator_traits<Derived> traits;
+ typedef typename traits::XprType XprType;
+ typedef indexed_based_stl_reverse_iterator_base<typename traits::non_const_iterator> non_const_iterator;
+ typedef indexed_based_stl_reverse_iterator_base<typename traits::const_iterator> const_iterator;
+ typedef std::conditional_t<internal::is_const<XprType>::value,non_const_iterator,const_iterator> other_iterator;
+ // NOTE: in C++03 we cannot declare friend classes through typedefs because we need to write friend class:
+ friend class indexed_based_stl_reverse_iterator_base<typename traits::const_iterator>;
+ friend class indexed_based_stl_reverse_iterator_base<typename traits::non_const_iterator>;
+public:
+ typedef Index difference_type;
+ typedef std::random_access_iterator_tag iterator_category;
+
+ indexed_based_stl_reverse_iterator_base() : mp_xpr(0), m_index(0) {}
+ indexed_based_stl_reverse_iterator_base(XprType& xpr, Index index) : mp_xpr(&xpr), m_index(index) {}
+
+ indexed_based_stl_reverse_iterator_base(const non_const_iterator& other)
+ : mp_xpr(other.mp_xpr), m_index(other.m_index)
+ {}
+
+ indexed_based_stl_reverse_iterator_base& operator=(const non_const_iterator& other)
+ {
+ mp_xpr = other.mp_xpr;
+ m_index = other.m_index;
+ return *this;
+ }
+
+ Derived& operator++() { --m_index; return derived(); }
+ Derived& operator--() { ++m_index; return derived(); }
+
+ Derived operator++(int) { Derived prev(derived()); operator++(); return prev;}
+ Derived operator--(int) { Derived prev(derived()); operator--(); return prev;}
+
+ friend Derived operator+(const indexed_based_stl_reverse_iterator_base& a, Index b) { Derived ret(a.derived()); ret += b; return ret; }
+ friend Derived operator-(const indexed_based_stl_reverse_iterator_base& a, Index b) { Derived ret(a.derived()); ret -= b; return ret; }
+ friend Derived operator+(Index a, const indexed_based_stl_reverse_iterator_base& b) { Derived ret(b.derived()); ret += a; return ret; }
+ friend Derived operator-(Index a, const indexed_based_stl_reverse_iterator_base& b) { Derived ret(b.derived()); ret -= a; return ret; }
+
+ Derived& operator+=(Index b) { m_index -= b; return derived(); }
+ Derived& operator-=(Index b) { m_index += b; return derived(); }
+
+ difference_type operator-(const indexed_based_stl_reverse_iterator_base& other) const
+ {
+ eigen_assert(mp_xpr == other.mp_xpr);
+ return other.m_index - m_index;
+ }
+
+ difference_type operator-(const other_iterator& other) const
+ {
+ eigen_assert(mp_xpr == other.mp_xpr);
+ return other.m_index - m_index;
+ }
+
+ bool operator==(const indexed_based_stl_reverse_iterator_base& other) const { eigen_assert(mp_xpr == other.mp_xpr); return m_index == other.m_index; }
+ bool operator!=(const indexed_based_stl_reverse_iterator_base& other) const { eigen_assert(mp_xpr == other.mp_xpr); return m_index != other.m_index; }
+ bool operator< (const indexed_based_stl_reverse_iterator_base& other) const { eigen_assert(mp_xpr == other.mp_xpr); return m_index > other.m_index; }
+ bool operator<=(const indexed_based_stl_reverse_iterator_base& other) const { eigen_assert(mp_xpr == other.mp_xpr); return m_index >= other.m_index; }
+ bool operator> (const indexed_based_stl_reverse_iterator_base& other) const { eigen_assert(mp_xpr == other.mp_xpr); return m_index < other.m_index; }
+ bool operator>=(const indexed_based_stl_reverse_iterator_base& other) const { eigen_assert(mp_xpr == other.mp_xpr); return m_index <= other.m_index; }
+
+ bool operator==(const other_iterator& other) const { eigen_assert(mp_xpr == other.mp_xpr); return m_index == other.m_index; }
+ bool operator!=(const other_iterator& other) const { eigen_assert(mp_xpr == other.mp_xpr); return m_index != other.m_index; }
+ bool operator< (const other_iterator& other) const { eigen_assert(mp_xpr == other.mp_xpr); return m_index > other.m_index; }
+ bool operator<=(const other_iterator& other) const { eigen_assert(mp_xpr == other.mp_xpr); return m_index >= other.m_index; }
+ bool operator> (const other_iterator& other) const { eigen_assert(mp_xpr == other.mp_xpr); return m_index < other.m_index; }
+ bool operator>=(const other_iterator& other) const { eigen_assert(mp_xpr == other.mp_xpr); return m_index <= other.m_index; }
+
+protected:
+
+ Derived& derived() { return static_cast<Derived&>(*this); }
+ const Derived& derived() const { return static_cast<const Derived&>(*this); }
+
+ XprType *mp_xpr;
+ Index m_index;
+};
+
+template<typename XprType>
+class pointer_based_stl_iterator
+{
+ enum { is_lvalue = internal::is_lvalue<XprType>::value };
+ typedef pointer_based_stl_iterator<std::remove_const_t<XprType>> non_const_iterator;
+ typedef pointer_based_stl_iterator<std::add_const_t<XprType>> const_iterator;
+ typedef std::conditional_t<internal::is_const<XprType>::value,non_const_iterator,const_iterator> other_iterator;
+ // NOTE: in C++03 we cannot declare friend classes through typedefs because we need to write friend class:
+ friend class pointer_based_stl_iterator<std::add_const_t<XprType>>;
+ friend class pointer_based_stl_iterator<std::remove_const_t<XprType>>;
+public:
+ typedef Index difference_type;
+ typedef typename XprType::Scalar value_type;
+ typedef std::random_access_iterator_tag iterator_category;
+ typedef std::conditional_t<bool(is_lvalue), value_type*, const value_type*> pointer;
+ typedef std::conditional_t<bool(is_lvalue), value_type&, const value_type&> reference;
+
+
+ pointer_based_stl_iterator() EIGEN_NO_THROW : m_ptr(0) {}
+ pointer_based_stl_iterator(XprType& xpr, Index index) EIGEN_NO_THROW : m_incr(xpr.innerStride())
+ {
+ m_ptr = xpr.data() + index * m_incr.value();
+ }
+
+ pointer_based_stl_iterator(const non_const_iterator& other) EIGEN_NO_THROW
+ : m_ptr(other.m_ptr), m_incr(other.m_incr)
+ {}
+
+ pointer_based_stl_iterator& operator=(const non_const_iterator& other) EIGEN_NO_THROW
+ {
+ m_ptr = other.m_ptr;
+ m_incr.setValue(other.m_incr);
+ return *this;
+ }
+
+ reference operator*() const { return *m_ptr; }
+ reference operator[](Index i) const { return *(m_ptr+i*m_incr.value()); }
+ pointer operator->() const { return m_ptr; }
+
+ pointer_based_stl_iterator& operator++() { m_ptr += m_incr.value(); return *this; }
+ pointer_based_stl_iterator& operator--() { m_ptr -= m_incr.value(); return *this; }
+
+ pointer_based_stl_iterator operator++(int) { pointer_based_stl_iterator prev(*this); operator++(); return prev;}
+ pointer_based_stl_iterator operator--(int) { pointer_based_stl_iterator prev(*this); operator--(); return prev;}
+
+ friend pointer_based_stl_iterator operator+(const pointer_based_stl_iterator& a, Index b) { pointer_based_stl_iterator ret(a); ret += b; return ret; }
+ friend pointer_based_stl_iterator operator-(const pointer_based_stl_iterator& a, Index b) { pointer_based_stl_iterator ret(a); ret -= b; return ret; }
+ friend pointer_based_stl_iterator operator+(Index a, const pointer_based_stl_iterator& b) { pointer_based_stl_iterator ret(b); ret += a; return ret; }
+ friend pointer_based_stl_iterator operator-(Index a, const pointer_based_stl_iterator& b) { pointer_based_stl_iterator ret(b); ret -= a; return ret; }
+
+ pointer_based_stl_iterator& operator+=(Index b) { m_ptr += b*m_incr.value(); return *this; }
+ pointer_based_stl_iterator& operator-=(Index b) { m_ptr -= b*m_incr.value(); return *this; }
+
+ difference_type operator-(const pointer_based_stl_iterator& other) const {
+ return (m_ptr - other.m_ptr)/m_incr.value();
+ }
+
+ difference_type operator-(const other_iterator& other) const {
+ return (m_ptr - other.m_ptr)/m_incr.value();
+ }
+
+ bool operator==(const pointer_based_stl_iterator& other) const { return m_ptr == other.m_ptr; }
+ bool operator!=(const pointer_based_stl_iterator& other) const { return m_ptr != other.m_ptr; }
+ bool operator< (const pointer_based_stl_iterator& other) const { return m_ptr < other.m_ptr; }
+ bool operator<=(const pointer_based_stl_iterator& other) const { return m_ptr <= other.m_ptr; }
+ bool operator> (const pointer_based_stl_iterator& other) const { return m_ptr > other.m_ptr; }
+ bool operator>=(const pointer_based_stl_iterator& other) const { return m_ptr >= other.m_ptr; }
+
+ bool operator==(const other_iterator& other) const { return m_ptr == other.m_ptr; }
+ bool operator!=(const other_iterator& other) const { return m_ptr != other.m_ptr; }
+ bool operator< (const other_iterator& other) const { return m_ptr < other.m_ptr; }
+ bool operator<=(const other_iterator& other) const { return m_ptr <= other.m_ptr; }
+ bool operator> (const other_iterator& other) const { return m_ptr > other.m_ptr; }
+ bool operator>=(const other_iterator& other) const { return m_ptr >= other.m_ptr; }
+
+protected:
+
+ pointer m_ptr;
+ internal::variable_if_dynamic<Index, XprType::InnerStrideAtCompileTime> m_incr;
+};
+
+template<typename XprType_>
+struct indexed_based_stl_iterator_traits<generic_randaccess_stl_iterator<XprType_> >
+{
+ typedef XprType_ XprType;
+ typedef generic_randaccess_stl_iterator<std::remove_const_t<XprType>> non_const_iterator;
+ typedef generic_randaccess_stl_iterator<std::add_const_t<XprType>> const_iterator;
+};
+
+template<typename XprType>
+class generic_randaccess_stl_iterator : public indexed_based_stl_iterator_base<generic_randaccess_stl_iterator<XprType> >
+{
+public:
+ typedef typename XprType::Scalar value_type;
+
+protected:
+
+ enum {
+ has_direct_access = (internal::traits<XprType>::Flags & DirectAccessBit) ? 1 : 0,
+ is_lvalue = internal::is_lvalue<XprType>::value
+ };
+
+ typedef indexed_based_stl_iterator_base<generic_randaccess_stl_iterator> Base;
+ using Base::m_index;
+ using Base::mp_xpr;
+
+ // TODO currently const Transpose/Reshape expressions never returns const references,
+ // so lets return by value too.
+ //typedef std::conditional_t<bool(has_direct_access), const value_type&, const value_type> read_only_ref_t;
+ typedef const value_type read_only_ref_t;
+
+public:
+
+ typedef std::conditional_t<bool(is_lvalue), value_type *, const value_type *> pointer;
+ typedef std::conditional_t<bool(is_lvalue), value_type&, read_only_ref_t> reference;
+
+ generic_randaccess_stl_iterator() : Base() {}
+ generic_randaccess_stl_iterator(XprType& xpr, Index index) : Base(xpr,index) {}
+ generic_randaccess_stl_iterator(const typename Base::non_const_iterator& other) : Base(other) {}
+ using Base::operator=;
+
+ reference operator*() const { return (*mp_xpr)(m_index); }
+ reference operator[](Index i) const { return (*mp_xpr)(m_index+i); }
+ pointer operator->() const { return &((*mp_xpr)(m_index)); }
+};
+
+template<typename XprType_, DirectionType Direction>
+struct indexed_based_stl_iterator_traits<subvector_stl_iterator<XprType_,Direction> >
+{
+ typedef XprType_ XprType;
+ typedef subvector_stl_iterator<std::remove_const_t<XprType>, Direction> non_const_iterator;
+ typedef subvector_stl_iterator<std::add_const_t<XprType>, Direction> const_iterator;
+};
+
+template<typename XprType, DirectionType Direction>
+class subvector_stl_iterator : public indexed_based_stl_iterator_base<subvector_stl_iterator<XprType,Direction> >
+{
+protected:
+
+ enum { is_lvalue = internal::is_lvalue<XprType>::value };
+
+ typedef indexed_based_stl_iterator_base<subvector_stl_iterator> Base;
+ using Base::m_index;
+ using Base::mp_xpr;
+
+ typedef std::conditional_t<Direction==Vertical,typename XprType::ColXpr,typename XprType::RowXpr> SubVectorType;
+ typedef std::conditional_t<Direction==Vertical,typename XprType::ConstColXpr,typename XprType::ConstRowXpr> ConstSubVectorType;
+
+
+public:
+ typedef std::conditional_t<bool(is_lvalue), SubVectorType, ConstSubVectorType> reference;
+ typedef typename reference::PlainObject value_type;
+
+private:
+ class subvector_stl_iterator_ptr
+ {
+ public:
+ subvector_stl_iterator_ptr(const reference &subvector) : m_subvector(subvector) {}
+ reference* operator->() { return &m_subvector; }
+ private:
+ reference m_subvector;
+ };
+public:
+
+ typedef subvector_stl_iterator_ptr pointer;
+
+ subvector_stl_iterator() : Base() {}
+ subvector_stl_iterator(XprType& xpr, Index index) : Base(xpr,index) {}
+
+ reference operator*() const { return (*mp_xpr).template subVector<Direction>(m_index); }
+ reference operator[](Index i) const { return (*mp_xpr).template subVector<Direction>(m_index+i); }
+ pointer operator->() const { return (*mp_xpr).template subVector<Direction>(m_index); }
+};
+
+template<typename XprType_, DirectionType Direction>
+struct indexed_based_stl_iterator_traits<subvector_stl_reverse_iterator<XprType_,Direction> >
+{
+ typedef XprType_ XprType;
+ typedef subvector_stl_reverse_iterator<std::remove_const_t<XprType>, Direction> non_const_iterator;
+ typedef subvector_stl_reverse_iterator<std::add_const_t<XprType>, Direction> const_iterator;
+};
+
+template<typename XprType, DirectionType Direction>
+class subvector_stl_reverse_iterator : public indexed_based_stl_reverse_iterator_base<subvector_stl_reverse_iterator<XprType,Direction> >
+{
+protected:
+
+ enum { is_lvalue = internal::is_lvalue<XprType>::value };
+
+ typedef indexed_based_stl_reverse_iterator_base<subvector_stl_reverse_iterator> Base;
+ using Base::m_index;
+ using Base::mp_xpr;
+
+ typedef std::conditional_t<Direction==Vertical,typename XprType::ColXpr,typename XprType::RowXpr> SubVectorType;
+ typedef std::conditional_t<Direction==Vertical,typename XprType::ConstColXpr,typename XprType::ConstRowXpr> ConstSubVectorType;
+
+
+public:
+ typedef std::conditional_t<bool(is_lvalue), SubVectorType, ConstSubVectorType> reference;
+ typedef typename reference::PlainObject value_type;
+
+private:
+ class subvector_stl_reverse_iterator_ptr
+ {
+ public:
+ subvector_stl_reverse_iterator_ptr(const reference &subvector) : m_subvector(subvector) {}
+ reference* operator->() { return &m_subvector; }
+ private:
+ reference m_subvector;
+ };
+public:
+
+ typedef subvector_stl_reverse_iterator_ptr pointer;
+
+ subvector_stl_reverse_iterator() : Base() {}
+ subvector_stl_reverse_iterator(XprType& xpr, Index index) : Base(xpr,index) {}
+
+ reference operator*() const { return (*mp_xpr).template subVector<Direction>(m_index); }
+ reference operator[](Index i) const { return (*mp_xpr).template subVector<Direction>(m_index+i); }
+ pointer operator->() const { return (*mp_xpr).template subVector<Direction>(m_index); }
+};
+
+} // namespace internal
+
+
+/** returns an iterator to the first element of the 1D vector or array
+ * \only_for_vectors
+ * \sa end(), cbegin()
+ */
+template<typename Derived>
+inline typename DenseBase<Derived>::iterator DenseBase<Derived>::begin()
+{
+ EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived);
+ return iterator(derived(), 0);
+}
+
+/** const version of begin() */
+template<typename Derived>
+inline typename DenseBase<Derived>::const_iterator DenseBase<Derived>::begin() const
+{
+ return cbegin();
+}
+
+/** returns a read-only const_iterator to the first element of the 1D vector or array
+ * \only_for_vectors
+ * \sa cend(), begin()
+ */
+template<typename Derived>
+inline typename DenseBase<Derived>::const_iterator DenseBase<Derived>::cbegin() const
+{
+ EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived);
+ return const_iterator(derived(), 0);
+}
+
+/** returns an iterator to the element following the last element of the 1D vector or array
+ * \only_for_vectors
+ * \sa begin(), cend()
+ */
+template<typename Derived>
+inline typename DenseBase<Derived>::iterator DenseBase<Derived>::end()
+{
+ EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived);
+ return iterator(derived(), size());
+}
+
+/** const version of end() */
+template<typename Derived>
+inline typename DenseBase<Derived>::const_iterator DenseBase<Derived>::end() const
+{
+ return cend();
+}
+
+/** returns a read-only const_iterator to the element following the last element of the 1D vector or array
+ * \only_for_vectors
+ * \sa begin(), cend()
+ */
+template<typename Derived>
+inline typename DenseBase<Derived>::const_iterator DenseBase<Derived>::cend() const
+{
+ EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived);
+ return const_iterator(derived(), size());
+}
+
+} // namespace Eigen
+
+#endif // EIGEN_STLITERATORS_H
diff --git a/Eigen/src/Core/Stride.h b/Eigen/src/Core/Stride.h
new file mode 100644
index 0000000..2832e80
--- /dev/null
+++ b/Eigen/src/Core/Stride.h
@@ -0,0 +1,122 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2010 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_STRIDE_H
+#define EIGEN_STRIDE_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+/** \class Stride
+ * \ingroup Core_Module
+ *
+ * \brief Holds strides information for Map
+ *
+ * This class holds the strides information for mapping arrays with strides with class Map.
+ *
+ * It holds two values: the inner stride and the outer stride.
+ *
+ * The inner stride is the pointer increment between two consecutive entries within a given row of a
+ * row-major matrix or within a given column of a column-major matrix.
+ *
+ * The outer stride is the pointer increment between two consecutive rows of a row-major matrix or
+ * between two consecutive columns of a column-major matrix.
+ *
+ * These two values can be passed either at compile-time as template parameters, or at runtime as
+ * arguments to the constructor.
+ *
+ * Indeed, this class takes two template parameters:
+ * \tparam OuterStrideAtCompileTime_ the outer stride, or Dynamic if you want to specify it at runtime.
+ * \tparam InnerStrideAtCompileTime_ the inner stride, or Dynamic if you want to specify it at runtime.
+ *
+ * Here is an example:
+ * \include Map_general_stride.cpp
+ * Output: \verbinclude Map_general_stride.out
+ *
+ * Both strides can be negative. However, a negative stride of -1 cannot be specified at compile time
+ * because of the ambiguity with Dynamic which is defined to -1 (historically, negative strides were
+ * not allowed).
+ *
+ * Note that for compile-time vectors (ColsAtCompileTime==1 or RowsAtCompile==1),
+ * the inner stride is the pointer increment between two consecutive elements,
+ * regardless of storage layout.
+ *
+ * \sa class InnerStride, class OuterStride, \ref TopicStorageOrders
+ */
+template<int OuterStrideAtCompileTime_, int InnerStrideAtCompileTime_>
+class Stride
+{
+ public:
+ typedef Eigen::Index Index; ///< \deprecated since Eigen 3.3
+ enum {
+ InnerStrideAtCompileTime = InnerStrideAtCompileTime_,
+ OuterStrideAtCompileTime = OuterStrideAtCompileTime_
+ };
+
+ /** Default constructor, for use when strides are fixed at compile time */
+ EIGEN_DEVICE_FUNC
+ Stride()
+ : m_outer(OuterStrideAtCompileTime), m_inner(InnerStrideAtCompileTime)
+ {
+ // FIXME: for Eigen 4 we should use DynamicIndex instead of Dynamic.
+ // FIXME: for Eigen 4 we should also unify this API with fix<>
+ eigen_assert(InnerStrideAtCompileTime != Dynamic && OuterStrideAtCompileTime != Dynamic);
+ }
+
+ /** Constructor allowing to pass the strides at runtime */
+ EIGEN_DEVICE_FUNC
+ Stride(Index outerStride, Index innerStride)
+ : m_outer(outerStride), m_inner(innerStride)
+ {
+ }
+
+ /** Copy constructor */
+ EIGEN_DEVICE_FUNC
+ Stride(const Stride& other)
+ : m_outer(other.outer()), m_inner(other.inner())
+ {}
+
+ /** \returns the outer stride */
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
+ inline Index outer() const { return m_outer.value(); }
+ /** \returns the inner stride */
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
+ inline Index inner() const { return m_inner.value(); }
+
+ protected:
+ internal::variable_if_dynamic<Index, OuterStrideAtCompileTime> m_outer;
+ internal::variable_if_dynamic<Index, InnerStrideAtCompileTime> m_inner;
+};
+
+/** \brief Convenience specialization of Stride to specify only an inner stride
+ * See class Map for some examples */
+template<int Value>
+class InnerStride : public Stride<0, Value>
+{
+ typedef Stride<0, Value> Base;
+ public:
+ EIGEN_DEVICE_FUNC InnerStride() : Base() {}
+ EIGEN_DEVICE_FUNC InnerStride(Index v) : Base(0, v) {} // FIXME making this explicit could break valid code
+};
+
+/** \brief Convenience specialization of Stride to specify only an outer stride
+ * See class Map for some examples */
+template<int Value>
+class OuterStride : public Stride<Value, 0>
+{
+ typedef Stride<Value, 0> Base;
+ public:
+ EIGEN_DEVICE_FUNC OuterStride() : Base() {}
+ EIGEN_DEVICE_FUNC OuterStride(Index v) : Base(v,0) {} // FIXME making this explicit could break valid code
+};
+
+} // end namespace Eigen
+
+#endif // EIGEN_STRIDE_H
diff --git a/Eigen/src/Core/Swap.h b/Eigen/src/Core/Swap.h
new file mode 100644
index 0000000..b2e7511
--- /dev/null
+++ b/Eigen/src/Core/Swap.h
@@ -0,0 +1,70 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_SWAP_H
+#define EIGEN_SWAP_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+
+// Overload default assignPacket behavior for swapping them
+template<typename DstEvaluatorTypeT, typename SrcEvaluatorTypeT>
+class generic_dense_assignment_kernel<DstEvaluatorTypeT, SrcEvaluatorTypeT, swap_assign_op<typename DstEvaluatorTypeT::Scalar>, Specialized>
+ : public generic_dense_assignment_kernel<DstEvaluatorTypeT, SrcEvaluatorTypeT, swap_assign_op<typename DstEvaluatorTypeT::Scalar>, BuiltIn>
+{
+protected:
+ typedef generic_dense_assignment_kernel<DstEvaluatorTypeT, SrcEvaluatorTypeT, swap_assign_op<typename DstEvaluatorTypeT::Scalar>, BuiltIn> Base;
+ using Base::m_dst;
+ using Base::m_src;
+ using Base::m_functor;
+
+public:
+ typedef typename Base::Scalar Scalar;
+ typedef typename Base::DstXprType DstXprType;
+ typedef swap_assign_op<Scalar> Functor;
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ generic_dense_assignment_kernel(DstEvaluatorTypeT &dst, const SrcEvaluatorTypeT &src, const Functor &func, DstXprType& dstExpr)
+ : Base(dst, src, func, dstExpr)
+ {}
+
+ template<int StoreMode, int LoadMode, typename PacketType>
+ EIGEN_STRONG_INLINE void assignPacket(Index row, Index col)
+ {
+ PacketType tmp = m_src.template packet<LoadMode,PacketType>(row,col);
+ const_cast<SrcEvaluatorTypeT&>(m_src).template writePacket<LoadMode>(row,col, m_dst.template packet<StoreMode,PacketType>(row,col));
+ m_dst.template writePacket<StoreMode>(row,col,tmp);
+ }
+
+ template<int StoreMode, int LoadMode, typename PacketType>
+ EIGEN_STRONG_INLINE void assignPacket(Index index)
+ {
+ PacketType tmp = m_src.template packet<LoadMode,PacketType>(index);
+ const_cast<SrcEvaluatorTypeT&>(m_src).template writePacket<LoadMode>(index, m_dst.template packet<StoreMode,PacketType>(index));
+ m_dst.template writePacket<StoreMode>(index,tmp);
+ }
+
+ // TODO find a simple way not to have to copy/paste this function from generic_dense_assignment_kernel, by simple I mean no CRTP (Gael)
+ template<int StoreMode, int LoadMode, typename PacketType>
+ EIGEN_STRONG_INLINE void assignPacketByOuterInner(Index outer, Index inner)
+ {
+ Index row = Base::rowIndexByOuterInner(outer, inner);
+ Index col = Base::colIndexByOuterInner(outer, inner);
+ assignPacket<StoreMode,LoadMode,PacketType>(row, col);
+ }
+};
+
+} // namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_SWAP_H
diff --git a/Eigen/src/Core/Transpose.h b/Eigen/src/Core/Transpose.h
new file mode 100644
index 0000000..74650ef
--- /dev/null
+++ b/Eigen/src/Core/Transpose.h
@@ -0,0 +1,466 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+// Copyright (C) 2009-2014 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_TRANSPOSE_H
+#define EIGEN_TRANSPOSE_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+template<typename MatrixType>
+struct traits<Transpose<MatrixType> > : public traits<MatrixType>
+{
+ typedef typename ref_selector<MatrixType>::type MatrixTypeNested;
+ typedef std::remove_reference_t<MatrixTypeNested> MatrixTypeNestedPlain;
+ enum {
+ RowsAtCompileTime = MatrixType::ColsAtCompileTime,
+ ColsAtCompileTime = MatrixType::RowsAtCompileTime,
+ MaxRowsAtCompileTime = MatrixType::MaxColsAtCompileTime,
+ MaxColsAtCompileTime = MatrixType::MaxRowsAtCompileTime,
+ FlagsLvalueBit = is_lvalue<MatrixType>::value ? LvalueBit : 0,
+ Flags0 = traits<MatrixTypeNestedPlain>::Flags & ~(LvalueBit | NestByRefBit),
+ Flags1 = Flags0 | FlagsLvalueBit,
+ Flags = Flags1 ^ RowMajorBit,
+ InnerStrideAtCompileTime = inner_stride_at_compile_time<MatrixType>::ret,
+ OuterStrideAtCompileTime = outer_stride_at_compile_time<MatrixType>::ret
+ };
+};
+}
+
+template<typename MatrixType, typename StorageKind> class TransposeImpl;
+
+/** \class Transpose
+ * \ingroup Core_Module
+ *
+ * \brief Expression of the transpose of a matrix
+ *
+ * \tparam MatrixType the type of the object of which we are taking the transpose
+ *
+ * This class represents an expression of the transpose of a matrix.
+ * It is the return type of MatrixBase::transpose() and MatrixBase::adjoint()
+ * and most of the time this is the only way it is used.
+ *
+ * \sa MatrixBase::transpose(), MatrixBase::adjoint()
+ */
+template<typename MatrixType> class Transpose
+ : public TransposeImpl<MatrixType,typename internal::traits<MatrixType>::StorageKind>
+{
+ public:
+
+ typedef typename internal::ref_selector<MatrixType>::non_const_type MatrixTypeNested;
+
+ typedef typename TransposeImpl<MatrixType,typename internal::traits<MatrixType>::StorageKind>::Base Base;
+ EIGEN_GENERIC_PUBLIC_INTERFACE(Transpose)
+ typedef internal::remove_all_t<MatrixType> NestedExpression;
+
+ EIGEN_DEVICE_FUNC
+ explicit EIGEN_STRONG_INLINE Transpose(MatrixType& matrix) : m_matrix(matrix) {}
+
+ EIGEN_INHERIT_ASSIGNMENT_OPERATORS(Transpose)
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE EIGEN_CONSTEXPR
+ Index rows() const EIGEN_NOEXCEPT { return m_matrix.cols(); }
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE EIGEN_CONSTEXPR
+ Index cols() const EIGEN_NOEXCEPT { return m_matrix.rows(); }
+
+ /** \returns the nested expression */
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ const internal::remove_all_t<MatrixTypeNested>&
+ nestedExpression() const { return m_matrix; }
+
+ /** \returns the nested expression */
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ std::remove_reference_t<MatrixTypeNested>&
+ nestedExpression() { return m_matrix; }
+
+ /** \internal */
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ void resize(Index nrows, Index ncols) {
+ m_matrix.resize(ncols,nrows);
+ }
+
+ protected:
+ typename internal::ref_selector<MatrixType>::non_const_type m_matrix;
+};
+
+namespace internal {
+
+template<typename MatrixType, bool HasDirectAccess = has_direct_access<MatrixType>::ret>
+struct TransposeImpl_base
+{
+ typedef typename dense_xpr_base<Transpose<MatrixType> >::type type;
+};
+
+template<typename MatrixType>
+struct TransposeImpl_base<MatrixType, false>
+{
+ typedef typename dense_xpr_base<Transpose<MatrixType> >::type type;
+};
+
+} // end namespace internal
+
+// Generic API dispatcher
+template<typename XprType, typename StorageKind>
+class TransposeImpl
+ : public internal::generic_xpr_base<Transpose<XprType> >::type
+{
+public:
+ typedef typename internal::generic_xpr_base<Transpose<XprType> >::type Base;
+};
+
+template<typename MatrixType> class TransposeImpl<MatrixType,Dense>
+ : public internal::TransposeImpl_base<MatrixType>::type
+{
+ public:
+
+ typedef typename internal::TransposeImpl_base<MatrixType>::type Base;
+ using Base::coeffRef;
+ EIGEN_DENSE_PUBLIC_INTERFACE(Transpose<MatrixType>)
+ EIGEN_INHERIT_ASSIGNMENT_OPERATORS(TransposeImpl)
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ Index innerStride() const { return derived().nestedExpression().innerStride(); }
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ Index outerStride() const { return derived().nestedExpression().outerStride(); }
+
+ typedef std::conditional_t<
+ internal::is_lvalue<MatrixType>::value,
+ Scalar,
+ const Scalar
+ > ScalarWithConstIfNotLvalue;
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ ScalarWithConstIfNotLvalue* data() { return derived().nestedExpression().data(); }
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ const Scalar* data() const { return derived().nestedExpression().data(); }
+
+ // FIXME: shall we keep the const version of coeffRef?
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ const Scalar& coeffRef(Index rowId, Index colId) const
+ {
+ return derived().nestedExpression().coeffRef(colId, rowId);
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ const Scalar& coeffRef(Index index) const
+ {
+ return derived().nestedExpression().coeffRef(index);
+ }
+ protected:
+ EIGEN_DEFAULT_EMPTY_CONSTRUCTOR_AND_DESTRUCTOR(TransposeImpl)
+};
+
+/** \returns an expression of the transpose of *this.
+ *
+ * Example: \include MatrixBase_transpose.cpp
+ * Output: \verbinclude MatrixBase_transpose.out
+ *
+ * \warning If you want to replace a matrix by its own transpose, do \b NOT do this:
+ * \code
+ * m = m.transpose(); // bug!!! caused by aliasing effect
+ * \endcode
+ * Instead, use the transposeInPlace() method:
+ * \code
+ * m.transposeInPlace();
+ * \endcode
+ * which gives Eigen good opportunities for optimization, or alternatively you can also do:
+ * \code
+ * m = m.transpose().eval();
+ * \endcode
+ *
+ * \sa transposeInPlace(), adjoint() */
+template<typename Derived>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+typename DenseBase<Derived>::TransposeReturnType
+DenseBase<Derived>::transpose()
+{
+ return TransposeReturnType(derived());
+}
+
+/** This is the const version of transpose().
+ *
+ * Make sure you read the warning for transpose() !
+ *
+ * \sa transposeInPlace(), adjoint() */
+template<typename Derived>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+const typename DenseBase<Derived>::ConstTransposeReturnType
+DenseBase<Derived>::transpose() const
+{
+ return ConstTransposeReturnType(derived());
+}
+
+/** \returns an expression of the adjoint (i.e. conjugate transpose) of *this.
+ *
+ * Example: \include MatrixBase_adjoint.cpp
+ * Output: \verbinclude MatrixBase_adjoint.out
+ *
+ * \warning If you want to replace a matrix by its own adjoint, do \b NOT do this:
+ * \code
+ * m = m.adjoint(); // bug!!! caused by aliasing effect
+ * \endcode
+ * Instead, use the adjointInPlace() method:
+ * \code
+ * m.adjointInPlace();
+ * \endcode
+ * which gives Eigen good opportunities for optimization, or alternatively you can also do:
+ * \code
+ * m = m.adjoint().eval();
+ * \endcode
+ *
+ * \sa adjointInPlace(), transpose(), conjugate(), class Transpose, class internal::scalar_conjugate_op */
+template<typename Derived>
+EIGEN_DEVICE_FUNC inline const typename MatrixBase<Derived>::AdjointReturnType
+MatrixBase<Derived>::adjoint() const
+{
+ return AdjointReturnType(this->transpose());
+}
+
+/***************************************************************************
+* "in place" transpose implementation
+***************************************************************************/
+
+namespace internal {
+
+template<typename MatrixType,
+ bool IsSquare = (MatrixType::RowsAtCompileTime == MatrixType::ColsAtCompileTime) && MatrixType::RowsAtCompileTime!=Dynamic,
+ bool MatchPacketSize =
+ (int(MatrixType::RowsAtCompileTime) == int(internal::packet_traits<typename MatrixType::Scalar>::size))
+ && (internal::evaluator<MatrixType>::Flags&PacketAccessBit) >
+struct inplace_transpose_selector;
+
+template<typename MatrixType>
+struct inplace_transpose_selector<MatrixType,true,false> { // square matrix
+ static void run(MatrixType& m) {
+ m.matrix().template triangularView<StrictlyUpper>().swap(m.matrix().transpose().template triangularView<StrictlyUpper>());
+ }
+};
+
+template<typename MatrixType>
+struct inplace_transpose_selector<MatrixType,true,true> { // PacketSize x PacketSize
+ static void run(MatrixType& m) {
+ typedef typename MatrixType::Scalar Scalar;
+ typedef typename internal::packet_traits<typename MatrixType::Scalar>::type Packet;
+ const Index PacketSize = internal::packet_traits<Scalar>::size;
+ const Index Alignment = internal::evaluator<MatrixType>::Alignment;
+ PacketBlock<Packet> A;
+ for (Index i=0; i<PacketSize; ++i)
+ A.packet[i] = m.template packetByOuterInner<Alignment>(i,0);
+ internal::ptranspose(A);
+ for (Index i=0; i<PacketSize; ++i)
+ m.template writePacket<Alignment>(m.rowIndexByOuterInner(i,0), m.colIndexByOuterInner(i,0), A.packet[i]);
+ }
+};
+
+
+template <typename MatrixType, Index Alignment>
+void BlockedInPlaceTranspose(MatrixType& m) {
+ typedef typename MatrixType::Scalar Scalar;
+ typedef typename internal::packet_traits<typename MatrixType::Scalar>::type Packet;
+ const Index PacketSize = internal::packet_traits<Scalar>::size;
+ eigen_assert(m.rows() == m.cols());
+ int row_start = 0;
+ for (; row_start + PacketSize <= m.rows(); row_start += PacketSize) {
+ for (int col_start = row_start; col_start + PacketSize <= m.cols(); col_start += PacketSize) {
+ PacketBlock<Packet> A;
+ if (row_start == col_start) {
+ for (Index i=0; i<PacketSize; ++i)
+ A.packet[i] = m.template packetByOuterInner<Alignment>(row_start + i,col_start);
+ internal::ptranspose(A);
+ for (Index i=0; i<PacketSize; ++i)
+ m.template writePacket<Alignment>(m.rowIndexByOuterInner(row_start + i, col_start), m.colIndexByOuterInner(row_start + i,col_start), A.packet[i]);
+ } else {
+ PacketBlock<Packet> B;
+ for (Index i=0; i<PacketSize; ++i) {
+ A.packet[i] = m.template packetByOuterInner<Alignment>(row_start + i,col_start);
+ B.packet[i] = m.template packetByOuterInner<Alignment>(col_start + i, row_start);
+ }
+ internal::ptranspose(A);
+ internal::ptranspose(B);
+ for (Index i=0; i<PacketSize; ++i) {
+ m.template writePacket<Alignment>(m.rowIndexByOuterInner(row_start + i, col_start), m.colIndexByOuterInner(row_start + i,col_start), B.packet[i]);
+ m.template writePacket<Alignment>(m.rowIndexByOuterInner(col_start + i, row_start), m.colIndexByOuterInner(col_start + i,row_start), A.packet[i]);
+ }
+ }
+ }
+ }
+ for (Index row = row_start; row < m.rows(); ++row) {
+ m.matrix().row(row).head(row).swap(
+ m.matrix().col(row).head(row).transpose());
+ }
+}
+
+template<typename MatrixType,bool MatchPacketSize>
+struct inplace_transpose_selector<MatrixType,false,MatchPacketSize> { // non square or dynamic matrix
+ static void run(MatrixType& m) {
+ typedef typename MatrixType::Scalar Scalar;
+ if (m.rows() == m.cols()) {
+ const Index PacketSize = internal::packet_traits<Scalar>::size;
+ if (!NumTraits<Scalar>::IsComplex && m.rows() >= PacketSize) {
+ if ((m.rows() % PacketSize) == 0)
+ BlockedInPlaceTranspose<MatrixType,internal::evaluator<MatrixType>::Alignment>(m);
+ else
+ BlockedInPlaceTranspose<MatrixType,Unaligned>(m);
+ }
+ else {
+ m.matrix().template triangularView<StrictlyUpper>().swap(m.matrix().transpose().template triangularView<StrictlyUpper>());
+ }
+ } else {
+ m = m.transpose().eval();
+ }
+ }
+};
+
+
+} // end namespace internal
+
+/** This is the "in place" version of transpose(): it replaces \c *this by its own transpose.
+ * Thus, doing
+ * \code
+ * m.transposeInPlace();
+ * \endcode
+ * has the same effect on m as doing
+ * \code
+ * m = m.transpose().eval();
+ * \endcode
+ * and is faster and also safer because in the latter line of code, forgetting the eval() results
+ * in a bug caused by \ref TopicAliasing "aliasing".
+ *
+ * Notice however that this method is only useful if you want to replace a matrix by its own transpose.
+ * If you just need the transpose of a matrix, use transpose().
+ *
+ * \note if the matrix is not square, then \c *this must be a resizable matrix.
+ * This excludes (non-square) fixed-size matrices, block-expressions and maps.
+ *
+ * \sa transpose(), adjoint(), adjointInPlace() */
+template<typename Derived>
+EIGEN_DEVICE_FUNC inline void DenseBase<Derived>::transposeInPlace()
+{
+ eigen_assert((rows() == cols() || (RowsAtCompileTime == Dynamic && ColsAtCompileTime == Dynamic))
+ && "transposeInPlace() called on a non-square non-resizable matrix");
+ internal::inplace_transpose_selector<Derived>::run(derived());
+}
+
+/***************************************************************************
+* "in place" adjoint implementation
+***************************************************************************/
+
+/** This is the "in place" version of adjoint(): it replaces \c *this by its own transpose.
+ * Thus, doing
+ * \code
+ * m.adjointInPlace();
+ * \endcode
+ * has the same effect on m as doing
+ * \code
+ * m = m.adjoint().eval();
+ * \endcode
+ * and is faster and also safer because in the latter line of code, forgetting the eval() results
+ * in a bug caused by aliasing.
+ *
+ * Notice however that this method is only useful if you want to replace a matrix by its own adjoint.
+ * If you just need the adjoint of a matrix, use adjoint().
+ *
+ * \note if the matrix is not square, then \c *this must be a resizable matrix.
+ * This excludes (non-square) fixed-size matrices, block-expressions and maps.
+ *
+ * \sa transpose(), adjoint(), transposeInPlace() */
+template<typename Derived>
+EIGEN_DEVICE_FUNC inline void MatrixBase<Derived>::adjointInPlace()
+{
+ derived() = adjoint().eval();
+}
+
+#ifndef EIGEN_NO_DEBUG
+
+// The following is to detect aliasing problems in most common cases.
+
+namespace internal {
+
+template<bool DestIsTransposed, typename OtherDerived>
+struct check_transpose_aliasing_compile_time_selector
+{
+ enum { ret = bool(blas_traits<OtherDerived>::IsTransposed) != DestIsTransposed };
+};
+
+template<bool DestIsTransposed, typename BinOp, typename DerivedA, typename DerivedB>
+struct check_transpose_aliasing_compile_time_selector<DestIsTransposed,CwiseBinaryOp<BinOp,DerivedA,DerivedB> >
+{
+ enum { ret = bool(blas_traits<DerivedA>::IsTransposed) != DestIsTransposed
+ || bool(blas_traits<DerivedB>::IsTransposed) != DestIsTransposed
+ };
+};
+
+template<typename Scalar, bool DestIsTransposed, typename OtherDerived>
+struct check_transpose_aliasing_run_time_selector
+{
+ static bool run(const Scalar* dest, const OtherDerived& src)
+ {
+ return (bool(blas_traits<OtherDerived>::IsTransposed) != DestIsTransposed) && (dest!=0 && dest==(const Scalar*)extract_data(src));
+ }
+};
+
+template<typename Scalar, bool DestIsTransposed, typename BinOp, typename DerivedA, typename DerivedB>
+struct check_transpose_aliasing_run_time_selector<Scalar,DestIsTransposed,CwiseBinaryOp<BinOp,DerivedA,DerivedB> >
+{
+ static bool run(const Scalar* dest, const CwiseBinaryOp<BinOp,DerivedA,DerivedB>& src)
+ {
+ return ((blas_traits<DerivedA>::IsTransposed != DestIsTransposed) && (dest!=0 && dest==(const Scalar*)extract_data(src.lhs())))
+ || ((blas_traits<DerivedB>::IsTransposed != DestIsTransposed) && (dest!=0 && dest==(const Scalar*)extract_data(src.rhs())));
+ }
+};
+
+// the following selector, checkTransposeAliasing_impl, based on MightHaveTransposeAliasing,
+// is because when the condition controlling the assert is known at compile time, ICC emits a warning.
+// This is actually a good warning: in expressions that don't have any transposing, the condition is
+// known at compile time to be false, and using that, we can avoid generating the code of the assert again
+// and again for all these expressions that don't need it.
+
+template<typename Derived, typename OtherDerived,
+ bool MightHaveTransposeAliasing
+ = check_transpose_aliasing_compile_time_selector
+ <blas_traits<Derived>::IsTransposed,OtherDerived>::ret
+ >
+struct checkTransposeAliasing_impl
+{
+ static void run(const Derived& dst, const OtherDerived& other)
+ {
+ eigen_assert((!check_transpose_aliasing_run_time_selector
+ <typename Derived::Scalar,blas_traits<Derived>::IsTransposed,OtherDerived>
+ ::run(extract_data(dst), other))
+ && "aliasing detected during transposition, use transposeInPlace() "
+ "or evaluate the rhs into a temporary using .eval()");
+
+ }
+};
+
+template<typename Derived, typename OtherDerived>
+struct checkTransposeAliasing_impl<Derived, OtherDerived, false>
+{
+ static void run(const Derived&, const OtherDerived&)
+ {
+ }
+};
+
+template<typename Dst, typename Src>
+void check_for_aliasing(const Dst &dst, const Src &src)
+{
+ if((!Dst::IsVectorAtCompileTime) && dst.rows()>1 && dst.cols()>1)
+ internal::checkTransposeAliasing_impl<Dst, Src>::run(dst, src);
+}
+
+} // end namespace internal
+
+#endif // EIGEN_NO_DEBUG
+
+} // end namespace Eigen
+
+#endif // EIGEN_TRANSPOSE_H
diff --git a/Eigen/src/Core/Transpositions.h b/Eigen/src/Core/Transpositions.h
new file mode 100644
index 0000000..84a9773
--- /dev/null
+++ b/Eigen/src/Core/Transpositions.h
@@ -0,0 +1,388 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2010-2011 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_TRANSPOSITIONS_H
+#define EIGEN_TRANSPOSITIONS_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+template<typename Derived>
+class TranspositionsBase
+{
+ typedef internal::traits<Derived> Traits;
+
+ public:
+
+ typedef typename Traits::IndicesType IndicesType;
+ typedef typename IndicesType::Scalar StorageIndex;
+ typedef Eigen::Index Index; ///< \deprecated since Eigen 3.3
+
+ EIGEN_DEVICE_FUNC
+ Derived& derived() { return *static_cast<Derived*>(this); }
+ EIGEN_DEVICE_FUNC
+ const Derived& derived() const { return *static_cast<const Derived*>(this); }
+
+ /** Copies the \a other transpositions into \c *this */
+ template<typename OtherDerived>
+ Derived& operator=(const TranspositionsBase<OtherDerived>& other)
+ {
+ indices() = other.indices();
+ return derived();
+ }
+
+ /** \returns the number of transpositions */
+ EIGEN_DEVICE_FUNC
+ Index size() const { return indices().size(); }
+ /** \returns the number of rows of the equivalent permutation matrix */
+ EIGEN_DEVICE_FUNC
+ Index rows() const { return indices().size(); }
+ /** \returns the number of columns of the equivalent permutation matrix */
+ EIGEN_DEVICE_FUNC
+ Index cols() const { return indices().size(); }
+
+ /** Direct access to the underlying index vector */
+ EIGEN_DEVICE_FUNC
+ inline const StorageIndex& coeff(Index i) const { return indices().coeff(i); }
+ /** Direct access to the underlying index vector */
+ inline StorageIndex& coeffRef(Index i) { return indices().coeffRef(i); }
+ /** Direct access to the underlying index vector */
+ inline const StorageIndex& operator()(Index i) const { return indices()(i); }
+ /** Direct access to the underlying index vector */
+ inline StorageIndex& operator()(Index i) { return indices()(i); }
+ /** Direct access to the underlying index vector */
+ inline const StorageIndex& operator[](Index i) const { return indices()(i); }
+ /** Direct access to the underlying index vector */
+ inline StorageIndex& operator[](Index i) { return indices()(i); }
+
+ /** const version of indices(). */
+ EIGEN_DEVICE_FUNC
+ const IndicesType& indices() const { return derived().indices(); }
+ /** \returns a reference to the stored array representing the transpositions. */
+ EIGEN_DEVICE_FUNC
+ IndicesType& indices() { return derived().indices(); }
+
+ /** Resizes to given size. */
+ inline void resize(Index newSize)
+ {
+ indices().resize(newSize);
+ }
+
+ /** Sets \c *this to represents an identity transformation */
+ void setIdentity()
+ {
+ for(StorageIndex i = 0; i < indices().size(); ++i)
+ coeffRef(i) = i;
+ }
+
+ // FIXME: do we want such methods ?
+ // might be useful when the target matrix expression is complex, e.g.:
+ // object.matrix().block(..,..,..,..) = trans * object.matrix().block(..,..,..,..);
+ /*
+ template<typename MatrixType>
+ void applyForwardToRows(MatrixType& mat) const
+ {
+ for(Index k=0 ; k<size() ; ++k)
+ if(m_indices(k)!=k)
+ mat.row(k).swap(mat.row(m_indices(k)));
+ }
+
+ template<typename MatrixType>
+ void applyBackwardToRows(MatrixType& mat) const
+ {
+ for(Index k=size()-1 ; k>=0 ; --k)
+ if(m_indices(k)!=k)
+ mat.row(k).swap(mat.row(m_indices(k)));
+ }
+ */
+
+ /** \returns the inverse transformation */
+ inline Transpose<TranspositionsBase> inverse() const
+ { return Transpose<TranspositionsBase>(derived()); }
+
+ /** \returns the tranpose transformation */
+ inline Transpose<TranspositionsBase> transpose() const
+ { return Transpose<TranspositionsBase>(derived()); }
+
+ protected:
+};
+
+namespace internal {
+template<int SizeAtCompileTime, int MaxSizeAtCompileTime, typename StorageIndex_>
+struct traits<Transpositions<SizeAtCompileTime,MaxSizeAtCompileTime,StorageIndex_> >
+ : traits<PermutationMatrix<SizeAtCompileTime,MaxSizeAtCompileTime,StorageIndex_> >
+{
+ typedef Matrix<StorageIndex_, SizeAtCompileTime, 1, 0, MaxSizeAtCompileTime, 1> IndicesType;
+ typedef TranspositionsStorage StorageKind;
+};
+}
+
+/** \class Transpositions
+ * \ingroup Core_Module
+ *
+ * \brief Represents a sequence of transpositions (row/column interchange)
+ *
+ * \tparam SizeAtCompileTime the number of transpositions, or Dynamic
+ * \tparam MaxSizeAtCompileTime the maximum number of transpositions, or Dynamic. This optional parameter defaults to SizeAtCompileTime. Most of the time, you should not have to specify it.
+ *
+ * This class represents a permutation transformation as a sequence of \em n transpositions
+ * \f$[T_{n-1} \ldots T_{i} \ldots T_{0}]\f$. It is internally stored as a vector of integers \c indices.
+ * Each transposition \f$ T_{i} \f$ applied on the left of a matrix (\f$ T_{i} M\f$) interchanges
+ * the rows \c i and \c indices[i] of the matrix \c M.
+ * A transposition applied on the right (e.g., \f$ M T_{i}\f$) yields a column interchange.
+ *
+ * Compared to the class PermutationMatrix, such a sequence of transpositions is what is
+ * computed during a decomposition with pivoting, and it is faster when applying the permutation in-place.
+ *
+ * To apply a sequence of transpositions to a matrix, simply use the operator * as in the following example:
+ * \code
+ * Transpositions tr;
+ * MatrixXf mat;
+ * mat = tr * mat;
+ * \endcode
+ * In this example, we detect that the matrix appears on both side, and so the transpositions
+ * are applied in-place without any temporary or extra copy.
+ *
+ * \sa class PermutationMatrix
+ */
+
+template<int SizeAtCompileTime, int MaxSizeAtCompileTime, typename StorageIndex_>
+class Transpositions : public TranspositionsBase<Transpositions<SizeAtCompileTime,MaxSizeAtCompileTime,StorageIndex_> >
+{
+ typedef internal::traits<Transpositions> Traits;
+ public:
+
+ typedef TranspositionsBase<Transpositions> Base;
+ typedef typename Traits::IndicesType IndicesType;
+ typedef typename IndicesType::Scalar StorageIndex;
+
+ inline Transpositions() {}
+
+ /** Copy constructor. */
+ template<typename OtherDerived>
+ inline Transpositions(const TranspositionsBase<OtherDerived>& other)
+ : m_indices(other.indices()) {}
+
+ /** Generic constructor from expression of the transposition indices. */
+ template<typename Other>
+ explicit inline Transpositions(const MatrixBase<Other>& indices) : m_indices(indices)
+ {}
+
+ /** Copies the \a other transpositions into \c *this */
+ template<typename OtherDerived>
+ Transpositions& operator=(const TranspositionsBase<OtherDerived>& other)
+ {
+ return Base::operator=(other);
+ }
+
+ /** Constructs an uninitialized permutation matrix of given size.
+ */
+ inline Transpositions(Index size) : m_indices(size)
+ {}
+
+ /** const version of indices(). */
+ EIGEN_DEVICE_FUNC
+ const IndicesType& indices() const { return m_indices; }
+ /** \returns a reference to the stored array representing the transpositions. */
+ EIGEN_DEVICE_FUNC
+ IndicesType& indices() { return m_indices; }
+
+ protected:
+
+ IndicesType m_indices;
+};
+
+
+namespace internal {
+template<int SizeAtCompileTime, int MaxSizeAtCompileTime, typename StorageIndex_, int PacketAccess_>
+struct traits<Map<Transpositions<SizeAtCompileTime,MaxSizeAtCompileTime,StorageIndex_>,PacketAccess_> >
+ : traits<PermutationMatrix<SizeAtCompileTime,MaxSizeAtCompileTime,StorageIndex_> >
+{
+ typedef Map<const Matrix<StorageIndex_,SizeAtCompileTime,1,0,MaxSizeAtCompileTime,1>, PacketAccess_> IndicesType;
+ typedef StorageIndex_ StorageIndex;
+ typedef TranspositionsStorage StorageKind;
+};
+}
+
+template<int SizeAtCompileTime, int MaxSizeAtCompileTime, typename StorageIndex_, int PacketAccess>
+class Map<Transpositions<SizeAtCompileTime,MaxSizeAtCompileTime,StorageIndex_>,PacketAccess>
+ : public TranspositionsBase<Map<Transpositions<SizeAtCompileTime,MaxSizeAtCompileTime,StorageIndex_>,PacketAccess> >
+{
+ typedef internal::traits<Map> Traits;
+ public:
+
+ typedef TranspositionsBase<Map> Base;
+ typedef typename Traits::IndicesType IndicesType;
+ typedef typename IndicesType::Scalar StorageIndex;
+
+ explicit inline Map(const StorageIndex* indicesPtr)
+ : m_indices(indicesPtr)
+ {}
+
+ inline Map(const StorageIndex* indicesPtr, Index size)
+ : m_indices(indicesPtr,size)
+ {}
+
+ /** Copies the \a other transpositions into \c *this */
+ template<typename OtherDerived>
+ Map& operator=(const TranspositionsBase<OtherDerived>& other)
+ {
+ return Base::operator=(other);
+ }
+
+ #ifndef EIGEN_PARSED_BY_DOXYGEN
+ /** This is a special case of the templated operator=. Its purpose is to
+ * prevent a default operator= from hiding the templated operator=.
+ */
+ Map& operator=(const Map& other)
+ {
+ m_indices = other.m_indices;
+ return *this;
+ }
+ #endif
+
+ /** const version of indices(). */
+ EIGEN_DEVICE_FUNC
+ const IndicesType& indices() const { return m_indices; }
+
+ /** \returns a reference to the stored array representing the transpositions. */
+ EIGEN_DEVICE_FUNC
+ IndicesType& indices() { return m_indices; }
+
+ protected:
+
+ IndicesType m_indices;
+};
+
+namespace internal {
+template<typename IndicesType_>
+struct traits<TranspositionsWrapper<IndicesType_> >
+ : traits<PermutationWrapper<IndicesType_> >
+{
+ typedef TranspositionsStorage StorageKind;
+};
+}
+
+template<typename IndicesType_>
+class TranspositionsWrapper
+ : public TranspositionsBase<TranspositionsWrapper<IndicesType_> >
+{
+ typedef internal::traits<TranspositionsWrapper> Traits;
+ public:
+
+ typedef TranspositionsBase<TranspositionsWrapper> Base;
+ typedef typename Traits::IndicesType IndicesType;
+ typedef typename IndicesType::Scalar StorageIndex;
+
+ explicit inline TranspositionsWrapper(IndicesType& indices)
+ : m_indices(indices)
+ {}
+
+ /** Copies the \a other transpositions into \c *this */
+ template<typename OtherDerived>
+ TranspositionsWrapper& operator=(const TranspositionsBase<OtherDerived>& other)
+ {
+ return Base::operator=(other);
+ }
+
+ /** const version of indices(). */
+ EIGEN_DEVICE_FUNC
+ const IndicesType& indices() const { return m_indices; }
+
+ /** \returns a reference to the stored array representing the transpositions. */
+ EIGEN_DEVICE_FUNC
+ IndicesType& indices() { return m_indices; }
+
+ protected:
+
+ typename IndicesType::Nested m_indices;
+};
+
+
+
+/** \returns the \a matrix with the \a transpositions applied to the columns.
+ */
+template<typename MatrixDerived, typename TranspositionsDerived>
+EIGEN_DEVICE_FUNC
+const Product<MatrixDerived, TranspositionsDerived, AliasFreeProduct>
+operator*(const MatrixBase<MatrixDerived> &matrix,
+ const TranspositionsBase<TranspositionsDerived>& transpositions)
+{
+ return Product<MatrixDerived, TranspositionsDerived, AliasFreeProduct>
+ (matrix.derived(), transpositions.derived());
+}
+
+/** \returns the \a matrix with the \a transpositions applied to the rows.
+ */
+template<typename TranspositionsDerived, typename MatrixDerived>
+EIGEN_DEVICE_FUNC
+const Product<TranspositionsDerived, MatrixDerived, AliasFreeProduct>
+operator*(const TranspositionsBase<TranspositionsDerived> &transpositions,
+ const MatrixBase<MatrixDerived>& matrix)
+{
+ return Product<TranspositionsDerived, MatrixDerived, AliasFreeProduct>
+ (transpositions.derived(), matrix.derived());
+}
+
+// Template partial specialization for transposed/inverse transpositions
+
+namespace internal {
+
+template<typename Derived>
+struct traits<Transpose<TranspositionsBase<Derived> > >
+ : traits<Derived>
+{};
+
+} // end namespace internal
+
+template<typename TranspositionsDerived>
+class Transpose<TranspositionsBase<TranspositionsDerived> >
+{
+ typedef TranspositionsDerived TranspositionType;
+ typedef typename TranspositionType::IndicesType IndicesType;
+ public:
+
+ explicit Transpose(const TranspositionType& t) : m_transpositions(t) {}
+
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
+ Index size() const EIGEN_NOEXCEPT { return m_transpositions.size(); }
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
+ Index rows() const EIGEN_NOEXCEPT { return m_transpositions.size(); }
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
+ Index cols() const EIGEN_NOEXCEPT { return m_transpositions.size(); }
+
+ /** \returns the \a matrix with the inverse transpositions applied to the columns.
+ */
+ template<typename OtherDerived> friend
+ const Product<OtherDerived, Transpose, AliasFreeProduct>
+ operator*(const MatrixBase<OtherDerived>& matrix, const Transpose& trt)
+ {
+ return Product<OtherDerived, Transpose, AliasFreeProduct>(matrix.derived(), trt);
+ }
+
+ /** \returns the \a matrix with the inverse transpositions applied to the rows.
+ */
+ template<typename OtherDerived>
+ const Product<Transpose, OtherDerived, AliasFreeProduct>
+ operator*(const MatrixBase<OtherDerived>& matrix) const
+ {
+ return Product<Transpose, OtherDerived, AliasFreeProduct>(*this, matrix.derived());
+ }
+
+ EIGEN_DEVICE_FUNC
+ const TranspositionType& nestedExpression() const { return m_transpositions; }
+
+ protected:
+ const TranspositionType& m_transpositions;
+};
+
+} // end namespace Eigen
+
+#endif // EIGEN_TRANSPOSITIONS_H
diff --git a/Eigen/src/Core/TriangularMatrix.h b/Eigen/src/Core/TriangularMatrix.h
new file mode 100644
index 0000000..c1bd13a
--- /dev/null
+++ b/Eigen/src/Core/TriangularMatrix.h
@@ -0,0 +1,1003 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+// Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_TRIANGULARMATRIX_H
+#define EIGEN_TRIANGULARMATRIX_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+
+template<int Side, typename TriangularType, typename Rhs> struct triangular_solve_retval;
+
+}
+
+/** \class TriangularBase
+ * \ingroup Core_Module
+ *
+ * \brief Base class for triangular part in a matrix
+ */
+template<typename Derived> class TriangularBase : public EigenBase<Derived>
+{
+ public:
+
+ enum {
+ Mode = internal::traits<Derived>::Mode,
+ RowsAtCompileTime = internal::traits<Derived>::RowsAtCompileTime,
+ ColsAtCompileTime = internal::traits<Derived>::ColsAtCompileTime,
+ MaxRowsAtCompileTime = internal::traits<Derived>::MaxRowsAtCompileTime,
+ MaxColsAtCompileTime = internal::traits<Derived>::MaxColsAtCompileTime,
+
+ SizeAtCompileTime = (internal::size_of_xpr_at_compile_time<Derived>::ret),
+ /**< This is equal to the number of coefficients, i.e. the number of
+ * rows times the number of columns, or to \a Dynamic if this is not
+ * known at compile-time. \sa RowsAtCompileTime, ColsAtCompileTime */
+
+ MaxSizeAtCompileTime = internal::size_at_compile_time(internal::traits<Derived>::MaxRowsAtCompileTime,
+ internal::traits<Derived>::MaxColsAtCompileTime)
+
+ };
+ typedef typename internal::traits<Derived>::Scalar Scalar;
+ typedef typename internal::traits<Derived>::StorageKind StorageKind;
+ typedef typename internal::traits<Derived>::StorageIndex StorageIndex;
+ typedef typename internal::traits<Derived>::FullMatrixType DenseMatrixType;
+ typedef DenseMatrixType DenseType;
+ typedef Derived const& Nested;
+
+ EIGEN_DEVICE_FUNC
+ inline TriangularBase() { eigen_assert(!((int(Mode) & int(UnitDiag)) && (int(Mode) & int(ZeroDiag)))); }
+
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
+ inline Index rows() const EIGEN_NOEXCEPT { return derived().rows(); }
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
+ inline Index cols() const EIGEN_NOEXCEPT { return derived().cols(); }
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
+ inline Index outerStride() const EIGEN_NOEXCEPT { return derived().outerStride(); }
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
+ inline Index innerStride() const EIGEN_NOEXCEPT { return derived().innerStride(); }
+
+ // dummy resize function
+ EIGEN_DEVICE_FUNC
+ void resize(Index rows, Index cols)
+ {
+ EIGEN_UNUSED_VARIABLE(rows);
+ EIGEN_UNUSED_VARIABLE(cols);
+ eigen_assert(rows==this->rows() && cols==this->cols());
+ }
+
+ EIGEN_DEVICE_FUNC
+ inline Scalar coeff(Index row, Index col) const { return derived().coeff(row,col); }
+ EIGEN_DEVICE_FUNC
+ inline Scalar& coeffRef(Index row, Index col) { return derived().coeffRef(row,col); }
+
+ /** \see MatrixBase::copyCoeff(row,col)
+ */
+ template<typename Other>
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE void copyCoeff(Index row, Index col, Other& other)
+ {
+ derived().coeffRef(row, col) = other.coeff(row, col);
+ }
+
+ EIGEN_DEVICE_FUNC
+ inline Scalar operator()(Index row, Index col) const
+ {
+ check_coordinates(row, col);
+ return coeff(row,col);
+ }
+ EIGEN_DEVICE_FUNC
+ inline Scalar& operator()(Index row, Index col)
+ {
+ check_coordinates(row, col);
+ return coeffRef(row,col);
+ }
+
+ #ifndef EIGEN_PARSED_BY_DOXYGEN
+ EIGEN_DEVICE_FUNC
+ inline const Derived& derived() const { return *static_cast<const Derived*>(this); }
+ EIGEN_DEVICE_FUNC
+ inline Derived& derived() { return *static_cast<Derived*>(this); }
+ #endif // not EIGEN_PARSED_BY_DOXYGEN
+
+ template<typename DenseDerived>
+ EIGEN_DEVICE_FUNC
+ void evalTo(MatrixBase<DenseDerived> &other) const;
+ template<typename DenseDerived>
+ EIGEN_DEVICE_FUNC
+ void evalToLazy(MatrixBase<DenseDerived> &other) const;
+
+ EIGEN_DEVICE_FUNC
+ DenseMatrixType toDenseMatrix() const
+ {
+ DenseMatrixType res(rows(), cols());
+ evalToLazy(res);
+ return res;
+ }
+
+ protected:
+
+ void check_coordinates(Index row, Index col) const
+ {
+ EIGEN_ONLY_USED_FOR_DEBUG(row);
+ EIGEN_ONLY_USED_FOR_DEBUG(col);
+ eigen_assert(col>=0 && col<cols() && row>=0 && row<rows());
+ const int mode = int(Mode) & ~SelfAdjoint;
+ EIGEN_ONLY_USED_FOR_DEBUG(mode);
+ eigen_assert((mode==Upper && col>=row)
+ || (mode==Lower && col<=row)
+ || ((mode==StrictlyUpper || mode==UnitUpper) && col>row)
+ || ((mode==StrictlyLower || mode==UnitLower) && col<row));
+ }
+
+ #ifdef EIGEN_INTERNAL_DEBUGGING
+ void check_coordinates_internal(Index row, Index col) const
+ {
+ check_coordinates(row, col);
+ }
+ #else
+ void check_coordinates_internal(Index , Index ) const {}
+ #endif
+
+};
+
+/** \class TriangularView
+ * \ingroup Core_Module
+ *
+ * \brief Expression of a triangular part in a matrix
+ *
+ * \tparam MatrixType the type of the object in which we are taking the triangular part
+ * \tparam Mode the kind of triangular matrix expression to construct. Can be #Upper,
+ * #Lower, #UnitUpper, #UnitLower, #StrictlyUpper, or #StrictlyLower.
+ * This is in fact a bit field; it must have either #Upper or #Lower,
+ * and additionally it may have #UnitDiag or #ZeroDiag or neither.
+ *
+ * This class represents a triangular part of a matrix, not necessarily square. Strictly speaking, for rectangular
+ * matrices one should speak of "trapezoid" parts. This class is the return type
+ * of MatrixBase::triangularView() and SparseMatrixBase::triangularView(), and most of the time this is the only way it is used.
+ *
+ * \sa MatrixBase::triangularView()
+ */
+namespace internal {
+template<typename MatrixType, unsigned int Mode_>
+struct traits<TriangularView<MatrixType, Mode_> > : traits<MatrixType>
+{
+ typedef typename ref_selector<MatrixType>::non_const_type MatrixTypeNested;
+ typedef std::remove_reference_t<MatrixTypeNested> MatrixTypeNestedNonRef;
+ typedef remove_all_t<MatrixTypeNested> MatrixTypeNestedCleaned;
+ typedef typename MatrixType::PlainObject FullMatrixType;
+ typedef MatrixType ExpressionType;
+ enum {
+ Mode = Mode_,
+ FlagsLvalueBit = is_lvalue<MatrixType>::value ? LvalueBit : 0,
+ Flags = (MatrixTypeNestedCleaned::Flags & (HereditaryBits | FlagsLvalueBit) & (~(PacketAccessBit | DirectAccessBit | LinearAccessBit)))
+ };
+};
+}
+
+template<typename MatrixType_, unsigned int Mode_, typename StorageKind> class TriangularViewImpl;
+
+template<typename MatrixType_, unsigned int Mode_> class TriangularView
+ : public TriangularViewImpl<MatrixType_, Mode_, typename internal::traits<MatrixType_>::StorageKind >
+{
+ public:
+
+ typedef TriangularViewImpl<MatrixType_, Mode_, typename internal::traits<MatrixType_>::StorageKind > Base;
+ typedef typename internal::traits<TriangularView>::Scalar Scalar;
+ typedef MatrixType_ MatrixType;
+
+ protected:
+ typedef typename internal::traits<TriangularView>::MatrixTypeNested MatrixTypeNested;
+ typedef typename internal::traits<TriangularView>::MatrixTypeNestedNonRef MatrixTypeNestedNonRef;
+
+ typedef internal::remove_all_t<typename MatrixType::ConjugateReturnType> MatrixConjugateReturnType;
+ typedef TriangularView<std::add_const_t<MatrixType>, Mode_> ConstTriangularView;
+
+ public:
+
+ typedef typename internal::traits<TriangularView>::StorageKind StorageKind;
+ typedef typename internal::traits<TriangularView>::MatrixTypeNestedCleaned NestedExpression;
+
+ enum {
+ Mode = Mode_,
+ Flags = internal::traits<TriangularView>::Flags,
+ TransposeMode = (Mode & Upper ? Lower : 0)
+ | (Mode & Lower ? Upper : 0)
+ | (Mode & (UnitDiag))
+ | (Mode & (ZeroDiag)),
+ IsVectorAtCompileTime = false
+ };
+
+ EIGEN_DEVICE_FUNC
+ explicit inline TriangularView(MatrixType& matrix) : m_matrix(matrix)
+ {}
+
+ EIGEN_INHERIT_ASSIGNMENT_OPERATORS(TriangularView)
+
+ /** \copydoc EigenBase::rows() */
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
+ inline Index rows() const EIGEN_NOEXCEPT { return m_matrix.rows(); }
+ /** \copydoc EigenBase::cols() */
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
+ inline Index cols() const EIGEN_NOEXCEPT { return m_matrix.cols(); }
+
+ /** \returns a const reference to the nested expression */
+ EIGEN_DEVICE_FUNC
+ const NestedExpression& nestedExpression() const { return m_matrix; }
+
+ /** \returns a reference to the nested expression */
+ EIGEN_DEVICE_FUNC
+ NestedExpression& nestedExpression() { return m_matrix; }
+
+ typedef TriangularView<const MatrixConjugateReturnType,Mode> ConjugateReturnType;
+ /** \sa MatrixBase::conjugate() const */
+ EIGEN_DEVICE_FUNC
+ inline const ConjugateReturnType conjugate() const
+ { return ConjugateReturnType(m_matrix.conjugate()); }
+
+ /** \returns an expression of the complex conjugate of \c *this if Cond==true,
+ * returns \c *this otherwise.
+ */
+ template<bool Cond>
+ EIGEN_DEVICE_FUNC
+ inline std::conditional_t<Cond,ConjugateReturnType,ConstTriangularView>
+ conjugateIf() const
+ {
+ typedef std::conditional_t<Cond,ConjugateReturnType,ConstTriangularView> ReturnType;
+ return ReturnType(m_matrix.template conjugateIf<Cond>());
+ }
+
+ typedef TriangularView<const typename MatrixType::AdjointReturnType,TransposeMode> AdjointReturnType;
+ /** \sa MatrixBase::adjoint() const */
+ EIGEN_DEVICE_FUNC
+ inline const AdjointReturnType adjoint() const
+ { return AdjointReturnType(m_matrix.adjoint()); }
+
+ typedef TriangularView<typename MatrixType::TransposeReturnType,TransposeMode> TransposeReturnType;
+ /** \sa MatrixBase::transpose() */
+ template<class Dummy=int>
+ EIGEN_DEVICE_FUNC
+ inline TransposeReturnType transpose(std::enable_if_t<Eigen::internal::is_lvalue<MatrixType>::value, Dummy*> = nullptr)
+ {
+ typename MatrixType::TransposeReturnType tmp(m_matrix);
+ return TransposeReturnType(tmp);
+ }
+
+ typedef TriangularView<const typename MatrixType::ConstTransposeReturnType,TransposeMode> ConstTransposeReturnType;
+ /** \sa MatrixBase::transpose() const */
+ EIGEN_DEVICE_FUNC
+ inline const ConstTransposeReturnType transpose() const
+ {
+ return ConstTransposeReturnType(m_matrix.transpose());
+ }
+
+ template<typename Other>
+ EIGEN_DEVICE_FUNC
+ inline const Solve<TriangularView, Other>
+ solve(const MatrixBase<Other>& other) const
+ { return Solve<TriangularView, Other>(*this, other.derived()); }
+
+ // workaround MSVC ICE
+ #if EIGEN_COMP_MSVC
+ template<int Side, typename Other>
+ EIGEN_DEVICE_FUNC
+ inline const internal::triangular_solve_retval<Side,TriangularView, Other>
+ solve(const MatrixBase<Other>& other) const
+ { return Base::template solve<Side>(other); }
+ #else
+ using Base::solve;
+ #endif
+
+ /** \returns a selfadjoint view of the referenced triangular part which must be either \c #Upper or \c #Lower.
+ *
+ * This is a shortcut for \code this->nestedExpression().selfadjointView<(*this)::Mode>() \endcode
+ * \sa MatrixBase::selfadjointView() */
+ EIGEN_DEVICE_FUNC
+ SelfAdjointView<MatrixTypeNestedNonRef,Mode> selfadjointView()
+ {
+ EIGEN_STATIC_ASSERT((Mode&(UnitDiag|ZeroDiag))==0,PROGRAMMING_ERROR);
+ return SelfAdjointView<MatrixTypeNestedNonRef,Mode>(m_matrix);
+ }
+
+ /** This is the const version of selfadjointView() */
+ EIGEN_DEVICE_FUNC
+ const SelfAdjointView<MatrixTypeNestedNonRef,Mode> selfadjointView() const
+ {
+ EIGEN_STATIC_ASSERT((Mode&(UnitDiag|ZeroDiag))==0,PROGRAMMING_ERROR);
+ return SelfAdjointView<MatrixTypeNestedNonRef,Mode>(m_matrix);
+ }
+
+
+ /** \returns the determinant of the triangular matrix
+ * \sa MatrixBase::determinant() */
+ EIGEN_DEVICE_FUNC
+ Scalar determinant() const
+ {
+ if (Mode & UnitDiag)
+ return 1;
+ else if (Mode & ZeroDiag)
+ return 0;
+ else
+ return m_matrix.diagonal().prod();
+ }
+
+ protected:
+
+ MatrixTypeNested m_matrix;
+};
+
+/** \ingroup Core_Module
+ *
+ * \brief Base class for a triangular part in a \b dense matrix
+ *
+ * This class is an abstract base class of class TriangularView, and objects of type TriangularViewImpl cannot be instantiated.
+ * It extends class TriangularView with additional methods which available for dense expressions only.
+ *
+ * \sa class TriangularView, MatrixBase::triangularView()
+ */
+template<typename MatrixType_, unsigned int Mode_> class TriangularViewImpl<MatrixType_,Mode_,Dense>
+ : public TriangularBase<TriangularView<MatrixType_, Mode_> >
+{
+ public:
+
+ typedef TriangularView<MatrixType_, Mode_> TriangularViewType;
+
+ typedef TriangularBase<TriangularViewType> Base;
+ typedef typename internal::traits<TriangularViewType>::Scalar Scalar;
+
+ typedef MatrixType_ MatrixType;
+ typedef typename MatrixType::PlainObject DenseMatrixType;
+ typedef DenseMatrixType PlainObject;
+
+ public:
+ using Base::evalToLazy;
+ using Base::derived;
+
+ typedef typename internal::traits<TriangularViewType>::StorageKind StorageKind;
+
+ enum {
+ Mode = Mode_,
+ Flags = internal::traits<TriangularViewType>::Flags
+ };
+
+ /** \returns the outer-stride of the underlying dense matrix
+ * \sa DenseCoeffsBase::outerStride() */
+ EIGEN_DEVICE_FUNC
+ inline Index outerStride() const { return derived().nestedExpression().outerStride(); }
+ /** \returns the inner-stride of the underlying dense matrix
+ * \sa DenseCoeffsBase::innerStride() */
+ EIGEN_DEVICE_FUNC
+ inline Index innerStride() const { return derived().nestedExpression().innerStride(); }
+
+ /** \sa MatrixBase::operator+=() */
+ template<typename Other>
+ EIGEN_DEVICE_FUNC
+ TriangularViewType& operator+=(const DenseBase<Other>& other) {
+ internal::call_assignment_no_alias(derived(), other.derived(), internal::add_assign_op<Scalar,typename Other::Scalar>());
+ return derived();
+ }
+ /** \sa MatrixBase::operator-=() */
+ template<typename Other>
+ EIGEN_DEVICE_FUNC
+ TriangularViewType& operator-=(const DenseBase<Other>& other) {
+ internal::call_assignment_no_alias(derived(), other.derived(), internal::sub_assign_op<Scalar,typename Other::Scalar>());
+ return derived();
+ }
+
+ /** \sa MatrixBase::operator*=() */
+ EIGEN_DEVICE_FUNC
+ TriangularViewType& operator*=(const typename internal::traits<MatrixType>::Scalar& other) { return *this = derived().nestedExpression() * other; }
+ /** \sa DenseBase::operator/=() */
+ EIGEN_DEVICE_FUNC
+ TriangularViewType& operator/=(const typename internal::traits<MatrixType>::Scalar& other) { return *this = derived().nestedExpression() / other; }
+
+ /** \sa MatrixBase::fill() */
+ EIGEN_DEVICE_FUNC
+ void fill(const Scalar& value) { setConstant(value); }
+ /** \sa MatrixBase::setConstant() */
+ EIGEN_DEVICE_FUNC
+ TriangularViewType& setConstant(const Scalar& value)
+ { return *this = MatrixType::Constant(derived().rows(), derived().cols(), value); }
+ /** \sa MatrixBase::setZero() */
+ EIGEN_DEVICE_FUNC
+ TriangularViewType& setZero() { return setConstant(Scalar(0)); }
+ /** \sa MatrixBase::setOnes() */
+ EIGEN_DEVICE_FUNC
+ TriangularViewType& setOnes() { return setConstant(Scalar(1)); }
+
+ /** \sa MatrixBase::coeff()
+ * \warning the coordinates must fit into the referenced triangular part
+ */
+ EIGEN_DEVICE_FUNC
+ inline Scalar coeff(Index row, Index col) const
+ {
+ Base::check_coordinates_internal(row, col);
+ return derived().nestedExpression().coeff(row, col);
+ }
+
+ /** \sa MatrixBase::coeffRef()
+ * \warning the coordinates must fit into the referenced triangular part
+ */
+ EIGEN_DEVICE_FUNC
+ inline Scalar& coeffRef(Index row, Index col)
+ {
+ EIGEN_STATIC_ASSERT_LVALUE(TriangularViewType);
+ Base::check_coordinates_internal(row, col);
+ return derived().nestedExpression().coeffRef(row, col);
+ }
+
+ /** Assigns a triangular matrix to a triangular part of a dense matrix */
+ template<typename OtherDerived>
+ EIGEN_DEVICE_FUNC
+ TriangularViewType& operator=(const TriangularBase<OtherDerived>& other);
+
+ /** Shortcut for\code *this = other.other.triangularView<(*this)::Mode>() \endcode */
+ template<typename OtherDerived>
+ EIGEN_DEVICE_FUNC
+ TriangularViewType& operator=(const MatrixBase<OtherDerived>& other);
+
+#ifndef EIGEN_PARSED_BY_DOXYGEN
+ EIGEN_DEVICE_FUNC
+ TriangularViewType& operator=(const TriangularViewImpl& other)
+ { return *this = other.derived().nestedExpression(); }
+
+ template<typename OtherDerived>
+ /** \deprecated */
+ EIGEN_DEPRECATED EIGEN_DEVICE_FUNC
+ void lazyAssign(const TriangularBase<OtherDerived>& other);
+
+ template<typename OtherDerived>
+ /** \deprecated */
+ EIGEN_DEPRECATED EIGEN_DEVICE_FUNC
+ void lazyAssign(const MatrixBase<OtherDerived>& other);
+#endif
+
+ /** Efficient triangular matrix times vector/matrix product */
+ template<typename OtherDerived>
+ EIGEN_DEVICE_FUNC
+ const Product<TriangularViewType,OtherDerived>
+ operator*(const MatrixBase<OtherDerived>& rhs) const
+ {
+ return Product<TriangularViewType,OtherDerived>(derived(), rhs.derived());
+ }
+
+ /** Efficient vector/matrix times triangular matrix product */
+ template<typename OtherDerived> friend
+ EIGEN_DEVICE_FUNC
+ const Product<OtherDerived,TriangularViewType>
+ operator*(const MatrixBase<OtherDerived>& lhs, const TriangularViewImpl& rhs)
+ {
+ return Product<OtherDerived,TriangularViewType>(lhs.derived(),rhs.derived());
+ }
+
+ /** \returns the product of the inverse of \c *this with \a other, \a *this being triangular.
+ *
+ * This function computes the inverse-matrix matrix product inverse(\c *this) * \a other if
+ * \a Side==OnTheLeft (the default), or the right-inverse-multiply \a other * inverse(\c *this) if
+ * \a Side==OnTheRight.
+ *
+ * Note that the template parameter \c Side can be omitted, in which case \c Side==OnTheLeft
+ *
+ * The matrix \c *this must be triangular and invertible (i.e., all the coefficients of the
+ * diagonal must be non zero). It works as a forward (resp. backward) substitution if \c *this
+ * is an upper (resp. lower) triangular matrix.
+ *
+ * Example: \include Triangular_solve.cpp
+ * Output: \verbinclude Triangular_solve.out
+ *
+ * This function returns an expression of the inverse-multiply and can works in-place if it is assigned
+ * to the same matrix or vector \a other.
+ *
+ * For users coming from BLAS, this function (and more specifically solveInPlace()) offer
+ * all the operations supported by the \c *TRSV and \c *TRSM BLAS routines.
+ *
+ * \sa TriangularView::solveInPlace()
+ */
+ template<int Side, typename Other>
+ inline const internal::triangular_solve_retval<Side,TriangularViewType, Other>
+ solve(const MatrixBase<Other>& other) const;
+
+ /** "in-place" version of TriangularView::solve() where the result is written in \a other
+ *
+ * \warning The parameter is only marked 'const' to make the C++ compiler accept a temporary expression here.
+ * This function will const_cast it, so constness isn't honored here.
+ *
+ * Note that the template parameter \c Side can be omitted, in which case \c Side==OnTheLeft
+ *
+ * See TriangularView:solve() for the details.
+ */
+ template<int Side, typename OtherDerived>
+ EIGEN_DEVICE_FUNC
+ void solveInPlace(const MatrixBase<OtherDerived>& other) const;
+
+ template<typename OtherDerived>
+ EIGEN_DEVICE_FUNC
+ void solveInPlace(const MatrixBase<OtherDerived>& other) const
+ { return solveInPlace<OnTheLeft>(other); }
+
+ /** Swaps the coefficients of the common triangular parts of two matrices */
+ template<typename OtherDerived>
+ EIGEN_DEVICE_FUNC
+#ifdef EIGEN_PARSED_BY_DOXYGEN
+ void swap(TriangularBase<OtherDerived> &other)
+#else
+ void swap(TriangularBase<OtherDerived> const & other)
+#endif
+ {
+ EIGEN_STATIC_ASSERT_LVALUE(OtherDerived);
+ call_assignment(derived(), other.const_cast_derived(), internal::swap_assign_op<Scalar>());
+ }
+
+ /** Shortcut for \code (*this).swap(other.triangularView<(*this)::Mode>()) \endcode */
+ template<typename OtherDerived>
+ /** \deprecated */
+ EIGEN_DEPRECATED EIGEN_DEVICE_FUNC
+ void swap(MatrixBase<OtherDerived> const & other)
+ {
+ EIGEN_STATIC_ASSERT_LVALUE(OtherDerived);
+ call_assignment(derived(), other.const_cast_derived(), internal::swap_assign_op<Scalar>());
+ }
+
+ template<typename RhsType, typename DstType>
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE void _solve_impl(const RhsType &rhs, DstType &dst) const {
+ if(!internal::is_same_dense(dst,rhs))
+ dst = rhs;
+ this->solveInPlace(dst);
+ }
+
+ template<typename ProductType>
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE TriangularViewType& _assignProduct(const ProductType& prod, const Scalar& alpha, bool beta);
+ protected:
+ EIGEN_DEFAULT_COPY_CONSTRUCTOR(TriangularViewImpl)
+ EIGEN_DEFAULT_EMPTY_CONSTRUCTOR_AND_DESTRUCTOR(TriangularViewImpl)
+
+};
+
+/***************************************************************************
+* Implementation of triangular evaluation/assignment
+***************************************************************************/
+
+#ifndef EIGEN_PARSED_BY_DOXYGEN
+// FIXME should we keep that possibility
+template<typename MatrixType, unsigned int Mode>
+template<typename OtherDerived>
+EIGEN_DEVICE_FUNC inline TriangularView<MatrixType, Mode>&
+TriangularViewImpl<MatrixType, Mode, Dense>::operator=(const MatrixBase<OtherDerived>& other)
+{
+ internal::call_assignment_no_alias(derived(), other.derived(), internal::assign_op<Scalar,typename OtherDerived::Scalar>());
+ return derived();
+}
+
+// FIXME should we keep that possibility
+template<typename MatrixType, unsigned int Mode>
+template<typename OtherDerived>
+EIGEN_DEVICE_FUNC void TriangularViewImpl<MatrixType, Mode, Dense>::lazyAssign(const MatrixBase<OtherDerived>& other)
+{
+ internal::call_assignment_no_alias(derived(), other.template triangularView<Mode>());
+}
+
+
+
+template<typename MatrixType, unsigned int Mode>
+template<typename OtherDerived>
+EIGEN_DEVICE_FUNC inline TriangularView<MatrixType, Mode>&
+TriangularViewImpl<MatrixType, Mode, Dense>::operator=(const TriangularBase<OtherDerived>& other)
+{
+ eigen_assert(Mode == int(OtherDerived::Mode));
+ internal::call_assignment(derived(), other.derived());
+ return derived();
+}
+
+template<typename MatrixType, unsigned int Mode>
+template<typename OtherDerived>
+EIGEN_DEVICE_FUNC void TriangularViewImpl<MatrixType, Mode, Dense>::lazyAssign(const TriangularBase<OtherDerived>& other)
+{
+ eigen_assert(Mode == int(OtherDerived::Mode));
+ internal::call_assignment_no_alias(derived(), other.derived());
+}
+#endif
+
+/***************************************************************************
+* Implementation of TriangularBase methods
+***************************************************************************/
+
+/** Assigns a triangular or selfadjoint matrix to a dense matrix.
+ * If the matrix is triangular, the opposite part is set to zero. */
+template<typename Derived>
+template<typename DenseDerived>
+EIGEN_DEVICE_FUNC void TriangularBase<Derived>::evalTo(MatrixBase<DenseDerived> &other) const
+{
+ evalToLazy(other.derived());
+}
+
+/***************************************************************************
+* Implementation of TriangularView methods
+***************************************************************************/
+
+/***************************************************************************
+* Implementation of MatrixBase methods
+***************************************************************************/
+
+/**
+ * \returns an expression of a triangular view extracted from the current matrix
+ *
+ * The parameter \a Mode can have the following values: \c #Upper, \c #StrictlyUpper, \c #UnitUpper,
+ * \c #Lower, \c #StrictlyLower, \c #UnitLower.
+ *
+ * Example: \include MatrixBase_triangularView.cpp
+ * Output: \verbinclude MatrixBase_triangularView.out
+ *
+ * \sa class TriangularView
+ */
+template<typename Derived>
+template<unsigned int Mode>
+EIGEN_DEVICE_FUNC
+typename MatrixBase<Derived>::template TriangularViewReturnType<Mode>::Type
+MatrixBase<Derived>::triangularView()
+{
+ return typename TriangularViewReturnType<Mode>::Type(derived());
+}
+
+/** This is the const version of MatrixBase::triangularView() */
+template<typename Derived>
+template<unsigned int Mode>
+EIGEN_DEVICE_FUNC
+typename MatrixBase<Derived>::template ConstTriangularViewReturnType<Mode>::Type
+MatrixBase<Derived>::triangularView() const
+{
+ return typename ConstTriangularViewReturnType<Mode>::Type(derived());
+}
+
+/** \returns true if *this is approximately equal to an upper triangular matrix,
+ * within the precision given by \a prec.
+ *
+ * \sa isLowerTriangular()
+ */
+template<typename Derived>
+bool MatrixBase<Derived>::isUpperTriangular(const RealScalar& prec) const
+{
+ RealScalar maxAbsOnUpperPart = static_cast<RealScalar>(-1);
+ for(Index j = 0; j < cols(); ++j)
+ {
+ Index maxi = numext::mini(j, rows()-1);
+ for(Index i = 0; i <= maxi; ++i)
+ {
+ RealScalar absValue = numext::abs(coeff(i,j));
+ if(absValue > maxAbsOnUpperPart) maxAbsOnUpperPart = absValue;
+ }
+ }
+ RealScalar threshold = maxAbsOnUpperPart * prec;
+ for(Index j = 0; j < cols(); ++j)
+ for(Index i = j+1; i < rows(); ++i)
+ if(numext::abs(coeff(i, j)) > threshold) return false;
+ return true;
+}
+
+/** \returns true if *this is approximately equal to a lower triangular matrix,
+ * within the precision given by \a prec.
+ *
+ * \sa isUpperTriangular()
+ */
+template<typename Derived>
+bool MatrixBase<Derived>::isLowerTriangular(const RealScalar& prec) const
+{
+ RealScalar maxAbsOnLowerPart = static_cast<RealScalar>(-1);
+ for(Index j = 0; j < cols(); ++j)
+ for(Index i = j; i < rows(); ++i)
+ {
+ RealScalar absValue = numext::abs(coeff(i,j));
+ if(absValue > maxAbsOnLowerPart) maxAbsOnLowerPart = absValue;
+ }
+ RealScalar threshold = maxAbsOnLowerPart * prec;
+ for(Index j = 1; j < cols(); ++j)
+ {
+ Index maxi = numext::mini(j, rows()-1);
+ for(Index i = 0; i < maxi; ++i)
+ if(numext::abs(coeff(i, j)) > threshold) return false;
+ }
+ return true;
+}
+
+
+/***************************************************************************
+****************************************************************************
+* Evaluators and Assignment of triangular expressions
+***************************************************************************
+***************************************************************************/
+
+namespace internal {
+
+
+// TODO currently a triangular expression has the form TriangularView<.,.>
+// in the future triangular-ness should be defined by the expression traits
+// such that Transpose<TriangularView<.,.> > is valid. (currently TriangularBase::transpose() is overloaded to make it work)
+template<typename MatrixType, unsigned int Mode>
+struct evaluator_traits<TriangularView<MatrixType,Mode> >
+{
+ typedef typename storage_kind_to_evaluator_kind<typename MatrixType::StorageKind>::Kind Kind;
+ typedef typename glue_shapes<typename evaluator_traits<MatrixType>::Shape, TriangularShape>::type Shape;
+};
+
+template<typename MatrixType, unsigned int Mode>
+struct unary_evaluator<TriangularView<MatrixType,Mode>, IndexBased>
+ : evaluator<internal::remove_all_t<MatrixType>>
+{
+ typedef TriangularView<MatrixType,Mode> XprType;
+ typedef evaluator<internal::remove_all_t<MatrixType>> Base;
+ EIGEN_DEVICE_FUNC
+ unary_evaluator(const XprType &xpr) : Base(xpr.nestedExpression()) {}
+};
+
+// Additional assignment kinds:
+struct Triangular2Triangular {};
+struct Triangular2Dense {};
+struct Dense2Triangular {};
+
+
+template<typename Kernel, unsigned int Mode, int UnrollCount, bool ClearOpposite> struct triangular_assignment_loop;
+
+
+/** \internal Specialization of the dense assignment kernel for triangular matrices.
+ * The main difference is that the triangular, diagonal, and opposite parts are processed through three different functions.
+ * \tparam UpLo must be either Lower or Upper
+ * \tparam Mode must be either 0, UnitDiag, ZeroDiag, or SelfAdjoint
+ */
+template<int UpLo, int Mode, int SetOpposite, typename DstEvaluatorTypeT, typename SrcEvaluatorTypeT, typename Functor, int Version = Specialized>
+class triangular_dense_assignment_kernel : public generic_dense_assignment_kernel<DstEvaluatorTypeT, SrcEvaluatorTypeT, Functor, Version>
+{
+protected:
+ typedef generic_dense_assignment_kernel<DstEvaluatorTypeT, SrcEvaluatorTypeT, Functor, Version> Base;
+ typedef typename Base::DstXprType DstXprType;
+ typedef typename Base::SrcXprType SrcXprType;
+ using Base::m_dst;
+ using Base::m_src;
+ using Base::m_functor;
+public:
+
+ typedef typename Base::DstEvaluatorType DstEvaluatorType;
+ typedef typename Base::SrcEvaluatorType SrcEvaluatorType;
+ typedef typename Base::Scalar Scalar;
+ typedef typename Base::AssignmentTraits AssignmentTraits;
+
+
+ EIGEN_DEVICE_FUNC triangular_dense_assignment_kernel(DstEvaluatorType &dst, const SrcEvaluatorType &src, const Functor &func, DstXprType& dstExpr)
+ : Base(dst, src, func, dstExpr)
+ {}
+
+#ifdef EIGEN_INTERNAL_DEBUGGING
+ EIGEN_DEVICE_FUNC void assignCoeff(Index row, Index col)
+ {
+ eigen_internal_assert(row!=col);
+ Base::assignCoeff(row,col);
+ }
+#else
+ using Base::assignCoeff;
+#endif
+
+ EIGEN_DEVICE_FUNC void assignDiagonalCoeff(Index id)
+ {
+ if(Mode==UnitDiag && SetOpposite) m_functor.assignCoeff(m_dst.coeffRef(id,id), Scalar(1));
+ else if(Mode==ZeroDiag && SetOpposite) m_functor.assignCoeff(m_dst.coeffRef(id,id), Scalar(0));
+ else if(Mode==0) Base::assignCoeff(id,id);
+ }
+
+ EIGEN_DEVICE_FUNC void assignOppositeCoeff(Index row, Index col)
+ {
+ eigen_internal_assert(row!=col);
+ if(SetOpposite)
+ m_functor.assignCoeff(m_dst.coeffRef(row,col), Scalar(0));
+ }
+};
+
+template<int Mode, bool SetOpposite, typename DstXprType, typename SrcXprType, typename Functor>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+void call_triangular_assignment_loop(DstXprType& dst, const SrcXprType& src, const Functor &func)
+{
+ typedef evaluator<DstXprType> DstEvaluatorType;
+ typedef evaluator<SrcXprType> SrcEvaluatorType;
+
+ SrcEvaluatorType srcEvaluator(src);
+
+ Index dstRows = src.rows();
+ Index dstCols = src.cols();
+ if((dst.rows()!=dstRows) || (dst.cols()!=dstCols))
+ dst.resize(dstRows, dstCols);
+ DstEvaluatorType dstEvaluator(dst);
+
+ typedef triangular_dense_assignment_kernel< Mode&(Lower|Upper),Mode&(UnitDiag|ZeroDiag|SelfAdjoint),SetOpposite,
+ DstEvaluatorType,SrcEvaluatorType,Functor> Kernel;
+ Kernel kernel(dstEvaluator, srcEvaluator, func, dst.const_cast_derived());
+
+ enum {
+ unroll = DstXprType::SizeAtCompileTime != Dynamic
+ && SrcEvaluatorType::CoeffReadCost < HugeCost
+ && DstXprType::SizeAtCompileTime * (int(DstEvaluatorType::CoeffReadCost) + int(SrcEvaluatorType::CoeffReadCost)) / 2 <= EIGEN_UNROLLING_LIMIT
+ };
+
+ triangular_assignment_loop<Kernel, Mode, unroll ? int(DstXprType::SizeAtCompileTime) : Dynamic, SetOpposite>::run(kernel);
+}
+
+template<int Mode, bool SetOpposite, typename DstXprType, typename SrcXprType>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+void call_triangular_assignment_loop(DstXprType& dst, const SrcXprType& src)
+{
+ call_triangular_assignment_loop<Mode,SetOpposite>(dst, src, internal::assign_op<typename DstXprType::Scalar,typename SrcXprType::Scalar>());
+}
+
+template<> struct AssignmentKind<TriangularShape,TriangularShape> { typedef Triangular2Triangular Kind; };
+template<> struct AssignmentKind<DenseShape,TriangularShape> { typedef Triangular2Dense Kind; };
+template<> struct AssignmentKind<TriangularShape,DenseShape> { typedef Dense2Triangular Kind; };
+
+
+template< typename DstXprType, typename SrcXprType, typename Functor>
+struct Assignment<DstXprType, SrcXprType, Functor, Triangular2Triangular>
+{
+ EIGEN_DEVICE_FUNC static void run(DstXprType &dst, const SrcXprType &src, const Functor &func)
+ {
+ eigen_assert(int(DstXprType::Mode) == int(SrcXprType::Mode));
+
+ call_triangular_assignment_loop<DstXprType::Mode, false>(dst, src, func);
+ }
+};
+
+template< typename DstXprType, typename SrcXprType, typename Functor>
+struct Assignment<DstXprType, SrcXprType, Functor, Triangular2Dense>
+{
+ EIGEN_DEVICE_FUNC static void run(DstXprType &dst, const SrcXprType &src, const Functor &func)
+ {
+ call_triangular_assignment_loop<SrcXprType::Mode, (int(SrcXprType::Mode) & int(SelfAdjoint)) == 0>(dst, src, func);
+ }
+};
+
+template< typename DstXprType, typename SrcXprType, typename Functor>
+struct Assignment<DstXprType, SrcXprType, Functor, Dense2Triangular>
+{
+ EIGEN_DEVICE_FUNC static void run(DstXprType &dst, const SrcXprType &src, const Functor &func)
+ {
+ call_triangular_assignment_loop<DstXprType::Mode, false>(dst, src, func);
+ }
+};
+
+
+template<typename Kernel, unsigned int Mode, int UnrollCount, bool SetOpposite>
+struct triangular_assignment_loop
+{
+ // FIXME: this is not very clean, perhaps this information should be provided by the kernel?
+ typedef typename Kernel::DstEvaluatorType DstEvaluatorType;
+ typedef typename DstEvaluatorType::XprType DstXprType;
+
+ enum {
+ col = (UnrollCount-1) / DstXprType::RowsAtCompileTime,
+ row = (UnrollCount-1) % DstXprType::RowsAtCompileTime
+ };
+
+ typedef typename Kernel::Scalar Scalar;
+
+ EIGEN_DEVICE_FUNC
+ static inline void run(Kernel &kernel)
+ {
+ triangular_assignment_loop<Kernel, Mode, UnrollCount-1, SetOpposite>::run(kernel);
+
+ if(row==col)
+ kernel.assignDiagonalCoeff(row);
+ else if( ((Mode&Lower) && row>col) || ((Mode&Upper) && row<col) )
+ kernel.assignCoeff(row,col);
+ else if(SetOpposite)
+ kernel.assignOppositeCoeff(row,col);
+ }
+};
+
+// prevent buggy user code from causing an infinite recursion
+template<typename Kernel, unsigned int Mode, bool SetOpposite>
+struct triangular_assignment_loop<Kernel, Mode, 0, SetOpposite>
+{
+ EIGEN_DEVICE_FUNC
+ static inline void run(Kernel &) {}
+};
+
+
+
+// TODO: experiment with a recursive assignment procedure splitting the current
+// triangular part into one rectangular and two triangular parts.
+
+
+template<typename Kernel, unsigned int Mode, bool SetOpposite>
+struct triangular_assignment_loop<Kernel, Mode, Dynamic, SetOpposite>
+{
+ typedef typename Kernel::Scalar Scalar;
+ EIGEN_DEVICE_FUNC
+ static inline void run(Kernel &kernel)
+ {
+ for(Index j = 0; j < kernel.cols(); ++j)
+ {
+ Index maxi = numext::mini(j, kernel.rows());
+ Index i = 0;
+ if (((Mode&Lower) && SetOpposite) || (Mode&Upper))
+ {
+ for(; i < maxi; ++i)
+ if(Mode&Upper) kernel.assignCoeff(i, j);
+ else kernel.assignOppositeCoeff(i, j);
+ }
+ else
+ i = maxi;
+
+ if(i<kernel.rows()) // then i==j
+ kernel.assignDiagonalCoeff(i++);
+
+ if (((Mode&Upper) && SetOpposite) || (Mode&Lower))
+ {
+ for(; i < kernel.rows(); ++i)
+ if(Mode&Lower) kernel.assignCoeff(i, j);
+ else kernel.assignOppositeCoeff(i, j);
+ }
+ }
+ }
+};
+
+} // end namespace internal
+
+/** Assigns a triangular or selfadjoint matrix to a dense matrix.
+ * If the matrix is triangular, the opposite part is set to zero. */
+template<typename Derived>
+template<typename DenseDerived>
+EIGEN_DEVICE_FUNC void TriangularBase<Derived>::evalToLazy(MatrixBase<DenseDerived> &other) const
+{
+ other.derived().resize(this->rows(), this->cols());
+ internal::call_triangular_assignment_loop<Derived::Mode, (int(Derived::Mode) & int(SelfAdjoint)) == 0 /* SetOpposite */>(other.derived(), derived().nestedExpression());
+}
+
+namespace internal {
+
+// Triangular = Product
+template< typename DstXprType, typename Lhs, typename Rhs, typename Scalar>
+struct Assignment<DstXprType, Product<Lhs,Rhs,DefaultProduct>, internal::assign_op<Scalar,typename Product<Lhs,Rhs,DefaultProduct>::Scalar>, Dense2Triangular>
+{
+ typedef Product<Lhs,Rhs,DefaultProduct> SrcXprType;
+ static void run(DstXprType &dst, const SrcXprType &src, const internal::assign_op<Scalar,typename SrcXprType::Scalar> &)
+ {
+ Index dstRows = src.rows();
+ Index dstCols = src.cols();
+ if((dst.rows()!=dstRows) || (dst.cols()!=dstCols))
+ dst.resize(dstRows, dstCols);
+
+ dst._assignProduct(src, Scalar(1), false);
+ }
+};
+
+// Triangular += Product
+template< typename DstXprType, typename Lhs, typename Rhs, typename Scalar>
+struct Assignment<DstXprType, Product<Lhs,Rhs,DefaultProduct>, internal::add_assign_op<Scalar,typename Product<Lhs,Rhs,DefaultProduct>::Scalar>, Dense2Triangular>
+{
+ typedef Product<Lhs,Rhs,DefaultProduct> SrcXprType;
+ static void run(DstXprType &dst, const SrcXprType &src, const internal::add_assign_op<Scalar,typename SrcXprType::Scalar> &)
+ {
+ dst._assignProduct(src, Scalar(1), true);
+ }
+};
+
+// Triangular -= Product
+template< typename DstXprType, typename Lhs, typename Rhs, typename Scalar>
+struct Assignment<DstXprType, Product<Lhs,Rhs,DefaultProduct>, internal::sub_assign_op<Scalar,typename Product<Lhs,Rhs,DefaultProduct>::Scalar>, Dense2Triangular>
+{
+ typedef Product<Lhs,Rhs,DefaultProduct> SrcXprType;
+ static void run(DstXprType &dst, const SrcXprType &src, const internal::sub_assign_op<Scalar,typename SrcXprType::Scalar> &)
+ {
+ dst._assignProduct(src, Scalar(-1), true);
+ }
+};
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_TRIANGULARMATRIX_H
diff --git a/Eigen/src/Core/VectorBlock.h b/Eigen/src/Core/VectorBlock.h
new file mode 100644
index 0000000..ee28da1
--- /dev/null
+++ b/Eigen/src/Core/VectorBlock.h
@@ -0,0 +1,95 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2010 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_VECTORBLOCK_H
+#define EIGEN_VECTORBLOCK_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+template<typename VectorType, int Size>
+struct traits<VectorBlock<VectorType, Size> >
+ : public traits<Block<VectorType,
+ traits<VectorType>::Flags & RowMajorBit ? 1 : Size,
+ traits<VectorType>::Flags & RowMajorBit ? Size : 1> >
+{
+};
+}
+
+/** \class VectorBlock
+ * \ingroup Core_Module
+ *
+ * \brief Expression of a fixed-size or dynamic-size sub-vector
+ *
+ * \tparam VectorType the type of the object in which we are taking a sub-vector
+ * \tparam Size size of the sub-vector we are taking at compile time (optional)
+ *
+ * This class represents an expression of either a fixed-size or dynamic-size sub-vector.
+ * It is the return type of DenseBase::segment(Index,Index) and DenseBase::segment<int>(Index) and
+ * most of the time this is the only way it is used.
+ *
+ * However, if you want to directly manipulate sub-vector expressions,
+ * for instance if you want to write a function returning such an expression, you
+ * will need to use this class.
+ *
+ * Here is an example illustrating the dynamic case:
+ * \include class_VectorBlock.cpp
+ * Output: \verbinclude class_VectorBlock.out
+ *
+ * \note Even though this expression has dynamic size, in the case where \a VectorType
+ * has fixed size, this expression inherits a fixed maximal size which means that evaluating
+ * it does not cause a dynamic memory allocation.
+ *
+ * Here is an example illustrating the fixed-size case:
+ * \include class_FixedVectorBlock.cpp
+ * Output: \verbinclude class_FixedVectorBlock.out
+ *
+ * \sa class Block, DenseBase::segment(Index,Index,Index,Index), DenseBase::segment(Index,Index)
+ */
+template<typename VectorType, int Size> class VectorBlock
+ : public Block<VectorType,
+ internal::traits<VectorType>::Flags & RowMajorBit ? 1 : Size,
+ internal::traits<VectorType>::Flags & RowMajorBit ? Size : 1>
+{
+ typedef Block<VectorType,
+ internal::traits<VectorType>::Flags & RowMajorBit ? 1 : Size,
+ internal::traits<VectorType>::Flags & RowMajorBit ? Size : 1> Base;
+ enum {
+ IsColVector = !(internal::traits<VectorType>::Flags & RowMajorBit)
+ };
+ public:
+ EIGEN_DENSE_PUBLIC_INTERFACE(VectorBlock)
+ EIGEN_STATIC_ASSERT_VECTOR_ONLY(VectorBlock)
+
+ using Base::operator=;
+
+ /** Dynamic-size constructor
+ */
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ VectorBlock(VectorType& vector, Index start, Index size)
+ : Base(vector,
+ IsColVector ? start : 0, IsColVector ? 0 : start,
+ IsColVector ? size : 1, IsColVector ? 1 : size)
+ { }
+
+ /** Fixed-size constructor
+ */
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ VectorBlock(VectorType& vector, Index start)
+ : Base(vector, IsColVector ? start : 0, IsColVector ? 0 : start)
+ { }
+};
+
+
+} // end namespace Eigen
+
+#endif // EIGEN_VECTORBLOCK_H
diff --git a/Eigen/src/Core/VectorwiseOp.h b/Eigen/src/Core/VectorwiseOp.h
new file mode 100644
index 0000000..b004f76
--- /dev/null
+++ b/Eigen/src/Core/VectorwiseOp.h
@@ -0,0 +1,785 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2019 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_PARTIAL_REDUX_H
+#define EIGEN_PARTIAL_REDUX_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+/** \class PartialReduxExpr
+ * \ingroup Core_Module
+ *
+ * \brief Generic expression of a partially reduxed matrix
+ *
+ * \tparam MatrixType the type of the matrix we are applying the redux operation
+ * \tparam MemberOp type of the member functor
+ * \tparam Direction indicates the direction of the redux (#Vertical or #Horizontal)
+ *
+ * This class represents an expression of a partial redux operator of a matrix.
+ * It is the return type of some VectorwiseOp functions,
+ * and most of the time this is the only way it is used.
+ *
+ * \sa class VectorwiseOp
+ */
+
+template< typename MatrixType, typename MemberOp, int Direction>
+class PartialReduxExpr;
+
+namespace internal {
+template<typename MatrixType, typename MemberOp, int Direction>
+struct traits<PartialReduxExpr<MatrixType, MemberOp, Direction> >
+ : traits<MatrixType>
+{
+ typedef typename MemberOp::result_type Scalar;
+ typedef typename traits<MatrixType>::StorageKind StorageKind;
+ typedef typename traits<MatrixType>::XprKind XprKind;
+ typedef typename MatrixType::Scalar InputScalar;
+ enum {
+ RowsAtCompileTime = Direction==Vertical ? 1 : MatrixType::RowsAtCompileTime,
+ ColsAtCompileTime = Direction==Horizontal ? 1 : MatrixType::ColsAtCompileTime,
+ MaxRowsAtCompileTime = Direction==Vertical ? 1 : MatrixType::MaxRowsAtCompileTime,
+ MaxColsAtCompileTime = Direction==Horizontal ? 1 : MatrixType::MaxColsAtCompileTime,
+ Flags = RowsAtCompileTime == 1 ? RowMajorBit : 0,
+ TraversalSize = Direction==Vertical ? MatrixType::RowsAtCompileTime : MatrixType::ColsAtCompileTime
+ };
+};
+}
+
+template< typename MatrixType, typename MemberOp, int Direction>
+class PartialReduxExpr : public internal::dense_xpr_base< PartialReduxExpr<MatrixType, MemberOp, Direction> >::type,
+ internal::no_assignment_operator
+{
+ public:
+
+ typedef typename internal::dense_xpr_base<PartialReduxExpr>::type Base;
+ EIGEN_DENSE_PUBLIC_INTERFACE(PartialReduxExpr)
+
+ EIGEN_DEVICE_FUNC
+ explicit PartialReduxExpr(const MatrixType& mat, const MemberOp& func = MemberOp())
+ : m_matrix(mat), m_functor(func) {}
+
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
+ Index rows() const EIGEN_NOEXCEPT { return (Direction==Vertical ? 1 : m_matrix.rows()); }
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
+ Index cols() const EIGEN_NOEXCEPT { return (Direction==Horizontal ? 1 : m_matrix.cols()); }
+
+ EIGEN_DEVICE_FUNC
+ typename MatrixType::Nested nestedExpression() const { return m_matrix; }
+
+ EIGEN_DEVICE_FUNC
+ const MemberOp& functor() const { return m_functor; }
+
+ protected:
+ typename MatrixType::Nested m_matrix;
+ const MemberOp m_functor;
+};
+
+template<typename A,typename B> struct partial_redux_dummy_func;
+
+#define EIGEN_MAKE_PARTIAL_REDUX_FUNCTOR(MEMBER,COST,VECTORIZABLE,BINARYOP) \
+ template <typename ResultType,typename Scalar> \
+ struct member_##MEMBER { \
+ typedef ResultType result_type; \
+ typedef BINARYOP<Scalar,Scalar> BinaryOp; \
+ template<int Size> struct Cost { enum { value = COST }; }; \
+ enum { Vectorizable = VECTORIZABLE }; \
+ template<typename XprType> \
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE \
+ ResultType operator()(const XprType& mat) const \
+ { return mat.MEMBER(); } \
+ BinaryOp binaryFunc() const { return BinaryOp(); } \
+ }
+
+#define EIGEN_MEMBER_FUNCTOR(MEMBER,COST) \
+ EIGEN_MAKE_PARTIAL_REDUX_FUNCTOR(MEMBER,COST,0,partial_redux_dummy_func)
+
+namespace internal {
+
+EIGEN_MEMBER_FUNCTOR(norm, (Size+5) * NumTraits<Scalar>::MulCost + (Size-1)*NumTraits<Scalar>::AddCost);
+EIGEN_MEMBER_FUNCTOR(stableNorm, (Size+5) * NumTraits<Scalar>::MulCost + (Size-1)*NumTraits<Scalar>::AddCost);
+EIGEN_MEMBER_FUNCTOR(blueNorm, (Size+5) * NumTraits<Scalar>::MulCost + (Size-1)*NumTraits<Scalar>::AddCost);
+EIGEN_MEMBER_FUNCTOR(hypotNorm, (Size-1) * functor_traits<scalar_hypot_op<Scalar> >::Cost );
+EIGEN_MEMBER_FUNCTOR(all, (Size-1)*NumTraits<Scalar>::AddCost);
+EIGEN_MEMBER_FUNCTOR(any, (Size-1)*NumTraits<Scalar>::AddCost);
+EIGEN_MEMBER_FUNCTOR(count, (Size-1)*NumTraits<Scalar>::AddCost);
+
+EIGEN_MAKE_PARTIAL_REDUX_FUNCTOR(sum, (Size-1)*NumTraits<Scalar>::AddCost, 1, internal::scalar_sum_op);
+EIGEN_MAKE_PARTIAL_REDUX_FUNCTOR(minCoeff, (Size-1)*NumTraits<Scalar>::AddCost, 1, internal::scalar_min_op);
+EIGEN_MAKE_PARTIAL_REDUX_FUNCTOR(maxCoeff, (Size-1)*NumTraits<Scalar>::AddCost, 1, internal::scalar_max_op);
+EIGEN_MAKE_PARTIAL_REDUX_FUNCTOR(prod, (Size-1)*NumTraits<Scalar>::MulCost, 1, internal::scalar_product_op);
+
+template <int p, typename ResultType,typename Scalar>
+struct member_lpnorm {
+ typedef ResultType result_type;
+ enum { Vectorizable = 0 };
+ template<int Size> struct Cost
+ { enum { value = (Size+5) * NumTraits<Scalar>::MulCost + (Size-1)*NumTraits<Scalar>::AddCost }; };
+ EIGEN_DEVICE_FUNC member_lpnorm() {}
+ template<typename XprType>
+ EIGEN_DEVICE_FUNC inline ResultType operator()(const XprType& mat) const
+ { return mat.template lpNorm<p>(); }
+};
+
+template <typename BinaryOpT, typename Scalar>
+struct member_redux {
+ typedef BinaryOpT BinaryOp;
+ typedef typename result_of<
+ BinaryOp(const Scalar&,const Scalar&)
+ >::type result_type;
+
+ enum { Vectorizable = functor_traits<BinaryOp>::PacketAccess };
+ template<int Size> struct Cost { enum { value = (Size-1) * functor_traits<BinaryOp>::Cost }; };
+ EIGEN_DEVICE_FUNC explicit member_redux(const BinaryOp func) : m_functor(func) {}
+ template<typename Derived>
+ EIGEN_DEVICE_FUNC inline result_type operator()(const DenseBase<Derived>& mat) const
+ { return mat.redux(m_functor); }
+ const BinaryOp& binaryFunc() const { return m_functor; }
+ const BinaryOp m_functor;
+};
+}
+
+/** \class VectorwiseOp
+ * \ingroup Core_Module
+ *
+ * \brief Pseudo expression providing broadcasting and partial reduction operations
+ *
+ * \tparam ExpressionType the type of the object on which to do partial reductions
+ * \tparam Direction indicates whether to operate on columns (#Vertical) or rows (#Horizontal)
+ *
+ * This class represents a pseudo expression with broadcasting and partial reduction features.
+ * It is the return type of DenseBase::colwise() and DenseBase::rowwise()
+ * and most of the time this is the only way it is explicitly used.
+ *
+ * To understand the logic of rowwise/colwise expression, let's consider a generic case `A.colwise().foo()`
+ * where `foo` is any method of `VectorwiseOp`. This expression is equivalent to applying `foo()` to each
+ * column of `A` and then re-assemble the outputs in a matrix expression:
+ * \code [A.col(0).foo(), A.col(1).foo(), ..., A.col(A.cols()-1).foo()] \endcode
+ *
+ * Example: \include MatrixBase_colwise.cpp
+ * Output: \verbinclude MatrixBase_colwise.out
+ *
+ * The begin() and end() methods are obviously exceptions to the previous rule as they
+ * return STL-compatible begin/end iterators to the rows or columns of the nested expression.
+ * Typical use cases include for-range-loop and calls to STL algorithms:
+ *
+ * Example: \include MatrixBase_colwise_iterator_cxx11.cpp
+ * Output: \verbinclude MatrixBase_colwise_iterator_cxx11.out
+ *
+ * For a partial reduction on an empty input, some rules apply.
+ * For the sake of clarity, let's consider a vertical reduction:
+ * - If the number of columns is zero, then a 1x0 row-major vector expression is returned.
+ * - Otherwise, if the number of rows is zero, then
+ * - a row vector of zeros is returned for sum-like reductions (sum, squaredNorm, norm, etc.)
+ * - a row vector of ones is returned for a product reduction (e.g., <code>MatrixXd(n,0).colwise().prod()</code>)
+ * - an assert is triggered for all other reductions (minCoeff,maxCoeff,redux(bin_op))
+ *
+ * \sa DenseBase::colwise(), DenseBase::rowwise(), class PartialReduxExpr
+ */
+template<typename ExpressionType, int Direction> class VectorwiseOp
+{
+ public:
+
+ typedef typename ExpressionType::Scalar Scalar;
+ typedef typename ExpressionType::RealScalar RealScalar;
+ typedef Eigen::Index Index; ///< \deprecated since Eigen 3.3
+ typedef typename internal::ref_selector<ExpressionType>::non_const_type ExpressionTypeNested;
+ typedef internal::remove_all_t<ExpressionTypeNested> ExpressionTypeNestedCleaned;
+
+ template<template<typename OutScalar,typename InputScalar> class Functor,
+ typename ReturnScalar=Scalar> struct ReturnType
+ {
+ typedef PartialReduxExpr<ExpressionType,
+ Functor<ReturnScalar,Scalar>,
+ Direction
+ > Type;
+ };
+
+ template<typename BinaryOp> struct ReduxReturnType
+ {
+ typedef PartialReduxExpr<ExpressionType,
+ internal::member_redux<BinaryOp,Scalar>,
+ Direction
+ > Type;
+ };
+
+ enum {
+ isVertical = (Direction==Vertical) ? 1 : 0,
+ isHorizontal = (Direction==Horizontal) ? 1 : 0
+ };
+
+ protected:
+
+ template<typename OtherDerived> struct ExtendedType {
+ typedef Replicate<OtherDerived,
+ isVertical ? 1 : ExpressionType::RowsAtCompileTime,
+ isHorizontal ? 1 : ExpressionType::ColsAtCompileTime> Type;
+ };
+
+ /** \internal
+ * Replicates a vector to match the size of \c *this */
+ template<typename OtherDerived>
+ EIGEN_DEVICE_FUNC
+ typename ExtendedType<OtherDerived>::Type
+ extendedTo(const DenseBase<OtherDerived>& other) const
+ {
+ EIGEN_STATIC_ASSERT(internal::check_implication(isVertical, OtherDerived::MaxColsAtCompileTime==1),
+ YOU_PASSED_A_ROW_VECTOR_BUT_A_COLUMN_VECTOR_WAS_EXPECTED)
+ EIGEN_STATIC_ASSERT(internal::check_implication(isHorizontal, OtherDerived::MaxRowsAtCompileTime==1),
+ YOU_PASSED_A_COLUMN_VECTOR_BUT_A_ROW_VECTOR_WAS_EXPECTED)
+ return typename ExtendedType<OtherDerived>::Type
+ (other.derived(),
+ isVertical ? 1 : m_matrix.rows(),
+ isHorizontal ? 1 : m_matrix.cols());
+ }
+
+ template<typename OtherDerived> struct OppositeExtendedType {
+ typedef Replicate<OtherDerived,
+ isHorizontal ? 1 : ExpressionType::RowsAtCompileTime,
+ isVertical ? 1 : ExpressionType::ColsAtCompileTime> Type;
+ };
+
+ /** \internal
+ * Replicates a vector in the opposite direction to match the size of \c *this */
+ template<typename OtherDerived>
+ EIGEN_DEVICE_FUNC
+ typename OppositeExtendedType<OtherDerived>::Type
+ extendedToOpposite(const DenseBase<OtherDerived>& other) const
+ {
+ EIGEN_STATIC_ASSERT(internal::check_implication(isHorizontal, OtherDerived::MaxColsAtCompileTime==1),
+ YOU_PASSED_A_ROW_VECTOR_BUT_A_COLUMN_VECTOR_WAS_EXPECTED)
+ EIGEN_STATIC_ASSERT(internal::check_implication(isVertical, OtherDerived::MaxRowsAtCompileTime==1),
+ YOU_PASSED_A_COLUMN_VECTOR_BUT_A_ROW_VECTOR_WAS_EXPECTED)
+ return typename OppositeExtendedType<OtherDerived>::Type
+ (other.derived(),
+ isHorizontal ? 1 : m_matrix.rows(),
+ isVertical ? 1 : m_matrix.cols());
+ }
+
+ public:
+ EIGEN_DEVICE_FUNC
+ explicit inline VectorwiseOp(ExpressionType& matrix) : m_matrix(matrix) {}
+
+ /** \internal */
+ EIGEN_DEVICE_FUNC
+ inline const ExpressionType& _expression() const { return m_matrix; }
+
+ #ifdef EIGEN_PARSED_BY_DOXYGEN
+ /** STL-like <a href="https://en.cppreference.com/w/cpp/named_req/RandomAccessIterator">RandomAccessIterator</a>
+ * iterator type over the columns or rows as returned by the begin() and end() methods.
+ */
+ random_access_iterator_type iterator;
+ /** This is the const version of iterator (aka read-only) */
+ random_access_iterator_type const_iterator;
+ #else
+ typedef internal::subvector_stl_iterator<ExpressionType, DirectionType(Direction)> iterator;
+ typedef internal::subvector_stl_iterator<const ExpressionType, DirectionType(Direction)> const_iterator;
+ typedef internal::subvector_stl_reverse_iterator<ExpressionType, DirectionType(Direction)> reverse_iterator;
+ typedef internal::subvector_stl_reverse_iterator<const ExpressionType, DirectionType(Direction)> const_reverse_iterator;
+ #endif
+
+ /** returns an iterator to the first row (rowwise) or column (colwise) of the nested expression.
+ * \sa end(), cbegin()
+ */
+ iterator begin() { return iterator (m_matrix, 0); }
+ /** const version of begin() */
+ const_iterator begin() const { return const_iterator(m_matrix, 0); }
+ /** const version of begin() */
+ const_iterator cbegin() const { return const_iterator(m_matrix, 0); }
+
+ /** returns a reverse iterator to the last row (rowwise) or column (colwise) of the nested expression.
+ * \sa rend(), crbegin()
+ */
+ reverse_iterator rbegin() { return reverse_iterator (m_matrix, m_matrix.template subVectors<DirectionType(Direction)>()-1); }
+ /** const version of rbegin() */
+ const_reverse_iterator rbegin() const { return const_reverse_iterator (m_matrix, m_matrix.template subVectors<DirectionType(Direction)>()-1); }
+ /** const version of rbegin() */
+ const_reverse_iterator crbegin() const { return const_reverse_iterator (m_matrix, m_matrix.template subVectors<DirectionType(Direction)>()-1); }
+
+ /** returns an iterator to the row (resp. column) following the last row (resp. column) of the nested expression
+ * \sa begin(), cend()
+ */
+ iterator end() { return iterator (m_matrix, m_matrix.template subVectors<DirectionType(Direction)>()); }
+ /** const version of end() */
+ const_iterator end() const { return const_iterator(m_matrix, m_matrix.template subVectors<DirectionType(Direction)>()); }
+ /** const version of end() */
+ const_iterator cend() const { return const_iterator(m_matrix, m_matrix.template subVectors<DirectionType(Direction)>()); }
+
+ /** returns a reverse iterator to the row (resp. column) before the first row (resp. column) of the nested expression
+ * \sa begin(), cend()
+ */
+ reverse_iterator rend() { return reverse_iterator (m_matrix, -1); }
+ /** const version of rend() */
+ const_reverse_iterator rend() const { return const_reverse_iterator (m_matrix, -1); }
+ /** const version of rend() */
+ const_reverse_iterator crend() const { return const_reverse_iterator (m_matrix, -1); }
+
+ /** \returns a row or column vector expression of \c *this reduxed by \a func
+ *
+ * The template parameter \a BinaryOp is the type of the functor
+ * of the custom redux operator. Note that func must be an associative operator.
+ *
+ * \warning the size along the reduction direction must be strictly positive,
+ * otherwise an assertion is triggered.
+ *
+ * \sa class VectorwiseOp, DenseBase::colwise(), DenseBase::rowwise()
+ */
+ template<typename BinaryOp>
+ EIGEN_DEVICE_FUNC
+ const typename ReduxReturnType<BinaryOp>::Type
+ redux(const BinaryOp& func = BinaryOp()) const
+ {
+ eigen_assert(redux_length()>0 && "you are using an empty matrix");
+ return typename ReduxReturnType<BinaryOp>::Type(_expression(), internal::member_redux<BinaryOp,Scalar>(func));
+ }
+
+ typedef typename ReturnType<internal::member_minCoeff>::Type MinCoeffReturnType;
+ typedef typename ReturnType<internal::member_maxCoeff>::Type MaxCoeffReturnType;
+ typedef PartialReduxExpr<const CwiseUnaryOp<internal::scalar_abs2_op<Scalar>, const ExpressionTypeNestedCleaned>,internal::member_sum<RealScalar,RealScalar>,Direction> SquaredNormReturnType;
+ typedef CwiseUnaryOp<internal::scalar_sqrt_op<RealScalar>, const SquaredNormReturnType> NormReturnType;
+ typedef typename ReturnType<internal::member_blueNorm,RealScalar>::Type BlueNormReturnType;
+ typedef typename ReturnType<internal::member_stableNorm,RealScalar>::Type StableNormReturnType;
+ typedef typename ReturnType<internal::member_hypotNorm,RealScalar>::Type HypotNormReturnType;
+ typedef typename ReturnType<internal::member_sum>::Type SumReturnType;
+ typedef EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(SumReturnType,Scalar,quotient) MeanReturnType;
+ typedef typename ReturnType<internal::member_all>::Type AllReturnType;
+ typedef typename ReturnType<internal::member_any>::Type AnyReturnType;
+ typedef PartialReduxExpr<ExpressionType, internal::member_count<Index,Scalar>, Direction> CountReturnType;
+ typedef typename ReturnType<internal::member_prod>::Type ProdReturnType;
+ typedef Reverse<const ExpressionType, Direction> ConstReverseReturnType;
+ typedef Reverse<ExpressionType, Direction> ReverseReturnType;
+
+ template<int p> struct LpNormReturnType {
+ typedef PartialReduxExpr<ExpressionType, internal::member_lpnorm<p,RealScalar,Scalar>,Direction> Type;
+ };
+
+ /** \returns a row (or column) vector expression of the smallest coefficient
+ * of each column (or row) of the referenced expression.
+ *
+ * \warning the size along the reduction direction must be strictly positive,
+ * otherwise an assertion is triggered.
+ *
+ * \warning the result is undefined if \c *this contains NaN.
+ *
+ * Example: \include PartialRedux_minCoeff.cpp
+ * Output: \verbinclude PartialRedux_minCoeff.out
+ *
+ * \sa DenseBase::minCoeff() */
+ EIGEN_DEVICE_FUNC
+ const MinCoeffReturnType minCoeff() const
+ {
+ eigen_assert(redux_length()>0 && "you are using an empty matrix");
+ return MinCoeffReturnType(_expression());
+ }
+
+ /** \returns a row (or column) vector expression of the largest coefficient
+ * of each column (or row) of the referenced expression.
+ *
+ * \warning the size along the reduction direction must be strictly positive,
+ * otherwise an assertion is triggered.
+ *
+ * \warning the result is undefined if \c *this contains NaN.
+ *
+ * Example: \include PartialRedux_maxCoeff.cpp
+ * Output: \verbinclude PartialRedux_maxCoeff.out
+ *
+ * \sa DenseBase::maxCoeff() */
+ EIGEN_DEVICE_FUNC
+ const MaxCoeffReturnType maxCoeff() const
+ {
+ eigen_assert(redux_length()>0 && "you are using an empty matrix");
+ return MaxCoeffReturnType(_expression());
+ }
+
+ /** \returns a row (or column) vector expression of the squared norm
+ * of each column (or row) of the referenced expression.
+ * This is a vector with real entries, even if the original matrix has complex entries.
+ *
+ * Example: \include PartialRedux_squaredNorm.cpp
+ * Output: \verbinclude PartialRedux_squaredNorm.out
+ *
+ * \sa DenseBase::squaredNorm() */
+ EIGEN_DEVICE_FUNC
+ const SquaredNormReturnType squaredNorm() const
+ { return SquaredNormReturnType(m_matrix.cwiseAbs2()); }
+
+ /** \returns a row (or column) vector expression of the norm
+ * of each column (or row) of the referenced expression.
+ * This is a vector with real entries, even if the original matrix has complex entries.
+ *
+ * Example: \include PartialRedux_norm.cpp
+ * Output: \verbinclude PartialRedux_norm.out
+ *
+ * \sa DenseBase::norm() */
+ EIGEN_DEVICE_FUNC
+ const NormReturnType norm() const
+ { return NormReturnType(squaredNorm()); }
+
+ /** \returns a row (or column) vector expression of the norm
+ * of each column (or row) of the referenced expression.
+ * This is a vector with real entries, even if the original matrix has complex entries.
+ *
+ * Example: \include PartialRedux_norm.cpp
+ * Output: \verbinclude PartialRedux_norm.out
+ *
+ * \sa DenseBase::norm() */
+ template<int p>
+ EIGEN_DEVICE_FUNC
+ const typename LpNormReturnType<p>::Type lpNorm() const
+ { return typename LpNormReturnType<p>::Type(_expression()); }
+
+
+ /** \returns a row (or column) vector expression of the norm
+ * of each column (or row) of the referenced expression, using
+ * Blue's algorithm.
+ * This is a vector with real entries, even if the original matrix has complex entries.
+ *
+ * \sa DenseBase::blueNorm() */
+ EIGEN_DEVICE_FUNC
+ const BlueNormReturnType blueNorm() const
+ { return BlueNormReturnType(_expression()); }
+
+
+ /** \returns a row (or column) vector expression of the norm
+ * of each column (or row) of the referenced expression, avoiding
+ * underflow and overflow.
+ * This is a vector with real entries, even if the original matrix has complex entries.
+ *
+ * \sa DenseBase::stableNorm() */
+ EIGEN_DEVICE_FUNC
+ const StableNormReturnType stableNorm() const
+ { return StableNormReturnType(_expression()); }
+
+
+ /** \returns a row (or column) vector expression of the norm
+ * of each column (or row) of the referenced expression, avoiding
+ * underflow and overflow using a concatenation of hypot() calls.
+ * This is a vector with real entries, even if the original matrix has complex entries.
+ *
+ * \sa DenseBase::hypotNorm() */
+ EIGEN_DEVICE_FUNC
+ const HypotNormReturnType hypotNorm() const
+ { return HypotNormReturnType(_expression()); }
+
+ /** \returns a row (or column) vector expression of the sum
+ * of each column (or row) of the referenced expression.
+ *
+ * Example: \include PartialRedux_sum.cpp
+ * Output: \verbinclude PartialRedux_sum.out
+ *
+ * \sa DenseBase::sum() */
+ EIGEN_DEVICE_FUNC
+ const SumReturnType sum() const
+ { return SumReturnType(_expression()); }
+
+ /** \returns a row (or column) vector expression of the mean
+ * of each column (or row) of the referenced expression.
+ *
+ * \sa DenseBase::mean() */
+ EIGEN_DEVICE_FUNC
+ const MeanReturnType mean() const
+ { return sum() / Scalar(Direction==Vertical?m_matrix.rows():m_matrix.cols()); }
+
+ /** \returns a row (or column) vector expression representing
+ * whether \b all coefficients of each respective column (or row) are \c true.
+ * This expression can be assigned to a vector with entries of type \c bool.
+ *
+ * \sa DenseBase::all() */
+ EIGEN_DEVICE_FUNC
+ const AllReturnType all() const
+ { return AllReturnType(_expression()); }
+
+ /** \returns a row (or column) vector expression representing
+ * whether \b at \b least one coefficient of each respective column (or row) is \c true.
+ * This expression can be assigned to a vector with entries of type \c bool.
+ *
+ * \sa DenseBase::any() */
+ EIGEN_DEVICE_FUNC
+ const AnyReturnType any() const
+ { return AnyReturnType(_expression()); }
+
+ /** \returns a row (or column) vector expression representing
+ * the number of \c true coefficients of each respective column (or row).
+ * This expression can be assigned to a vector whose entries have the same type as is used to
+ * index entries of the original matrix; for dense matrices, this is \c std::ptrdiff_t .
+ *
+ * Example: \include PartialRedux_count.cpp
+ * Output: \verbinclude PartialRedux_count.out
+ *
+ * \sa DenseBase::count() */
+ EIGEN_DEVICE_FUNC
+ const CountReturnType count() const
+ { return CountReturnType(_expression()); }
+
+ /** \returns a row (or column) vector expression of the product
+ * of each column (or row) of the referenced expression.
+ *
+ * Example: \include PartialRedux_prod.cpp
+ * Output: \verbinclude PartialRedux_prod.out
+ *
+ * \sa DenseBase::prod() */
+ EIGEN_DEVICE_FUNC
+ const ProdReturnType prod() const
+ { return ProdReturnType(_expression()); }
+
+
+ /** \returns a matrix expression
+ * where each column (or row) are reversed.
+ *
+ * Example: \include Vectorwise_reverse.cpp
+ * Output: \verbinclude Vectorwise_reverse.out
+ *
+ * \sa DenseBase::reverse() */
+ EIGEN_DEVICE_FUNC
+ const ConstReverseReturnType reverse() const
+ { return ConstReverseReturnType( _expression() ); }
+
+ /** \returns a writable matrix expression
+ * where each column (or row) are reversed.
+ *
+ * \sa reverse() const */
+ EIGEN_DEVICE_FUNC
+ ReverseReturnType reverse()
+ { return ReverseReturnType( _expression() ); }
+
+ typedef Replicate<ExpressionType,(isVertical?Dynamic:1),(isHorizontal?Dynamic:1)> ReplicateReturnType;
+ EIGEN_DEVICE_FUNC
+ const ReplicateReturnType replicate(Index factor) const;
+
+ /**
+ * \return an expression of the replication of each column (or row) of \c *this
+ *
+ * Example: \include DirectionWise_replicate.cpp
+ * Output: \verbinclude DirectionWise_replicate.out
+ *
+ * \sa VectorwiseOp::replicate(Index), DenseBase::replicate(), class Replicate
+ */
+ // NOTE implemented here because of sunstudio's compilation errors
+ // isVertical*Factor+isHorizontal instead of (isVertical?Factor:1) to handle CUDA bug with ternary operator
+ template<int Factor> const Replicate<ExpressionType,isVertical*Factor+isHorizontal,isHorizontal*Factor+isVertical>
+ EIGEN_DEVICE_FUNC
+ replicate(Index factor = Factor) const
+ {
+ return Replicate<ExpressionType,(isVertical?Factor:1),(isHorizontal?Factor:1)>
+ (_expression(),isVertical?factor:1,isHorizontal?factor:1);
+ }
+
+/////////// Artithmetic operators ///////////
+
+ /** Copies the vector \a other to each subvector of \c *this */
+ template<typename OtherDerived>
+ EIGEN_DEVICE_FUNC
+ ExpressionType& operator=(const DenseBase<OtherDerived>& other)
+ {
+ EIGEN_STATIC_ASSERT_VECTOR_ONLY(OtherDerived)
+ EIGEN_STATIC_ASSERT_SAME_XPR_KIND(ExpressionType, OtherDerived)
+ //eigen_assert((m_matrix.isNull()) == (other.isNull())); FIXME
+ return m_matrix = extendedTo(other.derived());
+ }
+
+ /** Adds the vector \a other to each subvector of \c *this */
+ template<typename OtherDerived>
+ EIGEN_DEVICE_FUNC
+ ExpressionType& operator+=(const DenseBase<OtherDerived>& other)
+ {
+ EIGEN_STATIC_ASSERT_VECTOR_ONLY(OtherDerived)
+ EIGEN_STATIC_ASSERT_SAME_XPR_KIND(ExpressionType, OtherDerived)
+ return m_matrix += extendedTo(other.derived());
+ }
+
+ /** Subtracts the vector \a other to each subvector of \c *this */
+ template<typename OtherDerived>
+ EIGEN_DEVICE_FUNC
+ ExpressionType& operator-=(const DenseBase<OtherDerived>& other)
+ {
+ EIGEN_STATIC_ASSERT_VECTOR_ONLY(OtherDerived)
+ EIGEN_STATIC_ASSERT_SAME_XPR_KIND(ExpressionType, OtherDerived)
+ return m_matrix -= extendedTo(other.derived());
+ }
+
+ /** Multiplies each subvector of \c *this by the vector \a other */
+ template<typename OtherDerived>
+ EIGEN_DEVICE_FUNC
+ ExpressionType& operator*=(const DenseBase<OtherDerived>& other)
+ {
+ EIGEN_STATIC_ASSERT_VECTOR_ONLY(OtherDerived)
+ EIGEN_STATIC_ASSERT_ARRAYXPR(ExpressionType)
+ EIGEN_STATIC_ASSERT_SAME_XPR_KIND(ExpressionType, OtherDerived)
+ m_matrix *= extendedTo(other.derived());
+ return m_matrix;
+ }
+
+ /** Divides each subvector of \c *this by the vector \a other */
+ template<typename OtherDerived>
+ EIGEN_DEVICE_FUNC
+ ExpressionType& operator/=(const DenseBase<OtherDerived>& other)
+ {
+ EIGEN_STATIC_ASSERT_VECTOR_ONLY(OtherDerived)
+ EIGEN_STATIC_ASSERT_ARRAYXPR(ExpressionType)
+ EIGEN_STATIC_ASSERT_SAME_XPR_KIND(ExpressionType, OtherDerived)
+ m_matrix /= extendedTo(other.derived());
+ return m_matrix;
+ }
+
+ /** Returns the expression of the sum of the vector \a other to each subvector of \c *this */
+ template<typename OtherDerived> EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC
+ CwiseBinaryOp<internal::scalar_sum_op<Scalar,typename OtherDerived::Scalar>,
+ const ExpressionTypeNestedCleaned,
+ const typename ExtendedType<OtherDerived>::Type>
+ operator+(const DenseBase<OtherDerived>& other) const
+ {
+ EIGEN_STATIC_ASSERT_VECTOR_ONLY(OtherDerived)
+ EIGEN_STATIC_ASSERT_SAME_XPR_KIND(ExpressionType, OtherDerived)
+ return m_matrix + extendedTo(other.derived());
+ }
+
+ /** Returns the expression of the difference between each subvector of \c *this and the vector \a other */
+ template<typename OtherDerived>
+ EIGEN_DEVICE_FUNC
+ CwiseBinaryOp<internal::scalar_difference_op<Scalar,typename OtherDerived::Scalar>,
+ const ExpressionTypeNestedCleaned,
+ const typename ExtendedType<OtherDerived>::Type>
+ operator-(const DenseBase<OtherDerived>& other) const
+ {
+ EIGEN_STATIC_ASSERT_VECTOR_ONLY(OtherDerived)
+ EIGEN_STATIC_ASSERT_SAME_XPR_KIND(ExpressionType, OtherDerived)
+ return m_matrix - extendedTo(other.derived());
+ }
+
+ /** Returns the expression where each subvector is the product of the vector \a other
+ * by the corresponding subvector of \c *this */
+ template<typename OtherDerived> EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC
+ CwiseBinaryOp<internal::scalar_product_op<Scalar>,
+ const ExpressionTypeNestedCleaned,
+ const typename ExtendedType<OtherDerived>::Type>
+ EIGEN_DEVICE_FUNC
+ operator*(const DenseBase<OtherDerived>& other) const
+ {
+ EIGEN_STATIC_ASSERT_VECTOR_ONLY(OtherDerived)
+ EIGEN_STATIC_ASSERT_ARRAYXPR(ExpressionType)
+ EIGEN_STATIC_ASSERT_SAME_XPR_KIND(ExpressionType, OtherDerived)
+ return m_matrix * extendedTo(other.derived());
+ }
+
+ /** Returns the expression where each subvector is the quotient of the corresponding
+ * subvector of \c *this by the vector \a other */
+ template<typename OtherDerived>
+ EIGEN_DEVICE_FUNC
+ CwiseBinaryOp<internal::scalar_quotient_op<Scalar>,
+ const ExpressionTypeNestedCleaned,
+ const typename ExtendedType<OtherDerived>::Type>
+ operator/(const DenseBase<OtherDerived>& other) const
+ {
+ EIGEN_STATIC_ASSERT_VECTOR_ONLY(OtherDerived)
+ EIGEN_STATIC_ASSERT_ARRAYXPR(ExpressionType)
+ EIGEN_STATIC_ASSERT_SAME_XPR_KIND(ExpressionType, OtherDerived)
+ return m_matrix / extendedTo(other.derived());
+ }
+
+ /** \returns an expression where each column (or row) of the referenced matrix are normalized.
+ * The referenced matrix is \b not modified.
+ * \sa MatrixBase::normalized(), normalize()
+ */
+ EIGEN_DEVICE_FUNC
+ CwiseBinaryOp<internal::scalar_quotient_op<Scalar>,
+ const ExpressionTypeNestedCleaned,
+ const typename OppositeExtendedType<NormReturnType>::Type>
+ normalized() const { return m_matrix.cwiseQuotient(extendedToOpposite(this->norm())); }
+
+
+ /** Normalize in-place each row or columns of the referenced matrix.
+ * \sa MatrixBase::normalize(), normalized()
+ */
+ EIGEN_DEVICE_FUNC void normalize() {
+ m_matrix = this->normalized();
+ }
+
+ EIGEN_DEVICE_FUNC inline void reverseInPlace();
+
+/////////// Geometry module ///////////
+
+ typedef Homogeneous<ExpressionType,Direction> HomogeneousReturnType;
+ EIGEN_DEVICE_FUNC
+ HomogeneousReturnType homogeneous() const;
+
+ typedef typename ExpressionType::PlainObject CrossReturnType;
+ template<typename OtherDerived>
+ EIGEN_DEVICE_FUNC
+ const CrossReturnType cross(const MatrixBase<OtherDerived>& other) const;
+
+ enum {
+ HNormalized_Size = Direction==Vertical ? internal::traits<ExpressionType>::RowsAtCompileTime
+ : internal::traits<ExpressionType>::ColsAtCompileTime,
+ HNormalized_SizeMinusOne = HNormalized_Size==Dynamic ? Dynamic : HNormalized_Size-1
+ };
+ typedef Block<const ExpressionType,
+ Direction==Vertical ? int(HNormalized_SizeMinusOne)
+ : int(internal::traits<ExpressionType>::RowsAtCompileTime),
+ Direction==Horizontal ? int(HNormalized_SizeMinusOne)
+ : int(internal::traits<ExpressionType>::ColsAtCompileTime)>
+ HNormalized_Block;
+ typedef Block<const ExpressionType,
+ Direction==Vertical ? 1 : int(internal::traits<ExpressionType>::RowsAtCompileTime),
+ Direction==Horizontal ? 1 : int(internal::traits<ExpressionType>::ColsAtCompileTime)>
+ HNormalized_Factors;
+ typedef CwiseBinaryOp<internal::scalar_quotient_op<typename internal::traits<ExpressionType>::Scalar>,
+ const HNormalized_Block,
+ const Replicate<HNormalized_Factors,
+ Direction==Vertical ? HNormalized_SizeMinusOne : 1,
+ Direction==Horizontal ? HNormalized_SizeMinusOne : 1> >
+ HNormalizedReturnType;
+
+ EIGEN_DEVICE_FUNC
+ const HNormalizedReturnType hnormalized() const;
+
+# ifdef EIGEN_VECTORWISEOP_PLUGIN
+# include EIGEN_VECTORWISEOP_PLUGIN
+# endif
+
+ protected:
+ Index redux_length() const
+ {
+ return Direction==Vertical ? m_matrix.rows() : m_matrix.cols();
+ }
+ ExpressionTypeNested m_matrix;
+};
+
+//const colwise moved to DenseBase.h due to CUDA compiler bug
+
+
+/** \returns a writable VectorwiseOp wrapper of *this providing additional partial reduction operations
+ *
+ * \sa rowwise(), class VectorwiseOp, \ref TutorialReductionsVisitorsBroadcasting
+ */
+template<typename Derived>
+EIGEN_DEVICE_FUNC inline typename DenseBase<Derived>::ColwiseReturnType
+DenseBase<Derived>::colwise()
+{
+ return ColwiseReturnType(derived());
+}
+
+//const rowwise moved to DenseBase.h due to CUDA compiler bug
+
+
+/** \returns a writable VectorwiseOp wrapper of *this providing additional partial reduction operations
+ *
+ * \sa colwise(), class VectorwiseOp, \ref TutorialReductionsVisitorsBroadcasting
+ */
+template<typename Derived>
+EIGEN_DEVICE_FUNC inline typename DenseBase<Derived>::RowwiseReturnType
+DenseBase<Derived>::rowwise()
+{
+ return RowwiseReturnType(derived());
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_PARTIAL_REDUX_H
diff --git a/Eigen/src/Core/Visitor.h b/Eigen/src/Core/Visitor.h
new file mode 100644
index 0000000..e1c17fc
--- /dev/null
+++ b/Eigen/src/Core/Visitor.h
@@ -0,0 +1,455 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_VISITOR_H
+#define EIGEN_VISITOR_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+
+template<typename Visitor, typename Derived, int UnrollCount, bool Vectorize=((Derived::PacketAccess!=0) && functor_traits<Visitor>::PacketAccess)>
+struct visitor_impl;
+
+template<typename Visitor, typename Derived, int UnrollCount>
+struct visitor_impl<Visitor, Derived, UnrollCount, false>
+{
+ enum {
+ col = Derived::IsRowMajor ? (UnrollCount-1) % Derived::ColsAtCompileTime
+ : (UnrollCount-1) / Derived::RowsAtCompileTime,
+ row = Derived::IsRowMajor ? (UnrollCount-1) / Derived::ColsAtCompileTime
+ : (UnrollCount-1) % Derived::RowsAtCompileTime
+ };
+
+ EIGEN_DEVICE_FUNC
+ static inline void run(const Derived &mat, Visitor& visitor)
+ {
+ visitor_impl<Visitor, Derived, UnrollCount-1>::run(mat, visitor);
+ visitor(mat.coeff(row, col), row, col);
+ }
+};
+
+template<typename Visitor, typename Derived>
+struct visitor_impl<Visitor, Derived, 1, false>
+{
+ EIGEN_DEVICE_FUNC
+ static inline void run(const Derived &mat, Visitor& visitor)
+ {
+ return visitor.init(mat.coeff(0, 0), 0, 0);
+ }
+};
+
+// This specialization enables visitors on empty matrices at compile-time
+template<typename Visitor, typename Derived>
+struct visitor_impl<Visitor, Derived, 0, false> {
+ EIGEN_DEVICE_FUNC
+ static inline void run(const Derived &/*mat*/, Visitor& /*visitor*/)
+ {}
+};
+
+template<typename Visitor, typename Derived>
+struct visitor_impl<Visitor, Derived, Dynamic, /*Vectorize=*/false>
+{
+ EIGEN_DEVICE_FUNC
+ static inline void run(const Derived& mat, Visitor& visitor)
+ {
+ visitor.init(mat.coeff(0,0), 0, 0);
+ if (Derived::IsRowMajor) {
+ for(Index i = 1; i < mat.cols(); ++i) {
+ visitor(mat.coeff(0, i), 0, i);
+ }
+ for(Index j = 1; j < mat.rows(); ++j) {
+ for(Index i = 0; i < mat.cols(); ++i) {
+ visitor(mat.coeff(j, i), j, i);
+ }
+ }
+ } else {
+ for(Index i = 1; i < mat.rows(); ++i) {
+ visitor(mat.coeff(i, 0), i, 0);
+ }
+ for(Index j = 1; j < mat.cols(); ++j) {
+ for(Index i = 0; i < mat.rows(); ++i) {
+ visitor(mat.coeff(i, j), i, j);
+ }
+ }
+ }
+ }
+};
+
+template<typename Visitor, typename Derived, int UnrollSize>
+struct visitor_impl<Visitor, Derived, UnrollSize, /*Vectorize=*/true>
+{
+ typedef typename Derived::Scalar Scalar;
+ typedef typename packet_traits<Scalar>::type Packet;
+
+ EIGEN_DEVICE_FUNC
+ static inline void run(const Derived& mat, Visitor& visitor)
+ {
+ const Index PacketSize = packet_traits<Scalar>::size;
+ visitor.init(mat.coeff(0,0), 0, 0);
+ if (Derived::IsRowMajor) {
+ for(Index i = 0; i < mat.rows(); ++i) {
+ Index j = i == 0 ? 1 : 0;
+ for(; j+PacketSize-1 < mat.cols(); j += PacketSize) {
+ Packet p = mat.packet(i, j);
+ visitor.packet(p, i, j);
+ }
+ for(; j < mat.cols(); ++j)
+ visitor(mat.coeff(i, j), i, j);
+ }
+ } else {
+ for(Index j = 0; j < mat.cols(); ++j) {
+ Index i = j == 0 ? 1 : 0;
+ for(; i+PacketSize-1 < mat.rows(); i += PacketSize) {
+ Packet p = mat.packet(i, j);
+ visitor.packet(p, i, j);
+ }
+ for(; i < mat.rows(); ++i)
+ visitor(mat.coeff(i, j), i, j);
+ }
+ }
+ }
+};
+
+// evaluator adaptor
+template<typename XprType>
+class visitor_evaluator
+{
+public:
+ typedef internal::evaluator<XprType> Evaluator;
+
+ enum {
+ PacketAccess = Evaluator::Flags & PacketAccessBit,
+ IsRowMajor = XprType::IsRowMajor,
+ RowsAtCompileTime = XprType::RowsAtCompileTime,
+ ColsAtCompileTime = XprType::ColsAtCompileTime,
+ CoeffReadCost = Evaluator::CoeffReadCost
+ };
+
+
+ EIGEN_DEVICE_FUNC
+ explicit visitor_evaluator(const XprType &xpr) : m_evaluator(xpr), m_xpr(xpr) { }
+
+ typedef typename XprType::Scalar Scalar;
+ typedef std::remove_const_t<typename XprType::CoeffReturnType> CoeffReturnType;
+ typedef std::remove_const_t<typename XprType::PacketReturnType> PacketReturnType;
+
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR Index rows() const EIGEN_NOEXCEPT { return m_xpr.rows(); }
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR Index cols() const EIGEN_NOEXCEPT { return m_xpr.cols(); }
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR Index size() const EIGEN_NOEXCEPT { return m_xpr.size(); }
+
+ EIGEN_DEVICE_FUNC CoeffReturnType coeff(Index row, Index col) const
+ { return m_evaluator.coeff(row, col); }
+ EIGEN_DEVICE_FUNC PacketReturnType packet(Index row, Index col) const
+ { return m_evaluator.template packet<Unaligned,PacketReturnType>(row, col); }
+
+protected:
+ Evaluator m_evaluator;
+ const XprType &m_xpr;
+};
+
+} // end namespace internal
+
+/** Applies the visitor \a visitor to the whole coefficients of the matrix or vector.
+ *
+ * The template parameter \a Visitor is the type of the visitor and provides the following interface:
+ * \code
+ * struct MyVisitor {
+ * // called for the first coefficient
+ * void init(const Scalar& value, Index i, Index j);
+ * // called for all other coefficients
+ * void operator() (const Scalar& value, Index i, Index j);
+ * };
+ * \endcode
+ *
+ * \note compared to one or two \em for \em loops, visitors offer automatic
+ * unrolling for small fixed size matrix.
+ *
+ * \note if the matrix is empty, then the visitor is left unchanged.
+ *
+ * \sa minCoeff(Index*,Index*), maxCoeff(Index*,Index*), DenseBase::redux()
+ */
+template<typename Derived>
+template<typename Visitor>
+EIGEN_DEVICE_FUNC
+void DenseBase<Derived>::visit(Visitor& visitor) const
+{
+ if(size()==0)
+ return;
+
+ typedef typename internal::visitor_evaluator<Derived> ThisEvaluator;
+ ThisEvaluator thisEval(derived());
+
+ enum {
+ unroll = SizeAtCompileTime != Dynamic
+ && SizeAtCompileTime * int(ThisEvaluator::CoeffReadCost) + (SizeAtCompileTime-1) * int(internal::functor_traits<Visitor>::Cost) <= EIGEN_UNROLLING_LIMIT
+ };
+ return internal::visitor_impl<Visitor, ThisEvaluator, unroll ? int(SizeAtCompileTime) : Dynamic>::run(thisEval, visitor);
+}
+
+namespace internal {
+
+/** \internal
+ * \brief Base class to implement min and max visitors
+ */
+template <typename Derived>
+struct coeff_visitor
+{
+ // default initialization to avoid countless invalid maybe-uninitialized warnings by gcc
+ EIGEN_DEVICE_FUNC
+ coeff_visitor() : row(-1), col(-1), res(0) {}
+ typedef typename Derived::Scalar Scalar;
+ Index row, col;
+ Scalar res;
+ EIGEN_DEVICE_FUNC
+ inline void init(const Scalar& value, Index i, Index j)
+ {
+ res = value;
+ row = i;
+ col = j;
+ }
+};
+
+
+template<typename Scalar, int NaNPropagation, bool is_min=true>
+struct minmax_compare {
+ typedef typename packet_traits<Scalar>::type Packet;
+ static EIGEN_DEVICE_FUNC inline bool compare(Scalar a, Scalar b) { return a < b; }
+ static EIGEN_DEVICE_FUNC inline Scalar predux(const Packet& p) { return predux_min<NaNPropagation>(p);}
+};
+
+template<typename Scalar, int NaNPropagation>
+struct minmax_compare<Scalar, NaNPropagation, false> {
+ typedef typename packet_traits<Scalar>::type Packet;
+ static EIGEN_DEVICE_FUNC inline bool compare(Scalar a, Scalar b) { return a > b; }
+ static EIGEN_DEVICE_FUNC inline Scalar predux(const Packet& p) { return predux_max<NaNPropagation>(p);}
+};
+
+template <typename Derived, bool is_min, int NaNPropagation>
+struct minmax_coeff_visitor : coeff_visitor<Derived>
+{
+ using Scalar = typename Derived::Scalar;
+ using Packet = typename packet_traits<Scalar>::type;
+ using Comparator = minmax_compare<Scalar, NaNPropagation, is_min>;
+
+ EIGEN_DEVICE_FUNC inline
+ void operator() (const Scalar& value, Index i, Index j)
+ {
+ if(Comparator::compare(value, this->res)) {
+ this->res = value;
+ this->row = i;
+ this->col = j;
+ }
+ }
+
+ EIGEN_DEVICE_FUNC inline
+ void packet(const Packet& p, Index i, Index j) {
+ const Index PacketSize = packet_traits<Scalar>::size;
+ Scalar value = Comparator::predux(p);
+ if (Comparator::compare(value, this->res)) {
+ const Packet range = preverse(plset<Packet>(Scalar(1)));
+ Packet mask = pcmp_eq(pset1<Packet>(value), p);
+ Index max_idx = PacketSize - static_cast<Index>(predux_max(pand(range, mask)));
+ this->res = value;
+ this->row = Derived::IsRowMajor ? i : i + max_idx;;
+ this->col = Derived::IsRowMajor ? j + max_idx : j;
+ }
+ }
+};
+
+// Suppress NaN. The only case in which we return NaN is if the matrix is all NaN, in which case,
+// the row=0, col=0 is returned for the location.
+template <typename Derived, bool is_min>
+struct minmax_coeff_visitor<Derived, is_min, PropagateNumbers> : coeff_visitor<Derived>
+{
+ typedef typename Derived::Scalar Scalar;
+ using Packet = typename packet_traits<Scalar>::type;
+ using Comparator = minmax_compare<Scalar, PropagateNumbers, is_min>;
+
+ EIGEN_DEVICE_FUNC inline
+ void operator() (const Scalar& value, Index i, Index j)
+ {
+ if ((!(numext::isnan)(value) && (numext::isnan)(this->res)) || Comparator::compare(value, this->res)) {
+ this->res = value;
+ this->row = i;
+ this->col = j;
+ }
+ }
+
+ EIGEN_DEVICE_FUNC inline
+ void packet(const Packet& p, Index i, Index j) {
+ const Index PacketSize = packet_traits<Scalar>::size;
+ Scalar value = Comparator::predux(p);
+ if ((!(numext::isnan)(value) && (numext::isnan)(this->res)) || Comparator::compare(value, this->res)) {
+ const Packet range = preverse(plset<Packet>(Scalar(1)));
+ /* mask will be zero for NaNs, so they will be ignored. */
+ Packet mask = pcmp_eq(pset1<Packet>(value), p);
+ Index max_idx = PacketSize - static_cast<Index>(predux_max(pand(range, mask)));
+ this->res = value;
+ this->row = Derived::IsRowMajor ? i : i + max_idx;;
+ this->col = Derived::IsRowMajor ? j + max_idx : j;
+ }
+ }
+
+};
+
+// Propagate NaN. If the matrix contains NaN, the location of the first NaN will be returned in
+// row and col.
+template <typename Derived, bool is_min>
+struct minmax_coeff_visitor<Derived, is_min, PropagateNaN> : coeff_visitor<Derived>
+{
+ typedef typename Derived::Scalar Scalar;
+ using Packet = typename packet_traits<Scalar>::type;
+ using Comparator = minmax_compare<Scalar, PropagateNaN, is_min>;
+
+ EIGEN_DEVICE_FUNC inline
+ void operator() (const Scalar& value, Index i, Index j)
+ {
+ const bool value_is_nan = (numext::isnan)(value);
+ if ((value_is_nan && !(numext::isnan)(this->res)) || Comparator::compare(value, this->res)) {
+ this->res = value;
+ this->row = i;
+ this->col = j;
+ }
+ }
+
+ EIGEN_DEVICE_FUNC inline
+ void packet(const Packet& p, Index i, Index j) {
+ const Index PacketSize = packet_traits<Scalar>::size;
+ Scalar value = Comparator::predux(p);
+ const bool value_is_nan = (numext::isnan)(value);
+ if ((value_is_nan && !(numext::isnan)(this->res)) || Comparator::compare(value, this->res)) {
+ const Packet range = preverse(plset<Packet>(Scalar(1)));
+ // If the value is NaN, pick the first position of a NaN, otherwise pick the first extremal value.
+ Packet mask = value_is_nan ? pnot(pcmp_eq(p, p)) : pcmp_eq(pset1<Packet>(value), p);
+ Index max_idx = PacketSize - static_cast<Index>(predux_max(pand(range, mask)));
+ this->res = value;
+ this->row = Derived::IsRowMajor ? i : i + max_idx;;
+ this->col = Derived::IsRowMajor ? j + max_idx : j;
+ }
+ }
+};
+
+template<typename Scalar, bool is_min, int NaNPropagation>
+struct functor_traits<minmax_coeff_visitor<Scalar, is_min, NaNPropagation> > {
+ enum {
+ Cost = NumTraits<Scalar>::AddCost,
+ PacketAccess = true
+ };
+};
+
+} // end namespace internal
+
+/** \fn DenseBase<Derived>::minCoeff(IndexType* rowId, IndexType* colId) const
+ * \returns the minimum of all coefficients of *this and puts in *row and *col its location.
+ *
+ * In case \c *this contains NaN, NaNPropagation determines the behavior:
+ * NaNPropagation == PropagateFast : undefined
+ * NaNPropagation == PropagateNaN : result is NaN
+ * NaNPropagation == PropagateNumbers : result is maximum of elements that are not NaN
+ * \warning the matrix must be not empty, otherwise an assertion is triggered.
+ *
+ * \sa DenseBase::minCoeff(Index*), DenseBase::maxCoeff(Index*,Index*), DenseBase::visit(), DenseBase::minCoeff()
+ */
+template<typename Derived>
+template<int NaNPropagation, typename IndexType>
+EIGEN_DEVICE_FUNC
+typename internal::traits<Derived>::Scalar
+DenseBase<Derived>::minCoeff(IndexType* rowId, IndexType* colId) const
+{
+ eigen_assert(this->rows()>0 && this->cols()>0 && "you are using an empty matrix");
+
+ internal::minmax_coeff_visitor<Derived, true, NaNPropagation> minVisitor;
+ this->visit(minVisitor);
+ *rowId = minVisitor.row;
+ if (colId) *colId = minVisitor.col;
+ return minVisitor.res;
+}
+
+/** \returns the minimum of all coefficients of *this and puts in *index its location.
+ *
+ * In case \c *this contains NaN, NaNPropagation determines the behavior:
+ * NaNPropagation == PropagateFast : undefined
+ * NaNPropagation == PropagateNaN : result is NaN
+ * NaNPropagation == PropagateNumbers : result is maximum of elements that are not NaN
+ * \warning the matrix must be not empty, otherwise an assertion is triggered.
+ *
+ * \sa DenseBase::minCoeff(IndexType*,IndexType*), DenseBase::maxCoeff(IndexType*,IndexType*), DenseBase::visit(), DenseBase::minCoeff()
+ */
+template<typename Derived>
+template<int NaNPropagation, typename IndexType>
+EIGEN_DEVICE_FUNC
+typename internal::traits<Derived>::Scalar
+DenseBase<Derived>::minCoeff(IndexType* index) const
+{
+ eigen_assert(this->rows()>0 && this->cols()>0 && "you are using an empty matrix");
+
+ EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
+ internal::minmax_coeff_visitor<Derived, true, NaNPropagation> minVisitor;
+ this->visit(minVisitor);
+ *index = IndexType((RowsAtCompileTime==1) ? minVisitor.col : minVisitor.row);
+ return minVisitor.res;
+}
+
+/** \fn DenseBase<Derived>::maxCoeff(IndexType* rowId, IndexType* colId) const
+ * \returns the maximum of all coefficients of *this and puts in *row and *col its location.
+ *
+ * In case \c *this contains NaN, NaNPropagation determines the behavior:
+ * NaNPropagation == PropagateFast : undefined
+ * NaNPropagation == PropagateNaN : result is NaN
+ * NaNPropagation == PropagateNumbers : result is maximum of elements that are not NaN
+ * \warning the matrix must be not empty, otherwise an assertion is triggered.
+ *
+ * \sa DenseBase::minCoeff(IndexType*,IndexType*), DenseBase::visit(), DenseBase::maxCoeff()
+ */
+template<typename Derived>
+template<int NaNPropagation, typename IndexType>
+EIGEN_DEVICE_FUNC
+typename internal::traits<Derived>::Scalar
+DenseBase<Derived>::maxCoeff(IndexType* rowPtr, IndexType* colPtr) const
+{
+ eigen_assert(this->rows()>0 && this->cols()>0 && "you are using an empty matrix");
+
+ internal::minmax_coeff_visitor<Derived, false, NaNPropagation> maxVisitor;
+ this->visit(maxVisitor);
+ *rowPtr = maxVisitor.row;
+ if (colPtr) *colPtr = maxVisitor.col;
+ return maxVisitor.res;
+}
+
+/** \returns the maximum of all coefficients of *this and puts in *index its location.
+ *
+ * In case \c *this contains NaN, NaNPropagation determines the behavior:
+ * NaNPropagation == PropagateFast : undefined
+ * NaNPropagation == PropagateNaN : result is NaN
+ * NaNPropagation == PropagateNumbers : result is maximum of elements that are not NaN
+ * \warning the matrix must be not empty, otherwise an assertion is triggered.
+ *
+ * \sa DenseBase::maxCoeff(IndexType*,IndexType*), DenseBase::minCoeff(IndexType*,IndexType*), DenseBase::visitor(), DenseBase::maxCoeff()
+ */
+template<typename Derived>
+template<int NaNPropagation, typename IndexType>
+EIGEN_DEVICE_FUNC
+typename internal::traits<Derived>::Scalar
+DenseBase<Derived>::maxCoeff(IndexType* index) const
+{
+ eigen_assert(this->rows()>0 && this->cols()>0 && "you are using an empty matrix");
+
+ EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
+ internal::minmax_coeff_visitor<Derived, false, NaNPropagation> maxVisitor;
+ this->visit(maxVisitor);
+ *index = (RowsAtCompileTime==1) ? maxVisitor.col : maxVisitor.row;
+ return maxVisitor.res;
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_VISITOR_H
diff --git a/Eigen/src/Core/arch/AVX/Complex.h b/Eigen/src/Core/arch/AVX/Complex.h
new file mode 100644
index 0000000..3abb5bd
--- /dev/null
+++ b/Eigen/src/Core/arch/AVX/Complex.h
@@ -0,0 +1,370 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2014 Benoit Steiner (benoit.steiner.goog@gmail.com)
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_COMPLEX_AVX_H
+#define EIGEN_COMPLEX_AVX_H
+
+#include "../../InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+
+//---------- float ----------
+struct Packet4cf
+{
+ EIGEN_STRONG_INLINE Packet4cf() {}
+ EIGEN_STRONG_INLINE explicit Packet4cf(const __m256& a) : v(a) {}
+ __m256 v;
+};
+
+#ifndef EIGEN_VECTORIZE_AVX512
+template<> struct packet_traits<std::complex<float> > : default_packet_traits
+{
+ typedef Packet4cf type;
+ typedef Packet2cf half;
+ enum {
+ Vectorizable = 1,
+ AlignedOnScalar = 1,
+ size = 4,
+ HasHalfPacket = 1,
+
+ HasAdd = 1,
+ HasSub = 1,
+ HasMul = 1,
+ HasDiv = 1,
+ HasNegate = 1,
+ HasSqrt = 1,
+ HasAbs = 0,
+ HasAbs2 = 0,
+ HasMin = 0,
+ HasMax = 0,
+ HasSetLinear = 0
+ };
+};
+#endif
+
+template<> struct unpacket_traits<Packet4cf> {
+ typedef std::complex<float> type;
+ typedef Packet2cf half;
+ typedef Packet8f as_real;
+ enum {
+ size=4,
+ alignment=Aligned32,
+ vectorizable=true,
+ masked_load_available=false,
+ masked_store_available=false
+ };
+};
+
+template<> EIGEN_STRONG_INLINE Packet4cf padd<Packet4cf>(const Packet4cf& a, const Packet4cf& b) { return Packet4cf(_mm256_add_ps(a.v,b.v)); }
+template<> EIGEN_STRONG_INLINE Packet4cf psub<Packet4cf>(const Packet4cf& a, const Packet4cf& b) { return Packet4cf(_mm256_sub_ps(a.v,b.v)); }
+template<> EIGEN_STRONG_INLINE Packet4cf pnegate(const Packet4cf& a)
+{
+ return Packet4cf(pnegate(a.v));
+}
+template<> EIGEN_STRONG_INLINE Packet4cf pconj(const Packet4cf& a)
+{
+ const __m256 mask = _mm256_castsi256_ps(_mm256_setr_epi32(0x00000000,0x80000000,0x00000000,0x80000000,0x00000000,0x80000000,0x00000000,0x80000000));
+ return Packet4cf(_mm256_xor_ps(a.v,mask));
+}
+
+template<> EIGEN_STRONG_INLINE Packet4cf pmul<Packet4cf>(const Packet4cf& a, const Packet4cf& b)
+{
+ __m256 tmp1 = _mm256_mul_ps(_mm256_moveldup_ps(a.v), b.v);
+ __m256 tmp2 = _mm256_mul_ps(_mm256_movehdup_ps(a.v), _mm256_permute_ps(b.v, _MM_SHUFFLE(2,3,0,1)));
+ __m256 result = _mm256_addsub_ps(tmp1, tmp2);
+ return Packet4cf(result);
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet4cf pcmp_eq(const Packet4cf& a, const Packet4cf& b) {
+ __m256 eq = _mm256_cmp_ps(a.v, b.v, _CMP_EQ_OQ);
+ return Packet4cf(_mm256_and_ps(eq, _mm256_permute_ps(eq, 0xb1)));
+}
+
+template<> EIGEN_STRONG_INLINE Packet4cf ptrue<Packet4cf>(const Packet4cf& a) { return Packet4cf(ptrue(Packet8f(a.v))); }
+template<> EIGEN_STRONG_INLINE Packet4cf pand <Packet4cf>(const Packet4cf& a, const Packet4cf& b) { return Packet4cf(_mm256_and_ps(a.v,b.v)); }
+template<> EIGEN_STRONG_INLINE Packet4cf por <Packet4cf>(const Packet4cf& a, const Packet4cf& b) { return Packet4cf(_mm256_or_ps(a.v,b.v)); }
+template<> EIGEN_STRONG_INLINE Packet4cf pxor <Packet4cf>(const Packet4cf& a, const Packet4cf& b) { return Packet4cf(_mm256_xor_ps(a.v,b.v)); }
+template<> EIGEN_STRONG_INLINE Packet4cf pandnot<Packet4cf>(const Packet4cf& a, const Packet4cf& b) { return Packet4cf(_mm256_andnot_ps(b.v,a.v)); }
+
+template<> EIGEN_STRONG_INLINE Packet4cf pload <Packet4cf>(const std::complex<float>* from) { EIGEN_DEBUG_ALIGNED_LOAD return Packet4cf(pload<Packet8f>(&numext::real_ref(*from))); }
+template<> EIGEN_STRONG_INLINE Packet4cf ploadu<Packet4cf>(const std::complex<float>* from) { EIGEN_DEBUG_UNALIGNED_LOAD return Packet4cf(ploadu<Packet8f>(&numext::real_ref(*from))); }
+
+
+template<> EIGEN_STRONG_INLINE Packet4cf pset1<Packet4cf>(const std::complex<float>& from)
+{
+ const float re = std::real(from);
+ const float im = std::imag(from);
+ return Packet4cf(_mm256_set_ps(im, re, im, re, im, re, im, re));
+}
+
+template<> EIGEN_STRONG_INLINE Packet4cf ploaddup<Packet4cf>(const std::complex<float>* from)
+{
+ // FIXME The following might be optimized using _mm256_movedup_pd
+ Packet2cf a = ploaddup<Packet2cf>(from);
+ Packet2cf b = ploaddup<Packet2cf>(from+1);
+ return Packet4cf(_mm256_insertf128_ps(_mm256_castps128_ps256(a.v), b.v, 1));
+}
+
+template<> EIGEN_STRONG_INLINE void pstore <std::complex<float> >(std::complex<float>* to, const Packet4cf& from) { EIGEN_DEBUG_ALIGNED_STORE pstore(&numext::real_ref(*to), from.v); }
+template<> EIGEN_STRONG_INLINE void pstoreu<std::complex<float> >(std::complex<float>* to, const Packet4cf& from) { EIGEN_DEBUG_UNALIGNED_STORE pstoreu(&numext::real_ref(*to), from.v); }
+
+template<> EIGEN_DEVICE_FUNC inline Packet4cf pgather<std::complex<float>, Packet4cf>(const std::complex<float>* from, Index stride)
+{
+ return Packet4cf(_mm256_set_ps(std::imag(from[3*stride]), std::real(from[3*stride]),
+ std::imag(from[2*stride]), std::real(from[2*stride]),
+ std::imag(from[1*stride]), std::real(from[1*stride]),
+ std::imag(from[0*stride]), std::real(from[0*stride])));
+}
+
+template<> EIGEN_DEVICE_FUNC inline void pscatter<std::complex<float>, Packet4cf>(std::complex<float>* to, const Packet4cf& from, Index stride)
+{
+ __m128 low = _mm256_extractf128_ps(from.v, 0);
+ to[stride*0] = std::complex<float>(_mm_cvtss_f32(_mm_shuffle_ps(low, low, 0)),
+ _mm_cvtss_f32(_mm_shuffle_ps(low, low, 1)));
+ to[stride*1] = std::complex<float>(_mm_cvtss_f32(_mm_shuffle_ps(low, low, 2)),
+ _mm_cvtss_f32(_mm_shuffle_ps(low, low, 3)));
+
+ __m128 high = _mm256_extractf128_ps(from.v, 1);
+ to[stride*2] = std::complex<float>(_mm_cvtss_f32(_mm_shuffle_ps(high, high, 0)),
+ _mm_cvtss_f32(_mm_shuffle_ps(high, high, 1)));
+ to[stride*3] = std::complex<float>(_mm_cvtss_f32(_mm_shuffle_ps(high, high, 2)),
+ _mm_cvtss_f32(_mm_shuffle_ps(high, high, 3)));
+
+}
+
+template<> EIGEN_STRONG_INLINE std::complex<float> pfirst<Packet4cf>(const Packet4cf& a)
+{
+ return pfirst(Packet2cf(_mm256_castps256_ps128(a.v)));
+}
+
+template<> EIGEN_STRONG_INLINE Packet4cf preverse(const Packet4cf& a) {
+ __m128 low = _mm256_extractf128_ps(a.v, 0);
+ __m128 high = _mm256_extractf128_ps(a.v, 1);
+ __m128d lowd = _mm_castps_pd(low);
+ __m128d highd = _mm_castps_pd(high);
+ low = _mm_castpd_ps(_mm_shuffle_pd(lowd,lowd,0x1));
+ high = _mm_castpd_ps(_mm_shuffle_pd(highd,highd,0x1));
+ __m256 result = _mm256_setzero_ps();
+ result = _mm256_insertf128_ps(result, low, 1);
+ result = _mm256_insertf128_ps(result, high, 0);
+ return Packet4cf(result);
+}
+
+template<> EIGEN_STRONG_INLINE std::complex<float> predux<Packet4cf>(const Packet4cf& a)
+{
+ return predux(padd(Packet2cf(_mm256_extractf128_ps(a.v,0)),
+ Packet2cf(_mm256_extractf128_ps(a.v,1))));
+}
+
+template<> EIGEN_STRONG_INLINE std::complex<float> predux_mul<Packet4cf>(const Packet4cf& a)
+{
+ return predux_mul(pmul(Packet2cf(_mm256_extractf128_ps(a.v, 0)),
+ Packet2cf(_mm256_extractf128_ps(a.v, 1))));
+}
+
+
+EIGEN_MAKE_CONJ_HELPER_CPLX_REAL(Packet4cf,Packet8f)
+
+template<> EIGEN_STRONG_INLINE Packet4cf pdiv<Packet4cf>(const Packet4cf& a, const Packet4cf& b)
+{
+ return pdiv_complex(a, b);
+}
+
+template<> EIGEN_STRONG_INLINE Packet4cf pcplxflip<Packet4cf>(const Packet4cf& x)
+{
+ return Packet4cf(_mm256_shuffle_ps(x.v, x.v, _MM_SHUFFLE(2, 3, 0 ,1)));
+}
+
+//---------- double ----------
+struct Packet2cd
+{
+ EIGEN_STRONG_INLINE Packet2cd() {}
+ EIGEN_STRONG_INLINE explicit Packet2cd(const __m256d& a) : v(a) {}
+ __m256d v;
+};
+
+#ifndef EIGEN_VECTORIZE_AVX512
+template<> struct packet_traits<std::complex<double> > : default_packet_traits
+{
+ typedef Packet2cd type;
+ typedef Packet1cd half;
+ enum {
+ Vectorizable = 1,
+ AlignedOnScalar = 0,
+ size = 2,
+ HasHalfPacket = 1,
+
+ HasAdd = 1,
+ HasSub = 1,
+ HasMul = 1,
+ HasDiv = 1,
+ HasNegate = 1,
+ HasSqrt = 1,
+ HasAbs = 0,
+ HasAbs2 = 0,
+ HasMin = 0,
+ HasMax = 0,
+ HasSetLinear = 0
+ };
+};
+#endif
+
+template<> struct unpacket_traits<Packet2cd> {
+ typedef std::complex<double> type;
+ typedef Packet1cd half;
+ typedef Packet4d as_real;
+ enum {
+ size=2,
+ alignment=Aligned32,
+ vectorizable=true,
+ masked_load_available=false,
+ masked_store_available=false
+ };
+};
+
+template<> EIGEN_STRONG_INLINE Packet2cd padd<Packet2cd>(const Packet2cd& a, const Packet2cd& b) { return Packet2cd(_mm256_add_pd(a.v,b.v)); }
+template<> EIGEN_STRONG_INLINE Packet2cd psub<Packet2cd>(const Packet2cd& a, const Packet2cd& b) { return Packet2cd(_mm256_sub_pd(a.v,b.v)); }
+template<> EIGEN_STRONG_INLINE Packet2cd pnegate(const Packet2cd& a) { return Packet2cd(pnegate(a.v)); }
+template<> EIGEN_STRONG_INLINE Packet2cd pconj(const Packet2cd& a)
+{
+ const __m256d mask = _mm256_castsi256_pd(_mm256_set_epi32(0x80000000,0x0,0x0,0x0,0x80000000,0x0,0x0,0x0));
+ return Packet2cd(_mm256_xor_pd(a.v,mask));
+}
+
+template<> EIGEN_STRONG_INLINE Packet2cd pmul<Packet2cd>(const Packet2cd& a, const Packet2cd& b)
+{
+ __m256d tmp1 = _mm256_shuffle_pd(a.v,a.v,0x0);
+ __m256d even = _mm256_mul_pd(tmp1, b.v);
+ __m256d tmp2 = _mm256_shuffle_pd(a.v,a.v,0xF);
+ __m256d tmp3 = _mm256_shuffle_pd(b.v,b.v,0x5);
+ __m256d odd = _mm256_mul_pd(tmp2, tmp3);
+ return Packet2cd(_mm256_addsub_pd(even, odd));
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet2cd pcmp_eq(const Packet2cd& a, const Packet2cd& b) {
+ __m256d eq = _mm256_cmp_pd(a.v, b.v, _CMP_EQ_OQ);
+ return Packet2cd(pand(eq, _mm256_permute_pd(eq, 0x5)));
+}
+
+template<> EIGEN_STRONG_INLINE Packet2cd ptrue<Packet2cd>(const Packet2cd& a) { return Packet2cd(ptrue(Packet4d(a.v))); }
+template<> EIGEN_STRONG_INLINE Packet2cd pand <Packet2cd>(const Packet2cd& a, const Packet2cd& b) { return Packet2cd(_mm256_and_pd(a.v,b.v)); }
+template<> EIGEN_STRONG_INLINE Packet2cd por <Packet2cd>(const Packet2cd& a, const Packet2cd& b) { return Packet2cd(_mm256_or_pd(a.v,b.v)); }
+template<> EIGEN_STRONG_INLINE Packet2cd pxor <Packet2cd>(const Packet2cd& a, const Packet2cd& b) { return Packet2cd(_mm256_xor_pd(a.v,b.v)); }
+template<> EIGEN_STRONG_INLINE Packet2cd pandnot<Packet2cd>(const Packet2cd& a, const Packet2cd& b) { return Packet2cd(_mm256_andnot_pd(b.v,a.v)); }
+
+template<> EIGEN_STRONG_INLINE Packet2cd pload <Packet2cd>(const std::complex<double>* from)
+{ EIGEN_DEBUG_ALIGNED_LOAD return Packet2cd(pload<Packet4d>((const double*)from)); }
+template<> EIGEN_STRONG_INLINE Packet2cd ploadu<Packet2cd>(const std::complex<double>* from)
+{ EIGEN_DEBUG_UNALIGNED_LOAD return Packet2cd(ploadu<Packet4d>((const double*)from)); }
+
+template<> EIGEN_STRONG_INLINE Packet2cd pset1<Packet2cd>(const std::complex<double>& from)
+{
+ // in case casting to a __m128d* is really not safe, then we can still fallback to this version: (much slower though)
+// return Packet2cd(_mm256_loadu2_m128d((const double*)&from,(const double*)&from));
+ return Packet2cd(_mm256_broadcast_pd((const __m128d*)(const void*)&from));
+}
+
+template<> EIGEN_STRONG_INLINE Packet2cd ploaddup<Packet2cd>(const std::complex<double>* from) { return pset1<Packet2cd>(*from); }
+
+template<> EIGEN_STRONG_INLINE void pstore <std::complex<double> >(std::complex<double> * to, const Packet2cd& from) { EIGEN_DEBUG_ALIGNED_STORE pstore((double*)to, from.v); }
+template<> EIGEN_STRONG_INLINE void pstoreu<std::complex<double> >(std::complex<double> * to, const Packet2cd& from) { EIGEN_DEBUG_UNALIGNED_STORE pstoreu((double*)to, from.v); }
+
+template<> EIGEN_DEVICE_FUNC inline Packet2cd pgather<std::complex<double>, Packet2cd>(const std::complex<double>* from, Index stride)
+{
+ return Packet2cd(_mm256_set_pd(std::imag(from[1*stride]), std::real(from[1*stride]),
+ std::imag(from[0*stride]), std::real(from[0*stride])));
+}
+
+template<> EIGEN_DEVICE_FUNC inline void pscatter<std::complex<double>, Packet2cd>(std::complex<double>* to, const Packet2cd& from, Index stride)
+{
+ __m128d low = _mm256_extractf128_pd(from.v, 0);
+ to[stride*0] = std::complex<double>(_mm_cvtsd_f64(low), _mm_cvtsd_f64(_mm_shuffle_pd(low, low, 1)));
+ __m128d high = _mm256_extractf128_pd(from.v, 1);
+ to[stride*1] = std::complex<double>(_mm_cvtsd_f64(high), _mm_cvtsd_f64(_mm_shuffle_pd(high, high, 1)));
+}
+
+template<> EIGEN_STRONG_INLINE std::complex<double> pfirst<Packet2cd>(const Packet2cd& a)
+{
+ __m128d low = _mm256_extractf128_pd(a.v, 0);
+ EIGEN_ALIGN16 double res[2];
+ _mm_store_pd(res, low);
+ return std::complex<double>(res[0],res[1]);
+}
+
+template<> EIGEN_STRONG_INLINE Packet2cd preverse(const Packet2cd& a) {
+ __m256d result = _mm256_permute2f128_pd(a.v, a.v, 1);
+ return Packet2cd(result);
+}
+
+template<> EIGEN_STRONG_INLINE std::complex<double> predux<Packet2cd>(const Packet2cd& a)
+{
+ return predux(padd(Packet1cd(_mm256_extractf128_pd(a.v,0)),
+ Packet1cd(_mm256_extractf128_pd(a.v,1))));
+}
+
+template<> EIGEN_STRONG_INLINE std::complex<double> predux_mul<Packet2cd>(const Packet2cd& a)
+{
+ return predux(pmul(Packet1cd(_mm256_extractf128_pd(a.v,0)),
+ Packet1cd(_mm256_extractf128_pd(a.v,1))));
+}
+
+EIGEN_MAKE_CONJ_HELPER_CPLX_REAL(Packet2cd,Packet4d)
+
+template<> EIGEN_STRONG_INLINE Packet2cd pdiv<Packet2cd>(const Packet2cd& a, const Packet2cd& b)
+{
+ return pdiv_complex(a, b);
+}
+
+template<> EIGEN_STRONG_INLINE Packet2cd pcplxflip<Packet2cd>(const Packet2cd& x)
+{
+ return Packet2cd(_mm256_shuffle_pd(x.v, x.v, 0x5));
+}
+
+EIGEN_DEVICE_FUNC inline void
+ptranspose(PacketBlock<Packet4cf,4>& kernel) {
+ __m256d P0 = _mm256_castps_pd(kernel.packet[0].v);
+ __m256d P1 = _mm256_castps_pd(kernel.packet[1].v);
+ __m256d P2 = _mm256_castps_pd(kernel.packet[2].v);
+ __m256d P3 = _mm256_castps_pd(kernel.packet[3].v);
+
+ __m256d T0 = _mm256_shuffle_pd(P0, P1, 15);
+ __m256d T1 = _mm256_shuffle_pd(P0, P1, 0);
+ __m256d T2 = _mm256_shuffle_pd(P2, P3, 15);
+ __m256d T3 = _mm256_shuffle_pd(P2, P3, 0);
+
+ kernel.packet[1].v = _mm256_castpd_ps(_mm256_permute2f128_pd(T0, T2, 32));
+ kernel.packet[3].v = _mm256_castpd_ps(_mm256_permute2f128_pd(T0, T2, 49));
+ kernel.packet[0].v = _mm256_castpd_ps(_mm256_permute2f128_pd(T1, T3, 32));
+ kernel.packet[2].v = _mm256_castpd_ps(_mm256_permute2f128_pd(T1, T3, 49));
+}
+
+EIGEN_DEVICE_FUNC inline void
+ptranspose(PacketBlock<Packet2cd,2>& kernel) {
+ __m256d tmp = _mm256_permute2f128_pd(kernel.packet[0].v, kernel.packet[1].v, 0+(2<<4));
+ kernel.packet[1].v = _mm256_permute2f128_pd(kernel.packet[0].v, kernel.packet[1].v, 1+(3<<4));
+ kernel.packet[0].v = tmp;
+}
+
+template<> EIGEN_STRONG_INLINE Packet2cd psqrt<Packet2cd>(const Packet2cd& a) {
+ return psqrt_complex<Packet2cd>(a);
+}
+
+template<> EIGEN_STRONG_INLINE Packet4cf psqrt<Packet4cf>(const Packet4cf& a) {
+ return psqrt_complex<Packet4cf>(a);
+}
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_COMPLEX_AVX_H
diff --git a/Eigen/src/Core/arch/AVX/MathFunctions.h b/Eigen/src/Core/arch/AVX/MathFunctions.h
new file mode 100644
index 0000000..cb7d7b8
--- /dev/null
+++ b/Eigen/src/Core/arch/AVX/MathFunctions.h
@@ -0,0 +1,205 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2014 Pedro Gonnet (pedro.gonnet@gmail.com)
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_MATH_FUNCTIONS_AVX_H
+#define EIGEN_MATH_FUNCTIONS_AVX_H
+
+/* The sin and cos functions of this file are loosely derived from
+ * Julien Pommier's sse math library: http://gruntthepeon.free.fr/ssemath/
+ */
+
+#include "../../InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+
+template <>
+EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet8f
+psin<Packet8f>(const Packet8f& _x) {
+ return psin_float(_x);
+}
+
+template <>
+EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet8f
+pcos<Packet8f>(const Packet8f& _x) {
+ return pcos_float(_x);
+}
+
+template <>
+EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet8f
+pasin<Packet8f>(const Packet8f& _x) {
+ return pasin_float(_x);
+}
+
+template <>
+EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet8f
+pacos<Packet8f>(const Packet8f& _x) {
+ return pacos_float(_x);
+}
+
+template <>
+EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet8f
+patan<Packet8f>(const Packet8f& _x) {
+ return patan_float(_x);
+}
+
+template <>
+EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet4d
+patan<Packet4d>(const Packet4d& _x) {
+ return patan_double(_x);
+}
+
+template <>
+EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet8f
+plog<Packet8f>(const Packet8f& _x) {
+ return plog_float(_x);
+}
+
+template <>
+EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet4d
+plog<Packet4d>(const Packet4d& _x) {
+ return plog_double(_x);
+}
+
+template <>
+EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet8f
+plog2<Packet8f>(const Packet8f& _x) {
+ return plog2_float(_x);
+}
+
+template <>
+EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet4d
+plog2<Packet4d>(const Packet4d& _x) {
+ return plog2_double(_x);
+}
+
+template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+Packet8f plog1p<Packet8f>(const Packet8f& _x) {
+ return generic_plog1p(_x);
+}
+
+template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+Packet8f pexpm1<Packet8f>(const Packet8f& _x) {
+ return generic_expm1(_x);
+}
+
+// Exponential function. Works by writing "x = m*log(2) + r" where
+// "m = floor(x/log(2)+1/2)" and "r" is the remainder. The result is then
+// "exp(x) = 2^m*exp(r)" where exp(r) is in the range [-1,1).
+template <>
+EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet8f
+pexp<Packet8f>(const Packet8f& _x) {
+ return pexp_float(_x);
+}
+
+// Hyperbolic Tangent function.
+template <>
+EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet8f
+ptanh<Packet8f>(const Packet8f& _x) {
+ return internal::generic_fast_tanh_float(_x);
+}
+
+// Exponential function for doubles.
+template <>
+EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet4d
+pexp<Packet4d>(const Packet4d& _x) {
+ return pexp_double(_x);
+}
+
+
+// Notice that for newer processors, it is counterproductive to use Newton
+// iteration for square root. In particular, Skylake and Zen2 processors
+// have approximately doubled throughput of the _mm_sqrt_ps instruction
+// compared to their predecessors.
+template <> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+Packet8f psqrt<Packet8f>(const Packet8f& _x) {
+ return _mm256_sqrt_ps(_x);
+}
+template <> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+Packet4d psqrt<Packet4d>(const Packet4d& _x) {
+ return _mm256_sqrt_pd(_x);
+}
+
+
+// Even on Skylake, using Newton iteration is a win for reciprocal square root.
+#if EIGEN_FAST_MATH
+template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+Packet8f prsqrt<Packet8f>(const Packet8f& a) {
+ // _mm256_rsqrt_ps returns -inf for negative denormals.
+ // _mm512_rsqrt**_ps returns -NaN for negative denormals. We may want
+ // consistency here.
+ // const Packet8f rsqrt = pselect(pcmp_lt(a, pzero(a)),
+ // pset1<Packet8f>(-NumTraits<float>::quiet_NaN()),
+ // _mm256_rsqrt_ps(a));
+ return generic_rsqrt_newton_step<Packet8f, /*Steps=*/1>::run(a, _mm256_rsqrt_ps(a));
+}
+
+template<> EIGEN_STRONG_INLINE Packet8f preciprocal<Packet8f>(const Packet8f& a) {
+ return generic_reciprocal_newton_step<Packet8f, /*Steps=*/1>::run(a, _mm256_rcp_ps(a));
+}
+
+#endif
+
+
+F16_PACKET_FUNCTION(Packet8f, Packet8h, psin)
+F16_PACKET_FUNCTION(Packet8f, Packet8h, pcos)
+F16_PACKET_FUNCTION(Packet8f, Packet8h, plog)
+F16_PACKET_FUNCTION(Packet8f, Packet8h, plog2)
+F16_PACKET_FUNCTION(Packet8f, Packet8h, plog1p)
+F16_PACKET_FUNCTION(Packet8f, Packet8h, pexpm1)
+F16_PACKET_FUNCTION(Packet8f, Packet8h, pexp)
+F16_PACKET_FUNCTION(Packet8f, Packet8h, ptanh)
+F16_PACKET_FUNCTION(Packet8f, Packet8h, psqrt)
+F16_PACKET_FUNCTION(Packet8f, Packet8h, prsqrt)
+F16_PACKET_FUNCTION(Packet8f, Packet8h, preciprocal)
+
+template <>
+EIGEN_STRONG_INLINE Packet8h pfrexp(const Packet8h& a, Packet8h& exponent) {
+ Packet8f fexponent;
+ const Packet8h out = float2half(pfrexp<Packet8f>(half2float(a), fexponent));
+ exponent = float2half(fexponent);
+ return out;
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet8h pldexp(const Packet8h& a, const Packet8h& exponent) {
+ return float2half(pldexp<Packet8f>(half2float(a), half2float(exponent)));
+}
+
+BF16_PACKET_FUNCTION(Packet8f, Packet8bf, psin)
+BF16_PACKET_FUNCTION(Packet8f, Packet8bf, pcos)
+BF16_PACKET_FUNCTION(Packet8f, Packet8bf, plog)
+BF16_PACKET_FUNCTION(Packet8f, Packet8bf, plog2)
+BF16_PACKET_FUNCTION(Packet8f, Packet8bf, plog1p)
+BF16_PACKET_FUNCTION(Packet8f, Packet8bf, pexpm1)
+BF16_PACKET_FUNCTION(Packet8f, Packet8bf, pexp)
+BF16_PACKET_FUNCTION(Packet8f, Packet8bf, ptanh)
+BF16_PACKET_FUNCTION(Packet8f, Packet8bf, psqrt)
+BF16_PACKET_FUNCTION(Packet8f, Packet8bf, prsqrt)
+BF16_PACKET_FUNCTION(Packet8f, Packet8bf, preciprocal)
+
+template <>
+EIGEN_STRONG_INLINE Packet8bf pfrexp(const Packet8bf& a, Packet8bf& exponent) {
+ Packet8f fexponent;
+ const Packet8bf out = F32ToBf16(pfrexp<Packet8f>(Bf16ToF32(a), fexponent));
+ exponent = F32ToBf16(fexponent);
+ return out;
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet8bf pldexp(const Packet8bf& a, const Packet8bf& exponent) {
+ return F32ToBf16(pldexp<Packet8f>(Bf16ToF32(a), Bf16ToF32(exponent)));
+}
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_MATH_FUNCTIONS_AVX_H
diff --git a/Eigen/src/Core/arch/AVX/PacketMath.h b/Eigen/src/Core/arch/AVX/PacketMath.h
new file mode 100644
index 0000000..ecbb73c
--- /dev/null
+++ b/Eigen/src/Core/arch/AVX/PacketMath.h
@@ -0,0 +1,2020 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2014 Benoit Steiner (benoit.steiner.goog@gmail.com)
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_PACKET_MATH_AVX_H
+#define EIGEN_PACKET_MATH_AVX_H
+
+#include "../../InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+
+#ifndef EIGEN_CACHEFRIENDLY_PRODUCT_THRESHOLD
+#define EIGEN_CACHEFRIENDLY_PRODUCT_THRESHOLD 8
+#endif
+
+#if !defined(EIGEN_VECTORIZE_AVX512) && !defined(EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS)
+#define EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS 16
+#endif
+
+#ifdef EIGEN_VECTORIZE_FMA
+#ifndef EIGEN_HAS_SINGLE_INSTRUCTION_MADD
+#define EIGEN_HAS_SINGLE_INSTRUCTION_MADD
+#endif
+#endif
+
+typedef __m256 Packet8f;
+typedef eigen_packet_wrapper<__m256i, 0> Packet8i;
+typedef __m256d Packet4d;
+#ifndef EIGEN_VECTORIZE_AVX512FP16
+typedef eigen_packet_wrapper<__m128i, 2> Packet8h;
+#endif
+typedef eigen_packet_wrapper<__m128i, 3> Packet8bf;
+
+#ifdef EIGEN_VECTORIZE_AVX2
+// Start from 3 to be compatible with AVX512
+typedef eigen_packet_wrapper<__m256i, 3> Packet4l;
+#endif
+
+template<> struct is_arithmetic<__m256> { enum { value = true }; };
+template<> struct is_arithmetic<__m256i> { enum { value = true }; };
+template<> struct is_arithmetic<__m256d> { enum { value = true }; };
+template<> struct is_arithmetic<Packet8i> { enum { value = true }; };
+#ifndef EIGEN_VECTORIZE_AVX512FP16
+template<> struct is_arithmetic<Packet8h> { enum { value = true }; };
+#endif
+template<> struct is_arithmetic<Packet8bf> { enum { value = true }; };
+#ifdef EIGEN_VECTORIZE_AVX2
+template<> struct is_arithmetic<Packet4l> { enum { value = true }; };
+#endif
+
+// Use the packet_traits defined in AVX512/PacketMath.h instead if we're going
+// to leverage AVX512 instructions.
+#ifndef EIGEN_VECTORIZE_AVX512
+template<> struct packet_traits<float> : default_packet_traits
+{
+ typedef Packet8f type;
+ typedef Packet4f half;
+ enum {
+ Vectorizable = 1,
+ AlignedOnScalar = 1,
+ size = 8,
+ HasHalfPacket = 1,
+
+ HasCmp = 1,
+ HasDiv = 1,
+ HasReciprocal = EIGEN_FAST_MATH,
+ HasSin = EIGEN_FAST_MATH,
+ HasCos = EIGEN_FAST_MATH,
+ HasACos = 1,
+ HasASin = 1,
+ HasATan = 1,
+ HasLog = 1,
+ HasLog1p = 1,
+ HasExpm1 = 1,
+ HasExp = 1,
+ HasNdtri = 1,
+ HasBessel = 1,
+ HasSqrt = 1,
+ HasRsqrt = 1,
+ HasTanh = EIGEN_FAST_MATH,
+ HasErf = EIGEN_FAST_MATH,
+ HasBlend = 1,
+ HasRound = 1,
+ HasFloor = 1,
+ HasCeil = 1,
+ HasRint = 1
+ };
+};
+template<> struct packet_traits<double> : default_packet_traits
+{
+ typedef Packet4d type;
+ typedef Packet2d half;
+ enum {
+ Vectorizable = 1,
+ AlignedOnScalar = 1,
+ size=4,
+ HasHalfPacket = 1,
+
+ HasCmp = 1,
+ HasDiv = 1,
+ HasLog = 1,
+ HasExp = 1,
+ HasSqrt = 1,
+ HasRsqrt = 1,
+ HasATan = 1,
+ HasBlend = 1,
+ HasRound = 1,
+ HasFloor = 1,
+ HasCeil = 1,
+ HasRint = 1
+ };
+};
+
+template <>
+struct packet_traits<Eigen::half> : default_packet_traits {
+ typedef Packet8h type;
+ // There is no half-size packet for Packet8h.
+ typedef Packet8h half;
+ enum {
+ Vectorizable = 1,
+ AlignedOnScalar = 1,
+ size = 8,
+ HasHalfPacket = 0,
+
+ HasCmp = 1,
+ HasAdd = 1,
+ HasSub = 1,
+ HasMul = 1,
+ HasDiv = 1,
+ HasSin = EIGEN_FAST_MATH,
+ HasCos = EIGEN_FAST_MATH,
+ HasNegate = 1,
+ HasAbs = 1,
+ HasAbs2 = 0,
+ HasMin = 1,
+ HasMax = 1,
+ HasConj = 1,
+ HasSetLinear = 0,
+ HasLog = 1,
+ HasLog1p = 1,
+ HasExpm1 = 1,
+ HasExp = 1,
+ HasSqrt = 1,
+ HasRsqrt = 1,
+ HasTanh = EIGEN_FAST_MATH,
+ HasErf = EIGEN_FAST_MATH,
+ HasBlend = 0,
+ HasRound = 1,
+ HasFloor = 1,
+ HasCeil = 1,
+ HasRint = 1,
+ HasBessel = 1,
+ HasNdtri = 1
+ };
+};
+
+template <>
+struct packet_traits<bfloat16> : default_packet_traits {
+ typedef Packet8bf type;
+ // There is no half-size packet for current Packet8bf.
+ // TODO: support as SSE path.
+ typedef Packet8bf half;
+ enum {
+ Vectorizable = 1,
+ AlignedOnScalar = 1,
+ size = 8,
+ HasHalfPacket = 0,
+
+ HasCmp = 1,
+ HasAdd = 1,
+ HasSub = 1,
+ HasMul = 1,
+ HasDiv = 1,
+ HasSin = EIGEN_FAST_MATH,
+ HasCos = EIGEN_FAST_MATH,
+ HasNegate = 1,
+ HasAbs = 1,
+ HasAbs2 = 0,
+ HasMin = 1,
+ HasMax = 1,
+ HasConj = 1,
+ HasSetLinear = 0,
+ HasLog = 1,
+ HasLog1p = 1,
+ HasExpm1 = 1,
+ HasExp = 1,
+ HasSqrt = 1,
+ HasRsqrt = 1,
+ HasTanh = EIGEN_FAST_MATH,
+ HasErf = EIGEN_FAST_MATH,
+ HasBlend = 0,
+ HasRound = 1,
+ HasFloor = 1,
+ HasCeil = 1,
+ HasRint = 1,
+ HasBessel = 1,
+ HasNdtri = 1
+ };
+};
+
+template<> struct packet_traits<int> : default_packet_traits
+{
+ typedef Packet8i type;
+ typedef Packet4i half;
+ enum {
+ Vectorizable = 1,
+ AlignedOnScalar = 1,
+ HasCmp = 1,
+ HasDiv = 1,
+ size=8
+ };
+};
+
+#ifdef EIGEN_VECTORIZE_AVX2
+template<> struct packet_traits<int64_t> : default_packet_traits
+{
+ typedef Packet4l type;
+ // There is no half-size packet for current Packet4l.
+ // TODO: support as SSE path.
+ typedef Packet4l half;
+ enum {
+ Vectorizable = 1,
+ AlignedOnScalar = 1,
+ HasCmp = 1,
+ size=4,
+
+ // requires AVX512
+ HasShift = 0,
+ };
+};
+#endif
+
+#endif
+
+template<> struct scalar_div_cost<float,true> { enum { value = 14 }; };
+template<> struct scalar_div_cost<double,true> { enum { value = 16 }; };
+
+template<> struct unpacket_traits<Packet8f> {
+ typedef float type;
+ typedef Packet4f half;
+ typedef Packet8i integer_packet;
+ typedef uint8_t mask_t;
+ enum {size=8, alignment=Aligned32, vectorizable=true, masked_load_available=true, masked_store_available=true
+#ifdef EIGEN_VECTORIZE_AVX512
+ , masked_fpops_available=true
+#endif
+ };
+};
+template<> struct unpacket_traits<Packet4d> {
+ typedef double type;
+ typedef Packet2d half;
+ enum {size=4, alignment=Aligned32, vectorizable=true, masked_load_available=false, masked_store_available=false};
+};
+template<> struct unpacket_traits<Packet8i> {
+ typedef int type;
+ typedef Packet4i half;
+ enum {size=8, alignment=Aligned32, vectorizable=true, masked_load_available=false, masked_store_available=false};
+};
+#ifdef EIGEN_VECTORIZE_AVX2
+template<> struct unpacket_traits<Packet4l> {
+ typedef int64_t type;
+ typedef Packet4l half;
+ enum {size=4, alignment=Aligned32, vectorizable=true, masked_load_available=false, masked_store_available=false};
+};
+#endif
+template<> struct unpacket_traits<Packet8bf> {
+ typedef bfloat16 type;
+ typedef Packet8bf half;
+ enum {size=8, alignment=Aligned16, vectorizable=true, masked_load_available=false, masked_store_available=false};
+};
+
+// Helper function for bit packing snippet of low precision comparison.
+// It packs the flags from 16x16 to 8x16.
+EIGEN_STRONG_INLINE __m128i Pack16To8(Packet8f rf) {
+ return _mm_packs_epi32(_mm256_extractf128_si256(_mm256_castps_si256(rf), 0),
+ _mm256_extractf128_si256(_mm256_castps_si256(rf), 1));
+}
+
+#ifdef EIGEN_VECTORIZE_AVX2
+template <>
+EIGEN_STRONG_INLINE Packet4l pset1<Packet4l>(const int64_t& from) {
+ return _mm256_set1_epi64x(from);
+}
+template <>
+EIGEN_STRONG_INLINE Packet4l pzero(const Packet4l& /*a*/) {
+ return _mm256_setzero_si256();
+}
+template <>
+EIGEN_STRONG_INLINE Packet4l peven_mask(const Packet4l& /*a*/) {
+ return _mm256_set_epi64x(0ll, -1ll, 0ll, -1ll);
+}
+template <>
+EIGEN_STRONG_INLINE Packet4l pload1<Packet4l>(const int64_t* from) {
+ return _mm256_set1_epi64x(*from);
+}
+template <>
+EIGEN_STRONG_INLINE Packet4l padd<Packet4l>(const Packet4l& a, const Packet4l& b) {
+ return _mm256_add_epi64(a, b);
+}
+template <>
+EIGEN_STRONG_INLINE Packet4l plset<Packet4l>(const int64_t& a) {
+ return padd(pset1<Packet4l>(a), Packet4l(_mm256_set_epi64x(3ll, 2ll, 1ll, 0ll)));
+}
+template <>
+EIGEN_STRONG_INLINE Packet4l psub<Packet4l>(const Packet4l& a, const Packet4l& b) {
+ return _mm256_sub_epi64(a, b);
+}
+template <>
+EIGEN_STRONG_INLINE Packet4l pnegate(const Packet4l& a) {
+ return psub(pzero(a), a);
+}
+template <>
+EIGEN_STRONG_INLINE Packet4l pconj(const Packet4l& a) {
+ return a;
+}
+template <>
+EIGEN_STRONG_INLINE Packet4l pcmp_le(const Packet4l& a, const Packet4l& b) {
+ return _mm256_xor_si256(_mm256_cmpgt_epi64(a, b), _mm256_set1_epi32(-1));
+}
+template <>
+EIGEN_STRONG_INLINE Packet4l pcmp_lt(const Packet4l& a, const Packet4l& b) {
+ return _mm256_cmpgt_epi64(b, a);
+}
+template <>
+EIGEN_STRONG_INLINE Packet4l pcmp_eq(const Packet4l& a, const Packet4l& b) {
+ return _mm256_cmpeq_epi64(a, b);
+}
+template <>
+EIGEN_STRONG_INLINE Packet4l ptrue<Packet4l>(const Packet4l& a) {
+ return _mm256_cmpeq_epi64(a, a);
+}
+template <>
+EIGEN_STRONG_INLINE Packet4l pand<Packet4l>(const Packet4l& a, const Packet4l& b) {
+ return _mm256_and_si256(a, b);
+}
+template <>
+EIGEN_STRONG_INLINE Packet4l por<Packet4l>(const Packet4l& a, const Packet4l& b) {
+ return _mm256_or_si256(a, b);
+}
+template <>
+EIGEN_STRONG_INLINE Packet4l pxor<Packet4l>(const Packet4l& a, const Packet4l& b) {
+ return _mm256_xor_si256(a, b);
+}
+template <>
+EIGEN_STRONG_INLINE Packet4l pandnot<Packet4l>(const Packet4l& a, const Packet4l& b) {
+ return _mm256_andnot_si256(b, a);
+}
+template <int N>
+EIGEN_STRONG_INLINE Packet4l plogical_shift_right(Packet4l a) {
+ return _mm256_srli_epi64(a, N);
+}
+template <int N>
+EIGEN_STRONG_INLINE Packet4l plogical_shift_left(Packet4l a) {
+ return _mm256_slli_epi64(a, N);
+}
+template <>
+EIGEN_STRONG_INLINE Packet4l pload<Packet4l>(const int64_t* from) {
+ EIGEN_DEBUG_ALIGNED_LOAD return _mm256_load_si256(reinterpret_cast<const __m256i*>(from));
+}
+template <>
+EIGEN_STRONG_INLINE Packet4l ploadu<Packet4l>(const int64_t* from) {
+ EIGEN_DEBUG_UNALIGNED_LOAD return _mm256_loadu_si256(reinterpret_cast<const __m256i*>(from));
+}
+// Loads 2 int64_ts from memory a returns the packet {a0, a0, a1, a1}
+template <>
+EIGEN_STRONG_INLINE Packet4l ploaddup<Packet4l>(const int64_t* from) {
+ const Packet4l a = _mm256_castsi128_si256(_mm_loadu_si128(reinterpret_cast<const __m128i*>(from)));
+ return _mm256_permutevar8x32_epi32(a, _mm256_setr_epi32(0, 1, 0, 1, 2, 3, 2, 3));
+}
+template <>
+EIGEN_STRONG_INLINE void pstore<int64_t>(int64_t* to, const Packet4l& from) {
+ EIGEN_DEBUG_ALIGNED_STORE _mm256_storeu_si256(reinterpret_cast<__m256i*>(to), from);
+}
+template <>
+EIGEN_STRONG_INLINE void pstoreu<int64_t>(int64_t* to, const Packet4l& from) {
+ EIGEN_DEBUG_UNALIGNED_STORE _mm256_storeu_si256(reinterpret_cast<__m256i*>(to), from);
+}
+template <>
+EIGEN_DEVICE_FUNC inline Packet4l pgather<int64_t, Packet4l>(const int64_t* from, Index stride) {
+ return _mm256_set_epi64x(from[3 * stride], from[2 * stride], from[1 * stride], from[0 * stride]);
+}
+template <>
+EIGEN_DEVICE_FUNC inline void pscatter<int64_t, Packet4l>(int64_t* to, const Packet4l& from, Index stride) {
+ __m128i low = _mm256_extractf128_si256(from, 0);
+ to[stride * 0] = _mm_extract_epi64(low, 0);
+ to[stride * 1] = _mm_extract_epi64(low, 1);
+
+ __m128i high = _mm256_extractf128_si256(from, 1);
+ to[stride * 2] = _mm_extract_epi64(high, 0);
+ to[stride * 3] = _mm_extract_epi64(high, 1);
+}
+template <>
+EIGEN_STRONG_INLINE void pstore1<Packet4l>(int64_t* to, const int64_t& a) {
+ Packet4l pa = pset1<Packet4l>(a);
+ pstore(to, pa);
+}
+template <>
+EIGEN_STRONG_INLINE int64_t pfirst<Packet4l>(const Packet4l& a) {
+ return _mm_cvtsi128_si64(_mm256_castsi256_si128(a));
+}
+template <>
+EIGEN_STRONG_INLINE int64_t predux<Packet4l>(const Packet4l& a) {
+ __m128i r = _mm_add_epi64(_mm256_castsi256_si128(a), _mm256_extractf128_si256(a, 1));
+ return _mm_extract_epi64(r, 0) + _mm_extract_epi64(r, 1);
+}
+#define MM256_SHUFFLE_EPI64(A, B, M) _mm256_shuffle_pd(_mm256_castsi256_pd(A), _mm256_castsi256_pd(B), M)
+EIGEN_DEVICE_FUNC inline void ptranspose(PacketBlock<Packet4l, 4>& kernel) {
+ __m256d T0 = MM256_SHUFFLE_EPI64(kernel.packet[0], kernel.packet[1], 15);
+ __m256d T1 = MM256_SHUFFLE_EPI64(kernel.packet[0], kernel.packet[1], 0);
+ __m256d T2 = MM256_SHUFFLE_EPI64(kernel.packet[2], kernel.packet[3], 15);
+ __m256d T3 = MM256_SHUFFLE_EPI64(kernel.packet[2], kernel.packet[3], 0);
+
+ kernel.packet[1] = _mm256_castpd_si256(_mm256_permute2f128_pd(T0, T2, 32));
+ kernel.packet[3] = _mm256_castpd_si256(_mm256_permute2f128_pd(T0, T2, 49));
+ kernel.packet[0] = _mm256_castpd_si256(_mm256_permute2f128_pd(T1, T3, 32));
+ kernel.packet[2] = _mm256_castpd_si256(_mm256_permute2f128_pd(T1, T3, 49));
+}
+template <>
+EIGEN_STRONG_INLINE Packet4l pmin<Packet4l>(const Packet4l& a, const Packet4l& b) {
+ __m256i cmp = _mm256_cmpgt_epi64(a, b);
+ __m256i a_min = _mm256_andnot_si256(cmp, a);
+ __m256i b_min = _mm256_and_si256(cmp, b);
+ return Packet4l(_mm256_or_si256(a_min, b_min));
+}
+template <>
+EIGEN_STRONG_INLINE Packet4l pmax<Packet4l>(const Packet4l& a, const Packet4l& b) {
+ __m256i cmp = _mm256_cmpgt_epi64(a, b);
+ __m256i a_min = _mm256_and_si256(cmp, a);
+ __m256i b_min = _mm256_andnot_si256(cmp, b);
+ return Packet4l(_mm256_or_si256(a_min, b_min));
+}
+template <>
+EIGEN_STRONG_INLINE Packet4l pabs<Packet4l>(const Packet4l& a) {
+ Packet4l pz = pzero<Packet4l>(a);
+ Packet4l cmp = _mm256_cmpgt_epi64(a, pz);
+ return psub(cmp, pxor(a, cmp));
+}
+template <>
+EIGEN_STRONG_INLINE Packet4l pmul<Packet4l>(const Packet4l& a, const Packet4l& b) {
+ // 64-bit mul requires avx512, so do this with 32-bit multiplication
+ __m256i upper32_a = _mm256_srli_epi64(a, 32);
+ __m256i upper32_b = _mm256_srli_epi64(b, 32);
+
+ // upper * lower
+ __m256i mul1 = _mm256_mul_epu32(upper32_a, b);
+ __m256i mul2 = _mm256_mul_epu32(upper32_b, a);
+ // Gives us both upper*upper and lower*lower
+ __m256i mul3 = _mm256_mul_epu32(a, b);
+
+ __m256i high = _mm256_slli_epi64(_mm256_add_epi64(mul1, mul2), 32);
+ return _mm256_add_epi64(high, mul3);
+}
+#endif
+
+template<> EIGEN_STRONG_INLINE Packet8f pset1<Packet8f>(const float& from) { return _mm256_set1_ps(from); }
+template<> EIGEN_STRONG_INLINE Packet4d pset1<Packet4d>(const double& from) { return _mm256_set1_pd(from); }
+template<> EIGEN_STRONG_INLINE Packet8i pset1<Packet8i>(const int& from) { return _mm256_set1_epi32(from); }
+
+template<> EIGEN_STRONG_INLINE Packet8f pset1frombits<Packet8f>(unsigned int from) { return _mm256_castsi256_ps(pset1<Packet8i>(from)); }
+template<> EIGEN_STRONG_INLINE Packet4d pset1frombits<Packet4d>(uint64_t from) { return _mm256_castsi256_pd(_mm256_set1_epi64x(from)); }
+
+template<> EIGEN_STRONG_INLINE Packet8f pzero(const Packet8f& /*a*/) { return _mm256_setzero_ps(); }
+template<> EIGEN_STRONG_INLINE Packet4d pzero(const Packet4d& /*a*/) { return _mm256_setzero_pd(); }
+template<> EIGEN_STRONG_INLINE Packet8i pzero(const Packet8i& /*a*/) { return _mm256_setzero_si256(); }
+
+
+template<> EIGEN_STRONG_INLINE Packet8f peven_mask(const Packet8f& /*a*/) { return _mm256_castsi256_ps(_mm256_set_epi32(0, -1, 0, -1, 0, -1, 0, -1)); }
+template<> EIGEN_STRONG_INLINE Packet8i peven_mask(const Packet8i& /*a*/) { return _mm256_set_epi32(0, -1, 0, -1, 0, -1, 0, -1); }
+template<> EIGEN_STRONG_INLINE Packet4d peven_mask(const Packet4d& /*a*/) { return _mm256_castsi256_pd(_mm256_set_epi32(0, 0, -1, -1, 0, 0, -1, -1)); }
+
+template<> EIGEN_STRONG_INLINE Packet8f pload1<Packet8f>(const float* from) { return _mm256_broadcast_ss(from); }
+template<> EIGEN_STRONG_INLINE Packet4d pload1<Packet4d>(const double* from) { return _mm256_broadcast_sd(from); }
+
+template<> EIGEN_STRONG_INLINE Packet8f padd<Packet8f>(const Packet8f& a, const Packet8f& b) { return _mm256_add_ps(a,b); }
+#ifdef EIGEN_VECTORIZE_AVX512
+template <>
+EIGEN_STRONG_INLINE Packet8f padd<Packet8f>(const Packet8f& a, const Packet8f& b, uint8_t umask) {
+ __mmask16 mask = static_cast<__mmask16>(umask & 0x00FF);
+ return _mm512_castps512_ps256(_mm512_maskz_add_ps(
+ mask,
+ _mm512_castps256_ps512(a),
+ _mm512_castps256_ps512(b)));
+}
+#endif
+template<> EIGEN_STRONG_INLINE Packet4d padd<Packet4d>(const Packet4d& a, const Packet4d& b) { return _mm256_add_pd(a,b); }
+template<> EIGEN_STRONG_INLINE Packet8i padd<Packet8i>(const Packet8i& a, const Packet8i& b) {
+#ifdef EIGEN_VECTORIZE_AVX2
+ return _mm256_add_epi32(a,b);
+#else
+ __m128i lo = _mm_add_epi32(_mm256_extractf128_si256(a, 0), _mm256_extractf128_si256(b, 0));
+ __m128i hi = _mm_add_epi32(_mm256_extractf128_si256(a, 1), _mm256_extractf128_si256(b, 1));
+ return _mm256_insertf128_si256(_mm256_castsi128_si256(lo), (hi), 1);
+#endif
+}
+
+template<> EIGEN_STRONG_INLINE Packet8f plset<Packet8f>(const float& a) { return padd(pset1<Packet8f>(a), _mm256_set_ps(7.0,6.0,5.0,4.0,3.0,2.0,1.0,0.0)); }
+template<> EIGEN_STRONG_INLINE Packet4d plset<Packet4d>(const double& a) { return padd(pset1<Packet4d>(a), _mm256_set_pd(3.0,2.0,1.0,0.0)); }
+template<> EIGEN_STRONG_INLINE Packet8i plset<Packet8i>(const int& a) { return padd(pset1<Packet8i>(a), (Packet8i)_mm256_set_epi32(7,6,5,4,3,2,1,0)); }
+
+template<> EIGEN_STRONG_INLINE Packet8f psub<Packet8f>(const Packet8f& a, const Packet8f& b) { return _mm256_sub_ps(a,b); }
+template<> EIGEN_STRONG_INLINE Packet4d psub<Packet4d>(const Packet4d& a, const Packet4d& b) { return _mm256_sub_pd(a,b); }
+template<> EIGEN_STRONG_INLINE Packet8i psub<Packet8i>(const Packet8i& a, const Packet8i& b) {
+#ifdef EIGEN_VECTORIZE_AVX2
+ return _mm256_sub_epi32(a,b);
+#else
+ __m128i lo = _mm_sub_epi32(_mm256_extractf128_si256(a, 0), _mm256_extractf128_si256(b, 0));
+ __m128i hi = _mm_sub_epi32(_mm256_extractf128_si256(a, 1), _mm256_extractf128_si256(b, 1));
+ return _mm256_insertf128_si256(_mm256_castsi128_si256(lo), (hi), 1);
+#endif
+}
+
+template<> EIGEN_STRONG_INLINE Packet8f pnegate(const Packet8f& a)
+{
+ return _mm256_sub_ps(_mm256_set1_ps(0.0),a);
+}
+template<> EIGEN_STRONG_INLINE Packet4d pnegate(const Packet4d& a)
+{
+ return _mm256_sub_pd(_mm256_set1_pd(0.0),a);
+}
+template<> EIGEN_STRONG_INLINE Packet8i pnegate(const Packet8i& a)
+{
+ return psub(pzero(a), a);
+}
+
+template<> EIGEN_STRONG_INLINE Packet8f pconj(const Packet8f& a) { return a; }
+template<> EIGEN_STRONG_INLINE Packet4d pconj(const Packet4d& a) { return a; }
+template<> EIGEN_STRONG_INLINE Packet8i pconj(const Packet8i& a) { return a; }
+
+template<> EIGEN_STRONG_INLINE Packet8f pmul<Packet8f>(const Packet8f& a, const Packet8f& b) { return _mm256_mul_ps(a,b); }
+template<> EIGEN_STRONG_INLINE Packet4d pmul<Packet4d>(const Packet4d& a, const Packet4d& b) { return _mm256_mul_pd(a,b); }
+template<> EIGEN_STRONG_INLINE Packet8i pmul<Packet8i>(const Packet8i& a, const Packet8i& b) {
+#ifdef EIGEN_VECTORIZE_AVX2
+ return _mm256_mullo_epi32(a,b);
+#else
+ const __m128i lo = _mm_mullo_epi32(_mm256_extractf128_si256(a, 0), _mm256_extractf128_si256(b, 0));
+ const __m128i hi = _mm_mullo_epi32(_mm256_extractf128_si256(a, 1), _mm256_extractf128_si256(b, 1));
+ return _mm256_insertf128_si256(_mm256_castsi128_si256(lo), (hi), 1);
+#endif
+}
+
+template<> EIGEN_STRONG_INLINE Packet8f pdiv<Packet8f>(const Packet8f& a, const Packet8f& b) { return _mm256_div_ps(a,b); }
+template<> EIGEN_STRONG_INLINE Packet4d pdiv<Packet4d>(const Packet4d& a, const Packet4d& b) { return _mm256_div_pd(a,b); }
+
+template<> EIGEN_STRONG_INLINE Packet8i pdiv<Packet8i>(const Packet8i& a, const Packet8i& b)
+{
+#ifdef EIGEN_VECTORIZE_AVX512
+ return _mm512_cvttpd_epi32(_mm512_div_pd(_mm512_cvtepi32_pd(a), _mm512_cvtepi32_pd(b)));
+#else
+ Packet4i lo = pdiv<Packet4i>(_mm256_extractf128_si256(a, 0), _mm256_extractf128_si256(b, 0));
+ Packet4i hi = pdiv<Packet4i>(_mm256_extractf128_si256(a, 1), _mm256_extractf128_si256(b, 1));
+ return _mm256_insertf128_si256(_mm256_castsi128_si256(lo), hi, 1);
+#endif
+}
+
+#ifdef EIGEN_VECTORIZE_FMA
+template <>
+EIGEN_STRONG_INLINE Packet8f pmadd(const Packet8f& a, const Packet8f& b, const Packet8f& c) {
+ return _mm256_fmadd_ps(a, b, c);
+}
+template <>
+EIGEN_STRONG_INLINE Packet4d pmadd(const Packet4d& a, const Packet4d& b, const Packet4d& c) {
+ return _mm256_fmadd_pd(a, b, c);
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet8f pmsub(const Packet8f& a, const Packet8f& b, const Packet8f& c) {
+ return _mm256_fmsub_ps(a, b, c);
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet4d pmsub(const Packet4d& a, const Packet4d& b, const Packet4d& c) {
+ return _mm256_fmsub_pd(a, b, c);
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet8f pnmadd(const Packet8f& a, const Packet8f& b, const Packet8f& c) {
+ return _mm256_fnmadd_ps(a, b, c);
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet4d pnmadd(const Packet4d& a, const Packet4d& b, const Packet4d& c) {
+ return _mm256_fnmadd_pd(a, b, c);
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet8f pnmsub(const Packet8f& a, const Packet8f& b, const Packet8f& c) {
+ return _mm256_fnmsub_ps(a, b, c);
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet4d pnmsub(const Packet4d& a, const Packet4d& b, const Packet4d& c) {
+ return _mm256_fnmsub_pd(a, b, c);
+}
+
+#endif
+
+template<> EIGEN_STRONG_INLINE Packet8f pcmp_le(const Packet8f& a, const Packet8f& b) { return _mm256_cmp_ps(a,b,_CMP_LE_OQ); }
+template<> EIGEN_STRONG_INLINE Packet8f pcmp_lt(const Packet8f& a, const Packet8f& b) { return _mm256_cmp_ps(a,b,_CMP_LT_OQ); }
+template<> EIGEN_STRONG_INLINE Packet8f pcmp_lt_or_nan(const Packet8f& a, const Packet8f& b) { return _mm256_cmp_ps(a, b, _CMP_NGE_UQ); }
+template<> EIGEN_STRONG_INLINE Packet8f pcmp_eq(const Packet8f& a, const Packet8f& b) { return _mm256_cmp_ps(a,b,_CMP_EQ_OQ); }
+
+template<> EIGEN_STRONG_INLINE Packet4d pcmp_le(const Packet4d& a, const Packet4d& b) { return _mm256_cmp_pd(a,b,_CMP_LE_OQ); }
+template<> EIGEN_STRONG_INLINE Packet4d pcmp_lt(const Packet4d& a, const Packet4d& b) { return _mm256_cmp_pd(a,b,_CMP_LT_OQ); }
+template<> EIGEN_STRONG_INLINE Packet4d pcmp_lt_or_nan(const Packet4d& a, const Packet4d& b) { return _mm256_cmp_pd(a, b, _CMP_NGE_UQ); }
+template<> EIGEN_STRONG_INLINE Packet4d pcmp_eq(const Packet4d& a, const Packet4d& b) { return _mm256_cmp_pd(a,b,_CMP_EQ_OQ); }
+
+template<> EIGEN_STRONG_INLINE Packet8i pcmp_le(const Packet8i& a, const Packet8i& b) {
+#ifdef EIGEN_VECTORIZE_AVX2
+ return _mm256_xor_si256(_mm256_cmpgt_epi32(a,b), _mm256_set1_epi32(-1));
+#else
+ __m128i lo = _mm_cmpgt_epi32(_mm256_extractf128_si256(a, 0), _mm256_extractf128_si256(b, 0));
+ lo = _mm_xor_si128(lo, _mm_set1_epi32(-1));
+ __m128i hi = _mm_cmpgt_epi32(_mm256_extractf128_si256(a, 1), _mm256_extractf128_si256(b, 1));
+ hi = _mm_xor_si128(hi, _mm_set1_epi32(-1));
+ return _mm256_insertf128_si256(_mm256_castsi128_si256(lo), (hi), 1);
+#endif
+}
+template<> EIGEN_STRONG_INLINE Packet8i pcmp_lt(const Packet8i& a, const Packet8i& b) {
+#ifdef EIGEN_VECTORIZE_AVX2
+ return _mm256_cmpgt_epi32(b,a);
+#else
+ __m128i lo = _mm_cmpgt_epi32(_mm256_extractf128_si256(b, 0), _mm256_extractf128_si256(a, 0));
+ __m128i hi = _mm_cmpgt_epi32(_mm256_extractf128_si256(b, 1), _mm256_extractf128_si256(a, 1));
+ return _mm256_insertf128_si256(_mm256_castsi128_si256(lo), (hi), 1);
+#endif
+}
+template<> EIGEN_STRONG_INLINE Packet8i pcmp_eq(const Packet8i& a, const Packet8i& b) {
+#ifdef EIGEN_VECTORIZE_AVX2
+ return _mm256_cmpeq_epi32(a,b);
+#else
+ __m128i lo = _mm_cmpeq_epi32(_mm256_extractf128_si256(a, 0), _mm256_extractf128_si256(b, 0));
+ __m128i hi = _mm_cmpeq_epi32(_mm256_extractf128_si256(a, 1), _mm256_extractf128_si256(b, 1));
+ return _mm256_insertf128_si256(_mm256_castsi128_si256(lo), (hi), 1);
+#endif
+}
+
+template<> EIGEN_STRONG_INLINE Packet8f pmin<Packet8f>(const Packet8f& a, const Packet8f& b) {
+#if EIGEN_COMP_GNUC && EIGEN_COMP_GNUC < 63
+ // There appears to be a bug in GCC, by which the optimizer may flip
+ // the argument order in calls to _mm_min_ps/_mm_max_ps, so we have to
+ // resort to inline ASM here. This is supposed to be fixed in gcc6.3,
+ // see also: https://gcc.gnu.org/bugzilla/show_bug.cgi?id=72867
+ Packet8f res;
+ asm("vminps %[a], %[b], %[res]" : [res] "=x" (res) : [a] "x" (a), [b] "x" (b));
+ return res;
+#else
+ // Arguments are swapped to match NaN propagation behavior of std::min.
+ return _mm256_min_ps(b,a);
+#endif
+}
+template<> EIGEN_STRONG_INLINE Packet4d pmin<Packet4d>(const Packet4d& a, const Packet4d& b) {
+#if EIGEN_COMP_GNUC && EIGEN_COMP_GNUC < 63
+ // See pmin above
+ Packet4d res;
+ asm("vminpd %[a], %[b], %[res]" : [res] "=x" (res) : [a] "x" (a), [b] "x" (b));
+ return res;
+#else
+ // Arguments are swapped to match NaN propagation behavior of std::min.
+ return _mm256_min_pd(b,a);
+#endif
+}
+template<> EIGEN_STRONG_INLINE Packet8i pmin<Packet8i>(const Packet8i& a, const Packet8i& b) {
+#ifdef EIGEN_VECTORIZE_AVX2
+ return _mm256_min_epi32(a, b);
+#else
+ __m128i lo = _mm_min_epi32(_mm256_extractf128_si256(a, 0), _mm256_extractf128_si256(b, 0));
+ __m128i hi = _mm_min_epi32(_mm256_extractf128_si256(a, 1), _mm256_extractf128_si256(b, 1));
+ return _mm256_insertf128_si256(_mm256_castsi128_si256(lo), (hi), 1);
+#endif
+}
+
+template<> EIGEN_STRONG_INLINE Packet8f pmax<Packet8f>(const Packet8f& a, const Packet8f& b) {
+#if EIGEN_COMP_GNUC && EIGEN_COMP_GNUC < 63
+ // See pmin above
+ Packet8f res;
+ asm("vmaxps %[a], %[b], %[res]" : [res] "=x" (res) : [a] "x" (a), [b] "x" (b));
+ return res;
+#else
+ // Arguments are swapped to match NaN propagation behavior of std::max.
+ return _mm256_max_ps(b,a);
+#endif
+}
+template<> EIGEN_STRONG_INLINE Packet4d pmax<Packet4d>(const Packet4d& a, const Packet4d& b) {
+#if EIGEN_COMP_GNUC && EIGEN_COMP_GNUC < 63
+ // See pmin above
+ Packet4d res;
+ asm("vmaxpd %[a], %[b], %[res]" : [res] "=x" (res) : [a] "x" (a), [b] "x" (b));
+ return res;
+#else
+ // Arguments are swapped to match NaN propagation behavior of std::max.
+ return _mm256_max_pd(b,a);
+#endif
+}
+template<> EIGEN_STRONG_INLINE Packet8i pmax<Packet8i>(const Packet8i& a, const Packet8i& b) {
+#ifdef EIGEN_VECTORIZE_AVX2
+ return _mm256_max_epi32(a, b);
+#else
+ __m128i lo = _mm_max_epi32(_mm256_extractf128_si256(a, 0), _mm256_extractf128_si256(b, 0));
+ __m128i hi = _mm_max_epi32(_mm256_extractf128_si256(a, 1), _mm256_extractf128_si256(b, 1));
+ return _mm256_insertf128_si256(_mm256_castsi128_si256(lo), (hi), 1);
+#endif
+}
+
+#ifdef EIGEN_VECTORIZE_AVX2
+template<> EIGEN_STRONG_INLINE Packet8i psign(const Packet8i& a) {
+ return _mm256_sign_epi32(_mm256_set1_epi32(1), a);
+}
+#endif
+
+// Add specializations for min/max with prescribed NaN progation.
+template<>
+EIGEN_STRONG_INLINE Packet8f pmin<PropagateNumbers, Packet8f>(const Packet8f& a, const Packet8f& b) {
+ return pminmax_propagate_numbers(a, b, pmin<Packet8f>);
+}
+template<>
+EIGEN_STRONG_INLINE Packet4d pmin<PropagateNumbers, Packet4d>(const Packet4d& a, const Packet4d& b) {
+ return pminmax_propagate_numbers(a, b, pmin<Packet4d>);
+}
+template<>
+EIGEN_STRONG_INLINE Packet8f pmax<PropagateNumbers, Packet8f>(const Packet8f& a, const Packet8f& b) {
+ return pminmax_propagate_numbers(a, b, pmax<Packet8f>);
+}
+template<>
+EIGEN_STRONG_INLINE Packet4d pmax<PropagateNumbers, Packet4d>(const Packet4d& a, const Packet4d& b) {
+ return pminmax_propagate_numbers(a, b, pmax<Packet4d>);
+}
+template<>
+EIGEN_STRONG_INLINE Packet8f pmin<PropagateNaN, Packet8f>(const Packet8f& a, const Packet8f& b) {
+ return pminmax_propagate_nan(a, b, pmin<Packet8f>);
+}
+template<>
+EIGEN_STRONG_INLINE Packet4d pmin<PropagateNaN, Packet4d>(const Packet4d& a, const Packet4d& b) {
+ return pminmax_propagate_nan(a, b, pmin<Packet4d>);
+}
+template<>
+EIGEN_STRONG_INLINE Packet8f pmax<PropagateNaN, Packet8f>(const Packet8f& a, const Packet8f& b) {
+ return pminmax_propagate_nan(a, b, pmax<Packet8f>);
+}
+template<>
+EIGEN_STRONG_INLINE Packet4d pmax<PropagateNaN, Packet4d>(const Packet4d& a, const Packet4d& b) {
+ return pminmax_propagate_nan(a, b, pmax<Packet4d>);
+}
+
+template<> EIGEN_STRONG_INLINE Packet8f print<Packet8f>(const Packet8f& a) { return _mm256_round_ps(a, _MM_FROUND_CUR_DIRECTION); }
+template<> EIGEN_STRONG_INLINE Packet4d print<Packet4d>(const Packet4d& a) { return _mm256_round_pd(a, _MM_FROUND_CUR_DIRECTION); }
+
+template<> EIGEN_STRONG_INLINE Packet8f pceil<Packet8f>(const Packet8f& a) { return _mm256_ceil_ps(a); }
+template<> EIGEN_STRONG_INLINE Packet4d pceil<Packet4d>(const Packet4d& a) { return _mm256_ceil_pd(a); }
+
+template<> EIGEN_STRONG_INLINE Packet8f pfloor<Packet8f>(const Packet8f& a) { return _mm256_floor_ps(a); }
+template<> EIGEN_STRONG_INLINE Packet4d pfloor<Packet4d>(const Packet4d& a) { return _mm256_floor_pd(a); }
+
+
+template<> EIGEN_STRONG_INLINE Packet8i ptrue<Packet8i>(const Packet8i& a) {
+#ifdef EIGEN_VECTORIZE_AVX2
+ // vpcmpeqd has lower latency than the more general vcmpps
+ return _mm256_cmpeq_epi32(a,a);
+#else
+ const __m256 b = _mm256_castsi256_ps(a);
+ return _mm256_castps_si256(_mm256_cmp_ps(b,b,_CMP_TRUE_UQ));
+#endif
+}
+
+template<> EIGEN_STRONG_INLINE Packet8f ptrue<Packet8f>(const Packet8f& a) {
+#ifdef EIGEN_VECTORIZE_AVX2
+ // vpcmpeqd has lower latency than the more general vcmpps
+ const __m256i b = _mm256_castps_si256(a);
+ return _mm256_castsi256_ps(_mm256_cmpeq_epi32(b,b));
+#else
+ return _mm256_cmp_ps(a,a,_CMP_TRUE_UQ);
+#endif
+}
+
+template<> EIGEN_STRONG_INLINE Packet4d ptrue<Packet4d>(const Packet4d& a) {
+#ifdef EIGEN_VECTORIZE_AVX2
+ // vpcmpeqq has lower latency than the more general vcmppd
+ const __m256i b = _mm256_castpd_si256(a);
+ return _mm256_castsi256_pd(_mm256_cmpeq_epi64(b,b));
+#else
+ return _mm256_cmp_pd(a,a,_CMP_TRUE_UQ);
+#endif
+}
+
+template<> EIGEN_STRONG_INLINE Packet8f pand<Packet8f>(const Packet8f& a, const Packet8f& b) { return _mm256_and_ps(a,b); }
+template<> EIGEN_STRONG_INLINE Packet4d pand<Packet4d>(const Packet4d& a, const Packet4d& b) { return _mm256_and_pd(a,b); }
+template<> EIGEN_STRONG_INLINE Packet8i pand<Packet8i>(const Packet8i& a, const Packet8i& b) {
+#ifdef EIGEN_VECTORIZE_AVX2
+ return _mm256_and_si256(a,b);
+#else
+ return _mm256_castps_si256(_mm256_and_ps(_mm256_castsi256_ps(a),_mm256_castsi256_ps(b)));
+#endif
+}
+
+template<> EIGEN_STRONG_INLINE Packet8f por<Packet8f>(const Packet8f& a, const Packet8f& b) { return _mm256_or_ps(a,b); }
+template<> EIGEN_STRONG_INLINE Packet4d por<Packet4d>(const Packet4d& a, const Packet4d& b) { return _mm256_or_pd(a,b); }
+template<> EIGEN_STRONG_INLINE Packet8i por<Packet8i>(const Packet8i& a, const Packet8i& b) {
+#ifdef EIGEN_VECTORIZE_AVX2
+ return _mm256_or_si256(a,b);
+#else
+ return _mm256_castps_si256(_mm256_or_ps(_mm256_castsi256_ps(a),_mm256_castsi256_ps(b)));
+#endif
+}
+
+template<> EIGEN_STRONG_INLINE Packet8f pxor<Packet8f>(const Packet8f& a, const Packet8f& b) { return _mm256_xor_ps(a,b); }
+template<> EIGEN_STRONG_INLINE Packet4d pxor<Packet4d>(const Packet4d& a, const Packet4d& b) { return _mm256_xor_pd(a,b); }
+template<> EIGEN_STRONG_INLINE Packet8i pxor<Packet8i>(const Packet8i& a, const Packet8i& b) {
+#ifdef EIGEN_VECTORIZE_AVX2
+ return _mm256_xor_si256(a,b);
+#else
+ return _mm256_castps_si256(_mm256_xor_ps(_mm256_castsi256_ps(a),_mm256_castsi256_ps(b)));
+#endif
+}
+
+template<> EIGEN_STRONG_INLINE Packet8f pandnot<Packet8f>(const Packet8f& a, const Packet8f& b) { return _mm256_andnot_ps(b,a); }
+template<> EIGEN_STRONG_INLINE Packet4d pandnot<Packet4d>(const Packet4d& a, const Packet4d& b) { return _mm256_andnot_pd(b,a); }
+template<> EIGEN_STRONG_INLINE Packet8i pandnot<Packet8i>(const Packet8i& a, const Packet8i& b) {
+#ifdef EIGEN_VECTORIZE_AVX2
+ return _mm256_andnot_si256(b,a);
+#else
+ return _mm256_castps_si256(_mm256_andnot_ps(_mm256_castsi256_ps(b),_mm256_castsi256_ps(a)));
+#endif
+}
+
+template<> EIGEN_STRONG_INLINE Packet8f pround<Packet8f>(const Packet8f& a)
+{
+ const Packet8f mask = pset1frombits<Packet8f>(static_cast<numext::uint32_t>(0x80000000u));
+ const Packet8f prev0dot5 = pset1frombits<Packet8f>(static_cast<numext::uint32_t>(0x3EFFFFFFu));
+ return _mm256_round_ps(padd(por(pand(a, mask), prev0dot5), a), _MM_FROUND_TO_ZERO);
+}
+template<> EIGEN_STRONG_INLINE Packet4d pround<Packet4d>(const Packet4d& a)
+{
+ const Packet4d mask = pset1frombits<Packet4d>(static_cast<numext::uint64_t>(0x8000000000000000ull));
+ const Packet4d prev0dot5 = pset1frombits<Packet4d>(static_cast<numext::uint64_t>(0x3FDFFFFFFFFFFFFFull));
+ return _mm256_round_pd(padd(por(pand(a, mask), prev0dot5), a), _MM_FROUND_TO_ZERO);
+}
+
+template<> EIGEN_STRONG_INLINE Packet8f pselect<Packet8f>(const Packet8f& mask, const Packet8f& a, const Packet8f& b)
+{ return _mm256_blendv_ps(b,a,mask); }
+template<> EIGEN_STRONG_INLINE Packet4d pselect<Packet4d>(const Packet4d& mask, const Packet4d& a, const Packet4d& b)
+{ return _mm256_blendv_pd(b,a,mask); }
+
+template<int N> EIGEN_STRONG_INLINE Packet8i parithmetic_shift_right(Packet8i a) {
+#ifdef EIGEN_VECTORIZE_AVX2
+ return _mm256_srai_epi32(a, N);
+#else
+ __m128i lo = _mm_srai_epi32(_mm256_extractf128_si256(a, 0), N);
+ __m128i hi = _mm_srai_epi32(_mm256_extractf128_si256(a, 1), N);
+ return _mm256_insertf128_si256(_mm256_castsi128_si256(lo), (hi), 1);
+#endif
+}
+
+template<int N> EIGEN_STRONG_INLINE Packet8i plogical_shift_right(Packet8i a) {
+#ifdef EIGEN_VECTORIZE_AVX2
+ return _mm256_srli_epi32(a, N);
+#else
+ __m128i lo = _mm_srli_epi32(_mm256_extractf128_si256(a, 0), N);
+ __m128i hi = _mm_srli_epi32(_mm256_extractf128_si256(a, 1), N);
+ return _mm256_insertf128_si256(_mm256_castsi128_si256(lo), (hi), 1);
+#endif
+}
+
+template<int N> EIGEN_STRONG_INLINE Packet8i plogical_shift_left(Packet8i a) {
+#ifdef EIGEN_VECTORIZE_AVX2
+ return _mm256_slli_epi32(a, N);
+#else
+ __m128i lo = _mm_slli_epi32(_mm256_extractf128_si256(a, 0), N);
+ __m128i hi = _mm_slli_epi32(_mm256_extractf128_si256(a, 1), N);
+ return _mm256_insertf128_si256(_mm256_castsi128_si256(lo), (hi), 1);
+#endif
+}
+
+template<> EIGEN_STRONG_INLINE Packet8f pload<Packet8f>(const float* from) { EIGEN_DEBUG_ALIGNED_LOAD return _mm256_load_ps(from); }
+template<> EIGEN_STRONG_INLINE Packet4d pload<Packet4d>(const double* from) { EIGEN_DEBUG_ALIGNED_LOAD return _mm256_load_pd(from); }
+template<> EIGEN_STRONG_INLINE Packet8i pload<Packet8i>(const int* from) { EIGEN_DEBUG_ALIGNED_LOAD return _mm256_load_si256(reinterpret_cast<const __m256i*>(from)); }
+
+template<> EIGEN_STRONG_INLINE Packet8f ploadu<Packet8f>(const float* from) { EIGEN_DEBUG_UNALIGNED_LOAD return _mm256_loadu_ps(from); }
+template<> EIGEN_STRONG_INLINE Packet4d ploadu<Packet4d>(const double* from) { EIGEN_DEBUG_UNALIGNED_LOAD return _mm256_loadu_pd(from); }
+template<> EIGEN_STRONG_INLINE Packet8i ploadu<Packet8i>(const int* from) { EIGEN_DEBUG_UNALIGNED_LOAD return _mm256_loadu_si256(reinterpret_cast<const __m256i*>(from)); }
+
+template<> EIGEN_STRONG_INLINE Packet8f ploadu<Packet8f>(const float* from, uint8_t umask) {
+#ifdef EIGEN_VECTORIZE_AVX512
+ __mmask16 mask = static_cast<__mmask16>(umask & 0x00FF);
+ EIGEN_DEBUG_UNALIGNED_LOAD return _mm512_castps512_ps256(_mm512_maskz_loadu_ps(mask, from));
+#else
+ Packet8i mask = _mm256_set1_epi8(static_cast<char>(umask));
+ const Packet8i bit_mask = _mm256_set_epi32(0xffffff7f, 0xffffffbf, 0xffffffdf, 0xffffffef, 0xfffffff7, 0xfffffffb, 0xfffffffd, 0xfffffffe);
+ mask = por<Packet8i>(mask, bit_mask);
+ mask = pcmp_eq<Packet8i>(mask, _mm256_set1_epi32(0xffffffff));
+ EIGEN_DEBUG_UNALIGNED_LOAD return _mm256_maskload_ps(from, mask);
+#endif
+}
+
+// Loads 4 floats from memory a returns the packet {a0, a0 a1, a1, a2, a2, a3, a3}
+template<> EIGEN_STRONG_INLINE Packet8f ploaddup<Packet8f>(const float* from)
+{
+ // TODO try to find a way to avoid the need of a temporary register
+// Packet8f tmp = _mm256_castps128_ps256(_mm_loadu_ps(from));
+// tmp = _mm256_insertf128_ps(tmp, _mm_movehl_ps(_mm256_castps256_ps128(tmp),_mm256_castps256_ps128(tmp)), 1);
+// return _mm256_unpacklo_ps(tmp,tmp);
+
+ // _mm256_insertf128_ps is very slow on Haswell, thus:
+ Packet8f tmp = _mm256_broadcast_ps((const __m128*)(const void*)from);
+ // mimic an "inplace" permutation of the lower 128bits using a blend
+ tmp = _mm256_blend_ps(tmp,_mm256_castps128_ps256(_mm_permute_ps( _mm256_castps256_ps128(tmp), _MM_SHUFFLE(1,0,1,0))), 15);
+ // then we can perform a consistent permutation on the global register to get everything in shape:
+ return _mm256_permute_ps(tmp, _MM_SHUFFLE(3,3,2,2));
+}
+// Loads 2 doubles from memory a returns the packet {a0, a0, a1, a1}
+template<> EIGEN_STRONG_INLINE Packet4d ploaddup<Packet4d>(const double* from)
+{
+ Packet4d tmp = _mm256_broadcast_pd((const __m128d*)(const void*)from);
+ return _mm256_permute_pd(tmp, 3<<2);
+}
+// Loads 4 integers from memory a returns the packet {a0, a0, a1, a1, a2, a2, a3, a3}
+template<> EIGEN_STRONG_INLINE Packet8i ploaddup<Packet8i>(const int* from)
+{
+#ifdef EIGEN_VECTORIZE_AVX2
+ const Packet8i a = _mm256_castsi128_si256(ploadu<Packet4i>(from));
+ return _mm256_permutevar8x32_epi32(a, _mm256_setr_epi32(0, 0, 1, 1, 2, 2, 3, 3));
+#else
+ __m256 tmp = _mm256_broadcast_ps((const __m128*)(const void*)from);
+ // mimic an "inplace" permutation of the lower 128bits using a blend
+ tmp = _mm256_blend_ps(tmp,_mm256_castps128_ps256(_mm_permute_ps( _mm256_castps256_ps128(tmp), _MM_SHUFFLE(1,0,1,0))), 15);
+ // then we can perform a consistent permutation on the global register to get everything in shape:
+ return _mm256_castps_si256(_mm256_permute_ps(tmp, _MM_SHUFFLE(3,3,2,2)));
+#endif
+}
+
+// Loads 2 floats from memory a returns the packet {a0, a0 a0, a0, a1, a1, a1, a1}
+template<> EIGEN_STRONG_INLINE Packet8f ploadquad<Packet8f>(const float* from)
+{
+ Packet8f tmp = _mm256_castps128_ps256(_mm_broadcast_ss(from));
+ return _mm256_insertf128_ps(tmp, _mm_broadcast_ss(from+1), 1);
+}
+template<> EIGEN_STRONG_INLINE Packet8i ploadquad<Packet8i>(const int* from)
+{
+ return _mm256_insertf128_si256(_mm256_set1_epi32(*from), _mm_set1_epi32(*(from+1)), 1);
+}
+
+template<> EIGEN_STRONG_INLINE void pstore<float>(float* to, const Packet8f& from) { EIGEN_DEBUG_ALIGNED_STORE _mm256_store_ps(to, from); }
+template<> EIGEN_STRONG_INLINE void pstore<double>(double* to, const Packet4d& from) { EIGEN_DEBUG_ALIGNED_STORE _mm256_store_pd(to, from); }
+template<> EIGEN_STRONG_INLINE void pstore<int>(int* to, const Packet8i& from) { EIGEN_DEBUG_ALIGNED_STORE _mm256_storeu_si256(reinterpret_cast<__m256i*>(to), from); }
+
+template<> EIGEN_STRONG_INLINE void pstoreu<float>(float* to, const Packet8f& from) { EIGEN_DEBUG_UNALIGNED_STORE _mm256_storeu_ps(to, from); }
+template<> EIGEN_STRONG_INLINE void pstoreu<double>(double* to, const Packet4d& from) { EIGEN_DEBUG_UNALIGNED_STORE _mm256_storeu_pd(to, from); }
+template<> EIGEN_STRONG_INLINE void pstoreu<int>(int* to, const Packet8i& from) { EIGEN_DEBUG_UNALIGNED_STORE _mm256_storeu_si256(reinterpret_cast<__m256i*>(to), from); }
+
+template<> EIGEN_STRONG_INLINE void pstoreu<float>(float* to, const Packet8f& from, uint8_t umask) {
+#ifdef EIGEN_VECTORIZE_AVX512
+ __mmask16 mask = static_cast<__mmask16>(umask & 0x00FF);
+ EIGEN_DEBUG_UNALIGNED_STORE return _mm512_mask_storeu_ps(to, mask, _mm512_castps256_ps512(from));
+#else
+ Packet8i mask = _mm256_set1_epi8(static_cast<char>(umask));
+ const Packet8i bit_mask = _mm256_set_epi32(0xffffff7f, 0xffffffbf, 0xffffffdf, 0xffffffef, 0xfffffff7, 0xfffffffb, 0xfffffffd, 0xfffffffe);
+ mask = por<Packet8i>(mask, bit_mask);
+ mask = pcmp_eq<Packet8i>(mask, _mm256_set1_epi32(0xffffffff));
+ EIGEN_DEBUG_UNALIGNED_STORE return _mm256_maskstore_ps(to, mask, from);
+#endif
+}
+
+// NOTE: leverage _mm256_i32gather_ps and _mm256_i32gather_pd if AVX2 instructions are available
+// NOTE: for the record the following seems to be slower: return _mm256_i32gather_ps(from, _mm256_set1_epi32(stride), 4);
+template<> EIGEN_DEVICE_FUNC inline Packet8f pgather<float, Packet8f>(const float* from, Index stride)
+{
+ return _mm256_set_ps(from[7*stride], from[6*stride], from[5*stride], from[4*stride],
+ from[3*stride], from[2*stride], from[1*stride], from[0*stride]);
+}
+template<> EIGEN_DEVICE_FUNC inline Packet4d pgather<double, Packet4d>(const double* from, Index stride)
+{
+ return _mm256_set_pd(from[3*stride], from[2*stride], from[1*stride], from[0*stride]);
+}
+template<> EIGEN_DEVICE_FUNC inline Packet8i pgather<int, Packet8i>(const int* from, Index stride)
+{
+ return _mm256_set_epi32(from[7*stride], from[6*stride], from[5*stride], from[4*stride],
+ from[3*stride], from[2*stride], from[1*stride], from[0*stride]);
+}
+
+template<> EIGEN_DEVICE_FUNC inline void pscatter<float, Packet8f>(float* to, const Packet8f& from, Index stride)
+{
+ __m128 low = _mm256_extractf128_ps(from, 0);
+ to[stride*0] = _mm_cvtss_f32(low);
+ to[stride*1] = _mm_cvtss_f32(_mm_shuffle_ps(low, low, 1));
+ to[stride*2] = _mm_cvtss_f32(_mm_shuffle_ps(low, low, 2));
+ to[stride*3] = _mm_cvtss_f32(_mm_shuffle_ps(low, low, 3));
+
+ __m128 high = _mm256_extractf128_ps(from, 1);
+ to[stride*4] = _mm_cvtss_f32(high);
+ to[stride*5] = _mm_cvtss_f32(_mm_shuffle_ps(high, high, 1));
+ to[stride*6] = _mm_cvtss_f32(_mm_shuffle_ps(high, high, 2));
+ to[stride*7] = _mm_cvtss_f32(_mm_shuffle_ps(high, high, 3));
+}
+template<> EIGEN_DEVICE_FUNC inline void pscatter<double, Packet4d>(double* to, const Packet4d& from, Index stride)
+{
+ __m128d low = _mm256_extractf128_pd(from, 0);
+ to[stride*0] = _mm_cvtsd_f64(low);
+ to[stride*1] = _mm_cvtsd_f64(_mm_shuffle_pd(low, low, 1));
+ __m128d high = _mm256_extractf128_pd(from, 1);
+ to[stride*2] = _mm_cvtsd_f64(high);
+ to[stride*3] = _mm_cvtsd_f64(_mm_shuffle_pd(high, high, 1));
+}
+template<> EIGEN_DEVICE_FUNC inline void pscatter<int, Packet8i>(int* to, const Packet8i& from, Index stride)
+{
+ __m128i low = _mm256_extractf128_si256(from, 0);
+ to[stride*0] = _mm_extract_epi32(low, 0);
+ to[stride*1] = _mm_extract_epi32(low, 1);
+ to[stride*2] = _mm_extract_epi32(low, 2);
+ to[stride*3] = _mm_extract_epi32(low, 3);
+
+ __m128i high = _mm256_extractf128_si256(from, 1);
+ to[stride*4] = _mm_extract_epi32(high, 0);
+ to[stride*5] = _mm_extract_epi32(high, 1);
+ to[stride*6] = _mm_extract_epi32(high, 2);
+ to[stride*7] = _mm_extract_epi32(high, 3);
+}
+
+template<> EIGEN_STRONG_INLINE void pstore1<Packet8f>(float* to, const float& a)
+{
+ Packet8f pa = pset1<Packet8f>(a);
+ pstore(to, pa);
+}
+template<> EIGEN_STRONG_INLINE void pstore1<Packet4d>(double* to, const double& a)
+{
+ Packet4d pa = pset1<Packet4d>(a);
+ pstore(to, pa);
+}
+template<> EIGEN_STRONG_INLINE void pstore1<Packet8i>(int* to, const int& a)
+{
+ Packet8i pa = pset1<Packet8i>(a);
+ pstore(to, pa);
+}
+
+#ifndef EIGEN_VECTORIZE_AVX512
+template<> EIGEN_STRONG_INLINE void prefetch<float>(const float* addr) { _mm_prefetch((SsePrefetchPtrType)(addr), _MM_HINT_T0); }
+template<> EIGEN_STRONG_INLINE void prefetch<double>(const double* addr) { _mm_prefetch((SsePrefetchPtrType)(addr), _MM_HINT_T0); }
+template<> EIGEN_STRONG_INLINE void prefetch<int>(const int* addr) { _mm_prefetch((SsePrefetchPtrType)(addr), _MM_HINT_T0); }
+#endif
+
+template<> EIGEN_STRONG_INLINE float pfirst<Packet8f>(const Packet8f& a) {
+ return _mm_cvtss_f32(_mm256_castps256_ps128(a));
+}
+template<> EIGEN_STRONG_INLINE double pfirst<Packet4d>(const Packet4d& a) {
+ return _mm_cvtsd_f64(_mm256_castpd256_pd128(a));
+}
+template<> EIGEN_STRONG_INLINE int pfirst<Packet8i>(const Packet8i& a) {
+ return _mm_cvtsi128_si32(_mm256_castsi256_si128(a));
+}
+
+
+template<> EIGEN_STRONG_INLINE Packet8f preverse(const Packet8f& a)
+{
+ __m256 tmp = _mm256_shuffle_ps(a,a,0x1b);
+ return _mm256_permute2f128_ps(tmp, tmp, 1);
+}
+template<> EIGEN_STRONG_INLINE Packet4d preverse(const Packet4d& a)
+{
+ __m256d tmp = _mm256_shuffle_pd(a,a,5);
+ return _mm256_permute2f128_pd(tmp, tmp, 1);
+ #if 0
+ // This version is unlikely to be faster as _mm256_shuffle_ps and _mm256_permute_pd
+ // exhibit the same latency/throughput, but it is here for future reference/benchmarking...
+ __m256d swap_halves = _mm256_permute2f128_pd(a,a,1);
+ return _mm256_permute_pd(swap_halves,5);
+ #endif
+}
+template<> EIGEN_STRONG_INLINE Packet8i preverse(const Packet8i& a)
+{
+ return _mm256_castps_si256(preverse(_mm256_castsi256_ps(a)));
+}
+
+#ifdef EIGEN_VECTORIZE_AVX2
+template<> EIGEN_STRONG_INLINE Packet4l preverse(const Packet4l& a)
+{
+ return _mm256_castpd_si256(preverse(_mm256_castsi256_pd(a)));
+}
+#endif
+
+// pabs should be ok
+template<> EIGEN_STRONG_INLINE Packet8f pabs(const Packet8f& a)
+{
+ const Packet8f mask = _mm256_castsi256_ps(_mm256_setr_epi32(0x7FFFFFFF,0x7FFFFFFF,0x7FFFFFFF,0x7FFFFFFF,0x7FFFFFFF,0x7FFFFFFF,0x7FFFFFFF,0x7FFFFFFF));
+ return _mm256_and_ps(a,mask);
+}
+template<> EIGEN_STRONG_INLINE Packet4d pabs(const Packet4d& a)
+{
+ const Packet4d mask = _mm256_castsi256_pd(_mm256_setr_epi32(0xFFFFFFFF,0x7FFFFFFF,0xFFFFFFFF,0x7FFFFFFF,0xFFFFFFFF,0x7FFFFFFF,0xFFFFFFFF,0x7FFFFFFF));
+ return _mm256_and_pd(a,mask);
+}
+template<> EIGEN_STRONG_INLINE Packet8i pabs(const Packet8i& a)
+{
+#ifdef EIGEN_VECTORIZE_AVX2
+ return _mm256_abs_epi32(a);
+#else
+ __m128i lo = _mm_abs_epi32(_mm256_extractf128_si256(a, 0));
+ __m128i hi = _mm_abs_epi32(_mm256_extractf128_si256(a, 1));
+ return _mm256_insertf128_si256(_mm256_castsi128_si256(lo), (hi), 1);
+#endif
+}
+
+template<> EIGEN_STRONG_INLINE Packet8f pfrexp<Packet8f>(const Packet8f& a, Packet8f& exponent) {
+ return pfrexp_generic(a,exponent);
+}
+
+// Extract exponent without existence of Packet4l.
+template<>
+EIGEN_STRONG_INLINE
+Packet4d pfrexp_generic_get_biased_exponent(const Packet4d& a) {
+ const Packet4d cst_exp_mask = pset1frombits<Packet4d>(static_cast<uint64_t>(0x7ff0000000000000ull));
+ __m256i a_expo = _mm256_castpd_si256(pand(a, cst_exp_mask));
+#ifdef EIGEN_VECTORIZE_AVX2
+ a_expo = _mm256_srli_epi64(a_expo, 52);
+ __m128i lo = _mm256_extractf128_si256(a_expo, 0);
+ __m128i hi = _mm256_extractf128_si256(a_expo, 1);
+#else
+ __m128i lo = _mm256_extractf128_si256(a_expo, 0);
+ __m128i hi = _mm256_extractf128_si256(a_expo, 1);
+ lo = _mm_srli_epi64(lo, 52);
+ hi = _mm_srli_epi64(hi, 52);
+#endif
+ Packet2d exponent_lo = _mm_cvtepi32_pd(vec4i_swizzle1(lo, 0, 2, 1, 3));
+ Packet2d exponent_hi = _mm_cvtepi32_pd(vec4i_swizzle1(hi, 0, 2, 1, 3));
+ Packet4d exponent = _mm256_insertf128_pd(_mm256_setzero_pd(), exponent_lo, 0);
+ exponent = _mm256_insertf128_pd(exponent, exponent_hi, 1);
+ return exponent;
+}
+
+
+template<> EIGEN_STRONG_INLINE Packet4d pfrexp<Packet4d>(const Packet4d& a, Packet4d& exponent) {
+ return pfrexp_generic(a, exponent);
+}
+
+template<> EIGEN_STRONG_INLINE Packet8f pldexp<Packet8f>(const Packet8f& a, const Packet8f& exponent) {
+ return pldexp_generic(a, exponent);
+}
+
+template<> EIGEN_STRONG_INLINE Packet4d pldexp<Packet4d>(const Packet4d& a, const Packet4d& exponent) {
+ // Clamp exponent to [-2099, 2099]
+ const Packet4d max_exponent = pset1<Packet4d>(2099.0);
+ const Packet4i e = _mm256_cvtpd_epi32(pmin(pmax(exponent, pnegate(max_exponent)), max_exponent));
+
+ // Split 2^e into four factors and multiply.
+ const Packet4i bias = pset1<Packet4i>(1023);
+ Packet4i b = parithmetic_shift_right<2>(e); // floor(e/4)
+
+ // 2^b
+ Packet4i hi = vec4i_swizzle1(padd(b, bias), 0, 2, 1, 3);
+ Packet4i lo = _mm_slli_epi64(hi, 52);
+ hi = _mm_slli_epi64(_mm_srli_epi64(hi, 32), 52);
+ Packet4d c = _mm256_castsi256_pd(_mm256_insertf128_si256(_mm256_castsi128_si256(lo), hi, 1));
+ Packet4d out = pmul(pmul(pmul(a, c), c), c); // a * 2^(3b)
+
+ // 2^(e - 3b)
+ b = psub(psub(psub(e, b), b), b); // e - 3b
+ hi = vec4i_swizzle1(padd(b, bias), 0, 2, 1, 3);
+ lo = _mm_slli_epi64(hi, 52);
+ hi = _mm_slli_epi64(_mm_srli_epi64(hi, 32), 52);
+ c = _mm256_castsi256_pd(_mm256_insertf128_si256(_mm256_castsi128_si256(lo), hi, 1));
+ out = pmul(out, c); // a * 2^e
+ return out;
+}
+
+template<> EIGEN_STRONG_INLINE float predux<Packet8f>(const Packet8f& a)
+{
+ return predux(Packet4f(_mm_add_ps(_mm256_castps256_ps128(a),_mm256_extractf128_ps(a,1))));
+}
+template<> EIGEN_STRONG_INLINE double predux<Packet4d>(const Packet4d& a)
+{
+ return predux(Packet2d(_mm_add_pd(_mm256_castpd256_pd128(a),_mm256_extractf128_pd(a,1))));
+}
+template<> EIGEN_STRONG_INLINE int predux<Packet8i>(const Packet8i& a)
+{
+ return predux(Packet4i(_mm_add_epi32(_mm256_castsi256_si128(a),_mm256_extractf128_si256(a,1))));
+}
+
+template<> EIGEN_STRONG_INLINE Packet4f predux_half_dowto4<Packet8f>(const Packet8f& a)
+{
+ return _mm_add_ps(_mm256_castps256_ps128(a),_mm256_extractf128_ps(a,1));
+}
+template<> EIGEN_STRONG_INLINE Packet4i predux_half_dowto4<Packet8i>(const Packet8i& a)
+{
+ return _mm_add_epi32(_mm256_castsi256_si128(a),_mm256_extractf128_si256(a,1));
+}
+
+template<> EIGEN_STRONG_INLINE float predux_mul<Packet8f>(const Packet8f& a)
+{
+ Packet8f tmp;
+ tmp = _mm256_mul_ps(a, _mm256_permute2f128_ps(a,a,1));
+ tmp = _mm256_mul_ps(tmp, _mm256_shuffle_ps(tmp,tmp,_MM_SHUFFLE(1,0,3,2)));
+ return pfirst(_mm256_mul_ps(tmp, _mm256_shuffle_ps(tmp,tmp,1)));
+}
+template<> EIGEN_STRONG_INLINE double predux_mul<Packet4d>(const Packet4d& a)
+{
+ Packet4d tmp;
+ tmp = _mm256_mul_pd(a, _mm256_permute2f128_pd(a,a,1));
+ return pfirst(_mm256_mul_pd(tmp, _mm256_shuffle_pd(tmp,tmp,1)));
+}
+
+template<> EIGEN_STRONG_INLINE float predux_min<Packet8f>(const Packet8f& a)
+{
+ Packet8f tmp = _mm256_min_ps(a, _mm256_permute2f128_ps(a,a,1));
+ tmp = _mm256_min_ps(tmp, _mm256_shuffle_ps(tmp,tmp,_MM_SHUFFLE(1,0,3,2)));
+ return pfirst(_mm256_min_ps(tmp, _mm256_shuffle_ps(tmp,tmp,1)));
+}
+template<> EIGEN_STRONG_INLINE double predux_min<Packet4d>(const Packet4d& a)
+{
+ Packet4d tmp = _mm256_min_pd(a, _mm256_permute2f128_pd(a,a,1));
+ return pfirst(_mm256_min_pd(tmp, _mm256_shuffle_pd(tmp, tmp, 1)));
+}
+
+template<> EIGEN_STRONG_INLINE float predux_max<Packet8f>(const Packet8f& a)
+{
+ Packet8f tmp = _mm256_max_ps(a, _mm256_permute2f128_ps(a,a,1));
+ tmp = _mm256_max_ps(tmp, _mm256_shuffle_ps(tmp,tmp,_MM_SHUFFLE(1,0,3,2)));
+ return pfirst(_mm256_max_ps(tmp, _mm256_shuffle_ps(tmp,tmp,1)));
+}
+
+template<> EIGEN_STRONG_INLINE double predux_max<Packet4d>(const Packet4d& a)
+{
+ Packet4d tmp = _mm256_max_pd(a, _mm256_permute2f128_pd(a,a,1));
+ return pfirst(_mm256_max_pd(tmp, _mm256_shuffle_pd(tmp, tmp, 1)));
+}
+
+// not needed yet
+// template<> EIGEN_STRONG_INLINE bool predux_all(const Packet8f& x)
+// {
+// return _mm256_movemask_ps(x)==0xFF;
+// }
+
+template<> EIGEN_STRONG_INLINE bool predux_any(const Packet8f& x)
+{
+ return _mm256_movemask_ps(x) != 0;
+}
+
+template<> EIGEN_STRONG_INLINE bool predux_any(const Packet8i& x)
+{
+ return _mm256_movemask_ps(_mm256_castsi256_ps(x)) != 0;
+}
+
+EIGEN_DEVICE_FUNC inline void
+ptranspose(PacketBlock<Packet8f,8>& kernel) {
+ __m256 T0 = _mm256_unpacklo_ps(kernel.packet[0], kernel.packet[1]);
+ __m256 T1 = _mm256_unpackhi_ps(kernel.packet[0], kernel.packet[1]);
+ __m256 T2 = _mm256_unpacklo_ps(kernel.packet[2], kernel.packet[3]);
+ __m256 T3 = _mm256_unpackhi_ps(kernel.packet[2], kernel.packet[3]);
+ __m256 T4 = _mm256_unpacklo_ps(kernel.packet[4], kernel.packet[5]);
+ __m256 T5 = _mm256_unpackhi_ps(kernel.packet[4], kernel.packet[5]);
+ __m256 T6 = _mm256_unpacklo_ps(kernel.packet[6], kernel.packet[7]);
+ __m256 T7 = _mm256_unpackhi_ps(kernel.packet[6], kernel.packet[7]);
+ __m256 S0 = _mm256_shuffle_ps(T0,T2,_MM_SHUFFLE(1,0,1,0));
+ __m256 S1 = _mm256_shuffle_ps(T0,T2,_MM_SHUFFLE(3,2,3,2));
+ __m256 S2 = _mm256_shuffle_ps(T1,T3,_MM_SHUFFLE(1,0,1,0));
+ __m256 S3 = _mm256_shuffle_ps(T1,T3,_MM_SHUFFLE(3,2,3,2));
+ __m256 S4 = _mm256_shuffle_ps(T4,T6,_MM_SHUFFLE(1,0,1,0));
+ __m256 S5 = _mm256_shuffle_ps(T4,T6,_MM_SHUFFLE(3,2,3,2));
+ __m256 S6 = _mm256_shuffle_ps(T5,T7,_MM_SHUFFLE(1,0,1,0));
+ __m256 S7 = _mm256_shuffle_ps(T5,T7,_MM_SHUFFLE(3,2,3,2));
+ kernel.packet[0] = _mm256_permute2f128_ps(S0, S4, 0x20);
+ kernel.packet[1] = _mm256_permute2f128_ps(S1, S5, 0x20);
+ kernel.packet[2] = _mm256_permute2f128_ps(S2, S6, 0x20);
+ kernel.packet[3] = _mm256_permute2f128_ps(S3, S7, 0x20);
+ kernel.packet[4] = _mm256_permute2f128_ps(S0, S4, 0x31);
+ kernel.packet[5] = _mm256_permute2f128_ps(S1, S5, 0x31);
+ kernel.packet[6] = _mm256_permute2f128_ps(S2, S6, 0x31);
+ kernel.packet[7] = _mm256_permute2f128_ps(S3, S7, 0x31);
+}
+
+EIGEN_DEVICE_FUNC inline void
+ptranspose(PacketBlock<Packet8f,4>& kernel) {
+ __m256 T0 = _mm256_unpacklo_ps(kernel.packet[0], kernel.packet[1]);
+ __m256 T1 = _mm256_unpackhi_ps(kernel.packet[0], kernel.packet[1]);
+ __m256 T2 = _mm256_unpacklo_ps(kernel.packet[2], kernel.packet[3]);
+ __m256 T3 = _mm256_unpackhi_ps(kernel.packet[2], kernel.packet[3]);
+
+ __m256 S0 = _mm256_shuffle_ps(T0,T2,_MM_SHUFFLE(1,0,1,0));
+ __m256 S1 = _mm256_shuffle_ps(T0,T2,_MM_SHUFFLE(3,2,3,2));
+ __m256 S2 = _mm256_shuffle_ps(T1,T3,_MM_SHUFFLE(1,0,1,0));
+ __m256 S3 = _mm256_shuffle_ps(T1,T3,_MM_SHUFFLE(3,2,3,2));
+
+ kernel.packet[0] = _mm256_permute2f128_ps(S0, S1, 0x20);
+ kernel.packet[1] = _mm256_permute2f128_ps(S2, S3, 0x20);
+ kernel.packet[2] = _mm256_permute2f128_ps(S0, S1, 0x31);
+ kernel.packet[3] = _mm256_permute2f128_ps(S2, S3, 0x31);
+}
+
+#define MM256_SHUFFLE_EPI32(A, B, M) \
+ _mm256_castps_si256(_mm256_shuffle_ps(_mm256_castsi256_ps(A), _mm256_castsi256_ps(B), M))
+
+#ifndef EIGEN_VECTORIZE_AVX2
+#define MM256_UNPACKLO_EPI32(A, B) \
+ _mm256_castps_si256(_mm256_unpacklo_ps(_mm256_castsi256_ps(A), _mm256_castsi256_ps(B)))
+#define MM256_UNPACKHI_EPI32(A, B) \
+ _mm256_castps_si256(_mm256_unpackhi_ps(_mm256_castsi256_ps(A), _mm256_castsi256_ps(B)))
+#else
+#define MM256_UNPACKLO_EPI32(A, B) _mm256_unpacklo_epi32(A, B)
+#define MM256_UNPACKHI_EPI32(A, B) _mm256_unpackhi_epi32(A, B)
+#endif
+
+
+EIGEN_DEVICE_FUNC inline void
+ptranspose(PacketBlock<Packet8i,8>& kernel) {
+ __m256i T0 = MM256_UNPACKLO_EPI32(kernel.packet[0], kernel.packet[1]);
+ __m256i T1 = MM256_UNPACKHI_EPI32(kernel.packet[0], kernel.packet[1]);
+ __m256i T2 = MM256_UNPACKLO_EPI32(kernel.packet[2], kernel.packet[3]);
+ __m256i T3 = MM256_UNPACKHI_EPI32(kernel.packet[2], kernel.packet[3]);
+ __m256i T4 = MM256_UNPACKLO_EPI32(kernel.packet[4], kernel.packet[5]);
+ __m256i T5 = MM256_UNPACKHI_EPI32(kernel.packet[4], kernel.packet[5]);
+ __m256i T6 = MM256_UNPACKLO_EPI32(kernel.packet[6], kernel.packet[7]);
+ __m256i T7 = MM256_UNPACKHI_EPI32(kernel.packet[6], kernel.packet[7]);
+ __m256i S0 = MM256_SHUFFLE_EPI32(T0,T2,_MM_SHUFFLE(1,0,1,0));
+ __m256i S1 = MM256_SHUFFLE_EPI32(T0,T2,_MM_SHUFFLE(3,2,3,2));
+ __m256i S2 = MM256_SHUFFLE_EPI32(T1,T3,_MM_SHUFFLE(1,0,1,0));
+ __m256i S3 = MM256_SHUFFLE_EPI32(T1,T3,_MM_SHUFFLE(3,2,3,2));
+ __m256i S4 = MM256_SHUFFLE_EPI32(T4,T6,_MM_SHUFFLE(1,0,1,0));
+ __m256i S5 = MM256_SHUFFLE_EPI32(T4,T6,_MM_SHUFFLE(3,2,3,2));
+ __m256i S6 = MM256_SHUFFLE_EPI32(T5,T7,_MM_SHUFFLE(1,0,1,0));
+ __m256i S7 = MM256_SHUFFLE_EPI32(T5,T7,_MM_SHUFFLE(3,2,3,2));
+ kernel.packet[0] = _mm256_permute2f128_si256(S0, S4, 0x20);
+ kernel.packet[1] = _mm256_permute2f128_si256(S1, S5, 0x20);
+ kernel.packet[2] = _mm256_permute2f128_si256(S2, S6, 0x20);
+ kernel.packet[3] = _mm256_permute2f128_si256(S3, S7, 0x20);
+ kernel.packet[4] = _mm256_permute2f128_si256(S0, S4, 0x31);
+ kernel.packet[5] = _mm256_permute2f128_si256(S1, S5, 0x31);
+ kernel.packet[6] = _mm256_permute2f128_si256(S2, S6, 0x31);
+ kernel.packet[7] = _mm256_permute2f128_si256(S3, S7, 0x31);
+}
+
+EIGEN_DEVICE_FUNC inline void
+ptranspose(PacketBlock<Packet8i,4>& kernel) {
+ __m256i T0 = MM256_UNPACKLO_EPI32(kernel.packet[0], kernel.packet[1]);
+ __m256i T1 = MM256_UNPACKHI_EPI32(kernel.packet[0], kernel.packet[1]);
+ __m256i T2 = MM256_UNPACKLO_EPI32(kernel.packet[2], kernel.packet[3]);
+ __m256i T3 = MM256_UNPACKHI_EPI32(kernel.packet[2], kernel.packet[3]);
+
+ __m256i S0 = MM256_SHUFFLE_EPI32(T0,T2,_MM_SHUFFLE(1,0,1,0));
+ __m256i S1 = MM256_SHUFFLE_EPI32(T0,T2,_MM_SHUFFLE(3,2,3,2));
+ __m256i S2 = MM256_SHUFFLE_EPI32(T1,T3,_MM_SHUFFLE(1,0,1,0));
+ __m256i S3 = MM256_SHUFFLE_EPI32(T1,T3,_MM_SHUFFLE(3,2,3,2));
+
+ kernel.packet[0] = _mm256_permute2f128_si256(S0, S1, 0x20);
+ kernel.packet[1] = _mm256_permute2f128_si256(S2, S3, 0x20);
+ kernel.packet[2] = _mm256_permute2f128_si256(S0, S1, 0x31);
+ kernel.packet[3] = _mm256_permute2f128_si256(S2, S3, 0x31);
+}
+
+EIGEN_DEVICE_FUNC inline void
+ptranspose(PacketBlock<Packet4d,4>& kernel) {
+ __m256d T0 = _mm256_shuffle_pd(kernel.packet[0], kernel.packet[1], 15);
+ __m256d T1 = _mm256_shuffle_pd(kernel.packet[0], kernel.packet[1], 0);
+ __m256d T2 = _mm256_shuffle_pd(kernel.packet[2], kernel.packet[3], 15);
+ __m256d T3 = _mm256_shuffle_pd(kernel.packet[2], kernel.packet[3], 0);
+
+ kernel.packet[1] = _mm256_permute2f128_pd(T0, T2, 32);
+ kernel.packet[3] = _mm256_permute2f128_pd(T0, T2, 49);
+ kernel.packet[0] = _mm256_permute2f128_pd(T1, T3, 32);
+ kernel.packet[2] = _mm256_permute2f128_pd(T1, T3, 49);
+}
+
+template<> EIGEN_STRONG_INLINE Packet8f pblend(const Selector<8>& ifPacket, const Packet8f& thenPacket, const Packet8f& elsePacket) {
+#ifdef EIGEN_VECTORIZE_AVX2
+ const __m256i zero = _mm256_setzero_si256();
+ const __m256i select = _mm256_set_epi32(ifPacket.select[7], ifPacket.select[6], ifPacket.select[5], ifPacket.select[4], ifPacket.select[3], ifPacket.select[2], ifPacket.select[1], ifPacket.select[0]);
+ __m256i false_mask = _mm256_cmpeq_epi32(zero, select);
+ return _mm256_blendv_ps(thenPacket, elsePacket, _mm256_castsi256_ps(false_mask));
+#else
+ const __m256 zero = _mm256_setzero_ps();
+ const __m256 select = _mm256_set_ps(ifPacket.select[7], ifPacket.select[6], ifPacket.select[5], ifPacket.select[4], ifPacket.select[3], ifPacket.select[2], ifPacket.select[1], ifPacket.select[0]);
+ __m256 false_mask = _mm256_cmp_ps(select, zero, _CMP_EQ_UQ);
+ return _mm256_blendv_ps(thenPacket, elsePacket, false_mask);
+#endif
+}
+
+template<> EIGEN_STRONG_INLINE Packet4d pblend(const Selector<4>& ifPacket, const Packet4d& thenPacket, const Packet4d& elsePacket) {
+#ifdef EIGEN_VECTORIZE_AVX2
+ const __m256i zero = _mm256_setzero_si256();
+ const __m256i select = _mm256_set_epi64x(ifPacket.select[3], ifPacket.select[2], ifPacket.select[1], ifPacket.select[0]);
+ __m256i false_mask = _mm256_cmpeq_epi64(select, zero);
+ return _mm256_blendv_pd(thenPacket, elsePacket, _mm256_castsi256_pd(false_mask));
+#else
+ const __m256d zero = _mm256_setzero_pd();
+ const __m256d select = _mm256_set_pd(ifPacket.select[3], ifPacket.select[2], ifPacket.select[1], ifPacket.select[0]);
+ __m256d false_mask = _mm256_cmp_pd(select, zero, _CMP_EQ_UQ);
+ return _mm256_blendv_pd(thenPacket, elsePacket, false_mask);
+#endif
+}
+
+// Packet math for Eigen::half
+#ifndef EIGEN_VECTORIZE_AVX512FP16
+template<> struct unpacket_traits<Packet8h> { typedef Eigen::half type; enum {size=8, alignment=Aligned16, vectorizable=true, masked_load_available=false, masked_store_available=false}; typedef Packet8h half; };
+#endif
+
+template<> EIGEN_STRONG_INLINE Packet8h pset1<Packet8h>(const Eigen::half& from) {
+ return _mm_set1_epi16(numext::bit_cast<numext::uint16_t>(from));
+}
+
+template<> EIGEN_STRONG_INLINE Eigen::half pfirst<Packet8h>(const Packet8h& from) {
+ return numext::bit_cast<Eigen::half>(static_cast<numext::uint16_t>(_mm_extract_epi16(from, 0)));
+}
+
+template<> EIGEN_STRONG_INLINE Packet8h pload<Packet8h>(const Eigen::half* from) {
+ return _mm_load_si128(reinterpret_cast<const __m128i*>(from));
+}
+
+template<> EIGEN_STRONG_INLINE Packet8h ploadu<Packet8h>(const Eigen::half* from) {
+ return _mm_loadu_si128(reinterpret_cast<const __m128i*>(from));
+}
+
+template<> EIGEN_STRONG_INLINE void pstore<Eigen::half>(Eigen::half* to, const Packet8h& from) {
+ _mm_store_si128(reinterpret_cast<__m128i*>(to), from);
+}
+
+template<> EIGEN_STRONG_INLINE void pstoreu<Eigen::half>(Eigen::half* to, const Packet8h& from) {
+ _mm_storeu_si128(reinterpret_cast<__m128i*>(to), from);
+}
+
+template<> EIGEN_STRONG_INLINE Packet8h
+ploaddup<Packet8h>(const Eigen::half* from) {
+ const numext::uint16_t a = numext::bit_cast<numext::uint16_t>(from[0]);
+ const numext::uint16_t b = numext::bit_cast<numext::uint16_t>(from[1]);
+ const numext::uint16_t c = numext::bit_cast<numext::uint16_t>(from[2]);
+ const numext::uint16_t d = numext::bit_cast<numext::uint16_t>(from[3]);
+ return _mm_set_epi16(d, d, c, c, b, b, a, a);
+}
+
+template<> EIGEN_STRONG_INLINE Packet8h
+ploadquad<Packet8h>(const Eigen::half* from) {
+ const numext::uint16_t a = numext::bit_cast<numext::uint16_t>(from[0]);
+ const numext::uint16_t b = numext::bit_cast<numext::uint16_t>(from[1]);
+ return _mm_set_epi16(b, b, b, b, a, a, a, a);
+}
+
+template<> EIGEN_STRONG_INLINE Packet8h ptrue(const Packet8h& a) {
+ return _mm_cmpeq_epi32(a, a);
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet8h pabs(const Packet8h& a) {
+ const __m128i sign_mask = _mm_set1_epi16(static_cast<numext::uint16_t>(0x8000));
+ return _mm_andnot_si128(sign_mask, a);
+}
+
+EIGEN_STRONG_INLINE Packet8f half2float(const Packet8h& a) {
+#ifdef EIGEN_HAS_FP16_C
+ return _mm256_cvtph_ps(a);
+#else
+ Eigen::internal::Packet8f pp = _mm256_castsi256_ps(_mm256_insertf128_si256(
+ _mm256_castsi128_si256(half2floatsse(a)), half2floatsse(_mm_srli_si128(a, 8)), 1));
+ return pp;
+#endif
+}
+
+EIGEN_STRONG_INLINE Packet8h float2half(const Packet8f& a) {
+#ifdef EIGEN_HAS_FP16_C
+ return _mm256_cvtps_ph(a, _MM_FROUND_TO_NEAREST_INT|_MM_FROUND_NO_EXC);
+#else
+ __m128i lo = float2half(_mm256_extractf128_ps(a, 0));
+ __m128i hi = float2half(_mm256_extractf128_ps(a, 1));
+ return _mm_packus_epi32(lo, hi);
+#endif
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet8h pmin<Packet8h>(const Packet8h& a,
+ const Packet8h& b) {
+ return float2half(pmin<Packet8f>(half2float(a), half2float(b)));
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet8h pmax<Packet8h>(const Packet8h& a,
+ const Packet8h& b) {
+ return float2half(pmax<Packet8f>(half2float(a), half2float(b)));
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet8h plset<Packet8h>(const half& a) {
+ return float2half(plset<Packet8f>(static_cast<float>(a)));
+}
+
+template<> EIGEN_STRONG_INLINE Packet8h por(const Packet8h& a,const Packet8h& b) {
+ // in some cases Packet4i is a wrapper around __m128i, so we either need to
+ // cast to Packet4i to directly call the intrinsics as below:
+ return _mm_or_si128(a,b);
+}
+template<> EIGEN_STRONG_INLINE Packet8h pxor(const Packet8h& a,const Packet8h& b) {
+ return _mm_xor_si128(a,b);
+}
+template<> EIGEN_STRONG_INLINE Packet8h pand(const Packet8h& a,const Packet8h& b) {
+ return _mm_and_si128(a,b);
+}
+template<> EIGEN_STRONG_INLINE Packet8h pandnot(const Packet8h& a,const Packet8h& b) {
+ return _mm_andnot_si128(b,a);
+}
+
+template<> EIGEN_STRONG_INLINE Packet8h pselect(const Packet8h& mask, const Packet8h& a, const Packet8h& b) {
+ return _mm_blendv_epi8(b, a, mask);
+}
+
+template<> EIGEN_STRONG_INLINE Packet8h pround<Packet8h>(const Packet8h& a) {
+ return float2half(pround<Packet8f>(half2float(a)));
+}
+
+template<> EIGEN_STRONG_INLINE Packet8h print<Packet8h>(const Packet8h& a) {
+ return float2half(print<Packet8f>(half2float(a)));
+}
+
+template<> EIGEN_STRONG_INLINE Packet8h pceil<Packet8h>(const Packet8h& a) {
+ return float2half(pceil<Packet8f>(half2float(a)));
+}
+
+template<> EIGEN_STRONG_INLINE Packet8h pfloor<Packet8h>(const Packet8h& a) {
+ return float2half(pfloor<Packet8f>(half2float(a)));
+}
+
+template<> EIGEN_STRONG_INLINE Packet8h pcmp_eq(const Packet8h& a,const Packet8h& b) {
+ return Pack16To8(pcmp_eq(half2float(a), half2float(b)));
+}
+
+template<> EIGEN_STRONG_INLINE Packet8h pcmp_le(const Packet8h& a,const Packet8h& b) {
+ return Pack16To8(pcmp_le(half2float(a), half2float(b)));
+}
+
+template<> EIGEN_STRONG_INLINE Packet8h pcmp_lt(const Packet8h& a,const Packet8h& b) {
+ return Pack16To8(pcmp_lt(half2float(a), half2float(b)));
+}
+
+template<> EIGEN_STRONG_INLINE Packet8h pcmp_lt_or_nan(const Packet8h& a,const Packet8h& b) {
+ return Pack16To8(pcmp_lt_or_nan(half2float(a), half2float(b)));
+}
+
+template<> EIGEN_STRONG_INLINE Packet8h pconj(const Packet8h& a) { return a; }
+
+template<> EIGEN_STRONG_INLINE Packet8h pnegate(const Packet8h& a) {
+ Packet8h sign_mask = _mm_set1_epi16(static_cast<numext::uint16_t>(0x8000));
+ return _mm_xor_si128(a, sign_mask);
+}
+
+#ifndef EIGEN_VECTORIZE_AVX512FP16
+template<> EIGEN_STRONG_INLINE Packet8h padd<Packet8h>(const Packet8h& a, const Packet8h& b) {
+ Packet8f af = half2float(a);
+ Packet8f bf = half2float(b);
+ Packet8f rf = padd(af, bf);
+ return float2half(rf);
+}
+
+template<> EIGEN_STRONG_INLINE Packet8h psub<Packet8h>(const Packet8h& a, const Packet8h& b) {
+ Packet8f af = half2float(a);
+ Packet8f bf = half2float(b);
+ Packet8f rf = psub(af, bf);
+ return float2half(rf);
+}
+
+template<> EIGEN_STRONG_INLINE Packet8h pmul<Packet8h>(const Packet8h& a, const Packet8h& b) {
+ Packet8f af = half2float(a);
+ Packet8f bf = half2float(b);
+ Packet8f rf = pmul(af, bf);
+ return float2half(rf);
+}
+
+template<> EIGEN_STRONG_INLINE Packet8h pdiv<Packet8h>(const Packet8h& a, const Packet8h& b) {
+ Packet8f af = half2float(a);
+ Packet8f bf = half2float(b);
+ Packet8f rf = pdiv(af, bf);
+ return float2half(rf);
+}
+#endif
+
+template<> EIGEN_STRONG_INLINE Packet8h pgather<Eigen::half, Packet8h>(const Eigen::half* from, Index stride)
+{
+ const numext::uint16_t s0 = numext::bit_cast<numext::uint16_t>(from[0*stride]);
+ const numext::uint16_t s1 = numext::bit_cast<numext::uint16_t>(from[1*stride]);
+ const numext::uint16_t s2 = numext::bit_cast<numext::uint16_t>(from[2*stride]);
+ const numext::uint16_t s3 = numext::bit_cast<numext::uint16_t>(from[3*stride]);
+ const numext::uint16_t s4 = numext::bit_cast<numext::uint16_t>(from[4*stride]);
+ const numext::uint16_t s5 = numext::bit_cast<numext::uint16_t>(from[5*stride]);
+ const numext::uint16_t s6 = numext::bit_cast<numext::uint16_t>(from[6*stride]);
+ const numext::uint16_t s7 = numext::bit_cast<numext::uint16_t>(from[7*stride]);
+ return _mm_set_epi16(s7, s6, s5, s4, s3, s2, s1, s0);
+}
+
+template<> EIGEN_STRONG_INLINE void pscatter<Eigen::half, Packet8h>(Eigen::half* to, const Packet8h& from, Index stride)
+{
+ EIGEN_ALIGN32 Eigen::half aux[8];
+ pstore(aux, from);
+ to[stride*0] = aux[0];
+ to[stride*1] = aux[1];
+ to[stride*2] = aux[2];
+ to[stride*3] = aux[3];
+ to[stride*4] = aux[4];
+ to[stride*5] = aux[5];
+ to[stride*6] = aux[6];
+ to[stride*7] = aux[7];
+}
+
+
+#ifndef EIGEN_VECTORIZE_AVX512FP16
+template<> EIGEN_STRONG_INLINE Eigen::half predux<Packet8h>(const Packet8h& a) {
+ Packet8f af = half2float(a);
+ float reduced = predux<Packet8f>(af);
+ return Eigen::half(reduced);
+}
+#endif
+
+template<> EIGEN_STRONG_INLINE Eigen::half predux_max<Packet8h>(const Packet8h& a) {
+ Packet8f af = half2float(a);
+ float reduced = predux_max<Packet8f>(af);
+ return Eigen::half(reduced);
+}
+
+template<> EIGEN_STRONG_INLINE Eigen::half predux_min<Packet8h>(const Packet8h& a) {
+ Packet8f af = half2float(a);
+ float reduced = predux_min<Packet8f>(af);
+ return Eigen::half(reduced);
+}
+
+template<> EIGEN_STRONG_INLINE Eigen::half predux_mul<Packet8h>(const Packet8h& a) {
+ Packet8f af = half2float(a);
+ float reduced = predux_mul<Packet8f>(af);
+ return Eigen::half(reduced);
+}
+
+template<> EIGEN_STRONG_INLINE Packet8h preverse(const Packet8h& a)
+{
+ __m128i m = _mm_setr_epi8(14,15,12,13,10,11,8,9,6,7,4,5,2,3,0,1);
+ return _mm_shuffle_epi8(a,m);
+}
+
+EIGEN_STRONG_INLINE void
+ptranspose(PacketBlock<Packet8h,8>& kernel) {
+ __m128i a = kernel.packet[0];
+ __m128i b = kernel.packet[1];
+ __m128i c = kernel.packet[2];
+ __m128i d = kernel.packet[3];
+ __m128i e = kernel.packet[4];
+ __m128i f = kernel.packet[5];
+ __m128i g = kernel.packet[6];
+ __m128i h = kernel.packet[7];
+
+ __m128i a03b03 = _mm_unpacklo_epi16(a, b);
+ __m128i c03d03 = _mm_unpacklo_epi16(c, d);
+ __m128i e03f03 = _mm_unpacklo_epi16(e, f);
+ __m128i g03h03 = _mm_unpacklo_epi16(g, h);
+ __m128i a47b47 = _mm_unpackhi_epi16(a, b);
+ __m128i c47d47 = _mm_unpackhi_epi16(c, d);
+ __m128i e47f47 = _mm_unpackhi_epi16(e, f);
+ __m128i g47h47 = _mm_unpackhi_epi16(g, h);
+
+ __m128i a01b01c01d01 = _mm_unpacklo_epi32(a03b03, c03d03);
+ __m128i a23b23c23d23 = _mm_unpackhi_epi32(a03b03, c03d03);
+ __m128i e01f01g01h01 = _mm_unpacklo_epi32(e03f03, g03h03);
+ __m128i e23f23g23h23 = _mm_unpackhi_epi32(e03f03, g03h03);
+ __m128i a45b45c45d45 = _mm_unpacklo_epi32(a47b47, c47d47);
+ __m128i a67b67c67d67 = _mm_unpackhi_epi32(a47b47, c47d47);
+ __m128i e45f45g45h45 = _mm_unpacklo_epi32(e47f47, g47h47);
+ __m128i e67f67g67h67 = _mm_unpackhi_epi32(e47f47, g47h47);
+
+ __m128i a0b0c0d0e0f0g0h0 = _mm_unpacklo_epi64(a01b01c01d01, e01f01g01h01);
+ __m128i a1b1c1d1e1f1g1h1 = _mm_unpackhi_epi64(a01b01c01d01, e01f01g01h01);
+ __m128i a2b2c2d2e2f2g2h2 = _mm_unpacklo_epi64(a23b23c23d23, e23f23g23h23);
+ __m128i a3b3c3d3e3f3g3h3 = _mm_unpackhi_epi64(a23b23c23d23, e23f23g23h23);
+ __m128i a4b4c4d4e4f4g4h4 = _mm_unpacklo_epi64(a45b45c45d45, e45f45g45h45);
+ __m128i a5b5c5d5e5f5g5h5 = _mm_unpackhi_epi64(a45b45c45d45, e45f45g45h45);
+ __m128i a6b6c6d6e6f6g6h6 = _mm_unpacklo_epi64(a67b67c67d67, e67f67g67h67);
+ __m128i a7b7c7d7e7f7g7h7 = _mm_unpackhi_epi64(a67b67c67d67, e67f67g67h67);
+
+ kernel.packet[0] = a0b0c0d0e0f0g0h0;
+ kernel.packet[1] = a1b1c1d1e1f1g1h1;
+ kernel.packet[2] = a2b2c2d2e2f2g2h2;
+ kernel.packet[3] = a3b3c3d3e3f3g3h3;
+ kernel.packet[4] = a4b4c4d4e4f4g4h4;
+ kernel.packet[5] = a5b5c5d5e5f5g5h5;
+ kernel.packet[6] = a6b6c6d6e6f6g6h6;
+ kernel.packet[7] = a7b7c7d7e7f7g7h7;
+}
+
+EIGEN_STRONG_INLINE void
+ptranspose(PacketBlock<Packet8h,4>& kernel) {
+ EIGEN_ALIGN32 Eigen::half in[4][8];
+ pstore<Eigen::half>(in[0], kernel.packet[0]);
+ pstore<Eigen::half>(in[1], kernel.packet[1]);
+ pstore<Eigen::half>(in[2], kernel.packet[2]);
+ pstore<Eigen::half>(in[3], kernel.packet[3]);
+
+ EIGEN_ALIGN32 Eigen::half out[4][8];
+
+ for (int i = 0; i < 4; ++i) {
+ for (int j = 0; j < 4; ++j) {
+ out[i][j] = in[j][2*i];
+ }
+ for (int j = 0; j < 4; ++j) {
+ out[i][j+4] = in[j][2*i+1];
+ }
+ }
+
+ kernel.packet[0] = pload<Packet8h>(out[0]);
+ kernel.packet[1] = pload<Packet8h>(out[1]);
+ kernel.packet[2] = pload<Packet8h>(out[2]);
+ kernel.packet[3] = pload<Packet8h>(out[3]);
+}
+
+// BFloat16 implementation.
+
+EIGEN_STRONG_INLINE Packet8f Bf16ToF32(const Packet8bf& a) {
+#ifdef EIGEN_VECTORIZE_AVX2
+ __m256i extend = _mm256_cvtepu16_epi32(a);
+ return _mm256_castsi256_ps(_mm256_slli_epi32(extend, 16));
+#else
+ __m128i lo = _mm_cvtepu16_epi32(a);
+ __m128i hi = _mm_cvtepu16_epi32(_mm_srli_si128(a, 8));
+ __m128i lo_shift = _mm_slli_epi32(lo, 16);
+ __m128i hi_shift = _mm_slli_epi32(hi, 16);
+ return _mm256_castsi256_ps(_mm256_insertf128_si256(_mm256_castsi128_si256(lo_shift), hi_shift, 1));
+#endif
+}
+
+// Convert float to bfloat16 according to round-to-nearest-even/denormals algorithm.
+EIGEN_STRONG_INLINE Packet8bf F32ToBf16(const Packet8f& a) {
+
+ __m256i input = _mm256_castps_si256(a);
+
+#ifdef EIGEN_VECTORIZE_AVX2
+ // uint32_t lsb = (input >> 16);
+ __m256i t = _mm256_srli_epi32(input, 16);
+ // uint32_t lsb = lsb & 1;
+ t = _mm256_and_si256(t, _mm256_set1_epi32(1));
+ // uint32_t rounding_bias = 0x7fff + lsb;
+ t = _mm256_add_epi32(t, _mm256_set1_epi32(0x7fff));
+ // input += rounding_bias;
+ t = _mm256_add_epi32(t, input);
+ // input = input >> 16;
+ t = _mm256_srli_epi32(t, 16);
+ // Check NaN before converting back to bf16
+ __m256 mask = _mm256_cmp_ps(a, a, _CMP_ORD_Q);
+ __m256i nan = _mm256_set1_epi32(0x7fc0);
+ t = _mm256_blendv_epi8(nan, t, _mm256_castps_si256(mask));
+ // output = numext::bit_cast<uint16_t>(input);
+ return _mm_packus_epi32(_mm256_extractf128_si256(t, 0),
+ _mm256_extractf128_si256(t, 1));
+#else
+ // uint32_t lsb = (input >> 16);
+ __m128i lo = _mm_srli_epi32(_mm256_extractf128_si256(input, 0), 16);
+ __m128i hi = _mm_srli_epi32(_mm256_extractf128_si256(input, 1), 16);
+ // uint32_t lsb = lsb & 1;
+ lo = _mm_and_si128(lo, _mm_set1_epi32(1));
+ hi = _mm_and_si128(hi, _mm_set1_epi32(1));
+ // uint32_t rounding_bias = 0x7fff + lsb;
+ lo = _mm_add_epi32(lo, _mm_set1_epi32(0x7fff));
+ hi = _mm_add_epi32(hi, _mm_set1_epi32(0x7fff));
+ // input += rounding_bias;
+ lo = _mm_add_epi32(lo, _mm256_extractf128_si256(input, 0));
+ hi = _mm_add_epi32(hi, _mm256_extractf128_si256(input, 1));
+ // input = input >> 16;
+ lo = _mm_srli_epi32(lo, 16);
+ hi = _mm_srli_epi32(hi, 16);
+ // Check NaN before converting back to bf16
+ __m256 mask = _mm256_cmp_ps(a, a, _CMP_ORD_Q);
+ __m128i nan = _mm_set1_epi32(0x7fc0);
+ lo = _mm_blendv_epi8(nan, lo, _mm_castps_si128(_mm256_castps256_ps128(mask)));
+ hi = _mm_blendv_epi8(nan, hi, _mm_castps_si128(_mm256_extractf128_ps(mask, 1)));
+ // output = numext::bit_cast<uint16_t>(input);
+ return _mm_packus_epi32(lo, hi);
+#endif
+}
+
+template<> EIGEN_STRONG_INLINE Packet8bf pset1<Packet8bf>(const bfloat16& from) {
+ return _mm_set1_epi16(numext::bit_cast<numext::uint16_t>(from));
+}
+
+template<> EIGEN_STRONG_INLINE bfloat16 pfirst<Packet8bf>(const Packet8bf& from) {
+ return numext::bit_cast<bfloat16>(static_cast<numext::uint16_t>(_mm_extract_epi16(from, 0)));
+}
+
+template<> EIGEN_STRONG_INLINE Packet8bf pload<Packet8bf>(const bfloat16* from) {
+ return _mm_load_si128(reinterpret_cast<const __m128i*>(from));
+}
+
+template<> EIGEN_STRONG_INLINE Packet8bf ploadu<Packet8bf>(const bfloat16* from) {
+ return _mm_loadu_si128(reinterpret_cast<const __m128i*>(from));
+}
+
+template<> EIGEN_STRONG_INLINE void pstore<bfloat16>(bfloat16* to, const Packet8bf& from) {
+ _mm_store_si128(reinterpret_cast<__m128i*>(to), from);
+}
+
+template<> EIGEN_STRONG_INLINE void pstoreu<bfloat16>(bfloat16* to, const Packet8bf& from) {
+ _mm_storeu_si128(reinterpret_cast<__m128i*>(to), from);
+}
+
+template<> EIGEN_STRONG_INLINE Packet8bf
+ploaddup<Packet8bf>(const bfloat16* from) {
+ const numext::uint16_t a = numext::bit_cast<numext::uint16_t>(from[0]);
+ const numext::uint16_t b = numext::bit_cast<numext::uint16_t>(from[1]);
+ const numext::uint16_t c = numext::bit_cast<numext::uint16_t>(from[2]);
+ const numext::uint16_t d = numext::bit_cast<numext::uint16_t>(from[3]);
+ return _mm_set_epi16(d, d, c, c, b, b, a, a);
+}
+
+template<> EIGEN_STRONG_INLINE Packet8bf
+ploadquad<Packet8bf>(const bfloat16* from) {
+ const numext::uint16_t a = numext::bit_cast<numext::uint16_t>(from[0]);
+ const numext::uint16_t b = numext::bit_cast<numext::uint16_t>(from[1]);
+ return _mm_set_epi16(b, b, b, b, a, a, a, a);
+}
+
+template<> EIGEN_STRONG_INLINE Packet8bf ptrue(const Packet8bf& a) {
+ return _mm_cmpeq_epi32(a, a);
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet8bf pabs(const Packet8bf& a) {
+ const __m128i sign_mask = _mm_set1_epi16(static_cast<numext::uint16_t>(0x8000));
+ return _mm_andnot_si128(sign_mask, a);
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet8bf pmin<Packet8bf>(const Packet8bf& a,
+ const Packet8bf& b) {
+ return F32ToBf16(pmin<Packet8f>(Bf16ToF32(a), Bf16ToF32(b)));
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet8bf pmax<Packet8bf>(const Packet8bf& a,
+ const Packet8bf& b) {
+ return F32ToBf16(pmax<Packet8f>(Bf16ToF32(a), Bf16ToF32(b)));
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet8bf plset<Packet8bf>(const bfloat16& a) {
+ return F32ToBf16(plset<Packet8f>(static_cast<float>(a)));
+}
+
+template<> EIGEN_STRONG_INLINE Packet8bf por(const Packet8bf& a,const Packet8bf& b) {
+ return _mm_or_si128(a,b);
+}
+template<> EIGEN_STRONG_INLINE Packet8bf pxor(const Packet8bf& a,const Packet8bf& b) {
+ return _mm_xor_si128(a,b);
+}
+template<> EIGEN_STRONG_INLINE Packet8bf pand(const Packet8bf& a,const Packet8bf& b) {
+ return _mm_and_si128(a,b);
+}
+template<> EIGEN_STRONG_INLINE Packet8bf pandnot(const Packet8bf& a,const Packet8bf& b) {
+ return _mm_andnot_si128(b,a);
+}
+
+template<> EIGEN_STRONG_INLINE Packet8bf pselect(const Packet8bf& mask, const Packet8bf& a, const Packet8bf& b) {
+ return _mm_blendv_epi8(b, a, mask);
+}
+
+template<> EIGEN_STRONG_INLINE Packet8bf pround<Packet8bf>(const Packet8bf& a)
+{
+ return F32ToBf16(pround<Packet8f>(Bf16ToF32(a)));
+}
+
+template<> EIGEN_STRONG_INLINE Packet8bf print<Packet8bf>(const Packet8bf& a) {
+ return F32ToBf16(print<Packet8f>(Bf16ToF32(a)));
+}
+
+template<> EIGEN_STRONG_INLINE Packet8bf pceil<Packet8bf>(const Packet8bf& a) {
+ return F32ToBf16(pceil<Packet8f>(Bf16ToF32(a)));
+}
+
+template<> EIGEN_STRONG_INLINE Packet8bf pfloor<Packet8bf>(const Packet8bf& a) {
+ return F32ToBf16(pfloor<Packet8f>(Bf16ToF32(a)));
+}
+
+template<> EIGEN_STRONG_INLINE Packet8bf pcmp_eq(const Packet8bf& a,const Packet8bf& b) {
+ return Pack16To8(pcmp_eq(Bf16ToF32(a), Bf16ToF32(b)));
+}
+
+template<> EIGEN_STRONG_INLINE Packet8bf pcmp_le(const Packet8bf& a,const Packet8bf& b) {
+ return Pack16To8(pcmp_le(Bf16ToF32(a), Bf16ToF32(b)));
+}
+
+template<> EIGEN_STRONG_INLINE Packet8bf pcmp_lt(const Packet8bf& a,const Packet8bf& b) {
+ return Pack16To8(pcmp_lt(Bf16ToF32(a), Bf16ToF32(b)));
+}
+
+template<> EIGEN_STRONG_INLINE Packet8bf pcmp_lt_or_nan(const Packet8bf& a,const Packet8bf& b) {
+ return Pack16To8(pcmp_lt_or_nan(Bf16ToF32(a), Bf16ToF32(b)));
+}
+
+template<> EIGEN_STRONG_INLINE Packet8bf pconj(const Packet8bf& a) { return a; }
+
+template<> EIGEN_STRONG_INLINE Packet8bf pnegate(const Packet8bf& a) {
+ Packet8bf sign_mask = _mm_set1_epi16(static_cast<numext::uint16_t>(0x8000));
+ return _mm_xor_si128(a, sign_mask);
+}
+
+template<> EIGEN_STRONG_INLINE Packet8bf padd<Packet8bf>(const Packet8bf& a, const Packet8bf& b) {
+ return F32ToBf16(padd<Packet8f>(Bf16ToF32(a), Bf16ToF32(b)));
+}
+
+template<> EIGEN_STRONG_INLINE Packet8bf psub<Packet8bf>(const Packet8bf& a, const Packet8bf& b) {
+ return F32ToBf16(psub<Packet8f>(Bf16ToF32(a), Bf16ToF32(b)));
+}
+
+template<> EIGEN_STRONG_INLINE Packet8bf pmul<Packet8bf>(const Packet8bf& a, const Packet8bf& b) {
+ return F32ToBf16(pmul<Packet8f>(Bf16ToF32(a), Bf16ToF32(b)));
+}
+
+template<> EIGEN_STRONG_INLINE Packet8bf pdiv<Packet8bf>(const Packet8bf& a, const Packet8bf& b) {
+ return F32ToBf16(pdiv<Packet8f>(Bf16ToF32(a), Bf16ToF32(b)));
+}
+
+
+template<> EIGEN_STRONG_INLINE Packet8bf pgather<bfloat16, Packet8bf>(const bfloat16* from, Index stride)
+{
+ const numext::uint16_t s0 = numext::bit_cast<numext::uint16_t>(from[0*stride]);
+ const numext::uint16_t s1 = numext::bit_cast<numext::uint16_t>(from[1*stride]);
+ const numext::uint16_t s2 = numext::bit_cast<numext::uint16_t>(from[2*stride]);
+ const numext::uint16_t s3 = numext::bit_cast<numext::uint16_t>(from[3*stride]);
+ const numext::uint16_t s4 = numext::bit_cast<numext::uint16_t>(from[4*stride]);
+ const numext::uint16_t s5 = numext::bit_cast<numext::uint16_t>(from[5*stride]);
+ const numext::uint16_t s6 = numext::bit_cast<numext::uint16_t>(from[6*stride]);
+ const numext::uint16_t s7 = numext::bit_cast<numext::uint16_t>(from[7*stride]);
+ return _mm_set_epi16(s7, s6, s5, s4, s3, s2, s1, s0);
+}
+
+template<> EIGEN_STRONG_INLINE void pscatter<bfloat16, Packet8bf>(bfloat16* to, const Packet8bf& from, Index stride)
+{
+ EIGEN_ALIGN32 bfloat16 aux[8];
+ pstore(aux, from);
+ to[stride*0] = aux[0];
+ to[stride*1] = aux[1];
+ to[stride*2] = aux[2];
+ to[stride*3] = aux[3];
+ to[stride*4] = aux[4];
+ to[stride*5] = aux[5];
+ to[stride*6] = aux[6];
+ to[stride*7] = aux[7];
+}
+
+template<> EIGEN_STRONG_INLINE bfloat16 predux<Packet8bf>(const Packet8bf& a) {
+ return static_cast<bfloat16>(predux<Packet8f>(Bf16ToF32(a)));
+}
+
+template<> EIGEN_STRONG_INLINE bfloat16 predux_max<Packet8bf>(const Packet8bf& a) {
+ return static_cast<bfloat16>(predux_max<Packet8f>(Bf16ToF32(a)));
+}
+
+template<> EIGEN_STRONG_INLINE bfloat16 predux_min<Packet8bf>(const Packet8bf& a) {
+ return static_cast<bfloat16>(predux_min<Packet8f>(Bf16ToF32(a)));
+}
+
+template<> EIGEN_STRONG_INLINE bfloat16 predux_mul<Packet8bf>(const Packet8bf& a) {
+ return static_cast<bfloat16>(predux_mul<Packet8f>(Bf16ToF32(a)));
+}
+
+template<> EIGEN_STRONG_INLINE Packet8bf preverse(const Packet8bf& a)
+{
+ __m128i m = _mm_setr_epi8(14,15,12,13,10,11,8,9,6,7,4,5,2,3,0,1);
+ return _mm_shuffle_epi8(a,m);
+}
+
+EIGEN_STRONG_INLINE void
+ptranspose(PacketBlock<Packet8bf,8>& kernel) {
+ __m128i a = kernel.packet[0];
+ __m128i b = kernel.packet[1];
+ __m128i c = kernel.packet[2];
+ __m128i d = kernel.packet[3];
+ __m128i e = kernel.packet[4];
+ __m128i f = kernel.packet[5];
+ __m128i g = kernel.packet[6];
+ __m128i h = kernel.packet[7];
+
+ __m128i a03b03 = _mm_unpacklo_epi16(a, b);
+ __m128i c03d03 = _mm_unpacklo_epi16(c, d);
+ __m128i e03f03 = _mm_unpacklo_epi16(e, f);
+ __m128i g03h03 = _mm_unpacklo_epi16(g, h);
+ __m128i a47b47 = _mm_unpackhi_epi16(a, b);
+ __m128i c47d47 = _mm_unpackhi_epi16(c, d);
+ __m128i e47f47 = _mm_unpackhi_epi16(e, f);
+ __m128i g47h47 = _mm_unpackhi_epi16(g, h);
+
+ __m128i a01b01c01d01 = _mm_unpacklo_epi32(a03b03, c03d03);
+ __m128i a23b23c23d23 = _mm_unpackhi_epi32(a03b03, c03d03);
+ __m128i e01f01g01h01 = _mm_unpacklo_epi32(e03f03, g03h03);
+ __m128i e23f23g23h23 = _mm_unpackhi_epi32(e03f03, g03h03);
+ __m128i a45b45c45d45 = _mm_unpacklo_epi32(a47b47, c47d47);
+ __m128i a67b67c67d67 = _mm_unpackhi_epi32(a47b47, c47d47);
+ __m128i e45f45g45h45 = _mm_unpacklo_epi32(e47f47, g47h47);
+ __m128i e67f67g67h67 = _mm_unpackhi_epi32(e47f47, g47h47);
+
+ kernel.packet[0] = _mm_unpacklo_epi64(a01b01c01d01, e01f01g01h01);
+ kernel.packet[1] = _mm_unpackhi_epi64(a01b01c01d01, e01f01g01h01);
+ kernel.packet[2] = _mm_unpacklo_epi64(a23b23c23d23, e23f23g23h23);
+ kernel.packet[3] = _mm_unpackhi_epi64(a23b23c23d23, e23f23g23h23);
+ kernel.packet[4] = _mm_unpacklo_epi64(a45b45c45d45, e45f45g45h45);
+ kernel.packet[5] = _mm_unpackhi_epi64(a45b45c45d45, e45f45g45h45);
+ kernel.packet[6] = _mm_unpacklo_epi64(a67b67c67d67, e67f67g67h67);
+ kernel.packet[7] = _mm_unpackhi_epi64(a67b67c67d67, e67f67g67h67);
+}
+
+EIGEN_STRONG_INLINE void
+ptranspose(PacketBlock<Packet8bf,4>& kernel) {
+ __m128i a = kernel.packet[0];
+ __m128i b = kernel.packet[1];
+ __m128i c = kernel.packet[2];
+ __m128i d = kernel.packet[3];
+
+ __m128i ab_03 = _mm_unpacklo_epi16(a, b);
+ __m128i cd_03 = _mm_unpacklo_epi16(c, d);
+ __m128i ab_47 = _mm_unpackhi_epi16(a, b);
+ __m128i cd_47 = _mm_unpackhi_epi16(c, d);
+
+ kernel.packet[0] = _mm_unpacklo_epi32(ab_03, cd_03);
+ kernel.packet[1] = _mm_unpackhi_epi32(ab_03, cd_03);
+ kernel.packet[2] = _mm_unpacklo_epi32(ab_47, cd_47);
+ kernel.packet[3] = _mm_unpackhi_epi32(ab_47, cd_47);
+}
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_PACKET_MATH_AVX_H
diff --git a/Eigen/src/Core/arch/AVX/TypeCasting.h b/Eigen/src/Core/arch/AVX/TypeCasting.h
new file mode 100644
index 0000000..320479b
--- /dev/null
+++ b/Eigen/src/Core/arch/AVX/TypeCasting.h
@@ -0,0 +1,117 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2015 Benoit Steiner <benoit.steiner.goog@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_TYPE_CASTING_AVX_H
+#define EIGEN_TYPE_CASTING_AVX_H
+
+#include "../../InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+
+// For now we use SSE to handle integers, so we can't use AVX instructions to cast
+// from int to float
+template <>
+struct type_casting_traits<float, int> {
+ enum {
+ VectorizedCast = 0,
+ SrcCoeffRatio = 1,
+ TgtCoeffRatio = 1
+ };
+};
+
+template <>
+struct type_casting_traits<int, float> {
+ enum {
+ VectorizedCast = 0,
+ SrcCoeffRatio = 1,
+ TgtCoeffRatio = 1
+ };
+};
+
+
+#ifndef EIGEN_VECTORIZE_AVX512
+
+template <>
+struct type_casting_traits<Eigen::half, float> {
+ enum {
+ VectorizedCast = 1,
+ SrcCoeffRatio = 1,
+ TgtCoeffRatio = 1
+ };
+};
+
+
+template <>
+struct type_casting_traits<float, Eigen::half> {
+ enum {
+ VectorizedCast = 1,
+ SrcCoeffRatio = 1,
+ TgtCoeffRatio = 1
+ };
+};
+
+template <>
+struct type_casting_traits<bfloat16, float> {
+ enum {
+ VectorizedCast = 1,
+ SrcCoeffRatio = 1,
+ TgtCoeffRatio = 1
+ };
+};
+
+template <>
+struct type_casting_traits<float, bfloat16> {
+ enum {
+ VectorizedCast = 1,
+ SrcCoeffRatio = 1,
+ TgtCoeffRatio = 1
+ };
+};
+
+#endif // EIGEN_VECTORIZE_AVX512
+
+template<> EIGEN_STRONG_INLINE Packet8i pcast<Packet8f, Packet8i>(const Packet8f& a) {
+ return _mm256_cvttps_epi32(a);
+}
+
+template<> EIGEN_STRONG_INLINE Packet8f pcast<Packet8i, Packet8f>(const Packet8i& a) {
+ return _mm256_cvtepi32_ps(a);
+}
+
+template<> EIGEN_STRONG_INLINE Packet8i preinterpret<Packet8i,Packet8f>(const Packet8f& a) {
+ return _mm256_castps_si256(a);
+}
+
+template<> EIGEN_STRONG_INLINE Packet8f preinterpret<Packet8f,Packet8i>(const Packet8i& a) {
+ return _mm256_castsi256_ps(a);
+}
+
+template<> EIGEN_STRONG_INLINE Packet8f pcast<Packet8h, Packet8f>(const Packet8h& a) {
+ return half2float(a);
+}
+
+template<> EIGEN_STRONG_INLINE Packet8f pcast<Packet8bf, Packet8f>(const Packet8bf& a) {
+ return Bf16ToF32(a);
+}
+
+template<> EIGEN_STRONG_INLINE Packet8h pcast<Packet8f, Packet8h>(const Packet8f& a) {
+ return float2half(a);
+}
+
+template<> EIGEN_STRONG_INLINE Packet8bf pcast<Packet8f, Packet8bf>(const Packet8f& a) {
+ return F32ToBf16(a);
+}
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_TYPE_CASTING_AVX_H
diff --git a/Eigen/src/Core/arch/AVX512/Complex.h b/Eigen/src/Core/arch/AVX512/Complex.h
new file mode 100644
index 0000000..6d8ee2b
--- /dev/null
+++ b/Eigen/src/Core/arch/AVX512/Complex.h
@@ -0,0 +1,382 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2018 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_COMPLEX_AVX512_H
+#define EIGEN_COMPLEX_AVX512_H
+
+#include "../../InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+
+//---------- float ----------
+struct Packet8cf
+{
+ EIGEN_STRONG_INLINE Packet8cf() {}
+ EIGEN_STRONG_INLINE explicit Packet8cf(const __m512& a) : v(a) {}
+ __m512 v;
+};
+
+template<> struct packet_traits<std::complex<float> > : default_packet_traits
+{
+ typedef Packet8cf type;
+ typedef Packet4cf half;
+ enum {
+ Vectorizable = 1,
+ AlignedOnScalar = 1,
+ size = 8,
+ HasHalfPacket = 1,
+
+ HasAdd = 1,
+ HasSub = 1,
+ HasMul = 1,
+ HasDiv = 1,
+ HasNegate = 1,
+ HasSqrt = 1,
+ HasAbs = 0,
+ HasAbs2 = 0,
+ HasMin = 0,
+ HasMax = 0,
+ HasSetLinear = 0
+ };
+};
+
+template<> struct unpacket_traits<Packet8cf> {
+ typedef std::complex<float> type;
+ typedef Packet4cf half;
+ typedef Packet16f as_real;
+ enum {
+ size = 8,
+ alignment=unpacket_traits<Packet16f>::alignment,
+ vectorizable=true,
+ masked_load_available=false,
+ masked_store_available=false
+ };
+};
+
+template<> EIGEN_STRONG_INLINE Packet8cf ptrue<Packet8cf>(const Packet8cf& a) { return Packet8cf(ptrue(Packet16f(a.v))); }
+template<> EIGEN_STRONG_INLINE Packet8cf padd<Packet8cf>(const Packet8cf& a, const Packet8cf& b) { return Packet8cf(_mm512_add_ps(a.v,b.v)); }
+template<> EIGEN_STRONG_INLINE Packet8cf psub<Packet8cf>(const Packet8cf& a, const Packet8cf& b) { return Packet8cf(_mm512_sub_ps(a.v,b.v)); }
+template<> EIGEN_STRONG_INLINE Packet8cf pnegate(const Packet8cf& a)
+{
+ return Packet8cf(pnegate(a.v));
+}
+template<> EIGEN_STRONG_INLINE Packet8cf pconj(const Packet8cf& a)
+{
+ const __m512 mask = _mm512_castsi512_ps(_mm512_setr_epi32(
+ 0x00000000,0x80000000,0x00000000,0x80000000,0x00000000,0x80000000,0x00000000,0x80000000,
+ 0x00000000,0x80000000,0x00000000,0x80000000,0x00000000,0x80000000,0x00000000,0x80000000));
+ return Packet8cf(pxor(a.v,mask));
+}
+
+template<> EIGEN_STRONG_INLINE Packet8cf pmul<Packet8cf>(const Packet8cf& a, const Packet8cf& b)
+{
+ __m512 tmp2 = _mm512_mul_ps(_mm512_movehdup_ps(a.v), _mm512_permute_ps(b.v, _MM_SHUFFLE(2,3,0,1)));
+ return Packet8cf(_mm512_fmaddsub_ps(_mm512_moveldup_ps(a.v), b.v, tmp2));
+}
+
+template<> EIGEN_STRONG_INLINE Packet8cf pand <Packet8cf>(const Packet8cf& a, const Packet8cf& b) { return Packet8cf(pand(a.v,b.v)); }
+template<> EIGEN_STRONG_INLINE Packet8cf por <Packet8cf>(const Packet8cf& a, const Packet8cf& b) { return Packet8cf(por(a.v,b.v)); }
+template<> EIGEN_STRONG_INLINE Packet8cf pxor <Packet8cf>(const Packet8cf& a, const Packet8cf& b) { return Packet8cf(pxor(a.v,b.v)); }
+template<> EIGEN_STRONG_INLINE Packet8cf pandnot<Packet8cf>(const Packet8cf& a, const Packet8cf& b) { return Packet8cf(pandnot(a.v,b.v)); }
+
+template <>
+EIGEN_STRONG_INLINE Packet8cf pcmp_eq(const Packet8cf& a, const Packet8cf& b) {
+ __m512 eq = pcmp_eq<Packet16f>(a.v, b.v);
+ return Packet8cf(pand(eq, _mm512_permute_ps(eq, 0xB1)));
+}
+
+template<> EIGEN_STRONG_INLINE Packet8cf pload <Packet8cf>(const std::complex<float>* from) { EIGEN_DEBUG_ALIGNED_LOAD return Packet8cf(pload<Packet16f>(&numext::real_ref(*from))); }
+template<> EIGEN_STRONG_INLINE Packet8cf ploadu<Packet8cf>(const std::complex<float>* from) { EIGEN_DEBUG_UNALIGNED_LOAD return Packet8cf(ploadu<Packet16f>(&numext::real_ref(*from))); }
+
+
+template<> EIGEN_STRONG_INLINE Packet8cf pset1<Packet8cf>(const std::complex<float>& from)
+{
+ const float re = std::real(from);
+ const float im = std::imag(from);
+ return Packet8cf(_mm512_set_ps(im, re, im, re, im, re, im, re, im, re, im, re, im, re, im, re));
+}
+
+template<> EIGEN_STRONG_INLINE Packet8cf ploaddup<Packet8cf>(const std::complex<float>* from)
+{
+ return Packet8cf( _mm512_castpd_ps( ploaddup<Packet8d>((const double*)(const void*)from )) );
+}
+template<> EIGEN_STRONG_INLINE Packet8cf ploadquad<Packet8cf>(const std::complex<float>* from)
+{
+ return Packet8cf( _mm512_castpd_ps( ploadquad<Packet8d>((const double*)(const void*)from )) );
+}
+
+template<> EIGEN_STRONG_INLINE void pstore <std::complex<float> >(std::complex<float>* to, const Packet8cf& from) { EIGEN_DEBUG_ALIGNED_STORE pstore(&numext::real_ref(*to), from.v); }
+template<> EIGEN_STRONG_INLINE void pstoreu<std::complex<float> >(std::complex<float>* to, const Packet8cf& from) { EIGEN_DEBUG_UNALIGNED_STORE pstoreu(&numext::real_ref(*to), from.v); }
+
+template<> EIGEN_DEVICE_FUNC inline Packet8cf pgather<std::complex<float>, Packet8cf>(const std::complex<float>* from, Index stride)
+{
+ return Packet8cf(_mm512_castpd_ps(pgather<double,Packet8d>((const double*)(const void*)from, stride)));
+}
+
+template<> EIGEN_DEVICE_FUNC inline void pscatter<std::complex<float>, Packet8cf>(std::complex<float>* to, const Packet8cf& from, Index stride)
+{
+ pscatter((double*)(void*)to, _mm512_castps_pd(from.v), stride);
+}
+
+template<> EIGEN_STRONG_INLINE std::complex<float> pfirst<Packet8cf>(const Packet8cf& a)
+{
+ return pfirst(Packet2cf(_mm512_castps512_ps128(a.v)));
+}
+
+template<> EIGEN_STRONG_INLINE Packet8cf preverse(const Packet8cf& a) {
+ return Packet8cf(_mm512_castsi512_ps(
+ _mm512_permutexvar_epi64( _mm512_set_epi32(0, 0, 0, 1, 0, 2, 0, 3, 0, 4, 0, 5, 0, 6, 0, 7),
+ _mm512_castps_si512(a.v))));
+}
+
+template<> EIGEN_STRONG_INLINE std::complex<float> predux<Packet8cf>(const Packet8cf& a)
+{
+ return predux(padd(Packet4cf(extract256<0>(a.v)),
+ Packet4cf(extract256<1>(a.v))));
+}
+
+template<> EIGEN_STRONG_INLINE std::complex<float> predux_mul<Packet8cf>(const Packet8cf& a)
+{
+ return predux_mul(pmul(Packet4cf(extract256<0>(a.v)),
+ Packet4cf(extract256<1>(a.v))));
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet4cf predux_half_dowto4<Packet8cf>(const Packet8cf& a) {
+ __m256 lane0 = extract256<0>(a.v);
+ __m256 lane1 = extract256<1>(a.v);
+ __m256 res = _mm256_add_ps(lane0, lane1);
+ return Packet4cf(res);
+}
+
+EIGEN_MAKE_CONJ_HELPER_CPLX_REAL(Packet8cf,Packet16f)
+
+template<> EIGEN_STRONG_INLINE Packet8cf pdiv<Packet8cf>(const Packet8cf& a, const Packet8cf& b)
+{
+ return pdiv_complex(a, b);
+}
+
+template<> EIGEN_STRONG_INLINE Packet8cf pcplxflip<Packet8cf>(const Packet8cf& x)
+{
+ return Packet8cf(_mm512_shuffle_ps(x.v, x.v, _MM_SHUFFLE(2, 3, 0 ,1)));
+}
+
+//---------- double ----------
+struct Packet4cd
+{
+ EIGEN_STRONG_INLINE Packet4cd() {}
+ EIGEN_STRONG_INLINE explicit Packet4cd(const __m512d& a) : v(a) {}
+ __m512d v;
+};
+
+template<> struct packet_traits<std::complex<double> > : default_packet_traits
+{
+ typedef Packet4cd type;
+ typedef Packet2cd half;
+ enum {
+ Vectorizable = 1,
+ AlignedOnScalar = 0,
+ size = 4,
+ HasHalfPacket = 1,
+
+ HasAdd = 1,
+ HasSub = 1,
+ HasMul = 1,
+ HasDiv = 1,
+ HasNegate = 1,
+ HasSqrt = 1,
+ HasAbs = 0,
+ HasAbs2 = 0,
+ HasMin = 0,
+ HasMax = 0,
+ HasSetLinear = 0
+ };
+};
+
+template<> struct unpacket_traits<Packet4cd> {
+ typedef std::complex<double> type;
+ typedef Packet2cd half;
+ typedef Packet8d as_real;
+ enum {
+ size = 4,
+ alignment = unpacket_traits<Packet8d>::alignment,
+ vectorizable=true,
+ masked_load_available=false,
+ masked_store_available=false
+ };
+};
+
+template<> EIGEN_STRONG_INLINE Packet4cd padd<Packet4cd>(const Packet4cd& a, const Packet4cd& b) { return Packet4cd(_mm512_add_pd(a.v,b.v)); }
+template<> EIGEN_STRONG_INLINE Packet4cd psub<Packet4cd>(const Packet4cd& a, const Packet4cd& b) { return Packet4cd(_mm512_sub_pd(a.v,b.v)); }
+template<> EIGEN_STRONG_INLINE Packet4cd pnegate(const Packet4cd& a) { return Packet4cd(pnegate(a.v)); }
+template<> EIGEN_STRONG_INLINE Packet4cd pconj(const Packet4cd& a)
+{
+ const __m512d mask = _mm512_castsi512_pd(
+ _mm512_set_epi32(0x80000000,0x0,0x0,0x0,0x80000000,0x0,0x0,0x0,
+ 0x80000000,0x0,0x0,0x0,0x80000000,0x0,0x0,0x0));
+ return Packet4cd(pxor(a.v,mask));
+}
+
+template<> EIGEN_STRONG_INLINE Packet4cd pmul<Packet4cd>(const Packet4cd& a, const Packet4cd& b)
+{
+ __m512d tmp1 = _mm512_shuffle_pd(a.v,a.v,0x0);
+ __m512d tmp2 = _mm512_shuffle_pd(a.v,a.v,0xFF);
+ __m512d tmp3 = _mm512_shuffle_pd(b.v,b.v,0x55);
+ __m512d odd = _mm512_mul_pd(tmp2, tmp3);
+ return Packet4cd(_mm512_fmaddsub_pd(tmp1, b.v, odd));
+}
+
+template<> EIGEN_STRONG_INLINE Packet4cd ptrue<Packet4cd>(const Packet4cd& a) { return Packet4cd(ptrue(Packet8d(a.v))); }
+template<> EIGEN_STRONG_INLINE Packet4cd pand <Packet4cd>(const Packet4cd& a, const Packet4cd& b) { return Packet4cd(pand(a.v,b.v)); }
+template<> EIGEN_STRONG_INLINE Packet4cd por <Packet4cd>(const Packet4cd& a, const Packet4cd& b) { return Packet4cd(por(a.v,b.v)); }
+template<> EIGEN_STRONG_INLINE Packet4cd pxor <Packet4cd>(const Packet4cd& a, const Packet4cd& b) { return Packet4cd(pxor(a.v,b.v)); }
+template<> EIGEN_STRONG_INLINE Packet4cd pandnot<Packet4cd>(const Packet4cd& a, const Packet4cd& b) { return Packet4cd(pandnot(a.v,b.v)); }
+
+template <>
+EIGEN_STRONG_INLINE Packet4cd pcmp_eq(const Packet4cd& a, const Packet4cd& b) {
+ __m512d eq = pcmp_eq<Packet8d>(a.v, b.v);
+ return Packet4cd(pand(eq, _mm512_permute_pd(eq, 0x55)));
+}
+
+template<> EIGEN_STRONG_INLINE Packet4cd pload <Packet4cd>(const std::complex<double>* from)
+{ EIGEN_DEBUG_ALIGNED_LOAD return Packet4cd(pload<Packet8d>((const double*)from)); }
+template<> EIGEN_STRONG_INLINE Packet4cd ploadu<Packet4cd>(const std::complex<double>* from)
+{ EIGEN_DEBUG_UNALIGNED_LOAD return Packet4cd(ploadu<Packet8d>((const double*)from)); }
+
+template<> EIGEN_STRONG_INLINE Packet4cd pset1<Packet4cd>(const std::complex<double>& from)
+{
+ return Packet4cd(_mm512_castps_pd(_mm512_broadcast_f32x4( _mm_castpd_ps(pset1<Packet1cd>(from).v))));
+}
+
+template<> EIGEN_STRONG_INLINE Packet4cd ploaddup<Packet4cd>(const std::complex<double>* from) {
+ return Packet4cd(_mm512_insertf64x4(
+ _mm512_castpd256_pd512(ploaddup<Packet2cd>(from).v), ploaddup<Packet2cd>(from+1).v, 1));
+}
+
+template<> EIGEN_STRONG_INLINE void pstore <std::complex<double> >(std::complex<double> * to, const Packet4cd& from) { EIGEN_DEBUG_ALIGNED_STORE pstore((double*)to, from.v); }
+template<> EIGEN_STRONG_INLINE void pstoreu<std::complex<double> >(std::complex<double> * to, const Packet4cd& from) { EIGEN_DEBUG_UNALIGNED_STORE pstoreu((double*)to, from.v); }
+
+template<> EIGEN_DEVICE_FUNC inline Packet4cd pgather<std::complex<double>, Packet4cd>(const std::complex<double>* from, Index stride)
+{
+ return Packet4cd(_mm512_insertf64x4(_mm512_castpd256_pd512(
+ _mm256_insertf128_pd(_mm256_castpd128_pd256(ploadu<Packet1cd>(from+0*stride).v), ploadu<Packet1cd>(from+1*stride).v,1)),
+ _mm256_insertf128_pd(_mm256_castpd128_pd256(ploadu<Packet1cd>(from+2*stride).v), ploadu<Packet1cd>(from+3*stride).v,1), 1));
+}
+
+template<> EIGEN_DEVICE_FUNC inline void pscatter<std::complex<double>, Packet4cd>(std::complex<double>* to, const Packet4cd& from, Index stride)
+{
+ __m512i fromi = _mm512_castpd_si512(from.v);
+ double* tod = (double*)(void*)to;
+ _mm_storeu_pd(tod+0*stride, _mm_castsi128_pd(_mm512_extracti32x4_epi32(fromi,0)) );
+ _mm_storeu_pd(tod+2*stride, _mm_castsi128_pd(_mm512_extracti32x4_epi32(fromi,1)) );
+ _mm_storeu_pd(tod+4*stride, _mm_castsi128_pd(_mm512_extracti32x4_epi32(fromi,2)) );
+ _mm_storeu_pd(tod+6*stride, _mm_castsi128_pd(_mm512_extracti32x4_epi32(fromi,3)) );
+}
+
+template<> EIGEN_STRONG_INLINE std::complex<double> pfirst<Packet4cd>(const Packet4cd& a)
+{
+ __m128d low = extract128<0>(a.v);
+ EIGEN_ALIGN16 double res[2];
+ _mm_store_pd(res, low);
+ return std::complex<double>(res[0],res[1]);
+}
+
+template<> EIGEN_STRONG_INLINE Packet4cd preverse(const Packet4cd& a) {
+ return Packet4cd(_mm512_shuffle_f64x2(a.v, a.v, (shuffle_mask<3,2,1,0>::mask)));
+}
+
+template<> EIGEN_STRONG_INLINE std::complex<double> predux<Packet4cd>(const Packet4cd& a)
+{
+ return predux(padd(Packet2cd(_mm512_extractf64x4_pd(a.v,0)),
+ Packet2cd(_mm512_extractf64x4_pd(a.v,1))));
+}
+
+template<> EIGEN_STRONG_INLINE std::complex<double> predux_mul<Packet4cd>(const Packet4cd& a)
+{
+ return predux_mul(pmul(Packet2cd(_mm512_extractf64x4_pd(a.v,0)),
+ Packet2cd(_mm512_extractf64x4_pd(a.v,1))));
+}
+
+EIGEN_MAKE_CONJ_HELPER_CPLX_REAL(Packet4cd,Packet8d)
+
+template<> EIGEN_STRONG_INLINE Packet4cd pdiv<Packet4cd>(const Packet4cd& a, const Packet4cd& b)
+{
+ return pdiv_complex(a, b);
+}
+
+template<> EIGEN_STRONG_INLINE Packet4cd pcplxflip<Packet4cd>(const Packet4cd& x)
+{
+ return Packet4cd(_mm512_permute_pd(x.v,0x55));
+}
+
+EIGEN_DEVICE_FUNC inline void
+ptranspose(PacketBlock<Packet8cf,4>& kernel) {
+ PacketBlock<Packet8d,4> pb;
+
+ pb.packet[0] = _mm512_castps_pd(kernel.packet[0].v);
+ pb.packet[1] = _mm512_castps_pd(kernel.packet[1].v);
+ pb.packet[2] = _mm512_castps_pd(kernel.packet[2].v);
+ pb.packet[3] = _mm512_castps_pd(kernel.packet[3].v);
+ ptranspose(pb);
+ kernel.packet[0].v = _mm512_castpd_ps(pb.packet[0]);
+ kernel.packet[1].v = _mm512_castpd_ps(pb.packet[1]);
+ kernel.packet[2].v = _mm512_castpd_ps(pb.packet[2]);
+ kernel.packet[3].v = _mm512_castpd_ps(pb.packet[3]);
+}
+
+EIGEN_DEVICE_FUNC inline void
+ptranspose(PacketBlock<Packet8cf,8>& kernel) {
+ PacketBlock<Packet8d,8> pb;
+
+ pb.packet[0] = _mm512_castps_pd(kernel.packet[0].v);
+ pb.packet[1] = _mm512_castps_pd(kernel.packet[1].v);
+ pb.packet[2] = _mm512_castps_pd(kernel.packet[2].v);
+ pb.packet[3] = _mm512_castps_pd(kernel.packet[3].v);
+ pb.packet[4] = _mm512_castps_pd(kernel.packet[4].v);
+ pb.packet[5] = _mm512_castps_pd(kernel.packet[5].v);
+ pb.packet[6] = _mm512_castps_pd(kernel.packet[6].v);
+ pb.packet[7] = _mm512_castps_pd(kernel.packet[7].v);
+ ptranspose(pb);
+ kernel.packet[0].v = _mm512_castpd_ps(pb.packet[0]);
+ kernel.packet[1].v = _mm512_castpd_ps(pb.packet[1]);
+ kernel.packet[2].v = _mm512_castpd_ps(pb.packet[2]);
+ kernel.packet[3].v = _mm512_castpd_ps(pb.packet[3]);
+ kernel.packet[4].v = _mm512_castpd_ps(pb.packet[4]);
+ kernel.packet[5].v = _mm512_castpd_ps(pb.packet[5]);
+ kernel.packet[6].v = _mm512_castpd_ps(pb.packet[6]);
+ kernel.packet[7].v = _mm512_castpd_ps(pb.packet[7]);
+}
+
+EIGEN_DEVICE_FUNC inline void
+ptranspose(PacketBlock<Packet4cd,4>& kernel) {
+ __m512d T0 = _mm512_shuffle_f64x2(kernel.packet[0].v, kernel.packet[1].v, (shuffle_mask<0,1,0,1>::mask)); // [a0 a1 b0 b1]
+ __m512d T1 = _mm512_shuffle_f64x2(kernel.packet[0].v, kernel.packet[1].v, (shuffle_mask<2,3,2,3>::mask)); // [a2 a3 b2 b3]
+ __m512d T2 = _mm512_shuffle_f64x2(kernel.packet[2].v, kernel.packet[3].v, (shuffle_mask<0,1,0,1>::mask)); // [c0 c1 d0 d1]
+ __m512d T3 = _mm512_shuffle_f64x2(kernel.packet[2].v, kernel.packet[3].v, (shuffle_mask<2,3,2,3>::mask)); // [c2 c3 d2 d3]
+
+ kernel.packet[3] = Packet4cd(_mm512_shuffle_f64x2(T1, T3, (shuffle_mask<1,3,1,3>::mask))); // [a3 b3 c3 d3]
+ kernel.packet[2] = Packet4cd(_mm512_shuffle_f64x2(T1, T3, (shuffle_mask<0,2,0,2>::mask))); // [a2 b2 c2 d2]
+ kernel.packet[1] = Packet4cd(_mm512_shuffle_f64x2(T0, T2, (shuffle_mask<1,3,1,3>::mask))); // [a1 b1 c1 d1]
+ kernel.packet[0] = Packet4cd(_mm512_shuffle_f64x2(T0, T2, (shuffle_mask<0,2,0,2>::mask))); // [a0 b0 c0 d0]
+}
+
+template<> EIGEN_STRONG_INLINE Packet4cd psqrt<Packet4cd>(const Packet4cd& a) {
+ return psqrt_complex<Packet4cd>(a);
+}
+
+template<> EIGEN_STRONG_INLINE Packet8cf psqrt<Packet8cf>(const Packet8cf& a) {
+ return psqrt_complex<Packet8cf>(a);
+}
+
+} // end namespace internal
+} // end namespace Eigen
+
+#endif // EIGEN_COMPLEX_AVX512_H
diff --git a/Eigen/src/Core/arch/AVX512/GemmKernel.h b/Eigen/src/Core/arch/AVX512/GemmKernel.h
new file mode 100644
index 0000000..cb7cfdf
--- /dev/null
+++ b/Eigen/src/Core/arch/AVX512/GemmKernel.h
@@ -0,0 +1,1235 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2022 Intel Corporation
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_CORE_ARCH_AVX512_GEMM_KERNEL_H
+#define EIGEN_CORE_ARCH_AVX512_GEMM_KERNEL_H
+
+#if EIGEN_COMP_MSVC
+#include <intrin.h>
+#else
+#include <x86intrin.h>
+#endif
+#include <immintrin.h>
+#include <type_traits>
+
+#include "../../InternalHeaderCheck.h"
+
+#if !defined(EIGEN_USE_AVX512_GEMM_KERNELS)
+// Disable new AVX512 kernels by default.
+#define EIGEN_USE_AVX512_GEMM_KERNELS 0
+#endif
+
+#define SECOND_FETCH (32)
+#if (EIGEN_COMP_GNUC_STRICT != 0) && !defined(EIGEN_ARCH_AVX512_GEMM_KERNEL_USE_LESS_A_REGS)
+// Use less registers to load A elements to workaround compiler spills. Loose a
+// bit of performance (less than ~2%).
+#define EIGEN_ARCH_AVX512_GEMM_KERNEL_USE_LESS_A_REGS
+#endif
+
+namespace Eigen {
+namespace internal {
+
+template <typename Scalar, bool is_unit_inc>
+class gemm_class {
+ using vec = typename packet_traits<Scalar>::type;
+ using vec_ymm = typename unpacket_traits<vec>::half;
+ using vec_xmm = typename unpacket_traits<vec_ymm>::half;
+ using umask_t = typename unpacket_traits<vec>::mask_t;
+
+ static constexpr bool is_f32 = sizeof(Scalar) == sizeof(float);
+ static constexpr bool is_f64 = sizeof(Scalar) == sizeof(double);
+
+#ifndef EIGEN_ARCH_AVX512_GEMM_KERNEL_USE_LESS_A_REGS
+ static constexpr bool use_less_a_regs = !is_unit_inc;
+#else
+ static constexpr bool use_less_a_regs = true;
+#endif
+#ifndef EIGEN_ARCH_AVX512_GEMM_KERNEL_USE_LESS_B_REGS
+ static constexpr bool use_less_b_regs = !is_unit_inc;
+#else
+ static constexpr bool use_less_b_regs = true;
+#endif
+
+ static constexpr int a_regs[] = {0, 1, 2, use_less_a_regs ? 0 : 3, use_less_a_regs ? 1 : 4, use_less_a_regs ? 2 : 5};
+ static constexpr int b_regs[] = {6, use_less_b_regs ? 6 : 7};
+ static constexpr int c_regs[] = {
+ 8, 16, 24, 9, 17, 25, 10, 18, 26, 11, 19, 27, 12, 20, 28, 13, 21, 29, 14, 22, 30, 15, 23, 31,
+ };
+
+ static constexpr int alpha_load_reg = 0;
+ static constexpr int c_load_regs[] = {1, 2, 6};
+
+ static constexpr int a_shift = 128;
+ static constexpr int b_shift = 128;
+
+ static constexpr int nelems_in_cache_line = is_f32 ? 16 : 8;
+ static constexpr int a_prefetch_size = nelems_in_cache_line * 2;
+ static constexpr int b_prefetch_size = nelems_in_cache_line * 8;
+
+ vec zmm[32];
+ umask_t mask;
+
+ // gemm arguments.
+ Index m;
+ const Index n, k, ldc;
+ const Index inc;
+ const Scalar *alpha;
+
+ const Scalar *a, *b;
+ Scalar *c;
+
+ const bool is_alpha1;
+ const bool is_beta0;
+
+ const Index a_stride, b_stride;
+ const Index a_off, b_off;
+
+ static EIGEN_ALWAYS_INLINE constexpr int div_up(int a, int b) { return a == 0 ? 0 : (a - 1) / b + 1; }
+
+ EIGEN_ALWAYS_INLINE void prefetch_a(const Scalar *a_addr) {
+ _mm_prefetch((char *)(a_prefetch_size + a_addr - a_shift), _MM_HINT_T0);
+ }
+
+ EIGEN_ALWAYS_INLINE void prefetch_b(const Scalar *b_addr) {
+ _mm_prefetch((char *)(b_prefetch_size + b_addr - b_shift), _MM_HINT_T0);
+ }
+
+ EIGEN_ALWAYS_INLINE void prefetch_x(const Scalar *x_addr) { _mm_prefetch((char *)(x_addr - a_shift), _MM_HINT_T2); }
+
+ EIGEN_ALWAYS_INLINE void prefetch_c(const Scalar *c_addr) {
+#if defined(__PRFCHW__) && __PRFCHW__ == 1
+ _m_prefetchw((void *)c_addr);
+#else
+ _mm_prefetch((char *)c_addr, _MM_HINT_T0);
+#endif
+ }
+
+ template <int nelems>
+ EIGEN_ALWAYS_INLINE void a_load(vec &a_reg, const Scalar *a_addr) {
+ switch (nelems * sizeof(*a_addr) * 8) {
+ default:
+ case 512 * 3:
+ a_reg = ploadu<vec>(a_addr);
+ break;
+ case 512 * 2:
+ a_reg = ploadu<vec>(a_addr);
+ break;
+ case 512 * 1:
+ a_reg = ploadu<vec>(a_addr);
+ break;
+ case 256 * 1:
+ a_reg = preinterpret<vec>(_mm512_broadcast_f64x4(ploadu<Packet4d>(reinterpret_cast<const double *>(a_addr))));
+ break;
+ case 128 * 1:
+ a_reg = preinterpret<vec>(_mm512_broadcast_f32x4(ploadu<Packet4f>(reinterpret_cast<const float *>(a_addr))));
+ break;
+ case 64 * 1:
+ a_reg = preinterpret<vec>(pload1<Packet8d>(reinterpret_cast<const double *>(a_addr)));
+ break;
+ case 32 * 1:
+ a_reg = pload1<vec>(a_addr);
+ break;
+ }
+ }
+
+ EIGEN_ALWAYS_INLINE void b_load(vec &b_reg, const Scalar *b_addr) { b_reg = pload1<vec>(b_addr); }
+
+ template <int nelems>
+ EIGEN_ALWAYS_INLINE void c_store(Scalar *mem, vec &src) {
+ if (is_unit_inc) {
+ switch (nelems * sizeof(*mem) * 8) {
+ default:
+ case 512 * 3:
+ pstoreu(mem, src);
+ break;
+ case 512 * 2:
+ pstoreu(mem, src);
+ break;
+ case 512 * 1:
+ pstoreu(mem, src);
+ break;
+ case 256 * 1:
+ pstoreu(mem, preinterpret<vec_ymm>(src));
+ break;
+ case 128 * 1:
+ pstoreu(mem, preinterpret<vec_xmm>(src));
+ break;
+ case 64 * 1:
+ pstorel(mem, preinterpret<vec_xmm>(src));
+ break;
+ case 32 * 1:
+ pstores(mem, preinterpret<vec_xmm>(src));
+ break;
+ }
+ } else {
+ switch (nelems * sizeof(*mem) * 8) {
+ default:
+ case 512 * 3:
+ pscatter(mem, src, inc);
+ break;
+ case 512 * 2:
+ pscatter(mem, src, inc);
+ break;
+ case 512 * 1:
+ pscatter(mem, src, inc);
+ break;
+ case 256 * 1:
+ pscatter(mem, src, inc, mask);
+ break;
+ case 128 * 1:
+ pscatter(mem, src, inc, mask);
+ break;
+ case 64 * 1:
+ pscatter(mem, src, inc, mask);
+ break;
+ case 32 * 1:
+ pscatter(mem, src, inc, mask);
+ break;
+ }
+ }
+ }
+
+ template <int nelems>
+ EIGEN_ALWAYS_INLINE void vaddm(vec &dst, const Scalar *mem, vec &src, vec ®) {
+ if (is_unit_inc) {
+ switch (nelems * sizeof(*mem) * 8) {
+ default:
+ case 512 * 3:
+ dst = padd(src, ploadu<vec>(mem));
+ break;
+ case 512 * 2:
+ dst = padd(src, ploadu<vec>(mem));
+ break;
+ case 512 * 1:
+ dst = padd(src, ploadu<vec>(mem));
+ break;
+ case 256 * 1:
+ dst = preinterpret<vec>(padd(preinterpret<vec_ymm>(src), ploadu<vec_ymm>(mem)));
+ break;
+ case 128 * 1:
+ dst = preinterpret<vec>(padd(preinterpret<vec_xmm>(src), ploadu<vec_xmm>(mem)));
+ break;
+ case 64 * 1:
+ dst = preinterpret<vec>(padd(preinterpret<vec_xmm>(src), ploadl<vec_xmm>(mem)));
+ break;
+ case 32 * 1:
+ dst = preinterpret<vec>(padds(preinterpret<vec_xmm>(src), ploads<vec_xmm>(mem)));
+ break;
+ }
+ } else {
+ // Zero out scratch register
+ reg = pzero(reg);
+
+ switch (nelems * sizeof(*mem) * 8) {
+ default:
+ case 512 * 3:
+ reg = pgather<Scalar, vec>(mem, inc);
+ dst = padd(src, reg);
+ break;
+ case 512 * 2:
+ reg = pgather<Scalar, vec>(mem, inc);
+ dst = padd(src, reg);
+ break;
+ case 512 * 1:
+ reg = pgather<Scalar, vec>(mem, inc);
+ dst = padd(src, reg);
+ break;
+ case 256 * 1:
+ reg = preinterpret<vec>(pgather<Scalar, vec_ymm>(mem, inc));
+ dst = preinterpret<vec>(padd(preinterpret<vec_ymm>(src), preinterpret<vec_ymm>(reg)));
+ break;
+ case 128 * 1:
+ reg = preinterpret<vec>(pgather<Scalar, vec_xmm>(mem, inc));
+ dst = preinterpret<vec>(padd(preinterpret<vec_xmm>(src), preinterpret<vec_xmm>(reg)));
+ break;
+ case 64 * 1:
+ if (is_f32) {
+ reg = pgather(reg, mem, inc, mask);
+ dst = preinterpret<vec>(padd(preinterpret<vec_xmm>(src), preinterpret<vec_xmm>(reg)));
+ } else {
+ dst = preinterpret<vec>(padd(preinterpret<vec_xmm>(src), ploadl<vec_xmm>(mem)));
+ }
+ break;
+ case 32 * 1:
+ dst = preinterpret<vec>(padds(preinterpret<vec_xmm>(src), ploads<vec_xmm>(mem)));
+ break;
+ }
+ }
+ }
+
+ EIGEN_STRONG_INLINE void vfmadd(vec &dst, const vec &src1, const vec &src2) {
+ dst = pmadd(src1, src2, dst);
+
+#if (EIGEN_COMP_GNUC != 0) || (EIGEN_COMP_CLANG != 0)
+ // Workaround register spills for gcc and clang
+ __asm__("#" : [dst] "+v"(dst) : [src1] "%v"(src1), [src2] "v"(src2));
+#endif
+ }
+
+ template <int nelems>
+ EIGEN_ALWAYS_INLINE void vfmaddm(vec &dst, const Scalar *mem, vec &src, vec &scale, vec ®) {
+ if (is_unit_inc) {
+ switch (nelems * sizeof(*mem) * 8) {
+ default:
+ case 512 * 3:
+ dst = pmadd(scale, src, ploadu<vec>(mem));
+ break;
+ case 512 * 2:
+ dst = pmadd(scale, src, ploadu<vec>(mem));
+ break;
+ case 512 * 1:
+ dst = pmadd(scale, src, ploadu<vec>(mem));
+ break;
+ case 256 * 1:
+ dst =
+ preinterpret<vec>(pmadd(preinterpret<vec_ymm>(scale), preinterpret<vec_ymm>(src), ploadu<vec_ymm>(mem)));
+ break;
+ case 128 * 1:
+ dst =
+ preinterpret<vec>(pmadd(preinterpret<vec_xmm>(scale), preinterpret<vec_xmm>(src), ploadu<vec_xmm>(mem)));
+ break;
+ case 64 * 1:
+ dst =
+ preinterpret<vec>(pmadd(preinterpret<vec_xmm>(scale), preinterpret<vec_xmm>(src), ploadl<vec_xmm>(mem)));
+ break;
+ case 32 * 1:
+ dst =
+ preinterpret<vec>(pmadds(preinterpret<vec_xmm>(scale), preinterpret<vec_xmm>(src), ploads<vec_xmm>(mem)));
+ break;
+ }
+ } else {
+ // Zero out scratch register
+ reg = pzero(reg);
+
+ switch (nelems * sizeof(*mem) * 8) {
+ default:
+ case 512 * 3:
+ reg = pgather<Scalar, vec>(mem, inc);
+ dst = pmadd(scale, src, reg);
+ break;
+ case 512 * 2:
+ reg = pgather<Scalar, vec>(mem, inc);
+ dst = pmadd(scale, src, reg);
+ break;
+ case 512 * 1:
+ reg = pgather<Scalar, vec>(mem, inc);
+ dst = pmadd(scale, src, reg);
+ break;
+ case 256 * 1:
+ reg = preinterpret<vec>(pgather<Scalar, vec_ymm>(mem, inc));
+ dst = preinterpret<vec>(
+ pmadd(preinterpret<vec_ymm>(scale), preinterpret<vec_ymm>(src), preinterpret<vec_ymm>(reg)));
+ break;
+ case 128 * 1:
+ reg = preinterpret<vec>(pgather<Scalar, vec_xmm>(mem, inc));
+ dst = preinterpret<vec>(
+ pmadd(preinterpret<vec_xmm>(scale), preinterpret<vec_xmm>(src), preinterpret<vec_xmm>(reg)));
+ break;
+ case 64 * 1:
+ if (is_f32) {
+ reg = pgather(reg, mem, inc, mask);
+ dst = preinterpret<vec>(
+ pmadd(preinterpret<vec_xmm>(scale), preinterpret<vec_xmm>(src), preinterpret<vec_xmm>(reg)));
+ } else {
+ dst = preinterpret<vec>(
+ pmadd(preinterpret<vec_xmm>(scale), preinterpret<vec_xmm>(src), ploadl<vec_xmm>(mem)));
+ }
+ break;
+ case 32 * 1:
+ dst =
+ preinterpret<vec>(pmadds(preinterpret<vec_xmm>(scale), preinterpret<vec_xmm>(src), ploads<vec_xmm>(mem)));
+ break;
+ }
+ }
+ }
+
+ template <int j, int endX, int i, int endY, int nelems>
+ EIGEN_ALWAYS_INLINE std::enable_if_t<(j > endX) || (i > endY)> a_loads(const Scalar *ao) {
+ EIGEN_UNUSED_VARIABLE(ao);
+ }
+
+ template <int j, int endX, int i, int endY, int nelems>
+ EIGEN_ALWAYS_INLINE std::enable_if_t<(j <= endX) && (i <= endY)> a_loads(const Scalar *ao) {
+ if (j < endX) {
+ if (i < endY) {
+ auto &a_reg = zmm[a_regs[i + (j % 2) * 3]];
+ const Scalar *a_addr = ao + nelems * j + nelems_in_cache_line * i - a_shift;
+ a_load<nelems>(a_reg, a_addr);
+
+ a_loads<j, endX, i + 1, endY, nelems>(ao);
+ } else {
+ a_loads<j + 1, endX, 0, endY, nelems>(ao);
+ }
+ }
+ }
+
+ template <int un, int max_b_unroll, int i, int um_vecs, int a_unroll, int b_unroll>
+ EIGEN_ALWAYS_INLINE std::enable_if_t<(un > max_b_unroll) || (i > um_vecs)> prefetch_cs(const Scalar *co1,
+ const Scalar *co2) {
+ EIGEN_UNUSED_VARIABLE(co1);
+ EIGEN_UNUSED_VARIABLE(co2);
+ }
+
+ /* C prefetch loop structure.
+ * for (int un = 0; un < 8; un++) {
+ * if (b_unroll >= un + 1) {
+ * if (un == 4) co2 = co1 + 4 * ldc;
+ *
+ * for (int i = 0; i < um_vecs; i++) {
+ * Scalar *co = (un + 1 <= 4) ? co1 : co2;
+ * auto co_off = (un % 4) * ldc + a_unroll - 1 + i * nelems_in_cache_line * sizeof *co;
+ * prefetch_c(co + co_off);
+ * }
+ * }
+ * }
+ */
+
+ template <int un, int max_b_unroll, int i, int um_vecs, int a_unroll, int b_unroll>
+ EIGEN_ALWAYS_INLINE std::enable_if_t<(un <= max_b_unroll) && (i <= um_vecs)> prefetch_cs(Scalar *&co1, Scalar *&co2) {
+ if (un < max_b_unroll) {
+ if (b_unroll >= un + 1) {
+ if (un == 4 && i == 0) co2 = co1 + 4 * ldc;
+
+ if (i < um_vecs) {
+ Scalar *co = (un + 1 <= 4) ? co1 : co2;
+ auto co_off = (un % 4) * ldc + a_unroll - 1 + i * nelems_in_cache_line * sizeof *co;
+ prefetch_c(co + co_off);
+
+ prefetch_cs<un, max_b_unroll, i + 1, um_vecs, a_unroll, b_unroll>(co1, co2);
+ } else {
+ prefetch_cs<un + 1, max_b_unroll, 0, um_vecs, a_unroll, b_unroll>(co1, co2);
+ }
+
+ } else {
+ prefetch_cs<un + 1, max_b_unroll, 0, um_vecs, a_unroll, b_unroll>(co1, co2);
+ }
+ }
+ }
+
+ // load_c
+ template <int i, int um_vecs, int idx, int nelems>
+ EIGEN_ALWAYS_INLINE std::enable_if_t<(i > um_vecs)> scale_load_c(const Scalar *cox, vec &alpha_reg) {
+ EIGEN_UNUSED_VARIABLE(cox);
+ EIGEN_UNUSED_VARIABLE(alpha_reg);
+ }
+
+ template <int i, int um_vecs, int idx, int nelems>
+ EIGEN_ALWAYS_INLINE std::enable_if_t<(i <= um_vecs)> scale_load_c(const Scalar *cox, vec &alpha_reg) {
+ if (i < um_vecs) {
+ auto &c_reg = zmm[c_regs[i + idx * 3]];
+ auto &c_load_reg = zmm[c_load_regs[i % 3]];
+ auto c_mem = cox;
+ if (is_unit_inc)
+ c_mem += i * nelems_in_cache_line;
+ else
+ c_mem += i * nelems_in_cache_line * inc;
+
+ if (!is_beta0 && is_alpha1)
+ vaddm<nelems>(c_reg, c_mem, c_reg, c_load_reg);
+ else if (!is_beta0 && !is_alpha1)
+ vfmaddm<nelems>(c_reg, c_mem, c_reg, alpha_reg, c_load_reg);
+ else if (is_beta0 && !is_alpha1)
+ c_reg = pmul(alpha_reg, c_reg);
+
+ scale_load_c<i + 1, um_vecs, idx, nelems>(cox, alpha_reg);
+ }
+ }
+
+ // store_c
+ template <int i, int um_vecs, int idx, int nelems>
+ EIGEN_ALWAYS_INLINE std::enable_if_t<(i > um_vecs)> write_c(Scalar *cox) {
+ EIGEN_UNUSED_VARIABLE(cox);
+ }
+
+ template <int i, int um_vecs, int idx, int nelems>
+ EIGEN_ALWAYS_INLINE std::enable_if_t<(i <= um_vecs)> write_c(Scalar *cox) {
+ if (i < um_vecs) {
+ auto &c_reg = zmm[c_regs[i + idx * 3]];
+ auto c_mem = cox;
+ if (is_unit_inc)
+ c_mem += i * nelems_in_cache_line;
+ else
+ c_mem += i * nelems_in_cache_line * inc;
+
+ c_store<nelems>(c_mem, c_reg);
+ c_reg = pzero(c_reg);
+
+ write_c<i + 1, um_vecs, idx, nelems>(cox);
+ }
+ }
+
+ /* C update loop structure.
+ * co2 = co1 + ldc;
+ *
+ * auto &alpha_reg = zmm[alpha_load_reg];
+ * if (!is_alpha1) alpha_reg = pload1<vec>(alpha);
+ *
+ * int idx = 0;
+ * for (pow = 1; pow <= 8; pow <<= 1) {
+ *
+ * if (b_unroll >= pow) {
+ * for (count = 1; count < (pow + 1) / 2 + 1; count++) {
+ * if (pow >= 4) co2 += ldc;
+ *
+ * const Scalar *cox = (idx == 0) ? co1 : co2;
+ *
+ * const int um_vecs = div_up(a_unroll, nelems_in_cache_line);
+ * scale_load_c<0, um_vecs, idx, a_unroll>(cox, alpha_reg);
+ * write_c<0, um_vecs, idx, a_unroll>(cox);
+ *
+ * idx++;
+ * }
+ * }
+ * }
+ *
+ * if (b_unroll == 1)
+ * co1 += ldc;
+ * else
+ * co1 = co2 + ldc;
+ */
+
+ template <int pow, int a_unroll, int idx>
+ EIGEN_ALWAYS_INLINE void c_update_1count(Scalar *&cox) {
+ if (pow >= 4) cox += ldc;
+
+ const int um_vecs = div_up(a_unroll, nelems_in_cache_line);
+ auto &alpha_reg = zmm[alpha_load_reg];
+
+ scale_load_c<0, um_vecs, idx, a_unroll>(cox, alpha_reg);
+ write_c<0, um_vecs, idx, a_unroll>(cox);
+ }
+
+ template <int pow, int a_unroll>
+ EIGEN_ALWAYS_INLINE void c_update_1pow(Scalar *&co1, Scalar *&co2) {
+ constexpr int idx = pow / 2;
+ Scalar *&cox = idx == 0 ? co1 : co2;
+
+ constexpr int max_count = (pow + 1) / 2;
+ static_assert(max_count <= 4, "Unsupported max_count.");
+
+ if (1 <= max_count) c_update_1count<pow, a_unroll, idx + 0>(cox);
+ if (2 <= max_count) c_update_1count<pow, a_unroll, idx + 1>(cox);
+ if (3 <= max_count) c_update_1count<pow, a_unroll, idx + 2>(cox);
+ if (4 <= max_count) c_update_1count<pow, a_unroll, idx + 3>(cox);
+ }
+
+ template <int max_b_unroll, int a_unroll, int b_unroll>
+ EIGEN_ALWAYS_INLINE void c_update(Scalar *&co1, Scalar *&co2) {
+ auto &alpha_reg = zmm[alpha_load_reg];
+
+ co2 = co1 + ldc;
+ if (!is_alpha1) alpha_reg = pload1<vec>(alpha);
+ if (!is_unit_inc && a_unroll < nelems_in_cache_line) mask = static_cast<umask_t>((1ull << a_unroll) - 1);
+
+ static_assert(max_b_unroll <= 8, "Unsupported max_b_unroll");
+
+ if (1 <= max_b_unroll && 1 <= b_unroll) c_update_1pow<1, a_unroll>(co1, co2);
+ if (2 <= max_b_unroll && 2 <= b_unroll) c_update_1pow<2, a_unroll>(co1, co2);
+ if (4 <= max_b_unroll && 4 <= b_unroll) c_update_1pow<4, a_unroll>(co1, co2);
+ if (8 <= max_b_unroll && 8 <= b_unroll) c_update_1pow<8, a_unroll>(co1, co2);
+
+ if (b_unroll == 1)
+ co1 += ldc;
+ else
+ co1 = co2 + ldc;
+ }
+
+ // compute
+ template <int um, int um_vecs, int idx, int uk, bool fetch_x, bool ktail>
+ EIGEN_ALWAYS_INLINE std::enable_if_t<(um > um_vecs)> compute(const Scalar *ao, const Scalar *bo, int &fetchA_idx,
+ int &fetchB_idx, vec &b_reg) {
+ EIGEN_UNUSED_VARIABLE(ao);
+ EIGEN_UNUSED_VARIABLE(bo);
+ EIGEN_UNUSED_VARIABLE(fetchA_idx);
+ EIGEN_UNUSED_VARIABLE(fetchB_idx);
+ EIGEN_UNUSED_VARIABLE(b_reg);
+ }
+
+ template <int um, int um_vecs, int idx, int uk, bool fetch_x, bool ktail>
+ EIGEN_ALWAYS_INLINE std::enable_if_t<(um <= um_vecs)> compute(const Scalar *ao, const Scalar *bo, int &fetchA_idx,
+ int &fetchB_idx, vec &b_reg) {
+ if (um < um_vecs) {
+ auto &c_reg = zmm[c_regs[um + idx * 3]];
+ auto &a_reg = zmm[a_regs[um + (uk % 2) * 3]];
+
+ vfmadd(c_reg, a_reg, b_reg);
+
+ if (!fetch_x && um == 0 &&
+ (((idx == 0 || idx == 6) && (uk % 2 == 0 || is_f64 || ktail)) ||
+ (idx == 3 && (uk % 2 == 1 || is_f64 || ktail)))) {
+ prefetch_a(ao + nelems_in_cache_line * fetchA_idx);
+ fetchA_idx++;
+ }
+
+ if (um == 0 && idx == 1 && (uk % 2 == 0 || is_f64 || ktail)) {
+ prefetch_b(bo + nelems_in_cache_line * fetchB_idx);
+ fetchB_idx++;
+ }
+
+ compute<um + 1, um_vecs, idx, uk, fetch_x, ktail>(ao, bo, fetchA_idx, fetchB_idx, b_reg);
+ }
+ }
+
+ // load_a
+ template <int um, int um_vecs, int uk, int nelems, bool ktail>
+ EIGEN_ALWAYS_INLINE std::enable_if_t<(um > um_vecs)> load_a(const Scalar *ao) {
+ EIGEN_UNUSED_VARIABLE(ao);
+ }
+
+ template <int um, int um_vecs, int uk, int nelems, bool ktail>
+ EIGEN_ALWAYS_INLINE std::enable_if_t<(um <= um_vecs)> load_a(const Scalar *ao) {
+ if (um < um_vecs) {
+ auto &a_reg = zmm[a_regs[um + (uk % 2) * 3]];
+ const Scalar *a_addr = ao + nelems * (1 + !ktail * !use_less_a_regs + uk) + nelems_in_cache_line * um - a_shift;
+ a_load<nelems>(a_reg, a_addr);
+
+ load_a<um + 1, um_vecs, uk, nelems, ktail>(ao);
+ }
+ }
+ template <int uk, int pow, int count, int um_vecs, int b_unroll, bool ktail, bool fetch_x, bool c_fetch>
+ EIGEN_ALWAYS_INLINE std::enable_if_t<(count > (pow + 1) / 2)> innerkernel_1pow(const Scalar *&aa,
+ const Scalar *const &ao,
+ const Scalar *const &bo, Scalar *&co2,
+ int &fetchA_idx, int &fetchB_idx) {
+ EIGEN_UNUSED_VARIABLE(aa);
+ EIGEN_UNUSED_VARIABLE(ao);
+ EIGEN_UNUSED_VARIABLE(bo);
+ EIGEN_UNUSED_VARIABLE(co2);
+ EIGEN_UNUSED_VARIABLE(fetchA_idx);
+ EIGEN_UNUSED_VARIABLE(fetchB_idx);
+ }
+
+ template <int uk, int pow, int count, int um_vecs, int b_unroll, bool ktail, bool fetch_x, bool c_fetch>
+ EIGEN_ALWAYS_INLINE std::enable_if_t<(count <= (pow + 1) / 2)> innerkernel_1pow(const Scalar *&aa,
+ const Scalar *const &ao,
+ const Scalar *const &bo, Scalar *&co2,
+ int &fetchA_idx, int &fetchB_idx) {
+ const int idx = (pow / 2) + count;
+
+ if (count < (pow + 1) / 2) {
+ auto &b_reg = zmm[b_regs[idx % 2]];
+
+ if (fetch_x && uk == 3 && idx == 0) prefetch_x(aa);
+ if (fetch_x && uk == 3 && idx == 4) aa += 8;
+
+ if (b_unroll >= pow) {
+ compute<0, um_vecs, idx, uk, fetch_x, ktail>(ao, bo, fetchA_idx, fetchB_idx, b_reg);
+
+ const Scalar *b_addr = bo + b_unroll * uk + idx + 1 + (b_unroll > 1) * !use_less_b_regs - b_shift;
+ b_load(b_reg, b_addr);
+ }
+
+ // Go to the next count.
+ innerkernel_1pow<uk, pow, count + 1, um_vecs, b_unroll, ktail, fetch_x, c_fetch>(aa, ao, bo, co2, fetchA_idx,
+ fetchB_idx);
+
+ } else {
+ // Maybe prefetch C data after count-loop.
+ if (pow == 2 && c_fetch) {
+ if (uk % 3 == 0 && uk > 0) {
+ co2 += ldc;
+ } else {
+ prefetch_c(co2 + (uk % 3) * nelems_in_cache_line);
+ }
+ }
+ }
+ }
+
+ template <int uk, int max_b_unroll, int a_unroll, int b_unroll, bool ktail, bool fetch_x, bool c_fetch>
+ EIGEN_ALWAYS_INLINE void innerkernel_1uk(const Scalar *&aa, const Scalar *const &ao, const Scalar *const &bo,
+ Scalar *&co2, int &fetchA_idx, int &fetchB_idx) {
+ const int um_vecs = div_up(a_unroll, nelems_in_cache_line);
+
+ if (max_b_unroll >= 1)
+ innerkernel_1pow<uk, 1, 0, um_vecs, b_unroll, ktail, fetch_x, c_fetch>(aa, ao, bo, co2, fetchA_idx, fetchB_idx);
+ if (max_b_unroll >= 2)
+ innerkernel_1pow<uk, 2, 0, um_vecs, b_unroll, ktail, fetch_x, c_fetch>(aa, ao, bo, co2, fetchA_idx, fetchB_idx);
+ if (max_b_unroll >= 4)
+ innerkernel_1pow<uk, 4, 0, um_vecs, b_unroll, ktail, fetch_x, c_fetch>(aa, ao, bo, co2, fetchA_idx, fetchB_idx);
+ if (max_b_unroll >= 8)
+ innerkernel_1pow<uk, 8, 0, um_vecs, b_unroll, ktail, fetch_x, c_fetch>(aa, ao, bo, co2, fetchA_idx, fetchB_idx);
+
+ // Load A after pow-loop.
+ load_a<0, um_vecs, uk, a_unroll, ktail>(ao);
+ }
+
+ /* Inner kernel loop structure.
+ * for (int uk = 0; uk < kfactor; uk++) {
+ * int idx = 0;
+ *
+ * for (pow = 1; pow < max_b_unroll << 1; pow <<= 1) {
+ * for (int count = 0; count < (pow + 1) / 2; count++) {
+ * auto &b_reg = zmm[b_regs[idx % 2]];
+ *
+ * if (fetch_x && uk == 3 && idx == 0) prefetch_x(aa);
+ * if (fetch_x && uk == 3 && idx == 4) aa += 8;
+ *
+ * if (b_unroll >= pow) {
+ * compute<0, um_vecs, idx, uk, fetchx, ktail>(ao, bo, fetchA_idx, fetchB_idx, b_reg);
+ *
+ * const Scalar *b_addr = bo + b_unroll * uk + idx + 1 + (b_unroll > 1) - b_shift ;
+ * b_load(b_reg, b_addr);
+ * }
+ * idx++;
+ * }
+ *
+ * Maybe prefetch C data.
+ * if (pow == 2 && c_fetch) {
+ * if (uk % 3 == 0 && uk > 0) {
+ * co2 += ldc;
+ * } else {
+ * prefetch_c(co2 + (uk % 3) * nelems_in_cache_line);
+ * }
+ * }
+ * }
+ *
+ * Load A.
+ * load_a<0, um_vecs, uk, ktail, a_unroll>(ao);
+ * }
+ *
+ * Advance A/B pointers after uk-loop.
+ * ao += a_unroll * kfactor;
+ * bo += b_unroll * kfactor;
+ */
+
+ template <int a_unroll, int b_unroll, int k_factor, int max_b_unroll, int max_k_factor, bool c_fetch>
+ EIGEN_ALWAYS_INLINE void innerkernel(const Scalar *&aa, const Scalar *&ao, const Scalar *&bo, Scalar *&co2) {
+ int fetchA_idx = 0;
+ int fetchB_idx = 0;
+
+ const bool fetch_x = k_factor == max_k_factor;
+ const bool ktail = k_factor == 1;
+
+ static_assert(k_factor <= 4 && k_factor > 0, "innerkernel maximum k_factor supported is 4");
+
+ if (k_factor > 0)
+ innerkernel_1uk<0, max_b_unroll, a_unroll, b_unroll, ktail, fetch_x, c_fetch>(aa, ao, bo, co2, fetchA_idx,
+ fetchB_idx);
+ if (k_factor > 1)
+ innerkernel_1uk<1, max_b_unroll, a_unroll, b_unroll, ktail, fetch_x, c_fetch>(aa, ao, bo, co2, fetchA_idx,
+ fetchB_idx);
+ if (k_factor > 2)
+ innerkernel_1uk<2, max_b_unroll, a_unroll, b_unroll, ktail, fetch_x, c_fetch>(aa, ao, bo, co2, fetchA_idx,
+ fetchB_idx);
+ if (k_factor > 3)
+ innerkernel_1uk<3, max_b_unroll, a_unroll, b_unroll, ktail, fetch_x, c_fetch>(aa, ao, bo, co2, fetchA_idx,
+ fetchB_idx);
+
+ // Advance A/B pointers after uk-loop.
+ ao += a_unroll * k_factor;
+ bo += b_unroll * k_factor;
+ }
+
+ template <int a_unroll, int b_unroll, int max_b_unroll>
+ EIGEN_ALWAYS_INLINE void kloop(const Scalar *&aa, const Scalar *&ao, const Scalar *&bo, Scalar *&co1, Scalar *&co2) {
+ const int um_vecs = div_up(a_unroll, nelems_in_cache_line);
+ if (!use_less_a_regs)
+ a_loads<0, 2, 0, um_vecs, a_unroll>(ao);
+ else
+ a_loads<0, 1, 0, um_vecs, a_unroll>(ao);
+
+ b_load(zmm[b_regs[0]], bo - b_shift + 0);
+ if (!use_less_b_regs) b_load(zmm[b_regs[1]], bo - b_shift + 1);
+
+#ifndef SECOND_FETCH
+ prefetch_cs<0, max_b_unroll, 0, um_vecs, a_unroll, b_unroll>(co1, co2);
+#endif // SECOND_FETCH
+
+ // Unrolling k-loop by a factor of 4.
+ const int max_k_factor = 4;
+ Index loop_count = k / max_k_factor;
+
+ if (loop_count > 0) {
+#ifdef SECOND_FETCH
+ loop_count -= SECOND_FETCH;
+#endif
+ while (loop_count > 0) {
+ innerkernel<a_unroll, b_unroll, max_k_factor, max_b_unroll, max_k_factor, 0>(aa, ao, bo, co2);
+ loop_count--;
+ }
+#ifdef SECOND_FETCH
+ co2 = co1 + nelems_in_cache_line - 1;
+
+ loop_count += b_unroll;
+ while (loop_count > 0) {
+ innerkernel<a_unroll, b_unroll, max_k_factor, max_b_unroll, max_k_factor, 1>(aa, ao, bo, co2);
+ loop_count--;
+ }
+
+ loop_count += SECOND_FETCH - b_unroll;
+ while (loop_count > 0) {
+ innerkernel<a_unroll, b_unroll, max_k_factor, max_b_unroll, max_k_factor, 0>(aa, ao, bo, co2);
+ loop_count--;
+ }
+#endif
+ }
+
+ // k-loop remainder handling.
+ loop_count = k % max_k_factor;
+ while (loop_count > 0) {
+ innerkernel<a_unroll, b_unroll, 1, max_b_unroll, max_k_factor, 0>(aa, ao, bo, co2);
+ loop_count--;
+ }
+
+ // Update C matrix.
+ c_update<max_b_unroll, a_unroll, b_unroll>(co1, co2);
+ }
+
+ template <int a_unroll, int b_unroll, int max_b_unroll>
+ EIGEN_ALWAYS_INLINE void nloop(const Scalar *&aa, const Scalar *&ao, const Scalar *&bo, Scalar *&co1, Scalar *&co2) {
+ // Set A matrix pointer.
+ ao = a + a_off * a_unroll;
+
+ // Set B matrix pointer if needed.
+ bo += b_unroll * b_off;
+
+ kloop<a_unroll, b_unroll, max_b_unroll>(aa, ao, bo, co1, co2);
+
+ // Advance B matrix pointer if needed.
+ bo += b_unroll * (b_stride - k - b_off);
+
+ // Advance prefetch A pointer.
+ aa += 16;
+ }
+
+ template <int a_unroll, int max_a_unroll, int max_b_unroll>
+ EIGEN_ALWAYS_INLINE void mloop(const Scalar *&ao, const Scalar *&bo, Scalar *&co1, Scalar *&co2) {
+ // Set prefetch A pointers.
+ const Scalar *aa = a + a_unroll * a_stride;
+
+ // Set C matrix pointers.
+ co1 = c;
+ if (a_unroll >= max_a_unroll) co2 = c + 2 * ldc;
+ if (is_unit_inc)
+ c += a_unroll;
+ else
+ c += a_unroll * inc;
+
+ // Set B matrix pointer.
+ bo = b;
+
+ // Main n-loop.
+ for (Index i = n / max_b_unroll; i > 0; i--) nloop<a_unroll, max_b_unroll, max_b_unroll>(aa, ao, bo, co1, co2);
+
+ // n-remainders.
+ if (n & 4 && max_b_unroll > 4) nloop<a_unroll, 4, max_b_unroll>(aa, ao, bo, co1, co2);
+#if 0
+ if (n & 2 && max_b_unroll > 2) nloop<a_unroll, 2, max_b_unroll>(aa, ao, bo, co1, co2);
+ if (n & 1 && max_b_unroll > 1) nloop<a_unroll, 1, max_b_unroll>(aa, ao, bo, co1, co2);
+#else
+ // Copy kernels don't support tails of n = 2 for single/double precision.
+ // Loop over ones.
+ int n_rem = 2 * ((n & 2) != 0) + 1 * ((n & 1) != 0);
+ while (n_rem > 0) {
+ nloop<a_unroll, 1, max_b_unroll>(aa, ao, bo, co1, co2);
+ n_rem--;
+ }
+#endif
+
+ // Advance A matrix pointer.
+ a = ao + a_unroll * (a_stride - k - a_off);
+ }
+
+ public:
+ // Compute kernel unrolling C matrix by max_a_unroll x max_b_unroll.
+ template <int max_a_unroll, int max_b_unroll>
+ EIGEN_ALWAYS_INLINE void compute_kern() {
+ a -= -a_shift;
+ b -= -b_shift;
+
+ const Scalar *ao = nullptr;
+ const Scalar *bo = nullptr;
+ Scalar *co1 = nullptr;
+ Scalar *co2 = nullptr;
+
+ // Main m-loop.
+ for (; m >= max_a_unroll; m -= max_a_unroll) mloop<max_a_unroll, max_a_unroll, max_b_unroll>(ao, bo, co1, co2);
+
+ // m-remainders.
+ if (m & 32 && max_a_unroll > 32) mloop<32, max_a_unroll, max_b_unroll>(ao, bo, co1, co2);
+ if (m & 16 && max_a_unroll > 16) mloop<16, max_a_unroll, max_b_unroll>(ao, bo, co1, co2);
+ if (m & 8 && max_a_unroll > 8) mloop<8, max_a_unroll, max_b_unroll>(ao, bo, co1, co2);
+ if (m & 4 && max_a_unroll > 4) mloop<4, max_a_unroll, max_b_unroll>(ao, bo, co1, co2);
+ if (m & 2 && max_a_unroll > 2 && is_f64) mloop<2, max_a_unroll, max_b_unroll>(ao, bo, co1, co2);
+ if (m & 1 && max_a_unroll > 1 && is_f64) mloop<1, max_a_unroll, max_b_unroll>(ao, bo, co1, co2);
+
+ // Copy kernels don't support tails of m = 2 for single precision.
+ // Loop over ones.
+ if (is_f32) {
+ int m_rem = 2 * ((m & 2) != 0) + 1 * ((m & 1) != 0);
+ while (m_rem > 0) {
+ mloop<1, max_a_unroll, max_b_unroll>(ao, bo, co1, co2);
+ m_rem--;
+ }
+ }
+ }
+
+ gemm_class(Index m_, Index n_, Index k_, Index ldc_, Index inc_, const Scalar *alpha_, const Scalar *a_,
+ const Scalar *b_, Scalar *c_, bool is_alpha1_, bool is_beta0_, Index a_stride_, Index b_stride_,
+ Index a_off_, Index b_off_)
+ : m(m_),
+ n(n_),
+ k(k_),
+ ldc(ldc_),
+ inc(inc_),
+ alpha(alpha_),
+ a(a_),
+ b(b_),
+ c(c_),
+ is_alpha1(is_alpha1_),
+ is_beta0(is_beta0_),
+ a_stride(a_stride_),
+ b_stride(b_stride_),
+ a_off(a_off_),
+ b_off(b_off_) {
+ // Zero out all accumulation registers.
+ zmm[8] = pzero(zmm[8]);
+ zmm[9] = pzero(zmm[9]);
+ zmm[10] = pzero(zmm[10]);
+ zmm[11] = pzero(zmm[11]);
+ zmm[12] = pzero(zmm[12]);
+ zmm[13] = pzero(zmm[13]);
+ zmm[14] = pzero(zmm[14]);
+ zmm[15] = pzero(zmm[15]);
+ zmm[16] = pzero(zmm[16]);
+ zmm[17] = pzero(zmm[17]);
+ zmm[18] = pzero(zmm[18]);
+ zmm[19] = pzero(zmm[19]);
+ zmm[20] = pzero(zmm[20]);
+ zmm[21] = pzero(zmm[21]);
+ zmm[22] = pzero(zmm[22]);
+ zmm[23] = pzero(zmm[23]);
+ zmm[24] = pzero(zmm[24]);
+ zmm[25] = pzero(zmm[25]);
+ zmm[26] = pzero(zmm[26]);
+ zmm[27] = pzero(zmm[27]);
+ zmm[28] = pzero(zmm[28]);
+ zmm[29] = pzero(zmm[29]);
+ zmm[30] = pzero(zmm[30]);
+ zmm[31] = pzero(zmm[31]);
+ }
+};
+
+// Compute kernel with max unroll support of:
+// Single precision:
+// max_a_unroll: 48, 32, 16, 8, 4, 2, 1
+// max_b_unroll: 8, 4, 2, 1
+// Double precision:
+// max_a_unroll: 24, 16, 8, 4, 2, 1
+// max_b_unroll: 8, 4, 2, 1
+template <typename Scalar, int max_a_unroll, int max_b_unroll, bool is_alpha1, bool is_beta0, bool is_unit_inc>
+EIGEN_DONT_INLINE void gemm_kern_avx512(Index m, Index n, Index k, Scalar *alpha, const Scalar *a, const Scalar *b,
+ Scalar *c, Index ldc, Index inc = 1, Index a_stride = -1, Index b_stride = -1,
+ Index a_off = 0, Index b_off = 0) {
+ if (a_stride == -1) a_stride = k;
+ if (b_stride == -1) b_stride = k;
+
+ gemm_class<Scalar, is_unit_inc> g(m, n, k, ldc, inc, alpha, a, b, c, is_alpha1, is_beta0, a_stride, b_stride, a_off,
+ b_off);
+ g.template compute_kern<max_a_unroll, max_b_unroll>();
+}
+
+// Template specializations of GEBP kernels with nr = 8.
+#if EIGEN_USE_AVX512_GEMM_KERNELS
+template <bool ConjLhs_, bool ConjRhs_, int PacketSize_>
+class gebp_traits<float, float, ConjLhs_, ConjRhs_, Architecture::Target, PacketSize_>
+ : public gebp_traits<float, float, ConjLhs_, ConjRhs_, Architecture::Generic, PacketSize_> {
+ using Base = gebp_traits<float, float, ConjLhs_, ConjRhs_, Architecture::Generic, PacketSize_>;
+
+ public:
+ enum { nr = Base::Vectorizable ? 8 : 4 };
+};
+
+template <bool ConjLhs_, bool ConjRhs_, int PacketSize_>
+class gebp_traits<double, double, ConjLhs_, ConjRhs_, Architecture::Target, PacketSize_>
+ : public gebp_traits<double, double, ConjLhs_, ConjRhs_, Architecture::Generic, PacketSize_> {
+ using Base = gebp_traits<double, double, ConjLhs_, ConjRhs_, Architecture::Generic, PacketSize_>;
+
+ public:
+ enum { nr = Base::Vectorizable ? 8 : 4 };
+};
+
+template <typename Scalar, typename Index, typename DataMapper, bool Conjugate, bool PanelMode>
+struct gemm_pack_rhs<Scalar, Index, DataMapper, 8, ColMajor, Conjugate, PanelMode> {
+ typedef typename packet_traits<Scalar>::type Packet;
+ typedef typename DataMapper::LinearMapper LinearMapper;
+ enum { PacketSize = packet_traits<Scalar>::size };
+ EIGEN_DONT_INLINE void operator()(Scalar *blockB, const DataMapper &rhs, Index depth, Index cols, Index stride = 0,
+ Index offset = 0);
+};
+
+template <typename Scalar, typename Index, typename DataMapper, bool Conjugate, bool PanelMode>
+EIGEN_DONT_INLINE void gemm_pack_rhs<Scalar, Index, DataMapper, 8, ColMajor, Conjugate, PanelMode>::operator()(
+ Scalar *blockB, const DataMapper &rhs, Index depth, Index cols, Index stride, Index offset) {
+ constexpr int nr = 8;
+ EIGEN_ASM_COMMENT("EIGEN PRODUCT PACK RHS COLMAJOR");
+ EIGEN_UNUSED_VARIABLE(stride);
+ EIGEN_UNUSED_VARIABLE(offset);
+ eigen_assert(((!PanelMode) && stride == 0 && offset == 0) || (PanelMode && stride >= depth && offset <= stride));
+ conj_if<NumTraits<Scalar>::IsComplex && Conjugate> cj;
+ Index packet_cols8 = nr >= 8 ? (cols / 8) * 8 : 0;
+ Index packet_cols4 = nr >= 4 ? (cols / 4) * 4 : 0;
+ Index count = 0;
+ const Index peeled_k = (depth / PacketSize) * PacketSize;
+ if (nr >= 8) {
+ for (Index j2 = 0; j2 < packet_cols8; j2 += 8) {
+ // skip what we have before
+ if (PanelMode) count += 8 * offset;
+ const LinearMapper dm0 = rhs.getLinearMapper(0, j2 + 0);
+ const LinearMapper dm1 = rhs.getLinearMapper(0, j2 + 1);
+ const LinearMapper dm2 = rhs.getLinearMapper(0, j2 + 2);
+ const LinearMapper dm3 = rhs.getLinearMapper(0, j2 + 3);
+ const LinearMapper dm4 = rhs.getLinearMapper(0, j2 + 4);
+ const LinearMapper dm5 = rhs.getLinearMapper(0, j2 + 5);
+ const LinearMapper dm6 = rhs.getLinearMapper(0, j2 + 6);
+ const LinearMapper dm7 = rhs.getLinearMapper(0, j2 + 7);
+ Index k = 0;
+ if ((PacketSize % 8) == 0) // TODO enable vectorized transposition for PacketSize==4
+ {
+ for (; k < peeled_k; k += PacketSize) {
+ PacketBlock<Packet, (PacketSize % 8) == 0 ? 8 : PacketSize> kernel;
+
+ kernel.packet[0] = dm0.template loadPacket<Packet>(k);
+ kernel.packet[1] = dm1.template loadPacket<Packet>(k);
+ kernel.packet[2] = dm2.template loadPacket<Packet>(k);
+ kernel.packet[3] = dm3.template loadPacket<Packet>(k);
+ kernel.packet[4] = dm4.template loadPacket<Packet>(k);
+ kernel.packet[5] = dm5.template loadPacket<Packet>(k);
+ kernel.packet[6] = dm6.template loadPacket<Packet>(k);
+ kernel.packet[7] = dm7.template loadPacket<Packet>(k);
+
+ ptranspose(kernel);
+
+ pstoreu(blockB + count + 0 * PacketSize, cj.pconj(kernel.packet[0]));
+ pstoreu(blockB + count + 1 * PacketSize, cj.pconj(kernel.packet[1 % PacketSize]));
+ pstoreu(blockB + count + 2 * PacketSize, cj.pconj(kernel.packet[2 % PacketSize]));
+ pstoreu(blockB + count + 3 * PacketSize, cj.pconj(kernel.packet[3 % PacketSize]));
+ pstoreu(blockB + count + 4 * PacketSize, cj.pconj(kernel.packet[4 % PacketSize]));
+ pstoreu(blockB + count + 5 * PacketSize, cj.pconj(kernel.packet[5 % PacketSize]));
+ pstoreu(blockB + count + 6 * PacketSize, cj.pconj(kernel.packet[6 % PacketSize]));
+ pstoreu(blockB + count + 7 * PacketSize, cj.pconj(kernel.packet[7 % PacketSize]));
+ count += 8 * PacketSize;
+ }
+ }
+ for (; k < depth; k++) {
+ blockB[count + 0] = cj(dm0(k));
+ blockB[count + 1] = cj(dm1(k));
+ blockB[count + 2] = cj(dm2(k));
+ blockB[count + 3] = cj(dm3(k));
+ blockB[count + 4] = cj(dm4(k));
+ blockB[count + 5] = cj(dm5(k));
+ blockB[count + 6] = cj(dm6(k));
+ blockB[count + 7] = cj(dm7(k));
+ count += 8;
+ }
+ // skip what we have after
+ if (PanelMode) count += 8 * (stride - offset - depth);
+ }
+ }
+
+ if (nr >= 4) {
+ for (Index j2 = packet_cols8; j2 < packet_cols4; j2 += 4) {
+ // skip what we have before
+ if (PanelMode) count += 4 * offset;
+ const LinearMapper dm0 = rhs.getLinearMapper(0, j2 + 0);
+ const LinearMapper dm1 = rhs.getLinearMapper(0, j2 + 1);
+ const LinearMapper dm2 = rhs.getLinearMapper(0, j2 + 2);
+ const LinearMapper dm3 = rhs.getLinearMapper(0, j2 + 3);
+
+ Index k = 0;
+ if ((PacketSize % 4) == 0) // TODO enable vectorized transposition for PacketSize==2 ??
+ {
+ for (; k < peeled_k; k += PacketSize) {
+ PacketBlock<Packet, (PacketSize % 4) == 0 ? 4 : PacketSize> kernel;
+ kernel.packet[0] = dm0.template loadPacket<Packet>(k);
+ kernel.packet[1 % PacketSize] = dm1.template loadPacket<Packet>(k);
+ kernel.packet[2 % PacketSize] = dm2.template loadPacket<Packet>(k);
+ kernel.packet[3 % PacketSize] = dm3.template loadPacket<Packet>(k);
+ ptranspose(kernel);
+ pstoreu(blockB + count + 0 * PacketSize, cj.pconj(kernel.packet[0]));
+ pstoreu(blockB + count + 1 * PacketSize, cj.pconj(kernel.packet[1 % PacketSize]));
+ pstoreu(blockB + count + 2 * PacketSize, cj.pconj(kernel.packet[2 % PacketSize]));
+ pstoreu(blockB + count + 3 * PacketSize, cj.pconj(kernel.packet[3 % PacketSize]));
+ count += 4 * PacketSize;
+ }
+ }
+ for (; k < depth; k++) {
+ blockB[count + 0] = cj(dm0(k));
+ blockB[count + 1] = cj(dm1(k));
+ blockB[count + 2] = cj(dm2(k));
+ blockB[count + 3] = cj(dm3(k));
+ count += 4;
+ }
+ // skip what we have after
+ if (PanelMode) count += 4 * (stride - offset - depth);
+ }
+ }
+
+ // copy the remaining columns one at a time (nr==1)
+ for (Index j2 = packet_cols4; j2 < cols; ++j2) {
+ if (PanelMode) count += offset;
+ const LinearMapper dm0 = rhs.getLinearMapper(0, j2);
+ for (Index k = 0; k < depth; k++) {
+ blockB[count] = cj(dm0(k));
+ count += 1;
+ }
+ if (PanelMode) count += (stride - offset - depth);
+ }
+}
+
+template <typename Scalar, typename Index, typename DataMapper, bool Conjugate, bool PanelMode>
+struct gemm_pack_rhs<Scalar, Index, DataMapper, 8, RowMajor, Conjugate, PanelMode> {
+ typedef typename packet_traits<Scalar>::type Packet;
+ typedef typename unpacket_traits<Packet>::half HalfPacket;
+ typedef typename unpacket_traits<typename unpacket_traits<Packet>::half>::half QuarterPacket;
+ typedef typename DataMapper::LinearMapper LinearMapper;
+ enum {
+ PacketSize = packet_traits<Scalar>::size,
+ HalfPacketSize = unpacket_traits<HalfPacket>::size,
+ QuarterPacketSize = unpacket_traits<QuarterPacket>::size
+ };
+ EIGEN_DONT_INLINE void operator()(Scalar *blockB, const DataMapper &rhs, Index depth, Index cols, Index stride = 0,
+ Index offset = 0) {
+ constexpr int nr = 8;
+ EIGEN_ASM_COMMENT("EIGEN PRODUCT PACK RHS ROWMAJOR");
+ EIGEN_UNUSED_VARIABLE(stride);
+ EIGEN_UNUSED_VARIABLE(offset);
+ eigen_assert(((!PanelMode) && stride == 0 && offset == 0) || (PanelMode && stride >= depth && offset <= stride));
+ const bool HasHalf = (int)HalfPacketSize < (int)PacketSize;
+ const bool HasQuarter = (int)QuarterPacketSize < (int)HalfPacketSize;
+ conj_if<NumTraits<Scalar>::IsComplex && Conjugate> cj;
+ Index packet_cols8 = nr >= 8 ? (cols / 8) * 8 : 0;
+ Index packet_cols4 = nr >= 4 ? (cols / 4) * 4 : 0;
+ Index count = 0;
+
+ if (nr >= 8) {
+ for (Index j2 = 0; j2 < packet_cols8; j2 += 8) {
+ // skip what we have before
+ if (PanelMode) count += 8 * offset;
+ for (Index k = 0; k < depth; k++) {
+ if (PacketSize == 8) {
+ // Packet A = ploadu<Packet>(&rhs.data()[k*rhs.stride() + j2]);
+ Packet A = rhs.template loadPacket<Packet>(k, j2);
+ pstoreu(blockB + count, cj.pconj(A));
+ } else if (HasHalf && HalfPacketSize == 8) {
+ HalfPacket A = rhs.template loadPacket<HalfPacket>(k, j2);
+ pstoreu(blockB + count, cj.pconj(A));
+ } else if (HasQuarter && QuarterPacketSize == 8) {
+ QuarterPacket A = rhs.template loadPacket<QuarterPacket>(k, j2);
+ pstoreu(blockB + count, cj.pconj(A));
+ } else if (PacketSize == 4) {
+ // Packet A = ploadu<Packet>(&rhs.data()[k*rhs.stride() + j2]);
+ // Packet B = ploadu<Packet>(&rhs.data()[k*rhs.stride() + j2 + PacketSize]);
+ Packet A = rhs.template loadPacket<Packet>(k, j2);
+ Packet B = rhs.template loadPacket<Packet>(k, j2 + PacketSize);
+ pstoreu(blockB + count, cj.pconj(A));
+ pstoreu(blockB + count + PacketSize, cj.pconj(B));
+ } else {
+ // const Scalar* b0 = &rhs.data()[k*rhs.stride() + j2];
+ const LinearMapper dm0 = rhs.getLinearMapper(k, j2);
+ blockB[count + 0] = cj(dm0(0));
+ blockB[count + 1] = cj(dm0(1));
+ blockB[count + 2] = cj(dm0(2));
+ blockB[count + 3] = cj(dm0(3));
+ blockB[count + 4] = cj(dm0(4));
+ blockB[count + 5] = cj(dm0(5));
+ blockB[count + 6] = cj(dm0(6));
+ blockB[count + 7] = cj(dm0(7));
+ }
+ count += 8;
+ }
+ // skip what we have after
+ if (PanelMode) count += 8 * (stride - offset - depth);
+ }
+ }
+
+ if (nr >= 4) {
+ for (Index j2 = packet_cols8; j2 < packet_cols4; j2 += 4) {
+ // skip what we have before
+ if (PanelMode) count += 4 * offset;
+ for (Index k = 0; k < depth; k++) {
+ if (PacketSize == 4) {
+ Packet A = rhs.template loadPacket<Packet>(k, j2);
+ pstoreu(blockB + count, cj.pconj(A));
+ count += PacketSize;
+ } else if (HasHalf && HalfPacketSize == 4) {
+ HalfPacket A = rhs.template loadPacket<HalfPacket>(k, j2);
+ pstoreu(blockB + count, cj.pconj(A));
+ count += HalfPacketSize;
+ } else if (HasQuarter && QuarterPacketSize == 4) {
+ QuarterPacket A = rhs.template loadPacket<QuarterPacket>(k, j2);
+ pstoreu(blockB + count, cj.pconj(A));
+ count += QuarterPacketSize;
+ } else {
+ const LinearMapper dm0 = rhs.getLinearMapper(k, j2);
+ blockB[count + 0] = cj(dm0(0));
+ blockB[count + 1] = cj(dm0(1));
+ blockB[count + 2] = cj(dm0(2));
+ blockB[count + 3] = cj(dm0(3));
+ count += 4;
+ }
+ }
+ // skip what we have after
+ if (PanelMode) count += 4 * (stride - offset - depth);
+ }
+ }
+ // copy the remaining columns one at a time (nr==1)
+ for (Index j2 = packet_cols4; j2 < cols; ++j2) {
+ if (PanelMode) count += offset;
+ for (Index k = 0; k < depth; k++) {
+ blockB[count] = cj(rhs(k, j2));
+ count += 1;
+ }
+ if (PanelMode) count += stride - offset - depth;
+ }
+ }
+};
+
+template <typename Scalar, typename Index, typename DataMapper, int mr, bool ConjugateLhs, bool ConjugateRhs>
+struct gebp_kernel<Scalar, Scalar, Index, DataMapper, mr, 8, ConjugateLhs, ConjugateRhs> {
+ EIGEN_ALWAYS_INLINE
+ void operator()(const DataMapper &res, const Scalar *blockA, const Scalar *blockB, Index rows, Index depth,
+ Index cols, Scalar alpha, Index strideA = -1, Index strideB = -1, Index offsetA = 0,
+ Index offsetB = 0);
+};
+
+template <typename Scalar, typename Index, typename DataMapper, int mr, bool ConjugateLhs, bool ConjugateRhs>
+EIGEN_ALWAYS_INLINE void gebp_kernel<Scalar, Scalar, Index, DataMapper, mr, 8, ConjugateLhs, ConjugateRhs>::operator()(
+ const DataMapper &res, const Scalar *blockA, const Scalar *blockB, Index rows, Index depth, Index cols,
+ Scalar alpha, Index strideA, Index strideB, Index offsetA, Index offsetB) {
+ if (res.incr() == 1) {
+ if (alpha == 1) {
+ gemm_kern_avx512<Scalar, mr, 8, true, false, true>(rows, cols, depth, &alpha, blockA, blockB,
+ (Scalar *)res.data(), res.stride(), res.incr(), strideA,
+ strideB, offsetA, offsetB);
+ } else {
+ gemm_kern_avx512<Scalar, mr, 8, false, false, true>(rows, cols, depth, &alpha, blockA, blockB,
+ (Scalar *)res.data(), res.stride(), res.incr(), strideA,
+ strideB, offsetA, offsetB);
+ }
+ } else {
+ if (alpha == 1) {
+ gemm_kern_avx512<Scalar, mr, 8, true, false, false>(rows, cols, depth, &alpha, blockA, blockB,
+ (Scalar *)res.data(), res.stride(), res.incr(), strideA,
+ strideB, offsetA, offsetB);
+ } else {
+ gemm_kern_avx512<Scalar, mr, 8, false, false, false>(rows, cols, depth, &alpha, blockA, blockB,
+ (Scalar *)res.data(), res.stride(), res.incr(), strideA,
+ strideB, offsetA, offsetB);
+ }
+ }
+}
+#endif // EIGEN_USE_AVX512_GEMM_KERNELS
+
+} // namespace internal
+} // namespace Eigen
+
+#undef SECOND_FETCH
+
+#endif // EIGEN_CORE_ARCH_AVX512_GEMM_KERNEL_H
diff --git a/Eigen/src/Core/arch/AVX512/MathFunctions.h b/Eigen/src/Core/arch/AVX512/MathFunctions.h
new file mode 100644
index 0000000..af47a85
--- /dev/null
+++ b/Eigen/src/Core/arch/AVX512/MathFunctions.h
@@ -0,0 +1,302 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2016 Pedro Gonnet (pedro.gonnet@gmail.com)
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef THIRD_PARTY_EIGEN3_EIGEN_SRC_CORE_ARCH_AVX512_MATHFUNCTIONS_H_
+#define THIRD_PARTY_EIGEN3_EIGEN_SRC_CORE_ARCH_AVX512_MATHFUNCTIONS_H_
+
+#include "../../InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+
+#if EIGEN_HAS_AVX512_MATH
+
+#define EIGEN_DECLARE_CONST_Packet16f(NAME, X) \
+ const Packet16f p16f_##NAME = pset1<Packet16f>(X)
+
+#define EIGEN_DECLARE_CONST_Packet16f_FROM_INT(NAME, X) \
+ const Packet16f p16f_##NAME = preinterpret<Packet16f,Packet16i>(pset1<Packet16i>(X))
+
+#define EIGEN_DECLARE_CONST_Packet8d(NAME, X) \
+ const Packet8d p8d_##NAME = pset1<Packet8d>(X)
+
+#define EIGEN_DECLARE_CONST_Packet8d_FROM_INT64(NAME, X) \
+ const Packet8d p8d_##NAME = _mm512_castsi512_pd(_mm512_set1_epi64(X))
+
+#define EIGEN_DECLARE_CONST_Packet16bf(NAME, X) \
+ const Packet16bf p16bf_##NAME = pset1<Packet16bf>(X)
+
+#define EIGEN_DECLARE_CONST_Packet16bf_FROM_INT(NAME, X) \
+ const Packet16bf p16bf_##NAME = preinterpret<Packet16bf,Packet16i>(pset1<Packet16i>(X))
+
+template <>
+EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet16f
+plog<Packet16f>(const Packet16f& _x) {
+ return plog_float(_x);
+}
+
+template <>
+EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet8d
+plog<Packet8d>(const Packet8d& _x) {
+ return plog_double(_x);
+}
+
+F16_PACKET_FUNCTION(Packet16f, Packet16h, plog)
+BF16_PACKET_FUNCTION(Packet16f, Packet16bf, plog)
+
+template <>
+EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet16f
+plog2<Packet16f>(const Packet16f& _x) {
+ return plog2_float(_x);
+}
+
+template <>
+EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet8d
+plog2<Packet8d>(const Packet8d& _x) {
+ return plog2_double(_x);
+}
+
+F16_PACKET_FUNCTION(Packet16f, Packet16h, plog2)
+BF16_PACKET_FUNCTION(Packet16f, Packet16bf, plog2)
+
+// Exponential function. Works by writing "x = m*log(2) + r" where
+// "m = floor(x/log(2)+1/2)" and "r" is the remainder. The result is then
+// "exp(x) = 2^m*exp(r)" where exp(r) is in the range [-1,1).
+template <>
+EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet16f
+pexp<Packet16f>(const Packet16f& _x) {
+ EIGEN_DECLARE_CONST_Packet16f(1, 1.0f);
+ EIGEN_DECLARE_CONST_Packet16f(half, 0.5f);
+ EIGEN_DECLARE_CONST_Packet16f(127, 127.0f);
+
+ EIGEN_DECLARE_CONST_Packet16f(exp_hi, 88.3762626647950f);
+ EIGEN_DECLARE_CONST_Packet16f(exp_lo, -88.3762626647949f);
+
+ EIGEN_DECLARE_CONST_Packet16f(cephes_LOG2EF, 1.44269504088896341f);
+
+ EIGEN_DECLARE_CONST_Packet16f(cephes_exp_p0, 1.9875691500E-4f);
+ EIGEN_DECLARE_CONST_Packet16f(cephes_exp_p1, 1.3981999507E-3f);
+ EIGEN_DECLARE_CONST_Packet16f(cephes_exp_p2, 8.3334519073E-3f);
+ EIGEN_DECLARE_CONST_Packet16f(cephes_exp_p3, 4.1665795894E-2f);
+ EIGEN_DECLARE_CONST_Packet16f(cephes_exp_p4, 1.6666665459E-1f);
+ EIGEN_DECLARE_CONST_Packet16f(cephes_exp_p5, 5.0000001201E-1f);
+
+ // Clamp x.
+ Packet16f x = pmax(pmin(_x, p16f_exp_hi), p16f_exp_lo);
+
+ // Express exp(x) as exp(m*ln(2) + r), start by extracting
+ // m = floor(x/ln(2) + 0.5).
+ Packet16f m = _mm512_floor_ps(pmadd(x, p16f_cephes_LOG2EF, p16f_half));
+
+ // Get r = x - m*ln(2). Note that we can do this without losing more than one
+ // ulp precision due to the FMA instruction.
+ EIGEN_DECLARE_CONST_Packet16f(nln2, -0.6931471805599453f);
+ Packet16f r = _mm512_fmadd_ps(m, p16f_nln2, x);
+ Packet16f r2 = pmul(r, r);
+ Packet16f r3 = pmul(r2, r);
+
+ // Evaluate the polynomial approximant,improved by instruction-level parallelism.
+ Packet16f y, y1, y2;
+ y = pmadd(p16f_cephes_exp_p0, r, p16f_cephes_exp_p1);
+ y1 = pmadd(p16f_cephes_exp_p3, r, p16f_cephes_exp_p4);
+ y2 = padd(r, p16f_1);
+ y = pmadd(y, r, p16f_cephes_exp_p2);
+ y1 = pmadd(y1, r, p16f_cephes_exp_p5);
+ y = pmadd(y, r3, y1);
+ y = pmadd(y, r2, y2);
+
+ // Build emm0 = 2^m.
+ Packet16i emm0 = _mm512_cvttps_epi32(padd(m, p16f_127));
+ emm0 = _mm512_slli_epi32(emm0, 23);
+
+ // Return 2^m * exp(r).
+ return pmax(pmul(y, _mm512_castsi512_ps(emm0)), _x);
+}
+
+template <>
+EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet8d
+pexp<Packet8d>(const Packet8d& _x) {
+ return pexp_double(_x);
+}
+
+F16_PACKET_FUNCTION(Packet16f, Packet16h, pexp)
+BF16_PACKET_FUNCTION(Packet16f, Packet16bf, pexp)
+
+template <>
+EIGEN_STRONG_INLINE Packet16h pfrexp(const Packet16h& a, Packet16h& exponent) {
+ Packet16f fexponent;
+ const Packet16h out = float2half(pfrexp<Packet16f>(half2float(a), fexponent));
+ exponent = float2half(fexponent);
+ return out;
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet16h pldexp(const Packet16h& a, const Packet16h& exponent) {
+ return float2half(pldexp<Packet16f>(half2float(a), half2float(exponent)));
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet16bf pfrexp(const Packet16bf& a, Packet16bf& exponent) {
+ Packet16f fexponent;
+ const Packet16bf out = F32ToBf16(pfrexp<Packet16f>(Bf16ToF32(a), fexponent));
+ exponent = F32ToBf16(fexponent);
+ return out;
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet16bf pldexp(const Packet16bf& a, const Packet16bf& exponent) {
+ return F32ToBf16(pldexp<Packet16f>(Bf16ToF32(a), Bf16ToF32(exponent)));
+}
+
+#if EIGEN_FAST_MATH
+template <>
+EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet16f
+psqrt<Packet16f>(const Packet16f& _x) {
+ return generic_sqrt_newton_step<Packet16f>::run(_x, _mm512_rsqrt14_ps(_x));
+}
+
+template <>
+EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet8d
+psqrt<Packet8d>(const Packet8d& _x) {
+ // Double requires 2 Newton-Raphson steps for convergence.
+ return generic_sqrt_newton_step<Packet8d, /*Steps=*/2>::run(_x, _mm512_rsqrt14_pd(_x));
+}
+#else
+template <>
+EIGEN_STRONG_INLINE Packet16f psqrt<Packet16f>(const Packet16f& x) {
+ return _mm512_sqrt_ps(x);
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet8d psqrt<Packet8d>(const Packet8d& x) {
+ return _mm512_sqrt_pd(x);
+}
+#endif
+
+F16_PACKET_FUNCTION(Packet16f, Packet16h, psqrt)
+BF16_PACKET_FUNCTION(Packet16f, Packet16bf, psqrt)
+
+// prsqrt for float.
+#if defined(EIGEN_VECTORIZE_AVX512ER)
+
+template <>
+EIGEN_STRONG_INLINE Packet16f prsqrt<Packet16f>(const Packet16f& x) {
+ return _mm512_rsqrt28_ps(x);
+}
+#elif EIGEN_FAST_MATH
+
+template <>
+EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet16f
+prsqrt<Packet16f>(const Packet16f& _x) {
+ return generic_rsqrt_newton_step<Packet16f, /*Steps=*/1>::run(_x, _mm512_rsqrt14_ps(_x));
+}
+#endif
+
+F16_PACKET_FUNCTION(Packet16f, Packet16h, prsqrt)
+BF16_PACKET_FUNCTION(Packet16f, Packet16bf, prsqrt)
+
+// prsqrt for double.
+#if EIGEN_FAST_MATH
+template <>
+EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet8d
+prsqrt<Packet8d>(const Packet8d& _x) {
+ #ifdef EIGEN_VECTORIZE_AVX512ER
+ return generic_rsqrt_newton_step<Packet8d, /*Steps=*/1>::run(_x, _mm512_rsqrt28_pd(_x));
+ #else
+ return generic_rsqrt_newton_step<Packet8d, /*Steps=*/2>::run(_x, _mm512_rsqrt14_pd(_x));
+ #endif
+}
+
+template<> EIGEN_STRONG_INLINE Packet16f preciprocal<Packet16f>(const Packet16f& a) {
+#ifdef EIGEN_VECTORIZE_AVX512ER
+ return _mm512_rcp28_ps(a);
+#else
+ return generic_reciprocal_newton_step<Packet16f, /*Steps=*/1>::run(a, _mm512_rcp14_ps(a));
+#endif
+}
+
+F16_PACKET_FUNCTION(Packet16f, Packet16h, preciprocal)
+BF16_PACKET_FUNCTION(Packet16f, Packet16bf, preciprocal)
+#endif
+
+template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+Packet16f plog1p<Packet16f>(const Packet16f& _x) {
+ return generic_plog1p(_x);
+}
+
+F16_PACKET_FUNCTION(Packet16f, Packet16h, plog1p)
+BF16_PACKET_FUNCTION(Packet16f, Packet16bf, plog1p)
+
+template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+Packet16f pexpm1<Packet16f>(const Packet16f& _x) {
+ return generic_expm1(_x);
+}
+
+F16_PACKET_FUNCTION(Packet16f, Packet16h, pexpm1)
+BF16_PACKET_FUNCTION(Packet16f, Packet16bf, pexpm1)
+
+#endif // EIGEN_HAS_AVX512_MATH
+
+
+template <>
+EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet16f
+psin<Packet16f>(const Packet16f& _x) {
+ return psin_float(_x);
+}
+
+template <>
+EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet16f
+pcos<Packet16f>(const Packet16f& _x) {
+ return pcos_float(_x);
+}
+
+template <>
+EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet16f
+pacos<Packet16f>(const Packet16f& _x) {
+ return pacos_float(_x);
+}
+
+template <>
+EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet16f
+pasin<Packet16f>(const Packet16f& _x) {
+ return pasin_float(_x);
+}
+
+template <>
+EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet16f
+patan<Packet16f>(const Packet16f& _x) {
+ return patan_float(_x);
+}
+
+template <>
+EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet8d
+patan<Packet8d>(const Packet8d& _x) {
+ return patan_double(_x);
+}
+
+template <>
+EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet16f
+ptanh<Packet16f>(const Packet16f& _x) {
+ return internal::generic_fast_tanh_float(_x);
+}
+
+F16_PACKET_FUNCTION(Packet16f, Packet16h, psin)
+F16_PACKET_FUNCTION(Packet16f, Packet16h, pcos)
+F16_PACKET_FUNCTION(Packet16f, Packet16h, ptanh)
+
+BF16_PACKET_FUNCTION(Packet16f, Packet16bf, psin)
+BF16_PACKET_FUNCTION(Packet16f, Packet16bf, pcos)
+BF16_PACKET_FUNCTION(Packet16f, Packet16bf, ptanh)
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // THIRD_PARTY_EIGEN3_EIGEN_SRC_CORE_ARCH_AVX512_MATHFUNCTIONS_H_
diff --git a/Eigen/src/Core/arch/AVX512/PacketMath.h b/Eigen/src/Core/arch/AVX512/PacketMath.h
new file mode 100644
index 0000000..5f37740
--- /dev/null
+++ b/Eigen/src/Core/arch/AVX512/PacketMath.h
@@ -0,0 +1,2735 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2016 Benoit Steiner (benoit.steiner.goog@gmail.com)
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_PACKET_MATH_AVX512_H
+#define EIGEN_PACKET_MATH_AVX512_H
+
+#include "../../InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+
+#ifndef EIGEN_CACHEFRIENDLY_PRODUCT_THRESHOLD
+#define EIGEN_CACHEFRIENDLY_PRODUCT_THRESHOLD 8
+#endif
+
+#ifndef EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS
+#define EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS 32
+#endif
+
+#ifdef EIGEN_VECTORIZE_FMA
+#ifndef EIGEN_HAS_SINGLE_INSTRUCTION_MADD
+#define EIGEN_HAS_SINGLE_INSTRUCTION_MADD
+#endif
+#endif
+
+// Disable the code for older versions of gcc that don't support many of the required avx512 math instrinsics.
+#if EIGEN_GNUC_AT_LEAST(5, 3) || EIGEN_COMP_CLANG || EIGEN_COMP_MSVC >= 1923 || EIGEN_COMP_ICC >= 1900
+#define EIGEN_HAS_AVX512_MATH 1
+#else
+#define EIGEN_HAS_AVX512_MATH 0
+#endif
+
+typedef __m512 Packet16f;
+typedef __m512i Packet16i;
+typedef __m512d Packet8d;
+#ifndef EIGEN_VECTORIZE_AVX512FP16
+typedef eigen_packet_wrapper<__m256i, 1> Packet16h;
+#endif
+typedef eigen_packet_wrapper<__m256i, 2> Packet16bf;
+
+template <>
+struct is_arithmetic<__m512> {
+ enum { value = true };
+};
+template <>
+struct is_arithmetic<__m512i> {
+ enum { value = true };
+};
+template <>
+struct is_arithmetic<__m512d> {
+ enum { value = true };
+};
+
+#ifndef EIGEN_VECTORIZE_AVX512FP16
+template<> struct is_arithmetic<Packet16h> { enum { value = true }; };
+
+template <>
+struct packet_traits<half> : default_packet_traits {
+ typedef Packet16h type;
+ // There is no half-size packet for Packet16h.
+ typedef Packet16h half;
+ enum {
+ Vectorizable = 1,
+ AlignedOnScalar = 1,
+ size = 16,
+ HasHalfPacket = 1,
+
+ HasCmp = 1,
+ HasAdd = 1,
+ HasSub = 1,
+ HasMul = 1,
+ HasDiv = 1,
+ HasNegate = 1,
+ HasAbs = 1,
+ HasAbs2 = 0,
+ HasMin = 1,
+ HasMax = 1,
+ HasConj = 1,
+ HasSetLinear = 0,
+ HasLog = EIGEN_HAS_AVX512_MATH,
+ HasLog1p = EIGEN_HAS_AVX512_MATH,
+ HasExp = EIGEN_HAS_AVX512_MATH,
+ HasExpm1 = EIGEN_HAS_AVX512_MATH,
+ HasSqrt = EIGEN_HAS_AVX512_MATH,
+ HasRsqrt = EIGEN_HAS_AVX512_MATH,
+ HasBessel = EIGEN_HAS_AVX512_MATH,
+ HasNdtri = EIGEN_HAS_AVX512_MATH,
+ HasSin = EIGEN_FAST_MATH,
+ HasCos = EIGEN_FAST_MATH,
+ HasTanh = EIGEN_FAST_MATH,
+ HasErf = EIGEN_FAST_MATH,
+ HasBlend = 0,
+ HasRound = 1,
+ HasFloor = 1,
+ HasCeil = 1,
+ HasRint = 1
+ };
+};
+#endif
+
+template<> struct packet_traits<float> : default_packet_traits
+{
+ typedef Packet16f type;
+ typedef Packet8f half;
+ enum {
+ Vectorizable = 1,
+ AlignedOnScalar = 1,
+ size = 16,
+ HasHalfPacket = 1,
+
+ HasAbs = 1,
+ HasMin = 1,
+ HasMax = 1,
+ HasConj = 1,
+ HasBlend = 0,
+ HasSin = EIGEN_FAST_MATH,
+ HasCos = EIGEN_FAST_MATH,
+ HasACos = 1,
+ HasASin = 1,
+ HasATan = 1,
+#if EIGEN_HAS_AVX512_MATH
+ HasLog = 1,
+ HasLog1p = 1,
+ HasExpm1 = 1,
+ HasNdtri = 1,
+ HasBessel = 1,
+ HasExp = 1,
+ HasSqrt = EIGEN_FAST_MATH,
+ HasRsqrt = EIGEN_FAST_MATH,
+ HasReciprocal = EIGEN_FAST_MATH,
+ HasTanh = EIGEN_FAST_MATH,
+ HasErf = EIGEN_FAST_MATH,
+#endif
+ HasCmp = 1,
+ HasDiv = 1,
+ HasRound = 1,
+ HasFloor = 1,
+ HasCeil = 1,
+ HasRint = 1
+ };
+ };
+template<> struct packet_traits<double> : default_packet_traits
+{
+ typedef Packet8d type;
+ typedef Packet4d half;
+ enum {
+ Vectorizable = 1,
+ AlignedOnScalar = 1,
+ size = 8,
+ HasHalfPacket = 1,
+#if EIGEN_HAS_AVX512_MATH
+ HasLog = 1,
+ HasExp = 1,
+ HasSqrt = EIGEN_FAST_MATH,
+ HasRsqrt = EIGEN_FAST_MATH,
+#endif
+ HasATan = 1,
+ HasCmp = 1,
+ HasDiv = 1,
+ HasRound = 1,
+ HasFloor = 1,
+ HasCeil = 1,
+ HasRint = 1
+ };
+};
+
+template<> struct packet_traits<int> : default_packet_traits
+{
+ typedef Packet16i type;
+ typedef Packet8i half;
+ enum {
+ Vectorizable = 1,
+ AlignedOnScalar = 1,
+ HasCmp = 1,
+ HasDiv = 1,
+ size=16
+ };
+};
+
+template <>
+struct unpacket_traits<Packet16f> {
+ typedef float type;
+ typedef Packet8f half;
+ typedef Packet16i integer_packet;
+ typedef uint16_t mask_t;
+ enum { size = 16, alignment=Aligned64, vectorizable=true, masked_load_available=true, masked_store_available=true, masked_fpops_available=true };
+};
+template <>
+struct unpacket_traits<Packet8d> {
+ typedef double type;
+ typedef Packet4d half;
+ typedef uint8_t mask_t;
+ enum { size = 8, alignment=Aligned64, vectorizable=true, masked_load_available=true, masked_store_available=true, masked_fpops_available=true };
+};
+template <>
+struct unpacket_traits<Packet16i> {
+ typedef int type;
+ typedef Packet8i half;
+ enum { size = 16, alignment=Aligned64, vectorizable=true, masked_load_available=false, masked_store_available=false };
+};
+
+#ifndef EIGEN_VECTORIZE_AVX512FP16
+template<>
+struct unpacket_traits<Packet16h> {
+ typedef Eigen::half type;
+ typedef Packet8h half;
+ enum {size=16, alignment=Aligned32, vectorizable=true, masked_load_available=false, masked_store_available=false};
+};
+#endif
+
+template <>
+EIGEN_STRONG_INLINE Packet16f pset1<Packet16f>(const float& from) {
+ return _mm512_set1_ps(from);
+}
+template <>
+EIGEN_STRONG_INLINE Packet8d pset1<Packet8d>(const double& from) {
+ return _mm512_set1_pd(from);
+}
+template <>
+EIGEN_STRONG_INLINE Packet16i pset1<Packet16i>(const int& from) {
+ return _mm512_set1_epi32(from);
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet16f pset1frombits<Packet16f>(unsigned int from) {
+ return _mm512_castsi512_ps(_mm512_set1_epi32(from));
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet8d pset1frombits<Packet8d>(const numext::uint64_t from) {
+ return _mm512_castsi512_pd(_mm512_set1_epi64(from));
+}
+
+template<> EIGEN_STRONG_INLINE Packet16f pzero(const Packet16f& /*a*/) { return _mm512_setzero_ps(); }
+template<> EIGEN_STRONG_INLINE Packet8d pzero(const Packet8d& /*a*/) { return _mm512_setzero_pd(); }
+template<> EIGEN_STRONG_INLINE Packet16i pzero(const Packet16i& /*a*/) { return _mm512_setzero_si512(); }
+
+template<> EIGEN_STRONG_INLINE Packet16f peven_mask(const Packet16f& /*a*/) {
+ return _mm512_castsi512_ps(_mm512_set_epi32(0, -1, 0, -1, 0, -1, 0, -1,
+ 0, -1, 0, -1, 0, -1, 0, -1));
+}
+template<> EIGEN_STRONG_INLINE Packet16i peven_mask(const Packet16i& /*a*/) {
+ return _mm512_set_epi32(0, -1, 0, -1, 0, -1, 0, -1,
+ 0, -1, 0, -1, 0, -1, 0, -1);
+}
+template<> EIGEN_STRONG_INLINE Packet8d peven_mask(const Packet8d& /*a*/) {
+ return _mm512_castsi512_pd(_mm512_set_epi32(0, 0, -1, -1, 0, 0, -1, -1,
+ 0, 0, -1, -1, 0, 0, -1, -1));
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet16f pload1<Packet16f>(const float* from) {
+#if (EIGEN_COMP_GNUC != 0) || (EIGEN_COMP_CLANG != 0)
+ // Inline asm here helps reduce some register spilling in TRSM kernels.
+ // See note in unrolls::gemm::microKernel in TrsmKernel.h
+ Packet16f ret;
+ __asm__ ("vbroadcastss %[mem], %[dst]" : [dst] "=v" (ret) : [mem] "m" (*from));
+ return ret;
+#else
+ return _mm512_broadcastss_ps(_mm_load_ps1(from));
+#endif
+}
+template <>
+EIGEN_STRONG_INLINE Packet8d pload1<Packet8d>(const double* from) {
+#if (EIGEN_COMP_GNUC != 0) || (EIGEN_COMP_CLANG != 0)
+ Packet8d ret;
+ __asm__ ("vbroadcastsd %[mem], %[dst]" : [dst] "=v" (ret) : [mem] "m" (*from));
+ return ret;
+#else
+ return _mm512_set1_pd(*from);
+#endif
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet16f plset<Packet16f>(const float& a) {
+ return _mm512_add_ps(
+ _mm512_set1_ps(a),
+ _mm512_set_ps(15.0f, 14.0f, 13.0f, 12.0f, 11.0f, 10.0f, 9.0f, 8.0f, 7.0f, 6.0f, 5.0f,
+ 4.0f, 3.0f, 2.0f, 1.0f, 0.0f));
+}
+template <>
+EIGEN_STRONG_INLINE Packet8d plset<Packet8d>(const double& a) {
+ return _mm512_add_pd(_mm512_set1_pd(a),
+ _mm512_set_pd(7.0, 6.0, 5.0, 4.0, 3.0, 2.0, 1.0, 0.0));
+}
+template <>
+EIGEN_STRONG_INLINE Packet16i plset<Packet16i>(const int& a) {
+ return _mm512_add_epi32(
+ _mm512_set1_epi32(a),
+ _mm512_set_epi32(15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0));
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet16f padd<Packet16f>(const Packet16f& a,
+ const Packet16f& b) {
+ return _mm512_add_ps(a, b);
+}
+template <>
+EIGEN_STRONG_INLINE Packet8d padd<Packet8d>(const Packet8d& a,
+ const Packet8d& b) {
+ return _mm512_add_pd(a, b);
+}
+template <>
+EIGEN_STRONG_INLINE Packet16i padd<Packet16i>(const Packet16i& a,
+ const Packet16i& b) {
+ return _mm512_add_epi32(a, b);
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet16f padd<Packet16f>(const Packet16f& a,
+ const Packet16f& b,
+ uint16_t umask) {
+ __mmask16 mask = static_cast<__mmask16>(umask);
+ return _mm512_maskz_add_ps(mask, a, b);
+}
+template <>
+EIGEN_STRONG_INLINE Packet8d padd<Packet8d>(const Packet8d& a,
+ const Packet8d& b,
+ uint8_t umask) {
+ __mmask8 mask = static_cast<__mmask8>(umask);
+ return _mm512_maskz_add_pd(mask, a, b);
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet16f psub<Packet16f>(const Packet16f& a,
+ const Packet16f& b) {
+ return _mm512_sub_ps(a, b);
+}
+template <>
+EIGEN_STRONG_INLINE Packet8d psub<Packet8d>(const Packet8d& a,
+ const Packet8d& b) {
+ return _mm512_sub_pd(a, b);
+}
+template <>
+EIGEN_STRONG_INLINE Packet16i psub<Packet16i>(const Packet16i& a,
+ const Packet16i& b) {
+ return _mm512_sub_epi32(a, b);
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet16f pnegate(const Packet16f& a) {
+ return _mm512_sub_ps(_mm512_set1_ps(0.0), a);
+}
+template <>
+EIGEN_STRONG_INLINE Packet8d pnegate(const Packet8d& a) {
+ return _mm512_sub_pd(_mm512_set1_pd(0.0), a);
+}
+template <>
+EIGEN_STRONG_INLINE Packet16i pnegate(const Packet16i& a) {
+ return _mm512_sub_epi32(_mm512_set1_epi32(0), a);
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet16f pconj(const Packet16f& a) {
+ return a;
+}
+template <>
+EIGEN_STRONG_INLINE Packet8d pconj(const Packet8d& a) {
+ return a;
+}
+template <>
+EIGEN_STRONG_INLINE Packet16i pconj(const Packet16i& a) {
+ return a;
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet16f pmul<Packet16f>(const Packet16f& a,
+ const Packet16f& b) {
+ return _mm512_mul_ps(a, b);
+}
+template <>
+EIGEN_STRONG_INLINE Packet8d pmul<Packet8d>(const Packet8d& a,
+ const Packet8d& b) {
+ return _mm512_mul_pd(a, b);
+}
+template <>
+EIGEN_STRONG_INLINE Packet16i pmul<Packet16i>(const Packet16i& a,
+ const Packet16i& b) {
+ return _mm512_mullo_epi32(a, b);
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet16f pdiv<Packet16f>(const Packet16f& a,
+ const Packet16f& b) {
+ return _mm512_div_ps(a, b);
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet8d pdiv<Packet8d>(const Packet8d& a,
+ const Packet8d& b) {
+ return _mm512_div_pd(a, b);
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet16i pdiv<Packet16i>(const Packet16i& a,
+ const Packet16i& b) {
+ Packet8i q_lo = pdiv<Packet8i>(_mm512_extracti64x4_epi64(a, 0), _mm512_extracti64x4_epi64(b,0));
+ Packet8i q_hi = pdiv<Packet8i>(_mm512_extracti64x4_epi64(a, 1), _mm512_extracti64x4_epi64(b, 1));
+ return _mm512_inserti64x4(_mm512_castsi256_si512(q_lo), q_hi, 1);
+}
+
+#ifdef EIGEN_VECTORIZE_FMA
+template <>
+EIGEN_STRONG_INLINE Packet16f pmadd(const Packet16f& a, const Packet16f& b,
+ const Packet16f& c) {
+ return _mm512_fmadd_ps(a, b, c);
+}
+template <>
+EIGEN_STRONG_INLINE Packet8d pmadd(const Packet8d& a, const Packet8d& b,
+ const Packet8d& c) {
+ return _mm512_fmadd_pd(a, b, c);
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet16f pmsub(const Packet16f& a, const Packet16f& b,
+ const Packet16f& c) {
+ return _mm512_fmsub_ps(a, b, c);
+}
+template <>
+EIGEN_STRONG_INLINE Packet8d pmsub(const Packet8d& a, const Packet8d& b,
+ const Packet8d& c) {
+ return _mm512_fmsub_pd(a, b, c);
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet16f pnmadd(const Packet16f& a, const Packet16f& b,
+ const Packet16f& c) {
+ return _mm512_fnmadd_ps(a, b, c);
+}
+template <>
+EIGEN_STRONG_INLINE Packet8d pnmadd(const Packet8d& a, const Packet8d& b,
+ const Packet8d& c) {
+ return _mm512_fnmadd_pd(a, b, c);
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet16f pnmsub(const Packet16f& a, const Packet16f& b,
+ const Packet16f& c) {
+ return _mm512_fnmsub_ps(a, b, c);
+}
+template <>
+EIGEN_STRONG_INLINE Packet8d pnmsub(const Packet8d& a, const Packet8d& b,
+ const Packet8d& c) {
+ return _mm512_fnmsub_pd(a, b, c);
+}
+#endif
+
+template <>
+EIGEN_DEVICE_FUNC inline Packet16f pselect(const Packet16f& mask,
+ const Packet16f& a,
+ const Packet16f& b) {
+ __mmask16 mask16 = _mm512_cmp_epi32_mask(
+ _mm512_castps_si512(mask), _mm512_setzero_epi32(), _MM_CMPINT_EQ);
+ return _mm512_mask_blend_ps(mask16, a, b);
+}
+
+template <>
+EIGEN_DEVICE_FUNC inline Packet8d pselect(const Packet8d& mask,
+ const Packet8d& a,
+ const Packet8d& b) {
+ __mmask8 mask8 = _mm512_cmp_epi64_mask(_mm512_castpd_si512(mask),
+ _mm512_setzero_epi32(), _MM_CMPINT_EQ);
+ return _mm512_mask_blend_pd(mask8, a, b);
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet16f pmin<Packet16f>(const Packet16f& a,
+ const Packet16f& b) {
+ // Arguments are reversed to match NaN propagation behavior of std::min.
+ return _mm512_min_ps(b, a);
+}
+template <>
+EIGEN_STRONG_INLINE Packet8d pmin<Packet8d>(const Packet8d& a,
+ const Packet8d& b) {
+ // Arguments are reversed to match NaN propagation behavior of std::min.
+ return _mm512_min_pd(b, a);
+}
+template <>
+EIGEN_STRONG_INLINE Packet16i pmin<Packet16i>(const Packet16i& a,
+ const Packet16i& b) {
+ return _mm512_min_epi32(b, a);
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet16f pmax<Packet16f>(const Packet16f& a,
+ const Packet16f& b) {
+ // Arguments are reversed to match NaN propagation behavior of std::max.
+ return _mm512_max_ps(b, a);
+}
+template <>
+EIGEN_STRONG_INLINE Packet8d pmax<Packet8d>(const Packet8d& a,
+ const Packet8d& b) {
+ // Arguments are reversed to match NaN propagation behavior of std::max.
+ return _mm512_max_pd(b, a);
+}
+template <>
+EIGEN_STRONG_INLINE Packet16i pmax<Packet16i>(const Packet16i& a,
+ const Packet16i& b) {
+ return _mm512_max_epi32(b, a);
+}
+
+// Add specializations for min/max with prescribed NaN progation.
+template<>
+EIGEN_STRONG_INLINE Packet16f pmin<PropagateNumbers, Packet16f>(const Packet16f& a, const Packet16f& b) {
+ return pminmax_propagate_numbers(a, b, pmin<Packet16f>);
+}
+template<>
+EIGEN_STRONG_INLINE Packet8d pmin<PropagateNumbers, Packet8d>(const Packet8d& a, const Packet8d& b) {
+ return pminmax_propagate_numbers(a, b, pmin<Packet8d>);
+}
+template<>
+EIGEN_STRONG_INLINE Packet16f pmax<PropagateNumbers, Packet16f>(const Packet16f& a, const Packet16f& b) {
+ return pminmax_propagate_numbers(a, b, pmax<Packet16f>);
+}
+template<>
+EIGEN_STRONG_INLINE Packet8d pmax<PropagateNumbers, Packet8d>(const Packet8d& a, const Packet8d& b) {
+ return pminmax_propagate_numbers(a, b, pmax<Packet8d>);
+}
+template<>
+EIGEN_STRONG_INLINE Packet16f pmin<PropagateNaN, Packet16f>(const Packet16f& a, const Packet16f& b) {
+ return pminmax_propagate_nan(a, b, pmin<Packet16f>);
+}
+template<>
+EIGEN_STRONG_INLINE Packet8d pmin<PropagateNaN, Packet8d>(const Packet8d& a, const Packet8d& b) {
+ return pminmax_propagate_nan(a, b, pmin<Packet8d>);
+}
+template<>
+EIGEN_STRONG_INLINE Packet16f pmax<PropagateNaN, Packet16f>(const Packet16f& a, const Packet16f& b) {
+ return pminmax_propagate_nan(a, b, pmax<Packet16f>);
+}
+template<>
+EIGEN_STRONG_INLINE Packet8d pmax<PropagateNaN, Packet8d>(const Packet8d& a, const Packet8d& b) {
+ return pminmax_propagate_nan(a, b, pmax<Packet8d>);
+}
+
+
+#ifdef EIGEN_VECTORIZE_AVX512DQ
+template<int I_> EIGEN_STRONG_INLINE Packet8f extract256(Packet16f x) { return _mm512_extractf32x8_ps(x,I_); }
+template<int I_> EIGEN_STRONG_INLINE Packet2d extract128(Packet8d x) { return _mm512_extractf64x2_pd(x,I_); }
+EIGEN_STRONG_INLINE Packet16f cat256(Packet8f a, Packet8f b) { return _mm512_insertf32x8(_mm512_castps256_ps512(a),b,1); }
+#else
+// AVX512F does not define _mm512_extractf32x8_ps to extract _m256 from _m512
+template<int I_> EIGEN_STRONG_INLINE Packet8f extract256(Packet16f x) {
+ return _mm256_castsi256_ps(_mm512_extracti64x4_epi64( _mm512_castps_si512(x),I_));
+}
+
+// AVX512F does not define _mm512_extractf64x2_pd to extract _m128 from _m512
+template<int I_> EIGEN_STRONG_INLINE Packet2d extract128(Packet8d x) {
+ return _mm_castsi128_pd(_mm512_extracti32x4_epi32( _mm512_castpd_si512(x),I_));
+}
+
+EIGEN_STRONG_INLINE Packet16f cat256(Packet8f a, Packet8f b) {
+ return _mm512_castsi512_ps(_mm512_inserti64x4(_mm512_castsi256_si512(_mm256_castps_si256(a)),
+ _mm256_castps_si256(b),1));
+}
+#endif
+
+// Helper function for bit packing snippet of low precision comparison.
+// It packs the flags from 32x16 to 16x16.
+EIGEN_STRONG_INLINE __m256i Pack32To16(Packet16f rf) {
+ // Split data into small pieces and handle with AVX instructions
+ // to guarantee internal order of vector.
+ // Operation:
+ // dst[15:0] := Saturate16(rf[31:0])
+ // dst[31:16] := Saturate16(rf[63:32])
+ // ...
+ // dst[255:240] := Saturate16(rf[255:224])
+ __m256i lo = _mm256_castps_si256(extract256<0>(rf));
+ __m256i hi = _mm256_castps_si256(extract256<1>(rf));
+ __m128i result_lo = _mm_packs_epi32(_mm256_extractf128_si256(lo, 0),
+ _mm256_extractf128_si256(lo, 1));
+ __m128i result_hi = _mm_packs_epi32(_mm256_extractf128_si256(hi, 0),
+ _mm256_extractf128_si256(hi, 1));
+ return _mm256_insertf128_si256(_mm256_castsi128_si256(result_lo), result_hi, 1);
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet16f pcmp_eq(const Packet16f& a, const Packet16f& b) {
+ __mmask16 mask = _mm512_cmp_ps_mask(a, b, _CMP_EQ_OQ);
+ return _mm512_castsi512_ps(
+ _mm512_mask_set1_epi32(_mm512_set1_epi32(0), mask, 0xffffffffu));
+}
+template<> EIGEN_STRONG_INLINE Packet16f pcmp_le(const Packet16f& a, const Packet16f& b) {
+ __mmask16 mask = _mm512_cmp_ps_mask(a, b, _CMP_LE_OQ);
+ return _mm512_castsi512_ps(
+ _mm512_mask_set1_epi32(_mm512_set1_epi32(0), mask, 0xffffffffu));
+}
+
+template<> EIGEN_STRONG_INLINE Packet16f pcmp_lt(const Packet16f& a, const Packet16f& b) {
+ __mmask16 mask = _mm512_cmp_ps_mask(a, b, _CMP_LT_OQ);
+ return _mm512_castsi512_ps(
+ _mm512_mask_set1_epi32(_mm512_set1_epi32(0), mask, 0xffffffffu));
+}
+
+template<> EIGEN_STRONG_INLINE Packet16f pcmp_lt_or_nan(const Packet16f& a, const Packet16f& b) {
+ __mmask16 mask = _mm512_cmp_ps_mask(a, b, _CMP_NGE_UQ);
+ return _mm512_castsi512_ps(
+ _mm512_mask_set1_epi32(_mm512_set1_epi32(0), mask, 0xffffffffu));
+}
+
+template<> EIGEN_STRONG_INLINE Packet16i pcmp_eq(const Packet16i& a, const Packet16i& b) {
+ __mmask16 mask = _mm512_cmp_epi32_mask(a, b, _MM_CMPINT_EQ);
+ return _mm512_mask_set1_epi32(_mm512_set1_epi32(0), mask, 0xffffffffu);
+}
+template<> EIGEN_STRONG_INLINE Packet16i pcmp_le(const Packet16i& a, const Packet16i& b) {
+ __mmask16 mask = _mm512_cmp_epi32_mask(a, b, _MM_CMPINT_LE);
+ return _mm512_mask_set1_epi32(_mm512_set1_epi32(0), mask, 0xffffffffu);
+}
+template<> EIGEN_STRONG_INLINE Packet16i pcmp_lt(const Packet16i& a, const Packet16i& b) {
+ __mmask16 mask = _mm512_cmp_epi32_mask(a, b, _MM_CMPINT_LT);
+ return _mm512_mask_set1_epi32(_mm512_set1_epi32(0), mask, 0xffffffffu);
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet8d pcmp_eq(const Packet8d& a, const Packet8d& b) {
+ __mmask8 mask = _mm512_cmp_pd_mask(a, b, _CMP_EQ_OQ);
+ return _mm512_castsi512_pd(
+ _mm512_mask_set1_epi64(_mm512_set1_epi64(0), mask, 0xffffffffffffffffu));
+}
+template <>
+EIGEN_STRONG_INLINE Packet8d pcmp_le(const Packet8d& a, const Packet8d& b) {
+ __mmask8 mask = _mm512_cmp_pd_mask(a, b, _CMP_LE_OQ);
+ return _mm512_castsi512_pd(
+ _mm512_mask_set1_epi64(_mm512_set1_epi64(0), mask, 0xffffffffffffffffu));
+}
+template <>
+EIGEN_STRONG_INLINE Packet8d pcmp_lt(const Packet8d& a, const Packet8d& b) {
+ __mmask8 mask = _mm512_cmp_pd_mask(a, b, _CMP_LT_OQ);
+ return _mm512_castsi512_pd(
+ _mm512_mask_set1_epi64(_mm512_set1_epi64(0), mask, 0xffffffffffffffffu));
+}
+template <>
+EIGEN_STRONG_INLINE Packet8d pcmp_lt_or_nan(const Packet8d& a, const Packet8d& b) {
+ __mmask8 mask = _mm512_cmp_pd_mask(a, b, _CMP_NGE_UQ);
+ return _mm512_castsi512_pd(
+ _mm512_mask_set1_epi64(_mm512_set1_epi64(0), mask, 0xffffffffffffffffu));
+}
+
+template<> EIGEN_STRONG_INLINE Packet16f print<Packet16f>(const Packet16f& a) { return _mm512_roundscale_ps(a, _MM_FROUND_CUR_DIRECTION); }
+template<> EIGEN_STRONG_INLINE Packet8d print<Packet8d>(const Packet8d& a) { return _mm512_roundscale_pd(a, _MM_FROUND_CUR_DIRECTION); }
+
+template<> EIGEN_STRONG_INLINE Packet16f pceil<Packet16f>(const Packet16f& a) { return _mm512_roundscale_ps(a, _MM_FROUND_TO_POS_INF); }
+template<> EIGEN_STRONG_INLINE Packet8d pceil<Packet8d>(const Packet8d& a) { return _mm512_roundscale_pd(a, _MM_FROUND_TO_POS_INF); }
+
+template<> EIGEN_STRONG_INLINE Packet16f pfloor<Packet16f>(const Packet16f& a) { return _mm512_roundscale_ps(a, _MM_FROUND_TO_NEG_INF); }
+template<> EIGEN_STRONG_INLINE Packet8d pfloor<Packet8d>(const Packet8d& a) { return _mm512_roundscale_pd(a, _MM_FROUND_TO_NEG_INF); }
+
+template <>
+EIGEN_STRONG_INLINE Packet16i ptrue<Packet16i>(const Packet16i& /*a*/) {
+ return _mm512_set1_epi32(0xffffffffu);
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet16f ptrue<Packet16f>(const Packet16f& a) {
+ return _mm512_castsi512_ps(ptrue<Packet16i>(_mm512_castps_si512(a)));
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet8d ptrue<Packet8d>(const Packet8d& a) {
+ return _mm512_castsi512_pd(ptrue<Packet16i>(_mm512_castpd_si512(a)));
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet16i pand<Packet16i>(const Packet16i& a,
+ const Packet16i& b) {
+ return _mm512_and_si512(a,b);
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet16f pand<Packet16f>(const Packet16f& a,
+ const Packet16f& b) {
+#ifdef EIGEN_VECTORIZE_AVX512DQ
+ return _mm512_and_ps(a, b);
+#else
+ return _mm512_castsi512_ps(pand(_mm512_castps_si512(a),_mm512_castps_si512(b)));
+#endif
+}
+template <>
+EIGEN_STRONG_INLINE Packet8d pand<Packet8d>(const Packet8d& a,
+ const Packet8d& b) {
+#ifdef EIGEN_VECTORIZE_AVX512DQ
+ return _mm512_and_pd(a, b);
+#else
+ Packet8d res = _mm512_undefined_pd();
+ Packet4d lane0_a = _mm512_extractf64x4_pd(a, 0);
+ Packet4d lane0_b = _mm512_extractf64x4_pd(b, 0);
+ res = _mm512_insertf64x4(res, _mm256_and_pd(lane0_a, lane0_b), 0);
+
+ Packet4d lane1_a = _mm512_extractf64x4_pd(a, 1);
+ Packet4d lane1_b = _mm512_extractf64x4_pd(b, 1);
+ return _mm512_insertf64x4(res, _mm256_and_pd(lane1_a, lane1_b), 1);
+#endif
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet16i por<Packet16i>(const Packet16i& a, const Packet16i& b) {
+ return _mm512_or_si512(a, b);
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet16f por<Packet16f>(const Packet16f& a, const Packet16f& b) {
+#ifdef EIGEN_VECTORIZE_AVX512DQ
+ return _mm512_or_ps(a, b);
+#else
+ return _mm512_castsi512_ps(por(_mm512_castps_si512(a),_mm512_castps_si512(b)));
+#endif
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet8d por<Packet8d>(const Packet8d& a,
+ const Packet8d& b) {
+#ifdef EIGEN_VECTORIZE_AVX512DQ
+ return _mm512_or_pd(a, b);
+#else
+ return _mm512_castsi512_pd(por(_mm512_castpd_si512(a),_mm512_castpd_si512(b)));
+#endif
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet16i pxor<Packet16i>(const Packet16i& a, const Packet16i& b) {
+ return _mm512_xor_si512(a, b);
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet16f pxor<Packet16f>(const Packet16f& a, const Packet16f& b) {
+#ifdef EIGEN_VECTORIZE_AVX512DQ
+ return _mm512_xor_ps(a, b);
+#else
+ return _mm512_castsi512_ps(pxor(_mm512_castps_si512(a),_mm512_castps_si512(b)));
+#endif
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet8d pxor<Packet8d>(const Packet8d& a, const Packet8d& b) {
+#ifdef EIGEN_VECTORIZE_AVX512DQ
+ return _mm512_xor_pd(a, b);
+#else
+ return _mm512_castsi512_pd(pxor(_mm512_castpd_si512(a),_mm512_castpd_si512(b)));
+#endif
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet16i pandnot<Packet16i>(const Packet16i& a, const Packet16i& b) {
+ return _mm512_andnot_si512(b, a);
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet16f pandnot<Packet16f>(const Packet16f& a, const Packet16f& b) {
+#ifdef EIGEN_VECTORIZE_AVX512DQ
+ return _mm512_andnot_ps(b, a);
+#else
+ return _mm512_castsi512_ps(pandnot(_mm512_castps_si512(a),_mm512_castps_si512(b)));
+#endif
+}
+template <>
+EIGEN_STRONG_INLINE Packet8d pandnot<Packet8d>(const Packet8d& a,const Packet8d& b) {
+#ifdef EIGEN_VECTORIZE_AVX512DQ
+ return _mm512_andnot_pd(b, a);
+#else
+ return _mm512_castsi512_pd(pandnot(_mm512_castpd_si512(a),_mm512_castpd_si512(b)));
+#endif
+}
+
+template<> EIGEN_STRONG_INLINE Packet16f pround<Packet16f>(const Packet16f& a)
+{
+ // Work-around for default std::round rounding mode.
+ const Packet16f mask = pset1frombits<Packet16f>(static_cast<numext::uint32_t>(0x80000000u));
+ const Packet16f prev0dot5 = pset1frombits<Packet16f>(static_cast<numext::uint32_t>(0x3EFFFFFFu));
+ return _mm512_roundscale_ps(padd(por(pand(a, mask), prev0dot5), a), _MM_FROUND_TO_ZERO);
+}
+template<> EIGEN_STRONG_INLINE Packet8d pround<Packet8d>(const Packet8d& a)
+{
+ // Work-around for default std::round rounding mode.
+ const Packet8d mask = pset1frombits<Packet8d>(static_cast<numext::uint64_t>(0x8000000000000000ull));
+ const Packet8d prev0dot5 = pset1frombits<Packet8d>(static_cast<numext::uint64_t>(0x3FDFFFFFFFFFFFFFull));
+ return _mm512_roundscale_pd(padd(por(pand(a, mask), prev0dot5), a), _MM_FROUND_TO_ZERO);
+}
+
+template<int N> EIGEN_STRONG_INLINE Packet16i parithmetic_shift_right(Packet16i a) {
+ return _mm512_srai_epi32(a, N);
+}
+
+template<int N> EIGEN_STRONG_INLINE Packet16i plogical_shift_right(Packet16i a) {
+ return _mm512_srli_epi32(a, N);
+}
+
+template<int N> EIGEN_STRONG_INLINE Packet16i plogical_shift_left(Packet16i a) {
+ return _mm512_slli_epi32(a, N);
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet16f pload<Packet16f>(const float* from) {
+ EIGEN_DEBUG_ALIGNED_LOAD return _mm512_load_ps(from);
+}
+template <>
+EIGEN_STRONG_INLINE Packet8d pload<Packet8d>(const double* from) {
+ EIGEN_DEBUG_ALIGNED_LOAD return _mm512_load_pd(from);
+}
+template <>
+EIGEN_STRONG_INLINE Packet16i pload<Packet16i>(const int* from) {
+ EIGEN_DEBUG_ALIGNED_LOAD return _mm512_load_si512(
+ reinterpret_cast<const __m512i*>(from));
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet16f ploadu<Packet16f>(const float* from) {
+ EIGEN_DEBUG_UNALIGNED_LOAD return _mm512_loadu_ps(from);
+}
+template <>
+EIGEN_STRONG_INLINE Packet8d ploadu<Packet8d>(const double* from) {
+ EIGEN_DEBUG_UNALIGNED_LOAD return _mm512_loadu_pd(from);
+}
+template <>
+EIGEN_STRONG_INLINE Packet16i ploadu<Packet16i>(const int* from) {
+ EIGEN_DEBUG_UNALIGNED_LOAD return _mm512_loadu_si512(
+ reinterpret_cast<const __m512i*>(from));
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet16f ploadu<Packet16f>(const float* from, uint16_t umask) {
+ __mmask16 mask = static_cast<__mmask16>(umask);
+ EIGEN_DEBUG_UNALIGNED_LOAD return _mm512_maskz_loadu_ps(mask, from);
+}
+template <>
+EIGEN_STRONG_INLINE Packet8d ploadu<Packet8d>(const double* from, uint8_t umask) {
+ __mmask8 mask = static_cast<__mmask8>(umask);
+ EIGEN_DEBUG_UNALIGNED_LOAD return _mm512_maskz_loadu_pd(mask, from);
+}
+
+// Loads 8 floats from memory a returns the packet
+// {a0, a0 a1, a1, a2, a2, a3, a3, a4, a4, a5, a5, a6, a6, a7, a7}
+template <>
+EIGEN_STRONG_INLINE Packet16f ploaddup<Packet16f>(const float* from) {
+ // an unaligned load is required here as there is no requirement
+ // on the alignment of input pointer 'from'
+ __m256i low_half = _mm256_loadu_si256(reinterpret_cast<const __m256i*>(from));
+ __m512 even_elements = _mm512_castsi512_ps(_mm512_cvtepu32_epi64(low_half));
+ __m512 pairs = _mm512_permute_ps(even_elements, _MM_SHUFFLE(2, 2, 0, 0));
+ return pairs;
+}
+
+#ifdef EIGEN_VECTORIZE_AVX512DQ
+// FIXME: this does not look optimal, better load a Packet4d and shuffle...
+// Loads 4 doubles from memory a returns the packet {a0, a0 a1, a1, a2, a2, a3,
+// a3}
+template <>
+EIGEN_STRONG_INLINE Packet8d ploaddup<Packet8d>(const double* from) {
+ __m512d x = _mm512_setzero_pd();
+ x = _mm512_insertf64x2(x, _mm_loaddup_pd(&from[0]), 0);
+ x = _mm512_insertf64x2(x, _mm_loaddup_pd(&from[1]), 1);
+ x = _mm512_insertf64x2(x, _mm_loaddup_pd(&from[2]), 2);
+ x = _mm512_insertf64x2(x, _mm_loaddup_pd(&from[3]), 3);
+ return x;
+}
+#else
+template <>
+EIGEN_STRONG_INLINE Packet8d ploaddup<Packet8d>(const double* from) {
+ __m512d x = _mm512_setzero_pd();
+ x = _mm512_mask_broadcastsd_pd(x, 0x3<<0, _mm_load_sd(from+0));
+ x = _mm512_mask_broadcastsd_pd(x, 0x3<<2, _mm_load_sd(from+1));
+ x = _mm512_mask_broadcastsd_pd(x, 0x3<<4, _mm_load_sd(from+2));
+ x = _mm512_mask_broadcastsd_pd(x, 0x3<<6, _mm_load_sd(from+3));
+ return x;
+}
+#endif
+
+// Loads 8 integers from memory and returns the packet
+// {a0, a0 a1, a1, a2, a2, a3, a3, a4, a4, a5, a5, a6, a6, a7, a7}
+template <>
+EIGEN_STRONG_INLINE Packet16i ploaddup<Packet16i>(const int* from) {
+ __m256i low_half = _mm256_loadu_si256(reinterpret_cast<const __m256i*>(from));
+ __m512 even_elements = _mm512_castsi512_ps(_mm512_cvtepu32_epi64(low_half));
+ __m512 pairs = _mm512_permute_ps(even_elements, _MM_SHUFFLE(2, 2, 0, 0));
+ return _mm512_castps_si512(pairs);
+}
+
+// Loads 4 floats from memory a returns the packet
+// {a0, a0 a0, a0, a1, a1, a1, a1, a2, a2, a2, a2, a3, a3, a3, a3}
+template <>
+EIGEN_STRONG_INLINE Packet16f ploadquad<Packet16f>(const float* from) {
+ Packet16f tmp = _mm512_castps128_ps512(ploadu<Packet4f>(from));
+ const Packet16i scatter_mask = _mm512_set_epi32(3,3,3,3, 2,2,2,2, 1,1,1,1, 0,0,0,0);
+ return _mm512_permutexvar_ps(scatter_mask, tmp);
+}
+
+// Loads 2 doubles from memory a returns the packet
+// {a0, a0 a0, a0, a1, a1, a1, a1}
+template <>
+EIGEN_STRONG_INLINE Packet8d ploadquad<Packet8d>(const double* from) {
+ __m256d lane0 = _mm256_set1_pd(*from);
+ __m256d lane1 = _mm256_set1_pd(*(from+1));
+ __m512d tmp = _mm512_undefined_pd();
+ tmp = _mm512_insertf64x4(tmp, lane0, 0);
+ return _mm512_insertf64x4(tmp, lane1, 1);
+}
+
+// Loads 4 integers from memory and returns the packet
+// {a0, a0 a0, a0, a1, a1, a1, a1, a2, a2, a2, a2, a3, a3, a3, a3}
+template <>
+EIGEN_STRONG_INLINE Packet16i ploadquad<Packet16i>(const int* from) {
+ Packet16i tmp = _mm512_castsi128_si512(ploadu<Packet4i>(from));
+ const Packet16i scatter_mask = _mm512_set_epi32(3,3,3,3, 2,2,2,2, 1,1,1,1, 0,0,0,0);
+ return _mm512_permutexvar_epi32(scatter_mask, tmp);
+}
+
+template <>
+EIGEN_STRONG_INLINE void pstore<float>(float* to, const Packet16f& from) {
+ EIGEN_DEBUG_ALIGNED_STORE _mm512_store_ps(to, from);
+}
+template <>
+EIGEN_STRONG_INLINE void pstore<double>(double* to, const Packet8d& from) {
+ EIGEN_DEBUG_ALIGNED_STORE _mm512_store_pd(to, from);
+}
+template <>
+EIGEN_STRONG_INLINE void pstore<int>(int* to, const Packet16i& from) {
+ EIGEN_DEBUG_ALIGNED_STORE _mm512_storeu_si512(reinterpret_cast<__m512i*>(to),
+ from);
+}
+
+template <>
+EIGEN_STRONG_INLINE void pstoreu<float>(float* to, const Packet16f& from) {
+ EIGEN_DEBUG_UNALIGNED_STORE _mm512_storeu_ps(to, from);
+}
+template <>
+EIGEN_STRONG_INLINE void pstoreu<double>(double* to, const Packet8d& from) {
+ EIGEN_DEBUG_UNALIGNED_STORE _mm512_storeu_pd(to, from);
+}
+template <>
+EIGEN_STRONG_INLINE void pstoreu<int>(int* to, const Packet16i& from) {
+ EIGEN_DEBUG_UNALIGNED_STORE _mm512_storeu_si512(
+ reinterpret_cast<__m512i*>(to), from);
+}
+template <>
+EIGEN_STRONG_INLINE void pstoreu<float>(float* to, const Packet16f& from, uint16_t umask) {
+ __mmask16 mask = static_cast<__mmask16>(umask);
+ EIGEN_DEBUG_UNALIGNED_STORE return _mm512_mask_storeu_ps(to, mask, from);
+}
+template <>
+EIGEN_STRONG_INLINE void pstoreu<double>(double* to, const Packet8d& from, uint8_t umask) {
+ __mmask8 mask = static_cast<__mmask8>(umask);
+ EIGEN_DEBUG_UNALIGNED_STORE return _mm512_mask_storeu_pd(to, mask, from);
+}
+
+template <typename Scalar, typename Packet>
+EIGEN_DEVICE_FUNC inline Packet pgather(const Packet& src, const Scalar* from,
+ Index stride, typename unpacket_traits<Packet>::mask_t umask);
+template <>
+EIGEN_DEVICE_FUNC inline Packet16f pgather<float, Packet16f>(const Packet16f& src,
+ const float* from,
+ Index stride,
+ uint16_t umask) {
+ Packet16i stride_vector = _mm512_set1_epi32(convert_index<int>(stride));
+ Packet16i stride_multiplier =
+ _mm512_set_epi32(15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0);
+ Packet16i indices = _mm512_mullo_epi32(stride_vector, stride_multiplier);
+ __mmask16 mask = static_cast<__mmask16>(umask);
+
+ return _mm512_mask_i32gather_ps(src, mask, indices, from, 4);
+}
+template <>
+EIGEN_DEVICE_FUNC inline Packet8d pgather<double, Packet8d>(const Packet8d& src,
+ const double* from,
+ Index stride,
+ uint8_t umask) {
+ Packet8i stride_vector = _mm256_set1_epi32(convert_index<int>(stride));
+ Packet8i stride_multiplier = _mm256_set_epi32(7, 6, 5, 4, 3, 2, 1, 0);
+ Packet8i indices = _mm256_mullo_epi32(stride_vector, stride_multiplier);
+ __mmask8 mask = static_cast<__mmask8>(umask);
+
+ return _mm512_mask_i32gather_pd(src, mask, indices, from, 8);
+}
+
+template <>
+EIGEN_DEVICE_FUNC inline Packet16f pgather<float, Packet16f>(const float* from,
+ Index stride) {
+ Packet16i stride_vector = _mm512_set1_epi32(convert_index<int>(stride));
+ Packet16i stride_multiplier =
+ _mm512_set_epi32(15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0);
+ Packet16i indices = _mm512_mullo_epi32(stride_vector, stride_multiplier);
+
+ return _mm512_i32gather_ps(indices, from, 4);
+}
+template <>
+EIGEN_DEVICE_FUNC inline Packet8d pgather<double, Packet8d>(const double* from,
+ Index stride) {
+ Packet8i stride_vector = _mm256_set1_epi32(convert_index<int>(stride));
+ Packet8i stride_multiplier = _mm256_set_epi32(7, 6, 5, 4, 3, 2, 1, 0);
+ Packet8i indices = _mm256_mullo_epi32(stride_vector, stride_multiplier);
+
+ return _mm512_i32gather_pd(indices, from, 8);
+}
+template <>
+EIGEN_DEVICE_FUNC inline Packet16i pgather<int, Packet16i>(const int* from,
+ Index stride) {
+ Packet16i stride_vector = _mm512_set1_epi32(convert_index<int>(stride));
+ Packet16i stride_multiplier =
+ _mm512_set_epi32(15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0);
+ Packet16i indices = _mm512_mullo_epi32(stride_vector, stride_multiplier);
+ return _mm512_i32gather_epi32(indices, from, 4);
+}
+
+template <typename Scalar, typename Packet>
+EIGEN_DEVICE_FUNC inline void pscatter(Scalar* to, const Packet& from,
+ Index stride, typename unpacket_traits<Packet>::mask_t umask);
+template <>
+EIGEN_DEVICE_FUNC inline void pscatter<float, Packet16f>(float* to,
+ const Packet16f& from,
+ Index stride,
+ uint16_t umask) {
+ Packet16i stride_vector = _mm512_set1_epi32(convert_index<int>(stride));
+ Packet16i stride_multiplier =
+ _mm512_set_epi32(15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0);
+ Packet16i indices = _mm512_mullo_epi32(stride_vector, stride_multiplier);
+ __mmask16 mask = static_cast<__mmask16>(umask);
+ _mm512_mask_i32scatter_ps(to, mask, indices, from, 4);
+}
+template <>
+EIGEN_DEVICE_FUNC inline void pscatter<double, Packet8d>(double* to,
+ const Packet8d& from,
+ Index stride,
+ uint8_t umask) {
+ Packet8i stride_vector = _mm256_set1_epi32(convert_index<int>(stride));
+ Packet8i stride_multiplier = _mm256_set_epi32(7, 6, 5, 4, 3, 2, 1, 0);
+ Packet8i indices = _mm256_mullo_epi32(stride_vector, stride_multiplier);
+ __mmask8 mask = static_cast<__mmask8>(umask);
+ _mm512_mask_i32scatter_pd(to, mask, indices, from, 8);
+}
+
+template <>
+EIGEN_DEVICE_FUNC inline void pscatter<float, Packet16f>(float* to,
+ const Packet16f& from,
+ Index stride) {
+ Packet16i stride_vector = _mm512_set1_epi32(convert_index<int>(stride));
+ Packet16i stride_multiplier =
+ _mm512_set_epi32(15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0);
+ Packet16i indices = _mm512_mullo_epi32(stride_vector, stride_multiplier);
+ _mm512_i32scatter_ps(to, indices, from, 4);
+}
+template <>
+EIGEN_DEVICE_FUNC inline void pscatter<double, Packet8d>(double* to,
+ const Packet8d& from,
+ Index stride) {
+ Packet8i stride_vector = _mm256_set1_epi32(convert_index<int>(stride));
+ Packet8i stride_multiplier = _mm256_set_epi32(7, 6, 5, 4, 3, 2, 1, 0);
+ Packet8i indices = _mm256_mullo_epi32(stride_vector, stride_multiplier);
+ _mm512_i32scatter_pd(to, indices, from, 8);
+}
+template <>
+EIGEN_DEVICE_FUNC inline void pscatter<int, Packet16i>(int* to,
+ const Packet16i& from,
+ Index stride) {
+ Packet16i stride_vector = _mm512_set1_epi32(convert_index<int>(stride));
+ Packet16i stride_multiplier =
+ _mm512_set_epi32(15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0);
+ Packet16i indices = _mm512_mullo_epi32(stride_vector, stride_multiplier);
+ _mm512_i32scatter_epi32(to, indices, from, 4);
+}
+
+template <>
+EIGEN_STRONG_INLINE void pstore1<Packet16f>(float* to, const float& a) {
+ Packet16f pa = pset1<Packet16f>(a);
+ pstore(to, pa);
+}
+template <>
+EIGEN_STRONG_INLINE void pstore1<Packet8d>(double* to, const double& a) {
+ Packet8d pa = pset1<Packet8d>(a);
+ pstore(to, pa);
+}
+template <>
+EIGEN_STRONG_INLINE void pstore1<Packet16i>(int* to, const int& a) {
+ Packet16i pa = pset1<Packet16i>(a);
+ pstore(to, pa);
+}
+
+template<> EIGEN_STRONG_INLINE void prefetch<float>(const float* addr) { _mm_prefetch((SsePrefetchPtrType)(addr), _MM_HINT_T0); }
+template<> EIGEN_STRONG_INLINE void prefetch<double>(const double* addr) { _mm_prefetch((SsePrefetchPtrType)(addr), _MM_HINT_T0); }
+template<> EIGEN_STRONG_INLINE void prefetch<int>(const int* addr) { _mm_prefetch((SsePrefetchPtrType)(addr), _MM_HINT_T0); }
+
+template <>
+EIGEN_STRONG_INLINE float pfirst<Packet16f>(const Packet16f& a) {
+ return _mm_cvtss_f32(_mm512_extractf32x4_ps(a, 0));
+}
+template <>
+EIGEN_STRONG_INLINE double pfirst<Packet8d>(const Packet8d& a) {
+ return _mm_cvtsd_f64(_mm256_extractf128_pd(_mm512_extractf64x4_pd(a, 0), 0));
+}
+template <>
+EIGEN_STRONG_INLINE int pfirst<Packet16i>(const Packet16i& a) {
+ return _mm_extract_epi32(_mm512_extracti32x4_epi32(a, 0), 0);
+}
+
+template<> EIGEN_STRONG_INLINE Packet16f preverse(const Packet16f& a)
+{
+ return _mm512_permutexvar_ps(_mm512_set_epi32(0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15), a);
+}
+
+template<> EIGEN_STRONG_INLINE Packet8d preverse(const Packet8d& a)
+{
+ return _mm512_permutexvar_pd(_mm512_set_epi32(0, 0, 0, 1, 0, 2, 0, 3, 0, 4, 0, 5, 0, 6, 0, 7), a);
+}
+
+template<> EIGEN_STRONG_INLINE Packet16i preverse(const Packet16i& a)
+{
+ return _mm512_permutexvar_epi32(_mm512_set_epi32(0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15), a);
+}
+
+template<> EIGEN_STRONG_INLINE Packet16f pabs(const Packet16f& a)
+{
+ // _mm512_abs_ps intrinsic not found, so hack around it
+ return _mm512_castsi512_ps(_mm512_and_si512(_mm512_castps_si512(a), _mm512_set1_epi32(0x7fffffff)));
+}
+template <>
+EIGEN_STRONG_INLINE Packet8d pabs(const Packet8d& a) {
+ // _mm512_abs_ps intrinsic not found, so hack around it
+ return _mm512_castsi512_pd(_mm512_and_si512(_mm512_castpd_si512(a),
+ _mm512_set1_epi64(0x7fffffffffffffff)));
+}
+template<> EIGEN_STRONG_INLINE Packet16i pabs(const Packet16i& a)
+{
+ return _mm512_abs_epi32(a);
+}
+
+template<>
+EIGEN_STRONG_INLINE Packet16f pfrexp<Packet16f>(const Packet16f& a, Packet16f& exponent){
+ return pfrexp_generic(a, exponent);
+}
+
+// Extract exponent without existence of Packet8l.
+template<>
+EIGEN_STRONG_INLINE
+Packet8d pfrexp_generic_get_biased_exponent(const Packet8d& a) {
+ const Packet8d cst_exp_mask = pset1frombits<Packet8d>(static_cast<uint64_t>(0x7ff0000000000000ull));
+ #ifdef EIGEN_VECTORIZE_AVX512DQ
+ return _mm512_cvtepi64_pd(_mm512_srli_epi64(_mm512_castpd_si512(pand(a, cst_exp_mask)), 52));
+ #else
+ return _mm512_cvtepi32_pd(_mm512_cvtepi64_epi32(_mm512_srli_epi64(_mm512_castpd_si512(pand(a, cst_exp_mask)), 52)));
+ #endif
+}
+
+template<>
+EIGEN_STRONG_INLINE Packet8d pfrexp<Packet8d>(const Packet8d& a, Packet8d& exponent) {
+ return pfrexp_generic(a, exponent);
+}
+
+template<> EIGEN_STRONG_INLINE Packet16f pldexp<Packet16f>(const Packet16f& a, const Packet16f& exponent) {
+ return pldexp_generic(a, exponent);
+}
+
+template<> EIGEN_STRONG_INLINE Packet8d pldexp<Packet8d>(const Packet8d& a, const Packet8d& exponent) {
+ // Clamp exponent to [-2099, 2099]
+ const Packet8d max_exponent = pset1<Packet8d>(2099.0);
+ const Packet8i e = _mm512_cvtpd_epi32(pmin(pmax(exponent, pnegate(max_exponent)), max_exponent));
+
+ // Split 2^e into four factors and multiply.
+ const Packet8i bias = pset1<Packet8i>(1023);
+ Packet8i b = parithmetic_shift_right<2>(e); // floor(e/4)
+
+ // 2^b
+ const Packet8i permute_idx = _mm256_setr_epi32(0, 4, 1, 5, 2, 6, 3, 7);
+ Packet8i hi = _mm256_permutevar8x32_epi32(padd(b, bias), permute_idx);
+ Packet8i lo = _mm256_slli_epi64(hi, 52);
+ hi = _mm256_slli_epi64(_mm256_srli_epi64(hi, 32), 52);
+ Packet8d c = _mm512_castsi512_pd(_mm512_inserti64x4(_mm512_castsi256_si512(lo), hi, 1));
+ Packet8d out = pmul(pmul(pmul(a, c), c), c); // a * 2^(3b)
+
+ // 2^(e - 3b)
+ b = psub(psub(psub(e, b), b), b); // e - 3b
+ hi = _mm256_permutevar8x32_epi32(padd(b, bias), permute_idx);
+ lo = _mm256_slli_epi64(hi, 52);
+ hi = _mm256_slli_epi64(_mm256_srli_epi64(hi, 32), 52);
+ c = _mm512_castsi512_pd(_mm512_inserti64x4(_mm512_castsi256_si512(lo), hi, 1));
+ out = pmul(out, c); // a * 2^e
+ return out;
+}
+
+#ifdef EIGEN_VECTORIZE_AVX512DQ
+// AVX512F does not define _mm512_extractf32x8_ps to extract _m256 from _m512
+#define EIGEN_EXTRACT_8f_FROM_16f(INPUT, OUTPUT) \
+ __m256 OUTPUT##_0 = _mm512_extractf32x8_ps(INPUT, 0); \
+ __m256 OUTPUT##_1 = _mm512_extractf32x8_ps(INPUT, 1)
+
+// AVX512F does not define _mm512_extracti32x8_epi32 to extract _m256i from _m512i
+#define EIGEN_EXTRACT_8i_FROM_16i(INPUT, OUTPUT) \
+ __m256i OUTPUT##_0 = _mm512_extracti32x8_epi32(INPUT, 0); \
+ __m256i OUTPUT##_1 = _mm512_extracti32x8_epi32(INPUT, 1)
+#else
+#define EIGEN_EXTRACT_8f_FROM_16f(INPUT, OUTPUT) \
+ __m256 OUTPUT##_0 = _mm256_insertf128_ps( \
+ _mm256_castps128_ps256(_mm512_extractf32x4_ps(INPUT, 0)), \
+ _mm512_extractf32x4_ps(INPUT, 1), 1); \
+ __m256 OUTPUT##_1 = _mm256_insertf128_ps( \
+ _mm256_castps128_ps256(_mm512_extractf32x4_ps(INPUT, 2)), \
+ _mm512_extractf32x4_ps(INPUT, 3), 1)
+
+#define EIGEN_EXTRACT_8i_FROM_16i(INPUT, OUTPUT) \
+ __m256i OUTPUT##_0 = _mm256_insertf128_si256( \
+ _mm256_castsi128_si256(_mm512_extracti32x4_epi32(INPUT, 0)), \
+ _mm512_extracti32x4_epi32(INPUT, 1), 1); \
+ __m256i OUTPUT##_1 = _mm256_insertf128_si256( \
+ _mm256_castsi128_si256(_mm512_extracti32x4_epi32(INPUT, 2)), \
+ _mm512_extracti32x4_epi32(INPUT, 3), 1)
+#endif
+
+#ifdef EIGEN_VECTORIZE_AVX512DQ
+#define EIGEN_INSERT_8f_INTO_16f(OUTPUT, INPUTA, INPUTB) \
+ OUTPUT = _mm512_insertf32x8(_mm512_castps256_ps512(INPUTA), INPUTB, 1);
+
+#define EIGEN_INSERT_8i_INTO_16i(OUTPUT, INPUTA, INPUTB) \
+ OUTPUT = _mm512_inserti32x8(_mm512_castsi256_si512(INPUTA), INPUTB, 1);
+#else
+#define EIGEN_INSERT_8f_INTO_16f(OUTPUT, INPUTA, INPUTB) \
+ OUTPUT = _mm512_undefined_ps(); \
+ OUTPUT = _mm512_insertf32x4(OUTPUT, _mm256_extractf128_ps(INPUTA, 0), 0); \
+ OUTPUT = _mm512_insertf32x4(OUTPUT, _mm256_extractf128_ps(INPUTA, 1), 1); \
+ OUTPUT = _mm512_insertf32x4(OUTPUT, _mm256_extractf128_ps(INPUTB, 0), 2); \
+ OUTPUT = _mm512_insertf32x4(OUTPUT, _mm256_extractf128_ps(INPUTB, 1), 3);
+
+#define EIGEN_INSERT_8i_INTO_16i(OUTPUT, INPUTA, INPUTB) \
+ OUTPUT = _mm512_undefined_epi32(); \
+ OUTPUT = _mm512_inserti32x4(OUTPUT, _mm256_extractf128_si256(INPUTA, 0), 0); \
+ OUTPUT = _mm512_inserti32x4(OUTPUT, _mm256_extractf128_si256(INPUTA, 1), 1); \
+ OUTPUT = _mm512_inserti32x4(OUTPUT, _mm256_extractf128_si256(INPUTB, 0), 2); \
+ OUTPUT = _mm512_inserti32x4(OUTPUT, _mm256_extractf128_si256(INPUTB, 1), 3);
+#endif
+
+template <>
+EIGEN_STRONG_INLINE float predux<Packet16f>(const Packet16f& a) {
+#ifdef EIGEN_VECTORIZE_AVX512DQ
+ __m256 lane0 = _mm512_extractf32x8_ps(a, 0);
+ __m256 lane1 = _mm512_extractf32x8_ps(a, 1);
+ Packet8f x = _mm256_add_ps(lane0, lane1);
+ return predux<Packet8f>(x);
+#else
+ __m128 lane0 = _mm512_extractf32x4_ps(a, 0);
+ __m128 lane1 = _mm512_extractf32x4_ps(a, 1);
+ __m128 lane2 = _mm512_extractf32x4_ps(a, 2);
+ __m128 lane3 = _mm512_extractf32x4_ps(a, 3);
+ __m128 sum = _mm_add_ps(_mm_add_ps(lane0, lane1), _mm_add_ps(lane2, lane3));
+ sum = _mm_hadd_ps(sum, sum);
+ sum = _mm_hadd_ps(sum, _mm_permute_ps(sum, 1));
+ return _mm_cvtss_f32(sum);
+#endif
+}
+template <>
+EIGEN_STRONG_INLINE double predux<Packet8d>(const Packet8d& a) {
+ __m256d lane0 = _mm512_extractf64x4_pd(a, 0);
+ __m256d lane1 = _mm512_extractf64x4_pd(a, 1);
+ __m256d sum = _mm256_add_pd(lane0, lane1);
+ __m256d tmp0 = _mm256_hadd_pd(sum, _mm256_permute2f128_pd(sum, sum, 1));
+ return _mm_cvtsd_f64(_mm256_castpd256_pd128(_mm256_hadd_pd(tmp0, tmp0)));
+}
+template <>
+EIGEN_STRONG_INLINE int predux<Packet16i>(const Packet16i& a) {
+#ifdef EIGEN_VECTORIZE_AVX512DQ
+ __m256i lane0 = _mm512_extracti32x8_epi32(a, 0);
+ __m256i lane1 = _mm512_extracti32x8_epi32(a, 1);
+ Packet8i x = _mm256_add_epi32(lane0, lane1);
+ return predux<Packet8i>(x);
+#else
+ __m128i lane0 = _mm512_extracti32x4_epi32(a, 0);
+ __m128i lane1 = _mm512_extracti32x4_epi32(a, 1);
+ __m128i lane2 = _mm512_extracti32x4_epi32(a, 2);
+ __m128i lane3 = _mm512_extracti32x4_epi32(a, 3);
+ __m128i sum = _mm_add_epi32(_mm_add_epi32(lane0, lane1), _mm_add_epi32(lane2, lane3));
+ sum = _mm_hadd_epi32(sum, sum);
+ sum = _mm_hadd_epi32(sum, _mm_castps_si128(_mm_permute_ps(_mm_castsi128_ps(sum), 1)));
+ return _mm_cvtsi128_si32(sum);
+#endif
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet8f predux_half_dowto4<Packet16f>(const Packet16f& a) {
+#ifdef EIGEN_VECTORIZE_AVX512DQ
+ __m256 lane0 = _mm512_extractf32x8_ps(a, 0);
+ __m256 lane1 = _mm512_extractf32x8_ps(a, 1);
+ return _mm256_add_ps(lane0, lane1);
+#else
+ __m128 lane0 = _mm512_extractf32x4_ps(a, 0);
+ __m128 lane1 = _mm512_extractf32x4_ps(a, 1);
+ __m128 lane2 = _mm512_extractf32x4_ps(a, 2);
+ __m128 lane3 = _mm512_extractf32x4_ps(a, 3);
+ __m128 sum0 = _mm_add_ps(lane0, lane2);
+ __m128 sum1 = _mm_add_ps(lane1, lane3);
+ return _mm256_insertf128_ps(_mm256_castps128_ps256(sum0), sum1, 1);
+#endif
+}
+template <>
+EIGEN_STRONG_INLINE Packet4d predux_half_dowto4<Packet8d>(const Packet8d& a) {
+ __m256d lane0 = _mm512_extractf64x4_pd(a, 0);
+ __m256d lane1 = _mm512_extractf64x4_pd(a, 1);
+ return _mm256_add_pd(lane0, lane1);
+}
+template <>
+EIGEN_STRONG_INLINE Packet8i predux_half_dowto4<Packet16i>(const Packet16i& a) {
+#ifdef EIGEN_VECTORIZE_AVX512DQ
+ __m256i lane0 = _mm512_extracti32x8_epi32(a, 0);
+ __m256i lane1 = _mm512_extracti32x8_epi32(a, 1);
+ return _mm256_add_epi32(lane0, lane1);
+#else
+ __m128i lane0 = _mm512_extracti32x4_epi32(a, 0);
+ __m128i lane1 = _mm512_extracti32x4_epi32(a, 1);
+ __m128i lane2 = _mm512_extracti32x4_epi32(a, 2);
+ __m128i lane3 = _mm512_extracti32x4_epi32(a, 3);
+ __m128i sum0 = _mm_add_epi32(lane0, lane2);
+ __m128i sum1 = _mm_add_epi32(lane1, lane3);
+ return _mm256_inserti128_si256(_mm256_castsi128_si256(sum0), sum1, 1);
+#endif
+}
+
+template <>
+EIGEN_STRONG_INLINE float predux_mul<Packet16f>(const Packet16f& a) {
+//#ifdef EIGEN_VECTORIZE_AVX512DQ
+#if 0
+ Packet8f lane0 = _mm512_extractf32x8_ps(a, 0);
+ Packet8f lane1 = _mm512_extractf32x8_ps(a, 1);
+ Packet8f res = pmul(lane0, lane1);
+ res = pmul(res, _mm256_permute2f128_ps(res, res, 1));
+ res = pmul(res, _mm_permute_ps(res, _MM_SHUFFLE(0, 0, 3, 2)));
+ return pfirst(pmul(res, _mm_permute_ps(res, _MM_SHUFFLE(0, 0, 0, 1))));
+#else
+ __m128 lane0 = _mm512_extractf32x4_ps(a, 0);
+ __m128 lane1 = _mm512_extractf32x4_ps(a, 1);
+ __m128 lane2 = _mm512_extractf32x4_ps(a, 2);
+ __m128 lane3 = _mm512_extractf32x4_ps(a, 3);
+ __m128 res = pmul(pmul(lane0, lane1), pmul(lane2, lane3));
+ res = pmul(res, _mm_permute_ps(res, _MM_SHUFFLE(0, 0, 3, 2)));
+ return pfirst(pmul(res, _mm_permute_ps(res, _MM_SHUFFLE(0, 0, 0, 1))));
+#endif
+}
+template <>
+EIGEN_STRONG_INLINE double predux_mul<Packet8d>(const Packet8d& a) {
+ __m256d lane0 = _mm512_extractf64x4_pd(a, 0);
+ __m256d lane1 = _mm512_extractf64x4_pd(a, 1);
+ __m256d res = pmul(lane0, lane1);
+ res = pmul(res, _mm256_permute2f128_pd(res, res, 1));
+ return pfirst(pmul(res, _mm256_shuffle_pd(res, res, 1)));
+}
+
+template <>
+EIGEN_STRONG_INLINE float predux_min<Packet16f>(const Packet16f& a) {
+ __m128 lane0 = _mm512_extractf32x4_ps(a, 0);
+ __m128 lane1 = _mm512_extractf32x4_ps(a, 1);
+ __m128 lane2 = _mm512_extractf32x4_ps(a, 2);
+ __m128 lane3 = _mm512_extractf32x4_ps(a, 3);
+ __m128 res = _mm_min_ps(_mm_min_ps(lane0, lane1), _mm_min_ps(lane2, lane3));
+ res = _mm_min_ps(res, _mm_permute_ps(res, _MM_SHUFFLE(0, 0, 3, 2)));
+ return pfirst(_mm_min_ps(res, _mm_permute_ps(res, _MM_SHUFFLE(0, 0, 0, 1))));
+}
+template <>
+EIGEN_STRONG_INLINE double predux_min<Packet8d>(const Packet8d& a) {
+ __m256d lane0 = _mm512_extractf64x4_pd(a, 0);
+ __m256d lane1 = _mm512_extractf64x4_pd(a, 1);
+ __m256d res = _mm256_min_pd(lane0, lane1);
+ res = _mm256_min_pd(res, _mm256_permute2f128_pd(res, res, 1));
+ return pfirst(_mm256_min_pd(res, _mm256_shuffle_pd(res, res, 1)));
+}
+
+template <>
+EIGEN_STRONG_INLINE float predux_max<Packet16f>(const Packet16f& a) {
+ __m128 lane0 = _mm512_extractf32x4_ps(a, 0);
+ __m128 lane1 = _mm512_extractf32x4_ps(a, 1);
+ __m128 lane2 = _mm512_extractf32x4_ps(a, 2);
+ __m128 lane3 = _mm512_extractf32x4_ps(a, 3);
+ __m128 res = _mm_max_ps(_mm_max_ps(lane0, lane1), _mm_max_ps(lane2, lane3));
+ res = _mm_max_ps(res, _mm_permute_ps(res, _MM_SHUFFLE(0, 0, 3, 2)));
+ return pfirst(_mm_max_ps(res, _mm_permute_ps(res, _MM_SHUFFLE(0, 0, 0, 1))));
+}
+
+template <>
+EIGEN_STRONG_INLINE double predux_max<Packet8d>(const Packet8d& a) {
+ __m256d lane0 = _mm512_extractf64x4_pd(a, 0);
+ __m256d lane1 = _mm512_extractf64x4_pd(a, 1);
+ __m256d res = _mm256_max_pd(lane0, lane1);
+ res = _mm256_max_pd(res, _mm256_permute2f128_pd(res, res, 1));
+ return pfirst(_mm256_max_pd(res, _mm256_shuffle_pd(res, res, 1)));
+}
+
+template<> EIGEN_STRONG_INLINE bool predux_any(const Packet16f& x)
+{
+ Packet16i xi = _mm512_castps_si512(x);
+ __mmask16 tmp = _mm512_test_epi32_mask(xi,xi);
+ return !_mm512_kortestz(tmp,tmp);
+}
+
+template<> EIGEN_STRONG_INLINE bool predux_any(const Packet16i& x)
+{
+ __mmask16 tmp = _mm512_test_epi32_mask(x,x);
+ return !_mm512_kortestz(tmp,tmp);
+}
+
+#define PACK_OUTPUT(OUTPUT, INPUT, INDEX, STRIDE) \
+ EIGEN_INSERT_8f_INTO_16f(OUTPUT[INDEX], INPUT[INDEX], INPUT[INDEX + STRIDE]);
+
+EIGEN_DEVICE_FUNC inline void ptranspose(PacketBlock<Packet16f, 16>& kernel) {
+ __m512 T0 = _mm512_unpacklo_ps(kernel.packet[0], kernel.packet[1]);
+ __m512 T1 = _mm512_unpackhi_ps(kernel.packet[0], kernel.packet[1]);
+ __m512 T2 = _mm512_unpacklo_ps(kernel.packet[2], kernel.packet[3]);
+ __m512 T3 = _mm512_unpackhi_ps(kernel.packet[2], kernel.packet[3]);
+ __m512 T4 = _mm512_unpacklo_ps(kernel.packet[4], kernel.packet[5]);
+ __m512 T5 = _mm512_unpackhi_ps(kernel.packet[4], kernel.packet[5]);
+ __m512 T6 = _mm512_unpacklo_ps(kernel.packet[6], kernel.packet[7]);
+ __m512 T7 = _mm512_unpackhi_ps(kernel.packet[6], kernel.packet[7]);
+ __m512 T8 = _mm512_unpacklo_ps(kernel.packet[8], kernel.packet[9]);
+ __m512 T9 = _mm512_unpackhi_ps(kernel.packet[8], kernel.packet[9]);
+ __m512 T10 = _mm512_unpacklo_ps(kernel.packet[10], kernel.packet[11]);
+ __m512 T11 = _mm512_unpackhi_ps(kernel.packet[10], kernel.packet[11]);
+ __m512 T12 = _mm512_unpacklo_ps(kernel.packet[12], kernel.packet[13]);
+ __m512 T13 = _mm512_unpackhi_ps(kernel.packet[12], kernel.packet[13]);
+ __m512 T14 = _mm512_unpacklo_ps(kernel.packet[14], kernel.packet[15]);
+ __m512 T15 = _mm512_unpackhi_ps(kernel.packet[14], kernel.packet[15]);
+ __m512 S0 = _mm512_shuffle_ps(T0, T2, _MM_SHUFFLE(1, 0, 1, 0));
+ __m512 S1 = _mm512_shuffle_ps(T0, T2, _MM_SHUFFLE(3, 2, 3, 2));
+ __m512 S2 = _mm512_shuffle_ps(T1, T3, _MM_SHUFFLE(1, 0, 1, 0));
+ __m512 S3 = _mm512_shuffle_ps(T1, T3, _MM_SHUFFLE(3, 2, 3, 2));
+ __m512 S4 = _mm512_shuffle_ps(T4, T6, _MM_SHUFFLE(1, 0, 1, 0));
+ __m512 S5 = _mm512_shuffle_ps(T4, T6, _MM_SHUFFLE(3, 2, 3, 2));
+ __m512 S6 = _mm512_shuffle_ps(T5, T7, _MM_SHUFFLE(1, 0, 1, 0));
+ __m512 S7 = _mm512_shuffle_ps(T5, T7, _MM_SHUFFLE(3, 2, 3, 2));
+ __m512 S8 = _mm512_shuffle_ps(T8, T10, _MM_SHUFFLE(1, 0, 1, 0));
+ __m512 S9 = _mm512_shuffle_ps(T8, T10, _MM_SHUFFLE(3, 2, 3, 2));
+ __m512 S10 = _mm512_shuffle_ps(T9, T11, _MM_SHUFFLE(1, 0, 1, 0));
+ __m512 S11 = _mm512_shuffle_ps(T9, T11, _MM_SHUFFLE(3, 2, 3, 2));
+ __m512 S12 = _mm512_shuffle_ps(T12, T14, _MM_SHUFFLE(1, 0, 1, 0));
+ __m512 S13 = _mm512_shuffle_ps(T12, T14, _MM_SHUFFLE(3, 2, 3, 2));
+ __m512 S14 = _mm512_shuffle_ps(T13, T15, _MM_SHUFFLE(1, 0, 1, 0));
+ __m512 S15 = _mm512_shuffle_ps(T13, T15, _MM_SHUFFLE(3, 2, 3, 2));
+
+ EIGEN_EXTRACT_8f_FROM_16f(S0, S0);
+ EIGEN_EXTRACT_8f_FROM_16f(S1, S1);
+ EIGEN_EXTRACT_8f_FROM_16f(S2, S2);
+ EIGEN_EXTRACT_8f_FROM_16f(S3, S3);
+ EIGEN_EXTRACT_8f_FROM_16f(S4, S4);
+ EIGEN_EXTRACT_8f_FROM_16f(S5, S5);
+ EIGEN_EXTRACT_8f_FROM_16f(S6, S6);
+ EIGEN_EXTRACT_8f_FROM_16f(S7, S7);
+ EIGEN_EXTRACT_8f_FROM_16f(S8, S8);
+ EIGEN_EXTRACT_8f_FROM_16f(S9, S9);
+ EIGEN_EXTRACT_8f_FROM_16f(S10, S10);
+ EIGEN_EXTRACT_8f_FROM_16f(S11, S11);
+ EIGEN_EXTRACT_8f_FROM_16f(S12, S12);
+ EIGEN_EXTRACT_8f_FROM_16f(S13, S13);
+ EIGEN_EXTRACT_8f_FROM_16f(S14, S14);
+ EIGEN_EXTRACT_8f_FROM_16f(S15, S15);
+
+ PacketBlock<Packet8f, 32> tmp;
+
+ tmp.packet[0] = _mm256_permute2f128_ps(S0_0, S4_0, 0x20);
+ tmp.packet[1] = _mm256_permute2f128_ps(S1_0, S5_0, 0x20);
+ tmp.packet[2] = _mm256_permute2f128_ps(S2_0, S6_0, 0x20);
+ tmp.packet[3] = _mm256_permute2f128_ps(S3_0, S7_0, 0x20);
+ tmp.packet[4] = _mm256_permute2f128_ps(S0_0, S4_0, 0x31);
+ tmp.packet[5] = _mm256_permute2f128_ps(S1_0, S5_0, 0x31);
+ tmp.packet[6] = _mm256_permute2f128_ps(S2_0, S6_0, 0x31);
+ tmp.packet[7] = _mm256_permute2f128_ps(S3_0, S7_0, 0x31);
+
+ tmp.packet[8] = _mm256_permute2f128_ps(S0_1, S4_1, 0x20);
+ tmp.packet[9] = _mm256_permute2f128_ps(S1_1, S5_1, 0x20);
+ tmp.packet[10] = _mm256_permute2f128_ps(S2_1, S6_1, 0x20);
+ tmp.packet[11] = _mm256_permute2f128_ps(S3_1, S7_1, 0x20);
+ tmp.packet[12] = _mm256_permute2f128_ps(S0_1, S4_1, 0x31);
+ tmp.packet[13] = _mm256_permute2f128_ps(S1_1, S5_1, 0x31);
+ tmp.packet[14] = _mm256_permute2f128_ps(S2_1, S6_1, 0x31);
+ tmp.packet[15] = _mm256_permute2f128_ps(S3_1, S7_1, 0x31);
+
+ // Second set of _m256 outputs
+ tmp.packet[16] = _mm256_permute2f128_ps(S8_0, S12_0, 0x20);
+ tmp.packet[17] = _mm256_permute2f128_ps(S9_0, S13_0, 0x20);
+ tmp.packet[18] = _mm256_permute2f128_ps(S10_0, S14_0, 0x20);
+ tmp.packet[19] = _mm256_permute2f128_ps(S11_0, S15_0, 0x20);
+ tmp.packet[20] = _mm256_permute2f128_ps(S8_0, S12_0, 0x31);
+ tmp.packet[21] = _mm256_permute2f128_ps(S9_0, S13_0, 0x31);
+ tmp.packet[22] = _mm256_permute2f128_ps(S10_0, S14_0, 0x31);
+ tmp.packet[23] = _mm256_permute2f128_ps(S11_0, S15_0, 0x31);
+
+ tmp.packet[24] = _mm256_permute2f128_ps(S8_1, S12_1, 0x20);
+ tmp.packet[25] = _mm256_permute2f128_ps(S9_1, S13_1, 0x20);
+ tmp.packet[26] = _mm256_permute2f128_ps(S10_1, S14_1, 0x20);
+ tmp.packet[27] = _mm256_permute2f128_ps(S11_1, S15_1, 0x20);
+ tmp.packet[28] = _mm256_permute2f128_ps(S8_1, S12_1, 0x31);
+ tmp.packet[29] = _mm256_permute2f128_ps(S9_1, S13_1, 0x31);
+ tmp.packet[30] = _mm256_permute2f128_ps(S10_1, S14_1, 0x31);
+ tmp.packet[31] = _mm256_permute2f128_ps(S11_1, S15_1, 0x31);
+
+ // Pack them into the output
+ PACK_OUTPUT(kernel.packet, tmp.packet, 0, 16);
+ PACK_OUTPUT(kernel.packet, tmp.packet, 1, 16);
+ PACK_OUTPUT(kernel.packet, tmp.packet, 2, 16);
+ PACK_OUTPUT(kernel.packet, tmp.packet, 3, 16);
+
+ PACK_OUTPUT(kernel.packet, tmp.packet, 4, 16);
+ PACK_OUTPUT(kernel.packet, tmp.packet, 5, 16);
+ PACK_OUTPUT(kernel.packet, tmp.packet, 6, 16);
+ PACK_OUTPUT(kernel.packet, tmp.packet, 7, 16);
+
+ PACK_OUTPUT(kernel.packet, tmp.packet, 8, 16);
+ PACK_OUTPUT(kernel.packet, tmp.packet, 9, 16);
+ PACK_OUTPUT(kernel.packet, tmp.packet, 10, 16);
+ PACK_OUTPUT(kernel.packet, tmp.packet, 11, 16);
+
+ PACK_OUTPUT(kernel.packet, tmp.packet, 12, 16);
+ PACK_OUTPUT(kernel.packet, tmp.packet, 13, 16);
+ PACK_OUTPUT(kernel.packet, tmp.packet, 14, 16);
+ PACK_OUTPUT(kernel.packet, tmp.packet, 15, 16);
+}
+#define PACK_OUTPUT_2(OUTPUT, INPUT, INDEX, STRIDE) \
+ EIGEN_INSERT_8f_INTO_16f(OUTPUT[INDEX], INPUT[2 * INDEX], \
+ INPUT[2 * INDEX + STRIDE]);
+
+EIGEN_DEVICE_FUNC inline void ptranspose(PacketBlock<Packet16f, 8>& kernel) {
+ __m512 T0 = _mm512_unpacklo_ps(kernel.packet[0],kernel.packet[1]);
+ __m512 T1 = _mm512_unpackhi_ps(kernel.packet[0],kernel.packet[1]);
+ __m512 T2 = _mm512_unpacklo_ps(kernel.packet[2],kernel.packet[3]);
+ __m512 T3 = _mm512_unpackhi_ps(kernel.packet[2],kernel.packet[3]);
+ __m512 T4 = _mm512_unpacklo_ps(kernel.packet[4],kernel.packet[5]);
+ __m512 T5 = _mm512_unpackhi_ps(kernel.packet[4],kernel.packet[5]);
+ __m512 T6 = _mm512_unpacklo_ps(kernel.packet[6],kernel.packet[7]);
+ __m512 T7 = _mm512_unpackhi_ps(kernel.packet[6],kernel.packet[7]);
+
+ kernel.packet[0] = _mm512_castpd_ps(_mm512_unpacklo_pd(_mm512_castps_pd(T0),_mm512_castps_pd(T2)));
+ kernel.packet[1] = _mm512_castpd_ps(_mm512_unpackhi_pd(_mm512_castps_pd(T0),_mm512_castps_pd(T2)));
+ kernel.packet[2] = _mm512_castpd_ps(_mm512_unpacklo_pd(_mm512_castps_pd(T1),_mm512_castps_pd(T3)));
+ kernel.packet[3] = _mm512_castpd_ps(_mm512_unpackhi_pd(_mm512_castps_pd(T1),_mm512_castps_pd(T3)));
+ kernel.packet[4] = _mm512_castpd_ps(_mm512_unpacklo_pd(_mm512_castps_pd(T4),_mm512_castps_pd(T6)));
+ kernel.packet[5] = _mm512_castpd_ps(_mm512_unpackhi_pd(_mm512_castps_pd(T4),_mm512_castps_pd(T6)));
+ kernel.packet[6] = _mm512_castpd_ps(_mm512_unpacklo_pd(_mm512_castps_pd(T5),_mm512_castps_pd(T7)));
+ kernel.packet[7] = _mm512_castpd_ps(_mm512_unpackhi_pd(_mm512_castps_pd(T5),_mm512_castps_pd(T7)));
+
+ T0 = _mm512_shuffle_f32x4(kernel.packet[0], kernel.packet[4], 0x44);
+ T1 = _mm512_shuffle_f32x4(kernel.packet[0], kernel.packet[4], 0xee);
+ T2 = _mm512_shuffle_f32x4(kernel.packet[1], kernel.packet[5], 0x44);
+ T3 = _mm512_shuffle_f32x4(kernel.packet[1], kernel.packet[5], 0xee);
+ T4 = _mm512_shuffle_f32x4(kernel.packet[2], kernel.packet[6], 0x44);
+ T5 = _mm512_shuffle_f32x4(kernel.packet[2], kernel.packet[6], 0xee);
+ T6 = _mm512_shuffle_f32x4(kernel.packet[3], kernel.packet[7], 0x44);
+ T7 = _mm512_shuffle_f32x4(kernel.packet[3], kernel.packet[7], 0xee);
+
+ kernel.packet[0] = _mm512_shuffle_f32x4(T0, T2, 0x88);
+ kernel.packet[2] = _mm512_shuffle_f32x4(T0, T2, 0xdd);
+ kernel.packet[1] = _mm512_shuffle_f32x4(T4, T6, 0x88);
+ kernel.packet[3] = _mm512_shuffle_f32x4(T4, T6, 0xdd);
+ kernel.packet[4] = _mm512_shuffle_f32x4(T1, T3, 0x88);
+ kernel.packet[6] = _mm512_shuffle_f32x4(T1, T3, 0xdd);
+ kernel.packet[5] = _mm512_shuffle_f32x4(T5, T7, 0x88);
+ kernel.packet[7] = _mm512_shuffle_f32x4(T5, T7, 0xdd);
+}
+
+EIGEN_DEVICE_FUNC inline void ptranspose(PacketBlock<Packet16f, 4>& kernel) {
+ __m512 T0 = _mm512_unpacklo_ps(kernel.packet[0], kernel.packet[1]);
+ __m512 T1 = _mm512_unpackhi_ps(kernel.packet[0], kernel.packet[1]);
+ __m512 T2 = _mm512_unpacklo_ps(kernel.packet[2], kernel.packet[3]);
+ __m512 T3 = _mm512_unpackhi_ps(kernel.packet[2], kernel.packet[3]);
+
+ __m512 S0 = _mm512_shuffle_ps(T0, T2, _MM_SHUFFLE(1, 0, 1, 0));
+ __m512 S1 = _mm512_shuffle_ps(T0, T2, _MM_SHUFFLE(3, 2, 3, 2));
+ __m512 S2 = _mm512_shuffle_ps(T1, T3, _MM_SHUFFLE(1, 0, 1, 0));
+ __m512 S3 = _mm512_shuffle_ps(T1, T3, _MM_SHUFFLE(3, 2, 3, 2));
+
+ EIGEN_EXTRACT_8f_FROM_16f(S0, S0);
+ EIGEN_EXTRACT_8f_FROM_16f(S1, S1);
+ EIGEN_EXTRACT_8f_FROM_16f(S2, S2);
+ EIGEN_EXTRACT_8f_FROM_16f(S3, S3);
+
+ PacketBlock<Packet8f, 8> tmp;
+
+ tmp.packet[0] = _mm256_permute2f128_ps(S0_0, S1_0, 0x20);
+ tmp.packet[1] = _mm256_permute2f128_ps(S2_0, S3_0, 0x20);
+ tmp.packet[2] = _mm256_permute2f128_ps(S0_0, S1_0, 0x31);
+ tmp.packet[3] = _mm256_permute2f128_ps(S2_0, S3_0, 0x31);
+
+ tmp.packet[4] = _mm256_permute2f128_ps(S0_1, S1_1, 0x20);
+ tmp.packet[5] = _mm256_permute2f128_ps(S2_1, S3_1, 0x20);
+ tmp.packet[6] = _mm256_permute2f128_ps(S0_1, S1_1, 0x31);
+ tmp.packet[7] = _mm256_permute2f128_ps(S2_1, S3_1, 0x31);
+
+ PACK_OUTPUT_2(kernel.packet, tmp.packet, 0, 1);
+ PACK_OUTPUT_2(kernel.packet, tmp.packet, 1, 1);
+ PACK_OUTPUT_2(kernel.packet, tmp.packet, 2, 1);
+ PACK_OUTPUT_2(kernel.packet, tmp.packet, 3, 1);
+}
+
+#define PACK_OUTPUT_SQ_D(OUTPUT, INPUT, INDEX, STRIDE) \
+ OUTPUT[INDEX] = _mm512_insertf64x4(OUTPUT[INDEX], INPUT[INDEX], 0); \
+ OUTPUT[INDEX] = _mm512_insertf64x4(OUTPUT[INDEX], INPUT[INDEX + STRIDE], 1);
+
+#define PACK_OUTPUT_D(OUTPUT, INPUT, INDEX, STRIDE) \
+ OUTPUT[INDEX] = _mm512_insertf64x4(OUTPUT[INDEX], INPUT[(2 * INDEX)], 0); \
+ OUTPUT[INDEX] = \
+ _mm512_insertf64x4(OUTPUT[INDEX], INPUT[(2 * INDEX) + STRIDE], 1);
+
+EIGEN_DEVICE_FUNC inline void ptranspose(PacketBlock<Packet8d, 4>& kernel) {
+ __m512d T0 = _mm512_shuffle_pd(kernel.packet[0], kernel.packet[1], 0);
+ __m512d T1 = _mm512_shuffle_pd(kernel.packet[0], kernel.packet[1], 0xff);
+ __m512d T2 = _mm512_shuffle_pd(kernel.packet[2], kernel.packet[3], 0);
+ __m512d T3 = _mm512_shuffle_pd(kernel.packet[2], kernel.packet[3], 0xff);
+
+ PacketBlock<Packet4d, 8> tmp;
+
+ tmp.packet[0] = _mm256_permute2f128_pd(_mm512_extractf64x4_pd(T0, 0),
+ _mm512_extractf64x4_pd(T2, 0), 0x20);
+ tmp.packet[1] = _mm256_permute2f128_pd(_mm512_extractf64x4_pd(T1, 0),
+ _mm512_extractf64x4_pd(T3, 0), 0x20);
+ tmp.packet[2] = _mm256_permute2f128_pd(_mm512_extractf64x4_pd(T0, 0),
+ _mm512_extractf64x4_pd(T2, 0), 0x31);
+ tmp.packet[3] = _mm256_permute2f128_pd(_mm512_extractf64x4_pd(T1, 0),
+ _mm512_extractf64x4_pd(T3, 0), 0x31);
+
+ tmp.packet[4] = _mm256_permute2f128_pd(_mm512_extractf64x4_pd(T0, 1),
+ _mm512_extractf64x4_pd(T2, 1), 0x20);
+ tmp.packet[5] = _mm256_permute2f128_pd(_mm512_extractf64x4_pd(T1, 1),
+ _mm512_extractf64x4_pd(T3, 1), 0x20);
+ tmp.packet[6] = _mm256_permute2f128_pd(_mm512_extractf64x4_pd(T0, 1),
+ _mm512_extractf64x4_pd(T2, 1), 0x31);
+ tmp.packet[7] = _mm256_permute2f128_pd(_mm512_extractf64x4_pd(T1, 1),
+ _mm512_extractf64x4_pd(T3, 1), 0x31);
+
+ PACK_OUTPUT_D(kernel.packet, tmp.packet, 0, 1);
+ PACK_OUTPUT_D(kernel.packet, tmp.packet, 1, 1);
+ PACK_OUTPUT_D(kernel.packet, tmp.packet, 2, 1);
+ PACK_OUTPUT_D(kernel.packet, tmp.packet, 3, 1);
+}
+
+EIGEN_DEVICE_FUNC inline void ptranspose(PacketBlock<Packet8d, 8>& kernel) {
+ __m512d T0 = _mm512_unpacklo_pd(kernel.packet[0],kernel.packet[1]);
+ __m512d T1 = _mm512_unpackhi_pd(kernel.packet[0],kernel.packet[1]);
+ __m512d T2 = _mm512_unpacklo_pd(kernel.packet[2],kernel.packet[3]);
+ __m512d T3 = _mm512_unpackhi_pd(kernel.packet[2],kernel.packet[3]);
+ __m512d T4 = _mm512_unpacklo_pd(kernel.packet[4],kernel.packet[5]);
+ __m512d T5 = _mm512_unpackhi_pd(kernel.packet[4],kernel.packet[5]);
+ __m512d T6 = _mm512_unpacklo_pd(kernel.packet[6],kernel.packet[7]);
+ __m512d T7 = _mm512_unpackhi_pd(kernel.packet[6],kernel.packet[7]);
+
+ kernel.packet[0] = _mm512_permutex_pd(T2, 0x4E);
+ kernel.packet[0] = _mm512_mask_blend_pd(0xCC, T0, kernel.packet[0]);
+ kernel.packet[2] = _mm512_permutex_pd(T0, 0x4E);
+ kernel.packet[2] = _mm512_mask_blend_pd(0xCC, kernel.packet[2], T2);
+ kernel.packet[1] = _mm512_permutex_pd(T3, 0x4E);
+ kernel.packet[1] = _mm512_mask_blend_pd(0xCC, T1, kernel.packet[1]);
+ kernel.packet[3] = _mm512_permutex_pd(T1, 0x4E);
+ kernel.packet[3] = _mm512_mask_blend_pd(0xCC, kernel.packet[3], T3);
+ kernel.packet[4] = _mm512_permutex_pd(T6, 0x4E);
+ kernel.packet[4] = _mm512_mask_blend_pd(0xCC, T4, kernel.packet[4]);
+ kernel.packet[6] = _mm512_permutex_pd(T4, 0x4E);
+ kernel.packet[6] = _mm512_mask_blend_pd(0xCC, kernel.packet[6], T6);
+ kernel.packet[5] = _mm512_permutex_pd(T7, 0x4E);
+ kernel.packet[5] = _mm512_mask_blend_pd(0xCC, T5, kernel.packet[5]);
+ kernel.packet[7] = _mm512_permutex_pd(T5, 0x4E);
+ kernel.packet[7] = _mm512_mask_blend_pd(0xCC, kernel.packet[7], T7);
+
+ T0 = _mm512_shuffle_f64x2(kernel.packet[4], kernel.packet[4], 0x4E);
+ T0 = _mm512_mask_blend_pd(0xF0, kernel.packet[0], T0);
+ T4 = _mm512_shuffle_f64x2(kernel.packet[0], kernel.packet[0], 0x4E);
+ T4 = _mm512_mask_blend_pd(0xF0, T4, kernel.packet[4]);
+ T1 = _mm512_shuffle_f64x2(kernel.packet[5], kernel.packet[5], 0x4E);
+ T1 = _mm512_mask_blend_pd(0xF0, kernel.packet[1], T1);
+ T5 = _mm512_shuffle_f64x2(kernel.packet[1], kernel.packet[1], 0x4E);
+ T5 = _mm512_mask_blend_pd(0xF0, T5, kernel.packet[5]);
+ T2 = _mm512_shuffle_f64x2(kernel.packet[6], kernel.packet[6], 0x4E);
+ T2 = _mm512_mask_blend_pd(0xF0, kernel.packet[2], T2);
+ T6 = _mm512_shuffle_f64x2(kernel.packet[2], kernel.packet[2], 0x4E);
+ T6 = _mm512_mask_blend_pd(0xF0, T6, kernel.packet[6]);
+ T3 = _mm512_shuffle_f64x2(kernel.packet[7], kernel.packet[7], 0x4E);
+ T3 = _mm512_mask_blend_pd(0xF0, kernel.packet[3], T3);
+ T7 = _mm512_shuffle_f64x2(kernel.packet[3], kernel.packet[3], 0x4E);
+ T7 = _mm512_mask_blend_pd(0xF0, T7, kernel.packet[7]);
+
+ kernel.packet[0] = T0; kernel.packet[1] = T1;
+ kernel.packet[2] = T2; kernel.packet[3] = T3;
+ kernel.packet[4] = T4; kernel.packet[5] = T5;
+ kernel.packet[6] = T6; kernel.packet[7] = T7;
+}
+
+#define PACK_OUTPUT_I32(OUTPUT, INPUT, INDEX, STRIDE) \
+ EIGEN_INSERT_8i_INTO_16i(OUTPUT[INDEX], INPUT[INDEX], INPUT[INDEX + STRIDE]);
+
+#define PACK_OUTPUT_I32_2(OUTPUT, INPUT, INDEX, STRIDE) \
+ EIGEN_INSERT_8i_INTO_16i(OUTPUT[INDEX], INPUT[2 * INDEX], \
+ INPUT[2 * INDEX + STRIDE]);
+
+#define SHUFFLE_EPI32(A, B, M) \
+ _mm512_castps_si512(_mm512_shuffle_ps(_mm512_castsi512_ps(A), _mm512_castsi512_ps(B), M))
+
+EIGEN_DEVICE_FUNC inline void ptranspose(PacketBlock<Packet16i, 16>& kernel) {
+ __m512i T0 = _mm512_unpacklo_epi32(kernel.packet[0], kernel.packet[1]);
+ __m512i T1 = _mm512_unpackhi_epi32(kernel.packet[0], kernel.packet[1]);
+ __m512i T2 = _mm512_unpacklo_epi32(kernel.packet[2], kernel.packet[3]);
+ __m512i T3 = _mm512_unpackhi_epi32(kernel.packet[2], kernel.packet[3]);
+ __m512i T4 = _mm512_unpacklo_epi32(kernel.packet[4], kernel.packet[5]);
+ __m512i T5 = _mm512_unpackhi_epi32(kernel.packet[4], kernel.packet[5]);
+ __m512i T6 = _mm512_unpacklo_epi32(kernel.packet[6], kernel.packet[7]);
+ __m512i T7 = _mm512_unpackhi_epi32(kernel.packet[6], kernel.packet[7]);
+ __m512i T8 = _mm512_unpacklo_epi32(kernel.packet[8], kernel.packet[9]);
+ __m512i T9 = _mm512_unpackhi_epi32(kernel.packet[8], kernel.packet[9]);
+ __m512i T10 = _mm512_unpacklo_epi32(kernel.packet[10], kernel.packet[11]);
+ __m512i T11 = _mm512_unpackhi_epi32(kernel.packet[10], kernel.packet[11]);
+ __m512i T12 = _mm512_unpacklo_epi32(kernel.packet[12], kernel.packet[13]);
+ __m512i T13 = _mm512_unpackhi_epi32(kernel.packet[12], kernel.packet[13]);
+ __m512i T14 = _mm512_unpacklo_epi32(kernel.packet[14], kernel.packet[15]);
+ __m512i T15 = _mm512_unpackhi_epi32(kernel.packet[14], kernel.packet[15]);
+ __m512i S0 = SHUFFLE_EPI32(T0, T2, _MM_SHUFFLE(1, 0, 1, 0));
+ __m512i S1 = SHUFFLE_EPI32(T0, T2, _MM_SHUFFLE(3, 2, 3, 2));
+ __m512i S2 = SHUFFLE_EPI32(T1, T3, _MM_SHUFFLE(1, 0, 1, 0));
+ __m512i S3 = SHUFFLE_EPI32(T1, T3, _MM_SHUFFLE(3, 2, 3, 2));
+ __m512i S4 = SHUFFLE_EPI32(T4, T6, _MM_SHUFFLE(1, 0, 1, 0));
+ __m512i S5 = SHUFFLE_EPI32(T4, T6, _MM_SHUFFLE(3, 2, 3, 2));
+ __m512i S6 = SHUFFLE_EPI32(T5, T7, _MM_SHUFFLE(1, 0, 1, 0));
+ __m512i S7 = SHUFFLE_EPI32(T5, T7, _MM_SHUFFLE(3, 2, 3, 2));
+ __m512i S8 = SHUFFLE_EPI32(T8, T10, _MM_SHUFFLE(1, 0, 1, 0));
+ __m512i S9 = SHUFFLE_EPI32(T8, T10, _MM_SHUFFLE(3, 2, 3, 2));
+ __m512i S10 = SHUFFLE_EPI32(T9, T11, _MM_SHUFFLE(1, 0, 1, 0));
+ __m512i S11 = SHUFFLE_EPI32(T9, T11, _MM_SHUFFLE(3, 2, 3, 2));
+ __m512i S12 = SHUFFLE_EPI32(T12, T14, _MM_SHUFFLE(1, 0, 1, 0));
+ __m512i S13 = SHUFFLE_EPI32(T12, T14, _MM_SHUFFLE(3, 2, 3, 2));
+ __m512i S14 = SHUFFLE_EPI32(T13, T15, _MM_SHUFFLE(1, 0, 1, 0));
+ __m512i S15 = SHUFFLE_EPI32(T13, T15, _MM_SHUFFLE(3, 2, 3, 2));
+
+ EIGEN_EXTRACT_8i_FROM_16i(S0, S0);
+ EIGEN_EXTRACT_8i_FROM_16i(S1, S1);
+ EIGEN_EXTRACT_8i_FROM_16i(S2, S2);
+ EIGEN_EXTRACT_8i_FROM_16i(S3, S3);
+ EIGEN_EXTRACT_8i_FROM_16i(S4, S4);
+ EIGEN_EXTRACT_8i_FROM_16i(S5, S5);
+ EIGEN_EXTRACT_8i_FROM_16i(S6, S6);
+ EIGEN_EXTRACT_8i_FROM_16i(S7, S7);
+ EIGEN_EXTRACT_8i_FROM_16i(S8, S8);
+ EIGEN_EXTRACT_8i_FROM_16i(S9, S9);
+ EIGEN_EXTRACT_8i_FROM_16i(S10, S10);
+ EIGEN_EXTRACT_8i_FROM_16i(S11, S11);
+ EIGEN_EXTRACT_8i_FROM_16i(S12, S12);
+ EIGEN_EXTRACT_8i_FROM_16i(S13, S13);
+ EIGEN_EXTRACT_8i_FROM_16i(S14, S14);
+ EIGEN_EXTRACT_8i_FROM_16i(S15, S15);
+
+ PacketBlock<Packet8i, 32> tmp;
+
+ tmp.packet[0] = _mm256_permute2f128_si256(S0_0, S4_0, 0x20);
+ tmp.packet[1] = _mm256_permute2f128_si256(S1_0, S5_0, 0x20);
+ tmp.packet[2] = _mm256_permute2f128_si256(S2_0, S6_0, 0x20);
+ tmp.packet[3] = _mm256_permute2f128_si256(S3_0, S7_0, 0x20);
+ tmp.packet[4] = _mm256_permute2f128_si256(S0_0, S4_0, 0x31);
+ tmp.packet[5] = _mm256_permute2f128_si256(S1_0, S5_0, 0x31);
+ tmp.packet[6] = _mm256_permute2f128_si256(S2_0, S6_0, 0x31);
+ tmp.packet[7] = _mm256_permute2f128_si256(S3_0, S7_0, 0x31);
+
+ tmp.packet[8] = _mm256_permute2f128_si256(S0_1, S4_1, 0x20);
+ tmp.packet[9] = _mm256_permute2f128_si256(S1_1, S5_1, 0x20);
+ tmp.packet[10] = _mm256_permute2f128_si256(S2_1, S6_1, 0x20);
+ tmp.packet[11] = _mm256_permute2f128_si256(S3_1, S7_1, 0x20);
+ tmp.packet[12] = _mm256_permute2f128_si256(S0_1, S4_1, 0x31);
+ tmp.packet[13] = _mm256_permute2f128_si256(S1_1, S5_1, 0x31);
+ tmp.packet[14] = _mm256_permute2f128_si256(S2_1, S6_1, 0x31);
+ tmp.packet[15] = _mm256_permute2f128_si256(S3_1, S7_1, 0x31);
+
+ // Second set of _m256 outputs
+ tmp.packet[16] = _mm256_permute2f128_si256(S8_0, S12_0, 0x20);
+ tmp.packet[17] = _mm256_permute2f128_si256(S9_0, S13_0, 0x20);
+ tmp.packet[18] = _mm256_permute2f128_si256(S10_0, S14_0, 0x20);
+ tmp.packet[19] = _mm256_permute2f128_si256(S11_0, S15_0, 0x20);
+ tmp.packet[20] = _mm256_permute2f128_si256(S8_0, S12_0, 0x31);
+ tmp.packet[21] = _mm256_permute2f128_si256(S9_0, S13_0, 0x31);
+ tmp.packet[22] = _mm256_permute2f128_si256(S10_0, S14_0, 0x31);
+ tmp.packet[23] = _mm256_permute2f128_si256(S11_0, S15_0, 0x31);
+
+ tmp.packet[24] = _mm256_permute2f128_si256(S8_1, S12_1, 0x20);
+ tmp.packet[25] = _mm256_permute2f128_si256(S9_1, S13_1, 0x20);
+ tmp.packet[26] = _mm256_permute2f128_si256(S10_1, S14_1, 0x20);
+ tmp.packet[27] = _mm256_permute2f128_si256(S11_1, S15_1, 0x20);
+ tmp.packet[28] = _mm256_permute2f128_si256(S8_1, S12_1, 0x31);
+ tmp.packet[29] = _mm256_permute2f128_si256(S9_1, S13_1, 0x31);
+ tmp.packet[30] = _mm256_permute2f128_si256(S10_1, S14_1, 0x31);
+ tmp.packet[31] = _mm256_permute2f128_si256(S11_1, S15_1, 0x31);
+
+ // Pack them into the output
+ PACK_OUTPUT_I32(kernel.packet, tmp.packet, 0, 16);
+ PACK_OUTPUT_I32(kernel.packet, tmp.packet, 1, 16);
+ PACK_OUTPUT_I32(kernel.packet, tmp.packet, 2, 16);
+ PACK_OUTPUT_I32(kernel.packet, tmp.packet, 3, 16);
+
+ PACK_OUTPUT_I32(kernel.packet, tmp.packet, 4, 16);
+ PACK_OUTPUT_I32(kernel.packet, tmp.packet, 5, 16);
+ PACK_OUTPUT_I32(kernel.packet, tmp.packet, 6, 16);
+ PACK_OUTPUT_I32(kernel.packet, tmp.packet, 7, 16);
+
+ PACK_OUTPUT_I32(kernel.packet, tmp.packet, 8, 16);
+ PACK_OUTPUT_I32(kernel.packet, tmp.packet, 9, 16);
+ PACK_OUTPUT_I32(kernel.packet, tmp.packet, 10, 16);
+ PACK_OUTPUT_I32(kernel.packet, tmp.packet, 11, 16);
+
+ PACK_OUTPUT_I32(kernel.packet, tmp.packet, 12, 16);
+ PACK_OUTPUT_I32(kernel.packet, tmp.packet, 13, 16);
+ PACK_OUTPUT_I32(kernel.packet, tmp.packet, 14, 16);
+ PACK_OUTPUT_I32(kernel.packet, tmp.packet, 15, 16);
+}
+
+EIGEN_DEVICE_FUNC inline void ptranspose(PacketBlock<Packet16i, 4>& kernel) {
+ __m512i T0 = _mm512_unpacklo_epi32(kernel.packet[0], kernel.packet[1]);
+ __m512i T1 = _mm512_unpackhi_epi32(kernel.packet[0], kernel.packet[1]);
+ __m512i T2 = _mm512_unpacklo_epi32(kernel.packet[2], kernel.packet[3]);
+ __m512i T3 = _mm512_unpackhi_epi32(kernel.packet[2], kernel.packet[3]);
+
+ __m512i S0 = SHUFFLE_EPI32(T0, T2, _MM_SHUFFLE(1, 0, 1, 0));
+ __m512i S1 = SHUFFLE_EPI32(T0, T2, _MM_SHUFFLE(3, 2, 3, 2));
+ __m512i S2 = SHUFFLE_EPI32(T1, T3, _MM_SHUFFLE(1, 0, 1, 0));
+ __m512i S3 = SHUFFLE_EPI32(T1, T3, _MM_SHUFFLE(3, 2, 3, 2));
+
+ EIGEN_EXTRACT_8i_FROM_16i(S0, S0);
+ EIGEN_EXTRACT_8i_FROM_16i(S1, S1);
+ EIGEN_EXTRACT_8i_FROM_16i(S2, S2);
+ EIGEN_EXTRACT_8i_FROM_16i(S3, S3);
+
+ PacketBlock<Packet8i, 8> tmp;
+
+ tmp.packet[0] = _mm256_permute2f128_si256(S0_0, S1_0, 0x20);
+ tmp.packet[1] = _mm256_permute2f128_si256(S2_0, S3_0, 0x20);
+ tmp.packet[2] = _mm256_permute2f128_si256(S0_0, S1_0, 0x31);
+ tmp.packet[3] = _mm256_permute2f128_si256(S2_0, S3_0, 0x31);
+
+ tmp.packet[4] = _mm256_permute2f128_si256(S0_1, S1_1, 0x20);
+ tmp.packet[5] = _mm256_permute2f128_si256(S2_1, S3_1, 0x20);
+ tmp.packet[6] = _mm256_permute2f128_si256(S0_1, S1_1, 0x31);
+ tmp.packet[7] = _mm256_permute2f128_si256(S2_1, S3_1, 0x31);
+
+ PACK_OUTPUT_I32_2(kernel.packet, tmp.packet, 0, 1);
+ PACK_OUTPUT_I32_2(kernel.packet, tmp.packet, 1, 1);
+ PACK_OUTPUT_I32_2(kernel.packet, tmp.packet, 2, 1);
+ PACK_OUTPUT_I32_2(kernel.packet, tmp.packet, 3, 1);
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet16f pblend(const Selector<16>& /*ifPacket*/,
+ const Packet16f& /*thenPacket*/,
+ const Packet16f& /*elsePacket*/) {
+ eigen_assert(false && "To be implemented");
+ return Packet16f();
+}
+template <>
+EIGEN_STRONG_INLINE Packet8d pblend(const Selector<8>& ifPacket,
+ const Packet8d& thenPacket,
+ const Packet8d& elsePacket) {
+ __mmask8 m = (ifPacket.select[0] )
+ | (ifPacket.select[1]<<1)
+ | (ifPacket.select[2]<<2)
+ | (ifPacket.select[3]<<3)
+ | (ifPacket.select[4]<<4)
+ | (ifPacket.select[5]<<5)
+ | (ifPacket.select[6]<<6)
+ | (ifPacket.select[7]<<7);
+ return _mm512_mask_blend_pd(m, elsePacket, thenPacket);
+}
+
+// Packet math for Eigen::half
+template<> EIGEN_STRONG_INLINE Packet16h pset1<Packet16h>(const Eigen::half& from) {
+ return _mm256_set1_epi16(from.x);
+}
+
+template<> EIGEN_STRONG_INLINE Eigen::half pfirst<Packet16h>(const Packet16h& from) {
+ return half_impl::raw_uint16_to_half(static_cast<unsigned short>(_mm256_extract_epi16(from, 0)));
+}
+
+template<> EIGEN_STRONG_INLINE Packet16h pload<Packet16h>(const Eigen::half* from) {
+ return _mm256_load_si256(reinterpret_cast<const __m256i*>(from));
+}
+
+template<> EIGEN_STRONG_INLINE Packet16h ploadu<Packet16h>(const Eigen::half* from) {
+ return _mm256_loadu_si256(reinterpret_cast<const __m256i*>(from));
+}
+
+template<> EIGEN_STRONG_INLINE void pstore<half>(Eigen::half* to, const Packet16h& from) {
+ // (void*) -> workaround clang warning:
+ // cast from 'Eigen::half *' to '__m256i *' increases required alignment from 2 to 32
+ _mm256_store_si256((__m256i*)(void*)to, from);
+}
+
+template<> EIGEN_STRONG_INLINE void pstoreu<half>(Eigen::half* to, const Packet16h& from) {
+ // (void*) -> workaround clang warning:
+ // cast from 'Eigen::half *' to '__m256i *' increases required alignment from 2 to 32
+ _mm256_storeu_si256((__m256i*)(void*)to, from);
+}
+
+template<> EIGEN_STRONG_INLINE Packet16h
+ploaddup<Packet16h>(const Eigen::half* from) {
+ unsigned short a = from[0].x;
+ unsigned short b = from[1].x;
+ unsigned short c = from[2].x;
+ unsigned short d = from[3].x;
+ unsigned short e = from[4].x;
+ unsigned short f = from[5].x;
+ unsigned short g = from[6].x;
+ unsigned short h = from[7].x;
+ return _mm256_set_epi16(h, h, g, g, f, f, e, e, d, d, c, c, b, b, a, a);
+}
+
+template<> EIGEN_STRONG_INLINE Packet16h
+ploadquad(const Eigen::half* from) {
+ unsigned short a = from[0].x;
+ unsigned short b = from[1].x;
+ unsigned short c = from[2].x;
+ unsigned short d = from[3].x;
+ return _mm256_set_epi16(d, d, d, d, c, c, c, c, b, b, b, b, a, a, a, a);
+}
+
+EIGEN_STRONG_INLINE Packet16f half2float(const Packet16h& a) {
+ return _mm512_cvtph_ps(a);
+}
+
+EIGEN_STRONG_INLINE Packet16h float2half(const Packet16f& a) {
+ return _mm512_cvtps_ph(a, _MM_FROUND_TO_NEAREST_INT|_MM_FROUND_NO_EXC);
+}
+
+template<> EIGEN_STRONG_INLINE Packet16h ptrue(const Packet16h& a) {
+ return Packet16h(ptrue(Packet8i(a)));
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet16h pabs(const Packet16h& a) {
+ const __m256i sign_mask = _mm256_set1_epi16(static_cast<numext::uint16_t>(0x8000));
+ return _mm256_andnot_si256(sign_mask, a);
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet16h pmin<Packet16h>(const Packet16h& a,
+ const Packet16h& b) {
+ return float2half(pmin<Packet16f>(half2float(a), half2float(b)));
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet16h pmax<Packet16h>(const Packet16h& a,
+ const Packet16h& b) {
+ return float2half(pmax<Packet16f>(half2float(a), half2float(b)));
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet16h plset<Packet16h>(const half& a) {
+ return float2half(plset<Packet16f>(static_cast<float>(a)));
+}
+
+template<> EIGEN_STRONG_INLINE Packet16h por(const Packet16h& a,const Packet16h& b) {
+ // in some cases Packet8i is a wrapper around __m256i, so we need to
+ // cast to Packet8i to call the correct overload.
+ return Packet16h(por(Packet8i(a),Packet8i(b)));
+}
+template<> EIGEN_STRONG_INLINE Packet16h pxor(const Packet16h& a,const Packet16h& b) {
+ return Packet16h(pxor(Packet8i(a),Packet8i(b)));
+}
+template<> EIGEN_STRONG_INLINE Packet16h pand(const Packet16h& a,const Packet16h& b) {
+ return Packet16h(pand(Packet8i(a),Packet8i(b)));
+}
+template<> EIGEN_STRONG_INLINE Packet16h pandnot(const Packet16h& a,const Packet16h& b) {
+ return Packet16h(pandnot(Packet8i(a),Packet8i(b)));
+}
+
+template<> EIGEN_STRONG_INLINE Packet16h pselect(const Packet16h& mask, const Packet16h& a, const Packet16h& b) {
+ return _mm256_blendv_epi8(b, a, mask);
+}
+
+template<> EIGEN_STRONG_INLINE Packet16h pround<Packet16h>(const Packet16h& a) {
+ return float2half(pround<Packet16f>(half2float(a)));
+}
+
+template<> EIGEN_STRONG_INLINE Packet16h print<Packet16h>(const Packet16h& a) {
+ return float2half(print<Packet16f>(half2float(a)));
+}
+
+template<> EIGEN_STRONG_INLINE Packet16h pceil<Packet16h>(const Packet16h& a) {
+ return float2half(pceil<Packet16f>(half2float(a)));
+}
+
+template<> EIGEN_STRONG_INLINE Packet16h pfloor<Packet16h>(const Packet16h& a) {
+ return float2half(pfloor<Packet16f>(half2float(a)));
+}
+
+template<> EIGEN_STRONG_INLINE Packet16h pcmp_eq(const Packet16h& a,const Packet16h& b) {
+ Packet16f af = half2float(a);
+ Packet16f bf = half2float(b);
+ return Pack32To16(pcmp_eq(af, bf));
+}
+
+template<> EIGEN_STRONG_INLINE Packet16h pcmp_le(const Packet16h& a,const Packet16h& b) {
+ return Pack32To16(pcmp_le(half2float(a), half2float(b)));
+}
+
+template<> EIGEN_STRONG_INLINE Packet16h pcmp_lt(const Packet16h& a,const Packet16h& b) {
+ return Pack32To16(pcmp_lt(half2float(a), half2float(b)));
+}
+
+template<> EIGEN_STRONG_INLINE Packet16h pcmp_lt_or_nan(const Packet16h& a,const Packet16h& b) {
+ return Pack32To16(pcmp_lt_or_nan(half2float(a), half2float(b)));
+}
+
+template<> EIGEN_STRONG_INLINE Packet16h pconj(const Packet16h& a) { return a; }
+
+template<> EIGEN_STRONG_INLINE Packet16h pnegate(const Packet16h& a) {
+ Packet16h sign_mask = _mm256_set1_epi16(static_cast<unsigned short>(0x8000));
+ return _mm256_xor_si256(a, sign_mask);
+}
+
+#ifndef EIGEN_VECTORIZE_AVX512FP16
+template<> EIGEN_STRONG_INLINE Packet16h padd<Packet16h>(const Packet16h& a, const Packet16h& b) {
+ Packet16f af = half2float(a);
+ Packet16f bf = half2float(b);
+ Packet16f rf = padd(af, bf);
+ return float2half(rf);
+}
+
+template<> EIGEN_STRONG_INLINE Packet16h psub<Packet16h>(const Packet16h& a, const Packet16h& b) {
+ Packet16f af = half2float(a);
+ Packet16f bf = half2float(b);
+ Packet16f rf = psub(af, bf);
+ return float2half(rf);
+}
+
+template<> EIGEN_STRONG_INLINE Packet16h pmul<Packet16h>(const Packet16h& a, const Packet16h& b) {
+ Packet16f af = half2float(a);
+ Packet16f bf = half2float(b);
+ Packet16f rf = pmul(af, bf);
+ return float2half(rf);
+}
+
+template<> EIGEN_STRONG_INLINE Packet16h pdiv<Packet16h>(const Packet16h& a, const Packet16h& b) {
+ Packet16f af = half2float(a);
+ Packet16f bf = half2float(b);
+ Packet16f rf = pdiv(af, bf);
+ return float2half(rf);
+}
+
+template<> EIGEN_STRONG_INLINE half predux<Packet16h>(const Packet16h& from) {
+ Packet16f from_float = half2float(from);
+ return half(predux(from_float));
+}
+
+#endif
+
+template <>
+EIGEN_STRONG_INLINE Packet8h predux_half_dowto4<Packet16h>(const Packet16h& a) {
+ Packet8h lane0 = _mm256_extractf128_si256(a, 0);
+ Packet8h lane1 = _mm256_extractf128_si256(a, 1);
+ return padd<Packet8h>(lane0, lane1);
+}
+
+template<> EIGEN_STRONG_INLINE Eigen::half predux_max<Packet16h>(const Packet16h& a) {
+ Packet16f af = half2float(a);
+ float reduced = predux_max<Packet16f>(af);
+ return Eigen::half(reduced);
+}
+
+template<> EIGEN_STRONG_INLINE Eigen::half predux_min<Packet16h>(const Packet16h& a) {
+ Packet16f af = half2float(a);
+ float reduced = predux_min<Packet16f>(af);
+ return Eigen::half(reduced);
+}
+
+template<> EIGEN_STRONG_INLINE half predux_mul<Packet16h>(const Packet16h& from) {
+ Packet16f from_float = half2float(from);
+ return half(predux_mul(from_float));
+}
+
+template<> EIGEN_STRONG_INLINE Packet16h preverse(const Packet16h& a)
+{
+ __m128i m = _mm_setr_epi8(14,15,12,13,10,11,8,9,6,7,4,5,2,3,0,1);
+ return _mm256_insertf128_si256(
+ _mm256_castsi128_si256(_mm_shuffle_epi8(_mm256_extractf128_si256(a,1),m)),
+ _mm_shuffle_epi8(_mm256_extractf128_si256(a,0),m), 1);
+}
+
+template<> EIGEN_STRONG_INLINE Packet16h pgather<Eigen::half, Packet16h>(const Eigen::half* from, Index stride)
+{
+ return _mm256_set_epi16(
+ from[15*stride].x, from[14*stride].x, from[13*stride].x, from[12*stride].x,
+ from[11*stride].x, from[10*stride].x, from[9*stride].x, from[8*stride].x,
+ from[7*stride].x, from[6*stride].x, from[5*stride].x, from[4*stride].x,
+ from[3*stride].x, from[2*stride].x, from[1*stride].x, from[0*stride].x);
+}
+
+template<> EIGEN_STRONG_INLINE void pscatter<half, Packet16h>(half* to, const Packet16h& from, Index stride)
+{
+ EIGEN_ALIGN64 half aux[16];
+ pstore(aux, from);
+ to[stride*0] = aux[0];
+ to[stride*1] = aux[1];
+ to[stride*2] = aux[2];
+ to[stride*3] = aux[3];
+ to[stride*4] = aux[4];
+ to[stride*5] = aux[5];
+ to[stride*6] = aux[6];
+ to[stride*7] = aux[7];
+ to[stride*8] = aux[8];
+ to[stride*9] = aux[9];
+ to[stride*10] = aux[10];
+ to[stride*11] = aux[11];
+ to[stride*12] = aux[12];
+ to[stride*13] = aux[13];
+ to[stride*14] = aux[14];
+ to[stride*15] = aux[15];
+}
+
+EIGEN_STRONG_INLINE void
+ptranspose(PacketBlock<Packet16h,16>& kernel) {
+ __m256i a = kernel.packet[0];
+ __m256i b = kernel.packet[1];
+ __m256i c = kernel.packet[2];
+ __m256i d = kernel.packet[3];
+ __m256i e = kernel.packet[4];
+ __m256i f = kernel.packet[5];
+ __m256i g = kernel.packet[6];
+ __m256i h = kernel.packet[7];
+ __m256i i = kernel.packet[8];
+ __m256i j = kernel.packet[9];
+ __m256i k = kernel.packet[10];
+ __m256i l = kernel.packet[11];
+ __m256i m = kernel.packet[12];
+ __m256i n = kernel.packet[13];
+ __m256i o = kernel.packet[14];
+ __m256i p = kernel.packet[15];
+
+ __m256i ab_07 = _mm256_unpacklo_epi16(a, b);
+ __m256i cd_07 = _mm256_unpacklo_epi16(c, d);
+ __m256i ef_07 = _mm256_unpacklo_epi16(e, f);
+ __m256i gh_07 = _mm256_unpacklo_epi16(g, h);
+ __m256i ij_07 = _mm256_unpacklo_epi16(i, j);
+ __m256i kl_07 = _mm256_unpacklo_epi16(k, l);
+ __m256i mn_07 = _mm256_unpacklo_epi16(m, n);
+ __m256i op_07 = _mm256_unpacklo_epi16(o, p);
+
+ __m256i ab_8f = _mm256_unpackhi_epi16(a, b);
+ __m256i cd_8f = _mm256_unpackhi_epi16(c, d);
+ __m256i ef_8f = _mm256_unpackhi_epi16(e, f);
+ __m256i gh_8f = _mm256_unpackhi_epi16(g, h);
+ __m256i ij_8f = _mm256_unpackhi_epi16(i, j);
+ __m256i kl_8f = _mm256_unpackhi_epi16(k, l);
+ __m256i mn_8f = _mm256_unpackhi_epi16(m, n);
+ __m256i op_8f = _mm256_unpackhi_epi16(o, p);
+
+ __m256i abcd_03 = _mm256_unpacklo_epi32(ab_07, cd_07);
+ __m256i abcd_47 = _mm256_unpackhi_epi32(ab_07, cd_07);
+ __m256i efgh_03 = _mm256_unpacklo_epi32(ef_07, gh_07);
+ __m256i efgh_47 = _mm256_unpackhi_epi32(ef_07, gh_07);
+ __m256i ijkl_03 = _mm256_unpacklo_epi32(ij_07, kl_07);
+ __m256i ijkl_47 = _mm256_unpackhi_epi32(ij_07, kl_07);
+ __m256i mnop_03 = _mm256_unpacklo_epi32(mn_07, op_07);
+ __m256i mnop_47 = _mm256_unpackhi_epi32(mn_07, op_07);
+
+ __m256i abcd_8b = _mm256_unpacklo_epi32(ab_8f, cd_8f);
+ __m256i abcd_cf = _mm256_unpackhi_epi32(ab_8f, cd_8f);
+ __m256i efgh_8b = _mm256_unpacklo_epi32(ef_8f, gh_8f);
+ __m256i efgh_cf = _mm256_unpackhi_epi32(ef_8f, gh_8f);
+ __m256i ijkl_8b = _mm256_unpacklo_epi32(ij_8f, kl_8f);
+ __m256i ijkl_cf = _mm256_unpackhi_epi32(ij_8f, kl_8f);
+ __m256i mnop_8b = _mm256_unpacklo_epi32(mn_8f, op_8f);
+ __m256i mnop_cf = _mm256_unpackhi_epi32(mn_8f, op_8f);
+
+ __m256i abcdefgh_01 = _mm256_unpacklo_epi64(abcd_03, efgh_03);
+ __m256i abcdefgh_23 = _mm256_unpackhi_epi64(abcd_03, efgh_03);
+ __m256i ijklmnop_01 = _mm256_unpacklo_epi64(ijkl_03, mnop_03);
+ __m256i ijklmnop_23 = _mm256_unpackhi_epi64(ijkl_03, mnop_03);
+ __m256i abcdefgh_45 = _mm256_unpacklo_epi64(abcd_47, efgh_47);
+ __m256i abcdefgh_67 = _mm256_unpackhi_epi64(abcd_47, efgh_47);
+ __m256i ijklmnop_45 = _mm256_unpacklo_epi64(ijkl_47, mnop_47);
+ __m256i ijklmnop_67 = _mm256_unpackhi_epi64(ijkl_47, mnop_47);
+ __m256i abcdefgh_89 = _mm256_unpacklo_epi64(abcd_8b, efgh_8b);
+ __m256i abcdefgh_ab = _mm256_unpackhi_epi64(abcd_8b, efgh_8b);
+ __m256i ijklmnop_89 = _mm256_unpacklo_epi64(ijkl_8b, mnop_8b);
+ __m256i ijklmnop_ab = _mm256_unpackhi_epi64(ijkl_8b, mnop_8b);
+ __m256i abcdefgh_cd = _mm256_unpacklo_epi64(abcd_cf, efgh_cf);
+ __m256i abcdefgh_ef = _mm256_unpackhi_epi64(abcd_cf, efgh_cf);
+ __m256i ijklmnop_cd = _mm256_unpacklo_epi64(ijkl_cf, mnop_cf);
+ __m256i ijklmnop_ef = _mm256_unpackhi_epi64(ijkl_cf, mnop_cf);
+
+ // NOTE: no unpacklo/hi instr in this case, so using permute instr.
+ __m256i a_p_0 = _mm256_permute2x128_si256(abcdefgh_01, ijklmnop_01, 0x20);
+ __m256i a_p_1 = _mm256_permute2x128_si256(abcdefgh_23, ijklmnop_23, 0x20);
+ __m256i a_p_2 = _mm256_permute2x128_si256(abcdefgh_45, ijklmnop_45, 0x20);
+ __m256i a_p_3 = _mm256_permute2x128_si256(abcdefgh_67, ijklmnop_67, 0x20);
+ __m256i a_p_4 = _mm256_permute2x128_si256(abcdefgh_89, ijklmnop_89, 0x20);
+ __m256i a_p_5 = _mm256_permute2x128_si256(abcdefgh_ab, ijklmnop_ab, 0x20);
+ __m256i a_p_6 = _mm256_permute2x128_si256(abcdefgh_cd, ijklmnop_cd, 0x20);
+ __m256i a_p_7 = _mm256_permute2x128_si256(abcdefgh_ef, ijklmnop_ef, 0x20);
+ __m256i a_p_8 = _mm256_permute2x128_si256(abcdefgh_01, ijklmnop_01, 0x31);
+ __m256i a_p_9 = _mm256_permute2x128_si256(abcdefgh_23, ijklmnop_23, 0x31);
+ __m256i a_p_a = _mm256_permute2x128_si256(abcdefgh_45, ijklmnop_45, 0x31);
+ __m256i a_p_b = _mm256_permute2x128_si256(abcdefgh_67, ijklmnop_67, 0x31);
+ __m256i a_p_c = _mm256_permute2x128_si256(abcdefgh_89, ijklmnop_89, 0x31);
+ __m256i a_p_d = _mm256_permute2x128_si256(abcdefgh_ab, ijklmnop_ab, 0x31);
+ __m256i a_p_e = _mm256_permute2x128_si256(abcdefgh_cd, ijklmnop_cd, 0x31);
+ __m256i a_p_f = _mm256_permute2x128_si256(abcdefgh_ef, ijklmnop_ef, 0x31);
+
+ kernel.packet[0] = a_p_0;
+ kernel.packet[1] = a_p_1;
+ kernel.packet[2] = a_p_2;
+ kernel.packet[3] = a_p_3;
+ kernel.packet[4] = a_p_4;
+ kernel.packet[5] = a_p_5;
+ kernel.packet[6] = a_p_6;
+ kernel.packet[7] = a_p_7;
+ kernel.packet[8] = a_p_8;
+ kernel.packet[9] = a_p_9;
+ kernel.packet[10] = a_p_a;
+ kernel.packet[11] = a_p_b;
+ kernel.packet[12] = a_p_c;
+ kernel.packet[13] = a_p_d;
+ kernel.packet[14] = a_p_e;
+ kernel.packet[15] = a_p_f;
+}
+
+EIGEN_STRONG_INLINE void
+ptranspose(PacketBlock<Packet16h,8>& kernel) {
+ EIGEN_ALIGN64 half in[8][16];
+ pstore<half>(in[0], kernel.packet[0]);
+ pstore<half>(in[1], kernel.packet[1]);
+ pstore<half>(in[2], kernel.packet[2]);
+ pstore<half>(in[3], kernel.packet[3]);
+ pstore<half>(in[4], kernel.packet[4]);
+ pstore<half>(in[5], kernel.packet[5]);
+ pstore<half>(in[6], kernel.packet[6]);
+ pstore<half>(in[7], kernel.packet[7]);
+
+ EIGEN_ALIGN64 half out[8][16];
+
+ for (int i = 0; i < 8; ++i) {
+ for (int j = 0; j < 8; ++j) {
+ out[i][j] = in[j][2*i];
+ }
+ for (int j = 0; j < 8; ++j) {
+ out[i][j+8] = in[j][2*i+1];
+ }
+ }
+
+ kernel.packet[0] = pload<Packet16h>(out[0]);
+ kernel.packet[1] = pload<Packet16h>(out[1]);
+ kernel.packet[2] = pload<Packet16h>(out[2]);
+ kernel.packet[3] = pload<Packet16h>(out[3]);
+ kernel.packet[4] = pload<Packet16h>(out[4]);
+ kernel.packet[5] = pload<Packet16h>(out[5]);
+ kernel.packet[6] = pload<Packet16h>(out[6]);
+ kernel.packet[7] = pload<Packet16h>(out[7]);
+}
+
+EIGEN_STRONG_INLINE void
+ptranspose(PacketBlock<Packet16h,4>& kernel) {
+ EIGEN_ALIGN64 half in[4][16];
+ pstore<half>(in[0], kernel.packet[0]);
+ pstore<half>(in[1], kernel.packet[1]);
+ pstore<half>(in[2], kernel.packet[2]);
+ pstore<half>(in[3], kernel.packet[3]);
+
+ EIGEN_ALIGN64 half out[4][16];
+
+ for (int i = 0; i < 4; ++i) {
+ for (int j = 0; j < 4; ++j) {
+ out[i][j] = in[j][4*i];
+ }
+ for (int j = 0; j < 4; ++j) {
+ out[i][j+4] = in[j][4*i+1];
+ }
+ for (int j = 0; j < 4; ++j) {
+ out[i][j+8] = in[j][4*i+2];
+ }
+ for (int j = 0; j < 4; ++j) {
+ out[i][j+12] = in[j][4*i+3];
+ }
+ }
+
+ kernel.packet[0] = pload<Packet16h>(out[0]);
+ kernel.packet[1] = pload<Packet16h>(out[1]);
+ kernel.packet[2] = pload<Packet16h>(out[2]);
+ kernel.packet[3] = pload<Packet16h>(out[3]);
+}
+
+template <> struct is_arithmetic<Packet16bf> { enum { value = true }; };
+
+template <>
+struct packet_traits<bfloat16> : default_packet_traits {
+ typedef Packet16bf type;
+ typedef Packet8bf half;
+ enum {
+ Vectorizable = 1,
+ AlignedOnScalar = 1,
+ size = 16,
+ HasHalfPacket = 1,
+ HasBlend = 0,
+ HasInsert = 1,
+ HasSin = EIGEN_FAST_MATH,
+ HasCos = EIGEN_FAST_MATH,
+#if EIGEN_HAS_AVX512_MATH
+#ifdef EIGEN_VECTORIZE_AVX512DQ
+ HasLog = 1, // Currently fails test with bad accuracy.
+ HasLog1p = 1,
+ HasExpm1 = 1,
+ HasNdtri = 1,
+ HasBessel = 1,
+#endif
+ HasExp = 1,
+ HasSqrt = EIGEN_FAST_MATH,
+ HasRsqrt = EIGEN_FAST_MATH,
+ HasTanh = EIGEN_FAST_MATH,
+ HasErf = EIGEN_FAST_MATH,
+#endif
+ HasCmp = 1,
+ HasDiv = 1
+ };
+};
+
+template <>
+struct unpacket_traits<Packet16bf>
+{
+ typedef bfloat16 type;
+ enum {size=16, alignment=Aligned32, vectorizable=true, masked_load_available=false, masked_store_available=false};
+ typedef Packet8bf half;
+};
+
+template <>
+EIGEN_STRONG_INLINE Packet16bf pset1<Packet16bf>(const bfloat16& from) {
+ return _mm256_set1_epi16(from.value);
+}
+
+template <>
+EIGEN_STRONG_INLINE bfloat16 pfirst<Packet16bf>(const Packet16bf& from) {
+ bfloat16 t;
+ t.value = static_cast<unsigned short>(_mm256_extract_epi16(from, 0));
+ return t;
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet16bf pload<Packet16bf>(const bfloat16* from) {
+ return _mm256_load_si256(reinterpret_cast<const __m256i*>(from));
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet16bf ploadu<Packet16bf>(const bfloat16* from) {
+ return _mm256_loadu_si256(reinterpret_cast<const __m256i*>(from));
+}
+
+template <>
+EIGEN_STRONG_INLINE void pstore<bfloat16>(bfloat16* to,
+ const Packet16bf& from) {
+ _mm256_store_si256(reinterpret_cast<__m256i*>(to), from);
+}
+
+template <>
+EIGEN_STRONG_INLINE void pstoreu<bfloat16>(bfloat16* to,
+ const Packet16bf& from) {
+ _mm256_storeu_si256(reinterpret_cast<__m256i*>(to), from);
+}
+
+template<> EIGEN_STRONG_INLINE Packet16bf
+ploaddup<Packet16bf>(const bfloat16* from) {
+ unsigned short a = from[0].value;
+ unsigned short b = from[1].value;
+ unsigned short c = from[2].value;
+ unsigned short d = from[3].value;
+ unsigned short e = from[4].value;
+ unsigned short f = from[5].value;
+ unsigned short g = from[6].value;
+ unsigned short h = from[7].value;
+ return _mm256_set_epi16(h, h, g, g, f, f, e, e, d, d, c, c, b, b, a, a);
+}
+
+template<> EIGEN_STRONG_INLINE Packet16bf
+ploadquad(const bfloat16* from) {
+ unsigned short a = from[0].value;
+ unsigned short b = from[1].value;
+ unsigned short c = from[2].value;
+ unsigned short d = from[3].value;
+ return _mm256_set_epi16(d, d, d, d, c, c, c, c, b, b, b, b, a, a, a, a);
+}
+
+EIGEN_STRONG_INLINE Packet16f Bf16ToF32(const Packet16bf& a) {
+ return _mm512_castsi512_ps(_mm512_slli_epi32(_mm512_cvtepu16_epi32(a), 16));
+}
+
+// Convert float to bfloat16 according to round-to-nearest-even/denormals algorithm.
+EIGEN_STRONG_INLINE Packet16bf F32ToBf16(const Packet16f& a) {
+ Packet16bf r;
+
+#if defined(EIGEN_VECTORIZE_AVX512BF16) && EIGEN_GNUC_AT_LEAST(10, 1)
+ // Since GCC 10.1 supports avx512bf16 and C style explicit cast
+ // (C++ static_cast is not supported yet), do conversion via intrinsic
+ // and register path for performance.
+ r = (__m256i)(_mm512_cvtneps_pbh(a));
+
+#else
+ __m512i t;
+ __m512i input = _mm512_castps_si512(a);
+ __m512i nan = _mm512_set1_epi32(0x7fc0);
+
+ // uint32_t lsb = (input >> 16) & 1;
+ t = _mm512_and_si512(_mm512_srli_epi32(input, 16), _mm512_set1_epi32(1));
+ // uint32_t rounding_bias = 0x7fff + lsb;
+ t = _mm512_add_epi32(t, _mm512_set1_epi32(0x7fff));
+ // input += rounding_bias;
+ t = _mm512_add_epi32(t, input);
+ // input = input >> 16;
+ t = _mm512_srli_epi32(t, 16);
+
+ // Check NaN before converting back to bf16
+ __mmask16 mask = _mm512_cmp_ps_mask(a, a, _CMP_ORD_Q);
+
+ t = _mm512_mask_blend_epi32(mask, nan, t);
+ // output.value = static_cast<uint16_t>(input);
+ r = _mm512_cvtepi32_epi16(t);
+#endif // EIGEN_VECTORIZE_AVX512BF16
+
+ return r;
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet16bf ptrue(const Packet16bf& a) {
+ return Packet16bf(ptrue<Packet8i>(Packet8i(a)));
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet16bf por(const Packet16bf& a, const Packet16bf& b) {
+ return Packet16bf(por<Packet8i>(Packet8i(a), Packet8i(b)));
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet16bf pxor(const Packet16bf& a, const Packet16bf& b) {
+ return Packet16bf(pxor<Packet8i>(Packet8i(a), Packet8i(b)));
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet16bf pand(const Packet16bf& a, const Packet16bf& b) {
+ return Packet16bf(pand<Packet8i>(Packet8i(a), Packet8i(b)));
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet16bf pandnot(const Packet16bf& a,
+ const Packet16bf& b) {
+ return Packet16bf(pandnot<Packet8i>(Packet8i(a), Packet8i(b)));
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet16bf pselect(const Packet16bf& mask,
+ const Packet16bf& a,
+ const Packet16bf& b) {
+ // Input mask is expected to be all 0/1, handle it with 8-bit
+ // intrinsic for performance.
+ return _mm256_blendv_epi8(b, a, mask);
+}
+
+template<> EIGEN_STRONG_INLINE Packet16bf pround<Packet16bf>(const Packet16bf& a)
+{
+ return F32ToBf16(pround<Packet16f>(Bf16ToF32(a)));
+}
+
+template<> EIGEN_STRONG_INLINE Packet16bf print<Packet16bf>(const Packet16bf& a) {
+ return F32ToBf16(print<Packet16f>(Bf16ToF32(a)));
+}
+
+template<> EIGEN_STRONG_INLINE Packet16bf pceil<Packet16bf>(const Packet16bf& a) {
+ return F32ToBf16(pceil<Packet16f>(Bf16ToF32(a)));
+}
+
+template<> EIGEN_STRONG_INLINE Packet16bf pfloor<Packet16bf>(const Packet16bf& a) {
+ return F32ToBf16(pfloor<Packet16f>(Bf16ToF32(a)));
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet16bf pcmp_eq(const Packet16bf& a,
+ const Packet16bf& b) {
+ return Pack32To16(pcmp_eq(Bf16ToF32(a), Bf16ToF32(b)));
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet16bf pcmp_le(const Packet16bf& a,
+ const Packet16bf& b) {
+ return Pack32To16(pcmp_le(Bf16ToF32(a), Bf16ToF32(b)));
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet16bf pcmp_lt(const Packet16bf& a,
+ const Packet16bf& b) {
+ return Pack32To16(pcmp_lt(Bf16ToF32(a), Bf16ToF32(b)));
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet16bf pcmp_lt_or_nan(const Packet16bf& a,
+ const Packet16bf& b) {
+ return Pack32To16(pcmp_lt_or_nan(Bf16ToF32(a), Bf16ToF32(b)));
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet16bf pnegate(const Packet16bf& a) {
+ Packet16bf sign_mask = _mm256_set1_epi16(static_cast<unsigned short>(0x8000));
+ return _mm256_xor_si256(a, sign_mask);
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet16bf pconj(const Packet16bf& a) {
+ return a;
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet16bf pabs(const Packet16bf& a) {
+ const __m256i sign_mask = _mm256_set1_epi16(static_cast<numext::uint16_t>(0x8000));
+ return _mm256_andnot_si256(sign_mask, a);
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet16bf padd<Packet16bf>(const Packet16bf& a,
+ const Packet16bf& b) {
+ return F32ToBf16(padd<Packet16f>(Bf16ToF32(a), Bf16ToF32(b)));
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet16bf psub<Packet16bf>(const Packet16bf& a,
+ const Packet16bf& b) {
+ return F32ToBf16(psub<Packet16f>(Bf16ToF32(a), Bf16ToF32(b)));
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet16bf pmul<Packet16bf>(const Packet16bf& a,
+ const Packet16bf& b) {
+ return F32ToBf16(pmul<Packet16f>(Bf16ToF32(a), Bf16ToF32(b)));
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet16bf pdiv<Packet16bf>(const Packet16bf& a,
+ const Packet16bf& b) {
+ return F32ToBf16(pdiv<Packet16f>(Bf16ToF32(a), Bf16ToF32(b)));
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet16bf pmin<Packet16bf>(const Packet16bf& a,
+ const Packet16bf& b) {
+ return F32ToBf16(pmin<Packet16f>(Bf16ToF32(a), Bf16ToF32(b)));
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet16bf pmax<Packet16bf>(const Packet16bf& a,
+ const Packet16bf& b) {
+ return F32ToBf16(pmax<Packet16f>(Bf16ToF32(a), Bf16ToF32(b)));
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet16bf plset<Packet16bf>(const bfloat16& a) {
+ return F32ToBf16(plset<Packet16f>(static_cast<float>(a)));
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet8bf predux_half_dowto4<Packet16bf>(const Packet16bf& a) {
+ Packet8bf lane0 = _mm256_extractf128_si256(a, 0);
+ Packet8bf lane1 = _mm256_extractf128_si256(a, 1);
+ return padd<Packet8bf>(lane0, lane1);
+}
+
+template <>
+EIGEN_STRONG_INLINE bfloat16 predux<Packet16bf>(const Packet16bf& p) {
+ return static_cast<bfloat16>(predux<Packet16f>(Bf16ToF32(p)));
+}
+
+template <>
+EIGEN_STRONG_INLINE bfloat16 predux_mul<Packet16bf>(const Packet16bf& from) {
+ return static_cast<bfloat16>(predux_mul<Packet16f>(Bf16ToF32(from)));
+}
+
+template <>
+EIGEN_STRONG_INLINE bfloat16 predux_min<Packet16bf>(const Packet16bf& from) {
+ return static_cast<bfloat16>(predux_min<Packet16f>(Bf16ToF32(from)));
+}
+
+template <>
+EIGEN_STRONG_INLINE bfloat16 predux_max<Packet16bf>(const Packet16bf& from) {
+ return static_cast<bfloat16>(predux_max<Packet16f>(Bf16ToF32(from)));
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet16bf preverse(const Packet16bf& a) {
+ __m256i m = _mm256_setr_epi8(14,15,12,13,10,11,8,9,6,7,4,5,2,3,0,1,
+ 14,15,12,13,10,11,8,9,6,7,4,5,2,3,0,1);
+
+ Packet16bf res;
+ // Swap hi and lo first because shuffle is in 128-bit lanes.
+ res = _mm256_permute2x128_si256(a, a, 1);
+ // Shuffle 8-bit values in src within 2*128-bit lanes.
+ return _mm256_shuffle_epi8(res, m);
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet16bf pgather<bfloat16, Packet16bf>(const bfloat16* from,
+ Index stride) {
+ return _mm256_set_epi16(
+ from[15*stride].value, from[14*stride].value, from[13*stride].value, from[12*stride].value,
+ from[11*stride].value, from[10*stride].value, from[9*stride].value, from[8*stride].value,
+ from[7*stride].value, from[6*stride].value, from[5*stride].value, from[4*stride].value,
+ from[3*stride].value, from[2*stride].value, from[1*stride].value, from[0*stride].value);
+}
+
+template <>
+EIGEN_STRONG_INLINE void pscatter<bfloat16, Packet16bf>(bfloat16* to,
+ const Packet16bf& from,
+ Index stride) {
+ EIGEN_ALIGN64 bfloat16 aux[16];
+ pstore(aux, from);
+ to[stride*0] = aux[0];
+ to[stride*1] = aux[1];
+ to[stride*2] = aux[2];
+ to[stride*3] = aux[3];
+ to[stride*4] = aux[4];
+ to[stride*5] = aux[5];
+ to[stride*6] = aux[6];
+ to[stride*7] = aux[7];
+ to[stride*8] = aux[8];
+ to[stride*9] = aux[9];
+ to[stride*10] = aux[10];
+ to[stride*11] = aux[11];
+ to[stride*12] = aux[12];
+ to[stride*13] = aux[13];
+ to[stride*14] = aux[14];
+ to[stride*15] = aux[15];
+}
+
+EIGEN_STRONG_INLINE void ptranspose(PacketBlock<Packet16bf,16>& kernel) {
+ __m256i a = kernel.packet[0];
+ __m256i b = kernel.packet[1];
+ __m256i c = kernel.packet[2];
+ __m256i d = kernel.packet[3];
+ __m256i e = kernel.packet[4];
+ __m256i f = kernel.packet[5];
+ __m256i g = kernel.packet[6];
+ __m256i h = kernel.packet[7];
+ __m256i i = kernel.packet[8];
+ __m256i j = kernel.packet[9];
+ __m256i k = kernel.packet[10];
+ __m256i l = kernel.packet[11];
+ __m256i m = kernel.packet[12];
+ __m256i n = kernel.packet[13];
+ __m256i o = kernel.packet[14];
+ __m256i p = kernel.packet[15];
+
+ __m256i ab_07 = _mm256_unpacklo_epi16(a, b);
+ __m256i cd_07 = _mm256_unpacklo_epi16(c, d);
+ __m256i ef_07 = _mm256_unpacklo_epi16(e, f);
+ __m256i gh_07 = _mm256_unpacklo_epi16(g, h);
+ __m256i ij_07 = _mm256_unpacklo_epi16(i, j);
+ __m256i kl_07 = _mm256_unpacklo_epi16(k, l);
+ __m256i mn_07 = _mm256_unpacklo_epi16(m, n);
+ __m256i op_07 = _mm256_unpacklo_epi16(o, p);
+
+ __m256i ab_8f = _mm256_unpackhi_epi16(a, b);
+ __m256i cd_8f = _mm256_unpackhi_epi16(c, d);
+ __m256i ef_8f = _mm256_unpackhi_epi16(e, f);
+ __m256i gh_8f = _mm256_unpackhi_epi16(g, h);
+ __m256i ij_8f = _mm256_unpackhi_epi16(i, j);
+ __m256i kl_8f = _mm256_unpackhi_epi16(k, l);
+ __m256i mn_8f = _mm256_unpackhi_epi16(m, n);
+ __m256i op_8f = _mm256_unpackhi_epi16(o, p);
+
+ __m256i abcd_03 = _mm256_unpacklo_epi32(ab_07, cd_07);
+ __m256i abcd_47 = _mm256_unpackhi_epi32(ab_07, cd_07);
+ __m256i efgh_03 = _mm256_unpacklo_epi32(ef_07, gh_07);
+ __m256i efgh_47 = _mm256_unpackhi_epi32(ef_07, gh_07);
+ __m256i ijkl_03 = _mm256_unpacklo_epi32(ij_07, kl_07);
+ __m256i ijkl_47 = _mm256_unpackhi_epi32(ij_07, kl_07);
+ __m256i mnop_03 = _mm256_unpacklo_epi32(mn_07, op_07);
+ __m256i mnop_47 = _mm256_unpackhi_epi32(mn_07, op_07);
+
+ __m256i abcd_8b = _mm256_unpacklo_epi32(ab_8f, cd_8f);
+ __m256i abcd_cf = _mm256_unpackhi_epi32(ab_8f, cd_8f);
+ __m256i efgh_8b = _mm256_unpacklo_epi32(ef_8f, gh_8f);
+ __m256i efgh_cf = _mm256_unpackhi_epi32(ef_8f, gh_8f);
+ __m256i ijkl_8b = _mm256_unpacklo_epi32(ij_8f, kl_8f);
+ __m256i ijkl_cf = _mm256_unpackhi_epi32(ij_8f, kl_8f);
+ __m256i mnop_8b = _mm256_unpacklo_epi32(mn_8f, op_8f);
+ __m256i mnop_cf = _mm256_unpackhi_epi32(mn_8f, op_8f);
+
+ __m256i abcdefgh_01 = _mm256_unpacklo_epi64(abcd_03, efgh_03);
+ __m256i abcdefgh_23 = _mm256_unpackhi_epi64(abcd_03, efgh_03);
+ __m256i ijklmnop_01 = _mm256_unpacklo_epi64(ijkl_03, mnop_03);
+ __m256i ijklmnop_23 = _mm256_unpackhi_epi64(ijkl_03, mnop_03);
+ __m256i abcdefgh_45 = _mm256_unpacklo_epi64(abcd_47, efgh_47);
+ __m256i abcdefgh_67 = _mm256_unpackhi_epi64(abcd_47, efgh_47);
+ __m256i ijklmnop_45 = _mm256_unpacklo_epi64(ijkl_47, mnop_47);
+ __m256i ijklmnop_67 = _mm256_unpackhi_epi64(ijkl_47, mnop_47);
+ __m256i abcdefgh_89 = _mm256_unpacklo_epi64(abcd_8b, efgh_8b);
+ __m256i abcdefgh_ab = _mm256_unpackhi_epi64(abcd_8b, efgh_8b);
+ __m256i ijklmnop_89 = _mm256_unpacklo_epi64(ijkl_8b, mnop_8b);
+ __m256i ijklmnop_ab = _mm256_unpackhi_epi64(ijkl_8b, mnop_8b);
+ __m256i abcdefgh_cd = _mm256_unpacklo_epi64(abcd_cf, efgh_cf);
+ __m256i abcdefgh_ef = _mm256_unpackhi_epi64(abcd_cf, efgh_cf);
+ __m256i ijklmnop_cd = _mm256_unpacklo_epi64(ijkl_cf, mnop_cf);
+ __m256i ijklmnop_ef = _mm256_unpackhi_epi64(ijkl_cf, mnop_cf);
+
+ // NOTE: no unpacklo/hi instr in this case, so using permute instr.
+ kernel.packet[0] = _mm256_permute2x128_si256(abcdefgh_01, ijklmnop_01, 0x20);
+ kernel.packet[1] = _mm256_permute2x128_si256(abcdefgh_23, ijklmnop_23, 0x20);
+ kernel.packet[2] = _mm256_permute2x128_si256(abcdefgh_45, ijklmnop_45, 0x20);
+ kernel.packet[3] = _mm256_permute2x128_si256(abcdefgh_67, ijklmnop_67, 0x20);
+ kernel.packet[4] = _mm256_permute2x128_si256(abcdefgh_89, ijklmnop_89, 0x20);
+ kernel.packet[5] = _mm256_permute2x128_si256(abcdefgh_ab, ijklmnop_ab, 0x20);
+ kernel.packet[6] = _mm256_permute2x128_si256(abcdefgh_cd, ijklmnop_cd, 0x20);
+ kernel.packet[7] = _mm256_permute2x128_si256(abcdefgh_ef, ijklmnop_ef, 0x20);
+ kernel.packet[8] = _mm256_permute2x128_si256(abcdefgh_01, ijklmnop_01, 0x31);
+ kernel.packet[9] = _mm256_permute2x128_si256(abcdefgh_23, ijklmnop_23, 0x31);
+ kernel.packet[10] = _mm256_permute2x128_si256(abcdefgh_45, ijklmnop_45, 0x31);
+ kernel.packet[11] = _mm256_permute2x128_si256(abcdefgh_67, ijklmnop_67, 0x31);
+ kernel.packet[12] = _mm256_permute2x128_si256(abcdefgh_89, ijklmnop_89, 0x31);
+ kernel.packet[13] = _mm256_permute2x128_si256(abcdefgh_ab, ijklmnop_ab, 0x31);
+ kernel.packet[14] = _mm256_permute2x128_si256(abcdefgh_cd, ijklmnop_cd, 0x31);
+ kernel.packet[15] = _mm256_permute2x128_si256(abcdefgh_ef, ijklmnop_ef, 0x31);
+}
+
+EIGEN_STRONG_INLINE void ptranspose(PacketBlock<Packet16bf,4>& kernel) {
+ __m256i a = kernel.packet[0];
+ __m256i b = kernel.packet[1];
+ __m256i c = kernel.packet[2];
+ __m256i d = kernel.packet[3];
+
+ __m256i ab_07 = _mm256_unpacklo_epi16(a, b);
+ __m256i cd_07 = _mm256_unpacklo_epi16(c, d);
+ __m256i ab_8f = _mm256_unpackhi_epi16(a, b);
+ __m256i cd_8f = _mm256_unpackhi_epi16(c, d);
+
+ __m256i abcd_03 = _mm256_unpacklo_epi32(ab_07, cd_07);
+ __m256i abcd_47 = _mm256_unpackhi_epi32(ab_07, cd_07);
+ __m256i abcd_8b = _mm256_unpacklo_epi32(ab_8f, cd_8f);
+ __m256i abcd_cf = _mm256_unpackhi_epi32(ab_8f, cd_8f);
+
+ // NOTE: no unpacklo/hi instr in this case, so using permute instr.
+ kernel.packet[0] = _mm256_permute2x128_si256(abcd_03, abcd_47, 0x20);
+ kernel.packet[1] = _mm256_permute2x128_si256(abcd_8b, abcd_cf, 0x20);
+ kernel.packet[2] = _mm256_permute2x128_si256(abcd_03, abcd_47, 0x31);
+ kernel.packet[3] = _mm256_permute2x128_si256(abcd_8b, abcd_cf, 0x31);
+}
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_PACKET_MATH_AVX512_H
diff --git a/Eigen/src/Core/arch/AVX512/PacketMathFP16.h b/Eigen/src/Core/arch/AVX512/PacketMathFP16.h
new file mode 100644
index 0000000..324d050
--- /dev/null
+++ b/Eigen/src/Core/arch/AVX512/PacketMathFP16.h
@@ -0,0 +1,870 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+//
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_PACKET_MATH_FP16_AVX512_H
+#define EIGEN_PACKET_MATH_FP16_AVX512_H
+
+#include "../../InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+
+// Disable the code for older versions of gcc that don't support many of the required avx512 math instrinsics.
+#if EIGEN_GNUC_AT_LEAST(5, 3) || EIGEN_COMP_CLANG || EIGEN_COMP_MSVC >= 1923 || EIGEN_COMP_ICC >= 1900
+#define EIGEN_HAS_AVX512_MATH 1
+#else
+#define EIGEN_HAS_AVX512_MATH 0
+#endif
+
+typedef __m512h Packet32h;
+typedef eigen_packet_wrapper<__m256i, 1> Packet16h;
+typedef eigen_packet_wrapper<__m128i, 2> Packet8h;
+
+template <>
+struct is_arithmetic<Packet8h> {
+ enum { value = true };
+};
+
+template <>
+struct packet_traits<half> : default_packet_traits {
+ typedef Packet32h type;
+ typedef Packet16h half;
+ enum {
+ Vectorizable = 1,
+ AlignedOnScalar = 1,
+ size = 32,
+ HasHalfPacket = 1,
+
+ HasCmp = 1,
+ HasAdd = 1,
+ HasSub = 1,
+ HasMul = 1,
+ HasDiv = 1,
+ HasNegate = 1,
+ HasAbs = 1,
+ HasAbs2 = 0,
+ HasMin = 1,
+ HasMax = 1,
+ HasConj = 1,
+ HasSetLinear = 0,
+ // These ones should be implemented in future
+ HasLog = EIGEN_HAS_AVX512_MATH,
+ HasLog1p = EIGEN_HAS_AVX512_MATH,
+ HasExp = EIGEN_HAS_AVX512_MATH,
+ HasExpm1 = EIGEN_HAS_AVX512_MATH,
+ HasSqrt = EIGEN_HAS_AVX512_MATH,
+ HasRsqrt = EIGEN_HAS_AVX512_MATH,
+ HasBessel = 0, // EIGEN_HAS_AVX512_MATH,
+ HasNdtri = 0, // EIGEN_HAS_AVX512_MATH,
+ HasSin = EIGEN_FAST_MATH,
+ HasCos = EIGEN_FAST_MATH,
+ HasTanh = EIGEN_FAST_MATH,
+ HasErf = 0, // EIGEN_FAST_MATH,
+ HasBlend = 0,
+ HasRound = 1,
+ HasFloor = 1,
+ HasCeil = 1,
+ HasRint = 1
+ };
+};
+
+template <>
+struct unpacket_traits<Packet32h> {
+ typedef Eigen::half type;
+ typedef Packet16h half;
+ enum {
+ size = 32,
+ alignment = Aligned64,
+ vectorizable = true,
+ masked_load_available = false,
+ masked_store_available = false
+ };
+};
+
+template <>
+struct unpacket_traits<Packet16h> {
+ typedef Eigen::half type;
+ typedef Packet8h half;
+ enum {
+ size = 16,
+ alignment = Aligned32,
+ vectorizable = true,
+ masked_load_available = false,
+ masked_store_available = false
+ };
+};
+
+template <>
+struct unpacket_traits<Packet8h> {
+ typedef Eigen::half type;
+ typedef Packet8h half;
+ enum {
+ size = 8,
+ alignment = Aligned16,
+ vectorizable = true,
+ masked_load_available = false,
+ masked_store_available = false
+ };
+};
+
+// Memory functions
+
+// pset1
+
+template <>
+EIGEN_STRONG_INLINE Packet32h pset1<Packet32h>(const Eigen::half& from) {
+ return _mm512_set1_ph(static_cast<_Float16>(from));
+}
+
+// pset1frombits
+template <>
+EIGEN_STRONG_INLINE Packet32h pset1frombits<Packet32h>(unsigned short from) {
+ return _mm512_castsi512_ph(_mm512_set1_epi16(from));
+}
+
+// pfirst
+
+template <>
+EIGEN_STRONG_INLINE Eigen::half pfirst<Packet32h>(const Packet32h& from) {
+#ifdef EIGEN_VECTORIZE_AVX512DQ
+ return half_impl::raw_uint16_to_half(
+ static_cast<unsigned short>(_mm256_extract_epi16(_mm512_extracti32x8_epi32(_mm512_castph_si512(from), 0), 0)));
+#else
+ Eigen::half dest[32];
+ _mm512_storeu_ph(dest, from);
+ return dest[0];
+#endif
+}
+
+// pload
+
+template <>
+EIGEN_STRONG_INLINE Packet32h pload<Packet32h>(const Eigen::half* from) {
+ EIGEN_DEBUG_ALIGNED_LOAD return _mm512_load_ph(from);
+}
+
+// ploadu
+
+template <>
+EIGEN_STRONG_INLINE Packet32h ploadu<Packet32h>(const Eigen::half* from) {
+ EIGEN_DEBUG_UNALIGNED_LOAD return _mm512_loadu_ph(from);
+}
+
+// pstore
+
+template <>
+EIGEN_STRONG_INLINE void pstore<half>(Eigen::half* to, const Packet32h& from) {
+ EIGEN_DEBUG_ALIGNED_STORE _mm512_store_ph(to, from);
+}
+
+// pstoreu
+
+template <>
+EIGEN_STRONG_INLINE void pstoreu<half>(Eigen::half* to, const Packet32h& from) {
+ EIGEN_DEBUG_UNALIGNED_STORE _mm512_storeu_ph(to, from);
+}
+
+// ploaddup
+template <>
+EIGEN_STRONG_INLINE Packet32h ploaddup<Packet32h>(const Eigen::half* from) {
+ __m512h a = _mm512_castph256_ph512(_mm256_loadu_ph(from));
+ return _mm512_permutexvar_ph(_mm512_set_epi16(15, 15, 14, 14, 13, 13, 12, 12, 11, 11, 10, 10, 9, 9, 8, 8, 7, 7, 6, 6,
+ 5, 5, 4, 4, 3, 3, 2, 2, 1, 1, 0, 0),
+ a);
+}
+
+// ploadquad
+template <>
+EIGEN_STRONG_INLINE Packet32h ploadquad<Packet32h>(const Eigen::half* from) {
+ __m512h a = _mm512_castph128_ph512(_mm_loadu_ph(from));
+ return _mm512_permutexvar_ph(
+ _mm512_set_epi16(7, 7, 7, 7, 6, 6, 6, 6, 5, 5, 5, 5, 4, 4, 4, 4, 3, 3, 3, 3, 2, 2, 2, 2, 1, 1, 1, 1, 0, 0, 0, 0),
+ a);
+}
+
+// pabs
+
+template <>
+EIGEN_STRONG_INLINE Packet32h pabs<Packet32h>(const Packet32h& a) {
+ return _mm512_abs_ph(a);
+}
+
+// pmin
+
+template <>
+EIGEN_STRONG_INLINE Packet32h pmin<Packet32h>(const Packet32h& a, const Packet32h& b) {
+ return _mm512_min_ph(a, b);
+}
+
+// pmax
+
+template <>
+EIGEN_STRONG_INLINE Packet32h pmax<Packet32h>(const Packet32h& a, const Packet32h& b) {
+ return _mm512_max_ph(a, b);
+}
+
+// plset
+template <>
+EIGEN_STRONG_INLINE Packet32h plset<Packet32h>(const half& a) {
+ return _mm512_add_ph(_mm512_set1_ph(a),
+ _mm512_set_ph(31.0f, 30.0f, 29.0f, 28.0f, 27.0f, 26.0f, 25.0f, 24.0f, 23.0f, 22.0f, 21.0f, 20.0f,
+ 19.0f, 18.0f, 17.0f, 16.0f, 15.0f, 14.0f, 13.0f, 12.0f, 11.0f, 10.0f, 9.0f, 8.0f,
+ 7.0f, 6.0f, 5.0f, 4.0f, 3.0f, 2.0f, 1.0f, 0.0f));
+}
+
+// por
+
+template <>
+EIGEN_STRONG_INLINE Packet32h por(const Packet32h& a, const Packet32h& b) {
+ return _mm512_castsi512_ph(_mm512_or_si512(_mm512_castph_si512(a), _mm512_castph_si512(b)));
+}
+
+// pxor
+
+template <>
+EIGEN_STRONG_INLINE Packet32h pxor(const Packet32h& a, const Packet32h& b) {
+ return _mm512_castsi512_ph(_mm512_xor_si512(_mm512_castph_si512(a), _mm512_castph_si512(b)));
+}
+
+// pand
+
+template <>
+EIGEN_STRONG_INLINE Packet32h pand(const Packet32h& a, const Packet32h& b) {
+ return _mm512_castsi512_ph(_mm512_and_si512(_mm512_castph_si512(a), _mm512_castph_si512(b)));
+}
+
+// pandnot
+
+template <>
+EIGEN_STRONG_INLINE Packet32h pandnot(const Packet32h& a, const Packet32h& b) {
+ return _mm512_castsi512_ph(_mm512_andnot_si512(_mm512_castph_si512(b), _mm512_castph_si512(a)));
+}
+
+// pselect
+
+template <>
+EIGEN_DEVICE_FUNC inline Packet32h pselect(const Packet32h& mask, const Packet32h& a, const Packet32h& b) {
+ __mmask32 mask32 = _mm512_cmp_epi16_mask(_mm512_castph_si512(mask), _mm512_setzero_epi32(), _MM_CMPINT_EQ);
+ return _mm512_mask_blend_ph(mask32, a, b);
+}
+
+// pcmp_eq
+
+template <>
+EIGEN_STRONG_INLINE Packet32h pcmp_eq(const Packet32h& a, const Packet32h& b) {
+ __mmask32 mask = _mm512_cmp_ph_mask(a, b, _CMP_EQ_OQ);
+ return _mm512_castsi512_ph(_mm512_mask_set1_epi16(_mm512_set1_epi32(0), mask, 0xffffu));
+}
+
+// pcmp_le
+
+template <>
+EIGEN_STRONG_INLINE Packet32h pcmp_le(const Packet32h& a, const Packet32h& b) {
+ __mmask32 mask = _mm512_cmp_ph_mask(a, b, _CMP_LE_OQ);
+ return _mm512_castsi512_ph(_mm512_mask_set1_epi16(_mm512_set1_epi32(0), mask, 0xffffu));
+}
+
+// pcmp_lt
+
+template <>
+EIGEN_STRONG_INLINE Packet32h pcmp_lt(const Packet32h& a, const Packet32h& b) {
+ __mmask32 mask = _mm512_cmp_ph_mask(a, b, _CMP_LT_OQ);
+ return _mm512_castsi512_ph(_mm512_mask_set1_epi16(_mm512_set1_epi32(0), mask, 0xffffu));
+}
+
+// pcmp_lt_or_nan
+
+template <>
+EIGEN_STRONG_INLINE Packet32h pcmp_lt_or_nan(const Packet32h& a, const Packet32h& b) {
+ __mmask32 mask = _mm512_cmp_ph_mask(a, b, _CMP_NGE_UQ);
+ return _mm512_castsi512_ph(_mm512_mask_set1_epi16(_mm512_set1_epi16(0), mask, 0xffffu));
+}
+
+// padd
+
+template <>
+EIGEN_STRONG_INLINE Packet32h padd<Packet32h>(const Packet32h& a, const Packet32h& b) {
+ return _mm512_add_ph(a, b);
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet16h padd<Packet16h>(const Packet16h& a, const Packet16h& b) {
+ return _mm256_castph_si256(_mm256_add_ph(_mm256_castsi256_ph(a), _mm256_castsi256_ph(b)));
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet8h padd<Packet8h>(const Packet8h& a, const Packet8h& b) {
+ return _mm_castph_si128(_mm_add_ph(_mm_castsi128_ph(a), _mm_castsi128_ph(b)));
+}
+
+// psub
+
+template <>
+EIGEN_STRONG_INLINE Packet32h psub<Packet32h>(const Packet32h& a, const Packet32h& b) {
+ return _mm512_sub_ph(a, b);
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet16h psub<Packet16h>(const Packet16h& a, const Packet16h& b) {
+ return _mm256_castph_si256(_mm256_sub_ph(_mm256_castsi256_ph(a), _mm256_castsi256_ph(b)));
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet8h psub<Packet8h>(const Packet8h& a, const Packet8h& b) {
+ return _mm_castph_si128(_mm_sub_ph(_mm_castsi128_ph(a), _mm_castsi128_ph(b)));
+}
+
+// pmul
+
+template <>
+EIGEN_STRONG_INLINE Packet32h pmul<Packet32h>(const Packet32h& a, const Packet32h& b) {
+ return _mm512_mul_ph(a, b);
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet16h pmul<Packet16h>(const Packet16h& a, const Packet16h& b) {
+ return _mm256_castph_si256(_mm256_mul_ph(_mm256_castsi256_ph(a), _mm256_castsi256_ph(b)));
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet8h pmul<Packet8h>(const Packet8h& a, const Packet8h& b) {
+ return _mm_castph_si128(_mm_mul_ph(_mm_castsi128_ph(a), _mm_castsi128_ph(b)));
+}
+
+// pdiv
+
+template <>
+EIGEN_STRONG_INLINE Packet32h pdiv<Packet32h>(const Packet32h& a, const Packet32h& b) {
+ return _mm512_div_ph(a, b);
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet16h pdiv<Packet16h>(const Packet16h& a, const Packet16h& b) {
+ return _mm256_castph_si256(_mm256_div_ph(_mm256_castsi256_ph(a), _mm256_castsi256_ph(b)));
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet8h pdiv<Packet8h>(const Packet8h& a, const Packet8h& b) {
+ return _mm_castph_si128(_mm_div_ph(_mm_castsi128_ph(a), _mm_castsi128_ph(b)));
+}
+
+// pround
+
+template <>
+EIGEN_STRONG_INLINE Packet32h pround<Packet32h>(const Packet32h& a) {
+ // Work-around for default std::round rounding mode.
+
+ // Mask for the sign bit
+ const Packet32h signMask = pset1frombits<Packet32h>(static_cast<numext::uint16_t>(0x8000u));
+ // The largest half-preicision float less than 0.5
+ const Packet32h prev0dot5 = pset1frombits<Packet32h>(static_cast<numext::uint16_t>(0x37FFu));
+
+ return _mm512_roundscale_ph(padd(por(pand(a, signMask), prev0dot5), a), _MM_FROUND_TO_ZERO);
+}
+
+// print
+
+template <>
+EIGEN_STRONG_INLINE Packet32h print<Packet32h>(const Packet32h& a) {
+ return _mm512_roundscale_ph(a, _MM_FROUND_CUR_DIRECTION);
+}
+
+// pceil
+
+template <>
+EIGEN_STRONG_INLINE Packet32h pceil<Packet32h>(const Packet32h& a) {
+ return _mm512_roundscale_ph(a, _MM_FROUND_TO_POS_INF);
+}
+
+// pfloor
+
+template <>
+EIGEN_STRONG_INLINE Packet32h pfloor<Packet32h>(const Packet32h& a) {
+ return _mm512_roundscale_ph(a, _MM_FROUND_TO_NEG_INF);
+}
+
+// predux
+template <>
+EIGEN_STRONG_INLINE half predux<Packet32h>(const Packet32h& a) {
+ return (half)_mm512_reduce_add_ph(a);
+}
+
+template <>
+EIGEN_STRONG_INLINE half predux<Packet16h>(const Packet16h& a) {
+ return (half)_mm256_reduce_add_ph(_mm256_castsi256_ph(a));
+}
+
+template <>
+EIGEN_STRONG_INLINE half predux<Packet8h>(const Packet8h& a) {
+ return (half)_mm_reduce_add_ph(_mm_castsi128_ph(a));
+}
+
+// predux_half_dowto4
+template <>
+EIGEN_STRONG_INLINE Packet16h predux_half_dowto4<Packet32h>(const Packet32h& a) {
+#ifdef EIGEN_VECTORIZE_AVX512DQ
+ __m256i lowHalf = _mm256_castps_si256(_mm512_extractf32x8_ps(_mm512_castph_ps(a), 0));
+ __m256i highHalf = _mm256_castps_si256(_mm512_extractf32x8_ps(_mm512_castph_ps(a), 1));
+
+ return Packet16h(padd<Packet16h>(lowHalf, highHalf));
+#else
+ Eigen::half data[32];
+ _mm512_storeu_ph(data, a);
+
+ __m256i lowHalf = _mm256_castph_si256(_mm256_loadu_ph(data));
+ __m256i highHalf = _mm256_castph_si256(_mm256_loadu_ph(data + 16));
+
+ return Packet16h(padd<Packet16h>(lowHalf, highHalf));
+#endif
+}
+
+// predux_max
+
+// predux_min
+
+// predux_mul
+
+#ifdef EIGEN_VECTORIZE_FMA
+
+// pmadd
+
+template <>
+EIGEN_STRONG_INLINE Packet32h pmadd(const Packet32h& a, const Packet32h& b, const Packet32h& c) {
+ return _mm512_fmadd_ph(a, b, c);
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet16h pmadd(const Packet16h& a, const Packet16h& b, const Packet16h& c) {
+ return _mm256_castph_si256(_mm256_fmadd_ph(_mm256_castsi256_ph(a), _mm256_castsi256_ph(b), _mm256_castsi256_ph(c)));
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet8h pmadd(const Packet8h& a, const Packet8h& b, const Packet8h& c) {
+ return _mm_castph_si128(_mm_fmadd_ph(_mm_castsi128_ph(a), _mm_castsi128_ph(b), _mm_castsi128_ph(c)));
+}
+
+// pmsub
+
+template <>
+EIGEN_STRONG_INLINE Packet32h pmsub(const Packet32h& a, const Packet32h& b, const Packet32h& c) {
+ return _mm512_fmsub_ph(a, b, c);
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet16h pmsub(const Packet16h& a, const Packet16h& b, const Packet16h& c) {
+ return _mm256_castph_si256(_mm256_fmsub_ph(_mm256_castsi256_ph(a), _mm256_castsi256_ph(b), _mm256_castsi256_ph(c)));
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet8h pmsub(const Packet8h& a, const Packet8h& b, const Packet8h& c) {
+ return _mm_castph_si128(_mm_fmsub_ph(_mm_castsi128_ph(a), _mm_castsi128_ph(b), _mm_castsi128_ph(c)));
+}
+
+// pnmadd
+
+template <>
+EIGEN_STRONG_INLINE Packet32h pnmadd(const Packet32h& a, const Packet32h& b, const Packet32h& c) {
+ return _mm512_fnmadd_ph(a, b, c);
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet16h pnmadd(const Packet16h& a, const Packet16h& b, const Packet16h& c) {
+ return _mm256_castph_si256(_mm256_fnmadd_ph(_mm256_castsi256_ph(a), _mm256_castsi256_ph(b), _mm256_castsi256_ph(c)));
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet8h pnmadd(const Packet8h& a, const Packet8h& b, const Packet8h& c) {
+ return _mm_castph_si128(_mm_fnmadd_ph(_mm_castsi128_ph(a), _mm_castsi128_ph(b), _mm_castsi128_ph(c)));
+}
+
+// pnmsub
+
+template <>
+EIGEN_STRONG_INLINE Packet32h pnmsub(const Packet32h& a, const Packet32h& b, const Packet32h& c) {
+ return _mm512_fnmsub_ph(a, b, c);
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet16h pnmsub(const Packet16h& a, const Packet16h& b, const Packet16h& c) {
+ return _mm256_castph_si256(_mm256_fnmsub_ph(_mm256_castsi256_ph(a), _mm256_castsi256_ph(b), _mm256_castsi256_ph(c)));
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet8h pnmsub(const Packet8h& a, const Packet8h& b, const Packet8h& c) {
+ return _mm_castph_si128(_mm_fnmsub_ph(_mm_castsi128_ph(a), _mm_castsi128_ph(b), _mm_castsi128_ph(c)));
+}
+
+#endif
+
+// pnegate
+
+template <>
+EIGEN_STRONG_INLINE Packet32h pnegate<Packet32h>(const Packet32h& a) {
+ return _mm512_sub_ph(_mm512_set1_ph(0.0), a);
+}
+
+// pconj
+
+template <>
+EIGEN_STRONG_INLINE Packet32h pconj<Packet32h>(const Packet32h& a) {
+ return a;
+}
+
+// psqrt
+
+template <>
+EIGEN_STRONG_INLINE Packet32h psqrt<Packet32h>(const Packet32h& a) {
+ return _mm512_sqrt_ph(a);
+}
+
+// prsqrt
+
+template <>
+EIGEN_STRONG_INLINE Packet32h prsqrt<Packet32h>(const Packet32h& a) {
+ return _mm512_rsqrt_ph(a);
+}
+
+// preciprocal
+
+template <>
+EIGEN_STRONG_INLINE Packet32h preciprocal<Packet32h>(const Packet32h& a) {
+ return _mm512_rcp_ph(a);
+}
+
+// ptranspose
+
+EIGEN_DEVICE_FUNC inline void ptranspose(PacketBlock<Packet32h, 32>& a) {
+ __m512i t[32];
+
+ EIGEN_UNROLL_LOOP
+ for (int i = 0; i < 16; i++) {
+ t[2 * i] = _mm512_unpacklo_epi16(_mm512_castph_si512(a.packet[2 * i]), _mm512_castph_si512(a.packet[2 * i + 1]));
+ t[2 * i + 1] =
+ _mm512_unpackhi_epi16(_mm512_castph_si512(a.packet[2 * i]), _mm512_castph_si512(a.packet[2 * i + 1]));
+ }
+
+ __m512i p[32];
+
+ EIGEN_UNROLL_LOOP
+ for (int i = 0; i < 8; i++) {
+ p[4 * i] = _mm512_unpacklo_epi32(t[4 * i], t[4 * i + 2]);
+ p[4 * i + 1] = _mm512_unpackhi_epi32(t[4 * i], t[4 * i + 2]);
+ p[4 * i + 2] = _mm512_unpacklo_epi32(t[4 * i + 1], t[4 * i + 3]);
+ p[4 * i + 3] = _mm512_unpackhi_epi32(t[4 * i + 1], t[4 * i + 3]);
+ }
+
+ __m512i q[32];
+
+ EIGEN_UNROLL_LOOP
+ for (int i = 0; i < 4; i++) {
+ q[8 * i] = _mm512_unpacklo_epi64(p[8 * i], p[8 * i + 4]);
+ q[8 * i + 1] = _mm512_unpackhi_epi64(p[8 * i], p[8 * i + 4]);
+ q[8 * i + 2] = _mm512_unpacklo_epi64(p[8 * i + 1], p[8 * i + 5]);
+ q[8 * i + 3] = _mm512_unpackhi_epi64(p[8 * i + 1], p[8 * i + 5]);
+ q[8 * i + 4] = _mm512_unpacklo_epi64(p[8 * i + 2], p[8 * i + 6]);
+ q[8 * i + 5] = _mm512_unpackhi_epi64(p[8 * i + 2], p[8 * i + 6]);
+ q[8 * i + 6] = _mm512_unpacklo_epi64(p[8 * i + 3], p[8 * i + 7]);
+ q[8 * i + 7] = _mm512_unpackhi_epi64(p[8 * i + 3], p[8 * i + 7]);
+ }
+
+ __m512i f[32];
+
+#define PACKET32H_TRANSPOSE_HELPER(X, Y) \
+ do { \
+ f[Y * 8] = _mm512_inserti32x4(f[Y * 8], _mm512_extracti32x4_epi32(q[X * 8], Y), X); \
+ f[Y * 8 + 1] = _mm512_inserti32x4(f[Y * 8 + 1], _mm512_extracti32x4_epi32(q[X * 8 + 1], Y), X); \
+ f[Y * 8 + 2] = _mm512_inserti32x4(f[Y * 8 + 2], _mm512_extracti32x4_epi32(q[X * 8 + 2], Y), X); \
+ f[Y * 8 + 3] = _mm512_inserti32x4(f[Y * 8 + 3], _mm512_extracti32x4_epi32(q[X * 8 + 3], Y), X); \
+ f[Y * 8 + 4] = _mm512_inserti32x4(f[Y * 8 + 4], _mm512_extracti32x4_epi32(q[X * 8 + 4], Y), X); \
+ f[Y * 8 + 5] = _mm512_inserti32x4(f[Y * 8 + 5], _mm512_extracti32x4_epi32(q[X * 8 + 5], Y), X); \
+ f[Y * 8 + 6] = _mm512_inserti32x4(f[Y * 8 + 6], _mm512_extracti32x4_epi32(q[X * 8 + 6], Y), X); \
+ f[Y * 8 + 7] = _mm512_inserti32x4(f[Y * 8 + 7], _mm512_extracti32x4_epi32(q[X * 8 + 7], Y), X); \
+ } while (false);
+
+ PACKET32H_TRANSPOSE_HELPER(0, 0);
+ PACKET32H_TRANSPOSE_HELPER(1, 1);
+ PACKET32H_TRANSPOSE_HELPER(2, 2);
+ PACKET32H_TRANSPOSE_HELPER(3, 3);
+
+ PACKET32H_TRANSPOSE_HELPER(1, 0);
+ PACKET32H_TRANSPOSE_HELPER(2, 0);
+ PACKET32H_TRANSPOSE_HELPER(3, 0);
+ PACKET32H_TRANSPOSE_HELPER(2, 1);
+ PACKET32H_TRANSPOSE_HELPER(3, 1);
+ PACKET32H_TRANSPOSE_HELPER(3, 2);
+
+ PACKET32H_TRANSPOSE_HELPER(0, 1);
+ PACKET32H_TRANSPOSE_HELPER(0, 2);
+ PACKET32H_TRANSPOSE_HELPER(0, 3);
+ PACKET32H_TRANSPOSE_HELPER(1, 2);
+ PACKET32H_TRANSPOSE_HELPER(1, 3);
+ PACKET32H_TRANSPOSE_HELPER(2, 3);
+
+#undef PACKET32H_TRANSPOSE_HELPER
+
+ EIGEN_UNROLL_LOOP
+ for (int i = 0; i < 32; i++) {
+ a.packet[i] = _mm512_castsi512_ph(f[i]);
+ }
+}
+
+EIGEN_DEVICE_FUNC inline void ptranspose(PacketBlock<Packet32h, 4>& a) {
+ __m512i p0, p1, p2, p3, t0, t1, t2, t3, a0, a1, a2, a3;
+ t0 = _mm512_unpacklo_epi16(_mm512_castph_si512(a.packet[0]), _mm512_castph_si512(a.packet[1]));
+ t1 = _mm512_unpackhi_epi16(_mm512_castph_si512(a.packet[0]), _mm512_castph_si512(a.packet[1]));
+ t2 = _mm512_unpacklo_epi16(_mm512_castph_si512(a.packet[2]), _mm512_castph_si512(a.packet[3]));
+ t3 = _mm512_unpackhi_epi16(_mm512_castph_si512(a.packet[2]), _mm512_castph_si512(a.packet[3]));
+
+ p0 = _mm512_unpacklo_epi32(t0, t2);
+ p1 = _mm512_unpackhi_epi32(t0, t2);
+ p2 = _mm512_unpacklo_epi32(t1, t3);
+ p3 = _mm512_unpackhi_epi32(t1, t3);
+
+ a0 = p0;
+ a1 = p1;
+ a2 = p2;
+ a3 = p3;
+
+ a0 = _mm512_inserti32x4(a0, _mm512_extracti32x4_epi32(p1, 0), 1);
+ a1 = _mm512_inserti32x4(a1, _mm512_extracti32x4_epi32(p0, 1), 0);
+
+ a0 = _mm512_inserti32x4(a0, _mm512_extracti32x4_epi32(p2, 0), 2);
+ a2 = _mm512_inserti32x4(a2, _mm512_extracti32x4_epi32(p0, 2), 0);
+
+ a0 = _mm512_inserti32x4(a0, _mm512_extracti32x4_epi32(p3, 0), 3);
+ a3 = _mm512_inserti32x4(a3, _mm512_extracti32x4_epi32(p0, 3), 0);
+
+ a1 = _mm512_inserti32x4(a1, _mm512_extracti32x4_epi32(p2, 1), 2);
+ a2 = _mm512_inserti32x4(a2, _mm512_extracti32x4_epi32(p1, 2), 1);
+
+ a2 = _mm512_inserti32x4(a2, _mm512_extracti32x4_epi32(p3, 2), 3);
+ a3 = _mm512_inserti32x4(a3, _mm512_extracti32x4_epi32(p2, 3), 2);
+
+ a1 = _mm512_inserti32x4(a1, _mm512_extracti32x4_epi32(p3, 1), 3);
+ a3 = _mm512_inserti32x4(a3, _mm512_extracti32x4_epi32(p1, 3), 1);
+
+ a.packet[0] = _mm512_castsi512_ph(a0);
+ a.packet[1] = _mm512_castsi512_ph(a1);
+ a.packet[2] = _mm512_castsi512_ph(a2);
+ a.packet[3] = _mm512_castsi512_ph(a3);
+}
+
+// preverse
+
+template <>
+EIGEN_STRONG_INLINE Packet32h preverse(const Packet32h& a) {
+ return _mm512_permutexvar_ph(_mm512_set_epi16(0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19,
+ 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31),
+ a);
+}
+
+// pscatter
+
+template <>
+EIGEN_STRONG_INLINE void pscatter<half, Packet32h>(half* to, const Packet32h& from, Index stride) {
+ EIGEN_ALIGN64 half aux[32];
+ pstore(aux, from);
+
+ EIGEN_UNROLL_LOOP
+ for (int i = 0; i < 32; i++) {
+ to[stride * i] = aux[i];
+ }
+}
+
+// pgather
+
+template <>
+EIGEN_STRONG_INLINE Packet32h pgather<Eigen::half, Packet32h>(const Eigen::half* from, Index stride) {
+ return _mm512_castsi512_ph(_mm512_set_epi16(
+ from[31 * stride].x, from[30 * stride].x, from[29 * stride].x, from[28 * stride].x, from[27 * stride].x,
+ from[26 * stride].x, from[25 * stride].x, from[24 * stride].x, from[23 * stride].x, from[22 * stride].x,
+ from[21 * stride].x, from[20 * stride].x, from[19 * stride].x, from[18 * stride].x, from[17 * stride].x,
+ from[16 * stride].x, from[15 * stride].x, from[14 * stride].x, from[13 * stride].x, from[12 * stride].x,
+ from[11 * stride].x, from[10 * stride].x, from[9 * stride].x, from[8 * stride].x, from[7 * stride].x,
+ from[6 * stride].x, from[5 * stride].x, from[4 * stride].x, from[3 * stride].x, from[2 * stride].x,
+ from[1 * stride].x, from[0 * stride].x));
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet16h pcos<Packet16h>(const Packet16h&);
+template <>
+EIGEN_STRONG_INLINE Packet16h psin<Packet16h>(const Packet16h&);
+template <>
+EIGEN_STRONG_INLINE Packet16h plog<Packet16h>(const Packet16h&);
+template <>
+EIGEN_STRONG_INLINE Packet16h plog2<Packet16h>(const Packet16h&);
+template <>
+EIGEN_STRONG_INLINE Packet16h plog1p<Packet16h>(const Packet16h&);
+template <>
+EIGEN_STRONG_INLINE Packet16h pexp<Packet16h>(const Packet16h&);
+template <>
+EIGEN_STRONG_INLINE Packet16h pexpm1<Packet16h>(const Packet16h&);
+template <>
+EIGEN_STRONG_INLINE Packet16h ptanh<Packet16h>(const Packet16h&);
+template <>
+EIGEN_STRONG_INLINE Packet16h pfrexp<Packet16h>(const Packet16h&, Packet16h&);
+template <>
+EIGEN_STRONG_INLINE Packet16h pldexp<Packet16h>(const Packet16h&, const Packet16h&);
+
+EIGEN_STRONG_INLINE Packet32h combine2Packet16h(const Packet16h& a, const Packet16h& b) {
+ __m512d result = _mm512_undefined_pd();
+ result = _mm512_insertf64x4(result, _mm256_castsi256_pd(a), 0);
+ result = _mm512_insertf64x4(result, _mm256_castsi256_pd(b), 1);
+ return _mm512_castpd_ph(result);
+}
+
+EIGEN_STRONG_INLINE void extract2Packet16h(const Packet32h& x, Packet16h& a, Packet16h& b) {
+ a = _mm256_castpd_si256(_mm512_extractf64x4_pd(_mm512_castph_pd(x), 0));
+ b = _mm256_castpd_si256(_mm512_extractf64x4_pd(_mm512_castph_pd(x), 1));
+}
+
+// psin
+template <>
+EIGEN_STRONG_INLINE Packet32h psin<Packet32h>(const Packet32h& a) {
+ Packet16h low;
+ Packet16h high;
+ extract2Packet16h(a, low, high);
+
+ Packet16h lowOut = psin(low);
+ Packet16h highOut = psin(high);
+
+ return combine2Packet16h(lowOut, highOut);
+}
+
+// pcos
+template <>
+EIGEN_STRONG_INLINE Packet32h pcos<Packet32h>(const Packet32h& a) {
+ Packet16h low;
+ Packet16h high;
+ extract2Packet16h(a, low, high);
+
+ Packet16h lowOut = pcos(low);
+ Packet16h highOut = pcos(high);
+
+ return combine2Packet16h(lowOut, highOut);
+}
+
+// plog
+template <>
+EIGEN_STRONG_INLINE Packet32h plog<Packet32h>(const Packet32h& a) {
+ Packet16h low;
+ Packet16h high;
+ extract2Packet16h(a, low, high);
+
+ Packet16h lowOut = plog(low);
+ Packet16h highOut = plog(high);
+
+ return combine2Packet16h(lowOut, highOut);
+}
+
+// plog2
+template <>
+EIGEN_STRONG_INLINE Packet32h plog2<Packet32h>(const Packet32h& a) {
+ Packet16h low;
+ Packet16h high;
+ extract2Packet16h(a, low, high);
+
+ Packet16h lowOut = plog2(low);
+ Packet16h highOut = plog2(high);
+
+ return combine2Packet16h(lowOut, highOut);
+}
+
+// plog1p
+template <>
+EIGEN_STRONG_INLINE Packet32h plog1p<Packet32h>(const Packet32h& a) {
+ Packet16h low;
+ Packet16h high;
+ extract2Packet16h(a, low, high);
+
+ Packet16h lowOut = plog1p(low);
+ Packet16h highOut = plog1p(high);
+
+ return combine2Packet16h(lowOut, highOut);
+}
+
+// pexp
+template <>
+EIGEN_STRONG_INLINE Packet32h pexp<Packet32h>(const Packet32h& a) {
+ Packet16h low;
+ Packet16h high;
+ extract2Packet16h(a, low, high);
+
+ Packet16h lowOut = pexp(low);
+ Packet16h highOut = pexp(high);
+
+ return combine2Packet16h(lowOut, highOut);
+}
+
+// pexpm1
+template <>
+EIGEN_STRONG_INLINE Packet32h pexpm1<Packet32h>(const Packet32h& a) {
+ Packet16h low;
+ Packet16h high;
+ extract2Packet16h(a, low, high);
+
+ Packet16h lowOut = pexpm1(low);
+ Packet16h highOut = pexpm1(high);
+
+ return combine2Packet16h(lowOut, highOut);
+}
+
+// ptanh
+template <>
+EIGEN_STRONG_INLINE Packet32h ptanh<Packet32h>(const Packet32h& a) {
+ Packet16h low;
+ Packet16h high;
+ extract2Packet16h(a, low, high);
+
+ Packet16h lowOut = ptanh(low);
+ Packet16h highOut = ptanh(high);
+
+ return combine2Packet16h(lowOut, highOut);
+}
+
+// pfrexp
+template <>
+EIGEN_STRONG_INLINE Packet32h pfrexp<Packet32h>(const Packet32h& a, Packet32h& exponent) {
+ Packet16h low;
+ Packet16h high;
+ extract2Packet16h(a, low, high);
+
+ Packet16h exp1 = _mm256_undefined_si256();
+ Packet16h exp2 = _mm256_undefined_si256();
+
+ Packet16h lowOut = pfrexp(low, exp1);
+ Packet16h highOut = pfrexp(high, exp2);
+
+ exponent = combine2Packet16h(exp1, exp2);
+
+ return combine2Packet16h(lowOut, highOut);
+}
+
+// pldexp
+template <>
+EIGEN_STRONG_INLINE Packet32h pldexp<Packet32h>(const Packet32h& a, const Packet32h& exponent) {
+ Packet16h low;
+ Packet16h high;
+ extract2Packet16h(a, low, high);
+
+ Packet16h exp1;
+ Packet16h exp2;
+ extract2Packet16h(exponent, exp1, exp2);
+
+ Packet16h lowOut = pldexp(low, exp1);
+ Packet16h highOut = pldexp(high, exp2);
+
+ return combine2Packet16h(lowOut, highOut);
+}
+
+} // end namespace internal
+} // end namespace Eigen
+
+#endif // EIGEN_PACKET_MATH_FP16_AVX512_H
\ No newline at end of file
diff --git a/Eigen/src/Core/arch/AVX512/TrsmKernel.h b/Eigen/src/Core/arch/AVX512/TrsmKernel.h
new file mode 100644
index 0000000..edd6ef3
--- /dev/null
+++ b/Eigen/src/Core/arch/AVX512/TrsmKernel.h
@@ -0,0 +1,1185 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2022 Intel Corporation
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_CORE_ARCH_AVX512_TRSM_KERNEL_H
+#define EIGEN_CORE_ARCH_AVX512_TRSM_KERNEL_H
+
+#include "../../InternalHeaderCheck.h"
+
+#if !defined(EIGEN_USE_AVX512_TRSM_KERNELS)
+#define EIGEN_USE_AVX512_TRSM_KERNELS 1
+#endif
+
+#if EIGEN_USE_AVX512_TRSM_KERNELS
+#if !defined(EIGEN_USE_AVX512_TRSM_R_KERNELS)
+#define EIGEN_USE_AVX512_TRSM_R_KERNELS 1
+#endif
+#if !defined(EIGEN_USE_AVX512_TRSM_L_KERNELS)
+#define EIGEN_USE_AVX512_TRSM_L_KERNELS 1
+#endif
+#else // EIGEN_USE_AVX512_TRSM_KERNELS == 0
+#define EIGEN_USE_AVX512_TRSM_R_KERNELS 0
+#define EIGEN_USE_AVX512_TRSM_L_KERNELS 0
+#endif
+
+// Need this for some std::min calls.
+#ifdef min
+#undef min
+#endif
+
+namespace Eigen {
+namespace internal {
+
+#define EIGEN_AVX_MAX_NUM_ACC (int64_t(24))
+#define EIGEN_AVX_MAX_NUM_ROW (int64_t(8)) // Denoted L in code.
+#define EIGEN_AVX_MAX_K_UNROL (int64_t(4))
+#define EIGEN_AVX_B_LOAD_SETS (int64_t(2))
+#define EIGEN_AVX_MAX_A_BCAST (int64_t(2))
+typedef Packet16f vecFullFloat;
+typedef Packet8d vecFullDouble;
+typedef Packet8f vecHalfFloat;
+typedef Packet4d vecHalfDouble;
+
+// Compile-time unrolls are implemented here.
+// Note: this depends on macros and typedefs above.
+#include "TrsmUnrolls.inc"
+
+#if (EIGEN_USE_AVX512_TRSM_KERNELS) && (EIGEN_COMP_CLANG != 0)
+/**
+ * For smaller problem sizes, and certain compilers, using the optimized kernels trsmKernelL/R directly
+ * is faster than the packed versions in TriangularSolverMatrix.h.
+ *
+ * The current heuristic is based on having having all arrays used in the largest gemm-update
+ * in triSolve fit in roughly L2Cap (percentage) of the L2 cache. These cutoffs are a bit conservative and could be
+ * larger for some trsm cases.
+ * The formula:
+ *
+ * (L*M + M*N + L*N)*sizeof(Scalar) < L2Cache*L2Cap
+ *
+ * L = number of rows to solve at a time
+ * N = number of rhs
+ * M = Dimension of triangular matrix
+ *
+ */
+#if !defined(EIGEN_ENABLE_AVX512_NOCOPY_TRSM_CUTOFFS)
+#define EIGEN_ENABLE_AVX512_NOCOPY_TRSM_CUTOFFS 1
+#endif
+
+#if EIGEN_ENABLE_AVX512_NOCOPY_TRSM_CUTOFFS
+
+#if EIGEN_USE_AVX512_TRSM_R_KERNELS
+#if !defined(EIGEN_ENABLE_AVX512_NOCOPY_TRSM_R_CUTOFFS)
+#define EIGEN_ENABLE_AVX512_NOCOPY_TRSM_R_CUTOFFS 1
+#endif // !defined(EIGEN_ENABLE_AVX512_NOCOPY_TRSM_R_CUTOFFS)
+#endif
+
+#if EIGEN_USE_AVX512_TRSM_L_KERNELS
+#if !defined(EIGEN_ENABLE_AVX512_NOCOPY_TRSM_L_CUTOFFS)
+#define EIGEN_ENABLE_AVX512_NOCOPY_TRSM_L_CUTOFFS 1
+#endif
+#endif // EIGEN_USE_AVX512_TRSM_L_KERNELS
+
+#else // EIGEN_ENABLE_AVX512_NOCOPY_TRSM_CUTOFFS == 0
+#define EIGEN_ENABLE_AVX512_NOCOPY_TRSM_R_CUTOFFS 0
+#define EIGEN_ENABLE_AVX512_NOCOPY_TRSM_L_CUTOFFS 0
+#endif // EIGEN_ENABLE_AVX512_NOCOPY_TRSM_CUTOFFS
+
+template <typename Scalar>
+int64_t avx512_trsm_cutoff(int64_t L2Size, int64_t N, double L2Cap) {
+ const int64_t U3 = 3 * packet_traits<Scalar>::size;
+ const int64_t MaxNb = 5 * U3;
+ int64_t Nb = std::min(MaxNb, N);
+ double cutoff_d =
+ (((L2Size * L2Cap) / (sizeof(Scalar))) - (EIGEN_AVX_MAX_NUM_ROW)*Nb) / ((EIGEN_AVX_MAX_NUM_ROW) + Nb);
+ int64_t cutoff_l = static_cast<int64_t>(cutoff_d);
+ return (cutoff_l / EIGEN_AVX_MAX_NUM_ROW) * EIGEN_AVX_MAX_NUM_ROW;
+}
+#else // !(EIGEN_USE_AVX512_TRSM_KERNELS) || !(EIGEN_COMP_CLANG != 0)
+#define EIGEN_ENABLE_AVX512_NOCOPY_TRSM_CUTOFFS 0
+#define EIGEN_ENABLE_AVX512_NOCOPY_TRSM_R_CUTOFFS 0
+#define EIGEN_ENABLE_AVX512_NOCOPY_TRSM_L_CUTOFFS 0
+#endif
+
+/**
+ * Used by gemmKernel for the case A/B row-major and C col-major.
+ */
+template <typename Scalar, typename vec, int64_t unrollM, int64_t unrollN, bool remM, bool remN>
+static EIGEN_ALWAYS_INLINE void transStoreC(PacketBlock<vec, EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS> &zmm,
+ Scalar *C_arr, int64_t LDC, int64_t remM_ = 0, int64_t remN_ = 0) {
+ EIGEN_UNUSED_VARIABLE(remN_);
+ EIGEN_UNUSED_VARIABLE(remM_);
+ using urolls = unrolls::trans<Scalar>;
+
+ constexpr int64_t U3 = urolls::PacketSize * 3;
+ constexpr int64_t U2 = urolls::PacketSize * 2;
+ constexpr int64_t U1 = urolls::PacketSize * 1;
+
+ static_assert(unrollN == U1 || unrollN == U2 || unrollN == U3, "unrollN should be a multiple of PacketSize");
+ static_assert(unrollM == EIGEN_AVX_MAX_NUM_ROW, "unrollM should be equal to EIGEN_AVX_MAX_NUM_ROW");
+
+ urolls::template transpose<unrollN, 0>(zmm);
+ EIGEN_IF_CONSTEXPR(unrollN > U2) urolls::template transpose<unrollN, 2>(zmm);
+ EIGEN_IF_CONSTEXPR(unrollN > U1) urolls::template transpose<unrollN, 1>(zmm);
+
+ static_assert((remN && unrollN == U1) || !remN, "When handling N remainder set unrollN=U1");
+ EIGEN_IF_CONSTEXPR(!remN) {
+ urolls::template storeC<std::min(unrollN, U1), unrollN, 0, remM>(C_arr, LDC, zmm, remM_);
+ EIGEN_IF_CONSTEXPR(unrollN > U1) {
+ constexpr int64_t unrollN_ = std::min(unrollN - U1, U1);
+ urolls::template storeC<unrollN_, unrollN, 1, remM>(C_arr + U1 * LDC, LDC, zmm, remM_);
+ }
+ EIGEN_IF_CONSTEXPR(unrollN > U2) {
+ constexpr int64_t unrollN_ = std::min(unrollN - U2, U1);
+ urolls::template storeC<unrollN_, unrollN, 2, remM>(C_arr + U2 * LDC, LDC, zmm, remM_);
+ }
+ }
+ else {
+ EIGEN_IF_CONSTEXPR((std::is_same<Scalar, float>::value)) {
+ // Note: without "if constexpr" this section of code will also be
+ // parsed by the compiler so each of the storeC will still be instantiated.
+ // We use enable_if in aux_storeC to set it to an empty function for
+ // these cases.
+ if (remN_ == 15)
+ urolls::template storeC<15, unrollN, 0, remM>(C_arr, LDC, zmm, remM_);
+ else if (remN_ == 14)
+ urolls::template storeC<14, unrollN, 0, remM>(C_arr, LDC, zmm, remM_);
+ else if (remN_ == 13)
+ urolls::template storeC<13, unrollN, 0, remM>(C_arr, LDC, zmm, remM_);
+ else if (remN_ == 12)
+ urolls::template storeC<12, unrollN, 0, remM>(C_arr, LDC, zmm, remM_);
+ else if (remN_ == 11)
+ urolls::template storeC<11, unrollN, 0, remM>(C_arr, LDC, zmm, remM_);
+ else if (remN_ == 10)
+ urolls::template storeC<10, unrollN, 0, remM>(C_arr, LDC, zmm, remM_);
+ else if (remN_ == 9)
+ urolls::template storeC<9, unrollN, 0, remM>(C_arr, LDC, zmm, remM_);
+ else if (remN_ == 8)
+ urolls::template storeC<8, unrollN, 0, remM>(C_arr, LDC, zmm, remM_);
+ else if (remN_ == 7)
+ urolls::template storeC<7, unrollN, 0, remM>(C_arr, LDC, zmm, remM_);
+ else if (remN_ == 6)
+ urolls::template storeC<6, unrollN, 0, remM>(C_arr, LDC, zmm, remM_);
+ else if (remN_ == 5)
+ urolls::template storeC<5, unrollN, 0, remM>(C_arr, LDC, zmm, remM_);
+ else if (remN_ == 4)
+ urolls::template storeC<4, unrollN, 0, remM>(C_arr, LDC, zmm, remM_);
+ else if (remN_ == 3)
+ urolls::template storeC<3, unrollN, 0, remM>(C_arr, LDC, zmm, remM_);
+ else if (remN_ == 2)
+ urolls::template storeC<2, unrollN, 0, remM>(C_arr, LDC, zmm, remM_);
+ else if (remN_ == 1)
+ urolls::template storeC<1, unrollN, 0, remM>(C_arr, LDC, zmm, remM_);
+ }
+ else {
+ if (remN_ == 7)
+ urolls::template storeC<7, unrollN, 0, remM>(C_arr, LDC, zmm, remM_);
+ else if (remN_ == 6)
+ urolls::template storeC<6, unrollN, 0, remM>(C_arr, LDC, zmm, remM_);
+ else if (remN_ == 5)
+ urolls::template storeC<5, unrollN, 0, remM>(C_arr, LDC, zmm, remM_);
+ else if (remN_ == 4)
+ urolls::template storeC<4, unrollN, 0, remM>(C_arr, LDC, zmm, remM_);
+ else if (remN_ == 3)
+ urolls::template storeC<3, unrollN, 0, remM>(C_arr, LDC, zmm, remM_);
+ else if (remN_ == 2)
+ urolls::template storeC<2, unrollN, 0, remM>(C_arr, LDC, zmm, remM_);
+ else if (remN_ == 1)
+ urolls::template storeC<1, unrollN, 0, remM>(C_arr, LDC, zmm, remM_);
+ }
+ }
+}
+
+/**
+ * GEMM like operation for trsm panel updates.
+ * Computes: C -= A*B
+ * K must be multipe of 4.
+ *
+ * Unrolls used are {1,2,4,8}x{U1,U2,U3};
+ * For good performance we want K to be large with M/N relatively small, but also large enough
+ * to use the {8,U3} unroll block.
+ *
+ * isARowMajor: is A_arr row-major?
+ * isCRowMajor: is C_arr row-major? (B_arr is assumed to be row-major).
+ * isAdd: C += A*B or C -= A*B (used by trsm)
+ * handleKRem: Handle arbitrary K? This is not needed for trsm.
+ */
+template <typename Scalar, bool isARowMajor, bool isCRowMajor, bool isAdd, bool handleKRem>
+void gemmKernel(Scalar *A_arr, Scalar *B_arr, Scalar *C_arr, int64_t M, int64_t N, int64_t K, int64_t LDA, int64_t LDB,
+ int64_t LDC) {
+ using urolls = unrolls::gemm<Scalar, isAdd>;
+ constexpr int64_t U3 = urolls::PacketSize * 3;
+ constexpr int64_t U2 = urolls::PacketSize * 2;
+ constexpr int64_t U1 = urolls::PacketSize * 1;
+ using vec = typename std::conditional<std::is_same<Scalar, float>::value, vecFullFloat, vecFullDouble>::type;
+ int64_t N_ = (N / U3) * U3;
+ int64_t M_ = (M / EIGEN_AVX_MAX_NUM_ROW) * EIGEN_AVX_MAX_NUM_ROW;
+ int64_t K_ = (K / EIGEN_AVX_MAX_K_UNROL) * EIGEN_AVX_MAX_K_UNROL;
+ int64_t j = 0;
+ for (; j < N_; j += U3) {
+ constexpr int64_t EIGEN_AVX_MAX_B_LOAD = EIGEN_AVX_B_LOAD_SETS * 3;
+ int64_t i = 0;
+ for (; i < M_; i += EIGEN_AVX_MAX_NUM_ROW) {
+ Scalar *A_t = &A_arr[idA<isARowMajor>(i, 0, LDA)], *B_t = &B_arr[0 * LDB + j];
+ PacketBlock<vec, EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS> zmm;
+ urolls::template setzero<3, EIGEN_AVX_MAX_NUM_ROW>(zmm);
+ for (int64_t k = 0; k < K_; k += EIGEN_AVX_MAX_K_UNROL) {
+ urolls::template microKernel<isARowMajor, 3, EIGEN_AVX_MAX_NUM_ROW, EIGEN_AVX_MAX_K_UNROL, EIGEN_AVX_MAX_B_LOAD,
+ EIGEN_AVX_MAX_A_BCAST>(B_t, A_t, LDB, LDA, zmm);
+ B_t += EIGEN_AVX_MAX_K_UNROL * LDB;
+ EIGEN_IF_CONSTEXPR(isARowMajor) A_t += EIGEN_AVX_MAX_K_UNROL;
+ else A_t += EIGEN_AVX_MAX_K_UNROL * LDA;
+ }
+ EIGEN_IF_CONSTEXPR(handleKRem) {
+ for (int64_t k = K_; k < K; k++) {
+ urolls::template microKernel<isARowMajor, 3, EIGEN_AVX_MAX_NUM_ROW, 1, EIGEN_AVX_B_LOAD_SETS * 3,
+ EIGEN_AVX_MAX_A_BCAST>(B_t, A_t, LDB, LDA, zmm);
+ B_t += LDB;
+ EIGEN_IF_CONSTEXPR(isARowMajor) A_t++;
+ else A_t += LDA;
+ }
+ }
+ EIGEN_IF_CONSTEXPR(isCRowMajor) {
+ urolls::template updateC<3, EIGEN_AVX_MAX_NUM_ROW>(&C_arr[i * LDC + j], LDC, zmm);
+ urolls::template storeC<3, EIGEN_AVX_MAX_NUM_ROW>(&C_arr[i * LDC + j], LDC, zmm);
+ }
+ else {
+ transStoreC<Scalar, vec, EIGEN_AVX_MAX_NUM_ROW, U3, false, false>(zmm, &C_arr[i + j * LDC], LDC);
+ }
+ }
+ if (M - i >= 4) { // Note: this block assumes EIGEN_AVX_MAX_NUM_ROW = 8. Should be removed otherwise
+ Scalar *A_t = &A_arr[idA<isARowMajor>(i, 0, LDA)];
+ Scalar *B_t = &B_arr[0 * LDB + j];
+ PacketBlock<vec, EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS> zmm;
+ urolls::template setzero<3, 4>(zmm);
+ for (int64_t k = 0; k < K_; k += EIGEN_AVX_MAX_K_UNROL) {
+ urolls::template microKernel<isARowMajor, 3, 4, EIGEN_AVX_MAX_K_UNROL, EIGEN_AVX_B_LOAD_SETS * 3,
+ EIGEN_AVX_MAX_A_BCAST>(B_t, A_t, LDB, LDA, zmm);
+ B_t += EIGEN_AVX_MAX_K_UNROL * LDB;
+ EIGEN_IF_CONSTEXPR(isARowMajor) A_t += EIGEN_AVX_MAX_K_UNROL;
+ else A_t += EIGEN_AVX_MAX_K_UNROL * LDA;
+ }
+ EIGEN_IF_CONSTEXPR(handleKRem) {
+ for (int64_t k = K_; k < K; k++) {
+ urolls::template microKernel<isARowMajor, 3, 4, 1, EIGEN_AVX_B_LOAD_SETS * 3, EIGEN_AVX_MAX_A_BCAST>(
+ B_t, A_t, LDB, LDA, zmm);
+ B_t += LDB;
+ EIGEN_IF_CONSTEXPR(isARowMajor) A_t++;
+ else A_t += LDA;
+ }
+ }
+ EIGEN_IF_CONSTEXPR(isCRowMajor) {
+ urolls::template updateC<3, 4>(&C_arr[i * LDC + j], LDC, zmm);
+ urolls::template storeC<3, 4>(&C_arr[i * LDC + j], LDC, zmm);
+ }
+ else {
+ transStoreC<Scalar, vec, EIGEN_AVX_MAX_NUM_ROW, U3, true, false>(zmm, &C_arr[i + j * LDC], LDC, 4);
+ }
+ i += 4;
+ }
+ if (M - i >= 2) {
+ Scalar *A_t = &A_arr[idA<isARowMajor>(i, 0, LDA)];
+ Scalar *B_t = &B_arr[0 * LDB + j];
+ PacketBlock<vec, EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS> zmm;
+ urolls::template setzero<3, 2>(zmm);
+ for (int64_t k = 0; k < K_; k += EIGEN_AVX_MAX_K_UNROL) {
+ urolls::template microKernel<isARowMajor, 3, 2, EIGEN_AVX_MAX_K_UNROL, EIGEN_AVX_B_LOAD_SETS * 3,
+ EIGEN_AVX_MAX_A_BCAST>(B_t, A_t, LDB, LDA, zmm);
+ B_t += EIGEN_AVX_MAX_K_UNROL * LDB;
+ EIGEN_IF_CONSTEXPR(isARowMajor) A_t += EIGEN_AVX_MAX_K_UNROL;
+ else A_t += EIGEN_AVX_MAX_K_UNROL * LDA;
+ }
+ EIGEN_IF_CONSTEXPR(handleKRem) {
+ for (int64_t k = K_; k < K; k++) {
+ urolls::template microKernel<isARowMajor, 3, 2, 1, EIGEN_AVX_B_LOAD_SETS * 3, EIGEN_AVX_MAX_A_BCAST>(
+ B_t, A_t, LDB, LDA, zmm);
+ B_t += LDB;
+ EIGEN_IF_CONSTEXPR(isARowMajor) A_t++;
+ else A_t += LDA;
+ }
+ }
+ EIGEN_IF_CONSTEXPR(isCRowMajor) {
+ urolls::template updateC<3, 2>(&C_arr[i * LDC + j], LDC, zmm);
+ urolls::template storeC<3, 2>(&C_arr[i * LDC + j], LDC, zmm);
+ }
+ else {
+ transStoreC<Scalar, vec, EIGEN_AVX_MAX_NUM_ROW, U3, true, false>(zmm, &C_arr[i + j * LDC], LDC, 2);
+ }
+ i += 2;
+ }
+ if (M - i > 0) {
+ Scalar *A_t = &A_arr[idA<isARowMajor>(i, 0, LDA)];
+ Scalar *B_t = &B_arr[0 * LDB + j];
+ PacketBlock<vec, EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS> zmm;
+ urolls::template setzero<3, 1>(zmm);
+ {
+ for (int64_t k = 0; k < K_; k += EIGEN_AVX_MAX_K_UNROL) {
+ urolls::template microKernel<isARowMajor, 3, 1, EIGEN_AVX_MAX_K_UNROL, EIGEN_AVX_B_LOAD_SETS * 3, 1>(
+ B_t, A_t, LDB, LDA, zmm);
+ B_t += EIGEN_AVX_MAX_K_UNROL * LDB;
+ EIGEN_IF_CONSTEXPR(isARowMajor) A_t += EIGEN_AVX_MAX_K_UNROL;
+ else A_t += EIGEN_AVX_MAX_K_UNROL * LDA;
+ }
+ EIGEN_IF_CONSTEXPR(handleKRem) {
+ for (int64_t k = K_; k < K; k++) {
+ urolls::template microKernel<isARowMajor, 3, 1, 1, EIGEN_AVX_B_LOAD_SETS * 3, 1>(B_t, A_t, LDB, LDA, zmm);
+ B_t += LDB;
+ EIGEN_IF_CONSTEXPR(isARowMajor) A_t++;
+ else A_t += LDA;
+ }
+ }
+ EIGEN_IF_CONSTEXPR(isCRowMajor) {
+ urolls::template updateC<3, 1>(&C_arr[i * LDC + j], LDC, zmm);
+ urolls::template storeC<3, 1>(&C_arr[i * LDC + j], LDC, zmm);
+ }
+ else {
+ transStoreC<Scalar, vec, EIGEN_AVX_MAX_NUM_ROW, U3, true, false>(zmm, &C_arr[i + j * LDC], LDC, 1);
+ }
+ }
+ }
+ }
+ if (N - j >= U2) {
+ constexpr int64_t EIGEN_AVX_MAX_B_LOAD = EIGEN_AVX_B_LOAD_SETS * 2;
+ int64_t i = 0;
+ for (; i < M_; i += EIGEN_AVX_MAX_NUM_ROW) {
+ Scalar *A_t = &A_arr[idA<isARowMajor>(i, 0, LDA)], *B_t = &B_arr[0 * LDB + j];
+ EIGEN_IF_CONSTEXPR(isCRowMajor) B_t = &B_arr[0 * LDB + j];
+ PacketBlock<vec, EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS> zmm;
+ urolls::template setzero<2, EIGEN_AVX_MAX_NUM_ROW>(zmm);
+ for (int64_t k = 0; k < K_; k += EIGEN_AVX_MAX_K_UNROL) {
+ urolls::template microKernel<isARowMajor, 2, EIGEN_AVX_MAX_NUM_ROW, EIGEN_AVX_MAX_K_UNROL, EIGEN_AVX_MAX_B_LOAD,
+ EIGEN_AVX_MAX_A_BCAST>(B_t, A_t, LDB, LDA, zmm);
+ B_t += EIGEN_AVX_MAX_K_UNROL * LDB;
+ EIGEN_IF_CONSTEXPR(isARowMajor) A_t += EIGEN_AVX_MAX_K_UNROL;
+ else A_t += EIGEN_AVX_MAX_K_UNROL * LDA;
+ }
+ EIGEN_IF_CONSTEXPR(handleKRem) {
+ for (int64_t k = K_; k < K; k++) {
+ urolls::template microKernel<isARowMajor, 2, EIGEN_AVX_MAX_NUM_ROW, 1, EIGEN_AVX_MAX_B_LOAD,
+ EIGEN_AVX_MAX_A_BCAST>(B_t, A_t, LDB, LDA, zmm);
+ B_t += LDB;
+ EIGEN_IF_CONSTEXPR(isARowMajor) A_t++;
+ else A_t += LDA;
+ }
+ }
+ EIGEN_IF_CONSTEXPR(isCRowMajor) {
+ urolls::template updateC<2, EIGEN_AVX_MAX_NUM_ROW>(&C_arr[i * LDC + j], LDC, zmm);
+ urolls::template storeC<2, EIGEN_AVX_MAX_NUM_ROW>(&C_arr[i * LDC + j], LDC, zmm);
+ }
+ else {
+ transStoreC<Scalar, vec, EIGEN_AVX_MAX_NUM_ROW, U2, false, false>(zmm, &C_arr[i + j * LDC], LDC);
+ }
+ }
+ if (M - i >= 4) { // Note: this block assumes EIGEN_AVX_MAX_NUM_ROW = 8. Should be removed otherwise
+ Scalar *A_t = &A_arr[idA<isARowMajor>(i, 0, LDA)];
+ Scalar *B_t = &B_arr[0 * LDB + j];
+ PacketBlock<vec, EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS> zmm;
+ urolls::template setzero<2, 4>(zmm);
+ for (int64_t k = 0; k < K_; k += EIGEN_AVX_MAX_K_UNROL) {
+ urolls::template microKernel<isARowMajor, 2, 4, EIGEN_AVX_MAX_K_UNROL, EIGEN_AVX_MAX_B_LOAD,
+ EIGEN_AVX_MAX_A_BCAST>(B_t, A_t, LDB, LDA, zmm);
+ B_t += EIGEN_AVX_MAX_K_UNROL * LDB;
+ EIGEN_IF_CONSTEXPR(isARowMajor) A_t += EIGEN_AVX_MAX_K_UNROL;
+ else A_t += EIGEN_AVX_MAX_K_UNROL * LDA;
+ }
+ EIGEN_IF_CONSTEXPR(handleKRem) {
+ for (int64_t k = K_; k < K; k++) {
+ urolls::template microKernel<isARowMajor, 2, 4, 1, EIGEN_AVX_MAX_B_LOAD, EIGEN_AVX_MAX_A_BCAST>(B_t, A_t, LDB,
+ LDA, zmm);
+ B_t += LDB;
+ EIGEN_IF_CONSTEXPR(isARowMajor) A_t++;
+ else A_t += LDA;
+ }
+ }
+ EIGEN_IF_CONSTEXPR(isCRowMajor) {
+ urolls::template updateC<2, 4>(&C_arr[i * LDC + j], LDC, zmm);
+ urolls::template storeC<2, 4>(&C_arr[i * LDC + j], LDC, zmm);
+ }
+ else {
+ transStoreC<Scalar, vec, EIGEN_AVX_MAX_NUM_ROW, U2, true, false>(zmm, &C_arr[i + j * LDC], LDC, 4);
+ }
+ i += 4;
+ }
+ if (M - i >= 2) {
+ Scalar *A_t = &A_arr[idA<isARowMajor>(i, 0, LDA)];
+ Scalar *B_t = &B_arr[0 * LDB + j];
+ PacketBlock<vec, EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS> zmm;
+ urolls::template setzero<2, 2>(zmm);
+ for (int64_t k = 0; k < K_; k += EIGEN_AVX_MAX_K_UNROL) {
+ urolls::template microKernel<isARowMajor, 2, 2, EIGEN_AVX_MAX_K_UNROL, EIGEN_AVX_MAX_B_LOAD,
+ EIGEN_AVX_MAX_A_BCAST>(B_t, A_t, LDB, LDA, zmm);
+ B_t += EIGEN_AVX_MAX_K_UNROL * LDB;
+ EIGEN_IF_CONSTEXPR(isARowMajor) A_t += EIGEN_AVX_MAX_K_UNROL;
+ else A_t += EIGEN_AVX_MAX_K_UNROL * LDA;
+ }
+ EIGEN_IF_CONSTEXPR(handleKRem) {
+ for (int64_t k = K_; k < K; k++) {
+ urolls::template microKernel<isARowMajor, 2, 2, 1, EIGEN_AVX_MAX_B_LOAD, EIGEN_AVX_MAX_A_BCAST>(B_t, A_t, LDB,
+ LDA, zmm);
+ B_t += LDB;
+ EIGEN_IF_CONSTEXPR(isARowMajor) A_t++;
+ else A_t += LDA;
+ }
+ }
+ EIGEN_IF_CONSTEXPR(isCRowMajor) {
+ urolls::template updateC<2, 2>(&C_arr[i * LDC + j], LDC, zmm);
+ urolls::template storeC<2, 2>(&C_arr[i * LDC + j], LDC, zmm);
+ }
+ else {
+ transStoreC<Scalar, vec, EIGEN_AVX_MAX_NUM_ROW, U2, true, false>(zmm, &C_arr[i + j * LDC], LDC, 2);
+ }
+ i += 2;
+ }
+ if (M - i > 0) {
+ Scalar *A_t = &A_arr[idA<isARowMajor>(i, 0, LDA)];
+ Scalar *B_t = &B_arr[0 * LDB + j];
+ PacketBlock<vec, EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS> zmm;
+ urolls::template setzero<2, 1>(zmm);
+ for (int64_t k = 0; k < K_; k += EIGEN_AVX_MAX_K_UNROL) {
+ urolls::template microKernel<isARowMajor, 2, 1, EIGEN_AVX_MAX_K_UNROL, EIGEN_AVX_MAX_B_LOAD, 1>(B_t, A_t, LDB,
+ LDA, zmm);
+ B_t += EIGEN_AVX_MAX_K_UNROL * LDB;
+ EIGEN_IF_CONSTEXPR(isARowMajor) A_t += EIGEN_AVX_MAX_K_UNROL;
+ else A_t += EIGEN_AVX_MAX_K_UNROL * LDA;
+ }
+ EIGEN_IF_CONSTEXPR(handleKRem) {
+ for (int64_t k = K_; k < K; k++) {
+ urolls::template microKernel<isARowMajor, 2, 1, 1, EIGEN_AVX_MAX_B_LOAD, 1>(B_t, A_t, LDB, LDA, zmm);
+ B_t += LDB;
+ EIGEN_IF_CONSTEXPR(isARowMajor) A_t++;
+ else A_t += LDA;
+ }
+ }
+ EIGEN_IF_CONSTEXPR(isCRowMajor) {
+ urolls::template updateC<2, 1>(&C_arr[i * LDC + j], LDC, zmm);
+ urolls::template storeC<2, 1>(&C_arr[i * LDC + j], LDC, zmm);
+ }
+ else {
+ transStoreC<Scalar, vec, EIGEN_AVX_MAX_NUM_ROW, U2, true, false>(zmm, &C_arr[i + j * LDC], LDC, 1);
+ }
+ }
+ j += U2;
+ }
+ if (N - j >= U1) {
+ constexpr int64_t EIGEN_AVX_MAX_B_LOAD = EIGEN_AVX_B_LOAD_SETS * 1;
+ int64_t i = 0;
+ for (; i < M_; i += EIGEN_AVX_MAX_NUM_ROW) {
+ Scalar *A_t = &A_arr[idA<isARowMajor>(i, 0, LDA)], *B_t = &B_arr[0 * LDB + j];
+ PacketBlock<vec, EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS> zmm;
+ urolls::template setzero<1, EIGEN_AVX_MAX_NUM_ROW>(zmm);
+ for (int64_t k = 0; k < K_; k += EIGEN_AVX_MAX_K_UNROL) {
+ urolls::template microKernel<isARowMajor, 1, EIGEN_AVX_MAX_NUM_ROW, EIGEN_AVX_MAX_K_UNROL, EIGEN_AVX_MAX_B_LOAD,
+ EIGEN_AVX_MAX_A_BCAST>(B_t, A_t, LDB, LDA, zmm);
+ B_t += EIGEN_AVX_MAX_K_UNROL * LDB;
+ EIGEN_IF_CONSTEXPR(isARowMajor) A_t += EIGEN_AVX_MAX_K_UNROL;
+ else A_t += EIGEN_AVX_MAX_K_UNROL * LDA;
+ }
+ EIGEN_IF_CONSTEXPR(handleKRem) {
+ for (int64_t k = K_; k < K; k++) {
+ urolls::template microKernel<isARowMajor, 1, EIGEN_AVX_MAX_NUM_ROW, 1, EIGEN_AVX_B_LOAD_SETS * 1,
+ EIGEN_AVX_MAX_A_BCAST>(B_t, A_t, LDB, LDA, zmm);
+ B_t += LDB;
+ EIGEN_IF_CONSTEXPR(isARowMajor) A_t++;
+ else A_t += LDA;
+ }
+ }
+ EIGEN_IF_CONSTEXPR(isCRowMajor) {
+ urolls::template updateC<1, EIGEN_AVX_MAX_NUM_ROW>(&C_arr[i * LDC + j], LDC, zmm);
+ urolls::template storeC<1, EIGEN_AVX_MAX_NUM_ROW>(&C_arr[i * LDC + j], LDC, zmm);
+ }
+ else {
+ transStoreC<Scalar, vec, EIGEN_AVX_MAX_NUM_ROW, U1, false, false>(zmm, &C_arr[i + j * LDC], LDC);
+ }
+ }
+ if (M - i >= 4) { // Note: this block assumes EIGEN_AVX_MAX_NUM_ROW = 8. Should be removed otherwise
+ Scalar *A_t = &A_arr[idA<isARowMajor>(i, 0, LDA)];
+ Scalar *B_t = &B_arr[0 * LDB + j];
+ PacketBlock<vec, EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS> zmm;
+ urolls::template setzero<1, 4>(zmm);
+ for (int64_t k = 0; k < K_; k += EIGEN_AVX_MAX_K_UNROL) {
+ urolls::template microKernel<isARowMajor, 1, 4, EIGEN_AVX_MAX_K_UNROL, EIGEN_AVX_MAX_B_LOAD,
+ EIGEN_AVX_MAX_A_BCAST>(B_t, A_t, LDB, LDA, zmm);
+ B_t += EIGEN_AVX_MAX_K_UNROL * LDB;
+ EIGEN_IF_CONSTEXPR(isARowMajor) A_t += EIGEN_AVX_MAX_K_UNROL;
+ else A_t += EIGEN_AVX_MAX_K_UNROL * LDA;
+ }
+ EIGEN_IF_CONSTEXPR(handleKRem) {
+ for (int64_t k = K_; k < K; k++) {
+ urolls::template microKernel<isARowMajor, 1, 4, 1, EIGEN_AVX_MAX_B_LOAD, EIGEN_AVX_MAX_A_BCAST>(B_t, A_t, LDB,
+ LDA, zmm);
+ B_t += LDB;
+ EIGEN_IF_CONSTEXPR(isARowMajor) A_t++;
+ else A_t += LDA;
+ }
+ }
+ EIGEN_IF_CONSTEXPR(isCRowMajor) {
+ urolls::template updateC<1, 4>(&C_arr[i * LDC + j], LDC, zmm);
+ urolls::template storeC<1, 4>(&C_arr[i * LDC + j], LDC, zmm);
+ }
+ else {
+ transStoreC<Scalar, vec, EIGEN_AVX_MAX_NUM_ROW, U1, true, false>(zmm, &C_arr[i + j * LDC], LDC, 4);
+ }
+ i += 4;
+ }
+ if (M - i >= 2) {
+ Scalar *A_t = &A_arr[idA<isARowMajor>(i, 0, LDA)];
+ Scalar *B_t = &B_arr[0 * LDB + j];
+ PacketBlock<vec, EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS> zmm;
+ urolls::template setzero<1, 2>(zmm);
+ for (int64_t k = 0; k < K_; k += EIGEN_AVX_MAX_K_UNROL) {
+ urolls::template microKernel<isARowMajor, 1, 2, EIGEN_AVX_MAX_K_UNROL, EIGEN_AVX_MAX_B_LOAD,
+ EIGEN_AVX_MAX_A_BCAST>(B_t, A_t, LDB, LDA, zmm);
+ B_t += EIGEN_AVX_MAX_K_UNROL * LDB;
+ EIGEN_IF_CONSTEXPR(isARowMajor) A_t += EIGEN_AVX_MAX_K_UNROL;
+ else A_t += EIGEN_AVX_MAX_K_UNROL * LDA;
+ }
+ EIGEN_IF_CONSTEXPR(handleKRem) {
+ for (int64_t k = K_; k < K; k++) {
+ urolls::template microKernel<isARowMajor, 1, 2, 1, EIGEN_AVX_MAX_B_LOAD, EIGEN_AVX_MAX_A_BCAST>(B_t, A_t, LDB,
+ LDA, zmm);
+ B_t += LDB;
+ EIGEN_IF_CONSTEXPR(isARowMajor) A_t++;
+ else A_t += LDA;
+ }
+ }
+ EIGEN_IF_CONSTEXPR(isCRowMajor) {
+ urolls::template updateC<1, 2>(&C_arr[i * LDC + j], LDC, zmm);
+ urolls::template storeC<1, 2>(&C_arr[i * LDC + j], LDC, zmm);
+ }
+ else {
+ transStoreC<Scalar, vec, EIGEN_AVX_MAX_NUM_ROW, U1, true, false>(zmm, &C_arr[i + j * LDC], LDC, 2);
+ }
+ i += 2;
+ }
+ if (M - i > 0) {
+ Scalar *A_t = &A_arr[idA<isARowMajor>(i, 0, LDA)];
+ Scalar *B_t = &B_arr[0 * LDB + j];
+ PacketBlock<vec, EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS> zmm;
+ urolls::template setzero<1, 1>(zmm);
+ {
+ for (int64_t k = 0; k < K_; k += EIGEN_AVX_MAX_K_UNROL) {
+ urolls::template microKernel<isARowMajor, 1, 1, EIGEN_AVX_MAX_K_UNROL, EIGEN_AVX_MAX_B_LOAD, 1>(B_t, A_t, LDB,
+ LDA, zmm);
+ B_t += EIGEN_AVX_MAX_K_UNROL * LDB;
+ EIGEN_IF_CONSTEXPR(isARowMajor) A_t += EIGEN_AVX_MAX_K_UNROL;
+ else A_t += EIGEN_AVX_MAX_K_UNROL * LDA;
+ }
+ EIGEN_IF_CONSTEXPR(handleKRem) {
+ for (int64_t k = K_; k < K; k++) {
+ urolls::template microKernel<isARowMajor, 1, 1, 1, EIGEN_AVX_B_LOAD_SETS * 1, 1>(B_t, A_t, LDB, LDA, zmm);
+ B_t += LDB;
+ EIGEN_IF_CONSTEXPR(isARowMajor) A_t++;
+ else A_t += LDA;
+ }
+ }
+ EIGEN_IF_CONSTEXPR(isCRowMajor) {
+ urolls::template updateC<1, 1>(&C_arr[i * LDC + j], LDC, zmm);
+ urolls::template storeC<1, 1>(&C_arr[i * LDC + j], LDC, zmm);
+ }
+ else {
+ transStoreC<Scalar, vec, EIGEN_AVX_MAX_NUM_ROW, U1, true, false>(zmm, &C_arr[i + j * LDC], LDC, 1);
+ }
+ }
+ }
+ j += U1;
+ }
+ if (N - j > 0) {
+ constexpr int64_t EIGEN_AVX_MAX_B_LOAD = EIGEN_AVX_B_LOAD_SETS * 1;
+ int64_t i = 0;
+ for (; i < M_; i += EIGEN_AVX_MAX_NUM_ROW) {
+ Scalar *A_t = &A_arr[idA<isARowMajor>(i, 0, LDA)];
+ Scalar *B_t = &B_arr[0 * LDB + j];
+ PacketBlock<vec, EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS> zmm;
+ urolls::template setzero<1, EIGEN_AVX_MAX_NUM_ROW>(zmm);
+ for (int64_t k = 0; k < K_; k += EIGEN_AVX_MAX_K_UNROL) {
+ urolls::template microKernel<isARowMajor, 1, EIGEN_AVX_MAX_NUM_ROW, EIGEN_AVX_MAX_K_UNROL, EIGEN_AVX_MAX_B_LOAD,
+ EIGEN_AVX_MAX_A_BCAST, true>(B_t, A_t, LDB, LDA, zmm, N - j);
+ B_t += EIGEN_AVX_MAX_K_UNROL * LDB;
+ EIGEN_IF_CONSTEXPR(isARowMajor) A_t += EIGEN_AVX_MAX_K_UNROL;
+ else A_t += EIGEN_AVX_MAX_K_UNROL * LDA;
+ }
+ EIGEN_IF_CONSTEXPR(handleKRem) {
+ for (int64_t k = K_; k < K; k++) {
+ urolls::template microKernel<isARowMajor, 1, EIGEN_AVX_MAX_NUM_ROW, 1, EIGEN_AVX_MAX_B_LOAD,
+ EIGEN_AVX_MAX_A_BCAST, true>(B_t, A_t, LDB, LDA, zmm, N - j);
+ B_t += LDB;
+ EIGEN_IF_CONSTEXPR(isARowMajor) A_t++;
+ else A_t += LDA;
+ }
+ }
+ EIGEN_IF_CONSTEXPR(isCRowMajor) {
+ urolls::template updateC<1, EIGEN_AVX_MAX_NUM_ROW, true>(&C_arr[i * LDC + j], LDC, zmm, N - j);
+ urolls::template storeC<1, EIGEN_AVX_MAX_NUM_ROW, true>(&C_arr[i * LDC + j], LDC, zmm, N - j);
+ }
+ else {
+ transStoreC<Scalar, vec, EIGEN_AVX_MAX_NUM_ROW, U1, false, true>(zmm, &C_arr[i + j * LDC], LDC, 0, N - j);
+ }
+ }
+ if (M - i >= 4) { // Note: this block assumes EIGEN_AVX_MAX_NUM_ROW = 8. Should be removed otherwise
+ Scalar *A_t = &A_arr[idA<isARowMajor>(i, 0, LDA)];
+ Scalar *B_t = &B_arr[0 * LDB + j];
+ PacketBlock<vec, EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS> zmm;
+ urolls::template setzero<1, 4>(zmm);
+ for (int64_t k = 0; k < K_; k += EIGEN_AVX_MAX_K_UNROL) {
+ urolls::template microKernel<isARowMajor, 1, 4, EIGEN_AVX_MAX_K_UNROL, EIGEN_AVX_MAX_B_LOAD,
+ EIGEN_AVX_MAX_A_BCAST, true>(B_t, A_t, LDB, LDA, zmm, N - j);
+ B_t += EIGEN_AVX_MAX_K_UNROL * LDB;
+ EIGEN_IF_CONSTEXPR(isARowMajor) A_t += EIGEN_AVX_MAX_K_UNROL;
+ else A_t += EIGEN_AVX_MAX_K_UNROL * LDA;
+ }
+ EIGEN_IF_CONSTEXPR(handleKRem) {
+ for (int64_t k = K_; k < K; k++) {
+ urolls::template microKernel<isARowMajor, 1, 4, 1, EIGEN_AVX_MAX_B_LOAD, EIGEN_AVX_MAX_A_BCAST, true>(
+ B_t, A_t, LDB, LDA, zmm, N - j);
+ B_t += LDB;
+ EIGEN_IF_CONSTEXPR(isARowMajor) A_t++;
+ else A_t += LDA;
+ }
+ }
+ EIGEN_IF_CONSTEXPR(isCRowMajor) {
+ urolls::template updateC<1, 4, true>(&C_arr[i * LDC + j], LDC, zmm, N - j);
+ urolls::template storeC<1, 4, true>(&C_arr[i * LDC + j], LDC, zmm, N - j);
+ }
+ else {
+ transStoreC<Scalar, vec, EIGEN_AVX_MAX_NUM_ROW, U1, true, true>(zmm, &C_arr[i + j * LDC], LDC, 4, N - j);
+ }
+ i += 4;
+ }
+ if (M - i >= 2) {
+ Scalar *A_t = &A_arr[idA<isARowMajor>(i, 0, LDA)];
+ Scalar *B_t = &B_arr[0 * LDB + j];
+ PacketBlock<vec, EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS> zmm;
+ urolls::template setzero<1, 2>(zmm);
+ for (int64_t k = 0; k < K_; k += EIGEN_AVX_MAX_K_UNROL) {
+ urolls::template microKernel<isARowMajor, 1, 2, EIGEN_AVX_MAX_K_UNROL, EIGEN_AVX_MAX_B_LOAD,
+ EIGEN_AVX_MAX_A_BCAST, true>(B_t, A_t, LDB, LDA, zmm, N - j);
+ B_t += EIGEN_AVX_MAX_K_UNROL * LDB;
+ EIGEN_IF_CONSTEXPR(isARowMajor) A_t += EIGEN_AVX_MAX_K_UNROL;
+ else A_t += EIGEN_AVX_MAX_K_UNROL * LDA;
+ }
+ EIGEN_IF_CONSTEXPR(handleKRem) {
+ for (int64_t k = K_; k < K; k++) {
+ urolls::template microKernel<isARowMajor, 1, 2, 1, EIGEN_AVX_MAX_B_LOAD, EIGEN_AVX_MAX_A_BCAST, true>(
+ B_t, A_t, LDB, LDA, zmm, N - j);
+ B_t += LDB;
+ EIGEN_IF_CONSTEXPR(isARowMajor) A_t++;
+ else A_t += LDA;
+ }
+ }
+ EIGEN_IF_CONSTEXPR(isCRowMajor) {
+ urolls::template updateC<1, 2, true>(&C_arr[i * LDC + j], LDC, zmm, N - j);
+ urolls::template storeC<1, 2, true>(&C_arr[i * LDC + j], LDC, zmm, N - j);
+ }
+ else {
+ transStoreC<Scalar, vec, EIGEN_AVX_MAX_NUM_ROW, U1, true, true>(zmm, &C_arr[i + j * LDC], LDC, 2, N - j);
+ }
+ i += 2;
+ }
+ if (M - i > 0) {
+ Scalar *A_t = &A_arr[idA<isARowMajor>(i, 0, LDA)];
+ Scalar *B_t = &B_arr[0 * LDB + j];
+ PacketBlock<vec, EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS> zmm;
+ urolls::template setzero<1, 1>(zmm);
+ for (int64_t k = 0; k < K_; k += EIGEN_AVX_MAX_K_UNROL) {
+ urolls::template microKernel<isARowMajor, 1, 1, EIGEN_AVX_MAX_K_UNROL, EIGEN_AVX_MAX_B_LOAD, 1, true>(
+ B_t, A_t, LDB, LDA, zmm, N - j);
+ B_t += EIGEN_AVX_MAX_K_UNROL * LDB;
+ EIGEN_IF_CONSTEXPR(isARowMajor) A_t += EIGEN_AVX_MAX_K_UNROL;
+ else A_t += EIGEN_AVX_MAX_K_UNROL * LDA;
+ }
+ EIGEN_IF_CONSTEXPR(handleKRem) {
+ for (int64_t k = K_; k < K; k++) {
+ urolls::template microKernel<isARowMajor, 1, 1, 1, EIGEN_AVX_MAX_B_LOAD, 1, true>(B_t, A_t, LDB, LDA, zmm,
+ N - j);
+ B_t += LDB;
+ EIGEN_IF_CONSTEXPR(isARowMajor) A_t++;
+ else A_t += LDA;
+ }
+ }
+ EIGEN_IF_CONSTEXPR(isCRowMajor) {
+ urolls::template updateC<1, 1, true>(&C_arr[i * LDC + j], LDC, zmm, N - j);
+ urolls::template storeC<1, 1, true>(&C_arr[i * LDC + j], LDC, zmm, N - j);
+ }
+ else {
+ transStoreC<Scalar, vec, EIGEN_AVX_MAX_NUM_ROW, U1, true, true>(zmm, &C_arr[i + j * LDC], LDC, 1, N - j);
+ }
+ }
+ }
+}
+
+/**
+ * Triangular solve kernel with A on left with K number of rhs. dim(A) = unrollM
+ *
+ * unrollM: dimension of A matrix (triangular matrix). unrollM should be <= EIGEN_AVX_MAX_NUM_ROW
+ * isFWDSolve: is forward solve?
+ * isUnitDiag: is the diagonal of A all ones?
+ * The B matrix (RHS) is assumed to be row-major
+ */
+template <typename Scalar, typename vec, int64_t unrollM, bool isARowMajor, bool isFWDSolve, bool isUnitDiag>
+static EIGEN_ALWAYS_INLINE void triSolveKernel(Scalar *A_arr, Scalar *B_arr, int64_t K, int64_t LDA, int64_t LDB) {
+ static_assert(unrollM <= EIGEN_AVX_MAX_NUM_ROW, "unrollM should be equal to EIGEN_AVX_MAX_NUM_ROW");
+ using urolls = unrolls::trsm<Scalar>;
+ constexpr int64_t U3 = urolls::PacketSize * 3;
+ constexpr int64_t U2 = urolls::PacketSize * 2;
+ constexpr int64_t U1 = urolls::PacketSize * 1;
+
+ PacketBlock<vec, EIGEN_AVX_MAX_NUM_ACC> RHSInPacket;
+ PacketBlock<vec, EIGEN_AVX_MAX_NUM_ROW> AInPacket;
+
+ int64_t k = 0;
+ while (K - k >= U3) {
+ urolls::template loadRHS<isFWDSolve, unrollM, 3>(B_arr + k, LDB, RHSInPacket);
+ urolls::template triSolveMicroKernel<isARowMajor, isFWDSolve, isUnitDiag, unrollM, 3>(A_arr, LDA, RHSInPacket,
+ AInPacket);
+ urolls::template storeRHS<isFWDSolve, unrollM, 3>(B_arr + k, LDB, RHSInPacket);
+ k += U3;
+ }
+ if (K - k >= U2) {
+ urolls::template loadRHS<isFWDSolve, unrollM, 2>(B_arr + k, LDB, RHSInPacket);
+ urolls::template triSolveMicroKernel<isARowMajor, isFWDSolve, isUnitDiag, unrollM, 2>(A_arr, LDA, RHSInPacket,
+ AInPacket);
+ urolls::template storeRHS<isFWDSolve, unrollM, 2>(B_arr + k, LDB, RHSInPacket);
+ k += U2;
+ }
+ if (K - k >= U1) {
+ urolls::template loadRHS<isFWDSolve, unrollM, 1>(B_arr + k, LDB, RHSInPacket);
+ urolls::template triSolveMicroKernel<isARowMajor, isFWDSolve, isUnitDiag, unrollM, 1>(A_arr, LDA, RHSInPacket,
+ AInPacket);
+ urolls::template storeRHS<isFWDSolve, unrollM, 1>(B_arr + k, LDB, RHSInPacket);
+ k += U1;
+ }
+ if (K - k > 0) {
+ // Handle remaining number of RHS
+ urolls::template loadRHS<isFWDSolve, unrollM, 1, true>(B_arr + k, LDB, RHSInPacket, K - k);
+ urolls::template triSolveMicroKernel<isARowMajor, isFWDSolve, isUnitDiag, unrollM, 1>(A_arr, LDA, RHSInPacket,
+ AInPacket);
+ urolls::template storeRHS<isFWDSolve, unrollM, 1, true>(B_arr + k, LDB, RHSInPacket, K - k);
+ }
+}
+
+/**
+ * Triangular solve routine with A on left and dimension of at most L with K number of rhs. This is essentially
+ * a wrapper for triSolveMicrokernel for M = {1,2,3,4,5,6,7,8}.
+ *
+ * isFWDSolve: is forward solve?
+ * isUnitDiag: is the diagonal of A all ones?
+ * The B matrix (RHS) is assumed to be row-major
+ */
+template <typename Scalar, bool isARowMajor, bool isFWDSolve, bool isUnitDiag>
+void triSolveKernelLxK(Scalar *A_arr, Scalar *B_arr, int64_t M, int64_t K, int64_t LDA, int64_t LDB) {
+ // Note: this assumes EIGEN_AVX_MAX_NUM_ROW = 8. Unrolls should be adjusted
+ // accordingly if EIGEN_AVX_MAX_NUM_ROW is smaller.
+ using vec = typename std::conditional<std::is_same<Scalar, float>::value, vecFullFloat, vecFullDouble>::type;
+ if (M == 8)
+ triSolveKernel<Scalar, vec, 8, isARowMajor, isFWDSolve, isUnitDiag>(A_arr, B_arr, K, LDA, LDB);
+ else if (M == 7)
+ triSolveKernel<Scalar, vec, 7, isARowMajor, isFWDSolve, isUnitDiag>(A_arr, B_arr, K, LDA, LDB);
+ else if (M == 6)
+ triSolveKernel<Scalar, vec, 6, isARowMajor, isFWDSolve, isUnitDiag>(A_arr, B_arr, K, LDA, LDB);
+ else if (M == 5)
+ triSolveKernel<Scalar, vec, 5, isARowMajor, isFWDSolve, isUnitDiag>(A_arr, B_arr, K, LDA, LDB);
+ else if (M == 4)
+ triSolveKernel<Scalar, vec, 4, isARowMajor, isFWDSolve, isUnitDiag>(A_arr, B_arr, K, LDA, LDB);
+ else if (M == 3)
+ triSolveKernel<Scalar, vec, 3, isARowMajor, isFWDSolve, isUnitDiag>(A_arr, B_arr, K, LDA, LDB);
+ else if (M == 2)
+ triSolveKernel<Scalar, vec, 2, isARowMajor, isFWDSolve, isUnitDiag>(A_arr, B_arr, K, LDA, LDB);
+ else if (M == 1)
+ triSolveKernel<Scalar, vec, 1, isARowMajor, isFWDSolve, isUnitDiag>(A_arr, B_arr, K, LDA, LDB);
+ return;
+}
+
+/**
+ * This routine is used to copy B to/from a temporary array (row-major) for cases where B is column-major.
+ *
+ * toTemp: true => copy to temporary array, false => copy from temporary array
+ * remM: true = need to handle remainder values for M (M < EIGEN_AVX_MAX_NUM_ROW)
+ *
+ */
+template <typename Scalar, bool toTemp = true, bool remM = false>
+static EIGEN_ALWAYS_INLINE void copyBToRowMajor(Scalar *B_arr, int64_t LDB, int64_t K, Scalar *B_temp, int64_t LDB_,
+ int64_t remM_ = 0) {
+ EIGEN_UNUSED_VARIABLE(remM_);
+ using urolls = unrolls::transB<Scalar>;
+ using vecHalf = typename std::conditional<std::is_same<Scalar, float>::value, vecHalfFloat, vecFullDouble>::type;
+ PacketBlock<vecHalf, EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS> ymm;
+ constexpr int64_t U3 = urolls::PacketSize * 3;
+ constexpr int64_t U2 = urolls::PacketSize * 2;
+ constexpr int64_t U1 = urolls::PacketSize * 1;
+ int64_t K_ = K / U3 * U3;
+ int64_t k = 0;
+
+ for (; k < K_; k += U3) {
+ urolls::template transB_kernel<U3, toTemp, remM>(B_arr + k * LDB, LDB, B_temp, LDB_, ymm, remM_);
+ B_temp += U3;
+ }
+ if (K - k >= U2) {
+ urolls::template transB_kernel<U2, toTemp, remM>(B_arr + k * LDB, LDB, B_temp, LDB_, ymm, remM_);
+ B_temp += U2;
+ k += U2;
+ }
+ if (K - k >= U1) {
+ urolls::template transB_kernel<U1, toTemp, remM>(B_arr + k * LDB, LDB, B_temp, LDB_, ymm, remM_);
+ B_temp += U1;
+ k += U1;
+ }
+ EIGEN_IF_CONSTEXPR(U1 > 8) {
+ // Note: without "if constexpr" this section of code will also be
+ // parsed by the compiler so there is an additional check in {load/store}BBlock
+ // to make sure the counter is not non-negative.
+ if (K - k >= 8) {
+ urolls::template transB_kernel<8, toTemp, remM>(B_arr + k * LDB, LDB, B_temp, LDB_, ymm, remM_);
+ B_temp += 8;
+ k += 8;
+ }
+ }
+ EIGEN_IF_CONSTEXPR(U1 > 4) {
+ // Note: without "if constexpr" this section of code will also be
+ // parsed by the compiler so there is an additional check in {load/store}BBlock
+ // to make sure the counter is not non-negative.
+ if (K - k >= 4) {
+ urolls::template transB_kernel<4, toTemp, remM>(B_arr + k * LDB, LDB, B_temp, LDB_, ymm, remM_);
+ B_temp += 4;
+ k += 4;
+ }
+ }
+ if (K - k >= 2) {
+ urolls::template transB_kernel<2, toTemp, remM>(B_arr + k * LDB, LDB, B_temp, LDB_, ymm, remM_);
+ B_temp += 2;
+ k += 2;
+ }
+ if (K - k >= 1) {
+ urolls::template transB_kernel<1, toTemp, remM>(B_arr + k * LDB, LDB, B_temp, LDB_, ymm, remM_);
+ B_temp += 1;
+ k += 1;
+ }
+}
+
+#if (EIGEN_USE_AVX512_TRSM_L_KERNELS) && defined(EIGEN_NO_MALLOC)
+/**
+ * Reduce blocking sizes so that the size of the temporary workspace needed is less than "limit" bytes,
+ * - kB must be at least psize
+ * - numM must be at least EIGEN_AVX_MAX_NUM_ROW
+ */
+template <typename Scalar, bool isBRowMajor>
+constexpr std::pair<int64_t, int64_t> trsmBlocking(const int64_t limit) {
+ constexpr int64_t psize = packet_traits<Scalar>::size;
+ int64_t kB = 15 * psize;
+ int64_t numM = 8 * EIGEN_AVX_MAX_NUM_ROW;
+ // If B is rowmajor, no temp workspace needed, so use default blocking sizes.
+ if (isBRowMajor) return {kB, numM};
+
+ // Very simple heuristic, prefer keeping kB as large as possible to fully use vector registers.
+ for (int64_t k = kB; k > psize; k -= psize) {
+ for (int64_t m = numM; m > EIGEN_AVX_MAX_NUM_ROW; m -= EIGEN_AVX_MAX_NUM_ROW) {
+ if ((((k + psize - 1) / psize + 4) * psize) * m * sizeof(Scalar) < limit) {
+ return {k, m};
+ }
+ }
+ }
+ return {psize, EIGEN_AVX_MAX_NUM_ROW}; // Minimum blocking size required
+}
+#endif // (EIGEN_USE_AVX512_TRSM_L_KERNELS) && defined(EIGEN_NO_MALLOC)
+
+/**
+ * Main triangular solve driver
+ *
+ * Triangular solve with A on the left.
+ * Scalar: Scalar precision, only float/double is supported.
+ * isARowMajor: is A row-major?
+ * isBRowMajor: is B row-major?
+ * isFWDSolve: is this forward solve or backward (true => forward)?
+ * isUnitDiag: is diagonal of A unit or nonunit (true => A has unit diagonal)?
+ *
+ * M: dimension of A
+ * numRHS: number of right hand sides (coincides with K dimension for gemm updates)
+ *
+ * Here are the mapping between the different TRSM cases (col-major) and triSolve:
+ *
+ * LLN (left , lower, A non-transposed) :: isARowMajor=false, isBRowMajor=false, isFWDSolve=true
+ * LUT (left , upper, A transposed) :: isARowMajor=true, isBRowMajor=false, isFWDSolve=true
+ * LUN (left , upper, A non-transposed) :: isARowMajor=false, isBRowMajor=false, isFWDSolve=false
+ * LLT (left , lower, A transposed) :: isARowMajor=true, isBRowMajor=false, isFWDSolve=false
+ * RUN (right, upper, A non-transposed) :: isARowMajor=true, isBRowMajor=true, isFWDSolve=true
+ * RLT (right, lower, A transposed) :: isARowMajor=false, isBRowMajor=true, isFWDSolve=true
+ * RUT (right, upper, A transposed) :: isARowMajor=false, isBRowMajor=true, isFWDSolve=false
+ * RLN (right, lower, A non-transposed) :: isARowMajor=true, isBRowMajor=true, isFWDSolve=false
+ *
+ * Note: For RXX cases M,numRHS should be swapped.
+ *
+ */
+template <typename Scalar, bool isARowMajor = true, bool isBRowMajor = true, bool isFWDSolve = true,
+ bool isUnitDiag = false>
+void triSolve(Scalar *A_arr, Scalar *B_arr, int64_t M, int64_t numRHS, int64_t LDA, int64_t LDB) {
+ constexpr int64_t psize = packet_traits<Scalar>::size;
+ /**
+ * The values for kB, numM were determined experimentally.
+ * kB: Number of RHS we process at a time.
+ * numM: number of rows of B we will store in a temporary array (see below.) This should be a multiple of L.
+ *
+ * kB was determined by initially setting kB = numRHS and benchmarking triSolve (TRSM-RUN case)
+ * performance with M=numRHS.
+ * It was observed that performance started to drop around M=numRHS=240. This is likely machine dependent.
+ *
+ * numM was chosen "arbitrarily". It should be relatively small so B_temp is not too large, but it should be
+ * large enough to allow GEMM updates to have larger "K"s (see below.) No benchmarking has been done so far to
+ * determine optimal values for numM.
+ */
+#if (EIGEN_USE_AVX512_TRSM_L_KERNELS) && defined(EIGEN_NO_MALLOC)
+ /**
+ * If EIGEN_NO_MALLOC is requested, we try to reduce kB and numM so the maximum temp workspace required is less
+ * than EIGEN_STACK_ALLOCATION_LIMIT. Actual workspace size may be less, depending on the number of vectors to
+ * solve.
+ * - kB must be at least psize
+ * - numM must be at least EIGEN_AVX_MAX_NUM_ROW
+ *
+ * If B is row-major, the blocking sizes are not reduced (no temp workspace needed).
+ */
+ constexpr std::pair<int64_t, int64_t> blocking_ = trsmBlocking<Scalar, isBRowMajor>(EIGEN_STACK_ALLOCATION_LIMIT);
+ constexpr int64_t kB = blocking_.first;
+ constexpr int64_t numM = blocking_.second;
+ /**
+ * If the temp workspace size exceeds EIGEN_STACK_ALLOCATION_LIMIT even with the minimum blocking sizes,
+ * we throw an assertion. Use -DEIGEN_USE_AVX512_TRSM_L_KERNELS=0 if necessary
+ */
+ static_assert(!(((((kB + psize - 1) / psize + 4) * psize) * numM * sizeof(Scalar) >= EIGEN_STACK_ALLOCATION_LIMIT) &&
+ !isBRowMajor),
+ "Temp workspace required is too large.");
+#else
+ constexpr int64_t kB = (3 * psize) * 5; // 5*U3
+ constexpr int64_t numM = 8 * EIGEN_AVX_MAX_NUM_ROW;
+#endif
+
+ int64_t sizeBTemp = 0;
+ Scalar *B_temp = NULL;
+ EIGEN_IF_CONSTEXPR(!isBRowMajor) {
+ /**
+ * If B is col-major, we copy it to a fixed-size temporary array of size at most ~numM*kB and
+ * transpose it to row-major. Call the solve routine, and copy+transpose it back to the original array.
+ * The updated row-major copy of B is reused in the GEMM updates.
+ */
+ sizeBTemp = (((std::min(kB, numRHS) + psize - 1) / psize + 4) * psize) * numM;
+ }
+
+#if !defined(EIGEN_NO_MALLOC)
+ EIGEN_IF_CONSTEXPR(!isBRowMajor) B_temp = (Scalar *)handmade_aligned_malloc(sizeof(Scalar) * sizeBTemp, 64);
+#elif (EIGEN_USE_AVX512_TRSM_L_KERNELS) && defined(EIGEN_NO_MALLOC)
+ // Use alloca if malloc not allowed, requested temp workspace size should be less than EIGEN_STACK_ALLOCATION_LIMIT
+ ei_declare_aligned_stack_constructed_variable(Scalar, B_temp_alloca, sizeBTemp, 0);
+ B_temp = B_temp_alloca;
+#endif
+
+ for (int64_t k = 0; k < numRHS; k += kB) {
+ int64_t bK = numRHS - k > kB ? kB : numRHS - k;
+ int64_t M_ = (M / EIGEN_AVX_MAX_NUM_ROW) * EIGEN_AVX_MAX_NUM_ROW, gemmOff = 0;
+
+ // bK rounded up to next multiple of L=EIGEN_AVX_MAX_NUM_ROW. When B_temp is used, we solve for bkL RHS
+ // instead of bK RHS in triSolveKernelLxK.
+ int64_t bkL = ((bK + (EIGEN_AVX_MAX_NUM_ROW - 1)) / EIGEN_AVX_MAX_NUM_ROW) * EIGEN_AVX_MAX_NUM_ROW;
+ const int64_t numScalarPerCache = 64 / sizeof(Scalar);
+ // Leading dimension of B_temp, will be a multiple of the cache line size.
+ int64_t LDT = ((bkL + (numScalarPerCache - 1)) / numScalarPerCache) * numScalarPerCache;
+ int64_t offsetBTemp = 0;
+ for (int64_t i = 0; i < M_; i += EIGEN_AVX_MAX_NUM_ROW) {
+ EIGEN_IF_CONSTEXPR(!isBRowMajor) {
+ int64_t indA_i = isFWDSolve ? i : M - 1 - i;
+ int64_t indB_i = isFWDSolve ? i : M - (i + EIGEN_AVX_MAX_NUM_ROW);
+ int64_t offB_1 = isFWDSolve ? offsetBTemp : sizeBTemp - EIGEN_AVX_MAX_NUM_ROW * LDT - offsetBTemp;
+ int64_t offB_2 = isFWDSolve ? offsetBTemp : sizeBTemp - LDT - offsetBTemp;
+ // Copy values from B to B_temp.
+ copyBToRowMajor<Scalar, true, false>(B_arr + indB_i + k * LDB, LDB, bK, B_temp + offB_1, LDT);
+ // Triangular solve with a small block of A and long horizontal blocks of B (or B_temp if B col-major)
+ triSolveKernelLxK<Scalar, isARowMajor, isFWDSolve, isUnitDiag>(
+ &A_arr[idA<isARowMajor>(indA_i, indA_i, LDA)], B_temp + offB_2, EIGEN_AVX_MAX_NUM_ROW, bkL, LDA, LDT);
+ // Copy values from B_temp back to B. B_temp will be reused in gemm call below.
+ copyBToRowMajor<Scalar, false, false>(B_arr + indB_i + k * LDB, LDB, bK, B_temp + offB_1, LDT);
+
+ offsetBTemp += EIGEN_AVX_MAX_NUM_ROW * LDT;
+ }
+ else {
+ int64_t ind = isFWDSolve ? i : M - 1 - i;
+ triSolveKernelLxK<Scalar, isARowMajor, isFWDSolve, isUnitDiag>(
+ &A_arr[idA<isARowMajor>(ind, ind, LDA)], B_arr + k + ind * LDB, EIGEN_AVX_MAX_NUM_ROW, bK, LDA, LDB);
+ }
+ if (i + EIGEN_AVX_MAX_NUM_ROW < M_) {
+ /**
+ * For the GEMM updates, we want "K" (K=i+8 in this case) to be large as soon as possible
+ * to reuse the accumulators in GEMM as much as possible. So we only update 8xbK blocks of
+ * B as follows:
+ *
+ * A B
+ * __
+ * |__|__ |__|
+ * |__|__|__ |__|
+ * |__|__|__|__ |__|
+ * |********|__| |**|
+ */
+ EIGEN_IF_CONSTEXPR(isBRowMajor) {
+ int64_t indA_i = isFWDSolve ? i + EIGEN_AVX_MAX_NUM_ROW : M - (i + 2 * EIGEN_AVX_MAX_NUM_ROW);
+ int64_t indA_j = isFWDSolve ? 0 : M - (i + EIGEN_AVX_MAX_NUM_ROW);
+ int64_t indB_i = isFWDSolve ? 0 : M - (i + EIGEN_AVX_MAX_NUM_ROW);
+ int64_t indB_i2 = isFWDSolve ? i + EIGEN_AVX_MAX_NUM_ROW : M - (i + 2 * EIGEN_AVX_MAX_NUM_ROW);
+ gemmKernel<Scalar, isARowMajor, isBRowMajor, false, false>(
+ &A_arr[idA<isARowMajor>(indA_i, indA_j, LDA)], B_arr + k + indB_i * LDB, B_arr + k + indB_i2 * LDB,
+ EIGEN_AVX_MAX_NUM_ROW, bK, i + EIGEN_AVX_MAX_NUM_ROW, LDA, LDB, LDB);
+ }
+ else {
+ if (offsetBTemp + EIGEN_AVX_MAX_NUM_ROW * LDT > sizeBTemp) {
+ /**
+ * Similar idea as mentioned above, but here we are limited by the number of updated values of B
+ * that can be stored (row-major) in B_temp.
+ *
+ * If there is not enough space to store the next batch of 8xbK of B in B_temp, we call GEMM
+ * update and partially update the remaining old values of B which depends on the new values
+ * of B stored in B_temp. These values are then no longer needed and can be overwritten.
+ */
+ int64_t indA_i = isFWDSolve ? i + EIGEN_AVX_MAX_NUM_ROW : 0;
+ int64_t indA_j = isFWDSolve ? gemmOff : M - (i + EIGEN_AVX_MAX_NUM_ROW);
+ int64_t indB_i = isFWDSolve ? i + EIGEN_AVX_MAX_NUM_ROW : 0;
+ int64_t offB_1 = isFWDSolve ? 0 : sizeBTemp - offsetBTemp;
+ gemmKernel<Scalar, isARowMajor, isBRowMajor, false, false>(
+ &A_arr[idA<isARowMajor>(indA_i, indA_j, LDA)], B_temp + offB_1, B_arr + indB_i + (k)*LDB,
+ M - (i + EIGEN_AVX_MAX_NUM_ROW), bK, i + EIGEN_AVX_MAX_NUM_ROW - gemmOff, LDA, LDT, LDB);
+ offsetBTemp = 0;
+ gemmOff = i + EIGEN_AVX_MAX_NUM_ROW;
+ } else {
+ /**
+ * If there is enough space in B_temp, we only update the next 8xbK values of B.
+ */
+ int64_t indA_i = isFWDSolve ? i + EIGEN_AVX_MAX_NUM_ROW : M - (i + 2 * EIGEN_AVX_MAX_NUM_ROW);
+ int64_t indA_j = isFWDSolve ? gemmOff : M - (i + EIGEN_AVX_MAX_NUM_ROW);
+ int64_t indB_i = isFWDSolve ? i + EIGEN_AVX_MAX_NUM_ROW : M - (i + 2 * EIGEN_AVX_MAX_NUM_ROW);
+ int64_t offB_1 = isFWDSolve ? 0 : sizeBTemp - offsetBTemp;
+ gemmKernel<Scalar, isARowMajor, isBRowMajor, false, false>(
+ &A_arr[idA<isARowMajor>(indA_i, indA_j, LDA)], B_temp + offB_1, B_arr + indB_i + (k)*LDB,
+ EIGEN_AVX_MAX_NUM_ROW, bK, i + EIGEN_AVX_MAX_NUM_ROW - gemmOff, LDA, LDT, LDB);
+ }
+ }
+ }
+ }
+ // Handle M remainder..
+ int64_t bM = M - M_;
+ if (bM > 0) {
+ if (M_ > 0) {
+ EIGEN_IF_CONSTEXPR(isBRowMajor) {
+ int64_t indA_i = isFWDSolve ? M_ : 0;
+ int64_t indA_j = isFWDSolve ? 0 : bM;
+ int64_t indB_i = isFWDSolve ? 0 : bM;
+ int64_t indB_i2 = isFWDSolve ? M_ : 0;
+ gemmKernel<Scalar, isARowMajor, isBRowMajor, false, false>(
+ &A_arr[idA<isARowMajor>(indA_i, indA_j, LDA)], B_arr + k + indB_i * LDB, B_arr + k + indB_i2 * LDB, bM,
+ bK, M_, LDA, LDB, LDB);
+ }
+ else {
+ int64_t indA_i = isFWDSolve ? M_ : 0;
+ int64_t indA_j = isFWDSolve ? gemmOff : bM;
+ int64_t indB_i = isFWDSolve ? M_ : 0;
+ int64_t offB_1 = isFWDSolve ? 0 : sizeBTemp - offsetBTemp;
+ gemmKernel<Scalar, isARowMajor, isBRowMajor, false, false>(&A_arr[idA<isARowMajor>(indA_i, indA_j, LDA)],
+ B_temp + offB_1, B_arr + indB_i + (k)*LDB, bM, bK,
+ M_ - gemmOff, LDA, LDT, LDB);
+ }
+ }
+ EIGEN_IF_CONSTEXPR(!isBRowMajor) {
+ int64_t indA_i = isFWDSolve ? M_ : M - 1 - M_;
+ int64_t indB_i = isFWDSolve ? M_ : 0;
+ int64_t offB_1 = isFWDSolve ? 0 : (bM - 1) * bkL;
+ copyBToRowMajor<Scalar, true, true>(B_arr + indB_i + k * LDB, LDB, bK, B_temp, bkL, bM);
+ triSolveKernelLxK<Scalar, isARowMajor, isFWDSolve, isUnitDiag>(&A_arr[idA<isARowMajor>(indA_i, indA_i, LDA)],
+ B_temp + offB_1, bM, bkL, LDA, bkL);
+ copyBToRowMajor<Scalar, false, true>(B_arr + indB_i + k * LDB, LDB, bK, B_temp, bkL, bM);
+ }
+ else {
+ int64_t ind = isFWDSolve ? M_ : M - 1 - M_;
+ triSolveKernelLxK<Scalar, isARowMajor, isFWDSolve, isUnitDiag>(&A_arr[idA<isARowMajor>(ind, ind, LDA)],
+ B_arr + k + ind * LDB, bM, bK, LDA, LDB);
+ }
+ }
+ }
+
+#if !defined(EIGEN_NO_MALLOC)
+ EIGEN_IF_CONSTEXPR(!isBRowMajor) handmade_aligned_free(B_temp);
+#endif
+}
+
+// Template specializations of trsmKernelL/R for float/double and inner strides of 1.
+#if (EIGEN_USE_AVX512_TRSM_KERNELS)
+#if (EIGEN_USE_AVX512_TRSM_R_KERNELS)
+template <typename Scalar, typename Index, int Mode, bool Conjugate, int TriStorageOrder, int OtherInnerStride>
+struct trsmKernelR;
+
+template <typename Index, int Mode, int TriStorageOrder>
+struct trsmKernelR<float, Index, Mode, false, TriStorageOrder, 1> {
+ static void kernel(Index size, Index otherSize, const float *_tri, Index triStride, float *_other, Index otherIncr,
+ Index otherStride);
+};
+
+template <typename Index, int Mode, int TriStorageOrder>
+struct trsmKernelR<double, Index, Mode, false, TriStorageOrder, 1> {
+ static void kernel(Index size, Index otherSize, const double *_tri, Index triStride, double *_other, Index otherIncr,
+ Index otherStride);
+};
+
+template <typename Index, int Mode, int TriStorageOrder>
+EIGEN_DONT_INLINE void trsmKernelR<float, Index, Mode, false, TriStorageOrder, 1>::kernel(
+ Index size, Index otherSize, const float *_tri, Index triStride, float *_other, Index otherIncr,
+ Index otherStride) {
+ EIGEN_UNUSED_VARIABLE(otherIncr);
+ triSolve<float, TriStorageOrder != RowMajor, true, (Mode & Lower) != Lower, (Mode & UnitDiag) != 0>(
+ const_cast<float *>(_tri), _other, size, otherSize, triStride, otherStride);
+}
+
+template <typename Index, int Mode, int TriStorageOrder>
+EIGEN_DONT_INLINE void trsmKernelR<double, Index, Mode, false, TriStorageOrder, 1>::kernel(
+ Index size, Index otherSize, const double *_tri, Index triStride, double *_other, Index otherIncr,
+ Index otherStride) {
+ EIGEN_UNUSED_VARIABLE(otherIncr);
+ triSolve<double, TriStorageOrder != RowMajor, true, (Mode & Lower) != Lower, (Mode & UnitDiag) != 0>(
+ const_cast<double *>(_tri), _other, size, otherSize, triStride, otherStride);
+}
+#endif // (EIGEN_USE_AVX512_TRSM_R_KERNELS)
+
+// These trsm kernels require temporary memory allocation
+#if (EIGEN_USE_AVX512_TRSM_L_KERNELS)
+template <typename Scalar, typename Index, int Mode, bool Conjugate, int TriStorageOrder, int OtherInnerStride>
+struct trsmKernelL;
+
+template <typename Index, int Mode, int TriStorageOrder>
+struct trsmKernelL<float, Index, Mode, false, TriStorageOrder, 1> {
+ static void kernel(Index size, Index otherSize, const float *_tri, Index triStride, float *_other, Index otherIncr,
+ Index otherStride);
+};
+
+template <typename Index, int Mode, int TriStorageOrder>
+struct trsmKernelL<double, Index, Mode, false, TriStorageOrder, 1> {
+ static void kernel(Index size, Index otherSize, const double *_tri, Index triStride, double *_other, Index otherIncr,
+ Index otherStride);
+};
+
+template <typename Index, int Mode, int TriStorageOrder>
+EIGEN_DONT_INLINE void trsmKernelL<float, Index, Mode, false, TriStorageOrder, 1>::kernel(
+ Index size, Index otherSize, const float *_tri, Index triStride, float *_other, Index otherIncr,
+ Index otherStride) {
+ EIGEN_UNUSED_VARIABLE(otherIncr);
+ triSolve<float, TriStorageOrder == RowMajor, false, (Mode & Lower) == Lower, (Mode & UnitDiag) != 0>(
+ const_cast<float *>(_tri), _other, size, otherSize, triStride, otherStride);
+}
+
+template <typename Index, int Mode, int TriStorageOrder>
+EIGEN_DONT_INLINE void trsmKernelL<double, Index, Mode, false, TriStorageOrder, 1>::kernel(
+ Index size, Index otherSize, const double *_tri, Index triStride, double *_other, Index otherIncr,
+ Index otherStride) {
+ EIGEN_UNUSED_VARIABLE(otherIncr);
+ triSolve<double, TriStorageOrder == RowMajor, false, (Mode & Lower) == Lower, (Mode & UnitDiag) != 0>(
+ const_cast<double *>(_tri), _other, size, otherSize, triStride, otherStride);
+}
+#endif // EIGEN_USE_AVX512_TRSM_L_KERNELS
+#endif // EIGEN_USE_AVX512_TRSM_KERNELS
+} // namespace internal
+} // namespace Eigen
+#endif // EIGEN_CORE_ARCH_AVX512_TRSM_KERNEL_H
diff --git a/Eigen/src/Core/arch/AVX512/TrsmUnrolls.inc b/Eigen/src/Core/arch/AVX512/TrsmUnrolls.inc
new file mode 100644
index 0000000..6b09424
--- /dev/null
+++ b/Eigen/src/Core/arch/AVX512/TrsmUnrolls.inc
@@ -0,0 +1,1212 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2022 Intel Corporation
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_CORE_ARCH_AVX512_TRSM_UNROLLS_H
+#define EIGEN_CORE_ARCH_AVX512_TRSM_UNROLLS_H
+
+template <bool isARowMajor = true>
+static EIGEN_ALWAYS_INLINE int64_t idA(int64_t i, int64_t j, int64_t LDA) {
+ EIGEN_IF_CONSTEXPR(isARowMajor) return i * LDA + j;
+ else return i + j * LDA;
+}
+
+/**
+ * This namespace contains various classes used to generate compile-time unrolls which are
+ * used throughout the trsm/gemm kernels. The unrolls are characterized as for-loops (1-D), nested
+ * for-loops (2-D), or triple nested for-loops (3-D). Unrolls are generated using template recursion
+ *
+ * Example, the 2-D for-loop is unrolled recursively by first flattening to a 1-D loop.
+ *
+ * for(startI = 0; startI < endI; startI++) for(startC = 0; startC < endI*endJ; startC++)
+ * for(startJ = 0; startJ < endJ; startJ++) ----> startI = (startC)/(endJ)
+ * func(startI,startJ) startJ = (startC)%(endJ)
+ * func(...)
+ *
+ * The 1-D loop can be unrolled recursively by using enable_if and defining an auxillary function
+ * with a template parameter used as a counter.
+ *
+ * template <endI, endJ, counter>
+ * std::enable_if_t<(counter <= 0)> <---- tail case.
+ * aux_func {}
+ *
+ * template <endI, endJ, counter>
+ * std::enable_if_t<(counter > 0)> <---- actual for-loop
+ * aux_func {
+ * startC = endI*endJ - counter
+ * startI = (startC)/(endJ)
+ * startJ = (startC)%(endJ)
+ * func(startI, startJ)
+ * aux_func<endI, endJ, counter-1>()
+ * }
+ *
+ * Note: Additional wrapper functions are provided for aux_func which hides the counter template
+ * parameter since counter usually depends on endI, endJ, etc...
+ *
+ * Conventions:
+ * 1) endX: specifies the terminal value for the for-loop, (ex: for(startX = 0; startX < endX; startX++))
+ *
+ * 2) rem, remM, remK template parameters are used for deciding whether to use masked operations for
+ * handling remaining tails (when sizes are not multiples of PacketSize or EIGEN_AVX_MAX_NUM_ROW)
+ */
+namespace unrolls {
+
+template <int64_t N>
+EIGEN_ALWAYS_INLINE auto remMask(int64_t m) {
+ EIGEN_IF_CONSTEXPR(N == 16) { return 0xFFFF >> (16 - m); }
+ else EIGEN_IF_CONSTEXPR(N == 8) {
+ return 0xFF >> (8 - m);
+ }
+ else EIGEN_IF_CONSTEXPR(N == 4) {
+ return 0x0F >> (4 - m);
+ }
+ return 0;
+}
+
+template <typename Packet>
+EIGEN_ALWAYS_INLINE void trans8x8blocks(PacketBlock<Packet, 8> &kernel);
+
+template <>
+EIGEN_ALWAYS_INLINE void trans8x8blocks(PacketBlock<Packet16f, 8> &kernel) {
+ __m512 T0 = _mm512_unpacklo_ps(kernel.packet[0], kernel.packet[1]);
+ __m512 T1 = _mm512_unpackhi_ps(kernel.packet[0], kernel.packet[1]);
+ __m512 T2 = _mm512_unpacklo_ps(kernel.packet[2], kernel.packet[3]);
+ __m512 T3 = _mm512_unpackhi_ps(kernel.packet[2], kernel.packet[3]);
+ __m512 T4 = _mm512_unpacklo_ps(kernel.packet[4], kernel.packet[5]);
+ __m512 T5 = _mm512_unpackhi_ps(kernel.packet[4], kernel.packet[5]);
+ __m512 T6 = _mm512_unpacklo_ps(kernel.packet[6], kernel.packet[7]);
+ __m512 T7 = _mm512_unpackhi_ps(kernel.packet[6], kernel.packet[7]);
+
+ kernel.packet[0] = _mm512_castpd_ps(_mm512_unpacklo_pd(_mm512_castps_pd(T0), _mm512_castps_pd(T2)));
+ kernel.packet[1] = _mm512_castpd_ps(_mm512_unpackhi_pd(_mm512_castps_pd(T0), _mm512_castps_pd(T2)));
+ kernel.packet[2] = _mm512_castpd_ps(_mm512_unpacklo_pd(_mm512_castps_pd(T1), _mm512_castps_pd(T3)));
+ kernel.packet[3] = _mm512_castpd_ps(_mm512_unpackhi_pd(_mm512_castps_pd(T1), _mm512_castps_pd(T3)));
+ kernel.packet[4] = _mm512_castpd_ps(_mm512_unpacklo_pd(_mm512_castps_pd(T4), _mm512_castps_pd(T6)));
+ kernel.packet[5] = _mm512_castpd_ps(_mm512_unpackhi_pd(_mm512_castps_pd(T4), _mm512_castps_pd(T6)));
+ kernel.packet[6] = _mm512_castpd_ps(_mm512_unpacklo_pd(_mm512_castps_pd(T5), _mm512_castps_pd(T7)));
+ kernel.packet[7] = _mm512_castpd_ps(_mm512_unpackhi_pd(_mm512_castps_pd(T5), _mm512_castps_pd(T7)));
+
+ T0 = _mm512_castpd_ps(_mm512_permutex_pd(_mm512_castps_pd(kernel.packet[4]), 0x4E));
+ T0 = _mm512_mask_blend_ps(0xF0F0, kernel.packet[0], T0);
+ T4 = _mm512_castpd_ps(_mm512_permutex_pd(_mm512_castps_pd(kernel.packet[0]), 0x4E));
+ T4 = _mm512_mask_blend_ps(0xF0F0, T4, kernel.packet[4]);
+ T1 = _mm512_castpd_ps(_mm512_permutex_pd(_mm512_castps_pd(kernel.packet[5]), 0x4E));
+ T1 = _mm512_mask_blend_ps(0xF0F0, kernel.packet[1], T1);
+ T5 = _mm512_castpd_ps(_mm512_permutex_pd(_mm512_castps_pd(kernel.packet[1]), 0x4E));
+ T5 = _mm512_mask_blend_ps(0xF0F0, T5, kernel.packet[5]);
+ T2 = _mm512_castpd_ps(_mm512_permutex_pd(_mm512_castps_pd(kernel.packet[6]), 0x4E));
+ T2 = _mm512_mask_blend_ps(0xF0F0, kernel.packet[2], T2);
+ T6 = _mm512_castpd_ps(_mm512_permutex_pd(_mm512_castps_pd(kernel.packet[2]), 0x4E));
+ T6 = _mm512_mask_blend_ps(0xF0F0, T6, kernel.packet[6]);
+ T3 = _mm512_castpd_ps(_mm512_permutex_pd(_mm512_castps_pd(kernel.packet[7]), 0x4E));
+ T3 = _mm512_mask_blend_ps(0xF0F0, kernel.packet[3], T3);
+ T7 = _mm512_castpd_ps(_mm512_permutex_pd(_mm512_castps_pd(kernel.packet[3]), 0x4E));
+ T7 = _mm512_mask_blend_ps(0xF0F0, T7, kernel.packet[7]);
+
+ kernel.packet[0] = T0;
+ kernel.packet[1] = T1;
+ kernel.packet[2] = T2;
+ kernel.packet[3] = T3;
+ kernel.packet[4] = T4;
+ kernel.packet[5] = T5;
+ kernel.packet[6] = T6;
+ kernel.packet[7] = T7;
+}
+
+template <>
+EIGEN_ALWAYS_INLINE void trans8x8blocks(PacketBlock<Packet8d, 8> &kernel) {
+ ptranspose(kernel);
+}
+
+/***
+ * Unrolls for tranposed C stores
+ */
+template <typename Scalar>
+class trans {
+ public:
+ using vec = typename std::conditional<std::is_same<Scalar, float>::value, vecFullFloat, vecFullDouble>::type;
+ using vecHalf = typename std::conditional<std::is_same<Scalar, float>::value, vecHalfFloat, vecFullDouble>::type;
+ static constexpr int64_t PacketSize = packet_traits<Scalar>::size;
+
+ /***********************************
+ * Auxillary Functions for:
+ * - storeC
+ ***********************************
+ */
+
+ /**
+ * aux_storeC
+ *
+ * 1-D unroll
+ * for(startN = 0; startN < endN; startN++)
+ *
+ * (endN <= PacketSize) is required to handle the fp32 case, see comments in transStoreC
+ *
+ **/
+ template <int64_t endN, int64_t counter, int64_t unrollN, int64_t packetIndexOffset, bool remM>
+ static EIGEN_ALWAYS_INLINE std::enable_if_t<(counter > 0 && endN <= PacketSize)> aux_storeC(
+ Scalar *C_arr, int64_t LDC, PacketBlock<vec, EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS> &zmm, int64_t remM_ = 0) {
+ constexpr int64_t counterReverse = endN - counter;
+ constexpr int64_t startN = counterReverse;
+
+ EIGEN_IF_CONSTEXPR(startN < EIGEN_AVX_MAX_NUM_ROW) {
+ EIGEN_IF_CONSTEXPR(remM) {
+ pstoreu<Scalar>(
+ C_arr + LDC * startN,
+ padd(ploadu<vecHalf>((const Scalar *)C_arr + LDC * startN, remMask<EIGEN_AVX_MAX_NUM_ROW>(remM_)),
+ preinterpret<vecHalf>(zmm.packet[packetIndexOffset + (unrollN / PacketSize) * startN]),
+ remMask<EIGEN_AVX_MAX_NUM_ROW>(remM_)),
+ remMask<EIGEN_AVX_MAX_NUM_ROW>(remM_));
+ }
+ else {
+ pstoreu<Scalar>(C_arr + LDC * startN,
+ padd(ploadu<vecHalf>((const Scalar *)C_arr + LDC * startN),
+ preinterpret<vecHalf>(zmm.packet[packetIndexOffset + (unrollN / PacketSize) * startN])));
+ }
+ }
+ else { // This block is only needed for fp32 case
+ // Reinterpret as __m512 for _mm512_shuffle_f32x4
+ vecFullFloat zmm2vecFullFloat = preinterpret<vecFullFloat>(
+ zmm.packet[packetIndexOffset + (unrollN / PacketSize) * (startN - EIGEN_AVX_MAX_NUM_ROW)]);
+ // Swap lower and upper half of avx register.
+ zmm.packet[packetIndexOffset + (unrollN / PacketSize) * (startN - EIGEN_AVX_MAX_NUM_ROW)] =
+ preinterpret<vec>(_mm512_shuffle_f32x4(zmm2vecFullFloat, zmm2vecFullFloat, 0b01001110));
+
+ EIGEN_IF_CONSTEXPR(remM) {
+ pstoreu<Scalar>(
+ C_arr + LDC * startN,
+ padd(ploadu<vecHalf>((const Scalar *)C_arr + LDC * startN, remMask<EIGEN_AVX_MAX_NUM_ROW>(remM_)),
+ preinterpret<vecHalf>(
+ zmm.packet[packetIndexOffset + (unrollN / PacketSize) * (startN - EIGEN_AVX_MAX_NUM_ROW)])),
+ remMask<EIGEN_AVX_MAX_NUM_ROW>(remM_));
+ }
+ else {
+ pstoreu<Scalar>(
+ C_arr + LDC * startN,
+ padd(ploadu<vecHalf>((const Scalar *)C_arr + LDC * startN),
+ preinterpret<vecHalf>(
+ zmm.packet[packetIndexOffset + (unrollN / PacketSize) * (startN - EIGEN_AVX_MAX_NUM_ROW)])));
+ }
+ }
+ aux_storeC<endN, counter - 1, unrollN, packetIndexOffset, remM>(C_arr, LDC, zmm, remM_);
+ }
+
+ template <int64_t endN, int64_t counter, int64_t unrollN, int64_t packetIndexOffset, bool remM>
+ static EIGEN_ALWAYS_INLINE std::enable_if_t<!(counter > 0 && endN <= PacketSize)> aux_storeC(
+ Scalar *C_arr, int64_t LDC, PacketBlock<vec, EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS> &zmm, int64_t remM_ = 0) {
+ EIGEN_UNUSED_VARIABLE(C_arr);
+ EIGEN_UNUSED_VARIABLE(LDC);
+ EIGEN_UNUSED_VARIABLE(zmm);
+ EIGEN_UNUSED_VARIABLE(remM_);
+ }
+
+ template <int64_t endN, int64_t unrollN, int64_t packetIndexOffset, bool remM>
+ static EIGEN_ALWAYS_INLINE void storeC(Scalar *C_arr, int64_t LDC,
+ PacketBlock<vec, EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS> &zmm,
+ int64_t remM_ = 0) {
+ aux_storeC<endN, endN, unrollN, packetIndexOffset, remM>(C_arr, LDC, zmm, remM_);
+ }
+
+ /**
+ * Transposes LxunrollN row major block of matrices stored EIGEN_AVX_MAX_NUM_ACC zmm registers to
+ * "unrollN"xL ymm registers to be stored col-major into C.
+ *
+ * For 8x48, the 8x48 block (row-major) is stored in zmm as follows:
+ *
+ * row0: zmm0 zmm1 zmm2
+ * row1: zmm3 zmm4 zmm5
+ * .
+ * .
+ * row7: zmm21 zmm22 zmm23
+ *
+ * For 8x32, the 8x32 block (row-major) is stored in zmm as follows:
+ *
+ * row0: zmm0 zmm1
+ * row1: zmm2 zmm3
+ * .
+ * .
+ * row7: zmm14 zmm15
+ *
+ *
+ * In general we will have {1,2,3} groups of avx registers each of size
+ * EIGEN_AVX_MAX_NUM_ROW. packetIndexOffset is used to select which "block" of
+ * avx registers are being transposed.
+ */
+ template <int64_t unrollN, int64_t packetIndexOffset>
+ static EIGEN_ALWAYS_INLINE void transpose(PacketBlock<vec, EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS> &zmm) {
+ // Note: this assumes EIGEN_AVX_MAX_NUM_ROW = 8. Unrolls should be adjusted
+ // accordingly if EIGEN_AVX_MAX_NUM_ROW is smaller.
+ constexpr int64_t zmmStride = unrollN / PacketSize;
+ PacketBlock<vec, EIGEN_AVX_MAX_NUM_ROW> r;
+ r.packet[0] = zmm.packet[packetIndexOffset + zmmStride * 0];
+ r.packet[1] = zmm.packet[packetIndexOffset + zmmStride * 1];
+ r.packet[2] = zmm.packet[packetIndexOffset + zmmStride * 2];
+ r.packet[3] = zmm.packet[packetIndexOffset + zmmStride * 3];
+ r.packet[4] = zmm.packet[packetIndexOffset + zmmStride * 4];
+ r.packet[5] = zmm.packet[packetIndexOffset + zmmStride * 5];
+ r.packet[6] = zmm.packet[packetIndexOffset + zmmStride * 6];
+ r.packet[7] = zmm.packet[packetIndexOffset + zmmStride * 7];
+ trans8x8blocks(r);
+ zmm.packet[packetIndexOffset + zmmStride * 0] = r.packet[0];
+ zmm.packet[packetIndexOffset + zmmStride * 1] = r.packet[1];
+ zmm.packet[packetIndexOffset + zmmStride * 2] = r.packet[2];
+ zmm.packet[packetIndexOffset + zmmStride * 3] = r.packet[3];
+ zmm.packet[packetIndexOffset + zmmStride * 4] = r.packet[4];
+ zmm.packet[packetIndexOffset + zmmStride * 5] = r.packet[5];
+ zmm.packet[packetIndexOffset + zmmStride * 6] = r.packet[6];
+ zmm.packet[packetIndexOffset + zmmStride * 7] = r.packet[7];
+ }
+};
+
+/**
+ * Unrolls for copyBToRowMajor
+ *
+ * Idea:
+ * 1) Load a block of right-hand sides to registers (using loadB).
+ * 2) Convert the block from column-major to row-major (transposeLxL)
+ * 3) Store the blocks from register either to a temp array (toTemp == true), or back to B (toTemp == false).
+ *
+ * We use at most EIGEN_AVX_MAX_NUM_ACC avx registers to store the blocks of B. The remaining registers are
+ * used as temps for transposing.
+ *
+ * Blocks will be of size Lx{U1,U2,U3}. packetIndexOffset is used to index between these subblocks
+ * For fp32, PacketSize = 2*EIGEN_AVX_MAX_NUM_ROW, so we reinterpret packets as packets half the size (zmm -> ymm).
+ */
+template <typename Scalar>
+class transB {
+ public:
+ using vec = typename std::conditional<std::is_same<Scalar, float>::value, vecFullFloat, vecFullDouble>::type;
+ using vecHalf = typename std::conditional<std::is_same<Scalar, float>::value, vecHalfFloat, vecFullDouble>::type;
+ static constexpr int64_t PacketSize = packet_traits<Scalar>::size;
+
+ /***********************************
+ * Auxillary Functions for:
+ * - loadB
+ * - storeB
+ * - loadBBlock
+ * - storeBBlock
+ ***********************************
+ */
+
+ /**
+ * aux_loadB
+ *
+ * 1-D unroll
+ * for(startN = 0; startN < endN; startN++)
+ **/
+ template <int64_t endN, int64_t counter, int64_t packetIndexOffset, bool remM>
+ static EIGEN_ALWAYS_INLINE std::enable_if_t<(counter > 0)> aux_loadB(
+ Scalar *B_arr, int64_t LDB, PacketBlock<vecHalf, EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS> &ymm,
+ int64_t remM_ = 0) {
+ constexpr int64_t counterReverse = endN - counter;
+ constexpr int64_t startN = counterReverse;
+
+ EIGEN_IF_CONSTEXPR(remM) {
+ ymm.packet[packetIndexOffset + startN] =
+ ploadu<vecHalf>((const Scalar *)&B_arr[startN * LDB], remMask<EIGEN_AVX_MAX_NUM_ROW>(remM_));
+ }
+ else ymm.packet[packetIndexOffset + startN] = ploadu<vecHalf>((const Scalar *)&B_arr[startN * LDB]);
+
+ aux_loadB<endN, counter - 1, packetIndexOffset, remM>(B_arr, LDB, ymm, remM_);
+ }
+
+ template <int64_t endN, int64_t counter, int64_t packetIndexOffset, bool remM>
+ static EIGEN_ALWAYS_INLINE std::enable_if_t<(counter <= 0)> aux_loadB(
+ Scalar *B_arr, int64_t LDB, PacketBlock<vecHalf, EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS> &ymm,
+ int64_t remM_ = 0) {
+ EIGEN_UNUSED_VARIABLE(B_arr);
+ EIGEN_UNUSED_VARIABLE(LDB);
+ EIGEN_UNUSED_VARIABLE(ymm);
+ EIGEN_UNUSED_VARIABLE(remM_);
+ }
+
+ /**
+ * aux_storeB
+ *
+ * 1-D unroll
+ * for(startN = 0; startN < endN; startN++)
+ **/
+ template <int64_t endN, int64_t counter, int64_t packetIndexOffset, bool remK, bool remM>
+ static EIGEN_ALWAYS_INLINE std::enable_if_t<(counter > 0)> aux_storeB(
+ Scalar *B_arr, int64_t LDB, PacketBlock<vecHalf, EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS> &ymm, int64_t rem_ = 0) {
+ constexpr int64_t counterReverse = endN - counter;
+ constexpr int64_t startN = counterReverse;
+
+ EIGEN_IF_CONSTEXPR(remK || remM) {
+ pstoreu<Scalar>(&B_arr[startN * LDB], ymm.packet[packetIndexOffset + startN],
+ remMask<EIGEN_AVX_MAX_NUM_ROW>(rem_));
+ }
+ else {
+ pstoreu<Scalar>(&B_arr[startN * LDB], ymm.packet[packetIndexOffset + startN]);
+ }
+
+ aux_storeB<endN, counter - 1, packetIndexOffset, remK, remM>(B_arr, LDB, ymm, rem_);
+ }
+
+ template <int64_t endN, int64_t counter, int64_t packetIndexOffset, bool remK, bool remM>
+ static EIGEN_ALWAYS_INLINE std::enable_if_t<(counter <= 0)> aux_storeB(
+ Scalar *B_arr, int64_t LDB, PacketBlock<vecHalf, EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS> &ymm, int64_t rem_ = 0) {
+ EIGEN_UNUSED_VARIABLE(B_arr);
+ EIGEN_UNUSED_VARIABLE(LDB);
+ EIGEN_UNUSED_VARIABLE(ymm);
+ EIGEN_UNUSED_VARIABLE(rem_);
+ }
+
+ /**
+ * aux_loadBBlock
+ *
+ * 1-D unroll
+ * for(startN = 0; startN < endN; startN += EIGEN_AVX_MAX_NUM_ROW)
+ **/
+ template <int64_t endN, int64_t counter, bool toTemp, bool remM>
+ static EIGEN_ALWAYS_INLINE std::enable_if_t<(counter > 0)> aux_loadBBlock(
+ Scalar *B_arr, int64_t LDB, Scalar *B_temp, int64_t LDB_,
+ PacketBlock<vecHalf, EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS> &ymm, int64_t remM_ = 0) {
+ constexpr int64_t counterReverse = endN - counter;
+ constexpr int64_t startN = counterReverse;
+ transB::template loadB<EIGEN_AVX_MAX_NUM_ROW, startN, false>(&B_temp[startN], LDB_, ymm);
+ aux_loadBBlock<endN, counter - EIGEN_AVX_MAX_NUM_ROW, toTemp, remM>(B_arr, LDB, B_temp, LDB_, ymm, remM_);
+ }
+
+ template <int64_t endN, int64_t counter, bool toTemp, bool remM>
+ static EIGEN_ALWAYS_INLINE std::enable_if_t<(counter <= 0)> aux_loadBBlock(
+ Scalar *B_arr, int64_t LDB, Scalar *B_temp, int64_t LDB_,
+ PacketBlock<vecHalf, EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS> &ymm, int64_t remM_ = 0) {
+ EIGEN_UNUSED_VARIABLE(B_arr);
+ EIGEN_UNUSED_VARIABLE(LDB);
+ EIGEN_UNUSED_VARIABLE(B_temp);
+ EIGEN_UNUSED_VARIABLE(LDB_);
+ EIGEN_UNUSED_VARIABLE(ymm);
+ EIGEN_UNUSED_VARIABLE(remM_);
+ }
+
+ /**
+ * aux_storeBBlock
+ *
+ * 1-D unroll
+ * for(startN = 0; startN < endN; startN += EIGEN_AVX_MAX_NUM_ROW)
+ **/
+ template <int64_t endN, int64_t counter, bool toTemp, bool remM, int64_t remK_>
+ static EIGEN_ALWAYS_INLINE std::enable_if_t<(counter > 0)> aux_storeBBlock(
+ Scalar *B_arr, int64_t LDB, Scalar *B_temp, int64_t LDB_,
+ PacketBlock<vecHalf, EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS> &ymm, int64_t remM_ = 0) {
+ constexpr int64_t counterReverse = endN - counter;
+ constexpr int64_t startN = counterReverse;
+
+ EIGEN_IF_CONSTEXPR(toTemp) {
+ transB::template storeB<EIGEN_AVX_MAX_NUM_ROW, startN, remK_ != 0, false>(&B_temp[startN], LDB_, ymm, remK_);
+ }
+ else {
+ transB::template storeB<std::min(EIGEN_AVX_MAX_NUM_ROW, endN), startN, false, remM>(&B_arr[0 + startN * LDB], LDB,
+ ymm, remM_);
+ }
+ aux_storeBBlock<endN, counter - EIGEN_AVX_MAX_NUM_ROW, toTemp, remM, remK_>(B_arr, LDB, B_temp, LDB_, ymm, remM_);
+ }
+
+ template <int64_t endN, int64_t counter, bool toTemp, bool remM, int64_t remK_>
+ static EIGEN_ALWAYS_INLINE std::enable_if_t<(counter <= 0)> aux_storeBBlock(
+ Scalar *B_arr, int64_t LDB, Scalar *B_temp, int64_t LDB_,
+ PacketBlock<vecHalf, EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS> &ymm, int64_t remM_ = 0) {
+ EIGEN_UNUSED_VARIABLE(B_arr);
+ EIGEN_UNUSED_VARIABLE(LDB);
+ EIGEN_UNUSED_VARIABLE(B_temp);
+ EIGEN_UNUSED_VARIABLE(LDB_);
+ EIGEN_UNUSED_VARIABLE(ymm);
+ EIGEN_UNUSED_VARIABLE(remM_);
+ }
+
+ /********************************************************
+ * Wrappers for aux_XXXX to hide counter parameter
+ ********************************************************/
+
+ template <int64_t endN, int64_t packetIndexOffset, bool remM>
+ static EIGEN_ALWAYS_INLINE void loadB(Scalar *B_arr, int64_t LDB,
+ PacketBlock<vecHalf, EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS> &ymm,
+ int64_t remM_ = 0) {
+ aux_loadB<endN, endN, packetIndexOffset, remM>(B_arr, LDB, ymm, remM_);
+ }
+
+ template <int64_t endN, int64_t packetIndexOffset, bool remK, bool remM>
+ static EIGEN_ALWAYS_INLINE void storeB(Scalar *B_arr, int64_t LDB,
+ PacketBlock<vecHalf, EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS> &ymm,
+ int64_t rem_ = 0) {
+ aux_storeB<endN, endN, packetIndexOffset, remK, remM>(B_arr, LDB, ymm, rem_);
+ }
+
+ template <int64_t unrollN, bool toTemp, bool remM>
+ static EIGEN_ALWAYS_INLINE void loadBBlock(Scalar *B_arr, int64_t LDB, Scalar *B_temp, int64_t LDB_,
+ PacketBlock<vecHalf, EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS> &ymm,
+ int64_t remM_ = 0) {
+ EIGEN_IF_CONSTEXPR(toTemp) { transB::template loadB<unrollN, 0, remM>(&B_arr[0], LDB, ymm, remM_); }
+ else {
+ aux_loadBBlock<unrollN, unrollN, toTemp, remM>(B_arr, LDB, B_temp, LDB_, ymm, remM_);
+ }
+ }
+
+ template <int64_t unrollN, bool toTemp, bool remM, int64_t remK_>
+ static EIGEN_ALWAYS_INLINE void storeBBlock(Scalar *B_arr, int64_t LDB, Scalar *B_temp, int64_t LDB_,
+ PacketBlock<vecHalf, EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS> &ymm,
+ int64_t remM_ = 0) {
+ aux_storeBBlock<unrollN, unrollN, toTemp, remM, remK_>(B_arr, LDB, B_temp, LDB_, ymm, remM_);
+ }
+
+ template <int64_t packetIndexOffset>
+ static EIGEN_ALWAYS_INLINE void transposeLxL(PacketBlock<vecHalf, EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS> &ymm) {
+ // Note: this assumes EIGEN_AVX_MAX_NUM_ROW = 8. Unrolls should be adjusted
+ // accordingly if EIGEN_AVX_MAX_NUM_ROW is smaller.
+ PacketBlock<vecHalf, EIGEN_AVX_MAX_NUM_ROW> r;
+ r.packet[0] = ymm.packet[packetIndexOffset + 0];
+ r.packet[1] = ymm.packet[packetIndexOffset + 1];
+ r.packet[2] = ymm.packet[packetIndexOffset + 2];
+ r.packet[3] = ymm.packet[packetIndexOffset + 3];
+ r.packet[4] = ymm.packet[packetIndexOffset + 4];
+ r.packet[5] = ymm.packet[packetIndexOffset + 5];
+ r.packet[6] = ymm.packet[packetIndexOffset + 6];
+ r.packet[7] = ymm.packet[packetIndexOffset + 7];
+ ptranspose(r);
+ ymm.packet[packetIndexOffset + 0] = r.packet[0];
+ ymm.packet[packetIndexOffset + 1] = r.packet[1];
+ ymm.packet[packetIndexOffset + 2] = r.packet[2];
+ ymm.packet[packetIndexOffset + 3] = r.packet[3];
+ ymm.packet[packetIndexOffset + 4] = r.packet[4];
+ ymm.packet[packetIndexOffset + 5] = r.packet[5];
+ ymm.packet[packetIndexOffset + 6] = r.packet[6];
+ ymm.packet[packetIndexOffset + 7] = r.packet[7];
+ }
+
+ template <int64_t unrollN, bool toTemp, bool remM>
+ static EIGEN_ALWAYS_INLINE void transB_kernel(Scalar *B_arr, int64_t LDB, Scalar *B_temp, int64_t LDB_,
+ PacketBlock<vecHalf, EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS> &ymm,
+ int64_t remM_ = 0) {
+ constexpr int64_t U3 = PacketSize * 3;
+ constexpr int64_t U2 = PacketSize * 2;
+ constexpr int64_t U1 = PacketSize * 1;
+ /**
+ * Unrolls needed for each case:
+ * - AVX512 fp32 48 32 16 8 4 2 1
+ * - AVX512 fp64 24 16 8 4 2 1
+ *
+ * For fp32 L and U1 are 1:2 so for U3/U2 cases the loads/stores need to be split up.
+ */
+ EIGEN_IF_CONSTEXPR(unrollN == U3) {
+ // load LxU3 B col major, transpose LxU3 row major
+ constexpr int64_t maxUBlock = std::min(3 * EIGEN_AVX_MAX_NUM_ROW, U3);
+ transB::template loadBBlock<maxUBlock, toTemp, remM>(B_arr, LDB, B_temp, LDB_, ymm, remM_);
+ transB::template transposeLxL<0 * EIGEN_AVX_MAX_NUM_ROW>(ymm);
+ transB::template transposeLxL<1 * EIGEN_AVX_MAX_NUM_ROW>(ymm);
+ transB::template transposeLxL<2 * EIGEN_AVX_MAX_NUM_ROW>(ymm);
+ transB::template storeBBlock<maxUBlock, toTemp, remM, 0>(B_arr, LDB, B_temp, LDB_, ymm, remM_);
+
+ EIGEN_IF_CONSTEXPR(maxUBlock < U3) {
+ transB::template loadBBlock<maxUBlock, toTemp, remM>(&B_arr[maxUBlock * LDB], LDB, &B_temp[maxUBlock], LDB_,
+ ymm, remM_);
+ transB::template transposeLxL<0 * EIGEN_AVX_MAX_NUM_ROW>(ymm);
+ transB::template transposeLxL<1 * EIGEN_AVX_MAX_NUM_ROW>(ymm);
+ transB::template transposeLxL<2 * EIGEN_AVX_MAX_NUM_ROW>(ymm);
+ transB::template storeBBlock<maxUBlock, toTemp, remM, 0>(&B_arr[maxUBlock * LDB], LDB, &B_temp[maxUBlock], LDB_,
+ ymm, remM_);
+ }
+ }
+ else EIGEN_IF_CONSTEXPR(unrollN == U2) {
+ // load LxU2 B col major, transpose LxU2 row major
+ constexpr int64_t maxUBlock = std::min(3 * EIGEN_AVX_MAX_NUM_ROW, U2);
+ transB::template loadBBlock<maxUBlock, toTemp, remM>(B_arr, LDB, B_temp, LDB_, ymm, remM_);
+ transB::template transposeLxL<0 * EIGEN_AVX_MAX_NUM_ROW>(ymm);
+ transB::template transposeLxL<1 * EIGEN_AVX_MAX_NUM_ROW>(ymm);
+ EIGEN_IF_CONSTEXPR(maxUBlock < U2) transB::template transposeLxL<2 * EIGEN_AVX_MAX_NUM_ROW>(ymm);
+ transB::template storeBBlock<maxUBlock, toTemp, remM, 0>(B_arr, LDB, B_temp, LDB_, ymm, remM_);
+
+ EIGEN_IF_CONSTEXPR(maxUBlock < U2) {
+ transB::template loadBBlock<EIGEN_AVX_MAX_NUM_ROW, toTemp, remM>(&B_arr[maxUBlock * LDB], LDB,
+ &B_temp[maxUBlock], LDB_, ymm, remM_);
+ transB::template transposeLxL<0>(ymm);
+ transB::template storeBBlock<EIGEN_AVX_MAX_NUM_ROW, toTemp, remM, 0>(&B_arr[maxUBlock * LDB], LDB,
+ &B_temp[maxUBlock], LDB_, ymm, remM_);
+ }
+ }
+ else EIGEN_IF_CONSTEXPR(unrollN == U1) {
+ // load LxU1 B col major, transpose LxU1 row major
+ transB::template loadBBlock<U1, toTemp, remM>(B_arr, LDB, B_temp, LDB_, ymm, remM_);
+ transB::template transposeLxL<0>(ymm);
+ EIGEN_IF_CONSTEXPR(EIGEN_AVX_MAX_NUM_ROW < U1) { transB::template transposeLxL<1 * EIGEN_AVX_MAX_NUM_ROW>(ymm); }
+ transB::template storeBBlock<U1, toTemp, remM, 0>(B_arr, LDB, B_temp, LDB_, ymm, remM_);
+ }
+ else EIGEN_IF_CONSTEXPR(unrollN == 8 && U1 > 8) {
+ // load Lx4 B col major, transpose Lx4 row major
+ transB::template loadBBlock<8, toTemp, remM>(B_arr, LDB, B_temp, LDB_, ymm, remM_);
+ transB::template transposeLxL<0>(ymm);
+ transB::template storeBBlock<8, toTemp, remM, 8>(B_arr, LDB, B_temp, LDB_, ymm, remM_);
+ }
+ else EIGEN_IF_CONSTEXPR(unrollN == 4 && U1 > 4) {
+ // load Lx4 B col major, transpose Lx4 row major
+ transB::template loadBBlock<4, toTemp, remM>(B_arr, LDB, B_temp, LDB_, ymm, remM_);
+ transB::template transposeLxL<0>(ymm);
+ transB::template storeBBlock<4, toTemp, remM, 4>(B_arr, LDB, B_temp, LDB_, ymm, remM_);
+ }
+ else EIGEN_IF_CONSTEXPR(unrollN == 2) {
+ // load Lx2 B col major, transpose Lx2 row major
+ transB::template loadBBlock<2, toTemp, remM>(B_arr, LDB, B_temp, LDB_, ymm, remM_);
+ transB::template transposeLxL<0>(ymm);
+ transB::template storeBBlock<2, toTemp, remM, 2>(B_arr, LDB, B_temp, LDB_, ymm, remM_);
+ }
+ else EIGEN_IF_CONSTEXPR(unrollN == 1) {
+ // load Lx1 B col major, transpose Lx1 row major
+ transB::template loadBBlock<1, toTemp, remM>(B_arr, LDB, B_temp, LDB_, ymm, remM_);
+ transB::template transposeLxL<0>(ymm);
+ transB::template storeBBlock<1, toTemp, remM, 1>(B_arr, LDB, B_temp, LDB_, ymm, remM_);
+ }
+ }
+};
+
+/**
+ * Unrolls for triSolveKernel
+ *
+ * Idea:
+ * 1) Load a block of right-hand sides to registers in RHSInPacket (using loadRHS).
+ * 2) Do triangular solve with RHSInPacket and a small block of A (triangular matrix)
+ * stored in AInPacket (using triSolveMicroKernel).
+ * 3) Store final results (in avx registers) back into memory (using storeRHS).
+ *
+ * RHSInPacket uses at most EIGEN_AVX_MAX_NUM_ACC avx registers and AInPacket uses at most
+ * EIGEN_AVX_MAX_NUM_ROW registers.
+ */
+template <typename Scalar>
+class trsm {
+ public:
+ using vec = typename std::conditional<std::is_same<Scalar, float>::value, vecFullFloat, vecFullDouble>::type;
+ static constexpr int64_t PacketSize = packet_traits<Scalar>::size;
+
+ /***********************************
+ * Auxillary Functions for:
+ * - loadRHS
+ * - storeRHS
+ * - divRHSByDiag
+ * - updateRHS
+ * - triSolveMicroKernel
+ ************************************/
+ /**
+ * aux_loadRHS
+ *
+ * 2-D unroll
+ * for(startM = 0; startM < endM; startM++)
+ * for(startK = 0; startK < endK; startK++)
+ **/
+ template <bool isFWDSolve, int64_t endM, int64_t endK, int64_t counter, bool krem>
+ static EIGEN_ALWAYS_INLINE std::enable_if_t<(counter > 0)> aux_loadRHS(
+ Scalar *B_arr, int64_t LDB, PacketBlock<vec, EIGEN_AVX_MAX_NUM_ACC> &RHSInPacket, int64_t rem = 0) {
+ constexpr int64_t counterReverse = endM * endK - counter;
+ constexpr int64_t startM = counterReverse / (endK);
+ constexpr int64_t startK = counterReverse % endK;
+
+ constexpr int64_t packetIndex = startM * endK + startK;
+ constexpr int64_t startM_ = isFWDSolve ? startM : -startM;
+ const int64_t rhsIndex = (startK * PacketSize) + startM_ * LDB;
+ EIGEN_IF_CONSTEXPR(krem) {
+ RHSInPacket.packet[packetIndex] = ploadu<vec>(&B_arr[rhsIndex], remMask<PacketSize>(rem));
+ }
+ else {
+ RHSInPacket.packet[packetIndex] = ploadu<vec>(&B_arr[rhsIndex]);
+ }
+ aux_loadRHS<isFWDSolve, endM, endK, counter - 1, krem>(B_arr, LDB, RHSInPacket, rem);
+ }
+
+ template <bool isFWDSolve, int64_t endM, int64_t endK, int64_t counter, bool krem>
+ static EIGEN_ALWAYS_INLINE std::enable_if_t<(counter <= 0)> aux_loadRHS(
+ Scalar *B_arr, int64_t LDB, PacketBlock<vec, EIGEN_AVX_MAX_NUM_ACC> &RHSInPacket, int64_t rem = 0) {
+ EIGEN_UNUSED_VARIABLE(B_arr);
+ EIGEN_UNUSED_VARIABLE(LDB);
+ EIGEN_UNUSED_VARIABLE(RHSInPacket);
+ EIGEN_UNUSED_VARIABLE(rem);
+ }
+
+ /**
+ * aux_storeRHS
+ *
+ * 2-D unroll
+ * for(startM = 0; startM < endM; startM++)
+ * for(startK = 0; startK < endK; startK++)
+ **/
+ template <bool isFWDSolve, int64_t endM, int64_t endK, int64_t counter, bool krem>
+ static EIGEN_ALWAYS_INLINE std::enable_if_t<(counter > 0)> aux_storeRHS(
+ Scalar *B_arr, int64_t LDB, PacketBlock<vec, EIGEN_AVX_MAX_NUM_ACC> &RHSInPacket, int64_t rem = 0) {
+ constexpr int64_t counterReverse = endM * endK - counter;
+ constexpr int64_t startM = counterReverse / (endK);
+ constexpr int64_t startK = counterReverse % endK;
+
+ constexpr int64_t packetIndex = startM * endK + startK;
+ constexpr int64_t startM_ = isFWDSolve ? startM : -startM;
+ const int64_t rhsIndex = (startK * PacketSize) + startM_ * LDB;
+ EIGEN_IF_CONSTEXPR(krem) {
+ pstoreu<Scalar>(&B_arr[rhsIndex], RHSInPacket.packet[packetIndex], remMask<PacketSize>(rem));
+ }
+ else {
+ pstoreu<Scalar>(&B_arr[rhsIndex], RHSInPacket.packet[packetIndex]);
+ }
+ aux_storeRHS<isFWDSolve, endM, endK, counter - 1, krem>(B_arr, LDB, RHSInPacket, rem);
+ }
+
+ template <bool isFWDSolve, int64_t endM, int64_t endK, int64_t counter, bool krem>
+ static EIGEN_ALWAYS_INLINE std::enable_if_t<(counter <= 0)> aux_storeRHS(
+ Scalar *B_arr, int64_t LDB, PacketBlock<vec, EIGEN_AVX_MAX_NUM_ACC> &RHSInPacket, int64_t rem = 0) {
+ EIGEN_UNUSED_VARIABLE(B_arr);
+ EIGEN_UNUSED_VARIABLE(LDB);
+ EIGEN_UNUSED_VARIABLE(RHSInPacket);
+ EIGEN_UNUSED_VARIABLE(rem);
+ }
+
+ /**
+ * aux_divRHSByDiag
+ *
+ * currM may be -1, (currM >=0) in enable_if checks for this
+ *
+ * 1-D unroll
+ * for(startK = 0; startK < endK; startK++)
+ **/
+ template <int64_t currM, int64_t endK, int64_t counter>
+ static EIGEN_ALWAYS_INLINE std::enable_if_t<(counter > 0 && currM >= 0)> aux_divRHSByDiag(
+ PacketBlock<vec, EIGEN_AVX_MAX_NUM_ACC> &RHSInPacket, PacketBlock<vec, EIGEN_AVX_MAX_NUM_ROW> &AInPacket) {
+ constexpr int64_t counterReverse = endK - counter;
+ constexpr int64_t startK = counterReverse;
+
+ constexpr int64_t packetIndex = currM * endK + startK;
+ RHSInPacket.packet[packetIndex] = pmul(AInPacket.packet[currM], RHSInPacket.packet[packetIndex]);
+ aux_divRHSByDiag<currM, endK, counter - 1>(RHSInPacket, AInPacket);
+ }
+
+ template <int64_t currM, int64_t endK, int64_t counter>
+ static EIGEN_ALWAYS_INLINE std::enable_if_t<!(counter > 0 && currM >= 0)> aux_divRHSByDiag(
+ PacketBlock<vec, EIGEN_AVX_MAX_NUM_ACC> &RHSInPacket, PacketBlock<vec, EIGEN_AVX_MAX_NUM_ROW> &AInPacket) {
+ EIGEN_UNUSED_VARIABLE(RHSInPacket);
+ EIGEN_UNUSED_VARIABLE(AInPacket);
+ }
+
+ /**
+ * aux_updateRHS
+ *
+ * 2-D unroll
+ * for(startM = initM; startM < endM; startM++)
+ * for(startK = 0; startK < endK; startK++)
+ **/
+ template <bool isARowMajor, bool isFWDSolve, bool isUnitDiag, int64_t initM, int64_t endM, int64_t endK,
+ int64_t counter, int64_t currentM>
+ static EIGEN_ALWAYS_INLINE std::enable_if_t<(counter > 0)> aux_updateRHS(
+ Scalar *A_arr, int64_t LDA, PacketBlock<vec, EIGEN_AVX_MAX_NUM_ACC> &RHSInPacket,
+ PacketBlock<vec, EIGEN_AVX_MAX_NUM_ROW> &AInPacket) {
+ constexpr int64_t counterReverse = (endM - initM) * endK - counter;
+ constexpr int64_t startM = initM + counterReverse / (endK);
+ constexpr int64_t startK = counterReverse % endK;
+
+ // For each row of A, first update all corresponding RHS
+ constexpr int64_t packetIndex = startM * endK + startK;
+ EIGEN_IF_CONSTEXPR(currentM > 0) {
+ RHSInPacket.packet[packetIndex] =
+ pnmadd(AInPacket.packet[startM], RHSInPacket.packet[(currentM - 1) * endK + startK],
+ RHSInPacket.packet[packetIndex]);
+ }
+
+ EIGEN_IF_CONSTEXPR(startK == endK - 1) {
+ // Once all RHS for previous row of A is updated, we broadcast the next element in the column A_{i, currentM}.
+ EIGEN_IF_CONSTEXPR(startM == currentM && !isUnitDiag) {
+ // If diagonal is not unit, we broadcast reciprocals of diagonals AinPacket.packet[currentM].
+ // This will be used in divRHSByDiag
+ EIGEN_IF_CONSTEXPR(isFWDSolve)
+ AInPacket.packet[currentM] = pset1<vec>(Scalar(1) / A_arr[idA<isARowMajor>(currentM, currentM, LDA)]);
+ else AInPacket.packet[currentM] = pset1<vec>(Scalar(1) / A_arr[idA<isARowMajor>(-currentM, -currentM, LDA)]);
+ }
+ else {
+ // Broadcast next off diagonal element of A
+ EIGEN_IF_CONSTEXPR(isFWDSolve)
+ AInPacket.packet[startM] = pset1<vec>(A_arr[idA<isARowMajor>(startM, currentM, LDA)]);
+ else AInPacket.packet[startM] = pset1<vec>(A_arr[idA<isARowMajor>(-startM, -currentM, LDA)]);
+ }
+ }
+
+ aux_updateRHS<isARowMajor, isFWDSolve, isUnitDiag, initM, endM, endK, counter - 1, currentM>(
+ A_arr, LDA, RHSInPacket, AInPacket);
+ }
+
+ template <bool isARowMajor, bool isFWDSolve, bool isUnitDiag, int64_t initM, int64_t endM, int64_t endK,
+ int64_t counter, int64_t currentM>
+ static EIGEN_ALWAYS_INLINE std::enable_if_t<(counter <= 0)> aux_updateRHS(
+ Scalar *A_arr, int64_t LDA, PacketBlock<vec, EIGEN_AVX_MAX_NUM_ACC> &RHSInPacket,
+ PacketBlock<vec, EIGEN_AVX_MAX_NUM_ROW> &AInPacket) {
+ EIGEN_UNUSED_VARIABLE(A_arr);
+ EIGEN_UNUSED_VARIABLE(LDA);
+ EIGEN_UNUSED_VARIABLE(RHSInPacket);
+ EIGEN_UNUSED_VARIABLE(AInPacket);
+ }
+
+ /**
+ * aux_triSolverMicroKernel
+ *
+ * 1-D unroll
+ * for(startM = 0; startM < endM; startM++)
+ **/
+ template <bool isARowMajor, bool isFWDSolve, bool isUnitDiag, int64_t endM, int64_t counter, int64_t numK>
+ static EIGEN_ALWAYS_INLINE std::enable_if_t<(counter > 0)> aux_triSolveMicroKernel(
+ Scalar *A_arr, int64_t LDA, PacketBlock<vec, EIGEN_AVX_MAX_NUM_ACC> &RHSInPacket,
+ PacketBlock<vec, EIGEN_AVX_MAX_NUM_ROW> &AInPacket) {
+ constexpr int64_t counterReverse = endM - counter;
+ constexpr int64_t startM = counterReverse;
+
+ constexpr int64_t currentM = startM;
+ // Divides the right-hand side in row startM, by digonal value of A
+ // broadcasted to AInPacket.packet[startM-1] in the previous iteration.
+ //
+ // Without "if constexpr" the compiler instantiates the case <-1, numK>
+ // this is handled with enable_if to prevent out-of-bound warnings
+ // from the compiler
+ EIGEN_IF_CONSTEXPR(!isUnitDiag && startM > 0)
+ trsm::template divRHSByDiag<startM - 1, numK>(RHSInPacket, AInPacket);
+
+ // After division, the rhs corresponding to subsequent rows of A can be partially updated
+ // We also broadcast the reciprocal of the next diagonal to AInPacket.packet[currentM] (if needed)
+ // to be used in the next iteration.
+ trsm::template updateRHS<isARowMajor, isFWDSolve, isUnitDiag, startM, endM, numK, currentM>(A_arr, LDA, RHSInPacket,
+ AInPacket);
+
+ // Handle division for the RHS corresponding to the final row of A.
+ EIGEN_IF_CONSTEXPR(!isUnitDiag && startM == endM - 1)
+ trsm::template divRHSByDiag<startM, numK>(RHSInPacket, AInPacket);
+
+ aux_triSolveMicroKernel<isARowMajor, isFWDSolve, isUnitDiag, endM, counter - 1, numK>(A_arr, LDA, RHSInPacket,
+ AInPacket);
+ }
+
+ template <bool isARowMajor, bool isFWDSolve, bool isUnitDiag, int64_t endM, int64_t counter, int64_t numK>
+ static EIGEN_ALWAYS_INLINE std::enable_if_t<(counter <= 0)> aux_triSolveMicroKernel(
+ Scalar *A_arr, int64_t LDA, PacketBlock<vec, EIGEN_AVX_MAX_NUM_ACC> &RHSInPacket,
+ PacketBlock<vec, EIGEN_AVX_MAX_NUM_ROW> &AInPacket) {
+ EIGEN_UNUSED_VARIABLE(A_arr);
+ EIGEN_UNUSED_VARIABLE(LDA);
+ EIGEN_UNUSED_VARIABLE(RHSInPacket);
+ EIGEN_UNUSED_VARIABLE(AInPacket);
+ }
+
+ /********************************************************
+ * Wrappers for aux_XXXX to hide counter parameter
+ ********************************************************/
+
+ /**
+ * Load endMxendK block of B to RHSInPacket
+ * Masked loads are used for cases where endK is not a multiple of PacketSize
+ */
+ template <bool isFWDSolve, int64_t endM, int64_t endK, bool krem = false>
+ static EIGEN_ALWAYS_INLINE void loadRHS(Scalar *B_arr, int64_t LDB,
+ PacketBlock<vec, EIGEN_AVX_MAX_NUM_ACC> &RHSInPacket, int64_t rem = 0) {
+ aux_loadRHS<isFWDSolve, endM, endK, endM * endK, krem>(B_arr, LDB, RHSInPacket, rem);
+ }
+
+ /**
+ * Load endMxendK block of B to RHSInPacket
+ * Masked loads are used for cases where endK is not a multiple of PacketSize
+ */
+ template <bool isFWDSolve, int64_t endM, int64_t endK, bool krem = false>
+ static EIGEN_ALWAYS_INLINE void storeRHS(Scalar *B_arr, int64_t LDB,
+ PacketBlock<vec, EIGEN_AVX_MAX_NUM_ACC> &RHSInPacket, int64_t rem = 0) {
+ aux_storeRHS<isFWDSolve, endM, endK, endM * endK, krem>(B_arr, LDB, RHSInPacket, rem);
+ }
+
+ /**
+ * Only used if Triangular matrix has non-unit diagonal values
+ */
+ template <int64_t currM, int64_t endK>
+ static EIGEN_ALWAYS_INLINE void divRHSByDiag(PacketBlock<vec, EIGEN_AVX_MAX_NUM_ACC> &RHSInPacket,
+ PacketBlock<vec, EIGEN_AVX_MAX_NUM_ROW> &AInPacket) {
+ aux_divRHSByDiag<currM, endK, endK>(RHSInPacket, AInPacket);
+ }
+
+ /**
+ * Update right-hand sides (stored in avx registers)
+ * Traversing along the column A_{i,currentM}, where currentM <= i <= endM, and broadcasting each value to AInPacket.
+ **/
+ template <bool isARowMajor, bool isFWDSolve, bool isUnitDiag, int64_t startM, int64_t endM, int64_t endK,
+ int64_t currentM>
+ static EIGEN_ALWAYS_INLINE void updateRHS(Scalar *A_arr, int64_t LDA,
+ PacketBlock<vec, EIGEN_AVX_MAX_NUM_ACC> &RHSInPacket,
+ PacketBlock<vec, EIGEN_AVX_MAX_NUM_ROW> &AInPacket) {
+ aux_updateRHS<isARowMajor, isFWDSolve, isUnitDiag, startM, endM, endK, (endM - startM) * endK, currentM>(
+ A_arr, LDA, RHSInPacket, AInPacket);
+ }
+
+ /**
+ * endM: dimension of A. 1 <= endM <= EIGEN_AVX_MAX_NUM_ROW
+ * numK: number of avx registers to use for each row of B (ex fp32: 48 rhs => 3 avx reg used). 1 <= endK <= 3.
+ * isFWDSolve: true => forward substitution, false => backwards substitution
+ * isUnitDiag: true => triangular matrix has unit diagonal.
+ */
+ template <bool isARowMajor, bool isFWDSolve, bool isUnitDiag, int64_t endM, int64_t numK>
+ static EIGEN_ALWAYS_INLINE void triSolveMicroKernel(Scalar *A_arr, int64_t LDA,
+ PacketBlock<vec, EIGEN_AVX_MAX_NUM_ACC> &RHSInPacket,
+ PacketBlock<vec, EIGEN_AVX_MAX_NUM_ROW> &AInPacket) {
+ static_assert(numK >= 1 && numK <= 3, "numK out of range");
+ aux_triSolveMicroKernel<isARowMajor, isFWDSolve, isUnitDiag, endM, endM, numK>(A_arr, LDA, RHSInPacket, AInPacket);
+ }
+};
+
+/**
+ * Unrolls for gemm kernel
+ *
+ * isAdd: true => C += A*B, false => C -= A*B
+ */
+template <typename Scalar, bool isAdd>
+class gemm {
+ public:
+ using vec = typename std::conditional<std::is_same<Scalar, float>::value, vecFullFloat, vecFullDouble>::type;
+ static constexpr int64_t PacketSize = packet_traits<Scalar>::size;
+
+ /***********************************
+ * Auxillary Functions for:
+ * - setzero
+ * - updateC
+ * - storeC
+ * - startLoadB
+ * - triSolveMicroKernel
+ ************************************/
+
+ /**
+ * aux_setzero
+ *
+ * 2-D unroll
+ * for(startM = 0; startM < endM; startM++)
+ * for(startN = 0; startN < endN; startN++)
+ **/
+ template <int64_t endM, int64_t endN, int64_t counter>
+ static EIGEN_ALWAYS_INLINE std::enable_if_t<(counter > 0)> aux_setzero(
+ PacketBlock<vec, EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS> &zmm) {
+ constexpr int64_t counterReverse = endM * endN - counter;
+ constexpr int64_t startM = counterReverse / (endN);
+ constexpr int64_t startN = counterReverse % endN;
+
+ zmm.packet[startN * endM + startM] = pzero(zmm.packet[startN * endM + startM]);
+ aux_setzero<endM, endN, counter - 1>(zmm);
+ }
+
+ template <int64_t endM, int64_t endN, int64_t counter>
+ static EIGEN_ALWAYS_INLINE std::enable_if_t<(counter <= 0)> aux_setzero(
+ PacketBlock<vec, EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS> &zmm) {
+ EIGEN_UNUSED_VARIABLE(zmm);
+ }
+
+ /**
+ * aux_updateC
+ *
+ * 2-D unroll
+ * for(startM = 0; startM < endM; startM++)
+ * for(startN = 0; startN < endN; startN++)
+ **/
+ template <int64_t endM, int64_t endN, int64_t counter, bool rem>
+ static EIGEN_ALWAYS_INLINE std::enable_if_t<(counter > 0)> aux_updateC(
+ Scalar *C_arr, int64_t LDC, PacketBlock<vec, EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS> &zmm, int64_t rem_ = 0) {
+ EIGEN_UNUSED_VARIABLE(rem_);
+ constexpr int64_t counterReverse = endM * endN - counter;
+ constexpr int64_t startM = counterReverse / (endN);
+ constexpr int64_t startN = counterReverse % endN;
+
+ EIGEN_IF_CONSTEXPR(rem)
+ zmm.packet[startN * endM + startM] =
+ padd(ploadu<vec>(&C_arr[(startN)*LDC + startM * PacketSize], remMask<PacketSize>(rem_)),
+ zmm.packet[startN * endM + startM], remMask<PacketSize>(rem_));
+ else zmm.packet[startN * endM + startM] =
+ padd(ploadu<vec>(&C_arr[(startN)*LDC + startM * PacketSize]), zmm.packet[startN * endM + startM]);
+ aux_updateC<endM, endN, counter - 1, rem>(C_arr, LDC, zmm, rem_);
+ }
+
+ template <int64_t endM, int64_t endN, int64_t counter, bool rem>
+ static EIGEN_ALWAYS_INLINE std::enable_if_t<(counter <= 0)> aux_updateC(
+ Scalar *C_arr, int64_t LDC, PacketBlock<vec, EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS> &zmm, int64_t rem_ = 0) {
+ EIGEN_UNUSED_VARIABLE(C_arr);
+ EIGEN_UNUSED_VARIABLE(LDC);
+ EIGEN_UNUSED_VARIABLE(zmm);
+ EIGEN_UNUSED_VARIABLE(rem_);
+ }
+
+ /**
+ * aux_storeC
+ *
+ * 2-D unroll
+ * for(startM = 0; startM < endM; startM++)
+ * for(startN = 0; startN < endN; startN++)
+ **/
+ template <int64_t endM, int64_t endN, int64_t counter, bool rem>
+ static EIGEN_ALWAYS_INLINE std::enable_if_t<(counter > 0)> aux_storeC(
+ Scalar *C_arr, int64_t LDC, PacketBlock<vec, EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS> &zmm, int64_t rem_ = 0) {
+ EIGEN_UNUSED_VARIABLE(rem_);
+ constexpr int64_t counterReverse = endM * endN - counter;
+ constexpr int64_t startM = counterReverse / (endN);
+ constexpr int64_t startN = counterReverse % endN;
+
+ EIGEN_IF_CONSTEXPR(rem)
+ pstoreu<Scalar>(&C_arr[(startN)*LDC + startM * PacketSize], zmm.packet[startN * endM + startM],
+ remMask<PacketSize>(rem_));
+ else pstoreu<Scalar>(&C_arr[(startN)*LDC + startM * PacketSize], zmm.packet[startN * endM + startM]);
+ aux_storeC<endM, endN, counter - 1, rem>(C_arr, LDC, zmm, rem_);
+ }
+
+ template <int64_t endM, int64_t endN, int64_t counter, bool rem>
+ static EIGEN_ALWAYS_INLINE std::enable_if_t<(counter <= 0)> aux_storeC(
+ Scalar *C_arr, int64_t LDC, PacketBlock<vec, EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS> &zmm, int64_t rem_ = 0) {
+ EIGEN_UNUSED_VARIABLE(C_arr);
+ EIGEN_UNUSED_VARIABLE(LDC);
+ EIGEN_UNUSED_VARIABLE(zmm);
+ EIGEN_UNUSED_VARIABLE(rem_);
+ }
+
+ /**
+ * aux_startLoadB
+ *
+ * 1-D unroll
+ * for(startL = 0; startL < endL; startL++)
+ **/
+ template <int64_t unrollM, int64_t unrollN, int64_t endL, int64_t counter, bool rem>
+ static EIGEN_ALWAYS_INLINE std::enable_if_t<(counter > 0)> aux_startLoadB(
+ Scalar *B_t, int64_t LDB, PacketBlock<vec, EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS> &zmm, int64_t rem_ = 0) {
+ EIGEN_UNUSED_VARIABLE(rem_);
+ constexpr int64_t counterReverse = endL - counter;
+ constexpr int64_t startL = counterReverse;
+
+ EIGEN_IF_CONSTEXPR(rem)
+ zmm.packet[unrollM * unrollN + startL] =
+ ploadu<vec>(&B_t[(startL / unrollM) * LDB + (startL % unrollM) * PacketSize], remMask<PacketSize>(rem_));
+ else zmm.packet[unrollM * unrollN + startL] =
+ ploadu<vec>(&B_t[(startL / unrollM) * LDB + (startL % unrollM) * PacketSize]);
+
+ aux_startLoadB<unrollM, unrollN, endL, counter - 1, rem>(B_t, LDB, zmm, rem_);
+ }
+
+ template <int64_t unrollM, int64_t unrollN, int64_t endL, int64_t counter, bool rem>
+ static EIGEN_ALWAYS_INLINE std::enable_if_t<(counter <= 0)> aux_startLoadB(
+ Scalar *B_t, int64_t LDB, PacketBlock<vec, EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS> &zmm, int64_t rem_ = 0) {
+ EIGEN_UNUSED_VARIABLE(B_t);
+ EIGEN_UNUSED_VARIABLE(LDB);
+ EIGEN_UNUSED_VARIABLE(zmm);
+ EIGEN_UNUSED_VARIABLE(rem_);
+ }
+
+ /**
+ * aux_startBCastA
+ *
+ * 1-D unroll
+ * for(startB = 0; startB < endB; startB++)
+ **/
+ template <bool isARowMajor, int64_t unrollM, int64_t unrollN, int64_t endB, int64_t counter, int64_t numLoad>
+ static EIGEN_ALWAYS_INLINE std::enable_if_t<(counter > 0)> aux_startBCastA(
+ Scalar *A_t, int64_t LDA, PacketBlock<vec, EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS> &zmm) {
+ constexpr int64_t counterReverse = endB - counter;
+ constexpr int64_t startB = counterReverse;
+
+ zmm.packet[unrollM * unrollN + numLoad + startB] = pload1<vec>(&A_t[idA<isARowMajor>(startB, 0, LDA)]);
+
+ aux_startBCastA<isARowMajor, unrollM, unrollN, endB, counter - 1, numLoad>(A_t, LDA, zmm);
+ }
+
+ template <bool isARowMajor, int64_t unrollM, int64_t unrollN, int64_t endB, int64_t counter, int64_t numLoad>
+ static EIGEN_ALWAYS_INLINE std::enable_if_t<(counter <= 0)> aux_startBCastA(
+ Scalar *A_t, int64_t LDA, PacketBlock<vec, EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS> &zmm) {
+ EIGEN_UNUSED_VARIABLE(A_t);
+ EIGEN_UNUSED_VARIABLE(LDA);
+ EIGEN_UNUSED_VARIABLE(zmm);
+ }
+
+ /**
+ * aux_loadB
+ * currK: current K
+ *
+ * 1-D unroll
+ * for(startM = 0; startM < endM; startM++)
+ **/
+ template <int64_t endM, int64_t counter, int64_t unrollN, int64_t currK, int64_t unrollK, int64_t numLoad,
+ int64_t numBCast, bool rem>
+ static EIGEN_ALWAYS_INLINE std::enable_if_t<(counter > 0)> aux_loadB(
+ Scalar *B_t, int64_t LDB, PacketBlock<vec, EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS> &zmm, int64_t rem_ = 0) {
+ EIGEN_UNUSED_VARIABLE(rem_);
+ if ((numLoad / endM + currK < unrollK)) {
+ constexpr int64_t counterReverse = endM - counter;
+ constexpr int64_t startM = counterReverse;
+
+ EIGEN_IF_CONSTEXPR(rem) {
+ zmm.packet[endM * unrollN + (startM + currK * endM) % numLoad] =
+ ploadu<vec>(&B_t[(numLoad / endM + currK) * LDB + startM * PacketSize], remMask<PacketSize>(rem_));
+ }
+ else {
+ zmm.packet[endM * unrollN + (startM + currK * endM) % numLoad] =
+ ploadu<vec>(&B_t[(numLoad / endM + currK) * LDB + startM * PacketSize]);
+ }
+
+ aux_loadB<endM, counter - 1, unrollN, currK, unrollK, numLoad, numBCast, rem>(B_t, LDB, zmm, rem_);
+ }
+ }
+
+ template <int64_t endM, int64_t counter, int64_t unrollN, int64_t currK, int64_t unrollK, int64_t numLoad,
+ int64_t numBCast, bool rem>
+ static EIGEN_ALWAYS_INLINE std::enable_if_t<(counter <= 0)> aux_loadB(
+ Scalar *B_t, int64_t LDB, PacketBlock<vec, EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS> &zmm, int64_t rem_ = 0) {
+ EIGEN_UNUSED_VARIABLE(B_t);
+ EIGEN_UNUSED_VARIABLE(LDB);
+ EIGEN_UNUSED_VARIABLE(zmm);
+ EIGEN_UNUSED_VARIABLE(rem_);
+ }
+
+ /**
+ * aux_microKernel
+ *
+ * 3-D unroll
+ * for(startM = 0; startM < endM; startM++)
+ * for(startN = 0; startN < endN; startN++)
+ * for(startK = 0; startK < endK; startK++)
+ **/
+ template <bool isARowMajor, int64_t endM, int64_t endN, int64_t endK, int64_t counter, int64_t numLoad,
+ int64_t numBCast, bool rem>
+ static EIGEN_ALWAYS_INLINE std::enable_if_t<(counter > 0)> aux_microKernel(
+ Scalar *B_t, Scalar *A_t, int64_t LDB, int64_t LDA, PacketBlock<vec, EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS> &zmm,
+ int64_t rem_ = 0) {
+ EIGEN_UNUSED_VARIABLE(rem_);
+ constexpr int64_t counterReverse = endM * endN * endK - counter;
+ constexpr int startK = counterReverse / (endM * endN);
+ constexpr int startN = (counterReverse / (endM)) % endN;
+ constexpr int startM = counterReverse % endM;
+
+ EIGEN_IF_CONSTEXPR(startK == 0 && startM == 0 && startN == 0) {
+ gemm::template startLoadB<endM, endN, numLoad, rem>(B_t, LDB, zmm, rem_);
+ gemm::template startBCastA<isARowMajor, endM, endN, numBCast, numLoad>(A_t, LDA, zmm);
+ }
+
+ {
+ // Interleave FMA and Bcast
+ EIGEN_IF_CONSTEXPR(isAdd) {
+ zmm.packet[startN * endM + startM] =
+ pmadd(zmm.packet[endM * endN + numLoad + (startN + startK * endN) % numBCast],
+ zmm.packet[endM * endN + (startM + startK * endM) % numLoad], zmm.packet[startN * endM + startM]);
+ }
+ else {
+ zmm.packet[startN * endM + startM] =
+ pnmadd(zmm.packet[endM * endN + numLoad + (startN + startK * endN) % numBCast],
+ zmm.packet[endM * endN + (startM + startK * endM) % numLoad], zmm.packet[startN * endM + startM]);
+ }
+ // Bcast
+ EIGEN_IF_CONSTEXPR(startM == endM - 1 && (numBCast + startN + startK * endN < endK * endN)) {
+ zmm.packet[endM * endN + numLoad + (startN + startK * endN) % numBCast] = pload1<vec>(&A_t[idA<isARowMajor>(
+ (numBCast + startN + startK * endN) % endN, (numBCast + startN + startK * endN) / endN, LDA)]);
+ }
+ }
+
+ // We have updated all accumlators, time to load next set of B's
+ EIGEN_IF_CONSTEXPR((startN == endN - 1) && (startM == endM - 1)) {
+ gemm::template loadB<endM, endN, startK, endK, numLoad, numBCast, rem>(B_t, LDB, zmm, rem_);
+ }
+ aux_microKernel<isARowMajor, endM, endN, endK, counter - 1, numLoad, numBCast, rem>(B_t, A_t, LDB, LDA, zmm, rem_);
+ }
+
+ template <bool isARowMajor, int64_t endM, int64_t endN, int64_t endK, int64_t counter, int64_t numLoad,
+ int64_t numBCast, bool rem>
+ static EIGEN_ALWAYS_INLINE std::enable_if_t<(counter <= 0)> aux_microKernel(
+ Scalar *B_t, Scalar *A_t, int64_t LDB, int64_t LDA, PacketBlock<vec, EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS> &zmm,
+ int64_t rem_ = 0) {
+ EIGEN_UNUSED_VARIABLE(B_t);
+ EIGEN_UNUSED_VARIABLE(A_t);
+ EIGEN_UNUSED_VARIABLE(LDB);
+ EIGEN_UNUSED_VARIABLE(LDA);
+ EIGEN_UNUSED_VARIABLE(zmm);
+ EIGEN_UNUSED_VARIABLE(rem_);
+ }
+
+ /********************************************************
+ * Wrappers for aux_XXXX to hide counter parameter
+ ********************************************************/
+
+ template <int64_t endM, int64_t endN>
+ static EIGEN_ALWAYS_INLINE void setzero(PacketBlock<vec, EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS> &zmm) {
+ aux_setzero<endM, endN, endM * endN>(zmm);
+ }
+
+ /**
+ * Ideally the compiler folds these into vaddp{s,d} with an embedded memory load.
+ */
+ template <int64_t endM, int64_t endN, bool rem = false>
+ static EIGEN_ALWAYS_INLINE void updateC(Scalar *C_arr, int64_t LDC,
+ PacketBlock<vec, EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS> &zmm,
+ int64_t rem_ = 0) {
+ EIGEN_UNUSED_VARIABLE(rem_);
+ aux_updateC<endM, endN, endM * endN, rem>(C_arr, LDC, zmm, rem_);
+ }
+
+ template <int64_t endM, int64_t endN, bool rem = false>
+ static EIGEN_ALWAYS_INLINE void storeC(Scalar *C_arr, int64_t LDC,
+ PacketBlock<vec, EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS> &zmm,
+ int64_t rem_ = 0) {
+ EIGEN_UNUSED_VARIABLE(rem_);
+ aux_storeC<endM, endN, endM * endN, rem>(C_arr, LDC, zmm, rem_);
+ }
+
+ /**
+ * Use numLoad registers for loading B at start of microKernel
+ */
+ template <int64_t unrollM, int64_t unrollN, int64_t endL, bool rem>
+ static EIGEN_ALWAYS_INLINE void startLoadB(Scalar *B_t, int64_t LDB,
+ PacketBlock<vec, EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS> &zmm,
+ int64_t rem_ = 0) {
+ EIGEN_UNUSED_VARIABLE(rem_);
+ aux_startLoadB<unrollM, unrollN, endL, endL, rem>(B_t, LDB, zmm, rem_);
+ }
+
+ /**
+ * Use numBCast registers for broadcasting A at start of microKernel
+ */
+ template <bool isARowMajor, int64_t unrollM, int64_t unrollN, int64_t endB, int64_t numLoad>
+ static EIGEN_ALWAYS_INLINE void startBCastA(Scalar *A_t, int64_t LDA,
+ PacketBlock<vec, EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS> &zmm) {
+ aux_startBCastA<isARowMajor, unrollM, unrollN, endB, endB, numLoad>(A_t, LDA, zmm);
+ }
+
+ /**
+ * Loads next set of B into vector registers between each K unroll.
+ */
+ template <int64_t endM, int64_t unrollN, int64_t currK, int64_t unrollK, int64_t numLoad, int64_t numBCast, bool rem>
+ static EIGEN_ALWAYS_INLINE void loadB(Scalar *B_t, int64_t LDB,
+ PacketBlock<vec, EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS> &zmm,
+ int64_t rem_ = 0) {
+ EIGEN_UNUSED_VARIABLE(rem_);
+ aux_loadB<endM, endM, unrollN, currK, unrollK, numLoad, numBCast, rem>(B_t, LDB, zmm, rem_);
+ }
+
+ /**
+ * Generates a microkernel for gemm (row-major) with unrolls {1,2,4,8}x{U1,U2,U3} to compute C -= A*B.
+ * A matrix can be row/col-major. B matrix is assumed row-major.
+ *
+ * isARowMajor: is A row major
+ * endM: Number registers per row
+ * endN: Number of rows
+ * endK: Loop unroll for K.
+ * numLoad: Number of registers for loading B.
+ * numBCast: Number of registers for broadcasting A.
+ *
+ * Ex: microkernel<isARowMajor,0,3,0,4,0,4,6,2>: 8x48 unroll (24 accumulators), k unrolled 4 times,
+ * 6 register for loading B, 2 for broadcasting A.
+ *
+ * Note: Ideally the microkernel should not have any register spilling.
+ * The avx instruction counts should be:
+ * - endK*endN vbroadcasts{s,d}
+ * - endK*endM vmovup{s,d}
+ * - endK*endN*endM FMAs
+ *
+ * From testing, there are no register spills with clang. There are register spills with GNU, which
+ * causes a performance hit.
+ */
+ template <bool isARowMajor, int64_t endM, int64_t endN, int64_t endK, int64_t numLoad, int64_t numBCast,
+ bool rem = false>
+ static EIGEN_ALWAYS_INLINE void microKernel(Scalar *B_t, Scalar *A_t, int64_t LDB, int64_t LDA,
+ PacketBlock<vec, EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS> &zmm,
+ int64_t rem_ = 0) {
+ EIGEN_UNUSED_VARIABLE(rem_);
+ aux_microKernel<isARowMajor, endM, endN, endK, endM * endN * endK, numLoad, numBCast, rem>(B_t, A_t, LDB, LDA, zmm,
+ rem_);
+ }
+};
+} // namespace unrolls
+
+#endif // EIGEN_CORE_ARCH_AVX512_TRSM_UNROLLS_H
diff --git a/Eigen/src/Core/arch/AVX512/TypeCasting.h b/Eigen/src/Core/arch/AVX512/TypeCasting.h
new file mode 100644
index 0000000..62a7429
--- /dev/null
+++ b/Eigen/src/Core/arch/AVX512/TypeCasting.h
@@ -0,0 +1,214 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2019 Rasmus Munk Larsen <rmlarsen@google.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_TYPE_CASTING_AVX512_H
+#define EIGEN_TYPE_CASTING_AVX512_H
+
+#include "../../InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+
+template<> EIGEN_STRONG_INLINE Packet16i pcast<Packet16f, Packet16i>(const Packet16f& a) {
+ return _mm512_cvttps_epi32(a);
+}
+
+template<> EIGEN_STRONG_INLINE Packet16f pcast<Packet16i, Packet16f>(const Packet16i& a) {
+ return _mm512_cvtepi32_ps(a);
+}
+
+template<> EIGEN_STRONG_INLINE Packet16i preinterpret<Packet16i, Packet16f>(const Packet16f& a) {
+ return _mm512_castps_si512(a);
+}
+
+template<> EIGEN_STRONG_INLINE Packet16f preinterpret<Packet16f, Packet16i>(const Packet16i& a) {
+ return _mm512_castsi512_ps(a);
+}
+
+template<> EIGEN_STRONG_INLINE Packet8d preinterpret<Packet8d, Packet16f>(const Packet16f& a) {
+ return _mm512_castps_pd(a);
+}
+
+template<> EIGEN_STRONG_INLINE Packet16f preinterpret<Packet16f, Packet8d>(const Packet8d& a) {
+ return _mm512_castpd_ps(a);
+}
+
+template<> EIGEN_STRONG_INLINE Packet8f preinterpret<Packet8f, Packet16f>(const Packet16f& a) {
+ return _mm512_castps512_ps256(a);
+}
+
+template<> EIGEN_STRONG_INLINE Packet4f preinterpret<Packet4f, Packet16f>(const Packet16f& a) {
+ return _mm512_castps512_ps128(a);
+}
+
+template<> EIGEN_STRONG_INLINE Packet4d preinterpret<Packet4d, Packet8d>(const Packet8d& a) {
+ return _mm512_castpd512_pd256(a);
+}
+
+template<> EIGEN_STRONG_INLINE Packet2d preinterpret<Packet2d, Packet8d>(const Packet8d& a) {
+ return _mm512_castpd512_pd128(a);
+}
+
+template<> EIGEN_STRONG_INLINE Packet16f preinterpret<Packet16f, Packet8f>(const Packet8f& a) {
+ return _mm512_castps256_ps512(a);
+}
+
+template<> EIGEN_STRONG_INLINE Packet16f preinterpret<Packet16f, Packet4f>(const Packet4f& a) {
+ return _mm512_castps128_ps512(a);
+}
+
+template<> EIGEN_STRONG_INLINE Packet8d preinterpret<Packet8d, Packet4d>(const Packet4d& a) {
+ return _mm512_castpd256_pd512(a);
+}
+
+template<> EIGEN_STRONG_INLINE Packet8d preinterpret<Packet8d, Packet2d>(const Packet2d& a) {
+ return _mm512_castpd128_pd512(a);
+}
+
+template<> EIGEN_STRONG_INLINE Packet16f preinterpret<Packet16f, Packet16f>(const Packet16f& a) {
+ return a;
+}
+
+template<> EIGEN_STRONG_INLINE Packet8d preinterpret<Packet8d, Packet8d>(const Packet8d& a) {
+ return a;
+}
+
+#ifndef EIGEN_VECTORIZE_AVX512FP16
+
+template <>
+struct type_casting_traits<half, float> {
+ enum {
+ VectorizedCast = 1,
+ SrcCoeffRatio = 1,
+ TgtCoeffRatio = 1
+ };
+};
+
+template<> EIGEN_STRONG_INLINE Packet16f pcast<Packet16h, Packet16f>(const Packet16h& a) {
+ return half2float(a);
+}
+
+template <>
+struct type_casting_traits<float, half> {
+ enum {
+ VectorizedCast = 1,
+ SrcCoeffRatio = 1,
+ TgtCoeffRatio = 1
+ };
+};
+
+template<> EIGEN_STRONG_INLINE Packet16h pcast<Packet16f, Packet16h>(const Packet16f& a) {
+ return float2half(a);
+}
+
+#endif
+
+template <>
+struct type_casting_traits<bfloat16, float> {
+ enum {
+ VectorizedCast = 1,
+ SrcCoeffRatio = 1,
+ TgtCoeffRatio = 1
+ };
+};
+
+template<> EIGEN_STRONG_INLINE Packet16f pcast<Packet16bf, Packet16f>(const Packet16bf& a) {
+ return Bf16ToF32(a);
+}
+
+template <>
+struct type_casting_traits<float, bfloat16> {
+ enum {
+ VectorizedCast = 1,
+ SrcCoeffRatio = 1,
+ TgtCoeffRatio = 1
+ };
+};
+
+template<> EIGEN_STRONG_INLINE Packet16bf pcast<Packet16f, Packet16bf>(const Packet16f& a) {
+ return F32ToBf16(a);
+}
+
+#ifdef EIGEN_VECTORIZE_AVX512FP16
+
+template <>
+struct type_casting_traits<half, float> {
+ enum {
+ VectorizedCast = 1,
+ SrcCoeffRatio = 1,
+ TgtCoeffRatio = 2
+ };
+};
+
+template <>
+struct type_casting_traits<float, half> {
+ enum {
+ VectorizedCast = 1,
+ SrcCoeffRatio = 2,
+ TgtCoeffRatio = 1
+ };
+};
+
+template <>
+EIGEN_STRONG_INLINE Packet16f pcast<Packet32h, Packet16f>(const Packet32h& a) {
+ // Discard second-half of input.
+ Packet16h low = _mm256_castpd_si256(_mm512_extractf64x4_pd(_mm512_castph_pd(a), 0));
+ return _mm512_cvtxph_ps(_mm256_castsi256_ph(low));
+}
+
+
+template <>
+EIGEN_STRONG_INLINE Packet32h pcast<Packet16f, Packet32h>(const Packet16f& a, const Packet16f& b) {
+ __m512d result = _mm512_undefined_pd();
+ result = _mm512_insertf64x4(result, _mm256_castsi256_pd(_mm512_cvtps_ph(a, _MM_FROUND_TO_NEAREST_INT|_MM_FROUND_NO_EXC)), 0);
+ result = _mm512_insertf64x4(result, _mm256_castsi256_pd(_mm512_cvtps_ph(b, _MM_FROUND_TO_NEAREST_INT|_MM_FROUND_NO_EXC)), 1);
+ return _mm512_castpd_ph(result);
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet8f pcast<Packet16h, Packet8f>(const Packet16h& a) {
+ // Discard second-half of input.
+ Packet8h low = _mm_castps_si128(_mm256_extractf32x4_ps(_mm256_castsi256_ps(a), 0));
+ return _mm256_cvtxph_ps(_mm_castsi128_ph(low));
+}
+
+
+template <>
+EIGEN_STRONG_INLINE Packet16h pcast<Packet8f, Packet16h>(const Packet8f& a, const Packet8f& b) {
+ __m256d result = _mm256_undefined_pd();
+ result = _mm256_insertf64x2(result, _mm_castsi128_pd(_mm256_cvtps_ph(a, _MM_FROUND_TO_NEAREST_INT|_MM_FROUND_NO_EXC)), 0);
+ result = _mm256_insertf64x2(result, _mm_castsi128_pd(_mm256_cvtps_ph(b, _MM_FROUND_TO_NEAREST_INT|_MM_FROUND_NO_EXC)), 1);
+ return _mm256_castpd_si256(result);
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet4f pcast<Packet8h, Packet4f>(const Packet8h& a) {
+ Packet8f full = _mm256_cvtxph_ps(_mm_castsi128_ph(a));
+ // Discard second-half of input.
+ return _mm256_extractf32x4_ps(full, 0);
+}
+
+
+template <>
+EIGEN_STRONG_INLINE Packet8h pcast<Packet4f, Packet8h>(const Packet4f& a, const Packet4f& b) {
+ __m256 result = _mm256_undefined_ps();
+ result = _mm256_insertf128_ps(result, a, 0);
+ result = _mm256_insertf128_ps(result, b, 1);
+ return _mm256_cvtps_ph(result, _MM_FROUND_TO_NEAREST_INT|_MM_FROUND_NO_EXC);
+}
+
+
+#endif
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_TYPE_CASTING_AVX512_H
diff --git a/Eigen/src/Core/arch/AltiVec/Complex.h b/Eigen/src/Core/arch/AltiVec/Complex.h
new file mode 100644
index 0000000..46812f9
--- /dev/null
+++ b/Eigen/src/Core/arch/AltiVec/Complex.h
@@ -0,0 +1,484 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2010 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2010-2016 Konstantinos Margaritis <markos@freevec.org>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_COMPLEX32_ALTIVEC_H
+#define EIGEN_COMPLEX32_ALTIVEC_H
+
+#include "../../InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+
+static Packet4ui p4ui_CONJ_XOR = vec_mergeh((Packet4ui)p4i_ZERO, (Packet4ui)p4f_MZERO);//{ 0x00000000, 0x80000000, 0x00000000, 0x80000000 };
+#ifdef __VSX__
+#if defined(_BIG_ENDIAN)
+static Packet2ul p2ul_CONJ_XOR1 = (Packet2ul) vec_sld((Packet4ui) p2d_MZERO, (Packet4ui) p2l_ZERO, 8);//{ 0x8000000000000000, 0x0000000000000000 };
+static Packet2ul p2ul_CONJ_XOR2 = (Packet2ul) vec_sld((Packet4ui) p2l_ZERO, (Packet4ui) p2d_MZERO, 8);//{ 0x8000000000000000, 0x0000000000000000 };
+#else
+static Packet2ul p2ul_CONJ_XOR1 = (Packet2ul) vec_sld((Packet4ui) p2l_ZERO, (Packet4ui) p2d_MZERO, 8);//{ 0x8000000000000000, 0x0000000000000000 };
+static Packet2ul p2ul_CONJ_XOR2 = (Packet2ul) vec_sld((Packet4ui) p2d_MZERO, (Packet4ui) p2l_ZERO, 8);//{ 0x8000000000000000, 0x0000000000000000 };
+#endif
+#endif
+
+//---------- float ----------
+struct Packet2cf
+{
+ EIGEN_STRONG_INLINE explicit Packet2cf() {}
+ EIGEN_STRONG_INLINE explicit Packet2cf(const Packet4f& a) : v(a) {}
+
+ EIGEN_STRONG_INLINE Packet2cf pmul(const Packet2cf& a, const Packet2cf& b)
+ {
+ Packet4f v1, v2;
+
+ // Permute and multiply the real parts of a and b
+ v1 = vec_perm(a.v, a.v, p16uc_PSET32_WODD);
+ // Get the imaginary parts of a
+ v2 = vec_perm(a.v, a.v, p16uc_PSET32_WEVEN);
+ // multiply a_re * b
+ v1 = vec_madd(v1, b.v, p4f_ZERO);
+ // multiply a_im * b and get the conjugate result
+ v2 = vec_madd(v2, b.v, p4f_ZERO);
+ v2 = reinterpret_cast<Packet4f>(pxor(v2, reinterpret_cast<Packet4f>(p4ui_CONJ_XOR)));
+ // permute back to a proper order
+ v2 = vec_perm(v2, v2, p16uc_COMPLEX32_REV);
+
+ return Packet2cf(padd<Packet4f>(v1, v2));
+ }
+
+ EIGEN_STRONG_INLINE Packet2cf& operator*=(const Packet2cf& b) {
+ v = pmul(Packet2cf(*this), b).v;
+ return *this;
+ }
+ EIGEN_STRONG_INLINE Packet2cf operator*(const Packet2cf& b) const {
+ return Packet2cf(*this) *= b;
+ }
+
+ EIGEN_STRONG_INLINE Packet2cf& operator+=(const Packet2cf& b) {
+ v = padd(v, b.v);
+ return *this;
+ }
+ EIGEN_STRONG_INLINE Packet2cf operator+(const Packet2cf& b) const {
+ return Packet2cf(*this) += b;
+ }
+ EIGEN_STRONG_INLINE Packet2cf& operator-=(const Packet2cf& b) {
+ v = psub(v, b.v);
+ return *this;
+ }
+ EIGEN_STRONG_INLINE Packet2cf operator-(const Packet2cf& b) const {
+ return Packet2cf(*this) -= b;
+ }
+ EIGEN_STRONG_INLINE Packet2cf operator-(void) const {
+ return Packet2cf(-v);
+ }
+
+ Packet4f v;
+};
+
+template<> struct packet_traits<std::complex<float> > : default_packet_traits
+{
+ typedef Packet2cf type;
+ typedef Packet2cf half;
+ typedef Packet4f as_real;
+ enum {
+ Vectorizable = 1,
+ AlignedOnScalar = 1,
+ size = 2,
+ HasHalfPacket = 0,
+
+ HasAdd = 1,
+ HasSub = 1,
+ HasMul = 1,
+ HasDiv = 1,
+ HasNegate = 1,
+ HasAbs = 0,
+ HasAbs2 = 0,
+ HasMin = 0,
+ HasMax = 0,
+ HasSqrt = 1,
+#ifdef __VSX__
+ HasBlend = 1,
+#endif
+ HasSetLinear = 0
+ };
+};
+
+template<> struct unpacket_traits<Packet2cf> { typedef std::complex<float> type; enum {size=2, alignment=Aligned16, vectorizable=true, masked_load_available=false, masked_store_available=false}; typedef Packet2cf half; typedef Packet4f as_real; };
+
+template<> EIGEN_STRONG_INLINE Packet2cf pset1<Packet2cf>(const std::complex<float>& from)
+{
+ Packet2cf res;
+#ifdef __VSX__
+ // Load a single std::complex<float> from memory and duplicate
+ //
+ // Using pload would read past the end of the reference in this case
+ // Using vec_xl_len + vec_splat, generates poor assembly
+ __asm__ ("lxvdsx %x0,%y1" : "=wa" (res.v) : "Z" (from));
+#else
+ if((std::ptrdiff_t(&from) % 16) == 0)
+ res.v = pload<Packet4f>((const float *)&from);
+ else
+ res.v = ploadu<Packet4f>((const float *)&from);
+ res.v = vec_perm(res.v, res.v, p16uc_PSET64_HI);
+#endif
+ return res;
+}
+
+template<> EIGEN_STRONG_INLINE Packet2cf pload<Packet2cf>(const std::complex<float>* from) { return Packet2cf(pload<Packet4f>((const float *) from)); }
+template<> EIGEN_STRONG_INLINE Packet2cf ploadu<Packet2cf>(const std::complex<float>* from) { return Packet2cf(ploadu<Packet4f>((const float*) from)); }
+template<> EIGEN_ALWAYS_INLINE Packet2cf pload_partial<Packet2cf>(const std::complex<float>* from, const Index n, const Index offset)
+{
+ return Packet2cf(pload_partial<Packet4f>((const float *) from, n * 2, offset * 2));
+}
+template<> EIGEN_ALWAYS_INLINE Packet2cf ploadu_partial<Packet2cf>(const std::complex<float>* from, const Index n)
+{
+ return Packet2cf(ploadu_partial<Packet4f>((const float*) from, n * 2));
+}
+template<> EIGEN_STRONG_INLINE Packet2cf ploaddup<Packet2cf>(const std::complex<float>* from) { return pset1<Packet2cf>(*from); }
+
+template<> EIGEN_STRONG_INLINE void pstore <std::complex<float> >(std::complex<float> * to, const Packet2cf& from) { pstore((float*)to, from.v); }
+template<> EIGEN_STRONG_INLINE void pstoreu<std::complex<float> >(std::complex<float> * to, const Packet2cf& from) { pstoreu((float*)to, from.v); }
+template<> EIGEN_ALWAYS_INLINE void pstore_partial <std::complex<float> >(std::complex<float> * to, const Packet2cf& from, const Index n, const Index offset) { pstore_partial((float*)to, from.v, n * 2, offset * 2); }
+template<> EIGEN_ALWAYS_INLINE void pstoreu_partial<std::complex<float> >(std::complex<float> * to, const Packet2cf& from, const Index n) { pstoreu_partial((float*)to, from.v, n * 2); }
+
+EIGEN_STRONG_INLINE Packet2cf pload2(const std::complex<float>& from0, const std::complex<float>& from1)
+{
+ Packet4f res0, res1;
+#ifdef __VSX__
+ // Load two std::complex<float> from memory and combine
+ __asm__ ("lxsdx %x0,%y1" : "=wa" (res0) : "Z" (from0));
+ __asm__ ("lxsdx %x0,%y1" : "=wa" (res1) : "Z" (from1));
+#ifdef _BIG_ENDIAN
+ __asm__ ("xxpermdi %x0, %x1, %x2, 0" : "=wa" (res0) : "wa" (res0), "wa" (res1));
+#else
+ __asm__ ("xxpermdi %x0, %x2, %x1, 0" : "=wa" (res0) : "wa" (res0), "wa" (res1));
+#endif
+#else
+ *reinterpret_cast<std::complex<float> *>(&res0) = from0;
+ *reinterpret_cast<std::complex<float> *>(&res1) = from1;
+ res0 = vec_perm(res0, res1, p16uc_TRANSPOSE64_HI);
+#endif
+ return Packet2cf(res0);
+}
+
+template<> EIGEN_ALWAYS_INLINE Packet2cf pload_ignore<Packet2cf>(const std::complex<float>* from)
+{
+ Packet2cf res;
+ res.v = pload_ignore<Packet4f>(reinterpret_cast<const float*>(from));
+ return res;
+}
+
+template<typename Scalar, typename Packet> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE Packet pgather_complex_size2(const Scalar* from, Index stride, const Index n = 2)
+{
+ eigen_assert(n <= unpacket_traits<Packet>::size && "number of elements will gather past end of packet");
+ EIGEN_ALIGN16 Scalar af[2];
+ for (Index i = 0; i < n; i++) {
+ af[i] = from[i*stride];
+ }
+ return pload_ignore<Packet>(af);
+}
+template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE Packet2cf pgather<std::complex<float>, Packet2cf>(const std::complex<float>* from, Index stride)
+{
+ return pgather_complex_size2<std::complex<float>, Packet2cf>(from, stride);
+}
+template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE Packet2cf pgather_partial<std::complex<float>, Packet2cf>(const std::complex<float>* from, Index stride, const Index n)
+{
+ return pgather_complex_size2<std::complex<float>, Packet2cf>(from, stride, n);
+}
+template<typename Scalar, typename Packet> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE void pscatter_complex_size2(Scalar* to, const Packet& from, Index stride, const Index n = 2)
+{
+ eigen_assert(n <= unpacket_traits<Packet>::size && "number of elements will scatter past end of packet");
+ EIGEN_ALIGN16 Scalar af[2];
+ pstore<Scalar>((Scalar *) af, from);
+ for (Index i = 0; i < n; i++) {
+ to[i*stride] = af[i];
+ }
+}
+template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE void pscatter<std::complex<float>, Packet2cf>(std::complex<float>* to, const Packet2cf& from, Index stride)
+{
+ pscatter_complex_size2<std::complex<float>, Packet2cf>(to, from, stride);
+}
+template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE void pscatter_partial<std::complex<float>, Packet2cf>(std::complex<float>* to, const Packet2cf& from, Index stride, const Index n)
+{
+ pscatter_complex_size2<std::complex<float>, Packet2cf>(to, from, stride, n);
+}
+
+template<> EIGEN_STRONG_INLINE Packet2cf padd<Packet2cf>(const Packet2cf& a, const Packet2cf& b) { return Packet2cf(a.v + b.v); }
+template<> EIGEN_STRONG_INLINE Packet2cf psub<Packet2cf>(const Packet2cf& a, const Packet2cf& b) { return Packet2cf(a.v - b.v); }
+template<> EIGEN_STRONG_INLINE Packet2cf pnegate(const Packet2cf& a) { return Packet2cf(pnegate(a.v)); }
+template<> EIGEN_STRONG_INLINE Packet2cf pconj(const Packet2cf& a) { return Packet2cf(pxor<Packet4f>(a.v, reinterpret_cast<Packet4f>(p4ui_CONJ_XOR))); }
+
+template<> EIGEN_STRONG_INLINE Packet2cf pand <Packet2cf>(const Packet2cf& a, const Packet2cf& b) { return Packet2cf(pand<Packet4f>(a.v, b.v)); }
+template<> EIGEN_STRONG_INLINE Packet2cf por <Packet2cf>(const Packet2cf& a, const Packet2cf& b) { return Packet2cf(por<Packet4f>(a.v, b.v)); }
+template<> EIGEN_STRONG_INLINE Packet2cf pxor <Packet2cf>(const Packet2cf& a, const Packet2cf& b) { return Packet2cf(pxor<Packet4f>(a.v, b.v)); }
+template<> EIGEN_STRONG_INLINE Packet2cf pandnot<Packet2cf>(const Packet2cf& a, const Packet2cf& b) { return Packet2cf(pandnot<Packet4f>(a.v, b.v)); }
+
+template<> EIGEN_STRONG_INLINE void prefetch<std::complex<float> >(const std::complex<float> * addr) { EIGEN_PPC_PREFETCH(addr); }
+
+template<> EIGEN_STRONG_INLINE std::complex<float> pfirst<Packet2cf>(const Packet2cf& a)
+{
+ EIGEN_ALIGN16 std::complex<float> res[2];
+ pstore((float *)&res, a.v);
+
+ return res[0];
+}
+
+template<> EIGEN_STRONG_INLINE Packet2cf preverse(const Packet2cf& a)
+{
+ Packet4f rev_a;
+ rev_a = vec_sld(a.v, a.v, 8);
+ return Packet2cf(rev_a);
+}
+
+template<> EIGEN_STRONG_INLINE std::complex<float> predux<Packet2cf>(const Packet2cf& a)
+{
+ Packet4f b;
+ b = vec_sld(a.v, a.v, 8);
+ b = padd<Packet4f>(a.v, b);
+ return pfirst<Packet2cf>(Packet2cf(b));
+}
+
+template<> EIGEN_STRONG_INLINE std::complex<float> predux_mul<Packet2cf>(const Packet2cf& a)
+{
+ Packet4f b;
+ Packet2cf prod;
+ b = vec_sld(a.v, a.v, 8);
+ prod = pmul<Packet2cf>(a, Packet2cf(b));
+
+ return pfirst<Packet2cf>(prod);
+}
+
+EIGEN_MAKE_CONJ_HELPER_CPLX_REAL(Packet2cf,Packet4f)
+
+template<> EIGEN_STRONG_INLINE Packet2cf pdiv<Packet2cf>(const Packet2cf& a, const Packet2cf& b)
+{
+ return pdiv_complex(a, b);
+}
+
+template<> EIGEN_STRONG_INLINE Packet2cf pcplxflip<Packet2cf>(const Packet2cf& x)
+{
+ return Packet2cf(vec_perm(x.v, x.v, p16uc_COMPLEX32_REV));
+}
+
+EIGEN_STRONG_INLINE void ptranspose(PacketBlock<Packet2cf,2>& kernel)
+{
+#ifdef __VSX__
+ Packet4f tmp = reinterpret_cast<Packet4f>(vec_mergeh(reinterpret_cast<Packet2d>(kernel.packet[0].v), reinterpret_cast<Packet2d>(kernel.packet[1].v)));
+ kernel.packet[1].v = reinterpret_cast<Packet4f>(vec_mergel(reinterpret_cast<Packet2d>(kernel.packet[0].v), reinterpret_cast<Packet2d>(kernel.packet[1].v)));
+#else
+ Packet4f tmp = vec_perm(kernel.packet[0].v, kernel.packet[1].v, p16uc_TRANSPOSE64_HI);
+ kernel.packet[1].v = vec_perm(kernel.packet[0].v, kernel.packet[1].v, p16uc_TRANSPOSE64_LO);
+#endif
+ kernel.packet[0].v = tmp;
+}
+
+template<> EIGEN_STRONG_INLINE Packet2cf pcmp_eq(const Packet2cf& a, const Packet2cf& b) {
+ Packet4f eq = reinterpret_cast<Packet4f>(vec_cmpeq(a.v,b.v));
+ return Packet2cf(vec_and(eq, vec_perm(eq, eq, p16uc_COMPLEX32_REV)));
+}
+
+#ifdef __VSX__
+template<> EIGEN_STRONG_INLINE Packet2cf pblend(const Selector<2>& ifPacket, const Packet2cf& thenPacket, const Packet2cf& elsePacket) {
+ Packet2cf result;
+ result.v = reinterpret_cast<Packet4f>(pblend<Packet2d>(ifPacket, reinterpret_cast<Packet2d>(thenPacket.v), reinterpret_cast<Packet2d>(elsePacket.v)));
+ return result;
+}
+#endif
+
+template<> EIGEN_STRONG_INLINE Packet2cf psqrt<Packet2cf>(const Packet2cf& a)
+{
+ return psqrt_complex<Packet2cf>(a);
+}
+
+//---------- double ----------
+#ifdef __VSX__
+struct Packet1cd
+{
+ EIGEN_STRONG_INLINE Packet1cd() {}
+ EIGEN_STRONG_INLINE explicit Packet1cd(const Packet2d& a) : v(a) {}
+
+ EIGEN_STRONG_INLINE Packet1cd pmul(const Packet1cd& a, const Packet1cd& b)
+ {
+ Packet2d a_re, a_im, v1, v2;
+
+ // Permute and multiply the real parts of a and b
+ a_re = vec_perm(a.v, a.v, p16uc_PSET64_HI);
+ // Get the imaginary parts of a
+ a_im = vec_perm(a.v, a.v, p16uc_PSET64_LO);
+ // multiply a_re * b
+ v1 = vec_madd(a_re, b.v, p2d_ZERO);
+ // multiply a_im * b and get the conjugate result
+ v2 = vec_madd(a_im, b.v, p2d_ZERO);
+ v2 = reinterpret_cast<Packet2d>(vec_sld(reinterpret_cast<Packet4ui>(v2), reinterpret_cast<Packet4ui>(v2), 8));
+ v2 = pxor(v2, reinterpret_cast<Packet2d>(p2ul_CONJ_XOR1));
+
+ return Packet1cd(padd<Packet2d>(v1, v2));
+ }
+
+ EIGEN_STRONG_INLINE Packet1cd& operator*=(const Packet1cd& b) {
+ v = pmul(Packet1cd(*this), b).v;
+ return *this;
+ }
+ EIGEN_STRONG_INLINE Packet1cd operator*(const Packet1cd& b) const {
+ return Packet1cd(*this) *= b;
+ }
+
+ EIGEN_STRONG_INLINE Packet1cd& operator+=(const Packet1cd& b) {
+ v = padd(v, b.v);
+ return *this;
+ }
+ EIGEN_STRONG_INLINE Packet1cd operator+(const Packet1cd& b) const {
+ return Packet1cd(*this) += b;
+ }
+ EIGEN_STRONG_INLINE Packet1cd& operator-=(const Packet1cd& b) {
+ v = psub(v, b.v);
+ return *this;
+ }
+ EIGEN_STRONG_INLINE Packet1cd operator-(const Packet1cd& b) const {
+ return Packet1cd(*this) -= b;
+ }
+ EIGEN_STRONG_INLINE Packet1cd operator-(void) const {
+ return Packet1cd(-v);
+ }
+
+ Packet2d v;
+};
+
+template<> struct packet_traits<std::complex<double> > : default_packet_traits
+{
+ typedef Packet1cd type;
+ typedef Packet1cd half;
+ typedef Packet2d as_real;
+ enum {
+ Vectorizable = 1,
+ AlignedOnScalar = 0,
+ size = 1,
+ HasHalfPacket = 0,
+
+ HasAdd = 1,
+ HasSub = 1,
+ HasMul = 1,
+ HasDiv = 1,
+ HasNegate = 1,
+ HasAbs = 0,
+ HasAbs2 = 0,
+ HasMin = 0,
+ HasMax = 0,
+ HasSqrt = 1,
+ HasSetLinear = 0
+ };
+};
+
+template<> struct unpacket_traits<Packet1cd> { typedef std::complex<double> type; enum {size=1, alignment=Aligned16, vectorizable=true, masked_load_available=false, masked_store_available=false}; typedef Packet1cd half; typedef Packet2d as_real; };
+
+template<> EIGEN_STRONG_INLINE Packet1cd pload <Packet1cd>(const std::complex<double>* from) { return Packet1cd(pload<Packet2d>((const double*)from)); }
+template<> EIGEN_STRONG_INLINE Packet1cd ploadu<Packet1cd>(const std::complex<double>* from) { return Packet1cd(ploadu<Packet2d>((const double*)from)); }
+template<> EIGEN_ALWAYS_INLINE Packet1cd pload_partial<Packet1cd>(const std::complex<double>* from, const Index n, const Index offset)
+{
+ return Packet1cd(pload_partial<Packet2d>((const double*)from, n * 2, offset * 2));
+}
+template<> EIGEN_ALWAYS_INLINE Packet1cd ploadu_partial<Packet1cd>(const std::complex<double>* from, const Index n)
+{
+ return Packet1cd(ploadu_partial<Packet2d>((const double*)from, n * 2));
+}
+template<> EIGEN_STRONG_INLINE void pstore <std::complex<double> >(std::complex<double> * to, const Packet1cd& from) { pstore((double*)to, from.v); }
+template<> EIGEN_STRONG_INLINE void pstoreu<std::complex<double> >(std::complex<double> * to, const Packet1cd& from) { pstoreu((double*)to, from.v); }
+template<> EIGEN_ALWAYS_INLINE void pstore_partial <std::complex<double> >(std::complex<double> * to, const Packet1cd& from, const Index n, const Index offset) { pstore_partial((double*)to, from.v, n * 2, offset * 2); }
+template<> EIGEN_ALWAYS_INLINE void pstoreu_partial<std::complex<double> >(std::complex<double> * to, const Packet1cd& from, const Index n) { pstoreu_partial((double*)to, from.v, n * 2); }
+
+template<> EIGEN_STRONG_INLINE Packet1cd pset1<Packet1cd>(const std::complex<double>& from)
+{ /* here we really have to use unaligned loads :( */ return ploadu<Packet1cd>(&from); }
+
+template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE Packet1cd pgather<std::complex<double>, Packet1cd>(const std::complex<double>* from, Index)
+{
+ return pload<Packet1cd>(from);
+}
+template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE Packet1cd pgather_partial<std::complex<double>, Packet1cd>(const std::complex<double>* from, Index, const Index)
+{
+ return pload<Packet1cd>(from);
+}
+template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE void pscatter<std::complex<double>, Packet1cd>(std::complex<double>* to, const Packet1cd& from, Index)
+{
+ pstore<std::complex<double> >(to, from);
+}
+template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE void pscatter_partial<std::complex<double>, Packet1cd>(std::complex<double>* to, const Packet1cd& from, Index, const Index)
+{
+ pstore<std::complex<double> >(to, from);
+}
+
+template<> EIGEN_STRONG_INLINE Packet1cd padd<Packet1cd>(const Packet1cd& a, const Packet1cd& b) { return Packet1cd(a.v + b.v); }
+template<> EIGEN_STRONG_INLINE Packet1cd psub<Packet1cd>(const Packet1cd& a, const Packet1cd& b) { return Packet1cd(a.v - b.v); }
+template<> EIGEN_STRONG_INLINE Packet1cd pnegate(const Packet1cd& a) { return Packet1cd(pnegate(Packet2d(a.v))); }
+template<> EIGEN_STRONG_INLINE Packet1cd pconj(const Packet1cd& a) { return Packet1cd(pxor(a.v, reinterpret_cast<Packet2d>(p2ul_CONJ_XOR2))); }
+
+template<> EIGEN_STRONG_INLINE Packet1cd pand <Packet1cd>(const Packet1cd& a, const Packet1cd& b) { return Packet1cd(pand(a.v,b.v)); }
+template<> EIGEN_STRONG_INLINE Packet1cd por <Packet1cd>(const Packet1cd& a, const Packet1cd& b) { return Packet1cd(por(a.v,b.v)); }
+template<> EIGEN_STRONG_INLINE Packet1cd pxor <Packet1cd>(const Packet1cd& a, const Packet1cd& b) { return Packet1cd(pxor(a.v,b.v)); }
+template<> EIGEN_STRONG_INLINE Packet1cd pandnot<Packet1cd>(const Packet1cd& a, const Packet1cd& b) { return Packet1cd(pandnot(a.v, b.v)); }
+
+template<> EIGEN_STRONG_INLINE Packet1cd ploaddup<Packet1cd>(const std::complex<double>* from) { return pset1<Packet1cd>(*from); }
+
+template<> EIGEN_STRONG_INLINE void prefetch<std::complex<double> >(const std::complex<double> * addr) { EIGEN_PPC_PREFETCH(addr); }
+
+template<> EIGEN_STRONG_INLINE std::complex<double> pfirst<Packet1cd>(const Packet1cd& a)
+{
+ EIGEN_ALIGN16 std::complex<double> res[1];
+ pstore<std::complex<double> >(res, a);
+
+ return res[0];
+}
+
+template<> EIGEN_STRONG_INLINE Packet1cd preverse(const Packet1cd& a) { return a; }
+
+template<> EIGEN_STRONG_INLINE std::complex<double> predux<Packet1cd>(const Packet1cd& a) { return pfirst(a); }
+
+template<> EIGEN_STRONG_INLINE std::complex<double> predux_mul<Packet1cd>(const Packet1cd& a) { return pfirst(a); }
+
+EIGEN_MAKE_CONJ_HELPER_CPLX_REAL(Packet1cd,Packet2d)
+
+template<> EIGEN_STRONG_INLINE Packet1cd pdiv<Packet1cd>(const Packet1cd& a, const Packet1cd& b)
+{
+ return pdiv_complex(a, b);
+}
+
+EIGEN_STRONG_INLINE Packet1cd pcplxflip/*<Packet1cd>*/(const Packet1cd& x)
+{
+ return Packet1cd(preverse(Packet2d(x.v)));
+}
+
+EIGEN_STRONG_INLINE void ptranspose(PacketBlock<Packet1cd,2>& kernel)
+{
+ Packet2d tmp = vec_mergeh(kernel.packet[0].v, kernel.packet[1].v);
+ kernel.packet[1].v = vec_mergel(kernel.packet[0].v, kernel.packet[1].v);
+ kernel.packet[0].v = tmp;
+}
+
+template<> EIGEN_STRONG_INLINE Packet1cd pcmp_eq(const Packet1cd& a, const Packet1cd& b) {
+ // Compare real and imaginary parts of a and b to get the mask vector:
+ // [re(a)==re(b), im(a)==im(b)]
+ Packet2d eq = reinterpret_cast<Packet2d>(vec_cmpeq(a.v,b.v));
+ // Swap real/imag elements in the mask in to get:
+ // [im(a)==im(b), re(a)==re(b)]
+ Packet2d eq_swapped = reinterpret_cast<Packet2d>(vec_sld(reinterpret_cast<Packet4ui>(eq), reinterpret_cast<Packet4ui>(eq), 8));
+ // Return re(a)==re(b) & im(a)==im(b) by computing bitwise AND of eq and eq_swapped
+ return Packet1cd(vec_and(eq, eq_swapped));
+}
+
+template<> EIGEN_STRONG_INLINE Packet1cd psqrt<Packet1cd>(const Packet1cd& a)
+{
+ return psqrt_complex<Packet1cd>(a);
+}
+
+#endif // __VSX__
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_COMPLEX32_ALTIVEC_H
diff --git a/Eigen/src/Core/arch/AltiVec/MathFunctions.h b/Eigen/src/Core/arch/AltiVec/MathFunctions.h
new file mode 100644
index 0000000..6f48d98
--- /dev/null
+++ b/Eigen/src/Core/arch/AltiVec/MathFunctions.h
@@ -0,0 +1,134 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2007 Julien Pommier
+// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2016 Konstantinos Margaritis <markos@freevec.org>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_MATH_FUNCTIONS_ALTIVEC_H
+#define EIGEN_MATH_FUNCTIONS_ALTIVEC_H
+
+#include "../../InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+
+template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+Packet4f plog<Packet4f>(const Packet4f& _x)
+{
+ return plog_float(_x);
+}
+
+template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+Packet4f pexp<Packet4f>(const Packet4f& _x)
+{
+ return pexp_float(_x);
+}
+
+template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+Packet4f psin<Packet4f>(const Packet4f& _x)
+{
+ return psin_float(_x);
+}
+
+template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+Packet4f pcos<Packet4f>(const Packet4f& _x)
+{
+ return pcos_float(_x);
+}
+
+template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+Packet4f pacos<Packet4f>(const Packet4f& _x)
+{
+ return pacos_float(_x);
+}
+
+template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+Packet4f pasin<Packet4f>(const Packet4f& _x)
+{
+ return pasin_float(_x);
+}
+
+template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+Packet4f patan<Packet4f>(const Packet4f& _x)
+{
+ return patan_float(_x);
+}
+
+#ifdef __VSX__
+#ifndef EIGEN_COMP_CLANG
+template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+Packet4f prsqrt<Packet4f>(const Packet4f& x)
+{
+ return vec_rsqrt(x);
+}
+
+template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+Packet2d prsqrt<Packet2d>(const Packet2d& x)
+{
+ return vec_rsqrt(x);
+}
+
+template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+Packet2d patan<Packet2d>(const Packet2d& _x)
+{
+ return patan_double(_x);
+}
+#endif
+
+template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+Packet4f psqrt<Packet4f>(const Packet4f& x)
+{
+ return vec_sqrt(x);
+}
+
+template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+Packet2d psqrt<Packet2d>(const Packet2d& x)
+{
+ return vec_sqrt(x);
+}
+
+template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+Packet2d pexp<Packet2d>(const Packet2d& _x)
+{
+ return pexp_double(_x);
+}
+
+template<> EIGEN_STRONG_INLINE Packet8bf psqrt<Packet8bf> (const Packet8bf& a){
+ BF16_TO_F32_UNARY_OP_WRAPPER(psqrt<Packet4f>, a);
+}
+
+#ifndef EIGEN_COMP_CLANG
+template<> EIGEN_STRONG_INLINE Packet8bf prsqrt<Packet8bf> (const Packet8bf& a){
+ BF16_TO_F32_UNARY_OP_WRAPPER(prsqrt<Packet4f>, a);
+}
+#endif
+#else
+template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+Packet4f psqrt<Packet4f>(const Packet4f& x)
+{
+ Packet4f a;
+ for (Index i = 0; i < packet_traits<float>::size; i++) {
+ a[i] = numext::sqrt(x[i]);
+ }
+ return a;
+}
+#endif
+
+// Hyperbolic Tangent function.
+template <>
+EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet4f
+ptanh<Packet4f>(const Packet4f& x) {
+ return internal::generic_fast_tanh_float(x);
+}
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_MATH_FUNCTIONS_ALTIVEC_H
diff --git a/Eigen/src/Core/arch/AltiVec/MatrixProduct.h b/Eigen/src/Core/arch/AltiVec/MatrixProduct.h
new file mode 100644
index 0000000..3b3b558
--- /dev/null
+++ b/Eigen/src/Core/arch/AltiVec/MatrixProduct.h
@@ -0,0 +1,2788 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2020 Everton Constantino (everton.constantino@ibm.com)
+// Copyright (C) 2021 Chip Kerchner (chip.kerchner@ibm.com)
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_MATRIX_PRODUCT_ALTIVEC_H
+#define EIGEN_MATRIX_PRODUCT_ALTIVEC_H
+
+#ifndef EIGEN_ALTIVEC_USE_CUSTOM_PACK
+#define EIGEN_ALTIVEC_USE_CUSTOM_PACK 1
+#endif
+
+#include "MatrixProductCommon.h"
+
+#if !defined(EIGEN_ALTIVEC_DISABLE_MMA)
+#define EIGEN_ALTIVEC_DISABLE_MMA 0
+#endif
+
+// Check for MMA builtin support.
+#if !EIGEN_ALTIVEC_DISABLE_MMA && defined(__has_builtin)
+#if __has_builtin(__builtin_mma_assemble_acc)
+ #define EIGEN_ALTIVEC_MMA_SUPPORT
+#endif
+#endif
+
+// Check if and how we should actually use MMA if supported.
+#if defined(EIGEN_ALTIVEC_MMA_SUPPORT)
+
+#if !defined(EIGEN_ALTIVEC_ENABLE_MMA_DYNAMIC_DISPATCH)
+#define EIGEN_ALTIVEC_ENABLE_MMA_DYNAMIC_DISPATCH 0
+#endif
+
+// Check if we want to enable dynamic dispatch. Not supported by LLVM.
+#if EIGEN_ALTIVEC_ENABLE_MMA_DYNAMIC_DISPATCH && !EIGEN_COMP_LLVM
+#define EIGEN_ALTIVEC_MMA_DYNAMIC_DISPATCH 1
+// Otherwise, use MMA by default if available.
+#elif defined(__MMA__)
+#define EIGEN_ALTIVEC_MMA_ONLY 1
+#endif
+
+#endif // EIGEN_ALTIVEC_MMA_SUPPORT
+
+#if defined(EIGEN_ALTIVEC_MMA_ONLY) || defined(EIGEN_ALTIVEC_MMA_DYNAMIC_DISPATCH)
+ #include "MatrixProductMMA.h"
+#endif
+
+/**************************************************************************************************
+ * TODO *
+ * - Check StorageOrder on dhs_pack (the innermost second loop seems unvectorized when it could). *
+ * - Check the possibility of transposing as GETREAL and GETIMAG when needed. *
+ **************************************************************************************************/
+#include "../../InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+
+/**************************
+ * Constants and typedefs *
+ **************************/
+template<typename Scalar>
+struct quad_traits
+{
+ typedef typename packet_traits<Scalar>::type vectortype;
+ typedef PacketBlock<vectortype,4> type;
+ typedef vectortype rhstype;
+ enum
+ {
+ vectorsize = packet_traits<Scalar>::size,
+ size = 4,
+ rows = 4
+ };
+};
+
+template<>
+struct quad_traits<double>
+{
+ typedef Packet2d vectortype;
+ typedef PacketBlock<vectortype,4> type;
+ typedef PacketBlock<Packet2d,2> rhstype;
+ enum
+ {
+ vectorsize = packet_traits<double>::size,
+ size = 2,
+ rows = 4
+ };
+};
+
+// MatrixProduct decomposes real/imaginary vectors into a real vector and an imaginary vector, this turned out
+// to be faster than Eigen's usual approach of having real/imaginary pairs on a single vector. This constants then
+// are responsible to extract from convert between Eigen's and MatrixProduct approach.
+
+const static Packet16uc p16uc_GETREAL32 = { 0, 1, 2, 3,
+ 8, 9, 10, 11,
+ 16, 17, 18, 19,
+ 24, 25, 26, 27};
+
+const static Packet16uc p16uc_GETIMAG32 = { 4, 5, 6, 7,
+ 12, 13, 14, 15,
+ 20, 21, 22, 23,
+ 28, 29, 30, 31};
+
+/*********************************************
+ * Single precision real and complex packing *
+ * *******************************************/
+
+/**
+ * Symm packing is related to packing of symmetric adjoint blocks, as expected the packing leaves
+ * the diagonal real, whatever is below it is copied from the respective upper diagonal element and
+ * conjugated. There's no PanelMode available for symm packing.
+ *
+ * Packing in general is supposed to leave the lhs block and the rhs block easy to be read by gemm using
+ * its respective rank-update instructions. The float32/64 versions are different because at this moment
+ * the size of the accumulator is fixed at 512-bits so you can't have a 4x4 accumulator of 64-bit elements.
+ *
+ * As mentioned earlier MatrixProduct breaks complex numbers into a real vector and a complex vector so packing has
+ * to take that into account, at the moment, we run pack the real part and then the imaginary part, this is the main
+ * reason why packing for complex is broken down into several different parts, also the reason why we endup having a
+ * float32/64 and complex float32/64 version.
+ **/
+template<typename Scalar, int StorageOrder>
+EIGEN_ALWAYS_INLINE std::complex<Scalar> getAdjointVal(Index i, Index j, const_blas_data_mapper<std::complex<Scalar>, Index, StorageOrder>& dt)
+{
+ std::complex<Scalar> v;
+ if(i < j)
+ {
+ v.real( dt(j,i).real());
+ v.imag(-dt(j,i).imag());
+ } else if(i > j)
+ {
+ v.real( dt(i,j).real());
+ v.imag( dt(i,j).imag());
+ } else {
+ v.real( dt(i,j).real());
+ v.imag((Scalar)0.0);
+ }
+ return v;
+}
+
+template<typename Scalar, int StorageOrder, int N>
+EIGEN_STRONG_INLINE void symm_pack_complex_rhs_helper(std::complex<Scalar>* blockB, const std::complex<Scalar>* _rhs, Index rhsStride, Index rows, Index cols, Index k2)
+{
+ const Index depth = k2 + rows;
+ const_blas_data_mapper<std::complex<Scalar>, Index, StorageOrder> rhs(_rhs, rhsStride);
+ const Index vectorSize = N*quad_traits<Scalar>::vectorsize;
+ const Index vectorDelta = vectorSize * rows;
+ Scalar* blockBf = reinterpret_cast<Scalar *>(blockB);
+
+ Index rir = 0, rii, j = 0;
+ for(; j + vectorSize <= cols; j+=vectorSize)
+ {
+ rii = rir + vectorDelta;
+
+ for(Index i = k2; i < depth; i++)
+ {
+ for(Index k = 0; k < vectorSize; k++)
+ {
+ std::complex<Scalar> v = getAdjointVal<Scalar, StorageOrder>(i, j + k, rhs);
+
+ blockBf[rir + k] = v.real();
+ blockBf[rii + k] = v.imag();
+ }
+ rir += vectorSize;
+ rii += vectorSize;
+ }
+
+ rir += vectorDelta;
+ }
+
+ for(; j < cols; j++)
+ {
+ rii = rir + rows;
+
+ for(Index i = k2; i < depth; i++)
+ {
+ std::complex<Scalar> v = getAdjointVal<Scalar, StorageOrder>(i, j, rhs);
+
+ blockBf[rir] = v.real();
+ blockBf[rii] = v.imag();
+
+ rir += 1;
+ rii += 1;
+ }
+
+ rir += rows;
+ }
+}
+
+template<typename Scalar, int StorageOrder>
+EIGEN_STRONG_INLINE void symm_pack_complex_lhs_helper(std::complex<Scalar>* blockA, const std::complex<Scalar>* _lhs, Index lhsStride, Index cols, Index rows)
+{
+ const Index depth = cols;
+ const_blas_data_mapper<std::complex<Scalar>, Index, StorageOrder> lhs(_lhs, lhsStride);
+ const Index vectorSize = quad_traits<Scalar>::vectorsize;
+ const Index vectorDelta = vectorSize * depth;
+ Scalar* blockAf = reinterpret_cast<Scalar *>(blockA);
+
+ Index rir = 0, rii, j = 0;
+ for(; j + vectorSize <= rows; j+=vectorSize)
+ {
+ rii = rir + vectorDelta;
+
+ for(Index i = 0; i < depth; i++)
+ {
+ for(Index k = 0; k < vectorSize; k++)
+ {
+ std::complex<Scalar> v = getAdjointVal<Scalar, StorageOrder>(j+k, i, lhs);
+
+ blockAf[rir + k] = v.real();
+ blockAf[rii + k] = v.imag();
+ }
+ rir += vectorSize;
+ rii += vectorSize;
+ }
+
+ rir += vectorDelta;
+ }
+
+ if (j < rows)
+ {
+ rii = rir + ((rows - j) * depth);
+
+ for(Index i = 0; i < depth; i++)
+ {
+ Index k = j;
+ for(; k < rows; k++)
+ {
+ std::complex<Scalar> v = getAdjointVal<Scalar, StorageOrder>(k, i, lhs);
+
+ blockAf[rir] = v.real();
+ blockAf[rii] = v.imag();
+
+ rir += 1;
+ rii += 1;
+ }
+ }
+ }
+}
+
+template<typename Scalar, int StorageOrder, int N>
+EIGEN_STRONG_INLINE void symm_pack_rhs_helper(Scalar* blockB, const Scalar* _rhs, Index rhsStride, Index rows, Index cols, Index k2)
+{
+ const Index depth = k2 + rows;
+ const_blas_data_mapper<Scalar, Index, StorageOrder> rhs(_rhs, rhsStride);
+ const Index vectorSize = quad_traits<Scalar>::vectorsize;
+
+ Index ri = 0, j = 0;
+ for(; j + N*vectorSize <= cols; j+=N*vectorSize)
+ {
+ Index i = k2;
+ for(; i < depth; i++)
+ {
+ for(Index k = 0; k < N*vectorSize; k++)
+ {
+ if(i <= j+k)
+ blockB[ri + k] = rhs(j+k, i);
+ else
+ blockB[ri + k] = rhs(i, j+k);
+ }
+ ri += N*vectorSize;
+ }
+ }
+
+ for(; j < cols; j++)
+ {
+ for(Index i = k2; i < depth; i++)
+ {
+ if(j <= i)
+ blockB[ri] = rhs(i, j);
+ else
+ blockB[ri] = rhs(j, i);
+ ri += 1;
+ }
+ }
+}
+
+template<typename Scalar, int StorageOrder>
+EIGEN_STRONG_INLINE void symm_pack_lhs_helper(Scalar* blockA, const Scalar* _lhs, Index lhsStride, Index cols, Index rows)
+{
+ const Index depth = cols;
+ const_blas_data_mapper<Scalar, Index, StorageOrder> lhs(_lhs, lhsStride);
+ const Index vectorSize = quad_traits<Scalar>::vectorsize;
+
+ Index ri = 0, j = 0;
+ for(; j + vectorSize <= rows; j+=vectorSize)
+ {
+ Index i = 0;
+
+ for(; i < depth; i++)
+ {
+ for(Index k = 0; k < vectorSize; k++)
+ {
+ if(i <= j+k)
+ blockA[ri + k] = lhs(j+k, i);
+ else
+ blockA[ri + k] = lhs(i, j+k);
+ }
+ ri += vectorSize;
+ }
+ }
+
+ if (j < rows)
+ {
+ for(Index i = 0; i < depth; i++)
+ {
+ Index k = j;
+ for(; k < rows; k++)
+ {
+ if(i <= k)
+ blockA[ri] = lhs(k, i);
+ else
+ blockA[ri] = lhs(i, k);
+ ri += 1;
+ }
+ }
+ }
+}
+
+template<typename Index, int nr, int StorageOrder>
+struct symm_pack_rhs<std::complex<float>, Index, nr, StorageOrder>
+{
+ void operator()(std::complex<float>* blockB, const std::complex<float>* _rhs, Index rhsStride, Index rows, Index cols, Index k2)
+ {
+ symm_pack_complex_rhs_helper<float, StorageOrder, 1>(blockB, _rhs, rhsStride, rows, cols, k2);
+ }
+};
+
+template<typename Index, int Pack1, int Pack2_dummy, int StorageOrder>
+struct symm_pack_lhs<std::complex<float>, Index, Pack1, Pack2_dummy, StorageOrder>
+{
+ void operator()(std::complex<float>* blockA, const std::complex<float>* _lhs, Index lhsStride, Index cols, Index rows)
+ {
+ symm_pack_complex_lhs_helper<float, StorageOrder>(blockA, _lhs, lhsStride, cols, rows);
+ }
+};
+
+// *********** symm_pack std::complex<float64> ***********
+
+template<typename Index, int nr, int StorageOrder>
+struct symm_pack_rhs<std::complex<double>, Index, nr, StorageOrder>
+{
+ void operator()(std::complex<double>* blockB, const std::complex<double>* _rhs, Index rhsStride, Index rows, Index cols, Index k2)
+ {
+ symm_pack_complex_rhs_helper<double, StorageOrder, 2>(blockB, _rhs, rhsStride, rows, cols, k2);
+ }
+};
+
+template<typename Index, int Pack1, int Pack2_dummy, int StorageOrder>
+struct symm_pack_lhs<std::complex<double>, Index, Pack1, Pack2_dummy, StorageOrder>
+{
+ void operator()(std::complex<double>* blockA, const std::complex<double>* _lhs, Index lhsStride, Index cols, Index rows)
+ {
+ symm_pack_complex_lhs_helper<double, StorageOrder>(blockA, _lhs, lhsStride, cols, rows);
+ }
+};
+
+// *********** symm_pack float32 ***********
+template<typename Index, int nr, int StorageOrder>
+struct symm_pack_rhs<float, Index, nr, StorageOrder>
+{
+ void operator()(float* blockB, const float* _rhs, Index rhsStride, Index rows, Index cols, Index k2)
+ {
+ symm_pack_rhs_helper<float, StorageOrder, 1>(blockB, _rhs, rhsStride, rows, cols, k2);
+ }
+};
+
+template<typename Index, int Pack1, int Pack2_dummy, int StorageOrder>
+struct symm_pack_lhs<float, Index, Pack1, Pack2_dummy, StorageOrder>
+{
+ void operator()(float* blockA, const float* _lhs, Index lhsStride, Index cols, Index rows)
+ {
+ symm_pack_lhs_helper<float, StorageOrder>(blockA, _lhs, lhsStride, cols, rows);
+ }
+};
+
+// *********** symm_pack float64 ***********
+template<typename Index, int nr, int StorageOrder>
+struct symm_pack_rhs<double, Index, nr, StorageOrder>
+{
+ void operator()(double* blockB, const double* _rhs, Index rhsStride, Index rows, Index cols, Index k2)
+ {
+ symm_pack_rhs_helper<double, StorageOrder, 2>(blockB, _rhs, rhsStride, rows, cols, k2);
+ }
+};
+
+template<typename Index, int Pack1, int Pack2_dummy, int StorageOrder>
+struct symm_pack_lhs<double, Index, Pack1, Pack2_dummy, StorageOrder>
+{
+ void operator()(double* blockA, const double* _lhs, Index lhsStride, Index cols, Index rows)
+ {
+ symm_pack_lhs_helper<double, StorageOrder>(blockA, _lhs, lhsStride, cols, rows);
+ }
+};
+
+/**
+ * PanelMode
+ * Packing might be called several times before being multiplied by gebp_kernel, this happens because
+ * on special occasions it fills part of block with other parts of the matrix. Two variables control
+ * how PanelMode should behave: offset and stride. The idea is that those variables represent whatever
+ * is going to be the real offset and stride in the future and this is what you should obey. The process
+ * is to behave as you would with normal packing but leave the start of each part with the correct offset
+ * and the end as well respecting the real stride the block will have. Gebp is aware of both blocks stride
+ * and offset and behaves accordingly.
+ **/
+
+template<typename Scalar, typename Packet, int N>
+EIGEN_ALWAYS_INLINE void storeBlock(Scalar* to, PacketBlock<Packet,N>& block)
+{
+ const Index size = 16 / sizeof(Scalar);
+ pstore<Scalar>(to + (0 * size), block.packet[0]);
+ pstore<Scalar>(to + (1 * size), block.packet[1]);
+ if (N > 2) {
+ pstore<Scalar>(to + (2 * size), block.packet[2]);
+ }
+ if (N > 3) {
+ pstore<Scalar>(to + (3 * size), block.packet[3]);
+ }
+}
+
+// General template for lhs & rhs complex packing.
+template<typename Scalar, typename DataMapper, typename Packet, typename PacketC, int StorageOrder, bool Conjugate, bool PanelMode, bool UseLhs>
+struct dhs_cpack {
+ EIGEN_STRONG_INLINE void operator()(std::complex<Scalar>* blockA, const DataMapper& lhs, Index depth, Index rows, Index stride, Index offset)
+ {
+ const Index vectorSize = quad_traits<Scalar>::vectorsize;
+ const Index vectorDelta = vectorSize * ((PanelMode) ? stride : depth);
+ Index rir = ((PanelMode) ? (vectorSize*offset) : 0), rii;
+ Scalar* blockAt = reinterpret_cast<Scalar *>(blockA);
+ Index j = 0;
+
+ for(; j + vectorSize <= rows; j+=vectorSize)
+ {
+ const DataMapper lhs2 = UseLhs ? lhs.getSubMapper(j, 0) : lhs.getSubMapper(0, j);
+ Index i = 0;
+
+ rii = rir + vectorDelta;
+
+ for(; i + vectorSize <= depth; i+=vectorSize)
+ {
+ PacketBlock<Packet,4> blockr, blocki;
+ PacketBlock<PacketC,8> cblock;
+
+ if (UseLhs) {
+ bload<DataMapper, PacketC, 2, StorageOrder, true, 4>(cblock, lhs2, 0, i);
+ } else {
+ bload<DataMapper, PacketC, 2, StorageOrder, true, 4>(cblock, lhs2, i, 0);
+ }
+
+ blockr.packet[0] = vec_perm(cblock.packet[0].v, cblock.packet[4].v, p16uc_GETREAL32);
+ blockr.packet[1] = vec_perm(cblock.packet[1].v, cblock.packet[5].v, p16uc_GETREAL32);
+ blockr.packet[2] = vec_perm(cblock.packet[2].v, cblock.packet[6].v, p16uc_GETREAL32);
+ blockr.packet[3] = vec_perm(cblock.packet[3].v, cblock.packet[7].v, p16uc_GETREAL32);
+
+ blocki.packet[0] = vec_perm(cblock.packet[0].v, cblock.packet[4].v, p16uc_GETIMAG32);
+ blocki.packet[1] = vec_perm(cblock.packet[1].v, cblock.packet[5].v, p16uc_GETIMAG32);
+ blocki.packet[2] = vec_perm(cblock.packet[2].v, cblock.packet[6].v, p16uc_GETIMAG32);
+ blocki.packet[3] = vec_perm(cblock.packet[3].v, cblock.packet[7].v, p16uc_GETIMAG32);
+
+ if(Conjugate)
+ {
+ blocki.packet[0] = -blocki.packet[0];
+ blocki.packet[1] = -blocki.packet[1];
+ blocki.packet[2] = -blocki.packet[2];
+ blocki.packet[3] = -blocki.packet[3];
+ }
+
+ if(((StorageOrder == RowMajor) && UseLhs) || (((StorageOrder == ColMajor) && !UseLhs)))
+ {
+ ptranspose(blockr);
+ ptranspose(blocki);
+ }
+
+ storeBlock<Scalar, Packet, 4>(blockAt + rir, blockr);
+ storeBlock<Scalar, Packet, 4>(blockAt + rii, blocki);
+
+ rir += 4*vectorSize;
+ rii += 4*vectorSize;
+ }
+ for(; i < depth; i++)
+ {
+ PacketBlock<Packet,1> blockr, blocki;
+ PacketBlock<PacketC,2> cblock;
+
+ if(((StorageOrder == ColMajor) && UseLhs) || (((StorageOrder == RowMajor) && !UseLhs)))
+ {
+ if (UseLhs) {
+ cblock.packet[0] = lhs2.template loadPacket<PacketC>(0, i);
+ cblock.packet[1] = lhs2.template loadPacket<PacketC>(2, i);
+ } else {
+ cblock.packet[0] = lhs2.template loadPacket<PacketC>(i, 0);
+ cblock.packet[1] = lhs2.template loadPacket<PacketC>(i, 2);
+ }
+ } else {
+ if (UseLhs) {
+ cblock.packet[0] = pload2(lhs2(0, i), lhs2(1, i));
+ cblock.packet[1] = pload2(lhs2(2, i), lhs2(3, i));
+ } else {
+ cblock.packet[0] = pload2(lhs2(i, 0), lhs2(i, 1));
+ cblock.packet[1] = pload2(lhs2(i, 2), lhs2(i, 3));
+ }
+ }
+
+ blockr.packet[0] = vec_perm(cblock.packet[0].v, cblock.packet[1].v, p16uc_GETREAL32);
+ blocki.packet[0] = vec_perm(cblock.packet[0].v, cblock.packet[1].v, p16uc_GETIMAG32);
+
+ if(Conjugate)
+ {
+ blocki.packet[0] = -blocki.packet[0];
+ }
+
+ pstore<Scalar>(blockAt + rir, blockr.packet[0]);
+ pstore<Scalar>(blockAt + rii, blocki.packet[0]);
+
+ rir += vectorSize;
+ rii += vectorSize;
+ }
+
+ rir += ((PanelMode) ? (vectorSize*(2*stride - depth)) : vectorDelta);
+ }
+
+ if (!UseLhs)
+ {
+ if(PanelMode) rir -= (offset*(vectorSize - 1));
+
+ for(; j < rows; j++)
+ {
+ const DataMapper lhs2 = lhs.getSubMapper(0, j);
+ rii = rir + ((PanelMode) ? stride : depth);
+
+ for(Index i = 0; i < depth; i++)
+ {
+ blockAt[rir] = lhs2(i, 0).real();
+
+ if(Conjugate)
+ blockAt[rii] = -lhs2(i, 0).imag();
+ else
+ blockAt[rii] = lhs2(i, 0).imag();
+
+ rir += 1;
+ rii += 1;
+ }
+
+ rir += ((PanelMode) ? (2*stride - depth) : depth);
+ }
+ } else {
+ if (j < rows)
+ {
+ if(PanelMode) rir += (offset*(rows - j - vectorSize));
+ rii = rir + (((PanelMode) ? stride : depth) * (rows - j));
+
+ for(Index i = 0; i < depth; i++)
+ {
+ Index k = j;
+ for(; k < rows; k++)
+ {
+ blockAt[rir] = lhs(k, i).real();
+
+ if(Conjugate)
+ blockAt[rii] = -lhs(k, i).imag();
+ else
+ blockAt[rii] = lhs(k, i).imag();
+
+ rir += 1;
+ rii += 1;
+ }
+ }
+ }
+ }
+ }
+};
+
+// General template for lhs & rhs packing.
+template<typename Scalar, typename DataMapper, typename Packet, int StorageOrder, bool PanelMode, bool UseLhs>
+struct dhs_pack{
+ EIGEN_STRONG_INLINE void operator()(Scalar* blockA, const DataMapper& lhs, Index depth, Index rows, Index stride, Index offset)
+ {
+ const Index vectorSize = quad_traits<Scalar>::vectorsize;
+ Index ri = 0, j = 0;
+
+ for(; j + vectorSize <= rows; j+=vectorSize)
+ {
+ const DataMapper lhs2 = UseLhs ? lhs.getSubMapper(j, 0) : lhs.getSubMapper(0, j);
+ Index i = 0;
+
+ if(PanelMode) ri += vectorSize*offset;
+
+ for(; i + vectorSize <= depth; i+=vectorSize)
+ {
+ PacketBlock<Packet,4> block;
+
+ if (UseLhs) {
+ bload<DataMapper, Packet, 4, StorageOrder, false, 4>(block, lhs2, 0, i);
+ } else {
+ bload<DataMapper, Packet, 4, StorageOrder, false, 4>(block, lhs2, i, 0);
+ }
+ if(((StorageOrder == RowMajor) && UseLhs) || ((StorageOrder == ColMajor) && !UseLhs))
+ {
+ ptranspose(block);
+ }
+
+ storeBlock<Scalar, Packet, 4>(blockA + ri, block);
+
+ ri += 4*vectorSize;
+ }
+ for(; i < depth; i++)
+ {
+ if(((StorageOrder == RowMajor) && UseLhs) || ((StorageOrder == ColMajor) && !UseLhs))
+ {
+ if (UseLhs) {
+ blockA[ri+0] = lhs2(0, i);
+ blockA[ri+1] = lhs2(1, i);
+ blockA[ri+2] = lhs2(2, i);
+ blockA[ri+3] = lhs2(3, i);
+ } else {
+ blockA[ri+0] = lhs2(i, 0);
+ blockA[ri+1] = lhs2(i, 1);
+ blockA[ri+2] = lhs2(i, 2);
+ blockA[ri+3] = lhs2(i, 3);
+ }
+ } else {
+ Packet lhsV;
+ if (UseLhs) {
+ lhsV = lhs2.template loadPacket<Packet>(0, i);
+ } else {
+ lhsV = lhs2.template loadPacket<Packet>(i, 0);
+ }
+ pstore<Scalar>(blockA + ri, lhsV);
+ }
+
+ ri += vectorSize;
+ }
+
+ if(PanelMode) ri += vectorSize*(stride - offset - depth);
+ }
+
+ if (!UseLhs)
+ {
+ if(PanelMode) ri += offset;
+
+ for(; j < rows; j++)
+ {
+ const DataMapper lhs2 = lhs.getSubMapper(0, j);
+ for(Index i = 0; i < depth; i++)
+ {
+ blockA[ri] = lhs2(i, 0);
+ ri += 1;
+ }
+
+ if(PanelMode) ri += stride - depth;
+ }
+ } else {
+ if (j < rows)
+ {
+ if(PanelMode) ri += offset*(rows - j);
+
+ for(Index i = 0; i < depth; i++)
+ {
+ Index k = j;
+ for(; k < rows; k++)
+ {
+ blockA[ri] = lhs(k, i);
+ ri += 1;
+ }
+ }
+ }
+ }
+ }
+};
+
+// General template for lhs packing, float64 specialization.
+template<typename DataMapper, int StorageOrder, bool PanelMode>
+struct dhs_pack<double, DataMapper, Packet2d, StorageOrder, PanelMode, true>
+{
+ EIGEN_STRONG_INLINE void operator()(double* blockA, const DataMapper& lhs, Index depth, Index rows, Index stride, Index offset)
+ {
+ const Index vectorSize = quad_traits<double>::vectorsize;
+ Index ri = 0, j = 0;
+
+ for(; j + vectorSize <= rows; j+=vectorSize)
+ {
+ const DataMapper lhs2 = lhs.getSubMapper(j, 0);
+ Index i = 0;
+
+ if(PanelMode) ri += vectorSize*offset;
+
+ for(; i + vectorSize <= depth; i+=vectorSize)
+ {
+ PacketBlock<Packet2d,2> block;
+ if(StorageOrder == RowMajor)
+ {
+ block.packet[0] = lhs2.template loadPacket<Packet2d>(0, i);
+ block.packet[1] = lhs2.template loadPacket<Packet2d>(1, i);
+
+ ptranspose(block);
+ } else {
+ block.packet[0] = lhs2.template loadPacket<Packet2d>(0, i + 0);
+ block.packet[1] = lhs2.template loadPacket<Packet2d>(0, i + 1);
+ }
+
+ storeBlock<double, Packet2d, 2>(blockA + ri, block);
+
+ ri += 2*vectorSize;
+ }
+ for(; i < depth; i++)
+ {
+ if(StorageOrder == RowMajor)
+ {
+ blockA[ri+0] = lhs2(0, i);
+ blockA[ri+1] = lhs2(1, i);
+ } else {
+ Packet2d lhsV = lhs2.template loadPacket<Packet2d>(0, i);
+ pstore<double>(blockA + ri, lhsV);
+ }
+
+ ri += vectorSize;
+ }
+
+ if(PanelMode) ri += vectorSize*(stride - offset - depth);
+ }
+
+ if (j < rows)
+ {
+ if(PanelMode) ri += offset*(rows - j);
+
+ for(Index i = 0; i < depth; i++)
+ {
+ Index k = j;
+ for(; k < rows; k++)
+ {
+ blockA[ri] = lhs(k, i);
+ ri += 1;
+ }
+ }
+ }
+ }
+};
+
+// General template for rhs packing, float64 specialization.
+template<typename DataMapper, int StorageOrder, bool PanelMode>
+struct dhs_pack<double, DataMapper, Packet2d, StorageOrder, PanelMode, false>
+{
+ EIGEN_STRONG_INLINE void operator()(double* blockB, const DataMapper& rhs, Index depth, Index cols, Index stride, Index offset)
+ {
+ const Index vectorSize = quad_traits<double>::vectorsize;
+ Index ri = 0, j = 0;
+
+ for(; j + 2*vectorSize <= cols; j+=2*vectorSize)
+ {
+ const DataMapper rhs2 = rhs.getSubMapper(0, j);
+ Index i = 0;
+
+ if(PanelMode) ri += offset*(2*vectorSize);
+
+ for(; i + vectorSize <= depth; i+=vectorSize)
+ {
+ PacketBlock<Packet2d,4> block;
+ if(StorageOrder == ColMajor)
+ {
+ PacketBlock<Packet2d,2> block1, block2;
+ block1.packet[0] = rhs2.template loadPacket<Packet2d>(i, 0);
+ block1.packet[1] = rhs2.template loadPacket<Packet2d>(i, 1);
+ block2.packet[0] = rhs2.template loadPacket<Packet2d>(i, 2);
+ block2.packet[1] = rhs2.template loadPacket<Packet2d>(i, 3);
+
+ ptranspose(block1);
+ ptranspose(block2);
+
+ pstore<double>(blockB + ri , block1.packet[0]);
+ pstore<double>(blockB + ri + 2, block2.packet[0]);
+ pstore<double>(blockB + ri + 4, block1.packet[1]);
+ pstore<double>(blockB + ri + 6, block2.packet[1]);
+ } else {
+ block.packet[0] = rhs2.template loadPacket<Packet2d>(i + 0, 0); //[a1 a2]
+ block.packet[1] = rhs2.template loadPacket<Packet2d>(i + 0, 2); //[a3 a4]
+ block.packet[2] = rhs2.template loadPacket<Packet2d>(i + 1, 0); //[b1 b2]
+ block.packet[3] = rhs2.template loadPacket<Packet2d>(i + 1, 2); //[b3 b4]
+
+ storeBlock<double, Packet2d, 4>(blockB + ri, block);
+ }
+
+ ri += 4*vectorSize;
+ }
+ for(; i < depth; i++)
+ {
+ if(StorageOrder == ColMajor)
+ {
+ blockB[ri+0] = rhs2(i, 0);
+ blockB[ri+1] = rhs2(i, 1);
+
+ ri += vectorSize;
+
+ blockB[ri+0] = rhs2(i, 2);
+ blockB[ri+1] = rhs2(i, 3);
+ } else {
+ Packet2d rhsV = rhs2.template loadPacket<Packet2d>(i, 0);
+ pstore<double>(blockB + ri, rhsV);
+
+ ri += vectorSize;
+
+ rhsV = rhs2.template loadPacket<Packet2d>(i, 2);
+ pstore<double>(blockB + ri, rhsV);
+ }
+ ri += vectorSize;
+ }
+
+ if(PanelMode) ri += (2*vectorSize)*(stride - offset - depth);
+ }
+
+ if(PanelMode) ri += offset;
+
+ for(; j < cols; j++)
+ {
+ const DataMapper rhs2 = rhs.getSubMapper(0, j);
+ for(Index i = 0; i < depth; i++)
+ {
+ blockB[ri] = rhs2(i, 0);
+ ri += 1;
+ }
+
+ if(PanelMode) ri += stride - depth;
+ }
+ }
+};
+
+// General template for lhs complex packing, float64 specialization.
+template<typename DataMapper, typename Packet, typename PacketC, int StorageOrder, bool Conjugate, bool PanelMode>
+struct dhs_cpack<double, DataMapper, Packet, PacketC, StorageOrder, Conjugate, PanelMode, true>
+{
+ EIGEN_STRONG_INLINE void operator()(std::complex<double>* blockA, const DataMapper& lhs, Index depth, Index rows, Index stride, Index offset)
+ {
+ const Index vectorSize = quad_traits<double>::vectorsize;
+ const Index vectorDelta = vectorSize * ((PanelMode) ? stride : depth);
+ Index rir = ((PanelMode) ? (vectorSize*offset) : 0), rii;
+ double* blockAt = reinterpret_cast<double *>(blockA);
+ Index j = 0;
+
+ for(; j + vectorSize <= rows; j+=vectorSize)
+ {
+ const DataMapper lhs2 = lhs.getSubMapper(j, 0);
+ Index i = 0;
+
+ rii = rir + vectorDelta;
+
+ for(; i + vectorSize <= depth; i+=vectorSize)
+ {
+ PacketBlock<Packet,2> blockr, blocki;
+ PacketBlock<PacketC,4> cblock;
+
+ if(StorageOrder == ColMajor)
+ {
+ cblock.packet[0] = lhs2.template loadPacket<PacketC>(0, i + 0); //[a1 a1i]
+ cblock.packet[1] = lhs2.template loadPacket<PacketC>(0, i + 1); //[b1 b1i]
+
+ cblock.packet[2] = lhs2.template loadPacket<PacketC>(1, i + 0); //[a2 a2i]
+ cblock.packet[3] = lhs2.template loadPacket<PacketC>(1, i + 1); //[b2 b2i]
+
+ blockr.packet[0] = vec_mergeh(cblock.packet[0].v, cblock.packet[2].v); //[a1 a2]
+ blockr.packet[1] = vec_mergeh(cblock.packet[1].v, cblock.packet[3].v); //[b1 b2]
+
+ blocki.packet[0] = vec_mergel(cblock.packet[0].v, cblock.packet[2].v);
+ blocki.packet[1] = vec_mergel(cblock.packet[1].v, cblock.packet[3].v);
+ } else {
+ cblock.packet[0] = lhs2.template loadPacket<PacketC>(0, i); //[a1 a1i]
+ cblock.packet[1] = lhs2.template loadPacket<PacketC>(1, i); //[a2 a2i]
+
+ cblock.packet[2] = lhs2.template loadPacket<PacketC>(0, i + 1); //[b1 b1i]
+ cblock.packet[3] = lhs2.template loadPacket<PacketC>(1, i + 1); //[b2 b2i
+
+ blockr.packet[0] = vec_mergeh(cblock.packet[0].v, cblock.packet[1].v); //[a1 a2]
+ blockr.packet[1] = vec_mergeh(cblock.packet[2].v, cblock.packet[3].v); //[b1 b2]
+
+ blocki.packet[0] = vec_mergel(cblock.packet[0].v, cblock.packet[1].v);
+ blocki.packet[1] = vec_mergel(cblock.packet[2].v, cblock.packet[3].v);
+ }
+
+ if(Conjugate)
+ {
+ blocki.packet[0] = -blocki.packet[0];
+ blocki.packet[1] = -blocki.packet[1];
+ }
+
+ storeBlock<double, Packet, 2>(blockAt + rir, blockr);
+ storeBlock<double, Packet, 2>(blockAt + rii, blocki);
+
+ rir += 2*vectorSize;
+ rii += 2*vectorSize;
+ }
+ for(; i < depth; i++)
+ {
+ PacketBlock<Packet,1> blockr, blocki;
+ PacketBlock<PacketC,2> cblock;
+
+ cblock.packet[0] = lhs2.template loadPacket<PacketC>(0, i);
+ cblock.packet[1] = lhs2.template loadPacket<PacketC>(1, i);
+
+ blockr.packet[0] = vec_mergeh(cblock.packet[0].v, cblock.packet[1].v);
+ blocki.packet[0] = vec_mergel(cblock.packet[0].v, cblock.packet[1].v);
+
+ if(Conjugate)
+ {
+ blocki.packet[0] = -blocki.packet[0];
+ }
+
+ pstore<double>(blockAt + rir, blockr.packet[0]);
+ pstore<double>(blockAt + rii, blocki.packet[0]);
+
+ rir += vectorSize;
+ rii += vectorSize;
+ }
+
+ rir += ((PanelMode) ? (vectorSize*(2*stride - depth)) : vectorDelta);
+ }
+
+ if (j < rows)
+ {
+ if(PanelMode) rir += (offset*(rows - j - vectorSize));
+ rii = rir + (((PanelMode) ? stride : depth) * (rows - j));
+
+ for(Index i = 0; i < depth; i++)
+ {
+ Index k = j;
+ for(; k < rows; k++)
+ {
+ blockAt[rir] = lhs(k, i).real();
+
+ if(Conjugate)
+ blockAt[rii] = -lhs(k, i).imag();
+ else
+ blockAt[rii] = lhs(k, i).imag();
+
+ rir += 1;
+ rii += 1;
+ }
+ }
+ }
+ }
+};
+
+// General template for rhs complex packing, float64 specialization.
+template<typename DataMapper, typename Packet, typename PacketC, int StorageOrder, bool Conjugate, bool PanelMode>
+struct dhs_cpack<double, DataMapper, Packet, PacketC, StorageOrder, Conjugate, PanelMode, false>
+{
+ EIGEN_STRONG_INLINE void operator()(std::complex<double>* blockB, const DataMapper& rhs, Index depth, Index cols, Index stride, Index offset)
+ {
+ const Index vectorSize = quad_traits<double>::vectorsize;
+ const Index vectorDelta = 2*vectorSize * ((PanelMode) ? stride : depth);
+ Index rir = ((PanelMode) ? (2*vectorSize*offset) : 0), rii;
+ double* blockBt = reinterpret_cast<double *>(blockB);
+ Index j = 0;
+
+ for(; j + 2*vectorSize <= cols; j+=2*vectorSize)
+ {
+ const DataMapper rhs2 = rhs.getSubMapper(0, j);
+ Index i = 0;
+
+ rii = rir + vectorDelta;
+
+ for(; i < depth; i++)
+ {
+ PacketBlock<PacketC,4> cblock;
+ PacketBlock<Packet,2> blockr, blocki;
+
+ bload<DataMapper, PacketC, 2, ColMajor, false, 4>(cblock, rhs2, i, 0);
+
+ blockr.packet[0] = vec_mergeh(cblock.packet[0].v, cblock.packet[1].v);
+ blockr.packet[1] = vec_mergeh(cblock.packet[2].v, cblock.packet[3].v);
+
+ blocki.packet[0] = vec_mergel(cblock.packet[0].v, cblock.packet[1].v);
+ blocki.packet[1] = vec_mergel(cblock.packet[2].v, cblock.packet[3].v);
+
+ if(Conjugate)
+ {
+ blocki.packet[0] = -blocki.packet[0];
+ blocki.packet[1] = -blocki.packet[1];
+ }
+
+ storeBlock<double, Packet, 2>(blockBt + rir, blockr);
+ storeBlock<double, Packet, 2>(blockBt + rii, blocki);
+
+ rir += 2*vectorSize;
+ rii += 2*vectorSize;
+ }
+
+ rir += ((PanelMode) ? (2*vectorSize*(2*stride - depth)) : vectorDelta);
+ }
+
+ if(PanelMode) rir -= (offset*(2*vectorSize - 1));
+
+ for(; j < cols; j++)
+ {
+ const DataMapper rhs2 = rhs.getSubMapper(0, j);
+ rii = rir + ((PanelMode) ? stride : depth);
+
+ for(Index i = 0; i < depth; i++)
+ {
+ blockBt[rir] = rhs2(i, 0).real();
+
+ if(Conjugate)
+ blockBt[rii] = -rhs2(i, 0).imag();
+ else
+ blockBt[rii] = rhs2(i, 0).imag();
+
+ rir += 1;
+ rii += 1;
+ }
+
+ rir += ((PanelMode) ? (2*stride - depth) : depth);
+ }
+ }
+};
+
+/**************
+ * GEMM utils *
+ **************/
+
+// 512-bits rank1-update of acc. It can either positive or negative accumulate (useful for complex gemm).
+template<typename Packet, bool NegativeAccumulate, int N>
+EIGEN_ALWAYS_INLINE void pger_common(PacketBlock<Packet,N>* acc, const Packet& lhsV, const Packet* rhsV)
+{
+ if(NegativeAccumulate)
+ {
+ for (int M = 0; M < N; M++) {
+ acc->packet[M] = vec_nmsub(lhsV, rhsV[M], acc->packet[M]);
+ }
+ } else {
+ for (int M = 0; M < N; M++) {
+ acc->packet[M] = vec_madd(lhsV, rhsV[M], acc->packet[M]);
+ }
+ }
+}
+
+template<int N, typename Scalar, typename Packet, bool NegativeAccumulate>
+EIGEN_ALWAYS_INLINE void pger(PacketBlock<Packet,N>* acc, const Scalar* lhs, const Packet* rhsV)
+{
+ Packet lhsV = pload<Packet>(lhs);
+
+ pger_common<Packet, NegativeAccumulate, N>(acc, lhsV, rhsV);
+}
+
+// 512-bits rank1-update of complex acc. It takes decoupled accumulators as entries. It also takes cares of mixed types real * complex and complex * real.
+template<int N, typename Packet, bool ConjugateLhs, bool ConjugateRhs, bool LhsIsReal, bool RhsIsReal>
+EIGEN_ALWAYS_INLINE void pgerc_common(PacketBlock<Packet,N>* accReal, PacketBlock<Packet,N>* accImag, const Packet &lhsV, Packet &lhsVi, const Packet* rhsV, const Packet* rhsVi)
+{
+ pger_common<Packet, false, N>(accReal, lhsV, rhsV);
+ if(LhsIsReal)
+ {
+ pger_common<Packet, ConjugateRhs, N>(accImag, lhsV, rhsVi);
+ EIGEN_UNUSED_VARIABLE(lhsVi);
+ } else {
+ if (!RhsIsReal) {
+ pger_common<Packet, ConjugateLhs == ConjugateRhs, N>(accReal, lhsVi, rhsVi);
+ pger_common<Packet, ConjugateRhs, N>(accImag, lhsV, rhsVi);
+ } else {
+ EIGEN_UNUSED_VARIABLE(rhsVi);
+ }
+ pger_common<Packet, ConjugateLhs, N>(accImag, lhsVi, rhsV);
+ }
+}
+
+template<int N, typename Scalar, typename Packet, bool ConjugateLhs, bool ConjugateRhs, bool LhsIsReal, bool RhsIsReal>
+EIGEN_ALWAYS_INLINE void pgerc(PacketBlock<Packet,N>* accReal, PacketBlock<Packet,N>* accImag, const Scalar* lhs_ptr, const Scalar* lhs_ptr_imag, const Packet* rhsV, const Packet* rhsVi)
+{
+ Packet lhsV = ploadLhs<Packet>(lhs_ptr);
+ Packet lhsVi;
+ if(!LhsIsReal) lhsVi = ploadLhs<Packet>(lhs_ptr_imag);
+ else EIGEN_UNUSED_VARIABLE(lhs_ptr_imag);
+
+ pgerc_common<N, Packet, ConjugateLhs, ConjugateRhs, LhsIsReal, RhsIsReal>(accReal, accImag, lhsV, lhsVi, rhsV, rhsVi);
+}
+
+template<typename Packet>
+EIGEN_ALWAYS_INLINE Packet ploadLhs(const __UNPACK_TYPE__(Packet)* lhs)
+{
+ return ploadu<Packet>(lhs);
+}
+
+// Zero the accumulator on PacketBlock.
+template<typename Packet, int N>
+EIGEN_ALWAYS_INLINE void bsetzero(PacketBlock<Packet,N>& acc)
+{
+ for (int M = 0; M < N; M++) {
+ acc.packet[M] = pset1<Packet>((__UNPACK_TYPE__(Packet))0);
+ }
+}
+
+template<typename Packet, int N>
+EIGEN_ALWAYS_INLINE void bscalec_common(PacketBlock<Packet,N>& acc, PacketBlock<Packet,N>& accZ, const Packet& pAlpha)
+{
+ for (int M = 0; M < N; M++) {
+ acc.packet[M] = vec_mul(accZ.packet[M], pAlpha);
+ }
+}
+
+template<typename Packet, int N>
+EIGEN_ALWAYS_INLINE void band(PacketBlock<Packet,N>& acc, const Packet& pMask)
+{
+ for (int M = 0; M < N; M++) {
+ acc.packet[M] = pand<Packet>(acc.packet[M], pMask);
+ }
+}
+
+// Complex version of PacketBlock scaling.
+template<typename Packet, int N, bool mask>
+EIGEN_ALWAYS_INLINE void bscalec(PacketBlock<Packet,N>& aReal, PacketBlock<Packet,N>& aImag, const Packet& bReal, const Packet& bImag, PacketBlock<Packet,N>& cReal, PacketBlock<Packet,N>& cImag, const Packet& pMask)
+{
+ if (mask && (sizeof(__UNPACK_TYPE__(Packet)) == sizeof(float))) {
+ band<Packet, N>(aReal, pMask);
+ band<Packet, N>(aImag, pMask);
+ } else {
+ EIGEN_UNUSED_VARIABLE(pMask);
+ }
+
+ bscalec_common<Packet, N>(cReal, aReal, bReal);
+
+ bscalec_common<Packet, N>(cImag, aImag, bReal);
+
+ pger_common<Packet, true, N>(&cReal, bImag, aImag.packet);
+
+ pger_common<Packet, false, N>(&cImag, bImag, aReal.packet);
+}
+
+// Load a PacketBlock, the N parameters make tunning gemm easier so we can add more accumulators as needed.
+//
+// full = operate (load) on the entire PacketBlock or only half
+template<typename DataMapper, typename Packet, const Index accCols, int StorageOrder, bool Complex, int N, bool full>
+EIGEN_ALWAYS_INLINE void bload(PacketBlock<Packet,N*(Complex?2:1)>& acc, const DataMapper& res, Index row, Index col)
+{
+ if (StorageOrder == RowMajor) {
+ for (int M = 0; M < N; M++) {
+ acc.packet[M] = res.template loadPacket<Packet>(row + M, col);
+ }
+ if (Complex) {
+ for (int M = 0; M < N; M++) {
+ acc.packet[M+N] = res.template loadPacket<Packet>(row + M, col + accCols);
+ }
+ }
+ } else {
+ for (int M = 0; M < N; M++) {
+ acc.packet[M] = res.template loadPacket<Packet>(row, col + M);
+ }
+ if (Complex && full) {
+ for (int M = 0; M < N; M++) {
+ acc.packet[M+N] = res.template loadPacket<Packet>(row + accCols, col + M);
+ }
+ }
+ }
+}
+
+template<typename DataMapper, typename Packet, int N>
+EIGEN_ALWAYS_INLINE void bstore(PacketBlock<Packet,N>& acc, const DataMapper& res, Index row)
+{
+ for (int M = 0; M < N; M++) {
+ res.template storePacket<Packet>(row, M, acc.packet[M]);
+ }
+}
+
+#ifdef USE_PARTIAL_PACKETS
+template<typename DataMapper, typename Packet, const Index accCols, bool Complex, Index N, bool full>
+EIGEN_ALWAYS_INLINE void bload_partial(PacketBlock<Packet,N*(Complex?2:1)>& acc, const DataMapper& res, Index row, Index elements)
+{
+ for (Index M = 0; M < N; M++) {
+ acc.packet[M] = res.template loadPacketPartial<Packet>(row, M, elements);
+ }
+ if (Complex && full) {
+ for (Index M = 0; M < N; M++) {
+ acc.packet[M+N] = res.template loadPacketPartial<Packet>(row + accCols, M, elements);
+ }
+ }
+}
+
+template<typename DataMapper, typename Packet, Index N>
+EIGEN_ALWAYS_INLINE void bstore_partial(PacketBlock<Packet,N>& acc, const DataMapper& res, Index row, Index elements)
+{
+ for (Index M = 0; M < N; M++) {
+ res.template storePacketPartial<Packet>(row, M, acc.packet[M], elements);
+ }
+}
+#endif
+
+#ifdef _ARCH_PWR10
+#define USE_P10_AND_PVIPR2_0 (EIGEN_COMP_LLVM || (__GNUC__ >= 11))
+#else
+#define USE_P10_AND_PVIPR2_0 0
+#endif
+
+#if !USE_P10_AND_PVIPR2_0
+const static Packet4i mask4[4] = { { 0, 0, 0, 0 }, { -1, 0, 0, 0 }, { -1, -1, 0, 0 }, { -1, -1, -1, 0 } };
+#endif
+
+template<typename Packet>
+EIGEN_ALWAYS_INLINE Packet bmask(const Index remaining_rows)
+{
+#if USE_P10_AND_PVIPR2_0
+#ifdef _BIG_ENDIAN
+ return Packet(vec_reve(vec_genwm((1 << remaining_rows) - 1)));
+#else
+ return Packet(vec_genwm((1 << remaining_rows) - 1));
+#endif
+#else
+ return Packet(mask4[remaining_rows]);
+#endif
+}
+
+template<>
+EIGEN_ALWAYS_INLINE Packet2d bmask<Packet2d>(const Index remaining_rows)
+{
+#if USE_P10_AND_PVIPR2_0
+ Packet2d mask2 = Packet2d(vec_gendm(remaining_rows));
+#ifdef _BIG_ENDIAN
+ return preverse(mask2);
+#else
+ return mask2;
+#endif
+#else
+ Packet2l ret = { -remaining_rows, 0 };
+ return Packet2d(ret);
+#endif
+}
+
+template<typename Packet, int N>
+EIGEN_ALWAYS_INLINE void bscale(PacketBlock<Packet,N>& acc, PacketBlock<Packet,N>& accZ, const Packet& pAlpha)
+{
+ for (int M = 0; M < N; M++) {
+ acc.packet[M] = pmadd<Packet>(pAlpha, accZ.packet[M], acc.packet[M]);
+ }
+}
+
+// Scale the PacketBlock vectors by alpha.
+template<typename Packet, int N, bool mask>
+EIGEN_ALWAYS_INLINE void bscale(PacketBlock<Packet,N>& acc, PacketBlock<Packet,N>& accZ, const Packet& pAlpha, const Packet& pMask)
+{
+ if (mask) {
+ band<Packet, N>(accZ, pMask);
+ } else {
+ EIGEN_UNUSED_VARIABLE(pMask);
+ }
+
+ bscale<Packet, N>(acc, accZ, pAlpha);
+}
+
+template<typename Packet, int N, bool real>
+EIGEN_ALWAYS_INLINE void pbroadcastN(const __UNPACK_TYPE__(Packet) *ap0,
+ const __UNPACK_TYPE__(Packet) *ap1, const __UNPACK_TYPE__(Packet) *ap2,
+ Packet& a0, Packet& a1, Packet& a2, Packet& a3)
+{
+ a0 = pset1<Packet>(ap0[0]);
+ if (N == 4) {
+ a1 = pset1<Packet>(ap0[1]);
+ a2 = pset1<Packet>(ap0[2]);
+ a3 = pset1<Packet>(ap0[3]);
+ EIGEN_UNUSED_VARIABLE(ap1);
+ EIGEN_UNUSED_VARIABLE(ap2);
+ } else {
+ if (N > 1) {
+ a1 = pset1<Packet>(ap1[0]);
+ } else {
+ EIGEN_UNUSED_VARIABLE(a1);
+ EIGEN_UNUSED_VARIABLE(ap1);
+ }
+ if (N > 2) {
+ a2 = pset1<Packet>(ap2[0]);
+ } else {
+ EIGEN_UNUSED_VARIABLE(a2);
+ EIGEN_UNUSED_VARIABLE(ap2);
+ }
+ }
+}
+
+template<> EIGEN_ALWAYS_INLINE void
+pbroadcastN<Packet4f,4,true>(const float *ap0, const float *, const float *,
+ Packet4f& a0, Packet4f& a1, Packet4f& a2, Packet4f& a3)
+{
+ pbroadcast4<Packet4f>(ap0, a0, a1, a2, a3);
+}
+
+template<> EIGEN_ALWAYS_INLINE void
+pbroadcastN<Packet4f,4,false>(const float *ap0, const float *ap1, const float *ap2,
+ Packet4f& a0, Packet4f& a1, Packet4f& a2, Packet4f& a3)
+{
+ pbroadcastN<Packet4f,4,true>(ap0, ap1, ap2, a0, a1, a2, a3);
+}
+
+template<>
+EIGEN_ALWAYS_INLINE void pbroadcastN<Packet2d,4,false>(const double* ap0, const double *,
+ const double *, Packet2d& a0, Packet2d& a1, Packet2d& a2, Packet2d& a3)
+{
+ a1 = pload<Packet2d>(ap0);
+ a3 = pload<Packet2d>(ap0 + 2);
+ a0 = vec_splat(a1, 0);
+ a1 = vec_splat(a1, 1);
+ a2 = vec_splat(a3, 0);
+ a3 = vec_splat(a3, 1);
+}
+
+// Grab two decouples real/imaginary PacketBlocks and return two coupled (real/imaginary pairs) PacketBlocks.
+template<typename Packet, typename Packetc, int N, bool full>
+EIGEN_ALWAYS_INLINE void bcouple_common(PacketBlock<Packet,N>& taccReal, PacketBlock<Packet,N>& taccImag, PacketBlock<Packetc, N>& acc1, PacketBlock<Packetc, N>& acc2)
+{
+ for (int M = 0; M < N; M++) {
+ acc1.packet[M].v = vec_mergeh(taccReal.packet[M], taccImag.packet[M]);
+ }
+
+ if (full) {
+ for (int M = 0; M < N; M++) {
+ acc2.packet[M].v = vec_mergel(taccReal.packet[M], taccImag.packet[M]);
+ }
+ }
+}
+
+template<typename Packet, typename Packetc, int N, bool full>
+EIGEN_ALWAYS_INLINE void bcouple(PacketBlock<Packet,N>& taccReal, PacketBlock<Packet,N>& taccImag, PacketBlock<Packetc,N*2>& tRes, PacketBlock<Packetc, N>& acc1, PacketBlock<Packetc, N>& acc2)
+{
+ bcouple_common<Packet, Packetc, N, full>(taccReal, taccImag, acc1, acc2);
+
+ for (int M = 0; M < N; M++) {
+ acc1.packet[M] = padd<Packetc>(tRes.packet[M], acc1.packet[M]);
+ }
+
+ if (full) {
+ for (int M = 0; M < N; M++) {
+ acc2.packet[M] = padd<Packetc>(tRes.packet[M+N], acc2.packet[M]);
+ }
+ }
+}
+
+// PEEL loop factor.
+#define PEEL 7
+#define PEEL_ROW 7
+
+#define MICRO_UNROLL(func) \
+ func(0) func(1) func(2) func(3) func(4) func(5) func(6) func(7)
+
+#define MICRO_NORMAL_ROWS \
+ accRows == quad_traits<Scalar>::rows || accRows == 1
+
+#define MICRO_NEW_ROWS ((MICRO_NORMAL_ROWS) ? accRows : 1)
+
+#define MICRO_RHS(ptr, N) rhs_##ptr##N
+
+#define MICRO_ZERO_PEEL(peel) \
+ if ((PEEL_ROW > peel) && (peel != 0)) { \
+ bsetzero<Packet, accRows>(accZero##peel); \
+ } else { \
+ EIGEN_UNUSED_VARIABLE(accZero##peel); \
+ }
+
+#define MICRO_ADD(ptr, N) \
+ if (MICRO_NORMAL_ROWS) { \
+ MICRO_RHS(ptr,0) += (accRows * N); \
+ } else { \
+ MICRO_RHS(ptr,0) += N; \
+ MICRO_RHS(ptr,1) += N; \
+ if (accRows == 3) { \
+ MICRO_RHS(ptr,2) += N; \
+ } \
+ }
+
+#define MICRO_ADD_ROWS(N) MICRO_ADD(ptr, N)
+
+#define MICRO_BROADCAST1(peel, ptr, rhsV, real) \
+ if (MICRO_NORMAL_ROWS) { \
+ pbroadcastN<Packet,accRows,real>(MICRO_RHS(ptr,0) + (accRows * peel), MICRO_RHS(ptr,0), MICRO_RHS(ptr,0), rhsV##peel[0], rhsV##peel[1], rhsV##peel[2], rhsV##peel[3]); \
+ } else { \
+ pbroadcastN<Packet,accRows,real>(MICRO_RHS(ptr,0) + peel, MICRO_RHS(ptr,1) + peel, MICRO_RHS(ptr,2) + peel, rhsV##peel[0], rhsV##peel[1], rhsV##peel[2], rhsV##peel[3]); \
+ }
+
+#define MICRO_BROADCAST(peel) MICRO_BROADCAST1(peel, ptr, rhsV, true)
+
+#define MICRO_BROADCAST_EXTRA1(ptr, rhsV, real) \
+ pbroadcastN<Packet,accRows,real>(MICRO_RHS(ptr,0), MICRO_RHS(ptr,1), MICRO_RHS(ptr,2), rhsV[0], rhsV[1], rhsV[2], rhsV[3]);
+
+#define MICRO_BROADCAST_EXTRA \
+ Packet rhsV[4]; \
+ MICRO_BROADCAST_EXTRA1(ptr, rhsV, true) \
+ MICRO_ADD_ROWS(1)
+
+#define MICRO_SRC2(ptr, N, M) \
+ if (MICRO_NORMAL_ROWS) { \
+ EIGEN_UNUSED_VARIABLE(strideB); \
+ EIGEN_UNUSED_VARIABLE(MICRO_RHS(ptr,1)); \
+ EIGEN_UNUSED_VARIABLE(MICRO_RHS(ptr,2)); \
+ } else { \
+ MICRO_RHS(ptr,1) = rhs_base + N + M; \
+ if (accRows == 3) { \
+ MICRO_RHS(ptr,2) = rhs_base + N*2 + M; \
+ } else { \
+ EIGEN_UNUSED_VARIABLE(MICRO_RHS(ptr,2)); \
+ } \
+ }
+
+#define MICRO_SRC2_PTR MICRO_SRC2(ptr, strideB, 0)
+
+#define MICRO_ZERO_PEEL_ROW MICRO_UNROLL(MICRO_ZERO_PEEL)
+
+#define MICRO_WORK_PEEL(peel) \
+ if (PEEL_ROW > peel) { \
+ MICRO_BROADCAST(peel) \
+ pger<accRows, Scalar, Packet, false>(&accZero##peel, lhs_ptr + (remaining_rows * peel), rhsV##peel); \
+ } else { \
+ EIGEN_UNUSED_VARIABLE(rhsV##peel); \
+ }
+
+#define MICRO_WORK_PEEL_ROW \
+ Packet rhsV0[4], rhsV1[4], rhsV2[4], rhsV3[4], rhsV4[4], rhsV5[4], rhsV6[4], rhsV7[4]; \
+ MICRO_UNROLL(MICRO_WORK_PEEL) \
+ lhs_ptr += (remaining_rows * PEEL_ROW); \
+ MICRO_ADD_ROWS(PEEL_ROW)
+
+#define MICRO_ADD_PEEL(peel, sum) \
+ if (PEEL_ROW > peel) { \
+ for (Index i = 0; i < accRows; i++) { \
+ accZero##sum.packet[i] += accZero##peel.packet[i]; \
+ } \
+ }
+
+#define MICRO_ADD_PEEL_ROW \
+ MICRO_ADD_PEEL(4, 0) MICRO_ADD_PEEL(5, 1) MICRO_ADD_PEEL(6, 2) MICRO_ADD_PEEL(7, 3) \
+ MICRO_ADD_PEEL(2, 0) MICRO_ADD_PEEL(3, 1) MICRO_ADD_PEEL(1, 0)
+
+#define MICRO_PREFETCHN1(ptr, N) \
+ EIGEN_POWER_PREFETCH(MICRO_RHS(ptr,0)); \
+ if (N == 2 || N == 3) { \
+ EIGEN_POWER_PREFETCH(MICRO_RHS(ptr,1)); \
+ if (N == 3) { \
+ EIGEN_POWER_PREFETCH(MICRO_RHS(ptr,2)); \
+ } \
+ }
+
+#define MICRO_PREFETCHN(N) MICRO_PREFETCHN1(ptr, N)
+
+#define MICRO_COMPLEX_PREFETCHN(N) \
+ MICRO_PREFETCHN1(ptr_real, N); \
+ if(!RhsIsReal) { \
+ MICRO_PREFETCHN1(ptr_imag, N); \
+ }
+
+template<typename Scalar, typename Packet, const Index accRows, const Index remaining_rows>
+EIGEN_ALWAYS_INLINE void MICRO_EXTRA_ROW(
+ const Scalar* &lhs_ptr,
+ const Scalar* &rhs_ptr0,
+ const Scalar* &rhs_ptr1,
+ const Scalar* &rhs_ptr2,
+ PacketBlock<Packet,accRows> &accZero)
+{
+ MICRO_BROADCAST_EXTRA
+ pger<accRows, Scalar, Packet, false>(&accZero, lhs_ptr, rhsV);
+ lhs_ptr += remaining_rows;
+}
+
+template<typename Scalar, typename Packet, typename DataMapper, const Index accRows, const Index accCols, const Index remaining_rows>
+EIGEN_ALWAYS_INLINE void gemm_unrolled_row_iteration(
+ const DataMapper& res,
+ const Scalar* lhs_base,
+ const Scalar* rhs_base,
+ Index depth,
+ Index strideA,
+ Index offsetA,
+ Index strideB,
+ Index row,
+ Index rows,
+ const Packet& pAlpha,
+ const Packet& pMask)
+{
+ const Scalar* rhs_ptr0 = rhs_base, * rhs_ptr1 = NULL, * rhs_ptr2 = NULL;
+ const Scalar* lhs_ptr = lhs_base + row*strideA + remaining_rows*offsetA;
+ PacketBlock<Packet,accRows> accZero0, accZero1, accZero2, accZero3, accZero4, accZero5, accZero6, accZero7, acc;
+
+ MICRO_SRC2_PTR
+ bsetzero<Packet, accRows>(accZero0);
+
+ Index remaining_depth = depth & -quad_traits<Scalar>::rows;
+ Index k = 0;
+ if (remaining_depth >= PEEL_ROW) {
+ MICRO_ZERO_PEEL_ROW
+ do
+ {
+ MICRO_PREFETCHN(accRows)
+ EIGEN_POWER_PREFETCH(lhs_ptr);
+ MICRO_WORK_PEEL_ROW
+ } while ((k += PEEL_ROW) + PEEL_ROW <= remaining_depth);
+ MICRO_ADD_PEEL_ROW
+ }
+ for(; k < depth; k++)
+ {
+ MICRO_EXTRA_ROW<Scalar, Packet, accRows, remaining_rows>(lhs_ptr, rhs_ptr0, rhs_ptr1, rhs_ptr2, accZero0);
+ }
+
+#ifdef USE_PARTIAL_PACKETS
+ EIGEN_UNUSED_VARIABLE(rows);
+ EIGEN_UNUSED_VARIABLE(pMask);
+ bload_partial<DataMapper, Packet, 0, false, accRows>(acc, res, row, remaining_rows);
+ bscale<Packet,accRows>(acc, accZero0, pAlpha);
+ bstore_partial<DataMapper, Packet, accRows>(acc, res, row, remaining_rows);
+#else
+ bload<DataMapper, Packet, 0, ColMajor, false, accRows>(acc, res, row, 0);
+ if ((accRows == 1) || (rows >= accCols))
+ {
+ bscale<Packet,accRows,true>(acc, accZero0, pAlpha, pMask);
+ bstore<DataMapper, Packet, accRows>(acc, res, row);
+ } else {
+ bscale<Packet,accRows,false>(acc, accZero0, pAlpha, pMask);
+ for(Index j = 0; j < accRows; j++) {
+ for(Index i = 0; i < remaining_rows; i++) {
+ res(row + i, j) = acc.packet[j][i];
+ }
+ }
+ }
+#endif
+}
+
+#define MICRO_EXTRA(MICRO_EXTRA_UNROLL, value, is_col) \
+ switch(value) { \
+ default: \
+ MICRO_EXTRA_UNROLL(1) \
+ break; \
+ case 2: \
+ if (is_col || (sizeof(Scalar) == sizeof(float))) { \
+ MICRO_EXTRA_UNROLL(2) \
+ } \
+ break; \
+ case 3: \
+ if (is_col || (sizeof(Scalar) == sizeof(float))) { \
+ MICRO_EXTRA_UNROLL(3) \
+ } \
+ break; \
+ }
+
+#define MICRO_EXTRA_ROWS(N) \
+ gemm_unrolled_row_iteration<Scalar, Packet, DataMapper, accRows, accCols, N>(res, lhs_base, rhs_base, depth, strideA, offsetA, strideB, row, rows, pAlpha, pMask);
+
+template<typename Scalar, typename Packet, typename DataMapper, const Index accRows, const Index accCols>
+EIGEN_ALWAYS_INLINE void gemm_extra_row(
+ const DataMapper& res,
+ const Scalar* lhs_base,
+ const Scalar* rhs_base,
+ Index depth,
+ Index strideA,
+ Index offsetA,
+ Index strideB,
+ Index row,
+ Index rows,
+ Index remaining_rows,
+ const Packet& pAlpha,
+ const Packet& pMask)
+{
+ MICRO_EXTRA(MICRO_EXTRA_ROWS, remaining_rows, false)
+}
+
+#define MICRO_UNROLL_WORK(func, func2, peel) \
+ MICRO_UNROLL(func2); \
+ func(0,peel) func(1,peel) func(2,peel) func(3,peel) \
+ func(4,peel) func(5,peel) func(6,peel) func(7,peel)
+
+#define MICRO_WORK_ONE(iter, peel) \
+ if (unroll_factor > iter) { \
+ pger_common<Packet, false, accRows>(&accZero##iter, lhsV##iter, rhsV##peel); \
+ }
+
+#define MICRO_TYPE_PEEL4(func, func2, peel) \
+ if (PEEL > peel) { \
+ Packet lhsV0, lhsV1, lhsV2, lhsV3, lhsV4, lhsV5, lhsV6, lhsV7; \
+ MICRO_BROADCAST(peel) \
+ MICRO_UNROLL_WORK(func, func2, peel) \
+ } else { \
+ EIGEN_UNUSED_VARIABLE(rhsV##peel); \
+ }
+
+#define MICRO_UNROLL_TYPE_PEEL(M, func, func1, func2) \
+ Packet rhsV0[M], rhsV1[M], rhsV2[M], rhsV3[M], rhsV4[M], rhsV5[M], rhsV6[M], rhsV7[M]; \
+ func(func1,func2,0) func(func1,func2,1) \
+ func(func1,func2,2) func(func1,func2,3) \
+ func(func1,func2,4) func(func1,func2,5) \
+ func(func1,func2,6) func(func1,func2,7)
+
+#define MICRO_UNROLL_TYPE_ONE(M, func, func1, func2) \
+ Packet rhsV0[M]; \
+ func(func1,func2,0)
+
+#define MICRO_UNROLL_TYPE(MICRO_TYPE, size) \
+ MICRO_TYPE(4, MICRO_TYPE_PEEL4, MICRO_WORK_ONE, MICRO_LOAD_ONE) \
+ MICRO_ADD_ROWS(size)
+
+#define MICRO_ONE_PEEL4 MICRO_UNROLL_TYPE(MICRO_UNROLL_TYPE_PEEL, PEEL)
+
+#define MICRO_ONE4 MICRO_UNROLL_TYPE(MICRO_UNROLL_TYPE_ONE, 1)
+
+#define MICRO_DST_PTR_ONE(iter) \
+ if (unroll_factor > iter) { \
+ bsetzero<Packet, accRows>(accZero##iter); \
+ } else { \
+ EIGEN_UNUSED_VARIABLE(accZero##iter); \
+ }
+
+#define MICRO_DST_PTR MICRO_UNROLL(MICRO_DST_PTR_ONE)
+
+#define MICRO_SRC_PTR MICRO_UNROLL(MICRO_SRC_PTR_ONE)
+
+#define MICRO_PREFETCH MICRO_UNROLL(MICRO_PREFETCH_ONE)
+
+#ifdef USE_PARTIAL_PACKETS
+#define MICRO_STORE_ONE(iter) \
+ if (unroll_factor > iter) { \
+ if (MICRO_NORMAL_PARTIAL(iter)) { \
+ bload<DataMapper, Packet, 0, ColMajor, false, accRows>(acc, res, row + iter*accCols, 0); \
+ bscale<Packet,accRows>(acc, accZero##iter, pAlpha); \
+ bstore<DataMapper, Packet, accRows>(acc, res, row + iter*accCols); \
+ } else { \
+ bload_partial<DataMapper, Packet, 0, false, accRows>(acc, res, row + iter*accCols, accCols2); \
+ bscale<Packet,accRows>(acc, accZero##iter, pAlpha); \
+ bstore_partial<DataMapper, Packet, accRows>(acc, res, row + iter*accCols, accCols2); \
+ } \
+ }
+#else
+#define MICRO_STORE_ONE(iter) \
+ if (unroll_factor > iter) { \
+ bload<DataMapper, Packet, 0, ColMajor, false, accRows>(acc, res, row + iter*accCols, 0); \
+ bscale<Packet,accRows,!(MICRO_NORMAL(iter))>(acc, accZero##iter, pAlpha, pMask); \
+ bstore<DataMapper, Packet, accRows>(acc, res, row + iter*accCols); \
+ }
+#endif
+
+#define MICRO_STORE MICRO_UNROLL(MICRO_STORE_ONE)
+
+#ifdef USE_PARTIAL_PACKETS
+template<int unroll_factor, typename Scalar, typename Packet, typename DataMapper, const Index accRows, const Index accCols, bool full>
+#else
+template<int unroll_factor, typename Scalar, typename Packet, typename DataMapper, const Index accRows, const Index accCols, const Index accCols2>
+#endif
+EIGEN_ALWAYS_INLINE void gemm_unrolled_iteration(
+ const DataMapper& res,
+ const Scalar* lhs_base,
+ const Scalar* rhs_base,
+ Index depth,
+ Index strideA,
+ Index offsetA,
+ Index strideB,
+ Index& row,
+ const Packet& pAlpha,
+#ifdef USE_PARTIAL_PACKETS
+ Index accCols2
+#else
+ const Packet& pMask
+#endif
+ )
+{
+ const Scalar* rhs_ptr0 = rhs_base, * rhs_ptr1 = NULL, * rhs_ptr2 = NULL;
+ const Scalar* lhs_ptr0 = NULL, * lhs_ptr1 = NULL, * lhs_ptr2 = NULL, * lhs_ptr3 = NULL, * lhs_ptr4 = NULL, * lhs_ptr5 = NULL, * lhs_ptr6 = NULL, * lhs_ptr7 = NULL;
+ PacketBlock<Packet,accRows> accZero0, accZero1, accZero2, accZero3, accZero4, accZero5, accZero6, accZero7;
+ PacketBlock<Packet,accRows> acc;
+
+ MICRO_SRC2_PTR
+ MICRO_SRC_PTR
+ MICRO_DST_PTR
+
+ Index k = 0;
+ for(; k + PEEL <= depth; k+= PEEL)
+ {
+ MICRO_PREFETCHN(accRows)
+ MICRO_PREFETCH
+ MICRO_ONE_PEEL4
+ }
+ for(; k < depth; k++)
+ {
+ MICRO_ONE4
+ }
+ MICRO_STORE
+
+ MICRO_UPDATE
+}
+
+#ifdef USE_PARTIAL_PACKETS
+#define MICRO_UNROLL_ITER2(N, M) \
+ gemm_unrolled_iteration<N + ((M) ? 1 : 0), Scalar, Packet, DataMapper, accRows, accCols, !M>(res3, lhs_base, rhs_base, depth, strideA, offsetA, strideB, row, pAlpha, M ? remaining_rows : accCols); \
+ if (M) return;
+#else
+#define MICRO_UNROLL_ITER2(N, M) \
+ gemm_unrolled_iteration<N + ((M) ? 1 : 0), Scalar, Packet, DataMapper, accRows, accCols, M ? M : accCols>(res3, lhs_base, rhs_base, depth, strideA, offsetA, strideB, row, pAlpha, pMask); \
+ if (M) return;
+#endif
+
+template<typename Scalar, typename Packet, typename DataMapper, const Index accRows, const Index accCols>
+EIGEN_ALWAYS_INLINE void gemm_cols(
+ const DataMapper& res,
+ const Scalar* blockA,
+ const Scalar* blockB,
+ Index depth,
+ Index strideA,
+ Index offsetA,
+ Index strideB,
+ Index offsetB,
+ Index col,
+ Index rows,
+ Index remaining_rows,
+ const Packet& pAlpha,
+ const Packet& pMask)
+{
+ const DataMapper res3 = res.getSubMapper(0, col);
+
+ const Scalar* rhs_base = blockB + col*strideB + MICRO_NEW_ROWS*offsetB;
+ const Scalar* lhs_base = blockA + accCols*offsetA;
+ Index row = 0;
+
+#define MAX_UNROLL 7
+ while(row + MAX_UNROLL*accCols <= rows) {
+ MICRO_UNROLL_ITER2(MAX_UNROLL, 0);
+ }
+ switch( (rows-row)/accCols ) {
+#if MAX_UNROLL > 7
+ case 7:
+ MICRO_UNROLL_ITER(MICRO_UNROLL_ITER2, 7)
+ break;
+#endif
+#if MAX_UNROLL > 6
+ case 6:
+ MICRO_UNROLL_ITER(MICRO_UNROLL_ITER2, 6)
+ break;
+#endif
+#if MAX_UNROLL > 5
+ case 5:
+ MICRO_UNROLL_ITER(MICRO_UNROLL_ITER2, 5)
+ break;
+#endif
+#if MAX_UNROLL > 4
+ case 4:
+ MICRO_UNROLL_ITER(MICRO_UNROLL_ITER2, 4)
+ break;
+#endif
+#if MAX_UNROLL > 3
+ case 3:
+ MICRO_UNROLL_ITER(MICRO_UNROLL_ITER2, 3)
+ break;
+#endif
+#if MAX_UNROLL > 2
+ case 2:
+ MICRO_UNROLL_ITER(MICRO_UNROLL_ITER2, 2)
+ break;
+#endif
+#if MAX_UNROLL > 1
+ case 1:
+ MICRO_UNROLL_ITER(MICRO_UNROLL_ITER2, 1)
+ break;
+#endif
+ default:
+ break;
+ }
+#undef MAX_UNROLL
+
+ if(remaining_rows > 0)
+ {
+ gemm_extra_row<Scalar, Packet, DataMapper, accRows, accCols>(res3, blockA, rhs_base, depth, strideA, offsetA, strideB, row, rows, remaining_rows, pAlpha, pMask);
+ }
+}
+
+#define MICRO_EXTRA_COLS(N) \
+ gemm_cols<Scalar, Packet, DataMapper, N, accCols>(res, blockA, blockB, depth, strideA, offsetA, strideB, offsetB, col, rows, remaining_rows, pAlpha, pMask);
+
+template<typename Scalar, typename Packet, typename DataMapper, const Index accCols>
+EIGEN_STRONG_INLINE void gemm_extra_cols(
+ const DataMapper& res,
+ const Scalar* blockA,
+ const Scalar* blockB,
+ Index depth,
+ Index strideA,
+ Index offsetA,
+ Index strideB,
+ Index offsetB,
+ Index col,
+ Index rows,
+ Index cols,
+ Index remaining_rows,
+ const Packet& pAlpha,
+ const Packet& pMask)
+{
+ MICRO_EXTRA(MICRO_EXTRA_COLS, cols-col, true)
+}
+
+/****************
+ * GEMM kernels *
+ * **************/
+template<typename Scalar, typename Packet, typename RhsPacket, typename DataMapper, const Index accRows, const Index accCols>
+EIGEN_STRONG_INLINE void gemm(const DataMapper& res, const Scalar* blockA, const Scalar* blockB, Index rows, Index depth, Index cols, Scalar alpha, Index strideA, Index strideB, Index offsetA, Index offsetB)
+{
+ const Index remaining_rows = rows % accCols;
+
+ if( strideA == -1 ) strideA = depth;
+ if( strideB == -1 ) strideB = depth;
+
+ const Packet pAlpha = pset1<Packet>(alpha);
+ const Packet pMask = bmask<Packet>(remaining_rows);
+
+ Index col = 0;
+ for(; col + accRows <= cols; col += accRows)
+ {
+ gemm_cols<Scalar, Packet, DataMapper, accRows, accCols>(res, blockA, blockB, depth, strideA, offsetA, strideB, offsetB, col, rows, remaining_rows, pAlpha, pMask);
+ }
+
+ if (col != cols)
+ {
+ gemm_extra_cols<Scalar, Packet, DataMapper, accCols>(res, blockA, blockB, depth, strideA, offsetA, strideB, offsetB, col, rows, cols, remaining_rows, pAlpha, pMask);
+ }
+}
+
+#define accColsC (accCols / 2)
+#define advanceRows ((LhsIsReal) ? 1 : 2)
+#define advanceCols ((RhsIsReal) ? 1 : 2)
+
+// PEEL_COMPLEX loop factor.
+#define PEEL_COMPLEX 3
+#define PEEL_COMPLEX_ROW 3
+
+#define MICRO_COMPLEX_UNROLL(func) \
+ func(0) func(1) func(2) func(3)
+
+#define MICRO_COMPLEX_ZERO_PEEL(peel) \
+ if ((PEEL_COMPLEX_ROW > peel) && (peel != 0)) { \
+ bsetzero<Packet, accRows>(accReal##peel); \
+ bsetzero<Packet, accRows>(accImag##peel); \
+ } else { \
+ EIGEN_UNUSED_VARIABLE(accReal##peel); \
+ EIGEN_UNUSED_VARIABLE(accImag##peel); \
+ }
+
+#define MICRO_COMPLEX_ADD_ROWS(N, used) \
+ MICRO_ADD(ptr_real, N) \
+ if (!RhsIsReal) { \
+ MICRO_ADD(ptr_imag, N) \
+ } else if (used) { \
+ EIGEN_UNUSED_VARIABLE(MICRO_RHS(ptr_imag,0)); \
+ EIGEN_UNUSED_VARIABLE(MICRO_RHS(ptr_imag,1)); \
+ EIGEN_UNUSED_VARIABLE(MICRO_RHS(ptr_imag,2)); \
+ }
+
+#define MICRO_COMPLEX_BROADCAST(peel) \
+ MICRO_BROADCAST1(peel, ptr_real, rhsV, false) \
+ if (!RhsIsReal) { \
+ MICRO_BROADCAST1(peel, ptr_imag, rhsVi, false) \
+ } else { \
+ EIGEN_UNUSED_VARIABLE(rhsVi##peel); \
+ }
+
+#define MICRO_COMPLEX_BROADCAST_EXTRA \
+ Packet rhsV[4], rhsVi[4]; \
+ MICRO_BROADCAST_EXTRA1(ptr_real, rhsV, false) \
+ if(!RhsIsReal) { \
+ MICRO_BROADCAST_EXTRA1(ptr_imag, rhsVi, false) \
+ } else { \
+ EIGEN_UNUSED_VARIABLE(rhsVi); \
+ } \
+ MICRO_COMPLEX_ADD_ROWS(1, true)
+
+#define MICRO_COMPLEX_SRC2_PTR \
+ MICRO_SRC2(ptr_real, strideB*advanceCols, 0) \
+ if (!RhsIsReal) { \
+ MICRO_RHS(ptr_imag,0) = rhs_base + MICRO_NEW_ROWS*strideB; \
+ MICRO_SRC2(ptr_imag, strideB*advanceCols, strideB) \
+ } else { \
+ EIGEN_UNUSED_VARIABLE(MICRO_RHS(ptr_imag,0)); \
+ EIGEN_UNUSED_VARIABLE(MICRO_RHS(ptr_imag,1)); \
+ EIGEN_UNUSED_VARIABLE(MICRO_RHS(ptr_imag,2)); \
+ }
+
+#define MICRO_COMPLEX_ZERO_PEEL_ROW MICRO_COMPLEX_UNROLL(MICRO_COMPLEX_ZERO_PEEL)
+
+#define MICRO_COMPLEX_WORK_PEEL(peel) \
+ if (PEEL_COMPLEX_ROW > peel) { \
+ MICRO_COMPLEX_BROADCAST(peel) \
+ pgerc<accRows, Scalar, Packet, ConjugateLhs, ConjugateRhs, LhsIsReal, RhsIsReal>(&accReal##peel, &accImag##peel, lhs_ptr_real + (remaining_rows * peel), lhs_ptr_imag + (remaining_rows * peel), rhsV##peel, rhsVi##peel); \
+ } else { \
+ EIGEN_UNUSED_VARIABLE(rhsV##peel); \
+ EIGEN_UNUSED_VARIABLE(rhsVi##peel); \
+ }
+
+#define MICRO_COMPLEX_ADD_COLS(size) \
+ lhs_ptr_real += (remaining_rows * size); \
+ if(!LhsIsReal) lhs_ptr_imag += (remaining_rows * size); \
+ else EIGEN_UNUSED_VARIABLE(lhs_ptr_imag);
+
+#define MICRO_COMPLEX_WORK_PEEL_ROW \
+ Packet rhsV0[4], rhsV1[4], rhsV2[4], rhsV3[4]; \
+ Packet rhsVi0[4], rhsVi1[4], rhsVi2[4], rhsVi3[4]; \
+ MICRO_COMPLEX_UNROLL(MICRO_COMPLEX_WORK_PEEL) \
+ MICRO_COMPLEX_ADD_COLS(PEEL_COMPLEX_ROW) \
+ MICRO_COMPLEX_ADD_ROWS(PEEL_COMPLEX_ROW, false)
+
+#define MICRO_COMPLEX_ADD_PEEL(peel, sum) \
+ if (PEEL_COMPLEX_ROW > peel) { \
+ for (Index i = 0; i < accRows; i++) { \
+ accReal##sum.packet[i] += accReal##peel.packet[i]; \
+ accImag##sum.packet[i] += accImag##peel.packet[i]; \
+ } \
+ }
+
+#define MICRO_COMPLEX_ADD_PEEL_ROW \
+ MICRO_COMPLEX_ADD_PEEL(2, 0) MICRO_COMPLEX_ADD_PEEL(3, 1) \
+ MICRO_COMPLEX_ADD_PEEL(1, 0)
+
+template<typename Scalar, typename Packet, const Index accRows, bool ConjugateLhs, bool ConjugateRhs, bool LhsIsReal, bool RhsIsReal, const Index remaining_rows>
+EIGEN_ALWAYS_INLINE void MICRO_COMPLEX_EXTRA_ROW(
+ const Scalar* &lhs_ptr_real, const Scalar* &lhs_ptr_imag,
+ const Scalar* &rhs_ptr_real0, const Scalar* &rhs_ptr_real1, const Scalar* &rhs_ptr_real2,
+ const Scalar* &rhs_ptr_imag0, const Scalar* &rhs_ptr_imag1, const Scalar* &rhs_ptr_imag2,
+ PacketBlock<Packet,accRows> &accReal, PacketBlock<Packet,accRows> &accImag)
+{
+ MICRO_COMPLEX_BROADCAST_EXTRA
+ pgerc<accRows, Scalar, Packet, ConjugateLhs, ConjugateRhs, LhsIsReal, RhsIsReal>(&accReal, &accImag, lhs_ptr_real, lhs_ptr_imag, rhsV, rhsVi);
+ MICRO_COMPLEX_ADD_COLS(1)
+}
+
+template<typename Scalar, typename Packet, typename Packetc, typename DataMapper, const Index accRows, const Index accCols, bool ConjugateLhs, bool ConjugateRhs, bool LhsIsReal, bool RhsIsReal, const Index remaining_rows>
+EIGEN_ALWAYS_INLINE void gemm_unrolled_complex_row_iteration(
+ const DataMapper& res,
+ const Scalar* lhs_base,
+ const Scalar* rhs_base,
+ Index depth,
+ Index strideA,
+ Index offsetA,
+ Index strideB,
+ Index row,
+ Index rows,
+ const Packet& pAlphaReal,
+ const Packet& pAlphaImag,
+ const Packet& pMask)
+{
+ const Scalar* rhs_ptr_real0 = rhs_base, * rhs_ptr_real1 = NULL, * rhs_ptr_real2 = NULL;
+ const Scalar* rhs_ptr_imag0 = NULL, * rhs_ptr_imag1 = NULL, * rhs_ptr_imag2 = NULL;
+ const Scalar* lhs_ptr_real = lhs_base + advanceRows*row*strideA + remaining_rows*offsetA;
+ const Scalar* lhs_ptr_imag = NULL;
+ if(!LhsIsReal) lhs_ptr_imag = lhs_ptr_real + remaining_rows*strideA;
+ else EIGEN_UNUSED_VARIABLE(lhs_ptr_imag);
+ PacketBlock<Packet,accRows> accReal0, accImag0, accReal1, accImag1, accReal2, accImag2, accReal3, accImag3;
+ PacketBlock<Packet,accRows> taccReal, taccImag;
+ PacketBlock<Packetc,accRows> acc0, acc1;
+ PacketBlock<Packetc,accRows*2> tRes;
+
+ MICRO_COMPLEX_SRC2_PTR
+
+ bsetzero<Packet, accRows>(accReal0);
+ bsetzero<Packet, accRows>(accImag0);
+
+ Index remaining_depth = depth & -quad_traits<Scalar>::rows;
+ Index k = 0;
+ if (remaining_depth >= PEEL_COMPLEX_ROW) {
+ MICRO_COMPLEX_ZERO_PEEL_ROW
+ do
+ {
+ MICRO_COMPLEX_PREFETCHN(accRows)
+ EIGEN_POWER_PREFETCH(lhs_ptr_real);
+ if(!LhsIsReal) {
+ EIGEN_POWER_PREFETCH(lhs_ptr_imag);
+ }
+ MICRO_COMPLEX_WORK_PEEL_ROW
+ } while ((k += PEEL_COMPLEX_ROW) + PEEL_COMPLEX_ROW <= remaining_depth);
+ MICRO_COMPLEX_ADD_PEEL_ROW
+ }
+ for(; k < depth; k++)
+ {
+ MICRO_COMPLEX_EXTRA_ROW<Scalar, Packet, accRows, ConjugateLhs, ConjugateRhs, LhsIsReal, RhsIsReal, remaining_rows>(lhs_ptr_real, lhs_ptr_imag, rhs_ptr_real0, rhs_ptr_real1, rhs_ptr_real2, rhs_ptr_imag0, rhs_ptr_imag1, rhs_ptr_imag2, accReal0, accImag0);
+ }
+
+ constexpr bool full = (remaining_rows > accColsC);
+ bload<DataMapper, Packetc, accColsC, ColMajor, true, accRows, full>(tRes, res, row, 0);
+ if ((accRows == 1) || (rows >= accCols))
+ {
+ bscalec<Packet,accRows,true>(accReal0, accImag0, pAlphaReal, pAlphaImag, taccReal, taccImag, pMask);
+ bcouple<Packet, Packetc, accRows, full>(taccReal, taccImag, tRes, acc0, acc1);
+ bstore<DataMapper, Packetc, accRows>(acc0, res, row + 0);
+ if (full) {
+ bstore<DataMapper, Packetc, accRows>(acc1, res, row + accColsC);
+ }
+ } else {
+ bscalec<Packet,accRows,false>(accReal0, accImag0, pAlphaReal, pAlphaImag, taccReal, taccImag, pMask);
+ bcouple<Packet, Packetc, accRows, full>(taccReal, taccImag, tRes, acc0, acc1);
+
+ if ((sizeof(Scalar) == sizeof(float)) && (remaining_rows == 1))
+ {
+ for(Index j = 0; j < accRows; j++) {
+ res(row + 0, j) = pfirst<Packetc>(acc0.packet[j]);
+ }
+ } else {
+ bstore<DataMapper, Packetc, accRows>(acc0, res, row + 0);
+ if (full) {
+ for(Index j = 0; j < accRows; j++) {
+ res(row + accColsC, j) = pfirst<Packetc>(acc1.packet[j]);
+ }
+ }
+ }
+ }
+}
+
+#define MICRO_COMPLEX_EXTRA_ROWS(N) \
+ gemm_unrolled_complex_row_iteration<Scalar, Packet, Packetc, DataMapper, accRows, accCols, ConjugateLhs, ConjugateRhs, LhsIsReal, RhsIsReal, N>(res, lhs_base, rhs_base, depth, strideA, offsetA, strideB, row, rows, pAlphaReal, pAlphaImag, pMask);
+
+template<typename Scalar, typename Packet, typename Packetc, typename DataMapper, const Index accRows, const Index accCols, bool ConjugateLhs, bool ConjugateRhs, bool LhsIsReal, bool RhsIsReal>
+EIGEN_ALWAYS_INLINE void gemm_complex_extra_row(
+ const DataMapper& res,
+ const Scalar* lhs_base,
+ const Scalar* rhs_base,
+ Index depth,
+ Index strideA,
+ Index offsetA,
+ Index strideB,
+ Index row,
+ Index rows,
+ Index remaining_rows,
+ const Packet& pAlphaReal,
+ const Packet& pAlphaImag,
+ const Packet& pMask)
+{
+ MICRO_EXTRA(MICRO_COMPLEX_EXTRA_ROWS, remaining_rows, false)
+}
+
+#define MICRO_COMPLEX_UNROLL_WORK(func, func2, peel) \
+ MICRO_COMPLEX_UNROLL(func2); \
+ func(0,peel) func(1,peel) func(2,peel) func(3,peel)
+
+#define MICRO_COMPLEX_WORK_ONE4(iter, peel) \
+ if (unroll_factor > iter) { \
+ pgerc_common<accRows, Packet, ConjugateLhs, ConjugateRhs, LhsIsReal, RhsIsReal>(&accReal##iter, &accImag##iter, lhsV##iter, lhsVi##iter, rhsV##peel, rhsVi##peel); \
+ }
+
+#define MICRO_COMPLEX_TYPE_PEEL4(func, func2, peel) \
+ if (PEEL_COMPLEX > peel) { \
+ Packet lhsV0, lhsV1, lhsV2, lhsV3; \
+ Packet lhsVi0, lhsVi1, lhsVi2, lhsVi3; \
+ MICRO_COMPLEX_BROADCAST(peel) \
+ MICRO_COMPLEX_UNROLL_WORK(func, func2, peel) \
+ } else { \
+ EIGEN_UNUSED_VARIABLE(rhsV##peel); \
+ EIGEN_UNUSED_VARIABLE(rhsVi##peel); \
+ }
+
+#define MICRO_COMPLEX_UNROLL_TYPE_PEEL(M, func, func1, func2) \
+ Packet rhsV0[M], rhsV1[M], rhsV2[M], rhsV3[M]; \
+ Packet rhsVi0[M], rhsVi1[M], rhsVi2[M], rhsVi3[M]; \
+ func(func1,func2,0) func(func1,func2,1) \
+ func(func1,func2,2) func(func1,func2,3)
+
+#define MICRO_COMPLEX_UNROLL_TYPE_ONE(M, func, func1, func2) \
+ Packet rhsV0[M], rhsVi0[M];\
+ func(func1,func2,0)
+
+#define MICRO_COMPLEX_UNROLL_TYPE(MICRO_COMPLEX_TYPE, size) \
+ MICRO_COMPLEX_TYPE(4, MICRO_COMPLEX_TYPE_PEEL4, MICRO_COMPLEX_WORK_ONE4, MICRO_COMPLEX_LOAD_ONE) \
+ MICRO_COMPLEX_ADD_ROWS(size, false)
+
+#define MICRO_COMPLEX_ONE_PEEL4 MICRO_COMPLEX_UNROLL_TYPE(MICRO_COMPLEX_UNROLL_TYPE_PEEL, PEEL_COMPLEX)
+
+#define MICRO_COMPLEX_ONE4 MICRO_COMPLEX_UNROLL_TYPE(MICRO_COMPLEX_UNROLL_TYPE_ONE, 1)
+
+#define MICRO_COMPLEX_DST_PTR_ONE(iter) \
+ if (unroll_factor > iter) { \
+ bsetzero<Packet, accRows>(accReal##iter); \
+ bsetzero<Packet, accRows>(accImag##iter); \
+ } else { \
+ EIGEN_UNUSED_VARIABLE(accReal##iter); \
+ EIGEN_UNUSED_VARIABLE(accImag##iter); \
+ }
+
+#define MICRO_COMPLEX_DST_PTR MICRO_COMPLEX_UNROLL(MICRO_COMPLEX_DST_PTR_ONE)
+
+#define MICRO_COMPLEX_SRC_PTR MICRO_COMPLEX_UNROLL(MICRO_COMPLEX_SRC_PTR_ONE)
+
+#define MICRO_COMPLEX_PREFETCH MICRO_COMPLEX_UNROLL(MICRO_COMPLEX_PREFETCH_ONE)
+
+#define MICRO_COMPLEX_STORE_ONE(iter) \
+ if (unroll_factor > iter) { \
+ constexpr bool full = ((MICRO_NORMAL(iter)) || (accCols2 > accColsC)); \
+ bload<DataMapper, Packetc, accColsC, ColMajor, true, accRows, full>(tRes, res, row + iter*accCols, 0); \
+ bscalec<Packet,accRows,!(MICRO_NORMAL(iter))>(accReal##iter, accImag##iter, pAlphaReal, pAlphaImag, taccReal, taccImag, pMask); \
+ bcouple<Packet, Packetc, accRows, full>(taccReal, taccImag, tRes, acc0, acc1); \
+ bstore<DataMapper, Packetc, accRows>(acc0, res, row + iter*accCols + 0); \
+ if (full) { \
+ bstore<DataMapper, Packetc, accRows>(acc1, res, row + iter*accCols + accColsC); \
+ } \
+ }
+
+#define MICRO_COMPLEX_STORE MICRO_COMPLEX_UNROLL(MICRO_COMPLEX_STORE_ONE)
+
+template<int unroll_factor, typename Scalar, typename Packet, typename Packetc, typename DataMapper, const Index accRows, const Index accCols, const Index accCols2, bool ConjugateLhs, bool ConjugateRhs, bool LhsIsReal, bool RhsIsReal>
+EIGEN_ALWAYS_INLINE void gemm_complex_unrolled_iteration(
+ const DataMapper& res,
+ const Scalar* lhs_base,
+ const Scalar* rhs_base,
+ Index depth,
+ Index strideA,
+ Index offsetA,
+ Index strideB,
+ Index& row,
+ const Packet& pAlphaReal,
+ const Packet& pAlphaImag,
+ const Packet& pMask)
+{
+ const Scalar* rhs_ptr_real0 = rhs_base, * rhs_ptr_real1 = NULL, * rhs_ptr_real2 = NULL;
+ const Scalar* rhs_ptr_imag0 = NULL, * rhs_ptr_imag1 = NULL, * rhs_ptr_imag2 = NULL;
+ const Index imag_delta = accCols*strideA;
+ const Index imag_delta2 = accCols2*strideA;
+ const Scalar* lhs_ptr_real0 = NULL, * lhs_ptr_real1 = NULL;
+ const Scalar* lhs_ptr_real2 = NULL, * lhs_ptr_real3 = NULL;
+ PacketBlock<Packet,accRows> accReal0, accImag0, accReal1, accImag1;
+ PacketBlock<Packet,accRows> accReal2, accImag2, accReal3, accImag3;
+ PacketBlock<Packet,accRows> taccReal, taccImag;
+ PacketBlock<Packetc,accRows> acc0, acc1;
+ PacketBlock<Packetc,accRows*2> tRes;
+
+ MICRO_COMPLEX_SRC2_PTR
+ MICRO_COMPLEX_SRC_PTR
+ MICRO_COMPLEX_DST_PTR
+
+ Index k = 0;
+ for(; k + PEEL_COMPLEX <= depth; k+= PEEL_COMPLEX)
+ {
+ MICRO_COMPLEX_PREFETCHN(accRows)
+ MICRO_COMPLEX_PREFETCH
+ MICRO_COMPLEX_ONE_PEEL4
+ }
+ for(; k < depth; k++)
+ {
+ MICRO_COMPLEX_ONE4
+ }
+ MICRO_COMPLEX_STORE
+
+ MICRO_COMPLEX_UPDATE
+}
+
+#define MICRO_COMPLEX_UNROLL_ITER2(N, M) \
+ gemm_complex_unrolled_iteration<N + (M ? 1 : 0), Scalar, Packet, Packetc, DataMapper, accRows, accCols, M ? M : accCols, ConjugateLhs, ConjugateRhs, LhsIsReal, RhsIsReal>(res3, lhs_base, rhs_base, depth, strideA, offsetA, strideB, row, pAlphaReal, pAlphaImag, pMask); \
+ if (M) return;
+
+template<typename Scalar, typename Packet, typename Packetc, typename DataMapper, const Index accRows, const Index accCols, bool ConjugateLhs, bool ConjugateRhs, bool LhsIsReal, bool RhsIsReal>
+EIGEN_ALWAYS_INLINE void gemm_complex_cols(
+ const DataMapper& res,
+ const Scalar* blockA,
+ const Scalar* blockB,
+ Index depth,
+ Index strideA,
+ Index offsetA,
+ Index strideB,
+ Index offsetB,
+ Index col,
+ Index rows,
+ Index remaining_rows,
+ const Packet& pAlphaReal,
+ const Packet& pAlphaImag,
+ const Packet& pMask)
+{
+ const DataMapper res3 = res.getSubMapper(0, col);
+
+ const Scalar* rhs_base = blockB + advanceCols*col*strideB + MICRO_NEW_ROWS*offsetB;
+ const Scalar* lhs_base = blockA + accCols*offsetA;
+ Index row = 0;
+
+#define MAX_COMPLEX_UNROLL 4
+ while(row + MAX_COMPLEX_UNROLL*accCols <= rows) {
+ MICRO_COMPLEX_UNROLL_ITER2(MAX_COMPLEX_UNROLL, 0);
+ }
+ switch( (rows-row)/accCols ) {
+#if MAX_COMPLEX_UNROLL > 4
+ case 4:
+ MICRO_COMPLEX_UNROLL_ITER(MICRO_COMPLEX_UNROLL_ITER2, 4)
+ break;
+#endif
+#if MAX_COMPLEX_UNROLL > 3
+ case 3:
+ MICRO_COMPLEX_UNROLL_ITER(MICRO_COMPLEX_UNROLL_ITER2, 3)
+ break;
+#endif
+#if MAX_COMPLEX_UNROLL > 2
+ case 2:
+ MICRO_COMPLEX_UNROLL_ITER(MICRO_COMPLEX_UNROLL_ITER2, 2)
+ break;
+#endif
+#if MAX_COMPLEX_UNROLL > 1
+ case 1:
+ MICRO_COMPLEX_UNROLL_ITER(MICRO_COMPLEX_UNROLL_ITER2, 1)
+ break;
+#endif
+ default:
+ break;
+ }
+#undef MAX_COMPLEX_UNROLL
+
+ if(remaining_rows > 0)
+ {
+ gemm_complex_extra_row<Scalar, Packet, Packetc, DataMapper, accRows, accCols, ConjugateLhs, ConjugateRhs, LhsIsReal, RhsIsReal>(res3, blockA, rhs_base, depth, strideA, offsetA, strideB, row, rows, remaining_rows, pAlphaReal, pAlphaImag, pMask);
+ }
+}
+
+#define MICRO_COMPLEX_EXTRA_COLS(N) \
+ gemm_complex_cols<Scalar, Packet, Packetc, DataMapper, N, accCols, ConjugateLhs, ConjugateRhs, LhsIsReal, RhsIsReal>(res, blockA, blockB, depth, strideA, offsetA, strideB, offsetB, col, rows, remaining_rows, pAlphaReal, pAlphaImag, pMask);
+
+template<typename Scalar, typename Packet, typename Packetc, typename DataMapper, const Index accCols, bool ConjugateLhs, bool ConjugateRhs, bool LhsIsReal, bool RhsIsReal>
+EIGEN_STRONG_INLINE void gemm_complex_extra_cols(
+ const DataMapper& res,
+ const Scalar* blockA,
+ const Scalar* blockB,
+ Index depth,
+ Index strideA,
+ Index offsetA,
+ Index strideB,
+ Index offsetB,
+ Index col,
+ Index rows,
+ Index cols,
+ Index remaining_rows,
+ const Packet& pAlphaReal,
+ const Packet& pAlphaImag,
+ const Packet& pMask)
+{
+ MICRO_EXTRA(MICRO_COMPLEX_EXTRA_COLS, cols-col, true)
+}
+
+template<typename LhsScalar, typename RhsScalar, typename Scalarc, typename Scalar, typename Packet, typename Packetc, typename RhsPacket, typename DataMapper, const Index accRows, const Index accCols, bool ConjugateLhs, bool ConjugateRhs, bool LhsIsReal, bool RhsIsReal>
+EIGEN_STRONG_INLINE void gemm_complex(const DataMapper& res, const LhsScalar* blockAc, const RhsScalar* blockBc, Index rows, Index depth, Index cols, Scalarc alpha, Index strideA, Index strideB, Index offsetA, Index offsetB)
+{
+ const Index remaining_rows = rows % accCols;
+
+ if( strideA == -1 ) strideA = depth;
+ if( strideB == -1 ) strideB = depth;
+
+ const Packet pAlphaReal = pset1<Packet>(alpha.real());
+ const Packet pAlphaImag = pset1<Packet>(alpha.imag());
+ const Packet pMask = bmask<Packet>(remaining_rows);
+
+ const Scalar* blockA = (Scalar *) blockAc;
+ const Scalar* blockB = (Scalar *) blockBc;
+
+ Index col = 0;
+ for(; col + accRows <= cols; col += accRows)
+ {
+ gemm_complex_cols<Scalar, Packet, Packetc, DataMapper, accRows, accCols, ConjugateLhs, ConjugateRhs, LhsIsReal, RhsIsReal>(res, blockA, blockB, depth, strideA, offsetA, strideB, offsetB, col, rows, remaining_rows, pAlphaReal, pAlphaImag, pMask);
+ }
+
+ if (col != cols)
+ {
+ gemm_complex_extra_cols<Scalar, Packet, Packetc, DataMapper, accCols, ConjugateLhs, ConjugateRhs, LhsIsReal, RhsIsReal>(res, blockA, blockB, depth, strideA, offsetA, strideB, offsetB, col, rows, cols, remaining_rows, pAlphaReal, pAlphaImag, pMask);
+ }
+}
+
+#undef accColsC
+#undef advanceCols
+#undef advanceRows
+
+#include "MatrixVectorProduct.h"
+
+/************************************
+ * ppc64le template specializations *
+ * **********************************/
+template<typename Index, typename DataMapper, int Pack1, int Pack2, typename Packet, bool Conjugate, bool PanelMode>
+struct gemm_pack_lhs<double, Index, DataMapper, Pack1, Pack2, Packet, ColMajor, Conjugate, PanelMode>
+{
+ void operator()(double* blockA, const DataMapper& lhs, Index depth, Index rows, Index stride=0, Index offset=0);
+};
+
+template<typename Index, typename DataMapper, int Pack1, int Pack2, typename Packet, bool Conjugate, bool PanelMode>
+void gemm_pack_lhs<double, Index, DataMapper, Pack1, Pack2, Packet, ColMajor, Conjugate, PanelMode>
+ ::operator()(double* blockA, const DataMapper& lhs, Index depth, Index rows, Index stride, Index offset)
+{
+ dhs_pack<double, DataMapper, Packet2d, ColMajor, PanelMode, true> pack;
+ pack(blockA, lhs, depth, rows, stride, offset);
+}
+
+template<typename Index, typename DataMapper, int Pack1, int Pack2, typename Packet, bool Conjugate, bool PanelMode>
+struct gemm_pack_lhs<double, Index, DataMapper, Pack1, Pack2, Packet, RowMajor, Conjugate, PanelMode>
+{
+ void operator()(double* blockA, const DataMapper& lhs, Index depth, Index rows, Index stride=0, Index offset=0);
+};
+
+template<typename Index, typename DataMapper, int Pack1, int Pack2, typename Packet, bool Conjugate, bool PanelMode>
+void gemm_pack_lhs<double, Index, DataMapper, Pack1, Pack2, Packet, RowMajor, Conjugate, PanelMode>
+ ::operator()(double* blockA, const DataMapper& lhs, Index depth, Index rows, Index stride, Index offset)
+{
+ dhs_pack<double, DataMapper, Packet2d, RowMajor, PanelMode, true> pack;
+ pack(blockA, lhs, depth, rows, stride, offset);
+}
+
+#if EIGEN_ALTIVEC_USE_CUSTOM_PACK
+template<typename Index, typename DataMapper, int nr, bool Conjugate, bool PanelMode>
+struct gemm_pack_rhs<double, Index, DataMapper, nr, ColMajor, Conjugate, PanelMode>
+{
+ void operator()(double* blockB, const DataMapper& rhs, Index depth, Index cols, Index stride=0, Index offset=0);
+};
+
+template<typename Index, typename DataMapper, int nr, bool Conjugate, bool PanelMode>
+void gemm_pack_rhs<double, Index, DataMapper, nr, ColMajor, Conjugate, PanelMode>
+ ::operator()(double* blockB, const DataMapper& rhs, Index depth, Index cols, Index stride, Index offset)
+{
+ dhs_pack<double, DataMapper, Packet2d, ColMajor, PanelMode, false> pack;
+ pack(blockB, rhs, depth, cols, stride, offset);
+}
+
+template<typename Index, typename DataMapper, int nr, bool Conjugate, bool PanelMode>
+struct gemm_pack_rhs<double, Index, DataMapper, nr, RowMajor, Conjugate, PanelMode>
+{
+ void operator()(double* blockB, const DataMapper& rhs, Index depth, Index cols, Index stride=0, Index offset=0);
+};
+
+template<typename Index, typename DataMapper, int nr, bool Conjugate, bool PanelMode>
+void gemm_pack_rhs<double, Index, DataMapper, nr, RowMajor, Conjugate, PanelMode>
+ ::operator()(double* blockB, const DataMapper& rhs, Index depth, Index cols, Index stride, Index offset)
+{
+ dhs_pack<double, DataMapper, Packet2d, RowMajor, PanelMode, false> pack;
+ pack(blockB, rhs, depth, cols, stride, offset);
+}
+#endif
+
+template<typename Index, typename DataMapper, int Pack1, int Pack2, typename Packet, bool Conjugate, bool PanelMode>
+struct gemm_pack_lhs<float, Index, DataMapper, Pack1, Pack2, Packet, RowMajor, Conjugate, PanelMode>
+{
+ void operator()(float* blockA, const DataMapper& lhs, Index depth, Index rows, Index stride=0, Index offset=0);
+};
+
+template<typename Index, typename DataMapper, int Pack1, int Pack2, typename Packet, bool Conjugate, bool PanelMode>
+void gemm_pack_lhs<float, Index, DataMapper, Pack1, Pack2, Packet, RowMajor, Conjugate, PanelMode>
+ ::operator()(float* blockA, const DataMapper& lhs, Index depth, Index rows, Index stride, Index offset)
+{
+ dhs_pack<float, DataMapper, Packet4f, RowMajor, PanelMode, true> pack;
+ pack(blockA, lhs, depth, rows, stride, offset);
+}
+
+template<typename Index, typename DataMapper, int Pack1, int Pack2, typename Packet, bool Conjugate, bool PanelMode>
+struct gemm_pack_lhs<float, Index, DataMapper, Pack1, Pack2, Packet, ColMajor, Conjugate, PanelMode>
+{
+ void operator()(float* blockA, const DataMapper& lhs, Index depth, Index rows, Index stride=0, Index offset=0);
+};
+
+template<typename Index, typename DataMapper, int Pack1, int Pack2, typename Packet, bool Conjugate, bool PanelMode>
+void gemm_pack_lhs<float, Index, DataMapper, Pack1, Pack2, Packet, ColMajor, Conjugate, PanelMode>
+ ::operator()(float* blockA, const DataMapper& lhs, Index depth, Index rows, Index stride, Index offset)
+{
+ dhs_pack<float, DataMapper, Packet4f, ColMajor, PanelMode, true> pack;
+ pack(blockA, lhs, depth, rows, stride, offset);
+}
+
+template<typename Index, typename DataMapper, int Pack1, int Pack2, typename Packet, bool Conjugate, bool PanelMode>
+struct gemm_pack_lhs<std::complex<float>, Index, DataMapper, Pack1, Pack2, Packet, RowMajor, Conjugate, PanelMode>
+{
+ void operator()(std::complex<float>* blockA, const DataMapper& lhs, Index depth, Index rows, Index stride=0, Index offset=0);
+};
+
+template<typename Index, typename DataMapper, int Pack1, int Pack2, typename Packet, bool Conjugate, bool PanelMode>
+void gemm_pack_lhs<std::complex<float>, Index, DataMapper, Pack1, Pack2, Packet, RowMajor, Conjugate, PanelMode>
+ ::operator()(std::complex<float>* blockA, const DataMapper& lhs, Index depth, Index rows, Index stride, Index offset)
+{
+ dhs_cpack<float, DataMapper, Packet4f, Packet2cf, RowMajor, Conjugate, PanelMode, true> pack;
+ pack(blockA, lhs, depth, rows, stride, offset);
+}
+
+template<typename Index, typename DataMapper, int Pack1, int Pack2, typename Packet, bool Conjugate, bool PanelMode>
+struct gemm_pack_lhs<std::complex<float>, Index, DataMapper, Pack1, Pack2, Packet, ColMajor, Conjugate, PanelMode>
+{
+ void operator()(std::complex<float>* blockA, const DataMapper& lhs, Index depth, Index rows, Index stride=0, Index offset=0);
+};
+
+template<typename Index, typename DataMapper, int Pack1, int Pack2, typename Packet, bool Conjugate, bool PanelMode>
+void gemm_pack_lhs<std::complex<float>, Index, DataMapper, Pack1, Pack2, Packet, ColMajor, Conjugate, PanelMode>
+ ::operator()(std::complex<float>* blockA, const DataMapper& lhs, Index depth, Index rows, Index stride, Index offset)
+{
+ dhs_cpack<float, DataMapper, Packet4f, Packet2cf, ColMajor, Conjugate, PanelMode, true> pack;
+ pack(blockA, lhs, depth, rows, stride, offset);
+}
+
+#if EIGEN_ALTIVEC_USE_CUSTOM_PACK
+template<typename Index, typename DataMapper, int nr, bool Conjugate, bool PanelMode>
+struct gemm_pack_rhs<float, Index, DataMapper, nr, ColMajor, Conjugate, PanelMode>
+{
+ void operator()(float* blockB, const DataMapper& rhs, Index depth, Index cols, Index stride=0, Index offset=0);
+};
+
+template<typename Index, typename DataMapper, int nr, bool Conjugate, bool PanelMode>
+void gemm_pack_rhs<float, Index, DataMapper, nr, ColMajor, Conjugate, PanelMode>
+ ::operator()(float* blockB, const DataMapper& rhs, Index depth, Index cols, Index stride, Index offset)
+{
+ dhs_pack<float, DataMapper, Packet4f, ColMajor, PanelMode, false> pack;
+ pack(blockB, rhs, depth, cols, stride, offset);
+}
+
+template<typename Index, typename DataMapper, int nr, bool Conjugate, bool PanelMode>
+struct gemm_pack_rhs<float, Index, DataMapper, nr, RowMajor, Conjugate, PanelMode>
+{
+ void operator()(float* blockB, const DataMapper& rhs, Index depth, Index cols, Index stride=0, Index offset=0);
+};
+
+template<typename Index, typename DataMapper, int nr, bool Conjugate, bool PanelMode>
+void gemm_pack_rhs<float, Index, DataMapper, nr, RowMajor, Conjugate, PanelMode>
+ ::operator()(float* blockB, const DataMapper& rhs, Index depth, Index cols, Index stride, Index offset)
+{
+ dhs_pack<float, DataMapper, Packet4f, RowMajor, PanelMode, false> pack;
+ pack(blockB, rhs, depth, cols, stride, offset);
+}
+#endif
+
+template<typename Index, typename DataMapper, int nr, bool Conjugate, bool PanelMode>
+struct gemm_pack_rhs<std::complex<float>, Index, DataMapper, nr, ColMajor, Conjugate, PanelMode>
+{
+ void operator()(std::complex<float>* blockB, const DataMapper& rhs, Index depth, Index cols, Index stride=0, Index offset=0);
+};
+
+template<typename Index, typename DataMapper, int nr, bool Conjugate, bool PanelMode>
+void gemm_pack_rhs<std::complex<float>, Index, DataMapper, nr, ColMajor, Conjugate, PanelMode>
+ ::operator()(std::complex<float>* blockB, const DataMapper& rhs, Index depth, Index cols, Index stride, Index offset)
+{
+ dhs_cpack<float, DataMapper, Packet4f, Packet2cf, ColMajor, Conjugate, PanelMode, false> pack;
+ pack(blockB, rhs, depth, cols, stride, offset);
+}
+
+template<typename Index, typename DataMapper, int nr, bool Conjugate, bool PanelMode>
+struct gemm_pack_rhs<std::complex<float>, Index, DataMapper, nr, RowMajor, Conjugate, PanelMode>
+{
+ void operator()(std::complex<float>* blockB, const DataMapper& rhs, Index depth, Index cols, Index stride=0, Index offset=0);
+};
+
+template<typename Index, typename DataMapper, int nr, bool Conjugate, bool PanelMode>
+void gemm_pack_rhs<std::complex<float>, Index, DataMapper, nr, RowMajor, Conjugate, PanelMode>
+ ::operator()(std::complex<float>* blockB, const DataMapper& rhs, Index depth, Index cols, Index stride, Index offset)
+{
+ dhs_cpack<float, DataMapper, Packet4f, Packet2cf, RowMajor, Conjugate, PanelMode, false> pack;
+ pack(blockB, rhs, depth, cols, stride, offset);
+}
+
+template<typename Index, typename DataMapper, int Pack1, int Pack2, typename Packet, bool Conjugate, bool PanelMode>
+struct gemm_pack_lhs<std::complex<double>, Index, DataMapper, Pack1, Pack2, Packet, RowMajor, Conjugate, PanelMode>
+{
+ void operator()(std::complex<double>* blockA, const DataMapper& lhs, Index depth, Index rows, Index stride=0, Index offset=0);
+};
+
+template<typename Index, typename DataMapper, int Pack1, int Pack2, typename Packet, bool Conjugate, bool PanelMode>
+void gemm_pack_lhs<std::complex<double>, Index, DataMapper, Pack1, Pack2, Packet, RowMajor, Conjugate, PanelMode>
+ ::operator()(std::complex<double>* blockA, const DataMapper& lhs, Index depth, Index rows, Index stride, Index offset)
+{
+ dhs_cpack<double, DataMapper, Packet2d, Packet1cd, RowMajor, Conjugate, PanelMode, true> pack;
+ pack(blockA, lhs, depth, rows, stride, offset);
+}
+
+template<typename Index, typename DataMapper, int Pack1, int Pack2, typename Packet, bool Conjugate, bool PanelMode>
+struct gemm_pack_lhs<std::complex<double>, Index, DataMapper, Pack1, Pack2, Packet, ColMajor, Conjugate, PanelMode>
+{
+ void operator()(std::complex<double>* blockA, const DataMapper& lhs, Index depth, Index rows, Index stride=0, Index offset=0);
+};
+
+template<typename Index, typename DataMapper, int Pack1, int Pack2, typename Packet, bool Conjugate, bool PanelMode>
+void gemm_pack_lhs<std::complex<double>, Index, DataMapper, Pack1, Pack2, Packet, ColMajor, Conjugate, PanelMode>
+ ::operator()(std::complex<double>* blockA, const DataMapper& lhs, Index depth, Index rows, Index stride, Index offset)
+{
+ dhs_cpack<double, DataMapper, Packet2d, Packet1cd, ColMajor, Conjugate, PanelMode, true> pack;
+ pack(blockA, lhs, depth, rows, stride, offset);
+}
+
+template<typename Index, typename DataMapper, int nr, bool Conjugate, bool PanelMode>
+struct gemm_pack_rhs<std::complex<double>, Index, DataMapper, nr, ColMajor, Conjugate, PanelMode>
+{
+ void operator()(std::complex<double>* blockB, const DataMapper& rhs, Index depth, Index cols, Index stride=0, Index offset=0);
+};
+
+template<typename Index, typename DataMapper, int nr, bool Conjugate, bool PanelMode>
+void gemm_pack_rhs<std::complex<double>, Index, DataMapper, nr, ColMajor, Conjugate, PanelMode>
+ ::operator()(std::complex<double>* blockB, const DataMapper& rhs, Index depth, Index cols, Index stride, Index offset)
+{
+ dhs_cpack<double, DataMapper, Packet2d, Packet1cd, ColMajor, Conjugate, PanelMode, false> pack;
+ pack(blockB, rhs, depth, cols, stride, offset);
+}
+
+template<typename Index, typename DataMapper, int nr, bool Conjugate, bool PanelMode>
+struct gemm_pack_rhs<std::complex<double>, Index, DataMapper, nr, RowMajor, Conjugate, PanelMode>
+{
+ void operator()(std::complex<double>* blockB, const DataMapper& rhs, Index depth, Index cols, Index stride=0, Index offset=0);
+};
+
+template<typename Index, typename DataMapper, int nr, bool Conjugate, bool PanelMode>
+void gemm_pack_rhs<std::complex<double>, Index, DataMapper, nr, RowMajor, Conjugate, PanelMode>
+ ::operator()(std::complex<double>* blockB, const DataMapper& rhs, Index depth, Index cols, Index stride, Index offset)
+{
+ dhs_cpack<double, DataMapper, Packet2d, Packet1cd, RowMajor, Conjugate, PanelMode, false> pack;
+ pack(blockB, rhs, depth, cols, stride, offset);
+}
+
+// ********* gebp specializations *********
+template<typename Index, typename DataMapper, int mr, int nr, bool ConjugateLhs, bool ConjugateRhs>
+struct gebp_kernel<float, float, Index, DataMapper, mr, nr, ConjugateLhs, ConjugateRhs>
+{
+ typedef typename quad_traits<float>::vectortype Packet;
+ typedef typename quad_traits<float>::rhstype RhsPacket;
+
+ void operator()(const DataMapper& res, const float* blockA, const float* blockB,
+ Index rows, Index depth, Index cols, float alpha,
+ Index strideA=-1, Index strideB=-1, Index offsetA=0, Index offsetB=0);
+};
+
+template<typename Index, typename DataMapper, int mr, int nr, bool ConjugateLhs, bool ConjugateRhs>
+void gebp_kernel<float, float, Index, DataMapper, mr, nr, ConjugateLhs, ConjugateRhs>
+ ::operator()(const DataMapper& res, const float* blockA, const float* blockB,
+ Index rows, Index depth, Index cols, float alpha,
+ Index strideA, Index strideB, Index offsetA, Index offsetB)
+ {
+ const Index accRows = quad_traits<float>::rows;
+ const Index accCols = quad_traits<float>::size;
+ void (*gemm_function)(const DataMapper&, const float*, const float*, Index, Index, Index, float, Index, Index, Index, Index);
+
+ #if defined(EIGEN_ALTIVEC_MMA_ONLY)
+ //generate with MMA only
+ gemm_function = &Eigen::internal::gemmMMA<float, Packet, RhsPacket, DataMapper, accRows, accCols>;
+ #elif defined(EIGEN_ALTIVEC_MMA_DYNAMIC_DISPATCH)
+ if (__builtin_cpu_supports ("arch_3_1") && __builtin_cpu_supports ("mma")){
+ gemm_function = &Eigen::internal::gemmMMA<float, Packet, RhsPacket, DataMapper, accRows, accCols>;
+ }
+ else{
+ gemm_function = &Eigen::internal::gemm<float, Packet, RhsPacket, DataMapper, accRows, accCols>;
+ }
+ #else
+ gemm_function = &Eigen::internal::gemm<float, Packet, RhsPacket, DataMapper, accRows, accCols>;
+ #endif
+ gemm_function(res, blockA, blockB, rows, depth, cols, alpha, strideA, strideB, offsetA, offsetB);
+ }
+
+template<typename Index, typename DataMapper, int mr, int nr, bool ConjugateLhs, bool ConjugateRhs>
+struct gebp_kernel<std::complex<float>, std::complex<float>, Index, DataMapper, mr, nr, ConjugateLhs, ConjugateRhs>
+{
+ typedef Packet4f Packet;
+ typedef Packet2cf Packetc;
+ typedef Packet4f RhsPacket;
+
+ void operator()(const DataMapper& res, const std::complex<float>* blockA, const std::complex<float>* blockB,
+ Index rows, Index depth, Index cols, std::complex<float> alpha,
+ Index strideA=-1, Index strideB=-1, Index offsetA=0, Index offsetB=0);
+};
+
+template<typename Index, typename DataMapper, int mr, int nr, bool ConjugateLhs, bool ConjugateRhs>
+void gebp_kernel<std::complex<float>, std::complex<float>, Index, DataMapper, mr, nr, ConjugateLhs, ConjugateRhs>
+ ::operator()(const DataMapper& res, const std::complex<float>* blockA, const std::complex<float>* blockB,
+ Index rows, Index depth, Index cols, std::complex<float> alpha,
+ Index strideA, Index strideB, Index offsetA, Index offsetB)
+ {
+ const Index accRows = quad_traits<float>::rows;
+ const Index accCols = quad_traits<float>::size;
+ void (*gemm_function)(const DataMapper&, const std::complex<float>*, const std::complex<float>*,
+ Index, Index, Index, std::complex<float>, Index, Index, Index, Index);
+
+ #if defined(EIGEN_ALTIVEC_MMA_ONLY)
+ //generate with MMA only
+ gemm_function = &Eigen::internal::gemm_complexMMA<std::complex<float>, std::complex<float>, std::complex<float>, float, Packet, Packetc, RhsPacket, DataMapper, accRows, accCols, ConjugateLhs, ConjugateRhs, false, false>;
+ #elif defined(EIGEN_ALTIVEC_MMA_DYNAMIC_DISPATCH)
+ if (__builtin_cpu_supports ("arch_3_1") && __builtin_cpu_supports ("mma")){
+ gemm_function = &Eigen::internal::gemm_complexMMA<std::complex<float>, std::complex<float>, std::complex<float>, float, Packet, Packetc, RhsPacket, DataMapper, accRows, accCols, ConjugateLhs, ConjugateRhs, false, false>;
+ }
+ else{
+ gemm_function = &Eigen::internal::gemm_complex<std::complex<float>, std::complex<float>, std::complex<float>, float, Packet, Packetc, RhsPacket, DataMapper, accRows, accCols, ConjugateLhs, ConjugateRhs, false, false>;
+ }
+ #else
+ gemm_function = &Eigen::internal::gemm_complex<std::complex<float>, std::complex<float>, std::complex<float>, float, Packet, Packetc, RhsPacket, DataMapper, accRows, accCols, ConjugateLhs, ConjugateRhs, false, false>;
+ #endif
+ gemm_function(res, blockA, blockB, rows, depth, cols, alpha, strideA, strideB, offsetA, offsetB);
+ }
+
+template<typename Index, typename DataMapper, int mr, int nr, bool ConjugateLhs, bool ConjugateRhs>
+struct gebp_kernel<float, std::complex<float>, Index, DataMapper, mr, nr, ConjugateLhs, ConjugateRhs>
+{
+ typedef Packet4f Packet;
+ typedef Packet2cf Packetc;
+ typedef Packet4f RhsPacket;
+
+ void operator()(const DataMapper& res, const float* blockA, const std::complex<float>* blockB,
+ Index rows, Index depth, Index cols, std::complex<float> alpha,
+ Index strideA=-1, Index strideB=-1, Index offsetA=0, Index offsetB=0);
+};
+
+template<typename Index, typename DataMapper, int mr, int nr, bool ConjugateLhs, bool ConjugateRhs>
+void gebp_kernel<float, std::complex<float>, Index, DataMapper, mr, nr, ConjugateLhs, ConjugateRhs>
+ ::operator()(const DataMapper& res, const float* blockA, const std::complex<float>* blockB,
+ Index rows, Index depth, Index cols, std::complex<float> alpha,
+ Index strideA, Index strideB, Index offsetA, Index offsetB)
+ {
+ const Index accRows = quad_traits<float>::rows;
+ const Index accCols = quad_traits<float>::size;
+ void (*gemm_function)(const DataMapper&, const float*, const std::complex<float>*,
+ Index, Index, Index, std::complex<float>, Index, Index, Index, Index);
+ #if defined(EIGEN_ALTIVEC_MMA_ONLY)
+ //generate with MMA only
+ gemm_function = &Eigen::internal::gemm_complexMMA<float, std::complex<float>, std::complex<float>, float, Packet, Packetc, RhsPacket, DataMapper, accRows, accCols, ConjugateLhs, ConjugateRhs, true, false>;
+ #elif defined(EIGEN_ALTIVEC_MMA_DYNAMIC_DISPATCH)
+ if (__builtin_cpu_supports ("arch_3_1") && __builtin_cpu_supports ("mma")){
+ gemm_function = &Eigen::internal::gemm_complexMMA<float, std::complex<float>, std::complex<float>, float, Packet, Packetc, RhsPacket, DataMapper, accRows, accCols, ConjugateLhs, ConjugateRhs, true, false>;
+ }
+ else{
+ gemm_function = &Eigen::internal::gemm_complex<float, std::complex<float>, std::complex<float>, float, Packet, Packetc, RhsPacket, DataMapper, accRows, accCols, ConjugateLhs, ConjugateRhs, true, false>;
+ }
+ #else
+ gemm_function = &Eigen::internal::gemm_complex<float, std::complex<float>, std::complex<float>, float, Packet, Packetc, RhsPacket, DataMapper, accRows, accCols, ConjugateLhs, ConjugateRhs, true, false>;
+ #endif
+ gemm_function(res, blockA, blockB, rows, depth, cols, alpha, strideA, strideB, offsetA, offsetB);
+ }
+
+template<typename Index, typename DataMapper, int mr, int nr, bool ConjugateLhs, bool ConjugateRhs>
+struct gebp_kernel<std::complex<float>, float, Index, DataMapper, mr, nr, ConjugateLhs, ConjugateRhs>
+{
+ typedef Packet4f Packet;
+ typedef Packet2cf Packetc;
+ typedef Packet4f RhsPacket;
+
+ void operator()(const DataMapper& res, const std::complex<float>* blockA, const float* blockB,
+ Index rows, Index depth, Index cols, std::complex<float> alpha,
+ Index strideA=-1, Index strideB=-1, Index offsetA=0, Index offsetB=0);
+};
+
+template<typename Index, typename DataMapper, int mr, int nr, bool ConjugateLhs, bool ConjugateRhs>
+void gebp_kernel<std::complex<float>, float, Index, DataMapper, mr, nr, ConjugateLhs, ConjugateRhs>
+ ::operator()(const DataMapper& res, const std::complex<float>* blockA, const float* blockB,
+ Index rows, Index depth, Index cols, std::complex<float> alpha,
+ Index strideA, Index strideB, Index offsetA, Index offsetB)
+ {
+ const Index accRows = quad_traits<float>::rows;
+ const Index accCols = quad_traits<float>::size;
+ void (*gemm_function)(const DataMapper&, const std::complex<float>*, const float*,
+ Index, Index, Index, std::complex<float>, Index, Index, Index, Index);
+ #if defined(EIGEN_ALTIVEC_MMA_ONLY)
+ //generate with MMA only
+ gemm_function = &Eigen::internal::gemm_complexMMA<std::complex<float>, float, std::complex<float>, float, Packet, Packetc, RhsPacket, DataMapper, accRows, accCols, ConjugateLhs, ConjugateRhs, false, true>;
+ #elif defined(EIGEN_ALTIVEC_MMA_DYNAMIC_DISPATCH)
+ if (__builtin_cpu_supports ("arch_3_1") && __builtin_cpu_supports ("mma")){
+ gemm_function = &Eigen::internal::gemm_complexMMA<std::complex<float>, float, std::complex<float>, float, Packet, Packetc, RhsPacket, DataMapper, accRows, accCols, ConjugateLhs, ConjugateRhs, false, true>;
+ }
+ else{
+ gemm_function = &Eigen::internal::gemm_complex<std::complex<float>, float, std::complex<float>, float, Packet, Packetc, RhsPacket, DataMapper, accRows, accCols, ConjugateLhs, ConjugateRhs, false, true>;
+ }
+ #else
+ gemm_function = &Eigen::internal::gemm_complex<std::complex<float>, float, std::complex<float>, float, Packet, Packetc, RhsPacket, DataMapper, accRows, accCols, ConjugateLhs, ConjugateRhs, false, true>;
+ #endif
+ gemm_function(res, blockA, blockB, rows, depth, cols, alpha, strideA, strideB, offsetA, offsetB);
+ }
+
+template<typename Index, typename DataMapper, int mr, int nr, bool ConjugateLhs, bool ConjugateRhs>
+struct gebp_kernel<double, double, Index, DataMapper, mr, nr, ConjugateLhs, ConjugateRhs>
+{
+ typedef typename quad_traits<double>::vectortype Packet;
+ typedef typename quad_traits<double>::rhstype RhsPacket;
+
+ void operator()(const DataMapper& res, const double* blockA, const double* blockB,
+ Index rows, Index depth, Index cols, double alpha,
+ Index strideA=-1, Index strideB=-1, Index offsetA=0, Index offsetB=0);
+};
+
+template<typename Index, typename DataMapper, int mr, int nr, bool ConjugateLhs, bool ConjugateRhs>
+void gebp_kernel<double, double, Index, DataMapper, mr, nr, ConjugateLhs, ConjugateRhs>
+ ::operator()(const DataMapper& res, const double* blockA, const double* blockB,
+ Index rows, Index depth, Index cols, double alpha,
+ Index strideA, Index strideB, Index offsetA, Index offsetB)
+ {
+ const Index accRows = quad_traits<double>::rows;
+ const Index accCols = quad_traits<double>::size;
+ void (*gemm_function)(const DataMapper&, const double*, const double*, Index, Index, Index, double, Index, Index, Index, Index);
+
+ #if defined(EIGEN_ALTIVEC_MMA_ONLY)
+ //generate with MMA only
+ gemm_function = &Eigen::internal::gemmMMA<double, Packet, RhsPacket, DataMapper, accRows, accCols>;
+ #elif defined(EIGEN_ALTIVEC_MMA_DYNAMIC_DISPATCH)
+ if (__builtin_cpu_supports ("arch_3_1") && __builtin_cpu_supports ("mma")){
+ gemm_function = &Eigen::internal::gemmMMA<double, Packet, RhsPacket, DataMapper, accRows, accCols>;
+ }
+ else{
+ gemm_function = &Eigen::internal::gemm<double, Packet, RhsPacket, DataMapper, accRows, accCols>;
+ }
+ #else
+ gemm_function = &Eigen::internal::gemm<double, Packet, RhsPacket, DataMapper, accRows, accCols>;
+ #endif
+ gemm_function(res, blockA, blockB, rows, depth, cols, alpha, strideA, strideB, offsetA, offsetB);
+ }
+
+template<typename Index, typename DataMapper, int mr, int nr, bool ConjugateLhs, bool ConjugateRhs>
+struct gebp_kernel<std::complex<double>, std::complex<double>, Index, DataMapper, mr, nr, ConjugateLhs, ConjugateRhs>
+{
+ typedef quad_traits<double>::vectortype Packet;
+ typedef Packet1cd Packetc;
+ typedef quad_traits<double>::rhstype RhsPacket;
+
+ void operator()(const DataMapper& res, const std::complex<double>* blockA, const std::complex<double>* blockB,
+ Index rows, Index depth, Index cols, std::complex<double> alpha,
+ Index strideA=-1, Index strideB=-1, Index offsetA=0, Index offsetB=0);
+};
+
+template<typename Index, typename DataMapper, int mr, int nr, bool ConjugateLhs, bool ConjugateRhs>
+void gebp_kernel<std::complex<double>, std::complex<double>, Index, DataMapper, mr, nr, ConjugateLhs, ConjugateRhs>
+ ::operator()(const DataMapper& res, const std::complex<double>* blockA, const std::complex<double>* blockB,
+ Index rows, Index depth, Index cols, std::complex<double> alpha,
+ Index strideA, Index strideB, Index offsetA, Index offsetB)
+ {
+ const Index accRows = quad_traits<double>::rows;
+ const Index accCols = quad_traits<double>::size;
+ void (*gemm_function)(const DataMapper&, const std::complex<double>*, const std::complex<double>*,
+ Index, Index, Index, std::complex<double>, Index, Index, Index, Index);
+ #if defined(EIGEN_ALTIVEC_MMA_ONLY)
+ //generate with MMA only
+ gemm_function = &Eigen::internal::gemm_complexMMA<std::complex<double>, std::complex<double>, std::complex<double>, double, Packet, Packetc, RhsPacket, DataMapper, accRows, accCols, ConjugateLhs, ConjugateRhs, false, false>;
+ #elif defined(EIGEN_ALTIVEC_MMA_DYNAMIC_DISPATCH)
+ if (__builtin_cpu_supports ("arch_3_1") && __builtin_cpu_supports ("mma")){
+ gemm_function = &Eigen::internal::gemm_complexMMA<std::complex<double>, std::complex<double>, std::complex<double>, double, Packet, Packetc, RhsPacket, DataMapper, accRows, accCols, ConjugateLhs, ConjugateRhs, false, false>;
+ }
+ else{
+ gemm_function = &Eigen::internal::gemm_complex<std::complex<double>, std::complex<double>, std::complex<double>, double, Packet, Packetc, RhsPacket, DataMapper, accRows, accCols, ConjugateLhs, ConjugateRhs, false, false>;
+ }
+ #else
+ gemm_function = &Eigen::internal::gemm_complex<std::complex<double>, std::complex<double>, std::complex<double>, double, Packet, Packetc, RhsPacket, DataMapper, accRows, accCols, ConjugateLhs, ConjugateRhs, false, false>;
+ #endif
+ gemm_function(res, blockA, blockB, rows, depth, cols, alpha, strideA, strideB, offsetA, offsetB);
+ }
+
+template<typename Index, typename DataMapper, int mr, int nr, bool ConjugateLhs, bool ConjugateRhs>
+struct gebp_kernel<std::complex<double>, double, Index, DataMapper, mr, nr, ConjugateLhs, ConjugateRhs>
+{
+ typedef quad_traits<double>::vectortype Packet;
+ typedef Packet1cd Packetc;
+ typedef quad_traits<double>::rhstype RhsPacket;
+
+ void operator()(const DataMapper& res, const std::complex<double>* blockA, const double* blockB,
+ Index rows, Index depth, Index cols, std::complex<double> alpha,
+ Index strideA=-1, Index strideB=-1, Index offsetA=0, Index offsetB=0);
+};
+
+template<typename Index, typename DataMapper, int mr, int nr, bool ConjugateLhs, bool ConjugateRhs>
+void gebp_kernel<std::complex<double>, double, Index, DataMapper, mr, nr, ConjugateLhs, ConjugateRhs>
+ ::operator()(const DataMapper& res, const std::complex<double>* blockA, const double* blockB,
+ Index rows, Index depth, Index cols, std::complex<double> alpha,
+ Index strideA, Index strideB, Index offsetA, Index offsetB)
+ {
+ const Index accRows = quad_traits<double>::rows;
+ const Index accCols = quad_traits<double>::size;
+ void (*gemm_function)(const DataMapper&, const std::complex<double>*, const double*,
+ Index, Index, Index, std::complex<double>, Index, Index, Index, Index);
+ #if defined(EIGEN_ALTIVEC_MMA_ONLY)
+ //generate with MMA only
+ gemm_function = &Eigen::internal::gemm_complexMMA<std::complex<double>, double, std::complex<double>, double, Packet, Packetc, RhsPacket, DataMapper, accRows, accCols, ConjugateLhs, ConjugateRhs, false, true>;
+ #elif defined(EIGEN_ALTIVEC_MMA_DYNAMIC_DISPATCH)
+ if (__builtin_cpu_supports ("arch_3_1") && __builtin_cpu_supports ("mma")){
+ gemm_function = &Eigen::internal::gemm_complexMMA<std::complex<double>, double, std::complex<double>, double, Packet, Packetc, RhsPacket, DataMapper, accRows, accCols, ConjugateLhs, ConjugateRhs, false, true>;
+ }
+ else{
+ gemm_function = &Eigen::internal::gemm_complex<std::complex<double>, double, std::complex<double>, double, Packet, Packetc, RhsPacket, DataMapper, accRows, accCols, ConjugateLhs, ConjugateRhs, false, true>;
+ }
+ #else
+ gemm_function = &Eigen::internal::gemm_complex<std::complex<double>, double, std::complex<double>, double, Packet, Packetc, RhsPacket, DataMapper, accRows, accCols, ConjugateLhs, ConjugateRhs, false, true>;
+ #endif
+ gemm_function(res, blockA, blockB, rows, depth, cols, alpha, strideA, strideB, offsetA, offsetB);
+ }
+
+template<typename Index, typename DataMapper, int mr, int nr, bool ConjugateLhs, bool ConjugateRhs>
+struct gebp_kernel<double, std::complex<double>, Index, DataMapper, mr, nr, ConjugateLhs, ConjugateRhs>
+{
+ typedef quad_traits<double>::vectortype Packet;
+ typedef Packet1cd Packetc;
+ typedef quad_traits<double>::rhstype RhsPacket;
+
+ void operator()(const DataMapper& res, const double* blockA, const std::complex<double>* blockB,
+ Index rows, Index depth, Index cols, std::complex<double> alpha,
+ Index strideA=-1, Index strideB=-1, Index offsetA=0, Index offsetB=0);
+};
+
+template<typename Index, typename DataMapper, int mr, int nr, bool ConjugateLhs, bool ConjugateRhs>
+void gebp_kernel<double, std::complex<double>, Index, DataMapper, mr, nr, ConjugateLhs, ConjugateRhs>
+ ::operator()(const DataMapper& res, const double* blockA, const std::complex<double>* blockB,
+ Index rows, Index depth, Index cols, std::complex<double> alpha,
+ Index strideA, Index strideB, Index offsetA, Index offsetB)
+ {
+ const Index accRows = quad_traits<double>::rows;
+ const Index accCols = quad_traits<double>::size;
+ void (*gemm_function)(const DataMapper&, const double*, const std::complex<double>*,
+ Index, Index, Index, std::complex<double>, Index, Index, Index, Index);
+ #if defined(EIGEN_ALTIVEC_MMA_ONLY)
+ //generate with MMA only
+ gemm_function = &Eigen::internal::gemm_complexMMA<double, std::complex<double>, std::complex<double>, double, Packet, Packetc, RhsPacket, DataMapper, accRows, accCols, ConjugateLhs, ConjugateRhs, true, false>;
+ #elif defined(EIGEN_ALTIVEC_MMA_DYNAMIC_DISPATCH)
+ if (__builtin_cpu_supports ("arch_3_1") && __builtin_cpu_supports ("mma")){
+ gemm_function = &Eigen::internal::gemm_complexMMA<double, std::complex<double>, std::complex<double>, double, Packet, Packetc, RhsPacket, DataMapper, accRows, accCols, ConjugateLhs, ConjugateRhs, true, false>;
+ }
+ else{
+ gemm_function = &Eigen::internal::gemm_complex<double, std::complex<double>, std::complex<double>, double, Packet, Packetc, RhsPacket, DataMapper, accRows, accCols, ConjugateLhs, ConjugateRhs, true, false>;
+ }
+ #else
+ gemm_function = &Eigen::internal::gemm_complex<double, std::complex<double>, std::complex<double>, double, Packet, Packetc, RhsPacket, DataMapper, accRows, accCols, ConjugateLhs, ConjugateRhs, true, false>;
+ #endif
+ gemm_function(res, blockA, blockB, rows, depth, cols, alpha, strideA, strideB, offsetA, offsetB);
+ }
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_MATRIX_PRODUCT_ALTIVEC_H
diff --git a/Eigen/src/Core/arch/AltiVec/MatrixProductCommon.h b/Eigen/src/Core/arch/AltiVec/MatrixProductCommon.h
new file mode 100644
index 0000000..28868ca
--- /dev/null
+++ b/Eigen/src/Core/arch/AltiVec/MatrixProductCommon.h
@@ -0,0 +1,216 @@
+//#define EIGEN_POWER_USE_PREFETCH // Use prefetching in gemm routines
+#ifdef EIGEN_POWER_USE_PREFETCH
+#define EIGEN_POWER_PREFETCH(p) prefetch(p)
+#else
+#define EIGEN_POWER_PREFETCH(p)
+#endif
+
+#ifdef _ARCH_PWR9
+#define USE_PARTIAL_PACKETS
+#endif
+
+#include "../../InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+
+template<typename Scalar, typename Packet, typename DataMapper, const Index accRows, const Index accCols>
+EIGEN_ALWAYS_INLINE void gemm_extra_row(
+ const DataMapper& res,
+ const Scalar* lhs_base,
+ const Scalar* rhs_base,
+ Index depth,
+ Index strideA,
+ Index offsetA,
+ Index strideB,
+ Index row,
+ Index rows,
+ Index remaining_rows,
+ const Packet& pAlpha,
+ const Packet& pMask);
+
+template<typename Scalar, typename Packet, typename DataMapper, const Index accCols, bool ConjugateLhs, bool ConjugateRhs, bool LhsIsReal, bool RhsIsReal>
+EIGEN_STRONG_INLINE void gemm_extra_cols(
+ const DataMapper& res,
+ const Scalar* blockA,
+ const Scalar* blockB,
+ Index depth,
+ Index strideA,
+ Index offsetA,
+ Index strideB,
+ Index offsetB,
+ Index col,
+ Index rows,
+ Index cols,
+ Index remaining_rows,
+ const Packet& pAlpha,
+ const Packet& pMask);
+
+template<typename Packet>
+EIGEN_ALWAYS_INLINE Packet bmask(const Index remaining_rows);
+
+template<typename Scalar, typename Packet, typename Packetc, typename DataMapper, const Index accRows, const Index accCols, bool ConjugateLhs, bool ConjugateRhs, bool LhsIsReal, bool RhsIsReal>
+EIGEN_ALWAYS_INLINE void gemm_complex_extra_row(
+ const DataMapper& res,
+ const Scalar* lhs_base,
+ const Scalar* rhs_base,
+ Index depth,
+ Index strideA,
+ Index offsetA,
+ Index strideB,
+ Index row,
+ Index rows,
+ Index remaining_rows,
+ const Packet& pAlphaReal,
+ const Packet& pAlphaImag,
+ const Packet& pMask);
+
+template<typename Scalar, typename Packet, typename Packetc, typename DataMapper, const Index accCols, bool ConjugateLhs, bool ConjugateRhs, bool LhsIsReal, bool RhsIsReal>
+EIGEN_STRONG_INLINE void gemm_complex_extra_cols(
+ const DataMapper& res,
+ const Scalar* blockA,
+ const Scalar* blockB,
+ Index depth,
+ Index strideA,
+ Index offsetA,
+ Index strideB,
+ Index offsetB,
+ Index col,
+ Index rows,
+ Index cols,
+ Index remaining_rows,
+ const Packet& pAlphaReal,
+ const Packet& pAlphaImag,
+ const Packet& pMask);
+
+template<typename Packet>
+EIGEN_ALWAYS_INLINE Packet ploadLhs(const __UNPACK_TYPE__(Packet)* lhs);
+
+template<typename DataMapper, typename Packet, const Index accCols, int StorageOrder, bool Complex, int N, bool full = true>
+EIGEN_ALWAYS_INLINE void bload(PacketBlock<Packet,N*(Complex?2:1)>& acc, const DataMapper& res, Index row, Index col);
+
+template<typename DataMapper, typename Packet, int N>
+EIGEN_ALWAYS_INLINE void bstore(PacketBlock<Packet,N>& acc, const DataMapper& res, Index row);
+
+#ifdef USE_PARTIAL_PACKETS
+template<typename DataMapper, typename Packet, const Index accCols, bool Complex, Index N, bool full = true>
+EIGEN_ALWAYS_INLINE void bload_partial(PacketBlock<Packet,N*(Complex?2:1)>& acc, const DataMapper& res, Index row, Index elements);
+
+template<typename DataMapper, typename Packet, Index N>
+EIGEN_ALWAYS_INLINE void bstore_partial(PacketBlock<Packet,N>& acc, const DataMapper& res, Index row, Index elements);
+#endif
+
+template<typename Packet, int N>
+EIGEN_ALWAYS_INLINE void bscale(PacketBlock<Packet,N>& acc, PacketBlock<Packet,N>& accZ, const Packet& pAlpha);
+
+template<typename Packet, int N, bool mask>
+EIGEN_ALWAYS_INLINE void bscale(PacketBlock<Packet,N>& acc, PacketBlock<Packet,N>& accZ, const Packet& pAlpha, const Packet& pMask);
+
+template<typename Packet, int N, bool mask>
+EIGEN_ALWAYS_INLINE void bscalec(PacketBlock<Packet,N>& aReal, PacketBlock<Packet,N>& aImag, const Packet& bReal, const Packet& bImag, PacketBlock<Packet,N>& cReal, PacketBlock<Packet,N>& cImag, const Packet& pMask);
+
+template<typename Packet, typename Packetc, int N, bool full>
+EIGEN_ALWAYS_INLINE void bcouple(PacketBlock<Packet,N>& taccReal, PacketBlock<Packet,N>& taccImag, PacketBlock<Packetc,N*2>& tRes, PacketBlock<Packetc, N>& acc1, PacketBlock<Packetc, N>& acc2);
+
+#define MICRO_NORMAL(iter) \
+ (accCols == accCols2) || (unroll_factor != (iter + 1))
+
+#define MICRO_UNROLL_ITER1(func, N) \
+ switch (remaining_rows) { \
+ default: \
+ func(N, 0) \
+ break; \
+ case 1: \
+ func(N, 1) \
+ break; \
+ case 2: \
+ if (sizeof(Scalar) == sizeof(float)) { \
+ func(N, 2) \
+ } \
+ break; \
+ case 3: \
+ if (sizeof(Scalar) == sizeof(float)) { \
+ func(N, 3) \
+ } \
+ break; \
+ }
+
+#ifdef USE_PARTIAL_PACKETS
+#define MICRO_UNROLL_ITER(func, N) \
+ if (remaining_rows) { \
+ func(N, true); \
+ } else { \
+ func(N, false); \
+ }
+
+#define MICRO_NORMAL_PARTIAL(iter) \
+ full || (unroll_factor != (iter + 1))
+#else
+#define MICRO_UNROLL_ITER(func, N) MICRO_UNROLL_ITER1(func, N)
+#endif
+
+#define MICRO_COMPLEX_UNROLL_ITER(func, N) MICRO_UNROLL_ITER1(func, N)
+
+#define MICRO_NORMAL_COLS(iter, a, b) ((MICRO_NORMAL(iter)) ? a : b)
+
+#define MICRO_LOAD1(lhs_ptr, iter) \
+ if (unroll_factor > iter) { \
+ lhsV##iter = ploadLhs<Packet>(lhs_ptr##iter); \
+ lhs_ptr##iter += MICRO_NORMAL_COLS(iter, accCols, accCols2); \
+ } else { \
+ EIGEN_UNUSED_VARIABLE(lhsV##iter); \
+ }
+
+#define MICRO_LOAD_ONE(iter) MICRO_LOAD1(lhs_ptr, iter)
+
+#define MICRO_COMPLEX_LOAD_ONE(iter) \
+ if (!LhsIsReal && (unroll_factor > iter)) { \
+ lhsVi##iter = ploadLhs<Packet>(lhs_ptr_real##iter + MICRO_NORMAL_COLS(iter, imag_delta, imag_delta2)); \
+ } else { \
+ EIGEN_UNUSED_VARIABLE(lhsVi##iter); \
+ } \
+ MICRO_LOAD1(lhs_ptr_real, iter) \
+
+#define MICRO_SRC_PTR1(lhs_ptr, advRows, iter) \
+ if (unroll_factor > iter) { \
+ lhs_ptr##iter = lhs_base + (row+(iter*accCols))*strideA*advRows - MICRO_NORMAL_COLS(iter, 0, (accCols-accCols2)*offsetA); \
+ } else { \
+ EIGEN_UNUSED_VARIABLE(lhs_ptr##iter); \
+ }
+
+#define MICRO_SRC_PTR_ONE(iter) MICRO_SRC_PTR1(lhs_ptr, 1, iter)
+
+#define MICRO_COMPLEX_SRC_PTR_ONE(iter) MICRO_SRC_PTR1(lhs_ptr_real, advanceRows, iter)
+
+#define MICRO_PREFETCH1(lhs_ptr, iter) \
+ if (unroll_factor > iter) { \
+ EIGEN_POWER_PREFETCH(lhs_ptr##iter); \
+ }
+
+#define MICRO_PREFETCH_ONE(iter) MICRO_PREFETCH1(lhs_ptr, iter)
+
+#define MICRO_COMPLEX_PREFETCH_ONE(iter) MICRO_PREFETCH1(lhs_ptr_real, iter)
+
+#ifdef USE_PARTIAL_PACKETS
+#define MICRO_UPDATE_MASK
+#else
+#define MICRO_UPDATE_MASK EIGEN_UNUSED_VARIABLE(pMask);
+#endif
+
+#define MICRO_UPDATE \
+ if (accCols == accCols2) { \
+ MICRO_UPDATE_MASK \
+ EIGEN_UNUSED_VARIABLE(offsetA); \
+ row += unroll_factor*accCols; \
+ }
+
+#define MICRO_COMPLEX_UPDATE \
+ MICRO_UPDATE \
+ if(LhsIsReal || (accCols == accCols2)) { \
+ EIGEN_UNUSED_VARIABLE(imag_delta2); \
+ }
+
+
+} // end namespace internal
+} // end namespace Eigen
diff --git a/Eigen/src/Core/arch/AltiVec/MatrixProductMMA.h b/Eigen/src/Core/arch/AltiVec/MatrixProductMMA.h
new file mode 100644
index 0000000..aa1cbf8
--- /dev/null
+++ b/Eigen/src/Core/arch/AltiVec/MatrixProductMMA.h
@@ -0,0 +1,755 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2020 Everton Constantino (everton.constantino@ibm.com)
+// Copyright (C) 2021 Chip Kerchner (chip.kerchner@ibm.com)
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_MATRIX_PRODUCT_MMA_ALTIVEC_H
+#define EIGEN_MATRIX_PRODUCT_MMA_ALTIVEC_H
+
+// If using dynamic dispatch, set the CPU target.
+#if defined(EIGEN_ALTIVEC_MMA_DYNAMIC_DISPATCH)
+#pragma GCC push_options
+#pragma GCC target("cpu=power10,htm")
+#endif
+
+#ifdef __has_builtin
+#if !__has_builtin(__builtin_vsx_assemble_pair)
+#define __builtin_vsx_assemble_pair __builtin_mma_assemble_pair
+#endif
+#if !__has_builtin(__builtin_vsx_disassemble_pair)
+#define __builtin_vsx_disassemble_pair __builtin_mma_disassemble_pair
+#endif
+#endif
+
+#include "../../InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+
+#define accColsC (accCols / 2)
+
+EIGEN_ALWAYS_INLINE void bsetzeroMMA(__vector_quad* acc)
+{
+ __builtin_mma_xxsetaccz(acc);
+}
+
+#ifdef USE_PARTIAL_PACKETS
+template<typename DataMapper, typename Packet, bool full>
+EIGEN_ALWAYS_INLINE void storeAccumulator(Index i, const DataMapper& data, const Packet& alpha, const Index elements, __vector_quad* acc)
+#else
+template<typename DataMapper, typename Packet, const Index accCols, const Index accCols2>
+EIGEN_ALWAYS_INLINE void storeAccumulator(Index i, const DataMapper& data, const Packet& alpha, const Packet& pMask, __vector_quad* acc)
+#endif
+{
+ PacketBlock<Packet, 4> result;
+ __builtin_mma_disassemble_acc(&result.packet, acc);
+
+ PacketBlock<Packet, 4> tRes;
+#ifdef USE_PARTIAL_PACKETS
+ if (full) {
+ EIGEN_UNUSED_VARIABLE(elements);
+ bload<DataMapper, Packet, 0, ColMajor, false, 4>(tRes, data, i, 0);
+ bscale<Packet, 4>(tRes, result, alpha);
+ bstore<DataMapper, Packet, 4>(tRes, data, i);
+ } else {
+ bload_partial<DataMapper, Packet, 0, false, 4>(tRes, data, i, elements);
+ bscale<Packet, 4>(tRes, result, alpha);
+ bstore_partial<DataMapper, Packet, 4>(tRes, data, i, elements);
+ }
+#else
+ bload<DataMapper, Packet, 0, ColMajor, false, 4>(tRes, data, i, 0);
+ bscale<Packet, 4, (accCols != accCols2)>(tRes, result, alpha, pMask);
+ bstore<DataMapper, Packet, 4>(tRes, data, i);
+#endif
+}
+
+template<typename DataMapper, typename Packet, typename Packetc, const Index accCols, const Index accCols2>
+EIGEN_ALWAYS_INLINE void storeComplexAccumulator(Index i, const DataMapper& data, const Packet& alphaReal, const Packet& alphaImag, const Packet& pMask, __vector_quad* accReal, __vector_quad* accImag)
+{
+ constexpr bool full = (accCols2 > accColsC);
+ PacketBlock<Packet, 4> resultReal, resultImag;
+ __builtin_mma_disassemble_acc(&resultReal.packet, accReal);
+ __builtin_mma_disassemble_acc(&resultImag.packet, accImag);
+
+ PacketBlock<Packetc, 8> tRes;
+ bload<DataMapper, Packetc, accColsC, ColMajor, true, 4, full>(tRes, data, i, 0);
+
+ PacketBlock<Packet, 4> taccReal, taccImag;
+ bscalec<Packet, 4, (accCols != accCols2)>(resultReal, resultImag, alphaReal, alphaImag, taccReal, taccImag, pMask);
+
+ PacketBlock<Packetc, 4> acc1, acc2;
+ bcouple<Packet, Packetc, 4, full>(taccReal, taccImag, tRes, acc1, acc2);
+
+ bstore<DataMapper, Packetc, 4>(acc1, data, i);
+ if (full) {
+ bstore<DataMapper, Packetc, 4>(acc2, data, i + accColsC);
+ }
+}
+
+// Defaults to float32, since Eigen still supports C++03 we can't use default template arguments
+template<typename LhsPacket, typename RhsPacket, bool NegativeAccumulate>
+EIGEN_ALWAYS_INLINE void pgerMMA(__vector_quad* acc, const RhsPacket& a, const LhsPacket& b)
+{
+ if(NegativeAccumulate)
+ {
+ __builtin_mma_xvf32gernp(acc, (__vector unsigned char)a, (__vector unsigned char)b);
+ } else {
+ __builtin_mma_xvf32gerpp(acc, (__vector unsigned char)a, (__vector unsigned char)b);
+ }
+}
+
+template<typename LhsPacket, typename RhsPacket, bool NegativeAccumulate>
+EIGEN_ALWAYS_INLINE void pgerMMA(__vector_quad* acc, const __vector_pair& a, const Packet2d& b)
+{
+ if(NegativeAccumulate)
+ {
+ __builtin_mma_xvf64gernp(acc, (__vector_pair)a, (__vector unsigned char)b);
+ } else {
+ __builtin_mma_xvf64gerpp(acc, (__vector_pair)a, (__vector unsigned char)b);
+ }
+}
+
+template<typename Packet, typename RhsPacket, bool ConjugateLhs, bool ConjugateRhs, bool LhsIsReal, bool RhsIsReal>
+EIGEN_ALWAYS_INLINE void pgercMMA(__vector_quad* accReal, __vector_quad* accImag, const Packet& lhsV, Packet& lhsVi, const RhsPacket& rhsV, RhsPacket& rhsVi)
+{
+ pgerMMA<Packet, RhsPacket, false>(accReal, rhsV, lhsV);
+ if(LhsIsReal) {
+ pgerMMA<Packet, RhsPacket, ConjugateRhs>(accImag, rhsVi, lhsV);
+ EIGEN_UNUSED_VARIABLE(lhsVi);
+ } else {
+ if(!RhsIsReal) {
+ pgerMMA<Packet, RhsPacket, ConjugateLhs == ConjugateRhs>(accReal, rhsVi, lhsVi);
+ pgerMMA<Packet, RhsPacket, ConjugateRhs>(accImag, rhsVi, lhsV);
+ } else {
+ EIGEN_UNUSED_VARIABLE(rhsVi);
+ }
+ pgerMMA<Packet, RhsPacket, ConjugateLhs>(accImag, rhsV, lhsVi);
+ }
+}
+
+// This is necessary because ploadRhs for double returns a pair of vectors when MMA is enabled.
+template<typename Packet>
+EIGEN_ALWAYS_INLINE Packet ploadRhs(const __UNPACK_TYPE__(Packet)* rhs)
+{
+ return ploadu<Packet>(rhs);
+}
+
+template<typename Scalar, typename Packet>
+EIGEN_ALWAYS_INLINE void ploadRhsMMA(const Scalar* rhs, Packet& rhsV)
+{
+ rhsV = ploadRhs<Packet>(rhs);
+}
+
+template<>
+EIGEN_ALWAYS_INLINE void ploadRhsMMA(const double* rhs, __vector_pair& rhsV)
+{
+#if EIGEN_COMP_LLVM
+ __builtin_vsx_assemble_pair(&rhsV,
+ reinterpret_cast<__vector unsigned char>(ploadRhs<Packet2d>(rhs + (sizeof(Packet2d) / sizeof(double)))),
+ reinterpret_cast<__vector unsigned char>(ploadRhs<Packet2d>(rhs)));
+#else
+ rhsV = *reinterpret_cast<__vector_pair *>(const_cast<double *>(rhs));
+#endif
+}
+
+EIGEN_ALWAYS_INLINE void ploadLhsMMA(const double* lhs, __vector_pair& lhsV)
+{
+ ploadRhsMMA(lhs, lhsV);
+}
+
+#if (EIGEN_COMP_LLVM || (__GNUC__ >= 11))
+#define VECTOR_PAIR_LOADS_LHS
+#endif
+
+// PEEL_MMA loop factor.
+#define PEEL_MMA 7
+
+#define MICRO_MMA_UNROLL(func) \
+ func(0) func(1) func(2) func(3) func(4) func(5) func(6) func(7)
+
+#define MICRO_MMA_WORK(func, type, peel) \
+ func(0,type,peel) func(1,type,peel) func(2,type,peel) func(3,type,peel) \
+ func(4,type,peel) func(5,type,peel) func(6,type,peel) func(7,type,peel)
+
+#define MICRO_MMA_WORK_ONE(iter, type, peel) \
+ if (unroll_factor > iter) { \
+ pgerMMA<Packet, type, false>(&accZero##iter, rhsV[peel], lhsV##iter); \
+ }
+
+#ifdef VECTOR_PAIR_LOADS_LHS
+#define MICRO_MMA_WORK_TWO(iter, type, peel) \
+ if (unroll_factor > iter) { \
+ pgerMMA<Packet, type, false>(&accZero##iter, rhsV[peel], lhsV2##iter.packet[peel & 1]); \
+ }
+
+#define MICRO_MMA_LOAD1_TWO(lhs_ptr, iter) \
+ if (unroll_factor > iter) { \
+ if (MICRO_NORMAL(iter)) { \
+ ploadLhsMMA(reinterpret_cast<const double*>(lhs_ptr##iter), plhsV##iter); \
+ __builtin_vsx_disassemble_pair(reinterpret_cast<void*>(&lhsV2##iter.packet), &plhsV##iter); \
+ lhs_ptr##iter += accCols*2; \
+ } else { \
+ lhsV2##iter.packet[0] = ploadLhs<Packet>(lhs_ptr##iter); \
+ lhsV2##iter.packet[1] = ploadLhs<Packet>(lhs_ptr##iter + accCols2); \
+ lhs_ptr##iter += accCols2*2; \
+ EIGEN_UNUSED_VARIABLE(plhsV##iter) \
+ } \
+ } else { \
+ EIGEN_UNUSED_VARIABLE(lhsV2##iter); \
+ EIGEN_UNUSED_VARIABLE(plhsV##iter) \
+ }
+
+#define MICRO_MMA_LOAD_TWO(iter) MICRO_MMA_LOAD1_TWO(lhs_ptr, iter)
+#endif
+
+#define MICRO_MMA_TYPE_PEEL(funcw, funcl, type, peel) \
+ if (PEEL_MMA > peel) { \
+ Packet lhsV0, lhsV1, lhsV2, lhsV3, lhsV4, lhsV5, lhsV6, lhsV7; \
+ ploadRhsMMA(rhs_ptr + (accRows * peel), rhsV[peel]); \
+ MICRO_MMA_UNROLL(funcl) \
+ MICRO_MMA_WORK(funcw, type, peel) \
+ }
+
+#ifndef VECTOR_PAIR_LOADS_LHS
+#define MICRO_MMA_UNROLL_TYPE_PEEL(funcw, funcl, type) \
+ type rhsV[8]; \
+ MICRO_MMA_TYPE_PEEL(funcw,funcl,type,0) MICRO_MMA_TYPE_PEEL(funcw,funcl,type,1) \
+ MICRO_MMA_TYPE_PEEL(funcw,funcl,type,2) MICRO_MMA_TYPE_PEEL(funcw,funcl,type,3) \
+ MICRO_MMA_TYPE_PEEL(funcw,funcl,type,4) MICRO_MMA_TYPE_PEEL(funcw,funcl,type,5) \
+ MICRO_MMA_TYPE_PEEL(funcw,funcl,type,6) MICRO_MMA_TYPE_PEEL(funcw,funcl,type,7)
+#else
+#define MICRO_MMA_TYPE_PEEL2(funcw1, funcl1, funcw2, funcl2, type, peel1, peel2) \
+ if (PEEL_MMA > peel2) { \
+ PacketBlock<Packet,2> lhsV20, lhsV21, lhsV22, lhsV23, lhsV24, lhsV25, lhsV26, lhsV27; \
+ __vector_pair plhsV0, plhsV1, plhsV2, plhsV3, plhsV4, plhsV5, plhsV6, plhsV7; \
+ if (sizeof(type) == 16) { \
+ ploadRhsMMA(reinterpret_cast<const double*>(rhs_ptr + (accRows * peel1)), prhsV##peel1); \
+ __builtin_vsx_disassemble_pair(reinterpret_cast<void*>(&rhsV[peel1]), &prhsV##peel1); \
+ } else { \
+ EIGEN_UNUSED_VARIABLE(prhsV##peel1); \
+ ploadRhsMMA(rhs_ptr + (accRows * peel1), rhsV[peel1]); \
+ ploadRhsMMA(rhs_ptr + (accRows * peel2), rhsV[peel2]); \
+ } \
+ MICRO_MMA_UNROLL(funcl2) \
+ MICRO_MMA_WORK(funcw2, type, peel1) \
+ MICRO_MMA_WORK(funcw2, type, peel2) \
+ } else { \
+ EIGEN_UNUSED_VARIABLE(prhsV##peel1); \
+ MICRO_MMA_TYPE_PEEL(funcw1, funcl1, type, peel1) \
+ }
+
+#define MICRO_MMA_UNROLL_TYPE_PEEL2(funcw1, funcl1, funcw2, funcl2, type) \
+ type rhsV[8]; \
+ __vector_pair prhsV0, prhsV2, prhsV4, prhsV6; \
+ MICRO_MMA_TYPE_PEEL2(funcw1,funcl1,funcw2,funcl2,type,0,1) \
+ MICRO_MMA_TYPE_PEEL2(funcw1,funcl1,funcw2,funcl2,type,2,3) \
+ MICRO_MMA_TYPE_PEEL2(funcw1,funcl1,funcw2,funcl2,type,4,5) \
+ MICRO_MMA_TYPE_PEEL2(funcw1,funcl1,funcw2,funcl2,type,6,7)
+#endif
+
+#define MICRO_MMA_UNROLL_TYPE_ONE(funcw, funcl, type) \
+ type rhsV[1]; \
+ MICRO_MMA_TYPE_PEEL(funcw,funcl,type,0)
+
+#define MICRO_MMA_UNROLL_TYPE(MICRO_MMA_TYPE, size) \
+ MICRO_MMA_TYPE(MICRO_MMA_WORK_ONE, MICRO_LOAD_ONE, RhsPacket) \
+ rhs_ptr += (accRows * size);
+
+#ifndef VECTOR_PAIR_LOADS_LHS
+#define MICRO_MMA_ONE_PEEL MICRO_MMA_UNROLL_TYPE(MICRO_MMA_UNROLL_TYPE_PEEL, PEEL_MMA)
+#else
+#define MICRO_MMA_UNROLL_TYPE2(MICRO_MMA_TYPE, size) \
+ MICRO_MMA_TYPE(MICRO_MMA_WORK_ONE, MICRO_LOAD_ONE, MICRO_MMA_WORK_TWO, MICRO_MMA_LOAD_TWO, RhsPacket) \
+ rhs_ptr += (accRows * size);
+
+#define MICRO_MMA_ONE_PEEL MICRO_MMA_UNROLL_TYPE2(MICRO_MMA_UNROLL_TYPE_PEEL2, PEEL_MMA)
+#endif
+
+#define MICRO_MMA_ONE MICRO_MMA_UNROLL_TYPE(MICRO_MMA_UNROLL_TYPE_ONE, 1)
+
+#define MICRO_MMA_DST_PTR_ONE(iter) \
+ if (unroll_factor > iter) { \
+ bsetzeroMMA(&accZero##iter); \
+ } else { \
+ EIGEN_UNUSED_VARIABLE(accZero##iter); \
+ }
+
+#define MICRO_MMA_DST_PTR MICRO_MMA_UNROLL(MICRO_MMA_DST_PTR_ONE)
+
+#define MICRO_MMA_SRC_PTR MICRO_MMA_UNROLL(MICRO_SRC_PTR_ONE)
+
+#define MICRO_MMA_PREFETCH MICRO_MMA_UNROLL(MICRO_PREFETCH_ONE)
+
+#ifdef USE_PARTIAL_PACKETS
+#define MICRO_MMA_STORE_ONE(iter) \
+ if (unroll_factor > iter) { \
+ storeAccumulator<DataMapper, Packet, MICRO_NORMAL_PARTIAL(iter)>(row + iter*accCols, res, pAlpha, accCols2, &accZero##iter); \
+ }
+#else
+#define MICRO_MMA_STORE_ONE(iter) \
+ if (unroll_factor > iter) { \
+ storeAccumulator<DataMapper, Packet, accCols, (unroll_factor != (iter + 1)) ? accCols : accCols2>(row + iter*accCols, res, pAlpha, pMask, &accZero##iter); \
+ }
+#endif
+
+#define MICRO_MMA_STORE MICRO_MMA_UNROLL(MICRO_MMA_STORE_ONE)
+
+#ifdef USE_PARTIAL_PACKETS
+template<int unroll_factor, typename Scalar, typename Packet, typename RhsPacket, typename DataMapper, const Index accRows, const Index accCols, bool full>
+#else
+template<int unroll_factor, typename Scalar, typename Packet, typename RhsPacket, typename DataMapper, const Index accRows, const Index accCols, const Index accCols2>
+#endif
+EIGEN_ALWAYS_INLINE void gemm_unrolled_MMA_iteration(
+ const DataMapper& res,
+ const Scalar* lhs_base,
+ const Scalar* rhs_base,
+ Index depth,
+ Index strideA,
+ Index offsetA,
+ Index& row,
+ const Packet& pAlpha,
+#ifdef USE_PARTIAL_PACKETS
+ Index accCols2
+#else
+ const Packet& pMask
+#endif
+ )
+{
+ const Scalar* rhs_ptr = rhs_base;
+ const Scalar* lhs_ptr0 = NULL, * lhs_ptr1 = NULL, * lhs_ptr2 = NULL, * lhs_ptr3 = NULL, * lhs_ptr4 = NULL, * lhs_ptr5 = NULL, * lhs_ptr6 = NULL, * lhs_ptr7 = NULL;
+ __vector_quad accZero0, accZero1, accZero2, accZero3, accZero4, accZero5, accZero6, accZero7;
+
+ MICRO_MMA_SRC_PTR
+ MICRO_MMA_DST_PTR
+
+ Index k = 0, depth2 = depth - PEEL_MMA;
+ for(; k <= depth2; k += PEEL_MMA)
+ {
+ EIGEN_POWER_PREFETCH(rhs_ptr);
+ MICRO_MMA_PREFETCH
+ MICRO_MMA_ONE_PEEL
+ }
+ for(; k < depth; k++)
+ {
+ MICRO_MMA_ONE
+ }
+ MICRO_MMA_STORE
+
+ MICRO_UPDATE
+}
+
+#ifdef USE_PARTIAL_PACKETS
+#define MICRO_MMA_UNROLL_ITER2(N, M) \
+ gemm_unrolled_MMA_iteration<N + (M ? 1 : 0), Scalar, Packet, RhsPacket, DataMapper, accRows, accCols, !M>(res3, lhs_base, rhs_base, depth, strideA, offsetA, row, pAlpha, M ? remaining_rows : accCols); \
+ if (M) return;
+#else
+#define MICRO_MMA_UNROLL_ITER2(N, M) \
+ gemm_unrolled_MMA_iteration<N + (M ? 1 : 0), Scalar, Packet, RhsPacket, DataMapper, accRows, accCols, M ? M : accCols>(res3, lhs_base, rhs_base, depth, strideA, offsetA, row, pAlpha, pMask); \
+ if (M) return;
+#endif
+
+template<typename Scalar, typename Packet, typename RhsPacket, typename DataMapper, const Index accRows, const Index accCols>
+EIGEN_ALWAYS_INLINE void gemmMMA_cols(
+ const DataMapper& res,
+ const Scalar* blockA,
+ const Scalar* blockB,
+ Index depth,
+ Index strideA,
+ Index offsetA,
+ Index strideB,
+ Index offsetB,
+ Index col,
+ Index rows,
+ Index remaining_rows,
+ const Packet& pAlpha,
+ const Packet& pMask)
+{
+ const DataMapper res3 = res.getSubMapper(0, col);
+
+ const Scalar* rhs_base = blockB + col*strideB + accRows*offsetB;
+ const Scalar* lhs_base = blockA + accCols*offsetA;
+ Index row = 0;
+
+#define MAX_MMA_UNROLL 7
+ while(row + MAX_MMA_UNROLL*accCols <= rows) {
+ MICRO_MMA_UNROLL_ITER2(MAX_MMA_UNROLL, 0);
+ }
+ switch( (rows-row)/accCols ) {
+#if MAX_MMA_UNROLL > 7
+ case 7:
+ MICRO_UNROLL_ITER(MICRO_MMA_UNROLL_ITER2, 7)
+ break;
+#endif
+#if MAX_MMA_UNROLL > 6
+ case 6:
+ MICRO_UNROLL_ITER(MICRO_MMA_UNROLL_ITER2, 6)
+ break;
+#endif
+#if MAX_MMA_UNROLL > 5
+ case 5:
+ MICRO_UNROLL_ITER(MICRO_MMA_UNROLL_ITER2, 5)
+ break;
+#endif
+#if MAX_MMA_UNROLL > 4
+ case 4:
+ MICRO_UNROLL_ITER(MICRO_MMA_UNROLL_ITER2, 4)
+ break;
+#endif
+#if MAX_MMA_UNROLL > 3
+ case 3:
+ MICRO_UNROLL_ITER(MICRO_MMA_UNROLL_ITER2, 3)
+ break;
+#endif
+#if MAX_MMA_UNROLL > 2
+ case 2:
+ MICRO_UNROLL_ITER(MICRO_MMA_UNROLL_ITER2, 2)
+ break;
+#endif
+#if MAX_MMA_UNROLL > 1
+ case 1:
+ MICRO_UNROLL_ITER(MICRO_MMA_UNROLL_ITER2, 1)
+ break;
+#endif
+ default:
+ break;
+ }
+#undef MAX_MMA_UNROLL
+
+ if(remaining_rows > 0)
+ {
+ gemm_extra_row<Scalar, Packet, DataMapper, accRows, accCols>(res3, blockA, rhs_base, depth, strideA, offsetA, strideB, row, rows, remaining_rows, pAlpha, pMask);
+ }
+}
+
+template<typename Scalar, typename Packet, typename RhsPacket, typename DataMapper, const Index accRows, const Index accCols>
+void gemmMMA(const DataMapper& res, const Scalar* blockA, const Scalar* blockB, Index rows, Index depth, Index cols, Scalar alpha, Index strideA, Index strideB, Index offsetA, Index offsetB)
+{
+ const Index remaining_rows = rows % accCols;
+
+ if( strideA == -1 ) strideA = depth;
+ if( strideB == -1 ) strideB = depth;
+
+ const Packet pAlpha = pset1<Packet>(alpha);
+ const Packet pMask = bmask<Packet>(remaining_rows);
+
+ typedef typename std::conditional_t<(sizeof(Scalar) == sizeof(float)), RhsPacket, __vector_pair> RhsPacket2;
+
+ Index col = 0;
+ for(; col + accRows <= cols; col += accRows)
+ {
+ gemmMMA_cols<Scalar, Packet, RhsPacket2, DataMapper, accRows, accCols>(res, blockA, blockB, depth, strideA, offsetA, strideB, offsetB, col, rows, remaining_rows, pAlpha, pMask);
+ }
+
+ if (col != cols)
+ {
+ gemm_extra_cols<Scalar, Packet, DataMapper, accCols>(res, blockA, blockB, depth, strideA, offsetA, strideB, offsetB, col, rows, cols, remaining_rows, pAlpha, pMask);
+ }
+}
+
+#define advanceRows ((LhsIsReal) ? 1 : 2)
+#define advanceCols ((RhsIsReal) ? 1 : 2)
+
+// PEEL_COMPLEX_MMA loop factor.
+#define PEEL_COMPLEX_MMA 3
+
+#define MICRO_COMPLEX_MMA_UNROLL(func) \
+ func(0) func(1) func(2) func(3)
+
+#define MICRO_COMPLEX_MMA_WORK(func, type, peel) \
+ func(0,type,peel) func(1,type,peel) func(2,type,peel) func(3,type,peel)
+
+#define MICRO_COMPLEX_MMA_WORK_ONE(iter, type, peel) \
+ if (unroll_factor > iter) { \
+ pgercMMA<Packet, type, ConjugateLhs, ConjugateRhs, LhsIsReal, RhsIsReal>(&accReal##iter, &accImag##iter, lhsV##iter, lhsVi##iter, rhsV[peel], rhsVi[peel]); \
+ }
+
+#ifdef VECTOR_PAIR_LOADS_LHS
+#define MICRO_COMPLEX_MMA_WORK_TWO(iter, type, peel) \
+ if (unroll_factor > iter) { \
+ pgercMMA<Packet, type, ConjugateLhs, ConjugateRhs, LhsIsReal, RhsIsReal>(&accReal##iter, &accImag##iter, lhsV2##iter.packet[peel & 1], lhsVi2##iter.packet[peel & 1], rhsV[peel], rhsVi[peel]); \
+ }
+
+#define MICRO_COMPLEX_MMA_LOAD1_TWO(lhs_ptr, iter) \
+ if (!LhsIsReal && (unroll_factor > iter)) { \
+ if (MICRO_NORMAL(iter)) { \
+ ploadLhsMMA(reinterpret_cast<const double*>(lhs_ptr_real##iter + imag_delta), plhsVi##iter); \
+ __builtin_vsx_disassemble_pair(reinterpret_cast<void*>(&lhsVi2##iter.packet), &plhsVi##iter); \
+ } else { \
+ lhsVi2##iter.packet[0] = ploadLhs<Packet>(lhs_ptr_real##iter + imag_delta2); \
+ lhsVi2##iter.packet[1] = ploadLhs<Packet>(lhs_ptr_real##iter + imag_delta2 + accCols2); \
+ EIGEN_UNUSED_VARIABLE(plhsVi##iter) \
+ } \
+ } else { \
+ EIGEN_UNUSED_VARIABLE(lhsVi2##iter); \
+ EIGEN_UNUSED_VARIABLE(plhsVi##iter) \
+ } \
+ MICRO_MMA_LOAD1_TWO(lhs_ptr_real, iter)
+
+#define MICRO_COMPLEX_MMA_LOAD_TWO(iter) MICRO_COMPLEX_MMA_LOAD1_TWO(lhs_ptr, iter)
+#endif
+
+#define MICRO_COMPLEX_MMA_TYPE_PEEL(funcw, funcl, type, peel) \
+ if (PEEL_COMPLEX_MMA > peel) { \
+ Packet lhsV0, lhsV1, lhsV2, lhsV3; \
+ Packet lhsVi0, lhsVi1, lhsVi2, lhsVi3; \
+ ploadRhsMMA(rhs_ptr_real + (accRows * peel), rhsV[peel]); \
+ if(!RhsIsReal) { \
+ ploadRhsMMA(rhs_ptr_imag + (accRows * peel), rhsVi[peel]); \
+ } \
+ MICRO_COMPLEX_MMA_UNROLL(funcl) \
+ MICRO_COMPLEX_MMA_WORK(funcw, type, peel) \
+ }
+
+#ifndef VECTOR_PAIR_LOADS_LHS
+#define MICRO_COMPLEX_MMA_UNROLL_TYPE_PEEL(funcw, funcl, type) \
+ type rhsV[4], rhsVi[4]; \
+ MICRO_COMPLEX_MMA_TYPE_PEEL(funcw,funcl,type,0) MICRO_COMPLEX_MMA_TYPE_PEEL(funcw,funcl,type,1) \
+ MICRO_COMPLEX_MMA_TYPE_PEEL(funcw,funcl,type,2) MICRO_COMPLEX_MMA_TYPE_PEEL(funcw,funcl,type,3)
+#else
+#define MICRO_COMPLEX_MMA_TYPE_PEEL2(funcw1, funcl1, funcw2, funcl2, type, peel1, peel2) \
+ if (PEEL_COMPLEX_MMA > peel2) { \
+ PacketBlock<Packet,2> lhsV20, lhsV21, lhsV22, lhsV23; \
+ PacketBlock<Packet,2> lhsVi20, lhsVi21, lhsVi22, lhsVi23; \
+ __vector_pair plhsV0, plhsV1, plhsV2, plhsV3; \
+ __vector_pair plhsVi0, plhsVi1, plhsVi2, plhsVi3; \
+ if (sizeof(type) == 16) { \
+ ploadRhsMMA(reinterpret_cast<const double*>(rhs_ptr_real + (accRows * peel1)), prhsV##peel1); \
+ __builtin_vsx_disassemble_pair(reinterpret_cast<void*>(&rhsV[peel1]), &prhsV##peel1); \
+ if(!RhsIsReal) { \
+ ploadRhsMMA(reinterpret_cast<const double*>(rhs_ptr_imag + (accRows * peel1)), prhsVi##peel1); \
+ __builtin_vsx_disassemble_pair(reinterpret_cast<void*>(&rhsVi[peel1]), &prhsVi##peel1); \
+ } else { \
+ EIGEN_UNUSED_VARIABLE(prhsVi##peel1); \
+ } \
+ } else { \
+ EIGEN_UNUSED_VARIABLE(prhsV##peel1); \
+ EIGEN_UNUSED_VARIABLE(prhsVi##peel1); \
+ ploadRhsMMA(rhs_ptr_real + (accRows * peel1), rhsV[peel1]); \
+ ploadRhsMMA(rhs_ptr_real + (accRows * peel2), rhsV[peel2]); \
+ if(!RhsIsReal) { \
+ ploadRhsMMA(rhs_ptr_imag + (accRows * peel1), rhsVi[peel1]); \
+ ploadRhsMMA(rhs_ptr_imag + (accRows * peel2), rhsVi[peel2]); \
+ } \
+ } \
+ MICRO_COMPLEX_MMA_UNROLL(funcl2) \
+ MICRO_COMPLEX_MMA_WORK(funcw2, type, peel1) \
+ MICRO_COMPLEX_MMA_WORK(funcw2, type, peel2) \
+ } else { \
+ EIGEN_UNUSED_VARIABLE(prhsV##peel1); \
+ EIGEN_UNUSED_VARIABLE(prhsVi##peel1); \
+ MICRO_COMPLEX_MMA_TYPE_PEEL(funcw1, funcl1, type, peel1) \
+ }
+
+#define MICRO_COMPLEX_MMA_UNROLL_TYPE_PEEL2(funcw1, funcl1, funcw2, funcl2, type) \
+ type rhsV[4], rhsVi[4]; \
+ __vector_pair prhsV0, prhsV2; \
+ __vector_pair prhsVi0, prhsVi2; \
+ MICRO_COMPLEX_MMA_TYPE_PEEL2(funcw1,funcl1,funcw2,funcl2,type,0,1) \
+ MICRO_COMPLEX_MMA_TYPE_PEEL2(funcw1,funcl1,funcw2,funcl2,type,2,3)
+#endif
+
+#define MICRO_COMPLEX_MMA_UNROLL_TYPE_ONE(funcw, funcl, type) \
+ type rhsV[1], rhsVi[1]; \
+ MICRO_COMPLEX_MMA_TYPE_PEEL(funcw,funcl,type,0)
+
+#define MICRO_COMPLEX_MMA_UNROLL_TYPE(MICRO_COMPLEX_MMA_TYPE, size) \
+ MICRO_COMPLEX_MMA_TYPE(MICRO_COMPLEX_MMA_WORK_ONE, MICRO_COMPLEX_LOAD_ONE, RhsPacket) \
+ rhs_ptr_real += (accRows * size); \
+ if(!RhsIsReal) rhs_ptr_imag += (accRows * size);
+
+#ifndef VECTOR_PAIR_LOADS_LHS
+#define MICRO_COMPLEX_MMA_ONE_PEEL MICRO_COMPLEX_MMA_UNROLL_TYPE(MICRO_COMPLEX_MMA_UNROLL_TYPE_PEEL, PEEL_COMPLEX_MMA)
+#else
+#define MICRO_COMPLEX_MMA_UNROLL_TYPE2(MICRO_COMPLEX_MMA_TYPE, size) \
+ MICRO_COMPLEX_MMA_TYPE(MICRO_COMPLEX_MMA_WORK_ONE, MICRO_COMPLEX_LOAD_ONE, MICRO_COMPLEX_MMA_WORK_TWO, MICRO_COMPLEX_MMA_LOAD_TWO, RhsPacket) \
+ rhs_ptr_real += (accRows * size); \
+ if(!RhsIsReal) rhs_ptr_imag += (accRows * size);
+
+#define MICRO_COMPLEX_MMA_ONE_PEEL MICRO_COMPLEX_MMA_UNROLL_TYPE2(MICRO_COMPLEX_MMA_UNROLL_TYPE_PEEL2, PEEL_COMPLEX_MMA)
+#endif
+
+#define MICRO_COMPLEX_MMA_ONE MICRO_COMPLEX_MMA_UNROLL_TYPE(MICRO_COMPLEX_MMA_UNROLL_TYPE_ONE, 1)
+
+#define MICRO_COMPLEX_MMA_DST_PTR_ONE(iter) \
+ if (unroll_factor > iter) { \
+ bsetzeroMMA(&accReal##iter); \
+ bsetzeroMMA(&accImag##iter); \
+ } else { \
+ EIGEN_UNUSED_VARIABLE(accReal##iter); \
+ EIGEN_UNUSED_VARIABLE(accImag##iter); \
+ }
+
+#define MICRO_COMPLEX_MMA_DST_PTR MICRO_COMPLEX_MMA_UNROLL(MICRO_COMPLEX_MMA_DST_PTR_ONE)
+
+#define MICRO_COMPLEX_MMA_SRC_PTR MICRO_COMPLEX_MMA_UNROLL(MICRO_COMPLEX_SRC_PTR_ONE)
+
+#define MICRO_COMPLEX_MMA_PREFETCH MICRO_COMPLEX_MMA_UNROLL(MICRO_COMPLEX_PREFETCH_ONE)
+
+#define MICRO_COMPLEX_MMA_STORE_ONE(iter) \
+ if (unroll_factor > iter) { \
+ storeComplexAccumulator<DataMapper, Packet, Packetc, accCols, (unroll_factor != (iter + 1)) ? accCols : accCols2>(row + iter*accCols, res, pAlphaReal, pAlphaImag, pMask, &accReal##iter, &accImag##iter); \
+ }
+
+#define MICRO_COMPLEX_MMA_STORE MICRO_COMPLEX_MMA_UNROLL(MICRO_COMPLEX_MMA_STORE_ONE)
+
+template<int unroll_factor, typename Scalar, typename Packet, typename Packetc, typename RhsPacket, typename DataMapper, const Index accRows, const Index accCols, const Index accCols2, bool ConjugateLhs, bool ConjugateRhs, bool LhsIsReal, bool RhsIsReal>
+EIGEN_ALWAYS_INLINE void gemm_complex_unrolled_MMA_iteration(
+ const DataMapper& res,
+ const Scalar* lhs_base,
+ const Scalar* rhs_base,
+ Index depth,
+ Index strideA,
+ Index offsetA,
+ Index strideB,
+ Index& row,
+ const Packet& pAlphaReal,
+ const Packet& pAlphaImag,
+ const Packet& pMask)
+{
+ const Scalar* rhs_ptr_real = rhs_base;
+ const Scalar* rhs_ptr_imag = NULL;
+ const Index imag_delta = accCols*strideA;
+ const Index imag_delta2 = accCols2*strideA;
+ if(!RhsIsReal) {
+ rhs_ptr_imag = rhs_base + accRows*strideB;
+ } else {
+ EIGEN_UNUSED_VARIABLE(rhs_ptr_imag);
+ }
+ const Scalar* lhs_ptr_real0 = NULL, * lhs_ptr_real1 = NULL;
+ const Scalar* lhs_ptr_real2 = NULL, * lhs_ptr_real3 = NULL;
+ __vector_quad accReal0, accImag0, accReal1, accImag1, accReal2, accImag2, accReal3, accImag3;
+
+ MICRO_COMPLEX_MMA_SRC_PTR
+ MICRO_COMPLEX_MMA_DST_PTR
+
+ Index k = 0, depth2 = depth - PEEL_COMPLEX_MMA;
+ for(; k <= depth2; k += PEEL_COMPLEX_MMA)
+ {
+ EIGEN_POWER_PREFETCH(rhs_ptr_real);
+ if(!RhsIsReal) {
+ EIGEN_POWER_PREFETCH(rhs_ptr_imag);
+ }
+ MICRO_COMPLEX_MMA_PREFETCH
+ MICRO_COMPLEX_MMA_ONE_PEEL
+ }
+ for(; k < depth; k++)
+ {
+ MICRO_COMPLEX_MMA_ONE
+ }
+ MICRO_COMPLEX_MMA_STORE
+
+ MICRO_COMPLEX_UPDATE
+}
+
+#define MICRO_COMPLEX_MMA_UNROLL_ITER2(N, M) \
+ gemm_complex_unrolled_MMA_iteration<N + (M ? 1 : 0), Scalar, Packet, Packetc, RhsPacket, DataMapper, accRows, accCols, M ? M : accCols, ConjugateLhs, ConjugateRhs, LhsIsReal, RhsIsReal>(res3, lhs_base, rhs_base, depth, strideA, offsetA, strideB, row, pAlphaReal, pAlphaImag, pMask); \
+ if (M) return;
+
+template<typename Scalar, typename Packet, typename Packetc, typename RhsPacket, typename DataMapper, const Index accRows, const Index accCols, bool ConjugateLhs, bool ConjugateRhs, bool LhsIsReal, bool RhsIsReal>
+EIGEN_ALWAYS_INLINE void gemmMMA_complex_cols(
+ const DataMapper& res,
+ const Scalar* blockA,
+ const Scalar* blockB,
+ Index depth,
+ Index strideA,
+ Index offsetA,
+ Index strideB,
+ Index offsetB,
+ Index col,
+ Index rows,
+ Index remaining_rows,
+ const Packet& pAlphaReal,
+ const Packet& pAlphaImag,
+ const Packet& pMask)
+{
+ const DataMapper res3 = res.getSubMapper(0, col);
+
+ const Scalar* rhs_base = blockB + advanceCols*col*strideB + accRows*offsetB;
+ const Scalar* lhs_base = blockA + accCols*offsetA;
+ Index row = 0;
+
+#define MAX_COMPLEX_MMA_UNROLL 4
+ while(row + MAX_COMPLEX_MMA_UNROLL*accCols <= rows) {
+ MICRO_COMPLEX_MMA_UNROLL_ITER2(MAX_COMPLEX_MMA_UNROLL, 0);
+ }
+ switch( (rows-row)/accCols ) {
+#if MAX_COMPLEX_MMA_UNROLL > 4
+ case 4:
+ MICRO_COMPLEX_UNROLL_ITER(MICRO_COMPLEX_MMA_UNROLL_ITER2, 4)
+ break;
+#endif
+#if MAX_COMPLEX_MMA_UNROLL > 3
+ case 3:
+ MICRO_COMPLEX_UNROLL_ITER(MICRO_COMPLEX_MMA_UNROLL_ITER2, 3)
+ break;
+#endif
+#if MAX_COMPLEX_MMA_UNROLL > 2
+ case 2:
+ MICRO_COMPLEX_UNROLL_ITER(MICRO_COMPLEX_MMA_UNROLL_ITER2, 2)
+ break;
+#endif
+#if MAX_COMPLEX_MMA_UNROLL > 1
+ case 1:
+ MICRO_COMPLEX_UNROLL_ITER(MICRO_COMPLEX_MMA_UNROLL_ITER2, 1)
+ break;
+#endif
+ default:
+ break;
+ }
+#undef MAX_COMPLEX_MMA_UNROLL
+
+ if(remaining_rows > 0)
+ {
+ gemm_complex_extra_row<Scalar, Packet, Packetc, DataMapper, accRows, accCols, ConjugateLhs, ConjugateRhs, LhsIsReal, RhsIsReal>(res3, blockA, rhs_base, depth, strideA, offsetA, strideB, row, rows, remaining_rows, pAlphaReal, pAlphaImag, pMask);
+ }
+}
+
+template<typename LhsScalar, typename RhsScalar, typename Scalarc, typename Scalar, typename Packet, typename Packetc, typename RhsPacket, typename DataMapper, const Index accRows, const Index accCols, bool ConjugateLhs, bool ConjugateRhs, bool LhsIsReal, bool RhsIsReal>
+void gemm_complexMMA(const DataMapper& res, const LhsScalar* blockAc, const RhsScalar* blockBc, Index rows, Index depth, Index cols, Scalarc alpha, Index strideA, Index strideB, Index offsetA, Index offsetB)
+{
+ const Index remaining_rows = rows % accCols;
+
+ if( strideA == -1 ) strideA = depth;
+ if( strideB == -1 ) strideB = depth;
+
+ const Packet pAlphaReal = pset1<Packet>(alpha.real());
+ const Packet pAlphaImag = pset1<Packet>(alpha.imag());
+ const Packet pMask = bmask<Packet>(remaining_rows);
+
+ const Scalar* blockA = (Scalar *) blockAc;
+ const Scalar* blockB = (Scalar *) blockBc;
+
+ typedef typename std::conditional_t<(sizeof(Scalar) == sizeof(float)), RhsPacket, __vector_pair> RhsPacket2;
+
+ Index col = 0;
+ for(; col + accRows <= cols; col += accRows)
+ {
+ gemmMMA_complex_cols<Scalar, Packet, Packetc, RhsPacket2, DataMapper, accRows, accCols, ConjugateLhs, ConjugateRhs, LhsIsReal, RhsIsReal>(res, blockA, blockB, depth, strideA, offsetA, strideB, offsetB, col, rows, remaining_rows, pAlphaReal, pAlphaImag, pMask);
+ }
+
+ if (col != cols)
+ {
+ gemm_complex_extra_cols<Scalar, Packet, Packetc, DataMapper, accCols, ConjugateLhs, ConjugateRhs, LhsIsReal, RhsIsReal>(res, blockA, blockB, depth, strideA, offsetA, strideB, offsetB, col, rows, cols, remaining_rows, pAlphaReal, pAlphaImag, pMask);
+ }
+}
+
+#undef accColsC
+#undef advanceRows
+#undef advanceCols
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#if defined(EIGEN_ALTIVEC_MMA_DYNAMIC_DISPATCH)
+#pragma GCC pop_options
+#endif
+
+#endif // EIGEN_MATRIX_PRODUCT_MMA_ALTIVEC_H
+
diff --git a/Eigen/src/Core/arch/AltiVec/MatrixVectorProduct.h b/Eigen/src/Core/arch/AltiVec/MatrixVectorProduct.h
new file mode 100644
index 0000000..9d00b93
--- /dev/null
+++ b/Eigen/src/Core/arch/AltiVec/MatrixVectorProduct.h
@@ -0,0 +1,2400 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2021 Chip Kerchner (chip.kerchner@ibm.com)
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_MATRIX_VECTOR_PRODUCT_ALTIVEC_H
+#define EIGEN_MATRIX_VECTOR_PRODUCT_ALTIVEC_H
+
+#include "../../InternalHeaderCheck.h"
+
+#if defined(__MMA__) && !EIGEN_ALTIVEC_DISABLE_MMA
+#if EIGEN_COMP_LLVM || (__GNUC__ > 10 || __GNUC_MINOR__ >= 3)
+#define USE_GEMV_MMA
+#endif
+
+#if !EIGEN_COMP_LLVM && (__GNUC__ == 10 && __GNUC_MINOR__ <= 3)
+// Only allow one vector_pair in buggy gcc - gcc 10.3 has a bug
+#define GCC_ONE_VECTORPAIR_BUG
+#endif
+#endif
+
+//#define USE_SLOWER_GEMV_MMA // MMA is currently not as fast as VSX in complex double GEMV (revisit when gcc is improved)
+
+//#define EIGEN_POWER_USE_GEMV_PREFETCH
+#ifdef EIGEN_POWER_USE_GEMV_PREFETCH
+#define EIGEN_POWER_GEMV_PREFETCH(p) prefetch(p)
+#else
+#define EIGEN_POWER_GEMV_PREFETCH(p)
+#endif
+
+#ifdef __has_builtin
+#if !__has_builtin(__builtin_vsx_assemble_pair)
+#define __builtin_vsx_assemble_pair __builtin_mma_assemble_pair
+#endif
+#if !__has_builtin(__builtin_vsx_disassemble_pair)
+#define __builtin_vsx_disassemble_pair __builtin_mma_disassemble_pair
+#endif
+#endif
+
+#if EIGEN_COMP_LLVM
+#define GEMV_BUILDPAIR_MMA(dst, src1, src2) \
+ __builtin_vsx_assemble_pair(&dst, (__vector unsigned char)src2, (__vector unsigned char)src1)
+#else
+#if (__GNUC__ <= 10)
+#if (__GNUC_MINOR__ > 3)
+#define GEMV_BUILDPAIR_MMA(dst, src1, src2) \
+ __builtin_vsx_assemble_pair(&dst, (__vector unsigned char)src2, (__vector unsigned char)src1)
+#else
+#define GEMV_BUILDPAIR_MMA(dst, src1, src2) \
+ __builtin_vsx_assemble_pair(&dst, (__vector unsigned char)src1, (__vector unsigned char)src2)
+#endif
+#else
+#define GEMV_BUILDPAIR_MMA(dst, src1, src2) \
+ __builtin_vsx_build_pair(&dst, (__vector unsigned char)src1, (__vector unsigned char)src2)
+#endif
+#endif
+
+#define GEMV_IS_COMPLEX_COMPLEX ((sizeof(LhsPacket) == 16) && (sizeof(RhsPacket) == 16))
+#define GEMV_IS_FLOAT (ResPacketSize == (16 / sizeof(float)))
+#define GEMV_IS_SCALAR (sizeof(ResPacket) != 16)
+#define GEMV_IS_COMPLEX_FLOAT (ResPacketSize == (16 / sizeof(std::complex<float>)))
+
+/** \internal multiply and add and store results */
+template<typename ResPacket, typename ResScalar>
+EIGEN_ALWAYS_INLINE void storeMaddData(ResScalar* res, ResPacket& palpha, ResPacket& data)
+{
+ pstoreu(res, pmadd(data, palpha, ploadu<ResPacket>(res)));
+}
+
+template<typename ResScalar>
+EIGEN_ALWAYS_INLINE void storeMaddData(ResScalar* res, ResScalar& alpha, ResScalar& data)
+{
+ *res += (alpha * data);
+}
+
+#define GEMV_UNROLL(func, N) \
+ func(0, N) func(1, N) func(2, N) func(3, N) \
+ func(4, N) func(5, N) func(6, N) func(7, N)
+
+#define GEMV_UNROLL_HALF(func, N) \
+ func(0, 0, 1, N) func(1, 2, 3, N) func(2, 4, 5, N) func(3, 6, 7, N)
+
+#define GEMV_GETN(N) (((N) * ResPacketSize) >> 2)
+
+#define GEMV_LOADPACKET_COL(iter) \
+ lhs.template load<LhsPacket, LhsAlignment>(i + ((iter) * LhsPacketSize), j)
+
+#ifdef USE_GEMV_MMA
+#define GEMV_UNROLL3(func, N, which) \
+ func(0, N, which) func(1, N, which) func(2, N, which) func(3, N, which) \
+ func(4, N, which) func(5, N, which) func(6, N, which) func(7, N, which)
+
+#define GEMV_UNUSED_VAR(iter, N, which) \
+ if (GEMV_GETN(N) <= iter) { \
+ EIGEN_UNUSED_VARIABLE(which##iter); \
+ }
+
+#define GEMV_UNUSED_EXTRA_VAR(iter, N, which) \
+ if (N <= iter) { \
+ EIGEN_UNUSED_VARIABLE(which##iter); \
+ }
+
+#define GEMV_UNUSED_EXTRA(N, which) \
+ GEMV_UNROLL3(GEMV_UNUSED_EXTRA_VAR, N, which)
+
+#define GEMV_UNUSED(N, which) \
+ GEMV_UNROLL3(GEMV_UNUSED_VAR, N, which)
+
+#define GEMV_INIT_MMA(iter, N) \
+ if (GEMV_GETN(N) > iter) { \
+ __builtin_mma_xxsetaccz(&e##iter); \
+ }
+
+#if EIGEN_COMP_LLVM
+#define GEMV_LOADPAIR_COL_MMA(iter1, iter2) \
+ GEMV_BUILDPAIR_MMA(b##iter1, GEMV_LOADPACKET_COL(iter2), GEMV_LOADPACKET_COL((iter2) + 1));
+#else
+#define GEMV_LOADPAIR_COL_MMA(iter1, iter2) \
+ const LhsScalar& src##iter1 = lhs(i + ((iter1 * 32) / sizeof(LhsScalar)), j); \
+ b##iter1 = *reinterpret_cast<__vector_pair *>(const_cast<LhsScalar *>(&src##iter1));
+#endif
+
+#define GEMV_LOAD1A_COL_MMA(iter, N) \
+ if (GEMV_GETN(N) > iter) { \
+ if (GEMV_IS_FLOAT) { \
+ g##iter = GEMV_LOADPACKET_COL(iter); \
+ EIGEN_UNUSED_VARIABLE(b##iter); \
+ } else { \
+ GEMV_LOADPAIR_COL_MMA(iter, iter << 1) \
+ EIGEN_UNUSED_VARIABLE(g##iter); \
+ } \
+ } else { \
+ EIGEN_UNUSED_VARIABLE(b##iter); \
+ EIGEN_UNUSED_VARIABLE(g##iter); \
+ }
+
+#define GEMV_WORK1A_COL_MMA(iter, N) \
+ if (GEMV_GETN(N) > iter) { \
+ if (GEMV_IS_FLOAT) { \
+ pger_vecMMA_acc<LhsPacket, RhsPacket, true>(&e##iter, a0, g##iter); \
+ } else { \
+ pger_vecMMA_acc<LhsPacket, RhsPacket, true>(&e##iter, b##iter, a0); \
+ } \
+ }
+
+#define GEMV_LOAD1B_COL_MMA(iter1, iter2, iter3, N) \
+ if (GEMV_GETN(N) > iter1) { \
+ if (GEMV_IS_FLOAT) { \
+ GEMV_LOADPAIR_COL_MMA(iter2, iter2) \
+ EIGEN_UNUSED_VARIABLE(b##iter3); \
+ } else { \
+ GEMV_LOADPAIR_COL_MMA(iter2, iter2 << 1) \
+ GEMV_LOADPAIR_COL_MMA(iter3, iter3 << 1) \
+ } \
+ } else { \
+ EIGEN_UNUSED_VARIABLE(b##iter2); \
+ EIGEN_UNUSED_VARIABLE(b##iter3); \
+ } \
+ EIGEN_UNUSED_VARIABLE(g##iter2); \
+ EIGEN_UNUSED_VARIABLE(g##iter3);
+
+#define GEMV_WORK1B_COL_MMA(iter1, iter2, iter3, N) \
+ if (GEMV_GETN(N) > iter1) { \
+ if (GEMV_IS_FLOAT) { \
+ LhsPacket h[2]; \
+ __builtin_vsx_disassemble_pair(reinterpret_cast<void*>(h), &b##iter2); \
+ pger_vecMMA_acc<LhsPacket, RhsPacket, true>(&e##iter2, a0, h[0]); \
+ pger_vecMMA_acc<LhsPacket, RhsPacket, true>(&e##iter3, a0, h[1]); \
+ } else { \
+ pger_vecMMA_acc<LhsPacket, RhsPacket, true>(&e##iter2, b##iter2, a0); \
+ pger_vecMMA_acc<LhsPacket, RhsPacket, true>(&e##iter3, b##iter3, a0); \
+ } \
+ }
+
+#if EIGEN_COMP_LLVM
+#define GEMV_LOAD_COL_MMA(N) \
+ if (GEMV_GETN(N) > 1) { \
+ GEMV_UNROLL_HALF(GEMV_LOAD1B_COL_MMA, (N >> 1)) \
+ } else { \
+ GEMV_UNROLL(GEMV_LOAD1A_COL_MMA, N) \
+ }
+
+#define GEMV_WORK_COL_MMA(N) \
+ if (GEMV_GETN(N) > 1) { \
+ GEMV_UNROLL_HALF(GEMV_WORK1B_COL_MMA, (N >> 1)) \
+ } else { \
+ GEMV_UNROLL(GEMV_WORK1A_COL_MMA, N) \
+ }
+#else
+#define GEMV_LOAD_COL_MMA(N) \
+ GEMV_UNROLL(GEMV_LOAD1A_COL_MMA, N)
+
+#define GEMV_WORK_COL_MMA(N) \
+ GEMV_UNROLL(GEMV_WORK1A_COL_MMA, N)
+#endif
+
+#define GEMV_DISASSEMBLE_MMA(iter, N) \
+ if (GEMV_GETN(N) > iter) { \
+ __builtin_mma_disassemble_acc(&result##iter.packet, &e##iter); \
+ if (!GEMV_IS_FLOAT) { \
+ result##iter.packet[0][1] = result##iter.packet[1][0]; \
+ result##iter.packet[2][1] = result##iter.packet[3][0]; \
+ } \
+ }
+
+#define GEMV_LOADPAIR2_COL_MMA(iter1, iter2) \
+ b##iter1 = *reinterpret_cast<__vector_pair *>(res + i + ((iter2) * ResPacketSize));
+
+#define GEMV_LOAD2_COL_MMA(iter1, iter2, iter3, N) \
+ if (GEMV_GETN(N) > iter1) { \
+ if (GEMV_IS_FLOAT) { \
+ GEMV_LOADPAIR2_COL_MMA(iter2, iter2); \
+ EIGEN_UNUSED_VARIABLE(b##iter3); \
+ } else { \
+ GEMV_LOADPAIR2_COL_MMA(iter2, iter2 << 1); \
+ GEMV_LOADPAIR2_COL_MMA(iter3, iter3 << 1); \
+ } \
+ } else { \
+ EIGEN_UNUSED_VARIABLE(b##iter2); \
+ EIGEN_UNUSED_VARIABLE(b##iter3); \
+ }
+
+#if EIGEN_COMP_LLVM
+#define GEMV_WORKPAIR2_COL_MMA(iter2, iter3, iter4) \
+ ResPacket f##iter2[2]; \
+ __builtin_vsx_disassemble_pair(reinterpret_cast<void*>(f##iter2), &b##iter2); \
+ f##iter2[0] = pmadd(result##iter2.packet[0], palpha, f##iter2[0]); \
+ f##iter2[1] = pmadd(result##iter3.packet[(iter2 == iter3) ? 2 : 0], palpha, f##iter2[1]); \
+ GEMV_BUILDPAIR_MMA(b##iter2, f##iter2[0], f##iter2[1]);
+#else
+#define GEMV_WORKPAIR2_COL_MMA(iter2, iter3, iter4) \
+ if (GEMV_IS_FLOAT) { \
+ __asm__ ("xvmaddasp %0,%x1,%x3\n\txvmaddasp %L0,%x2,%x3" : "+&d" (b##iter2) : "wa" (result##iter3.packet[0]), "wa" (result##iter2.packet[0]), "wa" (palpha)); \
+ } else { \
+ __asm__ ("xvmaddadp %0,%x1,%x3\n\txvmaddadp %L0,%x2,%x3" : "+&d" (b##iter2) : "wa" (result##iter2.packet[2]), "wa" (result##iter2.packet[0]), "wa" (palpha)); \
+ }
+#endif
+
+#define GEMV_WORK2_COL_MMA(iter1, iter2, iter3, N) \
+ if (GEMV_GETN(N) > iter1) { \
+ if (GEMV_IS_FLOAT) { \
+ GEMV_WORKPAIR2_COL_MMA(iter2, iter3, iter2); \
+ } else { \
+ GEMV_WORKPAIR2_COL_MMA(iter2, iter2, iter2 << 1); \
+ GEMV_WORKPAIR2_COL_MMA(iter3, iter3, iter3 << 1); \
+ } \
+ }
+
+#define GEMV_STOREPAIR2_COL_MMA(iter1, iter2) \
+ *reinterpret_cast<__vector_pair *>(res + i + ((iter2) * ResPacketSize)) = b##iter1;
+
+#define GEMV_STORE_COL_MMA(iter, N) \
+ if (GEMV_GETN(N) > iter) { \
+ if (GEMV_IS_FLOAT) { \
+ storeMaddData<ResPacket, ResScalar>(res + i + (iter * ResPacketSize), palpha, result##iter.packet[0]); \
+ } else { \
+ GEMV_LOADPAIR2_COL_MMA(iter, iter << 1) \
+ GEMV_WORKPAIR2_COL_MMA(iter, iter, iter << 1) \
+ GEMV_STOREPAIR2_COL_MMA(iter, iter << 1) \
+ } \
+ }
+
+#define GEMV_STORE2_COL_MMA(iter1, iter2, iter3, N) \
+ if (GEMV_GETN(N) > iter1) { \
+ if (GEMV_IS_FLOAT) { \
+ GEMV_STOREPAIR2_COL_MMA(iter2, iter2); \
+ } else { \
+ GEMV_STOREPAIR2_COL_MMA(iter2, iter2 << 1) \
+ GEMV_STOREPAIR2_COL_MMA(iter3, iter3 << 1) \
+ } \
+ }
+
+#define GEMV_PROCESS_COL_ONE_MMA(N) \
+ GEMV_UNROLL(GEMV_INIT_MMA, N) \
+ Index j = j2; \
+ __vector_pair b0, b1, b2, b3, b4, b5, b6, b7; \
+ do { \
+ LhsPacket g0, g1, g2, g3, g4, g5, g6, g7; \
+ RhsPacket a0 = pset1<RhsPacket>(rhs2(j, 0)); \
+ GEMV_UNROLL(GEMV_PREFETCH, N) \
+ GEMV_LOAD_COL_MMA(N) \
+ GEMV_WORK_COL_MMA(N) \
+ } while (++j < jend); \
+ GEMV_UNROLL(GEMV_DISASSEMBLE_MMA, N) \
+ if (GEMV_GETN(N) <= 1) { \
+ GEMV_UNROLL(GEMV_STORE_COL_MMA, N) \
+ } else { \
+ GEMV_UNROLL_HALF(GEMV_LOAD2_COL_MMA, (N >> 1)) \
+ GEMV_UNROLL_HALF(GEMV_WORK2_COL_MMA, (N >> 1)) \
+ GEMV_UNROLL_HALF(GEMV_STORE2_COL_MMA, (N >> 1)) \
+ } \
+ i += (ResPacketSize * N);
+#endif
+
+#define GEMV_INIT(iter, N) \
+ if (N > iter) { \
+ c##iter = pset1<ResPacket>(ResScalar(0)); \
+ } else { \
+ EIGEN_UNUSED_VARIABLE(c##iter); \
+ }
+
+#ifdef EIGEN_POWER_USE_GEMV_PREFETCH
+#define GEMV_PREFETCH(iter, N) \
+ if (GEMV_GETN(N) > ((iter >> 1) + ((N >> 1) * (iter & 1)))) { \
+ lhs.prefetch(i + (iter * LhsPacketSize) + prefetch_dist, j); \
+ }
+#else
+#define GEMV_PREFETCH(iter, N)
+#endif
+
+#define GEMV_WORK_COL(iter, N) \
+ if (N > iter) { \
+ c##iter = pcj.pmadd(GEMV_LOADPACKET_COL(iter), a0, c##iter); \
+ }
+
+#define GEMV_STORE_COL(iter, N) \
+ if (N > iter) { \
+ pstoreu(res + i + (iter * ResPacketSize), pmadd(c##iter, palpha, ploadu<ResPacket>(res + i + (iter * ResPacketSize)))); \
+ }
+
+/** \internal main macro for gemv_col - initialize accumulators, multiply and add inputs, and store results */
+#define GEMV_PROCESS_COL_ONE(N) \
+ GEMV_UNROLL(GEMV_INIT, N) \
+ Index j = j2; \
+ do { \
+ RhsPacket a0 = pset1<RhsPacket>(rhs2(j, 0)); \
+ GEMV_UNROLL(GEMV_PREFETCH, N) \
+ GEMV_UNROLL(GEMV_WORK_COL, N) \
+ } while (++j < jend); \
+ GEMV_UNROLL(GEMV_STORE_COL, N) \
+ i += (ResPacketSize * N);
+
+#ifdef USE_GEMV_MMA
+#define GEMV_PROCESS_COL(N) \
+ GEMV_PROCESS_COL_ONE_MMA(N)
+#else
+#define GEMV_PROCESS_COL(N) \
+ GEMV_PROCESS_COL_ONE(N)
+#endif
+
+/** \internal perform a matrix multiply and accumulate of packet a and packet b */
+#ifdef USE_GEMV_MMA
+template<typename LhsPacket, typename RhsPacket, bool accumulate>
+EIGEN_ALWAYS_INLINE void pger_vecMMA_acc(__vector_quad* acc, const RhsPacket& a, const LhsPacket& b)
+{
+ if (accumulate)
+ {
+ __builtin_mma_xvf32gerpp(acc, (__vector unsigned char)a, (__vector unsigned char)b);
+ }
+ else
+ {
+ __builtin_mma_xvf32ger(acc, (__vector unsigned char)a, (__vector unsigned char)b);
+ }
+}
+
+/** \internal perform a matrix multiply and accumulate of vector_pair a and packet b */
+template<typename LhsPacket, typename RhsPacket, bool accumulate>
+EIGEN_ALWAYS_INLINE void pger_vecMMA_acc(__vector_quad* acc, __vector_pair& a, const LhsPacket& b)
+{
+ if (accumulate)
+ {
+ __builtin_mma_xvf64gerpp(acc, a, (__vector unsigned char)b);
+ }
+ else
+ {
+ __builtin_mma_xvf64ger(acc, a, (__vector unsigned char)b);
+ }
+}
+#endif
+
+template<typename LhsScalar, typename LhsMapper, typename RhsScalar, typename RhsMapper, typename ResScalar>
+EIGEN_STRONG_INLINE void gemv_col(
+ Index rows, Index cols,
+ const LhsMapper& alhs,
+ const RhsMapper& rhs,
+ ResScalar* res, Index resIncr,
+ ResScalar alpha)
+{
+ typedef gemv_traits<LhsScalar, RhsScalar> Traits;
+
+ typedef typename Traits::LhsPacket LhsPacket;
+ typedef typename Traits::RhsPacket RhsPacket;
+ typedef typename Traits::ResPacket ResPacket;
+
+ EIGEN_UNUSED_VARIABLE(resIncr);
+ eigen_internal_assert(resIncr == 1);
+
+ // The following copy tells the compiler that lhs's attributes are not modified outside this function
+ // This helps GCC to generate proper code.
+ LhsMapper lhs(alhs);
+ RhsMapper rhs2(rhs);
+
+ conj_helper<LhsScalar, RhsScalar, false, false> cj;
+ conj_helper<LhsPacket, RhsPacket, false, false> pcj;
+
+ const Index lhsStride = lhs.stride();
+ // TODO: for padded aligned inputs, we could enable aligned reads
+ enum {
+ LhsAlignment = Unaligned,
+ ResPacketSize = Traits::ResPacketSize,
+ LhsPacketSize = Traits::LhsPacketSize,
+ RhsPacketSize = Traits::RhsPacketSize,
+ };
+
+#ifndef GCC_ONE_VECTORPAIR_BUG
+ const Index n8 = rows - 8 * ResPacketSize + 1;
+ const Index n4 = rows - 4 * ResPacketSize + 1;
+ const Index n2 = rows - 2 * ResPacketSize + 1;
+#endif
+ const Index n1 = rows - 1 * ResPacketSize + 1;
+#ifdef EIGEN_POWER_USE_GEMV_PREFETCH
+ const Index prefetch_dist = 64 * LhsPacketSize;
+#endif
+
+ // TODO: improve the following heuristic:
+ const Index block_cols = cols < 128 ? cols : (lhsStride * sizeof(LhsScalar) < 16000 ? 16 : 8);
+ ResPacket palpha = pset1<ResPacket>(alpha);
+
+ for (Index j2 = 0; j2 < cols; j2 += block_cols)
+ {
+ Index jend = numext::mini(j2 + block_cols, cols);
+ Index i = 0;
+ ResPacket c0, c1, c2, c3, c4, c5, c6, c7;
+#ifdef USE_GEMV_MMA
+ __vector_quad e0, e1, e2, e3, e4, e5, e6, e7;
+ PacketBlock<ResPacket, 4> result0, result1, result2, result3, result4, result5, result6, result7;
+ GEMV_UNUSED(8, e)
+ GEMV_UNUSED(8, result)
+ GEMV_UNUSED_EXTRA(1, c)
+#endif
+#ifndef GCC_ONE_VECTORPAIR_BUG
+ while (i < n8)
+ {
+ GEMV_PROCESS_COL(8)
+ }
+ if (i < n4)
+ {
+ GEMV_PROCESS_COL(4)
+ }
+ if (i < n2)
+ {
+ GEMV_PROCESS_COL(2)
+ }
+ if (i < n1)
+#else
+ while (i < n1)
+#endif
+ {
+ GEMV_PROCESS_COL_ONE(1)
+ }
+ for (;i < rows;++i)
+ {
+ ResScalar d0(0);
+ Index j = j2;
+ do {
+ d0 += cj.pmul(lhs(i, j), rhs2(j, 0));
+ } while (++j < jend);
+ res[i] += alpha * d0;
+ }
+ }
+}
+
+const Packet16uc p16uc_COMPLEX32_XORFLIP = { 0x44,0x55,0x66,0x77, 0x00,0x11,0x22,0x33, 0xcc,0xdd,0xee,0xff, 0x88,0x99,0xaa,0xbb };
+const Packet16uc p16uc_COMPLEX64_XORFLIP = { 0x88,0x99,0xaa,0xbb, 0xcc,0xdd,0xee,0xff, 0x00,0x11,0x22,0x33, 0x44,0x55,0x66,0x77 };
+
+#ifdef _BIG_ENDIAN
+const Packet16uc p16uc_COMPLEX32_CONJ_XOR = { 0x00,0x00,0x00,0x00, 0x80,0x00,0x00,0x00, 0x00,0x00,0x00,0x00, 0x80,0x00,0x00,0x00 };
+const Packet16uc p16uc_COMPLEX64_CONJ_XOR = { 0x00,0x00,0x00,0x00, 0x00,0x00,0x00,0x00, 0x80,0x00,0x00,0x00, 0x00,0x00,0x00,0x00 };
+const Packet16uc p16uc_COMPLEX32_CONJ_XOR2 = { 0x80,0x00,0x00,0x00, 0x00,0x00,0x00,0x00, 0x80,0x00,0x00,0x00, 0x00,0x00,0x00,0x00 };
+const Packet16uc p16uc_COMPLEX64_CONJ_XOR2 = { 0x80,0x00,0x00,0x00, 0x00,0x00,0x00,0x00, 0x00,0x00,0x00,0x00, 0x00,0x00,0x00,0x00 };
+const Packet16uc p16uc_COMPLEX32_NEGATE = { 0x80,0x00,0x00,0x00, 0x80,0x00,0x00,0x00, 0x80,0x00,0x00,0x00, 0x80,0x00,0x00,0x00 };
+const Packet16uc p16uc_COMPLEX64_NEGATE = { 0x80,0x00,0x00,0x00, 0x00,0x00,0x00,0x00, 0x80,0x00,0x00,0x00, 0x00,0x00,0x00,0x00 };
+#else
+const Packet16uc p16uc_COMPLEX32_CONJ_XOR = { 0x00,0x00,0x00,0x00, 0x00,0x00,0x00,0x80, 0x00,0x00,0x00,0x00, 0x00,0x00,0x00,0x80 };
+const Packet16uc p16uc_COMPLEX64_CONJ_XOR = { 0x00,0x00,0x00,0x00, 0x00,0x00,0x00,0x00, 0x00,0x00,0x00,0x00, 0x00,0x00,0x00,0x80 };
+const Packet16uc p16uc_COMPLEX32_CONJ_XOR2 = { 0x00,0x00,0x00,0x80, 0x00,0x00,0x00,0x00, 0x00,0x00,0x00,0x80, 0x00,0x00,0x00,0x00 };
+const Packet16uc p16uc_COMPLEX64_CONJ_XOR2 = { 0x00,0x00,0x00,0x00, 0x00,0x00,0x00,0x80, 0x00,0x00,0x00,0x00, 0x00,0x00,0x00,0x00 };
+const Packet16uc p16uc_COMPLEX32_NEGATE = { 0x00,0x00,0x00,0x80, 0x00,0x00,0x00,0x80, 0x00,0x00,0x00,0x80, 0x00,0x00,0x00,0x80 };
+const Packet16uc p16uc_COMPLEX64_NEGATE = { 0x00,0x00,0x00,0x00, 0x00,0x00,0x00,0x80, 0x00,0x00,0x00,0x00, 0x00,0x00,0x00,0x80 };
+#endif
+
+#ifdef _BIG_ENDIAN
+#define COMPLEX_DELTA 0
+#else
+#define COMPLEX_DELTA 2
+#endif
+
+/** \internal packet conjugate (same as pconj but uses the constants in pcplxflipconj for better code generation) */
+EIGEN_ALWAYS_INLINE Packet2cf pconj2(const Packet2cf& a) {
+ return Packet2cf(pxor(a.v, reinterpret_cast<Packet4f>(p16uc_COMPLEX32_CONJ_XOR)));
+}
+
+EIGEN_ALWAYS_INLINE Packet1cd pconj2(const Packet1cd& a) {
+ return Packet1cd(pxor(a.v, reinterpret_cast<Packet2d>(p16uc_COMPLEX64_CONJ_XOR)));
+}
+
+/** \internal packet conjugate with real & imaginary operation inverted */
+EIGEN_ALWAYS_INLINE Packet2cf pconjinv(const Packet2cf& a) {
+#ifdef __POWER8_VECTOR__
+ return Packet2cf(Packet4f(vec_neg(Packet2d(a.v))));
+#else
+ return Packet2cf(pxor(a.v, reinterpret_cast<Packet4f>(p16uc_COMPLEX32_CONJ_XOR2)));
+#endif
+}
+
+EIGEN_ALWAYS_INLINE Packet1cd pconjinv(const Packet1cd& a) {
+ return Packet1cd(pxor(a.v, reinterpret_cast<Packet2d>(p16uc_COMPLEX64_CONJ_XOR2)));
+}
+
+#if defined(_ARCH_PWR8) && (!EIGEN_COMP_LLVM || __clang_major__ >= 12)
+#define PERMXOR_GOOD // Clang had a bug with vec_permxor and endianness prior to version 12
+#endif
+
+/** \internal flip the real & imaginary results and packet conjugate */
+EIGEN_ALWAYS_INLINE Packet2cf pcplxflipconj(Packet2cf a)
+{
+#ifdef PERMXOR_GOOD
+ return Packet2cf(Packet4f(vec_permxor(Packet16uc(a.v), p16uc_COMPLEX32_CONJ_XOR, p16uc_COMPLEX32_XORFLIP)));
+#else
+ return pcplxflip(pconj2(a));
+#endif
+}
+
+EIGEN_ALWAYS_INLINE Packet1cd pcplxflipconj(Packet1cd a)
+{
+#ifdef PERMXOR_GOOD
+ return Packet1cd(Packet2d(vec_permxor(Packet16uc(a.v), p16uc_COMPLEX64_CONJ_XOR, p16uc_COMPLEX64_XORFLIP)));
+#else
+ return pcplxflip(pconj2(a));
+#endif
+}
+
+/** \internal packet conjugate and flip the real & imaginary results */
+EIGEN_ALWAYS_INLINE Packet2cf pcplxconjflip(Packet2cf a)
+{
+#ifdef PERMXOR_GOOD
+ return Packet2cf(Packet4f(vec_permxor(Packet16uc(a.v), p16uc_COMPLEX32_CONJ_XOR2, p16uc_COMPLEX32_XORFLIP)));
+#else
+ return pconj2(pcplxflip(a));
+#endif
+}
+
+EIGEN_ALWAYS_INLINE Packet1cd pcplxconjflip(Packet1cd a)
+{
+#ifdef PERMXOR_GOOD
+ return Packet1cd(Packet2d(vec_permxor(Packet16uc(a.v), p16uc_COMPLEX64_CONJ_XOR2, p16uc_COMPLEX64_XORFLIP)));
+#else
+ return pconj2(pcplxflip(a));
+#endif
+}
+
+/** \internal packet negate */
+EIGEN_ALWAYS_INLINE Packet2cf pnegate2(Packet2cf a)
+{
+#ifdef __POWER8_VECTOR__
+ return Packet2cf(vec_neg(a.v));
+#else
+ return Packet2cf(pxor(a.v, reinterpret_cast<Packet4f>(p16uc_COMPLEX32_NEGATE)));
+#endif
+}
+
+EIGEN_ALWAYS_INLINE Packet1cd pnegate2(Packet1cd a)
+{
+#ifdef __POWER8_VECTOR__
+ return Packet1cd(vec_neg(a.v));
+#else
+ return Packet1cd(pxor(a.v, reinterpret_cast<Packet2d>(p16uc_COMPLEX64_NEGATE)));
+#endif
+}
+
+/** \internal flip the real & imaginary results and negate */
+EIGEN_ALWAYS_INLINE Packet2cf pcplxflipnegate(Packet2cf a)
+{
+#ifdef PERMXOR_GOOD
+ return Packet2cf(Packet4f(vec_permxor(Packet16uc(a.v), p16uc_COMPLEX32_NEGATE, p16uc_COMPLEX32_XORFLIP)));
+#else
+ return pcplxflip(pnegate2(a));
+#endif
+}
+
+EIGEN_ALWAYS_INLINE Packet1cd pcplxflipnegate(Packet1cd a)
+{
+#ifdef PERMXOR_GOOD
+ return Packet1cd(Packet2d(vec_permxor(Packet16uc(a.v), p16uc_COMPLEX64_NEGATE, p16uc_COMPLEX64_XORFLIP)));
+#else
+ return pcplxflip(pnegate2(a));
+#endif
+}
+
+/** \internal flip the real & imaginary results */
+EIGEN_ALWAYS_INLINE Packet2cf pcplxflip2(Packet2cf a)
+{
+ return Packet2cf(Packet4f(vec_perm(Packet16uc(a.v), Packet16uc(a.v), p16uc_COMPLEX32_XORFLIP)));
+}
+
+EIGEN_ALWAYS_INLINE Packet1cd pcplxflip2(Packet1cd a)
+{
+#ifdef __VSX__
+ return Packet1cd(__builtin_vsx_xxpermdi(a.v, a.v, 2));
+#else
+ return Packet1cd(Packet2d(vec_perm(Packet16uc(a.v), Packet16uc(a.v), p16uc_COMPLEX64_XORFLIP)));
+#endif
+}
+
+/** \internal load half a vector with one complex value */
+EIGEN_ALWAYS_INLINE Packet4f pload_complex_half(std::complex<float>* src)
+{
+ Packet4f t;
+#ifdef __VSX__
+ // Load float64/two float32 (doubleword alignment)
+ __asm__("lxsdx %x0,%y1" : "=wa" (t) : "Z" (*src));
+#else
+ *reinterpret_cast<std::complex<float>*>(reinterpret_cast<float*>(&t) + COMPLEX_DELTA) = *src;
+#endif
+ return t;
+}
+
+/** \internal load two vectors from the real and imaginary portions of a complex value */
+template<typename RhsScalar>
+EIGEN_ALWAYS_INLINE void pload_realimag(RhsScalar* src, Packet4f& r, Packet4f& i)
+{
+#ifdef _ARCH_PWR9
+ __asm__("lxvwsx %x0,%y1" : "=wa" (r) : "Z" (*(reinterpret_cast<float*>(src) + 0)));
+ __asm__("lxvwsx %x0,%y1" : "=wa" (i) : "Z" (*(reinterpret_cast<float*>(src) + 1)));
+#else
+ Packet4f t = pload_complex_half(src);
+ r = vec_splat(t, COMPLEX_DELTA + 0);
+ i = vec_splat(t, COMPLEX_DELTA + 1);
+#endif
+}
+
+template<typename RhsScalar>
+EIGEN_ALWAYS_INLINE void pload_realimag(RhsScalar* src, Packet2d& r, Packet2d& i)
+{
+#ifdef __VSX__
+ __asm__("lxvdsx %x0,%y1" : "=wa" (r) : "Z" (*(reinterpret_cast<double*>(src) + 0)));
+ __asm__("lxvdsx %x0,%y1" : "=wa" (i) : "Z" (*(reinterpret_cast<double*>(src) + 1)));
+#else
+ Packet2d t = ploadu<Packet2d>(reinterpret_cast<double*>(src));
+ r = vec_splat(t, 0);
+ i = vec_splat(t, 1);
+#endif
+}
+
+#ifndef __POWER8_VECTOR__
+const Packet16uc p16uc_MERGEE = { 0x00, 0x01, 0x02, 0x03, 0x10, 0x11, 0x12, 0x13, 0x08, 0x09, 0x0A, 0x0B, 0x18, 0x19, 0x1A, 0x1B };
+
+const Packet16uc p16uc_MERGEO = { 0x04, 0x05, 0x06, 0x07, 0x14, 0x15, 0x16, 0x17, 0x0C, 0x0D, 0x0E, 0x0F, 0x1C, 0x1D, 0x1E, 0x1F };
+#endif
+
+/** \internal load two vectors from the interleaved real & imaginary values of src */
+template<typename RhsScalar>
+EIGEN_ALWAYS_INLINE void pload_realimag_row(RhsScalar* src, Packet4f& r, Packet4f& i)
+{
+ Packet4f t = ploadu<Packet4f>(reinterpret_cast<float*>(src));
+#ifdef __POWER8_VECTOR__
+ r = vec_mergee(t, t);
+ i = vec_mergeo(t, t);
+#else
+ r = vec_perm(t, t, p16uc_MERGEE);
+ i = vec_perm(t, t, p16uc_MERGEO);
+#endif
+}
+
+template<typename RhsScalar>
+EIGEN_ALWAYS_INLINE void pload_realimag_row(RhsScalar* src, Packet2d& r, Packet2d& i)
+{
+ return pload_realimag(src, r, i);
+}
+
+/** \internal load and splat a complex value into a vector - column-wise */
+EIGEN_ALWAYS_INLINE Packet4f pload_realimag_combine(std::complex<float>* src)
+{
+#ifdef __VSX__
+ Packet4f ret;
+ __asm__("lxvdsx %x0,%y1" : "=wa" (ret) : "Z" (*(reinterpret_cast<double*>(src) + 0)));
+ return ret;
+#else
+ return Packet4f(ploaddup<Packet2d>(reinterpret_cast<double *>(src)));
+#endif
+}
+
+EIGEN_ALWAYS_INLINE Packet2d pload_realimag_combine(std::complex<double>* src)
+{
+ return ploadu<Packet1cd>(src).v;
+}
+
+/** \internal load a complex value into a vector - row-wise */
+EIGEN_ALWAYS_INLINE Packet4f pload_realimag_combine_row(std::complex<float>* src)
+{
+ return ploadu<Packet2cf>(src).v;
+}
+
+EIGEN_ALWAYS_INLINE Packet2d pload_realimag_combine_row(std::complex<double>* src)
+{
+ return ploadu<Packet1cd>(src).v;
+}
+
+/** \internal load a scalar or a vector from complex location */
+template<typename ResPacket>
+EIGEN_ALWAYS_INLINE Packet4f pload_complex(std::complex<float>* src)
+{
+ if (GEMV_IS_SCALAR) {
+ return pload_complex_half(src);
+ }
+ else
+ {
+ return ploadu<Packet4f>(reinterpret_cast<float*>(src));
+ }
+}
+
+template<typename ResPacket>
+EIGEN_ALWAYS_INLINE Packet2d pload_complex(std::complex<double>* src)
+{
+ return ploadu<Packet2d>(reinterpret_cast<double*>(src));
+}
+
+/** \internal load from a complex vector and convert to a real vector */
+template<typename ResPacket>
+EIGEN_ALWAYS_INLINE Packet4f pload_complex(Packet2cf* src)
+{
+ return src->v;
+}
+
+template<typename ResPacket>
+EIGEN_ALWAYS_INLINE Packet2d pload_complex(Packet1cd* src)
+{
+ return src->v;
+}
+
+/** \internal load a full vector from complex location - column-wise */
+EIGEN_ALWAYS_INLINE Packet4f pload_complex_full(std::complex<float>* src)
+{
+ return Packet4f(ploaddup<Packet2d>(reinterpret_cast<double *>(src)));
+}
+
+EIGEN_ALWAYS_INLINE Packet2d pload_complex_full(std::complex<double>* src)
+{
+ return ploadu<Packet1cd>(src).v;
+}
+
+/** \internal load a full vector from complex location - row-wise */
+EIGEN_ALWAYS_INLINE Packet4f pload_complex_full_row(std::complex<float>* src)
+{
+ return ploadu<Packet2cf>(src).v;
+}
+
+EIGEN_ALWAYS_INLINE Packet2d pload_complex_full_row(std::complex<double>* src)
+{
+ return pload_complex_full(src);
+}
+
+/** \internal load a vector from a real-only scalar location - column-wise */
+EIGEN_ALWAYS_INLINE Packet4f pload_real(float* src)
+{
+ return pset1<Packet4f>(*src);
+}
+
+EIGEN_ALWAYS_INLINE Packet2d pload_real(double* src)
+{
+ return pset1<Packet2d>(*src);
+}
+
+EIGEN_ALWAYS_INLINE Packet4f pload_real(Packet4f& src)
+{
+ return src;
+}
+
+EIGEN_ALWAYS_INLINE Packet2d pload_real(Packet2d& src)
+{
+ return src;
+}
+
+/** \internal load a vector from a real-only vector location */
+EIGEN_ALWAYS_INLINE Packet4f pload_real_full(float* src)
+{
+ Packet4f ret = ploadu<Packet4f>(src);
+ return vec_mergeh(ret, ret);
+}
+
+EIGEN_ALWAYS_INLINE Packet2d pload_real_full(double* src)
+{
+ return pload_real(src);
+}
+
+EIGEN_ALWAYS_INLINE Packet4f pload_real_full(std::complex<float>* src)
+{
+ return pload_complex_full(src); // Just for compilation
+}
+
+EIGEN_ALWAYS_INLINE Packet2d pload_real_full(std::complex<double>* src)
+{
+ return pload_complex_full(src); // Just for compilation
+}
+
+/** \internal load a vector from a real-only scalar location - row-wise */
+template<typename ResPacket>
+EIGEN_ALWAYS_INLINE Packet4f pload_real_row(float* src)
+{
+ if (GEMV_IS_SCALAR) {
+ return pload_real_full(src);
+ }
+ else {
+ return ploadu<Packet4f>(src);
+ }
+}
+
+template<typename ResPacket>
+EIGEN_ALWAYS_INLINE Packet2d pload_real_row(double* src)
+{
+ return pload_real(src);
+}
+
+EIGEN_ALWAYS_INLINE Packet2cf padd(Packet2cf& a, std::complex<float>& b)
+{
+ EIGEN_UNUSED_VARIABLE(b);
+ return a; // Just for compilation
+}
+
+EIGEN_ALWAYS_INLINE Packet1cd padd(Packet1cd& a, std::complex<double>& b)
+{
+ EIGEN_UNUSED_VARIABLE(b);
+ return a; // Just for compilation
+}
+
+/** \internal set a scalar from complex location */
+template<typename Scalar, typename ResScalar>
+EIGEN_ALWAYS_INLINE Scalar pset1_realimag(ResScalar& alpha, int which, int conj)
+{
+ return (which) ? ((conj) ? -alpha.real() : alpha.real()) : ((conj) ? -alpha.imag() : alpha.imag());
+}
+
+/** \internal set a vector from complex location */
+template<typename Scalar, typename ResScalar, typename ResPacket, int which>
+EIGEN_ALWAYS_INLINE Packet2cf pset1_complex(std::complex<float>& alpha)
+{
+ Packet2cf ret;
+ ret.v[COMPLEX_DELTA + 0] = pset1_realimag<Scalar, ResScalar>(alpha, (which & 0x01), (which & 0x04));
+ ret.v[COMPLEX_DELTA + 1] = pset1_realimag<Scalar, ResScalar>(alpha, (which & 0x02), (which & 0x08));
+ ret.v[2 - COMPLEX_DELTA] = ret.v[COMPLEX_DELTA + 0];
+ ret.v[3 - COMPLEX_DELTA] = ret.v[COMPLEX_DELTA + 1];
+ return ret;
+}
+
+template<typename Scalar, typename ResScalar, typename ResPacket, int which>
+EIGEN_ALWAYS_INLINE Packet1cd pset1_complex(std::complex<double>& alpha)
+{
+ Packet1cd ret;
+ ret.v[0] = pset1_realimag<Scalar, ResScalar>(alpha, (which & 0x01), (which & 0x04));
+ ret.v[1] = pset1_realimag<Scalar, ResScalar>(alpha, (which & 0x02), (which & 0x08));
+ return ret;
+}
+
+/** \internal zero out a vector for real or complex forms */
+template<typename Packet>
+EIGEN_ALWAYS_INLINE Packet pset_zero()
+{
+ return pset1<Packet>(__UNPACK_TYPE__(Packet)(0));
+}
+
+template<>
+EIGEN_ALWAYS_INLINE Packet2cf pset_zero<Packet2cf>()
+{
+ return Packet2cf(pset1<Packet4f>(float(0)));
+}
+
+template<>
+EIGEN_ALWAYS_INLINE Packet1cd pset_zero<Packet1cd>()
+{
+ return Packet1cd(pset1<Packet2d>(double(0)));
+}
+
+/** \internal initialize a vector from another vector */
+template<typename Packet, typename LhsPacket, typename RhsPacket>
+EIGEN_ALWAYS_INLINE Packet pset_init(Packet& c1)
+{
+ if (GEMV_IS_COMPLEX_COMPLEX) {
+ EIGEN_UNUSED_VARIABLE(c1);
+ return pset_zero<Packet>();
+ }
+ else
+ {
+ return c1; // Intentionally left uninitialized
+ }
+}
+
+template<typename PResPacket, typename ResPacket, typename ResScalar, typename Scalar>
+struct alpha_store
+{
+ alpha_store<PResPacket, ResPacket, ResScalar, Scalar>(ResScalar& alpha) {
+ separate.r = pset1_complex<Scalar, ResScalar, ResPacket, 0x3>(alpha);
+ separate.i = pset1_complex<Scalar, ResScalar, ResPacket, 0x0>(alpha);
+ }
+ struct ri {
+ PResPacket r;
+ PResPacket i;
+ } separate;
+};
+
+/** \internal multiply and add for complex math */
+template<typename ScalarPacket, typename AlphaData>
+EIGEN_ALWAYS_INLINE ScalarPacket pmadd_complex(ScalarPacket& c0, ScalarPacket& c2, ScalarPacket& c4, AlphaData& b0)
+{
+ return pmadd(c2, b0.separate.i.v, pmadd(c0, b0.separate.r.v, c4));
+}
+
+/** \internal store and madd for complex math */
+template<typename Scalar, typename ScalarPacket, typename PResPacket, typename ResPacket, typename ResScalar, typename AlphaData>
+EIGEN_ALWAYS_INLINE void pstoreu_pmadd_complex(PResPacket& c0, AlphaData& b0, ResScalar* res)
+{
+ PResPacket c2 = pcplxflipconj(c0);
+ if (GEMV_IS_SCALAR) {
+ ScalarPacket c4 = ploadu<ScalarPacket>(reinterpret_cast<Scalar*>(res));
+ ScalarPacket c3 = pmadd_complex<ScalarPacket, AlphaData>(c0.v, c2.v, c4, b0);
+ pstoreu(reinterpret_cast<Scalar*>(res), c3);
+ } else {
+ ScalarPacket c4 = pload_complex<ResPacket>(res);
+ PResPacket c3 = PResPacket(pmadd_complex<ScalarPacket, AlphaData>(c0.v, c2.v, c4, b0));
+ pstoreu(res, c3);
+ }
+}
+
+template<typename ScalarPacket, typename PResPacket, typename ResPacket, typename ResScalar, typename AlphaData, Index ResPacketSize, Index iter2>
+EIGEN_ALWAYS_INLINE void pstoreu_pmadd_complex(PResPacket& c0, PResPacket& c1, AlphaData& b0, ResScalar* res)
+{
+ PResPacket c2 = pcplxflipconj(c0);
+ PResPacket c3 = pcplxflipconj(c1);
+#if !defined(_ARCH_PWR10)
+ ScalarPacket c4 = pload_complex<ResPacket>(res + (iter2 * ResPacketSize));
+ ScalarPacket c5 = pload_complex<ResPacket>(res + ((iter2 + 1) * ResPacketSize));
+ PResPacket c6 = PResPacket(pmadd_complex<ScalarPacket, AlphaData>(c0.v, c2.v, c4, b0));
+ PResPacket c7 = PResPacket(pmadd_complex<ScalarPacket, AlphaData>(c1.v, c3.v, c5, b0));
+ pstoreu(res + (iter2 * ResPacketSize), c6);
+ pstoreu(res + ((iter2 + 1) * ResPacketSize), c7);
+#else
+ __vector_pair a = *reinterpret_cast<__vector_pair *>(res + (iter2 * ResPacketSize));
+#if EIGEN_COMP_LLVM
+ PResPacket c6[2];
+ __builtin_vsx_disassemble_pair(reinterpret_cast<void*>(c6), &a);
+ c6[0] = PResPacket(pmadd_complex<ScalarPacket, AlphaData>(c0.v, c2.v, c6[0].v, b0));
+ c6[1] = PResPacket(pmadd_complex<ScalarPacket, AlphaData>(c1.v, c3.v, c6[1].v, b0));
+ GEMV_BUILDPAIR_MMA(a, c6[0].v, c6[1].v);
+#else
+ if (GEMV_IS_COMPLEX_FLOAT) {
+ __asm__ ("xvmaddasp %L0,%x1,%x2\n\txvmaddasp %0,%x1,%x3" : "+&d" (a) : "wa" (b0.separate.r.v), "wa" (c0.v), "wa" (c1.v));
+ __asm__ ("xvmaddasp %L0,%x1,%x2\n\txvmaddasp %0,%x1,%x3" : "+&d" (a) : "wa" (b0.separate.i.v), "wa" (c2.v), "wa" (c3.v));
+ } else {
+ __asm__ ("xvmaddadp %L0,%x1,%x2\n\txvmaddadp %0,%x1,%x3" : "+&d" (a) : "wa" (b0.separate.r.v), "wa" (c0.v), "wa" (c1.v));
+ __asm__ ("xvmaddadp %L0,%x1,%x2\n\txvmaddadp %0,%x1,%x3" : "+&d" (a) : "wa" (b0.separate.i.v), "wa" (c2.v), "wa" (c3.v));
+ }
+#endif
+ *reinterpret_cast<__vector_pair *>(res + (iter2 * ResPacketSize)) = a;
+#endif
+}
+
+/** \internal load lhs packet */
+template<typename Scalar, typename LhsScalar, typename LhsMapper, typename LhsPacket>
+EIGEN_ALWAYS_INLINE LhsPacket loadLhsPacket(LhsMapper& lhs, Index i, Index j)
+{
+ if (sizeof(Scalar) == sizeof(LhsScalar)) {
+ const LhsScalar& src = lhs(i + 0, j);
+ return LhsPacket(pload_real_full(const_cast<LhsScalar*>(&src)));
+ }
+ return lhs.template load<LhsPacket, Unaligned>(i + 0, j);
+}
+
+/** \internal madd for complex times complex */
+template<typename ComplexPacket, typename RealPacket, bool ConjugateLhs, bool ConjugateRhs, bool Negate>
+EIGEN_ALWAYS_INLINE RealPacket pmadd_complex_complex(RealPacket& a, RealPacket& b, RealPacket& c)
+{
+ if (ConjugateLhs && ConjugateRhs) {
+ return vec_madd(a, pconj2(ComplexPacket(b)).v, c);
+ }
+ else if (Negate && !ConjugateLhs && ConjugateRhs) {
+ return vec_nmsub(a, b, c);
+ }
+ else {
+ return vec_madd(a, b, c);
+ }
+}
+
+/** \internal madd for complex times real */
+template<typename ComplexPacket, typename RealPacket, bool Conjugate>
+EIGEN_ALWAYS_INLINE RealPacket pmadd_complex_real(RealPacket& a, RealPacket& b, RealPacket& c)
+{
+ if (Conjugate) {
+ return vec_madd(a, pconj2(ComplexPacket(b)).v, c);
+ }
+ else {
+ return vec_madd(a, b, c);
+ }
+}
+
+template<typename LhsPacket, typename RhsScalar, typename RhsPacket, typename PResPacket, bool ConjugateLhs, bool ConjugateRhs, int StorageOrder>
+EIGEN_ALWAYS_INLINE void gemv_mult_generic(LhsPacket& a0, RhsScalar* b, PResPacket& c0)
+{
+ conj_helper<LhsPacket, RhsPacket, ConjugateLhs, ConjugateRhs> pcj;
+ RhsPacket b0;
+ if (StorageOrder == ColMajor) {
+ b0 = pset1<RhsPacket>(*b);
+ }
+ else {
+ b0 = ploadu<RhsPacket>(b);
+ }
+ c0 = pcj.pmadd(a0, b0, c0);
+}
+
+/** \internal core multiply operation for vectors - complex times complex */
+template<typename ScalarPacket, typename LhsPacket, typename RhsScalar, typename RhsPacket, typename PResPacket, typename ResPacket, bool ConjugateLhs, bool ConjugateRhs, int StorageOrder>
+EIGEN_ALWAYS_INLINE void gemv_mult_complex_complex(LhsPacket& a0, RhsScalar* b, PResPacket& c0, ResPacket& c1)
+{
+ ScalarPacket br, bi;
+ if (StorageOrder == ColMajor) {
+ pload_realimag<RhsScalar>(b, br, bi);
+ }
+ else {
+ pload_realimag_row<RhsScalar>(b, br, bi);
+ }
+ if (ConjugateLhs && !ConjugateRhs) a0 = pconj2(a0);
+ LhsPacket a1 = pcplxflipconj(a0);
+ ScalarPacket cr = pmadd_complex_complex<LhsPacket, ScalarPacket, ConjugateLhs, ConjugateRhs, false>(a0.v, br, c0.v);
+ ScalarPacket ci = pmadd_complex_complex<LhsPacket, ScalarPacket, ConjugateLhs, ConjugateRhs, true>(a1.v, bi, c1.v);
+ c1 = ResPacket(ci);
+ c0 = PResPacket(cr);
+}
+
+/** \internal core multiply operation for vectors - real times complex */
+template<typename ScalarPacket, typename LhsPacket, typename RhsScalar, typename RhsPacket, typename PResPacket, typename ResPacket, bool ConjugateLhs, bool ConjugateRhs, int StorageOrder>
+EIGEN_ALWAYS_INLINE void gemv_mult_real_complex(LhsPacket& a0, RhsScalar* b, PResPacket& c0)
+{
+ ScalarPacket b0;
+ if (StorageOrder == ColMajor) {
+ b0 = pload_complex_full(b);
+ }
+ else {
+ b0 = pload_complex_full_row(b);
+ }
+ ScalarPacket cri = pmadd_complex_real<PResPacket, ScalarPacket, ConjugateRhs>(a0, b0, c0.v);
+ c0 = PResPacket(cri);
+}
+
+/** \internal core multiply operation for vectors - complex times real */
+template<typename ScalarPacket, typename LhsPacket, typename RhsScalar, typename RhsPacket, typename PResPacket, typename ResPacket, bool ConjugateLhs, bool ConjugateRhs, int StorageOrder>
+EIGEN_ALWAYS_INLINE void gemv_mult_complex_real(LhsPacket& a0, RhsScalar* b, PResPacket& c0)
+{
+ ScalarPacket a1 = pload_complex<ResPacket>(&a0);
+ ScalarPacket b0;
+ if (StorageOrder == ColMajor) {
+ b0 = pload_real(b);
+ }
+ else {
+ b0 = pload_real_row<ResPacket>(b);
+ }
+ ScalarPacket cri = pmadd_complex_real<PResPacket, ScalarPacket, ConjugateLhs>(a1, b0, c0.v);
+ c0 = PResPacket(cri);
+}
+
+#define GEMV_MULT_COMPLEX_COMPLEX(LhsType, RhsType, ResType) \
+template<typename ScalarPacket, typename LhsPacket, typename RhsScalar, typename RhsPacket, typename PResPacket, typename ResPacket, bool ConjugateLhs, bool ConjugateRhs, int StorageOrder> \
+EIGEN_ALWAYS_INLINE void gemv_mult_complex(LhsType& a0, RhsType* b, ResType& c0, ResType& c1) \
+{ \
+ gemv_mult_complex_complex<ScalarPacket, LhsPacket, RhsScalar, RhsPacket, PResPacket, ResPacket, ConjugateLhs, ConjugateRhs, StorageOrder>(a0, b, c0, c1); \
+}
+
+GEMV_MULT_COMPLEX_COMPLEX(Packet2cf, std::complex<float>, Packet2cf)
+GEMV_MULT_COMPLEX_COMPLEX(Packet1cd, std::complex<double>, Packet1cd)
+
+#define GEMV_MULT_REAL_COMPLEX(LhsType, RhsType, ResType) \
+template<typename ScalarPacket, typename LhsPacket, typename RhsScalar, typename RhsPacket, typename PResPacket, typename ResPacket, bool ConjugateLhs, bool ConjugateRhs, int StorageOrder> \
+EIGEN_ALWAYS_INLINE void gemv_mult_complex(LhsType& a0, RhsType* b, ResType& c0, RhsType&) \
+{ \
+ gemv_mult_real_complex<ScalarPacket, LhsPacket, RhsScalar, RhsPacket, PResPacket, ResPacket, ConjugateLhs, ConjugateRhs, StorageOrder>(a0, b, c0); \
+}
+
+GEMV_MULT_REAL_COMPLEX(float, std::complex<float>, Packet2cf)
+GEMV_MULT_REAL_COMPLEX(double, std::complex<double>, Packet1cd)
+GEMV_MULT_REAL_COMPLEX(Packet4f, std::complex<float>, Packet2cf)
+GEMV_MULT_REAL_COMPLEX(Packet2d, std::complex<double>, Packet1cd)
+
+#define GEMV_MULT_COMPLEX_REAL(LhsType, RhsType, ResType1, ResType2) \
+template<typename ScalarPacket, typename LhsPacket, typename RhsScalar, typename RhsPacket, typename PResPacket, typename ResPacket, bool ConjugateLhs, bool ConjugateRhs, int StorageOrder> \
+EIGEN_ALWAYS_INLINE void gemv_mult_complex(LhsType& a0, RhsType* b, ResType1& c0, ResType2&) \
+{ \
+ gemv_mult_complex_real<ScalarPacket, LhsPacket, RhsScalar, RhsPacket, PResPacket, ResPacket, ConjugateLhs, ConjugateRhs, StorageOrder>(a0, b, c0); \
+}
+
+GEMV_MULT_COMPLEX_REAL(Packet2cf, float, Packet2cf, std::complex<float>)
+GEMV_MULT_COMPLEX_REAL(Packet1cd, double, Packet1cd, std::complex<double>)
+GEMV_MULT_COMPLEX_REAL(std::complex<float>, float, Packet2cf, std::complex<float>)
+GEMV_MULT_COMPLEX_REAL(std::complex<double>, double, Packet1cd, std::complex<double>)
+
+#ifdef USE_GEMV_MMA
+/** \internal convert packet to real form */
+template<typename T>
+EIGEN_ALWAYS_INLINE T convertReal(T a)
+{
+ return a;
+}
+
+EIGEN_ALWAYS_INLINE Packet4f convertReal(Packet2cf a)
+{
+ return a.v;
+}
+
+EIGEN_ALWAYS_INLINE Packet2d convertReal(Packet1cd a)
+{
+ return a.v;
+}
+
+/** \internal convert packet to complex form */
+template<typename T>
+EIGEN_ALWAYS_INLINE T convertComplex(T a)
+{
+ return a;
+}
+
+EIGEN_ALWAYS_INLINE Packet2cf convertComplex(Packet4f a)
+{
+ return Packet2cf(a);
+}
+
+EIGEN_ALWAYS_INLINE Packet1cd convertComplex(Packet2d a)
+{
+ return Packet1cd(a);
+}
+
+/** \internal load a vector from a complex location (for MMA version) */
+template<typename ScalarPacket, typename LhsPacket, typename SLhsPacket, typename ResPacket>
+EIGEN_ALWAYS_INLINE void pload_complex_MMA(SLhsPacket& a)
+{
+ a = SLhsPacket(pload_complex<ResPacket>(&a));
+}
+
+template<typename ScalarPacket, typename LhsPacket, typename SLhsPacket, typename ResPacket>
+EIGEN_ALWAYS_INLINE void pload_complex_MMA(__vector_pair&)
+{
+ // Pass thru
+}
+
+/** \internal perform a matrix multiply and accumulate (positive and negative) of packet a and packet b */
+template<typename LhsPacket, typename RhsPacket, bool NegativeAccumulate>
+EIGEN_ALWAYS_INLINE void pger_vecMMA(__vector_quad* acc, RhsPacket& a, LhsPacket& b)
+{
+ if (NegativeAccumulate)
+ {
+ __builtin_mma_xvf32gernp(acc, (__vector unsigned char)a, (__vector unsigned char)b);
+ }
+ else {
+ __builtin_mma_xvf32gerpp(acc, (__vector unsigned char)a, (__vector unsigned char)b);
+ }
+}
+
+/** \internal perform a matrix multiply and accumulate (positive and negative) of vector_pair a and packet b */
+template<typename LhsPacket, typename RhsPacket, bool NegativeAccumulate>
+EIGEN_ALWAYS_INLINE void pger_vecMMA(__vector_quad* acc, __vector_pair& a, Packet2d& b)
+{
+ if (NegativeAccumulate)
+ {
+ __builtin_mma_xvf64gernp(acc, (__vector_pair)a, (__vector unsigned char)b);
+ }
+ else {
+ __builtin_mma_xvf64gerpp(acc, (__vector_pair)a, (__vector unsigned char)b);
+ }
+}
+
+template<typename LhsPacket, typename RhsPacket, bool NegativeAccumulate>
+EIGEN_ALWAYS_INLINE void pger_vecMMA(__vector_quad*, __vector_pair&, Packet4f&)
+{
+ // Just for compilation
+}
+
+/** \internal madd for complex times complex (MMA version) */
+template<typename RealPacket, typename LhsPacket, bool ConjugateLhs, bool ConjugateRhs, bool Negate>
+EIGEN_ALWAYS_INLINE void pmadd_complex_complex_MMA(LhsPacket& a, RealPacket& b, __vector_quad* c)
+{
+ if (ConjugateLhs && ConjugateRhs) {
+ RealPacket b2 = pconj2(convertComplex(b)).v;
+ return pger_vecMMA<RealPacket, RealPacket, false>(c, b2, a.v);
+ }
+ else if (Negate && !ConjugateLhs && ConjugateRhs) {
+ return pger_vecMMA<RealPacket, RealPacket, true>(c, b, a.v);
+ }
+ else {
+ return pger_vecMMA<RealPacket, RealPacket, false>(c, b, a.v);
+ }
+}
+
+template<typename RealPacket, typename LhsPacket, bool ConjugateLhs, bool ConjugateRhs, bool Negate>
+EIGEN_ALWAYS_INLINE void pmadd_complex_complex_MMA(__vector_pair& a, RealPacket& b, __vector_quad* c)
+{
+ if (ConjugateLhs && ConjugateRhs) {
+ RealPacket b2 = pconj2(convertComplex(b)).v;
+ return pger_vecMMA<RealPacket, __vector_pair, false>(c, a, b2);
+ }
+ else if (Negate && !ConjugateLhs && ConjugateRhs) {
+ return pger_vecMMA<RealPacket, __vector_pair, true>(c, a, b);
+ }
+ else {
+ return pger_vecMMA<RealPacket, __vector_pair, false>(c, a, b);
+ }
+}
+
+/** \internal madd for complex times real (MMA version) */
+template<typename RealPacket, typename LhsPacket, bool Conjugate, int StorageOrder>
+EIGEN_ALWAYS_INLINE void pmadd_complex_real_MMA(LhsPacket& a, RealPacket& b, __vector_quad* c)
+{
+ RealPacket a2 = convertReal(a);
+ if (Conjugate) {
+ RealPacket b2 = pconj2(convertComplex(b)).v;
+ if (StorageOrder == ColMajor) {
+ return pger_vecMMA<RealPacket, RealPacket, false>(c, b2, a2);
+ } else {
+ return pger_vecMMA<RealPacket, RealPacket, false>(c, a2, b2);
+ }
+ }
+ else {
+ if (StorageOrder == ColMajor) {
+ return pger_vecMMA<RealPacket, RealPacket, false>(c, b, a2);
+ } else {
+ return pger_vecMMA<RealPacket, RealPacket, false>(c, a2, b);
+ }
+ }
+}
+
+/** \internal madd for real times complex (MMA version) */
+template<typename RealPacket, typename LhsPacket, bool Conjugate, int StorageOrder>
+EIGEN_ALWAYS_INLINE void pmadd_complex_real_MMA(__vector_pair& a, RealPacket& b, __vector_quad* c)
+{
+ if (Conjugate) {
+ RealPacket b2 = pconj2(convertComplex(b)).v;
+ return pger_vecMMA<RealPacket, __vector_pair, false>(c, a, b2);
+ }
+ else {
+ return pger_vecMMA<RealPacket, __vector_pair, false>(c, a, b);
+ }
+}
+
+/** \internal core multiply operation for vectors (MMA version) - complex times complex */
+template<typename ScalarPacket, typename LhsPacket, typename SLhsPacket, typename RhsScalar, typename ResPacket, bool ConjugateLhs, bool ConjugateRhs, int StorageOrder>
+EIGEN_ALWAYS_INLINE void gemv_mult_complex_complex_MMA(SLhsPacket& a0, RhsScalar* b, __vector_quad* c0)
+{
+ ScalarPacket b0;
+ if (StorageOrder == ColMajor) {
+ b0 = pload_realimag_combine(b);
+ } else {
+ b0 = pload_realimag_combine_row(b);
+ }
+ pmadd_complex_complex_MMA<ScalarPacket, LhsPacket, ConjugateLhs, ConjugateRhs, false>(a0, b0, c0);
+}
+
+/** \internal core multiply operation for vectors (MMA version) - complex times real */
+template<typename ScalarPacket, typename LhsPacket, typename SLhsPacket, typename RhsScalar, typename ResPacket, bool ConjugateLhs, bool ConjugateRhs, int StorageOrder>
+EIGEN_ALWAYS_INLINE void gemv_mult_complex_real_MMA(SLhsPacket& a0, RhsScalar* b, __vector_quad* c0)
+{
+ pload_complex_MMA<ScalarPacket, LhsPacket, SLhsPacket, ResPacket>(a0);
+ ScalarPacket b0;
+ if (StorageOrder == ColMajor) {
+ b0 = pload_real(b);
+ }
+ else {
+ b0 = pload_real_row<ResPacket>(b);
+ }
+ pmadd_complex_real_MMA<ScalarPacket, LhsPacket, ConjugateLhs, ColMajor>(a0, b0, c0);
+}
+
+/** \internal core multiply operation for vectors (MMA version) - real times complex */
+template<typename ScalarPacket, typename LhsPacket, typename SLhsPacket, typename RhsScalar, typename ResPacket, bool ConjugateLhs, bool ConjugateRhs, int StorageOrder>
+EIGEN_ALWAYS_INLINE void gemv_mult_real_complex_MMA(SLhsPacket& a0, RhsScalar* b, __vector_quad* c0)
+{
+ ScalarPacket b0;
+ if (StorageOrder == ColMajor) {
+ b0 = pload_complex_full(b);
+ }
+ else {
+ b0 = pload_complex_full_row(b);
+ }
+ pmadd_complex_real_MMA<ScalarPacket, LhsPacket, ConjugateRhs, (sizeof(RhsScalar) == sizeof(std::complex<float>)) ? StorageOrder : ColMajor>(a0, b0, c0);
+}
+
+#define GEMV_MULT_COMPLEX_COMPLEX_MMA(LhsType, RhsType) \
+template<typename ScalarPacket, typename LhsScalar, typename LhsPacket, typename SLhsPacket, typename RhsScalar, typename RhsPacket, typename ResPacket, bool ConjugateLhs, bool ConjugateRhs, int StorageOrder> \
+EIGEN_ALWAYS_INLINE void gemv_mult_complex_MMA(LhsType& a0, RhsType* b, __vector_quad* c0) \
+{ \
+ gemv_mult_complex_complex_MMA<ScalarPacket, LhsPacket, SLhsPacket, RhsScalar, ResPacket, ConjugateLhs, ConjugateRhs, StorageOrder>(a0, b, c0); \
+}
+
+GEMV_MULT_COMPLEX_COMPLEX_MMA(Packet2cf, std::complex<float>)
+GEMV_MULT_COMPLEX_COMPLEX_MMA(__vector_pair, std::complex<float>)
+GEMV_MULT_COMPLEX_COMPLEX_MMA(Packet1cd, std::complex<double>)
+
+/** \internal core multiply operation for vectors (MMA version) - complex times complex */
+template<typename ScalarPacket, typename LhsScalar, typename LhsPacket, typename SLhsPacket, typename RhsScalar, typename RhsPacket, typename ResPacket, bool ConjugateLhs, bool ConjugateRhs, int StorageOrder>
+EIGEN_ALWAYS_INLINE void gemv_mult_complex_MMA(__vector_pair& a0, std::complex<double>* b, __vector_quad* c0)
+{
+ if (sizeof(LhsScalar) == 16) {
+ gemv_mult_complex_complex_MMA<ScalarPacket, LhsPacket, SLhsPacket, RhsScalar, ResPacket, ConjugateLhs, ConjugateRhs, StorageOrder>(a0, b, c0);
+ }
+ else {
+ gemv_mult_real_complex_MMA<ScalarPacket, LhsPacket, SLhsPacket, RhsScalar, ResPacket, ConjugateLhs, ConjugateRhs, StorageOrder>(a0, b, c0);
+ }
+}
+
+#define GEMV_MULT_REAL_COMPLEX_MMA(LhsType, RhsType) \
+template<typename ScalarPacket, typename LhsScalar, typename LhsPacket, typename SLhsPacket, typename RhsScalar, typename RhsPacket, typename ResPacket, bool ConjugateLhs, bool ConjugateRhs, int StorageOrder> \
+EIGEN_ALWAYS_INLINE void gemv_mult_complex_MMA(LhsType& a0, RhsType* b, __vector_quad* c0) \
+{ \
+ gemv_mult_real_complex_MMA<ScalarPacket, LhsPacket, SLhsPacket, RhsScalar, ResPacket, ConjugateLhs, ConjugateRhs, StorageOrder>(a0, b, c0); \
+}
+
+GEMV_MULT_REAL_COMPLEX_MMA(Packet4f, std::complex<float>)
+GEMV_MULT_REAL_COMPLEX_MMA(Packet2d, std::complex<double>)
+
+#define GEMV_MULT_COMPLEX_REAL_MMA(LhsType, RhsType) \
+template<typename ScalarPacket, typename LhsScalar, typename LhsPacket, typename SLhsPacket, typename RhsScalar, typename RhsPacket, typename ResPacket, bool ConjugateLhs, bool ConjugateRhs, int StorageOrder> \
+EIGEN_ALWAYS_INLINE void gemv_mult_complex_MMA(LhsType& a0, RhsType* b, __vector_quad* c0) \
+{ \
+ gemv_mult_complex_real_MMA<ScalarPacket, LhsPacket, SLhsPacket, RhsScalar, ResPacket, ConjugateLhs, ConjugateRhs, StorageOrder>(a0, b, c0); \
+}
+
+GEMV_MULT_COMPLEX_REAL_MMA(Packet2cf, float)
+GEMV_MULT_COMPLEX_REAL_MMA(Packet1cd, double)
+GEMV_MULT_COMPLEX_REAL_MMA(__vector_pair, float)
+GEMV_MULT_COMPLEX_REAL_MMA(__vector_pair, double)
+
+/** \internal disassemble MMA accumulator results into packets */
+template <typename Scalar, typename ScalarPacket, typename LhsPacket, typename RhsPacket, bool ConjugateLhs, bool ConjugateRhs>
+EIGEN_ALWAYS_INLINE void disassembleResults2(__vector_quad* c0, PacketBlock<ScalarPacket, 4>& result0)
+{
+ __builtin_mma_disassemble_acc(&result0.packet, c0);
+ if (sizeof(LhsPacket) == 16) {
+ if (sizeof(RhsPacket) == 16) {
+ ScalarPacket tmp0, tmp2;
+ tmp2 = vec_mergeh(result0.packet[2], result0.packet[3]);
+ tmp0 = vec_mergeh(result0.packet[0], result0.packet[1]);
+ result0.packet[3] = vec_mergel(result0.packet[3], result0.packet[2]);
+ result0.packet[1] = vec_mergel(result0.packet[1], result0.packet[0]);
+ result0.packet[2] = tmp2;
+ result0.packet[0] = tmp0;
+
+ if (ConjugateLhs) {
+ result0.packet[0] = pconj2(convertComplex(result0.packet[0])).v;
+ result0.packet[2] = pconj2(convertComplex(result0.packet[2])).v;
+ } else if (ConjugateRhs) {
+ result0.packet[1] = pconj2(convertComplex(result0.packet[1])).v;
+ result0.packet[3] = pconj2(convertComplex(result0.packet[3])).v;
+ } else {
+ result0.packet[1] = pconjinv(convertComplex(result0.packet[1])).v;
+ result0.packet[3] = pconjinv(convertComplex(result0.packet[3])).v;
+ }
+ result0.packet[0] = vec_add(result0.packet[0], result0.packet[1]);
+ result0.packet[2] = vec_add(result0.packet[2], result0.packet[3]);
+ } else {
+ result0.packet[0][1] = result0.packet[1][1];
+ result0.packet[2][1] = result0.packet[3][1];
+ }
+ }
+}
+
+template <typename Scalar, typename ScalarPacket, typename LhsPacket, typename RhsPacket, bool ConjugateLhs, bool ConjugateRhs>
+EIGEN_ALWAYS_INLINE void disassembleResults4(__vector_quad* c0, PacketBlock<ScalarPacket, 4>& result0)
+{
+ __builtin_mma_disassemble_acc(&result0.packet, c0);
+ if (GEMV_IS_COMPLEX_COMPLEX) {
+ if (ConjugateLhs) {
+ result0.packet[0] = pconj2(convertComplex(result0.packet[0])).v;
+ result0.packet[1] = pcplxflip2(convertComplex(result0.packet[1])).v;
+ } else {
+ if (ConjugateRhs) {
+ result0.packet[1] = pcplxconjflip(convertComplex(result0.packet[1])).v;
+ } else {
+ result0.packet[1] = pcplxflipconj(convertComplex(result0.packet[1])).v;
+ }
+ }
+ result0.packet[0] = vec_add(result0.packet[0], result0.packet[1]);
+ } else if (sizeof(LhsPacket) == sizeof(std::complex<float>)) {
+ if (ConjugateLhs) {
+ result0.packet[0] = pconj2(convertComplex(result0.packet[0])).v;
+ }
+ } else {
+ result0.packet[0] = vec_mergee(result0.packet[0], result0.packet[1]);
+ }
+}
+
+template <typename Scalar, typename ScalarPacket, int ResPacketSize, typename LhsPacket, typename RhsPacket, bool ConjugateLhs, bool ConjugateRhs>
+EIGEN_ALWAYS_INLINE void disassembleResults(__vector_quad* c0, PacketBlock<ScalarPacket, 4>& result0)
+{
+ if (!GEMV_IS_COMPLEX_FLOAT) {
+ disassembleResults2<Scalar, ScalarPacket, LhsPacket, RhsPacket, ConjugateLhs, ConjugateRhs>(c0, result0);
+ } else {
+ disassembleResults4<Scalar, ScalarPacket, LhsPacket, RhsPacket, ConjugateLhs, ConjugateRhs>(c0, result0);
+ }
+}
+#endif
+
+#define GEMV_GETN_COMPLEX(N) (((N) * ResPacketSize) >> 1)
+
+#define GEMV_LOADPACKET_COL_COMPLEX(iter) \
+ loadLhsPacket<Scalar, LhsScalar, LhsMapper, PLhsPacket>(lhs, i + ((iter) * ResPacketSize), j)
+
+#define GEMV_LOADPACKET_COL_COMPLEX_DATA(iter) \
+ convertReal(GEMV_LOADPACKET_COL_COMPLEX(iter))
+
+#ifdef USE_GEMV_MMA
+#define GEMV_INIT_COL_COMPLEX_MMA(iter, N) \
+ if (GEMV_GETN_COMPLEX(N) > iter) { \
+ __builtin_mma_xxsetaccz(&e0##iter); \
+ }
+
+#if EIGEN_COMP_LLVM
+#define GEMV_LOADPAIR_COL_COMPLEX_MMA(iter1, iter2) \
+ GEMV_BUILDPAIR_MMA(a##iter1, GEMV_LOADPACKET_COL_COMPLEX_DATA(iter2), GEMV_LOADPACKET_COL_COMPLEX_DATA((iter2) + 1)); \
+ EIGEN_UNUSED_VARIABLE(f##iter1);
+#else
+#define GEMV_LOADPAIR_COL_COMPLEX_MMA(iter1, iter2) \
+ if (sizeof(LhsPacket) == 16) { \
+ const LhsScalar& src = lhs(i + ((32 * iter1) / sizeof(LhsScalar)), j); \
+ a##iter1 = *reinterpret_cast<__vector_pair *>(const_cast<LhsScalar *>(&src)); \
+ EIGEN_UNUSED_VARIABLE(f##iter1); \
+ } else { \
+ f##iter1 = lhs.template load<PLhsPacket, Unaligned>(i + ((iter2) * ResPacketSize), j); \
+ GEMV_BUILDPAIR_MMA(a##iter1, vec_splat(convertReal(f##iter1), 0), vec_splat(convertReal(f##iter1), 1)); \
+ }
+#endif
+
+#define GEMV_LOAD1_COL_COMPLEX_MMA(iter, N) \
+ if (GEMV_GETN_COMPLEX(N) > iter) { \
+ if (GEMV_IS_COMPLEX_FLOAT) { \
+ f##iter = GEMV_LOADPACKET_COL_COMPLEX(iter); \
+ EIGEN_UNUSED_VARIABLE(a##iter); \
+ } else { \
+ GEMV_LOADPAIR_COL_COMPLEX_MMA(iter, iter << 1) \
+ } \
+ } else { \
+ EIGEN_UNUSED_VARIABLE(a##iter); \
+ EIGEN_UNUSED_VARIABLE(f##iter); \
+ }
+
+#define GEMV_WORK1_COL_COMPLEX_MMA(iter, N) \
+ if (GEMV_GETN_COMPLEX(N) > iter) { \
+ if (GEMV_IS_COMPLEX_FLOAT) { \
+ gemv_mult_complex_MMA<ScalarPacket, LhsScalar, PLhsPacket, PLhsPacket, RhsScalar, RhsPacket, ResPacket, ConjugateLhs, ConjugateRhs, ColMajor>(f##iter, b, &e0##iter); \
+ } else { \
+ gemv_mult_complex_MMA<ScalarPacket, LhsScalar, PLhsPacket, __vector_pair, RhsScalar, RhsPacket, ResPacket, ConjugateLhs, ConjugateRhs, ColMajor>(a##iter, b, &e0##iter); \
+ } \
+ }
+
+#define GEMV_LOADPAIR2_COL_COMPLEX_MMA(iter1, iter2) \
+ GEMV_BUILDPAIR_MMA(a##iter1, GEMV_LOADPACKET_COL_COMPLEX_DATA(iter2), GEMV_LOADPACKET_COL_COMPLEX_DATA((iter2) + 1));
+
+#define GEMV_LOAD2_COL_COMPLEX_MMA(iter1, iter2, iter3, N) \
+ if (GEMV_GETN_COMPLEX(N) > iter1) { \
+ if (GEMV_IS_COMPLEX_FLOAT) { \
+ GEMV_LOADPAIR2_COL_COMPLEX_MMA(iter2, iter2); \
+ EIGEN_UNUSED_VARIABLE(a##iter3) \
+ } else { \
+ GEMV_LOADPAIR2_COL_COMPLEX_MMA(iter2, iter2 << 1); \
+ GEMV_LOADPAIR2_COL_COMPLEX_MMA(iter3, iter3 << 1); \
+ } \
+ } else { \
+ EIGEN_UNUSED_VARIABLE(a##iter2); \
+ EIGEN_UNUSED_VARIABLE(a##iter3); \
+ } \
+ EIGEN_UNUSED_VARIABLE(f##iter2); \
+ EIGEN_UNUSED_VARIABLE(f##iter3);
+
+#define GEMV_WORK2_COL_COMPLEX_MMA(iter1, iter2, iter3, N) \
+ if (GEMV_GETN_COMPLEX(N) > iter1) { \
+ if (GEMV_IS_COMPLEX_FLOAT) { \
+ PLhsPacket g[2]; \
+ __builtin_vsx_disassemble_pair(reinterpret_cast<void*>(g), &a##iter2); \
+ gemv_mult_complex_MMA<ScalarPacket, LhsScalar, PLhsPacket, PLhsPacket, RhsScalar, RhsPacket, ResPacket, ConjugateLhs, ConjugateRhs, ColMajor>(g[0], b, &e0##iter2); \
+ gemv_mult_complex_MMA<ScalarPacket, LhsScalar, PLhsPacket, PLhsPacket, RhsScalar, RhsPacket, ResPacket, ConjugateLhs, ConjugateRhs, ColMajor>(g[1], b, &e0##iter3); \
+ } else { \
+ gemv_mult_complex_MMA<ScalarPacket, LhsScalar, PLhsPacket, __vector_pair, RhsScalar, RhsPacket, ResPacket, ConjugateLhs, ConjugateRhs, ColMajor>(a##iter2, b, &e0##iter2); \
+ gemv_mult_complex_MMA<ScalarPacket, LhsScalar, PLhsPacket, __vector_pair, RhsScalar, RhsPacket, ResPacket, ConjugateLhs, ConjugateRhs, ColMajor>(a##iter3, b, &e0##iter3); \
+ } \
+ }
+
+#if EIGEN_COMP_LLVM
+#define GEMV_LOAD_COL_COMPLEX_MMA(N) \
+ if (GEMV_GETN_COMPLEX(N) > 1) { \
+ GEMV_UNROLL_HALF(GEMV_LOAD2_COL_COMPLEX_MMA, (N >> 1)) \
+ } else { \
+ GEMV_UNROLL(GEMV_LOAD1_COL_COMPLEX_MMA, N) \
+ }
+
+#define GEMV_WORK_COL_COMPLEX_MMA(N) \
+ if (GEMV_GETN_COMPLEX(N) > 1) { \
+ GEMV_UNROLL_HALF(GEMV_WORK2_COL_COMPLEX_MMA, (N >> 1)) \
+ } else { \
+ GEMV_UNROLL(GEMV_WORK1_COL_COMPLEX_MMA, N) \
+ }
+#else
+#define GEMV_LOAD_COL_COMPLEX_MMA(N) \
+ GEMV_UNROLL(GEMV_LOAD1_COL_COMPLEX_MMA, N)
+
+#define GEMV_WORK_COL_COMPLEX_MMA(N) \
+ GEMV_UNROLL(GEMV_WORK1_COL_COMPLEX_MMA, N)
+#endif
+
+#define GEMV_DISASSEMBLE_COMPLEX_MMA(iter) \
+ disassembleResults<Scalar, ScalarPacket, ResPacketSize, LhsPacket, RhsPacket, ConjugateLhs, ConjugateRhs>(&e0##iter, result0##iter);
+
+#define GEMV_STORE_COL_COMPLEX_MMA(iter, N) \
+ if (GEMV_GETN_COMPLEX(N) > iter) { \
+ GEMV_DISASSEMBLE_COMPLEX_MMA(iter); \
+ c0##iter = PResPacket(result0##iter.packet[0]); \
+ if (GEMV_IS_COMPLEX_FLOAT) { \
+ pstoreu_pmadd_complex<Scalar, ScalarPacket, PResPacket, ResPacket, ResScalar, AlphaData>(c0##iter, alpha_data, res + i + (iter * ResPacketSize)); \
+ } else { \
+ pstoreu_pmadd_complex<Scalar, ScalarPacket, PResPacket, ResPacket, ResScalar, AlphaData>(c0##iter, alpha_data, res + i + ((iter << 1) * ResPacketSize)); \
+ c0##iter = PResPacket(result0##iter.packet[2]); \
+ pstoreu_pmadd_complex<Scalar, ScalarPacket, PResPacket, ResPacket, ResScalar, AlphaData>(c0##iter, alpha_data, res + i + (((iter << 1) + 1) * ResPacketSize)); \
+ } \
+ }
+
+#define GEMV_STORE2_COL_COMPLEX_MMA(iter1, iter2, iter3, N) \
+ if (GEMV_GETN_COMPLEX(N) > iter1) { \
+ GEMV_DISASSEMBLE_COMPLEX_MMA(iter2); \
+ GEMV_DISASSEMBLE_COMPLEX_MMA(iter3); \
+ c0##iter2 = PResPacket(result0##iter2.packet[0]); \
+ if (GEMV_IS_COMPLEX_FLOAT) { \
+ c0##iter3 = PResPacket(result0##iter3.packet[0]); \
+ pstoreu_pmadd_complex<ScalarPacket, PResPacket, ResPacket, ResScalar, AlphaData, ResPacketSize, iter2>(c0##iter2, c0##iter3, alpha_data, res + i); \
+ } else { \
+ c0##iter3 = PResPacket(result0##iter2.packet[2]); \
+ pstoreu_pmadd_complex<ScalarPacket, PResPacket, ResPacket, ResScalar, AlphaData, ResPacketSize, iter2 << 1>(c0##iter2, c0##iter3, alpha_data, res + i); \
+ c0##iter2 = PResPacket(result0##iter3.packet[0]); \
+ c0##iter3 = PResPacket(result0##iter3.packet[2]); \
+ pstoreu_pmadd_complex<ScalarPacket, PResPacket, ResPacket, ResScalar, AlphaData, ResPacketSize, iter3 << 1>(c0##iter2, c0##iter3, alpha_data, res + i); \
+ } \
+ }
+
+#define GEMV_PROCESS_COL_COMPLEX_ONE_MMA(N) \
+ GEMV_UNROLL(GEMV_INIT_COL_COMPLEX_MMA, N) \
+ Index j = j2; \
+ do { \
+ const RhsScalar& b1 = rhs2(j, 0); \
+ RhsScalar* b = const_cast<RhsScalar *>(&b1); \
+ GEMV_UNROLL(GEMV_PREFETCH, N) \
+ GEMV_LOAD_COL_COMPLEX_MMA(N) \
+ GEMV_WORK_COL_COMPLEX_MMA(N) \
+ } while (++j < jend); \
+ if (GEMV_GETN(N) <= 2) { \
+ GEMV_UNROLL(GEMV_STORE_COL_COMPLEX_MMA, N) \
+ } else { \
+ GEMV_UNROLL_HALF(GEMV_STORE2_COL_COMPLEX_MMA, (N >> 1)) \
+ } \
+ i += (ResPacketSize * N);
+#endif
+
+#define GEMV_INIT_COMPLEX(iter, N) \
+ if (N > iter) { \
+ c0##iter = pset_zero<PResPacket>(); \
+ c1##iter = pset_init<ResPacket, LhsPacket, RhsPacket>(c1##iter); \
+ } else { \
+ EIGEN_UNUSED_VARIABLE(c0##iter); \
+ EIGEN_UNUSED_VARIABLE(c1##iter); \
+ }
+
+#define GEMV_WORK_COL_COMPLEX(iter, N) \
+ if (N > iter) { \
+ f##iter = GEMV_LOADPACKET_COL_COMPLEX(iter); \
+ gemv_mult_complex<ScalarPacket, PLhsPacket, RhsScalar, RhsPacket, PResPacket, ResPacket, ConjugateLhs, ConjugateRhs, ColMajor>(f##iter, b, c0##iter, c1##iter); \
+ } else { \
+ EIGEN_UNUSED_VARIABLE(f##iter); \
+ }
+
+#define GEMV_STORE_COL_COMPLEX(iter, N) \
+ if (N > iter) { \
+ if (GEMV_IS_COMPLEX_COMPLEX) { \
+ c0##iter = padd(c0##iter, c1##iter); \
+ } \
+ pstoreu_pmadd_complex<Scalar, ScalarPacket, PResPacket, ResPacket, ResScalar, AlphaData>(c0##iter, alpha_data, res + i + (iter * ResPacketSize)); \
+ }
+
+/** \internal main macro for gemv_complex_col - initialize accumulators, multiply and add inputs, and store results */
+#define GEMV_PROCESS_COL_COMPLEX_ONE(N) \
+ GEMV_UNROLL(GEMV_INIT_COMPLEX, N) \
+ Index j = j2; \
+ do { \
+ const RhsScalar& b1 = rhs2(j, 0); \
+ RhsScalar* b = const_cast<RhsScalar *>(&b1); \
+ GEMV_UNROLL(GEMV_PREFETCH, N) \
+ GEMV_UNROLL(GEMV_WORK_COL_COMPLEX, N) \
+ } while (++j < jend); \
+ GEMV_UNROLL(GEMV_STORE_COL_COMPLEX, N) \
+ i += (ResPacketSize * N);
+
+#if defined(USE_GEMV_MMA) && (EIGEN_COMP_LLVM || defined(USE_SLOWER_GEMV_MMA))
+#define USE_GEMV_COL_COMPLEX_MMA
+#endif
+
+#ifdef USE_GEMV_COL_COMPLEX_MMA
+#define GEMV_PROCESS_COL_COMPLEX(N) \
+ GEMV_PROCESS_COL_COMPLEX_ONE_MMA(N)
+#else
+#if defined(USE_GEMV_MMA) && (__GNUC__ > 10)
+#define GEMV_PROCESS_COL_COMPLEX(N) \
+ if (sizeof(Scalar) != sizeof(LhsPacket)) { \
+ GEMV_PROCESS_COL_COMPLEX_ONE_MMA(N) \
+ } else { \
+ GEMV_PROCESS_COL_COMPLEX_ONE(N) \
+ }
+#else
+#define GEMV_PROCESS_COL_COMPLEX(N) \
+ GEMV_PROCESS_COL_COMPLEX_ONE(N)
+#endif
+#endif
+
+template<typename Scalar, typename LhsScalar, typename LhsMapper, bool ConjugateLhs, bool LhsIsReal, typename RhsScalar, typename RhsMapper, bool ConjugateRhs, bool RhsIsReal, typename ResScalar>
+EIGEN_STRONG_INLINE void gemv_complex_col(
+ Index rows, Index cols,
+ const LhsMapper& alhs,
+ const RhsMapper& rhs,
+ ResScalar* res, Index resIncr,
+ ResScalar alpha)
+{
+ typedef gemv_traits<LhsScalar, RhsScalar> Traits;
+
+ typedef typename Traits::LhsPacket LhsPacket;
+ typedef typename Traits::RhsPacket RhsPacket;
+ typedef typename Traits::ResPacket ResPacket;
+
+ typedef typename packet_traits<Scalar>::type ScalarPacket;
+ typedef typename packet_traits<LhsScalar>::type PLhsPacket;
+ typedef typename packet_traits<ResScalar>::type PResPacket;
+ typedef gemv_traits<ResPacket, ResPacket> PTraits;
+
+ EIGEN_UNUSED_VARIABLE(resIncr);
+ eigen_internal_assert(resIncr == 1);
+
+ // The following copy tells the compiler that lhs's attributes are not modified outside this function
+ // This helps GCC to generate proper code.
+ LhsMapper lhs(alhs);
+ RhsMapper rhs2(rhs);
+
+ conj_helper<LhsScalar, RhsScalar, ConjugateLhs, ConjugateRhs> cj;
+
+ const Index lhsStride = lhs.stride();
+ // TODO: for padded aligned inputs, we could enable aligned reads
+ enum {
+ LhsAlignment = Unaligned,
+ ResPacketSize = PTraits::ResPacketSize,
+ LhsPacketSize = PTraits::LhsPacketSize,
+ RhsPacketSize = PTraits::RhsPacketSize,
+ };
+#ifdef EIGEN_POWER_USE_GEMV_PREFETCH
+ const Index prefetch_dist = 64 * LhsPacketSize;
+#endif
+
+#ifndef GCC_ONE_VECTORPAIR_BUG
+ const Index n8 = rows - 8 * ResPacketSize + 1;
+ const Index n4 = rows - 4 * ResPacketSize + 1;
+ const Index n2 = rows - 2 * ResPacketSize + 1;
+#endif
+ const Index n1 = rows - 1 * ResPacketSize + 1;
+
+ // TODO: improve the following heuristic:
+ const Index block_cols = cols < 128 ? cols : (lhsStride * sizeof(LhsScalar) < 16000 ? 16 : 8);
+
+ typedef alpha_store<PResPacket, ResPacket, ResScalar, Scalar> AlphaData;
+ AlphaData alpha_data(alpha);
+
+ for (Index j2 = 0; j2 < cols; j2 += block_cols)
+ {
+ Index jend = numext::mini(j2 + block_cols, cols);
+ Index i = 0;
+ PResPacket c00, c01, c02, c03, c04, c05, c06, c07;
+ ResPacket c10, c11, c12, c13, c14, c15, c16, c17;
+ PLhsPacket f0, f1, f2, f3, f4, f5, f6, f7;
+#ifdef USE_GEMV_MMA
+ __vector_quad e00, e01, e02, e03, e04, e05, e06, e07;
+ __vector_pair a0, a1, a2, a3, a4, a5, a6, a7;
+ PacketBlock<ScalarPacket, 4> result00, result01, result02, result03, result04, result05, result06, result07;
+ GEMV_UNUSED(8, e0)
+ GEMV_UNUSED(8, result0)
+ GEMV_UNUSED(8, a)
+ GEMV_UNUSED(8, f)
+#if !defined(GCC_ONE_VECTORPAIR_BUG) && defined(USE_GEMV_COL_COMPLEX_MMA)
+ if (GEMV_IS_COMPLEX_COMPLEX || !GEMV_IS_COMPLEX_FLOAT)
+#endif
+#endif
+#ifndef GCC_ONE_VECTORPAIR_BUG
+ {
+ while (i < n8)
+ {
+ GEMV_PROCESS_COL_COMPLEX(8)
+ }
+ }
+ while (i < n4)
+ {
+ GEMV_PROCESS_COL_COMPLEX(4)
+ }
+ if (i < n2)
+ {
+ GEMV_PROCESS_COL_COMPLEX(2)
+ }
+ if (i < n1)
+#else
+ while (i < n1)
+#endif
+ {
+ GEMV_PROCESS_COL_COMPLEX_ONE(1)
+ }
+ for (;i < rows;++i)
+ {
+ ResScalar d0(0);
+ Index j = j2;
+ do {
+ d0 += cj.pmul(lhs(i, j), rhs2(j, 0));
+ } while (++j < jend);
+ res[i] += alpha * d0;
+ }
+ }
+}
+
+template <typename Scalar, int N> struct ScalarBlock {
+ Scalar scalar[N];
+};
+
+#ifdef USE_GEMV_MMA
+static Packet16uc p16uc_ELEMENT_3 = { 0x0c,0x0d,0x0e,0x0f, 0x1c,0x1d,0x1e,0x1f, 0x0c,0x0d,0x0e,0x0f, 0x1c,0x1d,0x1e,0x1f };
+
+/** \internal predux (add elements of a vector) from a MMA accumulator - real results */
+template<typename ResScalar, typename ResPacket>
+EIGEN_ALWAYS_INLINE ScalarBlock<ResScalar, 2> predux_real(__vector_quad* acc0, __vector_quad* acc1)
+{
+ PacketBlock<ResPacket, 4> result0, result1;
+ __builtin_mma_disassemble_acc(&result0.packet, acc0);
+ __builtin_mma_disassemble_acc(&result1.packet, acc1);
+ result0.packet[0] = vec_mergeh(result0.packet[0], result1.packet[0]);
+ result0.packet[1] = vec_mergeo(result0.packet[1], result1.packet[1]);
+ result0.packet[2] = vec_mergel(result0.packet[2], result1.packet[2]);
+ result0.packet[3] = vec_perm(result0.packet[3], result1.packet[3], p16uc_ELEMENT_3);
+ result0.packet[0] = vec_add(vec_add(result0.packet[0], result0.packet[2]), vec_add(result0.packet[1], result0.packet[3]));
+ return *reinterpret_cast<ScalarBlock<ResScalar, 2> *>(&result0.packet[0]);
+}
+
+template<>
+EIGEN_ALWAYS_INLINE ScalarBlock<double, 2> predux_real<double, Packet2d>(__vector_quad* acc0, __vector_quad* acc1)
+{
+ PacketBlock<Packet2d, 4> result0, result1;
+ __builtin_mma_disassemble_acc(&result0.packet, acc0);
+ __builtin_mma_disassemble_acc(&result1.packet, acc1);
+ result0.packet[0] = vec_add(vec_mergeh(result0.packet[0], result1.packet[0]), vec_mergel(result0.packet[1], result1.packet[1]));
+ return *reinterpret_cast<ScalarBlock<double, 2> *>(&result0.packet[0]);
+}
+
+/** \internal add complex results together */
+template<typename LhsPacket, typename RhsPacket, bool ConjugateLhs, bool ConjugateRhs>
+EIGEN_ALWAYS_INLINE ScalarBlock<std::complex<float>, 2> addComplexResults(PacketBlock<Packet4f, 4>& result0, PacketBlock<Packet4f, 4>& result1)
+{
+ ScalarBlock<std::complex<float>, 2> cc0;
+ result0.packet[0] = reinterpret_cast<Packet4f>(vec_mergeh(reinterpret_cast<Packet2d>(result0.packet[0]), reinterpret_cast<Packet2d>(result1.packet[0])));
+ result0.packet[2] = reinterpret_cast<Packet4f>(vec_mergel(reinterpret_cast<Packet2d>(result0.packet[2]), reinterpret_cast<Packet2d>(result1.packet[2])));
+ result0.packet[0] = vec_add(result0.packet[0], result0.packet[2]);
+ if (GEMV_IS_COMPLEX_COMPLEX) {
+ result0.packet[1] = reinterpret_cast<Packet4f>(vec_mergeh(reinterpret_cast<Packet2d>(result0.packet[1]), reinterpret_cast<Packet2d>(result1.packet[1])));
+ result0.packet[3] = reinterpret_cast<Packet4f>(vec_mergel(reinterpret_cast<Packet2d>(result0.packet[3]), reinterpret_cast<Packet2d>(result1.packet[3])));
+ result0.packet[1] = vec_add(result0.packet[1], result0.packet[3]);
+ if (ConjugateLhs) {
+ result0.packet[0] = pconj2(convertComplex(result0.packet[0])).v;
+ result0.packet[1] = pcplxflip2(convertComplex(result0.packet[1])).v;
+ } else if (ConjugateRhs) {
+ result0.packet[1] = pcplxconjflip(convertComplex(result0.packet[1])).v;
+ } else {
+ result0.packet[1] = pcplxflipconj(convertComplex(result0.packet[1])).v;
+ }
+ result0.packet[0] = vec_add(result0.packet[0], result0.packet[1]);
+ } else {
+ if (ConjugateLhs && (sizeof(LhsPacket) == sizeof(std::complex<float>))) {
+ result0.packet[0] = pconj2(convertComplex(result0.packet[0])).v;
+ }
+ }
+ cc0.scalar[0].real(result0.packet[0][0]);
+ cc0.scalar[0].imag(result0.packet[0][1]);
+ cc0.scalar[1].real(result0.packet[0][2]);
+ cc0.scalar[1].imag(result0.packet[0][3]);
+ return cc0;
+}
+
+template<typename LhsPacket, typename RhsPacket, bool ConjugateLhs, bool ConjugateRhs>
+EIGEN_ALWAYS_INLINE ScalarBlock<std::complex<double>, 2> addComplexResults(PacketBlock<Packet2d, 4>&, PacketBlock<Packet2d, 4>&)
+{
+ ScalarBlock<std::complex<double>, 2> cc0;
+ EIGEN_UNUSED_VARIABLE(cc0);
+ return cc0; // Just for compilation
+}
+
+/** \internal predux (add elements of a vector) from a MMA accumulator - complex results */
+template<typename ResScalar, typename ResPacket, typename LhsPacket, typename RhsPacket, bool ConjugateLhs, bool ConjugateRhs>
+EIGEN_ALWAYS_INLINE ScalarBlock<ResScalar, 2> predux_complex(__vector_quad* acc0, __vector_quad* acc1)
+{
+ PacketBlock<ResPacket, 4> result0, result1;
+ __builtin_mma_disassemble_acc(&result0.packet, acc0);
+ __builtin_mma_disassemble_acc(&result1.packet, acc1);
+ return addComplexResults<LhsPacket, RhsPacket, ConjugateLhs, ConjugateRhs>(result0, result1);
+}
+
+template<typename ResScalar, typename ResPacket>
+EIGEN_ALWAYS_INLINE ScalarBlock<ResScalar, 2> predux_real(__vector_quad* acc0)
+{
+ PacketBlock<ResPacket, 4> result0;
+ __builtin_mma_disassemble_acc(&result0.packet, acc0);
+ result0.packet[0] = vec_add(vec_mergeh(result0.packet[0], result0.packet[2]), vec_mergel(result0.packet[1], result0.packet[3]));
+ return *reinterpret_cast<ScalarBlock<ResScalar, 2> *>(&result0.packet[0]);
+}
+
+template<typename ResScalar, typename ResPacket, typename LhsPacket, typename RhsPacket, bool ConjugateLhs, bool ConjugateRhs>
+EIGEN_ALWAYS_INLINE ScalarBlock<ResScalar, 2> predux_complex(__vector_quad* acc0)
+{
+ ScalarBlock<ResScalar, 2> cc0;
+ PacketBlock<ResPacket, 4> result0;
+ __builtin_mma_disassemble_acc(&result0.packet, acc0);
+ if (GEMV_IS_COMPLEX_COMPLEX) {
+ if (ConjugateLhs) {
+ result0.packet[1] = pconjinv(convertComplex(result0.packet[1])).v;
+ result0.packet[3] = pconjinv(convertComplex(result0.packet[3])).v;
+ } else if (ConjugateRhs) {
+ result0.packet[0] = pconj2(convertComplex(result0.packet[0])).v;
+ result0.packet[2] = pconj2(convertComplex(result0.packet[2])).v;
+ } else {
+ result0.packet[1] = pconj2(convertComplex(result0.packet[1])).v;
+ result0.packet[3] = pconj2(convertComplex(result0.packet[3])).v;
+ }
+ result0.packet[0] = vec_add(result0.packet[0], __builtin_vsx_xxpermdi(result0.packet[1], result0.packet[1], 2));
+ result0.packet[2] = vec_add(result0.packet[2], __builtin_vsx_xxpermdi(result0.packet[3], result0.packet[3], 2));
+ } else {
+ result0.packet[0] = __builtin_vsx_xxpermdi(result0.packet[0], result0.packet[1], 1);
+ result0.packet[2] = __builtin_vsx_xxpermdi(result0.packet[2], result0.packet[3], 1);
+ }
+ cc0.scalar[0].real(result0.packet[0][0]);
+ cc0.scalar[0].imag(result0.packet[0][1]);
+ cc0.scalar[1].real(result0.packet[2][0]);
+ cc0.scalar[1].imag(result0.packet[2][1]);
+ return cc0;
+}
+#endif
+
+template<typename ResScalar, typename ResPacket>
+EIGEN_ALWAYS_INLINE ScalarBlock<ResScalar, 2> predux_real(ResPacket& a, ResPacket& b)
+{
+ ScalarBlock<ResScalar, 2> cc0;
+ cc0.scalar[0] = predux(a);
+ cc0.scalar[1] = predux(b);
+ return cc0;
+}
+
+template<typename ResScalar, typename ResPacket>
+EIGEN_ALWAYS_INLINE ScalarBlock<ResScalar, 2> predux_complex(ResPacket& a, ResPacket& b)
+{
+ return predux_real<ResScalar, ResPacket>(a, b);
+}
+
+#define GEMV_UNROLL_ROW(func, N) \
+ func(0, N) func(1, N) func(2, N) func(3, N) func(4, N) func(5, N) func(6, N) func(7, N)
+
+#define GEMV_UNROLL_ROW_HALF(func, N) \
+ func(0, 0, 1, N) func(1, 2, 3, N) func(2, 4, 5, N) func(3, 6, 7, N)
+
+#define GEMV_LOADPACKET_ROW(iter) \
+ lhs.template load<LhsPacket, Unaligned>(i + (iter), j)
+
+#ifdef USE_GEMV_MMA
+#define GEMV_UNROLL3_ROW(func, N, which) \
+ func(0, N, which) func(1, N, which) func(2, N, which) func(3, N, which) \
+ func(4, N, which) func(5, N, which) func(6, N, which) func(7, N, which)
+
+#define GEMV_UNUSED_ROW(N, which) \
+ GEMV_UNROLL3_ROW(GEMV_UNUSED_VAR, N, which)
+
+#define GEMV_INIT_ROW(iter, N) \
+ if (GEMV_GETN(N) > iter) { \
+ __builtin_mma_xxsetaccz(&c##iter); \
+ }
+
+#define GEMV_LOADPAIR_ROW(iter1, iter2) \
+ GEMV_BUILDPAIR_MMA(b##iter1, GEMV_LOADPACKET_ROW(iter2), GEMV_LOADPACKET_ROW((iter2) + 1));
+
+#define GEMV_WORK_ROW(iter, N) \
+ if (GEMV_GETN(N) > iter) { \
+ if (GEMV_IS_FLOAT) { \
+ pger_vecMMA_acc<LhsPacket, RhsPacket, true>(&c##iter, a0, GEMV_LOADPACKET_ROW(iter)); \
+ } else { \
+ __vector_pair b##iter; \
+ GEMV_LOADPAIR_ROW(iter, iter << 1) \
+ pger_vecMMA_acc<LhsPacket, RhsPacket, true>(&c##iter, b##iter, a0); \
+ } \
+ }
+
+#define GEMV_PREDUX2(iter1, iter2, iter3, N) \
+ if (N > iter1) { \
+ if (GEMV_IS_FLOAT) { \
+ cc##iter1 = predux_real<ResScalar, ResPacket>(&c##iter2, &c##iter3); \
+ } else { \
+ cc##iter1 = predux_real<ResScalar, ResPacket>(&c##iter1); \
+ } \
+ } else { \
+ EIGEN_UNUSED_VARIABLE(cc##iter1); \
+ }
+#else
+#define GEMV_INIT_ROW(iter, N) \
+ if (N > iter) { \
+ c##iter = pset1<ResPacket>(ResScalar(0)); \
+ } else { \
+ EIGEN_UNUSED_VARIABLE(c##iter); \
+ }
+
+#define GEMV_WORK_ROW(iter, N) \
+ if (N > iter) { \
+ c##iter = pcj.pmadd(GEMV_LOADPACKET_ROW(iter), a0, c##iter); \
+ }
+
+#define GEMV_PREDUX2(iter1, iter2, iter3, N) \
+ if (N > iter1) { \
+ cc##iter1 = predux_real<ResScalar, ResPacket>(c##iter2, c##iter3); \
+ } else { \
+ EIGEN_UNUSED_VARIABLE(cc##iter1); \
+ }
+#endif
+
+#define GEMV_MULT(iter1, iter2, iter3, N) \
+ if (N > iter1) { \
+ cc##iter1.scalar[0] += cj.pmul(lhs(i + iter2, j), a0); \
+ cc##iter1.scalar[1] += cj.pmul(lhs(i + iter3, j), a0); \
+ }
+
+#define GEMV_STORE_ROW(iter1, iter2, iter3, N) \
+ if (N > iter1) { \
+ storeMaddData<ResScalar>(res + ((i + iter2) * resIncr), alpha, cc##iter1.scalar[0]); \
+ storeMaddData<ResScalar>(res + ((i + iter3) * resIncr), alpha, cc##iter1.scalar[1]); \
+ }
+
+/** \internal main macro for gemv_row - initialize accumulators, multiply and add inputs, predux and store results */
+#define GEMV_PROCESS_ROW(N) \
+ for (; i < n##N; i += N) { \
+ GEMV_UNROLL_ROW(GEMV_INIT_ROW, N) \
+ Index j = 0; \
+ for (; j + LhsPacketSize <= cols; j += LhsPacketSize) { \
+ RhsPacket a0 = rhs2.template load<RhsPacket, Unaligned>(j); \
+ GEMV_UNROLL_ROW(GEMV_WORK_ROW, N) \
+ } \
+ GEMV_UNROLL_ROW_HALF(GEMV_PREDUX2, (N >> 1)) \
+ for (; j < cols; ++j) { \
+ RhsScalar a0 = rhs2(j); \
+ GEMV_UNROLL_ROW_HALF(GEMV_MULT, (N >> 1)) \
+ } \
+ GEMV_UNROLL_ROW_HALF(GEMV_STORE_ROW, (N >> 1)) \
+ }
+
+template<typename LhsScalar, typename LhsMapper, typename RhsScalar, typename RhsMapper, typename ResScalar>
+EIGEN_STRONG_INLINE void gemv_row(
+ Index rows, Index cols,
+ const LhsMapper& alhs,
+ const RhsMapper& rhs,
+ ResScalar* res, Index resIncr,
+ ResScalar alpha)
+{
+ typedef gemv_traits<LhsScalar, RhsScalar> Traits;
+
+ typedef typename Traits::LhsPacket LhsPacket;
+ typedef typename Traits::RhsPacket RhsPacket;
+ typedef typename Traits::ResPacket ResPacket;
+
+ // The following copy tells the compiler that lhs's attributes are not modified outside this function
+ // This helps GCC to generate proper code.
+ LhsMapper lhs(alhs);
+ typename RhsMapper::LinearMapper rhs2 = rhs.getLinearMapper(0, 0);
+
+ eigen_internal_assert(rhs.stride() == 1);
+ conj_helper<LhsScalar, RhsScalar, false, false> cj;
+ conj_helper<LhsPacket, RhsPacket, false, false> pcj;
+
+ // TODO: fine tune the following heuristic. The rationale is that if the matrix is very large,
+ // processing 8 rows at once might be counter productive wrt cache.
+#ifndef GCC_ONE_VECTORPAIR_BUG
+ const Index n8 = lhs.stride() * sizeof(LhsScalar) > 32000 ? (rows - 7) : (rows - 7);
+ const Index n4 = rows - 3;
+ const Index n2 = rows - 1;
+#endif
+
+ // TODO: for padded aligned inputs, we could enable aligned reads
+ enum {
+ LhsAlignment = Unaligned,
+ ResPacketSize = Traits::ResPacketSize,
+ LhsPacketSize = Traits::LhsPacketSize,
+ RhsPacketSize = Traits::RhsPacketSize,
+ };
+
+ Index i = 0;
+#ifdef USE_GEMV_MMA
+ __vector_quad c0, c1, c2, c3, c4, c5, c6, c7;
+ GEMV_UNUSED_ROW(8, c)
+#else
+ ResPacket c0, c1, c2, c3, c4, c5, c6, c7;
+#endif
+#ifndef GCC_ONE_VECTORPAIR_BUG
+ ScalarBlock<ResScalar, 2> cc0, cc1, cc2, cc3;
+ GEMV_PROCESS_ROW(8)
+ GEMV_PROCESS_ROW(4)
+ GEMV_PROCESS_ROW(2)
+#endif
+ for (; i < rows; ++i)
+ {
+ ResPacket d0 = pset1<ResPacket>(ResScalar(0));
+ Index j = 0;
+ for (; j + LhsPacketSize <= cols; j += LhsPacketSize)
+ {
+ RhsPacket b0 = rhs2.template load<RhsPacket, Unaligned>(j);
+
+ d0 = pcj.pmadd(lhs.template load<LhsPacket, LhsAlignment>(i + 0, j), b0, d0);
+ }
+ ResScalar dd0 = predux(d0);
+ for (; j < cols; ++j)
+ {
+ dd0 += cj.pmul(lhs(i, j), rhs2(j));
+ }
+ res[i * resIncr] += alpha * dd0;
+ }
+}
+
+#define EIGEN_POWER_GEMV_REAL_SPECIALIZE_COL(Scalar) \
+template<typename Index, typename LhsMapper, bool ConjugateLhs, typename RhsMapper, bool ConjugateRhs, int Version> \
+struct general_matrix_vector_product<Index, Scalar, LhsMapper, ColMajor, ConjugateLhs, Scalar, RhsMapper, ConjugateRhs, Version> \
+{ \
+ typedef typename ScalarBinaryOpTraits<Scalar, Scalar>::ReturnType ResScalar; \
+\
+ EIGEN_DEVICE_FUNC EIGEN_DONT_INLINE static void run( \
+ Index rows, Index cols, \
+ const LhsMapper& lhs, \
+ const RhsMapper& rhs, \
+ ResScalar* res, Index resIncr, \
+ ResScalar alpha) { \
+ gemv_col<Scalar, LhsMapper, Scalar, RhsMapper, ResScalar>(rows, cols, lhs, rhs, res, resIncr, alpha); \
+ } \
+};
+
+#define EIGEN_POWER_GEMV_REAL_SPECIALIZE_ROW(Scalar) \
+template<typename Index, typename LhsMapper, bool ConjugateLhs, typename RhsMapper, bool ConjugateRhs, int Version> \
+struct general_matrix_vector_product<Index, Scalar, LhsMapper, RowMajor, ConjugateLhs, Scalar, RhsMapper, ConjugateRhs, Version> \
+{ \
+ typedef typename ScalarBinaryOpTraits<Scalar, Scalar>::ReturnType ResScalar; \
+\
+ EIGEN_DEVICE_FUNC EIGEN_DONT_INLINE static void run( \
+ Index rows, Index cols, \
+ const LhsMapper& lhs, \
+ const RhsMapper& rhs, \
+ ResScalar* res, Index resIncr, \
+ ResScalar alpha) { \
+ gemv_row<Scalar, LhsMapper, Scalar, RhsMapper, ResScalar>(rows, cols, lhs, rhs, res, resIncr, alpha); \
+ } \
+};
+
+EIGEN_POWER_GEMV_REAL_SPECIALIZE_COL(float)
+EIGEN_POWER_GEMV_REAL_SPECIALIZE_COL(double)
+EIGEN_POWER_GEMV_REAL_SPECIALIZE_ROW(float)
+EIGEN_POWER_GEMV_REAL_SPECIALIZE_ROW(double)
+
+template<typename ResScalar, typename PResPacket, typename ResPacket, typename LhsPacket, typename RhsPacket>
+EIGEN_ALWAYS_INLINE ScalarBlock<ResScalar, 2> predux_complex(PResPacket& a0, PResPacket& b0, ResPacket& a1, ResPacket& b1)
+{
+ if (GEMV_IS_COMPLEX_COMPLEX) {
+ a0 = padd(a0, a1);
+ b0 = padd(b0, b1);
+ }
+ return predux_complex<ResScalar, PResPacket>(a0, b0);
+}
+
+#define GEMV_LOADPACKET_ROW_COMPLEX(iter) \
+ loadLhsPacket<Scalar, LhsScalar, LhsMapper, PLhsPacket>(lhs, i + (iter), j)
+
+#define GEMV_LOADPACKET_ROW_COMPLEX_DATA(iter) \
+ convertReal(GEMV_LOADPACKET_ROW_COMPLEX(iter))
+
+#define GEMV_PROCESS_ROW_COMPLEX_SINGLE_WORK(which, N) \
+ j = 0; \
+ for (; j + LhsPacketSize <= cols; j += LhsPacketSize) { \
+ const RhsScalar& b1 = rhs2(j); \
+ RhsScalar* b = const_cast<RhsScalar *>(&b1); \
+ GEMV_UNROLL_ROW(which, N) \
+ }
+
+#define GEMV_PROCESS_END_ROW_COMPLEX(N) \
+ for (; j < cols; ++j) { \
+ RhsScalar b0 = rhs2(j); \
+ GEMV_UNROLL_ROW_HALF(GEMV_MULT_COMPLEX, (N >> 1)) \
+ } \
+ GEMV_UNROLL_ROW_HALF(GEMV_STORE_ROW_COMPLEX, (N >> 1))
+
+#ifdef USE_GEMV_MMA
+#define GEMV_INIT_ROW_COMPLEX_MMA(iter, N) \
+ if (GEMV_GETN_COMPLEX(N) > iter) { \
+ __builtin_mma_xxsetaccz(&e0##iter); \
+ }
+
+#define GEMV_LOADPAIR_ROW_COMPLEX_MMA(iter1, iter2) \
+ GEMV_BUILDPAIR_MMA(a##iter1, GEMV_LOADPACKET_ROW_COMPLEX_DATA(iter2), GEMV_LOADPACKET_ROW_COMPLEX_DATA((iter2) + 1));
+
+#define GEMV_WORK_ROW_COMPLEX_MMA(iter, N) \
+ if (GEMV_GETN_COMPLEX(N) > iter) { \
+ if (GEMV_IS_COMPLEX_FLOAT) { \
+ PLhsPacket a##iter = GEMV_LOADPACKET_ROW_COMPLEX(iter); \
+ gemv_mult_complex_MMA<ScalarPacket, LhsScalar, PLhsPacket, PLhsPacket, RhsScalar, RhsPacket, ResPacket, ConjugateLhs, ConjugateRhs, RowMajor>(a##iter, b, &e0##iter); \
+ } else { \
+ __vector_pair a##iter; \
+ GEMV_LOADPAIR_ROW_COMPLEX_MMA(iter, iter << 1) \
+ gemv_mult_complex_MMA<ScalarPacket, LhsScalar, PLhsPacket, __vector_pair, RhsScalar, RhsPacket, ResPacket, ConjugateLhs, ConjugateRhs, RowMajor>(a##iter, b, &e0##iter); \
+ } \
+ }
+
+#define GEMV_PREDUX4_COMPLEX_MMA(iter1, iter2, iter3, N) \
+ if (N > iter1) { \
+ if (GEMV_IS_COMPLEX_FLOAT) { \
+ cc##iter1 = predux_complex<ResScalar, ScalarPacket, LhsPacket, RhsPacket, ConjugateLhs, ConjugateRhs>(&e0##iter2, &e0##iter3); \
+ } else { \
+ cc##iter1 = predux_complex<ResScalar, ScalarPacket, LhsPacket, RhsPacket, ConjugateLhs, ConjugateRhs>(&e0##iter1); \
+ } \
+ } else { \
+ EIGEN_UNUSED_VARIABLE(cc##iter1); \
+ }
+
+#define GEMV_PROCESS_ROW_COMPLEX_SINGLE_MMA(N) \
+ GEMV_UNROLL_ROW(GEMV_INIT_ROW_COMPLEX_MMA, N) \
+ GEMV_PROCESS_ROW_COMPLEX_SINGLE_WORK(GEMV_WORK_ROW_COMPLEX_MMA, N)
+
+#define GEMV_PROCESS_ROW_COMPLEX_ONE_MMA(N) \
+ for (; i < n##N; i += N) { \
+ GEMV_PROCESS_ROW_COMPLEX_SINGLE_MMA(N) \
+ GEMV_UNROLL_ROW_HALF(GEMV_PREDUX4_COMPLEX_MMA, (N >> 1)) \
+ GEMV_PROCESS_END_ROW_COMPLEX(N); \
+ }
+#endif
+
+#define GEMV_WORK_ROW_COMPLEX(iter, N) \
+ if (N > iter) { \
+ PLhsPacket a##iter = GEMV_LOADPACKET_ROW_COMPLEX(iter); \
+ gemv_mult_complex<ScalarPacket, PLhsPacket, RhsScalar, RhsPacket, PResPacket, ResPacket, ConjugateLhs, ConjugateRhs, RowMajor>(a##iter, b, c0##iter, c1##iter); \
+ }
+
+#define GEMV_PREDUX4_COMPLEX(iter1, iter2, iter3, N) \
+ if (N > iter1) { \
+ cc##iter1 = predux_complex<ResScalar, PResPacket, ResPacket, LhsPacket, RhsPacket>(c0##iter2, c0##iter3, c1##iter2, c1##iter3); \
+ } else { \
+ EIGEN_UNUSED_VARIABLE(cc##iter1); \
+ }
+
+#define GEMV_MULT_COMPLEX(iter1, iter2, iter3, N) \
+ if (N > iter1) { \
+ cc##iter1.scalar[0] += cj.pmul(lhs(i + iter2, j), b0); \
+ cc##iter1.scalar[1] += cj.pmul(lhs(i + iter3, j), b0); \
+ }
+
+#define GEMV_STORE_ROW_COMPLEX(iter1, iter2, iter3, N) \
+ if (N > iter1) { \
+ storeMaddData<ResScalar>(res + ((i + iter2) * resIncr), alpha, cc##iter1.scalar[0]); \
+ storeMaddData<ResScalar>(res + ((i + iter3) * resIncr), alpha, cc##iter1.scalar[1]); \
+ }
+
+#define GEMV_PROCESS_ROW_COMPLEX_SINGLE_NEW(N) \
+ GEMV_UNROLL_ROW(GEMV_INIT_COMPLEX, N) \
+ GEMV_PROCESS_ROW_COMPLEX_SINGLE_WORK(GEMV_WORK_ROW_COMPLEX, N)
+
+/** \internal main macro for gemv_complex_row - initialize accumulators, multiply and add inputs, predux and store results */
+#define GEMV_PROCESS_ROW_COMPLEX_ONE_NEW(N) \
+ for (; i < n##N; i += N) { \
+ GEMV_PROCESS_ROW_COMPLEX_SINGLE_NEW(N) \
+ GEMV_UNROLL_ROW_HALF(GEMV_PREDUX4_COMPLEX, (N >> 1)) \
+ GEMV_PROCESS_END_ROW_COMPLEX(N); \
+ }
+
+#define GEMV_PROCESS_ROW_COMPLEX_PREDUX_NEW(iter) \
+ if (GEMV_IS_COMPLEX_COMPLEX) { \
+ c0##iter = padd(c0##iter, c1##iter); \
+ } \
+ dd0 = predux(c0##iter);
+
+#if EIGEN_COMP_LLVM
+#define GEMV_PROCESS_ROW_COMPLEX_SINGLE(N) \
+ GEMV_PROCESS_ROW_COMPLEX_SINGLE_NEW(N)
+
+#define GEMV_PROCESS_ROW_COMPLEX_ONE(N) \
+ GEMV_PROCESS_ROW_COMPLEX_ONE_NEW(N)
+
+#define GEMV_PROCESS_ROW_COMPLEX_PREDUX(iter) \
+ GEMV_PROCESS_ROW_COMPLEX_PREDUX_NEW(iter)
+#else
+// gcc seems to be reading and writing registers unnecessarily to memory.
+// Use the old way for complex double until it is fixed.
+
+#define GEMV_LOADPACKET_ROW_COMPLEX_OLD(iter) \
+ lhs.template load<LhsPacket, LhsAlignment>(i + (iter), j)
+
+#define GEMV_INIT_COMPLEX_OLD(iter, N) \
+ EIGEN_UNUSED_VARIABLE(c0##iter); \
+ if (N > iter) { \
+ c1##iter = pset_zero<ResPacket>(); \
+ } else { \
+ EIGEN_UNUSED_VARIABLE(c1##iter); \
+ }
+
+#define GEMV_WORK_ROW_COMPLEX_OLD(iter, N) \
+ if (N > iter) { \
+ LhsPacket a##iter = GEMV_LOADPACKET_ROW_COMPLEX_OLD(iter); \
+ c1##iter = pcj.pmadd(a##iter, b0, c1##iter); \
+ }
+
+#define GEMV_PREDUX4_COMPLEX_OLD(iter1, iter2, iter3, N) \
+ if (N > iter1) { \
+ cc##iter1.scalar[0] = predux(c1##iter2); \
+ cc##iter1.scalar[1] = predux(c1##iter3); \
+ } else { \
+ EIGEN_UNUSED_VARIABLE(cc##iter1); \
+ }
+
+#define GEMV_PROCESS_ROW_COMPLEX_SINGLE_OLD(N) \
+ GEMV_UNROLL_ROW(GEMV_INIT_COMPLEX_OLD, N) \
+ j = 0; \
+ for (; j + LhsPacketSize <= cols; j += LhsPacketSize) { \
+ RhsPacket b0 = rhs2.template load<RhsPacket, Unaligned>(j); \
+ GEMV_UNROLL_ROW(GEMV_WORK_ROW_COMPLEX_OLD, N) \
+ }
+
+#define GEMV_PROCESS_ROW_COMPLEX_ONE_OLD(N) \
+ for (; i < n##N; i += N) { \
+ GEMV_PROCESS_ROW_COMPLEX_SINGLE_OLD(N) \
+ GEMV_UNROLL_ROW_HALF(GEMV_PREDUX4_COMPLEX_OLD, (N >> 1)) \
+ GEMV_PROCESS_END_ROW_COMPLEX(N) \
+ }
+
+#define GEMV_PROCESS_ROW_COMPLEX_PREDUX_OLD(iter) \
+ dd0 = predux(c1##iter);
+
+#if (__GNUC__ > 10)
+#define GEMV_PROCESS_ROW_COMPLEX_IS_NEW 1
+#else
+#define GEMV_PROCESS_ROW_COMPLEX_IS_NEW \
+ (sizeof(Scalar) == sizeof(float)) || GEMV_IS_COMPLEX_COMPLEX
+#endif
+
+#define GEMV_PROCESS_ROW_COMPLEX_SINGLE(N) \
+ if (GEMV_PROCESS_ROW_COMPLEX_IS_NEW) { \
+ GEMV_PROCESS_ROW_COMPLEX_SINGLE_NEW(N) \
+ } else { \
+ GEMV_PROCESS_ROW_COMPLEX_SINGLE_OLD(N) \
+ }
+
+#define GEMV_PROCESS_ROW_COMPLEX_ONE(N) \
+ if (GEMV_PROCESS_ROW_COMPLEX_IS_NEW) { \
+ GEMV_PROCESS_ROW_COMPLEX_ONE_NEW(N) \
+ } else { \
+ GEMV_PROCESS_ROW_COMPLEX_ONE_OLD(N) \
+ }
+
+#define GEMV_PROCESS_ROW_COMPLEX_PREDUX(iter) \
+ if (GEMV_PROCESS_ROW_COMPLEX_IS_NEW) { \
+ GEMV_PROCESS_ROW_COMPLEX_PREDUX_NEW(iter) \
+ } else { \
+ GEMV_PROCESS_ROW_COMPLEX_PREDUX_OLD(iter) \
+ }
+#endif
+
+#ifdef USE_GEMV_MMA
+#define GEMV_PROCESS_ROW_COMPLEX(N) \
+ GEMV_PROCESS_ROW_COMPLEX_ONE_MMA(N)
+#else
+#define GEMV_PROCESS_ROW_COMPLEX(N) \
+ GEMV_PROCESS_ROW_COMPLEX_ONE(N)
+#endif
+
+template<typename Scalar, typename LhsScalar, typename LhsMapper, bool ConjugateLhs, bool LhsIsReal, typename RhsScalar, typename RhsMapper, bool ConjugateRhs, bool RhsIsReal, typename ResScalar>
+EIGEN_STRONG_INLINE void gemv_complex_row(
+ Index rows, Index cols,
+ const LhsMapper& alhs,
+ const RhsMapper& rhs,
+ ResScalar* res, Index resIncr,
+ ResScalar alpha)
+{
+ typedef gemv_traits<LhsScalar, RhsScalar> Traits;
+
+ typedef typename Traits::LhsPacket LhsPacket;
+ typedef typename Traits::RhsPacket RhsPacket;
+ typedef typename Traits::ResPacket ResPacket;
+
+ typedef typename packet_traits<Scalar>::type ScalarPacket;
+ typedef typename packet_traits<LhsScalar>::type PLhsPacket;
+ typedef typename packet_traits<ResScalar>::type PResPacket;
+ typedef gemv_traits<ResPacket, ResPacket> PTraits;
+
+ // The following copy tells the compiler that lhs's attributes are not modified outside this function
+ // This helps GCC to generate proper code.
+ LhsMapper lhs(alhs);
+ typename RhsMapper::LinearMapper rhs2 = rhs.getLinearMapper(0, 0);
+
+ eigen_internal_assert(rhs.stride() == 1);
+ conj_helper<LhsScalar, RhsScalar, ConjugateLhs, ConjugateRhs> cj;
+#if !EIGEN_COMP_LLVM
+ conj_helper<LhsPacket, RhsPacket, ConjugateLhs, ConjugateRhs> pcj;
+#endif
+
+ // TODO: fine tune the following heuristic. The rationale is that if the matrix is very large,
+ // processing 8 rows at once might be counter productive wrt cache.
+#ifndef GCC_ONE_VECTORPAIR_BUG
+ const Index n8 = lhs.stride() * sizeof(LhsScalar) > 32000 ? (rows - 7) : (rows - 7);
+ const Index n4 = rows - 3;
+ const Index n2 = rows - 1;
+#endif
+
+ // TODO: for padded aligned inputs, we could enable aligned reads
+ enum {
+ LhsAlignment = Unaligned,
+ ResPacketSize = PTraits::ResPacketSize,
+ LhsPacketSize = PTraits::LhsPacketSize,
+ RhsPacketSize = PTraits::RhsPacketSize,
+ };
+
+ Index i = 0, j;
+ PResPacket c00, c01, c02, c03, c04, c05, c06, c07;
+ ResPacket c10, c11, c12, c13, c14, c15, c16, c17;
+#ifdef USE_GEMV_MMA
+ __vector_quad e00, e01, e02, e03, e04, e05, e06, e07;
+ GEMV_UNUSED_ROW(8, e0)
+ GEMV_UNUSED_EXTRA(1, c0)
+ GEMV_UNUSED_EXTRA(1, c1)
+#endif
+ ResScalar dd0;
+#ifndef GCC_ONE_VECTORPAIR_BUG
+ ScalarBlock<ResScalar, 2> cc0, cc1, cc2, cc3;
+#ifdef USE_GEMV_MMA
+ if (!GEMV_IS_COMPLEX_COMPLEX)
+#endif
+ {
+ GEMV_PROCESS_ROW_COMPLEX(8)
+ }
+ GEMV_PROCESS_ROW_COMPLEX(4)
+ GEMV_PROCESS_ROW_COMPLEX(2)
+#endif
+ for (; i < rows; ++i)
+ {
+ GEMV_PROCESS_ROW_COMPLEX_SINGLE(1)
+ GEMV_PROCESS_ROW_COMPLEX_PREDUX(0)
+ for (; j < cols; ++j)
+ {
+ dd0 += cj.pmul(lhs(i, j), rhs2(j));
+ }
+ res[i * resIncr] += alpha * dd0;
+ }
+}
+
+#define EIGEN_POWER_GEMV_COMPLEX_SPECIALIZE_COL(Scalar, LhsScalar, RhsScalar) \
+template<typename Index, typename LhsMapper, bool ConjugateLhs, typename RhsMapper, bool ConjugateRhs, int Version> \
+struct general_matrix_vector_product<Index, LhsScalar, LhsMapper, ColMajor, ConjugateLhs, RhsScalar, RhsMapper, ConjugateRhs, Version> \
+{ \
+ typedef typename ScalarBinaryOpTraits<LhsScalar, RhsScalar>::ReturnType ResScalar; \
+\
+ EIGEN_DEVICE_FUNC EIGEN_DONT_INLINE static void run( \
+ Index rows, Index cols, \
+ const LhsMapper& lhs, \
+ const RhsMapper& rhs, \
+ ResScalar* res, Index resIncr, \
+ ResScalar alpha) { \
+ gemv_complex_col<Scalar, LhsScalar, LhsMapper, ConjugateLhs, sizeof(Scalar) == sizeof(LhsScalar), RhsScalar, RhsMapper, ConjugateRhs, sizeof(Scalar) == sizeof(RhsScalar), ResScalar>(rows, cols, lhs, rhs, res, resIncr, alpha); \
+ } \
+};
+
+#define EIGEN_POWER_GEMV_COMPLEX_SPECIALIZE_ROW(Scalar, LhsScalar, RhsScalar) \
+template<typename Index, typename LhsMapper, bool ConjugateLhs, typename RhsMapper, bool ConjugateRhs, int Version> \
+struct general_matrix_vector_product<Index, LhsScalar, LhsMapper, RowMajor, ConjugateLhs, RhsScalar, RhsMapper, ConjugateRhs, Version> \
+{ \
+ typedef typename ScalarBinaryOpTraits<LhsScalar, RhsScalar>::ReturnType ResScalar; \
+\
+ EIGEN_DEVICE_FUNC EIGEN_DONT_INLINE static void run( \
+ Index rows, Index cols, \
+ const LhsMapper& lhs, \
+ const RhsMapper& rhs, \
+ ResScalar* res, Index resIncr, \
+ ResScalar alpha) { \
+ gemv_complex_row<Scalar, LhsScalar, LhsMapper, ConjugateLhs, sizeof(Scalar) == sizeof(LhsScalar), RhsScalar, RhsMapper, ConjugateRhs, sizeof(Scalar) == sizeof(RhsScalar), ResScalar>(rows, cols, lhs, rhs, res, resIncr, alpha); \
+ } \
+};
+
+EIGEN_POWER_GEMV_COMPLEX_SPECIALIZE_COL(float, float, std::complex<float>)
+EIGEN_POWER_GEMV_COMPLEX_SPECIALIZE_COL(float, std::complex<float>, float)
+EIGEN_POWER_GEMV_COMPLEX_SPECIALIZE_COL(float, std::complex<float>, std::complex<float>)
+EIGEN_POWER_GEMV_COMPLEX_SPECIALIZE_COL(double, double, std::complex<double>)
+EIGEN_POWER_GEMV_COMPLEX_SPECIALIZE_COL(double, std::complex<double>, double)
+EIGEN_POWER_GEMV_COMPLEX_SPECIALIZE_COL(double, std::complex<double>, std::complex<double>)
+EIGEN_POWER_GEMV_COMPLEX_SPECIALIZE_ROW(float, float, std::complex<float>)
+EIGEN_POWER_GEMV_COMPLEX_SPECIALIZE_ROW(float, std::complex<float>, float)
+EIGEN_POWER_GEMV_COMPLEX_SPECIALIZE_ROW(float, std::complex<float>, std::complex<float>)
+EIGEN_POWER_GEMV_COMPLEX_SPECIALIZE_ROW(double, double, std::complex<double>)
+EIGEN_POWER_GEMV_COMPLEX_SPECIALIZE_ROW(double, std::complex<double>, double)
+EIGEN_POWER_GEMV_COMPLEX_SPECIALIZE_ROW(double, std::complex<double>, std::complex<double>)
+
+#endif // EIGEN_MATRIX_VECTOR_PRODUCT_ALTIVEC_H
+
diff --git a/Eigen/src/Core/arch/AltiVec/PacketMath.h b/Eigen/src/Core/arch/AltiVec/PacketMath.h
new file mode 100644
index 0000000..37398de
--- /dev/null
+++ b/Eigen/src/Core/arch/AltiVec/PacketMath.h
@@ -0,0 +1,3151 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2016 Konstantinos Margaritis <markos@freevec.org>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_PACKET_MATH_ALTIVEC_H
+#define EIGEN_PACKET_MATH_ALTIVEC_H
+
+#include "../../InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+
+#ifndef EIGEN_CACHEFRIENDLY_PRODUCT_THRESHOLD
+#define EIGEN_CACHEFRIENDLY_PRODUCT_THRESHOLD 4
+#endif
+
+#ifndef EIGEN_HAS_SINGLE_INSTRUCTION_MADD
+#define EIGEN_HAS_SINGLE_INSTRUCTION_MADD
+#endif
+
+// NOTE Altivec has 32 registers, but Eigen only accepts a value of 8 or 16
+#ifndef EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS
+#define EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS 32
+#endif
+
+typedef __vector float Packet4f;
+typedef __vector int Packet4i;
+typedef __vector unsigned int Packet4ui;
+typedef __vector __bool int Packet4bi;
+typedef __vector short int Packet8s;
+typedef __vector unsigned short int Packet8us;
+typedef __vector signed char Packet16c;
+typedef __vector unsigned char Packet16uc;
+typedef eigen_packet_wrapper<__vector unsigned short int,0> Packet8bf;
+
+// We don't want to write the same code all the time, but we need to reuse the constants
+// and it doesn't really work to declare them global, so we define macros instead
+#define EIGEN_DECLARE_CONST_FAST_Packet4f(NAME,X) \
+ Packet4f p4f_##NAME = {X, X, X, X}
+
+#define EIGEN_DECLARE_CONST_FAST_Packet4i(NAME,X) \
+ Packet4i p4i_##NAME = vec_splat_s32(X)
+
+#define EIGEN_DECLARE_CONST_FAST_Packet4ui(NAME,X) \
+ Packet4ui p4ui_##NAME = {X, X, X, X}
+
+#define EIGEN_DECLARE_CONST_FAST_Packet8us(NAME,X) \
+ Packet8us p8us_##NAME = {X, X, X, X, X, X, X, X}
+
+#define EIGEN_DECLARE_CONST_FAST_Packet16uc(NAME,X) \
+ Packet16uc p16uc_##NAME = {X, X, X, X, X, X, X, X, X, X, X, X, X, X, X, X}
+
+#define EIGEN_DECLARE_CONST_Packet4f(NAME,X) \
+ Packet4f p4f_##NAME = pset1<Packet4f>(X)
+
+#define EIGEN_DECLARE_CONST_Packet4i(NAME,X) \
+ Packet4i p4i_##NAME = pset1<Packet4i>(X)
+
+#define EIGEN_DECLARE_CONST_Packet2d(NAME,X) \
+ Packet2d p2d_##NAME = pset1<Packet2d>(X)
+
+#define EIGEN_DECLARE_CONST_Packet2l(NAME,X) \
+ Packet2l p2l_##NAME = pset1<Packet2l>(X)
+
+#define EIGEN_DECLARE_CONST_Packet4f_FROM_INT(NAME,X) \
+ const Packet4f p4f_##NAME = reinterpret_cast<Packet4f>(pset1<Packet4i>(X))
+
+#define DST_CHAN 1
+#define DST_CTRL(size, count, stride) (((size) << 24) | ((count) << 16) | (stride))
+#define __UNPACK_TYPE__(PACKETNAME) typename unpacket_traits<PACKETNAME>::type
+
+// These constants are endian-agnostic
+static EIGEN_DECLARE_CONST_FAST_Packet4f(ZERO, 0); //{ 0.0, 0.0, 0.0, 0.0}
+static EIGEN_DECLARE_CONST_FAST_Packet4i(ZERO, 0); //{ 0, 0, 0, 0,}
+static EIGEN_DECLARE_CONST_FAST_Packet4i(ONE,1); //{ 1, 1, 1, 1}
+static EIGEN_DECLARE_CONST_FAST_Packet4i(MINUS16,-16); //{ -16, -16, -16, -16}
+static EIGEN_DECLARE_CONST_FAST_Packet4i(MINUS1,-1); //{ -1, -1, -1, -1}
+static EIGEN_DECLARE_CONST_FAST_Packet4ui(SIGN, 0x80000000u);
+static EIGEN_DECLARE_CONST_FAST_Packet4ui(PREV0DOT5, 0x3EFFFFFFu);
+#ifndef __POWER8_VECTOR__
+static EIGEN_DECLARE_CONST_FAST_Packet8us(ONE,1); //{ 1, 1, 1, 1, 1, 1, 1, 1}
+static EIGEN_DECLARE_CONST_FAST_Packet16uc(ONE,1);
+#endif
+static Packet4f p4f_MZERO = (Packet4f) vec_sl((Packet4ui)p4i_MINUS1, (Packet4ui)p4i_MINUS1); //{ 0x80000000, 0x80000000, 0x80000000, 0x80000000}
+#ifndef __VSX__
+static Packet4f p4f_ONE = vec_ctf(p4i_ONE, 0); //{ 1.0, 1.0, 1.0, 1.0}
+#endif
+
+static Packet4f p4f_COUNTDOWN = { 0.0, 1.0, 2.0, 3.0 };
+static Packet4i p4i_COUNTDOWN = { 0, 1, 2, 3 };
+static Packet8s p8s_COUNTDOWN = { 0, 1, 2, 3, 4, 5, 6, 7 };
+static Packet8us p8us_COUNTDOWN = { 0, 1, 2, 3, 4, 5, 6, 7 };
+
+static Packet16c p16c_COUNTDOWN = { 0, 1, 2, 3, 4, 5, 6, 7,
+ 8, 9, 10, 11, 12, 13, 14, 15};
+static Packet16uc p16uc_COUNTDOWN = { 0, 1, 2, 3, 4, 5, 6, 7,
+ 8, 9, 10, 11, 12, 13, 14, 15};
+
+static Packet16uc p16uc_REVERSE32 = { 12,13,14,15, 8,9,10,11, 4,5,6,7, 0,1,2,3 };
+static Packet16uc p16uc_REVERSE16 = { 14,15, 12,13, 10,11, 8,9, 6,7, 4,5, 2,3, 0,1 };
+#ifndef _ARCH_PWR9
+static Packet16uc p16uc_REVERSE8 = { 15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0 };
+#endif
+
+#ifdef _BIG_ENDIAN
+static Packet16uc p16uc_DUPLICATE32_HI = { 0,1,2,3, 0,1,2,3, 4,5,6,7, 4,5,6,7 };
+#endif
+static const Packet16uc p16uc_DUPLICATE16_EVEN= { 0,1 ,0,1, 4,5, 4,5, 8,9, 8,9, 12,13, 12,13 };
+static const Packet16uc p16uc_DUPLICATE16_ODD = { 2,3 ,2,3, 6,7, 6,7, 10,11, 10,11, 14,15, 14,15 };
+
+static Packet16uc p16uc_QUADRUPLICATE16_HI = { 0,1,0,1,0,1,0,1, 2,3,2,3,2,3,2,3 };
+
+// Handle endianness properly while loading constants
+// Define global static constants:
+#ifdef _BIG_ENDIAN
+static Packet16uc p16uc_FORWARD = vec_lvsl(0, (float*)0);
+static Packet16uc p16uc_PSET32_WODD = vec_sld((Packet16uc) vec_splat((Packet4ui)p16uc_FORWARD, 0), (Packet16uc) vec_splat((Packet4ui)p16uc_FORWARD, 2), 8);//{ 0,1,2,3, 0,1,2,3, 8,9,10,11, 8,9,10,11 };
+static Packet16uc p16uc_PSET32_WEVEN = vec_sld(p16uc_DUPLICATE32_HI, (Packet16uc) vec_splat((Packet4ui)p16uc_FORWARD, 3), 8);//{ 4,5,6,7, 4,5,6,7, 12,13,14,15, 12,13,14,15 };
+static Packet16uc p16uc_HALF64_0_16 = vec_sld((Packet16uc)p4i_ZERO, vec_splat((Packet16uc) vec_abs(p4i_MINUS16), 3), 8); //{ 0,0,0,0, 0,0,0,0, 16,16,16,16, 16,16,16,16};
+#else
+static Packet16uc p16uc_FORWARD = p16uc_REVERSE32;
+static Packet16uc p16uc_PSET32_WODD = vec_sld((Packet16uc) vec_splat((Packet4ui)p16uc_FORWARD, 1), (Packet16uc) vec_splat((Packet4ui)p16uc_FORWARD, 3), 8);//{ 0,1,2,3, 0,1,2,3, 8,9,10,11, 8,9,10,11 };
+static Packet16uc p16uc_PSET32_WEVEN = vec_sld((Packet16uc) vec_splat((Packet4ui)p16uc_FORWARD, 0), (Packet16uc) vec_splat((Packet4ui)p16uc_FORWARD, 2), 8);//{ 4,5,6,7, 4,5,6,7, 12,13,14,15, 12,13,14,15 };
+static Packet16uc p16uc_HALF64_0_16 = vec_sld(vec_splat((Packet16uc) vec_abs(p4i_MINUS16), 0), (Packet16uc)p4i_ZERO, 8); //{ 0,0,0,0, 0,0,0,0, 16,16,16,16, 16,16,16,16};
+#endif // _BIG_ENDIAN
+
+static Packet16uc p16uc_PSET64_HI = (Packet16uc) vec_mergeh((Packet4ui)p16uc_PSET32_WODD, (Packet4ui)p16uc_PSET32_WEVEN); //{ 0,1,2,3, 4,5,6,7, 0,1,2,3, 4,5,6,7 };
+static Packet16uc p16uc_PSET64_LO = (Packet16uc) vec_mergel((Packet4ui)p16uc_PSET32_WODD, (Packet4ui)p16uc_PSET32_WEVEN); //{ 8,9,10,11, 12,13,14,15, 8,9,10,11, 12,13,14,15 };
+static Packet16uc p16uc_TRANSPOSE64_HI = p16uc_PSET64_HI + p16uc_HALF64_0_16; //{ 0,1,2,3, 4,5,6,7, 16,17,18,19, 20,21,22,23};
+static Packet16uc p16uc_TRANSPOSE64_LO = p16uc_PSET64_LO + p16uc_HALF64_0_16; //{ 8,9,10,11, 12,13,14,15, 24,25,26,27, 28,29,30,31};
+
+static Packet16uc p16uc_COMPLEX32_REV = vec_sld(p16uc_REVERSE32, p16uc_REVERSE32, 8); //{ 4,5,6,7, 0,1,2,3, 12,13,14,15, 8,9,10,11 };
+
+#if EIGEN_HAS_BUILTIN(__builtin_prefetch) || EIGEN_COMP_GNUC
+ #define EIGEN_PPC_PREFETCH(ADDR) __builtin_prefetch(ADDR);
+#else
+ #define EIGEN_PPC_PREFETCH(ADDR) asm( " dcbt [%[addr]]\n" :: [addr] "r" (ADDR) : "cc" );
+#endif
+
+#if EIGEN_COMP_LLVM
+#define LOAD_STORE_UNROLL_16 _Pragma("unroll 16")
+#else
+#define LOAD_STORE_UNROLL_16 _Pragma("GCC unroll(16)")
+#endif
+
+template <>
+struct packet_traits<float> : default_packet_traits {
+ typedef Packet4f type;
+ typedef Packet4f half;
+ enum {
+ Vectorizable = 1,
+ AlignedOnScalar = 1,
+ size = 4,
+ HasHalfPacket = 1,
+
+ HasAdd = 1,
+ HasSub = 1,
+ HasMul = 1,
+ HasDiv = 1,
+ HasMin = 1,
+ HasMax = 1,
+ HasAbs = 1,
+ HasSin = EIGEN_FAST_MATH,
+ HasCos = EIGEN_FAST_MATH,
+ HasACos = 1,
+ HasASin = 1,
+ HasATan = 1,
+ HasLog = 1,
+ HasExp = 1,
+#ifdef __VSX__
+ HasSqrt = 1,
+#if !EIGEN_COMP_CLANG
+ HasRsqrt = 1,
+#else
+ HasRsqrt = 0,
+#endif
+ HasTanh = EIGEN_FAST_MATH,
+ HasErf = EIGEN_FAST_MATH,
+ HasRint = 1,
+#else
+ HasSqrt = 0,
+ HasRsqrt = 0,
+ HasTanh = 0,
+ HasErf = 0,
+ HasRint = 0,
+#endif
+ HasRound = 1,
+ HasFloor = 1,
+ HasCeil = 1,
+ HasNegate = 1,
+ HasBlend = 1
+ };
+};
+template <>
+struct packet_traits<bfloat16> : default_packet_traits {
+ typedef Packet8bf type;
+ typedef Packet8bf half;
+ enum {
+ Vectorizable = 1,
+ AlignedOnScalar = 1,
+ size = 8,
+ HasHalfPacket = 0,
+
+ HasAdd = 1,
+ HasSub = 1,
+ HasMul = 1,
+ HasDiv = 1,
+ HasMin = 1,
+ HasMax = 1,
+ HasAbs = 1,
+ HasSin = EIGEN_FAST_MATH,
+ HasCos = EIGEN_FAST_MATH,
+ HasLog = 1,
+ HasExp = 1,
+#ifdef __VSX__
+ HasSqrt = 1,
+#if !EIGEN_COMP_CLANG
+ HasRsqrt = 1,
+#else
+ HasRsqrt = 0,
+#endif
+ HasRint = 1,
+#else
+ HasSqrt = 0,
+ HasRsqrt = 0,
+ HasRint = 0,
+#endif
+ HasTanh = 0,
+ HasErf = 0,
+ HasRound = 1,
+ HasFloor = 1,
+ HasCeil = 1,
+ HasNegate = 1,
+ HasBlend = 1
+ };
+};
+
+template <>
+struct packet_traits<int> : default_packet_traits {
+ typedef Packet4i type;
+ typedef Packet4i half;
+ enum {
+ Vectorizable = 1,
+ AlignedOnScalar = 1,
+ size = 4,
+ HasHalfPacket = 0,
+
+ HasAdd = 1,
+ HasSub = 1,
+ HasShift = 1,
+ HasMul = 1,
+ HasDiv = 0,
+ HasBlend = 1,
+ HasCmp = 1
+ };
+};
+
+template <>
+struct packet_traits<short int> : default_packet_traits {
+ typedef Packet8s type;
+ typedef Packet8s half;
+ enum {
+ Vectorizable = 1,
+ AlignedOnScalar = 1,
+ size = 8,
+ HasHalfPacket = 0,
+
+ HasAdd = 1,
+ HasSub = 1,
+ HasMul = 1,
+ HasDiv = 0,
+ HasBlend = 1,
+ HasCmp = 1
+ };
+};
+
+template <>
+struct packet_traits<unsigned short int> : default_packet_traits {
+ typedef Packet8us type;
+ typedef Packet8us half;
+ enum {
+ Vectorizable = 1,
+ AlignedOnScalar = 1,
+ size = 8,
+ HasHalfPacket = 0,
+
+ HasAdd = 1,
+ HasSub = 1,
+ HasMul = 1,
+ HasDiv = 0,
+ HasBlend = 1,
+ HasCmp = 1
+ };
+};
+
+template <>
+struct packet_traits<signed char> : default_packet_traits {
+ typedef Packet16c type;
+ typedef Packet16c half;
+ enum {
+ Vectorizable = 1,
+ AlignedOnScalar = 1,
+ size = 16,
+ HasHalfPacket = 0,
+
+ HasAdd = 1,
+ HasSub = 1,
+ HasMul = 1,
+ HasDiv = 0,
+ HasBlend = 1,
+ HasCmp = 1
+ };
+};
+
+template <>
+struct packet_traits<unsigned char> : default_packet_traits {
+ typedef Packet16uc type;
+ typedef Packet16uc half;
+ enum {
+ Vectorizable = 1,
+ AlignedOnScalar = 1,
+ size = 16,
+ HasHalfPacket = 0,
+
+ HasAdd = 1,
+ HasSub = 1,
+ HasMul = 1,
+ HasDiv = 0,
+ HasBlend = 1,
+ HasCmp = 1
+ };
+};
+
+template<> struct unpacket_traits<Packet4f>
+{
+ typedef float type;
+ typedef Packet4f half;
+ typedef Packet4i integer_packet;
+ enum {size=4, alignment=Aligned16, vectorizable=true, masked_load_available=false, masked_store_available=false};
+};
+template<> struct unpacket_traits<Packet4i>
+{
+ typedef int type;
+ typedef Packet4i half;
+ enum {size=4, alignment=Aligned16, vectorizable=true, masked_load_available=false, masked_store_available=false};
+};
+template<> struct unpacket_traits<Packet8s>
+{
+ typedef short int type;
+ typedef Packet8s half;
+ enum {size=8, alignment=Aligned16, vectorizable=true, masked_load_available=false, masked_store_available=false};
+};
+template<> struct unpacket_traits<Packet8us>
+{
+ typedef unsigned short int type;
+ typedef Packet8us half;
+ enum {size=8, alignment=Aligned16, vectorizable=true, masked_load_available=false, masked_store_available=false};
+};
+
+template<> struct unpacket_traits<Packet16c>
+{
+ typedef signed char type;
+ typedef Packet16c half;
+ enum {size=16, alignment=Aligned16, vectorizable=true, masked_load_available=false, masked_store_available=false};
+};
+template<> struct unpacket_traits<Packet16uc>
+{
+ typedef unsigned char type;
+ typedef Packet16uc half;
+ enum {size=16, alignment=Aligned16, vectorizable=true, masked_load_available=false, masked_store_available=false};
+};
+
+template<> struct unpacket_traits<Packet8bf>
+{
+ typedef bfloat16 type;
+ typedef Packet8bf half;
+ enum {size=8, alignment=Aligned16, vectorizable=true, masked_load_available=false, masked_store_available=false};
+};
+inline std::ostream & operator <<(std::ostream & s, const Packet16c & v)
+{
+ union {
+ Packet16c v;
+ signed char n[16];
+ } vt;
+ vt.v = v;
+ for (int i=0; i< 16; i++)
+ s << vt.n[i] << ", ";
+ return s;
+}
+
+inline std::ostream & operator <<(std::ostream & s, const Packet16uc & v)
+{
+ union {
+ Packet16uc v;
+ unsigned char n[16];
+ } vt;
+ vt.v = v;
+ for (int i=0; i< 16; i++)
+ s << vt.n[i] << ", ";
+ return s;
+}
+
+inline std::ostream & operator <<(std::ostream & s, const Packet4f & v)
+{
+ union {
+ Packet4f v;
+ float n[4];
+ } vt;
+ vt.v = v;
+ s << vt.n[0] << ", " << vt.n[1] << ", " << vt.n[2] << ", " << vt.n[3];
+ return s;
+}
+
+inline std::ostream & operator <<(std::ostream & s, const Packet4i & v)
+{
+ union {
+ Packet4i v;
+ int n[4];
+ } vt;
+ vt.v = v;
+ s << vt.n[0] << ", " << vt.n[1] << ", " << vt.n[2] << ", " << vt.n[3];
+ return s;
+}
+
+inline std::ostream & operator <<(std::ostream & s, const Packet4ui & v)
+{
+ union {
+ Packet4ui v;
+ unsigned int n[4];
+ } vt;
+ vt.v = v;
+ s << vt.n[0] << ", " << vt.n[1] << ", " << vt.n[2] << ", " << vt.n[3];
+ return s;
+}
+
+template <typename Packet>
+EIGEN_STRONG_INLINE Packet pload_common(const __UNPACK_TYPE__(Packet)* from)
+{
+ // some versions of GCC throw "unused-but-set-parameter".
+ // ignoring these warnings for now.
+ EIGEN_UNUSED_VARIABLE(from);
+ EIGEN_DEBUG_ALIGNED_LOAD
+#ifdef __VSX__
+ return vec_xl(0, const_cast<__UNPACK_TYPE__(Packet)*>(from));
+#else
+ return vec_ld(0, from);
+#endif
+}
+
+// Need to define them first or we get specialization after instantiation errors
+template<> EIGEN_STRONG_INLINE Packet4f pload<Packet4f>(const float* from)
+{
+ return pload_common<Packet4f>(from);
+}
+
+template<> EIGEN_STRONG_INLINE Packet4i pload<Packet4i>(const int* from)
+{
+ return pload_common<Packet4i>(from);
+}
+
+template<> EIGEN_STRONG_INLINE Packet8s pload<Packet8s>(const short int* from)
+{
+ return pload_common<Packet8s>(from);
+}
+
+template<> EIGEN_STRONG_INLINE Packet8us pload<Packet8us>(const unsigned short int* from)
+{
+ return pload_common<Packet8us>(from);
+}
+
+template<> EIGEN_STRONG_INLINE Packet16c pload<Packet16c>(const signed char* from)
+{
+ return pload_common<Packet16c>(from);
+}
+
+template<> EIGEN_STRONG_INLINE Packet16uc pload<Packet16uc>(const unsigned char* from)
+{
+ return pload_common<Packet16uc>(from);
+}
+
+template<> EIGEN_STRONG_INLINE Packet8bf pload<Packet8bf>(const bfloat16* from)
+{
+ return pload_common<Packet8us>(reinterpret_cast<const unsigned short int*>(from));
+}
+
+template <typename Packet>
+EIGEN_ALWAYS_INLINE Packet pload_ignore(const __UNPACK_TYPE__(Packet)* from)
+{
+ // some versions of GCC throw "unused-but-set-parameter".
+ // ignoring these warnings for now.
+ EIGEN_UNUSED_VARIABLE(from);
+ EIGEN_DEBUG_ALIGNED_LOAD
+ // Ignore partial input memory initialized
+#if !EIGEN_COMP_LLVM
+ #pragma GCC diagnostic push
+ #pragma GCC diagnostic ignored "-Wmaybe-uninitialized"
+#endif
+#ifdef __VSX__
+ return vec_xl(0, const_cast<__UNPACK_TYPE__(Packet)*>(from));
+#else
+ return vec_ld(0, from);
+#endif
+#if !EIGEN_COMP_LLVM
+ #pragma GCC diagnostic pop
+#endif
+}
+
+template<> EIGEN_ALWAYS_INLINE Packet8bf pload_ignore<Packet8bf>(const bfloat16* from)
+{
+ return pload_ignore<Packet8us>(reinterpret_cast<const unsigned short int*>(from));
+}
+
+template <typename Packet>
+EIGEN_ALWAYS_INLINE Packet pload_partial_common(const __UNPACK_TYPE__(Packet)* from, const Index n, const Index offset)
+{
+ // some versions of GCC throw "unused-but-set-parameter".
+ // ignoring these warnings for now.
+ const Index packet_size = unpacket_traits<Packet>::size;
+ eigen_assert(n + offset <= packet_size && "number of elements plus offset will read past end of packet");
+ const Index size = sizeof(__UNPACK_TYPE__(Packet));
+#ifdef _ARCH_PWR9
+ EIGEN_UNUSED_VARIABLE(packet_size);
+ EIGEN_DEBUG_ALIGNED_LOAD
+ EIGEN_UNUSED_VARIABLE(from);
+ Packet load = vec_xl_len(const_cast<__UNPACK_TYPE__(Packet)*>(from), n * size);
+ if (offset) {
+ Packet16uc shift = pset1<Packet16uc>(offset * 8 * size);
+#ifdef _BIG_ENDIAN
+ load = Packet(vec_sro(Packet16uc(load), shift));
+#else
+ load = Packet(vec_slo(Packet16uc(load), shift));
+#endif
+ }
+ return load;
+#else
+ EIGEN_ALIGN16 __UNPACK_TYPE__(Packet) load[packet_size];
+ unsigned char* load2 = reinterpret_cast<unsigned char *>(load + offset);
+ unsigned char* from2 = reinterpret_cast<unsigned char *>(const_cast<__UNPACK_TYPE__(Packet)*>(from));
+ Index n2 = n * size;
+ Index i = 0;
+ if (16 <= n2) {
+ pstoreu(load2, ploadu<Packet16uc>(from2));
+ i += 16;
+ }
+ if (i + 8 <= n2) {
+ *reinterpret_cast<uint64_t *>(load2 + i) = *reinterpret_cast<uint64_t *>(from2 + i);
+ i += 8;
+ }
+ if (i + 4 <= n2) {
+ *reinterpret_cast<uint32_t *>(load2 + i) = *reinterpret_cast<uint32_t *>(from2 + i);
+ i += 4;
+ }
+ if (i + 2 <= n2) {
+ *reinterpret_cast<uint16_t *>(load2 + i) = *reinterpret_cast<uint16_t *>(from2 + i);
+ i += 2;
+ }
+ if (i < n2) {
+ *reinterpret_cast<uint8_t *>(load2 + i) = *reinterpret_cast<uint8_t *>(from2 + i);
+ }
+ return pload_ignore<Packet>(load);
+#endif
+}
+
+template<> EIGEN_ALWAYS_INLINE Packet4f pload_partial<Packet4f>(const float* from, const Index n, const Index offset)
+{
+ return pload_partial_common<Packet4f>(from, n, offset);
+}
+
+template<> EIGEN_ALWAYS_INLINE Packet4i pload_partial<Packet4i>(const int* from, const Index n, const Index offset)
+{
+ return pload_partial_common<Packet4i>(from, n, offset);
+}
+
+template<> EIGEN_ALWAYS_INLINE Packet8s pload_partial<Packet8s>(const short int* from, const Index n, const Index offset)
+{
+ return pload_partial_common<Packet8s>(from, n, offset);
+}
+
+template<> EIGEN_ALWAYS_INLINE Packet8us pload_partial<Packet8us>(const unsigned short int* from, const Index n, const Index offset)
+{
+ return pload_partial_common<Packet8us>(from, n, offset);
+}
+
+template<> EIGEN_ALWAYS_INLINE Packet8bf pload_partial<Packet8bf>(const bfloat16* from, const Index n, const Index offset)
+{
+ return pload_partial_common<Packet8us>(reinterpret_cast<const unsigned short int*>(from), n, offset);
+}
+
+template<> EIGEN_ALWAYS_INLINE Packet16c pload_partial<Packet16c>(const signed char* from, const Index n, const Index offset)
+{
+ return pload_partial_common<Packet16c>(from, n, offset);
+}
+
+template<> EIGEN_ALWAYS_INLINE Packet16uc pload_partial<Packet16uc>(const unsigned char* from, const Index n, const Index offset)
+{
+ return pload_partial_common<Packet16uc>(from, n, offset);
+}
+
+template <typename Packet>
+EIGEN_STRONG_INLINE void pstore_common(__UNPACK_TYPE__(Packet)* to, const Packet& from){
+ // some versions of GCC throw "unused-but-set-parameter" (float *to).
+ // ignoring these warnings for now.
+ EIGEN_UNUSED_VARIABLE(to);
+ EIGEN_DEBUG_ALIGNED_STORE
+#ifdef __VSX__
+ vec_xst(from, 0, to);
+#else
+ vec_st(from, 0, to);
+#endif
+}
+
+template<> EIGEN_STRONG_INLINE void pstore<float>(float* to, const Packet4f& from)
+{
+ pstore_common<Packet4f>(to, from);
+}
+
+template<> EIGEN_STRONG_INLINE void pstore<int>(int* to, const Packet4i& from)
+{
+ pstore_common<Packet4i>(to, from);
+}
+
+template<> EIGEN_STRONG_INLINE void pstore<short int>(short int* to, const Packet8s& from)
+{
+ pstore_common<Packet8s>(to, from);
+}
+
+template<> EIGEN_STRONG_INLINE void pstore<unsigned short int>(unsigned short int* to, const Packet8us& from)
+{
+ pstore_common<Packet8us>(to, from);
+}
+
+template<> EIGEN_STRONG_INLINE void pstore<bfloat16>(bfloat16* to, const Packet8bf& from)
+{
+ pstore_common<Packet8us>(reinterpret_cast<unsigned short int*>(to), from);
+}
+
+template<> EIGEN_STRONG_INLINE void pstore<signed char>(signed char* to, const Packet16c& from)
+{
+ pstore_common<Packet16c>(to, from);
+}
+
+template<> EIGEN_STRONG_INLINE void pstore<unsigned char>(unsigned char* to, const Packet16uc& from)
+{
+ pstore_common<Packet16uc>(to, from);
+}
+
+template<typename Packet> EIGEN_ALWAYS_INLINE void pstore_partial_common(__UNPACK_TYPE__(Packet)* to, const Packet& from, const Index n, const Index offset)
+{
+ // some versions of GCC throw "unused-but-set-parameter" (float *to).
+ // ignoring these warnings for now.
+ const Index packet_size = unpacket_traits<Packet>::size;
+ eigen_assert(n + offset <= packet_size && "number of elements plus offset will write past end of packet");
+ const Index size = sizeof(__UNPACK_TYPE__(Packet));
+#ifdef _ARCH_PWR9
+ EIGEN_UNUSED_VARIABLE(packet_size);
+ EIGEN_UNUSED_VARIABLE(to);
+ EIGEN_DEBUG_ALIGNED_STORE
+ Packet store = from;
+ if (offset) {
+ Packet16uc shift = pset1<Packet16uc>(offset * 8 * size);
+#ifdef _BIG_ENDIAN
+ store = Packet(vec_slo(Packet16uc(store), shift));
+#else
+ store = Packet(vec_sro(Packet16uc(store), shift));
+#endif
+ }
+ vec_xst_len(store, to, n * size);
+#else
+ EIGEN_ALIGN16 __UNPACK_TYPE__(Packet) store[packet_size];
+ pstore(store, from);
+ unsigned char* store2 = reinterpret_cast<unsigned char *>(store + offset);
+ unsigned char* to2 = reinterpret_cast<unsigned char *>(to);
+ Index n2 = n * size;
+ Index i = 0;
+ if (16 <= n2) {
+ pstore(to2, ploadu<Packet16uc>(store2));
+ i += 16;
+ }
+ if (i + 8 <= n2) {
+ *reinterpret_cast<uint64_t *>(to2 + i) = *reinterpret_cast<uint64_t *>(store2 + i);
+ i += 8;
+ }
+ if (i + 4 <= n2) {
+ *reinterpret_cast<uint32_t *>(to2 + i) = *reinterpret_cast<uint32_t *>(store2 + i);
+ i += 4;
+ }
+ if (i + 2 <= n2) {
+ *reinterpret_cast<uint16_t *>(to2 + i) = *reinterpret_cast<uint16_t *>(store2 + i);
+ i += 2;
+ }
+ if (i < n2) {
+ *reinterpret_cast<uint8_t *>(to2 + i) = *reinterpret_cast<uint8_t *>(store2 + i);
+ }
+#endif
+}
+
+template<> EIGEN_ALWAYS_INLINE void pstore_partial<float>(float* to, const Packet4f& from, const Index n, const Index offset)
+{
+ pstore_partial_common<Packet4f>(to, from, n, offset);
+}
+
+template<> EIGEN_ALWAYS_INLINE void pstore_partial<int>(int* to, const Packet4i& from, const Index n, const Index offset)
+{
+ pstore_partial_common<Packet4i>(to, from, n, offset);
+}
+
+template<> EIGEN_ALWAYS_INLINE void pstore_partial<short int>(short int* to, const Packet8s& from, const Index n, const Index offset)
+{
+ pstore_partial_common<Packet8s>(to, from, n, offset);
+}
+
+template<> EIGEN_ALWAYS_INLINE void pstore_partial<unsigned short int>(unsigned short int* to, const Packet8us& from, const Index n, const Index offset)
+{
+ pstore_partial_common<Packet8us>(to, from, n, offset);
+}
+
+template<> EIGEN_ALWAYS_INLINE void pstore_partial<bfloat16>(bfloat16* to, const Packet8bf& from, const Index n, const Index offset)
+{
+ pstore_partial_common<Packet8us>(reinterpret_cast<unsigned short int*>(to), from, n, offset);
+}
+
+template<> EIGEN_ALWAYS_INLINE void pstore_partial<signed char>(signed char* to, const Packet16c& from, const Index n, const Index offset)
+{
+ pstore_partial_common<Packet16c>(to, from, n, offset);
+}
+
+template<> EIGEN_ALWAYS_INLINE void pstore_partial<unsigned char>(unsigned char* to, const Packet16uc& from, const Index n, const Index offset)
+{
+ pstore_partial_common<Packet16uc>(to, from, n, offset);
+}
+
+template<typename Packet>
+EIGEN_STRONG_INLINE Packet pset1_size4(const __UNPACK_TYPE__(Packet)& from)
+{
+ Packet v = {from, from, from, from};
+ return v;
+}
+
+template<typename Packet>
+EIGEN_STRONG_INLINE Packet pset1_size8(const __UNPACK_TYPE__(Packet)& from)
+{
+ Packet v = {from, from, from, from, from, from, from, from};
+ return v;
+}
+
+template<typename Packet>
+EIGEN_STRONG_INLINE Packet pset1_size16(const __UNPACK_TYPE__(Packet)& from)
+{
+ Packet v = {from, from, from, from, from, from, from, from, from, from, from, from, from, from, from, from};
+ return v;
+}
+
+template<> EIGEN_STRONG_INLINE Packet4f pset1<Packet4f>(const float& from) {
+ return pset1_size4<Packet4f>(from);
+}
+
+template<> EIGEN_STRONG_INLINE Packet4i pset1<Packet4i>(const int& from) {
+ return pset1_size4<Packet4i>(from);
+}
+
+template<> EIGEN_STRONG_INLINE Packet8s pset1<Packet8s>(const short int& from) {
+ return pset1_size8<Packet8s>(from);
+}
+
+template<> EIGEN_STRONG_INLINE Packet8us pset1<Packet8us>(const unsigned short int& from) {
+ return pset1_size8<Packet8us>(from);
+}
+
+template<> EIGEN_STRONG_INLINE Packet16c pset1<Packet16c>(const signed char& from) {
+ return pset1_size16<Packet16c>(from);
+}
+
+template<> EIGEN_STRONG_INLINE Packet16uc pset1<Packet16uc>(const unsigned char& from) {
+ return pset1_size16<Packet16uc>(from);
+}
+
+template<> EIGEN_STRONG_INLINE Packet4f pset1frombits<Packet4f>(unsigned int from) {
+ return reinterpret_cast<Packet4f>(pset1<Packet4i>(from));
+}
+
+template<> EIGEN_STRONG_INLINE Packet8bf pset1<Packet8bf>(const bfloat16& from) {
+ return pset1_size8<Packet8us>(reinterpret_cast<const unsigned short int&>(from));
+}
+
+template<typename Packet> EIGEN_STRONG_INLINE void
+pbroadcast4_common(const __UNPACK_TYPE__(Packet) *a,
+ Packet& a0, Packet& a1, Packet& a2, Packet& a3)
+{
+ a3 = pload<Packet>(a);
+ a0 = vec_splat(a3, 0);
+ a1 = vec_splat(a3, 1);
+ a2 = vec_splat(a3, 2);
+ a3 = vec_splat(a3, 3);
+}
+
+template<> EIGEN_STRONG_INLINE void
+pbroadcast4<Packet4f>(const float *a,
+ Packet4f& a0, Packet4f& a1, Packet4f& a2, Packet4f& a3)
+{
+ pbroadcast4_common<Packet4f>(a, a0, a1, a2, a3);
+}
+template<> EIGEN_STRONG_INLINE void
+pbroadcast4<Packet4i>(const int *a,
+ Packet4i& a0, Packet4i& a1, Packet4i& a2, Packet4i& a3)
+{
+ pbroadcast4_common<Packet4i>(a, a0, a1, a2, a3);
+}
+
+template<typename Packet> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE Packet pgather_common(const __UNPACK_TYPE__(Packet)* from, Index stride, const Index n = unpacket_traits<Packet>::size)
+{
+ EIGEN_ALIGN16 __UNPACK_TYPE__(Packet) a[unpacket_traits<Packet>::size];
+ eigen_assert(n <= unpacket_traits<Packet>::size && "number of elements will gather past end of packet");
+ LOAD_STORE_UNROLL_16
+ for (Index i = 0; i < n; i++) {
+ a[i] = from[i*stride];
+ }
+ // Leave rest of the array uninitialized
+ return pload_ignore<Packet>(a);
+}
+
+template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE Packet4f pgather<float, Packet4f>(const float* from, Index stride)
+{
+ return pgather_common<Packet4f>(from, stride);
+}
+
+template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE Packet4i pgather<int, Packet4i>(const int* from, Index stride)
+{
+ return pgather_common<Packet4i>(from, stride);
+}
+
+template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE Packet8s pgather<short int, Packet8s>(const short int* from, Index stride)
+{
+ return pgather_common<Packet8s>(from, stride);
+}
+
+template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE Packet8us pgather<unsigned short int, Packet8us>(const unsigned short int* from, Index stride)
+{
+ return pgather_common<Packet8us>(from, stride);
+}
+
+template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE Packet8bf pgather<bfloat16, Packet8bf>(const bfloat16* from, Index stride)
+{
+ return pgather_common<Packet8bf>(from, stride);
+}
+
+template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE Packet16c pgather<signed char, Packet16c>(const signed char* from, Index stride)
+{
+ return pgather_common<Packet16c>(from, stride);
+}
+
+template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE Packet16uc pgather<unsigned char, Packet16uc>(const unsigned char* from, Index stride)
+{
+ return pgather_common<Packet16uc>(from, stride);
+}
+
+template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE Packet4f pgather_partial<float, Packet4f>(const float* from, Index stride, const Index n)
+{
+ return pgather_common<Packet4f>(from, stride, n);
+}
+
+template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE Packet4i pgather_partial<int, Packet4i>(const int* from, Index stride, const Index n)
+{
+ return pgather_common<Packet4i>(from, stride, n);
+}
+
+template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE Packet8s pgather_partial<short int, Packet8s>(const short int* from, Index stride, const Index n)
+{
+ return pgather_common<Packet8s>(from, stride, n);
+}
+
+template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE Packet8us pgather_partial<unsigned short int, Packet8us>(const unsigned short int* from, Index stride, const Index n)
+{
+ return pgather_common<Packet8us>(from, stride, n);
+}
+
+template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE Packet8bf pgather_partial<bfloat16, Packet8bf>(const bfloat16* from, Index stride, const Index n)
+{
+ return pgather_common<Packet8bf>(from, stride, n);
+}
+
+template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE Packet16c pgather_partial<signed char, Packet16c>(const signed char* from, Index stride, const Index n)
+{
+ return pgather_common<Packet16c>(from, stride, n);
+}
+
+template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE Packet16uc pgather_partial<unsigned char, Packet16uc>(const unsigned char* from, Index stride, const Index n)
+{
+ return pgather_common<Packet16uc>(from, stride, n);
+}
+
+template<typename Packet> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE void pscatter_common(__UNPACK_TYPE__(Packet)* to, const Packet& from, Index stride, const Index n = unpacket_traits<Packet>::size)
+{
+ EIGEN_ALIGN16 __UNPACK_TYPE__(Packet) a[unpacket_traits<Packet>::size];
+ eigen_assert(n <= unpacket_traits<Packet>::size && "number of elements will scatter past end of packet");
+ pstore<__UNPACK_TYPE__(Packet)>(a, from);
+ LOAD_STORE_UNROLL_16
+ for (Index i = 0; i < n; i++) {
+ to[i*stride] = a[i];
+ }
+}
+
+template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE void pscatter<float, Packet4f>(float* to, const Packet4f& from, Index stride)
+{
+ pscatter_common<Packet4f>(to, from, stride);
+}
+
+template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE void pscatter<int, Packet4i>(int* to, const Packet4i& from, Index stride)
+{
+ pscatter_common<Packet4i>(to, from, stride);
+}
+
+template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE void pscatter<short int, Packet8s>(short int* to, const Packet8s& from, Index stride)
+{
+ pscatter_common<Packet8s>(to, from, stride);
+}
+
+template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE void pscatter<unsigned short int, Packet8us>(unsigned short int* to, const Packet8us& from, Index stride)
+{
+ pscatter_common<Packet8us>(to, from, stride);
+}
+
+template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE void pscatter<bfloat16, Packet8bf>(bfloat16* to, const Packet8bf& from, Index stride)
+{
+ pscatter_common<Packet8bf>(to, from, stride);
+}
+
+template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE void pscatter<signed char, Packet16c>(signed char* to, const Packet16c& from, Index stride)
+{
+ pscatter_common<Packet16c>(to, from, stride);
+}
+
+template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE void pscatter<unsigned char, Packet16uc>(unsigned char* to, const Packet16uc& from, Index stride)
+{
+ pscatter_common<Packet16uc>(to, from, stride);
+}
+
+template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE void pscatter_partial<float, Packet4f>(float* to, const Packet4f& from, Index stride, const Index n)
+{
+ pscatter_common<Packet4f>(to, from, stride, n);
+}
+
+template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE void pscatter_partial<int, Packet4i>(int* to, const Packet4i& from, Index stride, const Index n)
+{
+ pscatter_common<Packet4i>(to, from, stride, n);
+}
+
+template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE void pscatter_partial<short int, Packet8s>(short int* to, const Packet8s& from, Index stride, const Index n)
+{
+ pscatter_common<Packet8s>(to, from, stride, n);
+}
+
+template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE void pscatter_partial<unsigned short int, Packet8us>(unsigned short int* to, const Packet8us& from, Index stride, const Index n)
+{
+ pscatter_common<Packet8us>(to, from, stride, n);
+}
+
+template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE void pscatter_partial<bfloat16, Packet8bf>(bfloat16* to, const Packet8bf& from, Index stride, const Index n)
+{
+ pscatter_common<Packet8bf>(to, from, stride, n);
+}
+
+template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE void pscatter_partial<signed char, Packet16c>(signed char* to, const Packet16c& from, Index stride, const Index n)
+{
+ pscatter_common<Packet16c>(to, from, stride, n);
+}
+
+template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE void pscatter_partial<unsigned char, Packet16uc>(unsigned char* to, const Packet16uc& from, Index stride, const Index n)
+{
+ pscatter_common<Packet16uc>(to, from, stride, n);
+}
+
+template<> EIGEN_STRONG_INLINE Packet4f plset<Packet4f>(const float& a) { return pset1<Packet4f>(a) + p4f_COUNTDOWN; }
+template<> EIGEN_STRONG_INLINE Packet4i plset<Packet4i>(const int& a) { return pset1<Packet4i>(a) + p4i_COUNTDOWN; }
+template<> EIGEN_STRONG_INLINE Packet8s plset<Packet8s>(const short int& a) { return pset1<Packet8s>(a) + p8s_COUNTDOWN; }
+template<> EIGEN_STRONG_INLINE Packet8us plset<Packet8us>(const unsigned short int& a) { return pset1<Packet8us>(a) + p8us_COUNTDOWN; }
+template<> EIGEN_STRONG_INLINE Packet16c plset<Packet16c>(const signed char& a) { return pset1<Packet16c>(a) + p16c_COUNTDOWN; }
+template<> EIGEN_STRONG_INLINE Packet16uc plset<Packet16uc>(const unsigned char& a) { return pset1<Packet16uc>(a) + p16uc_COUNTDOWN; }
+
+template<> EIGEN_STRONG_INLINE Packet4f padd<Packet4f> (const Packet4f& a, const Packet4f& b) { return a + b; }
+template<> EIGEN_STRONG_INLINE Packet4i padd<Packet4i> (const Packet4i& a, const Packet4i& b) { return a + b; }
+template<> EIGEN_STRONG_INLINE Packet4ui padd<Packet4ui> (const Packet4ui& a, const Packet4ui& b) { return a + b; }
+template<> EIGEN_STRONG_INLINE Packet8s padd<Packet8s> (const Packet8s& a, const Packet8s& b) { return a + b; }
+template<> EIGEN_STRONG_INLINE Packet8us padd<Packet8us> (const Packet8us& a, const Packet8us& b) { return a + b; }
+template<> EIGEN_STRONG_INLINE Packet16c padd<Packet16c> (const Packet16c& a, const Packet16c& b) { return a + b; }
+template<> EIGEN_STRONG_INLINE Packet16uc padd<Packet16uc>(const Packet16uc& a, const Packet16uc& b) { return a + b; }
+
+template<> EIGEN_STRONG_INLINE Packet4f psub<Packet4f> (const Packet4f& a, const Packet4f& b) { return a - b; }
+template<> EIGEN_STRONG_INLINE Packet4i psub<Packet4i> (const Packet4i& a, const Packet4i& b) { return a - b; }
+template<> EIGEN_STRONG_INLINE Packet8s psub<Packet8s> (const Packet8s& a, const Packet8s& b) { return a - b; }
+template<> EIGEN_STRONG_INLINE Packet8us psub<Packet8us> (const Packet8us& a, const Packet8us& b) { return a - b; }
+template<> EIGEN_STRONG_INLINE Packet16c psub<Packet16c> (const Packet16c& a, const Packet16c& b) { return a - b; }
+template<> EIGEN_STRONG_INLINE Packet16uc psub<Packet16uc>(const Packet16uc& a, const Packet16uc& b) { return a - b; }
+
+template<> EIGEN_STRONG_INLINE Packet4f pnegate(const Packet4f& a)
+{
+#ifdef __POWER8_VECTOR__
+ return vec_neg(a);
+#else
+ return p4f_ZERO - a;
+#endif
+}
+template<> EIGEN_STRONG_INLINE Packet4i pnegate(const Packet4i& a)
+{
+#ifdef __POWER8_VECTOR__
+ return vec_neg(a);
+#else
+ return p4i_ZERO - a;
+#endif
+}
+
+template<> EIGEN_STRONG_INLINE Packet4f pconj(const Packet4f& a) { return a; }
+template<> EIGEN_STRONG_INLINE Packet4i pconj(const Packet4i& a) { return a; }
+
+template<> EIGEN_STRONG_INLINE Packet4f pmul<Packet4f> (const Packet4f& a, const Packet4f& b) { return vec_madd(a,b, p4f_MZERO); }
+template<> EIGEN_STRONG_INLINE Packet4i pmul<Packet4i> (const Packet4i& a, const Packet4i& b) { return a * b; }
+template<> EIGEN_STRONG_INLINE Packet8s pmul<Packet8s> (const Packet8s& a, const Packet8s& b) { return vec_mul(a,b); }
+template<> EIGEN_STRONG_INLINE Packet8us pmul<Packet8us> (const Packet8us& a, const Packet8us& b) { return vec_mul(a,b); }
+template<> EIGEN_STRONG_INLINE Packet16c pmul<Packet16c> (const Packet16c& a, const Packet16c& b) { return vec_mul(a,b); }
+template<> EIGEN_STRONG_INLINE Packet16uc pmul<Packet16uc>(const Packet16uc& a, const Packet16uc& b) { return vec_mul(a,b); }
+
+
+template<> EIGEN_STRONG_INLINE Packet4f pdiv<Packet4f>(const Packet4f& a, const Packet4f& b)
+{
+#ifndef __VSX__ // VSX actually provides a div instruction
+ Packet4f t, y_0, y_1;
+
+ // Altivec does not offer a divide instruction, we have to do a reciprocal approximation
+ y_0 = vec_re(b);
+
+ // Do one Newton-Raphson iteration to get the needed accuracy
+ t = vec_nmsub(y_0, b, p4f_ONE);
+ y_1 = vec_madd(y_0, t, y_0);
+
+ return vec_madd(a, y_1, p4f_MZERO);
+#else
+ return vec_div(a, b);
+#endif
+}
+
+template<> EIGEN_STRONG_INLINE Packet4i pdiv<Packet4i>(const Packet4i& /*a*/, const Packet4i& /*b*/)
+{ eigen_assert(false && "packet integer division are not supported by AltiVec");
+ return pset1<Packet4i>(0);
+}
+
+// for some weird raisons, it has to be overloaded for packet of integers
+template<> EIGEN_STRONG_INLINE Packet4f pmadd(const Packet4f& a, const Packet4f& b, const Packet4f& c) { return vec_madd(a,b,c); }
+template<> EIGEN_STRONG_INLINE Packet4i pmadd(const Packet4i& a, const Packet4i& b, const Packet4i& c) { return a*b + c; }
+template<> EIGEN_STRONG_INLINE Packet8s pmadd(const Packet8s& a, const Packet8s& b, const Packet8s& c) { return vec_madd(a,b,c); }
+template<> EIGEN_STRONG_INLINE Packet8us pmadd(const Packet8us& a, const Packet8us& b, const Packet8us& c) { return vec_madd(a,b,c); }
+
+#ifdef __VSX__
+template<> EIGEN_STRONG_INLINE Packet4f pmsub(const Packet4f& a, const Packet4f& b, const Packet4f& c) { return vec_msub(a,b,c); }
+template<> EIGEN_STRONG_INLINE Packet4f pnmadd(const Packet4f& a, const Packet4f& b, const Packet4f& c) { return vec_nmsub(a,b,c); }
+template<> EIGEN_STRONG_INLINE Packet4f pnmsub(const Packet4f& a, const Packet4f& b, const Packet4f& c) { return vec_nmadd(a,b,c); }
+#endif
+
+template<> EIGEN_STRONG_INLINE Packet4f pmin<Packet4f>(const Packet4f& a, const Packet4f& b)
+{
+ #ifdef __VSX__
+ // NOTE: about 10% slower than vec_min, but consistent with std::min and SSE regarding NaN
+ Packet4f ret;
+ __asm__ ("xvcmpgesp %x0,%x1,%x2\n\txxsel %x0,%x1,%x2,%x0" : "=&wa" (ret) : "wa" (a), "wa" (b));
+ return ret;
+ #else
+ return vec_min(a, b);
+ #endif
+}
+template<> EIGEN_STRONG_INLINE Packet4i pmin<Packet4i>(const Packet4i& a, const Packet4i& b) { return vec_min(a, b); }
+template<> EIGEN_STRONG_INLINE Packet8s pmin<Packet8s>(const Packet8s& a, const Packet8s& b) { return vec_min(a, b); }
+template<> EIGEN_STRONG_INLINE Packet8us pmin<Packet8us>(const Packet8us& a, const Packet8us& b) { return vec_min(a, b); }
+template<> EIGEN_STRONG_INLINE Packet16c pmin<Packet16c>(const Packet16c& a, const Packet16c& b) { return vec_min(a, b); }
+template<> EIGEN_STRONG_INLINE Packet16uc pmin<Packet16uc>(const Packet16uc& a, const Packet16uc& b) { return vec_min(a, b); }
+
+
+template<> EIGEN_STRONG_INLINE Packet4f pmax<Packet4f>(const Packet4f& a, const Packet4f& b)
+{
+ #ifdef __VSX__
+ // NOTE: about 10% slower than vec_max, but consistent with std::max and SSE regarding NaN
+ Packet4f ret;
+ __asm__ ("xvcmpgtsp %x0,%x2,%x1\n\txxsel %x0,%x1,%x2,%x0" : "=&wa" (ret) : "wa" (a), "wa" (b));
+ return ret;
+ #else
+ return vec_max(a, b);
+ #endif
+}
+template<> EIGEN_STRONG_INLINE Packet4i pmax<Packet4i>(const Packet4i& a, const Packet4i& b) { return vec_max(a, b); }
+template<> EIGEN_STRONG_INLINE Packet8s pmax<Packet8s>(const Packet8s& a, const Packet8s& b) { return vec_max(a, b); }
+template<> EIGEN_STRONG_INLINE Packet8us pmax<Packet8us>(const Packet8us& a, const Packet8us& b) { return vec_max(a, b); }
+template<> EIGEN_STRONG_INLINE Packet16c pmax<Packet16c>(const Packet16c& a, const Packet16c& b) { return vec_max(a, b); }
+template<> EIGEN_STRONG_INLINE Packet16uc pmax<Packet16uc>(const Packet16uc& a, const Packet16uc& b) { return vec_max(a, b); }
+
+template<> EIGEN_STRONG_INLINE Packet4f pcmp_le(const Packet4f& a, const Packet4f& b) { return reinterpret_cast<Packet4f>(vec_cmple(a,b)); }
+template<> EIGEN_STRONG_INLINE Packet4f pcmp_lt(const Packet4f& a, const Packet4f& b) { return reinterpret_cast<Packet4f>(vec_cmplt(a,b)); }
+template<> EIGEN_STRONG_INLINE Packet4f pcmp_eq(const Packet4f& a, const Packet4f& b) { return reinterpret_cast<Packet4f>(vec_cmpeq(a,b)); }
+template<> EIGEN_STRONG_INLINE Packet4f pcmp_lt_or_nan(const Packet4f& a, const Packet4f& b) {
+ Packet4f c = reinterpret_cast<Packet4f>(vec_cmpge(a,b));
+ return vec_nor(c,c);
+}
+
+#ifdef __VSX__
+template<> EIGEN_STRONG_INLINE Packet4i pcmp_le(const Packet4i& a, const Packet4i& b) { return reinterpret_cast<Packet4i>(vec_cmple(a,b)); }
+#endif
+template<> EIGEN_STRONG_INLINE Packet4i pcmp_lt(const Packet4i& a, const Packet4i& b) { return reinterpret_cast<Packet4i>(vec_cmplt(a,b)); }
+template<> EIGEN_STRONG_INLINE Packet4i pcmp_eq(const Packet4i& a, const Packet4i& b) { return reinterpret_cast<Packet4i>(vec_cmpeq(a,b)); }
+#ifdef __VSX__
+template<> EIGEN_STRONG_INLINE Packet8s pcmp_le(const Packet8s& a, const Packet8s& b) { return reinterpret_cast<Packet8s>(vec_cmple(a,b)); }
+#endif
+template<> EIGEN_STRONG_INLINE Packet8s pcmp_lt(const Packet8s& a, const Packet8s& b) { return reinterpret_cast<Packet8s>(vec_cmplt(a,b)); }
+template<> EIGEN_STRONG_INLINE Packet8s pcmp_eq(const Packet8s& a, const Packet8s& b) { return reinterpret_cast<Packet8s>(vec_cmpeq(a,b)); }
+#ifdef __VSX__
+template<> EIGEN_STRONG_INLINE Packet8us pcmp_le(const Packet8us& a, const Packet8us& b) { return reinterpret_cast<Packet8us>(vec_cmple(a,b)); }
+#endif
+template<> EIGEN_STRONG_INLINE Packet8us pcmp_lt(const Packet8us& a, const Packet8us& b) { return reinterpret_cast<Packet8us>(vec_cmplt(a,b)); }
+template<> EIGEN_STRONG_INLINE Packet8us pcmp_eq(const Packet8us& a, const Packet8us& b) { return reinterpret_cast<Packet8us>(vec_cmpeq(a,b)); }
+#ifdef __VSX__
+template<> EIGEN_STRONG_INLINE Packet16c pcmp_le(const Packet16c& a, const Packet16c& b) { return reinterpret_cast<Packet16c>(vec_cmple(a,b)); }
+#endif
+template<> EIGEN_STRONG_INLINE Packet16c pcmp_lt(const Packet16c& a, const Packet16c& b) { return reinterpret_cast<Packet16c>(vec_cmplt(a,b)); }
+template<> EIGEN_STRONG_INLINE Packet16c pcmp_eq(const Packet16c& a, const Packet16c& b) { return reinterpret_cast<Packet16c>(vec_cmpeq(a,b)); }
+#ifdef __VSX__
+template<> EIGEN_STRONG_INLINE Packet16uc pcmp_le(const Packet16uc& a, const Packet16uc& b) { return reinterpret_cast<Packet16uc>(vec_cmple(a,b)); }
+#endif
+template<> EIGEN_STRONG_INLINE Packet16uc pcmp_lt(const Packet16uc& a, const Packet16uc& b) { return reinterpret_cast<Packet16uc>(vec_cmplt(a,b)); }
+template<> EIGEN_STRONG_INLINE Packet16uc pcmp_eq(const Packet16uc& a, const Packet16uc& b) { return reinterpret_cast<Packet16uc>(vec_cmpeq(a,b)); }
+
+template<> EIGEN_STRONG_INLINE Packet4f pand<Packet4f>(const Packet4f& a, const Packet4f& b) { return vec_and(a, b); }
+template<> EIGEN_STRONG_INLINE Packet4i pand<Packet4i>(const Packet4i& a, const Packet4i& b) { return vec_and(a, b); }
+template<> EIGEN_STRONG_INLINE Packet4ui pand<Packet4ui>(const Packet4ui& a, const Packet4ui& b) { return vec_and(a, b); }
+template<> EIGEN_STRONG_INLINE Packet8us pand<Packet8us>(const Packet8us& a, const Packet8us& b) { return vec_and(a, b); }
+template<> EIGEN_STRONG_INLINE Packet8bf pand<Packet8bf>(const Packet8bf& a, const Packet8bf& b) {
+ return pand<Packet8us>(a, b);
+}
+
+
+template<> EIGEN_STRONG_INLINE Packet4f por<Packet4f>(const Packet4f& a, const Packet4f& b) { return vec_or(a, b); }
+template<> EIGEN_STRONG_INLINE Packet4i por<Packet4i>(const Packet4i& a, const Packet4i& b) { return vec_or(a, b); }
+template<> EIGEN_STRONG_INLINE Packet8s por<Packet8s>(const Packet8s& a, const Packet8s& b) { return vec_or(a, b); }
+template<> EIGEN_STRONG_INLINE Packet8us por<Packet8us>(const Packet8us& a, const Packet8us& b) { return vec_or(a, b); }
+template<> EIGEN_STRONG_INLINE Packet8bf por<Packet8bf>(const Packet8bf& a, const Packet8bf& b) {
+ return por<Packet8us>(a, b);
+}
+
+template<> EIGEN_STRONG_INLINE Packet4f pxor<Packet4f>(const Packet4f& a, const Packet4f& b) { return vec_xor(a, b); }
+template<> EIGEN_STRONG_INLINE Packet4i pxor<Packet4i>(const Packet4i& a, const Packet4i& b) { return vec_xor(a, b); }
+template<> EIGEN_STRONG_INLINE Packet8bf pxor<Packet8bf>(const Packet8bf& a, const Packet8bf& b) {
+ return pxor<Packet8us>(a, b);
+}
+
+template<> EIGEN_STRONG_INLINE Packet4f pandnot<Packet4f>(const Packet4f& a, const Packet4f& b) { return vec_andc(a, b); }
+template<> EIGEN_STRONG_INLINE Packet4i pandnot<Packet4i>(const Packet4i& a, const Packet4i& b) { return vec_andc(a, b); }
+
+template<> EIGEN_STRONG_INLINE Packet4f pselect(const Packet4f& mask, const Packet4f& a, const Packet4f& b) {
+ return vec_sel(b, a, reinterpret_cast<Packet4ui>(mask));
+}
+
+template<> EIGEN_STRONG_INLINE Packet4f pround<Packet4f>(const Packet4f& a)
+{
+ Packet4f t = vec_add(reinterpret_cast<Packet4f>(vec_or(vec_and(reinterpret_cast<Packet4ui>(a), p4ui_SIGN), p4ui_PREV0DOT5)), a);
+ Packet4f res;
+
+#ifdef __VSX__
+ __asm__("xvrspiz %x0, %x1\n\t"
+ : "=&wa" (res)
+ : "wa" (t));
+#else
+ __asm__("vrfiz %0, %1\n\t"
+ : "=v" (res)
+ : "v" (t));
+#endif
+
+ return res;
+}
+template<> EIGEN_STRONG_INLINE Packet4f pceil<Packet4f>(const Packet4f& a) { return vec_ceil(a); }
+template<> EIGEN_STRONG_INLINE Packet4f pfloor<Packet4f>(const Packet4f& a) { return vec_floor(a); }
+#ifdef __VSX__
+template<> EIGEN_STRONG_INLINE Packet4f print<Packet4f>(const Packet4f& a)
+{
+ Packet4f res;
+
+ __asm__("xvrspic %x0, %x1\n\t"
+ : "=&wa" (res)
+ : "wa" (a));
+
+ return res;
+}
+#endif
+
+template<typename Packet> EIGEN_STRONG_INLINE Packet ploadu_common(const __UNPACK_TYPE__(Packet)* from)
+{
+ EIGEN_DEBUG_ALIGNED_LOAD
+#if defined(__VSX__) || !defined(_BIG_ENDIAN)
+ EIGEN_DEBUG_UNALIGNED_LOAD
+ return vec_xl(0, const_cast<__UNPACK_TYPE__(Packet)*>(from));
+#else
+ Packet16uc MSQ, LSQ;
+ Packet16uc mask;
+ MSQ = vec_ld(0, (unsigned char *)from); // most significant quadword
+ LSQ = vec_ld(15, (unsigned char *)from); // least significant quadword
+ mask = vec_lvsl(0, from); // create the permute mask
+ //TODO: Add static_cast here
+ return (Packet) vec_perm(MSQ, LSQ, mask); // align the data
+#endif
+}
+
+template<> EIGEN_STRONG_INLINE Packet4f ploadu<Packet4f>(const float* from)
+{
+ return ploadu_common<Packet4f>(from);
+}
+template<> EIGEN_STRONG_INLINE Packet4i ploadu<Packet4i>(const int* from)
+{
+ return ploadu_common<Packet4i>(from);
+}
+template<> EIGEN_STRONG_INLINE Packet8s ploadu<Packet8s>(const short int* from)
+{
+ return ploadu_common<Packet8s>(from);
+}
+template<> EIGEN_STRONG_INLINE Packet8us ploadu<Packet8us>(const unsigned short int* from)
+{
+ return ploadu_common<Packet8us>(from);
+}
+template<> EIGEN_STRONG_INLINE Packet8bf ploadu<Packet8bf>(const bfloat16* from)
+{
+ return ploadu_common<Packet8us>(reinterpret_cast<const unsigned short int*>(from));
+}
+template<> EIGEN_STRONG_INLINE Packet16c ploadu<Packet16c>(const signed char* from)
+{
+ return ploadu_common<Packet16c>(from);
+}
+template<> EIGEN_STRONG_INLINE Packet16uc ploadu<Packet16uc>(const unsigned char* from)
+{
+ return ploadu_common<Packet16uc>(from);
+}
+
+template<typename Packet> EIGEN_ALWAYS_INLINE Packet ploadu_partial_common(const __UNPACK_TYPE__(Packet)* from, const Index n)
+{
+ const Index packet_size = unpacket_traits<Packet>::size;
+ eigen_assert(n <= packet_size && "number of elements will read past end of packet");
+ const Index size = sizeof(__UNPACK_TYPE__(Packet));
+#ifdef _ARCH_PWR9
+ EIGEN_UNUSED_VARIABLE(packet_size);
+ EIGEN_DEBUG_ALIGNED_LOAD
+ EIGEN_DEBUG_UNALIGNED_LOAD
+ return vec_xl_len(const_cast<__UNPACK_TYPE__(Packet)*>(from), n * size);
+#else
+ EIGEN_ALIGN16 __UNPACK_TYPE__(Packet) load[packet_size];
+ unsigned char* load2 = reinterpret_cast<unsigned char *>(load);
+ unsigned char* from2 = reinterpret_cast<unsigned char *>(const_cast<__UNPACK_TYPE__(Packet)*>(from));
+ Index n2 = n * size;
+ Index i = 0;
+ if (16 <= n2) {
+ pstore(load2, ploadu<Packet16uc>(from2));
+ i += 16;
+ }
+ if (i + 8 <= n2) {
+ *reinterpret_cast<uint64_t *>(load2 + i) = *reinterpret_cast<uint64_t *>(from2 + i);
+ i += 8;
+ }
+ if (i + 4 <= n2) {
+ *reinterpret_cast<uint32_t *>(load2 + i) = *reinterpret_cast<uint32_t *>(from2 + i);
+ i += 4;
+ }
+ if (i + 2 <= n2) {
+ *reinterpret_cast<uint16_t *>(load2 + i) = *reinterpret_cast<uint16_t *>(from2 + i);
+ i += 2;
+ }
+ if (i < n2) {
+ *reinterpret_cast<uint8_t *>(load2 + i) = *reinterpret_cast<uint8_t *>(from2 + i);
+ }
+ return pload_ignore<Packet>(load);
+#endif
+}
+
+template<> EIGEN_ALWAYS_INLINE Packet4f ploadu_partial<Packet4f>(const float* from, const Index n)
+{
+ return ploadu_partial_common<Packet4f>(from, n);
+}
+template<> EIGEN_ALWAYS_INLINE Packet4i ploadu_partial<Packet4i>(const int* from, const Index n)
+{
+ return ploadu_partial_common<Packet4i>(from, n);
+}
+template<> EIGEN_ALWAYS_INLINE Packet8s ploadu_partial<Packet8s>(const short int* from, const Index n)
+{
+ return ploadu_partial_common<Packet8s>(from, n);
+}
+template<> EIGEN_ALWAYS_INLINE Packet8us ploadu_partial<Packet8us>(const unsigned short int* from, const Index n)
+{
+ return ploadu_partial_common<Packet8us>(from, n);
+}
+template<> EIGEN_ALWAYS_INLINE Packet8bf ploadu_partial<Packet8bf>(const bfloat16* from, const Index n)
+{
+ return ploadu_partial_common<Packet8us>(reinterpret_cast<const unsigned short int*>(from), n);
+}
+template<> EIGEN_ALWAYS_INLINE Packet16c ploadu_partial<Packet16c>(const signed char* from, const Index n)
+{
+ return ploadu_partial_common<Packet16c>(from, n);
+}
+template<> EIGEN_ALWAYS_INLINE Packet16uc ploadu_partial<Packet16uc>(const unsigned char* from, const Index n)
+{
+ return ploadu_partial_common<Packet16uc>(from, n);
+}
+
+template<typename Packet> EIGEN_STRONG_INLINE Packet ploaddup_common(const __UNPACK_TYPE__(Packet)* from)
+{
+ Packet p;
+ if((std::ptrdiff_t(from) % 16) == 0) p = pload<Packet>(from);
+ else p = ploadu<Packet>(from);
+ return vec_mergeh(p, p);
+}
+template<> EIGEN_STRONG_INLINE Packet4f ploaddup<Packet4f>(const float* from)
+{
+ return ploaddup_common<Packet4f>(from);
+}
+template<> EIGEN_STRONG_INLINE Packet4i ploaddup<Packet4i>(const int* from)
+{
+ return ploaddup_common<Packet4i>(from);
+}
+
+template<> EIGEN_STRONG_INLINE Packet8s ploaddup<Packet8s>(const short int* from)
+{
+ Packet8s p;
+ if((std::ptrdiff_t(from) % 16) == 0) p = pload<Packet8s>(from);
+ else p = ploadu<Packet8s>(from);
+ return vec_mergeh(p, p);
+}
+
+template<> EIGEN_STRONG_INLINE Packet8us ploaddup<Packet8us>(const unsigned short int* from)
+{
+ Packet8us p;
+ if((std::ptrdiff_t(from) % 16) == 0) p = pload<Packet8us>(from);
+ else p = ploadu<Packet8us>(from);
+ return vec_mergeh(p, p);
+}
+
+template<> EIGEN_STRONG_INLINE Packet8s ploadquad<Packet8s>(const short int* from)
+{
+ Packet8s p;
+ if((std::ptrdiff_t(from) % 16) == 0) p = pload<Packet8s>(from);
+ else p = ploadu<Packet8s>(from);
+ return vec_perm(p, p, p16uc_QUADRUPLICATE16_HI);
+}
+
+template<> EIGEN_STRONG_INLINE Packet8us ploadquad<Packet8us>(const unsigned short int* from)
+{
+ Packet8us p;
+ if((std::ptrdiff_t(from) % 16) == 0) p = pload<Packet8us>(from);
+ else p = ploadu<Packet8us>(from);
+ return vec_perm(p, p, p16uc_QUADRUPLICATE16_HI);
+}
+
+template<> EIGEN_STRONG_INLINE Packet8bf ploadquad<Packet8bf>(const bfloat16* from)
+{
+ return ploadquad<Packet8us>(reinterpret_cast<const unsigned short int*>(from));
+}
+
+template<> EIGEN_STRONG_INLINE Packet16c ploaddup<Packet16c>(const signed char* from)
+{
+ Packet16c p;
+ if((std::ptrdiff_t(from) % 16) == 0) p = pload<Packet16c>(from);
+ else p = ploadu<Packet16c>(from);
+ return vec_mergeh(p, p);
+}
+
+template<> EIGEN_STRONG_INLINE Packet16uc ploaddup<Packet16uc>(const unsigned char* from)
+{
+ Packet16uc p;
+ if((std::ptrdiff_t(from) % 16) == 0) p = pload<Packet16uc>(from);
+ else p = ploadu<Packet16uc>(from);
+ return vec_mergeh(p, p);
+}
+
+template<typename Packet> EIGEN_STRONG_INLINE void pstoreu_common(__UNPACK_TYPE__(Packet)* to, const Packet& from)
+{
+ EIGEN_DEBUG_UNALIGNED_STORE
+#if defined(__VSX__) || !defined(_BIG_ENDIAN)
+ vec_xst(from, 0, to);
+#else
+ // Taken from http://developer.apple.com/hardwaredrivers/ve/alignment.html
+ // Warning: not thread safe!
+ Packet16uc MSQ, LSQ, edges;
+ Packet16uc edgeAlign, align;
+
+ MSQ = vec_ld(0, (unsigned char *)to); // most significant quadword
+ LSQ = vec_ld(15, (unsigned char *)to); // least significant quadword
+ edgeAlign = vec_lvsl(0, to); // permute map to extract edges
+ edges=vec_perm(LSQ,MSQ,edgeAlign); // extract the edges
+ align = vec_lvsr( 0, to ); // permute map to misalign data
+ MSQ = vec_perm(edges,(Packet16uc)from,align); // misalign the data (MSQ)
+ LSQ = vec_perm((Packet16uc)from,edges,align); // misalign the data (LSQ)
+ vec_st( LSQ, 15, (unsigned char *)to ); // Store the LSQ part first
+ vec_st( MSQ, 0, (unsigned char *)to ); // Store the MSQ part second
+#endif
+}
+template<> EIGEN_STRONG_INLINE void pstoreu<float>(float* to, const Packet4f& from)
+{
+ pstoreu_common<Packet4f>(to, from);
+}
+template<> EIGEN_STRONG_INLINE void pstoreu<int>(int* to, const Packet4i& from)
+{
+ pstoreu_common<Packet4i>(to, from);
+}
+template<> EIGEN_STRONG_INLINE void pstoreu<short int>(short int* to, const Packet8s& from)
+{
+ pstoreu_common<Packet8s>(to, from);
+}
+template<> EIGEN_STRONG_INLINE void pstoreu<unsigned short int>(unsigned short int* to, const Packet8us& from)
+{
+ pstoreu_common<Packet8us>(to, from);
+}
+template<> EIGEN_STRONG_INLINE void pstoreu<bfloat16>(bfloat16* to, const Packet8bf& from)
+{
+ pstoreu_common<Packet8us>(reinterpret_cast<unsigned short int*>(to), from);
+}
+template<> EIGEN_STRONG_INLINE void pstoreu<signed char>(signed char* to, const Packet16c& from)
+{
+ pstoreu_common<Packet16c>(to, from);
+}
+template<> EIGEN_STRONG_INLINE void pstoreu<unsigned char>(unsigned char* to, const Packet16uc& from)
+{
+ pstoreu_common<Packet16uc>(to, from);
+}
+
+template<typename Packet> EIGEN_ALWAYS_INLINE void pstoreu_partial_common(__UNPACK_TYPE__(Packet)* to, const Packet& from, const Index n)
+{
+ const Index packet_size = unpacket_traits<Packet>::size;
+ eigen_assert(n <= packet_size && "number of elements will write past end of packet");
+ const Index size = sizeof(__UNPACK_TYPE__(Packet));
+#ifdef _ARCH_PWR9
+ EIGEN_UNUSED_VARIABLE(packet_size);
+ EIGEN_DEBUG_UNALIGNED_STORE
+ vec_xst_len(from, to, n * size);
+#else
+ EIGEN_ALIGN16 __UNPACK_TYPE__(Packet) store[packet_size];
+ pstore(store, from);
+ unsigned char* store2 = reinterpret_cast<unsigned char *>(store);
+ unsigned char* to2 = reinterpret_cast<unsigned char *>(to);
+ Index n2 = n * size;
+ Index i = 0;
+ if (16 <= n2) {
+ pstoreu(to2, pload<Packet16uc>(store2));
+ i += 16;
+ }
+ if (i + 8 <= n2) {
+ *reinterpret_cast<uint64_t *>(to2 + i) = *reinterpret_cast<uint64_t *>(store2 + i);
+ i += 8;
+ }
+ if (i + 4 <= n2) {
+ *reinterpret_cast<uint32_t *>(to2 + i) = *reinterpret_cast<uint32_t *>(store2 + i);
+ i += 4;
+ }
+ if (i + 2 <= n2) {
+ *reinterpret_cast<uint16_t *>(to2 + i) = *reinterpret_cast<uint16_t *>(store2 + i);
+ i += 2;
+ }
+ if (i < n2) {
+ *reinterpret_cast<uint8_t *>(to2 + i) = *reinterpret_cast<uint8_t *>(store2 + i);
+ }
+
+ LOAD_STORE_UNROLL_16
+ for (Index i = 0; i < n; i++) {
+ to[i] = from[i];
+ }
+#endif
+}
+
+template<> EIGEN_ALWAYS_INLINE void pstoreu_partial<float>(float* to, const Packet4f& from, const Index n)
+{
+ pstoreu_partial_common<Packet4f>(to, from, n);
+}
+template<> EIGEN_ALWAYS_INLINE void pstoreu_partial<int>(int* to, const Packet4i& from, const Index n)
+{
+ pstoreu_partial_common<Packet4i>(to, from, n);
+}
+template<> EIGEN_ALWAYS_INLINE void pstoreu_partial<short int>(short int* to, const Packet8s& from, const Index n)
+{
+ pstoreu_partial_common<Packet8s>(to, from, n);
+}
+template<> EIGEN_ALWAYS_INLINE void pstoreu_partial<unsigned short int>(unsigned short int* to, const Packet8us& from, const Index n)
+{
+ pstoreu_partial_common<Packet8us>(to, from, n);
+}
+template<> EIGEN_ALWAYS_INLINE void pstoreu_partial<bfloat16>(bfloat16* to, const Packet8bf& from, const Index n)
+{
+ pstoreu_partial_common<Packet8us>(reinterpret_cast<unsigned short int*>(to), from, n);
+}
+template<> EIGEN_ALWAYS_INLINE void pstoreu_partial<signed char>(signed char* to, const Packet16c& from, const Index n)
+{
+ pstoreu_partial_common<Packet16c>(to, from, n);
+}
+template<> EIGEN_ALWAYS_INLINE void pstoreu_partial<unsigned char>(unsigned char* to, const Packet16uc& from, const Index n)
+{
+ pstoreu_partial_common<Packet16uc>(to, from, n);
+}
+
+template<> EIGEN_STRONG_INLINE void prefetch<float>(const float* addr) { EIGEN_PPC_PREFETCH(addr); }
+template<> EIGEN_STRONG_INLINE void prefetch<int>(const int* addr) { EIGEN_PPC_PREFETCH(addr); }
+
+template<> EIGEN_STRONG_INLINE float pfirst<Packet4f>(const Packet4f& a) { EIGEN_ALIGN16 float x; vec_ste(a, 0, &x); return x; }
+template<> EIGEN_STRONG_INLINE int pfirst<Packet4i>(const Packet4i& a) { EIGEN_ALIGN16 int x; vec_ste(a, 0, &x); return x; }
+
+template<typename Packet> EIGEN_STRONG_INLINE __UNPACK_TYPE__(Packet) pfirst_common(const Packet& a) {
+ EIGEN_ALIGN16 __UNPACK_TYPE__(Packet) x;
+ vec_ste(a, 0, &x);
+ return x;
+}
+
+template<> EIGEN_STRONG_INLINE short int pfirst<Packet8s>(const Packet8s& a) {
+ return pfirst_common<Packet8s>(a);
+}
+
+template<> EIGEN_STRONG_INLINE unsigned short int pfirst<Packet8us>(const Packet8us& a) {
+ return pfirst_common<Packet8us>(a);
+}
+
+template<> EIGEN_STRONG_INLINE signed char pfirst<Packet16c>(const Packet16c& a)
+{
+ return pfirst_common<Packet16c>(a);
+}
+
+template<> EIGEN_STRONG_INLINE unsigned char pfirst<Packet16uc>(const Packet16uc& a)
+{
+ return pfirst_common<Packet16uc>(a);
+}
+
+template<> EIGEN_STRONG_INLINE Packet4f preverse(const Packet4f& a)
+{
+ return reinterpret_cast<Packet4f>(vec_perm(reinterpret_cast<Packet16uc>(a), reinterpret_cast<Packet16uc>(a), p16uc_REVERSE32));
+}
+template<> EIGEN_STRONG_INLINE Packet4i preverse(const Packet4i& a)
+{
+ return reinterpret_cast<Packet4i>(vec_perm(reinterpret_cast<Packet16uc>(a), reinterpret_cast<Packet16uc>(a), p16uc_REVERSE32));
+}
+template<> EIGEN_STRONG_INLINE Packet8s preverse(const Packet8s& a)
+{
+ return reinterpret_cast<Packet8s>(vec_perm(reinterpret_cast<Packet16uc>(a), reinterpret_cast<Packet16uc>(a), p16uc_REVERSE16));
+}
+template<> EIGEN_STRONG_INLINE Packet8us preverse(const Packet8us& a)
+{
+ return reinterpret_cast<Packet8us>(vec_perm(reinterpret_cast<Packet16uc>(a), reinterpret_cast<Packet16uc>(a), p16uc_REVERSE16));
+}
+template<> EIGEN_STRONG_INLINE Packet16c preverse(const Packet16c& a)
+{
+#ifdef _ARCH_PWR9
+ return vec_revb(a);
+#else
+ return vec_perm(a, a, p16uc_REVERSE8);
+#endif
+}
+template<> EIGEN_STRONG_INLINE Packet16uc preverse(const Packet16uc& a)
+{
+#ifdef _ARCH_PWR9
+ return vec_revb(a);
+#else
+ return vec_perm(a, a, p16uc_REVERSE8);
+#endif
+}
+template<> EIGEN_STRONG_INLINE Packet8bf preverse(const Packet8bf& a)
+{
+ return preverse<Packet8us>(a);
+}
+
+template<> EIGEN_STRONG_INLINE Packet4f pabs(const Packet4f& a) { return vec_abs(a); }
+template<> EIGEN_STRONG_INLINE Packet4i pabs(const Packet4i& a) { return vec_abs(a); }
+template<> EIGEN_STRONG_INLINE Packet8s pabs(const Packet8s& a) { return vec_abs(a); }
+template<> EIGEN_STRONG_INLINE Packet8us pabs(const Packet8us& a) { return a; }
+template<> EIGEN_STRONG_INLINE Packet16c pabs(const Packet16c& a) { return vec_abs(a); }
+template<> EIGEN_STRONG_INLINE Packet16uc pabs(const Packet16uc& a) { return a; }
+template<> EIGEN_STRONG_INLINE Packet8bf pabs(const Packet8bf& a) {
+ EIGEN_DECLARE_CONST_FAST_Packet8us(abs_mask,0x7FFF);
+ return pand<Packet8us>(p8us_abs_mask, a);
+}
+
+template<int N> EIGEN_STRONG_INLINE Packet4i parithmetic_shift_right(const Packet4i& a)
+{ return vec_sra(a,reinterpret_cast<Packet4ui>(pset1<Packet4i>(N))); }
+template<int N> EIGEN_STRONG_INLINE Packet4i plogical_shift_right(const Packet4i& a)
+{ return vec_sr(a,reinterpret_cast<Packet4ui>(pset1<Packet4i>(N))); }
+template<int N> EIGEN_STRONG_INLINE Packet4i plogical_shift_left(const Packet4i& a)
+{ return vec_sl(a,reinterpret_cast<Packet4ui>(pset1<Packet4i>(N))); }
+template<int N> EIGEN_STRONG_INLINE Packet4f plogical_shift_left(const Packet4f& a)
+{
+ const EIGEN_DECLARE_CONST_FAST_Packet4ui(mask, N);
+ Packet4ui r = vec_sl(reinterpret_cast<Packet4ui>(a), p4ui_mask);
+ return reinterpret_cast<Packet4f>(r);
+}
+
+template<int N> EIGEN_STRONG_INLINE Packet4f plogical_shift_right(const Packet4f& a)
+{
+ const EIGEN_DECLARE_CONST_FAST_Packet4ui(mask, N);
+ Packet4ui r = vec_sr(reinterpret_cast<Packet4ui>(a), p4ui_mask);
+ return reinterpret_cast<Packet4f>(r);
+}
+
+template<int N> EIGEN_STRONG_INLINE Packet4ui plogical_shift_right(const Packet4ui& a)
+{
+ const EIGEN_DECLARE_CONST_FAST_Packet4ui(mask, N);
+ return vec_sr(a, p4ui_mask);
+}
+
+template<int N> EIGEN_STRONG_INLINE Packet4ui plogical_shift_left(const Packet4ui& a)
+{
+ const EIGEN_DECLARE_CONST_FAST_Packet4ui(mask, N);
+ return vec_sl(a, p4ui_mask);
+}
+
+template<int N> EIGEN_STRONG_INLINE Packet8us plogical_shift_left(const Packet8us& a)
+{
+ const EIGEN_DECLARE_CONST_FAST_Packet8us(mask, N);
+ return vec_sl(a, p8us_mask);
+}
+template<int N> EIGEN_STRONG_INLINE Packet8us plogical_shift_right(const Packet8us& a)
+{
+ const EIGEN_DECLARE_CONST_FAST_Packet8us(mask, N);
+ return vec_sr(a, p8us_mask);
+}
+
+EIGEN_STRONG_INLINE Packet4f Bf16ToF32Even(const Packet8bf& bf){
+ return plogical_shift_left<16>(reinterpret_cast<Packet4f>(bf.m_val));
+}
+
+EIGEN_STRONG_INLINE Packet4f Bf16ToF32Odd(const Packet8bf& bf){
+ const EIGEN_DECLARE_CONST_FAST_Packet4ui(high_mask, 0xFFFF0000);
+ return pand<Packet4f>(
+ reinterpret_cast<Packet4f>(bf.m_val),
+ reinterpret_cast<Packet4f>(p4ui_high_mask)
+ );
+}
+
+// Simple interleaving of bool masks, prevents true values from being
+// converted to NaNs.
+EIGEN_STRONG_INLINE Packet8bf F32ToBf16Bool(Packet4f even, Packet4f odd) {
+ const EIGEN_DECLARE_CONST_FAST_Packet4ui(high_mask, 0xFFFF0000);
+ Packet4f bf_odd, bf_even;
+ bf_odd = pand(reinterpret_cast<Packet4f>(p4ui_high_mask), odd);
+ bf_even = plogical_shift_right<16>(even);
+ return reinterpret_cast<Packet8us>(por<Packet4f>(bf_even, bf_odd));
+}
+
+EIGEN_STRONG_INLINE Packet8bf F32ToBf16(Packet4f p4f){
+ Packet4ui input = reinterpret_cast<Packet4ui>(p4f);
+ Packet4ui lsb = plogical_shift_right<16>(input);
+ lsb = pand<Packet4ui>(lsb, reinterpret_cast<Packet4ui>(p4i_ONE));
+
+ EIGEN_DECLARE_CONST_FAST_Packet4ui(BIAS,0x7FFFu);
+ Packet4ui rounding_bias = padd<Packet4ui>(lsb, p4ui_BIAS);
+ input = padd<Packet4ui>(input, rounding_bias);
+
+ //Test NaN and Subnormal - Begin
+ const EIGEN_DECLARE_CONST_FAST_Packet4ui(exp_mask, 0x7F800000);
+ Packet4ui exp = pand<Packet4ui>(p4ui_exp_mask, reinterpret_cast<Packet4ui>(p4f));
+
+ const EIGEN_DECLARE_CONST_FAST_Packet4ui(mantissa_mask, 0x7FFFFF);
+ Packet4ui mantissa = pand<Packet4ui>(p4ui_mantissa_mask, reinterpret_cast<Packet4ui>(p4f));
+
+ const EIGEN_DECLARE_CONST_FAST_Packet4ui(max_exp, 0x7F800000);
+ Packet4bi is_max_exp = vec_cmpeq(exp, p4ui_max_exp);
+ Packet4bi is_zero_exp = vec_cmpeq(exp, reinterpret_cast<Packet4ui>(p4i_ZERO));
+
+ Packet4bi is_mant_zero = vec_cmpeq(mantissa, reinterpret_cast<Packet4ui>(p4i_ZERO));
+ Packet4ui nan_selector = pandnot<Packet4ui>(
+ reinterpret_cast<Packet4ui>(is_max_exp),
+ reinterpret_cast<Packet4ui>(is_mant_zero)
+ );
+
+ Packet4ui subnormal_selector = pandnot<Packet4ui>(
+ reinterpret_cast<Packet4ui>(is_zero_exp),
+ reinterpret_cast<Packet4ui>(is_mant_zero)
+ );
+
+ const EIGEN_DECLARE_CONST_FAST_Packet4ui(nan, 0x7FC00000);
+ input = vec_sel(input, p4ui_nan, nan_selector);
+ input = vec_sel(input, reinterpret_cast<Packet4ui>(p4f), subnormal_selector);
+ //Test NaN and Subnormal - End
+
+ input = plogical_shift_right<16>(input);
+ return reinterpret_cast<Packet8us>(input);
+}
+
+EIGEN_STRONG_INLINE Packet8bf F32ToBf16(Packet4f even, Packet4f odd){
+ Packet4f bf_odd, bf_even;
+ bf_odd = reinterpret_cast<Packet4f>(F32ToBf16(odd).m_val);
+ bf_odd = plogical_shift_left<16>(bf_odd);
+ bf_even = reinterpret_cast<Packet4f>(F32ToBf16(even).m_val);
+ return reinterpret_cast<Packet8us>(por<Packet4f>(bf_even, bf_odd));
+}
+#define BF16_TO_F32_UNARY_OP_WRAPPER(OP, A) \
+ Packet4f a_even = Bf16ToF32Even(A);\
+ Packet4f a_odd = Bf16ToF32Odd(A);\
+ Packet4f op_even = OP(a_even);\
+ Packet4f op_odd = OP(a_odd);\
+ return F32ToBf16(op_even, op_odd);\
+
+#define BF16_TO_F32_BINARY_OP_WRAPPER(OP, A, B) \
+ Packet4f a_even = Bf16ToF32Even(A);\
+ Packet4f a_odd = Bf16ToF32Odd(A);\
+ Packet4f b_even = Bf16ToF32Even(B);\
+ Packet4f b_odd = Bf16ToF32Odd(B);\
+ Packet4f op_even = OP(a_even, b_even);\
+ Packet4f op_odd = OP(a_odd, b_odd);\
+ return F32ToBf16(op_even, op_odd);\
+
+#define BF16_TO_F32_BINARY_OP_WRAPPER_BOOL(OP, A, B) \
+ Packet4f a_even = Bf16ToF32Even(A);\
+ Packet4f a_odd = Bf16ToF32Odd(A);\
+ Packet4f b_even = Bf16ToF32Even(B);\
+ Packet4f b_odd = Bf16ToF32Odd(B);\
+ Packet4f op_even = OP(a_even, b_even);\
+ Packet4f op_odd = OP(a_odd, b_odd);\
+ return F32ToBf16Bool(op_even, op_odd);\
+
+template<> EIGEN_STRONG_INLINE Packet8bf padd<Packet8bf>(const Packet8bf& a, const Packet8bf& b) {
+ BF16_TO_F32_BINARY_OP_WRAPPER(padd<Packet4f>, a, b);
+}
+
+template<> EIGEN_STRONG_INLINE Packet8bf pmul<Packet8bf>(const Packet8bf& a, const Packet8bf& b) {
+ BF16_TO_F32_BINARY_OP_WRAPPER(pmul<Packet4f>, a, b);
+}
+
+template<> EIGEN_STRONG_INLINE Packet8bf pdiv<Packet8bf>(const Packet8bf& a, const Packet8bf& b) {
+ BF16_TO_F32_BINARY_OP_WRAPPER(pdiv<Packet4f>, a, b);
+}
+
+template<> EIGEN_STRONG_INLINE Packet8bf pnegate<Packet8bf>(const Packet8bf& a) {
+ BF16_TO_F32_UNARY_OP_WRAPPER(pnegate<Packet4f>, a);
+}
+
+template<> EIGEN_STRONG_INLINE Packet8bf psub<Packet8bf>(const Packet8bf& a, const Packet8bf& b) {
+ BF16_TO_F32_BINARY_OP_WRAPPER(psub<Packet4f>, a, b);
+}
+
+template<> EIGEN_STRONG_INLINE Packet8bf pexp<Packet8bf> (const Packet8bf& a){
+ BF16_TO_F32_UNARY_OP_WRAPPER(pexp_float, a);
+}
+
+template<> EIGEN_STRONG_INLINE Packet4f pldexp<Packet4f>(const Packet4f& a, const Packet4f& exponent) {
+ return pldexp_generic(a,exponent);
+}
+template<> EIGEN_STRONG_INLINE Packet8bf pldexp<Packet8bf> (const Packet8bf& a, const Packet8bf& exponent){
+ BF16_TO_F32_BINARY_OP_WRAPPER(pldexp<Packet4f>, a, exponent);
+}
+
+template<> EIGEN_STRONG_INLINE Packet4f pfrexp<Packet4f>(const Packet4f& a, Packet4f& exponent) {
+ return pfrexp_generic(a,exponent);
+}
+template<> EIGEN_STRONG_INLINE Packet8bf pfrexp<Packet8bf> (const Packet8bf& a, Packet8bf& e){
+ Packet4f a_even = Bf16ToF32Even(a);
+ Packet4f a_odd = Bf16ToF32Odd(a);
+ Packet4f e_even;
+ Packet4f e_odd;
+ Packet4f op_even = pfrexp<Packet4f>(a_even, e_even);
+ Packet4f op_odd = pfrexp<Packet4f>(a_odd, e_odd);
+ e = F32ToBf16(e_even, e_odd);
+ return F32ToBf16(op_even, op_odd);
+}
+
+template<> EIGEN_STRONG_INLINE Packet8bf psin<Packet8bf> (const Packet8bf& a){
+ BF16_TO_F32_UNARY_OP_WRAPPER(psin_float, a);
+}
+template<> EIGEN_STRONG_INLINE Packet8bf pcos<Packet8bf> (const Packet8bf& a){
+ BF16_TO_F32_UNARY_OP_WRAPPER(pcos_float, a);
+}
+template<> EIGEN_STRONG_INLINE Packet8bf plog<Packet8bf> (const Packet8bf& a){
+ BF16_TO_F32_UNARY_OP_WRAPPER(plog_float, a);
+}
+template<> EIGEN_STRONG_INLINE Packet8bf pfloor<Packet8bf> (const Packet8bf& a){
+ BF16_TO_F32_UNARY_OP_WRAPPER(pfloor<Packet4f>, a);
+}
+template<> EIGEN_STRONG_INLINE Packet8bf pceil<Packet8bf> (const Packet8bf& a){
+ BF16_TO_F32_UNARY_OP_WRAPPER(pceil<Packet4f>, a);
+}
+template<> EIGEN_STRONG_INLINE Packet8bf pround<Packet8bf> (const Packet8bf& a){
+ BF16_TO_F32_UNARY_OP_WRAPPER(pround<Packet4f>, a);
+}
+#ifdef __VSX__
+template<> EIGEN_STRONG_INLINE Packet8bf print<Packet8bf> (const Packet8bf& a){
+ BF16_TO_F32_UNARY_OP_WRAPPER(print<Packet4f>, a);
+}
+#endif
+template<> EIGEN_STRONG_INLINE Packet8bf pmadd(const Packet8bf& a, const Packet8bf& b, const Packet8bf& c) {
+ Packet4f a_even = Bf16ToF32Even(a);
+ Packet4f a_odd = Bf16ToF32Odd(a);
+ Packet4f b_even = Bf16ToF32Even(b);
+ Packet4f b_odd = Bf16ToF32Odd(b);
+ Packet4f c_even = Bf16ToF32Even(c);
+ Packet4f c_odd = Bf16ToF32Odd(c);
+ Packet4f pmadd_even = pmadd<Packet4f>(a_even, b_even, c_even);
+ Packet4f pmadd_odd = pmadd<Packet4f>(a_odd, b_odd, c_odd);
+ return F32ToBf16(pmadd_even, pmadd_odd);
+}
+
+template<> EIGEN_STRONG_INLINE Packet8bf pmin<Packet8bf>(const Packet8bf& a, const Packet8bf& b) {
+ BF16_TO_F32_BINARY_OP_WRAPPER(pmin<Packet4f>, a, b);
+}
+
+template<> EIGEN_STRONG_INLINE Packet8bf pmax<Packet8bf>(const Packet8bf& a, const Packet8bf& b) {
+ BF16_TO_F32_BINARY_OP_WRAPPER(pmax<Packet4f>, a, b);
+}
+
+template<> EIGEN_STRONG_INLINE Packet8bf pcmp_lt(const Packet8bf& a, const Packet8bf& b) {
+ BF16_TO_F32_BINARY_OP_WRAPPER_BOOL(pcmp_lt<Packet4f>, a, b);
+}
+template<> EIGEN_STRONG_INLINE Packet8bf pcmp_lt_or_nan(const Packet8bf& a, const Packet8bf& b) {
+ BF16_TO_F32_BINARY_OP_WRAPPER_BOOL(pcmp_lt_or_nan<Packet4f>, a, b);
+}
+template<> EIGEN_STRONG_INLINE Packet8bf pcmp_le(const Packet8bf& a, const Packet8bf& b) {
+ BF16_TO_F32_BINARY_OP_WRAPPER_BOOL(pcmp_le<Packet4f>, a, b);
+}
+template<> EIGEN_STRONG_INLINE Packet8bf pcmp_eq(const Packet8bf& a, const Packet8bf& b) {
+ BF16_TO_F32_BINARY_OP_WRAPPER_BOOL(pcmp_eq<Packet4f>, a, b);
+}
+
+template<> EIGEN_STRONG_INLINE bfloat16 pfirst(const Packet8bf& a) {
+ return Eigen::bfloat16_impl::raw_uint16_to_bfloat16((pfirst<Packet8us>(a)));
+}
+
+template<> EIGEN_STRONG_INLINE Packet8bf ploaddup<Packet8bf>(const bfloat16* from)
+{
+ return ploaddup<Packet8us>(reinterpret_cast<const unsigned short int*>(from));
+}
+
+template<> EIGEN_STRONG_INLINE Packet8bf plset<Packet8bf>(const bfloat16& a) {
+ bfloat16 countdown[8] = { bfloat16(0), bfloat16(1), bfloat16(2), bfloat16(3),
+ bfloat16(4), bfloat16(5), bfloat16(6), bfloat16(7) };
+ return padd<Packet8bf>(pset1<Packet8bf>(a), pload<Packet8bf>(countdown));
+}
+
+template<> EIGEN_STRONG_INLINE float predux<Packet4f>(const Packet4f& a)
+{
+ Packet4f b, sum;
+ b = vec_sld(a, a, 8);
+ sum = a + b;
+ b = vec_sld(sum, sum, 4);
+ sum += b;
+ return pfirst(sum);
+}
+
+template<> EIGEN_STRONG_INLINE int predux<Packet4i>(const Packet4i& a)
+{
+ Packet4i sum;
+ sum = vec_sums(a, p4i_ZERO);
+#ifdef _BIG_ENDIAN
+ sum = vec_sld(sum, p4i_ZERO, 12);
+#else
+ sum = vec_sld(p4i_ZERO, sum, 4);
+#endif
+ return pfirst(sum);
+}
+
+template<> EIGEN_STRONG_INLINE bfloat16 predux<Packet8bf>(const Packet8bf& a)
+{
+ float redux_even = predux<Packet4f>(Bf16ToF32Even(a));
+ float redux_odd = predux<Packet4f>(Bf16ToF32Odd(a));
+ float f32_result = redux_even + redux_odd;
+ return bfloat16(f32_result);
+}
+template<typename Packet> EIGEN_STRONG_INLINE __UNPACK_TYPE__(Packet) predux_size8(const Packet& a)
+{
+ union{
+ Packet v;
+ __UNPACK_TYPE__(Packet) n[8];
+ } vt;
+ vt.v = a;
+
+ EIGEN_ALIGN16 int first_loader[4] = { vt.n[0], vt.n[1], vt.n[2], vt.n[3] };
+ EIGEN_ALIGN16 int second_loader[4] = { vt.n[4], vt.n[5], vt.n[6], vt.n[7] };
+ Packet4i first_half = pload<Packet4i>(first_loader);
+ Packet4i second_half = pload<Packet4i>(second_loader);
+
+ return static_cast<__UNPACK_TYPE__(Packet)>(predux(first_half) + predux(second_half));
+}
+
+template<> EIGEN_STRONG_INLINE short int predux<Packet8s>(const Packet8s& a)
+{
+ return predux_size8<Packet8s>(a);
+}
+
+template<> EIGEN_STRONG_INLINE unsigned short int predux<Packet8us>(const Packet8us& a)
+{
+ return predux_size8<Packet8us>(a);
+}
+
+template<typename Packet> EIGEN_STRONG_INLINE __UNPACK_TYPE__(Packet) predux_size16(const Packet& a)
+{
+ union{
+ Packet v;
+ __UNPACK_TYPE__(Packet) n[16];
+ } vt;
+ vt.v = a;
+
+ EIGEN_ALIGN16 int first_loader[4] = { vt.n[0], vt.n[1], vt.n[2], vt.n[3] };
+ EIGEN_ALIGN16 int second_loader[4] = { vt.n[4], vt.n[5], vt.n[6], vt.n[7] };
+ EIGEN_ALIGN16 int third_loader[4] = { vt.n[8], vt.n[9], vt.n[10], vt.n[11] };
+ EIGEN_ALIGN16 int fourth_loader[4] = { vt.n[12], vt.n[13], vt.n[14], vt.n[15] };
+
+ Packet4i first_quarter = pload<Packet4i>(first_loader);
+ Packet4i second_quarter = pload<Packet4i>(second_loader);
+ Packet4i third_quarter = pload<Packet4i>(third_loader);
+ Packet4i fourth_quarter = pload<Packet4i>(fourth_loader);
+
+ return static_cast<__UNPACK_TYPE__(Packet)>(predux(first_quarter) + predux(second_quarter)
+ + predux(third_quarter) + predux(fourth_quarter));
+}
+
+template<> EIGEN_STRONG_INLINE signed char predux<Packet16c>(const Packet16c& a)
+{
+ return predux_size16<Packet16c>(a);
+}
+
+template<> EIGEN_STRONG_INLINE unsigned char predux<Packet16uc>(const Packet16uc& a)
+{
+ return predux_size16<Packet16uc>(a);
+}
+
+// Other reduction functions:
+// mul
+template<> EIGEN_STRONG_INLINE float predux_mul<Packet4f>(const Packet4f& a)
+{
+ Packet4f prod;
+ prod = pmul(a, vec_sld(a, a, 8));
+ return pfirst(pmul(prod, vec_sld(prod, prod, 4)));
+}
+
+template<> EIGEN_STRONG_INLINE int predux_mul<Packet4i>(const Packet4i& a)
+{
+ EIGEN_ALIGN16 int aux[4];
+ pstore(aux, a);
+ return aux[0] * aux[1] * aux[2] * aux[3];
+}
+
+template<> EIGEN_STRONG_INLINE short int predux_mul<Packet8s>(const Packet8s& a)
+{
+ Packet8s pair, quad, octo;
+
+ pair = vec_mul(a, vec_sld(a, a, 8));
+ quad = vec_mul(pair, vec_sld(pair, pair, 4));
+ octo = vec_mul(quad, vec_sld(quad, quad, 2));
+
+ return pfirst(octo);
+}
+
+template<> EIGEN_STRONG_INLINE unsigned short int predux_mul<Packet8us>(const Packet8us& a)
+{
+ Packet8us pair, quad, octo;
+
+ pair = vec_mul(a, vec_sld(a, a, 8));
+ quad = vec_mul(pair, vec_sld(pair, pair, 4));
+ octo = vec_mul(quad, vec_sld(quad, quad, 2));
+
+ return pfirst(octo);
+}
+
+template<> EIGEN_STRONG_INLINE bfloat16 predux_mul<Packet8bf>(const Packet8bf& a)
+{
+ float redux_even = predux_mul<Packet4f>(Bf16ToF32Even(a));
+ float redux_odd = predux_mul<Packet4f>(Bf16ToF32Odd(a));
+ float f32_result = redux_even * redux_odd;
+ return bfloat16(f32_result);
+}
+
+
+template<> EIGEN_STRONG_INLINE signed char predux_mul<Packet16c>(const Packet16c& a)
+{
+ Packet16c pair, quad, octo, result;
+
+ pair = vec_mul(a, vec_sld(a, a, 8));
+ quad = vec_mul(pair, vec_sld(pair, pair, 4));
+ octo = vec_mul(quad, vec_sld(quad, quad, 2));
+ result = vec_mul(octo, vec_sld(octo, octo, 1));
+
+ return pfirst(result);
+}
+
+template<> EIGEN_STRONG_INLINE unsigned char predux_mul<Packet16uc>(const Packet16uc& a)
+{
+ Packet16uc pair, quad, octo, result;
+
+ pair = vec_mul(a, vec_sld(a, a, 8));
+ quad = vec_mul(pair, vec_sld(pair, pair, 4));
+ octo = vec_mul(quad, vec_sld(quad, quad, 2));
+ result = vec_mul(octo, vec_sld(octo, octo, 1));
+
+ return pfirst(result);
+}
+
+// min
+template<typename Packet> EIGEN_STRONG_INLINE
+__UNPACK_TYPE__(Packet) predux_min4(const Packet& a)
+{
+ Packet b, res;
+ b = vec_min(a, vec_sld(a, a, 8));
+ res = vec_min(b, vec_sld(b, b, 4));
+ return pfirst(res);
+}
+
+
+template<> EIGEN_STRONG_INLINE float predux_min<Packet4f>(const Packet4f& a)
+{
+ return predux_min4<Packet4f>(a);
+}
+
+template<> EIGEN_STRONG_INLINE int predux_min<Packet4i>(const Packet4i& a)
+{
+ return predux_min4<Packet4i>(a);
+}
+
+template<> EIGEN_STRONG_INLINE bfloat16 predux_min<Packet8bf>(const Packet8bf& a)
+{
+ float redux_even = predux_min<Packet4f>(Bf16ToF32Even(a));
+ float redux_odd = predux_min<Packet4f>(Bf16ToF32Odd(a));
+ float f32_result = (std::min)(redux_even, redux_odd);
+ return bfloat16(f32_result);
+}
+
+template<> EIGEN_STRONG_INLINE short int predux_min<Packet8s>(const Packet8s& a)
+{
+ Packet8s pair, quad, octo;
+
+ //pair = { Min(a0,a4), Min(a1,a5), Min(a2,a6), Min(a3,a7) }
+ pair = vec_min(a, vec_sld(a, a, 8));
+
+ //quad = { Min(a0, a4, a2, a6), Min(a1, a5, a3, a7) }
+ quad = vec_min(pair, vec_sld(pair, pair, 4));
+
+ //octo = { Min(a0, a4, a2, a6, a1, a5, a3, a7) }
+ octo = vec_min(quad, vec_sld(quad, quad, 2));
+ return pfirst(octo);
+}
+
+template<> EIGEN_STRONG_INLINE unsigned short int predux_min<Packet8us>(const Packet8us& a)
+{
+ Packet8us pair, quad, octo;
+
+ //pair = { Min(a0,a4), Min(a1,a5), Min(a2,a6), Min(a3,a7) }
+ pair = vec_min(a, vec_sld(a, a, 8));
+
+ //quad = { Min(a0, a4, a2, a6), Min(a1, a5, a3, a7) }
+ quad = vec_min(pair, vec_sld(pair, pair, 4));
+
+ //octo = { Min(a0, a4, a2, a6, a1, a5, a3, a7) }
+ octo = vec_min(quad, vec_sld(quad, quad, 2));
+ return pfirst(octo);
+}
+
+template<> EIGEN_STRONG_INLINE signed char predux_min<Packet16c>(const Packet16c& a)
+{
+ Packet16c pair, quad, octo, result;
+
+ pair = vec_min(a, vec_sld(a, a, 8));
+ quad = vec_min(pair, vec_sld(pair, pair, 4));
+ octo = vec_min(quad, vec_sld(quad, quad, 2));
+ result = vec_min(octo, vec_sld(octo, octo, 1));
+
+ return pfirst(result);
+}
+
+template<> EIGEN_STRONG_INLINE unsigned char predux_min<Packet16uc>(const Packet16uc& a)
+{
+ Packet16uc pair, quad, octo, result;
+
+ pair = vec_min(a, vec_sld(a, a, 8));
+ quad = vec_min(pair, vec_sld(pair, pair, 4));
+ octo = vec_min(quad, vec_sld(quad, quad, 2));
+ result = vec_min(octo, vec_sld(octo, octo, 1));
+
+ return pfirst(result);
+}
+// max
+template<typename Packet> EIGEN_STRONG_INLINE __UNPACK_TYPE__(Packet) predux_max4(const Packet& a)
+{
+ Packet b, res;
+ b = vec_max(a, vec_sld(a, a, 8));
+ res = vec_max(b, vec_sld(b, b, 4));
+ return pfirst(res);
+}
+
+template<> EIGEN_STRONG_INLINE float predux_max<Packet4f>(const Packet4f& a)
+{
+ return predux_max4<Packet4f>(a);
+}
+
+template<> EIGEN_STRONG_INLINE int predux_max<Packet4i>(const Packet4i& a)
+{
+ return predux_max4<Packet4i>(a);
+}
+
+template<> EIGEN_STRONG_INLINE bfloat16 predux_max<Packet8bf>(const Packet8bf& a)
+{
+ float redux_even = predux_max<Packet4f>(Bf16ToF32Even(a));
+ float redux_odd = predux_max<Packet4f>(Bf16ToF32Odd(a));
+ float f32_result = (std::max)(redux_even, redux_odd);
+ return bfloat16(f32_result);
+}
+
+template<> EIGEN_STRONG_INLINE short int predux_max<Packet8s>(const Packet8s& a)
+{
+ Packet8s pair, quad, octo;
+
+ //pair = { Max(a0,a4), Max(a1,a5), Max(a2,a6), Max(a3,a7) }
+ pair = vec_max(a, vec_sld(a, a, 8));
+
+ //quad = { Max(a0, a4, a2, a6), Max(a1, a5, a3, a7) }
+ quad = vec_max(pair, vec_sld(pair, pair, 4));
+
+ //octo = { Max(a0, a4, a2, a6, a1, a5, a3, a7) }
+ octo = vec_max(quad, vec_sld(quad, quad, 2));
+ return pfirst(octo);
+}
+
+template<> EIGEN_STRONG_INLINE unsigned short int predux_max<Packet8us>(const Packet8us& a)
+{
+ Packet8us pair, quad, octo;
+
+ //pair = { Max(a0,a4), Max(a1,a5), Max(a2,a6), Max(a3,a7) }
+ pair = vec_max(a, vec_sld(a, a, 8));
+
+ //quad = { Max(a0, a4, a2, a6), Max(a1, a5, a3, a7) }
+ quad = vec_max(pair, vec_sld(pair, pair, 4));
+
+ //octo = { Max(a0, a4, a2, a6, a1, a5, a3, a7) }
+ octo = vec_max(quad, vec_sld(quad, quad, 2));
+ return pfirst(octo);
+}
+
+template<> EIGEN_STRONG_INLINE signed char predux_max<Packet16c>(const Packet16c& a)
+{
+ Packet16c pair, quad, octo, result;
+
+ pair = vec_max(a, vec_sld(a, a, 8));
+ quad = vec_max(pair, vec_sld(pair, pair, 4));
+ octo = vec_max(quad, vec_sld(quad, quad, 2));
+ result = vec_max(octo, vec_sld(octo, octo, 1));
+
+ return pfirst(result);
+}
+
+template<> EIGEN_STRONG_INLINE unsigned char predux_max<Packet16uc>(const Packet16uc& a)
+{
+ Packet16uc pair, quad, octo, result;
+
+ pair = vec_max(a, vec_sld(a, a, 8));
+ quad = vec_max(pair, vec_sld(pair, pair, 4));
+ octo = vec_max(quad, vec_sld(quad, quad, 2));
+ result = vec_max(octo, vec_sld(octo, octo, 1));
+
+ return pfirst(result);
+}
+
+template<> EIGEN_STRONG_INLINE bool predux_any(const Packet4f& x)
+{
+ return vec_any_ne(x, pzero(x));
+}
+
+template <typename T> EIGEN_DEVICE_FUNC inline void
+ptranpose_common(PacketBlock<T,4>& kernel){
+ T t0, t1, t2, t3;
+ t0 = vec_mergeh(kernel.packet[0], kernel.packet[2]);
+ t1 = vec_mergel(kernel.packet[0], kernel.packet[2]);
+ t2 = vec_mergeh(kernel.packet[1], kernel.packet[3]);
+ t3 = vec_mergel(kernel.packet[1], kernel.packet[3]);
+ kernel.packet[0] = vec_mergeh(t0, t2);
+ kernel.packet[1] = vec_mergel(t0, t2);
+ kernel.packet[2] = vec_mergeh(t1, t3);
+ kernel.packet[3] = vec_mergel(t1, t3);
+}
+
+EIGEN_DEVICE_FUNC inline void
+ptranspose(PacketBlock<Packet4f,4>& kernel) {
+ ptranpose_common<Packet4f>(kernel);
+}
+
+EIGEN_DEVICE_FUNC inline void
+ptranspose(PacketBlock<Packet4i,4>& kernel) {
+ ptranpose_common<Packet4i>(kernel);
+}
+
+EIGEN_DEVICE_FUNC inline void
+ptranspose(PacketBlock<Packet8s,4>& kernel) {
+ Packet8s t0, t1, t2, t3;
+ t0 = vec_mergeh(kernel.packet[0], kernel.packet[2]);
+ t1 = vec_mergel(kernel.packet[0], kernel.packet[2]);
+ t2 = vec_mergeh(kernel.packet[1], kernel.packet[3]);
+ t3 = vec_mergel(kernel.packet[1], kernel.packet[3]);
+ kernel.packet[0] = vec_mergeh(t0, t2);
+ kernel.packet[1] = vec_mergel(t0, t2);
+ kernel.packet[2] = vec_mergeh(t1, t3);
+ kernel.packet[3] = vec_mergel(t1, t3);
+}
+
+EIGEN_DEVICE_FUNC inline void
+ptranspose(PacketBlock<Packet8us,4>& kernel) {
+ Packet8us t0, t1, t2, t3;
+ t0 = vec_mergeh(kernel.packet[0], kernel.packet[2]);
+ t1 = vec_mergel(kernel.packet[0], kernel.packet[2]);
+ t2 = vec_mergeh(kernel.packet[1], kernel.packet[3]);
+ t3 = vec_mergel(kernel.packet[1], kernel.packet[3]);
+ kernel.packet[0] = vec_mergeh(t0, t2);
+ kernel.packet[1] = vec_mergel(t0, t2);
+ kernel.packet[2] = vec_mergeh(t1, t3);
+ kernel.packet[3] = vec_mergel(t1, t3);
+}
+
+
+EIGEN_DEVICE_FUNC inline void
+ptranspose(PacketBlock<Packet8bf,4>& kernel) {
+ Packet8us t0, t1, t2, t3;
+
+ t0 = vec_mergeh(kernel.packet[0].m_val, kernel.packet[2].m_val);
+ t1 = vec_mergel(kernel.packet[0].m_val, kernel.packet[2].m_val);
+ t2 = vec_mergeh(kernel.packet[1].m_val, kernel.packet[3].m_val);
+ t3 = vec_mergel(kernel.packet[1].m_val, kernel.packet[3].m_val);
+ kernel.packet[0] = vec_mergeh(t0, t2);
+ kernel.packet[1] = vec_mergel(t0, t2);
+ kernel.packet[2] = vec_mergeh(t1, t3);
+ kernel.packet[3] = vec_mergel(t1, t3);
+}
+
+EIGEN_DEVICE_FUNC inline void
+ptranspose(PacketBlock<Packet16c,4>& kernel) {
+ Packet16c t0, t1, t2, t3;
+ t0 = vec_mergeh(kernel.packet[0], kernel.packet[2]);
+ t1 = vec_mergel(kernel.packet[0], kernel.packet[2]);
+ t2 = vec_mergeh(kernel.packet[1], kernel.packet[3]);
+ t3 = vec_mergel(kernel.packet[1], kernel.packet[3]);
+ kernel.packet[0] = vec_mergeh(t0, t2);
+ kernel.packet[1] = vec_mergel(t0, t2);
+ kernel.packet[2] = vec_mergeh(t1, t3);
+ kernel.packet[3] = vec_mergel(t1, t3);
+}
+
+
+EIGEN_DEVICE_FUNC inline void
+ptranspose(PacketBlock<Packet16uc,4>& kernel) {
+ Packet16uc t0, t1, t2, t3;
+ t0 = vec_mergeh(kernel.packet[0], kernel.packet[2]);
+ t1 = vec_mergel(kernel.packet[0], kernel.packet[2]);
+ t2 = vec_mergeh(kernel.packet[1], kernel.packet[3]);
+ t3 = vec_mergel(kernel.packet[1], kernel.packet[3]);
+ kernel.packet[0] = vec_mergeh(t0, t2);
+ kernel.packet[1] = vec_mergel(t0, t2);
+ kernel.packet[2] = vec_mergeh(t1, t3);
+ kernel.packet[3] = vec_mergel(t1, t3);
+}
+
+EIGEN_DEVICE_FUNC inline void
+ptranspose(PacketBlock<Packet8s,8>& kernel) {
+ Packet8s v[8], sum[8];
+
+ v[0] = vec_mergeh(kernel.packet[0], kernel.packet[4]);
+ v[1] = vec_mergel(kernel.packet[0], kernel.packet[4]);
+ v[2] = vec_mergeh(kernel.packet[1], kernel.packet[5]);
+ v[3] = vec_mergel(kernel.packet[1], kernel.packet[5]);
+ v[4] = vec_mergeh(kernel.packet[2], kernel.packet[6]);
+ v[5] = vec_mergel(kernel.packet[2], kernel.packet[6]);
+ v[6] = vec_mergeh(kernel.packet[3], kernel.packet[7]);
+ v[7] = vec_mergel(kernel.packet[3], kernel.packet[7]);
+ sum[0] = vec_mergeh(v[0], v[4]);
+ sum[1] = vec_mergel(v[0], v[4]);
+ sum[2] = vec_mergeh(v[1], v[5]);
+ sum[3] = vec_mergel(v[1], v[5]);
+ sum[4] = vec_mergeh(v[2], v[6]);
+ sum[5] = vec_mergel(v[2], v[6]);
+ sum[6] = vec_mergeh(v[3], v[7]);
+ sum[7] = vec_mergel(v[3], v[7]);
+
+ kernel.packet[0] = vec_mergeh(sum[0], sum[4]);
+ kernel.packet[1] = vec_mergel(sum[0], sum[4]);
+ kernel.packet[2] = vec_mergeh(sum[1], sum[5]);
+ kernel.packet[3] = vec_mergel(sum[1], sum[5]);
+ kernel.packet[4] = vec_mergeh(sum[2], sum[6]);
+ kernel.packet[5] = vec_mergel(sum[2], sum[6]);
+ kernel.packet[6] = vec_mergeh(sum[3], sum[7]);
+ kernel.packet[7] = vec_mergel(sum[3], sum[7]);
+}
+
+EIGEN_DEVICE_FUNC inline void
+ptranspose(PacketBlock<Packet8us,8>& kernel) {
+ Packet8us v[8], sum[8];
+
+ v[0] = vec_mergeh(kernel.packet[0], kernel.packet[4]);
+ v[1] = vec_mergel(kernel.packet[0], kernel.packet[4]);
+ v[2] = vec_mergeh(kernel.packet[1], kernel.packet[5]);
+ v[3] = vec_mergel(kernel.packet[1], kernel.packet[5]);
+ v[4] = vec_mergeh(kernel.packet[2], kernel.packet[6]);
+ v[5] = vec_mergel(kernel.packet[2], kernel.packet[6]);
+ v[6] = vec_mergeh(kernel.packet[3], kernel.packet[7]);
+ v[7] = vec_mergel(kernel.packet[3], kernel.packet[7]);
+ sum[0] = vec_mergeh(v[0], v[4]);
+ sum[1] = vec_mergel(v[0], v[4]);
+ sum[2] = vec_mergeh(v[1], v[5]);
+ sum[3] = vec_mergel(v[1], v[5]);
+ sum[4] = vec_mergeh(v[2], v[6]);
+ sum[5] = vec_mergel(v[2], v[6]);
+ sum[6] = vec_mergeh(v[3], v[7]);
+ sum[7] = vec_mergel(v[3], v[7]);
+
+ kernel.packet[0] = vec_mergeh(sum[0], sum[4]);
+ kernel.packet[1] = vec_mergel(sum[0], sum[4]);
+ kernel.packet[2] = vec_mergeh(sum[1], sum[5]);
+ kernel.packet[3] = vec_mergel(sum[1], sum[5]);
+ kernel.packet[4] = vec_mergeh(sum[2], sum[6]);
+ kernel.packet[5] = vec_mergel(sum[2], sum[6]);
+ kernel.packet[6] = vec_mergeh(sum[3], sum[7]);
+ kernel.packet[7] = vec_mergel(sum[3], sum[7]);
+}
+
+EIGEN_DEVICE_FUNC inline void
+ptranspose(PacketBlock<Packet8bf,8>& kernel) {
+ Packet8bf v[8], sum[8];
+
+ v[0] = vec_mergeh(kernel.packet[0].m_val, kernel.packet[4].m_val);
+ v[1] = vec_mergel(kernel.packet[0].m_val, kernel.packet[4].m_val);
+ v[2] = vec_mergeh(kernel.packet[1].m_val, kernel.packet[5].m_val);
+ v[3] = vec_mergel(kernel.packet[1].m_val, kernel.packet[5].m_val);
+ v[4] = vec_mergeh(kernel.packet[2].m_val, kernel.packet[6].m_val);
+ v[5] = vec_mergel(kernel.packet[2].m_val, kernel.packet[6].m_val);
+ v[6] = vec_mergeh(kernel.packet[3].m_val, kernel.packet[7].m_val);
+ v[7] = vec_mergel(kernel.packet[3].m_val, kernel.packet[7].m_val);
+ sum[0] = vec_mergeh(v[0].m_val, v[4].m_val);
+ sum[1] = vec_mergel(v[0].m_val, v[4].m_val);
+ sum[2] = vec_mergeh(v[1].m_val, v[5].m_val);
+ sum[3] = vec_mergel(v[1].m_val, v[5].m_val);
+ sum[4] = vec_mergeh(v[2].m_val, v[6].m_val);
+ sum[5] = vec_mergel(v[2].m_val, v[6].m_val);
+ sum[6] = vec_mergeh(v[3].m_val, v[7].m_val);
+ sum[7] = vec_mergel(v[3].m_val, v[7].m_val);
+
+ kernel.packet[0] = vec_mergeh(sum[0].m_val, sum[4].m_val);
+ kernel.packet[1] = vec_mergel(sum[0].m_val, sum[4].m_val);
+ kernel.packet[2] = vec_mergeh(sum[1].m_val, sum[5].m_val);
+ kernel.packet[3] = vec_mergel(sum[1].m_val, sum[5].m_val);
+ kernel.packet[4] = vec_mergeh(sum[2].m_val, sum[6].m_val);
+ kernel.packet[5] = vec_mergel(sum[2].m_val, sum[6].m_val);
+ kernel.packet[6] = vec_mergeh(sum[3].m_val, sum[7].m_val);
+ kernel.packet[7] = vec_mergel(sum[3].m_val, sum[7].m_val);
+}
+
+EIGEN_DEVICE_FUNC inline void
+ptranspose(PacketBlock<Packet16c,16>& kernel) {
+ Packet16c step1[16], step2[16], step3[16];
+
+ step1[0] = vec_mergeh(kernel.packet[0], kernel.packet[8]);
+ step1[1] = vec_mergel(kernel.packet[0], kernel.packet[8]);
+ step1[2] = vec_mergeh(kernel.packet[1], kernel.packet[9]);
+ step1[3] = vec_mergel(kernel.packet[1], kernel.packet[9]);
+ step1[4] = vec_mergeh(kernel.packet[2], kernel.packet[10]);
+ step1[5] = vec_mergel(kernel.packet[2], kernel.packet[10]);
+ step1[6] = vec_mergeh(kernel.packet[3], kernel.packet[11]);
+ step1[7] = vec_mergel(kernel.packet[3], kernel.packet[11]);
+ step1[8] = vec_mergeh(kernel.packet[4], kernel.packet[12]);
+ step1[9] = vec_mergel(kernel.packet[4], kernel.packet[12]);
+ step1[10] = vec_mergeh(kernel.packet[5], kernel.packet[13]);
+ step1[11] = vec_mergel(kernel.packet[5], kernel.packet[13]);
+ step1[12] = vec_mergeh(kernel.packet[6], kernel.packet[14]);
+ step1[13] = vec_mergel(kernel.packet[6], kernel.packet[14]);
+ step1[14] = vec_mergeh(kernel.packet[7], kernel.packet[15]);
+ step1[15] = vec_mergel(kernel.packet[7], kernel.packet[15]);
+
+ step2[0] = vec_mergeh(step1[0], step1[8]);
+ step2[1] = vec_mergel(step1[0], step1[8]);
+ step2[2] = vec_mergeh(step1[1], step1[9]);
+ step2[3] = vec_mergel(step1[1], step1[9]);
+ step2[4] = vec_mergeh(step1[2], step1[10]);
+ step2[5] = vec_mergel(step1[2], step1[10]);
+ step2[6] = vec_mergeh(step1[3], step1[11]);
+ step2[7] = vec_mergel(step1[3], step1[11]);
+ step2[8] = vec_mergeh(step1[4], step1[12]);
+ step2[9] = vec_mergel(step1[4], step1[12]);
+ step2[10] = vec_mergeh(step1[5], step1[13]);
+ step2[11] = vec_mergel(step1[5], step1[13]);
+ step2[12] = vec_mergeh(step1[6], step1[14]);
+ step2[13] = vec_mergel(step1[6], step1[14]);
+ step2[14] = vec_mergeh(step1[7], step1[15]);
+ step2[15] = vec_mergel(step1[7], step1[15]);
+
+ step3[0] = vec_mergeh(step2[0], step2[8]);
+ step3[1] = vec_mergel(step2[0], step2[8]);
+ step3[2] = vec_mergeh(step2[1], step2[9]);
+ step3[3] = vec_mergel(step2[1], step2[9]);
+ step3[4] = vec_mergeh(step2[2], step2[10]);
+ step3[5] = vec_mergel(step2[2], step2[10]);
+ step3[6] = vec_mergeh(step2[3], step2[11]);
+ step3[7] = vec_mergel(step2[3], step2[11]);
+ step3[8] = vec_mergeh(step2[4], step2[12]);
+ step3[9] = vec_mergel(step2[4], step2[12]);
+ step3[10] = vec_mergeh(step2[5], step2[13]);
+ step3[11] = vec_mergel(step2[5], step2[13]);
+ step3[12] = vec_mergeh(step2[6], step2[14]);
+ step3[13] = vec_mergel(step2[6], step2[14]);
+ step3[14] = vec_mergeh(step2[7], step2[15]);
+ step3[15] = vec_mergel(step2[7], step2[15]);
+
+ kernel.packet[0] = vec_mergeh(step3[0], step3[8]);
+ kernel.packet[1] = vec_mergel(step3[0], step3[8]);
+ kernel.packet[2] = vec_mergeh(step3[1], step3[9]);
+ kernel.packet[3] = vec_mergel(step3[1], step3[9]);
+ kernel.packet[4] = vec_mergeh(step3[2], step3[10]);
+ kernel.packet[5] = vec_mergel(step3[2], step3[10]);
+ kernel.packet[6] = vec_mergeh(step3[3], step3[11]);
+ kernel.packet[7] = vec_mergel(step3[3], step3[11]);
+ kernel.packet[8] = vec_mergeh(step3[4], step3[12]);
+ kernel.packet[9] = vec_mergel(step3[4], step3[12]);
+ kernel.packet[10] = vec_mergeh(step3[5], step3[13]);
+ kernel.packet[11] = vec_mergel(step3[5], step3[13]);
+ kernel.packet[12] = vec_mergeh(step3[6], step3[14]);
+ kernel.packet[13] = vec_mergel(step3[6], step3[14]);
+ kernel.packet[14] = vec_mergeh(step3[7], step3[15]);
+ kernel.packet[15] = vec_mergel(step3[7], step3[15]);
+}
+
+EIGEN_DEVICE_FUNC inline void
+ptranspose(PacketBlock<Packet16uc,16>& kernel) {
+ Packet16uc step1[16], step2[16], step3[16];
+
+ step1[0] = vec_mergeh(kernel.packet[0], kernel.packet[8]);
+ step1[1] = vec_mergel(kernel.packet[0], kernel.packet[8]);
+ step1[2] = vec_mergeh(kernel.packet[1], kernel.packet[9]);
+ step1[3] = vec_mergel(kernel.packet[1], kernel.packet[9]);
+ step1[4] = vec_mergeh(kernel.packet[2], kernel.packet[10]);
+ step1[5] = vec_mergel(kernel.packet[2], kernel.packet[10]);
+ step1[6] = vec_mergeh(kernel.packet[3], kernel.packet[11]);
+ step1[7] = vec_mergel(kernel.packet[3], kernel.packet[11]);
+ step1[8] = vec_mergeh(kernel.packet[4], kernel.packet[12]);
+ step1[9] = vec_mergel(kernel.packet[4], kernel.packet[12]);
+ step1[10] = vec_mergeh(kernel.packet[5], kernel.packet[13]);
+ step1[11] = vec_mergel(kernel.packet[5], kernel.packet[13]);
+ step1[12] = vec_mergeh(kernel.packet[6], kernel.packet[14]);
+ step1[13] = vec_mergel(kernel.packet[6], kernel.packet[14]);
+ step1[14] = vec_mergeh(kernel.packet[7], kernel.packet[15]);
+ step1[15] = vec_mergel(kernel.packet[7], kernel.packet[15]);
+
+ step2[0] = vec_mergeh(step1[0], step1[8]);
+ step2[1] = vec_mergel(step1[0], step1[8]);
+ step2[2] = vec_mergeh(step1[1], step1[9]);
+ step2[3] = vec_mergel(step1[1], step1[9]);
+ step2[4] = vec_mergeh(step1[2], step1[10]);
+ step2[5] = vec_mergel(step1[2], step1[10]);
+ step2[6] = vec_mergeh(step1[3], step1[11]);
+ step2[7] = vec_mergel(step1[3], step1[11]);
+ step2[8] = vec_mergeh(step1[4], step1[12]);
+ step2[9] = vec_mergel(step1[4], step1[12]);
+ step2[10] = vec_mergeh(step1[5], step1[13]);
+ step2[11] = vec_mergel(step1[5], step1[13]);
+ step2[12] = vec_mergeh(step1[6], step1[14]);
+ step2[13] = vec_mergel(step1[6], step1[14]);
+ step2[14] = vec_mergeh(step1[7], step1[15]);
+ step2[15] = vec_mergel(step1[7], step1[15]);
+
+ step3[0] = vec_mergeh(step2[0], step2[8]);
+ step3[1] = vec_mergel(step2[0], step2[8]);
+ step3[2] = vec_mergeh(step2[1], step2[9]);
+ step3[3] = vec_mergel(step2[1], step2[9]);
+ step3[4] = vec_mergeh(step2[2], step2[10]);
+ step3[5] = vec_mergel(step2[2], step2[10]);
+ step3[6] = vec_mergeh(step2[3], step2[11]);
+ step3[7] = vec_mergel(step2[3], step2[11]);
+ step3[8] = vec_mergeh(step2[4], step2[12]);
+ step3[9] = vec_mergel(step2[4], step2[12]);
+ step3[10] = vec_mergeh(step2[5], step2[13]);
+ step3[11] = vec_mergel(step2[5], step2[13]);
+ step3[12] = vec_mergeh(step2[6], step2[14]);
+ step3[13] = vec_mergel(step2[6], step2[14]);
+ step3[14] = vec_mergeh(step2[7], step2[15]);
+ step3[15] = vec_mergel(step2[7], step2[15]);
+
+ kernel.packet[0] = vec_mergeh(step3[0], step3[8]);
+ kernel.packet[1] = vec_mergel(step3[0], step3[8]);
+ kernel.packet[2] = vec_mergeh(step3[1], step3[9]);
+ kernel.packet[3] = vec_mergel(step3[1], step3[9]);
+ kernel.packet[4] = vec_mergeh(step3[2], step3[10]);
+ kernel.packet[5] = vec_mergel(step3[2], step3[10]);
+ kernel.packet[6] = vec_mergeh(step3[3], step3[11]);
+ kernel.packet[7] = vec_mergel(step3[3], step3[11]);
+ kernel.packet[8] = vec_mergeh(step3[4], step3[12]);
+ kernel.packet[9] = vec_mergel(step3[4], step3[12]);
+ kernel.packet[10] = vec_mergeh(step3[5], step3[13]);
+ kernel.packet[11] = vec_mergel(step3[5], step3[13]);
+ kernel.packet[12] = vec_mergeh(step3[6], step3[14]);
+ kernel.packet[13] = vec_mergel(step3[6], step3[14]);
+ kernel.packet[14] = vec_mergeh(step3[7], step3[15]);
+ kernel.packet[15] = vec_mergel(step3[7], step3[15]);
+}
+
+template<typename Packet> EIGEN_STRONG_INLINE
+Packet pblend4(const Selector<4>& ifPacket, const Packet& thenPacket, const Packet& elsePacket) {
+ Packet4ui select = { ifPacket.select[0], ifPacket.select[1], ifPacket.select[2], ifPacket.select[3] };
+#ifdef __POWER8_VECTOR__
+ Packet4ui mask = reinterpret_cast<Packet4ui>(vec_neg(reinterpret_cast<Packet4i>(select)));
+#else
+ Packet4ui mask = reinterpret_cast<Packet4ui>(vec_cmpeq(reinterpret_cast<Packet4ui>(select), reinterpret_cast<Packet4ui>(p4i_ONE)));
+#endif
+ return vec_sel(elsePacket, thenPacket, mask);
+}
+
+template<> EIGEN_STRONG_INLINE Packet4i pblend(const Selector<4>& ifPacket, const Packet4i& thenPacket, const Packet4i& elsePacket) {
+ return pblend4<Packet4i>(ifPacket, thenPacket, elsePacket);
+}
+
+template<> EIGEN_STRONG_INLINE Packet4f pblend(const Selector<4>& ifPacket, const Packet4f& thenPacket, const Packet4f& elsePacket) {
+ return pblend4<Packet4f>(ifPacket, thenPacket, elsePacket);
+}
+
+template<> EIGEN_STRONG_INLINE Packet8s pblend(const Selector<8>& ifPacket, const Packet8s& thenPacket, const Packet8s& elsePacket) {
+ Packet8us select = { ifPacket.select[0], ifPacket.select[1], ifPacket.select[2], ifPacket.select[3],
+ ifPacket.select[4], ifPacket.select[5], ifPacket.select[6], ifPacket.select[7] };
+#ifdef __POWER8_VECTOR__
+ Packet8us mask = reinterpret_cast<Packet8us>(vec_neg(reinterpret_cast<Packet8s>(select)));
+#else
+ Packet8us mask = reinterpret_cast<Packet8us>(vec_cmpeq(select, p8us_ONE));
+#endif
+ Packet8s result = vec_sel(elsePacket, thenPacket, mask);
+ return result;
+}
+
+template<> EIGEN_STRONG_INLINE Packet8us pblend(const Selector<8>& ifPacket, const Packet8us& thenPacket, const Packet8us& elsePacket) {
+ Packet8us select = { ifPacket.select[0], ifPacket.select[1], ifPacket.select[2], ifPacket.select[3],
+ ifPacket.select[4], ifPacket.select[5], ifPacket.select[6], ifPacket.select[7] };
+#ifdef __POWER8_VECTOR__
+ Packet8us mask = reinterpret_cast<Packet8us>(vec_neg(reinterpret_cast<Packet8s>(select)));
+#else
+ Packet8us mask = reinterpret_cast<Packet8us>(vec_cmpeq(reinterpret_cast<Packet8us>(select), p8us_ONE));
+#endif
+ return vec_sel(elsePacket, thenPacket, mask);
+}
+
+template<> EIGEN_STRONG_INLINE Packet8bf pblend(const Selector<8>& ifPacket, const Packet8bf& thenPacket, const Packet8bf& elsePacket) {
+ return pblend<Packet8us>(ifPacket, thenPacket, elsePacket);
+}
+
+template<> EIGEN_STRONG_INLINE Packet16c pblend(const Selector<16>& ifPacket, const Packet16c& thenPacket, const Packet16c& elsePacket) {
+ Packet16uc select = { ifPacket.select[0], ifPacket.select[1], ifPacket.select[2], ifPacket.select[3],
+ ifPacket.select[4], ifPacket.select[5], ifPacket.select[6], ifPacket.select[7],
+ ifPacket.select[8], ifPacket.select[9], ifPacket.select[10], ifPacket.select[11],
+ ifPacket.select[12], ifPacket.select[13], ifPacket.select[14], ifPacket.select[15] };
+
+#ifdef __POWER8_VECTOR__
+ Packet16uc mask = reinterpret_cast<Packet16uc>(vec_neg(reinterpret_cast<Packet16c>(select)));
+#else
+ Packet16uc mask = reinterpret_cast<Packet16uc>(vec_cmpeq(reinterpret_cast<Packet16uc>(select), p16uc_ONE));
+#endif
+ return vec_sel(elsePacket, thenPacket, mask);
+}
+
+template<> EIGEN_STRONG_INLINE Packet16uc pblend(const Selector<16>& ifPacket, const Packet16uc& thenPacket, const Packet16uc& elsePacket) {
+ Packet16uc select = { ifPacket.select[0], ifPacket.select[1], ifPacket.select[2], ifPacket.select[3],
+ ifPacket.select[4], ifPacket.select[5], ifPacket.select[6], ifPacket.select[7],
+ ifPacket.select[8], ifPacket.select[9], ifPacket.select[10], ifPacket.select[11],
+ ifPacket.select[12], ifPacket.select[13], ifPacket.select[14], ifPacket.select[15] };
+
+#ifdef __POWER8_VECTOR__
+ Packet16uc mask = reinterpret_cast<Packet16uc>(vec_neg(reinterpret_cast<Packet16c>(select)));
+#else
+ Packet16uc mask = reinterpret_cast<Packet16uc>(vec_cmpeq(reinterpret_cast<Packet16uc>(select), p16uc_ONE));
+#endif
+ return vec_sel(elsePacket, thenPacket, mask);
+}
+
+template <>
+struct type_casting_traits<float, int> {
+ enum {
+ VectorizedCast = 1,
+ SrcCoeffRatio = 1,
+ TgtCoeffRatio = 1
+ };
+};
+
+template <>
+struct type_casting_traits<int, float> {
+ enum {
+ VectorizedCast = 1,
+ SrcCoeffRatio = 1,
+ TgtCoeffRatio = 1
+ };
+};
+
+template <>
+struct type_casting_traits<bfloat16, unsigned short int> {
+ enum {
+ VectorizedCast = 1,
+ SrcCoeffRatio = 1,
+ TgtCoeffRatio = 1
+ };
+};
+
+template <>
+struct type_casting_traits<unsigned short int, bfloat16> {
+ enum {
+ VectorizedCast = 1,
+ SrcCoeffRatio = 1,
+ TgtCoeffRatio = 1
+ };
+};
+
+template<> EIGEN_STRONG_INLINE Packet4i pcast<Packet4f, Packet4i>(const Packet4f& a) {
+ return vec_cts(a,0);
+}
+
+template<> EIGEN_STRONG_INLINE Packet4ui pcast<Packet4f, Packet4ui>(const Packet4f& a) {
+ return vec_ctu(a,0);
+}
+
+template<> EIGEN_STRONG_INLINE Packet4f pcast<Packet4i, Packet4f>(const Packet4i& a) {
+ return vec_ctf(a,0);
+}
+
+template<> EIGEN_STRONG_INLINE Packet4f pcast<Packet4ui, Packet4f>(const Packet4ui& a) {
+ return vec_ctf(a,0);
+}
+
+template<> EIGEN_STRONG_INLINE Packet8us pcast<Packet8bf, Packet8us>(const Packet8bf& a) {
+ Packet4f float_even = Bf16ToF32Even(a);
+ Packet4f float_odd = Bf16ToF32Odd(a);
+ Packet4ui int_even = pcast<Packet4f, Packet4ui>(float_even);
+ Packet4ui int_odd = pcast<Packet4f, Packet4ui>(float_odd);
+ const EIGEN_DECLARE_CONST_FAST_Packet4ui(low_mask, 0x0000FFFF);
+ Packet4ui low_even = pand<Packet4ui>(int_even, p4ui_low_mask);
+ Packet4ui low_odd = pand<Packet4ui>(int_odd, p4ui_low_mask);
+
+ //Check values that are bigger than USHRT_MAX (0xFFFF)
+ Packet4bi overflow_selector;
+ if(vec_any_gt(int_even, p4ui_low_mask)){
+ overflow_selector = vec_cmpgt(int_even, p4ui_low_mask);
+ low_even = vec_sel(low_even, p4ui_low_mask, overflow_selector);
+ }
+ if(vec_any_gt(int_odd, p4ui_low_mask)){
+ overflow_selector = vec_cmpgt(int_odd, p4ui_low_mask);
+ low_odd = vec_sel(low_even, p4ui_low_mask, overflow_selector);
+ }
+
+ low_odd = plogical_shift_left<16>(low_odd);
+
+ Packet4ui int_final = por<Packet4ui>(low_even, low_odd);
+ return reinterpret_cast<Packet8us>(int_final);
+}
+
+template<> EIGEN_STRONG_INLINE Packet8bf pcast<Packet8us, Packet8bf>(const Packet8us& a) {
+ //short -> int -> float -> bfloat16
+ const EIGEN_DECLARE_CONST_FAST_Packet4ui(low_mask, 0x0000FFFF);
+ Packet4ui int_cast = reinterpret_cast<Packet4ui>(a);
+ Packet4ui int_even = pand<Packet4ui>(int_cast, p4ui_low_mask);
+ Packet4ui int_odd = plogical_shift_right<16>(int_cast);
+ Packet4f float_even = pcast<Packet4ui, Packet4f>(int_even);
+ Packet4f float_odd = pcast<Packet4ui, Packet4f>(int_odd);
+ return F32ToBf16(float_even, float_odd);
+}
+
+
+template<> EIGEN_STRONG_INLINE Packet4i preinterpret<Packet4i,Packet4f>(const Packet4f& a) {
+ return reinterpret_cast<Packet4i>(a);
+}
+
+template<> EIGEN_STRONG_INLINE Packet4f preinterpret<Packet4f,Packet4i>(const Packet4i& a) {
+ return reinterpret_cast<Packet4f>(a);
+}
+
+
+
+//---------- double ----------
+#ifdef __VSX__
+typedef __vector double Packet2d;
+typedef __vector unsigned long long Packet2ul;
+typedef __vector long long Packet2l;
+#if EIGEN_COMP_CLANG
+typedef Packet2ul Packet2bl;
+#else
+typedef __vector __bool long Packet2bl;
+#endif
+
+static Packet2l p2l_ONE = { 1, 1 };
+static Packet2l p2l_ZERO = reinterpret_cast<Packet2l>(p4i_ZERO);
+static Packet2ul p2ul_SIGN = { 0x8000000000000000ull, 0x8000000000000000ull };
+static Packet2ul p2ul_PREV0DOT5 = { 0x3FDFFFFFFFFFFFFFull, 0x3FDFFFFFFFFFFFFFull };
+static Packet2d p2d_ONE = { 1.0, 1.0 };
+static Packet2d p2d_ZERO = reinterpret_cast<Packet2d>(p4f_ZERO);
+static Packet2d p2d_MZERO = { numext::bit_cast<double>(0x8000000000000000ull),
+ numext::bit_cast<double>(0x8000000000000000ull) };
+
+#ifdef _BIG_ENDIAN
+static Packet2d p2d_COUNTDOWN = reinterpret_cast<Packet2d>(vec_sld(reinterpret_cast<Packet4f>(p2d_ZERO), reinterpret_cast<Packet4f>(p2d_ONE), 8));
+#else
+static Packet2d p2d_COUNTDOWN = reinterpret_cast<Packet2d>(vec_sld(reinterpret_cast<Packet4f>(p2d_ONE), reinterpret_cast<Packet4f>(p2d_ZERO), 8));
+#endif
+
+template<int index> Packet2d vec_splat_dbl(Packet2d& a)
+{
+ return vec_splat(a, index);
+}
+
+template<> struct packet_traits<double> : default_packet_traits
+{
+ typedef Packet2d type;
+ typedef Packet2d half;
+ enum {
+ Vectorizable = 1,
+ AlignedOnScalar = 1,
+ size=2,
+ HasHalfPacket = 1,
+
+ HasAdd = 1,
+ HasSub = 1,
+ HasMul = 1,
+ HasDiv = 1,
+ HasMin = 1,
+ HasMax = 1,
+ HasAbs = 1,
+ HasSin = 0,
+ HasCos = 0,
+ HasATan = 1,
+ HasLog = 0,
+ HasExp = 1,
+ HasSqrt = 1,
+ HasRsqrt = 1,
+ HasRound = 1,
+ HasFloor = 1,
+ HasCeil = 1,
+ HasRint = 1,
+ HasNegate = 1,
+ HasBlend = 1
+ };
+};
+
+template<> struct unpacket_traits<Packet2d> { typedef double type; enum {size=2, alignment=Aligned16, vectorizable=true, masked_load_available=false, masked_store_available=false}; typedef Packet2d half; };
+
+inline std::ostream & operator <<(std::ostream & s, const Packet2l & v)
+{
+ union {
+ Packet2l v;
+ int64_t n[2];
+ } vt;
+ vt.v = v;
+ s << vt.n[0] << ", " << vt.n[1];
+ return s;
+}
+
+inline std::ostream & operator <<(std::ostream & s, const Packet2d & v)
+{
+ union {
+ Packet2d v;
+ double n[2];
+ } vt;
+ vt.v = v;
+ s << vt.n[0] << ", " << vt.n[1];
+ return s;
+}
+
+// Need to define them first or we get specialization after instantiation errors
+template<> EIGEN_STRONG_INLINE Packet2d pload<Packet2d>(const double* from)
+{
+ EIGEN_DEBUG_ALIGNED_LOAD
+ return vec_xl(0, const_cast<double *>(from)); // cast needed by Clang
+}
+
+template<> EIGEN_ALWAYS_INLINE Packet2d pload_partial<Packet2d>(const double* from, const Index n, const Index offset)
+{
+ return pload_partial_common<Packet2d>(from, n, offset);
+}
+
+template<> EIGEN_STRONG_INLINE void pstore<double>(double* to, const Packet2d& from)
+{
+ EIGEN_DEBUG_ALIGNED_STORE
+ vec_xst(from, 0, to);
+}
+
+template<> EIGEN_ALWAYS_INLINE void pstore_partial<double>(double* to, const Packet2d& from, const Index n, const Index offset)
+{
+ pstore_partial_common<Packet2d>(to, from, n, offset);
+}
+
+template<> EIGEN_STRONG_INLINE Packet2d pset1<Packet2d>(const double& from) {
+ Packet2d v = {from, from};
+ return v;
+}
+
+template<> EIGEN_STRONG_INLINE Packet2d pset1frombits<Packet2d>(unsigned long from) {
+ Packet2l v = {static_cast<long long>(from), static_cast<long long>(from)};
+ return reinterpret_cast<Packet2d>(v);
+}
+
+template<> EIGEN_STRONG_INLINE void
+pbroadcast4<Packet2d>(const double *a,
+ Packet2d& a0, Packet2d& a1, Packet2d& a2, Packet2d& a3)
+{
+ //This way is faster than vec_splat (at least for doubles in Power 9)
+ a0 = pset1<Packet2d>(a[0]);
+ a1 = pset1<Packet2d>(a[1]);
+ a2 = pset1<Packet2d>(a[2]);
+ a3 = pset1<Packet2d>(a[3]);
+}
+
+template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE Packet2d pgather<double, Packet2d>(const double* from, Index stride)
+{
+ return pgather_common<Packet2d>(from, stride);
+}
+template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE Packet2d pgather_partial<double, Packet2d>(const double* from, Index stride, const Index n)
+{
+ return pgather_common<Packet2d>(from, stride, n);
+}
+template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE void pscatter<double, Packet2d>(double* to, const Packet2d& from, Index stride)
+{
+ pscatter_common<Packet2d>(to, from, stride);
+}
+template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE void pscatter_partial<double, Packet2d>(double* to, const Packet2d& from, Index stride, const Index n)
+{
+ pscatter_common<Packet2d>(to, from, stride, n);
+}
+
+template<> EIGEN_STRONG_INLINE Packet2d plset<Packet2d>(const double& a) { return pset1<Packet2d>(a) + p2d_COUNTDOWN; }
+
+template<> EIGEN_STRONG_INLINE Packet2d padd<Packet2d>(const Packet2d& a, const Packet2d& b) { return a + b; }
+
+template<> EIGEN_STRONG_INLINE Packet2d psub<Packet2d>(const Packet2d& a, const Packet2d& b) { return a - b; }
+
+template<> EIGEN_STRONG_INLINE Packet2d pnegate(const Packet2d& a)
+{
+#ifdef __POWER8_VECTOR__
+ return vec_neg(a);
+#else
+ return p2d_ZERO - a;
+#endif
+}
+
+template<> EIGEN_STRONG_INLINE Packet2d pconj(const Packet2d& a) { return a; }
+
+template<> EIGEN_STRONG_INLINE Packet2d pmul<Packet2d>(const Packet2d& a, const Packet2d& b) { return vec_madd(a,b,p2d_MZERO); }
+template<> EIGEN_STRONG_INLINE Packet2d pdiv<Packet2d>(const Packet2d& a, const Packet2d& b) { return vec_div(a,b); }
+
+// for some weird raisons, it has to be overloaded for packet of integers
+template<> EIGEN_STRONG_INLINE Packet2d pmadd(const Packet2d& a, const Packet2d& b, const Packet2d& c) { return vec_madd(a, b, c); }
+template<> EIGEN_STRONG_INLINE Packet2d pmsub(const Packet2d& a, const Packet2d& b, const Packet2d& c) { return vec_msub(a,b,c); }
+template<> EIGEN_STRONG_INLINE Packet2d pnmadd(const Packet2d& a, const Packet2d& b, const Packet2d& c) { return vec_nmsub(a,b,c); }
+template<> EIGEN_STRONG_INLINE Packet2d pnmsub(const Packet2d& a, const Packet2d& b, const Packet2d& c) { return vec_nmadd(a,b,c); }
+
+template<> EIGEN_STRONG_INLINE Packet2d pmin<Packet2d>(const Packet2d& a, const Packet2d& b)
+{
+ // NOTE: about 10% slower than vec_min, but consistent with std::min and SSE regarding NaN
+ Packet2d ret;
+ __asm__ ("xvcmpgedp %x0,%x1,%x2\n\txxsel %x0,%x1,%x2,%x0" : "=&wa" (ret) : "wa" (a), "wa" (b));
+ return ret;
+ }
+
+template<> EIGEN_STRONG_INLINE Packet2d pmax<Packet2d>(const Packet2d& a, const Packet2d& b)
+{
+ // NOTE: about 10% slower than vec_max, but consistent with std::max and SSE regarding NaN
+ Packet2d ret;
+ __asm__ ("xvcmpgtdp %x0,%x2,%x1\n\txxsel %x0,%x1,%x2,%x0" : "=&wa" (ret) : "wa" (a), "wa" (b));
+ return ret;
+}
+
+template<> EIGEN_STRONG_INLINE Packet2d pcmp_le(const Packet2d& a, const Packet2d& b) { return reinterpret_cast<Packet2d>(vec_cmple(a,b)); }
+template<> EIGEN_STRONG_INLINE Packet2d pcmp_lt(const Packet2d& a, const Packet2d& b) { return reinterpret_cast<Packet2d>(vec_cmplt(a,b)); }
+template<> EIGEN_STRONG_INLINE Packet2d pcmp_eq(const Packet2d& a, const Packet2d& b) { return reinterpret_cast<Packet2d>(vec_cmpeq(a,b)); }
+template<> EIGEN_STRONG_INLINE Packet2d pcmp_lt_or_nan(const Packet2d& a, const Packet2d& b) {
+ Packet2d c = reinterpret_cast<Packet2d>(vec_cmpge(a,b));
+ return vec_nor(c,c);
+}
+
+template<> EIGEN_STRONG_INLINE Packet2d pand<Packet2d>(const Packet2d& a, const Packet2d& b) { return vec_and(a, b); }
+
+template<> EIGEN_STRONG_INLINE Packet2d por<Packet2d>(const Packet2d& a, const Packet2d& b) { return vec_or(a, b); }
+
+template<> EIGEN_STRONG_INLINE Packet2d pxor<Packet2d>(const Packet2d& a, const Packet2d& b) { return vec_xor(a, b); }
+
+template<> EIGEN_STRONG_INLINE Packet2d pandnot<Packet2d>(const Packet2d& a, const Packet2d& b) { return vec_and(a, vec_nor(b, b)); }
+
+template<> EIGEN_STRONG_INLINE Packet2d pround<Packet2d>(const Packet2d& a)
+{
+ Packet2d t = vec_add(reinterpret_cast<Packet2d>(vec_or(vec_and(reinterpret_cast<Packet2ul>(a), p2ul_SIGN), p2ul_PREV0DOT5)), a);
+ Packet2d res;
+
+ __asm__("xvrdpiz %x0, %x1\n\t"
+ : "=&wa" (res)
+ : "wa" (t));
+
+ return res;
+}
+template<> EIGEN_STRONG_INLINE Packet2d pceil<Packet2d>(const Packet2d& a) { return vec_ceil(a); }
+template<> EIGEN_STRONG_INLINE Packet2d pfloor<Packet2d>(const Packet2d& a) { return vec_floor(a); }
+template<> EIGEN_STRONG_INLINE Packet2d print<Packet2d>(const Packet2d& a)
+{
+ Packet2d res;
+
+ __asm__("xvrdpic %x0, %x1\n\t"
+ : "=&wa" (res)
+ : "wa" (a));
+
+ return res;
+}
+
+template<> EIGEN_STRONG_INLINE Packet2d ploadu<Packet2d>(const double* from)
+{
+ EIGEN_DEBUG_UNALIGNED_LOAD
+ return vec_xl(0, const_cast<double*>(from));
+}
+
+template<> EIGEN_ALWAYS_INLINE Packet2d ploadu_partial<Packet2d>(const double* from, const Index n)
+{
+ return ploadu_partial_common<Packet2d>(from, n);
+}
+
+template<> EIGEN_STRONG_INLINE Packet2d ploaddup<Packet2d>(const double* from)
+{
+ Packet2d p;
+ if((std::ptrdiff_t(from) % 16) == 0) p = pload<Packet2d>(from);
+ else p = ploadu<Packet2d>(from);
+ return vec_splat_dbl<0>(p);
+}
+
+template<> EIGEN_STRONG_INLINE void pstoreu<double>(double* to, const Packet2d& from)
+{
+ EIGEN_DEBUG_UNALIGNED_STORE
+ vec_xst(from, 0, to);
+}
+
+template<> EIGEN_ALWAYS_INLINE void pstoreu_partial<double>(double* to, const Packet2d& from, const Index n)
+{
+ pstoreu_partial_common<Packet2d>(to, from, n);
+}
+
+template<> EIGEN_STRONG_INLINE void prefetch<double>(const double* addr) { EIGEN_PPC_PREFETCH(addr); }
+
+template<> EIGEN_STRONG_INLINE double pfirst<Packet2d>(const Packet2d& a) { EIGEN_ALIGN16 double x[2]; pstore<double>(x, a); return x[0]; }
+
+template<> EIGEN_STRONG_INLINE Packet2d preverse(const Packet2d& a)
+{
+ return vec_sld(a, a, 8);
+}
+template<> EIGEN_STRONG_INLINE Packet2d pabs(const Packet2d& a) { return vec_abs(a); }
+
+// VSX support varies between different compilers and even different
+// versions of the same compiler. For gcc version >= 4.9.3, we can use
+// vec_cts to efficiently convert Packet2d to Packet2l. Otherwise, use
+// a slow version that works with older compilers.
+// Update: apparently vec_cts/vec_ctf intrinsics for 64-bit doubles
+// are buggy, https://gcc.gnu.org/bugzilla/show_bug.cgi?id=70963
+template<>
+inline Packet2l pcast<Packet2d, Packet2l>(const Packet2d& x) {
+#if EIGEN_GNUC_AT_LEAST(5, 4) || \
+ (EIGEN_GNUC_AT(6, 1) && __GNUC_PATCHLEVEL__ >= 1)
+ return vec_cts(x, 0); // TODO: check clang version.
+#else
+ double tmp[2];
+ memcpy(tmp, &x, sizeof(tmp));
+ Packet2l l = { static_cast<long long>(tmp[0]),
+ static_cast<long long>(tmp[1]) };
+ return l;
+#endif
+}
+
+template<>
+inline Packet2d pcast<Packet2l, Packet2d>(const Packet2l& x) {
+ unsigned long long tmp[2];
+ memcpy(tmp, &x, sizeof(tmp));
+ Packet2d d = { static_cast<double>(tmp[0]),
+ static_cast<double>(tmp[1]) };
+ return d;
+}
+
+
+// Packet2l shifts.
+// For POWER8 we simply use vec_sr/l.
+//
+// Things are more complicated for POWER7. There is actually a
+// vec_xxsxdi intrinsic but it is not supported by some gcc versions.
+// So we need to shift by N % 32 and rearrage bytes.
+#ifdef __POWER8_VECTOR__
+
+template<int N>
+EIGEN_STRONG_INLINE Packet2l plogical_shift_left(const Packet2l& a) {
+ const Packet2ul shift = { N, N };
+ return vec_sl(a, shift);
+}
+
+template<int N>
+EIGEN_STRONG_INLINE Packet2l plogical_shift_right(const Packet2l& a) {
+ const Packet2ul shift = { N, N };
+ return vec_sr(a, shift);
+}
+
+#else
+
+// Shifts [A, B, C, D] to [B, 0, D, 0].
+// Used to implement left shifts for Packet2l.
+EIGEN_ALWAYS_INLINE Packet4i shift_even_left(const Packet4i& a) {
+ static const Packet16uc perm = {
+ 0x14, 0x15, 0x16, 0x17, 0x00, 0x01, 0x02, 0x03,
+ 0x1c, 0x1d, 0x1e, 0x1f, 0x08, 0x09, 0x0a, 0x0b };
+ #ifdef _BIG_ENDIAN
+ return vec_perm(p4i_ZERO, a, perm);
+ #else
+ return vec_perm(a, p4i_ZERO, perm);
+ #endif
+}
+
+// Shifts [A, B, C, D] to [0, A, 0, C].
+// Used to implement right shifts for Packet2l.
+EIGEN_ALWAYS_INLINE Packet4i shift_odd_right(const Packet4i& a) {
+ static const Packet16uc perm = {
+ 0x04, 0x05, 0x06, 0x07, 0x10, 0x11, 0x12, 0x13,
+ 0x0c, 0x0d, 0x0e, 0x0f, 0x18, 0x19, 0x1a, 0x1b };
+ #ifdef _BIG_ENDIAN
+ return vec_perm(p4i_ZERO, a, perm);
+ #else
+ return vec_perm(a, p4i_ZERO, perm);
+ #endif
+}
+
+template<int N, typename EnableIf = void>
+struct plogical_shift_left_impl;
+
+template<int N>
+struct plogical_shift_left_impl<N, std::enable_if_t<(N < 32) && (N >= 0)>> {
+ static EIGEN_STRONG_INLINE Packet2l run(const Packet2l& a) {
+ static const unsigned n = static_cast<unsigned>(N);
+ const Packet4ui shift = {n, n, n, n};
+ const Packet4i ai = reinterpret_cast<Packet4i>(a);
+ static const unsigned m = static_cast<unsigned>(32 - N);
+ const Packet4ui shift_right = {m, m, m, m};
+ const Packet4i out_hi = vec_sl(ai, shift);
+ const Packet4i out_lo = shift_even_left(vec_sr(ai, shift_right));
+ return reinterpret_cast<Packet2l>(por<Packet4i>(out_hi, out_lo));
+ }
+};
+
+template<int N>
+struct plogical_shift_left_impl<N, std::enable_if_t<(N >= 32)>> {
+ static EIGEN_STRONG_INLINE Packet2l run(const Packet2l& a) {
+ static const unsigned m = static_cast<unsigned>(N - 32);
+ const Packet4ui shift = {m, m, m, m};
+ const Packet4i ai = reinterpret_cast<Packet4i>(a);
+ return reinterpret_cast<Packet2l>(shift_even_left(vec_sl(ai, shift)));
+ }
+};
+
+template<int N>
+EIGEN_STRONG_INLINE Packet2l plogical_shift_left(const Packet2l& a) {
+ return plogical_shift_left_impl<N>::run(a);
+}
+
+template<int N, typename EnableIf = void>
+struct plogical_shift_right_impl;
+
+template<int N>
+struct plogical_shift_right_impl<N, std::enable_if_t<(N < 32) && (N >= 0)>> {
+ static EIGEN_STRONG_INLINE Packet2l run(const Packet2l& a) {
+ static const unsigned n = static_cast<unsigned>(N);
+ const Packet4ui shift = {n, n, n, n};
+ const Packet4i ai = reinterpret_cast<Packet4i>(a);
+ static const unsigned m = static_cast<unsigned>(32 - N);
+ const Packet4ui shift_left = {m, m, m, m};
+ const Packet4i out_lo = vec_sr(ai, shift);
+ const Packet4i out_hi = shift_odd_right(vec_sl(ai, shift_left));
+ return reinterpret_cast<Packet2l>(por<Packet4i>(out_hi, out_lo));
+ }
+};
+
+template<int N>
+struct plogical_shift_right_impl<N, std::enable_if_t<(N >= 32)>> {
+ static EIGEN_STRONG_INLINE Packet2l run(const Packet2l& a) {
+ static const unsigned m = static_cast<unsigned>(N - 32);
+ const Packet4ui shift = {m, m, m, m};
+ const Packet4i ai = reinterpret_cast<Packet4i>(a);
+ return reinterpret_cast<Packet2l>(shift_odd_right(vec_sr(ai, shift)));
+ }
+};
+
+template<int N>
+EIGEN_STRONG_INLINE Packet2l plogical_shift_right(const Packet2l& a) {
+ return plogical_shift_right_impl<N>::run(a);
+}
+#endif
+
+template<> EIGEN_STRONG_INLINE Packet2d pldexp<Packet2d>(const Packet2d& a, const Packet2d& exponent) {
+ // Clamp exponent to [-2099, 2099]
+ const Packet2d max_exponent = pset1<Packet2d>(2099.0);
+ const Packet2l e = pcast<Packet2d, Packet2l>(pmin(pmax(exponent, pnegate(max_exponent)), max_exponent));
+
+ // Split 2^e into four factors and multiply:
+ const Packet2l bias = { 1023, 1023 };
+ Packet2l b = plogical_shift_right<2>(e); // floor(e/4)
+ Packet2d c = reinterpret_cast<Packet2d>(plogical_shift_left<52>(b + bias));
+ Packet2d out = pmul(pmul(pmul(a, c), c), c); // a * 2^(3b)
+ b = psub(psub(psub(e, b), b), b); // e - 3b
+ c = reinterpret_cast<Packet2d>(plogical_shift_left<52>(b + bias)); // 2^(e - 3b)
+ out = pmul(out, c); // a * 2^e
+ return out;
+}
+
+
+// Extract exponent without existence of Packet2l.
+template<>
+EIGEN_STRONG_INLINE
+Packet2d pfrexp_generic_get_biased_exponent(const Packet2d& a) {
+ return pcast<Packet2l, Packet2d>(plogical_shift_right<52>(reinterpret_cast<Packet2l>(pabs(a))));
+}
+
+template<> EIGEN_STRONG_INLINE Packet2d pfrexp<Packet2d> (const Packet2d& a, Packet2d& exponent) {
+ return pfrexp_generic(a, exponent);
+}
+
+template<> EIGEN_STRONG_INLINE double predux<Packet2d>(const Packet2d& a)
+{
+ Packet2d b, sum;
+ b = reinterpret_cast<Packet2d>(vec_sld(reinterpret_cast<Packet4f>(a), reinterpret_cast<Packet4f>(a), 8));
+ sum = a + b;
+ return pfirst<Packet2d>(sum);
+}
+
+// Other reduction functions:
+// mul
+template<> EIGEN_STRONG_INLINE double predux_mul<Packet2d>(const Packet2d& a)
+{
+ return pfirst(pmul(a, reinterpret_cast<Packet2d>(vec_sld(reinterpret_cast<Packet4ui>(a), reinterpret_cast<Packet4ui>(a), 8))));
+}
+
+// min
+template<> EIGEN_STRONG_INLINE double predux_min<Packet2d>(const Packet2d& a)
+{
+ return pfirst(pmin(a, reinterpret_cast<Packet2d>(vec_sld(reinterpret_cast<Packet4ui>(a), reinterpret_cast<Packet4ui>(a), 8))));
+}
+
+// max
+template<> EIGEN_STRONG_INLINE double predux_max<Packet2d>(const Packet2d& a)
+{
+ return pfirst(pmax(a, reinterpret_cast<Packet2d>(vec_sld(reinterpret_cast<Packet4ui>(a), reinterpret_cast<Packet4ui>(a), 8))));
+}
+
+EIGEN_DEVICE_FUNC inline void
+ptranspose(PacketBlock<Packet2d,2>& kernel) {
+ Packet2d t0, t1;
+ t0 = vec_mergeh(kernel.packet[0], kernel.packet[1]);
+ t1 = vec_mergel(kernel.packet[0], kernel.packet[1]);
+ kernel.packet[0] = t0;
+ kernel.packet[1] = t1;
+}
+
+template<> EIGEN_STRONG_INLINE Packet2d pblend(const Selector<2>& ifPacket, const Packet2d& thenPacket, const Packet2d& elsePacket) {
+ Packet2l select = { ifPacket.select[0], ifPacket.select[1] };
+ Packet2bl mask = reinterpret_cast<Packet2bl>( vec_cmpeq(reinterpret_cast<Packet2d>(select), reinterpret_cast<Packet2d>(p2l_ONE)) );
+ return vec_sel(elsePacket, thenPacket, mask);
+}
+
+
+#endif // __VSX__
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_PACKET_MATH_ALTIVEC_H
diff --git a/Eigen/src/Core/arch/Default/BFloat16.h b/Eigen/src/Core/arch/Default/BFloat16.h
new file mode 100644
index 0000000..d2137d4
--- /dev/null
+++ b/Eigen/src/Core/arch/Default/BFloat16.h
@@ -0,0 +1,863 @@
+/* Copyright 2017 The TensorFlow Authors. All Rights Reserved.
+
+Licensed under the Apache License, Version 2.0 (the "License");
+you may not use this file except in compliance with the License.
+You may obtain a copy of the License at
+
+ http://www.apache.org/licenses/LICENSE-2.0
+
+Unless required by applicable law or agreed to in writing, software
+distributed under the License is distributed on an "AS IS" BASIS,
+WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+See the License for the specific language governing permissions and
+limitations under the License.
+==============================================================================*/
+
+#ifndef EIGEN_BFLOAT16_H
+#define EIGEN_BFLOAT16_H
+
+#include "../../InternalHeaderCheck.h"
+
+#if defined(EIGEN_HAS_HIP_BF16)
+// When compiling with GPU support, the "hip_bfloat16" base class as well as
+// some other routines are defined in the GPU compiler header files
+// (hip_bfloat16.h), and they are not tagged constexpr
+// As a consequence, we get compile failures when compiling Eigen with
+// GPU support. Hence the need to disable EIGEN_CONSTEXPR when building
+// Eigen with GPU support
+ #pragma push_macro("EIGEN_CONSTEXPR")
+ #undef EIGEN_CONSTEXPR
+ #define EIGEN_CONSTEXPR
+#endif
+
+#define BF16_PACKET_FUNCTION(PACKET_F, PACKET_BF16, METHOD) \
+ template <> \
+ EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED \
+ PACKET_BF16 METHOD<PACKET_BF16>(const PACKET_BF16& _x) { \
+ return F32ToBf16(METHOD<PACKET_F>(Bf16ToF32(_x))); \
+ }
+
+// Only use HIP GPU bf16 in kernels
+#if defined(EIGEN_HAS_HIP_BF16) && defined(EIGEN_GPU_COMPILE_PHASE)
+#define EIGEN_USE_HIP_BF16
+#endif
+
+namespace Eigen {
+
+struct bfloat16;
+
+namespace numext {
+template <>
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::bfloat16 bit_cast<Eigen::bfloat16, uint16_t>(const uint16_t& src);
+
+template <>
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC uint16_t bit_cast<uint16_t, Eigen::bfloat16>(const Eigen::bfloat16& src);
+} // namespace numext
+namespace bfloat16_impl {
+
+#if defined(EIGEN_USE_HIP_BF16)
+
+struct __bfloat16_raw : public hip_bfloat16 {
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR __bfloat16_raw() {}
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR __bfloat16_raw(hip_bfloat16 hb) : hip_bfloat16(hb) {}
+ explicit EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR __bfloat16_raw(unsigned short raw) : hip_bfloat16(raw) {}
+};
+
+#else
+
+// Make our own __bfloat16_raw definition.
+struct __bfloat16_raw {
+#if defined(EIGEN_HAS_HIP_BF16) && !defined(EIGEN_GPU_COMPILE_PHASE)
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR __bfloat16_raw() {}
+#else
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR __bfloat16_raw() : value(0) {}
+#endif
+ explicit EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR __bfloat16_raw(unsigned short raw) : value(raw) {}
+ unsigned short value;
+};
+
+#endif // defined(EIGEN_USE_HIP_BF16)
+
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR __bfloat16_raw raw_uint16_to_bfloat16(unsigned short value);
+template <bool AssumeArgumentIsNormalOrInfinityOrZero>
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC __bfloat16_raw float_to_bfloat16_rtne(float ff);
+// Forward declarations of template specializations, to avoid Visual C++ 2019 errors, saying:
+// > error C2908: explicit specialization; 'float_to_bfloat16_rtne' has already been instantiated
+template <>
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC __bfloat16_raw float_to_bfloat16_rtne<false>(float ff);
+template <>
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC __bfloat16_raw float_to_bfloat16_rtne<true>(float ff);
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC float bfloat16_to_float(__bfloat16_raw h);
+
+struct bfloat16_base : public __bfloat16_raw {
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR bfloat16_base() {}
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR bfloat16_base(const __bfloat16_raw& h) : __bfloat16_raw(h) {}
+};
+
+} // namespace bfloat16_impl
+
+// Class definition.
+struct bfloat16 : public bfloat16_impl::bfloat16_base {
+
+ typedef bfloat16_impl::__bfloat16_raw __bfloat16_raw;
+
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR bfloat16() {}
+
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR bfloat16(const __bfloat16_raw& h) : bfloat16_impl::bfloat16_base(h) {}
+
+ explicit EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR bfloat16(bool b)
+ : bfloat16_impl::bfloat16_base(bfloat16_impl::raw_uint16_to_bfloat16(b ? 0x3f80 : 0)) {}
+
+ template<class T>
+ explicit EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR bfloat16(T val)
+ : bfloat16_impl::bfloat16_base(bfloat16_impl::float_to_bfloat16_rtne<internal::is_integral<T>::value>(static_cast<float>(val))) {}
+
+ explicit EIGEN_DEVICE_FUNC bfloat16(float f)
+ : bfloat16_impl::bfloat16_base(bfloat16_impl::float_to_bfloat16_rtne<false>(f)) {}
+
+ // Following the convention of numpy, converting between complex and
+ // float will lead to loss of imag value.
+ template<typename RealScalar>
+ explicit EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR bfloat16(const std::complex<RealScalar>& val)
+ : bfloat16_impl::bfloat16_base(bfloat16_impl::float_to_bfloat16_rtne<false>(static_cast<float>(val.real()))) {}
+
+ EIGEN_DEVICE_FUNC operator float() const { // NOLINT: Allow implicit conversion to float, because it is lossless.
+ return bfloat16_impl::bfloat16_to_float(*this);
+ }
+};
+
+// TODO(majnemer): Get rid of this once we can rely on C++17 inline variables do
+// solve the ODR issue.
+namespace bfloat16_impl {
+template <typename = void>
+struct numeric_limits_bfloat16_impl {
+ static EIGEN_CONSTEXPR const bool is_specialized = true;
+ static EIGEN_CONSTEXPR const bool is_signed = true;
+ static EIGEN_CONSTEXPR const bool is_integer = false;
+ static EIGEN_CONSTEXPR const bool is_exact = false;
+ static EIGEN_CONSTEXPR const bool has_infinity = true;
+ static EIGEN_CONSTEXPR const bool has_quiet_NaN = true;
+ static EIGEN_CONSTEXPR const bool has_signaling_NaN = true;
+ static EIGEN_CONSTEXPR const std::float_denorm_style has_denorm = std::denorm_present;
+ static EIGEN_CONSTEXPR const bool has_denorm_loss = false;
+ static EIGEN_CONSTEXPR const std::float_round_style round_style = std::numeric_limits<float>::round_style;
+ static EIGEN_CONSTEXPR const bool is_iec559 = true;
+ // The C++ standard defines this as "true if the set of values representable
+ // by the type is finite." BFloat16 has finite precision.
+ static EIGEN_CONSTEXPR const bool is_bounded = true;
+ static EIGEN_CONSTEXPR const bool is_modulo = false;
+ static EIGEN_CONSTEXPR const int digits = 8;
+ static EIGEN_CONSTEXPR const int digits10 = 2;
+ static EIGEN_CONSTEXPR const int max_digits10 = 4;
+ static EIGEN_CONSTEXPR const int radix = std::numeric_limits<float>::radix;
+ static EIGEN_CONSTEXPR const int min_exponent = std::numeric_limits<float>::min_exponent;
+ static EIGEN_CONSTEXPR const int min_exponent10 = std::numeric_limits<float>::min_exponent10;
+ static EIGEN_CONSTEXPR const int max_exponent = std::numeric_limits<float>::max_exponent;
+ static EIGEN_CONSTEXPR const int max_exponent10 = std::numeric_limits<float>::max_exponent10;
+ static EIGEN_CONSTEXPR const bool traps = std::numeric_limits<float>::traps;
+ // IEEE754: "The implementer shall choose how tininess is detected, but shall
+ // detect tininess in the same way for all operations in radix two"
+ static EIGEN_CONSTEXPR const bool tinyness_before = std::numeric_limits<float>::tinyness_before;
+
+ static EIGEN_CONSTEXPR Eigen::bfloat16 (min)() { return Eigen::bfloat16_impl::raw_uint16_to_bfloat16(0x0080); }
+ static EIGEN_CONSTEXPR Eigen::bfloat16 lowest() { return Eigen::bfloat16_impl::raw_uint16_to_bfloat16(0xff7f); }
+ static EIGEN_CONSTEXPR Eigen::bfloat16 (max)() { return Eigen::bfloat16_impl::raw_uint16_to_bfloat16(0x7f7f); }
+ static EIGEN_CONSTEXPR Eigen::bfloat16 epsilon() { return Eigen::bfloat16_impl::raw_uint16_to_bfloat16(0x3c00); }
+ static EIGEN_CONSTEXPR Eigen::bfloat16 round_error() { return Eigen::bfloat16_impl::raw_uint16_to_bfloat16(0x3f00); }
+ static EIGEN_CONSTEXPR Eigen::bfloat16 infinity() { return Eigen::bfloat16_impl::raw_uint16_to_bfloat16(0x7f80); }
+ static EIGEN_CONSTEXPR Eigen::bfloat16 quiet_NaN() { return Eigen::bfloat16_impl::raw_uint16_to_bfloat16(0x7fc0); }
+ static EIGEN_CONSTEXPR Eigen::bfloat16 signaling_NaN() { return Eigen::bfloat16_impl::raw_uint16_to_bfloat16(0x7fa0); }
+ static EIGEN_CONSTEXPR Eigen::bfloat16 denorm_min() { return Eigen::bfloat16_impl::raw_uint16_to_bfloat16(0x0001); }
+};
+
+template<typename T>
+EIGEN_CONSTEXPR const bool numeric_limits_bfloat16_impl<T>::is_specialized;
+template<typename T>
+EIGEN_CONSTEXPR const bool numeric_limits_bfloat16_impl<T>::is_signed;
+template<typename T>
+EIGEN_CONSTEXPR const bool numeric_limits_bfloat16_impl<T>::is_integer;
+template<typename T>
+EIGEN_CONSTEXPR const bool numeric_limits_bfloat16_impl<T>::is_exact;
+template<typename T>
+EIGEN_CONSTEXPR const bool numeric_limits_bfloat16_impl<T>::has_infinity;
+template<typename T>
+EIGEN_CONSTEXPR const bool numeric_limits_bfloat16_impl<T>::has_quiet_NaN;
+template<typename T>
+EIGEN_CONSTEXPR const bool numeric_limits_bfloat16_impl<T>::has_signaling_NaN;
+template<typename T>
+EIGEN_CONSTEXPR const std::float_denorm_style numeric_limits_bfloat16_impl<T>::has_denorm;
+template<typename T>
+EIGEN_CONSTEXPR const bool numeric_limits_bfloat16_impl<T>::has_denorm_loss;
+template<typename T>
+EIGEN_CONSTEXPR const std::float_round_style numeric_limits_bfloat16_impl<T>::round_style;
+template<typename T>
+EIGEN_CONSTEXPR const bool numeric_limits_bfloat16_impl<T>::is_iec559;
+template<typename T>
+EIGEN_CONSTEXPR const bool numeric_limits_bfloat16_impl<T>::is_bounded;
+template<typename T>
+EIGEN_CONSTEXPR const bool numeric_limits_bfloat16_impl<T>::is_modulo;
+template<typename T>
+EIGEN_CONSTEXPR const int numeric_limits_bfloat16_impl<T>::digits;
+template<typename T>
+EIGEN_CONSTEXPR const int numeric_limits_bfloat16_impl<T>::digits10;
+template<typename T>
+EIGEN_CONSTEXPR const int numeric_limits_bfloat16_impl<T>::max_digits10;
+template<typename T>
+EIGEN_CONSTEXPR const int numeric_limits_bfloat16_impl<T>::radix;
+template<typename T>
+EIGEN_CONSTEXPR const int numeric_limits_bfloat16_impl<T>::min_exponent;
+template<typename T>
+EIGEN_CONSTEXPR const int numeric_limits_bfloat16_impl<T>::min_exponent10;
+template<typename T>
+EIGEN_CONSTEXPR const int numeric_limits_bfloat16_impl<T>::max_exponent;
+template<typename T>
+EIGEN_CONSTEXPR const int numeric_limits_bfloat16_impl<T>::max_exponent10;
+template<typename T>
+EIGEN_CONSTEXPR const bool numeric_limits_bfloat16_impl<T>::traps;
+template<typename T>
+EIGEN_CONSTEXPR const bool numeric_limits_bfloat16_impl<T>::tinyness_before;
+} // end namespace bfloat16_impl
+} // end namespace Eigen
+
+namespace std {
+// If std::numeric_limits<T> is specialized, should also specialize
+// std::numeric_limits<const T>, std::numeric_limits<volatile T>, and
+// std::numeric_limits<const volatile T>
+// https://stackoverflow.com/a/16519653/
+template<>
+class numeric_limits<Eigen::bfloat16> : public Eigen::bfloat16_impl::numeric_limits_bfloat16_impl<> {};
+template<>
+class numeric_limits<const Eigen::bfloat16> : public numeric_limits<Eigen::bfloat16> {};
+template<>
+class numeric_limits<volatile Eigen::bfloat16> : public numeric_limits<Eigen::bfloat16> {};
+template<>
+class numeric_limits<const volatile Eigen::bfloat16> : public numeric_limits<Eigen::bfloat16> {};
+} // end namespace std
+
+namespace Eigen {
+
+namespace bfloat16_impl {
+
+// We need to distinguish ‘clang as the CUDA compiler’ from ‘clang as the host compiler,
+// invoked by NVCC’ (e.g. on MacOS). The former needs to see both host and device implementation
+// of the functions, while the latter can only deal with one of them.
+#if !defined(EIGEN_HAS_NATIVE_BF16) || (EIGEN_COMP_CLANG && !EIGEN_COMP_NVCC) // Emulate support for bfloat16 floats
+
+#if EIGEN_COMP_CLANG && defined(EIGEN_CUDACC)
+// We need to provide emulated *host-side* BF16 operators for clang.
+#pragma push_macro("EIGEN_DEVICE_FUNC")
+#undef EIGEN_DEVICE_FUNC
+#if (defined(EIGEN_HAS_GPU_BF16) && defined(EIGEN_HAS_NATIVE_BF16))
+#define EIGEN_DEVICE_FUNC __host__
+#else // both host and device need emulated ops.
+#define EIGEN_DEVICE_FUNC __host__ __device__
+#endif
+#endif
+
+// Definitions for CPUs, mostly working through conversion
+// to/from fp32.
+
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bfloat16 operator + (const bfloat16& a, const bfloat16& b) {
+ return bfloat16(float(a) + float(b));
+}
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bfloat16 operator + (const bfloat16& a, const int& b) {
+ return bfloat16(float(a) + static_cast<float>(b));
+}
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bfloat16 operator + (const int& a, const bfloat16& b) {
+ return bfloat16(static_cast<float>(a) + float(b));
+}
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bfloat16 operator * (const bfloat16& a, const bfloat16& b) {
+ return bfloat16(float(a) * float(b));
+}
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bfloat16 operator - (const bfloat16& a, const bfloat16& b) {
+ return bfloat16(float(a) - float(b));
+}
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bfloat16 operator / (const bfloat16& a, const bfloat16& b) {
+ return bfloat16(float(a) / float(b));
+}
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bfloat16 operator - (const bfloat16& a) {
+ numext::uint16_t x = numext::bit_cast<uint16_t>(a) ^ 0x8000;
+ return numext::bit_cast<bfloat16>(x);
+}
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bfloat16& operator += (bfloat16& a, const bfloat16& b) {
+ a = bfloat16(float(a) + float(b));
+ return a;
+}
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bfloat16& operator *= (bfloat16& a, const bfloat16& b) {
+ a = bfloat16(float(a) * float(b));
+ return a;
+}
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bfloat16& operator -= (bfloat16& a, const bfloat16& b) {
+ a = bfloat16(float(a) - float(b));
+ return a;
+}
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bfloat16& operator /= (bfloat16& a, const bfloat16& b) {
+ a = bfloat16(float(a) / float(b));
+ return a;
+}
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bfloat16 operator++(bfloat16& a) {
+ a += bfloat16(1);
+ return a;
+}
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bfloat16 operator--(bfloat16& a) {
+ a -= bfloat16(1);
+ return a;
+}
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bfloat16 operator++(bfloat16& a, int) {
+ bfloat16 original_value = a;
+ ++a;
+ return original_value;
+}
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bfloat16 operator--(bfloat16& a, int) {
+ bfloat16 original_value = a;
+ --a;
+ return original_value;
+}
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bool operator == (const bfloat16& a, const bfloat16& b) {
+ return numext::equal_strict(float(a),float(b));
+}
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bool operator != (const bfloat16& a, const bfloat16& b) {
+ return numext::not_equal_strict(float(a), float(b));
+}
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bool operator < (const bfloat16& a, const bfloat16& b) {
+ return float(a) < float(b);
+}
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bool operator <= (const bfloat16& a, const bfloat16& b) {
+ return float(a) <= float(b);
+}
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bool operator > (const bfloat16& a, const bfloat16& b) {
+ return float(a) > float(b);
+}
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bool operator >= (const bfloat16& a, const bfloat16& b) {
+ return float(a) >= float(b);
+}
+
+#if EIGEN_COMP_CLANG && defined(EIGEN_CUDACC)
+#pragma pop_macro("EIGEN_DEVICE_FUNC")
+#endif
+#endif // Emulate support for bfloat16 floats
+
+// Division by an index. Do it in full float precision to avoid accuracy
+// issues in converting the denominator to bfloat16.
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bfloat16 operator / (const bfloat16& a, Index b) {
+ return bfloat16(static_cast<float>(a) / static_cast<float>(b));
+}
+
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC __bfloat16_raw truncate_to_bfloat16(const float v) {
+#if defined(EIGEN_USE_HIP_BF16)
+ return __bfloat16_raw(__bfloat16_raw::round_to_bfloat16(v, __bfloat16_raw::truncate));
+#else
+ __bfloat16_raw output;
+ if (numext::isnan EIGEN_NOT_A_MACRO(v)) {
+ output.value = std::signbit(v) ? 0xFFC0: 0x7FC0;
+ return output;
+ }
+ output.value = static_cast<numext::uint16_t>(numext::bit_cast<numext::uint32_t>(v) >> 16);
+ return output;
+#endif
+}
+
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR __bfloat16_raw raw_uint16_to_bfloat16(numext::uint16_t value) {
+#if defined(EIGEN_USE_HIP_BF16)
+ __bfloat16_raw bf;
+ bf.data = value;
+ return bf;
+#else
+ return __bfloat16_raw(value);
+#endif
+}
+
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR numext::uint16_t raw_bfloat16_as_uint16(const __bfloat16_raw& bf) {
+#if defined(EIGEN_USE_HIP_BF16)
+ return bf.data;
+#else
+ return bf.value;
+#endif
+}
+
+// float_to_bfloat16_rtne template specialization that does not make any
+// assumption about the value of its function argument (ff).
+template <>
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC __bfloat16_raw float_to_bfloat16_rtne<false>(float ff) {
+#if defined(EIGEN_USE_HIP_BF16)
+ return __bfloat16_raw(__bfloat16_raw::round_to_bfloat16(ff));
+#else
+ __bfloat16_raw output;
+
+ if (numext::isnan EIGEN_NOT_A_MACRO(ff)) {
+ // If the value is a NaN, squash it to a qNaN with msb of fraction set,
+ // this makes sure after truncation we don't end up with an inf.
+ //
+ // qNaN magic: All exponent bits set + most significant bit of fraction
+ // set.
+ output.value = std::signbit(ff) ? 0xFFC0: 0x7FC0;
+ } else {
+ // Fast rounding algorithm that rounds a half value to nearest even. This
+ // reduces expected error when we convert a large number of floats. Here
+ // is how it works:
+ //
+ // Definitions:
+ // To convert a float 32 to bfloat16, a float 32 can be viewed as 32 bits
+ // with the following tags:
+ //
+ // Sign | Exp (8 bits) | Frac (23 bits)
+ // S EEEEEEEE FFFFFFLRTTTTTTTTTTTTTTT
+ //
+ // S: Sign bit.
+ // E: Exponent bits.
+ // F: First 6 bits of fraction.
+ // L: Least significant bit of resulting bfloat16 if we truncate away the
+ // rest of the float32. This is also the 7th bit of fraction
+ // R: Rounding bit, 8th bit of fraction.
+ // T: Sticky bits, rest of fraction, 15 bits.
+ //
+ // To round half to nearest even, there are 3 cases where we want to round
+ // down (simply truncate the result of the bits away, which consists of
+ // rounding bit and sticky bits) and two cases where we want to round up
+ // (truncate then add one to the result).
+ //
+ // The fast converting algorithm simply adds lsb (L) to 0x7fff (15 bits of
+ // 1s) as the rounding bias, adds the rounding bias to the input, then
+ // truncates the last 16 bits away.
+ //
+ // To understand how it works, we can analyze this algorithm case by case:
+ //
+ // 1. L = 0, R = 0:
+ // Expect: round down, this is less than half value.
+ //
+ // Algorithm:
+ // - Rounding bias: 0x7fff + 0 = 0x7fff
+ // - Adding rounding bias to input may create any carry, depending on
+ // whether there is any value set to 1 in T bits.
+ // - R may be set to 1 if there is a carry.
+ // - L remains 0.
+ // - Note that this case also handles Inf and -Inf, where all fraction
+ // bits, including L, R and Ts are all 0. The output remains Inf after
+ // this algorithm.
+ //
+ // 2. L = 1, R = 0:
+ // Expect: round down, this is less than half value.
+ //
+ // Algorithm:
+ // - Rounding bias: 0x7fff + 1 = 0x8000
+ // - Adding rounding bias to input doesn't change sticky bits but
+ // adds 1 to rounding bit.
+ // - L remains 1.
+ //
+ // 3. L = 0, R = 1, all of T are 0:
+ // Expect: round down, this is exactly at half, the result is already
+ // even (L=0).
+ //
+ // Algorithm:
+ // - Rounding bias: 0x7fff + 0 = 0x7fff
+ // - Adding rounding bias to input sets all sticky bits to 1, but
+ // doesn't create a carry.
+ // - R remains 1.
+ // - L remains 0.
+ //
+ // 4. L = 1, R = 1:
+ // Expect: round up, this is exactly at half, the result needs to be
+ // round to the next even number.
+ //
+ // Algorithm:
+ // - Rounding bias: 0x7fff + 1 = 0x8000
+ // - Adding rounding bias to input doesn't change sticky bits, but
+ // creates a carry from rounding bit.
+ // - The carry sets L to 0, creates another carry bit and propagate
+ // forward to F bits.
+ // - If all the F bits are 1, a carry then propagates to the exponent
+ // bits, which then creates the minimum value with the next exponent
+ // value. Note that we won't have the case where exponents are all 1,
+ // since that's either a NaN (handled in the other if condition) or inf
+ // (handled in case 1).
+ //
+ // 5. L = 0, R = 1, any of T is 1:
+ // Expect: round up, this is greater than half.
+ //
+ // Algorithm:
+ // - Rounding bias: 0x7fff + 0 = 0x7fff
+ // - Adding rounding bias to input creates a carry from sticky bits,
+ // sets rounding bit to 0, then create another carry.
+ // - The second carry sets L to 1.
+ //
+ // Examples:
+ //
+ // Exact half value that is already even:
+ // Input:
+ // Sign | Exp (8 bit) | Frac (first 7 bit) | Frac (last 16 bit)
+ // S E E E E E E E E F F F F F F L RTTTTTTTTTTTTTTT
+ // 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1000000000000000
+ //
+ // This falls into case 3. We truncate the rest of 16 bits and no
+ // carry is created into F and L:
+ //
+ // Output:
+ // Sign | Exp (8 bit) | Frac (first 7 bit)
+ // S E E E E E E E E F F F F F F L
+ // 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0
+ //
+ // Exact half value, round to next even number:
+ // Input:
+ // Sign | Exp (8 bit) | Frac (first 7 bit) | Frac (last 16 bit)
+ // S E E E E E E E E F F F F F F L RTTTTTTTTTTTTTTT
+ // 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1000000000000000
+ //
+ // This falls into case 4. We create a carry from R and T,
+ // which then propagates into L and F:
+ //
+ // Output:
+ // Sign | Exp (8 bit) | Frac (first 7 bit)
+ // S E E E E E E E E F F F F F F L
+ // 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0
+ //
+ //
+ // Max denormal value round to min normal value:
+ // Input:
+ // Sign | Exp (8 bit) | Frac (first 7 bit) | Frac (last 16 bit)
+ // S E E E E E E E E F F F F F F L RTTTTTTTTTTTTTTT
+ // 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1111111111111111
+ //
+ // This falls into case 4. We create a carry from R and T,
+ // propagate into L and F, which then propagates into exponent
+ // bits:
+ //
+ // Output:
+ // Sign | Exp (8 bit) | Frac (first 7 bit)
+ // S E E E E E E E E F F F F F F L
+ // 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0
+ //
+ // Max normal value round to Inf:
+ // Input:
+ // Sign | Exp (8 bit) | Frac (first 7 bit) | Frac (last 16 bit)
+ // S E E E E E E E E F F F F F F L RTTTTTTTTTTTTTTT
+ // 0 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1111111111111111
+ //
+ // This falls into case 4. We create a carry from R and T,
+ // propagate into L and F, which then propagates into exponent
+ // bits:
+ //
+ // Sign | Exp (8 bit) | Frac (first 7 bit)
+ // S E E E E E E E E F F F F F F L
+ // 0 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0
+
+ // At this point, ff must be either a normal float, or +/-infinity.
+ output = float_to_bfloat16_rtne<true>(ff);
+ }
+ return output;
+#endif
+}
+
+// float_to_bfloat16_rtne template specialization that assumes that its function
+// argument (ff) is either a normal floating point number, or +/-infinity, or
+// zero. Used to improve the runtime performance of conversion from an integer
+// type to bfloat16.
+template <>
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC __bfloat16_raw float_to_bfloat16_rtne<true>(float ff) {
+#if defined(EIGEN_USE_HIP_BF16)
+ return __bfloat16_raw(__bfloat16_raw::round_to_bfloat16(ff));
+#else
+ numext::uint32_t input = numext::bit_cast<numext::uint32_t>(ff);
+ __bfloat16_raw output;
+
+ // Least significant bit of resulting bfloat.
+ numext::uint32_t lsb = (input >> 16) & 1;
+ numext::uint32_t rounding_bias = 0x7fff + lsb;
+ input += rounding_bias;
+ output.value = static_cast<numext::uint16_t>(input >> 16);
+ return output;
+#endif
+}
+
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC float bfloat16_to_float(__bfloat16_raw h) {
+#if defined(EIGEN_USE_HIP_BF16)
+ return static_cast<float>(h);
+#else
+ return numext::bit_cast<float>(static_cast<numext::uint32_t>(h.value) << 16);
+#endif
+}
+
+// --- standard functions ---
+
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bool (isinf)(const bfloat16& a) {
+ EIGEN_USING_STD(isinf);
+#if defined(EIGEN_USE_HIP_BF16)
+ return (isinf)(a); // Uses HIP hip_bfloat16 isinf operator
+#else
+ return (isinf)(float(a));
+#endif
+}
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bool (isnan)(const bfloat16& a) {
+ EIGEN_USING_STD(isnan);
+#if defined(EIGEN_USE_HIP_BF16)
+ return (isnan)(a); // Uses HIP hip_bfloat16 isnan operator
+#else
+ return (isnan)(float(a));
+#endif
+}
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bool (isfinite)(const bfloat16& a) {
+ return !(isinf EIGEN_NOT_A_MACRO (a)) && !(isnan EIGEN_NOT_A_MACRO (a));
+}
+
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bfloat16 abs(const bfloat16& a) {
+ numext::uint16_t x = numext::bit_cast<numext::uint16_t>(a) & 0x7FFF;
+ return numext::bit_cast<bfloat16>(x);
+}
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bfloat16 exp(const bfloat16& a) {
+ return bfloat16(::expf(float(a)));
+}
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bfloat16 expm1(const bfloat16& a) {
+ return bfloat16(numext::expm1(float(a)));
+}
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bfloat16 log(const bfloat16& a) {
+ return bfloat16(::logf(float(a)));
+}
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bfloat16 log1p(const bfloat16& a) {
+ return bfloat16(numext::log1p(float(a)));
+}
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bfloat16 log10(const bfloat16& a) {
+ return bfloat16(::log10f(float(a)));
+}
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bfloat16 log2(const bfloat16& a) {
+ return bfloat16(static_cast<float>(EIGEN_LOG2E) * ::logf(float(a)));
+}
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bfloat16 sqrt(const bfloat16& a) {
+ return bfloat16(::sqrtf(float(a)));
+}
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bfloat16 pow(const bfloat16& a, const bfloat16& b) {
+ return bfloat16(::powf(float(a), float(b)));
+}
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bfloat16 atan2(const bfloat16& a, const bfloat16& b) {
+ return bfloat16(::atan2f(float(a), float(b)));
+}
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bfloat16 sin(const bfloat16& a) {
+ return bfloat16(::sinf(float(a)));
+}
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bfloat16 cos(const bfloat16& a) {
+ return bfloat16(::cosf(float(a)));
+}
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bfloat16 tan(const bfloat16& a) {
+ return bfloat16(::tanf(float(a)));
+}
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bfloat16 asin(const bfloat16& a) {
+ return bfloat16(::asinf(float(a)));
+}
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bfloat16 acos(const bfloat16& a) {
+ return bfloat16(::acosf(float(a)));
+}
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bfloat16 atan(const bfloat16& a) {
+ return bfloat16(::atanf(float(a)));
+}
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bfloat16 sinh(const bfloat16& a) {
+ return bfloat16(::sinhf(float(a)));
+}
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bfloat16 cosh(const bfloat16& a) {
+ return bfloat16(::coshf(float(a)));
+}
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bfloat16 tanh(const bfloat16& a) {
+ return bfloat16(::tanhf(float(a)));
+}
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bfloat16 asinh(const bfloat16& a) {
+ return bfloat16(::asinhf(float(a)));
+}
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bfloat16 acosh(const bfloat16& a) {
+ return bfloat16(::acoshf(float(a)));
+}
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bfloat16 atanh(const bfloat16& a) {
+ return bfloat16(::atanhf(float(a)));
+}
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bfloat16 floor(const bfloat16& a) {
+ return bfloat16(::floorf(float(a)));
+}
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bfloat16 ceil(const bfloat16& a) {
+ return bfloat16(::ceilf(float(a)));
+}
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bfloat16 rint(const bfloat16& a) {
+ return bfloat16(::rintf(float(a)));
+}
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bfloat16 round(const bfloat16& a) {
+ return bfloat16(::roundf(float(a)));
+}
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bfloat16 fmod(const bfloat16& a, const bfloat16& b) {
+ return bfloat16(::fmodf(float(a), float(b)));
+}
+
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bfloat16 (min)(const bfloat16& a, const bfloat16& b) {
+ const float f1 = static_cast<float>(a);
+ const float f2 = static_cast<float>(b);
+ return f2 < f1 ? b : a;
+}
+
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bfloat16 (max)(const bfloat16& a, const bfloat16& b) {
+ const float f1 = static_cast<float>(a);
+ const float f2 = static_cast<float>(b);
+ return f1 < f2 ? b : a;
+}
+
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bfloat16 fmin(const bfloat16& a, const bfloat16& b) {
+ const float f1 = static_cast<float>(a);
+ const float f2 = static_cast<float>(b);
+ return bfloat16(::fminf(f1, f2));
+}
+
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bfloat16 fmax(const bfloat16& a, const bfloat16& b) {
+ const float f1 = static_cast<float>(a);
+ const float f2 = static_cast<float>(b);
+ return bfloat16(::fmaxf(f1, f2));
+}
+
+#ifndef EIGEN_NO_IO
+EIGEN_ALWAYS_INLINE std::ostream& operator << (std::ostream& os, const bfloat16& v) {
+ os << static_cast<float>(v);
+ return os;
+}
+#endif
+
+} // namespace bfloat16_impl
+
+namespace internal {
+
+template<>
+struct random_default_impl<bfloat16, false, false>
+{
+ static inline bfloat16 run(const bfloat16& x, const bfloat16& y)
+ {
+ return x + (y-x) * bfloat16(float(std::rand()) / float(RAND_MAX));
+ }
+ static inline bfloat16 run()
+ {
+ return run(bfloat16(-1.f), bfloat16(1.f));
+ }
+};
+
+template<> struct is_arithmetic<bfloat16> { enum { value = true }; };
+
+} // namespace internal
+
+template<> struct NumTraits<Eigen::bfloat16>
+ : GenericNumTraits<Eigen::bfloat16>
+{
+ enum {
+ IsSigned = true,
+ IsInteger = false,
+ IsComplex = false,
+ RequireInitialization = false
+ };
+
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR static EIGEN_STRONG_INLINE Eigen::bfloat16 epsilon() {
+ return bfloat16_impl::raw_uint16_to_bfloat16(0x3c00);
+ }
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR static EIGEN_STRONG_INLINE Eigen::bfloat16 dummy_precision() {
+ return bfloat16_impl::raw_uint16_to_bfloat16(0x3D4D); // bfloat16(5e-2f);
+ }
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR static EIGEN_STRONG_INLINE Eigen::bfloat16 highest() {
+ return bfloat16_impl::raw_uint16_to_bfloat16(0x7F7F);
+ }
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR static EIGEN_STRONG_INLINE Eigen::bfloat16 lowest() {
+ return bfloat16_impl::raw_uint16_to_bfloat16(0xFF7F);
+ }
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR static EIGEN_STRONG_INLINE Eigen::bfloat16 infinity() {
+ return bfloat16_impl::raw_uint16_to_bfloat16(0x7f80);
+ }
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR static EIGEN_STRONG_INLINE Eigen::bfloat16 quiet_NaN() {
+ return bfloat16_impl::raw_uint16_to_bfloat16(0x7fc0);
+ }
+};
+
+} // namespace Eigen
+
+
+#if defined(EIGEN_HAS_HIP_BF16)
+ #pragma pop_macro("EIGEN_CONSTEXPR")
+#endif
+
+namespace Eigen {
+namespace numext {
+
+template<>
+EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
+bool (isnan)(const Eigen::bfloat16& h) {
+ return (bfloat16_impl::isnan)(h);
+}
+
+template<>
+EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
+bool (isinf)(const Eigen::bfloat16& h) {
+ return (bfloat16_impl::isinf)(h);
+}
+
+template<>
+EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
+bool (isfinite)(const Eigen::bfloat16& h) {
+ return (bfloat16_impl::isfinite)(h);
+}
+
+template <>
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::bfloat16 bit_cast<Eigen::bfloat16, uint16_t>(const uint16_t& src) {
+ return Eigen::bfloat16_impl::raw_uint16_to_bfloat16(src);
+}
+
+template <>
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC uint16_t bit_cast<uint16_t, Eigen::bfloat16>(const Eigen::bfloat16& src) {
+ return Eigen::bfloat16_impl::raw_bfloat16_as_uint16(src);
+}
+
+} // namespace numext
+} // namespace Eigen
+
+#if EIGEN_HAS_STD_HASH
+namespace std {
+template <>
+struct hash<Eigen::bfloat16> {
+ EIGEN_STRONG_INLINE std::size_t operator()(const Eigen::bfloat16& a) const {
+ return static_cast<std::size_t>(Eigen::numext::bit_cast<Eigen::numext::uint16_t>(a));
+ }
+};
+} // namespace std
+#endif
+
+// Add the missing shfl* intrinsics.
+// The __shfl* functions are only valid on HIP or _CUDA_ARCH_ >= 300.
+// CUDA defines them for (__CUDA_ARCH__ >= 300 || !defined(__CUDA_ARCH__))
+//
+// HIP and CUDA prior to SDK 9.0 define
+// __shfl, __shfl_up, __shfl_down, __shfl_xor for int and float
+// CUDA since 9.0 deprecates those and instead defines
+// __shfl_sync, __shfl_up_sync, __shfl_down_sync, __shfl_xor_sync,
+// with native support for __half and __nv_bfloat16
+//
+// Note that the following are __device__ - only functions.
+#if defined(EIGEN_HIPCC)
+
+#if defined(EIGEN_HAS_HIP_BF16)
+
+__device__ EIGEN_STRONG_INLINE Eigen::bfloat16 __shfl(Eigen::bfloat16 var, int srcLane, int width=warpSize) {
+ const int ivar = static_cast<int>(Eigen::numext::bit_cast<Eigen::numext::uint16_t>(var));
+ return Eigen::numext::bit_cast<Eigen::bfloat16>(static_cast<Eigen::numext::uint16_t>(__shfl(ivar, srcLane, width)));
+}
+
+__device__ EIGEN_STRONG_INLINE Eigen::bfloat16 __shfl_up(Eigen::bfloat16 var, unsigned int delta, int width=warpSize) {
+ const int ivar = static_cast<int>(Eigen::numext::bit_cast<Eigen::numext::uint16_t>(var));
+ return Eigen::numext::bit_cast<Eigen::bfloat16>(static_cast<Eigen::numext::uint16_t>(__shfl_up(ivar, delta, width)));
+}
+
+__device__ EIGEN_STRONG_INLINE Eigen::bfloat16 __shfl_down(Eigen::bfloat16 var, unsigned int delta, int width=warpSize) {
+ const int ivar = static_cast<int>(Eigen::numext::bit_cast<Eigen::numext::uint16_t>(var));
+ return Eigen::numext::bit_cast<Eigen::bfloat16>(static_cast<Eigen::numext::uint16_t>(__shfl_down(ivar, delta, width)));
+}
+
+__device__ EIGEN_STRONG_INLINE Eigen::bfloat16 __shfl_xor(Eigen::bfloat16 var, int laneMask, int width=warpSize) {
+ const int ivar = static_cast<int>(Eigen::numext::bit_cast<Eigen::numext::uint16_t>(var));
+ return Eigen::numext::bit_cast<Eigen::bfloat16>(static_cast<Eigen::numext::uint16_t>(__shfl_xor(ivar, laneMask, width)));
+}
+
+#endif // HIP
+
+#endif // __shfl*
+
+#if defined(EIGEN_HIPCC)
+EIGEN_STRONG_INLINE __device__ Eigen::bfloat16 __ldg(const Eigen::bfloat16* ptr) {
+ return Eigen::bfloat16_impl::raw_uint16_to_bfloat16(__ldg(Eigen::numext::bit_cast<const Eigen::numext::uint16_t*>(ptr)));
+}
+#endif // __ldg
+
+#endif // EIGEN_BFLOAT16_H
diff --git a/Eigen/src/Core/arch/Default/ConjHelper.h b/Eigen/src/Core/arch/Default/ConjHelper.h
new file mode 100644
index 0000000..6b5afe3
--- /dev/null
+++ b/Eigen/src/Core/arch/Default/ConjHelper.h
@@ -0,0 +1,119 @@
+
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2017 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_ARCH_CONJ_HELPER_H
+#define EIGEN_ARCH_CONJ_HELPER_H
+
+#define EIGEN_MAKE_CONJ_HELPER_CPLX_REAL(PACKET_CPLX, PACKET_REAL) \
+ template <> \
+ struct conj_helper<PACKET_REAL, PACKET_CPLX, false, false> { \
+ EIGEN_STRONG_INLINE PACKET_CPLX pmadd(const PACKET_REAL& x, \
+ const PACKET_CPLX& y, \
+ const PACKET_CPLX& c) const { \
+ return padd(c, this->pmul(x, y)); \
+ } \
+ EIGEN_STRONG_INLINE PACKET_CPLX pmul(const PACKET_REAL& x, \
+ const PACKET_CPLX& y) const { \
+ return PACKET_CPLX(Eigen::internal::pmul<PACKET_REAL>(x, y.v)); \
+ } \
+ }; \
+ \
+ template <> \
+ struct conj_helper<PACKET_CPLX, PACKET_REAL, false, false> { \
+ EIGEN_STRONG_INLINE PACKET_CPLX pmadd(const PACKET_CPLX& x, \
+ const PACKET_REAL& y, \
+ const PACKET_CPLX& c) const { \
+ return padd(c, this->pmul(x, y)); \
+ } \
+ EIGEN_STRONG_INLINE PACKET_CPLX pmul(const PACKET_CPLX& x, \
+ const PACKET_REAL& y) const { \
+ return PACKET_CPLX(Eigen::internal::pmul<PACKET_REAL>(x.v, y)); \
+ } \
+ };
+
+#include "../../InternalHeaderCheck.h"
+
+namespace Eigen {
+namespace internal {
+
+template<bool Conjugate> struct conj_if;
+
+template<> struct conj_if<true> {
+ template<typename T>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE T operator()(const T& x) const { return numext::conj(x); }
+ template<typename T>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE T pconj(const T& x) const { return internal::pconj(x); }
+};
+
+template<> struct conj_if<false> {
+ template<typename T>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const T& operator()(const T& x) const { return x; }
+ template<typename T>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const T& pconj(const T& x) const { return x; }
+};
+
+// Generic Implementation, assume scalars since the packet-version is
+// specialized below.
+template<typename LhsType, typename RhsType, bool ConjLhs, bool ConjRhs>
+struct conj_helper {
+ typedef typename ScalarBinaryOpTraits<LhsType, RhsType>::ReturnType ResultType;
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE ResultType
+ pmadd(const LhsType& x, const RhsType& y, const ResultType& c) const
+ { return this->pmul(x, y) + c; }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE ResultType
+ pmul(const LhsType& x, const RhsType& y) const
+ { return conj_if<ConjLhs>()(x) * conj_if<ConjRhs>()(y); }
+};
+
+template<typename LhsScalar, typename RhsScalar>
+struct conj_helper<LhsScalar, RhsScalar, true, true> {
+ typedef typename ScalarBinaryOpTraits<LhsScalar,RhsScalar>::ReturnType ResultType;
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE ResultType
+ pmadd(const LhsScalar& x, const RhsScalar& y, const ResultType& c) const
+ { return this->pmul(x, y) + c; }
+
+ // We save a conjuation by using the identity conj(a)*conj(b) = conj(a*b).
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE ResultType
+ pmul(const LhsScalar& x, const RhsScalar& y) const
+ { return numext::conj(x * y); }
+};
+
+// Implementation with equal type, use packet operations.
+template<typename Packet, bool ConjLhs, bool ConjRhs>
+struct conj_helper<Packet, Packet, ConjLhs, ConjRhs>
+{
+ typedef Packet ResultType;
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet pmadd(const Packet& x, const Packet& y, const Packet& c) const
+ { return Eigen::internal::pmadd(conj_if<ConjLhs>().pconj(x), conj_if<ConjRhs>().pconj(y), c); }
+
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet pmul(const Packet& x, const Packet& y) const
+ { return Eigen::internal::pmul(conj_if<ConjLhs>().pconj(x), conj_if<ConjRhs>().pconj(y)); }
+};
+
+template<typename Packet>
+struct conj_helper<Packet, Packet, true, true>
+{
+ typedef Packet ResultType;
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet pmadd(const Packet& x, const Packet& y, const Packet& c) const
+ { return Eigen::internal::pmadd(pconj(x), pconj(y), c); }
+ // We save a conjuation by using the identity conj(a)*conj(b) = conj(a*b).
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet pmul(const Packet& x, const Packet& y) const
+ { return pconj(Eigen::internal::pmul(x, y)); }
+};
+
+} // namespace internal
+} // namespace Eigen
+
+#endif // EIGEN_ARCH_CONJ_HELPER_H
diff --git a/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h b/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h
new file mode 100644
index 0000000..3060214
--- /dev/null
+++ b/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h
@@ -0,0 +1,2198 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2007 Julien Pommier
+// Copyright (C) 2014 Pedro Gonnet (pedro.gonnet@gmail.com)
+// Copyright (C) 2009-2019 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+/* The exp and log functions of this file initially come from
+ * Julien Pommier's sse math library: http://gruntthepeon.free.fr/ssemath/
+ */
+
+#ifndef EIGEN_ARCH_GENERIC_PACKET_MATH_FUNCTIONS_H
+#define EIGEN_ARCH_GENERIC_PACKET_MATH_FUNCTIONS_H
+
+#include "../../InternalHeaderCheck.h"
+
+namespace Eigen {
+namespace internal {
+
+// Creates a Scalar integer type with same bit-width.
+template<typename T> struct make_integer;
+template<> struct make_integer<float> { typedef numext::int32_t type; };
+template<> struct make_integer<double> { typedef numext::int64_t type; };
+template<> struct make_integer<half> { typedef numext::int16_t type; };
+template<> struct make_integer<bfloat16> { typedef numext::int16_t type; };
+
+template<typename Packet> EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC
+Packet pfrexp_generic_get_biased_exponent(const Packet& a) {
+ typedef typename unpacket_traits<Packet>::type Scalar;
+ typedef typename unpacket_traits<Packet>::integer_packet PacketI;
+ static constexpr int mantissa_bits = numext::numeric_limits<Scalar>::digits - 1;
+ return pcast<PacketI, Packet>(plogical_shift_right<mantissa_bits>(preinterpret<PacketI>(pabs(a))));
+}
+
+// Safely applies frexp, correctly handles denormals.
+// Assumes IEEE floating point format.
+template<typename Packet> EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC
+Packet pfrexp_generic(const Packet& a, Packet& exponent) {
+ typedef typename unpacket_traits<Packet>::type Scalar;
+ typedef typename make_unsigned<typename make_integer<Scalar>::type>::type ScalarUI;
+ static constexpr int
+ TotalBits = sizeof(Scalar) * CHAR_BIT,
+ MantissaBits = numext::numeric_limits<Scalar>::digits - 1,
+ ExponentBits = TotalBits - MantissaBits - 1;
+
+ EIGEN_CONSTEXPR ScalarUI scalar_sign_mantissa_mask =
+ ~(((ScalarUI(1) << ExponentBits) - ScalarUI(1)) << MantissaBits); // ~0x7f800000
+ const Packet sign_mantissa_mask = pset1frombits<Packet>(static_cast<ScalarUI>(scalar_sign_mantissa_mask));
+ const Packet half = pset1<Packet>(Scalar(0.5));
+ const Packet zero = pzero(a);
+ const Packet normal_min = pset1<Packet>((numext::numeric_limits<Scalar>::min)()); // Minimum normal value, 2^-126
+
+ // To handle denormals, normalize by multiplying by 2^(int(MantissaBits)+1).
+ const Packet is_denormal = pcmp_lt(pabs(a), normal_min);
+ EIGEN_CONSTEXPR ScalarUI scalar_normalization_offset = ScalarUI(MantissaBits + 1); // 24
+ // The following cannot be constexpr because bfloat16(uint16_t) is not constexpr.
+ const Scalar scalar_normalization_factor = Scalar(ScalarUI(1) << int(scalar_normalization_offset)); // 2^24
+ const Packet normalization_factor = pset1<Packet>(scalar_normalization_factor);
+ const Packet normalized_a = pselect(is_denormal, pmul(a, normalization_factor), a);
+
+ // Determine exponent offset: -126 if normal, -126-24 if denormal
+ const Scalar scalar_exponent_offset = -Scalar((ScalarUI(1)<<(ExponentBits-1)) - ScalarUI(2)); // -126
+ Packet exponent_offset = pset1<Packet>(scalar_exponent_offset);
+ const Packet normalization_offset = pset1<Packet>(-Scalar(scalar_normalization_offset)); // -24
+ exponent_offset = pselect(is_denormal, padd(exponent_offset, normalization_offset), exponent_offset);
+
+ // Determine exponent and mantissa from normalized_a.
+ exponent = pfrexp_generic_get_biased_exponent(normalized_a);
+ // Zero, Inf and NaN return 'a' unmodified, exponent is zero
+ // (technically the exponent is unspecified for inf/NaN, but GCC/Clang set it to zero)
+ const Scalar scalar_non_finite_exponent = Scalar((ScalarUI(1) << ExponentBits) - ScalarUI(1)); // 255
+ const Packet non_finite_exponent = pset1<Packet>(scalar_non_finite_exponent);
+ const Packet is_zero_or_not_finite = por(pcmp_eq(a, zero), pcmp_eq(exponent, non_finite_exponent));
+ const Packet m = pselect(is_zero_or_not_finite, a, por(pand(normalized_a, sign_mantissa_mask), half));
+ exponent = pselect(is_zero_or_not_finite, zero, padd(exponent, exponent_offset));
+ return m;
+}
+
+// Safely applies ldexp, correctly handles overflows, underflows and denormals.
+// Assumes IEEE floating point format.
+template<typename Packet> EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC
+Packet pldexp_generic(const Packet& a, const Packet& exponent) {
+ // We want to return a * 2^exponent, allowing for all possible integer
+ // exponents without overflowing or underflowing in intermediate
+ // computations.
+ //
+ // Since 'a' and the output can be denormal, the maximum range of 'exponent'
+ // to consider for a float is:
+ // -255-23 -> 255+23
+ // Below -278 any finite float 'a' will become zero, and above +278 any
+ // finite float will become inf, including when 'a' is the smallest possible
+ // denormal.
+ //
+ // Unfortunately, 2^(278) cannot be represented using either one or two
+ // finite normal floats, so we must split the scale factor into at least
+ // three parts. It turns out to be faster to split 'exponent' into four
+ // factors, since [exponent>>2] is much faster to compute that [exponent/3].
+ //
+ // Set e = min(max(exponent, -278), 278);
+ // b = floor(e/4);
+ // out = ((((a * 2^(b)) * 2^(b)) * 2^(b)) * 2^(e-3*b))
+ //
+ // This will avoid any intermediate overflows and correctly handle 0, inf,
+ // NaN cases.
+ typedef typename unpacket_traits<Packet>::integer_packet PacketI;
+ typedef typename unpacket_traits<Packet>::type Scalar;
+ typedef typename unpacket_traits<PacketI>::type ScalarI;
+ static constexpr int
+ TotalBits = sizeof(Scalar) * CHAR_BIT,
+ MantissaBits = numext::numeric_limits<Scalar>::digits - 1,
+ ExponentBits = TotalBits - MantissaBits - 1;
+
+ const Packet max_exponent = pset1<Packet>(Scalar((ScalarI(1)<<ExponentBits) + ScalarI(MantissaBits - 1))); // 278
+ const PacketI bias = pset1<PacketI>((ScalarI(1)<<(ExponentBits-1)) - ScalarI(1)); // 127
+ const PacketI e = pcast<Packet, PacketI>(pmin(pmax(exponent, pnegate(max_exponent)), max_exponent));
+ PacketI b = parithmetic_shift_right<2>(e); // floor(e/4);
+ Packet c = preinterpret<Packet>(plogical_shift_left<MantissaBits>(padd(b, bias))); // 2^b
+ Packet out = pmul(pmul(pmul(a, c), c), c); // a * 2^(3b)
+ b = psub(psub(psub(e, b), b), b); // e - 3b
+ c = preinterpret<Packet>(plogical_shift_left<MantissaBits>(padd(b, bias))); // 2^(e-3*b)
+ out = pmul(out, c);
+ return out;
+}
+
+// Explicitly multiplies
+// a * (2^e)
+// clamping e to the range
+// [NumTraits<Scalar>::min_exponent()-2, NumTraits<Scalar>::max_exponent()]
+//
+// This is approx 7x faster than pldexp_impl, but will prematurely over/underflow
+// if 2^e doesn't fit into a normal floating-point Scalar.
+//
+// Assumes IEEE floating point format
+template<typename Packet>
+struct pldexp_fast_impl {
+ typedef typename unpacket_traits<Packet>::integer_packet PacketI;
+ typedef typename unpacket_traits<Packet>::type Scalar;
+ typedef typename unpacket_traits<PacketI>::type ScalarI;
+ static constexpr int
+ TotalBits = sizeof(Scalar) * CHAR_BIT,
+ MantissaBits = numext::numeric_limits<Scalar>::digits - 1,
+ ExponentBits = TotalBits - MantissaBits - 1;
+
+ static EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC
+ Packet run(const Packet& a, const Packet& exponent) {
+ const Packet bias = pset1<Packet>(Scalar((ScalarI(1)<<(ExponentBits-1)) - ScalarI(1))); // 127
+ const Packet limit = pset1<Packet>(Scalar((ScalarI(1)<<ExponentBits) - ScalarI(1))); // 255
+ // restrict biased exponent between 0 and 255 for float.
+ const PacketI e = pcast<Packet, PacketI>(pmin(pmax(padd(exponent, bias), pzero(limit)), limit)); // exponent + 127
+ // return a * (2^e)
+ return pmul(a, preinterpret<Packet>(plogical_shift_left<MantissaBits>(e)));
+ }
+};
+
+// Natural or base 2 logarithm.
+// Computes log(x) as log(2^e * m) = C*e + log(m), where the constant C =log(2)
+// and m is in the range [sqrt(1/2),sqrt(2)). In this range, the logarithm can
+// be easily approximated by a polynomial centered on m=1 for stability.
+// TODO(gonnet): Further reduce the interval allowing for lower-degree
+// polynomial interpolants -> ... -> profit!
+template <typename Packet, bool base2>
+EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+Packet plog_impl_float(const Packet _x)
+{
+ const Packet cst_1 = pset1<Packet>(1.0f);
+ const Packet cst_minus_inf = pset1frombits<Packet>(static_cast<Eigen::numext::uint32_t>(0xff800000u));
+ const Packet cst_pos_inf = pset1frombits<Packet>(static_cast<Eigen::numext::uint32_t>(0x7f800000u));
+
+ const Packet cst_cephes_SQRTHF = pset1<Packet>(0.707106781186547524f);
+ Packet e, x;
+ // extract significant in the range [0.5,1) and exponent
+ x = pfrexp(_x,e);
+
+ // part2: Shift the inputs from the range [0.5,1) to [sqrt(1/2),sqrt(2))
+ // and shift by -1. The values are then centered around 0, which improves
+ // the stability of the polynomial evaluation.
+ // if( x < SQRTHF ) {
+ // e -= 1;
+ // x = x + x - 1.0;
+ // } else { x = x - 1.0; }
+ Packet mask = pcmp_lt(x, cst_cephes_SQRTHF);
+ Packet tmp = pand(x, mask);
+ x = psub(x, cst_1);
+ e = psub(e, pand(cst_1, mask));
+ x = padd(x, tmp);
+
+ // Polynomial coefficients for rational (3,3) r(x) = p(x)/q(x)
+ // approximating log(1+x) on [sqrt(0.5)-1;sqrt(2)-1].
+ const Packet cst_p1 = pset1<Packet>(1.0000000190281136f);
+ const Packet cst_p2 = pset1<Packet>(1.0000000190281063f);
+ const Packet cst_p3 = pset1<Packet>(0.18256296349849254f);
+ const Packet cst_q1 = pset1<Packet>(1.4999999999999927f);
+ const Packet cst_q2 = pset1<Packet>(0.59923249590823520f);
+ const Packet cst_q3 = pset1<Packet>(0.049616247954120038f);
+
+ Packet p = pmadd(x, cst_p3, cst_p2);
+ p = pmadd(x, p, cst_p1);
+ p = pmul(x, p);
+ Packet q = pmadd(x, cst_q3, cst_q2);
+ q = pmadd(x, q, cst_q1);
+ q = pmadd(x, q, cst_1);
+ x = pdiv(p, q);
+
+ // Add the logarithm of the exponent back to the result of the interpolation.
+ if (base2) {
+ const Packet cst_log2e = pset1<Packet>(static_cast<float>(EIGEN_LOG2E));
+ x = pmadd(x, cst_log2e, e);
+ } else {
+ const Packet cst_ln2 = pset1<Packet>(static_cast<float>(EIGEN_LN2));
+ x = pmadd(e, cst_ln2, x);
+ }
+
+ Packet invalid_mask = pcmp_lt_or_nan(_x, pzero(_x));
+ Packet iszero_mask = pcmp_eq(_x,pzero(_x));
+ Packet pos_inf_mask = pcmp_eq(_x,cst_pos_inf);
+ // Filter out invalid inputs, i.e.:
+ // - negative arg will be NAN
+ // - 0 will be -INF
+ // - +INF will be +INF
+ return pselect(iszero_mask, cst_minus_inf,
+ por(pselect(pos_inf_mask,cst_pos_inf,x), invalid_mask));
+}
+
+template <typename Packet>
+EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+Packet plog_float(const Packet _x)
+{
+ return plog_impl_float<Packet, /* base2 */ false>(_x);
+}
+
+template <typename Packet>
+EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+Packet plog2_float(const Packet _x)
+{
+ return plog_impl_float<Packet, /* base2 */ true>(_x);
+}
+
+/* Returns the base e (2.718...) or base 2 logarithm of x.
+ * The argument is separated into its exponent and fractional parts.
+ * The logarithm of the fraction in the interval [sqrt(1/2), sqrt(2)],
+ * is approximated by
+ *
+ * log(1+x) = x - 0.5 x**2 + x**3 P(x)/Q(x).
+ *
+ * for more detail see: http://www.netlib.org/cephes/
+ */
+template <typename Packet, bool base2>
+EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+Packet plog_impl_double(const Packet _x)
+{
+ Packet x = _x;
+
+ const Packet cst_1 = pset1<Packet>(1.0);
+ const Packet cst_neg_half = pset1<Packet>(-0.5);
+ const Packet cst_minus_inf = pset1frombits<Packet>( static_cast<uint64_t>(0xfff0000000000000ull));
+ const Packet cst_pos_inf = pset1frombits<Packet>( static_cast<uint64_t>(0x7ff0000000000000ull));
+
+
+ // Polynomial Coefficients for log(1+x) = x - x**2/2 + x**3 P(x)/Q(x)
+ // 1/sqrt(2) <= x < sqrt(2)
+ const Packet cst_cephes_SQRTHF = pset1<Packet>(0.70710678118654752440E0);
+ const Packet cst_cephes_log_p0 = pset1<Packet>(1.01875663804580931796E-4);
+ const Packet cst_cephes_log_p1 = pset1<Packet>(4.97494994976747001425E-1);
+ const Packet cst_cephes_log_p2 = pset1<Packet>(4.70579119878881725854E0);
+ const Packet cst_cephes_log_p3 = pset1<Packet>(1.44989225341610930846E1);
+ const Packet cst_cephes_log_p4 = pset1<Packet>(1.79368678507819816313E1);
+ const Packet cst_cephes_log_p5 = pset1<Packet>(7.70838733755885391666E0);
+
+ const Packet cst_cephes_log_q0 = pset1<Packet>(1.0);
+ const Packet cst_cephes_log_q1 = pset1<Packet>(1.12873587189167450590E1);
+ const Packet cst_cephes_log_q2 = pset1<Packet>(4.52279145837532221105E1);
+ const Packet cst_cephes_log_q3 = pset1<Packet>(8.29875266912776603211E1);
+ const Packet cst_cephes_log_q4 = pset1<Packet>(7.11544750618563894466E1);
+ const Packet cst_cephes_log_q5 = pset1<Packet>(2.31251620126765340583E1);
+
+ Packet e;
+ // extract significant in the range [0.5,1) and exponent
+ x = pfrexp(x,e);
+
+ // Shift the inputs from the range [0.5,1) to [sqrt(1/2),sqrt(2))
+ // and shift by -1. The values are then centered around 0, which improves
+ // the stability of the polynomial evaluation.
+ // if( x < SQRTHF ) {
+ // e -= 1;
+ // x = x + x - 1.0;
+ // } else { x = x - 1.0; }
+ Packet mask = pcmp_lt(x, cst_cephes_SQRTHF);
+ Packet tmp = pand(x, mask);
+ x = psub(x, cst_1);
+ e = psub(e, pand(cst_1, mask));
+ x = padd(x, tmp);
+
+ Packet x2 = pmul(x, x);
+ Packet x3 = pmul(x2, x);
+
+ // Evaluate the polynomial approximant , probably to improve instruction-level parallelism.
+ // y = x - 0.5*x^2 + x^3 * polevl( x, P, 5 ) / p1evl( x, Q, 5 ) );
+ Packet y, y1, y_;
+ y = pmadd(cst_cephes_log_p0, x, cst_cephes_log_p1);
+ y1 = pmadd(cst_cephes_log_p3, x, cst_cephes_log_p4);
+ y = pmadd(y, x, cst_cephes_log_p2);
+ y1 = pmadd(y1, x, cst_cephes_log_p5);
+ y_ = pmadd(y, x3, y1);
+
+ y = pmadd(cst_cephes_log_q0, x, cst_cephes_log_q1);
+ y1 = pmadd(cst_cephes_log_q3, x, cst_cephes_log_q4);
+ y = pmadd(y, x, cst_cephes_log_q2);
+ y1 = pmadd(y1, x, cst_cephes_log_q5);
+ y = pmadd(y, x3, y1);
+
+ y_ = pmul(y_, x3);
+ y = pdiv(y_, y);
+
+ y = pmadd(cst_neg_half, x2, y);
+ x = padd(x, y);
+
+ // Add the logarithm of the exponent back to the result of the interpolation.
+ if (base2) {
+ const Packet cst_log2e = pset1<Packet>(static_cast<double>(EIGEN_LOG2E));
+ x = pmadd(x, cst_log2e, e);
+ } else {
+ const Packet cst_ln2 = pset1<Packet>(static_cast<double>(EIGEN_LN2));
+ x = pmadd(e, cst_ln2, x);
+ }
+
+ Packet invalid_mask = pcmp_lt_or_nan(_x, pzero(_x));
+ Packet iszero_mask = pcmp_eq(_x,pzero(_x));
+ Packet pos_inf_mask = pcmp_eq(_x,cst_pos_inf);
+ // Filter out invalid inputs, i.e.:
+ // - negative arg will be NAN
+ // - 0 will be -INF
+ // - +INF will be +INF
+ return pselect(iszero_mask, cst_minus_inf,
+ por(pselect(pos_inf_mask,cst_pos_inf,x), invalid_mask));
+}
+
+template <typename Packet>
+EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+Packet plog_double(const Packet _x)
+{
+ return plog_impl_double<Packet, /* base2 */ false>(_x);
+}
+
+template <typename Packet>
+EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+Packet plog2_double(const Packet _x)
+{
+ return plog_impl_double<Packet, /* base2 */ true>(_x);
+}
+
+/** \internal \returns log(1 + x) computed using W. Kahan's formula.
+ See: http://www.plunk.org/~hatch/rightway.php
+ */
+template<typename Packet>
+Packet generic_plog1p(const Packet& x)
+{
+ typedef typename unpacket_traits<Packet>::type ScalarType;
+ const Packet one = pset1<Packet>(ScalarType(1));
+ Packet xp1 = padd(x, one);
+ Packet small_mask = pcmp_eq(xp1, one);
+ Packet log1 = plog(xp1);
+ Packet inf_mask = pcmp_eq(xp1, log1);
+ Packet log_large = pmul(x, pdiv(log1, psub(xp1, one)));
+ return pselect(por(small_mask, inf_mask), x, log_large);
+}
+
+/** \internal \returns exp(x)-1 computed using W. Kahan's formula.
+ See: http://www.plunk.org/~hatch/rightway.php
+ */
+template<typename Packet>
+Packet generic_expm1(const Packet& x)
+{
+ typedef typename unpacket_traits<Packet>::type ScalarType;
+ const Packet one = pset1<Packet>(ScalarType(1));
+ const Packet neg_one = pset1<Packet>(ScalarType(-1));
+ Packet u = pexp(x);
+ Packet one_mask = pcmp_eq(u, one);
+ Packet u_minus_one = psub(u, one);
+ Packet neg_one_mask = pcmp_eq(u_minus_one, neg_one);
+ Packet logu = plog(u);
+ // The following comparison is to catch the case where
+ // exp(x) = +inf. It is written in this way to avoid having
+ // to form the constant +inf, which depends on the packet
+ // type.
+ Packet pos_inf_mask = pcmp_eq(logu, u);
+ Packet expm1 = pmul(u_minus_one, pdiv(x, logu));
+ expm1 = pselect(pos_inf_mask, u, expm1);
+ return pselect(one_mask,
+ x,
+ pselect(neg_one_mask,
+ neg_one,
+ expm1));
+}
+
+
+// Exponential function. Works by writing "x = m*log(2) + r" where
+// "m = floor(x/log(2)+1/2)" and "r" is the remainder. The result is then
+// "exp(x) = 2^m*exp(r)" where exp(r) is in the range [-1,1).
+// exp(r) is computed using a 6th order minimax polynomial approximation.
+template <typename Packet>
+EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+Packet pexp_float(const Packet _x)
+{
+ const Packet cst_zero = pset1<Packet>(0.0f);
+ const Packet cst_one = pset1<Packet>(1.0f);
+ const Packet cst_half = pset1<Packet>(0.5f);
+ const Packet cst_exp_hi = pset1<Packet>(88.723f);
+ const Packet cst_exp_lo = pset1<Packet>(-104.f);
+
+ const Packet cst_cephes_LOG2EF = pset1<Packet>(1.44269504088896341f);
+ const Packet cst_p2 = pset1<Packet>(0.49999988079071044921875f);
+ const Packet cst_p3 = pset1<Packet>(0.16666518151760101318359375f);
+ const Packet cst_p4 = pset1<Packet>(4.166965186595916748046875e-2f);
+ const Packet cst_p5 = pset1<Packet>(8.36894474923610687255859375e-3f);
+ const Packet cst_p6 = pset1<Packet>(1.37449637986719608306884765625e-3f);
+
+ // Clamp x.
+ Packet zero_mask = pcmp_lt(_x, cst_exp_lo);
+ Packet x = pmin(_x, cst_exp_hi);
+
+ // Express exp(x) as exp(m*ln(2) + r), start by extracting
+ // m = floor(x/ln(2) + 0.5).
+ Packet m = pfloor(pmadd(x, cst_cephes_LOG2EF, cst_half));
+
+ // Get r = x - m*ln(2). If no FMA instructions are available, m*ln(2) is
+ // subtracted out in two parts, m*C1+m*C2 = m*ln(2), to avoid accumulating
+ // truncation errors.
+ const Packet cst_cephes_exp_C1 = pset1<Packet>(-0.693359375f);
+ const Packet cst_cephes_exp_C2 = pset1<Packet>(2.12194440e-4f);
+ Packet r = pmadd(m, cst_cephes_exp_C1, x);
+ r = pmadd(m, cst_cephes_exp_C2, r);
+
+ // Evaluate the 6th order polynomial approximation to exp(r)
+ // with r in the interval [-ln(2)/2;ln(2)/2].
+ const Packet r2 = pmul(r, r);
+ Packet p_even = pmadd(r2, cst_p6, cst_p4);
+ const Packet p_odd = pmadd(r2, cst_p5, cst_p3);
+ p_even = pmadd(r2, p_even, cst_p2);
+ const Packet p_low = padd(r, cst_one);
+ Packet y = pmadd(r, p_odd, p_even);
+ y = pmadd(r2, y, p_low);
+
+ // Return 2^m * exp(r).
+ // TODO: replace pldexp with faster implementation since y in [-1, 1).
+ return pselect(zero_mask, cst_zero, pmax(pldexp(y,m), _x));
+}
+
+template <typename Packet>
+EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+Packet pexp_double(const Packet _x)
+{
+ Packet x = _x;
+ const Packet cst_zero = pset1<Packet>(0.0);
+ const Packet cst_1 = pset1<Packet>(1.0);
+ const Packet cst_2 = pset1<Packet>(2.0);
+ const Packet cst_half = pset1<Packet>(0.5);
+
+ const Packet cst_exp_hi = pset1<Packet>(709.784);
+ const Packet cst_exp_lo = pset1<Packet>(-709.784);
+
+ const Packet cst_cephes_LOG2EF = pset1<Packet>(1.4426950408889634073599);
+ const Packet cst_cephes_exp_p0 = pset1<Packet>(1.26177193074810590878e-4);
+ const Packet cst_cephes_exp_p1 = pset1<Packet>(3.02994407707441961300e-2);
+ const Packet cst_cephes_exp_p2 = pset1<Packet>(9.99999999999999999910e-1);
+ const Packet cst_cephes_exp_q0 = pset1<Packet>(3.00198505138664455042e-6);
+ const Packet cst_cephes_exp_q1 = pset1<Packet>(2.52448340349684104192e-3);
+ const Packet cst_cephes_exp_q2 = pset1<Packet>(2.27265548208155028766e-1);
+ const Packet cst_cephes_exp_q3 = pset1<Packet>(2.00000000000000000009e0);
+ const Packet cst_cephes_exp_C1 = pset1<Packet>(0.693145751953125);
+ const Packet cst_cephes_exp_C2 = pset1<Packet>(1.42860682030941723212e-6);
+
+ Packet tmp, fx;
+
+ // clamp x
+ Packet zero_mask = pcmp_lt(_x, cst_exp_lo);
+ x = pmin(x, cst_exp_hi);
+ // Express exp(x) as exp(g + n*log(2)).
+ fx = pmadd(cst_cephes_LOG2EF, x, cst_half);
+
+ // Get the integer modulus of log(2), i.e. the "n" described above.
+ fx = pfloor(fx);
+
+ // Get the remainder modulo log(2), i.e. the "g" described above. Subtract
+ // n*log(2) out in two steps, i.e. n*C1 + n*C2, C1+C2=log2 to get the last
+ // digits right.
+ tmp = pmul(fx, cst_cephes_exp_C1);
+ Packet z = pmul(fx, cst_cephes_exp_C2);
+ x = psub(x, tmp);
+ x = psub(x, z);
+
+ Packet x2 = pmul(x, x);
+
+ // Evaluate the numerator polynomial of the rational interpolant.
+ Packet px = cst_cephes_exp_p0;
+ px = pmadd(px, x2, cst_cephes_exp_p1);
+ px = pmadd(px, x2, cst_cephes_exp_p2);
+ px = pmul(px, x);
+
+ // Evaluate the denominator polynomial of the rational interpolant.
+ Packet qx = cst_cephes_exp_q0;
+ qx = pmadd(qx, x2, cst_cephes_exp_q1);
+ qx = pmadd(qx, x2, cst_cephes_exp_q2);
+ qx = pmadd(qx, x2, cst_cephes_exp_q3);
+
+ // I don't really get this bit, copied from the SSE2 routines, so...
+ // TODO(gonnet): Figure out what is going on here, perhaps find a better
+ // rational interpolant?
+ x = pdiv(px, psub(qx, px));
+ x = pmadd(cst_2, x, cst_1);
+
+ // Construct the result 2^n * exp(g) = e * x. The max is used to catch
+ // non-finite values in the input.
+ // TODO: replace pldexp with faster implementation since x in [-1, 1).
+ return pselect(zero_mask, cst_zero, pmax(pldexp(x,fx), _x));
+}
+
+// The following code is inspired by the following stack-overflow answer:
+// https://stackoverflow.com/questions/30463616/payne-hanek-algorithm-implementation-in-c/30465751#30465751
+// It has been largely optimized:
+// - By-pass calls to frexp.
+// - Aligned loads of required 96 bits of 2/pi. This is accomplished by
+// (1) balancing the mantissa and exponent to the required bits of 2/pi are
+// aligned on 8-bits, and (2) replicating the storage of the bits of 2/pi.
+// - Avoid a branch in rounding and extraction of the remaining fractional part.
+// Overall, I measured a speed up higher than x2 on x86-64.
+inline float trig_reduce_huge (float xf, Eigen::numext::int32_t *quadrant)
+{
+ using Eigen::numext::int32_t;
+ using Eigen::numext::uint32_t;
+ using Eigen::numext::int64_t;
+ using Eigen::numext::uint64_t;
+
+ const double pio2_62 = 3.4061215800865545e-19; // pi/2 * 2^-62
+ const uint64_t zero_dot_five = uint64_t(1) << 61; // 0.5 in 2.62-bit fixed-point format
+
+ // 192 bits of 2/pi for Payne-Hanek reduction
+ // Bits are introduced by packet of 8 to enable aligned reads.
+ static const uint32_t two_over_pi [] =
+ {
+ 0x00000028, 0x000028be, 0x0028be60, 0x28be60db,
+ 0xbe60db93, 0x60db9391, 0xdb939105, 0x9391054a,
+ 0x91054a7f, 0x054a7f09, 0x4a7f09d5, 0x7f09d5f4,
+ 0x09d5f47d, 0xd5f47d4d, 0xf47d4d37, 0x7d4d3770,
+ 0x4d377036, 0x377036d8, 0x7036d8a5, 0x36d8a566,
+ 0xd8a5664f, 0xa5664f10, 0x664f10e4, 0x4f10e410,
+ 0x10e41000, 0xe4100000
+ };
+
+ uint32_t xi = numext::bit_cast<uint32_t>(xf);
+ // Below, -118 = -126 + 8.
+ // -126 is to get the exponent,
+ // +8 is to enable alignment of 2/pi's bits on 8 bits.
+ // This is possible because the fractional part of x as only 24 meaningful bits.
+ uint32_t e = (xi >> 23) - 118;
+ // Extract the mantissa and shift it to align it wrt the exponent
+ xi = ((xi & 0x007fffffu)| 0x00800000u) << (e & 0x7);
+
+ uint32_t i = e >> 3;
+ uint32_t twoopi_1 = two_over_pi[i-1];
+ uint32_t twoopi_2 = two_over_pi[i+3];
+ uint32_t twoopi_3 = two_over_pi[i+7];
+
+ // Compute x * 2/pi in 2.62-bit fixed-point format.
+ uint64_t p;
+ p = uint64_t(xi) * twoopi_3;
+ p = uint64_t(xi) * twoopi_2 + (p >> 32);
+ p = (uint64_t(xi * twoopi_1) << 32) + p;
+
+ // Round to nearest: add 0.5 and extract integral part.
+ uint64_t q = (p + zero_dot_five) >> 62;
+ *quadrant = int(q);
+ // Now it remains to compute "r = x - q*pi/2" with high accuracy,
+ // since we have p=x/(pi/2) with high accuracy, we can more efficiently compute r as:
+ // r = (p-q)*pi/2,
+ // where the product can be be carried out with sufficient accuracy using double precision.
+ p -= q<<62;
+ return float(double(int64_t(p)) * pio2_62);
+}
+
+template<bool ComputeSine,typename Packet>
+EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+#if EIGEN_COMP_GNUC_STRICT
+__attribute__((optimize("-fno-unsafe-math-optimizations")))
+#endif
+Packet psincos_float(const Packet& _x)
+{
+ typedef typename unpacket_traits<Packet>::integer_packet PacketI;
+
+ const Packet cst_2oPI = pset1<Packet>(0.636619746685028076171875f); // 2/PI
+ const Packet cst_rounding_magic = pset1<Packet>(12582912); // 2^23 for rounding
+ const PacketI csti_1 = pset1<PacketI>(1);
+ const Packet cst_sign_mask = pset1frombits<Packet>(static_cast<Eigen::numext::uint32_t>(0x80000000u));
+
+ Packet x = pabs(_x);
+
+ // Scale x by 2/Pi to find x's octant.
+ Packet y = pmul(x, cst_2oPI);
+
+ // Rounding trick to find nearest integer:
+ Packet y_round = padd(y, cst_rounding_magic);
+ EIGEN_OPTIMIZATION_BARRIER(y_round)
+ PacketI y_int = preinterpret<PacketI>(y_round); // last 23 digits represent integer (if abs(x)<2^24)
+ y = psub(y_round, cst_rounding_magic); // nearest integer to x * (2/pi)
+
+ // Subtract y * Pi/2 to reduce x to the interval -Pi/4 <= x <= +Pi/4
+ // using "Extended precision modular arithmetic"
+ #if defined(EIGEN_HAS_SINGLE_INSTRUCTION_MADD)
+ // This version requires true FMA for high accuracy
+ // It provides a max error of 1ULP up to (with absolute_error < 5.9605e-08):
+ const float huge_th = ComputeSine ? 117435.992f : 71476.0625f;
+ x = pmadd(y, pset1<Packet>(-1.57079601287841796875f), x);
+ x = pmadd(y, pset1<Packet>(-3.1391647326017846353352069854736328125e-07f), x);
+ x = pmadd(y, pset1<Packet>(-5.390302529957764765544681040410068817436695098876953125e-15f), x);
+ #else
+ // Without true FMA, the previous set of coefficients maintain 1ULP accuracy
+ // up to x<15.7 (for sin), but accuracy is immediately lost for x>15.7.
+ // We thus use one more iteration to maintain 2ULPs up to reasonably large inputs.
+
+ // The following set of coefficients maintain 1ULP up to 9.43 and 14.16 for sin and cos respectively.
+ // and 2 ULP up to:
+ const float huge_th = ComputeSine ? 25966.f : 18838.f;
+ x = pmadd(y, pset1<Packet>(-1.5703125), x); // = 0xbfc90000
+ EIGEN_OPTIMIZATION_BARRIER(x)
+ x = pmadd(y, pset1<Packet>(-0.000483989715576171875), x); // = 0xb9fdc000
+ EIGEN_OPTIMIZATION_BARRIER(x)
+ x = pmadd(y, pset1<Packet>(1.62865035235881805419921875e-07), x); // = 0x342ee000
+ x = pmadd(y, pset1<Packet>(5.5644315544167710640977020375430583953857421875e-11), x); // = 0x2e74b9ee
+
+ // For the record, the following set of coefficients maintain 2ULP up
+ // to a slightly larger range:
+ // const float huge_th = ComputeSine ? 51981.f : 39086.125f;
+ // but it slightly fails to maintain 1ULP for two values of sin below pi.
+ // x = pmadd(y, pset1<Packet>(-3.140625/2.), x);
+ // x = pmadd(y, pset1<Packet>(-0.00048351287841796875), x);
+ // x = pmadd(y, pset1<Packet>(-3.13855707645416259765625e-07), x);
+ // x = pmadd(y, pset1<Packet>(-6.0771006282767103812147979624569416046142578125e-11), x);
+
+ // For the record, with only 3 iterations it is possible to maintain
+ // 1 ULP up to 3PI (maybe more) and 2ULP up to 255.
+ // The coefficients are: 0xbfc90f80, 0xb7354480, 0x2e74b9ee
+ #endif
+
+ if(predux_any(pcmp_le(pset1<Packet>(huge_th),pabs(_x))))
+ {
+ const int PacketSize = unpacket_traits<Packet>::size;
+ EIGEN_ALIGN_TO_BOUNDARY(sizeof(Packet)) float vals[PacketSize];
+ EIGEN_ALIGN_TO_BOUNDARY(sizeof(Packet)) float x_cpy[PacketSize];
+ EIGEN_ALIGN_TO_BOUNDARY(sizeof(Packet)) Eigen::numext::int32_t y_int2[PacketSize];
+ pstoreu(vals, pabs(_x));
+ pstoreu(x_cpy, x);
+ pstoreu(y_int2, y_int);
+ for(int k=0; k<PacketSize;++k)
+ {
+ float val = vals[k];
+ if(val>=huge_th && (numext::isfinite)(val))
+ x_cpy[k] = trig_reduce_huge(val,&y_int2[k]);
+ }
+ x = ploadu<Packet>(x_cpy);
+ y_int = ploadu<PacketI>(y_int2);
+ }
+
+ // Compute the sign to apply to the polynomial.
+ // sin: sign = second_bit(y_int) xor signbit(_x)
+ // cos: sign = second_bit(y_int+1)
+ Packet sign_bit = ComputeSine ? pxor(_x, preinterpret<Packet>(plogical_shift_left<30>(y_int)))
+ : preinterpret<Packet>(plogical_shift_left<30>(padd(y_int,csti_1)));
+ sign_bit = pand(sign_bit, cst_sign_mask); // clear all but left most bit
+
+ // Get the polynomial selection mask from the second bit of y_int
+ // We'll calculate both (sin and cos) polynomials and then select from the two.
+ Packet poly_mask = preinterpret<Packet>(pcmp_eq(pand(y_int, csti_1), pzero(y_int)));
+
+ Packet x2 = pmul(x,x);
+
+ // Evaluate the cos(x) polynomial. (-Pi/4 <= x <= Pi/4)
+ Packet y1 = pset1<Packet>(2.4372266125283204019069671630859375e-05f);
+ y1 = pmadd(y1, x2, pset1<Packet>(-0.00138865201734006404876708984375f ));
+ y1 = pmadd(y1, x2, pset1<Packet>(0.041666619479656219482421875f ));
+ y1 = pmadd(y1, x2, pset1<Packet>(-0.5f));
+ y1 = pmadd(y1, x2, pset1<Packet>(1.f));
+
+ // Evaluate the sin(x) polynomial. (Pi/4 <= x <= Pi/4)
+ // octave/matlab code to compute those coefficients:
+ // x = (0:0.0001:pi/4)';
+ // A = [x.^3 x.^5 x.^7];
+ // w = ((1.-(x/(pi/4)).^2).^5)*2000+1; # weights trading relative accuracy
+ // c = (A'*diag(w)*A)\(A'*diag(w)*(sin(x)-x)); # weighted LS, linear coeff forced to 1
+ // printf('%.64f\n %.64f\n%.64f\n', c(3), c(2), c(1))
+ //
+ Packet y2 = pset1<Packet>(-0.0001959234114083702898469196984621021329076029360294342041015625f);
+ y2 = pmadd(y2, x2, pset1<Packet>( 0.0083326873655616851693794799871284340042620897293090820312500000f));
+ y2 = pmadd(y2, x2, pset1<Packet>(-0.1666666203982298255503735617821803316473960876464843750000000000f));
+ y2 = pmul(y2, x2);
+ y2 = pmadd(y2, x, x);
+
+ // Select the correct result from the two polynomials.
+ y = ComputeSine ? pselect(poly_mask,y2,y1)
+ : pselect(poly_mask,y1,y2);
+
+ // Update the sign and filter huge inputs
+ return pxor(y, sign_bit);
+}
+
+template<typename Packet>
+EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+Packet psin_float(const Packet& x)
+{
+ return psincos_float<true>(x);
+}
+
+template<typename Packet>
+EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+Packet pcos_float(const Packet& x)
+{
+ return psincos_float<false>(x);
+}
+
+// Generic implementation of acos(x).
+template<typename Packet>
+EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+Packet pacos_float(const Packet& x_in) {
+ typedef typename unpacket_traits<Packet>::type Scalar;
+ static_assert(std::is_same<Scalar, float>::value, "Scalar type must be float");
+
+ const Packet cst_one = pset1<Packet>(Scalar(1));
+ const Packet cst_pi = pset1<Packet>(Scalar(EIGEN_PI));
+ const Packet p6 = pset1<Packet>(Scalar(2.26911413483321666717529296875e-3));
+ const Packet p5 = pset1<Packet>(Scalar(-1.1063250713050365447998046875e-2));
+ const Packet p4 = pset1<Packet>(Scalar(2.680264413356781005859375e-2));
+ const Packet p3 = pset1<Packet>(Scalar(-4.87488098442554473876953125e-2));
+ const Packet p2 = pset1<Packet>(Scalar(8.874166011810302734375e-2));
+ const Packet p1 = pset1<Packet>(Scalar(-0.2145837843418121337890625));
+ const Packet p0 = pset1<Packet>(Scalar(1.57079613208770751953125));
+
+ // For x in [0:1], we approximate acos(x)/sqrt(1-x), which is a smooth
+ // function, by a 6'th order polynomial.
+ // For x in [-1:0) we use that acos(-x) = pi - acos(x).
+ const Packet neg_mask = pcmp_lt(x_in, pzero(x_in));
+ Packet x = pabs(x_in);
+ const Packet invalid_mask = pcmp_lt(pset1<Packet>(1.0f), x);
+
+ // Evaluate the polynomial using Horner's rule:
+ // P(x) = p0 + x * (p1 + x * (p2 + ... (p5 + x * p6)) ... ) .
+ // We evaluate even and odd terms independently to increase
+ // instruction level parallelism.
+ Packet x2 = pmul(x_in,x_in);
+ Packet p_even = pmadd(p6, x2, p4);
+ Packet p_odd = pmadd(p5, x2, p3);
+ p_even = pmadd(p_even, x2, p2);
+ p_odd = pmadd(p_odd, x2, p1);
+ p_even = pmadd(p_even, x2, p0);
+ Packet p = pmadd(p_odd, x, p_even);
+
+ // The polynomial approximates acos(x)/sqrt(1-x), so
+ // multiply by sqrt(1-x) to get acos(x).
+ Packet denom = psqrt(psub(cst_one, x));
+ Packet result = pmul(denom, p);
+
+ // Undo mapping for negative arguments.
+ result = pselect(neg_mask, psub(cst_pi, result), result);
+ // Return NaN for arguments outside [-1:1].
+ return pselect(invalid_mask,
+ pset1<Packet>(std::numeric_limits<float>::quiet_NaN()),
+ result);
+}
+
+// Generic implementation of asin(x).
+template<typename Packet>
+EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+Packet pasin_float(const Packet& x_in) {
+ typedef typename unpacket_traits<Packet>::type Scalar;
+ static_assert(std::is_same<Scalar, float>::value, "Scalar type must be float");
+
+ // For |x| < 0.5 approximate asin(x)/x by an 8th order polynomial with
+ // even terms only.
+ const Packet p9 = pset1<Packet>(Scalar(5.08838854730129241943359375e-2f));
+ const Packet p7 = pset1<Packet>(Scalar(3.95139865577220916748046875e-2f));
+ const Packet p5 = pset1<Packet>(Scalar(7.550220191478729248046875e-2f));
+ const Packet p3 = pset1<Packet>(Scalar(0.16664917767047882080078125f));
+ const Packet p1 = pset1<Packet>(Scalar(1.00000011920928955078125f));
+
+ const Packet neg_mask = pcmp_lt(x_in, pzero(x_in));
+ Packet x = pabs(x_in);
+ const Packet invalid_mask = pcmp_lt(pset1<Packet>(1.0f), x);
+ // For arguments |x| > 0.5, we map x back to [0:0.5] using
+ // the transformation x_large = sqrt(0.5*(1-x)), and use the
+ // identity
+ // asin(x) = pi/2 - 2 * asin( sqrt( 0.5 * (1 - x)))
+ const Packet cst_half = pset1<Packet>(Scalar(0.5f));
+ const Packet cst_two = pset1<Packet>(Scalar(2));
+ Packet x_large = psqrt(pnmadd(cst_half, x, cst_half));
+ const Packet large_mask = pcmp_lt(cst_half, x);
+ x = pselect(large_mask, x_large, x);
+
+ // Compute polynomial.
+ // x * (p1 + x^2*(p3 + x^2*(p5 + x^2*(p7 + x^2*p9))))
+ Packet x2 = pmul(x, x);
+ Packet p = pmadd(p9, x2, p7);
+ p = pmadd(p, x2, p5);
+ p = pmadd(p, x2, p3);
+ p = pmadd(p, x2, p1);
+ p = pmul(p, x);
+
+ constexpr float kPiOverTwo = static_cast<float>(EIGEN_PI/2);
+ Packet p_large = pnmadd(cst_two, p, pset1<Packet>(kPiOverTwo));
+ p = pselect(large_mask, p_large, p);
+ // Flip the sign for negative arguments.
+ p = pselect(neg_mask, pnegate(p), p);
+
+ // Return NaN for arguments outside [-1:1].
+ return pselect(invalid_mask, pset1<Packet>(std::numeric_limits<float>::quiet_NaN()), p);
+}
+
+// Computes elementwise atan(x) for x in [-1:1] with 2 ulp accuracy.
+template<typename Packet>
+EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+Packet patan_reduced_float(const Packet& x) {
+ const Packet q0 = pset1<Packet>(-0.3333314359188079833984375f);
+ const Packet q2 = pset1<Packet>(0.19993579387664794921875f);
+ const Packet q4 = pset1<Packet>(-0.14209578931331634521484375f);
+ const Packet q6 = pset1<Packet>(0.1066047251224517822265625f);
+ const Packet q8 = pset1<Packet>(-7.5408883392810821533203125e-2f);
+ const Packet q10 = pset1<Packet>(4.3082617223262786865234375e-2f);
+ const Packet q12 = pset1<Packet>(-1.62907354533672332763671875e-2f);
+ const Packet q14 = pset1<Packet>(2.90188402868807315826416015625e-3f);
+
+ // Approximate atan(x) by a polynomial of the form
+ // P(x) = x + x^3 * Q(x^2),
+ // where Q(x^2) is a 7th order polynomial in x^2.
+ // We evaluate even and odd terms in x^2 in parallel
+ // to take advantage of instruction level parallelism
+ // and hardware with multiple FMA units.
+ const Packet x2 = pmul(x, x);
+ const Packet x4 = pmul(x2, x2);
+ Packet q_odd = pmadd(q14, x4, q10);
+ Packet q_even = pmadd(q12, x4, q8);
+ q_odd = pmadd(q_odd, x4, q6);
+ q_even = pmadd(q_even, x4, q4);
+ q_odd = pmadd(q_odd, x4, q2);
+ q_even = pmadd(q_even, x4, q0);
+ const Packet q = pmadd(q_odd, x2, q_even);
+ return pmadd(q, pmul(x, x2), x);
+}
+
+template<typename Packet>
+EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+Packet patan_float(const Packet& x_in) {
+ typedef typename unpacket_traits<Packet>::type Scalar;
+ static_assert(std::is_same<Scalar, float>::value, "Scalar type must be float");
+
+ const Packet cst_one = pset1<Packet>(1.0f);
+ constexpr float kPiOverTwo = static_cast<float>(EIGEN_PI/2);
+
+ // "Large": For |x| > 1, use atan(1/x) = sign(x)*pi/2 - atan(x).
+ // "Small": For |x| <= 1, approximate atan(x) directly by a polynomial
+ // calculated using Sollya.
+ const Packet neg_mask = pcmp_lt(x_in, pzero(x_in));
+ const Packet large_mask = pcmp_lt(cst_one, pabs(x_in));
+ const Packet large_shift = pselect(neg_mask, pset1<Packet>(-kPiOverTwo), pset1<Packet>(kPiOverTwo));
+ const Packet x = pselect(large_mask, preciprocal(x_in), x_in);
+ const Packet p = patan_reduced_float(x);
+
+ // Apply transformations according to the range reduction masks.
+ return pselect(large_mask, psub(large_shift, p), p);
+}
+
+// Computes elementwise atan(x) for x in [-tan(pi/8):tan(pi/8)]
+// with 2 ulp accuracy.
+template <typename Packet>
+EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet
+patan_reduced_double(const Packet& x) {
+ const Packet q0 =
+ pset1<Packet>(-0.33333333333330028569463365784031338989734649658203);
+ const Packet q2 =
+ pset1<Packet>(0.199999999990664090177006073645316064357757568359375);
+ const Packet q4 =
+ pset1<Packet>(-0.142857141937123677255527809393242932856082916259766);
+ const Packet q6 =
+ pset1<Packet>(0.111111065991039953404495577160560060292482376098633);
+ const Packet q8 =
+ pset1<Packet>(-9.0907812986129224452902519715280504897236824035645e-2);
+ const Packet q10 =
+ pset1<Packet>(7.6900542950704739442180368769186316058039665222168e-2);
+ const Packet q12 =
+ pset1<Packet>(-6.6410112986494976294871150912513257935643196105957e-2);
+ const Packet q14 =
+ pset1<Packet>(5.6920144995467943094258345126945641823112964630127e-2);
+ const Packet q16 =
+ pset1<Packet>(-4.3577020814990513608577771265117917209863662719727e-2);
+ const Packet q18 =
+ pset1<Packet>(2.1244050233624342527427586446719942614436149597168e-2);
+
+ // Approximate atan(x) on [0:tan(pi/8)] by a polynomial of the form
+ // P(x) = x + x^3 * Q(x^2),
+ // where Q(x^2) is a 9th order polynomial in x^2.
+ // We evaluate even and odd terms in x^2 in parallel
+ // to take advantage of instruction level parallelism
+ // and hardware with multiple FMA units.
+ const Packet x2 = pmul(x, x);
+ const Packet x4 = pmul(x2, x2);
+ Packet q_odd = pmadd(q18, x4, q14);
+ Packet q_even = pmadd(q16, x4, q12);
+ q_odd = pmadd(q_odd, x4, q10);
+ q_even = pmadd(q_even, x4, q8);
+ q_odd = pmadd(q_odd, x4, q6);
+ q_even = pmadd(q_even, x4, q4);
+ q_odd = pmadd(q_odd, x4, q2);
+ q_even = pmadd(q_even, x4, q0);
+ const Packet p = pmadd(q_odd, x2, q_even);
+ return pmadd(p, pmul(x, x2), x);
+}
+
+template<typename Packet>
+EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+Packet patan_double(const Packet& x_in) {
+ typedef typename unpacket_traits<Packet>::type Scalar;
+ static_assert(std::is_same<Scalar, double>::value, "Scalar type must be double");
+
+ const Packet cst_one = pset1<Packet>(1.0);
+ constexpr double kPiOverTwo = static_cast<double>(EIGEN_PI / 2);
+ const Packet cst_pi_over_two = pset1<Packet>(kPiOverTwo);
+ constexpr double kPiOverFour = static_cast<double>(EIGEN_PI / 4);
+ const Packet cst_pi_over_four = pset1<Packet>(kPiOverFour);
+ const Packet cst_large = pset1<Packet>(2.4142135623730950488016887); // tan(3*pi/8);
+ const Packet cst_medium = pset1<Packet>(0.4142135623730950488016887); // tan(pi/8);
+
+ const Packet neg_mask = pcmp_lt(x_in, pzero(x_in));
+ Packet x = pabs(x_in);
+
+ // Use the same range reduction strategy (to [0:tan(pi/8)]) as the
+ // Cephes library:
+ // "Large": For x >= tan(3*pi/8), use atan(1/x) = pi/2 - atan(x).
+ // "Medium": For x in [tan(pi/8) : tan(3*pi/8)),
+ // use atan(x) = pi/4 + atan((x-1)/(x+1)).
+ // "Small": For x < tan(pi/8), approximate atan(x) directly by a polynomial
+ // calculated using Sollya.
+ const Packet large_mask = pcmp_lt(cst_large, x);
+ x = pselect(large_mask, preciprocal(x), x);
+ const Packet medium_mask = pandnot(pcmp_lt(cst_medium, x), large_mask);
+ x = pselect(medium_mask, pdiv(psub(x, cst_one), padd(x, cst_one)), x);
+
+ // Compute approximation of p ~= atan(x') where x' is the argument reduced to
+ // [0:tan(pi/8)].
+ Packet p = patan_reduced_double(x);
+
+ // Apply transformations according to the range reduction masks.
+ p = pselect(large_mask, psub(cst_pi_over_two, p), p);
+ p = pselect(medium_mask, padd(cst_pi_over_four, p), p);
+ return pselect(neg_mask, pnegate(p), p);
+}
+
+template<typename Packet>
+EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+Packet pdiv_complex(const Packet& x, const Packet& y) {
+ typedef typename unpacket_traits<Packet>::as_real RealPacket;
+ // In the following we annotate the code for the case where the inputs
+ // are a pair length-2 SIMD vectors representing a single pair of complex
+ // numbers x = a + i*b, y = c + i*d.
+ const RealPacket y_abs = pabs(y.v); // |c|, |d|
+ const RealPacket y_abs_flip = pcplxflip(Packet(y_abs)).v; // |d|, |c|
+ const RealPacket y_max = pmax(y_abs, y_abs_flip); // max(|c|, |d|), max(|c|, |d|)
+ const RealPacket y_scaled = pdiv(y.v, y_max); // c / max(|c|, |d|), d / max(|c|, |d|)
+ // Compute scaled denominator.
+ const RealPacket y_scaled_sq = pmul(y_scaled, y_scaled); // c'**2, d'**2
+ const RealPacket denom = padd(y_scaled_sq, pcplxflip(Packet(y_scaled_sq)).v);
+ Packet result_scaled = pmul(x, pconj(Packet(y_scaled))); // a * c' + b * d', -a * d + b * c
+ // Divide elementwise by denom.
+ result_scaled = Packet(pdiv(result_scaled.v, denom));
+ // Rescale result
+ return Packet(pdiv(result_scaled.v, y_max));
+}
+
+template<typename Packet>
+EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+Packet psqrt_complex(const Packet& a) {
+ typedef typename unpacket_traits<Packet>::type Scalar;
+ typedef typename Scalar::value_type RealScalar;
+ typedef typename unpacket_traits<Packet>::as_real RealPacket;
+
+ // Computes the principal sqrt of the complex numbers in the input.
+ //
+ // For example, for packets containing 2 complex numbers stored in interleaved format
+ // a = [a0, a1] = [x0, y0, x1, y1],
+ // where x0 = real(a0), y0 = imag(a0) etc., this function returns
+ // b = [b0, b1] = [u0, v0, u1, v1],
+ // such that b0^2 = a0, b1^2 = a1.
+ //
+ // To derive the formula for the complex square roots, let's consider the equation for
+ // a single complex square root of the number x + i*y. We want to find real numbers
+ // u and v such that
+ // (u + i*v)^2 = x + i*y <=>
+ // u^2 - v^2 + i*2*u*v = x + i*v.
+ // By equating the real and imaginary parts we get:
+ // u^2 - v^2 = x
+ // 2*u*v = y.
+ //
+ // For x >= 0, this has the numerically stable solution
+ // u = sqrt(0.5 * (x + sqrt(x^2 + y^2)))
+ // v = 0.5 * (y / u)
+ // and for x < 0,
+ // v = sign(y) * sqrt(0.5 * (-x + sqrt(x^2 + y^2)))
+ // u = 0.5 * (y / v)
+ //
+ // To avoid unnecessary over- and underflow, we compute sqrt(x^2 + y^2) as
+ // l = max(|x|, |y|) * sqrt(1 + (min(|x|, |y|) / max(|x|, |y|))^2) ,
+
+ // In the following, without lack of generality, we have annotated the code, assuming
+ // that the input is a packet of 2 complex numbers.
+ //
+ // Step 1. Compute l = [l0, l0, l1, l1], where
+ // l0 = sqrt(x0^2 + y0^2), l1 = sqrt(x1^2 + y1^2)
+ // To avoid over- and underflow, we use the stable formula for each hypotenuse
+ // l0 = (min0 == 0 ? max0 : max0 * sqrt(1 + (min0/max0)**2)),
+ // where max0 = max(|x0|, |y0|), min0 = min(|x0|, |y0|), and similarly for l1.
+
+ RealPacket a_abs = pabs(a.v); // [|x0|, |y0|, |x1|, |y1|]
+ RealPacket a_abs_flip = pcplxflip(Packet(a_abs)).v; // [|y0|, |x0|, |y1|, |x1|]
+ RealPacket a_max = pmax(a_abs, a_abs_flip);
+ RealPacket a_min = pmin(a_abs, a_abs_flip);
+ RealPacket a_min_zero_mask = pcmp_eq(a_min, pzero(a_min));
+ RealPacket a_max_zero_mask = pcmp_eq(a_max, pzero(a_max));
+ RealPacket r = pdiv(a_min, a_max);
+ const RealPacket cst_one = pset1<RealPacket>(RealScalar(1));
+ RealPacket l = pmul(a_max, psqrt(padd(cst_one, pmul(r, r)))); // [l0, l0, l1, l1]
+ // Set l to a_max if a_min is zero.
+ l = pselect(a_min_zero_mask, a_max, l);
+
+ // Step 2. Compute [rho0, *, rho1, *], where
+ // rho0 = sqrt(0.5 * (l0 + |x0|)), rho1 = sqrt(0.5 * (l1 + |x1|))
+ // We don't care about the imaginary parts computed here. They will be overwritten later.
+ const RealPacket cst_half = pset1<RealPacket>(RealScalar(0.5));
+ Packet rho;
+ rho.v = psqrt(pmul(cst_half, padd(a_abs, l)));
+
+ // Step 3. Compute [rho0, eta0, rho1, eta1], where
+ // eta0 = (y0 / l0) / 2, and eta1 = (y1 / l1) / 2.
+ // set eta = 0 of input is 0 + i0.
+ RealPacket eta = pandnot(pmul(cst_half, pdiv(a.v, pcplxflip(rho).v)), a_max_zero_mask);
+ RealPacket real_mask = peven_mask(a.v);
+ Packet positive_real_result;
+ // Compute result for inputs with positive real part.
+ positive_real_result.v = pselect(real_mask, rho.v, eta);
+
+ // Step 4. Compute solution for inputs with negative real part:
+ // [|eta0|, sign(y0)*rho0, |eta1|, sign(y1)*rho1]
+ const RealPacket cst_imag_sign_mask =
+ pset1<Packet>(Scalar(RealScalar(0.0), RealScalar(-0.0))).v;
+ RealPacket imag_signs = pand(a.v, cst_imag_sign_mask);
+ Packet negative_real_result;
+ // Notice that rho is positive, so taking it's absolute value is a noop.
+ negative_real_result.v = por(pabs(pcplxflip(positive_real_result).v), imag_signs);
+
+ // Step 5. Select solution branch based on the sign of the real parts.
+ Packet negative_real_mask;
+ negative_real_mask.v = pcmp_lt(pand(real_mask, a.v), pzero(a.v));
+ negative_real_mask.v = por(negative_real_mask.v, pcplxflip(negative_real_mask).v);
+ Packet result = pselect(negative_real_mask, negative_real_result, positive_real_result);
+
+ // Step 6. Handle special cases for infinities:
+ // * If z is (x,+∞), the result is (+∞,+∞) even if x is NaN
+ // * If z is (x,-∞), the result is (+∞,-∞) even if x is NaN
+ // * If z is (-∞,y), the result is (0*|y|,+∞) for finite or NaN y
+ // * If z is (+∞,y), the result is (+∞,0*|y|) for finite or NaN y
+ const RealPacket cst_pos_inf = pset1<RealPacket>(NumTraits<RealScalar>::infinity());
+ Packet is_inf;
+ is_inf.v = pcmp_eq(a_abs, cst_pos_inf);
+ Packet is_real_inf;
+ is_real_inf.v = pand(is_inf.v, real_mask);
+ is_real_inf = por(is_real_inf, pcplxflip(is_real_inf));
+ // prepare packet of (+∞,0*|y|) or (0*|y|,+∞), depending on the sign of the infinite real part.
+ Packet real_inf_result;
+ real_inf_result.v = pmul(a_abs, pset1<Packet>(Scalar(RealScalar(1.0), RealScalar(0.0))).v);
+ real_inf_result.v = pselect(negative_real_mask.v, pcplxflip(real_inf_result).v, real_inf_result.v);
+ // prepare packet of (+∞,+∞) or (+∞,-∞), depending on the sign of the infinite imaginary part.
+ Packet is_imag_inf;
+ is_imag_inf.v = pandnot(is_inf.v, real_mask);
+ is_imag_inf = por(is_imag_inf, pcplxflip(is_imag_inf));
+ Packet imag_inf_result;
+ imag_inf_result.v = por(pand(cst_pos_inf, real_mask), pandnot(a.v, real_mask));
+
+ return pselect(is_imag_inf, imag_inf_result,
+ pselect(is_real_inf, real_inf_result,result));
+}
+
+
+template <typename Packet>
+struct psign_impl<
+ Packet,
+ std::enable_if_t<
+ !NumTraits<typename unpacket_traits<Packet>::type>::IsComplex &&
+ !NumTraits<typename unpacket_traits<Packet>::type>::IsInteger>> {
+ static EIGEN_DEVICE_FUNC inline Packet run(const Packet& a) {
+ using Scalar = typename unpacket_traits<Packet>::type;
+ const Packet cst_one = pset1<Packet>(Scalar(1));
+ const Packet cst_minus_one = pset1<Packet>(Scalar(-1));
+ const Packet cst_zero = pzero(a);
+
+ const Packet not_nan_mask = pcmp_eq(a, a);
+ const Packet positive_mask = pcmp_lt(cst_zero, a);
+ const Packet positive = pand(positive_mask, cst_one);
+ const Packet negative_mask = pcmp_lt(a, cst_zero);
+ const Packet negative = pand(negative_mask, cst_minus_one);
+
+ return pselect(not_nan_mask, por(positive, negative), a);
+ }
+};
+
+template <typename Packet>
+struct psign_impl<
+ Packet, std::enable_if_t<
+ !NumTraits<typename unpacket_traits<Packet>::type>::IsComplex &&
+ NumTraits<typename unpacket_traits<Packet>::type>::IsSigned &&
+ NumTraits<typename unpacket_traits<Packet>::type>::IsInteger>> {
+ static EIGEN_DEVICE_FUNC inline Packet run(const Packet& a) {
+ using Scalar = typename unpacket_traits<Packet>::type;
+ const Packet cst_one = pset1<Packet>(Scalar(1));
+ const Packet cst_minus_one = pset1<Packet>(Scalar(-1));
+ const Packet cst_zero = pzero(a);
+
+ const Packet positive_mask = pcmp_lt(cst_zero, a);
+ const Packet positive = pand(positive_mask, cst_one);
+ const Packet negative_mask = pcmp_lt(a, cst_zero);
+ const Packet negative = pand(negative_mask, cst_minus_one);
+
+ return por(positive, negative);
+ }
+};
+
+template <typename Packet>
+struct psign_impl<Packet, std::enable_if_t<!NumTraits<typename unpacket_traits<Packet>::type>::IsComplex &&
+ !NumTraits<typename unpacket_traits<Packet>::type>::IsSigned &&
+ NumTraits<typename unpacket_traits<Packet>::type>::IsInteger>> {
+ static EIGEN_DEVICE_FUNC inline Packet run(const Packet& a) {
+ using Scalar = typename unpacket_traits<Packet>::type;
+ const Packet cst_one = pset1<Packet>(Scalar(1));
+ const Packet cst_zero = pzero(a);
+
+ const Packet zero_mask = pcmp_eq(cst_zero, a);
+ return pandnot(cst_one, zero_mask);
+ }
+};
+
+// \internal \returns the the sign of a complex number z, defined as z / abs(z).
+template <typename Packet>
+struct psign_impl<Packet, std::enable_if_t<NumTraits<typename unpacket_traits<Packet>::type>::IsComplex &&
+ unpacket_traits<Packet>::vectorizable>> {
+ static EIGEN_DEVICE_FUNC inline Packet run(const Packet& a) {
+ typedef typename unpacket_traits<Packet>::type Scalar;
+ typedef typename Scalar::value_type RealScalar;
+ typedef typename unpacket_traits<Packet>::as_real RealPacket;
+
+ // Step 1. Compute (for each element z = x + i*y in a)
+ // l = abs(z) = sqrt(x^2 + y^2).
+ // To avoid over- and underflow, we use the stable formula for each hypotenuse
+ // l = (zmin == 0 ? zmax : zmax * sqrt(1 + (zmin/zmax)**2)),
+ // where zmax = max(|x|, |y|), zmin = min(|x|, |y|),
+ RealPacket a_abs = pabs(a.v);
+ RealPacket a_abs_flip = pcplxflip(Packet(a_abs)).v;
+ RealPacket a_max = pmax(a_abs, a_abs_flip);
+ RealPacket a_min = pmin(a_abs, a_abs_flip);
+ RealPacket a_min_zero_mask = pcmp_eq(a_min, pzero(a_min));
+ RealPacket a_max_zero_mask = pcmp_eq(a_max, pzero(a_max));
+ RealPacket r = pdiv(a_min, a_max);
+ const RealPacket cst_one = pset1<RealPacket>(RealScalar(1));
+ RealPacket l = pmul(a_max, psqrt(padd(cst_one, pmul(r, r)))); // [l0, l0, l1, l1]
+ // Set l to a_max if a_min is zero, since the roundtrip sqrt(a_max^2) may be
+ // lossy.
+ l = pselect(a_min_zero_mask, a_max, l);
+ // Step 2 compute a / abs(a).
+ RealPacket sign_as_real = pandnot(pdiv(a.v, l), a_max_zero_mask);
+ Packet sign;
+ sign.v = sign_as_real;
+ return sign;
+ }
+};
+
+// TODO(rmlarsen): The following set of utilities for double word arithmetic
+// should perhaps be refactored as a separate file, since it would be generally
+// useful for special function implementation etc. Writing the algorithms in
+// terms if a double word type would also make the code more readable.
+
+// This function splits x into the nearest integer n and fractional part r,
+// such that x = n + r holds exactly.
+template<typename Packet>
+EIGEN_STRONG_INLINE
+void absolute_split(const Packet& x, Packet& n, Packet& r) {
+ n = pround(x);
+ r = psub(x, n);
+}
+
+// This function computes the sum {s, r}, such that x + y = s_hi + s_lo
+// holds exactly, and s_hi = fl(x+y), if |x| >= |y|.
+template<typename Packet>
+EIGEN_STRONG_INLINE
+void fast_twosum(const Packet& x, const Packet& y, Packet& s_hi, Packet& s_lo) {
+ s_hi = padd(x, y);
+ const Packet t = psub(s_hi, x);
+ s_lo = psub(y, t);
+}
+
+#ifdef EIGEN_HAS_SINGLE_INSTRUCTION_MADD
+// This function implements the extended precision product of
+// a pair of floating point numbers. Given {x, y}, it computes the pair
+// {p_hi, p_lo} such that x * y = p_hi + p_lo holds exactly and
+// p_hi = fl(x * y).
+template<typename Packet>
+EIGEN_STRONG_INLINE
+void twoprod(const Packet& x, const Packet& y,
+ Packet& p_hi, Packet& p_lo) {
+ p_hi = pmul(x, y);
+ p_lo = pmadd(x, y, pnegate(p_hi));
+}
+
+#else
+
+// This function implements the Veltkamp splitting. Given a floating point
+// number x it returns the pair {x_hi, x_lo} such that x_hi + x_lo = x holds
+// exactly and that half of the significant of x fits in x_hi.
+// This is Algorithm 3 from Jean-Michel Muller, "Elementary Functions",
+// 3rd edition, Birkh\"auser, 2016.
+template<typename Packet>
+EIGEN_STRONG_INLINE
+void veltkamp_splitting(const Packet& x, Packet& x_hi, Packet& x_lo) {
+ typedef typename unpacket_traits<Packet>::type Scalar;
+ EIGEN_CONSTEXPR int shift = (NumTraits<Scalar>::digits() + 1) / 2;
+ const Scalar shift_scale = Scalar(uint64_t(1) << shift); // Scalar constructor not necessarily constexpr.
+ const Packet gamma = pmul(pset1<Packet>(shift_scale + Scalar(1)), x);
+ Packet rho = psub(x, gamma);
+ x_hi = padd(rho, gamma);
+ x_lo = psub(x, x_hi);
+}
+
+// This function implements Dekker's algorithm for products x * y.
+// Given floating point numbers {x, y} computes the pair
+// {p_hi, p_lo} such that x * y = p_hi + p_lo holds exactly and
+// p_hi = fl(x * y).
+template<typename Packet>
+EIGEN_STRONG_INLINE
+void twoprod(const Packet& x, const Packet& y,
+ Packet& p_hi, Packet& p_lo) {
+ Packet x_hi, x_lo, y_hi, y_lo;
+ veltkamp_splitting(x, x_hi, x_lo);
+ veltkamp_splitting(y, y_hi, y_lo);
+
+ p_hi = pmul(x, y);
+ p_lo = pmadd(x_hi, y_hi, pnegate(p_hi));
+ p_lo = pmadd(x_hi, y_lo, p_lo);
+ p_lo = pmadd(x_lo, y_hi, p_lo);
+ p_lo = pmadd(x_lo, y_lo, p_lo);
+}
+
+#endif // EIGEN_HAS_SINGLE_INSTRUCTION_MADD
+
+
+// This function implements Dekker's algorithm for the addition
+// of two double word numbers represented by {x_hi, x_lo} and {y_hi, y_lo}.
+// It returns the result as a pair {s_hi, s_lo} such that
+// x_hi + x_lo + y_hi + y_lo = s_hi + s_lo holds exactly.
+// This is Algorithm 5 from Jean-Michel Muller, "Elementary Functions",
+// 3rd edition, Birkh\"auser, 2016.
+template<typename Packet>
+EIGEN_STRONG_INLINE
+ void twosum(const Packet& x_hi, const Packet& x_lo,
+ const Packet& y_hi, const Packet& y_lo,
+ Packet& s_hi, Packet& s_lo) {
+ const Packet x_greater_mask = pcmp_lt(pabs(y_hi), pabs(x_hi));
+ Packet r_hi_1, r_lo_1;
+ fast_twosum(x_hi, y_hi,r_hi_1, r_lo_1);
+ Packet r_hi_2, r_lo_2;
+ fast_twosum(y_hi, x_hi,r_hi_2, r_lo_2);
+ const Packet r_hi = pselect(x_greater_mask, r_hi_1, r_hi_2);
+
+ const Packet s1 = padd(padd(y_lo, r_lo_1), x_lo);
+ const Packet s2 = padd(padd(x_lo, r_lo_2), y_lo);
+ const Packet s = pselect(x_greater_mask, s1, s2);
+
+ fast_twosum(r_hi, s, s_hi, s_lo);
+}
+
+// This is a version of twosum for double word numbers,
+// which assumes that |x_hi| >= |y_hi|.
+template<typename Packet>
+EIGEN_STRONG_INLINE
+ void fast_twosum(const Packet& x_hi, const Packet& x_lo,
+ const Packet& y_hi, const Packet& y_lo,
+ Packet& s_hi, Packet& s_lo) {
+ Packet r_hi, r_lo;
+ fast_twosum(x_hi, y_hi, r_hi, r_lo);
+ const Packet s = padd(padd(y_lo, r_lo), x_lo);
+ fast_twosum(r_hi, s, s_hi, s_lo);
+}
+
+// This is a version of twosum for adding a floating point number x to
+// double word number {y_hi, y_lo} number, with the assumption
+// that |x| >= |y_hi|.
+template<typename Packet>
+EIGEN_STRONG_INLINE
+void fast_twosum(const Packet& x,
+ const Packet& y_hi, const Packet& y_lo,
+ Packet& s_hi, Packet& s_lo) {
+ Packet r_hi, r_lo;
+ fast_twosum(x, y_hi, r_hi, r_lo);
+ const Packet s = padd(y_lo, r_lo);
+ fast_twosum(r_hi, s, s_hi, s_lo);
+}
+
+// This function implements the multiplication of a double word
+// number represented by {x_hi, x_lo} by a floating point number y.
+// It returns the result as a pair {p_hi, p_lo} such that
+// (x_hi + x_lo) * y = p_hi + p_lo hold with a relative error
+// of less than 2*2^{-2p}, where p is the number of significand bit
+// in the floating point type.
+// This is Algorithm 7 from Jean-Michel Muller, "Elementary Functions",
+// 3rd edition, Birkh\"auser, 2016.
+template<typename Packet>
+EIGEN_STRONG_INLINE
+void twoprod(const Packet& x_hi, const Packet& x_lo, const Packet& y,
+ Packet& p_hi, Packet& p_lo) {
+ Packet c_hi, c_lo1;
+ twoprod(x_hi, y, c_hi, c_lo1);
+ const Packet c_lo2 = pmul(x_lo, y);
+ Packet t_hi, t_lo1;
+ fast_twosum(c_hi, c_lo2, t_hi, t_lo1);
+ const Packet t_lo2 = padd(t_lo1, c_lo1);
+ fast_twosum(t_hi, t_lo2, p_hi, p_lo);
+}
+
+// This function implements the multiplication of two double word
+// numbers represented by {x_hi, x_lo} and {y_hi, y_lo}.
+// It returns the result as a pair {p_hi, p_lo} such that
+// (x_hi + x_lo) * (y_hi + y_lo) = p_hi + p_lo holds with a relative error
+// of less than 2*2^{-2p}, where p is the number of significand bit
+// in the floating point type.
+template<typename Packet>
+EIGEN_STRONG_INLINE
+void twoprod(const Packet& x_hi, const Packet& x_lo,
+ const Packet& y_hi, const Packet& y_lo,
+ Packet& p_hi, Packet& p_lo) {
+ Packet p_hi_hi, p_hi_lo;
+ twoprod(x_hi, x_lo, y_hi, p_hi_hi, p_hi_lo);
+ Packet p_lo_hi, p_lo_lo;
+ twoprod(x_hi, x_lo, y_lo, p_lo_hi, p_lo_lo);
+ fast_twosum(p_hi_hi, p_hi_lo, p_lo_hi, p_lo_lo, p_hi, p_lo);
+}
+
+// This function implements the division of double word {x_hi, x_lo}
+// by float y. This is Algorithm 15 from "Tight and rigourous error bounds
+// for basic building blocks of double-word arithmetic", Joldes, Muller, & Popescu,
+// 2017. https://hal.archives-ouvertes.fr/hal-01351529
+template <typename Packet>
+void doubleword_div_fp(const Packet& x_hi, const Packet& x_lo, const Packet& y,
+ Packet& z_hi, Packet& z_lo) {
+ const Packet t_hi = pdiv(x_hi, y);
+ Packet pi_hi, pi_lo;
+ twoprod(t_hi, y, pi_hi, pi_lo);
+ const Packet delta_hi = psub(x_hi, pi_hi);
+ const Packet delta_t = psub(delta_hi, pi_lo);
+ const Packet delta = padd(delta_t, x_lo);
+ const Packet t_lo = pdiv(delta, y);
+ fast_twosum(t_hi, t_lo, z_hi, z_lo);
+}
+
+// This function computes log2(x) and returns the result as a double word.
+template <typename Scalar>
+struct accurate_log2 {
+ template <typename Packet>
+ EIGEN_STRONG_INLINE
+ void operator()(const Packet& x, Packet& log2_x_hi, Packet& log2_x_lo) {
+ log2_x_hi = plog2(x);
+ log2_x_lo = pzero(x);
+ }
+};
+
+// This specialization uses a more accurate algorithm to compute log2(x) for
+// floats in [1/sqrt(2);sqrt(2)] with a relative accuracy of ~6.42e-10.
+// This additional accuracy is needed to counter the error-magnification
+// inherent in multiplying by a potentially large exponent in pow(x,y).
+// The minimax polynomial used was calculated using the Sollya tool.
+// See sollya.org.
+template <>
+struct accurate_log2<float> {
+ template <typename Packet>
+ EIGEN_STRONG_INLINE
+ void operator()(const Packet& z, Packet& log2_x_hi, Packet& log2_x_lo) {
+ // The function log(1+x)/x is approximated in the interval
+ // [1/sqrt(2)-1;sqrt(2)-1] by a degree 10 polynomial of the form
+ // Q(x) = (C0 + x * (C1 + x * (C2 + x * (C3 + x * P(x))))),
+ // where the degree 6 polynomial P(x) is evaluated in single precision,
+ // while the remaining 4 terms of Q(x), as well as the final multiplication by x
+ // to reconstruct log(1+x) are evaluated in extra precision using
+ // double word arithmetic. C0 through C3 are extra precise constants
+ // stored as double words.
+ //
+ // The polynomial coefficients were calculated using Sollya commands:
+ // > n = 10;
+ // > f = log2(1+x)/x;
+ // > interval = [sqrt(0.5)-1;sqrt(2)-1];
+ // > p = fpminimax(f,n,[|double,double,double,double,single...|],interval,relative,floating);
+
+ const Packet p6 = pset1<Packet>( 9.703654795885e-2f);
+ const Packet p5 = pset1<Packet>(-0.1690667718648f);
+ const Packet p4 = pset1<Packet>( 0.1720575392246f);
+ const Packet p3 = pset1<Packet>(-0.1789081543684f);
+ const Packet p2 = pset1<Packet>( 0.2050433009862f);
+ const Packet p1 = pset1<Packet>(-0.2404672354459f);
+ const Packet p0 = pset1<Packet>( 0.2885761857032f);
+
+ const Packet C3_hi = pset1<Packet>(-0.360674142838f);
+ const Packet C3_lo = pset1<Packet>(-6.13283912543e-09f);
+ const Packet C2_hi = pset1<Packet>(0.480897903442f);
+ const Packet C2_lo = pset1<Packet>(-1.44861207474e-08f);
+ const Packet C1_hi = pset1<Packet>(-0.721347510815f);
+ const Packet C1_lo = pset1<Packet>(-4.84483164698e-09f);
+ const Packet C0_hi = pset1<Packet>(1.44269502163f);
+ const Packet C0_lo = pset1<Packet>(2.01711713999e-08f);
+ const Packet one = pset1<Packet>(1.0f);
+
+ const Packet x = psub(z, one);
+ // Evaluate P(x) in working precision.
+ // We evaluate it in multiple parts to improve instruction level
+ // parallelism.
+ Packet x2 = pmul(x,x);
+ Packet p_even = pmadd(p6, x2, p4);
+ p_even = pmadd(p_even, x2, p2);
+ p_even = pmadd(p_even, x2, p0);
+ Packet p_odd = pmadd(p5, x2, p3);
+ p_odd = pmadd(p_odd, x2, p1);
+ Packet p = pmadd(p_odd, x, p_even);
+
+ // Now evaluate the low-order tems of Q(x) in double word precision.
+ // In the following, due to the alternating signs and the fact that
+ // |x| < sqrt(2)-1, we can assume that |C*_hi| >= q_i, and use
+ // fast_twosum instead of the slower twosum.
+ Packet q_hi, q_lo;
+ Packet t_hi, t_lo;
+ // C3 + x * p(x)
+ twoprod(p, x, t_hi, t_lo);
+ fast_twosum(C3_hi, C3_lo, t_hi, t_lo, q_hi, q_lo);
+ // C2 + x * p(x)
+ twoprod(q_hi, q_lo, x, t_hi, t_lo);
+ fast_twosum(C2_hi, C2_lo, t_hi, t_lo, q_hi, q_lo);
+ // C1 + x * p(x)
+ twoprod(q_hi, q_lo, x, t_hi, t_lo);
+ fast_twosum(C1_hi, C1_lo, t_hi, t_lo, q_hi, q_lo);
+ // C0 + x * p(x)
+ twoprod(q_hi, q_lo, x, t_hi, t_lo);
+ fast_twosum(C0_hi, C0_lo, t_hi, t_lo, q_hi, q_lo);
+
+ // log(z) ~= x * Q(x)
+ twoprod(q_hi, q_lo, x, log2_x_hi, log2_x_lo);
+ }
+};
+
+// This specialization uses a more accurate algorithm to compute log2(x) for
+// floats in [1/sqrt(2);sqrt(2)] with a relative accuracy of ~1.27e-18.
+// This additional accuracy is needed to counter the error-magnification
+// inherent in multiplying by a potentially large exponent in pow(x,y).
+// The minimax polynomial used was calculated using the Sollya tool.
+// See sollya.org.
+
+template <>
+struct accurate_log2<double> {
+ template <typename Packet>
+ EIGEN_STRONG_INLINE
+ void operator()(const Packet& x, Packet& log2_x_hi, Packet& log2_x_lo) {
+ // We use a transformation of variables:
+ // r = c * (x-1) / (x+1),
+ // such that
+ // log2(x) = log2((1 + r/c) / (1 - r/c)) = f(r).
+ // The function f(r) can be approximated well using an odd polynomial
+ // of the form
+ // P(r) = ((Q(r^2) * r^2 + C) * r^2 + 1) * r,
+ // For the implementation of log2<double> here, Q is of degree 6 with
+ // coefficient represented in working precision (double), while C is a
+ // constant represented in extra precision as a double word to achieve
+ // full accuracy.
+ //
+ // The polynomial coefficients were computed by the Sollya script:
+ //
+ // c = 2 / log(2);
+ // trans = c * (x-1)/(x+1);
+ // itrans = (1+x/c)/(1-x/c);
+ // interval=[trans(sqrt(0.5)); trans(sqrt(2))];
+ // print(interval);
+ // f = log2(itrans(x));
+ // p=fpminimax(f,[|1,3,5,7,9,11,13,15,17|],[|1,DD,double...|],interval,relative,floating);
+ const Packet q12 = pset1<Packet>(2.87074255468000586e-9);
+ const Packet q10 = pset1<Packet>(2.38957980901884082e-8);
+ const Packet q8 = pset1<Packet>(2.31032094540014656e-7);
+ const Packet q6 = pset1<Packet>(2.27279857398537278e-6);
+ const Packet q4 = pset1<Packet>(2.31271023278625638e-5);
+ const Packet q2 = pset1<Packet>(2.47556738444535513e-4);
+ const Packet q0 = pset1<Packet>(2.88543873228900172e-3);
+ const Packet C_hi = pset1<Packet>(0.0400377511598501157);
+ const Packet C_lo = pset1<Packet>(-4.77726582251425391e-19);
+ const Packet one = pset1<Packet>(1.0);
+
+ const Packet cst_2_log2e_hi = pset1<Packet>(2.88539008177792677);
+ const Packet cst_2_log2e_lo = pset1<Packet>(4.07660016854549667e-17);
+ // c * (x - 1)
+ Packet t_hi, t_lo;
+ // t = c * (x-1)
+ twoprod(cst_2_log2e_hi, cst_2_log2e_lo, psub(x, one), t_hi, t_lo);
+ // r = c * (x-1) / (x+1),
+ Packet r_hi, r_lo;
+ doubleword_div_fp(t_hi, t_lo, padd(x, one), r_hi, r_lo);
+
+ // r2 = r * r
+ Packet r2_hi, r2_lo;
+ twoprod(r_hi, r_lo, r_hi, r_lo, r2_hi, r2_lo);
+ // r4 = r2 * r2
+ Packet r4_hi, r4_lo;
+ twoprod(r2_hi, r2_lo, r2_hi, r2_lo, r4_hi, r4_lo);
+
+ // Evaluate Q(r^2) in working precision. We evaluate it in two parts
+ // (even and odd in r^2) to improve instruction level parallelism.
+ Packet q_even = pmadd(q12, r4_hi, q8);
+ Packet q_odd = pmadd(q10, r4_hi, q6);
+ q_even = pmadd(q_even, r4_hi, q4);
+ q_odd = pmadd(q_odd, r4_hi, q2);
+ q_even = pmadd(q_even, r4_hi, q0);
+ Packet q = pmadd(q_odd, r2_hi, q_even);
+
+ // Now evaluate the low order terms of P(x) in double word precision.
+ // In the following, due to the increasing magnitude of the coefficients
+ // and r being constrained to [-0.5, 0.5] we can use fast_twosum instead
+ // of the slower twosum.
+ // Q(r^2) * r^2
+ Packet p_hi, p_lo;
+ twoprod(r2_hi, r2_lo, q, p_hi, p_lo);
+ // Q(r^2) * r^2 + C
+ Packet p1_hi, p1_lo;
+ fast_twosum(C_hi, C_lo, p_hi, p_lo, p1_hi, p1_lo);
+ // (Q(r^2) * r^2 + C) * r^2
+ Packet p2_hi, p2_lo;
+ twoprod(r2_hi, r2_lo, p1_hi, p1_lo, p2_hi, p2_lo);
+ // ((Q(r^2) * r^2 + C) * r^2 + 1)
+ Packet p3_hi, p3_lo;
+ fast_twosum(one, p2_hi, p2_lo, p3_hi, p3_lo);
+
+ // log(z) ~= ((Q(r^2) * r^2 + C) * r^2 + 1) * r
+ twoprod(p3_hi, p3_lo, r_hi, r_lo, log2_x_hi, log2_x_lo);
+ }
+};
+
+// This function computes exp2(x) (i.e. 2**x).
+template <typename Scalar>
+struct fast_accurate_exp2 {
+ template <typename Packet>
+ EIGEN_STRONG_INLINE
+ Packet operator()(const Packet& x) {
+ // TODO(rmlarsen): Add a pexp2 packetop.
+ return pexp(pmul(pset1<Packet>(Scalar(EIGEN_LN2)), x));
+ }
+};
+
+// This specialization uses a faster algorithm to compute exp2(x) for floats
+// in [-0.5;0.5] with a relative accuracy of 1 ulp.
+// The minimax polynomial used was calculated using the Sollya tool.
+// See sollya.org.
+template <>
+struct fast_accurate_exp2<float> {
+ template <typename Packet>
+ EIGEN_STRONG_INLINE
+ Packet operator()(const Packet& x) {
+ // This function approximates exp2(x) by a degree 6 polynomial of the form
+ // Q(x) = 1 + x * (C + x * P(x)), where the degree 4 polynomial P(x) is evaluated in
+ // single precision, and the remaining steps are evaluated with extra precision using
+ // double word arithmetic. C is an extra precise constant stored as a double word.
+ //
+ // The polynomial coefficients were calculated using Sollya commands:
+ // > n = 6;
+ // > f = 2^x;
+ // > interval = [-0.5;0.5];
+ // > p = fpminimax(f,n,[|1,double,single...|],interval,relative,floating);
+
+ const Packet p4 = pset1<Packet>(1.539513905e-4f);
+ const Packet p3 = pset1<Packet>(1.340007293e-3f);
+ const Packet p2 = pset1<Packet>(9.618283249e-3f);
+ const Packet p1 = pset1<Packet>(5.550328270e-2f);
+ const Packet p0 = pset1<Packet>(0.2402264923f);
+
+ const Packet C_hi = pset1<Packet>(0.6931471825f);
+ const Packet C_lo = pset1<Packet>(2.36836577e-08f);
+ const Packet one = pset1<Packet>(1.0f);
+
+ // Evaluate P(x) in working precision.
+ // We evaluate even and odd parts of the polynomial separately
+ // to gain some instruction level parallelism.
+ Packet x2 = pmul(x,x);
+ Packet p_even = pmadd(p4, x2, p2);
+ Packet p_odd = pmadd(p3, x2, p1);
+ p_even = pmadd(p_even, x2, p0);
+ Packet p = pmadd(p_odd, x, p_even);
+
+ // Evaluate the remaining terms of Q(x) with extra precision using
+ // double word arithmetic.
+ Packet p_hi, p_lo;
+ // x * p(x)
+ twoprod(p, x, p_hi, p_lo);
+ // C + x * p(x)
+ Packet q1_hi, q1_lo;
+ twosum(p_hi, p_lo, C_hi, C_lo, q1_hi, q1_lo);
+ // x * (C + x * p(x))
+ Packet q2_hi, q2_lo;
+ twoprod(q1_hi, q1_lo, x, q2_hi, q2_lo);
+ // 1 + x * (C + x * p(x))
+ Packet q3_hi, q3_lo;
+ // Since |q2_hi| <= sqrt(2)-1 < 1, we can use fast_twosum
+ // for adding it to unity here.
+ fast_twosum(one, q2_hi, q3_hi, q3_lo);
+ return padd(q3_hi, padd(q2_lo, q3_lo));
+ }
+};
+
+// in [-0.5;0.5] with a relative accuracy of 1 ulp.
+// The minimax polynomial used was calculated using the Sollya tool.
+// See sollya.org.
+template <>
+struct fast_accurate_exp2<double> {
+ template <typename Packet>
+ EIGEN_STRONG_INLINE
+ Packet operator()(const Packet& x) {
+ // This function approximates exp2(x) by a degree 10 polynomial of the form
+ // Q(x) = 1 + x * (C + x * P(x)), where the degree 8 polynomial P(x) is evaluated in
+ // single precision, and the remaining steps are evaluated with extra precision using
+ // double word arithmetic. C is an extra precise constant stored as a double word.
+ //
+ // The polynomial coefficients were calculated using Sollya commands:
+ // > n = 11;
+ // > f = 2^x;
+ // > interval = [-0.5;0.5];
+ // > p = fpminimax(f,n,[|1,DD,double...|],interval,relative,floating);
+
+ const Packet p9 = pset1<Packet>(4.431642109085495276e-10);
+ const Packet p8 = pset1<Packet>(7.073829923303358410e-9);
+ const Packet p7 = pset1<Packet>(1.017822306737031311e-7);
+ const Packet p6 = pset1<Packet>(1.321543498017646657e-6);
+ const Packet p5 = pset1<Packet>(1.525273342728892877e-5);
+ const Packet p4 = pset1<Packet>(1.540353045780084423e-4);
+ const Packet p3 = pset1<Packet>(1.333355814685869807e-3);
+ const Packet p2 = pset1<Packet>(9.618129107593478832e-3);
+ const Packet p1 = pset1<Packet>(5.550410866481961247e-2);
+ const Packet p0 = pset1<Packet>(0.240226506959101332);
+ const Packet C_hi = pset1<Packet>(0.693147180559945286);
+ const Packet C_lo = pset1<Packet>(4.81927865669806721e-17);
+ const Packet one = pset1<Packet>(1.0);
+
+ // Evaluate P(x) in working precision.
+ // We evaluate even and odd parts of the polynomial separately
+ // to gain some instruction level parallelism.
+ Packet x2 = pmul(x,x);
+ Packet p_even = pmadd(p8, x2, p6);
+ Packet p_odd = pmadd(p9, x2, p7);
+ p_even = pmadd(p_even, x2, p4);
+ p_odd = pmadd(p_odd, x2, p5);
+ p_even = pmadd(p_even, x2, p2);
+ p_odd = pmadd(p_odd, x2, p3);
+ p_even = pmadd(p_even, x2, p0);
+ p_odd = pmadd(p_odd, x2, p1);
+ Packet p = pmadd(p_odd, x, p_even);
+
+ // Evaluate the remaining terms of Q(x) with extra precision using
+ // double word arithmetic.
+ Packet p_hi, p_lo;
+ // x * p(x)
+ twoprod(p, x, p_hi, p_lo);
+ // C + x * p(x)
+ Packet q1_hi, q1_lo;
+ twosum(p_hi, p_lo, C_hi, C_lo, q1_hi, q1_lo);
+ // x * (C + x * p(x))
+ Packet q2_hi, q2_lo;
+ twoprod(q1_hi, q1_lo, x, q2_hi, q2_lo);
+ // 1 + x * (C + x * p(x))
+ Packet q3_hi, q3_lo;
+ // Since |q2_hi| <= sqrt(2)-1 < 1, we can use fast_twosum
+ // for adding it to unity here.
+ fast_twosum(one, q2_hi, q3_hi, q3_lo);
+ return padd(q3_hi, padd(q2_lo, q3_lo));
+ }
+};
+
+// This function implements the non-trivial case of pow(x,y) where x is
+// positive and y is (possibly) non-integer.
+// Formally, pow(x,y) = exp2(y * log2(x)), where exp2(x) is shorthand for 2^x.
+// TODO(rmlarsen): We should probably add this as a packet up 'ppow', to make it
+// easier to specialize or turn off for specific types and/or backends.x
+template <typename Packet>
+EIGEN_STRONG_INLINE Packet generic_pow_impl(const Packet& x, const Packet& y) {
+ typedef typename unpacket_traits<Packet>::type Scalar;
+ // Split x into exponent e_x and mantissa m_x.
+ Packet e_x;
+ Packet m_x = pfrexp(x, e_x);
+
+ // Adjust m_x to lie in [1/sqrt(2):sqrt(2)] to minimize absolute error in log2(m_x).
+ EIGEN_CONSTEXPR Scalar sqrt_half = Scalar(0.70710678118654752440);
+ const Packet m_x_scale_mask = pcmp_lt(m_x, pset1<Packet>(sqrt_half));
+ m_x = pselect(m_x_scale_mask, pmul(pset1<Packet>(Scalar(2)), m_x), m_x);
+ e_x = pselect(m_x_scale_mask, psub(e_x, pset1<Packet>(Scalar(1))), e_x);
+
+ // Compute log2(m_x) with 6 extra bits of accuracy.
+ Packet rx_hi, rx_lo;
+ accurate_log2<Scalar>()(m_x, rx_hi, rx_lo);
+
+ // Compute the two terms {y * e_x, y * r_x} in f = y * log2(x) with doubled
+ // precision using double word arithmetic.
+ Packet f1_hi, f1_lo, f2_hi, f2_lo;
+ twoprod(e_x, y, f1_hi, f1_lo);
+ twoprod(rx_hi, rx_lo, y, f2_hi, f2_lo);
+ // Sum the two terms in f using double word arithmetic. We know
+ // that |e_x| > |log2(m_x)|, except for the case where e_x==0.
+ // This means that we can use fast_twosum(f1,f2).
+ // In the case e_x == 0, e_x * y = f1 = 0, so we don't lose any
+ // accuracy by violating the assumption of fast_twosum, because
+ // it's a no-op.
+ Packet f_hi, f_lo;
+ fast_twosum(f1_hi, f1_lo, f2_hi, f2_lo, f_hi, f_lo);
+
+ // Split f into integer and fractional parts.
+ Packet n_z, r_z;
+ absolute_split(f_hi, n_z, r_z);
+ r_z = padd(r_z, f_lo);
+ Packet n_r;
+ absolute_split(r_z, n_r, r_z);
+ n_z = padd(n_z, n_r);
+
+ // We now have an accurate split of f = n_z + r_z and can compute
+ // x^y = 2**{n_z + r_z) = exp2(r_z) * 2**{n_z}.
+ // Since r_z is in [-0.5;0.5], we compute the first factor to high accuracy
+ // using a specialized algorithm. Multiplication by the second factor can
+ // be done exactly using pldexp(), since it is an integer power of 2.
+ const Packet e_r = fast_accurate_exp2<Scalar>()(r_z);
+ return pldexp(e_r, n_z);
+}
+
+// Generic implementation of pow(x,y).
+template <typename Packet>
+EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet generic_pow(const Packet& x, const Packet& y) {
+ typedef typename unpacket_traits<Packet>::type Scalar;
+
+ const Packet cst_pos_inf = pset1<Packet>(NumTraits<Scalar>::infinity());
+ const Packet cst_neg_inf = pset1<Packet>(-NumTraits<Scalar>::infinity());
+ const Packet cst_zero = pset1<Packet>(Scalar(0));
+ const Packet cst_one = pset1<Packet>(Scalar(1));
+ const Packet cst_nan = pset1<Packet>(NumTraits<Scalar>::quiet_NaN());
+
+ const Packet abs_x = pabs(x);
+ // Predicates for sign and magnitude of x.
+ const Packet abs_x_is_zero = pcmp_eq(abs_x, cst_zero);
+ const Packet x_has_signbit = pcmp_eq(por(pand(x, cst_neg_inf), cst_pos_inf), cst_neg_inf);
+ const Packet x_is_neg = pandnot(x_has_signbit, abs_x_is_zero);
+ const Packet x_is_neg_zero = pand(x_has_signbit, abs_x_is_zero);
+ const Packet abs_x_is_inf = pcmp_eq(abs_x, cst_pos_inf);
+ const Packet abs_x_is_one = pcmp_eq(abs_x, cst_one);
+ const Packet abs_x_is_gt_one = pcmp_lt(cst_one, abs_x);
+ const Packet abs_x_is_lt_one = pcmp_lt(abs_x, cst_one);
+ const Packet x_is_one = pandnot(abs_x_is_one, x_is_neg);
+ const Packet x_is_neg_one = pand(abs_x_is_one, x_is_neg);
+ const Packet x_is_nan = pandnot(ptrue(x), pcmp_eq(x, x));
+
+ // Predicates for sign and magnitude of y.
+ const Packet abs_y = pabs(y);
+ const Packet y_is_one = pcmp_eq(y, cst_one);
+ const Packet abs_y_is_zero = pcmp_eq(abs_y, cst_zero);
+ const Packet y_is_neg = pcmp_lt(y, cst_zero);
+ const Packet y_is_pos = pandnot(ptrue(y), por(abs_y_is_zero, y_is_neg));
+ const Packet y_is_nan = pandnot(ptrue(y), pcmp_eq(y, y));
+ const Packet abs_y_is_inf = pcmp_eq(abs_y, cst_pos_inf);
+ EIGEN_CONSTEXPR Scalar huge_exponent =
+ (NumTraits<Scalar>::max_exponent() * Scalar(EIGEN_LN2)) / NumTraits<Scalar>::epsilon();
+ const Packet abs_y_is_huge = pcmp_le(pset1<Packet>(huge_exponent), pabs(y));
+
+ // Predicates for whether y is integer and/or even.
+ const Packet y_is_int = pcmp_eq(pfloor(y), y);
+ const Packet y_div_2 = pmul(y, pset1<Packet>(Scalar(0.5)));
+ const Packet y_is_even = pcmp_eq(pround(y_div_2), y_div_2);
+
+ // Predicates encoding special cases for the value of pow(x,y)
+ const Packet invalid_negative_x = pandnot(pandnot(pandnot(x_is_neg, abs_x_is_inf), y_is_int), abs_y_is_inf);
+ const Packet pow_is_nan = por(invalid_negative_x, por(x_is_nan, y_is_nan));
+ const Packet pow_is_one =
+ por(por(x_is_one, abs_y_is_zero), pand(x_is_neg_one, por(abs_y_is_inf, pandnot(y_is_even, invalid_negative_x))));
+ const Packet pow_is_zero = por(por(por(pand(abs_x_is_zero, y_is_pos), pand(abs_x_is_inf, y_is_neg)),
+ pand(pand(abs_x_is_lt_one, abs_y_is_huge), y_is_pos)),
+ pand(pand(abs_x_is_gt_one, abs_y_is_huge), y_is_neg));
+ const Packet pow_is_inf = por(por(por(pand(abs_x_is_zero, y_is_neg), pand(abs_x_is_inf, y_is_pos)),
+ pand(pand(abs_x_is_lt_one, abs_y_is_huge), y_is_neg)),
+ pand(pand(abs_x_is_gt_one, abs_y_is_huge), y_is_pos));
+ const Packet inf_val =
+ pselect(pandnot(pand(por(pand(abs_x_is_inf, x_is_neg), pand(x_is_neg_zero, y_is_neg)), y_is_int), y_is_even),
+ cst_neg_inf, cst_pos_inf);
+
+ // General computation of pow(x,y) for positive x or negative x and integer y.
+ const Packet negate_pow_abs = pandnot(x_is_neg, y_is_even);
+ const Packet pow_abs = generic_pow_impl(abs_x, y);
+ return pselect(
+ y_is_one, x,
+ pselect(pow_is_one, cst_one,
+ pselect(pow_is_nan, cst_nan,
+ pselect(pow_is_inf, inf_val,
+ pselect(pow_is_zero, cst_zero, pselect(negate_pow_abs, pnegate(pow_abs), pow_abs))))));
+}
+
+/* polevl (modified for Eigen)
+ *
+ * Evaluate polynomial
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * int N;
+ * Scalar x, y, coef[N+1];
+ *
+ * y = polevl<decltype(x), N>( x, coef);
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Evaluates polynomial of degree N:
+ *
+ * 2 N
+ * y = C + C x + C x +...+ C x
+ * 0 1 2 N
+ *
+ * Coefficients are stored in reverse order:
+ *
+ * coef[0] = C , ..., coef[N] = C .
+ * N 0
+ *
+ * The function p1evl() assumes that coef[N] = 1.0 and is
+ * omitted from the array. Its calling arguments are
+ * otherwise the same as polevl().
+ *
+ *
+ * The Eigen implementation is templatized. For best speed, store
+ * coef as a const array (constexpr), e.g.
+ *
+ * const double coef[] = {1.0, 2.0, 3.0, ...};
+ *
+ */
+template <typename Packet, int N>
+struct ppolevl {
+ static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet run(const Packet& x, const typename unpacket_traits<Packet>::type coeff[]) {
+ EIGEN_STATIC_ASSERT((N > 0), YOU_MADE_A_PROGRAMMING_MISTAKE);
+ return pmadd(ppolevl<Packet, N-1>::run(x, coeff), x, pset1<Packet>(coeff[N]));
+ }
+};
+
+template <typename Packet>
+struct ppolevl<Packet, 0> {
+ static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet run(const Packet& x, const typename unpacket_traits<Packet>::type coeff[]) {
+ EIGEN_UNUSED_VARIABLE(x);
+ return pset1<Packet>(coeff[0]);
+ }
+};
+
+/* chbevl (modified for Eigen)
+ *
+ * Evaluate Chebyshev series
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * int N;
+ * Scalar x, y, coef[N], chebevl();
+ *
+ * y = chbevl( x, coef, N );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Evaluates the series
+ *
+ * N-1
+ * - '
+ * y = > coef[i] T (x/2)
+ * - i
+ * i=0
+ *
+ * of Chebyshev polynomials Ti at argument x/2.
+ *
+ * Coefficients are stored in reverse order, i.e. the zero
+ * order term is last in the array. Note N is the number of
+ * coefficients, not the order.
+ *
+ * If coefficients are for the interval a to b, x must
+ * have been transformed to x -> 2(2x - b - a)/(b-a) before
+ * entering the routine. This maps x from (a, b) to (-1, 1),
+ * over which the Chebyshev polynomials are defined.
+ *
+ * If the coefficients are for the inverted interval, in
+ * which (a, b) is mapped to (1/b, 1/a), the transformation
+ * required is x -> 2(2ab/x - b - a)/(b-a). If b is infinity,
+ * this becomes x -> 4a/x - 1.
+ *
+ *
+ *
+ * SPEED:
+ *
+ * Taking advantage of the recurrence properties of the
+ * Chebyshev polynomials, the routine requires one more
+ * addition per loop than evaluating a nested polynomial of
+ * the same degree.
+ *
+ */
+
+template <typename Packet, int N>
+struct pchebevl {
+ EIGEN_DEVICE_FUNC
+ static EIGEN_STRONG_INLINE Packet run(Packet x, const typename unpacket_traits<Packet>::type coef[]) {
+ typedef typename unpacket_traits<Packet>::type Scalar;
+ Packet b0 = pset1<Packet>(coef[0]);
+ Packet b1 = pset1<Packet>(static_cast<Scalar>(0.f));
+ Packet b2;
+
+ for (int i = 1; i < N; i++) {
+ b2 = b1;
+ b1 = b0;
+ b0 = psub(pmadd(x, b1, pset1<Packet>(coef[i])), b2);
+ }
+
+ return pmul(pset1<Packet>(static_cast<Scalar>(0.5f)), psub(b0, b2));
+ }
+};
+
+namespace unary_pow {
+template <typename ScalarExponent, bool IsIntegerAtCompileTime = NumTraits<ScalarExponent>::IsInteger>
+struct is_odd {
+ static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE ScalarExponent run(const ScalarExponent& x) {
+ ScalarExponent xdiv2 = x / ScalarExponent(2);
+ ScalarExponent floorxdiv2 = numext::floor(xdiv2);
+ return xdiv2 != floorxdiv2;
+ }
+};
+template <typename ScalarExponent>
+struct is_odd<ScalarExponent, true> {
+ static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE ScalarExponent run(const ScalarExponent& x) {
+ return x % ScalarExponent(2);
+ }
+};
+
+template <typename Packet, typename ScalarExponent,
+ bool BaseIsIntegerType = NumTraits<typename unpacket_traits<Packet>::type>::IsInteger>
+struct do_div {
+ static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet run(const Packet& x, const ScalarExponent& exponent) {
+ typedef typename unpacket_traits<Packet>::type Scalar;
+ const Packet cst_pos_one = pset1<Packet>(Scalar(1));
+ return exponent < 0 ? pdiv(cst_pos_one, x) : x;
+ }
+};
+
+template <typename Packet, typename ScalarExponent>
+struct do_div<Packet, ScalarExponent, true> {
+ // pdiv not defined, nor necessary for integer base types
+ static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet run(const Packet& x, const ScalarExponent& exponent) {
+ EIGEN_UNUSED_VARIABLE(exponent);
+ return x;
+ }
+};
+
+template <typename Packet, typename ScalarExponent>
+static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet int_pow(const Packet& x, const ScalarExponent& exponent) {
+ typedef typename unpacket_traits<Packet>::type Scalar;
+ const Packet cst_pos_one = pset1<Packet>(Scalar(1));
+ if (exponent == 0) return cst_pos_one;
+ Packet result = x;
+ Packet y = cst_pos_one;
+ ScalarExponent m = numext::abs(exponent);
+ while (m > 1) {
+ bool odd = is_odd<ScalarExponent>::run(m);
+ if (odd) y = pmul(y, result);
+ result = pmul(result, result);
+ m = numext::floor(m / ScalarExponent(2));
+ }
+ result = pmul(y, result);
+ result = do_div<Packet, ScalarExponent>::run(result, exponent);
+ return result;
+}
+
+template <typename Packet>
+static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet gen_pow(const Packet& x,
+ const typename unpacket_traits<Packet>::type& exponent) {
+ const Packet exponent_packet = pset1<Packet>(exponent);
+ return generic_pow_impl(x, exponent_packet);
+}
+
+template <typename Packet, typename ScalarExponent>
+static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet handle_nonint_int_errors(const Packet& x, const Packet& powx,
+ const ScalarExponent& exponent) {
+ typedef typename unpacket_traits<Packet>::type Scalar;
+
+ // non-integer base, integer exponent case
+
+ const bool exponent_is_odd = is_odd<ScalarExponent>::run(exponent);
+ const bool exponent_is_neg = exponent < 0;
+
+ const Packet exp_is_odd = exponent_is_odd ? ptrue(x) : pzero(x);
+ const Packet exp_is_neg = exponent_is_neg ? ptrue(x) : pzero(x);
+
+ const Scalar pos_zero = Scalar(0);
+ const Scalar neg_zero = -Scalar(0);
+ const Scalar pos_one = Scalar(1);
+ const Scalar pos_inf = NumTraits<Scalar>::infinity();
+ const Scalar neg_inf = -NumTraits<Scalar>::infinity();
+
+ const Packet cst_pos_zero = pset1<Packet>(pos_zero);
+ const Packet cst_neg_zero = pset1<Packet>(neg_zero);
+ const Packet cst_pos_one = pset1<Packet>(pos_one);
+ const Packet cst_pos_inf = pset1<Packet>(pos_inf);
+ const Packet cst_neg_inf = pset1<Packet>(neg_inf);
+
+ const Packet abs_x = pabs(x);
+ const Packet abs_x_is_zero = pcmp_eq(abs_x, cst_pos_zero);
+ const Packet abs_x_is_one = pcmp_eq(abs_x, cst_pos_one);
+ const Packet abs_x_is_inf = pcmp_eq(abs_x, cst_pos_inf);
+
+ const Packet x_has_signbit = pcmp_eq(por(pand(x, cst_neg_inf), cst_pos_inf), cst_neg_inf);
+ const Packet x_is_neg = pandnot(x_has_signbit, abs_x_is_zero);
+ const Packet x_is_neg_zero = pand(x_has_signbit, abs_x_is_zero);
+
+ if (exponent == 0) {
+ return cst_pos_one;
+ }
+
+ Packet pow_is_pos_inf = pand(pandnot(abs_x_is_zero, x_is_neg_zero), pand(exp_is_odd, exp_is_neg));
+ pow_is_pos_inf = por(pow_is_pos_inf, pand(abs_x_is_zero, pandnot(exp_is_neg, exp_is_odd)));
+ pow_is_pos_inf = por(pow_is_pos_inf, pand(pand(abs_x_is_inf, x_is_neg), pandnot(pnot(exp_is_neg), exp_is_odd)));
+ pow_is_pos_inf = por(pow_is_pos_inf, pandnot(pandnot(abs_x_is_inf, x_is_neg), exp_is_neg));
+
+ Packet pow_is_neg_inf = pand(x_is_neg_zero, pand(exp_is_neg, exp_is_odd));
+ pow_is_neg_inf = por(pow_is_neg_inf, pand(pand(abs_x_is_inf, x_is_neg), pandnot(exp_is_odd, exp_is_neg)));
+
+ Packet pow_is_pos_zero = pandnot(abs_x_is_zero, exp_is_neg);
+ pow_is_pos_zero = por(pow_is_pos_zero, pand(pand(abs_x_is_inf, x_is_neg), pandnot(exp_is_neg, exp_is_odd)));
+ pow_is_pos_zero = por(pow_is_pos_zero, pand(pandnot(abs_x_is_inf, x_is_neg), exp_is_neg));
+
+ Packet pow_is_neg_zero = pand(x_is_neg_zero, pandnot(exp_is_odd, exp_is_neg));
+ pow_is_neg_zero = por(pow_is_neg_zero, pand(pand(abs_x_is_inf, x_is_neg), pand(exp_is_odd, exp_is_neg)));
+
+ Packet result = pselect(pow_is_neg_inf, cst_neg_inf, powx);
+ result = pselect(pow_is_neg_zero, cst_neg_zero, result);
+ result = pselect(pow_is_pos_zero, cst_pos_zero, result);
+ result = pselect(pow_is_pos_inf, cst_pos_inf, result);
+ result = pselect(pandnot(abs_x_is_one, x_is_neg), cst_pos_one, result);
+ return result;
+}
+
+template <typename Packet, typename ScalarExponent>
+static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet handle_nonint_nonint_errors(const Packet& x, const Packet& powx,
+ const ScalarExponent& exponent) {
+ typedef typename unpacket_traits<Packet>::type Scalar;
+
+ // non-integer base and exponent case
+
+ const bool exponent_is_fin = (numext::isfinite)(exponent);
+ const bool exponent_is_nan = (numext::isnan)(exponent);
+ const bool exponent_is_neg = exponent < 0;
+ const bool exponent_is_inf = !exponent_is_fin && !exponent_is_nan;
+
+ const Packet exp_is_neg = exponent_is_neg ? ptrue(x) : pzero(x);
+ const Packet exp_is_inf = exponent_is_inf ? ptrue(x) : pzero(x);
+
+ const Scalar pos_zero = Scalar(0);
+ const Scalar pos_one = Scalar(1);
+ const Scalar pos_inf = NumTraits<Scalar>::infinity();
+ const Scalar neg_inf = -NumTraits<Scalar>::infinity();
+ const Scalar nan = NumTraits<Scalar>::quiet_NaN();
+
+ const Packet cst_pos_zero = pset1<Packet>(pos_zero);
+ const Packet cst_pos_one = pset1<Packet>(pos_one);
+ const Packet cst_pos_inf = pset1<Packet>(pos_inf);
+ const Packet cst_neg_inf = pset1<Packet>(neg_inf);
+ const Packet cst_nan = pset1<Packet>(nan);
+
+ const Packet abs_x = pabs(x);
+ const Packet abs_x_is_zero = pcmp_eq(abs_x, cst_pos_zero);
+ const Packet abs_x_is_lt_one = pcmp_lt(abs_x, cst_pos_one);
+ const Packet abs_x_is_gt_one = pcmp_lt(cst_pos_one, abs_x);
+ const Packet abs_x_is_one = pcmp_eq(abs_x, cst_pos_one);
+ const Packet abs_x_is_inf = pcmp_eq(abs_x, cst_pos_inf);
+
+ const Packet x_has_signbit = pcmp_eq(por(pand(x, cst_neg_inf), cst_pos_inf), cst_neg_inf);
+ const Packet x_is_neg = pandnot(x_has_signbit, abs_x_is_zero);
+
+ if (exponent_is_nan) {
+ return pselect(pandnot(abs_x_is_one, x_is_neg), cst_pos_one, cst_nan);
+ }
+
+ Packet pow_is_pos_zero = pandnot(abs_x_is_zero, exp_is_neg);
+ pow_is_pos_zero = por(pow_is_pos_zero, pand(abs_x_is_gt_one, pand(exp_is_inf, exp_is_neg)));
+ pow_is_pos_zero = por(pow_is_pos_zero, pand(abs_x_is_lt_one, pandnot(exp_is_inf, exp_is_neg)));
+ pow_is_pos_zero = por(pow_is_pos_zero, pand(abs_x_is_inf, exp_is_neg));
+
+ const Packet pow_is_pos_one = pand(abs_x_is_one, exp_is_inf);
+
+ Packet pow_is_pos_inf = pand(abs_x_is_zero, exp_is_neg);
+ pow_is_pos_inf = por(pow_is_pos_inf, pand(abs_x_is_lt_one, pand(exp_is_inf, exp_is_neg)));
+ pow_is_pos_inf = por(pow_is_pos_inf, pand(abs_x_is_gt_one, pandnot(exp_is_inf, exp_is_neg)));
+ pow_is_pos_inf = por(pow_is_pos_inf, pandnot(abs_x_is_inf, exp_is_neg));
+
+ const Packet pow_is_nan = pandnot(pandnot(x_is_neg, abs_x_is_inf), exp_is_inf);
+
+ Packet result = pselect(pow_is_pos_inf, cst_pos_inf, powx);
+ result = pselect(pow_is_pos_one, cst_pos_one, result);
+ result = pselect(pow_is_pos_zero, cst_pos_zero, result);
+ result = pselect(pow_is_nan, cst_nan, result);
+ result = pselect(pandnot(abs_x_is_one, x_is_neg), cst_pos_one, result);
+ return result;
+}
+
+template <typename Packet, typename ScalarExponent>
+static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet handle_int_int(const Packet& x, const ScalarExponent& exponent) {
+ typedef typename unpacket_traits<Packet>::type Scalar;
+
+ // integer base, integer exponent case
+
+ // This routine handles negative and very large positive exponents
+ // Signed integer overflow and divide by zero is undefined behavior
+ // Unsigned intgers do not overflow
+
+ const bool exponent_is_odd = unary_pow::is_odd<ScalarExponent>::run(exponent);
+
+ const Scalar zero = Scalar(0);
+ const Scalar pos_one = Scalar(1);
+
+ const Packet cst_zero = pset1<Packet>(zero);
+ const Packet cst_pos_one = pset1<Packet>(pos_one);
+
+ const Packet abs_x = pabs(x);
+
+ const Packet pow_is_zero = exponent < 0 ? pcmp_lt(cst_pos_one, abs_x) : pzero(x);
+ const Packet pow_is_one = pcmp_eq(cst_pos_one, abs_x);
+ const Packet pow_is_neg = exponent_is_odd ? pcmp_lt(x, cst_zero) : pzero(x);
+
+ Packet result = pselect(pow_is_zero, cst_zero, x);
+ result = pselect(pandnot(pow_is_one, pow_is_neg), cst_pos_one, result);
+ result = pselect(pand(pow_is_one, pow_is_neg), pnegate(cst_pos_one), result);
+ return result;
+}
+} // end namespace unary_pow
+
+template <typename Packet, typename ScalarExponent,
+ bool BaseIsIntegerType = NumTraits<typename unpacket_traits<Packet>::type>::IsInteger,
+ bool ExponentIsIntegerType = NumTraits<ScalarExponent>::IsInteger>
+struct unary_pow_impl;
+
+template <typename Packet, typename ScalarExponent>
+struct unary_pow_impl<Packet, ScalarExponent, false, false> {
+ typedef typename unpacket_traits<Packet>::type Scalar;
+ static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet run(const Packet& x, const ScalarExponent& exponent) {
+ const bool exponent_is_integer = (numext::isfinite)(exponent) && numext::round(exponent) == exponent;
+ if (exponent_is_integer) {
+ Packet result = unary_pow::int_pow(x, exponent);
+ result = unary_pow::handle_nonint_int_errors(x, result, exponent);
+ return result;
+ } else {
+ Packet result = unary_pow::gen_pow(x, exponent);
+ result = unary_pow::handle_nonint_nonint_errors(x, result, exponent);
+ return result;
+ }
+ }
+};
+
+template <typename Packet, typename ScalarExponent>
+struct unary_pow_impl<Packet, ScalarExponent, false, true> {
+ typedef typename unpacket_traits<Packet>::type Scalar;
+ static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet run(const Packet& x, const ScalarExponent& exponent) {
+ Packet result = unary_pow::int_pow(x, exponent);
+ result = unary_pow::handle_nonint_int_errors(x, result, exponent);
+ return result;
+ }
+};
+
+template <typename Packet, typename ScalarExponent>
+struct unary_pow_impl<Packet, ScalarExponent, true, true> {
+ typedef typename unpacket_traits<Packet>::type Scalar;
+ static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet run(const Packet& x, const ScalarExponent& exponent) {
+ if (exponent < 0 || exponent > NumTraits<Scalar>::digits()) {
+ return unary_pow::handle_int_int(x, exponent);
+ }
+ else {
+ return unary_pow::int_pow(x, exponent);
+ }
+ }
+};
+
+} // end namespace internal
+} // end namespace Eigen
+
+#endif // EIGEN_ARCH_GENERIC_PACKET_MATH_FUNCTIONS_H
diff --git a/Eigen/src/Core/arch/Default/GenericPacketMathFunctionsFwd.h b/Eigen/src/Core/arch/Default/GenericPacketMathFunctionsFwd.h
new file mode 100644
index 0000000..179c55c
--- /dev/null
+++ b/Eigen/src/Core/arch/Default/GenericPacketMathFunctionsFwd.h
@@ -0,0 +1,128 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2019 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_ARCH_GENERIC_PACKET_MATH_FUNCTIONS_FWD_H
+#define EIGEN_ARCH_GENERIC_PACKET_MATH_FUNCTIONS_FWD_H
+
+#include "../../InternalHeaderCheck.h"
+
+namespace Eigen {
+namespace internal {
+
+// Forward declarations of the generic math functions
+// implemented in GenericPacketMathFunctions.h
+// This is needed to workaround a circular dependency.
+
+/***************************************************************************
+ * Some generic implementations to be used by implementors
+***************************************************************************/
+
+/** Default implementation of pfrexp.
+ * It is expected to be called by implementers of template<> pfrexp.
+ */
+template<typename Packet> EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC
+Packet pfrexp_generic(const Packet& a, Packet& exponent);
+
+// Extracts the biased exponent value from Packet p, and casts the results to
+// a floating-point Packet type. Used by pfrexp_generic. Override this if
+// there is no unpacket_traits<Packet>::integer_packet.
+template<typename Packet> EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC
+Packet pfrexp_generic_get_biased_exponent(const Packet& p);
+
+/** Default implementation of pldexp.
+ * It is expected to be called by implementers of template<> pldexp.
+ */
+template<typename Packet> EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC
+Packet pldexp_generic(const Packet& a, const Packet& exponent);
+
+/** \internal \returns log(x) for single precision float */
+template <typename Packet>
+EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+Packet plog_float(const Packet _x);
+
+/** \internal \returns log2(x) for single precision float */
+template <typename Packet>
+EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+Packet plog2_float(const Packet _x);
+
+/** \internal \returns log(x) for single precision float */
+template <typename Packet>
+EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+Packet plog_double(const Packet _x);
+
+/** \internal \returns log2(x) for single precision float */
+template <typename Packet>
+EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+Packet plog2_double(const Packet _x);
+
+/** \internal \returns log(1 + x) */
+template<typename Packet>
+Packet generic_plog1p(const Packet& x);
+
+/** \internal \returns exp(x)-1 */
+template<typename Packet>
+Packet generic_expm1(const Packet& x);
+
+/** \internal \returns exp(x) for single precision float */
+template <typename Packet>
+EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+Packet pexp_float(const Packet _x);
+
+/** \internal \returns exp(x) for double precision real numbers */
+template <typename Packet>
+EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+Packet pexp_double(const Packet _x);
+
+/** \internal \returns sin(x) for single precision float */
+template<typename Packet>
+EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+Packet psin_float(const Packet& x);
+
+/** \internal \returns cos(x) for single precision float */
+template<typename Packet>
+EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+Packet pcos_float(const Packet& x);
+
+/** \internal \returns asin(x) for single precision float */
+template<typename Packet>
+EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+Packet pasin_float(const Packet& x);
+
+/** \internal \returns acos(x) for single precision float */
+template<typename Packet>
+EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+Packet pacos_float(const Packet& x);
+
+/** \internal \returns atan(x) for single precision float */
+template<typename Packet>
+EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+Packet patan_float(const Packet& x);
+
+/** \internal \returns atan(x) for double precision float */
+template<typename Packet>
+EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+Packet patan_double(const Packet& x);
+
+/** \internal \returns sqrt(x) for complex types */
+template<typename Packet>
+EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+Packet psqrt_complex(const Packet& a);
+
+/** \internal \returns x / y for complex types */
+template<typename Packet>
+EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+Packet pdiv_complex(const Packet& x, const Packet& y);
+
+template <typename Packet, int N> struct ppolevl;
+
+
+} // end namespace internal
+} // end namespace Eigen
+
+#endif // EIGEN_ARCH_GENERIC_PACKET_MATH_FUNCTIONS_FWD_H
diff --git a/Eigen/src/Core/arch/Default/Half.h b/Eigen/src/Core/arch/Default/Half.h
new file mode 100644
index 0000000..75d6228
--- /dev/null
+++ b/Eigen/src/Core/arch/Default/Half.h
@@ -0,0 +1,1011 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+//
+// The conversion routines are Copyright (c) Fabian Giesen, 2016.
+// The original license follows:
+//
+// Copyright (c) Fabian Giesen, 2016
+// All rights reserved.
+// Redistribution and use in source and binary forms, with or without
+// modification, are permitted.
+// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+// LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
+// A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
+// HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
+// SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
+// LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
+// DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
+// THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
+// (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
+// OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+
+
+// Standard 16-bit float type, mostly useful for GPUs. Defines a new
+// type Eigen::half (inheriting either from CUDA's or HIP's __half struct) with
+// operator overloads such that it behaves basically as an arithmetic
+// type. It will be quite slow on CPUs (so it is recommended to stay
+// in fp32 for CPUs, except for simple parameter conversions, I/O
+// to disk and the likes), but fast on GPUs.
+
+
+#ifndef EIGEN_HALF_H
+#define EIGEN_HALF_H
+
+#include "../../InternalHeaderCheck.h"
+
+#if defined(EIGEN_HAS_GPU_FP16) || defined(EIGEN_HAS_ARM64_FP16_SCALAR_ARITHMETIC)
+// When compiling with GPU support, the "__half_raw" base class as well as
+// some other routines are defined in the GPU compiler header files
+// (cuda_fp16.h, hip_fp16.h), and they are not tagged constexpr
+// As a consequence, we get compile failures when compiling Eigen with
+// GPU support. Hence the need to disable EIGEN_CONSTEXPR when building
+// Eigen with GPU support
+ #pragma push_macro("EIGEN_CONSTEXPR")
+ #undef EIGEN_CONSTEXPR
+ #define EIGEN_CONSTEXPR
+#endif
+
+#define F16_PACKET_FUNCTION(PACKET_F, PACKET_F16, METHOD) \
+ template <> \
+ EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC EIGEN_UNUSED \
+ PACKET_F16 METHOD<PACKET_F16>(const PACKET_F16& _x) { \
+ return float2half(METHOD<PACKET_F>(half2float(_x))); \
+ }
+
+namespace Eigen {
+
+struct half;
+
+namespace half_impl {
+
+// We want to use the __half_raw struct from the HIP header file only during the device compile phase.
+// This is required because of a quirk in the way TensorFlow GPU builds are done.
+// When compiling TensorFlow source code with GPU support, files that
+// * contain GPU kernels (i.e. *.cu.cc files) are compiled via hipcc
+// * do not contain GPU kernels ( i.e. *.cc files) are compiled via gcc (typically)
+//
+// Tensorflow uses the Eigen::half type as its FP16 type, and there are functions that
+// * are defined in a file that gets compiled via hipcc AND
+// * have Eigen::half as a pass-by-value argument AND
+// * are called in a file that gets compiled via gcc
+//
+// In the scenario described above the caller and callee will see different versions
+// of the Eigen::half base class __half_raw, and they will be compiled by different compilers
+//
+// There appears to be an ABI mismatch between gcc and clang (which is called by hipcc) that results in
+// the callee getting corrupted values for the Eigen::half argument.
+//
+// Making the host side compile phase of hipcc use the same Eigen::half impl, as the gcc compile, resolves
+// this error, and hence the following convoluted #if condition
+#if !defined(EIGEN_HAS_GPU_FP16) || !defined(EIGEN_GPU_COMPILE_PHASE)
+// Make our own __half_raw definition that is similar to CUDA's.
+struct __half_raw {
+#if (defined(EIGEN_HAS_GPU_FP16) && !defined(EIGEN_GPU_COMPILE_PHASE))
+ // Eigen::half can be used as the datatype for shared memory declarations (in Eigen and TF)
+ // The element type for shared memory cannot have non-trivial constructors
+ // and hence the following special casing (which skips the zero-initilization).
+ // Note that this check gets done even in the host compilation phase, and
+ // hence the need for this
+ EIGEN_DEVICE_FUNC __half_raw() {}
+#else
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR __half_raw() : x(0) {}
+#endif
+#if defined(EIGEN_HAS_ARM64_FP16_SCALAR_ARITHMETIC)
+ explicit EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR __half_raw(numext::uint16_t raw) : x(numext::bit_cast<__fp16>(raw)) {
+ }
+ __fp16 x;
+#else
+ explicit EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR __half_raw(numext::uint16_t raw) : x(raw) {}
+ numext::uint16_t x;
+#endif
+};
+
+#elif defined(EIGEN_HAS_HIP_FP16)
+ // Nothing to do here
+ // HIP fp16 header file has a definition for __half_raw
+#elif defined(EIGEN_HAS_CUDA_FP16)
+ #if EIGEN_CUDA_SDK_VER < 90000
+ // In CUDA < 9.0, __half is the equivalent of CUDA 9's __half_raw
+ typedef __half __half_raw;
+ #endif // defined(EIGEN_HAS_CUDA_FP16)
+#elif defined(SYCL_DEVICE_ONLY)
+ typedef cl::sycl::half __half_raw;
+#endif
+
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR __half_raw raw_uint16_to_half(numext::uint16_t x);
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC __half_raw float_to_half_rtne(float ff);
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC float half_to_float(__half_raw h);
+
+struct half_base : public __half_raw {
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR half_base() {}
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR half_base(const __half_raw& h) : __half_raw(h) {}
+
+#if defined(EIGEN_HAS_GPU_FP16)
+ #if defined(EIGEN_HAS_HIP_FP16)
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR half_base(const __half& h) { x = __half_as_ushort(h); }
+ #elif defined(EIGEN_HAS_CUDA_FP16)
+ #if EIGEN_CUDA_SDK_VER >= 90000
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR half_base(const __half& h) : __half_raw(*(__half_raw*)&h) {}
+ #endif
+ #endif
+#endif
+};
+
+} // namespace half_impl
+
+// Class definition.
+struct half : public half_impl::half_base {
+
+ // Writing this out as separate #if-else blocks to make the code easier to follow
+ // The same applies to most #if-else blocks in this file
+#if !defined(EIGEN_HAS_GPU_FP16) || !defined(EIGEN_GPU_COMPILE_PHASE)
+ // Use the same base class for the following two scenarios
+ // * when compiling without GPU support enabled
+ // * during host compile phase when compiling with GPU support enabled
+ typedef half_impl::__half_raw __half_raw;
+#elif defined(EIGEN_HAS_HIP_FP16)
+ // Nothing to do here
+ // HIP fp16 header file has a definition for __half_raw
+#elif defined(EIGEN_HAS_CUDA_FP16)
+ // Note that EIGEN_CUDA_SDK_VER is set to 0 even when compiling with HIP, so
+ // (EIGEN_CUDA_SDK_VER < 90000) is true even for HIP! So keeping this within
+ // #if defined(EIGEN_HAS_CUDA_FP16) is needed
+ #if defined(EIGEN_CUDA_SDK_VER) && EIGEN_CUDA_SDK_VER < 90000
+ typedef half_impl::__half_raw __half_raw;
+ #endif
+#endif
+
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR half() {}
+
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR half(const __half_raw& h) : half_impl::half_base(h) {}
+
+#if defined(EIGEN_HAS_GPU_FP16)
+ #if defined(EIGEN_HAS_HIP_FP16)
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR half(const __half& h) : half_impl::half_base(h) {}
+ #elif defined(EIGEN_HAS_CUDA_FP16)
+ #if defined(EIGEN_CUDA_SDK_VER) && EIGEN_CUDA_SDK_VER >= 90000
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR half(const __half& h) : half_impl::half_base(h) {}
+ #endif
+ #endif
+#endif
+
+
+ explicit EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR half(bool b)
+ : half_impl::half_base(half_impl::raw_uint16_to_half(b ? 0x3c00 : 0)) {}
+ template<class T>
+ explicit EIGEN_DEVICE_FUNC half(T val)
+ : half_impl::half_base(half_impl::float_to_half_rtne(static_cast<float>(val))) {}
+ explicit EIGEN_DEVICE_FUNC half(float f)
+ : half_impl::half_base(half_impl::float_to_half_rtne(f)) {}
+
+ // Following the convention of numpy, converting between complex and
+ // float will lead to loss of imag value.
+ template<typename RealScalar>
+ explicit EIGEN_DEVICE_FUNC half(std::complex<RealScalar> c)
+ : half_impl::half_base(half_impl::float_to_half_rtne(static_cast<float>(c.real()))) {}
+
+ EIGEN_DEVICE_FUNC operator float() const { // NOLINT: Allow implicit conversion to float, because it is lossless.
+ return half_impl::half_to_float(*this);
+ }
+
+#if defined(EIGEN_HAS_GPU_FP16) && !defined(EIGEN_GPU_COMPILE_PHASE)
+ EIGEN_DEVICE_FUNC operator __half() const {
+ ::__half_raw hr;
+ hr.x = x;
+ return __half(hr);
+ }
+#endif
+};
+
+// TODO(majnemer): Get rid of this once we can rely on C++17 inline variables do
+// solve the ODR issue.
+namespace half_impl {
+template <typename = void>
+struct numeric_limits_half_impl {
+ static EIGEN_CONSTEXPR const bool is_specialized = true;
+ static EIGEN_CONSTEXPR const bool is_signed = true;
+ static EIGEN_CONSTEXPR const bool is_integer = false;
+ static EIGEN_CONSTEXPR const bool is_exact = false;
+ static EIGEN_CONSTEXPR const bool has_infinity = true;
+ static EIGEN_CONSTEXPR const bool has_quiet_NaN = true;
+ static EIGEN_CONSTEXPR const bool has_signaling_NaN = true;
+ static EIGEN_CONSTEXPR const std::float_denorm_style has_denorm = std::denorm_present;
+ static EIGEN_CONSTEXPR const bool has_denorm_loss = false;
+ static EIGEN_CONSTEXPR const std::float_round_style round_style = std::round_to_nearest;
+ static EIGEN_CONSTEXPR const bool is_iec559 = true;
+ // The C++ standard defines this as "true if the set of values representable
+ // by the type is finite." Half has finite precision.
+ static EIGEN_CONSTEXPR const bool is_bounded = true;
+ static EIGEN_CONSTEXPR const bool is_modulo = false;
+ static EIGEN_CONSTEXPR const int digits = 11;
+ static EIGEN_CONSTEXPR const int digits10 = 3; // according to http://half.sourceforge.net/structstd_1_1numeric__limits_3_01half__float_1_1half_01_4.html
+ static EIGEN_CONSTEXPR const int max_digits10 = 5; // according to http://half.sourceforge.net/structstd_1_1numeric__limits_3_01half__float_1_1half_01_4.html
+ static EIGEN_CONSTEXPR const int radix = std::numeric_limits<float>::radix;
+ static EIGEN_CONSTEXPR const int min_exponent = -13;
+ static EIGEN_CONSTEXPR const int min_exponent10 = -4;
+ static EIGEN_CONSTEXPR const int max_exponent = 16;
+ static EIGEN_CONSTEXPR const int max_exponent10 = 4;
+ static EIGEN_CONSTEXPR const bool traps = std::numeric_limits<float>::traps;
+ // IEEE754: "The implementer shall choose how tininess is detected, but shall
+ // detect tininess in the same way for all operations in radix two"
+ static EIGEN_CONSTEXPR const bool tinyness_before = std::numeric_limits<float>::tinyness_before;
+
+ static EIGEN_CONSTEXPR Eigen::half (min)() { return Eigen::half_impl::raw_uint16_to_half(0x0400); }
+ static EIGEN_CONSTEXPR Eigen::half lowest() { return Eigen::half_impl::raw_uint16_to_half(0xfbff); }
+ static EIGEN_CONSTEXPR Eigen::half (max)() { return Eigen::half_impl::raw_uint16_to_half(0x7bff); }
+ static EIGEN_CONSTEXPR Eigen::half epsilon() { return Eigen::half_impl::raw_uint16_to_half(0x1400); }
+ static EIGEN_CONSTEXPR Eigen::half round_error() { return Eigen::half_impl::raw_uint16_to_half(0x3800); }
+ static EIGEN_CONSTEXPR Eigen::half infinity() { return Eigen::half_impl::raw_uint16_to_half(0x7c00); }
+ static EIGEN_CONSTEXPR Eigen::half quiet_NaN() { return Eigen::half_impl::raw_uint16_to_half(0x7e00); }
+ static EIGEN_CONSTEXPR Eigen::half signaling_NaN() { return Eigen::half_impl::raw_uint16_to_half(0x7d00); }
+ static EIGEN_CONSTEXPR Eigen::half denorm_min() { return Eigen::half_impl::raw_uint16_to_half(0x0001); }
+};
+
+template<typename T>
+EIGEN_CONSTEXPR const bool numeric_limits_half_impl<T>::is_specialized;
+template<typename T>
+EIGEN_CONSTEXPR const bool numeric_limits_half_impl<T>::is_signed;
+template<typename T>
+EIGEN_CONSTEXPR const bool numeric_limits_half_impl<T>::is_integer;
+template<typename T>
+EIGEN_CONSTEXPR const bool numeric_limits_half_impl<T>::is_exact;
+template<typename T>
+EIGEN_CONSTEXPR const bool numeric_limits_half_impl<T>::has_infinity;
+template<typename T>
+EIGEN_CONSTEXPR const bool numeric_limits_half_impl<T>::has_quiet_NaN;
+template<typename T>
+EIGEN_CONSTEXPR const bool numeric_limits_half_impl<T>::has_signaling_NaN;
+template<typename T>
+EIGEN_CONSTEXPR const std::float_denorm_style numeric_limits_half_impl<T>::has_denorm;
+template<typename T>
+EIGEN_CONSTEXPR const bool numeric_limits_half_impl<T>::has_denorm_loss;
+template<typename T>
+EIGEN_CONSTEXPR const std::float_round_style numeric_limits_half_impl<T>::round_style;
+template<typename T>
+EIGEN_CONSTEXPR const bool numeric_limits_half_impl<T>::is_iec559;
+template<typename T>
+EIGEN_CONSTEXPR const bool numeric_limits_half_impl<T>::is_bounded;
+template<typename T>
+EIGEN_CONSTEXPR const bool numeric_limits_half_impl<T>::is_modulo;
+template<typename T>
+EIGEN_CONSTEXPR const int numeric_limits_half_impl<T>::digits;
+template<typename T>
+EIGEN_CONSTEXPR const int numeric_limits_half_impl<T>::digits10;
+template<typename T>
+EIGEN_CONSTEXPR const int numeric_limits_half_impl<T>::max_digits10;
+template<typename T>
+EIGEN_CONSTEXPR const int numeric_limits_half_impl<T>::radix;
+template<typename T>
+EIGEN_CONSTEXPR const int numeric_limits_half_impl<T>::min_exponent;
+template<typename T>
+EIGEN_CONSTEXPR const int numeric_limits_half_impl<T>::min_exponent10;
+template<typename T>
+EIGEN_CONSTEXPR const int numeric_limits_half_impl<T>::max_exponent;
+template<typename T>
+EIGEN_CONSTEXPR const int numeric_limits_half_impl<T>::max_exponent10;
+template<typename T>
+EIGEN_CONSTEXPR const bool numeric_limits_half_impl<T>::traps;
+template<typename T>
+EIGEN_CONSTEXPR const bool numeric_limits_half_impl<T>::tinyness_before;
+} // end namespace half_impl
+} // end namespace Eigen
+
+namespace std {
+// If std::numeric_limits<T> is specialized, should also specialize
+// std::numeric_limits<const T>, std::numeric_limits<volatile T>, and
+// std::numeric_limits<const volatile T>
+// https://stackoverflow.com/a/16519653/
+template<>
+class numeric_limits<Eigen::half> : public Eigen::half_impl::numeric_limits_half_impl<> {};
+template<>
+class numeric_limits<const Eigen::half> : public numeric_limits<Eigen::half> {};
+template<>
+class numeric_limits<volatile Eigen::half> : public numeric_limits<Eigen::half> {};
+template<>
+class numeric_limits<const volatile Eigen::half> : public numeric_limits<Eigen::half> {};
+} // end namespace std
+
+namespace Eigen {
+
+namespace half_impl {
+
+#if (defined(EIGEN_HAS_CUDA_FP16) && defined(EIGEN_CUDA_ARCH) && \
+ EIGEN_CUDA_ARCH >= 530) || \
+ (defined(EIGEN_HAS_HIP_FP16) && defined(HIP_DEVICE_COMPILE))
+// Note: We deliberately do *not* define this to 1 even if we have Arm's native
+// fp16 type since GPU halfs are rather different from native CPU halfs.
+// TODO: Rename to something like EIGEN_HAS_NATIVE_GPU_FP16
+#define EIGEN_HAS_NATIVE_FP16
+#endif
+
+// Intrinsics for native fp16 support. Note that on current hardware,
+// these are no faster than fp32 arithmetic (you need to use the half2
+// versions to get the ALU speed increased), but you do save the
+// conversion steps back and forth.
+
+#if defined(EIGEN_HAS_NATIVE_FP16)
+EIGEN_STRONG_INLINE __device__ half operator + (const half& a, const half& b) {
+#if defined(EIGEN_CUDA_SDK_VER) && EIGEN_CUDA_SDK_VER >= 90000
+ return __hadd(::__half(a), ::__half(b));
+#else
+ return __hadd(a, b);
+#endif
+}
+EIGEN_STRONG_INLINE __device__ half operator * (const half& a, const half& b) {
+ return __hmul(a, b);
+}
+EIGEN_STRONG_INLINE __device__ half operator - (const half& a, const half& b) {
+ return __hsub(a, b);
+}
+EIGEN_STRONG_INLINE __device__ half operator / (const half& a, const half& b) {
+#if defined(EIGEN_CUDA_SDK_VER) && EIGEN_CUDA_SDK_VER >= 90000
+ return __hdiv(a, b);
+#else
+ float num = __half2float(a);
+ float denom = __half2float(b);
+ return __float2half(num / denom);
+#endif
+}
+EIGEN_STRONG_INLINE __device__ half operator - (const half& a) {
+ return __hneg(a);
+}
+EIGEN_STRONG_INLINE __device__ half& operator += (half& a, const half& b) {
+ a = a + b;
+ return a;
+}
+EIGEN_STRONG_INLINE __device__ half& operator *= (half& a, const half& b) {
+ a = a * b;
+ return a;
+}
+EIGEN_STRONG_INLINE __device__ half& operator -= (half& a, const half& b) {
+ a = a - b;
+ return a;
+}
+EIGEN_STRONG_INLINE __device__ half& operator /= (half& a, const half& b) {
+ a = a / b;
+ return a;
+}
+EIGEN_STRONG_INLINE __device__ bool operator == (const half& a, const half& b) {
+ return __heq(a, b);
+}
+EIGEN_STRONG_INLINE __device__ bool operator != (const half& a, const half& b) {
+ return __hne(a, b);
+}
+EIGEN_STRONG_INLINE __device__ bool operator < (const half& a, const half& b) {
+ return __hlt(a, b);
+}
+EIGEN_STRONG_INLINE __device__ bool operator <= (const half& a, const half& b) {
+ return __hle(a, b);
+}
+EIGEN_STRONG_INLINE __device__ bool operator > (const half& a, const half& b) {
+ return __hgt(a, b);
+}
+EIGEN_STRONG_INLINE __device__ bool operator >= (const half& a, const half& b) {
+ return __hge(a, b);
+}
+#endif
+
+#if defined(EIGEN_HAS_ARM64_FP16_SCALAR_ARITHMETIC) && !defined(EIGEN_GPU_COMPILE_PHASE)
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half operator + (const half& a, const half& b) {
+ return half(vaddh_f16(a.x, b.x));
+}
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half operator * (const half& a, const half& b) {
+ return half(vmulh_f16(a.x, b.x));
+}
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half operator - (const half& a, const half& b) {
+ return half(vsubh_f16(a.x, b.x));
+}
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half operator / (const half& a, const half& b) {
+ return half(vdivh_f16(a.x, b.x));
+}
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half operator - (const half& a) {
+ return half(vnegh_f16(a.x));
+}
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half& operator += (half& a, const half& b) {
+ a = half(vaddh_f16(a.x, b.x));
+ return a;
+}
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half& operator *= (half& a, const half& b) {
+ a = half(vmulh_f16(a.x, b.x));
+ return a;
+}
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half& operator -= (half& a, const half& b) {
+ a = half(vsubh_f16(a.x, b.x));
+ return a;
+}
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half& operator /= (half& a, const half& b) {
+ a = half(vdivh_f16(a.x, b.x));
+ return a;
+}
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bool operator == (const half& a, const half& b) {
+ return vceqh_f16(a.x, b.x);
+}
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bool operator != (const half& a, const half& b) {
+ return !vceqh_f16(a.x, b.x);
+}
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bool operator < (const half& a, const half& b) {
+ return vclth_f16(a.x, b.x);
+}
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bool operator <= (const half& a, const half& b) {
+ return vcleh_f16(a.x, b.x);
+}
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bool operator > (const half& a, const half& b) {
+ return vcgth_f16(a.x, b.x);
+}
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bool operator >= (const half& a, const half& b) {
+ return vcgeh_f16(a.x, b.x);
+}
+// We need to distinguish ‘clang as the CUDA compiler’ from ‘clang as the host compiler,
+// invoked by NVCC’ (e.g. on MacOS). The former needs to see both host and device implementation
+// of the functions, while the latter can only deal with one of them.
+#elif !defined(EIGEN_HAS_NATIVE_FP16) || (EIGEN_COMP_CLANG && !EIGEN_COMP_NVCC) // Emulate support for half floats
+
+#if EIGEN_COMP_CLANG && defined(EIGEN_CUDACC)
+// We need to provide emulated *host-side* FP16 operators for clang.
+#pragma push_macro("EIGEN_DEVICE_FUNC")
+#undef EIGEN_DEVICE_FUNC
+#if defined(EIGEN_HAS_CUDA_FP16) && defined(EIGEN_HAS_NATIVE_FP16)
+#define EIGEN_DEVICE_FUNC __host__
+#else // both host and device need emulated ops.
+#define EIGEN_DEVICE_FUNC __host__ __device__
+#endif
+#endif
+
+// Definitions for CPUs and older HIP+CUDA, mostly working through conversion
+// to/from fp32.
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half operator + (const half& a, const half& b) {
+ return half(float(a) + float(b));
+}
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half operator * (const half& a, const half& b) {
+ return half(float(a) * float(b));
+}
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half operator - (const half& a, const half& b) {
+ return half(float(a) - float(b));
+}
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half operator / (const half& a, const half& b) {
+ return half(float(a) / float(b));
+}
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half operator - (const half& a) {
+ half result;
+ result.x = a.x ^ 0x8000;
+ return result;
+}
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half& operator += (half& a, const half& b) {
+ a = half(float(a) + float(b));
+ return a;
+}
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half& operator *= (half& a, const half& b) {
+ a = half(float(a) * float(b));
+ return a;
+}
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half& operator -= (half& a, const half& b) {
+ a = half(float(a) - float(b));
+ return a;
+}
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half& operator /= (half& a, const half& b) {
+ a = half(float(a) / float(b));
+ return a;
+}
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bool operator == (const half& a, const half& b) {
+ return numext::equal_strict(float(a),float(b));
+}
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bool operator != (const half& a, const half& b) {
+ return numext::not_equal_strict(float(a), float(b));
+}
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bool operator < (const half& a, const half& b) {
+ return float(a) < float(b);
+}
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bool operator <= (const half& a, const half& b) {
+ return float(a) <= float(b);
+}
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bool operator > (const half& a, const half& b) {
+ return float(a) > float(b);
+}
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bool operator >= (const half& a, const half& b) {
+ return float(a) >= float(b);
+}
+
+#if defined(__clang__) && defined(__CUDA__)
+#pragma pop_macro("EIGEN_DEVICE_FUNC")
+#endif
+#endif // Emulate support for half floats
+
+// Division by an index. Do it in full float precision to avoid accuracy
+// issues in converting the denominator to half.
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half operator / (const half& a, Index b) {
+ return half(static_cast<float>(a) / static_cast<float>(b));
+}
+
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half operator++(half& a) {
+ a += half(1);
+ return a;
+}
+
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half operator--(half& a) {
+ a -= half(1);
+ return a;
+}
+
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half operator++(half& a, int) {
+ half original_value = a;
+ ++a;
+ return original_value;
+}
+
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half operator--(half& a, int) {
+ half original_value = a;
+ --a;
+ return original_value;
+}
+
+// Conversion routines, including fallbacks for the host or older CUDA.
+// Note that newer Intel CPUs (Haswell or newer) have vectorized versions of
+// these in hardware. If we need more performance on older/other CPUs, they are
+// also possible to vectorize directly.
+
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR __half_raw raw_uint16_to_half(numext::uint16_t x) {
+ // We cannot simply do a "return __half_raw(x)" here, because __half_raw is union type
+ // in the hip_fp16 header file, and that will trigger a compile error
+ // On the other hand, having anything but a return statement also triggers a compile error
+ // because this is constexpr function.
+ // Fortunately, since we need to disable EIGEN_CONSTEXPR for GPU anyway, we can get out
+ // of this catch22 by having separate bodies for GPU / non GPU
+#if defined(EIGEN_HAS_GPU_FP16)
+ __half_raw h;
+ h.x = x;
+ return h;
+#else
+ return __half_raw(x);
+#endif
+}
+
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC numext::uint16_t raw_half_as_uint16(const __half_raw& h) {
+ // HIP/CUDA/Default have a member 'x' of type uint16_t.
+ // For ARM64 native half, the member 'x' is of type __fp16, so we need to bit-cast.
+ // For SYCL, cl::sycl::half is _Float16, so cast directly.
+#if defined(EIGEN_HAS_ARM64_FP16_SCALAR_ARITHMETIC)
+ return numext::bit_cast<numext::uint16_t>(h.x);
+#elif defined(SYCL_DEVICE_ONLY)
+ return numext::bit_cast<numext::uint16_t>(h);
+#else
+ return h.x;
+#endif
+}
+
+union float32_bits {
+ unsigned int u;
+ float f;
+};
+
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC __half_raw float_to_half_rtne(float ff) {
+#if (defined(EIGEN_HAS_CUDA_FP16) && defined(EIGEN_CUDA_ARCH) && EIGEN_CUDA_ARCH >= 300) || \
+ (defined(EIGEN_HAS_HIP_FP16) && defined(EIGEN_HIP_DEVICE_COMPILE))
+ __half tmp_ff = __float2half(ff);
+ return *(__half_raw*)&tmp_ff;
+
+#elif defined(EIGEN_HAS_FP16_C)
+ __half_raw h;
+ #if EIGEN_COMP_MSVC
+ // MSVC does not have scalar instructions.
+ h.x =_mm_extract_epi16(_mm_cvtps_ph(_mm_set_ss(ff), 0), 0);
+ #else
+ h.x = _cvtss_sh(ff, 0);
+ #endif
+ return h;
+
+#elif defined(EIGEN_HAS_ARM64_FP16_SCALAR_ARITHMETIC)
+ __half_raw h;
+ h.x = static_cast<__fp16>(ff);
+ return h;
+
+#else
+ float32_bits f; f.f = ff;
+
+ const float32_bits f32infty = { 255 << 23 };
+ const float32_bits f16max = { (127 + 16) << 23 };
+ const float32_bits denorm_magic = { ((127 - 15) + (23 - 10) + 1) << 23 };
+ unsigned int sign_mask = 0x80000000u;
+ __half_raw o;
+ o.x = static_cast<numext::uint16_t>(0x0u);
+
+ unsigned int sign = f.u & sign_mask;
+ f.u ^= sign;
+
+ // NOTE all the integer compares in this function can be safely
+ // compiled into signed compares since all operands are below
+ // 0x80000000. Important if you want fast straight SSE2 code
+ // (since there's no unsigned PCMPGTD).
+
+ if (f.u >= f16max.u) { // result is Inf or NaN (all exponent bits set)
+ o.x = (f.u > f32infty.u) ? 0x7e00 : 0x7c00; // NaN->qNaN and Inf->Inf
+ } else { // (De)normalized number or zero
+ if (f.u < (113 << 23)) { // resulting FP16 is subnormal or zero
+ // use a magic value to align our 10 mantissa bits at the bottom of
+ // the float. as long as FP addition is round-to-nearest-even this
+ // just works.
+ f.f += denorm_magic.f;
+
+ // and one integer subtract of the bias later, we have our final float!
+ o.x = static_cast<numext::uint16_t>(f.u - denorm_magic.u);
+ } else {
+ unsigned int mant_odd = (f.u >> 13) & 1; // resulting mantissa is odd
+
+ // update exponent, rounding bias part 1
+ // Equivalent to `f.u += ((unsigned int)(15 - 127) << 23) + 0xfff`, but
+ // without arithmetic overflow.
+ f.u += 0xc8000fffU;
+ // rounding bias part 2
+ f.u += mant_odd;
+ // take the bits!
+ o.x = static_cast<numext::uint16_t>(f.u >> 13);
+ }
+ }
+
+ o.x |= static_cast<numext::uint16_t>(sign >> 16);
+ return o;
+#endif
+}
+
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC float half_to_float(__half_raw h) {
+#if (defined(EIGEN_HAS_CUDA_FP16) && defined(EIGEN_CUDA_ARCH) && EIGEN_CUDA_ARCH >= 300) || \
+ (defined(EIGEN_HAS_HIP_FP16) && defined(EIGEN_HIP_DEVICE_COMPILE))
+ return __half2float(h);
+#elif defined(EIGEN_HAS_FP16_C)
+ #if EIGEN_COMP_MSVC
+ // MSVC does not have scalar instructions.
+ return _mm_cvtss_f32(_mm_cvtph_ps(_mm_set1_epi16(h.x)));
+ #else
+ return _cvtsh_ss(h.x);
+ #endif
+#elif defined(EIGEN_HAS_ARM64_FP16_SCALAR_ARITHMETIC)
+ return static_cast<float>(h.x);
+#else
+ const float32_bits magic = { 113 << 23 };
+ const unsigned int shifted_exp = 0x7c00 << 13; // exponent mask after shift
+ float32_bits o;
+
+ o.u = (h.x & 0x7fff) << 13; // exponent/mantissa bits
+ unsigned int exp = shifted_exp & o.u; // just the exponent
+ o.u += (127 - 15) << 23; // exponent adjust
+
+ // handle exponent special cases
+ if (exp == shifted_exp) { // Inf/NaN?
+ o.u += (128 - 16) << 23; // extra exp adjust
+ } else if (exp == 0) { // Zero/Denormal?
+ o.u += 1 << 23; // extra exp adjust
+ o.f -= magic.f; // renormalize
+ }
+
+ o.u |= (h.x & 0x8000) << 16; // sign bit
+ return o.f;
+#endif
+}
+
+// --- standard functions ---
+
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bool (isinf)(const half& a) {
+#ifdef EIGEN_HAS_ARM64_FP16_SCALAR_ARITHMETIC
+ return (numext::bit_cast<numext::uint16_t>(a.x) & 0x7fff) == 0x7c00;
+#else
+ return (a.x & 0x7fff) == 0x7c00;
+#endif
+}
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bool (isnan)(const half& a) {
+#if (defined(EIGEN_HAS_CUDA_FP16) && defined(EIGEN_CUDA_ARCH) && EIGEN_CUDA_ARCH >= 530) || \
+ (defined(EIGEN_HAS_HIP_FP16) && defined(EIGEN_HIP_DEVICE_COMPILE))
+ return __hisnan(a);
+#elif defined(EIGEN_HAS_ARM64_FP16_SCALAR_ARITHMETIC)
+ return (numext::bit_cast<numext::uint16_t>(a.x) & 0x7fff) > 0x7c00;
+#else
+ return (a.x & 0x7fff) > 0x7c00;
+#endif
+}
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bool (isfinite)(const half& a) {
+ return !(isinf EIGEN_NOT_A_MACRO (a)) && !(isnan EIGEN_NOT_A_MACRO (a));
+}
+
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half abs(const half& a) {
+#if defined(EIGEN_HAS_ARM64_FP16_SCALAR_ARITHMETIC)
+ return half(vabsh_f16(a.x));
+#else
+ half result;
+ result.x = a.x & 0x7FFF;
+ return result;
+#endif
+}
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half exp(const half& a) {
+#if (EIGEN_CUDA_SDK_VER >= 80000 && defined EIGEN_CUDA_ARCH && EIGEN_CUDA_ARCH >= 530) || \
+ defined(EIGEN_HIP_DEVICE_COMPILE)
+ return half(hexp(a));
+#else
+ return half(::expf(float(a)));
+#endif
+}
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half expm1(const half& a) {
+ return half(numext::expm1(float(a)));
+}
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half log(const half& a) {
+#if (defined(EIGEN_HAS_CUDA_FP16) && EIGEN_CUDA_SDK_VER >= 80000 && defined(EIGEN_CUDA_ARCH) && EIGEN_CUDA_ARCH >= 530) || \
+ (defined(EIGEN_HAS_HIP_FP16) && defined(EIGEN_HIP_DEVICE_COMPILE))
+ return half(::hlog(a));
+#else
+ return half(::logf(float(a)));
+#endif
+}
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half log1p(const half& a) {
+ return half(numext::log1p(float(a)));
+}
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half log10(const half& a) {
+ return half(::log10f(float(a)));
+}
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half log2(const half& a) {
+ return half(static_cast<float>(EIGEN_LOG2E) * ::logf(float(a)));
+}
+
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half sqrt(const half& a) {
+#if (EIGEN_CUDA_SDK_VER >= 80000 && defined EIGEN_CUDA_ARCH && EIGEN_CUDA_ARCH >= 530) || \
+ defined(EIGEN_HIP_DEVICE_COMPILE)
+ return half(hsqrt(a));
+#else
+ return half(::sqrtf(float(a)));
+#endif
+}
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half pow(const half& a, const half& b) {
+ return half(::powf(float(a), float(b)));
+}
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half atan2(const half& a, const half& b) {
+ return half(::atan2f(float(a), float(b)));
+}
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half sin(const half& a) {
+ return half(::sinf(float(a)));
+}
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half cos(const half& a) {
+ return half(::cosf(float(a)));
+}
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half tan(const half& a) {
+ return half(::tanf(float(a)));
+}
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half tanh(const half& a) {
+ return half(::tanhf(float(a)));
+}
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half asin(const half& a) {
+ return half(::asinf(float(a)));
+}
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half acos(const half& a) {
+ return half(::acosf(float(a)));
+}
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half floor(const half& a) {
+#if (EIGEN_CUDA_SDK_VER >= 80000 && defined EIGEN_CUDA_ARCH && EIGEN_CUDA_ARCH >= 300) || \
+ defined(EIGEN_HIP_DEVICE_COMPILE)
+ return half(hfloor(a));
+#else
+ return half(::floorf(float(a)));
+#endif
+}
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half ceil(const half& a) {
+#if (EIGEN_CUDA_SDK_VER >= 80000 && defined EIGEN_CUDA_ARCH && EIGEN_CUDA_ARCH >= 300) || \
+ defined(EIGEN_HIP_DEVICE_COMPILE)
+ return half(hceil(a));
+#else
+ return half(::ceilf(float(a)));
+#endif
+}
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half rint(const half& a) {
+ return half(::rintf(float(a)));
+}
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half round(const half& a) {
+ return half(::roundf(float(a)));
+}
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half fmod(const half& a, const half& b) {
+ return half(::fmodf(float(a), float(b)));
+}
+
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half (min)(const half& a, const half& b) {
+#if (defined(EIGEN_HAS_CUDA_FP16) && defined(EIGEN_CUDA_ARCH) && EIGEN_CUDA_ARCH >= 530) || \
+ (defined(EIGEN_HAS_HIP_FP16) && defined(EIGEN_HIP_DEVICE_COMPILE))
+ return __hlt(b, a) ? b : a;
+#else
+ const float f1 = static_cast<float>(a);
+ const float f2 = static_cast<float>(b);
+ return f2 < f1 ? b : a;
+#endif
+}
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half (max)(const half& a, const half& b) {
+#if (defined(EIGEN_HAS_CUDA_FP16) && defined(EIGEN_CUDA_ARCH) && EIGEN_CUDA_ARCH >= 530) || \
+ (defined(EIGEN_HAS_HIP_FP16) && defined(EIGEN_HIP_DEVICE_COMPILE))
+ return __hlt(a, b) ? b : a;
+#else
+ const float f1 = static_cast<float>(a);
+ const float f2 = static_cast<float>(b);
+ return f1 < f2 ? b : a;
+#endif
+}
+
+#ifndef EIGEN_NO_IO
+EIGEN_ALWAYS_INLINE std::ostream& operator << (std::ostream& os, const half& v) {
+ os << static_cast<float>(v);
+ return os;
+}
+#endif
+
+} // end namespace half_impl
+
+// import Eigen::half_impl::half into Eigen namespace
+// using half_impl::half;
+
+namespace internal {
+
+template<>
+struct random_default_impl<half, false, false>
+{
+ static inline half run(const half& x, const half& y)
+ {
+ return x + (y-x) * half(float(std::rand()) / float(RAND_MAX));
+ }
+ static inline half run()
+ {
+ return run(half(-1.f), half(1.f));
+ }
+};
+
+template<> struct is_arithmetic<half> { enum { value = true }; };
+
+} // end namespace internal
+
+template<> struct NumTraits<Eigen::half>
+ : GenericNumTraits<Eigen::half>
+{
+ enum {
+ IsSigned = true,
+ IsInteger = false,
+ IsComplex = false,
+ RequireInitialization = false
+ };
+
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR static EIGEN_STRONG_INLINE Eigen::half epsilon() {
+ return half_impl::raw_uint16_to_half(0x0800);
+ }
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR static EIGEN_STRONG_INLINE Eigen::half dummy_precision() {
+ return half_impl::raw_uint16_to_half(0x211f); // Eigen::half(1e-2f);
+ }
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR static EIGEN_STRONG_INLINE Eigen::half highest() {
+ return half_impl::raw_uint16_to_half(0x7bff);
+ }
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR static EIGEN_STRONG_INLINE Eigen::half lowest() {
+ return half_impl::raw_uint16_to_half(0xfbff);
+ }
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR static EIGEN_STRONG_INLINE Eigen::half infinity() {
+ return half_impl::raw_uint16_to_half(0x7c00);
+ }
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR static EIGEN_STRONG_INLINE Eigen::half quiet_NaN() {
+ return half_impl::raw_uint16_to_half(0x7e00);
+ }
+};
+
+} // end namespace Eigen
+
+#if defined(EIGEN_HAS_GPU_FP16) || defined(EIGEN_HAS_ARM64_FP16_SCALAR_ARITHMETIC)
+ #pragma pop_macro("EIGEN_CONSTEXPR")
+#endif
+
+namespace Eigen {
+namespace numext {
+
+#if defined(EIGEN_GPU_COMPILE_PHASE)
+
+template <>
+EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE bool(isnan)(const Eigen::half& h) {
+ return (half_impl::isnan)(h);
+}
+
+template <>
+EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE bool(isinf)(const Eigen::half& h) {
+ return (half_impl::isinf)(h);
+}
+
+template <>
+EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE bool(isfinite)(const Eigen::half& h) {
+ return (half_impl::isfinite)(h);
+}
+
+#endif
+
+template <>
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half bit_cast<Eigen::half, uint16_t>(const uint16_t& src) {
+ return Eigen::half(Eigen::half_impl::raw_uint16_to_half(src));
+}
+
+template <>
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC uint16_t bit_cast<uint16_t, Eigen::half>(const Eigen::half& src) {
+ return Eigen::half_impl::raw_half_as_uint16(src);
+}
+
+} // namespace numext
+} // namespace Eigen
+
+// Add the missing shfl* intrinsics.
+// The __shfl* functions are only valid on HIP or _CUDA_ARCH_ >= 300.
+// CUDA defines them for (__CUDA_ARCH__ >= 300 || !defined(__CUDA_ARCH__))
+//
+// HIP and CUDA prior to SDK 9.0 define
+// __shfl, __shfl_up, __shfl_down, __shfl_xor for int and float
+// CUDA since 9.0 deprecates those and instead defines
+// __shfl_sync, __shfl_up_sync, __shfl_down_sync, __shfl_xor_sync,
+// with native support for __half and __nv_bfloat16
+//
+// Note that the following are __device__ - only functions.
+#if (defined(EIGEN_CUDACC) && (!defined(EIGEN_CUDA_ARCH) || EIGEN_CUDA_ARCH >= 300)) \
+ || defined(EIGEN_HIPCC)
+
+#if defined(EIGEN_HAS_CUDA_FP16) && EIGEN_CUDA_SDK_VER >= 90000
+
+__device__ EIGEN_STRONG_INLINE Eigen::half __shfl_sync(unsigned mask, Eigen::half var, int srcLane, int width=warpSize) {
+ const __half h = var;
+ return static_cast<Eigen::half>(__shfl_sync(mask, h, srcLane, width));
+}
+
+__device__ EIGEN_STRONG_INLINE Eigen::half __shfl_up_sync(unsigned mask, Eigen::half var, unsigned int delta, int width=warpSize) {
+ const __half h = var;
+ return static_cast<Eigen::half>(__shfl_up_sync(mask, h, delta, width));
+}
+
+__device__ EIGEN_STRONG_INLINE Eigen::half __shfl_down_sync(unsigned mask, Eigen::half var, unsigned int delta, int width=warpSize) {
+ const __half h = var;
+ return static_cast<Eigen::half>(__shfl_down_sync(mask, h, delta, width));
+}
+
+__device__ EIGEN_STRONG_INLINE Eigen::half __shfl_xor_sync(unsigned mask, Eigen::half var, int laneMask, int width=warpSize) {
+ const __half h = var;
+ return static_cast<Eigen::half>(__shfl_xor_sync(mask, h, laneMask, width));
+}
+
+#else // HIP or CUDA SDK < 9.0
+
+__device__ EIGEN_STRONG_INLINE Eigen::half __shfl(Eigen::half var, int srcLane, int width=warpSize) {
+ const int ivar = static_cast<int>(Eigen::numext::bit_cast<Eigen::numext::uint16_t>(var));
+ return Eigen::numext::bit_cast<Eigen::half>(static_cast<Eigen::numext::uint16_t>(__shfl(ivar, srcLane, width)));
+}
+
+__device__ EIGEN_STRONG_INLINE Eigen::half __shfl_up(Eigen::half var, unsigned int delta, int width=warpSize) {
+ const int ivar = static_cast<int>(Eigen::numext::bit_cast<Eigen::numext::uint16_t>(var));
+ return Eigen::numext::bit_cast<Eigen::half>(static_cast<Eigen::numext::uint16_t>(__shfl_up(ivar, delta, width)));
+}
+
+__device__ EIGEN_STRONG_INLINE Eigen::half __shfl_down(Eigen::half var, unsigned int delta, int width=warpSize) {
+ const int ivar = static_cast<int>(Eigen::numext::bit_cast<Eigen::numext::uint16_t>(var));
+ return Eigen::numext::bit_cast<Eigen::half>(static_cast<Eigen::numext::uint16_t>(__shfl_down(ivar, delta, width)));
+}
+
+__device__ EIGEN_STRONG_INLINE Eigen::half __shfl_xor(Eigen::half var, int laneMask, int width=warpSize) {
+ const int ivar = static_cast<int>(Eigen::numext::bit_cast<Eigen::numext::uint16_t>(var));
+ return Eigen::numext::bit_cast<Eigen::half>(static_cast<Eigen::numext::uint16_t>(__shfl_xor(ivar, laneMask, width)));
+}
+
+#endif // HIP vs CUDA
+#endif // __shfl*
+
+// ldg() has an overload for __half_raw, but we also need one for Eigen::half.
+#if (defined(EIGEN_CUDACC) && (!defined(EIGEN_CUDA_ARCH) || EIGEN_CUDA_ARCH >= 350)) \
+ || defined(EIGEN_HIPCC)
+EIGEN_STRONG_INLINE __device__ Eigen::half __ldg(const Eigen::half* ptr) {
+ return Eigen::half_impl::raw_uint16_to_half(__ldg(reinterpret_cast<const Eigen::numext::uint16_t*>(ptr)));
+}
+#endif // __ldg
+
+#if EIGEN_HAS_STD_HASH
+namespace std {
+template <>
+struct hash<Eigen::half> {
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE std::size_t operator()(const Eigen::half& a) const {
+ return static_cast<std::size_t>(Eigen::numext::bit_cast<Eigen::numext::uint16_t>(a));
+ }
+};
+} // end namespace std
+#endif
+
+#endif // EIGEN_HALF_H
diff --git a/Eigen/src/Core/arch/Default/Settings.h b/Eigen/src/Core/arch/Default/Settings.h
new file mode 100644
index 0000000..a5c3ada
--- /dev/null
+++ b/Eigen/src/Core/arch/Default/Settings.h
@@ -0,0 +1,49 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2010 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+
+/* All the parameters defined in this file can be specialized in the
+ * architecture specific files, and/or by the user.
+ * More to come... */
+
+#ifndef EIGEN_DEFAULT_SETTINGS_H
+#define EIGEN_DEFAULT_SETTINGS_H
+
+/** Defines the maximal loop size to enable meta unrolling of loops.
+ * Note that the value here is expressed in Eigen's own notion of "number of FLOPS",
+ * it does not correspond to the number of iterations or the number of instructions
+ */
+#ifndef EIGEN_UNROLLING_LIMIT
+#define EIGEN_UNROLLING_LIMIT 110
+#endif
+
+/** Defines the threshold between a "small" and a "large" matrix.
+ * This threshold is mainly used to select the proper product implementation.
+ */
+#ifndef EIGEN_CACHEFRIENDLY_PRODUCT_THRESHOLD
+#define EIGEN_CACHEFRIENDLY_PRODUCT_THRESHOLD 8
+#endif
+
+/** Defines the maximal width of the blocks used in the triangular product and solver
+ * for vectors (level 2 blas xTRMV and xTRSV). The default is 8.
+ */
+#ifndef EIGEN_TUNE_TRIANGULAR_PANEL_WIDTH
+#define EIGEN_TUNE_TRIANGULAR_PANEL_WIDTH 8
+#endif
+
+
+/** Defines the default number of registers available for that architecture.
+ * Currently it must be 8 or 16. Other values will fail.
+ */
+#ifndef EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS
+#define EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS 8
+#endif
+
+#endif // EIGEN_DEFAULT_SETTINGS_H
diff --git a/Eigen/src/Core/arch/Default/TypeCasting.h b/Eigen/src/Core/arch/Default/TypeCasting.h
new file mode 100644
index 0000000..dc779a7
--- /dev/null
+++ b/Eigen/src/Core/arch/Default/TypeCasting.h
@@ -0,0 +1,116 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2016 Benoit Steiner <benoit.steiner.goog@gmail.com>
+// Copyright (C) 2019 Rasmus Munk Larsen <rmlarsen@google.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_GENERIC_TYPE_CASTING_H
+#define EIGEN_GENERIC_TYPE_CASTING_H
+
+#include "../../InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+
+template<>
+struct scalar_cast_op<float, Eigen::half> {
+ typedef Eigen::half result_type;
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Eigen::half operator() (const float& a) const {
+ #if (defined(EIGEN_HAS_CUDA_FP16) && defined(EIGEN_CUDA_ARCH) && EIGEN_CUDA_ARCH >= 300) || \
+ (defined(EIGEN_HAS_HIP_FP16) && defined(EIGEN_HIP_DEVICE_COMPILE))
+ return __float2half(a);
+ #else
+ return Eigen::half(a);
+ #endif
+ }
+};
+
+template<>
+struct functor_traits<scalar_cast_op<float, Eigen::half> >
+{ enum { Cost = NumTraits<float>::AddCost, PacketAccess = false }; };
+
+
+template<>
+struct scalar_cast_op<int, Eigen::half> {
+ typedef Eigen::half result_type;
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Eigen::half operator() (const int& a) const {
+ #if (defined(EIGEN_HAS_CUDA_FP16) && defined(EIGEN_CUDA_ARCH) && EIGEN_CUDA_ARCH >= 300) || \
+ (defined(EIGEN_HAS_HIP_FP16) && defined(EIGEN_HIP_DEVICE_COMPILE))
+ return __float2half(static_cast<float>(a));
+ #else
+ return Eigen::half(static_cast<float>(a));
+ #endif
+ }
+};
+
+template<>
+struct functor_traits<scalar_cast_op<int, Eigen::half> >
+{ enum { Cost = NumTraits<float>::AddCost, PacketAccess = false }; };
+
+
+template<>
+struct scalar_cast_op<Eigen::half, float> {
+ typedef float result_type;
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE float operator() (const Eigen::half& a) const {
+ #if (defined(EIGEN_HAS_CUDA_FP16) && defined(EIGEN_CUDA_ARCH) && EIGEN_CUDA_ARCH >= 300) || \
+ (defined(EIGEN_HAS_HIP_FP16) && defined(EIGEN_HIP_DEVICE_COMPILE))
+ return __half2float(a);
+ #else
+ return static_cast<float>(a);
+ #endif
+ }
+};
+
+template<>
+struct functor_traits<scalar_cast_op<Eigen::half, float> >
+{ enum { Cost = NumTraits<float>::AddCost, PacketAccess = false }; };
+
+
+template<>
+struct scalar_cast_op<float, Eigen::bfloat16> {
+ typedef Eigen::bfloat16 result_type;
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Eigen::bfloat16 operator() (const float& a) const {
+ return Eigen::bfloat16(a);
+ }
+};
+
+template<>
+struct functor_traits<scalar_cast_op<float, Eigen::bfloat16> >
+{ enum { Cost = NumTraits<float>::AddCost, PacketAccess = false }; };
+
+
+template<>
+struct scalar_cast_op<int, Eigen::bfloat16> {
+ typedef Eigen::bfloat16 result_type;
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Eigen::bfloat16 operator() (const int& a) const {
+ return Eigen::bfloat16(static_cast<float>(a));
+ }
+};
+
+template<>
+struct functor_traits<scalar_cast_op<int, Eigen::bfloat16> >
+{ enum { Cost = NumTraits<float>::AddCost, PacketAccess = false }; };
+
+
+template<>
+struct scalar_cast_op<Eigen::bfloat16, float> {
+ typedef float result_type;
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE float operator() (const Eigen::bfloat16& a) const {
+ return static_cast<float>(a);
+ }
+};
+
+template<>
+struct functor_traits<scalar_cast_op<Eigen::bfloat16, float> >
+{ enum { Cost = NumTraits<float>::AddCost, PacketAccess = false }; };
+
+
+}
+}
+
+#endif // EIGEN_GENERIC_TYPE_CASTING_H
diff --git a/Eigen/src/Core/arch/GPU/Complex.h b/Eigen/src/Core/arch/GPU/Complex.h
new file mode 100644
index 0000000..c2b4c38
--- /dev/null
+++ b/Eigen/src/Core/arch/GPU/Complex.h
@@ -0,0 +1,271 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>
+// Copyright (C) 2021 C. Antonio Sanchez <cantonios@google.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_COMPLEX_GPU_H
+#define EIGEN_COMPLEX_GPU_H
+
+// Many std::complex methods such as operator+, operator-, operator* and
+// operator/ are not constexpr. Due to this, GCC and older versions of clang do
+// not treat them as device functions and thus Eigen functors making use of
+// these operators fail to compile. Here, we manually specialize these
+// operators and functors for complex types when building for CUDA to enable
+// their use on-device.
+//
+// NOTES:
+// - Compound assignment operators +=,-=,*=,/=(Scalar) will not work on device,
+// since they are already specialized in the standard. Using them will result
+// in silent kernel failures.
+// - Compiling with MSVC and using +=,-=,*=,/=(std::complex<Scalar>) will lead
+// to duplicate definition errors, since these are already specialized in
+// Visual Studio's <complex> header (contrary to the standard). This is
+// preferable to removing such definitions, which will lead to silent kernel
+// failures.
+// - Compiling with ICC requires defining _USE_COMPLEX_SPECIALIZATION_ prior
+// to the first inclusion of <complex>.
+
+#if defined(EIGEN_GPUCC) && defined(EIGEN_GPU_COMPILE_PHASE)
+
+// ICC already specializes std::complex<float> and std::complex<double>
+// operators, preventing us from making them device functions here.
+// This will lead to silent runtime errors if the operators are used on device.
+//
+// To allow std::complex operator use on device, define _OVERRIDE_COMPLEX_SPECIALIZATION_
+// prior to first inclusion of <complex>. This prevents ICC from adding
+// its own specializations, so our custom ones below can be used instead.
+#if !(defined(EIGEN_COMP_ICC) && defined(_USE_COMPLEX_SPECIALIZATION_))
+
+// Import Eigen's internal operator specializations.
+#define EIGEN_USING_STD_COMPLEX_OPERATORS \
+ using Eigen::complex_operator_detail::operator+; \
+ using Eigen::complex_operator_detail::operator-; \
+ using Eigen::complex_operator_detail::operator*; \
+ using Eigen::complex_operator_detail::operator/; \
+ using Eigen::complex_operator_detail::operator+=; \
+ using Eigen::complex_operator_detail::operator-=; \
+ using Eigen::complex_operator_detail::operator*=; \
+ using Eigen::complex_operator_detail::operator/=; \
+ using Eigen::complex_operator_detail::operator==; \
+ using Eigen::complex_operator_detail::operator!=;
+
+#include "../../InternalHeaderCheck.h"
+
+namespace Eigen {
+
+// Specialized std::complex overloads.
+namespace complex_operator_detail {
+
+template<typename T>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+std::complex<T> complex_multiply(const std::complex<T>& a, const std::complex<T>& b) {
+ const T a_real = numext::real(a);
+ const T a_imag = numext::imag(a);
+ const T b_real = numext::real(b);
+ const T b_imag = numext::imag(b);
+ return std::complex<T>(
+ a_real * b_real - a_imag * b_imag,
+ a_imag * b_real + a_real * b_imag);
+}
+
+template<typename T>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+std::complex<T> complex_divide_fast(const std::complex<T>& a, const std::complex<T>& b) {
+ const T a_real = numext::real(a);
+ const T a_imag = numext::imag(a);
+ const T b_real = numext::real(b);
+ const T b_imag = numext::imag(b);
+ const T norm = (b_real * b_real + b_imag * b_imag);
+ return std::complex<T>((a_real * b_real + a_imag * b_imag) / norm,
+ (a_imag * b_real - a_real * b_imag) / norm);
+}
+
+template<typename T>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+std::complex<T> complex_divide_stable(const std::complex<T>& a, const std::complex<T>& b) {
+ const T a_real = numext::real(a);
+ const T a_imag = numext::imag(a);
+ const T b_real = numext::real(b);
+ const T b_imag = numext::imag(b);
+ // Smith's complex division (https://arxiv.org/pdf/1210.4539.pdf),
+ // guards against over/under-flow.
+ const bool scale_imag = numext::abs(b_imag) <= numext::abs(b_real);
+ const T rscale = scale_imag ? T(1) : b_real / b_imag;
+ const T iscale = scale_imag ? b_imag / b_real : T(1);
+ const T denominator = b_real * rscale + b_imag * iscale;
+ return std::complex<T>((a_real * rscale + a_imag * iscale) / denominator,
+ (a_imag * rscale - a_real * iscale) / denominator);
+}
+
+template<typename T>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+std::complex<T> complex_divide(const std::complex<T>& a, const std::complex<T>& b) {
+#if EIGEN_FAST_MATH
+ return complex_divide_fast(a, b);
+#else
+ return complex_divide_stable(a, b);
+#endif
+}
+
+// NOTE: We cannot specialize compound assignment operators with Scalar T,
+// (i.e. operator@=(const T&), for @=+,-,*,/)
+// since they are already specialized for float/double/long double within
+// the standard <complex> header. We also do not specialize the stream
+// operators.
+#define EIGEN_CREATE_STD_COMPLEX_OPERATOR_SPECIALIZATIONS(T) \
+ \
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE \
+std::complex<T> operator+(const std::complex<T>& a) { return a; } \
+ \
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE \
+std::complex<T> operator-(const std::complex<T>& a) { \
+ return std::complex<T>(-numext::real(a), -numext::imag(a)); \
+} \
+ \
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE \
+std::complex<T> operator+(const std::complex<T>& a, const std::complex<T>& b) { \
+ return std::complex<T>(numext::real(a) + numext::real(b), numext::imag(a) + numext::imag(b)); \
+} \
+ \
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE \
+std::complex<T> operator+(const std::complex<T>& a, const T& b) { \
+ return std::complex<T>(numext::real(a) + b, numext::imag(a)); \
+} \
+ \
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE \
+std::complex<T> operator+(const T& a, const std::complex<T>& b) { \
+ return std::complex<T>(a + numext::real(b), numext::imag(b)); \
+} \
+ \
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE \
+std::complex<T> operator-(const std::complex<T>& a, const std::complex<T>& b) { \
+ return std::complex<T>(numext::real(a) - numext::real(b), numext::imag(a) - numext::imag(b)); \
+} \
+ \
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE \
+std::complex<T> operator-(const std::complex<T>& a, const T& b) { \
+ return std::complex<T>(numext::real(a) - b, numext::imag(a)); \
+} \
+ \
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE \
+std::complex<T> operator-(const T& a, const std::complex<T>& b) { \
+ return std::complex<T>(a - numext::real(b), -numext::imag(b)); \
+} \
+ \
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE \
+std::complex<T> operator*(const std::complex<T>& a, const std::complex<T>& b) { \
+ return complex_multiply(a, b); \
+} \
+ \
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE \
+std::complex<T> operator*(const std::complex<T>& a, const T& b) { \
+ return std::complex<T>(numext::real(a) * b, numext::imag(a) * b); \
+} \
+ \
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE \
+std::complex<T> operator*(const T& a, const std::complex<T>& b) { \
+ return std::complex<T>(a * numext::real(b), a * numext::imag(b)); \
+} \
+ \
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE \
+std::complex<T> operator/(const std::complex<T>& a, const std::complex<T>& b) { \
+ return complex_divide(a, b); \
+} \
+ \
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE \
+std::complex<T> operator/(const std::complex<T>& a, const T& b) { \
+ return std::complex<T>(numext::real(a) / b, numext::imag(a) / b); \
+} \
+ \
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE \
+std::complex<T> operator/(const T& a, const std::complex<T>& b) { \
+ return complex_divide(std::complex<T>(a, 0), b); \
+} \
+ \
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE \
+std::complex<T>& operator+=(std::complex<T>& a, const std::complex<T>& b) { \
+ numext::real_ref(a) += numext::real(b); \
+ numext::imag_ref(a) += numext::imag(b); \
+ return a; \
+} \
+ \
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE \
+std::complex<T>& operator-=(std::complex<T>& a, const std::complex<T>& b) { \
+ numext::real_ref(a) -= numext::real(b); \
+ numext::imag_ref(a) -= numext::imag(b); \
+ return a; \
+} \
+ \
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE \
+std::complex<T>& operator*=(std::complex<T>& a, const std::complex<T>& b) { \
+ a = complex_multiply(a, b); \
+ return a; \
+} \
+ \
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE \
+std::complex<T>& operator/=(std::complex<T>& a, const std::complex<T>& b) { \
+ a = complex_divide(a, b); \
+ return a; \
+} \
+ \
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE \
+bool operator==(const std::complex<T>& a, const std::complex<T>& b) { \
+ return numext::real(a) == numext::real(b) && numext::imag(a) == numext::imag(b); \
+} \
+ \
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE \
+bool operator==(const std::complex<T>& a, const T& b) { \
+ return numext::real(a) == b && numext::imag(a) == 0; \
+} \
+ \
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE \
+bool operator==(const T& a, const std::complex<T>& b) { \
+ return a == numext::real(b) && 0 == numext::imag(b); \
+} \
+ \
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE \
+bool operator!=(const std::complex<T>& a, const std::complex<T>& b) { \
+ return !(a == b); \
+} \
+ \
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE \
+bool operator!=(const std::complex<T>& a, const T& b) { \
+ return !(a == b); \
+} \
+ \
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE \
+bool operator!=(const T& a, const std::complex<T>& b) { \
+ return !(a == b); \
+}
+
+// Do not specialize for long double, since that reduces to double on device.
+EIGEN_CREATE_STD_COMPLEX_OPERATOR_SPECIALIZATIONS(float)
+EIGEN_CREATE_STD_COMPLEX_OPERATOR_SPECIALIZATIONS(double)
+
+#undef EIGEN_CREATE_STD_COMPLEX_OPERATOR_SPECIALIZATIONS
+
+
+} // namespace complex_operator_detail
+
+EIGEN_USING_STD_COMPLEX_OPERATORS
+
+namespace numext {
+EIGEN_USING_STD_COMPLEX_OPERATORS
+} // namespace numext
+
+namespace internal {
+EIGEN_USING_STD_COMPLEX_OPERATORS
+
+} // namespace internal
+} // namespace Eigen
+
+#endif // !(EIGEN_COMP_ICC && _USE_COMPLEX_SPECIALIZATION_)
+
+#endif // EIGEN_GPUCC && EIGEN_GPU_COMPILE_PHASE
+
+#endif // EIGEN_COMPLEX_GPU_H
diff --git a/Eigen/src/Core/arch/GPU/MathFunctions.h b/Eigen/src/Core/arch/GPU/MathFunctions.h
new file mode 100644
index 0000000..ad61e95
--- /dev/null
+++ b/Eigen/src/Core/arch/GPU/MathFunctions.h
@@ -0,0 +1,105 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_MATH_FUNCTIONS_GPU_H
+#define EIGEN_MATH_FUNCTIONS_GPU_H
+
+#include "../../InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+
+// Make sure this is only available when targeting a GPU: we don't want to
+// introduce conflicts between these packet_traits definitions and the ones
+// we'll use on the host side (SSE, AVX, ...)
+#if defined(EIGEN_GPUCC) && defined(EIGEN_USE_GPU)
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+float4 plog<float4>(const float4& a)
+{
+ return make_float4(logf(a.x), logf(a.y), logf(a.z), logf(a.w));
+}
+
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+double2 plog<double2>(const double2& a)
+{
+ using ::log;
+ return make_double2(log(a.x), log(a.y));
+}
+
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+float4 plog1p<float4>(const float4& a)
+{
+ return make_float4(log1pf(a.x), log1pf(a.y), log1pf(a.z), log1pf(a.w));
+}
+
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+double2 plog1p<double2>(const double2& a)
+{
+ return make_double2(log1p(a.x), log1p(a.y));
+}
+
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+float4 pexp<float4>(const float4& a)
+{
+ return make_float4(expf(a.x), expf(a.y), expf(a.z), expf(a.w));
+}
+
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+double2 pexp<double2>(const double2& a)
+{
+ using ::exp;
+ return make_double2(exp(a.x), exp(a.y));
+}
+
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+float4 pexpm1<float4>(const float4& a)
+{
+ return make_float4(expm1f(a.x), expm1f(a.y), expm1f(a.z), expm1f(a.w));
+}
+
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+double2 pexpm1<double2>(const double2& a)
+{
+ return make_double2(expm1(a.x), expm1(a.y));
+}
+
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+float4 psqrt<float4>(const float4& a)
+{
+ return make_float4(sqrtf(a.x), sqrtf(a.y), sqrtf(a.z), sqrtf(a.w));
+}
+
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+double2 psqrt<double2>(const double2& a)
+{
+ using ::sqrt;
+ return make_double2(sqrt(a.x), sqrt(a.y));
+}
+
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+float4 prsqrt<float4>(const float4& a)
+{
+ return make_float4(rsqrtf(a.x), rsqrtf(a.y), rsqrtf(a.z), rsqrtf(a.w));
+}
+
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+double2 prsqrt<double2>(const double2& a)
+{
+ return make_double2(rsqrt(a.x), rsqrt(a.y));
+}
+
+
+#endif
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_MATH_FUNCTIONS_GPU_H
diff --git a/Eigen/src/Core/arch/GPU/PacketMath.h b/Eigen/src/Core/arch/GPU/PacketMath.h
new file mode 100644
index 0000000..e2bcf48
--- /dev/null
+++ b/Eigen/src/Core/arch/GPU/PacketMath.h
@@ -0,0 +1,1711 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_PACKET_MATH_GPU_H
+#define EIGEN_PACKET_MATH_GPU_H
+
+#include "../../InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+
+// Read-only data cached load available.
+#if defined(EIGEN_HIP_DEVICE_COMPILE) || (defined(EIGEN_CUDA_ARCH) && EIGEN_CUDA_ARCH >= 350)
+#define EIGEN_GPU_HAS_LDG 1
+#endif
+
+// FP16 math available.
+#if (defined(EIGEN_CUDA_ARCH) && EIGEN_CUDA_ARCH >= 530)
+#define EIGEN_CUDA_HAS_FP16_ARITHMETIC 1
+#endif
+
+#if defined(EIGEN_HIP_DEVICE_COMPILE) || defined(EIGEN_CUDA_HAS_FP16_ARITHMETIC)
+#define EIGEN_GPU_HAS_FP16_ARITHMETIC 1
+#endif
+
+// Make sure this is only available when targeting a GPU: we don't want to
+// introduce conflicts between these packet_traits definitions and the ones
+// we'll use on the host side (SSE, AVX, ...)
+#if defined(EIGEN_GPUCC) && defined(EIGEN_USE_GPU)
+
+template<> struct is_arithmetic<float4> { enum { value = true }; };
+template<> struct is_arithmetic<double2> { enum { value = true }; };
+
+template<> struct packet_traits<float> : default_packet_traits
+{
+ typedef float4 type;
+ typedef float4 half;
+ enum {
+ Vectorizable = 1,
+ AlignedOnScalar = 1,
+ size=4,
+ HasHalfPacket = 0,
+
+ HasDiv = 1,
+ HasSin = 0,
+ HasCos = 0,
+ HasLog = 1,
+ HasExp = 1,
+ HasSqrt = 1,
+ HasRsqrt = 1,
+ HasLGamma = 1,
+ HasDiGamma = 1,
+ HasZeta = 1,
+ HasPolygamma = 1,
+ HasErf = 1,
+ HasErfc = 1,
+ HasNdtri = 1,
+ HasBessel = 1,
+ HasIGamma = 1,
+ HasIGammaDerA = 1,
+ HasGammaSampleDerAlpha = 1,
+ HasIGammac = 1,
+ HasBetaInc = 1,
+
+ HasBlend = 0,
+ HasFloor = 1,
+ };
+};
+
+template<> struct packet_traits<double> : default_packet_traits
+{
+ typedef double2 type;
+ typedef double2 half;
+ enum {
+ Vectorizable = 1,
+ AlignedOnScalar = 1,
+ size=2,
+ HasHalfPacket = 0,
+
+ HasDiv = 1,
+ HasLog = 1,
+ HasExp = 1,
+ HasSqrt = 1,
+ HasRsqrt = 1,
+ HasLGamma = 1,
+ HasDiGamma = 1,
+ HasZeta = 1,
+ HasPolygamma = 1,
+ HasErf = 1,
+ HasErfc = 1,
+ HasNdtri = 1,
+ HasBessel = 1,
+ HasIGamma = 1,
+ HasIGammaDerA = 1,
+ HasGammaSampleDerAlpha = 1,
+ HasIGammac = 1,
+ HasBetaInc = 1,
+
+ HasBlend = 0,
+ HasFloor = 1,
+ };
+};
+
+
+template<> struct unpacket_traits<float4> { typedef float type; enum {size=4, alignment=Aligned16, vectorizable=true, masked_load_available=false, masked_store_available=false}; typedef float4 half; };
+template<> struct unpacket_traits<double2> { typedef double type; enum {size=2, alignment=Aligned16, vectorizable=true, masked_load_available=false, masked_store_available=false}; typedef double2 half; };
+
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE float4 pset1<float4>(const float& from) {
+ return make_float4(from, from, from, from);
+}
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE double2 pset1<double2>(const double& from) {
+ return make_double2(from, from);
+}
+
+// We need to distinguish ‘clang as the CUDA compiler’ from ‘clang as the host compiler,
+// invoked by NVCC’ (e.g. on MacOS). The former needs to see both host and device implementation
+// of the functions, while the latter can only deal with one of them.
+#if defined(EIGEN_CUDA_ARCH) || defined(EIGEN_HIPCC) || (defined(EIGEN_CUDACC) && EIGEN_COMP_CLANG && !EIGEN_COMP_NVCC)
+
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE float bitwise_and(const float& a,
+ const float& b) {
+ return __int_as_float(__float_as_int(a) & __float_as_int(b));
+}
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE double bitwise_and(const double& a,
+ const double& b) {
+ return __longlong_as_double(__double_as_longlong(a) &
+ __double_as_longlong(b));
+}
+
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE float bitwise_or(const float& a,
+ const float& b) {
+ return __int_as_float(__float_as_int(a) | __float_as_int(b));
+}
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE double bitwise_or(const double& a,
+ const double& b) {
+ return __longlong_as_double(__double_as_longlong(a) |
+ __double_as_longlong(b));
+}
+
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE float bitwise_xor(const float& a,
+ const float& b) {
+ return __int_as_float(__float_as_int(a) ^ __float_as_int(b));
+}
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE double bitwise_xor(const double& a,
+ const double& b) {
+ return __longlong_as_double(__double_as_longlong(a) ^
+ __double_as_longlong(b));
+}
+
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE float bitwise_andnot(const float& a,
+ const float& b) {
+ return __int_as_float(__float_as_int(a) & ~__float_as_int(b));
+}
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE double bitwise_andnot(const double& a,
+ const double& b) {
+ return __longlong_as_double(__double_as_longlong(a) &
+ ~__double_as_longlong(b));
+}
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE float eq_mask(const float& a,
+ const float& b) {
+ return __int_as_float(a == b ? 0xffffffffu : 0u);
+}
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE double eq_mask(const double& a,
+ const double& b) {
+ return __longlong_as_double(a == b ? 0xffffffffffffffffull : 0ull);
+}
+
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE float lt_mask(const float& a,
+ const float& b) {
+ return __int_as_float(a < b ? 0xffffffffu : 0u);
+}
+
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE double lt_mask(const double& a,
+ const double& b) {
+ return __longlong_as_double(a < b ? 0xffffffffffffffffull : 0ull);
+}
+
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE float le_mask(const float& a,
+ const float& b) {
+ return __int_as_float(a <= b ? 0xffffffffu : 0u);
+}
+
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE double le_mask(const double& a,
+ const double& b) {
+ return __longlong_as_double(a <= b ? 0xffffffffffffffffull : 0ull);
+}
+
+template <>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE float4 pand<float4>(const float4& a,
+ const float4& b) {
+ return make_float4(bitwise_and(a.x, b.x), bitwise_and(a.y, b.y),
+ bitwise_and(a.z, b.z), bitwise_and(a.w, b.w));
+}
+template <>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE double2 pand<double2>(const double2& a,
+ const double2& b) {
+ return make_double2(bitwise_and(a.x, b.x), bitwise_and(a.y, b.y));
+}
+
+template <>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE float4 por<float4>(const float4& a,
+ const float4& b) {
+ return make_float4(bitwise_or(a.x, b.x), bitwise_or(a.y, b.y),
+ bitwise_or(a.z, b.z), bitwise_or(a.w, b.w));
+}
+template <>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE double2 por<double2>(const double2& a,
+ const double2& b) {
+ return make_double2(bitwise_or(a.x, b.x), bitwise_or(a.y, b.y));
+}
+
+template <>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE float4 pxor<float4>(const float4& a,
+ const float4& b) {
+ return make_float4(bitwise_xor(a.x, b.x), bitwise_xor(a.y, b.y),
+ bitwise_xor(a.z, b.z), bitwise_xor(a.w, b.w));
+}
+template <>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE double2 pxor<double2>(const double2& a,
+ const double2& b) {
+ return make_double2(bitwise_xor(a.x, b.x), bitwise_xor(a.y, b.y));
+}
+
+template <>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE float4 pandnot<float4>(const float4& a,
+ const float4& b) {
+ return make_float4(bitwise_andnot(a.x, b.x), bitwise_andnot(a.y, b.y),
+ bitwise_andnot(a.z, b.z), bitwise_andnot(a.w, b.w));
+}
+template <>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE double2
+pandnot<double2>(const double2& a, const double2& b) {
+ return make_double2(bitwise_andnot(a.x, b.x), bitwise_andnot(a.y, b.y));
+}
+
+template <>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE float4 pcmp_eq<float4>(const float4& a,
+ const float4& b) {
+ return make_float4(eq_mask(a.x, b.x), eq_mask(a.y, b.y), eq_mask(a.z, b.z),
+ eq_mask(a.w, b.w));
+}
+template <>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE float4 pcmp_lt<float4>(const float4& a,
+ const float4& b) {
+ return make_float4(lt_mask(a.x, b.x), lt_mask(a.y, b.y), lt_mask(a.z, b.z),
+ lt_mask(a.w, b.w));
+}
+template <>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE float4 pcmp_le<float4>(const float4& a,
+ const float4& b) {
+ return make_float4(le_mask(a.x, b.x), le_mask(a.y, b.y), le_mask(a.z, b.z),
+ le_mask(a.w, b.w));
+}
+template <>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE double2
+pcmp_eq<double2>(const double2& a, const double2& b) {
+ return make_double2(eq_mask(a.x, b.x), eq_mask(a.y, b.y));
+}
+template <>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE double2
+pcmp_lt<double2>(const double2& a, const double2& b) {
+ return make_double2(lt_mask(a.x, b.x), lt_mask(a.y, b.y));
+}
+template <>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE double2
+pcmp_le<double2>(const double2& a, const double2& b) {
+ return make_double2(le_mask(a.x, b.x), le_mask(a.y, b.y));
+}
+#endif // defined(EIGEN_CUDA_ARCH) || defined(EIGEN_HIPCC) || (defined(EIGEN_CUDACC) && EIGEN_COMP_CLANG && !EIGEN_COMP_NVCC)
+
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE float4 plset<float4>(const float& a) {
+ return make_float4(a, a+1, a+2, a+3);
+}
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE double2 plset<double2>(const double& a) {
+ return make_double2(a, a+1);
+}
+
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE float4 padd<float4>(const float4& a, const float4& b) {
+ return make_float4(a.x+b.x, a.y+b.y, a.z+b.z, a.w+b.w);
+}
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE double2 padd<double2>(const double2& a, const double2& b) {
+ return make_double2(a.x+b.x, a.y+b.y);
+}
+
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE float4 psub<float4>(const float4& a, const float4& b) {
+ return make_float4(a.x-b.x, a.y-b.y, a.z-b.z, a.w-b.w);
+}
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE double2 psub<double2>(const double2& a, const double2& b) {
+ return make_double2(a.x-b.x, a.y-b.y);
+}
+
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE float4 pnegate(const float4& a) {
+ return make_float4(-a.x, -a.y, -a.z, -a.w);
+}
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE double2 pnegate(const double2& a) {
+ return make_double2(-a.x, -a.y);
+}
+
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE float4 pconj(const float4& a) { return a; }
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE double2 pconj(const double2& a) { return a; }
+
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE float4 pmul<float4>(const float4& a, const float4& b) {
+ return make_float4(a.x*b.x, a.y*b.y, a.z*b.z, a.w*b.w);
+}
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE double2 pmul<double2>(const double2& a, const double2& b) {
+ return make_double2(a.x*b.x, a.y*b.y);
+}
+
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE float4 pdiv<float4>(const float4& a, const float4& b) {
+ return make_float4(a.x/b.x, a.y/b.y, a.z/b.z, a.w/b.w);
+}
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE double2 pdiv<double2>(const double2& a, const double2& b) {
+ return make_double2(a.x/b.x, a.y/b.y);
+}
+
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE float4 pmin<float4>(const float4& a, const float4& b) {
+ return make_float4(fminf(a.x, b.x), fminf(a.y, b.y), fminf(a.z, b.z), fminf(a.w, b.w));
+}
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE double2 pmin<double2>(const double2& a, const double2& b) {
+ return make_double2(fmin(a.x, b.x), fmin(a.y, b.y));
+}
+
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE float4 pmax<float4>(const float4& a, const float4& b) {
+ return make_float4(fmaxf(a.x, b.x), fmaxf(a.y, b.y), fmaxf(a.z, b.z), fmaxf(a.w, b.w));
+}
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE double2 pmax<double2>(const double2& a, const double2& b) {
+ return make_double2(fmax(a.x, b.x), fmax(a.y, b.y));
+}
+
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE float4 pload<float4>(const float* from) {
+ return *reinterpret_cast<const float4*>(from);
+}
+
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE double2 pload<double2>(const double* from) {
+ return *reinterpret_cast<const double2*>(from);
+}
+
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE float4 ploadu<float4>(const float* from) {
+ return make_float4(from[0], from[1], from[2], from[3]);
+}
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE double2 ploadu<double2>(const double* from) {
+ return make_double2(from[0], from[1]);
+}
+
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE float4 ploaddup<float4>(const float* from) {
+ return make_float4(from[0], from[0], from[1], from[1]);
+}
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE double2 ploaddup<double2>(const double* from) {
+ return make_double2(from[0], from[0]);
+}
+
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void pstore<float>(float* to, const float4& from) {
+ *reinterpret_cast<float4*>(to) = from;
+}
+
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void pstore<double>(double* to, const double2& from) {
+ *reinterpret_cast<double2*>(to) = from;
+}
+
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void pstoreu<float>(float* to, const float4& from) {
+ to[0] = from.x;
+ to[1] = from.y;
+ to[2] = from.z;
+ to[3] = from.w;
+}
+
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void pstoreu<double>(double* to, const double2& from) {
+ to[0] = from.x;
+ to[1] = from.y;
+}
+
+template<>
+EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE float4 ploadt_ro<float4, Aligned>(const float* from) {
+#if defined(EIGEN_GPU_HAS_LDG)
+ return __ldg((const float4*)from);
+#else
+ return make_float4(from[0], from[1], from[2], from[3]);
+#endif
+}
+template<>
+EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE double2 ploadt_ro<double2, Aligned>(const double* from) {
+#if defined(EIGEN_GPU_HAS_LDG)
+ return __ldg((const double2*)from);
+#else
+ return make_double2(from[0], from[1]);
+#endif
+}
+
+template<>
+EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE float4 ploadt_ro<float4, Unaligned>(const float* from) {
+#if defined(EIGEN_GPU_HAS_LDG)
+ return make_float4(__ldg(from+0), __ldg(from+1), __ldg(from+2), __ldg(from+3));
+#else
+ return make_float4(from[0], from[1], from[2], from[3]);
+#endif
+}
+template<>
+EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE double2 ploadt_ro<double2, Unaligned>(const double* from) {
+#if defined(EIGEN_GPU_HAS_LDG)
+ return make_double2(__ldg(from+0), __ldg(from+1));
+#else
+ return make_double2(from[0], from[1]);
+#endif
+}
+
+template<> EIGEN_DEVICE_FUNC inline float4 pgather<float, float4>(const float* from, Index stride) {
+ return make_float4(from[0*stride], from[1*stride], from[2*stride], from[3*stride]);
+}
+
+template<> EIGEN_DEVICE_FUNC inline double2 pgather<double, double2>(const double* from, Index stride) {
+ return make_double2(from[0*stride], from[1*stride]);
+}
+
+template<> EIGEN_DEVICE_FUNC inline void pscatter<float, float4>(float* to, const float4& from, Index stride) {
+ to[stride*0] = from.x;
+ to[stride*1] = from.y;
+ to[stride*2] = from.z;
+ to[stride*3] = from.w;
+}
+template<> EIGEN_DEVICE_FUNC inline void pscatter<double, double2>(double* to, const double2& from, Index stride) {
+ to[stride*0] = from.x;
+ to[stride*1] = from.y;
+}
+
+template<> EIGEN_DEVICE_FUNC inline float pfirst<float4>(const float4& a) {
+ return a.x;
+}
+template<> EIGEN_DEVICE_FUNC inline double pfirst<double2>(const double2& a) {
+ return a.x;
+}
+
+template<> EIGEN_DEVICE_FUNC inline float predux<float4>(const float4& a) {
+ return a.x + a.y + a.z + a.w;
+}
+template<> EIGEN_DEVICE_FUNC inline double predux<double2>(const double2& a) {
+ return a.x + a.y;
+}
+
+template<> EIGEN_DEVICE_FUNC inline float predux_max<float4>(const float4& a) {
+ return fmaxf(fmaxf(a.x, a.y), fmaxf(a.z, a.w));
+}
+template<> EIGEN_DEVICE_FUNC inline double predux_max<double2>(const double2& a) {
+ return fmax(a.x, a.y);
+}
+
+template<> EIGEN_DEVICE_FUNC inline float predux_min<float4>(const float4& a) {
+ return fminf(fminf(a.x, a.y), fminf(a.z, a.w));
+}
+template<> EIGEN_DEVICE_FUNC inline double predux_min<double2>(const double2& a) {
+ return fmin(a.x, a.y);
+}
+
+template<> EIGEN_DEVICE_FUNC inline float predux_mul<float4>(const float4& a) {
+ return a.x * a.y * a.z * a.w;
+}
+template<> EIGEN_DEVICE_FUNC inline double predux_mul<double2>(const double2& a) {
+ return a.x * a.y;
+}
+
+template<> EIGEN_DEVICE_FUNC inline float4 pabs<float4>(const float4& a) {
+ return make_float4(fabsf(a.x), fabsf(a.y), fabsf(a.z), fabsf(a.w));
+}
+template<> EIGEN_DEVICE_FUNC inline double2 pabs<double2>(const double2& a) {
+ return make_double2(fabs(a.x), fabs(a.y));
+}
+
+template<> EIGEN_DEVICE_FUNC inline float4 pfloor<float4>(const float4& a) {
+ return make_float4(floorf(a.x), floorf(a.y), floorf(a.z), floorf(a.w));
+}
+template<> EIGEN_DEVICE_FUNC inline double2 pfloor<double2>(const double2& a) {
+ return make_double2(floor(a.x), floor(a.y));
+}
+
+EIGEN_DEVICE_FUNC inline void
+ptranspose(PacketBlock<float4,4>& kernel) {
+ float tmp = kernel.packet[0].y;
+ kernel.packet[0].y = kernel.packet[1].x;
+ kernel.packet[1].x = tmp;
+
+ tmp = kernel.packet[0].z;
+ kernel.packet[0].z = kernel.packet[2].x;
+ kernel.packet[2].x = tmp;
+
+ tmp = kernel.packet[0].w;
+ kernel.packet[0].w = kernel.packet[3].x;
+ kernel.packet[3].x = tmp;
+
+ tmp = kernel.packet[1].z;
+ kernel.packet[1].z = kernel.packet[2].y;
+ kernel.packet[2].y = tmp;
+
+ tmp = kernel.packet[1].w;
+ kernel.packet[1].w = kernel.packet[3].y;
+ kernel.packet[3].y = tmp;
+
+ tmp = kernel.packet[2].w;
+ kernel.packet[2].w = kernel.packet[3].z;
+ kernel.packet[3].z = tmp;
+}
+
+EIGEN_DEVICE_FUNC inline void
+ptranspose(PacketBlock<double2,2>& kernel) {
+ double tmp = kernel.packet[0].y;
+ kernel.packet[0].y = kernel.packet[1].x;
+ kernel.packet[1].x = tmp;
+}
+
+#endif // defined(EIGEN_GPUCC) && defined(EIGEN_USE_GPU)
+
+// Half-packet functions are not available on the host for CUDA 9.0-9.2, only
+// on device. There is no benefit to using them on the host anyways, since they are
+// emulated.
+#if (defined(EIGEN_HAS_CUDA_FP16) || defined(EIGEN_HAS_HIP_FP16)) && defined(EIGEN_GPU_COMPILE_PHASE)
+
+typedef ulonglong2 Packet4h2;
+template<> struct unpacket_traits<Packet4h2> { typedef Eigen::half type; enum {size=8, alignment=Aligned16, vectorizable=true, masked_load_available=false, masked_store_available=false}; typedef Packet4h2 half; };
+template<> struct is_arithmetic<Packet4h2> { enum { value = true }; };
+
+template<> struct unpacket_traits<half2> { typedef Eigen::half type; enum {size=2, alignment=Aligned16, vectorizable=true, masked_load_available=false, masked_store_available=false}; typedef half2 half; };
+template<> struct is_arithmetic<half2> { enum { value = true }; };
+
+template<> struct packet_traits<Eigen::half> : default_packet_traits
+{
+ typedef Packet4h2 type;
+ typedef Packet4h2 half;
+ enum {
+ Vectorizable = 1,
+ AlignedOnScalar = 1,
+ size=8,
+ HasHalfPacket = 0,
+ HasAdd = 1,
+ HasSub = 1,
+ HasMul = 1,
+ HasDiv = 1,
+ HasSqrt = 1,
+ HasRsqrt = 1,
+ HasExp = 1,
+ HasExpm1 = 1,
+ HasLog = 1,
+ HasLog1p = 1
+ };
+};
+
+template<>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 pset1<half2>(const Eigen::half& from) {
+ return __half2half2(from);
+}
+
+template <>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet4h2
+pset1<Packet4h2>(const Eigen::half& from) {
+ Packet4h2 r;
+ half2* p_alias = reinterpret_cast<half2*>(&r);
+ p_alias[0] = pset1<half2>(from);
+ p_alias[1] = pset1<half2>(from);
+ p_alias[2] = pset1<half2>(from);
+ p_alias[3] = pset1<half2>(from);
+ return r;
+}
+
+namespace {
+
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 pload(const Eigen::half* from) {
+ return *reinterpret_cast<const half2*>(from);
+}
+
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 ploadu(const Eigen::half* from) {
+ return __halves2half2(from[0], from[1]);
+}
+
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 ploaddup(const Eigen::half* from) {
+ return __halves2half2(from[0], from[0]);
+}
+
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void pstore(Eigen::half* to,
+ const half2& from) {
+ *reinterpret_cast<half2*>(to) = from;
+}
+
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void pstoreu(Eigen::half* to,
+ const half2& from) {
+ to[0] = __low2half(from);
+ to[1] = __high2half(from);
+}
+
+
+EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE half2 ploadt_ro_aligned(
+ const Eigen::half* from) {
+#if defined(EIGEN_GPU_HAS_LDG)
+ // Input is guaranteed to be properly aligned.
+ return __ldg(reinterpret_cast<const half2*>(from));
+#else
+ return __halves2half2(*(from+0), *(from+1));
+#endif
+}
+
+EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE half2 ploadt_ro_unaligned(
+ const Eigen::half* from) {
+#if defined(EIGEN_GPU_HAS_LDG)
+ return __halves2half2(__ldg(from+0), __ldg(from+1));
+#else
+ return __halves2half2(*(from+0), *(from+1));
+#endif
+}
+
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 pgather(const Eigen::half* from,
+ Index stride) {
+ return __halves2half2(from[0*stride], from[1*stride]);
+}
+
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void pscatter(
+ Eigen::half* to, const half2& from, Index stride) {
+ to[stride*0] = __low2half(from);
+ to[stride*1] = __high2half(from);
+}
+
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Eigen::half pfirst(const half2& a) {
+ return __low2half(a);
+}
+
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 pabs(const half2& a) {
+ half a1 = __low2half(a);
+ half a2 = __high2half(a);
+ half result1 = half_impl::raw_uint16_to_half(a1.x & 0x7FFF);
+ half result2 = half_impl::raw_uint16_to_half(a2.x & 0x7FFF);
+ return __halves2half2(result1, result2);
+}
+
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 ptrue(const half2& /*a*/) {
+ half true_half = half_impl::raw_uint16_to_half(0xffffu);
+ return pset1<half2>(true_half);
+}
+
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 pzero(const half2& /*a*/) {
+ half false_half = half_impl::raw_uint16_to_half(0x0000u);
+ return pset1<half2>(false_half);
+}
+
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void
+ptranspose(PacketBlock<half2,2>& kernel) {
+ __half a1 = __low2half(kernel.packet[0]);
+ __half a2 = __high2half(kernel.packet[0]);
+ __half b1 = __low2half(kernel.packet[1]);
+ __half b2 = __high2half(kernel.packet[1]);
+ kernel.packet[0] = __halves2half2(a1, b1);
+ kernel.packet[1] = __halves2half2(a2, b2);
+}
+
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 plset(const Eigen::half& a) {
+#if defined(EIGEN_GPU_HAS_FP16_ARITHMETIC)
+ return __halves2half2(a, __hadd(a, __float2half(1.0f)));
+#else
+ float f = __half2float(a) + 1.0f;
+ return __halves2half2(a, __float2half(f));
+#endif
+}
+
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 pselect(const half2& mask,
+ const half2& a,
+ const half2& b) {
+ half mask_low = __low2half(mask);
+ half mask_high = __high2half(mask);
+ half result_low = mask_low == half(0) ? __low2half(b) : __low2half(a);
+ half result_high = mask_high == half(0) ? __high2half(b) : __high2half(a);
+ return __halves2half2(result_low, result_high);
+}
+
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 pcmp_eq(const half2& a,
+ const half2& b) {
+ half true_half = half_impl::raw_uint16_to_half(0xffffu);
+ half false_half = half_impl::raw_uint16_to_half(0x0000u);
+ half a1 = __low2half(a);
+ half a2 = __high2half(a);
+ half b1 = __low2half(b);
+ half b2 = __high2half(b);
+ half eq1 = __half2float(a1) == __half2float(b1) ? true_half : false_half;
+ half eq2 = __half2float(a2) == __half2float(b2) ? true_half : false_half;
+ return __halves2half2(eq1, eq2);
+}
+
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 pcmp_lt(const half2& a,
+ const half2& b) {
+ half true_half = half_impl::raw_uint16_to_half(0xffffu);
+ half false_half = half_impl::raw_uint16_to_half(0x0000u);
+ half a1 = __low2half(a);
+ half a2 = __high2half(a);
+ half b1 = __low2half(b);
+ half b2 = __high2half(b);
+ half eq1 = __half2float(a1) < __half2float(b1) ? true_half : false_half;
+ half eq2 = __half2float(a2) < __half2float(b2) ? true_half : false_half;
+ return __halves2half2(eq1, eq2);
+}
+
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 pcmp_le(const half2& a,
+ const half2& b) {
+ half true_half = half_impl::raw_uint16_to_half(0xffffu);
+ half false_half = half_impl::raw_uint16_to_half(0x0000u);
+ half a1 = __low2half(a);
+ half a2 = __high2half(a);
+ half b1 = __low2half(b);
+ half b2 = __high2half(b);
+ half eq1 = __half2float(a1) <= __half2float(b1) ? true_half : false_half;
+ half eq2 = __half2float(a2) <= __half2float(b2) ? true_half : false_half;
+ return __halves2half2(eq1, eq2);
+}
+
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 pand(const half2& a,
+ const half2& b) {
+ half a1 = __low2half(a);
+ half a2 = __high2half(a);
+ half b1 = __low2half(b);
+ half b2 = __high2half(b);
+ half result1 = half_impl::raw_uint16_to_half(a1.x & b1.x);
+ half result2 = half_impl::raw_uint16_to_half(a2.x & b2.x);
+ return __halves2half2(result1, result2);
+}
+
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 por(const half2& a,
+ const half2& b) {
+ half a1 = __low2half(a);
+ half a2 = __high2half(a);
+ half b1 = __low2half(b);
+ half b2 = __high2half(b);
+ half result1 = half_impl::raw_uint16_to_half(a1.x | b1.x);
+ half result2 = half_impl::raw_uint16_to_half(a2.x | b2.x);
+ return __halves2half2(result1, result2);
+}
+
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 pxor(const half2& a,
+ const half2& b) {
+ half a1 = __low2half(a);
+ half a2 = __high2half(a);
+ half b1 = __low2half(b);
+ half b2 = __high2half(b);
+ half result1 = half_impl::raw_uint16_to_half(a1.x ^ b1.x);
+ half result2 = half_impl::raw_uint16_to_half(a2.x ^ b2.x);
+ return __halves2half2(result1, result2);
+}
+
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 pandnot(const half2& a,
+ const half2& b) {
+ half a1 = __low2half(a);
+ half a2 = __high2half(a);
+ half b1 = __low2half(b);
+ half b2 = __high2half(b);
+ half result1 = half_impl::raw_uint16_to_half(a1.x & ~b1.x);
+ half result2 = half_impl::raw_uint16_to_half(a2.x & ~b2.x);
+ return __halves2half2(result1, result2);
+}
+
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 padd(const half2& a,
+ const half2& b) {
+#if defined(EIGEN_GPU_HAS_FP16_ARITHMETIC)
+ return __hadd2(a, b);
+#else
+ float a1 = __low2float(a);
+ float a2 = __high2float(a);
+ float b1 = __low2float(b);
+ float b2 = __high2float(b);
+ float r1 = a1 + b1;
+ float r2 = a2 + b2;
+ return __floats2half2_rn(r1, r2);
+#endif
+}
+
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 psub(const half2& a,
+ const half2& b) {
+#if defined(EIGEN_GPU_HAS_FP16_ARITHMETIC)
+ return __hsub2(a, b);
+#else
+ float a1 = __low2float(a);
+ float a2 = __high2float(a);
+ float b1 = __low2float(b);
+ float b2 = __high2float(b);
+ float r1 = a1 - b1;
+ float r2 = a2 - b2;
+ return __floats2half2_rn(r1, r2);
+#endif
+}
+
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 pnegate(const half2& a) {
+#if defined(EIGEN_GPU_HAS_FP16_ARITHMETIC)
+ return __hneg2(a);
+#else
+ float a1 = __low2float(a);
+ float a2 = __high2float(a);
+ return __floats2half2_rn(-a1, -a2);
+#endif
+}
+
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 pconj(const half2& a) { return a; }
+
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 pmul(const half2& a,
+ const half2& b) {
+#if defined(EIGEN_GPU_HAS_FP16_ARITHMETIC)
+ return __hmul2(a, b);
+#else
+ float a1 = __low2float(a);
+ float a2 = __high2float(a);
+ float b1 = __low2float(b);
+ float b2 = __high2float(b);
+ float r1 = a1 * b1;
+ float r2 = a2 * b2;
+ return __floats2half2_rn(r1, r2);
+#endif
+}
+
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 pmadd(const half2& a,
+ const half2& b,
+ const half2& c) {
+#if defined(EIGEN_GPU_HAS_FP16_ARITHMETIC)
+ return __hfma2(a, b, c);
+#else
+ float a1 = __low2float(a);
+ float a2 = __high2float(a);
+ float b1 = __low2float(b);
+ float b2 = __high2float(b);
+ float c1 = __low2float(c);
+ float c2 = __high2float(c);
+ float r1 = a1 * b1 + c1;
+ float r2 = a2 * b2 + c2;
+ return __floats2half2_rn(r1, r2);
+#endif
+}
+
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 pdiv(const half2& a,
+ const half2& b) {
+#if defined(EIGEN_GPU_HAS_FP16_ARITHMETIC)
+ return __h2div(a, b);
+#else
+ float a1 = __low2float(a);
+ float a2 = __high2float(a);
+ float b1 = __low2float(b);
+ float b2 = __high2float(b);
+ float r1 = a1 / b1;
+ float r2 = a2 / b2;
+ return __floats2half2_rn(r1, r2);
+#endif
+}
+
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 pmin(const half2& a,
+ const half2& b) {
+ float a1 = __low2float(a);
+ float a2 = __high2float(a);
+ float b1 = __low2float(b);
+ float b2 = __high2float(b);
+ __half r1 = a1 < b1 ? __low2half(a) : __low2half(b);
+ __half r2 = a2 < b2 ? __high2half(a) : __high2half(b);
+ return __halves2half2(r1, r2);
+}
+
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 pmax(const half2& a,
+ const half2& b) {
+ float a1 = __low2float(a);
+ float a2 = __high2float(a);
+ float b1 = __low2float(b);
+ float b2 = __high2float(b);
+ __half r1 = a1 > b1 ? __low2half(a) : __low2half(b);
+ __half r2 = a2 > b2 ? __high2half(a) : __high2half(b);
+ return __halves2half2(r1, r2);
+}
+
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Eigen::half predux(const half2& a) {
+#if defined(EIGEN_GPU_HAS_FP16_ARITHMETIC)
+ return __hadd(__low2half(a), __high2half(a));
+#else
+ float a1 = __low2float(a);
+ float a2 = __high2float(a);
+ return Eigen::half(__float2half(a1 + a2));
+#endif
+}
+
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Eigen::half predux_max(const half2& a) {
+#if defined(EIGEN_GPU_HAS_FP16_ARITHMETIC)
+ __half first = __low2half(a);
+ __half second = __high2half(a);
+ return __hgt(first, second) ? first : second;
+#else
+ float a1 = __low2float(a);
+ float a2 = __high2float(a);
+ return a1 > a2 ? __low2half(a) : __high2half(a);
+#endif
+}
+
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Eigen::half predux_min(const half2& a) {
+#if defined(EIGEN_GPU_HAS_FP16_ARITHMETIC)
+ __half first = __low2half(a);
+ __half second = __high2half(a);
+ return __hlt(first, second) ? first : second;
+#else
+ float a1 = __low2float(a);
+ float a2 = __high2float(a);
+ return a1 < a2 ? __low2half(a) : __high2half(a);
+#endif
+}
+
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Eigen::half predux_mul(const half2& a) {
+#if defined(EIGEN_GPU_HAS_FP16_ARITHMETIC)
+ return __hmul(__low2half(a), __high2half(a));
+#else
+ float a1 = __low2float(a);
+ float a2 = __high2float(a);
+ return Eigen::half(__float2half(a1 * a2));
+#endif
+}
+
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 plog1p(const half2& a) {
+ float a1 = __low2float(a);
+ float a2 = __high2float(a);
+ float r1 = log1pf(a1);
+ float r2 = log1pf(a2);
+ return __floats2half2_rn(r1, r2);
+}
+
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 pexpm1(const half2& a) {
+ float a1 = __low2float(a);
+ float a2 = __high2float(a);
+ float r1 = expm1f(a1);
+ float r2 = expm1f(a2);
+ return __floats2half2_rn(r1, r2);
+}
+
+#if (EIGEN_CUDA_SDK_VER >= 80000 && defined(EIGEN_CUDA_HAS_FP16_ARITHMETIC)) || \
+ defined(EIGEN_HIP_DEVICE_COMPILE)
+
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+half2 plog(const half2& a) {
+ return h2log(a);
+}
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+half2 pexp(const half2& a) {
+ return h2exp(a);
+}
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+half2 psqrt(const half2& a) {
+ return h2sqrt(a);
+}
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+half2 prsqrt(const half2& a) {
+ return h2rsqrt(a);
+}
+
+#else
+
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 plog(const half2& a) {
+ float a1 = __low2float(a);
+ float a2 = __high2float(a);
+ float r1 = logf(a1);
+ float r2 = logf(a2);
+ return __floats2half2_rn(r1, r2);
+}
+
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 pexp(const half2& a) {
+ float a1 = __low2float(a);
+ float a2 = __high2float(a);
+ float r1 = expf(a1);
+ float r2 = expf(a2);
+ return __floats2half2_rn(r1, r2);
+}
+
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 psqrt(const half2& a) {
+ float a1 = __low2float(a);
+ float a2 = __high2float(a);
+ float r1 = sqrtf(a1);
+ float r2 = sqrtf(a2);
+ return __floats2half2_rn(r1, r2);
+}
+
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 prsqrt(const half2& a) {
+ float a1 = __low2float(a);
+ float a2 = __high2float(a);
+ float r1 = rsqrtf(a1);
+ float r2 = rsqrtf(a2);
+ return __floats2half2_rn(r1, r2);
+}
+#endif
+} // namespace
+
+template <>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet4h2
+pload<Packet4h2>(const Eigen::half* from) {
+ return *reinterpret_cast<const Packet4h2*>(from);
+}
+
+// unaligned load;
+template <>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet4h2
+ploadu<Packet4h2>(const Eigen::half* from) {
+ Packet4h2 r;
+ half2* p_alias = reinterpret_cast<half2*>(&r);
+ p_alias[0] = ploadu(from + 0);
+ p_alias[1] = ploadu(from + 2);
+ p_alias[2] = ploadu(from + 4);
+ p_alias[3] = ploadu(from + 6);
+ return r;
+}
+
+template <>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet4h2
+ploaddup<Packet4h2>(const Eigen::half* from) {
+ Packet4h2 r;
+ half2* p_alias = reinterpret_cast<half2*>(&r);
+ p_alias[0] = ploaddup(from + 0);
+ p_alias[1] = ploaddup(from + 1);
+ p_alias[2] = ploaddup(from + 2);
+ p_alias[3] = ploaddup(from + 3);
+ return r;
+}
+
+template <>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void pstore<Eigen::half>(
+ Eigen::half* to, const Packet4h2& from) {
+ *reinterpret_cast<Packet4h2*>(to) = from;
+}
+
+template <>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void pstoreu<Eigen::half>(
+ Eigen::half* to, const Packet4h2& from) {
+ const half2* from_alias = reinterpret_cast<const half2*>(&from);
+ pstoreu(to + 0,from_alias[0]);
+ pstoreu(to + 2,from_alias[1]);
+ pstoreu(to + 4,from_alias[2]);
+ pstoreu(to + 6,from_alias[3]);
+}
+
+template <>
+EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE Packet4h2
+ploadt_ro<Packet4h2, Aligned>(const Eigen::half* from) {
+#if defined(EIGEN_GPU_HAS_LDG)
+ Packet4h2 r;
+ r = __ldg(reinterpret_cast<const Packet4h2*>(from));
+ return r;
+#else
+ Packet4h2 r;
+ half2* r_alias = reinterpret_cast<half2*>(&r);
+ r_alias[0] = ploadt_ro_aligned(from + 0);
+ r_alias[1] = ploadt_ro_aligned(from + 2);
+ r_alias[2] = ploadt_ro_aligned(from + 4);
+ r_alias[3] = ploadt_ro_aligned(from + 6);
+ return r;
+#endif
+}
+
+template <>
+EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE Packet4h2
+ploadt_ro<Packet4h2, Unaligned>(const Eigen::half* from) {
+ Packet4h2 r;
+ half2* r_alias = reinterpret_cast<half2*>(&r);
+ r_alias[0] = ploadt_ro_unaligned(from + 0);
+ r_alias[1] = ploadt_ro_unaligned(from + 2);
+ r_alias[2] = ploadt_ro_unaligned(from + 4);
+ r_alias[3] = ploadt_ro_unaligned(from + 6);
+ return r;
+}
+
+template <>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet4h2
+pgather<Eigen::half, Packet4h2>(const Eigen::half* from, Index stride) {
+ Packet4h2 r;
+ half2* p_alias = reinterpret_cast<half2*>(&r);
+ p_alias[0] = __halves2half2(from[0 * stride], from[1 * stride]);
+ p_alias[1] = __halves2half2(from[2 * stride], from[3 * stride]);
+ p_alias[2] = __halves2half2(from[4 * stride], from[5 * stride]);
+ p_alias[3] = __halves2half2(from[6 * stride], from[7 * stride]);
+ return r;
+}
+
+template <>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void pscatter<Eigen::half, Packet4h2>(
+ Eigen::half* to, const Packet4h2& from, Index stride) {
+ const half2* from_alias = reinterpret_cast<const half2*>(&from);
+ pscatter(to + stride * 0, from_alias[0], stride);
+ pscatter(to + stride * 2, from_alias[1], stride);
+ pscatter(to + stride * 4, from_alias[2], stride);
+ pscatter(to + stride * 6, from_alias[3], stride);
+}
+
+template <>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Eigen::half pfirst<Packet4h2>(
+ const Packet4h2& a) {
+ return pfirst(*(reinterpret_cast<const half2*>(&a)));
+}
+
+template <>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet4h2 pabs<Packet4h2>(
+ const Packet4h2& a) {
+ Packet4h2 r;
+ half2* p_alias = reinterpret_cast<half2*>(&r);
+ const half2* a_alias = reinterpret_cast<const half2*>(&a);
+ p_alias[0] = pabs(a_alias[0]);
+ p_alias[1] = pabs(a_alias[1]);
+ p_alias[2] = pabs(a_alias[2]);
+ p_alias[3] = pabs(a_alias[3]);
+ return r;
+}
+
+template <>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet4h2 ptrue<Packet4h2>(
+ const Packet4h2& /*a*/) {
+ half true_half = half_impl::raw_uint16_to_half(0xffffu);
+ return pset1<Packet4h2>(true_half);
+}
+
+template <>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet4h2 pzero<Packet4h2>(const Packet4h2& /*a*/) {
+ half false_half = half_impl::raw_uint16_to_half(0x0000u);
+ return pset1<Packet4h2>(false_half);
+}
+
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void ptranspose_double(
+ double* d_row0, double* d_row1, double* d_row2, double* d_row3,
+ double* d_row4, double* d_row5, double* d_row6, double* d_row7) {
+ double d_tmp;
+ d_tmp = d_row0[1];
+ d_row0[1] = d_row4[0];
+ d_row4[0] = d_tmp;
+
+ d_tmp = d_row1[1];
+ d_row1[1] = d_row5[0];
+ d_row5[0] = d_tmp;
+
+ d_tmp = d_row2[1];
+ d_row2[1] = d_row6[0];
+ d_row6[0] = d_tmp;
+
+ d_tmp = d_row3[1];
+ d_row3[1] = d_row7[0];
+ d_row7[0] = d_tmp;
+}
+
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void ptranspose_half2(
+ half2* f_row0, half2* f_row1, half2* f_row2, half2* f_row3) {
+ half2 f_tmp;
+ f_tmp = f_row0[1];
+ f_row0[1] = f_row2[0];
+ f_row2[0] = f_tmp;
+
+ f_tmp = f_row1[1];
+ f_row1[1] = f_row3[0];
+ f_row3[0] = f_tmp;
+}
+
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void
+ptranspose_half(half2& f0, half2& f1) {
+ __half a1 = __low2half(f0);
+ __half a2 = __high2half(f0);
+ __half b1 = __low2half(f1);
+ __half b2 = __high2half(f1);
+ f0 = __halves2half2(a1, b1);
+ f1 = __halves2half2(a2, b2);
+}
+
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void
+ptranspose(PacketBlock<Packet4h2,8>& kernel) {
+ double* d_row0 = reinterpret_cast<double*>(&kernel.packet[0]);
+ double* d_row1 = reinterpret_cast<double*>(&kernel.packet[1]);
+ double* d_row2 = reinterpret_cast<double*>(&kernel.packet[2]);
+ double* d_row3 = reinterpret_cast<double*>(&kernel.packet[3]);
+ double* d_row4 = reinterpret_cast<double*>(&kernel.packet[4]);
+ double* d_row5 = reinterpret_cast<double*>(&kernel.packet[5]);
+ double* d_row6 = reinterpret_cast<double*>(&kernel.packet[6]);
+ double* d_row7 = reinterpret_cast<double*>(&kernel.packet[7]);
+ ptranspose_double(d_row0, d_row1, d_row2, d_row3,
+ d_row4, d_row5, d_row6, d_row7);
+
+
+ half2* f_row0 = reinterpret_cast<half2*>(d_row0);
+ half2* f_row1 = reinterpret_cast<half2*>(d_row1);
+ half2* f_row2 = reinterpret_cast<half2*>(d_row2);
+ half2* f_row3 = reinterpret_cast<half2*>(d_row3);
+ ptranspose_half2(f_row0, f_row1, f_row2, f_row3);
+ ptranspose_half(f_row0[0], f_row1[0]);
+ ptranspose_half(f_row0[1], f_row1[1]);
+ ptranspose_half(f_row2[0], f_row3[0]);
+ ptranspose_half(f_row2[1], f_row3[1]);
+
+ f_row0 = reinterpret_cast<half2*>(d_row0 + 1);
+ f_row1 = reinterpret_cast<half2*>(d_row1 + 1);
+ f_row2 = reinterpret_cast<half2*>(d_row2 + 1);
+ f_row3 = reinterpret_cast<half2*>(d_row3 + 1);
+ ptranspose_half2(f_row0, f_row1, f_row2, f_row3);
+ ptranspose_half(f_row0[0], f_row1[0]);
+ ptranspose_half(f_row0[1], f_row1[1]);
+ ptranspose_half(f_row2[0], f_row3[0]);
+ ptranspose_half(f_row2[1], f_row3[1]);
+
+ f_row0 = reinterpret_cast<half2*>(d_row4);
+ f_row1 = reinterpret_cast<half2*>(d_row5);
+ f_row2 = reinterpret_cast<half2*>(d_row6);
+ f_row3 = reinterpret_cast<half2*>(d_row7);
+ ptranspose_half2(f_row0, f_row1, f_row2, f_row3);
+ ptranspose_half(f_row0[0], f_row1[0]);
+ ptranspose_half(f_row0[1], f_row1[1]);
+ ptranspose_half(f_row2[0], f_row3[0]);
+ ptranspose_half(f_row2[1], f_row3[1]);
+
+ f_row0 = reinterpret_cast<half2*>(d_row4 + 1);
+ f_row1 = reinterpret_cast<half2*>(d_row5 + 1);
+ f_row2 = reinterpret_cast<half2*>(d_row6 + 1);
+ f_row3 = reinterpret_cast<half2*>(d_row7 + 1);
+ ptranspose_half2(f_row0, f_row1, f_row2, f_row3);
+ ptranspose_half(f_row0[0], f_row1[0]);
+ ptranspose_half(f_row0[1], f_row1[1]);
+ ptranspose_half(f_row2[0], f_row3[0]);
+ ptranspose_half(f_row2[1], f_row3[1]);
+
+}
+
+template <>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet4h2
+plset<Packet4h2>(const Eigen::half& a) {
+#if defined(EIGEN_HIP_DEVICE_COMPILE)
+
+ Packet4h2 r;
+ half2* p_alias = reinterpret_cast<half2*>(&r);
+ p_alias[0] = __halves2half2(a, __hadd(a, __float2half(1.0f)));
+ p_alias[1] = __halves2half2(__hadd(a, __float2half(2.0f)),
+ __hadd(a, __float2half(3.0f)));
+ p_alias[2] = __halves2half2(__hadd(a, __float2half(4.0f)),
+ __hadd(a, __float2half(5.0f)));
+ p_alias[3] = __halves2half2(__hadd(a, __float2half(6.0f)),
+ __hadd(a, __float2half(7.0f)));
+ return r;
+#elif defined(EIGEN_CUDA_HAS_FP16_ARITHMETIC)
+ Packet4h2 r;
+ half2* r_alias = reinterpret_cast<half2*>(&r);
+
+ half2 b = pset1<half2>(a);
+ half2 c;
+ half2 half_offset0 = __halves2half2(__float2half(0.0f),__float2half(2.0f));
+ half2 half_offset1 = __halves2half2(__float2half(4.0f),__float2half(6.0f));
+
+ c = __hadd2(b, half_offset0);
+ r_alias[0] = plset(__low2half(c));
+ r_alias[1] = plset(__high2half(c));
+
+ c = __hadd2(b, half_offset1);
+ r_alias[2] = plset(__low2half(c));
+ r_alias[3] = plset(__high2half(c));
+
+ return r;
+
+#else
+ float f = __half2float(a);
+ Packet4h2 r;
+ half2* p_alias = reinterpret_cast<half2*>(&r);
+ p_alias[0] = __halves2half2(a, __float2half(f + 1.0f));
+ p_alias[1] = __halves2half2(__float2half(f + 2.0f), __float2half(f + 3.0f));
+ p_alias[2] = __halves2half2(__float2half(f + 4.0f), __float2half(f + 5.0f));
+ p_alias[3] = __halves2half2(__float2half(f + 6.0f), __float2half(f + 7.0f));
+ return r;
+#endif
+}
+
+template <>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet4h2
+pselect<Packet4h2>(const Packet4h2& mask, const Packet4h2& a,
+ const Packet4h2& b) {
+ Packet4h2 r;
+ half2* r_alias = reinterpret_cast<half2*>(&r);
+ const half2* mask_alias = reinterpret_cast<const half2*>(&mask);
+ const half2* a_alias = reinterpret_cast<const half2*>(&a);
+ const half2* b_alias = reinterpret_cast<const half2*>(&b);
+ r_alias[0] = pselect(mask_alias[0], a_alias[0], b_alias[0]);
+ r_alias[1] = pselect(mask_alias[1], a_alias[1], b_alias[1]);
+ r_alias[2] = pselect(mask_alias[2], a_alias[2], b_alias[2]);
+ r_alias[3] = pselect(mask_alias[3], a_alias[3], b_alias[3]);
+ return r;
+}
+
+template <>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet4h2
+pcmp_eq<Packet4h2>(const Packet4h2& a, const Packet4h2& b) {
+ Packet4h2 r;
+ half2* r_alias = reinterpret_cast<half2*>(&r);
+ const half2* a_alias = reinterpret_cast<const half2*>(&a);
+ const half2* b_alias = reinterpret_cast<const half2*>(&b);
+ r_alias[0] = pcmp_eq(a_alias[0], b_alias[0]);
+ r_alias[1] = pcmp_eq(a_alias[1], b_alias[1]);
+ r_alias[2] = pcmp_eq(a_alias[2], b_alias[2]);
+ r_alias[3] = pcmp_eq(a_alias[3], b_alias[3]);
+ return r;
+}
+
+template <>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet4h2
+pcmp_lt<Packet4h2>(const Packet4h2& a, const Packet4h2& b) {
+ Packet4h2 r;
+ half2* r_alias = reinterpret_cast<half2*>(&r);
+ const half2* a_alias = reinterpret_cast<const half2*>(&a);
+ const half2* b_alias = reinterpret_cast<const half2*>(&b);
+ r_alias[0] = pcmp_lt(a_alias[0], b_alias[0]);
+ r_alias[1] = pcmp_lt(a_alias[1], b_alias[1]);
+ r_alias[2] = pcmp_lt(a_alias[2], b_alias[2]);
+ r_alias[3] = pcmp_lt(a_alias[3], b_alias[3]);
+ return r;
+}
+
+template <>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet4h2
+pcmp_le<Packet4h2>(const Packet4h2& a, const Packet4h2& b) {
+ Packet4h2 r;
+ half2* r_alias = reinterpret_cast<half2*>(&r);
+ const half2* a_alias = reinterpret_cast<const half2*>(&a);
+ const half2* b_alias = reinterpret_cast<const half2*>(&b);
+ r_alias[0] = pcmp_le(a_alias[0], b_alias[0]);
+ r_alias[1] = pcmp_le(a_alias[1], b_alias[1]);
+ r_alias[2] = pcmp_le(a_alias[2], b_alias[2]);
+ r_alias[3] = pcmp_le(a_alias[3], b_alias[3]);
+ return r;
+}
+
+template <>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet4h2 pand<Packet4h2>(
+ const Packet4h2& a, const Packet4h2& b) {
+ Packet4h2 r;
+ half2* r_alias = reinterpret_cast<half2*>(&r);
+ const half2* a_alias = reinterpret_cast<const half2*>(&a);
+ const half2* b_alias = reinterpret_cast<const half2*>(&b);
+ r_alias[0] = pand(a_alias[0], b_alias[0]);
+ r_alias[1] = pand(a_alias[1], b_alias[1]);
+ r_alias[2] = pand(a_alias[2], b_alias[2]);
+ r_alias[3] = pand(a_alias[3], b_alias[3]);
+ return r;
+}
+
+template <>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet4h2 por<Packet4h2>(
+ const Packet4h2& a, const Packet4h2& b) {
+ Packet4h2 r;
+ half2* r_alias = reinterpret_cast<half2*>(&r);
+ const half2* a_alias = reinterpret_cast<const half2*>(&a);
+ const half2* b_alias = reinterpret_cast<const half2*>(&b);
+ r_alias[0] = por(a_alias[0], b_alias[0]);
+ r_alias[1] = por(a_alias[1], b_alias[1]);
+ r_alias[2] = por(a_alias[2], b_alias[2]);
+ r_alias[3] = por(a_alias[3], b_alias[3]);
+ return r;
+}
+
+template <>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet4h2 pxor<Packet4h2>(
+ const Packet4h2& a, const Packet4h2& b) {
+ Packet4h2 r;
+ half2* r_alias = reinterpret_cast<half2*>(&r);
+ const half2* a_alias = reinterpret_cast<const half2*>(&a);
+ const half2* b_alias = reinterpret_cast<const half2*>(&b);
+ r_alias[0] = pxor(a_alias[0], b_alias[0]);
+ r_alias[1] = pxor(a_alias[1], b_alias[1]);
+ r_alias[2] = pxor(a_alias[2], b_alias[2]);
+ r_alias[3] = pxor(a_alias[3], b_alias[3]);
+ return r;
+}
+
+template <>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet4h2
+pandnot<Packet4h2>(const Packet4h2& a, const Packet4h2& b) {
+ Packet4h2 r;
+ half2* r_alias = reinterpret_cast<half2*>(&r);
+ const half2* a_alias = reinterpret_cast<const half2*>(&a);
+ const half2* b_alias = reinterpret_cast<const half2*>(&b);
+ r_alias[0] = pandnot(a_alias[0], b_alias[0]);
+ r_alias[1] = pandnot(a_alias[1], b_alias[1]);
+ r_alias[2] = pandnot(a_alias[2], b_alias[2]);
+ r_alias[3] = pandnot(a_alias[3], b_alias[3]);
+ return r;
+}
+
+template <>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet4h2 padd<Packet4h2>(
+ const Packet4h2& a, const Packet4h2& b) {
+ Packet4h2 r;
+ half2* r_alias = reinterpret_cast<half2*>(&r);
+ const half2* a_alias = reinterpret_cast<const half2*>(&a);
+ const half2* b_alias = reinterpret_cast<const half2*>(&b);
+ r_alias[0] = padd(a_alias[0], b_alias[0]);
+ r_alias[1] = padd(a_alias[1], b_alias[1]);
+ r_alias[2] = padd(a_alias[2], b_alias[2]);
+ r_alias[3] = padd(a_alias[3], b_alias[3]);
+ return r;
+}
+
+template <>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet4h2 psub<Packet4h2>(
+ const Packet4h2& a, const Packet4h2& b) {
+ Packet4h2 r;
+ half2* r_alias = reinterpret_cast<half2*>(&r);
+ const half2* a_alias = reinterpret_cast<const half2*>(&a);
+ const half2* b_alias = reinterpret_cast<const half2*>(&b);
+ r_alias[0] = psub(a_alias[0], b_alias[0]);
+ r_alias[1] = psub(a_alias[1], b_alias[1]);
+ r_alias[2] = psub(a_alias[2], b_alias[2]);
+ r_alias[3] = psub(a_alias[3], b_alias[3]);
+ return r;
+}
+
+template <>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet4h2 pnegate(const Packet4h2& a) {
+ Packet4h2 r;
+ half2* r_alias = reinterpret_cast<half2*>(&r);
+ const half2* a_alias = reinterpret_cast<const half2*>(&a);
+ r_alias[0] = pnegate(a_alias[0]);
+ r_alias[1] = pnegate(a_alias[1]);
+ r_alias[2] = pnegate(a_alias[2]);
+ r_alias[3] = pnegate(a_alias[3]);
+ return r;
+}
+
+template <>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet4h2 pconj(const Packet4h2& a) {
+ return a;
+}
+
+template <>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet4h2 pmul<Packet4h2>(
+ const Packet4h2& a, const Packet4h2& b) {
+ Packet4h2 r;
+ half2* r_alias = reinterpret_cast<half2*>(&r);
+ const half2* a_alias = reinterpret_cast<const half2*>(&a);
+ const half2* b_alias = reinterpret_cast<const half2*>(&b);
+ r_alias[0] = pmul(a_alias[0], b_alias[0]);
+ r_alias[1] = pmul(a_alias[1], b_alias[1]);
+ r_alias[2] = pmul(a_alias[2], b_alias[2]);
+ r_alias[3] = pmul(a_alias[3], b_alias[3]);
+ return r;
+}
+
+template <>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet4h2 pmadd<Packet4h2>(
+ const Packet4h2& a, const Packet4h2& b, const Packet4h2& c) {
+ Packet4h2 r;
+ half2* r_alias = reinterpret_cast<half2*>(&r);
+ const half2* a_alias = reinterpret_cast<const half2*>(&a);
+ const half2* b_alias = reinterpret_cast<const half2*>(&b);
+ const half2* c_alias = reinterpret_cast<const half2*>(&c);
+ r_alias[0] = pmadd(a_alias[0], b_alias[0], c_alias[0]);
+ r_alias[1] = pmadd(a_alias[1], b_alias[1], c_alias[1]);
+ r_alias[2] = pmadd(a_alias[2], b_alias[2], c_alias[2]);
+ r_alias[3] = pmadd(a_alias[3], b_alias[3], c_alias[3]);
+ return r;
+}
+
+template <>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet4h2 pdiv<Packet4h2>(
+ const Packet4h2& a, const Packet4h2& b) {
+ Packet4h2 r;
+ half2* r_alias = reinterpret_cast<half2*>(&r);
+ const half2* a_alias = reinterpret_cast<const half2*>(&a);
+ const half2* b_alias = reinterpret_cast<const half2*>(&b);
+ r_alias[0] = pdiv(a_alias[0], b_alias[0]);
+ r_alias[1] = pdiv(a_alias[1], b_alias[1]);
+ r_alias[2] = pdiv(a_alias[2], b_alias[2]);
+ r_alias[3] = pdiv(a_alias[3], b_alias[3]);
+ return r;
+}
+
+template <>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet4h2 pmin<Packet4h2>(
+ const Packet4h2& a, const Packet4h2& b) {
+ Packet4h2 r;
+ half2* r_alias = reinterpret_cast<half2*>(&r);
+ const half2* a_alias = reinterpret_cast<const half2*>(&a);
+ const half2* b_alias = reinterpret_cast<const half2*>(&b);
+ r_alias[0] = pmin(a_alias[0], b_alias[0]);
+ r_alias[1] = pmin(a_alias[1], b_alias[1]);
+ r_alias[2] = pmin(a_alias[2], b_alias[2]);
+ r_alias[3] = pmin(a_alias[3], b_alias[3]);
+ return r;
+}
+
+template <>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet4h2 pmax<Packet4h2>(
+ const Packet4h2& a, const Packet4h2& b) {
+ Packet4h2 r;
+ half2* r_alias = reinterpret_cast<half2*>(&r);
+ const half2* a_alias = reinterpret_cast<const half2*>(&a);
+ const half2* b_alias = reinterpret_cast<const half2*>(&b);
+ r_alias[0] = pmax(a_alias[0], b_alias[0]);
+ r_alias[1] = pmax(a_alias[1], b_alias[1]);
+ r_alias[2] = pmax(a_alias[2], b_alias[2]);
+ r_alias[3] = pmax(a_alias[3], b_alias[3]);
+ return r;
+}
+
+template <>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Eigen::half predux<Packet4h2>(
+ const Packet4h2& a) {
+ const half2* a_alias = reinterpret_cast<const half2*>(&a);
+
+ return predux(a_alias[0]) + predux(a_alias[1]) +
+ predux(a_alias[2]) + predux(a_alias[3]);
+}
+
+template <>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Eigen::half predux_max<Packet4h2>(
+ const Packet4h2& a) {
+ const half2* a_alias = reinterpret_cast<const half2*>(&a);
+ half2 m0 = __halves2half2(predux_max(a_alias[0]),
+ predux_max(a_alias[1]));
+ half2 m1 = __halves2half2(predux_max(a_alias[2]),
+ predux_max(a_alias[3]));
+ __half first = predux_max(m0);
+ __half second = predux_max(m1);
+#if defined(EIGEN_CUDA_HAS_FP16_ARITHMETIC)
+ return (__hgt(first, second) ? first : second);
+#else
+ float ffirst = __half2float(first);
+ float fsecond = __half2float(second);
+ return (ffirst > fsecond)? first: second;
+#endif
+}
+
+template <>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Eigen::half predux_min<Packet4h2>(
+ const Packet4h2& a) {
+ const half2* a_alias = reinterpret_cast<const half2*>(&a);
+ half2 m0 = __halves2half2(predux_min(a_alias[0]),
+ predux_min(a_alias[1]));
+ half2 m1 = __halves2half2(predux_min(a_alias[2]),
+ predux_min(a_alias[3]));
+ __half first = predux_min(m0);
+ __half second = predux_min(m1);
+#if defined(EIGEN_CUDA_HAS_FP16_ARITHMETIC)
+ return (__hlt(first, second) ? first : second);
+#else
+ float ffirst = __half2float(first);
+ float fsecond = __half2float(second);
+ return (ffirst < fsecond)? first: second;
+#endif
+}
+
+// likely overflow/underflow
+template <>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Eigen::half predux_mul<Packet4h2>(
+ const Packet4h2& a) {
+ const half2* a_alias = reinterpret_cast<const half2*>(&a);
+ return predux_mul(pmul(pmul(a_alias[0], a_alias[1]),
+ pmul(a_alias[2], a_alias[3])));
+}
+
+template <>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet4h2
+plog1p<Packet4h2>(const Packet4h2& a) {
+ Packet4h2 r;
+ half2* r_alias = reinterpret_cast<half2*>(&r);
+ const half2* a_alias = reinterpret_cast<const half2*>(&a);
+ r_alias[0] = plog1p(a_alias[0]);
+ r_alias[1] = plog1p(a_alias[1]);
+ r_alias[2] = plog1p(a_alias[2]);
+ r_alias[3] = plog1p(a_alias[3]);
+ return r;
+}
+
+template <>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet4h2
+pexpm1<Packet4h2>(const Packet4h2& a) {
+ Packet4h2 r;
+ half2* r_alias = reinterpret_cast<half2*>(&r);
+ const half2* a_alias = reinterpret_cast<const half2*>(&a);
+ r_alias[0] = pexpm1(a_alias[0]);
+ r_alias[1] = pexpm1(a_alias[1]);
+ r_alias[2] = pexpm1(a_alias[2]);
+ r_alias[3] = pexpm1(a_alias[3]);
+ return r;
+}
+
+template <>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet4h2 plog<Packet4h2>(const Packet4h2& a) {
+ Packet4h2 r;
+ half2* r_alias = reinterpret_cast<half2*>(&r);
+ const half2* a_alias = reinterpret_cast<const half2*>(&a);
+ r_alias[0] = plog(a_alias[0]);
+ r_alias[1] = plog(a_alias[1]);
+ r_alias[2] = plog(a_alias[2]);
+ r_alias[3] = plog(a_alias[3]);
+ return r;
+}
+
+template <>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet4h2 pexp<Packet4h2>(const Packet4h2& a) {
+ Packet4h2 r;
+ half2* r_alias = reinterpret_cast<half2*>(&r);
+ const half2* a_alias = reinterpret_cast<const half2*>(&a);
+ r_alias[0] = pexp(a_alias[0]);
+ r_alias[1] = pexp(a_alias[1]);
+ r_alias[2] = pexp(a_alias[2]);
+ r_alias[3] = pexp(a_alias[3]);
+ return r;
+}
+
+template <>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet4h2 psqrt<Packet4h2>(const Packet4h2& a) {
+ Packet4h2 r;
+ half2* r_alias = reinterpret_cast<half2*>(&r);
+ const half2* a_alias = reinterpret_cast<const half2*>(&a);
+ r_alias[0] = psqrt(a_alias[0]);
+ r_alias[1] = psqrt(a_alias[1]);
+ r_alias[2] = psqrt(a_alias[2]);
+ r_alias[3] = psqrt(a_alias[3]);
+ return r;
+}
+
+template <>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet4h2
+prsqrt<Packet4h2>(const Packet4h2& a) {
+ Packet4h2 r;
+ half2* r_alias = reinterpret_cast<half2*>(&r);
+ const half2* a_alias = reinterpret_cast<const half2*>(&a);
+ r_alias[0] = prsqrt(a_alias[0]);
+ r_alias[1] = prsqrt(a_alias[1]);
+ r_alias[2] = prsqrt(a_alias[2]);
+ r_alias[3] = prsqrt(a_alias[3]);
+ return r;
+}
+
+// The following specialized padd, pmul, pdiv, pmin, pmax, pset1 are needed for
+// the implementation of GPU half reduction.
+template<>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 padd<half2>(const half2& a,
+ const half2& b) {
+#if defined(EIGEN_GPU_HAS_FP16_ARITHMETIC)
+ return __hadd2(a, b);
+#else
+ float a1 = __low2float(a);
+ float a2 = __high2float(a);
+ float b1 = __low2float(b);
+ float b2 = __high2float(b);
+ float r1 = a1 + b1;
+ float r2 = a2 + b2;
+ return __floats2half2_rn(r1, r2);
+#endif
+}
+
+template<>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 pmul<half2>(const half2& a,
+ const half2& b) {
+#if defined(EIGEN_GPU_HAS_FP16_ARITHMETIC)
+ return __hmul2(a, b);
+#else
+ float a1 = __low2float(a);
+ float a2 = __high2float(a);
+ float b1 = __low2float(b);
+ float b2 = __high2float(b);
+ float r1 = a1 * b1;
+ float r2 = a2 * b2;
+ return __floats2half2_rn(r1, r2);
+#endif
+}
+
+template<>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 pdiv<half2>(const half2& a,
+ const half2& b) {
+#if defined(EIGEN_GPU_HAS_FP16_ARITHMETIC)
+ return __h2div(a, b);
+#else
+ float a1 = __low2float(a);
+ float a2 = __high2float(a);
+ float b1 = __low2float(b);
+ float b2 = __high2float(b);
+ float r1 = a1 / b1;
+ float r2 = a2 / b2;
+ return __floats2half2_rn(r1, r2);
+#endif
+}
+
+template<>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 pmin<half2>(const half2& a,
+ const half2& b) {
+ float a1 = __low2float(a);
+ float a2 = __high2float(a);
+ float b1 = __low2float(b);
+ float b2 = __high2float(b);
+ __half r1 = a1 < b1 ? __low2half(a) : __low2half(b);
+ __half r2 = a2 < b2 ? __high2half(a) : __high2half(b);
+ return __halves2half2(r1, r2);
+}
+
+template<>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 pmax<half2>(const half2& a,
+ const half2& b) {
+ float a1 = __low2float(a);
+ float a2 = __high2float(a);
+ float b1 = __low2float(b);
+ float b2 = __high2float(b);
+ __half r1 = a1 > b1 ? __low2half(a) : __low2half(b);
+ __half r2 = a2 > b2 ? __high2half(a) : __high2half(b);
+ return __halves2half2(r1, r2);
+}
+
+#endif // (defined(EIGEN_HAS_CUDA_FP16) || defined(EIGEN_HAS_HIP_FP16)) && defined(EIGEN_GPU_COMPILE_PHASE)
+
+#undef EIGEN_GPU_HAS_LDG
+#undef EIGEN_CUDA_HAS_FP16_ARITHMETIC
+#undef EIGEN_GPU_HAS_FP16_ARITHMETIC
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+
+#endif // EIGEN_PACKET_MATH_GPU_H
diff --git a/Eigen/src/Core/arch/GPU/Tuple.h b/Eigen/src/Core/arch/GPU/Tuple.h
new file mode 100644
index 0000000..e223ca1
--- /dev/null
+++ b/Eigen/src/Core/arch/GPU/Tuple.h
@@ -0,0 +1,302 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2021 The Eigen Team
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_TUPLE_GPU
+#define EIGEN_TUPLE_GPU
+
+#include <type_traits>
+#include <utility>
+
+// This is a replacement of std::tuple that can be used in device code.
+
+namespace Eigen {
+namespace internal {
+namespace tuple_impl {
+
+// Internal tuple implementation.
+template<size_t N, typename... Types>
+class TupleImpl;
+
+// Generic recursive tuple.
+template<size_t N, typename T1, typename... Ts>
+class TupleImpl<N, T1, Ts...> {
+ public:
+ // Tuple may contain Eigen types.
+ EIGEN_MAKE_ALIGNED_OPERATOR_NEW
+
+ // Default constructor, enable if all types are default-constructible.
+ template<typename U1 = T1, typename EnableIf = std::enable_if_t<
+ std::is_default_constructible<U1>::value
+ && reduce_all<std::is_default_constructible<Ts>::value...>::value
+ >>
+ EIGEN_CONSTEXPR EIGEN_DEVICE_FUNC
+ TupleImpl() : head_{}, tail_{} {}
+
+ // Element constructor.
+ template<typename U1, typename... Us,
+ // Only enable if...
+ typename EnableIf = std::enable_if_t<
+ // the number of input arguments match, and ...
+ sizeof...(Us) == sizeof...(Ts) && (
+ // this does not look like a copy/move constructor.
+ N > 1 || std::is_convertible<U1, T1>::value)
+ >>
+ EIGEN_CONSTEXPR EIGEN_DEVICE_FUNC
+ TupleImpl(U1&& arg1, Us&&... args)
+ : head_(std::forward<U1>(arg1)), tail_(std::forward<Us>(args)...) {}
+
+ // The first stored value.
+ EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
+ T1& head() {
+ return head_;
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
+ const T1& head() const {
+ return head_;
+ }
+
+ // The tail values.
+ EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
+ TupleImpl<N-1, Ts...>& tail() {
+ return tail_;
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
+ const TupleImpl<N-1, Ts...>& tail() const {
+ return tail_;
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ void swap(TupleImpl& other) {
+ using numext::swap;
+ swap(head_, other.head_);
+ swap(tail_, other.tail_);
+ }
+
+ template<typename... UTypes>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ TupleImpl& operator=(const TupleImpl<N, UTypes...>& other) {
+ head_ = other.head_;
+ tail_ = other.tail_;
+ return *this;
+ }
+
+ template<typename... UTypes>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ TupleImpl& operator=(TupleImpl<N, UTypes...>&& other) {
+ head_ = std::move(other.head_);
+ tail_ = std::move(other.tail_);
+ return *this;
+ }
+
+ private:
+ // Allow related tuples to reference head_/tail_.
+ template<size_t M, typename... UTypes>
+ friend class TupleImpl;
+
+ T1 head_;
+ TupleImpl<N-1, Ts...> tail_;
+};
+
+// Empty tuple specialization.
+template<>
+class TupleImpl<size_t(0)> {};
+
+template<typename TupleType>
+struct is_tuple : std::false_type {};
+
+template<typename... Types>
+struct is_tuple< TupleImpl<sizeof...(Types), Types...> > : std::true_type {};
+
+// Gets an element from a tuple.
+template<size_t Idx, typename T1, typename... Ts>
+struct tuple_get_impl {
+ using TupleType = TupleImpl<sizeof...(Ts) + 1, T1, Ts...>;
+ using ReturnType = typename tuple_get_impl<Idx - 1, Ts...>::ReturnType;
+
+ static EIGEN_CONSTEXPR EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
+ ReturnType& run(TupleType& tuple) {
+ return tuple_get_impl<Idx-1, Ts...>::run(tuple.tail());
+ }
+
+ static EIGEN_CONSTEXPR EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
+ const ReturnType& run(const TupleType& tuple) {
+ return tuple_get_impl<Idx-1, Ts...>::run(tuple.tail());
+ }
+};
+
+// Base case, getting the head element.
+template<typename T1, typename... Ts>
+struct tuple_get_impl<0, T1, Ts...> {
+ using TupleType = TupleImpl<sizeof...(Ts) + 1, T1, Ts...>;
+ using ReturnType = T1;
+
+ static EIGEN_CONSTEXPR EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
+ T1& run(TupleType& tuple) {
+ return tuple.head();
+ }
+
+ static EIGEN_CONSTEXPR EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
+ const T1& run(const TupleType& tuple) {
+ return tuple.head();
+ }
+};
+
+// Concatenates N Tuples.
+template<size_t NTuples, typename... Tuples>
+struct tuple_cat_impl;
+
+template<size_t NTuples, size_t N1, typename... Args1, size_t N2, typename... Args2, typename... Tuples>
+struct tuple_cat_impl<NTuples, TupleImpl<N1, Args1...>, TupleImpl<N2, Args2...>, Tuples...> {
+ using TupleType1 = TupleImpl<N1, Args1...>;
+ using TupleType2 = TupleImpl<N2, Args2...>;
+ using MergedTupleType = TupleImpl<N1 + N2, Args1..., Args2...>;
+
+ using ReturnType = typename tuple_cat_impl<NTuples-1, MergedTupleType, Tuples...>::ReturnType;
+
+ // Uses the index sequences to extract and merge elements from tuple1 and tuple2,
+ // then recursively calls again.
+ template<typename Tuple1, size_t... I1s, typename Tuple2, size_t... I2s, typename... MoreTuples>
+ static EIGEN_CONSTEXPR EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ ReturnType run(Tuple1&& tuple1, std::index_sequence<I1s...>,
+ Tuple2&& tuple2, std::index_sequence<I2s...>,
+ MoreTuples&&... tuples) {
+ return tuple_cat_impl<NTuples-1, MergedTupleType, Tuples...>::run(
+ MergedTupleType(tuple_get_impl<I1s, Args1...>::run(std::forward<Tuple1>(tuple1))...,
+ tuple_get_impl<I2s, Args2...>::run(std::forward<Tuple2>(tuple2))...),
+ std::forward<MoreTuples>(tuples)...);
+ }
+
+ // Concatenates the first two tuples.
+ template<typename Tuple1, typename Tuple2, typename... MoreTuples>
+ static EIGEN_CONSTEXPR EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ ReturnType run(Tuple1&& tuple1, Tuple2&& tuple2, MoreTuples&&... tuples) {
+ return run(std::forward<Tuple1>(tuple1), std::make_index_sequence<N1>{},
+ std::forward<Tuple2>(tuple2), std::make_index_sequence<N2>{},
+ std::forward<MoreTuples>(tuples)...);
+ }
+};
+
+// Base case with a single tuple.
+template<size_t N, typename... Args>
+struct tuple_cat_impl<1, TupleImpl<N, Args...> > {
+ using ReturnType = TupleImpl<N, Args...>;
+
+ template<typename Tuple1>
+ static EIGEN_CONSTEXPR EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ ReturnType run(Tuple1&& tuple1) {
+ return tuple1;
+ }
+};
+
+// Special case of no tuples.
+template<>
+struct tuple_cat_impl<0> {
+ using ReturnType = TupleImpl<0>;
+ static EIGEN_CONSTEXPR EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ ReturnType run() {return ReturnType{}; }
+};
+
+// For use in make_tuple, unwraps a reference_wrapper.
+template <typename T>
+struct unwrap_reference_wrapper { using type = T; };
+
+template <typename T>
+struct unwrap_reference_wrapper<std::reference_wrapper<T> > { using type = T&; };
+
+// For use in make_tuple, decays a type and unwraps a reference_wrapper.
+template <typename T>
+struct unwrap_decay {
+ using type = typename unwrap_reference_wrapper<typename std::decay<T>::type>::type;
+};
+
+/**
+ * Utility for determining a tuple's size.
+ */
+template<typename Tuple>
+struct tuple_size;
+
+template<typename... Types >
+struct tuple_size< TupleImpl<sizeof...(Types), Types...> > : std::integral_constant<size_t, sizeof...(Types)> {};
+
+/**
+ * Gets an element of a tuple.
+ * \tparam Idx index of the element.
+ * \tparam Types ... tuple element types.
+ * \param tuple the tuple.
+ * \return a reference to the desired element.
+ */
+template<size_t Idx, typename... Types>
+EIGEN_CONSTEXPR EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+const typename tuple_get_impl<Idx, Types...>::ReturnType&
+get(const TupleImpl<sizeof...(Types), Types...>& tuple) {
+ return tuple_get_impl<Idx, Types...>::run(tuple);
+}
+
+template<size_t Idx, typename... Types>
+EIGEN_CONSTEXPR EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+typename tuple_get_impl<Idx, Types...>::ReturnType&
+get(TupleImpl<sizeof...(Types), Types...>& tuple) {
+ return tuple_get_impl<Idx, Types...>::run(tuple);
+}
+
+/**
+ * Concatenate multiple tuples.
+ * \param tuples ... list of tuples.
+ * \return concatenated tuple.
+ */
+template<typename... Tuples,
+ typename EnableIf = std::enable_if_t<
+ internal::reduce_all<
+ is_tuple<typename std::decay<Tuples>::type>::value...>::value>>
+EIGEN_CONSTEXPR EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+typename tuple_cat_impl<sizeof...(Tuples), typename std::decay<Tuples>::type...>::ReturnType
+tuple_cat(Tuples&&... tuples) {
+ return tuple_cat_impl<sizeof...(Tuples), typename std::decay<Tuples>::type...>::run(std::forward<Tuples>(tuples)...);
+}
+
+/**
+ * Tie arguments together into a tuple.
+ */
+template <typename... Args, typename ReturnType = TupleImpl<sizeof...(Args), Args&...> >
+EIGEN_CONSTEXPR EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ReturnType tie(Args&... args) EIGEN_NOEXCEPT {
+ return ReturnType{args...};
+}
+
+/**
+ * Create a tuple of l-values with the supplied arguments.
+ */
+template <typename... Args, typename ReturnType = TupleImpl<sizeof...(Args), typename unwrap_decay<Args>::type...> >
+EIGEN_CONSTEXPR EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ReturnType make_tuple(Args&&... args) {
+ return ReturnType{std::forward<Args>(args)...};
+}
+
+/**
+ * Forward a set of arguments as a tuple.
+ */
+template <typename... Args>
+EIGEN_CONSTEXPR EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+TupleImpl<sizeof...(Args), Args...> forward_as_tuple(Args&&... args) {
+ return TupleImpl<sizeof...(Args), Args...>(std::forward<Args>(args)...);
+}
+
+/**
+ * Alternative to std::tuple that can be used on device.
+ */
+template<typename... Types>
+using tuple = TupleImpl<sizeof...(Types), Types...>;
+
+} // namespace tuple_impl
+} // namespace internal
+} // namespace Eigen
+
+#endif // EIGEN_TUPLE_GPU
diff --git a/Eigen/src/Core/arch/GPU/TypeCasting.h b/Eigen/src/Core/arch/GPU/TypeCasting.h
new file mode 100644
index 0000000..6e8ba27
--- /dev/null
+++ b/Eigen/src/Core/arch/GPU/TypeCasting.h
@@ -0,0 +1,81 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2016 Benoit Steiner <benoit.steiner.goog@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_TYPE_CASTING_GPU_H
+#define EIGEN_TYPE_CASTING_GPU_H
+
+#include "../../InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+
+#if (defined(EIGEN_HAS_CUDA_FP16) && defined(EIGEN_CUDA_ARCH) && EIGEN_CUDA_ARCH >= 300) || \
+ (defined(EIGEN_HAS_HIP_FP16) && defined(EIGEN_HIP_DEVICE_COMPILE))
+
+template <>
+struct type_casting_traits<Eigen::half, float> {
+ enum {
+ VectorizedCast = 1,
+ SrcCoeffRatio = 1,
+ TgtCoeffRatio = 2
+ };
+};
+
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE float4 pcast<half2, float4>(const half2& a, const half2& b) {
+ float2 r1 = __half22float2(a);
+ float2 r2 = __half22float2(b);
+ return make_float4(r1.x, r1.y, r2.x, r2.y);
+}
+
+
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet4h2 pcast<float4, Packet4h2>(const float4& a, const float4& b) {
+ Packet4h2 r;
+ half2* r_alias=reinterpret_cast<half2*>(&r);
+ r_alias[0]=__floats2half2_rn(a.x,a.y);
+ r_alias[1]=__floats2half2_rn(a.z,a.w);
+ r_alias[2]=__floats2half2_rn(b.x,b.y);
+ r_alias[3]=__floats2half2_rn(b.z,b.w);
+ return r;
+}
+
+template <>
+struct type_casting_traits<float, Eigen::half> {
+ enum {
+ VectorizedCast = 1,
+ SrcCoeffRatio = 2,
+ TgtCoeffRatio = 1
+ };
+};
+
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE float4 pcast<Packet4h2, float4>(const Packet4h2& a) {
+ // Simply discard the second half of the input
+ float4 r;
+ const half2* a_alias=reinterpret_cast<const half2*>(&a);
+ float2 r1 = __half22float2(a_alias[0]);
+ float2 r2 = __half22float2(a_alias[1]);
+ r.x=static_cast<float>(r1.x);
+ r.y=static_cast<float>(r1.y);
+ r.z=static_cast<float>(r2.x);
+ r.w=static_cast<float>(r2.y);
+ return r;
+}
+
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 pcast<float4, half2>(const float4& a) {
+ // Simply discard the second half of the input
+ return __floats2half2_rn(a.x, a.y);
+}
+
+#endif
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_TYPE_CASTING_GPU_H
diff --git a/Eigen/src/Core/arch/HIP/hcc/math_constants.h b/Eigen/src/Core/arch/HIP/hcc/math_constants.h
new file mode 100644
index 0000000..25375a0
--- /dev/null
+++ b/Eigen/src/Core/arch/HIP/hcc/math_constants.h
@@ -0,0 +1,23 @@
+/*
+ * math_constants.h -
+ * HIP equivalent of the CUDA header of the same name
+ */
+
+#ifndef __MATH_CONSTANTS_H__
+#define __MATH_CONSTANTS_H__
+
+/* single precision constants */
+
+#define HIPRT_INF_F __int_as_float(0x7f800000)
+#define HIPRT_NAN_F __int_as_float(0x7fffffff)
+#define HIPRT_MIN_DENORM_F __int_as_float(0x00000001)
+#define HIPRT_MAX_NORMAL_F __int_as_float(0x7f7fffff)
+#define HIPRT_NEG_ZERO_F __int_as_float(0x80000000)
+#define HIPRT_ZERO_F 0.0f
+#define HIPRT_ONE_F 1.0f
+
+/* double precision constants */
+#define HIPRT_INF __hiloint2double(0x7ff00000, 0x00000000)
+#define HIPRT_NAN __hiloint2double(0xfff80000, 0x00000000)
+
+#endif
diff --git a/Eigen/src/Core/arch/MSA/Complex.h b/Eigen/src/Core/arch/MSA/Complex.h
new file mode 100644
index 0000000..b11a9b4
--- /dev/null
+++ b/Eigen/src/Core/arch/MSA/Complex.h
@@ -0,0 +1,647 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2018 Wave Computing, Inc.
+// Written by:
+// Chris Larsen
+// Alexey Frunze (afrunze@wavecomp.com)
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_COMPLEX_MSA_H
+#define EIGEN_COMPLEX_MSA_H
+
+#include <iostream>
+
+#include "../../InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+
+//---------- float ----------
+struct Packet2cf {
+ EIGEN_STRONG_INLINE Packet2cf() {
+ }
+ EIGEN_STRONG_INLINE explicit Packet2cf(const std::complex<float>& a,
+ const std::complex<float>& b) {
+ Packet4f t = { std::real(a), std::imag(a), std::real(b), std::imag(b) };
+ v = t;
+ }
+ EIGEN_STRONG_INLINE explicit Packet2cf(const Packet4f& a) : v(a) {
+ }
+ EIGEN_STRONG_INLINE Packet2cf(const Packet2cf& a) : v(a.v) {
+ }
+ EIGEN_STRONG_INLINE Packet2cf& operator=(const Packet2cf& b) {
+ v = b.v;
+ return *this;
+ }
+ EIGEN_STRONG_INLINE Packet2cf conjugate(void) const {
+ return Packet2cf((Packet4f)__builtin_msa_bnegi_d((v2u64)v, 63));
+ }
+ EIGEN_STRONG_INLINE Packet2cf& operator*=(const Packet2cf& b) {
+ Packet4f v1, v2;
+
+ // Get the real values of a | a1_re | a1_re | a2_re | a2_re |
+ v1 = (Packet4f)__builtin_msa_ilvev_w((v4i32)v, (v4i32)v);
+ // Get the imag values of a | a1_im | a1_im | a2_im | a2_im |
+ v2 = (Packet4f)__builtin_msa_ilvod_w((v4i32)v, (v4i32)v);
+ // Multiply the real a with b
+ v1 = pmul(v1, b.v);
+ // Multiply the imag a with b
+ v2 = pmul(v2, b.v);
+ // Conjugate v2
+ v2 = Packet2cf(v2).conjugate().v;
+ // Swap real/imag elements in v2.
+ v2 = (Packet4f)__builtin_msa_shf_w((v4i32)v2, EIGEN_MSA_SHF_I8(1, 0, 3, 2));
+ // Add and return the result
+ v = padd(v1, v2);
+ return *this;
+ }
+ EIGEN_STRONG_INLINE Packet2cf operator*(const Packet2cf& b) const {
+ return Packet2cf(*this) *= b;
+ }
+ EIGEN_STRONG_INLINE Packet2cf& operator+=(const Packet2cf& b) {
+ v = padd(v, b.v);
+ return *this;
+ }
+ EIGEN_STRONG_INLINE Packet2cf operator+(const Packet2cf& b) const {
+ return Packet2cf(*this) += b;
+ }
+ EIGEN_STRONG_INLINE Packet2cf& operator-=(const Packet2cf& b) {
+ v = psub(v, b.v);
+ return *this;
+ }
+ EIGEN_STRONG_INLINE Packet2cf operator-(const Packet2cf& b) const {
+ return Packet2cf(*this) -= b;
+ }
+ EIGEN_STRONG_INLINE Packet2cf operator/(const Packet2cf& b) const {
+ return pdiv_complex(Packet2cf(*this), b);
+ }
+ EIGEN_STRONG_INLINE Packet2cf& operator/=(const Packet2cf& b) {
+ *this = Packet2cf(*this) / b;
+ return *this;
+ }
+ EIGEN_STRONG_INLINE Packet2cf operator-(void) const {
+ return Packet2cf(pnegate(v));
+ }
+
+ Packet4f v;
+};
+
+inline std::ostream& operator<<(std::ostream& os, const Packet2cf& value) {
+ os << "[ (" << value.v[0] << ", " << value.v[1]
+ << "i),"
+ " ("
+ << value.v[2] << ", " << value.v[3] << "i) ]";
+ return os;
+}
+
+template <>
+struct packet_traits<std::complex<float> > : default_packet_traits {
+ typedef Packet2cf type;
+ typedef Packet2cf half;
+ enum {
+ Vectorizable = 1,
+ AlignedOnScalar = 1,
+ size = 2,
+ HasHalfPacket = 0,
+
+ HasAdd = 1,
+ HasSub = 1,
+ HasMul = 1,
+ HasDiv = 1,
+ HasNegate = 1,
+ HasAbs = 0,
+ HasAbs2 = 0,
+ HasMin = 0,
+ HasMax = 0,
+ HasSetLinear = 0,
+ HasBlend = 1
+ };
+};
+
+template <>
+struct unpacket_traits<Packet2cf> {
+ typedef std::complex<float> type;
+ enum { size = 2, alignment = Aligned16, vectorizable=true, masked_load_available=false, masked_store_available=false };
+ typedef Packet2cf half;
+};
+
+template <>
+EIGEN_STRONG_INLINE Packet2cf pset1<Packet2cf>(const std::complex<float>& from) {
+ EIGEN_MSA_DEBUG;
+
+ float f0 = from.real(), f1 = from.imag();
+ Packet4f v0 = { f0, f0, f0, f0 };
+ Packet4f v1 = { f1, f1, f1, f1 };
+ return Packet2cf((Packet4f)__builtin_msa_ilvr_w((Packet4i)v1, (Packet4i)v0));
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet2cf padd<Packet2cf>(const Packet2cf& a, const Packet2cf& b) {
+ EIGEN_MSA_DEBUG;
+
+ return a + b;
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet2cf psub<Packet2cf>(const Packet2cf& a, const Packet2cf& b) {
+ EIGEN_MSA_DEBUG;
+
+ return a - b;
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet2cf pnegate(const Packet2cf& a) {
+ EIGEN_MSA_DEBUG;
+
+ return -a;
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet2cf pconj(const Packet2cf& a) {
+ EIGEN_MSA_DEBUG;
+
+ return a.conjugate();
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet2cf pmul<Packet2cf>(const Packet2cf& a, const Packet2cf& b) {
+ EIGEN_MSA_DEBUG;
+
+ return a * b;
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet2cf pand<Packet2cf>(const Packet2cf& a, const Packet2cf& b) {
+ EIGEN_MSA_DEBUG;
+
+ return Packet2cf(pand(a.v, b.v));
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet2cf por<Packet2cf>(const Packet2cf& a, const Packet2cf& b) {
+ EIGEN_MSA_DEBUG;
+
+ return Packet2cf(por(a.v, b.v));
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet2cf pxor<Packet2cf>(const Packet2cf& a, const Packet2cf& b) {
+ EIGEN_MSA_DEBUG;
+
+ return Packet2cf(pxor(a.v, b.v));
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet2cf pandnot<Packet2cf>(const Packet2cf& a, const Packet2cf& b) {
+ EIGEN_MSA_DEBUG;
+
+ return Packet2cf(pandnot(a.v, b.v));
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet2cf pload<Packet2cf>(const std::complex<float>* from) {
+ EIGEN_MSA_DEBUG;
+
+ EIGEN_DEBUG_ALIGNED_LOAD return Packet2cf(pload<Packet4f>((const float*)from));
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet2cf ploadu<Packet2cf>(const std::complex<float>* from) {
+ EIGEN_MSA_DEBUG;
+
+ EIGEN_DEBUG_UNALIGNED_LOAD return Packet2cf(ploadu<Packet4f>((const float*)from));
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet2cf ploaddup<Packet2cf>(const std::complex<float>* from) {
+ EIGEN_MSA_DEBUG;
+
+ return pset1<Packet2cf>(*from);
+}
+
+template <>
+EIGEN_STRONG_INLINE void pstore<std::complex<float> >(std::complex<float>* to,
+ const Packet2cf& from) {
+ EIGEN_MSA_DEBUG;
+
+ EIGEN_DEBUG_ALIGNED_STORE pstore<float>((float*)to, from.v);
+}
+
+template <>
+EIGEN_STRONG_INLINE void pstoreu<std::complex<float> >(std::complex<float>* to,
+ const Packet2cf& from) {
+ EIGEN_MSA_DEBUG;
+
+ EIGEN_DEBUG_UNALIGNED_STORE pstoreu<float>((float*)to, from.v);
+}
+
+template <>
+EIGEN_DEVICE_FUNC inline Packet2cf pgather<std::complex<float>, Packet2cf>(
+ const std::complex<float>* from, Index stride) {
+ EIGEN_MSA_DEBUG;
+
+ return Packet2cf(from[0 * stride], from[1 * stride]);
+}
+
+template <>
+EIGEN_DEVICE_FUNC inline void pscatter<std::complex<float>, Packet2cf>(std::complex<float>* to,
+ const Packet2cf& from,
+ Index stride) {
+ EIGEN_MSA_DEBUG;
+
+ *to = std::complex<float>(from.v[0], from.v[1]);
+ to += stride;
+ *to = std::complex<float>(from.v[2], from.v[3]);
+}
+
+template <>
+EIGEN_STRONG_INLINE void prefetch<std::complex<float> >(const std::complex<float>* addr) {
+ EIGEN_MSA_DEBUG;
+
+ prefetch(reinterpret_cast<const float*>(addr));
+}
+
+template <>
+EIGEN_STRONG_INLINE std::complex<float> pfirst<Packet2cf>(const Packet2cf& a) {
+ EIGEN_MSA_DEBUG;
+
+ return std::complex<float>(a.v[0], a.v[1]);
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet2cf preverse(const Packet2cf& a) {
+ EIGEN_MSA_DEBUG;
+
+ return Packet2cf((Packet4f)__builtin_msa_shf_w((v4i32)a.v, EIGEN_MSA_SHF_I8(2, 3, 0, 1)));
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet2cf pcplxflip<Packet2cf>(const Packet2cf& a) {
+ EIGEN_MSA_DEBUG;
+
+ return Packet2cf((Packet4f)__builtin_msa_shf_w((v4i32)a.v, EIGEN_MSA_SHF_I8(1, 0, 3, 2)));
+}
+
+template <>
+EIGEN_STRONG_INLINE std::complex<float> predux<Packet2cf>(const Packet2cf& a) {
+ EIGEN_MSA_DEBUG;
+
+ Packet4f value = (Packet4f)preverse((Packet2d)a.v);
+ value += a.v;
+ return std::complex<float>(value[0], value[1]);
+}
+
+template <>
+EIGEN_STRONG_INLINE std::complex<float> predux_mul<Packet2cf>(const Packet2cf& a) {
+ EIGEN_MSA_DEBUG;
+
+ return std::complex<float>((a.v[0] * a.v[2]) - (a.v[1] * a.v[3]),
+ (a.v[0] * a.v[3]) + (a.v[1] * a.v[2]));
+}
+
+EIGEN_MAKE_CONJ_HELPER_CPLX_REAL(Packet2cf, Packet4f)
+
+template <>
+EIGEN_STRONG_INLINE Packet2cf pdiv<Packet2cf>(const Packet2cf& a, const Packet2cf& b) {
+ EIGEN_MSA_DEBUG;
+
+ return a / b;
+}
+
+inline std::ostream& operator<<(std::ostream& os, const PacketBlock<Packet2cf, 2>& value) {
+ os << "[ " << value.packet[0] << ", " << std::endl << " " << value.packet[1] << " ]";
+ return os;
+}
+
+EIGEN_DEVICE_FUNC inline void ptranspose(PacketBlock<Packet2cf, 2>& kernel) {
+ EIGEN_MSA_DEBUG;
+
+ Packet4f tmp =
+ (Packet4f)__builtin_msa_ilvl_d((v2i64)kernel.packet[1].v, (v2i64)kernel.packet[0].v);
+ kernel.packet[0].v =
+ (Packet4f)__builtin_msa_ilvr_d((v2i64)kernel.packet[1].v, (v2i64)kernel.packet[0].v);
+ kernel.packet[1].v = tmp;
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet2cf pblend(const Selector<2>& ifPacket, const Packet2cf& thenPacket,
+ const Packet2cf& elsePacket) {
+ return (Packet2cf)(Packet4f)pblend<Packet2d>(ifPacket, (Packet2d)thenPacket.v,
+ (Packet2d)elsePacket.v);
+}
+
+//---------- double ----------
+
+struct Packet1cd {
+ EIGEN_STRONG_INLINE Packet1cd() {
+ }
+ EIGEN_STRONG_INLINE explicit Packet1cd(const std::complex<double>& a) {
+ v[0] = std::real(a);
+ v[1] = std::imag(a);
+ }
+ EIGEN_STRONG_INLINE explicit Packet1cd(const Packet2d& a) : v(a) {
+ }
+ EIGEN_STRONG_INLINE Packet1cd(const Packet1cd& a) : v(a.v) {
+ }
+ EIGEN_STRONG_INLINE Packet1cd& operator=(const Packet1cd& b) {
+ v = b.v;
+ return *this;
+ }
+ EIGEN_STRONG_INLINE Packet1cd conjugate(void) const {
+ static const v2u64 p2ul_CONJ_XOR = { 0x0, 0x8000000000000000 };
+ return (Packet1cd)pxor(v, (Packet2d)p2ul_CONJ_XOR);
+ }
+ EIGEN_STRONG_INLINE Packet1cd& operator*=(const Packet1cd& b) {
+ Packet2d v1, v2;
+
+ // Get the real values of a | a1_re | a1_re
+ v1 = (Packet2d)__builtin_msa_ilvev_d((v2i64)v, (v2i64)v);
+ // Get the imag values of a | a1_im | a1_im
+ v2 = (Packet2d)__builtin_msa_ilvod_d((v2i64)v, (v2i64)v);
+ // Multiply the real a with b
+ v1 = pmul(v1, b.v);
+ // Multiply the imag a with b
+ v2 = pmul(v2, b.v);
+ // Conjugate v2
+ v2 = Packet1cd(v2).conjugate().v;
+ // Swap real/imag elements in v2.
+ v2 = (Packet2d)__builtin_msa_shf_w((v4i32)v2, EIGEN_MSA_SHF_I8(2, 3, 0, 1));
+ // Add and return the result
+ v = padd(v1, v2);
+ return *this;
+ }
+ EIGEN_STRONG_INLINE Packet1cd operator*(const Packet1cd& b) const {
+ return Packet1cd(*this) *= b;
+ }
+ EIGEN_STRONG_INLINE Packet1cd& operator+=(const Packet1cd& b) {
+ v = padd(v, b.v);
+ return *this;
+ }
+ EIGEN_STRONG_INLINE Packet1cd operator+(const Packet1cd& b) const {
+ return Packet1cd(*this) += b;
+ }
+ EIGEN_STRONG_INLINE Packet1cd& operator-=(const Packet1cd& b) {
+ v = psub(v, b.v);
+ return *this;
+ }
+ EIGEN_STRONG_INLINE Packet1cd operator-(const Packet1cd& b) const {
+ return Packet1cd(*this) -= b;
+ }
+ EIGEN_STRONG_INLINE Packet1cd& operator/=(const Packet1cd& b) {
+ *this *= b.conjugate();
+ Packet2d s = pmul<Packet2d>(b.v, b.v);
+ s = padd(s, preverse<Packet2d>(s));
+ v = pdiv(v, s);
+ return *this;
+ }
+ EIGEN_STRONG_INLINE Packet1cd operator/(const Packet1cd& b) const {
+ return Packet1cd(*this) /= b;
+ }
+ EIGEN_STRONG_INLINE Packet1cd operator-(void) const {
+ return Packet1cd(pnegate(v));
+ }
+
+ Packet2d v;
+};
+
+inline std::ostream& operator<<(std::ostream& os, const Packet1cd& value) {
+ os << "[ (" << value.v[0] << ", " << value.v[1] << "i) ]";
+ return os;
+}
+
+template <>
+struct packet_traits<std::complex<double> > : default_packet_traits {
+ typedef Packet1cd type;
+ typedef Packet1cd half;
+ enum {
+ Vectorizable = 1,
+ AlignedOnScalar = 0,
+ size = 1,
+ HasHalfPacket = 0,
+
+ HasAdd = 1,
+ HasSub = 1,
+ HasMul = 1,
+ HasDiv = 1,
+ HasNegate = 1,
+ HasAbs = 0,
+ HasAbs2 = 0,
+ HasMin = 0,
+ HasMax = 0,
+ HasSetLinear = 0
+ };
+};
+
+template <>
+struct unpacket_traits<Packet1cd> {
+ typedef std::complex<double> type;
+ enum { size = 1, alignment = Aligned16, vectorizable=true, masked_load_available=false, masked_store_available=false };
+ typedef Packet1cd half;
+};
+
+template <>
+EIGEN_STRONG_INLINE Packet1cd pload<Packet1cd>(const std::complex<double>* from) {
+ EIGEN_MSA_DEBUG;
+
+ EIGEN_DEBUG_ALIGNED_LOAD return Packet1cd(pload<Packet2d>((const double*)from));
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet1cd ploadu<Packet1cd>(const std::complex<double>* from) {
+ EIGEN_MSA_DEBUG;
+
+ EIGEN_DEBUG_UNALIGNED_LOAD return Packet1cd(ploadu<Packet2d>((const double*)from));
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet1cd pset1<Packet1cd>(const std::complex<double>& from) {
+ EIGEN_MSA_DEBUG;
+
+ return Packet1cd(from);
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet1cd padd<Packet1cd>(const Packet1cd& a, const Packet1cd& b) {
+ EIGEN_MSA_DEBUG;
+
+ return a + b;
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet1cd psub<Packet1cd>(const Packet1cd& a, const Packet1cd& b) {
+ EIGEN_MSA_DEBUG;
+
+ return a - b;
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet1cd pnegate(const Packet1cd& a) {
+ EIGEN_MSA_DEBUG;
+
+ return -a;
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet1cd pconj(const Packet1cd& a) {
+ EIGEN_MSA_DEBUG;
+
+ return a.conjugate();
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet1cd pmul<Packet1cd>(const Packet1cd& a, const Packet1cd& b) {
+ EIGEN_MSA_DEBUG;
+
+ return a * b;
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet1cd pand<Packet1cd>(const Packet1cd& a, const Packet1cd& b) {
+ EIGEN_MSA_DEBUG;
+
+ return Packet1cd(pand(a.v, b.v));
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet1cd por<Packet1cd>(const Packet1cd& a, const Packet1cd& b) {
+ EIGEN_MSA_DEBUG;
+
+ return Packet1cd(por(a.v, b.v));
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet1cd pxor<Packet1cd>(const Packet1cd& a, const Packet1cd& b) {
+ EIGEN_MSA_DEBUG;
+
+ return Packet1cd(pxor(a.v, b.v));
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet1cd pandnot<Packet1cd>(const Packet1cd& a, const Packet1cd& b) {
+ EIGEN_MSA_DEBUG;
+
+ return Packet1cd(pandnot(a.v, b.v));
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet1cd ploaddup<Packet1cd>(const std::complex<double>* from) {
+ EIGEN_MSA_DEBUG;
+
+ return pset1<Packet1cd>(*from);
+}
+
+template <>
+EIGEN_STRONG_INLINE void pstore<std::complex<double> >(std::complex<double>* to,
+ const Packet1cd& from) {
+ EIGEN_MSA_DEBUG;
+
+ EIGEN_DEBUG_ALIGNED_STORE pstore<double>((double*)to, from.v);
+}
+
+template <>
+EIGEN_STRONG_INLINE void pstoreu<std::complex<double> >(std::complex<double>* to,
+ const Packet1cd& from) {
+ EIGEN_MSA_DEBUG;
+
+ EIGEN_DEBUG_UNALIGNED_STORE pstoreu<double>((double*)to, from.v);
+}
+
+template <>
+EIGEN_STRONG_INLINE void prefetch<std::complex<double> >(const std::complex<double>* addr) {
+ EIGEN_MSA_DEBUG;
+
+ prefetch(reinterpret_cast<const double*>(addr));
+}
+
+template <>
+EIGEN_DEVICE_FUNC inline Packet1cd pgather<std::complex<double>, Packet1cd>(
+ const std::complex<double>* from, Index stride __attribute__((unused))) {
+ EIGEN_MSA_DEBUG;
+
+ Packet1cd res;
+ res.v[0] = std::real(from[0]);
+ res.v[1] = std::imag(from[0]);
+ return res;
+}
+
+template <>
+EIGEN_DEVICE_FUNC inline void pscatter<std::complex<double>, Packet1cd>(std::complex<double>* to,
+ const Packet1cd& from,
+ Index stride
+ __attribute__((unused))) {
+ EIGEN_MSA_DEBUG;
+
+ pstore(to, from);
+}
+
+template <>
+EIGEN_STRONG_INLINE std::complex<double> pfirst<Packet1cd>(const Packet1cd& a) {
+ EIGEN_MSA_DEBUG;
+
+ return std::complex<double>(a.v[0], a.v[1]);
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet1cd preverse(const Packet1cd& a) {
+ EIGEN_MSA_DEBUG;
+
+ return a;
+}
+
+template <>
+EIGEN_STRONG_INLINE std::complex<double> predux<Packet1cd>(const Packet1cd& a) {
+ EIGEN_MSA_DEBUG;
+
+ return pfirst(a);
+}
+
+template <>
+EIGEN_STRONG_INLINE std::complex<double> predux_mul<Packet1cd>(const Packet1cd& a) {
+ EIGEN_MSA_DEBUG;
+
+ return pfirst(a);
+}
+
+EIGEN_MAKE_CONJ_HELPER_CPLX_REAL(Packet1cd, Packet2d)
+
+template <>
+EIGEN_STRONG_INLINE Packet1cd pdiv<Packet1cd>(const Packet1cd& a, const Packet1cd& b) {
+ EIGEN_MSA_DEBUG;
+
+ return a / b;
+}
+
+EIGEN_STRONG_INLINE Packet1cd pcplxflip /*<Packet1cd>*/ (const Packet1cd& x) {
+ EIGEN_MSA_DEBUG;
+
+ return Packet1cd(preverse(Packet2d(x.v)));
+}
+
+inline std::ostream& operator<<(std::ostream& os, const PacketBlock<Packet1cd, 2>& value) {
+ os << "[ " << value.packet[0] << ", " << std::endl << " " << value.packet[1] << " ]";
+ return os;
+}
+
+EIGEN_STRONG_INLINE void ptranspose(PacketBlock<Packet1cd, 2>& kernel) {
+ EIGEN_MSA_DEBUG;
+
+ Packet2d v1, v2;
+
+ v1 = (Packet2d)__builtin_msa_ilvev_d((v2i64)kernel.packet[0].v, (v2i64)kernel.packet[1].v);
+ // Get the imag values of a
+ v2 = (Packet2d)__builtin_msa_ilvod_d((v2i64)kernel.packet[0].v, (v2i64)kernel.packet[1].v);
+
+ kernel.packet[0].v = v1;
+ kernel.packet[1].v = v2;
+}
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_COMPLEX_MSA_H
diff --git a/Eigen/src/Core/arch/MSA/MathFunctions.h b/Eigen/src/Core/arch/MSA/MathFunctions.h
new file mode 100644
index 0000000..5932041
--- /dev/null
+++ b/Eigen/src/Core/arch/MSA/MathFunctions.h
@@ -0,0 +1,389 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2007 Julien Pommier
+// Copyright (C) 2014 Pedro Gonnet (pedro.gonnet@gmail.com)
+// Copyright (C) 2016 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// Copyright (C) 2018 Wave Computing, Inc.
+// Written by:
+// Chris Larsen
+// Alexey Frunze (afrunze@wavecomp.com)
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+/* The sin, cos, exp, and log functions of this file come from
+ * Julien Pommier's sse math library: http://gruntthepeon.free.fr/ssemath/
+ */
+
+/* The tanh function of this file is an adaptation of
+ * template<typename T> T generic_fast_tanh_float(const T&)
+ * from MathFunctionsImpl.h.
+ */
+
+#ifndef EIGEN_MATH_FUNCTIONS_MSA_H
+#define EIGEN_MATH_FUNCTIONS_MSA_H
+
+#include "../../InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+
+template <>
+EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet4f
+plog<Packet4f>(const Packet4f& _x) {
+ static EIGEN_DECLARE_CONST_Packet4f(cephes_SQRTHF, 0.707106781186547524f);
+ static EIGEN_DECLARE_CONST_Packet4f(cephes_log_p0, 7.0376836292e-2f);
+ static EIGEN_DECLARE_CONST_Packet4f(cephes_log_p1, -1.1514610310e-1f);
+ static EIGEN_DECLARE_CONST_Packet4f(cephes_log_p2, 1.1676998740e-1f);
+ static EIGEN_DECLARE_CONST_Packet4f(cephes_log_p3, -1.2420140846e-1f);
+ static EIGEN_DECLARE_CONST_Packet4f(cephes_log_p4, +1.4249322787e-1f);
+ static EIGEN_DECLARE_CONST_Packet4f(cephes_log_p5, -1.6668057665e-1f);
+ static EIGEN_DECLARE_CONST_Packet4f(cephes_log_p6, +2.0000714765e-1f);
+ static EIGEN_DECLARE_CONST_Packet4f(cephes_log_p7, -2.4999993993e-1f);
+ static EIGEN_DECLARE_CONST_Packet4f(cephes_log_p8, +3.3333331174e-1f);
+ static EIGEN_DECLARE_CONST_Packet4f(cephes_log_q1, -2.12194440e-4f);
+ static EIGEN_DECLARE_CONST_Packet4f(cephes_log_q2, 0.693359375f);
+ static EIGEN_DECLARE_CONST_Packet4f(half, 0.5f);
+ static EIGEN_DECLARE_CONST_Packet4f(1, 1.0f);
+
+ // Convert negative argument into NAN (quiet negative, to be specific).
+ Packet4f zero = (Packet4f)__builtin_msa_ldi_w(0);
+ Packet4i neg_mask = __builtin_msa_fclt_w(_x, zero);
+ Packet4i zero_mask = __builtin_msa_fceq_w(_x, zero);
+ Packet4f non_neg_x_or_nan = padd(_x, (Packet4f)neg_mask); // Add 0.0 or NAN.
+ Packet4f x = non_neg_x_or_nan;
+
+ // Extract exponent from x = mantissa * 2**exponent, where 1.0 <= mantissa < 2.0.
+ // N.B. the exponent is one less of what frexpf() would return.
+ Packet4i e_int = __builtin_msa_ftint_s_w(__builtin_msa_flog2_w(x));
+ // Multiply x by 2**(-exponent-1) to get 0.5 <= x < 1.0 as from frexpf().
+ x = __builtin_msa_fexp2_w(x, (Packet4i)__builtin_msa_nori_b((v16u8)e_int, 0));
+
+ /*
+ if (x < SQRTHF) {
+ x = x + x - 1.0;
+ } else {
+ e += 1;
+ x = x - 1.0;
+ }
+ */
+ Packet4f xx = padd(x, x);
+ Packet4i ge_mask = __builtin_msa_fcle_w(p4f_cephes_SQRTHF, x);
+ e_int = psub(e_int, ge_mask);
+ x = (Packet4f)__builtin_msa_bsel_v((v16u8)ge_mask, (v16u8)xx, (v16u8)x);
+ x = psub(x, p4f_1);
+ Packet4f e = __builtin_msa_ffint_s_w(e_int);
+
+ Packet4f x2 = pmul(x, x);
+ Packet4f x3 = pmul(x2, x);
+
+ Packet4f y, y1, y2;
+ y = pmadd(p4f_cephes_log_p0, x, p4f_cephes_log_p1);
+ y1 = pmadd(p4f_cephes_log_p3, x, p4f_cephes_log_p4);
+ y2 = pmadd(p4f_cephes_log_p6, x, p4f_cephes_log_p7);
+ y = pmadd(y, x, p4f_cephes_log_p2);
+ y1 = pmadd(y1, x, p4f_cephes_log_p5);
+ y2 = pmadd(y2, x, p4f_cephes_log_p8);
+ y = pmadd(y, x3, y1);
+ y = pmadd(y, x3, y2);
+ y = pmul(y, x3);
+
+ y = pmadd(e, p4f_cephes_log_q1, y);
+ x = __builtin_msa_fmsub_w(x, x2, p4f_half);
+ x = padd(x, y);
+ x = pmadd(e, p4f_cephes_log_q2, x);
+
+ // x is now the logarithm result candidate. We still need to handle the
+ // extreme arguments of zero and positive infinity, though.
+ // N.B. if the argument is +INFINITY, x is NAN because the polynomial terms
+ // contain infinities of both signs (see the coefficients and code above).
+ // INFINITY - INFINITY is NAN.
+
+ // If the argument is +INFINITY, make it the new result candidate.
+ // To achieve that we choose the smaller of the result candidate and the
+ // argument.
+ // This is correct for all finite pairs of values (the logarithm is smaller
+ // than the argument).
+ // This is also correct in the special case when the argument is +INFINITY
+ // and the result candidate is NAN. This is because the fmin.df instruction
+ // prefers non-NANs to NANs.
+ x = __builtin_msa_fmin_w(x, non_neg_x_or_nan);
+
+ // If the argument is zero (including -0.0), the result becomes -INFINITY.
+ Packet4i neg_infs = __builtin_msa_slli_w(zero_mask, 23);
+ x = (Packet4f)__builtin_msa_bsel_v((v16u8)zero_mask, (v16u8)x, (v16u8)neg_infs);
+
+ return x;
+}
+
+template <>
+EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet4f
+pexp<Packet4f>(const Packet4f& _x) {
+ // Limiting single-precision pexp's argument to [-128, +128] lets pexp
+ // reach 0 and INFINITY naturally.
+ static EIGEN_DECLARE_CONST_Packet4f(exp_lo, -128.0f);
+ static EIGEN_DECLARE_CONST_Packet4f(exp_hi, +128.0f);
+ static EIGEN_DECLARE_CONST_Packet4f(cephes_LOG2EF, 1.44269504088896341f);
+ static EIGEN_DECLARE_CONST_Packet4f(cephes_exp_C1, 0.693359375f);
+ static EIGEN_DECLARE_CONST_Packet4f(cephes_exp_C2, -2.12194440e-4f);
+ static EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p0, 1.9875691500e-4f);
+ static EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p1, 1.3981999507e-3f);
+ static EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p2, 8.3334519073e-3f);
+ static EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p3, 4.1665795894e-2f);
+ static EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p4, 1.6666665459e-1f);
+ static EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p5, 5.0000001201e-1f);
+ static EIGEN_DECLARE_CONST_Packet4f(half, 0.5f);
+ static EIGEN_DECLARE_CONST_Packet4f(1, 1.0f);
+
+ Packet4f x = _x;
+
+ // Clamp x.
+ x = (Packet4f)__builtin_msa_bsel_v((v16u8)__builtin_msa_fclt_w(x, p4f_exp_lo), (v16u8)x,
+ (v16u8)p4f_exp_lo);
+ x = (Packet4f)__builtin_msa_bsel_v((v16u8)__builtin_msa_fclt_w(p4f_exp_hi, x), (v16u8)x,
+ (v16u8)p4f_exp_hi);
+
+ // Round to nearest integer by adding 0.5 (with x's sign) and truncating.
+ Packet4f x2_add = (Packet4f)__builtin_msa_binsli_w((v4u32)p4f_half, (v4u32)x, 0);
+ Packet4f x2 = pmadd(x, p4f_cephes_LOG2EF, x2_add);
+ Packet4i x2_int = __builtin_msa_ftrunc_s_w(x2);
+ Packet4f x2_int_f = __builtin_msa_ffint_s_w(x2_int);
+
+ x = __builtin_msa_fmsub_w(x, x2_int_f, p4f_cephes_exp_C1);
+ x = __builtin_msa_fmsub_w(x, x2_int_f, p4f_cephes_exp_C2);
+
+ Packet4f z = pmul(x, x);
+
+ Packet4f y = p4f_cephes_exp_p0;
+ y = pmadd(y, x, p4f_cephes_exp_p1);
+ y = pmadd(y, x, p4f_cephes_exp_p2);
+ y = pmadd(y, x, p4f_cephes_exp_p3);
+ y = pmadd(y, x, p4f_cephes_exp_p4);
+ y = pmadd(y, x, p4f_cephes_exp_p5);
+ y = pmadd(y, z, x);
+ y = padd(y, p4f_1);
+
+ // y *= 2**exponent.
+ y = __builtin_msa_fexp2_w(y, x2_int);
+
+ return y;
+}
+
+template <>
+EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet4f
+ptanh<Packet4f>(const Packet4f& _x) {
+ static EIGEN_DECLARE_CONST_Packet4f(tanh_tiny, 1e-4f);
+ static EIGEN_DECLARE_CONST_Packet4f(tanh_hi, 9.0f);
+ // The monomial coefficients of the numerator polynomial (odd).
+ static EIGEN_DECLARE_CONST_Packet4f(alpha_1, 4.89352455891786e-3f);
+ static EIGEN_DECLARE_CONST_Packet4f(alpha_3, 6.37261928875436e-4f);
+ static EIGEN_DECLARE_CONST_Packet4f(alpha_5, 1.48572235717979e-5f);
+ static EIGEN_DECLARE_CONST_Packet4f(alpha_7, 5.12229709037114e-8f);
+ static EIGEN_DECLARE_CONST_Packet4f(alpha_9, -8.60467152213735e-11f);
+ static EIGEN_DECLARE_CONST_Packet4f(alpha_11, 2.00018790482477e-13f);
+ static EIGEN_DECLARE_CONST_Packet4f(alpha_13, -2.76076847742355e-16f);
+ // The monomial coefficients of the denominator polynomial (even).
+ static EIGEN_DECLARE_CONST_Packet4f(beta_0, 4.89352518554385e-3f);
+ static EIGEN_DECLARE_CONST_Packet4f(beta_2, 2.26843463243900e-3f);
+ static EIGEN_DECLARE_CONST_Packet4f(beta_4, 1.18534705686654e-4f);
+ static EIGEN_DECLARE_CONST_Packet4f(beta_6, 1.19825839466702e-6f);
+
+ Packet4f x = pabs(_x);
+ Packet4i tiny_mask = __builtin_msa_fclt_w(x, p4f_tanh_tiny);
+
+ // Clamp the inputs to the range [-9, 9] since anything outside
+ // this range is -/+1.0f in single-precision.
+ x = (Packet4f)__builtin_msa_bsel_v((v16u8)__builtin_msa_fclt_w(p4f_tanh_hi, x), (v16u8)x,
+ (v16u8)p4f_tanh_hi);
+
+ // Since the polynomials are odd/even, we need x**2.
+ Packet4f x2 = pmul(x, x);
+
+ // Evaluate the numerator polynomial p.
+ Packet4f p = pmadd(x2, p4f_alpha_13, p4f_alpha_11);
+ p = pmadd(x2, p, p4f_alpha_9);
+ p = pmadd(x2, p, p4f_alpha_7);
+ p = pmadd(x2, p, p4f_alpha_5);
+ p = pmadd(x2, p, p4f_alpha_3);
+ p = pmadd(x2, p, p4f_alpha_1);
+ p = pmul(x, p);
+
+ // Evaluate the denominator polynomial q.
+ Packet4f q = pmadd(x2, p4f_beta_6, p4f_beta_4);
+ q = pmadd(x2, q, p4f_beta_2);
+ q = pmadd(x2, q, p4f_beta_0);
+
+ // Divide the numerator by the denominator.
+ p = pdiv(p, q);
+
+ // Reinstate the sign.
+ p = (Packet4f)__builtin_msa_binsli_w((v4u32)p, (v4u32)_x, 0);
+
+ // When the argument is very small in magnitude it's more accurate to just return it.
+ p = (Packet4f)__builtin_msa_bsel_v((v16u8)tiny_mask, (v16u8)p, (v16u8)_x);
+
+ return p;
+}
+
+template <bool sine>
+Packet4f psincos_inner_msa_float(const Packet4f& _x) {
+ static EIGEN_DECLARE_CONST_Packet4f(sincos_max_arg, 13176795.0f); // Approx. (2**24) / (4/Pi).
+ static EIGEN_DECLARE_CONST_Packet4f(minus_cephes_DP1, -0.78515625f);
+ static EIGEN_DECLARE_CONST_Packet4f(minus_cephes_DP2, -2.4187564849853515625e-4f);
+ static EIGEN_DECLARE_CONST_Packet4f(minus_cephes_DP3, -3.77489497744594108e-8f);
+ static EIGEN_DECLARE_CONST_Packet4f(sincof_p0, -1.9515295891e-4f);
+ static EIGEN_DECLARE_CONST_Packet4f(sincof_p1, 8.3321608736e-3f);
+ static EIGEN_DECLARE_CONST_Packet4f(sincof_p2, -1.6666654611e-1f);
+ static EIGEN_DECLARE_CONST_Packet4f(coscof_p0, 2.443315711809948e-5f);
+ static EIGEN_DECLARE_CONST_Packet4f(coscof_p1, -1.388731625493765e-3f);
+ static EIGEN_DECLARE_CONST_Packet4f(coscof_p2, 4.166664568298827e-2f);
+ static EIGEN_DECLARE_CONST_Packet4f(cephes_FOPI, 1.27323954473516f); // 4/Pi.
+ static EIGEN_DECLARE_CONST_Packet4f(half, 0.5f);
+ static EIGEN_DECLARE_CONST_Packet4f(1, 1.0f);
+
+ Packet4f x = pabs(_x);
+
+ // Translate infinite arguments into NANs.
+ Packet4f zero_or_nan_if_inf = psub(_x, _x);
+ x = padd(x, zero_or_nan_if_inf);
+ // Prevent sin/cos from generating values larger than 1.0 in magnitude
+ // for very large arguments by setting x to 0.0.
+ Packet4i small_or_nan_mask = __builtin_msa_fcult_w(x, p4f_sincos_max_arg);
+ x = pand(x, (Packet4f)small_or_nan_mask);
+
+ // Scale x by 4/Pi to find x's octant.
+ Packet4f y = pmul(x, p4f_cephes_FOPI);
+ // Get the octant. We'll reduce x by this number of octants or by one more than it.
+ Packet4i y_int = __builtin_msa_ftrunc_s_w(y);
+ // x's from even-numbered octants will translate to octant 0: [0, +Pi/4].
+ // x's from odd-numbered octants will translate to octant -1: [-Pi/4, 0].
+ // Adjustment for odd-numbered octants: octant = (octant + 1) & (~1).
+ Packet4i y_int1 = __builtin_msa_addvi_w(y_int, 1);
+ Packet4i y_int2 = (Packet4i)__builtin_msa_bclri_w((Packet4ui)y_int1, 0); // bclri = bit-clear
+ y = __builtin_msa_ffint_s_w(y_int2);
+
+ // Compute the sign to apply to the polynomial.
+ Packet4i sign_mask = sine ? pxor(__builtin_msa_slli_w(y_int1, 29), (Packet4i)_x)
+ : __builtin_msa_slli_w(__builtin_msa_addvi_w(y_int, 3), 29);
+
+ // Get the polynomial selection mask.
+ // We'll calculate both (sin and cos) polynomials and then select from the two.
+ Packet4i poly_mask = __builtin_msa_ceqi_w(__builtin_msa_slli_w(y_int2, 30), 0);
+
+ // Reduce x by y octants to get: -Pi/4 <= x <= +Pi/4.
+ // The magic pass: "Extended precision modular arithmetic"
+ // x = ((x - y * DP1) - y * DP2) - y * DP3
+ Packet4f tmp1 = pmul(y, p4f_minus_cephes_DP1);
+ Packet4f tmp2 = pmul(y, p4f_minus_cephes_DP2);
+ Packet4f tmp3 = pmul(y, p4f_minus_cephes_DP3);
+ x = padd(x, tmp1);
+ x = padd(x, tmp2);
+ x = padd(x, tmp3);
+
+ // Evaluate the cos(x) polynomial.
+ y = p4f_coscof_p0;
+ Packet4f z = pmul(x, x);
+ y = pmadd(y, z, p4f_coscof_p1);
+ y = pmadd(y, z, p4f_coscof_p2);
+ y = pmul(y, z);
+ y = pmul(y, z);
+ y = __builtin_msa_fmsub_w(y, z, p4f_half);
+ y = padd(y, p4f_1);
+
+ // Evaluate the sin(x) polynomial.
+ Packet4f y2 = p4f_sincof_p0;
+ y2 = pmadd(y2, z, p4f_sincof_p1);
+ y2 = pmadd(y2, z, p4f_sincof_p2);
+ y2 = pmul(y2, z);
+ y2 = pmadd(y2, x, x);
+
+ // Select the correct result from the two polynomials.
+ y = sine ? (Packet4f)__builtin_msa_bsel_v((v16u8)poly_mask, (v16u8)y, (v16u8)y2)
+ : (Packet4f)__builtin_msa_bsel_v((v16u8)poly_mask, (v16u8)y2, (v16u8)y);
+
+ // Update the sign.
+ sign_mask = pxor(sign_mask, (Packet4i)y);
+ y = (Packet4f)__builtin_msa_binsli_w((v4u32)y, (v4u32)sign_mask, 0); // binsli = bit-insert-left
+ return y;
+}
+
+template <>
+EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet4f
+psin<Packet4f>(const Packet4f& x) {
+ return psincos_inner_msa_float</* sine */ true>(x);
+}
+
+template <>
+EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet4f
+pcos<Packet4f>(const Packet4f& x) {
+ return psincos_inner_msa_float</* sine */ false>(x);
+}
+
+template <>
+EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet2d
+pexp<Packet2d>(const Packet2d& _x) {
+ // Limiting double-precision pexp's argument to [-1024, +1024] lets pexp
+ // reach 0 and INFINITY naturally.
+ static EIGEN_DECLARE_CONST_Packet2d(exp_lo, -1024.0);
+ static EIGEN_DECLARE_CONST_Packet2d(exp_hi, +1024.0);
+ static EIGEN_DECLARE_CONST_Packet2d(cephes_LOG2EF, 1.4426950408889634073599);
+ static EIGEN_DECLARE_CONST_Packet2d(cephes_exp_C1, 0.693145751953125);
+ static EIGEN_DECLARE_CONST_Packet2d(cephes_exp_C2, 1.42860682030941723212e-6);
+ static EIGEN_DECLARE_CONST_Packet2d(cephes_exp_p0, 1.26177193074810590878e-4);
+ static EIGEN_DECLARE_CONST_Packet2d(cephes_exp_p1, 3.02994407707441961300e-2);
+ static EIGEN_DECLARE_CONST_Packet2d(cephes_exp_p2, 9.99999999999999999910e-1);
+ static EIGEN_DECLARE_CONST_Packet2d(cephes_exp_q0, 3.00198505138664455042e-6);
+ static EIGEN_DECLARE_CONST_Packet2d(cephes_exp_q1, 2.52448340349684104192e-3);
+ static EIGEN_DECLARE_CONST_Packet2d(cephes_exp_q2, 2.27265548208155028766e-1);
+ static EIGEN_DECLARE_CONST_Packet2d(cephes_exp_q3, 2.00000000000000000009e0);
+ static EIGEN_DECLARE_CONST_Packet2d(half, 0.5);
+ static EIGEN_DECLARE_CONST_Packet2d(1, 1.0);
+ static EIGEN_DECLARE_CONST_Packet2d(2, 2.0);
+
+ Packet2d x = _x;
+
+ // Clamp x.
+ x = (Packet2d)__builtin_msa_bsel_v((v16u8)__builtin_msa_fclt_d(x, p2d_exp_lo), (v16u8)x,
+ (v16u8)p2d_exp_lo);
+ x = (Packet2d)__builtin_msa_bsel_v((v16u8)__builtin_msa_fclt_d(p2d_exp_hi, x), (v16u8)x,
+ (v16u8)p2d_exp_hi);
+
+ // Round to nearest integer by adding 0.5 (with x's sign) and truncating.
+ Packet2d x2_add = (Packet2d)__builtin_msa_binsli_d((v2u64)p2d_half, (v2u64)x, 0);
+ Packet2d x2 = pmadd(x, p2d_cephes_LOG2EF, x2_add);
+ Packet2l x2_long = __builtin_msa_ftrunc_s_d(x2);
+ Packet2d x2_long_d = __builtin_msa_ffint_s_d(x2_long);
+
+ x = __builtin_msa_fmsub_d(x, x2_long_d, p2d_cephes_exp_C1);
+ x = __builtin_msa_fmsub_d(x, x2_long_d, p2d_cephes_exp_C2);
+
+ x2 = pmul(x, x);
+
+ Packet2d px = p2d_cephes_exp_p0;
+ px = pmadd(px, x2, p2d_cephes_exp_p1);
+ px = pmadd(px, x2, p2d_cephes_exp_p2);
+ px = pmul(px, x);
+
+ Packet2d qx = p2d_cephes_exp_q0;
+ qx = pmadd(qx, x2, p2d_cephes_exp_q1);
+ qx = pmadd(qx, x2, p2d_cephes_exp_q2);
+ qx = pmadd(qx, x2, p2d_cephes_exp_q3);
+
+ x = pdiv(px, psub(qx, px));
+ x = pmadd(p2d_2, x, p2d_1);
+
+ // x *= 2**exponent.
+ x = __builtin_msa_fexp2_d(x, x2_long);
+
+ return x;
+}
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_MATH_FUNCTIONS_MSA_H
diff --git a/Eigen/src/Core/arch/MSA/PacketMath.h b/Eigen/src/Core/arch/MSA/PacketMath.h
new file mode 100644
index 0000000..f03dbed
--- /dev/null
+++ b/Eigen/src/Core/arch/MSA/PacketMath.h
@@ -0,0 +1,1235 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2018 Wave Computing, Inc.
+// Written by:
+// Chris Larsen
+// Alexey Frunze (afrunze@wavecomp.com)
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_PACKET_MATH_MSA_H
+#define EIGEN_PACKET_MATH_MSA_H
+
+#include <iostream>
+#include <string>
+
+#include "../../InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+
+#ifndef EIGEN_CACHEFRIENDLY_PRODUCT_THRESHOLD
+#define EIGEN_CACHEFRIENDLY_PRODUCT_THRESHOLD 8
+#endif
+
+#ifndef EIGEN_HAS_SINGLE_INSTRUCTION_MADD
+#define EIGEN_HAS_SINGLE_INSTRUCTION_MADD
+#endif
+
+#ifndef EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS
+#define EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS 32
+#endif
+
+#if 0
+#define EIGEN_MSA_DEBUG \
+ static bool firstTime = true; \
+ do { \
+ if (firstTime) { \
+ std::cout << __FILE__ << ':' << __LINE__ << ':' << __FUNCTION__ << std::endl; \
+ firstTime = false; \
+ } \
+ } while (0)
+#else
+#define EIGEN_MSA_DEBUG
+#endif
+
+#define EIGEN_MSA_SHF_I8(a, b, c, d) (((d) << 6) | ((c) << 4) | ((b) << 2) | (a))
+
+typedef v4f32 Packet4f;
+typedef v4i32 Packet4i;
+typedef v4u32 Packet4ui;
+
+#define EIGEN_DECLARE_CONST_Packet4f(NAME, X) const Packet4f p4f_##NAME = { X, X, X, X }
+#define EIGEN_DECLARE_CONST_Packet4i(NAME, X) const Packet4i p4i_##NAME = { X, X, X, X }
+#define EIGEN_DECLARE_CONST_Packet4ui(NAME, X) const Packet4ui p4ui_##NAME = { X, X, X, X }
+
+inline std::ostream& operator<<(std::ostream& os, const Packet4f& value) {
+ os << "[ " << value[0] << ", " << value[1] << ", " << value[2] << ", " << value[3] << " ]";
+ return os;
+}
+
+inline std::ostream& operator<<(std::ostream& os, const Packet4i& value) {
+ os << "[ " << value[0] << ", " << value[1] << ", " << value[2] << ", " << value[3] << " ]";
+ return os;
+}
+
+inline std::ostream& operator<<(std::ostream& os, const Packet4ui& value) {
+ os << "[ " << value[0] << ", " << value[1] << ", " << value[2] << ", " << value[3] << " ]";
+ return os;
+}
+
+template <>
+struct packet_traits<float> : default_packet_traits {
+ typedef Packet4f type;
+ typedef Packet4f half; // Packet2f intrinsics not implemented yet
+ enum {
+ Vectorizable = 1,
+ AlignedOnScalar = 1,
+ size = 4,
+ HasHalfPacket = 0, // Packet2f intrinsics not implemented yet
+ // FIXME check the Has*
+ HasDiv = 1,
+ HasSin = EIGEN_FAST_MATH,
+ HasCos = EIGEN_FAST_MATH,
+ HasTanh = EIGEN_FAST_MATH,
+ HasErf = EIGEN_FAST_MATH,
+ HasLog = 1,
+ HasExp = 1,
+ HasSqrt = 1,
+ HasRsqrt = 1,
+ HasRound = 1,
+ HasFloor = 1,
+ HasCeil = 1,
+ HasBlend = 1
+ };
+};
+
+template <>
+struct packet_traits<int32_t> : default_packet_traits {
+ typedef Packet4i type;
+ typedef Packet4i half; // Packet2i intrinsics not implemented yet
+ enum {
+ Vectorizable = 1,
+ AlignedOnScalar = 1,
+ size = 4,
+ HasHalfPacket = 0, // Packet2i intrinsics not implemented yet
+ // FIXME check the Has*
+ HasDiv = 1,
+ HasBlend = 1
+ };
+};
+
+template <>
+struct unpacket_traits<Packet4f> {
+ typedef float type;
+ enum { size = 4, alignment = Aligned16, vectorizable=true, masked_load_available=false, masked_store_available=false };
+ typedef Packet4f half;
+};
+
+template <>
+struct unpacket_traits<Packet4i> {
+ typedef int32_t type;
+ enum { size = 4, alignment = Aligned16, vectorizable=true, masked_load_available=false, masked_store_available=false };
+ typedef Packet4i half;
+};
+
+template <>
+EIGEN_STRONG_INLINE Packet4f pset1<Packet4f>(const float& from) {
+ EIGEN_MSA_DEBUG;
+
+ Packet4f v = { from, from, from, from };
+ return v;
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet4i pset1<Packet4i>(const int32_t& from) {
+ EIGEN_MSA_DEBUG;
+
+ return __builtin_msa_fill_w(from);
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet4f pload1<Packet4f>(const float* from) {
+ EIGEN_MSA_DEBUG;
+
+ float f = *from;
+ Packet4f v = { f, f, f, f };
+ return v;
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet4i pload1<Packet4i>(const int32_t* from) {
+ EIGEN_MSA_DEBUG;
+
+ return __builtin_msa_fill_w(*from);
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet4f padd<Packet4f>(const Packet4f& a, const Packet4f& b) {
+ EIGEN_MSA_DEBUG;
+
+ return __builtin_msa_fadd_w(a, b);
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet4i padd<Packet4i>(const Packet4i& a, const Packet4i& b) {
+ EIGEN_MSA_DEBUG;
+
+ return __builtin_msa_addv_w(a, b);
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet4f plset<Packet4f>(const float& a) {
+ EIGEN_MSA_DEBUG;
+
+ static const Packet4f countdown = { 0.0f, 1.0f, 2.0f, 3.0f };
+ return padd(pset1<Packet4f>(a), countdown);
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet4i plset<Packet4i>(const int32_t& a) {
+ EIGEN_MSA_DEBUG;
+
+ static const Packet4i countdown = { 0, 1, 2, 3 };
+ return padd(pset1<Packet4i>(a), countdown);
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet4f psub<Packet4f>(const Packet4f& a, const Packet4f& b) {
+ EIGEN_MSA_DEBUG;
+
+ return __builtin_msa_fsub_w(a, b);
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet4i psub<Packet4i>(const Packet4i& a, const Packet4i& b) {
+ EIGEN_MSA_DEBUG;
+
+ return __builtin_msa_subv_w(a, b);
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet4f pnegate(const Packet4f& a) {
+ EIGEN_MSA_DEBUG;
+
+ return (Packet4f)__builtin_msa_bnegi_w((v4u32)a, 31);
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet4i pnegate(const Packet4i& a) {
+ EIGEN_MSA_DEBUG;
+
+ return __builtin_msa_addvi_w((v4i32)__builtin_msa_nori_b((v16u8)a, 0), 1);
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet4f pconj(const Packet4f& a) {
+ EIGEN_MSA_DEBUG;
+
+ return a;
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet4i pconj(const Packet4i& a) {
+ EIGEN_MSA_DEBUG;
+
+ return a;
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet4f pmul<Packet4f>(const Packet4f& a, const Packet4f& b) {
+ EIGEN_MSA_DEBUG;
+
+ return __builtin_msa_fmul_w(a, b);
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet4i pmul<Packet4i>(const Packet4i& a, const Packet4i& b) {
+ EIGEN_MSA_DEBUG;
+
+ return __builtin_msa_mulv_w(a, b);
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet4f pdiv<Packet4f>(const Packet4f& a, const Packet4f& b) {
+ EIGEN_MSA_DEBUG;
+
+ return __builtin_msa_fdiv_w(a, b);
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet4i pdiv<Packet4i>(const Packet4i& a, const Packet4i& b) {
+ EIGEN_MSA_DEBUG;
+
+ return __builtin_msa_div_s_w(a, b);
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet4f pmadd(const Packet4f& a, const Packet4f& b, const Packet4f& c) {
+ EIGEN_MSA_DEBUG;
+
+ return __builtin_msa_fmadd_w(c, a, b);
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet4i pmadd(const Packet4i& a, const Packet4i& b, const Packet4i& c) {
+ EIGEN_MSA_DEBUG;
+
+ // Use "asm" construct to avoid __builtin_msa_maddv_w GNU C bug.
+ Packet4i value = c;
+ __asm__("maddv.w %w[value], %w[a], %w[b]\n"
+ // Outputs
+ : [value] "+f"(value)
+ // Inputs
+ : [a] "f"(a), [b] "f"(b));
+ return value;
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet4f pand<Packet4f>(const Packet4f& a, const Packet4f& b) {
+ EIGEN_MSA_DEBUG;
+
+ return (Packet4f)__builtin_msa_and_v((v16u8)a, (v16u8)b);
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet4i pand<Packet4i>(const Packet4i& a, const Packet4i& b) {
+ EIGEN_MSA_DEBUG;
+
+ return (Packet4i)__builtin_msa_and_v((v16u8)a, (v16u8)b);
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet4f por<Packet4f>(const Packet4f& a, const Packet4f& b) {
+ EIGEN_MSA_DEBUG;
+
+ return (Packet4f)__builtin_msa_or_v((v16u8)a, (v16u8)b);
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet4i por<Packet4i>(const Packet4i& a, const Packet4i& b) {
+ EIGEN_MSA_DEBUG;
+
+ return (Packet4i)__builtin_msa_or_v((v16u8)a, (v16u8)b);
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet4f pxor<Packet4f>(const Packet4f& a, const Packet4f& b) {
+ EIGEN_MSA_DEBUG;
+
+ return (Packet4f)__builtin_msa_xor_v((v16u8)a, (v16u8)b);
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet4i pxor<Packet4i>(const Packet4i& a, const Packet4i& b) {
+ EIGEN_MSA_DEBUG;
+
+ return (Packet4i)__builtin_msa_xor_v((v16u8)a, (v16u8)b);
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet4f pandnot<Packet4f>(const Packet4f& a, const Packet4f& b) {
+ EIGEN_MSA_DEBUG;
+
+ return pand(a, (Packet4f)__builtin_msa_xori_b((v16u8)b, 255));
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet4i pandnot<Packet4i>(const Packet4i& a, const Packet4i& b) {
+ EIGEN_MSA_DEBUG;
+
+ return pand(a, (Packet4i)__builtin_msa_xori_b((v16u8)b, 255));
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet4f pmin<Packet4f>(const Packet4f& a, const Packet4f& b) {
+ EIGEN_MSA_DEBUG;
+
+#if EIGEN_FAST_MATH
+ // This prefers numbers to NaNs.
+ return __builtin_msa_fmin_w(a, b);
+#else
+ // This prefers NaNs to numbers.
+ Packet4i aNaN = __builtin_msa_fcun_w(a, a);
+ Packet4i aMinOrNaN = por(__builtin_msa_fclt_w(a, b), aNaN);
+ return (Packet4f)__builtin_msa_bsel_v((v16u8)aMinOrNaN, (v16u8)b, (v16u8)a);
+#endif
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet4i pmin<Packet4i>(const Packet4i& a, const Packet4i& b) {
+ EIGEN_MSA_DEBUG;
+
+ return __builtin_msa_min_s_w(a, b);
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet4f pmax<Packet4f>(const Packet4f& a, const Packet4f& b) {
+ EIGEN_MSA_DEBUG;
+
+#if EIGEN_FAST_MATH
+ // This prefers numbers to NaNs.
+ return __builtin_msa_fmax_w(a, b);
+#else
+ // This prefers NaNs to numbers.
+ Packet4i aNaN = __builtin_msa_fcun_w(a, a);
+ Packet4i aMaxOrNaN = por(__builtin_msa_fclt_w(b, a), aNaN);
+ return (Packet4f)__builtin_msa_bsel_v((v16u8)aMaxOrNaN, (v16u8)b, (v16u8)a);
+#endif
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet4i pmax<Packet4i>(const Packet4i& a, const Packet4i& b) {
+ EIGEN_MSA_DEBUG;
+
+ return __builtin_msa_max_s_w(a, b);
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet4f pload<Packet4f>(const float* from) {
+ EIGEN_MSA_DEBUG;
+
+ EIGEN_DEBUG_ALIGNED_LOAD return (Packet4f)__builtin_msa_ld_w(const_cast<float*>(from), 0);
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet4i pload<Packet4i>(const int32_t* from) {
+ EIGEN_MSA_DEBUG;
+
+ EIGEN_DEBUG_ALIGNED_LOAD return __builtin_msa_ld_w(const_cast<int32_t*>(from), 0);
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet4f ploadu<Packet4f>(const float* from) {
+ EIGEN_MSA_DEBUG;
+
+ EIGEN_DEBUG_UNALIGNED_LOAD return (Packet4f)__builtin_msa_ld_w(const_cast<float*>(from), 0);
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet4i ploadu<Packet4i>(const int32_t* from) {
+ EIGEN_MSA_DEBUG;
+
+ EIGEN_DEBUG_UNALIGNED_LOAD return (Packet4i)__builtin_msa_ld_w(const_cast<int32_t*>(from), 0);
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet4f ploaddup<Packet4f>(const float* from) {
+ EIGEN_MSA_DEBUG;
+
+ float f0 = from[0], f1 = from[1];
+ Packet4f v0 = { f0, f0, f0, f0 };
+ Packet4f v1 = { f1, f1, f1, f1 };
+ return (Packet4f)__builtin_msa_ilvr_d((v2i64)v1, (v2i64)v0);
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet4i ploaddup<Packet4i>(const int32_t* from) {
+ EIGEN_MSA_DEBUG;
+
+ int32_t i0 = from[0], i1 = from[1];
+ Packet4i v0 = { i0, i0, i0, i0 };
+ Packet4i v1 = { i1, i1, i1, i1 };
+ return (Packet4i)__builtin_msa_ilvr_d((v2i64)v1, (v2i64)v0);
+}
+
+template <>
+EIGEN_STRONG_INLINE void pstore<float>(float* to, const Packet4f& from) {
+ EIGEN_MSA_DEBUG;
+
+ EIGEN_DEBUG_ALIGNED_STORE __builtin_msa_st_w((Packet4i)from, to, 0);
+}
+
+template <>
+EIGEN_STRONG_INLINE void pstore<int32_t>(int32_t* to, const Packet4i& from) {
+ EIGEN_MSA_DEBUG;
+
+ EIGEN_DEBUG_ALIGNED_STORE __builtin_msa_st_w(from, to, 0);
+}
+
+template <>
+EIGEN_STRONG_INLINE void pstoreu<float>(float* to, const Packet4f& from) {
+ EIGEN_MSA_DEBUG;
+
+ EIGEN_DEBUG_UNALIGNED_STORE __builtin_msa_st_w((Packet4i)from, to, 0);
+}
+
+template <>
+EIGEN_STRONG_INLINE void pstoreu<int32_t>(int32_t* to, const Packet4i& from) {
+ EIGEN_MSA_DEBUG;
+
+ EIGEN_DEBUG_UNALIGNED_STORE __builtin_msa_st_w(from, to, 0);
+}
+
+template <>
+EIGEN_DEVICE_FUNC inline Packet4f pgather<float, Packet4f>(const float* from, Index stride) {
+ EIGEN_MSA_DEBUG;
+
+ float f = *from;
+ Packet4f v = { f, f, f, f };
+ v[1] = from[stride];
+ v[2] = from[2 * stride];
+ v[3] = from[3 * stride];
+ return v;
+}
+
+template <>
+EIGEN_DEVICE_FUNC inline Packet4i pgather<int32_t, Packet4i>(const int32_t* from, Index stride) {
+ EIGEN_MSA_DEBUG;
+
+ int32_t i = *from;
+ Packet4i v = { i, i, i, i };
+ v[1] = from[stride];
+ v[2] = from[2 * stride];
+ v[3] = from[3 * stride];
+ return v;
+}
+
+template <>
+EIGEN_DEVICE_FUNC inline void pscatter<float, Packet4f>(float* to, const Packet4f& from,
+ Index stride) {
+ EIGEN_MSA_DEBUG;
+
+ *to = from[0];
+ to += stride;
+ *to = from[1];
+ to += stride;
+ *to = from[2];
+ to += stride;
+ *to = from[3];
+}
+
+template <>
+EIGEN_DEVICE_FUNC inline void pscatter<int32_t, Packet4i>(int32_t* to, const Packet4i& from,
+ Index stride) {
+ EIGEN_MSA_DEBUG;
+
+ *to = from[0];
+ to += stride;
+ *to = from[1];
+ to += stride;
+ *to = from[2];
+ to += stride;
+ *to = from[3];
+}
+
+template <>
+EIGEN_STRONG_INLINE void prefetch<float>(const float* addr) {
+ EIGEN_MSA_DEBUG;
+
+ __builtin_prefetch(addr);
+}
+
+template <>
+EIGEN_STRONG_INLINE void prefetch<int32_t>(const int32_t* addr) {
+ EIGEN_MSA_DEBUG;
+
+ __builtin_prefetch(addr);
+}
+
+template <>
+EIGEN_STRONG_INLINE float pfirst<Packet4f>(const Packet4f& a) {
+ EIGEN_MSA_DEBUG;
+
+ return a[0];
+}
+
+template <>
+EIGEN_STRONG_INLINE int32_t pfirst<Packet4i>(const Packet4i& a) {
+ EIGEN_MSA_DEBUG;
+
+ return a[0];
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet4f preverse(const Packet4f& a) {
+ EIGEN_MSA_DEBUG;
+
+ return (Packet4f)__builtin_msa_shf_w((v4i32)a, EIGEN_MSA_SHF_I8(3, 2, 1, 0));
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet4i preverse(const Packet4i& a) {
+ EIGEN_MSA_DEBUG;
+
+ return __builtin_msa_shf_w(a, EIGEN_MSA_SHF_I8(3, 2, 1, 0));
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet4f pabs(const Packet4f& a) {
+ EIGEN_MSA_DEBUG;
+
+ return (Packet4f)__builtin_msa_bclri_w((v4u32)a, 31);
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet4i pabs(const Packet4i& a) {
+ EIGEN_MSA_DEBUG;
+
+ Packet4i zero = __builtin_msa_ldi_w(0);
+ return __builtin_msa_add_a_w(zero, a);
+}
+
+template <>
+EIGEN_STRONG_INLINE float predux<Packet4f>(const Packet4f& a) {
+ EIGEN_MSA_DEBUG;
+
+ Packet4f s = padd(a, (Packet4f)__builtin_msa_shf_w((v4i32)a, EIGEN_MSA_SHF_I8(2, 3, 0, 1)));
+ s = padd(s, (Packet4f)__builtin_msa_shf_w((v4i32)s, EIGEN_MSA_SHF_I8(1, 0, 3, 2)));
+ return s[0];
+}
+
+
+template <>
+EIGEN_STRONG_INLINE int32_t predux<Packet4i>(const Packet4i& a) {
+ EIGEN_MSA_DEBUG;
+
+ Packet4i s = padd(a, __builtin_msa_shf_w(a, EIGEN_MSA_SHF_I8(2, 3, 0, 1)));
+ s = padd(s, __builtin_msa_shf_w(s, EIGEN_MSA_SHF_I8(1, 0, 3, 2)));
+ return s[0];
+}
+
+// Other reduction functions:
+// mul
+template <>
+EIGEN_STRONG_INLINE float predux_mul<Packet4f>(const Packet4f& a) {
+ EIGEN_MSA_DEBUG;
+
+ Packet4f p = pmul(a, (Packet4f)__builtin_msa_shf_w((v4i32)a, EIGEN_MSA_SHF_I8(2, 3, 0, 1)));
+ p = pmul(p, (Packet4f)__builtin_msa_shf_w((v4i32)p, EIGEN_MSA_SHF_I8(1, 0, 3, 2)));
+ return p[0];
+}
+
+template <>
+EIGEN_STRONG_INLINE int32_t predux_mul<Packet4i>(const Packet4i& a) {
+ EIGEN_MSA_DEBUG;
+
+ Packet4i p = pmul(a, __builtin_msa_shf_w(a, EIGEN_MSA_SHF_I8(2, 3, 0, 1)));
+ p = pmul(p, __builtin_msa_shf_w(p, EIGEN_MSA_SHF_I8(1, 0, 3, 2)));
+ return p[0];
+}
+
+// min
+template <>
+EIGEN_STRONG_INLINE float predux_min<Packet4f>(const Packet4f& a) {
+ EIGEN_MSA_DEBUG;
+
+ // Swap 64-bit halves of a.
+ Packet4f swapped = (Packet4f)__builtin_msa_shf_w((Packet4i)a, EIGEN_MSA_SHF_I8(2, 3, 0, 1));
+#if !EIGEN_FAST_MATH
+ // Detect presence of NaNs from pairs a[0]-a[2] and a[1]-a[3] as two 32-bit
+ // masks of all zeroes/ones in low 64 bits.
+ v16u8 unord = (v16u8)__builtin_msa_fcun_w(a, swapped);
+ // Combine the two masks into one: 64 ones if no NaNs, otherwise 64 zeroes.
+ unord = (v16u8)__builtin_msa_ceqi_d((v2i64)unord, 0);
+#endif
+ // Continue with min computation.
+ Packet4f v = __builtin_msa_fmin_w(a, swapped);
+ v = __builtin_msa_fmin_w(
+ v, (Packet4f)__builtin_msa_shf_w((Packet4i)v, EIGEN_MSA_SHF_I8(1, 0, 3, 2)));
+#if !EIGEN_FAST_MATH
+ // Based on the mask select between v and 4 qNaNs.
+ v16u8 qnans = (v16u8)__builtin_msa_fill_w(0x7FC00000);
+ v = (Packet4f)__builtin_msa_bsel_v(unord, qnans, (v16u8)v);
+#endif
+ return v[0];
+}
+
+template <>
+EIGEN_STRONG_INLINE int32_t predux_min<Packet4i>(const Packet4i& a) {
+ EIGEN_MSA_DEBUG;
+
+ Packet4i m = pmin(a, __builtin_msa_shf_w(a, EIGEN_MSA_SHF_I8(2, 3, 0, 1)));
+ m = pmin(m, __builtin_msa_shf_w(m, EIGEN_MSA_SHF_I8(1, 0, 3, 2)));
+ return m[0];
+}
+
+// max
+template <>
+EIGEN_STRONG_INLINE float predux_max<Packet4f>(const Packet4f& a) {
+ EIGEN_MSA_DEBUG;
+
+ // Swap 64-bit halves of a.
+ Packet4f swapped = (Packet4f)__builtin_msa_shf_w((Packet4i)a, EIGEN_MSA_SHF_I8(2, 3, 0, 1));
+#if !EIGEN_FAST_MATH
+ // Detect presence of NaNs from pairs a[0]-a[2] and a[1]-a[3] as two 32-bit
+ // masks of all zeroes/ones in low 64 bits.
+ v16u8 unord = (v16u8)__builtin_msa_fcun_w(a, swapped);
+ // Combine the two masks into one: 64 ones if no NaNs, otherwise 64 zeroes.
+ unord = (v16u8)__builtin_msa_ceqi_d((v2i64)unord, 0);
+#endif
+ // Continue with max computation.
+ Packet4f v = __builtin_msa_fmax_w(a, swapped);
+ v = __builtin_msa_fmax_w(
+ v, (Packet4f)__builtin_msa_shf_w((Packet4i)v, EIGEN_MSA_SHF_I8(1, 0, 3, 2)));
+#if !EIGEN_FAST_MATH
+ // Based on the mask select between v and 4 qNaNs.
+ v16u8 qnans = (v16u8)__builtin_msa_fill_w(0x7FC00000);
+ v = (Packet4f)__builtin_msa_bsel_v(unord, qnans, (v16u8)v);
+#endif
+ return v[0];
+}
+
+template <>
+EIGEN_STRONG_INLINE int32_t predux_max<Packet4i>(const Packet4i& a) {
+ EIGEN_MSA_DEBUG;
+
+ Packet4i m = pmax(a, __builtin_msa_shf_w(a, EIGEN_MSA_SHF_I8(2, 3, 0, 1)));
+ m = pmax(m, __builtin_msa_shf_w(m, EIGEN_MSA_SHF_I8(1, 0, 3, 2)));
+ return m[0];
+}
+
+inline std::ostream& operator<<(std::ostream& os, const PacketBlock<Packet4f, 4>& value) {
+ os << "[ " << value.packet[0] << "," << std::endl
+ << " " << value.packet[1] << "," << std::endl
+ << " " << value.packet[2] << "," << std::endl
+ << " " << value.packet[3] << " ]";
+ return os;
+}
+
+EIGEN_DEVICE_FUNC inline void ptranspose(PacketBlock<Packet4f, 4>& kernel) {
+ EIGEN_MSA_DEBUG;
+
+ v4i32 tmp1, tmp2, tmp3, tmp4;
+
+ tmp1 = __builtin_msa_ilvr_w((v4i32)kernel.packet[1], (v4i32)kernel.packet[0]);
+ tmp2 = __builtin_msa_ilvr_w((v4i32)kernel.packet[3], (v4i32)kernel.packet[2]);
+ tmp3 = __builtin_msa_ilvl_w((v4i32)kernel.packet[1], (v4i32)kernel.packet[0]);
+ tmp4 = __builtin_msa_ilvl_w((v4i32)kernel.packet[3], (v4i32)kernel.packet[2]);
+
+ kernel.packet[0] = (Packet4f)__builtin_msa_ilvr_d((v2i64)tmp2, (v2i64)tmp1);
+ kernel.packet[1] = (Packet4f)__builtin_msa_ilvod_d((v2i64)tmp2, (v2i64)tmp1);
+ kernel.packet[2] = (Packet4f)__builtin_msa_ilvr_d((v2i64)tmp4, (v2i64)tmp3);
+ kernel.packet[3] = (Packet4f)__builtin_msa_ilvod_d((v2i64)tmp4, (v2i64)tmp3);
+}
+
+inline std::ostream& operator<<(std::ostream& os, const PacketBlock<Packet4i, 4>& value) {
+ os << "[ " << value.packet[0] << "," << std::endl
+ << " " << value.packet[1] << "," << std::endl
+ << " " << value.packet[2] << "," << std::endl
+ << " " << value.packet[3] << " ]";
+ return os;
+}
+
+EIGEN_DEVICE_FUNC inline void ptranspose(PacketBlock<Packet4i, 4>& kernel) {
+ EIGEN_MSA_DEBUG;
+
+ v4i32 tmp1, tmp2, tmp3, tmp4;
+
+ tmp1 = __builtin_msa_ilvr_w(kernel.packet[1], kernel.packet[0]);
+ tmp2 = __builtin_msa_ilvr_w(kernel.packet[3], kernel.packet[2]);
+ tmp3 = __builtin_msa_ilvl_w(kernel.packet[1], kernel.packet[0]);
+ tmp4 = __builtin_msa_ilvl_w(kernel.packet[3], kernel.packet[2]);
+
+ kernel.packet[0] = (Packet4i)__builtin_msa_ilvr_d((v2i64)tmp2, (v2i64)tmp1);
+ kernel.packet[1] = (Packet4i)__builtin_msa_ilvod_d((v2i64)tmp2, (v2i64)tmp1);
+ kernel.packet[2] = (Packet4i)__builtin_msa_ilvr_d((v2i64)tmp4, (v2i64)tmp3);
+ kernel.packet[3] = (Packet4i)__builtin_msa_ilvod_d((v2i64)tmp4, (v2i64)tmp3);
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet4f psqrt(const Packet4f& a) {
+ EIGEN_MSA_DEBUG;
+
+ return __builtin_msa_fsqrt_w(a);
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet4f prsqrt(const Packet4f& a) {
+ EIGEN_MSA_DEBUG;
+
+#if EIGEN_FAST_MATH
+ return __builtin_msa_frsqrt_w(a);
+#else
+ Packet4f ones = __builtin_msa_ffint_s_w(__builtin_msa_ldi_w(1));
+ return pdiv(ones, psqrt(a));
+#endif
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet4f pfloor<Packet4f>(const Packet4f& a) {
+ Packet4f v = a;
+ int32_t old_mode, new_mode;
+ asm volatile(
+ "cfcmsa %[old_mode], $1\n"
+ "ori %[new_mode], %[old_mode], 3\n" // 3 = round towards -INFINITY.
+ "ctcmsa $1, %[new_mode]\n"
+ "frint.w %w[v], %w[v]\n"
+ "ctcmsa $1, %[old_mode]\n"
+ : // outputs
+ [old_mode] "=r"(old_mode), [new_mode] "=r"(new_mode),
+ [v] "+f"(v)
+ : // inputs
+ : // clobbers
+ );
+ return v;
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet4f pceil<Packet4f>(const Packet4f& a) {
+ Packet4f v = a;
+ int32_t old_mode, new_mode;
+ asm volatile(
+ "cfcmsa %[old_mode], $1\n"
+ "ori %[new_mode], %[old_mode], 3\n"
+ "xori %[new_mode], %[new_mode], 1\n" // 2 = round towards +INFINITY.
+ "ctcmsa $1, %[new_mode]\n"
+ "frint.w %w[v], %w[v]\n"
+ "ctcmsa $1, %[old_mode]\n"
+ : // outputs
+ [old_mode] "=r"(old_mode), [new_mode] "=r"(new_mode),
+ [v] "+f"(v)
+ : // inputs
+ : // clobbers
+ );
+ return v;
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet4f pround<Packet4f>(const Packet4f& a) {
+ Packet4f v = a;
+ int32_t old_mode, new_mode;
+ asm volatile(
+ "cfcmsa %[old_mode], $1\n"
+ "ori %[new_mode], %[old_mode], 3\n"
+ "xori %[new_mode], %[new_mode], 3\n" // 0 = round to nearest, ties to even.
+ "ctcmsa $1, %[new_mode]\n"
+ "frint.w %w[v], %w[v]\n"
+ "ctcmsa $1, %[old_mode]\n"
+ : // outputs
+ [old_mode] "=r"(old_mode), [new_mode] "=r"(new_mode),
+ [v] "+f"(v)
+ : // inputs
+ : // clobbers
+ );
+ return v;
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet4f pblend(const Selector<4>& ifPacket, const Packet4f& thenPacket,
+ const Packet4f& elsePacket) {
+ Packet4ui select = { ifPacket.select[0], ifPacket.select[1], ifPacket.select[2],
+ ifPacket.select[3] };
+ Packet4i mask = __builtin_msa_ceqi_w((Packet4i)select, 0);
+ return (Packet4f)__builtin_msa_bsel_v((v16u8)mask, (v16u8)thenPacket, (v16u8)elsePacket);
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet4i pblend(const Selector<4>& ifPacket, const Packet4i& thenPacket,
+ const Packet4i& elsePacket) {
+ Packet4ui select = { ifPacket.select[0], ifPacket.select[1], ifPacket.select[2],
+ ifPacket.select[3] };
+ Packet4i mask = __builtin_msa_ceqi_w((Packet4i)select, 0);
+ return (Packet4i)__builtin_msa_bsel_v((v16u8)mask, (v16u8)thenPacket, (v16u8)elsePacket);
+}
+
+//---------- double ----------
+
+typedef v2f64 Packet2d;
+typedef v2i64 Packet2l;
+typedef v2u64 Packet2ul;
+
+#define EIGEN_DECLARE_CONST_Packet2d(NAME, X) const Packet2d p2d_##NAME = { X, X }
+#define EIGEN_DECLARE_CONST_Packet2l(NAME, X) const Packet2l p2l_##NAME = { X, X }
+#define EIGEN_DECLARE_CONST_Packet2ul(NAME, X) const Packet2ul p2ul_##NAME = { X, X }
+
+inline std::ostream& operator<<(std::ostream& os, const Packet2d& value) {
+ os << "[ " << value[0] << ", " << value[1] << " ]";
+ return os;
+}
+
+inline std::ostream& operator<<(std::ostream& os, const Packet2l& value) {
+ os << "[ " << value[0] << ", " << value[1] << " ]";
+ return os;
+}
+
+inline std::ostream& operator<<(std::ostream& os, const Packet2ul& value) {
+ os << "[ " << value[0] << ", " << value[1] << " ]";
+ return os;
+}
+
+template <>
+struct packet_traits<double> : default_packet_traits {
+ typedef Packet2d type;
+ typedef Packet2d half;
+ enum {
+ Vectorizable = 1,
+ AlignedOnScalar = 1,
+ size = 2,
+ HasHalfPacket = 0,
+ // FIXME check the Has*
+ HasDiv = 1,
+ HasExp = 1,
+ HasSqrt = 1,
+ HasRsqrt = 1,
+ HasRound = 1,
+ HasFloor = 1,
+ HasCeil = 1,
+ HasBlend = 1
+ };
+};
+
+template <>
+struct unpacket_traits<Packet2d> {
+ typedef double type;
+ enum { size = 2, alignment = Aligned16, vectorizable=true, masked_load_available=false, masked_store_available=false };
+ typedef Packet2d half;
+};
+
+template <>
+EIGEN_STRONG_INLINE Packet2d pset1<Packet2d>(const double& from) {
+ EIGEN_MSA_DEBUG;
+
+ Packet2d value = { from, from };
+ return value;
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet2d padd<Packet2d>(const Packet2d& a, const Packet2d& b) {
+ EIGEN_MSA_DEBUG;
+
+ return __builtin_msa_fadd_d(a, b);
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet2d plset<Packet2d>(const double& a) {
+ EIGEN_MSA_DEBUG;
+
+ static const Packet2d countdown = { 0.0, 1.0 };
+ return padd(pset1<Packet2d>(a), countdown);
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet2d psub<Packet2d>(const Packet2d& a, const Packet2d& b) {
+ EIGEN_MSA_DEBUG;
+
+ return __builtin_msa_fsub_d(a, b);
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet2d pnegate(const Packet2d& a) {
+ EIGEN_MSA_DEBUG;
+
+ return (Packet2d)__builtin_msa_bnegi_d((v2u64)a, 63);
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet2d pconj(const Packet2d& a) {
+ EIGEN_MSA_DEBUG;
+
+ return a;
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet2d pmul<Packet2d>(const Packet2d& a, const Packet2d& b) {
+ EIGEN_MSA_DEBUG;
+
+ return __builtin_msa_fmul_d(a, b);
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet2d pdiv<Packet2d>(const Packet2d& a, const Packet2d& b) {
+ EIGEN_MSA_DEBUG;
+
+ return __builtin_msa_fdiv_d(a, b);
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet2d pmadd(const Packet2d& a, const Packet2d& b, const Packet2d& c) {
+ EIGEN_MSA_DEBUG;
+
+ return __builtin_msa_fmadd_d(c, a, b);
+}
+
+// Logical Operations are not supported for float, so we have to reinterpret casts using MSA
+// intrinsics
+template <>
+EIGEN_STRONG_INLINE Packet2d pand<Packet2d>(const Packet2d& a, const Packet2d& b) {
+ EIGEN_MSA_DEBUG;
+
+ return (Packet2d)__builtin_msa_and_v((v16u8)a, (v16u8)b);
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet2d por<Packet2d>(const Packet2d& a, const Packet2d& b) {
+ EIGEN_MSA_DEBUG;
+
+ return (Packet2d)__builtin_msa_or_v((v16u8)a, (v16u8)b);
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet2d pxor<Packet2d>(const Packet2d& a, const Packet2d& b) {
+ EIGEN_MSA_DEBUG;
+
+ return (Packet2d)__builtin_msa_xor_v((v16u8)a, (v16u8)b);
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet2d pandnot<Packet2d>(const Packet2d& a, const Packet2d& b) {
+ EIGEN_MSA_DEBUG;
+
+ return pand(a, (Packet2d)__builtin_msa_xori_b((v16u8)b, 255));
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet2d pload<Packet2d>(const double* from) {
+ EIGEN_MSA_DEBUG;
+
+ EIGEN_DEBUG_UNALIGNED_LOAD return (Packet2d)__builtin_msa_ld_d(const_cast<double*>(from), 0);
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet2d pmin<Packet2d>(const Packet2d& a, const Packet2d& b) {
+ EIGEN_MSA_DEBUG;
+
+#if EIGEN_FAST_MATH
+ // This prefers numbers to NaNs.
+ return __builtin_msa_fmin_d(a, b);
+#else
+ // This prefers NaNs to numbers.
+ v2i64 aNaN = __builtin_msa_fcun_d(a, a);
+ v2i64 aMinOrNaN = por(__builtin_msa_fclt_d(a, b), aNaN);
+ return (Packet2d)__builtin_msa_bsel_v((v16u8)aMinOrNaN, (v16u8)b, (v16u8)a);
+#endif
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet2d pmax<Packet2d>(const Packet2d& a, const Packet2d& b) {
+ EIGEN_MSA_DEBUG;
+
+#if EIGEN_FAST_MATH
+ // This prefers numbers to NaNs.
+ return __builtin_msa_fmax_d(a, b);
+#else
+ // This prefers NaNs to numbers.
+ v2i64 aNaN = __builtin_msa_fcun_d(a, a);
+ v2i64 aMaxOrNaN = por(__builtin_msa_fclt_d(b, a), aNaN);
+ return (Packet2d)__builtin_msa_bsel_v((v16u8)aMaxOrNaN, (v16u8)b, (v16u8)a);
+#endif
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet2d ploadu<Packet2d>(const double* from) {
+ EIGEN_MSA_DEBUG;
+
+ EIGEN_DEBUG_UNALIGNED_LOAD return (Packet2d)__builtin_msa_ld_d(const_cast<double*>(from), 0);
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet2d ploaddup<Packet2d>(const double* from) {
+ EIGEN_MSA_DEBUG;
+
+ Packet2d value = { *from, *from };
+ return value;
+}
+
+template <>
+EIGEN_STRONG_INLINE void pstore<double>(double* to, const Packet2d& from) {
+ EIGEN_MSA_DEBUG;
+
+ EIGEN_DEBUG_ALIGNED_STORE __builtin_msa_st_d((v2i64)from, to, 0);
+}
+
+template <>
+EIGEN_STRONG_INLINE void pstoreu<double>(double* to, const Packet2d& from) {
+ EIGEN_MSA_DEBUG;
+
+ EIGEN_DEBUG_UNALIGNED_STORE __builtin_msa_st_d((v2i64)from, to, 0);
+}
+
+template <>
+EIGEN_DEVICE_FUNC inline Packet2d pgather<double, Packet2d>(const double* from, Index stride) {
+ EIGEN_MSA_DEBUG;
+
+ Packet2d value;
+ value[0] = *from;
+ from += stride;
+ value[1] = *from;
+ return value;
+}
+
+template <>
+EIGEN_DEVICE_FUNC inline void pscatter<double, Packet2d>(double* to, const Packet2d& from,
+ Index stride) {
+ EIGEN_MSA_DEBUG;
+
+ *to = from[0];
+ to += stride;
+ *to = from[1];
+}
+
+template <>
+EIGEN_STRONG_INLINE void prefetch<double>(const double* addr) {
+ EIGEN_MSA_DEBUG;
+
+ __builtin_prefetch(addr);
+}
+
+template <>
+EIGEN_STRONG_INLINE double pfirst<Packet2d>(const Packet2d& a) {
+ EIGEN_MSA_DEBUG;
+
+ return a[0];
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet2d preverse(const Packet2d& a) {
+ EIGEN_MSA_DEBUG;
+
+ return (Packet2d)__builtin_msa_shf_w((v4i32)a, EIGEN_MSA_SHF_I8(2, 3, 0, 1));
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet2d pabs(const Packet2d& a) {
+ EIGEN_MSA_DEBUG;
+
+ return (Packet2d)__builtin_msa_bclri_d((v2u64)a, 63);
+}
+
+template <>
+EIGEN_STRONG_INLINE double predux<Packet2d>(const Packet2d& a) {
+ EIGEN_MSA_DEBUG;
+
+ Packet2d s = padd(a, preverse(a));
+ return s[0];
+}
+
+// Other reduction functions:
+// mul
+template <>
+EIGEN_STRONG_INLINE double predux_mul<Packet2d>(const Packet2d& a) {
+ EIGEN_MSA_DEBUG;
+
+ Packet2d p = pmul(a, preverse(a));
+ return p[0];
+}
+
+// min
+template <>
+EIGEN_STRONG_INLINE double predux_min<Packet2d>(const Packet2d& a) {
+ EIGEN_MSA_DEBUG;
+
+#if EIGEN_FAST_MATH
+ Packet2d swapped = (Packet2d)__builtin_msa_shf_w((Packet4i)a, EIGEN_MSA_SHF_I8(2, 3, 0, 1));
+ Packet2d v = __builtin_msa_fmin_d(a, swapped);
+ return v[0];
+#else
+ double a0 = a[0], a1 = a[1];
+ return ((numext::isnan)(a0) || a0 < a1) ? a0 : a1;
+#endif
+}
+
+// max
+template <>
+EIGEN_STRONG_INLINE double predux_max<Packet2d>(const Packet2d& a) {
+ EIGEN_MSA_DEBUG;
+
+#if EIGEN_FAST_MATH
+ Packet2d swapped = (Packet2d)__builtin_msa_shf_w((Packet4i)a, EIGEN_MSA_SHF_I8(2, 3, 0, 1));
+ Packet2d v = __builtin_msa_fmax_d(a, swapped);
+ return v[0];
+#else
+ double a0 = a[0], a1 = a[1];
+ return ((numext::isnan)(a0) || a0 > a1) ? a0 : a1;
+#endif
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet2d psqrt(const Packet2d& a) {
+ EIGEN_MSA_DEBUG;
+
+ return __builtin_msa_fsqrt_d(a);
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet2d prsqrt(const Packet2d& a) {
+ EIGEN_MSA_DEBUG;
+
+#if EIGEN_FAST_MATH
+ return __builtin_msa_frsqrt_d(a);
+#else
+ Packet2d ones = __builtin_msa_ffint_s_d(__builtin_msa_ldi_d(1));
+ return pdiv(ones, psqrt(a));
+#endif
+}
+
+inline std::ostream& operator<<(std::ostream& os, const PacketBlock<Packet2d, 2>& value) {
+ os << "[ " << value.packet[0] << "," << std::endl << " " << value.packet[1] << " ]";
+ return os;
+}
+
+EIGEN_DEVICE_FUNC inline void ptranspose(PacketBlock<Packet2d, 2>& kernel) {
+ EIGEN_MSA_DEBUG;
+
+ Packet2d trn1 = (Packet2d)__builtin_msa_ilvev_d((v2i64)kernel.packet[1], (v2i64)kernel.packet[0]);
+ Packet2d trn2 = (Packet2d)__builtin_msa_ilvod_d((v2i64)kernel.packet[1], (v2i64)kernel.packet[0]);
+ kernel.packet[0] = trn1;
+ kernel.packet[1] = trn2;
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet2d pfloor<Packet2d>(const Packet2d& a) {
+ Packet2d v = a;
+ int32_t old_mode, new_mode;
+ asm volatile(
+ "cfcmsa %[old_mode], $1\n"
+ "ori %[new_mode], %[old_mode], 3\n" // 3 = round towards -INFINITY.
+ "ctcmsa $1, %[new_mode]\n"
+ "frint.d %w[v], %w[v]\n"
+ "ctcmsa $1, %[old_mode]\n"
+ : // outputs
+ [old_mode] "=r"(old_mode), [new_mode] "=r"(new_mode),
+ [v] "+f"(v)
+ : // inputs
+ : // clobbers
+ );
+ return v;
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet2d pceil<Packet2d>(const Packet2d& a) {
+ Packet2d v = a;
+ int32_t old_mode, new_mode;
+ asm volatile(
+ "cfcmsa %[old_mode], $1\n"
+ "ori %[new_mode], %[old_mode], 3\n"
+ "xori %[new_mode], %[new_mode], 1\n" // 2 = round towards +INFINITY.
+ "ctcmsa $1, %[new_mode]\n"
+ "frint.d %w[v], %w[v]\n"
+ "ctcmsa $1, %[old_mode]\n"
+ : // outputs
+ [old_mode] "=r"(old_mode), [new_mode] "=r"(new_mode),
+ [v] "+f"(v)
+ : // inputs
+ : // clobbers
+ );
+ return v;
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet2d pround<Packet2d>(const Packet2d& a) {
+ Packet2d v = a;
+ int32_t old_mode, new_mode;
+ asm volatile(
+ "cfcmsa %[old_mode], $1\n"
+ "ori %[new_mode], %[old_mode], 3\n"
+ "xori %[new_mode], %[new_mode], 3\n" // 0 = round to nearest, ties to even.
+ "ctcmsa $1, %[new_mode]\n"
+ "frint.d %w[v], %w[v]\n"
+ "ctcmsa $1, %[old_mode]\n"
+ : // outputs
+ [old_mode] "=r"(old_mode), [new_mode] "=r"(new_mode),
+ [v] "+f"(v)
+ : // inputs
+ : // clobbers
+ );
+ return v;
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet2d pblend(const Selector<2>& ifPacket, const Packet2d& thenPacket,
+ const Packet2d& elsePacket) {
+ Packet2ul select = { ifPacket.select[0], ifPacket.select[1] };
+ Packet2l mask = __builtin_msa_ceqi_d((Packet2l)select, 0);
+ return (Packet2d)__builtin_msa_bsel_v((v16u8)mask, (v16u8)thenPacket, (v16u8)elsePacket);
+}
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_PACKET_MATH_MSA_H
diff --git a/Eigen/src/Core/arch/NEON/Complex.h b/Eigen/src/Core/arch/NEON/Complex.h
new file mode 100644
index 0000000..008dd7a
--- /dev/null
+++ b/Eigen/src/Core/arch/NEON/Complex.h
@@ -0,0 +1,565 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2010 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2010 Konstantinos Margaritis <markos@freevec.org>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_COMPLEX_NEON_H
+#define EIGEN_COMPLEX_NEON_H
+
+#include "../../InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+
+inline uint32x4_t p4ui_CONJ_XOR()
+{
+// See bug 1325, clang fails to call vld1q_u64.
+#if EIGEN_COMP_CLANG || EIGEN_COMP_CASTXML
+ uint32x4_t ret = { 0x00000000, 0x80000000, 0x00000000, 0x80000000 };
+ return ret;
+#else
+ static const uint32_t conj_XOR_DATA[] = { 0x00000000, 0x80000000, 0x00000000, 0x80000000 };
+ return vld1q_u32( conj_XOR_DATA );
+#endif
+}
+
+inline uint32x2_t p2ui_CONJ_XOR()
+{
+ static const uint32_t conj_XOR_DATA[] = { 0x00000000, 0x80000000 };
+ return vld1_u32( conj_XOR_DATA );
+}
+
+//---------- float ----------
+
+struct Packet1cf
+{
+ EIGEN_STRONG_INLINE Packet1cf() {}
+ EIGEN_STRONG_INLINE explicit Packet1cf(const Packet2f& a) : v(a) {}
+ Packet2f v;
+};
+struct Packet2cf
+{
+ EIGEN_STRONG_INLINE Packet2cf() {}
+ EIGEN_STRONG_INLINE explicit Packet2cf(const Packet4f& a) : v(a) {}
+ Packet4f v;
+};
+
+template<> struct packet_traits<std::complex<float> > : default_packet_traits
+{
+ typedef Packet2cf type;
+ typedef Packet1cf half;
+ enum
+ {
+ Vectorizable = 1,
+ AlignedOnScalar = 1,
+ size = 2,
+ HasHalfPacket = 1,
+
+ HasAdd = 1,
+ HasSub = 1,
+ HasMul = 1,
+ HasDiv = 1,
+ HasNegate = 1,
+ HasAbs = 0,
+ HasAbs2 = 0,
+ HasMin = 0,
+ HasMax = 0,
+ HasSetLinear = 0
+ };
+};
+
+template<> struct unpacket_traits<Packet1cf>
+{
+ typedef std::complex<float> type;
+ typedef Packet1cf half;
+ typedef Packet2f as_real;
+ enum
+ {
+ size = 1,
+ alignment = Aligned16,
+ vectorizable = true,
+ masked_load_available = false,
+ masked_store_available = false
+ };
+};
+template<> struct unpacket_traits<Packet2cf>
+{
+ typedef std::complex<float> type;
+ typedef Packet1cf half;
+ typedef Packet4f as_real;
+ enum
+ {
+ size = 2,
+ alignment = Aligned16,
+ vectorizable = true,
+ masked_load_available = false,
+ masked_store_available = false
+ };
+};
+
+template<> EIGEN_STRONG_INLINE Packet1cf pcast<float,Packet1cf>(const float& a)
+{ return Packet1cf(vset_lane_f32(a, vdup_n_f32(0.f), 0)); }
+template<> EIGEN_STRONG_INLINE Packet2cf pcast<Packet2f,Packet2cf>(const Packet2f& a)
+{ return Packet2cf(vreinterpretq_f32_u64(vmovl_u32(vreinterpret_u32_f32(a)))); }
+
+template<> EIGEN_STRONG_INLINE Packet1cf pset1<Packet1cf>(const std::complex<float>& from)
+{ return Packet1cf(vld1_f32(reinterpret_cast<const float*>(&from))); }
+template<> EIGEN_STRONG_INLINE Packet2cf pset1<Packet2cf>(const std::complex<float>& from)
+{
+ const float32x2_t r64 = vld1_f32(reinterpret_cast<const float*>(&from));
+ return Packet2cf(vcombine_f32(r64, r64));
+}
+
+template<> EIGEN_STRONG_INLINE Packet1cf padd<Packet1cf>(const Packet1cf& a, const Packet1cf& b)
+{ return Packet1cf(padd<Packet2f>(a.v, b.v)); }
+template<> EIGEN_STRONG_INLINE Packet2cf padd<Packet2cf>(const Packet2cf& a, const Packet2cf& b)
+{ return Packet2cf(padd<Packet4f>(a.v, b.v)); }
+
+template<> EIGEN_STRONG_INLINE Packet1cf psub<Packet1cf>(const Packet1cf& a, const Packet1cf& b)
+{ return Packet1cf(psub<Packet2f>(a.v, b.v)); }
+template<> EIGEN_STRONG_INLINE Packet2cf psub<Packet2cf>(const Packet2cf& a, const Packet2cf& b)
+{ return Packet2cf(psub<Packet4f>(a.v, b.v)); }
+
+template<> EIGEN_STRONG_INLINE Packet1cf pnegate(const Packet1cf& a) { return Packet1cf(pnegate<Packet2f>(a.v)); }
+template<> EIGEN_STRONG_INLINE Packet2cf pnegate(const Packet2cf& a) { return Packet2cf(pnegate<Packet4f>(a.v)); }
+
+template<> EIGEN_STRONG_INLINE Packet1cf pconj(const Packet1cf& a)
+{
+ const Packet2ui b = vreinterpret_u32_f32(a.v);
+ return Packet1cf(vreinterpret_f32_u32(veor_u32(b, p2ui_CONJ_XOR())));
+}
+template<> EIGEN_STRONG_INLINE Packet2cf pconj(const Packet2cf& a)
+{
+ const Packet4ui b = vreinterpretq_u32_f32(a.v);
+ return Packet2cf(vreinterpretq_f32_u32(veorq_u32(b, p4ui_CONJ_XOR())));
+}
+
+template<> EIGEN_STRONG_INLINE Packet1cf pmul<Packet1cf>(const Packet1cf& a, const Packet1cf& b)
+{
+ Packet2f v1, v2;
+
+ // Get the real values of a | a1_re | a1_re |
+ v1 = vdup_lane_f32(a.v, 0);
+ // Get the imag values of a | a1_im | a1_im |
+ v2 = vdup_lane_f32(a.v, 1);
+ // Multiply the real a with b
+ v1 = vmul_f32(v1, b.v);
+ // Multiply the imag a with b
+ v2 = vmul_f32(v2, b.v);
+ // Conjugate v2
+ v2 = vreinterpret_f32_u32(veor_u32(vreinterpret_u32_f32(v2), p2ui_CONJ_XOR()));
+ // Swap real/imag elements in v2.
+ v2 = vrev64_f32(v2);
+ // Add and return the result
+ return Packet1cf(vadd_f32(v1, v2));
+}
+template<> EIGEN_STRONG_INLINE Packet2cf pmul<Packet2cf>(const Packet2cf& a, const Packet2cf& b)
+{
+ Packet4f v1, v2;
+
+ // Get the real values of a | a1_re | a1_re | a2_re | a2_re |
+ v1 = vcombine_f32(vdup_lane_f32(vget_low_f32(a.v), 0), vdup_lane_f32(vget_high_f32(a.v), 0));
+ // Get the imag values of a | a1_im | a1_im | a2_im | a2_im |
+ v2 = vcombine_f32(vdup_lane_f32(vget_low_f32(a.v), 1), vdup_lane_f32(vget_high_f32(a.v), 1));
+ // Multiply the real a with b
+ v1 = vmulq_f32(v1, b.v);
+ // Multiply the imag a with b
+ v2 = vmulq_f32(v2, b.v);
+ // Conjugate v2
+ v2 = vreinterpretq_f32_u32(veorq_u32(vreinterpretq_u32_f32(v2), p4ui_CONJ_XOR()));
+ // Swap real/imag elements in v2.
+ v2 = vrev64q_f32(v2);
+ // Add and return the result
+ return Packet2cf(vaddq_f32(v1, v2));
+}
+
+template<> EIGEN_STRONG_INLINE Packet1cf pcmp_eq(const Packet1cf& a, const Packet1cf& b)
+{
+ // Compare real and imaginary parts of a and b to get the mask vector:
+ // [re(a[0])==re(b[0]), im(a[0])==im(b[0])]
+ Packet2f eq = pcmp_eq<Packet2f>(a.v, b.v);
+ // Swap real/imag elements in the mask in to get:
+ // [im(a[0])==im(b[0]), re(a[0])==re(b[0])]
+ Packet2f eq_swapped = vrev64_f32(eq);
+ // Return re(a)==re(b) && im(a)==im(b) by computing bitwise AND of eq and eq_swapped
+ return Packet1cf(pand<Packet2f>(eq, eq_swapped));
+}
+template<> EIGEN_STRONG_INLINE Packet2cf pcmp_eq(const Packet2cf& a, const Packet2cf& b)
+{
+ // Compare real and imaginary parts of a and b to get the mask vector:
+ // [re(a[0])==re(b[0]), im(a[0])==im(b[0]), re(a[1])==re(b[1]), im(a[1])==im(b[1])]
+ Packet4f eq = pcmp_eq<Packet4f>(a.v, b.v);
+ // Swap real/imag elements in the mask in to get:
+ // [im(a[0])==im(b[0]), re(a[0])==re(b[0]), im(a[1])==im(b[1]), re(a[1])==re(b[1])]
+ Packet4f eq_swapped = vrev64q_f32(eq);
+ // Return re(a)==re(b) && im(a)==im(b) by computing bitwise AND of eq and eq_swapped
+ return Packet2cf(pand<Packet4f>(eq, eq_swapped));
+}
+
+template<> EIGEN_STRONG_INLINE Packet1cf pand<Packet1cf>(const Packet1cf& a, const Packet1cf& b)
+{ return Packet1cf(vreinterpret_f32_u32(vand_u32(vreinterpret_u32_f32(a.v), vreinterpret_u32_f32(b.v)))); }
+template<> EIGEN_STRONG_INLINE Packet2cf pand<Packet2cf>(const Packet2cf& a, const Packet2cf& b)
+{ return Packet2cf(vreinterpretq_f32_u32(vandq_u32(vreinterpretq_u32_f32(a.v), vreinterpretq_u32_f32(b.v)))); }
+
+template<> EIGEN_STRONG_INLINE Packet1cf por<Packet1cf>(const Packet1cf& a, const Packet1cf& b)
+{ return Packet1cf(vreinterpret_f32_u32(vorr_u32(vreinterpret_u32_f32(a.v), vreinterpret_u32_f32(b.v)))); }
+template<> EIGEN_STRONG_INLINE Packet2cf por<Packet2cf>(const Packet2cf& a, const Packet2cf& b)
+{ return Packet2cf(vreinterpretq_f32_u32(vorrq_u32(vreinterpretq_u32_f32(a.v), vreinterpretq_u32_f32(b.v)))); }
+
+template<> EIGEN_STRONG_INLINE Packet1cf pxor<Packet1cf>(const Packet1cf& a, const Packet1cf& b)
+{ return Packet1cf(vreinterpret_f32_u32(veor_u32(vreinterpret_u32_f32(a.v), vreinterpret_u32_f32(b.v)))); }
+template<> EIGEN_STRONG_INLINE Packet2cf pxor<Packet2cf>(const Packet2cf& a, const Packet2cf& b)
+{ return Packet2cf(vreinterpretq_f32_u32(veorq_u32(vreinterpretq_u32_f32(a.v), vreinterpretq_u32_f32(b.v)))); }
+
+template<> EIGEN_STRONG_INLINE Packet1cf pandnot<Packet1cf>(const Packet1cf& a, const Packet1cf& b)
+{ return Packet1cf(vreinterpret_f32_u32(vbic_u32(vreinterpret_u32_f32(a.v), vreinterpret_u32_f32(b.v)))); }
+template<> EIGEN_STRONG_INLINE Packet2cf pandnot<Packet2cf>(const Packet2cf& a, const Packet2cf& b)
+{ return Packet2cf(vreinterpretq_f32_u32(vbicq_u32(vreinterpretq_u32_f32(a.v), vreinterpretq_u32_f32(b.v)))); }
+
+template<> EIGEN_STRONG_INLINE Packet1cf pload<Packet1cf>(const std::complex<float>* from)
+{ EIGEN_DEBUG_ALIGNED_LOAD return Packet1cf(pload<Packet2f>((const float*)from)); }
+template<> EIGEN_STRONG_INLINE Packet2cf pload<Packet2cf>(const std::complex<float>* from)
+{ EIGEN_DEBUG_ALIGNED_LOAD return Packet2cf(pload<Packet4f>(reinterpret_cast<const float*>(from))); }
+
+template<> EIGEN_STRONG_INLINE Packet1cf ploadu<Packet1cf>(const std::complex<float>* from)
+{ EIGEN_DEBUG_UNALIGNED_LOAD return Packet1cf(ploadu<Packet2f>((const float*)from)); }
+template<> EIGEN_STRONG_INLINE Packet2cf ploadu<Packet2cf>(const std::complex<float>* from)
+{ EIGEN_DEBUG_UNALIGNED_LOAD return Packet2cf(ploadu<Packet4f>(reinterpret_cast<const float*>(from))); }
+
+template<> EIGEN_STRONG_INLINE Packet1cf ploaddup<Packet1cf>(const std::complex<float>* from)
+{ return pset1<Packet1cf>(*from); }
+template<> EIGEN_STRONG_INLINE Packet2cf ploaddup<Packet2cf>(const std::complex<float>* from)
+{ return pset1<Packet2cf>(*from); }
+
+template<> EIGEN_STRONG_INLINE void pstore <std::complex<float> >(std::complex<float> *to, const Packet1cf& from)
+{ EIGEN_DEBUG_ALIGNED_STORE pstore((float*)to, from.v); }
+template<> EIGEN_STRONG_INLINE void pstore <std::complex<float> >(std::complex<float> *to, const Packet2cf& from)
+{ EIGEN_DEBUG_ALIGNED_STORE pstore(reinterpret_cast<float*>(to), from.v); }
+
+template<> EIGEN_STRONG_INLINE void pstoreu<std::complex<float> >(std::complex<float> *to, const Packet1cf& from)
+{ EIGEN_DEBUG_UNALIGNED_STORE pstoreu((float*)to, from.v); }
+template<> EIGEN_STRONG_INLINE void pstoreu<std::complex<float> >(std::complex<float> *to, const Packet2cf& from)
+{ EIGEN_DEBUG_UNALIGNED_STORE pstoreu(reinterpret_cast<float*>(to), from.v); }
+
+template<> EIGEN_DEVICE_FUNC inline Packet1cf pgather<std::complex<float>, Packet1cf>(
+ const std::complex<float>* from, Index stride)
+{
+ const Packet2f tmp = vdup_n_f32(std::real(from[0*stride]));
+ return Packet1cf(vset_lane_f32(std::imag(from[0*stride]), tmp, 1));
+}
+template<> EIGEN_DEVICE_FUNC inline Packet2cf pgather<std::complex<float>, Packet2cf>(
+ const std::complex<float>* from, Index stride)
+{
+ Packet4f res = vdupq_n_f32(std::real(from[0*stride]));
+ res = vsetq_lane_f32(std::imag(from[0*stride]), res, 1);
+ res = vsetq_lane_f32(std::real(from[1*stride]), res, 2);
+ res = vsetq_lane_f32(std::imag(from[1*stride]), res, 3);
+ return Packet2cf(res);
+}
+
+template<> EIGEN_DEVICE_FUNC inline void pscatter<std::complex<float>, Packet1cf>(
+ std::complex<float>* to, const Packet1cf& from, Index stride)
+{ to[stride*0] = std::complex<float>(vget_lane_f32(from.v, 0), vget_lane_f32(from.v, 1)); }
+template<> EIGEN_DEVICE_FUNC inline void pscatter<std::complex<float>, Packet2cf>(
+ std::complex<float>* to, const Packet2cf& from, Index stride)
+{
+ to[stride*0] = std::complex<float>(vgetq_lane_f32(from.v, 0), vgetq_lane_f32(from.v, 1));
+ to[stride*1] = std::complex<float>(vgetq_lane_f32(from.v, 2), vgetq_lane_f32(from.v, 3));
+}
+
+template<> EIGEN_STRONG_INLINE void prefetch<std::complex<float> >(const std::complex<float> *addr)
+{ EIGEN_ARM_PREFETCH(reinterpret_cast<const float*>(addr)); }
+
+template<> EIGEN_STRONG_INLINE std::complex<float> pfirst<Packet1cf>(const Packet1cf& a)
+{
+ EIGEN_ALIGN16 std::complex<float> x;
+ vst1_f32(reinterpret_cast<float*>(&x), a.v);
+ return x;
+}
+template<> EIGEN_STRONG_INLINE std::complex<float> pfirst<Packet2cf>(const Packet2cf& a)
+{
+ EIGEN_ALIGN16 std::complex<float> x[2];
+ vst1q_f32(reinterpret_cast<float*>(x), a.v);
+ return x[0];
+}
+
+template<> EIGEN_STRONG_INLINE Packet1cf preverse(const Packet1cf& a) { return a; }
+template<> EIGEN_STRONG_INLINE Packet2cf preverse(const Packet2cf& a)
+{ return Packet2cf(vcombine_f32(vget_high_f32(a.v), vget_low_f32(a.v))); }
+
+template<> EIGEN_STRONG_INLINE Packet1cf pcplxflip<Packet1cf>(const Packet1cf& a)
+{ return Packet1cf(vrev64_f32(a.v)); }
+template<> EIGEN_STRONG_INLINE Packet2cf pcplxflip<Packet2cf>(const Packet2cf& a)
+{ return Packet2cf(vrev64q_f32(a.v)); }
+
+template<> EIGEN_STRONG_INLINE std::complex<float> predux<Packet1cf>(const Packet1cf& a)
+{
+ std::complex<float> s;
+ vst1_f32((float *)&s, a.v);
+ return s;
+}
+template<> EIGEN_STRONG_INLINE std::complex<float> predux<Packet2cf>(const Packet2cf& a)
+{
+ std::complex<float> s;
+ vst1_f32(reinterpret_cast<float*>(&s), vadd_f32(vget_low_f32(a.v), vget_high_f32(a.v)));
+ return s;
+}
+
+template<> EIGEN_STRONG_INLINE std::complex<float> predux_mul<Packet1cf>(const Packet1cf& a)
+{
+ std::complex<float> s;
+ vst1_f32((float *)&s, a.v);
+ return s;
+}
+template<> EIGEN_STRONG_INLINE std::complex<float> predux_mul<Packet2cf>(const Packet2cf& a)
+{
+ float32x2_t a1, a2, v1, v2, prod;
+ std::complex<float> s;
+
+ a1 = vget_low_f32(a.v);
+ a2 = vget_high_f32(a.v);
+ // Get the real values of a | a1_re | a1_re | a2_re | a2_re |
+ v1 = vdup_lane_f32(a1, 0);
+ // Get the real values of a | a1_im | a1_im | a2_im | a2_im |
+ v2 = vdup_lane_f32(a1, 1);
+ // Multiply the real a with b
+ v1 = vmul_f32(v1, a2);
+ // Multiply the imag a with b
+ v2 = vmul_f32(v2, a2);
+ // Conjugate v2
+ v2 = vreinterpret_f32_u32(veor_u32(vreinterpret_u32_f32(v2), p2ui_CONJ_XOR()));
+ // Swap real/imag elements in v2.
+ v2 = vrev64_f32(v2);
+ // Add v1, v2
+ prod = vadd_f32(v1, v2);
+
+ vst1_f32(reinterpret_cast<float*>(&s), prod);
+
+ return s;
+}
+
+EIGEN_MAKE_CONJ_HELPER_CPLX_REAL(Packet1cf,Packet2f)
+EIGEN_MAKE_CONJ_HELPER_CPLX_REAL(Packet2cf,Packet4f)
+
+template<> EIGEN_STRONG_INLINE Packet1cf pdiv<Packet1cf>(const Packet1cf& a, const Packet1cf& b)
+{
+ return pdiv_complex(a, b);
+}
+template<> EIGEN_STRONG_INLINE Packet2cf pdiv<Packet2cf>(const Packet2cf& a, const Packet2cf& b)
+{
+ return pdiv_complex(a, b);
+}
+
+EIGEN_DEVICE_FUNC inline void ptranspose(PacketBlock<Packet1cf, 1>& /*kernel*/) {}
+EIGEN_DEVICE_FUNC inline void ptranspose(PacketBlock<Packet2cf, 2>& kernel)
+{
+ Packet4f tmp = vcombine_f32(vget_high_f32(kernel.packet[0].v), vget_high_f32(kernel.packet[1].v));
+ kernel.packet[0].v = vcombine_f32(vget_low_f32(kernel.packet[0].v), vget_low_f32(kernel.packet[1].v));
+ kernel.packet[1].v = tmp;
+}
+
+template<> EIGEN_STRONG_INLINE Packet1cf psqrt<Packet1cf>(const Packet1cf& a) {
+ return psqrt_complex<Packet1cf>(a);
+}
+
+template<> EIGEN_STRONG_INLINE Packet2cf psqrt<Packet2cf>(const Packet2cf& a) {
+ return psqrt_complex<Packet2cf>(a);
+}
+
+//---------- double ----------
+#if EIGEN_ARCH_ARM64 && !EIGEN_APPLE_DOUBLE_NEON_BUG
+
+// See bug 1325, clang fails to call vld1q_u64.
+#if EIGEN_COMP_CLANG || EIGEN_COMP_CASTXML || EIGEN_COMP_CPE
+ static uint64x2_t p2ul_CONJ_XOR = {0x0, 0x8000000000000000};
+#else
+ const uint64_t p2ul_conj_XOR_DATA[] = { 0x0, 0x8000000000000000 };
+ static uint64x2_t p2ul_CONJ_XOR = vld1q_u64( p2ul_conj_XOR_DATA );
+#endif
+
+struct Packet1cd
+{
+ EIGEN_STRONG_INLINE Packet1cd() {}
+ EIGEN_STRONG_INLINE explicit Packet1cd(const Packet2d& a) : v(a) {}
+ Packet2d v;
+};
+
+template<> struct packet_traits<std::complex<double> > : default_packet_traits
+{
+ typedef Packet1cd type;
+ typedef Packet1cd half;
+ enum
+ {
+ Vectorizable = 1,
+ AlignedOnScalar = 0,
+ size = 1,
+ HasHalfPacket = 0,
+
+ HasAdd = 1,
+ HasSub = 1,
+ HasMul = 1,
+ HasDiv = 1,
+ HasNegate = 1,
+ HasAbs = 0,
+ HasAbs2 = 0,
+ HasMin = 0,
+ HasMax = 0,
+ HasSetLinear = 0
+ };
+};
+
+template<> struct unpacket_traits<Packet1cd>
+{
+ typedef std::complex<double> type;
+ typedef Packet1cd half;
+ typedef Packet2d as_real;
+ enum
+ {
+ size=1,
+ alignment=Aligned16,
+ vectorizable=true,
+ masked_load_available=false,
+ masked_store_available=false
+ };
+};
+
+template<> EIGEN_STRONG_INLINE Packet1cd pload<Packet1cd>(const std::complex<double>* from)
+{ EIGEN_DEBUG_ALIGNED_LOAD return Packet1cd(pload<Packet2d>(reinterpret_cast<const double*>(from))); }
+
+template<> EIGEN_STRONG_INLINE Packet1cd ploadu<Packet1cd>(const std::complex<double>* from)
+{ EIGEN_DEBUG_UNALIGNED_LOAD return Packet1cd(ploadu<Packet2d>(reinterpret_cast<const double*>(from))); }
+
+template<> EIGEN_STRONG_INLINE Packet1cd pset1<Packet1cd>(const std::complex<double>& from)
+{
+ /* here we really have to use unaligned loads :( */
+ return ploadu<Packet1cd>(&from);
+}
+
+template<> EIGEN_STRONG_INLINE Packet1cd padd<Packet1cd>(const Packet1cd& a, const Packet1cd& b)
+{ return Packet1cd(padd<Packet2d>(a.v, b.v)); }
+
+template<> EIGEN_STRONG_INLINE Packet1cd psub<Packet1cd>(const Packet1cd& a, const Packet1cd& b)
+{ return Packet1cd(psub<Packet2d>(a.v, b.v)); }
+
+template<> EIGEN_STRONG_INLINE Packet1cd pnegate(const Packet1cd& a)
+{ return Packet1cd(pnegate<Packet2d>(a.v)); }
+
+template<> EIGEN_STRONG_INLINE Packet1cd pconj(const Packet1cd& a)
+{ return Packet1cd(vreinterpretq_f64_u64(veorq_u64(vreinterpretq_u64_f64(a.v), p2ul_CONJ_XOR))); }
+
+template<> EIGEN_STRONG_INLINE Packet1cd pmul<Packet1cd>(const Packet1cd& a, const Packet1cd& b)
+{
+ Packet2d v1, v2;
+
+ // Get the real values of a
+ v1 = vdupq_lane_f64(vget_low_f64(a.v), 0);
+ // Get the imag values of a
+ v2 = vdupq_lane_f64(vget_high_f64(a.v), 0);
+ // Multiply the real a with b
+ v1 = vmulq_f64(v1, b.v);
+ // Multiply the imag a with b
+ v2 = vmulq_f64(v2, b.v);
+ // Conjugate v2
+ v2 = vreinterpretq_f64_u64(veorq_u64(vreinterpretq_u64_f64(v2), p2ul_CONJ_XOR));
+ // Swap real/imag elements in v2.
+ v2 = preverse<Packet2d>(v2);
+ // Add and return the result
+ return Packet1cd(vaddq_f64(v1, v2));
+}
+
+template<> EIGEN_STRONG_INLINE Packet1cd pcmp_eq(const Packet1cd& a, const Packet1cd& b)
+{
+ // Compare real and imaginary parts of a and b to get the mask vector:
+ // [re(a)==re(b), im(a)==im(b)]
+ Packet2d eq = pcmp_eq<Packet2d>(a.v, b.v);
+ // Swap real/imag elements in the mask in to get:
+ // [im(a)==im(b), re(a)==re(b)]
+ Packet2d eq_swapped = vreinterpretq_f64_u32(vrev64q_u32(vreinterpretq_u32_f64(eq)));
+ // Return re(a)==re(b) & im(a)==im(b) by computing bitwise AND of eq and eq_swapped
+ return Packet1cd(pand<Packet2d>(eq, eq_swapped));
+}
+
+template<> EIGEN_STRONG_INLINE Packet1cd pand<Packet1cd>(const Packet1cd& a, const Packet1cd& b)
+{ return Packet1cd(vreinterpretq_f64_u64(vandq_u64(vreinterpretq_u64_f64(a.v),vreinterpretq_u64_f64(b.v)))); }
+
+template<> EIGEN_STRONG_INLINE Packet1cd por<Packet1cd>(const Packet1cd& a, const Packet1cd& b)
+{ return Packet1cd(vreinterpretq_f64_u64(vorrq_u64(vreinterpretq_u64_f64(a.v),vreinterpretq_u64_f64(b.v)))); }
+
+template<> EIGEN_STRONG_INLINE Packet1cd pxor<Packet1cd>(const Packet1cd& a, const Packet1cd& b)
+{ return Packet1cd(vreinterpretq_f64_u64(veorq_u64(vreinterpretq_u64_f64(a.v),vreinterpretq_u64_f64(b.v)))); }
+
+template<> EIGEN_STRONG_INLINE Packet1cd pandnot<Packet1cd>(const Packet1cd& a, const Packet1cd& b)
+{ return Packet1cd(vreinterpretq_f64_u64(vbicq_u64(vreinterpretq_u64_f64(a.v),vreinterpretq_u64_f64(b.v)))); }
+
+template<> EIGEN_STRONG_INLINE Packet1cd ploaddup<Packet1cd>(const std::complex<double>* from)
+{ return pset1<Packet1cd>(*from); }
+
+template<> EIGEN_STRONG_INLINE void pstore <std::complex<double> >(std::complex<double> *to, const Packet1cd& from)
+{ EIGEN_DEBUG_ALIGNED_STORE pstore(reinterpret_cast<double*>(to), from.v); }
+
+template<> EIGEN_STRONG_INLINE void pstoreu<std::complex<double> >(std::complex<double> *to, const Packet1cd& from)
+{ EIGEN_DEBUG_UNALIGNED_STORE pstoreu(reinterpret_cast<double*>(to), from.v); }
+
+template<> EIGEN_STRONG_INLINE void prefetch<std::complex<double> >(const std::complex<double> *addr)
+{ EIGEN_ARM_PREFETCH(reinterpret_cast<const double*>(addr)); }
+
+template<> EIGEN_DEVICE_FUNC inline Packet1cd pgather<std::complex<double>, Packet1cd>(
+ const std::complex<double>* from, Index stride)
+{
+ Packet2d res = pset1<Packet2d>(0.0);
+ res = vsetq_lane_f64(std::real(from[0*stride]), res, 0);
+ res = vsetq_lane_f64(std::imag(from[0*stride]), res, 1);
+ return Packet1cd(res);
+}
+
+template<> EIGEN_DEVICE_FUNC inline void pscatter<std::complex<double>, Packet1cd>(
+ std::complex<double>* to, const Packet1cd& from, Index stride)
+{ to[stride*0] = std::complex<double>(vgetq_lane_f64(from.v, 0), vgetq_lane_f64(from.v, 1)); }
+
+template<> EIGEN_STRONG_INLINE std::complex<double> pfirst<Packet1cd>(const Packet1cd& a)
+{
+ EIGEN_ALIGN16 std::complex<double> res;
+ pstore<std::complex<double> >(&res, a);
+ return res;
+}
+
+template<> EIGEN_STRONG_INLINE Packet1cd preverse(const Packet1cd& a) { return a; }
+
+template<> EIGEN_STRONG_INLINE std::complex<double> predux<Packet1cd>(const Packet1cd& a) { return pfirst(a); }
+
+template<> EIGEN_STRONG_INLINE std::complex<double> predux_mul<Packet1cd>(const Packet1cd& a) { return pfirst(a); }
+
+EIGEN_MAKE_CONJ_HELPER_CPLX_REAL(Packet1cd,Packet2d)
+
+template<> EIGEN_STRONG_INLINE Packet1cd pdiv<Packet1cd>(const Packet1cd& a, const Packet1cd& b)
+{
+ return pdiv_complex(a, b);
+}
+
+EIGEN_STRONG_INLINE Packet1cd pcplxflip/*<Packet1cd>*/(const Packet1cd& x)
+{ return Packet1cd(preverse(Packet2d(x.v))); }
+
+EIGEN_STRONG_INLINE void ptranspose(PacketBlock<Packet1cd,2>& kernel)
+{
+ Packet2d tmp = vcombine_f64(vget_high_f64(kernel.packet[0].v), vget_high_f64(kernel.packet[1].v));
+ kernel.packet[0].v = vcombine_f64(vget_low_f64(kernel.packet[0].v), vget_low_f64(kernel.packet[1].v));
+ kernel.packet[1].v = tmp;
+}
+
+template<> EIGEN_STRONG_INLINE Packet1cd psqrt<Packet1cd>(const Packet1cd& a) {
+ return psqrt_complex<Packet1cd>(a);
+}
+
+#endif // EIGEN_ARCH_ARM64
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_COMPLEX_NEON_H
diff --git a/Eigen/src/Core/arch/NEON/GeneralBlockPanelKernel.h b/Eigen/src/Core/arch/NEON/GeneralBlockPanelKernel.h
new file mode 100644
index 0000000..e49e394
--- /dev/null
+++ b/Eigen/src/Core/arch/NEON/GeneralBlockPanelKernel.h
@@ -0,0 +1,259 @@
+#include "../../InternalHeaderCheck.h"
+
+namespace Eigen {
+namespace internal {
+
+#if EIGEN_ARCH_ARM && EIGEN_COMP_CLANG
+
+// Clang seems to excessively spill registers in the GEBP kernel on 32-bit arm.
+// Here we specialize gebp_traits to eliminate these register spills.
+// See #2138.
+template<>
+struct gebp_traits <float,float,false,false,Architecture::NEON,GEBPPacketFull>
+ : gebp_traits<float,float,false,false,Architecture::Generic,GEBPPacketFull>
+{
+ EIGEN_STRONG_INLINE void acc(const AccPacket& c, const ResPacket& alpha, ResPacket& r) const
+ {
+ // This volatile inline ASM both acts as a barrier to prevent reordering,
+ // as well as enforces strict register use.
+ asm volatile(
+ "vmla.f32 %q[r], %q[c], %q[alpha]"
+ : [r] "+w" (r)
+ : [c] "w" (c),
+ [alpha] "w" (alpha)
+ : );
+ }
+
+ template <typename LaneIdType>
+ EIGEN_STRONG_INLINE void madd(const Packet4f& a, const Packet4f& b,
+ Packet4f& c, Packet4f& tmp,
+ const LaneIdType&) const {
+ acc(a, b, c);
+ }
+
+ template <typename LaneIdType>
+ EIGEN_STRONG_INLINE void madd(const Packet4f& a, const QuadPacket<Packet4f>& b,
+ Packet4f& c, Packet4f& tmp,
+ const LaneIdType& lane) const {
+ madd(a, b.get(lane), c, tmp, lane);
+ }
+};
+
+#endif // EIGEN_ARCH_ARM && EIGEN_COMP_CLANG
+
+#if EIGEN_ARCH_ARM64
+
+#ifndef EIGEN_NEON_GEBP_NR
+#define EIGEN_NEON_GEBP_NR 8
+#endif
+
+template<>
+struct gebp_traits <float,float,false,false,Architecture::NEON,GEBPPacketFull>
+ : gebp_traits<float,float,false,false,Architecture::Generic,GEBPPacketFull>
+{
+ typedef float RhsPacket;
+ typedef float32x4_t RhsPacketx4;
+ enum { nr = EIGEN_NEON_GEBP_NR };
+ EIGEN_STRONG_INLINE void loadRhs(const RhsScalar* b, RhsPacket& dest) const {
+ dest = *b;
+ }
+
+ EIGEN_STRONG_INLINE void loadRhs(const RhsScalar* b, RhsPacketx4& dest) const
+ {
+ dest = vld1q_f32(b);
+ }
+
+ EIGEN_STRONG_INLINE void updateRhs(const RhsScalar* b, RhsPacket& dest) const
+ {
+ dest = *b;
+ }
+
+ EIGEN_STRONG_INLINE void updateRhs(const RhsScalar*, RhsPacketx4&) const
+ {}
+
+ EIGEN_STRONG_INLINE void loadRhsQuad(const RhsScalar* b, RhsPacket& dest) const
+ {
+ loadRhs(b,dest);
+ }
+
+ EIGEN_STRONG_INLINE void madd(const LhsPacket& a, const RhsPacket& b, AccPacket& c, RhsPacket& /*tmp*/, const FixedInt<0>&) const
+ {
+ c = vfmaq_n_f32(c, a, b);
+ }
+ // NOTE: Template parameter inference failed when compiled with Android NDK:
+ // "candidate template ignored: could not match 'FixedInt<N>' against 'Eigen::internal::FixedInt<0>".
+
+ EIGEN_STRONG_INLINE void madd(const LhsPacket& a, const RhsPacketx4& b, AccPacket& c, RhsPacket& /*tmp*/, const FixedInt<0>&) const
+ { madd_helper<0>(a, b, c); }
+ EIGEN_STRONG_INLINE void madd(const LhsPacket& a, const RhsPacketx4& b, AccPacket& c, RhsPacket& /*tmp*/, const FixedInt<1>&) const
+ { madd_helper<1>(a, b, c); }
+ EIGEN_STRONG_INLINE void madd(const LhsPacket& a, const RhsPacketx4& b, AccPacket& c, RhsPacket& /*tmp*/, const FixedInt<2>&) const
+ { madd_helper<2>(a, b, c); }
+ EIGEN_STRONG_INLINE void madd(const LhsPacket& a, const RhsPacketx4& b, AccPacket& c, RhsPacket& /*tmp*/, const FixedInt<3>&) const
+ { madd_helper<3>(a, b, c); }
+
+ private:
+ template<int LaneID>
+ EIGEN_STRONG_INLINE void madd_helper(const LhsPacket& a, const RhsPacketx4& b, AccPacket& c) const
+ {
+ #if EIGEN_COMP_GNUC_STRICT
+ // 1. workaround gcc issue https://gcc.gnu.org/bugzilla/show_bug.cgi?id=89101
+ // vfmaq_laneq_f32 is implemented through a costly dup, which was fixed in gcc9
+ // 2. workaround the gcc register split problem on arm64-neon
+ if(LaneID==0) asm("fmla %0.4s, %1.4s, %2.s[0]\n" : "+w" (c) : "w" (a), "w" (b) : );
+ else if(LaneID==1) asm("fmla %0.4s, %1.4s, %2.s[1]\n" : "+w" (c) : "w" (a), "w" (b) : );
+ else if(LaneID==2) asm("fmla %0.4s, %1.4s, %2.s[2]\n" : "+w" (c) : "w" (a), "w" (b) : );
+ else if(LaneID==3) asm("fmla %0.4s, %1.4s, %2.s[3]\n" : "+w" (c) : "w" (a), "w" (b) : );
+ #else
+ c = vfmaq_laneq_f32(c, a, b, LaneID);
+ #endif
+ }
+};
+
+
+template<>
+struct gebp_traits <double,double,false,false,Architecture::NEON>
+ : gebp_traits<double,double,false,false,Architecture::Generic>
+{
+ typedef double RhsPacket;
+ enum { nr = EIGEN_NEON_GEBP_NR };
+ struct RhsPacketx4 {
+ float64x2_t B_0, B_1;
+ };
+
+ EIGEN_STRONG_INLINE void loadRhs(const RhsScalar* b, RhsPacket& dest) const
+ {
+ dest = *b;
+ }
+
+ EIGEN_STRONG_INLINE void loadRhs(const RhsScalar* b, RhsPacketx4& dest) const
+ {
+ dest.B_0 = vld1q_f64(b);
+ dest.B_1 = vld1q_f64(b+2);
+ }
+
+ EIGEN_STRONG_INLINE void updateRhs(const RhsScalar* b, RhsPacket& dest) const
+ {
+ loadRhs(b,dest);
+ }
+
+ EIGEN_STRONG_INLINE void updateRhs(const RhsScalar*, RhsPacketx4&) const
+ {}
+
+ EIGEN_STRONG_INLINE void loadRhsQuad(const RhsScalar* b, RhsPacket& dest) const
+ {
+ loadRhs(b,dest);
+ }
+
+ EIGEN_STRONG_INLINE void madd(const LhsPacket& a, const RhsPacket& b, AccPacket& c, RhsPacket& /*tmp*/, const FixedInt<0>&) const
+ {
+ c = vfmaq_n_f64(c, a, b);
+ }
+
+ // NOTE: Template parameter inference failed when compiled with Android NDK:
+ // "candidate template ignored: could not match 'FixedInt<N>' against 'Eigen::internal::FixedInt<0>".
+
+ EIGEN_STRONG_INLINE void madd(const LhsPacket& a, const RhsPacketx4& b, AccPacket& c, RhsPacket& /*tmp*/, const FixedInt<0>&) const
+ { madd_helper<0>(a, b, c); }
+ EIGEN_STRONG_INLINE void madd(const LhsPacket& a, const RhsPacketx4& b, AccPacket& c, RhsPacket& /*tmp*/, const FixedInt<1>&) const
+ { madd_helper<1>(a, b, c); }
+ EIGEN_STRONG_INLINE void madd(const LhsPacket& a, const RhsPacketx4& b, AccPacket& c, RhsPacket& /*tmp*/, const FixedInt<2>&) const
+ { madd_helper<2>(a, b, c); }
+ EIGEN_STRONG_INLINE void madd(const LhsPacket& a, const RhsPacketx4& b, AccPacket& c, RhsPacket& /*tmp*/, const FixedInt<3>&) const
+ { madd_helper<3>(a, b, c); }
+
+ private:
+ template <int LaneID>
+ EIGEN_STRONG_INLINE void madd_helper(const LhsPacket& a, const RhsPacketx4& b, AccPacket& c) const
+ {
+ #if EIGEN_COMP_GNUC_STRICT
+ // 1. workaround gcc issue https://gcc.gnu.org/bugzilla/show_bug.cgi?id=89101
+ // vfmaq_laneq_f64 is implemented through a costly dup, which was fixed in gcc9
+ // 2. workaround the gcc register split problem on arm64-neon
+ if(LaneID==0) asm("fmla %0.2d, %1.2d, %2.d[0]\n" : "+w" (c) : "w" (a), "w" (b.B_0) : );
+ else if(LaneID==1) asm("fmla %0.2d, %1.2d, %2.d[1]\n" : "+w" (c) : "w" (a), "w" (b.B_0) : );
+ else if(LaneID==2) asm("fmla %0.2d, %1.2d, %2.d[0]\n" : "+w" (c) : "w" (a), "w" (b.B_1) : );
+ else if(LaneID==3) asm("fmla %0.2d, %1.2d, %2.d[1]\n" : "+w" (c) : "w" (a), "w" (b.B_1) : );
+ #else
+ if(LaneID==0) c = vfmaq_laneq_f64(c, a, b.B_0, 0);
+ else if(LaneID==1) c = vfmaq_laneq_f64(c, a, b.B_0, 1);
+ else if(LaneID==2) c = vfmaq_laneq_f64(c, a, b.B_1, 0);
+ else if(LaneID==3) c = vfmaq_laneq_f64(c, a, b.B_1, 1);
+ #endif
+ }
+};
+
+#if EIGEN_HAS_ARM64_FP16_VECTOR_ARITHMETIC
+
+template<>
+struct gebp_traits <half,half,false,false,Architecture::NEON>
+ : gebp_traits<half,half,false,false,Architecture::Generic>
+{
+ typedef half RhsPacket;
+ typedef float16x4_t RhsPacketx4;
+ typedef float16x4_t PacketHalf;
+ enum { nr = EIGEN_NEON_GEBP_NR };
+
+ EIGEN_STRONG_INLINE void loadRhs(const RhsScalar* b, RhsPacket& dest) const
+ {
+ dest = *b;
+ }
+
+ EIGEN_STRONG_INLINE void loadRhs(const RhsScalar* b, RhsPacketx4& dest) const
+ {
+ dest = vld1_f16((const __fp16 *)b);
+ }
+
+ EIGEN_STRONG_INLINE void updateRhs(const RhsScalar* b, RhsPacket& dest) const
+ {
+ dest = *b;
+ }
+
+ EIGEN_STRONG_INLINE void updateRhs(const RhsScalar*, RhsPacketx4&) const
+ {}
+
+ EIGEN_STRONG_INLINE void loadRhsQuad(const RhsScalar* b, RhsPacket& dest) const
+ {
+ loadRhs(b,dest);
+ }
+
+ EIGEN_STRONG_INLINE void madd(const LhsPacket& a, const RhsPacket& b, AccPacket& c, RhsPacket& /*tmp*/, const FixedInt<0>&) const
+ {
+ c = vfmaq_n_f16(c, a, b);
+ }
+ EIGEN_STRONG_INLINE void madd(const PacketHalf& a, const RhsPacket& b, PacketHalf& c, RhsPacket& /*tmp*/, const FixedInt<0>&) const
+ {
+ c = vfma_n_f16(c, a, b);
+ }
+
+ // NOTE: Template parameter inference failed when compiled with Android NDK:
+ // "candidate template ignored: could not match 'FixedInt<N>' against 'Eigen::internal::FixedInt<0>".
+ EIGEN_STRONG_INLINE void madd(const LhsPacket& a, const RhsPacketx4& b, AccPacket& c, RhsPacket& /*tmp*/, const FixedInt<0>&) const
+ { madd_helper<0>(a, b, c); }
+ EIGEN_STRONG_INLINE void madd(const LhsPacket& a, const RhsPacketx4& b, AccPacket& c, RhsPacket& /*tmp*/, const FixedInt<1>&) const
+ { madd_helper<1>(a, b, c); }
+ EIGEN_STRONG_INLINE void madd(const LhsPacket& a, const RhsPacketx4& b, AccPacket& c, RhsPacket& /*tmp*/, const FixedInt<2>&) const
+ { madd_helper<2>(a, b, c); }
+ EIGEN_STRONG_INLINE void madd(const LhsPacket& a, const RhsPacketx4& b, AccPacket& c, RhsPacket& /*tmp*/, const FixedInt<3>&) const
+ { madd_helper<3>(a, b, c); }
+ private:
+ template<int LaneID>
+ EIGEN_STRONG_INLINE void madd_helper(const LhsPacket& a, const RhsPacketx4& b, AccPacket& c) const
+ {
+ #if EIGEN_COMP_GNUC_STRICT
+ // 1. vfmaq_lane_f16 is implemented through a costly dup
+ // 2. workaround the gcc register split problem on arm64-neon
+ if(LaneID==0) asm("fmla %0.8h, %1.8h, %2.h[0]\n" : "+w" (c) : "w" (a), "w" (b) : );
+ else if(LaneID==1) asm("fmla %0.8h, %1.8h, %2.h[1]\n" : "+w" (c) : "w" (a), "w" (b) : );
+ else if(LaneID==2) asm("fmla %0.8h, %1.8h, %2.h[2]\n" : "+w" (c) : "w" (a), "w" (b) : );
+ else if(LaneID==3) asm("fmla %0.8h, %1.8h, %2.h[3]\n" : "+w" (c) : "w" (a), "w" (b) : );
+ #else
+ c = vfmaq_lane_f16(c, a, b, LaneID);
+ #endif
+ }
+};
+#endif // EIGEN_HAS_ARM64_FP16_VECTOR_ARITHMETIC
+#endif // EIGEN_ARCH_ARM64
+
+} // namespace internal
+} // namespace Eigen
diff --git a/Eigen/src/Core/arch/NEON/MathFunctions.h b/Eigen/src/Core/arch/NEON/MathFunctions.h
new file mode 100644
index 0000000..aea5149
--- /dev/null
+++ b/Eigen/src/Core/arch/NEON/MathFunctions.h
@@ -0,0 +1,114 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_MATH_FUNCTIONS_NEON_H
+#define EIGEN_MATH_FUNCTIONS_NEON_H
+
+#include "../../InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+
+template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet2f pexp<Packet2f>(const Packet2f& x)
+{ return pexp_float(x); }
+template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet4f pexp<Packet4f>(const Packet4f& x)
+{ return pexp_float(x); }
+
+template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet2f plog<Packet2f>(const Packet2f& x)
+{ return plog_float(x); }
+template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet4f plog<Packet4f>(const Packet4f& x)
+{ return plog_float(x); }
+
+template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet2f psin<Packet2f>(const Packet2f& x)
+{ return psin_float(x); }
+template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet4f psin<Packet4f>(const Packet4f& x)
+{ return psin_float(x); }
+
+template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet2f pcos<Packet2f>(const Packet2f& x)
+{ return pcos_float(x); }
+template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet4f pcos<Packet4f>(const Packet4f& x)
+{ return pcos_float(x); }
+
+template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet2f pacos<Packet2f>(const Packet2f& x)
+{ return pacos_float(x); }
+template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet4f pacos<Packet4f>(const Packet4f& x)
+{ return pacos_float(x); }
+
+template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet2f pasin<Packet2f>(const Packet2f& x)
+{ return pasin_float(x); }
+template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet4f pasin<Packet4f>(const Packet4f& x)
+{ return pasin_float(x); }
+
+template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet2f patan<Packet2f>(const Packet2f& x)
+{ return patan_float(x); }
+template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet4f patan<Packet4f>(const Packet4f& x)
+{ return patan_float(x); }
+
+// Hyperbolic Tangent function.
+template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet2f ptanh<Packet2f>(const Packet2f& x)
+{ return internal::generic_fast_tanh_float(x); }
+template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet4f ptanh<Packet4f>(const Packet4f& x)
+{ return internal::generic_fast_tanh_float(x); }
+
+#if EIGEN_HAS_ARM64_FP16_VECTOR_ARITHMETIC
+template <>
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC
+Packet4hf ptanh<Packet4hf>(const Packet4hf& x) {
+ // Convert to float, call the float ptanh, and then convert back.
+ return vcvt_f16_f32(ptanh<Packet4f>(vcvt_f32_f16(x)));
+}
+
+template <>
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC
+Packet8hf ptanh<Packet8hf>(const Packet8hf& x) {
+ // Convert each 4 halfs to float, call the float ptanh, and then convert back.
+ return vcombine_f16(
+ vcvt_f16_f32(ptanh<Packet4f>(vcvt_f32_f16(vget_low_f16(x)))),
+ vcvt_f16_f32(ptanh<Packet4f>(vcvt_high_f32_f16(x))));
+}
+#endif // EIGEN_HAS_ARM64_FP16_VECTOR_ARITHMETIC
+
+
+BF16_PACKET_FUNCTION(Packet4f, Packet4bf, psin)
+BF16_PACKET_FUNCTION(Packet4f, Packet4bf, pcos)
+BF16_PACKET_FUNCTION(Packet4f, Packet4bf, plog)
+BF16_PACKET_FUNCTION(Packet4f, Packet4bf, pexp)
+BF16_PACKET_FUNCTION(Packet4f, Packet4bf, ptanh)
+
+template <>
+EIGEN_STRONG_INLINE Packet4bf pfrexp(const Packet4bf& a, Packet4bf& exponent) {
+ Packet4f fexponent;
+ const Packet4bf out = F32ToBf16(pfrexp<Packet4f>(Bf16ToF32(a), fexponent));
+ exponent = F32ToBf16(fexponent);
+ return out;
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet4bf pldexp(const Packet4bf& a, const Packet4bf& exponent) {
+ return F32ToBf16(pldexp<Packet4f>(Bf16ToF32(a), Bf16ToF32(exponent)));
+}
+
+//---------- double ----------
+
+#if EIGEN_ARCH_ARM64 && !EIGEN_APPLE_DOUBLE_NEON_BUG
+template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet2d pexp<Packet2d>(const Packet2d& x)
+{ return pexp_double(x); }
+
+template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet2d plog<Packet2d>(const Packet2d& x)
+{ return plog_double(x); }
+
+template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet2d patan<Packet2d>(const Packet2d& x)
+{ return patan_double(x); }
+
+#endif
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_MATH_FUNCTIONS_NEON_H
diff --git a/Eigen/src/Core/arch/NEON/PacketMath.h b/Eigen/src/Core/arch/NEON/PacketMath.h
new file mode 100644
index 0000000..5cbf4ac
--- /dev/null
+++ b/Eigen/src/Core/arch/NEON/PacketMath.h
@@ -0,0 +1,4612 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2010 Konstantinos Margaritis <markos@freevec.org>
+// Heavily based on Gael's SSE version.
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_PACKET_MATH_NEON_H
+#define EIGEN_PACKET_MATH_NEON_H
+
+#include "../../InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+
+#ifndef EIGEN_CACHEFRIENDLY_PRODUCT_THRESHOLD
+#define EIGEN_CACHEFRIENDLY_PRODUCT_THRESHOLD 8
+#endif
+
+#ifndef EIGEN_HAS_SINGLE_INSTRUCTION_MADD
+#define EIGEN_HAS_SINGLE_INSTRUCTION_MADD
+#endif
+
+#ifndef EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS
+#if EIGEN_ARCH_ARM64
+#define EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS 32
+#else
+#define EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS 16
+#endif
+#endif
+
+#if EIGEN_COMP_MSVC_STRICT
+
+// In MSVC's arm_neon.h header file, all NEON vector types
+// are aliases to the same underlying type __n128.
+// We thus have to wrap them to make them different C++ types.
+// (See also bug 1428)
+typedef eigen_packet_wrapper<float32x2_t,0> Packet2f;
+typedef eigen_packet_wrapper<float32x4_t,1> Packet4f;
+typedef eigen_packet_wrapper<int32_t ,2> Packet4c;
+typedef eigen_packet_wrapper<int8x8_t ,3> Packet8c;
+typedef eigen_packet_wrapper<int8x16_t ,4> Packet16c;
+typedef eigen_packet_wrapper<uint32_t ,5> Packet4uc;
+typedef eigen_packet_wrapper<uint8x8_t ,6> Packet8uc;
+typedef eigen_packet_wrapper<uint8x16_t ,7> Packet16uc;
+typedef eigen_packet_wrapper<int16x4_t ,8> Packet4s;
+typedef eigen_packet_wrapper<int16x8_t ,9> Packet8s;
+typedef eigen_packet_wrapper<uint16x4_t ,10> Packet4us;
+typedef eigen_packet_wrapper<uint16x8_t ,11> Packet8us;
+typedef eigen_packet_wrapper<int32x2_t ,12> Packet2i;
+typedef eigen_packet_wrapper<int32x4_t ,13> Packet4i;
+typedef eigen_packet_wrapper<uint32x2_t ,14> Packet2ui;
+typedef eigen_packet_wrapper<uint32x4_t ,15> Packet4ui;
+typedef eigen_packet_wrapper<int64x2_t ,16> Packet2l;
+typedef eigen_packet_wrapper<uint64x2_t ,17> Packet2ul;
+
+#else
+
+typedef float32x2_t Packet2f;
+typedef float32x4_t Packet4f;
+typedef eigen_packet_wrapper<int32_t ,2> Packet4c;
+typedef int8x8_t Packet8c;
+typedef int8x16_t Packet16c;
+typedef eigen_packet_wrapper<uint32_t ,5> Packet4uc;
+typedef uint8x8_t Packet8uc;
+typedef uint8x16_t Packet16uc;
+typedef int16x4_t Packet4s;
+typedef int16x8_t Packet8s;
+typedef uint16x4_t Packet4us;
+typedef uint16x8_t Packet8us;
+typedef int32x2_t Packet2i;
+typedef int32x4_t Packet4i;
+typedef uint32x2_t Packet2ui;
+typedef uint32x4_t Packet4ui;
+typedef int64x2_t Packet2l;
+typedef uint64x2_t Packet2ul;
+
+#endif // EIGEN_COMP_MSVC_STRICT
+
+EIGEN_STRONG_INLINE Packet4f shuffle1(const Packet4f& m, int mask){
+ const float* a = reinterpret_cast<const float*>(&m);
+ Packet4f res = {*(a + (mask & 3)), *(a + ((mask >> 2) & 3)), *(a + ((mask >> 4) & 3 )), *(a + ((mask >> 6) & 3))};
+ return res;
+}
+
+// fuctionally equivalent to _mm_shuffle_ps in SSE when interleave
+// == false (i.e. shuffle<false>(m, n, mask) equals _mm_shuffle_ps(m, n, mask)),
+// interleave m and n when interleave == true. Currently used in LU/arch/InverseSize4.h
+// to enable a shared implementation for fast inversion of matrices of size 4.
+template<bool interleave>
+EIGEN_STRONG_INLINE Packet4f shuffle2(const Packet4f &m, const Packet4f &n, int mask)
+{
+ const float* a = reinterpret_cast<const float*>(&m);
+ const float* b = reinterpret_cast<const float*>(&n);
+ Packet4f res = {*(a + (mask & 3)), *(a + ((mask >> 2) & 3)), *(b + ((mask >> 4) & 3)), *(b + ((mask >> 6) & 3))};
+ return res;
+}
+
+template<>
+EIGEN_STRONG_INLINE Packet4f shuffle2<true>(const Packet4f &m, const Packet4f &n, int mask)
+{
+ const float* a = reinterpret_cast<const float*>(&m);
+ const float* b = reinterpret_cast<const float*>(&n);
+ Packet4f res = {*(a + (mask & 3)), *(b + ((mask >> 2) & 3)), *(a + ((mask >> 4) & 3)), *(b + ((mask >> 6) & 3))};
+ return res;
+}
+
+EIGEN_STRONG_INLINE static int eigen_neon_shuffle_mask(int p, int q, int r, int s) {return ((s)<<6|(r)<<4|(q)<<2|(p));}
+
+EIGEN_STRONG_INLINE Packet4f vec4f_swizzle1(const Packet4f& a, int p, int q, int r, int s)
+{
+ return shuffle1(a, eigen_neon_shuffle_mask(p, q, r, s));
+}
+EIGEN_STRONG_INLINE Packet4f vec4f_swizzle2(const Packet4f& a, const Packet4f& b, int p, int q, int r, int s)
+{
+ return shuffle2<false>(a,b,eigen_neon_shuffle_mask(p, q, r, s));
+}
+EIGEN_STRONG_INLINE Packet4f vec4f_movelh(const Packet4f& a, const Packet4f& b)
+{
+ return shuffle2<false>(a,b,eigen_neon_shuffle_mask(0, 1, 0, 1));
+}
+EIGEN_STRONG_INLINE Packet4f vec4f_movehl(const Packet4f& a, const Packet4f& b)
+{
+ return shuffle2<false>(b,a,eigen_neon_shuffle_mask(2, 3, 2, 3));
+}
+EIGEN_STRONG_INLINE Packet4f vec4f_unpacklo(const Packet4f& a, const Packet4f& b)
+{
+ return shuffle2<true>(a,b,eigen_neon_shuffle_mask(0, 0, 1, 1));
+}
+EIGEN_STRONG_INLINE Packet4f vec4f_unpackhi(const Packet4f& a, const Packet4f& b)
+{
+ return shuffle2<true>(a,b,eigen_neon_shuffle_mask(2, 2, 3, 3));
+}
+#define vec4f_duplane(a, p) \
+ vdupq_lane_f32(vget_low_f32(a), p)
+
+#define EIGEN_DECLARE_CONST_Packet4f(NAME,X) \
+ const Packet4f p4f_##NAME = pset1<Packet4f>(X)
+
+#define EIGEN_DECLARE_CONST_Packet4f_FROM_INT(NAME,X) \
+ const Packet4f p4f_##NAME = vreinterpretq_f32_u32(pset1<int32_t>(X))
+
+#define EIGEN_DECLARE_CONST_Packet4i(NAME,X) \
+ const Packet4i p4i_##NAME = pset1<Packet4i>(X)
+
+#if EIGEN_ARCH_ARM64
+ // __builtin_prefetch tends to do nothing on ARM64 compilers because the
+ // prefetch instructions there are too detailed for __builtin_prefetch to map
+ // meaningfully to them.
+ #define EIGEN_ARM_PREFETCH(ADDR) __asm__ __volatile__("prfm pldl1keep, [%[addr]]\n" ::[addr] "r"(ADDR) : );
+#elif EIGEN_HAS_BUILTIN(__builtin_prefetch) || EIGEN_COMP_GNUC
+ #define EIGEN_ARM_PREFETCH(ADDR) __builtin_prefetch(ADDR);
+#elif defined __pld
+ #define EIGEN_ARM_PREFETCH(ADDR) __pld(ADDR)
+#elif EIGEN_ARCH_ARM
+ #define EIGEN_ARM_PREFETCH(ADDR) __asm__ __volatile__ ("pld [%[addr]]\n" :: [addr] "r" (ADDR) : );
+#else
+ // by default no explicit prefetching
+ #define EIGEN_ARM_PREFETCH(ADDR)
+#endif
+
+template <>
+struct packet_traits<float> : default_packet_traits
+{
+ typedef Packet4f type;
+ typedef Packet2f half;
+ enum
+ {
+ Vectorizable = 1,
+ AlignedOnScalar = 1,
+ size = 4,
+ HasHalfPacket = 1,
+
+ HasAdd = 1,
+ HasSub = 1,
+ HasShift = 1,
+ HasMul = 1,
+ HasNegate = 1,
+ HasAbs = 1,
+ HasArg = 0,
+ HasAbs2 = 1,
+ HasAbsDiff = 1,
+ HasMin = 1,
+ HasMax = 1,
+ HasConj = 1,
+ HasSetLinear = 0,
+ HasBlend = 0,
+
+ HasDiv = 1,
+ HasFloor = 1,
+ HasCeil = 1,
+ HasRint = 1,
+
+ HasSin = EIGEN_FAST_MATH,
+ HasCos = EIGEN_FAST_MATH,
+ HasACos = 1,
+ HasASin = 1,
+ HasATan = 1,
+ HasLog = 1,
+ HasExp = 1,
+ HasSqrt = 1,
+ HasRsqrt = 1,
+ HasTanh = EIGEN_FAST_MATH,
+ HasErf = EIGEN_FAST_MATH,
+ HasBessel = 0, // Issues with accuracy.
+ HasNdtri = 0
+ };
+};
+
+template <>
+struct packet_traits<int8_t> : default_packet_traits
+{
+ typedef Packet16c type;
+ typedef Packet8c half;
+ enum
+ {
+ Vectorizable = 1,
+ AlignedOnScalar = 1,
+ size = 16,
+ HasHalfPacket = 1,
+
+ HasCmp = 1,
+ HasAdd = 1,
+ HasSub = 1,
+ HasShift = 1,
+ HasMul = 1,
+ HasNegate = 1,
+ HasAbs = 1,
+ HasAbsDiff = 1,
+ HasArg = 0,
+ HasAbs2 = 1,
+ HasMin = 1,
+ HasMax = 1,
+ HasConj = 1,
+ HasSetLinear = 0,
+ HasBlend = 0
+ };
+};
+
+template <>
+struct packet_traits<uint8_t> : default_packet_traits
+{
+ typedef Packet16uc type;
+ typedef Packet8uc half;
+ enum
+ {
+ Vectorizable = 1,
+ AlignedOnScalar = 1,
+ size = 16,
+ HasHalfPacket = 1,
+
+ HasCmp = 1,
+ HasAdd = 1,
+ HasSub = 1,
+ HasShift = 1,
+ HasMul = 1,
+ HasNegate = 0,
+ HasAbs = 1,
+ HasAbsDiff = 1,
+ HasArg = 0,
+ HasAbs2 = 1,
+ HasMin = 1,
+ HasMax = 1,
+ HasConj = 1,
+ HasSetLinear = 0,
+ HasBlend = 0,
+
+ HasSqrt = 1
+ };
+};
+
+template <>
+struct packet_traits<int16_t> : default_packet_traits
+{
+ typedef Packet8s type;
+ typedef Packet4s half;
+ enum
+ {
+ Vectorizable = 1,
+ AlignedOnScalar = 1,
+ size = 8,
+ HasHalfPacket = 1,
+
+ HasAdd = 1,
+ HasSub = 1,
+ HasShift = 1,
+ HasMul = 1,
+ HasNegate = 1,
+ HasAbs = 1,
+ HasAbsDiff = 1,
+ HasArg = 0,
+ HasAbs2 = 1,
+ HasMin = 1,
+ HasMax = 1,
+ HasConj = 1,
+ HasSetLinear = 0,
+ HasBlend = 0
+ };
+};
+
+template <>
+struct packet_traits<uint16_t> : default_packet_traits
+{
+ typedef Packet8us type;
+ typedef Packet4us half;
+ enum
+ {
+ Vectorizable = 1,
+ AlignedOnScalar = 1,
+ size = 8,
+ HasHalfPacket = 1,
+
+ HasAdd = 1,
+ HasSub = 1,
+ HasShift = 1,
+ HasMul = 1,
+ HasNegate = 0,
+ HasAbs = 0,
+ HasAbsDiff = 1,
+ HasArg = 0,
+ HasAbs2 = 1,
+ HasMin = 1,
+ HasMax = 1,
+ HasConj = 1,
+ HasSetLinear = 0,
+ HasBlend = 0,
+ HasSqrt = 1
+ };
+};
+
+template <>
+struct packet_traits<int32_t> : default_packet_traits
+{
+ typedef Packet4i type;
+ typedef Packet2i half;
+ enum
+ {
+ Vectorizable = 1,
+ AlignedOnScalar = 1,
+ size = 4,
+ HasHalfPacket = 1,
+
+ HasAdd = 1,
+ HasSub = 1,
+ HasShift = 1,
+ HasMul = 1,
+ HasNegate = 1,
+ HasAbs = 1,
+ HasArg = 0,
+ HasAbs2 = 1,
+ HasAbsDiff = 1,
+ HasMin = 1,
+ HasMax = 1,
+ HasConj = 1,
+ HasSetLinear = 0,
+ HasBlend = 0
+ };
+};
+
+template <>
+struct packet_traits<uint32_t> : default_packet_traits
+{
+ typedef Packet4ui type;
+ typedef Packet2ui half;
+ enum
+ {
+ Vectorizable = 1,
+ AlignedOnScalar = 1,
+ size = 4,
+ HasHalfPacket = 1,
+
+ HasAdd = 1,
+ HasSub = 1,
+ HasShift = 1,
+ HasMul = 1,
+ HasNegate = 0,
+ HasAbs = 0,
+ HasArg = 0,
+ HasAbs2 = 1,
+ HasAbsDiff = 1,
+ HasMin = 1,
+ HasMax = 1,
+ HasConj = 1,
+ HasSetLinear = 0,
+ HasBlend = 0,
+
+ HasSqrt = 1
+ };
+};
+
+template <>
+struct packet_traits<int64_t> : default_packet_traits
+{
+ typedef Packet2l type;
+ typedef Packet2l half;
+ enum
+ {
+ Vectorizable = 1,
+ AlignedOnScalar = 1,
+ size = 2,
+ HasHalfPacket = 0,
+
+ HasCmp = 1,
+ HasAdd = 1,
+ HasSub = 1,
+ HasShift = 1,
+ HasMul = 1,
+ HasNegate = 1,
+ HasAbs = 1,
+ HasArg = 0,
+ HasAbs2 = 1,
+ HasAbsDiff = 1,
+ HasMin = 1,
+ HasMax = 1,
+ HasConj = 1,
+ HasSetLinear = 0,
+ HasBlend = 0
+ };
+};
+
+template <>
+struct packet_traits<uint64_t> : default_packet_traits
+{
+ typedef Packet2ul type;
+ typedef Packet2ul half;
+ enum
+ {
+ Vectorizable = 1,
+ AlignedOnScalar = 1,
+ size = 2,
+ HasHalfPacket = 0,
+
+ HasCmp = 1,
+ HasAdd = 1,
+ HasSub = 1,
+ HasShift = 1,
+ HasMul = 1,
+ HasNegate = 0,
+ HasAbs = 0,
+ HasArg = 0,
+ HasAbs2 = 1,
+ HasAbsDiff = 1,
+ HasMin = 1,
+ HasMax = 1,
+ HasConj = 1,
+ HasSetLinear = 0,
+ HasBlend = 0
+ };
+};
+
+template<> struct unpacket_traits<Packet2f>
+{
+ typedef float type;
+ typedef Packet2f half;
+ typedef Packet2i integer_packet;
+ enum
+ {
+ size = 2,
+ alignment = Aligned16,
+ vectorizable = true,
+ masked_load_available = false,
+ masked_store_available = false
+ };
+};
+template<> struct unpacket_traits<Packet4f>
+{
+ typedef float type;
+ typedef Packet2f half;
+ typedef Packet4i integer_packet;
+ enum
+ {
+ size = 4,
+ alignment = Aligned16,
+ vectorizable = true,
+ masked_load_available = false,
+ masked_store_available = false
+ };
+};
+template<> struct unpacket_traits<Packet4c>
+{
+ typedef int8_t type;
+ typedef Packet4c half;
+ enum
+ {
+ size = 4,
+ alignment = Unaligned,
+ vectorizable = true,
+ masked_load_available = false,
+ masked_store_available = false
+ };
+};
+template<> struct unpacket_traits<Packet8c>
+{
+ typedef int8_t type;
+ typedef Packet4c half;
+ enum
+ {
+ size = 8,
+ alignment = Aligned16,
+ vectorizable = true,
+ masked_load_available = false,
+ masked_store_available = false
+ };
+};
+template<> struct unpacket_traits<Packet16c>
+{
+ typedef int8_t type;
+ typedef Packet8c half;
+ enum
+ {
+ size = 16,
+ alignment = Aligned16,
+ vectorizable = true,
+ masked_load_available = false,
+ masked_store_available = false
+ };
+};
+template<> struct unpacket_traits<Packet4uc>
+{
+ typedef uint8_t type;
+ typedef Packet4uc half;
+ enum
+ {
+ size = 4,
+ alignment = Unaligned,
+ vectorizable = true,
+ masked_load_available = false,
+ masked_store_available = false
+ };
+};
+template<> struct unpacket_traits<Packet8uc>
+{
+ typedef uint8_t type;
+ typedef Packet4uc half;
+ enum
+ {
+ size = 8,
+ alignment = Aligned16,
+ vectorizable = true,
+ masked_load_available = false,
+ masked_store_available = false
+ };
+};
+template<> struct unpacket_traits<Packet16uc>
+{
+ typedef uint8_t type;
+ typedef Packet8uc half;
+ enum
+ {
+ size = 16,
+ alignment = Aligned16,
+ vectorizable = true,
+ masked_load_available = false,
+ masked_store_available = false};
+};
+template<> struct unpacket_traits<Packet4s>
+{
+ typedef int16_t type;
+ typedef Packet4s half;
+ enum
+ {
+ size = 4,
+ alignment = Aligned16,
+ vectorizable = true,
+ masked_load_available = false,
+ masked_store_available = false
+ };
+};
+template<> struct unpacket_traits<Packet8s>
+{
+ typedef int16_t type;
+ typedef Packet4s half;
+ enum
+ {
+ size = 8,
+ alignment = Aligned16,
+ vectorizable = true,
+ masked_load_available = false,
+ masked_store_available = false
+ };
+};
+template<> struct unpacket_traits<Packet4us>
+{
+ typedef uint16_t type;
+ typedef Packet4us half;
+ enum
+ {
+ size = 4,
+ alignment = Aligned16,
+ vectorizable = true,
+ masked_load_available = false,
+ masked_store_available = false
+ };
+};
+template<> struct unpacket_traits<Packet8us>
+{
+ typedef uint16_t type;
+ typedef Packet4us half;
+ enum
+ {
+ size = 8,
+ alignment = Aligned16,
+ vectorizable = true,
+ masked_load_available = false,
+ masked_store_available = false
+ };
+};
+template<> struct unpacket_traits<Packet2i>
+{
+ typedef int32_t type;
+ typedef Packet2i half;
+ enum
+ {
+ size = 2,
+ alignment = Aligned16,
+ vectorizable = true,
+ masked_load_available = false,
+ masked_store_available = false
+ };
+};
+template<> struct unpacket_traits<Packet4i>
+{
+ typedef int32_t type;
+ typedef Packet2i half;
+ enum
+ {
+ size = 4,
+ alignment = Aligned16,
+ vectorizable = true,
+ masked_load_available = false,
+ masked_store_available = false
+ };
+};
+template<> struct unpacket_traits<Packet2ui>
+{
+ typedef uint32_t type;
+ typedef Packet2ui half;
+ enum
+ {
+ size = 2,
+ alignment = Aligned16,
+ vectorizable = true,
+ masked_load_available = false,
+ masked_store_available = false
+ };
+};
+template<> struct unpacket_traits<Packet4ui>
+{
+ typedef uint32_t type;
+ typedef Packet2ui half;
+ enum
+ {
+ size = 4,
+ alignment = Aligned16,
+ vectorizable = true,
+ masked_load_available = false,
+ masked_store_available = false
+ };
+};
+template<> struct unpacket_traits<Packet2l>
+{
+ typedef int64_t type;
+ typedef Packet2l half;
+ enum
+ {
+ size = 2,
+ alignment = Aligned16,
+ vectorizable = true,
+ masked_load_available = false,
+ masked_store_available = false
+ };
+};
+template<> struct unpacket_traits<Packet2ul>
+{
+ typedef uint64_t type;
+ typedef Packet2ul half;
+ enum
+ {
+ size = 2,
+ alignment = Aligned16,
+ vectorizable = true,
+ masked_load_available = false,
+ masked_store_available = false
+ };
+};
+
+template<> EIGEN_STRONG_INLINE Packet2f pset1<Packet2f>(const float& from) { return vdup_n_f32(from); }
+template<> EIGEN_STRONG_INLINE Packet4f pset1<Packet4f>(const float& from) { return vdupq_n_f32(from); }
+template<> EIGEN_STRONG_INLINE Packet4c pset1<Packet4c>(const int8_t& from)
+{ return vget_lane_s32(vreinterpret_s32_s8(vdup_n_s8(from)), 0); }
+template<> EIGEN_STRONG_INLINE Packet8c pset1<Packet8c>(const int8_t& from) { return vdup_n_s8(from); }
+template<> EIGEN_STRONG_INLINE Packet16c pset1<Packet16c>(const int8_t& from) { return vdupq_n_s8(from); }
+template<> EIGEN_STRONG_INLINE Packet4uc pset1<Packet4uc>(const uint8_t& from)
+{ return vget_lane_u32(vreinterpret_u32_u8(vdup_n_u8(from)), 0); }
+template<> EIGEN_STRONG_INLINE Packet8uc pset1<Packet8uc>(const uint8_t& from) { return vdup_n_u8(from); }
+template<> EIGEN_STRONG_INLINE Packet16uc pset1<Packet16uc>(const uint8_t& from) { return vdupq_n_u8(from); }
+template<> EIGEN_STRONG_INLINE Packet4s pset1<Packet4s>(const int16_t& from) { return vdup_n_s16(from); }
+template<> EIGEN_STRONG_INLINE Packet8s pset1<Packet8s>(const int16_t& from) { return vdupq_n_s16(from); }
+template<> EIGEN_STRONG_INLINE Packet4us pset1<Packet4us>(const uint16_t& from) { return vdup_n_u16(from); }
+template<> EIGEN_STRONG_INLINE Packet8us pset1<Packet8us>(const uint16_t& from) { return vdupq_n_u16(from); }
+template<> EIGEN_STRONG_INLINE Packet2i pset1<Packet2i>(const int32_t& from) { return vdup_n_s32(from); }
+template<> EIGEN_STRONG_INLINE Packet4i pset1<Packet4i>(const int32_t& from) { return vdupq_n_s32(from); }
+template<> EIGEN_STRONG_INLINE Packet2ui pset1<Packet2ui>(const uint32_t& from) { return vdup_n_u32(from); }
+template<> EIGEN_STRONG_INLINE Packet4ui pset1<Packet4ui>(const uint32_t& from) { return vdupq_n_u32(from); }
+template<> EIGEN_STRONG_INLINE Packet2l pset1<Packet2l>(const int64_t& from) { return vdupq_n_s64(from); }
+template<> EIGEN_STRONG_INLINE Packet2ul pset1<Packet2ul>(const uint64_t& from) { return vdupq_n_u64(from); }
+
+template<> EIGEN_STRONG_INLINE Packet2f pset1frombits<Packet2f>(uint32_t from)
+{ return vreinterpret_f32_u32(vdup_n_u32(from)); }
+template<> EIGEN_STRONG_INLINE Packet4f pset1frombits<Packet4f>(uint32_t from)
+{ return vreinterpretq_f32_u32(vdupq_n_u32(from)); }
+
+template<> EIGEN_STRONG_INLINE Packet2f plset<Packet2f>(const float& a)
+{
+ const float c[] = {0.0f,1.0f};
+ return vadd_f32(pset1<Packet2f>(a), vld1_f32(c));
+}
+template<> EIGEN_STRONG_INLINE Packet4f plset<Packet4f>(const float& a)
+{
+ const float c[] = {0.0f,1.0f,2.0f,3.0f};
+ return vaddq_f32(pset1<Packet4f>(a), vld1q_f32(c));
+}
+template<> EIGEN_STRONG_INLINE Packet4c plset<Packet4c>(const int8_t& a)
+{ return vget_lane_s32(vreinterpret_s32_s8(vadd_s8(vreinterpret_s8_u32(vdup_n_u32(0x03020100)), vdup_n_s8(a))), 0); }
+template<> EIGEN_STRONG_INLINE Packet8c plset<Packet8c>(const int8_t& a)
+{
+ const int8_t c[] = {0,1,2,3,4,5,6,7};
+ return vadd_s8(pset1<Packet8c>(a), vld1_s8(c));
+}
+template<> EIGEN_STRONG_INLINE Packet16c plset<Packet16c>(const int8_t& a)
+{
+ const int8_t c[] = {0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15};
+ return vaddq_s8(pset1<Packet16c>(a), vld1q_s8(c));
+}
+template<> EIGEN_STRONG_INLINE Packet4uc plset<Packet4uc>(const uint8_t& a)
+{ return vget_lane_u32(vreinterpret_u32_u8(vadd_u8(vreinterpret_u8_u32(vdup_n_u32(0x03020100)), vdup_n_u8(a))), 0); }
+template<> EIGEN_STRONG_INLINE Packet8uc plset<Packet8uc>(const uint8_t& a)
+{
+ const uint8_t c[] = {0,1,2,3,4,5,6,7};
+ return vadd_u8(pset1<Packet8uc>(a), vld1_u8(c));
+}
+template<> EIGEN_STRONG_INLINE Packet16uc plset<Packet16uc>(const uint8_t& a)
+{
+ const uint8_t c[] = {0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15};
+ return vaddq_u8(pset1<Packet16uc>(a), vld1q_u8(c));
+}
+template<> EIGEN_STRONG_INLINE Packet4s plset<Packet4s>(const int16_t& a)
+{
+ const int16_t c[] = {0,1,2,3};
+ return vadd_s16(pset1<Packet4s>(a), vld1_s16(c));
+}
+template<> EIGEN_STRONG_INLINE Packet4us plset<Packet4us>(const uint16_t& a)
+{
+ const uint16_t c[] = {0,1,2,3};
+ return vadd_u16(pset1<Packet4us>(a), vld1_u16(c));
+}
+template<> EIGEN_STRONG_INLINE Packet8s plset<Packet8s>(const int16_t& a)
+{
+ const int16_t c[] = {0,1,2,3,4,5,6,7};
+ return vaddq_s16(pset1<Packet8s>(a), vld1q_s16(c));
+}
+template<> EIGEN_STRONG_INLINE Packet8us plset<Packet8us>(const uint16_t& a)
+{
+ const uint16_t c[] = {0,1,2,3,4,5,6,7};
+ return vaddq_u16(pset1<Packet8us>(a), vld1q_u16(c));
+}
+template<> EIGEN_STRONG_INLINE Packet2i plset<Packet2i>(const int32_t& a)
+{
+ const int32_t c[] = {0,1};
+ return vadd_s32(pset1<Packet2i>(a), vld1_s32(c));
+}
+template<> EIGEN_STRONG_INLINE Packet4i plset<Packet4i>(const int32_t& a)
+{
+ const int32_t c[] = {0,1,2,3};
+ return vaddq_s32(pset1<Packet4i>(a), vld1q_s32(c));
+}
+template<> EIGEN_STRONG_INLINE Packet2ui plset<Packet2ui>(const uint32_t& a)
+{
+ const uint32_t c[] = {0,1};
+ return vadd_u32(pset1<Packet2ui>(a), vld1_u32(c));
+}
+template<> EIGEN_STRONG_INLINE Packet4ui plset<Packet4ui>(const uint32_t& a)
+{
+ const uint32_t c[] = {0,1,2,3};
+ return vaddq_u32(pset1<Packet4ui>(a), vld1q_u32(c));
+}
+template<> EIGEN_STRONG_INLINE Packet2l plset<Packet2l>(const int64_t& a)
+{
+ const int64_t c[] = {0,1};
+ return vaddq_s64(pset1<Packet2l>(a), vld1q_s64(c));
+}
+template<> EIGEN_STRONG_INLINE Packet2ul plset<Packet2ul>(const uint64_t& a)
+{
+ const uint64_t c[] = {0,1};
+ return vaddq_u64(pset1<Packet2ul>(a), vld1q_u64(c));
+}
+
+template<> EIGEN_STRONG_INLINE Packet2f padd<Packet2f>(const Packet2f& a, const Packet2f& b) { return vadd_f32(a,b); }
+template<> EIGEN_STRONG_INLINE Packet4f padd<Packet4f>(const Packet4f& a, const Packet4f& b) { return vaddq_f32(a,b); }
+template<> EIGEN_STRONG_INLINE Packet4c padd<Packet4c>(const Packet4c& a, const Packet4c& b)
+{
+ return vget_lane_s32(vreinterpret_s32_s8(vadd_s8(
+ vreinterpret_s8_s32(vdup_n_s32(a)),
+ vreinterpret_s8_s32(vdup_n_s32(b)))), 0);
+}
+template<> EIGEN_STRONG_INLINE Packet8c padd<Packet8c>(const Packet8c& a, const Packet8c& b) { return vadd_s8(a,b); }
+template<> EIGEN_STRONG_INLINE Packet16c padd<Packet16c>(const Packet16c& a, const Packet16c& b) { return vaddq_s8(a,b); }
+template<> EIGEN_STRONG_INLINE Packet4uc padd<Packet4uc>(const Packet4uc& a, const Packet4uc& b)
+{
+ return vget_lane_u32(vreinterpret_u32_u8(vadd_u8(
+ vreinterpret_u8_u32(vdup_n_u32(a)),
+ vreinterpret_u8_u32(vdup_n_u32(b)))), 0);
+}
+template<> EIGEN_STRONG_INLINE Packet8uc padd<Packet8uc>(const Packet8uc& a, const Packet8uc& b) { return vadd_u8(a,b); }
+template<> EIGEN_STRONG_INLINE Packet16uc padd<Packet16uc>(const Packet16uc& a, const Packet16uc& b) { return vaddq_u8(a,b); }
+template<> EIGEN_STRONG_INLINE Packet4s padd<Packet4s>(const Packet4s& a, const Packet4s& b) { return vadd_s16(a,b); }
+template<> EIGEN_STRONG_INLINE Packet8s padd<Packet8s>(const Packet8s& a, const Packet8s& b) { return vaddq_s16(a,b); }
+template<> EIGEN_STRONG_INLINE Packet4us padd<Packet4us>(const Packet4us& a, const Packet4us& b) { return vadd_u16(a,b); }
+template<> EIGEN_STRONG_INLINE Packet8us padd<Packet8us>(const Packet8us& a, const Packet8us& b) { return vaddq_u16(a,b); }
+template<> EIGEN_STRONG_INLINE Packet2i padd<Packet2i>(const Packet2i& a, const Packet2i& b) { return vadd_s32(a,b); }
+template<> EIGEN_STRONG_INLINE Packet4i padd<Packet4i>(const Packet4i& a, const Packet4i& b) { return vaddq_s32(a,b); }
+template<> EIGEN_STRONG_INLINE Packet2ui padd<Packet2ui>(const Packet2ui& a, const Packet2ui& b) { return vadd_u32(a,b); }
+template<> EIGEN_STRONG_INLINE Packet4ui padd<Packet4ui>(const Packet4ui& a, const Packet4ui& b) { return vaddq_u32(a,b); }
+template<> EIGEN_STRONG_INLINE Packet2l padd<Packet2l>(const Packet2l& a, const Packet2l& b) { return vaddq_s64(a,b); }
+template<> EIGEN_STRONG_INLINE Packet2ul padd<Packet2ul>(const Packet2ul& a, const Packet2ul& b) { return vaddq_u64(a,b); }
+
+template<> EIGEN_STRONG_INLINE Packet2f psub<Packet2f>(const Packet2f& a, const Packet2f& b) { return vsub_f32(a,b); }
+template<> EIGEN_STRONG_INLINE Packet4f psub<Packet4f>(const Packet4f& a, const Packet4f& b) { return vsubq_f32(a,b); }
+template<> EIGEN_STRONG_INLINE Packet4c psub<Packet4c>(const Packet4c& a, const Packet4c& b)
+{
+ return vget_lane_s32(vreinterpret_s32_s8(vsub_s8(
+ vreinterpret_s8_s32(vdup_n_s32(a)),
+ vreinterpret_s8_s32(vdup_n_s32(b)))), 0);
+}
+template<> EIGEN_STRONG_INLINE Packet8c psub<Packet8c>(const Packet8c& a, const Packet8c& b) { return vsub_s8(a,b); }
+template<> EIGEN_STRONG_INLINE Packet16c psub<Packet16c>(const Packet16c& a, const Packet16c& b) { return vsubq_s8(a,b); }
+template<> EIGEN_STRONG_INLINE Packet4uc psub<Packet4uc>(const Packet4uc& a, const Packet4uc& b)
+{
+ return vget_lane_u32(vreinterpret_u32_u8(vsub_u8(
+ vreinterpret_u8_u32(vdup_n_u32(a)),
+ vreinterpret_u8_u32(vdup_n_u32(b)))), 0);
+}
+template<> EIGEN_STRONG_INLINE Packet8uc psub<Packet8uc>(const Packet8uc& a, const Packet8uc& b) { return vsub_u8(a,b); }
+template<> EIGEN_STRONG_INLINE Packet16uc psub<Packet16uc>(const Packet16uc& a, const Packet16uc& b) { return vsubq_u8(a,b); }
+template<> EIGEN_STRONG_INLINE Packet4s psub<Packet4s>(const Packet4s& a, const Packet4s& b) { return vsub_s16(a,b); }
+template<> EIGEN_STRONG_INLINE Packet8s psub<Packet8s>(const Packet8s& a, const Packet8s& b) { return vsubq_s16(a,b); }
+template<> EIGEN_STRONG_INLINE Packet4us psub<Packet4us>(const Packet4us& a, const Packet4us& b) { return vsub_u16(a,b); }
+template<> EIGEN_STRONG_INLINE Packet8us psub<Packet8us>(const Packet8us& a, const Packet8us& b) { return vsubq_u16(a,b); }
+template<> EIGEN_STRONG_INLINE Packet2i psub<Packet2i>(const Packet2i& a, const Packet2i& b) { return vsub_s32(a,b); }
+template<> EIGEN_STRONG_INLINE Packet4i psub<Packet4i>(const Packet4i& a, const Packet4i& b) { return vsubq_s32(a,b); }
+template<> EIGEN_STRONG_INLINE Packet2ui psub<Packet2ui>(const Packet2ui& a, const Packet2ui& b) { return vsub_u32(a,b); }
+template<> EIGEN_STRONG_INLINE Packet4ui psub<Packet4ui>(const Packet4ui& a, const Packet4ui& b) { return vsubq_u32(a,b); }
+template<> EIGEN_STRONG_INLINE Packet2l psub<Packet2l>(const Packet2l& a, const Packet2l& b) { return vsubq_s64(a,b); }
+template<> EIGEN_STRONG_INLINE Packet2ul psub<Packet2ul>(const Packet2ul& a, const Packet2ul& b) { return vsubq_u64(a,b); }
+
+template<> EIGEN_STRONG_INLINE Packet2f pxor<Packet2f>(const Packet2f& a, const Packet2f& b);
+template<> EIGEN_STRONG_INLINE Packet2f paddsub<Packet2f>(const Packet2f& a, const Packet2f & b) {
+ Packet2f mask = {numext::bit_cast<float>(0x80000000u), 0.0f};
+ return padd(a, pxor(mask, b));
+}
+template<> EIGEN_STRONG_INLINE Packet4f pxor<Packet4f>(const Packet4f& a, const Packet4f& b);
+template<> EIGEN_STRONG_INLINE Packet4f paddsub<Packet4f>(const Packet4f& a, const Packet4f& b) {
+ Packet4f mask = {numext::bit_cast<float>(0x80000000u), 0.0f, numext::bit_cast<float>(0x80000000u), 0.0f};
+ return padd(a, pxor(mask, b));
+}
+
+template<> EIGEN_STRONG_INLINE Packet2f pnegate(const Packet2f& a) { return vneg_f32(a); }
+template<> EIGEN_STRONG_INLINE Packet4f pnegate(const Packet4f& a) { return vnegq_f32(a); }
+template<> EIGEN_STRONG_INLINE Packet4c pnegate(const Packet4c& a)
+{ return vget_lane_s32(vreinterpret_s32_s8(vneg_s8(vreinterpret_s8_s32(vdup_n_s32(a)))), 0); }
+template<> EIGEN_STRONG_INLINE Packet8c pnegate(const Packet8c& a) { return vneg_s8(a); }
+template<> EIGEN_STRONG_INLINE Packet16c pnegate(const Packet16c& a) { return vnegq_s8(a); }
+template<> EIGEN_STRONG_INLINE Packet4s pnegate(const Packet4s& a) { return vneg_s16(a); }
+template<> EIGEN_STRONG_INLINE Packet8s pnegate(const Packet8s& a) { return vnegq_s16(a); }
+template<> EIGEN_STRONG_INLINE Packet2i pnegate(const Packet2i& a) { return vneg_s32(a); }
+template<> EIGEN_STRONG_INLINE Packet4i pnegate(const Packet4i& a) { return vnegq_s32(a); }
+template<> EIGEN_STRONG_INLINE Packet2l pnegate(const Packet2l& a) {
+#if EIGEN_ARCH_ARM64
+ return vnegq_s64(a);
+#else
+ return vcombine_s64(
+ vdup_n_s64(-vgetq_lane_s64(a, 0)),
+ vdup_n_s64(-vgetq_lane_s64(a, 1)));
+#endif
+}
+
+template<> EIGEN_STRONG_INLINE Packet2f pconj(const Packet2f& a) { return a; }
+template<> EIGEN_STRONG_INLINE Packet4f pconj(const Packet4f& a) { return a; }
+template<> EIGEN_STRONG_INLINE Packet4c pconj(const Packet4c& a) { return a; }
+template<> EIGEN_STRONG_INLINE Packet8c pconj(const Packet8c& a) { return a; }
+template<> EIGEN_STRONG_INLINE Packet16c pconj(const Packet16c& a) { return a; }
+template<> EIGEN_STRONG_INLINE Packet4uc pconj(const Packet4uc& a) { return a; }
+template<> EIGEN_STRONG_INLINE Packet8uc pconj(const Packet8uc& a) { return a; }
+template<> EIGEN_STRONG_INLINE Packet16uc pconj(const Packet16uc& a) { return a; }
+template<> EIGEN_STRONG_INLINE Packet4s pconj(const Packet4s& a) { return a; }
+template<> EIGEN_STRONG_INLINE Packet8s pconj(const Packet8s& a) { return a; }
+template<> EIGEN_STRONG_INLINE Packet4us pconj(const Packet4us& a) { return a; }
+template<> EIGEN_STRONG_INLINE Packet8us pconj(const Packet8us& a) { return a; }
+template<> EIGEN_STRONG_INLINE Packet2i pconj(const Packet2i& a) { return a; }
+template<> EIGEN_STRONG_INLINE Packet4i pconj(const Packet4i& a) { return a; }
+template<> EIGEN_STRONG_INLINE Packet2ui pconj(const Packet2ui& a) { return a; }
+template<> EIGEN_STRONG_INLINE Packet4ui pconj(const Packet4ui& a) { return a; }
+template<> EIGEN_STRONG_INLINE Packet2l pconj(const Packet2l& a) { return a; }
+template<> EIGEN_STRONG_INLINE Packet2ul pconj(const Packet2ul& a) { return a; }
+
+template<> EIGEN_STRONG_INLINE Packet2f pmul<Packet2f>(const Packet2f& a, const Packet2f& b) { return vmul_f32(a,b); }
+template<> EIGEN_STRONG_INLINE Packet4f pmul<Packet4f>(const Packet4f& a, const Packet4f& b) { return vmulq_f32(a,b); }
+template<> EIGEN_STRONG_INLINE Packet4c pmul<Packet4c>(const Packet4c& a, const Packet4c& b)
+{
+ return vget_lane_s32(vreinterpret_s32_s8(vmul_s8(
+ vreinterpret_s8_s32(vdup_n_s32(a)),
+ vreinterpret_s8_s32(vdup_n_s32(b)))), 0);
+}
+template<> EIGEN_STRONG_INLINE Packet8c pmul<Packet8c>(const Packet8c& a, const Packet8c& b) { return vmul_s8(a,b); }
+template<> EIGEN_STRONG_INLINE Packet16c pmul<Packet16c>(const Packet16c& a, const Packet16c& b) { return vmulq_s8(a,b); }
+template<> EIGEN_STRONG_INLINE Packet4uc pmul<Packet4uc>(const Packet4uc& a, const Packet4uc& b)
+{
+ return vget_lane_u32(vreinterpret_u32_u8(vmul_u8(
+ vreinterpret_u8_u32(vdup_n_u32(a)),
+ vreinterpret_u8_u32(vdup_n_u32(b)))), 0);
+}
+template<> EIGEN_STRONG_INLINE Packet8uc pmul<Packet8uc>(const Packet8uc& a, const Packet8uc& b) { return vmul_u8(a,b); }
+template<> EIGEN_STRONG_INLINE Packet16uc pmul<Packet16uc>(const Packet16uc& a, const Packet16uc& b) { return vmulq_u8(a,b); }
+template<> EIGEN_STRONG_INLINE Packet4s pmul<Packet4s>(const Packet4s& a, const Packet4s& b) { return vmul_s16(a,b); }
+template<> EIGEN_STRONG_INLINE Packet8s pmul<Packet8s>(const Packet8s& a, const Packet8s& b) { return vmulq_s16(a,b); }
+template<> EIGEN_STRONG_INLINE Packet4us pmul<Packet4us>(const Packet4us& a, const Packet4us& b) { return vmul_u16(a,b); }
+template<> EIGEN_STRONG_INLINE Packet8us pmul<Packet8us>(const Packet8us& a, const Packet8us& b) { return vmulq_u16(a,b); }
+template<> EIGEN_STRONG_INLINE Packet2i pmul<Packet2i>(const Packet2i& a, const Packet2i& b) { return vmul_s32(a,b); }
+template<> EIGEN_STRONG_INLINE Packet4i pmul<Packet4i>(const Packet4i& a, const Packet4i& b) { return vmulq_s32(a,b); }
+template<> EIGEN_STRONG_INLINE Packet2ui pmul<Packet2ui>(const Packet2ui& a, const Packet2ui& b) { return vmul_u32(a,b); }
+template<> EIGEN_STRONG_INLINE Packet4ui pmul<Packet4ui>(const Packet4ui& a, const Packet4ui& b) { return vmulq_u32(a,b); }
+template<> EIGEN_STRONG_INLINE Packet2l pmul<Packet2l>(const Packet2l& a, const Packet2l& b) {
+ return vcombine_s64(
+ vdup_n_s64(vgetq_lane_s64(a, 0)*vgetq_lane_s64(b, 0)),
+ vdup_n_s64(vgetq_lane_s64(a, 1)*vgetq_lane_s64(b, 1)));
+}
+template<> EIGEN_STRONG_INLINE Packet2ul pmul<Packet2ul>(const Packet2ul& a, const Packet2ul& b) {
+ return vcombine_u64(
+ vdup_n_u64(vgetq_lane_u64(a, 0)*vgetq_lane_u64(b, 0)),
+ vdup_n_u64(vgetq_lane_u64(a, 1)*vgetq_lane_u64(b, 1)));
+}
+
+template<> EIGEN_STRONG_INLINE Packet2f pdiv<Packet2f>(const Packet2f& a, const Packet2f& b)
+{
+#if EIGEN_ARCH_ARM64
+ return vdiv_f32(a,b);
+#else
+ Packet2f inv, restep, div;
+
+ // NEON does not offer a divide instruction, we have to do a reciprocal approximation
+ // However NEON in contrast to other SIMD engines (AltiVec/SSE), offers
+ // a reciprocal estimate AND a reciprocal step -which saves a few instructions
+ // vrecpeq_f32() returns an estimate to 1/b, which we will finetune with
+ // Newton-Raphson and vrecpsq_f32()
+ inv = vrecpe_f32(b);
+
+ // This returns a differential, by which we will have to multiply inv to get a better
+ // approximation of 1/b.
+ restep = vrecps_f32(b, inv);
+ inv = vmul_f32(restep, inv);
+
+ // Finally, multiply a by 1/b and get the wanted result of the division.
+ div = vmul_f32(a, inv);
+
+ return div;
+#endif
+}
+template<> EIGEN_STRONG_INLINE Packet4f pdiv<Packet4f>(const Packet4f& a, const Packet4f& b)
+{
+#if EIGEN_ARCH_ARM64
+ return vdivq_f32(a,b);
+#else
+ Packet4f inv, restep, div;
+
+ // NEON does not offer a divide instruction, we have to do a reciprocal approximation
+ // However NEON in contrast to other SIMD engines (AltiVec/SSE), offers
+ // a reciprocal estimate AND a reciprocal step -which saves a few instructions
+ // vrecpeq_f32() returns an estimate to 1/b, which we will finetune with
+ // Newton-Raphson and vrecpsq_f32()
+ inv = vrecpeq_f32(b);
+
+ // This returns a differential, by which we will have to multiply inv to get a better
+ // approximation of 1/b.
+ restep = vrecpsq_f32(b, inv);
+ inv = vmulq_f32(restep, inv);
+
+ // Finally, multiply a by 1/b and get the wanted result of the division.
+ div = vmulq_f32(a, inv);
+
+ return div;
+#endif
+}
+
+template<> EIGEN_STRONG_INLINE Packet4c pdiv<Packet4c>(const Packet4c& /*a*/, const Packet4c& /*b*/)
+{
+ eigen_assert(false && "packet integer division are not supported by NEON");
+ return pset1<Packet4c>(0);
+}
+template<> EIGEN_STRONG_INLINE Packet8c pdiv<Packet8c>(const Packet8c& /*a*/, const Packet8c& /*b*/)
+{
+ eigen_assert(false && "packet integer division are not supported by NEON");
+ return pset1<Packet8c>(0);
+}
+template<> EIGEN_STRONG_INLINE Packet16c pdiv<Packet16c>(const Packet16c& /*a*/, const Packet16c& /*b*/)
+{
+ eigen_assert(false && "packet integer division are not supported by NEON");
+ return pset1<Packet16c>(0);
+}
+template<> EIGEN_STRONG_INLINE Packet4uc pdiv<Packet4uc>(const Packet4uc& /*a*/, const Packet4uc& /*b*/)
+{
+ eigen_assert(false && "packet integer division are not supported by NEON");
+ return pset1<Packet4uc>(0);
+}
+template<> EIGEN_STRONG_INLINE Packet8uc pdiv<Packet8uc>(const Packet8uc& /*a*/, const Packet8uc& /*b*/)
+{
+ eigen_assert(false && "packet integer division are not supported by NEON");
+ return pset1<Packet8uc>(0);
+}
+template<> EIGEN_STRONG_INLINE Packet16uc pdiv<Packet16uc>(const Packet16uc& /*a*/, const Packet16uc& /*b*/)
+{
+ eigen_assert(false && "packet integer division are not supported by NEON");
+ return pset1<Packet16uc>(0);
+}
+template<> EIGEN_STRONG_INLINE Packet4s pdiv<Packet4s>(const Packet4s& /*a*/, const Packet4s& /*b*/)
+{
+ eigen_assert(false && "packet integer division are not supported by NEON");
+ return pset1<Packet4s>(0);
+}
+template<> EIGEN_STRONG_INLINE Packet8s pdiv<Packet8s>(const Packet8s& /*a*/, const Packet8s& /*b*/)
+{
+ eigen_assert(false && "packet integer division are not supported by NEON");
+ return pset1<Packet8s>(0);
+}
+template<> EIGEN_STRONG_INLINE Packet4us pdiv<Packet4us>(const Packet4us& /*a*/, const Packet4us& /*b*/)
+{
+ eigen_assert(false && "packet integer division are not supported by NEON");
+ return pset1<Packet4us>(0);
+}
+template<> EIGEN_STRONG_INLINE Packet8us pdiv<Packet8us>(const Packet8us& /*a*/, const Packet8us& /*b*/)
+{
+ eigen_assert(false && "packet integer division are not supported by NEON");
+ return pset1<Packet8us>(0);
+}
+template<> EIGEN_STRONG_INLINE Packet2i pdiv<Packet2i>(const Packet2i& /*a*/, const Packet2i& /*b*/)
+{
+ eigen_assert(false && "packet integer division are not supported by NEON");
+ return pset1<Packet2i>(0);
+}
+template<> EIGEN_STRONG_INLINE Packet4i pdiv<Packet4i>(const Packet4i& /*a*/, const Packet4i& /*b*/)
+{
+ eigen_assert(false && "packet integer division are not supported by NEON");
+ return pset1<Packet4i>(0);
+}
+template<> EIGEN_STRONG_INLINE Packet2ui pdiv<Packet2ui>(const Packet2ui& /*a*/, const Packet2ui& /*b*/)
+{
+ eigen_assert(false && "packet integer division are not supported by NEON");
+ return pset1<Packet2ui>(0);
+}
+template<> EIGEN_STRONG_INLINE Packet4ui pdiv<Packet4ui>(const Packet4ui& /*a*/, const Packet4ui& /*b*/)
+{
+ eigen_assert(false && "packet integer division are not supported by NEON");
+ return pset1<Packet4ui>(0);
+}
+template<> EIGEN_STRONG_INLINE Packet2l pdiv<Packet2l>(const Packet2l& /*a*/, const Packet2l& /*b*/)
+{
+ eigen_assert(false && "packet integer division are not supported by NEON");
+ return pset1<Packet2l>(0LL);
+}
+template<> EIGEN_STRONG_INLINE Packet2ul pdiv<Packet2ul>(const Packet2ul& /*a*/, const Packet2ul& /*b*/)
+{
+ eigen_assert(false && "packet integer division are not supported by NEON");
+ return pset1<Packet2ul>(0ULL);
+}
+
+
+#ifdef __ARM_FEATURE_FMA
+template<> EIGEN_STRONG_INLINE Packet4f pmadd(const Packet4f& a, const Packet4f& b, const Packet4f& c)
+{ return vfmaq_f32(c,a,b); }
+template<> EIGEN_STRONG_INLINE Packet2f pmadd(const Packet2f& a, const Packet2f& b, const Packet2f& c)
+{ return vfma_f32(c,a,b); }
+#else
+template<> EIGEN_STRONG_INLINE Packet4f pmadd(const Packet4f& a, const Packet4f& b, const Packet4f& c)
+{
+ return vmlaq_f32(c,a,b);
+}
+template<> EIGEN_STRONG_INLINE Packet2f pmadd(const Packet2f& a, const Packet2f& b, const Packet2f& c)
+{
+ return vmla_f32(c,a,b);
+}
+#endif
+
+// No FMA instruction for int, so use MLA unconditionally.
+template<> EIGEN_STRONG_INLINE Packet4c pmadd(const Packet4c& a, const Packet4c& b, const Packet4c& c)
+{
+ return vget_lane_s32(vreinterpret_s32_s8(vmla_s8(
+ vreinterpret_s8_s32(vdup_n_s32(c)),
+ vreinterpret_s8_s32(vdup_n_s32(a)),
+ vreinterpret_s8_s32(vdup_n_s32(b)))), 0);
+}
+template<> EIGEN_STRONG_INLINE Packet8c pmadd(const Packet8c& a, const Packet8c& b, const Packet8c& c)
+{ return vmla_s8(c,a,b); }
+template<> EIGEN_STRONG_INLINE Packet16c pmadd(const Packet16c& a, const Packet16c& b, const Packet16c& c)
+{ return vmlaq_s8(c,a,b); }
+template<> EIGEN_STRONG_INLINE Packet4uc pmadd(const Packet4uc& a, const Packet4uc& b, const Packet4uc& c)
+{
+ return vget_lane_u32(vreinterpret_u32_u8(vmla_u8(
+ vreinterpret_u8_u32(vdup_n_u32(c)),
+ vreinterpret_u8_u32(vdup_n_u32(a)),
+ vreinterpret_u8_u32(vdup_n_u32(b)))), 0);
+}
+template<> EIGEN_STRONG_INLINE Packet8uc pmadd(const Packet8uc& a, const Packet8uc& b, const Packet8uc& c)
+{ return vmla_u8(c,a,b); }
+template<> EIGEN_STRONG_INLINE Packet16uc pmadd(const Packet16uc& a, const Packet16uc& b, const Packet16uc& c)
+{ return vmlaq_u8(c,a,b); }
+template<> EIGEN_STRONG_INLINE Packet4s pmadd(const Packet4s& a, const Packet4s& b, const Packet4s& c)
+{ return vmla_s16(c,a,b); }
+template<> EIGEN_STRONG_INLINE Packet8s pmadd(const Packet8s& a, const Packet8s& b, const Packet8s& c)
+{ return vmlaq_s16(c,a,b); }
+template<> EIGEN_STRONG_INLINE Packet4us pmadd(const Packet4us& a, const Packet4us& b, const Packet4us& c)
+{ return vmla_u16(c,a,b); }
+template<> EIGEN_STRONG_INLINE Packet8us pmadd(const Packet8us& a, const Packet8us& b, const Packet8us& c)
+{ return vmlaq_u16(c,a,b); }
+template<> EIGEN_STRONG_INLINE Packet2i pmadd(const Packet2i& a, const Packet2i& b, const Packet2i& c)
+{ return vmla_s32(c,a,b); }
+template<> EIGEN_STRONG_INLINE Packet4i pmadd(const Packet4i& a, const Packet4i& b, const Packet4i& c)
+{ return vmlaq_s32(c,a,b); }
+template<> EIGEN_STRONG_INLINE Packet2ui pmadd(const Packet2ui& a, const Packet2ui& b, const Packet2ui& c)
+{ return vmla_u32(c,a,b); }
+template<> EIGEN_STRONG_INLINE Packet4ui pmadd(const Packet4ui& a, const Packet4ui& b, const Packet4ui& c)
+{ return vmlaq_u32(c,a,b); }
+
+template<> EIGEN_STRONG_INLINE Packet2f pabsdiff<Packet2f>(const Packet2f& a, const Packet2f& b)
+{ return vabd_f32(a,b); }
+template<> EIGEN_STRONG_INLINE Packet4f pabsdiff<Packet4f>(const Packet4f& a, const Packet4f& b)
+{ return vabdq_f32(a,b); }
+template<> EIGEN_STRONG_INLINE Packet4c pabsdiff<Packet4c>(const Packet4c& a, const Packet4c& b)
+{
+ return vget_lane_s32(vreinterpret_s32_s8(vabd_s8(
+ vreinterpret_s8_s32(vdup_n_s32(a)),
+ vreinterpret_s8_s32(vdup_n_s32(b)))), 0);
+}
+template<> EIGEN_STRONG_INLINE Packet8c pabsdiff<Packet8c>(const Packet8c& a, const Packet8c& b)
+{ return vabd_s8(a,b); }
+template<> EIGEN_STRONG_INLINE Packet16c pabsdiff<Packet16c>(const Packet16c& a, const Packet16c& b)
+{ return vabdq_s8(a,b); }
+template<> EIGEN_STRONG_INLINE Packet4uc pabsdiff<Packet4uc>(const Packet4uc& a, const Packet4uc& b)
+{
+ return vget_lane_u32(vreinterpret_u32_u8(vabd_u8(
+ vreinterpret_u8_u32(vdup_n_u32(a)),
+ vreinterpret_u8_u32(vdup_n_u32(b)))), 0);
+}
+template<> EIGEN_STRONG_INLINE Packet8uc pabsdiff<Packet8uc>(const Packet8uc& a, const Packet8uc& b)
+{ return vabd_u8(a,b); }
+template<> EIGEN_STRONG_INLINE Packet16uc pabsdiff<Packet16uc>(const Packet16uc& a, const Packet16uc& b)
+{ return vabdq_u8(a,b); }
+template<> EIGEN_STRONG_INLINE Packet4s pabsdiff<Packet4s>(const Packet4s& a, const Packet4s& b)
+{ return vabd_s16(a,b); }
+template<> EIGEN_STRONG_INLINE Packet8s pabsdiff<Packet8s>(const Packet8s& a, const Packet8s& b)
+{ return vabdq_s16(a,b); }
+template<> EIGEN_STRONG_INLINE Packet4us pabsdiff<Packet4us>(const Packet4us& a, const Packet4us& b)
+{ return vabd_u16(a,b); }
+template<> EIGEN_STRONG_INLINE Packet8us pabsdiff<Packet8us>(const Packet8us& a, const Packet8us& b)
+{ return vabdq_u16(a,b); }
+template<> EIGEN_STRONG_INLINE Packet2i pabsdiff<Packet2i>(const Packet2i& a, const Packet2i& b)
+{ return vabd_s32(a,b); }
+template<> EIGEN_STRONG_INLINE Packet4i pabsdiff<Packet4i>(const Packet4i& a, const Packet4i& b)
+{ return vabdq_s32(a,b); }
+template<> EIGEN_STRONG_INLINE Packet2ui pabsdiff<Packet2ui>(const Packet2ui& a, const Packet2ui& b)
+{ return vabd_u32(a,b); }
+template<> EIGEN_STRONG_INLINE Packet4ui pabsdiff<Packet4ui>(const Packet4ui& a, const Packet4ui& b)
+{ return vabdq_u32(a,b); }
+
+template<> EIGEN_STRONG_INLINE Packet2f pmin<Packet2f>(const Packet2f& a, const Packet2f& b) { return vmin_f32(a,b); }
+template<> EIGEN_STRONG_INLINE Packet4f pmin<Packet4f>(const Packet4f& a, const Packet4f& b) { return vminq_f32(a,b); }
+
+#ifdef __ARM_FEATURE_NUMERIC_MAXMIN
+// numeric max and min are only available if ARM_FEATURE_NUMERIC_MAXMIN is defined (which can only be the case for Armv8 systems).
+template<> EIGEN_STRONG_INLINE Packet4f pmin<PropagateNumbers, Packet4f>(const Packet4f& a, const Packet4f& b) { return vminnmq_f32(a, b); }
+template<> EIGEN_STRONG_INLINE Packet2f pmin<PropagateNumbers, Packet2f>(const Packet2f& a, const Packet2f& b) { return vminnm_f32(a, b); }
+#endif
+
+template<> EIGEN_STRONG_INLINE Packet4f pmin<PropagateNaN, Packet4f>(const Packet4f& a, const Packet4f& b) { return pmin<Packet4f>(a, b); }
+
+template<> EIGEN_STRONG_INLINE Packet2f pmin<PropagateNaN, Packet2f>(const Packet2f& a, const Packet2f& b) { return pmin<Packet2f>(a, b); }
+
+template<> EIGEN_STRONG_INLINE Packet4c pmin<Packet4c>(const Packet4c& a, const Packet4c& b)
+{
+ return vget_lane_s32(vreinterpret_s32_s8(vmin_s8(
+ vreinterpret_s8_s32(vdup_n_s32(a)),
+ vreinterpret_s8_s32(vdup_n_s32(b)))), 0);
+}
+template<> EIGEN_STRONG_INLINE Packet8c pmin<Packet8c>(const Packet8c& a, const Packet8c& b) { return vmin_s8(a,b); }
+template<> EIGEN_STRONG_INLINE Packet16c pmin<Packet16c>(const Packet16c& a, const Packet16c& b) { return vminq_s8(a,b); }
+template<> EIGEN_STRONG_INLINE Packet4uc pmin<Packet4uc>(const Packet4uc& a, const Packet4uc& b)
+{
+ return vget_lane_u32(vreinterpret_u32_u8(vmin_u8(
+ vreinterpret_u8_u32(vdup_n_u32(a)),
+ vreinterpret_u8_u32(vdup_n_u32(b)))), 0);
+}
+template<> EIGEN_STRONG_INLINE Packet8uc pmin<Packet8uc>(const Packet8uc& a, const Packet8uc& b) { return vmin_u8(a,b); }
+template<> EIGEN_STRONG_INLINE Packet16uc pmin<Packet16uc>(const Packet16uc& a, const Packet16uc& b) { return vminq_u8(a,b); }
+template<> EIGEN_STRONG_INLINE Packet4s pmin<Packet4s>(const Packet4s& a, const Packet4s& b) { return vmin_s16(a,b); }
+template<> EIGEN_STRONG_INLINE Packet8s pmin<Packet8s>(const Packet8s& a, const Packet8s& b) { return vminq_s16(a,b); }
+template<> EIGEN_STRONG_INLINE Packet4us pmin<Packet4us>(const Packet4us& a, const Packet4us& b) { return vmin_u16(a,b); }
+template<> EIGEN_STRONG_INLINE Packet8us pmin<Packet8us>(const Packet8us& a, const Packet8us& b) { return vminq_u16(a,b); }
+template<> EIGEN_STRONG_INLINE Packet2i pmin<Packet2i>(const Packet2i& a, const Packet2i& b) { return vmin_s32(a,b); }
+template<> EIGEN_STRONG_INLINE Packet4i pmin<Packet4i>(const Packet4i& a, const Packet4i& b) { return vminq_s32(a,b); }
+template<> EIGEN_STRONG_INLINE Packet2ui pmin<Packet2ui>(const Packet2ui& a, const Packet2ui& b) { return vmin_u32(a,b); }
+template<> EIGEN_STRONG_INLINE Packet4ui pmin<Packet4ui>(const Packet4ui& a, const Packet4ui& b) { return vminq_u32(a,b); }
+template<> EIGEN_STRONG_INLINE Packet2l pmin<Packet2l>(const Packet2l& a, const Packet2l& b) {
+ return vcombine_s64(
+ vdup_n_s64((std::min)(vgetq_lane_s64(a, 0), vgetq_lane_s64(b, 0))),
+ vdup_n_s64((std::min)(vgetq_lane_s64(a, 1), vgetq_lane_s64(b, 1))));
+}
+template<> EIGEN_STRONG_INLINE Packet2ul pmin<Packet2ul>(const Packet2ul& a, const Packet2ul& b) {
+ return vcombine_u64(
+ vdup_n_u64((std::min)(vgetq_lane_u64(a, 0), vgetq_lane_u64(b, 0))),
+ vdup_n_u64((std::min)(vgetq_lane_u64(a, 1), vgetq_lane_u64(b, 1))));
+}
+
+template<> EIGEN_STRONG_INLINE Packet2f pmax<Packet2f>(const Packet2f& a, const Packet2f& b) { return vmax_f32(a,b); }
+template<> EIGEN_STRONG_INLINE Packet4f pmax<Packet4f>(const Packet4f& a, const Packet4f& b) { return vmaxq_f32(a,b); }
+
+#ifdef __ARM_FEATURE_NUMERIC_MAXMIN
+// numeric max and min are only available if ARM_FEATURE_NUMERIC_MAXMIN is defined (which can only be the case for Armv8 systems).
+template<> EIGEN_STRONG_INLINE Packet4f pmax<PropagateNumbers, Packet4f>(const Packet4f& a, const Packet4f& b) { return vmaxnmq_f32(a, b); }
+template<> EIGEN_STRONG_INLINE Packet2f pmax<PropagateNumbers, Packet2f>(const Packet2f& a, const Packet2f& b) { return vmaxnm_f32(a, b); }
+#endif
+
+template<> EIGEN_STRONG_INLINE Packet4f pmax<PropagateNaN, Packet4f>(const Packet4f& a, const Packet4f& b) { return pmax<Packet4f>(a, b); }
+
+template<> EIGEN_STRONG_INLINE Packet2f pmax<PropagateNaN, Packet2f>(const Packet2f& a, const Packet2f& b) { return pmax<Packet2f>(a, b); }
+
+template<> EIGEN_STRONG_INLINE Packet4c pmax<Packet4c>(const Packet4c& a, const Packet4c& b)
+{
+ return vget_lane_s32(vreinterpret_s32_s8(vmax_s8(
+ vreinterpret_s8_s32(vdup_n_s32(a)),
+ vreinterpret_s8_s32(vdup_n_s32(b)))), 0);
+}
+template<> EIGEN_STRONG_INLINE Packet8c pmax<Packet8c>(const Packet8c& a, const Packet8c& b) { return vmax_s8(a,b); }
+template<> EIGEN_STRONG_INLINE Packet16c pmax<Packet16c>(const Packet16c& a, const Packet16c& b) { return vmaxq_s8(a,b); }
+template<> EIGEN_STRONG_INLINE Packet4uc pmax<Packet4uc>(const Packet4uc& a, const Packet4uc& b)
+{
+ return vget_lane_u32(vreinterpret_u32_u8(vmax_u8(
+ vreinterpret_u8_u32(vdup_n_u32(a)),
+ vreinterpret_u8_u32(vdup_n_u32(b)))), 0);
+}
+template<> EIGEN_STRONG_INLINE Packet8uc pmax<Packet8uc>(const Packet8uc& a, const Packet8uc& b) { return vmax_u8(a,b); }
+template<> EIGEN_STRONG_INLINE Packet16uc pmax<Packet16uc>(const Packet16uc& a, const Packet16uc& b) { return vmaxq_u8(a,b); }
+template<> EIGEN_STRONG_INLINE Packet4s pmax<Packet4s>(const Packet4s& a, const Packet4s& b) { return vmax_s16(a,b); }
+template<> EIGEN_STRONG_INLINE Packet8s pmax<Packet8s>(const Packet8s& a, const Packet8s& b) { return vmaxq_s16(a,b); }
+template<> EIGEN_STRONG_INLINE Packet4us pmax<Packet4us>(const Packet4us& a, const Packet4us& b) { return vmax_u16(a,b); }
+template<> EIGEN_STRONG_INLINE Packet8us pmax<Packet8us>(const Packet8us& a, const Packet8us& b) { return vmaxq_u16(a,b); }
+template<> EIGEN_STRONG_INLINE Packet2i pmax<Packet2i>(const Packet2i& a, const Packet2i& b) { return vmax_s32(a,b); }
+template<> EIGEN_STRONG_INLINE Packet4i pmax<Packet4i>(const Packet4i& a, const Packet4i& b) { return vmaxq_s32(a,b); }
+template<> EIGEN_STRONG_INLINE Packet2ui pmax<Packet2ui>(const Packet2ui& a, const Packet2ui& b) { return vmax_u32(a,b); }
+template<> EIGEN_STRONG_INLINE Packet4ui pmax<Packet4ui>(const Packet4ui& a, const Packet4ui& b) { return vmaxq_u32(a,b); }
+template<> EIGEN_STRONG_INLINE Packet2l pmax<Packet2l>(const Packet2l& a, const Packet2l& b) {
+ return vcombine_s64(
+ vdup_n_s64((std::max)(vgetq_lane_s64(a, 0), vgetq_lane_s64(b, 0))),
+ vdup_n_s64((std::max)(vgetq_lane_s64(a, 1), vgetq_lane_s64(b, 1))));
+}
+template<> EIGEN_STRONG_INLINE Packet2ul pmax<Packet2ul>(const Packet2ul& a, const Packet2ul& b) {
+ return vcombine_u64(
+ vdup_n_u64((std::max)(vgetq_lane_u64(a, 0), vgetq_lane_u64(b, 0))),
+ vdup_n_u64((std::max)(vgetq_lane_u64(a, 1), vgetq_lane_u64(b, 1))));
+}
+
+template<> EIGEN_STRONG_INLINE Packet2f pcmp_le<Packet2f>(const Packet2f& a, const Packet2f& b)
+{ return vreinterpret_f32_u32(vcle_f32(a,b)); }
+template<> EIGEN_STRONG_INLINE Packet4f pcmp_le<Packet4f>(const Packet4f& a, const Packet4f& b)
+{ return vreinterpretq_f32_u32(vcleq_f32(a,b)); }
+template<> EIGEN_STRONG_INLINE Packet4c pcmp_le<Packet4c>(const Packet4c& a, const Packet4c& b)
+{
+ return vget_lane_s32(vreinterpret_s32_u8(vcle_s8(
+ vreinterpret_s8_s32(vdup_n_s32(a)),
+ vreinterpret_s8_s32(vdup_n_s32(b)))), 0);
+}
+template<> EIGEN_STRONG_INLINE Packet8c pcmp_le<Packet8c>(const Packet8c& a, const Packet8c& b)
+{ return vreinterpret_s8_u8(vcle_s8(a,b)); }
+template<> EIGEN_STRONG_INLINE Packet16c pcmp_le<Packet16c>(const Packet16c& a, const Packet16c& b)
+{ return vreinterpretq_s8_u8(vcleq_s8(a,b)); }
+template<> EIGEN_STRONG_INLINE Packet4uc pcmp_le<Packet4uc>(const Packet4uc& a, const Packet4uc& b)
+{
+ return vget_lane_u32(vreinterpret_u32_u8(vcle_u8(
+ vreinterpret_u8_u32(vdup_n_u32(a)),
+ vreinterpret_u8_u32(vdup_n_u32(b)))), 0);
+}
+template<> EIGEN_STRONG_INLINE Packet8uc pcmp_le<Packet8uc>(const Packet8uc& a, const Packet8uc& b)
+{ return vcle_u8(a,b); }
+template<> EIGEN_STRONG_INLINE Packet16uc pcmp_le<Packet16uc>(const Packet16uc& a, const Packet16uc& b)
+{ return vcleq_u8(a,b); }
+template<> EIGEN_STRONG_INLINE Packet4s pcmp_le<Packet4s>(const Packet4s& a, const Packet4s& b)
+{ return vreinterpret_s16_u16(vcle_s16(a,b)); }
+template<> EIGEN_STRONG_INLINE Packet8s pcmp_le<Packet8s>(const Packet8s& a, const Packet8s& b)
+{ return vreinterpretq_s16_u16(vcleq_s16(a,b)); }
+template<> EIGEN_STRONG_INLINE Packet4us pcmp_le<Packet4us>(const Packet4us& a, const Packet4us& b)
+{ return vcle_u16(a,b); }
+template<> EIGEN_STRONG_INLINE Packet8us pcmp_le<Packet8us>(const Packet8us& a, const Packet8us& b)
+{ return vcleq_u16(a,b); }
+template<> EIGEN_STRONG_INLINE Packet2i pcmp_le<Packet2i>(const Packet2i& a, const Packet2i& b)
+{ return vreinterpret_s32_u32(vcle_s32(a,b)); }
+template<> EIGEN_STRONG_INLINE Packet4i pcmp_le<Packet4i>(const Packet4i& a, const Packet4i& b)
+{ return vreinterpretq_s32_u32(vcleq_s32(a,b)); }
+template<> EIGEN_STRONG_INLINE Packet2ui pcmp_le<Packet2ui>(const Packet2ui& a, const Packet2ui& b)
+{ return vcle_u32(a,b); }
+template<> EIGEN_STRONG_INLINE Packet4ui pcmp_le<Packet4ui>(const Packet4ui& a, const Packet4ui& b)
+{ return vcleq_u32(a,b); }
+template<> EIGEN_STRONG_INLINE Packet2l pcmp_le<Packet2l>(const Packet2l& a, const Packet2l& b)
+{
+#if EIGEN_ARCH_ARM64
+ return vreinterpretq_s64_u64(vcleq_s64(a,b));
+#else
+ return vcombine_s64(
+ vdup_n_s64(vgetq_lane_s64(a, 0) <= vgetq_lane_s64(b, 0) ? numext::int64_t(-1) : 0),
+ vdup_n_s64(vgetq_lane_s64(a, 1) <= vgetq_lane_s64(b, 1) ? numext::int64_t(-1) : 0));
+#endif
+}
+template<> EIGEN_STRONG_INLINE Packet2ul pcmp_le<Packet2ul>(const Packet2ul& a, const Packet2ul& b)
+{
+#if EIGEN_ARCH_ARM64
+ return vcleq_u64(a,b);
+#else
+ return vcombine_u64(
+ vdup_n_u64(vgetq_lane_u64(a, 0) <= vgetq_lane_u64(b, 0) ? numext::uint64_t(-1) : 0),
+ vdup_n_u64(vgetq_lane_u64(a, 1) <= vgetq_lane_u64(b, 1) ? numext::uint64_t(-1) : 0));
+#endif
+}
+
+template<> EIGEN_STRONG_INLINE Packet2f pcmp_lt<Packet2f>(const Packet2f& a, const Packet2f& b)
+{ return vreinterpret_f32_u32(vclt_f32(a,b)); }
+template<> EIGEN_STRONG_INLINE Packet4f pcmp_lt<Packet4f>(const Packet4f& a, const Packet4f& b)
+{ return vreinterpretq_f32_u32(vcltq_f32(a,b)); }
+template<> EIGEN_STRONG_INLINE Packet4c pcmp_lt<Packet4c>(const Packet4c& a, const Packet4c& b)
+{
+ return vget_lane_s32(vreinterpret_s32_u8(vclt_s8(
+ vreinterpret_s8_s32(vdup_n_s32(a)),
+ vreinterpret_s8_s32(vdup_n_s32(b)))), 0);
+}
+template<> EIGEN_STRONG_INLINE Packet8c pcmp_lt<Packet8c>(const Packet8c& a, const Packet8c& b)
+{ return vreinterpret_s8_u8(vclt_s8(a,b)); }
+template<> EIGEN_STRONG_INLINE Packet16c pcmp_lt<Packet16c>(const Packet16c& a, const Packet16c& b)
+{ return vreinterpretq_s8_u8(vcltq_s8(a,b)); }
+template<> EIGEN_STRONG_INLINE Packet4uc pcmp_lt<Packet4uc>(const Packet4uc& a, const Packet4uc& b)
+{
+ return vget_lane_u32(vreinterpret_u32_u8(vclt_u8(
+ vreinterpret_u8_u32(vdup_n_u32(a)),
+ vreinterpret_u8_u32(vdup_n_u32(b)))), 0);
+}
+template<> EIGEN_STRONG_INLINE Packet8uc pcmp_lt<Packet8uc>(const Packet8uc& a, const Packet8uc& b)
+{ return vclt_u8(a,b); }
+template<> EIGEN_STRONG_INLINE Packet16uc pcmp_lt<Packet16uc>(const Packet16uc& a, const Packet16uc& b)
+{ return vcltq_u8(a,b); }
+template<> EIGEN_STRONG_INLINE Packet4s pcmp_lt<Packet4s>(const Packet4s& a, const Packet4s& b)
+{ return vreinterpret_s16_u16(vclt_s16(a,b)); }
+template<> EIGEN_STRONG_INLINE Packet8s pcmp_lt<Packet8s>(const Packet8s& a, const Packet8s& b)
+{ return vreinterpretq_s16_u16(vcltq_s16(a,b)); }
+template<> EIGEN_STRONG_INLINE Packet4us pcmp_lt<Packet4us>(const Packet4us& a, const Packet4us& b)
+{ return vclt_u16(a,b); }
+template<> EIGEN_STRONG_INLINE Packet8us pcmp_lt<Packet8us>(const Packet8us& a, const Packet8us& b)
+{ return vcltq_u16(a,b); }
+template<> EIGEN_STRONG_INLINE Packet2i pcmp_lt<Packet2i>(const Packet2i& a, const Packet2i& b)
+{ return vreinterpret_s32_u32(vclt_s32(a,b)); }
+template<> EIGEN_STRONG_INLINE Packet4i pcmp_lt<Packet4i>(const Packet4i& a, const Packet4i& b)
+{ return vreinterpretq_s32_u32(vcltq_s32(a,b)); }
+template<> EIGEN_STRONG_INLINE Packet2ui pcmp_lt<Packet2ui>(const Packet2ui& a, const Packet2ui& b)
+{ return vclt_u32(a,b); }
+template<> EIGEN_STRONG_INLINE Packet4ui pcmp_lt<Packet4ui>(const Packet4ui& a, const Packet4ui& b)
+{ return vcltq_u32(a,b); }
+template<> EIGEN_STRONG_INLINE Packet2l pcmp_lt<Packet2l>(const Packet2l& a, const Packet2l& b)
+{
+#if EIGEN_ARCH_ARM64
+ return vreinterpretq_s64_u64(vcltq_s64(a,b));
+#else
+ return vcombine_s64(
+ vdup_n_s64(vgetq_lane_s64(a, 0) < vgetq_lane_s64(b, 0) ? numext::int64_t(-1) : 0),
+ vdup_n_s64(vgetq_lane_s64(a, 1) < vgetq_lane_s64(b, 1) ? numext::int64_t(-1) : 0));
+#endif
+}
+template<> EIGEN_STRONG_INLINE Packet2ul pcmp_lt<Packet2ul>(const Packet2ul& a, const Packet2ul& b)
+{
+#if EIGEN_ARCH_ARM64
+ return vcltq_u64(a,b);
+#else
+ return vcombine_u64(
+ vdup_n_u64(vgetq_lane_u64(a, 0) < vgetq_lane_u64(b, 0) ? numext::uint64_t(-1) : 0),
+ vdup_n_u64(vgetq_lane_u64(a, 1) < vgetq_lane_u64(b, 1) ? numext::uint64_t(-1) : 0));
+#endif
+}
+
+template<> EIGEN_STRONG_INLINE Packet2f pcmp_eq<Packet2f>(const Packet2f& a, const Packet2f& b)
+{ return vreinterpret_f32_u32(vceq_f32(a,b)); }
+template<> EIGEN_STRONG_INLINE Packet4f pcmp_eq<Packet4f>(const Packet4f& a, const Packet4f& b)
+{ return vreinterpretq_f32_u32(vceqq_f32(a,b)); }
+template<> EIGEN_STRONG_INLINE Packet4c pcmp_eq<Packet4c>(const Packet4c& a, const Packet4c& b)
+{
+ return vget_lane_s32(vreinterpret_s32_u8(vceq_s8(
+ vreinterpret_s8_s32(vdup_n_s32(a)),
+ vreinterpret_s8_s32(vdup_n_s32(b)))), 0);
+}
+template<> EIGEN_STRONG_INLINE Packet8c pcmp_eq<Packet8c>(const Packet8c& a, const Packet8c& b)
+{ return vreinterpret_s8_u8(vceq_s8(a,b)); }
+template<> EIGEN_STRONG_INLINE Packet16c pcmp_eq<Packet16c>(const Packet16c& a, const Packet16c& b)
+{ return vreinterpretq_s8_u8(vceqq_s8(a,b)); }
+template<> EIGEN_STRONG_INLINE Packet4uc pcmp_eq<Packet4uc>(const Packet4uc& a, const Packet4uc& b)
+{
+ return vget_lane_u32(vreinterpret_u32_u8(vceq_u8(
+ vreinterpret_u8_u32(vdup_n_u32(a)),
+ vreinterpret_u8_u32(vdup_n_u32(b)))), 0);
+}
+template<> EIGEN_STRONG_INLINE Packet8uc pcmp_eq<Packet8uc>(const Packet8uc& a, const Packet8uc& b)
+{ return vceq_u8(a,b); }
+template<> EIGEN_STRONG_INLINE Packet16uc pcmp_eq<Packet16uc>(const Packet16uc& a, const Packet16uc& b)
+{ return vceqq_u8(a,b); }
+template<> EIGEN_STRONG_INLINE Packet4s pcmp_eq<Packet4s>(const Packet4s& a, const Packet4s& b)
+{ return vreinterpret_s16_u16(vceq_s16(a,b)); }
+template<> EIGEN_STRONG_INLINE Packet8s pcmp_eq<Packet8s>(const Packet8s& a, const Packet8s& b)
+{ return vreinterpretq_s16_u16(vceqq_s16(a,b)); }
+template<> EIGEN_STRONG_INLINE Packet4us pcmp_eq<Packet4us>(const Packet4us& a, const Packet4us& b)
+{ return vceq_u16(a,b); }
+template<> EIGEN_STRONG_INLINE Packet8us pcmp_eq<Packet8us>(const Packet8us& a, const Packet8us& b)
+{ return vceqq_u16(a,b); }
+template<> EIGEN_STRONG_INLINE Packet2i pcmp_eq<Packet2i>(const Packet2i& a, const Packet2i& b)
+{ return vreinterpret_s32_u32(vceq_s32(a,b)); }
+template<> EIGEN_STRONG_INLINE Packet4i pcmp_eq<Packet4i>(const Packet4i& a, const Packet4i& b)
+{ return vreinterpretq_s32_u32(vceqq_s32(a,b)); }
+template<> EIGEN_STRONG_INLINE Packet2ui pcmp_eq<Packet2ui>(const Packet2ui& a, const Packet2ui& b)
+{ return vceq_u32(a,b); }
+template<> EIGEN_STRONG_INLINE Packet4ui pcmp_eq<Packet4ui>(const Packet4ui& a, const Packet4ui& b)
+{ return vceqq_u32(a,b); }
+template<> EIGEN_STRONG_INLINE Packet2l pcmp_eq<Packet2l>(const Packet2l& a, const Packet2l& b)
+{
+#if EIGEN_ARCH_ARM64
+ return vreinterpretq_s64_u64(vceqq_s64(a,b));
+#else
+ return vcombine_s64(
+ vdup_n_s64(vgetq_lane_s64(a, 0) == vgetq_lane_s64(b, 0) ? numext::int64_t(-1) : 0),
+ vdup_n_s64(vgetq_lane_s64(a, 1) == vgetq_lane_s64(b, 1) ? numext::int64_t(-1) : 0));
+#endif
+}
+template<> EIGEN_STRONG_INLINE Packet2ul pcmp_eq<Packet2ul>(const Packet2ul& a, const Packet2ul& b)
+{
+#if EIGEN_ARCH_ARM64
+ return vceqq_u64(a,b);
+#else
+ return vcombine_u64(
+ vdup_n_u64(vgetq_lane_u64(a, 0) == vgetq_lane_u64(b, 0) ? numext::uint64_t(-1) : 0),
+ vdup_n_u64(vgetq_lane_u64(a, 1) == vgetq_lane_u64(b, 1) ? numext::uint64_t(-1) : 0));
+#endif
+}
+
+template<> EIGEN_STRONG_INLINE Packet2f pcmp_lt_or_nan<Packet2f>(const Packet2f& a, const Packet2f& b)
+{ return vreinterpret_f32_u32(vmvn_u32(vcge_f32(a,b))); }
+template<> EIGEN_STRONG_INLINE Packet4f pcmp_lt_or_nan<Packet4f>(const Packet4f& a, const Packet4f& b)
+{ return vreinterpretq_f32_u32(vmvnq_u32(vcgeq_f32(a,b))); }
+
+// Logical Operations are not supported for float, so we have to reinterpret casts using NEON intrinsics
+template<> EIGEN_STRONG_INLINE Packet2f pand<Packet2f>(const Packet2f& a, const Packet2f& b)
+{ return vreinterpret_f32_u32(vand_u32(vreinterpret_u32_f32(a),vreinterpret_u32_f32(b))); }
+template<> EIGEN_STRONG_INLINE Packet4f pand<Packet4f>(const Packet4f& a, const Packet4f& b)
+{ return vreinterpretq_f32_u32(vandq_u32(vreinterpretq_u32_f32(a),vreinterpretq_u32_f32(b))); }
+template<> EIGEN_STRONG_INLINE Packet4c pand<Packet4c>(const Packet4c& a, const Packet4c& b)
+{ return a & b; }
+template<> EIGEN_STRONG_INLINE Packet8c pand<Packet8c>(const Packet8c& a, const Packet8c& b)
+{ return vand_s8(a,b); }
+template<> EIGEN_STRONG_INLINE Packet16c pand<Packet16c>(const Packet16c& a, const Packet16c& b)
+{ return vandq_s8(a,b); }
+template<> EIGEN_STRONG_INLINE Packet4uc pand<Packet4uc>(const Packet4uc& a, const Packet4uc& b)
+{ return a & b; }
+template<> EIGEN_STRONG_INLINE Packet8uc pand<Packet8uc>(const Packet8uc& a, const Packet8uc& b)
+{ return vand_u8(a,b); }
+template<> EIGEN_STRONG_INLINE Packet16uc pand<Packet16uc>(const Packet16uc& a, const Packet16uc& b)
+{ return vandq_u8(a,b); }
+template<> EIGEN_STRONG_INLINE Packet4s pand<Packet4s>(const Packet4s& a, const Packet4s& b) { return vand_s16(a,b); }
+template<> EIGEN_STRONG_INLINE Packet8s pand<Packet8s>(const Packet8s& a, const Packet8s& b) { return vandq_s16(a,b); }
+template<> EIGEN_STRONG_INLINE Packet4us pand<Packet4us>(const Packet4us& a, const Packet4us& b)
+{ return vand_u16(a,b); }
+template<> EIGEN_STRONG_INLINE Packet8us pand<Packet8us>(const Packet8us& a, const Packet8us& b)
+{ return vandq_u16(a,b); }
+template<> EIGEN_STRONG_INLINE Packet2i pand<Packet2i>(const Packet2i& a, const Packet2i& b) { return vand_s32(a,b); }
+template<> EIGEN_STRONG_INLINE Packet4i pand<Packet4i>(const Packet4i& a, const Packet4i& b) { return vandq_s32(a,b); }
+template<> EIGEN_STRONG_INLINE Packet2ui pand<Packet2ui>(const Packet2ui& a, const Packet2ui& b)
+{ return vand_u32(a,b); }
+template<> EIGEN_STRONG_INLINE Packet4ui pand<Packet4ui>(const Packet4ui& a, const Packet4ui& b)
+{ return vandq_u32(a,b); }
+template<> EIGEN_STRONG_INLINE Packet2l pand<Packet2l>(const Packet2l& a, const Packet2l& b) { return vandq_s64(a,b); }
+template<> EIGEN_STRONG_INLINE Packet2ul pand<Packet2ul>(const Packet2ul& a, const Packet2ul& b)
+{ return vandq_u64(a,b); }
+
+template<> EIGEN_STRONG_INLINE Packet2f por<Packet2f>(const Packet2f& a, const Packet2f& b)
+{ return vreinterpret_f32_u32(vorr_u32(vreinterpret_u32_f32(a),vreinterpret_u32_f32(b))); }
+template<> EIGEN_STRONG_INLINE Packet4f por<Packet4f>(const Packet4f& a, const Packet4f& b)
+{ return vreinterpretq_f32_u32(vorrq_u32(vreinterpretq_u32_f32(a),vreinterpretq_u32_f32(b))); }
+template<> EIGEN_STRONG_INLINE Packet4c por<Packet4c>(const Packet4c& a, const Packet4c& b)
+{ return a | b; }
+template<> EIGEN_STRONG_INLINE Packet8c por<Packet8c>(const Packet8c& a, const Packet8c& b) { return vorr_s8(a,b); }
+template<> EIGEN_STRONG_INLINE Packet16c por<Packet16c>(const Packet16c& a, const Packet16c& b)
+{ return vorrq_s8(a,b); }
+template<> EIGEN_STRONG_INLINE Packet4uc por<Packet4uc>(const Packet4uc& a, const Packet4uc& b)
+{ return a | b; }
+template<> EIGEN_STRONG_INLINE Packet8uc por<Packet8uc>(const Packet8uc& a, const Packet8uc& b)
+{ return vorr_u8(a,b); }
+template<> EIGEN_STRONG_INLINE Packet16uc por<Packet16uc>(const Packet16uc& a, const Packet16uc& b)
+{ return vorrq_u8(a,b); }
+template<> EIGEN_STRONG_INLINE Packet4s por<Packet4s>(const Packet4s& a, const Packet4s& b)
+{ return vorr_s16(a,b); }
+template<> EIGEN_STRONG_INLINE Packet8s por<Packet8s>(const Packet8s& a, const Packet8s& b)
+{ return vorrq_s16(a,b); }
+template<> EIGEN_STRONG_INLINE Packet4us por<Packet4us>(const Packet4us& a, const Packet4us& b)
+{ return vorr_u16(a,b); }
+template<> EIGEN_STRONG_INLINE Packet8us por<Packet8us>(const Packet8us& a, const Packet8us& b)
+{ return vorrq_u16(a,b); }
+template<> EIGEN_STRONG_INLINE Packet2i por<Packet2i>(const Packet2i& a, const Packet2i& b) { return vorr_s32(a,b); }
+template<> EIGEN_STRONG_INLINE Packet4i por<Packet4i>(const Packet4i& a, const Packet4i& b) { return vorrq_s32(a,b); }
+template<> EIGEN_STRONG_INLINE Packet2ui por<Packet2ui>(const Packet2ui& a, const Packet2ui& b)
+{ return vorr_u32(a,b); }
+template<> EIGEN_STRONG_INLINE Packet4ui por<Packet4ui>(const Packet4ui& a, const Packet4ui& b)
+{ return vorrq_u32(a,b); }
+template<> EIGEN_STRONG_INLINE Packet2l por<Packet2l>(const Packet2l& a, const Packet2l& b)
+{ return vorrq_s64(a,b); }
+template<> EIGEN_STRONG_INLINE Packet2ul por<Packet2ul>(const Packet2ul& a, const Packet2ul& b)
+{ return vorrq_u64(a,b); }
+
+template<> EIGEN_STRONG_INLINE Packet2f pxor<Packet2f>(const Packet2f& a, const Packet2f& b)
+{ return vreinterpret_f32_u32(veor_u32(vreinterpret_u32_f32(a),vreinterpret_u32_f32(b))); }
+template<> EIGEN_STRONG_INLINE Packet4f pxor<Packet4f>(const Packet4f& a, const Packet4f& b)
+{ return vreinterpretq_f32_u32(veorq_u32(vreinterpretq_u32_f32(a),vreinterpretq_u32_f32(b))); }
+template<> EIGEN_STRONG_INLINE Packet4c pxor<Packet4c>(const Packet4c& a, const Packet4c& b)
+{ return a ^ b; }
+template<> EIGEN_STRONG_INLINE Packet8c pxor<Packet8c>(const Packet8c& a, const Packet8c& b)
+{ return veor_s8(a,b); }
+template<> EIGEN_STRONG_INLINE Packet16c pxor<Packet16c>(const Packet16c& a, const Packet16c& b)
+{ return veorq_s8(a,b); }
+template<> EIGEN_STRONG_INLINE Packet4uc pxor<Packet4uc>(const Packet4uc& a, const Packet4uc& b)
+{ return a ^ b; }
+template<> EIGEN_STRONG_INLINE Packet8uc pxor<Packet8uc>(const Packet8uc& a, const Packet8uc& b)
+{ return veor_u8(a,b); }
+template<> EIGEN_STRONG_INLINE Packet16uc pxor<Packet16uc>(const Packet16uc& a, const Packet16uc& b)
+{ return veorq_u8(a,b); }
+template<> EIGEN_STRONG_INLINE Packet4s pxor<Packet4s>(const Packet4s& a, const Packet4s& b) { return veor_s16(a,b); }
+template<> EIGEN_STRONG_INLINE Packet8s pxor<Packet8s>(const Packet8s& a, const Packet8s& b) { return veorq_s16(a,b); }
+template<> EIGEN_STRONG_INLINE Packet4us pxor<Packet4us>(const Packet4us& a, const Packet4us& b)
+{ return veor_u16(a,b); }
+template<> EIGEN_STRONG_INLINE Packet8us pxor<Packet8us>(const Packet8us& a, const Packet8us& b)
+{ return veorq_u16(a,b); }
+template<> EIGEN_STRONG_INLINE Packet2i pxor<Packet2i>(const Packet2i& a, const Packet2i& b) { return veor_s32(a,b); }
+template<> EIGEN_STRONG_INLINE Packet4i pxor<Packet4i>(const Packet4i& a, const Packet4i& b) { return veorq_s32(a,b); }
+template<> EIGEN_STRONG_INLINE Packet2ui pxor<Packet2ui>(const Packet2ui& a, const Packet2ui& b)
+{ return veor_u32(a,b); }
+template<> EIGEN_STRONG_INLINE Packet4ui pxor<Packet4ui>(const Packet4ui& a, const Packet4ui& b)
+{ return veorq_u32(a,b); }
+template<> EIGEN_STRONG_INLINE Packet2l pxor<Packet2l>(const Packet2l& a, const Packet2l& b)
+{ return veorq_s64(a,b); }
+template<> EIGEN_STRONG_INLINE Packet2ul pxor<Packet2ul>(const Packet2ul& a, const Packet2ul& b)
+{ return veorq_u64(a,b); }
+
+template<> EIGEN_STRONG_INLINE Packet2f pandnot<Packet2f>(const Packet2f& a, const Packet2f& b)
+{ return vreinterpret_f32_u32(vbic_u32(vreinterpret_u32_f32(a),vreinterpret_u32_f32(b))); }
+template<> EIGEN_STRONG_INLINE Packet4f pandnot<Packet4f>(const Packet4f& a, const Packet4f& b)
+{ return vreinterpretq_f32_u32(vbicq_u32(vreinterpretq_u32_f32(a),vreinterpretq_u32_f32(b))); }
+template<> EIGEN_STRONG_INLINE Packet4c pandnot<Packet4c>(const Packet4c& a, const Packet4c& b)
+{ return a & ~b; }
+template<> EIGEN_STRONG_INLINE Packet8c pandnot<Packet8c>(const Packet8c& a, const Packet8c& b) { return vbic_s8(a,b); }
+template<> EIGEN_STRONG_INLINE Packet16c pandnot<Packet16c>(const Packet16c& a, const Packet16c& b) { return vbicq_s8(a,b); }
+template<> EIGEN_STRONG_INLINE Packet4uc pandnot<Packet4uc>(const Packet4uc& a, const Packet4uc& b)
+{ return a & ~b; }
+template<> EIGEN_STRONG_INLINE Packet8uc pandnot<Packet8uc>(const Packet8uc& a, const Packet8uc& b)
+{ return vbic_u8(a,b); }
+template<> EIGEN_STRONG_INLINE Packet16uc pandnot<Packet16uc>(const Packet16uc& a, const Packet16uc& b)
+{ return vbicq_u8(a,b); }
+template<> EIGEN_STRONG_INLINE Packet4s pandnot<Packet4s>(const Packet4s& a, const Packet4s& b)
+{ return vbic_s16(a,b); }
+template<> EIGEN_STRONG_INLINE Packet8s pandnot<Packet8s>(const Packet8s& a, const Packet8s& b)
+{ return vbicq_s16(a,b); }
+template<> EIGEN_STRONG_INLINE Packet4us pandnot<Packet4us>(const Packet4us& a, const Packet4us& b)
+{ return vbic_u16(a,b); }
+template<> EIGEN_STRONG_INLINE Packet8us pandnot<Packet8us>(const Packet8us& a, const Packet8us& b)
+{ return vbicq_u16(a,b); }
+template<> EIGEN_STRONG_INLINE Packet2i pandnot<Packet2i>(const Packet2i& a, const Packet2i& b)
+{ return vbic_s32(a,b); }
+template<> EIGEN_STRONG_INLINE Packet4i pandnot<Packet4i>(const Packet4i& a, const Packet4i& b)
+{ return vbicq_s32(a,b); }
+template<> EIGEN_STRONG_INLINE Packet2ui pandnot<Packet2ui>(const Packet2ui& a, const Packet2ui& b)
+{ return vbic_u32(a,b); }
+template<> EIGEN_STRONG_INLINE Packet4ui pandnot<Packet4ui>(const Packet4ui& a, const Packet4ui& b)
+{ return vbicq_u32(a,b); }
+template<> EIGEN_STRONG_INLINE Packet2l pandnot<Packet2l>(const Packet2l& a, const Packet2l& b)
+{ return vbicq_s64(a,b); }
+template<> EIGEN_STRONG_INLINE Packet2ul pandnot<Packet2ul>(const Packet2ul& a, const Packet2ul& b)
+{ return vbicq_u64(a,b); }
+
+
+template<int N> EIGEN_STRONG_INLINE Packet4c parithmetic_shift_right(Packet4c& a)
+{ return vget_lane_s32(vreinterpret_s32_s8(vshr_n_s8(vreinterpret_s8_s32(vdup_n_s32(a)), N)), 0); }
+template<int N> EIGEN_STRONG_INLINE Packet8c parithmetic_shift_right(Packet8c a) { return vshr_n_s8(a,N); }
+template<int N> EIGEN_STRONG_INLINE Packet16c parithmetic_shift_right(Packet16c a) { return vshrq_n_s8(a,N); }
+template<int N> EIGEN_STRONG_INLINE Packet4uc parithmetic_shift_right(Packet4uc& a)
+{ return vget_lane_u32(vreinterpret_u32_u8(vshr_n_u8(vreinterpret_u8_u32(vdup_n_u32(a)), N)), 0); }
+template<int N> EIGEN_STRONG_INLINE Packet8uc parithmetic_shift_right(Packet8uc a) { return vshr_n_u8(a,N); }
+template<int N> EIGEN_STRONG_INLINE Packet16uc parithmetic_shift_right(Packet16uc a) { return vshrq_n_u8(a,N); }
+template<int N> EIGEN_STRONG_INLINE Packet4s parithmetic_shift_right(Packet4s a) { return vshr_n_s16(a,N); }
+template<int N> EIGEN_STRONG_INLINE Packet8s parithmetic_shift_right(Packet8s a) { return vshrq_n_s16(a,N); }
+template<int N> EIGEN_STRONG_INLINE Packet4us parithmetic_shift_right(Packet4us a) { return vshr_n_u16(a,N); }
+template<int N> EIGEN_STRONG_INLINE Packet8us parithmetic_shift_right(Packet8us a) { return vshrq_n_u16(a,N); }
+template<int N> EIGEN_STRONG_INLINE Packet2i parithmetic_shift_right(Packet2i a) { return vshr_n_s32(a,N); }
+template<int N> EIGEN_STRONG_INLINE Packet4i parithmetic_shift_right(Packet4i a) { return vshrq_n_s32(a,N); }
+template<int N> EIGEN_STRONG_INLINE Packet2ui parithmetic_shift_right(Packet2ui a) { return vshr_n_u32(a,N); }
+template<int N> EIGEN_STRONG_INLINE Packet4ui parithmetic_shift_right(Packet4ui a) { return vshrq_n_u32(a,N); }
+template<int N> EIGEN_STRONG_INLINE Packet2l parithmetic_shift_right(Packet2l a) { return vshrq_n_s64(a,N); }
+template<int N> EIGEN_STRONG_INLINE Packet2ul parithmetic_shift_right(Packet2ul a) { return vshrq_n_u64(a,N); }
+
+template<int N> EIGEN_STRONG_INLINE Packet4c plogical_shift_right(Packet4c& a)
+{ return vget_lane_s32(vreinterpret_s32_u8(vshr_n_u8(vreinterpret_u8_s32(vdup_n_s32(a)), N)), 0); }
+template<int N> EIGEN_STRONG_INLINE Packet8c plogical_shift_right(Packet8c a)
+{ return vreinterpret_s8_u8(vshr_n_u8(vreinterpret_u8_s8(a),N)); }
+template<int N> EIGEN_STRONG_INLINE Packet16c plogical_shift_right(Packet16c a)
+{ return vreinterpretq_s8_u8(vshrq_n_u8(vreinterpretq_u8_s8(a),N)); }
+template<int N> EIGEN_STRONG_INLINE Packet4uc plogical_shift_right(Packet4uc& a)
+{ return vget_lane_u32(vreinterpret_u32_s8(vshr_n_s8(vreinterpret_s8_u32(vdup_n_u32(a)), N)), 0); }
+template<int N> EIGEN_STRONG_INLINE Packet8uc plogical_shift_right(Packet8uc a) { return vshr_n_u8(a,N); }
+template<int N> EIGEN_STRONG_INLINE Packet16uc plogical_shift_right(Packet16uc a) { return vshrq_n_u8(a,N); }
+template<int N> EIGEN_STRONG_INLINE Packet4s plogical_shift_right(Packet4s a)
+{ return vreinterpret_s16_u16(vshr_n_u16(vreinterpret_u16_s16(a),N)); }
+template<int N> EIGEN_STRONG_INLINE Packet8s plogical_shift_right(Packet8s a)
+{ return vreinterpretq_s16_u16(vshrq_n_u16(vreinterpretq_u16_s16(a),N)); }
+template<int N> EIGEN_STRONG_INLINE Packet4us plogical_shift_right(Packet4us a) { return vshr_n_u16(a,N); }
+template<int N> EIGEN_STRONG_INLINE Packet8us plogical_shift_right(Packet8us a) { return vshrq_n_u16(a,N); }
+template<int N> EIGEN_STRONG_INLINE Packet2i plogical_shift_right(Packet2i a)
+{ return vreinterpret_s32_u32(vshr_n_u32(vreinterpret_u32_s32(a),N)); }
+template<int N> EIGEN_STRONG_INLINE Packet4i plogical_shift_right(Packet4i a)
+{ return vreinterpretq_s32_u32(vshrq_n_u32(vreinterpretq_u32_s32(a),N)); }
+template<int N> EIGEN_STRONG_INLINE Packet2ui plogical_shift_right(Packet2ui a) { return vshr_n_u32(a,N); }
+template<int N> EIGEN_STRONG_INLINE Packet4ui plogical_shift_right(Packet4ui a) { return vshrq_n_u32(a,N); }
+template<int N> EIGEN_STRONG_INLINE Packet2l plogical_shift_right(Packet2l a)
+{ return vreinterpretq_s64_u64(vshrq_n_u64(vreinterpretq_u64_s64(a),N)); }
+template<int N> EIGEN_STRONG_INLINE Packet2ul plogical_shift_right(Packet2ul a) { return vshrq_n_u64(a,N); }
+
+template<int N> EIGEN_STRONG_INLINE Packet4c plogical_shift_left(Packet4c& a)
+{ return vget_lane_s32(vreinterpret_s32_s8(vshl_n_s8(vreinterpret_s8_s32(vdup_n_s32(a)), N)), 0); }
+template<int N> EIGEN_STRONG_INLINE Packet8c plogical_shift_left(Packet8c a) { return vshl_n_s8(a,N); }
+template<int N> EIGEN_STRONG_INLINE Packet16c plogical_shift_left(Packet16c a) { return vshlq_n_s8(a,N); }
+template<int N> EIGEN_STRONG_INLINE Packet4uc plogical_shift_left(Packet4uc& a)
+{ return vget_lane_u32(vreinterpret_u32_u8(vshl_n_u8(vreinterpret_u8_u32(vdup_n_u32(a)), N)), 0); }
+template<int N> EIGEN_STRONG_INLINE Packet8uc plogical_shift_left(Packet8uc a) { return vshl_n_u8(a,N); }
+template<int N> EIGEN_STRONG_INLINE Packet16uc plogical_shift_left(Packet16uc a) { return vshlq_n_u8(a,N); }
+template<int N> EIGEN_STRONG_INLINE Packet4s plogical_shift_left(Packet4s a) { return vshl_n_s16(a,N); }
+template<int N> EIGEN_STRONG_INLINE Packet8s plogical_shift_left(Packet8s a) { return vshlq_n_s16(a,N); }
+template<int N> EIGEN_STRONG_INLINE Packet4us plogical_shift_left(Packet4us a) { return vshl_n_u16(a,N); }
+template<int N> EIGEN_STRONG_INLINE Packet8us plogical_shift_left(Packet8us a) { return vshlq_n_u16(a,N); }
+template<int N> EIGEN_STRONG_INLINE Packet2i plogical_shift_left(Packet2i a) { return vshl_n_s32(a,N); }
+template<int N> EIGEN_STRONG_INLINE Packet4i plogical_shift_left(Packet4i a) { return vshlq_n_s32(a,N); }
+template<int N> EIGEN_STRONG_INLINE Packet2ui plogical_shift_left(Packet2ui a) { return vshl_n_u32(a,N); }
+template<int N> EIGEN_STRONG_INLINE Packet4ui plogical_shift_left(Packet4ui a) { return vshlq_n_u32(a,N); }
+template<int N> EIGEN_STRONG_INLINE Packet2l plogical_shift_left(Packet2l a) { return vshlq_n_s64(a,N); }
+template<int N> EIGEN_STRONG_INLINE Packet2ul plogical_shift_left(Packet2ul a) { return vshlq_n_u64(a,N); }
+
+template<> EIGEN_STRONG_INLINE Packet2f pload<Packet2f>(const float* from)
+{ EIGEN_DEBUG_ALIGNED_LOAD return vld1_f32(from); }
+template<> EIGEN_STRONG_INLINE Packet4f pload<Packet4f>(const float* from)
+{ EIGEN_DEBUG_ALIGNED_LOAD return vld1q_f32(from); }
+template<> EIGEN_STRONG_INLINE Packet4c pload<Packet4c>(const int8_t* from)
+{
+ Packet4c res;
+ memcpy(&res, from, sizeof(Packet4c));
+ return res;
+}
+template<> EIGEN_STRONG_INLINE Packet8c pload<Packet8c>(const int8_t* from)
+{ EIGEN_DEBUG_ALIGNED_LOAD return vld1_s8(from); }
+template<> EIGEN_STRONG_INLINE Packet16c pload<Packet16c>(const int8_t* from)
+{ EIGEN_DEBUG_ALIGNED_LOAD return vld1q_s8(from); }
+template<> EIGEN_STRONG_INLINE Packet4uc pload<Packet4uc>(const uint8_t* from)
+{
+ Packet4uc res;
+ memcpy(&res, from, sizeof(Packet4uc));
+ return res;
+}
+template<> EIGEN_STRONG_INLINE Packet8uc pload<Packet8uc>(const uint8_t* from)
+{ EIGEN_DEBUG_ALIGNED_LOAD return vld1_u8(from); }
+template<> EIGEN_STRONG_INLINE Packet16uc pload<Packet16uc>(const uint8_t* from)
+{ EIGEN_DEBUG_ALIGNED_LOAD return vld1q_u8(from); }
+template<> EIGEN_STRONG_INLINE Packet4s pload<Packet4s>(const int16_t* from)
+{ EIGEN_DEBUG_ALIGNED_LOAD return vld1_s16(from); }
+template<> EIGEN_STRONG_INLINE Packet8s pload<Packet8s>(const int16_t* from)
+{ EIGEN_DEBUG_ALIGNED_LOAD return vld1q_s16(from); }
+template<> EIGEN_STRONG_INLINE Packet4us pload<Packet4us>(const uint16_t* from)
+{ EIGEN_DEBUG_ALIGNED_LOAD return vld1_u16(from); }
+template<> EIGEN_STRONG_INLINE Packet8us pload<Packet8us>(const uint16_t* from)
+{ EIGEN_DEBUG_ALIGNED_LOAD return vld1q_u16(from); }
+template<> EIGEN_STRONG_INLINE Packet2i pload<Packet2i>(const int32_t* from)
+{ EIGEN_DEBUG_ALIGNED_LOAD return vld1_s32(from); }
+template<> EIGEN_STRONG_INLINE Packet4i pload<Packet4i>(const int32_t* from)
+{ EIGEN_DEBUG_ALIGNED_LOAD return vld1q_s32(from); }
+template<> EIGEN_STRONG_INLINE Packet2ui pload<Packet2ui>(const uint32_t* from)
+{ EIGEN_DEBUG_ALIGNED_LOAD return vld1_u32(from); }
+template<> EIGEN_STRONG_INLINE Packet4ui pload<Packet4ui>(const uint32_t* from)
+{ EIGEN_DEBUG_ALIGNED_LOAD return vld1q_u32(from); }
+template<> EIGEN_STRONG_INLINE Packet2l pload<Packet2l>(const int64_t* from)
+{ EIGEN_DEBUG_ALIGNED_LOAD return vld1q_s64(from); }
+template<> EIGEN_STRONG_INLINE Packet2ul pload<Packet2ul>(const uint64_t* from)
+{ EIGEN_DEBUG_ALIGNED_LOAD return vld1q_u64(from); }
+
+template<> EIGEN_STRONG_INLINE Packet2f ploadu<Packet2f>(const float* from)
+{ EIGEN_DEBUG_UNALIGNED_LOAD return vld1_f32(from); }
+template<> EIGEN_STRONG_INLINE Packet4f ploadu<Packet4f>(const float* from)
+{ EIGEN_DEBUG_UNALIGNED_LOAD return vld1q_f32(from); }
+template<> EIGEN_STRONG_INLINE Packet4c ploadu<Packet4c>(const int8_t* from)
+{
+ Packet4c res;
+ memcpy(&res, from, sizeof(Packet4c));
+ return res;
+}
+template<> EIGEN_STRONG_INLINE Packet8c ploadu<Packet8c>(const int8_t* from)
+{ EIGEN_DEBUG_UNALIGNED_LOAD return vld1_s8(from); }
+template<> EIGEN_STRONG_INLINE Packet16c ploadu<Packet16c>(const int8_t* from)
+{ EIGEN_DEBUG_UNALIGNED_LOAD return vld1q_s8(from); }
+template<> EIGEN_STRONG_INLINE Packet4uc ploadu<Packet4uc>(const uint8_t* from)
+{
+ Packet4uc res;
+ memcpy(&res, from, sizeof(Packet4uc));
+ return res;
+}
+template<> EIGEN_STRONG_INLINE Packet8uc ploadu<Packet8uc>(const uint8_t* from)
+{ EIGEN_DEBUG_UNALIGNED_LOAD return vld1_u8(from); }
+template<> EIGEN_STRONG_INLINE Packet16uc ploadu<Packet16uc>(const uint8_t* from)
+{ EIGEN_DEBUG_UNALIGNED_LOAD return vld1q_u8(from); }
+template<> EIGEN_STRONG_INLINE Packet4s ploadu<Packet4s>(const int16_t* from)
+{ EIGEN_DEBUG_UNALIGNED_LOAD return vld1_s16(from); }
+template<> EIGEN_STRONG_INLINE Packet8s ploadu<Packet8s>(const int16_t* from)
+{ EIGEN_DEBUG_UNALIGNED_LOAD return vld1q_s16(from); }
+template<> EIGEN_STRONG_INLINE Packet4us ploadu<Packet4us>(const uint16_t* from)
+{ EIGEN_DEBUG_UNALIGNED_LOAD return vld1_u16(from); }
+template<> EIGEN_STRONG_INLINE Packet8us ploadu<Packet8us>(const uint16_t* from)
+{ EIGEN_DEBUG_UNALIGNED_LOAD return vld1q_u16(from); }
+template<> EIGEN_STRONG_INLINE Packet2i ploadu<Packet2i>(const int32_t* from)
+{ EIGEN_DEBUG_UNALIGNED_LOAD return vld1_s32(from); }
+template<> EIGEN_STRONG_INLINE Packet4i ploadu<Packet4i>(const int32_t* from)
+{ EIGEN_DEBUG_UNALIGNED_LOAD return vld1q_s32(from); }
+template<> EIGEN_STRONG_INLINE Packet2ui ploadu<Packet2ui>(const uint32_t* from)
+{ EIGEN_DEBUG_UNALIGNED_LOAD return vld1_u32(from); }
+template<> EIGEN_STRONG_INLINE Packet4ui ploadu<Packet4ui>(const uint32_t* from)
+{ EIGEN_DEBUG_UNALIGNED_LOAD return vld1q_u32(from); }
+template<> EIGEN_STRONG_INLINE Packet2l ploadu<Packet2l>(const int64_t* from)
+{ EIGEN_DEBUG_UNALIGNED_LOAD return vld1q_s64(from); }
+template<> EIGEN_STRONG_INLINE Packet2ul ploadu<Packet2ul>(const uint64_t* from)
+{ EIGEN_DEBUG_UNALIGNED_LOAD return vld1q_u64(from); }
+
+template<> EIGEN_STRONG_INLINE Packet2f ploaddup<Packet2f>(const float* from)
+{ return vld1_dup_f32(from); }
+template<> EIGEN_STRONG_INLINE Packet4f ploaddup<Packet4f>(const float* from)
+{ return vcombine_f32(vld1_dup_f32(from), vld1_dup_f32(from+1)); }
+template<> EIGEN_STRONG_INLINE Packet4c ploaddup<Packet4c>(const int8_t* from)
+{
+ const int8x8_t a = vreinterpret_s8_s32(vdup_n_s32(pload<Packet4c>(from)));
+ return vget_lane_s32(vreinterpret_s32_s8(vzip_s8(a,a).val[0]), 0);
+}
+template<> EIGEN_STRONG_INLINE Packet8c ploaddup<Packet8c>(const int8_t* from)
+{
+ const int8x8_t a = vld1_s8(from);
+ return vzip_s8(a,a).val[0];
+}
+template<> EIGEN_STRONG_INLINE Packet16c ploaddup<Packet16c>(const int8_t* from)
+{
+ const int8x8_t a = vld1_s8(from);
+ const int8x8x2_t b = vzip_s8(a,a);
+ return vcombine_s8(b.val[0], b.val[1]);
+}
+template<> EIGEN_STRONG_INLINE Packet4uc ploaddup<Packet4uc>(const uint8_t* from)
+{
+ const uint8x8_t a = vreinterpret_u8_u32(vdup_n_u32(pload<Packet4uc>(from)));
+ return vget_lane_u32(vreinterpret_u32_u8(vzip_u8(a,a).val[0]), 0);
+}
+template<> EIGEN_STRONG_INLINE Packet8uc ploaddup<Packet8uc>(const uint8_t* from)
+{
+ const uint8x8_t a = vld1_u8(from);
+ return vzip_u8(a,a).val[0];
+}
+template<> EIGEN_STRONG_INLINE Packet16uc ploaddup<Packet16uc>(const uint8_t* from)
+{
+ const uint8x8_t a = vld1_u8(from);
+ const uint8x8x2_t b = vzip_u8(a,a);
+ return vcombine_u8(b.val[0], b.val[1]);
+}
+template<> EIGEN_STRONG_INLINE Packet4s ploaddup<Packet4s>(const int16_t* from)
+{
+ return vreinterpret_s16_u32(vzip_u32(vreinterpret_u32_s16(vld1_dup_s16(from)),
+ vreinterpret_u32_s16(vld1_dup_s16(from+1))).val[0]);
+}
+template<> EIGEN_STRONG_INLINE Packet8s ploaddup<Packet8s>(const int16_t* from)
+{
+ const int16x4_t a = vld1_s16(from);
+ const int16x4x2_t b = vzip_s16(a,a);
+ return vcombine_s16(b.val[0], b.val[1]);
+}
+template<> EIGEN_STRONG_INLINE Packet4us ploaddup<Packet4us>(const uint16_t* from)
+{
+ return vreinterpret_u16_u32(vzip_u32(vreinterpret_u32_u16(vld1_dup_u16(from)),
+ vreinterpret_u32_u16(vld1_dup_u16(from+1))).val[0]);
+}
+template<> EIGEN_STRONG_INLINE Packet8us ploaddup<Packet8us>(const uint16_t* from)
+{
+ const uint16x4_t a = vld1_u16(from);
+ const uint16x4x2_t b = vzip_u16(a,a);
+ return vcombine_u16(b.val[0], b.val[1]);
+}
+template<> EIGEN_STRONG_INLINE Packet2i ploaddup<Packet2i>(const int32_t* from)
+{ return vld1_dup_s32(from); }
+template<> EIGEN_STRONG_INLINE Packet4i ploaddup<Packet4i>(const int32_t* from)
+{ return vcombine_s32(vld1_dup_s32(from), vld1_dup_s32(from+1)); }
+template<> EIGEN_STRONG_INLINE Packet2ui ploaddup<Packet2ui>(const uint32_t* from)
+{ return vld1_dup_u32(from); }
+template<> EIGEN_STRONG_INLINE Packet4ui ploaddup<Packet4ui>(const uint32_t* from)
+{ return vcombine_u32(vld1_dup_u32(from), vld1_dup_u32(from+1)); }
+template<> EIGEN_STRONG_INLINE Packet2l ploaddup<Packet2l>(const int64_t* from)
+{ return vld1q_dup_s64(from); }
+template<> EIGEN_STRONG_INLINE Packet2ul ploaddup<Packet2ul>(const uint64_t* from)
+{ return vld1q_dup_u64(from); }
+
+template<> EIGEN_STRONG_INLINE Packet4f ploadquad<Packet4f>(const float* from) { return vld1q_dup_f32(from); }
+template<> EIGEN_STRONG_INLINE Packet4c ploadquad<Packet4c>(const int8_t* from)
+{ return vget_lane_s32(vreinterpret_s32_s8(vld1_dup_s8(from)), 0); }
+template<> EIGEN_STRONG_INLINE Packet8c ploadquad<Packet8c>(const int8_t* from)
+{
+ return vreinterpret_s8_u32(vzip_u32(
+ vreinterpret_u32_s8(vld1_dup_s8(from)),
+ vreinterpret_u32_s8(vld1_dup_s8(from+1))).val[0]);
+}
+template<> EIGEN_STRONG_INLINE Packet16c ploadquad<Packet16c>(const int8_t* from)
+{
+ const int8x8_t a = vreinterpret_s8_u32(vzip_u32(
+ vreinterpret_u32_s8(vld1_dup_s8(from)),
+ vreinterpret_u32_s8(vld1_dup_s8(from+1))).val[0]);
+ const int8x8_t b = vreinterpret_s8_u32(vzip_u32(
+ vreinterpret_u32_s8(vld1_dup_s8(from+2)),
+ vreinterpret_u32_s8(vld1_dup_s8(from+3))).val[0]);
+ return vcombine_s8(a,b);
+}
+template<> EIGEN_STRONG_INLINE Packet4uc ploadquad<Packet4uc>(const uint8_t* from)
+{ return vget_lane_u32(vreinterpret_u32_u8(vld1_dup_u8(from)), 0); }
+template<> EIGEN_STRONG_INLINE Packet8uc ploadquad<Packet8uc>(const uint8_t* from)
+{
+ return vreinterpret_u8_u32(vzip_u32(
+ vreinterpret_u32_u8(vld1_dup_u8(from)),
+ vreinterpret_u32_u8(vld1_dup_u8(from+1))).val[0]);
+}
+template<> EIGEN_STRONG_INLINE Packet16uc ploadquad<Packet16uc>(const uint8_t* from)
+{
+ const uint8x8_t a = vreinterpret_u8_u32(vzip_u32(
+ vreinterpret_u32_u8(vld1_dup_u8(from)),
+ vreinterpret_u32_u8(vld1_dup_u8(from+1))).val[0]);
+ const uint8x8_t b = vreinterpret_u8_u32(vzip_u32(
+ vreinterpret_u32_u8(vld1_dup_u8(from+2)),
+ vreinterpret_u32_u8(vld1_dup_u8(from+3))).val[0]);
+ return vcombine_u8(a,b);
+}
+template<> EIGEN_STRONG_INLINE Packet8s ploadquad<Packet8s>(const int16_t* from)
+{ return vcombine_s16(vld1_dup_s16(from), vld1_dup_s16(from+1)); }
+template<> EIGEN_STRONG_INLINE Packet8us ploadquad<Packet8us>(const uint16_t* from)
+{ return vcombine_u16(vld1_dup_u16(from), vld1_dup_u16(from+1)); }
+template<> EIGEN_STRONG_INLINE Packet4i ploadquad<Packet4i>(const int32_t* from) { return vld1q_dup_s32(from); }
+template<> EIGEN_STRONG_INLINE Packet4ui ploadquad<Packet4ui>(const uint32_t* from) { return vld1q_dup_u32(from); }
+
+template<> EIGEN_STRONG_INLINE void pstore<float>(float* to, const Packet2f& from)
+{ EIGEN_DEBUG_ALIGNED_STORE vst1_f32(to,from); }
+template<> EIGEN_STRONG_INLINE void pstore<float>(float* to, const Packet4f& from)
+{ EIGEN_DEBUG_ALIGNED_STORE vst1q_f32(to,from); }
+template<> EIGEN_STRONG_INLINE void pstore<int8_t>(int8_t* to, const Packet4c& from)
+{ memcpy(to, &from, sizeof(from)); }
+template<> EIGEN_STRONG_INLINE void pstore<int8_t>(int8_t* to, const Packet8c& from)
+{ EIGEN_DEBUG_ALIGNED_STORE vst1_s8(to,from); }
+template<> EIGEN_STRONG_INLINE void pstore<int8_t>(int8_t* to, const Packet16c& from)
+{ EIGEN_DEBUG_ALIGNED_STORE vst1q_s8(to,from); }
+template<> EIGEN_STRONG_INLINE void pstore<uint8_t>(uint8_t* to, const Packet4uc& from)
+{ memcpy(to, &from, sizeof(from)); }
+template<> EIGEN_STRONG_INLINE void pstore<uint8_t>(uint8_t* to, const Packet8uc& from)
+{ EIGEN_DEBUG_ALIGNED_STORE vst1_u8(to,from); }
+template<> EIGEN_STRONG_INLINE void pstore<uint8_t>(uint8_t* to, const Packet16uc& from)
+{ EIGEN_DEBUG_ALIGNED_STORE vst1q_u8(to,from); }
+template<> EIGEN_STRONG_INLINE void pstore<int16_t>(int16_t* to, const Packet4s& from)
+{ EIGEN_DEBUG_ALIGNED_STORE vst1_s16(to,from); }
+template<> EIGEN_STRONG_INLINE void pstore<int16_t>(int16_t* to, const Packet8s& from)
+{ EIGEN_DEBUG_ALIGNED_STORE vst1q_s16(to,from); }
+template<> EIGEN_STRONG_INLINE void pstore<uint16_t>(uint16_t* to, const Packet4us& from)
+{ EIGEN_DEBUG_ALIGNED_STORE vst1_u16(to,from); }
+template<> EIGEN_STRONG_INLINE void pstore<uint16_t>(uint16_t* to, const Packet8us& from)
+{ EIGEN_DEBUG_ALIGNED_STORE vst1q_u16(to,from); }
+template<> EIGEN_STRONG_INLINE void pstore<int32_t>(int32_t* to, const Packet2i& from)
+{ EIGEN_DEBUG_ALIGNED_STORE vst1_s32(to,from); }
+template<> EIGEN_STRONG_INLINE void pstore<int32_t>(int32_t* to, const Packet4i& from)
+{ EIGEN_DEBUG_ALIGNED_STORE vst1q_s32(to,from); }
+template<> EIGEN_STRONG_INLINE void pstore<uint32_t>(uint32_t* to, const Packet2ui& from)
+{ EIGEN_DEBUG_ALIGNED_STORE vst1_u32(to,from); }
+template<> EIGEN_STRONG_INLINE void pstore<uint32_t>(uint32_t* to, const Packet4ui& from)
+{ EIGEN_DEBUG_ALIGNED_STORE vst1q_u32(to,from); }
+template<> EIGEN_STRONG_INLINE void pstore<int64_t>(int64_t* to, const Packet2l& from)
+{ EIGEN_DEBUG_ALIGNED_STORE vst1q_s64(to,from); }
+template<> EIGEN_STRONG_INLINE void pstore<uint64_t>(uint64_t* to, const Packet2ul& from)
+{ EIGEN_DEBUG_ALIGNED_STORE vst1q_u64(to,from); }
+
+template<> EIGEN_STRONG_INLINE void pstoreu<float>(float* to, const Packet2f& from)
+{ EIGEN_DEBUG_UNALIGNED_STORE vst1_f32(to,from); }
+template<> EIGEN_STRONG_INLINE void pstoreu<float>(float* to, const Packet4f& from)
+{ EIGEN_DEBUG_UNALIGNED_STORE vst1q_f32(to,from); }
+template<> EIGEN_STRONG_INLINE void pstoreu<int8_t>(int8_t* to, const Packet4c& from)
+{ memcpy(to, &from, sizeof(from)); }
+template<> EIGEN_STRONG_INLINE void pstoreu<int8_t>(int8_t* to, const Packet8c& from)
+{ EIGEN_DEBUG_UNALIGNED_STORE vst1_s8(to,from); }
+template<> EIGEN_STRONG_INLINE void pstoreu<int8_t>(int8_t* to, const Packet16c& from)
+{ EIGEN_DEBUG_UNALIGNED_STORE vst1q_s8(to,from); }
+template<> EIGEN_STRONG_INLINE void pstoreu<uint8_t>(uint8_t* to, const Packet4uc& from)
+{ memcpy(to, &from, sizeof(from)); }
+template<> EIGEN_STRONG_INLINE void pstoreu<uint8_t>(uint8_t* to, const Packet8uc& from)
+{ EIGEN_DEBUG_UNALIGNED_STORE vst1_u8(to,from); }
+template<> EIGEN_STRONG_INLINE void pstoreu<uint8_t>(uint8_t* to, const Packet16uc& from)
+{ EIGEN_DEBUG_UNALIGNED_STORE vst1q_u8(to,from); }
+template<> EIGEN_STRONG_INLINE void pstoreu<int16_t>(int16_t* to, const Packet4s& from)
+{ EIGEN_DEBUG_UNALIGNED_STORE vst1_s16(to,from); }
+template<> EIGEN_STRONG_INLINE void pstoreu<int16_t>(int16_t* to, const Packet8s& from)
+{ EIGEN_DEBUG_UNALIGNED_STORE vst1q_s16(to,from); }
+template<> EIGEN_STRONG_INLINE void pstoreu<uint16_t>(uint16_t* to, const Packet4us& from)
+{ EIGEN_DEBUG_UNALIGNED_STORE vst1_u16(to,from); }
+template<> EIGEN_STRONG_INLINE void pstoreu<uint16_t>(uint16_t* to, const Packet8us& from)
+{ EIGEN_DEBUG_UNALIGNED_STORE vst1q_u16(to,from); }
+template<> EIGEN_STRONG_INLINE void pstoreu<int32_t>(int32_t* to, const Packet2i& from)
+{ EIGEN_DEBUG_UNALIGNED_STORE vst1_s32(to,from); }
+template<> EIGEN_STRONG_INLINE void pstoreu<int32_t>(int32_t* to, const Packet4i& from)
+{ EIGEN_DEBUG_UNALIGNED_STORE vst1q_s32(to,from); }
+template<> EIGEN_STRONG_INLINE void pstoreu<uint32_t>(uint32_t* to, const Packet2ui& from)
+{ EIGEN_DEBUG_UNALIGNED_STORE vst1_u32(to,from); }
+template<> EIGEN_STRONG_INLINE void pstoreu<uint32_t>(uint32_t* to, const Packet4ui& from)
+{ EIGEN_DEBUG_UNALIGNED_STORE vst1q_u32(to,from); }
+template<> EIGEN_STRONG_INLINE void pstoreu<int64_t>(int64_t* to, const Packet2l& from)
+{ EIGEN_DEBUG_UNALIGNED_STORE vst1q_s64(to,from); }
+template<> EIGEN_STRONG_INLINE void pstoreu<uint64_t>(uint64_t* to, const Packet2ul& from)
+{ EIGEN_DEBUG_UNALIGNED_STORE vst1q_u64(to,from); }
+
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet2f pgather<float, Packet2f>(const float* from, Index stride)
+{
+ Packet2f res = vld1_dup_f32(from);
+ res = vld1_lane_f32(from + 1*stride, res, 1);
+ return res;
+}
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet4f pgather<float, Packet4f>(const float* from, Index stride)
+{
+ Packet4f res = vld1q_dup_f32(from);
+ res = vld1q_lane_f32(from + 1*stride, res, 1);
+ res = vld1q_lane_f32(from + 2*stride, res, 2);
+ res = vld1q_lane_f32(from + 3*stride, res, 3);
+ return res;
+}
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet4c pgather<int8_t, Packet4c>(const int8_t* from, Index stride)
+{
+ Packet4c res;
+ for (int i = 0; i != 4; i++)
+ reinterpret_cast<int8_t*>(&res)[i] = *(from + i * stride);
+ return res;
+}
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet8c pgather<int8_t, Packet8c>(const int8_t* from, Index stride)
+{
+ Packet8c res = vld1_dup_s8(from);
+ res = vld1_lane_s8(from + 1*stride, res, 1);
+ res = vld1_lane_s8(from + 2*stride, res, 2);
+ res = vld1_lane_s8(from + 3*stride, res, 3);
+ res = vld1_lane_s8(from + 4*stride, res, 4);
+ res = vld1_lane_s8(from + 5*stride, res, 5);
+ res = vld1_lane_s8(from + 6*stride, res, 6);
+ res = vld1_lane_s8(from + 7*stride, res, 7);
+ return res;
+}
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet16c pgather<int8_t, Packet16c>(const int8_t* from, Index stride)
+{
+ Packet16c res = vld1q_dup_s8(from);
+ res = vld1q_lane_s8(from + 1*stride, res, 1);
+ res = vld1q_lane_s8(from + 2*stride, res, 2);
+ res = vld1q_lane_s8(from + 3*stride, res, 3);
+ res = vld1q_lane_s8(from + 4*stride, res, 4);
+ res = vld1q_lane_s8(from + 5*stride, res, 5);
+ res = vld1q_lane_s8(from + 6*stride, res, 6);
+ res = vld1q_lane_s8(from + 7*stride, res, 7);
+ res = vld1q_lane_s8(from + 8*stride, res, 8);
+ res = vld1q_lane_s8(from + 9*stride, res, 9);
+ res = vld1q_lane_s8(from + 10*stride, res, 10);
+ res = vld1q_lane_s8(from + 11*stride, res, 11);
+ res = vld1q_lane_s8(from + 12*stride, res, 12);
+ res = vld1q_lane_s8(from + 13*stride, res, 13);
+ res = vld1q_lane_s8(from + 14*stride, res, 14);
+ res = vld1q_lane_s8(from + 15*stride, res, 15);
+ return res;
+}
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet4uc pgather<uint8_t, Packet4uc>(const uint8_t* from, Index stride)
+{
+ Packet4uc res;
+ for (int i = 0; i != 4; i++)
+ reinterpret_cast<uint8_t*>(&res)[i] = *(from + i * stride);
+ return res;
+}
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet8uc pgather<uint8_t, Packet8uc>(const uint8_t* from, Index stride)
+{
+ Packet8uc res = vld1_dup_u8(from);
+ res = vld1_lane_u8(from + 1*stride, res, 1);
+ res = vld1_lane_u8(from + 2*stride, res, 2);
+ res = vld1_lane_u8(from + 3*stride, res, 3);
+ res = vld1_lane_u8(from + 4*stride, res, 4);
+ res = vld1_lane_u8(from + 5*stride, res, 5);
+ res = vld1_lane_u8(from + 6*stride, res, 6);
+ res = vld1_lane_u8(from + 7*stride, res, 7);
+ return res;
+}
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet16uc pgather<uint8_t, Packet16uc>(const uint8_t* from, Index stride)
+{
+ Packet16uc res = vld1q_dup_u8(from);
+ res = vld1q_lane_u8(from + 1*stride, res, 1);
+ res = vld1q_lane_u8(from + 2*stride, res, 2);
+ res = vld1q_lane_u8(from + 3*stride, res, 3);
+ res = vld1q_lane_u8(from + 4*stride, res, 4);
+ res = vld1q_lane_u8(from + 5*stride, res, 5);
+ res = vld1q_lane_u8(from + 6*stride, res, 6);
+ res = vld1q_lane_u8(from + 7*stride, res, 7);
+ res = vld1q_lane_u8(from + 8*stride, res, 8);
+ res = vld1q_lane_u8(from + 9*stride, res, 9);
+ res = vld1q_lane_u8(from + 10*stride, res, 10);
+ res = vld1q_lane_u8(from + 11*stride, res, 11);
+ res = vld1q_lane_u8(from + 12*stride, res, 12);
+ res = vld1q_lane_u8(from + 13*stride, res, 13);
+ res = vld1q_lane_u8(from + 14*stride, res, 14);
+ res = vld1q_lane_u8(from + 15*stride, res, 15);
+ return res;
+}
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet4s pgather<int16_t, Packet4s>(const int16_t* from, Index stride)
+{
+ Packet4s res = vld1_dup_s16(from);
+ res = vld1_lane_s16(from + 1*stride, res, 1);
+ res = vld1_lane_s16(from + 2*stride, res, 2);
+ res = vld1_lane_s16(from + 3*stride, res, 3);
+ return res;
+}
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet8s pgather<int16_t, Packet8s>(const int16_t* from, Index stride)
+{
+ Packet8s res = vld1q_dup_s16(from);
+ res = vld1q_lane_s16(from + 1*stride, res, 1);
+ res = vld1q_lane_s16(from + 2*stride, res, 2);
+ res = vld1q_lane_s16(from + 3*stride, res, 3);
+ res = vld1q_lane_s16(from + 4*stride, res, 4);
+ res = vld1q_lane_s16(from + 5*stride, res, 5);
+ res = vld1q_lane_s16(from + 6*stride, res, 6);
+ res = vld1q_lane_s16(from + 7*stride, res, 7);
+ return res;
+}
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet4us pgather<uint16_t, Packet4us>(const uint16_t* from, Index stride)
+{
+ Packet4us res = vld1_dup_u16(from);
+ res = vld1_lane_u16(from + 1*stride, res, 1);
+ res = vld1_lane_u16(from + 2*stride, res, 2);
+ res = vld1_lane_u16(from + 3*stride, res, 3);
+ return res;
+}
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet8us pgather<uint16_t, Packet8us>(const uint16_t* from, Index stride)
+{
+ Packet8us res = vld1q_dup_u16(from);
+ res = vld1q_lane_u16(from + 1*stride, res, 1);
+ res = vld1q_lane_u16(from + 2*stride, res, 2);
+ res = vld1q_lane_u16(from + 3*stride, res, 3);
+ res = vld1q_lane_u16(from + 4*stride, res, 4);
+ res = vld1q_lane_u16(from + 5*stride, res, 5);
+ res = vld1q_lane_u16(from + 6*stride, res, 6);
+ res = vld1q_lane_u16(from + 7*stride, res, 7);
+ return res;
+}
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet2i pgather<int32_t, Packet2i>(const int32_t* from, Index stride)
+{
+ Packet2i res = vld1_dup_s32(from);
+ res = vld1_lane_s32(from + 1*stride, res, 1);
+ return res;
+}
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet4i pgather<int32_t, Packet4i>(const int32_t* from, Index stride)
+{
+ Packet4i res = vld1q_dup_s32(from);
+ res = vld1q_lane_s32(from + 1*stride, res, 1);
+ res = vld1q_lane_s32(from + 2*stride, res, 2);
+ res = vld1q_lane_s32(from + 3*stride, res, 3);
+ return res;
+}
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet2ui pgather<uint32_t, Packet2ui>(const uint32_t* from, Index stride)
+{
+ Packet2ui res = vld1_dup_u32(from);
+ res = vld1_lane_u32(from + 1*stride, res, 1);
+ return res;
+}
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet4ui pgather<uint32_t, Packet4ui>(const uint32_t* from, Index stride)
+{
+ Packet4ui res = vld1q_dup_u32(from);
+ res = vld1q_lane_u32(from + 1*stride, res, 1);
+ res = vld1q_lane_u32(from + 2*stride, res, 2);
+ res = vld1q_lane_u32(from + 3*stride, res, 3);
+ return res;
+}
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet2l pgather<int64_t, Packet2l>(const int64_t* from, Index stride)
+{
+ Packet2l res = vld1q_dup_s64(from);
+ res = vld1q_lane_s64(from + 1*stride, res, 1);
+ return res;
+}
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet2ul pgather<uint64_t, Packet2ul>(const uint64_t* from, Index stride)
+{
+ Packet2ul res = vld1q_dup_u64(from);
+ res = vld1q_lane_u64(from + 1*stride, res, 1);
+ return res;
+}
+
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void pscatter<float, Packet2f>(float* to, const Packet2f& from, Index stride)
+{
+ vst1_lane_f32(to + stride*0, from, 0);
+ vst1_lane_f32(to + stride*1, from, 1);
+}
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void pscatter<float, Packet4f>(float* to, const Packet4f& from, Index stride)
+{
+ vst1q_lane_f32(to + stride*0, from, 0);
+ vst1q_lane_f32(to + stride*1, from, 1);
+ vst1q_lane_f32(to + stride*2, from, 2);
+ vst1q_lane_f32(to + stride*3, from, 3);
+}
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void pscatter<int8_t, Packet4c>(int8_t* to, const Packet4c& from, Index stride)
+{
+ for (int i = 0; i != 4; i++)
+ *(to + i * stride) = reinterpret_cast<const int8_t*>(&from)[i];
+}
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void pscatter<int8_t, Packet8c>(int8_t* to, const Packet8c& from, Index stride)
+{
+ vst1_lane_s8(to + stride*0, from, 0);
+ vst1_lane_s8(to + stride*1, from, 1);
+ vst1_lane_s8(to + stride*2, from, 2);
+ vst1_lane_s8(to + stride*3, from, 3);
+ vst1_lane_s8(to + stride*4, from, 4);
+ vst1_lane_s8(to + stride*5, from, 5);
+ vst1_lane_s8(to + stride*6, from, 6);
+ vst1_lane_s8(to + stride*7, from, 7);
+}
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void pscatter<int8_t, Packet16c>(int8_t* to, const Packet16c& from, Index stride)
+{
+ vst1q_lane_s8(to + stride*0, from, 0);
+ vst1q_lane_s8(to + stride*1, from, 1);
+ vst1q_lane_s8(to + stride*2, from, 2);
+ vst1q_lane_s8(to + stride*3, from, 3);
+ vst1q_lane_s8(to + stride*4, from, 4);
+ vst1q_lane_s8(to + stride*5, from, 5);
+ vst1q_lane_s8(to + stride*6, from, 6);
+ vst1q_lane_s8(to + stride*7, from, 7);
+ vst1q_lane_s8(to + stride*8, from, 8);
+ vst1q_lane_s8(to + stride*9, from, 9);
+ vst1q_lane_s8(to + stride*10, from, 10);
+ vst1q_lane_s8(to + stride*11, from, 11);
+ vst1q_lane_s8(to + stride*12, from, 12);
+ vst1q_lane_s8(to + stride*13, from, 13);
+ vst1q_lane_s8(to + stride*14, from, 14);
+ vst1q_lane_s8(to + stride*15, from, 15);
+}
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void pscatter<uint8_t, Packet4uc>(uint8_t* to, const Packet4uc& from, Index stride)
+{
+ for (int i = 0; i != 4; i++)
+ *(to + i * stride) = reinterpret_cast<const uint8_t*>(&from)[i];
+}
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void pscatter<uint8_t, Packet8uc>(uint8_t* to, const Packet8uc& from, Index stride)
+{
+ vst1_lane_u8(to + stride*0, from, 0);
+ vst1_lane_u8(to + stride*1, from, 1);
+ vst1_lane_u8(to + stride*2, from, 2);
+ vst1_lane_u8(to + stride*3, from, 3);
+ vst1_lane_u8(to + stride*4, from, 4);
+ vst1_lane_u8(to + stride*5, from, 5);
+ vst1_lane_u8(to + stride*6, from, 6);
+ vst1_lane_u8(to + stride*7, from, 7);
+}
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void pscatter<uint8_t, Packet16uc>(uint8_t* to, const Packet16uc& from, Index stride)
+{
+ vst1q_lane_u8(to + stride*0, from, 0);
+ vst1q_lane_u8(to + stride*1, from, 1);
+ vst1q_lane_u8(to + stride*2, from, 2);
+ vst1q_lane_u8(to + stride*3, from, 3);
+ vst1q_lane_u8(to + stride*4, from, 4);
+ vst1q_lane_u8(to + stride*5, from, 5);
+ vst1q_lane_u8(to + stride*6, from, 6);
+ vst1q_lane_u8(to + stride*7, from, 7);
+ vst1q_lane_u8(to + stride*8, from, 8);
+ vst1q_lane_u8(to + stride*9, from, 9);
+ vst1q_lane_u8(to + stride*10, from, 10);
+ vst1q_lane_u8(to + stride*11, from, 11);
+ vst1q_lane_u8(to + stride*12, from, 12);
+ vst1q_lane_u8(to + stride*13, from, 13);
+ vst1q_lane_u8(to + stride*14, from, 14);
+ vst1q_lane_u8(to + stride*15, from, 15);
+}
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void pscatter<int16_t, Packet4s>(int16_t* to, const Packet4s& from, Index stride)
+{
+ vst1_lane_s16(to + stride*0, from, 0);
+ vst1_lane_s16(to + stride*1, from, 1);
+ vst1_lane_s16(to + stride*2, from, 2);
+ vst1_lane_s16(to + stride*3, from, 3);
+}
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void pscatter<int16_t, Packet8s>(int16_t* to, const Packet8s& from, Index stride)
+{
+ vst1q_lane_s16(to + stride*0, from, 0);
+ vst1q_lane_s16(to + stride*1, from, 1);
+ vst1q_lane_s16(to + stride*2, from, 2);
+ vst1q_lane_s16(to + stride*3, from, 3);
+ vst1q_lane_s16(to + stride*4, from, 4);
+ vst1q_lane_s16(to + stride*5, from, 5);
+ vst1q_lane_s16(to + stride*6, from, 6);
+ vst1q_lane_s16(to + stride*7, from, 7);
+}
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void pscatter<uint16_t, Packet4us>(uint16_t* to, const Packet4us& from, Index stride)
+{
+ vst1_lane_u16(to + stride*0, from, 0);
+ vst1_lane_u16(to + stride*1, from, 1);
+ vst1_lane_u16(to + stride*2, from, 2);
+ vst1_lane_u16(to + stride*3, from, 3);
+}
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void pscatter<uint16_t, Packet8us>(uint16_t* to, const Packet8us& from, Index stride)
+{
+ vst1q_lane_u16(to + stride*0, from, 0);
+ vst1q_lane_u16(to + stride*1, from, 1);
+ vst1q_lane_u16(to + stride*2, from, 2);
+ vst1q_lane_u16(to + stride*3, from, 3);
+ vst1q_lane_u16(to + stride*4, from, 4);
+ vst1q_lane_u16(to + stride*5, from, 5);
+ vst1q_lane_u16(to + stride*6, from, 6);
+ vst1q_lane_u16(to + stride*7, from, 7);
+}
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void pscatter<int32_t, Packet2i>(int32_t* to, const Packet2i& from, Index stride)
+{
+ vst1_lane_s32(to + stride*0, from, 0);
+ vst1_lane_s32(to + stride*1, from, 1);
+}
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void pscatter<int32_t, Packet4i>(int32_t* to, const Packet4i& from, Index stride)
+{
+ vst1q_lane_s32(to + stride*0, from, 0);
+ vst1q_lane_s32(to + stride*1, from, 1);
+ vst1q_lane_s32(to + stride*2, from, 2);
+ vst1q_lane_s32(to + stride*3, from, 3);
+}
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void pscatter<uint32_t, Packet2ui>(uint32_t* to, const Packet2ui& from, Index stride)
+{
+ vst1_lane_u32(to + stride*0, from, 0);
+ vst1_lane_u32(to + stride*1, from, 1);
+}
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void pscatter<uint32_t, Packet4ui>(uint32_t* to, const Packet4ui& from, Index stride)
+{
+ vst1q_lane_u32(to + stride*0, from, 0);
+ vst1q_lane_u32(to + stride*1, from, 1);
+ vst1q_lane_u32(to + stride*2, from, 2);
+ vst1q_lane_u32(to + stride*3, from, 3);
+}
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void pscatter<int64_t, Packet2l>(int64_t* to, const Packet2l& from, Index stride)
+{
+ vst1q_lane_s64(to + stride*0, from, 0);
+ vst1q_lane_s64(to + stride*1, from, 1);
+}
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void pscatter<uint64_t, Packet2ul>(uint64_t* to, const Packet2ul& from, Index stride)
+{
+ vst1q_lane_u64(to + stride*0, from, 0);
+ vst1q_lane_u64(to + stride*1, from, 1);
+}
+
+template<> EIGEN_STRONG_INLINE void prefetch<float>(const float* addr) { EIGEN_ARM_PREFETCH(addr); }
+template<> EIGEN_STRONG_INLINE void prefetch<int8_t>(const int8_t* addr) { EIGEN_ARM_PREFETCH(addr); }
+template<> EIGEN_STRONG_INLINE void prefetch<uint8_t>(const uint8_t* addr) { EIGEN_ARM_PREFETCH(addr); }
+template<> EIGEN_STRONG_INLINE void prefetch<int16_t>(const int16_t* addr) { EIGEN_ARM_PREFETCH(addr); }
+template<> EIGEN_STRONG_INLINE void prefetch<uint16_t>(const uint16_t* addr) { EIGEN_ARM_PREFETCH(addr); }
+template<> EIGEN_STRONG_INLINE void prefetch<int32_t>(const int32_t* addr) { EIGEN_ARM_PREFETCH(addr); }
+template<> EIGEN_STRONG_INLINE void prefetch<uint32_t>(const uint32_t* addr) { EIGEN_ARM_PREFETCH(addr); }
+template<> EIGEN_STRONG_INLINE void prefetch<int64_t>(const int64_t* addr) { EIGEN_ARM_PREFETCH(addr); }
+template<> EIGEN_STRONG_INLINE void prefetch<uint64_t>(const uint64_t* addr) { EIGEN_ARM_PREFETCH(addr); }
+
+template<> EIGEN_STRONG_INLINE float pfirst<Packet2f>(const Packet2f& a) { return vget_lane_f32(a,0); }
+template<> EIGEN_STRONG_INLINE float pfirst<Packet4f>(const Packet4f& a) { return vgetq_lane_f32(a,0); }
+template<> EIGEN_STRONG_INLINE int8_t pfirst<Packet4c>(const Packet4c& a) { return static_cast<int8_t>(a & 0xff); }
+template<> EIGEN_STRONG_INLINE int8_t pfirst<Packet8c>(const Packet8c& a) { return vget_lane_s8(a,0); }
+template<> EIGEN_STRONG_INLINE int8_t pfirst<Packet16c>(const Packet16c& a) { return vgetq_lane_s8(a,0); }
+template<> EIGEN_STRONG_INLINE uint8_t pfirst<Packet4uc>(const Packet4uc& a) { return static_cast<uint8_t>(a & 0xff); }
+template<> EIGEN_STRONG_INLINE uint8_t pfirst<Packet8uc>(const Packet8uc& a) { return vget_lane_u8(a,0); }
+template<> EIGEN_STRONG_INLINE uint8_t pfirst<Packet16uc>(const Packet16uc& a) { return vgetq_lane_u8(a,0); }
+template<> EIGEN_STRONG_INLINE int16_t pfirst<Packet4s>(const Packet4s& a) { return vget_lane_s16(a,0); }
+template<> EIGEN_STRONG_INLINE int16_t pfirst<Packet8s>(const Packet8s& a) { return vgetq_lane_s16(a,0); }
+template<> EIGEN_STRONG_INLINE uint16_t pfirst<Packet4us>(const Packet4us& a) { return vget_lane_u16(a,0); }
+template<> EIGEN_STRONG_INLINE uint16_t pfirst<Packet8us>(const Packet8us& a) { return vgetq_lane_u16(a,0); }
+template<> EIGEN_STRONG_INLINE int32_t pfirst<Packet2i>(const Packet2i& a) { return vget_lane_s32(a,0); }
+template<> EIGEN_STRONG_INLINE int32_t pfirst<Packet4i>(const Packet4i& a) { return vgetq_lane_s32(a,0); }
+template<> EIGEN_STRONG_INLINE uint32_t pfirst<Packet2ui>(const Packet2ui& a) { return vget_lane_u32(a,0); }
+template<> EIGEN_STRONG_INLINE uint32_t pfirst<Packet4ui>(const Packet4ui& a) { return vgetq_lane_u32(a,0); }
+template<> EIGEN_STRONG_INLINE int64_t pfirst<Packet2l>(const Packet2l& a) { return vgetq_lane_s64(a,0); }
+template<> EIGEN_STRONG_INLINE uint64_t pfirst<Packet2ul>(const Packet2ul& a) { return vgetq_lane_u64(a,0); }
+
+template<> EIGEN_STRONG_INLINE Packet2f preverse(const Packet2f& a) { return vrev64_f32(a); }
+template<> EIGEN_STRONG_INLINE Packet4f preverse(const Packet4f& a)
+{
+ const float32x4_t a_r64 = vrev64q_f32(a);
+ return vcombine_f32(vget_high_f32(a_r64), vget_low_f32(a_r64));
+}
+template<> EIGEN_STRONG_INLINE Packet4c preverse(const Packet4c& a)
+{ return vget_lane_s32(vreinterpret_s32_s8(vrev64_s8(vreinterpret_s8_s32(vdup_n_s32(a)))), 0); }
+template<> EIGEN_STRONG_INLINE Packet8c preverse(const Packet8c& a) { return vrev64_s8(a); }
+template<> EIGEN_STRONG_INLINE Packet16c preverse(const Packet16c& a)
+{
+ const int8x16_t a_r64 = vrev64q_s8(a);
+ return vcombine_s8(vget_high_s8(a_r64), vget_low_s8(a_r64));
+}
+template<> EIGEN_STRONG_INLINE Packet4uc preverse(const Packet4uc& a)
+{ return vget_lane_u32(vreinterpret_u32_u8(vrev64_u8(vreinterpret_u8_u32(vdup_n_u32(a)))), 0); }
+template<> EIGEN_STRONG_INLINE Packet8uc preverse(const Packet8uc& a) { return vrev64_u8(a); }
+template<> EIGEN_STRONG_INLINE Packet16uc preverse(const Packet16uc& a)
+{
+ const uint8x16_t a_r64 = vrev64q_u8(a);
+ return vcombine_u8(vget_high_u8(a_r64), vget_low_u8(a_r64));
+}
+template<> EIGEN_STRONG_INLINE Packet4s preverse(const Packet4s& a) { return vrev64_s16(a); }
+template<> EIGEN_STRONG_INLINE Packet8s preverse(const Packet8s& a)
+{
+ const int16x8_t a_r64 = vrev64q_s16(a);
+ return vcombine_s16(vget_high_s16(a_r64), vget_low_s16(a_r64));
+}
+template<> EIGEN_STRONG_INLINE Packet4us preverse(const Packet4us& a) { return vrev64_u16(a); }
+template<> EIGEN_STRONG_INLINE Packet8us preverse(const Packet8us& a)
+{
+ const uint16x8_t a_r64 = vrev64q_u16(a);
+ return vcombine_u16(vget_high_u16(a_r64), vget_low_u16(a_r64));
+}
+template<> EIGEN_STRONG_INLINE Packet2i preverse(const Packet2i& a) { return vrev64_s32(a); }
+template<> EIGEN_STRONG_INLINE Packet4i preverse(const Packet4i& a)
+{
+ const int32x4_t a_r64 = vrev64q_s32(a);
+ return vcombine_s32(vget_high_s32(a_r64), vget_low_s32(a_r64));
+}
+template<> EIGEN_STRONG_INLINE Packet2ui preverse(const Packet2ui& a) { return vrev64_u32(a); }
+template<> EIGEN_STRONG_INLINE Packet4ui preverse(const Packet4ui& a)
+{
+ const uint32x4_t a_r64 = vrev64q_u32(a);
+ return vcombine_u32(vget_high_u32(a_r64), vget_low_u32(a_r64));
+}
+template<> EIGEN_STRONG_INLINE Packet2l preverse(const Packet2l& a)
+{ return vcombine_s64(vget_high_s64(a), vget_low_s64(a)); }
+template<> EIGEN_STRONG_INLINE Packet2ul preverse(const Packet2ul& a)
+{ return vcombine_u64(vget_high_u64(a), vget_low_u64(a)); }
+
+template<> EIGEN_STRONG_INLINE Packet2f pabs(const Packet2f& a) { return vabs_f32(a); }
+template<> EIGEN_STRONG_INLINE Packet4f pabs(const Packet4f& a) { return vabsq_f32(a); }
+template<> EIGEN_STRONG_INLINE Packet4c pabs<Packet4c>(const Packet4c& a)
+{ return vget_lane_s32(vreinterpret_s32_s8(vabs_s8(vreinterpret_s8_s32(vdup_n_s32(a)))), 0); }
+template<> EIGEN_STRONG_INLINE Packet8c pabs(const Packet8c& a) { return vabs_s8(a); }
+template<> EIGEN_STRONG_INLINE Packet16c pabs(const Packet16c& a) { return vabsq_s8(a); }
+template<> EIGEN_STRONG_INLINE Packet4uc pabs(const Packet4uc& a) { return a; }
+template<> EIGEN_STRONG_INLINE Packet8uc pabs(const Packet8uc& a) { return a; }
+template<> EIGEN_STRONG_INLINE Packet16uc pabs(const Packet16uc& a) { return a; }
+template<> EIGEN_STRONG_INLINE Packet4s pabs(const Packet4s& a) { return vabs_s16(a); }
+template<> EIGEN_STRONG_INLINE Packet8s pabs(const Packet8s& a) { return vabsq_s16(a); }
+template<> EIGEN_STRONG_INLINE Packet4us pabs(const Packet4us& a) { return a; }
+template<> EIGEN_STRONG_INLINE Packet8us pabs(const Packet8us& a) { return a; }
+template<> EIGEN_STRONG_INLINE Packet2i pabs(const Packet2i& a) { return vabs_s32(a); }
+template<> EIGEN_STRONG_INLINE Packet4i pabs(const Packet4i& a) { return vabsq_s32(a); }
+template<> EIGEN_STRONG_INLINE Packet2ui pabs(const Packet2ui& a) { return a; }
+template<> EIGEN_STRONG_INLINE Packet4ui pabs(const Packet4ui& a) { return a; }
+template<> EIGEN_STRONG_INLINE Packet2l pabs(const Packet2l& a) {
+#if EIGEN_ARCH_ARM64
+ return vabsq_s64(a);
+#else
+ return vcombine_s64(
+ vdup_n_s64((std::abs)(vgetq_lane_s64(a, 0))),
+ vdup_n_s64((std::abs)(vgetq_lane_s64(a, 1))));
+#endif
+}
+template<> EIGEN_STRONG_INLINE Packet2ul pabs(const Packet2ul& a) { return a; }
+
+template<> EIGEN_STRONG_INLINE Packet2f pfrexp<Packet2f>(const Packet2f& a, Packet2f& exponent)
+{ return pfrexp_generic(a,exponent); }
+template<> EIGEN_STRONG_INLINE Packet4f pfrexp<Packet4f>(const Packet4f& a, Packet4f& exponent)
+{ return pfrexp_generic(a,exponent); }
+
+template<> EIGEN_STRONG_INLINE Packet2f pldexp<Packet2f>(const Packet2f& a, const Packet2f& exponent)
+{ return pldexp_generic(a,exponent); }
+template<> EIGEN_STRONG_INLINE Packet4f pldexp<Packet4f>(const Packet4f& a, const Packet4f& exponent)
+{ return pldexp_generic(a,exponent); }
+
+#if EIGEN_ARCH_ARM64
+template<> EIGEN_STRONG_INLINE float predux<Packet2f>(const Packet2f& a) { return vaddv_f32(a); }
+template<> EIGEN_STRONG_INLINE float predux<Packet4f>(const Packet4f& a) { return vaddvq_f32(a); }
+#else
+template<> EIGEN_STRONG_INLINE float predux<Packet2f>(const Packet2f& a) { return vget_lane_f32(vpadd_f32(a,a), 0); }
+template<> EIGEN_STRONG_INLINE float predux<Packet4f>(const Packet4f& a)
+{
+ const float32x2_t sum = vadd_f32(vget_low_f32(a), vget_high_f32(a));
+ return vget_lane_f32(vpadd_f32(sum, sum), 0);
+}
+#endif
+template<> EIGEN_STRONG_INLINE int8_t predux<Packet4c>(const Packet4c& a)
+{
+ const int8x8_t a_dup = vreinterpret_s8_s32(vdup_n_s32(a));
+ int8x8_t sum = vpadd_s8(a_dup, a_dup);
+ sum = vpadd_s8(sum, sum);
+ return vget_lane_s8(sum, 0);
+}
+#if EIGEN_ARCH_ARM64
+template<> EIGEN_STRONG_INLINE int8_t predux<Packet8c>(const Packet8c& a) { return vaddv_s8(a); }
+template<> EIGEN_STRONG_INLINE int8_t predux<Packet16c>(const Packet16c& a) { return vaddvq_s8(a); }
+#else
+template<> EIGEN_STRONG_INLINE int8_t predux<Packet8c>(const Packet8c& a)
+{
+ int8x8_t sum = vpadd_s8(a,a);
+ sum = vpadd_s8(sum, sum);
+ sum = vpadd_s8(sum, sum);
+ return vget_lane_s8(sum, 0);
+}
+template<> EIGEN_STRONG_INLINE int8_t predux<Packet16c>(const Packet16c& a)
+{
+ int8x8_t sum = vadd_s8(vget_low_s8(a), vget_high_s8(a));
+ sum = vpadd_s8(sum, sum);
+ sum = vpadd_s8(sum, sum);
+ sum = vpadd_s8(sum, sum);
+ return vget_lane_s8(sum, 0);
+}
+#endif
+template<> EIGEN_STRONG_INLINE uint8_t predux<Packet4uc>(const Packet4uc& a)
+{
+ const uint8x8_t a_dup = vreinterpret_u8_u32(vdup_n_u32(a));
+ uint8x8_t sum = vpadd_u8(a_dup, a_dup);
+ sum = vpadd_u8(sum, sum);
+ return vget_lane_u8(sum, 0);
+}
+#if EIGEN_ARCH_ARM64
+template<> EIGEN_STRONG_INLINE uint8_t predux<Packet8uc>(const Packet8uc& a) { return vaddv_u8(a); }
+template<> EIGEN_STRONG_INLINE uint8_t predux<Packet16uc>(const Packet16uc& a) { return vaddvq_u8(a); }
+template<> EIGEN_STRONG_INLINE int16_t predux<Packet4s>(const Packet4s& a) { return vaddv_s16(a); }
+template<> EIGEN_STRONG_INLINE int16_t predux<Packet8s>(const Packet8s& a) { return vaddvq_s16(a); }
+template<> EIGEN_STRONG_INLINE uint16_t predux<Packet4us>(const Packet4us& a) { return vaddv_u16(a); }
+template<> EIGEN_STRONG_INLINE uint16_t predux<Packet8us>(const Packet8us& a) { return vaddvq_u16(a); }
+template<> EIGEN_STRONG_INLINE int32_t predux<Packet2i>(const Packet2i& a) { return vaddv_s32(a); }
+template<> EIGEN_STRONG_INLINE int32_t predux<Packet4i>(const Packet4i& a) { return vaddvq_s32(a); }
+template<> EIGEN_STRONG_INLINE uint32_t predux<Packet2ui>(const Packet2ui& a) { return vaddv_u32(a); }
+template<> EIGEN_STRONG_INLINE uint32_t predux<Packet4ui>(const Packet4ui& a) { return vaddvq_u32(a); }
+template<> EIGEN_STRONG_INLINE int64_t predux<Packet2l>(const Packet2l& a) { return vaddvq_s64(a); }
+template<> EIGEN_STRONG_INLINE uint64_t predux<Packet2ul>(const Packet2ul& a) { return vaddvq_u64(a); }
+#else
+template<> EIGEN_STRONG_INLINE uint8_t predux<Packet8uc>(const Packet8uc& a)
+{
+ uint8x8_t sum = vpadd_u8(a,a);
+ sum = vpadd_u8(sum, sum);
+ sum = vpadd_u8(sum, sum);
+ return vget_lane_u8(sum, 0);
+}
+template<> EIGEN_STRONG_INLINE uint8_t predux<Packet16uc>(const Packet16uc& a)
+{
+ uint8x8_t sum = vadd_u8(vget_low_u8(a), vget_high_u8(a));
+ sum = vpadd_u8(sum, sum);
+ sum = vpadd_u8(sum, sum);
+ sum = vpadd_u8(sum, sum);
+ return vget_lane_u8(sum, 0);
+}
+template<> EIGEN_STRONG_INLINE int16_t predux<Packet4s>(const Packet4s& a)
+{
+ const int16x4_t sum = vpadd_s16(a,a);
+ return vget_lane_s16(vpadd_s16(sum, sum), 0);
+}
+template<> EIGEN_STRONG_INLINE int16_t predux<Packet8s>(const Packet8s& a)
+{
+ int16x4_t sum = vadd_s16(vget_low_s16(a), vget_high_s16(a));
+ sum = vpadd_s16(sum, sum);
+ sum = vpadd_s16(sum, sum);
+ return vget_lane_s16(sum, 0);
+}
+template<> EIGEN_STRONG_INLINE uint16_t predux<Packet4us>(const Packet4us& a)
+{
+ const uint16x4_t sum = vpadd_u16(a,a);
+ return vget_lane_u16(vpadd_u16(sum, sum), 0);
+}
+template<> EIGEN_STRONG_INLINE uint16_t predux<Packet8us>(const Packet8us& a)
+{
+ uint16x4_t sum = vadd_u16(vget_low_u16(a), vget_high_u16(a));
+ sum = vpadd_u16(sum, sum);
+ sum = vpadd_u16(sum, sum);
+ return vget_lane_u16(sum, 0);
+}
+template<> EIGEN_STRONG_INLINE int32_t predux<Packet2i>(const Packet2i& a) { return vget_lane_s32(vpadd_s32(a,a), 0); }
+template<> EIGEN_STRONG_INLINE int32_t predux<Packet4i>(const Packet4i& a)
+{
+ const int32x2_t sum = vadd_s32(vget_low_s32(a), vget_high_s32(a));
+ return vget_lane_s32(vpadd_s32(sum, sum), 0);
+}
+template<> EIGEN_STRONG_INLINE uint32_t predux<Packet2ui>(const Packet2ui& a) { return vget_lane_u32(vpadd_u32(a,a), 0); }
+template<> EIGEN_STRONG_INLINE uint32_t predux<Packet4ui>(const Packet4ui& a)
+{
+ const uint32x2_t sum = vadd_u32(vget_low_u32(a), vget_high_u32(a));
+ return vget_lane_u32(vpadd_u32(sum, sum), 0);
+}
+template<> EIGEN_STRONG_INLINE int64_t predux<Packet2l>(const Packet2l& a)
+{ return vgetq_lane_s64(a, 0) + vgetq_lane_s64(a, 1); }
+template<> EIGEN_STRONG_INLINE uint64_t predux<Packet2ul>(const Packet2ul& a)
+{ return vgetq_lane_u64(a, 0) + vgetq_lane_u64(a, 1); }
+#endif
+
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet4c predux_half_dowto4(const Packet8c& a)
+{
+ return vget_lane_s32(vreinterpret_s32_s8(vadd_s8(a,
+ vreinterpret_s8_s32(vrev64_s32(vreinterpret_s32_s8(a))))), 0);
+}
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet8c predux_half_dowto4(const Packet16c& a)
+{ return vadd_s8(vget_high_s8(a), vget_low_s8(a)); }
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet4uc predux_half_dowto4(const Packet8uc& a)
+{
+ return vget_lane_u32(vreinterpret_u32_u8(vadd_u8(a,
+ vreinterpret_u8_u32(vrev64_u32(vreinterpret_u32_u8(a))))), 0);
+}
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet8uc predux_half_dowto4(const Packet16uc& a)
+{ return vadd_u8(vget_high_u8(a), vget_low_u8(a)); }
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet4s predux_half_dowto4(const Packet8s& a)
+{ return vadd_s16(vget_high_s16(a), vget_low_s16(a)); }
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet4us predux_half_dowto4(const Packet8us& a)
+{ return vadd_u16(vget_high_u16(a), vget_low_u16(a)); }
+
+// Other reduction functions:
+// mul
+template<> EIGEN_STRONG_INLINE float predux_mul<Packet2f>(const Packet2f& a)
+{ return vget_lane_f32(a, 0) * vget_lane_f32(a, 1); }
+template<> EIGEN_STRONG_INLINE float predux_mul<Packet4f>(const Packet4f& a)
+{ return predux_mul(vmul_f32(vget_low_f32(a), vget_high_f32(a))); }
+template<> EIGEN_STRONG_INLINE int8_t predux_mul<Packet4c>(const Packet4c& a)
+{
+ int8x8_t prod = vreinterpret_s8_s32(vdup_n_s32(a));
+ prod = vmul_s8(prod, vrev16_s8(prod));
+ return vget_lane_s8(prod, 0) * vget_lane_s8(prod, 2);
+}
+template<> EIGEN_STRONG_INLINE int8_t predux_mul<Packet8c>(const Packet8c& a)
+{
+ int8x8_t prod = vmul_s8(a, vrev16_s8(a));
+ prod = vmul_s8(prod, vrev32_s8(prod));
+ return vget_lane_s8(prod, 0) * vget_lane_s8(prod, 4);
+}
+template<> EIGEN_STRONG_INLINE int8_t predux_mul<Packet16c>(const Packet16c& a)
+{ return predux_mul(vmul_s8(vget_low_s8(a), vget_high_s8(a))); }
+template<> EIGEN_STRONG_INLINE uint8_t predux_mul<Packet4uc>(const Packet4uc& a)
+{
+ uint8x8_t prod = vreinterpret_u8_u32(vdup_n_u32(a));
+ prod = vmul_u8(prod, vrev16_u8(prod));
+ return vget_lane_u8(prod, 0) * vget_lane_u8(prod, 2);
+}
+template<> EIGEN_STRONG_INLINE uint8_t predux_mul<Packet8uc>(const Packet8uc& a)
+{
+ uint8x8_t prod = vmul_u8(a, vrev16_u8(a));
+ prod = vmul_u8(prod, vrev32_u8(prod));
+ return vget_lane_u8(prod, 0) * vget_lane_u8(prod, 4);
+}
+template<> EIGEN_STRONG_INLINE uint8_t predux_mul<Packet16uc>(const Packet16uc& a)
+{ return predux_mul(vmul_u8(vget_low_u8(a), vget_high_u8(a))); }
+template<> EIGEN_STRONG_INLINE int16_t predux_mul<Packet4s>(const Packet4s& a)
+{
+ const int16x4_t prod = vmul_s16(a, vrev32_s16(a));
+ return vget_lane_s16(prod, 0) * vget_lane_s16(prod, 2);
+}
+template<> EIGEN_STRONG_INLINE int16_t predux_mul<Packet8s>(const Packet8s& a)
+{
+ int16x4_t prod;
+
+ // Get the product of a_lo * a_hi -> |a1*a5|a2*a6|a3*a7|a4*a8|
+ prod = vmul_s16(vget_low_s16(a), vget_high_s16(a));
+ // Swap and multiply |a1*a5*a2*a6|a3*a7*a4*a8|
+ prod = vmul_s16(prod, vrev32_s16(prod));
+ // Multiply |a1*a5*a2*a6*a3*a7*a4*a8|
+ return vget_lane_s16(prod, 0) * vget_lane_s16(prod, 2);
+}
+template<> EIGEN_STRONG_INLINE uint16_t predux_mul<Packet4us>(const Packet4us& a)
+{
+ const uint16x4_t prod = vmul_u16(a, vrev32_u16(a));
+ return vget_lane_u16(prod, 0) * vget_lane_u16(prod, 2);
+}
+template<> EIGEN_STRONG_INLINE uint16_t predux_mul<Packet8us>(const Packet8us& a)
+{
+ uint16x4_t prod;
+
+ // Get the product of a_lo * a_hi -> |a1*a5|a2*a6|a3*a7|a4*a8|
+ prod = vmul_u16(vget_low_u16(a), vget_high_u16(a));
+ // Swap and multiply |a1*a5*a2*a6|a3*a7*a4*a8|
+ prod = vmul_u16(prod, vrev32_u16(prod));
+ // Multiply |a1*a5*a2*a6*a3*a7*a4*a8|
+ return vget_lane_u16(prod, 0) * vget_lane_u16(prod, 2);
+}
+template<> EIGEN_STRONG_INLINE int32_t predux_mul<Packet2i>(const Packet2i& a)
+{ return vget_lane_s32(a, 0) * vget_lane_s32(a, 1); }
+template<> EIGEN_STRONG_INLINE int32_t predux_mul<Packet4i>(const Packet4i& a)
+{ return predux_mul(vmul_s32(vget_low_s32(a), vget_high_s32(a))); }
+template<> EIGEN_STRONG_INLINE uint32_t predux_mul<Packet2ui>(const Packet2ui& a)
+{ return vget_lane_u32(a, 0) * vget_lane_u32(a, 1); }
+template<> EIGEN_STRONG_INLINE uint32_t predux_mul<Packet4ui>(const Packet4ui& a)
+{ return predux_mul(vmul_u32(vget_low_u32(a), vget_high_u32(a))); }
+template<> EIGEN_STRONG_INLINE int64_t predux_mul<Packet2l>(const Packet2l& a)
+{ return vgetq_lane_s64(a, 0) * vgetq_lane_s64(a, 1); }
+template<> EIGEN_STRONG_INLINE uint64_t predux_mul<Packet2ul>(const Packet2ul& a)
+{ return vgetq_lane_u64(a, 0) * vgetq_lane_u64(a, 1); }
+
+// min
+#if EIGEN_ARCH_ARM64
+template<> EIGEN_STRONG_INLINE float predux_min<Packet2f>(const Packet2f& a) { return vminv_f32(a); }
+template<> EIGEN_STRONG_INLINE float predux_min<Packet4f>(const Packet4f& a) { return vminvq_f32(a); }
+#else
+template<> EIGEN_STRONG_INLINE float predux_min<Packet2f>(const Packet2f& a)
+{ return vget_lane_f32(vpmin_f32(a,a), 0); }
+template<> EIGEN_STRONG_INLINE float predux_min<Packet4f>(const Packet4f& a)
+{
+ const float32x2_t min = vmin_f32(vget_low_f32(a), vget_high_f32(a));
+ return vget_lane_f32(vpmin_f32(min, min), 0);
+}
+#endif
+template<> EIGEN_STRONG_INLINE int8_t predux_min<Packet4c>(const Packet4c& a)
+{
+ const int8x8_t a_dup = vreinterpret_s8_s32(vdup_n_s32(a));
+ int8x8_t min = vpmin_s8(a_dup, a_dup);
+ min = vpmin_s8(min, min);
+ return vget_lane_s8(min, 0);
+}
+#if EIGEN_ARCH_ARM64
+template<> EIGEN_STRONG_INLINE int8_t predux_min<Packet8c>(const Packet8c& a) { return vminv_s8(a); }
+template<> EIGEN_STRONG_INLINE int8_t predux_min<Packet16c>(const Packet16c& a) { return vminvq_s8(a); }
+#else
+template<> EIGEN_STRONG_INLINE int8_t predux_min<Packet8c>(const Packet8c& a)
+{
+ int8x8_t min = vpmin_s8(a,a);
+ min = vpmin_s8(min, min);
+ min = vpmin_s8(min, min);
+ return vget_lane_s8(min, 0);
+}
+template<> EIGEN_STRONG_INLINE int8_t predux_min<Packet16c>(const Packet16c& a)
+{
+ int8x8_t min = vmin_s8(vget_low_s8(a), vget_high_s8(a));
+ min = vpmin_s8(min, min);
+ min = vpmin_s8(min, min);
+ min = vpmin_s8(min, min);
+ return vget_lane_s8(min, 0);
+}
+#endif
+template<> EIGEN_STRONG_INLINE uint8_t predux_min<Packet4uc>(const Packet4uc& a)
+{
+ const uint8x8_t a_dup = vreinterpret_u8_u32(vdup_n_u32(a));
+ uint8x8_t min = vpmin_u8(a_dup, a_dup);
+ min = vpmin_u8(min, min);
+ return vget_lane_u8(min, 0);
+}
+#if EIGEN_ARCH_ARM64
+template<> EIGEN_STRONG_INLINE uint8_t predux_min<Packet8uc>(const Packet8uc& a) { return vminv_u8(a); }
+template<> EIGEN_STRONG_INLINE uint8_t predux_min<Packet16uc>(const Packet16uc& a) { return vminvq_u8(a); }
+template<> EIGEN_STRONG_INLINE int16_t predux_min<Packet4s>(const Packet4s& a) { return vminv_s16(a); }
+template<> EIGEN_STRONG_INLINE int16_t predux_min<Packet8s>(const Packet8s& a) { return vminvq_s16(a); }
+template<> EIGEN_STRONG_INLINE uint16_t predux_min<Packet4us>(const Packet4us& a) { return vminv_u16(a); }
+template<> EIGEN_STRONG_INLINE uint16_t predux_min<Packet8us>(const Packet8us& a) { return vminvq_u16(a); }
+template<> EIGEN_STRONG_INLINE int32_t predux_min<Packet2i>(const Packet2i& a) { return vminv_s32(a); }
+template<> EIGEN_STRONG_INLINE int32_t predux_min<Packet4i>(const Packet4i& a) { return vminvq_s32(a); }
+template<> EIGEN_STRONG_INLINE uint32_t predux_min<Packet2ui>(const Packet2ui& a) { return vminv_u32(a); }
+template<> EIGEN_STRONG_INLINE uint32_t predux_min<Packet4ui>(const Packet4ui& a) { return vminvq_u32(a); }
+#else
+template<> EIGEN_STRONG_INLINE uint8_t predux_min<Packet8uc>(const Packet8uc& a)
+{
+ uint8x8_t min = vpmin_u8(a,a);
+ min = vpmin_u8(min, min);
+ min = vpmin_u8(min, min);
+ return vget_lane_u8(min, 0);
+}
+template<> EIGEN_STRONG_INLINE uint8_t predux_min<Packet16uc>(const Packet16uc& a)
+{
+ uint8x8_t min = vmin_u8(vget_low_u8(a), vget_high_u8(a));
+ min = vpmin_u8(min, min);
+ min = vpmin_u8(min, min);
+ min = vpmin_u8(min, min);
+ return vget_lane_u8(min, 0);
+}
+template<> EIGEN_STRONG_INLINE int16_t predux_min<Packet4s>(const Packet4s& a)
+{
+ const int16x4_t min = vpmin_s16(a,a);
+ return vget_lane_s16(vpmin_s16(min, min), 0);
+}
+template<> EIGEN_STRONG_INLINE int16_t predux_min<Packet8s>(const Packet8s& a)
+{
+ int16x4_t min = vmin_s16(vget_low_s16(a), vget_high_s16(a));
+ min = vpmin_s16(min, min);
+ min = vpmin_s16(min, min);
+ return vget_lane_s16(min, 0);
+}
+template<> EIGEN_STRONG_INLINE uint16_t predux_min<Packet4us>(const Packet4us& a)
+{
+ const uint16x4_t min = vpmin_u16(a,a);
+ return vget_lane_u16(vpmin_u16(min, min), 0);
+}
+template<> EIGEN_STRONG_INLINE uint16_t predux_min<Packet8us>(const Packet8us& a)
+{
+ uint16x4_t min = vmin_u16(vget_low_u16(a), vget_high_u16(a));
+ min = vpmin_u16(min, min);
+ min = vpmin_u16(min, min);
+ return vget_lane_u16(min, 0);
+}
+template<> EIGEN_STRONG_INLINE int32_t predux_min<Packet2i>(const Packet2i& a)
+{ return vget_lane_s32(vpmin_s32(a,a), 0); }
+template<> EIGEN_STRONG_INLINE int32_t predux_min<Packet4i>(const Packet4i& a)
+{
+ const int32x2_t min = vmin_s32(vget_low_s32(a), vget_high_s32(a));
+ return vget_lane_s32(vpmin_s32(min, min), 0);
+}
+template<> EIGEN_STRONG_INLINE uint32_t predux_min<Packet2ui>(const Packet2ui& a)
+{ return vget_lane_u32(vpmin_u32(a,a), 0); }
+template<> EIGEN_STRONG_INLINE uint32_t predux_min<Packet4ui>(const Packet4ui& a)
+{
+ const uint32x2_t min = vmin_u32(vget_low_u32(a), vget_high_u32(a));
+ return vget_lane_u32(vpmin_u32(min, min), 0);
+}
+#endif
+template<> EIGEN_STRONG_INLINE int64_t predux_min<Packet2l>(const Packet2l& a)
+{ return (std::min)(vgetq_lane_s64(a, 0), vgetq_lane_s64(a, 1)); }
+template<> EIGEN_STRONG_INLINE uint64_t predux_min<Packet2ul>(const Packet2ul& a)
+{ return (std::min)(vgetq_lane_u64(a, 0), vgetq_lane_u64(a, 1)); }
+
+// max
+#if EIGEN_ARCH_ARM64
+template<> EIGEN_STRONG_INLINE float predux_max<Packet2f>(const Packet2f& a) { return vmaxv_f32(a); }
+template<> EIGEN_STRONG_INLINE float predux_max<Packet4f>(const Packet4f& a) { return vmaxvq_f32(a); }
+#else
+template<> EIGEN_STRONG_INLINE float predux_max<Packet2f>(const Packet2f& a)
+{ return vget_lane_f32(vpmax_f32(a,a), 0); }
+template<> EIGEN_STRONG_INLINE float predux_max<Packet4f>(const Packet4f& a)
+{
+ const float32x2_t max = vmax_f32(vget_low_f32(a), vget_high_f32(a));
+ return vget_lane_f32(vpmax_f32(max, max), 0);
+}
+#endif
+template<> EIGEN_STRONG_INLINE int8_t predux_max<Packet4c>(const Packet4c& a)
+{
+ const int8x8_t a_dup = vreinterpret_s8_s32(vdup_n_s32(a));
+ int8x8_t max = vpmax_s8(a_dup, a_dup);
+ max = vpmax_s8(max, max);
+ return vget_lane_s8(max, 0);
+}
+#if EIGEN_ARCH_ARM64
+template<> EIGEN_STRONG_INLINE int8_t predux_max<Packet8c>(const Packet8c& a) { return vmaxv_s8(a); }
+template<> EIGEN_STRONG_INLINE int8_t predux_max<Packet16c>(const Packet16c& a) { return vmaxvq_s8(a); }
+#else
+template<> EIGEN_STRONG_INLINE int8_t predux_max<Packet8c>(const Packet8c& a)
+{
+ int8x8_t max = vpmax_s8(a,a);
+ max = vpmax_s8(max, max);
+ max = vpmax_s8(max, max);
+ return vget_lane_s8(max, 0);
+}
+template<> EIGEN_STRONG_INLINE int8_t predux_max<Packet16c>(const Packet16c& a)
+{
+ int8x8_t max = vmax_s8(vget_low_s8(a), vget_high_s8(a));
+ max = vpmax_s8(max, max);
+ max = vpmax_s8(max, max);
+ max = vpmax_s8(max, max);
+ return vget_lane_s8(max, 0);
+}
+#endif
+template<> EIGEN_STRONG_INLINE uint8_t predux_max<Packet4uc>(const Packet4uc& a)
+{
+ const uint8x8_t a_dup = vreinterpret_u8_u32(vdup_n_u32(a));
+ uint8x8_t max = vpmax_u8(a_dup, a_dup);
+ max = vpmax_u8(max, max);
+ return vget_lane_u8(max, 0);
+}
+#if EIGEN_ARCH_ARM64
+template<> EIGEN_STRONG_INLINE uint8_t predux_max<Packet8uc>(const Packet8uc& a) { return vmaxv_u8(a); }
+template<> EIGEN_STRONG_INLINE uint8_t predux_max<Packet16uc>(const Packet16uc& a) { return vmaxvq_u8(a); }
+template<> EIGEN_STRONG_INLINE int16_t predux_max<Packet4s>(const Packet4s& a) { return vmaxv_s16(a); }
+template<> EIGEN_STRONG_INLINE int16_t predux_max<Packet8s>(const Packet8s& a) { return vmaxvq_s16(a); }
+template<> EIGEN_STRONG_INLINE uint16_t predux_max<Packet4us>(const Packet4us& a) { return vmaxv_u16(a); }
+template<> EIGEN_STRONG_INLINE uint16_t predux_max<Packet8us>(const Packet8us& a) { return vmaxvq_u16(a); }
+template<> EIGEN_STRONG_INLINE int32_t predux_max<Packet2i>(const Packet2i& a) { return vmaxv_s32(a); }
+template<> EIGEN_STRONG_INLINE int32_t predux_max<Packet4i>(const Packet4i& a) { return vmaxvq_s32(a); }
+template<> EIGEN_STRONG_INLINE uint32_t predux_max<Packet2ui>(const Packet2ui& a) { return vmaxv_u32(a); }
+template<> EIGEN_STRONG_INLINE uint32_t predux_max<Packet4ui>(const Packet4ui& a) { return vmaxvq_u32(a); }
+#else
+template<> EIGEN_STRONG_INLINE uint8_t predux_max<Packet8uc>(const Packet8uc& a)
+{
+ uint8x8_t max = vpmax_u8(a,a);
+ max = vpmax_u8(max, max);
+ max = vpmax_u8(max, max);
+ return vget_lane_u8(max, 0);
+}
+template<> EIGEN_STRONG_INLINE uint8_t predux_max<Packet16uc>(const Packet16uc& a)
+{
+ uint8x8_t max = vmax_u8(vget_low_u8(a), vget_high_u8(a));
+ max = vpmax_u8(max, max);
+ max = vpmax_u8(max, max);
+ max = vpmax_u8(max, max);
+ return vget_lane_u8(max, 0);
+}
+template<> EIGEN_STRONG_INLINE int16_t predux_max<Packet4s>(const Packet4s& a)
+{
+ const int16x4_t max = vpmax_s16(a,a);
+ return vget_lane_s16(vpmax_s16(max, max), 0);
+}
+template<> EIGEN_STRONG_INLINE int16_t predux_max<Packet8s>(const Packet8s& a)
+{
+ int16x4_t max = vmax_s16(vget_low_s16(a), vget_high_s16(a));
+ max = vpmax_s16(max, max);
+ max = vpmax_s16(max, max);
+ return vget_lane_s16(max, 0);
+}
+template<> EIGEN_STRONG_INLINE uint16_t predux_max<Packet4us>(const Packet4us& a)
+{
+ const uint16x4_t max = vpmax_u16(a,a);
+ return vget_lane_u16(vpmax_u16(max, max), 0);
+}
+template<> EIGEN_STRONG_INLINE uint16_t predux_max<Packet8us>(const Packet8us& a)
+{
+ uint16x4_t max = vmax_u16(vget_low_u16(a), vget_high_u16(a));
+ max = vpmax_u16(max, max);
+ max = vpmax_u16(max, max);
+ return vget_lane_u16(max, 0);
+}
+template<> EIGEN_STRONG_INLINE int32_t predux_max<Packet2i>(const Packet2i& a)
+{ return vget_lane_s32(vpmax_s32(a,a), 0); }
+template<> EIGEN_STRONG_INLINE int32_t predux_max<Packet4i>(const Packet4i& a)
+{
+ const int32x2_t max = vmax_s32(vget_low_s32(a), vget_high_s32(a));
+ return vget_lane_s32(vpmax_s32(max, max), 0);
+}
+template<> EIGEN_STRONG_INLINE uint32_t predux_max<Packet2ui>(const Packet2ui& a)
+{ return vget_lane_u32(vpmax_u32(a,a), 0); }
+template<> EIGEN_STRONG_INLINE uint32_t predux_max<Packet4ui>(const Packet4ui& a)
+{
+ const uint32x2_t max = vmax_u32(vget_low_u32(a), vget_high_u32(a));
+ return vget_lane_u32(vpmax_u32(max, max), 0);
+}
+#endif
+template<> EIGEN_STRONG_INLINE int64_t predux_max<Packet2l>(const Packet2l& a)
+{ return (std::max)(vgetq_lane_s64(a, 0), vgetq_lane_s64(a, 1)); }
+template<> EIGEN_STRONG_INLINE uint64_t predux_max<Packet2ul>(const Packet2ul& a)
+{ return (std::max)(vgetq_lane_u64(a, 0), vgetq_lane_u64(a, 1)); }
+
+template<> EIGEN_STRONG_INLINE bool predux_any(const Packet4f& x)
+{
+ uint32x2_t tmp = vorr_u32(vget_low_u32( vreinterpretq_u32_f32(x)),
+ vget_high_u32(vreinterpretq_u32_f32(x)));
+ return vget_lane_u32(vpmax_u32(tmp, tmp), 0);
+}
+
+// Helpers for ptranspose.
+namespace detail {
+
+template<typename Packet>
+void zip_in_place(Packet& p1, Packet& p2);
+
+template<>
+EIGEN_ALWAYS_INLINE void zip_in_place<Packet2f>(Packet2f& p1, Packet2f& p2) {
+ const float32x2x2_t tmp = vzip_f32(p1, p2);
+ p1 = tmp.val[0];
+ p2 = tmp.val[1];
+}
+
+template<>
+EIGEN_ALWAYS_INLINE void zip_in_place<Packet4f>(Packet4f& p1, Packet4f& p2) {
+ const float32x4x2_t tmp = vzipq_f32(p1, p2);
+ p1 = tmp.val[0];
+ p2 = tmp.val[1];
+}
+
+template<>
+EIGEN_ALWAYS_INLINE void zip_in_place<Packet8c>(Packet8c& p1, Packet8c& p2) {
+ const int8x8x2_t tmp = vzip_s8(p1, p2);
+ p1 = tmp.val[0];
+ p2 = tmp.val[1];
+}
+
+template<>
+EIGEN_ALWAYS_INLINE void zip_in_place<Packet16c>(Packet16c& p1, Packet16c& p2) {
+ const int8x16x2_t tmp = vzipq_s8(p1, p2);
+ p1 = tmp.val[0];
+ p2 = tmp.val[1];
+}
+
+template<>
+EIGEN_ALWAYS_INLINE void zip_in_place<Packet8uc>(Packet8uc& p1, Packet8uc& p2) {
+ const uint8x8x2_t tmp = vzip_u8(p1, p2);
+ p1 = tmp.val[0];
+ p2 = tmp.val[1];
+}
+
+template<>
+EIGEN_ALWAYS_INLINE void zip_in_place<Packet16uc>(Packet16uc& p1, Packet16uc& p2) {
+ const uint8x16x2_t tmp = vzipq_u8(p1, p2);
+ p1 = tmp.val[0];
+ p2 = tmp.val[1];
+}
+
+template<>
+EIGEN_ALWAYS_INLINE void zip_in_place<Packet2i>(Packet2i& p1, Packet2i& p2) {
+ const int32x2x2_t tmp = vzip_s32(p1, p2);
+ p1 = tmp.val[0];
+ p2 = tmp.val[1];
+}
+
+template<>
+EIGEN_ALWAYS_INLINE void zip_in_place<Packet4i>(Packet4i& p1, Packet4i& p2) {
+ const int32x4x2_t tmp = vzipq_s32(p1, p2);
+ p1 = tmp.val[0];
+ p2 = tmp.val[1];
+}
+
+template<>
+EIGEN_ALWAYS_INLINE void zip_in_place<Packet2ui>(Packet2ui& p1, Packet2ui& p2) {
+ const uint32x2x2_t tmp = vzip_u32(p1, p2);
+ p1 = tmp.val[0];
+ p2 = tmp.val[1];
+}
+
+template<>
+EIGEN_ALWAYS_INLINE void zip_in_place<Packet4ui>(Packet4ui& p1, Packet4ui& p2) {
+ const uint32x4x2_t tmp = vzipq_u32(p1, p2);
+ p1 = tmp.val[0];
+ p2 = tmp.val[1];
+}
+
+template<>
+EIGEN_ALWAYS_INLINE void zip_in_place<Packet4s>(Packet4s& p1, Packet4s& p2) {
+ const int16x4x2_t tmp = vzip_s16(p1, p2);
+ p1 = tmp.val[0];
+ p2 = tmp.val[1];
+}
+
+template<>
+EIGEN_ALWAYS_INLINE void zip_in_place<Packet8s>(Packet8s& p1, Packet8s& p2) {
+ const int16x8x2_t tmp = vzipq_s16(p1, p2);
+ p1 = tmp.val[0];
+ p2 = tmp.val[1];
+}
+
+template<>
+EIGEN_ALWAYS_INLINE void zip_in_place<Packet4us>(Packet4us& p1, Packet4us& p2) {
+ const uint16x4x2_t tmp = vzip_u16(p1, p2);
+ p1 = tmp.val[0];
+ p2 = tmp.val[1];
+}
+
+template<>
+EIGEN_ALWAYS_INLINE void zip_in_place<Packet8us>(Packet8us& p1, Packet8us& p2) {
+ const uint16x8x2_t tmp = vzipq_u16(p1, p2);
+ p1 = tmp.val[0];
+ p2 = tmp.val[1];
+}
+
+template<typename Packet>
+EIGEN_ALWAYS_INLINE void ptranspose_impl(PacketBlock<Packet, 2>& kernel) {
+ zip_in_place(kernel.packet[0], kernel.packet[1]);
+}
+
+template<typename Packet>
+EIGEN_ALWAYS_INLINE void ptranspose_impl(PacketBlock<Packet, 4>& kernel) {
+ zip_in_place(kernel.packet[0], kernel.packet[2]);
+ zip_in_place(kernel.packet[1], kernel.packet[3]);
+ zip_in_place(kernel.packet[0], kernel.packet[1]);
+ zip_in_place(kernel.packet[2], kernel.packet[3]);
+}
+
+template<typename Packet>
+EIGEN_ALWAYS_INLINE void ptranspose_impl(PacketBlock<Packet, 8>& kernel) {
+ zip_in_place(kernel.packet[0], kernel.packet[4]);
+ zip_in_place(kernel.packet[1], kernel.packet[5]);
+ zip_in_place(kernel.packet[2], kernel.packet[6]);
+ zip_in_place(kernel.packet[3], kernel.packet[7]);
+
+ zip_in_place(kernel.packet[0], kernel.packet[2]);
+ zip_in_place(kernel.packet[1], kernel.packet[3]);
+ zip_in_place(kernel.packet[4], kernel.packet[6]);
+ zip_in_place(kernel.packet[5], kernel.packet[7]);
+
+ zip_in_place(kernel.packet[0], kernel.packet[1]);
+ zip_in_place(kernel.packet[2], kernel.packet[3]);
+ zip_in_place(kernel.packet[4], kernel.packet[5]);
+ zip_in_place(kernel.packet[6], kernel.packet[7]);
+}
+
+template<typename Packet>
+EIGEN_ALWAYS_INLINE void ptranspose_impl(PacketBlock<Packet, 16>& kernel) {
+ EIGEN_UNROLL_LOOP
+ for (int i=0; i<4; ++i) {
+ const int m = (1 << i);
+ EIGEN_UNROLL_LOOP
+ for (int j=0; j<m; ++j) {
+ const int n = (1 << (3-i));
+ EIGEN_UNROLL_LOOP
+ for (int k=0; k<n; ++k) {
+ const int idx = 2*j*n+k;
+ zip_in_place(kernel.packet[idx], kernel.packet[idx + n]);
+ }
+ }
+ }
+}
+
+} // namespace detail
+
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void ptranspose(PacketBlock<Packet2f, 2>& kernel) {
+ detail::ptranspose_impl(kernel);
+}
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void ptranspose(PacketBlock<Packet4f, 4>& kernel) {
+ detail::ptranspose_impl(kernel);
+}
+
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void ptranspose(PacketBlock<Packet4c, 4>& kernel)
+{
+ const int8x8_t a = vreinterpret_s8_s32(vset_lane_s32(kernel.packet[2], vdup_n_s32(kernel.packet[0]), 1));
+ const int8x8_t b = vreinterpret_s8_s32(vset_lane_s32(kernel.packet[3], vdup_n_s32(kernel.packet[1]), 1));
+
+ const int8x8x2_t zip8 = vzip_s8(a,b);
+ const int16x4x2_t zip16 = vzip_s16(vreinterpret_s16_s8(zip8.val[0]), vreinterpret_s16_s8(zip8.val[1]));
+
+ kernel.packet[0] = vget_lane_s32(vreinterpret_s32_s16(zip16.val[0]), 0);
+ kernel.packet[1] = vget_lane_s32(vreinterpret_s32_s16(zip16.val[0]), 1);
+ kernel.packet[2] = vget_lane_s32(vreinterpret_s32_s16(zip16.val[1]), 0);
+ kernel.packet[3] = vget_lane_s32(vreinterpret_s32_s16(zip16.val[1]), 1);
+}
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void ptranspose(PacketBlock<Packet8c, 8>& kernel) {
+ detail::ptranspose_impl(kernel);
+}
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void ptranspose(PacketBlock<Packet8c, 4>& kernel) {
+ detail::ptranspose_impl(kernel);
+}
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void ptranspose(PacketBlock<Packet16c, 16>& kernel) {
+ detail::ptranspose_impl(kernel);
+}
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void ptranspose(PacketBlock<Packet16c, 8>& kernel) {
+ detail::ptranspose_impl(kernel);
+}
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void ptranspose(PacketBlock<Packet16c, 4>& kernel) {
+ detail::ptranspose_impl(kernel);
+}
+
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void ptranspose(PacketBlock<Packet4uc, 4>& kernel)
+{
+ const uint8x8_t a = vreinterpret_u8_u32(vset_lane_u32(kernel.packet[2], vdup_n_u32(kernel.packet[0]), 1));
+ const uint8x8_t b = vreinterpret_u8_u32(vset_lane_u32(kernel.packet[3], vdup_n_u32(kernel.packet[1]), 1));
+
+ const uint8x8x2_t zip8 = vzip_u8(a,b);
+ const uint16x4x2_t zip16 = vzip_u16(vreinterpret_u16_u8(zip8.val[0]), vreinterpret_u16_u8(zip8.val[1]));
+
+ kernel.packet[0] = vget_lane_u32(vreinterpret_u32_u16(zip16.val[0]), 0);
+ kernel.packet[1] = vget_lane_u32(vreinterpret_u32_u16(zip16.val[0]), 1);
+ kernel.packet[2] = vget_lane_u32(vreinterpret_u32_u16(zip16.val[1]), 0);
+ kernel.packet[3] = vget_lane_u32(vreinterpret_u32_u16(zip16.val[1]), 1);
+}
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void ptranspose(PacketBlock<Packet8uc, 8>& kernel) {
+ detail::ptranspose_impl(kernel);
+}
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void ptranspose(PacketBlock<Packet8uc, 4>& kernel) {
+ detail::ptranspose_impl(kernel);
+}
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void ptranspose(PacketBlock<Packet16uc, 16>& kernel) {
+ detail::ptranspose_impl(kernel);
+}
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void ptranspose(PacketBlock<Packet16uc, 8>& kernel) {
+ detail::ptranspose_impl(kernel);
+}
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void ptranspose(PacketBlock<Packet16uc, 4>& kernel) {
+ detail::ptranspose_impl(kernel);
+}
+
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void ptranspose(PacketBlock<Packet4s, 4>& kernel) {
+ detail::ptranspose_impl(kernel);
+}
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void ptranspose(PacketBlock<Packet8s, 8>& kernel) {
+ detail::ptranspose_impl(kernel);
+}
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void ptranspose(PacketBlock<Packet8s, 4>& kernel) {
+ detail::ptranspose_impl(kernel);
+}
+
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void ptranspose(PacketBlock<Packet4us, 4>& kernel) {
+ detail::ptranspose_impl(kernel);
+}
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void ptranspose(PacketBlock<Packet8us, 8>& kernel) {
+ detail::ptranspose_impl(kernel);
+}
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void ptranspose(PacketBlock<Packet8us, 4>& kernel) {
+ detail::ptranspose_impl(kernel);
+}
+
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void ptranspose(PacketBlock<Packet2i, 2>& kernel) {
+ detail::ptranspose_impl(kernel);
+}
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void ptranspose(PacketBlock<Packet4i, 4>& kernel) {
+ detail::ptranspose_impl(kernel);
+}
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void ptranspose(PacketBlock<Packet2ui, 2>& kernel) {
+ detail::zip_in_place(kernel.packet[0], kernel.packet[1]);
+}
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void ptranspose(PacketBlock<Packet4ui, 4>& kernel) {
+ detail::ptranspose_impl(kernel);
+}
+
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void
+ptranspose(PacketBlock<Packet2l, 2>& kernel)
+{
+#if EIGEN_ARCH_ARM64
+ const int64x2_t tmp1 = vzip1q_s64(kernel.packet[0], kernel.packet[1]);
+ kernel.packet[1] = vzip2q_s64(kernel.packet[0], kernel.packet[1]);
+ kernel.packet[0] = tmp1;
+#else
+ const int64x1_t tmp[2][2] = {
+ { vget_low_s64(kernel.packet[0]), vget_high_s64(kernel.packet[0]) },
+ { vget_low_s64(kernel.packet[1]), vget_high_s64(kernel.packet[1]) }
+ };
+
+ kernel.packet[0] = vcombine_s64(tmp[0][0], tmp[1][0]);
+ kernel.packet[1] = vcombine_s64(tmp[0][1], tmp[1][1]);
+#endif
+}
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void
+ptranspose(PacketBlock<Packet2ul, 2>& kernel)
+{
+#if EIGEN_ARCH_ARM64
+ const uint64x2_t tmp1 = vzip1q_u64(kernel.packet[0], kernel.packet[1]);
+ kernel.packet[1] = vzip2q_u64(kernel.packet[0], kernel.packet[1]);
+ kernel.packet[0] = tmp1;
+#else
+ const uint64x1_t tmp[2][2] = {
+ { vget_low_u64(kernel.packet[0]), vget_high_u64(kernel.packet[0]) },
+ { vget_low_u64(kernel.packet[1]), vget_high_u64(kernel.packet[1]) }
+ };
+
+ kernel.packet[0] = vcombine_u64(tmp[0][0], tmp[1][0]);
+ kernel.packet[1] = vcombine_u64(tmp[0][1], tmp[1][1]);
+#endif
+}
+
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet2f pselect( const Packet2f& mask, const Packet2f& a, const Packet2f& b)
+{ return vbsl_f32(vreinterpret_u32_f32(mask), a, b); }
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet4f pselect(const Packet4f& mask, const Packet4f& a, const Packet4f& b)
+{ return vbslq_f32(vreinterpretq_u32_f32(mask), a, b); }
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet8c pselect(const Packet8c& mask, const Packet8c& a, const Packet8c& b)
+{ return vbsl_s8(vreinterpret_u8_s8(mask), a, b); }
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet16c pselect(const Packet16c& mask, const Packet16c& a, const Packet16c& b)
+{ return vbslq_s8(vreinterpretq_u8_s8(mask), a, b); }
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet8uc pselect(const Packet8uc& mask, const Packet8uc& a, const Packet8uc& b)
+{ return vbsl_u8(mask, a, b); }
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet16uc pselect(const Packet16uc& mask, const Packet16uc& a, const Packet16uc& b)
+{ return vbslq_u8(mask, a, b); }
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet4s pselect(const Packet4s& mask, const Packet4s& a, const Packet4s& b)
+{ return vbsl_s16(vreinterpret_u16_s16(mask), a, b); }
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet8s pselect(const Packet8s& mask, const Packet8s& a, const Packet8s& b)
+{ return vbslq_s16(vreinterpretq_u16_s16(mask), a, b); }
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet4us pselect(const Packet4us& mask, const Packet4us& a, const Packet4us& b)
+{ return vbsl_u16(mask, a, b); }
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet8us pselect(const Packet8us& mask, const Packet8us& a, const Packet8us& b)
+{ return vbslq_u16(mask, a, b); }
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet2i pselect(const Packet2i& mask, const Packet2i& a, const Packet2i& b)
+{ return vbsl_s32(vreinterpret_u32_s32(mask), a, b); }
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet4i pselect(const Packet4i& mask, const Packet4i& a, const Packet4i& b)
+{ return vbslq_s32(vreinterpretq_u32_s32(mask), a, b); }
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet2ui pselect(const Packet2ui& mask, const Packet2ui& a, const Packet2ui& b)
+{ return vbsl_u32(mask, a, b); }
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet4ui pselect(const Packet4ui& mask, const Packet4ui& a, const Packet4ui& b)
+{ return vbslq_u32(mask, a, b); }
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet2l pselect(const Packet2l& mask, const Packet2l& a, const Packet2l& b)
+{ return vbslq_s64(vreinterpretq_u64_s64(mask), a, b); }
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet2ul pselect(const Packet2ul& mask, const Packet2ul& a, const Packet2ul& b)
+{ return vbslq_u64(mask, a, b); }
+
+// Use armv8 rounding intinsics if available.
+#if EIGEN_ARCH_ARMV8
+template<> EIGEN_STRONG_INLINE Packet2f print<Packet2f>(const Packet2f& a)
+{ return vrndn_f32(a); }
+
+template<> EIGEN_STRONG_INLINE Packet4f print<Packet4f>(const Packet4f& a)
+{ return vrndnq_f32(a); }
+
+template<> EIGEN_STRONG_INLINE Packet2f pfloor<Packet2f>(const Packet2f& a)
+{ return vrndm_f32(a); }
+
+template<> EIGEN_STRONG_INLINE Packet4f pfloor<Packet4f>(const Packet4f& a)
+{ return vrndmq_f32(a); }
+
+template<> EIGEN_STRONG_INLINE Packet2f pceil<Packet2f>(const Packet2f& a)
+{ return vrndp_f32(a); }
+
+template<> EIGEN_STRONG_INLINE Packet4f pceil<Packet4f>(const Packet4f& a)
+{ return vrndpq_f32(a); }
+
+#else
+
+template<> EIGEN_STRONG_INLINE Packet4f print(const Packet4f& a) {
+ // Adds and subtracts signum(a) * 2^23 to force rounding.
+ const Packet4f limit = pset1<Packet4f>(static_cast<float>(1<<23));
+ const Packet4f abs_a = pabs(a);
+ Packet4f r = padd(abs_a, limit);
+ // Don't compile-away addition and subtraction.
+ EIGEN_OPTIMIZATION_BARRIER(r);
+ r = psub(r, limit);
+ // If greater than limit, simply return a. Otherwise, account for sign.
+ r = pselect(pcmp_lt(abs_a, limit),
+ pselect(pcmp_lt(a, pzero(a)), pnegate(r), r), a);
+ return r;
+}
+
+template<> EIGEN_STRONG_INLINE Packet2f print(const Packet2f& a) {
+ // Adds and subtracts signum(a) * 2^23 to force rounding.
+ const Packet2f limit = pset1<Packet2f>(static_cast<float>(1<<23));
+ const Packet2f abs_a = pabs(a);
+ Packet2f r = padd(abs_a, limit);
+ // Don't compile-away addition and subtraction.
+ EIGEN_OPTIMIZATION_BARRIER(r);
+ r = psub(r, limit);
+ // If greater than limit, simply return a. Otherwise, account for sign.
+ r = pselect(pcmp_lt(abs_a, limit),
+ pselect(pcmp_lt(a, pzero(a)), pnegate(r), r), a);
+ return r;
+}
+
+template<> EIGEN_STRONG_INLINE Packet4f pfloor<Packet4f>(const Packet4f& a)
+{
+ const Packet4f cst_1 = pset1<Packet4f>(1.0f);
+ Packet4f tmp = print<Packet4f>(a);
+ // If greater, subtract one.
+ Packet4f mask = pcmp_lt(a, tmp);
+ mask = pand(mask, cst_1);
+ return psub(tmp, mask);
+}
+
+template<> EIGEN_STRONG_INLINE Packet2f pfloor<Packet2f>(const Packet2f& a)
+{
+ const Packet2f cst_1 = pset1<Packet2f>(1.0f);
+ Packet2f tmp = print<Packet2f>(a);
+ // If greater, subtract one.
+ Packet2f mask = pcmp_lt(a, tmp);
+ mask = pand(mask, cst_1);
+ return psub(tmp, mask);
+}
+
+template<> EIGEN_STRONG_INLINE Packet4f pceil<Packet4f>(const Packet4f& a)
+{
+ const Packet4f cst_1 = pset1<Packet4f>(1.0f);
+ Packet4f tmp = print<Packet4f>(a);
+ // If smaller, add one.
+ Packet4f mask = pcmp_lt(tmp, a);
+ mask = pand(mask, cst_1);
+ return padd(tmp, mask);
+}
+
+template<> EIGEN_STRONG_INLINE Packet2f pceil<Packet2f>(const Packet2f& a)
+{
+ const Packet2f cst_1 = pset1<Packet2f>(1.0);
+ Packet2f tmp = print<Packet2f>(a);
+ // If smaller, add one.
+ Packet2f mask = pcmp_lt(tmp, a);
+ mask = pand(mask, cst_1);
+ return padd(tmp, mask);
+}
+
+#endif
+
+/**
+ * Computes the integer square root
+ * @remarks The calculation is performed using an algorithm which iterates through each binary digit of the result
+ * and tests whether setting that digit to 1 would cause the square of the value to be greater than the argument
+ * value. The algorithm is described in detail here: http://ww1.microchip.com/downloads/en/AppNotes/91040a.pdf .
+ */
+template<> EIGEN_STRONG_INLINE Packet4uc psqrt(const Packet4uc& a) {
+ uint8x8_t x = vreinterpret_u8_u32(vdup_n_u32(a));
+ uint8x8_t res = vdup_n_u8(0);
+ uint8x8_t add = vdup_n_u8(0x8);
+ for (int i = 0; i < 4; i++)
+ {
+ const uint8x8_t temp = vorr_u8(res, add);
+ res = vbsl_u8(vcge_u8(x, vmul_u8(temp, temp)), temp, res);
+ add = vshr_n_u8(add, 1);
+ }
+ return vget_lane_u32(vreinterpret_u32_u8(res), 0);
+}
+/// @copydoc Eigen::internal::psqrt(const Packet4uc& a)
+template<> EIGEN_STRONG_INLINE Packet8uc psqrt(const Packet8uc& a) {
+ uint8x8_t res = vdup_n_u8(0);
+ uint8x8_t add = vdup_n_u8(0x8);
+ for (int i = 0; i < 4; i++)
+ {
+ const uint8x8_t temp = vorr_u8(res, add);
+ res = vbsl_u8(vcge_u8(a, vmul_u8(temp, temp)), temp, res);
+ add = vshr_n_u8(add, 1);
+ }
+ return res;
+}
+/// @copydoc Eigen::internal::psqrt(const Packet4uc& a)
+template<> EIGEN_STRONG_INLINE Packet16uc psqrt(const Packet16uc& a) {
+ uint8x16_t res = vdupq_n_u8(0);
+ uint8x16_t add = vdupq_n_u8(0x8);
+ for (int i = 0; i < 4; i++)
+ {
+ const uint8x16_t temp = vorrq_u8(res, add);
+ res = vbslq_u8(vcgeq_u8(a, vmulq_u8(temp, temp)), temp, res);
+ add = vshrq_n_u8(add, 1);
+ }
+ return res;
+}
+/// @copydoc Eigen::internal::psqrt(const Packet4uc& a)
+template<> EIGEN_STRONG_INLINE Packet4us psqrt(const Packet4us& a) {
+ uint16x4_t res = vdup_n_u16(0);
+ uint16x4_t add = vdup_n_u16(0x80);
+ for (int i = 0; i < 8; i++)
+ {
+ const uint16x4_t temp = vorr_u16(res, add);
+ res = vbsl_u16(vcge_u16(a, vmul_u16(temp, temp)), temp, res);
+ add = vshr_n_u16(add, 1);
+ }
+ return res;
+}
+/// @copydoc Eigen::internal::psqrt(const Packet4uc& a)
+template<> EIGEN_STRONG_INLINE Packet8us psqrt(const Packet8us& a) {
+ uint16x8_t res = vdupq_n_u16(0);
+ uint16x8_t add = vdupq_n_u16(0x80);
+ for (int i = 0; i < 8; i++)
+ {
+ const uint16x8_t temp = vorrq_u16(res, add);
+ res = vbslq_u16(vcgeq_u16(a, vmulq_u16(temp, temp)), temp, res);
+ add = vshrq_n_u16(add, 1);
+ }
+ return res;
+}
+/// @copydoc Eigen::internal::psqrt(const Packet4uc& a)
+template<> EIGEN_STRONG_INLINE Packet2ui psqrt(const Packet2ui& a) {
+ uint32x2_t res = vdup_n_u32(0);
+ uint32x2_t add = vdup_n_u32(0x8000);
+ for (int i = 0; i < 16; i++)
+ {
+ const uint32x2_t temp = vorr_u32(res, add);
+ res = vbsl_u32(vcge_u32(a, vmul_u32(temp, temp)), temp, res);
+ add = vshr_n_u32(add, 1);
+ }
+ return res;
+}
+/// @copydoc Eigen::internal::psqrt(const Packet4uc& a)
+template<> EIGEN_STRONG_INLINE Packet4ui psqrt(const Packet4ui& a) {
+ uint32x4_t res = vdupq_n_u32(0);
+ uint32x4_t add = vdupq_n_u32(0x8000);
+ for (int i = 0; i < 16; i++)
+ {
+ const uint32x4_t temp = vorrq_u32(res, add);
+ res = vbslq_u32(vcgeq_u32(a, vmulq_u32(temp, temp)), temp, res);
+ add = vshrq_n_u32(add, 1);
+ }
+ return res;
+}
+
+template<> EIGEN_STRONG_INLINE Packet4f prsqrt(const Packet4f& a) {
+ // Do Newton iterations for 1/sqrt(x).
+ return generic_rsqrt_newton_step<Packet4f, /*Steps=*/2>::run(a, vrsqrteq_f32(a));
+}
+
+template<> EIGEN_STRONG_INLINE Packet2f prsqrt(const Packet2f& a) {
+ // Compute approximate reciprocal sqrt.
+ return generic_rsqrt_newton_step<Packet2f, /*Steps=*/2>::run(a, vrsqrte_f32(a));
+}
+
+// Unfortunately vsqrt_f32 is only available for A64.
+#if EIGEN_ARCH_ARM64
+template<> EIGEN_STRONG_INLINE Packet4f psqrt(const Packet4f& _x){return vsqrtq_f32(_x);}
+template<> EIGEN_STRONG_INLINE Packet2f psqrt(const Packet2f& _x){return vsqrt_f32(_x); }
+#else
+template<> EIGEN_STRONG_INLINE Packet4f psqrt(const Packet4f& a) {
+ return generic_sqrt_newton_step<Packet4f>::run(a, prsqrt(a));
+}
+template<> EIGEN_STRONG_INLINE Packet2f psqrt(const Packet2f& a) {
+ return generic_sqrt_newton_step<Packet2f>::run(a, prsqrt(a));
+}
+#endif
+
+//---------- bfloat16 ----------
+// TODO: Add support for native armv8.6-a bfloat16_t
+
+// TODO: Guard if we have native bfloat16 support
+typedef eigen_packet_wrapper<uint16x4_t, 19> Packet4bf;
+
+template<> struct is_arithmetic<Packet4bf> { enum { value = true }; };
+
+template<> struct packet_traits<bfloat16> : default_packet_traits
+{
+ typedef Packet4bf type;
+ typedef Packet4bf half;
+ enum
+ {
+ Vectorizable = 1,
+ AlignedOnScalar = 1,
+ size = 4,
+ HasHalfPacket = 0,
+
+ HasCmp = 1,
+ HasAdd = 1,
+ HasSub = 1,
+ HasShift = 1,
+ HasMul = 1,
+ HasNegate = 1,
+ HasAbs = 1,
+ HasArg = 0,
+ HasAbs2 = 1,
+ HasAbsDiff = 1,
+ HasMin = 1,
+ HasMax = 1,
+ HasConj = 1,
+ HasSetLinear = 0,
+ HasBlend = 0,
+ HasDiv = 1,
+ HasFloor = 1,
+ HasCeil = 1,
+ HasRint = 1,
+
+ HasSin = EIGEN_FAST_MATH,
+ HasCos = EIGEN_FAST_MATH,
+ HasLog = 1,
+ HasExp = 1,
+ HasSqrt = 0,
+ HasTanh = EIGEN_FAST_MATH,
+ HasErf = EIGEN_FAST_MATH,
+ HasBessel = 0, // Issues with accuracy.
+ HasNdtri = 0
+ };
+};
+
+template<> struct unpacket_traits<Packet4bf>
+{
+ typedef bfloat16 type;
+ typedef Packet4bf half;
+ enum
+ {
+ size = 4,
+ alignment = Aligned16,
+ vectorizable = true,
+ masked_load_available = false,
+ masked_store_available = false
+ };
+};
+
+namespace detail {
+template<>
+EIGEN_ALWAYS_INLINE void zip_in_place<Packet4bf>(Packet4bf& p1, Packet4bf& p2) {
+ const uint16x4x2_t tmp = vzip_u16(p1, p2);
+ p1 = tmp.val[0];
+ p2 = tmp.val[1];
+}
+} // namespace detail
+
+EIGEN_STRONG_INLINE Packet4bf F32ToBf16(const Packet4f& p)
+{
+ // See the scalar implementation in BFloat16.h for a comprehensible explanation
+ // of this fast rounding algorithm
+ Packet4ui input = reinterpret_cast<Packet4ui>(p);
+
+ // lsb = (input >> 16) & 1
+ Packet4ui lsb = vandq_u32(vshrq_n_u32(input, 16), vdupq_n_u32(1));
+
+ // rounding_bias = 0x7fff + lsb
+ Packet4ui rounding_bias = vaddq_u32(lsb, vdupq_n_u32(0x7fff));
+
+ // input += rounding_bias
+ input = vaddq_u32(input, rounding_bias);
+
+ // input = input >> 16
+ input = vshrq_n_u32(input, 16);
+
+ // Replace float-nans by bfloat16-nans, that is 0x7fc0
+ const Packet4ui bf16_nan = vdupq_n_u32(0x7fc0);
+ const Packet4ui mask = vceqq_f32(p, p);
+ input = vbslq_u32(mask, input, bf16_nan);
+
+ // output = static_cast<uint16_t>(input)
+ return vmovn_u32(input);
+}
+
+EIGEN_STRONG_INLINE Packet4f Bf16ToF32(const Packet4bf& p)
+{
+ return reinterpret_cast<Packet4f>(vshlq_n_u32(vmovl_u16(p), 16));
+}
+
+EIGEN_STRONG_INLINE Packet4bf F32MaskToBf16Mask(const Packet4f& p) {
+ return vmovn_u32(vreinterpretq_u32_f32(p));
+}
+
+template<> EIGEN_STRONG_INLINE Packet4bf pset1<Packet4bf>(const bfloat16& from) {
+ return pset1<Packet4us>(from.value);
+}
+
+template<> EIGEN_STRONG_INLINE bfloat16 pfirst<Packet4bf>(const Packet4bf& from) {
+ return bfloat16_impl::raw_uint16_to_bfloat16(static_cast<uint16_t>(pfirst<Packet4us>(from)));
+}
+
+template<> EIGEN_STRONG_INLINE Packet4bf pload<Packet4bf>(const bfloat16* from)
+{
+ return pload<Packet4us>(reinterpret_cast<const uint16_t*>(from));
+}
+
+template<> EIGEN_STRONG_INLINE Packet4bf ploadu<Packet4bf>(const bfloat16* from)
+{
+ return ploadu<Packet4us>(reinterpret_cast<const uint16_t*>(from));
+}
+
+template<> EIGEN_STRONG_INLINE void pstore<bfloat16>(bfloat16* to, const Packet4bf& from)
+{
+ EIGEN_DEBUG_ALIGNED_STORE vst1_u16(reinterpret_cast<uint16_t*>(to), from);
+}
+
+template<> EIGEN_STRONG_INLINE void pstoreu<bfloat16>(bfloat16* to, const Packet4bf& from)
+{
+ EIGEN_DEBUG_UNALIGNED_STORE vst1_u16(reinterpret_cast<uint16_t*>(to), from);
+}
+
+template<> EIGEN_STRONG_INLINE Packet4bf ploaddup<Packet4bf>(const bfloat16* from)
+{
+ return ploaddup<Packet4us>(reinterpret_cast<const uint16_t*>(from));
+}
+
+template <> EIGEN_STRONG_INLINE Packet4bf pabs(const Packet4bf& a) {
+ return F32ToBf16(pabs<Packet4f>(Bf16ToF32(a)));
+}
+
+template <> EIGEN_STRONG_INLINE Packet4bf pmin<PropagateNumbers, Packet4bf>(const Packet4bf &a,
+ const Packet4bf &b)
+{
+ return F32ToBf16(pmin<PropagateNumbers, Packet4f>(Bf16ToF32(a), Bf16ToF32(b)));
+}
+template <> EIGEN_STRONG_INLINE Packet4bf pmin<PropagateNaN, Packet4bf>(const Packet4bf &a,
+ const Packet4bf &b)
+{
+ return F32ToBf16(pmin<PropagateNaN, Packet4f>(Bf16ToF32(a), Bf16ToF32(b)));
+}
+
+template <> EIGEN_STRONG_INLINE Packet4bf pmin<Packet4bf>(const Packet4bf &a,
+ const Packet4bf &b)
+{
+ return F32ToBf16(pmin<Packet4f>(Bf16ToF32(a), Bf16ToF32(b)));
+}
+
+template <> EIGEN_STRONG_INLINE Packet4bf pmax<PropagateNumbers, Packet4bf>(const Packet4bf &a,
+ const Packet4bf &b)
+{
+ return F32ToBf16(pmax<PropagateNumbers, Packet4f>(Bf16ToF32(a), Bf16ToF32(b)));
+}
+template <> EIGEN_STRONG_INLINE Packet4bf pmax<PropagateNaN, Packet4bf>(const Packet4bf &a,
+ const Packet4bf &b)
+{
+ return F32ToBf16(pmax<PropagateNaN, Packet4f>(Bf16ToF32(a), Bf16ToF32(b)));
+}
+
+template <> EIGEN_STRONG_INLINE Packet4bf pmax<Packet4bf>(const Packet4bf &a,
+ const Packet4bf &b)
+{
+ return F32ToBf16(pmax<Packet4f>(Bf16ToF32(a), Bf16ToF32(b)));
+}
+
+template<> EIGEN_STRONG_INLINE Packet4bf plset<Packet4bf>(const bfloat16& a)
+{
+ return F32ToBf16(plset<Packet4f>(static_cast<float>(a)));
+}
+
+template<> EIGEN_STRONG_INLINE Packet4bf por(const Packet4bf& a,const Packet4bf& b) {
+ return por<Packet4us>(a, b);
+}
+
+template<> EIGEN_STRONG_INLINE Packet4bf pxor(const Packet4bf& a,const Packet4bf& b) {
+ return pxor<Packet4us>(a, b);
+}
+
+template<> EIGEN_STRONG_INLINE Packet4bf pand(const Packet4bf& a,const Packet4bf& b) {
+ return pand<Packet4us>(a, b);
+}
+
+template<> EIGEN_STRONG_INLINE Packet4bf pandnot(const Packet4bf& a,const Packet4bf& b) {
+ return pandnot<Packet4us>(a, b);
+}
+
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet4bf pselect(const Packet4bf& mask, const Packet4bf& a,
+ const Packet4bf& b)
+{
+ return pselect<Packet4us>(mask, a, b);
+}
+
+template<> EIGEN_STRONG_INLINE Packet4bf print<Packet4bf>(const Packet4bf& a)
+{
+ return F32ToBf16(print<Packet4f>(Bf16ToF32(a)));
+}
+
+template<> EIGEN_STRONG_INLINE Packet4bf pfloor<Packet4bf>(const Packet4bf& a)
+{
+ return F32ToBf16(pfloor<Packet4f>(Bf16ToF32(a)));
+}
+
+template<> EIGEN_STRONG_INLINE Packet4bf pceil<Packet4bf>(const Packet4bf& a)
+{
+ return F32ToBf16(pceil<Packet4f>(Bf16ToF32(a)));
+}
+
+template<> EIGEN_STRONG_INLINE Packet4bf pconj(const Packet4bf& a) { return a; }
+
+template<> EIGEN_STRONG_INLINE Packet4bf padd<Packet4bf>(const Packet4bf& a, const Packet4bf& b) {
+ return F32ToBf16(padd<Packet4f>(Bf16ToF32(a), Bf16ToF32(b)));
+}
+
+template<> EIGEN_STRONG_INLINE Packet4bf psub<Packet4bf>(const Packet4bf& a, const Packet4bf& b) {
+ return F32ToBf16(psub<Packet4f>(Bf16ToF32(a), Bf16ToF32(b)));
+}
+
+template<> EIGEN_STRONG_INLINE Packet4bf pmul<Packet4bf>(const Packet4bf& a, const Packet4bf& b) {
+ return F32ToBf16(pmul<Packet4f>(Bf16ToF32(a), Bf16ToF32(b)));
+}
+
+template<> EIGEN_STRONG_INLINE Packet4bf pdiv<Packet4bf>(const Packet4bf& a, const Packet4bf& b) {
+ return F32ToBf16(pdiv<Packet4f>(Bf16ToF32(a), Bf16ToF32(b)));
+}
+
+template<>
+EIGEN_STRONG_INLINE Packet4bf pgather<bfloat16, Packet4bf>(const bfloat16* from, Index stride)
+{
+ return pgather<uint16_t, Packet4us>(reinterpret_cast<const uint16_t*>(from), stride);
+}
+
+template<>
+EIGEN_STRONG_INLINE void pscatter<bfloat16, Packet4bf>(bfloat16* to, const Packet4bf& from, Index stride)
+{
+ pscatter<uint16_t, Packet4us>(reinterpret_cast<uint16_t*>(to), from, stride);
+}
+
+template<> EIGEN_STRONG_INLINE bfloat16 predux<Packet4bf>(const Packet4bf& a)
+{
+ return static_cast<bfloat16>(predux<Packet4f>(Bf16ToF32(a)));
+}
+
+template<> EIGEN_STRONG_INLINE bfloat16 predux_max<Packet4bf>(const Packet4bf& a)
+{
+ return static_cast<bfloat16>(predux_max<Packet4f>(Bf16ToF32(a)));
+}
+
+template<> EIGEN_STRONG_INLINE bfloat16 predux_min<Packet4bf>(const Packet4bf& a)
+{
+ return static_cast<bfloat16>(predux_min<Packet4f>(Bf16ToF32(a)));
+}
+
+template<> EIGEN_STRONG_INLINE bfloat16 predux_mul<Packet4bf>(const Packet4bf& a)
+{
+ return static_cast<bfloat16>(predux_mul<Packet4f>(Bf16ToF32(a)));
+}
+
+template<> EIGEN_STRONG_INLINE Packet4bf preverse<Packet4bf>(const Packet4bf& a)
+{
+ return preverse<Packet4us>(a);
+}
+
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void ptranspose(PacketBlock<Packet4bf, 4>& kernel)
+{
+ detail::ptranspose_impl(kernel);
+}
+
+template<> EIGEN_STRONG_INLINE Packet4bf pabsdiff<Packet4bf>(const Packet4bf& a, const Packet4bf& b)
+{
+ return F32ToBf16(pabsdiff<Packet4f>(Bf16ToF32(a), Bf16ToF32(b)));
+}
+
+template<> EIGEN_STRONG_INLINE Packet4bf pcmp_eq<Packet4bf>(const Packet4bf& a, const Packet4bf& b)
+{
+ return F32MaskToBf16Mask(pcmp_eq<Packet4f>(Bf16ToF32(a), Bf16ToF32(b)));
+}
+
+template<> EIGEN_STRONG_INLINE Packet4bf pcmp_lt<Packet4bf>(const Packet4bf& a, const Packet4bf& b)
+{
+ return F32MaskToBf16Mask(pcmp_lt<Packet4f>(Bf16ToF32(a), Bf16ToF32(b)));
+}
+
+template<> EIGEN_STRONG_INLINE Packet4bf pcmp_lt_or_nan<Packet4bf>(const Packet4bf& a, const Packet4bf& b)
+{
+ return F32MaskToBf16Mask(pcmp_lt_or_nan<Packet4f>(Bf16ToF32(a), Bf16ToF32(b)));
+}
+
+template<> EIGEN_STRONG_INLINE Packet4bf pcmp_le<Packet4bf>(const Packet4bf& a, const Packet4bf& b)
+{
+ return F32MaskToBf16Mask(pcmp_le<Packet4f>(Bf16ToF32(a), Bf16ToF32(b)));
+}
+
+template<> EIGEN_STRONG_INLINE Packet4bf pnegate<Packet4bf>(const Packet4bf& a)
+{
+ return pxor<Packet4us>(a, pset1<Packet4us>(static_cast<uint16_t>(0x8000)));
+}
+
+//---------- double ----------
+
+// Clang 3.5 in the iOS toolchain has an ICE triggered by NEON intrisics for double.
+// Confirmed at least with __apple_build_version__ = 6000054.
+#ifdef __apple_build_version__
+// Let's hope that by the time __apple_build_version__ hits the 601* range, the bug will be fixed.
+// https://gist.github.com/yamaya/2924292 suggests that the 3 first digits are only updated with
+// major toolchain updates.
+#define EIGEN_APPLE_DOUBLE_NEON_BUG (__apple_build_version__ < 6010000)
+#else
+#define EIGEN_APPLE_DOUBLE_NEON_BUG 0
+#endif
+
+#if EIGEN_ARCH_ARM64 && !EIGEN_APPLE_DOUBLE_NEON_BUG
+
+// Bug 907: workaround missing declarations of the following two functions in the ADK
+// Defining these functions as templates ensures that if these intrinsics are
+// already defined in arm_neon.h, then our workaround doesn't cause a conflict
+// and has lower priority in overload resolution.
+template <typename T> uint64x2_t vreinterpretq_u64_f64(T a) { return (uint64x2_t) a; }
+
+template <typename T> float64x2_t vreinterpretq_f64_u64(T a) { return (float64x2_t) a; }
+
+typedef float64x2_t Packet2d;
+typedef float64x1_t Packet1d;
+
+// fuctionally equivalent to _mm_shuffle_pd in SSE (i.e. shuffle(m, n, mask) equals _mm_shuffle_pd(m,n,mask))
+// Currently used in LU/arch/InverseSize4.h to enable a shared implementation
+// for fast inversion of matrices of size 4.
+EIGEN_STRONG_INLINE Packet2d shuffle(const Packet2d& m, const Packet2d& n, int mask)
+{
+ const double* a = reinterpret_cast<const double*>(&m);
+ const double* b = reinterpret_cast<const double*>(&n);
+ Packet2d res = {*(a + (mask & 1)), *(b + ((mask >> 1) & 1))};
+ return res;
+}
+
+EIGEN_STRONG_INLINE Packet2d vec2d_swizzle2(const Packet2d& a, const Packet2d& b, int mask)
+{
+ return shuffle(a, b, mask);
+}
+EIGEN_STRONG_INLINE Packet2d vec2d_unpacklo(const Packet2d& a,const Packet2d& b)
+{
+ return shuffle(a, b, 0);
+}
+EIGEN_STRONG_INLINE Packet2d vec2d_unpackhi(const Packet2d& a,const Packet2d& b)
+{
+ return shuffle(a, b, 3);
+}
+#define vec2d_duplane(a, p) \
+ vdupq_laneq_f64(a, p)
+
+template<> struct packet_traits<double> : default_packet_traits
+{
+ typedef Packet2d type;
+ typedef Packet2d half;
+ enum
+ {
+ Vectorizable = 1,
+ AlignedOnScalar = 1,
+ size = 2,
+ HasHalfPacket = 0,
+
+ HasCmp = 1,
+ HasAdd = 1,
+ HasSub = 1,
+ HasShift = 1,
+ HasMul = 1,
+ HasNegate = 1,
+ HasAbs = 1,
+ HasArg = 0,
+ HasAbs2 = 1,
+ HasAbsDiff = 1,
+ HasMin = 1,
+ HasMax = 1,
+ HasConj = 1,
+ HasSetLinear = 0,
+ HasBlend = 0,
+
+ HasDiv = 1,
+ HasFloor = 1,
+ HasCeil = 1,
+ HasRint = 1,
+
+#if EIGEN_ARCH_ARM64 && !EIGEN_APPLE_DOUBLE_NEON_BUG
+ HasExp = 1,
+ HasLog = 1,
+ HasATan = 1,
+#endif
+ HasSin = 0,
+ HasCos = 0,
+ HasSqrt = 1,
+ HasRsqrt = 1,
+ HasTanh = 0,
+ HasErf = 0
+ };
+};
+
+template<> struct unpacket_traits<Packet2d>
+{
+ typedef double type;
+ typedef Packet2d half;
+ typedef Packet2l integer_packet;
+ enum
+ {
+ size = 2,
+ alignment = Aligned16,
+ vectorizable = true,
+ masked_load_available = false,
+ masked_store_available = false
+ };
+};
+
+template<> EIGEN_STRONG_INLINE Packet2d pset1<Packet2d>(const double& from) { return vdupq_n_f64(from); }
+
+template<> EIGEN_STRONG_INLINE Packet2d plset<Packet2d>(const double& a)
+{
+ const double c[] = {0.0,1.0};
+ return vaddq_f64(pset1<Packet2d>(a), vld1q_f64(c));
+}
+
+template<> EIGEN_STRONG_INLINE Packet2d padd<Packet2d>(const Packet2d& a, const Packet2d& b) { return vaddq_f64(a,b); }
+
+template<> EIGEN_STRONG_INLINE Packet2d psub<Packet2d>(const Packet2d& a, const Packet2d& b) { return vsubq_f64(a,b); }
+
+template<> EIGEN_STRONG_INLINE Packet2d pxor<Packet2d>(const Packet2d& , const Packet2d& );
+template<> EIGEN_STRONG_INLINE Packet2d paddsub<Packet2d>(const Packet2d& a, const Packet2d& b){
+ const Packet2d mask = {numext::bit_cast<double>(0x8000000000000000ull),0.0};
+ return padd(a, pxor(mask, b));
+}
+
+template<> EIGEN_STRONG_INLINE Packet2d pnegate(const Packet2d& a) { return vnegq_f64(a); }
+
+template<> EIGEN_STRONG_INLINE Packet2d pconj(const Packet2d& a) { return a; }
+
+template<> EIGEN_STRONG_INLINE Packet2d pmul<Packet2d>(const Packet2d& a, const Packet2d& b) { return vmulq_f64(a,b); }
+
+template<> EIGEN_STRONG_INLINE Packet2d pdiv<Packet2d>(const Packet2d& a, const Packet2d& b) { return vdivq_f64(a,b); }
+
+#ifdef __ARM_FEATURE_FMA
+// See bug 936. See above comment about FMA for float.
+template<> EIGEN_STRONG_INLINE Packet2d pmadd(const Packet2d& a, const Packet2d& b, const Packet2d& c)
+{ return vfmaq_f64(c,a,b); }
+#else
+template<> EIGEN_STRONG_INLINE Packet2d pmadd(const Packet2d& a, const Packet2d& b, const Packet2d& c)
+{ return vmlaq_f64(c,a,b); }
+#endif
+
+template<> EIGEN_STRONG_INLINE Packet2d pmin<Packet2d>(const Packet2d& a, const Packet2d& b) { return vminq_f64(a,b); }
+
+#ifdef __ARM_FEATURE_NUMERIC_MAXMIN
+// numeric max and min are only available if ARM_FEATURE_NUMERIC_MAXMIN is defined (which can only be the case for Armv8 systems).
+template<> EIGEN_STRONG_INLINE Packet2d pmin<PropagateNumbers, Packet2d>(const Packet2d& a, const Packet2d& b) { return vminnmq_f64(a, b); }
+template<> EIGEN_STRONG_INLINE Packet2d pmax<PropagateNumbers, Packet2d>(const Packet2d& a, const Packet2d& b) { return vmaxnmq_f64(a, b); }
+
+#endif
+
+template<> EIGEN_STRONG_INLINE Packet2d pmin<PropagateNaN, Packet2d>(const Packet2d& a, const Packet2d& b) { return pmin<Packet2d>(a, b); }
+
+template<> EIGEN_STRONG_INLINE Packet2d pmax<Packet2d>(const Packet2d& a, const Packet2d& b) { return vmaxq_f64(a,b); }
+
+
+template<> EIGEN_STRONG_INLINE Packet2d pmax<PropagateNaN, Packet2d>(const Packet2d& a, const Packet2d& b) { return pmax<Packet2d>(a, b); }
+
+// Logical Operations are not supported for float, so we have to reinterpret casts using NEON intrinsics
+template<> EIGEN_STRONG_INLINE Packet2d pand<Packet2d>(const Packet2d& a, const Packet2d& b)
+{ return vreinterpretq_f64_u64(vandq_u64(vreinterpretq_u64_f64(a),vreinterpretq_u64_f64(b))); }
+
+template<> EIGEN_STRONG_INLINE Packet2d por<Packet2d>(const Packet2d& a, const Packet2d& b)
+{ return vreinterpretq_f64_u64(vorrq_u64(vreinterpretq_u64_f64(a),vreinterpretq_u64_f64(b))); }
+
+template<> EIGEN_STRONG_INLINE Packet2d pxor<Packet2d>(const Packet2d& a, const Packet2d& b)
+{ return vreinterpretq_f64_u64(veorq_u64(vreinterpretq_u64_f64(a),vreinterpretq_u64_f64(b))); }
+
+template<> EIGEN_STRONG_INLINE Packet2d pandnot<Packet2d>(const Packet2d& a, const Packet2d& b)
+{ return vreinterpretq_f64_u64(vbicq_u64(vreinterpretq_u64_f64(a),vreinterpretq_u64_f64(b))); }
+
+template<> EIGEN_STRONG_INLINE Packet2d pcmp_le(const Packet2d& a, const Packet2d& b)
+{ return vreinterpretq_f64_u64(vcleq_f64(a,b)); }
+
+template<> EIGEN_STRONG_INLINE Packet2d pcmp_lt(const Packet2d& a, const Packet2d& b)
+{ return vreinterpretq_f64_u64(vcltq_f64(a,b)); }
+
+template<> EIGEN_STRONG_INLINE Packet2d pcmp_lt_or_nan(const Packet2d& a, const Packet2d& b)
+{ return vreinterpretq_f64_u32(vmvnq_u32(vreinterpretq_u32_u64(vcgeq_f64(a,b)))); }
+
+template<> EIGEN_STRONG_INLINE Packet2d pcmp_eq(const Packet2d& a, const Packet2d& b)
+{ return vreinterpretq_f64_u64(vceqq_f64(a,b)); }
+
+template<> EIGEN_STRONG_INLINE Packet2d pload<Packet2d>(const double* from)
+{ EIGEN_DEBUG_ALIGNED_LOAD return vld1q_f64(from); }
+
+template<> EIGEN_STRONG_INLINE Packet2d ploadu<Packet2d>(const double* from)
+{ EIGEN_DEBUG_UNALIGNED_LOAD return vld1q_f64(from); }
+
+template<> EIGEN_STRONG_INLINE Packet2d ploaddup<Packet2d>(const double* from) { return vld1q_dup_f64(from); }
+template<> EIGEN_STRONG_INLINE void pstore<double>(double* to, const Packet2d& from)
+{ EIGEN_DEBUG_ALIGNED_STORE vst1q_f64(to,from); }
+
+template<> EIGEN_STRONG_INLINE void pstoreu<double>(double* to, const Packet2d& from)
+{ EIGEN_DEBUG_UNALIGNED_STORE vst1q_f64(to,from); }
+
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet2d pgather<double, Packet2d>(const double* from, Index stride)
+{
+ Packet2d res = pset1<Packet2d>(0.0);
+ res = vld1q_lane_f64(from + 0*stride, res, 0);
+ res = vld1q_lane_f64(from + 1*stride, res, 1);
+ return res;
+}
+
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void pscatter<double, Packet2d>(double* to, const Packet2d& from, Index stride)
+{
+ vst1q_lane_f64(to + stride*0, from, 0);
+ vst1q_lane_f64(to + stride*1, from, 1);
+}
+
+template<> EIGEN_STRONG_INLINE void prefetch<double>(const double* addr) { EIGEN_ARM_PREFETCH(addr); }
+
+// FIXME only store the 2 first elements ?
+template<> EIGEN_STRONG_INLINE double pfirst<Packet2d>(const Packet2d& a) { return vgetq_lane_f64(a,0); }
+
+template<> EIGEN_STRONG_INLINE Packet2d preverse(const Packet2d& a)
+{ return vcombine_f64(vget_high_f64(a), vget_low_f64(a)); }
+
+template<> EIGEN_STRONG_INLINE Packet2d pabs(const Packet2d& a) { return vabsq_f64(a); }
+
+template<> EIGEN_STRONG_INLINE double predux<Packet2d>(const Packet2d& a)
+{ return vaddvq_f64(a); }
+
+// Other reduction functions:
+// mul
+#if EIGEN_COMP_CLANG && defined(__apple_build_version__)
+template<> EIGEN_STRONG_INLINE double predux_mul<Packet2d>(const Packet2d& a)
+{ return (vget_low_f64(a) * vget_high_f64(a))[0]; }
+#else
+template<> EIGEN_STRONG_INLINE double predux_mul<Packet2d>(const Packet2d& a)
+{ return vget_lane_f64(vget_low_f64(a) * vget_high_f64(a), 0); }
+#endif
+
+// min
+template<> EIGEN_STRONG_INLINE double predux_min<Packet2d>(const Packet2d& a)
+{ return vminvq_f64(a); }
+
+// max
+template<> EIGEN_STRONG_INLINE double predux_max<Packet2d>(const Packet2d& a)
+{ return vmaxvq_f64(a); }
+
+
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void
+ptranspose(PacketBlock<Packet2d, 2>& kernel)
+{
+ const float64x2_t tmp1 = vzip1q_f64(kernel.packet[0], kernel.packet[1]);
+ const float64x2_t tmp2 = vzip2q_f64(kernel.packet[0], kernel.packet[1]);
+
+ kernel.packet[0] = tmp1;
+ kernel.packet[1] = tmp2;
+}
+
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet2d pselect( const Packet2d& mask, const Packet2d& a, const Packet2d& b)
+{ return vbslq_f64(vreinterpretq_u64_f64(mask), a, b); }
+
+template<> EIGEN_STRONG_INLINE Packet2d print<Packet2d>(const Packet2d& a)
+{ return vrndnq_f64(a); }
+
+template<> EIGEN_STRONG_INLINE Packet2d pfloor<Packet2d>(const Packet2d& a)
+{ return vrndmq_f64(a); }
+
+template<> EIGEN_STRONG_INLINE Packet2d pceil<Packet2d>(const Packet2d& a)
+{ return vrndpq_f64(a); }
+
+template<> EIGEN_STRONG_INLINE Packet2d pldexp<Packet2d>(const Packet2d& a, const Packet2d& exponent)
+{ return pldexp_generic(a, exponent); }
+
+template<> EIGEN_STRONG_INLINE Packet2d pfrexp<Packet2d>(const Packet2d& a, Packet2d& exponent)
+{ return pfrexp_generic(a,exponent); }
+
+template<> EIGEN_STRONG_INLINE Packet2d pset1frombits<Packet2d>(uint64_t from)
+{ return vreinterpretq_f64_u64(vdupq_n_u64(from)); }
+
+template<> EIGEN_STRONG_INLINE Packet2d prsqrt(const Packet2d& a) {
+ // Do Newton iterations for 1/sqrt(x).
+ return generic_rsqrt_newton_step<Packet2d, /*Steps=*/3>::run(a, vrsqrteq_f64(a));
+}
+
+template<> EIGEN_STRONG_INLINE Packet2d psqrt(const Packet2d& _x){ return vsqrtq_f64(_x); }
+
+// Do we have an fp16 types and supporting Neon intrinsics?
+#if EIGEN_HAS_ARM64_FP16_VECTOR_ARITHMETIC
+typedef float16x4_t Packet4hf;
+typedef float16x8_t Packet8hf;
+
+template <>
+struct packet_traits<Eigen::half> : default_packet_traits {
+ typedef Packet8hf type;
+ typedef Packet4hf half;
+ enum {
+ Vectorizable = 1,
+ AlignedOnScalar = 1,
+ size = 8,
+ HasHalfPacket = 1,
+
+ HasCmp = 1,
+ HasCast = 1,
+ HasAdd = 1,
+ HasSub = 1,
+ HasShift = 1,
+ HasMul = 1,
+ HasNegate = 1,
+ HasAbs = 1,
+ HasArg = 0,
+ HasAbs2 = 1,
+ HasAbsDiff = 0,
+ HasMin = 1,
+ HasMax = 1,
+ HasConj = 1,
+ HasSetLinear = 0,
+ HasBlend = 0,
+ HasInsert = 1,
+ HasReduxp = 1,
+ HasDiv = 1,
+ HasFloor = 1,
+ HasCeil = 1,
+ HasRint = 1,
+ HasSin = 0,
+ HasCos = 0,
+ HasLog = 0,
+ HasExp = 0,
+ HasTanh = packet_traits<float>::HasTanh, // tanh<half> calls tanh<float>
+ HasSqrt = 1,
+ HasRsqrt = 1,
+ HasErf = EIGEN_FAST_MATH,
+ HasBessel = 0, // Issues with accuracy.
+ HasNdtri = 0
+ };
+};
+
+template <>
+struct unpacket_traits<Packet4hf> {
+ typedef Eigen::half type;
+ typedef Packet4hf half;
+ enum {
+ size = 4,
+ alignment = Aligned16,
+ vectorizable = true,
+ masked_load_available = false,
+ masked_store_available = false
+ };
+};
+
+template <>
+struct unpacket_traits<Packet8hf> {
+ typedef Eigen::half type;
+ typedef Packet4hf half;
+ enum {
+ size = 8,
+ alignment = Aligned16,
+ vectorizable = true,
+ masked_load_available = false,
+ masked_store_available = false
+ };
+};
+
+template<>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet4hf predux_half_dowto4<Packet8hf>(const Packet8hf& a) {
+ return vadd_f16(vget_low_f16(a), vget_high_f16(a));
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet8hf pset1<Packet8hf>(const Eigen::half& from) {
+ return vdupq_n_f16(from.x);
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet4hf pset1<Packet4hf>(const Eigen::half& from) {
+ return vdup_n_f16(from.x);
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet8hf plset<Packet8hf>(const Eigen::half& a) {
+ const float16_t f[] = {0, 1, 2, 3, 4, 5, 6, 7};
+ Packet8hf countdown = vld1q_f16(f);
+ return vaddq_f16(pset1<Packet8hf>(a), countdown);
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet4hf plset<Packet4hf>(const Eigen::half& a) {
+ const float16_t f[] = {0, 1, 2, 3};
+ Packet4hf countdown = vld1_f16(f);
+ return vadd_f16(pset1<Packet4hf>(a), countdown);
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet8hf padd<Packet8hf>(const Packet8hf& a, const Packet8hf& b) {
+ return vaddq_f16(a, b);
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet4hf padd<Packet4hf>(const Packet4hf& a, const Packet4hf& b) {
+ return vadd_f16(a, b);
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet8hf psub<Packet8hf>(const Packet8hf& a, const Packet8hf& b) {
+ return vsubq_f16(a, b);
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet4hf psub<Packet4hf>(const Packet4hf& a, const Packet4hf& b) {
+ return vsub_f16(a, b);
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet8hf pnegate(const Packet8hf& a) {
+ return vnegq_f16(a);
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet4hf pnegate(const Packet4hf& a) {
+ return vneg_f16(a);
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet8hf pconj(const Packet8hf& a) {
+ return a;
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet4hf pconj(const Packet4hf& a) {
+ return a;
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet8hf pmul<Packet8hf>(const Packet8hf& a, const Packet8hf& b) {
+ return vmulq_f16(a, b);
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet4hf pmul<Packet4hf>(const Packet4hf& a, const Packet4hf& b) {
+ return vmul_f16(a, b);
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet8hf pdiv<Packet8hf>(const Packet8hf& a, const Packet8hf& b) {
+ return vdivq_f16(a, b);
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet4hf pdiv<Packet4hf>(const Packet4hf& a, const Packet4hf& b) {
+ return vdiv_f16(a, b);
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet8hf pmadd(const Packet8hf& a, const Packet8hf& b, const Packet8hf& c) {
+ return vfmaq_f16(c, a, b);
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet4hf pmadd(const Packet4hf& a, const Packet4hf& b, const Packet4hf& c) {
+ return vfma_f16(c, a, b);
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet8hf pmin<Packet8hf>(const Packet8hf& a, const Packet8hf& b) {
+ return vminq_f16(a, b);
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet4hf pmin<Packet4hf>(const Packet4hf& a, const Packet4hf& b) {
+ return vmin_f16(a, b);
+}
+
+#ifdef __ARM_FEATURE_NUMERIC_MAXMIN
+// numeric max and min are only available if ARM_FEATURE_NUMERIC_MAXMIN is defined (which can only be the case for Armv8 systems).
+template<> EIGEN_STRONG_INLINE Packet4hf pmin<PropagateNumbers, Packet4hf>(const Packet4hf& a, const Packet4hf& b) { return vminnm_f16(a, b); }
+template<> EIGEN_STRONG_INLINE Packet8hf pmin<PropagateNumbers, Packet8hf>(const Packet8hf& a, const Packet8hf& b) { return vminnmq_f16(a, b); }
+#endif
+
+template<> EIGEN_STRONG_INLINE Packet4hf pmin<PropagateNaN, Packet4hf>(const Packet4hf& a, const Packet4hf& b) { return pmin<Packet4hf>(a, b); }
+
+template<> EIGEN_STRONG_INLINE Packet8hf pmin<PropagateNaN, Packet8hf>(const Packet8hf& a, const Packet8hf& b) { return pmin<Packet8hf>(a, b); }
+
+template <>
+EIGEN_STRONG_INLINE Packet8hf pmax<Packet8hf>(const Packet8hf& a, const Packet8hf& b) {
+ return vmaxq_f16(a, b);
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet4hf pmax<Packet4hf>(const Packet4hf& a, const Packet4hf& b) {
+ return vmax_f16(a, b);
+}
+
+#ifdef __ARM_FEATURE_NUMERIC_MAXMIN
+// numeric max and min are only available if ARM_FEATURE_NUMERIC_MAXMIN is defined (which can only be the case for Armv8 systems).
+template<> EIGEN_STRONG_INLINE Packet4hf pmax<PropagateNumbers, Packet4hf>(const Packet4hf& a, const Packet4hf& b) { return vmaxnm_f16(a, b); }
+template<> EIGEN_STRONG_INLINE Packet8hf pmax<PropagateNumbers, Packet8hf>(const Packet8hf& a, const Packet8hf& b) { return vmaxnmq_f16(a, b); }
+#endif
+
+template<> EIGEN_STRONG_INLINE Packet4hf pmax<PropagateNaN, Packet4hf>(const Packet4hf& a, const Packet4hf& b) { return pmax<Packet4hf>(a, b); }
+
+template<> EIGEN_STRONG_INLINE Packet8hf pmax<PropagateNaN, Packet8hf>(const Packet8hf& a, const Packet8hf& b) { return pmax<Packet8hf>(a, b); }
+
+#define EIGEN_MAKE_ARM_FP16_CMP_8(name) \
+ template <> \
+ EIGEN_STRONG_INLINE Packet8hf pcmp_##name(const Packet8hf& a, const Packet8hf& b) { \
+ return vreinterpretq_f16_u16(vc##name##q_f16(a, b)); \
+ }
+
+#define EIGEN_MAKE_ARM_FP16_CMP_4(name) \
+ template <> \
+ EIGEN_STRONG_INLINE Packet4hf pcmp_##name(const Packet4hf& a, const Packet4hf& b) { \
+ return vreinterpret_f16_u16(vc##name##_f16(a, b)); \
+ }
+
+EIGEN_MAKE_ARM_FP16_CMP_8(eq)
+EIGEN_MAKE_ARM_FP16_CMP_8(lt)
+EIGEN_MAKE_ARM_FP16_CMP_8(le)
+
+EIGEN_MAKE_ARM_FP16_CMP_4(eq)
+EIGEN_MAKE_ARM_FP16_CMP_4(lt)
+EIGEN_MAKE_ARM_FP16_CMP_4(le)
+
+#undef EIGEN_MAKE_ARM_FP16_CMP_8
+#undef EIGEN_MAKE_ARM_FP16_CMP_4
+
+template <>
+EIGEN_STRONG_INLINE Packet8hf pcmp_lt_or_nan<Packet8hf>(const Packet8hf& a, const Packet8hf& b) {
+ return vreinterpretq_f16_u16(vmvnq_u16(vcgeq_f16(a, b)));
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet4hf pcmp_lt_or_nan<Packet4hf>(const Packet4hf& a, const Packet4hf& b) {
+ return vreinterpret_f16_u16(vmvn_u16(vcge_f16(a, b)));
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet8hf print<Packet8hf>(const Packet8hf& a)
+{ return vrndnq_f16(a); }
+
+template <>
+EIGEN_STRONG_INLINE Packet4hf print<Packet4hf>(const Packet4hf& a)
+{ return vrndn_f16(a); }
+
+template <>
+EIGEN_STRONG_INLINE Packet8hf pfloor<Packet8hf>(const Packet8hf& a)
+{ return vrndmq_f16(a); }
+
+template <>
+EIGEN_STRONG_INLINE Packet4hf pfloor<Packet4hf>(const Packet4hf& a)
+{ return vrndm_f16(a); }
+
+template <>
+EIGEN_STRONG_INLINE Packet8hf pceil<Packet8hf>(const Packet8hf& a)
+{ return vrndpq_f16(a); }
+
+template <>
+EIGEN_STRONG_INLINE Packet4hf pceil<Packet4hf>(const Packet4hf& a)
+{ return vrndp_f16(a); }
+
+template <>
+EIGEN_STRONG_INLINE Packet8hf psqrt<Packet8hf>(const Packet8hf& a) {
+ return vsqrtq_f16(a);
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet4hf psqrt<Packet4hf>(const Packet4hf& a) {
+ return vsqrt_f16(a);
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet8hf pand<Packet8hf>(const Packet8hf& a, const Packet8hf& b) {
+ return vreinterpretq_f16_u16(vandq_u16(vreinterpretq_u16_f16(a), vreinterpretq_u16_f16(b)));
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet4hf pand<Packet4hf>(const Packet4hf& a, const Packet4hf& b) {
+ return vreinterpret_f16_u16(vand_u16(vreinterpret_u16_f16(a), vreinterpret_u16_f16(b)));
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet8hf por<Packet8hf>(const Packet8hf& a, const Packet8hf& b) {
+ return vreinterpretq_f16_u16(vorrq_u16(vreinterpretq_u16_f16(a), vreinterpretq_u16_f16(b)));
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet4hf por<Packet4hf>(const Packet4hf& a, const Packet4hf& b) {
+ return vreinterpret_f16_u16(vorr_u16(vreinterpret_u16_f16(a), vreinterpret_u16_f16(b)));
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet8hf pxor<Packet8hf>(const Packet8hf& a, const Packet8hf& b) {
+ return vreinterpretq_f16_u16(veorq_u16(vreinterpretq_u16_f16(a), vreinterpretq_u16_f16(b)));
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet4hf pxor<Packet4hf>(const Packet4hf& a, const Packet4hf& b) {
+ return vreinterpret_f16_u16(veor_u16(vreinterpret_u16_f16(a), vreinterpret_u16_f16(b)));
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet8hf pandnot<Packet8hf>(const Packet8hf& a, const Packet8hf& b) {
+ return vreinterpretq_f16_u16(vbicq_u16(vreinterpretq_u16_f16(a), vreinterpretq_u16_f16(b)));
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet4hf pandnot<Packet4hf>(const Packet4hf& a, const Packet4hf& b) {
+ return vreinterpret_f16_u16(vbic_u16(vreinterpret_u16_f16(a), vreinterpret_u16_f16(b)));
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet8hf pload<Packet8hf>(const Eigen::half* from) {
+ EIGEN_DEBUG_ALIGNED_LOAD return vld1q_f16(reinterpret_cast<const float16_t*>(from));
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet4hf pload<Packet4hf>(const Eigen::half* from) {
+ EIGEN_DEBUG_ALIGNED_LOAD return vld1_f16(reinterpret_cast<const float16_t*>(from));
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet8hf ploadu<Packet8hf>(const Eigen::half* from) {
+ EIGEN_DEBUG_UNALIGNED_LOAD return vld1q_f16(reinterpret_cast<const float16_t*>(from));
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet4hf ploadu<Packet4hf>(const Eigen::half* from) {
+ EIGEN_DEBUG_UNALIGNED_LOAD return vld1_f16(reinterpret_cast<const float16_t*>(from));
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet8hf ploaddup<Packet8hf>(const Eigen::half* from) {
+ Packet8hf packet;
+ packet[0] = from[0].x;
+ packet[1] = from[0].x;
+ packet[2] = from[1].x;
+ packet[3] = from[1].x;
+ packet[4] = from[2].x;
+ packet[5] = from[2].x;
+ packet[6] = from[3].x;
+ packet[7] = from[3].x;
+ return packet;
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet4hf ploaddup<Packet4hf>(const Eigen::half* from) {
+ float16x4_t packet;
+ float16_t* tmp;
+ tmp = (float16_t*)&packet;
+ tmp[0] = from[0].x;
+ tmp[1] = from[0].x;
+ tmp[2] = from[1].x;
+ tmp[3] = from[1].x;
+ return packet;
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet8hf ploadquad<Packet8hf>(const Eigen::half* from) {
+ Packet4hf lo, hi;
+ lo = vld1_dup_f16(reinterpret_cast<const float16_t*>(from));
+ hi = vld1_dup_f16(reinterpret_cast<const float16_t*>(from+1));
+ return vcombine_f16(lo, hi);
+}
+
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet8hf pinsertfirst(const Packet8hf& a, Eigen::half b) { return vsetq_lane_f16(b.x, a, 0); }
+
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet4hf pinsertfirst(const Packet4hf& a, Eigen::half b) { return vset_lane_f16(b.x, a, 0); }
+
+template <>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet8hf pselect(const Packet8hf& mask, const Packet8hf& a, const Packet8hf& b) {
+ return vbslq_f16(vreinterpretq_u16_f16(mask), a, b);
+}
+
+template <>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet4hf pselect(const Packet4hf& mask, const Packet4hf& a, const Packet4hf& b) {
+ return vbsl_f16(vreinterpret_u16_f16(mask), a, b);
+}
+
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet8hf pinsertlast(const Packet8hf& a, Eigen::half b) { return vsetq_lane_f16(b.x, a, 7); }
+
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet4hf pinsertlast(const Packet4hf& a, Eigen::half b) { return vset_lane_f16(b.x, a, 3); }
+
+template <>
+EIGEN_STRONG_INLINE void pstore<Eigen::half>(Eigen::half* to, const Packet8hf& from) {
+ EIGEN_DEBUG_ALIGNED_STORE vst1q_f16(reinterpret_cast<float16_t*>(to), from);
+}
+
+template <>
+EIGEN_STRONG_INLINE void pstore<Eigen::half>(Eigen::half* to, const Packet4hf& from) {
+ EIGEN_DEBUG_ALIGNED_STORE vst1_f16(reinterpret_cast<float16_t*>(to), from);
+}
+
+template <>
+EIGEN_STRONG_INLINE void pstoreu<Eigen::half>(Eigen::half* to, const Packet8hf& from) {
+ EIGEN_DEBUG_UNALIGNED_STORE vst1q_f16(reinterpret_cast<float16_t*>(to), from);
+}
+
+template <>
+EIGEN_STRONG_INLINE void pstoreu<Eigen::half>(Eigen::half* to, const Packet4hf& from) {
+ EIGEN_DEBUG_UNALIGNED_STORE vst1_f16(reinterpret_cast<float16_t*>(to), from);
+}
+
+template <>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet8hf pgather<Eigen::half, Packet8hf>(const Eigen::half* from, Index stride) {
+ Packet8hf res = pset1<Packet8hf>(Eigen::half(0.f));
+ res = vsetq_lane_f16(from[0 * stride].x, res, 0);
+ res = vsetq_lane_f16(from[1 * stride].x, res, 1);
+ res = vsetq_lane_f16(from[2 * stride].x, res, 2);
+ res = vsetq_lane_f16(from[3 * stride].x, res, 3);
+ res = vsetq_lane_f16(from[4 * stride].x, res, 4);
+ res = vsetq_lane_f16(from[5 * stride].x, res, 5);
+ res = vsetq_lane_f16(from[6 * stride].x, res, 6);
+ res = vsetq_lane_f16(from[7 * stride].x, res, 7);
+ return res;
+}
+
+template <>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet4hf pgather<Eigen::half, Packet4hf>(const Eigen::half* from, Index stride) {
+ Packet4hf res = pset1<Packet4hf>(Eigen::half(0.f));
+ res = vset_lane_f16(from[0 * stride].x, res, 0);
+ res = vset_lane_f16(from[1 * stride].x, res, 1);
+ res = vset_lane_f16(from[2 * stride].x, res, 2);
+ res = vset_lane_f16(from[3 * stride].x, res, 3);
+ return res;
+}
+
+template <>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void pscatter<Eigen::half, Packet8hf>(Eigen::half* to, const Packet8hf& from, Index stride) {
+ to[stride * 0].x = vgetq_lane_f16(from, 0);
+ to[stride * 1].x = vgetq_lane_f16(from, 1);
+ to[stride * 2].x = vgetq_lane_f16(from, 2);
+ to[stride * 3].x = vgetq_lane_f16(from, 3);
+ to[stride * 4].x = vgetq_lane_f16(from, 4);
+ to[stride * 5].x = vgetq_lane_f16(from, 5);
+ to[stride * 6].x = vgetq_lane_f16(from, 6);
+ to[stride * 7].x = vgetq_lane_f16(from, 7);
+}
+
+template <>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void pscatter<Eigen::half, Packet4hf>(Eigen::half* to, const Packet4hf& from, Index stride) {
+ to[stride * 0].x = vget_lane_f16(from, 0);
+ to[stride * 1].x = vget_lane_f16(from, 1);
+ to[stride * 2].x = vget_lane_f16(from, 2);
+ to[stride * 3].x = vget_lane_f16(from, 3);
+}
+
+template <>
+EIGEN_STRONG_INLINE void prefetch<Eigen::half>(const Eigen::half* addr) {
+ EIGEN_ARM_PREFETCH(addr);
+}
+
+template <>
+EIGEN_STRONG_INLINE Eigen::half pfirst<Packet8hf>(const Packet8hf& a) {
+ float16_t x[8];
+ vst1q_f16(x, a);
+ Eigen::half h;
+ h.x = x[0];
+ return h;
+}
+
+template <>
+EIGEN_STRONG_INLINE Eigen::half pfirst<Packet4hf>(const Packet4hf& a) {
+ float16_t x[4];
+ vst1_f16(x, a);
+ Eigen::half h;
+ h.x = x[0];
+ return h;
+}
+
+template<> EIGEN_STRONG_INLINE Packet8hf preverse(const Packet8hf& a) {
+ float16x4_t a_lo, a_hi;
+ Packet8hf a_r64;
+
+ a_r64 = vrev64q_f16(a);
+ a_lo = vget_low_f16(a_r64);
+ a_hi = vget_high_f16(a_r64);
+ return vcombine_f16(a_hi, a_lo);
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet4hf preverse<Packet4hf>(const Packet4hf& a) {
+ return vrev64_f16(a);
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet8hf pabs<Packet8hf>(const Packet8hf& a) {
+ return vabsq_f16(a);
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet4hf pabs<Packet4hf>(const Packet4hf& a) {
+ return vabs_f16(a);
+}
+
+template <>
+EIGEN_STRONG_INLINE Eigen::half predux<Packet8hf>(const Packet8hf& a) {
+ float16x4_t a_lo, a_hi, sum;
+
+ a_lo = vget_low_f16(a);
+ a_hi = vget_high_f16(a);
+ sum = vpadd_f16(a_lo, a_hi);
+ sum = vpadd_f16(sum, sum);
+ sum = vpadd_f16(sum, sum);
+
+ Eigen::half h;
+ h.x = vget_lane_f16(sum, 0);
+ return h;
+}
+
+template <>
+EIGEN_STRONG_INLINE Eigen::half predux<Packet4hf>(const Packet4hf& a) {
+ float16x4_t sum;
+
+ sum = vpadd_f16(a, a);
+ sum = vpadd_f16(sum, sum);
+ Eigen::half h;
+ h.x = vget_lane_f16(sum, 0);
+ return h;
+}
+
+template <>
+EIGEN_STRONG_INLINE Eigen::half predux_mul<Packet8hf>(const Packet8hf& a) {
+ float16x4_t a_lo, a_hi, prod;
+
+ a_lo = vget_low_f16(a);
+ a_hi = vget_high_f16(a);
+ prod = vmul_f16(a_lo, a_hi);
+ prod = vmul_f16(prod, vrev64_f16(prod));
+
+ Eigen::half h;
+ h.x = vmulh_f16(vget_lane_f16(prod, 0), vget_lane_f16(prod, 1));
+ return h;
+}
+
+template <>
+EIGEN_STRONG_INLINE Eigen::half predux_mul<Packet4hf>(const Packet4hf& a) {
+ float16x4_t prod;
+ prod = vmul_f16(a, vrev64_f16(a));
+ Eigen::half h;
+ h.x = vmulh_f16(vget_lane_f16(prod, 0), vget_lane_f16(prod, 1));
+ return h;
+}
+
+template <>
+EIGEN_STRONG_INLINE Eigen::half predux_min<Packet8hf>(const Packet8hf& a) {
+ Eigen::half h;
+ h.x = vminvq_f16(a);
+ return h;
+}
+
+template <>
+EIGEN_STRONG_INLINE Eigen::half predux_min<Packet4hf>(const Packet4hf& a) {
+ Eigen::half h;
+ h.x = vminv_f16(a);
+ return h;
+}
+
+template <>
+EIGEN_STRONG_INLINE Eigen::half predux_max<Packet8hf>(const Packet8hf& a) {
+ Eigen::half h;
+ h.x = vmaxvq_f16(a);
+ return h;
+}
+
+template <>
+EIGEN_STRONG_INLINE Eigen::half predux_max<Packet4hf>(const Packet4hf& a) {
+ Eigen::half h;
+ h.x = vmaxv_f16(a);
+ return h;
+}
+
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void ptranspose(PacketBlock<Packet8hf, 4>& kernel)
+{
+ const float16x8x2_t zip16_1 = vzipq_f16(kernel.packet[0], kernel.packet[1]);
+ const float16x8x2_t zip16_2 = vzipq_f16(kernel.packet[2], kernel.packet[3]);
+
+ const float32x4x2_t zip32_1 = vzipq_f32(vreinterpretq_f32_f16(zip16_1.val[0]), vreinterpretq_f32_f16(zip16_2.val[0]));
+ const float32x4x2_t zip32_2 = vzipq_f32(vreinterpretq_f32_f16(zip16_1.val[1]), vreinterpretq_f32_f16(zip16_2.val[1]));
+
+ kernel.packet[0] = vreinterpretq_f16_f32(zip32_1.val[0]);
+ kernel.packet[1] = vreinterpretq_f16_f32(zip32_1.val[1]);
+ kernel.packet[2] = vreinterpretq_f16_f32(zip32_2.val[0]);
+ kernel.packet[3] = vreinterpretq_f16_f32(zip32_2.val[1]);
+}
+
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void ptranspose(PacketBlock<Packet4hf, 4>& kernel) {
+ EIGEN_ALIGN16 float16x4x4_t tmp_x4;
+ float16_t* tmp = (float16_t*)&kernel;
+ tmp_x4 = vld4_f16(tmp);
+
+ kernel.packet[0] = tmp_x4.val[0];
+ kernel.packet[1] = tmp_x4.val[1];
+ kernel.packet[2] = tmp_x4.val[2];
+ kernel.packet[3] = tmp_x4.val[3];
+}
+
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void ptranspose(PacketBlock<Packet8hf, 8>& kernel) {
+ float16x8x2_t T_1[4];
+
+ T_1[0] = vuzpq_f16(kernel.packet[0], kernel.packet[1]);
+ T_1[1] = vuzpq_f16(kernel.packet[2], kernel.packet[3]);
+ T_1[2] = vuzpq_f16(kernel.packet[4], kernel.packet[5]);
+ T_1[3] = vuzpq_f16(kernel.packet[6], kernel.packet[7]);
+
+ float16x8x2_t T_2[4];
+ T_2[0] = vuzpq_f16(T_1[0].val[0], T_1[1].val[0]);
+ T_2[1] = vuzpq_f16(T_1[0].val[1], T_1[1].val[1]);
+ T_2[2] = vuzpq_f16(T_1[2].val[0], T_1[3].val[0]);
+ T_2[3] = vuzpq_f16(T_1[2].val[1], T_1[3].val[1]);
+
+ float16x8x2_t T_3[4];
+ T_3[0] = vuzpq_f16(T_2[0].val[0], T_2[2].val[0]);
+ T_3[1] = vuzpq_f16(T_2[0].val[1], T_2[2].val[1]);
+ T_3[2] = vuzpq_f16(T_2[1].val[0], T_2[3].val[0]);
+ T_3[3] = vuzpq_f16(T_2[1].val[1], T_2[3].val[1]);
+
+ kernel.packet[0] = T_3[0].val[0];
+ kernel.packet[1] = T_3[2].val[0];
+ kernel.packet[2] = T_3[1].val[0];
+ kernel.packet[3] = T_3[3].val[0];
+ kernel.packet[4] = T_3[0].val[1];
+ kernel.packet[5] = T_3[2].val[1];
+ kernel.packet[6] = T_3[1].val[1];
+ kernel.packet[7] = T_3[3].val[1];
+}
+#endif // end EIGEN_HAS_ARM64_FP16_VECTOR_ARITHMETIC
+
+#endif // EIGEN_ARCH_ARM64
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_PACKET_MATH_NEON_H
diff --git a/Eigen/src/Core/arch/NEON/TypeCasting.h b/Eigen/src/Core/arch/NEON/TypeCasting.h
new file mode 100644
index 0000000..e5ddab6
--- /dev/null
+++ b/Eigen/src/Core/arch/NEON/TypeCasting.h
@@ -0,0 +1,1421 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2018 Rasmus Munk Larsen <rmlarsen@google.com>
+// Copyright (C) 2020 Antonio Sanchez <cantonios@google.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_TYPE_CASTING_NEON_H
+#define EIGEN_TYPE_CASTING_NEON_H
+
+#include "../../InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+
+//==============================================================================
+// pcast, SrcType = float
+//==============================================================================
+template <>
+struct type_casting_traits<float, float> {
+ enum { VectorizedCast = 1, SrcCoeffRatio = 1, TgtCoeffRatio = 1 };
+};
+template <>
+EIGEN_STRONG_INLINE Packet4f pcast<Packet4f, Packet4f>(const Packet4f& a) {
+ return a;
+}
+template <>
+EIGEN_STRONG_INLINE Packet2f pcast<Packet2f, Packet2f>(const Packet2f& a) {
+ return a;
+}
+
+template <>
+struct type_casting_traits<float, numext::int64_t> {
+ enum { VectorizedCast = 1, SrcCoeffRatio = 1, TgtCoeffRatio = 2 };
+};
+template <>
+struct type_casting_traits<float, numext::uint64_t> {
+ enum { VectorizedCast = 1, SrcCoeffRatio = 1, TgtCoeffRatio = 2 };
+};
+// If float64 exists, first convert to that to keep as much precision as possible.
+#if EIGEN_ARCH_ARM64
+template <>
+EIGEN_STRONG_INLINE Packet2l pcast<Packet4f, Packet2l>(const Packet4f& a) {
+ // Discard second half of input.
+ return vcvtq_s64_f64(vcvt_f64_f32(vget_low_f32(a)));
+}
+template <>
+EIGEN_STRONG_INLINE Packet2ul pcast<Packet4f, Packet2ul>(const Packet4f& a) {
+ // Discard second half of input.
+ return vcvtq_u64_f64(vcvt_f64_f32(vget_low_f32(a)));
+}
+#else
+template <>
+EIGEN_STRONG_INLINE Packet2l pcast<Packet4f, Packet2l>(const Packet4f& a) {
+ // Discard second half of input.
+ return vmovl_s32(vget_low_s32(vcvtq_s32_f32(a)));
+}
+template <>
+EIGEN_STRONG_INLINE Packet2ul pcast<Packet4f, Packet2ul>(const Packet4f& a) {
+ // Discard second half of input.
+ return vmovl_u32(vget_low_u32(vcvtq_u32_f32(a)));
+}
+#endif // EIGEN_ARCH_ARM64
+
+template <>
+struct type_casting_traits<float, numext::int32_t> {
+ enum { VectorizedCast = 1, SrcCoeffRatio = 1, TgtCoeffRatio = 1 };
+};
+template <>
+EIGEN_STRONG_INLINE Packet4i pcast<Packet4f, Packet4i>(const Packet4f& a) {
+ return vcvtq_s32_f32(a);
+}
+template <>
+EIGEN_STRONG_INLINE Packet2i pcast<Packet2f, Packet2i>(const Packet2f& a) {
+ return vcvt_s32_f32(a);
+}
+
+template <>
+struct type_casting_traits<float, numext::uint32_t> {
+ enum { VectorizedCast = 1, SrcCoeffRatio = 1, TgtCoeffRatio = 1 };
+};
+template <>
+EIGEN_STRONG_INLINE Packet4ui pcast<Packet4f, Packet4ui>(const Packet4f& a) {
+ return vcvtq_u32_f32(a);
+}
+template <>
+EIGEN_STRONG_INLINE Packet2ui pcast<Packet2f, Packet2ui>(const Packet2f& a) {
+ return vcvt_u32_f32(a);
+}
+
+template <>
+struct type_casting_traits<float, numext::int16_t> {
+ enum { VectorizedCast = 1, SrcCoeffRatio = 2, TgtCoeffRatio = 1 };
+};
+template <>
+EIGEN_STRONG_INLINE Packet8s pcast<Packet4f, Packet8s>(const Packet4f& a, const Packet4f& b) {
+ return vcombine_s16(vmovn_s32(vcvtq_s32_f32(a)), vmovn_s32(vcvtq_s32_f32(b)));
+}
+template <>
+EIGEN_STRONG_INLINE Packet4s pcast<Packet2f, Packet4s>(const Packet2f& a, const Packet2f& b) {
+ return vmovn_s32(vcombine_s32(vcvt_s32_f32(a), vcvt_s32_f32(b)));
+}
+
+template <>
+struct type_casting_traits<float, numext::uint16_t> {
+ enum { VectorizedCast = 1, SrcCoeffRatio = 2, TgtCoeffRatio = 1 };
+};
+template <>
+EIGEN_STRONG_INLINE Packet8us pcast<Packet4f, Packet8us>(const Packet4f& a, const Packet4f& b) {
+ return vcombine_u16(vmovn_u32(vcvtq_u32_f32(a)), vmovn_u32(vcvtq_u32_f32(b)));
+}
+template <>
+EIGEN_STRONG_INLINE Packet4us pcast<Packet2f, Packet4us>(const Packet2f& a, const Packet2f& b) {
+ return vmovn_u32(vcombine_u32(vcvt_u32_f32(a), vcvt_u32_f32(b)));
+}
+
+template <>
+struct type_casting_traits<float, numext::int8_t> {
+ enum { VectorizedCast = 1, SrcCoeffRatio = 4, TgtCoeffRatio = 1 };
+};
+template <>
+EIGEN_STRONG_INLINE Packet16c pcast<Packet4f, Packet16c>(const Packet4f& a, const Packet4f& b, const Packet4f& c,
+ const Packet4f& d) {
+ const int16x8_t ab_s16 = pcast<Packet4f, Packet8s>(a, b);
+ const int16x8_t cd_s16 = pcast<Packet4f, Packet8s>(c, d);
+ return vcombine_s8(vmovn_s16(ab_s16), vmovn_s16(cd_s16));
+}
+template <>
+EIGEN_STRONG_INLINE Packet8c pcast<Packet2f, Packet8c>(const Packet2f& a, const Packet2f& b, const Packet2f& c,
+ const Packet2f& d) {
+ const int16x4_t ab_s16 = pcast<Packet2f, Packet4s>(a, b);
+ const int16x4_t cd_s16 = pcast<Packet2f, Packet4s>(c, d);
+ return vmovn_s16(vcombine_s16(ab_s16, cd_s16));
+}
+
+template <>
+struct type_casting_traits<float, numext::uint8_t> {
+ enum { VectorizedCast = 1, SrcCoeffRatio = 4, TgtCoeffRatio = 1 };
+};
+template <>
+EIGEN_STRONG_INLINE Packet16uc pcast<Packet4f, Packet16uc>(const Packet4f& a, const Packet4f& b, const Packet4f& c,
+ const Packet4f& d) {
+ const uint16x8_t ab_u16 = pcast<Packet4f, Packet8us>(a, b);
+ const uint16x8_t cd_u16 = pcast<Packet4f, Packet8us>(c, d);
+ return vcombine_u8(vmovn_u16(ab_u16), vmovn_u16(cd_u16));
+}
+template <>
+EIGEN_STRONG_INLINE Packet8uc pcast<Packet2f, Packet8uc>(const Packet2f& a, const Packet2f& b, const Packet2f& c,
+ const Packet2f& d) {
+ const uint16x4_t ab_u16 = pcast<Packet2f, Packet4us>(a, b);
+ const uint16x4_t cd_u16 = pcast<Packet2f, Packet4us>(c, d);
+ return vmovn_u16(vcombine_u16(ab_u16, cd_u16));
+}
+
+//==============================================================================
+// pcast, SrcType = int8_t
+//==============================================================================
+template <>
+struct type_casting_traits<numext::int8_t, float> {
+ enum { VectorizedCast = 1, SrcCoeffRatio = 1, TgtCoeffRatio = 4 };
+};
+template <>
+EIGEN_STRONG_INLINE Packet4f pcast<Packet16c, Packet4f>(const Packet16c& a) {
+ // Discard all but first 4 bytes.
+ return vcvtq_f32_s32(vmovl_s16(vget_low_s16(vmovl_s8(vget_low_s8(a)))));
+}
+template <>
+EIGEN_STRONG_INLINE Packet2f pcast<Packet8c, Packet2f>(const Packet8c& a) {
+ // Discard all but first 2 bytes.
+ return vcvt_f32_s32(vget_low_s32(vmovl_s16(vget_low_s16(vmovl_s8(a)))));
+}
+
+template <>
+struct type_casting_traits<numext::int8_t, numext::int64_t> {
+ enum { VectorizedCast = 1, SrcCoeffRatio = 1, TgtCoeffRatio = 8 };
+};
+template <>
+EIGEN_STRONG_INLINE Packet2l pcast<Packet16c, Packet2l>(const Packet16c& a) {
+ // Discard all but first two bytes.
+ return vmovl_s32(vget_low_s32(vmovl_s16(vget_low_s16(vmovl_s8(vget_low_s8(a))))));
+}
+
+template <>
+struct type_casting_traits<numext::int8_t, numext::uint64_t> {
+ enum { VectorizedCast = 1, SrcCoeffRatio = 1, TgtCoeffRatio = 8 };
+};
+template <>
+EIGEN_STRONG_INLINE Packet2ul pcast<Packet16c, Packet2ul>(const Packet16c& a) {
+ return vreinterpretq_u64_s64(pcast<Packet16c, Packet2l>(a));
+}
+
+template <>
+struct type_casting_traits<numext::int8_t, numext::int32_t> {
+ enum { VectorizedCast = 1, SrcCoeffRatio = 1, TgtCoeffRatio = 4 };
+};
+template <>
+EIGEN_STRONG_INLINE Packet4i pcast<Packet16c, Packet4i>(const Packet16c& a) {
+ // Discard all but first 4 bytes.
+ return vmovl_s16(vget_low_s16(vmovl_s8(vget_low_s8(a))));
+}
+template <>
+EIGEN_STRONG_INLINE Packet2i pcast<Packet8c, Packet2i>(const Packet8c& a) {
+ // Discard all but first 2 bytes.
+ return vget_low_s32(vmovl_s16(vget_low_s16(vmovl_s8(a))));
+}
+
+template <>
+struct type_casting_traits<numext::int8_t, numext::uint32_t> {
+ enum { VectorizedCast = 1, SrcCoeffRatio = 1, TgtCoeffRatio = 4 };
+};
+template <>
+EIGEN_STRONG_INLINE Packet4ui pcast<Packet16c, Packet4ui>(const Packet16c& a) {
+ return vreinterpretq_u32_s32(pcast<Packet16c, Packet4i>(a));
+}
+template <>
+EIGEN_STRONG_INLINE Packet2ui pcast<Packet8c, Packet2ui>(const Packet8c& a) {
+ return vreinterpret_u32_s32(pcast<Packet8c, Packet2i>(a));
+}
+
+template <>
+struct type_casting_traits<numext::int8_t, numext::int16_t> {
+ enum { VectorizedCast = 1, SrcCoeffRatio = 1, TgtCoeffRatio = 2 };
+};
+template <>
+EIGEN_STRONG_INLINE Packet8s pcast<Packet16c, Packet8s>(const Packet16c& a) {
+ // Discard second half of input.
+ return vmovl_s8(vget_low_s8(a));
+}
+template <>
+EIGEN_STRONG_INLINE Packet4s pcast<Packet8c, Packet4s>(const Packet8c& a) {
+ // Discard second half of input.
+ return vget_low_s16(vmovl_s8(a));
+}
+
+template <>
+struct type_casting_traits<numext::int8_t, numext::uint16_t> {
+ enum { VectorizedCast = 1, SrcCoeffRatio = 1, TgtCoeffRatio = 2 };
+};
+template <>
+EIGEN_STRONG_INLINE Packet8us pcast<Packet16c, Packet8us>(const Packet16c& a) {
+ return vreinterpretq_u16_s16(pcast<Packet16c, Packet8s>(a));
+}
+template <>
+EIGEN_STRONG_INLINE Packet4us pcast<Packet8c, Packet4us>(const Packet8c& a) {
+ return vreinterpret_u16_s16(pcast<Packet8c, Packet4s>(a));
+}
+
+template <>
+struct type_casting_traits<numext::int8_t, numext::int8_t> {
+ enum { VectorizedCast = 1, SrcCoeffRatio = 1, TgtCoeffRatio = 1 };
+};
+template <>
+EIGEN_STRONG_INLINE Packet16c pcast<Packet16c, Packet16c>(const Packet16c& a) {
+ return a;
+}
+template <>
+EIGEN_STRONG_INLINE Packet8c pcast<Packet8c, Packet8c>(const Packet8c& a) {
+ return a;
+}
+template <>
+EIGEN_STRONG_INLINE Packet4c pcast<Packet4c, Packet4c>(const Packet4c& a) {
+ return a;
+}
+
+template <>
+struct type_casting_traits<numext::int8_t, numext::uint8_t> {
+ enum { VectorizedCast = 1, SrcCoeffRatio = 1, TgtCoeffRatio = 1 };
+};
+template <>
+EIGEN_STRONG_INLINE Packet16uc pcast<Packet16c, Packet16uc>(const Packet16c& a) {
+ return vreinterpretq_u8_s8(a);
+}
+template <>
+EIGEN_STRONG_INLINE Packet8uc pcast<Packet8c, Packet8uc>(const Packet8c& a) {
+ return vreinterpret_u8_s8(a);
+}
+template <>
+EIGEN_STRONG_INLINE Packet4uc pcast<Packet4c, Packet4uc>(const Packet4c& a) {
+ return static_cast<Packet4uc>(a);
+}
+
+//==============================================================================
+// pcast, SrcType = uint8_t
+//==============================================================================
+template <>
+struct type_casting_traits<numext::uint8_t, float> {
+ enum { VectorizedCast = 1, SrcCoeffRatio = 1, TgtCoeffRatio = 4 };
+};
+template <>
+EIGEN_STRONG_INLINE Packet4f pcast<Packet16uc, Packet4f>(const Packet16uc& a) {
+ // Discard all but first 4 bytes.
+ return vcvtq_f32_u32(vmovl_u16(vget_low_u16(vmovl_u8(vget_low_u8(a)))));
+}
+template <>
+EIGEN_STRONG_INLINE Packet2f pcast<Packet8uc, Packet2f>(const Packet8uc& a) {
+ // Discard all but first 2 bytes.
+ return vcvt_f32_u32(vget_low_u32(vmovl_u16(vget_low_u16(vmovl_u8(a)))));
+}
+
+template <>
+struct type_casting_traits<numext::uint8_t, numext::uint64_t> {
+ enum { VectorizedCast = 1, SrcCoeffRatio = 1, TgtCoeffRatio = 8 };
+};
+template <>
+EIGEN_STRONG_INLINE Packet2ul pcast<Packet16uc, Packet2ul>(const Packet16uc& a) {
+ // Discard all but first two bytes.
+ return vmovl_u32(vget_low_u32(vmovl_u16(vget_low_u16(vmovl_u8(vget_low_u8(a))))));
+}
+
+template <>
+struct type_casting_traits<numext::uint8_t, numext::int64_t> {
+ enum { VectorizedCast = 1, SrcCoeffRatio = 1, TgtCoeffRatio = 8 };
+};
+template <>
+EIGEN_STRONG_INLINE Packet2l pcast<Packet16uc, Packet2l>(const Packet16uc& a) {
+ return vreinterpretq_s64_u64(pcast<Packet16uc, Packet2ul>(a));
+}
+
+template <>
+struct type_casting_traits<numext::uint8_t, numext::uint32_t> {
+ enum { VectorizedCast = 1, SrcCoeffRatio = 1, TgtCoeffRatio = 4 };
+};
+template <>
+EIGEN_STRONG_INLINE Packet4ui pcast<Packet16uc, Packet4ui>(const Packet16uc& a) {
+ // Discard all but first 4 bytes.
+ return vmovl_u16(vget_low_u16(vmovl_u8(vget_low_u8(a))));
+}
+template <>
+EIGEN_STRONG_INLINE Packet2ui pcast<Packet8uc, Packet2ui>(const Packet8uc& a) {
+ // Discard all but first 2 bytes.
+ return vget_low_u32(vmovl_u16(vget_low_u16(vmovl_u8(a))));
+}
+
+template <>
+struct type_casting_traits<numext::uint8_t, numext::int32_t> {
+ enum { VectorizedCast = 1, SrcCoeffRatio = 1, TgtCoeffRatio = 4 };
+};
+template <>
+EIGEN_STRONG_INLINE Packet4i pcast<Packet16uc, Packet4i>(const Packet16uc& a) {
+ return vreinterpretq_s32_u32(pcast<Packet16uc, Packet4ui>(a));
+}
+template <>
+EIGEN_STRONG_INLINE Packet2i pcast<Packet8uc, Packet2i>(const Packet8uc& a) {
+ return vreinterpret_s32_u32(pcast<Packet8uc, Packet2ui>(a));
+}
+
+template <>
+struct type_casting_traits<numext::uint8_t, numext::uint16_t> {
+ enum { VectorizedCast = 1, SrcCoeffRatio = 1, TgtCoeffRatio = 2 };
+};
+template <>
+EIGEN_STRONG_INLINE Packet8us pcast<Packet16uc, Packet8us>(const Packet16uc& a) {
+ // Discard second half of input.
+ return vmovl_u8(vget_low_u8(a));
+}
+template <>
+EIGEN_STRONG_INLINE Packet4us pcast<Packet8uc, Packet4us>(const Packet8uc& a) {
+ // Discard second half of input.
+ return vget_low_u16(vmovl_u8(a));
+}
+
+template <>
+struct type_casting_traits<numext::uint8_t, numext::int16_t> {
+ enum { VectorizedCast = 1, SrcCoeffRatio = 1, TgtCoeffRatio = 2 };
+};
+template <>
+EIGEN_STRONG_INLINE Packet8s pcast<Packet16uc, Packet8s>(const Packet16uc& a) {
+ return vreinterpretq_s16_u16(pcast<Packet16uc, Packet8us>(a));
+}
+template <>
+EIGEN_STRONG_INLINE Packet4s pcast<Packet8uc, Packet4s>(const Packet8uc& a) {
+ return vreinterpret_s16_u16(pcast<Packet8uc, Packet4us>(a));
+}
+
+template <>
+struct type_casting_traits<numext::uint8_t, numext::uint8_t> {
+ enum { VectorizedCast = 1, SrcCoeffRatio = 1, TgtCoeffRatio = 1 };
+};
+template <>
+EIGEN_STRONG_INLINE Packet16uc pcast<Packet16uc, Packet16uc>(const Packet16uc& a) {
+ return a;
+}
+template <>
+EIGEN_STRONG_INLINE Packet8uc pcast<Packet8uc, Packet8uc>(const Packet8uc& a) {
+ return a;
+}
+template <>
+EIGEN_STRONG_INLINE Packet4uc pcast<Packet4uc, Packet4uc>(const Packet4uc& a) {
+ return a;
+}
+
+template <>
+struct type_casting_traits<numext::uint8_t, numext::int8_t> {
+ enum { VectorizedCast = 1, SrcCoeffRatio = 1, TgtCoeffRatio = 1 };
+};
+template <>
+EIGEN_STRONG_INLINE Packet16c pcast<Packet16uc, Packet16c>(const Packet16uc& a) {
+ return vreinterpretq_s8_u8(a);
+}
+template <>
+EIGEN_STRONG_INLINE Packet8c pcast<Packet8uc, Packet8c>(const Packet8uc& a) {
+ return vreinterpret_s8_u8(a);
+}
+template <>
+EIGEN_STRONG_INLINE Packet4c pcast<Packet4uc, Packet4c>(const Packet4uc& a) {
+ return static_cast<Packet4c>(a);
+}
+
+//==============================================================================
+// pcast, SrcType = int16_t
+//==============================================================================
+template <>
+struct type_casting_traits<numext::int16_t, float> {
+ enum { VectorizedCast = 1, SrcCoeffRatio = 1, TgtCoeffRatio = 2 };
+};
+template <>
+EIGEN_STRONG_INLINE Packet4f pcast<Packet8s, Packet4f>(const Packet8s& a) {
+ // Discard second half of input.
+ return vcvtq_f32_s32(vmovl_s16(vget_low_s16(a)));
+}
+template <>
+EIGEN_STRONG_INLINE Packet2f pcast<Packet4s, Packet2f>(const Packet4s& a) {
+ // Discard second half of input.
+ return vcvt_f32_s32(vget_low_s32(vmovl_s16(a)));
+}
+
+template <>
+struct type_casting_traits<numext::int16_t, numext::int64_t> {
+ enum { VectorizedCast = 1, SrcCoeffRatio = 1, TgtCoeffRatio = 4 };
+};
+template <>
+EIGEN_STRONG_INLINE Packet2l pcast<Packet8s, Packet2l>(const Packet8s& a) {
+ // Discard all but first two values.
+ return vmovl_s32(vget_low_s32(vmovl_s16(vget_low_s16(a))));
+}
+
+template <>
+struct type_casting_traits<numext::int16_t, numext::uint64_t> {
+ enum { VectorizedCast = 1, SrcCoeffRatio = 1, TgtCoeffRatio = 4 };
+};
+template <>
+EIGEN_STRONG_INLINE Packet2ul pcast<Packet8s, Packet2ul>(const Packet8s& a) {
+ return vreinterpretq_u64_s64(pcast<Packet8s, Packet2l>(a));
+}
+
+template <>
+struct type_casting_traits<numext::int16_t, numext::int32_t> {
+ enum { VectorizedCast = 1, SrcCoeffRatio = 1, TgtCoeffRatio = 2 };
+};
+template <>
+EIGEN_STRONG_INLINE Packet4i pcast<Packet8s, Packet4i>(const Packet8s& a) {
+ // Discard second half of input.
+ return vmovl_s16(vget_low_s16(a));
+}
+template <>
+EIGEN_STRONG_INLINE Packet2i pcast<Packet4s, Packet2i>(const Packet4s& a) {
+ // Discard second half of input.
+ return vget_low_s32(vmovl_s16(a));
+}
+
+template <>
+struct type_casting_traits<numext::int16_t, numext::uint32_t> {
+ enum { VectorizedCast = 1, SrcCoeffRatio = 1, TgtCoeffRatio = 2 };
+};
+template <>
+EIGEN_STRONG_INLINE Packet4ui pcast<Packet8s, Packet4ui>(const Packet8s& a) {
+ return vreinterpretq_u32_s32(pcast<Packet8s, Packet4i>(a));
+}
+template <>
+EIGEN_STRONG_INLINE Packet2ui pcast<Packet4s, Packet2ui>(const Packet4s& a) {
+ return vreinterpret_u32_s32(pcast<Packet4s, Packet2i>(a));
+}
+
+template <>
+struct type_casting_traits<numext::int16_t, numext::int16_t> {
+ enum { VectorizedCast = 1, SrcCoeffRatio = 1, TgtCoeffRatio = 1 };
+};
+template <>
+EIGEN_STRONG_INLINE Packet8s pcast<Packet8s, Packet8s>(const Packet8s& a) {
+ return a;
+}
+template <>
+EIGEN_STRONG_INLINE Packet4s pcast<Packet4s, Packet4s>(const Packet4s& a) {
+ return a;
+}
+
+template <>
+struct type_casting_traits<numext::int16_t, numext::uint16_t> {
+ enum { VectorizedCast = 1, SrcCoeffRatio = 1, TgtCoeffRatio = 1 };
+};
+template <>
+EIGEN_STRONG_INLINE Packet8us pcast<Packet8s, Packet8us>(const Packet8s& a) {
+ return vreinterpretq_u16_s16(a);
+}
+template <>
+EIGEN_STRONG_INLINE Packet4us pcast<Packet4s, Packet4us>(const Packet4s& a) {
+ return vreinterpret_u16_s16(a);
+}
+
+template <>
+struct type_casting_traits<numext::int16_t, numext::int8_t> {
+ enum { VectorizedCast = 1, SrcCoeffRatio = 2, TgtCoeffRatio = 1 };
+};
+template <>
+EIGEN_STRONG_INLINE Packet16c pcast<Packet8s, Packet16c>(const Packet8s& a, const Packet8s& b) {
+ return vcombine_s8(vmovn_s16(a), vmovn_s16(b));
+}
+template <>
+EIGEN_STRONG_INLINE Packet8c pcast<Packet4s, Packet8c>(const Packet4s& a, const Packet4s& b) {
+ return vmovn_s16(vcombine_s16(a, b));
+}
+
+template <>
+struct type_casting_traits<numext::int16_t, numext::uint8_t> {
+ enum { VectorizedCast = 1, SrcCoeffRatio = 2, TgtCoeffRatio = 1 };
+};
+template <>
+EIGEN_STRONG_INLINE Packet16uc pcast<Packet8s, Packet16uc>(const Packet8s& a, const Packet8s& b) {
+ return vcombine_u8(vmovn_u16(vreinterpretq_u16_s16(a)), vmovn_u16(vreinterpretq_u16_s16(b)));
+}
+template <>
+EIGEN_STRONG_INLINE Packet8uc pcast<Packet4s, Packet8uc>(const Packet4s& a, const Packet4s& b) {
+ return vmovn_u16(vcombine_u16(vreinterpret_u16_s16(a), vreinterpret_u16_s16(b)));
+}
+
+//==============================================================================
+// pcast, SrcType = uint16_t
+//==============================================================================
+template <>
+struct type_casting_traits<numext::uint16_t, float> {
+ enum { VectorizedCast = 1, SrcCoeffRatio = 1, TgtCoeffRatio = 2 };
+};
+template <>
+EIGEN_STRONG_INLINE Packet4f pcast<Packet8us, Packet4f>(const Packet8us& a) {
+ // Discard second half of input.
+ return vcvtq_f32_u32(vmovl_u16(vget_low_u16(a)));
+}
+template <>
+EIGEN_STRONG_INLINE Packet2f pcast<Packet4us, Packet2f>(const Packet4us& a) {
+ // Discard second half of input.
+ return vcvt_f32_u32(vget_low_u32(vmovl_u16(a)));
+}
+
+template <>
+struct type_casting_traits<numext::uint16_t, numext::uint64_t> {
+ enum { VectorizedCast = 1, SrcCoeffRatio = 1, TgtCoeffRatio = 4 };
+};
+template <>
+EIGEN_STRONG_INLINE Packet2ul pcast<Packet8us, Packet2ul>(const Packet8us& a) {
+ // Discard all but first two values.
+ return vmovl_u32(vget_low_u32(vmovl_u16(vget_low_u16(a))));
+}
+
+template <>
+struct type_casting_traits<numext::uint16_t, numext::int64_t> {
+ enum { VectorizedCast = 1, SrcCoeffRatio = 1, TgtCoeffRatio = 4 };
+};
+template <>
+EIGEN_STRONG_INLINE Packet2l pcast<Packet8us, Packet2l>(const Packet8us& a) {
+ return vreinterpretq_s64_u64(pcast<Packet8us, Packet2ul>(a));
+}
+
+template <>
+struct type_casting_traits<numext::uint16_t, numext::uint32_t> {
+ enum { VectorizedCast = 1, SrcCoeffRatio = 1, TgtCoeffRatio = 2 };
+};
+template <>
+EIGEN_STRONG_INLINE Packet4ui pcast<Packet8us, Packet4ui>(const Packet8us& a) {
+ // Discard second half of input.
+ return vmovl_u16(vget_low_u16(a));
+}
+template <>
+EIGEN_STRONG_INLINE Packet2ui pcast<Packet4us, Packet2ui>(const Packet4us& a) {
+ // Discard second half of input.
+ return vget_low_u32(vmovl_u16(a));
+}
+
+template <>
+struct type_casting_traits<numext::uint16_t, numext::int32_t> {
+ enum { VectorizedCast = 1, SrcCoeffRatio = 1, TgtCoeffRatio = 2 };
+};
+template <>
+EIGEN_STRONG_INLINE Packet4i pcast<Packet8us, Packet4i>(const Packet8us& a) {
+ return vreinterpretq_s32_u32(pcast<Packet8us, Packet4ui>(a));
+}
+template <>
+EIGEN_STRONG_INLINE Packet2i pcast<Packet4us, Packet2i>(const Packet4us& a) {
+ return vreinterpret_s32_u32(pcast<Packet4us, Packet2ui>(a));
+}
+
+template <>
+struct type_casting_traits<numext::uint16_t, numext::uint16_t> {
+ enum { VectorizedCast = 1, SrcCoeffRatio = 1, TgtCoeffRatio = 1 };
+};
+template <>
+EIGEN_STRONG_INLINE Packet8us pcast<Packet8us, Packet8us>(const Packet8us& a) {
+ return a;
+}
+template <>
+EIGEN_STRONG_INLINE Packet4us pcast<Packet4us, Packet4us>(const Packet4us& a) {
+ return a;
+}
+
+template <>
+struct type_casting_traits<numext::uint16_t, numext::int16_t> {
+ enum { VectorizedCast = 1, SrcCoeffRatio = 1, TgtCoeffRatio = 1 };
+};
+template <>
+EIGEN_STRONG_INLINE Packet8s pcast<Packet8us, Packet8s>(const Packet8us& a) {
+ return vreinterpretq_s16_u16(a);
+}
+template <>
+EIGEN_STRONG_INLINE Packet4s pcast<Packet4us, Packet4s>(const Packet4us& a) {
+ return vreinterpret_s16_u16(a);
+}
+
+template <>
+struct type_casting_traits<numext::uint16_t, numext::uint8_t> {
+ enum { VectorizedCast = 1, SrcCoeffRatio = 2, TgtCoeffRatio = 1 };
+};
+template <>
+EIGEN_STRONG_INLINE Packet16uc pcast<Packet8us, Packet16uc>(const Packet8us& a, const Packet8us& b) {
+ return vcombine_u8(vmovn_u16(a), vmovn_u16(b));
+}
+template <>
+EIGEN_STRONG_INLINE Packet8uc pcast<Packet4us, Packet8uc>(const Packet4us& a, const Packet4us& b) {
+ return vmovn_u16(vcombine_u16(a, b));
+}
+
+template <>
+struct type_casting_traits<numext::uint16_t, numext::int8_t> {
+ enum { VectorizedCast = 1, SrcCoeffRatio = 2, TgtCoeffRatio = 1 };
+};
+template <>
+EIGEN_STRONG_INLINE Packet16c pcast<Packet8us, Packet16c>(const Packet8us& a, const Packet8us& b) {
+ return vreinterpretq_s8_u8(pcast<Packet8us, Packet16uc>(a, b));
+}
+template <>
+EIGEN_STRONG_INLINE Packet8c pcast<Packet4us, Packet8c>(const Packet4us& a, const Packet4us& b) {
+ return vreinterpret_s8_u8(pcast<Packet4us, Packet8uc>(a, b));
+}
+
+//==============================================================================
+// pcast, SrcType = int32_t
+//==============================================================================
+template <>
+struct type_casting_traits<numext::int32_t, float> {
+ enum { VectorizedCast = 1, SrcCoeffRatio = 1, TgtCoeffRatio = 1 };
+};
+template <>
+EIGEN_STRONG_INLINE Packet4f pcast<Packet4i, Packet4f>(const Packet4i& a) {
+ return vcvtq_f32_s32(a);
+}
+template <>
+EIGEN_STRONG_INLINE Packet2f pcast<Packet2i, Packet2f>(const Packet2i& a) {
+ return vcvt_f32_s32(a);
+}
+
+template <>
+struct type_casting_traits<numext::int32_t, numext::int64_t> {
+ enum { VectorizedCast = 1, SrcCoeffRatio = 1, TgtCoeffRatio = 2 };
+};
+template <>
+EIGEN_STRONG_INLINE Packet2l pcast<Packet4i, Packet2l>(const Packet4i& a) {
+ // Discard second half of input.
+ return vmovl_s32(vget_low_s32(a));
+}
+
+template <>
+struct type_casting_traits<numext::int32_t, numext::uint64_t> {
+ enum { VectorizedCast = 1, SrcCoeffRatio = 1, TgtCoeffRatio = 2 };
+};
+template <>
+EIGEN_STRONG_INLINE Packet2ul pcast<Packet4i, Packet2ul>(const Packet4i& a) {
+ return vreinterpretq_u64_s64(pcast<Packet4i, Packet2l>(a));
+}
+
+template <>
+struct type_casting_traits<numext::int32_t, numext::int32_t> {
+ enum { VectorizedCast = 1, SrcCoeffRatio = 1, TgtCoeffRatio = 1 };
+};
+template <>
+EIGEN_STRONG_INLINE Packet4i pcast<Packet4i, Packet4i>(const Packet4i& a) {
+ return a;
+}
+template <>
+EIGEN_STRONG_INLINE Packet2i pcast<Packet2i, Packet2i>(const Packet2i& a) {
+ return a;
+}
+
+template <>
+struct type_casting_traits<numext::int32_t, numext::uint32_t> {
+ enum { VectorizedCast = 1, SrcCoeffRatio = 1, TgtCoeffRatio = 1 };
+};
+template <>
+EIGEN_STRONG_INLINE Packet4ui pcast<Packet4i, Packet4ui>(const Packet4i& a) {
+ return vreinterpretq_u32_s32(a);
+}
+template <>
+EIGEN_STRONG_INLINE Packet2ui pcast<Packet2i, Packet2ui>(const Packet2i& a) {
+ return vreinterpret_u32_s32(a);
+}
+
+template <>
+struct type_casting_traits<numext::int32_t, numext::int16_t> {
+ enum { VectorizedCast = 1, SrcCoeffRatio = 2, TgtCoeffRatio = 1 };
+};
+template <>
+EIGEN_STRONG_INLINE Packet8s pcast<Packet4i, Packet8s>(const Packet4i& a, const Packet4i& b) {
+ return vcombine_s16(vmovn_s32(a), vmovn_s32(b));
+}
+template <>
+EIGEN_STRONG_INLINE Packet4s pcast<Packet2i, Packet4s>(const Packet2i& a, const Packet2i& b) {
+ return vmovn_s32(vcombine_s32(a, b));
+}
+
+template <>
+struct type_casting_traits<numext::int32_t, numext::uint16_t> {
+ enum { VectorizedCast = 1, SrcCoeffRatio = 2, TgtCoeffRatio = 1 };
+};
+template <>
+EIGEN_STRONG_INLINE Packet8us pcast<Packet4i, Packet8us>(const Packet4i& a, const Packet4i& b) {
+ return vcombine_u16(vmovn_u32(vreinterpretq_u32_s32(a)), vmovn_u32(vreinterpretq_u32_s32(b)));
+}
+template <>
+EIGEN_STRONG_INLINE Packet4us pcast<Packet2i, Packet4us>(const Packet2i& a, const Packet2i& b) {
+ return vmovn_u32(vreinterpretq_u32_s32(vcombine_s32(a, b)));
+}
+
+template <>
+struct type_casting_traits<numext::int32_t, numext::int8_t> {
+ enum { VectorizedCast = 1, SrcCoeffRatio = 4, TgtCoeffRatio = 1 };
+};
+template <>
+EIGEN_STRONG_INLINE Packet16c pcast<Packet4i, Packet16c>(const Packet4i& a, const Packet4i& b, const Packet4i& c,
+ const Packet4i& d) {
+ const int16x8_t ab_s16 = pcast<Packet4i, Packet8s>(a, b);
+ const int16x8_t cd_s16 = pcast<Packet4i, Packet8s>(c, d);
+ return vcombine_s8(vmovn_s16(ab_s16), vmovn_s16(cd_s16));
+}
+template <>
+EIGEN_STRONG_INLINE Packet8c pcast<Packet2i, Packet8c>(const Packet2i& a, const Packet2i& b, const Packet2i& c,
+ const Packet2i& d) {
+ const int16x4_t ab_s16 = vmovn_s32(vcombine_s32(a, b));
+ const int16x4_t cd_s16 = vmovn_s32(vcombine_s32(c, d));
+ return vmovn_s16(vcombine_s16(ab_s16, cd_s16));
+}
+
+template <>
+struct type_casting_traits<numext::int32_t, numext::uint8_t> {
+ enum { VectorizedCast = 1, SrcCoeffRatio = 4, TgtCoeffRatio = 1 };
+};
+template <>
+EIGEN_STRONG_INLINE Packet16uc pcast<Packet4i, Packet16uc>(const Packet4i& a, const Packet4i& b, const Packet4i& c,
+ const Packet4i& d) {
+ const uint16x8_t ab_u16 = pcast<Packet4i, Packet8us>(a, b);
+ const uint16x8_t cd_u16 = pcast<Packet4i, Packet8us>(c, d);
+ return vcombine_u8(vmovn_u16(ab_u16), vmovn_u16(cd_u16));
+}
+template <>
+EIGEN_STRONG_INLINE Packet8uc pcast<Packet2i, Packet8uc>(const Packet2i& a, const Packet2i& b, const Packet2i& c,
+ const Packet2i& d) {
+ const uint16x4_t ab_u16 = pcast<Packet2i, Packet4us>(a, b);
+ const uint16x4_t cd_u16 = pcast<Packet2i, Packet4us>(c, d);
+ return vmovn_u16(vcombine_u16(ab_u16, cd_u16));
+}
+
+//==============================================================================
+// pcast, SrcType = uint32_t
+//==============================================================================
+template <>
+struct type_casting_traits<numext::uint32_t, float> {
+ enum { VectorizedCast = 1, SrcCoeffRatio = 1, TgtCoeffRatio = 1 };
+};
+template <>
+EIGEN_STRONG_INLINE Packet4f pcast<Packet4ui, Packet4f>(const Packet4ui& a) {
+ return vcvtq_f32_u32(a);
+}
+template <>
+EIGEN_STRONG_INLINE Packet2f pcast<Packet2ui, Packet2f>(const Packet2ui& a) {
+ return vcvt_f32_u32(a);
+}
+
+template <>
+struct type_casting_traits<numext::uint32_t, numext::uint64_t> {
+ enum { VectorizedCast = 1, SrcCoeffRatio = 1, TgtCoeffRatio = 2 };
+};
+template <>
+EIGEN_STRONG_INLINE Packet2ul pcast<Packet4ui, Packet2ul>(const Packet4ui& a) {
+ // Discard second half of input.
+ return vmovl_u32(vget_low_u32(a));
+}
+
+template <>
+struct type_casting_traits<numext::uint32_t, numext::int64_t> {
+ enum { VectorizedCast = 1, SrcCoeffRatio = 1, TgtCoeffRatio = 2 };
+};
+template <>
+EIGEN_STRONG_INLINE Packet2l pcast<Packet4ui, Packet2l>(const Packet4ui& a) {
+ return vreinterpretq_s64_u64(pcast<Packet4ui, Packet2ul>(a));
+}
+
+template <>
+struct type_casting_traits<numext::uint32_t, numext::uint32_t> {
+ enum { VectorizedCast = 1, SrcCoeffRatio = 1, TgtCoeffRatio = 1 };
+};
+template <>
+EIGEN_STRONG_INLINE Packet4ui pcast<Packet4ui, Packet4ui>(const Packet4ui& a) {
+ return a;
+}
+template <>
+EIGEN_STRONG_INLINE Packet2ui pcast<Packet2ui, Packet2ui>(const Packet2ui& a) {
+ return a;
+}
+
+template <>
+struct type_casting_traits<numext::uint32_t, numext::int32_t> {
+ enum { VectorizedCast = 1, SrcCoeffRatio = 1, TgtCoeffRatio = 1 };
+};
+template <>
+EIGEN_STRONG_INLINE Packet4i pcast<Packet4ui, Packet4i>(const Packet4ui& a) {
+ return vreinterpretq_s32_u32(a);
+}
+template <>
+EIGEN_STRONG_INLINE Packet2i pcast<Packet2ui, Packet2i>(const Packet2ui& a) {
+ return vreinterpret_s32_u32(a);
+}
+
+template <>
+struct type_casting_traits<numext::uint32_t, numext::uint16_t> {
+ enum { VectorizedCast = 1, SrcCoeffRatio = 2, TgtCoeffRatio = 1 };
+};
+template <>
+EIGEN_STRONG_INLINE Packet8us pcast<Packet4ui, Packet8us>(const Packet4ui& a, const Packet4ui& b) {
+ return vcombine_u16(vmovn_u32(a), vmovn_u32(b));
+}
+template <>
+EIGEN_STRONG_INLINE Packet4us pcast<Packet2ui, Packet4us>(const Packet2ui& a, const Packet2ui& b) {
+ return vmovn_u32(vcombine_u32(a, b));
+}
+
+template <>
+struct type_casting_traits<numext::uint32_t, numext::int16_t> {
+ enum { VectorizedCast = 1, SrcCoeffRatio = 2, TgtCoeffRatio = 1 };
+};
+template <>
+EIGEN_STRONG_INLINE Packet8s pcast<Packet4ui, Packet8s>(const Packet4ui& a, const Packet4ui& b) {
+ return vreinterpretq_s16_u16(pcast<Packet4ui, Packet8us>(a, b));
+}
+template <>
+EIGEN_STRONG_INLINE Packet4s pcast<Packet2ui, Packet4s>(const Packet2ui& a, const Packet2ui& b) {
+ return vreinterpret_s16_u16(pcast<Packet2ui, Packet4us>(a, b));
+}
+
+template <>
+struct type_casting_traits<numext::uint32_t, numext::uint8_t> {
+ enum { VectorizedCast = 1, SrcCoeffRatio = 4, TgtCoeffRatio = 1 };
+};
+template <>
+EIGEN_STRONG_INLINE Packet16uc pcast<Packet4ui, Packet16uc>(const Packet4ui& a, const Packet4ui& b, const Packet4ui& c,
+ const Packet4ui& d) {
+ const uint16x8_t ab_u16 = vcombine_u16(vmovn_u32(a), vmovn_u32(b));
+ const uint16x8_t cd_u16 = vcombine_u16(vmovn_u32(c), vmovn_u32(d));
+ return vcombine_u8(vmovn_u16(ab_u16), vmovn_u16(cd_u16));
+}
+template <>
+EIGEN_STRONG_INLINE Packet8uc pcast<Packet2ui, Packet8uc>(const Packet2ui& a, const Packet2ui& b, const Packet2ui& c,
+ const Packet2ui& d) {
+ const uint16x4_t ab_u16 = vmovn_u32(vcombine_u32(a, b));
+ const uint16x4_t cd_u16 = vmovn_u32(vcombine_u32(c, d));
+ return vmovn_u16(vcombine_u16(ab_u16, cd_u16));
+}
+
+template <>
+struct type_casting_traits<numext::uint32_t, numext::int8_t> {
+ enum { VectorizedCast = 1, SrcCoeffRatio = 4, TgtCoeffRatio = 1 };
+};
+template <>
+EIGEN_STRONG_INLINE Packet16c pcast<Packet4ui, Packet16c>(const Packet4ui& a, const Packet4ui& b, const Packet4ui& c,
+ const Packet4ui& d) {
+ return vreinterpretq_s8_u8(pcast<Packet4ui, Packet16uc>(a, b, c, d));
+}
+template <>
+EIGEN_STRONG_INLINE Packet8c pcast<Packet2ui, Packet8c>(const Packet2ui& a, const Packet2ui& b, const Packet2ui& c,
+ const Packet2ui& d) {
+ return vreinterpret_s8_u8(pcast<Packet2ui, Packet8uc>(a, b, c, d));
+}
+
+//==============================================================================
+// pcast, SrcType = int64_t
+//==============================================================================
+template <>
+struct type_casting_traits<numext::int64_t, float> {
+ enum { VectorizedCast = 1, SrcCoeffRatio = 2, TgtCoeffRatio = 1 };
+};
+template <>
+EIGEN_STRONG_INLINE Packet4f pcast<Packet2l, Packet4f>(const Packet2l& a, const Packet2l& b) {
+ return vcvtq_f32_s32(vcombine_s32(vmovn_s64(a), vmovn_s64(b)));
+}
+
+template <>
+struct type_casting_traits<numext::int64_t, numext::int64_t> {
+ enum { VectorizedCast = 1, SrcCoeffRatio = 1, TgtCoeffRatio = 1 };
+};
+template <>
+EIGEN_STRONG_INLINE Packet2l pcast<Packet2l, Packet2l>(const Packet2l& a) {
+ return a;
+}
+
+template <>
+struct type_casting_traits<numext::int64_t, numext::uint64_t> {
+ enum { VectorizedCast = 1, SrcCoeffRatio = 1, TgtCoeffRatio = 1 };
+};
+template <>
+EIGEN_STRONG_INLINE Packet2ul pcast<Packet2l, Packet2ul>(const Packet2l& a) {
+ return vreinterpretq_u64_s64(a);
+}
+
+template <>
+struct type_casting_traits<numext::int64_t, numext::int32_t> {
+ enum { VectorizedCast = 1, SrcCoeffRatio = 2, TgtCoeffRatio = 1 };
+};
+template <>
+EIGEN_STRONG_INLINE Packet4i pcast<Packet2l, Packet4i>(const Packet2l& a, const Packet2l& b) {
+ return vcombine_s32(vmovn_s64(a), vmovn_s64(b));
+}
+
+template <>
+struct type_casting_traits<numext::int64_t, numext::uint32_t> {
+ enum { VectorizedCast = 1, SrcCoeffRatio = 2, TgtCoeffRatio = 1 };
+};
+template <>
+EIGEN_STRONG_INLINE Packet4ui pcast<Packet2l, Packet4ui>(const Packet2l& a, const Packet2l& b) {
+ return vcombine_u32(vmovn_u64(vreinterpretq_u64_s64(a)), vmovn_u64(vreinterpretq_u64_s64(b)));
+}
+
+template <>
+struct type_casting_traits<numext::int64_t, numext::int16_t> {
+ enum { VectorizedCast = 1, SrcCoeffRatio = 4, TgtCoeffRatio = 1 };
+};
+template <>
+EIGEN_STRONG_INLINE Packet8s pcast<Packet2l, Packet8s>(const Packet2l& a, const Packet2l& b, const Packet2l& c,
+ const Packet2l& d) {
+ const int32x4_t ab_s32 = pcast<Packet2l, Packet4i>(a, b);
+ const int32x4_t cd_s32 = pcast<Packet2l, Packet4i>(c, d);
+ return vcombine_s16(vmovn_s32(ab_s32), vmovn_s32(cd_s32));
+}
+
+template <>
+struct type_casting_traits<numext::int64_t, numext::uint16_t> {
+ enum { VectorizedCast = 1, SrcCoeffRatio = 4, TgtCoeffRatio = 1 };
+};
+template <>
+EIGEN_STRONG_INLINE Packet8us pcast<Packet2l, Packet8us>(const Packet2l& a, const Packet2l& b, const Packet2l& c,
+ const Packet2l& d) {
+ const uint32x4_t ab_u32 = pcast<Packet2l, Packet4ui>(a, b);
+ const uint32x4_t cd_u32 = pcast<Packet2l, Packet4ui>(c, d);
+ return vcombine_u16(vmovn_u32(ab_u32), vmovn_u32(cd_u32));
+}
+
+template <>
+struct type_casting_traits<numext::int64_t, numext::int8_t> {
+ enum { VectorizedCast = 1, SrcCoeffRatio = 8, TgtCoeffRatio = 1 };
+};
+template <>
+EIGEN_STRONG_INLINE Packet16c pcast<Packet2l, Packet16c>(const Packet2l& a, const Packet2l& b, const Packet2l& c,
+ const Packet2l& d, const Packet2l& e, const Packet2l& f,
+ const Packet2l& g, const Packet2l& h) {
+ const int16x8_t abcd_s16 = pcast<Packet2l, Packet8s>(a, b, c, d);
+ const int16x8_t efgh_s16 = pcast<Packet2l, Packet8s>(e, f, g, h);
+ return vcombine_s8(vmovn_s16(abcd_s16), vmovn_s16(efgh_s16));
+}
+
+template <>
+struct type_casting_traits<numext::int64_t, numext::uint8_t> {
+ enum { VectorizedCast = 1, SrcCoeffRatio = 8, TgtCoeffRatio = 1 };
+};
+template <>
+EIGEN_STRONG_INLINE Packet16uc pcast<Packet2l, Packet16uc>(const Packet2l& a, const Packet2l& b, const Packet2l& c,
+ const Packet2l& d, const Packet2l& e, const Packet2l& f,
+ const Packet2l& g, const Packet2l& h) {
+ const uint16x8_t abcd_u16 = pcast<Packet2l, Packet8us>(a, b, c, d);
+ const uint16x8_t efgh_u16 = pcast<Packet2l, Packet8us>(e, f, g, h);
+ return vcombine_u8(vmovn_u16(abcd_u16), vmovn_u16(efgh_u16));
+}
+
+//==============================================================================
+// pcast, SrcType = uint64_t
+//==============================================================================
+template <>
+struct type_casting_traits<numext::uint64_t, float> {
+ enum { VectorizedCast = 1, SrcCoeffRatio = 2, TgtCoeffRatio = 1 };
+};
+template <>
+EIGEN_STRONG_INLINE Packet4f pcast<Packet2ul, Packet4f>(const Packet2ul& a, const Packet2ul& b) {
+ return vcvtq_f32_u32(vcombine_u32(vmovn_u64(a), vmovn_u64(b)));
+}
+
+template <>
+struct type_casting_traits<numext::uint64_t, numext::uint64_t> {
+ enum { VectorizedCast = 1, SrcCoeffRatio = 1, TgtCoeffRatio = 1 };
+};
+template <>
+EIGEN_STRONG_INLINE Packet2ul pcast<Packet2ul, Packet2ul>(const Packet2ul& a) {
+ return a;
+}
+
+template <>
+struct type_casting_traits<numext::uint64_t, numext::int64_t> {
+ enum { VectorizedCast = 1, SrcCoeffRatio = 1, TgtCoeffRatio = 1 };
+};
+template <>
+EIGEN_STRONG_INLINE Packet2l pcast<Packet2ul, Packet2l>(const Packet2ul& a) {
+ return vreinterpretq_s64_u64(a);
+}
+
+template <>
+struct type_casting_traits<numext::uint64_t, numext::uint32_t> {
+ enum { VectorizedCast = 1, SrcCoeffRatio = 2, TgtCoeffRatio = 1 };
+};
+template <>
+EIGEN_STRONG_INLINE Packet4ui pcast<Packet2ul, Packet4ui>(const Packet2ul& a, const Packet2ul& b) {
+ return vcombine_u32(vmovn_u64(a), vmovn_u64(b));
+}
+
+template <>
+struct type_casting_traits<numext::uint64_t, numext::int32_t> {
+ enum { VectorizedCast = 1, SrcCoeffRatio = 2, TgtCoeffRatio = 1 };
+};
+template <>
+EIGEN_STRONG_INLINE Packet4i pcast<Packet2ul, Packet4i>(const Packet2ul& a, const Packet2ul& b) {
+ return vreinterpretq_s32_u32(pcast<Packet2ul, Packet4ui>(a, b));
+}
+
+template <>
+struct type_casting_traits<numext::uint64_t, numext::uint16_t> {
+ enum { VectorizedCast = 1, SrcCoeffRatio = 4, TgtCoeffRatio = 1 };
+};
+template <>
+EIGEN_STRONG_INLINE Packet8us pcast<Packet2ul, Packet8us>(const Packet2ul& a, const Packet2ul& b, const Packet2ul& c,
+ const Packet2ul& d) {
+ const uint16x4_t ab_u16 = vmovn_u32(vcombine_u32(vmovn_u64(a), vmovn_u64(b)));
+ const uint16x4_t cd_u16 = vmovn_u32(vcombine_u32(vmovn_u64(c), vmovn_u64(d)));
+ return vcombine_u16(ab_u16, cd_u16);
+}
+
+template <>
+struct type_casting_traits<numext::uint64_t, numext::int16_t> {
+ enum { VectorizedCast = 1, SrcCoeffRatio = 4, TgtCoeffRatio = 1 };
+};
+template <>
+EIGEN_STRONG_INLINE Packet8s pcast<Packet2ul, Packet8s>(const Packet2ul& a, const Packet2ul& b, const Packet2ul& c,
+ const Packet2ul& d) {
+ return vreinterpretq_s16_u16(pcast<Packet2ul, Packet8us>(a, b, c, d));
+}
+
+template <>
+struct type_casting_traits<numext::uint64_t, numext::uint8_t> {
+ enum { VectorizedCast = 1, SrcCoeffRatio = 8, TgtCoeffRatio = 1 };
+};
+template <>
+EIGEN_STRONG_INLINE Packet16uc pcast<Packet2ul, Packet16uc>(const Packet2ul& a, const Packet2ul& b, const Packet2ul& c,
+ const Packet2ul& d, const Packet2ul& e, const Packet2ul& f,
+ const Packet2ul& g, const Packet2ul& h) {
+ const uint16x8_t abcd_u16 = pcast<Packet2ul, Packet8us>(a, b, c, d);
+ const uint16x8_t efgh_u16 = pcast<Packet2ul, Packet8us>(e, f, g, h);
+ return vcombine_u8(vmovn_u16(abcd_u16), vmovn_u16(efgh_u16));
+}
+
+template <>
+struct type_casting_traits<numext::uint64_t, numext::int8_t> {
+ enum { VectorizedCast = 1, SrcCoeffRatio = 8, TgtCoeffRatio = 1 };
+};
+template <>
+EIGEN_STRONG_INLINE Packet16c pcast<Packet2ul, Packet16c>(const Packet2ul& a, const Packet2ul& b, const Packet2ul& c,
+ const Packet2ul& d, const Packet2ul& e, const Packet2ul& f,
+ const Packet2ul& g, const Packet2ul& h) {
+ return vreinterpretq_s8_u8(pcast<Packet2ul, Packet16uc>(a, b, c, d, e, f, g, h));
+}
+
+//==============================================================================
+// preinterpret
+//==============================================================================
+template <>
+EIGEN_STRONG_INLINE Packet2f preinterpret<Packet2f, Packet2i>(const Packet2i& a) {
+ return vreinterpret_f32_s32(a);
+}
+template <>
+EIGEN_STRONG_INLINE Packet2f preinterpret<Packet2f, Packet2ui>(const Packet2ui& a) {
+ return vreinterpret_f32_u32(a);
+}
+template <>
+EIGEN_STRONG_INLINE Packet4f preinterpret<Packet4f, Packet4i>(const Packet4i& a) {
+ return vreinterpretq_f32_s32(a);
+}
+template <>
+EIGEN_STRONG_INLINE Packet4f preinterpret<Packet4f, Packet4ui>(const Packet4ui& a) {
+ return vreinterpretq_f32_u32(a);
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet4c preinterpret<Packet4c, Packet4uc>(const Packet4uc& a) {
+ return static_cast<Packet4c>(a);
+}
+template <>
+EIGEN_STRONG_INLINE Packet8c preinterpret<Packet8c, Packet8uc>(const Packet8uc& a) {
+ return vreinterpret_s8_u8(a);
+}
+template <>
+EIGEN_STRONG_INLINE Packet16c preinterpret<Packet16c, Packet16uc>(const Packet16uc& a) {
+ return vreinterpretq_s8_u8(a);
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet4uc preinterpret<Packet4uc, Packet4c>(const Packet4c& a) {
+ return static_cast<Packet4uc>(a);
+}
+template <>
+EIGEN_STRONG_INLINE Packet8uc preinterpret<Packet8uc, Packet8c>(const Packet8c& a) {
+ return vreinterpret_u8_s8(a);
+}
+template <>
+EIGEN_STRONG_INLINE Packet16uc preinterpret<Packet16uc, Packet16c>(const Packet16c& a) {
+ return vreinterpretq_u8_s8(a);
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet4s preinterpret<Packet4s, Packet4us>(const Packet4us& a) {
+ return vreinterpret_s16_u16(a);
+}
+template <>
+EIGEN_STRONG_INLINE Packet8s preinterpret<Packet8s, Packet8us>(const Packet8us& a) {
+ return vreinterpretq_s16_u16(a);
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet4us preinterpret<Packet4us, Packet4s>(const Packet4s& a) {
+ return vreinterpret_u16_s16(a);
+}
+template <>
+EIGEN_STRONG_INLINE Packet8us preinterpret<Packet8us, Packet8s>(const Packet8s& a) {
+ return vreinterpretq_u16_s16(a);
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet2i preinterpret<Packet2i, Packet2f>(const Packet2f& a) {
+ return vreinterpret_s32_f32(a);
+}
+template <>
+EIGEN_STRONG_INLINE Packet2i preinterpret<Packet2i, Packet2ui>(const Packet2ui& a) {
+ return vreinterpret_s32_u32(a);
+}
+template <>
+EIGEN_STRONG_INLINE Packet4i preinterpret<Packet4i, Packet4f>(const Packet4f& a) {
+ return vreinterpretq_s32_f32(a);
+}
+template <>
+EIGEN_STRONG_INLINE Packet4i preinterpret<Packet4i, Packet4ui>(const Packet4ui& a) {
+ return vreinterpretq_s32_u32(a);
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet2ui preinterpret<Packet2ui, Packet2f>(const Packet2f& a) {
+ return vreinterpret_u32_f32(a);
+}
+template <>
+EIGEN_STRONG_INLINE Packet2ui preinterpret<Packet2ui, Packet2i>(const Packet2i& a) {
+ return vreinterpret_u32_s32(a);
+}
+template <>
+EIGEN_STRONG_INLINE Packet4ui preinterpret<Packet4ui, Packet4f>(const Packet4f& a) {
+ return vreinterpretq_u32_f32(a);
+}
+template <>
+EIGEN_STRONG_INLINE Packet4ui preinterpret<Packet4ui, Packet4i>(const Packet4i& a) {
+ return vreinterpretq_u32_s32(a);
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet2l preinterpret<Packet2l, Packet2ul>(const Packet2ul& a) {
+ return vreinterpretq_s64_u64(a);
+}
+template <>
+EIGEN_STRONG_INLINE Packet2ul preinterpret<Packet2ul, Packet2l>(const Packet2l& a) {
+ return vreinterpretq_u64_s64(a);
+}
+
+#if EIGEN_ARCH_ARM64
+
+//==============================================================================
+// pcast/preinterpret, Double
+//==============================================================================
+
+template <>
+struct type_casting_traits<double, double> {
+ enum { VectorizedCast = 1, SrcCoeffRatio = 1, TgtCoeffRatio = 1 };
+};
+template <>
+EIGEN_STRONG_INLINE Packet2d pcast<Packet2d, Packet2d>(const Packet2d& a) {
+ return a;
+}
+
+template <>
+struct type_casting_traits<double, float> {
+ enum { VectorizedCast = 1, SrcCoeffRatio = 2, TgtCoeffRatio = 1 };
+};
+template <>
+EIGEN_STRONG_INLINE Packet4f pcast<Packet2d, Packet4f>(const Packet2d& a, const Packet2d& b) {
+ return vcombine_f32(vcvt_f32_f64(a), vcvt_f32_f64(b));
+}
+
+template <>
+struct type_casting_traits<double, numext::int64_t> {
+ enum { VectorizedCast = 1, SrcCoeffRatio = 1, TgtCoeffRatio = 1 };
+};
+template <>
+EIGEN_STRONG_INLINE Packet2l pcast<Packet2d, Packet2l>(const Packet2d& a) {
+ return vcvtq_s64_f64(a);
+}
+
+template <>
+struct type_casting_traits<double, numext::uint64_t> {
+ enum { VectorizedCast = 1, SrcCoeffRatio = 1, TgtCoeffRatio = 1 };
+};
+template <>
+EIGEN_STRONG_INLINE Packet2ul pcast<Packet2d, Packet2ul>(const Packet2d& a) {
+ return vcvtq_u64_f64(a);
+}
+
+template <>
+struct type_casting_traits<double, numext::int32_t> {
+ enum { VectorizedCast = 1, SrcCoeffRatio = 2, TgtCoeffRatio = 1 };
+};
+template <>
+EIGEN_STRONG_INLINE Packet4i pcast<Packet2d, Packet4i>(const Packet2d& a, const Packet2d& b) {
+ return vcombine_s32(vmovn_s64(vcvtq_s64_f64(a)), vmovn_s64(vcvtq_s64_f64(b)));
+}
+
+template <>
+struct type_casting_traits<double, numext::uint32_t> {
+ enum { VectorizedCast = 1, SrcCoeffRatio = 2, TgtCoeffRatio = 1 };
+};
+template <>
+EIGEN_STRONG_INLINE Packet4ui pcast<Packet2d, Packet4ui>(const Packet2d& a, const Packet2d& b) {
+ return vcombine_u32(vmovn_u64(vcvtq_u64_f64(a)), vmovn_u64(vcvtq_u64_f64(b)));
+}
+
+template <>
+struct type_casting_traits<double, numext::int16_t> {
+ enum { VectorizedCast = 1, SrcCoeffRatio = 4, TgtCoeffRatio = 1 };
+};
+template <>
+EIGEN_STRONG_INLINE Packet8s pcast<Packet2d, Packet8s>(const Packet2d& a, const Packet2d& b, const Packet2d& c,
+ const Packet2d& d) {
+ const int32x4_t ab_s32 = pcast<Packet2d, Packet4i>(a, b);
+ const int32x4_t cd_s32 = pcast<Packet2d, Packet4i>(c, d);
+ return vcombine_s16(vmovn_s32(ab_s32), vmovn_s32(cd_s32));
+}
+
+template <>
+struct type_casting_traits<double, numext::uint16_t> {
+ enum { VectorizedCast = 1, SrcCoeffRatio = 4, TgtCoeffRatio = 1 };
+};
+template <>
+EIGEN_STRONG_INLINE Packet8us pcast<Packet2d, Packet8us>(const Packet2d& a, const Packet2d& b, const Packet2d& c,
+ const Packet2d& d) {
+ const uint32x4_t ab_u32 = pcast<Packet2d, Packet4ui>(a, b);
+ const uint32x4_t cd_u32 = pcast<Packet2d, Packet4ui>(c, d);
+ return vcombine_u16(vmovn_u32(ab_u32), vmovn_u32(cd_u32));
+}
+
+template <>
+struct type_casting_traits<double, numext::int8_t> {
+ enum { VectorizedCast = 1, SrcCoeffRatio = 8, TgtCoeffRatio = 1 };
+};
+template <>
+EIGEN_STRONG_INLINE Packet16c pcast<Packet2d, Packet16c>(const Packet2d& a, const Packet2d& b, const Packet2d& c,
+ const Packet2d& d, const Packet2d& e, const Packet2d& f,
+ const Packet2d& g, const Packet2d& h) {
+ const int16x8_t abcd_s16 = pcast<Packet2d, Packet8s>(a, b, c, d);
+ const int16x8_t efgh_s16 = pcast<Packet2d, Packet8s>(e, f, g, h);
+ return vcombine_s8(vmovn_s16(abcd_s16), vmovn_s16(efgh_s16));
+}
+
+template <>
+struct type_casting_traits<double, numext::uint8_t> {
+ enum { VectorizedCast = 1, SrcCoeffRatio = 8, TgtCoeffRatio = 1 };
+};
+template <>
+EIGEN_STRONG_INLINE Packet16uc pcast<Packet2d, Packet16uc>(const Packet2d& a, const Packet2d& b, const Packet2d& c,
+ const Packet2d& d, const Packet2d& e, const Packet2d& f,
+ const Packet2d& g, const Packet2d& h) {
+ const uint16x8_t abcd_u16 = pcast<Packet2d, Packet8us>(a, b, c, d);
+ const uint16x8_t efgh_u16 = pcast<Packet2d, Packet8us>(e, f, g, h);
+ return vcombine_u8(vmovn_u16(abcd_u16), vmovn_u16(efgh_u16));
+}
+
+template <>
+struct type_casting_traits<float, double> {
+ enum { VectorizedCast = 1, SrcCoeffRatio = 1, TgtCoeffRatio = 2 };
+};
+template <>
+EIGEN_STRONG_INLINE Packet2d pcast<Packet4f, Packet2d>(const Packet4f& a) {
+ // Discard second-half of input.
+ return vcvt_f64_f32(vget_low_f32(a));
+}
+
+template <>
+struct type_casting_traits<numext::int8_t, double> {
+ enum { VectorizedCast = 1, SrcCoeffRatio = 1, TgtCoeffRatio = 8 };
+};
+template <>
+EIGEN_STRONG_INLINE Packet2d pcast<Packet16c, Packet2d>(const Packet16c& a) {
+ // Discard all but first two values.
+ return vcvt_f64_f32(pcast<Packet8c, Packet2f>(vget_low_s8(a)));
+}
+
+template <>
+struct type_casting_traits<numext::uint8_t, double> {
+ enum { VectorizedCast = 1, SrcCoeffRatio = 1, TgtCoeffRatio = 8 };
+};
+template <>
+EIGEN_STRONG_INLINE Packet2d pcast<Packet16uc, Packet2d>(const Packet16uc& a) {
+ // Discard all but first two values.
+ return vcvt_f64_f32(pcast<Packet8uc, Packet2f>(vget_low_u8(a)));
+}
+
+template <>
+struct type_casting_traits<numext::int16_t, double> {
+ enum { VectorizedCast = 1, SrcCoeffRatio = 1, TgtCoeffRatio = 4 };
+};
+template <>
+EIGEN_STRONG_INLINE Packet2d pcast<Packet8s, Packet2d>(const Packet8s& a) {
+ // Discard all but first two values.
+ return vcvt_f64_f32(pcast<Packet4s, Packet2f>(vget_low_s16(a)));
+}
+
+template <>
+struct type_casting_traits<numext::uint16_t, double> {
+ enum { VectorizedCast = 1, SrcCoeffRatio = 1, TgtCoeffRatio = 4 };
+};
+template <>
+EIGEN_STRONG_INLINE Packet2d pcast<Packet8us, Packet2d>(const Packet8us& a) {
+ // Discard all but first two values.
+ return vcvt_f64_f32(pcast<Packet4us, Packet2f>(vget_low_u16(a)));
+}
+
+template <>
+struct type_casting_traits<numext::int32_t, double> {
+ enum { VectorizedCast = 1, SrcCoeffRatio = 1, TgtCoeffRatio = 2 };
+};
+template <>
+EIGEN_STRONG_INLINE Packet2d pcast<Packet4i, Packet2d>(const Packet4i& a) {
+ // Discard second half of input.
+ return vcvtq_f64_s64(vmovl_s32(vget_low_s32(a)));
+}
+
+template <>
+struct type_casting_traits<numext::uint32_t, double> {
+ enum { VectorizedCast = 1, SrcCoeffRatio = 1, TgtCoeffRatio = 2 };
+};
+template <>
+EIGEN_STRONG_INLINE Packet2d pcast<Packet4ui, Packet2d>(const Packet4ui& a) {
+ // Discard second half of input.
+ return vcvtq_f64_u64(vmovl_u32(vget_low_u32(a)));
+}
+
+template <>
+struct type_casting_traits<numext::int64_t, double> {
+ enum { VectorizedCast = 1, SrcCoeffRatio = 1, TgtCoeffRatio = 1 };
+};
+template <>
+EIGEN_STRONG_INLINE Packet2d pcast<Packet2l, Packet2d>(const Packet2l& a) {
+ return vcvtq_f64_s64(a);
+}
+
+template <>
+struct type_casting_traits<numext::uint64_t, double> {
+ enum { VectorizedCast = 1, SrcCoeffRatio = 1, TgtCoeffRatio = 1 };
+};
+template <>
+EIGEN_STRONG_INLINE Packet2d pcast<Packet2ul, Packet2d>(const Packet2ul& a) {
+ return vcvtq_f64_u64(a);
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet2d preinterpret<Packet2d, Packet2l>(const Packet2l& a) {
+ return vreinterpretq_f64_s64(a);
+}
+template <>
+EIGEN_STRONG_INLINE Packet2d preinterpret<Packet2d, Packet2ul>(const Packet2ul& a) {
+ return vreinterpretq_f64_u64(a);
+}
+template <>
+EIGEN_STRONG_INLINE Packet2l preinterpret<Packet2l, Packet2d>(const Packet2d& a) {
+ return vreinterpretq_s64_f64(a);
+}
+template <>
+EIGEN_STRONG_INLINE Packet2ul preinterpret<Packet2ul, Packet2d>(const Packet2d& a) {
+ return vreinterpretq_u64_f64(a);
+}
+template <>
+EIGEN_STRONG_INLINE Packet2d preinterpret<Packet2d, Packet4i>(const Packet4i& a) {
+ return vreinterpretq_f64_s32(a);
+}
+template <>
+EIGEN_STRONG_INLINE Packet4i preinterpret<Packet4i, Packet2d>(const Packet2d& a) {
+ return vreinterpretq_s32_f64(a);
+}
+
+#endif // EIGEN_ARCH_ARM64
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_TYPE_CASTING_NEON_H
diff --git a/Eigen/src/Core/arch/NEON/UnaryFunctors.h b/Eigen/src/Core/arch/NEON/UnaryFunctors.h
new file mode 100644
index 0000000..67f9dcf
--- /dev/null
+++ b/Eigen/src/Core/arch/NEON/UnaryFunctors.h
@@ -0,0 +1,63 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_NEON_UNARY_FUNCTORS_H
+#define EIGEN_NEON_UNARY_FUNCTORS_H
+
+#include "../../InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+
+#if EIGEN_HAS_ARM64_FP16_VECTOR_ARITHMETIC
+/** \internal
+ * \brief Template specialization of the logistic function for Eigen::half.
+ */
+template <>
+struct scalar_logistic_op<Eigen::half> {
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ Eigen::half operator()(const Eigen::half& x) const {
+ // Convert to float and call scalar_logistic_op<float>.
+ const scalar_logistic_op<float> float_op;
+ return Eigen::half(float_op(float(x)));
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ Eigen::half packetOp(const Eigen::half& x) const {
+ return this->operator()(x);
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ Packet4hf packetOp(const Packet4hf& x) const {
+ const scalar_logistic_op<float> float_op;
+ return vcvt_f16_f32(float_op.packetOp(vcvt_f32_f16(x)));
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ Packet8hf packetOp(const Packet8hf& x) const {
+ const scalar_logistic_op<float> float_op;
+ return vcombine_f16(
+ vcvt_f16_f32(float_op.packetOp(vcvt_f32_f16(vget_low_f16(x)))),
+ vcvt_f16_f32(float_op.packetOp(vcvt_high_f32_f16(x))));
+ }
+};
+
+template<>
+struct functor_traits<scalar_logistic_op<Eigen::half>> {
+ enum {
+ Cost = functor_traits<scalar_logistic_op<float>>::Cost,
+ PacketAccess = functor_traits<scalar_logistic_op<float>>::PacketAccess,
+ };
+};
+#endif // EIGEN_HAS_ARM64_FP16_VECTOR_ARITHMETIC
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_NEON_UNARY_FUNCTORS_H
diff --git a/Eigen/src/Core/arch/SSE/Complex.h b/Eigen/src/Core/arch/SSE/Complex.h
new file mode 100644
index 0000000..60308ce
--- /dev/null
+++ b/Eigen/src/Core/arch/SSE/Complex.h
@@ -0,0 +1,332 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2010 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_COMPLEX_SSE_H
+#define EIGEN_COMPLEX_SSE_H
+
+#include "../../InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+
+//---------- float ----------
+struct Packet2cf
+{
+ EIGEN_STRONG_INLINE Packet2cf() {}
+ EIGEN_STRONG_INLINE explicit Packet2cf(const __m128& a) : v(a) {}
+ Packet4f v;
+};
+
+// Use the packet_traits defined in AVX/PacketMath.h instead if we're going
+// to leverage AVX instructions.
+#ifndef EIGEN_VECTORIZE_AVX
+template<> struct packet_traits<std::complex<float> > : default_packet_traits
+{
+ typedef Packet2cf type;
+ typedef Packet2cf half;
+ enum {
+ Vectorizable = 1,
+ AlignedOnScalar = 1,
+ size = 2,
+ HasHalfPacket = 0,
+
+ HasAdd = 1,
+ HasSub = 1,
+ HasMul = 1,
+ HasDiv = 1,
+ HasNegate = 1,
+ HasSqrt = 1,
+ HasAbs = 0,
+ HasAbs2 = 0,
+ HasMin = 0,
+ HasMax = 0,
+ HasSetLinear = 0,
+ HasBlend = 1
+ };
+};
+#endif
+
+template<> struct unpacket_traits<Packet2cf> {
+ typedef std::complex<float> type;
+ typedef Packet2cf half;
+ typedef Packet4f as_real;
+ enum {
+ size=2,
+ alignment=Aligned16,
+ vectorizable=true,
+ masked_load_available=false,
+ masked_store_available=false
+ };
+};
+
+template<> EIGEN_STRONG_INLINE Packet2cf padd<Packet2cf>(const Packet2cf& a, const Packet2cf& b) { return Packet2cf(_mm_add_ps(a.v,b.v)); }
+template<> EIGEN_STRONG_INLINE Packet2cf psub<Packet2cf>(const Packet2cf& a, const Packet2cf& b) { return Packet2cf(_mm_sub_ps(a.v,b.v)); }
+
+template<> EIGEN_STRONG_INLINE Packet2cf pnegate(const Packet2cf& a)
+{
+ const __m128 mask = _mm_castsi128_ps(_mm_setr_epi32(0x80000000,0x80000000,0x80000000,0x80000000));
+ return Packet2cf(_mm_xor_ps(a.v,mask));
+}
+template<> EIGEN_STRONG_INLINE Packet2cf pconj(const Packet2cf& a)
+{
+ const __m128 mask = _mm_castsi128_ps(_mm_setr_epi32(0x00000000,0x80000000,0x00000000,0x80000000));
+ return Packet2cf(_mm_xor_ps(a.v,mask));
+}
+
+template<> EIGEN_STRONG_INLINE Packet2cf pmul<Packet2cf>(const Packet2cf& a, const Packet2cf& b)
+{
+ #ifdef EIGEN_VECTORIZE_SSE3
+ return Packet2cf(_mm_addsub_ps(_mm_mul_ps(_mm_moveldup_ps(a.v), b.v),
+ _mm_mul_ps(_mm_movehdup_ps(a.v),
+ vec4f_swizzle1(b.v, 1, 0, 3, 2))));
+// return Packet2cf(_mm_addsub_ps(_mm_mul_ps(vec4f_swizzle1(a.v, 0, 0, 2, 2), b.v),
+// _mm_mul_ps(vec4f_swizzle1(a.v, 1, 1, 3, 3),
+// vec4f_swizzle1(b.v, 1, 0, 3, 2))));
+ #else
+ const __m128 mask = _mm_castsi128_ps(_mm_setr_epi32(0x80000000,0x00000000,0x80000000,0x00000000));
+ return Packet2cf(_mm_add_ps(_mm_mul_ps(vec4f_swizzle1(a.v, 0, 0, 2, 2), b.v),
+ _mm_xor_ps(_mm_mul_ps(vec4f_swizzle1(a.v, 1, 1, 3, 3),
+ vec4f_swizzle1(b.v, 1, 0, 3, 2)), mask)));
+ #endif
+}
+
+template<> EIGEN_STRONG_INLINE Packet2cf ptrue <Packet2cf>(const Packet2cf& a) { return Packet2cf(ptrue(Packet4f(a.v))); }
+template<> EIGEN_STRONG_INLINE Packet2cf pand <Packet2cf>(const Packet2cf& a, const Packet2cf& b) { return Packet2cf(_mm_and_ps(a.v,b.v)); }
+template<> EIGEN_STRONG_INLINE Packet2cf por <Packet2cf>(const Packet2cf& a, const Packet2cf& b) { return Packet2cf(_mm_or_ps(a.v,b.v)); }
+template<> EIGEN_STRONG_INLINE Packet2cf pxor <Packet2cf>(const Packet2cf& a, const Packet2cf& b) { return Packet2cf(_mm_xor_ps(a.v,b.v)); }
+template<> EIGEN_STRONG_INLINE Packet2cf pandnot<Packet2cf>(const Packet2cf& a, const Packet2cf& b) { return Packet2cf(_mm_andnot_ps(b.v,a.v)); }
+
+template<> EIGEN_STRONG_INLINE Packet2cf pload <Packet2cf>(const std::complex<float>* from) { EIGEN_DEBUG_ALIGNED_LOAD return Packet2cf(pload<Packet4f>(&numext::real_ref(*from))); }
+template<> EIGEN_STRONG_INLINE Packet2cf ploadu<Packet2cf>(const std::complex<float>* from) { EIGEN_DEBUG_UNALIGNED_LOAD return Packet2cf(ploadu<Packet4f>(&numext::real_ref(*from))); }
+
+template<> EIGEN_STRONG_INLINE Packet2cf pset1<Packet2cf>(const std::complex<float>& from)
+{
+ const float re = std::real(from);
+ const float im = std::imag(from);
+ return Packet2cf(_mm_set_ps(im, re, im, re));
+}
+
+template<> EIGEN_STRONG_INLINE Packet2cf ploaddup<Packet2cf>(const std::complex<float>* from) { return pset1<Packet2cf>(*from); }
+
+template<> EIGEN_STRONG_INLINE void pstore <std::complex<float> >(std::complex<float> * to, const Packet2cf& from) { EIGEN_DEBUG_ALIGNED_STORE pstore(&numext::real_ref(*to), Packet4f(from.v)); }
+template<> EIGEN_STRONG_INLINE void pstoreu<std::complex<float> >(std::complex<float> * to, const Packet2cf& from) { EIGEN_DEBUG_UNALIGNED_STORE pstoreu(&numext::real_ref(*to), Packet4f(from.v)); }
+
+
+template<> EIGEN_DEVICE_FUNC inline Packet2cf pgather<std::complex<float>, Packet2cf>(const std::complex<float>* from, Index stride)
+{
+ return Packet2cf(_mm_set_ps(std::imag(from[1*stride]), std::real(from[1*stride]),
+ std::imag(from[0*stride]), std::real(from[0*stride])));
+}
+
+template<> EIGEN_DEVICE_FUNC inline void pscatter<std::complex<float>, Packet2cf>(std::complex<float>* to, const Packet2cf& from, Index stride)
+{
+ to[stride*0] = std::complex<float>(_mm_cvtss_f32(_mm_shuffle_ps(from.v, from.v, 0)),
+ _mm_cvtss_f32(_mm_shuffle_ps(from.v, from.v, 1)));
+ to[stride*1] = std::complex<float>(_mm_cvtss_f32(_mm_shuffle_ps(from.v, from.v, 2)),
+ _mm_cvtss_f32(_mm_shuffle_ps(from.v, from.v, 3)));
+}
+
+template<> EIGEN_STRONG_INLINE void prefetch<std::complex<float> >(const std::complex<float> * addr) { _mm_prefetch((SsePrefetchPtrType)(addr), _MM_HINT_T0); }
+
+template<> EIGEN_STRONG_INLINE std::complex<float> pfirst<Packet2cf>(const Packet2cf& a)
+{
+ alignas(alignof(__m64)) std::complex<float> res;
+ _mm_storel_pi((__m64*)&res, a.v);
+ return res;
+}
+
+template<> EIGEN_STRONG_INLINE Packet2cf preverse(const Packet2cf& a) { return Packet2cf(_mm_castpd_ps(preverse(Packet2d(_mm_castps_pd(a.v))))); }
+
+template<> EIGEN_STRONG_INLINE std::complex<float> predux<Packet2cf>(const Packet2cf& a)
+{
+ return pfirst(Packet2cf(_mm_add_ps(a.v, _mm_movehl_ps(a.v,a.v))));
+}
+
+template<> EIGEN_STRONG_INLINE std::complex<float> predux_mul<Packet2cf>(const Packet2cf& a)
+{
+ return pfirst(pmul(a, Packet2cf(_mm_movehl_ps(a.v,a.v))));
+}
+
+EIGEN_STRONG_INLINE Packet2cf pcplxflip/* <Packet2cf> */(const Packet2cf& x)
+{
+ return Packet2cf(vec4f_swizzle1(x.v, 1, 0, 3, 2));
+}
+
+EIGEN_MAKE_CONJ_HELPER_CPLX_REAL(Packet2cf,Packet4f)
+
+template<> EIGEN_STRONG_INLINE Packet2cf pdiv<Packet2cf>(const Packet2cf& a, const Packet2cf& b)
+{
+ return pdiv_complex(a, b);
+}
+
+//---------- double ----------
+struct Packet1cd
+{
+ EIGEN_STRONG_INLINE Packet1cd() {}
+ EIGEN_STRONG_INLINE explicit Packet1cd(const __m128d& a) : v(a) {}
+ Packet2d v;
+};
+
+// Use the packet_traits defined in AVX/PacketMath.h instead if we're going
+// to leverage AVX instructions.
+#ifndef EIGEN_VECTORIZE_AVX
+template<> struct packet_traits<std::complex<double> > : default_packet_traits
+{
+ typedef Packet1cd type;
+ typedef Packet1cd half;
+ enum {
+ Vectorizable = 1,
+ AlignedOnScalar = 0,
+ size = 1,
+ HasHalfPacket = 0,
+
+ HasAdd = 1,
+ HasSub = 1,
+ HasMul = 1,
+ HasDiv = 1,
+ HasNegate = 1,
+ HasSqrt = 1,
+ HasAbs = 0,
+ HasAbs2 = 0,
+ HasMin = 0,
+ HasMax = 0,
+ HasSetLinear = 0
+ };
+};
+#endif
+
+template<> struct unpacket_traits<Packet1cd> {
+ typedef std::complex<double> type;
+ typedef Packet1cd half;
+ typedef Packet2d as_real;
+ enum {
+ size=1,
+ alignment=Aligned16,
+ vectorizable=true,
+ masked_load_available=false,
+ masked_store_available=false
+ };
+};
+
+template<> EIGEN_STRONG_INLINE Packet1cd padd<Packet1cd>(const Packet1cd& a, const Packet1cd& b) { return Packet1cd(_mm_add_pd(a.v,b.v)); }
+template<> EIGEN_STRONG_INLINE Packet1cd psub<Packet1cd>(const Packet1cd& a, const Packet1cd& b) { return Packet1cd(_mm_sub_pd(a.v,b.v)); }
+template<> EIGEN_STRONG_INLINE Packet1cd pnegate(const Packet1cd& a) { return Packet1cd(pnegate(Packet2d(a.v))); }
+template<> EIGEN_STRONG_INLINE Packet1cd pconj(const Packet1cd& a)
+{
+ const __m128d mask = _mm_castsi128_pd(_mm_set_epi32(0x80000000,0x0,0x0,0x0));
+ return Packet1cd(_mm_xor_pd(a.v,mask));
+}
+
+template<> EIGEN_STRONG_INLINE Packet1cd pmul<Packet1cd>(const Packet1cd& a, const Packet1cd& b)
+{
+ #ifdef EIGEN_VECTORIZE_SSE3
+ return Packet1cd(_mm_addsub_pd(_mm_mul_pd(_mm_movedup_pd(a.v), b.v),
+ _mm_mul_pd(vec2d_swizzle1(a.v, 1, 1),
+ vec2d_swizzle1(b.v, 1, 0))));
+ #else
+ const __m128d mask = _mm_castsi128_pd(_mm_set_epi32(0x0,0x0,0x80000000,0x0));
+ return Packet1cd(_mm_add_pd(_mm_mul_pd(vec2d_swizzle1(a.v, 0, 0), b.v),
+ _mm_xor_pd(_mm_mul_pd(vec2d_swizzle1(a.v, 1, 1),
+ vec2d_swizzle1(b.v, 1, 0)), mask)));
+ #endif
+}
+
+template<> EIGEN_STRONG_INLINE Packet1cd ptrue <Packet1cd>(const Packet1cd& a) { return Packet1cd(ptrue(Packet2d(a.v))); }
+template<> EIGEN_STRONG_INLINE Packet1cd pand <Packet1cd>(const Packet1cd& a, const Packet1cd& b) { return Packet1cd(_mm_and_pd(a.v,b.v)); }
+template<> EIGEN_STRONG_INLINE Packet1cd por <Packet1cd>(const Packet1cd& a, const Packet1cd& b) { return Packet1cd(_mm_or_pd(a.v,b.v)); }
+template<> EIGEN_STRONG_INLINE Packet1cd pxor <Packet1cd>(const Packet1cd& a, const Packet1cd& b) { return Packet1cd(_mm_xor_pd(a.v,b.v)); }
+template<> EIGEN_STRONG_INLINE Packet1cd pandnot<Packet1cd>(const Packet1cd& a, const Packet1cd& b) { return Packet1cd(_mm_andnot_pd(b.v,a.v)); }
+
+// FIXME force unaligned load, this is a temporary fix
+template<> EIGEN_STRONG_INLINE Packet1cd pload <Packet1cd>(const std::complex<double>* from)
+{ EIGEN_DEBUG_ALIGNED_LOAD return Packet1cd(pload<Packet2d>((const double*)from)); }
+template<> EIGEN_STRONG_INLINE Packet1cd ploadu<Packet1cd>(const std::complex<double>* from)
+{ EIGEN_DEBUG_UNALIGNED_LOAD return Packet1cd(ploadu<Packet2d>((const double*)from)); }
+template<> EIGEN_STRONG_INLINE Packet1cd pset1<Packet1cd>(const std::complex<double>& from)
+{ /* here we really have to use unaligned loads :( */ return ploadu<Packet1cd>(&from); }
+
+template<> EIGEN_STRONG_INLINE Packet1cd ploaddup<Packet1cd>(const std::complex<double>* from) { return pset1<Packet1cd>(*from); }
+
+// FIXME force unaligned store, this is a temporary fix
+template<> EIGEN_STRONG_INLINE void pstore <std::complex<double> >(std::complex<double> * to, const Packet1cd& from) { EIGEN_DEBUG_ALIGNED_STORE pstore((double*)to, Packet2d(from.v)); }
+template<> EIGEN_STRONG_INLINE void pstoreu<std::complex<double> >(std::complex<double> * to, const Packet1cd& from) { EIGEN_DEBUG_UNALIGNED_STORE pstoreu((double*)to, Packet2d(from.v)); }
+
+template<> EIGEN_STRONG_INLINE void prefetch<std::complex<double> >(const std::complex<double> * addr) { _mm_prefetch((SsePrefetchPtrType)(addr), _MM_HINT_T0); }
+
+template<> EIGEN_STRONG_INLINE std::complex<double> pfirst<Packet1cd>(const Packet1cd& a)
+{
+ EIGEN_ALIGN16 double res[2];
+ _mm_store_pd(res, a.v);
+ return std::complex<double>(res[0],res[1]);
+}
+
+template<> EIGEN_STRONG_INLINE Packet1cd preverse(const Packet1cd& a) { return a; }
+
+template<> EIGEN_STRONG_INLINE std::complex<double> predux<Packet1cd>(const Packet1cd& a)
+{
+ return pfirst(a);
+}
+
+template<> EIGEN_STRONG_INLINE std::complex<double> predux_mul<Packet1cd>(const Packet1cd& a)
+{
+ return pfirst(a);
+}
+
+EIGEN_MAKE_CONJ_HELPER_CPLX_REAL(Packet1cd,Packet2d)
+
+template<> EIGEN_STRONG_INLINE Packet1cd pdiv<Packet1cd>(const Packet1cd& a, const Packet1cd& b)
+{
+ return pdiv_complex(a, b);
+}
+
+EIGEN_STRONG_INLINE Packet1cd pcplxflip/* <Packet1cd> */(const Packet1cd& x)
+{
+ return Packet1cd(preverse(Packet2d(x.v)));
+}
+
+EIGEN_DEVICE_FUNC inline void
+ptranspose(PacketBlock<Packet2cf,2>& kernel) {
+ __m128d w1 = _mm_castps_pd(kernel.packet[0].v);
+ __m128d w2 = _mm_castps_pd(kernel.packet[1].v);
+
+ __m128 tmp = _mm_castpd_ps(_mm_unpackhi_pd(w1, w2));
+ kernel.packet[0].v = _mm_castpd_ps(_mm_unpacklo_pd(w1, w2));
+ kernel.packet[1].v = tmp;
+}
+
+template<> EIGEN_STRONG_INLINE Packet2cf pcmp_eq(const Packet2cf& a, const Packet2cf& b)
+{
+ __m128 eq = _mm_cmpeq_ps(a.v, b.v);
+ return Packet2cf(pand<Packet4f>(eq, vec4f_swizzle1(eq, 1, 0, 3, 2)));
+}
+
+template<> EIGEN_STRONG_INLINE Packet1cd pcmp_eq(const Packet1cd& a, const Packet1cd& b)
+{
+ __m128d eq = _mm_cmpeq_pd(a.v, b.v);
+ return Packet1cd(pand<Packet2d>(eq, vec2d_swizzle1(eq, 1, 0)));
+}
+
+template<> EIGEN_STRONG_INLINE Packet2cf pblend(const Selector<2>& ifPacket, const Packet2cf& thenPacket, const Packet2cf& elsePacket) {
+ __m128d result = pblend<Packet2d>(ifPacket, _mm_castps_pd(thenPacket.v), _mm_castps_pd(elsePacket.v));
+ return Packet2cf(_mm_castpd_ps(result));
+}
+
+template<> EIGEN_STRONG_INLINE Packet1cd psqrt<Packet1cd>(const Packet1cd& a) {
+ return psqrt_complex<Packet1cd>(a);
+}
+
+template<> EIGEN_STRONG_INLINE Packet2cf psqrt<Packet2cf>(const Packet2cf& a) {
+ return psqrt_complex<Packet2cf>(a);
+}
+
+} // end namespace internal
+} // end namespace Eigen
+
+#endif // EIGEN_COMPLEX_SSE_H
diff --git a/Eigen/src/Core/arch/SSE/MathFunctions.h b/Eigen/src/Core/arch/SSE/MathFunctions.h
new file mode 100644
index 0000000..f98fb7a
--- /dev/null
+++ b/Eigen/src/Core/arch/SSE/MathFunctions.h
@@ -0,0 +1,167 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2007 Julien Pommier
+// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+/* The sin and cos and functions of this file come from
+ * Julien Pommier's sse math library: http://gruntthepeon.free.fr/ssemath/
+ */
+
+#ifndef EIGEN_MATH_FUNCTIONS_SSE_H
+#define EIGEN_MATH_FUNCTIONS_SSE_H
+
+#include "../../InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+
+template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+Packet4f plog<Packet4f>(const Packet4f& _x) {
+ return plog_float(_x);
+}
+
+template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+Packet2d plog<Packet2d>(const Packet2d& _x) {
+ return plog_double(_x);
+}
+
+template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+Packet4f plog2<Packet4f>(const Packet4f& _x) {
+ return plog2_float(_x);
+}
+
+template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+Packet2d plog2<Packet2d>(const Packet2d& _x) {
+ return plog2_double(_x);
+}
+
+template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+Packet4f plog1p<Packet4f>(const Packet4f& _x) {
+ return generic_plog1p(_x);
+}
+
+template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+Packet4f pexpm1<Packet4f>(const Packet4f& _x) {
+ return generic_expm1(_x);
+}
+
+template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+Packet4f pexp<Packet4f>(const Packet4f& _x)
+{
+ return pexp_float(_x);
+}
+
+template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+Packet2d pexp<Packet2d>(const Packet2d& x)
+{
+ return pexp_double(x);
+}
+
+template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+Packet4f psin<Packet4f>(const Packet4f& _x)
+{
+ return psin_float(_x);
+}
+
+template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+Packet4f pcos<Packet4f>(const Packet4f& _x)
+{
+ return pcos_float(_x);
+}
+
+template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+Packet4f pacos<Packet4f>(const Packet4f& _x)
+{
+ return pacos_float(_x);
+}
+
+template <> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+Packet2d patan<Packet2d>(const Packet2d& _x) {
+ return patan_double(_x);
+}
+
+template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+Packet4f pasin<Packet4f>(const Packet4f& _x)
+{
+ return pasin_float(_x);
+}
+
+template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+Packet4f patan<Packet4f>(const Packet4f& _x)
+{
+ return patan_float(_x);
+}
+
+// Notice that for newer processors, it is counterproductive to use Newton
+// iteration for square root. In particular, Skylake and Zen2 processors
+// have approximately doubled throughput of the _mm_sqrt_ps instruction
+// compared to their predecessors.
+template<>EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+Packet4f psqrt<Packet4f>(const Packet4f& x) { return _mm_sqrt_ps(x); }
+template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+Packet2d psqrt<Packet2d>(const Packet2d& x) { return _mm_sqrt_pd(x); }
+template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+Packet16b psqrt<Packet16b>(const Packet16b& x) { return x; }
+
+#if EIGEN_FAST_MATH
+// Even on Skylake, using Newton iteration is a win for reciprocal square root.
+template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED
+Packet4f prsqrt<Packet4f>(const Packet4f& x) {
+ return generic_rsqrt_newton_step<Packet4f, /*Steps=*/1>::run(x, _mm_rsqrt_ps(x));
+}
+
+#ifdef EIGEN_VECTORIZE_FMA
+// Trying to speed up reciprocal using Newton-Raphson is counterproductive
+// unless FMA is available. Without FMA pdiv(pset1<Packet>(Scalar(1),a)) is
+// 30% faster.
+template<> EIGEN_STRONG_INLINE Packet4f preciprocal<Packet4f>(const Packet4f& x) {
+ return generic_reciprocal_newton_step<Packet4f, /*Steps=*/1>::run(x, _mm_rcp_ps(x));
+}
+#endif
+
+#endif
+
+
+
+// Hyperbolic Tangent function.
+template <>
+EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet4f
+ptanh<Packet4f>(const Packet4f& x) {
+ return internal::generic_fast_tanh_float(x);
+}
+
+} // end namespace internal
+
+namespace numext {
+
+template<>
+EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
+float sqrt(const float &x)
+{
+ return internal::pfirst(internal::Packet4f(_mm_sqrt_ss(_mm_set_ss(x))));
+}
+
+template<>
+EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
+double sqrt(const double &x)
+{
+#if EIGEN_COMP_GNUC_STRICT
+ // This works around a GCC bug generating poor code for _mm_sqrt_pd
+ // See https://gitlab.com/libeigen/eigen/commit/8dca9f97e38970
+ return internal::pfirst(internal::Packet2d(__builtin_ia32_sqrtsd(_mm_set_sd(x))));
+#else
+ return internal::pfirst(internal::Packet2d(_mm_sqrt_pd(_mm_set_sd(x))));
+#endif
+}
+
+} // end namespace numex
+
+} // end namespace Eigen
+
+#endif // EIGEN_MATH_FUNCTIONS_SSE_H
diff --git a/Eigen/src/Core/arch/SSE/PacketMath.h b/Eigen/src/Core/arch/SSE/PacketMath.h
new file mode 100644
index 0000000..847ff07
--- /dev/null
+++ b/Eigen/src/Core/arch/SSE/PacketMath.h
@@ -0,0 +1,1668 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_PACKET_MATH_SSE_H
+#define EIGEN_PACKET_MATH_SSE_H
+
+#include "../../InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+
+#ifndef EIGEN_CACHEFRIENDLY_PRODUCT_THRESHOLD
+#define EIGEN_CACHEFRIENDLY_PRODUCT_THRESHOLD 8
+#endif
+
+#if !defined(EIGEN_VECTORIZE_AVX) && !defined(EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS)
+// 32 bits => 8 registers
+// 64 bits => 16 registers
+#define EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS (2*sizeof(void*))
+#endif
+
+#ifdef EIGEN_VECTORIZE_FMA
+#ifndef EIGEN_HAS_SINGLE_INSTRUCTION_MADD
+#define EIGEN_HAS_SINGLE_INSTRUCTION_MADD
+#endif
+#endif
+
+#if ((defined EIGEN_VECTORIZE_AVX) && (EIGEN_COMP_GNUC_STRICT || EIGEN_COMP_MINGW || EIGEN_COMP_LCC) && (__GXX_ABI_VERSION < 1004)) || EIGEN_OS_QNX
+// With GCC's default ABI version, a __m128 or __m256 are the same types and therefore we cannot
+// have overloads for both types without linking error.
+// One solution is to increase ABI version using -fabi-version=4 (or greater).
+// Otherwise, we workaround this inconvenience by wrapping 128bit types into the following helper
+// structure:
+typedef eigen_packet_wrapper<__m128> Packet4f;
+typedef eigen_packet_wrapper<__m128d> Packet2d;
+#else
+typedef __m128 Packet4f;
+typedef __m128d Packet2d;
+#endif
+
+typedef eigen_packet_wrapper<__m128i, 0> Packet4i;
+typedef eigen_packet_wrapper<__m128i, 1> Packet16b;
+
+template<> struct is_arithmetic<__m128> { enum { value = true }; };
+template<> struct is_arithmetic<__m128i> { enum { value = true }; };
+template<> struct is_arithmetic<__m128d> { enum { value = true }; };
+template<> struct is_arithmetic<Packet4i> { enum { value = true }; };
+template<> struct is_arithmetic<Packet16b> { enum { value = true }; };
+
+template<int p, int q, int r, int s>
+struct shuffle_mask{
+ enum { mask = (s)<<6|(r)<<4|(q)<<2|(p) };
+};
+
+// TODO: change the implementation of all swizzle* ops from macro to template,
+#define vec4f_swizzle1(v,p,q,r,s) \
+ Packet4f(_mm_castsi128_ps(_mm_shuffle_epi32( _mm_castps_si128(v), (shuffle_mask<p,q,r,s>::mask))))
+
+#define vec4i_swizzle1(v,p,q,r,s) \
+ Packet4i(_mm_shuffle_epi32( v, (shuffle_mask<p,q,r,s>::mask)))
+
+#define vec2d_swizzle1(v,p,q) \
+ Packet2d(_mm_castsi128_pd(_mm_shuffle_epi32( _mm_castpd_si128(v), (shuffle_mask<2*p,2*p+1,2*q,2*q+1>::mask))))
+
+#define vec4f_swizzle2(a,b,p,q,r,s) \
+ Packet4f(_mm_shuffle_ps( (a), (b), (shuffle_mask<p,q,r,s>::mask)))
+
+#define vec4i_swizzle2(a,b,p,q,r,s) \
+ Packet4i(_mm_castps_si128( (_mm_shuffle_ps( _mm_castsi128_ps(a), _mm_castsi128_ps(b), (shuffle_mask<p,q,r,s>::mask)))))
+
+EIGEN_STRONG_INLINE Packet4f vec4f_movelh(const Packet4f& a, const Packet4f& b)
+{
+ return Packet4f(_mm_movelh_ps(a,b));
+}
+EIGEN_STRONG_INLINE Packet4f vec4f_movehl(const Packet4f& a, const Packet4f& b)
+{
+ return Packet4f(_mm_movehl_ps(a,b));
+}
+EIGEN_STRONG_INLINE Packet4f vec4f_unpacklo(const Packet4f& a, const Packet4f& b)
+{
+ return Packet4f(_mm_unpacklo_ps(a,b));
+}
+EIGEN_STRONG_INLINE Packet4f vec4f_unpackhi(const Packet4f& a, const Packet4f& b)
+{
+ return Packet4f(_mm_unpackhi_ps(a,b));
+}
+#define vec4f_duplane(a,p) \
+ vec4f_swizzle2(a,a,p,p,p,p)
+
+#define vec2d_swizzle2(a,b,mask) \
+ Packet2d(_mm_shuffle_pd(a,b,mask))
+
+EIGEN_STRONG_INLINE Packet2d vec2d_unpacklo(const Packet2d& a, const Packet2d& b)
+{
+ return Packet2d(_mm_unpacklo_pd(a,b));
+}
+EIGEN_STRONG_INLINE Packet2d vec2d_unpackhi(const Packet2d& a, const Packet2d& b)
+{
+ return Packet2d(_mm_unpackhi_pd(a,b));
+}
+#define vec2d_duplane(a,p) \
+ vec2d_swizzle2(a,a,(p<<1)|p)
+
+#define EIGEN_DECLARE_CONST_Packet4f(NAME,X) \
+ const Packet4f p4f_##NAME = pset1<Packet4f>(X)
+
+#define EIGEN_DECLARE_CONST_Packet2d(NAME,X) \
+ const Packet2d p2d_##NAME = pset1<Packet2d>(X)
+
+#define EIGEN_DECLARE_CONST_Packet4f_FROM_INT(NAME,X) \
+ const Packet4f p4f_##NAME = pset1frombits<Packet4f>(X)
+
+#define EIGEN_DECLARE_CONST_Packet4i(NAME,X) \
+ const Packet4i p4i_##NAME = pset1<Packet4i>(X)
+
+
+// Use the packet_traits defined in AVX/PacketMath.h instead if we're going
+// to leverage AVX instructions.
+#ifndef EIGEN_VECTORIZE_AVX
+template <>
+struct packet_traits<float> : default_packet_traits {
+ typedef Packet4f type;
+ typedef Packet4f half;
+ enum {
+ Vectorizable = 1,
+ AlignedOnScalar = 1,
+ size = 4,
+ HasHalfPacket = 0,
+
+ HasCmp = 1,
+ HasDiv = 1,
+ HasReciprocal = EIGEN_FAST_MATH,
+ HasSin = EIGEN_FAST_MATH,
+ HasCos = EIGEN_FAST_MATH,
+ HasACos = 1,
+ HasASin = 1,
+ HasATan = 1,
+ HasLog = 1,
+ HasLog1p = 1,
+ HasExpm1 = 1,
+ HasNdtri = 1,
+ HasExp = 1,
+ HasBessel = 1,
+ HasSqrt = 1,
+ HasRsqrt = 1,
+ HasTanh = EIGEN_FAST_MATH,
+ HasErf = EIGEN_FAST_MATH,
+ HasBlend = 1,
+ HasCeil = 1,
+ HasFloor = 1,
+#ifdef EIGEN_VECTORIZE_SSE4_1
+ HasRound = 1,
+#endif
+ HasRint = 1,
+ HasSign = 0 // The manually vectorized version is slightly slower for SSE.
+ };
+};
+template <>
+struct packet_traits<double> : default_packet_traits {
+ typedef Packet2d type;
+ typedef Packet2d half;
+ enum {
+ Vectorizable = 1,
+ AlignedOnScalar = 1,
+ size=2,
+ HasHalfPacket = 0,
+
+ HasCmp = 1,
+ HasDiv = 1,
+ HasLog = 1,
+ HasExp = 1,
+ HasSqrt = 1,
+ HasRsqrt = 1,
+ HasATan = 1,
+ HasBlend = 1,
+ HasFloor = 1,
+ HasCeil = 1,
+#ifdef EIGEN_VECTORIZE_SSE4_1
+ HasRound = 1,
+#endif
+ HasRint = 1
+ };
+};
+template<> struct packet_traits<int> : default_packet_traits
+{
+ typedef Packet4i type;
+ typedef Packet4i half;
+ enum {
+ Vectorizable = 1,
+ AlignedOnScalar = 1,
+ HasCmp = 1,
+ HasDiv=1,
+ size=4,
+
+ HasShift = 1,
+ HasBlend = 1
+ };
+};
+#endif
+template<> struct packet_traits<bool> : default_packet_traits
+{
+ typedef Packet16b type;
+ typedef Packet16b half;
+ enum {
+ Vectorizable = 1,
+ AlignedOnScalar = 1,
+ HasHalfPacket = 0,
+ size=16,
+
+ HasAdd = 1,
+ HasSub = 1,
+ HasShift = 0,
+ HasMul = 1,
+ HasNegate = 1,
+ HasAbs = 0,
+ HasAbs2 = 0,
+ HasMin = 0,
+ HasMax = 0,
+ HasConj = 0,
+ HasSqrt = 1,
+ HasSign = 0 // Don't try to vectorize psign<bool> = identity.
+ };
+};
+
+template<> struct unpacket_traits<Packet4f> {
+ typedef float type;
+ typedef Packet4f half;
+ typedef Packet4i integer_packet;
+ enum {size=4, alignment=Aligned16, vectorizable=true, masked_load_available=false, masked_store_available=false};
+};
+template<> struct unpacket_traits<Packet2d> {
+ typedef double type;
+ typedef Packet2d half;
+ enum {size=2, alignment=Aligned16, vectorizable=true, masked_load_available=false, masked_store_available=false};
+};
+template<> struct unpacket_traits<Packet4i> {
+ typedef int type;
+ typedef Packet4i half;
+ enum {size=4, alignment=Aligned16, vectorizable=true, masked_load_available=false, masked_store_available=false};
+};
+template<> struct unpacket_traits<Packet16b> {
+ typedef bool type;
+ typedef Packet16b half;
+ enum {size=16, alignment=Aligned16, vectorizable=true, masked_load_available=false, masked_store_available=false};
+};
+
+#ifndef EIGEN_VECTORIZE_AVX
+template<> struct scalar_div_cost<float,true> { enum { value = 7 }; };
+template<> struct scalar_div_cost<double,true> { enum { value = 8 }; };
+#endif
+
+template<> EIGEN_STRONG_INLINE Packet4f pset1<Packet4f>(const float& from) { return _mm_set_ps1(from); }
+template<> EIGEN_STRONG_INLINE Packet2d pset1<Packet2d>(const double& from) { return _mm_set1_pd(from); }
+template<> EIGEN_STRONG_INLINE Packet4i pset1<Packet4i>(const int& from) { return _mm_set1_epi32(from); }
+template<> EIGEN_STRONG_INLINE Packet16b pset1<Packet16b>(const bool& from) { return _mm_set1_epi8(static_cast<char>(from)); }
+
+template<> EIGEN_STRONG_INLINE Packet4f pset1frombits<Packet4f>(unsigned int from) { return _mm_castsi128_ps(pset1<Packet4i>(from)); }
+template<> EIGEN_STRONG_INLINE Packet2d pset1frombits<Packet2d>(uint64_t from) { return _mm_castsi128_pd(_mm_set1_epi64x(from)); }
+
+template<> EIGEN_STRONG_INLINE Packet4f peven_mask(const Packet4f& /*a*/) { return _mm_castsi128_ps(_mm_set_epi32(0, -1, 0, -1)); }
+template<> EIGEN_STRONG_INLINE Packet4i peven_mask(const Packet4i& /*a*/) { return _mm_set_epi32(0, -1, 0, -1); }
+template<> EIGEN_STRONG_INLINE Packet2d peven_mask(const Packet2d& /*a*/) { return _mm_castsi128_pd(_mm_set_epi32(0, 0, -1, -1)); }
+
+template<> EIGEN_STRONG_INLINE Packet4f pzero(const Packet4f& /*a*/) { return _mm_setzero_ps(); }
+template<> EIGEN_STRONG_INLINE Packet2d pzero(const Packet2d& /*a*/) { return _mm_setzero_pd(); }
+template<> EIGEN_STRONG_INLINE Packet4i pzero(const Packet4i& /*a*/) { return _mm_setzero_si128(); }
+
+// GCC generates a shufps instruction for _mm_set1_ps/_mm_load1_ps instead of the more efficient pshufd instruction.
+// However, using inrinsics for pset1 makes gcc to generate crappy code in some cases (see bug 203)
+// Using inline assembly is also not an option because then gcc fails to reorder properly the instructions.
+// Therefore, we introduced the pload1 functions to be used in product kernels for which bug 203 does not apply.
+// Also note that with AVX, we want it to generate a vbroadcastss.
+#if EIGEN_COMP_GNUC_STRICT && (!defined __AVX__)
+template<> EIGEN_STRONG_INLINE Packet4f pload1<Packet4f>(const float *from) {
+ return vec4f_swizzle1(_mm_load_ss(from),0,0,0,0);
+}
+#endif
+
+template<> EIGEN_STRONG_INLINE Packet4f plset<Packet4f>(const float& a) { return _mm_add_ps(pset1<Packet4f>(a), _mm_set_ps(3,2,1,0)); }
+template<> EIGEN_STRONG_INLINE Packet2d plset<Packet2d>(const double& a) { return _mm_add_pd(pset1<Packet2d>(a),_mm_set_pd(1,0)); }
+template<> EIGEN_STRONG_INLINE Packet4i plset<Packet4i>(const int& a) { return _mm_add_epi32(pset1<Packet4i>(a),_mm_set_epi32(3,2,1,0)); }
+
+template<> EIGEN_STRONG_INLINE Packet4f padd<Packet4f>(const Packet4f& a, const Packet4f& b) { return _mm_add_ps(a,b); }
+template<> EIGEN_STRONG_INLINE Packet2d padd<Packet2d>(const Packet2d& a, const Packet2d& b) { return _mm_add_pd(a,b); }
+template<> EIGEN_STRONG_INLINE Packet4i padd<Packet4i>(const Packet4i& a, const Packet4i& b) { return _mm_add_epi32(a,b); }
+
+template<> EIGEN_STRONG_INLINE Packet16b padd<Packet16b>(const Packet16b& a, const Packet16b& b) { return _mm_or_si128(a,b); }
+
+template<typename Packet> EIGEN_STRONG_INLINE Packet padds(const Packet& a, const Packet& b);
+template<> EIGEN_STRONG_INLINE Packet4f padds<Packet4f>(const Packet4f& a, const Packet4f& b) { return _mm_add_ss(a,b); }
+template<> EIGEN_STRONG_INLINE Packet2d padds<Packet2d>(const Packet2d& a, const Packet2d& b) { return _mm_add_sd(a,b); }
+
+template<> EIGEN_STRONG_INLINE Packet4f psub<Packet4f>(const Packet4f& a, const Packet4f& b) { return _mm_sub_ps(a,b); }
+template<> EIGEN_STRONG_INLINE Packet2d psub<Packet2d>(const Packet2d& a, const Packet2d& b) { return _mm_sub_pd(a,b); }
+template<> EIGEN_STRONG_INLINE Packet4i psub<Packet4i>(const Packet4i& a, const Packet4i& b) { return _mm_sub_epi32(a,b); }
+template<> EIGEN_STRONG_INLINE Packet16b psub<Packet16b>(const Packet16b& a, const Packet16b& b) { return _mm_xor_si128(a,b); }
+
+template<> EIGEN_STRONG_INLINE Packet4f pxor<Packet4f>(const Packet4f& a, const Packet4f& b);
+template<> EIGEN_STRONG_INLINE Packet4f paddsub<Packet4f>(const Packet4f& a, const Packet4f& b)
+{
+#ifdef EIGEN_VECTORIZE_SSE3
+ return _mm_addsub_ps(a,b);
+#else
+ const Packet4f mask = _mm_castsi128_ps(_mm_setr_epi32(0x80000000,0x0,0x80000000,0x0));
+ return padd(a, pxor(mask, b));
+#endif
+}
+
+template<> EIGEN_STRONG_INLINE Packet2d pxor<Packet2d>(const Packet2d& , const Packet2d& );
+template<> EIGEN_STRONG_INLINE Packet2d paddsub<Packet2d>(const Packet2d& a, const Packet2d& b)
+{
+#ifdef EIGEN_VECTORIZE_SSE3
+ return _mm_addsub_pd(a,b);
+#else
+ const Packet2d mask = _mm_castsi128_pd(_mm_setr_epi32(0x0,0x80000000,0x0,0x0));
+ return padd(a, pxor(mask, b));
+#endif
+}
+
+template<> EIGEN_STRONG_INLINE Packet4f pnegate(const Packet4f& a)
+{
+ const Packet4f mask = _mm_castsi128_ps(_mm_setr_epi32(0x80000000,0x80000000,0x80000000,0x80000000));
+ return _mm_xor_ps(a,mask);
+}
+template<> EIGEN_STRONG_INLINE Packet2d pnegate(const Packet2d& a)
+{
+ const Packet2d mask = _mm_castsi128_pd(_mm_setr_epi32(0x0,0x80000000,0x0,0x80000000));
+ return _mm_xor_pd(a,mask);
+}
+template<> EIGEN_STRONG_INLINE Packet4i pnegate(const Packet4i& a)
+{
+ return psub(Packet4i(_mm_setr_epi32(0,0,0,0)), a);
+}
+
+template<> EIGEN_STRONG_INLINE Packet16b pnegate(const Packet16b& a)
+{
+ return psub(pset1<Packet16b>(false), a);
+}
+
+template<> EIGEN_STRONG_INLINE Packet4f pconj(const Packet4f& a) { return a; }
+template<> EIGEN_STRONG_INLINE Packet2d pconj(const Packet2d& a) { return a; }
+template<> EIGEN_STRONG_INLINE Packet4i pconj(const Packet4i& a) { return a; }
+
+template<> EIGEN_STRONG_INLINE Packet4f pmul<Packet4f>(const Packet4f& a, const Packet4f& b) { return _mm_mul_ps(a,b); }
+template<> EIGEN_STRONG_INLINE Packet2d pmul<Packet2d>(const Packet2d& a, const Packet2d& b) { return _mm_mul_pd(a,b); }
+template<> EIGEN_STRONG_INLINE Packet4i pmul<Packet4i>(const Packet4i& a, const Packet4i& b)
+{
+#ifdef EIGEN_VECTORIZE_SSE4_1
+ return _mm_mullo_epi32(a,b);
+#else
+ // this version is slightly faster than 4 scalar products
+ return vec4i_swizzle1(
+ vec4i_swizzle2(
+ _mm_mul_epu32(a,b),
+ _mm_mul_epu32(vec4i_swizzle1(a,1,0,3,2),
+ vec4i_swizzle1(b,1,0,3,2)),
+ 0,2,0,2),
+ 0,2,1,3);
+#endif
+}
+
+template<> EIGEN_STRONG_INLINE Packet16b pmul<Packet16b>(const Packet16b& a, const Packet16b& b) { return _mm_and_si128(a,b); }
+
+template<> EIGEN_STRONG_INLINE Packet4f pdiv<Packet4f>(const Packet4f& a, const Packet4f& b) { return _mm_div_ps(a,b); }
+template<> EIGEN_STRONG_INLINE Packet2d pdiv<Packet2d>(const Packet2d& a, const Packet2d& b) { return _mm_div_pd(a,b); }
+
+template <>
+EIGEN_STRONG_INLINE Packet4i pdiv<Packet4i>(const Packet4i& a,
+ const Packet4i& b) {
+#ifdef EIGEN_VECTORIZE_AVX
+ return _mm256_cvttpd_epi32(
+ _mm256_div_pd(_mm256_cvtepi32_pd(a), _mm256_cvtepi32_pd(b)));
+#else
+ __m128i q_lo = _mm_cvttpd_epi32(_mm_div_pd(_mm_cvtepi32_pd(a), _mm_cvtepi32_pd(b)));
+ __m128i q_hi =
+ _mm_cvttpd_epi32(_mm_div_pd(_mm_cvtepi32_pd(vec4i_swizzle1(a, 2, 3, 0, 1)),
+ _mm_cvtepi32_pd(vec4i_swizzle1(b, 2, 3, 0, 1))));
+ return vec4i_swizzle1(_mm_unpacklo_epi32(q_lo, q_hi), 0, 2, 1, 3);
+#endif
+}
+
+
+// for some weird raisons, it has to be overloaded for packet of integers
+template<> EIGEN_STRONG_INLINE Packet4i pmadd(const Packet4i& a, const Packet4i& b, const Packet4i& c) { return padd(pmul(a,b), c); }
+#ifdef EIGEN_VECTORIZE_FMA
+template<> EIGEN_STRONG_INLINE Packet4f pmadd(const Packet4f& a, const Packet4f& b, const Packet4f& c) { return _mm_fmadd_ps(a,b,c); }
+template<> EIGEN_STRONG_INLINE Packet2d pmadd(const Packet2d& a, const Packet2d& b, const Packet2d& c) { return _mm_fmadd_pd(a,b,c); }
+template<> EIGEN_STRONG_INLINE Packet4f pmsub(const Packet4f& a, const Packet4f& b, const Packet4f& c) { return _mm_fmsub_ps(a,b,c); }
+template<> EIGEN_STRONG_INLINE Packet2d pmsub(const Packet2d& a, const Packet2d& b, const Packet2d& c) { return _mm_fmsub_pd(a,b,c); }
+template<> EIGEN_STRONG_INLINE Packet4f pnmadd(const Packet4f& a, const Packet4f& b, const Packet4f& c) { return _mm_fnmadd_ps(a,b,c); }
+template<> EIGEN_STRONG_INLINE Packet2d pnmadd(const Packet2d& a, const Packet2d& b, const Packet2d& c) { return _mm_fnmadd_pd(a,b,c); }
+template<> EIGEN_STRONG_INLINE Packet4f pnmsub(const Packet4f& a, const Packet4f& b, const Packet4f& c) { return _mm_fnmsub_ps(a,b,c); }
+template<> EIGEN_STRONG_INLINE Packet2d pnmsub(const Packet2d& a, const Packet2d& b, const Packet2d& c) { return _mm_fnmsub_pd(a,b,c); }
+
+template<typename Packet> EIGEN_STRONG_INLINE Packet pmadds(const Packet& a, const Packet& b, const Packet& c);
+template<> EIGEN_STRONG_INLINE Packet4f pmadds<Packet4f>(const Packet4f& a, const Packet4f& b, const Packet4f& c) { return _mm_fmadd_ss(a,b,c); }
+template<> EIGEN_STRONG_INLINE Packet2d pmadds<Packet2d>(const Packet2d& a, const Packet2d& b, const Packet2d& c) { return _mm_fmadd_sd(a,b,c); }
+#endif
+
+#ifdef EIGEN_VECTORIZE_SSE4_1
+template<> EIGEN_DEVICE_FUNC inline Packet4f pselect(const Packet4f& mask, const Packet4f& a, const Packet4f& b) {
+ return _mm_blendv_ps(b,a,mask);
+}
+
+template<> EIGEN_DEVICE_FUNC inline Packet4i pselect(const Packet4i& mask, const Packet4i& a, const Packet4i& b) {
+ return _mm_castps_si128(_mm_blendv_ps(_mm_castsi128_ps(b),_mm_castsi128_ps(a),_mm_castsi128_ps(mask)));
+}
+
+template<> EIGEN_DEVICE_FUNC inline Packet2d pselect(const Packet2d& mask, const Packet2d& a, const Packet2d& b) { return _mm_blendv_pd(b,a,mask); }
+
+template<> EIGEN_DEVICE_FUNC inline Packet16b pselect(const Packet16b& mask, const Packet16b& a, const Packet16b& b) {
+ return _mm_blendv_epi8(b,a,mask);
+}
+#else
+template<> EIGEN_DEVICE_FUNC inline Packet16b pselect(const Packet16b& mask, const Packet16b& a, const Packet16b& b) {
+ Packet16b a_part = _mm_and_si128(mask, a);
+ Packet16b b_part = _mm_andnot_si128(mask, b);
+ return _mm_or_si128(a_part, b_part);
+}
+#endif
+
+template<> EIGEN_STRONG_INLINE Packet4i ptrue<Packet4i>(const Packet4i& a) { return _mm_cmpeq_epi32(a, a); }
+template<> EIGEN_STRONG_INLINE Packet16b ptrue<Packet16b>(const Packet16b& a) { return _mm_cmpeq_epi8(a, a); }
+template<> EIGEN_STRONG_INLINE Packet4f
+ptrue<Packet4f>(const Packet4f& a) {
+ Packet4i b = _mm_castps_si128(a);
+ return _mm_castsi128_ps(_mm_cmpeq_epi32(b, b));
+}
+template<> EIGEN_STRONG_INLINE Packet2d
+ptrue<Packet2d>(const Packet2d& a) {
+ Packet4i b = _mm_castpd_si128(a);
+ return _mm_castsi128_pd(_mm_cmpeq_epi32(b, b));
+}
+
+
+template<> EIGEN_STRONG_INLINE Packet4f pand<Packet4f>(const Packet4f& a, const Packet4f& b) { return _mm_and_ps(a,b); }
+template<> EIGEN_STRONG_INLINE Packet2d pand<Packet2d>(const Packet2d& a, const Packet2d& b) { return _mm_and_pd(a,b); }
+template<> EIGEN_STRONG_INLINE Packet4i pand<Packet4i>(const Packet4i& a, const Packet4i& b) { return _mm_and_si128(a,b); }
+template<> EIGEN_STRONG_INLINE Packet16b pand<Packet16b>(const Packet16b& a, const Packet16b& b) { return _mm_and_si128(a,b); }
+
+template<> EIGEN_STRONG_INLINE Packet4f por<Packet4f>(const Packet4f& a, const Packet4f& b) { return _mm_or_ps(a,b); }
+template<> EIGEN_STRONG_INLINE Packet2d por<Packet2d>(const Packet2d& a, const Packet2d& b) { return _mm_or_pd(a,b); }
+template<> EIGEN_STRONG_INLINE Packet4i por<Packet4i>(const Packet4i& a, const Packet4i& b) { return _mm_or_si128(a,b); }
+template<> EIGEN_STRONG_INLINE Packet16b por<Packet16b>(const Packet16b& a, const Packet16b& b) { return _mm_or_si128(a,b); }
+
+template<> EIGEN_STRONG_INLINE Packet4f pxor<Packet4f>(const Packet4f& a, const Packet4f& b) { return _mm_xor_ps(a,b); }
+template<> EIGEN_STRONG_INLINE Packet2d pxor<Packet2d>(const Packet2d& a, const Packet2d& b) { return _mm_xor_pd(a,b); }
+template<> EIGEN_STRONG_INLINE Packet4i pxor<Packet4i>(const Packet4i& a, const Packet4i& b) { return _mm_xor_si128(a,b); }
+template<> EIGEN_STRONG_INLINE Packet16b pxor<Packet16b>(const Packet16b& a, const Packet16b& b) { return _mm_xor_si128(a,b); }
+
+template<> EIGEN_STRONG_INLINE Packet4f pandnot<Packet4f>(const Packet4f& a, const Packet4f& b) { return _mm_andnot_ps(b,a); }
+template<> EIGEN_STRONG_INLINE Packet2d pandnot<Packet2d>(const Packet2d& a, const Packet2d& b) { return _mm_andnot_pd(b,a); }
+template<> EIGEN_STRONG_INLINE Packet4i pandnot<Packet4i>(const Packet4i& a, const Packet4i& b) { return _mm_andnot_si128(b,a); }
+
+template<> EIGEN_STRONG_INLINE Packet4f pcmp_le(const Packet4f& a, const Packet4f& b) { return _mm_cmple_ps(a,b); }
+template<> EIGEN_STRONG_INLINE Packet4f pcmp_lt(const Packet4f& a, const Packet4f& b) { return _mm_cmplt_ps(a,b); }
+template<> EIGEN_STRONG_INLINE Packet4f pcmp_lt_or_nan(const Packet4f& a, const Packet4f& b) { return _mm_cmpnge_ps(a,b); }
+template<> EIGEN_STRONG_INLINE Packet4f pcmp_eq(const Packet4f& a, const Packet4f& b) { return _mm_cmpeq_ps(a,b); }
+
+template<> EIGEN_STRONG_INLINE Packet2d pcmp_le(const Packet2d& a, const Packet2d& b) { return _mm_cmple_pd(a,b); }
+template<> EIGEN_STRONG_INLINE Packet2d pcmp_lt(const Packet2d& a, const Packet2d& b) { return _mm_cmplt_pd(a,b); }
+template<> EIGEN_STRONG_INLINE Packet2d pcmp_lt_or_nan(const Packet2d& a, const Packet2d& b) { return _mm_cmpnge_pd(a,b); }
+template<> EIGEN_STRONG_INLINE Packet2d pcmp_eq(const Packet2d& a, const Packet2d& b) { return _mm_cmpeq_pd(a,b); }
+
+template<> EIGEN_STRONG_INLINE Packet4i pcmp_lt(const Packet4i& a, const Packet4i& b) { return _mm_cmplt_epi32(a,b); }
+template<> EIGEN_STRONG_INLINE Packet4i pcmp_eq(const Packet4i& a, const Packet4i& b) { return _mm_cmpeq_epi32(a,b); }
+template<> EIGEN_STRONG_INLINE Packet16b pcmp_eq(const Packet16b& a, const Packet16b& b) { return _mm_cmpeq_epi8(a,b); }
+template<> EIGEN_STRONG_INLINE Packet4i pcmp_le(const Packet4i& a, const Packet4i& b) { return por(pcmp_lt(a,b), pcmp_eq(a,b)); }
+
+template<> EIGEN_STRONG_INLINE Packet4f pmin<Packet4f>(const Packet4f& a, const Packet4f& b) {
+#if EIGEN_COMP_GNUC_STRICT && EIGEN_COMP_GNUC < 63
+ // There appears to be a bug in GCC, by which the optimizer may
+ // flip the argument order in calls to _mm_min_ps, so we have to
+ // resort to inline ASM here. This is supposed to be fixed in gcc6.3,
+ // see also: https://gcc.gnu.org/bugzilla/show_bug.cgi?id=72867
+ #ifdef EIGEN_VECTORIZE_AVX
+ Packet4f res;
+ asm("vminps %[a], %[b], %[res]" : [res] "=x" (res) : [a] "x" (a), [b] "x" (b));
+ #else
+ Packet4f res = b;
+ asm("minps %[a], %[res]" : [res] "+x" (res) : [a] "x" (a));
+ #endif
+ return res;
+#else
+ // Arguments are reversed to match NaN propagation behavior of std::min.
+ return _mm_min_ps(b, a);
+#endif
+}
+template<> EIGEN_STRONG_INLINE Packet2d pmin<Packet2d>(const Packet2d& a, const Packet2d& b) {
+#if EIGEN_COMP_GNUC_STRICT && EIGEN_COMP_GNUC < 63
+ // There appears to be a bug in GCC, by which the optimizer may
+ // flip the argument order in calls to _mm_min_pd, so we have to
+ // resort to inline ASM here. This is supposed to be fixed in gcc6.3,
+ // see also: https://gcc.gnu.org/bugzilla/show_bug.cgi?id=72867
+ #ifdef EIGEN_VECTORIZE_AVX
+ Packet2d res;
+ asm("vminpd %[a], %[b], %[res]" : [res] "=x" (res) : [a] "x" (a), [b] "x" (b));
+ #else
+ Packet2d res = b;
+ asm("minpd %[a], %[res]" : [res] "+x" (res) : [a] "x" (a));
+ #endif
+ return res;
+#else
+ // Arguments are reversed to match NaN propagation behavior of std::min.
+ return _mm_min_pd(b, a);
+#endif
+}
+template<> EIGEN_STRONG_INLINE Packet4i pmin<Packet4i>(const Packet4i& a, const Packet4i& b)
+{
+#ifdef EIGEN_VECTORIZE_SSE4_1
+ return _mm_min_epi32(a,b);
+#else
+ // after some bench, this version *is* faster than a scalar implementation
+ Packet4i mask = _mm_cmplt_epi32(a,b);
+ return _mm_or_si128(_mm_and_si128(mask,a),_mm_andnot_si128(mask,b));
+#endif
+}
+
+
+template<> EIGEN_STRONG_INLINE Packet4f pmax<Packet4f>(const Packet4f& a, const Packet4f& b) {
+#if EIGEN_COMP_GNUC_STRICT && EIGEN_COMP_GNUC < 63
+ // There appears to be a bug in GCC, by which the optimizer may
+ // flip the argument order in calls to _mm_max_ps, so we have to
+ // resort to inline ASM here. This is supposed to be fixed in gcc6.3,
+ // see also: https://gcc.gnu.org/bugzilla/show_bug.cgi?id=72867
+ #ifdef EIGEN_VECTORIZE_AVX
+ Packet4f res;
+ asm("vmaxps %[a], %[b], %[res]" : [res] "=x" (res) : [a] "x" (a), [b] "x" (b));
+ #else
+ Packet4f res = b;
+ asm("maxps %[a], %[res]" : [res] "+x" (res) : [a] "x" (a));
+ #endif
+ return res;
+#else
+ // Arguments are reversed to match NaN propagation behavior of std::max.
+ return _mm_max_ps(b, a);
+#endif
+}
+template<> EIGEN_STRONG_INLINE Packet2d pmax<Packet2d>(const Packet2d& a, const Packet2d& b) {
+#if EIGEN_COMP_GNUC_STRICT && EIGEN_COMP_GNUC < 63
+ // There appears to be a bug in GCC, by which the optimizer may
+ // flip the argument order in calls to _mm_max_pd, so we have to
+ // resort to inline ASM here. This is supposed to be fixed in gcc6.3,
+ // see also: https://gcc.gnu.org/bugzilla/show_bug.cgi?id=72867
+ #ifdef EIGEN_VECTORIZE_AVX
+ Packet2d res;
+ asm("vmaxpd %[a], %[b], %[res]" : [res] "=x" (res) : [a] "x" (a), [b] "x" (b));
+ #else
+ Packet2d res = b;
+ asm("maxpd %[a], %[res]" : [res] "+x" (res) : [a] "x" (a));
+ #endif
+ return res;
+#else
+ // Arguments are reversed to match NaN propagation behavior of std::max.
+ return _mm_max_pd(b, a);
+#endif
+}
+template<> EIGEN_STRONG_INLINE Packet4i pmax<Packet4i>(const Packet4i& a, const Packet4i& b)
+{
+#ifdef EIGEN_VECTORIZE_SSE4_1
+ return _mm_max_epi32(a,b);
+#else
+ // after some bench, this version *is* faster than a scalar implementation
+ Packet4i mask = _mm_cmpgt_epi32(a,b);
+ return _mm_or_si128(_mm_and_si128(mask,a),_mm_andnot_si128(mask,b));
+#endif
+}
+
+template <typename Packet, typename Op>
+EIGEN_STRONG_INLINE Packet pminmax_propagate_numbers(const Packet& a, const Packet& b, Op op) {
+ // In this implementation, we take advantage of the fact that pmin/pmax for SSE
+ // always return a if either a or b is NaN.
+ Packet not_nan_mask_a = pcmp_eq(a, a);
+ Packet m = op(a, b);
+ return pselect<Packet>(not_nan_mask_a, m, b);
+}
+
+template <typename Packet, typename Op>
+EIGEN_STRONG_INLINE Packet pminmax_propagate_nan(const Packet& a, const Packet& b, Op op) {
+ // In this implementation, we take advantage of the fact that pmin/pmax for SSE
+ // always return a if either a or b is NaN.
+ Packet not_nan_mask_a = pcmp_eq(a, a);
+ Packet m = op(b, a);
+ return pselect<Packet>(not_nan_mask_a, m, a);
+}
+
+// Add specializations for min/max with prescribed NaN progation.
+template<>
+EIGEN_STRONG_INLINE Packet4f pmin<PropagateNumbers, Packet4f>(const Packet4f& a, const Packet4f& b) {
+ return pminmax_propagate_numbers(a, b, pmin<Packet4f>);
+}
+template<>
+EIGEN_STRONG_INLINE Packet2d pmin<PropagateNumbers, Packet2d>(const Packet2d& a, const Packet2d& b) {
+ return pminmax_propagate_numbers(a, b, pmin<Packet2d>);
+}
+template<>
+EIGEN_STRONG_INLINE Packet4f pmax<PropagateNumbers, Packet4f>(const Packet4f& a, const Packet4f& b) {
+ return pminmax_propagate_numbers(a, b, pmax<Packet4f>);
+}
+template<>
+EIGEN_STRONG_INLINE Packet2d pmax<PropagateNumbers, Packet2d>(const Packet2d& a, const Packet2d& b) {
+ return pminmax_propagate_numbers(a, b, pmax<Packet2d>);
+}
+template<>
+EIGEN_STRONG_INLINE Packet4f pmin<PropagateNaN, Packet4f>(const Packet4f& a, const Packet4f& b) {
+ return pminmax_propagate_nan(a, b, pmin<Packet4f>);
+}
+template<>
+EIGEN_STRONG_INLINE Packet2d pmin<PropagateNaN, Packet2d>(const Packet2d& a, const Packet2d& b) {
+ return pminmax_propagate_nan(a, b, pmin<Packet2d>);
+}
+template<>
+EIGEN_STRONG_INLINE Packet4f pmax<PropagateNaN, Packet4f>(const Packet4f& a, const Packet4f& b) {
+ return pminmax_propagate_nan(a, b, pmax<Packet4f>);
+}
+template<>
+EIGEN_STRONG_INLINE Packet2d pmax<PropagateNaN, Packet2d>(const Packet2d& a, const Packet2d& b) {
+ return pminmax_propagate_nan(a, b, pmax<Packet2d>);
+}
+
+template<int N> EIGEN_STRONG_INLINE Packet4i parithmetic_shift_right(const Packet4i& a) { return _mm_srai_epi32(a,N); }
+template<int N> EIGEN_STRONG_INLINE Packet4i plogical_shift_right (const Packet4i& a) { return _mm_srli_epi32(a,N); }
+template<int N> EIGEN_STRONG_INLINE Packet4i plogical_shift_left (const Packet4i& a) { return _mm_slli_epi32(a,N); }
+
+template<> EIGEN_STRONG_INLINE Packet4f pabs(const Packet4f& a)
+{
+ const Packet4f mask = _mm_castsi128_ps(_mm_setr_epi32(0x7FFFFFFF,0x7FFFFFFF,0x7FFFFFFF,0x7FFFFFFF));
+ return _mm_and_ps(a,mask);
+}
+template<> EIGEN_STRONG_INLINE Packet2d pabs(const Packet2d& a)
+{
+ const Packet2d mask = _mm_castsi128_pd(_mm_setr_epi32(0xFFFFFFFF,0x7FFFFFFF,0xFFFFFFFF,0x7FFFFFFF));
+ return _mm_and_pd(a,mask);
+}
+template<> EIGEN_STRONG_INLINE Packet4i pabs(const Packet4i& a)
+{
+ #ifdef EIGEN_VECTORIZE_SSSE3
+ return _mm_abs_epi32(a);
+ #else
+ Packet4i aux = _mm_srai_epi32(a,31);
+ return _mm_sub_epi32(_mm_xor_si128(a,aux),aux);
+ #endif
+}
+
+#ifdef EIGEN_VECTORIZE_SSE4_1
+template<> EIGEN_STRONG_INLINE Packet4f pround<Packet4f>(const Packet4f& a)
+{
+ // Unfortunately _mm_round_ps doesn't have a rounding mode to implement numext::round.
+ const Packet4f mask = pset1frombits<Packet4f>(0x80000000u);
+ const Packet4f prev0dot5 = pset1frombits<Packet4f>(0x3EFFFFFFu);
+ return _mm_round_ps(padd(por(pand(a, mask), prev0dot5), a), _MM_FROUND_TO_ZERO);
+}
+
+template<> EIGEN_STRONG_INLINE Packet2d pround<Packet2d>(const Packet2d& a)
+{
+ const Packet2d mask = _mm_castsi128_pd(_mm_set_epi64x(0x8000000000000000ull, 0x8000000000000000ull));
+ const Packet2d prev0dot5 = _mm_castsi128_pd(_mm_set_epi64x(0x3FDFFFFFFFFFFFFFull, 0x3FDFFFFFFFFFFFFFull));
+ return _mm_round_pd(padd(por(pand(a, mask), prev0dot5), a), _MM_FROUND_TO_ZERO);
+}
+
+template<> EIGEN_STRONG_INLINE Packet4f print<Packet4f>(const Packet4f& a) { return _mm_round_ps(a, _MM_FROUND_CUR_DIRECTION); }
+template<> EIGEN_STRONG_INLINE Packet2d print<Packet2d>(const Packet2d& a) { return _mm_round_pd(a, _MM_FROUND_CUR_DIRECTION); }
+
+template<> EIGEN_STRONG_INLINE Packet4f pceil<Packet4f>(const Packet4f& a) { return _mm_ceil_ps(a); }
+template<> EIGEN_STRONG_INLINE Packet2d pceil<Packet2d>(const Packet2d& a) { return _mm_ceil_pd(a); }
+
+template<> EIGEN_STRONG_INLINE Packet4f pfloor<Packet4f>(const Packet4f& a) { return _mm_floor_ps(a); }
+template<> EIGEN_STRONG_INLINE Packet2d pfloor<Packet2d>(const Packet2d& a) { return _mm_floor_pd(a); }
+#else
+template<> EIGEN_STRONG_INLINE Packet4f print(const Packet4f& a) {
+ // Adds and subtracts signum(a) * 2^23 to force rounding.
+ const Packet4f limit = pset1<Packet4f>(static_cast<float>(1<<23));
+ const Packet4f abs_a = pabs(a);
+ Packet4f r = padd(abs_a, limit);
+ // Don't compile-away addition and subtraction.
+ EIGEN_OPTIMIZATION_BARRIER(r);
+ r = psub(r, limit);
+ // If greater than limit, simply return a. Otherwise, account for sign.
+ r = pselect(pcmp_lt(abs_a, limit),
+ pselect(pcmp_lt(a, pzero(a)), pnegate(r), r), a);
+ return r;
+}
+
+template<> EIGEN_STRONG_INLINE Packet2d print(const Packet2d& a) {
+ // Adds and subtracts signum(a) * 2^52 to force rounding.
+ const Packet2d limit = pset1<Packet2d>(static_cast<double>(1ull<<52));
+ const Packet2d abs_a = pabs(a);
+ Packet2d r = padd(abs_a, limit);
+ // Don't compile-away addition and subtraction.
+ EIGEN_OPTIMIZATION_BARRIER(r);
+ r = psub(r, limit);
+ // If greater than limit, simply return a. Otherwise, account for sign.
+ r = pselect(pcmp_lt(abs_a, limit),
+ pselect(pcmp_lt(a, pzero(a)), pnegate(r), r), a);
+ return r;
+}
+
+template<> EIGEN_STRONG_INLINE Packet4f pfloor<Packet4f>(const Packet4f& a)
+{
+ const Packet4f cst_1 = pset1<Packet4f>(1.0f);
+ Packet4f tmp = print<Packet4f>(a);
+ // If greater, subtract one.
+ Packet4f mask = _mm_cmpgt_ps(tmp, a);
+ mask = pand(mask, cst_1);
+ return psub(tmp, mask);
+}
+
+template<> EIGEN_STRONG_INLINE Packet2d pfloor<Packet2d>(const Packet2d& a)
+{
+ const Packet2d cst_1 = pset1<Packet2d>(1.0);
+ Packet2d tmp = print<Packet2d>(a);
+ // If greater, subtract one.
+ Packet2d mask = _mm_cmpgt_pd(tmp, a);
+ mask = pand(mask, cst_1);
+ return psub(tmp, mask);
+}
+
+template<> EIGEN_STRONG_INLINE Packet4f pceil<Packet4f>(const Packet4f& a)
+{
+ const Packet4f cst_1 = pset1<Packet4f>(1.0f);
+ Packet4f tmp = print<Packet4f>(a);
+ // If smaller, add one.
+ Packet4f mask = _mm_cmplt_ps(tmp, a);
+ mask = pand(mask, cst_1);
+ return padd(tmp, mask);
+}
+
+template<> EIGEN_STRONG_INLINE Packet2d pceil<Packet2d>(const Packet2d& a)
+{
+ const Packet2d cst_1 = pset1<Packet2d>(1.0);
+ Packet2d tmp = print<Packet2d>(a);
+ // If smaller, add one.
+ Packet2d mask = _mm_cmplt_pd(tmp, a);
+ mask = pand(mask, cst_1);
+ return padd(tmp, mask);
+}
+#endif
+
+template<> EIGEN_STRONG_INLINE Packet4f pload<Packet4f>(const float* from) { EIGEN_DEBUG_ALIGNED_LOAD return _mm_load_ps(from); }
+template<> EIGEN_STRONG_INLINE Packet2d pload<Packet2d>(const double* from) { EIGEN_DEBUG_ALIGNED_LOAD return _mm_load_pd(from); }
+template<> EIGEN_STRONG_INLINE Packet4i pload<Packet4i>(const int* from) { EIGEN_DEBUG_ALIGNED_LOAD return _mm_load_si128(reinterpret_cast<const __m128i*>(from)); }
+template<> EIGEN_STRONG_INLINE Packet16b pload<Packet16b>(const bool* from) { EIGEN_DEBUG_ALIGNED_LOAD return _mm_load_si128(reinterpret_cast<const __m128i*>(from)); }
+
+#if EIGEN_COMP_MSVC
+ template<> EIGEN_STRONG_INLINE Packet4f ploadu<Packet4f>(const float* from) {
+ EIGEN_DEBUG_UNALIGNED_LOAD
+ return _mm_loadu_ps(from);
+ }
+#else
+// NOTE: with the code below, MSVC's compiler crashes!
+
+template<> EIGEN_STRONG_INLINE Packet4f ploadu<Packet4f>(const float* from)
+{
+ EIGEN_DEBUG_UNALIGNED_LOAD
+ return _mm_loadu_ps(from);
+}
+#endif
+
+template<> EIGEN_STRONG_INLINE Packet2d ploadu<Packet2d>(const double* from)
+{
+ EIGEN_DEBUG_UNALIGNED_LOAD
+ return _mm_loadu_pd(from);
+}
+template<> EIGEN_STRONG_INLINE Packet4i ploadu<Packet4i>(const int* from)
+{
+ EIGEN_DEBUG_UNALIGNED_LOAD
+ return _mm_loadu_si128(reinterpret_cast<const __m128i*>(from));
+}
+template<> EIGEN_STRONG_INLINE Packet16b ploadu<Packet16b>(const bool* from) {
+ EIGEN_DEBUG_UNALIGNED_LOAD
+ return _mm_loadu_si128(reinterpret_cast<const __m128i*>(from));
+}
+
+// Load lower part of packet zero extending.
+template<typename Packet> EIGEN_STRONG_INLINE Packet ploadl(const typename unpacket_traits<Packet>::type* from);
+template<> EIGEN_STRONG_INLINE Packet4f ploadl<Packet4f>(const float* from) { EIGEN_DEBUG_UNALIGNED_LOAD return _mm_castpd_ps(_mm_load_sd(reinterpret_cast<const double*>(from))); }
+template<> EIGEN_STRONG_INLINE Packet2d ploadl<Packet2d>(const double* from) { EIGEN_DEBUG_UNALIGNED_LOAD return _mm_load_sd(from); }
+
+// Load scalar
+template<typename Packet> EIGEN_STRONG_INLINE Packet ploads(const typename unpacket_traits<Packet>::type* from);
+template<> EIGEN_STRONG_INLINE Packet4f ploads<Packet4f>(const float* from) { EIGEN_DEBUG_UNALIGNED_LOAD return _mm_load_ss(from); }
+template<> EIGEN_STRONG_INLINE Packet2d ploads<Packet2d>(const double* from) { EIGEN_DEBUG_UNALIGNED_LOAD return _mm_load_sd(from); }
+
+template<> EIGEN_STRONG_INLINE Packet4f ploaddup<Packet4f>(const float* from)
+{
+ return vec4f_swizzle1(_mm_castpd_ps(_mm_load_sd(reinterpret_cast<const double*>(from))), 0, 0, 1, 1);
+}
+template<> EIGEN_STRONG_INLINE Packet2d ploaddup<Packet2d>(const double* from)
+{ return pset1<Packet2d>(from[0]); }
+template<> EIGEN_STRONG_INLINE Packet4i ploaddup<Packet4i>(const int* from)
+{
+ Packet4i tmp;
+ tmp = _mm_loadl_epi64(reinterpret_cast<const __m128i*>(from));
+ return vec4i_swizzle1(tmp, 0, 0, 1, 1);
+}
+
+// Loads 8 bools from memory and returns the packet
+// {b0, b0, b1, b1, b2, b2, b3, b3, b4, b4, b5, b5, b6, b6, b7, b7}
+template<> EIGEN_STRONG_INLINE Packet16b ploaddup<Packet16b>(const bool* from)
+{
+ __m128i tmp = _mm_castpd_si128(pload1<Packet2d>(reinterpret_cast<const double*>(from)));
+ return _mm_unpacklo_epi8(tmp, tmp);
+}
+
+// Loads 4 bools from memory and returns the packet
+// {b0, b0 b0, b0, b1, b1, b1, b1, b2, b2, b2, b2, b3, b3, b3, b3}
+template<> EIGEN_STRONG_INLINE Packet16b
+ploadquad<Packet16b>(const bool* from) {
+ __m128i tmp = _mm_castps_si128(pload1<Packet4f>(reinterpret_cast<const float*>(from)));
+ tmp = _mm_unpacklo_epi8(tmp, tmp);
+ return _mm_unpacklo_epi16(tmp, tmp);
+}
+
+template<> EIGEN_STRONG_INLINE void pstore<float>(float* to, const Packet4f& from) { EIGEN_DEBUG_ALIGNED_STORE _mm_store_ps(to, from); }
+template<> EIGEN_STRONG_INLINE void pstore<double>(double* to, const Packet2d& from) { EIGEN_DEBUG_ALIGNED_STORE _mm_store_pd(to, from); }
+template<> EIGEN_STRONG_INLINE void pstore<int>(int* to, const Packet4i& from) { EIGEN_DEBUG_ALIGNED_STORE _mm_store_si128(reinterpret_cast<__m128i*>(to), from); }
+template<> EIGEN_STRONG_INLINE void pstore<bool>(bool* to, const Packet16b& from) { EIGEN_DEBUG_ALIGNED_STORE _mm_store_si128(reinterpret_cast<__m128i*>(to), from); }
+
+template<> EIGEN_STRONG_INLINE void pstoreu<double>(double* to, const Packet2d& from) { EIGEN_DEBUG_UNALIGNED_STORE _mm_storeu_pd(to, from); }
+template<> EIGEN_STRONG_INLINE void pstoreu<float>(float* to, const Packet4f& from) { EIGEN_DEBUG_UNALIGNED_STORE _mm_storeu_ps(to, from); }
+template<> EIGEN_STRONG_INLINE void pstoreu<int>(int* to, const Packet4i& from) { EIGEN_DEBUG_UNALIGNED_STORE _mm_storeu_si128(reinterpret_cast<__m128i*>(to), from); }
+template<> EIGEN_STRONG_INLINE void pstoreu<bool>(bool* to, const Packet16b& from) { EIGEN_DEBUG_ALIGNED_STORE _mm_storeu_si128(reinterpret_cast<__m128i*>(to), from); }
+
+template<typename Scalar, typename Packet> EIGEN_STRONG_INLINE void pstorel(Scalar* to, const Packet& from);
+template<> EIGEN_STRONG_INLINE void pstorel(float* to, const Packet4f& from) { EIGEN_DEBUG_UNALIGNED_STORE _mm_storel_pi(reinterpret_cast<__m64*>(to), from); }
+template<> EIGEN_STRONG_INLINE void pstorel(double* to, const Packet2d& from) { EIGEN_DEBUG_UNALIGNED_STORE _mm_storel_pd(to, from); }
+
+template<typename Scalar, typename Packet> EIGEN_STRONG_INLINE void pstores(Scalar* to, const Packet& from);
+template<> EIGEN_STRONG_INLINE void pstores(float* to, const Packet4f& from) { EIGEN_DEBUG_UNALIGNED_STORE _mm_store_ss(to, from); }
+template<> EIGEN_STRONG_INLINE void pstores(double* to, const Packet2d& from) { EIGEN_DEBUG_UNALIGNED_STORE _mm_store_sd(to, from); }
+
+template<> EIGEN_DEVICE_FUNC inline Packet4f pgather<float, Packet4f>(const float* from, Index stride)
+{
+ return _mm_set_ps(from[3*stride], from[2*stride], from[1*stride], from[0*stride]);
+}
+template<> EIGEN_DEVICE_FUNC inline Packet2d pgather<double, Packet2d>(const double* from, Index stride)
+{
+ return _mm_set_pd(from[1*stride], from[0*stride]);
+}
+template<> EIGEN_DEVICE_FUNC inline Packet4i pgather<int, Packet4i>(const int* from, Index stride)
+{
+ return _mm_set_epi32(from[3*stride], from[2*stride], from[1*stride], from[0*stride]);
+}
+
+template<> EIGEN_DEVICE_FUNC inline Packet16b pgather<bool, Packet16b>(const bool* from, Index stride)
+{
+ return _mm_set_epi8(from[15*stride], from[14*stride], from[13*stride], from[12*stride],
+ from[11*stride], from[10*stride], from[9*stride], from[8*stride],
+ from[7*stride], from[6*stride], from[5*stride], from[4*stride],
+ from[3*stride], from[2*stride], from[1*stride], from[0*stride]);
+}
+
+template<> EIGEN_DEVICE_FUNC inline void pscatter<float, Packet4f>(float* to, const Packet4f& from, Index stride)
+{
+ to[stride*0] = _mm_cvtss_f32(from);
+ to[stride*1] = _mm_cvtss_f32(_mm_shuffle_ps(from, from, 1));
+ to[stride*2] = _mm_cvtss_f32(_mm_shuffle_ps(from, from, 2));
+ to[stride*3] = _mm_cvtss_f32(_mm_shuffle_ps(from, from, 3));
+}
+template<> EIGEN_DEVICE_FUNC inline void pscatter<double, Packet2d>(double* to, const Packet2d& from, Index stride)
+{
+ to[stride*0] = _mm_cvtsd_f64(from);
+ to[stride*1] = _mm_cvtsd_f64(_mm_shuffle_pd(from, from, 1));
+}
+template<> EIGEN_DEVICE_FUNC inline void pscatter<int, Packet4i>(int* to, const Packet4i& from, Index stride)
+{
+ to[stride*0] = _mm_cvtsi128_si32(from);
+ to[stride*1] = _mm_cvtsi128_si32(_mm_shuffle_epi32(from, 1));
+ to[stride*2] = _mm_cvtsi128_si32(_mm_shuffle_epi32(from, 2));
+ to[stride*3] = _mm_cvtsi128_si32(_mm_shuffle_epi32(from, 3));
+}
+template<> EIGEN_DEVICE_FUNC inline void pscatter<bool, Packet16b>(bool* to, const Packet16b& from, Index stride)
+{
+ to[4*stride*0] = _mm_cvtsi128_si32(from);
+ to[4*stride*1] = _mm_cvtsi128_si32(_mm_shuffle_epi32(from, 1));
+ to[4*stride*2] = _mm_cvtsi128_si32(_mm_shuffle_epi32(from, 2));
+ to[4*stride*3] = _mm_cvtsi128_si32(_mm_shuffle_epi32(from, 3));
+}
+
+
+// some compilers might be tempted to perform multiple moves instead of using a vector path.
+template<> EIGEN_STRONG_INLINE void pstore1<Packet4f>(float* to, const float& a)
+{
+ Packet4f pa = _mm_set_ss(a);
+ pstore(to, Packet4f(vec4f_swizzle1(pa,0,0,0,0)));
+}
+// some compilers might be tempted to perform multiple moves instead of using a vector path.
+template<> EIGEN_STRONG_INLINE void pstore1<Packet2d>(double* to, const double& a)
+{
+ Packet2d pa = _mm_set_sd(a);
+ pstore(to, Packet2d(vec2d_swizzle1(pa,0,0)));
+}
+
+#if EIGEN_COMP_PGI && EIGEN_COMP_PGI < 1900
+typedef const void * SsePrefetchPtrType;
+#else
+typedef const char * SsePrefetchPtrType;
+#endif
+
+#ifndef EIGEN_VECTORIZE_AVX
+template<> EIGEN_STRONG_INLINE void prefetch<float>(const float* addr) { _mm_prefetch((SsePrefetchPtrType)(addr), _MM_HINT_T0); }
+template<> EIGEN_STRONG_INLINE void prefetch<double>(const double* addr) { _mm_prefetch((SsePrefetchPtrType)(addr), _MM_HINT_T0); }
+template<> EIGEN_STRONG_INLINE void prefetch<int>(const int* addr) { _mm_prefetch((SsePrefetchPtrType)(addr), _MM_HINT_T0); }
+#endif
+
+#if EIGEN_COMP_MSVC_STRICT && EIGEN_OS_WIN64
+// The temporary variable fixes an internal compilation error in vs <= 2008 and a wrong-result bug in vs 2010
+// Direct of the struct members fixed bug #62.
+template<> EIGEN_STRONG_INLINE float pfirst<Packet4f>(const Packet4f& a) { return a.m128_f32[0]; }
+template<> EIGEN_STRONG_INLINE double pfirst<Packet2d>(const Packet2d& a) { return a.m128d_f64[0]; }
+template<> EIGEN_STRONG_INLINE int pfirst<Packet4i>(const Packet4i& a) { int x = _mm_cvtsi128_si32(a); return x; }
+#elif EIGEN_COMP_MSVC_STRICT
+// The temporary variable fixes an internal compilation error in vs <= 2008 and a wrong-result bug in vs 2010
+template<> EIGEN_STRONG_INLINE float pfirst<Packet4f>(const Packet4f& a) { float x = _mm_cvtss_f32(a); return x; }
+template<> EIGEN_STRONG_INLINE double pfirst<Packet2d>(const Packet2d& a) { double x = _mm_cvtsd_f64(a); return x; }
+template<> EIGEN_STRONG_INLINE int pfirst<Packet4i>(const Packet4i& a) { int x = _mm_cvtsi128_si32(a); return x; }
+#else
+template<> EIGEN_STRONG_INLINE float pfirst<Packet4f>(const Packet4f& a) { return _mm_cvtss_f32(a); }
+template<> EIGEN_STRONG_INLINE double pfirst<Packet2d>(const Packet2d& a) { return _mm_cvtsd_f64(a); }
+template<> EIGEN_STRONG_INLINE int pfirst<Packet4i>(const Packet4i& a) { return _mm_cvtsi128_si32(a); }
+#endif
+template<> EIGEN_STRONG_INLINE bool pfirst<Packet16b>(const Packet16b& a) { int x = _mm_cvtsi128_si32(a); return static_cast<bool>(x & 1); }
+
+template<> EIGEN_STRONG_INLINE Packet4f preverse(const Packet4f& a) { return _mm_shuffle_ps(a,a,0x1B); }
+template<> EIGEN_STRONG_INLINE Packet2d preverse(const Packet2d& a) { return _mm_shuffle_pd(a,a,0x1); }
+template<> EIGEN_STRONG_INLINE Packet4i preverse(const Packet4i& a) { return _mm_shuffle_epi32(a,0x1B); }
+template<> EIGEN_STRONG_INLINE Packet16b preverse(const Packet16b& a) {
+#ifdef EIGEN_VECTORIZE_SSSE3
+ __m128i mask = _mm_set_epi8(0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15);
+ return _mm_shuffle_epi8(a, mask);
+#else
+ Packet16b tmp = _mm_shuffle_epi32(a, _MM_SHUFFLE(0, 1, 2, 3));
+ tmp = _mm_shufflehi_epi16(_mm_shufflelo_epi16(tmp, _MM_SHUFFLE(2, 3, 0, 1)), _MM_SHUFFLE(2, 3, 0, 1));
+ return _mm_or_si128(_mm_slli_epi16(tmp, 8), _mm_srli_epi16(tmp, 8));
+#endif
+}
+
+template<> EIGEN_STRONG_INLINE Packet4f pfrexp<Packet4f>(const Packet4f& a, Packet4f& exponent) {
+ return pfrexp_generic(a,exponent);
+}
+
+// Extract exponent without existence of Packet2l.
+template<>
+EIGEN_STRONG_INLINE
+Packet2d pfrexp_generic_get_biased_exponent(const Packet2d& a) {
+ const Packet2d cst_exp_mask = pset1frombits<Packet2d>(static_cast<uint64_t>(0x7ff0000000000000ull));
+ __m128i a_expo = _mm_srli_epi64(_mm_castpd_si128(pand(a, cst_exp_mask)), 52);
+ return _mm_cvtepi32_pd(vec4i_swizzle1(a_expo, 0, 2, 1, 3));
+}
+
+template<> EIGEN_STRONG_INLINE Packet2d pfrexp<Packet2d>(const Packet2d& a, Packet2d& exponent) {
+ return pfrexp_generic(a, exponent);
+}
+
+template<> EIGEN_STRONG_INLINE Packet4f pldexp<Packet4f>(const Packet4f& a, const Packet4f& exponent) {
+ return pldexp_generic(a,exponent);
+}
+
+// We specialize pldexp here, since the generic implementation uses Packet2l, which is not well
+// supported by SSE, and has more range than is needed for exponents.
+template<> EIGEN_STRONG_INLINE Packet2d pldexp<Packet2d>(const Packet2d& a, const Packet2d& exponent) {
+ // Clamp exponent to [-2099, 2099]
+ const Packet2d max_exponent = pset1<Packet2d>(2099.0);
+ const Packet2d e = pmin(pmax(exponent, pnegate(max_exponent)), max_exponent);
+
+ // Convert e to integer and swizzle to low-order bits.
+ const Packet4i ei = vec4i_swizzle1(_mm_cvtpd_epi32(e), 0, 3, 1, 3);
+
+ // Split 2^e into four factors and multiply:
+ const Packet4i bias = _mm_set_epi32(0, 1023, 0, 1023);
+ Packet4i b = parithmetic_shift_right<2>(ei); // floor(e/4)
+ Packet2d c = _mm_castsi128_pd(_mm_slli_epi64(padd(b, bias), 52)); // 2^b
+ Packet2d out = pmul(pmul(pmul(a, c), c), c); // a * 2^(3b)
+ b = psub(psub(psub(ei, b), b), b); // e - 3b
+ c = _mm_castsi128_pd(_mm_slli_epi64(padd(b, bias), 52)); // 2^(e - 3b)
+ out = pmul(out, c); // a * 2^e
+ return out;
+}
+
+// with AVX, the default implementations based on pload1 are faster
+#ifndef __AVX__
+template<> EIGEN_STRONG_INLINE void
+pbroadcast4<Packet4f>(const float *a,
+ Packet4f& a0, Packet4f& a1, Packet4f& a2, Packet4f& a3)
+{
+ a3 = pload<Packet4f>(a);
+ a0 = vec4f_swizzle1(a3, 0,0,0,0);
+ a1 = vec4f_swizzle1(a3, 1,1,1,1);
+ a2 = vec4f_swizzle1(a3, 2,2,2,2);
+ a3 = vec4f_swizzle1(a3, 3,3,3,3);
+}
+template<> EIGEN_STRONG_INLINE void
+pbroadcast4<Packet2d>(const double *a,
+ Packet2d& a0, Packet2d& a1, Packet2d& a2, Packet2d& a3)
+{
+#ifdef EIGEN_VECTORIZE_SSE3
+ a0 = _mm_loaddup_pd(a+0);
+ a1 = _mm_loaddup_pd(a+1);
+ a2 = _mm_loaddup_pd(a+2);
+ a3 = _mm_loaddup_pd(a+3);
+#else
+ a1 = pload<Packet2d>(a);
+ a0 = vec2d_swizzle1(a1, 0,0);
+ a1 = vec2d_swizzle1(a1, 1,1);
+ a3 = pload<Packet2d>(a+2);
+ a2 = vec2d_swizzle1(a3, 0,0);
+ a3 = vec2d_swizzle1(a3, 1,1);
+#endif
+}
+#endif
+
+EIGEN_STRONG_INLINE void punpackp(Packet4f* vecs)
+{
+ vecs[1] = _mm_castsi128_ps(_mm_shuffle_epi32(_mm_castps_si128(vecs[0]), 0x55));
+ vecs[2] = _mm_castsi128_ps(_mm_shuffle_epi32(_mm_castps_si128(vecs[0]), 0xAA));
+ vecs[3] = _mm_castsi128_ps(_mm_shuffle_epi32(_mm_castps_si128(vecs[0]), 0xFF));
+ vecs[0] = _mm_castsi128_ps(_mm_shuffle_epi32(_mm_castps_si128(vecs[0]), 0x00));
+}
+
+template<> EIGEN_STRONG_INLINE float predux<Packet4f>(const Packet4f& a)
+{
+ // Disable SSE3 _mm_hadd_pd that is extremely slow on all existing Intel's architectures
+ // (from Nehalem to Haswell)
+// #ifdef EIGEN_VECTORIZE_SSE3
+// Packet4f tmp = _mm_add_ps(a, vec4f_swizzle1(a,2,3,2,3));
+// return pfirst<Packet4f>(_mm_hadd_ps(tmp, tmp));
+// #else
+ Packet4f tmp = _mm_add_ps(a, _mm_movehl_ps(a,a));
+ return pfirst<Packet4f>(_mm_add_ss(tmp, _mm_shuffle_ps(tmp,tmp, 1)));
+// #endif
+}
+
+template<> EIGEN_STRONG_INLINE double predux<Packet2d>(const Packet2d& a)
+{
+ // Disable SSE3 _mm_hadd_pd that is extremely slow on all existing Intel's architectures
+ // (from Nehalem to Haswell)
+// #ifdef EIGEN_VECTORIZE_SSE3
+// return pfirst<Packet2d>(_mm_hadd_pd(a, a));
+// #else
+ return pfirst<Packet2d>(_mm_add_sd(a, _mm_unpackhi_pd(a,a)));
+// #endif
+}
+
+#ifdef EIGEN_VECTORIZE_SSSE3
+template<> EIGEN_STRONG_INLINE int predux<Packet4i>(const Packet4i& a)
+{
+ Packet4i tmp0 = _mm_hadd_epi32(a,a);
+ return pfirst<Packet4i>(_mm_hadd_epi32(tmp0,tmp0));
+}
+
+#else
+template<> EIGEN_STRONG_INLINE int predux<Packet4i>(const Packet4i& a)
+{
+ Packet4i tmp = _mm_add_epi32(a, _mm_unpackhi_epi64(a,a));
+ return pfirst(tmp) + pfirst<Packet4i>(_mm_shuffle_epi32(tmp, 1));
+}
+#endif
+
+template<> EIGEN_STRONG_INLINE bool predux<Packet16b>(const Packet16b& a) {
+ Packet4i tmp = _mm_or_si128(a, _mm_unpackhi_epi64(a,a));
+ return (pfirst(tmp) != 0) || (pfirst<Packet4i>(_mm_shuffle_epi32(tmp, 1)) != 0);
+}
+
+// Other reduction functions:
+
+
+// mul
+template<> EIGEN_STRONG_INLINE float predux_mul<Packet4f>(const Packet4f& a)
+{
+ Packet4f tmp = _mm_mul_ps(a, _mm_movehl_ps(a,a));
+ return pfirst<Packet4f>(_mm_mul_ss(tmp, _mm_shuffle_ps(tmp,tmp, 1)));
+}
+template<> EIGEN_STRONG_INLINE double predux_mul<Packet2d>(const Packet2d& a)
+{
+ return pfirst<Packet2d>(_mm_mul_sd(a, _mm_unpackhi_pd(a,a)));
+}
+template<> EIGEN_STRONG_INLINE int predux_mul<Packet4i>(const Packet4i& a)
+{
+ // after some experiments, it is seems this is the fastest way to implement it
+ // for GCC (eg., reusing pmul is very slow !)
+ // TODO try to call _mm_mul_epu32 directly
+ EIGEN_ALIGN16 int aux[4];
+ pstore(aux, a);
+ return (aux[0] * aux[1]) * (aux[2] * aux[3]);
+}
+
+template<> EIGEN_STRONG_INLINE bool predux_mul<Packet16b>(const Packet16b& a) {
+ Packet4i tmp = _mm_and_si128(a, _mm_unpackhi_epi64(a,a));
+ return ((pfirst<Packet4i>(tmp) == 0x01010101) &&
+ (pfirst<Packet4i>(_mm_shuffle_epi32(tmp, 1)) == 0x01010101));
+}
+
+// min
+template<> EIGEN_STRONG_INLINE float predux_min<Packet4f>(const Packet4f& a)
+{
+ Packet4f tmp = _mm_min_ps(a, _mm_movehl_ps(a,a));
+ return pfirst<Packet4f>(_mm_min_ss(tmp, _mm_shuffle_ps(tmp,tmp, 1)));
+}
+template<> EIGEN_STRONG_INLINE double predux_min<Packet2d>(const Packet2d& a)
+{
+ return pfirst<Packet2d>(_mm_min_sd(a, _mm_unpackhi_pd(a,a)));
+}
+template<> EIGEN_STRONG_INLINE int predux_min<Packet4i>(const Packet4i& a)
+{
+#ifdef EIGEN_VECTORIZE_SSE4_1
+ Packet4i tmp = _mm_min_epi32(a, _mm_shuffle_epi32(a, _MM_SHUFFLE(0,0,3,2)));
+ return pfirst<Packet4i>(_mm_min_epi32(tmp,_mm_shuffle_epi32(tmp, 1)));
+#else
+ // after some experiments, it is seems this is the fastest way to implement it
+ // for GCC (eg., it does not like using std::min after the pstore !!)
+ EIGEN_ALIGN16 int aux[4];
+ pstore(aux, a);
+ int aux0 = aux[0]<aux[1] ? aux[0] : aux[1];
+ int aux2 = aux[2]<aux[3] ? aux[2] : aux[3];
+ return aux0<aux2 ? aux0 : aux2;
+#endif // EIGEN_VECTORIZE_SSE4_1
+}
+
+// max
+template<> EIGEN_STRONG_INLINE float predux_max<Packet4f>(const Packet4f& a)
+{
+ Packet4f tmp = _mm_max_ps(a, _mm_movehl_ps(a,a));
+ return pfirst<Packet4f>(_mm_max_ss(tmp, _mm_shuffle_ps(tmp,tmp, 1)));
+}
+template<> EIGEN_STRONG_INLINE double predux_max<Packet2d>(const Packet2d& a)
+{
+ return pfirst<Packet2d>(_mm_max_sd(a, _mm_unpackhi_pd(a,a)));
+}
+template<> EIGEN_STRONG_INLINE int predux_max<Packet4i>(const Packet4i& a)
+{
+#ifdef EIGEN_VECTORIZE_SSE4_1
+ Packet4i tmp = _mm_max_epi32(a, _mm_shuffle_epi32(a, _MM_SHUFFLE(0,0,3,2)));
+ return pfirst<Packet4i>(_mm_max_epi32(tmp,_mm_shuffle_epi32(tmp, 1)));
+#else
+ // after some experiments, it is seems this is the fastest way to implement it
+ // for GCC (eg., it does not like using std::min after the pstore !!)
+ EIGEN_ALIGN16 int aux[4];
+ pstore(aux, a);
+ int aux0 = aux[0]>aux[1] ? aux[0] : aux[1];
+ int aux2 = aux[2]>aux[3] ? aux[2] : aux[3];
+ return aux0>aux2 ? aux0 : aux2;
+#endif // EIGEN_VECTORIZE_SSE4_1
+}
+
+// not needed yet
+// template<> EIGEN_STRONG_INLINE bool predux_all(const Packet4f& x)
+// {
+// return _mm_movemask_ps(x) == 0xF;
+// }
+
+template<> EIGEN_STRONG_INLINE bool predux_any(const Packet4f& x)
+{
+ return _mm_movemask_ps(x) != 0x0;
+}
+
+template<> EIGEN_STRONG_INLINE bool predux_any(const Packet4i& x)
+{
+ return _mm_movemask_ps(_mm_castsi128_ps(x)) != 0x0;
+}
+
+EIGEN_DEVICE_FUNC inline void
+ptranspose(PacketBlock<Packet4f,4>& kernel) {
+ _MM_TRANSPOSE4_PS(kernel.packet[0], kernel.packet[1], kernel.packet[2], kernel.packet[3]);
+}
+
+EIGEN_DEVICE_FUNC inline void
+ptranspose(PacketBlock<Packet2d,2>& kernel) {
+ __m128d tmp = _mm_unpackhi_pd(kernel.packet[0], kernel.packet[1]);
+ kernel.packet[0] = _mm_unpacklo_pd(kernel.packet[0], kernel.packet[1]);
+ kernel.packet[1] = tmp;
+}
+
+EIGEN_DEVICE_FUNC inline void
+ptranspose(PacketBlock<Packet4i,4>& kernel) {
+ __m128i T0 = _mm_unpacklo_epi32(kernel.packet[0], kernel.packet[1]);
+ __m128i T1 = _mm_unpacklo_epi32(kernel.packet[2], kernel.packet[3]);
+ __m128i T2 = _mm_unpackhi_epi32(kernel.packet[0], kernel.packet[1]);
+ __m128i T3 = _mm_unpackhi_epi32(kernel.packet[2], kernel.packet[3]);
+
+ kernel.packet[0] = _mm_unpacklo_epi64(T0, T1);
+ kernel.packet[1] = _mm_unpackhi_epi64(T0, T1);
+ kernel.packet[2] = _mm_unpacklo_epi64(T2, T3);
+ kernel.packet[3] = _mm_unpackhi_epi64(T2, T3);
+}
+
+EIGEN_DEVICE_FUNC inline void
+ptranspose(PacketBlock<Packet16b,4>& kernel) {
+ __m128i T0 = _mm_unpacklo_epi8(kernel.packet[0], kernel.packet[1]);
+ __m128i T1 = _mm_unpackhi_epi8(kernel.packet[0], kernel.packet[1]);
+ __m128i T2 = _mm_unpacklo_epi8(kernel.packet[2], kernel.packet[3]);
+ __m128i T3 = _mm_unpackhi_epi8(kernel.packet[2], kernel.packet[3]);
+ kernel.packet[0] = _mm_unpacklo_epi16(T0, T2);
+ kernel.packet[1] = _mm_unpackhi_epi16(T0, T2);
+ kernel.packet[2] = _mm_unpacklo_epi16(T1, T3);
+ kernel.packet[3] = _mm_unpackhi_epi16(T1, T3);
+}
+
+EIGEN_DEVICE_FUNC inline void
+ptranspose(PacketBlock<Packet16b,16>& kernel) {
+ // If we number the elements in the input thus:
+ // kernel.packet[ 0] = {00, 01, 02, 03, 04, 05, 06, 07, 08, 09, 0a, 0b, 0c, 0d, 0e, 0f}
+ // kernel.packet[ 1] = {10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 1a, 1b, 1c, 1d, 1e, 1f}
+ // ...
+ // kernel.packet[15] = {f0, f1, f2, f3, f4, f5, f6, f7, f8, f9, fa, fb, fc, fd, fe, ff},
+ //
+ // the desired output is:
+ // kernel.packet[ 0] = {00, 10, 20, 30, 40, 50, 60, 70, 80, 90, a0, b0, c0, d0, e0, f0}
+ // kernel.packet[ 1] = {01, 11, 21, 31, 41, 51, 61, 71, 81, 91, a1, b1, c1, d1, e1, f1}
+ // ...
+ // kernel.packet[15] = {0f, 1f, 2f, 3f, 4f, 5f, 6f, 7f, 8f, 9f, af, bf, cf, df, ef, ff},
+ __m128i t0 = _mm_unpacklo_epi8(kernel.packet[0], kernel.packet[1]); // 00 10 01 11 02 12 03 13 04 14 05 15 06 16 07 17
+ __m128i t1 = _mm_unpackhi_epi8(kernel.packet[0], kernel.packet[1]); // 08 18 09 19 0a 1a 0b 1b 0c 1c 0d 1d 0e 1e 0f 1f
+ __m128i t2 = _mm_unpacklo_epi8(kernel.packet[2], kernel.packet[3]); // 20 30 21 31 22 32 ... 27 37
+ __m128i t3 = _mm_unpackhi_epi8(kernel.packet[2], kernel.packet[3]); // 28 38 29 39 2a 3a ... 2f 3f
+ __m128i t4 = _mm_unpacklo_epi8(kernel.packet[4], kernel.packet[5]); // 40 50 41 51 42 52 47 57
+ __m128i t5 = _mm_unpackhi_epi8(kernel.packet[4], kernel.packet[5]); // 48 58 49 59 4a 5a
+ __m128i t6 = _mm_unpacklo_epi8(kernel.packet[6], kernel.packet[7]);
+ __m128i t7 = _mm_unpackhi_epi8(kernel.packet[6], kernel.packet[7]);
+ __m128i t8 = _mm_unpacklo_epi8(kernel.packet[8], kernel.packet[9]);
+ __m128i t9 = _mm_unpackhi_epi8(kernel.packet[8], kernel.packet[9]);
+ __m128i ta = _mm_unpacklo_epi8(kernel.packet[10], kernel.packet[11]);
+ __m128i tb = _mm_unpackhi_epi8(kernel.packet[10], kernel.packet[11]);
+ __m128i tc = _mm_unpacklo_epi8(kernel.packet[12], kernel.packet[13]);
+ __m128i td = _mm_unpackhi_epi8(kernel.packet[12], kernel.packet[13]);
+ __m128i te = _mm_unpacklo_epi8(kernel.packet[14], kernel.packet[15]);
+ __m128i tf = _mm_unpackhi_epi8(kernel.packet[14], kernel.packet[15]);
+
+ __m128i s0 = _mm_unpacklo_epi16(t0, t2); // 00 10 20 30 01 11 21 31 02 12 22 32 03 13 23 33
+ __m128i s1 = _mm_unpackhi_epi16(t0, t2); // 04 14 24 34
+ __m128i s2 = _mm_unpacklo_epi16(t1, t3); // 08 18 28 38 ...
+ __m128i s3 = _mm_unpackhi_epi16(t1, t3); // 0c 1c 2c 3c ...
+ __m128i s4 = _mm_unpacklo_epi16(t4, t6); // 40 50 60 70 41 51 61 71 42 52 62 72 43 53 63 73
+ __m128i s5 = _mm_unpackhi_epi16(t4, t6); // 44 54 64 74 ...
+ __m128i s6 = _mm_unpacklo_epi16(t5, t7);
+ __m128i s7 = _mm_unpackhi_epi16(t5, t7);
+ __m128i s8 = _mm_unpacklo_epi16(t8, ta);
+ __m128i s9 = _mm_unpackhi_epi16(t8, ta);
+ __m128i sa = _mm_unpacklo_epi16(t9, tb);
+ __m128i sb = _mm_unpackhi_epi16(t9, tb);
+ __m128i sc = _mm_unpacklo_epi16(tc, te);
+ __m128i sd = _mm_unpackhi_epi16(tc, te);
+ __m128i se = _mm_unpacklo_epi16(td, tf);
+ __m128i sf = _mm_unpackhi_epi16(td, tf);
+
+ __m128i u0 = _mm_unpacklo_epi32(s0, s4); // 00 10 20 30 40 50 60 70 01 11 21 31 41 51 61 71
+ __m128i u1 = _mm_unpackhi_epi32(s0, s4); // 02 12 22 32 42 52 62 72 03 13 23 33 43 53 63 73
+ __m128i u2 = _mm_unpacklo_epi32(s1, s5);
+ __m128i u3 = _mm_unpackhi_epi32(s1, s5);
+ __m128i u4 = _mm_unpacklo_epi32(s2, s6);
+ __m128i u5 = _mm_unpackhi_epi32(s2, s6);
+ __m128i u6 = _mm_unpacklo_epi32(s3, s7);
+ __m128i u7 = _mm_unpackhi_epi32(s3, s7);
+ __m128i u8 = _mm_unpacklo_epi32(s8, sc);
+ __m128i u9 = _mm_unpackhi_epi32(s8, sc);
+ __m128i ua = _mm_unpacklo_epi32(s9, sd);
+ __m128i ub = _mm_unpackhi_epi32(s9, sd);
+ __m128i uc = _mm_unpacklo_epi32(sa, se);
+ __m128i ud = _mm_unpackhi_epi32(sa, se);
+ __m128i ue = _mm_unpacklo_epi32(sb, sf);
+ __m128i uf = _mm_unpackhi_epi32(sb, sf);
+
+ kernel.packet[0] = _mm_unpacklo_epi64(u0, u8);
+ kernel.packet[1] = _mm_unpackhi_epi64(u0, u8);
+ kernel.packet[2] = _mm_unpacklo_epi64(u1, u9);
+ kernel.packet[3] = _mm_unpackhi_epi64(u1, u9);
+ kernel.packet[4] = _mm_unpacklo_epi64(u2, ua);
+ kernel.packet[5] = _mm_unpackhi_epi64(u2, ua);
+ kernel.packet[6] = _mm_unpacklo_epi64(u3, ub);
+ kernel.packet[7] = _mm_unpackhi_epi64(u3, ub);
+ kernel.packet[8] = _mm_unpacklo_epi64(u4, uc);
+ kernel.packet[9] = _mm_unpackhi_epi64(u4, uc);
+ kernel.packet[10] = _mm_unpacklo_epi64(u5, ud);
+ kernel.packet[11] = _mm_unpackhi_epi64(u5, ud);
+ kernel.packet[12] = _mm_unpacklo_epi64(u6, ue);
+ kernel.packet[13] = _mm_unpackhi_epi64(u6, ue);
+ kernel.packet[14] = _mm_unpacklo_epi64(u7, uf);
+ kernel.packet[15] = _mm_unpackhi_epi64(u7, uf);
+}
+
+template<> EIGEN_STRONG_INLINE Packet4i pblend(const Selector<4>& ifPacket, const Packet4i& thenPacket, const Packet4i& elsePacket) {
+ const __m128i zero = _mm_setzero_si128();
+ const __m128i select = _mm_set_epi32(ifPacket.select[3], ifPacket.select[2], ifPacket.select[1], ifPacket.select[0]);
+ __m128i false_mask = _mm_cmpeq_epi32(select, zero);
+#ifdef EIGEN_VECTORIZE_SSE4_1
+ return _mm_blendv_epi8(thenPacket, elsePacket, false_mask);
+#else
+ return _mm_or_si128(_mm_andnot_si128(false_mask, thenPacket), _mm_and_si128(false_mask, elsePacket));
+#endif
+}
+template<> EIGEN_STRONG_INLINE Packet4f pblend(const Selector<4>& ifPacket, const Packet4f& thenPacket, const Packet4f& elsePacket) {
+ const __m128 zero = _mm_setzero_ps();
+ const __m128 select = _mm_set_ps(ifPacket.select[3], ifPacket.select[2], ifPacket.select[1], ifPacket.select[0]);
+ __m128 false_mask = _mm_cmpeq_ps(select, zero);
+#ifdef EIGEN_VECTORIZE_SSE4_1
+ return _mm_blendv_ps(thenPacket, elsePacket, false_mask);
+#else
+ return _mm_or_ps(_mm_andnot_ps(false_mask, thenPacket), _mm_and_ps(false_mask, elsePacket));
+#endif
+}
+template<> EIGEN_STRONG_INLINE Packet2d pblend(const Selector<2>& ifPacket, const Packet2d& thenPacket, const Packet2d& elsePacket) {
+ const __m128d zero = _mm_setzero_pd();
+ const __m128d select = _mm_set_pd(ifPacket.select[1], ifPacket.select[0]);
+ __m128d false_mask = _mm_cmpeq_pd(select, zero);
+#ifdef EIGEN_VECTORIZE_SSE4_1
+ return _mm_blendv_pd(thenPacket, elsePacket, false_mask);
+#else
+ return _mm_or_pd(_mm_andnot_pd(false_mask, thenPacket), _mm_and_pd(false_mask, elsePacket));
+#endif
+}
+
+// Scalar path for pmadd with FMA to ensure consistency with vectorized path.
+#ifdef EIGEN_VECTORIZE_FMA
+template<> EIGEN_STRONG_INLINE float pmadd(const float& a, const float& b, const float& c) {
+ return ::fmaf(a,b,c);
+}
+template<> EIGEN_STRONG_INLINE double pmadd(const double& a, const double& b, const double& c) {
+ return ::fma(a,b,c);
+}
+template<> EIGEN_STRONG_INLINE float pmsub(const float& a, const float& b, const float& c) {
+ return ::fmaf(a,b,-c);
+}
+template<> EIGEN_STRONG_INLINE double pmsub(const double& a, const double& b, const double& c) {
+ return ::fma(a,b,-c);
+}
+template<> EIGEN_STRONG_INLINE float pnmadd(const float& a, const float& b, const float& c) {
+ return ::fmaf(-a,b,c);
+}
+template<> EIGEN_STRONG_INLINE double pnmadd(const double& a, const double& b, const double& c) {
+ return ::fma(-a,b,c);
+}
+template<> EIGEN_STRONG_INLINE float pnmsub(const float& a, const float& b, const float& c) {
+ return ::fmaf(-a,b,-c);
+}
+template<> EIGEN_STRONG_INLINE double pnmsub(const double& a, const double& b, const double& c) {
+ return ::fma(-a,b,-c);
+}
+#endif
+
+#ifdef EIGEN_VECTORIZE_SSE4_1
+// Helpers for half->float and float->half conversions.
+// Currently only used by the AVX code.
+EIGEN_STRONG_INLINE __m128i half2floatsse(__m128i h) {
+ __m128i input = _mm_cvtepu16_epi32(h);
+
+ // Direct vectorization of half_to_float, C parts in the comments.
+ __m128i shifted_exp = _mm_set1_epi32(0x7c00 << 13);
+ // o.u = (h.x & 0x7fff) << 13; // exponent/mantissa bits
+ __m128i ou = _mm_slli_epi32(_mm_and_si128(input, _mm_set1_epi32(0x7fff)), 13);
+ // exp = shifted_exp & o.u; // just the exponent
+ __m128i exp = _mm_and_si128(ou, shifted_exp);
+ // o.u += (127 - 15) << 23;
+ ou = _mm_add_epi32(ou, _mm_set1_epi32((127 - 15) << 23));
+
+ // Inf/NaN?
+ __m128i naninf_mask = _mm_cmpeq_epi32(exp, shifted_exp);
+ // Inf/NaN adjust
+ __m128i naninf_adj =
+ _mm_and_si128(_mm_set1_epi32((128 - 16) << 23), naninf_mask);
+ // extra exp adjust for Inf/NaN
+ ou = _mm_add_epi32(ou, naninf_adj);
+
+ // Zero/Denormal?
+ __m128i zeroden_mask = _mm_cmpeq_epi32(exp, _mm_setzero_si128());
+ __m128i zeroden_adj = _mm_and_si128(zeroden_mask, _mm_set1_epi32(1 << 23));
+ // o.u += 1 << 23;
+ ou = _mm_add_epi32(ou, zeroden_adj);
+ // magic.u = 113 << 23
+ __m128i magic = _mm_and_si128(zeroden_mask, _mm_set1_epi32(113 << 23));
+ // o.f -= magic.f
+ ou = _mm_castps_si128(
+ _mm_sub_ps(_mm_castsi128_ps(ou), _mm_castsi128_ps(magic)));
+
+ __m128i sign =
+ _mm_slli_epi32(_mm_and_si128(input, _mm_set1_epi32(0x8000)), 16);
+ // o.u |= (h.x & 0x8000) << 16; // sign bit
+ ou = _mm_or_si128(ou, sign);
+ // return o.f;
+ // We are actually returning uint version, to make
+ // _mm256_insertf128_si256 work.
+ return ou;
+}
+
+EIGEN_STRONG_INLINE __m128i float2half(__m128 f) {
+ __m128i o = _mm_setzero_si128();
+
+ // unsigned int sign_mask = 0x80000000u;
+ __m128i sign = _mm_set1_epi32(0x80000000u);
+ // unsigned int sign = f.u & sign_mask;
+ sign = _mm_and_si128(sign, _mm_castps_si128(f));
+ // f.u ^= sign;
+ f = _mm_xor_ps(f, _mm_castsi128_ps(sign));
+
+ __m128i fu = _mm_castps_si128(f);
+
+ __m128i f16max = _mm_set1_epi32((127 + 16) << 23);
+ __m128i f32infty = _mm_set1_epi32(255 << 23);
+ // if (f.u >= f16max.u) // result is Inf or NaN (all exponent bits set)
+ // there is no _mm_cmpge_epi32, so use lt and swap operands
+ __m128i infnan_mask = _mm_cmplt_epi32(f16max, _mm_castps_si128(f));
+ __m128i inf_mask = _mm_cmpgt_epi32(_mm_castps_si128(f), f32infty);
+ __m128i nan_mask = _mm_andnot_si128(inf_mask, infnan_mask);
+ __m128i inf_value = _mm_and_si128(inf_mask, _mm_set1_epi32(0x7e00));
+ __m128i nan_value = _mm_and_si128(nan_mask, _mm_set1_epi32(0x7c00));
+ // o.x = (f.u > f32infty.u) ? 0x7e00 : 0x7c00; // NaN->qNaN and Inf->Inf
+ __m128i naninf_value = _mm_or_si128(inf_value, nan_value);
+
+ __m128i denorm_magic = _mm_set1_epi32(((127 - 15) + (23 - 10) + 1) << 23);
+ __m128i subnorm_mask =
+ _mm_cmplt_epi32(_mm_castps_si128(f), _mm_set1_epi32(113 << 23));
+ // f.f += denorm_magic.f;
+ f = _mm_add_ps(f, _mm_castsi128_ps(denorm_magic));
+ // f.u - denorm_magic.u
+ o = _mm_sub_epi32(_mm_castps_si128(f), denorm_magic);
+ o = _mm_and_si128(o, subnorm_mask);
+ // Correct result for inf/nan/zero/subnormal, 0 otherwise
+ o = _mm_or_si128(o, naninf_value);
+
+ __m128i mask = _mm_or_si128(infnan_mask, subnorm_mask);
+ o = _mm_and_si128(o, mask);
+
+ // mant_odd = (f.u >> 13) & 1;
+ __m128i mand_odd = _mm_and_si128(_mm_srli_epi32(fu, 13), _mm_set1_epi32(0x1));
+ // f.u += 0xc8000fffU;
+ fu = _mm_add_epi32(fu, _mm_set1_epi32(0xc8000fffU));
+ // f.u += mant_odd;
+ fu = _mm_add_epi32(fu, mand_odd);
+ fu = _mm_andnot_si128(mask, fu);
+ // f.u >> 13
+ fu = _mm_srli_epi32(fu, 13);
+ o = _mm_or_si128(fu, o);
+
+ // o.x |= static_cast<numext::uint16_t>(sign >> 16);
+ o = _mm_or_si128(o, _mm_srli_epi32(sign, 16));
+
+ // 16 bit values
+ return _mm_and_si128(o, _mm_set1_epi32(0xffff));
+}
+#endif
+
+// Packet math for Eigen::half
+// Disable the following code since it's broken on too many platforms / compilers.
+//#elif defined(EIGEN_VECTORIZE_SSE) && (!EIGEN_ARCH_x86_64) && (!EIGEN_COMP_MSVC)
+#if 0
+
+typedef struct {
+ __m64 x;
+} Packet4h;
+
+
+template<> struct is_arithmetic<Packet4h> { enum { value = true }; };
+
+template <>
+struct packet_traits<Eigen::half> : default_packet_traits {
+ typedef Packet4h type;
+ // There is no half-size packet for Packet4h.
+ typedef Packet4h half;
+ enum {
+ Vectorizable = 1,
+ AlignedOnScalar = 1,
+ size = 4,
+ HasHalfPacket = 0,
+ HasAdd = 1,
+ HasSub = 1,
+ HasMul = 1,
+ HasDiv = 1,
+ HasNegate = 0,
+ HasAbs = 0,
+ HasAbs2 = 0,
+ HasMin = 0,
+ HasMax = 0,
+ HasConj = 0,
+ HasSetLinear = 0,
+ HasSqrt = 0,
+ HasRsqrt = 0,
+ HasExp = 0,
+ HasLog = 0,
+ HasBlend = 0
+ };
+};
+
+
+template<> struct unpacket_traits<Packet4h> { typedef Eigen::half type; enum {size=4, alignment=Aligned16, vectorizable=true, masked_load_available=false, masked_store_available=false}; typedef Packet4h half; };
+
+template<> EIGEN_STRONG_INLINE Packet4h pset1<Packet4h>(const Eigen::half& from) {
+ Packet4h result;
+ result.x = _mm_set1_pi16(from.x);
+ return result;
+}
+
+template<> EIGEN_STRONG_INLINE Eigen::half pfirst<Packet4h>(const Packet4h& from) {
+ return half_impl::raw_uint16_to_half(static_cast<unsigned short>(_mm_cvtsi64_si32(from.x)));
+}
+
+template<> EIGEN_STRONG_INLINE Packet4h pconj(const Packet4h& a) { return a; }
+
+template<> EIGEN_STRONG_INLINE Packet4h padd<Packet4h>(const Packet4h& a, const Packet4h& b) {
+ __int64_t a64 = _mm_cvtm64_si64(a.x);
+ __int64_t b64 = _mm_cvtm64_si64(b.x);
+
+ Eigen::half h[4];
+
+ Eigen::half ha = half_impl::raw_uint16_to_half(static_cast<unsigned short>(a64));
+ Eigen::half hb = half_impl::raw_uint16_to_half(static_cast<unsigned short>(b64));
+ h[0] = ha + hb;
+ ha = half_impl::raw_uint16_to_half(static_cast<unsigned short>(a64 >> 16));
+ hb = half_impl::raw_uint16_to_half(static_cast<unsigned short>(b64 >> 16));
+ h[1] = ha + hb;
+ ha = half_impl::raw_uint16_to_half(static_cast<unsigned short>(a64 >> 32));
+ hb = half_impl::raw_uint16_to_half(static_cast<unsigned short>(b64 >> 32));
+ h[2] = ha + hb;
+ ha = half_impl::raw_uint16_to_half(static_cast<unsigned short>(a64 >> 48));
+ hb = half_impl::raw_uint16_to_half(static_cast<unsigned short>(b64 >> 48));
+ h[3] = ha + hb;
+ Packet4h result;
+ result.x = _mm_set_pi16(h[3].x, h[2].x, h[1].x, h[0].x);
+ return result;
+}
+
+template<> EIGEN_STRONG_INLINE Packet4h psub<Packet4h>(const Packet4h& a, const Packet4h& b) {
+ __int64_t a64 = _mm_cvtm64_si64(a.x);
+ __int64_t b64 = _mm_cvtm64_si64(b.x);
+
+ Eigen::half h[4];
+
+ Eigen::half ha = half_impl::raw_uint16_to_half(static_cast<unsigned short>(a64));
+ Eigen::half hb = half_impl::raw_uint16_to_half(static_cast<unsigned short>(b64));
+ h[0] = ha - hb;
+ ha = half_impl::raw_uint16_to_half(static_cast<unsigned short>(a64 >> 16));
+ hb = half_impl::raw_uint16_to_half(static_cast<unsigned short>(b64 >> 16));
+ h[1] = ha - hb;
+ ha = half_impl::raw_uint16_to_half(static_cast<unsigned short>(a64 >> 32));
+ hb = half_impl::raw_uint16_to_half(static_cast<unsigned short>(b64 >> 32));
+ h[2] = ha - hb;
+ ha = half_impl::raw_uint16_to_half(static_cast<unsigned short>(a64 >> 48));
+ hb = half_impl::raw_uint16_to_half(static_cast<unsigned short>(b64 >> 48));
+ h[3] = ha - hb;
+ Packet4h result;
+ result.x = _mm_set_pi16(h[3].x, h[2].x, h[1].x, h[0].x);
+ return result;
+}
+
+template<> EIGEN_STRONG_INLINE Packet4h pmul<Packet4h>(const Packet4h& a, const Packet4h& b) {
+ __int64_t a64 = _mm_cvtm64_si64(a.x);
+ __int64_t b64 = _mm_cvtm64_si64(b.x);
+
+ Eigen::half h[4];
+
+ Eigen::half ha = half_impl::raw_uint16_to_half(static_cast<unsigned short>(a64));
+ Eigen::half hb = half_impl::raw_uint16_to_half(static_cast<unsigned short>(b64));
+ h[0] = ha * hb;
+ ha = half_impl::raw_uint16_to_half(static_cast<unsigned short>(a64 >> 16));
+ hb = half_impl::raw_uint16_to_half(static_cast<unsigned short>(b64 >> 16));
+ h[1] = ha * hb;
+ ha = half_impl::raw_uint16_to_half(static_cast<unsigned short>(a64 >> 32));
+ hb = half_impl::raw_uint16_to_half(static_cast<unsigned short>(b64 >> 32));
+ h[2] = ha * hb;
+ ha = half_impl::raw_uint16_to_half(static_cast<unsigned short>(a64 >> 48));
+ hb = half_impl::raw_uint16_to_half(static_cast<unsigned short>(b64 >> 48));
+ h[3] = ha * hb;
+ Packet4h result;
+ result.x = _mm_set_pi16(h[3].x, h[2].x, h[1].x, h[0].x);
+ return result;
+}
+
+template<> EIGEN_STRONG_INLINE Packet4h pdiv<Packet4h>(const Packet4h& a, const Packet4h& b) {
+ __int64_t a64 = _mm_cvtm64_si64(a.x);
+ __int64_t b64 = _mm_cvtm64_si64(b.x);
+
+ Eigen::half h[4];
+
+ Eigen::half ha = half_impl::raw_uint16_to_half(static_cast<unsigned short>(a64));
+ Eigen::half hb = half_impl::raw_uint16_to_half(static_cast<unsigned short>(b64));
+ h[0] = ha / hb;
+ ha = half_impl::raw_uint16_to_half(static_cast<unsigned short>(a64 >> 16));
+ hb = half_impl::raw_uint16_to_half(static_cast<unsigned short>(b64 >> 16));
+ h[1] = ha / hb;
+ ha = half_impl::raw_uint16_to_half(static_cast<unsigned short>(a64 >> 32));
+ hb = half_impl::raw_uint16_to_half(static_cast<unsigned short>(b64 >> 32));
+ h[2] = ha / hb;
+ ha = half_impl::raw_uint16_to_half(static_cast<unsigned short>(a64 >> 48));
+ hb = half_impl::raw_uint16_to_half(static_cast<unsigned short>(b64 >> 48));
+ h[3] = ha / hb;
+ Packet4h result;
+ result.x = _mm_set_pi16(h[3].x, h[2].x, h[1].x, h[0].x);
+ return result;
+}
+
+template<> EIGEN_STRONG_INLINE Packet4h pload<Packet4h>(const Eigen::half* from) {
+ Packet4h result;
+ result.x = _mm_cvtsi64_m64(*reinterpret_cast<const __int64_t*>(from));
+ return result;
+}
+
+template<> EIGEN_STRONG_INLINE Packet4h ploadu<Packet4h>(const Eigen::half* from) {
+ Packet4h result;
+ result.x = _mm_cvtsi64_m64(*reinterpret_cast<const __int64_t*>(from));
+ return result;
+}
+
+template<> EIGEN_STRONG_INLINE void pstore<Eigen::half>(Eigen::half* to, const Packet4h& from) {
+ __int64_t r = _mm_cvtm64_si64(from.x);
+ *(reinterpret_cast<__int64_t*>(to)) = r;
+}
+
+template<> EIGEN_STRONG_INLINE void pstoreu<Eigen::half>(Eigen::half* to, const Packet4h& from) {
+ __int64_t r = _mm_cvtm64_si64(from.x);
+ *(reinterpret_cast<__int64_t*>(to)) = r;
+}
+
+template<> EIGEN_STRONG_INLINE Packet4h
+ploadquad<Packet4h>(const Eigen::half* from) {
+ return pset1<Packet4h>(*from);
+}
+
+template<> EIGEN_STRONG_INLINE Packet4h pgather<Eigen::half, Packet4h>(const Eigen::half* from, Index stride)
+{
+ Packet4h result;
+ result.x = _mm_set_pi16(from[3*stride].x, from[2*stride].x, from[1*stride].x, from[0*stride].x);
+ return result;
+}
+
+template<> EIGEN_STRONG_INLINE void pscatter<Eigen::half, Packet4h>(Eigen::half* to, const Packet4h& from, Index stride)
+{
+ __int64_t a = _mm_cvtm64_si64(from.x);
+ to[stride*0].x = static_cast<unsigned short>(a);
+ to[stride*1].x = static_cast<unsigned short>(a >> 16);
+ to[stride*2].x = static_cast<unsigned short>(a >> 32);
+ to[stride*3].x = static_cast<unsigned short>(a >> 48);
+}
+
+EIGEN_STRONG_INLINE void
+ptranspose(PacketBlock<Packet4h,4>& kernel) {
+ __m64 T0 = _mm_unpacklo_pi16(kernel.packet[0].x, kernel.packet[1].x);
+ __m64 T1 = _mm_unpacklo_pi16(kernel.packet[2].x, kernel.packet[3].x);
+ __m64 T2 = _mm_unpackhi_pi16(kernel.packet[0].x, kernel.packet[1].x);
+ __m64 T3 = _mm_unpackhi_pi16(kernel.packet[2].x, kernel.packet[3].x);
+
+ kernel.packet[0].x = _mm_unpacklo_pi32(T0, T1);
+ kernel.packet[1].x = _mm_unpackhi_pi32(T0, T1);
+ kernel.packet[2].x = _mm_unpacklo_pi32(T2, T3);
+ kernel.packet[3].x = _mm_unpackhi_pi32(T2, T3);
+}
+
+#endif
+
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#if EIGEN_COMP_PGI && EIGEN_COMP_PGI < 1900
+// PGI++ does not define the following intrinsics in C++ mode.
+static inline __m128 _mm_castpd_ps (__m128d x) { return reinterpret_cast<__m128&>(x); }
+static inline __m128i _mm_castpd_si128(__m128d x) { return reinterpret_cast<__m128i&>(x); }
+static inline __m128d _mm_castps_pd (__m128 x) { return reinterpret_cast<__m128d&>(x); }
+static inline __m128i _mm_castps_si128(__m128 x) { return reinterpret_cast<__m128i&>(x); }
+static inline __m128 _mm_castsi128_ps(__m128i x) { return reinterpret_cast<__m128&>(x); }
+static inline __m128d _mm_castsi128_pd(__m128i x) { return reinterpret_cast<__m128d&>(x); }
+#endif
+
+#endif // EIGEN_PACKET_MATH_SSE_H
diff --git a/Eigen/src/Core/arch/SSE/TypeCasting.h b/Eigen/src/Core/arch/SSE/TypeCasting.h
new file mode 100644
index 0000000..a6346ea
--- /dev/null
+++ b/Eigen/src/Core/arch/SSE/TypeCasting.h
@@ -0,0 +1,152 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2015 Benoit Steiner <benoit.steiner.goog@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_TYPE_CASTING_SSE_H
+#define EIGEN_TYPE_CASTING_SSE_H
+
+#include "../../InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+
+#ifndef EIGEN_VECTORIZE_AVX
+template <>
+struct type_casting_traits<float, int> {
+ enum {
+ VectorizedCast = 1,
+ SrcCoeffRatio = 1,
+ TgtCoeffRatio = 1
+ };
+};
+
+template <>
+struct type_casting_traits<int, float> {
+ enum {
+ VectorizedCast = 1,
+ SrcCoeffRatio = 1,
+ TgtCoeffRatio = 1
+ };
+};
+
+template <>
+struct type_casting_traits<double, float> {
+ enum {
+ VectorizedCast = 1,
+ SrcCoeffRatio = 2,
+ TgtCoeffRatio = 1
+ };
+};
+
+template <>
+struct type_casting_traits<float, double> {
+ enum {
+ VectorizedCast = 1,
+ SrcCoeffRatio = 1,
+ TgtCoeffRatio = 2
+ };
+};
+#endif
+
+template<> EIGEN_STRONG_INLINE Packet4i pcast<Packet4f, Packet4i>(const Packet4f& a) {
+ return _mm_cvttps_epi32(a);
+}
+
+template<> EIGEN_STRONG_INLINE Packet4f pcast<Packet4i, Packet4f>(const Packet4i& a) {
+ return _mm_cvtepi32_ps(a);
+}
+
+template<> EIGEN_STRONG_INLINE Packet4f pcast<Packet2d, Packet4f>(const Packet2d& a, const Packet2d& b) {
+ return _mm_shuffle_ps(_mm_cvtpd_ps(a), _mm_cvtpd_ps(b), (1 << 2) | (1 << 6));
+}
+
+template<> EIGEN_STRONG_INLINE Packet2d pcast<Packet4f, Packet2d>(const Packet4f& a) {
+ // Simply discard the second half of the input
+ return _mm_cvtps_pd(a);
+}
+
+template<> EIGEN_STRONG_INLINE Packet2d preinterpret<Packet2d, Packet4f>(const Packet4f& a) {
+ return _mm_castps_pd(a);
+}
+
+template<> EIGEN_STRONG_INLINE Packet4f preinterpret<Packet4f, Packet2d>(const Packet2d& a) {
+ return _mm_castpd_ps(a);
+}
+
+template<> EIGEN_STRONG_INLINE Packet4i preinterpret<Packet4i,Packet4f>(const Packet4f& a) {
+ return _mm_castps_si128(a);
+}
+
+template<> EIGEN_STRONG_INLINE Packet4f preinterpret<Packet4f,Packet4i>(const Packet4i& a) {
+ return _mm_castsi128_ps(a);
+}
+
+template<> EIGEN_STRONG_INLINE Packet2d preinterpret<Packet2d,Packet4i>(const Packet4i& a) {
+ return _mm_castsi128_pd(a);
+}
+
+template<> EIGEN_STRONG_INLINE Packet4i preinterpret<Packet4i,Packet2d>(const Packet2d& a) {
+ return _mm_castpd_si128(a);
+}
+
+// Disable the following code since it's broken on too many platforms / compilers.
+//#elif defined(EIGEN_VECTORIZE_SSE) && (!EIGEN_ARCH_x86_64) && (!EIGEN_COMP_MSVC)
+#if 0
+
+template <>
+struct type_casting_traits<Eigen::half, float> {
+ enum {
+ VectorizedCast = 1,
+ SrcCoeffRatio = 1,
+ TgtCoeffRatio = 1
+ };
+};
+
+template<> EIGEN_STRONG_INLINE Packet4f pcast<Packet4h, Packet4f>(const Packet4h& a) {
+ __int64_t a64 = _mm_cvtm64_si64(a.x);
+ Eigen::half h = raw_uint16_to_half(static_cast<unsigned short>(a64));
+ float f1 = static_cast<float>(h);
+ h = raw_uint16_to_half(static_cast<unsigned short>(a64 >> 16));
+ float f2 = static_cast<float>(h);
+ h = raw_uint16_to_half(static_cast<unsigned short>(a64 >> 32));
+ float f3 = static_cast<float>(h);
+ h = raw_uint16_to_half(static_cast<unsigned short>(a64 >> 48));
+ float f4 = static_cast<float>(h);
+ return _mm_set_ps(f4, f3, f2, f1);
+}
+
+template <>
+struct type_casting_traits<float, Eigen::half> {
+ enum {
+ VectorizedCast = 1,
+ SrcCoeffRatio = 1,
+ TgtCoeffRatio = 1
+ };
+};
+
+template<> EIGEN_STRONG_INLINE Packet4h pcast<Packet4f, Packet4h>(const Packet4f& a) {
+ EIGEN_ALIGN16 float aux[4];
+ pstore(aux, a);
+ Eigen::half h0(aux[0]);
+ Eigen::half h1(aux[1]);
+ Eigen::half h2(aux[2]);
+ Eigen::half h3(aux[3]);
+
+ Packet4h result;
+ result.x = _mm_set_pi16(h3.x, h2.x, h1.x, h0.x);
+ return result;
+}
+
+#endif
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_TYPE_CASTING_SSE_H
diff --git a/Eigen/src/Core/arch/SVE/MathFunctions.h b/Eigen/src/Core/arch/SVE/MathFunctions.h
new file mode 100644
index 0000000..8b588b1
--- /dev/null
+++ b/Eigen/src/Core/arch/SVE/MathFunctions.h
@@ -0,0 +1,46 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2020, Arm Limited and Contributors
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_MATH_FUNCTIONS_SVE_H
+#define EIGEN_MATH_FUNCTIONS_SVE_H
+
+#include "../../InternalHeaderCheck.h"
+
+namespace Eigen {
+namespace internal {
+
+template <>
+EIGEN_STRONG_INLINE PacketXf pexp<PacketXf>(const PacketXf& x) {
+ return pexp_float(x);
+}
+
+template <>
+EIGEN_STRONG_INLINE PacketXf plog<PacketXf>(const PacketXf& x) {
+ return plog_float(x);
+}
+
+template <>
+EIGEN_STRONG_INLINE PacketXf psin<PacketXf>(const PacketXf& x) {
+ return psin_float(x);
+}
+
+template <>
+EIGEN_STRONG_INLINE PacketXf pcos<PacketXf>(const PacketXf& x) {
+ return pcos_float(x);
+}
+
+// Hyperbolic Tangent function.
+template <>
+EIGEN_STRONG_INLINE PacketXf ptanh<PacketXf>(const PacketXf& x) {
+ return internal::generic_fast_tanh_float(x);
+}
+} // end namespace internal
+} // end namespace Eigen
+
+#endif // EIGEN_MATH_FUNCTIONS_SVE_H
diff --git a/Eigen/src/Core/arch/SVE/PacketMath.h b/Eigen/src/Core/arch/SVE/PacketMath.h
new file mode 100644
index 0000000..9c106b3
--- /dev/null
+++ b/Eigen/src/Core/arch/SVE/PacketMath.h
@@ -0,0 +1,754 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2020, Arm Limited and Contributors
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_PACKET_MATH_SVE_H
+#define EIGEN_PACKET_MATH_SVE_H
+
+#include "../../InternalHeaderCheck.h"
+
+namespace Eigen
+{
+namespace internal
+{
+#ifndef EIGEN_CACHEFRIENDLY_PRODUCT_THRESHOLD
+#define EIGEN_CACHEFRIENDLY_PRODUCT_THRESHOLD 8
+#endif
+
+#ifndef EIGEN_HAS_SINGLE_INSTRUCTION_MADD
+#define EIGEN_HAS_SINGLE_INSTRUCTION_MADD
+#endif
+
+#define EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS 32
+
+template <typename Scalar, int SVEVectorLength>
+struct sve_packet_size_selector {
+ enum { size = SVEVectorLength / (sizeof(Scalar) * CHAR_BIT) };
+};
+
+/********************************* int32 **************************************/
+typedef svint32_t PacketXi __attribute__((arm_sve_vector_bits(EIGEN_ARM64_SVE_VL)));
+
+template <>
+struct packet_traits<numext::int32_t> : default_packet_traits {
+ typedef PacketXi type;
+ typedef PacketXi half; // Half not implemented yet
+ enum {
+ Vectorizable = 1,
+ AlignedOnScalar = 1,
+ size = sve_packet_size_selector<numext::int32_t, EIGEN_ARM64_SVE_VL>::size,
+ HasHalfPacket = 0,
+
+ HasAdd = 1,
+ HasSub = 1,
+ HasShift = 1,
+ HasMul = 1,
+ HasNegate = 1,
+ HasAbs = 1,
+ HasArg = 0,
+ HasAbs2 = 1,
+ HasMin = 1,
+ HasMax = 1,
+ HasConj = 1,
+ HasSetLinear = 0,
+ HasBlend = 0,
+ HasReduxp = 0 // Not implemented in SVE
+ };
+};
+
+template <>
+struct unpacket_traits<PacketXi> {
+ typedef numext::int32_t type;
+ typedef PacketXi half; // Half not yet implemented
+ enum {
+ size = sve_packet_size_selector<numext::int32_t, EIGEN_ARM64_SVE_VL>::size,
+ alignment = Aligned64,
+ vectorizable = true,
+ masked_load_available = false,
+ masked_store_available = false
+ };
+};
+
+template <>
+EIGEN_STRONG_INLINE void prefetch<numext::int32_t>(const numext::int32_t* addr)
+{
+ svprfw(svptrue_b32(), addr, SV_PLDL1KEEP);
+}
+
+template <>
+EIGEN_STRONG_INLINE PacketXi pset1<PacketXi>(const numext::int32_t& from)
+{
+ return svdup_n_s32(from);
+}
+
+template <>
+EIGEN_STRONG_INLINE PacketXi plset<PacketXi>(const numext::int32_t& a)
+{
+ numext::int32_t c[packet_traits<numext::int32_t>::size];
+ for (int i = 0; i < packet_traits<numext::int32_t>::size; i++) c[i] = i;
+ return svadd_s32_z(svptrue_b32(), pset1<PacketXi>(a), svld1_s32(svptrue_b32(), c));
+}
+
+template <>
+EIGEN_STRONG_INLINE PacketXi padd<PacketXi>(const PacketXi& a, const PacketXi& b)
+{
+ return svadd_s32_z(svptrue_b32(), a, b);
+}
+
+template <>
+EIGEN_STRONG_INLINE PacketXi psub<PacketXi>(const PacketXi& a, const PacketXi& b)
+{
+ return svsub_s32_z(svptrue_b32(), a, b);
+}
+
+template <>
+EIGEN_STRONG_INLINE PacketXi pnegate(const PacketXi& a)
+{
+ return svneg_s32_z(svptrue_b32(), a);
+}
+
+template <>
+EIGEN_STRONG_INLINE PacketXi pconj(const PacketXi& a)
+{
+ return a;
+}
+
+template <>
+EIGEN_STRONG_INLINE PacketXi pmul<PacketXi>(const PacketXi& a, const PacketXi& b)
+{
+ return svmul_s32_z(svptrue_b32(), a, b);
+}
+
+template <>
+EIGEN_STRONG_INLINE PacketXi pdiv<PacketXi>(const PacketXi& a, const PacketXi& b)
+{
+ return svdiv_s32_z(svptrue_b32(), a, b);
+}
+
+template <>
+EIGEN_STRONG_INLINE PacketXi pmadd(const PacketXi& a, const PacketXi& b, const PacketXi& c)
+{
+ return svmla_s32_z(svptrue_b32(), c, a, b);
+}
+
+template <>
+EIGEN_STRONG_INLINE PacketXi pmin<PacketXi>(const PacketXi& a, const PacketXi& b)
+{
+ return svmin_s32_z(svptrue_b32(), a, b);
+}
+
+template <>
+EIGEN_STRONG_INLINE PacketXi pmax<PacketXi>(const PacketXi& a, const PacketXi& b)
+{
+ return svmax_s32_z(svptrue_b32(), a, b);
+}
+
+template <>
+EIGEN_STRONG_INLINE PacketXi pcmp_le<PacketXi>(const PacketXi& a, const PacketXi& b)
+{
+ return svdup_n_s32_z(svcmple_s32(svptrue_b32(), a, b), 0xffffffffu);
+}
+
+template <>
+EIGEN_STRONG_INLINE PacketXi pcmp_lt<PacketXi>(const PacketXi& a, const PacketXi& b)
+{
+ return svdup_n_s32_z(svcmplt_s32(svptrue_b32(), a, b), 0xffffffffu);
+}
+
+template <>
+EIGEN_STRONG_INLINE PacketXi pcmp_eq<PacketXi>(const PacketXi& a, const PacketXi& b)
+{
+ return svdup_n_s32_z(svcmpeq_s32(svptrue_b32(), a, b), 0xffffffffu);
+}
+
+template <>
+EIGEN_STRONG_INLINE PacketXi ptrue<PacketXi>(const PacketXi& /*a*/)
+{
+ return svdup_n_s32_z(svptrue_b32(), 0xffffffffu);
+}
+
+template <>
+EIGEN_STRONG_INLINE PacketXi pzero<PacketXi>(const PacketXi& /*a*/)
+{
+ return svdup_n_s32_z(svptrue_b32(), 0);
+}
+
+template <>
+EIGEN_STRONG_INLINE PacketXi pand<PacketXi>(const PacketXi& a, const PacketXi& b)
+{
+ return svand_s32_z(svptrue_b32(), a, b);
+}
+
+template <>
+EIGEN_STRONG_INLINE PacketXi por<PacketXi>(const PacketXi& a, const PacketXi& b)
+{
+ return svorr_s32_z(svptrue_b32(), a, b);
+}
+
+template <>
+EIGEN_STRONG_INLINE PacketXi pxor<PacketXi>(const PacketXi& a, const PacketXi& b)
+{
+ return sveor_s32_z(svptrue_b32(), a, b);
+}
+
+template <>
+EIGEN_STRONG_INLINE PacketXi pandnot<PacketXi>(const PacketXi& a, const PacketXi& b)
+{
+ return svbic_s32_z(svptrue_b32(), a, b);
+}
+
+template <int N>
+EIGEN_STRONG_INLINE PacketXi parithmetic_shift_right(PacketXi a)
+{
+ return svasrd_n_s32_z(svptrue_b32(), a, N);
+}
+
+template <int N>
+EIGEN_STRONG_INLINE PacketXi plogical_shift_right(PacketXi a)
+{
+ return svreinterpret_s32_u32(svlsr_n_u32_z(svptrue_b32(), svreinterpret_u32_s32(a), N));
+}
+
+template <int N>
+EIGEN_STRONG_INLINE PacketXi plogical_shift_left(PacketXi a)
+{
+ return svlsl_n_s32_z(svptrue_b32(), a, N);
+}
+
+template <>
+EIGEN_STRONG_INLINE PacketXi pload<PacketXi>(const numext::int32_t* from)
+{
+ EIGEN_DEBUG_ALIGNED_LOAD return svld1_s32(svptrue_b32(), from);
+}
+
+template <>
+EIGEN_STRONG_INLINE PacketXi ploadu<PacketXi>(const numext::int32_t* from)
+{
+ EIGEN_DEBUG_UNALIGNED_LOAD return svld1_s32(svptrue_b32(), from);
+}
+
+template <>
+EIGEN_STRONG_INLINE PacketXi ploaddup<PacketXi>(const numext::int32_t* from)
+{
+ svuint32_t indices = svindex_u32(0, 1); // index {base=0, base+step=1, base+step*2, ...}
+ indices = svzip1_u32(indices, indices); // index in the format {a0, a0, a1, a1, a2, a2, ...}
+ return svld1_gather_u32index_s32(svptrue_b32(), from, indices);
+}
+
+template <>
+EIGEN_STRONG_INLINE PacketXi ploadquad<PacketXi>(const numext::int32_t* from)
+{
+ svuint32_t indices = svindex_u32(0, 1); // index {base=0, base+step=1, base+step*2, ...}
+ indices = svzip1_u32(indices, indices); // index in the format {a0, a0, a1, a1, a2, a2, ...}
+ indices = svzip1_u32(indices, indices); // index in the format {a0, a0, a0, a0, a1, a1, a1, a1, ...}
+ return svld1_gather_u32index_s32(svptrue_b32(), from, indices);
+}
+
+template <>
+EIGEN_STRONG_INLINE void pstore<numext::int32_t>(numext::int32_t* to, const PacketXi& from)
+{
+ EIGEN_DEBUG_ALIGNED_STORE svst1_s32(svptrue_b32(), to, from);
+}
+
+template <>
+EIGEN_STRONG_INLINE void pstoreu<numext::int32_t>(numext::int32_t* to, const PacketXi& from)
+{
+ EIGEN_DEBUG_UNALIGNED_STORE svst1_s32(svptrue_b32(), to, from);
+}
+
+template <>
+EIGEN_DEVICE_FUNC inline PacketXi pgather<numext::int32_t, PacketXi>(const numext::int32_t* from, Index stride)
+{
+ // Indice format: {base=0, base+stride, base+stride*2, base+stride*3, ...}
+ svint32_t indices = svindex_s32(0, stride);
+ return svld1_gather_s32index_s32(svptrue_b32(), from, indices);
+}
+
+template <>
+EIGEN_DEVICE_FUNC inline void pscatter<numext::int32_t, PacketXi>(numext::int32_t* to, const PacketXi& from, Index stride)
+{
+ // Indice format: {base=0, base+stride, base+stride*2, base+stride*3, ...}
+ svint32_t indices = svindex_s32(0, stride);
+ svst1_scatter_s32index_s32(svptrue_b32(), to, indices, from);
+}
+
+template <>
+EIGEN_STRONG_INLINE numext::int32_t pfirst<PacketXi>(const PacketXi& a)
+{
+ // svlasta returns the first element if all predicate bits are 0
+ return svlasta_s32(svpfalse_b(), a);
+}
+
+template <>
+EIGEN_STRONG_INLINE PacketXi preverse(const PacketXi& a)
+{
+ return svrev_s32(a);
+}
+
+template <>
+EIGEN_STRONG_INLINE PacketXi pabs(const PacketXi& a)
+{
+ return svabs_s32_z(svptrue_b32(), a);
+}
+
+template <>
+EIGEN_STRONG_INLINE numext::int32_t predux<PacketXi>(const PacketXi& a)
+{
+ return static_cast<numext::int32_t>(svaddv_s32(svptrue_b32(), a));
+}
+
+template <>
+EIGEN_STRONG_INLINE numext::int32_t predux_mul<PacketXi>(const PacketXi& a)
+{
+ EIGEN_STATIC_ASSERT((EIGEN_ARM64_SVE_VL % 128 == 0),
+ EIGEN_INTERNAL_ERROR_PLEASE_FILE_A_BUG_REPORT);
+
+ // Multiply the vector by its reverse
+ svint32_t prod = svmul_s32_z(svptrue_b32(), a, svrev_s32(a));
+ svint32_t half_prod;
+
+ // Extract the high half of the vector. Depending on the VL more reductions need to be done
+ if (EIGEN_ARM64_SVE_VL >= 2048) {
+ half_prod = svtbl_s32(prod, svindex_u32(32, 1));
+ prod = svmul_s32_z(svptrue_b32(), prod, half_prod);
+ }
+ if (EIGEN_ARM64_SVE_VL >= 1024) {
+ half_prod = svtbl_s32(prod, svindex_u32(16, 1));
+ prod = svmul_s32_z(svptrue_b32(), prod, half_prod);
+ }
+ if (EIGEN_ARM64_SVE_VL >= 512) {
+ half_prod = svtbl_s32(prod, svindex_u32(8, 1));
+ prod = svmul_s32_z(svptrue_b32(), prod, half_prod);
+ }
+ if (EIGEN_ARM64_SVE_VL >= 256) {
+ half_prod = svtbl_s32(prod, svindex_u32(4, 1));
+ prod = svmul_s32_z(svptrue_b32(), prod, half_prod);
+ }
+ // Last reduction
+ half_prod = svtbl_s32(prod, svindex_u32(2, 1));
+ prod = svmul_s32_z(svptrue_b32(), prod, half_prod);
+
+ // The reduction is done to the first element.
+ return pfirst<PacketXi>(prod);
+}
+
+template <>
+EIGEN_STRONG_INLINE numext::int32_t predux_min<PacketXi>(const PacketXi& a)
+{
+ return svminv_s32(svptrue_b32(), a);
+}
+
+template <>
+EIGEN_STRONG_INLINE numext::int32_t predux_max<PacketXi>(const PacketXi& a)
+{
+ return svmaxv_s32(svptrue_b32(), a);
+}
+
+template <int N>
+EIGEN_DEVICE_FUNC inline void ptranspose(PacketBlock<PacketXi, N>& kernel) {
+ int buffer[packet_traits<numext::int32_t>::size * N] = {0};
+ int i = 0;
+
+ PacketXi stride_index = svindex_s32(0, N);
+
+ for (i = 0; i < N; i++) {
+ svst1_scatter_s32index_s32(svptrue_b32(), buffer + i, stride_index, kernel.packet[i]);
+ }
+ for (i = 0; i < N; i++) {
+ kernel.packet[i] = svld1_s32(svptrue_b32(), buffer + i * packet_traits<numext::int32_t>::size);
+ }
+}
+
+/********************************* float32 ************************************/
+
+typedef svfloat32_t PacketXf __attribute__((arm_sve_vector_bits(EIGEN_ARM64_SVE_VL)));
+
+template <>
+struct packet_traits<float> : default_packet_traits {
+ typedef PacketXf type;
+ typedef PacketXf half;
+
+ enum {
+ Vectorizable = 1,
+ AlignedOnScalar = 1,
+ size = sve_packet_size_selector<float, EIGEN_ARM64_SVE_VL>::size,
+ HasHalfPacket = 0,
+
+ HasAdd = 1,
+ HasSub = 1,
+ HasShift = 1,
+ HasMul = 1,
+ HasNegate = 1,
+ HasAbs = 1,
+ HasArg = 0,
+ HasAbs2 = 1,
+ HasMin = 1,
+ HasMax = 1,
+ HasConj = 1,
+ HasSetLinear = 0,
+ HasBlend = 0,
+ HasReduxp = 0, // Not implemented in SVE
+
+ HasDiv = 1,
+ HasFloor = 1,
+
+ HasSin = EIGEN_FAST_MATH,
+ HasCos = EIGEN_FAST_MATH,
+ HasLog = 1,
+ HasExp = 1,
+ HasSqrt = 0,
+ HasTanh = EIGEN_FAST_MATH,
+ HasErf = EIGEN_FAST_MATH
+ };
+};
+
+template <>
+struct unpacket_traits<PacketXf> {
+ typedef float type;
+ typedef PacketXf half; // Half not yet implemented
+ typedef PacketXi integer_packet;
+
+ enum {
+ size = sve_packet_size_selector<float, EIGEN_ARM64_SVE_VL>::size,
+ alignment = Aligned64,
+ vectorizable = true,
+ masked_load_available = false,
+ masked_store_available = false
+ };
+};
+
+template <>
+EIGEN_STRONG_INLINE PacketXf pset1<PacketXf>(const float& from)
+{
+ return svdup_n_f32(from);
+}
+
+template <>
+EIGEN_STRONG_INLINE PacketXf pset1frombits<PacketXf>(numext::uint32_t from)
+{
+ return svreinterpret_f32_u32(svdup_n_u32_z(svptrue_b32(), from));
+}
+
+template <>
+EIGEN_STRONG_INLINE PacketXf plset<PacketXf>(const float& a)
+{
+ float c[packet_traits<float>::size];
+ for (int i = 0; i < packet_traits<float>::size; i++) c[i] = i;
+ return svadd_f32_z(svptrue_b32(), pset1<PacketXf>(a), svld1_f32(svptrue_b32(), c));
+}
+
+template <>
+EIGEN_STRONG_INLINE PacketXf padd<PacketXf>(const PacketXf& a, const PacketXf& b)
+{
+ return svadd_f32_z(svptrue_b32(), a, b);
+}
+
+template <>
+EIGEN_STRONG_INLINE PacketXf psub<PacketXf>(const PacketXf& a, const PacketXf& b)
+{
+ return svsub_f32_z(svptrue_b32(), a, b);
+}
+
+template <>
+EIGEN_STRONG_INLINE PacketXf pnegate(const PacketXf& a)
+{
+ return svneg_f32_z(svptrue_b32(), a);
+}
+
+template <>
+EIGEN_STRONG_INLINE PacketXf pconj(const PacketXf& a)
+{
+ return a;
+}
+
+template <>
+EIGEN_STRONG_INLINE PacketXf pmul<PacketXf>(const PacketXf& a, const PacketXf& b)
+{
+ return svmul_f32_z(svptrue_b32(), a, b);
+}
+
+template <>
+EIGEN_STRONG_INLINE PacketXf pdiv<PacketXf>(const PacketXf& a, const PacketXf& b)
+{
+ return svdiv_f32_z(svptrue_b32(), a, b);
+}
+
+template <>
+EIGEN_STRONG_INLINE PacketXf pmadd(const PacketXf& a, const PacketXf& b, const PacketXf& c)
+{
+ return svmla_f32_z(svptrue_b32(), c, a, b);
+}
+
+template <>
+EIGEN_STRONG_INLINE PacketXf pmin<PacketXf>(const PacketXf& a, const PacketXf& b)
+{
+ return svmin_f32_z(svptrue_b32(), a, b);
+}
+
+template <>
+EIGEN_STRONG_INLINE PacketXf pmin<PropagateNaN, PacketXf>(const PacketXf& a, const PacketXf& b)
+{
+ return pmin<PacketXf>(a, b);
+}
+
+template <>
+EIGEN_STRONG_INLINE PacketXf pmin<PropagateNumbers, PacketXf>(const PacketXf& a, const PacketXf& b)
+{
+ return svminnm_f32_z(svptrue_b32(), a, b);
+}
+
+template <>
+EIGEN_STRONG_INLINE PacketXf pmax<PacketXf>(const PacketXf& a, const PacketXf& b)
+{
+ return svmax_f32_z(svptrue_b32(), a, b);
+}
+
+template <>
+EIGEN_STRONG_INLINE PacketXf pmax<PropagateNaN, PacketXf>(const PacketXf& a, const PacketXf& b)
+{
+ return pmax<PacketXf>(a, b);
+}
+
+template <>
+EIGEN_STRONG_INLINE PacketXf pmax<PropagateNumbers, PacketXf>(const PacketXf& a, const PacketXf& b)
+{
+ return svmaxnm_f32_z(svptrue_b32(), a, b);
+}
+
+// Float comparisons in SVE return svbool (predicate). Use svdup to set active
+// lanes to 1 (0xffffffffu) and inactive lanes to 0.
+template <>
+EIGEN_STRONG_INLINE PacketXf pcmp_le<PacketXf>(const PacketXf& a, const PacketXf& b)
+{
+ return svreinterpret_f32_u32(svdup_n_u32_z(svcmple_f32(svptrue_b32(), a, b), 0xffffffffu));
+}
+
+template <>
+EIGEN_STRONG_INLINE PacketXf pcmp_lt<PacketXf>(const PacketXf& a, const PacketXf& b)
+{
+ return svreinterpret_f32_u32(svdup_n_u32_z(svcmplt_f32(svptrue_b32(), a, b), 0xffffffffu));
+}
+
+template <>
+EIGEN_STRONG_INLINE PacketXf pcmp_eq<PacketXf>(const PacketXf& a, const PacketXf& b)
+{
+ return svreinterpret_f32_u32(svdup_n_u32_z(svcmpeq_f32(svptrue_b32(), a, b), 0xffffffffu));
+}
+
+// Do a predicate inverse (svnot_b_z) on the predicate resulted from the
+// greater/equal comparison (svcmpge_f32). Then fill a float vector with the
+// active elements.
+template <>
+EIGEN_STRONG_INLINE PacketXf pcmp_lt_or_nan<PacketXf>(const PacketXf& a, const PacketXf& b)
+{
+ return svreinterpret_f32_u32(svdup_n_u32_z(svnot_b_z(svptrue_b32(), svcmpge_f32(svptrue_b32(), a, b)), 0xffffffffu));
+}
+
+template <>
+EIGEN_STRONG_INLINE PacketXf pfloor<PacketXf>(const PacketXf& a)
+{
+ return svrintm_f32_z(svptrue_b32(), a);
+}
+
+template <>
+EIGEN_STRONG_INLINE PacketXf ptrue<PacketXf>(const PacketXf& /*a*/)
+{
+ return svreinterpret_f32_u32(svdup_n_u32_z(svptrue_b32(), 0xffffffffu));
+}
+
+// Logical Operations are not supported for float, so reinterpret casts
+template <>
+EIGEN_STRONG_INLINE PacketXf pand<PacketXf>(const PacketXf& a, const PacketXf& b)
+{
+ return svreinterpret_f32_u32(svand_u32_z(svptrue_b32(), svreinterpret_u32_f32(a), svreinterpret_u32_f32(b)));
+}
+
+template <>
+EIGEN_STRONG_INLINE PacketXf por<PacketXf>(const PacketXf& a, const PacketXf& b)
+{
+ return svreinterpret_f32_u32(svorr_u32_z(svptrue_b32(), svreinterpret_u32_f32(a), svreinterpret_u32_f32(b)));
+}
+
+template <>
+EIGEN_STRONG_INLINE PacketXf pxor<PacketXf>(const PacketXf& a, const PacketXf& b)
+{
+ return svreinterpret_f32_u32(sveor_u32_z(svptrue_b32(), svreinterpret_u32_f32(a), svreinterpret_u32_f32(b)));
+}
+
+template <>
+EIGEN_STRONG_INLINE PacketXf pandnot<PacketXf>(const PacketXf& a, const PacketXf& b)
+{
+ return svreinterpret_f32_u32(svbic_u32_z(svptrue_b32(), svreinterpret_u32_f32(a), svreinterpret_u32_f32(b)));
+}
+
+template <>
+EIGEN_STRONG_INLINE PacketXf pload<PacketXf>(const float* from)
+{
+ EIGEN_DEBUG_ALIGNED_LOAD return svld1_f32(svptrue_b32(), from);
+}
+
+template <>
+EIGEN_STRONG_INLINE PacketXf ploadu<PacketXf>(const float* from)
+{
+ EIGEN_DEBUG_UNALIGNED_LOAD return svld1_f32(svptrue_b32(), from);
+}
+
+template <>
+EIGEN_STRONG_INLINE PacketXf ploaddup<PacketXf>(const float* from)
+{
+ svuint32_t indices = svindex_u32(0, 1); // index {base=0, base+step=1, base+step*2, ...}
+ indices = svzip1_u32(indices, indices); // index in the format {a0, a0, a1, a1, a2, a2, ...}
+ return svld1_gather_u32index_f32(svptrue_b32(), from, indices);
+}
+
+template <>
+EIGEN_STRONG_INLINE PacketXf ploadquad<PacketXf>(const float* from)
+{
+ svuint32_t indices = svindex_u32(0, 1); // index {base=0, base+step=1, base+step*2, ...}
+ indices = svzip1_u32(indices, indices); // index in the format {a0, a0, a1, a1, a2, a2, ...}
+ indices = svzip1_u32(indices, indices); // index in the format {a0, a0, a0, a0, a1, a1, a1, a1, ...}
+ return svld1_gather_u32index_f32(svptrue_b32(), from, indices);
+}
+
+template <>
+EIGEN_STRONG_INLINE void pstore<float>(float* to, const PacketXf& from)
+{
+ EIGEN_DEBUG_ALIGNED_STORE svst1_f32(svptrue_b32(), to, from);
+}
+
+template <>
+EIGEN_STRONG_INLINE void pstoreu<float>(float* to, const PacketXf& from)
+{
+ EIGEN_DEBUG_UNALIGNED_STORE svst1_f32(svptrue_b32(), to, from);
+}
+
+template <>
+EIGEN_DEVICE_FUNC inline PacketXf pgather<float, PacketXf>(const float* from, Index stride)
+{
+ // Indice format: {base=0, base+stride, base+stride*2, base+stride*3, ...}
+ svint32_t indices = svindex_s32(0, stride);
+ return svld1_gather_s32index_f32(svptrue_b32(), from, indices);
+}
+
+template <>
+EIGEN_DEVICE_FUNC inline void pscatter<float, PacketXf>(float* to, const PacketXf& from, Index stride)
+{
+ // Indice format: {base=0, base+stride, base+stride*2, base+stride*3, ...}
+ svint32_t indices = svindex_s32(0, stride);
+ svst1_scatter_s32index_f32(svptrue_b32(), to, indices, from);
+}
+
+template <>
+EIGEN_STRONG_INLINE float pfirst<PacketXf>(const PacketXf& a)
+{
+ // svlasta returns the first element if all predicate bits are 0
+ return svlasta_f32(svpfalse_b(), a);
+}
+
+template <>
+EIGEN_STRONG_INLINE PacketXf preverse(const PacketXf& a)
+{
+ return svrev_f32(a);
+}
+
+template <>
+EIGEN_STRONG_INLINE PacketXf pabs(const PacketXf& a)
+{
+ return svabs_f32_z(svptrue_b32(), a);
+}
+
+// TODO(tellenbach): Should this go into MathFunctions.h? If so, change for
+// all vector extensions and the generic version.
+template <>
+EIGEN_STRONG_INLINE PacketXf pfrexp<PacketXf>(const PacketXf& a, PacketXf& exponent)
+{
+ return pfrexp_generic(a, exponent);
+}
+
+template <>
+EIGEN_STRONG_INLINE float predux<PacketXf>(const PacketXf& a)
+{
+ return svaddv_f32(svptrue_b32(), a);
+}
+
+// Other reduction functions:
+// mul
+// Only works for SVE Vls multiple of 128
+template <>
+EIGEN_STRONG_INLINE float predux_mul<PacketXf>(const PacketXf& a)
+{
+ EIGEN_STATIC_ASSERT((EIGEN_ARM64_SVE_VL % 128 == 0),
+ EIGEN_INTERNAL_ERROR_PLEASE_FILE_A_BUG_REPORT);
+ // Multiply the vector by its reverse
+ svfloat32_t prod = svmul_f32_z(svptrue_b32(), a, svrev_f32(a));
+ svfloat32_t half_prod;
+
+ // Extract the high half of the vector. Depending on the VL more reductions need to be done
+ if (EIGEN_ARM64_SVE_VL >= 2048) {
+ half_prod = svtbl_f32(prod, svindex_u32(32, 1));
+ prod = svmul_f32_z(svptrue_b32(), prod, half_prod);
+ }
+ if (EIGEN_ARM64_SVE_VL >= 1024) {
+ half_prod = svtbl_f32(prod, svindex_u32(16, 1));
+ prod = svmul_f32_z(svptrue_b32(), prod, half_prod);
+ }
+ if (EIGEN_ARM64_SVE_VL >= 512) {
+ half_prod = svtbl_f32(prod, svindex_u32(8, 1));
+ prod = svmul_f32_z(svptrue_b32(), prod, half_prod);
+ }
+ if (EIGEN_ARM64_SVE_VL >= 256) {
+ half_prod = svtbl_f32(prod, svindex_u32(4, 1));
+ prod = svmul_f32_z(svptrue_b32(), prod, half_prod);
+ }
+ // Last reduction
+ half_prod = svtbl_f32(prod, svindex_u32(2, 1));
+ prod = svmul_f32_z(svptrue_b32(), prod, half_prod);
+
+ // The reduction is done to the first element.
+ return pfirst<PacketXf>(prod);
+}
+
+template <>
+EIGEN_STRONG_INLINE float predux_min<PacketXf>(const PacketXf& a)
+{
+ return svminv_f32(svptrue_b32(), a);
+}
+
+template <>
+EIGEN_STRONG_INLINE float predux_max<PacketXf>(const PacketXf& a)
+{
+ return svmaxv_f32(svptrue_b32(), a);
+}
+
+template<int N>
+EIGEN_DEVICE_FUNC inline void ptranspose(PacketBlock<PacketXf, N>& kernel)
+{
+ float buffer[packet_traits<float>::size * N] = {0};
+ int i = 0;
+
+ PacketXi stride_index = svindex_s32(0, N);
+
+ for (i = 0; i < N; i++) {
+ svst1_scatter_s32index_f32(svptrue_b32(), buffer + i, stride_index, kernel.packet[i]);
+ }
+
+ for (i = 0; i < N; i++) {
+ kernel.packet[i] = svld1_f32(svptrue_b32(), buffer + i * packet_traits<float>::size);
+ }
+}
+
+template<>
+EIGEN_STRONG_INLINE PacketXf pldexp<PacketXf>(const PacketXf& a, const PacketXf& exponent)
+{
+ return pldexp_generic(a, exponent);
+}
+
+} // namespace internal
+} // namespace Eigen
+
+#endif // EIGEN_PACKET_MATH_SVE_H
diff --git a/Eigen/src/Core/arch/SVE/TypeCasting.h b/Eigen/src/Core/arch/SVE/TypeCasting.h
new file mode 100644
index 0000000..1067a41
--- /dev/null
+++ b/Eigen/src/Core/arch/SVE/TypeCasting.h
@@ -0,0 +1,51 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2020, Arm Limited and Contributors
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_TYPE_CASTING_SVE_H
+#define EIGEN_TYPE_CASTING_SVE_H
+
+#include "../../InternalHeaderCheck.h"
+
+namespace Eigen {
+namespace internal {
+
+template <>
+struct type_casting_traits<float, numext::int32_t> {
+ enum { VectorizedCast = 1, SrcCoeffRatio = 1, TgtCoeffRatio = 1 };
+};
+
+template <>
+struct type_casting_traits<numext::int32_t, float> {
+ enum { VectorizedCast = 1, SrcCoeffRatio = 1, TgtCoeffRatio = 1 };
+};
+
+template <>
+EIGEN_STRONG_INLINE PacketXf pcast<PacketXi, PacketXf>(const PacketXi& a) {
+ return svcvt_f32_s32_z(svptrue_b32(), a);
+}
+
+template <>
+EIGEN_STRONG_INLINE PacketXi pcast<PacketXf, PacketXi>(const PacketXf& a) {
+ return svcvt_s32_f32_z(svptrue_b32(), a);
+}
+
+template <>
+EIGEN_STRONG_INLINE PacketXf preinterpret<PacketXf, PacketXi>(const PacketXi& a) {
+ return svreinterpret_f32_s32(a);
+}
+
+template <>
+EIGEN_STRONG_INLINE PacketXi preinterpret<PacketXi, PacketXf>(const PacketXf& a) {
+ return svreinterpret_s32_f32(a);
+}
+
+} // namespace internal
+} // namespace Eigen
+
+#endif // EIGEN_TYPE_CASTING_SVE_H
diff --git a/Eigen/src/Core/arch/SYCL/InteropHeaders.h b/Eigen/src/Core/arch/SYCL/InteropHeaders.h
new file mode 100644
index 0000000..57bfb69
--- /dev/null
+++ b/Eigen/src/Core/arch/SYCL/InteropHeaders.h
@@ -0,0 +1,234 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Mehdi Goli Codeplay Software Ltd.
+// Ralph Potter Codeplay Software Ltd.
+// Luke Iwanski Codeplay Software Ltd.
+// Contact: <eigen@codeplay.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+/*****************************************************************
+ * InteropHeaders.h
+ *
+ * \brief:
+ * InteropHeaders
+ *
+ *****************************************************************/
+
+#ifndef EIGEN_INTEROP_HEADERS_SYCL_H
+#define EIGEN_INTEROP_HEADERS_SYCL_H
+
+#include "../../InternalHeaderCheck.h"
+
+namespace Eigen {
+
+#if !defined(EIGEN_DONT_VECTORIZE_SYCL)
+
+namespace internal {
+
+template <int has_blend, int lengths>
+struct sycl_packet_traits : default_packet_traits {
+ enum {
+ Vectorizable = 1,
+ AlignedOnScalar = 1,
+ size = lengths,
+ HasHalfPacket = 0,
+ HasDiv = 1,
+ HasLog = 1,
+ HasExp = 1,
+ HasSqrt = 1,
+ HasRsqrt = 1,
+ HasSin = 1,
+ HasCos = 1,
+ HasTan = 1,
+ HasASin = 1,
+ HasACos = 1,
+ HasATan = 1,
+ HasSinh = 1,
+ HasCosh = 1,
+ HasTanh = 1,
+ HasLGamma = 0,
+ HasDiGamma = 0,
+ HasZeta = 0,
+ HasPolygamma = 0,
+ HasErf = 0,
+ HasErfc = 0,
+ HasNdtri = 0,
+ HasIGamma = 0,
+ HasIGammac = 0,
+ HasBetaInc = 0,
+ HasBlend = has_blend,
+ // This flag is used to indicate whether packet comparison is supported.
+ // pcmp_eq, pcmp_lt and pcmp_le should be defined for it to be true.
+ HasCmp = 1,
+ HasMax = 1,
+ HasMin = 1,
+ HasMul = 1,
+ HasAdd = 1,
+ HasFloor = 1,
+ HasRound = 1,
+ HasRint = 1,
+ HasLog1p = 1,
+ HasExpm1 = 1,
+ HasCeil = 1,
+ };
+};
+
+#ifdef SYCL_DEVICE_ONLY
+#define SYCL_PACKET_TRAITS(packet_type, has_blend, unpacket_type, lengths) \
+ template <> \
+ struct packet_traits<unpacket_type> \
+ : sycl_packet_traits<has_blend, lengths> { \
+ typedef packet_type type; \
+ typedef packet_type half; \
+ };
+
+SYCL_PACKET_TRAITS(cl::sycl::cl_float4, 1, float, 4)
+SYCL_PACKET_TRAITS(cl::sycl::cl_float4, 1, const float, 4)
+SYCL_PACKET_TRAITS(cl::sycl::cl_double2, 0, double, 2)
+SYCL_PACKET_TRAITS(cl::sycl::cl_double2, 0, const double, 2)
+#undef SYCL_PACKET_TRAITS
+
+// Make sure this is only available when targeting a GPU: we don't want to
+// introduce conflicts between these packet_traits definitions and the ones
+// we'll use on the host side (SSE, AVX, ...)
+#define SYCL_ARITHMETIC(packet_type) \
+ template <> \
+ struct is_arithmetic<packet_type> { \
+ enum { value = true }; \
+ };
+SYCL_ARITHMETIC(cl::sycl::cl_float4)
+SYCL_ARITHMETIC(cl::sycl::cl_double2)
+#undef SYCL_ARITHMETIC
+
+#define SYCL_UNPACKET_TRAITS(packet_type, unpacket_type, lengths) \
+ template <> \
+ struct unpacket_traits<packet_type> { \
+ typedef unpacket_type type; \
+ enum { size = lengths, vectorizable = true, alignment = Aligned16 }; \
+ typedef packet_type half; \
+ };
+SYCL_UNPACKET_TRAITS(cl::sycl::cl_float4, float, 4)
+SYCL_UNPACKET_TRAITS(cl::sycl::cl_double2, double, 2)
+
+#undef SYCL_UNPACKET_TRAITS
+#endif
+
+} // end namespace internal
+
+#endif
+
+namespace TensorSycl {
+namespace internal {
+
+template <typename PacketReturnType, int PacketSize>
+struct PacketWrapper;
+// This function should never get called on the device
+#ifndef SYCL_DEVICE_ONLY
+template <typename PacketReturnType, int PacketSize>
+struct PacketWrapper {
+ typedef typename ::Eigen::internal::unpacket_traits<PacketReturnType>::type
+ Scalar;
+ template <typename Index>
+ EIGEN_DEVICE_FUNC static Scalar scalarize(Index, PacketReturnType &) {
+ eigen_assert(false && "THERE IS NO PACKETIZE VERSION FOR THE CHOSEN TYPE");
+ abort();
+ }
+ EIGEN_DEVICE_FUNC static PacketReturnType convert_to_packet_type(Scalar in,
+ Scalar) {
+ return ::Eigen::internal::template plset<PacketReturnType>(in);
+ }
+ EIGEN_DEVICE_FUNC static void set_packet(PacketReturnType, Scalar *) {
+ eigen_assert(false && "THERE IS NO PACKETIZE VERSION FOR THE CHOSEN TYPE");
+ abort();
+ }
+};
+
+#elif defined(SYCL_DEVICE_ONLY)
+template <typename PacketReturnType>
+struct PacketWrapper<PacketReturnType, 4> {
+ typedef typename ::Eigen::internal::unpacket_traits<PacketReturnType>::type
+ Scalar;
+ template <typename Index>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE static Scalar scalarize(Index index, PacketReturnType &in) {
+ switch (index) {
+ case 0:
+ return in.x();
+ case 1:
+ return in.y();
+ case 2:
+ return in.z();
+ case 3:
+ return in.w();
+ default:
+ //INDEX MUST BE BETWEEN 0 and 3.There is no abort function in SYCL kernel. so we cannot use abort here.
+ // The code will never reach here
+ __builtin_unreachable();
+ }
+ __builtin_unreachable();
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE static PacketReturnType convert_to_packet_type(
+ Scalar in, Scalar other) {
+ return PacketReturnType(in, other, other, other);
+ }
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE static void set_packet(PacketReturnType &lhs, Scalar *rhs) {
+ lhs = PacketReturnType(rhs[0], rhs[1], rhs[2], rhs[3]);
+ }
+};
+
+template <typename PacketReturnType>
+struct PacketWrapper<PacketReturnType, 1> {
+ typedef typename ::Eigen::internal::unpacket_traits<PacketReturnType>::type
+ Scalar;
+ template <typename Index>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE static Scalar scalarize(Index, PacketReturnType &in) {
+ return in;
+ }
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE static PacketReturnType convert_to_packet_type(Scalar in,
+ Scalar) {
+ return PacketReturnType(in);
+ }
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE static void set_packet(PacketReturnType &lhs, Scalar *rhs) {
+ lhs = rhs[0];
+ }
+};
+
+template <typename PacketReturnType>
+struct PacketWrapper<PacketReturnType, 2> {
+ typedef typename ::Eigen::internal::unpacket_traits<PacketReturnType>::type
+ Scalar;
+ template <typename Index>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE static Scalar scalarize(Index index, PacketReturnType &in) {
+ switch (index) {
+ case 0:
+ return in.x();
+ case 1:
+ return in.y();
+ default:
+ //INDEX MUST BE BETWEEN 0 and 1.There is no abort function in SYCL kernel. so we cannot use abort here.
+ // The code will never reach here
+ __builtin_unreachable();
+ }
+ __builtin_unreachable();
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE static PacketReturnType convert_to_packet_type(
+ Scalar in, Scalar other) {
+ return PacketReturnType(in, other);
+ }
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE static void set_packet(PacketReturnType &lhs, Scalar *rhs) {
+ lhs = PacketReturnType(rhs[0], rhs[1]);
+ }
+};
+
+#endif
+
+} // end namespace internal
+} // end namespace TensorSycl
+} // end namespace Eigen
+
+#endif // EIGEN_INTEROP_HEADERS_SYCL_H
diff --git a/Eigen/src/Core/arch/SYCL/MathFunctions.h b/Eigen/src/Core/arch/SYCL/MathFunctions.h
new file mode 100644
index 0000000..9eb46bb
--- /dev/null
+++ b/Eigen/src/Core/arch/SYCL/MathFunctions.h
@@ -0,0 +1,303 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Mehdi Goli Codeplay Software Ltd.
+// Ralph Potter Codeplay Software Ltd.
+// Luke Iwanski Codeplay Software Ltd.
+// Contact: <eigen@codeplay.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+/*****************************************************************
+ * MathFunctions.h
+ *
+ * \brief:
+ * MathFunctions
+ *
+ *****************************************************************/
+
+#ifndef EIGEN_MATH_FUNCTIONS_SYCL_H
+#define EIGEN_MATH_FUNCTIONS_SYCL_H
+#include "../../InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+
+// Make sure this is only available when targeting a GPU: we don't want to
+// introduce conflicts between these packet_traits definitions and the ones
+// we'll use on the host side (SSE, AVX, ...)
+#if defined(SYCL_DEVICE_ONLY)
+#define SYCL_PLOG(packet_type) \
+ template <> \
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE packet_type plog<packet_type>( \
+ const packet_type& a) { \
+ return cl::sycl::log(a); \
+ }
+
+SYCL_PLOG(cl::sycl::cl_float4)
+SYCL_PLOG(cl::sycl::cl_double2)
+#undef SYCL_PLOG
+
+#define SYCL_PLOG1P(packet_type) \
+ template <> \
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE packet_type plog1p<packet_type>( \
+ const packet_type& a) { \
+ return cl::sycl::log1p(a); \
+ }
+
+SYCL_PLOG1P(cl::sycl::cl_float4)
+SYCL_PLOG1P(cl::sycl::cl_double2)
+#undef SYCL_PLOG1P
+
+#define SYCL_PLOG10(packet_type) \
+ template <> \
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE packet_type plog10<packet_type>( \
+ const packet_type& a) { \
+ return cl::sycl::log10(a); \
+ }
+
+SYCL_PLOG10(cl::sycl::cl_float4)
+SYCL_PLOG10(cl::sycl::cl_double2)
+#undef SYCL_PLOG10
+
+#define SYCL_PEXP(packet_type) \
+ template <> \
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE packet_type pexp<packet_type>( \
+ const packet_type& a) { \
+ return cl::sycl::exp(a); \
+ }
+
+SYCL_PEXP(cl::sycl::cl_float4)
+SYCL_PEXP(cl::sycl::cl_float)
+SYCL_PEXP(cl::sycl::cl_double2)
+#undef SYCL_PEXP
+
+#define SYCL_PEXPM1(packet_type) \
+ template <> \
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE packet_type pexpm1<packet_type>( \
+ const packet_type& a) { \
+ return cl::sycl::expm1(a); \
+ }
+
+SYCL_PEXPM1(cl::sycl::cl_float4)
+SYCL_PEXPM1(cl::sycl::cl_double2)
+#undef SYCL_PEXPM1
+
+#define SYCL_PSQRT(packet_type) \
+ template <> \
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE packet_type psqrt<packet_type>( \
+ const packet_type& a) { \
+ return cl::sycl::sqrt(a); \
+ }
+
+SYCL_PSQRT(cl::sycl::cl_float4)
+SYCL_PSQRT(cl::sycl::cl_double2)
+#undef SYCL_PSQRT
+
+#define SYCL_PRSQRT(packet_type) \
+ template <> \
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE packet_type prsqrt<packet_type>( \
+ const packet_type& a) { \
+ return cl::sycl::rsqrt(a); \
+ }
+
+SYCL_PRSQRT(cl::sycl::cl_float4)
+SYCL_PRSQRT(cl::sycl::cl_double2)
+#undef SYCL_PRSQRT
+
+/** \internal \returns the hyperbolic sine of \a a (coeff-wise) */
+#define SYCL_PSIN(packet_type) \
+ template <> \
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE packet_type psin<packet_type>( \
+ const packet_type& a) { \
+ return cl::sycl::sin(a); \
+ }
+
+SYCL_PSIN(cl::sycl::cl_float4)
+SYCL_PSIN(cl::sycl::cl_double2)
+#undef SYCL_PSIN
+
+/** \internal \returns the hyperbolic cosine of \a a (coeff-wise) */
+#define SYCL_PCOS(packet_type) \
+ template <> \
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE packet_type pcos<packet_type>( \
+ const packet_type& a) { \
+ return cl::sycl::cos(a); \
+ }
+
+SYCL_PCOS(cl::sycl::cl_float4)
+SYCL_PCOS(cl::sycl::cl_double2)
+#undef SYCL_PCOS
+
+/** \internal \returns the hyperbolic tan of \a a (coeff-wise) */
+#define SYCL_PTAN(packet_type) \
+ template <> \
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE packet_type ptan<packet_type>( \
+ const packet_type& a) { \
+ return cl::sycl::tan(a); \
+ }
+
+SYCL_PTAN(cl::sycl::cl_float4)
+SYCL_PTAN(cl::sycl::cl_double2)
+#undef SYCL_PTAN
+
+/** \internal \returns the hyperbolic sine of \a a (coeff-wise) */
+#define SYCL_PASIN(packet_type) \
+ template <> \
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE packet_type pasin<packet_type>( \
+ const packet_type& a) { \
+ return cl::sycl::asin(a); \
+ }
+
+SYCL_PASIN(cl::sycl::cl_float4)
+SYCL_PASIN(cl::sycl::cl_double2)
+#undef SYCL_PASIN
+
+/** \internal \returns the hyperbolic cosine of \a a (coeff-wise) */
+#define SYCL_PACOS(packet_type) \
+ template <> \
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE packet_type pacos<packet_type>( \
+ const packet_type& a) { \
+ return cl::sycl::acos(a); \
+ }
+
+SYCL_PACOS(cl::sycl::cl_float4)
+SYCL_PACOS(cl::sycl::cl_double2)
+#undef SYCL_PACOS
+
+/** \internal \returns the hyperbolic tan of \a a (coeff-wise) */
+#define SYCL_PATAN(packet_type) \
+ template <> \
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE packet_type patan<packet_type>( \
+ const packet_type& a) { \
+ return cl::sycl::atan(a); \
+ }
+
+SYCL_PATAN(cl::sycl::cl_float4)
+SYCL_PATAN(cl::sycl::cl_double2)
+#undef SYCL_PATAN
+
+/** \internal \returns the hyperbolic sine of \a a (coeff-wise) */
+#define SYCL_PSINH(packet_type) \
+ template <> \
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE packet_type psinh<packet_type>( \
+ const packet_type& a) { \
+ return cl::sycl::sinh(a); \
+ }
+
+SYCL_PSINH(cl::sycl::cl_float4)
+SYCL_PSINH(cl::sycl::cl_double2)
+#undef SYCL_PSINH
+
+/** \internal \returns the hyperbolic cosine of \a a (coeff-wise) */
+#define SYCL_PCOSH(packet_type) \
+ template <> \
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE packet_type pcosh<packet_type>( \
+ const packet_type& a) { \
+ return cl::sycl::cosh(a); \
+ }
+
+SYCL_PCOSH(cl::sycl::cl_float4)
+SYCL_PCOSH(cl::sycl::cl_double2)
+#undef SYCL_PCOSH
+
+/** \internal \returns the hyperbolic tan of \a a (coeff-wise) */
+#define SYCL_PTANH(packet_type) \
+ template <> \
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE packet_type ptanh<packet_type>( \
+ const packet_type& a) { \
+ return cl::sycl::tanh(a); \
+ }
+
+SYCL_PTANH(cl::sycl::cl_float4)
+SYCL_PTANH(cl::sycl::cl_double2)
+#undef SYCL_PTANH
+
+#define SYCL_PCEIL(packet_type) \
+ template <> \
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE packet_type pceil<packet_type>( \
+ const packet_type& a) { \
+ return cl::sycl::ceil(a); \
+ }
+
+SYCL_PCEIL(cl::sycl::cl_float4)
+SYCL_PCEIL(cl::sycl::cl_double2)
+#undef SYCL_PCEIL
+
+#define SYCL_PROUND(packet_type) \
+ template <> \
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE packet_type pround<packet_type>( \
+ const packet_type& a) { \
+ return cl::sycl::round(a); \
+ }
+
+SYCL_PROUND(cl::sycl::cl_float4)
+SYCL_PROUND(cl::sycl::cl_double2)
+#undef SYCL_PROUND
+
+#define SYCL_PRINT(packet_type) \
+ template <> \
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE packet_type print<packet_type>( \
+ const packet_type& a) { \
+ return cl::sycl::rint(a); \
+ }
+
+SYCL_PRINT(cl::sycl::cl_float4)
+SYCL_PRINT(cl::sycl::cl_double2)
+#undef SYCL_PRINT
+
+#define SYCL_FLOOR(packet_type) \
+ template <> \
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE packet_type pfloor<packet_type>( \
+ const packet_type& a) { \
+ return cl::sycl::floor(a); \
+ }
+
+SYCL_FLOOR(cl::sycl::cl_float4)
+SYCL_FLOOR(cl::sycl::cl_double2)
+#undef SYCL_FLOOR
+
+#define SYCL_PMIN(packet_type, expr) \
+ template <> \
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE packet_type pmin<packet_type>( \
+ const packet_type& a, const packet_type& b) { \
+ return expr; \
+ }
+
+SYCL_PMIN(cl::sycl::cl_float4, cl::sycl::fmin(a, b))
+SYCL_PMIN(cl::sycl::cl_double2, cl::sycl::fmin(a, b))
+#undef SYCL_PMIN
+
+#define SYCL_PMAX(packet_type, expr) \
+ template <> \
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE packet_type pmax<packet_type>( \
+ const packet_type& a, const packet_type& b) { \
+ return expr; \
+ }
+
+SYCL_PMAX(cl::sycl::cl_float4, cl::sycl::fmax(a, b))
+SYCL_PMAX(cl::sycl::cl_double2, cl::sycl::fmax(a, b))
+#undef SYCL_PMAX
+
+#define SYCL_PLDEXP(packet_type) \
+ template <> \
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE packet_type pldexp( \
+ const packet_type& a, const packet_type& exponent) { \
+ return cl::sycl::ldexp( \
+ a, exponent.template convert<cl::sycl::cl_int, \
+ cl::sycl::rounding_mode::automatic>()); \
+ }
+
+SYCL_PLDEXP(cl::sycl::cl_float4)
+SYCL_PLDEXP(cl::sycl::cl_double2)
+#undef SYCL_PLDEXP
+
+#endif
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_MATH_FUNCTIONS_SYCL_H
diff --git a/Eigen/src/Core/arch/SYCL/PacketMath.h b/Eigen/src/Core/arch/SYCL/PacketMath.h
new file mode 100644
index 0000000..5bc3235
--- /dev/null
+++ b/Eigen/src/Core/arch/SYCL/PacketMath.h
@@ -0,0 +1,596 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Mehdi Goli Codeplay Software Ltd.
+// Ralph Potter Codeplay Software Ltd.
+// Luke Iwanski Codeplay Software Ltd.
+// Contact: <eigen@codeplay.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+/*****************************************************************
+ * PacketMath.h
+ *
+ * \brief:
+ * PacketMath
+ *
+ *****************************************************************/
+
+#ifndef EIGEN_PACKET_MATH_SYCL_H
+#define EIGEN_PACKET_MATH_SYCL_H
+#include <type_traits>
+#include "../../InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+#ifdef SYCL_DEVICE_ONLY
+
+#define SYCL_PLOADT_RO(address_space_target) \
+ template <typename packet_type, int Alignment> \
+ EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE packet_type ploadt_ro( \
+ typename cl::sycl::multi_ptr< \
+ const typename unpacket_traits<packet_type>::type, \
+ cl::sycl::access::address_space::address_space_target>::pointer_t \
+ from) { \
+ typedef typename unpacket_traits<packet_type>::type scalar; \
+ typedef cl::sycl::multi_ptr< \
+ scalar, cl::sycl::access::address_space::address_space_target> \
+ multi_ptr; \
+ auto res = packet_type( \
+ static_cast<typename unpacket_traits<packet_type>::type>(0)); \
+ res.load(0, multi_ptr(const_cast<typename multi_ptr::pointer_t>(from))); \
+ return res; \
+ }
+
+SYCL_PLOADT_RO(global_space)
+SYCL_PLOADT_RO(local_space)
+#undef SYCL_PLOADT_RO
+#endif
+
+template <typename packet_type, int Alignment, typename T>
+EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE packet_type
+ploadt_ro(const Eigen::TensorSycl::internal::RangeAccess<
+ cl::sycl::access::mode::read_write, T>& from) {
+ return ploadt_ro<packet_type, Alignment>(from.get_pointer());
+}
+
+#ifdef SYCL_DEVICE_ONLY
+#define SYCL_PLOAD(address_space_target, Alignment, AlignedType) \
+ template <typename packet_type> \
+ EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE packet_type pload##AlignedType( \
+ typename cl::sycl::multi_ptr< \
+ const typename unpacket_traits<packet_type>::type, \
+ cl::sycl::access::address_space::address_space_target>::pointer_t \
+ from) { \
+ return ploadt_ro<packet_type, Alignment>(from); \
+ }
+
+// global space
+SYCL_PLOAD(global_space, Unaligned, u)
+SYCL_PLOAD(global_space, Aligned, )
+// local space
+SYCL_PLOAD(local_space, Unaligned, u)
+SYCL_PLOAD(local_space, Aligned, )
+
+#undef SYCL_PLOAD
+#endif
+
+#define SYCL_PLOAD(Alignment, AlignedType) \
+ template <typename packet_type> \
+ EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE packet_type pload##AlignedType( \
+ const Eigen::TensorSycl::internal::RangeAccess< \
+ cl::sycl::access::mode::read_write, \
+ typename unpacket_traits<packet_type>::type> \
+ from) { \
+ return ploadt_ro<packet_type, Alignment>(from); \
+ }
+SYCL_PLOAD(Unaligned, u)
+SYCL_PLOAD(Aligned, )
+#undef SYCL_PLOAD
+
+#ifdef SYCL_DEVICE_ONLY
+/** \internal \returns a packet version of \a *from.
+ * The pointer \a from must be aligned on a \a Alignment bytes boundary. */
+#define SYCL_PLOADT(address_space_target) \
+ template <typename packet_type, int Alignment> \
+ EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE packet_type ploadt( \
+ typename cl::sycl::multi_ptr< \
+ const typename unpacket_traits<packet_type>::type, \
+ cl::sycl::access::address_space::address_space_target>::pointer_t \
+ from) { \
+ if (Alignment >= unpacket_traits<packet_type>::alignment) \
+ return pload<packet_type>(from); \
+ else \
+ return ploadu<packet_type>(from); \
+ }
+
+// global space
+SYCL_PLOADT(global_space)
+// local space
+SYCL_PLOADT(local_space)
+#undef SYCL_PLOADT
+#endif
+
+template <typename packet_type, int Alignment>
+EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE packet_type
+ploadt(const Eigen::TensorSycl::internal::RangeAccess<
+ cl::sycl::access::mode::read_write,
+ typename unpacket_traits<packet_type>::type>& from) {
+ return ploadt<packet_type, Alignment>(from.get_pointer());
+}
+#ifdef SYCL_DEVICE_ONLY
+
+// private_space
+#define SYCL_PLOADT_RO_SPECIAL(packet_type, Alignment) \
+ template <> \
+ EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE packet_type \
+ ploadt_ro<packet_type, Alignment>( \
+ const typename unpacket_traits<packet_type>::type* from) { \
+ typedef typename unpacket_traits<packet_type>::type scalar; \
+ auto res = packet_type(static_cast<scalar>(0)); \
+ res.template load<cl::sycl::access::address_space::private_space>( \
+ 0, const_cast<scalar*>(from)); \
+ return res; \
+ }
+
+SYCL_PLOADT_RO_SPECIAL(cl::sycl::cl_float4, Aligned)
+SYCL_PLOADT_RO_SPECIAL(cl::sycl::cl_double2, Aligned)
+SYCL_PLOADT_RO_SPECIAL(cl::sycl::cl_float4, Unaligned)
+SYCL_PLOADT_RO_SPECIAL(cl::sycl::cl_double2, Unaligned)
+
+#define SYCL_PLOAD_SPECIAL(packet_type, alignment_type) \
+ template <> \
+ EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE packet_type pload##alignment_type( \
+ const typename unpacket_traits<packet_type>::type* from) { \
+ typedef typename unpacket_traits<packet_type>::type scalar; \
+ auto res = packet_type(static_cast<scalar>(0)); \
+ res.template load<cl::sycl::access::address_space::private_space>( \
+ 0, const_cast<scalar*>(from)); \
+ return res; \
+ }
+SYCL_PLOAD_SPECIAL(cl::sycl::cl_float4, )
+SYCL_PLOAD_SPECIAL(cl::sycl::cl_double2, )
+SYCL_PLOAD_SPECIAL(cl::sycl::cl_float4, u)
+SYCL_PLOAD_SPECIAL(cl::sycl::cl_double2, u)
+
+#undef SYCL_PLOAD_SPECIAL
+
+#define SYCL_PSTORE(scalar, packet_type, address_space_target, alignment) \
+ template <> \
+ EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE void pstore##alignment( \
+ typename cl::sycl::multi_ptr< \
+ scalar, \
+ cl::sycl::access::address_space::address_space_target>::pointer_t \
+ to, \
+ const packet_type& from) { \
+ typedef cl::sycl::multi_ptr< \
+ scalar, cl::sycl::access::address_space::address_space_target> \
+ multi_ptr; \
+ from.store(0, multi_ptr(to)); \
+ }
+
+// global space
+SYCL_PSTORE(float, cl::sycl::cl_float4, global_space, )
+SYCL_PSTORE(float, cl::sycl::cl_float4, global_space, u)
+SYCL_PSTORE(double, cl::sycl::cl_double2, global_space, )
+SYCL_PSTORE(double, cl::sycl::cl_double2, global_space, u)
+SYCL_PSTORE(float, cl::sycl::cl_float4, local_space, )
+SYCL_PSTORE(float, cl::sycl::cl_float4, local_space, u)
+SYCL_PSTORE(double, cl::sycl::cl_double2, local_space, )
+SYCL_PSTORE(double, cl::sycl::cl_double2, local_space, u)
+
+SYCL_PSTORE(float, cl::sycl::cl_float4, private_space, )
+SYCL_PSTORE(float, cl::sycl::cl_float4, private_space, u)
+SYCL_PSTORE(double, cl::sycl::cl_double2, private_space, )
+SYCL_PSTORE(double, cl::sycl::cl_double2, private_space, u)
+#undef SYCL_PSTORE
+
+#define SYCL_PSTORE_T(address_space_target) \
+ template <typename scalar, typename packet_type, int Alignment> \
+ EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE void pstoret( \
+ typename cl::sycl::multi_ptr< \
+ scalar, \
+ cl::sycl::access::address_space::address_space_target>::pointer_t \
+ to, \
+ const packet_type& from) { \
+ if (Alignment) \
+ pstore(to, from); \
+ else \
+ pstoreu(to, from); \
+ }
+
+SYCL_PSTORE_T(global_space)
+
+SYCL_PSTORE_T(local_space)
+
+#undef SYCL_PSTORE_T
+
+#define SYCL_PSET1(packet_type) \
+ template <> \
+ EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE packet_type pset1<packet_type>( \
+ const typename unpacket_traits<packet_type>::type& from) { \
+ return packet_type(from); \
+ }
+
+// global space
+SYCL_PSET1(cl::sycl::cl_float4)
+SYCL_PSET1(cl::sycl::cl_double2)
+
+#undef SYCL_PSET1
+
+template <typename packet_type>
+struct get_base_packet {
+ template <typename sycl_multi_pointer>
+ static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE packet_type
+ get_ploaddup(sycl_multi_pointer) {}
+
+ template <typename sycl_multi_pointer>
+ static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE packet_type
+ get_pgather(sycl_multi_pointer, Index) {}
+};
+
+template <>
+struct get_base_packet<cl::sycl::cl_float4> {
+ template <typename sycl_multi_pointer>
+ static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE cl::sycl::cl_float4 get_ploaddup(
+ sycl_multi_pointer from) {
+ return cl::sycl::cl_float4(from[0], from[0], from[1], from[1]);
+ }
+ template <typename sycl_multi_pointer>
+ static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE cl::sycl::cl_float4 get_pgather(
+ sycl_multi_pointer from, Index stride) {
+ return cl::sycl::cl_float4(from[0 * stride], from[1 * stride],
+ from[2 * stride], from[3 * stride]);
+ }
+
+ template <typename sycl_multi_pointer>
+ static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void set_pscatter(
+ sycl_multi_pointer to, const cl::sycl::cl_float4& from, Index stride) {
+ auto tmp = stride;
+ to[0] = from.x();
+ to[tmp] = from.y();
+ to[tmp += stride] = from.z();
+ to[tmp += stride] = from.w();
+ }
+ static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE cl::sycl::cl_float4 set_plset(
+ const float& a) {
+ return cl::sycl::cl_float4(static_cast<float>(a), static_cast<float>(a + 1),
+ static_cast<float>(a + 2),
+ static_cast<float>(a + 3));
+ }
+};
+
+template <>
+struct get_base_packet<cl::sycl::cl_double2> {
+ template <typename sycl_multi_pointer>
+ static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE cl::sycl::cl_double2
+ get_ploaddup(const sycl_multi_pointer from) {
+ return cl::sycl::cl_double2(from[0], from[0]);
+ }
+
+ template <typename sycl_multi_pointer, typename Index>
+ static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE cl::sycl::cl_double2 get_pgather(
+ const sycl_multi_pointer from, Index stride) {
+ return cl::sycl::cl_double2(from[0 * stride], from[1 * stride]);
+ }
+
+ template <typename sycl_multi_pointer>
+ static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void set_pscatter(
+ sycl_multi_pointer to, const cl::sycl::cl_double2& from, Index stride) {
+ to[0] = from.x();
+ to[stride] = from.y();
+ }
+
+ static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE cl::sycl::cl_double2 set_plset(
+ const double& a) {
+ return cl::sycl::cl_double2(static_cast<double>(a),
+ static_cast<double>(a + 1));
+ }
+};
+
+#define SYCL_PLOAD_DUP(address_space_target) \
+ template <typename packet_type> \
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE packet_type ploaddup( \
+ typename cl::sycl::multi_ptr< \
+ const typename unpacket_traits<packet_type>::type, \
+ cl::sycl::access::address_space::address_space_target>::pointer_t \
+ from) { \
+ return get_base_packet<packet_type>::get_ploaddup(from); \
+ }
+
+// global space
+SYCL_PLOAD_DUP(global_space)
+// local_space
+SYCL_PLOAD_DUP(local_space)
+#undef SYCL_PLOAD_DUP
+
+#define SYCL_PLOAD_DUP_SPECILIZE(packet_type) \
+ template <> \
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE packet_type ploaddup<packet_type>( \
+ const typename unpacket_traits<packet_type>::type* from) { \
+ return get_base_packet<packet_type>::get_ploaddup(from); \
+ }
+
+SYCL_PLOAD_DUP_SPECILIZE(cl::sycl::cl_float4)
+SYCL_PLOAD_DUP_SPECILIZE(cl::sycl::cl_double2)
+
+#undef SYCL_PLOAD_DUP_SPECILIZE
+
+#define SYCL_PLSET(packet_type) \
+ template <> \
+ EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE packet_type plset<packet_type>( \
+ const typename unpacket_traits<packet_type>::type& a) { \
+ return get_base_packet<packet_type>::set_plset(a); \
+ }
+
+SYCL_PLSET(cl::sycl::cl_float4)
+SYCL_PLSET(cl::sycl::cl_double2)
+
+#undef SYCL_PLSET
+
+#define SYCL_PGATHER(address_space_target) \
+ template <typename Scalar, typename packet_type> \
+ EIGEN_DEVICE_FUNC inline packet_type pgather( \
+ typename cl::sycl::multi_ptr< \
+ const typename unpacket_traits<packet_type>::type, \
+ cl::sycl::access::address_space::address_space_target>::pointer_t \
+ from, \
+ Index stride) { \
+ return get_base_packet<packet_type>::get_pgather(from, stride); \
+ }
+
+// global space
+SYCL_PGATHER(global_space)
+// local space
+SYCL_PGATHER(local_space)
+
+#undef SYCL_PGATHER
+
+#define SYCL_PGATHER_SPECILIZE(scalar, packet_type) \
+ template <> \
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE packet_type \
+ pgather<scalar, packet_type>( \
+ const typename unpacket_traits<packet_type>::type* from, Index stride) { \
+ return get_base_packet<packet_type>::get_pgather(from, stride); \
+ }
+
+SYCL_PGATHER_SPECILIZE(float, cl::sycl::cl_float4)
+SYCL_PGATHER_SPECILIZE(double, cl::sycl::cl_double2)
+
+#undef SYCL_PGATHER_SPECILIZE
+
+#define SYCL_PSCATTER(address_space_target) \
+ template <typename Scalar, typename packet_type> \
+ EIGEN_DEVICE_FUNC inline void pscatter( \
+ typename cl::sycl::multi_ptr< \
+ typename unpacket_traits<packet_type>::type, \
+ cl::sycl::access::address_space::address_space_target>::pointer_t \
+ to, \
+ const packet_type& from, Index stride) { \
+ get_base_packet<packet_type>::set_pscatter(to, from, stride); \
+ }
+
+// global space
+SYCL_PSCATTER(global_space)
+// local space
+SYCL_PSCATTER(local_space)
+
+#undef SYCL_PSCATTER
+
+#define SYCL_PSCATTER_SPECILIZE(scalar, packet_type) \
+ template <> \
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void pscatter<scalar, packet_type>( \
+ typename unpacket_traits<packet_type>::type * to, \
+ const packet_type& from, Index stride) { \
+ get_base_packet<packet_type>::set_pscatter(to, from, stride); \
+ }
+
+SYCL_PSCATTER_SPECILIZE(float, cl::sycl::cl_float4)
+SYCL_PSCATTER_SPECILIZE(double, cl::sycl::cl_double2)
+
+#undef SYCL_PSCATTER_SPECILIZE
+
+#define SYCL_PMAD(packet_type) \
+ template <> \
+ EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE packet_type pmadd( \
+ const packet_type& a, const packet_type& b, const packet_type& c) { \
+ return cl::sycl::mad(a, b, c); \
+ }
+
+SYCL_PMAD(cl::sycl::cl_float4)
+SYCL_PMAD(cl::sycl::cl_double2)
+#undef SYCL_PMAD
+
+template <>
+EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE float pfirst<cl::sycl::cl_float4>(
+ const cl::sycl::cl_float4& a) {
+ return a.x();
+}
+template <>
+EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE double pfirst<cl::sycl::cl_double2>(
+ const cl::sycl::cl_double2& a) {
+ return a.x();
+}
+
+template <>
+EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE float predux<cl::sycl::cl_float4>(
+ const cl::sycl::cl_float4& a) {
+ return a.x() + a.y() + a.z() + a.w();
+}
+
+template <>
+EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE double predux<cl::sycl::cl_double2>(
+ const cl::sycl::cl_double2& a) {
+ return a.x() + a.y();
+}
+
+template <>
+EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE float predux_max<cl::sycl::cl_float4>(
+ const cl::sycl::cl_float4& a) {
+ return cl::sycl::fmax(cl::sycl::fmax(a.x(), a.y()),
+ cl::sycl::fmax(a.z(), a.w()));
+}
+template <>
+EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE double predux_max<cl::sycl::cl_double2>(
+ const cl::sycl::cl_double2& a) {
+ return cl::sycl::fmax(a.x(), a.y());
+}
+
+template <>
+EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE float predux_min<cl::sycl::cl_float4>(
+ const cl::sycl::cl_float4& a) {
+ return cl::sycl::fmin(cl::sycl::fmin(a.x(), a.y()),
+ cl::sycl::fmin(a.z(), a.w()));
+}
+template <>
+EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE double predux_min<cl::sycl::cl_double2>(
+ const cl::sycl::cl_double2& a) {
+ return cl::sycl::fmin(a.x(), a.y());
+}
+
+template <>
+EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE float predux_mul<cl::sycl::cl_float4>(
+ const cl::sycl::cl_float4& a) {
+ return a.x() * a.y() * a.z() * a.w();
+}
+template <>
+EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE double predux_mul<cl::sycl::cl_double2>(
+ const cl::sycl::cl_double2& a) {
+ return a.x() * a.y();
+}
+
+template <>
+EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE cl::sycl::cl_float4
+pabs<cl::sycl::cl_float4>(const cl::sycl::cl_float4& a) {
+ return cl::sycl::cl_float4(cl::sycl::fabs(a.x()), cl::sycl::fabs(a.y()),
+ cl::sycl::fabs(a.z()), cl::sycl::fabs(a.w()));
+}
+template <>
+EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE cl::sycl::cl_double2
+pabs<cl::sycl::cl_double2>(const cl::sycl::cl_double2& a) {
+ return cl::sycl::cl_double2(cl::sycl::fabs(a.x()), cl::sycl::fabs(a.y()));
+}
+
+template <typename Packet>
+EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE Packet sycl_pcmp_le(const Packet &a,
+ const Packet &b) {
+ return (a <= b).template as<Packet>();
+}
+
+template <typename Packet>
+EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE Packet sycl_pcmp_lt(const Packet &a,
+ const Packet &b) {
+ return (a < b).template as<Packet>();
+}
+
+template <typename Packet>
+EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE Packet sycl_pcmp_eq(const Packet &a,
+ const Packet &b) {
+ return (a == b).template as<Packet>();
+}
+
+#define SYCL_PCMP(OP, TYPE) \
+ template <> \
+ EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE TYPE pcmp_##OP<TYPE>(const TYPE &a, \
+ const TYPE &b) { \
+ return sycl_pcmp_##OP<TYPE>(a, b); \
+ }
+
+SYCL_PCMP(le, cl::sycl::cl_float4)
+SYCL_PCMP(lt, cl::sycl::cl_float4)
+SYCL_PCMP(eq, cl::sycl::cl_float4)
+SYCL_PCMP(le, cl::sycl::cl_double2)
+SYCL_PCMP(lt, cl::sycl::cl_double2)
+SYCL_PCMP(eq, cl::sycl::cl_double2)
+#undef SYCL_PCMP
+
+EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE void ptranspose(
+ PacketBlock<cl::sycl::cl_float4, 4>& kernel) {
+ float tmp = kernel.packet[0].y();
+ kernel.packet[0].y() = kernel.packet[1].x();
+ kernel.packet[1].x() = tmp;
+
+ tmp = kernel.packet[0].z();
+ kernel.packet[0].z() = kernel.packet[2].x();
+ kernel.packet[2].x() = tmp;
+
+ tmp = kernel.packet[0].w();
+ kernel.packet[0].w() = kernel.packet[3].x();
+ kernel.packet[3].x() = tmp;
+
+ tmp = kernel.packet[1].z();
+ kernel.packet[1].z() = kernel.packet[2].y();
+ kernel.packet[2].y() = tmp;
+
+ tmp = kernel.packet[1].w();
+ kernel.packet[1].w() = kernel.packet[3].y();
+ kernel.packet[3].y() = tmp;
+
+ tmp = kernel.packet[2].w();
+ kernel.packet[2].w() = kernel.packet[3].z();
+ kernel.packet[3].z() = tmp;
+}
+
+EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE void ptranspose(
+ PacketBlock<cl::sycl::cl_double2, 2>& kernel) {
+ double tmp = kernel.packet[0].y();
+ kernel.packet[0].y() = kernel.packet[1].x();
+ kernel.packet[1].x() = tmp;
+}
+
+template <>
+EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE cl::sycl::cl_float4 pblend(
+ const Selector<unpacket_traits<cl::sycl::cl_float4>::size>& ifPacket,
+ const cl::sycl::cl_float4& thenPacket,
+ const cl::sycl::cl_float4& elsePacket) {
+ cl::sycl::cl_int4 condition(
+ ifPacket.select[0] ? 0 : -1, ifPacket.select[1] ? 0 : -1,
+ ifPacket.select[2] ? 0 : -1, ifPacket.select[3] ? 0 : -1);
+ return cl::sycl::select(thenPacket, elsePacket, condition);
+}
+
+template <>
+inline cl::sycl::cl_double2 pblend(
+ const Selector<unpacket_traits<cl::sycl::cl_double2>::size>& ifPacket,
+ const cl::sycl::cl_double2& thenPacket,
+ const cl::sycl::cl_double2& elsePacket) {
+ cl::sycl::cl_long2 condition(ifPacket.select[0] ? 0 : -1,
+ ifPacket.select[1] ? 0 : -1);
+ return cl::sycl::select(thenPacket, elsePacket, condition);
+}
+#endif // SYCL_DEVICE_ONLY
+
+#define SYCL_PSTORE(alignment) \
+ template <typename packet_type> \
+ EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE void pstore##alignment( \
+ const Eigen::TensorSycl::internal::RangeAccess< \
+ cl::sycl::access::mode::read_write, \
+ typename unpacket_traits<packet_type>::type>& to, \
+ const packet_type& from) { \
+ pstore##alignment(to.get_pointer(), from); \
+ }
+
+// global space
+SYCL_PSTORE()
+SYCL_PSTORE(u)
+
+#undef SYCL_PSTORE
+
+template <typename scalar, typename packet_type, int Alignment>
+EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE void pstoret(
+ Eigen::TensorSycl::internal::RangeAccess<
+ cl::sycl::access::mode::read_write,
+ typename unpacket_traits<packet_type>::type>
+ to,
+ const packet_type& from) {
+ pstoret<scalar, packet_type, Alignment>(to.get_pointer(), from);
+}
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_PACKET_MATH_SYCL_H
diff --git a/Eigen/src/Core/arch/SYCL/SyclMemoryModel.h b/Eigen/src/Core/arch/SYCL/SyclMemoryModel.h
new file mode 100644
index 0000000..54eedfa
--- /dev/null
+++ b/Eigen/src/Core/arch/SYCL/SyclMemoryModel.h
@@ -0,0 +1,696 @@
+/***************************************************************************
+ * Copyright (C) 2017 Codeplay Software Limited
+ * This Source Code Form is subject to the terms of the Mozilla
+ * Public License v. 2.0. If a copy of the MPL was not distributed
+ * with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+ *
+ *
+ * SyclMemoryModel.h
+ *
+ * Description:
+ * Interface for SYCL buffers to behave as a non-dereferenceable pointer
+ * Interface for Placeholder accessor to behave as a pointer on both host
+ * and device
+ *
+ * Authors:
+ *
+ * Ruyman Reyes Codeplay Software Ltd.
+ * Mehdi Goli Codeplay Software Ltd.
+ * Vanya Yaneva Codeplay Software Ltd.
+ *
+ **************************************************************************/
+
+#if defined(EIGEN_USE_SYCL) && \
+ !defined(EIGEN_CXX11_TENSOR_TENSOR_SYCL_STORAGE_MEMORY_H)
+#define EIGEN_CXX11_TENSOR_TENSOR_SYCL_STORAGE_MEMORY_H
+
+#include <CL/sycl.hpp>
+#ifdef EIGEN_EXCEPTIONS
+#include <stdexcept>
+#endif
+#include <cstddef>
+#include <queue>
+#include <set>
+#include <unordered_map>
+
+#include "../../InternalHeaderCheck.h"
+
+namespace Eigen {
+namespace TensorSycl {
+namespace internal {
+
+using sycl_acc_target = cl::sycl::access::target;
+using sycl_acc_mode = cl::sycl::access::mode;
+
+/**
+ * Default values for template arguments
+ */
+using buffer_data_type_t = uint8_t;
+const sycl_acc_target default_acc_target = sycl_acc_target::global_buffer;
+const sycl_acc_mode default_acc_mode = sycl_acc_mode::read_write;
+
+/**
+ * PointerMapper
+ * Associates fake pointers with buffers.
+ *
+ */
+class PointerMapper {
+ public:
+ using base_ptr_t = std::intptr_t;
+
+ /* Structure of a virtual pointer
+ *
+ * |================================================|
+ * | POINTER ADDRESS |
+ * |================================================|
+ */
+ struct virtual_pointer_t {
+ /* Type for the pointers
+ */
+ base_ptr_t m_contents;
+
+ /** Conversions from virtual_pointer_t to
+ * void * should just reinterpret_cast the integer number
+ */
+ operator void *() const { return reinterpret_cast<void *>(m_contents); }
+
+ /**
+ * Convert back to the integer number.
+ */
+ operator base_ptr_t() const { return m_contents; }
+
+ /**
+ * Add a certain value to the pointer to create a
+ * new pointer to that offset
+ */
+ virtual_pointer_t operator+(size_t off) { return m_contents + off; }
+
+ /* Numerical order for sorting pointers in containers. */
+ bool operator<(virtual_pointer_t rhs) const {
+ return (static_cast<base_ptr_t>(m_contents) <
+ static_cast<base_ptr_t>(rhs.m_contents));
+ }
+
+ bool operator>(virtual_pointer_t rhs) const {
+ return (static_cast<base_ptr_t>(m_contents) >
+ static_cast<base_ptr_t>(rhs.m_contents));
+ }
+
+ /**
+ * Numerical order for sorting pointers in containers
+ */
+ bool operator==(virtual_pointer_t rhs) const {
+ return (static_cast<base_ptr_t>(m_contents) ==
+ static_cast<base_ptr_t>(rhs.m_contents));
+ }
+
+ /**
+ * Simple forward to the equality overload.
+ */
+ bool operator!=(virtual_pointer_t rhs) const {
+ return !(this->operator==(rhs));
+ }
+
+ /**
+ * Converts a void * into a virtual pointer structure.
+ * Note that this will only work if the void * was
+ * already a virtual_pointer_t, but we have no way of
+ * checking
+ */
+ virtual_pointer_t(const void *ptr)
+ : m_contents(reinterpret_cast<base_ptr_t>(ptr)){};
+
+ /**
+ * Creates a virtual_pointer_t from the given integer
+ * number
+ */
+ virtual_pointer_t(base_ptr_t u) : m_contents(u){};
+ };
+
+ /* Definition of a null pointer
+ */
+ const virtual_pointer_t null_virtual_ptr = nullptr;
+
+ /**
+ * Whether if a pointer is null or not.
+ * A pointer is nullptr if the value is of null_virtual_ptr
+ */
+ static inline bool is_nullptr(virtual_pointer_t ptr) {
+ return (static_cast<void *>(ptr) == nullptr);
+ }
+
+ /* basic type for all buffers
+ */
+ using buffer_t = cl::sycl::buffer<buffer_data_type_t>;
+
+ /**
+ * Node that stores information about a device allocation.
+ * Nodes are sorted by size to organise a free list of nodes
+ * that can be recovered.
+ */
+ struct pMapNode_t {
+ buffer_t m_buffer;
+ size_t m_size;
+ bool m_free;
+
+ pMapNode_t(buffer_t b, size_t size, bool f)
+ : m_buffer{b}, m_size{size}, m_free{f} {
+ m_buffer.set_final_data(nullptr);
+ }
+
+ bool operator<=(const pMapNode_t &rhs) { return (m_size <= rhs.m_size); }
+ };
+
+ /** Storage of the pointer / buffer tree
+ */
+ using pointerMap_t = std::map<virtual_pointer_t, pMapNode_t>;
+
+ /**
+ * Obtain the insertion point in the pointer map for
+ * a pointer of the given size.
+ * \param requiredSize Size attempted to reclaim
+ */
+ typename pointerMap_t::iterator get_insertion_point(size_t requiredSize) {
+ typename pointerMap_t::iterator retVal;
+ bool reuse = false;
+ if (!m_freeList.empty()) {
+ // try to re-use an existing block
+ for (auto freeElem : m_freeList) {
+ if (freeElem->second.m_size >= requiredSize) {
+ retVal = freeElem;
+ reuse = true;
+ // Element is not going to be free anymore
+ m_freeList.erase(freeElem);
+ break;
+ }
+ }
+ }
+ if (!reuse) {
+ retVal = std::prev(m_pointerMap.end());
+ }
+ return retVal;
+ }
+
+ /**
+ * Returns an iterator to the node that stores the information
+ * of the given virtual pointer from the given pointer map structure.
+ * If pointer is not found, throws std::out_of_range.
+ * If the pointer map structure is empty, throws std::out_of_range
+ *
+ * \param pMap the pointerMap_t structure storing all the pointers
+ * \param virtual_pointer_ptr The virtual pointer to obtain the node of
+ * \throws std::out:of_range if the pointer is not found or pMap is empty
+ */
+ typename pointerMap_t::iterator get_node(const virtual_pointer_t ptr) {
+ if (this->count() == 0) {
+ m_pointerMap.clear();
+ EIGEN_THROW_X(std::out_of_range("There are no pointers allocated\n"));
+
+ }
+ if (is_nullptr(ptr)) {
+ m_pointerMap.clear();
+ EIGEN_THROW_X(std::out_of_range("Cannot access null pointer\n"));
+ }
+ // The previous element to the lower bound is the node that
+ // holds this memory address
+ auto node = m_pointerMap.lower_bound(ptr);
+ // If the value of the pointer is not the one of the node
+ // then we return the previous one
+ if (node == std::end(m_pointerMap)) {
+ --node;
+ } else if (node->first != ptr) {
+ if (node == std::begin(m_pointerMap)) {
+ m_pointerMap.clear();
+ EIGEN_THROW_X(
+ std::out_of_range("The pointer is not registered in the map\n"));
+
+ }
+ --node;
+ }
+
+ return node;
+ }
+
+ /* get_buffer.
+ * Returns a buffer from the map using the pointer address
+ */
+ template <typename buffer_data_type = buffer_data_type_t>
+ cl::sycl::buffer<buffer_data_type, 1> get_buffer(
+ const virtual_pointer_t ptr) {
+
+ auto node = get_node(ptr);
+ auto& map_node = node->second;
+ eigen_assert(node->first == ptr || node->first < ptr);
+ eigen_assert(ptr < static_cast<virtual_pointer_t>(map_node.m_size +
+ node->first));
+ return map_node.m_buffer.reinterpret<buffer_data_type>(
+ cl::sycl::range<1>{map_node.m_size / sizeof(buffer_data_type)});
+ }
+
+ /**
+ * @brief Returns an accessor to the buffer of the given virtual pointer
+ * @param accessMode
+ * @param accessTarget
+ * @param ptr The virtual pointer
+ */
+ template <sycl_acc_mode access_mode = default_acc_mode,
+ sycl_acc_target access_target = default_acc_target,
+ typename buffer_data_type = buffer_data_type_t>
+ cl::sycl::accessor<buffer_data_type, 1, access_mode, access_target>
+ get_access(const virtual_pointer_t ptr) {
+ auto buf = get_buffer<buffer_data_type>(ptr);
+ return buf.template get_access<access_mode, access_target>();
+ }
+
+ /**
+ * @brief Returns an accessor to the buffer of the given virtual pointer
+ * in the given command group scope
+ * @param accessMode
+ * @param accessTarget
+ * @param ptr The virtual pointer
+ * @param cgh Reference to the command group scope
+ */
+ template <sycl_acc_mode access_mode = default_acc_mode,
+ sycl_acc_target access_target = default_acc_target,
+ typename buffer_data_type = buffer_data_type_t>
+ cl::sycl::accessor<buffer_data_type, 1, access_mode, access_target>
+ get_access(const virtual_pointer_t ptr, cl::sycl::handler &cgh) {
+ auto buf = get_buffer<buffer_data_type>(ptr);
+ return buf.template get_access<access_mode, access_target>(cgh);
+ }
+
+ /*
+ * Returns the offset from the base address of this pointer.
+ */
+ inline std::ptrdiff_t get_offset(const virtual_pointer_t ptr) {
+ // The previous element to the lower bound is the node that
+ // holds this memory address
+ auto node = get_node(ptr);
+ auto start = node->first;
+ eigen_assert(start == ptr || start < ptr);
+ eigen_assert(ptr < start + node->second.m_size);
+ return (ptr - start);
+ }
+
+ /*
+ * Returns the number of elements by which the given pointer is offset from
+ * the base address.
+ */
+ template <typename buffer_data_type>
+ inline size_t get_element_offset(const virtual_pointer_t ptr) {
+ return get_offset(ptr) / sizeof(buffer_data_type);
+ }
+
+ /**
+ * Constructs the PointerMapper structure.
+ */
+ PointerMapper(base_ptr_t baseAddress = 4096)
+ : m_pointerMap{}, m_freeList{}, m_baseAddress{baseAddress} {
+ if (m_baseAddress == 0) {
+ EIGEN_THROW_X(std::invalid_argument("Base address cannot be zero\n"));
+ }
+ };
+
+ /**
+ * PointerMapper cannot be copied or moved
+ */
+ PointerMapper(const PointerMapper &) = delete;
+
+ /**
+ * Empty the pointer list
+ */
+ inline void clear() {
+ m_freeList.clear();
+ m_pointerMap.clear();
+ }
+
+ /* add_pointer.
+ * Adds an existing pointer to the map and returns the virtual pointer id.
+ */
+ inline virtual_pointer_t add_pointer(const buffer_t &b) {
+ return add_pointer_impl(b);
+ }
+
+ /* add_pointer.
+ * Adds a pointer to the map and returns the virtual pointer id.
+ */
+ inline virtual_pointer_t add_pointer(buffer_t &&b) {
+ return add_pointer_impl(b);
+ }
+
+ /**
+ * @brief Fuses the given node with the previous nodes in the
+ * pointer map if they are free
+ *
+ * @param node A reference to the free node to be fused
+ */
+ void fuse_forward(typename pointerMap_t::iterator &node) {
+ while (node != std::prev(m_pointerMap.end())) {
+ // if following node is free
+ // remove it and extend the current node with its size
+ auto fwd_node = std::next(node);
+ if (!fwd_node->second.m_free) {
+ break;
+ }
+ auto fwd_size = fwd_node->second.m_size;
+ m_freeList.erase(fwd_node);
+ m_pointerMap.erase(fwd_node);
+
+ node->second.m_size += fwd_size;
+ }
+ }
+
+ /**
+ * @brief Fuses the given node with the following nodes in the
+ * pointer map if they are free
+ *
+ * @param node A reference to the free node to be fused
+ */
+ void fuse_backward(typename pointerMap_t::iterator &node) {
+ while (node != m_pointerMap.begin()) {
+ // if previous node is free, extend it
+ // with the size of the current one
+ auto prev_node = std::prev(node);
+ if (!prev_node->second.m_free) {
+ break;
+ }
+ prev_node->second.m_size += node->second.m_size;
+
+ // remove the current node
+ m_freeList.erase(node);
+ m_pointerMap.erase(node);
+
+ // point to the previous node
+ node = prev_node;
+ }
+ }
+
+ /* remove_pointer.
+ * Removes the given pointer from the map.
+ * The pointer is allowed to be reused only if ReUse if true.
+ */
+ template <bool ReUse = true>
+ void remove_pointer(const virtual_pointer_t ptr) {
+ if (is_nullptr(ptr)) {
+ return;
+ }
+ auto node = this->get_node(ptr);
+
+ node->second.m_free = true;
+ m_freeList.emplace(node);
+
+ // Fuse the node
+ // with free nodes before and after it
+ fuse_forward(node);
+ fuse_backward(node);
+
+ // If after fusing the node is the last one
+ // simply remove it (since it is free)
+ if (node == std::prev(m_pointerMap.end())) {
+ m_freeList.erase(node);
+ m_pointerMap.erase(node);
+ }
+ }
+
+ /* count.
+ * Return the number of active pointers (i.e, pointers that
+ * have been malloc but not freed).
+ */
+ size_t count() const { return (m_pointerMap.size() - m_freeList.size()); }
+
+ private:
+ /* add_pointer_impl.
+ * Adds a pointer to the map and returns the virtual pointer id.
+ * BufferT is either a const buffer_t& or a buffer_t&&.
+ */
+ template <class BufferT>
+ virtual_pointer_t add_pointer_impl(BufferT b) {
+ virtual_pointer_t retVal = nullptr;
+ size_t bufSize = b.get_count() * sizeof(buffer_data_type_t);
+ auto byte_buffer =
+ b.template reinterpret<buffer_data_type_t>(cl::sycl::range<1>{bufSize});
+ pMapNode_t p{byte_buffer, bufSize, false};
+
+ // If this is the first pointer:
+ if (m_pointerMap.empty()) {
+ virtual_pointer_t initialVal{m_baseAddress};
+ m_pointerMap.emplace(initialVal, p);
+ return initialVal;
+ }
+
+ auto lastElemIter = get_insertion_point(bufSize);
+ // We are recovering an existing free node
+ if (lastElemIter->second.m_free) {
+ lastElemIter->second.m_buffer = b;
+ lastElemIter->second.m_free = false;
+
+ // If the recovered node is bigger than the inserted one
+ // add a new free node with the remaining space
+ if (lastElemIter->second.m_size > bufSize) {
+ // create a new node with the remaining space
+ auto remainingSize = lastElemIter->second.m_size - bufSize;
+ pMapNode_t p2{b, remainingSize, true};
+
+ // update size of the current node
+ lastElemIter->second.m_size = bufSize;
+
+ // add the new free node
+ auto newFreePtr = lastElemIter->first + bufSize;
+ auto freeNode = m_pointerMap.emplace(newFreePtr, p2).first;
+ m_freeList.emplace(freeNode);
+ }
+
+ retVal = lastElemIter->first;
+ } else {
+ size_t lastSize = lastElemIter->second.m_size;
+ retVal = lastElemIter->first + lastSize;
+ m_pointerMap.emplace(retVal, p);
+ }
+ return retVal;
+ }
+
+ /**
+ * Compare two iterators to pointer map entries according to
+ * the size of the allocation on the device.
+ */
+ struct SortBySize {
+ bool operator()(typename pointerMap_t::iterator a,
+ typename pointerMap_t::iterator b) const {
+ return ((a->first < b->first) && (a->second <= b->second)) ||
+ ((a->first < b->first) && (b->second <= a->second));
+ }
+ };
+
+ /* Maps the pointer addresses to buffer and size pairs.
+ */
+ pointerMap_t m_pointerMap;
+
+ /* List of free nodes available for re-using
+ */
+ std::set<typename pointerMap_t::iterator, SortBySize> m_freeList;
+
+ /* Base address used when issuing the first virtual pointer, allows users
+ * to specify alignment. Cannot be zero. */
+ std::intptr_t m_baseAddress;
+};
+
+/* remove_pointer.
+ * Removes the given pointer from the map.
+ * The pointer is allowed to be reused only if ReUse if true.
+ */
+template <>
+inline void PointerMapper::remove_pointer<false>(const virtual_pointer_t ptr) {
+ if (is_nullptr(ptr)) {
+ return;
+ }
+ m_pointerMap.erase(this->get_node(ptr));
+}
+
+/**
+ * Malloc-like interface to the pointer-mapper.
+ * Given a size, creates a byte-typed buffer and returns a
+ * fake pointer to keep track of it.
+ * \param size Size in bytes of the desired allocation
+ * \throw cl::sycl::exception if error while creating the buffer
+ */
+inline void *SYCLmalloc(size_t size, PointerMapper &pMap) {
+ if (size == 0) {
+ return nullptr;
+ }
+ // Create a generic buffer of the given size
+ using buffer_t = cl::sycl::buffer<buffer_data_type_t, 1>;
+ auto thePointer = pMap.add_pointer(buffer_t(cl::sycl::range<1>{size}));
+ // Store the buffer on the global list
+ return static_cast<void *>(thePointer);
+}
+
+/**
+ * Free-like interface to the pointer mapper.
+ * Given a fake-pointer created with the virtual-pointer malloc,
+ * destroys the buffer and remove it from the list.
+ * If ReUse is false, the pointer is not added to the freeList,
+ * it should be false only for sub-buffers.
+ */
+template <bool ReUse = true, typename PointerMapper>
+inline void SYCLfree(void *ptr, PointerMapper &pMap) {
+ pMap.template remove_pointer<ReUse>(ptr);
+}
+
+/**
+ * Clear all the memory allocated by SYCL.
+ */
+template <typename PointerMapper>
+inline void SYCLfreeAll(PointerMapper &pMap) {
+ pMap.clear();
+}
+
+template <cl::sycl::access::mode AcMd, typename T>
+struct RangeAccess {
+ static const auto global_access = cl::sycl::access::target::global_buffer;
+ static const auto is_place_holder = cl::sycl::access::placeholder::true_t;
+ typedef T scalar_t;
+ typedef scalar_t &ref_t;
+ typedef typename cl::sycl::global_ptr<scalar_t>::pointer_t ptr_t;
+
+ // the accessor type does not necessarily the same as T
+ typedef cl::sycl::accessor<scalar_t, 1, AcMd, global_access, is_place_holder>
+ accessor;
+
+ typedef RangeAccess<AcMd, T> self_t;
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE RangeAccess(accessor access,
+ size_t offset,
+ std::intptr_t virtual_ptr)
+ : access_(access), offset_(offset), virtual_ptr_(virtual_ptr) {}
+
+ RangeAccess(cl::sycl::buffer<scalar_t, 1> buff =
+ cl::sycl::buffer<scalar_t, 1>(cl::sycl::range<1>(1)))
+ : access_{accessor{buff}}, offset_(0), virtual_ptr_(-1) {}
+
+ // This should be only used for null constructor on the host side
+ RangeAccess(std::nullptr_t) : RangeAccess() {}
+ // This template parameter must be removed and scalar_t should be replaced
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE ptr_t get_pointer() const {
+ return (access_.get_pointer().get() + offset_);
+ }
+ template <typename Index>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE self_t &operator+=(Index offset) {
+ offset_ += (offset);
+ return *this;
+ }
+ template <typename Index>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE self_t operator+(Index offset) const {
+ return self_t(access_, offset_ + offset, virtual_ptr_);
+ }
+ template <typename Index>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE self_t operator-(Index offset) const {
+ return self_t(access_, offset_ - offset, virtual_ptr_);
+ }
+ template <typename Index>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE self_t &operator-=(Index offset) {
+ offset_ -= offset;
+ return *this;
+ }
+
+ // THIS IS FOR NULL COMPARISON ONLY
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE friend bool operator==(
+ const RangeAccess &lhs, std::nullptr_t) {
+ return ((lhs.virtual_ptr_ == -1));
+ }
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE friend bool operator!=(
+ const RangeAccess &lhs, std::nullptr_t i) {
+ return !(lhs == i);
+ }
+
+ // THIS IS FOR NULL COMPARISON ONLY
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE friend bool operator==(
+ std::nullptr_t, const RangeAccess &rhs) {
+ return ((rhs.virtual_ptr_ == -1));
+ }
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE friend bool operator!=(
+ std::nullptr_t i, const RangeAccess &rhs) {
+ return !(i == rhs);
+ }
+ // Prefix operator (Increment and return value)
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE self_t &operator++() {
+ offset_++;
+ return (*this);
+ }
+
+ // Postfix operator (Return value and increment)
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE self_t operator++(int i) {
+ EIGEN_UNUSED_VARIABLE(i);
+ self_t temp_iterator(*this);
+ offset_++;
+ return temp_iterator;
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE std::ptrdiff_t get_size() const {
+ return (access_.get_count() - offset_);
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE std::ptrdiff_t get_offset() const {
+ return offset_;
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void set_offset(std::ptrdiff_t offset) {
+ offset_ = offset;
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE ref_t operator*() const {
+ return *get_pointer();
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE ref_t operator*() {
+ return *get_pointer();
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE ptr_t operator->() = delete;
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE ref_t operator[](int x) {
+ return *(get_pointer() + x);
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE ref_t operator[](int x) const {
+ return *(get_pointer() + x);
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE scalar_t *get_virtual_pointer() const {
+ return reinterpret_cast<scalar_t *>(virtual_ptr_ +
+ (offset_ * sizeof(scalar_t)));
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE explicit operator bool() const {
+ return (virtual_ptr_ != -1);
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE operator RangeAccess<AcMd, const T>() {
+ return RangeAccess<AcMd, const T>(access_, offset_, virtual_ptr_);
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ operator RangeAccess<AcMd, const T>() const {
+ return RangeAccess<AcMd, const T>(access_, offset_, virtual_ptr_);
+ }
+ // binding placeholder accessors to a command group handler for SYCL
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void bind(
+ cl::sycl::handler &cgh) const {
+ cgh.require(access_);
+ }
+
+ private:
+ accessor access_;
+ size_t offset_;
+ std::intptr_t virtual_ptr_; // the location of the buffer in the map
+};
+
+template <cl::sycl::access::mode AcMd, typename T>
+struct RangeAccess<AcMd, const T> : RangeAccess<AcMd, T> {
+ typedef RangeAccess<AcMd, T> Base;
+ using Base::Base;
+};
+
+} // namespace internal
+} // namespace TensorSycl
+} // namespace Eigen
+
+#endif // EIGEN_CXX11_TENSOR_TENSOR_SYCL_STORAGE_MEMORY_H
diff --git a/Eigen/src/Core/arch/SYCL/TypeCasting.h b/Eigen/src/Core/arch/SYCL/TypeCasting.h
new file mode 100644
index 0000000..613e823
--- /dev/null
+++ b/Eigen/src/Core/arch/SYCL/TypeCasting.h
@@ -0,0 +1,87 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Mehdi Goli Codeplay Software Ltd.
+// Ralph Potter Codeplay Software Ltd.
+// Luke Iwanski Codeplay Software Ltd.
+// Contact: <eigen@codeplay.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+/*****************************************************************
+ * TypeCasting.h
+ *
+ * \brief:
+ * TypeCasting
+ *
+ *****************************************************************/
+
+#ifndef EIGEN_TYPE_CASTING_SYCL_H
+#define EIGEN_TYPE_CASTING_SYCL_H
+
+#include "../../InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+#ifdef SYCL_DEVICE_ONLY
+template <>
+struct type_casting_traits<float, int> {
+ enum { VectorizedCast = 1, SrcCoeffRatio = 1, TgtCoeffRatio = 1 };
+};
+
+template <>
+EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE cl::sycl::cl_int4
+pcast<cl::sycl::cl_float4, cl::sycl::cl_int4>(const cl::sycl::cl_float4& a) {
+ return a
+ .template convert<cl::sycl::cl_int, cl::sycl::rounding_mode::automatic>();
+}
+
+template <>
+struct type_casting_traits<int, float> {
+ enum { VectorizedCast = 1, SrcCoeffRatio = 1, TgtCoeffRatio = 1 };
+};
+
+template <>
+EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE cl::sycl::cl_float4
+pcast<cl::sycl::cl_int4, cl::sycl::cl_float4>(const cl::sycl::cl_int4& a) {
+ return a.template convert<cl::sycl::cl_float,
+ cl::sycl::rounding_mode::automatic>();
+}
+
+template <>
+struct type_casting_traits<double, float> {
+ enum { VectorizedCast = 1, SrcCoeffRatio = 2, TgtCoeffRatio = 1 };
+};
+
+template <>
+EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE cl::sycl::cl_float4
+pcast<cl::sycl::cl_double2, cl::sycl::cl_float4>(
+ const cl::sycl::cl_double2& a, const cl::sycl::cl_double2& b) {
+ auto a1 = a.template convert<cl::sycl::cl_float,
+ cl::sycl::rounding_mode::automatic>();
+ auto b1 = b.template convert<cl::sycl::cl_float,
+ cl::sycl::rounding_mode::automatic>();
+ return cl::sycl::float4(a1.x(), a1.y(), b1.x(), b1.y());
+}
+
+template <>
+struct type_casting_traits<float, double> {
+ enum { VectorizedCast = 1, SrcCoeffRatio = 1, TgtCoeffRatio = 2 };
+};
+
+template <>
+EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE cl::sycl::cl_double2
+pcast<cl::sycl::cl_float4, cl::sycl::cl_double2>(const cl::sycl::cl_float4& a) {
+ // Simply discard the second half of the input
+ return cl::sycl::cl_double2(a.x(), a.y());
+}
+
+#endif
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_TYPE_CASTING_SYCL_H
diff --git a/Eigen/src/Core/arch/ZVector/Complex.h b/Eigen/src/Core/arch/ZVector/Complex.h
new file mode 100644
index 0000000..df5c8d4
--- /dev/null
+++ b/Eigen/src/Core/arch/ZVector/Complex.h
@@ -0,0 +1,428 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2010 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2016 Konstantinos Margaritis <markos@freevec.org>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_COMPLEX32_ZVECTOR_H
+#define EIGEN_COMPLEX32_ZVECTOR_H
+
+#include "../../InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+
+#if !defined(__ARCH__) || (defined(__ARCH__) && __ARCH__ >= 12)
+static Packet4ui p4ui_CONJ_XOR = { 0x00000000, 0x80000000, 0x00000000, 0x80000000 }; //vec_mergeh((Packet4ui)p4i_ZERO, (Packet4ui)p4f_MZERO);
+#endif
+
+static Packet2ul p2ul_CONJ_XOR1 = (Packet2ul) vec_sld((Packet4ui) p2d_ZERO_, (Packet4ui) p2l_ZERO, 8);//{ 0x8000000000000000, 0x0000000000000000 };
+static Packet2ul p2ul_CONJ_XOR2 = (Packet2ul) vec_sld((Packet4ui) p2l_ZERO, (Packet4ui) p2d_ZERO_, 8);//{ 0x8000000000000000, 0x0000000000000000 };
+
+struct Packet1cd
+{
+ EIGEN_STRONG_INLINE Packet1cd() {}
+ EIGEN_STRONG_INLINE explicit Packet1cd(const Packet2d& a) : v(a) {}
+ Packet2d v;
+};
+
+struct Packet2cf
+{
+ EIGEN_STRONG_INLINE Packet2cf() {}
+ EIGEN_STRONG_INLINE explicit Packet2cf(const Packet4f& a) : v(a) {}
+#if !defined(__ARCH__) || (defined(__ARCH__) && __ARCH__ < 12)
+ union {
+ Packet4f v;
+ Packet1cd cd[2];
+ };
+#else
+ Packet4f v;
+#endif
+};
+
+template<> struct packet_traits<std::complex<float> > : default_packet_traits
+{
+ typedef Packet2cf type;
+ typedef Packet2cf half;
+ enum {
+ Vectorizable = 1,
+ AlignedOnScalar = 1,
+ size = 2,
+ HasHalfPacket = 0,
+
+ HasAdd = 1,
+ HasSub = 1,
+ HasMul = 1,
+ HasDiv = 1,
+ HasNegate = 1,
+ HasAbs = 0,
+ HasAbs2 = 0,
+ HasMin = 0,
+ HasMax = 0,
+ HasBlend = 1,
+ HasSetLinear = 0
+ };
+};
+
+
+template<> struct packet_traits<std::complex<double> > : default_packet_traits
+{
+ typedef Packet1cd type;
+ typedef Packet1cd half;
+ enum {
+ Vectorizable = 1,
+ AlignedOnScalar = 1,
+ size = 1,
+ HasHalfPacket = 0,
+
+ HasAdd = 1,
+ HasSub = 1,
+ HasMul = 1,
+ HasDiv = 1,
+ HasNegate = 1,
+ HasAbs = 0,
+ HasAbs2 = 0,
+ HasMin = 0,
+ HasMax = 0,
+ HasSetLinear = 0
+ };
+};
+
+template<> struct unpacket_traits<Packet2cf> {
+ typedef std::complex<float> type;
+ enum {size=2, alignment=Aligned16, vectorizable=true, masked_load_available=false, masked_store_available=false};
+ typedef Packet2cf half;
+ typedef Packet4f as_real;
+};
+template<> struct unpacket_traits<Packet1cd> {
+ typedef std::complex<double> type;
+ enum {size=1, alignment=Aligned16, vectorizable=true, masked_load_available=false, masked_store_available=false};
+ typedef Packet1cd half;
+ typedef Packet2d as_real;
+};
+
+/* Forward declaration */
+EIGEN_STRONG_INLINE void ptranspose(PacketBlock<Packet2cf,2>& kernel);
+
+/* complex<double> first */
+template<> EIGEN_STRONG_INLINE Packet1cd pload <Packet1cd>(const std::complex<double>* from) { EIGEN_DEBUG_ALIGNED_LOAD return Packet1cd(pload<Packet2d>((const double*)from)); }
+template<> EIGEN_STRONG_INLINE Packet1cd ploadu<Packet1cd>(const std::complex<double>* from) { EIGEN_DEBUG_UNALIGNED_LOAD return Packet1cd(ploadu<Packet2d>((const double*)from)); }
+template<> EIGEN_STRONG_INLINE void pstore <std::complex<double> >(std::complex<double> * to, const Packet1cd& from) { EIGEN_DEBUG_ALIGNED_STORE pstore((double*)to, from.v); }
+template<> EIGEN_STRONG_INLINE void pstoreu<std::complex<double> >(std::complex<double> * to, const Packet1cd& from) { EIGEN_DEBUG_UNALIGNED_STORE pstoreu((double*)to, from.v); }
+
+template<> EIGEN_STRONG_INLINE Packet1cd pset1<Packet1cd>(const std::complex<double>& from)
+{ /* here we really have to use unaligned loads :( */ return ploadu<Packet1cd>(&from); }
+
+template<> EIGEN_DEVICE_FUNC inline Packet1cd pgather<std::complex<double>, Packet1cd>(const std::complex<double>* from, Index stride EIGEN_UNUSED)
+{
+ return pload<Packet1cd>(from);
+}
+template<> EIGEN_DEVICE_FUNC inline void pscatter<std::complex<double>, Packet1cd>(std::complex<double>* to, const Packet1cd& from, Index stride EIGEN_UNUSED)
+{
+ pstore<std::complex<double> >(to, from);
+}
+template<> EIGEN_STRONG_INLINE Packet1cd padd<Packet1cd>(const Packet1cd& a, const Packet1cd& b) { return Packet1cd(a.v + b.v); }
+template<> EIGEN_STRONG_INLINE Packet1cd psub<Packet1cd>(const Packet1cd& a, const Packet1cd& b) { return Packet1cd(a.v - b.v); }
+template<> EIGEN_STRONG_INLINE Packet1cd pnegate(const Packet1cd& a) { return Packet1cd(pnegate(Packet2d(a.v))); }
+template<> EIGEN_STRONG_INLINE Packet1cd pconj(const Packet1cd& a) { return Packet1cd((Packet2d)vec_xor((Packet2d)a.v, (Packet2d)p2ul_CONJ_XOR2)); }
+template<> EIGEN_STRONG_INLINE Packet1cd pmul<Packet1cd>(const Packet1cd& a, const Packet1cd& b)
+{
+ Packet2d a_re, a_im, v1, v2;
+
+ // Permute and multiply the real parts of a and b
+ a_re = vec_perm(a.v, a.v, p16uc_PSET64_HI);
+ // Get the imaginary parts of a
+ a_im = vec_perm(a.v, a.v, p16uc_PSET64_LO);
+ // multiply a_re * b
+ v1 = vec_madd(a_re, b.v, p2d_ZERO);
+ // multiply a_im * b and get the conjugate result
+ v2 = vec_madd(a_im, b.v, p2d_ZERO);
+ v2 = (Packet2d) vec_sld((Packet4ui)v2, (Packet4ui)v2, 8);
+ v2 = (Packet2d) vec_xor((Packet2d)v2, (Packet2d) p2ul_CONJ_XOR1);
+
+ return Packet1cd(v1 + v2);
+}
+template<> EIGEN_STRONG_INLINE Packet1cd pand <Packet1cd>(const Packet1cd& a, const Packet1cd& b) { return Packet1cd(vec_and(a.v,b.v)); }
+template<> EIGEN_STRONG_INLINE Packet1cd por <Packet1cd>(const Packet1cd& a, const Packet1cd& b) { return Packet1cd(vec_or(a.v,b.v)); }
+template<> EIGEN_STRONG_INLINE Packet1cd pxor <Packet1cd>(const Packet1cd& a, const Packet1cd& b) { return Packet1cd(vec_xor(a.v,b.v)); }
+template<> EIGEN_STRONG_INLINE Packet1cd pandnot <Packet1cd>(const Packet1cd& a, const Packet1cd& b) { return Packet1cd(vec_and(a.v, vec_nor(b.v,b.v))); }
+template<> EIGEN_STRONG_INLINE Packet1cd ploaddup<Packet1cd>(const std::complex<double>* from) { return pset1<Packet1cd>(*from); }
+template<> EIGEN_STRONG_INLINE Packet1cd pcmp_eq(const Packet1cd& a, const Packet1cd& b) {
+ Packet2d eq = vec_cmpeq (a.v, b.v);
+ Packet2d tmp = { eq[1], eq[0] };
+ return (Packet1cd)pand<Packet2d>(eq, tmp);
+}
+
+template<> EIGEN_STRONG_INLINE void prefetch<std::complex<double> >(const std::complex<double> * addr) { EIGEN_ZVECTOR_PREFETCH(addr); }
+
+template<> EIGEN_STRONG_INLINE std::complex<double> pfirst<Packet1cd>(const Packet1cd& a)
+{
+ EIGEN_ALIGN16 std::complex<double> res;
+ pstore<std::complex<double> >(&res, a);
+
+ return res;
+}
+
+template<> EIGEN_STRONG_INLINE Packet1cd preverse(const Packet1cd& a) { return a; }
+template<> EIGEN_STRONG_INLINE std::complex<double> predux<Packet1cd>(const Packet1cd& a)
+{
+ return pfirst(a);
+}
+template<> EIGEN_STRONG_INLINE std::complex<double> predux_mul<Packet1cd>(const Packet1cd& a)
+{
+ return pfirst(a);
+}
+EIGEN_MAKE_CONJ_HELPER_CPLX_REAL(Packet1cd,Packet2d)
+
+template<> EIGEN_STRONG_INLINE Packet1cd pdiv<Packet1cd>(const Packet1cd& a, const Packet1cd& b)
+{
+ return pdiv_complex(a, b);
+}
+
+EIGEN_STRONG_INLINE Packet1cd pcplxflip/*<Packet1cd>*/(const Packet1cd& x)
+{
+ return Packet1cd(preverse(Packet2d(x.v)));
+}
+
+EIGEN_STRONG_INLINE void ptranspose(PacketBlock<Packet1cd,2>& kernel)
+{
+ Packet2d tmp = vec_perm(kernel.packet[0].v, kernel.packet[1].v, p16uc_TRANSPOSE64_HI);
+ kernel.packet[1].v = vec_perm(kernel.packet[0].v, kernel.packet[1].v, p16uc_TRANSPOSE64_LO);
+ kernel.packet[0].v = tmp;
+}
+
+/* complex<float> follows */
+template<> EIGEN_STRONG_INLINE Packet2cf pload <Packet2cf>(const std::complex<float>* from) { EIGEN_DEBUG_ALIGNED_LOAD return Packet2cf(pload<Packet4f>((const float*)from)); }
+template<> EIGEN_STRONG_INLINE Packet2cf ploadu<Packet2cf>(const std::complex<float>* from) { EIGEN_DEBUG_UNALIGNED_LOAD return Packet2cf(ploadu<Packet4f>((const float*)from)); }
+template<> EIGEN_STRONG_INLINE void pstore <std::complex<float> >(std::complex<float> * to, const Packet2cf& from) { EIGEN_DEBUG_ALIGNED_STORE pstore((float*)to, from.v); }
+template<> EIGEN_STRONG_INLINE void pstoreu<std::complex<float> >(std::complex<float> * to, const Packet2cf& from) { EIGEN_DEBUG_UNALIGNED_STORE pstoreu((float*)to, from.v); }
+
+template<> EIGEN_STRONG_INLINE std::complex<float> pfirst<Packet2cf>(const Packet2cf& a)
+{
+ EIGEN_ALIGN16 std::complex<float> res[2];
+ pstore<std::complex<float> >(res, a);
+
+ return res[0];
+}
+
+
+#if !defined(__ARCH__) || (defined(__ARCH__) && __ARCH__ < 12)
+template<> EIGEN_STRONG_INLINE Packet2cf pset1<Packet2cf>(const std::complex<float>& from)
+{
+ Packet2cf res;
+ res.cd[0] = Packet1cd(vec_ld2f((const float *)&from));
+ res.cd[1] = res.cd[0];
+ return res;
+}
+#else
+template<> EIGEN_STRONG_INLINE Packet2cf pset1<Packet2cf>(const std::complex<float>& from)
+{
+ Packet2cf res;
+ if((std::ptrdiff_t(&from) % 16) == 0)
+ res.v = pload<Packet4f>((const float *)&from);
+ else
+ res.v = ploadu<Packet4f>((const float *)&from);
+ res.v = vec_perm(res.v, res.v, p16uc_PSET64_HI);
+ return res;
+}
+#endif
+
+template<> EIGEN_DEVICE_FUNC inline Packet2cf pgather<std::complex<float>, Packet2cf>(const std::complex<float>* from, Index stride)
+{
+ EIGEN_ALIGN16 std::complex<float> af[2];
+ af[0] = from[0*stride];
+ af[1] = from[1*stride];
+ return pload<Packet2cf>(af);
+}
+template<> EIGEN_DEVICE_FUNC inline void pscatter<std::complex<float>, Packet2cf>(std::complex<float>* to, const Packet2cf& from, Index stride)
+{
+ EIGEN_ALIGN16 std::complex<float> af[2];
+ pstore<std::complex<float> >((std::complex<float> *) af, from);
+ to[0*stride] = af[0];
+ to[1*stride] = af[1];
+}
+
+template<> EIGEN_STRONG_INLINE Packet2cf padd<Packet2cf>(const Packet2cf& a, const Packet2cf& b) { return Packet2cf(padd<Packet4f>(a.v, b.v)); }
+template<> EIGEN_STRONG_INLINE Packet2cf psub<Packet2cf>(const Packet2cf& a, const Packet2cf& b) { return Packet2cf(psub<Packet4f>(a.v, b.v)); }
+template<> EIGEN_STRONG_INLINE Packet2cf pnegate(const Packet2cf& a) { return Packet2cf(pnegate(Packet4f(a.v))); }
+
+template<> EIGEN_STRONG_INLINE Packet2cf pand <Packet2cf>(const Packet2cf& a, const Packet2cf& b) { return Packet2cf(pand<Packet4f>(a.v,b.v)); }
+template<> EIGEN_STRONG_INLINE Packet2cf por <Packet2cf>(const Packet2cf& a, const Packet2cf& b) { return Packet2cf(por<Packet4f>(a.v,b.v)); }
+template<> EIGEN_STRONG_INLINE Packet2cf pxor <Packet2cf>(const Packet2cf& a, const Packet2cf& b) { return Packet2cf(pxor<Packet4f>(a.v,b.v)); }
+template<> EIGEN_STRONG_INLINE Packet2cf pandnot<Packet2cf>(const Packet2cf& a, const Packet2cf& b) { return Packet2cf(pandnot<Packet4f>(a.v,b.v)); }
+
+template<> EIGEN_STRONG_INLINE Packet2cf ploaddup<Packet2cf>(const std::complex<float>* from) { return pset1<Packet2cf>(*from); }
+
+template<> EIGEN_STRONG_INLINE void prefetch<std::complex<float> >(const std::complex<float> * addr) { EIGEN_ZVECTOR_PREFETCH(addr); }
+
+
+#if !defined(__ARCH__) || (defined(__ARCH__) && __ARCH__ < 12)
+
+template<> EIGEN_STRONG_INLINE Packet2cf pcmp_eq(const Packet2cf& a, const Packet2cf& b) {
+ Packet4f eq = pcmp_eq<Packet4f> (a.v, b.v);
+ Packet2cf res;
+ Packet2d tmp1 = { eq.v4f[0][1], eq.v4f[0][0] };
+ Packet2d tmp2 = { eq.v4f[1][1], eq.v4f[1][0] };
+ res.v.v4f[0] = pand<Packet2d>(eq.v4f[0], tmp1);
+ res.v.v4f[1] = pand<Packet2d>(eq.v4f[1], tmp2);
+ return res;
+}
+
+template<> EIGEN_STRONG_INLINE Packet2cf pconj(const Packet2cf& a)
+{
+ Packet2cf res;
+ res.v.v4f[0] = pconj(Packet1cd(reinterpret_cast<Packet2d>(a.v.v4f[0]))).v;
+ res.v.v4f[1] = pconj(Packet1cd(reinterpret_cast<Packet2d>(a.v.v4f[1]))).v;
+ return res;
+}
+
+template<> EIGEN_STRONG_INLINE Packet2cf pmul<Packet2cf>(const Packet2cf& a, const Packet2cf& b)
+{
+ Packet2cf res;
+ res.v.v4f[0] = pmul(Packet1cd(reinterpret_cast<Packet2d>(a.v.v4f[0])), Packet1cd(reinterpret_cast<Packet2d>(b.v.v4f[0]))).v;
+ res.v.v4f[1] = pmul(Packet1cd(reinterpret_cast<Packet2d>(a.v.v4f[1])), Packet1cd(reinterpret_cast<Packet2d>(b.v.v4f[1]))).v;
+ return res;
+}
+
+template<> EIGEN_STRONG_INLINE Packet2cf preverse(const Packet2cf& a)
+{
+ Packet2cf res;
+ res.cd[0] = a.cd[1];
+ res.cd[1] = a.cd[0];
+ return res;
+}
+
+template<> EIGEN_STRONG_INLINE std::complex<float> predux<Packet2cf>(const Packet2cf& a)
+{
+ std::complex<float> res;
+ Packet1cd b = padd<Packet1cd>(a.cd[0], a.cd[1]);
+ vec_st2f(b.v, (float*)&res);
+ return res;
+}
+
+template<> EIGEN_STRONG_INLINE std::complex<float> predux_mul<Packet2cf>(const Packet2cf& a)
+{
+ std::complex<float> res;
+ Packet1cd b = pmul<Packet1cd>(a.cd[0], a.cd[1]);
+ vec_st2f(b.v, (float*)&res);
+ return res;
+}
+
+EIGEN_MAKE_CONJ_HELPER_CPLX_REAL(Packet2cf,Packet4f)
+
+template<> EIGEN_STRONG_INLINE Packet2cf pdiv<Packet2cf>(const Packet2cf& a, const Packet2cf& b)
+{
+ return pdiv_complex(a, b);
+}
+
+EIGEN_STRONG_INLINE Packet2cf pcplxflip/*<Packet2cf>*/(const Packet2cf& x)
+{
+ Packet2cf res;
+ res.cd[0] = pcplxflip(x.cd[0]);
+ res.cd[1] = pcplxflip(x.cd[1]);
+ return res;
+}
+
+EIGEN_STRONG_INLINE void ptranspose(PacketBlock<Packet2cf,2>& kernel)
+{
+ Packet1cd tmp = kernel.packet[0].cd[1];
+ kernel.packet[0].cd[1] = kernel.packet[1].cd[0];
+ kernel.packet[1].cd[0] = tmp;
+}
+
+template<> EIGEN_STRONG_INLINE Packet2cf pblend(const Selector<2>& ifPacket, const Packet2cf& thenPacket, const Packet2cf& elsePacket) {
+ Packet2cf result;
+ const Selector<4> ifPacket4 = { ifPacket.select[0], ifPacket.select[0], ifPacket.select[1], ifPacket.select[1] };
+ result.v = pblend<Packet4f>(ifPacket4, thenPacket.v, elsePacket.v);
+ return result;
+}
+#else
+template<> EIGEN_STRONG_INLINE Packet2cf pcmp_eq(const Packet2cf& a, const Packet2cf& b) {
+ Packet4f eq = vec_cmpeq (a.v, b.v);
+ Packet4f tmp = { eq[1], eq[0], eq[3], eq[2] };
+ return (Packet2cf)pand<Packet4f>(eq, tmp);
+}
+template<> EIGEN_STRONG_INLINE Packet2cf pconj(const Packet2cf& a) { return Packet2cf(pxor<Packet4f>(a.v, reinterpret_cast<Packet4f>(p4ui_CONJ_XOR))); }
+template<> EIGEN_STRONG_INLINE Packet2cf pmul<Packet2cf>(const Packet2cf& a, const Packet2cf& b)
+{
+ Packet4f a_re, a_im, prod, prod_im;
+
+ // Permute and multiply the real parts of a and b
+ a_re = vec_perm(a.v, a.v, p16uc_PSET32_WODD);
+
+ // Get the imaginary parts of a
+ a_im = vec_perm(a.v, a.v, p16uc_PSET32_WEVEN);
+
+ // multiply a_im * b and get the conjugate result
+ prod_im = a_im * b.v;
+ prod_im = pxor<Packet4f>(prod_im, reinterpret_cast<Packet4f>(p4ui_CONJ_XOR));
+ // permute back to a proper order
+ prod_im = vec_perm(prod_im, prod_im, p16uc_COMPLEX32_REV);
+
+ // multiply a_re * b, add prod_im
+ prod = pmadd<Packet4f>(a_re, b.v, prod_im);
+
+ return Packet2cf(prod);
+}
+
+template<> EIGEN_STRONG_INLINE Packet2cf preverse(const Packet2cf& a)
+{
+ Packet4f rev_a;
+ rev_a = vec_perm(a.v, a.v, p16uc_COMPLEX32_REV2);
+ return Packet2cf(rev_a);
+}
+
+template<> EIGEN_STRONG_INLINE std::complex<float> predux<Packet2cf>(const Packet2cf& a)
+{
+ Packet4f b;
+ b = vec_sld(a.v, a.v, 8);
+ b = padd<Packet4f>(a.v, b);
+ return pfirst<Packet2cf>(Packet2cf(b));
+}
+
+template<> EIGEN_STRONG_INLINE std::complex<float> predux_mul<Packet2cf>(const Packet2cf& a)
+{
+ Packet4f b;
+ Packet2cf prod;
+ b = vec_sld(a.v, a.v, 8);
+ prod = pmul<Packet2cf>(a, Packet2cf(b));
+
+ return pfirst<Packet2cf>(prod);
+}
+
+EIGEN_MAKE_CONJ_HELPER_CPLX_REAL(Packet2cf,Packet4f)
+
+template<> EIGEN_STRONG_INLINE Packet2cf pdiv<Packet2cf>(const Packet2cf& a, const Packet2cf& b)
+{
+ return pdiv_complex(a, b);
+}
+
+template<> EIGEN_STRONG_INLINE Packet2cf pcplxflip<Packet2cf>(const Packet2cf& x)
+{
+ return Packet2cf(vec_perm(x.v, x.v, p16uc_COMPLEX32_REV));
+}
+
+EIGEN_STRONG_INLINE void ptranspose(PacketBlock<Packet2cf,2>& kernel)
+{
+ Packet4f tmp = vec_perm(kernel.packet[0].v, kernel.packet[1].v, p16uc_TRANSPOSE64_HI);
+ kernel.packet[1].v = vec_perm(kernel.packet[0].v, kernel.packet[1].v, p16uc_TRANSPOSE64_LO);
+ kernel.packet[0].v = tmp;
+}
+
+template<> EIGEN_STRONG_INLINE Packet2cf pblend(const Selector<2>& ifPacket, const Packet2cf& thenPacket, const Packet2cf& elsePacket) {
+ Packet2cf result;
+ result.v = reinterpret_cast<Packet4f>(pblend<Packet2d>(ifPacket, reinterpret_cast<Packet2d>(thenPacket.v), reinterpret_cast<Packet2d>(elsePacket.v)));
+ return result;
+}
+#endif
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_COMPLEX32_ZVECTOR_H
diff --git a/Eigen/src/Core/arch/ZVector/MathFunctions.h b/Eigen/src/Core/arch/ZVector/MathFunctions.h
new file mode 100644
index 0000000..1f2da26
--- /dev/null
+++ b/Eigen/src/Core/arch/ZVector/MathFunctions.h
@@ -0,0 +1,235 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2007 Julien Pommier
+// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2016 Konstantinos Margaritis <markos@freevec.org>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+/* The sin, cos, exp, and log functions of this file come from
+ * Julien Pommier's sse math library: http://gruntthepeon.free.fr/ssemath/
+ */
+
+#ifndef EIGEN_MATH_FUNCTIONS_ZVECTOR_H
+#define EIGEN_MATH_FUNCTIONS_ZVECTOR_H
+
+#include "../../InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+
+#if !defined(__ARCH__) || (defined(__ARCH__) && __ARCH__ >= 12)
+static EIGEN_DECLARE_CONST_Packet4f(1 , 1.0f);
+static EIGEN_DECLARE_CONST_Packet4f(half, 0.5f);
+static EIGEN_DECLARE_CONST_Packet4i(0x7f, 0x7f);
+static EIGEN_DECLARE_CONST_Packet4i(23, 23);
+
+static EIGEN_DECLARE_CONST_Packet4f_FROM_INT(inv_mant_mask, ~0x7f800000);
+
+/* the smallest non denormalized float number */
+static EIGEN_DECLARE_CONST_Packet4f_FROM_INT(min_norm_pos, 0x00800000);
+static EIGEN_DECLARE_CONST_Packet4f_FROM_INT(minus_inf, 0xff800000); // -1.f/0.f
+static EIGEN_DECLARE_CONST_Packet4f_FROM_INT(minus_nan, 0xffffffff);
+
+/* natural logarithm computed for 4 simultaneous float
+ return NaN for x <= 0
+*/
+static EIGEN_DECLARE_CONST_Packet4f(cephes_SQRTHF, 0.707106781186547524f);
+static EIGEN_DECLARE_CONST_Packet4f(cephes_log_p0, 7.0376836292E-2f);
+static EIGEN_DECLARE_CONST_Packet4f(cephes_log_p1, - 1.1514610310E-1f);
+static EIGEN_DECLARE_CONST_Packet4f(cephes_log_p2, 1.1676998740E-1f);
+static EIGEN_DECLARE_CONST_Packet4f(cephes_log_p3, - 1.2420140846E-1f);
+static EIGEN_DECLARE_CONST_Packet4f(cephes_log_p4, + 1.4249322787E-1f);
+static EIGEN_DECLARE_CONST_Packet4f(cephes_log_p5, - 1.6668057665E-1f);
+static EIGEN_DECLARE_CONST_Packet4f(cephes_log_p6, + 2.0000714765E-1f);
+static EIGEN_DECLARE_CONST_Packet4f(cephes_log_p7, - 2.4999993993E-1f);
+static EIGEN_DECLARE_CONST_Packet4f(cephes_log_p8, + 3.3333331174E-1f);
+static EIGEN_DECLARE_CONST_Packet4f(cephes_log_q1, -2.12194440e-4f);
+static EIGEN_DECLARE_CONST_Packet4f(cephes_log_q2, 0.693359375f);
+
+static EIGEN_DECLARE_CONST_Packet4f(exp_hi, 88.3762626647950f);
+static EIGEN_DECLARE_CONST_Packet4f(exp_lo, -88.3762626647949f);
+
+static EIGEN_DECLARE_CONST_Packet4f(cephes_LOG2EF, 1.44269504088896341f);
+static EIGEN_DECLARE_CONST_Packet4f(cephes_exp_C1, 0.693359375f);
+static EIGEN_DECLARE_CONST_Packet4f(cephes_exp_C2, -2.12194440e-4f);
+
+static EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p0, 1.9875691500E-4f);
+static EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p1, 1.3981999507E-3f);
+static EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p2, 8.3334519073E-3f);
+static EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p3, 4.1665795894E-2f);
+static EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p4, 1.6666665459E-1f);
+static EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p5, 5.0000001201E-1f);
+#endif
+
+static EIGEN_DECLARE_CONST_Packet2d(1 , 1.0);
+static EIGEN_DECLARE_CONST_Packet2d(2 , 2.0);
+static EIGEN_DECLARE_CONST_Packet2d(half, 0.5);
+
+static EIGEN_DECLARE_CONST_Packet2d(exp_hi, 709.437);
+static EIGEN_DECLARE_CONST_Packet2d(exp_lo, -709.436139303);
+
+static EIGEN_DECLARE_CONST_Packet2d(cephes_LOG2EF, 1.4426950408889634073599);
+
+static EIGEN_DECLARE_CONST_Packet2d(cephes_exp_p0, 1.26177193074810590878e-4);
+static EIGEN_DECLARE_CONST_Packet2d(cephes_exp_p1, 3.02994407707441961300e-2);
+static EIGEN_DECLARE_CONST_Packet2d(cephes_exp_p2, 9.99999999999999999910e-1);
+
+static EIGEN_DECLARE_CONST_Packet2d(cephes_exp_q0, 3.00198505138664455042e-6);
+static EIGEN_DECLARE_CONST_Packet2d(cephes_exp_q1, 2.52448340349684104192e-3);
+static EIGEN_DECLARE_CONST_Packet2d(cephes_exp_q2, 2.27265548208155028766e-1);
+static EIGEN_DECLARE_CONST_Packet2d(cephes_exp_q3, 2.00000000000000000009e0);
+
+static EIGEN_DECLARE_CONST_Packet2d(cephes_exp_C1, 0.693145751953125);
+static EIGEN_DECLARE_CONST_Packet2d(cephes_exp_C2, 1.42860682030941723212e-6);
+
+template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+Packet2d pexp<Packet2d>(const Packet2d& _x)
+{
+ Packet2d x = _x;
+
+ Packet2d tmp, fx;
+ Packet2l emm0;
+
+ // clamp x
+ x = pmax(pmin(x, p2d_exp_hi), p2d_exp_lo);
+ /* express exp(x) as exp(g + n*log(2)) */
+ fx = pmadd(p2d_cephes_LOG2EF, x, p2d_half);
+
+ fx = vec_floor(fx);
+
+ tmp = pmul(fx, p2d_cephes_exp_C1);
+ Packet2d z = pmul(fx, p2d_cephes_exp_C2);
+ x = psub(x, tmp);
+ x = psub(x, z);
+
+ Packet2d x2 = pmul(x,x);
+
+ Packet2d px = p2d_cephes_exp_p0;
+ px = pmadd(px, x2, p2d_cephes_exp_p1);
+ px = pmadd(px, x2, p2d_cephes_exp_p2);
+ px = pmul (px, x);
+
+ Packet2d qx = p2d_cephes_exp_q0;
+ qx = pmadd(qx, x2, p2d_cephes_exp_q1);
+ qx = pmadd(qx, x2, p2d_cephes_exp_q2);
+ qx = pmadd(qx, x2, p2d_cephes_exp_q3);
+
+ x = pdiv(px,psub(qx,px));
+ x = pmadd(p2d_2,x,p2d_1);
+
+ // build 2^n
+ emm0 = vec_ctsl(fx, 0);
+
+ static const Packet2l p2l_1023 = { 1023, 1023 };
+ static const Packet2ul p2ul_52 = { 52, 52 };
+
+ emm0 = emm0 + p2l_1023;
+ emm0 = emm0 << reinterpret_cast<Packet2l>(p2ul_52);
+
+ // Altivec's max & min operators just drop silent NaNs. Check NaNs in
+ // inputs and return them unmodified.
+ Packet2ul isnumber_mask = reinterpret_cast<Packet2ul>(vec_cmpeq(_x, _x));
+ return vec_sel(_x, pmax(pmul(x, reinterpret_cast<Packet2d>(emm0)), _x),
+ isnumber_mask);
+}
+
+template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+Packet4f pexp<Packet4f>(const Packet4f& _x)
+{
+#if !defined(__ARCH__) || (defined(__ARCH__) && __ARCH__ >= 12)
+ Packet4f x = _x;
+
+ Packet4f tmp, fx;
+ Packet4i emm0;
+
+ // clamp x
+ x = pmax(pmin(x, p4f_exp_hi), p4f_exp_lo);
+
+ // express exp(x) as exp(g + n*log(2))
+ fx = pmadd(x, p4f_cephes_LOG2EF, p4f_half);
+
+ fx = pfloor(fx);
+
+ tmp = pmul(fx, p4f_cephes_exp_C1);
+ Packet4f z = pmul(fx, p4f_cephes_exp_C2);
+ x = psub(x, tmp);
+ x = psub(x, z);
+
+ z = pmul(x,x);
+
+ Packet4f y = p4f_cephes_exp_p0;
+ y = pmadd(y, x, p4f_cephes_exp_p1);
+ y = pmadd(y, x, p4f_cephes_exp_p2);
+ y = pmadd(y, x, p4f_cephes_exp_p3);
+ y = pmadd(y, x, p4f_cephes_exp_p4);
+ y = pmadd(y, x, p4f_cephes_exp_p5);
+ y = pmadd(y, z, x);
+ y = padd(y, p4f_1);
+
+ // build 2^n
+ emm0 = (Packet4i){ (int)fx[0], (int)fx[1], (int)fx[2], (int)fx[3] };
+ emm0 = emm0 + p4i_0x7f;
+ emm0 = emm0 << reinterpret_cast<Packet4i>(p4i_23);
+
+ return pmax(pmul(y, reinterpret_cast<Packet4f>(emm0)), _x);
+#else
+ Packet4f res;
+ res.v4f[0] = pexp<Packet2d>(_x.v4f[0]);
+ res.v4f[1] = pexp<Packet2d>(_x.v4f[1]);
+ return res;
+#endif
+}
+
+template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+Packet2d psqrt<Packet2d>(const Packet2d& x)
+{
+ return vec_sqrt(x);
+}
+
+template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+Packet4f psqrt<Packet4f>(const Packet4f& x)
+{
+ Packet4f res;
+#if !defined(__ARCH__) || (defined(__ARCH__) && __ARCH__ >= 12)
+ res = vec_sqrt(x);
+#else
+ res.v4f[0] = psqrt<Packet2d>(x.v4f[0]);
+ res.v4f[1] = psqrt<Packet2d>(x.v4f[1]);
+#endif
+ return res;
+}
+
+template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+Packet2d prsqrt<Packet2d>(const Packet2d& x) {
+ return pset1<Packet2d>(1.0) / psqrt<Packet2d>(x);
+}
+
+template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+Packet4f prsqrt<Packet4f>(const Packet4f& x) {
+ Packet4f res;
+#if !defined(__ARCH__) || (defined(__ARCH__) && __ARCH__ >= 12)
+ res = pset1<Packet4f>(1.0) / psqrt<Packet4f>(x);
+#else
+ res.v4f[0] = prsqrt<Packet2d>(x.v4f[0]);
+ res.v4f[1] = prsqrt<Packet2d>(x.v4f[1]);
+#endif
+ return res;
+}
+
+// Hyperbolic Tangent function.
+template <>
+EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet4f
+ptanh<Packet4f>(const Packet4f& x) {
+ return internal::generic_fast_tanh_float(x);
+}
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_MATH_FUNCTIONS_ZVECTOR_H
diff --git a/Eigen/src/Core/arch/ZVector/PacketMath.h b/Eigen/src/Core/arch/ZVector/PacketMath.h
new file mode 100644
index 0000000..26b6f0d
--- /dev/null
+++ b/Eigen/src/Core/arch/ZVector/PacketMath.h
@@ -0,0 +1,1062 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2016 Konstantinos Margaritis <markos@freevec.org>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_PACKET_MATH_ZVECTOR_H
+#define EIGEN_PACKET_MATH_ZVECTOR_H
+
+#include "../../InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+
+#ifndef EIGEN_CACHEFRIENDLY_PRODUCT_THRESHOLD
+#define EIGEN_CACHEFRIENDLY_PRODUCT_THRESHOLD 16
+#endif
+
+#ifndef EIGEN_HAS_SINGLE_INSTRUCTION_MADD
+#define EIGEN_HAS_SINGLE_INSTRUCTION_MADD
+#endif
+
+#ifndef EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS
+#define EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS 32
+#endif
+
+typedef __vector int Packet4i;
+typedef __vector unsigned int Packet4ui;
+typedef __vector __bool int Packet4bi;
+typedef __vector short int Packet8i;
+typedef __vector unsigned char Packet16uc;
+typedef __vector double Packet2d;
+typedef __vector unsigned long long Packet2ul;
+typedef __vector long long Packet2l;
+
+// Z14 has builtin support for float vectors
+#if !defined(__ARCH__) || (defined(__ARCH__) && __ARCH__ >= 12)
+typedef __vector float Packet4f;
+#else
+typedef struct {
+ Packet2d v4f[2];
+} Packet4f;
+#endif
+
+typedef union {
+ numext::int32_t i[4];
+ numext::uint32_t ui[4];
+ numext::int64_t l[2];
+ numext::uint64_t ul[2];
+ double d[2];
+ float f[4];
+ Packet4i v4i;
+ Packet4ui v4ui;
+ Packet2l v2l;
+ Packet2ul v2ul;
+ Packet2d v2d;
+#if !defined(__ARCH__) || (defined(__ARCH__) && __ARCH__ >= 12)
+ Packet4f v4f;
+#endif
+} Packet;
+
+// We don't want to write the same code all the time, but we need to reuse the constants
+// and it doesn't really work to declare them global, so we define macros instead
+
+#define EIGEN_DECLARE_CONST_FAST_Packet4i(NAME,X) \
+ Packet4i p4i_##NAME = reinterpret_cast<Packet4i>(vec_splat_s32(X))
+
+#define EIGEN_DECLARE_CONST_FAST_Packet2d(NAME,X) \
+ Packet2d p2d_##NAME = reinterpret_cast<Packet2d>(vec_splat_s64(X))
+
+#define EIGEN_DECLARE_CONST_FAST_Packet2l(NAME,X) \
+ Packet2l p2l_##NAME = reinterpret_cast<Packet2l>(vec_splat_s64(X))
+
+#define EIGEN_DECLARE_CONST_Packet4i(NAME,X) \
+ Packet4i p4i_##NAME = pset1<Packet4i>(X)
+
+#define EIGEN_DECLARE_CONST_Packet2d(NAME,X) \
+ Packet2d p2d_##NAME = pset1<Packet2d>(X)
+
+#define EIGEN_DECLARE_CONST_Packet2l(NAME,X) \
+ Packet2l p2l_##NAME = pset1<Packet2l>(X)
+
+// These constants are endian-agnostic
+static EIGEN_DECLARE_CONST_FAST_Packet4i(ZERO, 0); //{ 0, 0, 0, 0,}
+static EIGEN_DECLARE_CONST_FAST_Packet4i(ONE, 1); //{ 1, 1, 1, 1}
+
+static EIGEN_DECLARE_CONST_FAST_Packet2d(ZERO, 0);
+static EIGEN_DECLARE_CONST_FAST_Packet2l(ZERO, 0);
+static EIGEN_DECLARE_CONST_FAST_Packet2l(ONE, 1);
+
+static Packet2d p2d_ONE = { 1.0, 1.0 };
+static Packet2d p2d_ZERO_ = { numext::bit_cast<double>(0x8000000000000000ull),
+ numext::bit_cast<double>(0x8000000000000000ull) };
+
+#if !defined(__ARCH__) || (defined(__ARCH__) && __ARCH__ >= 12)
+#define EIGEN_DECLARE_CONST_FAST_Packet4f(NAME,X) \
+ Packet4f p4f_##NAME = reinterpret_cast<Packet4f>(vec_splat_s32(X))
+
+#define EIGEN_DECLARE_CONST_Packet4f(NAME,X) \
+ Packet4f p4f_##NAME = pset1<Packet4f>(X)
+
+#define EIGEN_DECLARE_CONST_Packet4f_FROM_INT(NAME,X) \
+ const Packet4f p4f_##NAME = reinterpret_cast<Packet4f>(pset1<Packet4i>(X))
+
+static EIGEN_DECLARE_CONST_FAST_Packet4f(ZERO, 0); //{ 0.0, 0.0, 0.0, 0.0}
+static EIGEN_DECLARE_CONST_FAST_Packet4i(MINUS1,-1); //{ -1, -1, -1, -1}
+static Packet4f p4f_MZERO = { 0x80000000, 0x80000000, 0x80000000, 0x80000000};
+#endif
+
+static Packet4i p4i_COUNTDOWN = { 0, 1, 2, 3 };
+static Packet4f p4f_COUNTDOWN = { 0.0, 1.0, 2.0, 3.0 };
+static Packet2d p2d_COUNTDOWN = reinterpret_cast<Packet2d>(vec_sld(reinterpret_cast<Packet16uc>(p2d_ZERO), reinterpret_cast<Packet16uc>(p2d_ONE), 8));
+
+static Packet16uc p16uc_PSET64_HI = { 0,1,2,3, 4,5,6,7, 0,1,2,3, 4,5,6,7 };
+static Packet16uc p16uc_DUPLICATE32_HI = { 0,1,2,3, 0,1,2,3, 4,5,6,7, 4,5,6,7 };
+
+// Mask alignment
+#define EIGEN_MASK_ALIGNMENT 0xfffffffffffffff0
+
+#define EIGEN_ALIGNED_PTR(x) ((std::ptrdiff_t)(x) & EIGEN_MASK_ALIGNMENT)
+
+// Handle endianness properly while loading constants
+// Define global static constants:
+
+static Packet16uc p16uc_FORWARD = { 0,1,2,3, 4,5,6,7, 8,9,10,11, 12,13,14,15 };
+static Packet16uc p16uc_REVERSE32 = { 12,13,14,15, 8,9,10,11, 4,5,6,7, 0,1,2,3 };
+static Packet16uc p16uc_REVERSE64 = { 8,9,10,11, 12,13,14,15, 0,1,2,3, 4,5,6,7 };
+
+static Packet16uc p16uc_PSET32_WODD = vec_sld((Packet16uc) vec_splat((Packet4ui)p16uc_FORWARD, 0), (Packet16uc) vec_splat((Packet4ui)p16uc_FORWARD, 2), 8);//{ 0,1,2,3, 0,1,2,3, 8,9,10,11, 8,9,10,11 };
+static Packet16uc p16uc_PSET32_WEVEN = vec_sld(p16uc_DUPLICATE32_HI, (Packet16uc) vec_splat((Packet4ui)p16uc_FORWARD, 3), 8);//{ 4,5,6,7, 4,5,6,7, 12,13,14,15, 12,13,14,15 };
+/*static Packet16uc p16uc_HALF64_0_16 = vec_sld((Packet16uc)p4i_ZERO, vec_splat((Packet16uc) vec_abs(p4i_MINUS16), 3), 8); //{ 0,0,0,0, 0,0,0,0, 16,16,16,16, 16,16,16,16};
+
+static Packet16uc p16uc_PSET64_HI = (Packet16uc) vec_mergeh((Packet4ui)p16uc_PSET32_WODD, (Packet4ui)p16uc_PSET32_WEVEN); //{ 0,1,2,3, 4,5,6,7, 0,1,2,3, 4,5,6,7 };*/
+static Packet16uc p16uc_PSET64_LO = (Packet16uc) vec_mergel((Packet4ui)p16uc_PSET32_WODD, (Packet4ui)p16uc_PSET32_WEVEN); //{ 8,9,10,11, 12,13,14,15, 8,9,10,11, 12,13,14,15 };
+/*static Packet16uc p16uc_TRANSPOSE64_HI = vec_add(p16uc_PSET64_HI, p16uc_HALF64_0_16); //{ 0,1,2,3, 4,5,6,7, 16,17,18,19, 20,21,22,23};
+static Packet16uc p16uc_TRANSPOSE64_LO = vec_add(p16uc_PSET64_LO, p16uc_HALF64_0_16); //{ 8,9,10,11, 12,13,14,15, 24,25,26,27, 28,29,30,31};*/
+static Packet16uc p16uc_TRANSPOSE64_HI = { 0,1,2,3, 4,5,6,7, 16,17,18,19, 20,21,22,23};
+static Packet16uc p16uc_TRANSPOSE64_LO = { 8,9,10,11, 12,13,14,15, 24,25,26,27, 28,29,30,31};
+
+static Packet16uc p16uc_COMPLEX32_REV = vec_sld(p16uc_REVERSE32, p16uc_REVERSE32, 8); //{ 4,5,6,7, 0,1,2,3, 12,13,14,15, 8,9,10,11 };
+
+static Packet16uc p16uc_COMPLEX32_REV2 = vec_sld(p16uc_FORWARD, p16uc_FORWARD, 8); //{ 8,9,10,11, 12,13,14,15, 0,1,2,3, 4,5,6,7 };
+
+
+#if EIGEN_HAS_BUILTIN(__builtin_prefetch) || EIGEN_COMP_GNUC
+ #define EIGEN_ZVECTOR_PREFETCH(ADDR) __builtin_prefetch(ADDR);
+#else
+ #define EIGEN_ZVECTOR_PREFETCH(ADDR) asm( " pfd [%[addr]]\n" :: [addr] "r" (ADDR) : "cc" );
+#endif
+
+template<> struct packet_traits<int> : default_packet_traits
+{
+ typedef Packet4i type;
+ typedef Packet4i half;
+ enum {
+ Vectorizable = 1,
+ AlignedOnScalar = 1,
+ size = 4,
+ HasHalfPacket = 0,
+
+ HasAdd = 1,
+ HasSub = 1,
+ HasMul = 1,
+ HasDiv = 1,
+ HasBlend = 1
+ };
+};
+
+template <>
+struct packet_traits<float> : default_packet_traits {
+ typedef Packet4f type;
+ typedef Packet4f half;
+ enum {
+ Vectorizable = 1,
+ AlignedOnScalar = 1,
+ size = 4,
+ HasHalfPacket = 0,
+
+ HasAdd = 1,
+ HasSub = 1,
+ HasMul = 1,
+ HasDiv = 1,
+ HasMin = 1,
+ HasMax = 1,
+ HasAbs = 1,
+ HasSin = 0,
+ HasCos = 0,
+ HasLog = 0,
+ HasExp = 1,
+ HasSqrt = 1,
+ HasRsqrt = 1,
+ HasTanh = 1,
+ HasErf = 1,
+ HasRound = 1,
+ HasFloor = 1,
+ HasCeil = 1,
+ HasNegate = 1,
+ HasBlend = 1
+ };
+};
+
+template<> struct packet_traits<double> : default_packet_traits
+{
+ typedef Packet2d type;
+ typedef Packet2d half;
+ enum {
+ Vectorizable = 1,
+ AlignedOnScalar = 1,
+ size=2,
+ HasHalfPacket = 1,
+
+ HasAdd = 1,
+ HasSub = 1,
+ HasMul = 1,
+ HasDiv = 1,
+ HasMin = 1,
+ HasMax = 1,
+ HasAbs = 1,
+ HasSin = 0,
+ HasCos = 0,
+ HasLog = 0,
+ HasExp = 1,
+ HasSqrt = 1,
+ HasRsqrt = 1,
+ HasRound = 1,
+ HasFloor = 1,
+ HasCeil = 1,
+ HasNegate = 1,
+ HasBlend = 1
+ };
+};
+
+template<> struct unpacket_traits<Packet4i> { typedef int type; enum {size=4, alignment=Aligned16, vectorizable=true, masked_load_available=false, masked_store_available=false}; typedef Packet4i half; };
+template<> struct unpacket_traits<Packet4f> { typedef float type; enum {size=4, alignment=Aligned16, vectorizable=true, masked_load_available=false, masked_store_available=false}; typedef Packet4f half; };
+template<> struct unpacket_traits<Packet2d> { typedef double type; enum {size=2, alignment=Aligned16, vectorizable=true, masked_load_available=false, masked_store_available=false}; typedef Packet2d half; };
+
+/* Forward declaration */
+EIGEN_DEVICE_FUNC inline void ptranspose(PacketBlock<Packet4f,4>& kernel);
+
+inline std::ostream & operator <<(std::ostream & s, const Packet4i & v)
+{
+ Packet vt;
+ vt.v4i = v;
+ s << vt.i[0] << ", " << vt.i[1] << ", " << vt.i[2] << ", " << vt.i[3];
+ return s;
+}
+
+inline std::ostream & operator <<(std::ostream & s, const Packet4ui & v)
+{
+ Packet vt;
+ vt.v4ui = v;
+ s << vt.ui[0] << ", " << vt.ui[1] << ", " << vt.ui[2] << ", " << vt.ui[3];
+ return s;
+}
+
+inline std::ostream & operator <<(std::ostream & s, const Packet2l & v)
+{
+ Packet vt;
+ vt.v2l = v;
+ s << vt.l[0] << ", " << vt.l[1];
+ return s;
+}
+
+inline std::ostream & operator <<(std::ostream & s, const Packet2ul & v)
+{
+ Packet vt;
+ vt.v2ul = v;
+ s << vt.ul[0] << ", " << vt.ul[1] ;
+ return s;
+}
+
+inline std::ostream & operator <<(std::ostream & s, const Packet2d & v)
+{
+ Packet vt;
+ vt.v2d = v;
+ s << vt.d[0] << ", " << vt.d[1];
+ return s;
+}
+
+#if !defined(__ARCH__) || (defined(__ARCH__) && __ARCH__ >= 12)
+inline std::ostream & operator <<(std::ostream & s, const Packet4f & v)
+{
+ Packet vt;
+ vt.v4f = v;
+ s << vt.f[0] << ", " << vt.f[1] << ", " << vt.f[2] << ", " << vt.f[3];
+ return s;
+}
+#endif
+
+template<> EIGEN_STRONG_INLINE Packet4i pload<Packet4i>(const int* from)
+{
+ // FIXME: No intrinsic yet
+ EIGEN_DEBUG_ALIGNED_LOAD
+ Packet *vfrom;
+ vfrom = (Packet *) from;
+ return vfrom->v4i;
+}
+
+template<> EIGEN_STRONG_INLINE Packet2d pload<Packet2d>(const double* from)
+{
+ // FIXME: No intrinsic yet
+ EIGEN_DEBUG_ALIGNED_LOAD
+ Packet *vfrom;
+ vfrom = (Packet *) from;
+ return vfrom->v2d;
+}
+
+template<> EIGEN_STRONG_INLINE void pstore<int>(int* to, const Packet4i& from)
+{
+ // FIXME: No intrinsic yet
+ EIGEN_DEBUG_ALIGNED_STORE
+ Packet *vto;
+ vto = (Packet *) to;
+ vto->v4i = from;
+}
+
+template<> EIGEN_STRONG_INLINE void pstore<double>(double* to, const Packet2d& from)
+{
+ // FIXME: No intrinsic yet
+ EIGEN_DEBUG_ALIGNED_STORE
+ Packet *vto;
+ vto = (Packet *) to;
+ vto->v2d = from;
+}
+
+template<> EIGEN_STRONG_INLINE Packet4i pset1<Packet4i>(const int& from)
+{
+ return vec_splats(from);
+}
+template<> EIGEN_STRONG_INLINE Packet2d pset1<Packet2d>(const double& from) {
+ return vec_splats(from);
+}
+
+template<> EIGEN_STRONG_INLINE void
+pbroadcast4<Packet4i>(const int *a,
+ Packet4i& a0, Packet4i& a1, Packet4i& a2, Packet4i& a3)
+{
+ a3 = pload<Packet4i>(a);
+ a0 = vec_splat(a3, 0);
+ a1 = vec_splat(a3, 1);
+ a2 = vec_splat(a3, 2);
+ a3 = vec_splat(a3, 3);
+}
+
+template<> EIGEN_STRONG_INLINE void
+pbroadcast4<Packet2d>(const double *a,
+ Packet2d& a0, Packet2d& a1, Packet2d& a2, Packet2d& a3)
+{
+ a1 = pload<Packet2d>(a);
+ a0 = vec_splat(a1, 0);
+ a1 = vec_splat(a1, 1);
+ a3 = pload<Packet2d>(a+2);
+ a2 = vec_splat(a3, 0);
+ a3 = vec_splat(a3, 1);
+}
+
+template<> EIGEN_DEVICE_FUNC inline Packet4i pgather<int, Packet4i>(const int* from, Index stride)
+{
+ EIGEN_ALIGN16 int ai[4];
+ ai[0] = from[0*stride];
+ ai[1] = from[1*stride];
+ ai[2] = from[2*stride];
+ ai[3] = from[3*stride];
+ return pload<Packet4i>(ai);
+}
+
+template<> EIGEN_DEVICE_FUNC inline Packet2d pgather<double, Packet2d>(const double* from, Index stride)
+{
+ EIGEN_ALIGN16 double af[2];
+ af[0] = from[0*stride];
+ af[1] = from[1*stride];
+ return pload<Packet2d>(af);
+}
+
+template<> EIGEN_DEVICE_FUNC inline void pscatter<int, Packet4i>(int* to, const Packet4i& from, Index stride)
+{
+ EIGEN_ALIGN16 int ai[4];
+ pstore<int>((int *)ai, from);
+ to[0*stride] = ai[0];
+ to[1*stride] = ai[1];
+ to[2*stride] = ai[2];
+ to[3*stride] = ai[3];
+}
+
+template<> EIGEN_DEVICE_FUNC inline void pscatter<double, Packet2d>(double* to, const Packet2d& from, Index stride)
+{
+ EIGEN_ALIGN16 double af[2];
+ pstore<double>(af, from);
+ to[0*stride] = af[0];
+ to[1*stride] = af[1];
+}
+
+template<> EIGEN_STRONG_INLINE Packet4i padd<Packet4i>(const Packet4i& a, const Packet4i& b) { return (a + b); }
+template<> EIGEN_STRONG_INLINE Packet2d padd<Packet2d>(const Packet2d& a, const Packet2d& b) { return (a + b); }
+
+template<> EIGEN_STRONG_INLINE Packet4i psub<Packet4i>(const Packet4i& a, const Packet4i& b) { return (a - b); }
+template<> EIGEN_STRONG_INLINE Packet2d psub<Packet2d>(const Packet2d& a, const Packet2d& b) { return (a - b); }
+
+template<> EIGEN_STRONG_INLINE Packet4i pmul<Packet4i>(const Packet4i& a, const Packet4i& b) { return (a * b); }
+template<> EIGEN_STRONG_INLINE Packet2d pmul<Packet2d>(const Packet2d& a, const Packet2d& b) { return (a * b); }
+
+template<> EIGEN_STRONG_INLINE Packet4i pdiv<Packet4i>(const Packet4i& a, const Packet4i& b) { return (a / b); }
+template<> EIGEN_STRONG_INLINE Packet2d pdiv<Packet2d>(const Packet2d& a, const Packet2d& b) { return (a / b); }
+
+template<> EIGEN_STRONG_INLINE Packet4i pnegate(const Packet4i& a) { return (-a); }
+template<> EIGEN_STRONG_INLINE Packet2d pnegate(const Packet2d& a) { return (-a); }
+
+template<> EIGEN_STRONG_INLINE Packet4i pconj(const Packet4i& a) { return a; }
+template<> EIGEN_STRONG_INLINE Packet2d pconj(const Packet2d& a) { return a; }
+
+template<> EIGEN_STRONG_INLINE Packet4i pmadd(const Packet4i& a, const Packet4i& b, const Packet4i& c) { return padd<Packet4i>(pmul<Packet4i>(a, b), c); }
+template<> EIGEN_STRONG_INLINE Packet2d pmadd(const Packet2d& a, const Packet2d& b, const Packet2d& c) { return vec_madd(a, b, c); }
+
+template<> EIGEN_STRONG_INLINE Packet4i plset<Packet4i>(const int& a) { return padd<Packet4i>(pset1<Packet4i>(a), p4i_COUNTDOWN); }
+template<> EIGEN_STRONG_INLINE Packet2d plset<Packet2d>(const double& a) { return padd<Packet2d>(pset1<Packet2d>(a), p2d_COUNTDOWN); }
+
+template<> EIGEN_STRONG_INLINE Packet4i pmin<Packet4i>(const Packet4i& a, const Packet4i& b) { return vec_min(a, b); }
+template<> EIGEN_STRONG_INLINE Packet2d pmin<Packet2d>(const Packet2d& a, const Packet2d& b) { return vec_min(a, b); }
+
+template<> EIGEN_STRONG_INLINE Packet4i pmax<Packet4i>(const Packet4i& a, const Packet4i& b) { return vec_max(a, b); }
+template<> EIGEN_STRONG_INLINE Packet2d pmax<Packet2d>(const Packet2d& a, const Packet2d& b) { return vec_max(a, b); }
+
+template<> EIGEN_STRONG_INLINE Packet4i pand<Packet4i>(const Packet4i& a, const Packet4i& b) { return vec_and(a, b); }
+template<> EIGEN_STRONG_INLINE Packet2d pand<Packet2d>(const Packet2d& a, const Packet2d& b) { return vec_and(a, b); }
+
+template<> EIGEN_STRONG_INLINE Packet4i por<Packet4i>(const Packet4i& a, const Packet4i& b) { return vec_or(a, b); }
+template<> EIGEN_STRONG_INLINE Packet2d por<Packet2d>(const Packet2d& a, const Packet2d& b) { return vec_or(a, b); }
+
+template<> EIGEN_STRONG_INLINE Packet4i pxor<Packet4i>(const Packet4i& a, const Packet4i& b) { return vec_xor(a, b); }
+template<> EIGEN_STRONG_INLINE Packet2d pxor<Packet2d>(const Packet2d& a, const Packet2d& b) { return vec_xor(a, b); }
+
+template<> EIGEN_STRONG_INLINE Packet4i pandnot<Packet4i>(const Packet4i& a, const Packet4i& b) { return pand<Packet4i>(a, vec_nor(b, b)); }
+template<> EIGEN_STRONG_INLINE Packet2d pandnot<Packet2d>(const Packet2d& a, const Packet2d& b) { return vec_and(a, vec_nor(b, b)); }
+
+template<> EIGEN_STRONG_INLINE Packet2d pround<Packet2d>(const Packet2d& a) { return vec_round(a); }
+template<> EIGEN_STRONG_INLINE Packet2d pceil<Packet2d>(const Packet2d& a) { return vec_ceil(a); }
+template<> EIGEN_STRONG_INLINE Packet2d pfloor<Packet2d>(const Packet2d& a) { return vec_floor(a); }
+
+template<> EIGEN_STRONG_INLINE Packet4i ploadu<Packet4i>(const int* from) { return pload<Packet4i>(from); }
+template<> EIGEN_STRONG_INLINE Packet2d ploadu<Packet2d>(const double* from) { return pload<Packet2d>(from); }
+
+
+template<> EIGEN_STRONG_INLINE Packet4i ploaddup<Packet4i>(const int* from)
+{
+ Packet4i p = pload<Packet4i>(from);
+ return vec_perm(p, p, p16uc_DUPLICATE32_HI);
+}
+
+template<> EIGEN_STRONG_INLINE Packet2d ploaddup<Packet2d>(const double* from)
+{
+ Packet2d p = pload<Packet2d>(from);
+ return vec_perm(p, p, p16uc_PSET64_HI);
+}
+
+template<> EIGEN_STRONG_INLINE void pstoreu<int>(int* to, const Packet4i& from) { pstore<int>(to, from); }
+template<> EIGEN_STRONG_INLINE void pstoreu<double>(double* to, const Packet2d& from) { pstore<double>(to, from); }
+
+template<> EIGEN_STRONG_INLINE void prefetch<int>(const int* addr) { EIGEN_ZVECTOR_PREFETCH(addr); }
+template<> EIGEN_STRONG_INLINE void prefetch<double>(const double* addr) { EIGEN_ZVECTOR_PREFETCH(addr); }
+
+template<> EIGEN_STRONG_INLINE int pfirst<Packet4i>(const Packet4i& a) { EIGEN_ALIGN16 int x[4]; pstore(x, a); return x[0]; }
+template<> EIGEN_STRONG_INLINE double pfirst<Packet2d>(const Packet2d& a) { EIGEN_ALIGN16 double x[2]; pstore(x, a); return x[0]; }
+
+template<> EIGEN_STRONG_INLINE Packet4i preverse(const Packet4i& a)
+{
+ return reinterpret_cast<Packet4i>(vec_perm(reinterpret_cast<Packet16uc>(a), reinterpret_cast<Packet16uc>(a), p16uc_REVERSE32));
+}
+
+template<> EIGEN_STRONG_INLINE Packet2d preverse(const Packet2d& a)
+{
+ return reinterpret_cast<Packet2d>(vec_perm(reinterpret_cast<Packet16uc>(a), reinterpret_cast<Packet16uc>(a), p16uc_REVERSE64));
+}
+
+template<> EIGEN_STRONG_INLINE Packet4i pabs<Packet4i>(const Packet4i& a) { return vec_abs(a); }
+template<> EIGEN_STRONG_INLINE Packet2d pabs<Packet2d>(const Packet2d& a) { return vec_abs(a); }
+
+template<> EIGEN_STRONG_INLINE int predux<Packet4i>(const Packet4i& a)
+{
+ Packet4i b, sum;
+ b = vec_sld(a, a, 8);
+ sum = padd<Packet4i>(a, b);
+ b = vec_sld(sum, sum, 4);
+ sum = padd<Packet4i>(sum, b);
+ return pfirst(sum);
+}
+
+template<> EIGEN_STRONG_INLINE double predux<Packet2d>(const Packet2d& a)
+{
+ Packet2d b, sum;
+ b = reinterpret_cast<Packet2d>(vec_sld(reinterpret_cast<Packet4i>(a), reinterpret_cast<Packet4i>(a), 8));
+ sum = padd<Packet2d>(a, b);
+ return pfirst(sum);
+}
+
+// Other reduction functions:
+// mul
+template<> EIGEN_STRONG_INLINE int predux_mul<Packet4i>(const Packet4i& a)
+{
+ EIGEN_ALIGN16 int aux[4];
+ pstore(aux, a);
+ return aux[0] * aux[1] * aux[2] * aux[3];
+}
+
+template<> EIGEN_STRONG_INLINE double predux_mul<Packet2d>(const Packet2d& a)
+{
+ return pfirst(pmul(a, reinterpret_cast<Packet2d>(vec_sld(reinterpret_cast<Packet4i>(a), reinterpret_cast<Packet4i>(a), 8))));
+}
+
+// min
+template<> EIGEN_STRONG_INLINE int predux_min<Packet4i>(const Packet4i& a)
+{
+ Packet4i b, res;
+ b = pmin<Packet4i>(a, vec_sld(a, a, 8));
+ res = pmin<Packet4i>(b, vec_sld(b, b, 4));
+ return pfirst(res);
+}
+
+template<> EIGEN_STRONG_INLINE double predux_min<Packet2d>(const Packet2d& a)
+{
+ return pfirst(pmin<Packet2d>(a, reinterpret_cast<Packet2d>(vec_sld(reinterpret_cast<Packet4i>(a), reinterpret_cast<Packet4i>(a), 8))));
+}
+
+// max
+template<> EIGEN_STRONG_INLINE int predux_max<Packet4i>(const Packet4i& a)
+{
+ Packet4i b, res;
+ b = pmax<Packet4i>(a, vec_sld(a, a, 8));
+ res = pmax<Packet4i>(b, vec_sld(b, b, 4));
+ return pfirst(res);
+}
+
+// max
+template<> EIGEN_STRONG_INLINE double predux_max<Packet2d>(const Packet2d& a)
+{
+ return pfirst(pmax<Packet2d>(a, reinterpret_cast<Packet2d>(vec_sld(reinterpret_cast<Packet4i>(a), reinterpret_cast<Packet4i>(a), 8))));
+}
+
+EIGEN_DEVICE_FUNC inline void
+ptranspose(PacketBlock<Packet4i,4>& kernel) {
+ Packet4i t0 = vec_mergeh(kernel.packet[0], kernel.packet[2]);
+ Packet4i t1 = vec_mergel(kernel.packet[0], kernel.packet[2]);
+ Packet4i t2 = vec_mergeh(kernel.packet[1], kernel.packet[3]);
+ Packet4i t3 = vec_mergel(kernel.packet[1], kernel.packet[3]);
+ kernel.packet[0] = vec_mergeh(t0, t2);
+ kernel.packet[1] = vec_mergel(t0, t2);
+ kernel.packet[2] = vec_mergeh(t1, t3);
+ kernel.packet[3] = vec_mergel(t1, t3);
+}
+
+EIGEN_DEVICE_FUNC inline void
+ptranspose(PacketBlock<Packet2d,2>& kernel) {
+ Packet2d t0 = vec_perm(kernel.packet[0], kernel.packet[1], p16uc_TRANSPOSE64_HI);
+ Packet2d t1 = vec_perm(kernel.packet[0], kernel.packet[1], p16uc_TRANSPOSE64_LO);
+ kernel.packet[0] = t0;
+ kernel.packet[1] = t1;
+}
+
+template<> EIGEN_STRONG_INLINE Packet4i pblend(const Selector<4>& ifPacket, const Packet4i& thenPacket, const Packet4i& elsePacket) {
+ Packet4ui select = { ifPacket.select[0], ifPacket.select[1], ifPacket.select[2], ifPacket.select[3] };
+ Packet4ui mask = vec_cmpeq(select, reinterpret_cast<Packet4ui>(p4i_ONE));
+ return vec_sel(elsePacket, thenPacket, mask);
+}
+
+
+template<> EIGEN_STRONG_INLINE Packet2d pblend(const Selector<2>& ifPacket, const Packet2d& thenPacket, const Packet2d& elsePacket) {
+ Packet2ul select = { ifPacket.select[0], ifPacket.select[1] };
+ Packet2ul mask = vec_cmpeq(select, reinterpret_cast<Packet2ul>(p2l_ONE));
+ return vec_sel(elsePacket, thenPacket, mask);
+}
+
+/* z13 has no vector float support so we emulate that with double
+ z14 has proper vector float support.
+*/
+#if !defined(__ARCH__) || (defined(__ARCH__) && __ARCH__ < 12)
+/* Helper function to simulate a vec_splat_packet4f
+ */
+template<int element> EIGEN_STRONG_INLINE Packet4f vec_splat_packet4f(const Packet4f& from)
+{
+ Packet4f splat;
+ switch (element) {
+ case 0:
+ splat.v4f[0] = vec_splat(from.v4f[0], 0);
+ splat.v4f[1] = splat.v4f[0];
+ break;
+ case 1:
+ splat.v4f[0] = vec_splat(from.v4f[0], 1);
+ splat.v4f[1] = splat.v4f[0];
+ break;
+ case 2:
+ splat.v4f[0] = vec_splat(from.v4f[1], 0);
+ splat.v4f[1] = splat.v4f[0];
+ break;
+ case 3:
+ splat.v4f[0] = vec_splat(from.v4f[1], 1);
+ splat.v4f[1] = splat.v4f[0];
+ break;
+ }
+ return splat;
+}
+
+template<> EIGEN_STRONG_INLINE Packet4f pload<Packet4f>(const float* from)
+{
+ // FIXME: No intrinsic yet
+ EIGEN_DEBUG_ALIGNED_LOAD
+ Packet4f vfrom;
+ vfrom.v4f[0] = vec_ld2f(&from[0]);
+ vfrom.v4f[1] = vec_ld2f(&from[2]);
+ return vfrom;
+}
+
+template<> EIGEN_STRONG_INLINE void pstore<float>(float* to, const Packet4f& from)
+{
+ // FIXME: No intrinsic yet
+ EIGEN_DEBUG_ALIGNED_STORE
+ vec_st2f(from.v4f[0], &to[0]);
+ vec_st2f(from.v4f[1], &to[2]);
+}
+
+template<> EIGEN_STRONG_INLINE Packet4f pset1<Packet4f>(const float& from)
+{
+ Packet4f to;
+ to.v4f[0] = pset1<Packet2d>(static_cast<const double&>(from));
+ to.v4f[1] = to.v4f[0];
+ return to;
+}
+
+template<> EIGEN_STRONG_INLINE void
+pbroadcast4<Packet4f>(const float *a,
+ Packet4f& a0, Packet4f& a1, Packet4f& a2, Packet4f& a3)
+{
+ a3 = pload<Packet4f>(a);
+ a0 = vec_splat_packet4f<0>(a3);
+ a1 = vec_splat_packet4f<1>(a3);
+ a2 = vec_splat_packet4f<2>(a3);
+ a3 = vec_splat_packet4f<3>(a3);
+}
+
+template<> EIGEN_DEVICE_FUNC inline Packet4f pgather<float, Packet4f>(const float* from, Index stride)
+{
+ EIGEN_ALIGN16 float ai[4];
+ ai[0] = from[0*stride];
+ ai[1] = from[1*stride];
+ ai[2] = from[2*stride];
+ ai[3] = from[3*stride];
+ return pload<Packet4f>(ai);
+}
+
+template<> EIGEN_DEVICE_FUNC inline void pscatter<float, Packet4f>(float* to, const Packet4f& from, Index stride)
+{
+ EIGEN_ALIGN16 float ai[4];
+ pstore<float>((float *)ai, from);
+ to[0*stride] = ai[0];
+ to[1*stride] = ai[1];
+ to[2*stride] = ai[2];
+ to[3*stride] = ai[3];
+}
+
+template<> EIGEN_STRONG_INLINE Packet4f padd<Packet4f>(const Packet4f& a, const Packet4f& b)
+{
+ Packet4f c;
+ c.v4f[0] = a.v4f[0] + b.v4f[0];
+ c.v4f[1] = a.v4f[1] + b.v4f[1];
+ return c;
+}
+
+template<> EIGEN_STRONG_INLINE Packet4f psub<Packet4f>(const Packet4f& a, const Packet4f& b)
+{
+ Packet4f c;
+ c.v4f[0] = a.v4f[0] - b.v4f[0];
+ c.v4f[1] = a.v4f[1] - b.v4f[1];
+ return c;
+}
+
+template<> EIGEN_STRONG_INLINE Packet4f pmul<Packet4f>(const Packet4f& a, const Packet4f& b)
+{
+ Packet4f c;
+ c.v4f[0] = a.v4f[0] * b.v4f[0];
+ c.v4f[1] = a.v4f[1] * b.v4f[1];
+ return c;
+}
+
+template<> EIGEN_STRONG_INLINE Packet4f pdiv<Packet4f>(const Packet4f& a, const Packet4f& b)
+{
+ Packet4f c;
+ c.v4f[0] = a.v4f[0] / b.v4f[0];
+ c.v4f[1] = a.v4f[1] / b.v4f[1];
+ return c;
+}
+
+template<> EIGEN_STRONG_INLINE Packet4f pnegate(const Packet4f& a)
+{
+ Packet4f c;
+ c.v4f[0] = -a.v4f[0];
+ c.v4f[1] = -a.v4f[1];
+ return c;
+}
+
+template<> EIGEN_STRONG_INLINE Packet4f pmadd(const Packet4f& a, const Packet4f& b, const Packet4f& c)
+{
+ Packet4f res;
+ res.v4f[0] = vec_madd(a.v4f[0], b.v4f[0], c.v4f[0]);
+ res.v4f[1] = vec_madd(a.v4f[1], b.v4f[1], c.v4f[1]);
+ return res;
+}
+
+template<> EIGEN_STRONG_INLINE Packet4f pmin<Packet4f>(const Packet4f& a, const Packet4f& b)
+{
+ Packet4f res;
+ res.v4f[0] = pmin(a.v4f[0], b.v4f[0]);
+ res.v4f[1] = pmin(a.v4f[1], b.v4f[1]);
+ return res;
+}
+
+template<> EIGEN_STRONG_INLINE Packet4f pmax<Packet4f>(const Packet4f& a, const Packet4f& b)
+{
+ Packet4f res;
+ res.v4f[0] = pmax(a.v4f[0], b.v4f[0]);
+ res.v4f[1] = pmax(a.v4f[1], b.v4f[1]);
+ return res;
+}
+
+template<> EIGEN_STRONG_INLINE Packet4f pand<Packet4f>(const Packet4f& a, const Packet4f& b)
+{
+ Packet4f res;
+ res.v4f[0] = pand(a.v4f[0], b.v4f[0]);
+ res.v4f[1] = pand(a.v4f[1], b.v4f[1]);
+ return res;
+}
+
+template<> EIGEN_STRONG_INLINE Packet4f por<Packet4f>(const Packet4f& a, const Packet4f& b)
+{
+ Packet4f res;
+ res.v4f[0] = por(a.v4f[0], b.v4f[0]);
+ res.v4f[1] = por(a.v4f[1], b.v4f[1]);
+ return res;
+}
+
+template<> EIGEN_STRONG_INLINE Packet4f pxor<Packet4f>(const Packet4f& a, const Packet4f& b)
+{
+ Packet4f res;
+ res.v4f[0] = pxor(a.v4f[0], b.v4f[0]);
+ res.v4f[1] = pxor(a.v4f[1], b.v4f[1]);
+ return res;
+}
+
+template<> EIGEN_STRONG_INLINE Packet4f pandnot<Packet4f>(const Packet4f& a, const Packet4f& b)
+{
+ Packet4f res;
+ res.v4f[0] = pandnot(a.v4f[0], b.v4f[0]);
+ res.v4f[1] = pandnot(a.v4f[1], b.v4f[1]);
+ return res;
+}
+
+template<> EIGEN_STRONG_INLINE Packet4f pround<Packet4f>(const Packet4f& a)
+{
+ Packet4f res;
+ res.v4f[0] = vec_round(a.v4f[0]);
+ res.v4f[1] = vec_round(a.v4f[1]);
+ return res;
+}
+
+template<> EIGEN_STRONG_INLINE Packet4f pceil<Packet4f>(const Packet4f& a)
+{
+ Packet4f res;
+ res.v4f[0] = vec_ceil(a.v4f[0]);
+ res.v4f[1] = vec_ceil(a.v4f[1]);
+ return res;
+}
+
+template<> EIGEN_STRONG_INLINE Packet4f pfloor<Packet4f>(const Packet4f& a)
+{
+ Packet4f res;
+ res.v4f[0] = vec_floor(a.v4f[0]);
+ res.v4f[1] = vec_floor(a.v4f[1]);
+ return res;
+}
+
+template<> EIGEN_STRONG_INLINE Packet4f ploaddup<Packet4f>(const float* from)
+{
+ Packet4f p = pload<Packet4f>(from);
+ p.v4f[1] = vec_splat(p.v4f[0], 1);
+ p.v4f[0] = vec_splat(p.v4f[0], 0);
+ return p;
+}
+
+template<> EIGEN_STRONG_INLINE float pfirst<Packet4f>(const Packet4f& a) { EIGEN_ALIGN16 float x[2]; vec_st2f(a.v4f[0], &x[0]); return x[0]; }
+
+template<> EIGEN_STRONG_INLINE Packet4f preverse(const Packet4f& a)
+{
+ Packet4f rev;
+ rev.v4f[0] = preverse<Packet2d>(a.v4f[1]);
+ rev.v4f[1] = preverse<Packet2d>(a.v4f[0]);
+ return rev;
+}
+
+template<> EIGEN_STRONG_INLINE Packet4f pabs<Packet4f>(const Packet4f& a)
+{
+ Packet4f res;
+ res.v4f[0] = pabs(a.v4f[0]);
+ res.v4f[1] = pabs(a.v4f[1]);
+ return res;
+}
+
+template<> EIGEN_STRONG_INLINE float predux<Packet4f>(const Packet4f& a)
+{
+ Packet2d sum;
+ sum = padd<Packet2d>(a.v4f[0], a.v4f[1]);
+ double first = predux<Packet2d>(sum);
+ return static_cast<float>(first);
+}
+
+template<> EIGEN_STRONG_INLINE float predux_mul<Packet4f>(const Packet4f& a)
+{
+ // Return predux_mul<Packet2d> of the subvectors product
+ return static_cast<float>(pfirst(predux_mul(pmul(a.v4f[0], a.v4f[1]))));
+}
+
+template<> EIGEN_STRONG_INLINE float predux_min<Packet4f>(const Packet4f& a)
+{
+ Packet2d b, res;
+ b = pmin<Packet2d>(a.v4f[0], a.v4f[1]);
+ res = pmin<Packet2d>(b, reinterpret_cast<Packet2d>(vec_sld(reinterpret_cast<Packet4i>(b), reinterpret_cast<Packet4i>(b), 8)));
+ return static_cast<float>(pfirst(res));
+}
+
+template<> EIGEN_STRONG_INLINE float predux_max<Packet4f>(const Packet4f& a)
+{
+ Packet2d b, res;
+ b = pmax<Packet2d>(a.v4f[0], a.v4f[1]);
+ res = pmax<Packet2d>(b, reinterpret_cast<Packet2d>(vec_sld(reinterpret_cast<Packet4i>(b), reinterpret_cast<Packet4i>(b), 8)));
+ return static_cast<float>(pfirst(res));
+}
+
+/* Split the Packet4f PacketBlock into 4 Packet2d PacketBlocks and transpose each one
+ */
+EIGEN_DEVICE_FUNC inline void
+ptranspose(PacketBlock<Packet4f,4>& kernel) {
+ PacketBlock<Packet2d,2> t0,t1,t2,t3;
+ // copy top-left 2x2 Packet2d block
+ t0.packet[0] = kernel.packet[0].v4f[0];
+ t0.packet[1] = kernel.packet[1].v4f[0];
+
+ // copy top-right 2x2 Packet2d block
+ t1.packet[0] = kernel.packet[0].v4f[1];
+ t1.packet[1] = kernel.packet[1].v4f[1];
+
+ // copy bottom-left 2x2 Packet2d block
+ t2.packet[0] = kernel.packet[2].v4f[0];
+ t2.packet[1] = kernel.packet[3].v4f[0];
+
+ // copy bottom-right 2x2 Packet2d block
+ t3.packet[0] = kernel.packet[2].v4f[1];
+ t3.packet[1] = kernel.packet[3].v4f[1];
+
+ // Transpose all 2x2 blocks
+ ptranspose(t0);
+ ptranspose(t1);
+ ptranspose(t2);
+ ptranspose(t3);
+
+ // Copy back transposed blocks, but exchange t1 and t2 due to transposition
+ kernel.packet[0].v4f[0] = t0.packet[0];
+ kernel.packet[0].v4f[1] = t2.packet[0];
+ kernel.packet[1].v4f[0] = t0.packet[1];
+ kernel.packet[1].v4f[1] = t2.packet[1];
+ kernel.packet[2].v4f[0] = t1.packet[0];
+ kernel.packet[2].v4f[1] = t3.packet[0];
+ kernel.packet[3].v4f[0] = t1.packet[1];
+ kernel.packet[3].v4f[1] = t3.packet[1];
+}
+
+template<> EIGEN_STRONG_INLINE Packet4f pblend(const Selector<4>& ifPacket, const Packet4f& thenPacket, const Packet4f& elsePacket) {
+ Packet2ul select_hi = { ifPacket.select[0], ifPacket.select[1] };
+ Packet2ul select_lo = { ifPacket.select[2], ifPacket.select[3] };
+ Packet2ul mask_hi = vec_cmpeq(select_hi, reinterpret_cast<Packet2ul>(p2l_ONE));
+ Packet2ul mask_lo = vec_cmpeq(select_lo, reinterpret_cast<Packet2ul>(p2l_ONE));
+ Packet4f result;
+ result.v4f[0] = vec_sel(elsePacket.v4f[0], thenPacket.v4f[0], mask_hi);
+ result.v4f[1] = vec_sel(elsePacket.v4f[1], thenPacket.v4f[1], mask_lo);
+ return result;
+}
+
+template<> Packet4f EIGEN_STRONG_INLINE pcmp_le<Packet4f>(const Packet4f& a, const Packet4f& b)
+{
+ Packet4f res;
+ res.v4f[0] = pcmp_le(a.v4f[0], b.v4f[0]);
+ res.v4f[1] = pcmp_le(a.v4f[1], b.v4f[1]);
+ return res;
+}
+
+template<> Packet4f EIGEN_STRONG_INLINE pcmp_lt<Packet4f>(const Packet4f& a, const Packet4f& b)
+{
+ Packet4f res;
+ res.v4f[0] = pcmp_lt(a.v4f[0], b.v4f[0]);
+ res.v4f[1] = pcmp_lt(a.v4f[1], b.v4f[1]);
+ return res;
+}
+
+template<> Packet4f EIGEN_STRONG_INLINE pcmp_eq<Packet4f>(const Packet4f& a, const Packet4f& b)
+{
+ Packet4f res;
+ res.v4f[0] = pcmp_eq(a.v4f[0], b.v4f[0]);
+ res.v4f[1] = pcmp_eq(a.v4f[1], b.v4f[1]);
+ return res;
+}
+
+#else
+template<> EIGEN_STRONG_INLINE Packet4f pload<Packet4f>(const float* from)
+{
+ // FIXME: No intrinsic yet
+ EIGEN_DEBUG_ALIGNED_LOAD
+ Packet *vfrom;
+ vfrom = (Packet *) from;
+ return vfrom->v4f;
+}
+
+template<> EIGEN_STRONG_INLINE void pstore<float>(float* to, const Packet4f& from)
+{
+ // FIXME: No intrinsic yet
+ EIGEN_DEBUG_ALIGNED_STORE
+ Packet *vto;
+ vto = (Packet *) to;
+ vto->v4f = from;
+}
+
+template<> EIGEN_STRONG_INLINE Packet4f pset1<Packet4f>(const float& from)
+{
+ return vec_splats(from);
+}
+
+template<> EIGEN_STRONG_INLINE void
+pbroadcast4<Packet4f>(const float *a,
+ Packet4f& a0, Packet4f& a1, Packet4f& a2, Packet4f& a3)
+{
+ a3 = pload<Packet4f>(a);
+ a0 = vec_splat(a3, 0);
+ a1 = vec_splat(a3, 1);
+ a2 = vec_splat(a3, 2);
+ a3 = vec_splat(a3, 3);
+}
+
+template<> EIGEN_DEVICE_FUNC inline Packet4f pgather<float, Packet4f>(const float* from, Index stride)
+{
+ EIGEN_ALIGN16 float af[4];
+ af[0] = from[0*stride];
+ af[1] = from[1*stride];
+ af[2] = from[2*stride];
+ af[3] = from[3*stride];
+ return pload<Packet4f>(af);
+}
+
+template<> EIGEN_DEVICE_FUNC inline void pscatter<float, Packet4f>(float* to, const Packet4f& from, Index stride)
+{
+ EIGEN_ALIGN16 float af[4];
+ pstore<float>((float*)af, from);
+ to[0*stride] = af[0];
+ to[1*stride] = af[1];
+ to[2*stride] = af[2];
+ to[3*stride] = af[3];
+}
+
+template<> EIGEN_STRONG_INLINE Packet4f padd<Packet4f>(const Packet4f& a, const Packet4f& b) { return (a + b); }
+template<> EIGEN_STRONG_INLINE Packet4f psub<Packet4f>(const Packet4f& a, const Packet4f& b) { return (a - b); }
+template<> EIGEN_STRONG_INLINE Packet4f pmul<Packet4f>(const Packet4f& a, const Packet4f& b) { return (a * b); }
+template<> EIGEN_STRONG_INLINE Packet4f pdiv<Packet4f>(const Packet4f& a, const Packet4f& b) { return (a / b); }
+template<> EIGEN_STRONG_INLINE Packet4f pnegate<Packet4f>(const Packet4f& a) { return (-a); }
+template<> EIGEN_STRONG_INLINE Packet4f pconj<Packet4f> (const Packet4f& a) { return a; }
+template<> EIGEN_STRONG_INLINE Packet4f pmadd<Packet4f> (const Packet4f& a, const Packet4f& b, const Packet4f& c) { return vec_madd(a, b, c); }
+template<> EIGEN_STRONG_INLINE Packet4f pmin<Packet4f> (const Packet4f& a, const Packet4f& b) { return vec_min(a, b); }
+template<> EIGEN_STRONG_INLINE Packet4f pmax<Packet4f> (const Packet4f& a, const Packet4f& b) { return vec_max(a, b); }
+template<> EIGEN_STRONG_INLINE Packet4f pand<Packet4f> (const Packet4f& a, const Packet4f& b) { return vec_and(a, b); }
+template<> EIGEN_STRONG_INLINE Packet4f por<Packet4f> (const Packet4f& a, const Packet4f& b) { return vec_or(a, b); }
+template<> EIGEN_STRONG_INLINE Packet4f pxor<Packet4f> (const Packet4f& a, const Packet4f& b) { return vec_xor(a, b); }
+template<> EIGEN_STRONG_INLINE Packet4f pandnot<Packet4f>(const Packet4f& a, const Packet4f& b) { return vec_and(a, vec_nor(b, b)); }
+template<> EIGEN_STRONG_INLINE Packet4f pround<Packet4f> (const Packet4f& a) { return vec_round(a); }
+template<> EIGEN_STRONG_INLINE Packet4f pceil<Packet4f> (const Packet4f& a) { return vec_ceil(a); }
+template<> EIGEN_STRONG_INLINE Packet4f pfloor<Packet4f> (const Packet4f& a) { return vec_floor(a); }
+template<> EIGEN_STRONG_INLINE Packet4f pabs<Packet4f> (const Packet4f& a) { return vec_abs(a); }
+template<> EIGEN_STRONG_INLINE float pfirst<Packet4f>(const Packet4f& a) { EIGEN_ALIGN16 float x[4]; pstore(x, a); return x[0]; }
+
+template<> EIGEN_STRONG_INLINE Packet4f ploaddup<Packet4f>(const float* from)
+{
+ Packet4f p = pload<Packet4f>(from);
+ return vec_perm(p, p, p16uc_DUPLICATE32_HI);
+}
+
+template<> EIGEN_STRONG_INLINE Packet4f preverse(const Packet4f& a)
+{
+ return reinterpret_cast<Packet4f>(vec_perm(reinterpret_cast<Packet16uc>(a), reinterpret_cast<Packet16uc>(a), p16uc_REVERSE32));
+}
+
+template<> EIGEN_STRONG_INLINE float predux<Packet4f>(const Packet4f& a)
+{
+ Packet4f b, sum;
+ b = vec_sld(a, a, 8);
+ sum = padd<Packet4f>(a, b);
+ b = vec_sld(sum, sum, 4);
+ sum = padd<Packet4f>(sum, b);
+ return pfirst(sum);
+}
+
+// Other reduction functions:
+// mul
+template<> EIGEN_STRONG_INLINE float predux_mul<Packet4f>(const Packet4f& a)
+{
+ Packet4f prod;
+ prod = pmul(a, vec_sld(a, a, 8));
+ return pfirst(pmul(prod, vec_sld(prod, prod, 4)));
+}
+
+// min
+template<> EIGEN_STRONG_INLINE float predux_min<Packet4f>(const Packet4f& a)
+{
+ Packet4f b, res;
+ b = pmin<Packet4f>(a, vec_sld(a, a, 8));
+ res = pmin<Packet4f>(b, vec_sld(b, b, 4));
+ return pfirst(res);
+}
+
+// max
+template<> EIGEN_STRONG_INLINE float predux_max<Packet4f>(const Packet4f& a)
+{
+ Packet4f b, res;
+ b = pmax<Packet4f>(a, vec_sld(a, a, 8));
+ res = pmax<Packet4f>(b, vec_sld(b, b, 4));
+ return pfirst(res);
+}
+
+EIGEN_DEVICE_FUNC inline void
+ptranspose(PacketBlock<Packet4f,4>& kernel) {
+ Packet4f t0 = vec_mergeh(kernel.packet[0], kernel.packet[2]);
+ Packet4f t1 = vec_mergel(kernel.packet[0], kernel.packet[2]);
+ Packet4f t2 = vec_mergeh(kernel.packet[1], kernel.packet[3]);
+ Packet4f t3 = vec_mergel(kernel.packet[1], kernel.packet[3]);
+ kernel.packet[0] = vec_mergeh(t0, t2);
+ kernel.packet[1] = vec_mergel(t0, t2);
+ kernel.packet[2] = vec_mergeh(t1, t3);
+ kernel.packet[3] = vec_mergel(t1, t3);
+}
+
+template<> EIGEN_STRONG_INLINE Packet4f pblend(const Selector<4>& ifPacket, const Packet4f& thenPacket, const Packet4f& elsePacket) {
+ Packet4ui select = { ifPacket.select[0], ifPacket.select[1], ifPacket.select[2], ifPacket.select[3] };
+ Packet4ui mask = vec_cmpeq(select, reinterpret_cast<Packet4ui>(p4i_ONE));
+ return vec_sel(elsePacket, thenPacket, mask);
+}
+
+#endif
+
+template<> EIGEN_STRONG_INLINE void prefetch<float>(const float* addr) { EIGEN_ZVECTOR_PREFETCH(addr); }
+template<> EIGEN_STRONG_INLINE Packet4f ploadu<Packet4f> (const float* from) { return pload<Packet4f>(from); }
+template<> EIGEN_STRONG_INLINE void pstoreu<float>(float* to, const Packet4f& from) { pstore<float>(to, from); }
+template<> EIGEN_STRONG_INLINE Packet4f plset<Packet4f> (const float& a) { return padd<Packet4f>(pset1<Packet4f>(a), p4f_COUNTDOWN); }
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_PACKET_MATH_ZVECTOR_H
diff --git a/Eigen/src/Core/functors/AssignmentFunctors.h b/Eigen/src/Core/functors/AssignmentFunctors.h
new file mode 100644
index 0000000..c9d80e6
--- /dev/null
+++ b/Eigen/src/Core/functors/AssignmentFunctors.h
@@ -0,0 +1,173 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2010 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_ASSIGNMENT_FUNCTORS_H
+#define EIGEN_ASSIGNMENT_FUNCTORS_H
+
+#include "../InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+
+/** \internal
+ * \brief Template functor for scalar/packet assignment
+ *
+ */
+template<typename DstScalar,typename SrcScalar> struct assign_op {
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void assignCoeff(DstScalar& a, const SrcScalar& b) const { a = b; }
+
+ template<int Alignment, typename Packet>
+ EIGEN_STRONG_INLINE void assignPacket(DstScalar* a, const Packet& b) const
+ { internal::pstoret<DstScalar,Packet,Alignment>(a,b); }
+};
+
+// Empty overload for void type (used by PermutationMatrix)
+template<typename DstScalar> struct assign_op<DstScalar,void> {};
+
+template<typename DstScalar,typename SrcScalar>
+struct functor_traits<assign_op<DstScalar,SrcScalar> > {
+ enum {
+ Cost = NumTraits<DstScalar>::ReadCost,
+ PacketAccess = is_same<DstScalar,SrcScalar>::value && packet_traits<DstScalar>::Vectorizable && packet_traits<SrcScalar>::Vectorizable
+ };
+};
+
+/** \internal
+ * \brief Template functor for scalar/packet assignment with addition
+ *
+ */
+template<typename DstScalar,typename SrcScalar> struct add_assign_op {
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void assignCoeff(DstScalar& a, const SrcScalar& b) const { a += b; }
+
+ template<int Alignment, typename Packet>
+ EIGEN_STRONG_INLINE void assignPacket(DstScalar* a, const Packet& b) const
+ { internal::pstoret<DstScalar,Packet,Alignment>(a,internal::padd(internal::ploadt<Packet,Alignment>(a),b)); }
+};
+template<typename DstScalar,typename SrcScalar>
+struct functor_traits<add_assign_op<DstScalar,SrcScalar> > {
+ enum {
+ Cost = NumTraits<DstScalar>::ReadCost + NumTraits<DstScalar>::AddCost,
+ PacketAccess = is_same<DstScalar,SrcScalar>::value && packet_traits<DstScalar>::HasAdd
+ };
+};
+
+/** \internal
+ * \brief Template functor for scalar/packet assignment with subtraction
+ *
+ */
+template<typename DstScalar,typename SrcScalar> struct sub_assign_op {
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void assignCoeff(DstScalar& a, const SrcScalar& b) const { a -= b; }
+
+ template<int Alignment, typename Packet>
+ EIGEN_STRONG_INLINE void assignPacket(DstScalar* a, const Packet& b) const
+ { internal::pstoret<DstScalar,Packet,Alignment>(a,internal::psub(internal::ploadt<Packet,Alignment>(a),b)); }
+};
+template<typename DstScalar,typename SrcScalar>
+struct functor_traits<sub_assign_op<DstScalar,SrcScalar> > {
+ enum {
+ Cost = NumTraits<DstScalar>::ReadCost + NumTraits<DstScalar>::AddCost,
+ PacketAccess = is_same<DstScalar,SrcScalar>::value && packet_traits<DstScalar>::HasSub
+ };
+};
+
+/** \internal
+ * \brief Template functor for scalar/packet assignment with multiplication
+ *
+ */
+template<typename DstScalar, typename SrcScalar=DstScalar>
+struct mul_assign_op {
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void assignCoeff(DstScalar& a, const SrcScalar& b) const { a *= b; }
+
+ template<int Alignment, typename Packet>
+ EIGEN_STRONG_INLINE void assignPacket(DstScalar* a, const Packet& b) const
+ { internal::pstoret<DstScalar,Packet,Alignment>(a,internal::pmul(internal::ploadt<Packet,Alignment>(a),b)); }
+};
+template<typename DstScalar, typename SrcScalar>
+struct functor_traits<mul_assign_op<DstScalar,SrcScalar> > {
+ enum {
+ Cost = NumTraits<DstScalar>::ReadCost + NumTraits<DstScalar>::MulCost,
+ PacketAccess = is_same<DstScalar,SrcScalar>::value && packet_traits<DstScalar>::HasMul
+ };
+};
+
+/** \internal
+ * \brief Template functor for scalar/packet assignment with diviving
+ *
+ */
+template<typename DstScalar, typename SrcScalar=DstScalar> struct div_assign_op {
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void assignCoeff(DstScalar& a, const SrcScalar& b) const { a /= b; }
+
+ template<int Alignment, typename Packet>
+ EIGEN_STRONG_INLINE void assignPacket(DstScalar* a, const Packet& b) const
+ { internal::pstoret<DstScalar,Packet,Alignment>(a,internal::pdiv(internal::ploadt<Packet,Alignment>(a),b)); }
+};
+template<typename DstScalar, typename SrcScalar>
+struct functor_traits<div_assign_op<DstScalar,SrcScalar> > {
+ enum {
+ Cost = NumTraits<DstScalar>::ReadCost + NumTraits<DstScalar>::MulCost,
+ PacketAccess = is_same<DstScalar,SrcScalar>::value && packet_traits<DstScalar>::HasDiv
+ };
+};
+
+/** \internal
+ * \brief Template functor for scalar/packet assignment with swapping
+ *
+ * It works as follow. For a non-vectorized evaluation loop, we have:
+ * for(i) func(A.coeffRef(i), B.coeff(i));
+ * where B is a SwapWrapper expression. The trick is to make SwapWrapper::coeff behaves like a non-const coeffRef.
+ * Actually, SwapWrapper might not even be needed since even if B is a plain expression, since it has to be writable
+ * B.coeff already returns a const reference to the underlying scalar value.
+ *
+ * The case of a vectorized loop is more tricky:
+ * for(i,j) func.assignPacket<A_Align>(&A.coeffRef(i,j), B.packet<B_Align>(i,j));
+ * Here, B must be a SwapWrapper whose packet function actually returns a proxy object holding a Scalar*,
+ * the actual alignment and Packet type.
+ *
+ */
+template<typename Scalar> struct swap_assign_op {
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void assignCoeff(Scalar& a, const Scalar& b) const
+ {
+#ifdef EIGEN_GPUCC
+ // FIXME is there some kind of cuda::swap?
+ Scalar t=b; const_cast<Scalar&>(b)=a; a=t;
+#else
+ using std::swap;
+ swap(a,const_cast<Scalar&>(b));
+#endif
+ }
+};
+template<typename Scalar>
+struct functor_traits<swap_assign_op<Scalar> > {
+ enum {
+ Cost = 3 * NumTraits<Scalar>::ReadCost,
+ PacketAccess =
+ #if defined(EIGEN_VECTORIZE_AVX) && EIGEN_COMP_CLANG && (EIGEN_COMP_CLANG<800 || defined(__apple_build_version__))
+ // This is a partial workaround for a bug in clang generating bad code
+ // when mixing 256/512 bits loads and 128 bits moves.
+ // See http://eigen.tuxfamily.org/bz/show_bug.cgi?id=1684
+ // https://bugs.llvm.org/show_bug.cgi?id=40815
+ 0
+ #else
+ packet_traits<Scalar>::Vectorizable
+ #endif
+ };
+};
+
+} // namespace internal
+
+} // namespace Eigen
+
+#endif // EIGEN_ASSIGNMENT_FUNCTORS_H
diff --git a/Eigen/src/Core/functors/BinaryFunctors.h b/Eigen/src/Core/functors/BinaryFunctors.h
new file mode 100644
index 0000000..eaa4352
--- /dev/null
+++ b/Eigen/src/Core/functors/BinaryFunctors.h
@@ -0,0 +1,628 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2010 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_BINARY_FUNCTORS_H
+#define EIGEN_BINARY_FUNCTORS_H
+
+#include "../InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+
+//---------- associative binary functors ----------
+
+template<typename Arg1, typename Arg2>
+struct binary_op_base
+{
+ typedef Arg1 first_argument_type;
+ typedef Arg2 second_argument_type;
+};
+
+/** \internal
+ * \brief Template functor to compute the sum of two scalars
+ *
+ * \sa class CwiseBinaryOp, MatrixBase::operator+, class VectorwiseOp, DenseBase::sum()
+ */
+template<typename LhsScalar,typename RhsScalar>
+struct scalar_sum_op : binary_op_base<LhsScalar,RhsScalar>
+{
+ typedef typename ScalarBinaryOpTraits<LhsScalar,RhsScalar,scalar_sum_op>::ReturnType result_type;
+#ifdef EIGEN_SCALAR_BINARY_OP_PLUGIN
+ scalar_sum_op() {
+ EIGEN_SCALAR_BINARY_OP_PLUGIN
+ }
+#endif
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE result_type operator() (const LhsScalar& a, const RhsScalar& b) const { return a + b; }
+ template<typename Packet>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet packetOp(const Packet& a, const Packet& b) const
+ { return internal::padd(a,b); }
+ template<typename Packet>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE result_type predux(const Packet& a) const
+ { return internal::predux(a); }
+};
+template<typename LhsScalar,typename RhsScalar>
+struct functor_traits<scalar_sum_op<LhsScalar,RhsScalar> > {
+ enum {
+ Cost = (int(NumTraits<LhsScalar>::AddCost) + int(NumTraits<RhsScalar>::AddCost)) / 2, // rough estimate!
+ PacketAccess = is_same<LhsScalar,RhsScalar>::value && packet_traits<LhsScalar>::HasAdd && packet_traits<RhsScalar>::HasAdd
+ // TODO vectorize mixed sum
+ };
+};
+
+
+template<>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE bool scalar_sum_op<bool,bool>::operator() (const bool& a, const bool& b) const { return a || b; }
+
+
+/** \internal
+ * \brief Template functor to compute the product of two scalars
+ *
+ * \sa class CwiseBinaryOp, Cwise::operator*(), class VectorwiseOp, MatrixBase::redux()
+ */
+template<typename LhsScalar,typename RhsScalar>
+struct scalar_product_op : binary_op_base<LhsScalar,RhsScalar>
+{
+ typedef typename ScalarBinaryOpTraits<LhsScalar,RhsScalar,scalar_product_op>::ReturnType result_type;
+#ifdef EIGEN_SCALAR_BINARY_OP_PLUGIN
+ scalar_product_op() {
+ EIGEN_SCALAR_BINARY_OP_PLUGIN
+ }
+#endif
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE result_type operator() (const LhsScalar& a, const RhsScalar& b) const { return a * b; }
+ template<typename Packet>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet packetOp(const Packet& a, const Packet& b) const
+ { return internal::pmul(a,b); }
+ template<typename Packet>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE result_type predux(const Packet& a) const
+ { return internal::predux_mul(a); }
+};
+template<typename LhsScalar,typename RhsScalar>
+struct functor_traits<scalar_product_op<LhsScalar,RhsScalar> > {
+ enum {
+ Cost = (int(NumTraits<LhsScalar>::MulCost) + int(NumTraits<RhsScalar>::MulCost))/2, // rough estimate!
+ PacketAccess = is_same<LhsScalar,RhsScalar>::value && packet_traits<LhsScalar>::HasMul && packet_traits<RhsScalar>::HasMul
+ // TODO vectorize mixed product
+ };
+};
+
+template<>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE bool scalar_product_op<bool,bool>::operator() (const bool& a, const bool& b) const { return a && b; }
+
+
+/** \internal
+ * \brief Template functor to compute the conjugate product of two scalars
+ *
+ * This is a short cut for conj(x) * y which is needed for optimization purpose; in Eigen2 support mode, this becomes x * conj(y)
+ */
+template<typename LhsScalar,typename RhsScalar>
+struct scalar_conj_product_op : binary_op_base<LhsScalar,RhsScalar>
+{
+
+ enum {
+ Conj = NumTraits<LhsScalar>::IsComplex
+ };
+
+ typedef typename ScalarBinaryOpTraits<LhsScalar,RhsScalar,scalar_conj_product_op>::ReturnType result_type;
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE result_type operator() (const LhsScalar& a, const RhsScalar& b) const
+ { return conj_helper<LhsScalar,RhsScalar,Conj,false>().pmul(a,b); }
+
+ template<typename Packet>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet packetOp(const Packet& a, const Packet& b) const
+ { return conj_helper<Packet,Packet,Conj,false>().pmul(a,b); }
+};
+template<typename LhsScalar,typename RhsScalar>
+struct functor_traits<scalar_conj_product_op<LhsScalar,RhsScalar> > {
+ enum {
+ Cost = NumTraits<LhsScalar>::MulCost,
+ PacketAccess = internal::is_same<LhsScalar, RhsScalar>::value && packet_traits<LhsScalar>::HasMul
+ };
+};
+
+/** \internal
+ * \brief Template functor to compute the min of two scalars
+ *
+ * \sa class CwiseBinaryOp, MatrixBase::cwiseMin, class VectorwiseOp, MatrixBase::minCoeff()
+ */
+template<typename LhsScalar,typename RhsScalar, int NaNPropagation>
+struct scalar_min_op : binary_op_base<LhsScalar,RhsScalar>
+{
+ typedef typename ScalarBinaryOpTraits<LhsScalar,RhsScalar,scalar_min_op>::ReturnType result_type;
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE result_type operator() (const LhsScalar& a, const RhsScalar& b) const {
+ return internal::pmin<NaNPropagation>(a, b);
+ }
+ template<typename Packet>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet packetOp(const Packet& a, const Packet& b) const
+ {
+ return internal::pmin<NaNPropagation>(a,b);
+ }
+ template<typename Packet>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE result_type predux(const Packet& a) const
+ {
+ return internal::predux_min<NaNPropagation>(a);
+ }
+};
+
+template<typename LhsScalar,typename RhsScalar, int NaNPropagation>
+struct functor_traits<scalar_min_op<LhsScalar,RhsScalar, NaNPropagation> > {
+ enum {
+ Cost = (NumTraits<LhsScalar>::AddCost+NumTraits<RhsScalar>::AddCost)/2,
+ PacketAccess = internal::is_same<LhsScalar, RhsScalar>::value && packet_traits<LhsScalar>::HasMin
+ };
+};
+
+/** \internal
+ * \brief Template functor to compute the max of two scalars
+ *
+ * \sa class CwiseBinaryOp, MatrixBase::cwiseMax, class VectorwiseOp, MatrixBase::maxCoeff()
+ */
+template<typename LhsScalar,typename RhsScalar, int NaNPropagation>
+struct scalar_max_op : binary_op_base<LhsScalar,RhsScalar>
+{
+ typedef typename ScalarBinaryOpTraits<LhsScalar,RhsScalar,scalar_max_op>::ReturnType result_type;
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE result_type operator() (const LhsScalar& a, const RhsScalar& b) const {
+ return internal::pmax<NaNPropagation>(a,b);
+ }
+ template<typename Packet>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet packetOp(const Packet& a, const Packet& b) const
+ {
+ return internal::pmax<NaNPropagation>(a,b);
+ }
+ template<typename Packet>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE result_type predux(const Packet& a) const
+ {
+ return internal::predux_max<NaNPropagation>(a);
+ }
+};
+
+template<typename LhsScalar,typename RhsScalar, int NaNPropagation>
+struct functor_traits<scalar_max_op<LhsScalar,RhsScalar, NaNPropagation> > {
+ enum {
+ Cost = (NumTraits<LhsScalar>::AddCost+NumTraits<RhsScalar>::AddCost)/2,
+ PacketAccess = internal::is_same<LhsScalar, RhsScalar>::value && packet_traits<LhsScalar>::HasMax
+ };
+};
+
+/** \internal
+ * \brief Template functors for comparison of two scalars
+ * \todo Implement packet-comparisons
+ */
+template<typename LhsScalar, typename RhsScalar, ComparisonName cmp> struct scalar_cmp_op;
+
+template<typename LhsScalar, typename RhsScalar, ComparisonName cmp>
+struct functor_traits<scalar_cmp_op<LhsScalar,RhsScalar, cmp> > {
+ enum {
+ Cost = (NumTraits<LhsScalar>::AddCost+NumTraits<RhsScalar>::AddCost)/2,
+ PacketAccess = is_same<LhsScalar, RhsScalar>::value &&
+ packet_traits<LhsScalar>::HasCmp &&
+ // Since return type is bool, we currently require the inputs
+ // to be bool to enable packet access.
+ is_same<LhsScalar, bool>::value
+ };
+};
+
+template<ComparisonName Cmp, typename LhsScalar, typename RhsScalar>
+struct result_of<scalar_cmp_op<LhsScalar, RhsScalar, Cmp>(LhsScalar,RhsScalar)> {
+ typedef bool type;
+};
+
+
+template<typename LhsScalar, typename RhsScalar>
+struct scalar_cmp_op<LhsScalar,RhsScalar, cmp_EQ> : binary_op_base<LhsScalar,RhsScalar>
+{
+ typedef bool result_type;
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE bool operator()(const LhsScalar& a, const RhsScalar& b) const {return a==b;}
+ template<typename Packet>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet packetOp(const Packet& a, const Packet& b) const
+ { return internal::pcmp_eq(a,b); }
+};
+template<typename LhsScalar, typename RhsScalar>
+struct scalar_cmp_op<LhsScalar,RhsScalar, cmp_LT> : binary_op_base<LhsScalar,RhsScalar>
+{
+ typedef bool result_type;
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE bool operator()(const LhsScalar& a, const RhsScalar& b) const {return a<b;}
+ template<typename Packet>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet packetOp(const Packet& a, const Packet& b) const
+ { return internal::pcmp_lt(a,b); }
+};
+template<typename LhsScalar, typename RhsScalar>
+struct scalar_cmp_op<LhsScalar,RhsScalar, cmp_LE> : binary_op_base<LhsScalar,RhsScalar>
+{
+ typedef bool result_type;
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE bool operator()(const LhsScalar& a, const RhsScalar& b) const {return a<=b;}
+ template<typename Packet>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet packetOp(const Packet& a, const Packet& b) const
+ { return internal::pcmp_le(a,b); }
+};
+template<typename LhsScalar, typename RhsScalar>
+struct scalar_cmp_op<LhsScalar,RhsScalar, cmp_GT> : binary_op_base<LhsScalar,RhsScalar>
+{
+ typedef bool result_type;
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE bool operator()(const LhsScalar& a, const RhsScalar& b) const {return a>b;}
+ template<typename Packet>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet packetOp(const Packet& a, const Packet& b) const
+ { return internal::pcmp_lt(b,a); }
+};
+template<typename LhsScalar, typename RhsScalar>
+struct scalar_cmp_op<LhsScalar,RhsScalar, cmp_GE> : binary_op_base<LhsScalar,RhsScalar>
+{
+ typedef bool result_type;
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE bool operator()(const LhsScalar& a, const RhsScalar& b) const {return a>=b;}
+ template<typename Packet>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet packetOp(const Packet& a, const Packet& b) const
+ { return internal::pcmp_le(b,a); }
+};
+template<typename LhsScalar, typename RhsScalar>
+struct scalar_cmp_op<LhsScalar,RhsScalar, cmp_UNORD> : binary_op_base<LhsScalar,RhsScalar>
+{
+ typedef bool result_type;
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE bool operator()(const LhsScalar& a, const RhsScalar& b) const {return !(a<=b || b<=a);}
+ template<typename Packet>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet packetOp(const Packet& a, const Packet& b) const
+ { return internal::pcmp_eq(internal::por(internal::pcmp_le(a, b), internal::pcmp_le(b, a)), internal::pzero(a)); }
+};
+template<typename LhsScalar, typename RhsScalar>
+struct scalar_cmp_op<LhsScalar,RhsScalar, cmp_NEQ> : binary_op_base<LhsScalar,RhsScalar>
+{
+ typedef bool result_type;
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE bool operator()(const LhsScalar& a, const RhsScalar& b) const {return a!=b;}
+ template<typename Packet>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet packetOp(const Packet& a, const Packet& b) const
+ { return internal::pcmp_eq(internal::pcmp_eq(a, b), internal::pzero(a)); }
+};
+
+/** \internal
+ * \brief Template functor to compute the hypot of two \b positive \b and \b real scalars
+ *
+ * \sa MatrixBase::stableNorm(), class Redux
+ */
+template<typename Scalar>
+struct scalar_hypot_op<Scalar,Scalar> : binary_op_base<Scalar,Scalar>
+{
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar operator() (const Scalar &x, const Scalar &y) const
+ {
+ // This functor is used by hypotNorm only for which it is faster to first apply abs
+ // on all coefficients prior to reduction through hypot.
+ // This way we avoid calling abs on positive and real entries, and this also permits
+ // to seamlessly handle complexes. Otherwise we would have to handle both real and complexes
+ // through the same functor...
+ return internal::positive_real_hypot(x,y);
+ }
+};
+template<typename Scalar>
+struct functor_traits<scalar_hypot_op<Scalar,Scalar> > {
+ enum
+ {
+ Cost = 3 * NumTraits<Scalar>::AddCost +
+ 2 * NumTraits<Scalar>::MulCost +
+ 2 * scalar_div_cost<Scalar,false>::value,
+ PacketAccess = false
+ };
+};
+
+/** \internal
+ * \brief Template functor to compute the pow of two scalars
+ * See the specification of pow in https://en.cppreference.com/w/cpp/numeric/math/pow
+ */
+template<typename Scalar, typename Exponent>
+struct scalar_pow_op : binary_op_base<Scalar,Exponent>
+{
+ typedef typename ScalarBinaryOpTraits<Scalar,Exponent,scalar_pow_op>::ReturnType result_type;
+#ifdef EIGEN_SCALAR_BINARY_OP_PLUGIN
+ scalar_pow_op() {
+ typedef Scalar LhsScalar;
+ typedef Exponent RhsScalar;
+ EIGEN_SCALAR_BINARY_OP_PLUGIN
+ }
+#endif
+
+ EIGEN_DEVICE_FUNC
+ inline result_type operator() (const Scalar& a, const Exponent& b) const { return numext::pow(a, b); }
+
+ template<typename Packet>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Packet packetOp(const Packet& a, const Packet& b) const
+ {
+ return generic_pow(a,b);
+ }
+};
+
+template<typename Scalar, typename Exponent>
+struct functor_traits<scalar_pow_op<Scalar,Exponent> > {
+ enum {
+ Cost = 5 * NumTraits<Scalar>::MulCost,
+ PacketAccess = (!NumTraits<Scalar>::IsComplex && !NumTraits<Scalar>::IsInteger &&
+ packet_traits<Scalar>::HasExp && packet_traits<Scalar>::HasLog &&
+ packet_traits<Scalar>::HasRound && packet_traits<Scalar>::HasCmp &&
+ // Temporarily disable packet access for half/bfloat16 until
+ // accuracy is improved.
+ !is_same<Scalar, half>::value && !is_same<Scalar, bfloat16>::value
+ )
+ };
+};
+
+//---------- non associative binary functors ----------
+
+/** \internal
+ * \brief Template functor to compute the difference of two scalars
+ *
+ * \sa class CwiseBinaryOp, MatrixBase::operator-
+ */
+template<typename LhsScalar,typename RhsScalar>
+struct scalar_difference_op : binary_op_base<LhsScalar,RhsScalar>
+{
+ typedef typename ScalarBinaryOpTraits<LhsScalar,RhsScalar,scalar_difference_op>::ReturnType result_type;
+#ifdef EIGEN_SCALAR_BINARY_OP_PLUGIN
+ scalar_difference_op() {
+ EIGEN_SCALAR_BINARY_OP_PLUGIN
+ }
+#endif
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const result_type operator() (const LhsScalar& a, const RhsScalar& b) const { return a - b; }
+ template<typename Packet>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Packet packetOp(const Packet& a, const Packet& b) const
+ { return internal::psub(a,b); }
+};
+template<typename LhsScalar,typename RhsScalar>
+struct functor_traits<scalar_difference_op<LhsScalar,RhsScalar> > {
+ enum {
+ Cost = (int(NumTraits<LhsScalar>::AddCost) + int(NumTraits<RhsScalar>::AddCost)) / 2,
+ PacketAccess = is_same<LhsScalar,RhsScalar>::value && packet_traits<LhsScalar>::HasSub && packet_traits<RhsScalar>::HasSub
+ };
+};
+
+template <typename Packet, bool IsInteger = NumTraits<typename unpacket_traits<Packet>::type>::IsInteger>
+struct maybe_raise_div_by_zero {
+ static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void run(Packet x) {
+ EIGEN_UNUSED_VARIABLE(x);
+ }
+};
+
+#ifndef EIGEN_GPU_COMPILE_PHASE
+template <typename Packet>
+struct maybe_raise_div_by_zero<Packet, true> {
+ static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void run(Packet x) {
+ if (EIGEN_PREDICT_FALSE(predux_any(pcmp_eq(x, pzero(x))))) {
+ std::raise(SIGFPE);
+ }
+ }
+};
+#endif
+
+/** \internal
+ * \brief Template functor to compute the quotient of two scalars
+ *
+ * \sa class CwiseBinaryOp, Cwise::operator/()
+ */
+template<typename LhsScalar,typename RhsScalar>
+struct scalar_quotient_op : binary_op_base<LhsScalar,RhsScalar>
+{
+ typedef typename ScalarBinaryOpTraits<LhsScalar,RhsScalar,scalar_quotient_op>::ReturnType result_type;
+#ifdef EIGEN_SCALAR_BINARY_OP_PLUGIN
+ scalar_quotient_op() {
+ EIGEN_SCALAR_BINARY_OP_PLUGIN
+ }
+#endif
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const result_type operator() (const LhsScalar& a, const RhsScalar& b) const { return a / b; }
+ template<typename Packet>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Packet packetOp(const Packet& a, const Packet& b) const {
+ maybe_raise_div_by_zero<Packet>::run(b);
+ return internal::pdiv(a,b);
+ }
+};
+template<typename LhsScalar,typename RhsScalar>
+struct functor_traits<scalar_quotient_op<LhsScalar,RhsScalar> > {
+ typedef typename scalar_quotient_op<LhsScalar,RhsScalar>::result_type result_type;
+ enum {
+ PacketAccess = is_same<LhsScalar,RhsScalar>::value && packet_traits<LhsScalar>::HasDiv && packet_traits<RhsScalar>::HasDiv,
+ Cost = scalar_div_cost<result_type,PacketAccess>::value
+ };
+};
+
+
+
+/** \internal
+ * \brief Template functor to compute the and of two booleans
+ *
+ * \sa class CwiseBinaryOp, ArrayBase::operator&&
+ */
+struct scalar_boolean_and_op {
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE bool operator() (const bool& a, const bool& b) const { return a && b; }
+ template<typename Packet>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Packet packetOp(const Packet& a, const Packet& b) const
+ { return internal::pand(a,b); }
+};
+template<> struct functor_traits<scalar_boolean_and_op> {
+ enum {
+ Cost = NumTraits<bool>::AddCost,
+ PacketAccess = true
+ };
+};
+
+/** \internal
+ * \brief Template functor to compute the or of two booleans
+ *
+ * \sa class CwiseBinaryOp, ArrayBase::operator||
+ */
+struct scalar_boolean_or_op {
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE bool operator() (const bool& a, const bool& b) const { return a || b; }
+ template<typename Packet>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Packet packetOp(const Packet& a, const Packet& b) const
+ { return internal::por(a,b); }
+};
+template<> struct functor_traits<scalar_boolean_or_op> {
+ enum {
+ Cost = NumTraits<bool>::AddCost,
+ PacketAccess = true
+ };
+};
+
+/** \internal
+ * \brief Template functor to compute the xor of two booleans
+ *
+ * \sa class CwiseBinaryOp, ArrayBase::operator^
+ */
+struct scalar_boolean_xor_op {
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE bool operator() (const bool& a, const bool& b) const { return a ^ b; }
+ template<typename Packet>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Packet packetOp(const Packet& a, const Packet& b) const
+ { return internal::pxor(a,b); }
+};
+template<> struct functor_traits<scalar_boolean_xor_op> {
+ enum {
+ Cost = NumTraits<bool>::AddCost,
+ PacketAccess = true
+ };
+};
+
+/** \internal
+ * \brief Template functor to compute the absolute difference of two scalars
+ *
+ * \sa class CwiseBinaryOp, MatrixBase::absolute_difference
+ */
+template<typename LhsScalar,typename RhsScalar>
+struct scalar_absolute_difference_op : binary_op_base<LhsScalar,RhsScalar>
+{
+ typedef typename ScalarBinaryOpTraits<LhsScalar,RhsScalar,scalar_absolute_difference_op>::ReturnType result_type;
+#ifdef EIGEN_SCALAR_BINARY_OP_PLUGIN
+ scalar_absolute_difference_op() {
+ EIGEN_SCALAR_BINARY_OP_PLUGIN
+ }
+#endif
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const result_type operator() (const LhsScalar& a, const RhsScalar& b) const
+ { return numext::absdiff(a,b); }
+ template<typename Packet>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Packet packetOp(const Packet& a, const Packet& b) const
+ { return internal::pabsdiff(a,b); }
+};
+template<typename LhsScalar,typename RhsScalar>
+struct functor_traits<scalar_absolute_difference_op<LhsScalar,RhsScalar> > {
+ enum {
+ Cost = (NumTraits<LhsScalar>::AddCost+NumTraits<RhsScalar>::AddCost)/2,
+ PacketAccess = is_same<LhsScalar,RhsScalar>::value && packet_traits<LhsScalar>::HasAbsDiff
+ };
+};
+
+
+template <typename LhsScalar, typename RhsScalar>
+struct scalar_atan2_op {
+ using Scalar = LhsScalar;
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE std::enable_if_t<is_same<LhsScalar,RhsScalar>::value, Scalar>
+ operator()(const Scalar& y, const Scalar& x) const {
+ EIGEN_USING_STD(atan2);
+ return static_cast<Scalar>(atan2(y, x));
+ }
+ template <typename Packet>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ std::enable_if_t<is_same<LhsScalar, RhsScalar>::value, Packet>
+ packetOp(const Packet& y, const Packet& x) const {
+ // See https://en.cppreference.com/w/cpp/numeric/math/atan2
+ // for how corner cases are supposed to be handled according to the
+ // IEEE floating-point standard (IEC 60559).
+ const Packet kSignMask = pset1<Packet>(-Scalar(0));
+ const Packet kPi = pset1<Packet>(Scalar(EIGEN_PI));
+ const Packet kPiO2 = pset1<Packet>(Scalar(EIGEN_PI / 2));
+ const Packet kPiO4 = pset1<Packet>(Scalar(EIGEN_PI / 4));
+ const Packet k3PiO4 = pset1<Packet>(Scalar(3.0 * (EIGEN_PI / 4)));
+
+ // Various predicates about the inputs.
+ Packet x_signbit = pand(x, kSignMask);
+ Packet x_has_signbit = pcmp_lt(por(x_signbit, kPi), pzero(x));
+ Packet x_is_zero = pcmp_eq(x, pzero(x));
+ Packet x_neg = pandnot(x_has_signbit, x_is_zero);
+
+ Packet y_signbit = pand(y, kSignMask);
+ Packet y_is_zero = pcmp_eq(y, pzero(y));
+ Packet x_is_not_nan = pcmp_eq(x, x);
+ Packet y_is_not_nan = pcmp_eq(y, y);
+
+ // Compute the normal case. Notice that we expect that
+ // finite/infinite = +/-0 here.
+ Packet result = patan(pdiv(y, x));
+
+ // Compute shift for when x != 0 and y != 0.
+ Packet shift = pselect(x_neg, por(kPi, y_signbit), pzero(x));
+
+ // Special cases:
+ // Handle x = +/-inf && y = +/-inf.
+ Packet is_not_nan = pcmp_eq(result, result);
+ result =
+ pselect(is_not_nan, padd(shift, result),
+ pselect(x_neg, por(k3PiO4, y_signbit), por(kPiO4, y_signbit)));
+ // Handle x == +/-0.
+ result = pselect(
+ x_is_zero, pselect(y_is_zero, pzero(y), por(y_signbit, kPiO2)), result);
+ // Handle y == +/-0.
+ result = pselect(
+ y_is_zero,
+ pselect(x_has_signbit, por(y_signbit, kPi), por(y_signbit, pzero(y))),
+ result);
+ // Handle NaN inputs.
+ Packet kQNaN = pset1<Packet>(NumTraits<Scalar>::quiet_NaN());
+ return pselect(pand(x_is_not_nan, y_is_not_nan), result, kQNaN);
+ }
+};
+
+template<typename LhsScalar,typename RhsScalar>
+ struct functor_traits<scalar_atan2_op<LhsScalar, RhsScalar>> {
+ enum {
+ PacketAccess = is_same<LhsScalar,RhsScalar>::value && packet_traits<LhsScalar>::HasATan && packet_traits<LhsScalar>::HasDiv && !NumTraits<LhsScalar>::IsInteger && !NumTraits<LhsScalar>::IsComplex,
+ Cost =
+ scalar_div_cost<LhsScalar, PacketAccess>::value + 5 * NumTraits<LhsScalar>::MulCost + 5 * NumTraits<LhsScalar>::AddCost
+ };
+};
+
+//---------- binary functors bound to a constant, thus appearing as a unary functor ----------
+
+// The following two classes permits to turn any binary functor into a unary one with one argument bound to a constant value.
+// They are analogues to std::binder1st/binder2nd but with the following differences:
+// - they are compatible with packetOp
+// - they are portable across C++ versions (the std::binder* are deprecated in C++11)
+template<typename BinaryOp> struct bind1st_op : BinaryOp {
+
+ typedef typename BinaryOp::first_argument_type first_argument_type;
+ typedef typename BinaryOp::second_argument_type second_argument_type;
+ typedef typename BinaryOp::result_type result_type;
+
+ EIGEN_DEVICE_FUNC explicit bind1st_op(const first_argument_type &val) : m_value(val) {}
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const result_type operator() (const second_argument_type& b) const { return BinaryOp::operator()(m_value,b); }
+
+ template<typename Packet>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Packet packetOp(const Packet& b) const
+ { return BinaryOp::packetOp(internal::pset1<Packet>(m_value), b); }
+
+ first_argument_type m_value;
+};
+template<typename BinaryOp> struct functor_traits<bind1st_op<BinaryOp> > : functor_traits<BinaryOp> {};
+
+
+template<typename BinaryOp> struct bind2nd_op : BinaryOp {
+
+ typedef typename BinaryOp::first_argument_type first_argument_type;
+ typedef typename BinaryOp::second_argument_type second_argument_type;
+ typedef typename BinaryOp::result_type result_type;
+
+ EIGEN_DEVICE_FUNC explicit bind2nd_op(const second_argument_type &val) : m_value(val) {}
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const result_type operator() (const first_argument_type& a) const { return BinaryOp::operator()(a,m_value); }
+
+ template<typename Packet>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Packet packetOp(const Packet& a) const
+ { return BinaryOp::packetOp(a,internal::pset1<Packet>(m_value)); }
+
+ second_argument_type m_value;
+};
+template<typename BinaryOp> struct functor_traits<bind2nd_op<BinaryOp> > : functor_traits<BinaryOp> {};
+
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_BINARY_FUNCTORS_H
diff --git a/Eigen/src/Core/functors/NullaryFunctors.h b/Eigen/src/Core/functors/NullaryFunctors.h
new file mode 100644
index 0000000..e099d4a
--- /dev/null
+++ b/Eigen/src/Core/functors/NullaryFunctors.h
@@ -0,0 +1,190 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2016 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_NULLARY_FUNCTORS_H
+#define EIGEN_NULLARY_FUNCTORS_H
+
+#include "../InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+
+template<typename Scalar>
+struct scalar_constant_op {
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE scalar_constant_op(const scalar_constant_op& other) : m_other(other.m_other) { }
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE scalar_constant_op(const Scalar& other) : m_other(other) { }
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar operator() () const { return m_other; }
+ template<typename PacketType>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const PacketType packetOp() const { return internal::pset1<PacketType>(m_other); }
+ const Scalar m_other;
+};
+template<typename Scalar>
+struct functor_traits<scalar_constant_op<Scalar> >
+{ enum { Cost = 0 /* as the constant value should be loaded in register only once for the whole expression */,
+ PacketAccess = packet_traits<Scalar>::Vectorizable, IsRepeatable = true }; };
+
+template<typename Scalar> struct scalar_identity_op {
+ template<typename IndexType>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar operator() (IndexType row, IndexType col) const { return row==col ? Scalar(1) : Scalar(0); }
+};
+template<typename Scalar>
+struct functor_traits<scalar_identity_op<Scalar> >
+{ enum { Cost = NumTraits<Scalar>::AddCost, PacketAccess = false, IsRepeatable = true }; };
+
+template <typename Scalar, bool IsInteger> struct linspaced_op_impl;
+
+template <typename Scalar>
+struct linspaced_op_impl<Scalar,/*IsInteger*/false>
+{
+ typedef typename NumTraits<Scalar>::Real RealScalar;
+
+ EIGEN_DEVICE_FUNC linspaced_op_impl(const Scalar& low, const Scalar& high, Index num_steps) :
+ m_low(low), m_high(high), m_size1(num_steps==1 ? 1 : num_steps-1), m_step(num_steps==1 ? Scalar() : Scalar((high-low)/RealScalar(num_steps-1))),
+ m_flip(numext::abs(high)<numext::abs(low))
+ {}
+
+ template<typename IndexType>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar operator() (IndexType i) const {
+ if(m_flip)
+ return (i==0)? m_low : Scalar(m_high - RealScalar(m_size1-i)*m_step);
+ else
+ return (i==m_size1)? m_high : Scalar(m_low + RealScalar(i)*m_step);
+ }
+
+ template<typename Packet, typename IndexType>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Packet packetOp(IndexType i) const
+ {
+ // Principle:
+ // [low, ..., low] + ( [step, ..., step] * ( [i, ..., i] + [0, ..., size] ) )
+ if(m_flip)
+ {
+ Packet pi = plset<Packet>(Scalar(i-m_size1));
+ Packet res = padd(pset1<Packet>(m_high), pmul(pset1<Packet>(m_step), pi));
+ if (EIGEN_PREDICT_TRUE(i != 0)) return res;
+ Packet mask = pcmp_lt(pset1<Packet>(0), plset<Packet>(0));
+ return pselect<Packet>(mask, res, pset1<Packet>(m_low));
+ }
+ else
+ {
+ Packet pi = plset<Packet>(Scalar(i));
+ Packet res = padd(pset1<Packet>(m_low), pmul(pset1<Packet>(m_step), pi));
+ if(EIGEN_PREDICT_TRUE(i != m_size1-unpacket_traits<Packet>::size+1)) return res;
+ Packet mask = pcmp_lt(plset<Packet>(0), pset1<Packet>(unpacket_traits<Packet>::size-1));
+ return pselect<Packet>(mask, res, pset1<Packet>(m_high));
+ }
+ }
+
+ const Scalar m_low;
+ const Scalar m_high;
+ const Index m_size1;
+ const Scalar m_step;
+ const bool m_flip;
+};
+
+template <typename Scalar>
+struct linspaced_op_impl<Scalar,/*IsInteger*/true>
+{
+ EIGEN_DEVICE_FUNC linspaced_op_impl(const Scalar& low, const Scalar& high, Index num_steps) :
+ m_low(low),
+ m_multiplier((high-low)/convert_index<Scalar>(num_steps<=1 ? 1 : num_steps-1)),
+ m_divisor(convert_index<Scalar>((high>=low?num_steps:-num_steps)+(high-low))/((numext::abs(high-low)+1)==0?1:(numext::abs(high-low)+1))),
+ m_use_divisor(num_steps>1 && (numext::abs(high-low)+1)<num_steps)
+ {}
+
+ template<typename IndexType>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ const Scalar operator() (IndexType i) const
+ {
+ if(m_use_divisor) return m_low + convert_index<Scalar>(i)/m_divisor;
+ else return m_low + convert_index<Scalar>(i)*m_multiplier;
+ }
+
+ const Scalar m_low;
+ const Scalar m_multiplier;
+ const Scalar m_divisor;
+ const bool m_use_divisor;
+};
+
+// ----- Linspace functor ----------------------------------------------------------------
+
+// Forward declaration (we default to random access which does not really give
+// us a speed gain when using packet access but it allows to use the functor in
+// nested expressions).
+template <typename Scalar> struct linspaced_op;
+template <typename Scalar> struct functor_traits< linspaced_op<Scalar> >
+{
+ enum
+ {
+ Cost = 1,
+ PacketAccess = (!NumTraits<Scalar>::IsInteger) && packet_traits<Scalar>::HasSetLinear && packet_traits<Scalar>::HasBlend,
+ /*&& ((!NumTraits<Scalar>::IsInteger) || packet_traits<Scalar>::HasDiv),*/ // <- vectorization for integer is currently disabled
+ IsRepeatable = true
+ };
+};
+template <typename Scalar> struct linspaced_op
+{
+ EIGEN_DEVICE_FUNC linspaced_op(const Scalar& low, const Scalar& high, Index num_steps)
+ : impl((num_steps==1 ? high : low),high,num_steps)
+ {}
+
+ template<typename IndexType>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar operator() (IndexType i) const { return impl(i); }
+
+ template<typename Packet,typename IndexType>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Packet packetOp(IndexType i) const { return impl.template packetOp<Packet>(i); }
+
+ // This proxy object handles the actual required temporaries and the different
+ // implementations (integer vs. floating point).
+ const linspaced_op_impl<Scalar,NumTraits<Scalar>::IsInteger> impl;
+};
+
+// Linear access is automatically determined from the operator() prototypes available for the given functor.
+// If it exposes an operator()(i,j), then we assume the i and j coefficients are required independently
+// and linear access is not possible. In all other cases, linear access is enabled.
+// Users should not have to deal with this structure.
+template<typename Functor> struct functor_has_linear_access { enum { ret = !has_binary_operator<Functor>::value }; };
+
+// For unreliable compilers, let's specialize the has_*ary_operator
+// helpers so that at least built-in nullary functors work fine.
+#if !( EIGEN_COMP_MSVC || EIGEN_COMP_GNUC || (EIGEN_COMP_ICC>=1600))
+template<typename Scalar,typename IndexType>
+struct has_nullary_operator<scalar_constant_op<Scalar>,IndexType> { enum { value = 1}; };
+template<typename Scalar,typename IndexType>
+struct has_unary_operator<scalar_constant_op<Scalar>,IndexType> { enum { value = 0}; };
+template<typename Scalar,typename IndexType>
+struct has_binary_operator<scalar_constant_op<Scalar>,IndexType> { enum { value = 0}; };
+
+template<typename Scalar,typename IndexType>
+struct has_nullary_operator<scalar_identity_op<Scalar>,IndexType> { enum { value = 0}; };
+template<typename Scalar,typename IndexType>
+struct has_unary_operator<scalar_identity_op<Scalar>,IndexType> { enum { value = 0}; };
+template<typename Scalar,typename IndexType>
+struct has_binary_operator<scalar_identity_op<Scalar>,IndexType> { enum { value = 1}; };
+
+template<typename Scalar,typename IndexType>
+struct has_nullary_operator<linspaced_op<Scalar>,IndexType> { enum { value = 0}; };
+template<typename Scalar,typename IndexType>
+struct has_unary_operator<linspaced_op<Scalar>,IndexType> { enum { value = 1}; };
+template<typename Scalar,typename IndexType>
+struct has_binary_operator<linspaced_op<Scalar>,IndexType> { enum { value = 0}; };
+
+template<typename Scalar,typename IndexType>
+struct has_nullary_operator<scalar_random_op<Scalar>,IndexType> { enum { value = 1}; };
+template<typename Scalar,typename IndexType>
+struct has_unary_operator<scalar_random_op<Scalar>,IndexType> { enum { value = 0}; };
+template<typename Scalar,typename IndexType>
+struct has_binary_operator<scalar_random_op<Scalar>,IndexType> { enum { value = 0}; };
+#endif
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_NULLARY_FUNCTORS_H
diff --git a/Eigen/src/Core/functors/StlFunctors.h b/Eigen/src/Core/functors/StlFunctors.h
new file mode 100644
index 0000000..5971075
--- /dev/null
+++ b/Eigen/src/Core/functors/StlFunctors.h
@@ -0,0 +1,157 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2010 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_STL_FUNCTORS_H
+#define EIGEN_STL_FUNCTORS_H
+
+#include "../InternalHeaderCheck.h"
+
+namespace Eigen {
+
+// Portable replacements for certain functors.
+namespace numext {
+
+template<typename T = void>
+struct equal_to {
+ typedef bool result_type;
+ EIGEN_DEVICE_FUNC bool operator()(const T& lhs, const T& rhs) const {
+ return lhs == rhs;
+ }
+};
+
+template<typename T = void>
+struct not_equal_to {
+ typedef bool result_type;
+ EIGEN_DEVICE_FUNC bool operator()(const T& lhs, const T& rhs) const {
+ return lhs != rhs;
+ }
+};
+
+}
+
+
+namespace internal {
+
+// default functor traits for STL functors:
+
+template<typename T>
+struct functor_traits<std::multiplies<T> >
+{ enum { Cost = NumTraits<T>::MulCost, PacketAccess = false }; };
+
+template<typename T>
+struct functor_traits<std::divides<T> >
+{ enum { Cost = NumTraits<T>::MulCost, PacketAccess = false }; };
+
+template<typename T>
+struct functor_traits<std::plus<T> >
+{ enum { Cost = NumTraits<T>::AddCost, PacketAccess = false }; };
+
+template<typename T>
+struct functor_traits<std::minus<T> >
+{ enum { Cost = NumTraits<T>::AddCost, PacketAccess = false }; };
+
+template<typename T>
+struct functor_traits<std::negate<T> >
+{ enum { Cost = NumTraits<T>::AddCost, PacketAccess = false }; };
+
+template<typename T>
+struct functor_traits<std::logical_or<T> >
+{ enum { Cost = 1, PacketAccess = false }; };
+
+template<typename T>
+struct functor_traits<std::logical_and<T> >
+{ enum { Cost = 1, PacketAccess = false }; };
+
+template<typename T>
+struct functor_traits<std::logical_not<T> >
+{ enum { Cost = 1, PacketAccess = false }; };
+
+template<typename T>
+struct functor_traits<std::greater<T> >
+{ enum { Cost = 1, PacketAccess = false }; };
+
+template<typename T>
+struct functor_traits<std::less<T> >
+{ enum { Cost = 1, PacketAccess = false }; };
+
+template<typename T>
+struct functor_traits<std::greater_equal<T> >
+{ enum { Cost = 1, PacketAccess = false }; };
+
+template<typename T>
+struct functor_traits<std::less_equal<T> >
+{ enum { Cost = 1, PacketAccess = false }; };
+
+template<typename T>
+struct functor_traits<std::equal_to<T> >
+{ enum { Cost = 1, PacketAccess = false }; };
+
+template<typename T>
+struct functor_traits<numext::equal_to<T> >
+ : functor_traits<std::equal_to<T> > {};
+
+template<typename T>
+struct functor_traits<std::not_equal_to<T> >
+{ enum { Cost = 1, PacketAccess = false }; };
+
+template<typename T>
+struct functor_traits<numext::not_equal_to<T> >
+ : functor_traits<std::not_equal_to<T> > {};
+
+#if (EIGEN_COMP_CXXVER < 17)
+// std::unary_negate is deprecated since c++17 and will be removed in c++20
+template<typename T>
+struct functor_traits<std::unary_negate<T> >
+{ enum { Cost = 1 + functor_traits<T>::Cost, PacketAccess = false }; };
+
+// std::binary_negate is deprecated since c++17 and will be removed in c++20
+template<typename T>
+struct functor_traits<std::binary_negate<T> >
+{ enum { Cost = 1 + functor_traits<T>::Cost, PacketAccess = false }; };
+#endif
+
+#ifdef EIGEN_STDEXT_SUPPORT
+
+template<typename T0,typename T1>
+struct functor_traits<std::project1st<T0,T1> >
+{ enum { Cost = 0, PacketAccess = false }; };
+
+template<typename T0,typename T1>
+struct functor_traits<std::project2nd<T0,T1> >
+{ enum { Cost = 0, PacketAccess = false }; };
+
+template<typename T0,typename T1>
+struct functor_traits<std::select2nd<std::pair<T0,T1> > >
+{ enum { Cost = 0, PacketAccess = false }; };
+
+template<typename T0,typename T1>
+struct functor_traits<std::select1st<std::pair<T0,T1> > >
+{ enum { Cost = 0, PacketAccess = false }; };
+
+template<typename T0,typename T1>
+struct functor_traits<std::unary_compose<T0,T1> >
+{ enum { Cost = functor_traits<T0>::Cost + functor_traits<T1>::Cost, PacketAccess = false }; };
+
+template<typename T0,typename T1,typename T2>
+struct functor_traits<std::binary_compose<T0,T1,T2> >
+{ enum { Cost = functor_traits<T0>::Cost + functor_traits<T1>::Cost + functor_traits<T2>::Cost, PacketAccess = false }; };
+
+#endif // EIGEN_STDEXT_SUPPORT
+
+// allow to add new functors and specializations of functor_traits from outside Eigen.
+// this macro is really needed because functor_traits must be specialized after it is declared but before it is used...
+#ifdef EIGEN_FUNCTORS_PLUGIN
+#include EIGEN_FUNCTORS_PLUGIN
+#endif
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_STL_FUNCTORS_H
diff --git a/Eigen/src/Core/functors/TernaryFunctors.h b/Eigen/src/Core/functors/TernaryFunctors.h
new file mode 100644
index 0000000..41c0d5f
--- /dev/null
+++ b/Eigen/src/Core/functors/TernaryFunctors.h
@@ -0,0 +1,27 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2016 Eugene Brevdo <ebrevdo@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_TERNARY_FUNCTORS_H
+#define EIGEN_TERNARY_FUNCTORS_H
+
+#include "../InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+
+//---------- associative ternary functors ----------
+
+
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_TERNARY_FUNCTORS_H
diff --git a/Eigen/src/Core/functors/UnaryFunctors.h b/Eigen/src/Core/functors/UnaryFunctors.h
new file mode 100644
index 0000000..3485369
--- /dev/null
+++ b/Eigen/src/Core/functors/UnaryFunctors.h
@@ -0,0 +1,1162 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2016 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_UNARY_FUNCTORS_H
+#define EIGEN_UNARY_FUNCTORS_H
+
+#include "../InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+
+/** \internal
+ * \brief Template functor to compute the opposite of a scalar
+ *
+ * \sa class CwiseUnaryOp, MatrixBase::operator-
+ */
+template<typename Scalar> struct scalar_opposite_op {
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar operator() (const Scalar& a) const { return -a; }
+ template<typename Packet>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Packet packetOp(const Packet& a) const
+ { return internal::pnegate(a); }
+};
+template<typename Scalar>
+struct functor_traits<scalar_opposite_op<Scalar> >
+{ enum {
+ Cost = NumTraits<Scalar>::AddCost,
+ PacketAccess = packet_traits<Scalar>::HasNegate };
+};
+
+/** \internal
+ * \brief Template functor to compute the absolute value of a scalar
+ *
+ * \sa class CwiseUnaryOp, Cwise::abs
+ */
+template<typename Scalar> struct scalar_abs_op {
+ typedef typename NumTraits<Scalar>::Real result_type;
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const result_type operator() (const Scalar& a) const { return numext::abs(a); }
+ template<typename Packet>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Packet packetOp(const Packet& a) const
+ { return internal::pabs(a); }
+};
+template<typename Scalar>
+struct functor_traits<scalar_abs_op<Scalar> >
+{
+ enum {
+ Cost = NumTraits<Scalar>::AddCost,
+ PacketAccess = packet_traits<Scalar>::HasAbs
+ };
+};
+
+/** \internal
+ * \brief Template functor to compute the score of a scalar, to chose a pivot
+ *
+ * \sa class CwiseUnaryOp
+ */
+template<typename Scalar> struct scalar_score_coeff_op : scalar_abs_op<Scalar>
+{
+ typedef void Score_is_abs;
+};
+template<typename Scalar>
+struct functor_traits<scalar_score_coeff_op<Scalar> > : functor_traits<scalar_abs_op<Scalar> > {};
+
+/* Avoid recomputing abs when we know the score and they are the same. Not a true Eigen functor. */
+template<typename Scalar, typename=void> struct abs_knowing_score
+{
+ typedef typename NumTraits<Scalar>::Real result_type;
+ template<typename Score>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const result_type operator() (const Scalar& a, const Score&) const { return numext::abs(a); }
+};
+template<typename Scalar> struct abs_knowing_score<Scalar, typename scalar_score_coeff_op<Scalar>::Score_is_abs>
+{
+ typedef typename NumTraits<Scalar>::Real result_type;
+ template<typename Scal>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const result_type operator() (const Scal&, const result_type& a) const { return a; }
+};
+
+/** \internal
+ * \brief Template functor to compute the squared absolute value of a scalar
+ *
+ * \sa class CwiseUnaryOp, Cwise::abs2
+ */
+template<typename Scalar> struct scalar_abs2_op {
+ typedef typename NumTraits<Scalar>::Real result_type;
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE const result_type operator() (const Scalar& a) const { return numext::abs2(a); }
+ template<typename Packet>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Packet packetOp(const Packet& a) const
+ { return internal::pmul(a,a); }
+};
+template<typename Scalar>
+struct functor_traits<scalar_abs2_op<Scalar> >
+{ enum { Cost = NumTraits<Scalar>::MulCost, PacketAccess = packet_traits<Scalar>::HasAbs2 }; };
+
+/** \internal
+ * \brief Template functor to compute the conjugate of a complex value
+ *
+ * \sa class CwiseUnaryOp, MatrixBase::conjugate()
+ */
+template<typename Scalar> struct scalar_conjugate_op {
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE const Scalar operator() (const Scalar& a) const { return numext::conj(a); }
+ template<typename Packet>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Packet packetOp(const Packet& a) const { return internal::pconj(a); }
+};
+template<typename Scalar>
+struct functor_traits<scalar_conjugate_op<Scalar> >
+{
+ enum {
+ Cost = 0,
+ // Yes the cost is zero even for complexes because in most cases for which
+ // the cost is used, conjugation turns to be a no-op. Some examples:
+ // cost(a*conj(b)) == cost(a*b)
+ // cost(a+conj(b)) == cost(a+b)
+ // <etc.
+ // If we don't set it to zero, then:
+ // A.conjugate().lazyProduct(B.conjugate())
+ // will bake its operands. We definitely don't want that!
+ PacketAccess = packet_traits<Scalar>::HasConj
+ };
+};
+
+/** \internal
+ * \brief Template functor to compute the phase angle of a complex
+ *
+ * \sa class CwiseUnaryOp, Cwise::arg
+ */
+template<typename Scalar> struct scalar_arg_op {
+ typedef typename NumTraits<Scalar>::Real result_type;
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const result_type operator() (const Scalar& a) const { return numext::arg(a); }
+ template<typename Packet>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Packet packetOp(const Packet& a) const
+ { return internal::parg(a); }
+};
+template<typename Scalar>
+struct functor_traits<scalar_arg_op<Scalar> >
+{
+ enum {
+ Cost = NumTraits<Scalar>::IsComplex ? 5 * NumTraits<Scalar>::MulCost : NumTraits<Scalar>::AddCost,
+ PacketAccess = packet_traits<Scalar>::HasArg
+ };
+};
+/** \internal
+ * \brief Template functor to cast a scalar to another type
+ *
+ * \sa class CwiseUnaryOp, MatrixBase::cast()
+ */
+template<typename Scalar, typename NewType>
+struct scalar_cast_op {
+ typedef NewType result_type;
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const NewType operator() (const Scalar& a) const { return cast<Scalar, NewType>(a); }
+};
+template<typename Scalar, typename NewType>
+struct functor_traits<scalar_cast_op<Scalar,NewType> >
+{ enum { Cost = is_same<Scalar, NewType>::value ? 0 : NumTraits<NewType>::AddCost, PacketAccess = false }; };
+
+/** \internal
+ * \brief Template functor to arithmetically shift a scalar right by a number of bits
+ *
+ * \sa class CwiseUnaryOp, MatrixBase::shift_right()
+ */
+template<typename Scalar, int N>
+struct scalar_shift_right_op {
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar operator() (const Scalar& a) const
+ { return a >> N; }
+ template<typename Packet>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Packet packetOp(const Packet& a) const
+ { return internal::parithmetic_shift_right<N>(a); }
+};
+template<typename Scalar, int N>
+struct functor_traits<scalar_shift_right_op<Scalar,N> >
+{ enum { Cost = NumTraits<Scalar>::AddCost, PacketAccess = packet_traits<Scalar>::HasShift }; };
+
+/** \internal
+ * \brief Template functor to logically shift a scalar left by a number of bits
+ *
+ * \sa class CwiseUnaryOp, MatrixBase::shift_left()
+ */
+template<typename Scalar, int N>
+struct scalar_shift_left_op {
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar operator() (const Scalar& a) const
+ { return a << N; }
+ template<typename Packet>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Packet packetOp(const Packet& a) const
+ { return internal::plogical_shift_left<N>(a); }
+};
+template<typename Scalar, int N>
+struct functor_traits<scalar_shift_left_op<Scalar,N> >
+{ enum { Cost = NumTraits<Scalar>::AddCost, PacketAccess = packet_traits<Scalar>::HasShift }; };
+
+/** \internal
+ * \brief Template functor to extract the real part of a complex
+ *
+ * \sa class CwiseUnaryOp, MatrixBase::real()
+ */
+template<typename Scalar>
+struct scalar_real_op {
+ typedef typename NumTraits<Scalar>::Real result_type;
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE result_type operator() (const Scalar& a) const { return numext::real(a); }
+};
+template<typename Scalar>
+struct functor_traits<scalar_real_op<Scalar> >
+{ enum { Cost = 0, PacketAccess = false }; };
+
+/** \internal
+ * \brief Template functor to extract the imaginary part of a complex
+ *
+ * \sa class CwiseUnaryOp, MatrixBase::imag()
+ */
+template<typename Scalar>
+struct scalar_imag_op {
+ typedef typename NumTraits<Scalar>::Real result_type;
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE result_type operator() (const Scalar& a) const { return numext::imag(a); }
+};
+template<typename Scalar>
+struct functor_traits<scalar_imag_op<Scalar> >
+{ enum { Cost = 0, PacketAccess = false }; };
+
+/** \internal
+ * \brief Template functor to extract the real part of a complex as a reference
+ *
+ * \sa class CwiseUnaryOp, MatrixBase::real()
+ */
+template<typename Scalar>
+struct scalar_real_ref_op {
+ typedef typename NumTraits<Scalar>::Real result_type;
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE result_type& operator() (const Scalar& a) const { return numext::real_ref(*const_cast<Scalar*>(&a)); }
+};
+template<typename Scalar>
+struct functor_traits<scalar_real_ref_op<Scalar> >
+{ enum { Cost = 0, PacketAccess = false }; };
+
+/** \internal
+ * \brief Template functor to extract the imaginary part of a complex as a reference
+ *
+ * \sa class CwiseUnaryOp, MatrixBase::imag()
+ */
+template<typename Scalar>
+struct scalar_imag_ref_op {
+ typedef typename NumTraits<Scalar>::Real result_type;
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE result_type& operator() (const Scalar& a) const { return numext::imag_ref(*const_cast<Scalar*>(&a)); }
+};
+template<typename Scalar>
+struct functor_traits<scalar_imag_ref_op<Scalar> >
+{ enum { Cost = 0, PacketAccess = false }; };
+
+/** \internal
+ *
+ * \brief Template functor to compute the exponential of a scalar
+ *
+ * \sa class CwiseUnaryOp, Cwise::exp()
+ */
+template<typename Scalar> struct scalar_exp_op {
+ EIGEN_DEVICE_FUNC inline const Scalar operator() (const Scalar& a) const { return internal::pexp(a); }
+ template <typename Packet>
+ EIGEN_DEVICE_FUNC inline Packet packetOp(const Packet& a) const { return internal::pexp(a); }
+};
+template <typename Scalar>
+struct functor_traits<scalar_exp_op<Scalar> > {
+ enum {
+ PacketAccess = packet_traits<Scalar>::HasExp,
+ // The following numbers are based on the AVX implementation.
+#ifdef EIGEN_VECTORIZE_FMA
+ // Haswell can issue 2 add/mul/madd per cycle.
+ Cost =
+ (sizeof(Scalar) == 4
+ // float: 8 pmadd, 4 pmul, 2 padd/psub, 6 other
+ ? (8 * NumTraits<Scalar>::AddCost + 6 * NumTraits<Scalar>::MulCost)
+ // double: 7 pmadd, 5 pmul, 3 padd/psub, 1 div, 13 other
+ : (14 * NumTraits<Scalar>::AddCost +
+ 6 * NumTraits<Scalar>::MulCost +
+ scalar_div_cost<Scalar,packet_traits<Scalar>::HasDiv>::value))
+#else
+ Cost =
+ (sizeof(Scalar) == 4
+ // float: 7 pmadd, 6 pmul, 4 padd/psub, 10 other
+ ? (21 * NumTraits<Scalar>::AddCost + 13 * NumTraits<Scalar>::MulCost)
+ // double: 7 pmadd, 5 pmul, 3 padd/psub, 1 div, 13 other
+ : (23 * NumTraits<Scalar>::AddCost +
+ 12 * NumTraits<Scalar>::MulCost +
+ scalar_div_cost<Scalar,packet_traits<Scalar>::HasDiv>::value))
+#endif
+ };
+};
+
+/** \internal
+ *
+ * \brief Template functor to compute the exponential of a scalar - 1.
+ *
+ * \sa class CwiseUnaryOp, ArrayBase::expm1()
+ */
+template<typename Scalar> struct scalar_expm1_op {
+ EIGEN_DEVICE_FUNC inline const Scalar operator() (const Scalar& a) const { return numext::expm1(a); }
+ template <typename Packet>
+ EIGEN_DEVICE_FUNC inline Packet packetOp(const Packet& a) const { return internal::pexpm1(a); }
+};
+template <typename Scalar>
+struct functor_traits<scalar_expm1_op<Scalar> > {
+ enum {
+ PacketAccess = packet_traits<Scalar>::HasExpm1,
+ Cost = functor_traits<scalar_exp_op<Scalar> >::Cost // TODO measure cost of expm1
+ };
+};
+
+/** \internal
+ *
+ * \brief Template functor to compute the logarithm of a scalar
+ *
+ * \sa class CwiseUnaryOp, ArrayBase::log()
+ */
+template<typename Scalar> struct scalar_log_op {
+ EIGEN_DEVICE_FUNC inline const Scalar operator() (const Scalar& a) const { return numext::log(a); }
+ template <typename Packet>
+ EIGEN_DEVICE_FUNC inline Packet packetOp(const Packet& a) const { return internal::plog(a); }
+};
+template <typename Scalar>
+struct functor_traits<scalar_log_op<Scalar> > {
+ enum {
+ PacketAccess = packet_traits<Scalar>::HasLog,
+ Cost =
+ (PacketAccess
+ // The following numbers are based on the AVX implementation.
+#ifdef EIGEN_VECTORIZE_FMA
+ // 8 pmadd, 6 pmul, 8 padd/psub, 16 other, can issue 2 add/mul/madd per cycle.
+ ? (20 * NumTraits<Scalar>::AddCost + 7 * NumTraits<Scalar>::MulCost)
+#else
+ // 8 pmadd, 6 pmul, 8 padd/psub, 20 other
+ ? (36 * NumTraits<Scalar>::AddCost + 14 * NumTraits<Scalar>::MulCost)
+#endif
+ // Measured cost of std::log.
+ : sizeof(Scalar)==4 ? 40 : 85)
+ };
+};
+
+/** \internal
+ *
+ * \brief Template functor to compute the logarithm of 1 plus a scalar value
+ *
+ * \sa class CwiseUnaryOp, ArrayBase::log1p()
+ */
+template<typename Scalar> struct scalar_log1p_op {
+ EIGEN_DEVICE_FUNC inline const Scalar operator() (const Scalar& a) const { return numext::log1p(a); }
+ template <typename Packet>
+ EIGEN_DEVICE_FUNC inline Packet packetOp(const Packet& a) const { return internal::plog1p(a); }
+};
+template <typename Scalar>
+struct functor_traits<scalar_log1p_op<Scalar> > {
+ enum {
+ PacketAccess = packet_traits<Scalar>::HasLog1p,
+ Cost = functor_traits<scalar_log_op<Scalar> >::Cost // TODO measure cost of log1p
+ };
+};
+
+/** \internal
+ *
+ * \brief Template functor to compute the base-10 logarithm of a scalar
+ *
+ * \sa class CwiseUnaryOp, Cwise::log10()
+ */
+template<typename Scalar> struct scalar_log10_op {
+ EIGEN_DEVICE_FUNC inline const Scalar operator() (const Scalar& a) const { EIGEN_USING_STD(log10) return log10(a); }
+ template <typename Packet>
+ EIGEN_DEVICE_FUNC inline Packet packetOp(const Packet& a) const { return internal::plog10(a); }
+};
+template<typename Scalar>
+struct functor_traits<scalar_log10_op<Scalar> >
+{ enum { Cost = 5 * NumTraits<Scalar>::MulCost, PacketAccess = packet_traits<Scalar>::HasLog10 }; };
+
+/** \internal
+ *
+ * \brief Template functor to compute the base-2 logarithm of a scalar
+ *
+ * \sa class CwiseUnaryOp, Cwise::log2()
+ */
+template<typename Scalar> struct scalar_log2_op {
+ EIGEN_DEVICE_FUNC inline const Scalar operator() (const Scalar& a) const { return Scalar(EIGEN_LOG2E) * numext::log(a); }
+ template <typename Packet>
+ EIGEN_DEVICE_FUNC inline Packet packetOp(const Packet& a) const { return internal::plog2(a); }
+};
+template<typename Scalar>
+struct functor_traits<scalar_log2_op<Scalar> >
+{ enum { Cost = 5 * NumTraits<Scalar>::MulCost, PacketAccess = packet_traits<Scalar>::HasLog }; };
+
+/** \internal
+ * \brief Template functor to compute the square root of a scalar
+ * \sa class CwiseUnaryOp, Cwise::sqrt()
+ */
+template<typename Scalar> struct scalar_sqrt_op {
+ EIGEN_DEVICE_FUNC inline const Scalar operator() (const Scalar& a) const { return numext::sqrt(a); }
+ template <typename Packet>
+ EIGEN_DEVICE_FUNC inline Packet packetOp(const Packet& a) const { return internal::psqrt(a); }
+};
+template <typename Scalar>
+struct functor_traits<scalar_sqrt_op<Scalar> > {
+ enum {
+#if EIGEN_FAST_MATH
+ // The following numbers are based on the AVX implementation.
+ Cost = (sizeof(Scalar) == 8 ? 28
+ // 4 pmul, 1 pmadd, 3 other
+ : (3 * NumTraits<Scalar>::AddCost +
+ 5 * NumTraits<Scalar>::MulCost)),
+#else
+ // The following numbers are based on min VSQRT throughput on Haswell.
+ Cost = (sizeof(Scalar) == 8 ? 28 : 14),
+#endif
+ PacketAccess = packet_traits<Scalar>::HasSqrt
+ };
+};
+
+// Boolean specialization to eliminate -Wimplicit-conversion-floating-point-to-bool warnings.
+template<> struct scalar_sqrt_op<bool> {
+ EIGEN_DEPRECATED EIGEN_DEVICE_FUNC inline bool operator() (const bool& a) const { return a; }
+ template <typename Packet>
+ EIGEN_DEPRECATED EIGEN_DEVICE_FUNC inline Packet packetOp(const Packet& a) const { return a; }
+};
+template <>
+struct functor_traits<scalar_sqrt_op<bool> > {
+ enum { Cost = 1, PacketAccess = packet_traits<bool>::Vectorizable };
+};
+
+/** \internal
+ * \brief Template functor to compute the reciprocal square root of a scalar
+ * \sa class CwiseUnaryOp, Cwise::rsqrt()
+ */
+template<typename Scalar> struct scalar_rsqrt_op {
+ EIGEN_DEVICE_FUNC inline const Scalar operator() (const Scalar& a) const { return numext::rsqrt(a); }
+ template <typename Packet>
+ EIGEN_DEVICE_FUNC inline Packet packetOp(const Packet& a) const { return internal::prsqrt(a); }
+};
+
+template<typename Scalar>
+struct functor_traits<scalar_rsqrt_op<Scalar> >
+{ enum {
+ Cost = 5 * NumTraits<Scalar>::MulCost,
+ PacketAccess = packet_traits<Scalar>::HasRsqrt
+ };
+};
+
+/** \internal
+ * \brief Template functor to compute the cosine of a scalar
+ * \sa class CwiseUnaryOp, ArrayBase::cos()
+ */
+template<typename Scalar> struct scalar_cos_op {
+ EIGEN_DEVICE_FUNC inline Scalar operator() (const Scalar& a) const { return numext::cos(a); }
+ template <typename Packet>
+ EIGEN_DEVICE_FUNC inline Packet packetOp(const Packet& a) const { return internal::pcos(a); }
+};
+template<typename Scalar>
+struct functor_traits<scalar_cos_op<Scalar> >
+{
+ enum {
+ Cost = 5 * NumTraits<Scalar>::MulCost,
+ PacketAccess = packet_traits<Scalar>::HasCos
+ };
+};
+
+/** \internal
+ * \brief Template functor to compute the sine of a scalar
+ * \sa class CwiseUnaryOp, ArrayBase::sin()
+ */
+template<typename Scalar> struct scalar_sin_op {
+ EIGEN_DEVICE_FUNC inline const Scalar operator() (const Scalar& a) const { return numext::sin(a); }
+ template <typename Packet>
+ EIGEN_DEVICE_FUNC inline Packet packetOp(const Packet& a) const { return internal::psin(a); }
+};
+template<typename Scalar>
+struct functor_traits<scalar_sin_op<Scalar> >
+{
+ enum {
+ Cost = 5 * NumTraits<Scalar>::MulCost,
+ PacketAccess = packet_traits<Scalar>::HasSin
+ };
+};
+
+
+/** \internal
+ * \brief Template functor to compute the tan of a scalar
+ * \sa class CwiseUnaryOp, ArrayBase::tan()
+ */
+template<typename Scalar> struct scalar_tan_op {
+ EIGEN_DEVICE_FUNC inline const Scalar operator() (const Scalar& a) const { return numext::tan(a); }
+ template <typename Packet>
+ EIGEN_DEVICE_FUNC inline Packet packetOp(const Packet& a) const { return internal::ptan(a); }
+};
+template<typename Scalar>
+struct functor_traits<scalar_tan_op<Scalar> >
+{
+ enum {
+ Cost = 5 * NumTraits<Scalar>::MulCost,
+ PacketAccess = packet_traits<Scalar>::HasTan
+ };
+};
+
+/** \internal
+ * \brief Template functor to compute the arc cosine of a scalar
+ * \sa class CwiseUnaryOp, ArrayBase::acos()
+ */
+template<typename Scalar> struct scalar_acos_op {
+ EIGEN_DEVICE_FUNC inline const Scalar operator() (const Scalar& a) const { return numext::acos(a); }
+ template <typename Packet>
+ EIGEN_DEVICE_FUNC inline Packet packetOp(const Packet& a) const { return internal::pacos(a); }
+};
+template<typename Scalar>
+struct functor_traits<scalar_acos_op<Scalar> >
+{
+ enum {
+ Cost = 5 * NumTraits<Scalar>::MulCost,
+ PacketAccess = packet_traits<Scalar>::HasACos
+ };
+};
+
+/** \internal
+ * \brief Template functor to compute the arc sine of a scalar
+ * \sa class CwiseUnaryOp, ArrayBase::asin()
+ */
+template<typename Scalar> struct scalar_asin_op {
+ EIGEN_DEVICE_FUNC inline const Scalar operator() (const Scalar& a) const { return numext::asin(a); }
+ template <typename Packet>
+ EIGEN_DEVICE_FUNC inline Packet packetOp(const Packet& a) const { return internal::pasin(a); }
+};
+template<typename Scalar>
+struct functor_traits<scalar_asin_op<Scalar> >
+{
+ enum {
+ Cost = 5 * NumTraits<Scalar>::MulCost,
+ PacketAccess = packet_traits<Scalar>::HasASin
+ };
+};
+
+
+/** \internal
+ * \brief Template functor to compute the atan of a scalar
+ * \sa class CwiseUnaryOp, ArrayBase::atan()
+ */
+template<typename Scalar> struct scalar_atan_op {
+ EIGEN_DEVICE_FUNC inline const Scalar operator() (const Scalar& a) const { return numext::atan(a); }
+ template <typename Packet>
+ EIGEN_DEVICE_FUNC inline Packet packetOp(const Packet& a) const { return internal::patan(a); }
+};
+template<typename Scalar>
+struct functor_traits<scalar_atan_op<Scalar> >
+{
+ enum {
+ Cost = 5 * NumTraits<Scalar>::MulCost,
+ PacketAccess = packet_traits<Scalar>::HasATan
+ };
+};
+
+/** \internal
+ * \brief Template functor to compute the tanh of a scalar
+ * \sa class CwiseUnaryOp, ArrayBase::tanh()
+ */
+template <typename Scalar>
+struct scalar_tanh_op {
+ EIGEN_DEVICE_FUNC inline const Scalar operator()(const Scalar& a) const { return numext::tanh(a); }
+ template <typename Packet>
+ EIGEN_DEVICE_FUNC inline Packet packetOp(const Packet& x) const { return ptanh(x); }
+};
+
+template <typename Scalar>
+struct functor_traits<scalar_tanh_op<Scalar> > {
+ enum {
+ PacketAccess = packet_traits<Scalar>::HasTanh,
+ Cost = ( (EIGEN_FAST_MATH && is_same<Scalar,float>::value)
+// The following numbers are based on the AVX implementation,
+#ifdef EIGEN_VECTORIZE_FMA
+ // Haswell can issue 2 add/mul/madd per cycle.
+ // 9 pmadd, 2 pmul, 1 div, 2 other
+ ? (2 * NumTraits<Scalar>::AddCost +
+ 6 * NumTraits<Scalar>::MulCost +
+ scalar_div_cost<Scalar,packet_traits<Scalar>::HasDiv>::value)
+#else
+ ? (11 * NumTraits<Scalar>::AddCost +
+ 11 * NumTraits<Scalar>::MulCost +
+ scalar_div_cost<Scalar,packet_traits<Scalar>::HasDiv>::value)
+#endif
+ // This number assumes a naive implementation of tanh
+ : (6 * NumTraits<Scalar>::AddCost +
+ 3 * NumTraits<Scalar>::MulCost +
+ 2 * scalar_div_cost<Scalar,packet_traits<Scalar>::HasDiv>::value +
+ functor_traits<scalar_exp_op<Scalar> >::Cost))
+ };
+};
+
+/** \internal
+ * \brief Template functor to compute the atanh of a scalar
+ * \sa class CwiseUnaryOp, ArrayBase::atanh()
+ */
+template <typename Scalar>
+struct scalar_atanh_op {
+ EIGEN_DEVICE_FUNC inline const Scalar operator()(const Scalar& a) const { return numext::atanh(a); }
+};
+
+template <typename Scalar>
+struct functor_traits<scalar_atanh_op<Scalar> > {
+ enum { Cost = 5 * NumTraits<Scalar>::MulCost, PacketAccess = false };
+};
+
+/** \internal
+ * \brief Template functor to compute the sinh of a scalar
+ * \sa class CwiseUnaryOp, ArrayBase::sinh()
+ */
+template<typename Scalar> struct scalar_sinh_op {
+ EIGEN_DEVICE_FUNC inline const Scalar operator() (const Scalar& a) const { return numext::sinh(a); }
+ template <typename Packet>
+ EIGEN_DEVICE_FUNC inline Packet packetOp(const Packet& a) const { return internal::psinh(a); }
+};
+template<typename Scalar>
+struct functor_traits<scalar_sinh_op<Scalar> >
+{
+ enum {
+ Cost = 5 * NumTraits<Scalar>::MulCost,
+ PacketAccess = packet_traits<Scalar>::HasSinh
+ };
+};
+
+/** \internal
+ * \brief Template functor to compute the asinh of a scalar
+ * \sa class CwiseUnaryOp, ArrayBase::asinh()
+ */
+template <typename Scalar>
+struct scalar_asinh_op {
+ EIGEN_DEVICE_FUNC inline const Scalar operator()(const Scalar& a) const { return numext::asinh(a); }
+};
+
+template <typename Scalar>
+struct functor_traits<scalar_asinh_op<Scalar> > {
+ enum { Cost = 5 * NumTraits<Scalar>::MulCost, PacketAccess = false };
+};
+
+/** \internal
+ * \brief Template functor to compute the cosh of a scalar
+ * \sa class CwiseUnaryOp, ArrayBase::cosh()
+ */
+template<typename Scalar> struct scalar_cosh_op {
+ EIGEN_DEVICE_FUNC inline const Scalar operator() (const Scalar& a) const { return numext::cosh(a); }
+ template <typename Packet>
+ EIGEN_DEVICE_FUNC inline Packet packetOp(const Packet& a) const { return internal::pcosh(a); }
+};
+template<typename Scalar>
+struct functor_traits<scalar_cosh_op<Scalar> >
+{
+ enum {
+ Cost = 5 * NumTraits<Scalar>::MulCost,
+ PacketAccess = packet_traits<Scalar>::HasCosh
+ };
+};
+
+/** \internal
+ * \brief Template functor to compute the acosh of a scalar
+ * \sa class CwiseUnaryOp, ArrayBase::acosh()
+ */
+template <typename Scalar>
+struct scalar_acosh_op {
+ EIGEN_DEVICE_FUNC inline const Scalar operator()(const Scalar& a) const { return numext::acosh(a); }
+};
+
+template <typename Scalar>
+struct functor_traits<scalar_acosh_op<Scalar> > {
+ enum { Cost = 5 * NumTraits<Scalar>::MulCost, PacketAccess = false };
+};
+
+/** \internal
+ * \brief Template functor to compute the inverse of a scalar
+ * \sa class CwiseUnaryOp, Cwise::inverse()
+ */
+template<typename Scalar>
+struct scalar_inverse_op {
+ EIGEN_DEVICE_FUNC inline Scalar operator() (const Scalar& a) const { return Scalar(1)/a; }
+ template<typename Packet>
+ EIGEN_DEVICE_FUNC inline const Packet packetOp(const Packet& a) const
+ { return internal::preciprocal(a); }
+};
+template <typename Scalar>
+struct functor_traits<scalar_inverse_op<Scalar> > {
+ enum {
+ PacketAccess = packet_traits<Scalar>::HasDiv,
+ // If packet_traits<Scalar>::HasReciprocal then the Estimated cost is that
+ // of computing an approximation plus a single Newton-Raphson step, which
+ // consists of 1 pmul + 1 pmadd.
+ Cost = (packet_traits<Scalar>::HasReciprocal
+ ? 4 * NumTraits<Scalar>::MulCost
+ : scalar_div_cost<Scalar, PacketAccess>::value)
+ };
+};
+
+/** \internal
+ * \brief Template functor to compute the square of a scalar
+ * \sa class CwiseUnaryOp, Cwise::square()
+ */
+template<typename Scalar>
+struct scalar_square_op {
+ EIGEN_DEVICE_FUNC inline Scalar operator() (const Scalar& a) const { return a*a; }
+ template<typename Packet>
+ EIGEN_DEVICE_FUNC inline const Packet packetOp(const Packet& a) const
+ { return internal::pmul(a,a); }
+};
+template<typename Scalar>
+struct functor_traits<scalar_square_op<Scalar> >
+{ enum { Cost = NumTraits<Scalar>::MulCost, PacketAccess = packet_traits<Scalar>::HasMul }; };
+
+// Boolean specialization to avoid -Wint-in-bool-context warnings on GCC.
+template<>
+struct scalar_square_op<bool> {
+ EIGEN_DEPRECATED EIGEN_DEVICE_FUNC inline bool operator() (const bool& a) const { return a; }
+ template<typename Packet>
+ EIGEN_DEPRECATED EIGEN_DEVICE_FUNC inline const Packet packetOp(const Packet& a) const
+ { return a; }
+};
+template<>
+struct functor_traits<scalar_square_op<bool> >
+{ enum { Cost = 0, PacketAccess = packet_traits<bool>::Vectorizable }; };
+
+/** \internal
+ * \brief Template functor to compute the cube of a scalar
+ * \sa class CwiseUnaryOp, Cwise::cube()
+ */
+template<typename Scalar>
+struct scalar_cube_op {
+ EIGEN_DEVICE_FUNC inline Scalar operator() (const Scalar& a) const { return a*a*a; }
+ template<typename Packet>
+ EIGEN_DEVICE_FUNC inline const Packet packetOp(const Packet& a) const
+ { return internal::pmul(a,pmul(a,a)); }
+};
+template<typename Scalar>
+struct functor_traits<scalar_cube_op<Scalar> >
+{ enum { Cost = 2*NumTraits<Scalar>::MulCost, PacketAccess = packet_traits<Scalar>::HasMul }; };
+
+// Boolean specialization to avoid -Wint-in-bool-context warnings on GCC.
+template<>
+struct scalar_cube_op<bool> {
+ EIGEN_DEPRECATED EIGEN_DEVICE_FUNC inline bool operator() (const bool& a) const { return a; }
+ template<typename Packet>
+ EIGEN_DEPRECATED EIGEN_DEVICE_FUNC inline const Packet packetOp(const Packet& a) const
+ { return a; }
+};
+template<>
+struct functor_traits<scalar_cube_op<bool> >
+{ enum { Cost = 0, PacketAccess = packet_traits<bool>::Vectorizable }; };
+
+/** \internal
+ * \brief Template functor to compute the rounded value of a scalar
+ * \sa class CwiseUnaryOp, ArrayBase::round()
+ */
+template<typename Scalar> struct scalar_round_op {
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar operator() (const Scalar& a) const { return numext::round(a); }
+ template <typename Packet>
+ EIGEN_DEVICE_FUNC inline Packet packetOp(const Packet& a) const { return internal::pround(a); }
+};
+template<typename Scalar>
+struct functor_traits<scalar_round_op<Scalar> >
+{
+ enum {
+ Cost = NumTraits<Scalar>::MulCost,
+ PacketAccess = packet_traits<Scalar>::HasRound
+ };
+};
+
+/** \internal
+ * \brief Template functor to compute the floor of a scalar
+ * \sa class CwiseUnaryOp, ArrayBase::floor()
+ */
+template<typename Scalar> struct scalar_floor_op {
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar operator() (const Scalar& a) const { return numext::floor(a); }
+ template <typename Packet>
+ EIGEN_DEVICE_FUNC inline Packet packetOp(const Packet& a) const { return internal::pfloor(a); }
+};
+template<typename Scalar>
+struct functor_traits<scalar_floor_op<Scalar> >
+{
+ enum {
+ Cost = NumTraits<Scalar>::MulCost,
+ PacketAccess = packet_traits<Scalar>::HasFloor
+ };
+};
+
+/** \internal
+ * \brief Template functor to compute the rounded (with current rounding mode) value of a scalar
+ * \sa class CwiseUnaryOp, ArrayBase::rint()
+ */
+template<typename Scalar> struct scalar_rint_op {
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar operator() (const Scalar& a) const { return numext::rint(a); }
+ template <typename Packet>
+ EIGEN_DEVICE_FUNC inline Packet packetOp(const Packet& a) const { return internal::print(a); }
+};
+template<typename Scalar>
+struct functor_traits<scalar_rint_op<Scalar> >
+{
+ enum {
+ Cost = NumTraits<Scalar>::MulCost,
+ PacketAccess = packet_traits<Scalar>::HasRint
+ };
+};
+
+/** \internal
+ * \brief Template functor to compute the ceil of a scalar
+ * \sa class CwiseUnaryOp, ArrayBase::ceil()
+ */
+template<typename Scalar> struct scalar_ceil_op {
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar operator() (const Scalar& a) const { return numext::ceil(a); }
+ template <typename Packet>
+ EIGEN_DEVICE_FUNC inline Packet packetOp(const Packet& a) const { return internal::pceil(a); }
+};
+template<typename Scalar>
+struct functor_traits<scalar_ceil_op<Scalar> >
+{
+ enum {
+ Cost = NumTraits<Scalar>::MulCost,
+ PacketAccess = packet_traits<Scalar>::HasCeil
+ };
+};
+
+/** \internal
+ * \brief Template functor to compute whether a scalar is NaN
+ * \sa class CwiseUnaryOp, ArrayBase::isnan()
+ */
+template<typename Scalar> struct scalar_isnan_op {
+ typedef bool result_type;
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE result_type operator() (const Scalar& a) const {
+#if defined(SYCL_DEVICE_ONLY)
+ return numext::isnan(a);
+#else
+ return (numext::isnan)(a);
+#endif
+ }
+};
+template<typename Scalar>
+struct functor_traits<scalar_isnan_op<Scalar> >
+{
+ enum {
+ Cost = NumTraits<Scalar>::MulCost,
+ PacketAccess = false
+ };
+};
+
+/** \internal
+ * \brief Template functor to check whether a scalar is +/-inf
+ * \sa class CwiseUnaryOp, ArrayBase::isinf()
+ */
+template<typename Scalar> struct scalar_isinf_op {
+ typedef bool result_type;
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE result_type operator() (const Scalar& a) const {
+#if defined(SYCL_DEVICE_ONLY)
+ return numext::isinf(a);
+#else
+ return (numext::isinf)(a);
+#endif
+ }
+};
+template<typename Scalar>
+struct functor_traits<scalar_isinf_op<Scalar> >
+{
+ enum {
+ Cost = NumTraits<Scalar>::MulCost,
+ PacketAccess = false
+ };
+};
+
+/** \internal
+ * \brief Template functor to check whether a scalar has a finite value
+ * \sa class CwiseUnaryOp, ArrayBase::isfinite()
+ */
+template<typename Scalar> struct scalar_isfinite_op {
+ typedef bool result_type;
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE result_type operator() (const Scalar& a) const {
+#if defined(SYCL_DEVICE_ONLY)
+ return numext::isfinite(a);
+#else
+ return (numext::isfinite)(a);
+#endif
+ }
+};
+template<typename Scalar>
+struct functor_traits<scalar_isfinite_op<Scalar> >
+{
+ enum {
+ Cost = NumTraits<Scalar>::MulCost,
+ PacketAccess = false
+ };
+};
+
+/** \internal
+ * \brief Template functor to compute the logical not of a boolean
+ *
+ * \sa class CwiseUnaryOp, ArrayBase::operator!
+ */
+template<typename Scalar> struct scalar_boolean_not_op {
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE bool operator() (const bool& a) const { return !a; }
+};
+template<typename Scalar>
+struct functor_traits<scalar_boolean_not_op<Scalar> > {
+ enum {
+ Cost = NumTraits<bool>::AddCost,
+ PacketAccess = false
+ };
+};
+
+/** \internal
+ * \brief Template functor to compute the signum of a scalar
+ * \sa class CwiseUnaryOp, Cwise::sign()
+ */
+template<typename Scalar>
+struct scalar_sign_op {
+ EIGEN_DEVICE_FUNC inline const Scalar operator() (const Scalar& a) const
+ {
+ return numext::sign(a);
+ }
+
+ template <typename Packet>
+ EIGEN_DEVICE_FUNC inline Packet packetOp(const Packet& a) const {
+ return internal::psign(a);
+ }
+};
+
+template<typename Scalar>
+struct functor_traits<scalar_sign_op<Scalar> >
+{ enum {
+ Cost =
+ NumTraits<Scalar>::IsComplex
+ ? ( 8*NumTraits<Scalar>::MulCost ) // roughly
+ : ( 3*NumTraits<Scalar>::AddCost),
+ PacketAccess = packet_traits<Scalar>::HasSign && packet_traits<Scalar>::Vectorizable
+ };
+};
+
+/** \internal
+ * \brief Template functor to compute the logistic function of a scalar
+ * \sa class CwiseUnaryOp, ArrayBase::logistic()
+ */
+template <typename T>
+struct scalar_logistic_op {
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE T operator()(const T& x) const {
+ return packetOp(x);
+ }
+
+ template <typename Packet> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ Packet packetOp(const Packet& x) const {
+ const Packet one = pset1<Packet>(T(1));
+ const Packet inf = pset1<Packet>(NumTraits<T>::infinity());
+ const Packet e = pexp(x);
+ const Packet inf_mask = pcmp_eq(e, inf);
+ return pselect(inf_mask, one, pdiv(e, padd(one, e)));
+ }
+};
+
+// TODO(rmlarsen): Enable the following on host when integer_packet is defined
+// for the relevant packet types.
+#ifdef EIGEN_GPU_CC
+
+/** \internal
+ * \brief Template specialization of the logistic function for float.
+ * Computes S(x) = exp(x) / (1 + exp(x)), where exp(x) is implemented
+ * using an algorithm partly adopted from the implementation of
+ * pexp_float. See the individual steps described in the code below.
+ * Note that compared to pexp, we use an additional outer multiplicative
+ * range reduction step using the identity exp(x) = exp(x/2)^2.
+ * This prevert us from having to call ldexp on values that could produce
+ * a denormal result, which allows us to call the faster implementation in
+ * pldexp_fast_impl<Packet>::run(p, m).
+ * The final squaring, however, doubles the error bound on the final
+ * approximation. Exhaustive testing shows that we have a worst case error
+ * of 4.5 ulps (compared to computing S(x) in double precision), which is
+ * acceptable.
+ */
+template <>
+struct scalar_logistic_op<float> {
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE float operator()(const float& x) const {
+ // Truncate at the first point where the interpolant is exactly one.
+ const float cst_exp_hi = 16.6355324f;
+ const float e = numext::exp(numext::mini(x, cst_exp_hi));
+ return e / (1.0f + e);
+ }
+
+ template <typename Packet>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet
+ packetOp(const Packet& _x) const {
+ const Packet cst_zero = pset1<Packet>(0.0f);
+ const Packet cst_one = pset1<Packet>(1.0f);
+ const Packet cst_half = pset1<Packet>(0.5f);
+ // Truncate at the first point where the interpolant is exactly one.
+ const Packet cst_exp_hi = pset1<Packet>(16.6355324f);
+ const Packet cst_exp_lo = pset1<Packet>(-104.f);
+
+ // Clamp x to the non-trivial range where S(x). Outside this
+ // interval the correctly rounded value of S(x) is either zero
+ // or one.
+ Packet zero_mask = pcmp_lt(_x, cst_exp_lo);
+ Packet x = pmin(_x, cst_exp_hi);
+
+ // 1. Multiplicative range reduction:
+ // Reduce the range of x by a factor of 2. This avoids having
+ // to compute exp(x) accurately where the result is a denormalized
+ // value.
+ x = pmul(x, cst_half);
+
+ // 2. Subtractive range reduction:
+ // Express exp(x) as exp(m*ln(2) + r) = 2^m*exp(r), start by extracting
+ // m = floor(x/ln(2) + 0.5), such that x = m*ln(2) + r.
+ const Packet cst_cephes_LOG2EF = pset1<Packet>(1.44269504088896341f);
+ Packet m = pfloor(pmadd(x, cst_cephes_LOG2EF, cst_half));
+ // Get r = x - m*ln(2). We use a trick from Cephes where the term
+ // m*ln(2) is subtracted out in two parts, m*C1+m*C2 = m*ln(2),
+ // to avoid accumulating truncation errors.
+ const Packet cst_cephes_exp_C1 = pset1<Packet>(-0.693359375f);
+ const Packet cst_cephes_exp_C2 = pset1<Packet>(2.12194440e-4f);
+ Packet r = pmadd(m, cst_cephes_exp_C1, x);
+ r = pmadd(m, cst_cephes_exp_C2, r);
+
+ // 3. Compute an approximation to exp(r) using a degree 5 minimax polynomial.
+ // We compute even and odd terms separately to increase instruction level
+ // parallelism.
+ Packet r2 = pmul(r, r);
+ const Packet cst_p2 = pset1<Packet>(0.49999141693115234375f);
+ const Packet cst_p3 = pset1<Packet>(0.16666877269744873046875f);
+ const Packet cst_p4 = pset1<Packet>(4.1898667812347412109375e-2f);
+ const Packet cst_p5 = pset1<Packet>(8.33471305668354034423828125e-3f);
+
+ const Packet p_even = pmadd(r2, cst_p4, cst_p2);
+ const Packet p_odd = pmadd(r2, cst_p5, cst_p3);
+ const Packet p_low = padd(r, cst_one);
+ Packet p = pmadd(r, p_odd, p_even);
+ p = pmadd(r2, p, p_low);
+
+ // 4. Undo subtractive range reduction exp(m*ln(2) + r) = 2^m * exp(r).
+ Packet e = pldexp_fast_impl<Packet>::run(p, m);
+
+ // 5. Undo multiplicative range reduction by using exp(r) = exp(r/2)^2.
+ e = pmul(e, e);
+
+ // Return exp(x) / (1 + exp(x))
+ return pselect(zero_mask, cst_zero, pdiv(e, padd(cst_one, e)));
+ }
+};
+#endif // #ifndef EIGEN_GPU_COMPILE_PHASE
+
+
+template <typename T>
+struct functor_traits<scalar_logistic_op<T> > {
+ enum {
+ // The cost estimate for float here here is for the common(?) case where
+ // all arguments are greater than -9.
+ Cost = scalar_div_cost<T, packet_traits<T>::HasDiv>::value +
+ (internal::is_same<T, float>::value
+ ? NumTraits<T>::AddCost * 15 + NumTraits<T>::MulCost * 11
+ : NumTraits<T>::AddCost * 2 +
+ functor_traits<scalar_exp_op<T> >::Cost),
+ PacketAccess =
+ packet_traits<T>::HasAdd && packet_traits<T>::HasDiv &&
+ (internal::is_same<T, float>::value
+ ? packet_traits<T>::HasMul && packet_traits<T>::HasMax &&
+ packet_traits<T>::HasMin
+ : packet_traits<T>::HasNegate && packet_traits<T>::HasExp)
+ };
+};
+
+template <typename Scalar, typename ExponentScalar,
+ bool IsBaseInteger = NumTraits<Scalar>::IsInteger,
+ bool IsExponentInteger = NumTraits<ExponentScalar>::IsInteger,
+ bool IsBaseComplex = NumTraits<Scalar>::IsComplex,
+ bool IsExponentComplex = NumTraits<ExponentScalar>::IsComplex>
+struct scalar_unary_pow_op {
+ typedef typename internal::promote_scalar_arg<
+ Scalar, ExponentScalar,
+ internal::has_ReturnType<ScalarBinaryOpTraits<Scalar,ExponentScalar,scalar_unary_pow_op> >::value>::type PromotedExponent;
+ typedef typename ScalarBinaryOpTraits<Scalar, PromotedExponent, scalar_unary_pow_op>::ReturnType result_type;
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE scalar_unary_pow_op(const ExponentScalar& exponent) : m_exponent(exponent) {}
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE result_type operator()(const Scalar& a) const {
+ EIGEN_USING_STD(pow);
+ return static_cast<result_type>(pow(a, m_exponent));
+ }
+
+ private:
+ const ExponentScalar m_exponent;
+ scalar_unary_pow_op() {}
+};
+
+template <typename T>
+constexpr int exponent_digits() {
+ return CHAR_BIT * sizeof(T) - NumTraits<T>::digits() - NumTraits<T>::IsSigned;
+}
+
+template<typename From, typename To>
+struct is_floating_exactly_representable {
+ // TODO(rmlarsen): Add radix to NumTraits and enable this check.
+ // (NumTraits<To>::radix == NumTraits<From>::radix) &&
+ static constexpr bool value = (exponent_digits<To>() >= exponent_digits<From>() &&
+ NumTraits<To>::digits() >= NumTraits<From>::digits());
+};
+
+
+// Specialization for real, non-integer types, non-complex types.
+template <typename Scalar, typename ExponentScalar>
+struct scalar_unary_pow_op<Scalar, ExponentScalar, false, false, false, false> {
+ template <bool IsExactlyRepresentable = is_floating_exactly_representable<ExponentScalar, Scalar>::value>
+ std::enable_if_t<IsExactlyRepresentable, void> check_is_representable() const {}
+
+ // Issue a deprecation warning if we do a narrowing conversion on the exponent.
+ template <bool IsExactlyRepresentable = is_floating_exactly_representable<ExponentScalar, Scalar>::value>
+ EIGEN_DEPRECATED std::enable_if_t<!IsExactlyRepresentable, void> check_is_representable() const {}
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ scalar_unary_pow_op(const ExponentScalar& exponent) : m_exponent(static_cast<Scalar>(exponent)) {
+ check_is_representable();
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar operator()(const Scalar& a) const {
+ EIGEN_USING_STD(pow);
+ return static_cast<Scalar>(pow(a, m_exponent));
+ }
+ template <typename Packet>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet packetOp(const Packet& a) const {
+ return unary_pow_impl<Packet, Scalar>::run(a, m_exponent);
+ }
+
+ private:
+ const Scalar m_exponent;
+ scalar_unary_pow_op() {}
+};
+
+template <typename Scalar, typename ExponentScalar, bool BaseIsInteger>
+struct scalar_unary_pow_op<Scalar, ExponentScalar, BaseIsInteger, true, false, false> {
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE scalar_unary_pow_op(const ExponentScalar& exponent) : m_exponent(exponent) {}
+ // TODO: error handling logic for complex^real_integer
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar operator()(const Scalar& a) const {
+ return unary_pow_impl<Scalar, ExponentScalar>::run(a, m_exponent);
+ }
+ template <typename Packet>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet packetOp(const Packet& a) const {
+ return unary_pow_impl<Packet, ExponentScalar>::run(a, m_exponent);
+ }
+
+ private:
+ const ExponentScalar m_exponent;
+ scalar_unary_pow_op() {}
+};
+
+template <typename Scalar, typename ExponentScalar>
+struct functor_traits<scalar_unary_pow_op<Scalar, ExponentScalar>> {
+ enum {
+ GenPacketAccess = functor_traits<scalar_pow_op<Scalar, ExponentScalar>>::PacketAccess,
+ IntPacketAccess = !NumTraits<Scalar>::IsComplex && packet_traits<Scalar>::HasMul && (packet_traits<Scalar>::HasDiv || NumTraits<Scalar>::IsInteger) && packet_traits<Scalar>::HasCmp,
+ PacketAccess = NumTraits<ExponentScalar>::IsInteger ? IntPacketAccess : (IntPacketAccess && GenPacketAccess),
+ Cost = functor_traits<scalar_pow_op<Scalar, ExponentScalar>>::Cost
+ };
+};
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_FUNCTORS_H
diff --git a/Eigen/src/Core/products/GeneralBlockPanelKernel.h b/Eigen/src/Core/products/GeneralBlockPanelKernel.h
new file mode 100644
index 0000000..179d41c
--- /dev/null
+++ b/Eigen/src/Core/products/GeneralBlockPanelKernel.h
@@ -0,0 +1,3288 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_GENERAL_BLOCK_PANEL_H
+#define EIGEN_GENERAL_BLOCK_PANEL_H
+
+
+#include "../InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+
+enum GEBPPacketSizeType {
+ GEBPPacketFull = 0,
+ GEBPPacketHalf,
+ GEBPPacketQuarter
+};
+
+template<typename LhsScalar_, typename RhsScalar_, bool ConjLhs_=false, bool ConjRhs_=false, int Arch=Architecture::Target, int PacketSize_=GEBPPacketFull>
+class gebp_traits;
+
+
+/** \internal \returns b if a<=0, and returns a otherwise. */
+inline std::ptrdiff_t manage_caching_sizes_helper(std::ptrdiff_t a, std::ptrdiff_t b)
+{
+ return a<=0 ? b : a;
+}
+
+#if defined(EIGEN_DEFAULT_L1_CACHE_SIZE)
+#define EIGEN_SET_DEFAULT_L1_CACHE_SIZE(val) EIGEN_DEFAULT_L1_CACHE_SIZE
+#else
+#define EIGEN_SET_DEFAULT_L1_CACHE_SIZE(val) val
+#endif // defined(EIGEN_DEFAULT_L1_CACHE_SIZE)
+
+#if defined(EIGEN_DEFAULT_L2_CACHE_SIZE)
+#define EIGEN_SET_DEFAULT_L2_CACHE_SIZE(val) EIGEN_DEFAULT_L2_CACHE_SIZE
+#else
+#define EIGEN_SET_DEFAULT_L2_CACHE_SIZE(val) val
+#endif // defined(EIGEN_DEFAULT_L2_CACHE_SIZE)
+
+#if defined(EIGEN_DEFAULT_L3_CACHE_SIZE)
+#define EIGEN_SET_DEFAULT_L3_CACHE_SIZE(val) EIGEN_DEFAULT_L3_CACHE_SIZE
+#else
+#define EIGEN_SET_DEFAULT_L3_CACHE_SIZE(val) val
+#endif // defined(EIGEN_DEFAULT_L3_CACHE_SIZE)
+
+#if EIGEN_ARCH_i386_OR_x86_64
+const std::ptrdiff_t defaultL1CacheSize = EIGEN_SET_DEFAULT_L1_CACHE_SIZE(32*1024);
+const std::ptrdiff_t defaultL2CacheSize = EIGEN_SET_DEFAULT_L2_CACHE_SIZE(256*1024);
+const std::ptrdiff_t defaultL3CacheSize = EIGEN_SET_DEFAULT_L3_CACHE_SIZE(2*1024*1024);
+#elif EIGEN_ARCH_PPC
+const std::ptrdiff_t defaultL1CacheSize = EIGEN_SET_DEFAULT_L1_CACHE_SIZE(64*1024);
+const std::ptrdiff_t defaultL2CacheSize = EIGEN_SET_DEFAULT_L2_CACHE_SIZE(512*1024);
+const std::ptrdiff_t defaultL3CacheSize = EIGEN_SET_DEFAULT_L3_CACHE_SIZE(4*1024*1024);
+#else
+const std::ptrdiff_t defaultL1CacheSize = EIGEN_SET_DEFAULT_L1_CACHE_SIZE(16*1024);
+const std::ptrdiff_t defaultL2CacheSize = EIGEN_SET_DEFAULT_L2_CACHE_SIZE(512*1024);
+const std::ptrdiff_t defaultL3CacheSize = EIGEN_SET_DEFAULT_L3_CACHE_SIZE(512*1024);
+#endif
+
+#undef EIGEN_SET_DEFAULT_L1_CACHE_SIZE
+#undef EIGEN_SET_DEFAULT_L2_CACHE_SIZE
+#undef EIGEN_SET_DEFAULT_L3_CACHE_SIZE
+
+/** \internal */
+struct CacheSizes {
+ CacheSizes(): m_l1(-1),m_l2(-1),m_l3(-1) {
+ int l1CacheSize, l2CacheSize, l3CacheSize;
+ queryCacheSizes(l1CacheSize, l2CacheSize, l3CacheSize);
+ m_l1 = manage_caching_sizes_helper(l1CacheSize, defaultL1CacheSize);
+ m_l2 = manage_caching_sizes_helper(l2CacheSize, defaultL2CacheSize);
+ m_l3 = manage_caching_sizes_helper(l3CacheSize, defaultL3CacheSize);
+ }
+
+ std::ptrdiff_t m_l1;
+ std::ptrdiff_t m_l2;
+ std::ptrdiff_t m_l3;
+};
+
+/** \internal */
+inline void manage_caching_sizes(Action action, std::ptrdiff_t* l1, std::ptrdiff_t* l2, std::ptrdiff_t* l3)
+{
+ static CacheSizes m_cacheSizes;
+
+ if(action==SetAction)
+ {
+ // set the cpu cache size and cache all block sizes from a global cache size in byte
+ eigen_internal_assert(l1!=0 && l2!=0);
+ m_cacheSizes.m_l1 = *l1;
+ m_cacheSizes.m_l2 = *l2;
+ m_cacheSizes.m_l3 = *l3;
+ }
+ else if(action==GetAction)
+ {
+ eigen_internal_assert(l1!=0 && l2!=0);
+ *l1 = m_cacheSizes.m_l1;
+ *l2 = m_cacheSizes.m_l2;
+ *l3 = m_cacheSizes.m_l3;
+ }
+ else
+ {
+ eigen_internal_assert(false);
+ }
+}
+
+/* Helper for computeProductBlockingSizes.
+ *
+ * Given a m x k times k x n matrix product of scalar types \c LhsScalar and \c RhsScalar,
+ * this function computes the blocking size parameters along the respective dimensions
+ * for matrix products and related algorithms. The blocking sizes depends on various
+ * parameters:
+ * - the L1 and L2 cache sizes,
+ * - the register level blocking sizes defined by gebp_traits,
+ * - the number of scalars that fit into a packet (when vectorization is enabled).
+ *
+ * \sa setCpuCacheSizes */
+
+template<typename LhsScalar, typename RhsScalar, int KcFactor, typename Index>
+void evaluateProductBlockingSizesHeuristic(Index& k, Index& m, Index& n, Index num_threads = 1)
+{
+ typedef gebp_traits<LhsScalar,RhsScalar> Traits;
+
+ // Explanations:
+ // Let's recall that the product algorithms form mc x kc vertical panels A' on the lhs and
+ // kc x nc blocks B' on the rhs. B' has to fit into L2/L3 cache. Moreover, A' is processed
+ // per mr x kc horizontal small panels where mr is the blocking size along the m dimension
+ // at the register level. This small horizontal panel has to stay within L1 cache.
+ std::ptrdiff_t l1, l2, l3;
+ manage_caching_sizes(GetAction, &l1, &l2, &l3);
+ #ifdef EIGEN_VECTORIZE_AVX512
+ // We need to find a rationale for that, but without this adjustment,
+ // performance with AVX512 is pretty bad, like -20% slower.
+ // One reason is that with increasing packet-size, the blocking size k
+ // has to become pretty small if we want that 1 lhs panel fit within L1.
+ // For instance, with the 3pX4 kernel and double, the size of the lhs+rhs panels are:
+ // k*(3*64 + 4*8) Bytes, with l1=32kBytes, and k%8=0, we have k=144.
+ // This is quite small for a good reuse of the accumulation registers.
+ l1 *= 4;
+ #endif
+
+ if (num_threads > 1) {
+ typedef typename Traits::ResScalar ResScalar;
+ enum {
+ kdiv = KcFactor * (Traits::mr * sizeof(LhsScalar) + Traits::nr * sizeof(RhsScalar)),
+ ksub = Traits::mr * Traits::nr * sizeof(ResScalar),
+ kr = 8,
+ mr = Traits::mr,
+ nr = Traits::nr
+ };
+ // Increasing k gives us more time to prefetch the content of the "C"
+ // registers. However once the latency is hidden there is no point in
+ // increasing the value of k, so we'll cap it at 320 (value determined
+ // experimentally).
+ // To avoid that k vanishes, we make k_cache at least as big as kr
+ const Index k_cache = numext::maxi<Index>(kr, (numext::mini<Index>)((l1-ksub)/kdiv, 320));
+ if (k_cache < k) {
+ k = k_cache - (k_cache % kr);
+ eigen_internal_assert(k > 0);
+ }
+
+ const Index n_cache = (l2-l1) / (nr * sizeof(RhsScalar) * k);
+ const Index n_per_thread = numext::div_ceil(n, num_threads);
+ if (n_cache <= n_per_thread) {
+ // Don't exceed the capacity of the l2 cache.
+ eigen_internal_assert(n_cache >= static_cast<Index>(nr));
+ n = n_cache - (n_cache % nr);
+ eigen_internal_assert(n > 0);
+ } else {
+ n = (numext::mini<Index>)(n, (n_per_thread + nr - 1) - ((n_per_thread + nr - 1) % nr));
+ }
+
+ if (l3 > l2) {
+ // l3 is shared between all cores, so we'll give each thread its own chunk of l3.
+ const Index m_cache = (l3-l2) / (sizeof(LhsScalar) * k * num_threads);
+ const Index m_per_thread = numext::div_ceil(m, num_threads);
+ if(m_cache < m_per_thread && m_cache >= static_cast<Index>(mr)) {
+ m = m_cache - (m_cache % mr);
+ eigen_internal_assert(m > 0);
+ } else {
+ m = (numext::mini<Index>)(m, (m_per_thread + mr - 1) - ((m_per_thread + mr - 1) % mr));
+ }
+ }
+ }
+ else {
+ // In unit tests we do not want to use extra large matrices,
+ // so we reduce the cache size to check the blocking strategy is not flawed
+#ifdef EIGEN_DEBUG_SMALL_PRODUCT_BLOCKS
+ l1 = 9*1024;
+ l2 = 32*1024;
+ l3 = 512*1024;
+#endif
+
+ // Early return for small problems because the computation below are time consuming for small problems.
+ // Perhaps it would make more sense to consider k*n*m??
+ // Note that for very tiny problem, this function should be bypassed anyway
+ // because we use the coefficient-based implementation for them.
+ if((numext::maxi)(k,(numext::maxi)(m,n))<48)
+ return;
+
+ typedef typename Traits::ResScalar ResScalar;
+ enum {
+ k_peeling = 8,
+ k_div = KcFactor * (Traits::mr * sizeof(LhsScalar) + Traits::nr * sizeof(RhsScalar)),
+ k_sub = Traits::mr * Traits::nr * sizeof(ResScalar)
+ };
+
+ // ---- 1st level of blocking on L1, yields kc ----
+
+ // Blocking on the third dimension (i.e., k) is chosen so that an horizontal panel
+ // of size mr x kc of the lhs plus a vertical panel of kc x nr of the rhs both fits within L1 cache.
+ // We also include a register-level block of the result (mx x nr).
+ // (In an ideal world only the lhs panel would stay in L1)
+ // Moreover, kc has to be a multiple of 8 to be compatible with loop peeling, leading to a maximum blocking size of:
+ const Index max_kc = numext::maxi<Index>(((l1-k_sub)/k_div) & (~(k_peeling-1)),1);
+ const Index old_k = k;
+ if(k>max_kc)
+ {
+ // We are really blocking on the third dimension:
+ // -> reduce blocking size to make sure the last block is as large as possible
+ // while keeping the same number of sweeps over the result.
+ k = (k%max_kc)==0 ? max_kc
+ : max_kc - k_peeling * ((max_kc-1-(k%max_kc))/(k_peeling*(k/max_kc+1)));
+
+ eigen_internal_assert(((old_k/k) == (old_k/max_kc)) && "the number of sweeps has to remain the same");
+ }
+
+ // ---- 2nd level of blocking on max(L2,L3), yields nc ----
+
+ // TODO find a reliable way to get the actual amount of cache per core to use for 2nd level blocking, that is:
+ // actual_l2 = max(l2, l3/nb_core_sharing_l3)
+ // The number below is quite conservative: it is better to underestimate the cache size rather than overestimating it)
+ // For instance, it corresponds to 6MB of L3 shared among 4 cores.
+ #ifdef EIGEN_DEBUG_SMALL_PRODUCT_BLOCKS
+ const Index actual_l2 = l3;
+ #else
+ const Index actual_l2 = 1572864; // == 1.5 MB
+ #endif
+
+ // Here, nc is chosen such that a block of kc x nc of the rhs fit within half of L2.
+ // The second half is implicitly reserved to access the result and lhs coefficients.
+ // When k<max_kc, then nc can arbitrarily growth. In practice, it seems to be fruitful
+ // to limit this growth: we bound nc to growth by a factor x1.5.
+ // However, if the entire lhs block fit within L1, then we are not going to block on the rows at all,
+ // and it becomes fruitful to keep the packed rhs blocks in L1 if there is enough remaining space.
+ Index max_nc;
+ const Index lhs_bytes = m * k * sizeof(LhsScalar);
+ const Index remaining_l1 = l1- k_sub - lhs_bytes;
+ if(remaining_l1 >= Index(Traits::nr*sizeof(RhsScalar))*k)
+ {
+ // L1 blocking
+ max_nc = remaining_l1 / (k*sizeof(RhsScalar));
+ }
+ else
+ {
+ // L2 blocking
+ max_nc = (3*actual_l2)/(2*2*max_kc*sizeof(RhsScalar));
+ }
+ // WARNING Below, we assume that Traits::nr is a power of two.
+ Index nc = numext::mini<Index>(actual_l2/(2*k*sizeof(RhsScalar)), max_nc) & (~(Traits::nr-1));
+ if(n>nc)
+ {
+ // We are really blocking over the columns:
+ // -> reduce blocking size to make sure the last block is as large as possible
+ // while keeping the same number of sweeps over the packed lhs.
+ // Here we allow one more sweep if this gives us a perfect match, thus the commented "-1"
+ n = (n%nc)==0 ? nc
+ : (nc - Traits::nr * ((nc/*-1*/-(n%nc))/(Traits::nr*(n/nc+1))));
+ }
+ else if(old_k==k)
+ {
+ // So far, no blocking at all, i.e., kc==k, and nc==n.
+ // In this case, let's perform a blocking over the rows such that the packed lhs data is kept in cache L1/L2
+ // TODO: part of this blocking strategy is now implemented within the kernel itself, so the L1-based heuristic here should be obsolete.
+ Index problem_size = k*n*sizeof(LhsScalar);
+ Index actual_lm = actual_l2;
+ Index max_mc = m;
+ if(problem_size<=1024)
+ {
+ // problem is small enough to keep in L1
+ // Let's choose m such that lhs's block fit in 1/3 of L1
+ actual_lm = l1;
+ }
+ else if(l3!=0 && problem_size<=32768)
+ {
+ // we have both L2 and L3, and problem is small enough to be kept in L2
+ // Let's choose m such that lhs's block fit in 1/3 of L2
+ actual_lm = l2;
+ max_mc = (numext::mini<Index>)(576,max_mc);
+ }
+ Index mc = (numext::mini<Index>)(actual_lm/(3*k*sizeof(LhsScalar)), max_mc);
+ if (mc > Traits::mr) mc -= mc % Traits::mr;
+ else if (mc==0) return;
+ m = (m%mc)==0 ? mc
+ : (mc - Traits::mr * ((mc/*-1*/-(m%mc))/(Traits::mr*(m/mc+1))));
+ }
+ }
+}
+
+template <typename Index>
+inline bool useSpecificBlockingSizes(Index& k, Index& m, Index& n)
+{
+#ifdef EIGEN_TEST_SPECIFIC_BLOCKING_SIZES
+ if (EIGEN_TEST_SPECIFIC_BLOCKING_SIZES) {
+ k = numext::mini<Index>(k, EIGEN_TEST_SPECIFIC_BLOCKING_SIZE_K);
+ m = numext::mini<Index>(m, EIGEN_TEST_SPECIFIC_BLOCKING_SIZE_M);
+ n = numext::mini<Index>(n, EIGEN_TEST_SPECIFIC_BLOCKING_SIZE_N);
+ return true;
+ }
+#else
+ EIGEN_UNUSED_VARIABLE(k)
+ EIGEN_UNUSED_VARIABLE(m)
+ EIGEN_UNUSED_VARIABLE(n)
+#endif
+ return false;
+}
+
+/** \brief Computes the blocking parameters for a m x k times k x n matrix product
+ *
+ * \param[in,out] k Input: the third dimension of the product. Output: the blocking size along the same dimension.
+ * \param[in,out] m Input: the number of rows of the left hand side. Output: the blocking size along the same dimension.
+ * \param[in,out] n Input: the number of columns of the right hand side. Output: the blocking size along the same dimension.
+ *
+ * Given a m x k times k x n matrix product of scalar types \c LhsScalar and \c RhsScalar,
+ * this function computes the blocking size parameters along the respective dimensions
+ * for matrix products and related algorithms.
+ *
+ * The blocking size parameters may be evaluated:
+ * - either by a heuristic based on cache sizes;
+ * - or using fixed prescribed values (for testing purposes).
+ *
+ * \sa setCpuCacheSizes */
+
+template<typename LhsScalar, typename RhsScalar, int KcFactor, typename Index>
+void computeProductBlockingSizes(Index& k, Index& m, Index& n, Index num_threads = 1)
+{
+ if (!useSpecificBlockingSizes(k, m, n)) {
+ evaluateProductBlockingSizesHeuristic<LhsScalar, RhsScalar, KcFactor, Index>(k, m, n, num_threads);
+ }
+}
+
+template<typename LhsScalar, typename RhsScalar, typename Index>
+inline void computeProductBlockingSizes(Index& k, Index& m, Index& n, Index num_threads = 1)
+{
+ computeProductBlockingSizes<LhsScalar,RhsScalar,1,Index>(k, m, n, num_threads);
+}
+
+template <typename RhsPacket, typename RhsPacketx4, int registers_taken>
+struct RhsPanelHelper {
+ private:
+ static constexpr int remaining_registers = (std::max)(int(EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS) - registers_taken, 0);
+ public:
+ typedef std::conditional_t<remaining_registers>=4, RhsPacketx4, RhsPacket> type;
+};
+
+template <typename Packet>
+struct QuadPacket
+{
+ Packet B_0, B1, B2, B3;
+ const Packet& get(const FixedInt<0>&) const { return B_0; }
+ const Packet& get(const FixedInt<1>&) const { return B1; }
+ const Packet& get(const FixedInt<2>&) const { return B2; }
+ const Packet& get(const FixedInt<3>&) const { return B3; }
+};
+
+template <int N, typename T1, typename T2, typename T3>
+struct packet_conditional { typedef T3 type; };
+
+template <typename T1, typename T2, typename T3>
+struct packet_conditional<GEBPPacketFull, T1, T2, T3> { typedef T1 type; };
+
+template <typename T1, typename T2, typename T3>
+struct packet_conditional<GEBPPacketHalf, T1, T2, T3> { typedef T2 type; };
+
+#define PACKET_DECL_COND_POSTFIX(postfix, name, packet_size) \
+ typedef typename packet_conditional<packet_size, \
+ typename packet_traits<name ## Scalar>::type, \
+ typename packet_traits<name ## Scalar>::half, \
+ typename unpacket_traits<typename packet_traits<name ## Scalar>::half>::half>::type \
+ name ## Packet ## postfix
+
+#define PACKET_DECL_COND(name, packet_size) \
+ typedef typename packet_conditional<packet_size, \
+ typename packet_traits<name ## Scalar>::type, \
+ typename packet_traits<name ## Scalar>::half, \
+ typename unpacket_traits<typename packet_traits<name ## Scalar>::half>::half>::type \
+ name ## Packet
+
+#define PACKET_DECL_COND_SCALAR_POSTFIX(postfix, packet_size) \
+ typedef typename packet_conditional<packet_size, \
+ typename packet_traits<Scalar>::type, \
+ typename packet_traits<Scalar>::half, \
+ typename unpacket_traits<typename packet_traits<Scalar>::half>::half>::type \
+ ScalarPacket ## postfix
+
+#define PACKET_DECL_COND_SCALAR(packet_size) \
+ typedef typename packet_conditional<packet_size, \
+ typename packet_traits<Scalar>::type, \
+ typename packet_traits<Scalar>::half, \
+ typename unpacket_traits<typename packet_traits<Scalar>::half>::half>::type \
+ ScalarPacket
+
+/* Vectorization logic
+ * real*real: unpack rhs to constant packets, ...
+ *
+ * cd*cd : unpack rhs to (b_r,b_r), (b_i,b_i), mul to get (a_r b_r,a_i b_r) (a_r b_i,a_i b_i),
+ * storing each res packet into two packets (2x2),
+ * at the end combine them: swap the second and addsub them
+ * cf*cf : same but with 2x4 blocks
+ * cplx*real : unpack rhs to constant packets, ...
+ * real*cplx : load lhs as (a0,a0,a1,a1), and mul as usual
+ */
+template<typename LhsScalar_, typename RhsScalar_, bool ConjLhs_, bool ConjRhs_, int Arch, int PacketSize_>
+class gebp_traits
+{
+public:
+ typedef LhsScalar_ LhsScalar;
+ typedef RhsScalar_ RhsScalar;
+ typedef typename ScalarBinaryOpTraits<LhsScalar, RhsScalar>::ReturnType ResScalar;
+
+ PACKET_DECL_COND_POSTFIX(_, Lhs, PacketSize_);
+ PACKET_DECL_COND_POSTFIX(_, Rhs, PacketSize_);
+ PACKET_DECL_COND_POSTFIX(_, Res, PacketSize_);
+
+ enum {
+ ConjLhs = ConjLhs_,
+ ConjRhs = ConjRhs_,
+ Vectorizable = unpacket_traits<LhsPacket_>::vectorizable && unpacket_traits<RhsPacket_>::vectorizable,
+ LhsPacketSize = Vectorizable ? unpacket_traits<LhsPacket_>::size : 1,
+ RhsPacketSize = Vectorizable ? unpacket_traits<RhsPacket_>::size : 1,
+ ResPacketSize = Vectorizable ? unpacket_traits<ResPacket_>::size : 1,
+
+ NumberOfRegisters = EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS,
+
+ // register block size along the N direction must be 1 or 4
+ nr = 4,
+
+ // register block size along the M direction (currently, this one cannot be modified)
+ default_mr = (plain_enum_min(16, NumberOfRegisters)/2/nr)*LhsPacketSize,
+#if defined(EIGEN_HAS_SINGLE_INSTRUCTION_MADD) && !defined(EIGEN_VECTORIZE_ALTIVEC) && !defined(EIGEN_VECTORIZE_VSX) \
+ && ((!EIGEN_COMP_MSVC) || (EIGEN_COMP_MSVC>=1914))
+ // we assume 16 registers or more
+ // See bug 992, if the scalar type is not vectorizable but that EIGEN_HAS_SINGLE_INSTRUCTION_MADD is defined,
+ // then using 3*LhsPacketSize triggers non-implemented paths in syrk.
+ // Bug 1515: MSVC prior to v19.14 yields to register spilling.
+ mr = Vectorizable ? 3*LhsPacketSize : default_mr,
+#else
+ mr = default_mr,
+#endif
+
+ LhsProgress = LhsPacketSize,
+ RhsProgress = 1
+ };
+
+
+ typedef std::conditional_t<Vectorizable,LhsPacket_,LhsScalar> LhsPacket;
+ typedef std::conditional_t<Vectorizable,RhsPacket_,RhsScalar> RhsPacket;
+ typedef std::conditional_t<Vectorizable,ResPacket_,ResScalar> ResPacket;
+ typedef LhsPacket LhsPacket4Packing;
+
+ typedef QuadPacket<RhsPacket> RhsPacketx4;
+ typedef ResPacket AccPacket;
+
+ EIGEN_STRONG_INLINE void initAcc(AccPacket& p)
+ {
+ p = pset1<ResPacket>(ResScalar(0));
+ }
+
+ template<typename RhsPacketType>
+ EIGEN_STRONG_INLINE void loadRhs(const RhsScalar* b, RhsPacketType& dest) const
+ {
+ dest = pset1<RhsPacketType>(*b);
+ }
+
+ EIGEN_STRONG_INLINE void loadRhs(const RhsScalar* b, RhsPacketx4& dest) const
+ {
+ pbroadcast4(b, dest.B_0, dest.B1, dest.B2, dest.B3);
+ }
+
+ template<typename RhsPacketType>
+ EIGEN_STRONG_INLINE void updateRhs(const RhsScalar* b, RhsPacketType& dest) const
+ {
+ loadRhs(b, dest);
+ }
+
+ EIGEN_STRONG_INLINE void updateRhs(const RhsScalar*, RhsPacketx4&) const
+ {
+ }
+
+ EIGEN_STRONG_INLINE void loadRhsQuad(const RhsScalar* b, RhsPacket& dest) const
+ {
+ dest = ploadquad<RhsPacket>(b);
+ }
+
+ template<typename LhsPacketType>
+ EIGEN_STRONG_INLINE void loadLhs(const LhsScalar* a, LhsPacketType& dest) const
+ {
+ dest = pload<LhsPacketType>(a);
+ }
+
+ template<typename LhsPacketType>
+ EIGEN_STRONG_INLINE void loadLhsUnaligned(const LhsScalar* a, LhsPacketType& dest) const
+ {
+ dest = ploadu<LhsPacketType>(a);
+ }
+
+ template<typename LhsPacketType, typename RhsPacketType, typename AccPacketType, typename LaneIdType>
+ EIGEN_STRONG_INLINE void madd(const LhsPacketType& a, const RhsPacketType& b, AccPacketType& c, RhsPacketType& tmp, const LaneIdType&) const
+ {
+ conj_helper<LhsPacketType,RhsPacketType,ConjLhs,ConjRhs> cj;
+ // It would be a lot cleaner to call pmadd all the time. Unfortunately if we
+ // let gcc allocate the register in which to store the result of the pmul
+ // (in the case where there is no FMA) gcc fails to figure out how to avoid
+ // spilling register.
+#ifdef EIGEN_HAS_SINGLE_INSTRUCTION_MADD
+ EIGEN_UNUSED_VARIABLE(tmp);
+ c = cj.pmadd(a,b,c);
+#else
+ tmp = b; tmp = cj.pmul(a,tmp); c = padd(c,tmp);
+#endif
+ }
+
+ template<typename LhsPacketType, typename AccPacketType, typename LaneIdType>
+ EIGEN_STRONG_INLINE void madd(const LhsPacketType& a, const RhsPacketx4& b, AccPacketType& c, RhsPacket& tmp, const LaneIdType& lane) const
+ {
+ madd(a, b.get(lane), c, tmp, lane);
+ }
+
+ EIGEN_STRONG_INLINE void acc(const AccPacket& c, const ResPacket& alpha, ResPacket& r) const
+ {
+ r = pmadd(c,alpha,r);
+ }
+
+ template<typename ResPacketHalf>
+ EIGEN_STRONG_INLINE void acc(const ResPacketHalf& c, const ResPacketHalf& alpha, ResPacketHalf& r) const
+ {
+ r = pmadd(c,alpha,r);
+ }
+
+};
+
+template<typename RealScalar, bool ConjLhs_, int Arch, int PacketSize_>
+class gebp_traits<std::complex<RealScalar>, RealScalar, ConjLhs_, false, Arch, PacketSize_>
+{
+public:
+ typedef std::complex<RealScalar> LhsScalar;
+ typedef RealScalar RhsScalar;
+ typedef typename ScalarBinaryOpTraits<LhsScalar, RhsScalar>::ReturnType ResScalar;
+
+ PACKET_DECL_COND_POSTFIX(_, Lhs, PacketSize_);
+ PACKET_DECL_COND_POSTFIX(_, Rhs, PacketSize_);
+ PACKET_DECL_COND_POSTFIX(_, Res, PacketSize_);
+
+ enum {
+ ConjLhs = ConjLhs_,
+ ConjRhs = false,
+ Vectorizable = unpacket_traits<LhsPacket_>::vectorizable && unpacket_traits<RhsPacket_>::vectorizable,
+ LhsPacketSize = Vectorizable ? unpacket_traits<LhsPacket_>::size : 1,
+ RhsPacketSize = Vectorizable ? unpacket_traits<RhsPacket_>::size : 1,
+ ResPacketSize = Vectorizable ? unpacket_traits<ResPacket_>::size : 1,
+
+ NumberOfRegisters = EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS,
+ nr = 4,
+#if defined(EIGEN_HAS_SINGLE_INSTRUCTION_MADD) && !defined(EIGEN_VECTORIZE_ALTIVEC) && !defined(EIGEN_VECTORIZE_VSX)
+ // we assume 16 registers
+ mr = 3*LhsPacketSize,
+#else
+ mr = (plain_enum_min(16, NumberOfRegisters)/2/nr)*LhsPacketSize,
+#endif
+
+ LhsProgress = LhsPacketSize,
+ RhsProgress = 1
+ };
+
+ typedef std::conditional_t<Vectorizable,LhsPacket_,LhsScalar> LhsPacket;
+ typedef std::conditional_t<Vectorizable,RhsPacket_,RhsScalar> RhsPacket;
+ typedef std::conditional_t<Vectorizable,ResPacket_,ResScalar> ResPacket;
+ typedef LhsPacket LhsPacket4Packing;
+
+ typedef QuadPacket<RhsPacket> RhsPacketx4;
+
+ typedef ResPacket AccPacket;
+
+ EIGEN_STRONG_INLINE void initAcc(AccPacket& p)
+ {
+ p = pset1<ResPacket>(ResScalar(0));
+ }
+
+ template<typename RhsPacketType>
+ EIGEN_STRONG_INLINE void loadRhs(const RhsScalar* b, RhsPacketType& dest) const
+ {
+ dest = pset1<RhsPacketType>(*b);
+ }
+
+ EIGEN_STRONG_INLINE void loadRhs(const RhsScalar* b, RhsPacketx4& dest) const
+ {
+ pbroadcast4(b, dest.B_0, dest.B1, dest.B2, dest.B3);
+ }
+
+ template<typename RhsPacketType>
+ EIGEN_STRONG_INLINE void updateRhs(const RhsScalar* b, RhsPacketType& dest) const
+ {
+ loadRhs(b, dest);
+ }
+
+ EIGEN_STRONG_INLINE void updateRhs(const RhsScalar*, RhsPacketx4&) const
+ {}
+
+ EIGEN_STRONG_INLINE void loadRhsQuad(const RhsScalar* b, RhsPacket& dest) const
+ {
+ loadRhsQuad_impl(b,dest, std::conditional_t<RhsPacketSize==16,true_type,false_type>());
+ }
+
+ EIGEN_STRONG_INLINE void loadRhsQuad_impl(const RhsScalar* b, RhsPacket& dest, const true_type&) const
+ {
+ // FIXME we can do better!
+ // what we want here is a ploadheight
+ RhsScalar tmp[4] = {b[0],b[0],b[1],b[1]};
+ dest = ploadquad<RhsPacket>(tmp);
+ }
+
+ EIGEN_STRONG_INLINE void loadRhsQuad_impl(const RhsScalar* b, RhsPacket& dest, const false_type&) const
+ {
+ eigen_internal_assert(RhsPacketSize<=8);
+ dest = pset1<RhsPacket>(*b);
+ }
+
+ EIGEN_STRONG_INLINE void loadLhs(const LhsScalar* a, LhsPacket& dest) const
+ {
+ dest = pload<LhsPacket>(a);
+ }
+
+ template<typename LhsPacketType>
+ EIGEN_STRONG_INLINE void loadLhsUnaligned(const LhsScalar* a, LhsPacketType& dest) const
+ {
+ dest = ploadu<LhsPacketType>(a);
+ }
+
+ template <typename LhsPacketType, typename RhsPacketType, typename AccPacketType, typename LaneIdType>
+ EIGEN_STRONG_INLINE void madd(const LhsPacketType& a, const RhsPacketType& b, AccPacketType& c, RhsPacketType& tmp, const LaneIdType&) const
+ {
+ madd_impl(a, b, c, tmp, std::conditional_t<Vectorizable,true_type,false_type>());
+ }
+
+ template <typename LhsPacketType, typename RhsPacketType, typename AccPacketType>
+ EIGEN_STRONG_INLINE void madd_impl(const LhsPacketType& a, const RhsPacketType& b, AccPacketType& c, RhsPacketType& tmp, const true_type&) const
+ {
+#ifdef EIGEN_HAS_SINGLE_INSTRUCTION_MADD
+ EIGEN_UNUSED_VARIABLE(tmp);
+ c.v = pmadd(a.v,b,c.v);
+#else
+ tmp = b; tmp = pmul(a.v,tmp); c.v = padd(c.v,tmp);
+#endif
+ }
+
+ EIGEN_STRONG_INLINE void madd_impl(const LhsScalar& a, const RhsScalar& b, ResScalar& c, RhsScalar& /*tmp*/, const false_type&) const
+ {
+ c += a * b;
+ }
+
+ template<typename LhsPacketType, typename AccPacketType, typename LaneIdType>
+ EIGEN_STRONG_INLINE void madd(const LhsPacketType& a, const RhsPacketx4& b, AccPacketType& c, RhsPacket& tmp, const LaneIdType& lane) const
+ {
+ madd(a, b.get(lane), c, tmp, lane);
+ }
+
+ template <typename ResPacketType, typename AccPacketType>
+ EIGEN_STRONG_INLINE void acc(const AccPacketType& c, const ResPacketType& alpha, ResPacketType& r) const
+ {
+ conj_helper<ResPacketType,ResPacketType,ConjLhs,false> cj;
+ r = cj.pmadd(c,alpha,r);
+ }
+
+protected:
+};
+
+template<typename Packet>
+struct DoublePacket
+{
+ Packet first;
+ Packet second;
+};
+
+template<typename Packet>
+DoublePacket<Packet> padd(const DoublePacket<Packet> &a, const DoublePacket<Packet> &b)
+{
+ DoublePacket<Packet> res;
+ res.first = padd(a.first, b.first);
+ res.second = padd(a.second,b.second);
+ return res;
+}
+
+// note that for DoublePacket<RealPacket> the "4" in "downto4"
+// corresponds to the number of complexes, so it means "8"
+// it terms of real coefficients.
+
+template<typename Packet>
+const DoublePacket<Packet>&
+predux_half_dowto4(const DoublePacket<Packet> &a,
+ std::enable_if_t<unpacket_traits<Packet>::size<=8>* = 0)
+{
+ return a;
+}
+
+template<typename Packet>
+DoublePacket<typename unpacket_traits<Packet>::half>
+predux_half_dowto4(const DoublePacket<Packet> &a,
+ std::enable_if_t<unpacket_traits<Packet>::size==16>* = 0)
+{
+ // yes, that's pretty hackish :(
+ DoublePacket<typename unpacket_traits<Packet>::half> res;
+ typedef std::complex<typename unpacket_traits<Packet>::type> Cplx;
+ typedef typename packet_traits<Cplx>::type CplxPacket;
+ res.first = predux_half_dowto4(CplxPacket(a.first)).v;
+ res.second = predux_half_dowto4(CplxPacket(a.second)).v;
+ return res;
+}
+
+// same here, "quad" actually means "8" in terms of real coefficients
+template<typename Scalar, typename RealPacket>
+void loadQuadToDoublePacket(const Scalar* b, DoublePacket<RealPacket>& dest,
+ std::enable_if_t<unpacket_traits<RealPacket>::size<=8>* = 0)
+{
+ dest.first = pset1<RealPacket>(numext::real(*b));
+ dest.second = pset1<RealPacket>(numext::imag(*b));
+}
+
+template<typename Scalar, typename RealPacket>
+void loadQuadToDoublePacket(const Scalar* b, DoublePacket<RealPacket>& dest,
+ std::enable_if_t<unpacket_traits<RealPacket>::size==16>* = 0)
+{
+ // yes, that's pretty hackish too :(
+ typedef typename NumTraits<Scalar>::Real RealScalar;
+ RealScalar r[4] = {numext::real(b[0]), numext::real(b[0]), numext::real(b[1]), numext::real(b[1])};
+ RealScalar i[4] = {numext::imag(b[0]), numext::imag(b[0]), numext::imag(b[1]), numext::imag(b[1])};
+ dest.first = ploadquad<RealPacket>(r);
+ dest.second = ploadquad<RealPacket>(i);
+}
+
+
+template<typename Packet> struct unpacket_traits<DoublePacket<Packet> > {
+ typedef DoublePacket<typename unpacket_traits<Packet>::half> half;
+};
+// template<typename Packet>
+// DoublePacket<Packet> pmadd(const DoublePacket<Packet> &a, const DoublePacket<Packet> &b)
+// {
+// DoublePacket<Packet> res;
+// res.first = padd(a.first, b.first);
+// res.second = padd(a.second,b.second);
+// return res;
+// }
+
+template<typename RealScalar, bool ConjLhs_, bool ConjRhs_, int Arch, int PacketSize_>
+class gebp_traits<std::complex<RealScalar>, std::complex<RealScalar>, ConjLhs_, ConjRhs_, Arch, PacketSize_ >
+{
+public:
+ typedef std::complex<RealScalar> Scalar;
+ typedef std::complex<RealScalar> LhsScalar;
+ typedef std::complex<RealScalar> RhsScalar;
+ typedef std::complex<RealScalar> ResScalar;
+
+ PACKET_DECL_COND_POSTFIX(_, Lhs, PacketSize_);
+ PACKET_DECL_COND_POSTFIX(_, Rhs, PacketSize_);
+ PACKET_DECL_COND_POSTFIX(_, Res, PacketSize_);
+ PACKET_DECL_COND(Real, PacketSize_);
+ PACKET_DECL_COND_SCALAR(PacketSize_);
+
+ enum {
+ ConjLhs = ConjLhs_,
+ ConjRhs = ConjRhs_,
+ Vectorizable = unpacket_traits<RealPacket>::vectorizable
+ && unpacket_traits<ScalarPacket>::vectorizable,
+ ResPacketSize = Vectorizable ? unpacket_traits<ResPacket_>::size : 1,
+ LhsPacketSize = Vectorizable ? unpacket_traits<LhsPacket_>::size : 1,
+ RhsPacketSize = Vectorizable ? unpacket_traits<RhsScalar>::size : 1,
+ RealPacketSize = Vectorizable ? unpacket_traits<RealPacket>::size : 1,
+
+ // FIXME: should depend on NumberOfRegisters
+ nr = 4,
+ mr = ResPacketSize,
+
+ LhsProgress = ResPacketSize,
+ RhsProgress = 1
+ };
+
+ typedef DoublePacket<RealPacket> DoublePacketType;
+
+ typedef std::conditional_t<Vectorizable,ScalarPacket,Scalar> LhsPacket4Packing;
+ typedef std::conditional_t<Vectorizable,RealPacket, Scalar> LhsPacket;
+ typedef std::conditional_t<Vectorizable,DoublePacketType,Scalar> RhsPacket;
+ typedef std::conditional_t<Vectorizable,ScalarPacket,Scalar> ResPacket;
+ typedef std::conditional_t<Vectorizable,DoublePacketType,Scalar> AccPacket;
+
+ // this actually holds 8 packets!
+ typedef QuadPacket<RhsPacket> RhsPacketx4;
+
+ EIGEN_STRONG_INLINE void initAcc(Scalar& p) { p = Scalar(0); }
+
+ EIGEN_STRONG_INLINE void initAcc(DoublePacketType& p)
+ {
+ p.first = pset1<RealPacket>(RealScalar(0));
+ p.second = pset1<RealPacket>(RealScalar(0));
+ }
+
+ // Scalar path
+ EIGEN_STRONG_INLINE void loadRhs(const RhsScalar* b, ScalarPacket& dest) const
+ {
+ dest = pset1<ScalarPacket>(*b);
+ }
+
+ // Vectorized path
+ template<typename RealPacketType>
+ EIGEN_STRONG_INLINE void loadRhs(const RhsScalar* b, DoublePacket<RealPacketType>& dest) const
+ {
+ dest.first = pset1<RealPacketType>(numext::real(*b));
+ dest.second = pset1<RealPacketType>(numext::imag(*b));
+ }
+
+ EIGEN_STRONG_INLINE void loadRhs(const RhsScalar* b, RhsPacketx4& dest) const
+ {
+ loadRhs(b, dest.B_0);
+ loadRhs(b + 1, dest.B1);
+ loadRhs(b + 2, dest.B2);
+ loadRhs(b + 3, dest.B3);
+ }
+
+ // Scalar path
+ EIGEN_STRONG_INLINE void updateRhs(const RhsScalar* b, ScalarPacket& dest) const
+ {
+ loadRhs(b, dest);
+ }
+
+ // Vectorized path
+ template<typename RealPacketType>
+ EIGEN_STRONG_INLINE void updateRhs(const RhsScalar* b, DoublePacket<RealPacketType>& dest) const
+ {
+ loadRhs(b, dest);
+ }
+
+ EIGEN_STRONG_INLINE void updateRhs(const RhsScalar*, RhsPacketx4&) const {}
+
+ EIGEN_STRONG_INLINE void loadRhsQuad(const RhsScalar* b, ResPacket& dest) const
+ {
+ loadRhs(b,dest);
+ }
+ EIGEN_STRONG_INLINE void loadRhsQuad(const RhsScalar* b, DoublePacketType& dest) const
+ {
+ loadQuadToDoublePacket(b,dest);
+ }
+
+ // nothing special here
+ EIGEN_STRONG_INLINE void loadLhs(const LhsScalar* a, LhsPacket& dest) const
+ {
+ dest = pload<LhsPacket>((const typename unpacket_traits<LhsPacket>::type*)(a));
+ }
+
+ template<typename LhsPacketType>
+ EIGEN_STRONG_INLINE void loadLhsUnaligned(const LhsScalar* a, LhsPacketType& dest) const
+ {
+ dest = ploadu<LhsPacketType>((const typename unpacket_traits<LhsPacketType>::type*)(a));
+ }
+
+ template<typename LhsPacketType, typename RhsPacketType, typename ResPacketType, typename TmpType, typename LaneIdType>
+ EIGEN_STRONG_INLINE
+ std::enable_if_t<!is_same<RhsPacketType,RhsPacketx4>::value>
+ madd(const LhsPacketType& a, const RhsPacketType& b, DoublePacket<ResPacketType>& c, TmpType& /*tmp*/, const LaneIdType&) const
+ {
+ c.first = padd(pmul(a,b.first), c.first);
+ c.second = padd(pmul(a,b.second),c.second);
+ }
+
+ template<typename LaneIdType>
+ EIGEN_STRONG_INLINE void madd(const LhsPacket& a, const RhsPacket& b, ResPacket& c, RhsPacket& /*tmp*/, const LaneIdType&) const
+ {
+ c = cj.pmadd(a,b,c);
+ }
+
+ template<typename LhsPacketType, typename AccPacketType, typename LaneIdType>
+ EIGEN_STRONG_INLINE void madd(const LhsPacketType& a, const RhsPacketx4& b, AccPacketType& c, RhsPacket& tmp, const LaneIdType& lane) const
+ {
+ madd(a, b.get(lane), c, tmp, lane);
+ }
+
+ EIGEN_STRONG_INLINE void acc(const Scalar& c, const Scalar& alpha, Scalar& r) const { r += alpha * c; }
+
+ template<typename RealPacketType, typename ResPacketType>
+ EIGEN_STRONG_INLINE void acc(const DoublePacket<RealPacketType>& c, const ResPacketType& alpha, ResPacketType& r) const
+ {
+ // assemble c
+ ResPacketType tmp;
+ if((!ConjLhs)&&(!ConjRhs))
+ {
+ tmp = pcplxflip(pconj(ResPacketType(c.second)));
+ tmp = padd(ResPacketType(c.first),tmp);
+ }
+ else if((!ConjLhs)&&(ConjRhs))
+ {
+ tmp = pconj(pcplxflip(ResPacketType(c.second)));
+ tmp = padd(ResPacketType(c.first),tmp);
+ }
+ else if((ConjLhs)&&(!ConjRhs))
+ {
+ tmp = pcplxflip(ResPacketType(c.second));
+ tmp = padd(pconj(ResPacketType(c.first)),tmp);
+ }
+ else if((ConjLhs)&&(ConjRhs))
+ {
+ tmp = pcplxflip(ResPacketType(c.second));
+ tmp = psub(pconj(ResPacketType(c.first)),tmp);
+ }
+
+ r = pmadd(tmp,alpha,r);
+ }
+
+protected:
+ conj_helper<LhsScalar,RhsScalar,ConjLhs,ConjRhs> cj;
+};
+
+template<typename RealScalar, bool ConjRhs_, int Arch, int PacketSize_>
+class gebp_traits<RealScalar, std::complex<RealScalar>, false, ConjRhs_, Arch, PacketSize_ >
+{
+public:
+ typedef std::complex<RealScalar> Scalar;
+ typedef RealScalar LhsScalar;
+ typedef Scalar RhsScalar;
+ typedef Scalar ResScalar;
+
+ PACKET_DECL_COND_POSTFIX(_, Lhs, PacketSize_);
+ PACKET_DECL_COND_POSTFIX(_, Rhs, PacketSize_);
+ PACKET_DECL_COND_POSTFIX(_, Res, PacketSize_);
+ PACKET_DECL_COND_POSTFIX(_, Real, PacketSize_);
+ PACKET_DECL_COND_SCALAR_POSTFIX(_, PacketSize_);
+
+#undef PACKET_DECL_COND_SCALAR_POSTFIX
+#undef PACKET_DECL_COND_POSTFIX
+#undef PACKET_DECL_COND_SCALAR
+#undef PACKET_DECL_COND
+
+ enum {
+ ConjLhs = false,
+ ConjRhs = ConjRhs_,
+ Vectorizable = unpacket_traits<RealPacket_>::vectorizable
+ && unpacket_traits<ScalarPacket_>::vectorizable,
+ LhsPacketSize = Vectorizable ? unpacket_traits<LhsPacket_>::size : 1,
+ RhsPacketSize = Vectorizable ? unpacket_traits<RhsPacket_>::size : 1,
+ ResPacketSize = Vectorizable ? unpacket_traits<ResPacket_>::size : 1,
+
+ NumberOfRegisters = EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS,
+ // FIXME: should depend on NumberOfRegisters
+ nr = 4,
+ mr = (plain_enum_min(16, NumberOfRegisters)/2/nr)*ResPacketSize,
+
+ LhsProgress = ResPacketSize,
+ RhsProgress = 1
+ };
+
+ typedef std::conditional_t<Vectorizable,LhsPacket_,LhsScalar> LhsPacket;
+ typedef std::conditional_t<Vectorizable,RhsPacket_,RhsScalar> RhsPacket;
+ typedef std::conditional_t<Vectorizable,ResPacket_,ResScalar> ResPacket;
+ typedef LhsPacket LhsPacket4Packing;
+ typedef QuadPacket<RhsPacket> RhsPacketx4;
+ typedef ResPacket AccPacket;
+
+ EIGEN_STRONG_INLINE void initAcc(AccPacket& p)
+ {
+ p = pset1<ResPacket>(ResScalar(0));
+ }
+
+ template<typename RhsPacketType>
+ EIGEN_STRONG_INLINE void loadRhs(const RhsScalar* b, RhsPacketType& dest) const
+ {
+ dest = pset1<RhsPacketType>(*b);
+ }
+
+ EIGEN_STRONG_INLINE void loadRhs(const RhsScalar* b, RhsPacketx4& dest) const
+ {
+ pbroadcast4(b, dest.B_0, dest.B1, dest.B2, dest.B3);
+ }
+
+ template<typename RhsPacketType>
+ EIGEN_STRONG_INLINE void updateRhs(const RhsScalar* b, RhsPacketType& dest) const
+ {
+ loadRhs(b, dest);
+ }
+
+ EIGEN_STRONG_INLINE void updateRhs(const RhsScalar*, RhsPacketx4&) const
+ {}
+
+ EIGEN_STRONG_INLINE void loadLhs(const LhsScalar* a, LhsPacket& dest) const
+ {
+ dest = ploaddup<LhsPacket>(a);
+ }
+
+ EIGEN_STRONG_INLINE void loadRhsQuad(const RhsScalar* b, RhsPacket& dest) const
+ {
+ dest = ploadquad<RhsPacket>(b);
+ }
+
+ template<typename LhsPacketType>
+ EIGEN_STRONG_INLINE void loadLhsUnaligned(const LhsScalar* a, LhsPacketType& dest) const
+ {
+ dest = ploaddup<LhsPacketType>(a);
+ }
+
+ template <typename LhsPacketType, typename RhsPacketType, typename AccPacketType, typename LaneIdType>
+ EIGEN_STRONG_INLINE void madd(const LhsPacketType& a, const RhsPacketType& b, AccPacketType& c, RhsPacketType& tmp, const LaneIdType&) const
+ {
+ madd_impl(a, b, c, tmp, std::conditional_t<Vectorizable,true_type,false_type>());
+ }
+
+ template <typename LhsPacketType, typename RhsPacketType, typename AccPacketType>
+ EIGEN_STRONG_INLINE void madd_impl(const LhsPacketType& a, const RhsPacketType& b, AccPacketType& c, RhsPacketType& tmp, const true_type&) const
+ {
+#ifdef EIGEN_HAS_SINGLE_INSTRUCTION_MADD
+ EIGEN_UNUSED_VARIABLE(tmp);
+ c.v = pmadd(a,b.v,c.v);
+#else
+ tmp = b; tmp.v = pmul(a,tmp.v); c = padd(c,tmp);
+#endif
+
+ }
+
+ EIGEN_STRONG_INLINE void madd_impl(const LhsScalar& a, const RhsScalar& b, ResScalar& c, RhsScalar& /*tmp*/, const false_type&) const
+ {
+ c += a * b;
+ }
+
+ template<typename LhsPacketType, typename AccPacketType, typename LaneIdType>
+ EIGEN_STRONG_INLINE void madd(const LhsPacketType& a, const RhsPacketx4& b, AccPacketType& c, RhsPacket& tmp, const LaneIdType& lane) const
+ {
+ madd(a, b.get(lane), c, tmp, lane);
+ }
+
+ template <typename ResPacketType, typename AccPacketType>
+ EIGEN_STRONG_INLINE void acc(const AccPacketType& c, const ResPacketType& alpha, ResPacketType& r) const
+ {
+ conj_helper<ResPacketType,ResPacketType,false,ConjRhs> cj;
+ r = cj.pmadd(alpha,c,r);
+ }
+
+protected:
+
+};
+
+/* optimized General packed Block * packed Panel product kernel
+ *
+ * Mixing type logic: C += A * B
+ * | A | B | comments
+ * |real |cplx | no vectorization yet, would require to pack A with duplication
+ * |cplx |real | easy vectorization
+ */
+template<typename LhsScalar, typename RhsScalar, typename Index, typename DataMapper, int mr, int nr, bool ConjugateLhs, bool ConjugateRhs>
+struct gebp_kernel
+{
+ typedef gebp_traits<LhsScalar,RhsScalar,ConjugateLhs,ConjugateRhs,Architecture::Target> Traits;
+ typedef gebp_traits<LhsScalar,RhsScalar,ConjugateLhs,ConjugateRhs,Architecture::Target,GEBPPacketHalf> HalfTraits;
+ typedef gebp_traits<LhsScalar,RhsScalar,ConjugateLhs,ConjugateRhs,Architecture::Target,GEBPPacketQuarter> QuarterTraits;
+
+ typedef typename Traits::ResScalar ResScalar;
+ typedef typename Traits::LhsPacket LhsPacket;
+ typedef typename Traits::RhsPacket RhsPacket;
+ typedef typename Traits::ResPacket ResPacket;
+ typedef typename Traits::AccPacket AccPacket;
+ typedef typename Traits::RhsPacketx4 RhsPacketx4;
+
+ typedef typename RhsPanelHelper<RhsPacket, RhsPacketx4, 15>::type RhsPanel15;
+ typedef typename RhsPanelHelper<RhsPacket, RhsPacketx4, 27>::type RhsPanel27;
+
+ typedef gebp_traits<RhsScalar,LhsScalar,ConjugateRhs,ConjugateLhs,Architecture::Target> SwappedTraits;
+
+ typedef typename SwappedTraits::ResScalar SResScalar;
+ typedef typename SwappedTraits::LhsPacket SLhsPacket;
+ typedef typename SwappedTraits::RhsPacket SRhsPacket;
+ typedef typename SwappedTraits::ResPacket SResPacket;
+ typedef typename SwappedTraits::AccPacket SAccPacket;
+
+ typedef typename HalfTraits::LhsPacket LhsPacketHalf;
+ typedef typename HalfTraits::RhsPacket RhsPacketHalf;
+ typedef typename HalfTraits::ResPacket ResPacketHalf;
+ typedef typename HalfTraits::AccPacket AccPacketHalf;
+
+ typedef typename QuarterTraits::LhsPacket LhsPacketQuarter;
+ typedef typename QuarterTraits::RhsPacket RhsPacketQuarter;
+ typedef typename QuarterTraits::ResPacket ResPacketQuarter;
+ typedef typename QuarterTraits::AccPacket AccPacketQuarter;
+
+ typedef typename DataMapper::LinearMapper LinearMapper;
+
+ enum {
+ Vectorizable = Traits::Vectorizable,
+ LhsProgress = Traits::LhsProgress,
+ LhsProgressHalf = HalfTraits::LhsProgress,
+ LhsProgressQuarter = QuarterTraits::LhsProgress,
+ RhsProgress = Traits::RhsProgress,
+ RhsProgressHalf = HalfTraits::RhsProgress,
+ RhsProgressQuarter = QuarterTraits::RhsProgress,
+ ResPacketSize = Traits::ResPacketSize
+ };
+
+ EIGEN_DONT_INLINE
+ void operator()(const DataMapper& res, const LhsScalar* blockA, const RhsScalar* blockB,
+ Index rows, Index depth, Index cols, ResScalar alpha,
+ Index strideA=-1, Index strideB=-1, Index offsetA=0, Index offsetB=0);
+};
+
+template<typename LhsScalar, typename RhsScalar, typename Index, typename DataMapper, int mr, int nr, bool ConjugateLhs, bool ConjugateRhs,
+int SwappedLhsProgress = gebp_traits<RhsScalar,LhsScalar,ConjugateRhs,ConjugateLhs,Architecture::Target>::LhsProgress>
+struct last_row_process_16_packets
+{
+ typedef gebp_traits<LhsScalar,RhsScalar,ConjugateLhs,ConjugateRhs,Architecture::Target> Traits;
+ typedef gebp_traits<RhsScalar,LhsScalar,ConjugateRhs,ConjugateLhs,Architecture::Target> SwappedTraits;
+
+ typedef typename Traits::ResScalar ResScalar;
+ typedef typename SwappedTraits::LhsPacket SLhsPacket;
+ typedef typename SwappedTraits::RhsPacket SRhsPacket;
+ typedef typename SwappedTraits::ResPacket SResPacket;
+ typedef typename SwappedTraits::AccPacket SAccPacket;
+
+ EIGEN_STRONG_INLINE void operator()(const DataMapper& res, SwappedTraits &straits, const LhsScalar* blA,
+ const RhsScalar* blB, Index depth, const Index endk, Index i, Index j2,
+ ResScalar alpha, SAccPacket &C0)
+ {
+ EIGEN_UNUSED_VARIABLE(res);
+ EIGEN_UNUSED_VARIABLE(straits);
+ EIGEN_UNUSED_VARIABLE(blA);
+ EIGEN_UNUSED_VARIABLE(blB);
+ EIGEN_UNUSED_VARIABLE(depth);
+ EIGEN_UNUSED_VARIABLE(endk);
+ EIGEN_UNUSED_VARIABLE(i);
+ EIGEN_UNUSED_VARIABLE(j2);
+ EIGEN_UNUSED_VARIABLE(alpha);
+ EIGEN_UNUSED_VARIABLE(C0);
+ }
+};
+
+
+template<typename LhsScalar, typename RhsScalar, typename Index, typename DataMapper, int mr, int nr, bool ConjugateLhs, bool ConjugateRhs>
+struct last_row_process_16_packets<LhsScalar, RhsScalar, Index, DataMapper, mr, nr, ConjugateLhs, ConjugateRhs, 16> {
+ typedef gebp_traits<LhsScalar,RhsScalar,ConjugateLhs,ConjugateRhs,Architecture::Target> Traits;
+ typedef gebp_traits<RhsScalar,LhsScalar,ConjugateRhs,ConjugateLhs,Architecture::Target> SwappedTraits;
+
+ typedef typename Traits::ResScalar ResScalar;
+ typedef typename SwappedTraits::LhsPacket SLhsPacket;
+ typedef typename SwappedTraits::RhsPacket SRhsPacket;
+ typedef typename SwappedTraits::ResPacket SResPacket;
+ typedef typename SwappedTraits::AccPacket SAccPacket;
+
+ EIGEN_STRONG_INLINE void operator()(const DataMapper& res, SwappedTraits &straits, const LhsScalar* blA,
+ const RhsScalar* blB, Index depth, const Index endk, Index i, Index j2,
+ ResScalar alpha, SAccPacket &C0)
+ {
+ typedef typename unpacket_traits<typename unpacket_traits<SResPacket>::half>::half SResPacketQuarter;
+ typedef typename unpacket_traits<typename unpacket_traits<SLhsPacket>::half>::half SLhsPacketQuarter;
+ typedef typename unpacket_traits<typename unpacket_traits<SRhsPacket>::half>::half SRhsPacketQuarter;
+ typedef typename unpacket_traits<typename unpacket_traits<SAccPacket>::half>::half SAccPacketQuarter;
+
+ SResPacketQuarter R = res.template gatherPacket<SResPacketQuarter>(i, j2);
+ SResPacketQuarter alphav = pset1<SResPacketQuarter>(alpha);
+
+ if (depth - endk > 0)
+ {
+ // We have to handle the last row(s) of the rhs, which
+ // correspond to a half-packet
+ SAccPacketQuarter c0 = predux_half_dowto4(predux_half_dowto4(C0));
+
+ for (Index kk = endk; kk < depth; kk++)
+ {
+ SLhsPacketQuarter a0;
+ SRhsPacketQuarter b0;
+ straits.loadLhsUnaligned(blB, a0);
+ straits.loadRhs(blA, b0);
+ straits.madd(a0,b0,c0,b0, fix<0>);
+ blB += SwappedTraits::LhsProgress/4;
+ blA += 1;
+ }
+ straits.acc(c0, alphav, R);
+ }
+ else
+ {
+ straits.acc(predux_half_dowto4(predux_half_dowto4(C0)), alphav, R);
+ }
+ res.scatterPacket(i, j2, R);
+ }
+};
+
+template<int nr, Index LhsProgress, Index RhsProgress, typename LhsScalar, typename RhsScalar, typename ResScalar, typename AccPacket, typename LhsPacket, typename RhsPacket, typename ResPacket, typename GEBPTraits, typename LinearMapper, typename DataMapper>
+struct lhs_process_one_packet
+{
+ typedef typename GEBPTraits::RhsPacketx4 RhsPacketx4;
+
+ EIGEN_STRONG_INLINE void peeled_kc_onestep(Index K, const LhsScalar* blA, const RhsScalar* blB, GEBPTraits traits, LhsPacket *A0, RhsPacketx4 *rhs_panel, RhsPacket *T0, AccPacket *C0, AccPacket *C1, AccPacket *C2, AccPacket *C3)
+ {
+ EIGEN_ASM_COMMENT("begin step of gebp micro kernel 1X4");
+ EIGEN_ASM_COMMENT("Note: these asm comments work around bug 935!");
+ traits.loadLhs(&blA[(0+1*K)*LhsProgress], *A0);
+ traits.loadRhs(&blB[(0+4*K)*RhsProgress], *rhs_panel);
+ traits.madd(*A0, *rhs_panel, *C0, *T0, fix<0>);
+ traits.madd(*A0, *rhs_panel, *C1, *T0, fix<1>);
+ traits.madd(*A0, *rhs_panel, *C2, *T0, fix<2>);
+ traits.madd(*A0, *rhs_panel, *C3, *T0, fix<3>);
+ #if EIGEN_GNUC_AT_LEAST(6,0) && defined(EIGEN_VECTORIZE_SSE) && !(EIGEN_COMP_LCC)
+ __asm__ ("" : "+x,m" (*A0));
+ #endif
+ EIGEN_ASM_COMMENT("end step of gebp micro kernel 1X4");
+ }
+
+ EIGEN_STRONG_INLINE void operator()(
+ const DataMapper& res, const LhsScalar* blockA, const RhsScalar* blockB, ResScalar alpha,
+ Index peelStart, Index peelEnd, Index strideA, Index strideB, Index offsetA, Index offsetB,
+ int prefetch_res_offset, Index peeled_kc, Index pk, Index cols, Index depth, Index packet_cols4)
+ {
+ GEBPTraits traits;
+ Index packet_cols8 = nr>=8 ? (cols/8) * 8 : 0;
+ // loops on each largest micro horizontal panel of lhs
+ // (LhsProgress x depth)
+ for(Index i=peelStart; i<peelEnd; i+=LhsProgress)
+ {
+#if EIGEN_ARCH_ARM64
+ EIGEN_IF_CONSTEXPR(nr>=8) {
+ for(Index j2=0; j2<packet_cols8; j2+=8)
+ {
+ const LhsScalar* blA = &blockA[i*strideA+offsetA*(LhsProgress)];
+ prefetch(&blA[0]);
+
+ // gets res block as register
+ AccPacket C0, C1, C2, C3, C4, C5, C6, C7;
+ traits.initAcc(C0);
+ traits.initAcc(C1);
+ traits.initAcc(C2);
+ traits.initAcc(C3);
+ traits.initAcc(C4);
+ traits.initAcc(C5);
+ traits.initAcc(C6);
+ traits.initAcc(C7);
+
+ LinearMapper r0 = res.getLinearMapper(i, j2 + 0);
+ LinearMapper r1 = res.getLinearMapper(i, j2 + 1);
+ LinearMapper r2 = res.getLinearMapper(i, j2 + 2);
+ LinearMapper r3 = res.getLinearMapper(i, j2 + 3);
+ LinearMapper r4 = res.getLinearMapper(i, j2 + 4);
+ LinearMapper r5 = res.getLinearMapper(i, j2 + 5);
+ LinearMapper r6 = res.getLinearMapper(i, j2 + 6);
+ LinearMapper r7 = res.getLinearMapper(i, j2 + 7);
+ r0.prefetch(prefetch_res_offset);
+ r1.prefetch(prefetch_res_offset);
+ r2.prefetch(prefetch_res_offset);
+ r3.prefetch(prefetch_res_offset);
+ r4.prefetch(prefetch_res_offset);
+ r5.prefetch(prefetch_res_offset);
+ r6.prefetch(prefetch_res_offset);
+ r7.prefetch(prefetch_res_offset);
+ const RhsScalar* blB = &blockB[j2*strideB+offsetB*8];
+ prefetch(&blB[0]);
+
+ LhsPacket A0;
+ for(Index k=0; k<peeled_kc; k+=pk)
+ {
+ RhsPacketx4 rhs_panel;
+ RhsPacket T0;
+#define EIGEN_GEBGP_ONESTEP(K) \
+ do { \
+ EIGEN_ASM_COMMENT("begin step of gebp micro kernel 1pX8"); \
+ traits.loadLhs(&blA[(0 + 1 * K) * LhsProgress], A0); \
+ traits.loadRhs(&blB[(0 + 8 * K) * RhsProgress], rhs_panel); \
+ traits.madd(A0, rhs_panel, C0, T0, fix<0>); \
+ traits.updateRhs(&blB[(1 + 8 * K) * RhsProgress], rhs_panel); \
+ traits.madd(A0, rhs_panel, C1, T0, fix<1>); \
+ traits.updateRhs(&blB[(2 + 8 * K) * RhsProgress], rhs_panel); \
+ traits.madd(A0, rhs_panel, C2, T0, fix<2>); \
+ traits.updateRhs(&blB[(3 + 8 * K) * RhsProgress], rhs_panel); \
+ traits.madd(A0, rhs_panel, C3, T0, fix<3>); \
+ traits.loadRhs(&blB[(4 + 8 * K) * RhsProgress], rhs_panel); \
+ traits.madd(A0, rhs_panel, C4, T0, fix<0>); \
+ traits.updateRhs(&blB[(5 + 8 * K) * RhsProgress], rhs_panel); \
+ traits.madd(A0, rhs_panel, C5, T0, fix<1>); \
+ traits.updateRhs(&blB[(6 + 8 * K) * RhsProgress], rhs_panel); \
+ traits.madd(A0, rhs_panel, C6, T0, fix<2>); \
+ traits.updateRhs(&blB[(7 + 8 * K) * RhsProgress], rhs_panel); \
+ traits.madd(A0, rhs_panel, C7, T0, fix<3>); \
+ EIGEN_ASM_COMMENT("end step of gebp micro kernel 1pX8"); \
+ } while (false)
+
+ EIGEN_ASM_COMMENT("begin gebp micro kernel 1pX8");
+
+ EIGEN_GEBGP_ONESTEP(0);
+ EIGEN_GEBGP_ONESTEP(1);
+ EIGEN_GEBGP_ONESTEP(2);
+ EIGEN_GEBGP_ONESTEP(3);
+ EIGEN_GEBGP_ONESTEP(4);
+ EIGEN_GEBGP_ONESTEP(5);
+ EIGEN_GEBGP_ONESTEP(6);
+ EIGEN_GEBGP_ONESTEP(7);
+
+ blB += pk*8*RhsProgress;
+ blA += pk*(1*LhsProgress);
+
+ EIGEN_ASM_COMMENT("end gebp micro kernel 1pX8");
+ }
+ // process remaining peeled loop
+ for(Index k=peeled_kc; k<depth; k++)
+ {
+ RhsPacketx4 rhs_panel;
+ RhsPacket T0;
+ EIGEN_GEBGP_ONESTEP(0);
+ blB += 8*RhsProgress;
+ blA += 1*LhsProgress;
+ }
+
+#undef EIGEN_GEBGP_ONESTEP
+
+ ResPacket R0, R1;
+ ResPacket alphav = pset1<ResPacket>(alpha);
+
+ R0 = r0.template loadPacket<ResPacket>(0);
+ R1 = r1.template loadPacket<ResPacket>(0);
+ traits.acc(C0, alphav, R0);
+ traits.acc(C1, alphav, R1);
+ r0.storePacket(0, R0);
+ r1.storePacket(0, R1);
+
+ R0 = r2.template loadPacket<ResPacket>(0);
+ R1 = r3.template loadPacket<ResPacket>(0);
+ traits.acc(C2, alphav, R0);
+ traits.acc(C3, alphav, R1);
+ r2.storePacket(0, R0);
+ r3.storePacket(0, R1);
+
+ R0 = r4.template loadPacket<ResPacket>(0);
+ R1 = r5.template loadPacket<ResPacket>(0);
+ traits.acc(C4, alphav, R0);
+ traits.acc(C5, alphav, R1);
+ r4.storePacket(0, R0);
+ r5.storePacket(0, R1);
+
+ R0 = r6.template loadPacket<ResPacket>(0);
+ R1 = r7.template loadPacket<ResPacket>(0);
+ traits.acc(C6, alphav, R0);
+ traits.acc(C7, alphav, R1);
+ r6.storePacket(0, R0);
+ r7.storePacket(0, R1);
+ }
+ }
+#endif
+
+ // loops on each largest micro vertical panel of rhs (depth * nr)
+ for(Index j2=packet_cols8; j2<packet_cols4; j2+=4)
+ {
+ // We select a LhsProgress x nr micro block of res
+ // which is entirely stored into 1 x nr registers.
+
+ const LhsScalar* blA = &blockA[i*strideA+offsetA*(LhsProgress)];
+ prefetch(&blA[0]);
+
+ // gets res block as register
+ AccPacket C0, C1, C2, C3;
+ traits.initAcc(C0);
+ traits.initAcc(C1);
+ traits.initAcc(C2);
+ traits.initAcc(C3);
+ // To improve instruction pipelining, let's double the accumulation registers:
+ // even k will accumulate in C*, while odd k will accumulate in D*.
+ // This trick is crutial to get good performance with FMA, otherwise it is
+ // actually faster to perform separated MUL+ADD because of a naturally
+ // better instruction-level parallelism.
+ AccPacket D0, D1, D2, D3;
+ traits.initAcc(D0);
+ traits.initAcc(D1);
+ traits.initAcc(D2);
+ traits.initAcc(D3);
+
+ LinearMapper r0 = res.getLinearMapper(i, j2 + 0);
+ LinearMapper r1 = res.getLinearMapper(i, j2 + 1);
+ LinearMapper r2 = res.getLinearMapper(i, j2 + 2);
+ LinearMapper r3 = res.getLinearMapper(i, j2 + 3);
+
+ r0.prefetch(prefetch_res_offset);
+ r1.prefetch(prefetch_res_offset);
+ r2.prefetch(prefetch_res_offset);
+ r3.prefetch(prefetch_res_offset);
+
+ // performs "inner" products
+ const RhsScalar* blB = &blockB[j2*strideB+offsetB*4];
+ prefetch(&blB[0]);
+ LhsPacket A0, A1;
+
+ for(Index k=0; k<peeled_kc; k+=pk)
+ {
+ EIGEN_ASM_COMMENT("begin gebp micro kernel 1/half/quarterX4");
+ RhsPacketx4 rhs_panel;
+ RhsPacket T0;
+
+ internal::prefetch(blB+(48+0));
+ peeled_kc_onestep(0, blA, blB, traits, &A0, &rhs_panel, &T0, &C0, &C1, &C2, &C3);
+ peeled_kc_onestep(1, blA, blB, traits, &A1, &rhs_panel, &T0, &D0, &D1, &D2, &D3);
+ peeled_kc_onestep(2, blA, blB, traits, &A0, &rhs_panel, &T0, &C0, &C1, &C2, &C3);
+ peeled_kc_onestep(3, blA, blB, traits, &A1, &rhs_panel, &T0, &D0, &D1, &D2, &D3);
+ internal::prefetch(blB+(48+16));
+ peeled_kc_onestep(4, blA, blB, traits, &A0, &rhs_panel, &T0, &C0, &C1, &C2, &C3);
+ peeled_kc_onestep(5, blA, blB, traits, &A1, &rhs_panel, &T0, &D0, &D1, &D2, &D3);
+ peeled_kc_onestep(6, blA, blB, traits, &A0, &rhs_panel, &T0, &C0, &C1, &C2, &C3);
+ peeled_kc_onestep(7, blA, blB, traits, &A1, &rhs_panel, &T0, &D0, &D1, &D2, &D3);
+
+ blB += pk*4*RhsProgress;
+ blA += pk*LhsProgress;
+
+ EIGEN_ASM_COMMENT("end gebp micro kernel 1/half/quarterX4");
+ }
+ C0 = padd(C0,D0);
+ C1 = padd(C1,D1);
+ C2 = padd(C2,D2);
+ C3 = padd(C3,D3);
+
+ // process remaining peeled loop
+ for(Index k=peeled_kc; k<depth; k++)
+ {
+ RhsPacketx4 rhs_panel;
+ RhsPacket T0;
+ peeled_kc_onestep(0, blA, blB, traits, &A0, &rhs_panel, &T0, &C0, &C1, &C2, &C3);
+ blB += 4*RhsProgress;
+ blA += LhsProgress;
+ }
+
+ ResPacket R0, R1;
+ ResPacket alphav = pset1<ResPacket>(alpha);
+
+ R0 = r0.template loadPacket<ResPacket>(0);
+ R1 = r1.template loadPacket<ResPacket>(0);
+ traits.acc(C0, alphav, R0);
+ traits.acc(C1, alphav, R1);
+ r0.storePacket(0, R0);
+ r1.storePacket(0, R1);
+
+ R0 = r2.template loadPacket<ResPacket>(0);
+ R1 = r3.template loadPacket<ResPacket>(0);
+ traits.acc(C2, alphav, R0);
+ traits.acc(C3, alphav, R1);
+ r2.storePacket(0, R0);
+ r3.storePacket(0, R1);
+ }
+
+ // Deal with remaining columns of the rhs
+ for(Index j2=packet_cols4; j2<cols; j2++)
+ {
+ // One column at a time
+ const LhsScalar* blA = &blockA[i*strideA+offsetA*(LhsProgress)];
+ prefetch(&blA[0]);
+
+ // gets res block as register
+ AccPacket C0;
+ traits.initAcc(C0);
+
+ LinearMapper r0 = res.getLinearMapper(i, j2);
+
+ // performs "inner" products
+ const RhsScalar* blB = &blockB[j2*strideB+offsetB];
+ LhsPacket A0;
+
+ for(Index k= 0; k<peeled_kc; k+=pk)
+ {
+ EIGEN_ASM_COMMENT("begin gebp micro kernel 1/half/quarterX1");
+ RhsPacket B_0;
+
+#define EIGEN_GEBGP_ONESTEP(K) \
+ do { \
+ EIGEN_ASM_COMMENT("begin step of gebp micro kernel 1/half/quarterX1"); \
+ EIGEN_ASM_COMMENT("Note: these asm comments work around bug 935!"); \
+ /* FIXME: why unaligned???? */ \
+ traits.loadLhsUnaligned(&blA[(0+1*K)*LhsProgress], A0); \
+ traits.loadRhs(&blB[(0+K)*RhsProgress], B_0); \
+ traits.madd(A0, B_0, C0, B_0, fix<0>); \
+ EIGEN_ASM_COMMENT("end step of gebp micro kernel 1/half/quarterX1"); \
+ } while(false);
+
+ EIGEN_GEBGP_ONESTEP(0);
+ EIGEN_GEBGP_ONESTEP(1);
+ EIGEN_GEBGP_ONESTEP(2);
+ EIGEN_GEBGP_ONESTEP(3);
+ EIGEN_GEBGP_ONESTEP(4);
+ EIGEN_GEBGP_ONESTEP(5);
+ EIGEN_GEBGP_ONESTEP(6);
+ EIGEN_GEBGP_ONESTEP(7);
+
+ blB += pk*RhsProgress;
+ blA += pk*LhsProgress;
+
+ EIGEN_ASM_COMMENT("end gebp micro kernel 1/half/quarterX1");
+ }
+
+ // process remaining peeled loop
+ for(Index k=peeled_kc; k<depth; k++)
+ {
+ RhsPacket B_0;
+ EIGEN_GEBGP_ONESTEP(0);
+ blB += RhsProgress;
+ blA += LhsProgress;
+ }
+#undef EIGEN_GEBGP_ONESTEP
+ ResPacket R0;
+ ResPacket alphav = pset1<ResPacket>(alpha);
+ R0 = r0.template loadPacket<ResPacket>(0);
+ traits.acc(C0, alphav, R0);
+ r0.storePacket(0, R0);
+ }
+ }
+ }
+};
+
+template<int nr, Index LhsProgress, Index RhsProgress, typename LhsScalar, typename RhsScalar, typename ResScalar, typename AccPacket, typename LhsPacket, typename RhsPacket, typename ResPacket, typename GEBPTraits, typename LinearMapper, typename DataMapper>
+struct lhs_process_fraction_of_packet : lhs_process_one_packet<nr, LhsProgress, RhsProgress, LhsScalar, RhsScalar, ResScalar, AccPacket, LhsPacket, RhsPacket, ResPacket, GEBPTraits, LinearMapper, DataMapper>
+{
+
+EIGEN_STRONG_INLINE void peeled_kc_onestep(Index K, const LhsScalar* blA, const RhsScalar* blB, GEBPTraits traits, LhsPacket *A0, RhsPacket *B_0, RhsPacket *B1, RhsPacket *B2, RhsPacket *B3, AccPacket *C0, AccPacket *C1, AccPacket *C2, AccPacket *C3)
+ {
+ EIGEN_ASM_COMMENT("begin step of gebp micro kernel 1X4");
+ EIGEN_ASM_COMMENT("Note: these asm comments work around bug 935!");
+ traits.loadLhsUnaligned(&blA[(0+1*K)*(LhsProgress)], *A0);
+ traits.broadcastRhs(&blB[(0+4*K)*RhsProgress], *B_0, *B1, *B2, *B3);
+ traits.madd(*A0, *B_0, *C0, *B_0);
+ traits.madd(*A0, *B1, *C1, *B1);
+ traits.madd(*A0, *B2, *C2, *B2);
+ traits.madd(*A0, *B3, *C3, *B3);
+ EIGEN_ASM_COMMENT("end step of gebp micro kernel 1X4");
+ }
+};
+
+template<typename LhsScalar, typename RhsScalar, typename Index, typename DataMapper, int mr, int nr, bool ConjugateLhs, bool ConjugateRhs>
+EIGEN_DONT_INLINE
+void gebp_kernel<LhsScalar,RhsScalar,Index,DataMapper,mr,nr,ConjugateLhs,ConjugateRhs>
+ ::operator()(const DataMapper& res, const LhsScalar* blockA, const RhsScalar* blockB,
+ Index rows, Index depth, Index cols, ResScalar alpha,
+ Index strideA, Index strideB, Index offsetA, Index offsetB)
+ {
+ Traits traits;
+ SwappedTraits straits;
+
+ if(strideA==-1) strideA = depth;
+ if(strideB==-1) strideB = depth;
+ conj_helper<LhsScalar,RhsScalar,ConjugateLhs,ConjugateRhs> cj;
+ Index packet_cols4 = nr>=4 ? (cols/4) * 4 : 0;
+ Index packet_cols8 = nr>=8 ? (cols/8) * 8 : 0;
+ const Index peeled_mc3 = mr>=3*Traits::LhsProgress ? (rows/(3*LhsProgress))*(3*LhsProgress) : 0;
+ const Index peeled_mc2 = mr>=2*Traits::LhsProgress ? peeled_mc3+((rows-peeled_mc3)/(2*LhsProgress))*(2*LhsProgress) : 0;
+ const Index peeled_mc1 = mr>=1*Traits::LhsProgress ? peeled_mc2+((rows-peeled_mc2)/(1*LhsProgress))*(1*LhsProgress) : 0;
+ const Index peeled_mc_half = mr>=LhsProgressHalf ? peeled_mc1+((rows-peeled_mc1)/(LhsProgressHalf))*(LhsProgressHalf) : 0;
+ const Index peeled_mc_quarter = mr>=LhsProgressQuarter ? peeled_mc_half+((rows-peeled_mc_half)/(LhsProgressQuarter))*(LhsProgressQuarter) : 0;
+ enum { pk = 8 }; // NOTE Such a large peeling factor is important for large matrices (~ +5% when >1000 on Haswell)
+ const Index peeled_kc = depth & ~(pk-1);
+ const int prefetch_res_offset = 32/sizeof(ResScalar);
+// const Index depth2 = depth & ~1;
+
+ //---------- Process 3 * LhsProgress rows at once ----------
+ // This corresponds to 3*LhsProgress x nr register blocks.
+ // Usually, make sense only with FMA
+ if(mr>=3*Traits::LhsProgress)
+ {
+ // Here, the general idea is to loop on each largest micro horizontal panel of the lhs (3*Traits::LhsProgress x depth)
+ // and on each largest micro vertical panel of the rhs (depth * nr).
+ // Blocking sizes, i.e., 'depth' has been computed so that the micro horizontal panel of the lhs fit in L1.
+ // However, if depth is too small, we can extend the number of rows of these horizontal panels.
+ // This actual number of rows is computed as follow:
+ const Index l1 = defaultL1CacheSize; // in Bytes, TODO, l1 should be passed to this function.
+ // The max(1, ...) here is needed because we may be using blocking params larger than what our known l1 cache size
+ // suggests we should be using: either because our known l1 cache size is inaccurate (e.g. on Android, we can only guess),
+ // or because we are testing specific blocking sizes.
+ const Index actual_panel_rows = (3*LhsProgress) * std::max<Index>(1,( (l1 - sizeof(ResScalar)*mr*nr - depth*nr*sizeof(RhsScalar)) / (depth * sizeof(LhsScalar) * 3*LhsProgress) ));
+ for(Index i1=0; i1<peeled_mc3; i1+=actual_panel_rows)
+ {
+ const Index actual_panel_end = (std::min)(i1+actual_panel_rows, peeled_mc3);
+#if EIGEN_ARCH_ARM64
+ EIGEN_IF_CONSTEXPR(nr>=8) {
+ for(Index j2=0; j2<packet_cols8; j2+=8)
+ {
+ for(Index i=i1; i<actual_panel_end; i+=3*LhsProgress)
+ {
+ const LhsScalar* blA = &blockA[i*strideA+offsetA*(3*LhsProgress)];
+ prefetch(&blA[0]);
+ // gets res block as register
+ AccPacket C0, C1, C2, C3, C4, C5, C6, C7,
+ C8, C9, C10, C11, C12, C13, C14, C15,
+ C16, C17, C18, C19, C20, C21, C22, C23;
+ traits.initAcc(C0); traits.initAcc(C1); traits.initAcc(C2); traits.initAcc(C3);
+ traits.initAcc(C4); traits.initAcc(C5); traits.initAcc(C6); traits.initAcc(C7);
+ traits.initAcc(C8); traits.initAcc(C9); traits.initAcc(C10); traits.initAcc(C11);
+ traits.initAcc(C12); traits.initAcc(C13); traits.initAcc(C14); traits.initAcc(C15);
+ traits.initAcc(C16); traits.initAcc(C17); traits.initAcc(C18); traits.initAcc(C19);
+ traits.initAcc(C20); traits.initAcc(C21); traits.initAcc(C22); traits.initAcc(C23);
+
+ LinearMapper r0 = res.getLinearMapper(i, j2 + 0);
+ LinearMapper r1 = res.getLinearMapper(i, j2 + 1);
+ LinearMapper r2 = res.getLinearMapper(i, j2 + 2);
+ LinearMapper r3 = res.getLinearMapper(i, j2 + 3);
+ LinearMapper r4 = res.getLinearMapper(i, j2 + 4);
+ LinearMapper r5 = res.getLinearMapper(i, j2 + 5);
+ LinearMapper r6 = res.getLinearMapper(i, j2 + 6);
+ LinearMapper r7 = res.getLinearMapper(i, j2 + 7);
+
+ r0.prefetch(0);
+ r1.prefetch(0);
+ r2.prefetch(0);
+ r3.prefetch(0);
+ r4.prefetch(0);
+ r5.prefetch(0);
+ r6.prefetch(0);
+ r7.prefetch(0);
+
+ // performs "inner" products
+ const RhsScalar* blB = &blockB[j2*strideB+offsetB*8];
+ prefetch(&blB[0]);
+ LhsPacket A0, A1;
+ for(Index k=0; k<peeled_kc; k+=pk)
+ {
+ EIGEN_ASM_COMMENT("begin gebp micro kernel 3pX8");
+ // 27 registers are taken (24 for acc, 3 for lhs).
+ RhsPanel27 rhs_panel;
+ RhsPacket T0;
+ LhsPacket A2;
+ #if EIGEN_COMP_GNUC_STRICT && EIGEN_ARCH_ARM64 && defined(EIGEN_VECTORIZE_NEON) && !(EIGEN_GNUC_AT_LEAST(9,0))
+ // see http://eigen.tuxfamily.org/bz/show_bug.cgi?id=1633
+ // without this workaround A0, A1, and A2 are loaded in the same register,
+ // which is not good for pipelining
+ #define EIGEN_GEBP_3Px8_REGISTER_ALLOC_WORKAROUND __asm__ ("" : "+w,m" (A0), "+w,m" (A1), "+w,m" (A2));
+ #else
+ #define EIGEN_GEBP_3Px8_REGISTER_ALLOC_WORKAROUND
+ #endif
+
+#define EIGEN_GEBP_ONESTEP(K) \
+ do { \
+ EIGEN_ASM_COMMENT("begin step of gebp micro kernel 3pX8"); \
+ traits.loadLhs(&blA[(0 + 3 * K) * LhsProgress], A0); \
+ traits.loadLhs(&blA[(1 + 3 * K) * LhsProgress], A1); \
+ traits.loadLhs(&blA[(2 + 3 * K) * LhsProgress], A2); \
+ EIGEN_GEBP_3Px8_REGISTER_ALLOC_WORKAROUND \
+ traits.loadRhs(blB + (0 + 8 * K) * Traits::RhsProgress, rhs_panel); \
+ traits.madd(A0, rhs_panel, C0, T0, fix<0>); \
+ traits.madd(A1, rhs_panel, C8, T0, fix<0>); \
+ traits.madd(A2, rhs_panel, C16, T0, fix<0>); \
+ traits.updateRhs(blB + (1 + 8 * K) * Traits::RhsProgress, rhs_panel); \
+ traits.madd(A0, rhs_panel, C1, T0, fix<1>); \
+ traits.madd(A1, rhs_panel, C9, T0, fix<1>); \
+ traits.madd(A2, rhs_panel, C17, T0, fix<1>); \
+ traits.updateRhs(blB + (2 + 8 * K) * Traits::RhsProgress, rhs_panel); \
+ traits.madd(A0, rhs_panel, C2, T0, fix<2>); \
+ traits.madd(A1, rhs_panel, C10, T0, fix<2>); \
+ traits.madd(A2, rhs_panel, C18, T0, fix<2>); \
+ traits.updateRhs(blB + (3 + 8 * K) * Traits::RhsProgress, rhs_panel); \
+ traits.madd(A0, rhs_panel, C3, T0, fix<3>); \
+ traits.madd(A1, rhs_panel, C11, T0, fix<3>); \
+ traits.madd(A2, rhs_panel, C19, T0, fix<3>); \
+ traits.loadRhs(blB + (4 + 8 * K) * Traits::RhsProgress, rhs_panel); \
+ traits.madd(A0, rhs_panel, C4, T0, fix<0>); \
+ traits.madd(A1, rhs_panel, C12, T0, fix<0>); \
+ traits.madd(A2, rhs_panel, C20, T0, fix<0>); \
+ traits.updateRhs(blB + (5 + 8 * K) * Traits::RhsProgress, rhs_panel); \
+ traits.madd(A0, rhs_panel, C5, T0, fix<1>); \
+ traits.madd(A1, rhs_panel, C13, T0, fix<1>); \
+ traits.madd(A2, rhs_panel, C21, T0, fix<1>); \
+ traits.updateRhs(blB + (6 + 8 * K) * Traits::RhsProgress, rhs_panel); \
+ traits.madd(A0, rhs_panel, C6, T0, fix<2>); \
+ traits.madd(A1, rhs_panel, C14, T0, fix<2>); \
+ traits.madd(A2, rhs_panel, C22, T0, fix<2>); \
+ traits.updateRhs(blB + (7 + 8 * K) * Traits::RhsProgress, rhs_panel); \
+ traits.madd(A0, rhs_panel, C7, T0, fix<3>); \
+ traits.madd(A1, rhs_panel, C15, T0, fix<3>); \
+ traits.madd(A2, rhs_panel, C23, T0, fix<3>); \
+ EIGEN_ASM_COMMENT("end step of gebp micro kernel 3pX8"); \
+ } while (false)
+
+ EIGEN_GEBP_ONESTEP(0);
+ EIGEN_GEBP_ONESTEP(1);
+ EIGEN_GEBP_ONESTEP(2);
+ EIGEN_GEBP_ONESTEP(3);
+ EIGEN_GEBP_ONESTEP(4);
+ EIGEN_GEBP_ONESTEP(5);
+ EIGEN_GEBP_ONESTEP(6);
+ EIGEN_GEBP_ONESTEP(7);
+
+ blB += pk * 8 * RhsProgress;
+ blA += pk * 3 * Traits::LhsProgress;
+ EIGEN_ASM_COMMENT("end gebp micro kernel 3pX8");
+ }
+
+ // process remaining peeled loop
+ for (Index k = peeled_kc; k < depth; k++)
+ {
+
+ RhsPanel27 rhs_panel;
+ RhsPacket T0;
+ LhsPacket A2;
+ EIGEN_GEBP_ONESTEP(0);
+ blB += 8 * RhsProgress;
+ blA += 3 * Traits::LhsProgress;
+ }
+
+ #undef EIGEN_GEBP_ONESTEP
+
+ ResPacket R0, R1, R2;
+ ResPacket alphav = pset1<ResPacket>(alpha);
+
+ R0 = r0.template loadPacket<ResPacket>(0 * Traits::ResPacketSize);
+ R1 = r0.template loadPacket<ResPacket>(1 * Traits::ResPacketSize);
+ R2 = r0.template loadPacket<ResPacket>(2 * Traits::ResPacketSize);
+ traits.acc(C0, alphav, R0);
+ traits.acc(C8, alphav, R1);
+ traits.acc(C16, alphav, R2);
+ r0.storePacket(0 * Traits::ResPacketSize, R0);
+ r0.storePacket(1 * Traits::ResPacketSize, R1);
+ r0.storePacket(2 * Traits::ResPacketSize, R2);
+
+ R0 = r1.template loadPacket<ResPacket>(0 * Traits::ResPacketSize);
+ R1 = r1.template loadPacket<ResPacket>(1 * Traits::ResPacketSize);
+ R2 = r1.template loadPacket<ResPacket>(2 * Traits::ResPacketSize);
+ traits.acc(C1, alphav, R0);
+ traits.acc(C9, alphav, R1);
+ traits.acc(C17, alphav, R2);
+ r1.storePacket(0 * Traits::ResPacketSize, R0);
+ r1.storePacket(1 * Traits::ResPacketSize, R1);
+ r1.storePacket(2 * Traits::ResPacketSize, R2);
+
+ R0 = r2.template loadPacket<ResPacket>(0 * Traits::ResPacketSize);
+ R1 = r2.template loadPacket<ResPacket>(1 * Traits::ResPacketSize);
+ R2 = r2.template loadPacket<ResPacket>(2 * Traits::ResPacketSize);
+ traits.acc(C2, alphav, R0);
+ traits.acc(C10, alphav, R1);
+ traits.acc(C18, alphav, R2);
+ r2.storePacket(0 * Traits::ResPacketSize, R0);
+ r2.storePacket(1 * Traits::ResPacketSize, R1);
+ r2.storePacket(2 * Traits::ResPacketSize, R2);
+
+ R0 = r3.template loadPacket<ResPacket>(0 * Traits::ResPacketSize);
+ R1 = r3.template loadPacket<ResPacket>(1 * Traits::ResPacketSize);
+ R2 = r3.template loadPacket<ResPacket>(2 * Traits::ResPacketSize);
+ traits.acc(C3, alphav, R0);
+ traits.acc(C11, alphav, R1);
+ traits.acc(C19, alphav, R2);
+ r3.storePacket(0 * Traits::ResPacketSize, R0);
+ r3.storePacket(1 * Traits::ResPacketSize, R1);
+ r3.storePacket(2 * Traits::ResPacketSize, R2);
+
+ R0 = r4.template loadPacket<ResPacket>(0 * Traits::ResPacketSize);
+ R1 = r4.template loadPacket<ResPacket>(1 * Traits::ResPacketSize);
+ R2 = r4.template loadPacket<ResPacket>(2 * Traits::ResPacketSize);
+ traits.acc(C4, alphav, R0);
+ traits.acc(C12, alphav, R1);
+ traits.acc(C20, alphav, R2);
+ r4.storePacket(0 * Traits::ResPacketSize, R0);
+ r4.storePacket(1 * Traits::ResPacketSize, R1);
+ r4.storePacket(2 * Traits::ResPacketSize, R2);
+
+ R0 = r5.template loadPacket<ResPacket>(0 * Traits::ResPacketSize);
+ R1 = r5.template loadPacket<ResPacket>(1 * Traits::ResPacketSize);
+ R2 = r5.template loadPacket<ResPacket>(2 * Traits::ResPacketSize);
+ traits.acc(C5, alphav, R0);
+ traits.acc(C13, alphav, R1);
+ traits.acc(C21, alphav, R2);
+ r5.storePacket(0 * Traits::ResPacketSize, R0);
+ r5.storePacket(1 * Traits::ResPacketSize, R1);
+ r5.storePacket(2 * Traits::ResPacketSize, R2);
+
+ R0 = r6.template loadPacket<ResPacket>(0 * Traits::ResPacketSize);
+ R1 = r6.template loadPacket<ResPacket>(1 * Traits::ResPacketSize);
+ R2 = r6.template loadPacket<ResPacket>(2 * Traits::ResPacketSize);
+ traits.acc(C6, alphav, R0);
+ traits.acc(C14, alphav, R1);
+ traits.acc(C22, alphav, R2);
+ r6.storePacket(0 * Traits::ResPacketSize, R0);
+ r6.storePacket(1 * Traits::ResPacketSize, R1);
+ r6.storePacket(2 * Traits::ResPacketSize, R2);
+
+ R0 = r7.template loadPacket<ResPacket>(0 * Traits::ResPacketSize);
+ R1 = r7.template loadPacket<ResPacket>(1 * Traits::ResPacketSize);
+ R2 = r7.template loadPacket<ResPacket>(2 * Traits::ResPacketSize);
+ traits.acc(C7, alphav, R0);
+ traits.acc(C15, alphav, R1);
+ traits.acc(C23, alphav, R2);
+ r7.storePacket(0 * Traits::ResPacketSize, R0);
+ r7.storePacket(1 * Traits::ResPacketSize, R1);
+ r7.storePacket(2 * Traits::ResPacketSize, R2);
+ }
+ }
+ }
+#endif
+ for(Index j2=packet_cols8; j2<packet_cols4; j2+=4)
+ {
+ for(Index i=i1; i<actual_panel_end; i+=3*LhsProgress)
+ {
+
+ // We selected a 3*Traits::LhsProgress x nr micro block of res which is entirely
+ // stored into 3 x nr registers.
+
+ const LhsScalar* blA = &blockA[i*strideA+offsetA*(3*LhsProgress)];
+ prefetch(&blA[0]);
+
+ // gets res block as register
+ AccPacket C0, C1, C2, C3,
+ C4, C5, C6, C7,
+ C8, C9, C10, C11;
+ traits.initAcc(C0); traits.initAcc(C1); traits.initAcc(C2); traits.initAcc(C3);
+ traits.initAcc(C4); traits.initAcc(C5); traits.initAcc(C6); traits.initAcc(C7);
+ traits.initAcc(C8); traits.initAcc(C9); traits.initAcc(C10); traits.initAcc(C11);
+
+ LinearMapper r0 = res.getLinearMapper(i, j2 + 0);
+ LinearMapper r1 = res.getLinearMapper(i, j2 + 1);
+ LinearMapper r2 = res.getLinearMapper(i, j2 + 2);
+ LinearMapper r3 = res.getLinearMapper(i, j2 + 3);
+
+ r0.prefetch(0);
+ r1.prefetch(0);
+ r2.prefetch(0);
+ r3.prefetch(0);
+
+ // performs "inner" products
+ const RhsScalar* blB = &blockB[j2*strideB+offsetB*4];
+ prefetch(&blB[0]);
+ LhsPacket A0, A1;
+
+ for(Index k=0; k<peeled_kc; k+=pk)
+ {
+ EIGEN_ASM_COMMENT("begin gebp micro kernel 3pX4");
+ // 15 registers are taken (12 for acc, 3 for lhs).
+ RhsPanel15 rhs_panel;
+ RhsPacket T0;
+ LhsPacket A2;
+ #if EIGEN_COMP_GNUC_STRICT && EIGEN_ARCH_ARM64 && defined(EIGEN_VECTORIZE_NEON) && !(EIGEN_GNUC_AT_LEAST(9,0))
+ // see http://eigen.tuxfamily.org/bz/show_bug.cgi?id=1633
+ // without this workaround A0, A1, and A2 are loaded in the same register,
+ // which is not good for pipelining
+ #define EIGEN_GEBP_3PX4_REGISTER_ALLOC_WORKAROUND __asm__ ("" : "+w,m" (A0), "+w,m" (A1), "+w,m" (A2));
+ #else
+ #define EIGEN_GEBP_3PX4_REGISTER_ALLOC_WORKAROUND
+ #endif
+#define EIGEN_GEBP_ONESTEP(K) \
+ do { \
+ EIGEN_ASM_COMMENT("begin step of gebp micro kernel 3pX4"); \
+ EIGEN_ASM_COMMENT("Note: these asm comments work around bug 935!"); \
+ internal::prefetch(blA + (3 * K + 16) * LhsProgress); \
+ if (EIGEN_ARCH_ARM || EIGEN_ARCH_MIPS) { \
+ internal::prefetch(blB + (4 * K + 16) * RhsProgress); \
+ } /* Bug 953 */ \
+ traits.loadLhs(&blA[(0 + 3 * K) * LhsProgress], A0); \
+ traits.loadLhs(&blA[(1 + 3 * K) * LhsProgress], A1); \
+ traits.loadLhs(&blA[(2 + 3 * K) * LhsProgress], A2); \
+ EIGEN_GEBP_3PX4_REGISTER_ALLOC_WORKAROUND \
+ traits.loadRhs(blB + (0+4*K) * Traits::RhsProgress, rhs_panel); \
+ traits.madd(A0, rhs_panel, C0, T0, fix<0>); \
+ traits.madd(A1, rhs_panel, C4, T0, fix<0>); \
+ traits.madd(A2, rhs_panel, C8, T0, fix<0>); \
+ traits.updateRhs(blB + (1+4*K) * Traits::RhsProgress, rhs_panel); \
+ traits.madd(A0, rhs_panel, C1, T0, fix<1>); \
+ traits.madd(A1, rhs_panel, C5, T0, fix<1>); \
+ traits.madd(A2, rhs_panel, C9, T0, fix<1>); \
+ traits.updateRhs(blB + (2+4*K) * Traits::RhsProgress, rhs_panel); \
+ traits.madd(A0, rhs_panel, C2, T0, fix<2>); \
+ traits.madd(A1, rhs_panel, C6, T0, fix<2>); \
+ traits.madd(A2, rhs_panel, C10, T0, fix<2>); \
+ traits.updateRhs(blB + (3+4*K) * Traits::RhsProgress, rhs_panel); \
+ traits.madd(A0, rhs_panel, C3, T0, fix<3>); \
+ traits.madd(A1, rhs_panel, C7, T0, fix<3>); \
+ traits.madd(A2, rhs_panel, C11, T0, fix<3>); \
+ EIGEN_ASM_COMMENT("end step of gebp micro kernel 3pX4"); \
+ } while (false)
+
+ internal::prefetch(blB);
+ EIGEN_GEBP_ONESTEP(0);
+ EIGEN_GEBP_ONESTEP(1);
+ EIGEN_GEBP_ONESTEP(2);
+ EIGEN_GEBP_ONESTEP(3);
+ EIGEN_GEBP_ONESTEP(4);
+ EIGEN_GEBP_ONESTEP(5);
+ EIGEN_GEBP_ONESTEP(6);
+ EIGEN_GEBP_ONESTEP(7);
+
+ blB += pk*4*RhsProgress;
+ blA += pk*3*Traits::LhsProgress;
+
+ EIGEN_ASM_COMMENT("end gebp micro kernel 3pX4");
+ }
+ // process remaining peeled loop
+ for(Index k=peeled_kc; k<depth; k++)
+ {
+ RhsPanel15 rhs_panel;
+ RhsPacket T0;
+ LhsPacket A2;
+ EIGEN_GEBP_ONESTEP(0);
+ blB += 4*RhsProgress;
+ blA += 3*Traits::LhsProgress;
+ }
+
+#undef EIGEN_GEBP_ONESTEP
+
+ ResPacket R0, R1, R2;
+ ResPacket alphav = pset1<ResPacket>(alpha);
+
+ R0 = r0.template loadPacket<ResPacket>(0 * Traits::ResPacketSize);
+ R1 = r0.template loadPacket<ResPacket>(1 * Traits::ResPacketSize);
+ R2 = r0.template loadPacket<ResPacket>(2 * Traits::ResPacketSize);
+ traits.acc(C0, alphav, R0);
+ traits.acc(C4, alphav, R1);
+ traits.acc(C8, alphav, R2);
+ r0.storePacket(0 * Traits::ResPacketSize, R0);
+ r0.storePacket(1 * Traits::ResPacketSize, R1);
+ r0.storePacket(2 * Traits::ResPacketSize, R2);
+
+ R0 = r1.template loadPacket<ResPacket>(0 * Traits::ResPacketSize);
+ R1 = r1.template loadPacket<ResPacket>(1 * Traits::ResPacketSize);
+ R2 = r1.template loadPacket<ResPacket>(2 * Traits::ResPacketSize);
+ traits.acc(C1, alphav, R0);
+ traits.acc(C5, alphav, R1);
+ traits.acc(C9, alphav, R2);
+ r1.storePacket(0 * Traits::ResPacketSize, R0);
+ r1.storePacket(1 * Traits::ResPacketSize, R1);
+ r1.storePacket(2 * Traits::ResPacketSize, R2);
+
+ R0 = r2.template loadPacket<ResPacket>(0 * Traits::ResPacketSize);
+ R1 = r2.template loadPacket<ResPacket>(1 * Traits::ResPacketSize);
+ R2 = r2.template loadPacket<ResPacket>(2 * Traits::ResPacketSize);
+ traits.acc(C2, alphav, R0);
+ traits.acc(C6, alphav, R1);
+ traits.acc(C10, alphav, R2);
+ r2.storePacket(0 * Traits::ResPacketSize, R0);
+ r2.storePacket(1 * Traits::ResPacketSize, R1);
+ r2.storePacket(2 * Traits::ResPacketSize, R2);
+
+ R0 = r3.template loadPacket<ResPacket>(0 * Traits::ResPacketSize);
+ R1 = r3.template loadPacket<ResPacket>(1 * Traits::ResPacketSize);
+ R2 = r3.template loadPacket<ResPacket>(2 * Traits::ResPacketSize);
+ traits.acc(C3, alphav, R0);
+ traits.acc(C7, alphav, R1);
+ traits.acc(C11, alphav, R2);
+ r3.storePacket(0 * Traits::ResPacketSize, R0);
+ r3.storePacket(1 * Traits::ResPacketSize, R1);
+ r3.storePacket(2 * Traits::ResPacketSize, R2);
+ }
+ }
+
+ // Deal with remaining columns of the rhs
+ for(Index j2=packet_cols4; j2<cols; j2++)
+ {
+ for(Index i=i1; i<actual_panel_end; i+=3*LhsProgress)
+ {
+ // One column at a time
+ const LhsScalar* blA = &blockA[i*strideA+offsetA*(3*Traits::LhsProgress)];
+ prefetch(&blA[0]);
+
+ // gets res block as register
+ AccPacket C0, C4, C8;
+ traits.initAcc(C0);
+ traits.initAcc(C4);
+ traits.initAcc(C8);
+
+ LinearMapper r0 = res.getLinearMapper(i, j2);
+ r0.prefetch(0);
+
+ // performs "inner" products
+ const RhsScalar* blB = &blockB[j2*strideB+offsetB];
+ LhsPacket A0, A1, A2;
+
+ for(Index k=0; k<peeled_kc; k+=pk)
+ {
+ EIGEN_ASM_COMMENT("begin gebp micro kernel 3pX1");
+ RhsPacket B_0;
+#define EIGEN_GEBGP_ONESTEP(K) \
+ do { \
+ EIGEN_ASM_COMMENT("begin step of gebp micro kernel 3pX1"); \
+ EIGEN_ASM_COMMENT("Note: these asm comments work around bug 935!"); \
+ traits.loadLhs(&blA[(0 + 3 * K) * LhsProgress], A0); \
+ traits.loadLhs(&blA[(1 + 3 * K) * LhsProgress], A1); \
+ traits.loadLhs(&blA[(2 + 3 * K) * LhsProgress], A2); \
+ traits.loadRhs(&blB[(0 + K) * RhsProgress], B_0); \
+ traits.madd(A0, B_0, C0, B_0, fix<0>); \
+ traits.madd(A1, B_0, C4, B_0, fix<0>); \
+ traits.madd(A2, B_0, C8, B_0, fix<0>); \
+ EIGEN_ASM_COMMENT("end step of gebp micro kernel 3pX1"); \
+ } while (false)
+
+ EIGEN_GEBGP_ONESTEP(0);
+ EIGEN_GEBGP_ONESTEP(1);
+ EIGEN_GEBGP_ONESTEP(2);
+ EIGEN_GEBGP_ONESTEP(3);
+ EIGEN_GEBGP_ONESTEP(4);
+ EIGEN_GEBGP_ONESTEP(5);
+ EIGEN_GEBGP_ONESTEP(6);
+ EIGEN_GEBGP_ONESTEP(7);
+
+ blB += int(pk) * int(RhsProgress);
+ blA += int(pk) * 3 * int(Traits::LhsProgress);
+
+ EIGEN_ASM_COMMENT("end gebp micro kernel 3pX1");
+ }
+
+ // process remaining peeled loop
+ for(Index k=peeled_kc; k<depth; k++)
+ {
+ RhsPacket B_0;
+ EIGEN_GEBGP_ONESTEP(0);
+ blB += RhsProgress;
+ blA += 3*Traits::LhsProgress;
+ }
+#undef EIGEN_GEBGP_ONESTEP
+ ResPacket R0, R1, R2;
+ ResPacket alphav = pset1<ResPacket>(alpha);
+
+ R0 = r0.template loadPacket<ResPacket>(0 * Traits::ResPacketSize);
+ R1 = r0.template loadPacket<ResPacket>(1 * Traits::ResPacketSize);
+ R2 = r0.template loadPacket<ResPacket>(2 * Traits::ResPacketSize);
+ traits.acc(C0, alphav, R0);
+ traits.acc(C4, alphav, R1);
+ traits.acc(C8, alphav, R2);
+ r0.storePacket(0 * Traits::ResPacketSize, R0);
+ r0.storePacket(1 * Traits::ResPacketSize, R1);
+ r0.storePacket(2 * Traits::ResPacketSize, R2);
+ }
+ }
+ }
+ }
+
+ //---------- Process 2 * LhsProgress rows at once ----------
+ if(mr>=2*Traits::LhsProgress)
+ {
+ const Index l1 = defaultL1CacheSize; // in Bytes, TODO, l1 should be passed to this function.
+ // The max(1, ...) here is needed because we may be using blocking params larger than what our known l1 cache size
+ // suggests we should be using: either because our known l1 cache size is inaccurate (e.g. on Android, we can only guess),
+ // or because we are testing specific blocking sizes.
+ Index actual_panel_rows = (2*LhsProgress) * std::max<Index>(1,( (l1 - sizeof(ResScalar)*mr*nr - depth*nr*sizeof(RhsScalar)) / (depth * sizeof(LhsScalar) * 2*LhsProgress) ));
+
+ for(Index i1=peeled_mc3; i1<peeled_mc2; i1+=actual_panel_rows)
+ {
+ Index actual_panel_end = (std::min)(i1+actual_panel_rows, peeled_mc2);
+#if EIGEN_ARCH_ARM64
+ EIGEN_IF_CONSTEXPR(nr>=8) {
+ for(Index j2=0; j2<packet_cols8; j2+=8)
+ {
+ for(Index i=i1; i<actual_panel_end; i+=2*LhsProgress)
+ {
+ const LhsScalar* blA = &blockA[i*strideA+offsetA*(2*Traits::LhsProgress)];
+ prefetch(&blA[0]);
+
+ AccPacket C0, C1, C2, C3, C4, C5, C6, C7,
+ C8, C9, C10, C11, C12, C13, C14, C15;
+ traits.initAcc(C0); traits.initAcc(C1); traits.initAcc(C2); traits.initAcc(C3);
+ traits.initAcc(C4); traits.initAcc(C5); traits.initAcc(C6); traits.initAcc(C7);
+ traits.initAcc(C8); traits.initAcc(C9); traits.initAcc(C10); traits.initAcc(C11);
+ traits.initAcc(C12); traits.initAcc(C13); traits.initAcc(C14); traits.initAcc(C15);
+
+ LinearMapper r0 = res.getLinearMapper(i, j2 + 0);
+ LinearMapper r1 = res.getLinearMapper(i, j2 + 1);
+ LinearMapper r2 = res.getLinearMapper(i, j2 + 2);
+ LinearMapper r3 = res.getLinearMapper(i, j2 + 3);
+ LinearMapper r4 = res.getLinearMapper(i, j2 + 4);
+ LinearMapper r5 = res.getLinearMapper(i, j2 + 5);
+ LinearMapper r6 = res.getLinearMapper(i, j2 + 6);
+ LinearMapper r7 = res.getLinearMapper(i, j2 + 7);
+ r0.prefetch(prefetch_res_offset);
+ r1.prefetch(prefetch_res_offset);
+ r2.prefetch(prefetch_res_offset);
+ r3.prefetch(prefetch_res_offset);
+ r4.prefetch(prefetch_res_offset);
+ r5.prefetch(prefetch_res_offset);
+ r6.prefetch(prefetch_res_offset);
+ r7.prefetch(prefetch_res_offset);
+
+ const RhsScalar* blB = &blockB[j2*strideB+offsetB*8];
+ prefetch(&blB[0]);
+ LhsPacket A0, A1;
+ for(Index k=0; k<peeled_kc; k+=pk)
+ {
+ RhsPacketx4 rhs_panel;
+ RhsPacket T0;
+ // NOTE: the begin/end asm comments below work around bug 935!
+ // but they are not enough for gcc>=6 without FMA (bug 1637)
+ #if EIGEN_GNUC_AT_LEAST(6,0) && defined(EIGEN_VECTORIZE_SSE)
+ #define EIGEN_GEBP_2Px8_SPILLING_WORKAROUND __asm__ ("" : [a0] "+x,m" (A0),[a1] "+x,m" (A1));
+ #else
+ #define EIGEN_GEBP_2Px8_SPILLING_WORKAROUND
+ #endif
+#define EIGEN_GEBGP_ONESTEP(K) \
+ do { \
+ EIGEN_ASM_COMMENT("begin step of gebp micro kernel 2pX8"); \
+ traits.loadLhs(&blA[(0 + 2 * K) * LhsProgress], A0); \
+ traits.loadLhs(&blA[(1 + 2 * K) * LhsProgress], A1); \
+ traits.loadRhs(&blB[(0 + 8 * K) * RhsProgress], rhs_panel); \
+ traits.madd(A0, rhs_panel, C0, T0, fix<0>); \
+ traits.madd(A1, rhs_panel, C8, T0, fix<0>); \
+ traits.updateRhs(&blB[(1 + 8 * K) * RhsProgress], rhs_panel); \
+ traits.madd(A0, rhs_panel, C1, T0, fix<1>); \
+ traits.madd(A1, rhs_panel, C9, T0, fix<1>); \
+ traits.updateRhs(&blB[(2 + 8 * K) * RhsProgress], rhs_panel); \
+ traits.madd(A0, rhs_panel, C2, T0, fix<2>); \
+ traits.madd(A1, rhs_panel, C10, T0, fix<2>); \
+ traits.updateRhs(&blB[(3 + 8 * K) * RhsProgress], rhs_panel); \
+ traits.madd(A0, rhs_panel, C3, T0, fix<3>); \
+ traits.madd(A1, rhs_panel, C11, T0, fix<3>); \
+ traits.loadRhs(&blB[(4 + 8 * K) * RhsProgress], rhs_panel); \
+ traits.madd(A0, rhs_panel, C4, T0, fix<0>); \
+ traits.madd(A1, rhs_panel, C12, T0, fix<0>); \
+ traits.updateRhs(&blB[(5 + 8 * K) * RhsProgress], rhs_panel); \
+ traits.madd(A0, rhs_panel, C5, T0, fix<1>); \
+ traits.madd(A1, rhs_panel, C13, T0, fix<1>); \
+ traits.updateRhs(&blB[(6 + 8 * K) * RhsProgress], rhs_panel); \
+ traits.madd(A0, rhs_panel, C6, T0, fix<2>); \
+ traits.madd(A1, rhs_panel, C14, T0, fix<2>); \
+ traits.updateRhs(&blB[(7 + 8 * K) * RhsProgress], rhs_panel); \
+ traits.madd(A0, rhs_panel, C7, T0, fix<3>); \
+ traits.madd(A1, rhs_panel, C15, T0, fix<3>); \
+ EIGEN_GEBP_2Px8_SPILLING_WORKAROUND \
+ EIGEN_ASM_COMMENT("end step of gebp micro kernel 2pX8"); \
+ } while (false)
+
+ EIGEN_ASM_COMMENT("begin gebp micro kernel 2pX8");
+
+ EIGEN_GEBGP_ONESTEP(0);
+ EIGEN_GEBGP_ONESTEP(1);
+ EIGEN_GEBGP_ONESTEP(2);
+ EIGEN_GEBGP_ONESTEP(3);
+ EIGEN_GEBGP_ONESTEP(4);
+ EIGEN_GEBGP_ONESTEP(5);
+ EIGEN_GEBGP_ONESTEP(6);
+ EIGEN_GEBGP_ONESTEP(7);
+
+ blB += pk*8*RhsProgress;
+ blA += pk*(2*Traits::LhsProgress);
+
+ EIGEN_ASM_COMMENT("end gebp micro kernel 2pX8");
+ }
+ // process remaining peeled loop
+ for(Index k=peeled_kc; k<depth; k++)
+ {
+ RhsPacketx4 rhs_panel;
+ RhsPacket T0;
+ EIGEN_GEBGP_ONESTEP(0);
+ blB += 8*RhsProgress;
+ blA += 2*Traits::LhsProgress;
+ }
+
+#undef EIGEN_GEBGP_ONESTEP
+
+ ResPacket R0, R1, R2, R3;
+ ResPacket alphav = pset1<ResPacket>(alpha);
+
+ R0 = r0.template loadPacket<ResPacket>(0 * Traits::ResPacketSize);
+ R1 = r0.template loadPacket<ResPacket>(1 * Traits::ResPacketSize);
+ R2 = r1.template loadPacket<ResPacket>(0 * Traits::ResPacketSize);
+ R3 = r1.template loadPacket<ResPacket>(1 * Traits::ResPacketSize);
+ traits.acc(C0, alphav, R0);
+ traits.acc(C8, alphav, R1);
+ traits.acc(C1, alphav, R2);
+ traits.acc(C9, alphav, R3);
+ r0.storePacket(0 * Traits::ResPacketSize, R0);
+ r0.storePacket(1 * Traits::ResPacketSize, R1);
+ r1.storePacket(0 * Traits::ResPacketSize, R2);
+ r1.storePacket(1 * Traits::ResPacketSize, R3);
+
+ R0 = r2.template loadPacket<ResPacket>(0 * Traits::ResPacketSize);
+ R1 = r2.template loadPacket<ResPacket>(1 * Traits::ResPacketSize);
+ R2 = r3.template loadPacket<ResPacket>(0 * Traits::ResPacketSize);
+ R3 = r3.template loadPacket<ResPacket>(1 * Traits::ResPacketSize);
+ traits.acc(C2, alphav, R0);
+ traits.acc(C10, alphav, R1);
+ traits.acc(C3, alphav, R2);
+ traits.acc(C11, alphav, R3);
+ r2.storePacket(0 * Traits::ResPacketSize, R0);
+ r2.storePacket(1 * Traits::ResPacketSize, R1);
+ r3.storePacket(0 * Traits::ResPacketSize, R2);
+ r3.storePacket(1 * Traits::ResPacketSize, R3);
+
+ R0 = r4.template loadPacket<ResPacket>(0 * Traits::ResPacketSize);
+ R1 = r4.template loadPacket<ResPacket>(1 * Traits::ResPacketSize);
+ R2 = r5.template loadPacket<ResPacket>(0 * Traits::ResPacketSize);
+ R3 = r5.template loadPacket<ResPacket>(1 * Traits::ResPacketSize);
+ traits.acc(C4, alphav, R0);
+ traits.acc(C12, alphav, R1);
+ traits.acc(C5, alphav, R2);
+ traits.acc(C13, alphav, R3);
+ r4.storePacket(0 * Traits::ResPacketSize, R0);
+ r4.storePacket(1 * Traits::ResPacketSize, R1);
+ r5.storePacket(0 * Traits::ResPacketSize, R2);
+ r5.storePacket(1 * Traits::ResPacketSize, R3);
+
+ R0 = r6.template loadPacket<ResPacket>(0 * Traits::ResPacketSize);
+ R1 = r6.template loadPacket<ResPacket>(1 * Traits::ResPacketSize);
+ R2 = r7.template loadPacket<ResPacket>(0 * Traits::ResPacketSize);
+ R3 = r7.template loadPacket<ResPacket>(1 * Traits::ResPacketSize);
+ traits.acc(C6, alphav, R0);
+ traits.acc(C14, alphav, R1);
+ traits.acc(C7, alphav, R2);
+ traits.acc(C15, alphav, R3);
+ r6.storePacket(0 * Traits::ResPacketSize, R0);
+ r6.storePacket(1 * Traits::ResPacketSize, R1);
+ r7.storePacket(0 * Traits::ResPacketSize, R2);
+ r7.storePacket(1 * Traits::ResPacketSize, R3);
+ }
+ }
+ }
+#endif
+ for(Index j2=packet_cols8; j2<packet_cols4; j2+=4)
+ {
+ for(Index i=i1; i<actual_panel_end; i+=2*LhsProgress)
+ {
+
+ // We selected a 2*Traits::LhsProgress x nr micro block of res which is entirely
+ // stored into 2 x nr registers.
+
+ const LhsScalar* blA = &blockA[i*strideA+offsetA*(2*Traits::LhsProgress)];
+ prefetch(&blA[0]);
+
+ // gets res block as register
+ AccPacket C0, C1, C2, C3,
+ C4, C5, C6, C7;
+ traits.initAcc(C0); traits.initAcc(C1); traits.initAcc(C2); traits.initAcc(C3);
+ traits.initAcc(C4); traits.initAcc(C5); traits.initAcc(C6); traits.initAcc(C7);
+
+ LinearMapper r0 = res.getLinearMapper(i, j2 + 0);
+ LinearMapper r1 = res.getLinearMapper(i, j2 + 1);
+ LinearMapper r2 = res.getLinearMapper(i, j2 + 2);
+ LinearMapper r3 = res.getLinearMapper(i, j2 + 3);
+
+ r0.prefetch(prefetch_res_offset);
+ r1.prefetch(prefetch_res_offset);
+ r2.prefetch(prefetch_res_offset);
+ r3.prefetch(prefetch_res_offset);
+
+ // performs "inner" products
+ const RhsScalar* blB = &blockB[j2*strideB+offsetB*4];
+ prefetch(&blB[0]);
+ LhsPacket A0, A1;
+
+ for(Index k=0; k<peeled_kc; k+=pk)
+ {
+ EIGEN_ASM_COMMENT("begin gebp micro kernel 2pX4");
+ RhsPacketx4 rhs_panel;
+ RhsPacket T0;
+
+ // NOTE: the begin/end asm comments below work around bug 935!
+ // but they are not enough for gcc>=6 without FMA (bug 1637)
+ #if EIGEN_GNUC_AT_LEAST(6,0) && defined(EIGEN_VECTORIZE_SSE) && !(EIGEN_COMP_LCC)
+ #define EIGEN_GEBP_2PX4_SPILLING_WORKAROUND __asm__ ("" : [a0] "+x,m" (A0),[a1] "+x,m" (A1));
+ #else
+ #define EIGEN_GEBP_2PX4_SPILLING_WORKAROUND
+ #endif
+#define EIGEN_GEBGP_ONESTEP(K) \
+ do { \
+ EIGEN_ASM_COMMENT("begin step of gebp micro kernel 2pX4"); \
+ traits.loadLhs(&blA[(0 + 2 * K) * LhsProgress], A0); \
+ traits.loadLhs(&blA[(1 + 2 * K) * LhsProgress], A1); \
+ traits.loadRhs(&blB[(0 + 4 * K) * RhsProgress], rhs_panel); \
+ traits.madd(A0, rhs_panel, C0, T0, fix<0>); \
+ traits.madd(A1, rhs_panel, C4, T0, fix<0>); \
+ traits.madd(A0, rhs_panel, C1, T0, fix<1>); \
+ traits.madd(A1, rhs_panel, C5, T0, fix<1>); \
+ traits.madd(A0, rhs_panel, C2, T0, fix<2>); \
+ traits.madd(A1, rhs_panel, C6, T0, fix<2>); \
+ traits.madd(A0, rhs_panel, C3, T0, fix<3>); \
+ traits.madd(A1, rhs_panel, C7, T0, fix<3>); \
+ EIGEN_GEBP_2PX4_SPILLING_WORKAROUND \
+ EIGEN_ASM_COMMENT("end step of gebp micro kernel 2pX4"); \
+ } while (false)
+
+ internal::prefetch(blB+(48+0));
+ EIGEN_GEBGP_ONESTEP(0);
+ EIGEN_GEBGP_ONESTEP(1);
+ EIGEN_GEBGP_ONESTEP(2);
+ EIGEN_GEBGP_ONESTEP(3);
+ internal::prefetch(blB+(48+16));
+ EIGEN_GEBGP_ONESTEP(4);
+ EIGEN_GEBGP_ONESTEP(5);
+ EIGEN_GEBGP_ONESTEP(6);
+ EIGEN_GEBGP_ONESTEP(7);
+
+ blB += pk*4*RhsProgress;
+ blA += pk*(2*Traits::LhsProgress);
+
+ EIGEN_ASM_COMMENT("end gebp micro kernel 2pX4");
+ }
+ // process remaining peeled loop
+ for(Index k=peeled_kc; k<depth; k++)
+ {
+ RhsPacketx4 rhs_panel;
+ RhsPacket T0;
+ EIGEN_GEBGP_ONESTEP(0);
+ blB += 4*RhsProgress;
+ blA += 2*Traits::LhsProgress;
+ }
+#undef EIGEN_GEBGP_ONESTEP
+
+ ResPacket R0, R1, R2, R3;
+ ResPacket alphav = pset1<ResPacket>(alpha);
+
+ R0 = r0.template loadPacket<ResPacket>(0 * Traits::ResPacketSize);
+ R1 = r0.template loadPacket<ResPacket>(1 * Traits::ResPacketSize);
+ R2 = r1.template loadPacket<ResPacket>(0 * Traits::ResPacketSize);
+ R3 = r1.template loadPacket<ResPacket>(1 * Traits::ResPacketSize);
+ traits.acc(C0, alphav, R0);
+ traits.acc(C4, alphav, R1);
+ traits.acc(C1, alphav, R2);
+ traits.acc(C5, alphav, R3);
+ r0.storePacket(0 * Traits::ResPacketSize, R0);
+ r0.storePacket(1 * Traits::ResPacketSize, R1);
+ r1.storePacket(0 * Traits::ResPacketSize, R2);
+ r1.storePacket(1 * Traits::ResPacketSize, R3);
+
+ R0 = r2.template loadPacket<ResPacket>(0 * Traits::ResPacketSize);
+ R1 = r2.template loadPacket<ResPacket>(1 * Traits::ResPacketSize);
+ R2 = r3.template loadPacket<ResPacket>(0 * Traits::ResPacketSize);
+ R3 = r3.template loadPacket<ResPacket>(1 * Traits::ResPacketSize);
+ traits.acc(C2, alphav, R0);
+ traits.acc(C6, alphav, R1);
+ traits.acc(C3, alphav, R2);
+ traits.acc(C7, alphav, R3);
+ r2.storePacket(0 * Traits::ResPacketSize, R0);
+ r2.storePacket(1 * Traits::ResPacketSize, R1);
+ r3.storePacket(0 * Traits::ResPacketSize, R2);
+ r3.storePacket(1 * Traits::ResPacketSize, R3);
+ }
+ }
+
+ // Deal with remaining columns of the rhs
+ for(Index j2=packet_cols4; j2<cols; j2++)
+ {
+ for(Index i=i1; i<actual_panel_end; i+=2*LhsProgress)
+ {
+ // One column at a time
+ const LhsScalar* blA = &blockA[i*strideA+offsetA*(2*Traits::LhsProgress)];
+ prefetch(&blA[0]);
+
+ // gets res block as register
+ AccPacket C0, C4;
+ traits.initAcc(C0);
+ traits.initAcc(C4);
+
+ LinearMapper r0 = res.getLinearMapper(i, j2);
+ r0.prefetch(prefetch_res_offset);
+
+ // performs "inner" products
+ const RhsScalar* blB = &blockB[j2*strideB+offsetB];
+ LhsPacket A0, A1;
+
+ for(Index k=0; k<peeled_kc; k+=pk)
+ {
+ EIGEN_ASM_COMMENT("begin gebp micro kernel 2pX1");
+ RhsPacket B_0, B1;
+
+#define EIGEN_GEBGP_ONESTEP(K) \
+ do { \
+ EIGEN_ASM_COMMENT("begin step of gebp micro kernel 2pX1"); \
+ EIGEN_ASM_COMMENT("Note: these asm comments work around bug 935!"); \
+ traits.loadLhs(&blA[(0+2*K)*LhsProgress], A0); \
+ traits.loadLhs(&blA[(1+2*K)*LhsProgress], A1); \
+ traits.loadRhs(&blB[(0+K)*RhsProgress], B_0); \
+ traits.madd(A0, B_0, C0, B1, fix<0>); \
+ traits.madd(A1, B_0, C4, B_0, fix<0>); \
+ EIGEN_ASM_COMMENT("end step of gebp micro kernel 2pX1"); \
+ } while(false)
+
+ EIGEN_GEBGP_ONESTEP(0);
+ EIGEN_GEBGP_ONESTEP(1);
+ EIGEN_GEBGP_ONESTEP(2);
+ EIGEN_GEBGP_ONESTEP(3);
+ EIGEN_GEBGP_ONESTEP(4);
+ EIGEN_GEBGP_ONESTEP(5);
+ EIGEN_GEBGP_ONESTEP(6);
+ EIGEN_GEBGP_ONESTEP(7);
+
+ blB += int(pk) * int(RhsProgress);
+ blA += int(pk) * 2 * int(Traits::LhsProgress);
+
+ EIGEN_ASM_COMMENT("end gebp micro kernel 2pX1");
+ }
+
+ // process remaining peeled loop
+ for(Index k=peeled_kc; k<depth; k++)
+ {
+ RhsPacket B_0, B1;
+ EIGEN_GEBGP_ONESTEP(0);
+ blB += RhsProgress;
+ blA += 2*Traits::LhsProgress;
+ }
+#undef EIGEN_GEBGP_ONESTEP
+ ResPacket R0, R1;
+ ResPacket alphav = pset1<ResPacket>(alpha);
+
+ R0 = r0.template loadPacket<ResPacket>(0 * Traits::ResPacketSize);
+ R1 = r0.template loadPacket<ResPacket>(1 * Traits::ResPacketSize);
+ traits.acc(C0, alphav, R0);
+ traits.acc(C4, alphav, R1);
+ r0.storePacket(0 * Traits::ResPacketSize, R0);
+ r0.storePacket(1 * Traits::ResPacketSize, R1);
+ }
+ }
+ }
+ }
+ //---------- Process 1 * LhsProgress rows at once ----------
+ if(mr>=1*Traits::LhsProgress)
+ {
+ lhs_process_one_packet<nr, LhsProgress, RhsProgress, LhsScalar, RhsScalar, ResScalar, AccPacket, LhsPacket, RhsPacket, ResPacket, Traits, LinearMapper, DataMapper> p;
+ p(res, blockA, blockB, alpha, peeled_mc2, peeled_mc1, strideA, strideB, offsetA, offsetB, prefetch_res_offset, peeled_kc, pk, cols, depth, packet_cols4);
+ }
+ //---------- Process LhsProgressHalf rows at once ----------
+ if((LhsProgressHalf < LhsProgress) && mr>=LhsProgressHalf)
+ {
+ lhs_process_fraction_of_packet<nr, LhsProgressHalf, RhsProgressHalf, LhsScalar, RhsScalar, ResScalar, AccPacketHalf, LhsPacketHalf, RhsPacketHalf, ResPacketHalf, HalfTraits, LinearMapper, DataMapper> p;
+ p(res, blockA, blockB, alpha, peeled_mc1, peeled_mc_half, strideA, strideB, offsetA, offsetB, prefetch_res_offset, peeled_kc, pk, cols, depth, packet_cols4);
+ }
+ //---------- Process LhsProgressQuarter rows at once ----------
+ if((LhsProgressQuarter < LhsProgressHalf) && mr>=LhsProgressQuarter)
+ {
+ lhs_process_fraction_of_packet<nr, LhsProgressQuarter, RhsProgressQuarter, LhsScalar, RhsScalar, ResScalar, AccPacketQuarter, LhsPacketQuarter, RhsPacketQuarter, ResPacketQuarter, QuarterTraits, LinearMapper, DataMapper> p;
+ p(res, blockA, blockB, alpha, peeled_mc_half, peeled_mc_quarter, strideA, strideB, offsetA, offsetB, prefetch_res_offset, peeled_kc, pk, cols, depth, packet_cols4);
+ }
+ //---------- Process remaining rows, 1 at once ----------
+ if(peeled_mc_quarter<rows)
+ {
+#if EIGEN_ARCH_ARM64
+ EIGEN_IF_CONSTEXPR(nr>=8) {
+ // loop on each panel of the rhs
+ for(Index j2=0; j2<packet_cols8; j2+=8)
+ {
+ // loop on each row of the lhs (1*LhsProgress x depth)
+ for(Index i=peeled_mc_quarter; i<rows; i+=1)
+ {
+ const LhsScalar* blA = &blockA[i*strideA+offsetA];
+ prefetch(&blA[0]);
+ // gets a 1 x 1 res block as registers
+ ResScalar C0(0),C1(0),C2(0),C3(0),C4(0),C5(0),C6(0),C7(0);
+ const RhsScalar* blB = &blockB[j2*strideB+offsetB*8];
+ for(Index k=0; k<depth; k++)
+ {
+ LhsScalar A0 = blA[k];
+ RhsScalar B_0;
+
+ B_0 = blB[0];
+ C0 = cj.pmadd(A0, B_0, C0);
+
+ B_0 = blB[1];
+ C1 = cj.pmadd(A0, B_0, C1);
+
+ B_0 = blB[2];
+ C2 = cj.pmadd(A0, B_0, C2);
+
+ B_0 = blB[3];
+ C3 = cj.pmadd(A0, B_0, C3);
+
+ B_0 = blB[4];
+ C4 = cj.pmadd(A0, B_0, C4);
+
+ B_0 = blB[5];
+ C5 = cj.pmadd(A0, B_0, C5);
+
+ B_0 = blB[6];
+ C6 = cj.pmadd(A0, B_0, C6);
+
+ B_0 = blB[7];
+ C7 = cj.pmadd(A0, B_0, C7);
+
+ blB += 8;
+ }
+ res(i, j2 + 0) += alpha * C0;
+ res(i, j2 + 1) += alpha * C1;
+ res(i, j2 + 2) += alpha * C2;
+ res(i, j2 + 3) += alpha * C3;
+ res(i, j2 + 4) += alpha * C4;
+ res(i, j2 + 5) += alpha * C5;
+ res(i, j2 + 6) += alpha * C6;
+ res(i, j2 + 7) += alpha * C7;
+ }
+ }
+ }
+#endif
+
+ for(Index j2=packet_cols8; j2<packet_cols4; j2+=4)
+ {
+ // loop on each row of the lhs (1*LhsProgress x depth)
+ for(Index i=peeled_mc_quarter; i<rows; i+=1)
+ {
+ const LhsScalar* blA = &blockA[i*strideA+offsetA];
+ prefetch(&blA[0]);
+ const RhsScalar* blB = &blockB[j2*strideB+offsetB*4];
+
+ // If LhsProgress is 8 or 16, it assumes that there is a
+ // half or quarter packet, respectively, of the same size as
+ // nr (which is currently 4) for the return type.
+ const int SResPacketHalfSize = unpacket_traits<typename unpacket_traits<SResPacket>::half>::size;
+ const int SResPacketQuarterSize = unpacket_traits<typename unpacket_traits<typename unpacket_traits<SResPacket>::half>::half>::size;
+ if ((SwappedTraits::LhsProgress % 4) == 0 &&
+ (SwappedTraits::LhsProgress<=16) &&
+ (SwappedTraits::LhsProgress!=8 || SResPacketHalfSize==nr) &&
+ (SwappedTraits::LhsProgress!=16 || SResPacketQuarterSize==nr))
+ {
+ SAccPacket C0, C1, C2, C3;
+ straits.initAcc(C0);
+ straits.initAcc(C1);
+ straits.initAcc(C2);
+ straits.initAcc(C3);
+
+ const Index spk = (std::max)(1,SwappedTraits::LhsProgress/4);
+ const Index endk = (depth/spk)*spk;
+ const Index endk4 = (depth/(spk*4))*(spk*4);
+
+ Index k=0;
+ for(; k<endk4; k+=4*spk)
+ {
+ SLhsPacket A0,A1;
+ SRhsPacket B_0,B_1;
+
+ straits.loadLhsUnaligned(blB+0*SwappedTraits::LhsProgress, A0);
+ straits.loadLhsUnaligned(blB+1*SwappedTraits::LhsProgress, A1);
+
+ straits.loadRhsQuad(blA+0*spk, B_0);
+ straits.loadRhsQuad(blA+1*spk, B_1);
+ straits.madd(A0,B_0,C0,B_0, fix<0>);
+ straits.madd(A1,B_1,C1,B_1, fix<0>);
+
+ straits.loadLhsUnaligned(blB+2*SwappedTraits::LhsProgress, A0);
+ straits.loadLhsUnaligned(blB+3*SwappedTraits::LhsProgress, A1);
+ straits.loadRhsQuad(blA+2*spk, B_0);
+ straits.loadRhsQuad(blA+3*spk, B_1);
+ straits.madd(A0,B_0,C2,B_0, fix<0>);
+ straits.madd(A1,B_1,C3,B_1, fix<0>);
+
+ blB += 4*SwappedTraits::LhsProgress;
+ blA += 4*spk;
+ }
+ C0 = padd(padd(C0,C1),padd(C2,C3));
+ for(; k<endk; k+=spk)
+ {
+ SLhsPacket A0;
+ SRhsPacket B_0;
+
+ straits.loadLhsUnaligned(blB, A0);
+ straits.loadRhsQuad(blA, B_0);
+ straits.madd(A0,B_0,C0,B_0, fix<0>);
+
+ blB += SwappedTraits::LhsProgress;
+ blA += spk;
+ }
+ if(SwappedTraits::LhsProgress==8)
+ {
+ // Special case where we have to first reduce the accumulation register C0
+ typedef std::conditional_t<SwappedTraits::LhsProgress>=8,typename unpacket_traits<SResPacket>::half,SResPacket> SResPacketHalf;
+ typedef std::conditional_t<SwappedTraits::LhsProgress>=8,typename unpacket_traits<SLhsPacket>::half,SLhsPacket> SLhsPacketHalf;
+ typedef std::conditional_t<SwappedTraits::LhsProgress>=8,typename unpacket_traits<SRhsPacket>::half,SRhsPacket> SRhsPacketHalf;
+ typedef std::conditional_t<SwappedTraits::LhsProgress>=8,typename unpacket_traits<SAccPacket>::half,SAccPacket> SAccPacketHalf;
+
+ SResPacketHalf R = res.template gatherPacket<SResPacketHalf>(i, j2);
+ SResPacketHalf alphav = pset1<SResPacketHalf>(alpha);
+
+ if(depth-endk>0)
+ {
+ // We have to handle the last row of the rhs which corresponds to a half-packet
+ SLhsPacketHalf a0;
+ SRhsPacketHalf b0;
+ straits.loadLhsUnaligned(blB, a0);
+ straits.loadRhs(blA, b0);
+ SAccPacketHalf c0 = predux_half_dowto4(C0);
+ straits.madd(a0,b0,c0,b0, fix<0>);
+ straits.acc(c0, alphav, R);
+ }
+ else
+ {
+ straits.acc(predux_half_dowto4(C0), alphav, R);
+ }
+ res.scatterPacket(i, j2, R);
+ }
+ else if (SwappedTraits::LhsProgress==16)
+ {
+ // Special case where we have to first reduce the
+ // accumulation register C0. We specialize the block in
+ // template form, so that LhsProgress < 16 paths don't
+ // fail to compile
+ last_row_process_16_packets<LhsScalar, RhsScalar, Index, DataMapper, mr, nr, ConjugateLhs, ConjugateRhs> p;
+ p(res, straits, blA, blB, depth, endk, i, j2,alpha, C0);
+ }
+ else
+ {
+ SResPacket R = res.template gatherPacket<SResPacket>(i, j2);
+ SResPacket alphav = pset1<SResPacket>(alpha);
+ straits.acc(C0, alphav, R);
+ res.scatterPacket(i, j2, R);
+ }
+ }
+ else // scalar path
+ {
+ // get a 1 x 4 res block as registers
+ ResScalar C0(0), C1(0), C2(0), C3(0);
+
+ for(Index k=0; k<depth; k++)
+ {
+ LhsScalar A0;
+ RhsScalar B_0, B_1;
+
+ A0 = blA[k];
+
+ B_0 = blB[0];
+ B_1 = blB[1];
+ C0 = cj.pmadd(A0,B_0,C0);
+ C1 = cj.pmadd(A0,B_1,C1);
+
+ B_0 = blB[2];
+ B_1 = blB[3];
+ C2 = cj.pmadd(A0,B_0,C2);
+ C3 = cj.pmadd(A0,B_1,C3);
+
+ blB += 4;
+ }
+ res(i, j2 + 0) += alpha * C0;
+ res(i, j2 + 1) += alpha * C1;
+ res(i, j2 + 2) += alpha * C2;
+ res(i, j2 + 3) += alpha * C3;
+ }
+ }
+ }
+ // remaining columns
+ for(Index j2=packet_cols4; j2<cols; j2++)
+ {
+ // loop on each row of the lhs (1*LhsProgress x depth)
+ for(Index i=peeled_mc_quarter; i<rows; i+=1)
+ {
+ const LhsScalar* blA = &blockA[i*strideA+offsetA];
+ prefetch(&blA[0]);
+ // gets a 1 x 1 res block as registers
+ ResScalar C0(0);
+ const RhsScalar* blB = &blockB[j2*strideB+offsetB];
+ for(Index k=0; k<depth; k++)
+ {
+ LhsScalar A0 = blA[k];
+ RhsScalar B_0 = blB[k];
+ C0 = cj.pmadd(A0, B_0, C0);
+ }
+ res(i, j2) += alpha * C0;
+ }
+ }
+ }
+ }
+
+
+// pack a block of the lhs
+// The traversal is as follow (mr==4):
+// 0 4 8 12 ...
+// 1 5 9 13 ...
+// 2 6 10 14 ...
+// 3 7 11 15 ...
+//
+// 16 20 24 28 ...
+// 17 21 25 29 ...
+// 18 22 26 30 ...
+// 19 23 27 31 ...
+//
+// 32 33 34 35 ...
+// 36 36 38 39 ...
+template<typename Scalar, typename Index, typename DataMapper, int Pack1, int Pack2, typename Packet, bool Conjugate, bool PanelMode>
+struct gemm_pack_lhs<Scalar, Index, DataMapper, Pack1, Pack2, Packet, ColMajor, Conjugate, PanelMode>
+{
+ typedef typename DataMapper::LinearMapper LinearMapper;
+ EIGEN_DONT_INLINE void operator()(Scalar* blockA, const DataMapper& lhs, Index depth, Index rows, Index stride=0, Index offset=0);
+};
+
+template<typename Scalar, typename Index, typename DataMapper, int Pack1, int Pack2, typename Packet, bool Conjugate, bool PanelMode>
+EIGEN_DONT_INLINE void gemm_pack_lhs<Scalar, Index, DataMapper, Pack1, Pack2, Packet, ColMajor, Conjugate, PanelMode>
+ ::operator()(Scalar* blockA, const DataMapper& lhs, Index depth, Index rows, Index stride, Index offset)
+{
+ typedef typename unpacket_traits<Packet>::half HalfPacket;
+ typedef typename unpacket_traits<typename unpacket_traits<Packet>::half>::half QuarterPacket;
+ enum { PacketSize = unpacket_traits<Packet>::size,
+ HalfPacketSize = unpacket_traits<HalfPacket>::size,
+ QuarterPacketSize = unpacket_traits<QuarterPacket>::size,
+ HasHalf = (int)HalfPacketSize < (int)PacketSize,
+ HasQuarter = (int)QuarterPacketSize < (int)HalfPacketSize};
+
+ EIGEN_ASM_COMMENT("EIGEN PRODUCT PACK LHS");
+ EIGEN_UNUSED_VARIABLE(stride);
+ EIGEN_UNUSED_VARIABLE(offset);
+ eigen_assert(((!PanelMode) && stride==0 && offset==0) || (PanelMode && stride>=depth && offset<=stride));
+ eigen_assert( ((Pack1%PacketSize)==0 && Pack1<=4*PacketSize) || (Pack1<=4) );
+ conj_if<NumTraits<Scalar>::IsComplex && Conjugate> cj;
+ Index count = 0;
+
+ const Index peeled_mc3 = Pack1>=3*PacketSize ? (rows/(3*PacketSize))*(3*PacketSize) : 0;
+ const Index peeled_mc2 = Pack1>=2*PacketSize ? peeled_mc3+((rows-peeled_mc3)/(2*PacketSize))*(2*PacketSize) : 0;
+ const Index peeled_mc1 = Pack1>=1*PacketSize ? peeled_mc2+((rows-peeled_mc2)/(1*PacketSize))*(1*PacketSize) : 0;
+ const Index peeled_mc_half = Pack1>=HalfPacketSize ? peeled_mc1+((rows-peeled_mc1)/(HalfPacketSize))*(HalfPacketSize) : 0;
+ const Index peeled_mc_quarter = Pack1>=QuarterPacketSize ? (rows/(QuarterPacketSize))*(QuarterPacketSize) : 0;
+ const Index last_lhs_progress = rows > peeled_mc_quarter ? (rows - peeled_mc_quarter) & ~1 : 0;
+ const Index peeled_mc0 = Pack2>=PacketSize ? peeled_mc_quarter
+ : Pack2>1 && last_lhs_progress ? (rows/last_lhs_progress)*last_lhs_progress : 0;
+
+ Index i=0;
+
+ // Pack 3 packets
+ if(Pack1>=3*PacketSize)
+ {
+ for(; i<peeled_mc3; i+=3*PacketSize)
+ {
+ if(PanelMode) count += (3*PacketSize) * offset;
+
+ for(Index k=0; k<depth; k++)
+ {
+ Packet A, B, C;
+ A = lhs.template loadPacket<Packet>(i+0*PacketSize, k);
+ B = lhs.template loadPacket<Packet>(i+1*PacketSize, k);
+ C = lhs.template loadPacket<Packet>(i+2*PacketSize, k);
+ pstore(blockA+count, cj.pconj(A)); count+=PacketSize;
+ pstore(blockA+count, cj.pconj(B)); count+=PacketSize;
+ pstore(blockA+count, cj.pconj(C)); count+=PacketSize;
+ }
+ if(PanelMode) count += (3*PacketSize) * (stride-offset-depth);
+ }
+ }
+ // Pack 2 packets
+ if(Pack1>=2*PacketSize)
+ {
+ for(; i<peeled_mc2; i+=2*PacketSize)
+ {
+ if(PanelMode) count += (2*PacketSize) * offset;
+
+ for(Index k=0; k<depth; k++)
+ {
+ Packet A, B;
+ A = lhs.template loadPacket<Packet>(i+0*PacketSize, k);
+ B = lhs.template loadPacket<Packet>(i+1*PacketSize, k);
+ pstore(blockA+count, cj.pconj(A)); count+=PacketSize;
+ pstore(blockA+count, cj.pconj(B)); count+=PacketSize;
+ }
+ if(PanelMode) count += (2*PacketSize) * (stride-offset-depth);
+ }
+ }
+ // Pack 1 packets
+ if(Pack1>=1*PacketSize)
+ {
+ for(; i<peeled_mc1; i+=1*PacketSize)
+ {
+ if(PanelMode) count += (1*PacketSize) * offset;
+
+ for(Index k=0; k<depth; k++)
+ {
+ Packet A;
+ A = lhs.template loadPacket<Packet>(i+0*PacketSize, k);
+ pstore(blockA+count, cj.pconj(A));
+ count+=PacketSize;
+ }
+ if(PanelMode) count += (1*PacketSize) * (stride-offset-depth);
+ }
+ }
+ // Pack half packets
+ if(HasHalf && Pack1>=HalfPacketSize)
+ {
+ for(; i<peeled_mc_half; i+=HalfPacketSize)
+ {
+ if(PanelMode) count += (HalfPacketSize) * offset;
+
+ for(Index k=0; k<depth; k++)
+ {
+ HalfPacket A;
+ A = lhs.template loadPacket<HalfPacket>(i+0*(HalfPacketSize), k);
+ pstoreu(blockA+count, cj.pconj(A));
+ count+=HalfPacketSize;
+ }
+ if(PanelMode) count += (HalfPacketSize) * (stride-offset-depth);
+ }
+ }
+ // Pack quarter packets
+ if(HasQuarter && Pack1>=QuarterPacketSize)
+ {
+ for(; i<peeled_mc_quarter; i+=QuarterPacketSize)
+ {
+ if(PanelMode) count += (QuarterPacketSize) * offset;
+
+ for(Index k=0; k<depth; k++)
+ {
+ QuarterPacket A;
+ A = lhs.template loadPacket<QuarterPacket>(i+0*(QuarterPacketSize), k);
+ pstoreu(blockA+count, cj.pconj(A));
+ count+=QuarterPacketSize;
+ }
+ if(PanelMode) count += (QuarterPacketSize) * (stride-offset-depth);
+ }
+ }
+ // Pack2 may be *smaller* than PacketSize—that happens for
+ // products like real * complex, where we have to go half the
+ // progress on the lhs in order to duplicate those operands to
+ // address both real & imaginary parts on the rhs. This portion will
+ // pack those half ones until they match the number expected on the
+ // last peeling loop at this point (for the rhs).
+ if(Pack2<PacketSize && Pack2>1)
+ {
+ for(; i<peeled_mc0; i+=last_lhs_progress)
+ {
+ if(PanelMode) count += last_lhs_progress * offset;
+
+ for(Index k=0; k<depth; k++)
+ for(Index w=0; w<last_lhs_progress; w++)
+ blockA[count++] = cj(lhs(i+w, k));
+
+ if(PanelMode) count += last_lhs_progress * (stride-offset-depth);
+ }
+ }
+ // Pack scalars
+ for(; i<rows; i++)
+ {
+ if(PanelMode) count += offset;
+ for(Index k=0; k<depth; k++)
+ blockA[count++] = cj(lhs(i, k));
+ if(PanelMode) count += (stride-offset-depth);
+ }
+}
+
+template<typename Scalar, typename Index, typename DataMapper, int Pack1, int Pack2, typename Packet, bool Conjugate, bool PanelMode>
+struct gemm_pack_lhs<Scalar, Index, DataMapper, Pack1, Pack2, Packet, RowMajor, Conjugate, PanelMode>
+{
+ typedef typename DataMapper::LinearMapper LinearMapper;
+ EIGEN_DONT_INLINE void operator()(Scalar* blockA, const DataMapper& lhs, Index depth, Index rows, Index stride=0, Index offset=0);
+};
+
+template<typename Scalar, typename Index, typename DataMapper, int Pack1, int Pack2, typename Packet, bool Conjugate, bool PanelMode>
+EIGEN_DONT_INLINE void gemm_pack_lhs<Scalar, Index, DataMapper, Pack1, Pack2, Packet, RowMajor, Conjugate, PanelMode>
+ ::operator()(Scalar* blockA, const DataMapper& lhs, Index depth, Index rows, Index stride, Index offset)
+{
+ typedef typename unpacket_traits<Packet>::half HalfPacket;
+ typedef typename unpacket_traits<typename unpacket_traits<Packet>::half>::half QuarterPacket;
+ enum { PacketSize = unpacket_traits<Packet>::size,
+ HalfPacketSize = unpacket_traits<HalfPacket>::size,
+ QuarterPacketSize = unpacket_traits<QuarterPacket>::size,
+ HasHalf = (int)HalfPacketSize < (int)PacketSize,
+ HasQuarter = (int)QuarterPacketSize < (int)HalfPacketSize};
+
+ EIGEN_ASM_COMMENT("EIGEN PRODUCT PACK LHS");
+ EIGEN_UNUSED_VARIABLE(stride);
+ EIGEN_UNUSED_VARIABLE(offset);
+ eigen_assert(((!PanelMode) && stride==0 && offset==0) || (PanelMode && stride>=depth && offset<=stride));
+ conj_if<NumTraits<Scalar>::IsComplex && Conjugate> cj;
+ Index count = 0;
+ bool gone_half = false, gone_quarter = false, gone_last = false;
+
+ Index i = 0;
+ Index pack = Pack1;
+ Index psize = PacketSize;
+ while(pack>0)
+ {
+ Index remaining_rows = rows-i;
+ Index peeled_mc = gone_last ? Pack2>1 ? (rows/pack)*pack : 0 : i+(remaining_rows/pack)*pack;
+ Index starting_pos = i;
+ for(; i<peeled_mc; i+=pack)
+ {
+ if(PanelMode) count += pack * offset;
+
+ Index k=0;
+ if(pack>=psize && psize >= QuarterPacketSize)
+ {
+ const Index peeled_k = (depth/psize)*psize;
+ for(; k<peeled_k; k+=psize)
+ {
+ for (Index m = 0; m < pack; m += psize)
+ {
+ if (psize == PacketSize) {
+ PacketBlock<Packet> kernel;
+ for (Index p = 0; p < psize; ++p) kernel.packet[p] = lhs.template loadPacket<Packet>(i+p+m, k);
+ ptranspose(kernel);
+ for (Index p = 0; p < psize; ++p) pstore(blockA+count+m+(pack)*p, cj.pconj(kernel.packet[p]));
+ } else if (HasHalf && psize == HalfPacketSize) {
+ gone_half = true;
+ PacketBlock<HalfPacket> kernel_half;
+ for (Index p = 0; p < psize; ++p) kernel_half.packet[p] = lhs.template loadPacket<HalfPacket>(i+p+m, k);
+ ptranspose(kernel_half);
+ for (Index p = 0; p < psize; ++p) pstore(blockA+count+m+(pack)*p, cj.pconj(kernel_half.packet[p]));
+ } else if (HasQuarter && psize == QuarterPacketSize) {
+ gone_quarter = true;
+ PacketBlock<QuarterPacket> kernel_quarter;
+ for (Index p = 0; p < psize; ++p) kernel_quarter.packet[p] = lhs.template loadPacket<QuarterPacket>(i+p+m, k);
+ ptranspose(kernel_quarter);
+ for (Index p = 0; p < psize; ++p) pstore(blockA+count+m+(pack)*p, cj.pconj(kernel_quarter.packet[p]));
+ }
+ }
+ count += psize*pack;
+ }
+ }
+
+ for(; k<depth; k++)
+ {
+ Index w=0;
+ for(; w<pack-3; w+=4)
+ {
+ Scalar a(cj(lhs(i+w+0, k))),
+ b(cj(lhs(i+w+1, k))),
+ c(cj(lhs(i+w+2, k))),
+ d(cj(lhs(i+w+3, k)));
+ blockA[count++] = a;
+ blockA[count++] = b;
+ blockA[count++] = c;
+ blockA[count++] = d;
+ }
+ if(pack%4)
+ for(;w<pack;++w)
+ blockA[count++] = cj(lhs(i+w, k));
+ }
+
+ if(PanelMode) count += pack * (stride-offset-depth);
+ }
+
+ pack -= psize;
+ Index left = rows - i;
+ if (pack <= 0) {
+ if (!gone_last &&
+ (starting_pos == i || left >= psize/2 || left >= psize/4) &&
+ ((psize/2 == HalfPacketSize && HasHalf && !gone_half) ||
+ (psize/2 == QuarterPacketSize && HasQuarter && !gone_quarter))) {
+ psize /= 2;
+ pack = psize;
+ continue;
+ }
+ // Pack2 may be *smaller* than PacketSize—that happens for
+ // products like real * complex, where we have to go half the
+ // progress on the lhs in order to duplicate those operands to
+ // address both real & imaginary parts on the rhs. This portion will
+ // pack those half ones until they match the number expected on the
+ // last peeling loop at this point (for the rhs).
+ if (Pack2 < PacketSize && !gone_last) {
+ gone_last = true;
+ psize = pack = left & ~1;
+ }
+ }
+ }
+
+ for(; i<rows; i++)
+ {
+ if(PanelMode) count += offset;
+ for(Index k=0; k<depth; k++)
+ blockA[count++] = cj(lhs(i, k));
+ if(PanelMode) count += (stride-offset-depth);
+ }
+}
+
+// copy a complete panel of the rhs
+// this version is optimized for column major matrices
+// The traversal order is as follow: (nr==4):
+// 0 1 2 3 12 13 14 15 24 27
+// 4 5 6 7 16 17 18 19 25 28
+// 8 9 10 11 20 21 22 23 26 29
+// . . . . . . . . . .
+template<typename Scalar, typename Index, typename DataMapper, int nr, bool Conjugate, bool PanelMode>
+struct gemm_pack_rhs<Scalar, Index, DataMapper, nr, ColMajor, Conjugate, PanelMode>
+{
+ typedef typename packet_traits<Scalar>::type Packet;
+ typedef typename DataMapper::LinearMapper LinearMapper;
+ enum { PacketSize = packet_traits<Scalar>::size };
+ EIGEN_DONT_INLINE void operator()(Scalar* blockB, const DataMapper& rhs, Index depth, Index cols, Index stride=0, Index offset=0);
+};
+
+template<typename Scalar, typename Index, typename DataMapper, int nr, bool Conjugate, bool PanelMode>
+EIGEN_DONT_INLINE void gemm_pack_rhs<Scalar, Index, DataMapper, nr, ColMajor, Conjugate, PanelMode>
+ ::operator()(Scalar* blockB, const DataMapper& rhs, Index depth, Index cols, Index stride, Index offset)
+{
+ EIGEN_ASM_COMMENT("EIGEN PRODUCT PACK RHS COLMAJOR");
+ EIGEN_UNUSED_VARIABLE(stride);
+ EIGEN_UNUSED_VARIABLE(offset);
+ eigen_assert(((!PanelMode) && stride==0 && offset==0) || (PanelMode && stride>=depth && offset<=stride));
+ conj_if<NumTraits<Scalar>::IsComplex && Conjugate> cj;
+ Index packet_cols8 = nr>=8 ? (cols/8) * 8 : 0;
+ Index packet_cols4 = nr>=4 ? (cols/4) * 4 : 0;
+ Index count = 0;
+ const Index peeled_k = (depth/PacketSize)*PacketSize;
+
+#if EIGEN_ARCH_ARM64
+ EIGEN_IF_CONSTEXPR(nr>=8)
+ {
+ for(Index j2=0; j2<packet_cols8; j2+=8)
+ {
+ // skip what we have before
+ if(PanelMode) count += 8 * offset;
+ const LinearMapper dm0 = rhs.getLinearMapper(0, j2 + 0);
+ const LinearMapper dm1 = rhs.getLinearMapper(0, j2 + 1);
+ const LinearMapper dm2 = rhs.getLinearMapper(0, j2 + 2);
+ const LinearMapper dm3 = rhs.getLinearMapper(0, j2 + 3);
+ const LinearMapper dm4 = rhs.getLinearMapper(0, j2 + 4);
+ const LinearMapper dm5 = rhs.getLinearMapper(0, j2 + 5);
+ const LinearMapper dm6 = rhs.getLinearMapper(0, j2 + 6);
+ const LinearMapper dm7 = rhs.getLinearMapper(0, j2 + 7);
+ Index k = 0;
+ if (PacketSize % 2 == 0 && PacketSize <= 8) // 2 4 8
+ {
+ for (; k < peeled_k; k += PacketSize)
+ {
+ if (PacketSize == 2)
+ {
+ PacketBlock<Packet, PacketSize==2 ?2:PacketSize> kernel0, kernel1, kernel2, kernel3;
+ kernel0.packet[0%PacketSize] = dm0.template loadPacket<Packet>(k);
+ kernel0.packet[1%PacketSize] = dm1.template loadPacket<Packet>(k);
+ kernel1.packet[0%PacketSize] = dm2.template loadPacket<Packet>(k);
+ kernel1.packet[1%PacketSize] = dm3.template loadPacket<Packet>(k);
+ kernel2.packet[0%PacketSize] = dm4.template loadPacket<Packet>(k);
+ kernel2.packet[1%PacketSize] = dm5.template loadPacket<Packet>(k);
+ kernel3.packet[0%PacketSize] = dm6.template loadPacket<Packet>(k);
+ kernel3.packet[1%PacketSize] = dm7.template loadPacket<Packet>(k);
+ ptranspose(kernel0);
+ ptranspose(kernel1);
+ ptranspose(kernel2);
+ ptranspose(kernel3);
+
+ pstoreu(blockB + count + 0 * PacketSize, cj.pconj(kernel0.packet[0 % PacketSize]));
+ pstoreu(blockB + count + 1 * PacketSize, cj.pconj(kernel1.packet[0 % PacketSize]));
+ pstoreu(blockB + count + 2 * PacketSize, cj.pconj(kernel2.packet[0 % PacketSize]));
+ pstoreu(blockB + count + 3 * PacketSize, cj.pconj(kernel3.packet[0 % PacketSize]));
+
+ pstoreu(blockB + count + 4 * PacketSize, cj.pconj(kernel0.packet[1 % PacketSize]));
+ pstoreu(blockB + count + 5 * PacketSize, cj.pconj(kernel1.packet[1 % PacketSize]));
+ pstoreu(blockB + count + 6 * PacketSize, cj.pconj(kernel2.packet[1 % PacketSize]));
+ pstoreu(blockB + count + 7 * PacketSize, cj.pconj(kernel3.packet[1 % PacketSize]));
+ count+=8*PacketSize;
+ }
+ else if (PacketSize == 4)
+ {
+ PacketBlock<Packet, PacketSize == 4?4:PacketSize> kernel0, kernel1;
+
+ kernel0.packet[0%PacketSize] = dm0.template loadPacket<Packet>(k);
+ kernel0.packet[1%PacketSize] = dm1.template loadPacket<Packet>(k);
+ kernel0.packet[2%PacketSize] = dm2.template loadPacket<Packet>(k);
+ kernel0.packet[3%PacketSize] = dm3.template loadPacket<Packet>(k);
+ kernel1.packet[0%PacketSize] = dm4.template loadPacket<Packet>(k);
+ kernel1.packet[1%PacketSize] = dm5.template loadPacket<Packet>(k);
+ kernel1.packet[2%PacketSize] = dm6.template loadPacket<Packet>(k);
+ kernel1.packet[3%PacketSize] = dm7.template loadPacket<Packet>(k);
+ ptranspose(kernel0);
+ ptranspose(kernel1);
+
+ pstoreu(blockB+count+0*PacketSize, cj.pconj(kernel0.packet[0%PacketSize]));
+ pstoreu(blockB+count+1*PacketSize, cj.pconj(kernel1.packet[0%PacketSize]));
+ pstoreu(blockB+count+2*PacketSize, cj.pconj(kernel0.packet[1%PacketSize]));
+ pstoreu(blockB+count+3*PacketSize, cj.pconj(kernel1.packet[1%PacketSize]));
+ pstoreu(blockB+count+4*PacketSize, cj.pconj(kernel0.packet[2%PacketSize]));
+ pstoreu(blockB+count+5*PacketSize, cj.pconj(kernel1.packet[2%PacketSize]));
+ pstoreu(blockB+count+6*PacketSize, cj.pconj(kernel0.packet[3%PacketSize]));
+ pstoreu(blockB+count+7*PacketSize, cj.pconj(kernel1.packet[3%PacketSize]));
+ count+=8*PacketSize;
+ }
+ else if (PacketSize == 8)
+ {
+ PacketBlock<Packet, PacketSize==8?8:PacketSize> kernel0;
+
+ kernel0.packet[0%PacketSize] = dm0.template loadPacket<Packet>(k);
+ kernel0.packet[1%PacketSize] = dm1.template loadPacket<Packet>(k);
+ kernel0.packet[2%PacketSize] = dm2.template loadPacket<Packet>(k);
+ kernel0.packet[3%PacketSize] = dm3.template loadPacket<Packet>(k);
+ kernel0.packet[4%PacketSize] = dm4.template loadPacket<Packet>(k);
+ kernel0.packet[5%PacketSize] = dm5.template loadPacket<Packet>(k);
+ kernel0.packet[6%PacketSize] = dm6.template loadPacket<Packet>(k);
+ kernel0.packet[7%PacketSize] = dm7.template loadPacket<Packet>(k);
+ ptranspose(kernel0);
+
+ pstoreu(blockB+count+0*PacketSize, cj.pconj(kernel0.packet[0%PacketSize]));
+ pstoreu(blockB+count+1*PacketSize, cj.pconj(kernel0.packet[1%PacketSize]));
+ pstoreu(blockB+count+2*PacketSize, cj.pconj(kernel0.packet[2%PacketSize]));
+ pstoreu(blockB+count+3*PacketSize, cj.pconj(kernel0.packet[3%PacketSize]));
+ pstoreu(blockB+count+4*PacketSize, cj.pconj(kernel0.packet[4%PacketSize]));
+ pstoreu(blockB+count+5*PacketSize, cj.pconj(kernel0.packet[5%PacketSize]));
+ pstoreu(blockB+count+6*PacketSize, cj.pconj(kernel0.packet[6%PacketSize]));
+ pstoreu(blockB+count+7*PacketSize, cj.pconj(kernel0.packet[7%PacketSize]));
+ count+=8*PacketSize;
+ }
+ }
+ }
+
+ for(; k<depth; k++)
+ {
+ blockB[count+0] = cj(dm0(k));
+ blockB[count+1] = cj(dm1(k));
+ blockB[count+2] = cj(dm2(k));
+ blockB[count+3] = cj(dm3(k));
+ blockB[count+4] = cj(dm4(k));
+ blockB[count+5] = cj(dm5(k));
+ blockB[count+6] = cj(dm6(k));
+ blockB[count+7] = cj(dm7(k));
+ count += 8;
+ }
+ // skip what we have after
+ if(PanelMode) count += 8 * (stride-offset-depth);
+ }
+ }
+#endif
+
+ EIGEN_IF_CONSTEXPR(nr>=4)
+ {
+ for(Index j2=packet_cols8; j2<packet_cols4; j2+=4)
+ {
+ // skip what we have before
+ if(PanelMode) count += 4 * offset;
+ const LinearMapper dm0 = rhs.getLinearMapper(0, j2 + 0);
+ const LinearMapper dm1 = rhs.getLinearMapper(0, j2 + 1);
+ const LinearMapper dm2 = rhs.getLinearMapper(0, j2 + 2);
+ const LinearMapper dm3 = rhs.getLinearMapper(0, j2 + 3);
+
+ Index k=0;
+ if((PacketSize%4)==0) // TODO enable vectorized transposition for PacketSize==2 ??
+ {
+ for(; k<peeled_k; k+=PacketSize) {
+ PacketBlock<Packet,(PacketSize%4)==0?4:PacketSize> kernel;
+ kernel.packet[0 ] = dm0.template loadPacket<Packet>(k);
+ kernel.packet[1%PacketSize] = dm1.template loadPacket<Packet>(k);
+ kernel.packet[2%PacketSize] = dm2.template loadPacket<Packet>(k);
+ kernel.packet[3%PacketSize] = dm3.template loadPacket<Packet>(k);
+ ptranspose(kernel);
+ pstoreu(blockB+count+0*PacketSize, cj.pconj(kernel.packet[0]));
+ pstoreu(blockB+count+1*PacketSize, cj.pconj(kernel.packet[1%PacketSize]));
+ pstoreu(blockB+count+2*PacketSize, cj.pconj(kernel.packet[2%PacketSize]));
+ pstoreu(blockB+count+3*PacketSize, cj.pconj(kernel.packet[3%PacketSize]));
+ count+=4*PacketSize;
+ }
+ }
+ for(; k<depth; k++)
+ {
+ blockB[count+0] = cj(dm0(k));
+ blockB[count+1] = cj(dm1(k));
+ blockB[count+2] = cj(dm2(k));
+ blockB[count+3] = cj(dm3(k));
+ count += 4;
+ }
+ // skip what we have after
+ if(PanelMode) count += 4 * (stride-offset-depth);
+ }
+ }
+
+ // copy the remaining columns one at a time (nr==1)
+ for(Index j2=packet_cols4; j2<cols; ++j2)
+ {
+ if(PanelMode) count += offset;
+ const LinearMapper dm0 = rhs.getLinearMapper(0, j2);
+ for(Index k=0; k<depth; k++)
+ {
+ blockB[count] = cj(dm0(k));
+ count += 1;
+ }
+ if(PanelMode) count += (stride-offset-depth);
+ }
+}
+
+// this version is optimized for row major matrices
+template<typename Scalar, typename Index, typename DataMapper, int nr, bool Conjugate, bool PanelMode>
+struct gemm_pack_rhs<Scalar, Index, DataMapper, nr, RowMajor, Conjugate, PanelMode>
+{
+ typedef typename packet_traits<Scalar>::type Packet;
+ typedef typename unpacket_traits<Packet>::half HalfPacket;
+ typedef typename unpacket_traits<typename unpacket_traits<Packet>::half>::half QuarterPacket;
+ typedef typename DataMapper::LinearMapper LinearMapper;
+ enum { PacketSize = packet_traits<Scalar>::size,
+ HalfPacketSize = unpacket_traits<HalfPacket>::size,
+ QuarterPacketSize = unpacket_traits<QuarterPacket>::size};
+ EIGEN_DONT_INLINE void operator()(Scalar* blockB, const DataMapper& rhs, Index depth, Index cols, Index stride=0, Index offset=0)
+ {
+ EIGEN_ASM_COMMENT("EIGEN PRODUCT PACK RHS ROWMAJOR");
+ EIGEN_UNUSED_VARIABLE(stride);
+ EIGEN_UNUSED_VARIABLE(offset);
+ eigen_assert(((!PanelMode) && stride==0 && offset==0) || (PanelMode && stride>=depth && offset<=stride));
+ const bool HasHalf = (int)HalfPacketSize < (int)PacketSize;
+ const bool HasQuarter = (int)QuarterPacketSize < (int)HalfPacketSize;
+ conj_if<NumTraits<Scalar>::IsComplex && Conjugate> cj;
+ Index packet_cols8 = nr>=8 ? (cols/8) * 8 : 0;
+ Index packet_cols4 = nr>=4 ? (cols/4) * 4 : 0;
+ Index count = 0;
+
+#if EIGEN_ARCH_ARM64
+ EIGEN_IF_CONSTEXPR(nr>=8)
+ {
+ for(Index j2=0; j2<packet_cols8; j2+=8)
+ {
+ // skip what we have before
+ if(PanelMode) count += 8 * offset;
+ for(Index k=0; k<depth; k++)
+ {
+ if (PacketSize==8) {
+ Packet A = rhs.template loadPacket<Packet>(k, j2);
+ pstoreu(blockB+count, cj.pconj(A));
+ count += PacketSize;
+ } else if (PacketSize==4) {
+ Packet A = rhs.template loadPacket<Packet>(k, j2);
+ Packet B = rhs.template loadPacket<Packet>(k, j2 + 4);
+ pstoreu(blockB+count, cj.pconj(A));
+ pstoreu(blockB+count+PacketSize, cj.pconj(B));
+ count += 2*PacketSize;
+ } else {
+ const LinearMapper dm0 = rhs.getLinearMapper(k, j2);
+ blockB[count+0] = cj(dm0(0));
+ blockB[count+1] = cj(dm0(1));
+ blockB[count+2] = cj(dm0(2));
+ blockB[count+3] = cj(dm0(3));
+ blockB[count+4] = cj(dm0(4));
+ blockB[count+5] = cj(dm0(5));
+ blockB[count+6] = cj(dm0(6));
+ blockB[count+7] = cj(dm0(7));
+ count += 8;
+ }
+ }
+ // skip what we have after
+ if(PanelMode) count += 8 * (stride-offset-depth);
+ }
+ }
+#endif
+
+ if(nr>=4)
+ {
+ for(Index j2=packet_cols8; j2<packet_cols4; j2+=4)
+ {
+ // skip what we have before
+ if(PanelMode) count += 4 * offset;
+ for(Index k=0; k<depth; k++)
+ {
+ if (PacketSize==4) {
+ Packet A = rhs.template loadPacket<Packet>(k, j2);
+ pstoreu(blockB+count, cj.pconj(A));
+ count += PacketSize;
+ } else if (HasHalf && HalfPacketSize==4) {
+ HalfPacket A = rhs.template loadPacket<HalfPacket>(k, j2);
+ pstoreu(blockB+count, cj.pconj(A));
+ count += HalfPacketSize;
+ } else if (HasQuarter && QuarterPacketSize==4) {
+ QuarterPacket A = rhs.template loadPacket<QuarterPacket>(k, j2);
+ pstoreu(blockB+count, cj.pconj(A));
+ count += QuarterPacketSize;
+ } else {
+ const LinearMapper dm0 = rhs.getLinearMapper(k, j2);
+ blockB[count+0] = cj(dm0(0));
+ blockB[count+1] = cj(dm0(1));
+ blockB[count+2] = cj(dm0(2));
+ blockB[count+3] = cj(dm0(3));
+ count += 4;
+ }
+ }
+ // skip what we have after
+ if(PanelMode) count += 4 * (stride-offset-depth);
+ }
+ }
+ // copy the remaining columns one at a time (nr==1)
+ for(Index j2=packet_cols4; j2<cols; ++j2)
+ {
+ if(PanelMode) count += offset;
+ for(Index k=0; k<depth; k++)
+ {
+ blockB[count] = cj(rhs(k, j2));
+ count += 1;
+ }
+ if(PanelMode) count += stride-offset-depth;
+ }
+ }
+};
+
+} // end namespace internal
+
+/** \returns the currently set level 1 cpu cache size (in bytes) used to estimate the ideal blocking size parameters.
+ * \sa setCpuCacheSize */
+inline std::ptrdiff_t l1CacheSize()
+{
+ std::ptrdiff_t l1, l2, l3;
+ internal::manage_caching_sizes(GetAction, &l1, &l2, &l3);
+ return l1;
+}
+
+/** \returns the currently set level 2 cpu cache size (in bytes) used to estimate the ideal blocking size parameters.
+ * \sa setCpuCacheSize */
+inline std::ptrdiff_t l2CacheSize()
+{
+ std::ptrdiff_t l1, l2, l3;
+ internal::manage_caching_sizes(GetAction, &l1, &l2, &l3);
+ return l2;
+}
+
+/** \returns the currently set level 3 cpu cache size (in bytes) used to estimate the ideal blocking size paramete\
+rs.
+* \sa setCpuCacheSize */
+inline std::ptrdiff_t l3CacheSize()
+{
+ std::ptrdiff_t l1, l2, l3;
+ internal::manage_caching_sizes(GetAction, &l1, &l2, &l3);
+ return l3;
+}
+
+/** Set the cpu L1 and L2 cache sizes (in bytes).
+ * These values are use to adjust the size of the blocks
+ * for the algorithms working per blocks.
+ *
+ * \sa computeProductBlockingSizes */
+inline void setCpuCacheSizes(std::ptrdiff_t l1, std::ptrdiff_t l2, std::ptrdiff_t l3)
+{
+ internal::manage_caching_sizes(SetAction, &l1, &l2, &l3);
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_GENERAL_BLOCK_PANEL_H
diff --git a/Eigen/src/Core/products/GeneralMatrixMatrix.h b/Eigen/src/Core/products/GeneralMatrixMatrix.h
new file mode 100644
index 0000000..38bddac
--- /dev/null
+++ b/Eigen/src/Core/products/GeneralMatrixMatrix.h
@@ -0,0 +1,514 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_GENERAL_MATRIX_MATRIX_H
+#define EIGEN_GENERAL_MATRIX_MATRIX_H
+
+#include "../InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+
+template<typename LhsScalar_, typename RhsScalar_> class level3_blocking;
+
+/* Specialization for a row-major destination matrix => simple transposition of the product */
+template<
+ typename Index,
+ typename LhsScalar, int LhsStorageOrder, bool ConjugateLhs,
+ typename RhsScalar, int RhsStorageOrder, bool ConjugateRhs,
+ int ResInnerStride>
+struct general_matrix_matrix_product<Index,LhsScalar,LhsStorageOrder,ConjugateLhs,RhsScalar,RhsStorageOrder,ConjugateRhs,RowMajor,ResInnerStride>
+{
+ typedef gebp_traits<RhsScalar,LhsScalar> Traits;
+
+ typedef typename ScalarBinaryOpTraits<LhsScalar, RhsScalar>::ReturnType ResScalar;
+ static EIGEN_STRONG_INLINE void run(
+ Index rows, Index cols, Index depth,
+ const LhsScalar* lhs, Index lhsStride,
+ const RhsScalar* rhs, Index rhsStride,
+ ResScalar* res, Index resIncr, Index resStride,
+ ResScalar alpha,
+ level3_blocking<RhsScalar,LhsScalar>& blocking,
+ GemmParallelInfo<Index>* info = 0)
+ {
+ // transpose the product such that the result is column major
+ general_matrix_matrix_product<Index,
+ RhsScalar, RhsStorageOrder==RowMajor ? ColMajor : RowMajor, ConjugateRhs,
+ LhsScalar, LhsStorageOrder==RowMajor ? ColMajor : RowMajor, ConjugateLhs,
+ ColMajor,ResInnerStride>
+ ::run(cols,rows,depth,rhs,rhsStride,lhs,lhsStride,res,resIncr,resStride,alpha,blocking,info);
+ }
+};
+
+/* Specialization for a col-major destination matrix
+ * => Blocking algorithm following Goto's paper */
+template<
+ typename Index,
+ typename LhsScalar, int LhsStorageOrder, bool ConjugateLhs,
+ typename RhsScalar, int RhsStorageOrder, bool ConjugateRhs,
+ int ResInnerStride>
+struct general_matrix_matrix_product<Index,LhsScalar,LhsStorageOrder,ConjugateLhs,RhsScalar,RhsStorageOrder,ConjugateRhs,ColMajor,ResInnerStride>
+{
+
+typedef gebp_traits<LhsScalar,RhsScalar> Traits;
+
+typedef typename ScalarBinaryOpTraits<LhsScalar, RhsScalar>::ReturnType ResScalar;
+static void run(Index rows, Index cols, Index depth,
+ const LhsScalar* _lhs, Index lhsStride,
+ const RhsScalar* _rhs, Index rhsStride,
+ ResScalar* _res, Index resIncr, Index resStride,
+ ResScalar alpha,
+ level3_blocking<LhsScalar,RhsScalar>& blocking,
+ GemmParallelInfo<Index>* info = 0)
+{
+ typedef const_blas_data_mapper<LhsScalar, Index, LhsStorageOrder> LhsMapper;
+ typedef const_blas_data_mapper<RhsScalar, Index, RhsStorageOrder> RhsMapper;
+ typedef blas_data_mapper<typename Traits::ResScalar, Index, ColMajor,Unaligned,ResInnerStride> ResMapper;
+ LhsMapper lhs(_lhs, lhsStride);
+ RhsMapper rhs(_rhs, rhsStride);
+ ResMapper res(_res, resStride, resIncr);
+
+ Index kc = blocking.kc(); // cache block size along the K direction
+ Index mc = (std::min)(rows,blocking.mc()); // cache block size along the M direction
+ Index nc = (std::min)(cols,blocking.nc()); // cache block size along the N direction
+
+ gemm_pack_lhs<LhsScalar, Index, LhsMapper, Traits::mr, Traits::LhsProgress, typename Traits::LhsPacket4Packing, LhsStorageOrder> pack_lhs;
+ gemm_pack_rhs<RhsScalar, Index, RhsMapper, Traits::nr, RhsStorageOrder> pack_rhs;
+ gebp_kernel<LhsScalar, RhsScalar, Index, ResMapper, Traits::mr, Traits::nr, ConjugateLhs, ConjugateRhs> gebp;
+
+#ifdef EIGEN_HAS_OPENMP
+ if(info)
+ {
+ // this is the parallel version!
+ int tid = omp_get_thread_num();
+ int threads = omp_get_num_threads();
+
+ LhsScalar* blockA = blocking.blockA();
+ eigen_internal_assert(blockA!=0);
+
+ std::size_t sizeB = kc*nc;
+ ei_declare_aligned_stack_constructed_variable(RhsScalar, blockB, sizeB, 0);
+
+ // For each horizontal panel of the rhs, and corresponding vertical panel of the lhs...
+ for(Index k=0; k<depth; k+=kc)
+ {
+ const Index actual_kc = (std::min)(k+kc,depth)-k; // => rows of B', and cols of the A'
+
+ // In order to reduce the chance that a thread has to wait for the other,
+ // let's start by packing B'.
+ pack_rhs(blockB, rhs.getSubMapper(k,0), actual_kc, nc);
+
+ // Pack A_k to A' in a parallel fashion:
+ // each thread packs the sub block A_k,i to A'_i where i is the thread id.
+
+ // However, before copying to A'_i, we have to make sure that no other thread is still using it,
+ // i.e., we test that info[tid].users equals 0.
+ // Then, we set info[tid].users to the number of threads to mark that all other threads are going to use it.
+ while(info[tid].users!=0) {}
+ info[tid].users = threads;
+
+ pack_lhs(blockA+info[tid].lhs_start*actual_kc, lhs.getSubMapper(info[tid].lhs_start,k), actual_kc, info[tid].lhs_length);
+
+ // Notify the other threads that the part A'_i is ready to go.
+ info[tid].sync = k;
+
+ // Computes C_i += A' * B' per A'_i
+ for(int shift=0; shift<threads; ++shift)
+ {
+ int i = (tid+shift)%threads;
+
+ // At this point we have to make sure that A'_i has been updated by the thread i,
+ // we use testAndSetOrdered to mimic a volatile access.
+ // However, no need to wait for the B' part which has been updated by the current thread!
+ if (shift>0) {
+ while(info[i].sync!=k) {
+ }
+ }
+
+ gebp(res.getSubMapper(info[i].lhs_start, 0), blockA+info[i].lhs_start*actual_kc, blockB, info[i].lhs_length, actual_kc, nc, alpha);
+ }
+
+ // Then keep going as usual with the remaining B'
+ for(Index j=nc; j<cols; j+=nc)
+ {
+ const Index actual_nc = (std::min)(j+nc,cols)-j;
+
+ // pack B_k,j to B'
+ pack_rhs(blockB, rhs.getSubMapper(k,j), actual_kc, actual_nc);
+
+ // C_j += A' * B'
+ gebp(res.getSubMapper(0, j), blockA, blockB, rows, actual_kc, actual_nc, alpha);
+ }
+
+ // Release all the sub blocks A'_i of A' for the current thread,
+ // i.e., we simply decrement the number of users by 1
+ for(Index i=0; i<threads; ++i)
+ info[i].users -= 1;
+ }
+ }
+ else
+#endif // EIGEN_HAS_OPENMP
+ {
+ EIGEN_UNUSED_VARIABLE(info);
+
+ // this is the sequential version!
+ std::size_t sizeA = kc*mc;
+ std::size_t sizeB = kc*nc;
+
+ ei_declare_aligned_stack_constructed_variable(LhsScalar, blockA, sizeA, blocking.blockA());
+ ei_declare_aligned_stack_constructed_variable(RhsScalar, blockB, sizeB, blocking.blockB());
+
+ const bool pack_rhs_once = mc!=rows && kc==depth && nc==cols;
+
+ // For each horizontal panel of the rhs, and corresponding panel of the lhs...
+ for(Index i2=0; i2<rows; i2+=mc)
+ {
+ const Index actual_mc = (std::min)(i2+mc,rows)-i2;
+
+ for(Index k2=0; k2<depth; k2+=kc)
+ {
+ const Index actual_kc = (std::min)(k2+kc,depth)-k2;
+
+ // OK, here we have selected one horizontal panel of rhs and one vertical panel of lhs.
+ // => Pack lhs's panel into a sequential chunk of memory (L2/L3 caching)
+ // Note that this panel will be read as many times as the number of blocks in the rhs's
+ // horizontal panel which is, in practice, a very low number.
+ pack_lhs(blockA, lhs.getSubMapper(i2,k2), actual_kc, actual_mc);
+
+ // For each kc x nc block of the rhs's horizontal panel...
+ for(Index j2=0; j2<cols; j2+=nc)
+ {
+ const Index actual_nc = (std::min)(j2+nc,cols)-j2;
+
+ // We pack the rhs's block into a sequential chunk of memory (L2 caching)
+ // Note that this block will be read a very high number of times, which is equal to the number of
+ // micro horizontal panel of the large rhs's panel (e.g., rows/12 times).
+ if((!pack_rhs_once) || i2==0)
+ pack_rhs(blockB, rhs.getSubMapper(k2,j2), actual_kc, actual_nc);
+
+ // Everything is packed, we can now call the panel * block kernel:
+ gebp(res.getSubMapper(i2, j2), blockA, blockB, actual_mc, actual_kc, actual_nc, alpha);
+ }
+ }
+ }
+ }
+}
+
+};
+
+/*********************************************************************************
+* Specialization of generic_product_impl for "large" GEMM, i.e.,
+* implementation of the high level wrapper to general_matrix_matrix_product
+**********************************************************************************/
+
+template<typename Scalar, typename Index, typename Gemm, typename Lhs, typename Rhs, typename Dest, typename BlockingType>
+struct gemm_functor
+{
+ gemm_functor(const Lhs& lhs, const Rhs& rhs, Dest& dest, const Scalar& actualAlpha, BlockingType& blocking)
+ : m_lhs(lhs), m_rhs(rhs), m_dest(dest), m_actualAlpha(actualAlpha), m_blocking(blocking)
+ {}
+
+ void initParallelSession(Index num_threads) const
+ {
+ m_blocking.initParallel(m_lhs.rows(), m_rhs.cols(), m_lhs.cols(), num_threads);
+ m_blocking.allocateA();
+ }
+
+ void operator() (Index row, Index rows, Index col=0, Index cols=-1, GemmParallelInfo<Index>* info=0) const
+ {
+ if(cols==-1)
+ cols = m_rhs.cols();
+
+ Gemm::run(rows, cols, m_lhs.cols(),
+ &m_lhs.coeffRef(row,0), m_lhs.outerStride(),
+ &m_rhs.coeffRef(0,col), m_rhs.outerStride(),
+ (Scalar*)&(m_dest.coeffRef(row,col)), m_dest.innerStride(), m_dest.outerStride(),
+ m_actualAlpha, m_blocking, info);
+ }
+
+ typedef typename Gemm::Traits Traits;
+
+ protected:
+ const Lhs& m_lhs;
+ const Rhs& m_rhs;
+ Dest& m_dest;
+ Scalar m_actualAlpha;
+ BlockingType& m_blocking;
+};
+
+template<int StorageOrder, typename LhsScalar, typename RhsScalar, int MaxRows, int MaxCols, int MaxDepth, int KcFactor=1,
+bool FiniteAtCompileTime = MaxRows!=Dynamic && MaxCols!=Dynamic && MaxDepth != Dynamic> class gemm_blocking_space;
+
+template<typename LhsScalar_, typename RhsScalar_>
+class level3_blocking
+{
+ typedef LhsScalar_ LhsScalar;
+ typedef RhsScalar_ RhsScalar;
+
+ protected:
+ LhsScalar* m_blockA;
+ RhsScalar* m_blockB;
+
+ Index m_mc;
+ Index m_nc;
+ Index m_kc;
+
+ public:
+
+ level3_blocking()
+ : m_blockA(0), m_blockB(0), m_mc(0), m_nc(0), m_kc(0)
+ {}
+
+ inline Index mc() const { return m_mc; }
+ inline Index nc() const { return m_nc; }
+ inline Index kc() const { return m_kc; }
+
+ inline LhsScalar* blockA() { return m_blockA; }
+ inline RhsScalar* blockB() { return m_blockB; }
+};
+
+template<int StorageOrder, typename LhsScalar_, typename RhsScalar_, int MaxRows, int MaxCols, int MaxDepth, int KcFactor>
+class gemm_blocking_space<StorageOrder,LhsScalar_,RhsScalar_,MaxRows, MaxCols, MaxDepth, KcFactor, true /* == FiniteAtCompileTime */>
+ : public level3_blocking<
+ std::conditional_t<StorageOrder==RowMajor,RhsScalar_,LhsScalar_>,
+ std::conditional_t<StorageOrder==RowMajor,LhsScalar_,RhsScalar_>>
+{
+ enum {
+ Transpose = StorageOrder==RowMajor,
+ ActualRows = Transpose ? MaxCols : MaxRows,
+ ActualCols = Transpose ? MaxRows : MaxCols
+ };
+ typedef std::conditional_t<Transpose,RhsScalar_,LhsScalar_> LhsScalar;
+ typedef std::conditional_t<Transpose,LhsScalar_,RhsScalar_> RhsScalar;
+ enum {
+ SizeA = ActualRows * MaxDepth,
+ SizeB = ActualCols * MaxDepth
+ };
+
+#if EIGEN_MAX_STATIC_ALIGN_BYTES >= EIGEN_DEFAULT_ALIGN_BYTES
+ EIGEN_ALIGN_MAX LhsScalar m_staticA[SizeA];
+ EIGEN_ALIGN_MAX RhsScalar m_staticB[SizeB];
+#else
+ EIGEN_ALIGN_MAX char m_staticA[SizeA * sizeof(LhsScalar) + EIGEN_DEFAULT_ALIGN_BYTES-1];
+ EIGEN_ALIGN_MAX char m_staticB[SizeB * sizeof(RhsScalar) + EIGEN_DEFAULT_ALIGN_BYTES-1];
+#endif
+
+ public:
+
+ gemm_blocking_space(Index /*rows*/, Index /*cols*/, Index /*depth*/, Index /*num_threads*/, bool /*full_rows = false*/)
+ {
+ this->m_mc = ActualRows;
+ this->m_nc = ActualCols;
+ this->m_kc = MaxDepth;
+#if EIGEN_MAX_STATIC_ALIGN_BYTES >= EIGEN_DEFAULT_ALIGN_BYTES
+ this->m_blockA = m_staticA;
+ this->m_blockB = m_staticB;
+#else
+ this->m_blockA = reinterpret_cast<LhsScalar*>((internal::UIntPtr(m_staticA) + (EIGEN_DEFAULT_ALIGN_BYTES-1)) & ~std::size_t(EIGEN_DEFAULT_ALIGN_BYTES-1));
+ this->m_blockB = reinterpret_cast<RhsScalar*>((internal::UIntPtr(m_staticB) + (EIGEN_DEFAULT_ALIGN_BYTES-1)) & ~std::size_t(EIGEN_DEFAULT_ALIGN_BYTES-1));
+#endif
+ }
+
+ void initParallel(Index, Index, Index, Index)
+ {}
+
+ inline void allocateA() {}
+ inline void allocateB() {}
+ inline void allocateAll() {}
+};
+
+template<int StorageOrder, typename LhsScalar_, typename RhsScalar_, int MaxRows, int MaxCols, int MaxDepth, int KcFactor>
+class gemm_blocking_space<StorageOrder,LhsScalar_,RhsScalar_,MaxRows, MaxCols, MaxDepth, KcFactor, false>
+ : public level3_blocking<
+ std::conditional_t<StorageOrder==RowMajor,RhsScalar_,LhsScalar_>,
+ std::conditional_t<StorageOrder==RowMajor,LhsScalar_,RhsScalar_>>
+{
+ enum {
+ Transpose = StorageOrder==RowMajor
+ };
+ typedef std::conditional_t<Transpose,RhsScalar_,LhsScalar_> LhsScalar;
+ typedef std::conditional_t<Transpose,LhsScalar_,RhsScalar_> RhsScalar;
+
+ Index m_sizeA;
+ Index m_sizeB;
+
+ public:
+
+ gemm_blocking_space(Index rows, Index cols, Index depth, Index num_threads, bool l3_blocking)
+ {
+ this->m_mc = Transpose ? cols : rows;
+ this->m_nc = Transpose ? rows : cols;
+ this->m_kc = depth;
+
+ if(l3_blocking)
+ {
+ computeProductBlockingSizes<LhsScalar,RhsScalar,KcFactor>(this->m_kc, this->m_mc, this->m_nc, num_threads);
+ }
+ else // no l3 blocking
+ {
+ Index n = this->m_nc;
+ computeProductBlockingSizes<LhsScalar,RhsScalar,KcFactor>(this->m_kc, this->m_mc, n, num_threads);
+ }
+
+ m_sizeA = this->m_mc * this->m_kc;
+ m_sizeB = this->m_kc * this->m_nc;
+ }
+
+ void initParallel(Index rows, Index cols, Index depth, Index num_threads)
+ {
+ this->m_mc = Transpose ? cols : rows;
+ this->m_nc = Transpose ? rows : cols;
+ this->m_kc = depth;
+
+ eigen_internal_assert(this->m_blockA==0 && this->m_blockB==0);
+ Index m = this->m_mc;
+ computeProductBlockingSizes<LhsScalar,RhsScalar,KcFactor>(this->m_kc, m, this->m_nc, num_threads);
+ m_sizeA = this->m_mc * this->m_kc;
+ m_sizeB = this->m_kc * this->m_nc;
+ }
+
+ void allocateA()
+ {
+ if(this->m_blockA==0)
+ this->m_blockA = aligned_new<LhsScalar>(m_sizeA);
+ }
+
+ void allocateB()
+ {
+ if(this->m_blockB==0)
+ this->m_blockB = aligned_new<RhsScalar>(m_sizeB);
+ }
+
+ void allocateAll()
+ {
+ allocateA();
+ allocateB();
+ }
+
+ ~gemm_blocking_space()
+ {
+ aligned_delete(this->m_blockA, m_sizeA);
+ aligned_delete(this->m_blockB, m_sizeB);
+ }
+};
+
+} // end namespace internal
+
+namespace internal {
+
+template<typename Lhs, typename Rhs>
+struct generic_product_impl<Lhs,Rhs,DenseShape,DenseShape,GemmProduct>
+ : generic_product_impl_base<Lhs,Rhs,generic_product_impl<Lhs,Rhs,DenseShape,DenseShape,GemmProduct> >
+{
+ typedef typename Product<Lhs,Rhs>::Scalar Scalar;
+ typedef typename Lhs::Scalar LhsScalar;
+ typedef typename Rhs::Scalar RhsScalar;
+
+ typedef internal::blas_traits<Lhs> LhsBlasTraits;
+ typedef typename LhsBlasTraits::DirectLinearAccessType ActualLhsType;
+ typedef internal::remove_all_t<ActualLhsType> ActualLhsTypeCleaned;
+
+ typedef internal::blas_traits<Rhs> RhsBlasTraits;
+ typedef typename RhsBlasTraits::DirectLinearAccessType ActualRhsType;
+ typedef internal::remove_all_t<ActualRhsType> ActualRhsTypeCleaned;
+
+ enum {
+ MaxDepthAtCompileTime = min_size_prefer_fixed(Lhs::MaxColsAtCompileTime, Rhs::MaxRowsAtCompileTime)
+ };
+
+ typedef generic_product_impl<Lhs,Rhs,DenseShape,DenseShape,CoeffBasedProductMode> lazyproduct;
+
+ template<typename Dst>
+ static void evalTo(Dst& dst, const Lhs& lhs, const Rhs& rhs)
+ {
+ // See http://eigen.tuxfamily.org/bz/show_bug.cgi?id=404 for a discussion and helper program
+ // to determine the following heuristic.
+ // EIGEN_GEMM_TO_COEFFBASED_THRESHOLD is typically defined to 20 in GeneralProduct.h,
+ // unless it has been specialized by the user or for a given architecture.
+ // Note that the condition rhs.rows()>0 was required because lazy product is (was?) not happy with empty inputs.
+ // I'm not sure it is still required.
+ if((rhs.rows()+dst.rows()+dst.cols())<EIGEN_GEMM_TO_COEFFBASED_THRESHOLD && rhs.rows()>0)
+ lazyproduct::eval_dynamic(dst, lhs, rhs, internal::assign_op<typename Dst::Scalar,Scalar>());
+ else
+ {
+ dst.setZero();
+ scaleAndAddTo(dst, lhs, rhs, Scalar(1));
+ }
+ }
+
+ template<typename Dst>
+ static void addTo(Dst& dst, const Lhs& lhs, const Rhs& rhs)
+ {
+ if((rhs.rows()+dst.rows()+dst.cols())<EIGEN_GEMM_TO_COEFFBASED_THRESHOLD && rhs.rows()>0)
+ lazyproduct::eval_dynamic(dst, lhs, rhs, internal::add_assign_op<typename Dst::Scalar,Scalar>());
+ else
+ scaleAndAddTo(dst,lhs, rhs, Scalar(1));
+ }
+
+ template<typename Dst>
+ static void subTo(Dst& dst, const Lhs& lhs, const Rhs& rhs)
+ {
+ if((rhs.rows()+dst.rows()+dst.cols())<EIGEN_GEMM_TO_COEFFBASED_THRESHOLD && rhs.rows()>0)
+ lazyproduct::eval_dynamic(dst, lhs, rhs, internal::sub_assign_op<typename Dst::Scalar,Scalar>());
+ else
+ scaleAndAddTo(dst, lhs, rhs, Scalar(-1));
+ }
+
+ template<typename Dest>
+ static void scaleAndAddTo(Dest& dst, const Lhs& a_lhs, const Rhs& a_rhs, const Scalar& alpha)
+ {
+ eigen_assert(dst.rows()==a_lhs.rows() && dst.cols()==a_rhs.cols());
+ if(a_lhs.cols()==0 || a_lhs.rows()==0 || a_rhs.cols()==0)
+ return;
+
+ if (dst.cols() == 1)
+ {
+ // Fallback to GEMV if either the lhs or rhs is a runtime vector
+ typename Dest::ColXpr dst_vec(dst.col(0));
+ return internal::generic_product_impl<Lhs,typename Rhs::ConstColXpr,DenseShape,DenseShape,GemvProduct>
+ ::scaleAndAddTo(dst_vec, a_lhs, a_rhs.col(0), alpha);
+ }
+ else if (dst.rows() == 1)
+ {
+ // Fallback to GEMV if either the lhs or rhs is a runtime vector
+ typename Dest::RowXpr dst_vec(dst.row(0));
+ return internal::generic_product_impl<typename Lhs::ConstRowXpr,Rhs,DenseShape,DenseShape,GemvProduct>
+ ::scaleAndAddTo(dst_vec, a_lhs.row(0), a_rhs, alpha);
+ }
+
+ add_const_on_value_type_t<ActualLhsType> lhs = LhsBlasTraits::extract(a_lhs);
+ add_const_on_value_type_t<ActualRhsType> rhs = RhsBlasTraits::extract(a_rhs);
+
+ Scalar actualAlpha = combine_scalar_factors(alpha, a_lhs, a_rhs);
+
+ typedef internal::gemm_blocking_space<(Dest::Flags&RowMajorBit) ? RowMajor : ColMajor,LhsScalar,RhsScalar,
+ Dest::MaxRowsAtCompileTime,Dest::MaxColsAtCompileTime,MaxDepthAtCompileTime> BlockingType;
+
+ typedef internal::gemm_functor<
+ Scalar, Index,
+ internal::general_matrix_matrix_product<
+ Index,
+ LhsScalar, (ActualLhsTypeCleaned::Flags&RowMajorBit) ? RowMajor : ColMajor, bool(LhsBlasTraits::NeedToConjugate),
+ RhsScalar, (ActualRhsTypeCleaned::Flags&RowMajorBit) ? RowMajor : ColMajor, bool(RhsBlasTraits::NeedToConjugate),
+ (Dest::Flags&RowMajorBit) ? RowMajor : ColMajor,
+ Dest::InnerStrideAtCompileTime>,
+ ActualLhsTypeCleaned, ActualRhsTypeCleaned, Dest, BlockingType> GemmFunctor;
+
+ BlockingType blocking(dst.rows(), dst.cols(), lhs.cols(), 1, true);
+ internal::parallelize_gemm<(Dest::MaxRowsAtCompileTime>32 || Dest::MaxRowsAtCompileTime==Dynamic)>
+ (GemmFunctor(lhs, rhs, dst, actualAlpha, blocking), a_lhs.rows(), a_rhs.cols(), a_lhs.cols(), Dest::Flags&RowMajorBit);
+ }
+};
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_GENERAL_MATRIX_MATRIX_H
diff --git a/Eigen/src/Core/products/GeneralMatrixMatrixTriangular.h b/Eigen/src/Core/products/GeneralMatrixMatrixTriangular.h
new file mode 100644
index 0000000..716f2ca
--- /dev/null
+++ b/Eigen/src/Core/products/GeneralMatrixMatrixTriangular.h
@@ -0,0 +1,319 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009-2010 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_GENERAL_MATRIX_MATRIX_TRIANGULAR_H
+#define EIGEN_GENERAL_MATRIX_MATRIX_TRIANGULAR_H
+
+#include "../InternalHeaderCheck.h"
+
+namespace Eigen {
+
+template<typename Scalar, typename Index, int StorageOrder, int UpLo, bool ConjLhs, bool ConjRhs>
+struct selfadjoint_rank1_update;
+
+namespace internal {
+
+/**********************************************************************
+* This file implements a general A * B product while
+* evaluating only one triangular part of the product.
+* This is a more general version of self adjoint product (C += A A^T)
+* as the level 3 SYRK Blas routine.
+**********************************************************************/
+
+// forward declarations (defined at the end of this file)
+template<typename LhsScalar, typename RhsScalar, typename Index, int mr, int nr, bool ConjLhs, bool ConjRhs, int ResInnerStride, int UpLo>
+struct tribb_kernel;
+
+/* Optimized matrix-matrix product evaluating only one triangular half */
+template <typename Index,
+ typename LhsScalar, int LhsStorageOrder, bool ConjugateLhs,
+ typename RhsScalar, int RhsStorageOrder, bool ConjugateRhs,
+ int ResStorageOrder, int ResInnerStride, int UpLo, int Version = Specialized>
+struct general_matrix_matrix_triangular_product;
+
+// as usual if the result is row major => we transpose the product
+template <typename Index, typename LhsScalar, int LhsStorageOrder, bool ConjugateLhs,
+ typename RhsScalar, int RhsStorageOrder, bool ConjugateRhs,
+ int ResInnerStride, int UpLo, int Version>
+struct general_matrix_matrix_triangular_product<Index,LhsScalar,LhsStorageOrder,ConjugateLhs,RhsScalar,RhsStorageOrder,ConjugateRhs,RowMajor,ResInnerStride,UpLo,Version>
+{
+ typedef typename ScalarBinaryOpTraits<LhsScalar, RhsScalar>::ReturnType ResScalar;
+ static EIGEN_STRONG_INLINE void run(Index size, Index depth,const LhsScalar* lhs, Index lhsStride,
+ const RhsScalar* rhs, Index rhsStride, ResScalar* res, Index resIncr, Index resStride,
+ const ResScalar& alpha, level3_blocking<RhsScalar,LhsScalar>& blocking)
+ {
+ general_matrix_matrix_triangular_product<Index,
+ RhsScalar, RhsStorageOrder==RowMajor ? ColMajor : RowMajor, ConjugateRhs,
+ LhsScalar, LhsStorageOrder==RowMajor ? ColMajor : RowMajor, ConjugateLhs,
+ ColMajor, ResInnerStride, UpLo==Lower?Upper:Lower>
+ ::run(size,depth,rhs,rhsStride,lhs,lhsStride,res,resIncr,resStride,alpha,blocking);
+ }
+};
+
+template <typename Index, typename LhsScalar, int LhsStorageOrder, bool ConjugateLhs,
+ typename RhsScalar, int RhsStorageOrder, bool ConjugateRhs,
+ int ResInnerStride, int UpLo, int Version>
+struct general_matrix_matrix_triangular_product<Index,LhsScalar,LhsStorageOrder,ConjugateLhs,RhsScalar,RhsStorageOrder,ConjugateRhs,ColMajor,ResInnerStride,UpLo,Version>
+{
+ typedef typename ScalarBinaryOpTraits<LhsScalar, RhsScalar>::ReturnType ResScalar;
+ static EIGEN_STRONG_INLINE void run(Index size, Index depth,const LhsScalar* _lhs, Index lhsStride,
+ const RhsScalar* _rhs, Index rhsStride,
+ ResScalar* _res, Index resIncr, Index resStride,
+ const ResScalar& alpha, level3_blocking<LhsScalar,RhsScalar>& blocking)
+ {
+ typedef gebp_traits<LhsScalar,RhsScalar> Traits;
+
+ typedef const_blas_data_mapper<LhsScalar, Index, LhsStorageOrder> LhsMapper;
+ typedef const_blas_data_mapper<RhsScalar, Index, RhsStorageOrder> RhsMapper;
+ typedef blas_data_mapper<typename Traits::ResScalar, Index, ColMajor, Unaligned, ResInnerStride> ResMapper;
+ LhsMapper lhs(_lhs,lhsStride);
+ RhsMapper rhs(_rhs,rhsStride);
+ ResMapper res(_res, resStride, resIncr);
+
+ Index kc = blocking.kc();
+ Index mc = (std::min)(size,blocking.mc());
+
+ // !!! mc must be a multiple of nr:
+ if(mc > Traits::nr)
+ mc = (mc/Traits::nr)*Traits::nr;
+
+ std::size_t sizeA = kc*mc;
+ std::size_t sizeB = kc*size;
+
+ ei_declare_aligned_stack_constructed_variable(LhsScalar, blockA, sizeA, blocking.blockA());
+ ei_declare_aligned_stack_constructed_variable(RhsScalar, blockB, sizeB, blocking.blockB());
+
+ gemm_pack_lhs<LhsScalar, Index, LhsMapper, Traits::mr, Traits::LhsProgress, typename Traits::LhsPacket4Packing, LhsStorageOrder> pack_lhs;
+ gemm_pack_rhs<RhsScalar, Index, RhsMapper, Traits::nr, RhsStorageOrder> pack_rhs;
+ gebp_kernel<LhsScalar, RhsScalar, Index, ResMapper, Traits::mr, Traits::nr, ConjugateLhs, ConjugateRhs> gebp;
+ tribb_kernel<LhsScalar, RhsScalar, Index, Traits::mr, Traits::nr, ConjugateLhs, ConjugateRhs, ResInnerStride, UpLo> sybb;
+
+ for(Index k2=0; k2<depth; k2+=kc)
+ {
+ const Index actual_kc = (std::min)(k2+kc,depth)-k2;
+
+ // note that the actual rhs is the transpose/adjoint of mat
+ pack_rhs(blockB, rhs.getSubMapper(k2,0), actual_kc, size);
+
+ for(Index i2=0; i2<size; i2+=mc)
+ {
+ const Index actual_mc = (std::min)(i2+mc,size)-i2;
+
+ pack_lhs(blockA, lhs.getSubMapper(i2, k2), actual_kc, actual_mc);
+
+ // the selected actual_mc * size panel of res is split into three different part:
+ // 1 - before the diagonal => processed with gebp or skipped
+ // 2 - the actual_mc x actual_mc symmetric block => processed with a special kernel
+ // 3 - after the diagonal => processed with gebp or skipped
+ if (UpLo==Lower)
+ gebp(res.getSubMapper(i2, 0), blockA, blockB, actual_mc, actual_kc,
+ (std::min)(size,i2), alpha, -1, -1, 0, 0);
+
+ sybb(_res+resStride*i2 + resIncr*i2, resIncr, resStride, blockA, blockB + actual_kc*i2, actual_mc, actual_kc, alpha);
+
+ if (UpLo==Upper)
+ {
+ Index j2 = i2+actual_mc;
+ gebp(res.getSubMapper(i2, j2), blockA, blockB+actual_kc*j2, actual_mc,
+ actual_kc, (std::max)(Index(0), size-j2), alpha, -1, -1, 0, 0);
+ }
+ }
+ }
+ }
+};
+
+// Optimized packed Block * packed Block product kernel evaluating only one given triangular part
+// This kernel is built on top of the gebp kernel:
+// - the current destination block is processed per panel of actual_mc x BlockSize
+// where BlockSize is set to the minimal value allowing gebp to be as fast as possible
+// - then, as usual, each panel is split into three parts along the diagonal,
+// the sub blocks above and below the diagonal are processed as usual,
+// while the triangular block overlapping the diagonal is evaluated into a
+// small temporary buffer which is then accumulated into the result using a
+// triangular traversal.
+template<typename LhsScalar, typename RhsScalar, typename Index, int mr, int nr, bool ConjLhs, bool ConjRhs, int ResInnerStride, int UpLo>
+struct tribb_kernel
+{
+ typedef gebp_traits<LhsScalar,RhsScalar,ConjLhs,ConjRhs> Traits;
+ typedef typename Traits::ResScalar ResScalar;
+
+ enum {
+ BlockSize = meta_least_common_multiple<plain_enum_max(mr, nr), plain_enum_min(mr,nr)>::ret
+ };
+ void operator()(ResScalar* _res, Index resIncr, Index resStride, const LhsScalar* blockA, const RhsScalar* blockB, Index size, Index depth, const ResScalar& alpha)
+ {
+ typedef blas_data_mapper<ResScalar, Index, ColMajor, Unaligned, ResInnerStride> ResMapper;
+ typedef blas_data_mapper<ResScalar, Index, ColMajor, Unaligned> BufferMapper;
+ ResMapper res(_res, resStride, resIncr);
+ gebp_kernel<LhsScalar, RhsScalar, Index, ResMapper, mr, nr, ConjLhs, ConjRhs> gebp_kernel1;
+ gebp_kernel<LhsScalar, RhsScalar, Index, BufferMapper, mr, nr, ConjLhs, ConjRhs> gebp_kernel2;
+
+ Matrix<ResScalar,BlockSize,BlockSize,ColMajor> buffer((internal::constructor_without_unaligned_array_assert()));
+
+ // let's process the block per panel of actual_mc x BlockSize,
+ // again, each is split into three parts, etc.
+ for (Index j=0; j<size; j+=BlockSize)
+ {
+ Index actualBlockSize = std::min<Index>(BlockSize,size - j);
+ const RhsScalar* actual_b = blockB+j*depth;
+
+ if(UpLo==Upper)
+ gebp_kernel1(res.getSubMapper(0, j), blockA, actual_b, j, depth, actualBlockSize, alpha,
+ -1, -1, 0, 0);
+
+ // selfadjoint micro block
+ {
+ Index i = j;
+ buffer.setZero();
+ // 1 - apply the kernel on the temporary buffer
+ gebp_kernel2(BufferMapper(buffer.data(), BlockSize), blockA+depth*i, actual_b, actualBlockSize, depth, actualBlockSize, alpha,
+ -1, -1, 0, 0);
+
+ // 2 - triangular accumulation
+ for(Index j1=0; j1<actualBlockSize; ++j1)
+ {
+ typename ResMapper::LinearMapper r = res.getLinearMapper(i,j+j1);
+ for(Index i1=UpLo==Lower ? j1 : 0;
+ UpLo==Lower ? i1<actualBlockSize : i1<=j1; ++i1)
+ r(i1) += buffer(i1,j1);
+ }
+ }
+
+ if(UpLo==Lower)
+ {
+ Index i = j+actualBlockSize;
+ gebp_kernel1(res.getSubMapper(i, j), blockA+depth*i, actual_b, size-i,
+ depth, actualBlockSize, alpha, -1, -1, 0, 0);
+ }
+ }
+ }
+};
+
+} // end namespace internal
+
+// high level API
+
+template<typename MatrixType, typename ProductType, int UpLo, bool IsOuterProduct>
+struct general_product_to_triangular_selector;
+
+
+template<typename MatrixType, typename ProductType, int UpLo>
+struct general_product_to_triangular_selector<MatrixType,ProductType,UpLo,true>
+{
+ static void run(MatrixType& mat, const ProductType& prod, const typename MatrixType::Scalar& alpha, bool beta)
+ {
+ typedef typename MatrixType::Scalar Scalar;
+
+ typedef internal::remove_all_t<typename ProductType::LhsNested> Lhs;
+ typedef internal::blas_traits<Lhs> LhsBlasTraits;
+ typedef typename LhsBlasTraits::DirectLinearAccessType ActualLhs;
+ typedef internal::remove_all_t<ActualLhs> ActualLhs_;
+ internal::add_const_on_value_type_t<ActualLhs> actualLhs = LhsBlasTraits::extract(prod.lhs());
+
+ typedef internal::remove_all_t<typename ProductType::RhsNested> Rhs;
+ typedef internal::blas_traits<Rhs> RhsBlasTraits;
+ typedef typename RhsBlasTraits::DirectLinearAccessType ActualRhs;
+ typedef internal::remove_all_t<ActualRhs> ActualRhs_;
+ internal::add_const_on_value_type_t<ActualRhs> actualRhs = RhsBlasTraits::extract(prod.rhs());
+
+ Scalar actualAlpha = alpha * LhsBlasTraits::extractScalarFactor(prod.lhs().derived()) * RhsBlasTraits::extractScalarFactor(prod.rhs().derived());
+
+ if(!beta)
+ mat.template triangularView<UpLo>().setZero();
+
+ enum {
+ StorageOrder = (internal::traits<MatrixType>::Flags&RowMajorBit) ? RowMajor : ColMajor,
+ UseLhsDirectly = ActualLhs_::InnerStrideAtCompileTime==1,
+ UseRhsDirectly = ActualRhs_::InnerStrideAtCompileTime==1
+ };
+
+ internal::gemv_static_vector_if<Scalar,Lhs::SizeAtCompileTime,Lhs::MaxSizeAtCompileTime,!UseLhsDirectly> static_lhs;
+ ei_declare_aligned_stack_constructed_variable(Scalar, actualLhsPtr, actualLhs.size(),
+ (UseLhsDirectly ? const_cast<Scalar*>(actualLhs.data()) : static_lhs.data()));
+ if(!UseLhsDirectly) Map<typename ActualLhs_::PlainObject>(actualLhsPtr, actualLhs.size()) = actualLhs;
+
+ internal::gemv_static_vector_if<Scalar,Rhs::SizeAtCompileTime,Rhs::MaxSizeAtCompileTime,!UseRhsDirectly> static_rhs;
+ ei_declare_aligned_stack_constructed_variable(Scalar, actualRhsPtr, actualRhs.size(),
+ (UseRhsDirectly ? const_cast<Scalar*>(actualRhs.data()) : static_rhs.data()));
+ if(!UseRhsDirectly) Map<typename ActualRhs_::PlainObject>(actualRhsPtr, actualRhs.size()) = actualRhs;
+
+
+ selfadjoint_rank1_update<Scalar,Index,StorageOrder,UpLo,
+ LhsBlasTraits::NeedToConjugate && NumTraits<Scalar>::IsComplex,
+ RhsBlasTraits::NeedToConjugate && NumTraits<Scalar>::IsComplex>
+ ::run(actualLhs.size(), mat.data(), mat.outerStride(), actualLhsPtr, actualRhsPtr, actualAlpha);
+ }
+};
+
+template<typename MatrixType, typename ProductType, int UpLo>
+struct general_product_to_triangular_selector<MatrixType,ProductType,UpLo,false>
+{
+ static void run(MatrixType& mat, const ProductType& prod, const typename MatrixType::Scalar& alpha, bool beta)
+ {
+ typedef internal::remove_all_t<typename ProductType::LhsNested> Lhs;
+ typedef internal::blas_traits<Lhs> LhsBlasTraits;
+ typedef typename LhsBlasTraits::DirectLinearAccessType ActualLhs;
+ typedef internal::remove_all_t<ActualLhs> ActualLhs_;
+ internal::add_const_on_value_type_t<ActualLhs> actualLhs = LhsBlasTraits::extract(prod.lhs());
+
+ typedef internal::remove_all_t<typename ProductType::RhsNested> Rhs;
+ typedef internal::blas_traits<Rhs> RhsBlasTraits;
+ typedef typename RhsBlasTraits::DirectLinearAccessType ActualRhs;
+ typedef internal::remove_all_t<ActualRhs> ActualRhs_;
+ internal::add_const_on_value_type_t<ActualRhs> actualRhs = RhsBlasTraits::extract(prod.rhs());
+
+ typename ProductType::Scalar actualAlpha = alpha * LhsBlasTraits::extractScalarFactor(prod.lhs().derived()) * RhsBlasTraits::extractScalarFactor(prod.rhs().derived());
+
+ if(!beta)
+ mat.template triangularView<UpLo>().setZero();
+
+ enum {
+ IsRowMajor = (internal::traits<MatrixType>::Flags&RowMajorBit) ? 1 : 0,
+ LhsIsRowMajor = ActualLhs_::Flags&RowMajorBit ? 1 : 0,
+ RhsIsRowMajor = ActualRhs_::Flags&RowMajorBit ? 1 : 0,
+ SkipDiag = (UpLo&(UnitDiag|ZeroDiag))!=0
+ };
+
+ Index size = mat.cols();
+ if(SkipDiag)
+ size--;
+ Index depth = actualLhs.cols();
+
+ typedef internal::gemm_blocking_space<IsRowMajor ? RowMajor : ColMajor,typename Lhs::Scalar,typename Rhs::Scalar,
+ MatrixType::MaxColsAtCompileTime, MatrixType::MaxColsAtCompileTime, ActualRhs_::MaxColsAtCompileTime> BlockingType;
+
+ BlockingType blocking(size, size, depth, 1, false);
+
+ internal::general_matrix_matrix_triangular_product<Index,
+ typename Lhs::Scalar, LhsIsRowMajor ? RowMajor : ColMajor, LhsBlasTraits::NeedToConjugate,
+ typename Rhs::Scalar, RhsIsRowMajor ? RowMajor : ColMajor, RhsBlasTraits::NeedToConjugate,
+ IsRowMajor ? RowMajor : ColMajor, MatrixType::InnerStrideAtCompileTime, UpLo&(Lower|Upper)>
+ ::run(size, depth,
+ &actualLhs.coeffRef(SkipDiag&&(UpLo&Lower)==Lower ? 1 : 0,0), actualLhs.outerStride(),
+ &actualRhs.coeffRef(0,SkipDiag&&(UpLo&Upper)==Upper ? 1 : 0), actualRhs.outerStride(),
+ mat.data() + (SkipDiag ? (bool(IsRowMajor) != ((UpLo&Lower)==Lower) ? mat.innerStride() : mat.outerStride() ) : 0),
+ mat.innerStride(), mat.outerStride(), actualAlpha, blocking);
+ }
+};
+
+template<typename MatrixType, unsigned int UpLo>
+template<typename ProductType>
+EIGEN_DEVICE_FUNC TriangularView<MatrixType,UpLo>& TriangularViewImpl<MatrixType,UpLo,Dense>::_assignProduct(const ProductType& prod, const Scalar& alpha, bool beta)
+{
+ EIGEN_STATIC_ASSERT((UpLo&UnitDiag)==0, WRITING_TO_TRIANGULAR_PART_WITH_UNIT_DIAGONAL_IS_NOT_SUPPORTED);
+ eigen_assert(derived().nestedExpression().rows() == prod.rows() && derived().cols() == prod.cols());
+
+ general_product_to_triangular_selector<MatrixType, ProductType, UpLo, internal::traits<ProductType>::InnerSize==1>::run(derived().nestedExpression().const_cast_derived(), prod, alpha, beta);
+
+ return derived();
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_GENERAL_MATRIX_MATRIX_TRIANGULAR_H
diff --git a/Eigen/src/Core/products/GeneralMatrixMatrixTriangular_BLAS.h b/Eigen/src/Core/products/GeneralMatrixMatrixTriangular_BLAS.h
new file mode 100644
index 0000000..45ad5da
--- /dev/null
+++ b/Eigen/src/Core/products/GeneralMatrixMatrixTriangular_BLAS.h
@@ -0,0 +1,147 @@
+/*
+ Copyright (c) 2011, Intel Corporation. All rights reserved.
+
+ Redistribution and use in source and binary forms, with or without modification,
+ are permitted provided that the following conditions are met:
+
+ * Redistributions of source code must retain the above copyright notice, this
+ list of conditions and the following disclaimer.
+ * Redistributions in binary form must reproduce the above copyright notice,
+ this list of conditions and the following disclaimer in the documentation
+ and/or other materials provided with the distribution.
+ * Neither the name of Intel Corporation nor the names of its contributors may
+ be used to endorse or promote products derived from this software without
+ specific prior written permission.
+
+ THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
+ ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
+ WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
+ DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR
+ ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
+ (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
+ LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON
+ ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
+ (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
+ SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+
+ ********************************************************************************
+ * Content : Eigen bindings to BLAS F77
+ * Level 3 BLAS SYRK/HERK implementation.
+ ********************************************************************************
+*/
+
+#ifndef EIGEN_GENERAL_MATRIX_MATRIX_TRIANGULAR_BLAS_H
+#define EIGEN_GENERAL_MATRIX_MATRIX_TRIANGULAR_BLAS_H
+
+#include "../InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+
+template <typename Index, typename Scalar, int AStorageOrder, bool ConjugateA, int ResStorageOrder, int UpLo>
+struct general_matrix_matrix_rankupdate :
+ general_matrix_matrix_triangular_product<
+ Index,Scalar,AStorageOrder,ConjugateA,Scalar,AStorageOrder,ConjugateA,ResStorageOrder,1,UpLo,BuiltIn> {};
+
+
+// try to go to BLAS specialization
+#define EIGEN_BLAS_RANKUPDATE_SPECIALIZE(Scalar) \
+template <typename Index, int LhsStorageOrder, bool ConjugateLhs, \
+ int RhsStorageOrder, bool ConjugateRhs, int UpLo> \
+struct general_matrix_matrix_triangular_product<Index,Scalar,LhsStorageOrder,ConjugateLhs, \
+ Scalar,RhsStorageOrder,ConjugateRhs,ColMajor,1,UpLo,Specialized> { \
+ static EIGEN_STRONG_INLINE void run(Index size, Index depth,const Scalar* lhs, Index lhsStride, \
+ const Scalar* rhs, Index rhsStride, Scalar* res, Index resIncr, Index resStride, Scalar alpha, level3_blocking<Scalar, Scalar>& blocking) \
+ { \
+ if ( lhs==rhs && ((UpLo&(Lower|Upper))==UpLo) ) { \
+ general_matrix_matrix_rankupdate<Index,Scalar,LhsStorageOrder,ConjugateLhs,ColMajor,UpLo> \
+ ::run(size,depth,lhs,lhsStride,rhs,rhsStride,res,resStride,alpha,blocking); \
+ } else { \
+ general_matrix_matrix_triangular_product<Index, \
+ Scalar, LhsStorageOrder, ConjugateLhs, \
+ Scalar, RhsStorageOrder, ConjugateRhs, \
+ ColMajor, 1, UpLo, BuiltIn> \
+ ::run(size,depth,lhs,lhsStride,rhs,rhsStride,res,resIncr,resStride,alpha,blocking); \
+ } \
+ } \
+};
+
+EIGEN_BLAS_RANKUPDATE_SPECIALIZE(double)
+EIGEN_BLAS_RANKUPDATE_SPECIALIZE(float)
+// TODO handle complex cases
+// EIGEN_BLAS_RANKUPDATE_SPECIALIZE(dcomplex)
+// EIGEN_BLAS_RANKUPDATE_SPECIALIZE(scomplex)
+
+// SYRK for float/double
+#define EIGEN_BLAS_RANKUPDATE_R(EIGTYPE, BLASTYPE, BLASFUNC) \
+template <typename Index, int AStorageOrder, bool ConjugateA, int UpLo> \
+struct general_matrix_matrix_rankupdate<Index,EIGTYPE,AStorageOrder,ConjugateA,ColMajor,UpLo> { \
+ enum { \
+ IsLower = (UpLo&Lower) == Lower, \
+ LowUp = IsLower ? Lower : Upper, \
+ conjA = ((AStorageOrder==ColMajor) && ConjugateA) ? 1 : 0 \
+ }; \
+ static EIGEN_STRONG_INLINE void run(Index size, Index depth,const EIGTYPE* lhs, Index lhsStride, \
+ const EIGTYPE* /*rhs*/, Index /*rhsStride*/, EIGTYPE* res, Index resStride, EIGTYPE alpha, level3_blocking<EIGTYPE, EIGTYPE>& /*blocking*/) \
+ { \
+ /* typedef Matrix<EIGTYPE, Dynamic, Dynamic, RhsStorageOrder> MatrixRhs;*/ \
+\
+ BlasIndex lda=convert_index<BlasIndex>(lhsStride), ldc=convert_index<BlasIndex>(resStride), n=convert_index<BlasIndex>(size), k=convert_index<BlasIndex>(depth); \
+ char uplo=((IsLower) ? 'L' : 'U'), trans=((AStorageOrder==RowMajor) ? 'T':'N'); \
+ EIGTYPE beta(1); \
+ BLASFUNC(&uplo, &trans, &n, &k, (const BLASTYPE*)&numext::real_ref(alpha), lhs, &lda, (const BLASTYPE*)&numext::real_ref(beta), res, &ldc); \
+ } \
+};
+
+// HERK for complex data
+#define EIGEN_BLAS_RANKUPDATE_C(EIGTYPE, BLASTYPE, RTYPE, BLASFUNC) \
+template <typename Index, int AStorageOrder, bool ConjugateA, int UpLo> \
+struct general_matrix_matrix_rankupdate<Index,EIGTYPE,AStorageOrder,ConjugateA,ColMajor,UpLo> { \
+ enum { \
+ IsLower = (UpLo&Lower) == Lower, \
+ LowUp = IsLower ? Lower : Upper, \
+ conjA = (((AStorageOrder==ColMajor) && ConjugateA) || ((AStorageOrder==RowMajor) && !ConjugateA)) ? 1 : 0 \
+ }; \
+ static EIGEN_STRONG_INLINE void run(Index size, Index depth,const EIGTYPE* lhs, Index lhsStride, \
+ const EIGTYPE* /*rhs*/, Index /*rhsStride*/, EIGTYPE* res, Index resStride, EIGTYPE alpha, level3_blocking<EIGTYPE, EIGTYPE>& /*blocking*/) \
+ { \
+ typedef Matrix<EIGTYPE, Dynamic, Dynamic, AStorageOrder> MatrixType; \
+\
+ BlasIndex lda=convert_index<BlasIndex>(lhsStride), ldc=convert_index<BlasIndex>(resStride), n=convert_index<BlasIndex>(size), k=convert_index<BlasIndex>(depth); \
+ char uplo=((IsLower) ? 'L' : 'U'), trans=((AStorageOrder==RowMajor) ? 'C':'N'); \
+ RTYPE alpha_, beta_; \
+ const EIGTYPE* a_ptr; \
+\
+ alpha_ = alpha.real(); \
+ beta_ = 1.0; \
+/* Copy with conjugation in some cases*/ \
+ MatrixType a; \
+ if (conjA) { \
+ Map<const MatrixType, 0, OuterStride<> > mapA(lhs,n,k,OuterStride<>(lhsStride)); \
+ a = mapA.conjugate(); \
+ lda = a.outerStride(); \
+ a_ptr = a.data(); \
+ } else a_ptr=lhs; \
+ BLASFUNC(&uplo, &trans, &n, &k, &alpha_, (BLASTYPE*)a_ptr, &lda, &beta_, (BLASTYPE*)res, &ldc); \
+ } \
+};
+
+#ifdef EIGEN_USE_MKL
+EIGEN_BLAS_RANKUPDATE_R(double, double, dsyrk)
+EIGEN_BLAS_RANKUPDATE_R(float, float, ssyrk)
+#else
+EIGEN_BLAS_RANKUPDATE_R(double, double, dsyrk_)
+EIGEN_BLAS_RANKUPDATE_R(float, float, ssyrk_)
+#endif
+
+// TODO hanlde complex cases
+// EIGEN_BLAS_RANKUPDATE_C(dcomplex, double, double, zherk_)
+// EIGEN_BLAS_RANKUPDATE_C(scomplex, float, float, cherk_)
+
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_GENERAL_MATRIX_MATRIX_TRIANGULAR_BLAS_H
diff --git a/Eigen/src/Core/products/GeneralMatrixMatrix_BLAS.h b/Eigen/src/Core/products/GeneralMatrixMatrix_BLAS.h
new file mode 100644
index 0000000..490fe67
--- /dev/null
+++ b/Eigen/src/Core/products/GeneralMatrixMatrix_BLAS.h
@@ -0,0 +1,126 @@
+/*
+ Copyright (c) 2011, Intel Corporation. All rights reserved.
+
+ Redistribution and use in source and binary forms, with or without modification,
+ are permitted provided that the following conditions are met:
+
+ * Redistributions of source code must retain the above copyright notice, this
+ list of conditions and the following disclaimer.
+ * Redistributions in binary form must reproduce the above copyright notice,
+ this list of conditions and the following disclaimer in the documentation
+ and/or other materials provided with the distribution.
+ * Neither the name of Intel Corporation nor the names of its contributors may
+ be used to endorse or promote products derived from this software without
+ specific prior written permission.
+
+ THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
+ ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
+ WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
+ DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR
+ ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
+ (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
+ LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON
+ ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
+ (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
+ SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+
+ ********************************************************************************
+ * Content : Eigen bindings to BLAS F77
+ * General matrix-matrix product functionality based on ?GEMM.
+ ********************************************************************************
+*/
+
+#ifndef EIGEN_GENERAL_MATRIX_MATRIX_BLAS_H
+#define EIGEN_GENERAL_MATRIX_MATRIX_BLAS_H
+
+#include "../InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+
+/**********************************************************************
+* This file implements general matrix-matrix multiplication using BLAS
+* gemm function via partial specialization of
+* general_matrix_matrix_product::run(..) method for float, double,
+* std::complex<float> and std::complex<double> types
+**********************************************************************/
+
+// gemm specialization
+
+#define GEMM_SPECIALIZATION(EIGTYPE, EIGPREFIX, BLASTYPE, BLASFUNC) \
+template< \
+ typename Index, \
+ int LhsStorageOrder, bool ConjugateLhs, \
+ int RhsStorageOrder, bool ConjugateRhs> \
+struct general_matrix_matrix_product<Index,EIGTYPE,LhsStorageOrder,ConjugateLhs,EIGTYPE,RhsStorageOrder,ConjugateRhs,ColMajor,1> \
+{ \
+typedef gebp_traits<EIGTYPE,EIGTYPE> Traits; \
+\
+static void run(Index rows, Index cols, Index depth, \
+ const EIGTYPE* _lhs, Index lhsStride, \
+ const EIGTYPE* _rhs, Index rhsStride, \
+ EIGTYPE* res, Index resIncr, Index resStride, \
+ EIGTYPE alpha, \
+ level3_blocking<EIGTYPE, EIGTYPE>& /*blocking*/, \
+ GemmParallelInfo<Index>* /*info = 0*/) \
+{ \
+ using std::conj; \
+\
+ EIGEN_ONLY_USED_FOR_DEBUG(resIncr); \
+ eigen_assert(resIncr == 1); \
+ char transa, transb; \
+ BlasIndex m, n, k, lda, ldb, ldc; \
+ const EIGTYPE *a, *b; \
+ EIGTYPE beta(1); \
+ MatrixX##EIGPREFIX a_tmp, b_tmp; \
+\
+/* Set transpose options */ \
+ transa = (LhsStorageOrder==RowMajor) ? ((ConjugateLhs) ? 'C' : 'T') : 'N'; \
+ transb = (RhsStorageOrder==RowMajor) ? ((ConjugateRhs) ? 'C' : 'T') : 'N'; \
+\
+/* Set m, n, k */ \
+ m = convert_index<BlasIndex>(rows); \
+ n = convert_index<BlasIndex>(cols); \
+ k = convert_index<BlasIndex>(depth); \
+\
+/* Set lda, ldb, ldc */ \
+ lda = convert_index<BlasIndex>(lhsStride); \
+ ldb = convert_index<BlasIndex>(rhsStride); \
+ ldc = convert_index<BlasIndex>(resStride); \
+\
+/* Set a, b, c */ \
+ if ((LhsStorageOrder==ColMajor) && (ConjugateLhs)) { \
+ Map<const MatrixX##EIGPREFIX, 0, OuterStride<> > lhs(_lhs,m,k,OuterStride<>(lhsStride)); \
+ a_tmp = lhs.conjugate(); \
+ a = a_tmp.data(); \
+ lda = convert_index<BlasIndex>(a_tmp.outerStride()); \
+ } else a = _lhs; \
+\
+ if ((RhsStorageOrder==ColMajor) && (ConjugateRhs)) { \
+ Map<const MatrixX##EIGPREFIX, 0, OuterStride<> > rhs(_rhs,k,n,OuterStride<>(rhsStride)); \
+ b_tmp = rhs.conjugate(); \
+ b = b_tmp.data(); \
+ ldb = convert_index<BlasIndex>(b_tmp.outerStride()); \
+ } else b = _rhs; \
+\
+ BLASFUNC(&transa, &transb, &m, &n, &k, (const BLASTYPE*)&numext::real_ref(alpha), (const BLASTYPE*)a, &lda, (const BLASTYPE*)b, &ldb, (const BLASTYPE*)&numext::real_ref(beta), (BLASTYPE*)res, &ldc); \
+}};
+
+#ifdef EIGEN_USE_MKL
+GEMM_SPECIALIZATION(double, d, double, dgemm)
+GEMM_SPECIALIZATION(float, f, float, sgemm)
+GEMM_SPECIALIZATION(dcomplex, cd, MKL_Complex16, zgemm)
+GEMM_SPECIALIZATION(scomplex, cf, MKL_Complex8, cgemm)
+#else
+GEMM_SPECIALIZATION(double, d, double, dgemm_)
+GEMM_SPECIALIZATION(float, f, float, sgemm_)
+GEMM_SPECIALIZATION(dcomplex, cd, double, zgemm_)
+GEMM_SPECIALIZATION(scomplex, cf, float, cgemm_)
+#endif
+
+} // end namespase internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_GENERAL_MATRIX_MATRIX_BLAS_H
diff --git a/Eigen/src/Core/products/GeneralMatrixVector.h b/Eigen/src/Core/products/GeneralMatrixVector.h
new file mode 100644
index 0000000..7307994
--- /dev/null
+++ b/Eigen/src/Core/products/GeneralMatrixVector.h
@@ -0,0 +1,520 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2016 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_GENERAL_MATRIX_VECTOR_H
+#define EIGEN_GENERAL_MATRIX_VECTOR_H
+
+#include "../InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+
+enum GEMVPacketSizeType {
+ GEMVPacketFull = 0,
+ GEMVPacketHalf,
+ GEMVPacketQuarter
+};
+
+template <int N, typename T1, typename T2, typename T3>
+struct gemv_packet_cond { typedef T3 type; };
+
+template <typename T1, typename T2, typename T3>
+struct gemv_packet_cond<GEMVPacketFull, T1, T2, T3> { typedef T1 type; };
+
+template <typename T1, typename T2, typename T3>
+struct gemv_packet_cond<GEMVPacketHalf, T1, T2, T3> { typedef T2 type; };
+
+template<typename LhsScalar, typename RhsScalar, int PacketSize_=GEMVPacketFull>
+class gemv_traits
+{
+ typedef typename ScalarBinaryOpTraits<LhsScalar, RhsScalar>::ReturnType ResScalar;
+
+#define PACKET_DECL_COND_POSTFIX(postfix, name, packet_size) \
+ typedef typename gemv_packet_cond<packet_size, \
+ typename packet_traits<name ## Scalar>::type, \
+ typename packet_traits<name ## Scalar>::half, \
+ typename unpacket_traits<typename packet_traits<name ## Scalar>::half>::half>::type \
+ name ## Packet ## postfix
+
+ PACKET_DECL_COND_POSTFIX(_, Lhs, PacketSize_);
+ PACKET_DECL_COND_POSTFIX(_, Rhs, PacketSize_);
+ PACKET_DECL_COND_POSTFIX(_, Res, PacketSize_);
+#undef PACKET_DECL_COND_POSTFIX
+
+public:
+ enum {
+ Vectorizable = unpacket_traits<LhsPacket_>::vectorizable &&
+ unpacket_traits<RhsPacket_>::vectorizable &&
+ int(unpacket_traits<LhsPacket_>::size)==int(unpacket_traits<RhsPacket_>::size),
+ LhsPacketSize = Vectorizable ? unpacket_traits<LhsPacket_>::size : 1,
+ RhsPacketSize = Vectorizable ? unpacket_traits<RhsPacket_>::size : 1,
+ ResPacketSize = Vectorizable ? unpacket_traits<ResPacket_>::size : 1
+ };
+
+ typedef std::conditional_t<Vectorizable,LhsPacket_,LhsScalar> LhsPacket;
+ typedef std::conditional_t<Vectorizable,RhsPacket_,RhsScalar> RhsPacket;
+ typedef std::conditional_t<Vectorizable,ResPacket_,ResScalar> ResPacket;
+};
+
+
+/* Optimized col-major matrix * vector product:
+ * This algorithm processes the matrix per vertical panels,
+ * which are then processed horizontally per chunck of 8*PacketSize x 1 vertical segments.
+ *
+ * Mixing type logic: C += alpha * A * B
+ * | A | B |alpha| comments
+ * |real |cplx |cplx | no vectorization
+ * |real |cplx |real | alpha is converted to a cplx when calling the run function, no vectorization
+ * |cplx |real |cplx | invalid, the caller has to do tmp: = A * B; C += alpha*tmp
+ * |cplx |real |real | optimal case, vectorization possible via real-cplx mul
+ *
+ * The same reasoning apply for the transposed case.
+ */
+template<typename Index, typename LhsScalar, typename LhsMapper, bool ConjugateLhs, typename RhsScalar, typename RhsMapper, bool ConjugateRhs, int Version>
+struct general_matrix_vector_product<Index,LhsScalar,LhsMapper,ColMajor,ConjugateLhs,RhsScalar,RhsMapper,ConjugateRhs,Version>
+{
+ typedef gemv_traits<LhsScalar,RhsScalar> Traits;
+ typedef gemv_traits<LhsScalar,RhsScalar,GEMVPacketHalf> HalfTraits;
+ typedef gemv_traits<LhsScalar,RhsScalar,GEMVPacketQuarter> QuarterTraits;
+
+ typedef typename ScalarBinaryOpTraits<LhsScalar, RhsScalar>::ReturnType ResScalar;
+
+ typedef typename Traits::LhsPacket LhsPacket;
+ typedef typename Traits::RhsPacket RhsPacket;
+ typedef typename Traits::ResPacket ResPacket;
+
+ typedef typename HalfTraits::LhsPacket LhsPacketHalf;
+ typedef typename HalfTraits::RhsPacket RhsPacketHalf;
+ typedef typename HalfTraits::ResPacket ResPacketHalf;
+
+ typedef typename QuarterTraits::LhsPacket LhsPacketQuarter;
+ typedef typename QuarterTraits::RhsPacket RhsPacketQuarter;
+ typedef typename QuarterTraits::ResPacket ResPacketQuarter;
+
+EIGEN_DEVICE_FUNC EIGEN_DONT_INLINE static void run(
+ Index rows, Index cols,
+ const LhsMapper& lhs,
+ const RhsMapper& rhs,
+ ResScalar* res, Index resIncr,
+ RhsScalar alpha);
+};
+
+template<typename Index, typename LhsScalar, typename LhsMapper, bool ConjugateLhs, typename RhsScalar, typename RhsMapper, bool ConjugateRhs, int Version>
+EIGEN_DEVICE_FUNC EIGEN_DONT_INLINE void general_matrix_vector_product<Index,LhsScalar,LhsMapper,ColMajor,ConjugateLhs,RhsScalar,RhsMapper,ConjugateRhs,Version>::run(
+ Index rows, Index cols,
+ const LhsMapper& alhs,
+ const RhsMapper& rhs,
+ ResScalar* res, Index resIncr,
+ RhsScalar alpha)
+{
+ EIGEN_UNUSED_VARIABLE(resIncr);
+ eigen_internal_assert(resIncr==1);
+
+ // The following copy tells the compiler that lhs's attributes are not modified outside this function
+ // This helps GCC to generate propoer code.
+ LhsMapper lhs(alhs);
+
+ conj_helper<LhsScalar,RhsScalar,ConjugateLhs,ConjugateRhs> cj;
+ conj_helper<LhsPacket,RhsPacket,ConjugateLhs,ConjugateRhs> pcj;
+ conj_helper<LhsPacketHalf,RhsPacketHalf,ConjugateLhs,ConjugateRhs> pcj_half;
+ conj_helper<LhsPacketQuarter,RhsPacketQuarter,ConjugateLhs,ConjugateRhs> pcj_quarter;
+
+ const Index lhsStride = lhs.stride();
+ // TODO: for padded aligned inputs, we could enable aligned reads
+ enum { LhsAlignment = Unaligned,
+ ResPacketSize = Traits::ResPacketSize,
+ ResPacketSizeHalf = HalfTraits::ResPacketSize,
+ ResPacketSizeQuarter = QuarterTraits::ResPacketSize,
+ LhsPacketSize = Traits::LhsPacketSize,
+ HasHalf = (int)ResPacketSizeHalf < (int)ResPacketSize,
+ HasQuarter = (int)ResPacketSizeQuarter < (int)ResPacketSizeHalf
+ };
+
+ const Index n8 = rows-8*ResPacketSize+1;
+ const Index n4 = rows-4*ResPacketSize+1;
+ const Index n3 = rows-3*ResPacketSize+1;
+ const Index n2 = rows-2*ResPacketSize+1;
+ const Index n1 = rows-1*ResPacketSize+1;
+ const Index n_half = rows-1*ResPacketSizeHalf+1;
+ const Index n_quarter = rows-1*ResPacketSizeQuarter+1;
+
+ // TODO: improve the following heuristic:
+ const Index block_cols = cols<128 ? cols : (lhsStride*sizeof(LhsScalar)<32000?16:4);
+ ResPacket palpha = pset1<ResPacket>(alpha);
+ ResPacketHalf palpha_half = pset1<ResPacketHalf>(alpha);
+ ResPacketQuarter palpha_quarter = pset1<ResPacketQuarter>(alpha);
+
+ for(Index j2=0; j2<cols; j2+=block_cols)
+ {
+ Index jend = numext::mini(j2+block_cols,cols);
+ Index i=0;
+ for(; i<n8; i+=ResPacketSize*8)
+ {
+ ResPacket c0 = pset1<ResPacket>(ResScalar(0)),
+ c1 = pset1<ResPacket>(ResScalar(0)),
+ c2 = pset1<ResPacket>(ResScalar(0)),
+ c3 = pset1<ResPacket>(ResScalar(0)),
+ c4 = pset1<ResPacket>(ResScalar(0)),
+ c5 = pset1<ResPacket>(ResScalar(0)),
+ c6 = pset1<ResPacket>(ResScalar(0)),
+ c7 = pset1<ResPacket>(ResScalar(0));
+
+ for(Index j=j2; j<jend; j+=1)
+ {
+ RhsPacket b0 = pset1<RhsPacket>(rhs(j,0));
+ c0 = pcj.pmadd(lhs.template load<LhsPacket,LhsAlignment>(i+LhsPacketSize*0,j),b0,c0);
+ c1 = pcj.pmadd(lhs.template load<LhsPacket,LhsAlignment>(i+LhsPacketSize*1,j),b0,c1);
+ c2 = pcj.pmadd(lhs.template load<LhsPacket,LhsAlignment>(i+LhsPacketSize*2,j),b0,c2);
+ c3 = pcj.pmadd(lhs.template load<LhsPacket,LhsAlignment>(i+LhsPacketSize*3,j),b0,c3);
+ c4 = pcj.pmadd(lhs.template load<LhsPacket,LhsAlignment>(i+LhsPacketSize*4,j),b0,c4);
+ c5 = pcj.pmadd(lhs.template load<LhsPacket,LhsAlignment>(i+LhsPacketSize*5,j),b0,c5);
+ c6 = pcj.pmadd(lhs.template load<LhsPacket,LhsAlignment>(i+LhsPacketSize*6,j),b0,c6);
+ c7 = pcj.pmadd(lhs.template load<LhsPacket,LhsAlignment>(i+LhsPacketSize*7,j),b0,c7);
+ }
+ pstoreu(res+i+ResPacketSize*0, pmadd(c0,palpha,ploadu<ResPacket>(res+i+ResPacketSize*0)));
+ pstoreu(res+i+ResPacketSize*1, pmadd(c1,palpha,ploadu<ResPacket>(res+i+ResPacketSize*1)));
+ pstoreu(res+i+ResPacketSize*2, pmadd(c2,palpha,ploadu<ResPacket>(res+i+ResPacketSize*2)));
+ pstoreu(res+i+ResPacketSize*3, pmadd(c3,palpha,ploadu<ResPacket>(res+i+ResPacketSize*3)));
+ pstoreu(res+i+ResPacketSize*4, pmadd(c4,palpha,ploadu<ResPacket>(res+i+ResPacketSize*4)));
+ pstoreu(res+i+ResPacketSize*5, pmadd(c5,palpha,ploadu<ResPacket>(res+i+ResPacketSize*5)));
+ pstoreu(res+i+ResPacketSize*6, pmadd(c6,palpha,ploadu<ResPacket>(res+i+ResPacketSize*6)));
+ pstoreu(res+i+ResPacketSize*7, pmadd(c7,palpha,ploadu<ResPacket>(res+i+ResPacketSize*7)));
+ }
+ if(i<n4)
+ {
+ ResPacket c0 = pset1<ResPacket>(ResScalar(0)),
+ c1 = pset1<ResPacket>(ResScalar(0)),
+ c2 = pset1<ResPacket>(ResScalar(0)),
+ c3 = pset1<ResPacket>(ResScalar(0));
+
+ for(Index j=j2; j<jend; j+=1)
+ {
+ RhsPacket b0 = pset1<RhsPacket>(rhs(j,0));
+ c0 = pcj.pmadd(lhs.template load<LhsPacket,LhsAlignment>(i+LhsPacketSize*0,j),b0,c0);
+ c1 = pcj.pmadd(lhs.template load<LhsPacket,LhsAlignment>(i+LhsPacketSize*1,j),b0,c1);
+ c2 = pcj.pmadd(lhs.template load<LhsPacket,LhsAlignment>(i+LhsPacketSize*2,j),b0,c2);
+ c3 = pcj.pmadd(lhs.template load<LhsPacket,LhsAlignment>(i+LhsPacketSize*3,j),b0,c3);
+ }
+ pstoreu(res+i+ResPacketSize*0, pmadd(c0,palpha,ploadu<ResPacket>(res+i+ResPacketSize*0)));
+ pstoreu(res+i+ResPacketSize*1, pmadd(c1,palpha,ploadu<ResPacket>(res+i+ResPacketSize*1)));
+ pstoreu(res+i+ResPacketSize*2, pmadd(c2,palpha,ploadu<ResPacket>(res+i+ResPacketSize*2)));
+ pstoreu(res+i+ResPacketSize*3, pmadd(c3,palpha,ploadu<ResPacket>(res+i+ResPacketSize*3)));
+
+ i+=ResPacketSize*4;
+ }
+ if(i<n3)
+ {
+ ResPacket c0 = pset1<ResPacket>(ResScalar(0)),
+ c1 = pset1<ResPacket>(ResScalar(0)),
+ c2 = pset1<ResPacket>(ResScalar(0));
+
+ for(Index j=j2; j<jend; j+=1)
+ {
+ RhsPacket b0 = pset1<RhsPacket>(rhs(j,0));
+ c0 = pcj.pmadd(lhs.template load<LhsPacket,LhsAlignment>(i+LhsPacketSize*0,j),b0,c0);
+ c1 = pcj.pmadd(lhs.template load<LhsPacket,LhsAlignment>(i+LhsPacketSize*1,j),b0,c1);
+ c2 = pcj.pmadd(lhs.template load<LhsPacket,LhsAlignment>(i+LhsPacketSize*2,j),b0,c2);
+ }
+ pstoreu(res+i+ResPacketSize*0, pmadd(c0,palpha,ploadu<ResPacket>(res+i+ResPacketSize*0)));
+ pstoreu(res+i+ResPacketSize*1, pmadd(c1,palpha,ploadu<ResPacket>(res+i+ResPacketSize*1)));
+ pstoreu(res+i+ResPacketSize*2, pmadd(c2,palpha,ploadu<ResPacket>(res+i+ResPacketSize*2)));
+
+ i+=ResPacketSize*3;
+ }
+ if(i<n2)
+ {
+ ResPacket c0 = pset1<ResPacket>(ResScalar(0)),
+ c1 = pset1<ResPacket>(ResScalar(0));
+
+ for(Index j=j2; j<jend; j+=1)
+ {
+ RhsPacket b0 = pset1<RhsPacket>(rhs(j,0));
+ c0 = pcj.pmadd(lhs.template load<LhsPacket,LhsAlignment>(i+LhsPacketSize*0,j),b0,c0);
+ c1 = pcj.pmadd(lhs.template load<LhsPacket,LhsAlignment>(i+LhsPacketSize*1,j),b0,c1);
+ }
+ pstoreu(res+i+ResPacketSize*0, pmadd(c0,palpha,ploadu<ResPacket>(res+i+ResPacketSize*0)));
+ pstoreu(res+i+ResPacketSize*1, pmadd(c1,palpha,ploadu<ResPacket>(res+i+ResPacketSize*1)));
+ i+=ResPacketSize*2;
+ }
+ if(i<n1)
+ {
+ ResPacket c0 = pset1<ResPacket>(ResScalar(0));
+ for(Index j=j2; j<jend; j+=1)
+ {
+ RhsPacket b0 = pset1<RhsPacket>(rhs(j,0));
+ c0 = pcj.pmadd(lhs.template load<LhsPacket,LhsAlignment>(i+0,j),b0,c0);
+ }
+ pstoreu(res+i+ResPacketSize*0, pmadd(c0,palpha,ploadu<ResPacket>(res+i+ResPacketSize*0)));
+ i+=ResPacketSize;
+ }
+ if(HasHalf && i<n_half)
+ {
+ ResPacketHalf c0 = pset1<ResPacketHalf>(ResScalar(0));
+ for(Index j=j2; j<jend; j+=1)
+ {
+ RhsPacketHalf b0 = pset1<RhsPacketHalf>(rhs(j,0));
+ c0 = pcj_half.pmadd(lhs.template load<LhsPacketHalf,LhsAlignment>(i+0,j),b0,c0);
+ }
+ pstoreu(res+i+ResPacketSizeHalf*0, pmadd(c0,palpha_half,ploadu<ResPacketHalf>(res+i+ResPacketSizeHalf*0)));
+ i+=ResPacketSizeHalf;
+ }
+ if(HasQuarter && i<n_quarter)
+ {
+ ResPacketQuarter c0 = pset1<ResPacketQuarter>(ResScalar(0));
+ for(Index j=j2; j<jend; j+=1)
+ {
+ RhsPacketQuarter b0 = pset1<RhsPacketQuarter>(rhs(j,0));
+ c0 = pcj_quarter.pmadd(lhs.template load<LhsPacketQuarter,LhsAlignment>(i+0,j),b0,c0);
+ }
+ pstoreu(res+i+ResPacketSizeQuarter*0, pmadd(c0,palpha_quarter,ploadu<ResPacketQuarter>(res+i+ResPacketSizeQuarter*0)));
+ i+=ResPacketSizeQuarter;
+ }
+ for(;i<rows;++i)
+ {
+ ResScalar c0(0);
+ for(Index j=j2; j<jend; j+=1)
+ c0 += cj.pmul(lhs(i,j), rhs(j,0));
+ res[i] += alpha*c0;
+ }
+ }
+}
+
+/* Optimized row-major matrix * vector product:
+ * This algorithm processes 4 rows at once that allows to both reduce
+ * the number of load/stores of the result by a factor 4 and to reduce
+ * the instruction dependency. Moreover, we know that all bands have the
+ * same alignment pattern.
+ *
+ * Mixing type logic:
+ * - alpha is always a complex (or converted to a complex)
+ * - no vectorization
+ */
+template<typename Index, typename LhsScalar, typename LhsMapper, bool ConjugateLhs, typename RhsScalar, typename RhsMapper, bool ConjugateRhs, int Version>
+struct general_matrix_vector_product<Index,LhsScalar,LhsMapper,RowMajor,ConjugateLhs,RhsScalar,RhsMapper,ConjugateRhs,Version>
+{
+ typedef gemv_traits<LhsScalar,RhsScalar> Traits;
+ typedef gemv_traits<LhsScalar,RhsScalar,GEMVPacketHalf> HalfTraits;
+ typedef gemv_traits<LhsScalar,RhsScalar,GEMVPacketQuarter> QuarterTraits;
+
+ typedef typename ScalarBinaryOpTraits<LhsScalar, RhsScalar>::ReturnType ResScalar;
+
+ typedef typename Traits::LhsPacket LhsPacket;
+ typedef typename Traits::RhsPacket RhsPacket;
+ typedef typename Traits::ResPacket ResPacket;
+
+ typedef typename HalfTraits::LhsPacket LhsPacketHalf;
+ typedef typename HalfTraits::RhsPacket RhsPacketHalf;
+ typedef typename HalfTraits::ResPacket ResPacketHalf;
+
+ typedef typename QuarterTraits::LhsPacket LhsPacketQuarter;
+ typedef typename QuarterTraits::RhsPacket RhsPacketQuarter;
+ typedef typename QuarterTraits::ResPacket ResPacketQuarter;
+
+EIGEN_DEVICE_FUNC EIGEN_DONT_INLINE static void run(
+ Index rows, Index cols,
+ const LhsMapper& lhs,
+ const RhsMapper& rhs,
+ ResScalar* res, Index resIncr,
+ ResScalar alpha);
+};
+
+template<typename Index, typename LhsScalar, typename LhsMapper, bool ConjugateLhs, typename RhsScalar, typename RhsMapper, bool ConjugateRhs, int Version>
+EIGEN_DEVICE_FUNC EIGEN_DONT_INLINE void general_matrix_vector_product<Index,LhsScalar,LhsMapper,RowMajor,ConjugateLhs,RhsScalar,RhsMapper,ConjugateRhs,Version>::run(
+ Index rows, Index cols,
+ const LhsMapper& alhs,
+ const RhsMapper& rhs,
+ ResScalar* res, Index resIncr,
+ ResScalar alpha)
+{
+ // The following copy tells the compiler that lhs's attributes are not modified outside this function
+ // This helps GCC to generate propoer code.
+ LhsMapper lhs(alhs);
+
+ eigen_internal_assert(rhs.stride()==1);
+ conj_helper<LhsScalar,RhsScalar,ConjugateLhs,ConjugateRhs> cj;
+ conj_helper<LhsPacket,RhsPacket,ConjugateLhs,ConjugateRhs> pcj;
+ conj_helper<LhsPacketHalf,RhsPacketHalf,ConjugateLhs,ConjugateRhs> pcj_half;
+ conj_helper<LhsPacketQuarter,RhsPacketQuarter,ConjugateLhs,ConjugateRhs> pcj_quarter;
+
+ // TODO: fine tune the following heuristic. The rationale is that if the matrix is very large,
+ // processing 8 rows at once might be counter productive wrt cache.
+ const Index n8 = lhs.stride()*sizeof(LhsScalar)>32000 ? 0 : rows-7;
+ const Index n4 = rows-3;
+ const Index n2 = rows-1;
+
+ // TODO: for padded aligned inputs, we could enable aligned reads
+ enum { LhsAlignment = Unaligned,
+ ResPacketSize = Traits::ResPacketSize,
+ ResPacketSizeHalf = HalfTraits::ResPacketSize,
+ ResPacketSizeQuarter = QuarterTraits::ResPacketSize,
+ LhsPacketSize = Traits::LhsPacketSize,
+ LhsPacketSizeHalf = HalfTraits::LhsPacketSize,
+ LhsPacketSizeQuarter = QuarterTraits::LhsPacketSize,
+ HasHalf = (int)ResPacketSizeHalf < (int)ResPacketSize,
+ HasQuarter = (int)ResPacketSizeQuarter < (int)ResPacketSizeHalf
+ };
+
+ Index i=0;
+ for(; i<n8; i+=8)
+ {
+ ResPacket c0 = pset1<ResPacket>(ResScalar(0)),
+ c1 = pset1<ResPacket>(ResScalar(0)),
+ c2 = pset1<ResPacket>(ResScalar(0)),
+ c3 = pset1<ResPacket>(ResScalar(0)),
+ c4 = pset1<ResPacket>(ResScalar(0)),
+ c5 = pset1<ResPacket>(ResScalar(0)),
+ c6 = pset1<ResPacket>(ResScalar(0)),
+ c7 = pset1<ResPacket>(ResScalar(0));
+
+ Index j=0;
+ for(; j+LhsPacketSize<=cols; j+=LhsPacketSize)
+ {
+ RhsPacket b0 = rhs.template load<RhsPacket, Unaligned>(j,0);
+
+ c0 = pcj.pmadd(lhs.template load<LhsPacket,LhsAlignment>(i+0,j),b0,c0);
+ c1 = pcj.pmadd(lhs.template load<LhsPacket,LhsAlignment>(i+1,j),b0,c1);
+ c2 = pcj.pmadd(lhs.template load<LhsPacket,LhsAlignment>(i+2,j),b0,c2);
+ c3 = pcj.pmadd(lhs.template load<LhsPacket,LhsAlignment>(i+3,j),b0,c3);
+ c4 = pcj.pmadd(lhs.template load<LhsPacket,LhsAlignment>(i+4,j),b0,c4);
+ c5 = pcj.pmadd(lhs.template load<LhsPacket,LhsAlignment>(i+5,j),b0,c5);
+ c6 = pcj.pmadd(lhs.template load<LhsPacket,LhsAlignment>(i+6,j),b0,c6);
+ c7 = pcj.pmadd(lhs.template load<LhsPacket,LhsAlignment>(i+7,j),b0,c7);
+ }
+ ResScalar cc0 = predux(c0);
+ ResScalar cc1 = predux(c1);
+ ResScalar cc2 = predux(c2);
+ ResScalar cc3 = predux(c3);
+ ResScalar cc4 = predux(c4);
+ ResScalar cc5 = predux(c5);
+ ResScalar cc6 = predux(c6);
+ ResScalar cc7 = predux(c7);
+ for(; j<cols; ++j)
+ {
+ RhsScalar b0 = rhs(j,0);
+
+ cc0 += cj.pmul(lhs(i+0,j), b0);
+ cc1 += cj.pmul(lhs(i+1,j), b0);
+ cc2 += cj.pmul(lhs(i+2,j), b0);
+ cc3 += cj.pmul(lhs(i+3,j), b0);
+ cc4 += cj.pmul(lhs(i+4,j), b0);
+ cc5 += cj.pmul(lhs(i+5,j), b0);
+ cc6 += cj.pmul(lhs(i+6,j), b0);
+ cc7 += cj.pmul(lhs(i+7,j), b0);
+ }
+ res[(i+0)*resIncr] += alpha*cc0;
+ res[(i+1)*resIncr] += alpha*cc1;
+ res[(i+2)*resIncr] += alpha*cc2;
+ res[(i+3)*resIncr] += alpha*cc3;
+ res[(i+4)*resIncr] += alpha*cc4;
+ res[(i+5)*resIncr] += alpha*cc5;
+ res[(i+6)*resIncr] += alpha*cc6;
+ res[(i+7)*resIncr] += alpha*cc7;
+ }
+ for(; i<n4; i+=4)
+ {
+ ResPacket c0 = pset1<ResPacket>(ResScalar(0)),
+ c1 = pset1<ResPacket>(ResScalar(0)),
+ c2 = pset1<ResPacket>(ResScalar(0)),
+ c3 = pset1<ResPacket>(ResScalar(0));
+
+ Index j=0;
+ for(; j+LhsPacketSize<=cols; j+=LhsPacketSize)
+ {
+ RhsPacket b0 = rhs.template load<RhsPacket, Unaligned>(j,0);
+
+ c0 = pcj.pmadd(lhs.template load<LhsPacket,LhsAlignment>(i+0,j),b0,c0);
+ c1 = pcj.pmadd(lhs.template load<LhsPacket,LhsAlignment>(i+1,j),b0,c1);
+ c2 = pcj.pmadd(lhs.template load<LhsPacket,LhsAlignment>(i+2,j),b0,c2);
+ c3 = pcj.pmadd(lhs.template load<LhsPacket,LhsAlignment>(i+3,j),b0,c3);
+ }
+ ResScalar cc0 = predux(c0);
+ ResScalar cc1 = predux(c1);
+ ResScalar cc2 = predux(c2);
+ ResScalar cc3 = predux(c3);
+ for(; j<cols; ++j)
+ {
+ RhsScalar b0 = rhs(j,0);
+
+ cc0 += cj.pmul(lhs(i+0,j), b0);
+ cc1 += cj.pmul(lhs(i+1,j), b0);
+ cc2 += cj.pmul(lhs(i+2,j), b0);
+ cc3 += cj.pmul(lhs(i+3,j), b0);
+ }
+ res[(i+0)*resIncr] += alpha*cc0;
+ res[(i+1)*resIncr] += alpha*cc1;
+ res[(i+2)*resIncr] += alpha*cc2;
+ res[(i+3)*resIncr] += alpha*cc3;
+ }
+ for(; i<n2; i+=2)
+ {
+ ResPacket c0 = pset1<ResPacket>(ResScalar(0)),
+ c1 = pset1<ResPacket>(ResScalar(0));
+
+ Index j=0;
+ for(; j+LhsPacketSize<=cols; j+=LhsPacketSize)
+ {
+ RhsPacket b0 = rhs.template load<RhsPacket, Unaligned>(j,0);
+
+ c0 = pcj.pmadd(lhs.template load<LhsPacket,LhsAlignment>(i+0,j),b0,c0);
+ c1 = pcj.pmadd(lhs.template load<LhsPacket,LhsAlignment>(i+1,j),b0,c1);
+ }
+ ResScalar cc0 = predux(c0);
+ ResScalar cc1 = predux(c1);
+ for(; j<cols; ++j)
+ {
+ RhsScalar b0 = rhs(j,0);
+
+ cc0 += cj.pmul(lhs(i+0,j), b0);
+ cc1 += cj.pmul(lhs(i+1,j), b0);
+ }
+ res[(i+0)*resIncr] += alpha*cc0;
+ res[(i+1)*resIncr] += alpha*cc1;
+ }
+ for(; i<rows; ++i)
+ {
+ ResPacket c0 = pset1<ResPacket>(ResScalar(0));
+ ResPacketHalf c0_h = pset1<ResPacketHalf>(ResScalar(0));
+ ResPacketQuarter c0_q = pset1<ResPacketQuarter>(ResScalar(0));
+ Index j=0;
+ for(; j+LhsPacketSize<=cols; j+=LhsPacketSize)
+ {
+ RhsPacket b0 = rhs.template load<RhsPacket,Unaligned>(j,0);
+ c0 = pcj.pmadd(lhs.template load<LhsPacket,LhsAlignment>(i,j),b0,c0);
+ }
+ ResScalar cc0 = predux(c0);
+ if (HasHalf) {
+ for(; j+LhsPacketSizeHalf<=cols; j+=LhsPacketSizeHalf)
+ {
+ RhsPacketHalf b0 = rhs.template load<RhsPacketHalf,Unaligned>(j,0);
+ c0_h = pcj_half.pmadd(lhs.template load<LhsPacketHalf,LhsAlignment>(i,j),b0,c0_h);
+ }
+ cc0 += predux(c0_h);
+ }
+ if (HasQuarter) {
+ for(; j+LhsPacketSizeQuarter<=cols; j+=LhsPacketSizeQuarter)
+ {
+ RhsPacketQuarter b0 = rhs.template load<RhsPacketQuarter,Unaligned>(j,0);
+ c0_q = pcj_quarter.pmadd(lhs.template load<LhsPacketQuarter,LhsAlignment>(i,j),b0,c0_q);
+ }
+ cc0 += predux(c0_q);
+ }
+ for(; j<cols; ++j)
+ {
+ cc0 += cj.pmul(lhs(i,j), rhs(j,0));
+ }
+ res[i*resIncr] += alpha*cc0;
+ }
+}
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_GENERAL_MATRIX_VECTOR_H
diff --git a/Eigen/src/Core/products/GeneralMatrixVector_BLAS.h b/Eigen/src/Core/products/GeneralMatrixVector_BLAS.h
new file mode 100644
index 0000000..f77e2e4
--- /dev/null
+++ b/Eigen/src/Core/products/GeneralMatrixVector_BLAS.h
@@ -0,0 +1,138 @@
+/*
+ Copyright (c) 2011, Intel Corporation. All rights reserved.
+
+ Redistribution and use in source and binary forms, with or without modification,
+ are permitted provided that the following conditions are met:
+
+ * Redistributions of source code must retain the above copyright notice, this
+ list of conditions and the following disclaimer.
+ * Redistributions in binary form must reproduce the above copyright notice,
+ this list of conditions and the following disclaimer in the documentation
+ and/or other materials provided with the distribution.
+ * Neither the name of Intel Corporation nor the names of its contributors may
+ be used to endorse or promote products derived from this software without
+ specific prior written permission.
+
+ THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
+ ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
+ WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
+ DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR
+ ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
+ (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
+ LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON
+ ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
+ (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
+ SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+
+ ********************************************************************************
+ * Content : Eigen bindings to BLAS F77
+ * General matrix-vector product functionality based on ?GEMV.
+ ********************************************************************************
+*/
+
+#ifndef EIGEN_GENERAL_MATRIX_VECTOR_BLAS_H
+#define EIGEN_GENERAL_MATRIX_VECTOR_BLAS_H
+
+#include "../InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+
+/**********************************************************************
+* This file implements general matrix-vector multiplication using BLAS
+* gemv function via partial specialization of
+* general_matrix_vector_product::run(..) method for float, double,
+* std::complex<float> and std::complex<double> types
+**********************************************************************/
+
+// gemv specialization
+
+template<typename Index, typename LhsScalar, int StorageOrder, bool ConjugateLhs, typename RhsScalar, bool ConjugateRhs>
+struct general_matrix_vector_product_gemv;
+
+#define EIGEN_BLAS_GEMV_SPECIALIZE(Scalar) \
+template<typename Index, bool ConjugateLhs, bool ConjugateRhs> \
+struct general_matrix_vector_product<Index,Scalar,const_blas_data_mapper<Scalar,Index,ColMajor>,ColMajor,ConjugateLhs,Scalar,const_blas_data_mapper<Scalar,Index,RowMajor>,ConjugateRhs,Specialized> { \
+static void run( \
+ Index rows, Index cols, \
+ const const_blas_data_mapper<Scalar,Index,ColMajor> &lhs, \
+ const const_blas_data_mapper<Scalar,Index,RowMajor> &rhs, \
+ Scalar* res, Index resIncr, Scalar alpha) \
+{ \
+ if (ConjugateLhs) { \
+ general_matrix_vector_product<Index,Scalar,const_blas_data_mapper<Scalar,Index,ColMajor>,ColMajor,ConjugateLhs,Scalar,const_blas_data_mapper<Scalar,Index,RowMajor>,ConjugateRhs,BuiltIn>::run( \
+ rows, cols, lhs, rhs, res, resIncr, alpha); \
+ } else { \
+ general_matrix_vector_product_gemv<Index,Scalar,ColMajor,ConjugateLhs,Scalar,ConjugateRhs>::run( \
+ rows, cols, lhs.data(), lhs.stride(), rhs.data(), rhs.stride(), res, resIncr, alpha); \
+ } \
+} \
+}; \
+template<typename Index, bool ConjugateLhs, bool ConjugateRhs> \
+struct general_matrix_vector_product<Index,Scalar,const_blas_data_mapper<Scalar,Index,RowMajor>,RowMajor,ConjugateLhs,Scalar,const_blas_data_mapper<Scalar,Index,ColMajor>,ConjugateRhs,Specialized> { \
+static void run( \
+ Index rows, Index cols, \
+ const const_blas_data_mapper<Scalar,Index,RowMajor> &lhs, \
+ const const_blas_data_mapper<Scalar,Index,ColMajor> &rhs, \
+ Scalar* res, Index resIncr, Scalar alpha) \
+{ \
+ general_matrix_vector_product_gemv<Index,Scalar,RowMajor,ConjugateLhs,Scalar,ConjugateRhs>::run( \
+ rows, cols, lhs.data(), lhs.stride(), rhs.data(), rhs.stride(), res, resIncr, alpha); \
+} \
+}; \
+
+EIGEN_BLAS_GEMV_SPECIALIZE(double)
+EIGEN_BLAS_GEMV_SPECIALIZE(float)
+EIGEN_BLAS_GEMV_SPECIALIZE(dcomplex)
+EIGEN_BLAS_GEMV_SPECIALIZE(scomplex)
+
+#define EIGEN_BLAS_GEMV_SPECIALIZATION(EIGTYPE,BLASTYPE,BLASFUNC) \
+template<typename Index, int LhsStorageOrder, bool ConjugateLhs, bool ConjugateRhs> \
+struct general_matrix_vector_product_gemv<Index,EIGTYPE,LhsStorageOrder,ConjugateLhs,EIGTYPE,ConjugateRhs> \
+{ \
+typedef Matrix<EIGTYPE,Dynamic,1,ColMajor> GEMVVector;\
+\
+static void run( \
+ Index rows, Index cols, \
+ const EIGTYPE* lhs, Index lhsStride, \
+ const EIGTYPE* rhs, Index rhsIncr, \
+ EIGTYPE* res, Index resIncr, EIGTYPE alpha) \
+{ \
+ BlasIndex m=convert_index<BlasIndex>(rows), n=convert_index<BlasIndex>(cols), \
+ lda=convert_index<BlasIndex>(lhsStride), incx=convert_index<BlasIndex>(rhsIncr), incy=convert_index<BlasIndex>(resIncr); \
+ const EIGTYPE beta(1); \
+ const EIGTYPE *x_ptr; \
+ char trans=(LhsStorageOrder==ColMajor) ? 'N' : (ConjugateLhs) ? 'C' : 'T'; \
+ if (LhsStorageOrder==RowMajor) { \
+ m = convert_index<BlasIndex>(cols); \
+ n = convert_index<BlasIndex>(rows); \
+ }\
+ GEMVVector x_tmp; \
+ if (ConjugateRhs) { \
+ Map<const GEMVVector, 0, InnerStride<> > map_x(rhs,cols,1,InnerStride<>(incx)); \
+ x_tmp=map_x.conjugate(); \
+ x_ptr=x_tmp.data(); \
+ incx=1; \
+ } else x_ptr=rhs; \
+ BLASFUNC(&trans, &m, &n, (const BLASTYPE*)&numext::real_ref(alpha), (const BLASTYPE*)lhs, &lda, (const BLASTYPE*)x_ptr, &incx, (const BLASTYPE*)&numext::real_ref(beta), (BLASTYPE*)res, &incy); \
+}\
+};
+
+#ifdef EIGEN_USE_MKL
+EIGEN_BLAS_GEMV_SPECIALIZATION(double, double, dgemv)
+EIGEN_BLAS_GEMV_SPECIALIZATION(float, float, sgemv)
+EIGEN_BLAS_GEMV_SPECIALIZATION(dcomplex, MKL_Complex16, zgemv)
+EIGEN_BLAS_GEMV_SPECIALIZATION(scomplex, MKL_Complex8 , cgemv)
+#else
+EIGEN_BLAS_GEMV_SPECIALIZATION(double, double, dgemv_)
+EIGEN_BLAS_GEMV_SPECIALIZATION(float, float, sgemv_)
+EIGEN_BLAS_GEMV_SPECIALIZATION(dcomplex, double, zgemv_)
+EIGEN_BLAS_GEMV_SPECIALIZATION(scomplex, float, cgemv_)
+#endif
+
+} // end namespase internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_GENERAL_MATRIX_VECTOR_BLAS_H
diff --git a/Eigen/src/Core/products/Parallelizer.h b/Eigen/src/Core/products/Parallelizer.h
new file mode 100644
index 0000000..da4affb
--- /dev/null
+++ b/Eigen/src/Core/products/Parallelizer.h
@@ -0,0 +1,173 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2010 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_PARALLELIZER_H
+#define EIGEN_PARALLELIZER_H
+
+#include "../InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+
+/** \internal */
+inline void manage_multi_threading(Action action, int* v)
+{
+ static int m_maxThreads = -1;
+ EIGEN_UNUSED_VARIABLE(m_maxThreads)
+
+ if(action==SetAction)
+ {
+ eigen_internal_assert(v!=0);
+ m_maxThreads = *v;
+ }
+ else if(action==GetAction)
+ {
+ eigen_internal_assert(v!=0);
+ #ifdef EIGEN_HAS_OPENMP
+ if(m_maxThreads>0)
+ *v = m_maxThreads;
+ else
+ *v = omp_get_max_threads();
+ #else
+ *v = 1;
+ #endif
+ }
+ else
+ {
+ eigen_internal_assert(false);
+ }
+}
+
+}
+
+/** Must be call first when calling Eigen from multiple threads */
+inline void initParallel()
+{
+ int nbt;
+ internal::manage_multi_threading(GetAction, &nbt);
+ std::ptrdiff_t l1, l2, l3;
+ internal::manage_caching_sizes(GetAction, &l1, &l2, &l3);
+}
+
+/** \returns the max number of threads reserved for Eigen
+ * \sa setNbThreads */
+inline int nbThreads()
+{
+ int ret;
+ internal::manage_multi_threading(GetAction, &ret);
+ return ret;
+}
+
+/** Sets the max number of threads reserved for Eigen
+ * \sa nbThreads */
+inline void setNbThreads(int v)
+{
+ internal::manage_multi_threading(SetAction, &v);
+}
+
+namespace internal {
+
+template<typename Index> struct GemmParallelInfo
+{
+
+#ifdef EIGEN_HAS_OPENMP
+ GemmParallelInfo() : sync(-1), users(0), lhs_start(0), lhs_length(0) {}
+ std::atomic<Index> sync;
+ std::atomic<int> users;
+#else
+ GemmParallelInfo() : lhs_start(0), lhs_length(0) {}
+#endif
+
+ Index lhs_start;
+ Index lhs_length;
+};
+
+template<bool Condition, typename Functor, typename Index>
+void parallelize_gemm(const Functor& func, Index rows, Index cols, Index depth, bool transpose)
+{
+ // TODO when EIGEN_USE_BLAS is defined,
+ // we should still enable OMP for other scalar types
+ // Without C++11, we have to disable GEMM's parallelization on
+ // non x86 architectures because there volatile is not enough for our purpose.
+ // See bug 1572.
+#if (! defined(EIGEN_HAS_OPENMP)) || defined(EIGEN_USE_BLAS)
+ // FIXME the transpose variable is only needed to properly split
+ // the matrix product when multithreading is enabled. This is a temporary
+ // fix to support row-major destination matrices. This whole
+ // parallelizer mechanism has to be redesigned anyway.
+ EIGEN_UNUSED_VARIABLE(depth);
+ EIGEN_UNUSED_VARIABLE(transpose);
+ func(0,rows, 0,cols);
+#else
+
+ // Dynamically check whether we should enable or disable OpenMP.
+ // The conditions are:
+ // - the max number of threads we can create is greater than 1
+ // - we are not already in a parallel code
+ // - the sizes are large enough
+
+ // compute the maximal number of threads from the size of the product:
+ // This first heuristic takes into account that the product kernel is fully optimized when working with nr columns at once.
+ Index size = transpose ? rows : cols;
+ Index pb_max_threads = std::max<Index>(1,size / Functor::Traits::nr);
+
+ // compute the maximal number of threads from the total amount of work:
+ double work = static_cast<double>(rows) * static_cast<double>(cols) *
+ static_cast<double>(depth);
+ double kMinTaskSize = 50000; // FIXME improve this heuristic.
+ pb_max_threads = std::max<Index>(1, std::min<Index>(pb_max_threads, static_cast<Index>( work / kMinTaskSize ) ));
+
+ // compute the number of threads we are going to use
+ Index threads = std::min<Index>(nbThreads(), pb_max_threads);
+
+ // if multi-threading is explicitly disabled, not useful, or if we already are in a parallel session,
+ // then abort multi-threading
+ // FIXME omp_get_num_threads()>1 only works for openmp, what if the user does not use openmp?
+ if((!Condition) || (threads==1) || (omp_get_num_threads()>1))
+ return func(0,rows, 0,cols);
+
+ Eigen::initParallel();
+ func.initParallelSession(threads);
+
+ if(transpose)
+ std::swap(rows,cols);
+
+ ei_declare_aligned_stack_constructed_variable(GemmParallelInfo<Index>,info,threads,0);
+
+ #pragma omp parallel num_threads(threads)
+ {
+ Index i = omp_get_thread_num();
+ // Note that the actual number of threads might be lower than the number of request ones.
+ Index actual_threads = omp_get_num_threads();
+
+ Index blockCols = (cols / actual_threads) & ~Index(0x3);
+ Index blockRows = (rows / actual_threads);
+ blockRows = (blockRows/Functor::Traits::mr)*Functor::Traits::mr;
+
+ Index r0 = i*blockRows;
+ Index actualBlockRows = (i+1==actual_threads) ? rows-r0 : blockRows;
+
+ Index c0 = i*blockCols;
+ Index actualBlockCols = (i+1==actual_threads) ? cols-c0 : blockCols;
+
+ info[i].lhs_start = r0;
+ info[i].lhs_length = actualBlockRows;
+
+ if(transpose) func(c0, actualBlockCols, 0, rows, info);
+ else func(0, rows, c0, actualBlockCols, info);
+ }
+#endif
+}
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_PARALLELIZER_H
diff --git a/Eigen/src/Core/products/SelfadjointMatrixMatrix.h b/Eigen/src/Core/products/SelfadjointMatrixMatrix.h
new file mode 100644
index 0000000..c7bb445
--- /dev/null
+++ b/Eigen/src/Core/products/SelfadjointMatrixMatrix.h
@@ -0,0 +1,546 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_SELFADJOINT_MATRIX_MATRIX_H
+#define EIGEN_SELFADJOINT_MATRIX_MATRIX_H
+
+#include "../InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+
+// pack a selfadjoint block diagonal for use with the gebp_kernel
+template<typename Scalar, typename Index, int Pack1, int Pack2_dummy, int StorageOrder>
+struct symm_pack_lhs
+{
+ template<int BlockRows> inline
+ void pack(Scalar* blockA, const const_blas_data_mapper<Scalar,Index,StorageOrder>& lhs, Index cols, Index i, Index& count)
+ {
+ // normal copy
+ for(Index k=0; k<i; k++)
+ for(Index w=0; w<BlockRows; w++)
+ blockA[count++] = lhs(i+w,k); // normal
+ // symmetric copy
+ Index h = 0;
+ for(Index k=i; k<i+BlockRows; k++)
+ {
+ for(Index w=0; w<h; w++)
+ blockA[count++] = numext::conj(lhs(k, i+w)); // transposed
+
+ blockA[count++] = numext::real(lhs(k,k)); // real (diagonal)
+
+ for(Index w=h+1; w<BlockRows; w++)
+ blockA[count++] = lhs(i+w, k); // normal
+ ++h;
+ }
+ // transposed copy
+ for(Index k=i+BlockRows; k<cols; k++)
+ for(Index w=0; w<BlockRows; w++)
+ blockA[count++] = numext::conj(lhs(k, i+w)); // transposed
+ }
+ void operator()(Scalar* blockA, const Scalar* _lhs, Index lhsStride, Index cols, Index rows)
+ {
+ typedef typename unpacket_traits<typename packet_traits<Scalar>::type>::half HalfPacket;
+ typedef typename unpacket_traits<typename unpacket_traits<typename packet_traits<Scalar>::type>::half>::half QuarterPacket;
+ enum { PacketSize = packet_traits<Scalar>::size,
+ HalfPacketSize = unpacket_traits<HalfPacket>::size,
+ QuarterPacketSize = unpacket_traits<QuarterPacket>::size,
+ HasHalf = (int)HalfPacketSize < (int)PacketSize,
+ HasQuarter = (int)QuarterPacketSize < (int)HalfPacketSize};
+
+ const_blas_data_mapper<Scalar,Index,StorageOrder> lhs(_lhs,lhsStride);
+ Index count = 0;
+ //Index peeled_mc3 = (rows/Pack1)*Pack1;
+
+ const Index peeled_mc3 = Pack1>=3*PacketSize ? (rows/(3*PacketSize))*(3*PacketSize) : 0;
+ const Index peeled_mc2 = Pack1>=2*PacketSize ? peeled_mc3+((rows-peeled_mc3)/(2*PacketSize))*(2*PacketSize) : 0;
+ const Index peeled_mc1 = Pack1>=1*PacketSize ? peeled_mc2+((rows-peeled_mc2)/(1*PacketSize))*(1*PacketSize) : 0;
+ const Index peeled_mc_half = Pack1>=HalfPacketSize ? peeled_mc1+((rows-peeled_mc1)/(HalfPacketSize))*(HalfPacketSize) : 0;
+ const Index peeled_mc_quarter = Pack1>=QuarterPacketSize ? peeled_mc_half+((rows-peeled_mc_half)/(QuarterPacketSize))*(QuarterPacketSize) : 0;
+
+ if(Pack1>=3*PacketSize)
+ for(Index i=0; i<peeled_mc3; i+=3*PacketSize)
+ pack<3*PacketSize>(blockA, lhs, cols, i, count);
+
+ if(Pack1>=2*PacketSize)
+ for(Index i=peeled_mc3; i<peeled_mc2; i+=2*PacketSize)
+ pack<2*PacketSize>(blockA, lhs, cols, i, count);
+
+ if(Pack1>=1*PacketSize)
+ for(Index i=peeled_mc2; i<peeled_mc1; i+=1*PacketSize)
+ pack<1*PacketSize>(blockA, lhs, cols, i, count);
+
+ if(HasHalf && Pack1>=HalfPacketSize)
+ for(Index i=peeled_mc1; i<peeled_mc_half; i+=HalfPacketSize)
+ pack<HalfPacketSize>(blockA, lhs, cols, i, count);
+
+ if(HasQuarter && Pack1>=QuarterPacketSize)
+ for(Index i=peeled_mc_half; i<peeled_mc_quarter; i+=QuarterPacketSize)
+ pack<QuarterPacketSize>(blockA, lhs, cols, i, count);
+
+ // do the same with mr==1
+ for(Index i=peeled_mc_quarter; i<rows; i++)
+ {
+ for(Index k=0; k<i; k++)
+ blockA[count++] = lhs(i, k); // normal
+
+ blockA[count++] = numext::real(lhs(i, i)); // real (diagonal)
+
+ for(Index k=i+1; k<cols; k++)
+ blockA[count++] = numext::conj(lhs(k, i)); // transposed
+ }
+ }
+};
+
+template<typename Scalar, typename Index, int nr, int StorageOrder>
+struct symm_pack_rhs
+{
+ enum { PacketSize = packet_traits<Scalar>::size };
+ void operator()(Scalar* blockB, const Scalar* _rhs, Index rhsStride, Index rows, Index cols, Index k2)
+ {
+ Index end_k = k2 + rows;
+ Index count = 0;
+ const_blas_data_mapper<Scalar,Index,StorageOrder> rhs(_rhs,rhsStride);
+ Index packet_cols8 = nr>=8 ? (cols/8) * 8 : 0;
+ Index packet_cols4 = nr>=4 ? (cols/4) * 4 : 0;
+
+ // first part: normal case
+ for(Index j2=0; j2<k2; j2+=nr)
+ {
+ for(Index k=k2; k<end_k; k++)
+ {
+ blockB[count+0] = rhs(k,j2+0);
+ blockB[count+1] = rhs(k,j2+1);
+ if (nr>=4)
+ {
+ blockB[count+2] = rhs(k,j2+2);
+ blockB[count+3] = rhs(k,j2+3);
+ }
+ if (nr>=8)
+ {
+ blockB[count+4] = rhs(k,j2+4);
+ blockB[count+5] = rhs(k,j2+5);
+ blockB[count+6] = rhs(k,j2+6);
+ blockB[count+7] = rhs(k,j2+7);
+ }
+ count += nr;
+ }
+ }
+
+ // second part: diagonal block
+ Index end8 = nr>=8 ? (std::min)(k2+rows,packet_cols8) : k2;
+ if(nr>=8)
+ {
+ for(Index j2=k2; j2<end8; j2+=8)
+ {
+ // again we can split vertically in three different parts (transpose, symmetric, normal)
+ // transpose
+ for(Index k=k2; k<j2; k++)
+ {
+ blockB[count+0] = numext::conj(rhs(j2+0,k));
+ blockB[count+1] = numext::conj(rhs(j2+1,k));
+ blockB[count+2] = numext::conj(rhs(j2+2,k));
+ blockB[count+3] = numext::conj(rhs(j2+3,k));
+ blockB[count+4] = numext::conj(rhs(j2+4,k));
+ blockB[count+5] = numext::conj(rhs(j2+5,k));
+ blockB[count+6] = numext::conj(rhs(j2+6,k));
+ blockB[count+7] = numext::conj(rhs(j2+7,k));
+ count += 8;
+ }
+ // symmetric
+ Index h = 0;
+ for(Index k=j2; k<j2+8; k++)
+ {
+ // normal
+ for (Index w=0 ; w<h; ++w)
+ blockB[count+w] = rhs(k,j2+w);
+
+ blockB[count+h] = numext::real(rhs(k,k));
+
+ // transpose
+ for (Index w=h+1 ; w<8; ++w)
+ blockB[count+w] = numext::conj(rhs(j2+w,k));
+ count += 8;
+ ++h;
+ }
+ // normal
+ for(Index k=j2+8; k<end_k; k++)
+ {
+ blockB[count+0] = rhs(k,j2+0);
+ blockB[count+1] = rhs(k,j2+1);
+ blockB[count+2] = rhs(k,j2+2);
+ blockB[count+3] = rhs(k,j2+3);
+ blockB[count+4] = rhs(k,j2+4);
+ blockB[count+5] = rhs(k,j2+5);
+ blockB[count+6] = rhs(k,j2+6);
+ blockB[count+7] = rhs(k,j2+7);
+ count += 8;
+ }
+ }
+ }
+ if(nr>=4)
+ {
+ for(Index j2=end8; j2<(std::min)(k2+rows,packet_cols4); j2+=4)
+ {
+ // again we can split vertically in three different parts (transpose, symmetric, normal)
+ // transpose
+ for(Index k=k2; k<j2; k++)
+ {
+ blockB[count+0] = numext::conj(rhs(j2+0,k));
+ blockB[count+1] = numext::conj(rhs(j2+1,k));
+ blockB[count+2] = numext::conj(rhs(j2+2,k));
+ blockB[count+3] = numext::conj(rhs(j2+3,k));
+ count += 4;
+ }
+ // symmetric
+ Index h = 0;
+ for(Index k=j2; k<j2+4; k++)
+ {
+ // normal
+ for (Index w=0 ; w<h; ++w)
+ blockB[count+w] = rhs(k,j2+w);
+
+ blockB[count+h] = numext::real(rhs(k,k));
+
+ // transpose
+ for (Index w=h+1 ; w<4; ++w)
+ blockB[count+w] = numext::conj(rhs(j2+w,k));
+ count += 4;
+ ++h;
+ }
+ // normal
+ for(Index k=j2+4; k<end_k; k++)
+ {
+ blockB[count+0] = rhs(k,j2+0);
+ blockB[count+1] = rhs(k,j2+1);
+ blockB[count+2] = rhs(k,j2+2);
+ blockB[count+3] = rhs(k,j2+3);
+ count += 4;
+ }
+ }
+ }
+
+ // third part: transposed
+ if(nr>=8)
+ {
+ for(Index j2=k2+rows; j2<packet_cols8; j2+=8)
+ {
+ for(Index k=k2; k<end_k; k++)
+ {
+ blockB[count+0] = numext::conj(rhs(j2+0,k));
+ blockB[count+1] = numext::conj(rhs(j2+1,k));
+ blockB[count+2] = numext::conj(rhs(j2+2,k));
+ blockB[count+3] = numext::conj(rhs(j2+3,k));
+ blockB[count+4] = numext::conj(rhs(j2+4,k));
+ blockB[count+5] = numext::conj(rhs(j2+5,k));
+ blockB[count+6] = numext::conj(rhs(j2+6,k));
+ blockB[count+7] = numext::conj(rhs(j2+7,k));
+ count += 8;
+ }
+ }
+ }
+ if(nr>=4)
+ {
+ for(Index j2=(std::max)(packet_cols8,k2+rows); j2<packet_cols4; j2+=4)
+ {
+ for(Index k=k2; k<end_k; k++)
+ {
+ blockB[count+0] = numext::conj(rhs(j2+0,k));
+ blockB[count+1] = numext::conj(rhs(j2+1,k));
+ blockB[count+2] = numext::conj(rhs(j2+2,k));
+ blockB[count+3] = numext::conj(rhs(j2+3,k));
+ count += 4;
+ }
+ }
+ }
+
+ // copy the remaining columns one at a time (=> the same with nr==1)
+ for(Index j2=packet_cols4; j2<cols; ++j2)
+ {
+ // transpose
+ Index half = (std::min)(end_k,j2);
+ for(Index k=k2; k<half; k++)
+ {
+ blockB[count] = numext::conj(rhs(j2,k));
+ count += 1;
+ }
+
+ if(half==j2 && half<k2+rows)
+ {
+ blockB[count] = numext::real(rhs(j2,j2));
+ count += 1;
+ }
+ else
+ half--;
+
+ // normal
+ for(Index k=half+1; k<k2+rows; k++)
+ {
+ blockB[count] = rhs(k,j2);
+ count += 1;
+ }
+ }
+ }
+};
+
+/* Optimized selfadjoint matrix * matrix (_SYMM) product built on top of
+ * the general matrix matrix product.
+ */
+template <typename Scalar, typename Index,
+ int LhsStorageOrder, bool LhsSelfAdjoint, bool ConjugateLhs,
+ int RhsStorageOrder, bool RhsSelfAdjoint, bool ConjugateRhs,
+ int ResStorageOrder, int ResInnerStride>
+struct product_selfadjoint_matrix;
+
+template <typename Scalar, typename Index,
+ int LhsStorageOrder, bool LhsSelfAdjoint, bool ConjugateLhs,
+ int RhsStorageOrder, bool RhsSelfAdjoint, bool ConjugateRhs,
+ int ResInnerStride>
+struct product_selfadjoint_matrix<Scalar,Index,LhsStorageOrder,LhsSelfAdjoint,ConjugateLhs, RhsStorageOrder,RhsSelfAdjoint,ConjugateRhs,RowMajor,ResInnerStride>
+{
+
+ static EIGEN_STRONG_INLINE void run(
+ Index rows, Index cols,
+ const Scalar* lhs, Index lhsStride,
+ const Scalar* rhs, Index rhsStride,
+ Scalar* res, Index resIncr, Index resStride,
+ const Scalar& alpha, level3_blocking<Scalar,Scalar>& blocking)
+ {
+ product_selfadjoint_matrix<Scalar, Index,
+ logical_xor(RhsSelfAdjoint,RhsStorageOrder==RowMajor) ? ColMajor : RowMajor,
+ RhsSelfAdjoint, NumTraits<Scalar>::IsComplex && logical_xor(RhsSelfAdjoint, ConjugateRhs),
+ logical_xor(LhsSelfAdjoint,LhsStorageOrder==RowMajor) ? ColMajor : RowMajor,
+ LhsSelfAdjoint, NumTraits<Scalar>::IsComplex && logical_xor(LhsSelfAdjoint, ConjugateLhs),
+ ColMajor,ResInnerStride>
+ ::run(cols, rows, rhs, rhsStride, lhs, lhsStride, res, resIncr, resStride, alpha, blocking);
+ }
+};
+
+template <typename Scalar, typename Index,
+ int LhsStorageOrder, bool ConjugateLhs,
+ int RhsStorageOrder, bool ConjugateRhs,
+ int ResInnerStride>
+struct product_selfadjoint_matrix<Scalar,Index,LhsStorageOrder,true,ConjugateLhs, RhsStorageOrder,false,ConjugateRhs,ColMajor,ResInnerStride>
+{
+
+ static EIGEN_DONT_INLINE void run(
+ Index rows, Index cols,
+ const Scalar* _lhs, Index lhsStride,
+ const Scalar* _rhs, Index rhsStride,
+ Scalar* res, Index resIncr, Index resStride,
+ const Scalar& alpha, level3_blocking<Scalar,Scalar>& blocking);
+};
+
+template <typename Scalar, typename Index,
+ int LhsStorageOrder, bool ConjugateLhs,
+ int RhsStorageOrder, bool ConjugateRhs,
+ int ResInnerStride>
+EIGEN_DONT_INLINE void product_selfadjoint_matrix<Scalar,Index,LhsStorageOrder,true,ConjugateLhs, RhsStorageOrder,false,ConjugateRhs,ColMajor,ResInnerStride>::run(
+ Index rows, Index cols,
+ const Scalar* _lhs, Index lhsStride,
+ const Scalar* _rhs, Index rhsStride,
+ Scalar* _res, Index resIncr, Index resStride,
+ const Scalar& alpha, level3_blocking<Scalar,Scalar>& blocking)
+ {
+ Index size = rows;
+
+ typedef gebp_traits<Scalar,Scalar> Traits;
+
+ typedef const_blas_data_mapper<Scalar, Index, LhsStorageOrder> LhsMapper;
+ typedef const_blas_data_mapper<Scalar, Index, (LhsStorageOrder == RowMajor) ? ColMajor : RowMajor> LhsTransposeMapper;
+ typedef const_blas_data_mapper<Scalar, Index, RhsStorageOrder> RhsMapper;
+ typedef blas_data_mapper<typename Traits::ResScalar, Index, ColMajor, Unaligned, ResInnerStride> ResMapper;
+ LhsMapper lhs(_lhs,lhsStride);
+ LhsTransposeMapper lhs_transpose(_lhs,lhsStride);
+ RhsMapper rhs(_rhs,rhsStride);
+ ResMapper res(_res, resStride, resIncr);
+
+ Index kc = blocking.kc(); // cache block size along the K direction
+ Index mc = (std::min)(rows,blocking.mc()); // cache block size along the M direction
+ // kc must be smaller than mc
+ kc = (std::min)(kc,mc);
+ std::size_t sizeA = kc*mc;
+ std::size_t sizeB = kc*cols;
+ ei_declare_aligned_stack_constructed_variable(Scalar, blockA, sizeA, blocking.blockA());
+ ei_declare_aligned_stack_constructed_variable(Scalar, blockB, sizeB, blocking.blockB());
+
+ gebp_kernel<Scalar, Scalar, Index, ResMapper, Traits::mr, Traits::nr, ConjugateLhs, ConjugateRhs> gebp_kernel;
+ symm_pack_lhs<Scalar, Index, Traits::mr, Traits::LhsProgress, LhsStorageOrder> pack_lhs;
+ gemm_pack_rhs<Scalar, Index, RhsMapper, Traits::nr,RhsStorageOrder> pack_rhs;
+ gemm_pack_lhs<Scalar, Index, LhsTransposeMapper, Traits::mr, Traits::LhsProgress, typename Traits::LhsPacket4Packing, LhsStorageOrder==RowMajor?ColMajor:RowMajor, true> pack_lhs_transposed;
+
+ for(Index k2=0; k2<size; k2+=kc)
+ {
+ const Index actual_kc = (std::min)(k2+kc,size)-k2;
+
+ // we have selected one row panel of rhs and one column panel of lhs
+ // pack rhs's panel into a sequential chunk of memory
+ // and expand each coeff to a constant packet for further reuse
+ pack_rhs(blockB, rhs.getSubMapper(k2,0), actual_kc, cols);
+
+ // the select lhs's panel has to be split in three different parts:
+ // 1 - the transposed panel above the diagonal block => transposed packed copy
+ // 2 - the diagonal block => special packed copy
+ // 3 - the panel below the diagonal block => generic packed copy
+ for(Index i2=0; i2<k2; i2+=mc)
+ {
+ const Index actual_mc = (std::min)(i2+mc,k2)-i2;
+ // transposed packed copy
+ pack_lhs_transposed(blockA, lhs_transpose.getSubMapper(i2, k2), actual_kc, actual_mc);
+
+ gebp_kernel(res.getSubMapper(i2, 0), blockA, blockB, actual_mc, actual_kc, cols, alpha);
+ }
+ // the block diagonal
+ {
+ const Index actual_mc = (std::min)(k2+kc,size)-k2;
+ // symmetric packed copy
+ pack_lhs(blockA, &lhs(k2,k2), lhsStride, actual_kc, actual_mc);
+
+ gebp_kernel(res.getSubMapper(k2, 0), blockA, blockB, actual_mc, actual_kc, cols, alpha);
+ }
+
+ for(Index i2=k2+kc; i2<size; i2+=mc)
+ {
+ const Index actual_mc = (std::min)(i2+mc,size)-i2;
+ gemm_pack_lhs<Scalar, Index, LhsMapper, Traits::mr, Traits::LhsProgress, typename Traits::LhsPacket4Packing, LhsStorageOrder,false>()
+ (blockA, lhs.getSubMapper(i2, k2), actual_kc, actual_mc);
+
+ gebp_kernel(res.getSubMapper(i2, 0), blockA, blockB, actual_mc, actual_kc, cols, alpha);
+ }
+ }
+ }
+
+// matrix * selfadjoint product
+template <typename Scalar, typename Index,
+ int LhsStorageOrder, bool ConjugateLhs,
+ int RhsStorageOrder, bool ConjugateRhs,
+ int ResInnerStride>
+struct product_selfadjoint_matrix<Scalar,Index,LhsStorageOrder,false,ConjugateLhs, RhsStorageOrder,true,ConjugateRhs,ColMajor,ResInnerStride>
+{
+
+ static EIGEN_DONT_INLINE void run(
+ Index rows, Index cols,
+ const Scalar* _lhs, Index lhsStride,
+ const Scalar* _rhs, Index rhsStride,
+ Scalar* res, Index resIncr, Index resStride,
+ const Scalar& alpha, level3_blocking<Scalar,Scalar>& blocking);
+};
+
+template <typename Scalar, typename Index,
+ int LhsStorageOrder, bool ConjugateLhs,
+ int RhsStorageOrder, bool ConjugateRhs,
+ int ResInnerStride>
+EIGEN_DONT_INLINE void product_selfadjoint_matrix<Scalar,Index,LhsStorageOrder,false,ConjugateLhs, RhsStorageOrder,true,ConjugateRhs,ColMajor,ResInnerStride>::run(
+ Index rows, Index cols,
+ const Scalar* _lhs, Index lhsStride,
+ const Scalar* _rhs, Index rhsStride,
+ Scalar* _res, Index resIncr, Index resStride,
+ const Scalar& alpha, level3_blocking<Scalar,Scalar>& blocking)
+ {
+ Index size = cols;
+
+ typedef gebp_traits<Scalar,Scalar> Traits;
+
+ typedef const_blas_data_mapper<Scalar, Index, LhsStorageOrder> LhsMapper;
+ typedef blas_data_mapper<typename Traits::ResScalar, Index, ColMajor, Unaligned, ResInnerStride> ResMapper;
+ LhsMapper lhs(_lhs,lhsStride);
+ ResMapper res(_res,resStride, resIncr);
+
+ Index kc = blocking.kc(); // cache block size along the K direction
+ Index mc = (std::min)(rows,blocking.mc()); // cache block size along the M direction
+ std::size_t sizeA = kc*mc;
+ std::size_t sizeB = kc*cols;
+ ei_declare_aligned_stack_constructed_variable(Scalar, blockA, sizeA, blocking.blockA());
+ ei_declare_aligned_stack_constructed_variable(Scalar, blockB, sizeB, blocking.blockB());
+
+ gebp_kernel<Scalar, Scalar, Index, ResMapper, Traits::mr, Traits::nr, ConjugateLhs, ConjugateRhs> gebp_kernel;
+ gemm_pack_lhs<Scalar, Index, LhsMapper, Traits::mr, Traits::LhsProgress, typename Traits::LhsPacket4Packing, LhsStorageOrder> pack_lhs;
+ symm_pack_rhs<Scalar, Index, Traits::nr,RhsStorageOrder> pack_rhs;
+
+ for(Index k2=0; k2<size; k2+=kc)
+ {
+ const Index actual_kc = (std::min)(k2+kc,size)-k2;
+
+ pack_rhs(blockB, _rhs, rhsStride, actual_kc, cols, k2);
+
+ // => GEPP
+ for(Index i2=0; i2<rows; i2+=mc)
+ {
+ const Index actual_mc = (std::min)(i2+mc,rows)-i2;
+ pack_lhs(blockA, lhs.getSubMapper(i2, k2), actual_kc, actual_mc);
+
+ gebp_kernel(res.getSubMapper(i2, 0), blockA, blockB, actual_mc, actual_kc, cols, alpha);
+ }
+ }
+ }
+
+} // end namespace internal
+
+/***************************************************************************
+* Wrapper to product_selfadjoint_matrix
+***************************************************************************/
+
+namespace internal {
+
+template<typename Lhs, int LhsMode, typename Rhs, int RhsMode>
+struct selfadjoint_product_impl<Lhs,LhsMode,false,Rhs,RhsMode,false>
+{
+ typedef typename Product<Lhs,Rhs>::Scalar Scalar;
+
+ typedef internal::blas_traits<Lhs> LhsBlasTraits;
+ typedef typename LhsBlasTraits::DirectLinearAccessType ActualLhsType;
+ typedef internal::blas_traits<Rhs> RhsBlasTraits;
+ typedef typename RhsBlasTraits::DirectLinearAccessType ActualRhsType;
+
+ enum {
+ LhsIsUpper = (LhsMode&(Upper|Lower))==Upper,
+ LhsIsSelfAdjoint = (LhsMode&SelfAdjoint)==SelfAdjoint,
+ RhsIsUpper = (RhsMode&(Upper|Lower))==Upper,
+ RhsIsSelfAdjoint = (RhsMode&SelfAdjoint)==SelfAdjoint
+ };
+
+ template<typename Dest>
+ static void run(Dest &dst, const Lhs &a_lhs, const Rhs &a_rhs, const Scalar& alpha)
+ {
+ eigen_assert(dst.rows()==a_lhs.rows() && dst.cols()==a_rhs.cols());
+
+ add_const_on_value_type_t<ActualLhsType> lhs = LhsBlasTraits::extract(a_lhs);
+ add_const_on_value_type_t<ActualRhsType> rhs = RhsBlasTraits::extract(a_rhs);
+
+ Scalar actualAlpha = alpha * LhsBlasTraits::extractScalarFactor(a_lhs)
+ * RhsBlasTraits::extractScalarFactor(a_rhs);
+
+ typedef internal::gemm_blocking_space<(Dest::Flags&RowMajorBit) ? RowMajor : ColMajor,Scalar,Scalar,
+ Lhs::MaxRowsAtCompileTime, Rhs::MaxColsAtCompileTime, Lhs::MaxColsAtCompileTime,1> BlockingType;
+
+ BlockingType blocking(lhs.rows(), rhs.cols(), lhs.cols(), 1, false);
+
+ internal::product_selfadjoint_matrix<Scalar, Index,
+ internal::logical_xor(LhsIsUpper, internal::traits<Lhs>::Flags &RowMajorBit) ? RowMajor : ColMajor, LhsIsSelfAdjoint,
+ NumTraits<Scalar>::IsComplex && internal::logical_xor(LhsIsUpper, bool(LhsBlasTraits::NeedToConjugate)),
+ internal::logical_xor(RhsIsUpper, internal::traits<Rhs>::Flags &RowMajorBit) ? RowMajor : ColMajor, RhsIsSelfAdjoint,
+ NumTraits<Scalar>::IsComplex && internal::logical_xor(RhsIsUpper, bool(RhsBlasTraits::NeedToConjugate)),
+ internal::traits<Dest>::Flags&RowMajorBit ? RowMajor : ColMajor,
+ Dest::InnerStrideAtCompileTime>
+ ::run(
+ lhs.rows(), rhs.cols(), // sizes
+ &lhs.coeffRef(0,0), lhs.outerStride(), // lhs info
+ &rhs.coeffRef(0,0), rhs.outerStride(), // rhs info
+ &dst.coeffRef(0,0), dst.innerStride(), dst.outerStride(), // result info
+ actualAlpha, blocking // alpha
+ );
+ }
+};
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_SELFADJOINT_MATRIX_MATRIX_H
diff --git a/Eigen/src/Core/products/SelfadjointMatrixMatrix_BLAS.h b/Eigen/src/Core/products/SelfadjointMatrixMatrix_BLAS.h
new file mode 100644
index 0000000..0e371da
--- /dev/null
+++ b/Eigen/src/Core/products/SelfadjointMatrixMatrix_BLAS.h
@@ -0,0 +1,297 @@
+/*
+ Copyright (c) 2011, Intel Corporation. All rights reserved.
+
+ Redistribution and use in source and binary forms, with or without modification,
+ are permitted provided that the following conditions are met:
+
+ * Redistributions of source code must retain the above copyright notice, this
+ list of conditions and the following disclaimer.
+ * Redistributions in binary form must reproduce the above copyright notice,
+ this list of conditions and the following disclaimer in the documentation
+ and/or other materials provided with the distribution.
+ * Neither the name of Intel Corporation nor the names of its contributors may
+ be used to endorse or promote products derived from this software without
+ specific prior written permission.
+
+ THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
+ ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
+ WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
+ DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR
+ ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
+ (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
+ LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON
+ ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
+ (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
+ SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+//
+ ********************************************************************************
+ * Content : Eigen bindings to BLAS F77
+ * Self adjoint matrix * matrix product functionality based on ?SYMM/?HEMM.
+ ********************************************************************************
+*/
+
+#ifndef EIGEN_SELFADJOINT_MATRIX_MATRIX_BLAS_H
+#define EIGEN_SELFADJOINT_MATRIX_MATRIX_BLAS_H
+
+#include "../InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+
+
+/* Optimized selfadjoint matrix * matrix (?SYMM/?HEMM) product */
+
+#define EIGEN_BLAS_SYMM_L(EIGTYPE, BLASTYPE, EIGPREFIX, BLASFUNC) \
+template <typename Index, \
+ int LhsStorageOrder, bool ConjugateLhs, \
+ int RhsStorageOrder, bool ConjugateRhs> \
+struct product_selfadjoint_matrix<EIGTYPE,Index,LhsStorageOrder,true,ConjugateLhs,RhsStorageOrder,false,ConjugateRhs,ColMajor,1> \
+{\
+\
+ static void run( \
+ Index rows, Index cols, \
+ const EIGTYPE* _lhs, Index lhsStride, \
+ const EIGTYPE* _rhs, Index rhsStride, \
+ EIGTYPE* res, Index resIncr, Index resStride, \
+ EIGTYPE alpha, level3_blocking<EIGTYPE, EIGTYPE>& /*blocking*/) \
+ { \
+ EIGEN_ONLY_USED_FOR_DEBUG(resIncr); \
+ eigen_assert(resIncr == 1); \
+ char side='L', uplo='L'; \
+ BlasIndex m, n, lda, ldb, ldc; \
+ const EIGTYPE *a, *b; \
+ EIGTYPE beta(1); \
+ MatrixX##EIGPREFIX b_tmp; \
+\
+/* Set transpose options */ \
+/* Set m, n, k */ \
+ m = convert_index<BlasIndex>(rows); \
+ n = convert_index<BlasIndex>(cols); \
+\
+/* Set lda, ldb, ldc */ \
+ lda = convert_index<BlasIndex>(lhsStride); \
+ ldb = convert_index<BlasIndex>(rhsStride); \
+ ldc = convert_index<BlasIndex>(resStride); \
+\
+/* Set a, b, c */ \
+ if (LhsStorageOrder==RowMajor) uplo='U'; \
+ a = _lhs; \
+\
+ if (RhsStorageOrder==RowMajor) { \
+ Map<const MatrixX##EIGPREFIX, 0, OuterStride<> > rhs(_rhs,n,m,OuterStride<>(rhsStride)); \
+ b_tmp = rhs.adjoint(); \
+ b = b_tmp.data(); \
+ ldb = convert_index<BlasIndex>(b_tmp.outerStride()); \
+ } else b = _rhs; \
+\
+ BLASFUNC(&side, &uplo, &m, &n, (const BLASTYPE*)&numext::real_ref(alpha), (const BLASTYPE*)a, &lda, (const BLASTYPE*)b, &ldb, (const BLASTYPE*)&numext::real_ref(beta), (BLASTYPE*)res, &ldc); \
+\
+ } \
+};
+
+
+#define EIGEN_BLAS_HEMM_L(EIGTYPE, BLASTYPE, EIGPREFIX, BLASFUNC) \
+template <typename Index, \
+ int LhsStorageOrder, bool ConjugateLhs, \
+ int RhsStorageOrder, bool ConjugateRhs> \
+struct product_selfadjoint_matrix<EIGTYPE,Index,LhsStorageOrder,true,ConjugateLhs,RhsStorageOrder,false,ConjugateRhs,ColMajor,1> \
+{\
+ static void run( \
+ Index rows, Index cols, \
+ const EIGTYPE* _lhs, Index lhsStride, \
+ const EIGTYPE* _rhs, Index rhsStride, \
+ EIGTYPE* res, Index resIncr, Index resStride, \
+ EIGTYPE alpha, level3_blocking<EIGTYPE, EIGTYPE>& /*blocking*/) \
+ { \
+ EIGEN_ONLY_USED_FOR_DEBUG(resIncr); \
+ eigen_assert(resIncr == 1); \
+ char side='L', uplo='L'; \
+ BlasIndex m, n, lda, ldb, ldc; \
+ const EIGTYPE *a, *b; \
+ EIGTYPE beta(1); \
+ MatrixX##EIGPREFIX b_tmp; \
+ Matrix<EIGTYPE, Dynamic, Dynamic, LhsStorageOrder> a_tmp; \
+\
+/* Set transpose options */ \
+/* Set m, n, k */ \
+ m = convert_index<BlasIndex>(rows); \
+ n = convert_index<BlasIndex>(cols); \
+\
+/* Set lda, ldb, ldc */ \
+ lda = convert_index<BlasIndex>(lhsStride); \
+ ldb = convert_index<BlasIndex>(rhsStride); \
+ ldc = convert_index<BlasIndex>(resStride); \
+\
+/* Set a, b, c */ \
+ if (((LhsStorageOrder==ColMajor) && ConjugateLhs) || ((LhsStorageOrder==RowMajor) && (!ConjugateLhs))) { \
+ Map<const Matrix<EIGTYPE, Dynamic, Dynamic, LhsStorageOrder>, 0, OuterStride<> > lhs(_lhs,m,m,OuterStride<>(lhsStride)); \
+ a_tmp = lhs.conjugate(); \
+ a = a_tmp.data(); \
+ lda = convert_index<BlasIndex>(a_tmp.outerStride()); \
+ } else a = _lhs; \
+ if (LhsStorageOrder==RowMajor) uplo='U'; \
+\
+ if (RhsStorageOrder==ColMajor && (!ConjugateRhs)) { \
+ b = _rhs; } \
+ else { \
+ if (RhsStorageOrder==ColMajor && ConjugateRhs) { \
+ Map<const MatrixX##EIGPREFIX, 0, OuterStride<> > rhs(_rhs,m,n,OuterStride<>(rhsStride)); \
+ b_tmp = rhs.conjugate(); \
+ } else \
+ if (ConjugateRhs) { \
+ Map<const MatrixX##EIGPREFIX, 0, OuterStride<> > rhs(_rhs,n,m,OuterStride<>(rhsStride)); \
+ b_tmp = rhs.adjoint(); \
+ } else { \
+ Map<const MatrixX##EIGPREFIX, 0, OuterStride<> > rhs(_rhs,n,m,OuterStride<>(rhsStride)); \
+ b_tmp = rhs.transpose(); \
+ } \
+ b = b_tmp.data(); \
+ ldb = convert_index<BlasIndex>(b_tmp.outerStride()); \
+ } \
+\
+ BLASFUNC(&side, &uplo, &m, &n, (const BLASTYPE*)&numext::real_ref(alpha), (const BLASTYPE*)a, &lda, (const BLASTYPE*)b, &ldb, (const BLASTYPE*)&numext::real_ref(beta), (BLASTYPE*)res, &ldc); \
+\
+ } \
+};
+
+#ifdef EIGEN_USE_MKL
+EIGEN_BLAS_SYMM_L(double, double, d, dsymm)
+EIGEN_BLAS_SYMM_L(float, float, f, ssymm)
+EIGEN_BLAS_HEMM_L(dcomplex, MKL_Complex16, cd, zhemm)
+EIGEN_BLAS_HEMM_L(scomplex, MKL_Complex8, cf, chemm)
+#else
+EIGEN_BLAS_SYMM_L(double, double, d, dsymm_)
+EIGEN_BLAS_SYMM_L(float, float, f, ssymm_)
+EIGEN_BLAS_HEMM_L(dcomplex, double, cd, zhemm_)
+EIGEN_BLAS_HEMM_L(scomplex, float, cf, chemm_)
+#endif
+
+/* Optimized matrix * selfadjoint matrix (?SYMM/?HEMM) product */
+
+#define EIGEN_BLAS_SYMM_R(EIGTYPE, BLASTYPE, EIGPREFIX, BLASFUNC) \
+template <typename Index, \
+ int LhsStorageOrder, bool ConjugateLhs, \
+ int RhsStorageOrder, bool ConjugateRhs> \
+struct product_selfadjoint_matrix<EIGTYPE,Index,LhsStorageOrder,false,ConjugateLhs,RhsStorageOrder,true,ConjugateRhs,ColMajor,1> \
+{\
+\
+ static void run( \
+ Index rows, Index cols, \
+ const EIGTYPE* _lhs, Index lhsStride, \
+ const EIGTYPE* _rhs, Index rhsStride, \
+ EIGTYPE* res, Index resIncr, Index resStride, \
+ EIGTYPE alpha, level3_blocking<EIGTYPE, EIGTYPE>& /*blocking*/) \
+ { \
+ EIGEN_ONLY_USED_FOR_DEBUG(resIncr); \
+ eigen_assert(resIncr == 1); \
+ char side='R', uplo='L'; \
+ BlasIndex m, n, lda, ldb, ldc; \
+ const EIGTYPE *a, *b; \
+ EIGTYPE beta(1); \
+ MatrixX##EIGPREFIX b_tmp; \
+\
+/* Set m, n, k */ \
+ m = convert_index<BlasIndex>(rows); \
+ n = convert_index<BlasIndex>(cols); \
+\
+/* Set lda, ldb, ldc */ \
+ lda = convert_index<BlasIndex>(rhsStride); \
+ ldb = convert_index<BlasIndex>(lhsStride); \
+ ldc = convert_index<BlasIndex>(resStride); \
+\
+/* Set a, b, c */ \
+ if (RhsStorageOrder==RowMajor) uplo='U'; \
+ a = _rhs; \
+\
+ if (LhsStorageOrder==RowMajor) { \
+ Map<const MatrixX##EIGPREFIX, 0, OuterStride<> > lhs(_lhs,n,m,OuterStride<>(rhsStride)); \
+ b_tmp = lhs.adjoint(); \
+ b = b_tmp.data(); \
+ ldb = convert_index<BlasIndex>(b_tmp.outerStride()); \
+ } else b = _lhs; \
+\
+ BLASFUNC(&side, &uplo, &m, &n, (const BLASTYPE*)&numext::real_ref(alpha), (const BLASTYPE*)a, &lda, (const BLASTYPE*)b, &ldb, (const BLASTYPE*)&numext::real_ref(beta), (BLASTYPE*)res, &ldc); \
+\
+ } \
+};
+
+
+#define EIGEN_BLAS_HEMM_R(EIGTYPE, BLASTYPE, EIGPREFIX, BLASFUNC) \
+template <typename Index, \
+ int LhsStorageOrder, bool ConjugateLhs, \
+ int RhsStorageOrder, bool ConjugateRhs> \
+struct product_selfadjoint_matrix<EIGTYPE,Index,LhsStorageOrder,false,ConjugateLhs,RhsStorageOrder,true,ConjugateRhs,ColMajor,1> \
+{\
+ static void run( \
+ Index rows, Index cols, \
+ const EIGTYPE* _lhs, Index lhsStride, \
+ const EIGTYPE* _rhs, Index rhsStride, \
+ EIGTYPE* res, Index resIncr, Index resStride, \
+ EIGTYPE alpha, level3_blocking<EIGTYPE, EIGTYPE>& /*blocking*/) \
+ { \
+ EIGEN_ONLY_USED_FOR_DEBUG(resIncr); \
+ eigen_assert(resIncr == 1); \
+ char side='R', uplo='L'; \
+ BlasIndex m, n, lda, ldb, ldc; \
+ const EIGTYPE *a, *b; \
+ EIGTYPE beta(1); \
+ MatrixX##EIGPREFIX b_tmp; \
+ Matrix<EIGTYPE, Dynamic, Dynamic, RhsStorageOrder> a_tmp; \
+\
+/* Set m, n, k */ \
+ m = convert_index<BlasIndex>(rows); \
+ n = convert_index<BlasIndex>(cols); \
+\
+/* Set lda, ldb, ldc */ \
+ lda = convert_index<BlasIndex>(rhsStride); \
+ ldb = convert_index<BlasIndex>(lhsStride); \
+ ldc = convert_index<BlasIndex>(resStride); \
+\
+/* Set a, b, c */ \
+ if (((RhsStorageOrder==ColMajor) && ConjugateRhs) || ((RhsStorageOrder==RowMajor) && (!ConjugateRhs))) { \
+ Map<const Matrix<EIGTYPE, Dynamic, Dynamic, RhsStorageOrder>, 0, OuterStride<> > rhs(_rhs,n,n,OuterStride<>(rhsStride)); \
+ a_tmp = rhs.conjugate(); \
+ a = a_tmp.data(); \
+ lda = convert_index<BlasIndex>(a_tmp.outerStride()); \
+ } else a = _rhs; \
+ if (RhsStorageOrder==RowMajor) uplo='U'; \
+\
+ if (LhsStorageOrder==ColMajor && (!ConjugateLhs)) { \
+ b = _lhs; } \
+ else { \
+ if (LhsStorageOrder==ColMajor && ConjugateLhs) { \
+ Map<const MatrixX##EIGPREFIX, 0, OuterStride<> > lhs(_lhs,m,n,OuterStride<>(lhsStride)); \
+ b_tmp = lhs.conjugate(); \
+ } else \
+ if (ConjugateLhs) { \
+ Map<const MatrixX##EIGPREFIX, 0, OuterStride<> > lhs(_lhs,n,m,OuterStride<>(lhsStride)); \
+ b_tmp = lhs.adjoint(); \
+ } else { \
+ Map<const MatrixX##EIGPREFIX, 0, OuterStride<> > lhs(_lhs,n,m,OuterStride<>(lhsStride)); \
+ b_tmp = lhs.transpose(); \
+ } \
+ b = b_tmp.data(); \
+ ldb = convert_index<BlasIndex>(b_tmp.outerStride()); \
+ } \
+\
+ BLASFUNC(&side, &uplo, &m, &n, (const BLASTYPE*)&numext::real_ref(alpha), (const BLASTYPE*)a, &lda, (const BLASTYPE*)b, &ldb, (const BLASTYPE*)&numext::real_ref(beta), (BLASTYPE*)res, &ldc); \
+ } \
+};
+
+#ifdef EIGEN_USE_MKL
+EIGEN_BLAS_SYMM_R(double, double, d, dsymm)
+EIGEN_BLAS_SYMM_R(float, float, f, ssymm)
+EIGEN_BLAS_HEMM_R(dcomplex, MKL_Complex16, cd, zhemm)
+EIGEN_BLAS_HEMM_R(scomplex, MKL_Complex8, cf, chemm)
+#else
+EIGEN_BLAS_SYMM_R(double, double, d, dsymm_)
+EIGEN_BLAS_SYMM_R(float, float, f, ssymm_)
+EIGEN_BLAS_HEMM_R(dcomplex, double, cd, zhemm_)
+EIGEN_BLAS_HEMM_R(scomplex, float, cf, chemm_)
+#endif
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_SELFADJOINT_MATRIX_MATRIX_BLAS_H
diff --git a/Eigen/src/Core/products/SelfadjointMatrixVector.h b/Eigen/src/Core/products/SelfadjointMatrixVector.h
new file mode 100644
index 0000000..a62b6b5
--- /dev/null
+++ b/Eigen/src/Core/products/SelfadjointMatrixVector.h
@@ -0,0 +1,264 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_SELFADJOINT_MATRIX_VECTOR_H
+#define EIGEN_SELFADJOINT_MATRIX_VECTOR_H
+
+#include "../InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+
+/* Optimized selfadjoint matrix * vector product:
+ * This algorithm processes 2 columns at once that allows to both reduce
+ * the number of load/stores of the result by a factor 2 and to reduce
+ * the instruction dependency.
+ */
+
+template<typename Scalar, typename Index, int StorageOrder, int UpLo, bool ConjugateLhs, bool ConjugateRhs, int Version=Specialized>
+struct selfadjoint_matrix_vector_product;
+
+template<typename Scalar, typename Index, int StorageOrder, int UpLo, bool ConjugateLhs, bool ConjugateRhs, int Version>
+struct selfadjoint_matrix_vector_product
+
+{
+static EIGEN_DONT_INLINE EIGEN_DEVICE_FUNC
+void run(
+ Index size,
+ const Scalar* lhs, Index lhsStride,
+ const Scalar* rhs,
+ Scalar* res,
+ Scalar alpha);
+};
+
+template<typename Scalar, typename Index, int StorageOrder, int UpLo, bool ConjugateLhs, bool ConjugateRhs, int Version>
+EIGEN_DONT_INLINE EIGEN_DEVICE_FUNC
+void selfadjoint_matrix_vector_product<Scalar,Index,StorageOrder,UpLo,ConjugateLhs,ConjugateRhs,Version>::run(
+ Index size,
+ const Scalar* lhs, Index lhsStride,
+ const Scalar* rhs,
+ Scalar* res,
+ Scalar alpha)
+{
+ typedef typename packet_traits<Scalar>::type Packet;
+ typedef typename NumTraits<Scalar>::Real RealScalar;
+ const Index PacketSize = sizeof(Packet)/sizeof(Scalar);
+
+ enum {
+ IsRowMajor = StorageOrder==RowMajor ? 1 : 0,
+ IsLower = UpLo == Lower ? 1 : 0,
+ FirstTriangular = IsRowMajor == IsLower
+ };
+
+ conj_helper<Scalar,Scalar,NumTraits<Scalar>::IsComplex && logical_xor(ConjugateLhs, IsRowMajor), ConjugateRhs> cj0;
+ conj_helper<Scalar,Scalar,NumTraits<Scalar>::IsComplex && logical_xor(ConjugateLhs, !IsRowMajor), ConjugateRhs> cj1;
+ conj_helper<RealScalar,Scalar,false, ConjugateRhs> cjd;
+
+ conj_helper<Packet,Packet,NumTraits<Scalar>::IsComplex && logical_xor(ConjugateLhs, IsRowMajor), ConjugateRhs> pcj0;
+ conj_helper<Packet,Packet,NumTraits<Scalar>::IsComplex && logical_xor(ConjugateLhs, !IsRowMajor), ConjugateRhs> pcj1;
+
+ Scalar cjAlpha = ConjugateRhs ? numext::conj(alpha) : alpha;
+
+ Index bound = numext::maxi(Index(0), size-8) & 0xfffffffe;
+ if (FirstTriangular)
+ bound = size - bound;
+
+ for (Index j=FirstTriangular ? bound : 0;
+ j<(FirstTriangular ? size : bound);j+=2)
+ {
+ const Scalar* EIGEN_RESTRICT A0 = lhs + j*lhsStride;
+ const Scalar* EIGEN_RESTRICT A1 = lhs + (j+1)*lhsStride;
+
+ Scalar t0 = cjAlpha * rhs[j];
+ Packet ptmp0 = pset1<Packet>(t0);
+ Scalar t1 = cjAlpha * rhs[j+1];
+ Packet ptmp1 = pset1<Packet>(t1);
+
+ Scalar t2(0);
+ Packet ptmp2 = pset1<Packet>(t2);
+ Scalar t3(0);
+ Packet ptmp3 = pset1<Packet>(t3);
+
+ Index starti = FirstTriangular ? 0 : j+2;
+ Index endi = FirstTriangular ? j : size;
+ Index alignedStart = (starti) + internal::first_default_aligned(&res[starti], endi-starti);
+ Index alignedEnd = alignedStart + ((endi-alignedStart)/(PacketSize))*(PacketSize);
+
+ res[j] += cjd.pmul(numext::real(A0[j]), t0);
+ res[j+1] += cjd.pmul(numext::real(A1[j+1]), t1);
+ if(FirstTriangular)
+ {
+ res[j] += cj0.pmul(A1[j], t1);
+ t3 += cj1.pmul(A1[j], rhs[j]);
+ }
+ else
+ {
+ res[j+1] += cj0.pmul(A0[j+1],t0);
+ t2 += cj1.pmul(A0[j+1], rhs[j+1]);
+ }
+
+ for (Index i=starti; i<alignedStart; ++i)
+ {
+ res[i] += cj0.pmul(A0[i], t0) + cj0.pmul(A1[i],t1);
+ t2 += cj1.pmul(A0[i], rhs[i]);
+ t3 += cj1.pmul(A1[i], rhs[i]);
+ }
+ // Yes this an optimization for gcc 4.3 and 4.4 (=> huge speed up)
+ // gcc 4.2 does this optimization automatically.
+ const Scalar* EIGEN_RESTRICT a0It = A0 + alignedStart;
+ const Scalar* EIGEN_RESTRICT a1It = A1 + alignedStart;
+ const Scalar* EIGEN_RESTRICT rhsIt = rhs + alignedStart;
+ Scalar* EIGEN_RESTRICT resIt = res + alignedStart;
+ for (Index i=alignedStart; i<alignedEnd; i+=PacketSize)
+ {
+ Packet A0i = ploadu<Packet>(a0It); a0It += PacketSize;
+ Packet A1i = ploadu<Packet>(a1It); a1It += PacketSize;
+ Packet Bi = ploadu<Packet>(rhsIt); rhsIt += PacketSize; // FIXME should be aligned in most cases
+ Packet Xi = pload <Packet>(resIt);
+
+ Xi = pcj0.pmadd(A0i,ptmp0, pcj0.pmadd(A1i,ptmp1,Xi));
+ ptmp2 = pcj1.pmadd(A0i, Bi, ptmp2);
+ ptmp3 = pcj1.pmadd(A1i, Bi, ptmp3);
+ pstore(resIt,Xi); resIt += PacketSize;
+ }
+ for (Index i=alignedEnd; i<endi; i++)
+ {
+ res[i] += cj0.pmul(A0[i], t0) + cj0.pmul(A1[i],t1);
+ t2 += cj1.pmul(A0[i], rhs[i]);
+ t3 += cj1.pmul(A1[i], rhs[i]);
+ }
+
+ res[j] += alpha * (t2 + predux(ptmp2));
+ res[j+1] += alpha * (t3 + predux(ptmp3));
+ }
+ for (Index j=FirstTriangular ? 0 : bound;j<(FirstTriangular ? bound : size);j++)
+ {
+ const Scalar* EIGEN_RESTRICT A0 = lhs + j*lhsStride;
+
+ Scalar t1 = cjAlpha * rhs[j];
+ Scalar t2(0);
+ res[j] += cjd.pmul(numext::real(A0[j]), t1);
+ for (Index i=FirstTriangular ? 0 : j+1; i<(FirstTriangular ? j : size); i++)
+ {
+ res[i] += cj0.pmul(A0[i], t1);
+ t2 += cj1.pmul(A0[i], rhs[i]);
+ }
+ res[j] += alpha * t2;
+ }
+}
+
+} // end namespace internal
+
+/***************************************************************************
+* Wrapper to product_selfadjoint_vector
+***************************************************************************/
+
+namespace internal {
+
+template<typename Lhs, int LhsMode, typename Rhs>
+struct selfadjoint_product_impl<Lhs,LhsMode,false,Rhs,0,true>
+{
+ typedef typename Product<Lhs,Rhs>::Scalar Scalar;
+
+ typedef internal::blas_traits<Lhs> LhsBlasTraits;
+ typedef typename LhsBlasTraits::DirectLinearAccessType ActualLhsType;
+ typedef internal::remove_all_t<ActualLhsType> ActualLhsTypeCleaned;
+
+ typedef internal::blas_traits<Rhs> RhsBlasTraits;
+ typedef typename RhsBlasTraits::DirectLinearAccessType ActualRhsType;
+ typedef internal::remove_all_t<ActualRhsType> ActualRhsTypeCleaned;
+
+ enum { LhsUpLo = LhsMode&(Upper|Lower) };
+
+ template<typename Dest>
+ static EIGEN_DEVICE_FUNC
+ void run(Dest& dest, const Lhs &a_lhs, const Rhs &a_rhs, const Scalar& alpha)
+ {
+ typedef typename Dest::Scalar ResScalar;
+ typedef typename Rhs::Scalar RhsScalar;
+ typedef Map<Matrix<ResScalar,Dynamic,1>, plain_enum_min(AlignedMax,internal::packet_traits<ResScalar>::size)> MappedDest;
+
+ eigen_assert(dest.rows()==a_lhs.rows() && dest.cols()==a_rhs.cols());
+
+ add_const_on_value_type_t<ActualLhsType> lhs = LhsBlasTraits::extract(a_lhs);
+ add_const_on_value_type_t<ActualRhsType> rhs = RhsBlasTraits::extract(a_rhs);
+
+ Scalar actualAlpha = alpha * LhsBlasTraits::extractScalarFactor(a_lhs)
+ * RhsBlasTraits::extractScalarFactor(a_rhs);
+
+ enum {
+ EvalToDest = (Dest::InnerStrideAtCompileTime==1),
+ UseRhs = (ActualRhsTypeCleaned::InnerStrideAtCompileTime==1)
+ };
+
+ internal::gemv_static_vector_if<ResScalar,Dest::SizeAtCompileTime,Dest::MaxSizeAtCompileTime,!EvalToDest> static_dest;
+ internal::gemv_static_vector_if<RhsScalar,ActualRhsTypeCleaned::SizeAtCompileTime,ActualRhsTypeCleaned::MaxSizeAtCompileTime,!UseRhs> static_rhs;
+
+ ei_declare_aligned_stack_constructed_variable(ResScalar,actualDestPtr,dest.size(),
+ EvalToDest ? dest.data() : static_dest.data());
+
+ ei_declare_aligned_stack_constructed_variable(RhsScalar,actualRhsPtr,rhs.size(),
+ UseRhs ? const_cast<RhsScalar*>(rhs.data()) : static_rhs.data());
+
+ if(!EvalToDest)
+ {
+ #ifdef EIGEN_DENSE_STORAGE_CTOR_PLUGIN
+ Index size = dest.size();
+ EIGEN_DENSE_STORAGE_CTOR_PLUGIN
+ #endif
+ MappedDest(actualDestPtr, dest.size()) = dest;
+ }
+
+ if(!UseRhs)
+ {
+ #ifdef EIGEN_DENSE_STORAGE_CTOR_PLUGIN
+ Index size = rhs.size();
+ EIGEN_DENSE_STORAGE_CTOR_PLUGIN
+ #endif
+ Map<typename ActualRhsTypeCleaned::PlainObject>(actualRhsPtr, rhs.size()) = rhs;
+ }
+
+
+ internal::selfadjoint_matrix_vector_product<Scalar, Index, (internal::traits<ActualLhsTypeCleaned>::Flags&RowMajorBit) ? RowMajor : ColMajor,
+ int(LhsUpLo), bool(LhsBlasTraits::NeedToConjugate), bool(RhsBlasTraits::NeedToConjugate)>::run
+ (
+ lhs.rows(), // size
+ &lhs.coeffRef(0,0), lhs.outerStride(), // lhs info
+ actualRhsPtr, // rhs info
+ actualDestPtr, // result info
+ actualAlpha // scale factor
+ );
+
+ if(!EvalToDest)
+ dest = MappedDest(actualDestPtr, dest.size());
+ }
+};
+
+template<typename Lhs, typename Rhs, int RhsMode>
+struct selfadjoint_product_impl<Lhs,0,true,Rhs,RhsMode,false>
+{
+ typedef typename Product<Lhs,Rhs>::Scalar Scalar;
+ enum { RhsUpLo = RhsMode&(Upper|Lower) };
+
+ template<typename Dest>
+ static void run(Dest& dest, const Lhs &a_lhs, const Rhs &a_rhs, const Scalar& alpha)
+ {
+ // let's simply transpose the product
+ Transpose<Dest> destT(dest);
+ selfadjoint_product_impl<Transpose<const Rhs>, int(RhsUpLo)==Upper ? Lower : Upper, false,
+ Transpose<const Lhs>, 0, true>::run(destT, a_rhs.transpose(), a_lhs.transpose(), alpha);
+ }
+};
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_SELFADJOINT_MATRIX_VECTOR_H
diff --git a/Eigen/src/Core/products/SelfadjointMatrixVector_BLAS.h b/Eigen/src/Core/products/SelfadjointMatrixVector_BLAS.h
new file mode 100644
index 0000000..99a8ccd
--- /dev/null
+++ b/Eigen/src/Core/products/SelfadjointMatrixVector_BLAS.h
@@ -0,0 +1,120 @@
+/*
+ Copyright (c) 2011, Intel Corporation. All rights reserved.
+
+ Redistribution and use in source and binary forms, with or without modification,
+ are permitted provided that the following conditions are met:
+
+ * Redistributions of source code must retain the above copyright notice, this
+ list of conditions and the following disclaimer.
+ * Redistributions in binary form must reproduce the above copyright notice,
+ this list of conditions and the following disclaimer in the documentation
+ and/or other materials provided with the distribution.
+ * Neither the name of Intel Corporation nor the names of its contributors may
+ be used to endorse or promote products derived from this software without
+ specific prior written permission.
+
+ THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
+ ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
+ WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
+ DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR
+ ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
+ (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
+ LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON
+ ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
+ (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
+ SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+
+ ********************************************************************************
+ * Content : Eigen bindings to BLAS F77
+ * Selfadjoint matrix-vector product functionality based on ?SYMV/HEMV.
+ ********************************************************************************
+*/
+
+#ifndef EIGEN_SELFADJOINT_MATRIX_VECTOR_BLAS_H
+#define EIGEN_SELFADJOINT_MATRIX_VECTOR_BLAS_H
+
+#include "../InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+
+/**********************************************************************
+* This file implements selfadjoint matrix-vector multiplication using BLAS
+**********************************************************************/
+
+// symv/hemv specialization
+
+template<typename Scalar, typename Index, int StorageOrder, int UpLo, bool ConjugateLhs, bool ConjugateRhs>
+struct selfadjoint_matrix_vector_product_symv :
+ selfadjoint_matrix_vector_product<Scalar,Index,StorageOrder,UpLo,ConjugateLhs,ConjugateRhs,BuiltIn> {};
+
+#define EIGEN_BLAS_SYMV_SPECIALIZE(Scalar) \
+template<typename Index, int StorageOrder, int UpLo, bool ConjugateLhs, bool ConjugateRhs> \
+struct selfadjoint_matrix_vector_product<Scalar,Index,StorageOrder,UpLo,ConjugateLhs,ConjugateRhs,Specialized> { \
+static void run( \
+ Index size, const Scalar* lhs, Index lhsStride, \
+ const Scalar* _rhs, Scalar* res, Scalar alpha) { \
+ enum {\
+ IsColMajor = StorageOrder==ColMajor \
+ }; \
+ if (IsColMajor == ConjugateLhs) {\
+ selfadjoint_matrix_vector_product<Scalar,Index,StorageOrder,UpLo,ConjugateLhs,ConjugateRhs,BuiltIn>::run( \
+ size, lhs, lhsStride, _rhs, res, alpha); \
+ } else {\
+ selfadjoint_matrix_vector_product_symv<Scalar,Index,StorageOrder,UpLo,ConjugateLhs,ConjugateRhs>::run( \
+ size, lhs, lhsStride, _rhs, res, alpha); \
+ }\
+ } \
+}; \
+
+EIGEN_BLAS_SYMV_SPECIALIZE(double)
+EIGEN_BLAS_SYMV_SPECIALIZE(float)
+EIGEN_BLAS_SYMV_SPECIALIZE(dcomplex)
+EIGEN_BLAS_SYMV_SPECIALIZE(scomplex)
+
+#define EIGEN_BLAS_SYMV_SPECIALIZATION(EIGTYPE,BLASTYPE,BLASFUNC) \
+template<typename Index, int StorageOrder, int UpLo, bool ConjugateLhs, bool ConjugateRhs> \
+struct selfadjoint_matrix_vector_product_symv<EIGTYPE,Index,StorageOrder,UpLo,ConjugateLhs,ConjugateRhs> \
+{ \
+typedef Matrix<EIGTYPE,Dynamic,1,ColMajor> SYMVVector;\
+\
+static void run( \
+Index size, const EIGTYPE* lhs, Index lhsStride, \
+const EIGTYPE* _rhs, EIGTYPE* res, EIGTYPE alpha) \
+{ \
+ enum {\
+ IsRowMajor = StorageOrder==RowMajor ? 1 : 0, \
+ IsLower = UpLo == Lower ? 1 : 0 \
+ }; \
+ BlasIndex n=convert_index<BlasIndex>(size), lda=convert_index<BlasIndex>(lhsStride), incx=1, incy=1; \
+ EIGTYPE beta(1); \
+ const EIGTYPE *x_ptr; \
+ char uplo=(IsRowMajor) ? (IsLower ? 'U' : 'L') : (IsLower ? 'L' : 'U'); \
+ SYMVVector x_tmp; \
+ if (ConjugateRhs) { \
+ Map<const SYMVVector, 0 > map_x(_rhs,size,1); \
+ x_tmp=map_x.conjugate(); \
+ x_ptr=x_tmp.data(); \
+ } else x_ptr=_rhs; \
+ BLASFUNC(&uplo, &n, (const BLASTYPE*)&numext::real_ref(alpha), (const BLASTYPE*)lhs, &lda, (const BLASTYPE*)x_ptr, &incx, (const BLASTYPE*)&numext::real_ref(beta), (BLASTYPE*)res, &incy); \
+}\
+};
+
+#ifdef EIGEN_USE_MKL
+EIGEN_BLAS_SYMV_SPECIALIZATION(double, double, dsymv)
+EIGEN_BLAS_SYMV_SPECIALIZATION(float, float, ssymv)
+EIGEN_BLAS_SYMV_SPECIALIZATION(dcomplex, MKL_Complex16, zhemv)
+EIGEN_BLAS_SYMV_SPECIALIZATION(scomplex, MKL_Complex8, chemv)
+#else
+EIGEN_BLAS_SYMV_SPECIALIZATION(double, double, dsymv_)
+EIGEN_BLAS_SYMV_SPECIALIZATION(float, float, ssymv_)
+EIGEN_BLAS_SYMV_SPECIALIZATION(dcomplex, double, zhemv_)
+EIGEN_BLAS_SYMV_SPECIALIZATION(scomplex, float, chemv_)
+#endif
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_SELFADJOINT_MATRIX_VECTOR_BLAS_H
diff --git a/Eigen/src/Core/products/SelfadjointProduct.h b/Eigen/src/Core/products/SelfadjointProduct.h
new file mode 100644
index 0000000..4cbc1f7
--- /dev/null
+++ b/Eigen/src/Core/products/SelfadjointProduct.h
@@ -0,0 +1,135 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_SELFADJOINT_PRODUCT_H
+#define EIGEN_SELFADJOINT_PRODUCT_H
+
+/**********************************************************************
+* This file implements a self adjoint product: C += A A^T updating only
+* half of the selfadjoint matrix C.
+* It corresponds to the level 3 SYRK and level 2 SYR Blas routines.
+**********************************************************************/
+
+#include "../InternalHeaderCheck.h"
+
+namespace Eigen {
+
+
+template<typename Scalar, typename Index, int UpLo, bool ConjLhs, bool ConjRhs>
+struct selfadjoint_rank1_update<Scalar,Index,ColMajor,UpLo,ConjLhs,ConjRhs>
+{
+ static void run(Index size, Scalar* mat, Index stride, const Scalar* vecX, const Scalar* vecY, const Scalar& alpha)
+ {
+ internal::conj_if<ConjRhs> cj;
+ typedef Map<const Matrix<Scalar,Dynamic,1> > OtherMap;
+ typedef std::conditional_t<ConjLhs,typename OtherMap::ConjugateReturnType,const OtherMap&> ConjLhsType;
+ for (Index i=0; i<size; ++i)
+ {
+ Map<Matrix<Scalar,Dynamic,1> >(mat+stride*i+(UpLo==Lower ? i : 0), (UpLo==Lower ? size-i : (i+1)))
+ += (alpha * cj(vecY[i])) * ConjLhsType(OtherMap(vecX+(UpLo==Lower ? i : 0),UpLo==Lower ? size-i : (i+1)));
+ }
+ }
+};
+
+template<typename Scalar, typename Index, int UpLo, bool ConjLhs, bool ConjRhs>
+struct selfadjoint_rank1_update<Scalar,Index,RowMajor,UpLo,ConjLhs,ConjRhs>
+{
+ static void run(Index size, Scalar* mat, Index stride, const Scalar* vecX, const Scalar* vecY, const Scalar& alpha)
+ {
+ selfadjoint_rank1_update<Scalar,Index,ColMajor,UpLo==Lower?Upper:Lower,ConjRhs,ConjLhs>::run(size,mat,stride,vecY,vecX,alpha);
+ }
+};
+
+template<typename MatrixType, typename OtherType, int UpLo, bool OtherIsVector = OtherType::IsVectorAtCompileTime>
+struct selfadjoint_product_selector;
+
+template<typename MatrixType, typename OtherType, int UpLo>
+struct selfadjoint_product_selector<MatrixType,OtherType,UpLo,true>
+{
+ static void run(MatrixType& mat, const OtherType& other, const typename MatrixType::Scalar& alpha)
+ {
+ typedef typename MatrixType::Scalar Scalar;
+ typedef internal::blas_traits<OtherType> OtherBlasTraits;
+ typedef typename OtherBlasTraits::DirectLinearAccessType ActualOtherType;
+ typedef internal::remove_all_t<ActualOtherType> ActualOtherType_;
+ internal::add_const_on_value_type_t<ActualOtherType> actualOther = OtherBlasTraits::extract(other.derived());
+
+ Scalar actualAlpha = alpha * OtherBlasTraits::extractScalarFactor(other.derived());
+
+ enum {
+ StorageOrder = (internal::traits<MatrixType>::Flags&RowMajorBit) ? RowMajor : ColMajor,
+ UseOtherDirectly = ActualOtherType_::InnerStrideAtCompileTime==1
+ };
+ internal::gemv_static_vector_if<Scalar,OtherType::SizeAtCompileTime,OtherType::MaxSizeAtCompileTime,!UseOtherDirectly> static_other;
+
+ ei_declare_aligned_stack_constructed_variable(Scalar, actualOtherPtr, other.size(),
+ (UseOtherDirectly ? const_cast<Scalar*>(actualOther.data()) : static_other.data()));
+
+ if(!UseOtherDirectly)
+ Map<typename ActualOtherType_::PlainObject>(actualOtherPtr, actualOther.size()) = actualOther;
+
+ selfadjoint_rank1_update<Scalar,Index,StorageOrder,UpLo,
+ OtherBlasTraits::NeedToConjugate && NumTraits<Scalar>::IsComplex,
+ (!OtherBlasTraits::NeedToConjugate) && NumTraits<Scalar>::IsComplex>
+ ::run(other.size(), mat.data(), mat.outerStride(), actualOtherPtr, actualOtherPtr, actualAlpha);
+ }
+};
+
+template<typename MatrixType, typename OtherType, int UpLo>
+struct selfadjoint_product_selector<MatrixType,OtherType,UpLo,false>
+{
+ static void run(MatrixType& mat, const OtherType& other, const typename MatrixType::Scalar& alpha)
+ {
+ typedef typename MatrixType::Scalar Scalar;
+ typedef internal::blas_traits<OtherType> OtherBlasTraits;
+ typedef typename OtherBlasTraits::DirectLinearAccessType ActualOtherType;
+ typedef internal::remove_all_t<ActualOtherType> ActualOtherType_;
+ internal::add_const_on_value_type_t<ActualOtherType> actualOther = OtherBlasTraits::extract(other.derived());
+
+ Scalar actualAlpha = alpha * OtherBlasTraits::extractScalarFactor(other.derived());
+
+ enum {
+ IsRowMajor = (internal::traits<MatrixType>::Flags&RowMajorBit) ? 1 : 0,
+ OtherIsRowMajor = ActualOtherType_::Flags&RowMajorBit ? 1 : 0
+ };
+
+ Index size = mat.cols();
+ Index depth = actualOther.cols();
+
+ typedef internal::gemm_blocking_space<IsRowMajor ? RowMajor : ColMajor,Scalar,Scalar,
+ MatrixType::MaxColsAtCompileTime, MatrixType::MaxColsAtCompileTime, ActualOtherType_::MaxColsAtCompileTime> BlockingType;
+
+ BlockingType blocking(size, size, depth, 1, false);
+
+
+ internal::general_matrix_matrix_triangular_product<Index,
+ Scalar, OtherIsRowMajor ? RowMajor : ColMajor, OtherBlasTraits::NeedToConjugate && NumTraits<Scalar>::IsComplex,
+ Scalar, OtherIsRowMajor ? ColMajor : RowMajor, (!OtherBlasTraits::NeedToConjugate) && NumTraits<Scalar>::IsComplex,
+ IsRowMajor ? RowMajor : ColMajor, MatrixType::InnerStrideAtCompileTime, UpLo>
+ ::run(size, depth,
+ actualOther.data(), actualOther.outerStride(), actualOther.data(), actualOther.outerStride(),
+ mat.data(), mat.innerStride(), mat.outerStride(), actualAlpha, blocking);
+ }
+};
+
+// high level API
+
+template<typename MatrixType, unsigned int UpLo>
+template<typename DerivedU>
+EIGEN_DEVICE_FUNC SelfAdjointView<MatrixType,UpLo>& SelfAdjointView<MatrixType,UpLo>
+::rankUpdate(const MatrixBase<DerivedU>& u, const Scalar& alpha)
+{
+ selfadjoint_product_selector<MatrixType,DerivedU,UpLo>::run(_expression().const_cast_derived(), u.derived(), alpha);
+
+ return *this;
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_SELFADJOINT_PRODUCT_H
diff --git a/Eigen/src/Core/products/SelfadjointRank2Update.h b/Eigen/src/Core/products/SelfadjointRank2Update.h
new file mode 100644
index 0000000..fb199ad
--- /dev/null
+++ b/Eigen/src/Core/products/SelfadjointRank2Update.h
@@ -0,0 +1,95 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_SELFADJOINTRANK2UPTADE_H
+#define EIGEN_SELFADJOINTRANK2UPTADE_H
+
+#include "../InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+
+/* Optimized selfadjoint matrix += alpha * uv' + conj(alpha)*vu'
+ * It corresponds to the Level2 syr2 BLAS routine
+ */
+
+template<typename Scalar, typename Index, typename UType, typename VType, int UpLo>
+struct selfadjoint_rank2_update_selector;
+
+template<typename Scalar, typename Index, typename UType, typename VType>
+struct selfadjoint_rank2_update_selector<Scalar,Index,UType,VType,Lower>
+{
+ static EIGEN_DEVICE_FUNC
+ void run(Scalar* mat, Index stride, const UType& u, const VType& v, const Scalar& alpha)
+ {
+ const Index size = u.size();
+ for (Index i=0; i<size; ++i)
+ {
+ Map<Matrix<Scalar,Dynamic,1> >(mat+stride*i+i, size-i) +=
+ (numext::conj(alpha) * numext::conj(u.coeff(i))) * v.tail(size-i)
+ + (alpha * numext::conj(v.coeff(i))) * u.tail(size-i);
+ }
+ }
+};
+
+template<typename Scalar, typename Index, typename UType, typename VType>
+struct selfadjoint_rank2_update_selector<Scalar,Index,UType,VType,Upper>
+{
+ static void run(Scalar* mat, Index stride, const UType& u, const VType& v, const Scalar& alpha)
+ {
+ const Index size = u.size();
+ for (Index i=0; i<size; ++i)
+ Map<Matrix<Scalar,Dynamic,1> >(mat+stride*i, i+1) +=
+ (numext::conj(alpha) * numext::conj(u.coeff(i))) * v.head(i+1)
+ + (alpha * numext::conj(v.coeff(i))) * u.head(i+1);
+ }
+};
+
+template<bool Cond, typename T>
+using conj_expr_if = std::conditional<!Cond, const T&, CwiseUnaryOp<scalar_conjugate_op<typename traits<T>::Scalar>,T>>;
+
+} // end namespace internal
+
+template<typename MatrixType, unsigned int UpLo>
+template<typename DerivedU, typename DerivedV>
+EIGEN_DEVICE_FUNC SelfAdjointView<MatrixType,UpLo>& SelfAdjointView<MatrixType,UpLo>
+::rankUpdate(const MatrixBase<DerivedU>& u, const MatrixBase<DerivedV>& v, const Scalar& alpha)
+{
+ typedef internal::blas_traits<DerivedU> UBlasTraits;
+ typedef typename UBlasTraits::DirectLinearAccessType ActualUType;
+ typedef internal::remove_all_t<ActualUType> ActualUType_;
+ internal::add_const_on_value_type_t<ActualUType> actualU = UBlasTraits::extract(u.derived());
+
+ typedef internal::blas_traits<DerivedV> VBlasTraits;
+ typedef typename VBlasTraits::DirectLinearAccessType ActualVType;
+ typedef internal::remove_all_t<ActualVType> ActualVType_;
+ internal::add_const_on_value_type_t<ActualVType> actualV = VBlasTraits::extract(v.derived());
+
+ // If MatrixType is row major, then we use the routine for lower triangular in the upper triangular case and
+ // vice versa, and take the complex conjugate of all coefficients and vector entries.
+
+ enum { IsRowMajor = (internal::traits<MatrixType>::Flags&RowMajorBit) ? 1 : 0 };
+ Scalar actualAlpha = alpha * UBlasTraits::extractScalarFactor(u.derived())
+ * numext::conj(VBlasTraits::extractScalarFactor(v.derived()));
+ if (IsRowMajor)
+ actualAlpha = numext::conj(actualAlpha);
+
+ typedef internal::remove_all_t<typename internal::conj_expr_if<int(IsRowMajor) ^ int(UBlasTraits::NeedToConjugate), ActualUType_>::type> UType;
+ typedef internal::remove_all_t<typename internal::conj_expr_if<int(IsRowMajor) ^ int(VBlasTraits::NeedToConjugate), ActualVType_>::type> VType;
+ internal::selfadjoint_rank2_update_selector<Scalar, Index, UType, VType,
+ (IsRowMajor ? int(UpLo==Upper ? Lower : Upper) : UpLo)>
+ ::run(_expression().const_cast_derived().data(),_expression().outerStride(),UType(actualU),VType(actualV),actualAlpha);
+
+ return *this;
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_SELFADJOINTRANK2UPTADE_H
diff --git a/Eigen/src/Core/products/TriangularMatrixMatrix.h b/Eigen/src/Core/products/TriangularMatrixMatrix.h
new file mode 100644
index 0000000..770107a
--- /dev/null
+++ b/Eigen/src/Core/products/TriangularMatrixMatrix.h
@@ -0,0 +1,474 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_TRIANGULAR_MATRIX_MATRIX_H
+#define EIGEN_TRIANGULAR_MATRIX_MATRIX_H
+
+#include "../InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+
+// template<typename Scalar, int mr, int StorageOrder, bool Conjugate, int Mode>
+// struct gemm_pack_lhs_triangular
+// {
+// Matrix<Scalar,mr,mr,
+// void operator()(Scalar* blockA, const EIGEN_RESTRICT Scalar* lhs_, int lhsStride, int depth, int rows)
+// {
+// conj_if<NumTraits<Scalar>::IsComplex && Conjugate> cj;
+// const_blas_data_mapper<Scalar, StorageOrder> lhs(lhs_,lhsStride);
+// int count = 0;
+// const int peeled_mc = (rows/mr)*mr;
+// for(int i=0; i<peeled_mc; i+=mr)
+// {
+// for(int k=0; k<depth; k++)
+// for(int w=0; w<mr; w++)
+// blockA[count++] = cj(lhs(i+w, k));
+// }
+// for(int i=peeled_mc; i<rows; i++)
+// {
+// for(int k=0; k<depth; k++)
+// blockA[count++] = cj(lhs(i, k));
+// }
+// }
+// };
+
+/* Optimized triangular matrix * matrix (_TRMM++) product built on top of
+ * the general matrix matrix product.
+ */
+template <typename Scalar, typename Index,
+ int Mode, bool LhsIsTriangular,
+ int LhsStorageOrder, bool ConjugateLhs,
+ int RhsStorageOrder, bool ConjugateRhs,
+ int ResStorageOrder, int ResInnerStride,
+ int Version = Specialized>
+struct product_triangular_matrix_matrix;
+
+template <typename Scalar, typename Index,
+ int Mode, bool LhsIsTriangular,
+ int LhsStorageOrder, bool ConjugateLhs,
+ int RhsStorageOrder, bool ConjugateRhs,
+ int ResInnerStride, int Version>
+struct product_triangular_matrix_matrix<Scalar,Index,Mode,LhsIsTriangular,
+ LhsStorageOrder,ConjugateLhs,
+ RhsStorageOrder,ConjugateRhs,RowMajor,ResInnerStride,Version>
+{
+ static EIGEN_STRONG_INLINE void run(
+ Index rows, Index cols, Index depth,
+ const Scalar* lhs, Index lhsStride,
+ const Scalar* rhs, Index rhsStride,
+ Scalar* res, Index resIncr, Index resStride,
+ const Scalar& alpha, level3_blocking<Scalar,Scalar>& blocking)
+ {
+ product_triangular_matrix_matrix<Scalar, Index,
+ (Mode&(UnitDiag|ZeroDiag)) | ((Mode&Upper) ? Lower : Upper),
+ (!LhsIsTriangular),
+ RhsStorageOrder==RowMajor ? ColMajor : RowMajor,
+ ConjugateRhs,
+ LhsStorageOrder==RowMajor ? ColMajor : RowMajor,
+ ConjugateLhs,
+ ColMajor, ResInnerStride>
+ ::run(cols, rows, depth, rhs, rhsStride, lhs, lhsStride, res, resIncr, resStride, alpha, blocking);
+ }
+};
+
+// implements col-major += alpha * op(triangular) * op(general)
+template <typename Scalar, typename Index, int Mode,
+ int LhsStorageOrder, bool ConjugateLhs,
+ int RhsStorageOrder, bool ConjugateRhs,
+ int ResInnerStride, int Version>
+struct product_triangular_matrix_matrix<Scalar,Index,Mode,true,
+ LhsStorageOrder,ConjugateLhs,
+ RhsStorageOrder,ConjugateRhs,ColMajor,ResInnerStride,Version>
+{
+
+ typedef gebp_traits<Scalar,Scalar> Traits;
+ enum {
+ SmallPanelWidth = 2 * plain_enum_max(Traits::mr, Traits::nr),
+ IsLower = (Mode&Lower) == Lower,
+ SetDiag = (Mode&(ZeroDiag|UnitDiag)) ? 0 : 1
+ };
+
+ static EIGEN_DONT_INLINE void run(
+ Index _rows, Index _cols, Index _depth,
+ const Scalar* lhs_, Index lhsStride,
+ const Scalar* rhs_, Index rhsStride,
+ Scalar* res, Index resIncr, Index resStride,
+ const Scalar& alpha, level3_blocking<Scalar,Scalar>& blocking);
+};
+
+template <typename Scalar, typename Index, int Mode,
+ int LhsStorageOrder, bool ConjugateLhs,
+ int RhsStorageOrder, bool ConjugateRhs,
+ int ResInnerStride, int Version>
+EIGEN_DONT_INLINE void product_triangular_matrix_matrix<Scalar,Index,Mode,true,
+ LhsStorageOrder,ConjugateLhs,
+ RhsStorageOrder,ConjugateRhs,ColMajor,ResInnerStride,Version>::run(
+ Index _rows, Index _cols, Index _depth,
+ const Scalar* lhs_, Index lhsStride,
+ const Scalar* rhs_, Index rhsStride,
+ Scalar* res_, Index resIncr, Index resStride,
+ const Scalar& alpha, level3_blocking<Scalar,Scalar>& blocking)
+ {
+ // strip zeros
+ Index diagSize = (std::min)(_rows,_depth);
+ Index rows = IsLower ? _rows : diagSize;
+ Index depth = IsLower ? diagSize : _depth;
+ Index cols = _cols;
+
+ typedef const_blas_data_mapper<Scalar, Index, LhsStorageOrder> LhsMapper;
+ typedef const_blas_data_mapper<Scalar, Index, RhsStorageOrder> RhsMapper;
+ typedef blas_data_mapper<typename Traits::ResScalar, Index, ColMajor, Unaligned, ResInnerStride> ResMapper;
+ LhsMapper lhs(lhs_,lhsStride);
+ RhsMapper rhs(rhs_,rhsStride);
+ ResMapper res(res_, resStride, resIncr);
+
+ Index kc = blocking.kc(); // cache block size along the K direction
+ Index mc = (std::min)(rows,blocking.mc()); // cache block size along the M direction
+ // The small panel size must not be larger than blocking size.
+ // Usually this should never be the case because SmallPanelWidth^2 is very small
+ // compared to L2 cache size, but let's be safe:
+ Index panelWidth = (std::min)(Index(SmallPanelWidth),(std::min)(kc,mc));
+
+ std::size_t sizeA = kc*mc;
+ std::size_t sizeB = kc*cols;
+
+ ei_declare_aligned_stack_constructed_variable(Scalar, blockA, sizeA, blocking.blockA());
+ ei_declare_aligned_stack_constructed_variable(Scalar, blockB, sizeB, blocking.blockB());
+
+ // To work around an "error: member reference base type 'Matrix<...>
+ // (Eigen::internal::constructor_without_unaligned_array_assert (*)())' is
+ // not a structure or union" compilation error in nvcc (tested V8.0.61),
+ // create a dummy internal::constructor_without_unaligned_array_assert
+ // object to pass to the Matrix constructor.
+ internal::constructor_without_unaligned_array_assert a;
+ Matrix<Scalar,SmallPanelWidth,SmallPanelWidth,LhsStorageOrder> triangularBuffer(a);
+ triangularBuffer.setZero();
+ if((Mode&ZeroDiag)==ZeroDiag)
+ triangularBuffer.diagonal().setZero();
+ else
+ triangularBuffer.diagonal().setOnes();
+
+ gebp_kernel<Scalar, Scalar, Index, ResMapper, Traits::mr, Traits::nr, ConjugateLhs, ConjugateRhs> gebp_kernel;
+ gemm_pack_lhs<Scalar, Index, LhsMapper, Traits::mr, Traits::LhsProgress, typename Traits::LhsPacket4Packing, LhsStorageOrder> pack_lhs;
+ gemm_pack_rhs<Scalar, Index, RhsMapper, Traits::nr,RhsStorageOrder> pack_rhs;
+
+ for(Index k2=IsLower ? depth : 0;
+ IsLower ? k2>0 : k2<depth;
+ IsLower ? k2-=kc : k2+=kc)
+ {
+ Index actual_kc = (std::min)(IsLower ? k2 : depth-k2, kc);
+ Index actual_k2 = IsLower ? k2-actual_kc : k2;
+
+ // align blocks with the end of the triangular part for trapezoidal lhs
+ if((!IsLower)&&(k2<rows)&&(k2+actual_kc>rows))
+ {
+ actual_kc = rows-k2;
+ k2 = k2+actual_kc-kc;
+ }
+
+ pack_rhs(blockB, rhs.getSubMapper(actual_k2,0), actual_kc, cols);
+
+ // the selected lhs's panel has to be split in three different parts:
+ // 1 - the part which is zero => skip it
+ // 2 - the diagonal block => special kernel
+ // 3 - the dense panel below (lower case) or above (upper case) the diagonal block => GEPP
+
+ // the block diagonal, if any:
+ if(IsLower || actual_k2<rows)
+ {
+ // for each small vertical panels of lhs
+ for (Index k1=0; k1<actual_kc; k1+=panelWidth)
+ {
+ Index actualPanelWidth = std::min<Index>(actual_kc-k1, panelWidth);
+ Index lengthTarget = IsLower ? actual_kc-k1-actualPanelWidth : k1;
+ Index startBlock = actual_k2+k1;
+ Index blockBOffset = k1;
+
+ // => GEBP with the micro triangular block
+ // The trick is to pack this micro block while filling the opposite triangular part with zeros.
+ // To this end we do an extra triangular copy to a small temporary buffer
+ for (Index k=0;k<actualPanelWidth;++k)
+ {
+ if (SetDiag)
+ triangularBuffer.coeffRef(k,k) = lhs(startBlock+k,startBlock+k);
+ for (Index i=IsLower ? k+1 : 0; IsLower ? i<actualPanelWidth : i<k; ++i)
+ triangularBuffer.coeffRef(i,k) = lhs(startBlock+i,startBlock+k);
+ }
+ pack_lhs(blockA, LhsMapper(triangularBuffer.data(), triangularBuffer.outerStride()), actualPanelWidth, actualPanelWidth);
+
+ gebp_kernel(res.getSubMapper(startBlock, 0), blockA, blockB,
+ actualPanelWidth, actualPanelWidth, cols, alpha,
+ actualPanelWidth, actual_kc, 0, blockBOffset);
+
+ // GEBP with remaining micro panel
+ if (lengthTarget>0)
+ {
+ Index startTarget = IsLower ? actual_k2+k1+actualPanelWidth : actual_k2;
+
+ pack_lhs(blockA, lhs.getSubMapper(startTarget,startBlock), actualPanelWidth, lengthTarget);
+
+ gebp_kernel(res.getSubMapper(startTarget, 0), blockA, blockB,
+ lengthTarget, actualPanelWidth, cols, alpha,
+ actualPanelWidth, actual_kc, 0, blockBOffset);
+ }
+ }
+ }
+ // the part below (lower case) or above (upper case) the diagonal => GEPP
+ {
+ Index start = IsLower ? k2 : 0;
+ Index end = IsLower ? rows : (std::min)(actual_k2,rows);
+ for(Index i2=start; i2<end; i2+=mc)
+ {
+ const Index actual_mc = (std::min)(i2+mc,end)-i2;
+ gemm_pack_lhs<Scalar, Index, LhsMapper, Traits::mr,Traits::LhsProgress, typename Traits::LhsPacket4Packing, LhsStorageOrder,false>()
+ (blockA, lhs.getSubMapper(i2, actual_k2), actual_kc, actual_mc);
+
+ gebp_kernel(res.getSubMapper(i2, 0), blockA, blockB, actual_mc,
+ actual_kc, cols, alpha, -1, -1, 0, 0);
+ }
+ }
+ }
+ }
+
+// implements col-major += alpha * op(general) * op(triangular)
+template <typename Scalar, typename Index, int Mode,
+ int LhsStorageOrder, bool ConjugateLhs,
+ int RhsStorageOrder, bool ConjugateRhs,
+ int ResInnerStride, int Version>
+struct product_triangular_matrix_matrix<Scalar,Index,Mode,false,
+ LhsStorageOrder,ConjugateLhs,
+ RhsStorageOrder,ConjugateRhs,ColMajor,ResInnerStride,Version>
+{
+ typedef gebp_traits<Scalar,Scalar> Traits;
+ enum {
+ SmallPanelWidth = plain_enum_max(Traits::mr, Traits::nr),
+ IsLower = (Mode&Lower) == Lower,
+ SetDiag = (Mode&(ZeroDiag|UnitDiag)) ? 0 : 1
+ };
+
+ static EIGEN_DONT_INLINE void run(
+ Index _rows, Index _cols, Index _depth,
+ const Scalar* lhs_, Index lhsStride,
+ const Scalar* rhs_, Index rhsStride,
+ Scalar* res, Index resIncr, Index resStride,
+ const Scalar& alpha, level3_blocking<Scalar,Scalar>& blocking);
+};
+
+template <typename Scalar, typename Index, int Mode,
+ int LhsStorageOrder, bool ConjugateLhs,
+ int RhsStorageOrder, bool ConjugateRhs,
+ int ResInnerStride, int Version>
+EIGEN_DONT_INLINE void product_triangular_matrix_matrix<Scalar,Index,Mode,false,
+ LhsStorageOrder,ConjugateLhs,
+ RhsStorageOrder,ConjugateRhs,ColMajor,ResInnerStride,Version>::run(
+ Index _rows, Index _cols, Index _depth,
+ const Scalar* lhs_, Index lhsStride,
+ const Scalar* rhs_, Index rhsStride,
+ Scalar* res_, Index resIncr, Index resStride,
+ const Scalar& alpha, level3_blocking<Scalar,Scalar>& blocking)
+ {
+ const Index PacketBytes = packet_traits<Scalar>::size*sizeof(Scalar);
+ // strip zeros
+ Index diagSize = (std::min)(_cols,_depth);
+ Index rows = _rows;
+ Index depth = IsLower ? _depth : diagSize;
+ Index cols = IsLower ? diagSize : _cols;
+
+ typedef const_blas_data_mapper<Scalar, Index, LhsStorageOrder> LhsMapper;
+ typedef const_blas_data_mapper<Scalar, Index, RhsStorageOrder> RhsMapper;
+ typedef blas_data_mapper<typename Traits::ResScalar, Index, ColMajor, Unaligned, ResInnerStride> ResMapper;
+ LhsMapper lhs(lhs_,lhsStride);
+ RhsMapper rhs(rhs_,rhsStride);
+ ResMapper res(res_, resStride, resIncr);
+
+ Index kc = blocking.kc(); // cache block size along the K direction
+ Index mc = (std::min)(rows,blocking.mc()); // cache block size along the M direction
+
+ std::size_t sizeA = kc*mc;
+ std::size_t sizeB = kc*cols+EIGEN_MAX_ALIGN_BYTES/sizeof(Scalar);
+
+ ei_declare_aligned_stack_constructed_variable(Scalar, blockA, sizeA, blocking.blockA());
+ ei_declare_aligned_stack_constructed_variable(Scalar, blockB, sizeB, blocking.blockB());
+
+ internal::constructor_without_unaligned_array_assert a;
+ Matrix<Scalar,SmallPanelWidth,SmallPanelWidth,RhsStorageOrder> triangularBuffer(a);
+ triangularBuffer.setZero();
+ if((Mode&ZeroDiag)==ZeroDiag)
+ triangularBuffer.diagonal().setZero();
+ else
+ triangularBuffer.diagonal().setOnes();
+
+ gebp_kernel<Scalar, Scalar, Index, ResMapper, Traits::mr, Traits::nr, ConjugateLhs, ConjugateRhs> gebp_kernel;
+ gemm_pack_lhs<Scalar, Index, LhsMapper, Traits::mr, Traits::LhsProgress, typename Traits::LhsPacket4Packing, LhsStorageOrder> pack_lhs;
+ gemm_pack_rhs<Scalar, Index, RhsMapper, Traits::nr,RhsStorageOrder> pack_rhs;
+ gemm_pack_rhs<Scalar, Index, RhsMapper, Traits::nr,RhsStorageOrder,false,true> pack_rhs_panel;
+
+ for(Index k2=IsLower ? 0 : depth;
+ IsLower ? k2<depth : k2>0;
+ IsLower ? k2+=kc : k2-=kc)
+ {
+ Index actual_kc = (std::min)(IsLower ? depth-k2 : k2, kc);
+ Index actual_k2 = IsLower ? k2 : k2-actual_kc;
+
+ // align blocks with the end of the triangular part for trapezoidal rhs
+ if(IsLower && (k2<cols) && (actual_k2+actual_kc>cols))
+ {
+ actual_kc = cols-k2;
+ k2 = actual_k2 + actual_kc - kc;
+ }
+
+ // remaining size
+ Index rs = IsLower ? (std::min)(cols,actual_k2) : cols - k2;
+ // size of the triangular part
+ Index ts = (IsLower && actual_k2>=cols) ? 0 : actual_kc;
+
+ Scalar* geb = blockB+ts*ts;
+ geb = geb + internal::first_aligned<PacketBytes>(geb,PacketBytes/sizeof(Scalar));
+
+ pack_rhs(geb, rhs.getSubMapper(actual_k2,IsLower ? 0 : k2), actual_kc, rs);
+
+ // pack the triangular part of the rhs padding the unrolled blocks with zeros
+ if(ts>0)
+ {
+ for (Index j2=0; j2<actual_kc; j2+=SmallPanelWidth)
+ {
+ Index actualPanelWidth = std::min<Index>(actual_kc-j2, SmallPanelWidth);
+ Index actual_j2 = actual_k2 + j2;
+ Index panelOffset = IsLower ? j2+actualPanelWidth : 0;
+ Index panelLength = IsLower ? actual_kc-j2-actualPanelWidth : j2;
+ // general part
+ pack_rhs_panel(blockB+j2*actual_kc,
+ rhs.getSubMapper(actual_k2+panelOffset, actual_j2),
+ panelLength, actualPanelWidth,
+ actual_kc, panelOffset);
+
+ // append the triangular part via a temporary buffer
+ for (Index j=0;j<actualPanelWidth;++j)
+ {
+ if (SetDiag)
+ triangularBuffer.coeffRef(j,j) = rhs(actual_j2+j,actual_j2+j);
+ for (Index k=IsLower ? j+1 : 0; IsLower ? k<actualPanelWidth : k<j; ++k)
+ triangularBuffer.coeffRef(k,j) = rhs(actual_j2+k,actual_j2+j);
+ }
+
+ pack_rhs_panel(blockB+j2*actual_kc,
+ RhsMapper(triangularBuffer.data(), triangularBuffer.outerStride()),
+ actualPanelWidth, actualPanelWidth,
+ actual_kc, j2);
+ }
+ }
+
+ for (Index i2=0; i2<rows; i2+=mc)
+ {
+ const Index actual_mc = (std::min)(mc,rows-i2);
+ pack_lhs(blockA, lhs.getSubMapper(i2, actual_k2), actual_kc, actual_mc);
+
+ // triangular kernel
+ if(ts>0)
+ {
+ for (Index j2=0; j2<actual_kc; j2+=SmallPanelWidth)
+ {
+ Index actualPanelWidth = std::min<Index>(actual_kc-j2, SmallPanelWidth);
+ Index panelLength = IsLower ? actual_kc-j2 : j2+actualPanelWidth;
+ Index blockOffset = IsLower ? j2 : 0;
+
+ gebp_kernel(res.getSubMapper(i2, actual_k2 + j2),
+ blockA, blockB+j2*actual_kc,
+ actual_mc, panelLength, actualPanelWidth,
+ alpha,
+ actual_kc, actual_kc, // strides
+ blockOffset, blockOffset);// offsets
+ }
+ }
+ gebp_kernel(res.getSubMapper(i2, IsLower ? 0 : k2),
+ blockA, geb, actual_mc, actual_kc, rs,
+ alpha,
+ -1, -1, 0, 0);
+ }
+ }
+ }
+
+/***************************************************************************
+* Wrapper to product_triangular_matrix_matrix
+***************************************************************************/
+
+} // end namespace internal
+
+namespace internal {
+template<int Mode, bool LhsIsTriangular, typename Lhs, typename Rhs>
+struct triangular_product_impl<Mode,LhsIsTriangular,Lhs,false,Rhs,false>
+{
+ template<typename Dest> static void run(Dest& dst, const Lhs &a_lhs, const Rhs &a_rhs, const typename Dest::Scalar& alpha)
+ {
+ typedef typename Lhs::Scalar LhsScalar;
+ typedef typename Rhs::Scalar RhsScalar;
+ typedef typename Dest::Scalar Scalar;
+
+ typedef internal::blas_traits<Lhs> LhsBlasTraits;
+ typedef typename LhsBlasTraits::DirectLinearAccessType ActualLhsType;
+ typedef internal::remove_all_t<ActualLhsType> ActualLhsTypeCleaned;
+ typedef internal::blas_traits<Rhs> RhsBlasTraits;
+ typedef typename RhsBlasTraits::DirectLinearAccessType ActualRhsType;
+ typedef internal::remove_all_t<ActualRhsType> ActualRhsTypeCleaned;
+
+ internal::add_const_on_value_type_t<ActualLhsType> lhs = LhsBlasTraits::extract(a_lhs);
+ internal::add_const_on_value_type_t<ActualRhsType> rhs = RhsBlasTraits::extract(a_rhs);
+
+ LhsScalar lhs_alpha = LhsBlasTraits::extractScalarFactor(a_lhs);
+ RhsScalar rhs_alpha = RhsBlasTraits::extractScalarFactor(a_rhs);
+ Scalar actualAlpha = alpha * lhs_alpha * rhs_alpha;
+
+ typedef internal::gemm_blocking_space<(Dest::Flags&RowMajorBit) ? RowMajor : ColMajor,Scalar,Scalar,
+ Lhs::MaxRowsAtCompileTime, Rhs::MaxColsAtCompileTime, Lhs::MaxColsAtCompileTime,4> BlockingType;
+
+ enum { IsLower = (Mode&Lower) == Lower };
+ Index stripedRows = ((!LhsIsTriangular) || (IsLower)) ? lhs.rows() : (std::min)(lhs.rows(),lhs.cols());
+ Index stripedCols = ((LhsIsTriangular) || (!IsLower)) ? rhs.cols() : (std::min)(rhs.cols(),rhs.rows());
+ Index stripedDepth = LhsIsTriangular ? ((!IsLower) ? lhs.cols() : (std::min)(lhs.cols(),lhs.rows()))
+ : ((IsLower) ? rhs.rows() : (std::min)(rhs.rows(),rhs.cols()));
+
+ BlockingType blocking(stripedRows, stripedCols, stripedDepth, 1, false);
+
+ internal::product_triangular_matrix_matrix<Scalar, Index,
+ Mode, LhsIsTriangular,
+ (internal::traits<ActualLhsTypeCleaned>::Flags&RowMajorBit) ? RowMajor : ColMajor, LhsBlasTraits::NeedToConjugate,
+ (internal::traits<ActualRhsTypeCleaned>::Flags&RowMajorBit) ? RowMajor : ColMajor, RhsBlasTraits::NeedToConjugate,
+ (internal::traits<Dest >::Flags&RowMajorBit) ? RowMajor : ColMajor, Dest::InnerStrideAtCompileTime>
+ ::run(
+ stripedRows, stripedCols, stripedDepth, // sizes
+ &lhs.coeffRef(0,0), lhs.outerStride(), // lhs info
+ &rhs.coeffRef(0,0), rhs.outerStride(), // rhs info
+ &dst.coeffRef(0,0), dst.innerStride(), dst.outerStride(), // result info
+ actualAlpha, blocking
+ );
+
+ // Apply correction if the diagonal is unit and a scalar factor was nested:
+ if ((Mode&UnitDiag)==UnitDiag)
+ {
+ if (LhsIsTriangular && !numext::is_exactly_one(lhs_alpha))
+ {
+ Index diagSize = (std::min)(lhs.rows(),lhs.cols());
+ dst.topRows(diagSize) -= ((lhs_alpha-LhsScalar(1))*a_rhs).topRows(diagSize);
+ }
+ else if ((!LhsIsTriangular) && !numext::is_exactly_one(rhs_alpha))
+ {
+ Index diagSize = (std::min)(rhs.rows(),rhs.cols());
+ dst.leftCols(diagSize) -= (rhs_alpha-RhsScalar(1))*a_lhs.leftCols(diagSize);
+ }
+ }
+ }
+};
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_TRIANGULAR_MATRIX_MATRIX_H
diff --git a/Eigen/src/Core/products/TriangularMatrixMatrix_BLAS.h b/Eigen/src/Core/products/TriangularMatrixMatrix_BLAS.h
new file mode 100644
index 0000000..1eb57d3
--- /dev/null
+++ b/Eigen/src/Core/products/TriangularMatrixMatrix_BLAS.h
@@ -0,0 +1,319 @@
+/*
+ Copyright (c) 2011, Intel Corporation. All rights reserved.
+
+ Redistribution and use in source and binary forms, with or without modification,
+ are permitted provided that the following conditions are met:
+
+ * Redistributions of source code must retain the above copyright notice, this
+ list of conditions and the following disclaimer.
+ * Redistributions in binary form must reproduce the above copyright notice,
+ this list of conditions and the following disclaimer in the documentation
+ and/or other materials provided with the distribution.
+ * Neither the name of Intel Corporation nor the names of its contributors may
+ be used to endorse or promote products derived from this software without
+ specific prior written permission.
+
+ THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
+ ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
+ WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
+ DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR
+ ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
+ (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
+ LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON
+ ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
+ (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
+ SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+
+ ********************************************************************************
+ * Content : Eigen bindings to BLAS F77
+ * Triangular matrix * matrix product functionality based on ?TRMM.
+ ********************************************************************************
+*/
+
+#ifndef EIGEN_TRIANGULAR_MATRIX_MATRIX_BLAS_H
+#define EIGEN_TRIANGULAR_MATRIX_MATRIX_BLAS_H
+
+#include "../InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+
+
+template <typename Scalar, typename Index,
+ int Mode, bool LhsIsTriangular,
+ int LhsStorageOrder, bool ConjugateLhs,
+ int RhsStorageOrder, bool ConjugateRhs,
+ int ResStorageOrder>
+struct product_triangular_matrix_matrix_trmm :
+ product_triangular_matrix_matrix<Scalar,Index,Mode,
+ LhsIsTriangular,LhsStorageOrder,ConjugateLhs,
+ RhsStorageOrder, ConjugateRhs, ResStorageOrder, 1, BuiltIn> {};
+
+
+// try to go to BLAS specialization
+#define EIGEN_BLAS_TRMM_SPECIALIZE(Scalar, LhsIsTriangular) \
+template <typename Index, int Mode, \
+ int LhsStorageOrder, bool ConjugateLhs, \
+ int RhsStorageOrder, bool ConjugateRhs> \
+struct product_triangular_matrix_matrix<Scalar,Index, Mode, LhsIsTriangular, \
+ LhsStorageOrder,ConjugateLhs, RhsStorageOrder,ConjugateRhs,ColMajor,1,Specialized> { \
+ static inline void run(Index _rows, Index _cols, Index _depth, const Scalar* _lhs, Index lhsStride,\
+ const Scalar* _rhs, Index rhsStride, Scalar* res, Index resIncr, Index resStride, Scalar alpha, level3_blocking<Scalar,Scalar>& blocking) { \
+ EIGEN_ONLY_USED_FOR_DEBUG(resIncr); \
+ eigen_assert(resIncr == 1); \
+ product_triangular_matrix_matrix_trmm<Scalar,Index,Mode, \
+ LhsIsTriangular,LhsStorageOrder,ConjugateLhs, \
+ RhsStorageOrder, ConjugateRhs, ColMajor>::run( \
+ _rows, _cols, _depth, _lhs, lhsStride, _rhs, rhsStride, res, resStride, alpha, blocking); \
+ } \
+};
+
+EIGEN_BLAS_TRMM_SPECIALIZE(double, true)
+EIGEN_BLAS_TRMM_SPECIALIZE(double, false)
+EIGEN_BLAS_TRMM_SPECIALIZE(dcomplex, true)
+EIGEN_BLAS_TRMM_SPECIALIZE(dcomplex, false)
+EIGEN_BLAS_TRMM_SPECIALIZE(float, true)
+EIGEN_BLAS_TRMM_SPECIALIZE(float, false)
+EIGEN_BLAS_TRMM_SPECIALIZE(scomplex, true)
+EIGEN_BLAS_TRMM_SPECIALIZE(scomplex, false)
+
+// implements col-major += alpha * op(triangular) * op(general)
+#define EIGEN_BLAS_TRMM_L(EIGTYPE, BLASTYPE, EIGPREFIX, BLASFUNC) \
+template <typename Index, int Mode, \
+ int LhsStorageOrder, bool ConjugateLhs, \
+ int RhsStorageOrder, bool ConjugateRhs> \
+struct product_triangular_matrix_matrix_trmm<EIGTYPE,Index,Mode,true, \
+ LhsStorageOrder,ConjugateLhs,RhsStorageOrder,ConjugateRhs,ColMajor> \
+{ \
+ enum { \
+ IsLower = (Mode&Lower) == Lower, \
+ SetDiag = (Mode&(ZeroDiag|UnitDiag)) ? 0 : 1, \
+ IsUnitDiag = (Mode&UnitDiag) ? 1 : 0, \
+ IsZeroDiag = (Mode&ZeroDiag) ? 1 : 0, \
+ LowUp = IsLower ? Lower : Upper, \
+ conjA = ((LhsStorageOrder==ColMajor) && ConjugateLhs) ? 1 : 0 \
+ }; \
+\
+ static void run( \
+ Index _rows, Index _cols, Index _depth, \
+ const EIGTYPE* _lhs, Index lhsStride, \
+ const EIGTYPE* _rhs, Index rhsStride, \
+ EIGTYPE* res, Index resStride, \
+ EIGTYPE alpha, level3_blocking<EIGTYPE,EIGTYPE>& blocking) \
+ { \
+ Index diagSize = (std::min)(_rows,_depth); \
+ Index rows = IsLower ? _rows : diagSize; \
+ Index depth = IsLower ? diagSize : _depth; \
+ Index cols = _cols; \
+\
+ typedef Matrix<EIGTYPE, Dynamic, Dynamic, LhsStorageOrder> MatrixLhs; \
+ typedef Matrix<EIGTYPE, Dynamic, Dynamic, RhsStorageOrder> MatrixRhs; \
+\
+/* Non-square case - doesn't fit to BLAS ?TRMM. Fall to default triangular product or call BLAS ?GEMM*/ \
+ if (rows != depth) { \
+\
+ /* FIXME handle mkl_domain_get_max_threads */ \
+ /*int nthr = mkl_domain_get_max_threads(EIGEN_BLAS_DOMAIN_BLAS);*/ int nthr = 1;\
+\
+ if (((nthr==1) && (((std::max)(rows,depth)-diagSize)/(double)diagSize < 0.5))) { \
+ /* Most likely no benefit to call TRMM or GEMM from BLAS */ \
+ product_triangular_matrix_matrix<EIGTYPE,Index,Mode,true, \
+ LhsStorageOrder,ConjugateLhs, RhsStorageOrder, ConjugateRhs, ColMajor, 1, BuiltIn>::run( \
+ _rows, _cols, _depth, _lhs, lhsStride, _rhs, rhsStride, res, 1, resStride, alpha, blocking); \
+ /*std::cout << "TRMM_L: A is not square! Go to Eigen TRMM implementation!\n";*/ \
+ } else { \
+ /* Make sense to call GEMM */ \
+ Map<const MatrixLhs, 0, OuterStride<> > lhsMap(_lhs,rows,depth,OuterStride<>(lhsStride)); \
+ MatrixLhs aa_tmp=lhsMap.template triangularView<Mode>(); \
+ BlasIndex aStride = convert_index<BlasIndex>(aa_tmp.outerStride()); \
+ gemm_blocking_space<ColMajor,EIGTYPE,EIGTYPE,Dynamic,Dynamic,Dynamic> gemm_blocking(_rows,_cols,_depth, 1, true); \
+ general_matrix_matrix_product<Index,EIGTYPE,LhsStorageOrder,ConjugateLhs,EIGTYPE,RhsStorageOrder,ConjugateRhs,ColMajor,1>::run( \
+ rows, cols, depth, aa_tmp.data(), aStride, _rhs, rhsStride, res, 1, resStride, alpha, gemm_blocking, 0); \
+\
+ /*std::cout << "TRMM_L: A is not square! Go to BLAS GEMM implementation! " << nthr<<" \n";*/ \
+ } \
+ return; \
+ } \
+ char side = 'L', transa, uplo, diag = 'N'; \
+ EIGTYPE *b; \
+ const EIGTYPE *a; \
+ BlasIndex m, n, lda, ldb; \
+\
+/* Set m, n */ \
+ m = convert_index<BlasIndex>(diagSize); \
+ n = convert_index<BlasIndex>(cols); \
+\
+/* Set trans */ \
+ transa = (LhsStorageOrder==RowMajor) ? ((ConjugateLhs) ? 'C' : 'T') : 'N'; \
+\
+/* Set b, ldb */ \
+ Map<const MatrixRhs, 0, OuterStride<> > rhs(_rhs,depth,cols,OuterStride<>(rhsStride)); \
+ MatrixX##EIGPREFIX b_tmp; \
+\
+ if (ConjugateRhs) b_tmp = rhs.conjugate(); else b_tmp = rhs; \
+ b = b_tmp.data(); \
+ ldb = convert_index<BlasIndex>(b_tmp.outerStride()); \
+\
+/* Set uplo */ \
+ uplo = IsLower ? 'L' : 'U'; \
+ if (LhsStorageOrder==RowMajor) uplo = (uplo == 'L') ? 'U' : 'L'; \
+/* Set a, lda */ \
+ Map<const MatrixLhs, 0, OuterStride<> > lhs(_lhs,rows,depth,OuterStride<>(lhsStride)); \
+ MatrixLhs a_tmp; \
+\
+ if ((conjA!=0) || (SetDiag==0)) { \
+ if (conjA) a_tmp = lhs.conjugate(); else a_tmp = lhs; \
+ if (IsZeroDiag) \
+ a_tmp.diagonal().setZero(); \
+ else if (IsUnitDiag) \
+ a_tmp.diagonal().setOnes();\
+ a = a_tmp.data(); \
+ lda = convert_index<BlasIndex>(a_tmp.outerStride()); \
+ } else { \
+ a = _lhs; \
+ lda = convert_index<BlasIndex>(lhsStride); \
+ } \
+ /*std::cout << "TRMM_L: A is square! Go to BLAS TRMM implementation! \n";*/ \
+/* call ?trmm*/ \
+ BLASFUNC(&side, &uplo, &transa, &diag, &m, &n, (const BLASTYPE*)&numext::real_ref(alpha), (const BLASTYPE*)a, &lda, (BLASTYPE*)b, &ldb); \
+\
+/* Add op(a_triangular)*b into res*/ \
+ Map<MatrixX##EIGPREFIX, 0, OuterStride<> > res_tmp(res,rows,cols,OuterStride<>(resStride)); \
+ res_tmp=res_tmp+b_tmp; \
+ } \
+};
+
+#ifdef EIGEN_USE_MKL
+EIGEN_BLAS_TRMM_L(double, double, d, dtrmm)
+EIGEN_BLAS_TRMM_L(dcomplex, MKL_Complex16, cd, ztrmm)
+EIGEN_BLAS_TRMM_L(float, float, f, strmm)
+EIGEN_BLAS_TRMM_L(scomplex, MKL_Complex8, cf, ctrmm)
+#else
+EIGEN_BLAS_TRMM_L(double, double, d, dtrmm_)
+EIGEN_BLAS_TRMM_L(dcomplex, double, cd, ztrmm_)
+EIGEN_BLAS_TRMM_L(float, float, f, strmm_)
+EIGEN_BLAS_TRMM_L(scomplex, float, cf, ctrmm_)
+#endif
+
+// implements col-major += alpha * op(general) * op(triangular)
+#define EIGEN_BLAS_TRMM_R(EIGTYPE, BLASTYPE, EIGPREFIX, BLASFUNC) \
+template <typename Index, int Mode, \
+ int LhsStorageOrder, bool ConjugateLhs, \
+ int RhsStorageOrder, bool ConjugateRhs> \
+struct product_triangular_matrix_matrix_trmm<EIGTYPE,Index,Mode,false, \
+ LhsStorageOrder,ConjugateLhs,RhsStorageOrder,ConjugateRhs,ColMajor> \
+{ \
+ enum { \
+ IsLower = (Mode&Lower) == Lower, \
+ SetDiag = (Mode&(ZeroDiag|UnitDiag)) ? 0 : 1, \
+ IsUnitDiag = (Mode&UnitDiag) ? 1 : 0, \
+ IsZeroDiag = (Mode&ZeroDiag) ? 1 : 0, \
+ LowUp = IsLower ? Lower : Upper, \
+ conjA = ((RhsStorageOrder==ColMajor) && ConjugateRhs) ? 1 : 0 \
+ }; \
+\
+ static void run( \
+ Index _rows, Index _cols, Index _depth, \
+ const EIGTYPE* _lhs, Index lhsStride, \
+ const EIGTYPE* _rhs, Index rhsStride, \
+ EIGTYPE* res, Index resStride, \
+ EIGTYPE alpha, level3_blocking<EIGTYPE,EIGTYPE>& blocking) \
+ { \
+ Index diagSize = (std::min)(_cols,_depth); \
+ Index rows = _rows; \
+ Index depth = IsLower ? _depth : diagSize; \
+ Index cols = IsLower ? diagSize : _cols; \
+\
+ typedef Matrix<EIGTYPE, Dynamic, Dynamic, LhsStorageOrder> MatrixLhs; \
+ typedef Matrix<EIGTYPE, Dynamic, Dynamic, RhsStorageOrder> MatrixRhs; \
+\
+/* Non-square case - doesn't fit to BLAS ?TRMM. Fall to default triangular product or call BLAS ?GEMM*/ \
+ if (cols != depth) { \
+\
+ int nthr = 1 /*mkl_domain_get_max_threads(EIGEN_BLAS_DOMAIN_BLAS)*/; \
+\
+ if ((nthr==1) && (((std::max)(cols,depth)-diagSize)/(double)diagSize < 0.5)) { \
+ /* Most likely no benefit to call TRMM or GEMM from BLAS*/ \
+ product_triangular_matrix_matrix<EIGTYPE,Index,Mode,false, \
+ LhsStorageOrder,ConjugateLhs, RhsStorageOrder, ConjugateRhs, ColMajor, 1, BuiltIn>::run( \
+ _rows, _cols, _depth, _lhs, lhsStride, _rhs, rhsStride, res, 1, resStride, alpha, blocking); \
+ /*std::cout << "TRMM_R: A is not square! Go to Eigen TRMM implementation!\n";*/ \
+ } else { \
+ /* Make sense to call GEMM */ \
+ Map<const MatrixRhs, 0, OuterStride<> > rhsMap(_rhs,depth,cols, OuterStride<>(rhsStride)); \
+ MatrixRhs aa_tmp=rhsMap.template triangularView<Mode>(); \
+ BlasIndex aStride = convert_index<BlasIndex>(aa_tmp.outerStride()); \
+ gemm_blocking_space<ColMajor,EIGTYPE,EIGTYPE,Dynamic,Dynamic,Dynamic> gemm_blocking(_rows,_cols,_depth, 1, true); \
+ general_matrix_matrix_product<Index,EIGTYPE,LhsStorageOrder,ConjugateLhs,EIGTYPE,RhsStorageOrder,ConjugateRhs,ColMajor,1>::run( \
+ rows, cols, depth, _lhs, lhsStride, aa_tmp.data(), aStride, res, 1, resStride, alpha, gemm_blocking, 0); \
+\
+ /*std::cout << "TRMM_R: A is not square! Go to BLAS GEMM implementation! " << nthr<<" \n";*/ \
+ } \
+ return; \
+ } \
+ char side = 'R', transa, uplo, diag = 'N'; \
+ EIGTYPE *b; \
+ const EIGTYPE *a; \
+ BlasIndex m, n, lda, ldb; \
+\
+/* Set m, n */ \
+ m = convert_index<BlasIndex>(rows); \
+ n = convert_index<BlasIndex>(diagSize); \
+\
+/* Set trans */ \
+ transa = (RhsStorageOrder==RowMajor) ? ((ConjugateRhs) ? 'C' : 'T') : 'N'; \
+\
+/* Set b, ldb */ \
+ Map<const MatrixLhs, 0, OuterStride<> > lhs(_lhs,rows,depth,OuterStride<>(lhsStride)); \
+ MatrixX##EIGPREFIX b_tmp; \
+\
+ if (ConjugateLhs) b_tmp = lhs.conjugate(); else b_tmp = lhs; \
+ b = b_tmp.data(); \
+ ldb = convert_index<BlasIndex>(b_tmp.outerStride()); \
+\
+/* Set uplo */ \
+ uplo = IsLower ? 'L' : 'U'; \
+ if (RhsStorageOrder==RowMajor) uplo = (uplo == 'L') ? 'U' : 'L'; \
+/* Set a, lda */ \
+ Map<const MatrixRhs, 0, OuterStride<> > rhs(_rhs,depth,cols, OuterStride<>(rhsStride)); \
+ MatrixRhs a_tmp; \
+\
+ if ((conjA!=0) || (SetDiag==0)) { \
+ if (conjA) a_tmp = rhs.conjugate(); else a_tmp = rhs; \
+ if (IsZeroDiag) \
+ a_tmp.diagonal().setZero(); \
+ else if (IsUnitDiag) \
+ a_tmp.diagonal().setOnes();\
+ a = a_tmp.data(); \
+ lda = convert_index<BlasIndex>(a_tmp.outerStride()); \
+ } else { \
+ a = _rhs; \
+ lda = convert_index<BlasIndex>(rhsStride); \
+ } \
+ /*std::cout << "TRMM_R: A is square! Go to BLAS TRMM implementation! \n";*/ \
+/* call ?trmm*/ \
+ BLASFUNC(&side, &uplo, &transa, &diag, &m, &n, (const BLASTYPE*)&numext::real_ref(alpha), (const BLASTYPE*)a, &lda, (BLASTYPE*)b, &ldb); \
+\
+/* Add op(a_triangular)*b into res*/ \
+ Map<MatrixX##EIGPREFIX, 0, OuterStride<> > res_tmp(res,rows,cols,OuterStride<>(resStride)); \
+ res_tmp=res_tmp+b_tmp; \
+ } \
+};
+
+#ifdef EIGEN_USE_MKL
+EIGEN_BLAS_TRMM_R(double, double, d, dtrmm)
+EIGEN_BLAS_TRMM_R(dcomplex, MKL_Complex16, cd, ztrmm)
+EIGEN_BLAS_TRMM_R(float, float, f, strmm)
+EIGEN_BLAS_TRMM_R(scomplex, MKL_Complex8, cf, ctrmm)
+#else
+EIGEN_BLAS_TRMM_R(double, double, d, dtrmm_)
+EIGEN_BLAS_TRMM_R(dcomplex, double, cd, ztrmm_)
+EIGEN_BLAS_TRMM_R(float, float, f, strmm_)
+EIGEN_BLAS_TRMM_R(scomplex, float, cf, ctrmm_)
+#endif
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_TRIANGULAR_MATRIX_MATRIX_BLAS_H
diff --git a/Eigen/src/Core/products/TriangularMatrixVector.h b/Eigen/src/Core/products/TriangularMatrixVector.h
new file mode 100644
index 0000000..df15e81
--- /dev/null
+++ b/Eigen/src/Core/products/TriangularMatrixVector.h
@@ -0,0 +1,351 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_TRIANGULARMATRIXVECTOR_H
+#define EIGEN_TRIANGULARMATRIXVECTOR_H
+
+#include "../InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+
+template<typename Index, int Mode, typename LhsScalar, bool ConjLhs, typename RhsScalar, bool ConjRhs, int StorageOrder, int Version=Specialized>
+struct triangular_matrix_vector_product;
+
+template<typename Index, int Mode, typename LhsScalar, bool ConjLhs, typename RhsScalar, bool ConjRhs, int Version>
+struct triangular_matrix_vector_product<Index,Mode,LhsScalar,ConjLhs,RhsScalar,ConjRhs,ColMajor,Version>
+{
+ typedef typename ScalarBinaryOpTraits<LhsScalar, RhsScalar>::ReturnType ResScalar;
+ enum {
+ IsLower = ((Mode&Lower)==Lower),
+ HasUnitDiag = (Mode & UnitDiag)==UnitDiag,
+ HasZeroDiag = (Mode & ZeroDiag)==ZeroDiag
+ };
+ static EIGEN_DONT_INLINE void run(Index _rows, Index _cols, const LhsScalar* _lhs, Index lhsStride,
+ const RhsScalar* _rhs, Index rhsIncr, ResScalar* _res, Index resIncr, const RhsScalar& alpha);
+};
+
+template<typename Index, int Mode, typename LhsScalar, bool ConjLhs, typename RhsScalar, bool ConjRhs, int Version>
+EIGEN_DONT_INLINE void triangular_matrix_vector_product<Index,Mode,LhsScalar,ConjLhs,RhsScalar,ConjRhs,ColMajor,Version>
+ ::run(Index _rows, Index _cols, const LhsScalar* _lhs, Index lhsStride,
+ const RhsScalar* _rhs, Index rhsIncr, ResScalar* _res, Index resIncr, const RhsScalar& alpha)
+ {
+ static const Index PanelWidth = EIGEN_TUNE_TRIANGULAR_PANEL_WIDTH;
+ Index size = (std::min)(_rows,_cols);
+ Index rows = IsLower ? _rows : (std::min)(_rows,_cols);
+ Index cols = IsLower ? (std::min)(_rows,_cols) : _cols;
+
+ typedef Map<const Matrix<LhsScalar,Dynamic,Dynamic,ColMajor>, 0, OuterStride<> > LhsMap;
+ const LhsMap lhs(_lhs,rows,cols,OuterStride<>(lhsStride));
+ typename conj_expr_if<ConjLhs,LhsMap>::type cjLhs(lhs);
+
+ typedef Map<const Matrix<RhsScalar,Dynamic,1>, 0, InnerStride<> > RhsMap;
+ const RhsMap rhs(_rhs,cols,InnerStride<>(rhsIncr));
+ typename conj_expr_if<ConjRhs,RhsMap>::type cjRhs(rhs);
+
+ typedef Map<Matrix<ResScalar,Dynamic,1> > ResMap;
+ ResMap res(_res,rows);
+
+ typedef const_blas_data_mapper<LhsScalar,Index,ColMajor> LhsMapper;
+ typedef const_blas_data_mapper<RhsScalar,Index,RowMajor> RhsMapper;
+
+ for (Index pi=0; pi<size; pi+=PanelWidth)
+ {
+ Index actualPanelWidth = (std::min)(PanelWidth, size-pi);
+ for (Index k=0; k<actualPanelWidth; ++k)
+ {
+ Index i = pi + k;
+ Index s = IsLower ? ((HasUnitDiag||HasZeroDiag) ? i+1 : i ) : pi;
+ Index r = IsLower ? actualPanelWidth-k : k+1;
+ if ((!(HasUnitDiag||HasZeroDiag)) || (--r)>0)
+ res.segment(s,r) += (alpha * cjRhs.coeff(i)) * cjLhs.col(i).segment(s,r);
+ if (HasUnitDiag)
+ res.coeffRef(i) += alpha * cjRhs.coeff(i);
+ }
+ Index r = IsLower ? rows - pi - actualPanelWidth : pi;
+ if (r>0)
+ {
+ Index s = IsLower ? pi+actualPanelWidth : 0;
+ general_matrix_vector_product<Index,LhsScalar,LhsMapper,ColMajor,ConjLhs,RhsScalar,RhsMapper,ConjRhs,BuiltIn>::run(
+ r, actualPanelWidth,
+ LhsMapper(&lhs.coeffRef(s,pi), lhsStride),
+ RhsMapper(&rhs.coeffRef(pi), rhsIncr),
+ &res.coeffRef(s), resIncr, alpha);
+ }
+ }
+ if((!IsLower) && cols>size)
+ {
+ general_matrix_vector_product<Index,LhsScalar,LhsMapper,ColMajor,ConjLhs,RhsScalar,RhsMapper,ConjRhs>::run(
+ rows, cols-size,
+ LhsMapper(&lhs.coeffRef(0,size), lhsStride),
+ RhsMapper(&rhs.coeffRef(size), rhsIncr),
+ _res, resIncr, alpha);
+ }
+ }
+
+template<typename Index, int Mode, typename LhsScalar, bool ConjLhs, typename RhsScalar, bool ConjRhs,int Version>
+struct triangular_matrix_vector_product<Index,Mode,LhsScalar,ConjLhs,RhsScalar,ConjRhs,RowMajor,Version>
+{
+ typedef typename ScalarBinaryOpTraits<LhsScalar, RhsScalar>::ReturnType ResScalar;
+ enum {
+ IsLower = ((Mode&Lower)==Lower),
+ HasUnitDiag = (Mode & UnitDiag)==UnitDiag,
+ HasZeroDiag = (Mode & ZeroDiag)==ZeroDiag
+ };
+ static EIGEN_DONT_INLINE void run(Index _rows, Index _cols, const LhsScalar* _lhs, Index lhsStride,
+ const RhsScalar* _rhs, Index rhsIncr, ResScalar* _res, Index resIncr, const ResScalar& alpha);
+};
+
+template<typename Index, int Mode, typename LhsScalar, bool ConjLhs, typename RhsScalar, bool ConjRhs,int Version>
+EIGEN_DONT_INLINE void triangular_matrix_vector_product<Index,Mode,LhsScalar,ConjLhs,RhsScalar,ConjRhs,RowMajor,Version>
+ ::run(Index _rows, Index _cols, const LhsScalar* _lhs, Index lhsStride,
+ const RhsScalar* _rhs, Index rhsIncr, ResScalar* _res, Index resIncr, const ResScalar& alpha)
+ {
+ static const Index PanelWidth = EIGEN_TUNE_TRIANGULAR_PANEL_WIDTH;
+ Index diagSize = (std::min)(_rows,_cols);
+ Index rows = IsLower ? _rows : diagSize;
+ Index cols = IsLower ? diagSize : _cols;
+
+ typedef Map<const Matrix<LhsScalar,Dynamic,Dynamic,RowMajor>, 0, OuterStride<> > LhsMap;
+ const LhsMap lhs(_lhs,rows,cols,OuterStride<>(lhsStride));
+ typename conj_expr_if<ConjLhs,LhsMap>::type cjLhs(lhs);
+
+ typedef Map<const Matrix<RhsScalar,Dynamic,1> > RhsMap;
+ const RhsMap rhs(_rhs,cols);
+ typename conj_expr_if<ConjRhs,RhsMap>::type cjRhs(rhs);
+
+ typedef Map<Matrix<ResScalar,Dynamic,1>, 0, InnerStride<> > ResMap;
+ ResMap res(_res,rows,InnerStride<>(resIncr));
+
+ typedef const_blas_data_mapper<LhsScalar,Index,RowMajor> LhsMapper;
+ typedef const_blas_data_mapper<RhsScalar,Index,RowMajor> RhsMapper;
+
+ for (Index pi=0; pi<diagSize; pi+=PanelWidth)
+ {
+ Index actualPanelWidth = (std::min)(PanelWidth, diagSize-pi);
+ for (Index k=0; k<actualPanelWidth; ++k)
+ {
+ Index i = pi + k;
+ Index s = IsLower ? pi : ((HasUnitDiag||HasZeroDiag) ? i+1 : i);
+ Index r = IsLower ? k+1 : actualPanelWidth-k;
+ if ((!(HasUnitDiag||HasZeroDiag)) || (--r)>0)
+ res.coeffRef(i) += alpha * (cjLhs.row(i).segment(s,r).cwiseProduct(cjRhs.segment(s,r).transpose())).sum();
+ if (HasUnitDiag)
+ res.coeffRef(i) += alpha * cjRhs.coeff(i);
+ }
+ Index r = IsLower ? pi : cols - pi - actualPanelWidth;
+ if (r>0)
+ {
+ Index s = IsLower ? 0 : pi + actualPanelWidth;
+ general_matrix_vector_product<Index,LhsScalar,LhsMapper,RowMajor,ConjLhs,RhsScalar,RhsMapper,ConjRhs,BuiltIn>::run(
+ actualPanelWidth, r,
+ LhsMapper(&lhs.coeffRef(pi,s), lhsStride),
+ RhsMapper(&rhs.coeffRef(s), rhsIncr),
+ &res.coeffRef(pi), resIncr, alpha);
+ }
+ }
+ if(IsLower && rows>diagSize)
+ {
+ general_matrix_vector_product<Index,LhsScalar,LhsMapper,RowMajor,ConjLhs,RhsScalar,RhsMapper,ConjRhs>::run(
+ rows-diagSize, cols,
+ LhsMapper(&lhs.coeffRef(diagSize,0), lhsStride),
+ RhsMapper(&rhs.coeffRef(0), rhsIncr),
+ &res.coeffRef(diagSize), resIncr, alpha);
+ }
+ }
+
+/***************************************************************************
+* Wrapper to product_triangular_vector
+***************************************************************************/
+
+template<int Mode,int StorageOrder>
+struct trmv_selector;
+
+} // end namespace internal
+
+namespace internal {
+
+template<int Mode, typename Lhs, typename Rhs>
+struct triangular_product_impl<Mode,true,Lhs,false,Rhs,true>
+{
+ template<typename Dest> static void run(Dest& dst, const Lhs &lhs, const Rhs &rhs, const typename Dest::Scalar& alpha)
+ {
+ eigen_assert(dst.rows()==lhs.rows() && dst.cols()==rhs.cols());
+
+ internal::trmv_selector<Mode,(int(internal::traits<Lhs>::Flags)&RowMajorBit) ? RowMajor : ColMajor>::run(lhs, rhs, dst, alpha);
+ }
+};
+
+template<int Mode, typename Lhs, typename Rhs>
+struct triangular_product_impl<Mode,false,Lhs,true,Rhs,false>
+{
+ template<typename Dest> static void run(Dest& dst, const Lhs &lhs, const Rhs &rhs, const typename Dest::Scalar& alpha)
+ {
+ eigen_assert(dst.rows()==lhs.rows() && dst.cols()==rhs.cols());
+
+ Transpose<Dest> dstT(dst);
+ internal::trmv_selector<(Mode & (UnitDiag|ZeroDiag)) | ((Mode & Lower) ? Upper : Lower),
+ (int(internal::traits<Rhs>::Flags)&RowMajorBit) ? ColMajor : RowMajor>
+ ::run(rhs.transpose(),lhs.transpose(), dstT, alpha);
+ }
+};
+
+} // end namespace internal
+
+namespace internal {
+
+// TODO: find a way to factorize this piece of code with gemv_selector since the logic is exactly the same.
+
+template<int Mode> struct trmv_selector<Mode,ColMajor>
+{
+ template<typename Lhs, typename Rhs, typename Dest>
+ static void run(const Lhs &lhs, const Rhs &rhs, Dest& dest, const typename Dest::Scalar& alpha)
+ {
+ typedef typename Lhs::Scalar LhsScalar;
+ typedef typename Rhs::Scalar RhsScalar;
+ typedef typename Dest::Scalar ResScalar;
+
+ typedef internal::blas_traits<Lhs> LhsBlasTraits;
+ typedef typename LhsBlasTraits::DirectLinearAccessType ActualLhsType;
+ typedef internal::blas_traits<Rhs> RhsBlasTraits;
+ typedef typename RhsBlasTraits::DirectLinearAccessType ActualRhsType;
+
+ typedef Map<Matrix<ResScalar,Dynamic,1>, plain_enum_min(AlignedMax,internal::packet_traits<ResScalar>::size)> MappedDest;
+
+ add_const_on_value_type_t<ActualLhsType> actualLhs = LhsBlasTraits::extract(lhs);
+ add_const_on_value_type_t<ActualRhsType> actualRhs = RhsBlasTraits::extract(rhs);
+
+ LhsScalar lhs_alpha = LhsBlasTraits::extractScalarFactor(lhs);
+ RhsScalar rhs_alpha = RhsBlasTraits::extractScalarFactor(rhs);
+ ResScalar actualAlpha = alpha * lhs_alpha * rhs_alpha;
+
+ enum {
+ // FIXME find a way to allow an inner stride on the result if packet_traits<Scalar>::size==1
+ // on, the other hand it is good for the cache to pack the vector anyways...
+ EvalToDestAtCompileTime = Dest::InnerStrideAtCompileTime==1,
+ ComplexByReal = (NumTraits<LhsScalar>::IsComplex) && (!NumTraits<RhsScalar>::IsComplex),
+ MightCannotUseDest = (Dest::InnerStrideAtCompileTime!=1) || ComplexByReal
+ };
+
+ gemv_static_vector_if<ResScalar,Dest::SizeAtCompileTime,Dest::MaxSizeAtCompileTime,MightCannotUseDest> static_dest;
+
+ bool alphaIsCompatible = (!ComplexByReal) || numext::is_exactly_zero(numext::imag(actualAlpha));
+ bool evalToDest = EvalToDestAtCompileTime && alphaIsCompatible;
+
+ RhsScalar compatibleAlpha = get_factor<ResScalar,RhsScalar>::run(actualAlpha);
+
+ ei_declare_aligned_stack_constructed_variable(ResScalar,actualDestPtr,dest.size(),
+ evalToDest ? dest.data() : static_dest.data());
+
+ if(!evalToDest)
+ {
+ #ifdef EIGEN_DENSE_STORAGE_CTOR_PLUGIN
+ Index size = dest.size();
+ EIGEN_DENSE_STORAGE_CTOR_PLUGIN
+ #endif
+ if(!alphaIsCompatible)
+ {
+ MappedDest(actualDestPtr, dest.size()).setZero();
+ compatibleAlpha = RhsScalar(1);
+ }
+ else
+ MappedDest(actualDestPtr, dest.size()) = dest;
+ }
+
+ internal::triangular_matrix_vector_product
+ <Index,Mode,
+ LhsScalar, LhsBlasTraits::NeedToConjugate,
+ RhsScalar, RhsBlasTraits::NeedToConjugate,
+ ColMajor>
+ ::run(actualLhs.rows(),actualLhs.cols(),
+ actualLhs.data(),actualLhs.outerStride(),
+ actualRhs.data(),actualRhs.innerStride(),
+ actualDestPtr,1,compatibleAlpha);
+
+ if (!evalToDest)
+ {
+ if(!alphaIsCompatible)
+ dest += actualAlpha * MappedDest(actualDestPtr, dest.size());
+ else
+ dest = MappedDest(actualDestPtr, dest.size());
+ }
+
+ if ( ((Mode&UnitDiag)==UnitDiag) && !numext::is_exactly_one(lhs_alpha) )
+ {
+ Index diagSize = (std::min)(lhs.rows(),lhs.cols());
+ dest.head(diagSize) -= (lhs_alpha-LhsScalar(1))*rhs.head(diagSize);
+ }
+ }
+};
+
+template<int Mode> struct trmv_selector<Mode,RowMajor>
+{
+ template<typename Lhs, typename Rhs, typename Dest>
+ static void run(const Lhs &lhs, const Rhs &rhs, Dest& dest, const typename Dest::Scalar& alpha)
+ {
+ typedef typename Lhs::Scalar LhsScalar;
+ typedef typename Rhs::Scalar RhsScalar;
+ typedef typename Dest::Scalar ResScalar;
+
+ typedef internal::blas_traits<Lhs> LhsBlasTraits;
+ typedef typename LhsBlasTraits::DirectLinearAccessType ActualLhsType;
+ typedef internal::blas_traits<Rhs> RhsBlasTraits;
+ typedef typename RhsBlasTraits::DirectLinearAccessType ActualRhsType;
+ typedef internal::remove_all_t<ActualRhsType> ActualRhsTypeCleaned;
+
+ std::add_const_t<ActualLhsType> actualLhs = LhsBlasTraits::extract(lhs);
+ std::add_const_t<ActualRhsType> actualRhs = RhsBlasTraits::extract(rhs);
+
+ LhsScalar lhs_alpha = LhsBlasTraits::extractScalarFactor(lhs);
+ RhsScalar rhs_alpha = RhsBlasTraits::extractScalarFactor(rhs);
+ ResScalar actualAlpha = alpha * lhs_alpha * rhs_alpha;
+
+ enum {
+ DirectlyUseRhs = ActualRhsTypeCleaned::InnerStrideAtCompileTime==1
+ };
+
+ gemv_static_vector_if<RhsScalar,ActualRhsTypeCleaned::SizeAtCompileTime,ActualRhsTypeCleaned::MaxSizeAtCompileTime,!DirectlyUseRhs> static_rhs;
+
+ ei_declare_aligned_stack_constructed_variable(RhsScalar,actualRhsPtr,actualRhs.size(),
+ DirectlyUseRhs ? const_cast<RhsScalar*>(actualRhs.data()) : static_rhs.data());
+
+ if(!DirectlyUseRhs)
+ {
+ #ifdef EIGEN_DENSE_STORAGE_CTOR_PLUGIN
+ Index size = actualRhs.size();
+ EIGEN_DENSE_STORAGE_CTOR_PLUGIN
+ #endif
+ Map<typename ActualRhsTypeCleaned::PlainObject>(actualRhsPtr, actualRhs.size()) = actualRhs;
+ }
+
+ internal::triangular_matrix_vector_product
+ <Index,Mode,
+ LhsScalar, LhsBlasTraits::NeedToConjugate,
+ RhsScalar, RhsBlasTraits::NeedToConjugate,
+ RowMajor>
+ ::run(actualLhs.rows(),actualLhs.cols(),
+ actualLhs.data(),actualLhs.outerStride(),
+ actualRhsPtr,1,
+ dest.data(),dest.innerStride(),
+ actualAlpha);
+
+ if ( ((Mode&UnitDiag)==UnitDiag) && !numext::is_exactly_one(lhs_alpha) )
+ {
+ Index diagSize = (std::min)(lhs.rows(),lhs.cols());
+ dest.head(diagSize) -= (lhs_alpha-LhsScalar(1))*rhs.head(diagSize);
+ }
+ }
+};
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_TRIANGULARMATRIXVECTOR_H
diff --git a/Eigen/src/Core/products/TriangularMatrixVector_BLAS.h b/Eigen/src/Core/products/TriangularMatrixVector_BLAS.h
new file mode 100644
index 0000000..7a4d59e
--- /dev/null
+++ b/Eigen/src/Core/products/TriangularMatrixVector_BLAS.h
@@ -0,0 +1,257 @@
+/*
+ Copyright (c) 2011, Intel Corporation. All rights reserved.
+
+ Redistribution and use in source and binary forms, with or without modification,
+ are permitted provided that the following conditions are met:
+
+ * Redistributions of source code must retain the above copyright notice, this
+ list of conditions and the following disclaimer.
+ * Redistributions in binary form must reproduce the above copyright notice,
+ this list of conditions and the following disclaimer in the documentation
+ and/or other materials provided with the distribution.
+ * Neither the name of Intel Corporation nor the names of its contributors may
+ be used to endorse or promote products derived from this software without
+ specific prior written permission.
+
+ THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
+ ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
+ WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
+ DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR
+ ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
+ (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
+ LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON
+ ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
+ (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
+ SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+
+ ********************************************************************************
+ * Content : Eigen bindings to BLAS F77
+ * Triangular matrix-vector product functionality based on ?TRMV.
+ ********************************************************************************
+*/
+
+#ifndef EIGEN_TRIANGULAR_MATRIX_VECTOR_BLAS_H
+#define EIGEN_TRIANGULAR_MATRIX_VECTOR_BLAS_H
+
+#include "../InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+
+/**********************************************************************
+* This file implements triangular matrix-vector multiplication using BLAS
+**********************************************************************/
+
+// trmv/hemv specialization
+
+template<typename Index, int Mode, typename LhsScalar, bool ConjLhs, typename RhsScalar, bool ConjRhs, int StorageOrder>
+struct triangular_matrix_vector_product_trmv :
+ triangular_matrix_vector_product<Index,Mode,LhsScalar,ConjLhs,RhsScalar,ConjRhs,StorageOrder,BuiltIn> {};
+
+#define EIGEN_BLAS_TRMV_SPECIALIZE(Scalar) \
+template<typename Index, int Mode, bool ConjLhs, bool ConjRhs> \
+struct triangular_matrix_vector_product<Index,Mode,Scalar,ConjLhs,Scalar,ConjRhs,ColMajor,Specialized> { \
+ static void run(Index _rows, Index _cols, const Scalar* _lhs, Index lhsStride, \
+ const Scalar* _rhs, Index rhsIncr, Scalar* _res, Index resIncr, Scalar alpha) { \
+ triangular_matrix_vector_product_trmv<Index,Mode,Scalar,ConjLhs,Scalar,ConjRhs,ColMajor>::run( \
+ _rows, _cols, _lhs, lhsStride, _rhs, rhsIncr, _res, resIncr, alpha); \
+ } \
+}; \
+template<typename Index, int Mode, bool ConjLhs, bool ConjRhs> \
+struct triangular_matrix_vector_product<Index,Mode,Scalar,ConjLhs,Scalar,ConjRhs,RowMajor,Specialized> { \
+ static void run(Index _rows, Index _cols, const Scalar* _lhs, Index lhsStride, \
+ const Scalar* _rhs, Index rhsIncr, Scalar* _res, Index resIncr, Scalar alpha) { \
+ triangular_matrix_vector_product_trmv<Index,Mode,Scalar,ConjLhs,Scalar,ConjRhs,RowMajor>::run( \
+ _rows, _cols, _lhs, lhsStride, _rhs, rhsIncr, _res, resIncr, alpha); \
+ } \
+};
+
+EIGEN_BLAS_TRMV_SPECIALIZE(double)
+EIGEN_BLAS_TRMV_SPECIALIZE(float)
+EIGEN_BLAS_TRMV_SPECIALIZE(dcomplex)
+EIGEN_BLAS_TRMV_SPECIALIZE(scomplex)
+
+// implements col-major: res += alpha * op(triangular) * vector
+#define EIGEN_BLAS_TRMV_CM(EIGTYPE, BLASTYPE, EIGPREFIX, BLASPREFIX, BLASPOSTFIX) \
+template<typename Index, int Mode, bool ConjLhs, bool ConjRhs> \
+struct triangular_matrix_vector_product_trmv<Index,Mode,EIGTYPE,ConjLhs,EIGTYPE,ConjRhs,ColMajor> { \
+ enum { \
+ IsLower = (Mode&Lower) == Lower, \
+ SetDiag = (Mode&(ZeroDiag|UnitDiag)) ? 0 : 1, \
+ IsUnitDiag = (Mode&UnitDiag) ? 1 : 0, \
+ IsZeroDiag = (Mode&ZeroDiag) ? 1 : 0, \
+ LowUp = IsLower ? Lower : Upper \
+ }; \
+ static void run(Index _rows, Index _cols, const EIGTYPE* _lhs, Index lhsStride, \
+ const EIGTYPE* _rhs, Index rhsIncr, EIGTYPE* _res, Index resIncr, EIGTYPE alpha) \
+ { \
+ if (ConjLhs || IsZeroDiag) { \
+ triangular_matrix_vector_product<Index,Mode,EIGTYPE,ConjLhs,EIGTYPE,ConjRhs,ColMajor,BuiltIn>::run( \
+ _rows, _cols, _lhs, lhsStride, _rhs, rhsIncr, _res, resIncr, alpha); \
+ return; \
+ }\
+ Index size = (std::min)(_rows,_cols); \
+ Index rows = IsLower ? _rows : size; \
+ Index cols = IsLower ? size : _cols; \
+\
+ typedef VectorX##EIGPREFIX VectorRhs; \
+ EIGTYPE *x, *y;\
+\
+/* Set x*/ \
+ Map<const VectorRhs, 0, InnerStride<> > rhs(_rhs,cols,InnerStride<>(rhsIncr)); \
+ VectorRhs x_tmp; \
+ if (ConjRhs) x_tmp = rhs.conjugate(); else x_tmp = rhs; \
+ x = x_tmp.data(); \
+\
+/* Square part handling */\
+\
+ char trans, uplo, diag; \
+ BlasIndex m, n, lda, incx, incy; \
+ EIGTYPE const *a; \
+ EIGTYPE beta(1); \
+\
+/* Set m, n */ \
+ n = convert_index<BlasIndex>(size); \
+ lda = convert_index<BlasIndex>(lhsStride); \
+ incx = 1; \
+ incy = convert_index<BlasIndex>(resIncr); \
+\
+/* Set uplo, trans and diag*/ \
+ trans = 'N'; \
+ uplo = IsLower ? 'L' : 'U'; \
+ diag = IsUnitDiag ? 'U' : 'N'; \
+\
+/* call ?TRMV*/ \
+ BLASPREFIX##trmv##BLASPOSTFIX(&uplo, &trans, &diag, &n, (const BLASTYPE*)_lhs, &lda, (BLASTYPE*)x, &incx); \
+\
+/* Add op(a_tr)rhs into res*/ \
+ BLASPREFIX##axpy##BLASPOSTFIX(&n, (const BLASTYPE*)&numext::real_ref(alpha),(const BLASTYPE*)x, &incx, (BLASTYPE*)_res, &incy); \
+/* Non-square case - doesn't fit to BLAS ?TRMV. Fall to default triangular product*/ \
+ if (size<(std::max)(rows,cols)) { \
+ if (ConjRhs) x_tmp = rhs.conjugate(); else x_tmp = rhs; \
+ x = x_tmp.data(); \
+ if (size<rows) { \
+ y = _res + size*resIncr; \
+ a = _lhs + size; \
+ m = convert_index<BlasIndex>(rows-size); \
+ n = convert_index<BlasIndex>(size); \
+ } \
+ else { \
+ x += size; \
+ y = _res; \
+ a = _lhs + size*lda; \
+ m = convert_index<BlasIndex>(size); \
+ n = convert_index<BlasIndex>(cols-size); \
+ } \
+ BLASPREFIX##gemv##BLASPOSTFIX(&trans, &m, &n, (const BLASTYPE*)&numext::real_ref(alpha), (const BLASTYPE*)a, &lda, (const BLASTYPE*)x, &incx, (const BLASTYPE*)&numext::real_ref(beta), (BLASTYPE*)y, &incy); \
+ } \
+ } \
+};
+
+#ifdef EIGEN_USE_MKL
+EIGEN_BLAS_TRMV_CM(double, double, d, d,)
+EIGEN_BLAS_TRMV_CM(dcomplex, MKL_Complex16, cd, z,)
+EIGEN_BLAS_TRMV_CM(float, float, f, s,)
+EIGEN_BLAS_TRMV_CM(scomplex, MKL_Complex8, cf, c,)
+#else
+EIGEN_BLAS_TRMV_CM(double, double, d, d, _)
+EIGEN_BLAS_TRMV_CM(dcomplex, double, cd, z, _)
+EIGEN_BLAS_TRMV_CM(float, float, f, s, _)
+EIGEN_BLAS_TRMV_CM(scomplex, float, cf, c, _)
+#endif
+
+// implements row-major: res += alpha * op(triangular) * vector
+#define EIGEN_BLAS_TRMV_RM(EIGTYPE, BLASTYPE, EIGPREFIX, BLASPREFIX, BLASPOSTFIX) \
+template<typename Index, int Mode, bool ConjLhs, bool ConjRhs> \
+struct triangular_matrix_vector_product_trmv<Index,Mode,EIGTYPE,ConjLhs,EIGTYPE,ConjRhs,RowMajor> { \
+ enum { \
+ IsLower = (Mode&Lower) == Lower, \
+ SetDiag = (Mode&(ZeroDiag|UnitDiag)) ? 0 : 1, \
+ IsUnitDiag = (Mode&UnitDiag) ? 1 : 0, \
+ IsZeroDiag = (Mode&ZeroDiag) ? 1 : 0, \
+ LowUp = IsLower ? Lower : Upper \
+ }; \
+ static void run(Index _rows, Index _cols, const EIGTYPE* _lhs, Index lhsStride, \
+ const EIGTYPE* _rhs, Index rhsIncr, EIGTYPE* _res, Index resIncr, EIGTYPE alpha) \
+ { \
+ if (IsZeroDiag) { \
+ triangular_matrix_vector_product<Index,Mode,EIGTYPE,ConjLhs,EIGTYPE,ConjRhs,RowMajor,BuiltIn>::run( \
+ _rows, _cols, _lhs, lhsStride, _rhs, rhsIncr, _res, resIncr, alpha); \
+ return; \
+ }\
+ Index size = (std::min)(_rows,_cols); \
+ Index rows = IsLower ? _rows : size; \
+ Index cols = IsLower ? size : _cols; \
+\
+ typedef VectorX##EIGPREFIX VectorRhs; \
+ EIGTYPE *x, *y;\
+\
+/* Set x*/ \
+ Map<const VectorRhs, 0, InnerStride<> > rhs(_rhs,cols,InnerStride<>(rhsIncr)); \
+ VectorRhs x_tmp; \
+ if (ConjRhs) x_tmp = rhs.conjugate(); else x_tmp = rhs; \
+ x = x_tmp.data(); \
+\
+/* Square part handling */\
+\
+ char trans, uplo, diag; \
+ BlasIndex m, n, lda, incx, incy; \
+ EIGTYPE const *a; \
+ EIGTYPE beta(1); \
+\
+/* Set m, n */ \
+ n = convert_index<BlasIndex>(size); \
+ lda = convert_index<BlasIndex>(lhsStride); \
+ incx = 1; \
+ incy = convert_index<BlasIndex>(resIncr); \
+\
+/* Set uplo, trans and diag*/ \
+ trans = ConjLhs ? 'C' : 'T'; \
+ uplo = IsLower ? 'U' : 'L'; \
+ diag = IsUnitDiag ? 'U' : 'N'; \
+\
+/* call ?TRMV*/ \
+ BLASPREFIX##trmv##BLASPOSTFIX(&uplo, &trans, &diag, &n, (const BLASTYPE*)_lhs, &lda, (BLASTYPE*)x, &incx); \
+\
+/* Add op(a_tr)rhs into res*/ \
+ BLASPREFIX##axpy##BLASPOSTFIX(&n, (const BLASTYPE*)&numext::real_ref(alpha),(const BLASTYPE*)x, &incx, (BLASTYPE*)_res, &incy); \
+/* Non-square case - doesn't fit to BLAS ?TRMV. Fall to default triangular product*/ \
+ if (size<(std::max)(rows,cols)) { \
+ if (ConjRhs) x_tmp = rhs.conjugate(); else x_tmp = rhs; \
+ x = x_tmp.data(); \
+ if (size<rows) { \
+ y = _res + size*resIncr; \
+ a = _lhs + size*lda; \
+ m = convert_index<BlasIndex>(rows-size); \
+ n = convert_index<BlasIndex>(size); \
+ } \
+ else { \
+ x += size; \
+ y = _res; \
+ a = _lhs + size; \
+ m = convert_index<BlasIndex>(size); \
+ n = convert_index<BlasIndex>(cols-size); \
+ } \
+ BLASPREFIX##gemv##BLASPOSTFIX(&trans, &n, &m, (const BLASTYPE*)&numext::real_ref(alpha), (const BLASTYPE*)a, &lda, (const BLASTYPE*)x, &incx, (const BLASTYPE*)&numext::real_ref(beta), (BLASTYPE*)y, &incy); \
+ } \
+ } \
+};
+
+#ifdef EIGEN_USE_MKL
+EIGEN_BLAS_TRMV_RM(double, double, d, d,)
+EIGEN_BLAS_TRMV_RM(dcomplex, MKL_Complex16, cd, z,)
+EIGEN_BLAS_TRMV_RM(float, float, f, s,)
+EIGEN_BLAS_TRMV_RM(scomplex, MKL_Complex8, cf, c,)
+#else
+EIGEN_BLAS_TRMV_RM(double, double, d, d,_)
+EIGEN_BLAS_TRMV_RM(dcomplex, double, cd, z,_)
+EIGEN_BLAS_TRMV_RM(float, float, f, s,_)
+EIGEN_BLAS_TRMV_RM(scomplex, float, cf, c,_)
+#endif
+
+} // end namespase internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_TRIANGULAR_MATRIX_VECTOR_BLAS_H
diff --git a/Eigen/src/Core/products/TriangularSolverMatrix.h b/Eigen/src/Core/products/TriangularSolverMatrix.h
new file mode 100644
index 0000000..b148d9c
--- /dev/null
+++ b/Eigen/src/Core/products/TriangularSolverMatrix.h
@@ -0,0 +1,449 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Modifications Copyright (C) 2022 Intel Corporation
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_TRIANGULAR_SOLVER_MATRIX_H
+#define EIGEN_TRIANGULAR_SOLVER_MATRIX_H
+
+#include "../InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+
+template <typename Scalar, typename Index, int Mode, bool Conjugate, int TriStorageOrder,int OtherInnerStride>
+struct trsmKernelL {
+ // Generic Implementation of triangular solve for triangular matrix on left and multiple rhs.
+ // Handles non-packed matrices.
+ static void kernel(
+ Index size, Index otherSize,
+ const Scalar* _tri, Index triStride,
+ Scalar* _other, Index otherIncr, Index otherStride);
+};
+
+template <typename Scalar, typename Index, int Mode, bool Conjugate, int TriStorageOrder,int OtherInnerStride>
+struct trsmKernelR {
+ // Generic Implementation of triangular solve for triangular matrix on right and multiple lhs.
+ // Handles non-packed matrices.
+ static void kernel(
+ Index size, Index otherSize,
+ const Scalar* _tri, Index triStride,
+ Scalar* _other, Index otherIncr, Index otherStride);
+};
+
+template <typename Scalar, typename Index, int Mode, bool Conjugate, int TriStorageOrder,int OtherInnerStride>
+EIGEN_STRONG_INLINE void trsmKernelL<Scalar, Index, Mode, Conjugate, TriStorageOrder, OtherInnerStride>::kernel(
+ Index size, Index otherSize,
+ const Scalar* _tri, Index triStride,
+ Scalar* _other, Index otherIncr, Index otherStride)
+ {
+ typedef const_blas_data_mapper<Scalar, Index, TriStorageOrder> TriMapper;
+ typedef blas_data_mapper<Scalar, Index, ColMajor, Unaligned, OtherInnerStride> OtherMapper;
+ TriMapper tri(_tri, triStride);
+ OtherMapper other(_other, otherStride, otherIncr);
+
+ enum { IsLower = (Mode&Lower) == Lower };
+ conj_if<Conjugate> conj;
+
+ // tr solve
+ for (Index k=0; k<size; ++k)
+ {
+ // TODO write a small kernel handling this (can be shared with trsv)
+ Index i = IsLower ? k : -k-1;
+ Index rs = size - k - 1; // remaining size
+ Index s = TriStorageOrder==RowMajor ? (IsLower ? 0 : i+1)
+ : IsLower ? i+1 : i-rs;
+
+ Scalar a = (Mode & UnitDiag) ? Scalar(1) : Scalar(1)/conj(tri(i,i));
+ for (Index j=0; j<otherSize; ++j)
+ {
+ if (TriStorageOrder==RowMajor)
+ {
+ Scalar b(0);
+ const Scalar* l = &tri(i,s);
+ typename OtherMapper::LinearMapper r = other.getLinearMapper(s,j);
+ for (Index i3=0; i3<k; ++i3)
+ b += conj(l[i3]) * r(i3);
+
+ other(i,j) = (other(i,j) - b)*a;
+ }
+ else
+ {
+ Scalar& otherij = other(i,j);
+ otherij *= a;
+ Scalar b = otherij;
+ typename OtherMapper::LinearMapper r = other.getLinearMapper(s,j);
+ typename TriMapper::LinearMapper l = tri.getLinearMapper(s,i);
+ for (Index i3=0;i3<rs;++i3)
+ r(i3) -= b * conj(l(i3));
+ }
+ }
+ }
+ }
+
+
+template <typename Scalar, typename Index, int Mode, bool Conjugate, int TriStorageOrder, int OtherInnerStride>
+EIGEN_STRONG_INLINE void trsmKernelR<Scalar, Index, Mode, Conjugate, TriStorageOrder, OtherInnerStride>::kernel(
+ Index size, Index otherSize,
+ const Scalar* _tri, Index triStride,
+ Scalar* _other, Index otherIncr, Index otherStride)
+{
+ typedef typename NumTraits<Scalar>::Real RealScalar;
+ typedef blas_data_mapper<Scalar, Index, ColMajor, Unaligned, OtherInnerStride> LhsMapper;
+ typedef const_blas_data_mapper<Scalar, Index, TriStorageOrder> RhsMapper;
+ LhsMapper lhs(_other, otherStride, otherIncr);
+ RhsMapper rhs(_tri, triStride);
+
+ enum {
+ RhsStorageOrder = TriStorageOrder,
+ IsLower = (Mode&Lower) == Lower
+ };
+ conj_if<Conjugate> conj;
+
+ for (Index k=0; k<size; ++k)
+ {
+ Index j = IsLower ? size-k-1 : k;
+
+ typename LhsMapper::LinearMapper r = lhs.getLinearMapper(0,j);
+ for (Index k3=0; k3<k; ++k3)
+ {
+ Scalar b = conj(rhs(IsLower ? j+1+k3 : k3,j));
+ typename LhsMapper::LinearMapper a = lhs.getLinearMapper(0,IsLower ? j+1+k3 : k3);
+ for (Index i=0; i<otherSize; ++i)
+ r(i) -= a(i) * b;
+ }
+ if((Mode & UnitDiag)==0)
+ {
+ Scalar inv_rjj = RealScalar(1)/conj(rhs(j,j));
+ for (Index i=0; i<otherSize; ++i)
+ r(i) *= inv_rjj;
+ }
+ }
+}
+
+
+// if the rhs is row major, let's transpose the product
+template <typename Scalar, typename Index, int Side, int Mode, bool Conjugate, int TriStorageOrder, int OtherInnerStride>
+struct triangular_solve_matrix<Scalar,Index,Side,Mode,Conjugate,TriStorageOrder,RowMajor,OtherInnerStride>
+{
+ static void run(
+ Index size, Index cols,
+ const Scalar* tri, Index triStride,
+ Scalar* _other, Index otherIncr, Index otherStride,
+ level3_blocking<Scalar,Scalar>& blocking)
+ {
+ triangular_solve_matrix<
+ Scalar, Index, Side==OnTheLeft?OnTheRight:OnTheLeft,
+ (Mode&UnitDiag) | ((Mode&Upper) ? Lower : Upper),
+ NumTraits<Scalar>::IsComplex && Conjugate,
+ TriStorageOrder==RowMajor ? ColMajor : RowMajor, ColMajor, OtherInnerStride>
+ ::run(size, cols, tri, triStride, _other, otherIncr, otherStride, blocking);
+ }
+};
+
+/* Optimized triangular solver with multiple right hand side and the triangular matrix on the left
+ */
+template <typename Scalar, typename Index, int Mode, bool Conjugate, int TriStorageOrder,int OtherInnerStride>
+struct triangular_solve_matrix<Scalar,Index,OnTheLeft,Mode,Conjugate,TriStorageOrder,ColMajor,OtherInnerStride>
+{
+ static EIGEN_DONT_INLINE void run(
+ Index size, Index otherSize,
+ const Scalar* _tri, Index triStride,
+ Scalar* _other, Index otherIncr, Index otherStride,
+ level3_blocking<Scalar,Scalar>& blocking);
+};
+
+template <typename Scalar, typename Index, int Mode, bool Conjugate, int TriStorageOrder, int OtherInnerStride>
+EIGEN_DONT_INLINE void triangular_solve_matrix<Scalar,Index,OnTheLeft,Mode,Conjugate,TriStorageOrder,ColMajor,OtherInnerStride>::run(
+ Index size, Index otherSize,
+ const Scalar* _tri, Index triStride,
+ Scalar* _other, Index otherIncr, Index otherStride,
+ level3_blocking<Scalar,Scalar>& blocking)
+ {
+ Index cols = otherSize;
+
+ std::ptrdiff_t l1, l2, l3;
+ manage_caching_sizes(GetAction, &l1, &l2, &l3);
+
+#if defined(EIGEN_VECTORIZE_AVX512) && EIGEN_USE_AVX512_TRSM_L_KERNELS && EIGEN_ENABLE_AVX512_NOCOPY_TRSM_L_CUTOFFS
+ EIGEN_IF_CONSTEXPR( (OtherInnerStride == 1 &&
+ (std::is_same<Scalar,float>::value ||
+ std::is_same<Scalar,double>::value)) ) {
+ // Very rough cutoffs to determine when to call trsm w/o packing
+ // For small problem sizes trsmKernel compiled with clang is generally faster.
+ // TODO: Investigate better heuristics for cutoffs.
+ double L2Cap = 0.5; // 50% of L2 size
+ if (size < avx512_trsm_cutoff<Scalar>(l2, cols, L2Cap)) {
+ trsmKernelL<Scalar, Index, Mode, Conjugate, TriStorageOrder, 1>::kernel(
+ size, cols, _tri, triStride, _other, 1, otherStride);
+ return;
+ }
+ }
+#endif
+
+ typedef const_blas_data_mapper<Scalar, Index, TriStorageOrder> TriMapper;
+ typedef blas_data_mapper<Scalar, Index, ColMajor, Unaligned, OtherInnerStride> OtherMapper;
+ TriMapper tri(_tri, triStride);
+ OtherMapper other(_other, otherStride, otherIncr);
+
+ typedef gebp_traits<Scalar,Scalar> Traits;
+
+ enum {
+ SmallPanelWidth = plain_enum_max(Traits::mr, Traits::nr),
+ IsLower = (Mode&Lower) == Lower
+ };
+
+ Index kc = blocking.kc(); // cache block size along the K direction
+ Index mc = (std::min)(size,blocking.mc()); // cache block size along the M direction
+
+ std::size_t sizeA = kc*mc;
+ std::size_t sizeB = kc*cols;
+
+ ei_declare_aligned_stack_constructed_variable(Scalar, blockA, sizeA, blocking.blockA());
+ ei_declare_aligned_stack_constructed_variable(Scalar, blockB, sizeB, blocking.blockB());
+
+ gebp_kernel<Scalar, Scalar, Index, OtherMapper, Traits::mr, Traits::nr, Conjugate, false> gebp_kernel;
+ gemm_pack_lhs<Scalar, Index, TriMapper, Traits::mr, Traits::LhsProgress, typename Traits::LhsPacket4Packing, TriStorageOrder> pack_lhs;
+ gemm_pack_rhs<Scalar, Index, OtherMapper, Traits::nr, ColMajor, false, true> pack_rhs;
+
+ // the goal here is to subdivise the Rhs panels such that we keep some cache
+ // coherence when accessing the rhs elements
+ Index subcols = cols>0 ? l2/(4 * sizeof(Scalar) * std::max<Index>(otherStride,size)) : 0;
+ subcols = std::max<Index>((subcols/Traits::nr)*Traits::nr, Traits::nr);
+
+ for(Index k2=IsLower ? 0 : size;
+ IsLower ? k2<size : k2>0;
+ IsLower ? k2+=kc : k2-=kc)
+ {
+ const Index actual_kc = (std::min)(IsLower ? size-k2 : k2, kc);
+
+ // We have selected and packed a big horizontal panel R1 of rhs. Let B be the packed copy of this panel,
+ // and R2 the remaining part of rhs. The corresponding vertical panel of lhs is split into
+ // A11 (the triangular part) and A21 the remaining rectangular part.
+ // Then the high level algorithm is:
+ // - B = R1 => general block copy (done during the next step)
+ // - R1 = A11^-1 B => tricky part
+ // - update B from the new R1 => actually this has to be performed continuously during the above step
+ // - R2 -= A21 * B => GEPP
+
+ // The tricky part: compute R1 = A11^-1 B while updating B from R1
+ // The idea is to split A11 into multiple small vertical panels.
+ // Each panel can be split into a small triangular part T1k which is processed without optimization,
+ // and the remaining small part T2k which is processed using gebp with appropriate block strides
+ for(Index j2=0; j2<cols; j2+=subcols)
+ {
+ Index actual_cols = (std::min)(cols-j2,subcols);
+ // for each small vertical panels [T1k^T, T2k^T]^T of lhs
+ for (Index k1=0; k1<actual_kc; k1+=SmallPanelWidth)
+ {
+ Index actualPanelWidth = std::min<Index>(actual_kc-k1, SmallPanelWidth);
+ // tr solve
+ {
+ Index i = IsLower ? k2+k1 : k2-k1;
+#if defined(EIGEN_VECTORIZE_AVX512) && EIGEN_USE_AVX512_TRSM_L_KERNELS
+ EIGEN_IF_CONSTEXPR( (OtherInnerStride == 1 &&
+ (std::is_same<Scalar,float>::value ||
+ std::is_same<Scalar,double>::value)) ) {
+ i = IsLower ? k2 + k1: k2 - k1 - actualPanelWidth;
+ }
+#endif
+ trsmKernelL<Scalar, Index, Mode, Conjugate, TriStorageOrder, OtherInnerStride>::kernel(
+ actualPanelWidth, actual_cols,
+ _tri + i + (i)*triStride, triStride,
+ _other + i*OtherInnerStride + j2*otherStride, otherIncr, otherStride);
+ }
+
+ Index lengthTarget = actual_kc-k1-actualPanelWidth;
+ Index startBlock = IsLower ? k2+k1 : k2-k1-actualPanelWidth;
+ Index blockBOffset = IsLower ? k1 : lengthTarget;
+
+ // update the respective rows of B from other
+ pack_rhs(blockB+actual_kc*j2, other.getSubMapper(startBlock,j2), actualPanelWidth, actual_cols, actual_kc, blockBOffset);
+
+ // GEBP
+ if (lengthTarget>0)
+ {
+ Index startTarget = IsLower ? k2+k1+actualPanelWidth : k2-actual_kc;
+
+ pack_lhs(blockA, tri.getSubMapper(startTarget,startBlock), actualPanelWidth, lengthTarget);
+
+ gebp_kernel(other.getSubMapper(startTarget,j2), blockA, blockB+actual_kc*j2, lengthTarget, actualPanelWidth, actual_cols, Scalar(-1),
+ actualPanelWidth, actual_kc, 0, blockBOffset);
+ }
+ }
+ }
+
+ // R2 -= A21 * B => GEPP
+ {
+ Index start = IsLower ? k2+kc : 0;
+ Index end = IsLower ? size : k2-kc;
+ for(Index i2=start; i2<end; i2+=mc)
+ {
+ const Index actual_mc = (std::min)(mc,end-i2);
+ if (actual_mc>0)
+ {
+ pack_lhs(blockA, tri.getSubMapper(i2, IsLower ? k2 : k2-kc), actual_kc, actual_mc);
+
+ gebp_kernel(other.getSubMapper(i2, 0), blockA, blockB, actual_mc, actual_kc, cols, Scalar(-1), -1, -1, 0, 0);
+ }
+ }
+ }
+ }
+ }
+
+/* Optimized triangular solver with multiple left hand sides and the triangular matrix on the right
+ */
+template <typename Scalar, typename Index, int Mode, bool Conjugate, int TriStorageOrder, int OtherInnerStride>
+struct triangular_solve_matrix<Scalar,Index,OnTheRight,Mode,Conjugate,TriStorageOrder,ColMajor,OtherInnerStride>
+{
+ static EIGEN_DONT_INLINE void run(
+ Index size, Index otherSize,
+ const Scalar* _tri, Index triStride,
+ Scalar* _other, Index otherIncr, Index otherStride,
+ level3_blocking<Scalar,Scalar>& blocking);
+};
+
+template <typename Scalar, typename Index, int Mode, bool Conjugate, int TriStorageOrder, int OtherInnerStride>
+EIGEN_DONT_INLINE void triangular_solve_matrix<Scalar,Index,OnTheRight,Mode,Conjugate,TriStorageOrder,ColMajor,OtherInnerStride>::run(
+ Index size, Index otherSize,
+ const Scalar* _tri, Index triStride,
+ Scalar* _other, Index otherIncr, Index otherStride,
+ level3_blocking<Scalar,Scalar>& blocking)
+ {
+ Index rows = otherSize;
+
+#if defined(EIGEN_VECTORIZE_AVX512) && EIGEN_USE_AVX512_TRSM_R_KERNELS && EIGEN_ENABLE_AVX512_NOCOPY_TRSM_R_CUTOFFS
+ EIGEN_IF_CONSTEXPR( (OtherInnerStride == 1 &&
+ (std::is_same<Scalar,float>::value ||
+ std::is_same<Scalar,double>::value)) ) {
+ // TODO: Investigate better heuristics for cutoffs.
+ std::ptrdiff_t l1, l2, l3;
+ manage_caching_sizes(GetAction, &l1, &l2, &l3);
+ double L2Cap = 0.5; // 50% of L2 size
+ if (size < avx512_trsm_cutoff<Scalar>(l2, rows, L2Cap)) {
+ trsmKernelR<Scalar, Index, Mode, Conjugate, TriStorageOrder, OtherInnerStride>::
+ kernel(size, rows, _tri, triStride, _other, 1, otherStride);
+ return;
+ }
+ }
+#endif
+
+ typedef blas_data_mapper<Scalar, Index, ColMajor, Unaligned, OtherInnerStride> LhsMapper;
+ typedef const_blas_data_mapper<Scalar, Index, TriStorageOrder> RhsMapper;
+ LhsMapper lhs(_other, otherStride, otherIncr);
+ RhsMapper rhs(_tri, triStride);
+
+ typedef gebp_traits<Scalar,Scalar> Traits;
+ enum {
+ RhsStorageOrder = TriStorageOrder,
+ SmallPanelWidth = plain_enum_max(Traits::mr, Traits::nr),
+ IsLower = (Mode&Lower) == Lower
+ };
+
+ Index kc = blocking.kc(); // cache block size along the K direction
+ Index mc = (std::min)(rows,blocking.mc()); // cache block size along the M direction
+
+ std::size_t sizeA = kc*mc;
+ std::size_t sizeB = kc*size;
+
+ ei_declare_aligned_stack_constructed_variable(Scalar, blockA, sizeA, blocking.blockA());
+ ei_declare_aligned_stack_constructed_variable(Scalar, blockB, sizeB, blocking.blockB());
+
+ gebp_kernel<Scalar, Scalar, Index, LhsMapper, Traits::mr, Traits::nr, false, Conjugate> gebp_kernel;
+ gemm_pack_rhs<Scalar, Index, RhsMapper, Traits::nr, RhsStorageOrder> pack_rhs;
+ gemm_pack_rhs<Scalar, Index, RhsMapper, Traits::nr, RhsStorageOrder,false,true> pack_rhs_panel;
+ gemm_pack_lhs<Scalar, Index, LhsMapper, Traits::mr, Traits::LhsProgress, typename Traits::LhsPacket4Packing, ColMajor, false, true> pack_lhs_panel;
+
+ for(Index k2=IsLower ? size : 0;
+ IsLower ? k2>0 : k2<size;
+ IsLower ? k2-=kc : k2+=kc)
+ {
+ const Index actual_kc = (std::min)(IsLower ? k2 : size-k2, kc);
+ Index actual_k2 = IsLower ? k2-actual_kc : k2 ;
+
+ Index startPanel = IsLower ? 0 : k2+actual_kc;
+ Index rs = IsLower ? actual_k2 : size - actual_k2 - actual_kc;
+ Scalar* geb = blockB+actual_kc*actual_kc;
+
+ if (rs>0) pack_rhs(geb, rhs.getSubMapper(actual_k2,startPanel), actual_kc, rs);
+
+ // triangular packing (we only pack the panels off the diagonal,
+ // neglecting the blocks overlapping the diagonal
+ {
+ for (Index j2=0; j2<actual_kc; j2+=SmallPanelWidth)
+ {
+ Index actualPanelWidth = std::min<Index>(actual_kc-j2, SmallPanelWidth);
+ Index actual_j2 = actual_k2 + j2;
+ Index panelOffset = IsLower ? j2+actualPanelWidth : 0;
+ Index panelLength = IsLower ? actual_kc-j2-actualPanelWidth : j2;
+
+ if (panelLength>0)
+ pack_rhs_panel(blockB+j2*actual_kc,
+ rhs.getSubMapper(actual_k2+panelOffset, actual_j2),
+ panelLength, actualPanelWidth,
+ actual_kc, panelOffset);
+ }
+ }
+
+ for(Index i2=0; i2<rows; i2+=mc)
+ {
+ const Index actual_mc = (std::min)(mc,rows-i2);
+
+ // triangular solver kernel
+ {
+ // for each small block of the diagonal (=> vertical panels of rhs)
+ for (Index j2 = IsLower
+ ? (actual_kc - ((actual_kc%SmallPanelWidth) ? Index(actual_kc%SmallPanelWidth)
+ : Index(SmallPanelWidth)))
+ : 0;
+ IsLower ? j2>=0 : j2<actual_kc;
+ IsLower ? j2-=SmallPanelWidth : j2+=SmallPanelWidth)
+ {
+ Index actualPanelWidth = std::min<Index>(actual_kc-j2, SmallPanelWidth);
+ Index absolute_j2 = actual_k2 + j2;
+ Index panelOffset = IsLower ? j2+actualPanelWidth : 0;
+ Index panelLength = IsLower ? actual_kc - j2 - actualPanelWidth : j2;
+
+ // GEBP
+ if(panelLength>0)
+ {
+ gebp_kernel(lhs.getSubMapper(i2,absolute_j2),
+ blockA, blockB+j2*actual_kc,
+ actual_mc, panelLength, actualPanelWidth,
+ Scalar(-1),
+ actual_kc, actual_kc, // strides
+ panelOffset, panelOffset); // offsets
+ }
+
+ {
+ // unblocked triangular solve
+ trsmKernelR<Scalar, Index, Mode, Conjugate, TriStorageOrder, OtherInnerStride>::
+ kernel(actualPanelWidth, actual_mc,
+ _tri + absolute_j2 + absolute_j2*triStride, triStride,
+ _other + i2*OtherInnerStride + absolute_j2*otherStride, otherIncr, otherStride);
+ }
+ // pack the just computed part of lhs to A
+ pack_lhs_panel(blockA, lhs.getSubMapper(i2,absolute_j2),
+ actualPanelWidth, actual_mc,
+ actual_kc, j2);
+ }
+ }
+
+ if (rs>0)
+ gebp_kernel(lhs.getSubMapper(i2, startPanel), blockA, geb,
+ actual_mc, actual_kc, rs, Scalar(-1),
+ -1, -1, 0, 0);
+ }
+ }
+ }
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_TRIANGULAR_SOLVER_MATRIX_H
diff --git a/Eigen/src/Core/products/TriangularSolverMatrix_BLAS.h b/Eigen/src/Core/products/TriangularSolverMatrix_BLAS.h
new file mode 100644
index 0000000..2b63388
--- /dev/null
+++ b/Eigen/src/Core/products/TriangularSolverMatrix_BLAS.h
@@ -0,0 +1,169 @@
+/*
+ Copyright (c) 2011, Intel Corporation. All rights reserved.
+
+ Redistribution and use in source and binary forms, with or without modification,
+ are permitted provided that the following conditions are met:
+
+ * Redistributions of source code must retain the above copyright notice, this
+ list of conditions and the following disclaimer.
+ * Redistributions in binary form must reproduce the above copyright notice,
+ this list of conditions and the following disclaimer in the documentation
+ and/or other materials provided with the distribution.
+ * Neither the name of Intel Corporation nor the names of its contributors may
+ be used to endorse or promote products derived from this software without
+ specific prior written permission.
+
+ THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
+ ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
+ WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
+ DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR
+ ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
+ (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
+ LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON
+ ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
+ (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
+ SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+
+ ********************************************************************************
+ * Content : Eigen bindings to BLAS F77
+ * Triangular matrix * matrix product functionality based on ?TRMM.
+ ********************************************************************************
+*/
+
+#ifndef EIGEN_TRIANGULAR_SOLVER_MATRIX_BLAS_H
+#define EIGEN_TRIANGULAR_SOLVER_MATRIX_BLAS_H
+
+#include "../InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+
+// implements LeftSide op(triangular)^-1 * general
+#define EIGEN_BLAS_TRSM_L(EIGTYPE, BLASTYPE, BLASFUNC) \
+template <typename Index, int Mode, bool Conjugate, int TriStorageOrder> \
+struct triangular_solve_matrix<EIGTYPE,Index,OnTheLeft,Mode,Conjugate,TriStorageOrder,ColMajor,1> \
+{ \
+ enum { \
+ IsLower = (Mode&Lower) == Lower, \
+ IsUnitDiag = (Mode&UnitDiag) ? 1 : 0, \
+ IsZeroDiag = (Mode&ZeroDiag) ? 1 : 0, \
+ conjA = ((TriStorageOrder==ColMajor) && Conjugate) ? 1 : 0 \
+ }; \
+ static void run( \
+ Index size, Index otherSize, \
+ const EIGTYPE* _tri, Index triStride, \
+ EIGTYPE* _other, Index otherIncr, Index otherStride, level3_blocking<EIGTYPE,EIGTYPE>& /*blocking*/) \
+ { \
+ EIGEN_ONLY_USED_FOR_DEBUG(otherIncr); \
+ eigen_assert(otherIncr == 1); \
+ BlasIndex m = convert_index<BlasIndex>(size), n = convert_index<BlasIndex>(otherSize), lda, ldb; \
+ char side = 'L', uplo, diag='N', transa; \
+ /* Set alpha_ */ \
+ EIGTYPE alpha(1); \
+ ldb = convert_index<BlasIndex>(otherStride);\
+\
+ const EIGTYPE *a; \
+/* Set trans */ \
+ transa = (TriStorageOrder==RowMajor) ? ((Conjugate) ? 'C' : 'T') : 'N'; \
+/* Set uplo */ \
+ uplo = IsLower ? 'L' : 'U'; \
+ if (TriStorageOrder==RowMajor) uplo = (uplo == 'L') ? 'U' : 'L'; \
+/* Set a, lda */ \
+ typedef Matrix<EIGTYPE, Dynamic, Dynamic, TriStorageOrder> MatrixTri; \
+ Map<const MatrixTri, 0, OuterStride<> > tri(_tri,size,size,OuterStride<>(triStride)); \
+ MatrixTri a_tmp; \
+\
+ if (conjA) { \
+ a_tmp = tri.conjugate(); \
+ a = a_tmp.data(); \
+ lda = convert_index<BlasIndex>(a_tmp.outerStride()); \
+ } else { \
+ a = _tri; \
+ lda = convert_index<BlasIndex>(triStride); \
+ } \
+ if (IsUnitDiag) diag='U'; \
+/* call ?trsm*/ \
+ BLASFUNC(&side, &uplo, &transa, &diag, &m, &n, (const BLASTYPE*)&numext::real_ref(alpha), (const BLASTYPE*)a, &lda, (BLASTYPE*)_other, &ldb); \
+ } \
+};
+
+#ifdef EIGEN_USE_MKL
+EIGEN_BLAS_TRSM_L(double, double, dtrsm)
+EIGEN_BLAS_TRSM_L(dcomplex, MKL_Complex16, ztrsm)
+EIGEN_BLAS_TRSM_L(float, float, strsm)
+EIGEN_BLAS_TRSM_L(scomplex, MKL_Complex8, ctrsm)
+#else
+EIGEN_BLAS_TRSM_L(double, double, dtrsm_)
+EIGEN_BLAS_TRSM_L(dcomplex, double, ztrsm_)
+EIGEN_BLAS_TRSM_L(float, float, strsm_)
+EIGEN_BLAS_TRSM_L(scomplex, float, ctrsm_)
+#endif
+
+// implements RightSide general * op(triangular)^-1
+#define EIGEN_BLAS_TRSM_R(EIGTYPE, BLASTYPE, BLASFUNC) \
+template <typename Index, int Mode, bool Conjugate, int TriStorageOrder> \
+struct triangular_solve_matrix<EIGTYPE,Index,OnTheRight,Mode,Conjugate,TriStorageOrder,ColMajor,1> \
+{ \
+ enum { \
+ IsLower = (Mode&Lower) == Lower, \
+ IsUnitDiag = (Mode&UnitDiag) ? 1 : 0, \
+ IsZeroDiag = (Mode&ZeroDiag) ? 1 : 0, \
+ conjA = ((TriStorageOrder==ColMajor) && Conjugate) ? 1 : 0 \
+ }; \
+ static void run( \
+ Index size, Index otherSize, \
+ const EIGTYPE* _tri, Index triStride, \
+ EIGTYPE* _other, Index otherIncr, Index otherStride, level3_blocking<EIGTYPE,EIGTYPE>& /*blocking*/) \
+ { \
+ EIGEN_ONLY_USED_FOR_DEBUG(otherIncr); \
+ eigen_assert(otherIncr == 1); \
+ BlasIndex m = convert_index<BlasIndex>(otherSize), n = convert_index<BlasIndex>(size), lda, ldb; \
+ char side = 'R', uplo, diag='N', transa; \
+ /* Set alpha_ */ \
+ EIGTYPE alpha(1); \
+ ldb = convert_index<BlasIndex>(otherStride);\
+\
+ const EIGTYPE *a; \
+/* Set trans */ \
+ transa = (TriStorageOrder==RowMajor) ? ((Conjugate) ? 'C' : 'T') : 'N'; \
+/* Set uplo */ \
+ uplo = IsLower ? 'L' : 'U'; \
+ if (TriStorageOrder==RowMajor) uplo = (uplo == 'L') ? 'U' : 'L'; \
+/* Set a, lda */ \
+ typedef Matrix<EIGTYPE, Dynamic, Dynamic, TriStorageOrder> MatrixTri; \
+ Map<const MatrixTri, 0, OuterStride<> > tri(_tri,size,size,OuterStride<>(triStride)); \
+ MatrixTri a_tmp; \
+\
+ if (conjA) { \
+ a_tmp = tri.conjugate(); \
+ a = a_tmp.data(); \
+ lda = convert_index<BlasIndex>(a_tmp.outerStride()); \
+ } else { \
+ a = _tri; \
+ lda = convert_index<BlasIndex>(triStride); \
+ } \
+ if (IsUnitDiag) diag='U'; \
+/* call ?trsm*/ \
+ BLASFUNC(&side, &uplo, &transa, &diag, &m, &n, (const BLASTYPE*)&numext::real_ref(alpha), (const BLASTYPE*)a, &lda, (BLASTYPE*)_other, &ldb); \
+ /*std::cout << "TRMS_L specialization!\n";*/ \
+ } \
+};
+
+#ifdef EIGEN_USE_MKL
+EIGEN_BLAS_TRSM_R(double, double, dtrsm)
+EIGEN_BLAS_TRSM_R(dcomplex, MKL_Complex16, ztrsm)
+EIGEN_BLAS_TRSM_R(float, float, strsm)
+EIGEN_BLAS_TRSM_R(scomplex, MKL_Complex8, ctrsm)
+#else
+EIGEN_BLAS_TRSM_R(double, double, dtrsm_)
+EIGEN_BLAS_TRSM_R(dcomplex, double, ztrsm_)
+EIGEN_BLAS_TRSM_R(float, float, strsm_)
+EIGEN_BLAS_TRSM_R(scomplex, float, ctrsm_)
+#endif
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_TRIANGULAR_SOLVER_MATRIX_BLAS_H
diff --git a/Eigen/src/Core/products/TriangularSolverVector.h b/Eigen/src/Core/products/TriangularSolverVector.h
new file mode 100644
index 0000000..b8fbb5b
--- /dev/null
+++ b/Eigen/src/Core/products/TriangularSolverVector.h
@@ -0,0 +1,149 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2010 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_TRIANGULAR_SOLVER_VECTOR_H
+#define EIGEN_TRIANGULAR_SOLVER_VECTOR_H
+
+#include "../InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+
+template<typename LhsScalar, typename RhsScalar, typename Index, int Mode, bool Conjugate, int StorageOrder>
+struct triangular_solve_vector<LhsScalar, RhsScalar, Index, OnTheRight, Mode, Conjugate, StorageOrder>
+{
+ static void run(Index size, const LhsScalar* _lhs, Index lhsStride, RhsScalar* rhs)
+ {
+ triangular_solve_vector<LhsScalar,RhsScalar,Index,OnTheLeft,
+ ((Mode&Upper)==Upper ? Lower : Upper) | (Mode&UnitDiag),
+ Conjugate,StorageOrder==RowMajor?ColMajor:RowMajor
+ >::run(size, _lhs, lhsStride, rhs);
+ }
+};
+
+// forward and backward substitution, row-major, rhs is a vector
+template<typename LhsScalar, typename RhsScalar, typename Index, int Mode, bool Conjugate>
+struct triangular_solve_vector<LhsScalar, RhsScalar, Index, OnTheLeft, Mode, Conjugate, RowMajor>
+{
+ enum {
+ IsLower = ((Mode&Lower)==Lower)
+ };
+ static void run(Index size, const LhsScalar* _lhs, Index lhsStride, RhsScalar* rhs)
+ {
+ typedef Map<const Matrix<LhsScalar,Dynamic,Dynamic,RowMajor>, 0, OuterStride<> > LhsMap;
+ const LhsMap lhs(_lhs,size,size,OuterStride<>(lhsStride));
+
+ typedef const_blas_data_mapper<LhsScalar,Index,RowMajor> LhsMapper;
+ typedef const_blas_data_mapper<RhsScalar,Index,ColMajor> RhsMapper;
+
+ std::conditional_t<
+ Conjugate,
+ const CwiseUnaryOp<typename internal::scalar_conjugate_op<LhsScalar>,LhsMap>,
+ const LhsMap&> cjLhs(lhs);
+ static const Index PanelWidth = EIGEN_TUNE_TRIANGULAR_PANEL_WIDTH;
+ for(Index pi=IsLower ? 0 : size;
+ IsLower ? pi<size : pi>0;
+ IsLower ? pi+=PanelWidth : pi-=PanelWidth)
+ {
+ Index actualPanelWidth = (std::min)(IsLower ? size - pi : pi, PanelWidth);
+
+ Index r = IsLower ? pi : size - pi; // remaining size
+ if (r > 0)
+ {
+ // let's directly call the low level product function because:
+ // 1 - it is faster to compile
+ // 2 - it is slightly faster at runtime
+ Index startRow = IsLower ? pi : pi-actualPanelWidth;
+ Index startCol = IsLower ? 0 : pi;
+
+ general_matrix_vector_product<Index,LhsScalar,LhsMapper,RowMajor,Conjugate,RhsScalar,RhsMapper,false>::run(
+ actualPanelWidth, r,
+ LhsMapper(&lhs.coeffRef(startRow,startCol), lhsStride),
+ RhsMapper(rhs + startCol, 1),
+ rhs + startRow, 1,
+ RhsScalar(-1));
+ }
+
+ for(Index k=0; k<actualPanelWidth; ++k)
+ {
+ Index i = IsLower ? pi+k : pi-k-1;
+ Index s = IsLower ? pi : i+1;
+ if (k>0)
+ rhs[i] -= (cjLhs.row(i).segment(s,k).transpose().cwiseProduct(Map<const Matrix<RhsScalar,Dynamic,1> >(rhs+s,k))).sum();
+
+ if((!(Mode & UnitDiag)) && !is_identically_zero(rhs[i]))
+ rhs[i] /= cjLhs(i,i);
+ }
+ }
+ }
+};
+
+// forward and backward substitution, column-major, rhs is a vector
+template<typename LhsScalar, typename RhsScalar, typename Index, int Mode, bool Conjugate>
+struct triangular_solve_vector<LhsScalar, RhsScalar, Index, OnTheLeft, Mode, Conjugate, ColMajor>
+{
+ enum {
+ IsLower = ((Mode&Lower)==Lower)
+ };
+ static void run(Index size, const LhsScalar* _lhs, Index lhsStride, RhsScalar* rhs)
+ {
+ typedef Map<const Matrix<LhsScalar,Dynamic,Dynamic,ColMajor>, 0, OuterStride<> > LhsMap;
+ const LhsMap lhs(_lhs,size,size,OuterStride<>(lhsStride));
+ typedef const_blas_data_mapper<LhsScalar,Index,ColMajor> LhsMapper;
+ typedef const_blas_data_mapper<RhsScalar,Index,ColMajor> RhsMapper;
+ std::conditional_t<Conjugate,
+ const CwiseUnaryOp<typename internal::scalar_conjugate_op<LhsScalar>,LhsMap>,
+ const LhsMap&
+ > cjLhs(lhs);
+ static const Index PanelWidth = EIGEN_TUNE_TRIANGULAR_PANEL_WIDTH;
+
+ for(Index pi=IsLower ? 0 : size;
+ IsLower ? pi<size : pi>0;
+ IsLower ? pi+=PanelWidth : pi-=PanelWidth)
+ {
+ Index actualPanelWidth = (std::min)(IsLower ? size - pi : pi, PanelWidth);
+ Index startBlock = IsLower ? pi : pi-actualPanelWidth;
+ Index endBlock = IsLower ? pi + actualPanelWidth : 0;
+
+ for(Index k=0; k<actualPanelWidth; ++k)
+ {
+ Index i = IsLower ? pi+k : pi-k-1;
+ if(!is_identically_zero(rhs[i]))
+ {
+ if(!(Mode & UnitDiag))
+ rhs[i] /= cjLhs.coeff(i,i);
+
+ Index r = actualPanelWidth - k - 1; // remaining size
+ Index s = IsLower ? i+1 : i-r;
+ if (r>0)
+ Map<Matrix<RhsScalar,Dynamic,1> >(rhs+s,r) -= rhs[i] * cjLhs.col(i).segment(s,r);
+ }
+ }
+ Index r = IsLower ? size - endBlock : startBlock; // remaining size
+ if (r > 0)
+ {
+ // let's directly call the low level product function because:
+ // 1 - it is faster to compile
+ // 2 - it is slightly faster at runtime
+ general_matrix_vector_product<Index,LhsScalar,LhsMapper,ColMajor,Conjugate,RhsScalar,RhsMapper,false>::run(
+ r, actualPanelWidth,
+ LhsMapper(&lhs.coeffRef(endBlock,startBlock), lhsStride),
+ RhsMapper(rhs+startBlock, 1),
+ rhs+endBlock, 1, RhsScalar(-1));
+ }
+ }
+ }
+};
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_TRIANGULAR_SOLVER_VECTOR_H
diff --git a/Eigen/src/Core/util/BlasUtil.h b/Eigen/src/Core/util/BlasUtil.h
new file mode 100644
index 0000000..3f00077
--- /dev/null
+++ b/Eigen/src/Core/util/BlasUtil.h
@@ -0,0 +1,652 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009-2010 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_BLASUTIL_H
+#define EIGEN_BLASUTIL_H
+
+// This file contains many lightweight helper classes used to
+// implement and control fast level 2 and level 3 BLAS-like routines.
+
+#include "../InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+
+// forward declarations
+template<typename LhsScalar, typename RhsScalar, typename Index, typename DataMapper, int mr, int nr, bool ConjugateLhs=false, bool ConjugateRhs=false>
+struct gebp_kernel;
+
+template<typename Scalar, typename Index, typename DataMapper, int nr, int StorageOrder, bool Conjugate = false, bool PanelMode=false>
+struct gemm_pack_rhs;
+
+template<typename Scalar, typename Index, typename DataMapper, int Pack1, int Pack2, typename Packet, int StorageOrder, bool Conjugate = false, bool PanelMode = false>
+struct gemm_pack_lhs;
+
+template<
+ typename Index,
+ typename LhsScalar, int LhsStorageOrder, bool ConjugateLhs,
+ typename RhsScalar, int RhsStorageOrder, bool ConjugateRhs,
+ int ResStorageOrder, int ResInnerStride>
+struct general_matrix_matrix_product;
+
+template<typename Index,
+ typename LhsScalar, typename LhsMapper, int LhsStorageOrder, bool ConjugateLhs,
+ typename RhsScalar, typename RhsMapper, bool ConjugateRhs, int Version=Specialized>
+struct general_matrix_vector_product;
+
+template<typename From,typename To> struct get_factor {
+ EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE To run(const From& x) { return To(x); }
+};
+
+template<typename Scalar> struct get_factor<Scalar,typename NumTraits<Scalar>::Real> {
+ EIGEN_DEVICE_FUNC
+ static EIGEN_STRONG_INLINE typename NumTraits<Scalar>::Real run(const Scalar& x) { return numext::real(x); }
+};
+
+
+template<typename Scalar, typename Index>
+class BlasVectorMapper {
+ public:
+ EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE BlasVectorMapper(Scalar *data) : m_data(data) {}
+
+ EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE Scalar operator()(Index i) const {
+ return m_data[i];
+ }
+ template <typename Packet, int AlignmentType>
+ EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE Packet load(Index i) const {
+ return ploadt<Packet, AlignmentType>(m_data + i);
+ }
+
+ template <typename Packet>
+ EIGEN_DEVICE_FUNC bool aligned(Index i) const {
+ return (UIntPtr(m_data+i)%sizeof(Packet))==0;
+ }
+
+ protected:
+ Scalar* m_data;
+};
+
+template<typename Scalar, typename Index, int AlignmentType, int Incr=1>
+class BlasLinearMapper;
+
+template<typename Scalar, typename Index, int AlignmentType>
+class BlasLinearMapper<Scalar,Index,AlignmentType>
+{
+public:
+ EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE BlasLinearMapper(Scalar *data, Index incr=1)
+ : m_data(data)
+ {
+ EIGEN_ONLY_USED_FOR_DEBUG(incr);
+ eigen_assert(incr==1);
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE void prefetch(Index i) const {
+ internal::prefetch(&operator()(i));
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE Scalar& operator()(Index i) const {
+ return m_data[i];
+ }
+
+ template<typename PacketType>
+ EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE PacketType loadPacket(Index i) const {
+ return ploadt<PacketType, AlignmentType>(m_data + i);
+ }
+
+ template<typename PacketType>
+ EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE PacketType loadPacketPartial(Index i, Index n, Index offset = 0) const {
+ return ploadt_partial<PacketType, AlignmentType>(m_data + i, n, offset);
+ }
+
+ template<typename PacketType, int AlignmentT>
+ EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE PacketType load(Index i) const {
+ return ploadt<PacketType, AlignmentT>(m_data + i);
+ }
+
+ template<typename PacketType>
+ EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE void storePacket(Index i, const PacketType &p) const {
+ pstoret<Scalar, PacketType, AlignmentType>(m_data + i, p);
+ }
+
+ template<typename PacketType>
+ EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE void storePacketPartial(Index i, const PacketType &p, Index n, Index offset = 0) const {
+ pstoret_partial<Scalar, PacketType, AlignmentType>(m_data + i, p, n, offset);
+ }
+
+protected:
+ Scalar *m_data;
+};
+
+// Lightweight helper class to access matrix coefficients.
+template<typename Scalar, typename Index, int StorageOrder, int AlignmentType = Unaligned, int Incr = 1>
+class blas_data_mapper;
+
+// TMP to help PacketBlock store implementation.
+// There's currently no known use case for PacketBlock load.
+// The default implementation assumes ColMajor order.
+// It always store each packet sequentially one `stride` apart.
+template<typename Index, typename Scalar, typename Packet, int n, int idx, int StorageOrder>
+struct PacketBlockManagement
+{
+ PacketBlockManagement<Index, Scalar, Packet, n, idx - 1, StorageOrder> pbm;
+ EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE void store(Scalar *to, const Index stride, Index i, Index j, const PacketBlock<Packet, n> &block) const {
+ pbm.store(to, stride, i, j, block);
+ pstoreu<Scalar>(to + i + (j + idx)*stride, block.packet[idx]);
+ }
+};
+
+// PacketBlockManagement specialization to take care of RowMajor order without ifs.
+template<typename Index, typename Scalar, typename Packet, int n, int idx>
+struct PacketBlockManagement<Index, Scalar, Packet, n, idx, RowMajor>
+{
+ PacketBlockManagement<Index, Scalar, Packet, n, idx - 1, RowMajor> pbm;
+ EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE void store(Scalar *to, const Index stride, Index i, Index j, const PacketBlock<Packet, n> &block) const {
+ pbm.store(to, stride, i, j, block);
+ pstoreu<Scalar>(to + j + (i + idx)*stride, block.packet[idx]);
+ }
+};
+
+template<typename Index, typename Scalar, typename Packet, int n, int StorageOrder>
+struct PacketBlockManagement<Index, Scalar, Packet, n, -1, StorageOrder>
+{
+ EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE void store(Scalar *to, const Index stride, Index i, Index j, const PacketBlock<Packet, n> &block) const {
+ EIGEN_UNUSED_VARIABLE(to);
+ EIGEN_UNUSED_VARIABLE(stride);
+ EIGEN_UNUSED_VARIABLE(i);
+ EIGEN_UNUSED_VARIABLE(j);
+ EIGEN_UNUSED_VARIABLE(block);
+ }
+};
+
+template<typename Index, typename Scalar, typename Packet, int n>
+struct PacketBlockManagement<Index, Scalar, Packet, n, -1, RowMajor>
+{
+ EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE void store(Scalar *to, const Index stride, Index i, Index j, const PacketBlock<Packet, n> &block) const {
+ EIGEN_UNUSED_VARIABLE(to);
+ EIGEN_UNUSED_VARIABLE(stride);
+ EIGEN_UNUSED_VARIABLE(i);
+ EIGEN_UNUSED_VARIABLE(j);
+ EIGEN_UNUSED_VARIABLE(block);
+ }
+};
+
+template<typename Scalar, typename Index, int StorageOrder, int AlignmentType>
+class blas_data_mapper<Scalar,Index,StorageOrder,AlignmentType,1>
+{
+public:
+ typedef BlasLinearMapper<Scalar, Index, AlignmentType> LinearMapper;
+ typedef BlasVectorMapper<Scalar, Index> VectorMapper;
+
+ EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE blas_data_mapper(Scalar* data, Index stride, Index incr=1)
+ : m_data(data), m_stride(stride)
+ {
+ EIGEN_ONLY_USED_FOR_DEBUG(incr);
+ eigen_assert(incr==1);
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE blas_data_mapper<Scalar, Index, StorageOrder, AlignmentType>
+ getSubMapper(Index i, Index j) const {
+ return blas_data_mapper<Scalar, Index, StorageOrder, AlignmentType>(&operator()(i, j), m_stride);
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE LinearMapper getLinearMapper(Index i, Index j) const {
+ return LinearMapper(&operator()(i, j));
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE VectorMapper getVectorMapper(Index i, Index j) const {
+ return VectorMapper(&operator()(i, j));
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE void prefetch(Index i, Index j) const {
+ internal::prefetch(&operator()(i, j));
+ }
+
+ EIGEN_DEVICE_FUNC
+ EIGEN_ALWAYS_INLINE Scalar& operator()(Index i, Index j) const {
+ return m_data[StorageOrder==RowMajor ? j + i*m_stride : i + j*m_stride];
+ }
+
+ template<typename PacketType>
+ EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE PacketType loadPacket(Index i, Index j) const {
+ return ploadt<PacketType, AlignmentType>(&operator()(i, j));
+ }
+
+ template<typename PacketType>
+ EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE PacketType loadPacketPartial(Index i, Index j, Index n, Index offset = 0) const {
+ return ploadt_partial<PacketType, AlignmentType>(&operator()(i, j), n, offset);
+ }
+
+ template <typename PacketT, int AlignmentT>
+ EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE PacketT load(Index i, Index j) const {
+ return ploadt<PacketT, AlignmentT>(&operator()(i, j));
+ }
+
+ template<typename PacketType>
+ EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE void storePacket(Index i, Index j, const PacketType &p) const {
+ pstoret<Scalar, PacketType, AlignmentType>(&operator()(i, j), p);
+ }
+
+ template<typename PacketType>
+ EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE void storePacketPartial(Index i, Index j, const PacketType &p, Index n, Index offset = 0) const {
+ pstoret_partial<Scalar, PacketType, AlignmentType>(&operator()(i, j), p, n, offset);
+ }
+
+ template<typename SubPacket>
+ EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE void scatterPacket(Index i, Index j, const SubPacket &p) const {
+ pscatter<Scalar, SubPacket>(&operator()(i, j), p, m_stride);
+ }
+
+ template<typename SubPacket>
+ EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE SubPacket gatherPacket(Index i, Index j) const {
+ return pgather<Scalar, SubPacket>(&operator()(i, j), m_stride);
+ }
+
+ EIGEN_DEVICE_FUNC const Index stride() const { return m_stride; }
+ EIGEN_DEVICE_FUNC const Index incr() const { return 1; }
+ EIGEN_DEVICE_FUNC const Scalar* data() const { return m_data; }
+
+ EIGEN_DEVICE_FUNC Index firstAligned(Index size) const {
+ if (UIntPtr(m_data)%sizeof(Scalar)) {
+ return -1;
+ }
+ return internal::first_default_aligned(m_data, size);
+ }
+
+ template<typename SubPacket, int n>
+ EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE void storePacketBlock(Index i, Index j, const PacketBlock<SubPacket, n> &block) const {
+ PacketBlockManagement<Index, Scalar, SubPacket, n, n-1, StorageOrder> pbm;
+ pbm.store(m_data, m_stride, i, j, block);
+ }
+protected:
+ Scalar* EIGEN_RESTRICT m_data;
+ const Index m_stride;
+};
+
+// Implementation of non-natural increment (i.e. inner-stride != 1)
+// The exposed API is not complete yet compared to the Incr==1 case
+// because some features makes less sense in this case.
+template<typename Scalar, typename Index, int AlignmentType, int Incr>
+class BlasLinearMapper
+{
+public:
+ EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE BlasLinearMapper(Scalar *data,Index incr) : m_data(data), m_incr(incr) {}
+
+ EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE void prefetch(int i) const {
+ internal::prefetch(&operator()(i));
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE Scalar& operator()(Index i) const {
+ return m_data[i*m_incr.value()];
+ }
+
+ template<typename PacketType>
+ EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE PacketType loadPacket(Index i) const {
+ return pgather<Scalar,PacketType>(m_data + i*m_incr.value(), m_incr.value());
+ }
+
+ template<typename PacketType>
+ EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE PacketType loadPacketPartial(Index i, Index n, Index /*offset*/ = 0) const {
+ return pgather_partial<Scalar,PacketType>(m_data + i*m_incr.value(), m_incr.value(), n);
+ }
+
+ template<typename PacketType>
+ EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE void storePacket(Index i, const PacketType &p) const {
+ pscatter<Scalar, PacketType>(m_data + i*m_incr.value(), p, m_incr.value());
+ }
+
+ template<typename PacketType>
+ EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE void storePacketPartial(Index i, const PacketType &p, Index n, Index /*offset*/ = 0) const {
+ pscatter_partial<Scalar, PacketType>(m_data + i*m_incr.value(), p, m_incr.value(), n);
+ }
+
+protected:
+ Scalar *m_data;
+ const internal::variable_if_dynamic<Index,Incr> m_incr;
+};
+
+template<typename Scalar, typename Index, int StorageOrder, int AlignmentType,int Incr>
+class blas_data_mapper
+{
+public:
+ typedef BlasLinearMapper<Scalar, Index, AlignmentType,Incr> LinearMapper;
+
+ EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE blas_data_mapper(Scalar* data, Index stride, Index incr) : m_data(data), m_stride(stride), m_incr(incr) {}
+
+ EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE blas_data_mapper
+ getSubMapper(Index i, Index j) const {
+ return blas_data_mapper(&operator()(i, j), m_stride, m_incr.value());
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE LinearMapper getLinearMapper(Index i, Index j) const {
+ return LinearMapper(&operator()(i, j), m_incr.value());
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE void prefetch(Index i, Index j) const {
+ internal::prefetch(&operator()(i, j));
+ }
+
+ EIGEN_DEVICE_FUNC
+ EIGEN_ALWAYS_INLINE Scalar& operator()(Index i, Index j) const {
+ return m_data[StorageOrder==RowMajor ? j*m_incr.value() + i*m_stride : i*m_incr.value() + j*m_stride];
+ }
+
+ template<typename PacketType>
+ EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE PacketType loadPacket(Index i, Index j) const {
+ return pgather<Scalar,PacketType>(&operator()(i, j),m_incr.value());
+ }
+
+ template<typename PacketType>
+ EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE PacketType loadPacketPartial(Index i, Index j, Index n, Index /*offset*/ = 0) const {
+ return pgather_partial<Scalar,PacketType>(&operator()(i, j),m_incr.value(),n);
+ }
+
+ template <typename PacketT, int AlignmentT>
+ EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE PacketT load(Index i, Index j) const {
+ return pgather<Scalar,PacketT>(&operator()(i, j),m_incr.value());
+ }
+
+ template<typename PacketType>
+ EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE void storePacket(Index i, Index j, const PacketType &p) const {
+ pscatter<Scalar, PacketType>(&operator()(i, j), p, m_incr.value());
+ }
+
+ template<typename PacketType>
+ EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE void storePacketPartial(Index i, Index j, const PacketType &p, Index n, Index /*offset*/ = 0) const {
+ pscatter_partial<Scalar, PacketType>(&operator()(i, j), p, m_incr.value(), n);
+ }
+
+ template<typename SubPacket>
+ EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE void scatterPacket(Index i, Index j, const SubPacket &p) const {
+ pscatter<Scalar, SubPacket>(&operator()(i, j), p, m_stride);
+ }
+
+ template<typename SubPacket>
+ EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE SubPacket gatherPacket(Index i, Index j) const {
+ return pgather<Scalar, SubPacket>(&operator()(i, j), m_stride);
+ }
+
+ // storePacketBlock_helper defines a way to access values inside the PacketBlock, this is essentially required by the Complex types.
+ template<typename SubPacket, typename Scalar_, int n, int idx>
+ struct storePacketBlock_helper
+ {
+ storePacketBlock_helper<SubPacket, Scalar_, n, idx-1> spbh;
+ EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE void store(const blas_data_mapper<Scalar, Index, StorageOrder, AlignmentType, Incr>* sup, Index i, Index j, const PacketBlock<SubPacket, n>& block) const {
+ spbh.store(sup, i,j,block);
+ for(int l = 0; l < unpacket_traits<SubPacket>::size; l++)
+ {
+ Scalar_ *v = &sup->operator()(i+l, j+idx);
+ *v = block.packet[idx][l];
+ }
+ }
+ };
+
+ template<typename SubPacket, int n, int idx>
+ struct storePacketBlock_helper<SubPacket, std::complex<float>, n, idx>
+ {
+ storePacketBlock_helper<SubPacket, std::complex<float>, n, idx-1> spbh;
+ EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE void store(const blas_data_mapper<Scalar, Index, StorageOrder, AlignmentType, Incr>* sup, Index i, Index j, const PacketBlock<SubPacket, n>& block) const {
+ spbh.store(sup,i,j,block);
+ for(int l = 0; l < unpacket_traits<SubPacket>::size; l++)
+ {
+ std::complex<float> *v = &sup->operator()(i+l, j+idx);
+ v->real(block.packet[idx].v[2*l+0]);
+ v->imag(block.packet[idx].v[2*l+1]);
+ }
+ }
+ };
+
+ template<typename SubPacket, int n, int idx>
+ struct storePacketBlock_helper<SubPacket, std::complex<double>, n, idx>
+ {
+ storePacketBlock_helper<SubPacket, std::complex<double>, n, idx-1> spbh;
+ EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE void store(const blas_data_mapper<Scalar, Index, StorageOrder, AlignmentType, Incr>* sup, Index i, Index j, const PacketBlock<SubPacket, n>& block) const {
+ spbh.store(sup,i,j,block);
+ for(int l = 0; l < unpacket_traits<SubPacket>::size; l++)
+ {
+ std::complex<double> *v = &sup->operator()(i+l, j+idx);
+ v->real(block.packet[idx].v[2*l+0]);
+ v->imag(block.packet[idx].v[2*l+1]);
+ }
+ }
+ };
+
+ template<typename SubPacket, typename Scalar_, int n>
+ struct storePacketBlock_helper<SubPacket, Scalar_, n, -1>
+ {
+ EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE void store(const blas_data_mapper<Scalar, Index, StorageOrder, AlignmentType, Incr>*, Index, Index, const PacketBlock<SubPacket, n>& ) const {
+ }
+ };
+
+ template<typename SubPacket, int n>
+ struct storePacketBlock_helper<SubPacket, std::complex<float>, n, -1>
+ {
+ EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE void store(const blas_data_mapper<Scalar, Index, StorageOrder, AlignmentType, Incr>*, Index, Index, const PacketBlock<SubPacket, n>& ) const {
+ }
+ };
+
+ template<typename SubPacket, int n>
+ struct storePacketBlock_helper<SubPacket, std::complex<double>, n, -1>
+ {
+ EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE void store(const blas_data_mapper<Scalar, Index, StorageOrder, AlignmentType, Incr>*, Index, Index, const PacketBlock<SubPacket, n>& ) const {
+ }
+ };
+ // This function stores a PacketBlock on m_data, this approach is really quite slow compare to Incr=1 and should be avoided when possible.
+ template<typename SubPacket, int n>
+ EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE void storePacketBlock(Index i, Index j, const PacketBlock<SubPacket, n>&block) const {
+ storePacketBlock_helper<SubPacket, Scalar, n, n-1> spb;
+ spb.store(this, i,j,block);
+ }
+
+ EIGEN_DEVICE_FUNC const Index stride() const { return m_stride; }
+ EIGEN_DEVICE_FUNC const Index incr() const { return m_incr.value(); }
+ EIGEN_DEVICE_FUNC Scalar* data() const { return m_data; }
+protected:
+ Scalar* EIGEN_RESTRICT m_data;
+ const Index m_stride;
+ const internal::variable_if_dynamic<Index,Incr> m_incr;
+};
+
+// lightweight helper class to access matrix coefficients (const version)
+template<typename Scalar, typename Index, int StorageOrder>
+class const_blas_data_mapper : public blas_data_mapper<const Scalar, Index, StorageOrder> {
+ public:
+ EIGEN_ALWAYS_INLINE const_blas_data_mapper(const Scalar *data, Index stride) : blas_data_mapper<const Scalar, Index, StorageOrder>(data, stride) {}
+
+ EIGEN_ALWAYS_INLINE const_blas_data_mapper<Scalar, Index, StorageOrder> getSubMapper(Index i, Index j) const {
+ return const_blas_data_mapper<Scalar, Index, StorageOrder>(&(this->operator()(i, j)), this->m_stride);
+ }
+};
+
+
+/* Helper class to analyze the factors of a Product expression.
+ * In particular it allows to pop out operator-, scalar multiples,
+ * and conjugate */
+template<typename XprType> struct blas_traits
+{
+ typedef typename traits<XprType>::Scalar Scalar;
+ typedef const XprType& ExtractType;
+ typedef XprType ExtractType_;
+ enum {
+ IsComplex = NumTraits<Scalar>::IsComplex,
+ IsTransposed = false,
+ NeedToConjugate = false,
+ HasUsableDirectAccess = ( (int(XprType::Flags)&DirectAccessBit)
+ && ( bool(XprType::IsVectorAtCompileTime)
+ || int(inner_stride_at_compile_time<XprType>::ret) == 1)
+ ) ? 1 : 0,
+ HasScalarFactor = false
+ };
+ typedef std::conditional_t<bool(HasUsableDirectAccess),
+ ExtractType,
+ typename ExtractType_::PlainObject
+ > DirectLinearAccessType;
+ static inline EIGEN_DEVICE_FUNC ExtractType extract(const XprType& x) { return x; }
+ static inline EIGEN_DEVICE_FUNC const Scalar extractScalarFactor(const XprType&) { return Scalar(1); }
+};
+
+// pop conjugate
+template<typename Scalar, typename NestedXpr>
+struct blas_traits<CwiseUnaryOp<scalar_conjugate_op<Scalar>, NestedXpr> >
+ : blas_traits<NestedXpr>
+{
+ typedef blas_traits<NestedXpr> Base;
+ typedef CwiseUnaryOp<scalar_conjugate_op<Scalar>, NestedXpr> XprType;
+ typedef typename Base::ExtractType ExtractType;
+
+ enum {
+ IsComplex = NumTraits<Scalar>::IsComplex,
+ NeedToConjugate = Base::NeedToConjugate ? 0 : IsComplex
+ };
+ static inline ExtractType extract(const XprType& x) { return Base::extract(x.nestedExpression()); }
+ static inline Scalar extractScalarFactor(const XprType& x) { return conj(Base::extractScalarFactor(x.nestedExpression())); }
+};
+
+// pop scalar multiple
+template<typename Scalar, typename NestedXpr, typename Plain>
+struct blas_traits<CwiseBinaryOp<scalar_product_op<Scalar>, const CwiseNullaryOp<scalar_constant_op<Scalar>,Plain>, NestedXpr> >
+ : blas_traits<NestedXpr>
+{
+ enum {
+ HasScalarFactor = true
+ };
+ typedef blas_traits<NestedXpr> Base;
+ typedef CwiseBinaryOp<scalar_product_op<Scalar>, const CwiseNullaryOp<scalar_constant_op<Scalar>,Plain>, NestedXpr> XprType;
+ typedef typename Base::ExtractType ExtractType;
+ static inline EIGEN_DEVICE_FUNC ExtractType extract(const XprType& x) { return Base::extract(x.rhs()); }
+ static inline EIGEN_DEVICE_FUNC Scalar extractScalarFactor(const XprType& x)
+ { return x.lhs().functor().m_other * Base::extractScalarFactor(x.rhs()); }
+};
+template<typename Scalar, typename NestedXpr, typename Plain>
+struct blas_traits<CwiseBinaryOp<scalar_product_op<Scalar>, NestedXpr, const CwiseNullaryOp<scalar_constant_op<Scalar>,Plain> > >
+ : blas_traits<NestedXpr>
+{
+ enum {
+ HasScalarFactor = true
+ };
+ typedef blas_traits<NestedXpr> Base;
+ typedef CwiseBinaryOp<scalar_product_op<Scalar>, NestedXpr, const CwiseNullaryOp<scalar_constant_op<Scalar>,Plain> > XprType;
+ typedef typename Base::ExtractType ExtractType;
+ static inline ExtractType extract(const XprType& x) { return Base::extract(x.lhs()); }
+ static inline Scalar extractScalarFactor(const XprType& x)
+ { return Base::extractScalarFactor(x.lhs()) * x.rhs().functor().m_other; }
+};
+template<typename Scalar, typename Plain1, typename Plain2>
+struct blas_traits<CwiseBinaryOp<scalar_product_op<Scalar>, const CwiseNullaryOp<scalar_constant_op<Scalar>,Plain1>,
+ const CwiseNullaryOp<scalar_constant_op<Scalar>,Plain2> > >
+ : blas_traits<CwiseNullaryOp<scalar_constant_op<Scalar>,Plain1> >
+{};
+
+// pop opposite
+template<typename Scalar, typename NestedXpr>
+struct blas_traits<CwiseUnaryOp<scalar_opposite_op<Scalar>, NestedXpr> >
+ : blas_traits<NestedXpr>
+{
+ enum {
+ HasScalarFactor = true
+ };
+ typedef blas_traits<NestedXpr> Base;
+ typedef CwiseUnaryOp<scalar_opposite_op<Scalar>, NestedXpr> XprType;
+ typedef typename Base::ExtractType ExtractType;
+ static inline ExtractType extract(const XprType& x) { return Base::extract(x.nestedExpression()); }
+ static inline Scalar extractScalarFactor(const XprType& x)
+ { return - Base::extractScalarFactor(x.nestedExpression()); }
+};
+
+// pop/push transpose
+template<typename NestedXpr>
+struct blas_traits<Transpose<NestedXpr> >
+ : blas_traits<NestedXpr>
+{
+ typedef typename NestedXpr::Scalar Scalar;
+ typedef blas_traits<NestedXpr> Base;
+ typedef Transpose<NestedXpr> XprType;
+ typedef Transpose<const typename Base::ExtractType_> ExtractType; // const to get rid of a compile error; anyway blas traits are only used on the RHS
+ typedef Transpose<const typename Base::ExtractType_> ExtractType_;
+ typedef std::conditional_t<bool(Base::HasUsableDirectAccess),
+ ExtractType,
+ typename ExtractType::PlainObject
+ > DirectLinearAccessType;
+ enum {
+ IsTransposed = Base::IsTransposed ? 0 : 1
+ };
+ static inline ExtractType extract(const XprType& x) { return ExtractType(Base::extract(x.nestedExpression())); }
+ static inline Scalar extractScalarFactor(const XprType& x) { return Base::extractScalarFactor(x.nestedExpression()); }
+};
+
+template<typename T>
+struct blas_traits<const T>
+ : blas_traits<T>
+{};
+
+template<typename T, bool HasUsableDirectAccess=blas_traits<T>::HasUsableDirectAccess>
+struct extract_data_selector {
+ EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE static const typename T::Scalar* run(const T& m)
+ {
+ return blas_traits<T>::extract(m).data();
+ }
+};
+
+template<typename T>
+struct extract_data_selector<T,false> {
+ static typename T::Scalar* run(const T&) { return 0; }
+};
+
+template<typename T>
+EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE const typename T::Scalar* extract_data(const T& m)
+{
+ return extract_data_selector<T>::run(m);
+}
+
+/**
+ * \c combine_scalar_factors extracts and multiplies factors from GEMM and GEMV products.
+ * There is a specialization for booleans
+ */
+template<typename ResScalar, typename Lhs, typename Rhs>
+struct combine_scalar_factors_impl
+{
+ EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE static ResScalar run(const Lhs& lhs, const Rhs& rhs)
+ {
+ return blas_traits<Lhs>::extractScalarFactor(lhs) * blas_traits<Rhs>::extractScalarFactor(rhs);
+ }
+ EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE static ResScalar run(const ResScalar& alpha, const Lhs& lhs, const Rhs& rhs)
+ {
+ return alpha * blas_traits<Lhs>::extractScalarFactor(lhs) * blas_traits<Rhs>::extractScalarFactor(rhs);
+ }
+};
+template<typename Lhs, typename Rhs>
+struct combine_scalar_factors_impl<bool, Lhs, Rhs>
+{
+ EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE static bool run(const Lhs& lhs, const Rhs& rhs)
+ {
+ return blas_traits<Lhs>::extractScalarFactor(lhs) && blas_traits<Rhs>::extractScalarFactor(rhs);
+ }
+ EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE static bool run(const bool& alpha, const Lhs& lhs, const Rhs& rhs)
+ {
+ return alpha && blas_traits<Lhs>::extractScalarFactor(lhs) && blas_traits<Rhs>::extractScalarFactor(rhs);
+ }
+};
+
+template<typename ResScalar, typename Lhs, typename Rhs>
+EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE ResScalar combine_scalar_factors(const ResScalar& alpha, const Lhs& lhs, const Rhs& rhs)
+{
+ return combine_scalar_factors_impl<ResScalar,Lhs,Rhs>::run(alpha, lhs, rhs);
+}
+template<typename ResScalar, typename Lhs, typename Rhs>
+EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE ResScalar combine_scalar_factors(const Lhs& lhs, const Rhs& rhs)
+{
+ return combine_scalar_factors_impl<ResScalar,Lhs,Rhs>::run(lhs, rhs);
+}
+
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_BLASUTIL_H
diff --git a/Eigen/src/Core/util/ConfigureVectorization.h b/Eigen/src/Core/util/ConfigureVectorization.h
new file mode 100644
index 0000000..7c1a08b
--- /dev/null
+++ b/Eigen/src/Core/util/ConfigureVectorization.h
@@ -0,0 +1,507 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2018 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2020, Arm Limited and Contributors
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_CONFIGURE_VECTORIZATION_H
+#define EIGEN_CONFIGURE_VECTORIZATION_H
+
+//------------------------------------------------------------------------------------------
+// Static and dynamic alignment control
+//
+// The main purpose of this section is to define EIGEN_MAX_ALIGN_BYTES and EIGEN_MAX_STATIC_ALIGN_BYTES
+// as the maximal boundary in bytes on which dynamically and statically allocated data may be alignment respectively.
+// The values of EIGEN_MAX_ALIGN_BYTES and EIGEN_MAX_STATIC_ALIGN_BYTES can be specified by the user. If not,
+// a default value is automatically computed based on architecture, compiler, and OS.
+//
+// This section also defines macros EIGEN_ALIGN_TO_BOUNDARY(N) and the shortcuts EIGEN_ALIGN{8,16,32,_MAX}
+// to be used to declare statically aligned buffers.
+//------------------------------------------------------------------------------------------
+
+
+/* EIGEN_ALIGN_TO_BOUNDARY(n) forces data to be n-byte aligned. This is used to satisfy SIMD requirements.
+ * However, we do that EVEN if vectorization (EIGEN_VECTORIZE) is disabled,
+ * so that vectorization doesn't affect binary compatibility.
+ *
+ * If we made alignment depend on whether or not EIGEN_VECTORIZE is defined, it would be impossible to link
+ * vectorized and non-vectorized code.
+ */
+#if (defined EIGEN_CUDACC)
+ #define EIGEN_ALIGN_TO_BOUNDARY(n) __align__(n)
+ #define EIGEN_ALIGNOF(x) __alignof(x)
+#else
+ #define EIGEN_ALIGN_TO_BOUNDARY(n) alignas(n)
+ #define EIGEN_ALIGNOF(x) alignof(x)
+#endif
+
+// If the user explicitly disable vectorization, then we also disable alignment
+#if defined(EIGEN_DONT_VECTORIZE)
+ #if defined(EIGEN_GPUCC)
+ // GPU code is always vectorized and requires memory alignment for
+ // statically allocated buffers.
+ #define EIGEN_IDEAL_MAX_ALIGN_BYTES 16
+ #else
+ #define EIGEN_IDEAL_MAX_ALIGN_BYTES 0
+ #endif
+#elif defined(__AVX512F__)
+ // 64 bytes static alignment is preferred only if really required
+ #define EIGEN_IDEAL_MAX_ALIGN_BYTES 64
+#elif defined(__AVX__)
+ // 32 bytes static alignment is preferred only if really required
+ #define EIGEN_IDEAL_MAX_ALIGN_BYTES 32
+#else
+ #define EIGEN_IDEAL_MAX_ALIGN_BYTES 16
+#endif
+
+
+// EIGEN_MIN_ALIGN_BYTES defines the minimal value for which the notion of explicit alignment makes sense
+#define EIGEN_MIN_ALIGN_BYTES 16
+
+// Defined the boundary (in bytes) on which the data needs to be aligned. Note
+// that unless EIGEN_ALIGN is defined and not equal to 0, the data may not be
+// aligned at all regardless of the value of this #define.
+
+#if (defined(EIGEN_DONT_ALIGN_STATICALLY) || defined(EIGEN_DONT_ALIGN)) && defined(EIGEN_MAX_STATIC_ALIGN_BYTES) && EIGEN_MAX_STATIC_ALIGN_BYTES>0
+#error EIGEN_MAX_STATIC_ALIGN_BYTES and EIGEN_DONT_ALIGN[_STATICALLY] are both defined with EIGEN_MAX_STATIC_ALIGN_BYTES!=0. Use EIGEN_MAX_STATIC_ALIGN_BYTES=0 as a synonym of EIGEN_DONT_ALIGN_STATICALLY.
+#endif
+
+// EIGEN_DONT_ALIGN_STATICALLY and EIGEN_DONT_ALIGN are deprecated
+// They imply EIGEN_MAX_STATIC_ALIGN_BYTES=0
+#if defined(EIGEN_DONT_ALIGN_STATICALLY) || defined(EIGEN_DONT_ALIGN)
+ #ifdef EIGEN_MAX_STATIC_ALIGN_BYTES
+ #undef EIGEN_MAX_STATIC_ALIGN_BYTES
+ #endif
+ #define EIGEN_MAX_STATIC_ALIGN_BYTES 0
+#endif
+
+#ifndef EIGEN_MAX_STATIC_ALIGN_BYTES
+
+ // Try to automatically guess what is the best default value for EIGEN_MAX_STATIC_ALIGN_BYTES
+
+ // 16 byte alignment is only useful for vectorization. Since it affects the ABI, we need to enable
+ // 16 byte alignment on all platforms where vectorization might be enabled. In theory we could always
+ // enable alignment, but it can be a cause of problems on some platforms, so we just disable it in
+ // certain common platform (compiler+architecture combinations) to avoid these problems.
+ // Only static alignment is really problematic (relies on nonstandard compiler extensions),
+ // try to keep heap alignment even when we have to disable static alignment.
+ #if EIGEN_COMP_GNUC && !(EIGEN_ARCH_i386_OR_x86_64 || EIGEN_ARCH_ARM_OR_ARM64 || EIGEN_ARCH_PPC || EIGEN_ARCH_IA64 || EIGEN_ARCH_MIPS)
+ #define EIGEN_GCC_AND_ARCH_DOESNT_WANT_STACK_ALIGNMENT 1
+ #else
+ #define EIGEN_GCC_AND_ARCH_DOESNT_WANT_STACK_ALIGNMENT 0
+ #endif
+
+ // static alignment is completely disabled with GCC 3, Sun Studio, and QCC/QNX
+ #if !EIGEN_GCC_AND_ARCH_DOESNT_WANT_STACK_ALIGNMENT \
+ && !EIGEN_COMP_SUNCC \
+ && !EIGEN_OS_QNX
+ #define EIGEN_ARCH_WANTS_STACK_ALIGNMENT 1
+ #else
+ #define EIGEN_ARCH_WANTS_STACK_ALIGNMENT 0
+ #endif
+
+ #if EIGEN_ARCH_WANTS_STACK_ALIGNMENT
+ #define EIGEN_MAX_STATIC_ALIGN_BYTES EIGEN_IDEAL_MAX_ALIGN_BYTES
+ #else
+ #define EIGEN_MAX_STATIC_ALIGN_BYTES 0
+ #endif
+
+#endif
+
+// If EIGEN_MAX_ALIGN_BYTES is defined, then it is considered as an upper bound for EIGEN_MAX_STATIC_ALIGN_BYTES
+#if defined(EIGEN_MAX_ALIGN_BYTES) && EIGEN_MAX_ALIGN_BYTES<EIGEN_MAX_STATIC_ALIGN_BYTES
+#undef EIGEN_MAX_STATIC_ALIGN_BYTES
+#define EIGEN_MAX_STATIC_ALIGN_BYTES EIGEN_MAX_ALIGN_BYTES
+#endif
+
+#if EIGEN_MAX_STATIC_ALIGN_BYTES==0 && !defined(EIGEN_DISABLE_UNALIGNED_ARRAY_ASSERT)
+ #define EIGEN_DISABLE_UNALIGNED_ARRAY_ASSERT
+#endif
+
+// At this stage, EIGEN_MAX_STATIC_ALIGN_BYTES>0 is the true test whether we want to align arrays on the stack or not.
+// It takes into account both the user choice to explicitly enable/disable alignment (by setting EIGEN_MAX_STATIC_ALIGN_BYTES)
+// and the architecture config (EIGEN_ARCH_WANTS_STACK_ALIGNMENT).
+// Henceforth, only EIGEN_MAX_STATIC_ALIGN_BYTES should be used.
+
+
+// Shortcuts to EIGEN_ALIGN_TO_BOUNDARY
+#define EIGEN_ALIGN8 EIGEN_ALIGN_TO_BOUNDARY(8)
+#define EIGEN_ALIGN16 EIGEN_ALIGN_TO_BOUNDARY(16)
+#define EIGEN_ALIGN32 EIGEN_ALIGN_TO_BOUNDARY(32)
+#define EIGEN_ALIGN64 EIGEN_ALIGN_TO_BOUNDARY(64)
+#if EIGEN_MAX_STATIC_ALIGN_BYTES>0
+#define EIGEN_ALIGN_MAX EIGEN_ALIGN_TO_BOUNDARY(EIGEN_MAX_STATIC_ALIGN_BYTES)
+#else
+#define EIGEN_ALIGN_MAX
+#endif
+
+
+// Dynamic alignment control
+
+#if defined(EIGEN_DONT_ALIGN) && defined(EIGEN_MAX_ALIGN_BYTES) && EIGEN_MAX_ALIGN_BYTES>0
+#error EIGEN_MAX_ALIGN_BYTES and EIGEN_DONT_ALIGN are both defined with EIGEN_MAX_ALIGN_BYTES!=0. Use EIGEN_MAX_ALIGN_BYTES=0 as a synonym of EIGEN_DONT_ALIGN.
+#endif
+
+#ifdef EIGEN_DONT_ALIGN
+ #ifdef EIGEN_MAX_ALIGN_BYTES
+ #undef EIGEN_MAX_ALIGN_BYTES
+ #endif
+ #define EIGEN_MAX_ALIGN_BYTES 0
+#elif !defined(EIGEN_MAX_ALIGN_BYTES)
+ #define EIGEN_MAX_ALIGN_BYTES EIGEN_IDEAL_MAX_ALIGN_BYTES
+#endif
+
+#if EIGEN_IDEAL_MAX_ALIGN_BYTES > EIGEN_MAX_ALIGN_BYTES
+#define EIGEN_DEFAULT_ALIGN_BYTES EIGEN_IDEAL_MAX_ALIGN_BYTES
+#else
+#define EIGEN_DEFAULT_ALIGN_BYTES EIGEN_MAX_ALIGN_BYTES
+#endif
+
+
+#ifndef EIGEN_UNALIGNED_VECTORIZE
+#define EIGEN_UNALIGNED_VECTORIZE 1
+#endif
+
+//----------------------------------------------------------------------
+
+// if alignment is disabled, then disable vectorization. Note: EIGEN_MAX_ALIGN_BYTES is the proper check, it takes into
+// account both the user's will (EIGEN_MAX_ALIGN_BYTES,EIGEN_DONT_ALIGN) and our own platform checks
+#if EIGEN_MAX_ALIGN_BYTES==0
+ #ifndef EIGEN_DONT_VECTORIZE
+ #define EIGEN_DONT_VECTORIZE
+ #endif
+#endif
+
+
+// The following (except #include <malloc.h> and _M_IX86_FP ??) can likely be
+// removed as gcc 4.1 and msvc 2008 are not supported anyways.
+#if EIGEN_COMP_MSVC
+ #include <malloc.h> // for _aligned_malloc -- need it regardless of whether vectorization is enabled
+ // a user reported that in 64-bit mode, MSVC doesn't care to define _M_IX86_FP.
+ #if (defined(_M_IX86_FP) && (_M_IX86_FP >= 2)) || EIGEN_ARCH_x86_64
+ #define EIGEN_SSE2_ON_MSVC_2008_OR_LATER
+ #endif
+#else
+ #if (defined __SSE2__) && ( (!EIGEN_COMP_GNUC) || EIGEN_COMP_ICC || EIGEN_COMP_GNUC )
+ #define EIGEN_SSE2_ON_NON_MSVC_BUT_NOT_OLD_GCC
+ #endif
+#endif
+
+#if !(defined(EIGEN_DONT_VECTORIZE) || defined(EIGEN_GPUCC))
+
+ #if defined (EIGEN_SSE2_ON_NON_MSVC_BUT_NOT_OLD_GCC) || defined(EIGEN_SSE2_ON_MSVC_2008_OR_LATER)
+
+ // Defines symbols for compile-time detection of which instructions are
+ // used.
+ // EIGEN_VECTORIZE_YY is defined if and only if the instruction set YY is used
+ #define EIGEN_VECTORIZE
+ #define EIGEN_VECTORIZE_SSE
+ #define EIGEN_VECTORIZE_SSE2
+
+ // Detect sse3/ssse3/sse4:
+ // gcc and icc defines __SSE3__, ...
+ // there is no way to know about this on msvc. You can define EIGEN_VECTORIZE_SSE* if you
+ // want to force the use of those instructions with msvc.
+ #ifdef __SSE3__
+ #define EIGEN_VECTORIZE_SSE3
+ #endif
+ #ifdef __SSSE3__
+ #define EIGEN_VECTORIZE_SSSE3
+ #endif
+ #ifdef __SSE4_1__
+ #define EIGEN_VECTORIZE_SSE4_1
+ #endif
+ #ifdef __SSE4_2__
+ #define EIGEN_VECTORIZE_SSE4_2
+ #endif
+ #ifdef __AVX__
+ #ifndef EIGEN_USE_SYCL
+ #define EIGEN_VECTORIZE_AVX
+ #endif
+ #define EIGEN_VECTORIZE_SSE3
+ #define EIGEN_VECTORIZE_SSSE3
+ #define EIGEN_VECTORIZE_SSE4_1
+ #define EIGEN_VECTORIZE_SSE4_2
+ #endif
+ #ifdef __AVX2__
+ #ifndef EIGEN_USE_SYCL
+ #define EIGEN_VECTORIZE_AVX2
+ #define EIGEN_VECTORIZE_AVX
+ #endif
+ #define EIGEN_VECTORIZE_SSE3
+ #define EIGEN_VECTORIZE_SSSE3
+ #define EIGEN_VECTORIZE_SSE4_1
+ #define EIGEN_VECTORIZE_SSE4_2
+ #endif
+ #if defined(__FMA__) || (EIGEN_COMP_MSVC && defined(__AVX2__))
+ // MSVC does not expose a switch dedicated for FMA
+ // For MSVC, AVX2 => FMA
+ #define EIGEN_VECTORIZE_FMA
+ #endif
+ #if defined(__AVX512F__)
+ #ifndef EIGEN_VECTORIZE_FMA
+ #if EIGEN_COMP_GNUC
+ #error Please add -mfma to your compiler flags: compiling with -mavx512f alone without SSE/AVX FMA is not supported (bug 1638).
+ #else
+ #error Please enable FMA in your compiler flags (e.g. -mfma): compiling with AVX512 alone without SSE/AVX FMA is not supported (bug 1638).
+ #endif
+ #endif
+ #ifndef EIGEN_USE_SYCL
+ #define EIGEN_VECTORIZE_AVX512
+ #define EIGEN_VECTORIZE_AVX2
+ #define EIGEN_VECTORIZE_AVX
+ #endif
+ #define EIGEN_VECTORIZE_FMA
+ #define EIGEN_VECTORIZE_SSE3
+ #define EIGEN_VECTORIZE_SSSE3
+ #define EIGEN_VECTORIZE_SSE4_1
+ #define EIGEN_VECTORIZE_SSE4_2
+ #ifndef EIGEN_USE_SYCL
+ #ifdef __AVX512DQ__
+ #define EIGEN_VECTORIZE_AVX512DQ
+ #endif
+ #ifdef __AVX512ER__
+ #define EIGEN_VECTORIZE_AVX512ER
+ #endif
+ #ifdef __AVX512BF16__
+ #define EIGEN_VECTORIZE_AVX512BF16
+ #endif
+ #ifdef __AVX512FP16__
+ #ifdef __AVX512VL__
+ #define EIGEN_VECTORIZE_AVX512FP16
+ #else
+ #if EIGEN_COMP_GNUC
+ #error Please add -mavx512vl to your compiler flags: compiling with -mavx512fp16 alone without AVX512-VL is not supported.
+ #else
+ #error Please enable AVX512-VL in your compiler flags (e.g. -mavx512vl): compiling with AVX512-FP16 alone without AVX512-VL is not supported.
+ #endif
+ #endif
+ #endif
+ #endif
+ #endif
+
+ // Disable AVX support on broken xcode versions
+ #if defined(__apple_build_version__) && (__apple_build_version__ == 11000033 ) && ( __MAC_OS_X_VERSION_MIN_REQUIRED == 101500 )
+ // A nasty bug in the clang compiler shipped with xcode in a common compilation situation
+ // when XCode 11.0 and Mac deployment target macOS 10.15 is https://trac.macports.org/ticket/58776#no1
+ #ifdef EIGEN_VECTORIZE_AVX
+ #undef EIGEN_VECTORIZE_AVX
+ #warning "Disabling AVX support: clang compiler shipped with XCode 11.[012] generates broken assembly with -macosx-version-min=10.15 and AVX enabled. "
+ #ifdef EIGEN_VECTORIZE_AVX2
+ #undef EIGEN_VECTORIZE_AVX2
+ #endif
+ #ifdef EIGEN_VECTORIZE_FMA
+ #undef EIGEN_VECTORIZE_FMA
+ #endif
+ #ifdef EIGEN_VECTORIZE_AVX512
+ #undef EIGEN_VECTORIZE_AVX512
+ #endif
+ #ifdef EIGEN_VECTORIZE_AVX512DQ
+ #undef EIGEN_VECTORIZE_AVX512DQ
+ #endif
+ #ifdef EIGEN_VECTORIZE_AVX512ER
+ #undef EIGEN_VECTORIZE_AVX512ER
+ #endif
+ #endif
+ // NOTE: Confirmed test failures in XCode 11.0, and XCode 11.2 with -macosx-version-min=10.15 and AVX
+ // NOTE using -macosx-version-min=10.15 with Xcode 11.0 results in runtime segmentation faults in many tests, 11.2 produce core dumps in 3 tests
+ // NOTE using -macosx-version-min=10.14 produces functioning and passing tests in all cases
+ // NOTE __clang_version__ "11.0.0 (clang-1100.0.33.8)" XCode 11.0 <- Produces many segfault and core dumping tests
+ // with -macosx-version-min=10.15 and AVX
+ // NOTE __clang_version__ "11.0.0 (clang-1100.0.33.12)" XCode 11.2 <- Produces 3 core dumping tests with
+ // -macosx-version-min=10.15 and AVX
+ #endif
+
+ // include files
+
+ // This extern "C" works around a MINGW-w64 compilation issue
+ // https://sourceforge.net/tracker/index.php?func=detail&aid=3018394&group_id=202880&atid=983354
+ // In essence, intrin.h is included by windows.h and also declares intrinsics (just as emmintrin.h etc. below do).
+ // However, intrin.h uses an extern "C" declaration, and g++ thus complains of duplicate declarations
+ // with conflicting linkage. The linkage for intrinsics doesn't matter, but at that stage the compiler doesn't know;
+ // so, to avoid compile errors when windows.h is included after Eigen/Core, ensure intrinsics are extern "C" here too.
+ // notice that since these are C headers, the extern "C" is theoretically needed anyways.
+ extern "C" {
+ // In theory we should only include immintrin.h and not the other *mmintrin.h header files directly.
+ // Doing so triggers some issues with ICC. However old gcc versions seems to not have this file, thus:
+ #if EIGEN_COMP_ICC >= 1110 || EIGEN_COMP_EMSCRIPTEN
+ #include <immintrin.h>
+ #else
+ #include <mmintrin.h>
+ #include <emmintrin.h>
+ #include <xmmintrin.h>
+ #ifdef EIGEN_VECTORIZE_SSE3
+ #include <pmmintrin.h>
+ #endif
+ #ifdef EIGEN_VECTORIZE_SSSE3
+ #include <tmmintrin.h>
+ #endif
+ #ifdef EIGEN_VECTORIZE_SSE4_1
+ #include <smmintrin.h>
+ #endif
+ #ifdef EIGEN_VECTORIZE_SSE4_2
+ #include <nmmintrin.h>
+ #endif
+ #if defined(EIGEN_VECTORIZE_AVX) || defined(EIGEN_VECTORIZE_AVX512)
+ #include <immintrin.h>
+ #endif
+ #endif
+ } // end extern "C"
+
+ #elif defined __VSX__
+
+ #define EIGEN_VECTORIZE
+ #define EIGEN_VECTORIZE_VSX
+ #include <altivec.h>
+ // We need to #undef all these ugly tokens defined in <altivec.h>
+ // => use __vector instead of vector
+ #undef bool
+ #undef vector
+ #undef pixel
+
+ #elif defined __ALTIVEC__
+
+ #define EIGEN_VECTORIZE
+ #define EIGEN_VECTORIZE_ALTIVEC
+ #include <altivec.h>
+ // We need to #undef all these ugly tokens defined in <altivec.h>
+ // => use __vector instead of vector
+ #undef bool
+ #undef vector
+ #undef pixel
+
+ #elif ((defined __ARM_NEON) || (defined __ARM_NEON__)) && !(defined EIGEN_ARM64_USE_SVE)
+
+ #define EIGEN_VECTORIZE
+ #define EIGEN_VECTORIZE_NEON
+ #include <arm_neon.h>
+
+ // We currently require SVE to be enabled explicitly via EIGEN_ARM64_USE_SVE and
+ // will not select the backend automatically
+ #elif (defined __ARM_FEATURE_SVE) && (defined EIGEN_ARM64_USE_SVE)
+
+ #define EIGEN_VECTORIZE
+ #define EIGEN_VECTORIZE_SVE
+ #include <arm_sve.h>
+
+ // Since we depend on knowing SVE vector lengths at compile-time, we need
+ // to ensure a fixed lengths is set
+ #if defined __ARM_FEATURE_SVE_BITS
+ #define EIGEN_ARM64_SVE_VL __ARM_FEATURE_SVE_BITS
+ #else
+#error "Eigen requires a fixed SVE lector length but EIGEN_ARM64_SVE_VL is not set."
+#endif
+
+#elif (defined __s390x__ && defined __VEC__)
+
+#define EIGEN_VECTORIZE
+#define EIGEN_VECTORIZE_ZVECTOR
+#include <vecintrin.h>
+
+#elif defined __mips_msa
+
+// Limit MSA optimizations to little-endian CPUs for now.
+// TODO: Perhaps, eventually support MSA optimizations on big-endian CPUs?
+#if defined(__BYTE_ORDER__) && (__BYTE_ORDER__ == __ORDER_LITTLE_ENDIAN__)
+#if defined(__LP64__)
+#define EIGEN_MIPS_64
+#else
+#define EIGEN_MIPS_32
+#endif
+#define EIGEN_VECTORIZE
+#define EIGEN_VECTORIZE_MSA
+#include <msa.h>
+#endif
+
+#endif
+#endif
+
+// Following the Arm ACLE arm_neon.h should also include arm_fp16.h but not all
+// compilers seem to follow this. We therefore include it explicitly.
+// See also: https://bugs.llvm.org/show_bug.cgi?id=47955
+#if defined(EIGEN_HAS_ARM64_FP16_SCALAR_ARITHMETIC)
+ #include <arm_fp16.h>
+#endif
+
+#if defined(__F16C__) && (!defined(EIGEN_GPUCC) && (!EIGEN_COMP_CLANG || EIGEN_COMP_CLANG>=380))
+ // We can use the optimized fp16 to float and float to fp16 conversion routines
+ #define EIGEN_HAS_FP16_C
+
+ #if EIGEN_COMP_GNUC
+ // Make sure immintrin.h is included, even if e.g. vectorization is
+ // explicitly disabled (see also issue #2395).
+ // Note that FP16C intrinsics for gcc and clang are included by immintrin.h,
+ // as opposed to emmintrin.h as suggested by Intel:
+ // https://software.intel.com/sites/landingpage/IntrinsicsGuide/#othertechs=FP16C&expand=1711
+ #include <immintrin.h>
+ #endif
+#endif
+
+#if defined EIGEN_CUDACC
+ #define EIGEN_VECTORIZE_GPU
+ #include <vector_types.h>
+ #if EIGEN_CUDA_SDK_VER >= 70500
+ #define EIGEN_HAS_CUDA_FP16
+ #endif
+#endif
+
+#if defined(EIGEN_HAS_CUDA_FP16)
+ #include <cuda_runtime_api.h>
+ #include <cuda_fp16.h>
+#endif
+
+#if defined(EIGEN_HIPCC)
+ #define EIGEN_VECTORIZE_GPU
+ #include <hip/hip_vector_types.h>
+ #define EIGEN_HAS_HIP_FP16
+ #include <hip/hip_fp16.h>
+ #define EIGEN_HAS_HIP_BF16
+ #include <hip/hip_bfloat16.h>
+#endif
+
+
+/** \brief Namespace containing all symbols from the %Eigen library. */
+#include "../InternalHeaderCheck.h"
+
+namespace Eigen {
+
+inline static const char *SimdInstructionSetsInUse(void) {
+#if defined(EIGEN_VECTORIZE_AVX512)
+ return "AVX512, FMA, AVX2, AVX, SSE, SSE2, SSE3, SSSE3, SSE4.1, SSE4.2";
+#elif defined(EIGEN_VECTORIZE_AVX)
+ return "AVX SSE, SSE2, SSE3, SSSE3, SSE4.1, SSE4.2";
+#elif defined(EIGEN_VECTORIZE_SSE4_2)
+ return "SSE, SSE2, SSE3, SSSE3, SSE4.1, SSE4.2";
+#elif defined(EIGEN_VECTORIZE_SSE4_1)
+ return "SSE, SSE2, SSE3, SSSE3, SSE4.1";
+#elif defined(EIGEN_VECTORIZE_SSSE3)
+ return "SSE, SSE2, SSE3, SSSE3";
+#elif defined(EIGEN_VECTORIZE_SSE3)
+ return "SSE, SSE2, SSE3";
+#elif defined(EIGEN_VECTORIZE_SSE2)
+ return "SSE, SSE2";
+#elif defined(EIGEN_VECTORIZE_ALTIVEC)
+ return "AltiVec";
+#elif defined(EIGEN_VECTORIZE_VSX)
+ return "VSX";
+#elif defined(EIGEN_VECTORIZE_NEON)
+ return "ARM NEON";
+#elif defined(EIGEN_VECTORIZE_SVE)
+ return "ARM SVE";
+#elif defined(EIGEN_VECTORIZE_ZVECTOR)
+ return "S390X ZVECTOR";
+#elif defined(EIGEN_VECTORIZE_MSA)
+ return "MIPS MSA";
+#else
+ return "None";
+#endif
+}
+
+} // end namespace Eigen
+
+
+#endif // EIGEN_CONFIGURE_VECTORIZATION_H
diff --git a/Eigen/src/Core/util/Constants.h b/Eigen/src/Core/util/Constants.h
new file mode 100644
index 0000000..0175087
--- /dev/null
+++ b/Eigen/src/Core/util/Constants.h
@@ -0,0 +1,568 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2015 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2007-2009 Benoit Jacob <jacob.benoit.1@gmail.com>
+// Copyright (C) 2020, Arm Limited and Contributors
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_CONSTANTS_H
+#define EIGEN_CONSTANTS_H
+
+#include "../InternalHeaderCheck.h"
+
+namespace Eigen {
+
+/** This value means that a positive quantity (e.g., a size) is not known at compile-time, and that instead the value is
+ * stored in some runtime variable.
+ *
+ * Changing the value of Dynamic breaks the ABI, as Dynamic is often used as a template parameter for Matrix.
+ */
+const int Dynamic = -1;
+
+/** This value means that a signed quantity (e.g., a signed index) is not known at compile-time, and that instead its value
+ * has to be specified at runtime.
+ */
+const int DynamicIndex = 0xffffff;
+
+/** This value means that the increment to go from one value to another in a sequence is not constant for each step.
+ */
+const int UndefinedIncr = 0xfffffe;
+
+/** This value means +Infinity; it is currently used only as the p parameter to MatrixBase::lpNorm<int>().
+ * The value Infinity there means the L-infinity norm.
+ */
+const int Infinity = -1;
+
+/** This value means that the cost to evaluate an expression coefficient is either very expensive or
+ * cannot be known at compile time.
+ *
+ * This value has to be positive to (1) simplify cost computation, and (2) allow to distinguish between a very expensive and very very expensive expressions.
+ * It thus must also be large enough to make sure unrolling won't happen and that sub expressions will be evaluated, but not too large to avoid overflow.
+ */
+const int HugeCost = 10000;
+
+/** \defgroup flags Flags
+ * \ingroup Core_Module
+ *
+ * These are the possible bits which can be OR'ed to constitute the flags of a matrix or
+ * expression.
+ *
+ * It is important to note that these flags are a purely compile-time notion. They are a compile-time property of
+ * an expression type, implemented as enum's. They are not stored in memory at runtime, and they do not incur any
+ * runtime overhead.
+ *
+ * \sa MatrixBase::Flags
+ */
+
+/** \ingroup flags
+ *
+ * for a matrix, this means that the storage order is row-major.
+ * If this bit is not set, the storage order is column-major.
+ * For an expression, this determines the storage order of
+ * the matrix created by evaluation of that expression.
+ * \sa \blank \ref TopicStorageOrders */
+const unsigned int RowMajorBit = 0x1;
+
+/** \ingroup flags
+ * means the expression should be evaluated by the calling expression */
+const unsigned int EvalBeforeNestingBit = 0x2;
+
+/** \ingroup flags
+ * \deprecated
+ * means the expression should be evaluated before any assignment */
+EIGEN_DEPRECATED
+const unsigned int EvalBeforeAssigningBit = 0x4; // FIXME deprecated
+
+/** \ingroup flags
+ *
+ * Short version: means the expression might be vectorized
+ *
+ * Long version: means that the coefficients can be handled by packets
+ * and start at a memory location whose alignment meets the requirements
+ * of the present CPU architecture for optimized packet access. In the fixed-size
+ * case, there is the additional condition that it be possible to access all the
+ * coefficients by packets (this implies the requirement that the size be a multiple of 16 bytes,
+ * and that any nontrivial strides don't break the alignment). In the dynamic-size case,
+ * there is no such condition on the total size and strides, so it might not be possible to access
+ * all coeffs by packets.
+ *
+ * \note This bit can be set regardless of whether vectorization is actually enabled.
+ * To check for actual vectorizability, see \a ActualPacketAccessBit.
+ */
+const unsigned int PacketAccessBit = 0x8;
+
+#ifdef EIGEN_VECTORIZE
+/** \ingroup flags
+ *
+ * If vectorization is enabled (EIGEN_VECTORIZE is defined) this constant
+ * is set to the value \a PacketAccessBit.
+ *
+ * If vectorization is not enabled (EIGEN_VECTORIZE is not defined) this constant
+ * is set to the value 0.
+ */
+const unsigned int ActualPacketAccessBit = PacketAccessBit;
+#else
+const unsigned int ActualPacketAccessBit = 0x0;
+#endif
+
+/** \ingroup flags
+ *
+ * Short version: means the expression can be seen as 1D vector.
+ *
+ * Long version: means that one can access the coefficients
+ * of this expression by coeff(int), and coeffRef(int) in the case of a lvalue expression. These
+ * index-based access methods are guaranteed
+ * to not have to do any runtime computation of a (row, col)-pair from the index, so that it
+ * is guaranteed that whenever it is available, index-based access is at least as fast as
+ * (row,col)-based access. Expressions for which that isn't possible don't have the LinearAccessBit.
+ *
+ * If both PacketAccessBit and LinearAccessBit are set, then the
+ * packets of this expression can be accessed by packet(int), and writePacket(int) in the case of a
+ * lvalue expression.
+ *
+ * Typically, all vector expressions have the LinearAccessBit, but there is one exception:
+ * Product expressions don't have it, because it would be troublesome for vectorization, even when the
+ * Product is a vector expression. Thus, vector Product expressions allow index-based coefficient access but
+ * not index-based packet access, so they don't have the LinearAccessBit.
+ */
+const unsigned int LinearAccessBit = 0x10;
+
+/** \ingroup flags
+ *
+ * Means the expression has a coeffRef() method, i.e. is writable as its individual coefficients are directly addressable.
+ * This rules out read-only expressions.
+ *
+ * Note that DirectAccessBit and LvalueBit are mutually orthogonal, as there are examples of expression having one but note
+ * the other:
+ * \li writable expressions that don't have a very simple memory layout as a strided array, have LvalueBit but not DirectAccessBit
+ * \li Map-to-const expressions, for example Map<const Matrix>, have DirectAccessBit but not LvalueBit
+ *
+ * Expressions having LvalueBit also have their coeff() method returning a const reference instead of returning a new value.
+ */
+const unsigned int LvalueBit = 0x20;
+
+/** \ingroup flags
+ *
+ * Means that the underlying array of coefficients can be directly accessed as a plain strided array. The memory layout
+ * of the array of coefficients must be exactly the natural one suggested by rows(), cols(),
+ * outerStride(), innerStride(), and the RowMajorBit. This rules out expressions such as Diagonal, whose coefficients,
+ * though referencable, do not have such a regular memory layout.
+ *
+ * See the comment on LvalueBit for an explanation of how LvalueBit and DirectAccessBit are mutually orthogonal.
+ */
+const unsigned int DirectAccessBit = 0x40;
+
+/** \deprecated \ingroup flags
+ *
+ * means the first coefficient packet is guaranteed to be aligned.
+ * An expression cannot have the AlignedBit without the PacketAccessBit flag.
+ * In other words, this means we are allow to perform an aligned packet access to the first element regardless
+ * of the expression kind:
+ * \code
+ * expression.packet<Aligned>(0);
+ * \endcode
+ */
+EIGEN_DEPRECATED const unsigned int AlignedBit = 0x80;
+
+const unsigned int NestByRefBit = 0x100;
+
+/** \ingroup flags
+ *
+ * for an expression, this means that the storage order
+ * can be either row-major or column-major.
+ * The precise choice will be decided at evaluation time or when
+ * combined with other expressions.
+ * \sa \blank \ref RowMajorBit, \ref TopicStorageOrders */
+const unsigned int NoPreferredStorageOrderBit = 0x200;
+
+/** \ingroup flags
+ *
+ * Means that the underlying coefficients can be accessed through pointers to the sparse (un)compressed storage format,
+ * that is, the expression provides:
+ * \code
+ inline const Scalar* valuePtr() const;
+ inline const Index* innerIndexPtr() const;
+ inline const Index* outerIndexPtr() const;
+ inline const Index* innerNonZeroPtr() const;
+ \endcode
+ */
+const unsigned int CompressedAccessBit = 0x400;
+
+
+// list of flags that are inherited by default
+const unsigned int HereditaryBits = RowMajorBit
+ | EvalBeforeNestingBit;
+
+/** \defgroup enums Enumerations
+ * \ingroup Core_Module
+ *
+ * Various enumerations used in %Eigen. Many of these are used as template parameters.
+ */
+
+/** \ingroup enums
+ * Enum containing possible values for the \c Mode or \c UpLo parameter of
+ * MatrixBase::selfadjointView() and MatrixBase::triangularView(), and selfadjoint solvers. */
+enum UpLoType {
+ /** View matrix as a lower triangular matrix. */
+ Lower=0x1,
+ /** View matrix as an upper triangular matrix. */
+ Upper=0x2,
+ /** %Matrix has ones on the diagonal; to be used in combination with #Lower or #Upper. */
+ UnitDiag=0x4,
+ /** %Matrix has zeros on the diagonal; to be used in combination with #Lower or #Upper. */
+ ZeroDiag=0x8,
+ /** View matrix as a lower triangular matrix with ones on the diagonal. */
+ UnitLower=UnitDiag|Lower,
+ /** View matrix as an upper triangular matrix with ones on the diagonal. */
+ UnitUpper=UnitDiag|Upper,
+ /** View matrix as a lower triangular matrix with zeros on the diagonal. */
+ StrictlyLower=ZeroDiag|Lower,
+ /** View matrix as an upper triangular matrix with zeros on the diagonal. */
+ StrictlyUpper=ZeroDiag|Upper,
+ /** Used in BandMatrix and SelfAdjointView to indicate that the matrix is self-adjoint. */
+ SelfAdjoint=0x10,
+ /** Used to support symmetric, non-selfadjoint, complex matrices. */
+ Symmetric=0x20
+};
+
+/** \ingroup enums
+ * Enum for indicating whether a buffer is aligned or not. */
+enum AlignmentType {
+ Unaligned=0, /**< Data pointer has no specific alignment. */
+ Aligned8=8, /**< Data pointer is aligned on a 8 bytes boundary. */
+ Aligned16=16, /**< Data pointer is aligned on a 16 bytes boundary. */
+ Aligned32=32, /**< Data pointer is aligned on a 32 bytes boundary. */
+ Aligned64=64, /**< Data pointer is aligned on a 64 bytes boundary. */
+ Aligned128=128, /**< Data pointer is aligned on a 128 bytes boundary. */
+ AlignedMask=255,
+ Aligned=16, /**< \deprecated Synonym for Aligned16. */
+#if EIGEN_MAX_ALIGN_BYTES==128
+ AlignedMax = Aligned128
+#elif EIGEN_MAX_ALIGN_BYTES==64
+ AlignedMax = Aligned64
+#elif EIGEN_MAX_ALIGN_BYTES==32
+ AlignedMax = Aligned32
+#elif EIGEN_MAX_ALIGN_BYTES==16
+ AlignedMax = Aligned16
+#elif EIGEN_MAX_ALIGN_BYTES==8
+ AlignedMax = Aligned8
+#elif EIGEN_MAX_ALIGN_BYTES==0
+ AlignedMax = Unaligned
+#else
+#error Invalid value for EIGEN_MAX_ALIGN_BYTES
+#endif
+};
+
+/** \ingroup enums
+ * Enum containing possible values for the \p Direction parameter of
+ * Reverse, PartialReduxExpr and VectorwiseOp. */
+enum DirectionType {
+ /** For Reverse, all columns are reversed;
+ * for PartialReduxExpr and VectorwiseOp, act on columns. */
+ Vertical,
+ /** For Reverse, all rows are reversed;
+ * for PartialReduxExpr and VectorwiseOp, act on rows. */
+ Horizontal,
+ /** For Reverse, both rows and columns are reversed;
+ * not used for PartialReduxExpr and VectorwiseOp. */
+ BothDirections
+};
+
+/** \internal \ingroup enums
+ * Enum to specify how to traverse the entries of a matrix. */
+enum TraversalType {
+ /** \internal Default traversal, no vectorization, no index-based access */
+ DefaultTraversal,
+ /** \internal No vectorization, use index-based access to have only one for loop instead of 2 nested loops */
+ LinearTraversal,
+ /** \internal Equivalent to a slice vectorization for fixed-size matrices having good alignment
+ * and good size */
+ InnerVectorizedTraversal,
+ /** \internal Vectorization path using a single loop plus scalar loops for the
+ * unaligned boundaries */
+ LinearVectorizedTraversal,
+ /** \internal Generic vectorization path using one vectorized loop per row/column with some
+ * scalar loops to handle the unaligned boundaries */
+ SliceVectorizedTraversal,
+ /** \internal Special case to properly handle incompatible scalar types or other defecting cases*/
+ InvalidTraversal,
+ /** \internal Evaluate all entries at once */
+ AllAtOnceTraversal
+};
+
+/** \internal \ingroup enums
+ * Enum to specify whether to unroll loops when traversing over the entries of a matrix. */
+enum UnrollingType {
+ /** \internal Do not unroll loops. */
+ NoUnrolling,
+ /** \internal Unroll only the inner loop, but not the outer loop. */
+ InnerUnrolling,
+ /** \internal Unroll both the inner and the outer loop. If there is only one loop,
+ * because linear traversal is used, then unroll that loop. */
+ CompleteUnrolling
+};
+
+/** \internal \ingroup enums
+ * Enum to specify whether to use the default (built-in) implementation or the specialization. */
+enum SpecializedType {
+ Specialized,
+ BuiltIn
+};
+
+/** \ingroup enums
+ * Enum containing possible values for the \p Options_ template parameter of
+ * Matrix, Array and BandMatrix. */
+enum StorageOptions {
+ /** Storage order is column major (see \ref TopicStorageOrders). */
+ ColMajor = 0,
+ /** Storage order is row major (see \ref TopicStorageOrders). */
+ RowMajor = 0x1, // it is only a coincidence that this is equal to RowMajorBit -- don't rely on that
+ /** Align the matrix itself if it is vectorizable fixed-size */
+ AutoAlign = 0,
+ /** Don't require alignment for the matrix itself (the array of coefficients, if dynamically allocated, may still be requested to be aligned) */ // FIXME --- clarify the situation
+ DontAlign = 0x2
+};
+
+/** \ingroup enums
+ * Enum for specifying whether to apply or solve on the left or right. */
+enum SideType {
+ /** Apply transformation on the left. */
+ OnTheLeft = 1,
+ /** Apply transformation on the right. */
+ OnTheRight = 2
+};
+
+/** \ingroup enums
+ * Enum for specifying NaN-propagation behavior, e.g. for coeff-wise min/max. */
+enum NaNPropagationOptions {
+ /** Implementation defined behavior if NaNs are present. */
+ PropagateFast = 0,
+ /** Always propagate NaNs. */
+ PropagateNaN,
+ /** Always propagate not-NaNs. */
+ PropagateNumbers
+};
+
+/* the following used to be written as:
+ *
+ * struct NoChange_t {};
+ * namespace {
+ * EIGEN_UNUSED NoChange_t NoChange;
+ * }
+ *
+ * on the ground that it feels dangerous to disambiguate overloaded functions on enum/integer types.
+ * However, this leads to "variable declared but never referenced" warnings on Intel Composer XE,
+ * and we do not know how to get rid of them (bug 450).
+ */
+
+enum NoChange_t { NoChange };
+enum Sequential_t { Sequential };
+enum Default_t { Default };
+
+/** \internal \ingroup enums
+ * Used in AmbiVector. */
+enum AmbiVectorMode {
+ IsDense = 0,
+ IsSparse
+};
+
+/** \ingroup enums
+ * Used as template parameter in DenseCoeffBase and MapBase to indicate
+ * which accessors should be provided. */
+enum AccessorLevels {
+ /** Read-only access via a member function. */
+ ReadOnlyAccessors,
+ /** Read/write access via member functions. */
+ WriteAccessors,
+ /** Direct read-only access to the coefficients. */
+ DirectAccessors,
+ /** Direct read/write access to the coefficients. */
+ DirectWriteAccessors
+};
+
+/** \ingroup enums
+ * Enum with options to give to various decompositions. */
+enum DecompositionOptions {
+ /** \internal Not used (meant for LDLT?). */
+ Pivoting = 0x01,
+ /** \internal Not used (meant for LDLT?). */
+ NoPivoting = 0x02,
+ /** Used in JacobiSVD to indicate that the square matrix U is to be computed. */
+ ComputeFullU = 0x04,
+ /** Used in JacobiSVD to indicate that the thin matrix U is to be computed. */
+ ComputeThinU = 0x08,
+ /** Used in JacobiSVD to indicate that the square matrix V is to be computed. */
+ ComputeFullV = 0x10,
+ /** Used in JacobiSVD to indicate that the thin matrix V is to be computed. */
+ ComputeThinV = 0x20,
+ /** Used in SelfAdjointEigenSolver and GeneralizedSelfAdjointEigenSolver to specify
+ * that only the eigenvalues are to be computed and not the eigenvectors. */
+ EigenvaluesOnly = 0x40,
+ /** Used in SelfAdjointEigenSolver and GeneralizedSelfAdjointEigenSolver to specify
+ * that both the eigenvalues and the eigenvectors are to be computed. */
+ ComputeEigenvectors = 0x80,
+ /** \internal */
+ EigVecMask = EigenvaluesOnly | ComputeEigenvectors,
+ /** Used in GeneralizedSelfAdjointEigenSolver to indicate that it should
+ * solve the generalized eigenproblem \f$ Ax = \lambda B x \f$. */
+ Ax_lBx = 0x100,
+ /** Used in GeneralizedSelfAdjointEigenSolver to indicate that it should
+ * solve the generalized eigenproblem \f$ ABx = \lambda x \f$. */
+ ABx_lx = 0x200,
+ /** Used in GeneralizedSelfAdjointEigenSolver to indicate that it should
+ * solve the generalized eigenproblem \f$ BAx = \lambda x \f$. */
+ BAx_lx = 0x400,
+ /** \internal */
+ GenEigMask = Ax_lBx | ABx_lx | BAx_lx
+};
+
+/** \ingroup enums
+ * Possible values for the \p QRPreconditioner template parameter of JacobiSVD. */
+enum QRPreconditioners {
+ /** Use a QR decomposition with column pivoting as the first step. */
+ ColPivHouseholderQRPreconditioner = 0x0,
+ /** Do not specify what is to be done if the SVD of a non-square matrix is asked for. */
+ NoQRPreconditioner = 0x40,
+ /** Use a QR decomposition without pivoting as the first step. */
+ HouseholderQRPreconditioner = 0x80,
+ /** Use a QR decomposition with full pivoting as the first step. */
+ FullPivHouseholderQRPreconditioner = 0xC0,
+ /** Used to disable the QR Preconditioner in BDCSVD. */
+ DisableQRDecomposition = NoQRPreconditioner
+};
+
+#ifdef Success
+#error The preprocessor symbol 'Success' is defined, possibly by the X11 header file X.h
+#endif
+
+/** \ingroup enums
+ * Enum for reporting the status of a computation. */
+enum ComputationInfo {
+ /** Computation was successful. */
+ Success = 0,
+ /** The provided data did not satisfy the prerequisites. */
+ NumericalIssue = 1,
+ /** Iterative procedure did not converge. */
+ NoConvergence = 2,
+ /** The inputs are invalid, or the algorithm has been improperly called.
+ * When assertions are enabled, such errors trigger an assert. */
+ InvalidInput = 3
+};
+
+/** \ingroup enums
+ * Enum used to specify how a particular transformation is stored in a matrix.
+ * \sa Transform, Hyperplane::transform(). */
+enum TransformTraits {
+ /** Transformation is an isometry. */
+ Isometry = 0x1,
+ /** Transformation is an affine transformation stored as a (Dim+1)^2 matrix whose last row is
+ * assumed to be [0 ... 0 1]. */
+ Affine = 0x2,
+ /** Transformation is an affine transformation stored as a (Dim) x (Dim+1) matrix. */
+ AffineCompact = 0x10 | Affine,
+ /** Transformation is a general projective transformation stored as a (Dim+1)^2 matrix. */
+ Projective = 0x20
+};
+
+/** \internal \ingroup enums
+ * Enum used to choose between implementation depending on the computer architecture. */
+namespace Architecture
+{
+ enum Type {
+ Generic = 0x0,
+ SSE = 0x1,
+ AltiVec = 0x2,
+ VSX = 0x3,
+ NEON = 0x4,
+ MSA = 0x5,
+ SVE = 0x6,
+#if defined EIGEN_VECTORIZE_SSE
+ Target = SSE
+#elif defined EIGEN_VECTORIZE_ALTIVEC
+ Target = AltiVec
+#elif defined EIGEN_VECTORIZE_VSX
+ Target = VSX
+#elif defined EIGEN_VECTORIZE_NEON
+ Target = NEON
+#elif defined EIGEN_VECTORIZE_SVE
+ Target = SVE
+#elif defined EIGEN_VECTORIZE_MSA
+ Target = MSA
+#else
+ Target = Generic
+#endif
+ };
+}
+
+/** \internal \ingroup enums
+ * Enum used as template parameter in Product and product evaluators. */
+enum ProductImplType
+{ DefaultProduct=0, LazyProduct, AliasFreeProduct, CoeffBasedProductMode, LazyCoeffBasedProductMode, OuterProduct, InnerProduct, GemvProduct, GemmProduct };
+
+/** \internal \ingroup enums
+ * Enum used in experimental parallel implementation. */
+enum Action {GetAction, SetAction};
+
+/** The type used to identify a dense storage. */
+struct Dense {};
+
+/** The type used to identify a general sparse storage. */
+struct Sparse {};
+
+/** The type used to identify a general solver (factored) storage. */
+struct SolverStorage {};
+
+/** The type used to identify a permutation storage. */
+struct PermutationStorage {};
+
+/** The type used to identify a permutation storage. */
+struct TranspositionsStorage {};
+
+/** The type used to identify a matrix expression */
+struct MatrixXpr {};
+
+/** The type used to identify an array expression */
+struct ArrayXpr {};
+
+// An evaluator must define its shape. By default, it can be one of the following:
+struct DenseShape { static std::string debugName() { return "DenseShape"; } };
+struct SolverShape { static std::string debugName() { return "SolverShape"; } };
+struct HomogeneousShape { static std::string debugName() { return "HomogeneousShape"; } };
+struct DiagonalShape { static std::string debugName() { return "DiagonalShape"; } };
+struct SkewSymmetricShape { static std::string debugName() { return "SkewSymmetricShape"; } };
+struct BandShape { static std::string debugName() { return "BandShape"; } };
+struct TriangularShape { static std::string debugName() { return "TriangularShape"; } };
+struct SelfAdjointShape { static std::string debugName() { return "SelfAdjointShape"; } };
+struct PermutationShape { static std::string debugName() { return "PermutationShape"; } };
+struct TranspositionsShape { static std::string debugName() { return "TranspositionsShape"; } };
+struct SparseShape { static std::string debugName() { return "SparseShape"; } };
+
+namespace internal {
+
+ // random access iterators based on coeff*() accessors.
+struct IndexBased {};
+
+// evaluator based on iterators to access coefficients.
+struct IteratorBased {};
+
+/** \internal
+ * Constants for comparison functors
+ */
+enum ComparisonName : unsigned int {
+ cmp_EQ = 0,
+ cmp_LT = 1,
+ cmp_LE = 2,
+ cmp_UNORD = 3,
+ cmp_NEQ = 4,
+ cmp_GT = 5,
+ cmp_GE = 6
+};
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_CONSTANTS_H
diff --git a/Eigen/src/Core/util/DisableStupidWarnings.h b/Eigen/src/Core/util/DisableStupidWarnings.h
new file mode 100644
index 0000000..0865fb6
--- /dev/null
+++ b/Eigen/src/Core/util/DisableStupidWarnings.h
@@ -0,0 +1,138 @@
+#ifndef EIGEN_WARNINGS_DISABLED
+#define EIGEN_WARNINGS_DISABLED
+
+#if defined(_MSC_VER)
+ // 4100 - unreferenced formal parameter (occurred e.g. in aligned_allocator::destroy(pointer p))
+ // 4101 - unreferenced local variable
+ // 4127 - conditional expression is constant
+ // 4181 - qualifier applied to reference type ignored
+ // 4211 - nonstandard extension used : redefined extern to static
+ // 4244 - 'argument' : conversion from 'type1' to 'type2', possible loss of data
+ // 4273 - QtAlignedMalloc, inconsistent DLL linkage
+ // 4324 - structure was padded due to declspec(align())
+ // 4503 - decorated name length exceeded, name was truncated
+ // 4512 - assignment operator could not be generated
+ // 4522 - 'class' : multiple assignment operators specified
+ // 4700 - uninitialized local variable 'xyz' used
+ // 4714 - function marked as __forceinline not inlined
+ // 4717 - 'function' : recursive on all control paths, function will cause runtime stack overflow
+ // 4800 - 'type' : forcing value to bool 'true' or 'false' (performance warning)
+ #ifndef EIGEN_PERMANENTLY_DISABLE_STUPID_WARNINGS
+ #pragma warning( push )
+ #endif
+ #pragma warning( disable : 4100 4101 4127 4181 4211 4244 4273 4324 4503 4512 4522 4700 4714 4717 4800)
+
+#elif defined __INTEL_COMPILER
+ // 2196 - routine is both "inline" and "noinline" ("noinline" assumed)
+ // ICC 12 generates this warning even without any inline keyword, when defining class methods 'inline' i.e. inside of class body
+ // typedef that may be a reference type.
+ // 279 - controlling expression is constant
+ // ICC 12 generates this warning on assert(constant_expression_depending_on_template_params) and frankly this is a legitimate use case.
+ // 1684 - conversion from pointer to same-sized integral type (potential portability problem)
+ // 2259 - non-pointer conversion from "Eigen::Index={ptrdiff_t={long}}" to "int" may lose significant bits
+ #ifndef EIGEN_PERMANENTLY_DISABLE_STUPID_WARNINGS
+ #pragma warning push
+ #endif
+ #pragma warning disable 2196 279 1684 2259
+
+#elif defined __clang__
+ #ifndef EIGEN_PERMANENTLY_DISABLE_STUPID_WARNINGS
+ #pragma clang diagnostic push
+ #endif
+ #if defined(__has_warning)
+ // -Wconstant-logical-operand - warning: use of logical && with constant operand; switch to bitwise & or remove constant
+ // this is really a stupid warning as it warns on compile-time expressions involving enums
+ #if __has_warning("-Wconstant-logical-operand")
+ #pragma clang diagnostic ignored "-Wconstant-logical-operand"
+ #endif
+ #if __has_warning("-Wimplicit-int-float-conversion")
+ #pragma clang diagnostic ignored "-Wimplicit-int-float-conversion"
+ #endif
+ #if ( defined(__ALTIVEC__) || defined(__VSX__) ) && __cplusplus < 201103L
+ // warning: generic selections are a C11-specific feature
+ // ignoring warnings thrown at vec_ctf in Altivec/PacketMath.h
+ #if __has_warning("-Wc11-extensions")
+ #pragma clang diagnostic ignored "-Wc11-extensions"
+ #endif
+ #endif
+ #endif
+
+#elif defined __GNUC__ && !defined(__FUJITSU)
+
+ #if (!defined(EIGEN_PERMANENTLY_DISABLE_STUPID_WARNINGS)) && (__GNUC__ > 4 || (__GNUC__ == 4 && __GNUC_MINOR__ >= 6))
+ #pragma GCC diagnostic push
+ #endif
+ // g++ warns about local variables shadowing member functions, which is too strict
+ #pragma GCC diagnostic ignored "-Wshadow"
+ #if __GNUC__ == 4 && __GNUC_MINOR__ < 8
+ // Until g++-4.7 there are warnings when comparing unsigned int vs 0, even in templated functions:
+ #pragma GCC diagnostic ignored "-Wtype-limits"
+ #endif
+ #if __GNUC__>=6
+ #pragma GCC diagnostic ignored "-Wignored-attributes"
+ #endif
+ #if __GNUC__==7
+ // See: https://gcc.gnu.org/bugzilla/show_bug.cgi?id=89325
+ #pragma GCC diagnostic ignored "-Wattributes"
+ #endif
+#endif
+
+#if defined __NVCC__
+ // MSVC 14.16 (required by CUDA 9.*) does not support the _Pragma keyword, so
+ // we instead use Microsoft's __pragma extension.
+ #if defined _MSC_VER
+ #define EIGEN_MAKE_PRAGMA(X) __pragma(#X)
+ #else
+ #define EIGEN_MAKE_PRAGMA(X) _Pragma(#X)
+ #endif
+ #if defined __NVCC_DIAG_PRAGMA_SUPPORT__
+ #define EIGEN_NV_DIAG_SUPPRESS(X) EIGEN_MAKE_PRAGMA(nv_diag_suppress X)
+ #else
+ #define EIGEN_NV_DIAG_SUPPRESS(X) EIGEN_MAKE_PRAGMA(diag_suppress X)
+ #endif
+
+ EIGEN_NV_DIAG_SUPPRESS(boolean_controlling_expr_is_constant)
+ // Disable the "statement is unreachable" message
+ EIGEN_NV_DIAG_SUPPRESS(code_is_unreachable)
+ // Disable the "dynamic initialization in unreachable code" message
+ EIGEN_NV_DIAG_SUPPRESS(initialization_not_reachable)
+ // Disable the "invalid error number" message that we get with older versions of nvcc
+ EIGEN_NV_DIAG_SUPPRESS(1222)
+ // Disable the "calling a __host__ function from a __host__ __device__ function is not allowed" messages (yes, there are many of them and they seem to change with every version of the compiler)
+ EIGEN_NV_DIAG_SUPPRESS(2527)
+ EIGEN_NV_DIAG_SUPPRESS(2529)
+ EIGEN_NV_DIAG_SUPPRESS(2651)
+ EIGEN_NV_DIAG_SUPPRESS(2653)
+ EIGEN_NV_DIAG_SUPPRESS(2668)
+ EIGEN_NV_DIAG_SUPPRESS(2669)
+ EIGEN_NV_DIAG_SUPPRESS(2670)
+ EIGEN_NV_DIAG_SUPPRESS(2671)
+ EIGEN_NV_DIAG_SUPPRESS(2735)
+ EIGEN_NV_DIAG_SUPPRESS(2737)
+ EIGEN_NV_DIAG_SUPPRESS(2739)
+ EIGEN_NV_DIAG_SUPPRESS(2885)
+ EIGEN_NV_DIAG_SUPPRESS(2888)
+ EIGEN_NV_DIAG_SUPPRESS(2976)
+ EIGEN_NV_DIAG_SUPPRESS(2979)
+ EIGEN_NV_DIAG_SUPPRESS(20011)
+ EIGEN_NV_DIAG_SUPPRESS(20014)
+ // Disable the "// __device__ annotation is ignored on a function(...) that is
+ // explicitly defaulted on its first declaration" message.
+ // The __device__ annotation seems to actually be needed in some cases,
+ // otherwise resulting in kernel runtime errors.
+ EIGEN_NV_DIAG_SUPPRESS(2886)
+ EIGEN_NV_DIAG_SUPPRESS(2977)
+ EIGEN_NV_DIAG_SUPPRESS(20012)
+ #undef EIGEN_NV_DIAG_SUPPRESS
+ #undef EIGEN_MAKE_PRAGMA
+#endif
+
+#else
+// warnings already disabled:
+# ifndef EIGEN_WARNINGS_DISABLED_2
+# define EIGEN_WARNINGS_DISABLED_2
+# elif defined(EIGEN_INTERNAL_DEBUGGING)
+# error "Do not include \"DisableStupidWarnings.h\" recursively more than twice!"
+# endif
+
+#endif // not EIGEN_WARNINGS_DISABLED
diff --git a/Eigen/src/Core/util/ForwardDeclarations.h b/Eigen/src/Core/util/ForwardDeclarations.h
new file mode 100644
index 0000000..503d651
--- /dev/null
+++ b/Eigen/src/Core/util/ForwardDeclarations.h
@@ -0,0 +1,309 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2007-2010 Benoit Jacob <jacob.benoit.1@gmail.com>
+// Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_FORWARDDECLARATIONS_H
+#define EIGEN_FORWARDDECLARATIONS_H
+
+#include "../InternalHeaderCheck.h"
+
+namespace Eigen {
+namespace internal {
+
+template<typename T> struct traits;
+
+// here we say once and for all that traits<const T> == traits<T>
+// When constness must affect traits, it has to be constness on template parameters on which T itself depends.
+// For example, traits<Map<const T> > != traits<Map<T> >, but
+// traits<const Map<T> > == traits<Map<T> >
+template<typename T> struct traits<const T> : traits<T> {};
+
+template<typename Derived> struct has_direct_access
+{
+ enum { ret = (traits<Derived>::Flags & DirectAccessBit) ? 1 : 0 };
+};
+
+template<typename Derived> struct accessors_level
+{
+ enum { has_direct_access = (traits<Derived>::Flags & DirectAccessBit) ? 1 : 0,
+ has_write_access = (traits<Derived>::Flags & LvalueBit) ? 1 : 0,
+ value = has_direct_access ? (has_write_access ? DirectWriteAccessors : DirectAccessors)
+ : (has_write_access ? WriteAccessors : ReadOnlyAccessors)
+ };
+};
+
+template<typename T> struct evaluator_traits;
+
+template< typename T> struct evaluator;
+
+} // end namespace internal
+
+template<typename T> struct NumTraits;
+
+template<typename Derived> struct EigenBase;
+template<typename Derived> class DenseBase;
+template<typename Derived> class PlainObjectBase;
+template<typename Derived, int Level> class DenseCoeffsBase;
+
+template<typename Scalar_, int Rows_, int Cols_,
+ int Options_ = AutoAlign |
+ ( (Rows_==1 && Cols_!=1) ? Eigen::RowMajor
+ : (Cols_==1 && Rows_!=1) ? Eigen::ColMajor
+ : EIGEN_DEFAULT_MATRIX_STORAGE_ORDER_OPTION ),
+ int MaxRows_ = Rows_,
+ int MaxCols_ = Cols_
+> class Matrix;
+
+template<typename Derived> class MatrixBase;
+template<typename Derived> class ArrayBase;
+
+template<typename ExpressionType, unsigned int Added, unsigned int Removed> class Flagged;
+template<typename ExpressionType, template <typename> class StorageBase > class NoAlias;
+template<typename ExpressionType> class NestByValue;
+template<typename ExpressionType> class ForceAlignedAccess;
+template<typename ExpressionType> class SwapWrapper;
+
+template<typename XprType, int BlockRows=Dynamic, int BlockCols=Dynamic, bool InnerPanel = false> class Block;
+template<typename XprType, typename RowIndices, typename ColIndices> class IndexedView;
+template<typename XprType, int Rows=Dynamic, int Cols=Dynamic, int Order=0> class Reshaped;
+
+template<typename MatrixType, int Size=Dynamic> class VectorBlock;
+template<typename MatrixType> class Transpose;
+template<typename MatrixType> class Conjugate;
+template<typename NullaryOp, typename MatrixType> class CwiseNullaryOp;
+template<typename UnaryOp, typename MatrixType> class CwiseUnaryOp;
+template<typename BinaryOp, typename Lhs, typename Rhs> class CwiseBinaryOp;
+template<typename TernaryOp, typename Arg1, typename Arg2, typename Arg3> class CwiseTernaryOp;
+template<typename Decomposition, typename Rhstype> class Solve;
+template<typename XprType> class Inverse;
+
+template<typename Lhs, typename Rhs, int Option = DefaultProduct> class Product;
+
+template<typename Derived> class DiagonalBase;
+template<typename DiagonalVectorType_> class DiagonalWrapper;
+template<typename Scalar_, int SizeAtCompileTime, int MaxSizeAtCompileTime=SizeAtCompileTime> class DiagonalMatrix;
+template<typename MatrixType, typename DiagonalType, int ProductOrder> class DiagonalProduct;
+template<typename MatrixType, int Index = 0> class Diagonal;
+template<typename Derived> class SkewSymmetricBase;
+template<typename VectorType_> class SkewSymmetricWrapper;
+template<typename Scalar_> class SkewSymmetricMatrix3;
+template<int SizeAtCompileTime, int MaxSizeAtCompileTime = SizeAtCompileTime, typename IndexType=int> class PermutationMatrix;
+template<int SizeAtCompileTime, int MaxSizeAtCompileTime = SizeAtCompileTime, typename IndexType=int> class Transpositions;
+template<typename Derived> class PermutationBase;
+template<typename Derived> class TranspositionsBase;
+template<typename IndicesType_> class PermutationWrapper;
+template<typename IndicesType_> class TranspositionsWrapper;
+
+template<typename Derived,
+ int Level = internal::accessors_level<Derived>::has_write_access ? WriteAccessors : ReadOnlyAccessors
+> class MapBase;
+template<int OuterStrideAtCompileTime, int InnerStrideAtCompileTime> class Stride;
+template<int Value = Dynamic> class InnerStride;
+template<int Value = Dynamic> class OuterStride;
+template<typename MatrixType, int MapOptions=Unaligned, typename StrideType = Stride<0,0> > class Map;
+template<typename Derived> class RefBase;
+template<typename PlainObjectType, int Options = 0,
+ typename StrideType = typename std::conditional_t<PlainObjectType::IsVectorAtCompileTime,InnerStride<1>,OuterStride<> > > class Ref;
+template<typename ViewOp, typename MatrixType, typename StrideType = Stride<0,0>> class CwiseUnaryView;
+
+template<typename Derived> class TriangularBase;
+template<typename MatrixType, unsigned int Mode> class TriangularView;
+template<typename MatrixType, unsigned int Mode> class SelfAdjointView;
+template<typename MatrixType> class SparseView;
+template<typename ExpressionType> class WithFormat;
+template<typename MatrixType> struct CommaInitializer;
+template<typename Derived> class ReturnByValue;
+template<typename ExpressionType> class ArrayWrapper;
+template<typename ExpressionType> class MatrixWrapper;
+template<typename Derived> class SolverBase;
+template<typename XprType> class InnerIterator;
+
+namespace internal {
+template<typename XprType> class generic_randaccess_stl_iterator;
+template<typename XprType> class pointer_based_stl_iterator;
+template<typename XprType, DirectionType Direction> class subvector_stl_iterator;
+template<typename XprType, DirectionType Direction> class subvector_stl_reverse_iterator;
+template<typename DecompositionType> struct kernel_retval_base;
+template<typename DecompositionType> struct kernel_retval;
+template<typename DecompositionType> struct image_retval_base;
+template<typename DecompositionType> struct image_retval;
+} // end namespace internal
+
+namespace internal {
+template<typename Scalar_, int Rows=Dynamic, int Cols=Dynamic, int Supers=Dynamic, int Subs=Dynamic, int Options=0> class BandMatrix;
+}
+
+namespace internal {
+template<typename Lhs, typename Rhs> struct product_type;
+
+template<bool> struct EnableIf;
+
+/** \internal
+ * \class product_evaluator
+ * Products need their own evaluator with more template arguments allowing for
+ * easier partial template specializations.
+ */
+template< typename T,
+ int ProductTag = internal::product_type<typename T::Lhs,typename T::Rhs>::ret,
+ typename LhsShape = typename evaluator_traits<typename T::Lhs>::Shape,
+ typename RhsShape = typename evaluator_traits<typename T::Rhs>::Shape,
+ typename LhsScalar = typename traits<typename T::Lhs>::Scalar,
+ typename RhsScalar = typename traits<typename T::Rhs>::Scalar
+ > struct product_evaluator;
+}
+
+template<typename Lhs, typename Rhs,
+ int ProductType = internal::product_type<Lhs,Rhs>::value>
+struct ProductReturnType;
+
+// this is a workaround for sun CC
+template<typename Lhs, typename Rhs> struct LazyProductReturnType;
+
+namespace internal {
+
+// Provides scalar/packet-wise product and product with accumulation
+// with optional conjugation of the arguments.
+template<typename LhsScalar, typename RhsScalar, bool ConjLhs=false, bool ConjRhs=false> struct conj_helper;
+
+template<typename LhsScalar,typename RhsScalar=LhsScalar> struct scalar_sum_op;
+template<typename LhsScalar,typename RhsScalar=LhsScalar> struct scalar_difference_op;
+template<typename LhsScalar,typename RhsScalar=LhsScalar> struct scalar_conj_product_op;
+template<typename LhsScalar,typename RhsScalar=LhsScalar, int NaNPropagation=PropagateFast> struct scalar_min_op;
+template<typename LhsScalar,typename RhsScalar=LhsScalar, int NaNPropagation=PropagateFast> struct scalar_max_op;
+template<typename Scalar> struct scalar_opposite_op;
+template<typename Scalar> struct scalar_conjugate_op;
+template<typename Scalar> struct scalar_real_op;
+template<typename Scalar> struct scalar_imag_op;
+template<typename Scalar> struct scalar_abs_op;
+template<typename Scalar> struct scalar_abs2_op;
+template<typename LhsScalar,typename RhsScalar=LhsScalar> struct scalar_absolute_difference_op;
+template<typename Scalar> struct scalar_sqrt_op;
+template<typename Scalar> struct scalar_rsqrt_op;
+template<typename Scalar> struct scalar_exp_op;
+template<typename Scalar> struct scalar_log_op;
+template<typename Scalar> struct scalar_cos_op;
+template<typename Scalar> struct scalar_sin_op;
+template<typename Scalar> struct scalar_acos_op;
+template<typename Scalar> struct scalar_asin_op;
+template<typename Scalar> struct scalar_tan_op;
+template<typename Scalar> struct scalar_inverse_op;
+template<typename Scalar> struct scalar_square_op;
+template<typename Scalar> struct scalar_cube_op;
+template<typename Scalar, typename NewType> struct scalar_cast_op;
+template<typename Scalar> struct scalar_random_op;
+template<typename Scalar> struct scalar_constant_op;
+template<typename Scalar> struct scalar_identity_op;
+template<typename Scalar> struct scalar_sign_op;
+template <typename Scalar, typename ScalarExponent>
+struct scalar_pow_op;
+template <typename Scalar, typename ScalarExponent, bool BaseIsInteger, bool ExponentIsInteger, bool BaseIsComplex,
+ bool ExponentIsComplex>
+struct scalar_unary_pow_op;
+template<typename LhsScalar,typename RhsScalar=LhsScalar> struct scalar_hypot_op;
+template<typename LhsScalar,typename RhsScalar=LhsScalar> struct scalar_product_op;
+template<typename LhsScalar,typename RhsScalar=LhsScalar> struct scalar_quotient_op;
+
+// SpecialFunctions module
+template<typename Scalar> struct scalar_lgamma_op;
+template<typename Scalar> struct scalar_digamma_op;
+template<typename Scalar> struct scalar_erf_op;
+template<typename Scalar> struct scalar_erfc_op;
+template<typename Scalar> struct scalar_ndtri_op;
+template<typename Scalar> struct scalar_igamma_op;
+template<typename Scalar> struct scalar_igammac_op;
+template<typename Scalar> struct scalar_zeta_op;
+template<typename Scalar> struct scalar_betainc_op;
+
+// Bessel functions in SpecialFunctions module
+template<typename Scalar> struct scalar_bessel_i0_op;
+template<typename Scalar> struct scalar_bessel_i0e_op;
+template<typename Scalar> struct scalar_bessel_i1_op;
+template<typename Scalar> struct scalar_bessel_i1e_op;
+template<typename Scalar> struct scalar_bessel_j0_op;
+template<typename Scalar> struct scalar_bessel_y0_op;
+template<typename Scalar> struct scalar_bessel_j1_op;
+template<typename Scalar> struct scalar_bessel_y1_op;
+template<typename Scalar> struct scalar_bessel_k0_op;
+template<typename Scalar> struct scalar_bessel_k0e_op;
+template<typename Scalar> struct scalar_bessel_k1_op;
+template<typename Scalar> struct scalar_bessel_k1e_op;
+
+
+} // end namespace internal
+
+struct IOFormat;
+
+// Array module
+template<typename Scalar_, int Rows_, int Cols_,
+ int Options_ = AutoAlign |
+ ( (Rows_==1 && Cols_!=1) ? Eigen::RowMajor
+ : (Cols_==1 && Rows_!=1) ? Eigen::ColMajor
+ : EIGEN_DEFAULT_MATRIX_STORAGE_ORDER_OPTION ),
+ int MaxRows_ = Rows_, int MaxCols_ = Cols_> class Array;
+template<typename ConditionMatrixType, typename ThenMatrixType, typename ElseMatrixType> class Select;
+template<typename MatrixType, typename BinaryOp, int Direction> class PartialReduxExpr;
+template<typename ExpressionType, int Direction> class VectorwiseOp;
+template<typename MatrixType,int RowFactor,int ColFactor> class Replicate;
+template<typename MatrixType, int Direction = BothDirections> class Reverse;
+
+template<typename MatrixType> class FullPivLU;
+template<typename MatrixType> class PartialPivLU;
+namespace internal {
+template<typename MatrixType> struct inverse_impl;
+}
+template<typename MatrixType> class HouseholderQR;
+template<typename MatrixType> class ColPivHouseholderQR;
+template<typename MatrixType> class FullPivHouseholderQR;
+template<typename MatrixType> class CompleteOrthogonalDecomposition;
+template<typename MatrixType> class SVDBase;
+template<typename MatrixType, int Options = 0> class JacobiSVD;
+template<typename MatrixType, int Options = 0> class BDCSVD;
+template<typename MatrixType, int UpLo = Lower> class LLT;
+template<typename MatrixType, int UpLo = Lower> class LDLT;
+template<typename VectorsType, typename CoeffsType, int Side=OnTheLeft> class HouseholderSequence;
+template<typename Scalar> class JacobiRotation;
+
+// Geometry module:
+template<typename Derived, int Dim_> class RotationBase;
+template<typename Lhs, typename Rhs> class Cross;
+template<typename Derived> class QuaternionBase;
+template<typename Scalar> class Rotation2D;
+template<typename Scalar> class AngleAxis;
+template<typename Scalar,int Dim> class Translation;
+template<typename Scalar,int Dim> class AlignedBox;
+template<typename Scalar, int Options = AutoAlign> class Quaternion;
+template<typename Scalar,int Dim,int Mode,int Options_=AutoAlign> class Transform;
+template <typename Scalar_, int AmbientDim_, int Options=AutoAlign> class ParametrizedLine;
+template <typename Scalar_, int AmbientDim_, int Options=AutoAlign> class Hyperplane;
+template<typename Scalar> class UniformScaling;
+template<typename MatrixType,int Direction> class Homogeneous;
+
+// Sparse module:
+template<typename Derived> class SparseMatrixBase;
+
+// MatrixFunctions module
+template<typename Derived> struct MatrixExponentialReturnValue;
+template<typename Derived> class MatrixFunctionReturnValue;
+template<typename Derived> class MatrixSquareRootReturnValue;
+template<typename Derived> class MatrixLogarithmReturnValue;
+template<typename Derived> class MatrixPowerReturnValue;
+template<typename Derived> class MatrixComplexPowerReturnValue;
+
+namespace internal {
+template <typename Scalar>
+struct stem_function
+{
+ typedef std::complex<typename NumTraits<Scalar>::Real> ComplexScalar;
+ typedef ComplexScalar type(ComplexScalar, int);
+};
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_FORWARDDECLARATIONS_H
diff --git a/Eigen/src/Core/util/IndexedViewHelper.h b/Eigen/src/Core/util/IndexedViewHelper.h
new file mode 100644
index 0000000..19fa45d
--- /dev/null
+++ b/Eigen/src/Core/util/IndexedViewHelper.h
@@ -0,0 +1,195 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2017 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+
+#ifndef EIGEN_INDEXED_VIEW_HELPER_H
+#define EIGEN_INDEXED_VIEW_HELPER_H
+
+#include "../InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+struct symbolic_last_tag {};
+} // namespace internal
+
+namespace placeholders {
+
+typedef symbolic::SymbolExpr<internal::symbolic_last_tag> last_t;
+
+/** \var last
+ * \ingroup Core_Module
+ *
+ * Can be used as a parameter to Eigen::seq and Eigen::seqN functions to symbolically reference the last element/row/columns
+ * of the underlying vector or matrix once passed to DenseBase::operator()(const RowIndices&, const ColIndices&).
+ *
+ * This symbolic placeholder supports standard arithmetic operations.
+ *
+ * A typical usage example would be:
+ * \code
+ * using namespace Eigen;
+ * using Eigen::placeholders::last;
+ * VectorXd v(n);
+ * v(seq(2,last-2)).setOnes();
+ * \endcode
+ *
+ * \sa end
+ */
+static const last_t last;
+
+} // namespace placeholders
+
+namespace internal {
+
+// Replace symbolic last/end "keywords" by their true runtime value
+inline Index eval_expr_given_size(Index x, Index /* size */) { return x; }
+
+template<int N>
+FixedInt<N> eval_expr_given_size(FixedInt<N> x, Index /*size*/) { return x; }
+
+template<typename Derived>
+Index eval_expr_given_size(const symbolic::BaseExpr<Derived> &x, Index size)
+{
+ return x.derived().eval(Eigen::placeholders::last=size-1);
+}
+
+// Extract increment/step at compile time
+template<typename T, typename EnableIf = void> struct get_compile_time_incr {
+ enum { value = UndefinedIncr };
+};
+
+// Analogue of std::get<0>(x), but tailored for our needs.
+template<typename T>
+EIGEN_CONSTEXPR Index first(const T& x) EIGEN_NOEXCEPT { return x.first(); }
+
+// IndexedViewCompatibleType/makeIndexedViewCompatible turn an arbitrary object of type T into something usable by MatrixSlice
+// The generic implementation is a no-op
+template<typename T,int XprSize,typename EnableIf=void>
+struct IndexedViewCompatibleType {
+ typedef T type;
+};
+
+template<typename T,typename Q>
+const T& makeIndexedViewCompatible(const T& x, Index /*size*/, Q) { return x; }
+
+//--------------------------------------------------------------------------------
+// Handling of a single Index
+//--------------------------------------------------------------------------------
+
+struct SingleRange {
+ enum {
+ SizeAtCompileTime = 1
+ };
+ SingleRange(Index val) : m_value(val) {}
+ Index operator[](Index) const { return m_value; }
+ static EIGEN_CONSTEXPR Index size() EIGEN_NOEXCEPT { return 1; }
+ Index first() const EIGEN_NOEXCEPT { return m_value; }
+ Index m_value;
+};
+
+template<> struct get_compile_time_incr<SingleRange> {
+ enum { value = 1 }; // 1 or 0 ??
+};
+
+// Turn a single index into something that looks like an array (i.e., that exposes a .size(), and operator[](int) methods)
+template<typename T, int XprSize>
+struct IndexedViewCompatibleType<T,XprSize,std::enable_if_t<internal::is_integral<T>::value>> {
+ // Here we could simply use Array, but maybe it's less work for the compiler to use
+ // a simpler wrapper as SingleRange
+ //typedef Eigen::Array<Index,1,1> type;
+ typedef SingleRange type;
+};
+
+template<typename T, int XprSize>
+struct IndexedViewCompatibleType<T, XprSize, std::enable_if_t<symbolic::is_symbolic<T>::value>> {
+ typedef SingleRange type;
+};
+
+
+template<typename T>
+std::enable_if_t<symbolic::is_symbolic<T>::value,SingleRange>
+makeIndexedViewCompatible(const T& id, Index size, SpecializedType) {
+ return eval_expr_given_size(id,size);
+}
+
+//--------------------------------------------------------------------------------
+// Handling of all
+//--------------------------------------------------------------------------------
+
+struct all_t { all_t() {} };
+
+// Convert a symbolic 'all' into a usable range type
+template<int XprSize>
+struct AllRange {
+ enum { SizeAtCompileTime = XprSize };
+ AllRange(Index size = XprSize) : m_size(size) {}
+ EIGEN_CONSTEXPR Index operator[](Index i) const EIGEN_NOEXCEPT { return i; }
+ EIGEN_CONSTEXPR Index size() const EIGEN_NOEXCEPT { return m_size.value(); }
+ EIGEN_CONSTEXPR Index first() const EIGEN_NOEXCEPT { return 0; }
+ variable_if_dynamic<Index,XprSize> m_size;
+};
+
+template<int XprSize>
+struct IndexedViewCompatibleType<all_t,XprSize> {
+ typedef AllRange<XprSize> type;
+};
+
+template<typename XprSizeType>
+inline AllRange<get_fixed_value<XprSizeType>::value> makeIndexedViewCompatible(all_t , XprSizeType size, SpecializedType) {
+ return AllRange<get_fixed_value<XprSizeType>::value>(size);
+}
+
+template<int Size> struct get_compile_time_incr<AllRange<Size> > {
+ enum { value = 1 };
+};
+
+} // end namespace internal
+
+namespace placeholders {
+
+typedef symbolic::AddExpr<symbolic::SymbolExpr<internal::symbolic_last_tag>,symbolic::ValueExpr<Eigen::internal::FixedInt<1> > > lastp1_t;
+typedef Eigen::internal::all_t all_t;
+
+/** \var lastp1
+ * \ingroup Core_Module
+ *
+ * Can be used as a parameter to Eigen::seq and Eigen::seqN functions to symbolically
+ * reference the last+1 element/row/columns of the underlying vector or matrix once
+ * passed to DenseBase::operator()(const RowIndices&, const ColIndices&).
+ *
+ * This symbolic placeholder supports standard arithmetic operations.
+ * It is essentially an alias to last+fix<1>.
+ *
+ * \sa last
+ */
+#ifdef EIGEN_PARSED_BY_DOXYGEN
+static const auto lastp1 = last+fix<1>;
+#else
+// Using a FixedExpr<1> expression is important here to make sure the compiler
+// can fully optimize the computation starting indices with zero overhead.
+static const lastp1_t lastp1(last+fix<1>());
+#endif
+
+/** \var end
+ * \ingroup Core_Module
+ * \sa lastp1
+ */
+static const lastp1_t end = lastp1;
+
+/** \var all
+ * \ingroup Core_Module
+ * Can be used as a parameter to DenseBase::operator()(const RowIndices&, const ColIndices&) to index all rows or columns
+ */
+static const Eigen::internal::all_t all;
+
+} // namespace placeholders
+
+} // end namespace Eigen
+
+#endif // EIGEN_INDEXED_VIEW_HELPER_H
diff --git a/Eigen/src/Core/util/IntegralConstant.h b/Eigen/src/Core/util/IntegralConstant.h
new file mode 100644
index 0000000..ea275bd
--- /dev/null
+++ b/Eigen/src/Core/util/IntegralConstant.h
@@ -0,0 +1,252 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2017 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+
+#ifndef EIGEN_INTEGRAL_CONSTANT_H
+#define EIGEN_INTEGRAL_CONSTANT_H
+
+#include "../InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+
+template<int N> class FixedInt;
+template<int N> class VariableAndFixedInt;
+
+/** \internal
+ * \class FixedInt
+ *
+ * This class embeds a compile-time integer \c N.
+ *
+ * It is similar to c++11 std::integral_constant<int,N> but with some additional features
+ * such as:
+ * - implicit conversion to int
+ * - arithmetic and some bitwise operators: -, +, *, /, %, &, |
+ * - c++98/14 compatibility with fix<N> and fix<N>() syntax to define integral constants.
+ *
+ * It is strongly discouraged to directly deal with this class FixedInt. Instances are expected to
+ * be created by the user using Eigen::fix<N> or Eigen::fix<N>().
+ * \code
+ * internal::cleanup_index_type<T>::type
+ * internal::cleanup_index_type<T,DynamicKey>::type
+ * \endcode
+ * where T can a FixedInt<N>, a pointer to function FixedInt<N> (*)(), or numerous other integer-like representations.
+ * \c DynamicKey is either Dynamic (default) or DynamicIndex and used to identify true compile-time values.
+ *
+ * For convenience, you can extract the compile-time value \c N in a generic way using the following helper:
+ * \code
+ * internal::get_fixed_value<T,DefaultVal>::value
+ * \endcode
+ * that will give you \c N if T equals FixedInt<N> or FixedInt<N> (*)(), and \c DefaultVal if T does not embed any compile-time value (e.g., T==int).
+ *
+ * \sa fix<N>, class VariableAndFixedInt
+ */
+template<int N> class FixedInt
+{
+public:
+ static const int value = N;
+ EIGEN_CONSTEXPR operator int() const { return value; }
+
+ EIGEN_CONSTEXPR
+ FixedInt() = default;
+
+ EIGEN_CONSTEXPR
+ FixedInt(std::integral_constant<int,N>) {}
+
+ EIGEN_CONSTEXPR
+ FixedInt( VariableAndFixedInt<N> other) {
+ #ifndef EIGEN_INTERNAL_DEBUGGING
+ EIGEN_UNUSED_VARIABLE(other);
+ #endif
+ eigen_internal_assert(int(other)==N);
+ }
+
+ EIGEN_CONSTEXPR
+ FixedInt<-N> operator-() const { return FixedInt<-N>(); }
+
+ template<int M>
+ EIGEN_CONSTEXPR
+ FixedInt<N+M> operator+( FixedInt<M>) const { return FixedInt<N+M>(); }
+
+ template<int M>
+ EIGEN_CONSTEXPR
+ FixedInt<N-M> operator-( FixedInt<M>) const { return FixedInt<N-M>(); }
+
+ template<int M>
+ EIGEN_CONSTEXPR
+ FixedInt<N*M> operator*( FixedInt<M>) const { return FixedInt<N*M>(); }
+
+ template<int M>
+ EIGEN_CONSTEXPR
+ FixedInt<N/M> operator/( FixedInt<M>) const { return FixedInt<N/M>(); }
+
+ template<int M>
+ EIGEN_CONSTEXPR
+ FixedInt<N%M> operator%( FixedInt<M>) const { return FixedInt<N%M>(); }
+
+ template<int M>
+ EIGEN_CONSTEXPR
+ FixedInt<N|M> operator|( FixedInt<M>) const { return FixedInt<N|M>(); }
+
+ template<int M>
+ EIGEN_CONSTEXPR
+ FixedInt<N&M> operator&( FixedInt<M>) const { return FixedInt<N&M>(); }
+
+ // Needed in C++14 to allow fix<N>():
+ EIGEN_CONSTEXPR FixedInt operator() () const { return *this; }
+
+ VariableAndFixedInt<N> operator() (int val) const { return VariableAndFixedInt<N>(val); }
+};
+
+/** \internal
+ * \class VariableAndFixedInt
+ *
+ * This class embeds both a compile-time integer \c N and a runtime integer.
+ * Both values are supposed to be equal unless the compile-time value \c N has a special
+ * value meaning that the runtime-value should be used. Depending on the context, this special
+ * value can be either Eigen::Dynamic (for positive quantities) or Eigen::DynamicIndex (for
+ * quantities that can be negative).
+ *
+ * It is the return-type of the function Eigen::fix<N>(int), and most of the time this is the only
+ * way it is used. It is strongly discouraged to directly deal with instances of VariableAndFixedInt.
+ * Indeed, in order to write generic code, it is the responsibility of the callee to properly convert
+ * it to either a true compile-time quantity (i.e. a FixedInt<N>), or to a runtime quantity (e.g., an Index)
+ * using the following generic helper:
+ * \code
+ * internal::cleanup_index_type<T>::type
+ * internal::cleanup_index_type<T,DynamicKey>::type
+ * \endcode
+ * where T can be a template instantiation of VariableAndFixedInt or numerous other integer-like representations.
+ * \c DynamicKey is either Dynamic (default) or DynamicIndex and used to identify true compile-time values.
+ *
+ * For convenience, you can also extract the compile-time value \c N using the following helper:
+ * \code
+ * internal::get_fixed_value<T,DefaultVal>::value
+ * \endcode
+ * that will give you \c N if T equals VariableAndFixedInt<N>, and \c DefaultVal if T does not embed any compile-time value (e.g., T==int).
+ *
+ * \sa fix<N>(int), class FixedInt
+ */
+template<int N> class VariableAndFixedInt
+{
+public:
+ static const int value = N;
+ operator int() const { return m_value; }
+ VariableAndFixedInt(int val) { m_value = val; }
+protected:
+ int m_value;
+};
+
+template<typename T, int Default=Dynamic> struct get_fixed_value {
+ static const int value = Default;
+};
+
+template<int N,int Default> struct get_fixed_value<FixedInt<N>,Default> {
+ static const int value = N;
+};
+
+template<int N,int Default> struct get_fixed_value<VariableAndFixedInt<N>,Default> {
+ static const int value = N ;
+};
+
+template<typename T, int N, int Default>
+struct get_fixed_value<variable_if_dynamic<T,N>,Default> {
+ static const int value = N;
+};
+
+template<typename T> EIGEN_DEVICE_FUNC Index get_runtime_value(const T &x) { return x; }
+
+// Cleanup integer/FixedInt/VariableAndFixedInt/etc types:
+
+// By default, no cleanup:
+template<typename T, int DynamicKey=Dynamic, typename EnableIf=void> struct cleanup_index_type { typedef T type; };
+
+// Convert any integral type (e.g., short, int, unsigned int, etc.) to Eigen::Index
+template<typename T, int DynamicKey> struct cleanup_index_type<T,DynamicKey,std::enable_if_t<internal::is_integral<T>::value>> { typedef Index type; };
+
+// If VariableAndFixedInt does not match DynamicKey, then we turn it to a pure compile-time value:
+template<int N, int DynamicKey> struct cleanup_index_type<VariableAndFixedInt<N>, DynamicKey> { typedef FixedInt<N> type; };
+// If VariableAndFixedInt matches DynamicKey, then we turn it to a pure runtime-value (aka Index):
+template<int DynamicKey> struct cleanup_index_type<VariableAndFixedInt<DynamicKey>, DynamicKey> { typedef Index type; };
+
+template<int N, int DynamicKey> struct cleanup_index_type<std::integral_constant<int,N>, DynamicKey> { typedef FixedInt<N> type; };
+
+} // end namespace internal
+
+#ifndef EIGEN_PARSED_BY_DOXYGEN
+
+template<int N>
+constexpr internal::FixedInt<N> fix{};
+
+#else // EIGEN_PARSED_BY_DOXYGEN
+
+/** \var fix<N>()
+ * \ingroup Core_Module
+ *
+ * This \em identifier permits to construct an object embedding a compile-time integer \c N.
+ *
+ * \tparam N the compile-time integer value
+ *
+ * It is typically used in conjunction with the Eigen::seq and Eigen::seqN functions to pass compile-time values to them:
+ * \code
+ * seqN(10,fix<4>,fix<-3>) // <=> [10 7 4 1]
+ * \endcode
+ *
+ * See also the function fix(int) to pass both a compile-time and runtime value.
+ *
+ * In c++14, it is implemented as:
+ * \code
+ * template<int N> static const internal::FixedInt<N> fix{};
+ * \endcode
+ * where internal::FixedInt<N> is an internal template class similar to
+ * <a href="http://en.cppreference.com/w/cpp/types/integral_constant">\c std::integral_constant </a><tt> <int,N> </tt>
+ * Here, \c fix<N> is thus an object of type \c internal::FixedInt<N>.
+ *
+ * \sa fix<N>(int), seq, seqN
+ */
+template<int N>
+static const auto fix();
+
+/** \fn fix<N>(int)
+ * \ingroup Core_Module
+ *
+ * This function returns an object embedding both a compile-time integer \c N, and a fallback runtime value \a val.
+ *
+ * \tparam N the compile-time integer value
+ * \param val the fallback runtime integer value
+ *
+ * This function is a more general version of the \ref fix identifier/function that can be used in template code
+ * where the compile-time value could turn out to actually mean "undefined at compile-time". For positive integers
+ * such as a size or a dimension, this case is identified by Eigen::Dynamic, whereas runtime signed integers
+ * (e.g., an increment/stride) are identified as Eigen::DynamicIndex. In such a case, the runtime value \a val
+ * will be used as a fallback.
+ *
+ * A typical use case would be:
+ * \code
+ * template<typename Derived> void foo(const MatrixBase<Derived> &mat) {
+ * const int N = Derived::RowsAtCompileTime==Dynamic ? Dynamic : Derived::RowsAtCompileTime/2;
+ * const int n = mat.rows()/2;
+ * ... mat( seqN(0,fix<N>(n) ) ...;
+ * }
+ * \endcode
+ * In this example, the function Eigen::seqN knows that the second argument is expected to be a size.
+ * If the passed compile-time value N equals Eigen::Dynamic, then the proxy object returned by fix will be dissmissed, and converted to an Eigen::Index of value \c n.
+ * Otherwise, the runtime-value \c n will be dissmissed, and the returned ArithmeticSequence will be of the exact same type as <tt> seqN(0,fix<N>) </tt>.
+ *
+ * \sa fix, seqN, class ArithmeticSequence
+ */
+template<int N>
+static const auto fix(int val);
+
+#endif // EIGEN_PARSED_BY_DOXYGEN
+
+} // end namespace Eigen
+
+#endif // EIGEN_INTEGRAL_CONSTANT_H
diff --git a/Eigen/src/Core/util/MKL_support.h b/Eigen/src/Core/util/MKL_support.h
new file mode 100644
index 0000000..9cf5f6f
--- /dev/null
+++ b/Eigen/src/Core/util/MKL_support.h
@@ -0,0 +1,139 @@
+/*
+ Copyright (c) 2011, Intel Corporation. All rights reserved.
+
+ Redistribution and use in source and binary forms, with or without modification,
+ are permitted provided that the following conditions are met:
+
+ * Redistributions of source code must retain the above copyright notice, this
+ list of conditions and the following disclaimer.
+ * Redistributions in binary form must reproduce the above copyright notice,
+ this list of conditions and the following disclaimer in the documentation
+ and/or other materials provided with the distribution.
+ * Neither the name of Intel Corporation nor the names of its contributors may
+ be used to endorse or promote products derived from this software without
+ specific prior written permission.
+
+ THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
+ ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
+ WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
+ DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR
+ ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
+ (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
+ LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON
+ ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
+ (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
+ SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+
+ ********************************************************************************
+ * Content : Eigen bindings to Intel(R) MKL
+ * Include file with common MKL declarations
+ ********************************************************************************
+*/
+
+#ifndef EIGEN_MKL_SUPPORT_H
+#define EIGEN_MKL_SUPPORT_H
+
+#ifdef EIGEN_USE_MKL_ALL
+ #ifndef EIGEN_USE_BLAS
+ #define EIGEN_USE_BLAS
+ #endif
+ #ifndef EIGEN_USE_LAPACKE
+ #define EIGEN_USE_LAPACKE
+ #endif
+ #ifndef EIGEN_USE_MKL_VML
+ #define EIGEN_USE_MKL_VML
+ #endif
+#endif
+
+#ifdef EIGEN_USE_LAPACKE_STRICT
+ #define EIGEN_USE_LAPACKE
+#endif
+
+#if defined(EIGEN_USE_MKL_VML) && !defined(EIGEN_USE_MKL)
+ #define EIGEN_USE_MKL
+#endif
+
+
+#if defined EIGEN_USE_MKL
+# if (!defined MKL_DIRECT_CALL) && (!defined EIGEN_MKL_NO_DIRECT_CALL)
+# define MKL_DIRECT_CALL
+# define MKL_DIRECT_CALL_JUST_SET
+# endif
+# include <mkl.h>
+/*Check IMKL version for compatibility: < 10.3 is not usable with Eigen*/
+# ifndef INTEL_MKL_VERSION
+# undef EIGEN_USE_MKL /* INTEL_MKL_VERSION is not even defined on older versions */
+# elif INTEL_MKL_VERSION < 100305 /* the intel-mkl-103-release-notes say this was when the lapacke.h interface was added*/
+# undef EIGEN_USE_MKL
+# endif
+# ifndef EIGEN_USE_MKL
+ /*If the MKL version is too old, undef everything*/
+# undef EIGEN_USE_MKL_ALL
+# undef EIGEN_USE_LAPACKE
+# undef EIGEN_USE_MKL_VML
+# undef EIGEN_USE_LAPACKE_STRICT
+# undef EIGEN_USE_LAPACKE
+# ifdef MKL_DIRECT_CALL_JUST_SET
+# undef MKL_DIRECT_CALL
+# endif
+# endif
+#endif
+
+#if defined EIGEN_USE_MKL
+
+#define EIGEN_MKL_VML_THRESHOLD 128
+
+/* MKL_DOMAIN_BLAS, etc are defined only in 10.3 update 7 */
+/* MKL_BLAS, etc are not defined in 11.2 */
+#ifdef MKL_DOMAIN_ALL
+#define EIGEN_MKL_DOMAIN_ALL MKL_DOMAIN_ALL
+#else
+#define EIGEN_MKL_DOMAIN_ALL MKL_ALL
+#endif
+
+#ifdef MKL_DOMAIN_BLAS
+#define EIGEN_MKL_DOMAIN_BLAS MKL_DOMAIN_BLAS
+#else
+#define EIGEN_MKL_DOMAIN_BLAS MKL_BLAS
+#endif
+
+#ifdef MKL_DOMAIN_FFT
+#define EIGEN_MKL_DOMAIN_FFT MKL_DOMAIN_FFT
+#else
+#define EIGEN_MKL_DOMAIN_FFT MKL_FFT
+#endif
+
+#ifdef MKL_DOMAIN_VML
+#define EIGEN_MKL_DOMAIN_VML MKL_DOMAIN_VML
+#else
+#define EIGEN_MKL_DOMAIN_VML MKL_VML
+#endif
+
+#ifdef MKL_DOMAIN_PARDISO
+#define EIGEN_MKL_DOMAIN_PARDISO MKL_DOMAIN_PARDISO
+#else
+#define EIGEN_MKL_DOMAIN_PARDISO MKL_PARDISO
+#endif
+#endif
+
+#if defined(EIGEN_USE_BLAS) && !defined(EIGEN_USE_MKL)
+#include "../../misc/blas.h"
+#endif
+
+#include "../InternalHeaderCheck.h"
+
+namespace Eigen {
+
+typedef std::complex<double> dcomplex;
+typedef std::complex<float> scomplex;
+
+#if defined(EIGEN_USE_MKL)
+typedef MKL_INT BlasIndex;
+#else
+typedef int BlasIndex;
+#endif
+
+} // end namespace Eigen
+
+
+#endif // EIGEN_MKL_SUPPORT_H
diff --git a/Eigen/src/Core/util/Macros.h b/Eigen/src/Core/util/Macros.h
new file mode 100644
index 0000000..d8a67a4
--- /dev/null
+++ b/Eigen/src/Core/util/Macros.h
@@ -0,0 +1,1268 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2015 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_MACROS_H
+#define EIGEN_MACROS_H
+#include "../InternalHeaderCheck.h"
+
+//------------------------------------------------------------------------------------------
+// Eigen version and basic defaults
+//------------------------------------------------------------------------------------------
+
+#define EIGEN_WORLD_VERSION 3
+#define EIGEN_MAJOR_VERSION 4
+#define EIGEN_MINOR_VERSION 90
+
+#define EIGEN_VERSION_AT_LEAST(x,y,z) (EIGEN_WORLD_VERSION>x || (EIGEN_WORLD_VERSION>=x && \
+ (EIGEN_MAJOR_VERSION>y || (EIGEN_MAJOR_VERSION>=y && \
+ EIGEN_MINOR_VERSION>=z))))
+
+#ifdef EIGEN_DEFAULT_TO_ROW_MAJOR
+#define EIGEN_DEFAULT_MATRIX_STORAGE_ORDER_OPTION Eigen::RowMajor
+#else
+#define EIGEN_DEFAULT_MATRIX_STORAGE_ORDER_OPTION Eigen::ColMajor
+#endif
+
+#ifndef EIGEN_DEFAULT_DENSE_INDEX_TYPE
+#define EIGEN_DEFAULT_DENSE_INDEX_TYPE std::ptrdiff_t
+#endif
+
+// Upperbound on the C++ version to use.
+// Expected values are 03, 11, 14, 17, etc.
+// By default, let's use an arbitrarily large C++ version.
+#ifndef EIGEN_MAX_CPP_VER
+#define EIGEN_MAX_CPP_VER 99
+#endif
+
+/** Allows to disable some optimizations which might affect the accuracy of the result.
+ * Such optimization are enabled by default, and set EIGEN_FAST_MATH to 0 to disable them.
+ * They currently include:
+ * - single precision ArrayBase::sin() and ArrayBase::cos() for SSE and AVX vectorization.
+ */
+#ifndef EIGEN_FAST_MATH
+#define EIGEN_FAST_MATH 1
+#endif
+
+#ifndef EIGEN_STACK_ALLOCATION_LIMIT
+// 131072 == 128 KB
+#if defined(__AVX512F__)
+ #define EIGEN_STACK_ALLOCATION_LIMIT 0
+#else
+ #define EIGEN_STACK_ALLOCATION_LIMIT 16384
+#endif
+#endif
+
+//------------------------------------------------------------------------------------------
+// Compiler identification, EIGEN_COMP_*
+//------------------------------------------------------------------------------------------
+
+/// \internal EIGEN_COMP_GNUC set to 1 for all compilers compatible with GCC
+#ifdef __GNUC__
+ #define EIGEN_COMP_GNUC (__GNUC__*10+__GNUC_MINOR__)
+#else
+ #define EIGEN_COMP_GNUC 0
+#endif
+
+/// \internal EIGEN_COMP_CLANG set to major+minor version (e.g., 307 for clang 3.7) if the compiler is clang
+#if defined(__clang__)
+ #define EIGEN_COMP_CLANG (__clang_major__*100+__clang_minor__)
+#else
+ #define EIGEN_COMP_CLANG 0
+#endif
+
+/// \internal EIGEN_COMP_CASTXML set to 1 if being preprocessed by CastXML
+#if defined(__castxml__)
+ #define EIGEN_COMP_CASTXML 1
+#else
+ #define EIGEN_COMP_CASTXML 0
+#endif
+
+/// \internal EIGEN_COMP_LLVM set to 1 if the compiler backend is llvm
+#if defined(__llvm__)
+ #define EIGEN_COMP_LLVM 1
+#else
+ #define EIGEN_COMP_LLVM 0
+#endif
+
+/// \internal EIGEN_COMP_ICC set to __INTEL_COMPILER if the compiler is Intel icc compiler, 0 otherwise
+#if defined(__INTEL_COMPILER)
+ #define EIGEN_COMP_ICC __INTEL_COMPILER
+#else
+ #define EIGEN_COMP_ICC 0
+#endif
+
+/// \internal EIGEN_COMP_CLANGICC set to __INTEL_CLANG_COMPILER if the compiler is Intel icx compiler, 0 otherwise
+#if defined(__INTEL_CLANG_COMPILER)
+ #define EIGEN_COMP_CLANGICC __INTEL_CLANG_COMPILER
+#else
+ #define EIGEN_COMP_CLANGICC 0
+#endif
+
+/// \internal EIGEN_COMP_MINGW set to 1 if the compiler is mingw
+#if defined(__MINGW32__)
+ #define EIGEN_COMP_MINGW 1
+#else
+ #define EIGEN_COMP_MINGW 0
+#endif
+
+/// \internal EIGEN_COMP_SUNCC set to 1 if the compiler is Solaris Studio
+#if defined(__SUNPRO_CC)
+ #define EIGEN_COMP_SUNCC 1
+#else
+ #define EIGEN_COMP_SUNCC 0
+#endif
+
+/// \internal EIGEN_COMP_MSVC set to _MSC_VER if the compiler is Microsoft Visual C++, 0 otherwise.
+#if defined(_MSC_VER)
+ #define EIGEN_COMP_MSVC _MSC_VER
+#else
+ #define EIGEN_COMP_MSVC 0
+#endif
+
+#if defined(__NVCC__)
+#if defined(__CUDACC_VER_MAJOR__) && (__CUDACC_VER_MAJOR__ >= 9)
+ #define EIGEN_COMP_NVCC ((__CUDACC_VER_MAJOR__ * 10000) + (__CUDACC_VER_MINOR__ * 100))
+#elif defined(__CUDACC_VER__)
+ #define EIGEN_COMP_NVCC __CUDACC_VER__
+#else
+ #error "NVCC did not define compiler version."
+#endif
+#else
+ #define EIGEN_COMP_NVCC 0
+#endif
+
+// For the record, here is a table summarizing the possible values for EIGEN_COMP_MSVC:
+// name ver MSC_VER
+// 2015 14 1900
+// "15" 15 1900
+// 2017-14.1 15.0 1910
+// 2017-14.11 15.3 1911
+// 2017-14.12 15.5 1912
+// 2017-14.13 15.6 1913
+// 2017-14.14 15.7 1914
+// 2017 15.8 1915
+// 2017 15.9 1916
+// 2019 RTW 16.0 1920
+
+/// \internal EIGEN_COMP_MSVC_LANG set to _MSVC_LANG if the compiler is Microsoft Visual C++, 0 otherwise.
+#if defined(_MSVC_LANG)
+ #define EIGEN_COMP_MSVC_LANG _MSVC_LANG
+#else
+ #define EIGEN_COMP_MSVC_LANG 0
+#endif
+
+// For the record, here is a table summarizing the possible values for EIGEN_COMP_MSVC_LANG:
+// MSVC option Standard MSVC_LANG
+// /std:c++14 (default as of VS 2019) C++14 201402L
+// /std:c++17 C++17 201703L
+// /std:c++latest >C++17 >201703L
+
+/// \internal EIGEN_COMP_MSVC_STRICT set to 1 if the compiler is really Microsoft Visual C++ and not ,e.g., ICC or clang-cl
+#if EIGEN_COMP_MSVC && !(EIGEN_COMP_ICC || EIGEN_COMP_LLVM || EIGEN_COMP_CLANG)
+ #define EIGEN_COMP_MSVC_STRICT _MSC_VER
+#else
+ #define EIGEN_COMP_MSVC_STRICT 0
+#endif
+
+/// \internal EIGEN_COMP_IBM set to xlc version if the compiler is IBM XL C++
+// XLC version
+// 3.1 0x0301
+// 4.5 0x0405
+// 5.0 0x0500
+// 12.1 0x0C01
+#if defined(__IBMCPP__) || defined(__xlc__) || defined(__ibmxl__)
+ #define EIGEN_COMP_IBM __xlC__
+#else
+ #define EIGEN_COMP_IBM 0
+#endif
+
+/// \internal EIGEN_COMP_PGI set to PGI version if the compiler is Portland Group Compiler
+#if defined(__PGI)
+ #define EIGEN_COMP_PGI (__PGIC__*100+__PGIC_MINOR__)
+#else
+ #define EIGEN_COMP_PGI 0
+#endif
+
+/// \internal EIGEN_COMP_ARM set to 1 if the compiler is ARM Compiler
+#if defined(__CC_ARM) || defined(__ARMCC_VERSION)
+ #define EIGEN_COMP_ARM 1
+#else
+ #define EIGEN_COMP_ARM 0
+#endif
+
+/// \internal EIGEN_COMP_EMSCRIPTEN set to 1 if the compiler is Emscripten Compiler
+#if defined(__EMSCRIPTEN__)
+ #define EIGEN_COMP_EMSCRIPTEN 1
+#else
+ #define EIGEN_COMP_EMSCRIPTEN 0
+#endif
+
+/// \internal EIGEN_COMP_FCC set to FCC version if the compiler is Fujitsu Compiler (traditional mode)
+/// \note The Fujitsu C/C++ compiler uses the traditional mode based
+/// on EDG g++ 6.1 by default or if envoked with the -Nnoclang flag
+#if defined(__FUJITSU)
+ #define EIGEN_COMP_FCC (__FCC_major__*100+__FCC_minor__*10+__FCC_patchlevel__)
+#else
+ #define EIGEN_COMP_FCC 0
+#endif
+
+/// \internal EIGEN_COMP_CLANGFCC set to FCC version if the compiler is Fujitsu Compiler (Clang mode)
+/// \note The Fujitsu C/C++ compiler uses the non-traditional mode
+/// based on Clang 7.1.0 if envoked with the -Nclang flag
+#if defined(__CLANG_FUJITSU)
+ #define EIGEN_COMP_CLANGFCC (__FCC_major__*100+__FCC_minor__*10+__FCC_patchlevel__)
+#else
+ #define EIGEN_COMP_CLANGFCC 0
+#endif
+
+/// \internal EIGEN_COMP_CPE set to CPE version if the compiler is HPE Cray Compiler (GCC based)
+/// \note This is the SVE-enabled C/C++ compiler from the HPE Cray
+/// Programming Environment (CPE) based on Cray GCC 8.1
+#if defined(_CRAYC) && !defined(__clang__)
+ #define EIGEN_COMP_CPE (_RELEASE_MAJOR*100+_RELEASE_MINOR*10+_RELEASE_PATCHLEVEL)
+#else
+ #define EIGEN_COMP_CPE 0
+#endif
+
+/// \internal EIGEN_COMP_CLANGCPE set to CPE version if the compiler is HPE Cray Compiler (Clang based)
+/// \note This is the C/C++ compiler from the HPE Cray Programming
+/// Environment (CPE) based on Cray Clang 11.0 without SVE-support
+#if defined(_CRAYC) && defined(__clang__)
+ #define EIGEN_COMP_CLANGCPE (_RELEASE_MAJOR*100+_RELEASE_MINOR*10+_RELEASE_PATCHLEVEL)
+#else
+ #define EIGEN_COMP_CLANGCPE 0
+#endif
+
+/// \internal EIGEN_COMP_LCC set to 1 if the compiler is MCST-LCC (MCST eLbrus Compiler Collection)
+#if defined(__LCC__) && defined(__MCST__)
+ #define EIGEN_COMP_LCC (__LCC__*100+__LCC_MINOR__)
+#else
+ #define EIGEN_COMP_LCC 0
+#endif
+
+
+/// \internal EIGEN_GNUC_STRICT set to 1 if the compiler is really GCC and not a compatible compiler (e.g., ICC, clang, mingw, etc.)
+#if EIGEN_COMP_GNUC && !(EIGEN_COMP_CLANG || EIGEN_COMP_ICC || EIGEN_COMP_CLANGICC || EIGEN_COMP_MINGW || EIGEN_COMP_PGI || EIGEN_COMP_IBM || EIGEN_COMP_ARM || EIGEN_COMP_EMSCRIPTEN || EIGEN_COMP_FCC || EIGEN_COMP_CLANGFCC || EIGEN_COMP_CPE || EIGEN_COMP_CLANGCPE || EIGEN_COMP_LCC)
+ #define EIGEN_COMP_GNUC_STRICT 1
+#else
+ #define EIGEN_COMP_GNUC_STRICT 0
+#endif
+
+
+#if EIGEN_COMP_GNUC
+ #define EIGEN_GNUC_AT_LEAST(x,y) ((__GNUC__==x && __GNUC_MINOR__>=y) || __GNUC__>x)
+ #define EIGEN_GNUC_AT_MOST(x,y) ((__GNUC__==x && __GNUC_MINOR__<=y) || __GNUC__<x)
+ #define EIGEN_GNUC_AT(x,y) ( __GNUC__==x && __GNUC_MINOR__==y )
+#else
+ #define EIGEN_GNUC_AT_LEAST(x,y) 0
+ #define EIGEN_GNUC_AT_MOST(x,y) 0
+ #define EIGEN_GNUC_AT(x,y) 0
+#endif
+
+
+//------------------------------------------------------------------------------------------
+// Architecture identification, EIGEN_ARCH_*
+//------------------------------------------------------------------------------------------
+
+
+#if defined(__x86_64__) || (defined(_M_X64) && !defined(_M_ARM64EC)) || defined(__amd64)
+ #define EIGEN_ARCH_x86_64 1
+#else
+ #define EIGEN_ARCH_x86_64 0
+#endif
+
+#if defined(__i386__) || defined(_M_IX86) || defined(_X86_) || defined(__i386)
+ #define EIGEN_ARCH_i386 1
+#else
+ #define EIGEN_ARCH_i386 0
+#endif
+
+#if EIGEN_ARCH_x86_64 || EIGEN_ARCH_i386
+ #define EIGEN_ARCH_i386_OR_x86_64 1
+#else
+ #define EIGEN_ARCH_i386_OR_x86_64 0
+#endif
+
+/// \internal EIGEN_ARCH_ARM set to 1 if the architecture is ARM
+#if defined(__arm__)
+ #define EIGEN_ARCH_ARM 1
+#else
+ #define EIGEN_ARCH_ARM 0
+#endif
+
+/// \internal EIGEN_ARCH_ARM64 set to 1 if the architecture is ARM64
+#if defined(__aarch64__) || defined(_M_ARM64) || defined(_M_ARM64EC)
+ #define EIGEN_ARCH_ARM64 1
+#else
+ #define EIGEN_ARCH_ARM64 0
+#endif
+
+/// \internal EIGEN_ARCH_ARM_OR_ARM64 set to 1 if the architecture is ARM or ARM64
+#if EIGEN_ARCH_ARM || EIGEN_ARCH_ARM64
+ #define EIGEN_ARCH_ARM_OR_ARM64 1
+#else
+ #define EIGEN_ARCH_ARM_OR_ARM64 0
+#endif
+
+/// \internal EIGEN_ARCH_ARMV8 set to 1 if the architecture is armv8 or greater.
+#if EIGEN_ARCH_ARM_OR_ARM64 && defined(__ARM_ARCH) && __ARM_ARCH >= 8
+#define EIGEN_ARCH_ARMV8 1
+#else
+#define EIGEN_ARCH_ARMV8 0
+#endif
+
+
+/// \internal EIGEN_HAS_ARM64_FP16 set to 1 if the architecture provides an IEEE
+/// compliant Arm fp16 type
+#if EIGEN_ARCH_ARM64
+ #ifndef EIGEN_HAS_ARM64_FP16
+ #if defined(__ARM_FP16_FORMAT_IEEE)
+ #define EIGEN_HAS_ARM64_FP16 1
+ #else
+ #define EIGEN_HAS_ARM64_FP16 0
+ #endif
+ #endif
+#endif
+
+/// \internal EIGEN_HAS_ARM64_FP16_VECTOR_ARITHMETIC set to 1 if the architecture
+/// supports Neon vector intrinsics for fp16.
+#if EIGEN_ARCH_ARM64
+ #ifndef EIGEN_HAS_ARM64_FP16_VECTOR_ARITHMETIC
+ #if defined(__ARM_FEATURE_FP16_VECTOR_ARITHMETIC)
+ #define EIGEN_HAS_ARM64_FP16_VECTOR_ARITHMETIC 1
+ #else
+ #define EIGEN_HAS_ARM64_FP16_VECTOR_ARITHMETIC 0
+ #endif
+ #endif
+#endif
+
+/// \internal EIGEN_HAS_ARM64_FP16_SCALAR_ARITHMETIC set to 1 if the architecture
+/// supports Neon scalar intrinsics for fp16.
+#if EIGEN_ARCH_ARM64
+ #ifndef EIGEN_HAS_ARM64_FP16_SCALAR_ARITHMETIC
+ #if defined(__ARM_FEATURE_FP16_SCALAR_ARITHMETIC)
+ #define EIGEN_HAS_ARM64_FP16_SCALAR_ARITHMETIC 1
+ #endif
+ #endif
+#endif
+
+/// \internal EIGEN_ARCH_MIPS set to 1 if the architecture is MIPS
+#if defined(__mips__) || defined(__mips)
+ #define EIGEN_ARCH_MIPS 1
+#else
+ #define EIGEN_ARCH_MIPS 0
+#endif
+
+/// \internal EIGEN_ARCH_SPARC set to 1 if the architecture is SPARC
+#if defined(__sparc__) || defined(__sparc)
+ #define EIGEN_ARCH_SPARC 1
+#else
+ #define EIGEN_ARCH_SPARC 0
+#endif
+
+/// \internal EIGEN_ARCH_IA64 set to 1 if the architecture is Intel Itanium
+#if defined(__ia64__)
+ #define EIGEN_ARCH_IA64 1
+#else
+ #define EIGEN_ARCH_IA64 0
+#endif
+
+/// \internal EIGEN_ARCH_PPC set to 1 if the architecture is PowerPC
+#if defined(__powerpc__) || defined(__ppc__) || defined(_M_PPC)
+ #define EIGEN_ARCH_PPC 1
+#else
+ #define EIGEN_ARCH_PPC 0
+#endif
+
+
+
+//------------------------------------------------------------------------------------------
+// Operating system identification, EIGEN_OS_*
+//------------------------------------------------------------------------------------------
+
+/// \internal EIGEN_OS_UNIX set to 1 if the OS is a unix variant
+#if defined(__unix__) || defined(__unix)
+ #define EIGEN_OS_UNIX 1
+#else
+ #define EIGEN_OS_UNIX 0
+#endif
+
+/// \internal EIGEN_OS_LINUX set to 1 if the OS is based on Linux kernel
+#if defined(__linux__)
+ #define EIGEN_OS_LINUX 1
+#else
+ #define EIGEN_OS_LINUX 0
+#endif
+
+/// \internal EIGEN_OS_ANDROID set to 1 if the OS is Android
+// note: ANDROID is defined when using ndk_build, __ANDROID__ is defined when using a standalone toolchain.
+#if defined(__ANDROID__) || defined(ANDROID)
+ #define EIGEN_OS_ANDROID 1
+#else
+ #define EIGEN_OS_ANDROID 0
+#endif
+
+/// \internal EIGEN_OS_GNULINUX set to 1 if the OS is GNU Linux and not Linux-based OS (e.g., not android)
+#if defined(__gnu_linux__) && !(EIGEN_OS_ANDROID)
+ #define EIGEN_OS_GNULINUX 1
+#else
+ #define EIGEN_OS_GNULINUX 0
+#endif
+
+/// \internal EIGEN_OS_BSD set to 1 if the OS is a BSD variant
+#if defined(__FreeBSD__) || defined(__NetBSD__) || defined(__OpenBSD__) || defined(__bsdi__) || defined(__DragonFly__)
+ #define EIGEN_OS_BSD 1
+#else
+ #define EIGEN_OS_BSD 0
+#endif
+
+/// \internal EIGEN_OS_MAC set to 1 if the OS is MacOS
+#if defined(__APPLE__)
+ #define EIGEN_OS_MAC 1
+#else
+ #define EIGEN_OS_MAC 0
+#endif
+
+/// \internal EIGEN_OS_QNX set to 1 if the OS is QNX
+#if defined(__QNX__)
+ #define EIGEN_OS_QNX 1
+#else
+ #define EIGEN_OS_QNX 0
+#endif
+
+/// \internal EIGEN_OS_WIN set to 1 if the OS is Windows based
+#if defined(_WIN32)
+ #define EIGEN_OS_WIN 1
+#else
+ #define EIGEN_OS_WIN 0
+#endif
+
+/// \internal EIGEN_OS_WIN64 set to 1 if the OS is Windows 64bits
+#if defined(_WIN64)
+ #define EIGEN_OS_WIN64 1
+#else
+ #define EIGEN_OS_WIN64 0
+#endif
+
+/// \internal EIGEN_OS_WINCE set to 1 if the OS is Windows CE
+#if defined(_WIN32_WCE)
+ #define EIGEN_OS_WINCE 1
+#else
+ #define EIGEN_OS_WINCE 0
+#endif
+
+/// \internal EIGEN_OS_CYGWIN set to 1 if the OS is Windows/Cygwin
+#if defined(__CYGWIN__)
+ #define EIGEN_OS_CYGWIN 1
+#else
+ #define EIGEN_OS_CYGWIN 0
+#endif
+
+/// \internal EIGEN_OS_WIN_STRICT set to 1 if the OS is really Windows and not some variants
+#if EIGEN_OS_WIN && !( EIGEN_OS_WINCE || EIGEN_OS_CYGWIN )
+ #define EIGEN_OS_WIN_STRICT 1
+#else
+ #define EIGEN_OS_WIN_STRICT 0
+#endif
+
+/// \internal EIGEN_OS_SUN set to __SUNPRO_C if the OS is SUN
+// compiler solaris __SUNPRO_C
+// version studio
+// 5.7 10 0x570
+// 5.8 11 0x580
+// 5.9 12 0x590
+// 5.10 12.1 0x5100
+// 5.11 12.2 0x5110
+// 5.12 12.3 0x5120
+#if (defined(sun) || defined(__sun)) && !(defined(__SVR4) || defined(__svr4__))
+ #define EIGEN_OS_SUN __SUNPRO_C
+#else
+ #define EIGEN_OS_SUN 0
+#endif
+
+/// \internal EIGEN_OS_SOLARIS set to 1 if the OS is Solaris
+#if (defined(sun) || defined(__sun)) && (defined(__SVR4) || defined(__svr4__))
+ #define EIGEN_OS_SOLARIS 1
+#else
+ #define EIGEN_OS_SOLARIS 0
+#endif
+
+
+//------------------------------------------------------------------------------------------
+// Detect GPU compilers and architectures
+//------------------------------------------------------------------------------------------
+
+// NVCC is not supported as the target platform for HIPCC
+// Note that this also makes EIGEN_CUDACC and EIGEN_HIPCC mutually exclusive
+#if defined(__NVCC__) && defined(__HIPCC__)
+ #error "NVCC as the target platform for HIPCC is currently not supported."
+#endif
+
+#if defined(__CUDACC__) && !defined(EIGEN_NO_CUDA)
+ // Means the compiler is either nvcc or clang with CUDA enabled
+ #define EIGEN_CUDACC __CUDACC__
+#endif
+
+#if defined(__CUDA_ARCH__) && !defined(EIGEN_NO_CUDA)
+ // Means we are generating code for the device
+ #define EIGEN_CUDA_ARCH __CUDA_ARCH__
+#endif
+
+#if defined(EIGEN_CUDACC)
+#include <cuda.h>
+ #define EIGEN_CUDA_SDK_VER (CUDA_VERSION * 10)
+#else
+ #define EIGEN_CUDA_SDK_VER 0
+#endif
+
+#if defined(__HIPCC__) && !defined(EIGEN_NO_HIP)
+ // Means the compiler is HIPCC (analogous to EIGEN_CUDACC, but for HIP)
+ #define EIGEN_HIPCC __HIPCC__
+
+ // We need to include hip_runtime.h here because it pulls in
+ // ++ hip_common.h which contains the define for __HIP_DEVICE_COMPILE__
+ // ++ host_defines.h which contains the defines for the __host__ and __device__ macros
+ #include <hip/hip_runtime.h>
+
+ #if defined(__HIP_DEVICE_COMPILE__)
+ // analogous to EIGEN_CUDA_ARCH, but for HIP
+ #define EIGEN_HIP_DEVICE_COMPILE __HIP_DEVICE_COMPILE__
+ #endif
+
+ // For HIP (ROCm 3.5 and higher), we need to explicitly set the launch_bounds attribute
+ // value to 1024. The compiler assigns a default value of 256 when the attribute is not
+ // specified. This results in failures on the HIP platform, for cases when a GPU kernel
+ // without an explicit launch_bounds attribute is called with a threads_per_block value
+ // greater than 256.
+ //
+ // This is a regression in functioanlity and is expected to be fixed within the next
+ // couple of ROCm releases (compiler will go back to using 1024 value as the default)
+ //
+ // In the meantime, we will use a "only enabled for HIP" macro to set the launch_bounds
+ // attribute.
+
+ #define EIGEN_HIP_LAUNCH_BOUNDS_1024 __launch_bounds__(1024)
+
+#endif
+
+#if !defined(EIGEN_HIP_LAUNCH_BOUNDS_1024)
+#define EIGEN_HIP_LAUNCH_BOUNDS_1024
+#endif // !defined(EIGEN_HIP_LAUNCH_BOUNDS_1024)
+
+// Unify CUDA/HIPCC
+
+#if defined(EIGEN_CUDACC) || defined(EIGEN_HIPCC)
+//
+// If either EIGEN_CUDACC or EIGEN_HIPCC is defined, then define EIGEN_GPUCC
+//
+#define EIGEN_GPUCC
+//
+// EIGEN_HIPCC implies the HIP compiler and is used to tweak Eigen code for use in HIP kernels
+// EIGEN_CUDACC implies the CUDA compiler and is used to tweak Eigen code for use in CUDA kernels
+//
+// In most cases the same tweaks are required to the Eigen code to enable in both the HIP and CUDA kernels.
+// For those cases, the corresponding code should be guarded with
+// #if defined(EIGEN_GPUCC)
+// instead of
+// #if defined(EIGEN_CUDACC) || defined(EIGEN_HIPCC)
+//
+// For cases where the tweak is specific to HIP, the code should be guarded with
+// #if defined(EIGEN_HIPCC)
+//
+// For cases where the tweak is specific to CUDA, the code should be guarded with
+// #if defined(EIGEN_CUDACC)
+//
+#endif
+
+#if defined(EIGEN_CUDA_ARCH) || defined(EIGEN_HIP_DEVICE_COMPILE)
+//
+// If either EIGEN_CUDA_ARCH or EIGEN_HIP_DEVICE_COMPILE is defined, then define EIGEN_GPU_COMPILE_PHASE
+//
+#define EIGEN_GPU_COMPILE_PHASE
+//
+// GPU compilers (HIPCC, NVCC) typically do two passes over the source code,
+// + one to compile the source for the "host" (ie CPU)
+// + another to compile the source for the "device" (ie. GPU)
+//
+// Code that needs to enabled only during the either the "host" or "device" compilation phase
+// needs to be guarded with a macro that indicates the current compilation phase
+//
+// EIGEN_HIP_DEVICE_COMPILE implies the device compilation phase in HIP
+// EIGEN_CUDA_ARCH implies the device compilation phase in CUDA
+//
+// In most cases, the "host" / "device" specific code is the same for both HIP and CUDA
+// For those cases, the code should be guarded with
+// #if defined(EIGEN_GPU_COMPILE_PHASE)
+// instead of
+// #if defined(EIGEN_CUDA_ARCH) || defined(EIGEN_HIP_DEVICE_COMPILE)
+//
+// For cases where the tweak is specific to HIP, the code should be guarded with
+// #if defined(EIGEN_HIP_DEVICE_COMPILE)
+//
+// For cases where the tweak is specific to CUDA, the code should be guarded with
+// #if defined(EIGEN_CUDA_ARCH)
+//
+#endif
+
+#if defined(EIGEN_USE_SYCL) && defined(__SYCL_DEVICE_ONLY__)
+// EIGEN_USE_SYCL is a user-defined macro while __SYCL_DEVICE_ONLY__ is a compiler-defined macro.
+// In most cases we want to check if both macros are defined which can be done using the define below.
+#define SYCL_DEVICE_ONLY
+#endif
+
+//------------------------------------------------------------------------------------------
+// Detect Compiler/Architecture/OS specific features
+//------------------------------------------------------------------------------------------
+
+// Cross compiler wrapper around LLVM's __has_builtin
+#ifdef __has_builtin
+# define EIGEN_HAS_BUILTIN(x) __has_builtin(x)
+#else
+# define EIGEN_HAS_BUILTIN(x) 0
+#endif
+
+// A Clang feature extension to determine compiler features.
+// We use it to determine 'cxx_rvalue_references'
+#ifndef __has_feature
+# define __has_feature(x) 0
+#endif
+
+// The macro EIGEN_CPLUSPLUS is a replacement for __cplusplus/_MSVC_LANG that
+// works for both platforms, indicating the C++ standard version number.
+//
+// With MSVC, without defining /Zc:__cplusplus, the __cplusplus macro will
+// report 199711L regardless of the language standard specified via /std.
+// We need to rely on _MSVC_LANG instead, which is only available after
+// VS2015.3.
+#if EIGEN_COMP_MSVC_LANG > 0
+#define EIGEN_CPLUSPLUS EIGEN_COMP_MSVC_LANG
+#elif EIGEN_COMP_MSVC >= 1900
+#define EIGEN_CPLUSPLUS 201103L
+#elif defined(__cplusplus)
+#define EIGEN_CPLUSPLUS __cplusplus
+#else
+#define EIGEN_CPLUSPLUS 0
+#endif
+
+// The macro EIGEN_COMP_CXXVER defines the c++ version expected by the compiler.
+// For instance, if compiling with gcc and -std=c++17, then EIGEN_COMP_CXXVER
+// is defined to 17.
+#if EIGEN_CPLUSPLUS > 201703L
+ #define EIGEN_COMP_CXXVER 20
+#elif EIGEN_CPLUSPLUS > 201402L
+ #define EIGEN_COMP_CXXVER 17
+#elif EIGEN_CPLUSPLUS > 201103L
+ #define EIGEN_COMP_CXXVER 14
+#elif EIGEN_CPLUSPLUS >= 201103L
+ #define EIGEN_COMP_CXXVER 11
+#else
+ #define EIGEN_COMP_CXXVER 03
+#endif
+
+
+// The macros EIGEN_HAS_CXX?? defines a rough estimate of available c++ features
+// but in practice we should not rely on them but rather on the availability of
+// individual features as defined later.
+// This is why there is no EIGEN_HAS_CXX17.
+#if EIGEN_MAX_CPP_VER<14 || EIGEN_COMP_CXXVER<14 || (EIGEN_COMP_MSVC && EIGEN_COMP_MSVC < 1900) || \
+ (EIGEN_COMP_ICC && EIGEN_COMP_ICC < 1500) || (EIGEN_COMP_NVCC && EIGEN_COMP_NVCC < 80000) || \
+ (EIGEN_COMP_CLANG && ((EIGEN_COMP_CLANG<309) || (defined(__apple_build_version__) && (__apple_build_version__ < 9000000)))) || \
+ (EIGEN_COMP_GNUC_STRICT && EIGEN_COMP_GNUC<51)
+#error This compiler appears to be too old to be supported by Eigen
+#endif
+
+// Does the compiler support C99?
+// Need to include <cmath> to make sure _GLIBCXX_USE_C99 gets defined
+#include <cmath>
+#ifndef EIGEN_HAS_C99_MATH
+#if ((defined(__STDC_VERSION__) && (__STDC_VERSION__ >= 199901)) \
+ || (defined(__GNUC__) && defined(_GLIBCXX_USE_C99)) \
+ || (defined(_LIBCPP_VERSION) && !defined(_MSC_VER)) \
+ || (EIGEN_COMP_MSVC) || defined(SYCL_DEVICE_ONLY))
+ #define EIGEN_HAS_C99_MATH 1
+#else
+ #define EIGEN_HAS_C99_MATH 0
+#endif
+#endif
+
+// Does the compiler support std::hash?
+#ifndef EIGEN_HAS_STD_HASH
+// The std::hash struct is defined in C++11 but is not labelled as a __device__
+// function and is not constexpr, so cannot be used on device.
+#if !defined(EIGEN_GPU_COMPILE_PHASE)
+#define EIGEN_HAS_STD_HASH 1
+#else
+#define EIGEN_HAS_STD_HASH 0
+#endif
+#endif // EIGEN_HAS_STD_HASH
+
+#ifndef EIGEN_HAS_STD_INVOKE_RESULT
+#if EIGEN_MAX_CPP_VER >= 17 && EIGEN_COMP_CXXVER >= 17
+#define EIGEN_HAS_STD_INVOKE_RESULT 1
+#else
+#define EIGEN_HAS_STD_INVOKE_RESULT 0
+#endif
+#endif
+
+#define EIGEN_CONSTEXPR constexpr
+
+// NOTE: the required Apple's clang version is very conservative
+// and it could be that XCode 9 works just fine.
+// NOTE: the MSVC version is based on https://en.cppreference.com/w/cpp/compiler_support
+// and not tested.
+#ifndef EIGEN_HAS_CXX17_OVERALIGN
+#if EIGEN_MAX_CPP_VER>=17 && EIGEN_COMP_CXXVER>=17 && ( \
+ (EIGEN_COMP_MSVC >= 1912) \
+ || (EIGEN_GNUC_AT_LEAST(7,0)) \
+ || ((!defined(__apple_build_version__)) && (EIGEN_COMP_CLANG>=500)) \
+ || (( defined(__apple_build_version__)) && (__apple_build_version__>=10000000)) \
+ )
+#define EIGEN_HAS_CXX17_OVERALIGN 1
+#else
+#define EIGEN_HAS_CXX17_OVERALIGN 0
+#endif
+#endif
+
+#if defined(EIGEN_CUDACC)
+ // While available already with c++11, this is useful mostly starting with c++14 and relaxed constexpr rules
+ #if defined(__NVCC__)
+ // nvcc considers constexpr functions as __host__ __device__ with the option --expt-relaxed-constexpr
+ #ifdef __CUDACC_RELAXED_CONSTEXPR__
+ #define EIGEN_CONSTEXPR_ARE_DEVICE_FUNC
+ #endif
+ #elif defined(__clang__) && defined(__CUDA__) && __has_feature(cxx_relaxed_constexpr)
+ // clang++ always considers constexpr functions as implicitly __host__ __device__
+ #define EIGEN_CONSTEXPR_ARE_DEVICE_FUNC
+ #endif
+#endif
+
+// Does the compiler support the __int128 and __uint128_t extensions for 128-bit
+// integer arithmetic?
+//
+// Clang and GCC define __SIZEOF_INT128__ when these extensions are supported,
+// but we avoid using them in certain cases:
+//
+// * Building using Clang for Windows, where the Clang runtime library has
+// 128-bit support only on LP64 architectures, but Windows is LLP64.
+#ifndef EIGEN_HAS_BUILTIN_INT128
+#if defined(__SIZEOF_INT128__) && !(EIGEN_OS_WIN && EIGEN_COMP_CLANG)
+#define EIGEN_HAS_BUILTIN_INT128 1
+#else
+#define EIGEN_HAS_BUILTIN_INT128 0
+#endif
+#endif
+
+//------------------------------------------------------------------------------------------
+// Preprocessor programming helpers
+//------------------------------------------------------------------------------------------
+
+// This macro can be used to prevent from macro expansion, e.g.:
+// std::max EIGEN_NOT_A_MACRO(a,b)
+#define EIGEN_NOT_A_MACRO
+
+#define EIGEN_DEBUG_VAR(x) std::cerr << #x << " = " << x << std::endl;
+
+// concatenate two tokens
+#define EIGEN_CAT2(a,b) a ## b
+#define EIGEN_CAT(a,b) EIGEN_CAT2(a,b)
+
+#define EIGEN_COMMA ,
+
+// convert a token to a string
+#define EIGEN_MAKESTRING2(a) #a
+#define EIGEN_MAKESTRING(a) EIGEN_MAKESTRING2(a)
+
+// EIGEN_STRONG_INLINE is a stronger version of the inline, using __forceinline on MSVC,
+// but it still doesn't use GCC's always_inline. This is useful in (common) situations where MSVC needs forceinline
+// but GCC is still doing fine with just inline.
+#ifndef EIGEN_STRONG_INLINE
+#if (EIGEN_COMP_MSVC || EIGEN_COMP_ICC) && !defined(EIGEN_GPUCC)
+#define EIGEN_STRONG_INLINE __forceinline
+#else
+#define EIGEN_STRONG_INLINE inline
+#endif
+#endif
+
+// EIGEN_ALWAYS_INLINE is the strongest, it has the effect of making the function inline and adding every possible
+// attribute to maximize inlining. This should only be used when really necessary: in particular,
+// it uses __attribute__((always_inline)) on GCC, which most of the time is useless and can severely harm compile times.
+// FIXME with the always_inline attribute,
+#if EIGEN_COMP_GNUC && !defined(SYCL_DEVICE_ONLY)
+#define EIGEN_ALWAYS_INLINE __attribute__((always_inline)) inline
+#else
+#define EIGEN_ALWAYS_INLINE EIGEN_STRONG_INLINE
+#endif
+
+#if EIGEN_COMP_GNUC
+#define EIGEN_DONT_INLINE __attribute__((noinline))
+#elif EIGEN_COMP_MSVC
+#define EIGEN_DONT_INLINE __declspec(noinline)
+#else
+#define EIGEN_DONT_INLINE
+#endif
+
+#if EIGEN_COMP_GNUC
+#define EIGEN_PERMISSIVE_EXPR __extension__
+#else
+#define EIGEN_PERMISSIVE_EXPR
+#endif
+
+// GPU stuff
+
+// Disable some features when compiling with GPU compilers (NVCC/clang-cuda/SYCL/HIPCC)
+#if defined(EIGEN_CUDACC) || defined(SYCL_DEVICE_ONLY) || defined(EIGEN_HIPCC)
+ // Do not try asserts on device code
+ #ifndef EIGEN_NO_DEBUG
+ #define EIGEN_NO_DEBUG
+ #endif
+
+ #ifdef EIGEN_INTERNAL_DEBUGGING
+ #undef EIGEN_INTERNAL_DEBUGGING
+ #endif
+
+ #ifdef EIGEN_EXCEPTIONS
+ #undef EIGEN_EXCEPTIONS
+ #endif
+#endif
+
+#if defined(SYCL_DEVICE_ONLY)
+ #ifndef EIGEN_DONT_VECTORIZE
+ #define EIGEN_DONT_VECTORIZE
+ #endif
+ #define EIGEN_DEVICE_FUNC __attribute__((flatten)) __attribute__((always_inline))
+// All functions callable from CUDA/HIP code must be qualified with __device__
+#elif defined(EIGEN_GPUCC)
+ #define EIGEN_DEVICE_FUNC __host__ __device__
+#else
+ #define EIGEN_DEVICE_FUNC
+#endif
+
+
+// this macro allows to get rid of linking errors about multiply defined functions.
+// - static is not very good because it prevents definitions from different object files to be merged.
+// So static causes the resulting linked executable to be bloated with multiple copies of the same function.
+// - inline is not perfect either as it unwantedly hints the compiler toward inlining the function.
+#define EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_DEVICE_FUNC
+#define EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_DEVICE_FUNC inline
+
+#ifdef NDEBUG
+# ifndef EIGEN_NO_DEBUG
+# define EIGEN_NO_DEBUG
+# endif
+#endif
+
+// eigen_plain_assert is where we implement the workaround for the assert() bug in GCC <= 4.3, see bug 89
+#ifdef EIGEN_NO_DEBUG
+ #ifdef SYCL_DEVICE_ONLY // used to silence the warning on SYCL device
+ #define eigen_plain_assert(x) EIGEN_UNUSED_VARIABLE(x)
+ #else
+ #define eigen_plain_assert(x)
+ #endif
+#else
+ #define eigen_plain_assert(x) assert(x)
+#endif
+
+// eigen_assert can be overridden
+#ifndef eigen_assert
+#define eigen_assert(x) eigen_plain_assert(x)
+#endif
+
+#ifdef EIGEN_INTERNAL_DEBUGGING
+#define eigen_internal_assert(x) eigen_assert(x)
+#else
+#define eigen_internal_assert(x)
+#endif
+
+#ifdef EIGEN_NO_DEBUG
+#define EIGEN_ONLY_USED_FOR_DEBUG(x) EIGEN_UNUSED_VARIABLE(x)
+#else
+#define EIGEN_ONLY_USED_FOR_DEBUG(x)
+#endif
+
+#ifndef EIGEN_NO_DEPRECATED_WARNING
+ #if EIGEN_COMP_GNUC
+ #define EIGEN_DEPRECATED __attribute__((deprecated))
+ #elif EIGEN_COMP_MSVC
+ #define EIGEN_DEPRECATED __declspec(deprecated)
+ #else
+ #define EIGEN_DEPRECATED
+ #endif
+#else
+ #define EIGEN_DEPRECATED
+#endif
+
+#if EIGEN_COMP_GNUC
+#define EIGEN_UNUSED __attribute__((unused))
+#else
+#define EIGEN_UNUSED
+#endif
+
+#if EIGEN_COMP_GNUC
+ #define EIGEN_PRAGMA(tokens) _Pragma(#tokens)
+ #define EIGEN_DIAGNOSTICS(tokens) EIGEN_PRAGMA(GCC diagnostic tokens)
+ #define EIGEN_DIAGNOSTICS_OFF(msc, gcc) EIGEN_DIAGNOSTICS(gcc)
+#elif EIGEN_COMP_MSVC
+ #define EIGEN_PRAGMA(tokens) __pragma(tokens)
+ #define EIGEN_DIAGNOSTICS(tokens) EIGEN_PRAGMA(warning(tokens))
+ #define EIGEN_DIAGNOSTICS_OFF(msc, gcc) EIGEN_DIAGNOSTICS(msc)
+#else
+ #define EIGEN_PRAGMA(tokens)
+ #define EIGEN_DIAGNOSTICS(tokens)
+ #define EIGEN_DIAGNOSTICS_OFF(msc, gcc)
+#endif
+
+#define EIGEN_DISABLE_DEPRECATED_WARNING EIGEN_DIAGNOSTICS_OFF(disable : 4996, ignored "-Wdeprecated-declarations")
+
+// Suppresses 'unused variable' warnings.
+namespace Eigen {
+ namespace internal {
+ template<typename T> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr void ignore_unused_variable(const T&) {}
+ }
+}
+#define EIGEN_UNUSED_VARIABLE(var) Eigen::internal::ignore_unused_variable(var);
+
+#if !defined(EIGEN_ASM_COMMENT)
+ #if EIGEN_COMP_GNUC && (EIGEN_ARCH_i386_OR_x86_64 || EIGEN_ARCH_ARM_OR_ARM64)
+ #define EIGEN_ASM_COMMENT(X) __asm__("#" X)
+ #else
+ #define EIGEN_ASM_COMMENT(X)
+ #endif
+#endif
+
+
+// Acts as a barrier preventing operations involving `X` from crossing. This
+// occurs, for example, in the fast rounding trick where a magic constant is
+// added then subtracted, which is otherwise compiled away with -ffast-math.
+//
+// See bug 1674
+#if !defined(EIGEN_OPTIMIZATION_BARRIER)
+ #if EIGEN_COMP_GNUC
+ // According to https://gcc.gnu.org/onlinedocs/gcc/Constraints.html:
+ // X: Any operand whatsoever.
+ // r: A register operand is allowed provided that it is in a general
+ // register.
+ // g: Any register, memory or immediate integer operand is allowed, except
+ // for registers that are not general registers.
+ // w: (AArch32/AArch64) Floating point register, Advanced SIMD vector
+ // register or SVE vector register.
+ // x: (SSE) Any SSE register.
+ // (AArch64) Like w, but restricted to registers 0 to 15 inclusive.
+ // v: (PowerPC) An Altivec vector register.
+ // wa:(PowerPC) A VSX register.
+ //
+ // "X" (uppercase) should work for all cases, though this seems to fail for
+ // some versions of GCC for arm/aarch64 with
+ // "error: inconsistent operand constraints in an 'asm'"
+ // Clang x86_64/arm/aarch64 seems to require "g" to support both scalars and
+ // vectors, otherwise
+ // "error: non-trivial scalar-to-vector conversion, possible invalid
+ // constraint for vector type"
+ //
+ // GCC for ppc64le generates an internal compiler error with x/X/g.
+ // GCC for AVX generates an internal compiler error with X.
+ //
+ // Tested on icc/gcc/clang for sse, avx, avx2, avx512dq
+ // gcc for arm, aarch64,
+ // gcc for ppc64le,
+ // both vectors and scalars.
+ //
+ // Note that this is restricted to plain types - this will not work
+ // directly for std::complex<T>, Eigen::half, Eigen::bfloat16. For these,
+ // you will need to apply to the underlying POD type.
+ #if EIGEN_ARCH_PPC && EIGEN_COMP_GNUC_STRICT
+ // This seems to be broken on clang. Packet4f is loaded into a single
+ // register rather than a vector, zeroing out some entries. Integer
+ // types also generate a compile error.
+ // General, Altivec, VSX.
+ #define EIGEN_OPTIMIZATION_BARRIER(X) __asm__ ("" : "+r,v,wa" (X));
+ #elif EIGEN_ARCH_ARM_OR_ARM64
+ #ifdef __ARM_FP
+ // General, VFP or NEON.
+ // Clang doesn't like "r",
+ // error: non-trivial scalar-to-vector conversion, possible invalid
+ // constraint for vector typ
+ #define EIGEN_OPTIMIZATION_BARRIER(X) __asm__ ("" : "+g,w" (X));
+ #else
+ // Arm without VFP or NEON.
+ // "w" constraint will not compile.
+ #define EIGEN_OPTIMIZATION_BARRIER(X) __asm__ ("" : "+g" (X));
+ #endif
+ #elif EIGEN_ARCH_i386_OR_x86_64
+ // General, SSE.
+ #define EIGEN_OPTIMIZATION_BARRIER(X) __asm__ ("" : "+g,x" (X));
+ #else
+ // Not implemented for other architectures.
+ #define EIGEN_OPTIMIZATION_BARRIER(X)
+ #endif
+ #else
+ // Not implemented for other compilers.
+ #define EIGEN_OPTIMIZATION_BARRIER(X)
+ #endif
+#endif
+
+#if EIGEN_COMP_MSVC
+ // NOTE MSVC often gives C4127 warnings with compiletime if statements. See bug 1362.
+ // This workaround is ugly, but it does the job.
+# define EIGEN_CONST_CONDITIONAL(cond) (void)0, cond
+#else
+# define EIGEN_CONST_CONDITIONAL(cond) cond
+#endif
+
+#ifdef EIGEN_DONT_USE_RESTRICT_KEYWORD
+ #define EIGEN_RESTRICT
+#endif
+#ifndef EIGEN_RESTRICT
+ #define EIGEN_RESTRICT __restrict
+#endif
+
+
+#ifndef EIGEN_DEFAULT_IO_FORMAT
+#ifdef EIGEN_MAKING_DOCS
+// format used in Eigen's documentation
+// needed to define it here as escaping characters in CMake add_definition's argument seems very problematic.
+#define EIGEN_DEFAULT_IO_FORMAT Eigen::IOFormat(3, 0, " ", "\n", "", "")
+#else
+#define EIGEN_DEFAULT_IO_FORMAT Eigen::IOFormat()
+#endif
+#endif
+
+// just an empty macro !
+#define EIGEN_EMPTY
+
+
+// When compiling CUDA/HIP device code with NVCC or HIPCC
+// pull in math functions from the global namespace.
+// In host mode, and when device code is compiled with clang,
+// use the std versions.
+#if (defined(EIGEN_CUDA_ARCH) && defined(__NVCC__)) || defined(EIGEN_HIP_DEVICE_COMPILE)
+ #define EIGEN_USING_STD(FUNC) using ::FUNC;
+#else
+ #define EIGEN_USING_STD(FUNC) using std::FUNC;
+#endif
+
+#if EIGEN_COMP_MSVC_STRICT && EIGEN_COMP_NVCC
+ // Wwhen compiling with NVCC, using the base operator is necessary,
+ // otherwise we get duplicate definition errors
+ // For later MSVC versions, we require explicit operator= definition, otherwise we get
+ // use of implicitly deleted operator errors.
+ // (cf Bugs 920, 1000, 1324, 2291)
+ #define EIGEN_INHERIT_ASSIGNMENT_EQUAL_OPERATOR(Derived) \
+ using Base::operator =;
+#elif EIGEN_COMP_CLANG // workaround clang bug (see http://forum.kde.org/viewtopic.php?f=74&t=102653)
+ #define EIGEN_INHERIT_ASSIGNMENT_EQUAL_OPERATOR(Derived) \
+ using Base::operator =; \
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& operator=(const Derived& other) { Base::operator=(other); return *this; } \
+ template <typename OtherDerived> \
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& operator=(const DenseBase<OtherDerived>& other) { Base::operator=(other.derived()); return *this; }
+#else
+ #define EIGEN_INHERIT_ASSIGNMENT_EQUAL_OPERATOR(Derived) \
+ using Base::operator =; \
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& operator=(const Derived& other) \
+ { \
+ Base::operator=(other); \
+ return *this; \
+ }
+#endif
+
+
+/**
+ * \internal
+ * \brief Macro to explicitly define the default copy constructor.
+ * This is necessary, because the implicit definition is deprecated if the copy-assignment is overridden.
+ */
+#define EIGEN_DEFAULT_COPY_CONSTRUCTOR(CLASS) EIGEN_DEVICE_FUNC CLASS(const CLASS&) = default;
+
+
+
+/** \internal
+ * \brief Macro to manually inherit assignment operators.
+ * This is necessary, because the implicitly defined assignment operator gets deleted when a custom operator= is defined.
+ * With C++11 or later this also default-implements the copy-constructor
+ */
+#define EIGEN_INHERIT_ASSIGNMENT_OPERATORS(Derived) \
+ EIGEN_INHERIT_ASSIGNMENT_EQUAL_OPERATOR(Derived) \
+ EIGEN_DEFAULT_COPY_CONSTRUCTOR(Derived)
+
+/** \internal
+ * \brief Macro to manually define default constructors and destructors.
+ * This is necessary when the copy constructor is re-defined.
+ * For empty helper classes this should usually be protected, to avoid accidentally creating empty objects.
+ *
+ * Hiding the default destructor lead to problems in C++03 mode together with boost::multiprecision
+ */
+#define EIGEN_DEFAULT_EMPTY_CONSTRUCTOR_AND_DESTRUCTOR(Derived) \
+ EIGEN_DEVICE_FUNC Derived() = default; \
+ EIGEN_DEVICE_FUNC ~Derived() = default;
+
+
+
+
+
+/**
+* Just a side note. Commenting within defines works only by documenting
+* behind the object (via '!<'). Comments cannot be multi-line and thus
+* we have these extra long lines. What is confusing doxygen over here is
+* that we use '\' and basically have a bunch of typedefs with their
+* documentation in a single line.
+**/
+
+#define EIGEN_GENERIC_PUBLIC_INTERFACE(Derived) \
+ typedef typename Eigen::internal::traits<Derived>::Scalar Scalar; /*!< \brief Numeric type, e.g. float, double, int or std::complex<float>. */ \
+ typedef typename Eigen::NumTraits<Scalar>::Real RealScalar; /*!< \brief The underlying numeric type for composed scalar types. \details In cases where Scalar is e.g. std::complex<T>, T were corresponding to RealScalar. */ \
+ typedef typename Base::CoeffReturnType CoeffReturnType; /*!< \brief The return type for coefficient access. \details Depending on whether the object allows direct coefficient access (e.g. for a MatrixXd), this type is either 'const Scalar&' or simply 'Scalar' for objects that do not allow direct coefficient access. */ \
+ typedef typename Eigen::internal::ref_selector<Derived>::type Nested; \
+ typedef typename Eigen::internal::traits<Derived>::StorageKind StorageKind; \
+ typedef typename Eigen::internal::traits<Derived>::StorageIndex StorageIndex; \
+ enum CompileTimeTraits \
+ { RowsAtCompileTime = Eigen::internal::traits<Derived>::RowsAtCompileTime, \
+ ColsAtCompileTime = Eigen::internal::traits<Derived>::ColsAtCompileTime, \
+ Flags = Eigen::internal::traits<Derived>::Flags, \
+ SizeAtCompileTime = Base::SizeAtCompileTime, \
+ MaxSizeAtCompileTime = Base::MaxSizeAtCompileTime, \
+ IsVectorAtCompileTime = Base::IsVectorAtCompileTime }; \
+ using Base::derived; \
+ using Base::const_cast_derived;
+
+
+// FIXME Maybe the EIGEN_DENSE_PUBLIC_INTERFACE could be removed as importing PacketScalar is rarely needed
+#define EIGEN_DENSE_PUBLIC_INTERFACE(Derived) \
+ EIGEN_GENERIC_PUBLIC_INTERFACE(Derived) \
+ typedef typename Base::PacketScalar PacketScalar;
+
+
+#if EIGEN_HAS_BUILTIN(__builtin_expect) || EIGEN_COMP_GNUC
+#define EIGEN_PREDICT_FALSE(x) (__builtin_expect(x, false))
+#define EIGEN_PREDICT_TRUE(x) (__builtin_expect(false || (x), true))
+#else
+#define EIGEN_PREDICT_FALSE(x) (x)
+#define EIGEN_PREDICT_TRUE(x) (x)
+#endif
+
+// the expression type of a standard coefficient wise binary operation
+#define EIGEN_CWISE_BINARY_RETURN_TYPE(LHS,RHS,OPNAME) \
+ CwiseBinaryOp< \
+ EIGEN_CAT(EIGEN_CAT(internal::scalar_,OPNAME),_op)< \
+ typename internal::traits<LHS>::Scalar, \
+ typename internal::traits<RHS>::Scalar \
+ >, \
+ const LHS, \
+ const RHS \
+ >
+
+#define EIGEN_MAKE_CWISE_BINARY_OP(METHOD,OPNAME) \
+ template<typename OtherDerived> \
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const EIGEN_CWISE_BINARY_RETURN_TYPE(Derived,OtherDerived,OPNAME) \
+ (METHOD)(const EIGEN_CURRENT_STORAGE_BASE_CLASS<OtherDerived> &other) const \
+ { \
+ return EIGEN_CWISE_BINARY_RETURN_TYPE(Derived,OtherDerived,OPNAME)(derived(), other.derived()); \
+ }
+
+#define EIGEN_SCALAR_BINARY_SUPPORTED(OPNAME,TYPEA,TYPEB) \
+ (Eigen::internal::has_ReturnType<Eigen::ScalarBinaryOpTraits<TYPEA,TYPEB,EIGEN_CAT(EIGEN_CAT(Eigen::internal::scalar_,OPNAME),_op)<TYPEA,TYPEB> > >::value)
+
+#define EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(EXPR,SCALAR,OPNAME) \
+ CwiseBinaryOp<EIGEN_CAT(EIGEN_CAT(internal::scalar_,OPNAME),_op)<typename internal::traits<EXPR>::Scalar,SCALAR>, const EXPR, \
+ const typename internal::plain_constant_type<EXPR,SCALAR>::type>
+
+#define EIGEN_SCALAR_BINARYOP_EXPR_RETURN_TYPE(SCALAR,EXPR,OPNAME) \
+ CwiseBinaryOp<EIGEN_CAT(EIGEN_CAT(internal::scalar_,OPNAME),_op)<SCALAR,typename internal::traits<EXPR>::Scalar>, \
+ const typename internal::plain_constant_type<EXPR,SCALAR>::type, const EXPR>
+
+#define EIGEN_MAKE_SCALAR_BINARY_OP_ONTHERIGHT(METHOD,OPNAME) \
+ template <typename T> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE \
+ const EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(Derived,typename internal::promote_scalar_arg<Scalar EIGEN_COMMA T EIGEN_COMMA EIGEN_SCALAR_BINARY_SUPPORTED(OPNAME,Scalar,T)>::type,OPNAME)\
+ (METHOD)(const T& scalar) const { \
+ typedef typename internal::promote_scalar_arg<Scalar,T,EIGEN_SCALAR_BINARY_SUPPORTED(OPNAME,Scalar,T)>::type PromotedT; \
+ return EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(Derived,PromotedT,OPNAME)(derived(), \
+ typename internal::plain_constant_type<Derived,PromotedT>::type(derived().rows(), derived().cols(), internal::scalar_constant_op<PromotedT>(scalar))); \
+ }
+
+#define EIGEN_MAKE_SCALAR_BINARY_OP_ONTHELEFT(METHOD,OPNAME) \
+ template <typename T> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE friend \
+ const EIGEN_SCALAR_BINARYOP_EXPR_RETURN_TYPE(typename internal::promote_scalar_arg<Scalar EIGEN_COMMA T EIGEN_COMMA EIGEN_SCALAR_BINARY_SUPPORTED(OPNAME,T,Scalar)>::type,Derived,OPNAME) \
+ (METHOD)(const T& scalar, const StorageBaseType& matrix) { \
+ typedef typename internal::promote_scalar_arg<Scalar,T,EIGEN_SCALAR_BINARY_SUPPORTED(OPNAME,T,Scalar)>::type PromotedT; \
+ return EIGEN_SCALAR_BINARYOP_EXPR_RETURN_TYPE(PromotedT,Derived,OPNAME)( \
+ typename internal::plain_constant_type<Derived,PromotedT>::type(matrix.derived().rows(), matrix.derived().cols(), internal::scalar_constant_op<PromotedT>(scalar)), matrix.derived()); \
+ }
+
+#define EIGEN_MAKE_SCALAR_BINARY_OP(METHOD,OPNAME) \
+ EIGEN_MAKE_SCALAR_BINARY_OP_ONTHELEFT(METHOD,OPNAME) \
+ EIGEN_MAKE_SCALAR_BINARY_OP_ONTHERIGHT(METHOD,OPNAME)
+
+
+#if (defined(_CPPUNWIND) || defined(__EXCEPTIONS)) && !defined(EIGEN_CUDA_ARCH) && !defined(EIGEN_EXCEPTIONS) && !defined(EIGEN_USE_SYCL) && !defined(EIGEN_HIP_DEVICE_COMPILE)
+ #define EIGEN_EXCEPTIONS
+#endif
+
+
+#ifdef EIGEN_EXCEPTIONS
+# define EIGEN_THROW_X(X) throw X
+# define EIGEN_THROW throw
+# define EIGEN_TRY try
+# define EIGEN_CATCH(X) catch (X)
+#else
+# if defined(EIGEN_CUDA_ARCH)
+# define EIGEN_THROW_X(X) asm("trap;")
+# define EIGEN_THROW asm("trap;")
+# elif defined(EIGEN_HIP_DEVICE_COMPILE)
+# define EIGEN_THROW_X(X) asm("s_trap 0")
+# define EIGEN_THROW asm("s_trap 0")
+# else
+# define EIGEN_THROW_X(X) std::abort()
+# define EIGEN_THROW std::abort()
+# endif
+# define EIGEN_TRY if (true)
+# define EIGEN_CATCH(X) else
+#endif
+
+
+#define EIGEN_NOEXCEPT noexcept
+#define EIGEN_NOEXCEPT_IF(x) noexcept(x)
+#define EIGEN_NO_THROW noexcept(true)
+#define EIGEN_EXCEPTION_SPEC(X) noexcept(false)
+
+
+// The all function is used to enable a variadic version of eigen_assert which can take a parameter pack as its input.
+namespace Eigen {
+namespace internal {
+
+inline bool all(){ return true; }
+
+template<typename T, typename ...Ts>
+bool all(T t, Ts ... ts){ return t && all(ts...); }
+
+}
+}
+
+// provide override and final specifiers if they are available:
+#define EIGEN_OVERRIDE override
+#define EIGEN_FINAL final
+
+// Wrapping #pragma unroll in a macro since it is required for SYCL
+#if defined(SYCL_DEVICE_ONLY)
+ #if defined(_MSC_VER)
+ #define EIGEN_UNROLL_LOOP __pragma(unroll)
+ #else
+ #define EIGEN_UNROLL_LOOP _Pragma("unroll")
+ #endif
+#else
+ #define EIGEN_UNROLL_LOOP
+#endif
+
+// Notice: Use this macro with caution. The code in the if body should still
+// compile with C++14.
+#if defined(EIGEN_HAS_CXX17_IFCONSTEXPR)
+#define EIGEN_IF_CONSTEXPR(X) if constexpr (X)
+#else
+#define EIGEN_IF_CONSTEXPR(X) if (X)
+#endif
+
+#endif // EIGEN_MACROS_H
diff --git a/Eigen/src/Core/util/Memory.h b/Eigen/src/Core/util/Memory.h
new file mode 100644
index 0000000..385f4f4
--- /dev/null
+++ b/Eigen/src/Core/util/Memory.h
@@ -0,0 +1,1231 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2015 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2008-2009 Benoit Jacob <jacob.benoit.1@gmail.com>
+// Copyright (C) 2009 Kenneth Riddile <kfriddile@yahoo.com>
+// Copyright (C) 2010 Hauke Heibel <hauke.heibel@gmail.com>
+// Copyright (C) 2010 Thomas Capricelli <orzel@freehackers.org>
+// Copyright (C) 2013 Pavel Holoborodko <pavel@holoborodko.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+
+/*****************************************************************************
+*** Platform checks for aligned malloc functions ***
+*****************************************************************************/
+
+#ifndef EIGEN_MEMORY_H
+#define EIGEN_MEMORY_H
+
+#ifndef EIGEN_MALLOC_ALREADY_ALIGNED
+
+// Try to determine automatically if malloc is already aligned.
+
+// On 64-bit systems, glibc's malloc returns 16-byte-aligned pointers, see:
+// http://www.gnu.org/s/libc/manual/html_node/Aligned-Memory-Blocks.html
+// This is true at least since glibc 2.8.
+// This leaves the question how to detect 64-bit. According to this document,
+// http://gcc.fyxm.net/summit/2003/Porting%20to%2064%20bit.pdf
+// page 114, "[The] LP64 model [...] is used by all 64-bit UNIX ports" so it's indeed
+// quite safe, at least within the context of glibc, to equate 64-bit with LP64.
+#if defined(__GLIBC__) && ((__GLIBC__>=2 && __GLIBC_MINOR__ >= 8) || __GLIBC__>2) \
+ && defined(__LP64__) && ! defined( __SANITIZE_ADDRESS__ ) && (EIGEN_DEFAULT_ALIGN_BYTES == 16)
+ #define EIGEN_GLIBC_MALLOC_ALREADY_ALIGNED 1
+#else
+ #define EIGEN_GLIBC_MALLOC_ALREADY_ALIGNED 0
+#endif
+
+// FreeBSD 6 seems to have 16-byte aligned malloc
+// See http://svn.freebsd.org/viewvc/base/stable/6/lib/libc/stdlib/malloc.c?view=markup
+// FreeBSD 7 seems to have 16-byte aligned malloc except on ARM and MIPS architectures
+// See http://svn.freebsd.org/viewvc/base/stable/7/lib/libc/stdlib/malloc.c?view=markup
+#if defined(__FreeBSD__) && !(EIGEN_ARCH_ARM || EIGEN_ARCH_MIPS) && (EIGEN_DEFAULT_ALIGN_BYTES == 16)
+ #define EIGEN_FREEBSD_MALLOC_ALREADY_ALIGNED 1
+#else
+ #define EIGEN_FREEBSD_MALLOC_ALREADY_ALIGNED 0
+#endif
+
+#if (EIGEN_OS_MAC && (EIGEN_DEFAULT_ALIGN_BYTES == 16)) \
+ || (EIGEN_OS_WIN64 && (EIGEN_DEFAULT_ALIGN_BYTES == 16)) \
+ || EIGEN_GLIBC_MALLOC_ALREADY_ALIGNED \
+ || EIGEN_FREEBSD_MALLOC_ALREADY_ALIGNED
+ #define EIGEN_MALLOC_ALREADY_ALIGNED 1
+#else
+ #define EIGEN_MALLOC_ALREADY_ALIGNED 0
+#endif
+
+#endif
+
+#include "../InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+
+EIGEN_DEVICE_FUNC
+inline void throw_std_bad_alloc()
+{
+ #ifdef EIGEN_EXCEPTIONS
+ throw std::bad_alloc();
+ #else
+ std::size_t huge = static_cast<std::size_t>(-1);
+ #if defined(EIGEN_HIPCC)
+ //
+ // calls to "::operator new" are to be treated as opaque function calls (i.e no inlining),
+ // and as a consequence the code in the #else block triggers the hipcc warning :
+ // "no overloaded function has restriction specifiers that are compatible with the ambient context"
+ //
+ // "throw_std_bad_alloc" has the EIGEN_DEVICE_FUNC attribute, so it seems that hipcc expects
+ // the same on "operator new"
+ // Reverting code back to the old version in this #if block for the hipcc compiler
+ //
+ new int[huge];
+ #else
+ void* unused = ::operator new(huge);
+ EIGEN_UNUSED_VARIABLE(unused);
+ #endif
+ #endif
+}
+
+/*****************************************************************************
+*** Implementation of handmade aligned functions ***
+*****************************************************************************/
+
+/* ----- Hand made implementations of aligned malloc/free and realloc ----- */
+
+/** \internal Like malloc, but the returned pointer is guaranteed to be 16-byte aligned.
+ * Fast, but wastes 16 additional bytes of memory. Does not throw any exception.
+ */
+EIGEN_DEVICE_FUNC inline void* handmade_aligned_malloc(std::size_t size, std::size_t alignment = EIGEN_DEFAULT_ALIGN_BYTES)
+{
+ eigen_assert(alignment >= sizeof(void*) && (alignment & (alignment-1)) == 0 && "Alignment must be at least sizeof(void*) and a power of 2");
+
+ EIGEN_USING_STD(malloc)
+ void *original = malloc(size+alignment);
+
+ if (original == 0) return 0;
+ void *aligned = reinterpret_cast<void*>((reinterpret_cast<std::size_t>(original) & ~(std::size_t(alignment-1))) + alignment);
+ *(reinterpret_cast<void**>(aligned) - 1) = original;
+ return aligned;
+}
+
+/** \internal Frees memory allocated with handmade_aligned_malloc */
+EIGEN_DEVICE_FUNC inline void handmade_aligned_free(void *ptr)
+{
+ if (ptr) {
+ EIGEN_USING_STD(free)
+ free(*(reinterpret_cast<void**>(ptr) - 1));
+ }
+}
+
+/** \internal
+ * \brief Reallocates aligned memory.
+ * Since we know that our handmade version is based on std::malloc
+ * we can use std::realloc to implement efficient reallocation.
+ */
+inline void* handmade_aligned_realloc(void* ptr, std::size_t size, std::size_t = 0)
+{
+ if (ptr == 0) return handmade_aligned_malloc(size);
+ void *original = *(reinterpret_cast<void**>(ptr) - 1);
+ std::ptrdiff_t previous_offset = static_cast<char *>(ptr)-static_cast<char *>(original);
+ original = std::realloc(original,size+EIGEN_DEFAULT_ALIGN_BYTES);
+ if (original == 0) return 0;
+ void *aligned = reinterpret_cast<void*>((reinterpret_cast<std::size_t>(original) & ~(std::size_t(EIGEN_DEFAULT_ALIGN_BYTES-1))) + EIGEN_DEFAULT_ALIGN_BYTES);
+ void *previous_aligned = static_cast<char *>(original)+previous_offset;
+ if(aligned!=previous_aligned)
+ std::memmove(aligned, previous_aligned, size);
+
+ *(reinterpret_cast<void**>(aligned) - 1) = original;
+ return aligned;
+}
+
+/*****************************************************************************
+*** Implementation of portable aligned versions of malloc/free/realloc ***
+*****************************************************************************/
+
+#ifdef EIGEN_NO_MALLOC
+EIGEN_DEVICE_FUNC inline void check_that_malloc_is_allowed()
+{
+ eigen_assert(false && "heap allocation is forbidden (EIGEN_NO_MALLOC is defined)");
+}
+#elif defined EIGEN_RUNTIME_NO_MALLOC
+EIGEN_DEVICE_FUNC inline bool is_malloc_allowed_impl(bool update, bool new_value = false)
+{
+ static bool value = true;
+ if (update == 1)
+ value = new_value;
+ return value;
+}
+EIGEN_DEVICE_FUNC inline bool is_malloc_allowed() { return is_malloc_allowed_impl(false); }
+EIGEN_DEVICE_FUNC inline bool set_is_malloc_allowed(bool new_value) { return is_malloc_allowed_impl(true, new_value); }
+EIGEN_DEVICE_FUNC inline void check_that_malloc_is_allowed()
+{
+ eigen_assert(is_malloc_allowed() && "heap allocation is forbidden (EIGEN_RUNTIME_NO_MALLOC is defined and g_is_malloc_allowed is false)");
+}
+#else
+EIGEN_DEVICE_FUNC inline void check_that_malloc_is_allowed()
+{}
+#endif
+
+/** \internal Allocates \a size bytes. The returned pointer is guaranteed to have 16 or 32 bytes alignment depending on the requirements.
+ * On allocation error, the returned pointer is null, and std::bad_alloc is thrown.
+ */
+EIGEN_DEVICE_FUNC inline void* aligned_malloc(std::size_t size)
+{
+ check_that_malloc_is_allowed();
+
+ void *result;
+ #if (EIGEN_DEFAULT_ALIGN_BYTES==0) || EIGEN_MALLOC_ALREADY_ALIGNED
+
+ EIGEN_USING_STD(malloc)
+ result = malloc(size);
+
+ #if EIGEN_DEFAULT_ALIGN_BYTES==16
+ eigen_assert((size<16 || (std::size_t(result)%16)==0) && "System's malloc returned an unaligned pointer. Compile with EIGEN_MALLOC_ALREADY_ALIGNED=0 to fallback to handmade aligned memory allocator.");
+ #endif
+ #else
+ result = handmade_aligned_malloc(size);
+ #endif
+
+ if(!result && size)
+ throw_std_bad_alloc();
+
+ return result;
+}
+
+/** \internal Frees memory allocated with aligned_malloc. */
+EIGEN_DEVICE_FUNC inline void aligned_free(void *ptr)
+{
+ #if (EIGEN_DEFAULT_ALIGN_BYTES==0) || EIGEN_MALLOC_ALREADY_ALIGNED
+
+ EIGEN_USING_STD(free)
+ free(ptr);
+
+ #else
+ handmade_aligned_free(ptr);
+ #endif
+}
+
+/**
+ * \internal
+ * \brief Reallocates an aligned block of memory.
+ * \throws std::bad_alloc on allocation failure
+ */
+inline void* aligned_realloc(void *ptr, std::size_t new_size, std::size_t old_size)
+{
+ if (ptr == 0) return aligned_malloc(new_size);
+ EIGEN_UNUSED_VARIABLE(old_size)
+
+ void *result;
+#if (EIGEN_DEFAULT_ALIGN_BYTES==0) || EIGEN_MALLOC_ALREADY_ALIGNED
+ result = std::realloc(ptr,new_size);
+#else
+ result = handmade_aligned_realloc(ptr,new_size,old_size);
+#endif
+
+ if (!result && new_size)
+ throw_std_bad_alloc();
+
+#ifdef EIGEN_RUNTIME_NO_MALLOC
+ if (result != ptr)
+ check_that_malloc_is_allowed();
+#endif
+
+ return result;
+}
+
+/*****************************************************************************
+*** Implementation of conditionally aligned functions ***
+*****************************************************************************/
+
+/** \internal Allocates \a size bytes. If Align is true, then the returned ptr is 16-byte-aligned.
+ * On allocation error, the returned pointer is null, and a std::bad_alloc is thrown.
+ */
+template<bool Align> EIGEN_DEVICE_FUNC inline void* conditional_aligned_malloc(std::size_t size)
+{
+ return aligned_malloc(size);
+}
+
+template<> EIGEN_DEVICE_FUNC inline void* conditional_aligned_malloc<false>(std::size_t size)
+{
+ check_that_malloc_is_allowed();
+
+ EIGEN_USING_STD(malloc)
+ void *result = malloc(size);
+
+ if(!result && size)
+ throw_std_bad_alloc();
+ return result;
+}
+
+/** \internal Frees memory allocated with conditional_aligned_malloc */
+template<bool Align> EIGEN_DEVICE_FUNC inline void conditional_aligned_free(void *ptr)
+{
+ aligned_free(ptr);
+}
+
+template<> EIGEN_DEVICE_FUNC inline void conditional_aligned_free<false>(void *ptr)
+{
+ EIGEN_USING_STD(free)
+ free(ptr);
+}
+
+template<bool Align> inline void* conditional_aligned_realloc(void* ptr, std::size_t new_size, std::size_t old_size)
+{
+ return aligned_realloc(ptr, new_size, old_size);
+}
+
+template<> inline void* conditional_aligned_realloc<false>(void* ptr, std::size_t new_size, std::size_t)
+{
+ return std::realloc(ptr, new_size);
+}
+
+/*****************************************************************************
+*** Construction/destruction of array elements ***
+*****************************************************************************/
+
+/** \internal Destructs the elements of an array.
+ * The \a size parameters tells on how many objects to call the destructor of T.
+ */
+template<typename T> EIGEN_DEVICE_FUNC inline void destruct_elements_of_array(T *ptr, std::size_t size)
+{
+ // always destruct an array starting from the end.
+ if(ptr)
+ while(size) ptr[--size].~T();
+}
+
+/** \internal Constructs the elements of an array.
+ * The \a size parameter tells on how many objects to call the constructor of T.
+ */
+template<typename T> EIGEN_DEVICE_FUNC inline T* default_construct_elements_of_array(T *ptr, std::size_t size)
+{
+ std::size_t i=0;
+ EIGEN_TRY
+ {
+ for (i = 0; i < size; ++i) ::new (ptr + i) T;
+ }
+ EIGEN_CATCH(...)
+ {
+ destruct_elements_of_array(ptr, i);
+ EIGEN_THROW;
+ }
+ return ptr;
+}
+
+/** \internal Copy-constructs the elements of an array.
+ * The \a size parameter tells on how many objects to copy.
+ */
+template<typename T> EIGEN_DEVICE_FUNC inline T* copy_construct_elements_of_array(T *ptr, const T* src, std::size_t size)
+{
+ std::size_t i=0;
+ EIGEN_TRY
+ {
+ for (i = 0; i < size; ++i) ::new (ptr + i) T(*(src + i));
+ }
+ EIGEN_CATCH(...)
+ {
+ destruct_elements_of_array(ptr, i);
+ EIGEN_THROW;
+ }
+ return ptr;
+}
+
+/** \internal Move-constructs the elements of an array.
+ * The \a size parameter tells on how many objects to move.
+ */
+template<typename T> EIGEN_DEVICE_FUNC inline T* move_construct_elements_of_array(T *ptr, T* src, std::size_t size)
+{
+ std::size_t i=0;
+ EIGEN_TRY
+ {
+ for (i = 0; i < size; ++i) ::new (ptr + i) T(std::move(*(src + i)));
+ }
+ EIGEN_CATCH(...)
+ {
+ destruct_elements_of_array(ptr, i);
+ EIGEN_THROW;
+ }
+ return ptr;
+}
+
+/*****************************************************************************
+*** Implementation of aligned new/delete-like functions ***
+*****************************************************************************/
+
+template<typename T>
+EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE void check_size_for_overflow(std::size_t size)
+{
+ if(size > std::size_t(-1) / sizeof(T))
+ throw_std_bad_alloc();
+}
+
+/** \internal Allocates \a size objects of type T. The returned pointer is guaranteed to have 16 bytes alignment.
+ * On allocation error, the returned pointer is undefined, but a std::bad_alloc is thrown.
+ * The default constructor of T is called.
+ */
+template<typename T> EIGEN_DEVICE_FUNC inline T* aligned_new(std::size_t size)
+{
+ check_size_for_overflow<T>(size);
+ T *result = static_cast<T*>(aligned_malloc(sizeof(T)*size));
+ EIGEN_TRY
+ {
+ return default_construct_elements_of_array(result, size);
+ }
+ EIGEN_CATCH(...)
+ {
+ aligned_free(result);
+ EIGEN_THROW;
+ }
+ return result;
+}
+
+template<typename T, bool Align> EIGEN_DEVICE_FUNC inline T* conditional_aligned_new(std::size_t size)
+{
+ check_size_for_overflow<T>(size);
+ T *result = static_cast<T*>(conditional_aligned_malloc<Align>(sizeof(T)*size));
+ EIGEN_TRY
+ {
+ return default_construct_elements_of_array(result, size);
+ }
+ EIGEN_CATCH(...)
+ {
+ conditional_aligned_free<Align>(result);
+ EIGEN_THROW;
+ }
+ return result;
+}
+
+/** \internal Deletes objects constructed with aligned_new
+ * The \a size parameters tells on how many objects to call the destructor of T.
+ */
+template<typename T> EIGEN_DEVICE_FUNC inline void aligned_delete(T *ptr, std::size_t size)
+{
+ destruct_elements_of_array<T>(ptr, size);
+ Eigen::internal::aligned_free(ptr);
+}
+
+/** \internal Deletes objects constructed with conditional_aligned_new
+ * The \a size parameters tells on how many objects to call the destructor of T.
+ */
+template<typename T, bool Align> EIGEN_DEVICE_FUNC inline void conditional_aligned_delete(T *ptr, std::size_t size)
+{
+ destruct_elements_of_array<T>(ptr, size);
+ conditional_aligned_free<Align>(ptr);
+}
+
+template<typename T, bool Align> EIGEN_DEVICE_FUNC inline T* conditional_aligned_realloc_new(T* pts, std::size_t new_size, std::size_t old_size)
+{
+ check_size_for_overflow<T>(new_size);
+ check_size_for_overflow<T>(old_size);
+
+ // If elements need to be explicitly initialized, we cannot simply realloc
+ // (or memcpy) the memory block - each element needs to be reconstructed.
+ // Otherwise, objects that contain internal pointers like mpfr or
+ // AnnoyingScalar can be pointing to the wrong thing.
+ T* result = static_cast<T*>(conditional_aligned_malloc<Align>(sizeof(T)*new_size));
+ EIGEN_TRY
+ {
+ // Move-construct initial elements.
+ std::size_t copy_size = (std::min)(old_size, new_size);
+ move_construct_elements_of_array(result, pts, copy_size);
+
+ // Default-construct remaining elements.
+ if (new_size > old_size) {
+ default_construct_elements_of_array(result + copy_size, new_size - old_size);
+ }
+
+ // Delete old elements.
+ conditional_aligned_delete<T, Align>(pts, old_size);
+ }
+ EIGEN_CATCH(...)
+ {
+ conditional_aligned_free<Align>(result);
+ EIGEN_THROW;
+ }
+
+ return result;
+}
+
+
+template<typename T, bool Align> EIGEN_DEVICE_FUNC inline T* conditional_aligned_new_auto(std::size_t size)
+{
+ if(size==0)
+ return 0; // short-cut. Also fixes Bug 884
+ check_size_for_overflow<T>(size);
+ T *result = static_cast<T*>(conditional_aligned_malloc<Align>(sizeof(T)*size));
+ if(NumTraits<T>::RequireInitialization)
+ {
+ EIGEN_TRY
+ {
+ default_construct_elements_of_array(result, size);
+ }
+ EIGEN_CATCH(...)
+ {
+ conditional_aligned_free<Align>(result);
+ EIGEN_THROW;
+ }
+ }
+ return result;
+}
+
+template<typename T, bool Align> inline T* conditional_aligned_realloc_new_auto(T* pts, std::size_t new_size, std::size_t old_size)
+{
+ if (NumTraits<T>::RequireInitialization) {
+ return conditional_aligned_realloc_new<T, Align>(pts, new_size, old_size);
+ }
+
+ check_size_for_overflow<T>(new_size);
+ check_size_for_overflow<T>(old_size);
+ return static_cast<T*>(conditional_aligned_realloc<Align>(static_cast<void*>(pts), sizeof(T)*new_size, sizeof(T)*old_size));
+}
+
+template<typename T, bool Align> EIGEN_DEVICE_FUNC inline void conditional_aligned_delete_auto(T *ptr, std::size_t size)
+{
+ if(NumTraits<T>::RequireInitialization)
+ destruct_elements_of_array<T>(ptr, size);
+ conditional_aligned_free<Align>(ptr);
+}
+
+/****************************************************************************/
+
+/** \internal Returns the index of the first element of the array that is well aligned with respect to the requested \a Alignment.
+ *
+ * \tparam Alignment requested alignment in Bytes.
+ * \param array the address of the start of the array
+ * \param size the size of the array
+ *
+ * \note If no element of the array is well aligned or the requested alignment is not a multiple of a scalar,
+ * the size of the array is returned. For example with SSE, the requested alignment is typically 16-bytes. If
+ * packet size for the given scalar type is 1, then everything is considered well-aligned.
+ *
+ * \note Otherwise, if the Alignment is larger that the scalar size, we rely on the assumptions that sizeof(Scalar) is a
+ * power of 2. On the other hand, we do not assume that the array address is a multiple of sizeof(Scalar), as that fails for
+ * example with Scalar=double on certain 32-bit platforms, see bug #79.
+ *
+ * There is also the variant first_aligned(const MatrixBase&) defined in DenseCoeffsBase.h.
+ * \sa first_default_aligned()
+ */
+template<int Alignment, typename Scalar, typename Index>
+EIGEN_DEVICE_FUNC inline Index first_aligned(const Scalar* array, Index size)
+{
+ const Index ScalarSize = sizeof(Scalar);
+ const Index AlignmentSize = Alignment / ScalarSize;
+ const Index AlignmentMask = AlignmentSize-1;
+
+ if(AlignmentSize<=1)
+ {
+ // Either the requested alignment if smaller than a scalar, or it exactly match a 1 scalar
+ // so that all elements of the array have the same alignment.
+ return 0;
+ }
+ else if( (UIntPtr(array) & (sizeof(Scalar)-1)) || (Alignment%ScalarSize)!=0)
+ {
+ // The array is not aligned to the size of a single scalar, or the requested alignment is not a multiple of the scalar size.
+ // Consequently, no element of the array is well aligned.
+ return size;
+ }
+ else
+ {
+ Index first = (AlignmentSize - (Index((UIntPtr(array)/sizeof(Scalar))) & AlignmentMask)) & AlignmentMask;
+ return (first < size) ? first : size;
+ }
+}
+
+/** \internal Returns the index of the first element of the array that is well aligned with respect the largest packet requirement.
+ * \sa first_aligned(Scalar*,Index) and first_default_aligned(DenseBase<Derived>) */
+template<typename Scalar, typename Index>
+EIGEN_DEVICE_FUNC inline Index first_default_aligned(const Scalar* array, Index size)
+{
+ typedef typename packet_traits<Scalar>::type DefaultPacketType;
+ return first_aligned<unpacket_traits<DefaultPacketType>::alignment>(array, size);
+}
+
+/** \internal Returns the smallest integer multiple of \a base and greater or equal to \a size
+ */
+template<typename Index>
+inline Index first_multiple(Index size, Index base)
+{
+ return ((size+base-1)/base)*base;
+}
+
+// std::copy is much slower than memcpy, so let's introduce a smart_copy which
+// use memcpy on trivial types, i.e., on types that does not require an initialization ctor.
+template<typename T, bool UseMemcpy> struct smart_copy_helper;
+
+template<typename T> EIGEN_DEVICE_FUNC void smart_copy(const T* start, const T* end, T* target)
+{
+ smart_copy_helper<T,!NumTraits<T>::RequireInitialization>::run(start, end, target);
+}
+
+template<typename T> struct smart_copy_helper<T,true> {
+ EIGEN_DEVICE_FUNC static inline void run(const T* start, const T* end, T* target)
+ {
+ IntPtr size = IntPtr(end)-IntPtr(start);
+ if(size==0) return;
+ eigen_internal_assert(start!=0 && end!=0 && target!=0);
+ EIGEN_USING_STD(memcpy)
+ memcpy(target, start, size);
+ }
+};
+
+template<typename T> struct smart_copy_helper<T,false> {
+ EIGEN_DEVICE_FUNC static inline void run(const T* start, const T* end, T* target)
+ { std::copy(start, end, target); }
+};
+
+// intelligent memmove. falls back to std::memmove for POD types, uses std::copy otherwise.
+template<typename T, bool UseMemmove> struct smart_memmove_helper;
+
+template<typename T> void smart_memmove(const T* start, const T* end, T* target)
+{
+ smart_memmove_helper<T,!NumTraits<T>::RequireInitialization>::run(start, end, target);
+}
+
+template<typename T> struct smart_memmove_helper<T,true> {
+ static inline void run(const T* start, const T* end, T* target)
+ {
+ IntPtr size = IntPtr(end)-IntPtr(start);
+ if(size==0) return;
+ eigen_internal_assert(start!=0 && end!=0 && target!=0);
+ std::memmove(target, start, size);
+ }
+};
+
+template<typename T> struct smart_memmove_helper<T,false> {
+ static inline void run(const T* start, const T* end, T* target)
+ {
+ if (UIntPtr(target) < UIntPtr(start))
+ {
+ std::copy(start, end, target);
+ }
+ else
+ {
+ std::ptrdiff_t count = (std::ptrdiff_t(end)-std::ptrdiff_t(start)) / sizeof(T);
+ std::copy_backward(start, end, target + count);
+ }
+ }
+};
+
+template<typename T> EIGEN_DEVICE_FUNC T* smart_move(T* start, T* end, T* target)
+{
+ return std::move(start, end, target);
+}
+
+/*****************************************************************************
+*** Implementation of runtime stack allocation (falling back to malloc) ***
+*****************************************************************************/
+
+// you can overwrite Eigen's default behavior regarding alloca by defining EIGEN_ALLOCA
+// to the appropriate stack allocation function
+#if ! defined EIGEN_ALLOCA && ! defined EIGEN_GPU_COMPILE_PHASE
+ #if EIGEN_OS_LINUX || EIGEN_OS_MAC || (defined alloca)
+ #define EIGEN_ALLOCA alloca
+ #elif EIGEN_COMP_MSVC
+ #define EIGEN_ALLOCA _alloca
+ #endif
+#endif
+
+// With clang -Oz -mthumb, alloca changes the stack pointer in a way that is
+// not allowed in Thumb2. -DEIGEN_STACK_ALLOCATION_LIMIT=0 doesn't work because
+// the compiler still emits bad code because stack allocation checks use "<=".
+// TODO: Eliminate after https://bugs.llvm.org/show_bug.cgi?id=23772
+// is fixed.
+#if defined(__clang__) && defined(__thumb__)
+ #undef EIGEN_ALLOCA
+#endif
+
+// This helper class construct the allocated memory, and takes care of destructing and freeing the handled data
+// at destruction time. In practice this helper class is mainly useful to avoid memory leak in case of exceptions.
+template<typename T> class aligned_stack_memory_handler : noncopyable
+{
+ public:
+ /* Creates a stack_memory_handler responsible for the buffer \a ptr of size \a size.
+ * Note that \a ptr can be 0 regardless of the other parameters.
+ * This constructor takes care of constructing/initializing the elements of the buffer if required by the scalar type T (see NumTraits<T>::RequireInitialization).
+ * In this case, the buffer elements will also be destructed when this handler will be destructed.
+ * Finally, if \a dealloc is true, then the pointer \a ptr is freed.
+ **/
+ EIGEN_DEVICE_FUNC
+ aligned_stack_memory_handler(T* ptr, std::size_t size, bool dealloc)
+ : m_ptr(ptr), m_size(size), m_deallocate(dealloc)
+ {
+ if(NumTraits<T>::RequireInitialization && m_ptr)
+ Eigen::internal::default_construct_elements_of_array(m_ptr, size);
+ }
+ EIGEN_DEVICE_FUNC
+ ~aligned_stack_memory_handler()
+ {
+ if(NumTraits<T>::RequireInitialization && m_ptr)
+ Eigen::internal::destruct_elements_of_array<T>(m_ptr, m_size);
+ if(m_deallocate)
+ Eigen::internal::aligned_free(m_ptr);
+ }
+ protected:
+ T* m_ptr;
+ std::size_t m_size;
+ bool m_deallocate;
+};
+
+#ifdef EIGEN_ALLOCA
+
+template<typename Xpr, int NbEvaluations,
+ bool MapExternalBuffer = nested_eval<Xpr,NbEvaluations>::Evaluate && Xpr::MaxSizeAtCompileTime==Dynamic
+ >
+struct local_nested_eval_wrapper
+{
+ static constexpr bool NeedExternalBuffer = false;
+ typedef typename Xpr::Scalar Scalar;
+ typedef typename nested_eval<Xpr,NbEvaluations>::type ObjectType;
+ ObjectType object;
+
+ EIGEN_DEVICE_FUNC
+ local_nested_eval_wrapper(const Xpr& xpr, Scalar* ptr) : object(xpr)
+ {
+ EIGEN_UNUSED_VARIABLE(ptr);
+ eigen_internal_assert(ptr==0);
+ }
+};
+
+template<typename Xpr, int NbEvaluations>
+struct local_nested_eval_wrapper<Xpr,NbEvaluations,true>
+{
+ static constexpr bool NeedExternalBuffer = true;
+ typedef typename Xpr::Scalar Scalar;
+ typedef typename plain_object_eval<Xpr>::type PlainObject;
+ typedef Map<PlainObject,EIGEN_DEFAULT_ALIGN_BYTES> ObjectType;
+ ObjectType object;
+
+ EIGEN_DEVICE_FUNC
+ local_nested_eval_wrapper(const Xpr& xpr, Scalar* ptr)
+ : object(ptr==0 ? reinterpret_cast<Scalar*>(Eigen::internal::aligned_malloc(sizeof(Scalar)*xpr.size())) : ptr, xpr.rows(), xpr.cols()),
+ m_deallocate(ptr==0)
+ {
+ if(NumTraits<Scalar>::RequireInitialization && object.data())
+ Eigen::internal::default_construct_elements_of_array(object.data(), object.size());
+ object = xpr;
+ }
+
+ EIGEN_DEVICE_FUNC
+ ~local_nested_eval_wrapper()
+ {
+ if(NumTraits<Scalar>::RequireInitialization && object.data())
+ Eigen::internal::destruct_elements_of_array(object.data(), object.size());
+ if(m_deallocate)
+ Eigen::internal::aligned_free(object.data());
+ }
+
+private:
+ bool m_deallocate;
+};
+
+#endif // EIGEN_ALLOCA
+
+template<typename T> class scoped_array : noncopyable
+{
+ T* m_ptr;
+public:
+ explicit scoped_array(std::ptrdiff_t size)
+ {
+ m_ptr = new T[size];
+ }
+ ~scoped_array()
+ {
+ delete[] m_ptr;
+ }
+ T& operator[](std::ptrdiff_t i) { return m_ptr[i]; }
+ const T& operator[](std::ptrdiff_t i) const { return m_ptr[i]; }
+ T* &ptr() { return m_ptr; }
+ const T* ptr() const { return m_ptr; }
+ operator const T*() const { return m_ptr; }
+};
+
+template<typename T> void swap(scoped_array<T> &a,scoped_array<T> &b)
+{
+ std::swap(a.ptr(),b.ptr());
+}
+
+} // end namespace internal
+
+/** \internal
+ *
+ * The macro ei_declare_aligned_stack_constructed_variable(TYPE,NAME,SIZE,BUFFER) declares, allocates,
+ * and construct an aligned buffer named NAME of SIZE elements of type TYPE on the stack
+ * if the size in bytes is smaller than EIGEN_STACK_ALLOCATION_LIMIT, and if stack allocation is supported by the platform
+ * (currently, this is Linux, OSX and Visual Studio only). Otherwise the memory is allocated on the heap.
+ * The allocated buffer is automatically deleted when exiting the scope of this declaration.
+ * If BUFFER is non null, then the declared variable is simply an alias for BUFFER, and no allocation/deletion occurs.
+ * Here is an example:
+ * \code
+ * {
+ * ei_declare_aligned_stack_constructed_variable(float,data,size,0);
+ * // use data[0] to data[size-1]
+ * }
+ * \endcode
+ * The underlying stack allocation function can controlled with the EIGEN_ALLOCA preprocessor token.
+ *
+ * The macro ei_declare_local_nested_eval(XPR_T,XPR,N,NAME) is analogue to
+ * \code
+ * typename internal::nested_eval<XPRT_T,N>::type NAME(XPR);
+ * \endcode
+ * with the advantage of using aligned stack allocation even if the maximal size of XPR at compile time is unknown.
+ * This is accomplished through alloca if this later is supported and if the required number of bytes
+ * is below EIGEN_STACK_ALLOCATION_LIMIT.
+ */
+#ifdef EIGEN_ALLOCA
+
+ #if EIGEN_DEFAULT_ALIGN_BYTES>0
+ // We always manually re-align the result of EIGEN_ALLOCA.
+ // If alloca is already aligned, the compiler should be smart enough to optimize away the re-alignment.
+ #define EIGEN_ALIGNED_ALLOCA(SIZE) reinterpret_cast<void*>((internal::UIntPtr(EIGEN_ALLOCA(SIZE+EIGEN_DEFAULT_ALIGN_BYTES-1)) + EIGEN_DEFAULT_ALIGN_BYTES-1) & ~(std::size_t(EIGEN_DEFAULT_ALIGN_BYTES-1)))
+ #else
+ #define EIGEN_ALIGNED_ALLOCA(SIZE) EIGEN_ALLOCA(SIZE)
+ #endif
+
+ #define ei_declare_aligned_stack_constructed_variable(TYPE,NAME,SIZE,BUFFER) \
+ Eigen::internal::check_size_for_overflow<TYPE>(SIZE); \
+ TYPE* NAME = (BUFFER)!=0 ? (BUFFER) \
+ : reinterpret_cast<TYPE*>( \
+ (sizeof(TYPE)*SIZE<=EIGEN_STACK_ALLOCATION_LIMIT) ? EIGEN_ALIGNED_ALLOCA(sizeof(TYPE)*SIZE) \
+ : Eigen::internal::aligned_malloc(sizeof(TYPE)*SIZE) ); \
+ Eigen::internal::aligned_stack_memory_handler<TYPE> EIGEN_CAT(NAME,_stack_memory_destructor)((BUFFER)==0 ? NAME : 0,SIZE,sizeof(TYPE)*SIZE>EIGEN_STACK_ALLOCATION_LIMIT)
+
+
+ #define ei_declare_local_nested_eval(XPR_T,XPR,N,NAME) \
+ Eigen::internal::local_nested_eval_wrapper<XPR_T,N> EIGEN_CAT(NAME,_wrapper)(XPR, reinterpret_cast<typename XPR_T::Scalar*>( \
+ ( (Eigen::internal::local_nested_eval_wrapper<XPR_T,N>::NeedExternalBuffer) && ((sizeof(typename XPR_T::Scalar)*XPR.size())<=EIGEN_STACK_ALLOCATION_LIMIT) ) \
+ ? EIGEN_ALIGNED_ALLOCA( sizeof(typename XPR_T::Scalar)*XPR.size() ) : 0 ) ) ; \
+ typename Eigen::internal::local_nested_eval_wrapper<XPR_T,N>::ObjectType NAME(EIGEN_CAT(NAME,_wrapper).object)
+
+#else
+
+ #define ei_declare_aligned_stack_constructed_variable(TYPE,NAME,SIZE,BUFFER) \
+ Eigen::internal::check_size_for_overflow<TYPE>(SIZE); \
+ TYPE* NAME = (BUFFER)!=0 ? BUFFER : reinterpret_cast<TYPE*>(Eigen::internal::aligned_malloc(sizeof(TYPE)*SIZE)); \
+ Eigen::internal::aligned_stack_memory_handler<TYPE> EIGEN_CAT(NAME,_stack_memory_destructor)((BUFFER)==0 ? NAME : 0,SIZE,true)
+
+
+#define ei_declare_local_nested_eval(XPR_T,XPR,N,NAME) typename Eigen::internal::nested_eval<XPR_T,N>::type NAME(XPR)
+
+#endif
+
+
+/*****************************************************************************
+*** Implementation of EIGEN_MAKE_ALIGNED_OPERATOR_NEW [_IF] ***
+*****************************************************************************/
+
+#if EIGEN_HAS_CXX17_OVERALIGN
+
+// C++17 -> no need to bother about alignment anymore :)
+
+#define EIGEN_MAKE_ALIGNED_OPERATOR_NEW_NOTHROW(NeedsToAlign)
+#define EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF(NeedsToAlign)
+#define EIGEN_MAKE_ALIGNED_OPERATOR_NEW
+#define EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE(Scalar,Size)
+
+#else
+
+// HIP does not support new/delete on device.
+#if EIGEN_MAX_ALIGN_BYTES!=0 && !defined(EIGEN_HIP_DEVICE_COMPILE)
+ #define EIGEN_MAKE_ALIGNED_OPERATOR_NEW_NOTHROW(NeedsToAlign) \
+ EIGEN_DEVICE_FUNC \
+ void* operator new(std::size_t size, const std::nothrow_t&) EIGEN_NO_THROW { \
+ EIGEN_TRY { return Eigen::internal::conditional_aligned_malloc<NeedsToAlign>(size); } \
+ EIGEN_CATCH (...) { return 0; } \
+ }
+ #define EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF(NeedsToAlign) \
+ EIGEN_DEVICE_FUNC \
+ void *operator new(std::size_t size) { \
+ return Eigen::internal::conditional_aligned_malloc<NeedsToAlign>(size); \
+ } \
+ EIGEN_DEVICE_FUNC \
+ void *operator new[](std::size_t size) { \
+ return Eigen::internal::conditional_aligned_malloc<NeedsToAlign>(size); \
+ } \
+ EIGEN_DEVICE_FUNC \
+ void operator delete(void * ptr) EIGEN_NO_THROW { Eigen::internal::conditional_aligned_free<NeedsToAlign>(ptr); } \
+ EIGEN_DEVICE_FUNC \
+ void operator delete[](void * ptr) EIGEN_NO_THROW { Eigen::internal::conditional_aligned_free<NeedsToAlign>(ptr); } \
+ EIGEN_DEVICE_FUNC \
+ void operator delete(void * ptr, std::size_t /* sz */) EIGEN_NO_THROW { Eigen::internal::conditional_aligned_free<NeedsToAlign>(ptr); } \
+ EIGEN_DEVICE_FUNC \
+ void operator delete[](void * ptr, std::size_t /* sz */) EIGEN_NO_THROW { Eigen::internal::conditional_aligned_free<NeedsToAlign>(ptr); } \
+ /* in-place new and delete. since (at least afaik) there is no actual */ \
+ /* memory allocated we can safely let the default implementation handle */ \
+ /* this particular case. */ \
+ EIGEN_DEVICE_FUNC \
+ static void *operator new(std::size_t size, void *ptr) { return ::operator new(size,ptr); } \
+ EIGEN_DEVICE_FUNC \
+ static void *operator new[](std::size_t size, void* ptr) { return ::operator new[](size,ptr); } \
+ EIGEN_DEVICE_FUNC \
+ void operator delete(void * memory, void *ptr) EIGEN_NO_THROW { return ::operator delete(memory,ptr); } \
+ EIGEN_DEVICE_FUNC \
+ void operator delete[](void * memory, void *ptr) EIGEN_NO_THROW { return ::operator delete[](memory,ptr); } \
+ /* nothrow-new (returns zero instead of std::bad_alloc) */ \
+ EIGEN_MAKE_ALIGNED_OPERATOR_NEW_NOTHROW(NeedsToAlign) \
+ EIGEN_DEVICE_FUNC \
+ void operator delete(void *ptr, const std::nothrow_t&) EIGEN_NO_THROW { \
+ Eigen::internal::conditional_aligned_free<NeedsToAlign>(ptr); \
+ } \
+ typedef void eigen_aligned_operator_new_marker_type;
+#else
+ #define EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF(NeedsToAlign)
+#endif
+
+#define EIGEN_MAKE_ALIGNED_OPERATOR_NEW EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF(true)
+#define EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE(Scalar,Size) \
+ EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF(bool( \
+ ((Size)!=Eigen::Dynamic) && \
+ (((EIGEN_MAX_ALIGN_BYTES>=16) && ((sizeof(Scalar)*(Size))%(EIGEN_MAX_ALIGN_BYTES )==0)) || \
+ ((EIGEN_MAX_ALIGN_BYTES>=32) && ((sizeof(Scalar)*(Size))%(EIGEN_MAX_ALIGN_BYTES/2)==0)) || \
+ ((EIGEN_MAX_ALIGN_BYTES>=64) && ((sizeof(Scalar)*(Size))%(EIGEN_MAX_ALIGN_BYTES/4)==0)) )))
+
+#endif
+
+/****************************************************************************/
+
+/** \class aligned_allocator
+* \ingroup Core_Module
+*
+* \brief STL compatible allocator to use with types requiring a non-standard alignment.
+*
+* The memory is aligned as for dynamically aligned matrix/array types such as MatrixXd.
+* By default, it will thus provide at least 16 bytes alignment and more in following cases:
+* - 32 bytes alignment if AVX is enabled.
+* - 64 bytes alignment if AVX512 is enabled.
+*
+* This can be controlled using the \c EIGEN_MAX_ALIGN_BYTES macro as documented
+* \link TopicPreprocessorDirectivesPerformance there \endlink.
+*
+* Example:
+* \code
+* // Matrix4f requires 16 bytes alignment:
+* std::map< int, Matrix4f, std::less<int>,
+* aligned_allocator<std::pair<const int, Matrix4f> > > my_map_mat4;
+* // Vector3f does not require 16 bytes alignment, no need to use Eigen's allocator:
+* std::map< int, Vector3f > my_map_vec3;
+* \endcode
+*
+* \sa \blank \ref TopicStlContainers.
+*/
+template<class T>
+class aligned_allocator : public std::allocator<T>
+{
+public:
+ typedef std::size_t size_type;
+ typedef std::ptrdiff_t difference_type;
+ typedef T* pointer;
+ typedef const T* const_pointer;
+ typedef T& reference;
+ typedef const T& const_reference;
+ typedef T value_type;
+
+ template<class U>
+ struct rebind
+ {
+ typedef aligned_allocator<U> other;
+ };
+
+ aligned_allocator() : std::allocator<T>() {}
+
+ aligned_allocator(const aligned_allocator& other) : std::allocator<T>(other) {}
+
+ template<class U>
+ aligned_allocator(const aligned_allocator<U>& other) : std::allocator<T>(other) {}
+
+ ~aligned_allocator() {}
+
+ #if EIGEN_COMP_GNUC_STRICT && EIGEN_GNUC_AT_LEAST(7,0)
+ // In gcc std::allocator::max_size() is bugged making gcc triggers a warning:
+ // eigen/Eigen/src/Core/util/Memory.h:189:12: warning: argument 1 value '18446744073709551612' exceeds maximum object size 9223372036854775807
+ // See https://gcc.gnu.org/bugzilla/show_bug.cgi?id=87544
+ size_type max_size() const {
+ return (std::numeric_limits<std::ptrdiff_t>::max)()/sizeof(T);
+ }
+ #endif
+
+ pointer allocate(size_type num, const void* /*hint*/ = 0)
+ {
+ internal::check_size_for_overflow<T>(num);
+ return static_cast<pointer>( internal::aligned_malloc(num * sizeof(T)) );
+ }
+
+ void deallocate(pointer p, size_type /*num*/)
+ {
+ internal::aligned_free(p);
+ }
+};
+
+//---------- Cache sizes ----------
+
+#if !defined(EIGEN_NO_CPUID)
+# if EIGEN_COMP_GNUC && EIGEN_ARCH_i386_OR_x86_64
+# if defined(__PIC__) && EIGEN_ARCH_i386
+ // Case for x86 with PIC
+# define EIGEN_CPUID(abcd,func,id) \
+ __asm__ __volatile__ ("xchgl %%ebx, %k1;cpuid; xchgl %%ebx,%k1": "=a" (abcd[0]), "=&r" (abcd[1]), "=c" (abcd[2]), "=d" (abcd[3]) : "a" (func), "c" (id));
+# elif defined(__PIC__) && EIGEN_ARCH_x86_64
+ // Case for x64 with PIC. In theory this is only a problem with recent gcc and with medium or large code model, not with the default small code model.
+ // However, we cannot detect which code model is used, and the xchg overhead is negligible anyway.
+# define EIGEN_CPUID(abcd,func,id) \
+ __asm__ __volatile__ ("xchg{q}\t{%%}rbx, %q1; cpuid; xchg{q}\t{%%}rbx, %q1": "=a" (abcd[0]), "=&r" (abcd[1]), "=c" (abcd[2]), "=d" (abcd[3]) : "0" (func), "2" (id));
+# else
+ // Case for x86_64 or x86 w/o PIC
+# define EIGEN_CPUID(abcd,func,id) \
+ __asm__ __volatile__ ("cpuid": "=a" (abcd[0]), "=b" (abcd[1]), "=c" (abcd[2]), "=d" (abcd[3]) : "0" (func), "2" (id) );
+# endif
+# elif EIGEN_COMP_MSVC
+# if EIGEN_ARCH_i386_OR_x86_64
+# define EIGEN_CPUID(abcd,func,id) __cpuidex((int*)abcd,func,id)
+# endif
+# endif
+#endif
+
+namespace internal {
+
+#ifdef EIGEN_CPUID
+
+inline bool cpuid_is_vendor(int abcd[4], const int vendor[3])
+{
+ return abcd[1]==vendor[0] && abcd[3]==vendor[1] && abcd[2]==vendor[2];
+}
+
+inline void queryCacheSizes_intel_direct(int& l1, int& l2, int& l3)
+{
+ int abcd[4];
+ l1 = l2 = l3 = 0;
+ int cache_id = 0;
+ int cache_type = 0;
+ do {
+ abcd[0] = abcd[1] = abcd[2] = abcd[3] = 0;
+ EIGEN_CPUID(abcd,0x4,cache_id);
+ cache_type = (abcd[0] & 0x0F) >> 0;
+ if(cache_type==1||cache_type==3) // data or unified cache
+ {
+ int cache_level = (abcd[0] & 0xE0) >> 5; // A[7:5]
+ int ways = (abcd[1] & 0xFFC00000) >> 22; // B[31:22]
+ int partitions = (abcd[1] & 0x003FF000) >> 12; // B[21:12]
+ int line_size = (abcd[1] & 0x00000FFF) >> 0; // B[11:0]
+ int sets = (abcd[2]); // C[31:0]
+
+ int cache_size = (ways+1) * (partitions+1) * (line_size+1) * (sets+1);
+
+ switch(cache_level)
+ {
+ case 1: l1 = cache_size; break;
+ case 2: l2 = cache_size; break;
+ case 3: l3 = cache_size; break;
+ default: break;
+ }
+ }
+ cache_id++;
+ } while(cache_type>0 && cache_id<16);
+}
+
+inline void queryCacheSizes_intel_codes(int& l1, int& l2, int& l3)
+{
+ int abcd[4];
+ abcd[0] = abcd[1] = abcd[2] = abcd[3] = 0;
+ l1 = l2 = l3 = 0;
+ EIGEN_CPUID(abcd,0x00000002,0);
+ unsigned char * bytes = reinterpret_cast<unsigned char *>(abcd)+2;
+ bool check_for_p2_core2 = false;
+ for(int i=0; i<14; ++i)
+ {
+ switch(bytes[i])
+ {
+ case 0x0A: l1 = 8; break; // 0Ah data L1 cache, 8 KB, 2 ways, 32 byte lines
+ case 0x0C: l1 = 16; break; // 0Ch data L1 cache, 16 KB, 4 ways, 32 byte lines
+ case 0x0E: l1 = 24; break; // 0Eh data L1 cache, 24 KB, 6 ways, 64 byte lines
+ case 0x10: l1 = 16; break; // 10h data L1 cache, 16 KB, 4 ways, 32 byte lines (IA-64)
+ case 0x15: l1 = 16; break; // 15h code L1 cache, 16 KB, 4 ways, 32 byte lines (IA-64)
+ case 0x2C: l1 = 32; break; // 2Ch data L1 cache, 32 KB, 8 ways, 64 byte lines
+ case 0x30: l1 = 32; break; // 30h code L1 cache, 32 KB, 8 ways, 64 byte lines
+ case 0x60: l1 = 16; break; // 60h data L1 cache, 16 KB, 8 ways, 64 byte lines, sectored
+ case 0x66: l1 = 8; break; // 66h data L1 cache, 8 KB, 4 ways, 64 byte lines, sectored
+ case 0x67: l1 = 16; break; // 67h data L1 cache, 16 KB, 4 ways, 64 byte lines, sectored
+ case 0x68: l1 = 32; break; // 68h data L1 cache, 32 KB, 4 ways, 64 byte lines, sectored
+ case 0x1A: l2 = 96; break; // code and data L2 cache, 96 KB, 6 ways, 64 byte lines (IA-64)
+ case 0x22: l3 = 512; break; // code and data L3 cache, 512 KB, 4 ways (!), 64 byte lines, dual-sectored
+ case 0x23: l3 = 1024; break; // code and data L3 cache, 1024 KB, 8 ways, 64 byte lines, dual-sectored
+ case 0x25: l3 = 2048; break; // code and data L3 cache, 2048 KB, 8 ways, 64 byte lines, dual-sectored
+ case 0x29: l3 = 4096; break; // code and data L3 cache, 4096 KB, 8 ways, 64 byte lines, dual-sectored
+ case 0x39: l2 = 128; break; // code and data L2 cache, 128 KB, 4 ways, 64 byte lines, sectored
+ case 0x3A: l2 = 192; break; // code and data L2 cache, 192 KB, 6 ways, 64 byte lines, sectored
+ case 0x3B: l2 = 128; break; // code and data L2 cache, 128 KB, 2 ways, 64 byte lines, sectored
+ case 0x3C: l2 = 256; break; // code and data L2 cache, 256 KB, 4 ways, 64 byte lines, sectored
+ case 0x3D: l2 = 384; break; // code and data L2 cache, 384 KB, 6 ways, 64 byte lines, sectored
+ case 0x3E: l2 = 512; break; // code and data L2 cache, 512 KB, 4 ways, 64 byte lines, sectored
+ case 0x40: l2 = 0; break; // no integrated L2 cache (P6 core) or L3 cache (P4 core)
+ case 0x41: l2 = 128; break; // code and data L2 cache, 128 KB, 4 ways, 32 byte lines
+ case 0x42: l2 = 256; break; // code and data L2 cache, 256 KB, 4 ways, 32 byte lines
+ case 0x43: l2 = 512; break; // code and data L2 cache, 512 KB, 4 ways, 32 byte lines
+ case 0x44: l2 = 1024; break; // code and data L2 cache, 1024 KB, 4 ways, 32 byte lines
+ case 0x45: l2 = 2048; break; // code and data L2 cache, 2048 KB, 4 ways, 32 byte lines
+ case 0x46: l3 = 4096; break; // code and data L3 cache, 4096 KB, 4 ways, 64 byte lines
+ case 0x47: l3 = 8192; break; // code and data L3 cache, 8192 KB, 8 ways, 64 byte lines
+ case 0x48: l2 = 3072; break; // code and data L2 cache, 3072 KB, 12 ways, 64 byte lines
+ case 0x49: if(l2!=0) l3 = 4096; else {check_for_p2_core2=true; l3 = l2 = 4096;} break;// code and data L3 cache, 4096 KB, 16 ways, 64 byte lines (P4) or L2 for core2
+ case 0x4A: l3 = 6144; break; // code and data L3 cache, 6144 KB, 12 ways, 64 byte lines
+ case 0x4B: l3 = 8192; break; // code and data L3 cache, 8192 KB, 16 ways, 64 byte lines
+ case 0x4C: l3 = 12288; break; // code and data L3 cache, 12288 KB, 12 ways, 64 byte lines
+ case 0x4D: l3 = 16384; break; // code and data L3 cache, 16384 KB, 16 ways, 64 byte lines
+ case 0x4E: l2 = 6144; break; // code and data L2 cache, 6144 KB, 24 ways, 64 byte lines
+ case 0x78: l2 = 1024; break; // code and data L2 cache, 1024 KB, 4 ways, 64 byte lines
+ case 0x79: l2 = 128; break; // code and data L2 cache, 128 KB, 8 ways, 64 byte lines, dual-sectored
+ case 0x7A: l2 = 256; break; // code and data L2 cache, 256 KB, 8 ways, 64 byte lines, dual-sectored
+ case 0x7B: l2 = 512; break; // code and data L2 cache, 512 KB, 8 ways, 64 byte lines, dual-sectored
+ case 0x7C: l2 = 1024; break; // code and data L2 cache, 1024 KB, 8 ways, 64 byte lines, dual-sectored
+ case 0x7D: l2 = 2048; break; // code and data L2 cache, 2048 KB, 8 ways, 64 byte lines
+ case 0x7E: l2 = 256; break; // code and data L2 cache, 256 KB, 8 ways, 128 byte lines, sect. (IA-64)
+ case 0x7F: l2 = 512; break; // code and data L2 cache, 512 KB, 2 ways, 64 byte lines
+ case 0x80: l2 = 512; break; // code and data L2 cache, 512 KB, 8 ways, 64 byte lines
+ case 0x81: l2 = 128; break; // code and data L2 cache, 128 KB, 8 ways, 32 byte lines
+ case 0x82: l2 = 256; break; // code and data L2 cache, 256 KB, 8 ways, 32 byte lines
+ case 0x83: l2 = 512; break; // code and data L2 cache, 512 KB, 8 ways, 32 byte lines
+ case 0x84: l2 = 1024; break; // code and data L2 cache, 1024 KB, 8 ways, 32 byte lines
+ case 0x85: l2 = 2048; break; // code and data L2 cache, 2048 KB, 8 ways, 32 byte lines
+ case 0x86: l2 = 512; break; // code and data L2 cache, 512 KB, 4 ways, 64 byte lines
+ case 0x87: l2 = 1024; break; // code and data L2 cache, 1024 KB, 8 ways, 64 byte lines
+ case 0x88: l3 = 2048; break; // code and data L3 cache, 2048 KB, 4 ways, 64 byte lines (IA-64)
+ case 0x89: l3 = 4096; break; // code and data L3 cache, 4096 KB, 4 ways, 64 byte lines (IA-64)
+ case 0x8A: l3 = 8192; break; // code and data L3 cache, 8192 KB, 4 ways, 64 byte lines (IA-64)
+ case 0x8D: l3 = 3072; break; // code and data L3 cache, 3072 KB, 12 ways, 128 byte lines (IA-64)
+
+ default: break;
+ }
+ }
+ if(check_for_p2_core2 && l2 == l3)
+ l3 = 0;
+ l1 *= 1024;
+ l2 *= 1024;
+ l3 *= 1024;
+}
+
+inline void queryCacheSizes_intel(int& l1, int& l2, int& l3, int max_std_funcs)
+{
+ if(max_std_funcs>=4)
+ queryCacheSizes_intel_direct(l1,l2,l3);
+ else if(max_std_funcs>=2)
+ queryCacheSizes_intel_codes(l1,l2,l3);
+ else
+ l1 = l2 = l3 = 0;
+}
+
+inline void queryCacheSizes_amd(int& l1, int& l2, int& l3)
+{
+ int abcd[4];
+ abcd[0] = abcd[1] = abcd[2] = abcd[3] = 0;
+
+ // First query the max supported function.
+ EIGEN_CPUID(abcd,0x80000000,0);
+ if(static_cast<numext::uint32_t>(abcd[0]) >= static_cast<numext::uint32_t>(0x80000006))
+ {
+ EIGEN_CPUID(abcd,0x80000005,0);
+ l1 = (abcd[2] >> 24) * 1024; // C[31:24] = L1 size in KB
+ abcd[0] = abcd[1] = abcd[2] = abcd[3] = 0;
+ EIGEN_CPUID(abcd,0x80000006,0);
+ l2 = (abcd[2] >> 16) * 1024; // C[31;16] = l2 cache size in KB
+ l3 = ((abcd[3] & 0xFFFC000) >> 18) * 512 * 1024; // D[31;18] = l3 cache size in 512KB
+ }
+ else
+ {
+ l1 = l2 = l3 = 0;
+ }
+}
+#endif
+
+/** \internal
+ * Queries and returns the cache sizes in Bytes of the L1, L2, and L3 data caches respectively */
+inline void queryCacheSizes(int& l1, int& l2, int& l3)
+{
+ #ifdef EIGEN_CPUID
+ int abcd[4];
+ const int GenuineIntel[] = {0x756e6547, 0x49656e69, 0x6c65746e};
+ const int AuthenticAMD[] = {0x68747541, 0x69746e65, 0x444d4163};
+ const int AMDisbetter_[] = {0x69444d41, 0x74656273, 0x21726574}; // "AMDisbetter!"
+
+ // identify the CPU vendor
+ EIGEN_CPUID(abcd,0x0,0);
+ int max_std_funcs = abcd[0];
+ if(cpuid_is_vendor(abcd,GenuineIntel))
+ queryCacheSizes_intel(l1,l2,l3,max_std_funcs);
+ else if(cpuid_is_vendor(abcd,AuthenticAMD) || cpuid_is_vendor(abcd,AMDisbetter_))
+ queryCacheSizes_amd(l1,l2,l3);
+ else
+ // by default let's use Intel's API
+ queryCacheSizes_intel(l1,l2,l3,max_std_funcs);
+
+ // here is the list of other vendors:
+// ||cpuid_is_vendor(abcd,"VIA VIA VIA ")
+// ||cpuid_is_vendor(abcd,"CyrixInstead")
+// ||cpuid_is_vendor(abcd,"CentaurHauls")
+// ||cpuid_is_vendor(abcd,"GenuineTMx86")
+// ||cpuid_is_vendor(abcd,"TransmetaCPU")
+// ||cpuid_is_vendor(abcd,"RiseRiseRise")
+// ||cpuid_is_vendor(abcd,"Geode by NSC")
+// ||cpuid_is_vendor(abcd,"SiS SiS SiS ")
+// ||cpuid_is_vendor(abcd,"UMC UMC UMC ")
+// ||cpuid_is_vendor(abcd,"NexGenDriven")
+ #else
+ l1 = l2 = l3 = -1;
+ #endif
+}
+
+/** \internal
+ * \returns the size in Bytes of the L1 data cache */
+inline int queryL1CacheSize()
+{
+ int l1(-1), l2, l3;
+ queryCacheSizes(l1,l2,l3);
+ return l1;
+}
+
+/** \internal
+ * \returns the size in Bytes of the L2 or L3 cache if this later is present */
+inline int queryTopLevelCacheSize()
+{
+ int l1, l2(-1), l3(-1);
+ queryCacheSizes(l1,l2,l3);
+ return (std::max)(l2,l3);
+}
+
+
+
+/** \internal
+ * This wraps C++20's std::construct_at, using placement new instead if it is not available.
+ */
+
+#if EIGEN_COMP_CXXVER >= 20
+using std::construct_at;
+#else
+template<class T, class... Args>
+EIGEN_DEVICE_FUNC T* construct_at( T* p, Args&&... args )
+{
+ return ::new (const_cast<void*>(static_cast<const volatile void*>(p)))
+ T(std::forward<Args>(args)...);
+}
+#endif
+
+/** \internal
+ * This wraps C++17's std::destroy_at. If it's not available it calls the destructor.
+ * The wrapper is not a full replacement for C++20's std::destroy_at as it cannot
+ * be applied to std::array.
+ */
+#if EIGEN_COMP_CXXVER >= 17
+using std::destroy_at;
+#else
+template<class T>
+EIGEN_DEVICE_FUNC void destroy_at(T* p)
+{
+ p->~T();
+}
+#endif
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_MEMORY_H
diff --git a/Eigen/src/Core/util/Meta.h b/Eigen/src/Core/util/Meta.h
new file mode 100644
index 0000000..32152ac
--- /dev/null
+++ b/Eigen/src/Core/util/Meta.h
@@ -0,0 +1,540 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2015 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_META_H
+#define EIGEN_META_H
+
+#include "../InternalHeaderCheck.h"
+
+#if defined(EIGEN_GPU_COMPILE_PHASE)
+
+ #include <cfloat>
+
+ #if defined(EIGEN_CUDA_ARCH)
+ #include <math_constants.h>
+ #endif
+
+ #if defined(EIGEN_HIP_DEVICE_COMPILE)
+ #include "Eigen/src/Core/arch/HIP/hcc/math_constants.h"
+ #endif
+
+#endif
+
+// Recent versions of ICC require <cstdint> for pointer types below.
+#define EIGEN_ICC_NEEDS_CSTDINT (EIGEN_COMP_ICC>=1600)
+
+// Define portable (u)int{32,64} types
+#include <cstdint>
+
+namespace Eigen {
+namespace numext {
+typedef std::uint8_t uint8_t;
+typedef std::int8_t int8_t;
+typedef std::uint16_t uint16_t;
+typedef std::int16_t int16_t;
+typedef std::uint32_t uint32_t;
+typedef std::int32_t int32_t;
+typedef std::uint64_t uint64_t;
+typedef std::int64_t int64_t;
+}
+}
+
+namespace Eigen {
+
+typedef EIGEN_DEFAULT_DENSE_INDEX_TYPE DenseIndex;
+
+/**
+ * \brief The Index type as used for the API.
+ * \details To change this, \c \#define the preprocessor symbol \c EIGEN_DEFAULT_DENSE_INDEX_TYPE.
+ * \sa \blank \ref TopicPreprocessorDirectives, StorageIndex.
+ */
+
+typedef EIGEN_DEFAULT_DENSE_INDEX_TYPE Index;
+
+namespace internal {
+
+/** \internal
+ * \file Meta.h
+ * This file contains generic metaprogramming classes which are not specifically related to Eigen.
+ * \note In case you wonder, yes we're aware that Boost already provides all these features,
+ * we however don't want to add a dependency to Boost.
+ */
+
+// Only recent versions of ICC complain about using ptrdiff_t to hold pointers,
+// and older versions do not provide *intptr_t types.
+#if EIGEN_ICC_NEEDS_CSTDINT
+typedef std::intptr_t IntPtr;
+typedef std::uintptr_t UIntPtr;
+#else
+typedef std::ptrdiff_t IntPtr;
+typedef std::size_t UIntPtr;
+#endif
+#undef EIGEN_ICC_NEEDS_CSTDINT
+
+struct true_type { enum { value = 1 }; };
+struct false_type { enum { value = 0 }; };
+
+template<bool Condition>
+struct bool_constant;
+
+template<>
+struct bool_constant<true> : true_type {};
+
+template<>
+struct bool_constant<false> : false_type {};
+
+// Third-party libraries rely on these.
+using std::conditional;
+using std::remove_reference;
+using std::remove_pointer;
+using std::remove_const;
+
+template<typename T> struct remove_all { typedef T type; };
+template<typename T> struct remove_all<const T> { typedef typename remove_all<T>::type type; };
+template<typename T> struct remove_all<T const&> { typedef typename remove_all<T>::type type; };
+template<typename T> struct remove_all<T&> { typedef typename remove_all<T>::type type; };
+template<typename T> struct remove_all<T const*> { typedef typename remove_all<T>::type type; };
+template<typename T> struct remove_all<T*> { typedef typename remove_all<T>::type type; };
+
+template<typename T>
+using remove_all_t = typename remove_all<T>::type;
+
+template<typename T> struct is_arithmetic { enum { value = false }; };
+template<> struct is_arithmetic<float> { enum { value = true }; };
+template<> struct is_arithmetic<double> { enum { value = true }; };
+template<> struct is_arithmetic<long double> { enum { value = true }; };
+template<> struct is_arithmetic<bool> { enum { value = true }; };
+template<> struct is_arithmetic<char> { enum { value = true }; };
+template<> struct is_arithmetic<signed char> { enum { value = true }; };
+template<> struct is_arithmetic<unsigned char> { enum { value = true }; };
+template<> struct is_arithmetic<signed short> { enum { value = true }; };
+template<> struct is_arithmetic<unsigned short>{ enum { value = true }; };
+template<> struct is_arithmetic<signed int> { enum { value = true }; };
+template<> struct is_arithmetic<unsigned int> { enum { value = true }; };
+template<> struct is_arithmetic<signed long> { enum { value = true }; };
+template<> struct is_arithmetic<unsigned long> { enum { value = true }; };
+
+template<typename T, typename U> struct is_same { enum { value = 0 }; };
+template<typename T> struct is_same<T,T> { enum { value = 1 }; };
+
+template< class T >
+struct is_void : is_same<void, std::remove_const_t<T>> {};
+
+template<> struct is_arithmetic<signed long long> { enum { value = true }; };
+template<> struct is_arithmetic<unsigned long long> { enum { value = true }; };
+using std::is_integral;
+
+using std::make_unsigned;
+
+template <typename T> struct is_const { enum { value = 0 }; };
+template <typename T> struct is_const<T const> { enum { value = 1 }; };
+
+template<typename T> struct add_const_on_value_type { typedef const T type; };
+template<typename T> struct add_const_on_value_type<T&> { typedef T const& type; };
+template<typename T> struct add_const_on_value_type<T*> { typedef T const* type; };
+template<typename T> struct add_const_on_value_type<T* const> { typedef T const* const type; };
+template<typename T> struct add_const_on_value_type<T const* const> { typedef T const* const type; };
+
+template<typename T>
+using add_const_on_value_type_t = typename add_const_on_value_type<T>::type;
+
+using std::is_convertible;
+
+/** \internal
+ * A base class do disable default copy ctor and copy assignment operator.
+ */
+class noncopyable
+{
+ EIGEN_DEVICE_FUNC noncopyable(const noncopyable&);
+ EIGEN_DEVICE_FUNC const noncopyable& operator=(const noncopyable&);
+protected:
+ EIGEN_DEVICE_FUNC noncopyable() {}
+ EIGEN_DEVICE_FUNC ~noncopyable() {}
+};
+
+/** \internal
+ * Provides access to the number of elements in the object of as a compile-time constant expression.
+ * It "returns" Eigen::Dynamic if the size cannot be resolved at compile-time (default).
+ *
+ * Similar to std::tuple_size, but more general.
+ *
+ * It currently supports:
+ * - any types T defining T::SizeAtCompileTime
+ * - plain C arrays as T[N]
+ * - std::array (c++11)
+ * - some internal types such as SingleRange and AllRange
+ *
+ * The second template parameter eases SFINAE-based specializations.
+ */
+template<typename T, typename EnableIf = void> struct array_size {
+ enum { value = Dynamic };
+};
+
+template<typename T> struct array_size<T, std::enable_if_t<((T::SizeAtCompileTime&0)==0)>> {
+ enum { value = T::SizeAtCompileTime };
+};
+
+template<typename T, int N> struct array_size<const T (&)[N]> {
+ enum { value = N };
+};
+template<typename T, int N> struct array_size<T (&)[N]> {
+ enum { value = N };
+};
+
+template<typename T, std::size_t N> struct array_size<const std::array<T,N> > {
+ enum { value = N };
+};
+template<typename T, std::size_t N> struct array_size<std::array<T,N> > {
+ enum { value = N };
+};
+
+
+/** \internal
+ * Analogue of the std::ssize free function.
+ * It returns the signed size of the container or view \a x of type \c T
+ *
+ * It currently supports:
+ * - any types T defining a member T::size() const
+ * - plain C arrays as T[N]
+ *
+ * For C++20, this function just forwards to `std::ssize`, or any ADL discoverable `ssize` function.
+ */
+#if EIGEN_COMP_CXXVER < 20 || EIGEN_GNUC_AT_MOST(9,4)
+template <typename T>
+EIGEN_CONSTEXPR auto index_list_size(const T& x) {
+ using R = std::common_type_t<std::ptrdiff_t, std::make_signed_t<decltype(x.size())>>;
+ return static_cast<R>(x.size());
+}
+
+template<typename T, std::ptrdiff_t N>
+EIGEN_CONSTEXPR std::ptrdiff_t index_list_size(const T (&)[N]) { return N; }
+#else
+template <typename T>
+EIGEN_CONSTEXPR auto index_list_size(T&& x) {
+ using std::ssize;
+ return ssize(std::forward<T>(x));
+}
+#endif // EIGEN_COMP_CXXVER
+
+/** \internal
+ * Convenient struct to get the result type of a nullary, unary, binary, or
+ * ternary functor.
+ *
+ * Pre C++17:
+ * This uses std::result_of. However, note the `type` member removes
+ * const and converts references/pointers to their corresponding value type.
+ *
+ * Post C++17: Uses std::invoke_result
+ */
+#if EIGEN_HAS_STD_INVOKE_RESULT
+template<typename T> struct result_of;
+
+template<typename F, typename... ArgTypes>
+struct result_of<F(ArgTypes...)> {
+ typedef typename std::invoke_result<F, ArgTypes...>::type type1;
+ typedef remove_all_t<type1> type;
+};
+
+template<typename F, typename... ArgTypes>
+struct invoke_result {
+ typedef typename std::invoke_result<F, ArgTypes...>::type type1;
+ typedef remove_all_t<type1> type;
+};
+#else
+template<typename T> struct result_of {
+ typedef typename std::result_of<T>::type type1;
+ typedef remove_all_t<type1> type;
+};
+
+template<typename F, typename... ArgTypes>
+struct invoke_result {
+ typedef typename result_of<F(ArgTypes...)>::type type1;
+ typedef remove_all_t<type1> type;
+};
+#endif
+
+// Reduces a sequence of bools to true if all are true, false otherwise.
+template<bool... values>
+using reduce_all = std::is_same<std::integer_sequence<bool, values..., true>,
+ std::integer_sequence<bool, true, values...> >;
+
+// Reduces a sequence of bools to true if any are true, false if all false.
+template<bool... values>
+using reduce_any = std::integral_constant<bool,
+ !std::is_same<std::integer_sequence<bool, values..., false>, std::integer_sequence<bool, false, values...> >::value>;
+
+struct meta_yes { char a[1]; };
+struct meta_no { char a[2]; };
+
+// Check whether T::ReturnType does exist
+template <typename T>
+struct has_ReturnType
+{
+ template <typename C> static meta_yes testFunctor(C const *, typename C::ReturnType const * = 0);
+ template <typename C> static meta_no testFunctor(...);
+
+ enum { value = sizeof(testFunctor<T>(static_cast<T*>(0))) == sizeof(meta_yes) };
+};
+
+template<typename T> const T* return_ptr();
+
+template <typename T, typename IndexType=Index>
+struct has_nullary_operator
+{
+ template <typename C> static meta_yes testFunctor(C const *,std::enable_if_t<(sizeof(return_ptr<C>()->operator()())>0)> * = 0);
+ static meta_no testFunctor(...);
+
+ enum { value = sizeof(testFunctor(static_cast<T*>(0))) == sizeof(meta_yes) };
+};
+
+template <typename T, typename IndexType=Index>
+struct has_unary_operator
+{
+ template <typename C> static meta_yes testFunctor(C const *,std::enable_if_t<(sizeof(return_ptr<C>()->operator()(IndexType(0)))>0)> * = 0);
+ static meta_no testFunctor(...);
+
+ enum { value = sizeof(testFunctor(static_cast<T*>(0))) == sizeof(meta_yes) };
+};
+
+template <typename T, typename IndexType=Index>
+struct has_binary_operator
+{
+ template <typename C> static meta_yes testFunctor(C const *,std::enable_if_t<(sizeof(return_ptr<C>()->operator()(IndexType(0),IndexType(0)))>0)> * = 0);
+ static meta_no testFunctor(...);
+
+ enum { value = sizeof(testFunctor(static_cast<T*>(0))) == sizeof(meta_yes) };
+};
+
+/** \internal In short, it computes int(sqrt(\a Y)) with \a Y an integer.
+ * Usage example: \code meta_sqrt<1023>::ret \endcode
+ */
+template<int Y,
+ int InfX = 0,
+ int SupX = ((Y==1) ? 1 : Y/2),
+ bool Done = ((SupX - InfX) <= 1 || ((SupX * SupX <= Y) && ((SupX + 1) * (SupX + 1) > Y)))>
+class meta_sqrt
+{
+ enum {
+ MidX = (InfX+SupX)/2,
+ TakeInf = MidX*MidX > Y ? 1 : 0,
+ NewInf = int(TakeInf) ? InfX : int(MidX),
+ NewSup = int(TakeInf) ? int(MidX) : SupX
+ };
+ public:
+ enum { ret = meta_sqrt<Y,NewInf,NewSup>::ret };
+};
+
+template<int Y, int InfX, int SupX>
+class meta_sqrt<Y, InfX, SupX, true> { public: enum { ret = (SupX*SupX <= Y) ? SupX : InfX }; };
+
+
+/** \internal Computes the least common multiple of two positive integer A and B
+ * at compile-time.
+ */
+template<int A, int B, int K=1, bool Done = ((A*K)%B)==0, bool Big=(A>=B)>
+struct meta_least_common_multiple
+{
+ enum { ret = meta_least_common_multiple<A,B,K+1>::ret };
+};
+template<int A, int B, int K, bool Done>
+struct meta_least_common_multiple<A,B,K,Done,false>
+{
+ enum { ret = meta_least_common_multiple<B,A,K>::ret };
+};
+template<int A, int B, int K>
+struct meta_least_common_multiple<A,B,K,true,true>
+{
+ enum { ret = A*K };
+};
+
+
+/** \internal determines whether the product of two numeric types is allowed and what the return type is */
+template<typename T, typename U> struct scalar_product_traits
+{
+ enum { Defined = 0 };
+};
+
+// FIXME quick workaround around current limitation of result_of
+// template<typename Scalar, typename ArgType0, typename ArgType1>
+// struct result_of<scalar_product_op<Scalar>(ArgType0,ArgType1)> {
+// typedef typename scalar_product_traits<remove_all_t<ArgType0>, remove_all_t<ArgType1>>::ReturnType type;
+// };
+
+/** \internal Obtains a POD type suitable to use as storage for an object of a size
+ * of at most Len bytes, aligned as specified by \c Align.
+ */
+template<unsigned Len, unsigned Align>
+struct aligned_storage {
+ struct type {
+ EIGEN_ALIGN_TO_BOUNDARY(Align) unsigned char data[Len];
+ };
+};
+
+} // end namespace internal
+
+template<typename T> struct NumTraits;
+
+namespace numext {
+
+#if defined(EIGEN_GPU_COMPILE_PHASE)
+template<typename T> EIGEN_DEVICE_FUNC void swap(T &a, T &b) { T tmp = b; b = a; a = tmp; }
+#else
+template<typename T> EIGEN_STRONG_INLINE void swap(T &a, T &b) { std::swap(a,b); }
+#endif
+
+using std::numeric_limits;
+
+// Integer division with rounding up.
+// T is assumed to be an integer type with a>=0, and b>0
+template<typename T>
+EIGEN_DEVICE_FUNC
+T div_ceil(const T &a, const T &b)
+{
+ return (a+b-1) / b;
+}
+
+// The aim of the following functions is to bypass -Wfloat-equal warnings
+// when we really want a strict equality comparison on floating points.
+template<typename X, typename Y> EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC
+bool equal_strict(const X& x,const Y& y) { return x == y; }
+
+#if !defined(EIGEN_GPU_COMPILE_PHASE) || (!defined(EIGEN_CUDA_ARCH) && defined(EIGEN_CONSTEXPR_ARE_DEVICE_FUNC))
+template<> EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC
+bool equal_strict(const float& x,const float& y) { return std::equal_to<float>()(x,y); }
+
+template<> EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC
+bool equal_strict(const double& x,const double& y) { return std::equal_to<double>()(x,y); }
+#endif
+
+/**
+ * \internal Performs an exact comparison of x to zero, e.g. to decide whether a term can be ignored.
+ * Use this to to bypass -Wfloat-equal warnings when exact zero is what needs to be tested.
+*/
+template<typename X> EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC
+bool is_exactly_zero(const X& x) { return equal_strict(x, typename NumTraits<X>::Literal{0}); }
+
+/**
+ * \internal Performs an exact comparison of x to one, e.g. to decide whether a factor needs to be multiplied.
+ * Use this to to bypass -Wfloat-equal warnings when exact one is what needs to be tested.
+*/
+template<typename X> EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC
+bool is_exactly_one(const X& x) { return equal_strict(x, typename NumTraits<X>::Literal{1}); }
+
+template<typename X, typename Y> EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC
+bool not_equal_strict(const X& x,const Y& y) { return x != y; }
+
+#if !defined(EIGEN_GPU_COMPILE_PHASE) || (!defined(EIGEN_CUDA_ARCH) && defined(EIGEN_CONSTEXPR_ARE_DEVICE_FUNC))
+template<> EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC
+bool not_equal_strict(const float& x,const float& y) { return std::not_equal_to<float>()(x,y); }
+
+template<> EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC
+bool not_equal_strict(const double& x,const double& y) { return std::not_equal_to<double>()(x,y); }
+#endif
+
+} // end namespace numext
+
+namespace internal {
+
+template<typename Scalar>
+struct is_identically_zero_impl {
+ static inline bool run(const Scalar& s) {
+ return numext::is_exactly_zero(s);
+ }
+};
+
+template<typename Scalar> EIGEN_STRONG_INLINE
+bool is_identically_zero(const Scalar& s) { return is_identically_zero_impl<Scalar>::run(s); }
+
+/// \internal Returns true if its argument is of integer or enum type.
+/// FIXME this has the same purpose as `is_valid_index_type` in XprHelper.h
+template<typename A>
+constexpr bool is_int_or_enum_v = std::is_enum<A>::value || std::is_integral<A>::value;
+
+/// \internal Gets the minimum of two values which may be integers or enums
+template<typename A, typename B>
+inline constexpr int plain_enum_min(A a, B b) {
+ static_assert(is_int_or_enum_v<A>, "Argument a must be an integer or enum");
+ static_assert(is_int_or_enum_v<B>, "Argument b must be an integer or enum");
+ return ((int) a <= (int) b) ? (int) a : (int) b;
+}
+
+/// \internal Gets the maximum of two values which may be integers or enums
+template<typename A, typename B>
+inline constexpr int plain_enum_max(A a, B b) {
+ static_assert(is_int_or_enum_v<A>, "Argument a must be an integer or enum");
+ static_assert(is_int_or_enum_v<B>, "Argument b must be an integer or enum");
+ return ((int) a >= (int) b) ? (int) a : (int) b;
+}
+
+/**
+ * \internal
+ * `min_size_prefer_dynamic` gives the min between compile-time sizes. 0 has absolute priority, followed by 1,
+ * followed by Dynamic, followed by other finite values. The reason for giving Dynamic the priority over
+ * finite values is that min(3, Dynamic) should be Dynamic, since that could be anything between 0 and 3.
+ */
+template<typename A, typename B>
+inline constexpr int min_size_prefer_dynamic(A a, B b) {
+ static_assert(is_int_or_enum_v<A>, "Argument a must be an integer or enum");
+ static_assert(is_int_or_enum_v<B>, "Argument b must be an integer or enum");
+ if ((int) a == 0 || (int) b == 0) return 0;
+ if ((int) a == 1 || (int) b == 1) return 1;
+ if ((int) a == Dynamic || (int) b == Dynamic) return Dynamic;
+ return plain_enum_min(a, b);
+}
+
+/**
+ * \internal
+ * min_size_prefer_fixed is a variant of `min_size_prefer_dynamic` comparing MaxSizes. The difference is that finite values
+ * now have priority over Dynamic, so that min(3, Dynamic) gives 3. Indeed, whatever the actual value is
+ * (between 0 and 3), it is not more than 3.
+ */
+template<typename A, typename B>
+inline constexpr int min_size_prefer_fixed(A a, B b) {
+ static_assert(is_int_or_enum_v<A>, "Argument a must be an integer or enum");
+ static_assert(is_int_or_enum_v<B>, "Argument b must be an integer or enum");
+ if ((int) a == 0 || (int) b == 0) return 0;
+ if ((int) a == 1 || (int) b == 1) return 1;
+ if ((int) a == Dynamic && (int) b == Dynamic) return Dynamic;
+ if ((int) a == Dynamic) return (int) b;
+ if ((int) b == Dynamic) return (int) a;
+ return plain_enum_min(a, b);
+}
+
+/// \internal see `min_size_prefer_fixed`. No need for a separate variant for MaxSizes here.
+template<typename A, typename B>
+inline constexpr int max_size_prefer_dynamic(A a, B b) {
+ static_assert(is_int_or_enum_v<A>, "Argument a must be an integer or enum");
+ static_assert(is_int_or_enum_v<B>, "Argument b must be an integer or enum");
+ if ((int) a == Dynamic || (int) b == Dynamic) return Dynamic;
+ return plain_enum_max(a, b);
+}
+
+/// \internal Calculate logical XOR at compile time
+inline constexpr bool logical_xor(bool a, bool b) {
+ return a != b;
+}
+
+/// \internal Calculate logical IMPLIES at compile time
+inline constexpr bool check_implication(bool a, bool b) {
+ return !a || b;
+}
+
+/// \internal Provide fallback for std::is_constant_evaluated for pre-C++20.
+#if EIGEN_COMP_CXXVER >= 20
+using std::is_constant_evaluated;
+#else
+constexpr bool is_constant_evaluated() { return false; }
+#endif
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_META_H
diff --git a/Eigen/src/Core/util/NonMPL2.h b/Eigen/src/Core/util/NonMPL2.h
new file mode 100644
index 0000000..1af67cf
--- /dev/null
+++ b/Eigen/src/Core/util/NonMPL2.h
@@ -0,0 +1,3 @@
+#ifdef EIGEN_MPL2_ONLY
+#error Including non-MPL2 code in EIGEN_MPL2_ONLY mode
+#endif
diff --git a/Eigen/src/Core/util/ReenableStupidWarnings.h b/Eigen/src/Core/util/ReenableStupidWarnings.h
new file mode 100644
index 0000000..7021e6d
--- /dev/null
+++ b/Eigen/src/Core/util/ReenableStupidWarnings.h
@@ -0,0 +1,39 @@
+#ifdef EIGEN_WARNINGS_DISABLED_2
+// "DisableStupidWarnings.h" was included twice recursively: Do not re-enable warnings yet!
+# undef EIGEN_WARNINGS_DISABLED_2
+
+#elif defined(EIGEN_WARNINGS_DISABLED)
+#undef EIGEN_WARNINGS_DISABLED
+
+#ifndef EIGEN_PERMANENTLY_DISABLE_STUPID_WARNINGS
+ #ifdef _MSC_VER
+ #pragma warning( pop )
+ #elif defined __INTEL_COMPILER
+ #pragma warning pop
+ #elif defined __clang__
+ #pragma clang diagnostic pop
+ #elif defined __GNUC__ && !defined(__FUJITSU) && (__GNUC__ > 4 || (__GNUC__ == 4 && __GNUC_MINOR__ >= 6))
+ #pragma GCC diagnostic pop
+ #endif
+
+ #if defined __NVCC__
+// Don't re-enable the diagnostic messages, as it turns out these messages need
+// to be disabled at the point of the template instantiation (i.e the user code)
+// otherwise they'll be triggered by nvcc.
+// #define EIGEN_MAKE_PRAGMA(X) _Pragma(#X)
+// #if __NVCC_DIAG_PRAGMA_SUPPORT__
+// #define EIGEN_NV_DIAG_DEFAULT(X) EIGEN_MAKE_PRAGMA(nv_diag_default X)
+// #else
+// #define EIGEN_NV_DIAG_DEFAULT(X) EIGEN_MAKE_PRAGMA(diag_default X)
+// #endif
+// EIGEN_NV_DIAG_DEFAULT(code_is_unreachable)
+// EIGEN_NV_DIAG_DEFAULT(initialization_not_reachable)
+// EIGEN_NV_DIAG_DEFAULT(2651)
+// EIGEN_NV_DIAG_DEFAULT(2653)
+// #undef EIGEN_NV_DIAG_DEFAULT
+// #undef EIGEN_MAKE_PRAGMA
+ #endif
+
+#endif
+
+#endif // EIGEN_WARNINGS_DISABLED
diff --git a/Eigen/src/Core/util/ReshapedHelper.h b/Eigen/src/Core/util/ReshapedHelper.h
new file mode 100644
index 0000000..6daea03
--- /dev/null
+++ b/Eigen/src/Core/util/ReshapedHelper.h
@@ -0,0 +1,52 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2017 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+
+#ifndef EIGEN_RESHAPED_HELPER_H
+#define EIGEN_RESHAPED_HELPER_H
+
+#include "../InternalHeaderCheck.h"
+
+namespace Eigen {
+
+enum AutoSize_t { AutoSize };
+const int AutoOrder = 2;
+
+namespace internal {
+
+template<typename SizeType,typename OtherSize, int TotalSize>
+struct get_compiletime_reshape_size {
+ enum { value = get_fixed_value<SizeType>::value };
+};
+
+template<typename SizeType>
+Index get_runtime_reshape_size(SizeType size, Index /*other*/, Index /*total*/) {
+ return internal::get_runtime_value(size);
+}
+
+template<typename OtherSize, int TotalSize>
+struct get_compiletime_reshape_size<AutoSize_t,OtherSize,TotalSize> {
+ enum {
+ other_size = get_fixed_value<OtherSize>::value,
+ value = (TotalSize==Dynamic || other_size==Dynamic) ? Dynamic : TotalSize / other_size };
+};
+
+inline Index get_runtime_reshape_size(AutoSize_t /*size*/, Index other, Index total) {
+ return total/other;
+}
+
+constexpr inline int get_compiletime_reshape_order(int flags, int order) {
+ return order == AutoOrder ? flags & RowMajorBit : order;
+}
+
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_RESHAPED_HELPER_H
diff --git a/Eigen/src/Core/util/Serializer.h b/Eigen/src/Core/util/Serializer.h
new file mode 100644
index 0000000..cbfc04a
--- /dev/null
+++ b/Eigen/src/Core/util/Serializer.h
@@ -0,0 +1,220 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2021 The Eigen Team
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_SERIALIZER_H
+#define EIGEN_SERIALIZER_H
+
+#include <type_traits>
+
+// The Serializer class encodes data into a memory buffer so it can be later
+// reconstructed. This is mainly used to send objects back-and-forth between
+// the CPU and GPU.
+
+namespace Eigen {
+
+/**
+ * Serializes an object to a memory buffer.
+ *
+ * Useful for transferring data (e.g. back-and-forth to a device).
+ */
+template<typename T, typename EnableIf = void>
+class Serializer;
+
+// Specialization for POD types.
+template<typename T>
+class Serializer<T, typename std::enable_if_t<
+ std::is_trivial<T>::value
+ && std::is_standard_layout<T>::value>> {
+ public:
+
+ /**
+ * Determines the required size of the serialization buffer for a value.
+ *
+ * \param value the value to serialize.
+ * \return the required size.
+ */
+ EIGEN_DEVICE_FUNC size_t size(const T& value) const {
+ return sizeof(value);
+ }
+
+ /**
+ * Serializes a value to a byte buffer.
+ * \param dest the destination buffer; if this is nullptr, does nothing.
+ * \param end the end of the destination buffer.
+ * \param value the value to serialize.
+ * \return the next memory address past the end of the serialized data.
+ */
+ EIGEN_DEVICE_FUNC uint8_t* serialize(uint8_t* dest, uint8_t* end, const T& value) {
+ if (EIGEN_PREDICT_FALSE(dest == nullptr)) return nullptr;
+ if (EIGEN_PREDICT_FALSE(dest + sizeof(value) > end)) return nullptr;
+ EIGEN_USING_STD(memcpy)
+ memcpy(dest, &value, sizeof(value));
+ return dest + sizeof(value);
+ }
+
+ /**
+ * Deserializes a value from a byte buffer.
+ * \param src the source buffer; if this is nullptr, does nothing.
+ * \param end the end of the source buffer.
+ * \param value the value to populate.
+ * \return the next unprocessed memory address; nullptr if parsing errors are detected.
+ */
+ EIGEN_DEVICE_FUNC const uint8_t* deserialize(const uint8_t* src, const uint8_t* end, T& value) const {
+ if (EIGEN_PREDICT_FALSE(src == nullptr)) return nullptr;
+ if (EIGEN_PREDICT_FALSE(src + sizeof(value) > end)) return nullptr;
+ EIGEN_USING_STD(memcpy)
+ memcpy(&value, src, sizeof(value));
+ return src + sizeof(value);
+ }
+};
+
+// Specialization for DenseBase.
+// Serializes [rows, cols, data...].
+template<typename Derived>
+class Serializer<DenseBase<Derived>, void> {
+ public:
+ typedef typename Derived::Scalar Scalar;
+
+ struct Header {
+ typename Derived::Index rows;
+ typename Derived::Index cols;
+ };
+
+ EIGEN_DEVICE_FUNC size_t size(const Derived& value) const {
+ return sizeof(Header) + sizeof(Scalar) * value.size();
+ }
+
+ EIGEN_DEVICE_FUNC uint8_t* serialize(uint8_t* dest, uint8_t* end, const Derived& value) {
+ if (EIGEN_PREDICT_FALSE(dest == nullptr)) return nullptr;
+ if (EIGEN_PREDICT_FALSE(dest + size(value) > end)) return nullptr;
+ const size_t header_bytes = sizeof(Header);
+ const size_t data_bytes = sizeof(Scalar) * value.size();
+ Header header = {value.rows(), value.cols()};
+ EIGEN_USING_STD(memcpy)
+ memcpy(dest, &header, header_bytes);
+ dest += header_bytes;
+ memcpy(dest, value.data(), data_bytes);
+ return dest + data_bytes;
+ }
+
+ EIGEN_DEVICE_FUNC const uint8_t* deserialize(const uint8_t* src, const uint8_t* end, Derived& value) const {
+ if (EIGEN_PREDICT_FALSE(src == nullptr)) return nullptr;
+ if (EIGEN_PREDICT_FALSE(src + sizeof(Header) > end)) return nullptr;
+ const size_t header_bytes = sizeof(Header);
+ Header header;
+ EIGEN_USING_STD(memcpy)
+ memcpy(&header, src, header_bytes);
+ src += header_bytes;
+ const size_t data_bytes = sizeof(Scalar) * header.rows * header.cols;
+ if (EIGEN_PREDICT_FALSE(src + data_bytes > end)) return nullptr;
+ value.resize(header.rows, header.cols);
+ memcpy(value.data(), src, data_bytes);
+ return src + data_bytes;
+ }
+};
+
+template<typename Scalar, int Rows, int Cols, int Options, int MaxRows, int MaxCols>
+class Serializer<Matrix<Scalar, Rows, Cols, Options, MaxRows, MaxCols> > : public
+ Serializer<DenseBase<Matrix<Scalar, Rows, Cols, Options, MaxRows, MaxCols> > > {};
+
+template<typename Scalar, int Rows, int Cols, int Options, int MaxRows, int MaxCols>
+class Serializer<Array<Scalar, Rows, Cols, Options, MaxRows, MaxCols> > : public
+ Serializer<DenseBase<Array<Scalar, Rows, Cols, Options, MaxRows, MaxCols> > > {};
+
+namespace internal {
+
+// Recursive serialization implementation helper.
+template<size_t N, typename... Types>
+struct serialize_impl;
+
+template<size_t N, typename T1, typename... Ts>
+struct serialize_impl<N, T1, Ts...> {
+ using Serializer = Eigen::Serializer<typename std::decay<T1>::type>;
+
+ static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ size_t serialize_size(const T1& value, const Ts&... args) {
+ Serializer serializer;
+ size_t size = serializer.size(value);
+ return size + serialize_impl<N-1, Ts...>::serialize_size(args...);
+ }
+
+ static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ uint8_t* serialize(uint8_t* dest, uint8_t* end, const T1& value, const Ts&... args) {
+ Serializer serializer;
+ dest = serializer.serialize(dest, end, value);
+ return serialize_impl<N-1, Ts...>::serialize(dest, end, args...);
+ }
+
+ static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ const uint8_t* deserialize(const uint8_t* src, const uint8_t* end, T1& value, Ts&... args) {
+ Serializer serializer;
+ src = serializer.deserialize(src, end, value);
+ return serialize_impl<N-1, Ts...>::deserialize(src, end, args...);
+ }
+};
+
+// Base case.
+template<>
+struct serialize_impl<0> {
+ static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ size_t serialize_size() { return 0; }
+
+ static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ uint8_t* serialize(uint8_t* dest, uint8_t* /*end*/) { return dest; }
+
+ static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ const uint8_t* deserialize(const uint8_t* src, const uint8_t* /*end*/) { return src; }
+};
+
+} // namespace internal
+
+
+/**
+ * Determine the buffer size required to serialize a set of values.
+ *
+ * \param args ... arguments to serialize in sequence.
+ * \return the total size of the required buffer.
+ */
+template<typename... Args>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+size_t serialize_size(const Args&... args) {
+ return internal::serialize_impl<sizeof...(args), Args...>::serialize_size(args...);
+}
+
+/**
+ * Serialize a set of values to the byte buffer.
+ *
+ * \param dest output byte buffer; if this is nullptr, does nothing.
+ * \param end the end of the output byte buffer.
+ * \param args ... arguments to serialize in sequence.
+ * \return the next address after all serialized values.
+ */
+template<typename... Args>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+uint8_t* serialize(uint8_t* dest, uint8_t* end, const Args&... args) {
+ return internal::serialize_impl<sizeof...(args), Args...>::serialize(dest, end, args...);
+}
+
+/**
+ * Deserialize a set of values from the byte buffer.
+ *
+ * \param src input byte buffer; if this is nullptr, does nothing.
+ * \param end the end of input byte buffer.
+ * \param args ... arguments to deserialize in sequence.
+ * \return the next address after all parsed values; nullptr if parsing errors are detected.
+ */
+template<typename... Args>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+const uint8_t* deserialize(const uint8_t* src, const uint8_t* end, Args&... args) {
+ return internal::serialize_impl<sizeof...(args), Args...>::deserialize(src, end, args...);
+}
+
+} // namespace Eigen
+
+#endif // EIGEN_SERIALIZER_H
diff --git a/Eigen/src/Core/util/StaticAssert.h b/Eigen/src/Core/util/StaticAssert.h
new file mode 100644
index 0000000..c938eb8
--- /dev/null
+++ b/Eigen/src/Core/util/StaticAssert.h
@@ -0,0 +1,115 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_STATIC_ASSERT_H
+#define EIGEN_STATIC_ASSERT_H
+
+/* Some notes on Eigen's static assertion mechanism:
+ *
+ * - in EIGEN_STATIC_ASSERT(CONDITION,MSG) the parameter CONDITION must be a compile time boolean
+ * expression, and MSG an enum listed in struct internal::static_assertion<true>
+ *
+ * - currently EIGEN_STATIC_ASSERT can only be used in function scope
+ *
+ */
+
+#ifndef EIGEN_STATIC_ASSERT
+#ifndef EIGEN_NO_STATIC_ASSERT
+
+#define EIGEN_STATIC_ASSERT(X,MSG) static_assert(X,#MSG);
+
+#else // EIGEN_NO_STATIC_ASSERT
+
+#define EIGEN_STATIC_ASSERT(CONDITION,MSG)
+
+#endif // EIGEN_NO_STATIC_ASSERT
+#endif // EIGEN_STATIC_ASSERT
+
+// static assertion failing if the type \a TYPE is not a vector type
+#define EIGEN_STATIC_ASSERT_VECTOR_ONLY(TYPE) \
+ EIGEN_STATIC_ASSERT(TYPE::IsVectorAtCompileTime, \
+ YOU_TRIED_CALLING_A_VECTOR_METHOD_ON_A_MATRIX)
+
+// static assertion failing if the type \a TYPE is not fixed-size
+#define EIGEN_STATIC_ASSERT_FIXED_SIZE(TYPE) \
+ EIGEN_STATIC_ASSERT(TYPE::SizeAtCompileTime!=Eigen::Dynamic, \
+ YOU_CALLED_A_FIXED_SIZE_METHOD_ON_A_DYNAMIC_SIZE_MATRIX_OR_VECTOR)
+
+// static assertion failing if the type \a TYPE is not dynamic-size
+#define EIGEN_STATIC_ASSERT_DYNAMIC_SIZE(TYPE) \
+ EIGEN_STATIC_ASSERT(TYPE::SizeAtCompileTime==Eigen::Dynamic, \
+ YOU_CALLED_A_DYNAMIC_SIZE_METHOD_ON_A_FIXED_SIZE_MATRIX_OR_VECTOR)
+
+// static assertion failing if the type \a TYPE is not a vector type of the given size
+#define EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(TYPE, SIZE) \
+ EIGEN_STATIC_ASSERT(TYPE::IsVectorAtCompileTime && TYPE::SizeAtCompileTime==SIZE, \
+ THIS_METHOD_IS_ONLY_FOR_VECTORS_OF_A_SPECIFIC_SIZE)
+
+// static assertion failing if the type \a TYPE is not a vector type of the given size
+#define EIGEN_STATIC_ASSERT_MATRIX_SPECIFIC_SIZE(TYPE, ROWS, COLS) \
+ EIGEN_STATIC_ASSERT(TYPE::RowsAtCompileTime==ROWS && TYPE::ColsAtCompileTime==COLS, \
+ THIS_METHOD_IS_ONLY_FOR_MATRICES_OF_A_SPECIFIC_SIZE)
+
+// static assertion failing if the two vector expression types are not compatible (same fixed-size or dynamic size)
+#define EIGEN_STATIC_ASSERT_SAME_VECTOR_SIZE(TYPE0,TYPE1) \
+ EIGEN_STATIC_ASSERT( \
+ (int(TYPE0::SizeAtCompileTime)==Eigen::Dynamic \
+ || int(TYPE1::SizeAtCompileTime)==Eigen::Dynamic \
+ || int(TYPE0::SizeAtCompileTime)==int(TYPE1::SizeAtCompileTime)),\
+ YOU_MIXED_VECTORS_OF_DIFFERENT_SIZES)
+
+#define EIGEN_PREDICATE_SAME_MATRIX_SIZE(TYPE0,TYPE1) \
+ ( \
+ (int(Eigen::internal::size_of_xpr_at_compile_time<TYPE0>::ret)==0 && int(Eigen::internal::size_of_xpr_at_compile_time<TYPE1>::ret)==0) \
+ || (\
+ (int(TYPE0::RowsAtCompileTime)==Eigen::Dynamic \
+ || int(TYPE1::RowsAtCompileTime)==Eigen::Dynamic \
+ || int(TYPE0::RowsAtCompileTime)==int(TYPE1::RowsAtCompileTime)) \
+ && (int(TYPE0::ColsAtCompileTime)==Eigen::Dynamic \
+ || int(TYPE1::ColsAtCompileTime)==Eigen::Dynamic \
+ || int(TYPE0::ColsAtCompileTime)==int(TYPE1::ColsAtCompileTime))\
+ ) \
+ )
+
+#define EIGEN_STATIC_ASSERT_NON_INTEGER(TYPE) \
+ EIGEN_STATIC_ASSERT(!Eigen::NumTraits<TYPE>::IsInteger, THIS_FUNCTION_IS_NOT_FOR_INTEGER_NUMERIC_TYPES)
+
+
+// static assertion failing if it is guaranteed at compile-time that the two matrix expression types have different sizes
+#define EIGEN_STATIC_ASSERT_SAME_MATRIX_SIZE(TYPE0,TYPE1) \
+ EIGEN_STATIC_ASSERT( \
+ EIGEN_PREDICATE_SAME_MATRIX_SIZE(TYPE0,TYPE1),\
+ YOU_MIXED_MATRICES_OF_DIFFERENT_SIZES)
+
+#define EIGEN_STATIC_ASSERT_SIZE_1x1(TYPE) \
+ EIGEN_STATIC_ASSERT((TYPE::RowsAtCompileTime == 1 || TYPE::RowsAtCompileTime == Eigen::Dynamic) && \
+ (TYPE::ColsAtCompileTime == 1 || TYPE::ColsAtCompileTime == Eigen::Dynamic), \
+ THIS_METHOD_IS_ONLY_FOR_1x1_EXPRESSIONS)
+
+#define EIGEN_STATIC_ASSERT_LVALUE(Derived) \
+ EIGEN_STATIC_ASSERT(Eigen::internal::is_lvalue<Derived>::value, \
+ THIS_EXPRESSION_IS_NOT_A_LVALUE__IT_IS_READ_ONLY)
+
+#define EIGEN_STATIC_ASSERT_ARRAYXPR(Derived) \
+ EIGEN_STATIC_ASSERT((Eigen::internal::is_same<typename Eigen::internal::traits<Derived>::XprKind, ArrayXpr>::value), \
+ THIS_METHOD_IS_ONLY_FOR_ARRAYS_NOT_MATRICES)
+
+#define EIGEN_STATIC_ASSERT_SAME_XPR_KIND(Derived1, Derived2) \
+ EIGEN_STATIC_ASSERT((Eigen::internal::is_same<typename Eigen::internal::traits<Derived1>::XprKind, \
+ typename Eigen::internal::traits<Derived2>::XprKind \
+ >::value), \
+ YOU_CANNOT_MIX_ARRAYS_AND_MATRICES)
+
+// Check that a cost value is positive, and that is stay within a reasonable range
+// TODO this check could be enabled for internal debugging only
+#define EIGEN_INTERNAL_CHECK_COST_VALUE(C) \
+ EIGEN_STATIC_ASSERT((C)>=0 && (C)<=HugeCost*HugeCost, EIGEN_INTERNAL_ERROR_PLEASE_FILE_A_BUG_REPORT__INVALID_COST_VALUE);
+
+#endif // EIGEN_STATIC_ASSERT_H
diff --git a/Eigen/src/Core/util/SymbolicIndex.h b/Eigen/src/Core/util/SymbolicIndex.h
new file mode 100644
index 0000000..3b19185
--- /dev/null
+++ b/Eigen/src/Core/util/SymbolicIndex.h
@@ -0,0 +1,262 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2017 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_SYMBOLIC_INDEX_H
+#define EIGEN_SYMBOLIC_INDEX_H
+
+#include "../InternalHeaderCheck.h"
+
+namespace Eigen {
+
+/** \namespace Eigen::symbolic
+ * \ingroup Core_Module
+ *
+ * This namespace defines a set of classes and functions to build and evaluate symbolic expressions of scalar type Index.
+ * Here is a simple example:
+ *
+ * \code
+ * // First step, defines symbols:
+ * struct x_tag {}; static const symbolic::SymbolExpr<x_tag> x;
+ * struct y_tag {}; static const symbolic::SymbolExpr<y_tag> y;
+ * struct z_tag {}; static const symbolic::SymbolExpr<z_tag> z;
+ *
+ * // Defines an expression:
+ * auto expr = (x+3)/y+z;
+ *
+ * // And evaluate it: (c++14)
+ * std::cout << expr.eval(x=6,y=3,z=-13) << "\n";
+ *
+ * \endcode
+ *
+ * It is currently only used internally to define and manipulate the
+ * Eigen::placeholders::last and Eigen::placeholders::lastp1 symbols in
+ * Eigen::seq and Eigen::seqN.
+ *
+ */
+namespace symbolic {
+
+template<typename Tag> class Symbol;
+template<typename Arg0> class NegateExpr;
+template<typename Arg1,typename Arg2> class AddExpr;
+template<typename Arg1,typename Arg2> class ProductExpr;
+template<typename Arg1,typename Arg2> class QuotientExpr;
+
+// A simple wrapper around an integral value to provide the eval method.
+// We could also use a free-function symbolic_eval...
+template<typename IndexType=Index>
+class ValueExpr {
+public:
+ ValueExpr(IndexType val) : m_value(val) {}
+ template<typename T>
+ IndexType eval_impl(const T&) const { return m_value; }
+protected:
+ IndexType m_value;
+};
+
+// Specialization for compile-time value,
+// It is similar to ValueExpr(N) but this version helps the compiler to generate better code.
+template<int N>
+class ValueExpr<internal::FixedInt<N> > {
+public:
+ ValueExpr() {}
+ template<typename T>
+ EIGEN_CONSTEXPR Index eval_impl(const T&) const { return N; }
+};
+
+
+/** \class BaseExpr
+ * \ingroup Core_Module
+ * Common base class of any symbolic expressions
+ */
+template<typename Derived>
+class BaseExpr
+{
+public:
+ const Derived& derived() const { return *static_cast<const Derived*>(this); }
+
+ /** Evaluate the expression given the \a values of the symbols.
+ *
+ * \param values defines the values of the symbols, it can either be a SymbolValue or a std::tuple of SymbolValue
+ * as constructed by SymbolExpr::operator= operator.
+ *
+ */
+ template<typename T>
+ Index eval(const T& values) const { return derived().eval_impl(values); }
+
+ template<typename... Types>
+ Index eval(Types&&... values) const { return derived().eval_impl(std::make_tuple(values...)); }
+
+ NegateExpr<Derived> operator-() const { return NegateExpr<Derived>(derived()); }
+
+ AddExpr<Derived,ValueExpr<> > operator+(Index b) const
+ { return AddExpr<Derived,ValueExpr<> >(derived(), b); }
+ AddExpr<Derived,ValueExpr<> > operator-(Index a) const
+ { return AddExpr<Derived,ValueExpr<> >(derived(), -a); }
+ ProductExpr<Derived,ValueExpr<> > operator*(Index a) const
+ { return ProductExpr<Derived,ValueExpr<> >(derived(),a); }
+ QuotientExpr<Derived,ValueExpr<> > operator/(Index a) const
+ { return QuotientExpr<Derived,ValueExpr<> >(derived(),a); }
+
+ friend AddExpr<Derived,ValueExpr<> > operator+(Index a, const BaseExpr& b)
+ { return AddExpr<Derived,ValueExpr<> >(b.derived(), a); }
+ friend AddExpr<NegateExpr<Derived>,ValueExpr<> > operator-(Index a, const BaseExpr& b)
+ { return AddExpr<NegateExpr<Derived>,ValueExpr<> >(-b.derived(), a); }
+ friend ProductExpr<ValueExpr<>,Derived> operator*(Index a, const BaseExpr& b)
+ { return ProductExpr<ValueExpr<>,Derived>(a,b.derived()); }
+ friend QuotientExpr<ValueExpr<>,Derived> operator/(Index a, const BaseExpr& b)
+ { return QuotientExpr<ValueExpr<>,Derived>(a,b.derived()); }
+
+ template<int N>
+ AddExpr<Derived,ValueExpr<internal::FixedInt<N> > > operator+(internal::FixedInt<N>) const
+ { return AddExpr<Derived,ValueExpr<internal::FixedInt<N> > >(derived(), ValueExpr<internal::FixedInt<N> >()); }
+ template<int N>
+ AddExpr<Derived,ValueExpr<internal::FixedInt<-N> > > operator-(internal::FixedInt<N>) const
+ { return AddExpr<Derived,ValueExpr<internal::FixedInt<-N> > >(derived(), ValueExpr<internal::FixedInt<-N> >()); }
+ template<int N>
+ ProductExpr<Derived,ValueExpr<internal::FixedInt<N> > > operator*(internal::FixedInt<N>) const
+ { return ProductExpr<Derived,ValueExpr<internal::FixedInt<N> > >(derived(),ValueExpr<internal::FixedInt<N> >()); }
+ template<int N>
+ QuotientExpr<Derived,ValueExpr<internal::FixedInt<N> > > operator/(internal::FixedInt<N>) const
+ { return QuotientExpr<Derived,ValueExpr<internal::FixedInt<N> > >(derived(),ValueExpr<internal::FixedInt<N> >()); }
+
+ template<int N>
+ friend AddExpr<Derived,ValueExpr<internal::FixedInt<N> > > operator+(internal::FixedInt<N>, const BaseExpr& b)
+ { return AddExpr<Derived,ValueExpr<internal::FixedInt<N> > >(b.derived(), ValueExpr<internal::FixedInt<N> >()); }
+ template<int N>
+ friend AddExpr<NegateExpr<Derived>,ValueExpr<internal::FixedInt<N> > > operator-(internal::FixedInt<N>, const BaseExpr& b)
+ { return AddExpr<NegateExpr<Derived>,ValueExpr<internal::FixedInt<N> > >(-b.derived(), ValueExpr<internal::FixedInt<N> >()); }
+ template<int N>
+ friend ProductExpr<ValueExpr<internal::FixedInt<N> >,Derived> operator*(internal::FixedInt<N>, const BaseExpr& b)
+ { return ProductExpr<ValueExpr<internal::FixedInt<N> >,Derived>(ValueExpr<internal::FixedInt<N> >(),b.derived()); }
+ template<int N>
+ friend QuotientExpr<ValueExpr<internal::FixedInt<N> >,Derived> operator/(internal::FixedInt<N>, const BaseExpr& b)
+ { return QuotientExpr<ValueExpr<internal::FixedInt<N> > ,Derived>(ValueExpr<internal::FixedInt<N> >(),b.derived()); }
+
+
+ template<typename OtherDerived>
+ AddExpr<Derived,OtherDerived> operator+(const BaseExpr<OtherDerived> &b) const
+ { return AddExpr<Derived,OtherDerived>(derived(), b.derived()); }
+
+ template<typename OtherDerived>
+ AddExpr<Derived,NegateExpr<OtherDerived> > operator-(const BaseExpr<OtherDerived> &b) const
+ { return AddExpr<Derived,NegateExpr<OtherDerived> >(derived(), -b.derived()); }
+
+ template<typename OtherDerived>
+ ProductExpr<Derived,OtherDerived> operator*(const BaseExpr<OtherDerived> &b) const
+ { return ProductExpr<Derived,OtherDerived>(derived(), b.derived()); }
+
+ template<typename OtherDerived>
+ QuotientExpr<Derived,OtherDerived> operator/(const BaseExpr<OtherDerived> &b) const
+ { return QuotientExpr<Derived,OtherDerived>(derived(), b.derived()); }
+};
+
+template<typename T>
+struct is_symbolic {
+ // BaseExpr has no conversion ctor, so we only have to check whether T can be statically cast to its base class BaseExpr<T>.
+ enum { value = internal::is_convertible<T,BaseExpr<T> >::value };
+};
+
+/** Represents the actual value of a symbol identified by its tag
+ *
+ * It is the return type of SymbolValue::operator=, and most of the time this is only way it is used.
+ */
+template<typename Tag>
+class SymbolValue
+{
+public:
+ /** Default constructor from the value \a val */
+ SymbolValue(Index val) : m_value(val) {}
+
+ /** \returns the stored value of the symbol */
+ Index value() const { return m_value; }
+protected:
+ Index m_value;
+};
+
+/** Expression of a symbol uniquely identified by the template parameter type \c tag */
+template<typename tag>
+class SymbolExpr : public BaseExpr<SymbolExpr<tag> >
+{
+public:
+ /** Alias to the template parameter \c tag */
+ typedef tag Tag;
+
+ SymbolExpr() {}
+
+ /** Associate the value \a val to the given symbol \c *this, uniquely identified by its \c Tag.
+ *
+ * The returned object should be passed to ExprBase::eval() to evaluate a given expression with this specified runtime-time value.
+ */
+ SymbolValue<Tag> operator=(Index val) const {
+ return SymbolValue<Tag>(val);
+ }
+
+ Index eval_impl(const SymbolValue<Tag> &values) const { return values.value(); }
+
+ // C++14 versions suitable for multiple symbols
+ template<typename... Types>
+ Index eval_impl(const std::tuple<Types...>& values) const { return std::get<SymbolValue<Tag> >(values).value(); }
+};
+
+template<typename Arg0>
+class NegateExpr : public BaseExpr<NegateExpr<Arg0> >
+{
+public:
+ NegateExpr(const Arg0& arg0) : m_arg0(arg0) {}
+
+ template<typename T>
+ Index eval_impl(const T& values) const { return -m_arg0.eval_impl(values); }
+protected:
+ Arg0 m_arg0;
+};
+
+template<typename Arg0, typename Arg1>
+class AddExpr : public BaseExpr<AddExpr<Arg0,Arg1> >
+{
+public:
+ AddExpr(const Arg0& arg0, const Arg1& arg1) : m_arg0(arg0), m_arg1(arg1) {}
+
+ template<typename T>
+ Index eval_impl(const T& values) const { return m_arg0.eval_impl(values) + m_arg1.eval_impl(values); }
+protected:
+ Arg0 m_arg0;
+ Arg1 m_arg1;
+};
+
+template<typename Arg0, typename Arg1>
+class ProductExpr : public BaseExpr<ProductExpr<Arg0,Arg1> >
+{
+public:
+ ProductExpr(const Arg0& arg0, const Arg1& arg1) : m_arg0(arg0), m_arg1(arg1) {}
+
+ template<typename T>
+ Index eval_impl(const T& values) const { return m_arg0.eval_impl(values) * m_arg1.eval_impl(values); }
+protected:
+ Arg0 m_arg0;
+ Arg1 m_arg1;
+};
+
+template<typename Arg0, typename Arg1>
+class QuotientExpr : public BaseExpr<QuotientExpr<Arg0,Arg1> >
+{
+public:
+ QuotientExpr(const Arg0& arg0, const Arg1& arg1) : m_arg0(arg0), m_arg1(arg1) {}
+
+ template<typename T>
+ Index eval_impl(const T& values) const { return m_arg0.eval_impl(values) / m_arg1.eval_impl(values); }
+protected:
+ Arg0 m_arg0;
+ Arg1 m_arg1;
+};
+
+} // end namespace symbolic
+
+} // end namespace Eigen
+
+#endif // EIGEN_SYMBOLIC_INDEX_H
diff --git a/Eigen/src/Core/util/XprHelper.h b/Eigen/src/Core/util/XprHelper.h
new file mode 100644
index 0000000..b5f91bf
--- /dev/null
+++ b/Eigen/src/Core/util/XprHelper.h
@@ -0,0 +1,840 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_XPRHELPER_H
+#define EIGEN_XPRHELPER_H
+
+#include "../InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+
+template<typename IndexDest, typename IndexSrc>
+EIGEN_DEVICE_FUNC
+inline IndexDest convert_index(const IndexSrc& idx) {
+ // for sizeof(IndexDest)>=sizeof(IndexSrc) compilers should be able to optimize this away:
+ eigen_internal_assert(idx <= NumTraits<IndexDest>::highest() && "Index value to big for target type");
+ return IndexDest(idx);
+}
+
+// true if T can be considered as an integral index (i.e., and integral type or enum)
+template<typename T> struct is_valid_index_type
+{
+ enum { value = internal::is_integral<T>::value || std::is_enum<T>::value
+ };
+};
+
+// true if both types are not valid index types
+template<typename RowIndices, typename ColIndices>
+struct valid_indexed_view_overload {
+ enum { value = !(internal::is_valid_index_type<RowIndices>::value && internal::is_valid_index_type<ColIndices>::value) };
+};
+
+// promote_scalar_arg is an helper used in operation between an expression and a scalar, like:
+// expression * scalar
+// Its role is to determine how the type T of the scalar operand should be promoted given the scalar type ExprScalar of the given expression.
+// The IsSupported template parameter must be provided by the caller as: internal::has_ReturnType<ScalarBinaryOpTraits<ExprScalar,T,op> >::value using the proper order for ExprScalar and T.
+// Then the logic is as follows:
+// - if the operation is natively supported as defined by IsSupported, then the scalar type is not promoted, and T is returned.
+// - otherwise, NumTraits<ExprScalar>::Literal is returned if T is implicitly convertible to NumTraits<ExprScalar>::Literal AND that this does not imply a float to integer conversion.
+// - otherwise, ExprScalar is returned if T is implicitly convertible to ExprScalar AND that this does not imply a float to integer conversion.
+// - In all other cases, the promoted type is not defined, and the respective operation is thus invalid and not available (SFINAE).
+template<typename ExprScalar,typename T, bool IsSupported>
+struct promote_scalar_arg;
+
+template<typename S,typename T>
+struct promote_scalar_arg<S,T,true>
+{
+ typedef T type;
+};
+
+// Recursively check safe conversion to PromotedType, and then ExprScalar if they are different.
+template<typename ExprScalar,typename T,typename PromotedType,
+ bool ConvertibleToLiteral = internal::is_convertible<T,PromotedType>::value,
+ bool IsSafe = NumTraits<T>::IsInteger || !NumTraits<PromotedType>::IsInteger>
+struct promote_scalar_arg_unsupported;
+
+// Start recursion with NumTraits<ExprScalar>::Literal
+template<typename S,typename T>
+struct promote_scalar_arg<S,T,false> : promote_scalar_arg_unsupported<S,T,typename NumTraits<S>::Literal> {};
+
+// We found a match!
+template<typename S,typename T, typename PromotedType>
+struct promote_scalar_arg_unsupported<S,T,PromotedType,true,true>
+{
+ typedef PromotedType type;
+};
+
+// No match, but no real-to-integer issues, and ExprScalar and current PromotedType are different,
+// so let's try to promote to ExprScalar
+template<typename ExprScalar,typename T, typename PromotedType>
+struct promote_scalar_arg_unsupported<ExprScalar,T,PromotedType,false,true>
+ : promote_scalar_arg_unsupported<ExprScalar,T,ExprScalar>
+{};
+
+// Unsafe real-to-integer, let's stop.
+template<typename S,typename T, typename PromotedType, bool ConvertibleToLiteral>
+struct promote_scalar_arg_unsupported<S,T,PromotedType,ConvertibleToLiteral,false> {};
+
+// T is not even convertible to ExprScalar, let's stop.
+template<typename S,typename T>
+struct promote_scalar_arg_unsupported<S,T,S,false,true> {};
+
+//classes inheriting no_assignment_operator don't generate a default operator=.
+class no_assignment_operator
+{
+ private:
+ no_assignment_operator& operator=(const no_assignment_operator&);
+ protected:
+ EIGEN_DEFAULT_COPY_CONSTRUCTOR(no_assignment_operator)
+ EIGEN_DEFAULT_EMPTY_CONSTRUCTOR_AND_DESTRUCTOR(no_assignment_operator)
+};
+
+/** \internal return the index type with the largest number of bits */
+template<typename I1, typename I2>
+struct promote_index_type
+{
+ typedef std::conditional_t<(sizeof(I1)<sizeof(I2)), I2, I1> type;
+};
+
+/** \internal If the template parameter Value is Dynamic, this class is just a wrapper around a T variable that
+ * can be accessed using value() and setValue().
+ * Otherwise, this class is an empty structure and value() just returns the template parameter Value.
+ */
+template<typename T, int Value> class variable_if_dynamic
+{
+ public:
+ EIGEN_DEFAULT_EMPTY_CONSTRUCTOR_AND_DESTRUCTOR(variable_if_dynamic)
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE explicit variable_if_dynamic(T v) { EIGEN_ONLY_USED_FOR_DEBUG(v); eigen_assert(v == T(Value)); }
+ EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE EIGEN_CONSTEXPR
+ T value() { return T(Value); }
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE EIGEN_CONSTEXPR
+ operator T() const { return T(Value); }
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ void setValue(T v) const { EIGEN_ONLY_USED_FOR_DEBUG(v); eigen_assert(v == T(Value)); }
+};
+
+template<typename T> class variable_if_dynamic<T, Dynamic>
+{
+ T m_value;
+ public:
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE explicit variable_if_dynamic(T value = 0) EIGEN_NO_THROW : m_value(value) {}
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE T value() const { return m_value; }
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE operator T() const { return m_value; }
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void setValue(T value) { m_value = value; }
+};
+
+/** \internal like variable_if_dynamic but for DynamicIndex
+ */
+template<typename T, int Value> class variable_if_dynamicindex
+{
+ public:
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE explicit variable_if_dynamicindex(T v) { EIGEN_ONLY_USED_FOR_DEBUG(v); eigen_assert(v == T(Value)); }
+ EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE EIGEN_CONSTEXPR
+ T value() { return T(Value); }
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ void setValue(T) {}
+};
+
+template<typename T> class variable_if_dynamicindex<T, DynamicIndex>
+{
+ T m_value;
+ EIGEN_DEVICE_FUNC variable_if_dynamicindex() { eigen_assert(false); }
+ public:
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE explicit variable_if_dynamicindex(T value) : m_value(value) {}
+ EIGEN_DEVICE_FUNC T EIGEN_STRONG_INLINE value() const { return m_value; }
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void setValue(T value) { m_value = value; }
+};
+
+template<typename T> struct functor_traits
+{
+ enum
+ {
+ Cost = 10,
+ PacketAccess = false,
+ IsRepeatable = false
+ };
+};
+
+template<typename T> struct packet_traits;
+
+template<typename T> struct unpacket_traits;
+
+template<int Size, typename PacketType,
+ bool Stop = Size==Dynamic || (Size%unpacket_traits<PacketType>::size)==0 || is_same<PacketType,typename unpacket_traits<PacketType>::half>::value>
+struct find_best_packet_helper;
+
+template< int Size, typename PacketType>
+struct find_best_packet_helper<Size,PacketType,true>
+{
+ typedef PacketType type;
+};
+
+template<int Size, typename PacketType>
+struct find_best_packet_helper<Size,PacketType,false>
+{
+ typedef typename find_best_packet_helper<Size,typename unpacket_traits<PacketType>::half>::type type;
+};
+
+template<typename T, int Size>
+struct find_best_packet
+{
+ typedef typename find_best_packet_helper<Size,typename packet_traits<T>::type>::type type;
+};
+
+#if EIGEN_MAX_STATIC_ALIGN_BYTES>0
+constexpr inline int compute_default_alignment_helper(int ArrayBytes, int AlignmentBytes) {
+ if((ArrayBytes % AlignmentBytes) == 0) {
+ return AlignmentBytes;
+ } else if (EIGEN_MIN_ALIGN_BYTES<AlignmentBytes) {
+ return compute_default_alignment_helper(ArrayBytes, AlignmentBytes/2);
+ } else {
+ return 0;
+ }
+}
+#else
+// If static alignment is disabled, no need to bother.
+// This also avoids a division by zero
+constexpr inline int compute_default_alignment_helper(int ArrayBytes, int AlignmentBytes) {
+ EIGEN_UNUSED_VARIABLE(ArrayBytes);
+ EIGEN_UNUSED_VARIABLE(AlignmentBytes);
+ return 0;
+}
+#endif
+
+template<typename T, int Size> struct compute_default_alignment {
+ enum { value = compute_default_alignment_helper(Size*sizeof(T), EIGEN_MAX_STATIC_ALIGN_BYTES) };
+};
+
+template<typename T> struct compute_default_alignment<T,Dynamic> {
+ enum { value = EIGEN_MAX_ALIGN_BYTES };
+};
+
+template<typename Scalar_, int Rows_, int Cols_,
+ int Options_ = AutoAlign |
+ ( (Rows_==1 && Cols_!=1) ? RowMajor
+ : (Cols_==1 && Rows_!=1) ? ColMajor
+ : EIGEN_DEFAULT_MATRIX_STORAGE_ORDER_OPTION ),
+ int MaxRows_ = Rows_,
+ int MaxCols_ = Cols_
+> class make_proper_matrix_type
+{
+ enum {
+ IsColVector = Cols_==1 && Rows_!=1,
+ IsRowVector = Rows_==1 && Cols_!=1,
+ Options = IsColVector ? (Options_ | ColMajor) & ~RowMajor
+ : IsRowVector ? (Options_ | RowMajor) & ~ColMajor
+ : Options_
+ };
+ public:
+ typedef Matrix<Scalar_, Rows_, Cols_, Options, MaxRows_, MaxCols_> type;
+};
+
+constexpr inline unsigned compute_matrix_flags(int Options) {
+ unsigned row_major_bit = Options&RowMajor ? RowMajorBit : 0;
+ // FIXME currently we still have to handle DirectAccessBit at the expression level to handle DenseCoeffsBase<>
+ // and then propagate this information to the evaluator's flags.
+ // However, I (Gael) think that DirectAccessBit should only matter at the evaluation stage.
+ return DirectAccessBit | LvalueBit | NestByRefBit | row_major_bit;
+}
+
+constexpr inline int size_at_compile_time(int rows, int cols) {
+ return (rows==Dynamic || cols==Dynamic) ? Dynamic : rows * cols;
+}
+
+template<typename XprType> struct size_of_xpr_at_compile_time
+{
+ enum { ret = size_at_compile_time(traits<XprType>::RowsAtCompileTime, traits<XprType>::ColsAtCompileTime) };
+};
+
+/* plain_matrix_type : the difference from eval is that plain_matrix_type is always a plain matrix type,
+ * whereas eval is a const reference in the case of a matrix
+ */
+
+template<typename T, typename StorageKind = typename traits<T>::StorageKind> struct plain_matrix_type;
+template<typename T, typename BaseClassType, int Flags> struct plain_matrix_type_dense;
+template<typename T> struct plain_matrix_type<T,Dense>
+{
+ typedef typename plain_matrix_type_dense<T,typename traits<T>::XprKind, traits<T>::Flags>::type type;
+};
+template<typename T> struct plain_matrix_type<T,DiagonalShape>
+{
+ typedef typename T::PlainObject type;
+};
+
+template<typename T> struct plain_matrix_type<T,SkewSymmetricShape>
+{
+ typedef typename T::PlainObject type;
+};
+
+template<typename T, int Flags> struct plain_matrix_type_dense<T,MatrixXpr,Flags>
+{
+ typedef Matrix<typename traits<T>::Scalar,
+ traits<T>::RowsAtCompileTime,
+ traits<T>::ColsAtCompileTime,
+ AutoAlign | (Flags&RowMajorBit ? RowMajor : ColMajor),
+ traits<T>::MaxRowsAtCompileTime,
+ traits<T>::MaxColsAtCompileTime
+ > type;
+};
+
+template<typename T, int Flags> struct plain_matrix_type_dense<T,ArrayXpr,Flags>
+{
+ typedef Array<typename traits<T>::Scalar,
+ traits<T>::RowsAtCompileTime,
+ traits<T>::ColsAtCompileTime,
+ AutoAlign | (Flags&RowMajorBit ? RowMajor : ColMajor),
+ traits<T>::MaxRowsAtCompileTime,
+ traits<T>::MaxColsAtCompileTime
+ > type;
+};
+
+/* eval : the return type of eval(). For matrices, this is just a const reference
+ * in order to avoid a useless copy
+ */
+
+template<typename T, typename StorageKind = typename traits<T>::StorageKind> struct eval;
+
+template<typename T> struct eval<T,Dense>
+{
+ typedef typename plain_matrix_type<T>::type type;
+// typedef typename T::PlainObject type;
+// typedef T::Matrix<typename traits<T>::Scalar,
+// traits<T>::RowsAtCompileTime,
+// traits<T>::ColsAtCompileTime,
+// AutoAlign | (traits<T>::Flags&RowMajorBit ? RowMajor : ColMajor),
+// traits<T>::MaxRowsAtCompileTime,
+// traits<T>::MaxColsAtCompileTime
+// > type;
+};
+
+template<typename T> struct eval<T,DiagonalShape>
+{
+ typedef typename plain_matrix_type<T>::type type;
+};
+
+template<typename T> struct eval<T,SkewSymmetricShape>
+{
+ typedef typename plain_matrix_type<T>::type type;
+};
+
+// for matrices, no need to evaluate, just use a const reference to avoid a useless copy
+template<typename Scalar_, int Rows_, int Cols_, int Options_, int MaxRows_, int MaxCols_>
+struct eval<Matrix<Scalar_, Rows_, Cols_, Options_, MaxRows_, MaxCols_>, Dense>
+{
+ typedef const Matrix<Scalar_, Rows_, Cols_, Options_, MaxRows_, MaxCols_>& type;
+};
+
+template<typename Scalar_, int Rows_, int Cols_, int Options_, int MaxRows_, int MaxCols_>
+struct eval<Array<Scalar_, Rows_, Cols_, Options_, MaxRows_, MaxCols_>, Dense>
+{
+ typedef const Array<Scalar_, Rows_, Cols_, Options_, MaxRows_, MaxCols_>& type;
+};
+
+
+/* similar to plain_matrix_type, but using the evaluator's Flags */
+template<typename T, typename StorageKind = typename traits<T>::StorageKind> struct plain_object_eval;
+
+template<typename T>
+struct plain_object_eval<T,Dense>
+{
+ typedef typename plain_matrix_type_dense<T,typename traits<T>::XprKind, evaluator<T>::Flags>::type type;
+};
+
+
+/* plain_matrix_type_column_major : same as plain_matrix_type but guaranteed to be column-major
+ */
+template<typename T> struct plain_matrix_type_column_major
+{
+ enum { Rows = traits<T>::RowsAtCompileTime,
+ Cols = traits<T>::ColsAtCompileTime,
+ MaxRows = traits<T>::MaxRowsAtCompileTime,
+ MaxCols = traits<T>::MaxColsAtCompileTime
+ };
+ typedef Matrix<typename traits<T>::Scalar,
+ Rows,
+ Cols,
+ (MaxRows==1&&MaxCols!=1) ? RowMajor : ColMajor,
+ MaxRows,
+ MaxCols
+ > type;
+};
+
+/* plain_matrix_type_row_major : same as plain_matrix_type but guaranteed to be row-major
+ */
+template<typename T> struct plain_matrix_type_row_major
+{
+ enum { Rows = traits<T>::RowsAtCompileTime,
+ Cols = traits<T>::ColsAtCompileTime,
+ MaxRows = traits<T>::MaxRowsAtCompileTime,
+ MaxCols = traits<T>::MaxColsAtCompileTime
+ };
+ typedef Matrix<typename traits<T>::Scalar,
+ Rows,
+ Cols,
+ (MaxCols==1&&MaxRows!=1) ? ColMajor : RowMajor,
+ MaxRows,
+ MaxCols
+ > type;
+};
+
+/** \internal The reference selector for template expressions. The idea is that we don't
+ * need to use references for expressions since they are light weight proxy
+ * objects which should generate no copying overhead. */
+template <typename T>
+struct ref_selector
+{
+ typedef std::conditional_t<
+ bool(traits<T>::Flags & NestByRefBit),
+ T const&,
+ const T
+ > type;
+
+ typedef std::conditional_t<
+ bool(traits<T>::Flags & NestByRefBit),
+ T &,
+ T
+ > non_const_type;
+};
+
+/** \internal Adds the const qualifier on the value-type of T2 if and only if T1 is a const type */
+template<typename T1, typename T2>
+struct transfer_constness
+{
+ typedef std::conditional_t<
+ bool(internal::is_const<T1>::value),
+ add_const_on_value_type_t<T2>,
+ T2
+ > type;
+};
+
+
+// However, we still need a mechanism to detect whether an expression which is evaluated multiple time
+// has to be evaluated into a temporary.
+// That's the purpose of this new nested_eval helper:
+/** \internal Determines how a given expression should be nested when evaluated multiple times.
+ * For example, when you do a * (b+c), Eigen will determine how the expression b+c should be
+ * evaluated into the bigger product expression. The choice is between nesting the expression b+c as-is, or
+ * evaluating that expression b+c into a temporary variable d, and nest d so that the resulting expression is
+ * a*d. Evaluating can be beneficial for example if every coefficient access in the resulting expression causes
+ * many coefficient accesses in the nested expressions -- as is the case with matrix product for example.
+ *
+ * \tparam T the type of the expression being nested.
+ * \tparam n the number of coefficient accesses in the nested expression for each coefficient access in the bigger expression.
+ * \tparam PlainObject the type of the temporary if needed.
+ */
+template<typename T, int n, typename PlainObject = typename plain_object_eval<T>::type> struct nested_eval
+{
+ enum {
+ ScalarReadCost = NumTraits<typename traits<T>::Scalar>::ReadCost,
+ CoeffReadCost = evaluator<T>::CoeffReadCost, // NOTE What if an evaluator evaluate itself into a temporary?
+ // Then CoeffReadCost will be small (e.g., 1) but we still have to evaluate, especially if n>1.
+ // This situation is already taken care by the EvalBeforeNestingBit flag, which is turned ON
+ // for all evaluator creating a temporary. This flag is then propagated by the parent evaluators.
+ // Another solution could be to count the number of temps?
+ NAsInteger = n == Dynamic ? HugeCost : n,
+ CostEval = (NAsInteger+1) * ScalarReadCost + CoeffReadCost,
+ CostNoEval = NAsInteger * CoeffReadCost,
+ Evaluate = (int(evaluator<T>::Flags) & EvalBeforeNestingBit) || (int(CostEval) < int(CostNoEval))
+ };
+
+ typedef std::conditional_t<Evaluate, PlainObject, typename ref_selector<T>::type> type;
+};
+
+template<typename T>
+EIGEN_DEVICE_FUNC
+inline T* const_cast_ptr(const T* ptr)
+{
+ return const_cast<T*>(ptr);
+}
+
+template<typename Derived, typename XprKind = typename traits<Derived>::XprKind>
+struct dense_xpr_base
+{
+ /* dense_xpr_base should only ever be used on dense expressions, thus falling either into the MatrixXpr or into the ArrayXpr cases */
+};
+
+template<typename Derived>
+struct dense_xpr_base<Derived, MatrixXpr>
+{
+ typedef MatrixBase<Derived> type;
+};
+
+template<typename Derived>
+struct dense_xpr_base<Derived, ArrayXpr>
+{
+ typedef ArrayBase<Derived> type;
+};
+
+template<typename Derived, typename XprKind = typename traits<Derived>::XprKind, typename StorageKind = typename traits<Derived>::StorageKind>
+struct generic_xpr_base;
+
+template<typename Derived, typename XprKind>
+struct generic_xpr_base<Derived, XprKind, Dense>
+{
+ typedef typename dense_xpr_base<Derived,XprKind>::type type;
+};
+
+template<typename XprType, typename CastType> struct cast_return_type
+{
+ typedef typename XprType::Scalar CurrentScalarType;
+ typedef remove_all_t<CastType> CastType_;
+ typedef typename CastType_::Scalar NewScalarType;
+ typedef std::conditional_t<is_same<CurrentScalarType,NewScalarType>::value,
+ const XprType&,CastType> type;
+};
+
+template <typename A, typename B> struct promote_storage_type;
+
+template <typename A> struct promote_storage_type<A,A>
+{
+ typedef A ret;
+};
+template <typename A> struct promote_storage_type<A, const A>
+{
+ typedef A ret;
+};
+template <typename A> struct promote_storage_type<const A, A>
+{
+ typedef A ret;
+};
+
+/** \internal Specify the "storage kind" of applying a coefficient-wise
+ * binary operations between two expressions of kinds A and B respectively.
+ * The template parameter Functor permits to specialize the resulting storage kind wrt to
+ * the functor.
+ * The default rules are as follows:
+ * \code
+ * A op A -> A
+ * A op dense -> dense
+ * dense op B -> dense
+ * sparse op dense -> sparse
+ * dense op sparse -> sparse
+ * \endcode
+ */
+template <typename A, typename B, typename Functor> struct cwise_promote_storage_type;
+
+template <typename A, typename Functor> struct cwise_promote_storage_type<A,A,Functor> { typedef A ret; };
+template <typename Functor> struct cwise_promote_storage_type<Dense,Dense,Functor> { typedef Dense ret; };
+template <typename A, typename Functor> struct cwise_promote_storage_type<A,Dense,Functor> { typedef Dense ret; };
+template <typename B, typename Functor> struct cwise_promote_storage_type<Dense,B,Functor> { typedef Dense ret; };
+template <typename Functor> struct cwise_promote_storage_type<Sparse,Dense,Functor> { typedef Sparse ret; };
+template <typename Functor> struct cwise_promote_storage_type<Dense,Sparse,Functor> { typedef Sparse ret; };
+
+template <typename LhsKind, typename RhsKind, int LhsOrder, int RhsOrder> struct cwise_promote_storage_order {
+ enum { value = LhsOrder };
+};
+
+template <typename LhsKind, int LhsOrder, int RhsOrder> struct cwise_promote_storage_order<LhsKind,Sparse,LhsOrder,RhsOrder> { enum { value = RhsOrder }; };
+template <typename RhsKind, int LhsOrder, int RhsOrder> struct cwise_promote_storage_order<Sparse,RhsKind,LhsOrder,RhsOrder> { enum { value = LhsOrder }; };
+template <int Order> struct cwise_promote_storage_order<Sparse,Sparse,Order,Order> { enum { value = Order }; };
+
+
+/** \internal Specify the "storage kind" of multiplying an expression of kind A with kind B.
+ * The template parameter ProductTag permits to specialize the resulting storage kind wrt to
+ * some compile-time properties of the product: GemmProduct, GemvProduct, OuterProduct, InnerProduct.
+ * The default rules are as follows:
+ * \code
+ * K * K -> K
+ * dense * K -> dense
+ * K * dense -> dense
+ * diag * K -> K
+ * K * diag -> K
+ * Perm * K -> K
+ * K * Perm -> K
+ * \endcode
+ */
+template <typename A, typename B, int ProductTag> struct product_promote_storage_type;
+
+template <typename A, int ProductTag> struct product_promote_storage_type<A, A, ProductTag> { typedef A ret;};
+template <int ProductTag> struct product_promote_storage_type<Dense, Dense, ProductTag> { typedef Dense ret;};
+template <typename A, int ProductTag> struct product_promote_storage_type<A, Dense, ProductTag> { typedef Dense ret; };
+template <typename B, int ProductTag> struct product_promote_storage_type<Dense, B, ProductTag> { typedef Dense ret; };
+
+template <typename A, int ProductTag> struct product_promote_storage_type<A, DiagonalShape, ProductTag> { typedef A ret; };
+template <typename B, int ProductTag> struct product_promote_storage_type<DiagonalShape, B, ProductTag> { typedef B ret; };
+template <int ProductTag> struct product_promote_storage_type<Dense, DiagonalShape, ProductTag> { typedef Dense ret; };
+template <int ProductTag> struct product_promote_storage_type<DiagonalShape, Dense, ProductTag> { typedef Dense ret; };
+
+template <typename A, int ProductTag> struct product_promote_storage_type<A, SkewSymmetricShape, ProductTag> { typedef A ret; };
+template <typename B, int ProductTag> struct product_promote_storage_type<SkewSymmetricShape, B, ProductTag> { typedef B ret; };
+template <int ProductTag> struct product_promote_storage_type<Dense, SkewSymmetricShape, ProductTag> { typedef Dense ret; };
+template <int ProductTag> struct product_promote_storage_type<SkewSymmetricShape, Dense, ProductTag> { typedef Dense ret; };
+template <int ProductTag> struct product_promote_storage_type<SkewSymmetricShape, SkewSymmetricShape, ProductTag> { typedef Dense ret; };
+
+template <typename A, int ProductTag> struct product_promote_storage_type<A, PermutationStorage, ProductTag> { typedef A ret; };
+template <typename B, int ProductTag> struct product_promote_storage_type<PermutationStorage, B, ProductTag> { typedef B ret; };
+template <int ProductTag> struct product_promote_storage_type<Dense, PermutationStorage, ProductTag> { typedef Dense ret; };
+template <int ProductTag> struct product_promote_storage_type<PermutationStorage, Dense, ProductTag> { typedef Dense ret; };
+
+/** \internal gives the plain matrix or array type to store a row/column/diagonal of a matrix type.
+ * \tparam Scalar optional parameter allowing to pass a different scalar type than the one of the MatrixType.
+ */
+template<typename ExpressionType, typename Scalar = typename ExpressionType::Scalar>
+struct plain_row_type
+{
+ typedef Matrix<Scalar, 1, ExpressionType::ColsAtCompileTime,
+ int(ExpressionType::PlainObject::Options) | int(RowMajor), 1, ExpressionType::MaxColsAtCompileTime> MatrixRowType;
+ typedef Array<Scalar, 1, ExpressionType::ColsAtCompileTime,
+ int(ExpressionType::PlainObject::Options) | int(RowMajor), 1, ExpressionType::MaxColsAtCompileTime> ArrayRowType;
+
+ typedef std::conditional_t<
+ is_same< typename traits<ExpressionType>::XprKind, MatrixXpr >::value,
+ MatrixRowType,
+ ArrayRowType
+ > type;
+};
+
+template<typename ExpressionType, typename Scalar = typename ExpressionType::Scalar>
+struct plain_col_type
+{
+ typedef Matrix<Scalar, ExpressionType::RowsAtCompileTime, 1,
+ ExpressionType::PlainObject::Options & ~RowMajor, ExpressionType::MaxRowsAtCompileTime, 1> MatrixColType;
+ typedef Array<Scalar, ExpressionType::RowsAtCompileTime, 1,
+ ExpressionType::PlainObject::Options & ~RowMajor, ExpressionType::MaxRowsAtCompileTime, 1> ArrayColType;
+
+ typedef std::conditional_t<
+ is_same< typename traits<ExpressionType>::XprKind, MatrixXpr >::value,
+ MatrixColType,
+ ArrayColType
+ > type;
+};
+
+template<typename ExpressionType, typename Scalar = typename ExpressionType::Scalar>
+struct plain_diag_type
+{
+ enum { diag_size = internal::min_size_prefer_dynamic(ExpressionType::RowsAtCompileTime, ExpressionType::ColsAtCompileTime),
+ max_diag_size = min_size_prefer_fixed(ExpressionType::MaxRowsAtCompileTime,
+ ExpressionType::MaxColsAtCompileTime)
+ };
+ typedef Matrix<Scalar, diag_size, 1, ExpressionType::PlainObject::Options & ~RowMajor, max_diag_size, 1> MatrixDiagType;
+ typedef Array<Scalar, diag_size, 1, ExpressionType::PlainObject::Options & ~RowMajor, max_diag_size, 1> ArrayDiagType;
+
+ typedef std::conditional_t<
+ is_same< typename traits<ExpressionType>::XprKind, MatrixXpr >::value,
+ MatrixDiagType,
+ ArrayDiagType
+ > type;
+};
+
+template<typename Expr,typename Scalar = typename Expr::Scalar>
+struct plain_constant_type
+{
+ enum { Options = (traits<Expr>::Flags&RowMajorBit)?RowMajor:0 };
+
+ typedef Array<Scalar, traits<Expr>::RowsAtCompileTime, traits<Expr>::ColsAtCompileTime,
+ Options, traits<Expr>::MaxRowsAtCompileTime,traits<Expr>::MaxColsAtCompileTime> array_type;
+
+ typedef Matrix<Scalar, traits<Expr>::RowsAtCompileTime, traits<Expr>::ColsAtCompileTime,
+ Options, traits<Expr>::MaxRowsAtCompileTime,traits<Expr>::MaxColsAtCompileTime> matrix_type;
+
+ typedef CwiseNullaryOp<scalar_constant_op<Scalar>, const std::conditional_t<is_same< typename traits<Expr>::XprKind, MatrixXpr >::value, matrix_type, array_type> > type;
+};
+
+template<typename ExpressionType>
+struct is_lvalue
+{
+ enum { value = (!bool(is_const<ExpressionType>::value)) &&
+ bool(traits<ExpressionType>::Flags & LvalueBit) };
+};
+
+template<typename T> struct is_diagonal
+{ enum { ret = false }; };
+
+template<typename T> struct is_diagonal<DiagonalBase<T> >
+{ enum { ret = true }; };
+
+template<typename T> struct is_diagonal<DiagonalWrapper<T> >
+{ enum { ret = true }; };
+
+template<typename T, int S> struct is_diagonal<DiagonalMatrix<T,S> >
+{ enum { ret = true }; };
+
+
+template<typename T> struct is_identity
+{ enum { value = false }; };
+
+template<typename T> struct is_identity<CwiseNullaryOp<internal::scalar_identity_op<typename T::Scalar>, T> >
+{ enum { value = true }; };
+
+
+template<typename S1, typename S2> struct glue_shapes;
+template<> struct glue_shapes<DenseShape,TriangularShape> { typedef TriangularShape type; };
+
+template<typename T1, typename T2>
+struct possibly_same_dense {
+ enum { value = has_direct_access<T1>::ret && has_direct_access<T2>::ret && is_same<typename T1::Scalar,typename T2::Scalar>::value };
+};
+
+template<typename T1, typename T2>
+EIGEN_DEVICE_FUNC
+bool is_same_dense(const T1 &mat1, const T2 &mat2, std::enable_if_t<possibly_same_dense<T1,T2>::value> * = 0)
+{
+ return (mat1.data()==mat2.data()) && (mat1.innerStride()==mat2.innerStride()) && (mat1.outerStride()==mat2.outerStride());
+}
+
+template<typename T1, typename T2>
+EIGEN_DEVICE_FUNC
+bool is_same_dense(const T1 &, const T2 &, std::enable_if_t<!possibly_same_dense<T1,T2>::value> * = 0)
+{
+ return false;
+}
+
+// Internal helper defining the cost of a scalar division for the type T.
+// The default heuristic can be specialized for each scalar type and architecture.
+template<typename T,bool Vectorized=false,typename EnableIf = void>
+struct scalar_div_cost {
+ enum { value = 8*NumTraits<T>::MulCost };
+};
+
+template<typename T,bool Vectorized>
+struct scalar_div_cost<std::complex<T>, Vectorized> {
+ enum { value = 2*scalar_div_cost<T>::value
+ + 6*NumTraits<T>::MulCost
+ + 3*NumTraits<T>::AddCost
+ };
+};
+
+
+template<bool Vectorized>
+struct scalar_div_cost<signed long,Vectorized, std::conditional_t<sizeof(long)==8,void,false_type>> { enum { value = 24 }; };
+template<bool Vectorized>
+struct scalar_div_cost<unsigned long,Vectorized, std::conditional_t<sizeof(long)==8,void,false_type>> { enum { value = 21 }; };
+
+
+#ifdef EIGEN_DEBUG_ASSIGN
+std::string demangle_traversal(int t)
+{
+ if(t==DefaultTraversal) return "DefaultTraversal";
+ if(t==LinearTraversal) return "LinearTraversal";
+ if(t==InnerVectorizedTraversal) return "InnerVectorizedTraversal";
+ if(t==LinearVectorizedTraversal) return "LinearVectorizedTraversal";
+ if(t==SliceVectorizedTraversal) return "SliceVectorizedTraversal";
+ return "?";
+}
+std::string demangle_unrolling(int t)
+{
+ if(t==NoUnrolling) return "NoUnrolling";
+ if(t==InnerUnrolling) return "InnerUnrolling";
+ if(t==CompleteUnrolling) return "CompleteUnrolling";
+ return "?";
+}
+std::string demangle_flags(int f)
+{
+ std::string res;
+ if(f&RowMajorBit) res += " | RowMajor";
+ if(f&PacketAccessBit) res += " | Packet";
+ if(f&LinearAccessBit) res += " | Linear";
+ if(f&LvalueBit) res += " | Lvalue";
+ if(f&DirectAccessBit) res += " | Direct";
+ if(f&NestByRefBit) res += " | NestByRef";
+ if(f&NoPreferredStorageOrderBit) res += " | NoPreferredStorageOrderBit";
+
+ return res;
+}
+#endif
+
+} // end namespace internal
+
+
+/** \class ScalarBinaryOpTraits
+ * \ingroup Core_Module
+ *
+ * \brief Determines whether the given binary operation of two numeric types is allowed and what the scalar return type is.
+ *
+ * This class permits to control the scalar return type of any binary operation performed on two different scalar types through (partial) template specializations.
+ *
+ * For instance, let \c U1, \c U2 and \c U3 be three user defined scalar types for which most operations between instances of \c U1 and \c U2 returns an \c U3.
+ * You can let %Eigen knows that by defining:
+ \code
+ template<typename BinaryOp>
+ struct ScalarBinaryOpTraits<U1,U2,BinaryOp> { typedef U3 ReturnType; };
+ template<typename BinaryOp>
+ struct ScalarBinaryOpTraits<U2,U1,BinaryOp> { typedef U3 ReturnType; };
+ \endcode
+ * You can then explicitly disable some particular operations to get more explicit error messages:
+ \code
+ template<>
+ struct ScalarBinaryOpTraits<U1,U2,internal::scalar_max_op<U1,U2> > {};
+ \endcode
+ * Or customize the return type for individual operation:
+ \code
+ template<>
+ struct ScalarBinaryOpTraits<U1,U2,internal::scalar_sum_op<U1,U2> > { typedef U1 ReturnType; };
+ \endcode
+ *
+ * By default, the following generic combinations are supported:
+ <table class="manual">
+ <tr><th>ScalarA</th><th>ScalarB</th><th>BinaryOp</th><th>ReturnType</th><th>Note</th></tr>
+ <tr ><td>\c T </td><td>\c T </td><td>\c * </td><td>\c T </td><td></td></tr>
+ <tr class="alt"><td>\c NumTraits<T>::Real </td><td>\c T </td><td>\c * </td><td>\c T </td><td>Only if \c NumTraits<T>::IsComplex </td></tr>
+ <tr ><td>\c T </td><td>\c NumTraits<T>::Real </td><td>\c * </td><td>\c T </td><td>Only if \c NumTraits<T>::IsComplex </td></tr>
+ </table>
+ *
+ * \sa CwiseBinaryOp
+ */
+template<typename ScalarA, typename ScalarB, typename BinaryOp=internal::scalar_product_op<ScalarA,ScalarB> >
+struct ScalarBinaryOpTraits
+#ifndef EIGEN_PARSED_BY_DOXYGEN
+ // for backward compatibility, use the hints given by the (deprecated) internal::scalar_product_traits class.
+ : internal::scalar_product_traits<ScalarA,ScalarB>
+#endif // EIGEN_PARSED_BY_DOXYGEN
+{};
+
+template<typename T, typename BinaryOp>
+struct ScalarBinaryOpTraits<T,T,BinaryOp>
+{
+ typedef T ReturnType;
+};
+
+template <typename T, typename BinaryOp>
+struct ScalarBinaryOpTraits<T, typename NumTraits<std::enable_if_t<NumTraits<T>::IsComplex,T>>::Real, BinaryOp>
+{
+ typedef T ReturnType;
+};
+template <typename T, typename BinaryOp>
+struct ScalarBinaryOpTraits<typename NumTraits<std::enable_if_t<NumTraits<T>::IsComplex,T>>::Real, T, BinaryOp>
+{
+ typedef T ReturnType;
+};
+
+// For Matrix * Permutation
+template<typename T, typename BinaryOp>
+struct ScalarBinaryOpTraits<T,void,BinaryOp>
+{
+ typedef T ReturnType;
+};
+
+// For Permutation * Matrix
+template<typename T, typename BinaryOp>
+struct ScalarBinaryOpTraits<void,T,BinaryOp>
+{
+ typedef T ReturnType;
+};
+
+// for Permutation*Permutation
+template<typename BinaryOp>
+struct ScalarBinaryOpTraits<void,void,BinaryOp>
+{
+ typedef void ReturnType;
+};
+
+// We require Lhs and Rhs to have "compatible" scalar types.
+// It is tempting to always allow mixing different types but remember that this is often impossible in the vectorized paths.
+// So allowing mixing different types gives very unexpected errors when enabling vectorization, when the user tries to
+// add together a float matrix and a double matrix.
+#define EIGEN_CHECK_BINARY_COMPATIBILIY(BINOP,LHS,RHS) \
+ EIGEN_STATIC_ASSERT((Eigen::internal::has_ReturnType<ScalarBinaryOpTraits<LHS, RHS,BINOP> >::value), \
+ YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY)
+
+} // end namespace Eigen
+
+#endif // EIGEN_XPRHELPER_H
diff --git a/Eigen/src/Eigenvalues/ComplexEigenSolver.h b/Eigen/src/Eigenvalues/ComplexEigenSolver.h
new file mode 100644
index 0000000..1cfc0ca
--- /dev/null
+++ b/Eigen/src/Eigenvalues/ComplexEigenSolver.h
@@ -0,0 +1,343 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009 Claire Maurice
+// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2010,2012 Jitse Niesen <jitse@maths.leeds.ac.uk>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_COMPLEX_EIGEN_SOLVER_H
+#define EIGEN_COMPLEX_EIGEN_SOLVER_H
+
+#include "./ComplexSchur.h"
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+/** \eigenvalues_module \ingroup Eigenvalues_Module
+ *
+ *
+ * \class ComplexEigenSolver
+ *
+ * \brief Computes eigenvalues and eigenvectors of general complex matrices
+ *
+ * \tparam MatrixType_ the type of the matrix of which we are
+ * computing the eigendecomposition; this is expected to be an
+ * instantiation of the Matrix class template.
+ *
+ * The eigenvalues and eigenvectors of a matrix \f$ A \f$ are scalars
+ * \f$ \lambda \f$ and vectors \f$ v \f$ such that \f$ Av = \lambda v
+ * \f$. If \f$ D \f$ is a diagonal matrix with the eigenvalues on
+ * the diagonal, and \f$ V \f$ is a matrix with the eigenvectors as
+ * its columns, then \f$ A V = V D \f$. The matrix \f$ V \f$ is
+ * almost always invertible, in which case we have \f$ A = V D V^{-1}
+ * \f$. This is called the eigendecomposition.
+ *
+ * The main function in this class is compute(), which computes the
+ * eigenvalues and eigenvectors of a given function. The
+ * documentation for that function contains an example showing the
+ * main features of the class.
+ *
+ * \sa class EigenSolver, class SelfAdjointEigenSolver
+ */
+template<typename MatrixType_> class ComplexEigenSolver
+{
+ public:
+
+ /** \brief Synonym for the template parameter \p MatrixType_. */
+ typedef MatrixType_ MatrixType;
+
+ enum {
+ RowsAtCompileTime = MatrixType::RowsAtCompileTime,
+ ColsAtCompileTime = MatrixType::ColsAtCompileTime,
+ Options = MatrixType::Options,
+ MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime,
+ MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime
+ };
+
+ /** \brief Scalar type for matrices of type #MatrixType. */
+ typedef typename MatrixType::Scalar Scalar;
+ typedef typename NumTraits<Scalar>::Real RealScalar;
+ typedef Eigen::Index Index; ///< \deprecated since Eigen 3.3
+
+ /** \brief Complex scalar type for #MatrixType.
+ *
+ * This is \c std::complex<Scalar> if #Scalar is real (e.g.,
+ * \c float or \c double) and just \c Scalar if #Scalar is
+ * complex.
+ */
+ typedef std::complex<RealScalar> ComplexScalar;
+
+ /** \brief Type for vector of eigenvalues as returned by eigenvalues().
+ *
+ * This is a column vector with entries of type #ComplexScalar.
+ * The length of the vector is the size of #MatrixType.
+ */
+ typedef Matrix<ComplexScalar, ColsAtCompileTime, 1, Options&(~RowMajor), MaxColsAtCompileTime, 1> EigenvalueType;
+
+ /** \brief Type for matrix of eigenvectors as returned by eigenvectors().
+ *
+ * This is a square matrix with entries of type #ComplexScalar.
+ * The size is the same as the size of #MatrixType.
+ */
+ typedef Matrix<ComplexScalar, RowsAtCompileTime, ColsAtCompileTime, Options, MaxRowsAtCompileTime, MaxColsAtCompileTime> EigenvectorType;
+
+ /** \brief Default constructor.
+ *
+ * The default constructor is useful in cases in which the user intends to
+ * perform decompositions via compute().
+ */
+ ComplexEigenSolver()
+ : m_eivec(),
+ m_eivalues(),
+ m_schur(),
+ m_isInitialized(false),
+ m_eigenvectorsOk(false),
+ m_matX()
+ {}
+
+ /** \brief Default Constructor with memory preallocation
+ *
+ * Like the default constructor but with preallocation of the internal data
+ * according to the specified problem \a size.
+ * \sa ComplexEigenSolver()
+ */
+ explicit ComplexEigenSolver(Index size)
+ : m_eivec(size, size),
+ m_eivalues(size),
+ m_schur(size),
+ m_isInitialized(false),
+ m_eigenvectorsOk(false),
+ m_matX(size, size)
+ {}
+
+ /** \brief Constructor; computes eigendecomposition of given matrix.
+ *
+ * \param[in] matrix Square matrix whose eigendecomposition is to be computed.
+ * \param[in] computeEigenvectors If true, both the eigenvectors and the
+ * eigenvalues are computed; if false, only the eigenvalues are
+ * computed.
+ *
+ * This constructor calls compute() to compute the eigendecomposition.
+ */
+ template<typename InputType>
+ explicit ComplexEigenSolver(const EigenBase<InputType>& matrix, bool computeEigenvectors = true)
+ : m_eivec(matrix.rows(),matrix.cols()),
+ m_eivalues(matrix.cols()),
+ m_schur(matrix.rows()),
+ m_isInitialized(false),
+ m_eigenvectorsOk(false),
+ m_matX(matrix.rows(),matrix.cols())
+ {
+ compute(matrix.derived(), computeEigenvectors);
+ }
+
+ /** \brief Returns the eigenvectors of given matrix.
+ *
+ * \returns A const reference to the matrix whose columns are the eigenvectors.
+ *
+ * \pre Either the constructor
+ * ComplexEigenSolver(const MatrixType& matrix, bool) or the member
+ * function compute(const MatrixType& matrix, bool) has been called before
+ * to compute the eigendecomposition of a matrix, and
+ * \p computeEigenvectors was set to true (the default).
+ *
+ * This function returns a matrix whose columns are the eigenvectors. Column
+ * \f$ k \f$ is an eigenvector corresponding to eigenvalue number \f$ k
+ * \f$ as returned by eigenvalues(). The eigenvectors are normalized to
+ * have (Euclidean) norm equal to one. The matrix returned by this
+ * function is the matrix \f$ V \f$ in the eigendecomposition \f$ A = V D
+ * V^{-1} \f$, if it exists.
+ *
+ * Example: \include ComplexEigenSolver_eigenvectors.cpp
+ * Output: \verbinclude ComplexEigenSolver_eigenvectors.out
+ */
+ const EigenvectorType& eigenvectors() const
+ {
+ eigen_assert(m_isInitialized && "ComplexEigenSolver is not initialized.");
+ eigen_assert(m_eigenvectorsOk && "The eigenvectors have not been computed together with the eigenvalues.");
+ return m_eivec;
+ }
+
+ /** \brief Returns the eigenvalues of given matrix.
+ *
+ * \returns A const reference to the column vector containing the eigenvalues.
+ *
+ * \pre Either the constructor
+ * ComplexEigenSolver(const MatrixType& matrix, bool) or the member
+ * function compute(const MatrixType& matrix, bool) has been called before
+ * to compute the eigendecomposition of a matrix.
+ *
+ * This function returns a column vector containing the
+ * eigenvalues. Eigenvalues are repeated according to their
+ * algebraic multiplicity, so there are as many eigenvalues as
+ * rows in the matrix. The eigenvalues are not sorted in any particular
+ * order.
+ *
+ * Example: \include ComplexEigenSolver_eigenvalues.cpp
+ * Output: \verbinclude ComplexEigenSolver_eigenvalues.out
+ */
+ const EigenvalueType& eigenvalues() const
+ {
+ eigen_assert(m_isInitialized && "ComplexEigenSolver is not initialized.");
+ return m_eivalues;
+ }
+
+ /** \brief Computes eigendecomposition of given matrix.
+ *
+ * \param[in] matrix Square matrix whose eigendecomposition is to be computed.
+ * \param[in] computeEigenvectors If true, both the eigenvectors and the
+ * eigenvalues are computed; if false, only the eigenvalues are
+ * computed.
+ * \returns Reference to \c *this
+ *
+ * This function computes the eigenvalues of the complex matrix \p matrix.
+ * The eigenvalues() function can be used to retrieve them. If
+ * \p computeEigenvectors is true, then the eigenvectors are also computed
+ * and can be retrieved by calling eigenvectors().
+ *
+ * The matrix is first reduced to Schur form using the
+ * ComplexSchur class. The Schur decomposition is then used to
+ * compute the eigenvalues and eigenvectors.
+ *
+ * The cost of the computation is dominated by the cost of the
+ * Schur decomposition, which is \f$ O(n^3) \f$ where \f$ n \f$
+ * is the size of the matrix.
+ *
+ * Example: \include ComplexEigenSolver_compute.cpp
+ * Output: \verbinclude ComplexEigenSolver_compute.out
+ */
+ template<typename InputType>
+ ComplexEigenSolver& compute(const EigenBase<InputType>& matrix, bool computeEigenvectors = true);
+
+ /** \brief Reports whether previous computation was successful.
+ *
+ * \returns \c Success if computation was successful, \c NoConvergence otherwise.
+ */
+ ComputationInfo info() const
+ {
+ eigen_assert(m_isInitialized && "ComplexEigenSolver is not initialized.");
+ return m_schur.info();
+ }
+
+ /** \brief Sets the maximum number of iterations allowed. */
+ ComplexEigenSolver& setMaxIterations(Index maxIters)
+ {
+ m_schur.setMaxIterations(maxIters);
+ return *this;
+ }
+
+ /** \brief Returns the maximum number of iterations. */
+ Index getMaxIterations()
+ {
+ return m_schur.getMaxIterations();
+ }
+
+ protected:
+
+ EIGEN_STATIC_ASSERT_NON_INTEGER(Scalar)
+
+ EigenvectorType m_eivec;
+ EigenvalueType m_eivalues;
+ ComplexSchur<MatrixType> m_schur;
+ bool m_isInitialized;
+ bool m_eigenvectorsOk;
+ EigenvectorType m_matX;
+
+ private:
+ void doComputeEigenvectors(RealScalar matrixnorm);
+ void sortEigenvalues(bool computeEigenvectors);
+};
+
+
+template<typename MatrixType>
+template<typename InputType>
+ComplexEigenSolver<MatrixType>&
+ComplexEigenSolver<MatrixType>::compute(const EigenBase<InputType>& matrix, bool computeEigenvectors)
+{
+ // this code is inspired from Jampack
+ eigen_assert(matrix.cols() == matrix.rows());
+
+ // Do a complex Schur decomposition, A = U T U^*
+ // The eigenvalues are on the diagonal of T.
+ m_schur.compute(matrix.derived(), computeEigenvectors);
+
+ if(m_schur.info() == Success)
+ {
+ m_eivalues = m_schur.matrixT().diagonal();
+ if(computeEigenvectors)
+ doComputeEigenvectors(m_schur.matrixT().norm());
+ sortEigenvalues(computeEigenvectors);
+ }
+
+ m_isInitialized = true;
+ m_eigenvectorsOk = computeEigenvectors;
+ return *this;
+}
+
+
+template<typename MatrixType>
+void ComplexEigenSolver<MatrixType>::doComputeEigenvectors(RealScalar matrixnorm)
+{
+ const Index n = m_eivalues.size();
+
+ matrixnorm = numext::maxi(matrixnorm,(std::numeric_limits<RealScalar>::min)());
+
+ // Compute X such that T = X D X^(-1), where D is the diagonal of T.
+ // The matrix X is unit triangular.
+ m_matX = EigenvectorType::Zero(n, n);
+ for(Index k=n-1 ; k>=0 ; k--)
+ {
+ m_matX.coeffRef(k,k) = ComplexScalar(1.0,0.0);
+ // Compute X(i,k) using the (i,k) entry of the equation X T = D X
+ for(Index i=k-1 ; i>=0 ; i--)
+ {
+ m_matX.coeffRef(i,k) = -m_schur.matrixT().coeff(i,k);
+ if(k-i-1>0)
+ m_matX.coeffRef(i,k) -= (m_schur.matrixT().row(i).segment(i+1,k-i-1) * m_matX.col(k).segment(i+1,k-i-1)).value();
+ ComplexScalar z = m_schur.matrixT().coeff(i,i) - m_schur.matrixT().coeff(k,k);
+ if(z==ComplexScalar(0))
+ {
+ // If the i-th and k-th eigenvalue are equal, then z equals 0.
+ // Use a small value instead, to prevent division by zero.
+ numext::real_ref(z) = NumTraits<RealScalar>::epsilon() * matrixnorm;
+ }
+ m_matX.coeffRef(i,k) = m_matX.coeff(i,k) / z;
+ }
+ }
+
+ // Compute V as V = U X; now A = U T U^* = U X D X^(-1) U^* = V D V^(-1)
+ m_eivec.noalias() = m_schur.matrixU() * m_matX;
+ // .. and normalize the eigenvectors
+ for(Index k=0 ; k<n ; k++)
+ {
+ m_eivec.col(k).normalize();
+ }
+}
+
+
+template<typename MatrixType>
+void ComplexEigenSolver<MatrixType>::sortEigenvalues(bool computeEigenvectors)
+{
+ const Index n = m_eivalues.size();
+ for (Index i=0; i<n; i++)
+ {
+ Index k;
+ m_eivalues.cwiseAbs().tail(n-i).minCoeff(&k);
+ if (k != 0)
+ {
+ k += i;
+ std::swap(m_eivalues[k],m_eivalues[i]);
+ if(computeEigenvectors)
+ m_eivec.col(i).swap(m_eivec.col(k));
+ }
+ }
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_COMPLEX_EIGEN_SOLVER_H
diff --git a/Eigen/src/Eigenvalues/ComplexSchur.h b/Eigen/src/Eigenvalues/ComplexSchur.h
new file mode 100644
index 0000000..80a28fb
--- /dev/null
+++ b/Eigen/src/Eigenvalues/ComplexSchur.h
@@ -0,0 +1,464 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009 Claire Maurice
+// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2010,2012 Jitse Niesen <jitse@maths.leeds.ac.uk>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_COMPLEX_SCHUR_H
+#define EIGEN_COMPLEX_SCHUR_H
+
+#include "./HessenbergDecomposition.h"
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+template<typename MatrixType, bool IsComplex> struct complex_schur_reduce_to_hessenberg;
+}
+
+/** \eigenvalues_module \ingroup Eigenvalues_Module
+ *
+ *
+ * \class ComplexSchur
+ *
+ * \brief Performs a complex Schur decomposition of a real or complex square matrix
+ *
+ * \tparam MatrixType_ the type of the matrix of which we are
+ * computing the Schur decomposition; this is expected to be an
+ * instantiation of the Matrix class template.
+ *
+ * Given a real or complex square matrix A, this class computes the
+ * Schur decomposition: \f$ A = U T U^*\f$ where U is a unitary
+ * complex matrix, and T is a complex upper triangular matrix. The
+ * diagonal of the matrix T corresponds to the eigenvalues of the
+ * matrix A.
+ *
+ * Call the function compute() to compute the Schur decomposition of
+ * a given matrix. Alternatively, you can use the
+ * ComplexSchur(const MatrixType&, bool) constructor which computes
+ * the Schur decomposition at construction time. Once the
+ * decomposition is computed, you can use the matrixU() and matrixT()
+ * functions to retrieve the matrices U and V in the decomposition.
+ *
+ * \note This code is inspired from Jampack
+ *
+ * \sa class RealSchur, class EigenSolver, class ComplexEigenSolver
+ */
+template<typename MatrixType_> class ComplexSchur
+{
+ public:
+ typedef MatrixType_ MatrixType;
+ enum {
+ RowsAtCompileTime = MatrixType::RowsAtCompileTime,
+ ColsAtCompileTime = MatrixType::ColsAtCompileTime,
+ Options = MatrixType::Options,
+ MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime,
+ MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime
+ };
+
+ /** \brief Scalar type for matrices of type \p MatrixType_. */
+ typedef typename MatrixType::Scalar Scalar;
+ typedef typename NumTraits<Scalar>::Real RealScalar;
+ typedef Eigen::Index Index; ///< \deprecated since Eigen 3.3
+
+ /** \brief Complex scalar type for \p MatrixType_.
+ *
+ * This is \c std::complex<Scalar> if #Scalar is real (e.g.,
+ * \c float or \c double) and just \c Scalar if #Scalar is
+ * complex.
+ */
+ typedef std::complex<RealScalar> ComplexScalar;
+
+ /** \brief Type for the matrices in the Schur decomposition.
+ *
+ * This is a square matrix with entries of type #ComplexScalar.
+ * The size is the same as the size of \p MatrixType_.
+ */
+ typedef Matrix<ComplexScalar, RowsAtCompileTime, ColsAtCompileTime, Options, MaxRowsAtCompileTime, MaxColsAtCompileTime> ComplexMatrixType;
+
+ /** \brief Default constructor.
+ *
+ * \param [in] size Positive integer, size of the matrix whose Schur decomposition will be computed.
+ *
+ * The default constructor is useful in cases in which the user
+ * intends to perform decompositions via compute(). The \p size
+ * parameter is only used as a hint. It is not an error to give a
+ * wrong \p size, but it may impair performance.
+ *
+ * \sa compute() for an example.
+ */
+ explicit ComplexSchur(Index size = RowsAtCompileTime==Dynamic ? 1 : RowsAtCompileTime)
+ : m_matT(size,size),
+ m_matU(size,size),
+ m_hess(size),
+ m_isInitialized(false),
+ m_matUisUptodate(false),
+ m_maxIters(-1)
+ {}
+
+ /** \brief Constructor; computes Schur decomposition of given matrix.
+ *
+ * \param[in] matrix Square matrix whose Schur decomposition is to be computed.
+ * \param[in] computeU If true, both T and U are computed; if false, only T is computed.
+ *
+ * This constructor calls compute() to compute the Schur decomposition.
+ *
+ * \sa matrixT() and matrixU() for examples.
+ */
+ template<typename InputType>
+ explicit ComplexSchur(const EigenBase<InputType>& matrix, bool computeU = true)
+ : m_matT(matrix.rows(),matrix.cols()),
+ m_matU(matrix.rows(),matrix.cols()),
+ m_hess(matrix.rows()),
+ m_isInitialized(false),
+ m_matUisUptodate(false),
+ m_maxIters(-1)
+ {
+ compute(matrix.derived(), computeU);
+ }
+
+ /** \brief Returns the unitary matrix in the Schur decomposition.
+ *
+ * \returns A const reference to the matrix U.
+ *
+ * It is assumed that either the constructor
+ * ComplexSchur(const MatrixType& matrix, bool computeU) or the
+ * member function compute(const MatrixType& matrix, bool computeU)
+ * has been called before to compute the Schur decomposition of a
+ * matrix, and that \p computeU was set to true (the default
+ * value).
+ *
+ * Example: \include ComplexSchur_matrixU.cpp
+ * Output: \verbinclude ComplexSchur_matrixU.out
+ */
+ const ComplexMatrixType& matrixU() const
+ {
+ eigen_assert(m_isInitialized && "ComplexSchur is not initialized.");
+ eigen_assert(m_matUisUptodate && "The matrix U has not been computed during the ComplexSchur decomposition.");
+ return m_matU;
+ }
+
+ /** \brief Returns the triangular matrix in the Schur decomposition.
+ *
+ * \returns A const reference to the matrix T.
+ *
+ * It is assumed that either the constructor
+ * ComplexSchur(const MatrixType& matrix, bool computeU) or the
+ * member function compute(const MatrixType& matrix, bool computeU)
+ * has been called before to compute the Schur decomposition of a
+ * matrix.
+ *
+ * Note that this function returns a plain square matrix. If you want to reference
+ * only the upper triangular part, use:
+ * \code schur.matrixT().triangularView<Upper>() \endcode
+ *
+ * Example: \include ComplexSchur_matrixT.cpp
+ * Output: \verbinclude ComplexSchur_matrixT.out
+ */
+ const ComplexMatrixType& matrixT() const
+ {
+ eigen_assert(m_isInitialized && "ComplexSchur is not initialized.");
+ return m_matT;
+ }
+
+ /** \brief Computes Schur decomposition of given matrix.
+ *
+ * \param[in] matrix Square matrix whose Schur decomposition is to be computed.
+ * \param[in] computeU If true, both T and U are computed; if false, only T is computed.
+
+ * \returns Reference to \c *this
+ *
+ * The Schur decomposition is computed by first reducing the
+ * matrix to Hessenberg form using the class
+ * HessenbergDecomposition. The Hessenberg matrix is then reduced
+ * to triangular form by performing QR iterations with a single
+ * shift. The cost of computing the Schur decomposition depends
+ * on the number of iterations; as a rough guide, it may be taken
+ * on the number of iterations; as a rough guide, it may be taken
+ * to be \f$25n^3\f$ complex flops, or \f$10n^3\f$ complex flops
+ * if \a computeU is false.
+ *
+ * Example: \include ComplexSchur_compute.cpp
+ * Output: \verbinclude ComplexSchur_compute.out
+ *
+ * \sa compute(const MatrixType&, bool, Index)
+ */
+ template<typename InputType>
+ ComplexSchur& compute(const EigenBase<InputType>& matrix, bool computeU = true);
+
+ /** \brief Compute Schur decomposition from a given Hessenberg matrix
+ * \param[in] matrixH Matrix in Hessenberg form H
+ * \param[in] matrixQ orthogonal matrix Q that transform a matrix A to H : A = Q H Q^T
+ * \param computeU Computes the matriX U of the Schur vectors
+ * \return Reference to \c *this
+ *
+ * This routine assumes that the matrix is already reduced in Hessenberg form matrixH
+ * using either the class HessenbergDecomposition or another mean.
+ * It computes the upper quasi-triangular matrix T of the Schur decomposition of H
+ * When computeU is true, this routine computes the matrix U such that
+ * A = U T U^T = (QZ) T (QZ)^T = Q H Q^T where A is the initial matrix
+ *
+ * NOTE Q is referenced if computeU is true; so, if the initial orthogonal matrix
+ * is not available, the user should give an identity matrix (Q.setIdentity())
+ *
+ * \sa compute(const MatrixType&, bool)
+ */
+ template<typename HessMatrixType, typename OrthMatrixType>
+ ComplexSchur& computeFromHessenberg(const HessMatrixType& matrixH, const OrthMatrixType& matrixQ, bool computeU=true);
+
+ /** \brief Reports whether previous computation was successful.
+ *
+ * \returns \c Success if computation was successful, \c NoConvergence otherwise.
+ */
+ ComputationInfo info() const
+ {
+ eigen_assert(m_isInitialized && "ComplexSchur is not initialized.");
+ return m_info;
+ }
+
+ /** \brief Sets the maximum number of iterations allowed.
+ *
+ * If not specified by the user, the maximum number of iterations is m_maxIterationsPerRow times the size
+ * of the matrix.
+ */
+ ComplexSchur& setMaxIterations(Index maxIters)
+ {
+ m_maxIters = maxIters;
+ return *this;
+ }
+
+ /** \brief Returns the maximum number of iterations. */
+ Index getMaxIterations()
+ {
+ return m_maxIters;
+ }
+
+ /** \brief Maximum number of iterations per row.
+ *
+ * If not otherwise specified, the maximum number of iterations is this number times the size of the
+ * matrix. It is currently set to 30.
+ */
+ static const int m_maxIterationsPerRow = 30;
+
+ protected:
+ ComplexMatrixType m_matT, m_matU;
+ HessenbergDecomposition<MatrixType> m_hess;
+ ComputationInfo m_info;
+ bool m_isInitialized;
+ bool m_matUisUptodate;
+ Index m_maxIters;
+
+ private:
+ bool subdiagonalEntryIsNeglegible(Index i);
+ ComplexScalar computeShift(Index iu, Index iter);
+ void reduceToTriangularForm(bool computeU);
+ friend struct internal::complex_schur_reduce_to_hessenberg<MatrixType, NumTraits<Scalar>::IsComplex>;
+};
+
+/** If m_matT(i+1,i) is negligible in floating point arithmetic
+ * compared to m_matT(i,i) and m_matT(j,j), then set it to zero and
+ * return true, else return false. */
+template<typename MatrixType>
+inline bool ComplexSchur<MatrixType>::subdiagonalEntryIsNeglegible(Index i)
+{
+ RealScalar d = numext::norm1(m_matT.coeff(i,i)) + numext::norm1(m_matT.coeff(i+1,i+1));
+ RealScalar sd = numext::norm1(m_matT.coeff(i+1,i));
+ if (internal::isMuchSmallerThan(sd, d, NumTraits<RealScalar>::epsilon()))
+ {
+ m_matT.coeffRef(i+1,i) = ComplexScalar(0);
+ return true;
+ }
+ return false;
+}
+
+
+/** Compute the shift in the current QR iteration. */
+template<typename MatrixType>
+typename ComplexSchur<MatrixType>::ComplexScalar ComplexSchur<MatrixType>::computeShift(Index iu, Index iter)
+{
+ using std::abs;
+ if (iter == 10 || iter == 20)
+ {
+ // exceptional shift, taken from http://www.netlib.org/eispack/comqr.f
+ return abs(numext::real(m_matT.coeff(iu,iu-1))) + abs(numext::real(m_matT.coeff(iu-1,iu-2)));
+ }
+
+ // compute the shift as one of the eigenvalues of t, the 2x2
+ // diagonal block on the bottom of the active submatrix
+ Matrix<ComplexScalar,2,2> t = m_matT.template block<2,2>(iu-1,iu-1);
+ RealScalar normt = t.cwiseAbs().sum();
+ t /= normt; // the normalization by sf is to avoid under/overflow
+
+ ComplexScalar b = t.coeff(0,1) * t.coeff(1,0);
+ ComplexScalar c = t.coeff(0,0) - t.coeff(1,1);
+ ComplexScalar disc = sqrt(c*c + RealScalar(4)*b);
+ ComplexScalar det = t.coeff(0,0) * t.coeff(1,1) - b;
+ ComplexScalar trace = t.coeff(0,0) + t.coeff(1,1);
+ ComplexScalar eival1 = (trace + disc) / RealScalar(2);
+ ComplexScalar eival2 = (trace - disc) / RealScalar(2);
+ RealScalar eival1_norm = numext::norm1(eival1);
+ RealScalar eival2_norm = numext::norm1(eival2);
+ // A division by zero can only occur if eival1==eival2==0.
+ // In this case, det==0, and all we have to do is checking that eival2_norm!=0
+ if(eival1_norm > eival2_norm)
+ eival2 = det / eival1;
+ else if(!numext::is_exactly_zero(eival2_norm))
+ eival1 = det / eival2;
+
+ // choose the eigenvalue closest to the bottom entry of the diagonal
+ if(numext::norm1(eival1-t.coeff(1,1)) < numext::norm1(eival2-t.coeff(1,1)))
+ return normt * eival1;
+ else
+ return normt * eival2;
+}
+
+
+template<typename MatrixType>
+template<typename InputType>
+ComplexSchur<MatrixType>& ComplexSchur<MatrixType>::compute(const EigenBase<InputType>& matrix, bool computeU)
+{
+ m_matUisUptodate = false;
+ eigen_assert(matrix.cols() == matrix.rows());
+
+ if(matrix.cols() == 1)
+ {
+ m_matT = matrix.derived().template cast<ComplexScalar>();
+ if(computeU) m_matU = ComplexMatrixType::Identity(1,1);
+ m_info = Success;
+ m_isInitialized = true;
+ m_matUisUptodate = computeU;
+ return *this;
+ }
+
+ internal::complex_schur_reduce_to_hessenberg<MatrixType, NumTraits<Scalar>::IsComplex>::run(*this, matrix.derived(), computeU);
+ computeFromHessenberg(m_matT, m_matU, computeU);
+ return *this;
+}
+
+template<typename MatrixType>
+template<typename HessMatrixType, typename OrthMatrixType>
+ComplexSchur<MatrixType>& ComplexSchur<MatrixType>::computeFromHessenberg(const HessMatrixType& matrixH, const OrthMatrixType& matrixQ, bool computeU)
+{
+ m_matT = matrixH;
+ if(computeU)
+ m_matU = matrixQ;
+ reduceToTriangularForm(computeU);
+ return *this;
+}
+namespace internal {
+
+/* Reduce given matrix to Hessenberg form */
+template<typename MatrixType, bool IsComplex>
+struct complex_schur_reduce_to_hessenberg
+{
+ // this is the implementation for the case IsComplex = true
+ static void run(ComplexSchur<MatrixType>& _this, const MatrixType& matrix, bool computeU)
+ {
+ _this.m_hess.compute(matrix);
+ _this.m_matT = _this.m_hess.matrixH();
+ if(computeU) _this.m_matU = _this.m_hess.matrixQ();
+ }
+};
+
+template<typename MatrixType>
+struct complex_schur_reduce_to_hessenberg<MatrixType, false>
+{
+ static void run(ComplexSchur<MatrixType>& _this, const MatrixType& matrix, bool computeU)
+ {
+ typedef typename ComplexSchur<MatrixType>::ComplexScalar ComplexScalar;
+
+ // Note: m_hess is over RealScalar; m_matT and m_matU is over ComplexScalar
+ _this.m_hess.compute(matrix);
+ _this.m_matT = _this.m_hess.matrixH().template cast<ComplexScalar>();
+ if(computeU)
+ {
+ // This may cause an allocation which seems to be avoidable
+ MatrixType Q = _this.m_hess.matrixQ();
+ _this.m_matU = Q.template cast<ComplexScalar>();
+ }
+ }
+};
+
+} // end namespace internal
+
+// Reduce the Hessenberg matrix m_matT to triangular form by QR iteration.
+template<typename MatrixType>
+void ComplexSchur<MatrixType>::reduceToTriangularForm(bool computeU)
+{
+ Index maxIters = m_maxIters;
+ if (maxIters == -1)
+ maxIters = m_maxIterationsPerRow * m_matT.rows();
+
+ // The matrix m_matT is divided in three parts.
+ // Rows 0,...,il-1 are decoupled from the rest because m_matT(il,il-1) is zero.
+ // Rows il,...,iu is the part we are working on (the active submatrix).
+ // Rows iu+1,...,end are already brought in triangular form.
+ Index iu = m_matT.cols() - 1;
+ Index il;
+ Index iter = 0; // number of iterations we are working on the (iu,iu) element
+ Index totalIter = 0; // number of iterations for whole matrix
+
+ while(true)
+ {
+ // find iu, the bottom row of the active submatrix
+ while(iu > 0)
+ {
+ if(!subdiagonalEntryIsNeglegible(iu-1)) break;
+ iter = 0;
+ --iu;
+ }
+
+ // if iu is zero then we are done; the whole matrix is triangularized
+ if(iu==0) break;
+
+ // if we spent too many iterations, we give up
+ iter++;
+ totalIter++;
+ if(totalIter > maxIters) break;
+
+ // find il, the top row of the active submatrix
+ il = iu-1;
+ while(il > 0 && !subdiagonalEntryIsNeglegible(il-1))
+ {
+ --il;
+ }
+
+ /* perform the QR step using Givens rotations. The first rotation
+ creates a bulge; the (il+2,il) element becomes nonzero. This
+ bulge is chased down to the bottom of the active submatrix. */
+
+ ComplexScalar shift = computeShift(iu, iter);
+ JacobiRotation<ComplexScalar> rot;
+ rot.makeGivens(m_matT.coeff(il,il) - shift, m_matT.coeff(il+1,il));
+ m_matT.rightCols(m_matT.cols()-il).applyOnTheLeft(il, il+1, rot.adjoint());
+ m_matT.topRows((std::min)(il+2,iu)+1).applyOnTheRight(il, il+1, rot);
+ if(computeU) m_matU.applyOnTheRight(il, il+1, rot);
+
+ for(Index i=il+1 ; i<iu ; i++)
+ {
+ rot.makeGivens(m_matT.coeffRef(i,i-1), m_matT.coeffRef(i+1,i-1), &m_matT.coeffRef(i,i-1));
+ m_matT.coeffRef(i+1,i-1) = ComplexScalar(0);
+ m_matT.rightCols(m_matT.cols()-i).applyOnTheLeft(i, i+1, rot.adjoint());
+ m_matT.topRows((std::min)(i+2,iu)+1).applyOnTheRight(i, i+1, rot);
+ if(computeU) m_matU.applyOnTheRight(i, i+1, rot);
+ }
+ }
+
+ if(totalIter <= maxIters)
+ m_info = Success;
+ else
+ m_info = NoConvergence;
+
+ m_isInitialized = true;
+ m_matUisUptodate = computeU;
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_COMPLEX_SCHUR_H
diff --git a/Eigen/src/Eigenvalues/ComplexSchur_LAPACKE.h b/Eigen/src/Eigenvalues/ComplexSchur_LAPACKE.h
new file mode 100644
index 0000000..144eb2a
--- /dev/null
+++ b/Eigen/src/Eigenvalues/ComplexSchur_LAPACKE.h
@@ -0,0 +1,93 @@
+/*
+ Copyright (c) 2011, Intel Corporation. All rights reserved.
+
+ Redistribution and use in source and binary forms, with or without modification,
+ are permitted provided that the following conditions are met:
+
+ * Redistributions of source code must retain the above copyright notice, this
+ list of conditions and the following disclaimer.
+ * Redistributions in binary form must reproduce the above copyright notice,
+ this list of conditions and the following disclaimer in the documentation
+ and/or other materials provided with the distribution.
+ * Neither the name of Intel Corporation nor the names of its contributors may
+ be used to endorse or promote products derived from this software without
+ specific prior written permission.
+
+ THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
+ ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
+ WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
+ DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR
+ ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
+ (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
+ LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON
+ ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
+ (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
+ SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+
+ ********************************************************************************
+ * Content : Eigen bindings to LAPACKe
+ * Complex Schur needed to complex unsymmetrical eigenvalues/eigenvectors.
+ ********************************************************************************
+*/
+
+#ifndef EIGEN_COMPLEX_SCHUR_LAPACKE_H
+#define EIGEN_COMPLEX_SCHUR_LAPACKE_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+/** \internal Specialization for the data types supported by LAPACKe */
+
+#define EIGEN_LAPACKE_SCHUR_COMPLEX(EIGTYPE, LAPACKE_TYPE, LAPACKE_PREFIX, LAPACKE_PREFIX_U, EIGCOLROW, LAPACKE_COLROW) \
+template<> template<typename InputType> inline \
+ComplexSchur<Matrix<EIGTYPE, Dynamic, Dynamic, EIGCOLROW> >& \
+ComplexSchur<Matrix<EIGTYPE, Dynamic, Dynamic, EIGCOLROW> >::compute(const EigenBase<InputType>& matrix, bool computeU) \
+{ \
+ typedef Matrix<EIGTYPE, Dynamic, Dynamic, EIGCOLROW> MatrixType; \
+ typedef MatrixType::RealScalar RealScalar; \
+ typedef std::complex<RealScalar> ComplexScalar; \
+\
+ eigen_assert(matrix.cols() == matrix.rows()); \
+\
+ m_matUisUptodate = false; \
+ if(matrix.cols() == 1) \
+ { \
+ m_matT = matrix.derived().template cast<ComplexScalar>(); \
+ if(computeU) m_matU = ComplexMatrixType::Identity(1,1); \
+ m_info = Success; \
+ m_isInitialized = true; \
+ m_matUisUptodate = computeU; \
+ return *this; \
+ } \
+ lapack_int n = internal::convert_index<lapack_int>(matrix.cols()), sdim, info; \
+ lapack_int matrix_order = LAPACKE_COLROW; \
+ char jobvs, sort='N'; \
+ LAPACK_##LAPACKE_PREFIX_U##_SELECT1 select = 0; \
+ jobvs = (computeU) ? 'V' : 'N'; \
+ m_matU.resize(n, n); \
+ lapack_int ldvs = internal::convert_index<lapack_int>(m_matU.outerStride()); \
+ m_matT = matrix; \
+ lapack_int lda = internal::convert_index<lapack_int>(m_matT.outerStride()); \
+ Matrix<EIGTYPE, Dynamic, Dynamic> w; \
+ w.resize(n, 1);\
+ info = LAPACKE_##LAPACKE_PREFIX##gees( matrix_order, jobvs, sort, select, n, (LAPACKE_TYPE*)m_matT.data(), lda, &sdim, (LAPACKE_TYPE*)w.data(), (LAPACKE_TYPE*)m_matU.data(), ldvs ); \
+ if(info == 0) \
+ m_info = Success; \
+ else \
+ m_info = NoConvergence; \
+\
+ m_isInitialized = true; \
+ m_matUisUptodate = computeU; \
+ return *this; \
+\
+}
+
+EIGEN_LAPACKE_SCHUR_COMPLEX(dcomplex, lapack_complex_double, z, Z, ColMajor, LAPACK_COL_MAJOR)
+EIGEN_LAPACKE_SCHUR_COMPLEX(scomplex, lapack_complex_float, c, C, ColMajor, LAPACK_COL_MAJOR)
+EIGEN_LAPACKE_SCHUR_COMPLEX(dcomplex, lapack_complex_double, z, Z, RowMajor, LAPACK_ROW_MAJOR)
+EIGEN_LAPACKE_SCHUR_COMPLEX(scomplex, lapack_complex_float, c, C, RowMajor, LAPACK_ROW_MAJOR)
+
+} // end namespace Eigen
+
+#endif // EIGEN_COMPLEX_SCHUR_LAPACKE_H
diff --git a/Eigen/src/Eigenvalues/EigenSolver.h b/Eigen/src/Eigenvalues/EigenSolver.h
new file mode 100644
index 0000000..f6ff140
--- /dev/null
+++ b/Eigen/src/Eigenvalues/EigenSolver.h
@@ -0,0 +1,624 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2010,2012 Jitse Niesen <jitse@maths.leeds.ac.uk>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_EIGENSOLVER_H
+#define EIGEN_EIGENSOLVER_H
+
+#include "./RealSchur.h"
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+/** \eigenvalues_module \ingroup Eigenvalues_Module
+ *
+ *
+ * \class EigenSolver
+ *
+ * \brief Computes eigenvalues and eigenvectors of general matrices
+ *
+ * \tparam MatrixType_ the type of the matrix of which we are computing the
+ * eigendecomposition; this is expected to be an instantiation of the Matrix
+ * class template. Currently, only real matrices are supported.
+ *
+ * The eigenvalues and eigenvectors of a matrix \f$ A \f$ are scalars
+ * \f$ \lambda \f$ and vectors \f$ v \f$ such that \f$ Av = \lambda v \f$. If
+ * \f$ D \f$ is a diagonal matrix with the eigenvalues on the diagonal, and
+ * \f$ V \f$ is a matrix with the eigenvectors as its columns, then \f$ A V =
+ * V D \f$. The matrix \f$ V \f$ is almost always invertible, in which case we
+ * have \f$ A = V D V^{-1} \f$. This is called the eigendecomposition.
+ *
+ * The eigenvalues and eigenvectors of a matrix may be complex, even when the
+ * matrix is real. However, we can choose real matrices \f$ V \f$ and \f$ D
+ * \f$ satisfying \f$ A V = V D \f$, just like the eigendecomposition, if the
+ * matrix \f$ D \f$ is not required to be diagonal, but if it is allowed to
+ * have blocks of the form
+ * \f[ \begin{bmatrix} u & v \\ -v & u \end{bmatrix} \f]
+ * (where \f$ u \f$ and \f$ v \f$ are real numbers) on the diagonal. These
+ * blocks correspond to complex eigenvalue pairs \f$ u \pm iv \f$. We call
+ * this variant of the eigendecomposition the pseudo-eigendecomposition.
+ *
+ * Call the function compute() to compute the eigenvalues and eigenvectors of
+ * a given matrix. Alternatively, you can use the
+ * EigenSolver(const MatrixType&, bool) constructor which computes the
+ * eigenvalues and eigenvectors at construction time. Once the eigenvalue and
+ * eigenvectors are computed, they can be retrieved with the eigenvalues() and
+ * eigenvectors() functions. The pseudoEigenvalueMatrix() and
+ * pseudoEigenvectors() methods allow the construction of the
+ * pseudo-eigendecomposition.
+ *
+ * The documentation for EigenSolver(const MatrixType&, bool) contains an
+ * example of the typical use of this class.
+ *
+ * \note The implementation is adapted from
+ * <a href="http://math.nist.gov/javanumerics/jama/">JAMA</a> (public domain).
+ * Their code is based on EISPACK.
+ *
+ * \sa MatrixBase::eigenvalues(), class ComplexEigenSolver, class SelfAdjointEigenSolver
+ */
+template<typename MatrixType_> class EigenSolver
+{
+ public:
+
+ /** \brief Synonym for the template parameter \p MatrixType_. */
+ typedef MatrixType_ MatrixType;
+
+ enum {
+ RowsAtCompileTime = MatrixType::RowsAtCompileTime,
+ ColsAtCompileTime = MatrixType::ColsAtCompileTime,
+ Options = MatrixType::Options,
+ MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime,
+ MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime
+ };
+
+ /** \brief Scalar type for matrices of type #MatrixType. */
+ typedef typename MatrixType::Scalar Scalar;
+ typedef typename NumTraits<Scalar>::Real RealScalar;
+ typedef Eigen::Index Index; ///< \deprecated since Eigen 3.3
+
+ /** \brief Complex scalar type for #MatrixType.
+ *
+ * This is \c std::complex<Scalar> if #Scalar is real (e.g.,
+ * \c float or \c double) and just \c Scalar if #Scalar is
+ * complex.
+ */
+ typedef std::complex<RealScalar> ComplexScalar;
+
+ /** \brief Type for vector of eigenvalues as returned by eigenvalues().
+ *
+ * This is a column vector with entries of type #ComplexScalar.
+ * The length of the vector is the size of #MatrixType.
+ */
+ typedef Matrix<ComplexScalar, ColsAtCompileTime, 1, Options & ~RowMajor, MaxColsAtCompileTime, 1> EigenvalueType;
+
+ /** \brief Type for matrix of eigenvectors as returned by eigenvectors().
+ *
+ * This is a square matrix with entries of type #ComplexScalar.
+ * The size is the same as the size of #MatrixType.
+ */
+ typedef Matrix<ComplexScalar, RowsAtCompileTime, ColsAtCompileTime, Options, MaxRowsAtCompileTime, MaxColsAtCompileTime> EigenvectorsType;
+
+ /** \brief Default constructor.
+ *
+ * The default constructor is useful in cases in which the user intends to
+ * perform decompositions via EigenSolver::compute(const MatrixType&, bool).
+ *
+ * \sa compute() for an example.
+ */
+ EigenSolver() : m_eivec(), m_eivalues(), m_isInitialized(false), m_eigenvectorsOk(false), m_realSchur(), m_matT(), m_tmp() {}
+
+ /** \brief Default constructor with memory preallocation
+ *
+ * Like the default constructor but with preallocation of the internal data
+ * according to the specified problem \a size.
+ * \sa EigenSolver()
+ */
+ explicit EigenSolver(Index size)
+ : m_eivec(size, size),
+ m_eivalues(size),
+ m_isInitialized(false),
+ m_eigenvectorsOk(false),
+ m_realSchur(size),
+ m_matT(size, size),
+ m_tmp(size)
+ {}
+
+ /** \brief Constructor; computes eigendecomposition of given matrix.
+ *
+ * \param[in] matrix Square matrix whose eigendecomposition is to be computed.
+ * \param[in] computeEigenvectors If true, both the eigenvectors and the
+ * eigenvalues are computed; if false, only the eigenvalues are
+ * computed.
+ *
+ * This constructor calls compute() to compute the eigenvalues
+ * and eigenvectors.
+ *
+ * Example: \include EigenSolver_EigenSolver_MatrixType.cpp
+ * Output: \verbinclude EigenSolver_EigenSolver_MatrixType.out
+ *
+ * \sa compute()
+ */
+ template<typename InputType>
+ explicit EigenSolver(const EigenBase<InputType>& matrix, bool computeEigenvectors = true)
+ : m_eivec(matrix.rows(), matrix.cols()),
+ m_eivalues(matrix.cols()),
+ m_isInitialized(false),
+ m_eigenvectorsOk(false),
+ m_realSchur(matrix.cols()),
+ m_matT(matrix.rows(), matrix.cols()),
+ m_tmp(matrix.cols())
+ {
+ compute(matrix.derived(), computeEigenvectors);
+ }
+
+ /** \brief Returns the eigenvectors of given matrix.
+ *
+ * \returns %Matrix whose columns are the (possibly complex) eigenvectors.
+ *
+ * \pre Either the constructor
+ * EigenSolver(const MatrixType&,bool) or the member function
+ * compute(const MatrixType&, bool) has been called before, and
+ * \p computeEigenvectors was set to true (the default).
+ *
+ * Column \f$ k \f$ of the returned matrix is an eigenvector corresponding
+ * to eigenvalue number \f$ k \f$ as returned by eigenvalues(). The
+ * eigenvectors are normalized to have (Euclidean) norm equal to one. The
+ * matrix returned by this function is the matrix \f$ V \f$ in the
+ * eigendecomposition \f$ A = V D V^{-1} \f$, if it exists.
+ *
+ * Example: \include EigenSolver_eigenvectors.cpp
+ * Output: \verbinclude EigenSolver_eigenvectors.out
+ *
+ * \sa eigenvalues(), pseudoEigenvectors()
+ */
+ EigenvectorsType eigenvectors() const;
+
+ /** \brief Returns the pseudo-eigenvectors of given matrix.
+ *
+ * \returns Const reference to matrix whose columns are the pseudo-eigenvectors.
+ *
+ * \pre Either the constructor
+ * EigenSolver(const MatrixType&,bool) or the member function
+ * compute(const MatrixType&, bool) has been called before, and
+ * \p computeEigenvectors was set to true (the default).
+ *
+ * The real matrix \f$ V \f$ returned by this function and the
+ * block-diagonal matrix \f$ D \f$ returned by pseudoEigenvalueMatrix()
+ * satisfy \f$ AV = VD \f$.
+ *
+ * Example: \include EigenSolver_pseudoEigenvectors.cpp
+ * Output: \verbinclude EigenSolver_pseudoEigenvectors.out
+ *
+ * \sa pseudoEigenvalueMatrix(), eigenvectors()
+ */
+ const MatrixType& pseudoEigenvectors() const
+ {
+ eigen_assert(m_isInitialized && "EigenSolver is not initialized.");
+ eigen_assert(m_eigenvectorsOk && "The eigenvectors have not been computed together with the eigenvalues.");
+ return m_eivec;
+ }
+
+ /** \brief Returns the block-diagonal matrix in the pseudo-eigendecomposition.
+ *
+ * \returns A block-diagonal matrix.
+ *
+ * \pre Either the constructor
+ * EigenSolver(const MatrixType&,bool) or the member function
+ * compute(const MatrixType&, bool) has been called before.
+ *
+ * The matrix \f$ D \f$ returned by this function is real and
+ * block-diagonal. The blocks on the diagonal are either 1-by-1 or 2-by-2
+ * blocks of the form
+ * \f$ \begin{bmatrix} u & v \\ -v & u \end{bmatrix} \f$.
+ * These blocks are not sorted in any particular order.
+ * The matrix \f$ D \f$ and the matrix \f$ V \f$ returned by
+ * pseudoEigenvectors() satisfy \f$ AV = VD \f$.
+ *
+ * \sa pseudoEigenvectors() for an example, eigenvalues()
+ */
+ MatrixType pseudoEigenvalueMatrix() const;
+
+ /** \brief Returns the eigenvalues of given matrix.
+ *
+ * \returns A const reference to the column vector containing the eigenvalues.
+ *
+ * \pre Either the constructor
+ * EigenSolver(const MatrixType&,bool) or the member function
+ * compute(const MatrixType&, bool) has been called before.
+ *
+ * The eigenvalues are repeated according to their algebraic multiplicity,
+ * so there are as many eigenvalues as rows in the matrix. The eigenvalues
+ * are not sorted in any particular order.
+ *
+ * Example: \include EigenSolver_eigenvalues.cpp
+ * Output: \verbinclude EigenSolver_eigenvalues.out
+ *
+ * \sa eigenvectors(), pseudoEigenvalueMatrix(),
+ * MatrixBase::eigenvalues()
+ */
+ const EigenvalueType& eigenvalues() const
+ {
+ eigen_assert(m_isInitialized && "EigenSolver is not initialized.");
+ return m_eivalues;
+ }
+
+ /** \brief Computes eigendecomposition of given matrix.
+ *
+ * \param[in] matrix Square matrix whose eigendecomposition is to be computed.
+ * \param[in] computeEigenvectors If true, both the eigenvectors and the
+ * eigenvalues are computed; if false, only the eigenvalues are
+ * computed.
+ * \returns Reference to \c *this
+ *
+ * This function computes the eigenvalues of the real matrix \p matrix.
+ * The eigenvalues() function can be used to retrieve them. If
+ * \p computeEigenvectors is true, then the eigenvectors are also computed
+ * and can be retrieved by calling eigenvectors().
+ *
+ * The matrix is first reduced to real Schur form using the RealSchur
+ * class. The Schur decomposition is then used to compute the eigenvalues
+ * and eigenvectors.
+ *
+ * The cost of the computation is dominated by the cost of the
+ * Schur decomposition, which is very approximately \f$ 25n^3 \f$
+ * (where \f$ n \f$ is the size of the matrix) if \p computeEigenvectors
+ * is true, and \f$ 10n^3 \f$ if \p computeEigenvectors is false.
+ *
+ * This method reuses of the allocated data in the EigenSolver object.
+ *
+ * Example: \include EigenSolver_compute.cpp
+ * Output: \verbinclude EigenSolver_compute.out
+ */
+ template<typename InputType>
+ EigenSolver& compute(const EigenBase<InputType>& matrix, bool computeEigenvectors = true);
+
+ /** \returns NumericalIssue if the input contains INF or NaN values or overflow occurred. Returns Success otherwise. */
+ ComputationInfo info() const
+ {
+ eigen_assert(m_isInitialized && "EigenSolver is not initialized.");
+ return m_info;
+ }
+
+ /** \brief Sets the maximum number of iterations allowed. */
+ EigenSolver& setMaxIterations(Index maxIters)
+ {
+ m_realSchur.setMaxIterations(maxIters);
+ return *this;
+ }
+
+ /** \brief Returns the maximum number of iterations. */
+ Index getMaxIterations()
+ {
+ return m_realSchur.getMaxIterations();
+ }
+
+ private:
+ void doComputeEigenvectors();
+
+ protected:
+
+ static void check_template_parameters()
+ {
+ EIGEN_STATIC_ASSERT_NON_INTEGER(Scalar);
+ EIGEN_STATIC_ASSERT(!NumTraits<Scalar>::IsComplex, NUMERIC_TYPE_MUST_BE_REAL);
+ }
+
+ MatrixType m_eivec;
+ EigenvalueType m_eivalues;
+ bool m_isInitialized;
+ bool m_eigenvectorsOk;
+ ComputationInfo m_info;
+ RealSchur<MatrixType> m_realSchur;
+ MatrixType m_matT;
+
+ typedef Matrix<Scalar, ColsAtCompileTime, 1, Options & ~RowMajor, MaxColsAtCompileTime, 1> ColumnVectorType;
+ ColumnVectorType m_tmp;
+};
+
+template<typename MatrixType>
+MatrixType EigenSolver<MatrixType>::pseudoEigenvalueMatrix() const
+{
+ eigen_assert(m_isInitialized && "EigenSolver is not initialized.");
+ const RealScalar precision = RealScalar(2)*NumTraits<RealScalar>::epsilon();
+ Index n = m_eivalues.rows();
+ MatrixType matD = MatrixType::Zero(n,n);
+ for (Index i=0; i<n; ++i)
+ {
+ if (internal::isMuchSmallerThan(numext::imag(m_eivalues.coeff(i)), numext::real(m_eivalues.coeff(i)), precision))
+ matD.coeffRef(i,i) = numext::real(m_eivalues.coeff(i));
+ else
+ {
+ matD.template block<2,2>(i,i) << numext::real(m_eivalues.coeff(i)), numext::imag(m_eivalues.coeff(i)),
+ -numext::imag(m_eivalues.coeff(i)), numext::real(m_eivalues.coeff(i));
+ ++i;
+ }
+ }
+ return matD;
+}
+
+template<typename MatrixType>
+typename EigenSolver<MatrixType>::EigenvectorsType EigenSolver<MatrixType>::eigenvectors() const
+{
+ eigen_assert(m_isInitialized && "EigenSolver is not initialized.");
+ eigen_assert(m_eigenvectorsOk && "The eigenvectors have not been computed together with the eigenvalues.");
+ const RealScalar precision = RealScalar(2)*NumTraits<RealScalar>::epsilon();
+ Index n = m_eivec.cols();
+ EigenvectorsType matV(n,n);
+ for (Index j=0; j<n; ++j)
+ {
+ if (internal::isMuchSmallerThan(numext::imag(m_eivalues.coeff(j)), numext::real(m_eivalues.coeff(j)), precision) || j+1==n)
+ {
+ // we have a real eigen value
+ matV.col(j) = m_eivec.col(j).template cast<ComplexScalar>();
+ matV.col(j).normalize();
+ }
+ else
+ {
+ // we have a pair of complex eigen values
+ for (Index i=0; i<n; ++i)
+ {
+ matV.coeffRef(i,j) = ComplexScalar(m_eivec.coeff(i,j), m_eivec.coeff(i,j+1));
+ matV.coeffRef(i,j+1) = ComplexScalar(m_eivec.coeff(i,j), -m_eivec.coeff(i,j+1));
+ }
+ matV.col(j).normalize();
+ matV.col(j+1).normalize();
+ ++j;
+ }
+ }
+ return matV;
+}
+
+template<typename MatrixType>
+template<typename InputType>
+EigenSolver<MatrixType>&
+EigenSolver<MatrixType>::compute(const EigenBase<InputType>& matrix, bool computeEigenvectors)
+{
+ check_template_parameters();
+
+ using std::sqrt;
+ using std::abs;
+ using numext::isfinite;
+ eigen_assert(matrix.cols() == matrix.rows());
+
+ // Reduce to real Schur form.
+ m_realSchur.compute(matrix.derived(), computeEigenvectors);
+
+ m_info = m_realSchur.info();
+
+ if (m_info == Success)
+ {
+ m_matT = m_realSchur.matrixT();
+ if (computeEigenvectors)
+ m_eivec = m_realSchur.matrixU();
+
+ // Compute eigenvalues from matT
+ m_eivalues.resize(matrix.cols());
+ Index i = 0;
+ while (i < matrix.cols())
+ {
+ if (i == matrix.cols() - 1 || m_matT.coeff(i+1, i) == Scalar(0))
+ {
+ m_eivalues.coeffRef(i) = m_matT.coeff(i, i);
+ if(!(isfinite)(m_eivalues.coeffRef(i)))
+ {
+ m_isInitialized = true;
+ m_eigenvectorsOk = false;
+ m_info = NumericalIssue;
+ return *this;
+ }
+ ++i;
+ }
+ else
+ {
+ Scalar p = Scalar(0.5) * (m_matT.coeff(i, i) - m_matT.coeff(i+1, i+1));
+ Scalar z;
+ // Compute z = sqrt(abs(p * p + m_matT.coeff(i+1, i) * m_matT.coeff(i, i+1)));
+ // without overflow
+ {
+ Scalar t0 = m_matT.coeff(i+1, i);
+ Scalar t1 = m_matT.coeff(i, i+1);
+ Scalar maxval = numext::maxi<Scalar>(abs(p),numext::maxi<Scalar>(abs(t0),abs(t1)));
+ t0 /= maxval;
+ t1 /= maxval;
+ Scalar p0 = p/maxval;
+ z = maxval * sqrt(abs(p0 * p0 + t0 * t1));
+ }
+
+ m_eivalues.coeffRef(i) = ComplexScalar(m_matT.coeff(i+1, i+1) + p, z);
+ m_eivalues.coeffRef(i+1) = ComplexScalar(m_matT.coeff(i+1, i+1) + p, -z);
+ if(!((isfinite)(m_eivalues.coeffRef(i)) && (isfinite)(m_eivalues.coeffRef(i+1))))
+ {
+ m_isInitialized = true;
+ m_eigenvectorsOk = false;
+ m_info = NumericalIssue;
+ return *this;
+ }
+ i += 2;
+ }
+ }
+
+ // Compute eigenvectors.
+ if (computeEigenvectors)
+ doComputeEigenvectors();
+ }
+
+ m_isInitialized = true;
+ m_eigenvectorsOk = computeEigenvectors;
+
+ return *this;
+}
+
+
+template<typename MatrixType>
+void EigenSolver<MatrixType>::doComputeEigenvectors()
+{
+ using std::abs;
+ const Index size = m_eivec.cols();
+ const Scalar eps = NumTraits<Scalar>::epsilon();
+
+ // inefficient! this is already computed in RealSchur
+ Scalar norm(0);
+ for (Index j = 0; j < size; ++j)
+ {
+ norm += m_matT.row(j).segment((std::max)(j-1,Index(0)), size-(std::max)(j-1,Index(0))).cwiseAbs().sum();
+ }
+
+ // Backsubstitute to find vectors of upper triangular form
+ if (norm == Scalar(0))
+ {
+ return;
+ }
+
+ for (Index n = size-1; n >= 0; n--)
+ {
+ Scalar p = m_eivalues.coeff(n).real();
+ Scalar q = m_eivalues.coeff(n).imag();
+
+ // Scalar vector
+ if (q == Scalar(0))
+ {
+ Scalar lastr(0), lastw(0);
+ Index l = n;
+
+ m_matT.coeffRef(n,n) = Scalar(1);
+ for (Index i = n-1; i >= 0; i--)
+ {
+ Scalar w = m_matT.coeff(i,i) - p;
+ Scalar r = m_matT.row(i).segment(l,n-l+1).dot(m_matT.col(n).segment(l, n-l+1));
+
+ if (m_eivalues.coeff(i).imag() < Scalar(0))
+ {
+ lastw = w;
+ lastr = r;
+ }
+ else
+ {
+ l = i;
+ if (m_eivalues.coeff(i).imag() == Scalar(0))
+ {
+ if (w != Scalar(0))
+ m_matT.coeffRef(i,n) = -r / w;
+ else
+ m_matT.coeffRef(i,n) = -r / (eps * norm);
+ }
+ else // Solve real equations
+ {
+ Scalar x = m_matT.coeff(i,i+1);
+ Scalar y = m_matT.coeff(i+1,i);
+ Scalar denom = (m_eivalues.coeff(i).real() - p) * (m_eivalues.coeff(i).real() - p) + m_eivalues.coeff(i).imag() * m_eivalues.coeff(i).imag();
+ Scalar t = (x * lastr - lastw * r) / denom;
+ m_matT.coeffRef(i,n) = t;
+ if (abs(x) > abs(lastw))
+ m_matT.coeffRef(i+1,n) = (-r - w * t) / x;
+ else
+ m_matT.coeffRef(i+1,n) = (-lastr - y * t) / lastw;
+ }
+
+ // Overflow control
+ Scalar t = abs(m_matT.coeff(i,n));
+ if ((eps * t) * t > Scalar(1))
+ m_matT.col(n).tail(size-i) /= t;
+ }
+ }
+ }
+ else if (q < Scalar(0) && n > 0) // Complex vector
+ {
+ Scalar lastra(0), lastsa(0), lastw(0);
+ Index l = n-1;
+
+ // Last vector component imaginary so matrix is triangular
+ if (abs(m_matT.coeff(n,n-1)) > abs(m_matT.coeff(n-1,n)))
+ {
+ m_matT.coeffRef(n-1,n-1) = q / m_matT.coeff(n,n-1);
+ m_matT.coeffRef(n-1,n) = -(m_matT.coeff(n,n) - p) / m_matT.coeff(n,n-1);
+ }
+ else
+ {
+ ComplexScalar cc = ComplexScalar(Scalar(0),-m_matT.coeff(n-1,n)) / ComplexScalar(m_matT.coeff(n-1,n-1)-p,q);
+ m_matT.coeffRef(n-1,n-1) = numext::real(cc);
+ m_matT.coeffRef(n-1,n) = numext::imag(cc);
+ }
+ m_matT.coeffRef(n,n-1) = Scalar(0);
+ m_matT.coeffRef(n,n) = Scalar(1);
+ for (Index i = n-2; i >= 0; i--)
+ {
+ Scalar ra = m_matT.row(i).segment(l, n-l+1).dot(m_matT.col(n-1).segment(l, n-l+1));
+ Scalar sa = m_matT.row(i).segment(l, n-l+1).dot(m_matT.col(n).segment(l, n-l+1));
+ Scalar w = m_matT.coeff(i,i) - p;
+
+ if (m_eivalues.coeff(i).imag() < Scalar(0))
+ {
+ lastw = w;
+ lastra = ra;
+ lastsa = sa;
+ }
+ else
+ {
+ l = i;
+ if (m_eivalues.coeff(i).imag() == RealScalar(0))
+ {
+ ComplexScalar cc = ComplexScalar(-ra,-sa) / ComplexScalar(w,q);
+ m_matT.coeffRef(i,n-1) = numext::real(cc);
+ m_matT.coeffRef(i,n) = numext::imag(cc);
+ }
+ else
+ {
+ // Solve complex equations
+ Scalar x = m_matT.coeff(i,i+1);
+ Scalar y = m_matT.coeff(i+1,i);
+ Scalar vr = (m_eivalues.coeff(i).real() - p) * (m_eivalues.coeff(i).real() - p) + m_eivalues.coeff(i).imag() * m_eivalues.coeff(i).imag() - q * q;
+ Scalar vi = (m_eivalues.coeff(i).real() - p) * Scalar(2) * q;
+ if ((vr == Scalar(0)) && (vi == Scalar(0)))
+ vr = eps * norm * (abs(w) + abs(q) + abs(x) + abs(y) + abs(lastw));
+
+ ComplexScalar cc = ComplexScalar(x*lastra-lastw*ra+q*sa,x*lastsa-lastw*sa-q*ra) / ComplexScalar(vr,vi);
+ m_matT.coeffRef(i,n-1) = numext::real(cc);
+ m_matT.coeffRef(i,n) = numext::imag(cc);
+ if (abs(x) > (abs(lastw) + abs(q)))
+ {
+ m_matT.coeffRef(i+1,n-1) = (-ra - w * m_matT.coeff(i,n-1) + q * m_matT.coeff(i,n)) / x;
+ m_matT.coeffRef(i+1,n) = (-sa - w * m_matT.coeff(i,n) - q * m_matT.coeff(i,n-1)) / x;
+ }
+ else
+ {
+ cc = ComplexScalar(-lastra-y*m_matT.coeff(i,n-1),-lastsa-y*m_matT.coeff(i,n)) / ComplexScalar(lastw,q);
+ m_matT.coeffRef(i+1,n-1) = numext::real(cc);
+ m_matT.coeffRef(i+1,n) = numext::imag(cc);
+ }
+ }
+
+ // Overflow control
+ Scalar t = numext::maxi<Scalar>(abs(m_matT.coeff(i,n-1)),abs(m_matT.coeff(i,n)));
+ if ((eps * t) * t > Scalar(1))
+ m_matT.block(i, n-1, size-i, 2) /= t;
+
+ }
+ }
+
+ // We handled a pair of complex conjugate eigenvalues, so need to skip them both
+ n--;
+ }
+ else
+ {
+ eigen_assert(0 && "Internal bug in EigenSolver (INF or NaN has not been detected)"); // this should not happen
+ }
+ }
+
+ // Back transformation to get eigenvectors of original matrix
+ for (Index j = size-1; j >= 0; j--)
+ {
+ m_tmp.noalias() = m_eivec.leftCols(j+1) * m_matT.col(j).segment(0, j+1);
+ m_eivec.col(j) = m_tmp;
+ }
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_EIGENSOLVER_H
diff --git a/Eigen/src/Eigenvalues/GeneralizedEigenSolver.h b/Eigen/src/Eigenvalues/GeneralizedEigenSolver.h
new file mode 100644
index 0000000..d62c411
--- /dev/null
+++ b/Eigen/src/Eigenvalues/GeneralizedEigenSolver.h
@@ -0,0 +1,414 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2012-2016 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2010,2012 Jitse Niesen <jitse@maths.leeds.ac.uk>
+// Copyright (C) 2016 Tobias Wood <tobias@spinicist.org.uk>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_GENERALIZEDEIGENSOLVER_H
+#define EIGEN_GENERALIZEDEIGENSOLVER_H
+
+#include "./RealQZ.h"
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+/** \eigenvalues_module \ingroup Eigenvalues_Module
+ *
+ *
+ * \class GeneralizedEigenSolver
+ *
+ * \brief Computes the generalized eigenvalues and eigenvectors of a pair of general matrices
+ *
+ * \tparam MatrixType_ the type of the matrices of which we are computing the
+ * eigen-decomposition; this is expected to be an instantiation of the Matrix
+ * class template. Currently, only real matrices are supported.
+ *
+ * The generalized eigenvalues and eigenvectors of a matrix pair \f$ A \f$ and \f$ B \f$ are scalars
+ * \f$ \lambda \f$ and vectors \f$ v \f$ such that \f$ Av = \lambda Bv \f$. If
+ * \f$ D \f$ is a diagonal matrix with the eigenvalues on the diagonal, and
+ * \f$ V \f$ is a matrix with the eigenvectors as its columns, then \f$ A V =
+ * B V D \f$. The matrix \f$ V \f$ is almost always invertible, in which case we
+ * have \f$ A = B V D V^{-1} \f$. This is called the generalized eigen-decomposition.
+ *
+ * The generalized eigenvalues and eigenvectors of a matrix pair may be complex, even when the
+ * matrices are real. Moreover, the generalized eigenvalue might be infinite if the matrix B is
+ * singular. To workaround this difficulty, the eigenvalues are provided as a pair of complex \f$ \alpha \f$
+ * and real \f$ \beta \f$ such that: \f$ \lambda_i = \alpha_i / \beta_i \f$. If \f$ \beta_i \f$ is (nearly) zero,
+ * then one can consider the well defined left eigenvalue \f$ \mu = \beta_i / \alpha_i\f$ such that:
+ * \f$ \mu_i A v_i = B v_i \f$, or even \f$ \mu_i u_i^T A = u_i^T B \f$ where \f$ u_i \f$ is
+ * called the left eigenvector.
+ *
+ * Call the function compute() to compute the generalized eigenvalues and eigenvectors of
+ * a given matrix pair. Alternatively, you can use the
+ * GeneralizedEigenSolver(const MatrixType&, const MatrixType&, bool) constructor which computes the
+ * eigenvalues and eigenvectors at construction time. Once the eigenvalue and
+ * eigenvectors are computed, they can be retrieved with the eigenvalues() and
+ * eigenvectors() functions.
+ *
+ * Here is an usage example of this class:
+ * Example: \include GeneralizedEigenSolver.cpp
+ * Output: \verbinclude GeneralizedEigenSolver.out
+ *
+ * \sa MatrixBase::eigenvalues(), class ComplexEigenSolver, class SelfAdjointEigenSolver
+ */
+template<typename MatrixType_> class GeneralizedEigenSolver
+{
+ public:
+
+ /** \brief Synonym for the template parameter \p MatrixType_. */
+ typedef MatrixType_ MatrixType;
+
+ enum {
+ RowsAtCompileTime = MatrixType::RowsAtCompileTime,
+ ColsAtCompileTime = MatrixType::ColsAtCompileTime,
+ Options = MatrixType::Options,
+ MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime,
+ MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime
+ };
+
+ /** \brief Scalar type for matrices of type #MatrixType. */
+ typedef typename MatrixType::Scalar Scalar;
+ typedef typename NumTraits<Scalar>::Real RealScalar;
+ typedef Eigen::Index Index; ///< \deprecated since Eigen 3.3
+
+ /** \brief Complex scalar type for #MatrixType.
+ *
+ * This is \c std::complex<Scalar> if #Scalar is real (e.g.,
+ * \c float or \c double) and just \c Scalar if #Scalar is
+ * complex.
+ */
+ typedef std::complex<RealScalar> ComplexScalar;
+
+ /** \brief Type for vector of real scalar values eigenvalues as returned by betas().
+ *
+ * This is a column vector with entries of type #Scalar.
+ * The length of the vector is the size of #MatrixType.
+ */
+ typedef Matrix<Scalar, ColsAtCompileTime, 1, Options & ~RowMajor, MaxColsAtCompileTime, 1> VectorType;
+
+ /** \brief Type for vector of complex scalar values eigenvalues as returned by alphas().
+ *
+ * This is a column vector with entries of type #ComplexScalar.
+ * The length of the vector is the size of #MatrixType.
+ */
+ typedef Matrix<ComplexScalar, ColsAtCompileTime, 1, Options & ~RowMajor, MaxColsAtCompileTime, 1> ComplexVectorType;
+
+ /** \brief Expression type for the eigenvalues as returned by eigenvalues().
+ */
+ typedef CwiseBinaryOp<internal::scalar_quotient_op<ComplexScalar,Scalar>,ComplexVectorType,VectorType> EigenvalueType;
+
+ /** \brief Type for matrix of eigenvectors as returned by eigenvectors().
+ *
+ * This is a square matrix with entries of type #ComplexScalar.
+ * The size is the same as the size of #MatrixType.
+ */
+ typedef Matrix<ComplexScalar, RowsAtCompileTime, ColsAtCompileTime, Options, MaxRowsAtCompileTime, MaxColsAtCompileTime> EigenvectorsType;
+
+ /** \brief Default constructor.
+ *
+ * The default constructor is useful in cases in which the user intends to
+ * perform decompositions via EigenSolver::compute(const MatrixType&, bool).
+ *
+ * \sa compute() for an example.
+ */
+ GeneralizedEigenSolver()
+ : m_eivec(),
+ m_alphas(),
+ m_betas(),
+ m_computeEigenvectors(false),
+ m_isInitialized(false),
+ m_realQZ()
+ {}
+
+ /** \brief Default constructor with memory preallocation
+ *
+ * Like the default constructor but with preallocation of the internal data
+ * according to the specified problem \a size.
+ * \sa GeneralizedEigenSolver()
+ */
+ explicit GeneralizedEigenSolver(Index size)
+ : m_eivec(size, size),
+ m_alphas(size),
+ m_betas(size),
+ m_computeEigenvectors(false),
+ m_isInitialized(false),
+ m_realQZ(size),
+ m_tmp(size)
+ {}
+
+ /** \brief Constructor; computes the generalized eigendecomposition of given matrix pair.
+ *
+ * \param[in] A Square matrix whose eigendecomposition is to be computed.
+ * \param[in] B Square matrix whose eigendecomposition is to be computed.
+ * \param[in] computeEigenvectors If true, both the eigenvectors and the
+ * eigenvalues are computed; if false, only the eigenvalues are computed.
+ *
+ * This constructor calls compute() to compute the generalized eigenvalues
+ * and eigenvectors.
+ *
+ * \sa compute()
+ */
+ GeneralizedEigenSolver(const MatrixType& A, const MatrixType& B, bool computeEigenvectors = true)
+ : m_eivec(A.rows(), A.cols()),
+ m_alphas(A.cols()),
+ m_betas(A.cols()),
+ m_computeEigenvectors(false),
+ m_isInitialized(false),
+ m_realQZ(A.cols()),
+ m_tmp(A.cols())
+ {
+ compute(A, B, computeEigenvectors);
+ }
+
+ /* \brief Returns the computed generalized eigenvectors.
+ *
+ * \returns %Matrix whose columns are the (possibly complex) right eigenvectors.
+ * i.e. the eigenvectors that solve (A - l*B)x = 0. The ordering matches the eigenvalues.
+ *
+ * \pre Either the constructor
+ * GeneralizedEigenSolver(const MatrixType&,const MatrixType&, bool) or the member function
+ * compute(const MatrixType&, const MatrixType& bool) has been called before, and
+ * \p computeEigenvectors was set to true (the default).
+ *
+ * \sa eigenvalues()
+ */
+ EigenvectorsType eigenvectors() const {
+ eigen_assert(info() == Success && "GeneralizedEigenSolver failed to compute eigenvectors");
+ eigen_assert(m_computeEigenvectors && "Eigenvectors for GeneralizedEigenSolver were not calculated");
+ return m_eivec;
+ }
+
+ /** \brief Returns an expression of the computed generalized eigenvalues.
+ *
+ * \returns An expression of the column vector containing the eigenvalues.
+ *
+ * It is a shortcut for \code this->alphas().cwiseQuotient(this->betas()); \endcode
+ * Not that betas might contain zeros. It is therefore not recommended to use this function,
+ * but rather directly deal with the alphas and betas vectors.
+ *
+ * \pre Either the constructor
+ * GeneralizedEigenSolver(const MatrixType&,const MatrixType&,bool) or the member function
+ * compute(const MatrixType&,const MatrixType&,bool) has been called before.
+ *
+ * The eigenvalues are repeated according to their algebraic multiplicity,
+ * so there are as many eigenvalues as rows in the matrix. The eigenvalues
+ * are not sorted in any particular order.
+ *
+ * \sa alphas(), betas(), eigenvectors()
+ */
+ EigenvalueType eigenvalues() const
+ {
+ eigen_assert(info() == Success && "GeneralizedEigenSolver failed to compute eigenvalues.");
+ return EigenvalueType(m_alphas,m_betas);
+ }
+
+ /** \returns A const reference to the vectors containing the alpha values
+ *
+ * This vector permits to reconstruct the j-th eigenvalues as alphas(i)/betas(j).
+ *
+ * \sa betas(), eigenvalues() */
+ const ComplexVectorType& alphas() const
+ {
+ eigen_assert(info() == Success && "GeneralizedEigenSolver failed to compute alphas.");
+ return m_alphas;
+ }
+
+ /** \returns A const reference to the vectors containing the beta values
+ *
+ * This vector permits to reconstruct the j-th eigenvalues as alphas(i)/betas(j).
+ *
+ * \sa alphas(), eigenvalues() */
+ const VectorType& betas() const
+ {
+ eigen_assert(info() == Success && "GeneralizedEigenSolver failed to compute betas.");
+ return m_betas;
+ }
+
+ /** \brief Computes generalized eigendecomposition of given matrix.
+ *
+ * \param[in] A Square matrix whose eigendecomposition is to be computed.
+ * \param[in] B Square matrix whose eigendecomposition is to be computed.
+ * \param[in] computeEigenvectors If true, both the eigenvectors and the
+ * eigenvalues are computed; if false, only the eigenvalues are
+ * computed.
+ * \returns Reference to \c *this
+ *
+ * This function computes the eigenvalues of the real matrix \p matrix.
+ * The eigenvalues() function can be used to retrieve them. If
+ * \p computeEigenvectors is true, then the eigenvectors are also computed
+ * and can be retrieved by calling eigenvectors().
+ *
+ * The matrix is first reduced to real generalized Schur form using the RealQZ
+ * class. The generalized Schur decomposition is then used to compute the eigenvalues
+ * and eigenvectors.
+ *
+ * The cost of the computation is dominated by the cost of the
+ * generalized Schur decomposition.
+ *
+ * This method reuses of the allocated data in the GeneralizedEigenSolver object.
+ */
+ GeneralizedEigenSolver& compute(const MatrixType& A, const MatrixType& B, bool computeEigenvectors = true);
+
+ ComputationInfo info() const
+ {
+ eigen_assert(m_isInitialized && "EigenSolver is not initialized.");
+ return m_realQZ.info();
+ }
+
+ /** Sets the maximal number of iterations allowed.
+ */
+ GeneralizedEigenSolver& setMaxIterations(Index maxIters)
+ {
+ m_realQZ.setMaxIterations(maxIters);
+ return *this;
+ }
+
+ protected:
+
+ EIGEN_STATIC_ASSERT_NON_INTEGER(Scalar)
+ EIGEN_STATIC_ASSERT(!NumTraits<Scalar>::IsComplex, NUMERIC_TYPE_MUST_BE_REAL)
+
+ EigenvectorsType m_eivec;
+ ComplexVectorType m_alphas;
+ VectorType m_betas;
+ bool m_computeEigenvectors;
+ bool m_isInitialized;
+ RealQZ<MatrixType> m_realQZ;
+ ComplexVectorType m_tmp;
+};
+
+template<typename MatrixType>
+GeneralizedEigenSolver<MatrixType>&
+GeneralizedEigenSolver<MatrixType>::compute(const MatrixType& A, const MatrixType& B, bool computeEigenvectors)
+{
+ using std::sqrt;
+ using std::abs;
+ eigen_assert(A.cols() == A.rows() && B.cols() == A.rows() && B.cols() == B.rows());
+ Index size = A.cols();
+ // Reduce to generalized real Schur form:
+ // A = Q S Z and B = Q T Z
+ m_realQZ.compute(A, B, computeEigenvectors);
+ if (m_realQZ.info() == Success)
+ {
+ // Resize storage
+ m_alphas.resize(size);
+ m_betas.resize(size);
+ if (computeEigenvectors)
+ {
+ m_eivec.resize(size,size);
+ m_tmp.resize(size);
+ }
+
+ // Aliases:
+ Map<VectorType> v(reinterpret_cast<Scalar*>(m_tmp.data()), size);
+ ComplexVectorType &cv = m_tmp;
+ const MatrixType &mS = m_realQZ.matrixS();
+ const MatrixType &mT = m_realQZ.matrixT();
+
+ Index i = 0;
+ while (i < size)
+ {
+ if (i == size - 1 || mS.coeff(i+1, i) == Scalar(0))
+ {
+ // Real eigenvalue
+ m_alphas.coeffRef(i) = mS.diagonal().coeff(i);
+ m_betas.coeffRef(i) = mT.diagonal().coeff(i);
+ if (computeEigenvectors)
+ {
+ v.setConstant(Scalar(0.0));
+ v.coeffRef(i) = Scalar(1.0);
+ // For singular eigenvalues do nothing more
+ if(abs(m_betas.coeffRef(i)) >= (std::numeric_limits<RealScalar>::min)())
+ {
+ // Non-singular eigenvalue
+ const Scalar alpha = real(m_alphas.coeffRef(i));
+ const Scalar beta = m_betas.coeffRef(i);
+ for (Index j = i-1; j >= 0; j--)
+ {
+ const Index st = j+1;
+ const Index sz = i-j;
+ if (j > 0 && mS.coeff(j, j-1) != Scalar(0))
+ {
+ // 2x2 block
+ Matrix<Scalar, 2, 1> rhs = (alpha*mT.template block<2,Dynamic>(j-1,st,2,sz) - beta*mS.template block<2,Dynamic>(j-1,st,2,sz)) .lazyProduct( v.segment(st,sz) );
+ Matrix<Scalar, 2, 2> lhs = beta * mS.template block<2,2>(j-1,j-1) - alpha * mT.template block<2,2>(j-1,j-1);
+ v.template segment<2>(j-1) = lhs.partialPivLu().solve(rhs);
+ j--;
+ }
+ else
+ {
+ v.coeffRef(j) = -v.segment(st,sz).transpose().cwiseProduct(beta*mS.block(j,st,1,sz) - alpha*mT.block(j,st,1,sz)).sum() / (beta*mS.coeffRef(j,j) - alpha*mT.coeffRef(j,j));
+ }
+ }
+ }
+ m_eivec.col(i).real().noalias() = m_realQZ.matrixZ().transpose() * v;
+ m_eivec.col(i).real().normalize();
+ m_eivec.col(i).imag().setConstant(0);
+ }
+ ++i;
+ }
+ else
+ {
+ // We need to extract the generalized eigenvalues of the pair of a general 2x2 block S and a positive diagonal 2x2 block T
+ // Then taking beta=T_00*T_11, we can avoid any division, and alpha is the eigenvalues of A = (U^-1 * S * U) * diag(T_11,T_00):
+
+ // T = [a 0]
+ // [0 b]
+ RealScalar a = mT.diagonal().coeff(i),
+ b = mT.diagonal().coeff(i+1);
+ const RealScalar beta = m_betas.coeffRef(i) = m_betas.coeffRef(i+1) = a*b;
+
+ // ^^ NOTE: using diagonal()(i) instead of coeff(i,i) workarounds a MSVC bug.
+ Matrix<RealScalar,2,2> S2 = mS.template block<2,2>(i,i) * Matrix<Scalar,2,1>(b,a).asDiagonal();
+
+ Scalar p = Scalar(0.5) * (S2.coeff(0,0) - S2.coeff(1,1));
+ Scalar z = sqrt(abs(p * p + S2.coeff(1,0) * S2.coeff(0,1)));
+ const ComplexScalar alpha = ComplexScalar(S2.coeff(1,1) + p, (beta > 0) ? z : -z);
+ m_alphas.coeffRef(i) = conj(alpha);
+ m_alphas.coeffRef(i+1) = alpha;
+
+ if (computeEigenvectors) {
+ // Compute eigenvector in position (i+1) and then position (i) is just the conjugate
+ cv.setZero();
+ cv.coeffRef(i+1) = Scalar(1.0);
+ // here, the "static_cast" workaound expression template issues.
+ cv.coeffRef(i) = -(static_cast<Scalar>(beta*mS.coeffRef(i,i+1)) - alpha*mT.coeffRef(i,i+1))
+ / (static_cast<Scalar>(beta*mS.coeffRef(i,i)) - alpha*mT.coeffRef(i,i));
+ for (Index j = i-1; j >= 0; j--)
+ {
+ const Index st = j+1;
+ const Index sz = i+1-j;
+ if (j > 0 && mS.coeff(j, j-1) != Scalar(0))
+ {
+ // 2x2 block
+ Matrix<ComplexScalar, 2, 1> rhs = (alpha*mT.template block<2,Dynamic>(j-1,st,2,sz) - beta*mS.template block<2,Dynamic>(j-1,st,2,sz)) .lazyProduct( cv.segment(st,sz) );
+ Matrix<ComplexScalar, 2, 2> lhs = beta * mS.template block<2,2>(j-1,j-1) - alpha * mT.template block<2,2>(j-1,j-1);
+ cv.template segment<2>(j-1) = lhs.partialPivLu().solve(rhs);
+ j--;
+ } else {
+ cv.coeffRef(j) = cv.segment(st,sz).transpose().cwiseProduct(beta*mS.block(j,st,1,sz) - alpha*mT.block(j,st,1,sz)).sum()
+ / (alpha*mT.coeffRef(j,j) - static_cast<Scalar>(beta*mS.coeffRef(j,j)));
+ }
+ }
+ m_eivec.col(i+1).noalias() = (m_realQZ.matrixZ().transpose() * cv);
+ m_eivec.col(i+1).normalize();
+ m_eivec.col(i) = m_eivec.col(i+1).conjugate();
+ }
+ i += 2;
+ }
+ }
+ }
+ m_computeEigenvectors = computeEigenvectors;
+ m_isInitialized = true;
+ return *this;
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_GENERALIZEDEIGENSOLVER_H
diff --git a/Eigen/src/Eigenvalues/GeneralizedSelfAdjointEigenSolver.h b/Eigen/src/Eigenvalues/GeneralizedSelfAdjointEigenSolver.h
new file mode 100644
index 0000000..dab66ca
--- /dev/null
+++ b/Eigen/src/Eigenvalues/GeneralizedSelfAdjointEigenSolver.h
@@ -0,0 +1,228 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2010 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2010 Jitse Niesen <jitse@maths.leeds.ac.uk>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_GENERALIZEDSELFADJOINTEIGENSOLVER_H
+#define EIGEN_GENERALIZEDSELFADJOINTEIGENSOLVER_H
+
+#include "./Tridiagonalization.h"
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+/** \eigenvalues_module \ingroup Eigenvalues_Module
+ *
+ *
+ * \class GeneralizedSelfAdjointEigenSolver
+ *
+ * \brief Computes eigenvalues and eigenvectors of the generalized selfadjoint eigen problem
+ *
+ * \tparam MatrixType_ the type of the matrix of which we are computing the
+ * eigendecomposition; this is expected to be an instantiation of the Matrix
+ * class template.
+ *
+ * This class solves the generalized eigenvalue problem
+ * \f$ Av = \lambda Bv \f$. In this case, the matrix \f$ A \f$ should be
+ * selfadjoint and the matrix \f$ B \f$ should be positive definite.
+ *
+ * Only the \b lower \b triangular \b part of the input matrix is referenced.
+ *
+ * Call the function compute() to compute the eigenvalues and eigenvectors of
+ * a given matrix. Alternatively, you can use the
+ * GeneralizedSelfAdjointEigenSolver(const MatrixType&, const MatrixType&, int)
+ * constructor which computes the eigenvalues and eigenvectors at construction time.
+ * Once the eigenvalue and eigenvectors are computed, they can be retrieved with the eigenvalues()
+ * and eigenvectors() functions.
+ *
+ * The documentation for GeneralizedSelfAdjointEigenSolver(const MatrixType&, const MatrixType&, int)
+ * contains an example of the typical use of this class.
+ *
+ * \sa class SelfAdjointEigenSolver, class EigenSolver, class ComplexEigenSolver
+ */
+template<typename MatrixType_>
+class GeneralizedSelfAdjointEigenSolver : public SelfAdjointEigenSolver<MatrixType_>
+{
+ typedef SelfAdjointEigenSolver<MatrixType_> Base;
+ public:
+
+ typedef MatrixType_ MatrixType;
+
+ /** \brief Default constructor for fixed-size matrices.
+ *
+ * The default constructor is useful in cases in which the user intends to
+ * perform decompositions via compute(). This constructor
+ * can only be used if \p MatrixType_ is a fixed-size matrix; use
+ * GeneralizedSelfAdjointEigenSolver(Index) for dynamic-size matrices.
+ */
+ GeneralizedSelfAdjointEigenSolver() : Base() {}
+
+ /** \brief Constructor, pre-allocates memory for dynamic-size matrices.
+ *
+ * \param [in] size Positive integer, size of the matrix whose
+ * eigenvalues and eigenvectors will be computed.
+ *
+ * This constructor is useful for dynamic-size matrices, when the user
+ * intends to perform decompositions via compute(). The \p size
+ * parameter is only used as a hint. It is not an error to give a wrong
+ * \p size, but it may impair performance.
+ *
+ * \sa compute() for an example
+ */
+ explicit GeneralizedSelfAdjointEigenSolver(Index size)
+ : Base(size)
+ {}
+
+ /** \brief Constructor; computes generalized eigendecomposition of given matrix pencil.
+ *
+ * \param[in] matA Selfadjoint matrix in matrix pencil.
+ * Only the lower triangular part of the matrix is referenced.
+ * \param[in] matB Positive-definite matrix in matrix pencil.
+ * Only the lower triangular part of the matrix is referenced.
+ * \param[in] options A or-ed set of flags {#ComputeEigenvectors,#EigenvaluesOnly} | {#Ax_lBx,#ABx_lx,#BAx_lx}.
+ * Default is #ComputeEigenvectors|#Ax_lBx.
+ *
+ * This constructor calls compute(const MatrixType&, const MatrixType&, int)
+ * to compute the eigenvalues and (if requested) the eigenvectors of the
+ * generalized eigenproblem \f$ Ax = \lambda B x \f$ with \a matA the
+ * selfadjoint matrix \f$ A \f$ and \a matB the positive definite matrix
+ * \f$ B \f$. Each eigenvector \f$ x \f$ satisfies the property
+ * \f$ x^* B x = 1 \f$. The eigenvectors are computed if
+ * \a options contains ComputeEigenvectors.
+ *
+ * In addition, the two following variants can be solved via \p options:
+ * - \c ABx_lx: \f$ ABx = \lambda x \f$
+ * - \c BAx_lx: \f$ BAx = \lambda x \f$
+ *
+ * Example: \include SelfAdjointEigenSolver_SelfAdjointEigenSolver_MatrixType2.cpp
+ * Output: \verbinclude SelfAdjointEigenSolver_SelfAdjointEigenSolver_MatrixType2.out
+ *
+ * \sa compute(const MatrixType&, const MatrixType&, int)
+ */
+ GeneralizedSelfAdjointEigenSolver(const MatrixType& matA, const MatrixType& matB,
+ int options = ComputeEigenvectors|Ax_lBx)
+ : Base(matA.cols())
+ {
+ compute(matA, matB, options);
+ }
+
+ /** \brief Computes generalized eigendecomposition of given matrix pencil.
+ *
+ * \param[in] matA Selfadjoint matrix in matrix pencil.
+ * Only the lower triangular part of the matrix is referenced.
+ * \param[in] matB Positive-definite matrix in matrix pencil.
+ * Only the lower triangular part of the matrix is referenced.
+ * \param[in] options A or-ed set of flags {#ComputeEigenvectors,#EigenvaluesOnly} | {#Ax_lBx,#ABx_lx,#BAx_lx}.
+ * Default is #ComputeEigenvectors|#Ax_lBx.
+ *
+ * \returns Reference to \c *this
+ *
+ * According to \p options, this function computes eigenvalues and (if requested)
+ * the eigenvectors of one of the following three generalized eigenproblems:
+ * - \c Ax_lBx: \f$ Ax = \lambda B x \f$
+ * - \c ABx_lx: \f$ ABx = \lambda x \f$
+ * - \c BAx_lx: \f$ BAx = \lambda x \f$
+ * with \a matA the selfadjoint matrix \f$ A \f$ and \a matB the positive definite
+ * matrix \f$ B \f$.
+ * In addition, each eigenvector \f$ x \f$ satisfies the property \f$ x^* B x = 1 \f$.
+ *
+ * The eigenvalues() function can be used to retrieve
+ * the eigenvalues. If \p options contains ComputeEigenvectors, then the
+ * eigenvectors are also computed and can be retrieved by calling
+ * eigenvectors().
+ *
+ * The implementation uses LLT to compute the Cholesky decomposition
+ * \f$ B = LL^* \f$ and computes the classical eigendecomposition
+ * of the selfadjoint matrix \f$ L^{-1} A (L^*)^{-1} \f$ if \p options contains Ax_lBx
+ * and of \f$ L^{*} A L \f$ otherwise. This solves the
+ * generalized eigenproblem, because any solution of the generalized
+ * eigenproblem \f$ Ax = \lambda B x \f$ corresponds to a solution
+ * \f$ L^{-1} A (L^*)^{-1} (L^* x) = \lambda (L^* x) \f$ of the
+ * eigenproblem for \f$ L^{-1} A (L^*)^{-1} \f$. Similar statements
+ * can be made for the two other variants.
+ *
+ * Example: \include SelfAdjointEigenSolver_compute_MatrixType2.cpp
+ * Output: \verbinclude SelfAdjointEigenSolver_compute_MatrixType2.out
+ *
+ * \sa GeneralizedSelfAdjointEigenSolver(const MatrixType&, const MatrixType&, int)
+ */
+ GeneralizedSelfAdjointEigenSolver& compute(const MatrixType& matA, const MatrixType& matB,
+ int options = ComputeEigenvectors|Ax_lBx);
+
+ protected:
+
+};
+
+
+template<typename MatrixType>
+GeneralizedSelfAdjointEigenSolver<MatrixType>& GeneralizedSelfAdjointEigenSolver<MatrixType>::
+compute(const MatrixType& matA, const MatrixType& matB, int options)
+{
+ eigen_assert(matA.cols()==matA.rows() && matB.rows()==matA.rows() && matB.cols()==matB.rows());
+ eigen_assert((options&~(EigVecMask|GenEigMask))==0
+ && (options&EigVecMask)!=EigVecMask
+ && ((options&GenEigMask)==0 || (options&GenEigMask)==Ax_lBx
+ || (options&GenEigMask)==ABx_lx || (options&GenEigMask)==BAx_lx)
+ && "invalid option parameter");
+
+ bool computeEigVecs = ((options&EigVecMask)==0) || ((options&EigVecMask)==ComputeEigenvectors);
+
+ // Compute the cholesky decomposition of matB = L L' = U'U
+ LLT<MatrixType> cholB(matB);
+
+ int type = (options&GenEigMask);
+ if(type==0)
+ type = Ax_lBx;
+
+ if(type==Ax_lBx)
+ {
+ // compute C = inv(L) A inv(L')
+ MatrixType matC = matA.template selfadjointView<Lower>();
+ cholB.matrixL().template solveInPlace<OnTheLeft>(matC);
+ cholB.matrixU().template solveInPlace<OnTheRight>(matC);
+
+ Base::compute(matC, computeEigVecs ? ComputeEigenvectors : EigenvaluesOnly );
+
+ // transform back the eigen vectors: evecs = inv(U) * evecs
+ if(computeEigVecs)
+ cholB.matrixU().solveInPlace(Base::m_eivec);
+ }
+ else if(type==ABx_lx)
+ {
+ // compute C = L' A L
+ MatrixType matC = matA.template selfadjointView<Lower>();
+ matC = matC * cholB.matrixL();
+ matC = cholB.matrixU() * matC;
+
+ Base::compute(matC, computeEigVecs ? ComputeEigenvectors : EigenvaluesOnly);
+
+ // transform back the eigen vectors: evecs = inv(U) * evecs
+ if(computeEigVecs)
+ cholB.matrixU().solveInPlace(Base::m_eivec);
+ }
+ else if(type==BAx_lx)
+ {
+ // compute C = L' A L
+ MatrixType matC = matA.template selfadjointView<Lower>();
+ matC = matC * cholB.matrixL();
+ matC = cholB.matrixU() * matC;
+
+ Base::compute(matC, computeEigVecs ? ComputeEigenvectors : EigenvaluesOnly);
+
+ // transform back the eigen vectors: evecs = L * evecs
+ if(computeEigVecs)
+ Base::m_eivec = cholB.matrixL() * Base::m_eivec;
+ }
+
+ return *this;
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_GENERALIZEDSELFADJOINTEIGENSOLVER_H
diff --git a/Eigen/src/Eigenvalues/HessenbergDecomposition.h b/Eigen/src/Eigenvalues/HessenbergDecomposition.h
new file mode 100644
index 0000000..fafab99
--- /dev/null
+++ b/Eigen/src/Eigenvalues/HessenbergDecomposition.h
@@ -0,0 +1,376 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2010 Jitse Niesen <jitse@maths.leeds.ac.uk>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_HESSENBERGDECOMPOSITION_H
+#define EIGEN_HESSENBERGDECOMPOSITION_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+
+template<typename MatrixType> struct HessenbergDecompositionMatrixHReturnType;
+template<typename MatrixType>
+struct traits<HessenbergDecompositionMatrixHReturnType<MatrixType> >
+{
+ typedef MatrixType ReturnType;
+};
+
+}
+
+/** \eigenvalues_module \ingroup Eigenvalues_Module
+ *
+ *
+ * \class HessenbergDecomposition
+ *
+ * \brief Reduces a square matrix to Hessenberg form by an orthogonal similarity transformation
+ *
+ * \tparam MatrixType_ the type of the matrix of which we are computing the Hessenberg decomposition
+ *
+ * This class performs an Hessenberg decomposition of a matrix \f$ A \f$. In
+ * the real case, the Hessenberg decomposition consists of an orthogonal
+ * matrix \f$ Q \f$ and a Hessenberg matrix \f$ H \f$ such that \f$ A = Q H
+ * Q^T \f$. An orthogonal matrix is a matrix whose inverse equals its
+ * transpose (\f$ Q^{-1} = Q^T \f$). A Hessenberg matrix has zeros below the
+ * subdiagonal, so it is almost upper triangular. The Hessenberg decomposition
+ * of a complex matrix is \f$ A = Q H Q^* \f$ with \f$ Q \f$ unitary (that is,
+ * \f$ Q^{-1} = Q^* \f$).
+ *
+ * Call the function compute() to compute the Hessenberg decomposition of a
+ * given matrix. Alternatively, you can use the
+ * HessenbergDecomposition(const MatrixType&) constructor which computes the
+ * Hessenberg decomposition at construction time. Once the decomposition is
+ * computed, you can use the matrixH() and matrixQ() functions to construct
+ * the matrices H and Q in the decomposition.
+ *
+ * The documentation for matrixH() contains an example of the typical use of
+ * this class.
+ *
+ * \sa class ComplexSchur, class Tridiagonalization, \ref QR_Module "QR Module"
+ */
+template<typename MatrixType_> class HessenbergDecomposition
+{
+ public:
+
+ /** \brief Synonym for the template parameter \p MatrixType_. */
+ typedef MatrixType_ MatrixType;
+
+ enum {
+ Size = MatrixType::RowsAtCompileTime,
+ SizeMinusOne = Size == Dynamic ? Dynamic : Size - 1,
+ Options = MatrixType::Options,
+ MaxSize = MatrixType::MaxRowsAtCompileTime,
+ MaxSizeMinusOne = MaxSize == Dynamic ? Dynamic : MaxSize - 1
+ };
+
+ /** \brief Scalar type for matrices of type #MatrixType. */
+ typedef typename MatrixType::Scalar Scalar;
+ typedef Eigen::Index Index; ///< \deprecated since Eigen 3.3
+
+ /** \brief Type for vector of Householder coefficients.
+ *
+ * This is column vector with entries of type #Scalar. The length of the
+ * vector is one less than the size of #MatrixType, if it is a fixed-side
+ * type.
+ */
+ typedef Matrix<Scalar, SizeMinusOne, 1, Options & ~RowMajor, MaxSizeMinusOne, 1> CoeffVectorType;
+
+ /** \brief Return type of matrixQ() */
+ typedef HouseholderSequence<MatrixType,internal::remove_all_t<typename CoeffVectorType::ConjugateReturnType>> HouseholderSequenceType;
+
+ typedef internal::HessenbergDecompositionMatrixHReturnType<MatrixType> MatrixHReturnType;
+
+ /** \brief Default constructor; the decomposition will be computed later.
+ *
+ * \param [in] size The size of the matrix whose Hessenberg decomposition will be computed.
+ *
+ * The default constructor is useful in cases in which the user intends to
+ * perform decompositions via compute(). The \p size parameter is only
+ * used as a hint. It is not an error to give a wrong \p size, but it may
+ * impair performance.
+ *
+ * \sa compute() for an example.
+ */
+ explicit HessenbergDecomposition(Index size = Size==Dynamic ? 2 : Size)
+ : m_matrix(size,size),
+ m_temp(size),
+ m_isInitialized(false)
+ {
+ if(size>1)
+ m_hCoeffs.resize(size-1);
+ }
+
+ /** \brief Constructor; computes Hessenberg decomposition of given matrix.
+ *
+ * \param[in] matrix Square matrix whose Hessenberg decomposition is to be computed.
+ *
+ * This constructor calls compute() to compute the Hessenberg
+ * decomposition.
+ *
+ * \sa matrixH() for an example.
+ */
+ template<typename InputType>
+ explicit HessenbergDecomposition(const EigenBase<InputType>& matrix)
+ : m_matrix(matrix.derived()),
+ m_temp(matrix.rows()),
+ m_isInitialized(false)
+ {
+ if(matrix.rows()<2)
+ {
+ m_isInitialized = true;
+ return;
+ }
+ m_hCoeffs.resize(matrix.rows()-1,1);
+ _compute(m_matrix, m_hCoeffs, m_temp);
+ m_isInitialized = true;
+ }
+
+ /** \brief Computes Hessenberg decomposition of given matrix.
+ *
+ * \param[in] matrix Square matrix whose Hessenberg decomposition is to be computed.
+ * \returns Reference to \c *this
+ *
+ * The Hessenberg decomposition is computed by bringing the columns of the
+ * matrix successively in the required form using Householder reflections
+ * (see, e.g., Algorithm 7.4.2 in Golub \& Van Loan, <i>%Matrix
+ * Computations</i>). The cost is \f$ 10n^3/3 \f$ flops, where \f$ n \f$
+ * denotes the size of the given matrix.
+ *
+ * This method reuses of the allocated data in the HessenbergDecomposition
+ * object.
+ *
+ * Example: \include HessenbergDecomposition_compute.cpp
+ * Output: \verbinclude HessenbergDecomposition_compute.out
+ */
+ template<typename InputType>
+ HessenbergDecomposition& compute(const EigenBase<InputType>& matrix)
+ {
+ m_matrix = matrix.derived();
+ if(matrix.rows()<2)
+ {
+ m_isInitialized = true;
+ return *this;
+ }
+ m_hCoeffs.resize(matrix.rows()-1,1);
+ _compute(m_matrix, m_hCoeffs, m_temp);
+ m_isInitialized = true;
+ return *this;
+ }
+
+ /** \brief Returns the Householder coefficients.
+ *
+ * \returns a const reference to the vector of Householder coefficients
+ *
+ * \pre Either the constructor HessenbergDecomposition(const MatrixType&)
+ * or the member function compute(const MatrixType&) has been called
+ * before to compute the Hessenberg decomposition of a matrix.
+ *
+ * The Householder coefficients allow the reconstruction of the matrix
+ * \f$ Q \f$ in the Hessenberg decomposition from the packed data.
+ *
+ * \sa packedMatrix(), \ref Householder_Module "Householder module"
+ */
+ const CoeffVectorType& householderCoefficients() const
+ {
+ eigen_assert(m_isInitialized && "HessenbergDecomposition is not initialized.");
+ return m_hCoeffs;
+ }
+
+ /** \brief Returns the internal representation of the decomposition
+ *
+ * \returns a const reference to a matrix with the internal representation
+ * of the decomposition.
+ *
+ * \pre Either the constructor HessenbergDecomposition(const MatrixType&)
+ * or the member function compute(const MatrixType&) has been called
+ * before to compute the Hessenberg decomposition of a matrix.
+ *
+ * The returned matrix contains the following information:
+ * - the upper part and lower sub-diagonal represent the Hessenberg matrix H
+ * - the rest of the lower part contains the Householder vectors that, combined with
+ * Householder coefficients returned by householderCoefficients(),
+ * allows to reconstruct the matrix Q as
+ * \f$ Q = H_{N-1} \ldots H_1 H_0 \f$.
+ * Here, the matrices \f$ H_i \f$ are the Householder transformations
+ * \f$ H_i = (I - h_i v_i v_i^T) \f$
+ * where \f$ h_i \f$ is the \f$ i \f$th Householder coefficient and
+ * \f$ v_i \f$ is the Householder vector defined by
+ * \f$ v_i = [ 0, \ldots, 0, 1, M(i+2,i), \ldots, M(N-1,i) ]^T \f$
+ * with M the matrix returned by this function.
+ *
+ * See LAPACK for further details on this packed storage.
+ *
+ * Example: \include HessenbergDecomposition_packedMatrix.cpp
+ * Output: \verbinclude HessenbergDecomposition_packedMatrix.out
+ *
+ * \sa householderCoefficients()
+ */
+ const MatrixType& packedMatrix() const
+ {
+ eigen_assert(m_isInitialized && "HessenbergDecomposition is not initialized.");
+ return m_matrix;
+ }
+
+ /** \brief Reconstructs the orthogonal matrix Q in the decomposition
+ *
+ * \returns object representing the matrix Q
+ *
+ * \pre Either the constructor HessenbergDecomposition(const MatrixType&)
+ * or the member function compute(const MatrixType&) has been called
+ * before to compute the Hessenberg decomposition of a matrix.
+ *
+ * This function returns a light-weight object of template class
+ * HouseholderSequence. You can either apply it directly to a matrix or
+ * you can convert it to a matrix of type #MatrixType.
+ *
+ * \sa matrixH() for an example, class HouseholderSequence
+ */
+ HouseholderSequenceType matrixQ() const
+ {
+ eigen_assert(m_isInitialized && "HessenbergDecomposition is not initialized.");
+ return HouseholderSequenceType(m_matrix, m_hCoeffs.conjugate())
+ .setLength(m_matrix.rows() - 1)
+ .setShift(1);
+ }
+
+ /** \brief Constructs the Hessenberg matrix H in the decomposition
+ *
+ * \returns expression object representing the matrix H
+ *
+ * \pre Either the constructor HessenbergDecomposition(const MatrixType&)
+ * or the member function compute(const MatrixType&) has been called
+ * before to compute the Hessenberg decomposition of a matrix.
+ *
+ * The object returned by this function constructs the Hessenberg matrix H
+ * when it is assigned to a matrix or otherwise evaluated. The matrix H is
+ * constructed from the packed matrix as returned by packedMatrix(): The
+ * upper part (including the subdiagonal) of the packed matrix contains
+ * the matrix H. It may sometimes be better to directly use the packed
+ * matrix instead of constructing the matrix H.
+ *
+ * Example: \include HessenbergDecomposition_matrixH.cpp
+ * Output: \verbinclude HessenbergDecomposition_matrixH.out
+ *
+ * \sa matrixQ(), packedMatrix()
+ */
+ MatrixHReturnType matrixH() const
+ {
+ eigen_assert(m_isInitialized && "HessenbergDecomposition is not initialized.");
+ return MatrixHReturnType(*this);
+ }
+
+ private:
+
+ typedef Matrix<Scalar, 1, Size, int(Options) | int(RowMajor), 1, MaxSize> VectorType;
+ typedef typename NumTraits<Scalar>::Real RealScalar;
+ static void _compute(MatrixType& matA, CoeffVectorType& hCoeffs, VectorType& temp);
+
+ protected:
+ MatrixType m_matrix;
+ CoeffVectorType m_hCoeffs;
+ VectorType m_temp;
+ bool m_isInitialized;
+};
+
+/** \internal
+ * Performs a tridiagonal decomposition of \a matA in place.
+ *
+ * \param matA the input selfadjoint matrix
+ * \param hCoeffs returned Householder coefficients
+ *
+ * The result is written in the lower triangular part of \a matA.
+ *
+ * Implemented from Golub's "%Matrix Computations", algorithm 8.3.1.
+ *
+ * \sa packedMatrix()
+ */
+template<typename MatrixType>
+void HessenbergDecomposition<MatrixType>::_compute(MatrixType& matA, CoeffVectorType& hCoeffs, VectorType& temp)
+{
+ eigen_assert(matA.rows()==matA.cols());
+ Index n = matA.rows();
+ temp.resize(n);
+ for (Index i = 0; i<n-1; ++i)
+ {
+ // let's consider the vector v = i-th column starting at position i+1
+ Index remainingSize = n-i-1;
+ RealScalar beta;
+ Scalar h;
+ matA.col(i).tail(remainingSize).makeHouseholderInPlace(h, beta);
+ matA.col(i).coeffRef(i+1) = beta;
+ hCoeffs.coeffRef(i) = h;
+
+ // Apply similarity transformation to remaining columns,
+ // i.e., compute A = H A H'
+
+ // A = H A
+ matA.bottomRightCorner(remainingSize, remainingSize)
+ .applyHouseholderOnTheLeft(matA.col(i).tail(remainingSize-1), h, &temp.coeffRef(0));
+
+ // A = A H'
+ matA.rightCols(remainingSize)
+ .applyHouseholderOnTheRight(matA.col(i).tail(remainingSize-1), numext::conj(h), &temp.coeffRef(0));
+ }
+}
+
+namespace internal {
+
+/** \eigenvalues_module \ingroup Eigenvalues_Module
+ *
+ *
+ * \brief Expression type for return value of HessenbergDecomposition::matrixH()
+ *
+ * \tparam MatrixType type of matrix in the Hessenberg decomposition
+ *
+ * Objects of this type represent the Hessenberg matrix in the Hessenberg
+ * decomposition of some matrix. The object holds a reference to the
+ * HessenbergDecomposition class until the it is assigned or evaluated for
+ * some other reason (the reference should remain valid during the life time
+ * of this object). This class is the return type of
+ * HessenbergDecomposition::matrixH(); there is probably no other use for this
+ * class.
+ */
+template<typename MatrixType> struct HessenbergDecompositionMatrixHReturnType
+: public ReturnByValue<HessenbergDecompositionMatrixHReturnType<MatrixType> >
+{
+ public:
+ /** \brief Constructor.
+ *
+ * \param[in] hess Hessenberg decomposition
+ */
+ HessenbergDecompositionMatrixHReturnType(const HessenbergDecomposition<MatrixType>& hess) : m_hess(hess) { }
+
+ /** \brief Hessenberg matrix in decomposition.
+ *
+ * \param[out] result Hessenberg matrix in decomposition \p hess which
+ * was passed to the constructor
+ */
+ template <typename ResultType>
+ inline void evalTo(ResultType& result) const
+ {
+ result = m_hess.packedMatrix();
+ Index n = result.rows();
+ if (n>2)
+ result.bottomLeftCorner(n-2, n-2).template triangularView<Lower>().setZero();
+ }
+
+ Index rows() const { return m_hess.packedMatrix().rows(); }
+ Index cols() const { return m_hess.packedMatrix().cols(); }
+
+ protected:
+ const HessenbergDecomposition<MatrixType>& m_hess;
+};
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_HESSENBERGDECOMPOSITION_H
diff --git a/Eigen/src/Eigenvalues/InternalHeaderCheck.h b/Eigen/src/Eigenvalues/InternalHeaderCheck.h
new file mode 100644
index 0000000..374cbd4
--- /dev/null
+++ b/Eigen/src/Eigenvalues/InternalHeaderCheck.h
@@ -0,0 +1,3 @@
+#ifndef EIGEN_EIGENVALUES_MODULE_H
+#error "Please include Eigen/Eigenvalues instead of including headers inside the src directory directly."
+#endif
diff --git a/Eigen/src/Eigenvalues/MatrixBaseEigenvalues.h b/Eigen/src/Eigenvalues/MatrixBaseEigenvalues.h
new file mode 100644
index 0000000..c8df260
--- /dev/null
+++ b/Eigen/src/Eigenvalues/MatrixBaseEigenvalues.h
@@ -0,0 +1,160 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2010 Jitse Niesen <jitse@maths.leeds.ac.uk>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_MATRIXBASEEIGENVALUES_H
+#define EIGEN_MATRIXBASEEIGENVALUES_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+
+template<typename Derived, bool IsComplex>
+struct eigenvalues_selector
+{
+ // this is the implementation for the case IsComplex = true
+ static inline typename MatrixBase<Derived>::EigenvaluesReturnType const
+ run(const MatrixBase<Derived>& m)
+ {
+ typedef typename Derived::PlainObject PlainObject;
+ PlainObject m_eval(m);
+ return ComplexEigenSolver<PlainObject>(m_eval, false).eigenvalues();
+ }
+};
+
+template<typename Derived>
+struct eigenvalues_selector<Derived, false>
+{
+ static inline typename MatrixBase<Derived>::EigenvaluesReturnType const
+ run(const MatrixBase<Derived>& m)
+ {
+ typedef typename Derived::PlainObject PlainObject;
+ PlainObject m_eval(m);
+ return EigenSolver<PlainObject>(m_eval, false).eigenvalues();
+ }
+};
+
+} // end namespace internal
+
+/** \brief Computes the eigenvalues of a matrix
+ * \returns Column vector containing the eigenvalues.
+ *
+ * \eigenvalues_module
+ * This function computes the eigenvalues with the help of the EigenSolver
+ * class (for real matrices) or the ComplexEigenSolver class (for complex
+ * matrices).
+ *
+ * The eigenvalues are repeated according to their algebraic multiplicity,
+ * so there are as many eigenvalues as rows in the matrix.
+ *
+ * The SelfAdjointView class provides a better algorithm for selfadjoint
+ * matrices.
+ *
+ * Example: \include MatrixBase_eigenvalues.cpp
+ * Output: \verbinclude MatrixBase_eigenvalues.out
+ *
+ * \sa EigenSolver::eigenvalues(), ComplexEigenSolver::eigenvalues(),
+ * SelfAdjointView::eigenvalues()
+ */
+template<typename Derived>
+inline typename MatrixBase<Derived>::EigenvaluesReturnType
+MatrixBase<Derived>::eigenvalues() const
+{
+ return internal::eigenvalues_selector<Derived, NumTraits<Scalar>::IsComplex>::run(derived());
+}
+
+/** \brief Computes the eigenvalues of a matrix
+ * \returns Column vector containing the eigenvalues.
+ *
+ * \eigenvalues_module
+ * This function computes the eigenvalues with the help of the
+ * SelfAdjointEigenSolver class. The eigenvalues are repeated according to
+ * their algebraic multiplicity, so there are as many eigenvalues as rows in
+ * the matrix.
+ *
+ * Example: \include SelfAdjointView_eigenvalues.cpp
+ * Output: \verbinclude SelfAdjointView_eigenvalues.out
+ *
+ * \sa SelfAdjointEigenSolver::eigenvalues(), MatrixBase::eigenvalues()
+ */
+template<typename MatrixType, unsigned int UpLo>
+EIGEN_DEVICE_FUNC inline typename SelfAdjointView<MatrixType, UpLo>::EigenvaluesReturnType
+SelfAdjointView<MatrixType, UpLo>::eigenvalues() const
+{
+ PlainObject thisAsMatrix(*this);
+ return SelfAdjointEigenSolver<PlainObject>(thisAsMatrix, false).eigenvalues();
+}
+
+
+
+/** \brief Computes the L2 operator norm
+ * \returns Operator norm of the matrix.
+ *
+ * \eigenvalues_module
+ * This function computes the L2 operator norm of a matrix, which is also
+ * known as the spectral norm. The norm of a matrix \f$ A \f$ is defined to be
+ * \f[ \|A\|_2 = \max_x \frac{\|Ax\|_2}{\|x\|_2} \f]
+ * where the maximum is over all vectors and the norm on the right is the
+ * Euclidean vector norm. The norm equals the largest singular value, which is
+ * the square root of the largest eigenvalue of the positive semi-definite
+ * matrix \f$ A^*A \f$.
+ *
+ * The current implementation uses the eigenvalues of \f$ A^*A \f$, as computed
+ * by SelfAdjointView::eigenvalues(), to compute the operator norm of a
+ * matrix. The SelfAdjointView class provides a better algorithm for
+ * selfadjoint matrices.
+ *
+ * Example: \include MatrixBase_operatorNorm.cpp
+ * Output: \verbinclude MatrixBase_operatorNorm.out
+ *
+ * \sa SelfAdjointView::eigenvalues(), SelfAdjointView::operatorNorm()
+ */
+template<typename Derived>
+inline typename MatrixBase<Derived>::RealScalar
+MatrixBase<Derived>::operatorNorm() const
+{
+ using std::sqrt;
+ typename Derived::PlainObject m_eval(derived());
+ // FIXME if it is really guaranteed that the eigenvalues are already sorted,
+ // then we don't need to compute a maxCoeff() here, comparing the 1st and last ones is enough.
+ return sqrt((m_eval*m_eval.adjoint())
+ .eval()
+ .template selfadjointView<Lower>()
+ .eigenvalues()
+ .maxCoeff()
+ );
+}
+
+/** \brief Computes the L2 operator norm
+ * \returns Operator norm of the matrix.
+ *
+ * \eigenvalues_module
+ * This function computes the L2 operator norm of a self-adjoint matrix. For a
+ * self-adjoint matrix, the operator norm is the largest eigenvalue.
+ *
+ * The current implementation uses the eigenvalues of the matrix, as computed
+ * by eigenvalues(), to compute the operator norm of the matrix.
+ *
+ * Example: \include SelfAdjointView_operatorNorm.cpp
+ * Output: \verbinclude SelfAdjointView_operatorNorm.out
+ *
+ * \sa eigenvalues(), MatrixBase::operatorNorm()
+ */
+template<typename MatrixType, unsigned int UpLo>
+EIGEN_DEVICE_FUNC inline typename SelfAdjointView<MatrixType, UpLo>::RealScalar
+SelfAdjointView<MatrixType, UpLo>::operatorNorm() const
+{
+ return eigenvalues().cwiseAbs().maxCoeff();
+}
+
+} // end namespace Eigen
+
+#endif
diff --git a/Eigen/src/Eigenvalues/RealQZ.h b/Eigen/src/Eigenvalues/RealQZ.h
new file mode 100644
index 0000000..545918f
--- /dev/null
+++ b/Eigen/src/Eigenvalues/RealQZ.h
@@ -0,0 +1,659 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2012 Alexey Korepanov <kaikaikai@yandex.ru>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_REAL_QZ_H
+#define EIGEN_REAL_QZ_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+ /** \eigenvalues_module \ingroup Eigenvalues_Module
+ *
+ *
+ * \class RealQZ
+ *
+ * \brief Performs a real QZ decomposition of a pair of square matrices
+ *
+ * \tparam MatrixType_ the type of the matrix of which we are computing the
+ * real QZ decomposition; this is expected to be an instantiation of the
+ * Matrix class template.
+ *
+ * Given a real square matrices A and B, this class computes the real QZ
+ * decomposition: \f$ A = Q S Z \f$, \f$ B = Q T Z \f$ where Q and Z are
+ * real orthogonal matrixes, T is upper-triangular matrix, and S is upper
+ * quasi-triangular matrix. An orthogonal matrix is a matrix whose
+ * inverse is equal to its transpose, \f$ U^{-1} = U^T \f$. A quasi-triangular
+ * matrix is a block-triangular matrix whose diagonal consists of 1-by-1
+ * blocks and 2-by-2 blocks where further reduction is impossible due to
+ * complex eigenvalues.
+ *
+ * The eigenvalues of the pencil \f$ A - z B \f$ can be obtained from
+ * 1x1 and 2x2 blocks on the diagonals of S and T.
+ *
+ * Call the function compute() to compute the real QZ decomposition of a
+ * given pair of matrices. Alternatively, you can use the
+ * RealQZ(const MatrixType& B, const MatrixType& B, bool computeQZ)
+ * constructor which computes the real QZ decomposition at construction
+ * time. Once the decomposition is computed, you can use the matrixS(),
+ * matrixT(), matrixQ() and matrixZ() functions to retrieve the matrices
+ * S, T, Q and Z in the decomposition. If computeQZ==false, some time
+ * is saved by not computing matrices Q and Z.
+ *
+ * Example: \include RealQZ_compute.cpp
+ * Output: \include RealQZ_compute.out
+ *
+ * \note The implementation is based on the algorithm in "Matrix Computations"
+ * by Gene H. Golub and Charles F. Van Loan, and a paper "An algorithm for
+ * generalized eigenvalue problems" by C.B.Moler and G.W.Stewart.
+ *
+ * \sa class RealSchur, class ComplexSchur, class EigenSolver, class ComplexEigenSolver
+ */
+
+ template<typename MatrixType_> class RealQZ
+ {
+ public:
+ typedef MatrixType_ MatrixType;
+ enum {
+ RowsAtCompileTime = MatrixType::RowsAtCompileTime,
+ ColsAtCompileTime = MatrixType::ColsAtCompileTime,
+ Options = MatrixType::Options,
+ MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime,
+ MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime
+ };
+ typedef typename MatrixType::Scalar Scalar;
+ typedef std::complex<typename NumTraits<Scalar>::Real> ComplexScalar;
+ typedef Eigen::Index Index; ///< \deprecated since Eigen 3.3
+
+ typedef Matrix<ComplexScalar, ColsAtCompileTime, 1, Options & ~RowMajor, MaxColsAtCompileTime, 1> EigenvalueType;
+ typedef Matrix<Scalar, ColsAtCompileTime, 1, Options & ~RowMajor, MaxColsAtCompileTime, 1> ColumnVectorType;
+
+ /** \brief Default constructor.
+ *
+ * \param [in] size Positive integer, size of the matrix whose QZ decomposition will be computed.
+ *
+ * The default constructor is useful in cases in which the user intends to
+ * perform decompositions via compute(). The \p size parameter is only
+ * used as a hint. It is not an error to give a wrong \p size, but it may
+ * impair performance.
+ *
+ * \sa compute() for an example.
+ */
+ explicit RealQZ(Index size = RowsAtCompileTime==Dynamic ? 1 : RowsAtCompileTime) :
+ m_S(size, size),
+ m_T(size, size),
+ m_Q(size, size),
+ m_Z(size, size),
+ m_workspace(size*2),
+ m_maxIters(400),
+ m_isInitialized(false),
+ m_computeQZ(true)
+ {}
+
+ /** \brief Constructor; computes real QZ decomposition of given matrices
+ *
+ * \param[in] A Matrix A.
+ * \param[in] B Matrix B.
+ * \param[in] computeQZ If false, A and Z are not computed.
+ *
+ * This constructor calls compute() to compute the QZ decomposition.
+ */
+ RealQZ(const MatrixType& A, const MatrixType& B, bool computeQZ = true) :
+ m_S(A.rows(),A.cols()),
+ m_T(A.rows(),A.cols()),
+ m_Q(A.rows(),A.cols()),
+ m_Z(A.rows(),A.cols()),
+ m_workspace(A.rows()*2),
+ m_maxIters(400),
+ m_isInitialized(false),
+ m_computeQZ(true)
+ {
+ compute(A, B, computeQZ);
+ }
+
+ /** \brief Returns matrix Q in the QZ decomposition.
+ *
+ * \returns A const reference to the matrix Q.
+ */
+ const MatrixType& matrixQ() const {
+ eigen_assert(m_isInitialized && "RealQZ is not initialized.");
+ eigen_assert(m_computeQZ && "The matrices Q and Z have not been computed during the QZ decomposition.");
+ return m_Q;
+ }
+
+ /** \brief Returns matrix Z in the QZ decomposition.
+ *
+ * \returns A const reference to the matrix Z.
+ */
+ const MatrixType& matrixZ() const {
+ eigen_assert(m_isInitialized && "RealQZ is not initialized.");
+ eigen_assert(m_computeQZ && "The matrices Q and Z have not been computed during the QZ decomposition.");
+ return m_Z;
+ }
+
+ /** \brief Returns matrix S in the QZ decomposition.
+ *
+ * \returns A const reference to the matrix S.
+ */
+ const MatrixType& matrixS() const {
+ eigen_assert(m_isInitialized && "RealQZ is not initialized.");
+ return m_S;
+ }
+
+ /** \brief Returns matrix S in the QZ decomposition.
+ *
+ * \returns A const reference to the matrix S.
+ */
+ const MatrixType& matrixT() const {
+ eigen_assert(m_isInitialized && "RealQZ is not initialized.");
+ return m_T;
+ }
+
+ /** \brief Computes QZ decomposition of given matrix.
+ *
+ * \param[in] A Matrix A.
+ * \param[in] B Matrix B.
+ * \param[in] computeQZ If false, A and Z are not computed.
+ * \returns Reference to \c *this
+ */
+ RealQZ& compute(const MatrixType& A, const MatrixType& B, bool computeQZ = true);
+
+ /** \brief Reports whether previous computation was successful.
+ *
+ * \returns \c Success if computation was successful, \c NoConvergence otherwise.
+ */
+ ComputationInfo info() const
+ {
+ eigen_assert(m_isInitialized && "RealQZ is not initialized.");
+ return m_info;
+ }
+
+ /** \brief Returns number of performed QR-like iterations.
+ */
+ Index iterations() const
+ {
+ eigen_assert(m_isInitialized && "RealQZ is not initialized.");
+ return m_global_iter;
+ }
+
+ /** Sets the maximal number of iterations allowed to converge to one eigenvalue
+ * or decouple the problem.
+ */
+ RealQZ& setMaxIterations(Index maxIters)
+ {
+ m_maxIters = maxIters;
+ return *this;
+ }
+
+ private:
+
+ MatrixType m_S, m_T, m_Q, m_Z;
+ Matrix<Scalar,Dynamic,1> m_workspace;
+ ComputationInfo m_info;
+ Index m_maxIters;
+ bool m_isInitialized;
+ bool m_computeQZ;
+ Scalar m_normOfT, m_normOfS;
+ Index m_global_iter;
+
+ typedef Matrix<Scalar,3,1> Vector3s;
+ typedef Matrix<Scalar,2,1> Vector2s;
+ typedef Matrix<Scalar,2,2> Matrix2s;
+ typedef JacobiRotation<Scalar> JRs;
+
+ void hessenbergTriangular();
+ void computeNorms();
+ Index findSmallSubdiagEntry(Index iu);
+ Index findSmallDiagEntry(Index f, Index l);
+ void splitOffTwoRows(Index i);
+ void pushDownZero(Index z, Index f, Index l);
+ void step(Index f, Index l, Index iter);
+
+ }; // RealQZ
+
+ /** \internal Reduces S and T to upper Hessenberg - triangular form */
+ template<typename MatrixType>
+ void RealQZ<MatrixType>::hessenbergTriangular()
+ {
+
+ const Index dim = m_S.cols();
+
+ // perform QR decomposition of T, overwrite T with R, save Q
+ HouseholderQR<MatrixType> qrT(m_T);
+ m_T = qrT.matrixQR();
+ m_T.template triangularView<StrictlyLower>().setZero();
+ m_Q = qrT.householderQ();
+ // overwrite S with Q* S
+ m_S.applyOnTheLeft(m_Q.adjoint());
+ // init Z as Identity
+ if (m_computeQZ)
+ m_Z = MatrixType::Identity(dim,dim);
+ // reduce S to upper Hessenberg with Givens rotations
+ for (Index j=0; j<=dim-3; j++) {
+ for (Index i=dim-1; i>=j+2; i--) {
+ JRs G;
+ // kill S(i,j)
+ if(!numext::is_exactly_zero(m_S.coeff(i, j)))
+ {
+ G.makeGivens(m_S.coeff(i-1,j), m_S.coeff(i,j), &m_S.coeffRef(i-1, j));
+ m_S.coeffRef(i,j) = Scalar(0.0);
+ m_S.rightCols(dim-j-1).applyOnTheLeft(i-1,i,G.adjoint());
+ m_T.rightCols(dim-i+1).applyOnTheLeft(i-1,i,G.adjoint());
+ // update Q
+ if (m_computeQZ)
+ m_Q.applyOnTheRight(i-1,i,G);
+ }
+ // kill T(i,i-1)
+ if(!numext::is_exactly_zero(m_T.coeff(i, i - 1)))
+ {
+ G.makeGivens(m_T.coeff(i,i), m_T.coeff(i,i-1), &m_T.coeffRef(i,i));
+ m_T.coeffRef(i,i-1) = Scalar(0.0);
+ m_S.applyOnTheRight(i,i-1,G);
+ m_T.topRows(i).applyOnTheRight(i,i-1,G);
+ // update Z
+ if (m_computeQZ)
+ m_Z.applyOnTheLeft(i,i-1,G.adjoint());
+ }
+ }
+ }
+ }
+
+ /** \internal Computes vector L1 norms of S and T when in Hessenberg-Triangular form already */
+ template<typename MatrixType>
+ inline void RealQZ<MatrixType>::computeNorms()
+ {
+ const Index size = m_S.cols();
+ m_normOfS = Scalar(0.0);
+ m_normOfT = Scalar(0.0);
+ for (Index j = 0; j < size; ++j)
+ {
+ m_normOfS += m_S.col(j).segment(0, (std::min)(size,j+2)).cwiseAbs().sum();
+ m_normOfT += m_T.row(j).segment(j, size - j).cwiseAbs().sum();
+ }
+ }
+
+
+ /** \internal Look for single small sub-diagonal element S(res, res-1) and return res (or 0) */
+ template<typename MatrixType>
+ inline Index RealQZ<MatrixType>::findSmallSubdiagEntry(Index iu)
+ {
+ using std::abs;
+ Index res = iu;
+ while (res > 0)
+ {
+ Scalar s = abs(m_S.coeff(res-1,res-1)) + abs(m_S.coeff(res,res));
+ if (numext::is_exactly_zero(s))
+ s = m_normOfS;
+ if (abs(m_S.coeff(res,res-1)) < NumTraits<Scalar>::epsilon() * s)
+ break;
+ res--;
+ }
+ return res;
+ }
+
+ /** \internal Look for single small diagonal element T(res, res) for res between f and l, and return res (or f-1) */
+ template<typename MatrixType>
+ inline Index RealQZ<MatrixType>::findSmallDiagEntry(Index f, Index l)
+ {
+ using std::abs;
+ Index res = l;
+ while (res >= f) {
+ if (abs(m_T.coeff(res,res)) <= NumTraits<Scalar>::epsilon() * m_normOfT)
+ break;
+ res--;
+ }
+ return res;
+ }
+
+ /** \internal decouple 2x2 diagonal block in rows i, i+1 if eigenvalues are real */
+ template<typename MatrixType>
+ inline void RealQZ<MatrixType>::splitOffTwoRows(Index i)
+ {
+ using std::abs;
+ using std::sqrt;
+ const Index dim=m_S.cols();
+ if (numext::is_exactly_zero(abs(m_S.coeff(i + 1, i))))
+ return;
+ Index j = findSmallDiagEntry(i,i+1);
+ if (j==i-1)
+ {
+ // block of (S T^{-1})
+ Matrix2s STi = m_T.template block<2,2>(i,i).template triangularView<Upper>().
+ template solve<OnTheRight>(m_S.template block<2,2>(i,i));
+ Scalar p = Scalar(0.5)*(STi(0,0)-STi(1,1));
+ Scalar q = p*p + STi(1,0)*STi(0,1);
+ if (q>=0) {
+ Scalar z = sqrt(q);
+ // one QR-like iteration for ABi - lambda I
+ // is enough - when we know exact eigenvalue in advance,
+ // convergence is immediate
+ JRs G;
+ if (p>=0)
+ G.makeGivens(p + z, STi(1,0));
+ else
+ G.makeGivens(p - z, STi(1,0));
+ m_S.rightCols(dim-i).applyOnTheLeft(i,i+1,G.adjoint());
+ m_T.rightCols(dim-i).applyOnTheLeft(i,i+1,G.adjoint());
+ // update Q
+ if (m_computeQZ)
+ m_Q.applyOnTheRight(i,i+1,G);
+
+ G.makeGivens(m_T.coeff(i+1,i+1), m_T.coeff(i+1,i));
+ m_S.topRows(i+2).applyOnTheRight(i+1,i,G);
+ m_T.topRows(i+2).applyOnTheRight(i+1,i,G);
+ // update Z
+ if (m_computeQZ)
+ m_Z.applyOnTheLeft(i+1,i,G.adjoint());
+
+ m_S.coeffRef(i+1,i) = Scalar(0.0);
+ m_T.coeffRef(i+1,i) = Scalar(0.0);
+ }
+ }
+ else
+ {
+ pushDownZero(j,i,i+1);
+ }
+ }
+
+ /** \internal use zero in T(z,z) to zero S(l,l-1), working in block f..l */
+ template<typename MatrixType>
+ inline void RealQZ<MatrixType>::pushDownZero(Index z, Index f, Index l)
+ {
+ JRs G;
+ const Index dim = m_S.cols();
+ for (Index zz=z; zz<l; zz++)
+ {
+ // push 0 down
+ Index firstColS = zz>f ? (zz-1) : zz;
+ G.makeGivens(m_T.coeff(zz, zz+1), m_T.coeff(zz+1, zz+1));
+ m_S.rightCols(dim-firstColS).applyOnTheLeft(zz,zz+1,G.adjoint());
+ m_T.rightCols(dim-zz).applyOnTheLeft(zz,zz+1,G.adjoint());
+ m_T.coeffRef(zz+1,zz+1) = Scalar(0.0);
+ // update Q
+ if (m_computeQZ)
+ m_Q.applyOnTheRight(zz,zz+1,G);
+ // kill S(zz+1, zz-1)
+ if (zz>f)
+ {
+ G.makeGivens(m_S.coeff(zz+1, zz), m_S.coeff(zz+1,zz-1));
+ m_S.topRows(zz+2).applyOnTheRight(zz, zz-1,G);
+ m_T.topRows(zz+1).applyOnTheRight(zz, zz-1,G);
+ m_S.coeffRef(zz+1,zz-1) = Scalar(0.0);
+ // update Z
+ if (m_computeQZ)
+ m_Z.applyOnTheLeft(zz,zz-1,G.adjoint());
+ }
+ }
+ // finally kill S(l,l-1)
+ G.makeGivens(m_S.coeff(l,l), m_S.coeff(l,l-1));
+ m_S.applyOnTheRight(l,l-1,G);
+ m_T.applyOnTheRight(l,l-1,G);
+ m_S.coeffRef(l,l-1)=Scalar(0.0);
+ // update Z
+ if (m_computeQZ)
+ m_Z.applyOnTheLeft(l,l-1,G.adjoint());
+ }
+
+ /** \internal QR-like iterative step for block f..l */
+ template<typename MatrixType>
+ inline void RealQZ<MatrixType>::step(Index f, Index l, Index iter)
+ {
+ using std::abs;
+ const Index dim = m_S.cols();
+
+ // x, y, z
+ Scalar x, y, z;
+ if (iter==10)
+ {
+ // Wilkinson ad hoc shift
+ const Scalar
+ a11=m_S.coeff(f+0,f+0), a12=m_S.coeff(f+0,f+1),
+ a21=m_S.coeff(f+1,f+0), a22=m_S.coeff(f+1,f+1), a32=m_S.coeff(f+2,f+1),
+ b12=m_T.coeff(f+0,f+1),
+ b11i=Scalar(1.0)/m_T.coeff(f+0,f+0),
+ b22i=Scalar(1.0)/m_T.coeff(f+1,f+1),
+ a87=m_S.coeff(l-1,l-2),
+ a98=m_S.coeff(l-0,l-1),
+ b77i=Scalar(1.0)/m_T.coeff(l-2,l-2),
+ b88i=Scalar(1.0)/m_T.coeff(l-1,l-1);
+ Scalar ss = abs(a87*b77i) + abs(a98*b88i),
+ lpl = Scalar(1.5)*ss,
+ ll = ss*ss;
+ x = ll + a11*a11*b11i*b11i - lpl*a11*b11i + a12*a21*b11i*b22i
+ - a11*a21*b12*b11i*b11i*b22i;
+ y = a11*a21*b11i*b11i - lpl*a21*b11i + a21*a22*b11i*b22i
+ - a21*a21*b12*b11i*b11i*b22i;
+ z = a21*a32*b11i*b22i;
+ }
+ else if (iter==16)
+ {
+ // another exceptional shift
+ x = m_S.coeff(f,f)/m_T.coeff(f,f)-m_S.coeff(l,l)/m_T.coeff(l,l) + m_S.coeff(l,l-1)*m_T.coeff(l-1,l) /
+ (m_T.coeff(l-1,l-1)*m_T.coeff(l,l));
+ y = m_S.coeff(f+1,f)/m_T.coeff(f,f);
+ z = 0;
+ }
+ else if (iter>23 && !(iter%8))
+ {
+ // extremely exceptional shift
+ x = internal::random<Scalar>(-1.0,1.0);
+ y = internal::random<Scalar>(-1.0,1.0);
+ z = internal::random<Scalar>(-1.0,1.0);
+ }
+ else
+ {
+ // Compute the shifts: (x,y,z,0...) = (AB^-1 - l1 I) (AB^-1 - l2 I) e1
+ // where l1 and l2 are the eigenvalues of the 2x2 matrix C = U V^-1 where
+ // U and V are 2x2 bottom right sub matrices of A and B. Thus:
+ // = AB^-1AB^-1 + l1 l2 I - (l1+l2)(AB^-1)
+ // = AB^-1AB^-1 + det(M) - tr(M)(AB^-1)
+ // Since we are only interested in having x, y, z with a correct ratio, we have:
+ const Scalar
+ a11 = m_S.coeff(f,f), a12 = m_S.coeff(f,f+1),
+ a21 = m_S.coeff(f+1,f), a22 = m_S.coeff(f+1,f+1),
+ a32 = m_S.coeff(f+2,f+1),
+
+ a88 = m_S.coeff(l-1,l-1), a89 = m_S.coeff(l-1,l),
+ a98 = m_S.coeff(l,l-1), a99 = m_S.coeff(l,l),
+
+ b11 = m_T.coeff(f,f), b12 = m_T.coeff(f,f+1),
+ b22 = m_T.coeff(f+1,f+1),
+
+ b88 = m_T.coeff(l-1,l-1), b89 = m_T.coeff(l-1,l),
+ b99 = m_T.coeff(l,l);
+
+ x = ( (a88/b88 - a11/b11)*(a99/b99 - a11/b11) - (a89/b99)*(a98/b88) + (a98/b88)*(b89/b99)*(a11/b11) ) * (b11/a21)
+ + a12/b22 - (a11/b11)*(b12/b22);
+ y = (a22/b22-a11/b11) - (a21/b11)*(b12/b22) - (a88/b88-a11/b11) - (a99/b99-a11/b11) + (a98/b88)*(b89/b99);
+ z = a32/b22;
+ }
+
+ JRs G;
+
+ for (Index k=f; k<=l-2; k++)
+ {
+ // variables for Householder reflections
+ Vector2s essential2;
+ Scalar tau, beta;
+
+ Vector3s hr(x,y,z);
+
+ // Q_k to annihilate S(k+1,k-1) and S(k+2,k-1)
+ hr.makeHouseholderInPlace(tau, beta);
+ essential2 = hr.template bottomRows<2>();
+ Index fc=(std::max)(k-1,Index(0)); // first col to update
+ m_S.template middleRows<3>(k).rightCols(dim-fc).applyHouseholderOnTheLeft(essential2, tau, m_workspace.data());
+ m_T.template middleRows<3>(k).rightCols(dim-fc).applyHouseholderOnTheLeft(essential2, tau, m_workspace.data());
+ if (m_computeQZ)
+ m_Q.template middleCols<3>(k).applyHouseholderOnTheRight(essential2, tau, m_workspace.data());
+ if (k>f)
+ m_S.coeffRef(k+2,k-1) = m_S.coeffRef(k+1,k-1) = Scalar(0.0);
+
+ // Z_{k1} to annihilate T(k+2,k+1) and T(k+2,k)
+ hr << m_T.coeff(k+2,k+2),m_T.coeff(k+2,k),m_T.coeff(k+2,k+1);
+ hr.makeHouseholderInPlace(tau, beta);
+ essential2 = hr.template bottomRows<2>();
+ {
+ Index lr = (std::min)(k+4,dim); // last row to update
+ Map<Matrix<Scalar,Dynamic,1> > tmp(m_workspace.data(),lr);
+ // S
+ tmp = m_S.template middleCols<2>(k).topRows(lr) * essential2;
+ tmp += m_S.col(k+2).head(lr);
+ m_S.col(k+2).head(lr) -= tau*tmp;
+ m_S.template middleCols<2>(k).topRows(lr) -= (tau*tmp) * essential2.adjoint();
+ // T
+ tmp = m_T.template middleCols<2>(k).topRows(lr) * essential2;
+ tmp += m_T.col(k+2).head(lr);
+ m_T.col(k+2).head(lr) -= tau*tmp;
+ m_T.template middleCols<2>(k).topRows(lr) -= (tau*tmp) * essential2.adjoint();
+ }
+ if (m_computeQZ)
+ {
+ // Z
+ Map<Matrix<Scalar,1,Dynamic> > tmp(m_workspace.data(),dim);
+ tmp = essential2.adjoint()*(m_Z.template middleRows<2>(k));
+ tmp += m_Z.row(k+2);
+ m_Z.row(k+2) -= tau*tmp;
+ m_Z.template middleRows<2>(k) -= essential2 * (tau*tmp);
+ }
+ m_T.coeffRef(k+2,k) = m_T.coeffRef(k+2,k+1) = Scalar(0.0);
+
+ // Z_{k2} to annihilate T(k+1,k)
+ G.makeGivens(m_T.coeff(k+1,k+1), m_T.coeff(k+1,k));
+ m_S.applyOnTheRight(k+1,k,G);
+ m_T.applyOnTheRight(k+1,k,G);
+ // update Z
+ if (m_computeQZ)
+ m_Z.applyOnTheLeft(k+1,k,G.adjoint());
+ m_T.coeffRef(k+1,k) = Scalar(0.0);
+
+ // update x,y,z
+ x = m_S.coeff(k+1,k);
+ y = m_S.coeff(k+2,k);
+ if (k < l-2)
+ z = m_S.coeff(k+3,k);
+ } // loop over k
+
+ // Q_{n-1} to annihilate y = S(l,l-2)
+ G.makeGivens(x,y);
+ m_S.applyOnTheLeft(l-1,l,G.adjoint());
+ m_T.applyOnTheLeft(l-1,l,G.adjoint());
+ if (m_computeQZ)
+ m_Q.applyOnTheRight(l-1,l,G);
+ m_S.coeffRef(l,l-2) = Scalar(0.0);
+
+ // Z_{n-1} to annihilate T(l,l-1)
+ G.makeGivens(m_T.coeff(l,l),m_T.coeff(l,l-1));
+ m_S.applyOnTheRight(l,l-1,G);
+ m_T.applyOnTheRight(l,l-1,G);
+ if (m_computeQZ)
+ m_Z.applyOnTheLeft(l,l-1,G.adjoint());
+ m_T.coeffRef(l,l-1) = Scalar(0.0);
+ }
+
+ template<typename MatrixType>
+ RealQZ<MatrixType>& RealQZ<MatrixType>::compute(const MatrixType& A_in, const MatrixType& B_in, bool computeQZ)
+ {
+
+ const Index dim = A_in.cols();
+
+ eigen_assert (A_in.rows()==dim && A_in.cols()==dim
+ && B_in.rows()==dim && B_in.cols()==dim
+ && "Need square matrices of the same dimension");
+
+ m_isInitialized = true;
+ m_computeQZ = computeQZ;
+ m_S = A_in; m_T = B_in;
+ m_workspace.resize(dim*2);
+ m_global_iter = 0;
+
+ // entrance point: hessenberg triangular decomposition
+ hessenbergTriangular();
+ // compute L1 vector norms of T, S into m_normOfS, m_normOfT
+ computeNorms();
+
+ Index l = dim-1,
+ f,
+ local_iter = 0;
+
+ while (l>0 && local_iter<m_maxIters)
+ {
+ f = findSmallSubdiagEntry(l);
+ // now rows and columns f..l (including) decouple from the rest of the problem
+ if (f>0) m_S.coeffRef(f,f-1) = Scalar(0.0);
+ if (f == l) // One root found
+ {
+ l--;
+ local_iter = 0;
+ }
+ else if (f == l-1) // Two roots found
+ {
+ splitOffTwoRows(f);
+ l -= 2;
+ local_iter = 0;
+ }
+ else // No convergence yet
+ {
+ // if there's zero on diagonal of T, we can isolate an eigenvalue with Givens rotations
+ Index z = findSmallDiagEntry(f,l);
+ if (z>=f)
+ {
+ // zero found
+ pushDownZero(z,f,l);
+ }
+ else
+ {
+ // We are sure now that S.block(f,f, l-f+1,l-f+1) is underuced upper-Hessenberg
+ // and T.block(f,f, l-f+1,l-f+1) is invertible uper-triangular, which allows to
+ // apply a QR-like iteration to rows and columns f..l.
+ step(f,l, local_iter);
+ local_iter++;
+ m_global_iter++;
+ }
+ }
+ }
+ // check if we converged before reaching iterations limit
+ m_info = (local_iter<m_maxIters) ? Success : NoConvergence;
+
+ // For each non triangular 2x2 diagonal block of S,
+ // reduce the respective 2x2 diagonal block of T to positive diagonal form using 2x2 SVD.
+ // This step is not mandatory for QZ, but it does help further extraction of eigenvalues/eigenvectors,
+ // and is in par with Lapack/Matlab QZ.
+ if(m_info==Success)
+ {
+ for(Index i=0; i<dim-1; ++i)
+ {
+ if(!numext::is_exactly_zero(m_S.coeff(i + 1, i)))
+ {
+ JacobiRotation<Scalar> j_left, j_right;
+ internal::real_2x2_jacobi_svd(m_T, i, i+1, &j_left, &j_right);
+
+ // Apply resulting Jacobi rotations
+ m_S.applyOnTheLeft(i,i+1,j_left);
+ m_S.applyOnTheRight(i,i+1,j_right);
+ m_T.applyOnTheLeft(i,i+1,j_left);
+ m_T.applyOnTheRight(i,i+1,j_right);
+ m_T(i+1,i) = m_T(i,i+1) = Scalar(0);
+
+ if(m_computeQZ) {
+ m_Q.applyOnTheRight(i,i+1,j_left.transpose());
+ m_Z.applyOnTheLeft(i,i+1,j_right.transpose());
+ }
+
+ i++;
+ }
+ }
+ }
+
+ return *this;
+ } // end compute
+
+} // end namespace Eigen
+
+#endif //EIGEN_REAL_QZ
diff --git a/Eigen/src/Eigenvalues/RealSchur.h b/Eigen/src/Eigenvalues/RealSchur.h
new file mode 100644
index 0000000..9817666
--- /dev/null
+++ b/Eigen/src/Eigenvalues/RealSchur.h
@@ -0,0 +1,560 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2010,2012 Jitse Niesen <jitse@maths.leeds.ac.uk>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_REAL_SCHUR_H
+#define EIGEN_REAL_SCHUR_H
+
+#include "./HessenbergDecomposition.h"
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+/** \eigenvalues_module \ingroup Eigenvalues_Module
+ *
+ *
+ * \class RealSchur
+ *
+ * \brief Performs a real Schur decomposition of a square matrix
+ *
+ * \tparam MatrixType_ the type of the matrix of which we are computing the
+ * real Schur decomposition; this is expected to be an instantiation of the
+ * Matrix class template.
+ *
+ * Given a real square matrix A, this class computes the real Schur
+ * decomposition: \f$ A = U T U^T \f$ where U is a real orthogonal matrix and
+ * T is a real quasi-triangular matrix. An orthogonal matrix is a matrix whose
+ * inverse is equal to its transpose, \f$ U^{-1} = U^T \f$. A quasi-triangular
+ * matrix is a block-triangular matrix whose diagonal consists of 1-by-1
+ * blocks and 2-by-2 blocks with complex eigenvalues. The eigenvalues of the
+ * blocks on the diagonal of T are the same as the eigenvalues of the matrix
+ * A, and thus the real Schur decomposition is used in EigenSolver to compute
+ * the eigendecomposition of a matrix.
+ *
+ * Call the function compute() to compute the real Schur decomposition of a
+ * given matrix. Alternatively, you can use the RealSchur(const MatrixType&, bool)
+ * constructor which computes the real Schur decomposition at construction
+ * time. Once the decomposition is computed, you can use the matrixU() and
+ * matrixT() functions to retrieve the matrices U and T in the decomposition.
+ *
+ * The documentation of RealSchur(const MatrixType&, bool) contains an example
+ * of the typical use of this class.
+ *
+ * \note The implementation is adapted from
+ * <a href="http://math.nist.gov/javanumerics/jama/">JAMA</a> (public domain).
+ * Their code is based on EISPACK.
+ *
+ * \sa class ComplexSchur, class EigenSolver, class ComplexEigenSolver
+ */
+template<typename MatrixType_> class RealSchur
+{
+ public:
+ typedef MatrixType_ MatrixType;
+ enum {
+ RowsAtCompileTime = MatrixType::RowsAtCompileTime,
+ ColsAtCompileTime = MatrixType::ColsAtCompileTime,
+ Options = MatrixType::Options,
+ MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime,
+ MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime
+ };
+ typedef typename MatrixType::Scalar Scalar;
+ typedef std::complex<typename NumTraits<Scalar>::Real> ComplexScalar;
+ typedef Eigen::Index Index; ///< \deprecated since Eigen 3.3
+
+ typedef Matrix<ComplexScalar, ColsAtCompileTime, 1, Options & ~RowMajor, MaxColsAtCompileTime, 1> EigenvalueType;
+ typedef Matrix<Scalar, ColsAtCompileTime, 1, Options & ~RowMajor, MaxColsAtCompileTime, 1> ColumnVectorType;
+
+ /** \brief Default constructor.
+ *
+ * \param [in] size Positive integer, size of the matrix whose Schur decomposition will be computed.
+ *
+ * The default constructor is useful in cases in which the user intends to
+ * perform decompositions via compute(). The \p size parameter is only
+ * used as a hint. It is not an error to give a wrong \p size, but it may
+ * impair performance.
+ *
+ * \sa compute() for an example.
+ */
+ explicit RealSchur(Index size = RowsAtCompileTime==Dynamic ? 1 : RowsAtCompileTime)
+ : m_matT(size, size),
+ m_matU(size, size),
+ m_workspaceVector(size),
+ m_hess(size),
+ m_isInitialized(false),
+ m_matUisUptodate(false),
+ m_maxIters(-1)
+ { }
+
+ /** \brief Constructor; computes real Schur decomposition of given matrix.
+ *
+ * \param[in] matrix Square matrix whose Schur decomposition is to be computed.
+ * \param[in] computeU If true, both T and U are computed; if false, only T is computed.
+ *
+ * This constructor calls compute() to compute the Schur decomposition.
+ *
+ * Example: \include RealSchur_RealSchur_MatrixType.cpp
+ * Output: \verbinclude RealSchur_RealSchur_MatrixType.out
+ */
+ template<typename InputType>
+ explicit RealSchur(const EigenBase<InputType>& matrix, bool computeU = true)
+ : m_matT(matrix.rows(),matrix.cols()),
+ m_matU(matrix.rows(),matrix.cols()),
+ m_workspaceVector(matrix.rows()),
+ m_hess(matrix.rows()),
+ m_isInitialized(false),
+ m_matUisUptodate(false),
+ m_maxIters(-1)
+ {
+ compute(matrix.derived(), computeU);
+ }
+
+ /** \brief Returns the orthogonal matrix in the Schur decomposition.
+ *
+ * \returns A const reference to the matrix U.
+ *
+ * \pre Either the constructor RealSchur(const MatrixType&, bool) or the
+ * member function compute(const MatrixType&, bool) has been called before
+ * to compute the Schur decomposition of a matrix, and \p computeU was set
+ * to true (the default value).
+ *
+ * \sa RealSchur(const MatrixType&, bool) for an example
+ */
+ const MatrixType& matrixU() const
+ {
+ eigen_assert(m_isInitialized && "RealSchur is not initialized.");
+ eigen_assert(m_matUisUptodate && "The matrix U has not been computed during the RealSchur decomposition.");
+ return m_matU;
+ }
+
+ /** \brief Returns the quasi-triangular matrix in the Schur decomposition.
+ *
+ * \returns A const reference to the matrix T.
+ *
+ * \pre Either the constructor RealSchur(const MatrixType&, bool) or the
+ * member function compute(const MatrixType&, bool) has been called before
+ * to compute the Schur decomposition of a matrix.
+ *
+ * \sa RealSchur(const MatrixType&, bool) for an example
+ */
+ const MatrixType& matrixT() const
+ {
+ eigen_assert(m_isInitialized && "RealSchur is not initialized.");
+ return m_matT;
+ }
+
+ /** \brief Computes Schur decomposition of given matrix.
+ *
+ * \param[in] matrix Square matrix whose Schur decomposition is to be computed.
+ * \param[in] computeU If true, both T and U are computed; if false, only T is computed.
+ * \returns Reference to \c *this
+ *
+ * The Schur decomposition is computed by first reducing the matrix to
+ * Hessenberg form using the class HessenbergDecomposition. The Hessenberg
+ * matrix is then reduced to triangular form by performing Francis QR
+ * iterations with implicit double shift. The cost of computing the Schur
+ * decomposition depends on the number of iterations; as a rough guide, it
+ * may be taken to be \f$25n^3\f$ flops if \a computeU is true and
+ * \f$10n^3\f$ flops if \a computeU is false.
+ *
+ * Example: \include RealSchur_compute.cpp
+ * Output: \verbinclude RealSchur_compute.out
+ *
+ * \sa compute(const MatrixType&, bool, Index)
+ */
+ template<typename InputType>
+ RealSchur& compute(const EigenBase<InputType>& matrix, bool computeU = true);
+
+ /** \brief Computes Schur decomposition of a Hessenberg matrix H = Z T Z^T
+ * \param[in] matrixH Matrix in Hessenberg form H
+ * \param[in] matrixQ orthogonal matrix Q that transform a matrix A to H : A = Q H Q^T
+ * \param computeU Computes the matriX U of the Schur vectors
+ * \return Reference to \c *this
+ *
+ * This routine assumes that the matrix is already reduced in Hessenberg form matrixH
+ * using either the class HessenbergDecomposition or another mean.
+ * It computes the upper quasi-triangular matrix T of the Schur decomposition of H
+ * When computeU is true, this routine computes the matrix U such that
+ * A = U T U^T = (QZ) T (QZ)^T = Q H Q^T where A is the initial matrix
+ *
+ * NOTE Q is referenced if computeU is true; so, if the initial orthogonal matrix
+ * is not available, the user should give an identity matrix (Q.setIdentity())
+ *
+ * \sa compute(const MatrixType&, bool)
+ */
+ template<typename HessMatrixType, typename OrthMatrixType>
+ RealSchur& computeFromHessenberg(const HessMatrixType& matrixH, const OrthMatrixType& matrixQ, bool computeU);
+ /** \brief Reports whether previous computation was successful.
+ *
+ * \returns \c Success if computation was successful, \c NoConvergence otherwise.
+ */
+ ComputationInfo info() const
+ {
+ eigen_assert(m_isInitialized && "RealSchur is not initialized.");
+ return m_info;
+ }
+
+ /** \brief Sets the maximum number of iterations allowed.
+ *
+ * If not specified by the user, the maximum number of iterations is m_maxIterationsPerRow times the size
+ * of the matrix.
+ */
+ RealSchur& setMaxIterations(Index maxIters)
+ {
+ m_maxIters = maxIters;
+ return *this;
+ }
+
+ /** \brief Returns the maximum number of iterations. */
+ Index getMaxIterations()
+ {
+ return m_maxIters;
+ }
+
+ /** \brief Maximum number of iterations per row.
+ *
+ * If not otherwise specified, the maximum number of iterations is this number times the size of the
+ * matrix. It is currently set to 40.
+ */
+ static const int m_maxIterationsPerRow = 40;
+
+ private:
+
+ MatrixType m_matT;
+ MatrixType m_matU;
+ ColumnVectorType m_workspaceVector;
+ HessenbergDecomposition<MatrixType> m_hess;
+ ComputationInfo m_info;
+ bool m_isInitialized;
+ bool m_matUisUptodate;
+ Index m_maxIters;
+
+ typedef Matrix<Scalar,3,1> Vector3s;
+
+ Scalar computeNormOfT();
+ Index findSmallSubdiagEntry(Index iu, const Scalar& considerAsZero);
+ void splitOffTwoRows(Index iu, bool computeU, const Scalar& exshift);
+ void computeShift(Index iu, Index iter, Scalar& exshift, Vector3s& shiftInfo);
+ void initFrancisQRStep(Index il, Index iu, const Vector3s& shiftInfo, Index& im, Vector3s& firstHouseholderVector);
+ void performFrancisQRStep(Index il, Index im, Index iu, bool computeU, const Vector3s& firstHouseholderVector, Scalar* workspace);
+};
+
+
+template<typename MatrixType>
+template<typename InputType>
+RealSchur<MatrixType>& RealSchur<MatrixType>::compute(const EigenBase<InputType>& matrix, bool computeU)
+{
+ const Scalar considerAsZero = (std::numeric_limits<Scalar>::min)();
+
+ eigen_assert(matrix.cols() == matrix.rows());
+ Index maxIters = m_maxIters;
+ if (maxIters == -1)
+ maxIters = m_maxIterationsPerRow * matrix.rows();
+
+ Scalar scale = matrix.derived().cwiseAbs().maxCoeff();
+ if(scale<considerAsZero)
+ {
+ m_matT.setZero(matrix.rows(),matrix.cols());
+ if(computeU)
+ m_matU.setIdentity(matrix.rows(),matrix.cols());
+ m_info = Success;
+ m_isInitialized = true;
+ m_matUisUptodate = computeU;
+ return *this;
+ }
+
+ // Step 1. Reduce to Hessenberg form
+ m_hess.compute(matrix.derived()/scale);
+
+ // Step 2. Reduce to real Schur form
+ // Note: we copy m_hess.matrixQ() into m_matU here and not in computeFromHessenberg
+ // to be able to pass our working-space buffer for the Householder to Dense evaluation.
+ m_workspaceVector.resize(matrix.cols());
+ if(computeU)
+ m_hess.matrixQ().evalTo(m_matU, m_workspaceVector);
+ computeFromHessenberg(m_hess.matrixH(), m_matU, computeU);
+
+ m_matT *= scale;
+
+ return *this;
+}
+template<typename MatrixType>
+template<typename HessMatrixType, typename OrthMatrixType>
+RealSchur<MatrixType>& RealSchur<MatrixType>::computeFromHessenberg(const HessMatrixType& matrixH, const OrthMatrixType& matrixQ, bool computeU)
+{
+ using std::abs;
+
+ m_matT = matrixH;
+ m_workspaceVector.resize(m_matT.cols());
+ if(computeU && !internal::is_same_dense(m_matU,matrixQ))
+ m_matU = matrixQ;
+
+ Index maxIters = m_maxIters;
+ if (maxIters == -1)
+ maxIters = m_maxIterationsPerRow * matrixH.rows();
+ Scalar* workspace = &m_workspaceVector.coeffRef(0);
+
+ // The matrix m_matT is divided in three parts.
+ // Rows 0,...,il-1 are decoupled from the rest because m_matT(il,il-1) is zero.
+ // Rows il,...,iu is the part we are working on (the active window).
+ // Rows iu+1,...,end are already brought in triangular form.
+ Index iu = m_matT.cols() - 1;
+ Index iter = 0; // iteration count for current eigenvalue
+ Index totalIter = 0; // iteration count for whole matrix
+ Scalar exshift(0); // sum of exceptional shifts
+ Scalar norm = computeNormOfT();
+ // sub-diagonal entries smaller than considerAsZero will be treated as zero.
+ // We use eps^2 to enable more precision in small eigenvalues.
+ Scalar considerAsZero = numext::maxi<Scalar>( norm * numext::abs2(NumTraits<Scalar>::epsilon()),
+ (std::numeric_limits<Scalar>::min)() );
+
+ if(!numext::is_exactly_zero(norm))
+ {
+ while (iu >= 0)
+ {
+ Index il = findSmallSubdiagEntry(iu,considerAsZero);
+
+ // Check for convergence
+ if (il == iu) // One root found
+ {
+ m_matT.coeffRef(iu,iu) = m_matT.coeff(iu,iu) + exshift;
+ if (iu > 0)
+ m_matT.coeffRef(iu, iu-1) = Scalar(0);
+ iu--;
+ iter = 0;
+ }
+ else if (il == iu-1) // Two roots found
+ {
+ splitOffTwoRows(iu, computeU, exshift);
+ iu -= 2;
+ iter = 0;
+ }
+ else // No convergence yet
+ {
+ // The firstHouseholderVector vector has to be initialized to something to get rid of a silly GCC warning (-O1 -Wall -DNDEBUG )
+ Vector3s firstHouseholderVector = Vector3s::Zero(), shiftInfo;
+ computeShift(iu, iter, exshift, shiftInfo);
+ iter = iter + 1;
+ totalIter = totalIter + 1;
+ if (totalIter > maxIters) break;
+ Index im;
+ initFrancisQRStep(il, iu, shiftInfo, im, firstHouseholderVector);
+ performFrancisQRStep(il, im, iu, computeU, firstHouseholderVector, workspace);
+ }
+ }
+ }
+ if(totalIter <= maxIters)
+ m_info = Success;
+ else
+ m_info = NoConvergence;
+
+ m_isInitialized = true;
+ m_matUisUptodate = computeU;
+ return *this;
+}
+
+/** \internal Computes and returns vector L1 norm of T */
+template<typename MatrixType>
+inline typename MatrixType::Scalar RealSchur<MatrixType>::computeNormOfT()
+{
+ const Index size = m_matT.cols();
+ // FIXME to be efficient the following would requires a triangular reduxion code
+ // Scalar norm = m_matT.upper().cwiseAbs().sum()
+ // + m_matT.bottomLeftCorner(size-1,size-1).diagonal().cwiseAbs().sum();
+ Scalar norm(0);
+ for (Index j = 0; j < size; ++j)
+ norm += m_matT.col(j).segment(0, (std::min)(size,j+2)).cwiseAbs().sum();
+ return norm;
+}
+
+/** \internal Look for single small sub-diagonal element and returns its index */
+template<typename MatrixType>
+inline Index RealSchur<MatrixType>::findSmallSubdiagEntry(Index iu, const Scalar& considerAsZero)
+{
+ using std::abs;
+ Index res = iu;
+ while (res > 0)
+ {
+ Scalar s = abs(m_matT.coeff(res-1,res-1)) + abs(m_matT.coeff(res,res));
+
+ s = numext::maxi<Scalar>(s * NumTraits<Scalar>::epsilon(), considerAsZero);
+
+ if (abs(m_matT.coeff(res,res-1)) <= s)
+ break;
+ res--;
+ }
+ return res;
+}
+
+/** \internal Update T given that rows iu-1 and iu decouple from the rest. */
+template<typename MatrixType>
+inline void RealSchur<MatrixType>::splitOffTwoRows(Index iu, bool computeU, const Scalar& exshift)
+{
+ using std::sqrt;
+ using std::abs;
+ const Index size = m_matT.cols();
+
+ // The eigenvalues of the 2x2 matrix [a b; c d] are
+ // trace +/- sqrt(discr/4) where discr = tr^2 - 4*det, tr = a + d, det = ad - bc
+ Scalar p = Scalar(0.5) * (m_matT.coeff(iu-1,iu-1) - m_matT.coeff(iu,iu));
+ Scalar q = p * p + m_matT.coeff(iu,iu-1) * m_matT.coeff(iu-1,iu); // q = tr^2 / 4 - det = discr/4
+ m_matT.coeffRef(iu,iu) += exshift;
+ m_matT.coeffRef(iu-1,iu-1) += exshift;
+
+ if (q >= Scalar(0)) // Two real eigenvalues
+ {
+ Scalar z = sqrt(abs(q));
+ JacobiRotation<Scalar> rot;
+ if (p >= Scalar(0))
+ rot.makeGivens(p + z, m_matT.coeff(iu, iu-1));
+ else
+ rot.makeGivens(p - z, m_matT.coeff(iu, iu-1));
+
+ m_matT.rightCols(size-iu+1).applyOnTheLeft(iu-1, iu, rot.adjoint());
+ m_matT.topRows(iu+1).applyOnTheRight(iu-1, iu, rot);
+ m_matT.coeffRef(iu, iu-1) = Scalar(0);
+ if (computeU)
+ m_matU.applyOnTheRight(iu-1, iu, rot);
+ }
+
+ if (iu > 1)
+ m_matT.coeffRef(iu-1, iu-2) = Scalar(0);
+}
+
+/** \internal Form shift in shiftInfo, and update exshift if an exceptional shift is performed. */
+template<typename MatrixType>
+inline void RealSchur<MatrixType>::computeShift(Index iu, Index iter, Scalar& exshift, Vector3s& shiftInfo)
+{
+ using std::sqrt;
+ using std::abs;
+ shiftInfo.coeffRef(0) = m_matT.coeff(iu,iu);
+ shiftInfo.coeffRef(1) = m_matT.coeff(iu-1,iu-1);
+ shiftInfo.coeffRef(2) = m_matT.coeff(iu,iu-1) * m_matT.coeff(iu-1,iu);
+
+ // Wilkinson's original ad hoc shift
+ if (iter == 10)
+ {
+ exshift += shiftInfo.coeff(0);
+ for (Index i = 0; i <= iu; ++i)
+ m_matT.coeffRef(i,i) -= shiftInfo.coeff(0);
+ Scalar s = abs(m_matT.coeff(iu,iu-1)) + abs(m_matT.coeff(iu-1,iu-2));
+ shiftInfo.coeffRef(0) = Scalar(0.75) * s;
+ shiftInfo.coeffRef(1) = Scalar(0.75) * s;
+ shiftInfo.coeffRef(2) = Scalar(-0.4375) * s * s;
+ }
+
+ // MATLAB's new ad hoc shift
+ if (iter == 30)
+ {
+ Scalar s = (shiftInfo.coeff(1) - shiftInfo.coeff(0)) / Scalar(2.0);
+ s = s * s + shiftInfo.coeff(2);
+ if (s > Scalar(0))
+ {
+ s = sqrt(s);
+ if (shiftInfo.coeff(1) < shiftInfo.coeff(0))
+ s = -s;
+ s = s + (shiftInfo.coeff(1) - shiftInfo.coeff(0)) / Scalar(2.0);
+ s = shiftInfo.coeff(0) - shiftInfo.coeff(2) / s;
+ exshift += s;
+ for (Index i = 0; i <= iu; ++i)
+ m_matT.coeffRef(i,i) -= s;
+ shiftInfo.setConstant(Scalar(0.964));
+ }
+ }
+}
+
+/** \internal Compute index im at which Francis QR step starts and the first Householder vector. */
+template<typename MatrixType>
+inline void RealSchur<MatrixType>::initFrancisQRStep(Index il, Index iu, const Vector3s& shiftInfo, Index& im, Vector3s& firstHouseholderVector)
+{
+ using std::abs;
+ Vector3s& v = firstHouseholderVector; // alias to save typing
+
+ for (im = iu-2; im >= il; --im)
+ {
+ const Scalar Tmm = m_matT.coeff(im,im);
+ const Scalar r = shiftInfo.coeff(0) - Tmm;
+ const Scalar s = shiftInfo.coeff(1) - Tmm;
+ v.coeffRef(0) = (r * s - shiftInfo.coeff(2)) / m_matT.coeff(im+1,im) + m_matT.coeff(im,im+1);
+ v.coeffRef(1) = m_matT.coeff(im+1,im+1) - Tmm - r - s;
+ v.coeffRef(2) = m_matT.coeff(im+2,im+1);
+ if (im == il) {
+ break;
+ }
+ const Scalar lhs = m_matT.coeff(im,im-1) * (abs(v.coeff(1)) + abs(v.coeff(2)));
+ const Scalar rhs = v.coeff(0) * (abs(m_matT.coeff(im-1,im-1)) + abs(Tmm) + abs(m_matT.coeff(im+1,im+1)));
+ if (abs(lhs) < NumTraits<Scalar>::epsilon() * rhs)
+ break;
+ }
+}
+
+/** \internal Perform a Francis QR step involving rows il:iu and columns im:iu. */
+template<typename MatrixType>
+inline void RealSchur<MatrixType>::performFrancisQRStep(Index il, Index im, Index iu, bool computeU, const Vector3s& firstHouseholderVector, Scalar* workspace)
+{
+ eigen_assert(im >= il);
+ eigen_assert(im <= iu-2);
+
+ const Index size = m_matT.cols();
+
+ for (Index k = im; k <= iu-2; ++k)
+ {
+ bool firstIteration = (k == im);
+
+ Vector3s v;
+ if (firstIteration)
+ v = firstHouseholderVector;
+ else
+ v = m_matT.template block<3,1>(k,k-1);
+
+ Scalar tau, beta;
+ Matrix<Scalar, 2, 1> ess;
+ v.makeHouseholder(ess, tau, beta);
+
+ if (!numext::is_exactly_zero(beta)) // if v is not zero
+ {
+ if (firstIteration && k > il)
+ m_matT.coeffRef(k,k-1) = -m_matT.coeff(k,k-1);
+ else if (!firstIteration)
+ m_matT.coeffRef(k,k-1) = beta;
+
+ // These Householder transformations form the O(n^3) part of the algorithm
+ m_matT.block(k, k, 3, size-k).applyHouseholderOnTheLeft(ess, tau, workspace);
+ m_matT.block(0, k, (std::min)(iu,k+3) + 1, 3).applyHouseholderOnTheRight(ess, tau, workspace);
+ if (computeU)
+ m_matU.block(0, k, size, 3).applyHouseholderOnTheRight(ess, tau, workspace);
+ }
+ }
+
+ Matrix<Scalar, 2, 1> v = m_matT.template block<2,1>(iu-1, iu-2);
+ Scalar tau, beta;
+ Matrix<Scalar, 1, 1> ess;
+ v.makeHouseholder(ess, tau, beta);
+
+ if (!numext::is_exactly_zero(beta)) // if v is not zero
+ {
+ m_matT.coeffRef(iu-1, iu-2) = beta;
+ m_matT.block(iu-1, iu-1, 2, size-iu+1).applyHouseholderOnTheLeft(ess, tau, workspace);
+ m_matT.block(0, iu-1, iu+1, 2).applyHouseholderOnTheRight(ess, tau, workspace);
+ if (computeU)
+ m_matU.block(0, iu-1, size, 2).applyHouseholderOnTheRight(ess, tau, workspace);
+ }
+
+ // clean up pollution due to round-off errors
+ for (Index i = im+2; i <= iu; ++i)
+ {
+ m_matT.coeffRef(i,i-2) = Scalar(0);
+ if (i > im+2)
+ m_matT.coeffRef(i,i-3) = Scalar(0);
+ }
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_REAL_SCHUR_H
diff --git a/Eigen/src/Eigenvalues/RealSchur_LAPACKE.h b/Eigen/src/Eigenvalues/RealSchur_LAPACKE.h
new file mode 100644
index 0000000..0a6ed21
--- /dev/null
+++ b/Eigen/src/Eigenvalues/RealSchur_LAPACKE.h
@@ -0,0 +1,79 @@
+/*
+ Copyright (c) 2011, Intel Corporation. All rights reserved.
+
+ Redistribution and use in source and binary forms, with or without modification,
+ are permitted provided that the following conditions are met:
+
+ * Redistributions of source code must retain the above copyright notice, this
+ list of conditions and the following disclaimer.
+ * Redistributions in binary form must reproduce the above copyright notice,
+ this list of conditions and the following disclaimer in the documentation
+ and/or other materials provided with the distribution.
+ * Neither the name of Intel Corporation nor the names of its contributors may
+ be used to endorse or promote products derived from this software without
+ specific prior written permission.
+
+ THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
+ ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
+ WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
+ DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR
+ ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
+ (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
+ LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON
+ ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
+ (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
+ SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+
+ ********************************************************************************
+ * Content : Eigen bindings to LAPACKe
+ * Real Schur needed to real unsymmetrical eigenvalues/eigenvectors.
+ ********************************************************************************
+*/
+
+#ifndef EIGEN_REAL_SCHUR_LAPACKE_H
+#define EIGEN_REAL_SCHUR_LAPACKE_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+/** \internal Specialization for the data types supported by LAPACKe */
+
+#define EIGEN_LAPACKE_SCHUR_REAL(EIGTYPE, LAPACKE_TYPE, LAPACKE_PREFIX, LAPACKE_PREFIX_U, EIGCOLROW, LAPACKE_COLROW) \
+template<> template<typename InputType> inline \
+RealSchur<Matrix<EIGTYPE, Dynamic, Dynamic, EIGCOLROW> >& \
+RealSchur<Matrix<EIGTYPE, Dynamic, Dynamic, EIGCOLROW> >::compute(const EigenBase<InputType>& matrix, bool computeU) \
+{ \
+ eigen_assert(matrix.cols() == matrix.rows()); \
+\
+ lapack_int n = internal::convert_index<lapack_int>(matrix.cols()), sdim, info; \
+ lapack_int matrix_order = LAPACKE_COLROW; \
+ char jobvs, sort='N'; \
+ LAPACK_##LAPACKE_PREFIX_U##_SELECT2 select = 0; \
+ jobvs = (computeU) ? 'V' : 'N'; \
+ m_matU.resize(n, n); \
+ lapack_int ldvs = internal::convert_index<lapack_int>(m_matU.outerStride()); \
+ m_matT = matrix; \
+ lapack_int lda = internal::convert_index<lapack_int>(m_matT.outerStride()); \
+ Matrix<EIGTYPE, Dynamic, Dynamic> wr, wi; \
+ wr.resize(n, 1); wi.resize(n, 1); \
+ info = LAPACKE_##LAPACKE_PREFIX##gees( matrix_order, jobvs, sort, select, n, (LAPACKE_TYPE*)m_matT.data(), lda, &sdim, (LAPACKE_TYPE*)wr.data(), (LAPACKE_TYPE*)wi.data(), (LAPACKE_TYPE*)m_matU.data(), ldvs ); \
+ if(info == 0) \
+ m_info = Success; \
+ else \
+ m_info = NoConvergence; \
+\
+ m_isInitialized = true; \
+ m_matUisUptodate = computeU; \
+ return *this; \
+\
+}
+
+EIGEN_LAPACKE_SCHUR_REAL(double, double, d, D, ColMajor, LAPACK_COL_MAJOR)
+EIGEN_LAPACKE_SCHUR_REAL(float, float, s, S, ColMajor, LAPACK_COL_MAJOR)
+EIGEN_LAPACKE_SCHUR_REAL(double, double, d, D, RowMajor, LAPACK_ROW_MAJOR)
+EIGEN_LAPACKE_SCHUR_REAL(float, float, s, S, RowMajor, LAPACK_ROW_MAJOR)
+
+} // end namespace Eigen
+
+#endif // EIGEN_REAL_SCHUR_LAPACKE_H
diff --git a/Eigen/src/Eigenvalues/SelfAdjointEigenSolver.h b/Eigen/src/Eigenvalues/SelfAdjointEigenSolver.h
new file mode 100644
index 0000000..d196ec0
--- /dev/null
+++ b/Eigen/src/Eigenvalues/SelfAdjointEigenSolver.h
@@ -0,0 +1,900 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2010 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2010 Jitse Niesen <jitse@maths.leeds.ac.uk>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_SELFADJOINTEIGENSOLVER_H
+#define EIGEN_SELFADJOINTEIGENSOLVER_H
+
+#include "./Tridiagonalization.h"
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+template<typename MatrixType_>
+class GeneralizedSelfAdjointEigenSolver;
+
+namespace internal {
+template<typename SolverType,int Size,bool IsComplex> struct direct_selfadjoint_eigenvalues;
+
+template<typename MatrixType, typename DiagType, typename SubDiagType>
+EIGEN_DEVICE_FUNC
+ComputationInfo computeFromTridiagonal_impl(DiagType& diag, SubDiagType& subdiag, const Index maxIterations, bool computeEigenvectors, MatrixType& eivec);
+}
+
+/** \eigenvalues_module \ingroup Eigenvalues_Module
+ *
+ *
+ * \class SelfAdjointEigenSolver
+ *
+ * \brief Computes eigenvalues and eigenvectors of selfadjoint matrices
+ *
+ * \tparam MatrixType_ the type of the matrix of which we are computing the
+ * eigendecomposition; this is expected to be an instantiation of the Matrix
+ * class template.
+ *
+ * A matrix \f$ A \f$ is selfadjoint if it equals its adjoint. For real
+ * matrices, this means that the matrix is symmetric: it equals its
+ * transpose. This class computes the eigenvalues and eigenvectors of a
+ * selfadjoint matrix. These are the scalars \f$ \lambda \f$ and vectors
+ * \f$ v \f$ such that \f$ Av = \lambda v \f$. The eigenvalues of a
+ * selfadjoint matrix are always real. If \f$ D \f$ is a diagonal matrix with
+ * the eigenvalues on the diagonal, and \f$ V \f$ is a matrix with the
+ * eigenvectors as its columns, then \f$ A = V D V^{-1} \f$. This is called the
+ * eigendecomposition.
+ *
+ * For a selfadjoint matrix, \f$ V \f$ is unitary, meaning its inverse is equal
+ * to its adjoint, \f$ V^{-1} = V^{\dagger} \f$. If \f$ A \f$ is real, then
+ * \f$ V \f$ is also real and therefore orthogonal, meaning its inverse is
+ * equal to its transpose, \f$ V^{-1} = V^T \f$.
+ *
+ * The algorithm exploits the fact that the matrix is selfadjoint, making it
+ * faster and more accurate than the general purpose eigenvalue algorithms
+ * implemented in EigenSolver and ComplexEigenSolver.
+ *
+ * Only the \b lower \b triangular \b part of the input matrix is referenced.
+ *
+ * Call the function compute() to compute the eigenvalues and eigenvectors of
+ * a given matrix. Alternatively, you can use the
+ * SelfAdjointEigenSolver(const MatrixType&, int) constructor which computes
+ * the eigenvalues and eigenvectors at construction time. Once the eigenvalue
+ * and eigenvectors are computed, they can be retrieved with the eigenvalues()
+ * and eigenvectors() functions.
+ *
+ * The documentation for SelfAdjointEigenSolver(const MatrixType&, int)
+ * contains an example of the typical use of this class.
+ *
+ * To solve the \em generalized eigenvalue problem \f$ Av = \lambda Bv \f$ and
+ * the likes, see the class GeneralizedSelfAdjointEigenSolver.
+ *
+ * \sa MatrixBase::eigenvalues(), class EigenSolver, class ComplexEigenSolver
+ */
+template<typename MatrixType_> class SelfAdjointEigenSolver
+{
+ public:
+
+ typedef MatrixType_ MatrixType;
+ enum {
+ Size = MatrixType::RowsAtCompileTime,
+ ColsAtCompileTime = MatrixType::ColsAtCompileTime,
+ Options = MatrixType::Options,
+ MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime
+ };
+
+ /** \brief Scalar type for matrices of type \p MatrixType_. */
+ typedef typename MatrixType::Scalar Scalar;
+ typedef Eigen::Index Index; ///< \deprecated since Eigen 3.3
+
+ typedef Matrix<Scalar,Size,Size,ColMajor,MaxColsAtCompileTime,MaxColsAtCompileTime> EigenvectorsType;
+
+ /** \brief Real scalar type for \p MatrixType_.
+ *
+ * This is just \c Scalar if #Scalar is real (e.g., \c float or
+ * \c double), and the type of the real part of \c Scalar if #Scalar is
+ * complex.
+ */
+ typedef typename NumTraits<Scalar>::Real RealScalar;
+
+ friend struct internal::direct_selfadjoint_eigenvalues<SelfAdjointEigenSolver,Size,NumTraits<Scalar>::IsComplex>;
+
+ /** \brief Type for vector of eigenvalues as returned by eigenvalues().
+ *
+ * This is a column vector with entries of type #RealScalar.
+ * The length of the vector is the size of \p MatrixType_.
+ */
+ typedef typename internal::plain_col_type<MatrixType, RealScalar>::type RealVectorType;
+ typedef Tridiagonalization<MatrixType> TridiagonalizationType;
+ typedef typename TridiagonalizationType::SubDiagonalType SubDiagonalType;
+
+ /** \brief Default constructor for fixed-size matrices.
+ *
+ * The default constructor is useful in cases in which the user intends to
+ * perform decompositions via compute(). This constructor
+ * can only be used if \p MatrixType_ is a fixed-size matrix; use
+ * SelfAdjointEigenSolver(Index) for dynamic-size matrices.
+ *
+ * Example: \include SelfAdjointEigenSolver_SelfAdjointEigenSolver.cpp
+ * Output: \verbinclude SelfAdjointEigenSolver_SelfAdjointEigenSolver.out
+ */
+ EIGEN_DEVICE_FUNC
+ SelfAdjointEigenSolver()
+ : m_eivec(),
+ m_eivalues(),
+ m_subdiag(),
+ m_hcoeffs(),
+ m_info(InvalidInput),
+ m_isInitialized(false),
+ m_eigenvectorsOk(false)
+ { }
+
+ /** \brief Constructor, pre-allocates memory for dynamic-size matrices.
+ *
+ * \param [in] size Positive integer, size of the matrix whose
+ * eigenvalues and eigenvectors will be computed.
+ *
+ * This constructor is useful for dynamic-size matrices, when the user
+ * intends to perform decompositions via compute(). The \p size
+ * parameter is only used as a hint. It is not an error to give a wrong
+ * \p size, but it may impair performance.
+ *
+ * \sa compute() for an example
+ */
+ EIGEN_DEVICE_FUNC
+ explicit SelfAdjointEigenSolver(Index size)
+ : m_eivec(size, size),
+ m_eivalues(size),
+ m_subdiag(size > 1 ? size - 1 : 1),
+ m_hcoeffs(size > 1 ? size - 1 : 1),
+ m_isInitialized(false),
+ m_eigenvectorsOk(false)
+ {}
+
+ /** \brief Constructor; computes eigendecomposition of given matrix.
+ *
+ * \param[in] matrix Selfadjoint matrix whose eigendecomposition is to
+ * be computed. Only the lower triangular part of the matrix is referenced.
+ * \param[in] options Can be #ComputeEigenvectors (default) or #EigenvaluesOnly.
+ *
+ * This constructor calls compute(const MatrixType&, int) to compute the
+ * eigenvalues of the matrix \p matrix. The eigenvectors are computed if
+ * \p options equals #ComputeEigenvectors.
+ *
+ * Example: \include SelfAdjointEigenSolver_SelfAdjointEigenSolver_MatrixType.cpp
+ * Output: \verbinclude SelfAdjointEigenSolver_SelfAdjointEigenSolver_MatrixType.out
+ *
+ * \sa compute(const MatrixType&, int)
+ */
+ template<typename InputType>
+ EIGEN_DEVICE_FUNC
+ explicit SelfAdjointEigenSolver(const EigenBase<InputType>& matrix, int options = ComputeEigenvectors)
+ : m_eivec(matrix.rows(), matrix.cols()),
+ m_eivalues(matrix.cols()),
+ m_subdiag(matrix.rows() > 1 ? matrix.rows() - 1 : 1),
+ m_hcoeffs(matrix.cols() > 1 ? matrix.cols() - 1 : 1),
+ m_isInitialized(false),
+ m_eigenvectorsOk(false)
+ {
+ compute(matrix.derived(), options);
+ }
+
+ /** \brief Computes eigendecomposition of given matrix.
+ *
+ * \param[in] matrix Selfadjoint matrix whose eigendecomposition is to
+ * be computed. Only the lower triangular part of the matrix is referenced.
+ * \param[in] options Can be #ComputeEigenvectors (default) or #EigenvaluesOnly.
+ * \returns Reference to \c *this
+ *
+ * This function computes the eigenvalues of \p matrix. The eigenvalues()
+ * function can be used to retrieve them. If \p options equals #ComputeEigenvectors,
+ * then the eigenvectors are also computed and can be retrieved by
+ * calling eigenvectors().
+ *
+ * This implementation uses a symmetric QR algorithm. The matrix is first
+ * reduced to tridiagonal form using the Tridiagonalization class. The
+ * tridiagonal matrix is then brought to diagonal form with implicit
+ * symmetric QR steps with Wilkinson shift. Details can be found in
+ * Section 8.3 of Golub \& Van Loan, <i>%Matrix Computations</i>.
+ *
+ * The cost of the computation is about \f$ 9n^3 \f$ if the eigenvectors
+ * are required and \f$ 4n^3/3 \f$ if they are not required.
+ *
+ * This method reuses the memory in the SelfAdjointEigenSolver object that
+ * was allocated when the object was constructed, if the size of the
+ * matrix does not change.
+ *
+ * Example: \include SelfAdjointEigenSolver_compute_MatrixType.cpp
+ * Output: \verbinclude SelfAdjointEigenSolver_compute_MatrixType.out
+ *
+ * \sa SelfAdjointEigenSolver(const MatrixType&, int)
+ */
+ template<typename InputType>
+ EIGEN_DEVICE_FUNC
+ SelfAdjointEigenSolver& compute(const EigenBase<InputType>& matrix, int options = ComputeEigenvectors);
+
+ /** \brief Computes eigendecomposition of given matrix using a closed-form algorithm
+ *
+ * This is a variant of compute(const MatrixType&, int options) which
+ * directly solves the underlying polynomial equation.
+ *
+ * Currently only 2x2 and 3x3 matrices for which the sizes are known at compile time are supported (e.g., Matrix3d).
+ *
+ * This method is usually significantly faster than the QR iterative algorithm
+ * but it might also be less accurate. It is also worth noting that
+ * for 3x3 matrices it involves trigonometric operations which are
+ * not necessarily available for all scalar types.
+ *
+ * For the 3x3 case, we observed the following worst case relative error regarding the eigenvalues:
+ * - double: 1e-8
+ * - float: 1e-3
+ *
+ * \sa compute(const MatrixType&, int options)
+ */
+ EIGEN_DEVICE_FUNC
+ SelfAdjointEigenSolver& computeDirect(const MatrixType& matrix, int options = ComputeEigenvectors);
+
+ /**
+ *\brief Computes the eigen decomposition from a tridiagonal symmetric matrix
+ *
+ * \param[in] diag The vector containing the diagonal of the matrix.
+ * \param[in] subdiag The subdiagonal of the matrix.
+ * \param[in] options Can be #ComputeEigenvectors (default) or #EigenvaluesOnly.
+ * \returns Reference to \c *this
+ *
+ * This function assumes that the matrix has been reduced to tridiagonal form.
+ *
+ * \sa compute(const MatrixType&, int) for more information
+ */
+ SelfAdjointEigenSolver& computeFromTridiagonal(const RealVectorType& diag, const SubDiagonalType& subdiag , int options=ComputeEigenvectors);
+
+ /** \brief Returns the eigenvectors of given matrix.
+ *
+ * \returns A const reference to the matrix whose columns are the eigenvectors.
+ *
+ * \pre The eigenvectors have been computed before.
+ *
+ * Column \f$ k \f$ of the returned matrix is an eigenvector corresponding
+ * to eigenvalue number \f$ k \f$ as returned by eigenvalues(). The
+ * eigenvectors are normalized to have (Euclidean) norm equal to one. If
+ * this object was used to solve the eigenproblem for the selfadjoint
+ * matrix \f$ A \f$, then the matrix returned by this function is the
+ * matrix \f$ V \f$ in the eigendecomposition \f$ A = V D V^{-1} \f$.
+ *
+ * For a selfadjoint matrix, \f$ V \f$ is unitary, meaning its inverse is equal
+ * to its adjoint, \f$ V^{-1} = V^{\dagger} \f$. If \f$ A \f$ is real, then
+ * \f$ V \f$ is also real and therefore orthogonal, meaning its inverse is
+ * equal to its transpose, \f$ V^{-1} = V^T \f$.
+ *
+ * Example: \include SelfAdjointEigenSolver_eigenvectors.cpp
+ * Output: \verbinclude SelfAdjointEigenSolver_eigenvectors.out
+ *
+ * \sa eigenvalues()
+ */
+ EIGEN_DEVICE_FUNC
+ const EigenvectorsType& eigenvectors() const
+ {
+ eigen_assert(m_isInitialized && "SelfAdjointEigenSolver is not initialized.");
+ eigen_assert(m_eigenvectorsOk && "The eigenvectors have not been computed together with the eigenvalues.");
+ return m_eivec;
+ }
+
+ /** \brief Returns the eigenvalues of given matrix.
+ *
+ * \returns A const reference to the column vector containing the eigenvalues.
+ *
+ * \pre The eigenvalues have been computed before.
+ *
+ * The eigenvalues are repeated according to their algebraic multiplicity,
+ * so there are as many eigenvalues as rows in the matrix. The eigenvalues
+ * are sorted in increasing order.
+ *
+ * Example: \include SelfAdjointEigenSolver_eigenvalues.cpp
+ * Output: \verbinclude SelfAdjointEigenSolver_eigenvalues.out
+ *
+ * \sa eigenvectors(), MatrixBase::eigenvalues()
+ */
+ EIGEN_DEVICE_FUNC
+ const RealVectorType& eigenvalues() const
+ {
+ eigen_assert(m_isInitialized && "SelfAdjointEigenSolver is not initialized.");
+ return m_eivalues;
+ }
+
+ /** \brief Computes the positive-definite square root of the matrix.
+ *
+ * \returns the positive-definite square root of the matrix
+ *
+ * \pre The eigenvalues and eigenvectors of a positive-definite matrix
+ * have been computed before.
+ *
+ * The square root of a positive-definite matrix \f$ A \f$ is the
+ * positive-definite matrix whose square equals \f$ A \f$. This function
+ * uses the eigendecomposition \f$ A = V D V^{-1} \f$ to compute the
+ * square root as \f$ A^{1/2} = V D^{1/2} V^{-1} \f$.
+ *
+ * Example: \include SelfAdjointEigenSolver_operatorSqrt.cpp
+ * Output: \verbinclude SelfAdjointEigenSolver_operatorSqrt.out
+ *
+ * \sa operatorInverseSqrt(), <a href="unsupported/group__MatrixFunctions__Module.html">MatrixFunctions Module</a>
+ */
+ EIGEN_DEVICE_FUNC
+ MatrixType operatorSqrt() const
+ {
+ eigen_assert(m_isInitialized && "SelfAdjointEigenSolver is not initialized.");
+ eigen_assert(m_eigenvectorsOk && "The eigenvectors have not been computed together with the eigenvalues.");
+ return m_eivec * m_eivalues.cwiseSqrt().asDiagonal() * m_eivec.adjoint();
+ }
+
+ /** \brief Computes the inverse square root of the matrix.
+ *
+ * \returns the inverse positive-definite square root of the matrix
+ *
+ * \pre The eigenvalues and eigenvectors of a positive-definite matrix
+ * have been computed before.
+ *
+ * This function uses the eigendecomposition \f$ A = V D V^{-1} \f$ to
+ * compute the inverse square root as \f$ V D^{-1/2} V^{-1} \f$. This is
+ * cheaper than first computing the square root with operatorSqrt() and
+ * then its inverse with MatrixBase::inverse().
+ *
+ * Example: \include SelfAdjointEigenSolver_operatorInverseSqrt.cpp
+ * Output: \verbinclude SelfAdjointEigenSolver_operatorInverseSqrt.out
+ *
+ * \sa operatorSqrt(), MatrixBase::inverse(), <a href="unsupported/group__MatrixFunctions__Module.html">MatrixFunctions Module</a>
+ */
+ EIGEN_DEVICE_FUNC
+ MatrixType operatorInverseSqrt() const
+ {
+ eigen_assert(m_isInitialized && "SelfAdjointEigenSolver is not initialized.");
+ eigen_assert(m_eigenvectorsOk && "The eigenvectors have not been computed together with the eigenvalues.");
+ return m_eivec * m_eivalues.cwiseInverse().cwiseSqrt().asDiagonal() * m_eivec.adjoint();
+ }
+
+ /** \brief Reports whether previous computation was successful.
+ *
+ * \returns \c Success if computation was successful, \c NoConvergence otherwise.
+ */
+ EIGEN_DEVICE_FUNC
+ ComputationInfo info() const
+ {
+ eigen_assert(m_isInitialized && "SelfAdjointEigenSolver is not initialized.");
+ return m_info;
+ }
+
+ /** \brief Maximum number of iterations.
+ *
+ * The algorithm terminates if it does not converge within m_maxIterations * n iterations, where n
+ * denotes the size of the matrix. This value is currently set to 30 (copied from LAPACK).
+ */
+ static const int m_maxIterations = 30;
+
+ protected:
+ EIGEN_STATIC_ASSERT_NON_INTEGER(Scalar)
+
+ EigenvectorsType m_eivec;
+ RealVectorType m_eivalues;
+ typename TridiagonalizationType::SubDiagonalType m_subdiag;
+ typename TridiagonalizationType::CoeffVectorType m_hcoeffs;
+ ComputationInfo m_info;
+ bool m_isInitialized;
+ bool m_eigenvectorsOk;
+};
+
+namespace internal {
+/** \internal
+ *
+ * \eigenvalues_module \ingroup Eigenvalues_Module
+ *
+ * Performs a QR step on a tridiagonal symmetric matrix represented as a
+ * pair of two vectors \a diag and \a subdiag.
+ *
+ * \param diag the diagonal part of the input selfadjoint tridiagonal matrix
+ * \param subdiag the sub-diagonal part of the input selfadjoint tridiagonal matrix
+ * \param start starting index of the submatrix to work on
+ * \param end last+1 index of the submatrix to work on
+ * \param matrixQ pointer to the column-major matrix holding the eigenvectors, can be 0
+ * \param n size of the input matrix
+ *
+ * For compilation efficiency reasons, this procedure does not use eigen expression
+ * for its arguments.
+ *
+ * Implemented from Golub's "Matrix Computations", algorithm 8.3.2:
+ * "implicit symmetric QR step with Wilkinson shift"
+ */
+template<int StorageOrder,typename RealScalar, typename Scalar, typename Index>
+EIGEN_DEVICE_FUNC
+static void tridiagonal_qr_step(RealScalar* diag, RealScalar* subdiag, Index start, Index end, Scalar* matrixQ, Index n);
+}
+
+template<typename MatrixType>
+template<typename InputType>
+EIGEN_DEVICE_FUNC
+SelfAdjointEigenSolver<MatrixType>& SelfAdjointEigenSolver<MatrixType>
+::compute(const EigenBase<InputType>& a_matrix, int options)
+{
+ const InputType &matrix(a_matrix.derived());
+
+ EIGEN_USING_STD(abs);
+ eigen_assert(matrix.cols() == matrix.rows());
+ eigen_assert((options&~(EigVecMask|GenEigMask))==0
+ && (options&EigVecMask)!=EigVecMask
+ && "invalid option parameter");
+ bool computeEigenvectors = (options&ComputeEigenvectors)==ComputeEigenvectors;
+ Index n = matrix.cols();
+ m_eivalues.resize(n,1);
+
+ if(n==1)
+ {
+ m_eivec = matrix;
+ m_eivalues.coeffRef(0,0) = numext::real(m_eivec.coeff(0,0));
+ if(computeEigenvectors)
+ m_eivec.setOnes(n,n);
+ m_info = Success;
+ m_isInitialized = true;
+ m_eigenvectorsOk = computeEigenvectors;
+ return *this;
+ }
+
+ // declare some aliases
+ RealVectorType& diag = m_eivalues;
+ EigenvectorsType& mat = m_eivec;
+
+ // map the matrix coefficients to [-1:1] to avoid over- and underflow.
+ mat = matrix.template triangularView<Lower>();
+ RealScalar scale = mat.cwiseAbs().maxCoeff();
+ if(numext::is_exactly_zero(scale)) scale = RealScalar(1);
+ mat.template triangularView<Lower>() /= scale;
+ m_subdiag.resize(n-1);
+ m_hcoeffs.resize(n-1);
+ internal::tridiagonalization_inplace(mat, diag, m_subdiag, m_hcoeffs, computeEigenvectors);
+
+ m_info = internal::computeFromTridiagonal_impl(diag, m_subdiag, m_maxIterations, computeEigenvectors, m_eivec);
+
+ // scale back the eigen values
+ m_eivalues *= scale;
+
+ m_isInitialized = true;
+ m_eigenvectorsOk = computeEigenvectors;
+ return *this;
+}
+
+template<typename MatrixType>
+SelfAdjointEigenSolver<MatrixType>& SelfAdjointEigenSolver<MatrixType>
+::computeFromTridiagonal(const RealVectorType& diag, const SubDiagonalType& subdiag , int options)
+{
+ //TODO : Add an option to scale the values beforehand
+ bool computeEigenvectors = (options&ComputeEigenvectors)==ComputeEigenvectors;
+
+ m_eivalues = diag;
+ m_subdiag = subdiag;
+ if (computeEigenvectors)
+ {
+ m_eivec.setIdentity(diag.size(), diag.size());
+ }
+ m_info = internal::computeFromTridiagonal_impl(m_eivalues, m_subdiag, m_maxIterations, computeEigenvectors, m_eivec);
+
+ m_isInitialized = true;
+ m_eigenvectorsOk = computeEigenvectors;
+ return *this;
+}
+
+namespace internal {
+/**
+ * \internal
+ * \brief Compute the eigendecomposition from a tridiagonal matrix
+ *
+ * \param[in,out] diag : On input, the diagonal of the matrix, on output the eigenvalues
+ * \param[in,out] subdiag : The subdiagonal part of the matrix (entries are modified during the decomposition)
+ * \param[in] maxIterations : the maximum number of iterations
+ * \param[in] computeEigenvectors : whether the eigenvectors have to be computed or not
+ * \param[out] eivec : The matrix to store the eigenvectors if computeEigenvectors==true. Must be allocated on input.
+ * \returns \c Success or \c NoConvergence
+ */
+template<typename MatrixType, typename DiagType, typename SubDiagType>
+EIGEN_DEVICE_FUNC
+ComputationInfo computeFromTridiagonal_impl(DiagType& diag, SubDiagType& subdiag, const Index maxIterations, bool computeEigenvectors, MatrixType& eivec)
+{
+ ComputationInfo info;
+ typedef typename MatrixType::Scalar Scalar;
+
+ Index n = diag.size();
+ Index end = n-1;
+ Index start = 0;
+ Index iter = 0; // total number of iterations
+
+ typedef typename DiagType::RealScalar RealScalar;
+ const RealScalar considerAsZero = (std::numeric_limits<RealScalar>::min)();
+ const RealScalar precision_inv = RealScalar(1)/NumTraits<RealScalar>::epsilon();
+ while (end>0)
+ {
+ for (Index i = start; i<end; ++i) {
+ if (numext::abs(subdiag[i]) < considerAsZero) {
+ subdiag[i] = RealScalar(0);
+ } else {
+ // abs(subdiag[i]) <= epsilon * sqrt(abs(diag[i]) + abs(diag[i+1]))
+ // Scaled to prevent underflows.
+ const RealScalar scaled_subdiag = precision_inv * subdiag[i];
+ if (scaled_subdiag * scaled_subdiag <= (numext::abs(diag[i])+numext::abs(diag[i+1]))) {
+ subdiag[i] = RealScalar(0);
+ }
+ }
+ }
+
+ // find the largest unreduced block at the end of the matrix.
+ while (end>0 && numext::is_exactly_zero(subdiag[end - 1]))
+ {
+ end--;
+ }
+ if (end<=0)
+ break;
+
+ // if we spent too many iterations, we give up
+ iter++;
+ if(iter > maxIterations * n) break;
+
+ start = end - 1;
+ while (start>0 && !numext::is_exactly_zero(subdiag[start - 1]))
+ start--;
+
+ internal::tridiagonal_qr_step<MatrixType::Flags&RowMajorBit ? RowMajor : ColMajor>(diag.data(), subdiag.data(), start, end, computeEigenvectors ? eivec.data() : (Scalar*)0, n);
+ }
+ if (iter <= maxIterations * n)
+ info = Success;
+ else
+ info = NoConvergence;
+
+ // Sort eigenvalues and corresponding vectors.
+ // TODO make the sort optional ?
+ // TODO use a better sort algorithm !!
+ if (info == Success)
+ {
+ for (Index i = 0; i < n-1; ++i)
+ {
+ Index k;
+ diag.segment(i,n-i).minCoeff(&k);
+ if (k > 0)
+ {
+ numext::swap(diag[i], diag[k+i]);
+ if(computeEigenvectors)
+ eivec.col(i).swap(eivec.col(k+i));
+ }
+ }
+ }
+ return info;
+}
+
+template<typename SolverType,int Size,bool IsComplex> struct direct_selfadjoint_eigenvalues
+{
+ EIGEN_DEVICE_FUNC
+ static inline void run(SolverType& eig, const typename SolverType::MatrixType& A, int options)
+ { eig.compute(A,options); }
+};
+
+template<typename SolverType> struct direct_selfadjoint_eigenvalues<SolverType,3,false>
+{
+ typedef typename SolverType::MatrixType MatrixType;
+ typedef typename SolverType::RealVectorType VectorType;
+ typedef typename SolverType::Scalar Scalar;
+ typedef typename SolverType::EigenvectorsType EigenvectorsType;
+
+
+ /** \internal
+ * Computes the roots of the characteristic polynomial of \a m.
+ * For numerical stability m.trace() should be near zero and to avoid over- or underflow m should be normalized.
+ */
+ EIGEN_DEVICE_FUNC
+ static inline void computeRoots(const MatrixType& m, VectorType& roots)
+ {
+ EIGEN_USING_STD(sqrt)
+ EIGEN_USING_STD(atan2)
+ EIGEN_USING_STD(cos)
+ EIGEN_USING_STD(sin)
+ const Scalar s_inv3 = Scalar(1)/Scalar(3);
+ const Scalar s_sqrt3 = sqrt(Scalar(3));
+
+ // The characteristic equation is x^3 - c2*x^2 + c1*x - c0 = 0. The
+ // eigenvalues are the roots to this equation, all guaranteed to be
+ // real-valued, because the matrix is symmetric.
+ Scalar c0 = m(0,0)*m(1,1)*m(2,2) + Scalar(2)*m(1,0)*m(2,0)*m(2,1) - m(0,0)*m(2,1)*m(2,1) - m(1,1)*m(2,0)*m(2,0) - m(2,2)*m(1,0)*m(1,0);
+ Scalar c1 = m(0,0)*m(1,1) - m(1,0)*m(1,0) + m(0,0)*m(2,2) - m(2,0)*m(2,0) + m(1,1)*m(2,2) - m(2,1)*m(2,1);
+ Scalar c2 = m(0,0) + m(1,1) + m(2,2);
+
+ // Construct the parameters used in classifying the roots of the equation
+ // and in solving the equation for the roots in closed form.
+ Scalar c2_over_3 = c2*s_inv3;
+ Scalar a_over_3 = (c2*c2_over_3 - c1)*s_inv3;
+ a_over_3 = numext::maxi(a_over_3, Scalar(0));
+
+ Scalar half_b = Scalar(0.5)*(c0 + c2_over_3*(Scalar(2)*c2_over_3*c2_over_3 - c1));
+
+ Scalar q = a_over_3*a_over_3*a_over_3 - half_b*half_b;
+ q = numext::maxi(q, Scalar(0));
+
+ // Compute the eigenvalues by solving for the roots of the polynomial.
+ Scalar rho = sqrt(a_over_3);
+ Scalar theta = atan2(sqrt(q),half_b)*s_inv3; // since sqrt(q) > 0, atan2 is in [0, pi] and theta is in [0, pi/3]
+ Scalar cos_theta = cos(theta);
+ Scalar sin_theta = sin(theta);
+ // roots are already sorted, since cos is monotonically decreasing on [0, pi]
+ roots(0) = c2_over_3 - rho*(cos_theta + s_sqrt3*sin_theta); // == 2*rho*cos(theta+2pi/3)
+ roots(1) = c2_over_3 - rho*(cos_theta - s_sqrt3*sin_theta); // == 2*rho*cos(theta+ pi/3)
+ roots(2) = c2_over_3 + Scalar(2)*rho*cos_theta;
+ }
+
+ EIGEN_DEVICE_FUNC
+ static inline bool extract_kernel(MatrixType& mat, Ref<VectorType> res, Ref<VectorType> representative)
+ {
+ EIGEN_USING_STD(abs);
+ EIGEN_USING_STD(sqrt);
+ Index i0;
+ // Find non-zero column i0 (by construction, there must exist a non zero coefficient on the diagonal):
+ mat.diagonal().cwiseAbs().maxCoeff(&i0);
+ // mat.col(i0) is a good candidate for an orthogonal vector to the current eigenvector,
+ // so let's save it:
+ representative = mat.col(i0);
+ Scalar n0, n1;
+ VectorType c0, c1;
+ n0 = (c0 = representative.cross(mat.col((i0+1)%3))).squaredNorm();
+ n1 = (c1 = representative.cross(mat.col((i0+2)%3))).squaredNorm();
+ if(n0>n1) res = c0/sqrt(n0);
+ else res = c1/sqrt(n1);
+
+ return true;
+ }
+
+ EIGEN_DEVICE_FUNC
+ static inline void run(SolverType& solver, const MatrixType& mat, int options)
+ {
+ eigen_assert(mat.cols() == 3 && mat.cols() == mat.rows());
+ eigen_assert((options&~(EigVecMask|GenEigMask))==0
+ && (options&EigVecMask)!=EigVecMask
+ && "invalid option parameter");
+ bool computeEigenvectors = (options&ComputeEigenvectors)==ComputeEigenvectors;
+
+ EigenvectorsType& eivecs = solver.m_eivec;
+ VectorType& eivals = solver.m_eivalues;
+
+ // Shift the matrix to the mean eigenvalue and map the matrix coefficients to [-1:1] to avoid over- and underflow.
+ Scalar shift = mat.trace() / Scalar(3);
+ // TODO Avoid this copy. Currently it is necessary to suppress bogus values when determining maxCoeff and for computing the eigenvectors later
+ MatrixType scaledMat = mat.template selfadjointView<Lower>();
+ scaledMat.diagonal().array() -= shift;
+ Scalar scale = scaledMat.cwiseAbs().maxCoeff();
+ if(scale > 0) scaledMat /= scale; // TODO for scale==0 we could save the remaining operations
+
+ // compute the eigenvalues
+ computeRoots(scaledMat,eivals);
+
+ // compute the eigenvectors
+ if(computeEigenvectors)
+ {
+ if((eivals(2)-eivals(0))<=Eigen::NumTraits<Scalar>::epsilon())
+ {
+ // All three eigenvalues are numerically the same
+ eivecs.setIdentity();
+ }
+ else
+ {
+ MatrixType tmp;
+ tmp = scaledMat;
+
+ // Compute the eigenvector of the most distinct eigenvalue
+ Scalar d0 = eivals(2) - eivals(1);
+ Scalar d1 = eivals(1) - eivals(0);
+ Index k(0), l(2);
+ if(d0 > d1)
+ {
+ numext::swap(k,l);
+ d0 = d1;
+ }
+
+ // Compute the eigenvector of index k
+ {
+ tmp.diagonal().array () -= eivals(k);
+ // By construction, 'tmp' is of rank 2, and its kernel corresponds to the respective eigenvector.
+ extract_kernel(tmp, eivecs.col(k), eivecs.col(l));
+ }
+
+ // Compute eigenvector of index l
+ if(d0<=2*Eigen::NumTraits<Scalar>::epsilon()*d1)
+ {
+ // If d0 is too small, then the two other eigenvalues are numerically the same,
+ // and thus we only have to ortho-normalize the near orthogonal vector we saved above.
+ eivecs.col(l) -= eivecs.col(k).dot(eivecs.col(l))*eivecs.col(l);
+ eivecs.col(l).normalize();
+ }
+ else
+ {
+ tmp = scaledMat;
+ tmp.diagonal().array () -= eivals(l);
+
+ VectorType dummy;
+ extract_kernel(tmp, eivecs.col(l), dummy);
+ }
+
+ // Compute last eigenvector from the other two
+ eivecs.col(1) = eivecs.col(2).cross(eivecs.col(0)).normalized();
+ }
+ }
+
+ // Rescale back to the original size.
+ eivals *= scale;
+ eivals.array() += shift;
+
+ solver.m_info = Success;
+ solver.m_isInitialized = true;
+ solver.m_eigenvectorsOk = computeEigenvectors;
+ }
+};
+
+// 2x2 direct eigenvalues decomposition, code from Hauke Heibel
+template<typename SolverType>
+struct direct_selfadjoint_eigenvalues<SolverType,2,false>
+{
+ typedef typename SolverType::MatrixType MatrixType;
+ typedef typename SolverType::RealVectorType VectorType;
+ typedef typename SolverType::Scalar Scalar;
+ typedef typename SolverType::EigenvectorsType EigenvectorsType;
+
+ EIGEN_DEVICE_FUNC
+ static inline void computeRoots(const MatrixType& m, VectorType& roots)
+ {
+ EIGEN_USING_STD(sqrt);
+ const Scalar t0 = Scalar(0.5) * sqrt( numext::abs2(m(0,0)-m(1,1)) + Scalar(4)*numext::abs2(m(1,0)));
+ const Scalar t1 = Scalar(0.5) * (m(0,0) + m(1,1));
+ roots(0) = t1 - t0;
+ roots(1) = t1 + t0;
+ }
+
+ EIGEN_DEVICE_FUNC
+ static inline void run(SolverType& solver, const MatrixType& mat, int options)
+ {
+ EIGEN_USING_STD(sqrt);
+ EIGEN_USING_STD(abs);
+
+ eigen_assert(mat.cols() == 2 && mat.cols() == mat.rows());
+ eigen_assert((options&~(EigVecMask|GenEigMask))==0
+ && (options&EigVecMask)!=EigVecMask
+ && "invalid option parameter");
+ bool computeEigenvectors = (options&ComputeEigenvectors)==ComputeEigenvectors;
+
+ EigenvectorsType& eivecs = solver.m_eivec;
+ VectorType& eivals = solver.m_eivalues;
+
+ // Shift the matrix to the mean eigenvalue and map the matrix coefficients to [-1:1] to avoid over- and underflow.
+ Scalar shift = mat.trace() / Scalar(2);
+ MatrixType scaledMat = mat;
+ scaledMat.coeffRef(0,1) = mat.coeff(1,0);
+ scaledMat.diagonal().array() -= shift;
+ Scalar scale = scaledMat.cwiseAbs().maxCoeff();
+ if(scale > Scalar(0))
+ scaledMat /= scale;
+
+ // Compute the eigenvalues
+ computeRoots(scaledMat,eivals);
+
+ // compute the eigen vectors
+ if(computeEigenvectors)
+ {
+ if((eivals(1)-eivals(0))<=abs(eivals(1))*Eigen::NumTraits<Scalar>::epsilon())
+ {
+ eivecs.setIdentity();
+ }
+ else
+ {
+ scaledMat.diagonal().array () -= eivals(1);
+ Scalar a2 = numext::abs2(scaledMat(0,0));
+ Scalar c2 = numext::abs2(scaledMat(1,1));
+ Scalar b2 = numext::abs2(scaledMat(1,0));
+ if(a2>c2)
+ {
+ eivecs.col(1) << -scaledMat(1,0), scaledMat(0,0);
+ eivecs.col(1) /= sqrt(a2+b2);
+ }
+ else
+ {
+ eivecs.col(1) << -scaledMat(1,1), scaledMat(1,0);
+ eivecs.col(1) /= sqrt(c2+b2);
+ }
+
+ eivecs.col(0) << eivecs.col(1).unitOrthogonal();
+ }
+ }
+
+ // Rescale back to the original size.
+ eivals *= scale;
+ eivals.array() += shift;
+
+ solver.m_info = Success;
+ solver.m_isInitialized = true;
+ solver.m_eigenvectorsOk = computeEigenvectors;
+ }
+};
+
+}
+
+template<typename MatrixType>
+EIGEN_DEVICE_FUNC
+SelfAdjointEigenSolver<MatrixType>& SelfAdjointEigenSolver<MatrixType>
+::computeDirect(const MatrixType& matrix, int options)
+{
+ internal::direct_selfadjoint_eigenvalues<SelfAdjointEigenSolver,Size,NumTraits<Scalar>::IsComplex>::run(*this,matrix,options);
+ return *this;
+}
+
+namespace internal {
+
+// Francis implicit QR step.
+template<int StorageOrder,typename RealScalar, typename Scalar, typename Index>
+EIGEN_DEVICE_FUNC
+static void tridiagonal_qr_step(RealScalar* diag, RealScalar* subdiag, Index start, Index end, Scalar* matrixQ, Index n)
+{
+ // Wilkinson Shift.
+ RealScalar td = (diag[end-1] - diag[end])*RealScalar(0.5);
+ RealScalar e = subdiag[end-1];
+ // Note that thanks to scaling, e^2 or td^2 cannot overflow, however they can still
+ // underflow thus leading to inf/NaN values when using the following commented code:
+ // RealScalar e2 = numext::abs2(subdiag[end-1]);
+ // RealScalar mu = diag[end] - e2 / (td + (td>0 ? 1 : -1) * sqrt(td*td + e2));
+ // This explain the following, somewhat more complicated, version:
+ RealScalar mu = diag[end];
+ if(numext::is_exactly_zero(td)) {
+ mu -= numext::abs(e);
+ } else if (!numext::is_exactly_zero(e)) {
+ const RealScalar e2 = numext::abs2(e);
+ const RealScalar h = numext::hypot(td,e);
+ if(numext::is_exactly_zero(e2)) {
+ mu -= e / ((td + (td>RealScalar(0) ? h : -h)) / e);
+ } else {
+ mu -= e2 / (td + (td>RealScalar(0) ? h : -h));
+ }
+ }
+
+ RealScalar x = diag[start] - mu;
+ RealScalar z = subdiag[start];
+ // If z ever becomes zero, the Givens rotation will be the identity and
+ // z will stay zero for all future iterations.
+ for (Index k = start; k < end && !numext::is_exactly_zero(z); ++k)
+ {
+ JacobiRotation<RealScalar> rot;
+ rot.makeGivens(x, z);
+
+ // do T = G' T G
+ RealScalar sdk = rot.s() * diag[k] + rot.c() * subdiag[k];
+ RealScalar dkp1 = rot.s() * subdiag[k] + rot.c() * diag[k+1];
+
+ diag[k] = rot.c() * (rot.c() * diag[k] - rot.s() * subdiag[k]) - rot.s() * (rot.c() * subdiag[k] - rot.s() * diag[k+1]);
+ diag[k+1] = rot.s() * sdk + rot.c() * dkp1;
+ subdiag[k] = rot.c() * sdk - rot.s() * dkp1;
+
+ if (k > start)
+ subdiag[k - 1] = rot.c() * subdiag[k-1] - rot.s() * z;
+
+ // "Chasing the bulge" to return to triangular form.
+ x = subdiag[k];
+ if (k < end - 1)
+ {
+ z = -rot.s() * subdiag[k+1];
+ subdiag[k + 1] = rot.c() * subdiag[k+1];
+ }
+
+ // apply the givens rotation to the unit matrix Q = Q * G
+ if (matrixQ)
+ {
+ // FIXME if StorageOrder == RowMajor this operation is not very efficient
+ Map<Matrix<Scalar,Dynamic,Dynamic,StorageOrder> > q(matrixQ,n,n);
+ q.applyOnTheRight(k,k+1,rot);
+ }
+ }
+}
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_SELFADJOINTEIGENSOLVER_H
diff --git a/Eigen/src/Eigenvalues/SelfAdjointEigenSolver_LAPACKE.h b/Eigen/src/Eigenvalues/SelfAdjointEigenSolver_LAPACKE.h
new file mode 100644
index 0000000..b24de67
--- /dev/null
+++ b/Eigen/src/Eigenvalues/SelfAdjointEigenSolver_LAPACKE.h
@@ -0,0 +1,89 @@
+/*
+ Copyright (c) 2011, Intel Corporation. All rights reserved.
+
+ Redistribution and use in source and binary forms, with or without modification,
+ are permitted provided that the following conditions are met:
+
+ * Redistributions of source code must retain the above copyright notice, this
+ list of conditions and the following disclaimer.
+ * Redistributions in binary form must reproduce the above copyright notice,
+ this list of conditions and the following disclaimer in the documentation
+ and/or other materials provided with the distribution.
+ * Neither the name of Intel Corporation nor the names of its contributors may
+ be used to endorse or promote products derived from this software without
+ specific prior written permission.
+
+ THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
+ ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
+ WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
+ DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR
+ ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
+ (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
+ LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON
+ ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
+ (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
+ SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+
+ ********************************************************************************
+ * Content : Eigen bindings to LAPACKe
+ * Self-adjoint eigenvalues/eigenvectors.
+ ********************************************************************************
+*/
+
+#ifndef EIGEN_SAEIGENSOLVER_LAPACKE_H
+#define EIGEN_SAEIGENSOLVER_LAPACKE_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+/** \internal Specialization for the data types supported by LAPACKe */
+
+#define EIGEN_LAPACKE_EIG_SELFADJ_2(EIGTYPE, LAPACKE_TYPE, LAPACKE_RTYPE, LAPACKE_NAME, EIGCOLROW ) \
+template<> template<typename InputType> inline \
+SelfAdjointEigenSolver<Matrix<EIGTYPE, Dynamic, Dynamic, EIGCOLROW> >& \
+SelfAdjointEigenSolver<Matrix<EIGTYPE, Dynamic, Dynamic, EIGCOLROW> >::compute(const EigenBase<InputType>& matrix, int options) \
+{ \
+ eigen_assert(matrix.cols() == matrix.rows()); \
+ eigen_assert((options&~(EigVecMask|GenEigMask))==0 \
+ && (options&EigVecMask)!=EigVecMask \
+ && "invalid option parameter"); \
+ bool computeEigenvectors = (options&ComputeEigenvectors)==ComputeEigenvectors; \
+ lapack_int n = internal::convert_index<lapack_int>(matrix.cols()), lda, info; \
+ m_eivalues.resize(n,1); \
+ m_subdiag.resize(n-1); \
+ m_eivec = matrix; \
+\
+ if(n==1) \
+ { \
+ m_eivalues.coeffRef(0,0) = numext::real(m_eivec.coeff(0,0)); \
+ if(computeEigenvectors) m_eivec.setOnes(n,n); \
+ m_info = Success; \
+ m_isInitialized = true; \
+ m_eigenvectorsOk = computeEigenvectors; \
+ return *this; \
+ } \
+\
+ lda = internal::convert_index<lapack_int>(m_eivec.outerStride()); \
+ char jobz, uplo='L'/*, range='A'*/; \
+ jobz = computeEigenvectors ? 'V' : 'N'; \
+\
+ info = LAPACKE_##LAPACKE_NAME( LAPACK_COL_MAJOR, jobz, uplo, n, (LAPACKE_TYPE*)m_eivec.data(), lda, (LAPACKE_RTYPE*)m_eivalues.data() ); \
+ m_info = (info==0) ? Success : NoConvergence; \
+ m_isInitialized = true; \
+ m_eigenvectorsOk = computeEigenvectors; \
+ return *this; \
+}
+
+#define EIGEN_LAPACKE_EIG_SELFADJ(EIGTYPE, LAPACKE_TYPE, LAPACKE_RTYPE, LAPACKE_NAME ) \
+ EIGEN_LAPACKE_EIG_SELFADJ_2(EIGTYPE, LAPACKE_TYPE, LAPACKE_RTYPE, LAPACKE_NAME, ColMajor ) \
+ EIGEN_LAPACKE_EIG_SELFADJ_2(EIGTYPE, LAPACKE_TYPE, LAPACKE_RTYPE, LAPACKE_NAME, RowMajor )
+
+EIGEN_LAPACKE_EIG_SELFADJ(double, double, double, dsyev)
+EIGEN_LAPACKE_EIG_SELFADJ(float, float, float, ssyev)
+EIGEN_LAPACKE_EIG_SELFADJ(dcomplex, lapack_complex_double, double, zheev)
+EIGEN_LAPACKE_EIG_SELFADJ(scomplex, lapack_complex_float, float, cheev)
+
+} // end namespace Eigen
+
+#endif // EIGEN_SAEIGENSOLVER_H
diff --git a/Eigen/src/Eigenvalues/Tridiagonalization.h b/Eigen/src/Eigenvalues/Tridiagonalization.h
new file mode 100644
index 0000000..9b002fe
--- /dev/null
+++ b/Eigen/src/Eigenvalues/Tridiagonalization.h
@@ -0,0 +1,562 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2010 Jitse Niesen <jitse@maths.leeds.ac.uk>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_TRIDIAGONALIZATION_H
+#define EIGEN_TRIDIAGONALIZATION_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+
+template<typename MatrixType> struct TridiagonalizationMatrixTReturnType;
+template<typename MatrixType>
+struct traits<TridiagonalizationMatrixTReturnType<MatrixType> >
+ : public traits<typename MatrixType::PlainObject>
+{
+ typedef typename MatrixType::PlainObject ReturnType; // FIXME shall it be a BandMatrix?
+ enum { Flags = 0 };
+};
+
+template<typename MatrixType, typename CoeffVectorType>
+EIGEN_DEVICE_FUNC
+void tridiagonalization_inplace(MatrixType& matA, CoeffVectorType& hCoeffs);
+}
+
+/** \eigenvalues_module \ingroup Eigenvalues_Module
+ *
+ *
+ * \class Tridiagonalization
+ *
+ * \brief Tridiagonal decomposition of a selfadjoint matrix
+ *
+ * \tparam MatrixType_ the type of the matrix of which we are computing the
+ * tridiagonal decomposition; this is expected to be an instantiation of the
+ * Matrix class template.
+ *
+ * This class performs a tridiagonal decomposition of a selfadjoint matrix \f$ A \f$ such that:
+ * \f$ A = Q T Q^* \f$ where \f$ Q \f$ is unitary and \f$ T \f$ a real symmetric tridiagonal matrix.
+ *
+ * A tridiagonal matrix is a matrix which has nonzero elements only on the
+ * main diagonal and the first diagonal below and above it. The Hessenberg
+ * decomposition of a selfadjoint matrix is in fact a tridiagonal
+ * decomposition. This class is used in SelfAdjointEigenSolver to compute the
+ * eigenvalues and eigenvectors of a selfadjoint matrix.
+ *
+ * Call the function compute() to compute the tridiagonal decomposition of a
+ * given matrix. Alternatively, you can use the Tridiagonalization(const MatrixType&)
+ * constructor which computes the tridiagonal Schur decomposition at
+ * construction time. Once the decomposition is computed, you can use the
+ * matrixQ() and matrixT() functions to retrieve the matrices Q and T in the
+ * decomposition.
+ *
+ * The documentation of Tridiagonalization(const MatrixType&) contains an
+ * example of the typical use of this class.
+ *
+ * \sa class HessenbergDecomposition, class SelfAdjointEigenSolver
+ */
+template<typename MatrixType_> class Tridiagonalization
+{
+ public:
+
+ /** \brief Synonym for the template parameter \p MatrixType_. */
+ typedef MatrixType_ MatrixType;
+
+ typedef typename MatrixType::Scalar Scalar;
+ typedef typename NumTraits<Scalar>::Real RealScalar;
+ typedef Eigen::Index Index; ///< \deprecated since Eigen 3.3
+
+ enum {
+ Size = MatrixType::RowsAtCompileTime,
+ SizeMinusOne = Size == Dynamic ? Dynamic : (Size > 1 ? Size - 1 : 1),
+ Options = MatrixType::Options,
+ MaxSize = MatrixType::MaxRowsAtCompileTime,
+ MaxSizeMinusOne = MaxSize == Dynamic ? Dynamic : (MaxSize > 1 ? MaxSize - 1 : 1)
+ };
+
+ typedef Matrix<Scalar, SizeMinusOne, 1, Options & ~RowMajor, MaxSizeMinusOne, 1> CoeffVectorType;
+ typedef typename internal::plain_col_type<MatrixType, RealScalar>::type DiagonalType;
+ typedef Matrix<RealScalar, SizeMinusOne, 1, Options & ~RowMajor, MaxSizeMinusOne, 1> SubDiagonalType;
+ typedef internal::remove_all_t<typename MatrixType::RealReturnType> MatrixTypeRealView;
+ typedef internal::TridiagonalizationMatrixTReturnType<MatrixTypeRealView> MatrixTReturnType;
+
+ typedef std::conditional_t<NumTraits<Scalar>::IsComplex,
+ internal::add_const_on_value_type_t<typename Diagonal<const MatrixType>::RealReturnType>,
+ const Diagonal<const MatrixType>
+ > DiagonalReturnType;
+
+ typedef std::conditional_t<NumTraits<Scalar>::IsComplex,
+ internal::add_const_on_value_type_t<typename Diagonal<const MatrixType, -1>::RealReturnType>,
+ const Diagonal<const MatrixType, -1>
+ > SubDiagonalReturnType;
+
+ /** \brief Return type of matrixQ() */
+ typedef HouseholderSequence<MatrixType,internal::remove_all_t<typename CoeffVectorType::ConjugateReturnType>> HouseholderSequenceType;
+
+ /** \brief Default constructor.
+ *
+ * \param [in] size Positive integer, size of the matrix whose tridiagonal
+ * decomposition will be computed.
+ *
+ * The default constructor is useful in cases in which the user intends to
+ * perform decompositions via compute(). The \p size parameter is only
+ * used as a hint. It is not an error to give a wrong \p size, but it may
+ * impair performance.
+ *
+ * \sa compute() for an example.
+ */
+ explicit Tridiagonalization(Index size = Size==Dynamic ? 2 : Size)
+ : m_matrix(size,size),
+ m_hCoeffs(size > 1 ? size-1 : 1),
+ m_isInitialized(false)
+ {}
+
+ /** \brief Constructor; computes tridiagonal decomposition of given matrix.
+ *
+ * \param[in] matrix Selfadjoint matrix whose tridiagonal decomposition
+ * is to be computed.
+ *
+ * This constructor calls compute() to compute the tridiagonal decomposition.
+ *
+ * Example: \include Tridiagonalization_Tridiagonalization_MatrixType.cpp
+ * Output: \verbinclude Tridiagonalization_Tridiagonalization_MatrixType.out
+ */
+ template<typename InputType>
+ explicit Tridiagonalization(const EigenBase<InputType>& matrix)
+ : m_matrix(matrix.derived()),
+ m_hCoeffs(matrix.cols() > 1 ? matrix.cols()-1 : 1),
+ m_isInitialized(false)
+ {
+ internal::tridiagonalization_inplace(m_matrix, m_hCoeffs);
+ m_isInitialized = true;
+ }
+
+ /** \brief Computes tridiagonal decomposition of given matrix.
+ *
+ * \param[in] matrix Selfadjoint matrix whose tridiagonal decomposition
+ * is to be computed.
+ * \returns Reference to \c *this
+ *
+ * The tridiagonal decomposition is computed by bringing the columns of
+ * the matrix successively in the required form using Householder
+ * reflections. The cost is \f$ 4n^3/3 \f$ flops, where \f$ n \f$ denotes
+ * the size of the given matrix.
+ *
+ * This method reuses of the allocated data in the Tridiagonalization
+ * object, if the size of the matrix does not change.
+ *
+ * Example: \include Tridiagonalization_compute.cpp
+ * Output: \verbinclude Tridiagonalization_compute.out
+ */
+ template<typename InputType>
+ Tridiagonalization& compute(const EigenBase<InputType>& matrix)
+ {
+ m_matrix = matrix.derived();
+ m_hCoeffs.resize(matrix.rows()-1, 1);
+ internal::tridiagonalization_inplace(m_matrix, m_hCoeffs);
+ m_isInitialized = true;
+ return *this;
+ }
+
+ /** \brief Returns the Householder coefficients.
+ *
+ * \returns a const reference to the vector of Householder coefficients
+ *
+ * \pre Either the constructor Tridiagonalization(const MatrixType&) or
+ * the member function compute(const MatrixType&) has been called before
+ * to compute the tridiagonal decomposition of a matrix.
+ *
+ * The Householder coefficients allow the reconstruction of the matrix
+ * \f$ Q \f$ in the tridiagonal decomposition from the packed data.
+ *
+ * Example: \include Tridiagonalization_householderCoefficients.cpp
+ * Output: \verbinclude Tridiagonalization_householderCoefficients.out
+ *
+ * \sa packedMatrix(), \ref Householder_Module "Householder module"
+ */
+ inline CoeffVectorType householderCoefficients() const
+ {
+ eigen_assert(m_isInitialized && "Tridiagonalization is not initialized.");
+ return m_hCoeffs;
+ }
+
+ /** \brief Returns the internal representation of the decomposition
+ *
+ * \returns a const reference to a matrix with the internal representation
+ * of the decomposition.
+ *
+ * \pre Either the constructor Tridiagonalization(const MatrixType&) or
+ * the member function compute(const MatrixType&) has been called before
+ * to compute the tridiagonal decomposition of a matrix.
+ *
+ * The returned matrix contains the following information:
+ * - the strict upper triangular part is equal to the input matrix A.
+ * - the diagonal and lower sub-diagonal represent the real tridiagonal
+ * symmetric matrix T.
+ * - the rest of the lower part contains the Householder vectors that,
+ * combined with Householder coefficients returned by
+ * householderCoefficients(), allows to reconstruct the matrix Q as
+ * \f$ Q = H_{N-1} \ldots H_1 H_0 \f$.
+ * Here, the matrices \f$ H_i \f$ are the Householder transformations
+ * \f$ H_i = (I - h_i v_i v_i^T) \f$
+ * where \f$ h_i \f$ is the \f$ i \f$th Householder coefficient and
+ * \f$ v_i \f$ is the Householder vector defined by
+ * \f$ v_i = [ 0, \ldots, 0, 1, M(i+2,i), \ldots, M(N-1,i) ]^T \f$
+ * with M the matrix returned by this function.
+ *
+ * See LAPACK for further details on this packed storage.
+ *
+ * Example: \include Tridiagonalization_packedMatrix.cpp
+ * Output: \verbinclude Tridiagonalization_packedMatrix.out
+ *
+ * \sa householderCoefficients()
+ */
+ inline const MatrixType& packedMatrix() const
+ {
+ eigen_assert(m_isInitialized && "Tridiagonalization is not initialized.");
+ return m_matrix;
+ }
+
+ /** \brief Returns the unitary matrix Q in the decomposition
+ *
+ * \returns object representing the matrix Q
+ *
+ * \pre Either the constructor Tridiagonalization(const MatrixType&) or
+ * the member function compute(const MatrixType&) has been called before
+ * to compute the tridiagonal decomposition of a matrix.
+ *
+ * This function returns a light-weight object of template class
+ * HouseholderSequence. You can either apply it directly to a matrix or
+ * you can convert it to a matrix of type #MatrixType.
+ *
+ * \sa Tridiagonalization(const MatrixType&) for an example,
+ * matrixT(), class HouseholderSequence
+ */
+ HouseholderSequenceType matrixQ() const
+ {
+ eigen_assert(m_isInitialized && "Tridiagonalization is not initialized.");
+ return HouseholderSequenceType(m_matrix, m_hCoeffs.conjugate())
+ .setLength(m_matrix.rows() - 1)
+ .setShift(1);
+ }
+
+ /** \brief Returns an expression of the tridiagonal matrix T in the decomposition
+ *
+ * \returns expression object representing the matrix T
+ *
+ * \pre Either the constructor Tridiagonalization(const MatrixType&) or
+ * the member function compute(const MatrixType&) has been called before
+ * to compute the tridiagonal decomposition of a matrix.
+ *
+ * Currently, this function can be used to extract the matrix T from internal
+ * data and copy it to a dense matrix object. In most cases, it may be
+ * sufficient to directly use the packed matrix or the vector expressions
+ * returned by diagonal() and subDiagonal() instead of creating a new
+ * dense copy matrix with this function.
+ *
+ * \sa Tridiagonalization(const MatrixType&) for an example,
+ * matrixQ(), packedMatrix(), diagonal(), subDiagonal()
+ */
+ MatrixTReturnType matrixT() const
+ {
+ eigen_assert(m_isInitialized && "Tridiagonalization is not initialized.");
+ return MatrixTReturnType(m_matrix.real());
+ }
+
+ /** \brief Returns the diagonal of the tridiagonal matrix T in the decomposition.
+ *
+ * \returns expression representing the diagonal of T
+ *
+ * \pre Either the constructor Tridiagonalization(const MatrixType&) or
+ * the member function compute(const MatrixType&) has been called before
+ * to compute the tridiagonal decomposition of a matrix.
+ *
+ * Example: \include Tridiagonalization_diagonal.cpp
+ * Output: \verbinclude Tridiagonalization_diagonal.out
+ *
+ * \sa matrixT(), subDiagonal()
+ */
+ DiagonalReturnType diagonal() const;
+
+ /** \brief Returns the subdiagonal of the tridiagonal matrix T in the decomposition.
+ *
+ * \returns expression representing the subdiagonal of T
+ *
+ * \pre Either the constructor Tridiagonalization(const MatrixType&) or
+ * the member function compute(const MatrixType&) has been called before
+ * to compute the tridiagonal decomposition of a matrix.
+ *
+ * \sa diagonal() for an example, matrixT()
+ */
+ SubDiagonalReturnType subDiagonal() const;
+
+ protected:
+
+ MatrixType m_matrix;
+ CoeffVectorType m_hCoeffs;
+ bool m_isInitialized;
+};
+
+template<typename MatrixType>
+typename Tridiagonalization<MatrixType>::DiagonalReturnType
+Tridiagonalization<MatrixType>::diagonal() const
+{
+ eigen_assert(m_isInitialized && "Tridiagonalization is not initialized.");
+ return m_matrix.diagonal().real();
+}
+
+template<typename MatrixType>
+typename Tridiagonalization<MatrixType>::SubDiagonalReturnType
+Tridiagonalization<MatrixType>::subDiagonal() const
+{
+ eigen_assert(m_isInitialized && "Tridiagonalization is not initialized.");
+ return m_matrix.template diagonal<-1>().real();
+}
+
+namespace internal {
+
+/** \internal
+ * Performs a tridiagonal decomposition of the selfadjoint matrix \a matA in-place.
+ *
+ * \param[in,out] matA On input the selfadjoint matrix. Only the \b lower triangular part is referenced.
+ * On output, the strict upper part is left unchanged, and the lower triangular part
+ * represents the T and Q matrices in packed format has detailed below.
+ * \param[out] hCoeffs returned Householder coefficients (see below)
+ *
+ * On output, the tridiagonal selfadjoint matrix T is stored in the diagonal
+ * and lower sub-diagonal of the matrix \a matA.
+ * The unitary matrix Q is represented in a compact way as a product of
+ * Householder reflectors \f$ H_i \f$ such that:
+ * \f$ Q = H_{N-1} \ldots H_1 H_0 \f$.
+ * The Householder reflectors are defined as
+ * \f$ H_i = (I - h_i v_i v_i^T) \f$
+ * where \f$ h_i = hCoeffs[i]\f$ is the \f$ i \f$th Householder coefficient and
+ * \f$ v_i \f$ is the Householder vector defined by
+ * \f$ v_i = [ 0, \ldots, 0, 1, matA(i+2,i), \ldots, matA(N-1,i) ]^T \f$.
+ *
+ * Implemented from Golub's "Matrix Computations", algorithm 8.3.1.
+ *
+ * \sa Tridiagonalization::packedMatrix()
+ */
+template<typename MatrixType, typename CoeffVectorType>
+EIGEN_DEVICE_FUNC
+void tridiagonalization_inplace(MatrixType& matA, CoeffVectorType& hCoeffs)
+{
+ using numext::conj;
+ typedef typename MatrixType::Scalar Scalar;
+ typedef typename MatrixType::RealScalar RealScalar;
+ Index n = matA.rows();
+ eigen_assert(n==matA.cols());
+ eigen_assert(n==hCoeffs.size()+1 || n==1);
+
+ for (Index i = 0; i<n-1; ++i)
+ {
+ Index remainingSize = n-i-1;
+ RealScalar beta;
+ Scalar h;
+ matA.col(i).tail(remainingSize).makeHouseholderInPlace(h, beta);
+
+ // Apply similarity transformation to remaining columns,
+ // i.e., A = H A H' where H = I - h v v' and v = matA.col(i).tail(n-i-1)
+ matA.col(i).coeffRef(i+1) = 1;
+
+ hCoeffs.tail(n-i-1).noalias() = (matA.bottomRightCorner(remainingSize,remainingSize).template selfadjointView<Lower>()
+ * (conj(h) * matA.col(i).tail(remainingSize)));
+
+ hCoeffs.tail(n-i-1) += (conj(h)*RealScalar(-0.5)*(hCoeffs.tail(remainingSize).dot(matA.col(i).tail(remainingSize)))) * matA.col(i).tail(n-i-1);
+
+ matA.bottomRightCorner(remainingSize, remainingSize).template selfadjointView<Lower>()
+ .rankUpdate(matA.col(i).tail(remainingSize), hCoeffs.tail(remainingSize), Scalar(-1));
+
+ matA.col(i).coeffRef(i+1) = beta;
+ hCoeffs.coeffRef(i) = h;
+ }
+}
+
+// forward declaration, implementation at the end of this file
+template<typename MatrixType,
+ int Size=MatrixType::ColsAtCompileTime,
+ bool IsComplex=NumTraits<typename MatrixType::Scalar>::IsComplex>
+struct tridiagonalization_inplace_selector;
+
+/** \brief Performs a full tridiagonalization in place
+ *
+ * \param[in,out] mat On input, the selfadjoint matrix whose tridiagonal
+ * decomposition is to be computed. Only the lower triangular part referenced.
+ * The rest is left unchanged. On output, the orthogonal matrix Q
+ * in the decomposition if \p extractQ is true.
+ * \param[out] diag The diagonal of the tridiagonal matrix T in the
+ * decomposition.
+ * \param[out] subdiag The subdiagonal of the tridiagonal matrix T in
+ * the decomposition.
+ * \param[in] extractQ If true, the orthogonal matrix Q in the
+ * decomposition is computed and stored in \p mat.
+ *
+ * Computes the tridiagonal decomposition of the selfadjoint matrix \p mat in place
+ * such that \f$ mat = Q T Q^* \f$ where \f$ Q \f$ is unitary and \f$ T \f$ a real
+ * symmetric tridiagonal matrix.
+ *
+ * The tridiagonal matrix T is passed to the output parameters \p diag and \p subdiag. If
+ * \p extractQ is true, then the orthogonal matrix Q is passed to \p mat. Otherwise the lower
+ * part of the matrix \p mat is destroyed.
+ *
+ * The vectors \p diag and \p subdiag are not resized. The function
+ * assumes that they are already of the correct size. The length of the
+ * vector \p diag should equal the number of rows in \p mat, and the
+ * length of the vector \p subdiag should be one left.
+ *
+ * This implementation contains an optimized path for 3-by-3 matrices
+ * which is especially useful for plane fitting.
+ *
+ * \note Currently, it requires two temporary vectors to hold the intermediate
+ * Householder coefficients, and to reconstruct the matrix Q from the Householder
+ * reflectors.
+ *
+ * Example (this uses the same matrix as the example in
+ * Tridiagonalization::Tridiagonalization(const MatrixType&)):
+ * \include Tridiagonalization_decomposeInPlace.cpp
+ * Output: \verbinclude Tridiagonalization_decomposeInPlace.out
+ *
+ * \sa class Tridiagonalization
+ */
+template<typename MatrixType, typename DiagonalType, typename SubDiagonalType, typename CoeffVectorType>
+EIGEN_DEVICE_FUNC
+void tridiagonalization_inplace(MatrixType& mat, DiagonalType& diag, SubDiagonalType& subdiag,
+ CoeffVectorType& hcoeffs, bool extractQ)
+{
+ eigen_assert(mat.cols()==mat.rows() && diag.size()==mat.rows() && subdiag.size()==mat.rows()-1);
+ tridiagonalization_inplace_selector<MatrixType>::run(mat, diag, subdiag, hcoeffs, extractQ);
+}
+
+/** \internal
+ * General full tridiagonalization
+ */
+template<typename MatrixType, int Size, bool IsComplex>
+struct tridiagonalization_inplace_selector
+{
+ typedef typename Tridiagonalization<MatrixType>::HouseholderSequenceType HouseholderSequenceType;
+ template<typename DiagonalType, typename SubDiagonalType, typename CoeffVectorType>
+ static EIGEN_DEVICE_FUNC
+ void run(MatrixType& mat, DiagonalType& diag, SubDiagonalType& subdiag, CoeffVectorType& hCoeffs, bool extractQ)
+ {
+ tridiagonalization_inplace(mat, hCoeffs);
+ diag = mat.diagonal().real();
+ subdiag = mat.template diagonal<-1>().real();
+ if(extractQ)
+ mat = HouseholderSequenceType(mat, hCoeffs.conjugate())
+ .setLength(mat.rows() - 1)
+ .setShift(1);
+ }
+};
+
+/** \internal
+ * Specialization for 3x3 real matrices.
+ * Especially useful for plane fitting.
+ */
+template<typename MatrixType>
+struct tridiagonalization_inplace_selector<MatrixType,3,false>
+{
+ typedef typename MatrixType::Scalar Scalar;
+ typedef typename MatrixType::RealScalar RealScalar;
+
+ template<typename DiagonalType, typename SubDiagonalType, typename CoeffVectorType>
+ static void run(MatrixType& mat, DiagonalType& diag, SubDiagonalType& subdiag, CoeffVectorType&, bool extractQ)
+ {
+ using std::sqrt;
+ const RealScalar tol = (std::numeric_limits<RealScalar>::min)();
+ diag[0] = mat(0,0);
+ RealScalar v1norm2 = numext::abs2(mat(2,0));
+ if(v1norm2 <= tol)
+ {
+ diag[1] = mat(1,1);
+ diag[2] = mat(2,2);
+ subdiag[0] = mat(1,0);
+ subdiag[1] = mat(2,1);
+ if (extractQ)
+ mat.setIdentity();
+ }
+ else
+ {
+ RealScalar beta = sqrt(numext::abs2(mat(1,0)) + v1norm2);
+ RealScalar invBeta = RealScalar(1)/beta;
+ Scalar m01 = mat(1,0) * invBeta;
+ Scalar m02 = mat(2,0) * invBeta;
+ Scalar q = RealScalar(2)*m01*mat(2,1) + m02*(mat(2,2) - mat(1,1));
+ diag[1] = mat(1,1) + m02*q;
+ diag[2] = mat(2,2) - m02*q;
+ subdiag[0] = beta;
+ subdiag[1] = mat(2,1) - m01 * q;
+ if (extractQ)
+ {
+ mat << 1, 0, 0,
+ 0, m01, m02,
+ 0, m02, -m01;
+ }
+ }
+ }
+};
+
+/** \internal
+ * Trivial specialization for 1x1 matrices
+ */
+template<typename MatrixType, bool IsComplex>
+struct tridiagonalization_inplace_selector<MatrixType,1,IsComplex>
+{
+ typedef typename MatrixType::Scalar Scalar;
+
+ template<typename DiagonalType, typename SubDiagonalType, typename CoeffVectorType>
+ static EIGEN_DEVICE_FUNC
+ void run(MatrixType& mat, DiagonalType& diag, SubDiagonalType&, CoeffVectorType&, bool extractQ)
+ {
+ diag(0,0) = numext::real(mat(0,0));
+ if(extractQ)
+ mat(0,0) = Scalar(1);
+ }
+};
+
+/** \internal
+ * \eigenvalues_module \ingroup Eigenvalues_Module
+ *
+ * \brief Expression type for return value of Tridiagonalization::matrixT()
+ *
+ * \tparam MatrixType type of underlying dense matrix
+ */
+template<typename MatrixType> struct TridiagonalizationMatrixTReturnType
+: public ReturnByValue<TridiagonalizationMatrixTReturnType<MatrixType> >
+{
+ public:
+ /** \brief Constructor.
+ *
+ * \param[in] mat The underlying dense matrix
+ */
+ TridiagonalizationMatrixTReturnType(const MatrixType& mat) : m_matrix(mat) { }
+
+ template <typename ResultType>
+ inline void evalTo(ResultType& result) const
+ {
+ result.setZero();
+ result.template diagonal<1>() = m_matrix.template diagonal<-1>().conjugate();
+ result.diagonal() = m_matrix.diagonal();
+ result.template diagonal<-1>() = m_matrix.template diagonal<-1>();
+ }
+
+ EIGEN_CONSTEXPR Index rows() const EIGEN_NOEXCEPT { return m_matrix.rows(); }
+ EIGEN_CONSTEXPR Index cols() const EIGEN_NOEXCEPT { return m_matrix.cols(); }
+
+ protected:
+ typename MatrixType::Nested m_matrix;
+};
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_TRIDIAGONALIZATION_H
diff --git a/Eigen/src/Geometry/AlignedBox.h b/Eigen/src/Geometry/AlignedBox.h
new file mode 100644
index 0000000..a824817
--- /dev/null
+++ b/Eigen/src/Geometry/AlignedBox.h
@@ -0,0 +1,488 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+// Function void Eigen::AlignedBox::transform(const Transform& transform)
+// is provided under the following license agreement:
+//
+// Software License Agreement (BSD License)
+//
+// Copyright (c) 2011-2014, Willow Garage, Inc.
+// Copyright (c) 2014-2015, Open Source Robotics Foundation
+// All rights reserved.
+//
+// Redistribution and use in source and binary forms, with or without
+// modification, are permitted provided that the following conditions
+// are met:
+//
+// * Redistributions of source code must retain the above copyright
+// notice, this list of conditions and the following disclaimer.
+// * Redistributions in binary form must reproduce the above
+// copyright notice, this list of conditions and the following
+// disclaimer in the documentation and/or other materials provided
+// with the distribution.
+// * Neither the name of Open Source Robotics Foundation nor the names of its
+// contributors may be used to endorse or promote products derived
+// from this software without specific prior written permission.
+//
+// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+// LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
+// FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
+// COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
+// INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
+// BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
+// LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
+// CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+// LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
+// ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+// POSSIBILITY OF SUCH DAMAGE.
+
+#ifndef EIGEN_ALIGNEDBOX_H
+#define EIGEN_ALIGNEDBOX_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+/** \geometry_module \ingroup Geometry_Module
+ *
+ *
+ * \class AlignedBox
+ *
+ * \brief An axis aligned box
+ *
+ * \tparam Scalar_ the type of the scalar coefficients
+ * \tparam AmbientDim_ the dimension of the ambient space, can be a compile time value or Dynamic.
+ *
+ * This class represents an axis aligned box as a pair of the minimal and maximal corners.
+ * \warning The result of most methods is undefined when applied to an empty box. You can check for empty boxes using isEmpty().
+ * \sa alignedboxtypedefs
+ */
+template <typename Scalar_, int AmbientDim_>
+class AlignedBox
+{
+public:
+EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE(Scalar_,AmbientDim_)
+ enum { AmbientDimAtCompileTime = AmbientDim_ };
+ typedef Scalar_ Scalar;
+ typedef NumTraits<Scalar> ScalarTraits;
+ typedef Eigen::Index Index; ///< \deprecated since Eigen 3.3
+ typedef typename ScalarTraits::Real RealScalar;
+ typedef typename ScalarTraits::NonInteger NonInteger;
+ typedef Matrix<Scalar,AmbientDimAtCompileTime,1> VectorType;
+ typedef CwiseBinaryOp<internal::scalar_sum_op<Scalar>, const VectorType, const VectorType> VectorTypeSum;
+
+ /** Define constants to name the corners of a 1D, 2D or 3D axis aligned bounding box */
+ enum CornerType
+ {
+ /** 1D names @{ */
+ Min=0, Max=1,
+ /** @} */
+
+ /** Identifier for 2D corner @{ */
+ BottomLeft=0, BottomRight=1,
+ TopLeft=2, TopRight=3,
+ /** @} */
+
+ /** Identifier for 3D corner @{ */
+ BottomLeftFloor=0, BottomRightFloor=1,
+ TopLeftFloor=2, TopRightFloor=3,
+ BottomLeftCeil=4, BottomRightCeil=5,
+ TopLeftCeil=6, TopRightCeil=7
+ /** @} */
+ };
+
+
+ /** Default constructor initializing a null box. */
+ EIGEN_DEVICE_FUNC inline AlignedBox()
+ { if (EIGEN_CONST_CONDITIONAL(AmbientDimAtCompileTime!=Dynamic)) setEmpty(); }
+
+ /** Constructs a null box with \a _dim the dimension of the ambient space. */
+ EIGEN_DEVICE_FUNC inline explicit AlignedBox(Index _dim) : m_min(_dim), m_max(_dim)
+ { setEmpty(); }
+
+ /** Constructs a box with extremities \a _min and \a _max.
+ * \warning If either component of \a _min is larger than the same component of \a _max, the constructed box is empty. */
+ template<typename OtherVectorType1, typename OtherVectorType2>
+ EIGEN_DEVICE_FUNC inline AlignedBox(const OtherVectorType1& _min, const OtherVectorType2& _max) : m_min(_min), m_max(_max) {}
+
+ /** Constructs a box containing a single point \a p. */
+ template<typename Derived>
+ EIGEN_DEVICE_FUNC inline explicit AlignedBox(const MatrixBase<Derived>& p) : m_min(p), m_max(m_min)
+ { }
+
+ EIGEN_DEVICE_FUNC ~AlignedBox() {}
+
+ /** \returns the dimension in which the box holds */
+ EIGEN_DEVICE_FUNC inline Index dim() const { return AmbientDimAtCompileTime==Dynamic ? m_min.size() : Index(AmbientDimAtCompileTime); }
+
+ /** \deprecated use isEmpty() */
+ EIGEN_DEVICE_FUNC inline bool isNull() const { return isEmpty(); }
+
+ /** \deprecated use setEmpty() */
+ EIGEN_DEVICE_FUNC inline void setNull() { setEmpty(); }
+
+ /** \returns true if the box is empty.
+ * \sa setEmpty */
+ EIGEN_DEVICE_FUNC inline bool isEmpty() const { return (m_min.array() > m_max.array()).any(); }
+
+ /** Makes \c *this an empty box.
+ * \sa isEmpty */
+ EIGEN_DEVICE_FUNC inline void setEmpty()
+ {
+ m_min.setConstant( ScalarTraits::highest() );
+ m_max.setConstant( ScalarTraits::lowest() );
+ }
+
+ /** \returns the minimal corner */
+ EIGEN_DEVICE_FUNC inline const VectorType& (min)() const { return m_min; }
+ /** \returns a non const reference to the minimal corner */
+ EIGEN_DEVICE_FUNC inline VectorType& (min)() { return m_min; }
+ /** \returns the maximal corner */
+ EIGEN_DEVICE_FUNC inline const VectorType& (max)() const { return m_max; }
+ /** \returns a non const reference to the maximal corner */
+ EIGEN_DEVICE_FUNC inline VectorType& (max)() { return m_max; }
+
+ /** \returns the center of the box */
+ EIGEN_DEVICE_FUNC inline const EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(VectorTypeSum, RealScalar, quotient)
+ center() const
+ { return (m_min+m_max)/RealScalar(2); }
+
+ /** \returns the lengths of the sides of the bounding box.
+ * Note that this function does not get the same
+ * result for integral or floating scalar types: see
+ */
+ EIGEN_DEVICE_FUNC inline const CwiseBinaryOp< internal::scalar_difference_op<Scalar,Scalar>, const VectorType, const VectorType> sizes() const
+ { return m_max - m_min; }
+
+ /** \returns the volume of the bounding box */
+ EIGEN_DEVICE_FUNC inline Scalar volume() const
+ { return sizes().prod(); }
+
+ /** \returns an expression for the bounding box diagonal vector
+ * if the length of the diagonal is needed: diagonal().norm()
+ * will provide it.
+ */
+ EIGEN_DEVICE_FUNC inline CwiseBinaryOp< internal::scalar_difference_op<Scalar,Scalar>, const VectorType, const VectorType> diagonal() const
+ { return sizes(); }
+
+ /** \returns the vertex of the bounding box at the corner defined by
+ * the corner-id corner. It works only for a 1D, 2D or 3D bounding box.
+ * For 1D bounding boxes corners are named by 2 enum constants:
+ * BottomLeft and BottomRight.
+ * For 2D bounding boxes, corners are named by 4 enum constants:
+ * BottomLeft, BottomRight, TopLeft, TopRight.
+ * For 3D bounding boxes, the following names are added:
+ * BottomLeftCeil, BottomRightCeil, TopLeftCeil, TopRightCeil.
+ */
+ EIGEN_DEVICE_FUNC inline VectorType corner(CornerType corner) const
+ {
+ EIGEN_STATIC_ASSERT(AmbientDim_ <= 3, THIS_METHOD_IS_ONLY_FOR_VECTORS_OF_A_SPECIFIC_SIZE);
+
+ VectorType res;
+
+ Index mult = 1;
+ for(Index d=0; d<dim(); ++d)
+ {
+ if( mult & corner ) res[d] = m_max[d];
+ else res[d] = m_min[d];
+ mult *= 2;
+ }
+ return res;
+ }
+
+ /** \returns a random point inside the bounding box sampled with
+ * a uniform distribution */
+ EIGEN_DEVICE_FUNC inline VectorType sample() const
+ {
+ VectorType r(dim());
+ for(Index d=0; d<dim(); ++d)
+ {
+ if(!ScalarTraits::IsInteger)
+ {
+ r[d] = m_min[d] + (m_max[d]-m_min[d])
+ * internal::random<Scalar>(Scalar(0), Scalar(1));
+ }
+ else
+ r[d] = internal::random(m_min[d], m_max[d]);
+ }
+ return r;
+ }
+
+ /** \returns true if the point \a p is inside the box \c *this. */
+ template<typename Derived>
+ EIGEN_DEVICE_FUNC inline bool contains(const MatrixBase<Derived>& p) const
+ {
+ typename internal::nested_eval<Derived,2>::type p_n(p.derived());
+ return (m_min.array()<=p_n.array()).all() && (p_n.array()<=m_max.array()).all();
+ }
+
+ /** \returns true if the box \a b is entirely inside the box \c *this. */
+ EIGEN_DEVICE_FUNC inline bool contains(const AlignedBox& b) const
+ { return (m_min.array()<=(b.min)().array()).all() && ((b.max)().array()<=m_max.array()).all(); }
+
+ /** \returns true if the box \a b is intersecting the box \c *this.
+ * \sa intersection, clamp */
+ EIGEN_DEVICE_FUNC inline bool intersects(const AlignedBox& b) const
+ { return (m_min.array()<=(b.max)().array()).all() && ((b.min)().array()<=m_max.array()).all(); }
+
+ /** Extends \c *this such that it contains the point \a p and returns a reference to \c *this.
+ * \sa extend(const AlignedBox&) */
+ template<typename Derived>
+ EIGEN_DEVICE_FUNC inline AlignedBox& extend(const MatrixBase<Derived>& p)
+ {
+ typename internal::nested_eval<Derived,2>::type p_n(p.derived());
+ m_min = m_min.cwiseMin(p_n);
+ m_max = m_max.cwiseMax(p_n);
+ return *this;
+ }
+
+ /** Extends \c *this such that it contains the box \a b and returns a reference to \c *this.
+ * \sa merged, extend(const MatrixBase&) */
+ EIGEN_DEVICE_FUNC inline AlignedBox& extend(const AlignedBox& b)
+ {
+ m_min = m_min.cwiseMin(b.m_min);
+ m_max = m_max.cwiseMax(b.m_max);
+ return *this;
+ }
+
+ /** Clamps \c *this by the box \a b and returns a reference to \c *this.
+ * \note If the boxes don't intersect, the resulting box is empty.
+ * \sa intersection(), intersects() */
+ EIGEN_DEVICE_FUNC inline AlignedBox& clamp(const AlignedBox& b)
+ {
+ m_min = m_min.cwiseMax(b.m_min);
+ m_max = m_max.cwiseMin(b.m_max);
+ return *this;
+ }
+
+ /** Returns an AlignedBox that is the intersection of \a b and \c *this
+ * \note If the boxes don't intersect, the resulting box is empty.
+ * \sa intersects(), clamp, contains() */
+ EIGEN_DEVICE_FUNC inline AlignedBox intersection(const AlignedBox& b) const
+ {return AlignedBox(m_min.cwiseMax(b.m_min), m_max.cwiseMin(b.m_max)); }
+
+ /** Returns an AlignedBox that is the union of \a b and \c *this.
+ * \note Merging with an empty box may result in a box bigger than \c *this.
+ * \sa extend(const AlignedBox&) */
+ EIGEN_DEVICE_FUNC inline AlignedBox merged(const AlignedBox& b) const
+ { return AlignedBox(m_min.cwiseMin(b.m_min), m_max.cwiseMax(b.m_max)); }
+
+ /** Translate \c *this by the vector \a t and returns a reference to \c *this. */
+ template<typename Derived>
+ EIGEN_DEVICE_FUNC inline AlignedBox& translate(const MatrixBase<Derived>& a_t)
+ {
+ const typename internal::nested_eval<Derived,2>::type t(a_t.derived());
+ m_min += t;
+ m_max += t;
+ return *this;
+ }
+
+ /** \returns a copy of \c *this translated by the vector \a t. */
+ template<typename Derived>
+ EIGEN_DEVICE_FUNC inline AlignedBox translated(const MatrixBase<Derived>& a_t) const
+ {
+ AlignedBox result(m_min, m_max);
+ result.translate(a_t);
+ return result;
+ }
+
+ /** \returns the squared distance between the point \a p and the box \c *this,
+ * and zero if \a p is inside the box.
+ * \sa exteriorDistance(const MatrixBase&), squaredExteriorDistance(const AlignedBox&)
+ */
+ template<typename Derived>
+ EIGEN_DEVICE_FUNC inline Scalar squaredExteriorDistance(const MatrixBase<Derived>& p) const;
+
+ /** \returns the squared distance between the boxes \a b and \c *this,
+ * and zero if the boxes intersect.
+ * \sa exteriorDistance(const AlignedBox&), squaredExteriorDistance(const MatrixBase&)
+ */
+ EIGEN_DEVICE_FUNC inline Scalar squaredExteriorDistance(const AlignedBox& b) const;
+
+ /** \returns the distance between the point \a p and the box \c *this,
+ * and zero if \a p is inside the box.
+ * \sa squaredExteriorDistance(const MatrixBase&), exteriorDistance(const AlignedBox&)
+ */
+ template<typename Derived>
+ EIGEN_DEVICE_FUNC inline NonInteger exteriorDistance(const MatrixBase<Derived>& p) const
+ { EIGEN_USING_STD(sqrt) return sqrt(NonInteger(squaredExteriorDistance(p))); }
+
+ /** \returns the distance between the boxes \a b and \c *this,
+ * and zero if the boxes intersect.
+ * \sa squaredExteriorDistance(const AlignedBox&), exteriorDistance(const MatrixBase&)
+ */
+ EIGEN_DEVICE_FUNC inline NonInteger exteriorDistance(const AlignedBox& b) const
+ { EIGEN_USING_STD(sqrt) return sqrt(NonInteger(squaredExteriorDistance(b))); }
+
+ /**
+ * Specialization of transform for pure translation.
+ */
+ template<int Mode, int Options>
+ EIGEN_DEVICE_FUNC inline void transform(
+ const typename Transform<Scalar, AmbientDimAtCompileTime, Mode, Options>::TranslationType& translation)
+ {
+ this->translate(translation);
+ }
+
+ /**
+ * Transforms this box by \a transform and recomputes it to
+ * still be an axis-aligned box.
+ *
+ * \note This method is provided under BSD license (see the top of this file).
+ */
+ template<int Mode, int Options>
+ EIGEN_DEVICE_FUNC inline void transform(const Transform<Scalar, AmbientDimAtCompileTime, Mode, Options>& transform)
+ {
+ // Only Affine and Isometry transforms are currently supported.
+ EIGEN_STATIC_ASSERT(Mode == Affine || Mode == AffineCompact || Mode == Isometry, THIS_METHOD_IS_ONLY_FOR_SPECIFIC_TRANSFORMATIONS);
+
+ // Method adapted from FCL src/shape/geometric_shapes_utility.cpp#computeBV<AABB, Box>(...)
+ // https://github.com/flexible-collision-library/fcl/blob/fcl-0.4/src/shape/geometric_shapes_utility.cpp#L292
+ //
+ // Here's a nice explanation why it works: https://zeuxcg.org/2010/10/17/aabb-from-obb-with-component-wise-abs/
+
+ // two times rotated extent
+ const VectorType rotated_extent_2 = transform.linear().cwiseAbs() * sizes();
+ // two times new center
+ const VectorType rotated_center_2 = transform.linear() * (this->m_max + this->m_min) +
+ Scalar(2) * transform.translation();
+
+ this->m_max = (rotated_center_2 + rotated_extent_2) / Scalar(2);
+ this->m_min = (rotated_center_2 - rotated_extent_2) / Scalar(2);
+ }
+
+ /**
+ * \returns a copy of \c *this transformed by \a transform and recomputed to
+ * still be an axis-aligned box.
+ */
+ template<int Mode, int Options>
+ EIGEN_DEVICE_FUNC AlignedBox transformed(const Transform<Scalar, AmbientDimAtCompileTime, Mode, Options>& transform) const
+ {
+ AlignedBox result(m_min, m_max);
+ result.transform(transform);
+ return result;
+ }
+
+ /** \returns \c *this with scalar type casted to \a NewScalarType
+ *
+ * Note that if \a NewScalarType is equal to the current scalar type of \c *this
+ * then this function smartly returns a const reference to \c *this.
+ */
+ template<typename NewScalarType>
+ EIGEN_DEVICE_FUNC inline typename internal::cast_return_type<AlignedBox,
+ AlignedBox<NewScalarType,AmbientDimAtCompileTime> >::type cast() const
+ {
+ return typename internal::cast_return_type<AlignedBox,
+ AlignedBox<NewScalarType,AmbientDimAtCompileTime> >::type(*this);
+ }
+
+ /** Copy constructor with scalar type conversion */
+ template<typename OtherScalarType>
+ EIGEN_DEVICE_FUNC inline explicit AlignedBox(const AlignedBox<OtherScalarType,AmbientDimAtCompileTime>& other)
+ {
+ m_min = (other.min)().template cast<Scalar>();
+ m_max = (other.max)().template cast<Scalar>();
+ }
+
+ /** \returns \c true if \c *this is approximately equal to \a other, within the precision
+ * determined by \a prec.
+ *
+ * \sa MatrixBase::isApprox() */
+ EIGEN_DEVICE_FUNC bool isApprox(const AlignedBox& other, const RealScalar& prec = ScalarTraits::dummy_precision()) const
+ { return m_min.isApprox(other.m_min, prec) && m_max.isApprox(other.m_max, prec); }
+
+protected:
+
+ VectorType m_min, m_max;
+};
+
+
+
+template<typename Scalar,int AmbientDim>
+template<typename Derived>
+EIGEN_DEVICE_FUNC inline Scalar AlignedBox<Scalar,AmbientDim>::squaredExteriorDistance(const MatrixBase<Derived>& a_p) const
+{
+ typename internal::nested_eval<Derived,2*AmbientDim>::type p(a_p.derived());
+ Scalar dist2(0);
+ Scalar aux;
+ for (Index k=0; k<dim(); ++k)
+ {
+ if( m_min[k] > p[k] )
+ {
+ aux = m_min[k] - p[k];
+ dist2 += aux*aux;
+ }
+ else if( p[k] > m_max[k] )
+ {
+ aux = p[k] - m_max[k];
+ dist2 += aux*aux;
+ }
+ }
+ return dist2;
+}
+
+template<typename Scalar,int AmbientDim>
+EIGEN_DEVICE_FUNC inline Scalar AlignedBox<Scalar,AmbientDim>::squaredExteriorDistance(const AlignedBox& b) const
+{
+ Scalar dist2(0);
+ Scalar aux;
+ for (Index k=0; k<dim(); ++k)
+ {
+ if( m_min[k] > b.m_max[k] )
+ {
+ aux = m_min[k] - b.m_max[k];
+ dist2 += aux*aux;
+ }
+ else if( b.m_min[k] > m_max[k] )
+ {
+ aux = b.m_min[k] - m_max[k];
+ dist2 += aux*aux;
+ }
+ }
+ return dist2;
+}
+
+/** \defgroup alignedboxtypedefs Global aligned box typedefs
+ *
+ * \ingroup Geometry_Module
+ *
+ * Eigen defines several typedef shortcuts for most common aligned box types.
+ *
+ * The general patterns are the following:
+ *
+ * \c AlignedBoxSizeType where \c Size can be \c 1, \c 2,\c 3,\c 4 for fixed size boxes or \c X for dynamic size,
+ * and where \c Type can be \c i for integer, \c f for float, \c d for double.
+ *
+ * For example, \c AlignedBox3d is a fixed-size 3x3 aligned box type of doubles, and \c AlignedBoxXf is a dynamic-size aligned box of floats.
+ *
+ * \sa class AlignedBox
+ */
+
+#define EIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, Size, SizeSuffix) \
+/** \ingroup alignedboxtypedefs */ \
+typedef AlignedBox<Type, Size> AlignedBox##SizeSuffix##TypeSuffix;
+
+#define EIGEN_MAKE_TYPEDEFS_ALL_SIZES(Type, TypeSuffix) \
+EIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, 1, 1) \
+EIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, 2, 2) \
+EIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, 3, 3) \
+EIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, 4, 4) \
+EIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, Dynamic, X)
+
+EIGEN_MAKE_TYPEDEFS_ALL_SIZES(int, i)
+EIGEN_MAKE_TYPEDEFS_ALL_SIZES(float, f)
+EIGEN_MAKE_TYPEDEFS_ALL_SIZES(double, d)
+
+#undef EIGEN_MAKE_TYPEDEFS_ALL_SIZES
+#undef EIGEN_MAKE_TYPEDEFS
+
+} // end namespace Eigen
+
+#endif // EIGEN_ALIGNEDBOX_H
diff --git a/Eigen/src/Geometry/AngleAxis.h b/Eigen/src/Geometry/AngleAxis.h
new file mode 100644
index 0000000..c23a908
--- /dev/null
+++ b/Eigen/src/Geometry/AngleAxis.h
@@ -0,0 +1,249 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_ANGLEAXIS_H
+#define EIGEN_ANGLEAXIS_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+/** \geometry_module \ingroup Geometry_Module
+ *
+ * \class AngleAxis
+ *
+ * \brief Represents a 3D rotation as a rotation angle around an arbitrary 3D axis
+ *
+ * \param Scalar_ the scalar type, i.e., the type of the coefficients.
+ *
+ * \warning When setting up an AngleAxis object, the axis vector \b must \b be \b normalized.
+ *
+ * The following two typedefs are provided for convenience:
+ * \li \c AngleAxisf for \c float
+ * \li \c AngleAxisd for \c double
+ *
+ * Combined with MatrixBase::Unit{X,Y,Z}, AngleAxis can be used to easily
+ * mimic Euler-angles. Here is an example:
+ * \include AngleAxis_mimic_euler.cpp
+ * Output: \verbinclude AngleAxis_mimic_euler.out
+ *
+ * \note This class is not aimed to be used to store a rotation transformation,
+ * but rather to make easier the creation of other rotation (Quaternion, rotation Matrix)
+ * and transformation objects.
+ *
+ * \sa class Quaternion, class Transform, MatrixBase::UnitX()
+ */
+
+namespace internal {
+template<typename Scalar_> struct traits<AngleAxis<Scalar_> >
+{
+ typedef Scalar_ Scalar;
+};
+}
+
+template<typename Scalar_>
+class AngleAxis : public RotationBase<AngleAxis<Scalar_>,3>
+{
+ typedef RotationBase<AngleAxis<Scalar_>,3> Base;
+
+public:
+
+ using Base::operator*;
+
+ enum { Dim = 3 };
+ /** the scalar type of the coefficients */
+ typedef Scalar_ Scalar;
+ typedef Matrix<Scalar,3,3> Matrix3;
+ typedef Matrix<Scalar,3,1> Vector3;
+ typedef Quaternion<Scalar> QuaternionType;
+
+protected:
+
+ Vector3 m_axis;
+ Scalar m_angle;
+
+public:
+
+ /** Default constructor without initialization. */
+ EIGEN_DEVICE_FUNC AngleAxis() {}
+ /** Constructs and initialize the angle-axis rotation from an \a angle in radian
+ * and an \a axis which \b must \b be \b normalized.
+ *
+ * \warning If the \a axis vector is not normalized, then the angle-axis object
+ * represents an invalid rotation. */
+ template<typename Derived>
+ EIGEN_DEVICE_FUNC
+ inline AngleAxis(const Scalar& angle, const MatrixBase<Derived>& axis) : m_axis(axis), m_angle(angle) {}
+ /** Constructs and initialize the angle-axis rotation from a quaternion \a q.
+ * This function implicitly normalizes the quaternion \a q.
+ */
+ template<typename QuatDerived>
+ EIGEN_DEVICE_FUNC inline explicit AngleAxis(const QuaternionBase<QuatDerived>& q) { *this = q; }
+ /** Constructs and initialize the angle-axis rotation from a 3x3 rotation matrix. */
+ template<typename Derived>
+ EIGEN_DEVICE_FUNC inline explicit AngleAxis(const MatrixBase<Derived>& m) { *this = m; }
+
+ /** \returns the value of the rotation angle in radian */
+ EIGEN_DEVICE_FUNC Scalar angle() const { return m_angle; }
+ /** \returns a read-write reference to the stored angle in radian */
+ EIGEN_DEVICE_FUNC Scalar& angle() { return m_angle; }
+
+ /** \returns the rotation axis */
+ EIGEN_DEVICE_FUNC const Vector3& axis() const { return m_axis; }
+ /** \returns a read-write reference to the stored rotation axis.
+ *
+ * \warning The rotation axis must remain a \b unit vector.
+ */
+ EIGEN_DEVICE_FUNC Vector3& axis() { return m_axis; }
+
+ /** Concatenates two rotations */
+ EIGEN_DEVICE_FUNC inline QuaternionType operator* (const AngleAxis& other) const
+ { return QuaternionType(*this) * QuaternionType(other); }
+
+ /** Concatenates two rotations */
+ EIGEN_DEVICE_FUNC inline QuaternionType operator* (const QuaternionType& other) const
+ { return QuaternionType(*this) * other; }
+
+ /** Concatenates two rotations */
+ friend EIGEN_DEVICE_FUNC inline QuaternionType operator* (const QuaternionType& a, const AngleAxis& b)
+ { return a * QuaternionType(b); }
+
+ /** \returns the inverse rotation, i.e., an angle-axis with opposite rotation angle */
+ EIGEN_DEVICE_FUNC AngleAxis inverse() const
+ { return AngleAxis(-m_angle, m_axis); }
+
+ template<class QuatDerived>
+ EIGEN_DEVICE_FUNC AngleAxis& operator=(const QuaternionBase<QuatDerived>& q);
+ template<typename Derived>
+ EIGEN_DEVICE_FUNC AngleAxis& operator=(const MatrixBase<Derived>& m);
+
+ template<typename Derived>
+ EIGEN_DEVICE_FUNC AngleAxis& fromRotationMatrix(const MatrixBase<Derived>& m);
+ EIGEN_DEVICE_FUNC Matrix3 toRotationMatrix(void) const;
+
+ /** \returns \c *this with scalar type casted to \a NewScalarType
+ *
+ * Note that if \a NewScalarType is equal to the current scalar type of \c *this
+ * then this function smartly returns a const reference to \c *this.
+ */
+ template<typename NewScalarType>
+ EIGEN_DEVICE_FUNC inline typename internal::cast_return_type<AngleAxis,AngleAxis<NewScalarType> >::type cast() const
+ { return typename internal::cast_return_type<AngleAxis,AngleAxis<NewScalarType> >::type(*this); }
+
+ /** Copy constructor with scalar type conversion */
+ template<typename OtherScalarType>
+ EIGEN_DEVICE_FUNC inline explicit AngleAxis(const AngleAxis<OtherScalarType>& other)
+ {
+ m_axis = other.axis().template cast<Scalar>();
+ m_angle = Scalar(other.angle());
+ }
+
+ EIGEN_DEVICE_FUNC static inline const AngleAxis Identity() { return AngleAxis(Scalar(0), Vector3::UnitX()); }
+
+ /** \returns \c true if \c *this is approximately equal to \a other, within the precision
+ * determined by \a prec.
+ *
+ * \sa MatrixBase::isApprox() */
+ EIGEN_DEVICE_FUNC bool isApprox(const AngleAxis& other, const typename NumTraits<Scalar>::Real& prec = NumTraits<Scalar>::dummy_precision()) const
+ { return m_axis.isApprox(other.m_axis, prec) && internal::isApprox(m_angle,other.m_angle, prec); }
+};
+
+/** \ingroup Geometry_Module
+ * single precision angle-axis type */
+typedef AngleAxis<float> AngleAxisf;
+/** \ingroup Geometry_Module
+ * double precision angle-axis type */
+typedef AngleAxis<double> AngleAxisd;
+
+/** Set \c *this from a \b unit quaternion.
+ *
+ * The resulting axis is normalized, and the computed angle is in the [0,pi] range.
+ *
+ * This function implicitly normalizes the quaternion \a q.
+ */
+template<typename Scalar>
+template<typename QuatDerived>
+EIGEN_DEVICE_FUNC AngleAxis<Scalar>& AngleAxis<Scalar>::operator=(const QuaternionBase<QuatDerived>& q)
+{
+ EIGEN_USING_STD(atan2)
+ EIGEN_USING_STD(abs)
+ Scalar n = q.vec().norm();
+ if(n<NumTraits<Scalar>::epsilon())
+ n = q.vec().stableNorm();
+
+ if (n != Scalar(0))
+ {
+ m_angle = Scalar(2)*atan2(n, abs(q.w()));
+ if(q.w() < Scalar(0))
+ n = -n;
+ m_axis = q.vec() / n;
+ }
+ else
+ {
+ m_angle = Scalar(0);
+ m_axis << Scalar(1), Scalar(0), Scalar(0);
+ }
+ return *this;
+}
+
+/** Set \c *this from a 3x3 rotation matrix \a mat.
+ */
+template<typename Scalar>
+template<typename Derived>
+EIGEN_DEVICE_FUNC AngleAxis<Scalar>& AngleAxis<Scalar>::operator=(const MatrixBase<Derived>& mat)
+{
+ // Since a direct conversion would not be really faster,
+ // let's use the robust Quaternion implementation:
+ return *this = QuaternionType(mat);
+}
+
+/**
+* \brief Sets \c *this from a 3x3 rotation matrix.
+**/
+template<typename Scalar>
+template<typename Derived>
+EIGEN_DEVICE_FUNC AngleAxis<Scalar>& AngleAxis<Scalar>::fromRotationMatrix(const MatrixBase<Derived>& mat)
+{
+ return *this = QuaternionType(mat);
+}
+
+/** Constructs and \returns an equivalent 3x3 rotation matrix.
+ */
+template<typename Scalar>
+typename AngleAxis<Scalar>::Matrix3
+EIGEN_DEVICE_FUNC AngleAxis<Scalar>::toRotationMatrix(void) const
+{
+ EIGEN_USING_STD(sin)
+ EIGEN_USING_STD(cos)
+ Matrix3 res;
+ Vector3 sin_axis = sin(m_angle) * m_axis;
+ Scalar c = cos(m_angle);
+ Vector3 cos1_axis = (Scalar(1)-c) * m_axis;
+
+ Scalar tmp;
+ tmp = cos1_axis.x() * m_axis.y();
+ res.coeffRef(0,1) = tmp - sin_axis.z();
+ res.coeffRef(1,0) = tmp + sin_axis.z();
+
+ tmp = cos1_axis.x() * m_axis.z();
+ res.coeffRef(0,2) = tmp + sin_axis.y();
+ res.coeffRef(2,0) = tmp - sin_axis.y();
+
+ tmp = cos1_axis.y() * m_axis.z();
+ res.coeffRef(1,2) = tmp - sin_axis.x();
+ res.coeffRef(2,1) = tmp + sin_axis.x();
+
+ res.diagonal() = (cos1_axis.cwiseProduct(m_axis)).array() + c;
+
+ return res;
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_ANGLEAXIS_H
diff --git a/Eigen/src/Geometry/EulerAngles.h b/Eigen/src/Geometry/EulerAngles.h
new file mode 100644
index 0000000..2b99960
--- /dev/null
+++ b/Eigen/src/Geometry/EulerAngles.h
@@ -0,0 +1,116 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_EULERANGLES_H
+#define EIGEN_EULERANGLES_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+/** \geometry_module \ingroup Geometry_Module
+ *
+ *
+ * \returns the Euler-angles of the rotation matrix \c *this using the convention defined by the triplet (\a a0,\a a1,\a a2)
+ *
+ * Each of the three parameters \a a0,\a a1,\a a2 represents the respective rotation axis as an integer in {0,1,2}.
+ * For instance, in:
+ * \code Vector3f ea = mat.eulerAngles(2, 0, 2); \endcode
+ * "2" represents the z axis and "0" the x axis, etc. The returned angles are such that
+ * we have the following equality:
+ * \code
+ * mat == AngleAxisf(ea[0], Vector3f::UnitZ())
+ * * AngleAxisf(ea[1], Vector3f::UnitX())
+ * * AngleAxisf(ea[2], Vector3f::UnitZ()); \endcode
+ * This corresponds to the right-multiply conventions (with right hand side frames).
+ *
+ * The returned angles are in the ranges [0:pi]x[-pi:pi]x[-pi:pi].
+ *
+ * \sa class AngleAxis
+ */
+template<typename Derived>
+EIGEN_DEVICE_FUNC inline Matrix<typename MatrixBase<Derived>::Scalar,3,1>
+MatrixBase<Derived>::eulerAngles(Index a0, Index a1, Index a2) const
+{
+ EIGEN_USING_STD(atan2)
+ EIGEN_USING_STD(sin)
+ EIGEN_USING_STD(cos)
+ /* Implemented from Graphics Gems IV */
+ EIGEN_STATIC_ASSERT_MATRIX_SPECIFIC_SIZE(Derived,3,3)
+
+ Matrix<Scalar,3,1> res;
+ typedef Matrix<typename Derived::Scalar,2,1> Vector2;
+
+ const Index odd = ((a0+1)%3 == a1) ? 0 : 1;
+ const Index i = a0;
+ const Index j = (a0 + 1 + odd)%3;
+ const Index k = (a0 + 2 - odd)%3;
+
+ if (a0==a2)
+ {
+ res[0] = atan2(coeff(j,i), coeff(k,i));
+ if((odd && res[0]<Scalar(0)) || ((!odd) && res[0]>Scalar(0)))
+ {
+ if(res[0] > Scalar(0)) {
+ res[0] -= Scalar(EIGEN_PI);
+ }
+ else {
+ res[0] += Scalar(EIGEN_PI);
+ }
+ Scalar s2 = Vector2(coeff(j,i), coeff(k,i)).norm();
+ res[1] = -atan2(s2, coeff(i,i));
+ }
+ else
+ {
+ Scalar s2 = Vector2(coeff(j,i), coeff(k,i)).norm();
+ res[1] = atan2(s2, coeff(i,i));
+ }
+
+ // With a=(0,1,0), we have i=0; j=1; k=2, and after computing the first two angles,
+ // we can compute their respective rotation, and apply its inverse to M. Since the result must
+ // be a rotation around x, we have:
+ //
+ // c2 s1.s2 c1.s2 1 0 0
+ // 0 c1 -s1 * M = 0 c3 s3
+ // -s2 s1.c2 c1.c2 0 -s3 c3
+ //
+ // Thus: m11.c1 - m21.s1 = c3 & m12.c1 - m22.s1 = s3
+
+ Scalar s1 = sin(res[0]);
+ Scalar c1 = cos(res[0]);
+ res[2] = atan2(c1*coeff(j,k)-s1*coeff(k,k), c1*coeff(j,j) - s1 * coeff(k,j));
+ }
+ else
+ {
+ res[0] = atan2(coeff(j,k), coeff(k,k));
+ Scalar c2 = Vector2(coeff(i,i), coeff(i,j)).norm();
+ if((odd && res[0]<Scalar(0)) || ((!odd) && res[0]>Scalar(0))) {
+ if(res[0] > Scalar(0)) {
+ res[0] -= Scalar(EIGEN_PI);
+ }
+ else {
+ res[0] += Scalar(EIGEN_PI);
+ }
+ res[1] = atan2(-coeff(i,k), -c2);
+ }
+ else
+ res[1] = atan2(-coeff(i,k), c2);
+ Scalar s1 = sin(res[0]);
+ Scalar c1 = cos(res[0]);
+ res[2] = atan2(s1*coeff(k,i)-c1*coeff(j,i), c1*coeff(j,j) - s1 * coeff(k,j));
+ }
+ if (!odd)
+ res = -res;
+
+ return res;
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_EULERANGLES_H
diff --git a/Eigen/src/Geometry/Homogeneous.h b/Eigen/src/Geometry/Homogeneous.h
new file mode 100644
index 0000000..538cf83
--- /dev/null
+++ b/Eigen/src/Geometry/Homogeneous.h
@@ -0,0 +1,503 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009-2010 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_HOMOGENEOUS_H
+#define EIGEN_HOMOGENEOUS_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+/** \geometry_module \ingroup Geometry_Module
+ *
+ * \class Homogeneous
+ *
+ * \brief Expression of one (or a set of) homogeneous vector(s)
+ *
+ * \param MatrixType the type of the object in which we are making homogeneous
+ *
+ * This class represents an expression of one (or a set of) homogeneous vector(s).
+ * It is the return type of MatrixBase::homogeneous() and most of the time
+ * this is the only way it is used.
+ *
+ * \sa MatrixBase::homogeneous()
+ */
+
+namespace internal {
+
+template<typename MatrixType,int Direction>
+struct traits<Homogeneous<MatrixType,Direction> >
+ : traits<MatrixType>
+{
+ typedef typename traits<MatrixType>::StorageKind StorageKind;
+ typedef typename ref_selector<MatrixType>::type MatrixTypeNested;
+ typedef std::remove_reference_t<MatrixTypeNested> MatrixTypeNested_;
+ enum {
+ RowsPlusOne = (MatrixType::RowsAtCompileTime != Dynamic) ?
+ int(MatrixType::RowsAtCompileTime) + 1 : Dynamic,
+ ColsPlusOne = (MatrixType::ColsAtCompileTime != Dynamic) ?
+ int(MatrixType::ColsAtCompileTime) + 1 : Dynamic,
+ RowsAtCompileTime = Direction==Vertical ? RowsPlusOne : MatrixType::RowsAtCompileTime,
+ ColsAtCompileTime = Direction==Horizontal ? ColsPlusOne : MatrixType::ColsAtCompileTime,
+ MaxRowsAtCompileTime = RowsAtCompileTime,
+ MaxColsAtCompileTime = ColsAtCompileTime,
+ TmpFlags = MatrixTypeNested_::Flags & HereditaryBits,
+ Flags = ColsAtCompileTime==1 ? (TmpFlags & ~RowMajorBit)
+ : RowsAtCompileTime==1 ? (TmpFlags | RowMajorBit)
+ : TmpFlags
+ };
+};
+
+template<typename MatrixType,typename Lhs> struct homogeneous_left_product_impl;
+template<typename MatrixType,typename Rhs> struct homogeneous_right_product_impl;
+
+} // end namespace internal
+
+template<typename MatrixType,int Direction_> class Homogeneous
+ : public MatrixBase<Homogeneous<MatrixType,Direction_> >, internal::no_assignment_operator
+{
+ public:
+
+ typedef MatrixType NestedExpression;
+ enum { Direction = Direction_ };
+
+ typedef MatrixBase<Homogeneous> Base;
+ EIGEN_DENSE_PUBLIC_INTERFACE(Homogeneous)
+
+ EIGEN_DEVICE_FUNC explicit inline Homogeneous(const MatrixType& matrix)
+ : m_matrix(matrix)
+ {}
+
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
+ inline Index rows() const EIGEN_NOEXCEPT { return m_matrix.rows() + (int(Direction)==Vertical ? 1 : 0); }
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
+ inline Index cols() const EIGEN_NOEXCEPT { return m_matrix.cols() + (int(Direction)==Horizontal ? 1 : 0); }
+
+ EIGEN_DEVICE_FUNC const NestedExpression& nestedExpression() const { return m_matrix; }
+
+ template<typename Rhs>
+ EIGEN_DEVICE_FUNC inline const Product<Homogeneous,Rhs>
+ operator* (const MatrixBase<Rhs>& rhs) const
+ {
+ eigen_assert(int(Direction)==Horizontal);
+ return Product<Homogeneous,Rhs>(*this,rhs.derived());
+ }
+
+ template<typename Lhs> friend
+ EIGEN_DEVICE_FUNC inline const Product<Lhs,Homogeneous>
+ operator* (const MatrixBase<Lhs>& lhs, const Homogeneous& rhs)
+ {
+ eigen_assert(int(Direction)==Vertical);
+ return Product<Lhs,Homogeneous>(lhs.derived(),rhs);
+ }
+
+ template<typename Scalar, int Dim, int Mode, int Options> friend
+ EIGEN_DEVICE_FUNC inline const Product<Transform<Scalar,Dim,Mode,Options>, Homogeneous >
+ operator* (const Transform<Scalar,Dim,Mode,Options>& lhs, const Homogeneous& rhs)
+ {
+ eigen_assert(int(Direction)==Vertical);
+ return Product<Transform<Scalar,Dim,Mode,Options>, Homogeneous>(lhs,rhs);
+ }
+
+ template<typename Func>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE typename internal::result_of<Func(Scalar,Scalar)>::type
+ redux(const Func& func) const
+ {
+ return func(m_matrix.redux(func), Scalar(1));
+ }
+
+ protected:
+ typename MatrixType::Nested m_matrix;
+};
+
+/** \geometry_module \ingroup Geometry_Module
+ *
+ * \returns a vector expression that is one longer than the vector argument, with the value 1 symbolically appended as the last coefficient.
+ *
+ * This can be used to convert affine coordinates to homogeneous coordinates.
+ *
+ * \only_for_vectors
+ *
+ * Example: \include MatrixBase_homogeneous.cpp
+ * Output: \verbinclude MatrixBase_homogeneous.out
+ *
+ * \sa VectorwiseOp::homogeneous(), class Homogeneous
+ */
+template<typename Derived>
+EIGEN_DEVICE_FUNC inline typename MatrixBase<Derived>::HomogeneousReturnType
+MatrixBase<Derived>::homogeneous() const
+{
+ EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived);
+ return HomogeneousReturnType(derived());
+}
+
+/** \geometry_module \ingroup Geometry_Module
+ *
+ * \returns an expression where the value 1 is symbolically appended as the final coefficient to each column (or row) of the matrix.
+ *
+ * This can be used to convert affine coordinates to homogeneous coordinates.
+ *
+ * Example: \include VectorwiseOp_homogeneous.cpp
+ * Output: \verbinclude VectorwiseOp_homogeneous.out
+ *
+ * \sa MatrixBase::homogeneous(), class Homogeneous */
+template<typename ExpressionType, int Direction>
+EIGEN_DEVICE_FUNC inline Homogeneous<ExpressionType,Direction>
+VectorwiseOp<ExpressionType,Direction>::homogeneous() const
+{
+ return HomogeneousReturnType(_expression());
+}
+
+/** \geometry_module \ingroup Geometry_Module
+ *
+ * \brief homogeneous normalization
+ *
+ * \returns a vector expression of the N-1 first coefficients of \c *this divided by that last coefficient.
+ *
+ * This can be used to convert homogeneous coordinates to affine coordinates.
+ *
+ * It is essentially a shortcut for:
+ * \code
+ this->head(this->size()-1)/this->coeff(this->size()-1);
+ \endcode
+ *
+ * Example: \include MatrixBase_hnormalized.cpp
+ * Output: \verbinclude MatrixBase_hnormalized.out
+ *
+ * \sa VectorwiseOp::hnormalized() */
+template<typename Derived>
+EIGEN_DEVICE_FUNC inline const typename MatrixBase<Derived>::HNormalizedReturnType
+MatrixBase<Derived>::hnormalized() const
+{
+ EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived);
+ return ConstStartMinusOne(derived(),0,0,
+ ColsAtCompileTime==1?size()-1:1,
+ ColsAtCompileTime==1?1:size()-1) / coeff(size()-1);
+}
+
+/** \geometry_module \ingroup Geometry_Module
+ *
+ * \brief column or row-wise homogeneous normalization
+ *
+ * \returns an expression of the first N-1 coefficients of each column (or row) of \c *this divided by the last coefficient of each column (or row).
+ *
+ * This can be used to convert homogeneous coordinates to affine coordinates.
+ *
+ * It is conceptually equivalent to calling MatrixBase::hnormalized() to each column (or row) of \c *this.
+ *
+ * Example: \include DirectionWise_hnormalized.cpp
+ * Output: \verbinclude DirectionWise_hnormalized.out
+ *
+ * \sa MatrixBase::hnormalized() */
+template<typename ExpressionType, int Direction>
+EIGEN_DEVICE_FUNC inline const typename VectorwiseOp<ExpressionType,Direction>::HNormalizedReturnType
+VectorwiseOp<ExpressionType,Direction>::hnormalized() const
+{
+ return HNormalized_Block(_expression(),0,0,
+ Direction==Vertical ? _expression().rows()-1 : _expression().rows(),
+ Direction==Horizontal ? _expression().cols()-1 : _expression().cols()).cwiseQuotient(
+ Replicate<HNormalized_Factors,
+ Direction==Vertical ? HNormalized_SizeMinusOne : 1,
+ Direction==Horizontal ? HNormalized_SizeMinusOne : 1>
+ (HNormalized_Factors(_expression(),
+ Direction==Vertical ? _expression().rows()-1:0,
+ Direction==Horizontal ? _expression().cols()-1:0,
+ Direction==Vertical ? 1 : _expression().rows(),
+ Direction==Horizontal ? 1 : _expression().cols()),
+ Direction==Vertical ? _expression().rows()-1 : 1,
+ Direction==Horizontal ? _expression().cols()-1 : 1));
+}
+
+namespace internal {
+
+template<typename MatrixOrTransformType>
+struct take_matrix_for_product
+{
+ typedef MatrixOrTransformType type;
+ EIGEN_DEVICE_FUNC static const type& run(const type &x) { return x; }
+};
+
+template<typename Scalar, int Dim, int Mode,int Options>
+struct take_matrix_for_product<Transform<Scalar, Dim, Mode, Options> >
+{
+ typedef Transform<Scalar, Dim, Mode, Options> TransformType;
+ typedef std::add_const_t<typename TransformType::ConstAffinePart> type;
+ EIGEN_DEVICE_FUNC static type run (const TransformType& x) { return x.affine(); }
+};
+
+template<typename Scalar, int Dim, int Options>
+struct take_matrix_for_product<Transform<Scalar, Dim, Projective, Options> >
+{
+ typedef Transform<Scalar, Dim, Projective, Options> TransformType;
+ typedef typename TransformType::MatrixType type;
+ EIGEN_DEVICE_FUNC static const type& run (const TransformType& x) { return x.matrix(); }
+};
+
+template<typename MatrixType,typename Lhs>
+struct traits<homogeneous_left_product_impl<Homogeneous<MatrixType,Vertical>,Lhs> >
+{
+ typedef typename take_matrix_for_product<Lhs>::type LhsMatrixType;
+ typedef remove_all_t<MatrixType> MatrixTypeCleaned;
+ typedef remove_all_t<LhsMatrixType> LhsMatrixTypeCleaned;
+ typedef typename make_proper_matrix_type<
+ typename traits<MatrixTypeCleaned>::Scalar,
+ LhsMatrixTypeCleaned::RowsAtCompileTime,
+ MatrixTypeCleaned::ColsAtCompileTime,
+ MatrixTypeCleaned::PlainObject::Options,
+ LhsMatrixTypeCleaned::MaxRowsAtCompileTime,
+ MatrixTypeCleaned::MaxColsAtCompileTime>::type ReturnType;
+};
+
+template<typename MatrixType,typename Lhs>
+struct homogeneous_left_product_impl<Homogeneous<MatrixType,Vertical>,Lhs>
+ : public ReturnByValue<homogeneous_left_product_impl<Homogeneous<MatrixType,Vertical>,Lhs> >
+{
+ typedef typename traits<homogeneous_left_product_impl>::LhsMatrixType LhsMatrixType;
+ typedef remove_all_t<LhsMatrixType> LhsMatrixTypeCleaned;
+ typedef remove_all_t<typename LhsMatrixTypeCleaned::Nested> LhsMatrixTypeNested;
+ EIGEN_DEVICE_FUNC homogeneous_left_product_impl(const Lhs& lhs, const MatrixType& rhs)
+ : m_lhs(take_matrix_for_product<Lhs>::run(lhs)),
+ m_rhs(rhs)
+ {}
+
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
+ inline Index rows() const EIGEN_NOEXCEPT { return m_lhs.rows(); }
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
+ inline Index cols() const EIGEN_NOEXCEPT { return m_rhs.cols(); }
+
+ template<typename Dest> EIGEN_DEVICE_FUNC void evalTo(Dest& dst) const
+ {
+ // FIXME investigate how to allow lazy evaluation of this product when possible
+ dst = Block<const LhsMatrixTypeNested,
+ LhsMatrixTypeNested::RowsAtCompileTime,
+ LhsMatrixTypeNested::ColsAtCompileTime==Dynamic?Dynamic:LhsMatrixTypeNested::ColsAtCompileTime-1>
+ (m_lhs,0,0,m_lhs.rows(),m_lhs.cols()-1) * m_rhs;
+ dst += m_lhs.col(m_lhs.cols()-1).rowwise()
+ .template replicate<MatrixType::ColsAtCompileTime>(m_rhs.cols());
+ }
+
+ typename LhsMatrixTypeCleaned::Nested m_lhs;
+ typename MatrixType::Nested m_rhs;
+};
+
+template<typename MatrixType,typename Rhs>
+struct traits<homogeneous_right_product_impl<Homogeneous<MatrixType,Horizontal>,Rhs> >
+{
+ typedef typename make_proper_matrix_type<typename traits<MatrixType>::Scalar,
+ MatrixType::RowsAtCompileTime,
+ Rhs::ColsAtCompileTime,
+ MatrixType::PlainObject::Options,
+ MatrixType::MaxRowsAtCompileTime,
+ Rhs::MaxColsAtCompileTime>::type ReturnType;
+};
+
+template<typename MatrixType,typename Rhs>
+struct homogeneous_right_product_impl<Homogeneous<MatrixType,Horizontal>,Rhs>
+ : public ReturnByValue<homogeneous_right_product_impl<Homogeneous<MatrixType,Horizontal>,Rhs> >
+{
+ typedef remove_all_t<typename Rhs::Nested> RhsNested;
+ EIGEN_DEVICE_FUNC homogeneous_right_product_impl(const MatrixType& lhs, const Rhs& rhs)
+ : m_lhs(lhs), m_rhs(rhs)
+ {}
+
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR inline Index rows() const EIGEN_NOEXCEPT { return m_lhs.rows(); }
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR inline Index cols() const EIGEN_NOEXCEPT { return m_rhs.cols(); }
+
+ template<typename Dest> EIGEN_DEVICE_FUNC void evalTo(Dest& dst) const
+ {
+ // FIXME investigate how to allow lazy evaluation of this product when possible
+ dst = m_lhs * Block<const RhsNested,
+ RhsNested::RowsAtCompileTime==Dynamic?Dynamic:RhsNested::RowsAtCompileTime-1,
+ RhsNested::ColsAtCompileTime>
+ (m_rhs,0,0,m_rhs.rows()-1,m_rhs.cols());
+ dst += m_rhs.row(m_rhs.rows()-1).colwise()
+ .template replicate<MatrixType::RowsAtCompileTime>(m_lhs.rows());
+ }
+
+ typename MatrixType::Nested m_lhs;
+ typename Rhs::Nested m_rhs;
+};
+
+template<typename ArgType,int Direction>
+struct evaluator_traits<Homogeneous<ArgType,Direction> >
+{
+ typedef typename storage_kind_to_evaluator_kind<typename ArgType::StorageKind>::Kind Kind;
+ typedef HomogeneousShape Shape;
+};
+
+template<> struct AssignmentKind<DenseShape,HomogeneousShape> { typedef Dense2Dense Kind; };
+
+
+template<typename ArgType,int Direction>
+struct unary_evaluator<Homogeneous<ArgType,Direction>, IndexBased>
+ : evaluator<typename Homogeneous<ArgType,Direction>::PlainObject >
+{
+ typedef Homogeneous<ArgType,Direction> XprType;
+ typedef typename XprType::PlainObject PlainObject;
+ typedef evaluator<PlainObject> Base;
+
+ EIGEN_DEVICE_FUNC explicit unary_evaluator(const XprType& op)
+ : Base(), m_temp(op)
+ {
+ internal::construct_at<Base>(this, m_temp);
+ }
+
+protected:
+ PlainObject m_temp;
+};
+
+// dense = homogeneous
+template< typename DstXprType, typename ArgType, typename Scalar>
+struct Assignment<DstXprType, Homogeneous<ArgType,Vertical>, internal::assign_op<Scalar,typename ArgType::Scalar>, Dense2Dense>
+{
+ typedef Homogeneous<ArgType,Vertical> SrcXprType;
+ EIGEN_DEVICE_FUNC static void run(DstXprType &dst, const SrcXprType &src, const internal::assign_op<Scalar,typename ArgType::Scalar> &)
+ {
+ Index dstRows = src.rows();
+ Index dstCols = src.cols();
+ if((dst.rows()!=dstRows) || (dst.cols()!=dstCols))
+ dst.resize(dstRows, dstCols);
+
+ dst.template topRows<ArgType::RowsAtCompileTime>(src.nestedExpression().rows()) = src.nestedExpression();
+ dst.row(dst.rows()-1).setOnes();
+ }
+};
+
+// dense = homogeneous
+template< typename DstXprType, typename ArgType, typename Scalar>
+struct Assignment<DstXprType, Homogeneous<ArgType,Horizontal>, internal::assign_op<Scalar,typename ArgType::Scalar>, Dense2Dense>
+{
+ typedef Homogeneous<ArgType,Horizontal> SrcXprType;
+ EIGEN_DEVICE_FUNC static void run(DstXprType &dst, const SrcXprType &src, const internal::assign_op<Scalar,typename ArgType::Scalar> &)
+ {
+ Index dstRows = src.rows();
+ Index dstCols = src.cols();
+ if((dst.rows()!=dstRows) || (dst.cols()!=dstCols))
+ dst.resize(dstRows, dstCols);
+
+ dst.template leftCols<ArgType::ColsAtCompileTime>(src.nestedExpression().cols()) = src.nestedExpression();
+ dst.col(dst.cols()-1).setOnes();
+ }
+};
+
+template<typename LhsArg, typename Rhs, int ProductTag>
+struct generic_product_impl<Homogeneous<LhsArg,Horizontal>, Rhs, HomogeneousShape, DenseShape, ProductTag>
+{
+ template<typename Dest>
+ EIGEN_DEVICE_FUNC static void evalTo(Dest& dst, const Homogeneous<LhsArg,Horizontal>& lhs, const Rhs& rhs)
+ {
+ homogeneous_right_product_impl<Homogeneous<LhsArg,Horizontal>, Rhs>(lhs.nestedExpression(), rhs).evalTo(dst);
+ }
+};
+
+template<typename Lhs,typename Rhs>
+struct homogeneous_right_product_refactoring_helper
+{
+ enum {
+ Dim = Lhs::ColsAtCompileTime,
+ Rows = Lhs::RowsAtCompileTime
+ };
+ typedef typename Rhs::template ConstNRowsBlockXpr<Dim>::Type LinearBlockConst;
+ typedef std::remove_const_t<LinearBlockConst> LinearBlock;
+ typedef typename Rhs::ConstRowXpr ConstantColumn;
+ typedef Replicate<const ConstantColumn,Rows,1> ConstantBlock;
+ typedef Product<Lhs,LinearBlock,LazyProduct> LinearProduct;
+ typedef CwiseBinaryOp<internal::scalar_sum_op<typename Lhs::Scalar,typename Rhs::Scalar>, const LinearProduct, const ConstantBlock> Xpr;
+};
+
+template<typename Lhs, typename Rhs, int ProductTag>
+struct product_evaluator<Product<Lhs, Rhs, LazyProduct>, ProductTag, HomogeneousShape, DenseShape>
+ : public evaluator<typename homogeneous_right_product_refactoring_helper<typename Lhs::NestedExpression,Rhs>::Xpr>
+{
+ typedef Product<Lhs, Rhs, LazyProduct> XprType;
+ typedef homogeneous_right_product_refactoring_helper<typename Lhs::NestedExpression,Rhs> helper;
+ typedef typename helper::ConstantBlock ConstantBlock;
+ typedef typename helper::Xpr RefactoredXpr;
+ typedef evaluator<RefactoredXpr> Base;
+
+ EIGEN_DEVICE_FUNC explicit product_evaluator(const XprType& xpr)
+ : Base( xpr.lhs().nestedExpression() .lazyProduct( xpr.rhs().template topRows<helper::Dim>(xpr.lhs().nestedExpression().cols()) )
+ + ConstantBlock(xpr.rhs().row(xpr.rhs().rows()-1),xpr.lhs().rows(), 1) )
+ {}
+};
+
+template<typename Lhs, typename RhsArg, int ProductTag>
+struct generic_product_impl<Lhs, Homogeneous<RhsArg,Vertical>, DenseShape, HomogeneousShape, ProductTag>
+{
+ template<typename Dest>
+ EIGEN_DEVICE_FUNC static void evalTo(Dest& dst, const Lhs& lhs, const Homogeneous<RhsArg,Vertical>& rhs)
+ {
+ homogeneous_left_product_impl<Homogeneous<RhsArg,Vertical>, Lhs>(lhs, rhs.nestedExpression()).evalTo(dst);
+ }
+};
+
+// TODO: the following specialization is to address a regression from 3.2 to 3.3
+// In the future, this path should be optimized.
+template<typename Lhs, typename RhsArg, int ProductTag>
+struct generic_product_impl<Lhs, Homogeneous<RhsArg,Vertical>, TriangularShape, HomogeneousShape, ProductTag>
+{
+ template<typename Dest>
+ static void evalTo(Dest& dst, const Lhs& lhs, const Homogeneous<RhsArg,Vertical>& rhs)
+ {
+ dst.noalias() = lhs * rhs.eval();
+ }
+};
+
+template<typename Lhs,typename Rhs>
+struct homogeneous_left_product_refactoring_helper
+{
+ enum {
+ Dim = Rhs::RowsAtCompileTime,
+ Cols = Rhs::ColsAtCompileTime
+ };
+ typedef typename Lhs::template ConstNColsBlockXpr<Dim>::Type LinearBlockConst;
+ typedef std::remove_const_t<LinearBlockConst> LinearBlock;
+ typedef typename Lhs::ConstColXpr ConstantColumn;
+ typedef Replicate<const ConstantColumn,1,Cols> ConstantBlock;
+ typedef Product<LinearBlock,Rhs,LazyProduct> LinearProduct;
+ typedef CwiseBinaryOp<internal::scalar_sum_op<typename Lhs::Scalar,typename Rhs::Scalar>, const LinearProduct, const ConstantBlock> Xpr;
+};
+
+template<typename Lhs, typename Rhs, int ProductTag>
+struct product_evaluator<Product<Lhs, Rhs, LazyProduct>, ProductTag, DenseShape, HomogeneousShape>
+ : public evaluator<typename homogeneous_left_product_refactoring_helper<Lhs,typename Rhs::NestedExpression>::Xpr>
+{
+ typedef Product<Lhs, Rhs, LazyProduct> XprType;
+ typedef homogeneous_left_product_refactoring_helper<Lhs,typename Rhs::NestedExpression> helper;
+ typedef typename helper::ConstantBlock ConstantBlock;
+ typedef typename helper::Xpr RefactoredXpr;
+ typedef evaluator<RefactoredXpr> Base;
+
+ EIGEN_DEVICE_FUNC explicit product_evaluator(const XprType& xpr)
+ : Base( xpr.lhs().template leftCols<helper::Dim>(xpr.rhs().nestedExpression().rows()) .lazyProduct( xpr.rhs().nestedExpression() )
+ + ConstantBlock(xpr.lhs().col(xpr.lhs().cols()-1),1,xpr.rhs().cols()) )
+ {}
+};
+
+template<typename Scalar, int Dim, int Mode,int Options, typename RhsArg, int ProductTag>
+struct generic_product_impl<Transform<Scalar,Dim,Mode,Options>, Homogeneous<RhsArg,Vertical>, DenseShape, HomogeneousShape, ProductTag>
+{
+ typedef Transform<Scalar,Dim,Mode,Options> TransformType;
+ template<typename Dest>
+ EIGEN_DEVICE_FUNC static void evalTo(Dest& dst, const TransformType& lhs, const Homogeneous<RhsArg,Vertical>& rhs)
+ {
+ homogeneous_left_product_impl<Homogeneous<RhsArg,Vertical>, TransformType>(lhs, rhs.nestedExpression()).evalTo(dst);
+ }
+};
+
+template<typename ExpressionType, int Side, bool Transposed>
+struct permutation_matrix_product<ExpressionType, Side, Transposed, HomogeneousShape>
+ : public permutation_matrix_product<ExpressionType, Side, Transposed, DenseShape>
+{};
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_HOMOGENEOUS_H
diff --git a/Eigen/src/Geometry/Hyperplane.h b/Eigen/src/Geometry/Hyperplane.h
new file mode 100644
index 0000000..ad6aae9
--- /dev/null
+++ b/Eigen/src/Geometry/Hyperplane.h
@@ -0,0 +1,284 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_HYPERPLANE_H
+#define EIGEN_HYPERPLANE_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+/** \geometry_module \ingroup Geometry_Module
+ *
+ * \class Hyperplane
+ *
+ * \brief A hyperplane
+ *
+ * A hyperplane is an affine subspace of dimension n-1 in a space of dimension n.
+ * For example, a hyperplane in a plane is a line; a hyperplane in 3-space is a plane.
+ *
+ * \tparam Scalar_ the scalar type, i.e., the type of the coefficients
+ * \tparam AmbientDim_ the dimension of the ambient space, can be a compile time value or Dynamic.
+ * Notice that the dimension of the hyperplane is AmbientDim_-1.
+ *
+ * This class represents an hyperplane as the zero set of the implicit equation
+ * \f$ n \cdot x + d = 0 \f$ where \f$ n \f$ is a unit normal vector of the plane (linear part)
+ * and \f$ d \f$ is the distance (offset) to the origin.
+ */
+template <typename Scalar_, int AmbientDim_, int Options_>
+class Hyperplane
+{
+public:
+ EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE(Scalar_,AmbientDim_==Dynamic ? Dynamic : AmbientDim_+1)
+ enum {
+ AmbientDimAtCompileTime = AmbientDim_,
+ Options = Options_
+ };
+ typedef Scalar_ Scalar;
+ typedef typename NumTraits<Scalar>::Real RealScalar;
+ typedef Eigen::Index Index; ///< \deprecated since Eigen 3.3
+ typedef Matrix<Scalar,AmbientDimAtCompileTime,1> VectorType;
+ typedef Matrix<Scalar,Index(AmbientDimAtCompileTime)==Dynamic
+ ? Dynamic
+ : Index(AmbientDimAtCompileTime)+1,1,Options> Coefficients;
+ typedef Block<Coefficients,AmbientDimAtCompileTime,1> NormalReturnType;
+ typedef const Block<const Coefficients,AmbientDimAtCompileTime,1> ConstNormalReturnType;
+
+ /** Default constructor without initialization */
+ EIGEN_DEVICE_FUNC inline Hyperplane() {}
+
+ template<int OtherOptions>
+ EIGEN_DEVICE_FUNC Hyperplane(const Hyperplane<Scalar,AmbientDimAtCompileTime,OtherOptions>& other)
+ : m_coeffs(other.coeffs())
+ {}
+
+ /** Constructs a dynamic-size hyperplane with \a _dim the dimension
+ * of the ambient space */
+ EIGEN_DEVICE_FUNC inline explicit Hyperplane(Index _dim) : m_coeffs(_dim+1) {}
+
+ /** Construct a plane from its normal \a n and a point \a e onto the plane.
+ * \warning the vector normal is assumed to be normalized.
+ */
+ EIGEN_DEVICE_FUNC inline Hyperplane(const VectorType& n, const VectorType& e)
+ : m_coeffs(n.size()+1)
+ {
+ normal() = n;
+ offset() = -n.dot(e);
+ }
+
+ /** Constructs a plane from its normal \a n and distance to the origin \a d
+ * such that the algebraic equation of the plane is \f$ n \cdot x + d = 0 \f$.
+ * \warning the vector normal is assumed to be normalized.
+ */
+ EIGEN_DEVICE_FUNC inline Hyperplane(const VectorType& n, const Scalar& d)
+ : m_coeffs(n.size()+1)
+ {
+ normal() = n;
+ offset() = d;
+ }
+
+ /** Constructs a hyperplane passing through the two points. If the dimension of the ambient space
+ * is greater than 2, then there isn't uniqueness, so an arbitrary choice is made.
+ */
+ EIGEN_DEVICE_FUNC static inline Hyperplane Through(const VectorType& p0, const VectorType& p1)
+ {
+ Hyperplane result(p0.size());
+ result.normal() = (p1 - p0).unitOrthogonal();
+ result.offset() = -p0.dot(result.normal());
+ return result;
+ }
+
+ /** Constructs a hyperplane passing through the three points. The dimension of the ambient space
+ * is required to be exactly 3.
+ */
+ EIGEN_DEVICE_FUNC static inline Hyperplane Through(const VectorType& p0, const VectorType& p1, const VectorType& p2)
+ {
+ EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(VectorType, 3)
+ Hyperplane result(p0.size());
+ VectorType v0(p2 - p0), v1(p1 - p0);
+ result.normal() = v0.cross(v1);
+ RealScalar norm = result.normal().norm();
+ if(norm <= v0.norm() * v1.norm() * NumTraits<RealScalar>::epsilon())
+ {
+ Matrix<Scalar,2,3> m; m << v0.transpose(), v1.transpose();
+ JacobiSVD<Matrix<Scalar,2,3>, ComputeFullV> svd(m);
+ result.normal() = svd.matrixV().col(2);
+ }
+ else
+ result.normal() /= norm;
+ result.offset() = -p0.dot(result.normal());
+ return result;
+ }
+
+ /** Constructs a hyperplane passing through the parametrized line \a parametrized.
+ * If the dimension of the ambient space is greater than 2, then there isn't uniqueness,
+ * so an arbitrary choice is made.
+ */
+ // FIXME to be consistent with the rest this could be implemented as a static Through function ??
+ EIGEN_DEVICE_FUNC explicit Hyperplane(const ParametrizedLine<Scalar, AmbientDimAtCompileTime>& parametrized)
+ {
+ normal() = parametrized.direction().unitOrthogonal();
+ offset() = -parametrized.origin().dot(normal());
+ }
+
+ EIGEN_DEVICE_FUNC ~Hyperplane() {}
+
+ /** \returns the dimension in which the plane holds */
+ EIGEN_DEVICE_FUNC inline Index dim() const { return AmbientDimAtCompileTime==Dynamic ? m_coeffs.size()-1 : Index(AmbientDimAtCompileTime); }
+
+ /** normalizes \c *this */
+ EIGEN_DEVICE_FUNC void normalize(void)
+ {
+ m_coeffs /= normal().norm();
+ }
+
+ /** \returns the signed distance between the plane \c *this and a point \a p.
+ * \sa absDistance()
+ */
+ EIGEN_DEVICE_FUNC inline Scalar signedDistance(const VectorType& p) const { return normal().dot(p) + offset(); }
+
+ /** \returns the absolute distance between the plane \c *this and a point \a p.
+ * \sa signedDistance()
+ */
+ EIGEN_DEVICE_FUNC inline Scalar absDistance(const VectorType& p) const { return numext::abs(signedDistance(p)); }
+
+ /** \returns the projection of a point \a p onto the plane \c *this.
+ */
+ EIGEN_DEVICE_FUNC inline VectorType projection(const VectorType& p) const { return p - signedDistance(p) * normal(); }
+
+ /** \returns a constant reference to the unit normal vector of the plane, which corresponds
+ * to the linear part of the implicit equation.
+ */
+ EIGEN_DEVICE_FUNC inline ConstNormalReturnType normal() const { return ConstNormalReturnType(m_coeffs,0,0,dim(),1); }
+
+ /** \returns a non-constant reference to the unit normal vector of the plane, which corresponds
+ * to the linear part of the implicit equation.
+ */
+ EIGEN_DEVICE_FUNC inline NormalReturnType normal() { return NormalReturnType(m_coeffs,0,0,dim(),1); }
+
+ /** \returns the distance to the origin, which is also the "constant term" of the implicit equation
+ * \warning the vector normal is assumed to be normalized.
+ */
+ EIGEN_DEVICE_FUNC inline const Scalar& offset() const { return m_coeffs.coeff(dim()); }
+
+ /** \returns a non-constant reference to the distance to the origin, which is also the constant part
+ * of the implicit equation */
+ EIGEN_DEVICE_FUNC inline Scalar& offset() { return m_coeffs(dim()); }
+
+ /** \returns a constant reference to the coefficients c_i of the plane equation:
+ * \f$ c_0*x_0 + ... + c_{d-1}*x_{d-1} + c_d = 0 \f$
+ */
+ EIGEN_DEVICE_FUNC inline const Coefficients& coeffs() const { return m_coeffs; }
+
+ /** \returns a non-constant reference to the coefficients c_i of the plane equation:
+ * \f$ c_0*x_0 + ... + c_{d-1}*x_{d-1} + c_d = 0 \f$
+ */
+ EIGEN_DEVICE_FUNC inline Coefficients& coeffs() { return m_coeffs; }
+
+ /** \returns the intersection of *this with \a other.
+ *
+ * \warning The ambient space must be a plane, i.e. have dimension 2, so that \c *this and \a other are lines.
+ *
+ * \note If \a other is approximately parallel to *this, this method will return any point on *this.
+ */
+ EIGEN_DEVICE_FUNC VectorType intersection(const Hyperplane& other) const
+ {
+ EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(VectorType, 2)
+ Scalar det = coeffs().coeff(0) * other.coeffs().coeff(1) - coeffs().coeff(1) * other.coeffs().coeff(0);
+ // since the line equations ax+by=c are normalized with a^2+b^2=1, the following tests
+ // whether the two lines are approximately parallel.
+ if(internal::isMuchSmallerThan(det, Scalar(1)))
+ { // special case where the two lines are approximately parallel. Pick any point on the first line.
+ if(numext::abs(coeffs().coeff(1))>numext::abs(coeffs().coeff(0)))
+ return VectorType(coeffs().coeff(1), -coeffs().coeff(2)/coeffs().coeff(1)-coeffs().coeff(0));
+ else
+ return VectorType(-coeffs().coeff(2)/coeffs().coeff(0)-coeffs().coeff(1), coeffs().coeff(0));
+ }
+ else
+ { // general case
+ Scalar invdet = Scalar(1) / det;
+ return VectorType(invdet*(coeffs().coeff(1)*other.coeffs().coeff(2)-other.coeffs().coeff(1)*coeffs().coeff(2)),
+ invdet*(other.coeffs().coeff(0)*coeffs().coeff(2)-coeffs().coeff(0)*other.coeffs().coeff(2)));
+ }
+ }
+
+ /** Applies the transformation matrix \a mat to \c *this and returns a reference to \c *this.
+ *
+ * \param mat the Dim x Dim transformation matrix
+ * \param traits specifies whether the matrix \a mat represents an #Isometry
+ * or a more generic #Affine transformation. The default is #Affine.
+ */
+ template<typename XprType>
+ EIGEN_DEVICE_FUNC inline Hyperplane& transform(const MatrixBase<XprType>& mat, TransformTraits traits = Affine)
+ {
+ if (traits==Affine)
+ {
+ normal() = mat.inverse().transpose() * normal();
+ m_coeffs /= normal().norm();
+ }
+ else if (traits==Isometry)
+ normal() = mat * normal();
+ else
+ {
+ eigen_assert(0 && "invalid traits value in Hyperplane::transform()");
+ }
+ return *this;
+ }
+
+ /** Applies the transformation \a t to \c *this and returns a reference to \c *this.
+ *
+ * \param t the transformation of dimension Dim
+ * \param traits specifies whether the transformation \a t represents an #Isometry
+ * or a more generic #Affine transformation. The default is #Affine.
+ * Other kind of transformations are not supported.
+ */
+ template<int TrOptions>
+ EIGEN_DEVICE_FUNC inline Hyperplane& transform(const Transform<Scalar,AmbientDimAtCompileTime,Affine,TrOptions>& t,
+ TransformTraits traits = Affine)
+ {
+ transform(t.linear(), traits);
+ offset() -= normal().dot(t.translation());
+ return *this;
+ }
+
+ /** \returns \c *this with scalar type casted to \a NewScalarType
+ *
+ * Note that if \a NewScalarType is equal to the current scalar type of \c *this
+ * then this function smartly returns a const reference to \c *this.
+ */
+ template<typename NewScalarType>
+ EIGEN_DEVICE_FUNC inline typename internal::cast_return_type<Hyperplane,
+ Hyperplane<NewScalarType,AmbientDimAtCompileTime,Options> >::type cast() const
+ {
+ return typename internal::cast_return_type<Hyperplane,
+ Hyperplane<NewScalarType,AmbientDimAtCompileTime,Options> >::type(*this);
+ }
+
+ /** Copy constructor with scalar type conversion */
+ template<typename OtherScalarType,int OtherOptions>
+ EIGEN_DEVICE_FUNC inline explicit Hyperplane(const Hyperplane<OtherScalarType,AmbientDimAtCompileTime,OtherOptions>& other)
+ { m_coeffs = other.coeffs().template cast<Scalar>(); }
+
+ /** \returns \c true if \c *this is approximately equal to \a other, within the precision
+ * determined by \a prec.
+ *
+ * \sa MatrixBase::isApprox() */
+ template<int OtherOptions>
+ EIGEN_DEVICE_FUNC bool isApprox(const Hyperplane<Scalar,AmbientDimAtCompileTime,OtherOptions>& other, const typename NumTraits<Scalar>::Real& prec = NumTraits<Scalar>::dummy_precision()) const
+ { return m_coeffs.isApprox(other.m_coeffs, prec); }
+
+protected:
+
+ Coefficients m_coeffs;
+};
+
+} // end namespace Eigen
+
+#endif // EIGEN_HYPERPLANE_H
diff --git a/Eigen/src/Geometry/InternalHeaderCheck.h b/Eigen/src/Geometry/InternalHeaderCheck.h
new file mode 100644
index 0000000..a1159a3
--- /dev/null
+++ b/Eigen/src/Geometry/InternalHeaderCheck.h
@@ -0,0 +1,3 @@
+#ifndef EIGEN_GEOMETRY_MODULE_H
+#error "Please include Eigen/Geometry instead of including headers inside the src directory directly."
+#endif
diff --git a/Eigen/src/Geometry/OrthoMethods.h b/Eigen/src/Geometry/OrthoMethods.h
new file mode 100644
index 0000000..dc6a762
--- /dev/null
+++ b/Eigen/src/Geometry/OrthoMethods.h
@@ -0,0 +1,237 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_ORTHOMETHODS_H
+#define EIGEN_ORTHOMETHODS_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+/** \geometry_module \ingroup Geometry_Module
+ *
+ * \returns the cross product of \c *this and \a other
+ *
+ * Here is a very good explanation of cross-product: http://xkcd.com/199/
+ *
+ * With complex numbers, the cross product is implemented as
+ * \f$ (\mathbf{a}+i\mathbf{b}) \times (\mathbf{c}+i\mathbf{d}) = (\mathbf{a} \times \mathbf{c} - \mathbf{b} \times \mathbf{d}) - i(\mathbf{a} \times \mathbf{d} - \mathbf{b} \times \mathbf{c})\f$
+ *
+ * \sa MatrixBase::cross3()
+ */
+template<typename Derived>
+template<typename OtherDerived>
+#ifndef EIGEN_PARSED_BY_DOXYGEN
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+typename MatrixBase<Derived>::template cross_product_return_type<OtherDerived>::type
+#else
+typename MatrixBase<Derived>::PlainObject
+#endif
+MatrixBase<Derived>::cross(const MatrixBase<OtherDerived>& other) const
+{
+ EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(Derived,3)
+ EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(OtherDerived,3)
+
+ // Note that there is no need for an expression here since the compiler
+ // optimize such a small temporary very well (even within a complex expression)
+ typename internal::nested_eval<Derived,2>::type lhs(derived());
+ typename internal::nested_eval<OtherDerived,2>::type rhs(other.derived());
+ return typename cross_product_return_type<OtherDerived>::type(
+ numext::conj(lhs.coeff(1) * rhs.coeff(2) - lhs.coeff(2) * rhs.coeff(1)),
+ numext::conj(lhs.coeff(2) * rhs.coeff(0) - lhs.coeff(0) * rhs.coeff(2)),
+ numext::conj(lhs.coeff(0) * rhs.coeff(1) - lhs.coeff(1) * rhs.coeff(0))
+ );
+}
+
+namespace internal {
+
+template< int Arch,typename VectorLhs,typename VectorRhs,
+ typename Scalar = typename VectorLhs::Scalar,
+ bool Vectorizable = bool((VectorLhs::Flags&VectorRhs::Flags)&PacketAccessBit)>
+struct cross3_impl {
+ EIGEN_DEVICE_FUNC static inline typename internal::plain_matrix_type<VectorLhs>::type
+ run(const VectorLhs& lhs, const VectorRhs& rhs)
+ {
+ return typename internal::plain_matrix_type<VectorLhs>::type(
+ numext::conj(lhs.coeff(1) * rhs.coeff(2) - lhs.coeff(2) * rhs.coeff(1)),
+ numext::conj(lhs.coeff(2) * rhs.coeff(0) - lhs.coeff(0) * rhs.coeff(2)),
+ numext::conj(lhs.coeff(0) * rhs.coeff(1) - lhs.coeff(1) * rhs.coeff(0)),
+ 0
+ );
+ }
+};
+
+}
+
+/** \geometry_module \ingroup Geometry_Module
+ *
+ * \returns the cross product of \c *this and \a other using only the x, y, and z coefficients
+ *
+ * The size of \c *this and \a other must be four. This function is especially useful
+ * when using 4D vectors instead of 3D ones to get advantage of SSE/AltiVec vectorization.
+ *
+ * \sa MatrixBase::cross()
+ */
+template<typename Derived>
+template<typename OtherDerived>
+EIGEN_DEVICE_FUNC inline typename MatrixBase<Derived>::PlainObject
+MatrixBase<Derived>::cross3(const MatrixBase<OtherDerived>& other) const
+{
+ EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(Derived,4)
+ EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(OtherDerived,4)
+
+ typedef typename internal::nested_eval<Derived,2>::type DerivedNested;
+ typedef typename internal::nested_eval<OtherDerived,2>::type OtherDerivedNested;
+ DerivedNested lhs(derived());
+ OtherDerivedNested rhs(other.derived());
+
+ return internal::cross3_impl<Architecture::Target,
+ internal::remove_all_t<DerivedNested>,
+ internal::remove_all_t<OtherDerivedNested>>::run(lhs,rhs);
+}
+
+/** \geometry_module \ingroup Geometry_Module
+ *
+ * \returns a matrix expression of the cross product of each column or row
+ * of the referenced expression with the \a other vector.
+ *
+ * The referenced matrix must have one dimension equal to 3.
+ * The result matrix has the same dimensions than the referenced one.
+ *
+ * \sa MatrixBase::cross() */
+template<typename ExpressionType, int Direction>
+template<typename OtherDerived>
+EIGEN_DEVICE_FUNC
+const typename VectorwiseOp<ExpressionType,Direction>::CrossReturnType
+VectorwiseOp<ExpressionType,Direction>::cross(const MatrixBase<OtherDerived>& other) const
+{
+ EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(OtherDerived,3)
+ EIGEN_STATIC_ASSERT((internal::is_same<Scalar, typename OtherDerived::Scalar>::value),
+ YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY)
+
+ typename internal::nested_eval<ExpressionType,2>::type mat(_expression());
+ typename internal::nested_eval<OtherDerived,2>::type vec(other.derived());
+
+ CrossReturnType res(_expression().rows(),_expression().cols());
+ if(Direction==Vertical)
+ {
+ eigen_assert(CrossReturnType::RowsAtCompileTime==3 && "the matrix must have exactly 3 rows");
+ res.row(0) = (mat.row(1) * vec.coeff(2) - mat.row(2) * vec.coeff(1)).conjugate();
+ res.row(1) = (mat.row(2) * vec.coeff(0) - mat.row(0) * vec.coeff(2)).conjugate();
+ res.row(2) = (mat.row(0) * vec.coeff(1) - mat.row(1) * vec.coeff(0)).conjugate();
+ }
+ else
+ {
+ eigen_assert(CrossReturnType::ColsAtCompileTime==3 && "the matrix must have exactly 3 columns");
+ res.col(0) = (mat.col(1) * vec.coeff(2) - mat.col(2) * vec.coeff(1)).conjugate();
+ res.col(1) = (mat.col(2) * vec.coeff(0) - mat.col(0) * vec.coeff(2)).conjugate();
+ res.col(2) = (mat.col(0) * vec.coeff(1) - mat.col(1) * vec.coeff(0)).conjugate();
+ }
+ return res;
+}
+
+namespace internal {
+
+template<typename Derived, int Size = Derived::SizeAtCompileTime>
+struct unitOrthogonal_selector
+{
+ typedef typename plain_matrix_type<Derived>::type VectorType;
+ typedef typename traits<Derived>::Scalar Scalar;
+ typedef typename NumTraits<Scalar>::Real RealScalar;
+ typedef Matrix<Scalar,2,1> Vector2;
+ EIGEN_DEVICE_FUNC
+ static inline VectorType run(const Derived& src)
+ {
+ VectorType perp = VectorType::Zero(src.size());
+ Index maxi = 0;
+ Index sndi = 0;
+ src.cwiseAbs().maxCoeff(&maxi);
+ if (maxi==0)
+ sndi = 1;
+ RealScalar invnm = RealScalar(1)/(Vector2() << src.coeff(sndi),src.coeff(maxi)).finished().norm();
+ perp.coeffRef(maxi) = -numext::conj(src.coeff(sndi)) * invnm;
+ perp.coeffRef(sndi) = numext::conj(src.coeff(maxi)) * invnm;
+
+ return perp;
+ }
+};
+
+template<typename Derived>
+struct unitOrthogonal_selector<Derived,3>
+{
+ typedef typename plain_matrix_type<Derived>::type VectorType;
+ typedef typename traits<Derived>::Scalar Scalar;
+ typedef typename NumTraits<Scalar>::Real RealScalar;
+ EIGEN_DEVICE_FUNC
+ static inline VectorType run(const Derived& src)
+ {
+ VectorType perp;
+ /* Let us compute the crossed product of *this with a vector
+ * that is not too close to being colinear to *this.
+ */
+
+ /* unless the x and y coords are both close to zero, we can
+ * simply take ( -y, x, 0 ) and normalize it.
+ */
+ if((!isMuchSmallerThan(src.x(), src.z()))
+ || (!isMuchSmallerThan(src.y(), src.z())))
+ {
+ RealScalar invnm = RealScalar(1)/src.template head<2>().norm();
+ perp.coeffRef(0) = -numext::conj(src.y())*invnm;
+ perp.coeffRef(1) = numext::conj(src.x())*invnm;
+ perp.coeffRef(2) = 0;
+ }
+ /* if both x and y are close to zero, then the vector is close
+ * to the z-axis, so it's far from colinear to the x-axis for instance.
+ * So we take the crossed product with (1,0,0) and normalize it.
+ */
+ else
+ {
+ RealScalar invnm = RealScalar(1)/src.template tail<2>().norm();
+ perp.coeffRef(0) = 0;
+ perp.coeffRef(1) = -numext::conj(src.z())*invnm;
+ perp.coeffRef(2) = numext::conj(src.y())*invnm;
+ }
+
+ return perp;
+ }
+};
+
+template<typename Derived>
+struct unitOrthogonal_selector<Derived,2>
+{
+ typedef typename plain_matrix_type<Derived>::type VectorType;
+ EIGEN_DEVICE_FUNC
+ static inline VectorType run(const Derived& src)
+ { return VectorType(-numext::conj(src.y()), numext::conj(src.x())).normalized(); }
+};
+
+} // end namespace internal
+
+/** \geometry_module \ingroup Geometry_Module
+ *
+ * \returns a unit vector which is orthogonal to \c *this
+ *
+ * The size of \c *this must be at least 2. If the size is exactly 2,
+ * then the returned vector is a counter clock wise rotation of \c *this, i.e., (-y,x).normalized().
+ *
+ * \sa cross()
+ */
+template<typename Derived>
+EIGEN_DEVICE_FUNC typename MatrixBase<Derived>::PlainObject
+MatrixBase<Derived>::unitOrthogonal() const
+{
+ EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
+ return internal::unitOrthogonal_selector<Derived>::run(derived());
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_ORTHOMETHODS_H
diff --git a/Eigen/src/Geometry/ParametrizedLine.h b/Eigen/src/Geometry/ParametrizedLine.h
new file mode 100644
index 0000000..7576922
--- /dev/null
+++ b/Eigen/src/Geometry/ParametrizedLine.h
@@ -0,0 +1,234 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_PARAMETRIZEDLINE_H
+#define EIGEN_PARAMETRIZEDLINE_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+/** \geometry_module \ingroup Geometry_Module
+ *
+ * \class ParametrizedLine
+ *
+ * \brief A parametrized line
+ *
+ * A parametrized line is defined by an origin point \f$ \mathbf{o} \f$ and a unit
+ * direction vector \f$ \mathbf{d} \f$ such that the line corresponds to
+ * the set \f$ l(t) = \mathbf{o} + t \mathbf{d} \f$, \f$ t \in \mathbf{R} \f$.
+ *
+ * \tparam Scalar_ the scalar type, i.e., the type of the coefficients
+ * \tparam AmbientDim_ the dimension of the ambient space, can be a compile time value or Dynamic.
+ */
+template <typename Scalar_, int AmbientDim_, int Options_>
+class ParametrizedLine
+{
+public:
+ EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE(Scalar_,AmbientDim_)
+ enum {
+ AmbientDimAtCompileTime = AmbientDim_,
+ Options = Options_
+ };
+ typedef Scalar_ Scalar;
+ typedef typename NumTraits<Scalar>::Real RealScalar;
+ typedef Eigen::Index Index; ///< \deprecated since Eigen 3.3
+ typedef Matrix<Scalar,AmbientDimAtCompileTime,1,Options> VectorType;
+
+ /** Default constructor without initialization */
+ EIGEN_DEVICE_FUNC inline ParametrizedLine() {}
+
+ template<int OtherOptions>
+ EIGEN_DEVICE_FUNC ParametrizedLine(const ParametrizedLine<Scalar,AmbientDimAtCompileTime,OtherOptions>& other)
+ : m_origin(other.origin()), m_direction(other.direction())
+ {}
+
+ /** Constructs a dynamic-size line with \a _dim the dimension
+ * of the ambient space */
+ EIGEN_DEVICE_FUNC inline explicit ParametrizedLine(Index _dim) : m_origin(_dim), m_direction(_dim) {}
+
+ /** Initializes a parametrized line of direction \a direction and origin \a origin.
+ * \warning the vector direction is assumed to be normalized.
+ */
+ EIGEN_DEVICE_FUNC ParametrizedLine(const VectorType& origin, const VectorType& direction)
+ : m_origin(origin), m_direction(direction) {}
+
+ template <int OtherOptions>
+ EIGEN_DEVICE_FUNC explicit ParametrizedLine(const Hyperplane<Scalar_, AmbientDim_, OtherOptions>& hyperplane);
+
+ /** Constructs a parametrized line going from \a p0 to \a p1. */
+ EIGEN_DEVICE_FUNC static inline ParametrizedLine Through(const VectorType& p0, const VectorType& p1)
+ { return ParametrizedLine(p0, (p1-p0).normalized()); }
+
+ EIGEN_DEVICE_FUNC ~ParametrizedLine() {}
+
+ /** \returns the dimension in which the line holds */
+ EIGEN_DEVICE_FUNC inline Index dim() const { return m_direction.size(); }
+
+ EIGEN_DEVICE_FUNC const VectorType& origin() const { return m_origin; }
+ EIGEN_DEVICE_FUNC VectorType& origin() { return m_origin; }
+
+ EIGEN_DEVICE_FUNC const VectorType& direction() const { return m_direction; }
+ EIGEN_DEVICE_FUNC VectorType& direction() { return m_direction; }
+
+ /** \returns the squared distance of a point \a p to its projection onto the line \c *this.
+ * \sa distance()
+ */
+ EIGEN_DEVICE_FUNC RealScalar squaredDistance(const VectorType& p) const
+ {
+ VectorType diff = p - origin();
+ return (diff - direction().dot(diff) * direction()).squaredNorm();
+ }
+ /** \returns the distance of a point \a p to its projection onto the line \c *this.
+ * \sa squaredDistance()
+ */
+ EIGEN_DEVICE_FUNC RealScalar distance(const VectorType& p) const { EIGEN_USING_STD(sqrt) return sqrt(squaredDistance(p)); }
+
+ /** \returns the projection of a point \a p onto the line \c *this. */
+ EIGEN_DEVICE_FUNC VectorType projection(const VectorType& p) const
+ { return origin() + direction().dot(p-origin()) * direction(); }
+
+ EIGEN_DEVICE_FUNC VectorType pointAt(const Scalar& t) const;
+
+ template <int OtherOptions>
+ EIGEN_DEVICE_FUNC Scalar intersectionParameter(const Hyperplane<Scalar_, AmbientDim_, OtherOptions>& hyperplane) const;
+
+ template <int OtherOptions>
+ EIGEN_DEVICE_FUNC Scalar intersection(const Hyperplane<Scalar_, AmbientDim_, OtherOptions>& hyperplane) const;
+
+ template <int OtherOptions>
+ EIGEN_DEVICE_FUNC VectorType intersectionPoint(const Hyperplane<Scalar_, AmbientDim_, OtherOptions>& hyperplane) const;
+
+ /** Applies the transformation matrix \a mat to \c *this and returns a reference to \c *this.
+ *
+ * \param mat the Dim x Dim transformation matrix
+ * \param traits specifies whether the matrix \a mat represents an #Isometry
+ * or a more generic #Affine transformation. The default is #Affine.
+ */
+ template<typename XprType>
+ EIGEN_DEVICE_FUNC inline ParametrizedLine& transform(const MatrixBase<XprType>& mat, TransformTraits traits = Affine)
+ {
+ if (traits==Affine)
+ direction() = (mat * direction()).normalized();
+ else if (traits==Isometry)
+ direction() = mat * direction();
+ else
+ {
+ eigen_assert(0 && "invalid traits value in ParametrizedLine::transform()");
+ }
+ origin() = mat * origin();
+ return *this;
+ }
+
+ /** Applies the transformation \a t to \c *this and returns a reference to \c *this.
+ *
+ * \param t the transformation of dimension Dim
+ * \param traits specifies whether the transformation \a t represents an #Isometry
+ * or a more generic #Affine transformation. The default is #Affine.
+ * Other kind of transformations are not supported.
+ */
+ template<int TrOptions>
+ EIGEN_DEVICE_FUNC inline ParametrizedLine& transform(const Transform<Scalar,AmbientDimAtCompileTime,Affine,TrOptions>& t,
+ TransformTraits traits = Affine)
+ {
+ transform(t.linear(), traits);
+ origin() += t.translation();
+ return *this;
+ }
+
+/** \returns \c *this with scalar type casted to \a NewScalarType
+ *
+ * Note that if \a NewScalarType is equal to the current scalar type of \c *this
+ * then this function smartly returns a const reference to \c *this.
+ */
+ template<typename NewScalarType>
+ EIGEN_DEVICE_FUNC inline typename internal::cast_return_type<ParametrizedLine,
+ ParametrizedLine<NewScalarType,AmbientDimAtCompileTime,Options> >::type cast() const
+ {
+ return typename internal::cast_return_type<ParametrizedLine,
+ ParametrizedLine<NewScalarType,AmbientDimAtCompileTime,Options> >::type(*this);
+ }
+
+ /** Copy constructor with scalar type conversion */
+ template<typename OtherScalarType,int OtherOptions>
+ EIGEN_DEVICE_FUNC inline explicit ParametrizedLine(const ParametrizedLine<OtherScalarType,AmbientDimAtCompileTime,OtherOptions>& other)
+ {
+ m_origin = other.origin().template cast<Scalar>();
+ m_direction = other.direction().template cast<Scalar>();
+ }
+
+ /** \returns \c true if \c *this is approximately equal to \a other, within the precision
+ * determined by \a prec.
+ *
+ * \sa MatrixBase::isApprox() */
+ EIGEN_DEVICE_FUNC bool isApprox(const ParametrizedLine& other, const typename NumTraits<Scalar>::Real& prec = NumTraits<Scalar>::dummy_precision()) const
+ { return m_origin.isApprox(other.m_origin, prec) && m_direction.isApprox(other.m_direction, prec); }
+
+protected:
+
+ VectorType m_origin, m_direction;
+};
+
+/** Constructs a parametrized line from a 2D hyperplane
+ *
+ * \warning the ambient space must have dimension 2 such that the hyperplane actually describes a line
+ */
+template <typename Scalar_, int AmbientDim_, int Options_>
+template <int OtherOptions>
+EIGEN_DEVICE_FUNC inline ParametrizedLine<Scalar_, AmbientDim_,Options_>::ParametrizedLine(const Hyperplane<Scalar_, AmbientDim_,OtherOptions>& hyperplane)
+{
+ EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(VectorType, 2)
+ direction() = hyperplane.normal().unitOrthogonal();
+ origin() = -hyperplane.normal()*hyperplane.offset();
+}
+
+/** \returns the point at \a t along this line
+ */
+template <typename Scalar_, int AmbientDim_, int Options_>
+EIGEN_DEVICE_FUNC inline typename ParametrizedLine<Scalar_, AmbientDim_,Options_>::VectorType
+ParametrizedLine<Scalar_, AmbientDim_,Options_>::pointAt(const Scalar_& t) const
+{
+ return origin() + (direction()*t);
+}
+
+/** \returns the parameter value of the intersection between \c *this and the given \a hyperplane
+ */
+template <typename Scalar_, int AmbientDim_, int Options_>
+template <int OtherOptions>
+EIGEN_DEVICE_FUNC inline Scalar_ ParametrizedLine<Scalar_, AmbientDim_,Options_>::intersectionParameter(const Hyperplane<Scalar_, AmbientDim_, OtherOptions>& hyperplane) const
+{
+ return -(hyperplane.offset()+hyperplane.normal().dot(origin()))
+ / hyperplane.normal().dot(direction());
+}
+
+
+/** \deprecated use intersectionParameter()
+ * \returns the parameter value of the intersection between \c *this and the given \a hyperplane
+ */
+template <typename Scalar_, int AmbientDim_, int Options_>
+template <int OtherOptions>
+EIGEN_DEVICE_FUNC inline Scalar_ ParametrizedLine<Scalar_, AmbientDim_,Options_>::intersection(const Hyperplane<Scalar_, AmbientDim_, OtherOptions>& hyperplane) const
+{
+ return intersectionParameter(hyperplane);
+}
+
+/** \returns the point of the intersection between \c *this and the given hyperplane
+ */
+template <typename Scalar_, int AmbientDim_, int Options_>
+template <int OtherOptions>
+EIGEN_DEVICE_FUNC inline typename ParametrizedLine<Scalar_, AmbientDim_,Options_>::VectorType
+ParametrizedLine<Scalar_, AmbientDim_,Options_>::intersectionPoint(const Hyperplane<Scalar_, AmbientDim_, OtherOptions>& hyperplane) const
+{
+ return pointAt(intersectionParameter(hyperplane));
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_PARAMETRIZEDLINE_H
diff --git a/Eigen/src/Geometry/Quaternion.h b/Eigen/src/Geometry/Quaternion.h
new file mode 100644
index 0000000..0aca4c4
--- /dev/null
+++ b/Eigen/src/Geometry/Quaternion.h
@@ -0,0 +1,867 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2010 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2009 Mathieu Gautier <mathieu.gautier@cea.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_QUATERNION_H
+#define EIGEN_QUATERNION_H
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+
+/***************************************************************************
+* Definition of QuaternionBase<Derived>
+* The implementation is at the end of the file
+***************************************************************************/
+
+namespace internal {
+template<typename Other,
+ int OtherRows=Other::RowsAtCompileTime,
+ int OtherCols=Other::ColsAtCompileTime>
+struct quaternionbase_assign_impl;
+}
+
+/** \geometry_module \ingroup Geometry_Module
+ * \class QuaternionBase
+ * \brief Base class for quaternion expressions
+ * \tparam Derived derived type (CRTP)
+ * \sa class Quaternion
+ */
+template<class Derived>
+class QuaternionBase : public RotationBase<Derived, 3>
+{
+ public:
+ typedef RotationBase<Derived, 3> Base;
+
+ using Base::operator*;
+ using Base::derived;
+
+ typedef typename internal::traits<Derived>::Scalar Scalar;
+ typedef typename NumTraits<Scalar>::Real RealScalar;
+ typedef typename internal::traits<Derived>::Coefficients Coefficients;
+ typedef typename Coefficients::CoeffReturnType CoeffReturnType;
+ typedef std::conditional_t<bool(internal::traits<Derived>::Flags&LvalueBit),
+ Scalar&, CoeffReturnType> NonConstCoeffReturnType;
+
+
+ enum {
+ Flags = Eigen::internal::traits<Derived>::Flags
+ };
+
+ // typedef typename Matrix<Scalar,4,1> Coefficients;
+ /** the type of a 3D vector */
+ typedef Matrix<Scalar,3,1> Vector3;
+ /** the equivalent rotation matrix type */
+ typedef Matrix<Scalar,3,3> Matrix3;
+ /** the equivalent angle-axis type */
+ typedef AngleAxis<Scalar> AngleAxisType;
+
+
+
+ /** \returns the \c x coefficient */
+ EIGEN_DEVICE_FUNC inline CoeffReturnType x() const { return this->derived().coeffs().coeff(0); }
+ /** \returns the \c y coefficient */
+ EIGEN_DEVICE_FUNC inline CoeffReturnType y() const { return this->derived().coeffs().coeff(1); }
+ /** \returns the \c z coefficient */
+ EIGEN_DEVICE_FUNC inline CoeffReturnType z() const { return this->derived().coeffs().coeff(2); }
+ /** \returns the \c w coefficient */
+ EIGEN_DEVICE_FUNC inline CoeffReturnType w() const { return this->derived().coeffs().coeff(3); }
+
+ /** \returns a reference to the \c x coefficient (if Derived is a non-const lvalue) */
+ EIGEN_DEVICE_FUNC inline NonConstCoeffReturnType x() { return this->derived().coeffs().x(); }
+ /** \returns a reference to the \c y coefficient (if Derived is a non-const lvalue) */
+ EIGEN_DEVICE_FUNC inline NonConstCoeffReturnType y() { return this->derived().coeffs().y(); }
+ /** \returns a reference to the \c z coefficient (if Derived is a non-const lvalue) */
+ EIGEN_DEVICE_FUNC inline NonConstCoeffReturnType z() { return this->derived().coeffs().z(); }
+ /** \returns a reference to the \c w coefficient (if Derived is a non-const lvalue) */
+ EIGEN_DEVICE_FUNC inline NonConstCoeffReturnType w() { return this->derived().coeffs().w(); }
+
+ /** \returns a read-only vector expression of the imaginary part (x,y,z) */
+ EIGEN_DEVICE_FUNC inline const VectorBlock<const Coefficients,3> vec() const { return coeffs().template head<3>(); }
+
+ /** \returns a vector expression of the imaginary part (x,y,z) */
+ EIGEN_DEVICE_FUNC inline VectorBlock<Coefficients,3> vec() { return coeffs().template head<3>(); }
+
+ /** \returns a read-only vector expression of the coefficients (x,y,z,w) */
+ EIGEN_DEVICE_FUNC inline const typename internal::traits<Derived>::Coefficients& coeffs() const { return derived().coeffs(); }
+
+ /** \returns a vector expression of the coefficients (x,y,z,w) */
+ EIGEN_DEVICE_FUNC inline typename internal::traits<Derived>::Coefficients& coeffs() { return derived().coeffs(); }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE QuaternionBase<Derived>& operator=(const QuaternionBase<Derived>& other);
+ template<class OtherDerived> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& operator=(const QuaternionBase<OtherDerived>& other);
+
+// disabled this copy operator as it is giving very strange compilation errors when compiling
+// test_stdvector with GCC 4.4.2. This looks like a GCC bug though, so feel free to re-enable it if it's
+// useful; however notice that we already have the templated operator= above and e.g. in MatrixBase
+// we didn't have to add, in addition to templated operator=, such a non-templated copy operator.
+// Derived& operator=(const QuaternionBase& other)
+// { return operator=<Derived>(other); }
+
+ EIGEN_DEVICE_FUNC Derived& operator=(const AngleAxisType& aa);
+ template<class OtherDerived> EIGEN_DEVICE_FUNC Derived& operator=(const MatrixBase<OtherDerived>& m);
+
+ /** \returns a quaternion representing an identity rotation
+ * \sa MatrixBase::Identity()
+ */
+ EIGEN_DEVICE_FUNC static inline Quaternion<Scalar> Identity() { return Quaternion<Scalar>(Scalar(1), Scalar(0), Scalar(0), Scalar(0)); }
+
+ /** \sa QuaternionBase::Identity(), MatrixBase::setIdentity()
+ */
+ EIGEN_DEVICE_FUNC inline QuaternionBase& setIdentity() { coeffs() << Scalar(0), Scalar(0), Scalar(0), Scalar(1); return *this; }
+
+ /** \returns the squared norm of the quaternion's coefficients
+ * \sa QuaternionBase::norm(), MatrixBase::squaredNorm()
+ */
+ EIGEN_DEVICE_FUNC inline Scalar squaredNorm() const { return coeffs().squaredNorm(); }
+
+ /** \returns the norm of the quaternion's coefficients
+ * \sa QuaternionBase::squaredNorm(), MatrixBase::norm()
+ */
+ EIGEN_DEVICE_FUNC inline Scalar norm() const { return coeffs().norm(); }
+
+ /** Normalizes the quaternion \c *this
+ * \sa normalized(), MatrixBase::normalize() */
+ EIGEN_DEVICE_FUNC inline void normalize() { coeffs().normalize(); }
+ /** \returns a normalized copy of \c *this
+ * \sa normalize(), MatrixBase::normalized() */
+ EIGEN_DEVICE_FUNC inline Quaternion<Scalar> normalized() const { return Quaternion<Scalar>(coeffs().normalized()); }
+
+ /** \returns the dot product of \c *this and \a other
+ * Geometrically speaking, the dot product of two unit quaternions
+ * corresponds to the cosine of half the angle between the two rotations.
+ * \sa angularDistance()
+ */
+ template<class OtherDerived> EIGEN_DEVICE_FUNC inline Scalar dot(const QuaternionBase<OtherDerived>& other) const { return coeffs().dot(other.coeffs()); }
+
+ template<class OtherDerived> EIGEN_DEVICE_FUNC Scalar angularDistance(const QuaternionBase<OtherDerived>& other) const;
+
+ /** \returns an equivalent 3x3 rotation matrix */
+ EIGEN_DEVICE_FUNC inline Matrix3 toRotationMatrix() const;
+
+ /** \returns the quaternion which transform \a a into \a b through a rotation */
+ template<typename Derived1, typename Derived2>
+ EIGEN_DEVICE_FUNC Derived& setFromTwoVectors(const MatrixBase<Derived1>& a, const MatrixBase<Derived2>& b);
+
+ template<class OtherDerived> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Quaternion<Scalar> operator* (const QuaternionBase<OtherDerived>& q) const;
+ template<class OtherDerived> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& operator*= (const QuaternionBase<OtherDerived>& q);
+
+ /** \returns the quaternion describing the inverse rotation */
+ EIGEN_DEVICE_FUNC Quaternion<Scalar> inverse() const;
+
+ /** \returns the conjugated quaternion */
+ EIGEN_DEVICE_FUNC Quaternion<Scalar> conjugate() const;
+
+ template<class OtherDerived> EIGEN_DEVICE_FUNC Quaternion<Scalar> slerp(const Scalar& t, const QuaternionBase<OtherDerived>& other) const;
+
+ /** \returns true if each coefficients of \c *this and \a other are all exactly equal.
+ * \warning When using floating point scalar values you probably should rather use a
+ * fuzzy comparison such as isApprox()
+ * \sa isApprox(), operator!= */
+ template<class OtherDerived>
+ EIGEN_DEVICE_FUNC inline bool operator==(const QuaternionBase<OtherDerived>& other) const
+ { return coeffs() == other.coeffs(); }
+
+ /** \returns true if at least one pair of coefficients of \c *this and \a other are not exactly equal to each other.
+ * \warning When using floating point scalar values you probably should rather use a
+ * fuzzy comparison such as isApprox()
+ * \sa isApprox(), operator== */
+ template<class OtherDerived>
+ EIGEN_DEVICE_FUNC inline bool operator!=(const QuaternionBase<OtherDerived>& other) const
+ { return coeffs() != other.coeffs(); }
+
+ /** \returns \c true if \c *this is approximately equal to \a other, within the precision
+ * determined by \a prec.
+ *
+ * \sa MatrixBase::isApprox() */
+ template<class OtherDerived>
+ EIGEN_DEVICE_FUNC bool isApprox(const QuaternionBase<OtherDerived>& other, const RealScalar& prec = NumTraits<Scalar>::dummy_precision()) const
+ { return coeffs().isApprox(other.coeffs(), prec); }
+
+ /** return the result vector of \a v through the rotation*/
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Vector3 _transformVector(const Vector3& v) const;
+
+ #ifdef EIGEN_PARSED_BY_DOXYGEN
+ /** \returns \c *this with scalar type casted to \a NewScalarType
+ *
+ * Note that if \a NewScalarType is equal to the current scalar type of \c *this
+ * then this function smartly returns a const reference to \c *this.
+ */
+ template<typename NewScalarType>
+ EIGEN_DEVICE_FUNC inline typename internal::cast_return_type<Derived,Quaternion<NewScalarType> >::type cast() const;
+
+ #else
+
+ template<typename NewScalarType>
+ EIGEN_DEVICE_FUNC inline
+ std::enable_if_t<internal::is_same<Scalar,NewScalarType>::value,const Derived&> cast() const
+ {
+ return derived();
+ }
+
+ template<typename NewScalarType>
+ EIGEN_DEVICE_FUNC inline
+ std::enable_if_t<!internal::is_same<Scalar,NewScalarType>::value,Quaternion<NewScalarType> > cast() const
+ {
+ return Quaternion<NewScalarType>(coeffs().template cast<NewScalarType>());
+ }
+ #endif
+
+#ifndef EIGEN_NO_IO
+ friend std::ostream& operator<<(std::ostream& s, const QuaternionBase<Derived>& q) {
+ s << q.x() << "i + " << q.y() << "j + " << q.z() << "k" << " + " << q.w();
+ return s;
+ }
+#endif
+
+#ifdef EIGEN_QUATERNIONBASE_PLUGIN
+# include EIGEN_QUATERNIONBASE_PLUGIN
+#endif
+protected:
+ EIGEN_DEFAULT_COPY_CONSTRUCTOR(QuaternionBase)
+ EIGEN_DEFAULT_EMPTY_CONSTRUCTOR_AND_DESTRUCTOR(QuaternionBase)
+};
+
+/***************************************************************************
+* Definition/implementation of Quaternion<Scalar>
+***************************************************************************/
+
+/** \geometry_module \ingroup Geometry_Module
+ *
+ * \class Quaternion
+ *
+ * \brief The quaternion class used to represent 3D orientations and rotations
+ *
+ * \tparam Scalar_ the scalar type, i.e., the type of the coefficients
+ * \tparam Options_ controls the memory alignment of the coefficients. Can be \# AutoAlign or \# DontAlign. Default is AutoAlign.
+ *
+ * This class represents a quaternion \f$ w+xi+yj+zk \f$ that is a convenient representation of
+ * orientations and rotations of objects in three dimensions. Compared to other representations
+ * like Euler angles or 3x3 matrices, quaternions offer the following advantages:
+ * \li \b compact storage (4 scalars)
+ * \li \b efficient to compose (28 flops),
+ * \li \b stable spherical interpolation
+ *
+ * The following two typedefs are provided for convenience:
+ * \li \c Quaternionf for \c float
+ * \li \c Quaterniond for \c double
+ *
+ * \warning Operations interpreting the quaternion as rotation have undefined behavior if the quaternion is not normalized.
+ *
+ * \sa class AngleAxis, class Transform
+ */
+
+namespace internal {
+template<typename Scalar_,int Options_>
+struct traits<Quaternion<Scalar_,Options_> >
+{
+ typedef Quaternion<Scalar_,Options_> PlainObject;
+ typedef Scalar_ Scalar;
+ typedef Matrix<Scalar_,4,1,Options_> Coefficients;
+ enum{
+ Alignment = internal::traits<Coefficients>::Alignment,
+ Flags = LvalueBit
+ };
+};
+}
+
+template<typename Scalar_, int Options_>
+class Quaternion : public QuaternionBase<Quaternion<Scalar_,Options_> >
+{
+public:
+ typedef QuaternionBase<Quaternion<Scalar_,Options_> > Base;
+ enum { NeedsAlignment = internal::traits<Quaternion>::Alignment>0 };
+
+ typedef Scalar_ Scalar;
+
+ EIGEN_INHERIT_ASSIGNMENT_OPERATORS(Quaternion)
+ using Base::operator*=;
+
+ typedef typename internal::traits<Quaternion>::Coefficients Coefficients;
+ typedef typename Base::AngleAxisType AngleAxisType;
+
+ /** Default constructor leaving the quaternion uninitialized. */
+ EIGEN_DEVICE_FUNC inline Quaternion() {}
+
+ /** Constructs and initializes the quaternion \f$ w+xi+yj+zk \f$ from
+ * its four coefficients \a w, \a x, \a y and \a z.
+ *
+ * \warning Note the order of the arguments: the real \a w coefficient first,
+ * while internally the coefficients are stored in the following order:
+ * [\c x, \c y, \c z, \c w]
+ */
+ EIGEN_DEVICE_FUNC inline Quaternion(const Scalar& w, const Scalar& x, const Scalar& y, const Scalar& z) : m_coeffs(x, y, z, w){}
+
+ /** Constructs and initialize a quaternion from the array data */
+ EIGEN_DEVICE_FUNC explicit inline Quaternion(const Scalar* data) : m_coeffs(data) {}
+
+ /** Copy constructor */
+ template<class Derived> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Quaternion(const QuaternionBase<Derived>& other) { this->Base::operator=(other); }
+
+ /** Constructs and initializes a quaternion from the angle-axis \a aa */
+ EIGEN_DEVICE_FUNC explicit inline Quaternion(const AngleAxisType& aa) { *this = aa; }
+
+ /** Constructs and initializes a quaternion from either:
+ * - a rotation matrix expression,
+ * - a 4D vector expression representing quaternion coefficients in the order [\c x, \c y, \c z, \c w].
+ */
+ template<typename Derived>
+ EIGEN_DEVICE_FUNC explicit inline Quaternion(const MatrixBase<Derived>& other) { *this = other; }
+
+ /** Explicit copy constructor with scalar conversion */
+ template<typename OtherScalar, int OtherOptions>
+ EIGEN_DEVICE_FUNC explicit inline Quaternion(const Quaternion<OtherScalar, OtherOptions>& other)
+ { m_coeffs = other.coeffs().template cast<Scalar>(); }
+
+ // We define a copy constructor, which means we don't get an implicit move constructor or assignment operator.
+ /** Default move constructor */
+ EIGEN_DEVICE_FUNC inline Quaternion(Quaternion&& other) EIGEN_NOEXCEPT_IF(std::is_nothrow_move_constructible<Scalar>::value)
+ : m_coeffs(std::move(other.coeffs()))
+ {}
+
+ /** Default move assignment operator */
+ EIGEN_DEVICE_FUNC Quaternion& operator=(Quaternion&& other) EIGEN_NOEXCEPT_IF(std::is_nothrow_move_assignable<Scalar>::value)
+ {
+ m_coeffs = std::move(other.coeffs());
+ return *this;
+ }
+
+ EIGEN_DEVICE_FUNC static Quaternion UnitRandom();
+
+ template<typename Derived1, typename Derived2>
+ EIGEN_DEVICE_FUNC static Quaternion FromTwoVectors(const MatrixBase<Derived1>& a, const MatrixBase<Derived2>& b);
+
+ EIGEN_DEVICE_FUNC inline Coefficients& coeffs() { return m_coeffs;}
+ EIGEN_DEVICE_FUNC inline const Coefficients& coeffs() const { return m_coeffs;}
+
+ EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF(bool(NeedsAlignment))
+
+#ifdef EIGEN_QUATERNION_PLUGIN
+# include EIGEN_QUATERNION_PLUGIN
+#endif
+
+protected:
+ Coefficients m_coeffs;
+
+#ifndef EIGEN_PARSED_BY_DOXYGEN
+ EIGEN_STATIC_ASSERT( (Options_ & DontAlign) == Options_,
+ INVALID_MATRIX_TEMPLATE_PARAMETERS)
+#endif
+};
+
+/** \ingroup Geometry_Module
+ * single precision quaternion type */
+typedef Quaternion<float> Quaternionf;
+/** \ingroup Geometry_Module
+ * double precision quaternion type */
+typedef Quaternion<double> Quaterniond;
+
+/***************************************************************************
+* Specialization of Map<Quaternion<Scalar>>
+***************************************************************************/
+
+namespace internal {
+ template<typename Scalar_, int Options_>
+ struct traits<Map<Quaternion<Scalar_>, Options_> > : traits<Quaternion<Scalar_, (int(Options_)&Aligned)==Aligned ? AutoAlign : DontAlign> >
+ {
+ typedef Map<Matrix<Scalar_,4,1>, Options_> Coefficients;
+ };
+}
+
+namespace internal {
+ template<typename Scalar_, int Options_>
+ struct traits<Map<const Quaternion<Scalar_>, Options_> > : traits<Quaternion<Scalar_, (int(Options_)&Aligned)==Aligned ? AutoAlign : DontAlign> >
+ {
+ typedef Map<const Matrix<Scalar_,4,1>, Options_> Coefficients;
+ typedef traits<Quaternion<Scalar_, (int(Options_)&Aligned)==Aligned ? AutoAlign : DontAlign> > TraitsBase;
+ enum {
+ Flags = TraitsBase::Flags & ~LvalueBit
+ };
+ };
+}
+
+/** \ingroup Geometry_Module
+ * \brief Quaternion expression mapping a constant memory buffer
+ *
+ * \tparam Scalar_ the type of the Quaternion coefficients
+ * \tparam Options_ see class Map
+ *
+ * This is a specialization of class Map for Quaternion. This class allows to view
+ * a 4 scalar memory buffer as an Eigen's Quaternion object.
+ *
+ * \sa class Map, class Quaternion, class QuaternionBase
+ */
+template<typename Scalar_, int Options_>
+class Map<const Quaternion<Scalar_>, Options_ >
+ : public QuaternionBase<Map<const Quaternion<Scalar_>, Options_> >
+{
+ public:
+ typedef QuaternionBase<Map<const Quaternion<Scalar_>, Options_> > Base;
+
+ typedef Scalar_ Scalar;
+ typedef typename internal::traits<Map>::Coefficients Coefficients;
+ EIGEN_INHERIT_ASSIGNMENT_OPERATORS(Map)
+ using Base::operator*=;
+
+ /** Constructs a Mapped Quaternion object from the pointer \a coeffs
+ *
+ * The pointer \a coeffs must reference the four coefficients of Quaternion in the following order:
+ * \code *coeffs == {x, y, z, w} \endcode
+ *
+ * If the template parameter Options_ is set to #Aligned, then the pointer coeffs must be aligned. */
+ EIGEN_DEVICE_FUNC explicit EIGEN_STRONG_INLINE Map(const Scalar* coeffs) : m_coeffs(coeffs) {}
+
+ EIGEN_DEVICE_FUNC inline const Coefficients& coeffs() const { return m_coeffs;}
+
+ protected:
+ const Coefficients m_coeffs;
+};
+
+/** \ingroup Geometry_Module
+ * \brief Expression of a quaternion from a memory buffer
+ *
+ * \tparam Scalar_ the type of the Quaternion coefficients
+ * \tparam Options_ see class Map
+ *
+ * This is a specialization of class Map for Quaternion. This class allows to view
+ * a 4 scalar memory buffer as an Eigen's Quaternion object.
+ *
+ * \sa class Map, class Quaternion, class QuaternionBase
+ */
+template<typename Scalar_, int Options_>
+class Map<Quaternion<Scalar_>, Options_ >
+ : public QuaternionBase<Map<Quaternion<Scalar_>, Options_> >
+{
+ public:
+ typedef QuaternionBase<Map<Quaternion<Scalar_>, Options_> > Base;
+
+ typedef Scalar_ Scalar;
+ typedef typename internal::traits<Map>::Coefficients Coefficients;
+ EIGEN_INHERIT_ASSIGNMENT_OPERATORS(Map)
+ using Base::operator*=;
+
+ /** Constructs a Mapped Quaternion object from the pointer \a coeffs
+ *
+ * The pointer \a coeffs must reference the four coefficients of Quaternion in the following order:
+ * \code *coeffs == {x, y, z, w} \endcode
+ *
+ * If the template parameter Options_ is set to #Aligned, then the pointer coeffs must be aligned. */
+ EIGEN_DEVICE_FUNC explicit EIGEN_STRONG_INLINE Map(Scalar* coeffs) : m_coeffs(coeffs) {}
+
+ EIGEN_DEVICE_FUNC inline Coefficients& coeffs() { return m_coeffs; }
+ EIGEN_DEVICE_FUNC inline const Coefficients& coeffs() const { return m_coeffs; }
+
+ protected:
+ Coefficients m_coeffs;
+};
+
+/** \ingroup Geometry_Module
+ * Map an unaligned array of single precision scalars as a quaternion */
+typedef Map<Quaternion<float>, 0> QuaternionMapf;
+/** \ingroup Geometry_Module
+ * Map an unaligned array of double precision scalars as a quaternion */
+typedef Map<Quaternion<double>, 0> QuaternionMapd;
+/** \ingroup Geometry_Module
+ * Map a 16-byte aligned array of single precision scalars as a quaternion */
+typedef Map<Quaternion<float>, Aligned> QuaternionMapAlignedf;
+/** \ingroup Geometry_Module
+ * Map a 16-byte aligned array of double precision scalars as a quaternion */
+typedef Map<Quaternion<double>, Aligned> QuaternionMapAlignedd;
+
+/***************************************************************************
+* Implementation of QuaternionBase methods
+***************************************************************************/
+
+// Generic Quaternion * Quaternion product
+// This product can be specialized for a given architecture via the Arch template argument.
+namespace internal {
+template<int Arch, class Derived1, class Derived2, typename Scalar> struct quat_product
+{
+ EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE Quaternion<Scalar> run(const QuaternionBase<Derived1>& a, const QuaternionBase<Derived2>& b){
+ return Quaternion<Scalar>
+ (
+ a.w() * b.w() - a.x() * b.x() - a.y() * b.y() - a.z() * b.z(),
+ a.w() * b.x() + a.x() * b.w() + a.y() * b.z() - a.z() * b.y(),
+ a.w() * b.y() + a.y() * b.w() + a.z() * b.x() - a.x() * b.z(),
+ a.w() * b.z() + a.z() * b.w() + a.x() * b.y() - a.y() * b.x()
+ );
+ }
+};
+}
+
+/** \returns the concatenation of two rotations as a quaternion-quaternion product */
+template <class Derived>
+template <class OtherDerived>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Quaternion<typename internal::traits<Derived>::Scalar>
+QuaternionBase<Derived>::operator* (const QuaternionBase<OtherDerived>& other) const
+{
+ EIGEN_STATIC_ASSERT((internal::is_same<typename Derived::Scalar, typename OtherDerived::Scalar>::value),
+ YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY)
+ return internal::quat_product<Architecture::Target, Derived, OtherDerived,
+ typename internal::traits<Derived>::Scalar>::run(*this, other);
+}
+
+/** \sa operator*(Quaternion) */
+template <class Derived>
+template <class OtherDerived>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& QuaternionBase<Derived>::operator*= (const QuaternionBase<OtherDerived>& other)
+{
+ derived() = derived() * other.derived();
+ return derived();
+}
+
+/** Rotation of a vector by a quaternion.
+ * \remarks If the quaternion is used to rotate several points (>1)
+ * then it is much more efficient to first convert it to a 3x3 Matrix.
+ * Comparison of the operation cost for n transformations:
+ * - Quaternion2: 30n
+ * - Via a Matrix3: 24 + 15n
+ */
+template <class Derived>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE typename QuaternionBase<Derived>::Vector3
+QuaternionBase<Derived>::_transformVector(const Vector3& v) const
+{
+ // Note that this algorithm comes from the optimization by hand
+ // of the conversion to a Matrix followed by a Matrix/Vector product.
+ // It appears to be much faster than the common algorithm found
+ // in the literature (30 versus 39 flops). It also requires two
+ // Vector3 as temporaries.
+ Vector3 uv = this->vec().cross(v);
+ uv += uv;
+ return v + this->w() * uv + this->vec().cross(uv);
+}
+
+template<class Derived>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE QuaternionBase<Derived>& QuaternionBase<Derived>::operator=(const QuaternionBase<Derived>& other)
+{
+ coeffs() = other.coeffs();
+ return derived();
+}
+
+template<class Derived>
+template<class OtherDerived>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& QuaternionBase<Derived>::operator=(const QuaternionBase<OtherDerived>& other)
+{
+ coeffs() = other.coeffs();
+ return derived();
+}
+
+/** Set \c *this from an angle-axis \a aa and returns a reference to \c *this
+ */
+template<class Derived>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& QuaternionBase<Derived>::operator=(const AngleAxisType& aa)
+{
+ EIGEN_USING_STD(cos)
+ EIGEN_USING_STD(sin)
+ Scalar ha = Scalar(0.5)*aa.angle(); // Scalar(0.5) to suppress precision loss warnings
+ this->w() = cos(ha);
+ this->vec() = sin(ha) * aa.axis();
+ return derived();
+}
+
+/** Set \c *this from the expression \a xpr:
+ * - if \a xpr is a 4x1 vector, then \a xpr is assumed to be a quaternion
+ * - if \a xpr is a 3x3 matrix, then \a xpr is assumed to be rotation matrix
+ * and \a xpr is converted to a quaternion
+ */
+
+template<class Derived>
+template<class MatrixDerived>
+EIGEN_DEVICE_FUNC inline Derived& QuaternionBase<Derived>::operator=(const MatrixBase<MatrixDerived>& xpr)
+{
+ EIGEN_STATIC_ASSERT((internal::is_same<typename Derived::Scalar, typename MatrixDerived::Scalar>::value),
+ YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY)
+ internal::quaternionbase_assign_impl<MatrixDerived>::run(*this, xpr.derived());
+ return derived();
+}
+
+/** Convert the quaternion to a 3x3 rotation matrix. The quaternion is required to
+ * be normalized, otherwise the result is undefined.
+ */
+template<class Derived>
+EIGEN_DEVICE_FUNC inline typename QuaternionBase<Derived>::Matrix3
+QuaternionBase<Derived>::toRotationMatrix(void) const
+{
+ // NOTE if inlined, then gcc 4.2 and 4.4 get rid of the temporary (not gcc 4.3 !!)
+ // if not inlined then the cost of the return by value is huge ~ +35%,
+ // however, not inlining this function is an order of magnitude slower, so
+ // it has to be inlined, and so the return by value is not an issue
+ Matrix3 res;
+
+ const Scalar tx = Scalar(2)*this->x();
+ const Scalar ty = Scalar(2)*this->y();
+ const Scalar tz = Scalar(2)*this->z();
+ const Scalar twx = tx*this->w();
+ const Scalar twy = ty*this->w();
+ const Scalar twz = tz*this->w();
+ const Scalar txx = tx*this->x();
+ const Scalar txy = ty*this->x();
+ const Scalar txz = tz*this->x();
+ const Scalar tyy = ty*this->y();
+ const Scalar tyz = tz*this->y();
+ const Scalar tzz = tz*this->z();
+
+ res.coeffRef(0,0) = Scalar(1)-(tyy+tzz);
+ res.coeffRef(0,1) = txy-twz;
+ res.coeffRef(0,2) = txz+twy;
+ res.coeffRef(1,0) = txy+twz;
+ res.coeffRef(1,1) = Scalar(1)-(txx+tzz);
+ res.coeffRef(1,2) = tyz-twx;
+ res.coeffRef(2,0) = txz-twy;
+ res.coeffRef(2,1) = tyz+twx;
+ res.coeffRef(2,2) = Scalar(1)-(txx+tyy);
+
+ return res;
+}
+
+/** Sets \c *this to be a quaternion representing a rotation between
+ * the two arbitrary vectors \a a and \a b. In other words, the built
+ * rotation represent a rotation sending the line of direction \a a
+ * to the line of direction \a b, both lines passing through the origin.
+ *
+ * \returns a reference to \c *this.
+ *
+ * Note that the two input vectors do \b not have to be normalized, and
+ * do not need to have the same norm.
+ */
+template<class Derived>
+template<typename Derived1, typename Derived2>
+EIGEN_DEVICE_FUNC inline Derived& QuaternionBase<Derived>::setFromTwoVectors(const MatrixBase<Derived1>& a, const MatrixBase<Derived2>& b)
+{
+ EIGEN_USING_STD(sqrt)
+ Vector3 v0 = a.normalized();
+ Vector3 v1 = b.normalized();
+ Scalar c = v1.dot(v0);
+
+ // if dot == -1, vectors are nearly opposites
+ // => accurately compute the rotation axis by computing the
+ // intersection of the two planes. This is done by solving:
+ // x^T v0 = 0
+ // x^T v1 = 0
+ // under the constraint:
+ // ||x|| = 1
+ // which yields a singular value problem
+ if (c < Scalar(-1)+NumTraits<Scalar>::dummy_precision())
+ {
+ c = numext::maxi(c,Scalar(-1));
+ Matrix<Scalar,2,3> m; m << v0.transpose(), v1.transpose();
+ JacobiSVD<Matrix<Scalar,2,3>, ComputeFullV> svd(m);
+ Vector3 axis = svd.matrixV().col(2);
+
+ Scalar w2 = (Scalar(1)+c)*Scalar(0.5);
+ this->w() = sqrt(w2);
+ this->vec() = axis * sqrt(Scalar(1) - w2);
+ return derived();
+ }
+ Vector3 axis = v0.cross(v1);
+ Scalar s = sqrt((Scalar(1)+c)*Scalar(2));
+ Scalar invs = Scalar(1)/s;
+ this->vec() = axis * invs;
+ this->w() = s * Scalar(0.5);
+
+ return derived();
+}
+
+/** \returns a random unit quaternion following a uniform distribution law on SO(3)
+ *
+ * \note The implementation is based on http://planning.cs.uiuc.edu/node198.html
+ */
+template<typename Scalar, int Options>
+EIGEN_DEVICE_FUNC Quaternion<Scalar,Options> Quaternion<Scalar,Options>::UnitRandom()
+{
+ EIGEN_USING_STD(sqrt)
+ EIGEN_USING_STD(sin)
+ EIGEN_USING_STD(cos)
+ const Scalar u1 = internal::random<Scalar>(0, 1),
+ u2 = internal::random<Scalar>(0, 2*EIGEN_PI),
+ u3 = internal::random<Scalar>(0, 2*EIGEN_PI);
+ const Scalar a = sqrt(Scalar(1) - u1),
+ b = sqrt(u1);
+ return Quaternion (a * sin(u2), a * cos(u2), b * sin(u3), b * cos(u3));
+}
+
+
+/** Returns a quaternion representing a rotation between
+ * the two arbitrary vectors \a a and \a b. In other words, the built
+ * rotation represent a rotation sending the line of direction \a a
+ * to the line of direction \a b, both lines passing through the origin.
+ *
+ * \returns resulting quaternion
+ *
+ * Note that the two input vectors do \b not have to be normalized, and
+ * do not need to have the same norm.
+ */
+template<typename Scalar, int Options>
+template<typename Derived1, typename Derived2>
+EIGEN_DEVICE_FUNC Quaternion<Scalar,Options> Quaternion<Scalar,Options>::FromTwoVectors(const MatrixBase<Derived1>& a, const MatrixBase<Derived2>& b)
+{
+ Quaternion quat;
+ quat.setFromTwoVectors(a, b);
+ return quat;
+}
+
+
+/** \returns the multiplicative inverse of \c *this
+ * Note that in most cases, i.e., if you simply want the opposite rotation,
+ * and/or the quaternion is normalized, then it is enough to use the conjugate.
+ *
+ * \sa QuaternionBase::conjugate()
+ */
+template <class Derived>
+EIGEN_DEVICE_FUNC inline Quaternion<typename internal::traits<Derived>::Scalar> QuaternionBase<Derived>::inverse() const
+{
+ // FIXME should this function be called multiplicativeInverse and conjugate() be called inverse() or opposite() ??
+ Scalar n2 = this->squaredNorm();
+ if (n2 > Scalar(0))
+ return Quaternion<Scalar>(conjugate().coeffs() / n2);
+ else
+ {
+ // return an invalid result to flag the error
+ return Quaternion<Scalar>(Coefficients::Zero());
+ }
+}
+
+// Generic conjugate of a Quaternion
+namespace internal {
+template<int Arch, class Derived, typename Scalar> struct quat_conj
+{
+ EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE Quaternion<Scalar> run(const QuaternionBase<Derived>& q){
+ return Quaternion<Scalar>(q.w(),-q.x(),-q.y(),-q.z());
+ }
+};
+}
+
+/** \returns the conjugate of the \c *this which is equal to the multiplicative inverse
+ * if the quaternion is normalized.
+ * The conjugate of a quaternion represents the opposite rotation.
+ *
+ * \sa Quaternion2::inverse()
+ */
+template <class Derived>
+EIGEN_DEVICE_FUNC inline Quaternion<typename internal::traits<Derived>::Scalar>
+QuaternionBase<Derived>::conjugate() const
+{
+ return internal::quat_conj<Architecture::Target, Derived,
+ typename internal::traits<Derived>::Scalar>::run(*this);
+
+}
+
+/** \returns the angle (in radian) between two rotations
+ * \sa dot()
+ */
+template <class Derived>
+template <class OtherDerived>
+EIGEN_DEVICE_FUNC inline typename internal::traits<Derived>::Scalar
+QuaternionBase<Derived>::angularDistance(const QuaternionBase<OtherDerived>& other) const
+{
+ EIGEN_USING_STD(atan2)
+ Quaternion<Scalar> d = (*this) * other.conjugate();
+ return Scalar(2) * atan2( d.vec().norm(), numext::abs(d.w()) );
+}
+
+
+
+/** \returns the spherical linear interpolation between the two quaternions
+ * \c *this and \a other at the parameter \a t in [0;1].
+ *
+ * This represents an interpolation for a constant motion between \c *this and \a other,
+ * see also http://en.wikipedia.org/wiki/Slerp.
+ */
+template <class Derived>
+template <class OtherDerived>
+EIGEN_DEVICE_FUNC Quaternion<typename internal::traits<Derived>::Scalar>
+QuaternionBase<Derived>::slerp(const Scalar& t, const QuaternionBase<OtherDerived>& other) const
+{
+ EIGEN_USING_STD(acos)
+ EIGEN_USING_STD(sin)
+ const Scalar one = Scalar(1) - NumTraits<Scalar>::epsilon();
+ Scalar d = this->dot(other);
+ Scalar absD = numext::abs(d);
+
+ Scalar scale0;
+ Scalar scale1;
+
+ if(absD>=one)
+ {
+ scale0 = Scalar(1) - t;
+ scale1 = t;
+ }
+ else
+ {
+ // theta is the angle between the 2 quaternions
+ Scalar theta = acos(absD);
+ Scalar sinTheta = sin(theta);
+
+ scale0 = sin( ( Scalar(1) - t ) * theta) / sinTheta;
+ scale1 = sin( ( t * theta) ) / sinTheta;
+ }
+ if(d<Scalar(0)) scale1 = -scale1;
+
+ return Quaternion<Scalar>(scale0 * coeffs() + scale1 * other.coeffs());
+}
+
+namespace internal {
+
+// set from a rotation matrix
+template<typename Other>
+struct quaternionbase_assign_impl<Other,3,3>
+{
+ typedef typename Other::Scalar Scalar;
+ template<class Derived> EIGEN_DEVICE_FUNC static inline void run(QuaternionBase<Derived>& q, const Other& a_mat)
+ {
+ const typename internal::nested_eval<Other,2>::type mat(a_mat);
+ EIGEN_USING_STD(sqrt)
+ // This algorithm comes from "Quaternion Calculus and Fast Animation",
+ // Ken Shoemake, 1987 SIGGRAPH course notes
+ Scalar t = mat.trace();
+ if (t > Scalar(0))
+ {
+ t = sqrt(t + Scalar(1.0));
+ q.w() = Scalar(0.5)*t;
+ t = Scalar(0.5)/t;
+ q.x() = (mat.coeff(2,1) - mat.coeff(1,2)) * t;
+ q.y() = (mat.coeff(0,2) - mat.coeff(2,0)) * t;
+ q.z() = (mat.coeff(1,0) - mat.coeff(0,1)) * t;
+ }
+ else
+ {
+ Index i = 0;
+ if (mat.coeff(1,1) > mat.coeff(0,0))
+ i = 1;
+ if (mat.coeff(2,2) > mat.coeff(i,i))
+ i = 2;
+ Index j = (i+1)%3;
+ Index k = (j+1)%3;
+
+ t = sqrt(mat.coeff(i,i)-mat.coeff(j,j)-mat.coeff(k,k) + Scalar(1.0));
+ q.coeffs().coeffRef(i) = Scalar(0.5) * t;
+ t = Scalar(0.5)/t;
+ q.w() = (mat.coeff(k,j)-mat.coeff(j,k))*t;
+ q.coeffs().coeffRef(j) = (mat.coeff(j,i)+mat.coeff(i,j))*t;
+ q.coeffs().coeffRef(k) = (mat.coeff(k,i)+mat.coeff(i,k))*t;
+ }
+ }
+};
+
+// set from a vector of coefficients assumed to be a quaternion
+template<typename Other>
+struct quaternionbase_assign_impl<Other,4,1>
+{
+ typedef typename Other::Scalar Scalar;
+ template<class Derived> EIGEN_DEVICE_FUNC static inline void run(QuaternionBase<Derived>& q, const Other& vec)
+ {
+ q.coeffs() = vec;
+ }
+};
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_QUATERNION_H
diff --git a/Eigen/src/Geometry/Rotation2D.h b/Eigen/src/Geometry/Rotation2D.h
new file mode 100644
index 0000000..aa7f863
--- /dev/null
+++ b/Eigen/src/Geometry/Rotation2D.h
@@ -0,0 +1,201 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_ROTATION2D_H
+#define EIGEN_ROTATION2D_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+/** \geometry_module \ingroup Geometry_Module
+ *
+ * \class Rotation2D
+ *
+ * \brief Represents a rotation/orientation in a 2 dimensional space.
+ *
+ * \tparam Scalar_ the scalar type, i.e., the type of the coefficients
+ *
+ * This class is equivalent to a single scalar representing a counter clock wise rotation
+ * as a single angle in radian. It provides some additional features such as the automatic
+ * conversion from/to a 2x2 rotation matrix. Moreover this class aims to provide a similar
+ * interface to Quaternion in order to facilitate the writing of generic algorithms
+ * dealing with rotations.
+ *
+ * \sa class Quaternion, class Transform
+ */
+
+namespace internal {
+
+template<typename Scalar_> struct traits<Rotation2D<Scalar_> >
+{
+ typedef Scalar_ Scalar;
+};
+} // end namespace internal
+
+template<typename Scalar_>
+class Rotation2D : public RotationBase<Rotation2D<Scalar_>,2>
+{
+ typedef RotationBase<Rotation2D<Scalar_>,2> Base;
+
+public:
+
+ using Base::operator*;
+
+ enum { Dim = 2 };
+ /** the scalar type of the coefficients */
+ typedef Scalar_ Scalar;
+ typedef Matrix<Scalar,2,1> Vector2;
+ typedef Matrix<Scalar,2,2> Matrix2;
+
+protected:
+
+ Scalar m_angle;
+
+public:
+
+ /** Construct a 2D counter clock wise rotation from the angle \a a in radian. */
+ EIGEN_DEVICE_FUNC explicit inline Rotation2D(const Scalar& a) : m_angle(a) {}
+
+ /** Default constructor wihtout initialization. The represented rotation is undefined. */
+ EIGEN_DEVICE_FUNC Rotation2D() {}
+
+ /** Construct a 2D rotation from a 2x2 rotation matrix \a mat.
+ *
+ * \sa fromRotationMatrix()
+ */
+ template<typename Derived>
+ EIGEN_DEVICE_FUNC explicit Rotation2D(const MatrixBase<Derived>& m)
+ {
+ fromRotationMatrix(m.derived());
+ }
+
+ /** \returns the rotation angle */
+ EIGEN_DEVICE_FUNC inline Scalar angle() const { return m_angle; }
+
+ /** \returns a read-write reference to the rotation angle */
+ EIGEN_DEVICE_FUNC inline Scalar& angle() { return m_angle; }
+
+ /** \returns the rotation angle in [0,2pi] */
+ EIGEN_DEVICE_FUNC inline Scalar smallestPositiveAngle() const {
+ Scalar tmp = numext::fmod(m_angle,Scalar(2*EIGEN_PI));
+ return tmp<Scalar(0) ? tmp + Scalar(2*EIGEN_PI) : tmp;
+ }
+
+ /** \returns the rotation angle in [-pi,pi] */
+ EIGEN_DEVICE_FUNC inline Scalar smallestAngle() const {
+ Scalar tmp = numext::fmod(m_angle,Scalar(2*EIGEN_PI));
+ if(tmp>Scalar(EIGEN_PI)) tmp -= Scalar(2*EIGEN_PI);
+ else if(tmp<-Scalar(EIGEN_PI)) tmp += Scalar(2*EIGEN_PI);
+ return tmp;
+ }
+
+ /** \returns the inverse rotation */
+ EIGEN_DEVICE_FUNC inline Rotation2D inverse() const { return Rotation2D(-m_angle); }
+
+ /** Concatenates two rotations */
+ EIGEN_DEVICE_FUNC inline Rotation2D operator*(const Rotation2D& other) const
+ { return Rotation2D(m_angle + other.m_angle); }
+
+ /** Concatenates two rotations */
+ EIGEN_DEVICE_FUNC inline Rotation2D& operator*=(const Rotation2D& other)
+ { m_angle += other.m_angle; return *this; }
+
+ /** Applies the rotation to a 2D vector */
+ EIGEN_DEVICE_FUNC Vector2 operator* (const Vector2& vec) const
+ { return toRotationMatrix() * vec; }
+
+ template<typename Derived>
+ EIGEN_DEVICE_FUNC Rotation2D& fromRotationMatrix(const MatrixBase<Derived>& m);
+ EIGEN_DEVICE_FUNC Matrix2 toRotationMatrix() const;
+
+ /** Set \c *this from a 2x2 rotation matrix \a mat.
+ * In other words, this function extract the rotation angle from the rotation matrix.
+ *
+ * This method is an alias for fromRotationMatrix()
+ *
+ * \sa fromRotationMatrix()
+ */
+ template<typename Derived>
+ EIGEN_DEVICE_FUNC Rotation2D& operator=(const MatrixBase<Derived>& m)
+ { return fromRotationMatrix(m.derived()); }
+
+ /** \returns the spherical interpolation between \c *this and \a other using
+ * parameter \a t. It is in fact equivalent to a linear interpolation.
+ */
+ EIGEN_DEVICE_FUNC inline Rotation2D slerp(const Scalar& t, const Rotation2D& other) const
+ {
+ Scalar dist = Rotation2D(other.m_angle-m_angle).smallestAngle();
+ return Rotation2D(m_angle + dist*t);
+ }
+
+ /** \returns \c *this with scalar type casted to \a NewScalarType
+ *
+ * Note that if \a NewScalarType is equal to the current scalar type of \c *this
+ * then this function smartly returns a const reference to \c *this.
+ */
+ template<typename NewScalarType>
+ EIGEN_DEVICE_FUNC inline typename internal::cast_return_type<Rotation2D,Rotation2D<NewScalarType> >::type cast() const
+ { return typename internal::cast_return_type<Rotation2D,Rotation2D<NewScalarType> >::type(*this); }
+
+ /** Copy constructor with scalar type conversion */
+ template<typename OtherScalarType>
+ EIGEN_DEVICE_FUNC inline explicit Rotation2D(const Rotation2D<OtherScalarType>& other)
+ {
+ m_angle = Scalar(other.angle());
+ }
+
+ EIGEN_DEVICE_FUNC static inline Rotation2D Identity() { return Rotation2D(0); }
+
+ /** \returns \c true if \c *this is approximately equal to \a other, within the precision
+ * determined by \a prec.
+ *
+ * \sa MatrixBase::isApprox() */
+ EIGEN_DEVICE_FUNC bool isApprox(const Rotation2D& other, const typename NumTraits<Scalar>::Real& prec = NumTraits<Scalar>::dummy_precision()) const
+ { return internal::isApprox(m_angle,other.m_angle, prec); }
+
+};
+
+/** \ingroup Geometry_Module
+ * single precision 2D rotation type */
+typedef Rotation2D<float> Rotation2Df;
+/** \ingroup Geometry_Module
+ * double precision 2D rotation type */
+typedef Rotation2D<double> Rotation2Dd;
+
+/** Set \c *this from a 2x2 rotation matrix \a mat.
+ * In other words, this function extract the rotation angle
+ * from the rotation matrix.
+ */
+template<typename Scalar>
+template<typename Derived>
+EIGEN_DEVICE_FUNC Rotation2D<Scalar>& Rotation2D<Scalar>::fromRotationMatrix(const MatrixBase<Derived>& mat)
+{
+ EIGEN_USING_STD(atan2)
+ EIGEN_STATIC_ASSERT(Derived::RowsAtCompileTime==2 && Derived::ColsAtCompileTime==2,YOU_MADE_A_PROGRAMMING_MISTAKE)
+ m_angle = atan2(mat.coeff(1,0), mat.coeff(0,0));
+ return *this;
+}
+
+/** Constructs and \returns an equivalent 2x2 rotation matrix.
+ */
+template<typename Scalar>
+typename Rotation2D<Scalar>::Matrix2
+EIGEN_DEVICE_FUNC Rotation2D<Scalar>::toRotationMatrix(void) const
+{
+ EIGEN_USING_STD(sin)
+ EIGEN_USING_STD(cos)
+ Scalar sinA = sin(m_angle);
+ Scalar cosA = cos(m_angle);
+ return (Matrix2() << cosA, -sinA, sinA, cosA).finished();
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_ROTATION2D_H
diff --git a/Eigen/src/Geometry/RotationBase.h b/Eigen/src/Geometry/RotationBase.h
new file mode 100644
index 0000000..f21277f
--- /dev/null
+++ b/Eigen/src/Geometry/RotationBase.h
@@ -0,0 +1,208 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_ROTATIONBASE_H
+#define EIGEN_ROTATIONBASE_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+// forward declaration
+namespace internal {
+template<typename RotationDerived, typename MatrixType, bool IsVector=MatrixType::IsVectorAtCompileTime>
+struct rotation_base_generic_product_selector;
+}
+
+/** \class RotationBase
+ *
+ * \brief Common base class for compact rotation representations
+ *
+ * \tparam Derived is the derived type, i.e., a rotation type
+ * \tparam Dim_ the dimension of the space
+ */
+template<typename Derived, int Dim_>
+class RotationBase
+{
+ public:
+ enum { Dim = Dim_ };
+ /** the scalar type of the coefficients */
+ typedef typename internal::traits<Derived>::Scalar Scalar;
+
+ /** corresponding linear transformation matrix type */
+ typedef Matrix<Scalar,Dim,Dim> RotationMatrixType;
+ typedef Matrix<Scalar,Dim,1> VectorType;
+
+ public:
+ EIGEN_DEVICE_FUNC inline const Derived& derived() const { return *static_cast<const Derived*>(this); }
+ EIGEN_DEVICE_FUNC inline Derived& derived() { return *static_cast<Derived*>(this); }
+
+ /** \returns an equivalent rotation matrix */
+ EIGEN_DEVICE_FUNC inline RotationMatrixType toRotationMatrix() const { return derived().toRotationMatrix(); }
+
+ /** \returns an equivalent rotation matrix
+ * This function is added to be conform with the Transform class' naming scheme.
+ */
+ EIGEN_DEVICE_FUNC inline RotationMatrixType matrix() const { return derived().toRotationMatrix(); }
+
+ /** \returns the inverse rotation */
+ EIGEN_DEVICE_FUNC inline Derived inverse() const { return derived().inverse(); }
+
+ /** \returns the concatenation of the rotation \c *this with a translation \a t */
+ EIGEN_DEVICE_FUNC inline Transform<Scalar,Dim,Isometry> operator*(const Translation<Scalar,Dim>& t) const
+ { return Transform<Scalar,Dim,Isometry>(*this) * t; }
+
+ /** \returns the concatenation of the rotation \c *this with a uniform scaling \a s */
+ EIGEN_DEVICE_FUNC inline RotationMatrixType operator*(const UniformScaling<Scalar>& s) const
+ { return toRotationMatrix() * s.factor(); }
+
+ /** \returns the concatenation of the rotation \c *this with a generic expression \a e
+ * \a e can be:
+ * - a DimxDim linear transformation matrix
+ * - a DimxDim diagonal matrix (axis aligned scaling)
+ * - a vector of size Dim
+ */
+ template<typename OtherDerived>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE typename internal::rotation_base_generic_product_selector<Derived,OtherDerived,OtherDerived::IsVectorAtCompileTime>::ReturnType
+ operator*(const EigenBase<OtherDerived>& e) const
+ { return internal::rotation_base_generic_product_selector<Derived,OtherDerived>::run(derived(), e.derived()); }
+
+ /** \returns the concatenation of a linear transformation \a l with the rotation \a r */
+ template<typename OtherDerived> friend
+ EIGEN_DEVICE_FUNC inline RotationMatrixType operator*(const EigenBase<OtherDerived>& l, const Derived& r)
+ { return l.derived() * r.toRotationMatrix(); }
+
+ /** \returns the concatenation of a scaling \a l with the rotation \a r */
+ EIGEN_DEVICE_FUNC friend inline Transform<Scalar,Dim,Affine> operator*(const DiagonalMatrix<Scalar,Dim>& l, const Derived& r)
+ {
+ Transform<Scalar,Dim,Affine> res(r);
+ res.linear().applyOnTheLeft(l);
+ return res;
+ }
+
+ /** \returns the concatenation of the rotation \c *this with a transformation \a t */
+ template<int Mode, int Options>
+ EIGEN_DEVICE_FUNC inline Transform<Scalar,Dim,Mode> operator*(const Transform<Scalar,Dim,Mode,Options>& t) const
+ { return toRotationMatrix() * t; }
+
+ template<typename OtherVectorType>
+ EIGEN_DEVICE_FUNC inline VectorType _transformVector(const OtherVectorType& v) const
+ { return toRotationMatrix() * v; }
+};
+
+namespace internal {
+
+// implementation of the generic product rotation * matrix
+template<typename RotationDerived, typename MatrixType>
+struct rotation_base_generic_product_selector<RotationDerived,MatrixType,false>
+{
+ enum { Dim = RotationDerived::Dim };
+ typedef Matrix<typename RotationDerived::Scalar,Dim,Dim> ReturnType;
+ EIGEN_DEVICE_FUNC static inline ReturnType run(const RotationDerived& r, const MatrixType& m)
+ { return r.toRotationMatrix() * m; }
+};
+
+template<typename RotationDerived, typename Scalar, int Dim, int MaxDim>
+struct rotation_base_generic_product_selector< RotationDerived, DiagonalMatrix<Scalar,Dim,MaxDim>, false >
+{
+ typedef Transform<Scalar,Dim,Affine> ReturnType;
+ EIGEN_DEVICE_FUNC static inline ReturnType run(const RotationDerived& r, const DiagonalMatrix<Scalar,Dim,MaxDim>& m)
+ {
+ ReturnType res(r);
+ res.linear() *= m;
+ return res;
+ }
+};
+
+template<typename RotationDerived,typename OtherVectorType>
+struct rotation_base_generic_product_selector<RotationDerived,OtherVectorType,true>
+{
+ enum { Dim = RotationDerived::Dim };
+ typedef Matrix<typename RotationDerived::Scalar,Dim,1> ReturnType;
+ EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE ReturnType run(const RotationDerived& r, const OtherVectorType& v)
+ {
+ return r._transformVector(v);
+ }
+};
+
+} // end namespace internal
+
+/** \geometry_module
+ *
+ * \brief Constructs a Dim x Dim rotation matrix from the rotation \a r
+ */
+template<typename Scalar_, int Rows_, int Cols_, int Storage_, int MaxRows_, int MaxCols_>
+template<typename OtherDerived>
+EIGEN_DEVICE_FUNC Matrix<Scalar_, Rows_, Cols_, Storage_, MaxRows_, MaxCols_>
+::Matrix(const RotationBase<OtherDerived,ColsAtCompileTime>& r)
+{
+ EIGEN_STATIC_ASSERT_MATRIX_SPECIFIC_SIZE(Matrix,int(OtherDerived::Dim),int(OtherDerived::Dim))
+ *this = r.toRotationMatrix();
+}
+
+/** \geometry_module
+ *
+ * \brief Set a Dim x Dim rotation matrix from the rotation \a r
+ */
+template<typename Scalar_, int Rows_, int Cols_, int Storage_, int MaxRows_, int MaxCols_>
+template<typename OtherDerived>
+EIGEN_DEVICE_FUNC Matrix<Scalar_, Rows_, Cols_, Storage_, MaxRows_, MaxCols_>&
+Matrix<Scalar_, Rows_, Cols_, Storage_, MaxRows_, MaxCols_>
+::operator=(const RotationBase<OtherDerived,ColsAtCompileTime>& r)
+{
+ EIGEN_STATIC_ASSERT_MATRIX_SPECIFIC_SIZE(Matrix,int(OtherDerived::Dim),int(OtherDerived::Dim))
+ return *this = r.toRotationMatrix();
+}
+
+namespace internal {
+
+/** \internal
+ *
+ * Helper function to return an arbitrary rotation object to a rotation matrix.
+ *
+ * \tparam Scalar the numeric type of the matrix coefficients
+ * \tparam Dim the dimension of the current space
+ *
+ * It returns a Dim x Dim fixed size matrix.
+ *
+ * Default specializations are provided for:
+ * - any scalar type (2D),
+ * - any matrix expression,
+ * - any type based on RotationBase (e.g., Quaternion, AngleAxis, Rotation2D)
+ *
+ * Currently toRotationMatrix is only used by Transform.
+ *
+ * \sa class Transform, class Rotation2D, class Quaternion, class AngleAxis
+ */
+template<typename Scalar, int Dim>
+EIGEN_DEVICE_FUNC static inline Matrix<Scalar,2,2> toRotationMatrix(const Scalar& s)
+{
+ EIGEN_STATIC_ASSERT(Dim==2,YOU_MADE_A_PROGRAMMING_MISTAKE)
+ return Rotation2D<Scalar>(s).toRotationMatrix();
+}
+
+template<typename Scalar, int Dim, typename OtherDerived>
+EIGEN_DEVICE_FUNC static inline Matrix<Scalar,Dim,Dim> toRotationMatrix(const RotationBase<OtherDerived,Dim>& r)
+{
+ return r.toRotationMatrix();
+}
+
+template<typename Scalar, int Dim, typename OtherDerived>
+EIGEN_DEVICE_FUNC static inline const MatrixBase<OtherDerived>& toRotationMatrix(const MatrixBase<OtherDerived>& mat)
+{
+ EIGEN_STATIC_ASSERT(OtherDerived::RowsAtCompileTime==Dim && OtherDerived::ColsAtCompileTime==Dim,
+ YOU_MADE_A_PROGRAMMING_MISTAKE)
+ return mat;
+}
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_ROTATIONBASE_H
diff --git a/Eigen/src/Geometry/Scaling.h b/Eigen/src/Geometry/Scaling.h
new file mode 100644
index 0000000..8bcdce6
--- /dev/null
+++ b/Eigen/src/Geometry/Scaling.h
@@ -0,0 +1,195 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_SCALING_H
+#define EIGEN_SCALING_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+/** \geometry_module \ingroup Geometry_Module
+ *
+ * \class UniformScaling
+ *
+ * \brief Represents a generic uniform scaling transformation
+ *
+ * \tparam Scalar_ the scalar type, i.e., the type of the coefficients.
+ *
+ * This class represent a uniform scaling transformation. It is the return
+ * type of Scaling(Scalar), and most of the time this is the only way it
+ * is used. In particular, this class is not aimed to be used to store a scaling transformation,
+ * but rather to make easier the constructions and updates of Transform objects.
+ *
+ * To represent an axis aligned scaling, use the DiagonalMatrix class.
+ *
+ * \sa Scaling(), class DiagonalMatrix, MatrixBase::asDiagonal(), class Translation, class Transform
+ */
+
+namespace internal
+{
+ // This helper helps nvcc+MSVC to properly parse this file.
+ // See bug 1412.
+ template <typename Scalar, int Dim, int Mode>
+ struct uniformscaling_times_affine_returntype
+ {
+ enum
+ {
+ NewMode = int(Mode) == int(Isometry) ? Affine : Mode
+ };
+ typedef Transform <Scalar, Dim, NewMode> type;
+ };
+}
+
+template<typename Scalar_>
+class UniformScaling
+{
+public:
+ /** the scalar type of the coefficients */
+ typedef Scalar_ Scalar;
+
+protected:
+
+ Scalar m_factor;
+
+public:
+
+ /** Default constructor without initialization. */
+ UniformScaling() {}
+ /** Constructs and initialize a uniform scaling transformation */
+ explicit inline UniformScaling(const Scalar& s) : m_factor(s) {}
+
+ inline const Scalar& factor() const { return m_factor; }
+ inline Scalar& factor() { return m_factor; }
+
+ /** Concatenates two uniform scaling */
+ inline UniformScaling operator* (const UniformScaling& other) const
+ { return UniformScaling(m_factor * other.factor()); }
+
+ /** Concatenates a uniform scaling and a translation */
+ template<int Dim>
+ inline Transform<Scalar,Dim,Affine> operator* (const Translation<Scalar,Dim>& t) const;
+
+ /** Concatenates a uniform scaling and an affine transformation */
+ template<int Dim, int Mode, int Options>
+ inline typename
+ internal::uniformscaling_times_affine_returntype<Scalar,Dim,Mode>::type
+ operator* (const Transform<Scalar, Dim, Mode, Options>& t) const
+ {
+ typename internal::uniformscaling_times_affine_returntype<Scalar,Dim,Mode>::type res = t;
+ res.prescale(factor());
+ return res;
+ }
+
+ /** Concatenates a uniform scaling and a linear transformation matrix */
+ // TODO returns an expression
+ template<typename Derived>
+ inline typename Eigen::internal::plain_matrix_type<Derived>::type operator* (const MatrixBase<Derived>& other) const
+ { return other * m_factor; }
+
+ template<typename Derived,int Dim>
+ inline Matrix<Scalar,Dim,Dim> operator*(const RotationBase<Derived,Dim>& r) const
+ { return r.toRotationMatrix() * m_factor; }
+
+ /** \returns the inverse scaling */
+ inline UniformScaling inverse() const
+ { return UniformScaling(Scalar(1)/m_factor); }
+
+ /** \returns \c *this with scalar type casted to \a NewScalarType
+ *
+ * Note that if \a NewScalarType is equal to the current scalar type of \c *this
+ * then this function smartly returns a const reference to \c *this.
+ */
+ template<typename NewScalarType>
+ inline UniformScaling<NewScalarType> cast() const
+ { return UniformScaling<NewScalarType>(NewScalarType(m_factor)); }
+
+ /** Copy constructor with scalar type conversion */
+ template<typename OtherScalarType>
+ inline explicit UniformScaling(const UniformScaling<OtherScalarType>& other)
+ { m_factor = Scalar(other.factor()); }
+
+ /** \returns \c true if \c *this is approximately equal to \a other, within the precision
+ * determined by \a prec.
+ *
+ * \sa MatrixBase::isApprox() */
+ bool isApprox(const UniformScaling& other, const typename NumTraits<Scalar>::Real& prec = NumTraits<Scalar>::dummy_precision()) const
+ { return internal::isApprox(m_factor, other.factor(), prec); }
+
+};
+
+/** \addtogroup Geometry_Module */
+//@{
+
+/** Concatenates a linear transformation matrix and a uniform scaling
+ * \relates UniformScaling
+ */
+// NOTE this operator is defined in MatrixBase and not as a friend function
+// of UniformScaling to fix an internal crash of Intel's ICC
+template<typename Derived,typename Scalar>
+EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(Derived,Scalar,product)
+operator*(const MatrixBase<Derived>& matrix, const UniformScaling<Scalar>& s)
+{ return matrix.derived() * s.factor(); }
+
+/** Constructs a uniform scaling from scale factor \a s */
+inline UniformScaling<float> Scaling(float s) { return UniformScaling<float>(s); }
+/** Constructs a uniform scaling from scale factor \a s */
+inline UniformScaling<double> Scaling(double s) { return UniformScaling<double>(s); }
+/** Constructs a uniform scaling from scale factor \a s */
+template<typename RealScalar>
+inline UniformScaling<std::complex<RealScalar> > Scaling(const std::complex<RealScalar>& s)
+{ return UniformScaling<std::complex<RealScalar> >(s); }
+
+/** Constructs a 2D axis aligned scaling */
+template<typename Scalar>
+inline DiagonalMatrix<Scalar,2> Scaling(const Scalar& sx, const Scalar& sy)
+{ return DiagonalMatrix<Scalar,2>(sx, sy); }
+/** Constructs a 3D axis aligned scaling */
+template<typename Scalar>
+inline DiagonalMatrix<Scalar,3> Scaling(const Scalar& sx, const Scalar& sy, const Scalar& sz)
+{ return DiagonalMatrix<Scalar,3>(sx, sy, sz); }
+
+/** Constructs an axis aligned scaling expression from vector expression \a coeffs
+ * This is an alias for coeffs.asDiagonal()
+ */
+template<typename Derived>
+inline const DiagonalWrapper<const Derived> Scaling(const MatrixBase<Derived>& coeffs)
+{ return coeffs.asDiagonal(); }
+
+/** Constructs an axis aligned scaling expression from vector \a coeffs when passed as an rvalue reference */
+template<typename Derived>
+inline typename DiagonalWrapper<const Derived>::PlainObject Scaling(MatrixBase<Derived>&& coeffs)
+{ return typename DiagonalWrapper<const Derived>::PlainObject(std::move(coeffs.derived())); }
+
+/** \deprecated */
+typedef DiagonalMatrix<float, 2> AlignedScaling2f;
+/** \deprecated */
+typedef DiagonalMatrix<double,2> AlignedScaling2d;
+/** \deprecated */
+typedef DiagonalMatrix<float, 3> AlignedScaling3f;
+/** \deprecated */
+typedef DiagonalMatrix<double,3> AlignedScaling3d;
+//@}
+
+template<typename Scalar>
+template<int Dim>
+inline Transform<Scalar,Dim,Affine>
+UniformScaling<Scalar>::operator* (const Translation<Scalar,Dim>& t) const
+{
+ Transform<Scalar,Dim,Affine> res;
+ res.matrix().setZero();
+ res.linear().diagonal().fill(factor());
+ res.translation() = factor() * t.vector();
+ res(Dim,Dim) = Scalar(1);
+ return res;
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_SCALING_H
diff --git a/Eigen/src/Geometry/Transform.h b/Eigen/src/Geometry/Transform.h
new file mode 100644
index 0000000..fd0ae7e
--- /dev/null
+++ b/Eigen/src/Geometry/Transform.h
@@ -0,0 +1,1570 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2009 Benoit Jacob <jacob.benoit.1@gmail.com>
+// Copyright (C) 2010 Hauke Heibel <hauke.heibel@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_TRANSFORM_H
+#define EIGEN_TRANSFORM_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+
+template<typename Transform>
+struct transform_traits
+{
+ enum
+ {
+ Dim = Transform::Dim,
+ HDim = Transform::HDim,
+ Mode = Transform::Mode,
+ IsProjective = (int(Mode)==int(Projective))
+ };
+};
+
+template< typename TransformType,
+ typename MatrixType,
+ int Case = transform_traits<TransformType>::IsProjective ? 0
+ : int(MatrixType::RowsAtCompileTime) == int(transform_traits<TransformType>::HDim) ? 1
+ : 2,
+ int RhsCols = MatrixType::ColsAtCompileTime>
+struct transform_right_product_impl;
+
+template< typename Other,
+ int Mode,
+ int Options,
+ int Dim,
+ int HDim,
+ int OtherRows=Other::RowsAtCompileTime,
+ int OtherCols=Other::ColsAtCompileTime>
+struct transform_left_product_impl;
+
+template< typename Lhs,
+ typename Rhs,
+ bool AnyProjective =
+ transform_traits<Lhs>::IsProjective ||
+ transform_traits<Rhs>::IsProjective>
+struct transform_transform_product_impl;
+
+template< typename Other,
+ int Mode,
+ int Options,
+ int Dim,
+ int HDim,
+ int OtherRows=Other::RowsAtCompileTime,
+ int OtherCols=Other::ColsAtCompileTime>
+struct transform_construct_from_matrix;
+
+template<typename TransformType> struct transform_take_affine_part;
+
+template<typename Scalar_, int Dim_, int Mode_, int Options_>
+struct traits<Transform<Scalar_,Dim_,Mode_,Options_> >
+{
+ typedef Scalar_ Scalar;
+ typedef Eigen::Index StorageIndex;
+ typedef Dense StorageKind;
+ enum {
+ Dim1 = Dim_==Dynamic ? Dim_ : Dim_ + 1,
+ RowsAtCompileTime = Mode_==Projective ? Dim1 : Dim_,
+ ColsAtCompileTime = Dim1,
+ MaxRowsAtCompileTime = RowsAtCompileTime,
+ MaxColsAtCompileTime = ColsAtCompileTime,
+ Flags = 0
+ };
+};
+
+template<int Mode> struct transform_make_affine;
+
+} // end namespace internal
+
+/** \geometry_module \ingroup Geometry_Module
+ *
+ * \class Transform
+ *
+ * \brief Represents an homogeneous transformation in a N dimensional space
+ *
+ * \tparam Scalar_ the scalar type, i.e., the type of the coefficients
+ * \tparam Dim_ the dimension of the space
+ * \tparam Mode_ the type of the transformation. Can be:
+ * - #Affine: the transformation is stored as a (Dim+1)^2 matrix,
+ * where the last row is assumed to be [0 ... 0 1].
+ * - #AffineCompact: the transformation is stored as a (Dim)x(Dim+1) matrix.
+ * - #Projective: the transformation is stored as a (Dim+1)^2 matrix
+ * without any assumption.
+ * - #Isometry: same as #Affine with the additional assumption that
+ * the linear part represents a rotation. This assumption is exploited
+ * to speed up some functions such as inverse() and rotation().
+ * \tparam Options_ has the same meaning as in class Matrix. It allows to specify DontAlign and/or RowMajor.
+ * These Options are passed directly to the underlying matrix type.
+ *
+ * The homography is internally represented and stored by a matrix which
+ * is available through the matrix() method. To understand the behavior of
+ * this class you have to think a Transform object as its internal
+ * matrix representation. The chosen convention is right multiply:
+ *
+ * \code v' = T * v \endcode
+ *
+ * Therefore, an affine transformation matrix M is shaped like this:
+ *
+ * \f$ \left( \begin{array}{cc}
+ * linear & translation\\
+ * 0 ... 0 & 1
+ * \end{array} \right) \f$
+ *
+ * Note that for a projective transformation the last row can be anything,
+ * and then the interpretation of different parts might be slightly different.
+ *
+ * However, unlike a plain matrix, the Transform class provides many features
+ * simplifying both its assembly and usage. In particular, it can be composed
+ * with any other transformations (Transform,Translation,RotationBase,DiagonalMatrix)
+ * and can be directly used to transform implicit homogeneous vectors. All these
+ * operations are handled via the operator*. For the composition of transformations,
+ * its principle consists to first convert the right/left hand sides of the product
+ * to a compatible (Dim+1)^2 matrix and then perform a pure matrix product.
+ * Of course, internally, operator* tries to perform the minimal number of operations
+ * according to the nature of each terms. Likewise, when applying the transform
+ * to points, the latters are automatically promoted to homogeneous vectors
+ * before doing the matrix product. The conventions to homogeneous representations
+ * are performed as follow:
+ *
+ * \b Translation t (Dim)x(1):
+ * \f$ \left( \begin{array}{cc}
+ * I & t \\
+ * 0\,...\,0 & 1
+ * \end{array} \right) \f$
+ *
+ * \b Rotation R (Dim)x(Dim):
+ * \f$ \left( \begin{array}{cc}
+ * R & 0\\
+ * 0\,...\,0 & 1
+ * \end{array} \right) \f$
+ *<!--
+ * \b Linear \b Matrix L (Dim)x(Dim):
+ * \f$ \left( \begin{array}{cc}
+ * L & 0\\
+ * 0\,...\,0 & 1
+ * \end{array} \right) \f$
+ *
+ * \b Affine \b Matrix A (Dim)x(Dim+1):
+ * \f$ \left( \begin{array}{c}
+ * A\\
+ * 0\,...\,0\,1
+ * \end{array} \right) \f$
+ *-->
+ * \b Scaling \b DiagonalMatrix S (Dim)x(Dim):
+ * \f$ \left( \begin{array}{cc}
+ * S & 0\\
+ * 0\,...\,0 & 1
+ * \end{array} \right) \f$
+ *
+ * \b Column \b point v (Dim)x(1):
+ * \f$ \left( \begin{array}{c}
+ * v\\
+ * 1
+ * \end{array} \right) \f$
+ *
+ * \b Set \b of \b column \b points V1...Vn (Dim)x(n):
+ * \f$ \left( \begin{array}{ccc}
+ * v_1 & ... & v_n\\
+ * 1 & ... & 1
+ * \end{array} \right) \f$
+ *
+ * The concatenation of a Transform object with any kind of other transformation
+ * always returns a Transform object.
+ *
+ * A little exception to the "as pure matrix product" rule is the case of the
+ * transformation of non homogeneous vectors by an affine transformation. In
+ * that case the last matrix row can be ignored, and the product returns non
+ * homogeneous vectors.
+ *
+ * Since, for instance, a Dim x Dim matrix is interpreted as a linear transformation,
+ * it is not possible to directly transform Dim vectors stored in a Dim x Dim matrix.
+ * The solution is either to use a Dim x Dynamic matrix or explicitly request a
+ * vector transformation by making the vector homogeneous:
+ * \code
+ * m' = T * m.colwise().homogeneous();
+ * \endcode
+ * Note that there is zero overhead.
+ *
+ * Conversion methods from/to Qt's QMatrix and QTransform are available if the
+ * preprocessor token EIGEN_QT_SUPPORT is defined.
+ *
+ * This class can be extended with the help of the plugin mechanism described on the page
+ * \ref TopicCustomizing_Plugins by defining the preprocessor symbol \c EIGEN_TRANSFORM_PLUGIN.
+ *
+ * \sa class Matrix, class Quaternion
+ */
+template<typename Scalar_, int Dim_, int Mode_, int Options_>
+class Transform
+{
+public:
+ EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE(Scalar_,Dim_==Dynamic ? Dynamic : (Dim_+1)*(Dim_+1))
+ enum {
+ Mode = Mode_,
+ Options = Options_,
+ Dim = Dim_, ///< space dimension in which the transformation holds
+ HDim = Dim_+1, ///< size of a respective homogeneous vector
+ Rows = int(Mode)==(AffineCompact) ? Dim : HDim
+ };
+ /** the scalar type of the coefficients */
+ typedef Scalar_ Scalar;
+ typedef Eigen::Index StorageIndex;
+ typedef Eigen::Index Index; ///< \deprecated since Eigen 3.3
+ /** type of the matrix used to represent the transformation */
+ typedef typename internal::make_proper_matrix_type<Scalar,Rows,HDim,Options>::type MatrixType;
+ /** constified MatrixType */
+ typedef const MatrixType ConstMatrixType;
+ /** type of the matrix used to represent the linear part of the transformation */
+ typedef Matrix<Scalar,Dim,Dim,Options> LinearMatrixType;
+ /** type of read/write reference to the linear part of the transformation */
+ typedef Block<MatrixType,Dim,Dim,int(Mode)==(AffineCompact) && (int(Options)&RowMajor)==0> LinearPart;
+ /** type of read reference to the linear part of the transformation */
+ typedef const Block<ConstMatrixType,Dim,Dim,int(Mode)==(AffineCompact) && (int(Options)&RowMajor)==0> ConstLinearPart;
+ /** type of read/write reference to the affine part of the transformation */
+ typedef std::conditional_t<int(Mode)==int(AffineCompact),
+ MatrixType&,
+ Block<MatrixType,Dim,HDim> > AffinePart;
+ /** type of read reference to the affine part of the transformation */
+ typedef std::conditional_t<int(Mode)==int(AffineCompact),
+ const MatrixType&,
+ const Block<const MatrixType,Dim,HDim> > ConstAffinePart;
+ /** type of a vector */
+ typedef Matrix<Scalar,Dim,1> VectorType;
+ /** type of a read/write reference to the translation part of the rotation */
+ typedef Block<MatrixType,Dim,1,!(internal::traits<MatrixType>::Flags & RowMajorBit)> TranslationPart;
+ /** type of a read reference to the translation part of the rotation */
+ typedef const Block<ConstMatrixType,Dim,1,!(internal::traits<MatrixType>::Flags & RowMajorBit)> ConstTranslationPart;
+ /** corresponding translation type */
+ typedef Translation<Scalar,Dim> TranslationType;
+
+ // this intermediate enum is needed to avoid an ICE with gcc 3.4 and 4.0
+ enum { TransformTimeDiagonalMode = ((Mode==int(Isometry))?Affine:int(Mode)) };
+ /** The return type of the product between a diagonal matrix and a transform */
+ typedef Transform<Scalar,Dim,TransformTimeDiagonalMode> TransformTimeDiagonalReturnType;
+
+protected:
+
+ MatrixType m_matrix;
+
+public:
+
+ /** Default constructor without initialization of the meaningful coefficients.
+ * If Mode==Affine or Mode==Isometry, then the last row is set to [0 ... 0 1] */
+ EIGEN_DEVICE_FUNC inline Transform()
+ {
+ check_template_params();
+ internal::transform_make_affine<(int(Mode)==Affine || int(Mode)==Isometry) ? Affine : AffineCompact>::run(m_matrix);
+ }
+
+ EIGEN_DEVICE_FUNC inline explicit Transform(const TranslationType& t)
+ {
+ check_template_params();
+ *this = t;
+ }
+ EIGEN_DEVICE_FUNC inline explicit Transform(const UniformScaling<Scalar>& s)
+ {
+ check_template_params();
+ *this = s;
+ }
+ template<typename Derived>
+ EIGEN_DEVICE_FUNC inline explicit Transform(const RotationBase<Derived, Dim>& r)
+ {
+ check_template_params();
+ *this = r;
+ }
+
+ typedef internal::transform_take_affine_part<Transform> take_affine_part;
+
+ /** Constructs and initializes a transformation from a Dim^2 or a (Dim+1)^2 matrix. */
+ template<typename OtherDerived>
+ EIGEN_DEVICE_FUNC inline explicit Transform(const EigenBase<OtherDerived>& other)
+ {
+ EIGEN_STATIC_ASSERT((internal::is_same<Scalar,typename OtherDerived::Scalar>::value),
+ YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY);
+
+ check_template_params();
+ internal::transform_construct_from_matrix<OtherDerived,Mode,Options,Dim,HDim>::run(this, other.derived());
+ }
+
+ /** Set \c *this from a Dim^2 or (Dim+1)^2 matrix. */
+ template<typename OtherDerived>
+ EIGEN_DEVICE_FUNC inline Transform& operator=(const EigenBase<OtherDerived>& other)
+ {
+ EIGEN_STATIC_ASSERT((internal::is_same<Scalar,typename OtherDerived::Scalar>::value),
+ YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY);
+
+ internal::transform_construct_from_matrix<OtherDerived,Mode,Options,Dim,HDim>::run(this, other.derived());
+ return *this;
+ }
+
+ template<int OtherOptions>
+ EIGEN_DEVICE_FUNC inline Transform(const Transform<Scalar,Dim,Mode,OtherOptions>& other)
+ {
+ check_template_params();
+ // only the options change, we can directly copy the matrices
+ m_matrix = other.matrix();
+ }
+
+ template<int OtherMode,int OtherOptions>
+ EIGEN_DEVICE_FUNC inline Transform(const Transform<Scalar,Dim,OtherMode,OtherOptions>& other)
+ {
+ check_template_params();
+ // prevent conversions as:
+ // Affine | AffineCompact | Isometry = Projective
+ EIGEN_STATIC_ASSERT(internal::check_implication(OtherMode==int(Projective), Mode==int(Projective)),
+ YOU_PERFORMED_AN_INVALID_TRANSFORMATION_CONVERSION)
+
+ // prevent conversions as:
+ // Isometry = Affine | AffineCompact
+ EIGEN_STATIC_ASSERT(internal::check_implication(OtherMode==int(Affine)||OtherMode==int(AffineCompact), Mode!=int(Isometry)),
+ YOU_PERFORMED_AN_INVALID_TRANSFORMATION_CONVERSION)
+
+ enum { ModeIsAffineCompact = Mode == int(AffineCompact),
+ OtherModeIsAffineCompact = OtherMode == int(AffineCompact)
+ };
+
+ if(EIGEN_CONST_CONDITIONAL(ModeIsAffineCompact == OtherModeIsAffineCompact))
+ {
+ // We need the block expression because the code is compiled for all
+ // combinations of transformations and will trigger a compile time error
+ // if one tries to assign the matrices directly
+ m_matrix.template block<Dim,Dim+1>(0,0) = other.matrix().template block<Dim,Dim+1>(0,0);
+ makeAffine();
+ }
+ else if(EIGEN_CONST_CONDITIONAL(OtherModeIsAffineCompact))
+ {
+ typedef typename Transform<Scalar,Dim,OtherMode,OtherOptions>::MatrixType OtherMatrixType;
+ internal::transform_construct_from_matrix<OtherMatrixType,Mode,Options,Dim,HDim>::run(this, other.matrix());
+ }
+ else
+ {
+ // here we know that Mode == AffineCompact and OtherMode != AffineCompact.
+ // if OtherMode were Projective, the static assert above would already have caught it.
+ // So the only possibility is that OtherMode == Affine
+ linear() = other.linear();
+ translation() = other.translation();
+ }
+ }
+
+ template<typename OtherDerived>
+ EIGEN_DEVICE_FUNC Transform(const ReturnByValue<OtherDerived>& other)
+ {
+ check_template_params();
+ other.evalTo(*this);
+ }
+
+ template<typename OtherDerived>
+ EIGEN_DEVICE_FUNC Transform& operator=(const ReturnByValue<OtherDerived>& other)
+ {
+ other.evalTo(*this);
+ return *this;
+ }
+
+ #ifdef EIGEN_QT_SUPPORT
+ #if (QT_VERSION < QT_VERSION_CHECK(6, 0, 0))
+ inline Transform(const QMatrix& other);
+ inline Transform& operator=(const QMatrix& other);
+ inline QMatrix toQMatrix(void) const;
+ #endif
+ inline Transform(const QTransform& other);
+ inline Transform& operator=(const QTransform& other);
+ inline QTransform toQTransform(void) const;
+ #endif
+
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR Index rows() const EIGEN_NOEXCEPT { return int(Mode)==int(Projective) ? m_matrix.cols() : (m_matrix.cols()-1); }
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR Index cols() const EIGEN_NOEXCEPT { return m_matrix.cols(); }
+
+ /** shortcut for m_matrix(row,col);
+ * \sa MatrixBase::operator(Index,Index) const */
+ EIGEN_DEVICE_FUNC inline Scalar operator() (Index row, Index col) const { return m_matrix(row,col); }
+ /** shortcut for m_matrix(row,col);
+ * \sa MatrixBase::operator(Index,Index) */
+ EIGEN_DEVICE_FUNC inline Scalar& operator() (Index row, Index col) { return m_matrix(row,col); }
+
+ /** \returns a read-only expression of the transformation matrix */
+ EIGEN_DEVICE_FUNC inline const MatrixType& matrix() const { return m_matrix; }
+ /** \returns a writable expression of the transformation matrix */
+ EIGEN_DEVICE_FUNC inline MatrixType& matrix() { return m_matrix; }
+
+ /** \returns a read-only expression of the linear part of the transformation */
+ EIGEN_DEVICE_FUNC inline ConstLinearPart linear() const { return ConstLinearPart(m_matrix,0,0); }
+ /** \returns a writable expression of the linear part of the transformation */
+ EIGEN_DEVICE_FUNC inline LinearPart linear() { return LinearPart(m_matrix,0,0); }
+
+ /** \returns a read-only expression of the Dim x HDim affine part of the transformation */
+ EIGEN_DEVICE_FUNC inline ConstAffinePart affine() const { return take_affine_part::run(m_matrix); }
+ /** \returns a writable expression of the Dim x HDim affine part of the transformation */
+ EIGEN_DEVICE_FUNC inline AffinePart affine() { return take_affine_part::run(m_matrix); }
+
+ /** \returns a read-only expression of the translation vector of the transformation */
+ EIGEN_DEVICE_FUNC inline ConstTranslationPart translation() const { return ConstTranslationPart(m_matrix,0,Dim); }
+ /** \returns a writable expression of the translation vector of the transformation */
+ EIGEN_DEVICE_FUNC inline TranslationPart translation() { return TranslationPart(m_matrix,0,Dim); }
+
+ /** \returns an expression of the product between the transform \c *this and a matrix expression \a other.
+ *
+ * The right-hand-side \a other can be either:
+ * \li an homogeneous vector of size Dim+1,
+ * \li a set of homogeneous vectors of size Dim+1 x N,
+ * \li a transformation matrix of size Dim+1 x Dim+1.
+ *
+ * Moreover, if \c *this represents an affine transformation (i.e., Mode!=Projective), then \a other can also be:
+ * \li a point of size Dim (computes: \code this->linear() * other + this->translation()\endcode),
+ * \li a set of N points as a Dim x N matrix (computes: \code (this->linear() * other).colwise() + this->translation()\endcode),
+ *
+ * In all cases, the return type is a matrix or vector of same sizes as the right-hand-side \a other.
+ *
+ * If you want to interpret \a other as a linear or affine transformation, then first convert it to a Transform<> type,
+ * or do your own cooking.
+ *
+ * Finally, if you want to apply Affine transformations to vectors, then explicitly apply the linear part only:
+ * \code
+ * Affine3f A;
+ * Vector3f v1, v2;
+ * v2 = A.linear() * v1;
+ * \endcode
+ *
+ */
+ // note: this function is defined here because some compilers cannot find the respective declaration
+ template<typename OtherDerived>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename internal::transform_right_product_impl<Transform, OtherDerived>::ResultType
+ operator * (const EigenBase<OtherDerived> &other) const
+ { return internal::transform_right_product_impl<Transform, OtherDerived>::run(*this,other.derived()); }
+
+ /** \returns the product expression of a transformation matrix \a a times a transform \a b
+ *
+ * The left hand side \a other can be either:
+ * \li a linear transformation matrix of size Dim x Dim,
+ * \li an affine transformation matrix of size Dim x Dim+1,
+ * \li a general transformation matrix of size Dim+1 x Dim+1.
+ */
+ template<typename OtherDerived> friend
+ EIGEN_DEVICE_FUNC inline const typename internal::transform_left_product_impl<OtherDerived,Mode,Options,Dim_,Dim_+1>::ResultType
+ operator * (const EigenBase<OtherDerived> &a, const Transform &b)
+ { return internal::transform_left_product_impl<OtherDerived,Mode,Options,Dim,HDim>::run(a.derived(),b); }
+
+ /** \returns The product expression of a transform \a a times a diagonal matrix \a b
+ *
+ * The rhs diagonal matrix is interpreted as an affine scaling transformation. The
+ * product results in a Transform of the same type (mode) as the lhs only if the lhs
+ * mode is no isometry. In that case, the returned transform is an affinity.
+ */
+ template<typename DiagonalDerived>
+ EIGEN_DEVICE_FUNC inline const TransformTimeDiagonalReturnType
+ operator * (const DiagonalBase<DiagonalDerived> &b) const
+ {
+ TransformTimeDiagonalReturnType res(*this);
+ res.linearExt() *= b;
+ return res;
+ }
+
+ /** \returns The product expression of a diagonal matrix \a a times a transform \a b
+ *
+ * The lhs diagonal matrix is interpreted as an affine scaling transformation. The
+ * product results in a Transform of the same type (mode) as the lhs only if the lhs
+ * mode is no isometry. In that case, the returned transform is an affinity.
+ */
+ template<typename DiagonalDerived>
+ EIGEN_DEVICE_FUNC friend inline TransformTimeDiagonalReturnType
+ operator * (const DiagonalBase<DiagonalDerived> &a, const Transform &b)
+ {
+ TransformTimeDiagonalReturnType res;
+ res.linear().noalias() = a*b.linear();
+ res.translation().noalias() = a*b.translation();
+ if (EIGEN_CONST_CONDITIONAL(Mode!=int(AffineCompact)))
+ res.matrix().row(Dim) = b.matrix().row(Dim);
+ return res;
+ }
+
+ template<typename OtherDerived>
+ EIGEN_DEVICE_FUNC inline Transform& operator*=(const EigenBase<OtherDerived>& other) { return *this = *this * other; }
+
+ /** Concatenates two transformations */
+ EIGEN_DEVICE_FUNC inline const Transform operator * (const Transform& other) const
+ {
+ return internal::transform_transform_product_impl<Transform,Transform>::run(*this,other);
+ }
+
+ #if EIGEN_COMP_ICC
+private:
+ // this intermediate structure permits to workaround a bug in ICC 11:
+ // error: template instantiation resulted in unexpected function type of "Eigen::Transform<double, 3, 32, 0>
+ // (const Eigen::Transform<double, 3, 2, 0> &) const"
+ // (the meaning of a name may have changed since the template declaration -- the type of the template is:
+ // "Eigen::internal::transform_transform_product_impl<Eigen::Transform<double, 3, 32, 0>,
+ // Eigen::Transform<double, 3, Mode, Options>, <expression>>::ResultType (const Eigen::Transform<double, 3, Mode, Options> &) const")
+ //
+ template<int OtherMode,int OtherOptions> struct icc_11_workaround
+ {
+ typedef internal::transform_transform_product_impl<Transform,Transform<Scalar,Dim,OtherMode,OtherOptions> > ProductType;
+ typedef typename ProductType::ResultType ResultType;
+ };
+
+public:
+ /** Concatenates two different transformations */
+ template<int OtherMode,int OtherOptions>
+ inline typename icc_11_workaround<OtherMode,OtherOptions>::ResultType
+ operator * (const Transform<Scalar,Dim,OtherMode,OtherOptions>& other) const
+ {
+ typedef typename icc_11_workaround<OtherMode,OtherOptions>::ProductType ProductType;
+ return ProductType::run(*this,other);
+ }
+ #else
+ /** Concatenates two different transformations */
+ template<int OtherMode,int OtherOptions>
+ EIGEN_DEVICE_FUNC inline typename internal::transform_transform_product_impl<Transform,Transform<Scalar,Dim,OtherMode,OtherOptions> >::ResultType
+ operator * (const Transform<Scalar,Dim,OtherMode,OtherOptions>& other) const
+ {
+ return internal::transform_transform_product_impl<Transform,Transform<Scalar,Dim,OtherMode,OtherOptions> >::run(*this,other);
+ }
+ #endif
+
+ /** \sa MatrixBase::setIdentity() */
+ EIGEN_DEVICE_FUNC void setIdentity() { m_matrix.setIdentity(); }
+
+ /**
+ * \brief Returns an identity transformation.
+ * \todo In the future this function should be returning a Transform expression.
+ */
+ EIGEN_DEVICE_FUNC static const Transform Identity()
+ {
+ return Transform(MatrixType::Identity());
+ }
+
+ template<typename OtherDerived>
+ EIGEN_DEVICE_FUNC
+ inline Transform& scale(const MatrixBase<OtherDerived> &other);
+
+ template<typename OtherDerived>
+ EIGEN_DEVICE_FUNC
+ inline Transform& prescale(const MatrixBase<OtherDerived> &other);
+
+ EIGEN_DEVICE_FUNC inline Transform& scale(const Scalar& s);
+ EIGEN_DEVICE_FUNC inline Transform& prescale(const Scalar& s);
+
+ template<typename OtherDerived>
+ EIGEN_DEVICE_FUNC
+ inline Transform& translate(const MatrixBase<OtherDerived> &other);
+
+ template<typename OtherDerived>
+ EIGEN_DEVICE_FUNC
+ inline Transform& pretranslate(const MatrixBase<OtherDerived> &other);
+
+ template<typename RotationType>
+ EIGEN_DEVICE_FUNC
+ inline Transform& rotate(const RotationType& rotation);
+
+ template<typename RotationType>
+ EIGEN_DEVICE_FUNC
+ inline Transform& prerotate(const RotationType& rotation);
+
+ EIGEN_DEVICE_FUNC Transform& shear(const Scalar& sx, const Scalar& sy);
+ EIGEN_DEVICE_FUNC Transform& preshear(const Scalar& sx, const Scalar& sy);
+
+ EIGEN_DEVICE_FUNC inline Transform& operator=(const TranslationType& t);
+
+ EIGEN_DEVICE_FUNC
+ inline Transform& operator*=(const TranslationType& t) { return translate(t.vector()); }
+
+ EIGEN_DEVICE_FUNC inline Transform operator*(const TranslationType& t) const;
+
+ EIGEN_DEVICE_FUNC
+ inline Transform& operator=(const UniformScaling<Scalar>& t);
+
+ EIGEN_DEVICE_FUNC
+ inline Transform& operator*=(const UniformScaling<Scalar>& s) { return scale(s.factor()); }
+
+ EIGEN_DEVICE_FUNC
+ inline TransformTimeDiagonalReturnType operator*(const UniformScaling<Scalar>& s) const
+ {
+ TransformTimeDiagonalReturnType res = *this;
+ res.scale(s.factor());
+ return res;
+ }
+
+ EIGEN_DEVICE_FUNC
+ inline Transform& operator*=(const DiagonalMatrix<Scalar,Dim>& s) { linearExt() *= s; return *this; }
+
+ template<typename Derived>
+ EIGEN_DEVICE_FUNC inline Transform& operator=(const RotationBase<Derived,Dim>& r);
+ template<typename Derived>
+ EIGEN_DEVICE_FUNC inline Transform& operator*=(const RotationBase<Derived,Dim>& r) { return rotate(r.toRotationMatrix()); }
+ template<typename Derived>
+ EIGEN_DEVICE_FUNC inline Transform operator*(const RotationBase<Derived,Dim>& r) const;
+
+ typedef std::conditional_t<int(Mode)==Isometry,ConstLinearPart,const LinearMatrixType> RotationReturnType;
+ EIGEN_DEVICE_FUNC RotationReturnType rotation() const;
+
+ template<typename RotationMatrixType, typename ScalingMatrixType>
+ EIGEN_DEVICE_FUNC
+ void computeRotationScaling(RotationMatrixType *rotation, ScalingMatrixType *scaling) const;
+ template<typename ScalingMatrixType, typename RotationMatrixType>
+ EIGEN_DEVICE_FUNC
+ void computeScalingRotation(ScalingMatrixType *scaling, RotationMatrixType *rotation) const;
+
+ template<typename PositionDerived, typename OrientationType, typename ScaleDerived>
+ EIGEN_DEVICE_FUNC
+ Transform& fromPositionOrientationScale(const MatrixBase<PositionDerived> &position,
+ const OrientationType& orientation, const MatrixBase<ScaleDerived> &scale);
+
+ EIGEN_DEVICE_FUNC
+ inline Transform inverse(TransformTraits traits = (TransformTraits)Mode) const;
+
+ /** \returns a const pointer to the column major internal matrix */
+ EIGEN_DEVICE_FUNC const Scalar* data() const { return m_matrix.data(); }
+ /** \returns a non-const pointer to the column major internal matrix */
+ EIGEN_DEVICE_FUNC Scalar* data() { return m_matrix.data(); }
+
+ /** \returns \c *this with scalar type casted to \a NewScalarType
+ *
+ * Note that if \a NewScalarType is equal to the current scalar type of \c *this
+ * then this function smartly returns a const reference to \c *this.
+ */
+ template<typename NewScalarType>
+ EIGEN_DEVICE_FUNC inline typename internal::cast_return_type<Transform,Transform<NewScalarType,Dim,Mode,Options> >::type cast() const
+ { return typename internal::cast_return_type<Transform,Transform<NewScalarType,Dim,Mode,Options> >::type(*this); }
+
+ /** Copy constructor with scalar type conversion */
+ template<typename OtherScalarType>
+ EIGEN_DEVICE_FUNC inline explicit Transform(const Transform<OtherScalarType,Dim,Mode,Options>& other)
+ {
+ check_template_params();
+ m_matrix = other.matrix().template cast<Scalar>();
+ }
+
+ /** \returns \c true if \c *this is approximately equal to \a other, within the precision
+ * determined by \a prec.
+ *
+ * \sa MatrixBase::isApprox() */
+ EIGEN_DEVICE_FUNC bool isApprox(const Transform& other, const typename NumTraits<Scalar>::Real& prec = NumTraits<Scalar>::dummy_precision()) const
+ { return m_matrix.isApprox(other.m_matrix, prec); }
+
+ /** Sets the last row to [0 ... 0 1]
+ */
+ EIGEN_DEVICE_FUNC void makeAffine()
+ {
+ internal::transform_make_affine<int(Mode)>::run(m_matrix);
+ }
+
+ /** \internal
+ * \returns the Dim x Dim linear part if the transformation is affine,
+ * and the HDim x Dim part for projective transformations.
+ */
+ EIGEN_DEVICE_FUNC inline Block<MatrixType,int(Mode)==int(Projective)?HDim:Dim,Dim> linearExt()
+ { return m_matrix.template block<int(Mode)==int(Projective)?HDim:Dim,Dim>(0,0); }
+ /** \internal
+ * \returns the Dim x Dim linear part if the transformation is affine,
+ * and the HDim x Dim part for projective transformations.
+ */
+ EIGEN_DEVICE_FUNC inline const Block<MatrixType,int(Mode)==int(Projective)?HDim:Dim,Dim> linearExt() const
+ { return m_matrix.template block<int(Mode)==int(Projective)?HDim:Dim,Dim>(0,0); }
+
+ /** \internal
+ * \returns the translation part if the transformation is affine,
+ * and the last column for projective transformations.
+ */
+ EIGEN_DEVICE_FUNC inline Block<MatrixType,int(Mode)==int(Projective)?HDim:Dim,1> translationExt()
+ { return m_matrix.template block<int(Mode)==int(Projective)?HDim:Dim,1>(0,Dim); }
+ /** \internal
+ * \returns the translation part if the transformation is affine,
+ * and the last column for projective transformations.
+ */
+ EIGEN_DEVICE_FUNC inline const Block<MatrixType,int(Mode)==int(Projective)?HDim:Dim,1> translationExt() const
+ { return m_matrix.template block<int(Mode)==int(Projective)?HDim:Dim,1>(0,Dim); }
+
+
+ #ifdef EIGEN_TRANSFORM_PLUGIN
+ #include EIGEN_TRANSFORM_PLUGIN
+ #endif
+
+protected:
+ #ifndef EIGEN_PARSED_BY_DOXYGEN
+ EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE void check_template_params()
+ {
+ EIGEN_STATIC_ASSERT((Options & (DontAlign|RowMajor)) == Options, INVALID_MATRIX_TEMPLATE_PARAMETERS)
+ }
+ #endif
+
+};
+
+/** \ingroup Geometry_Module */
+typedef Transform<float,2,Isometry> Isometry2f;
+/** \ingroup Geometry_Module */
+typedef Transform<float,3,Isometry> Isometry3f;
+/** \ingroup Geometry_Module */
+typedef Transform<double,2,Isometry> Isometry2d;
+/** \ingroup Geometry_Module */
+typedef Transform<double,3,Isometry> Isometry3d;
+
+/** \ingroup Geometry_Module */
+typedef Transform<float,2,Affine> Affine2f;
+/** \ingroup Geometry_Module */
+typedef Transform<float,3,Affine> Affine3f;
+/** \ingroup Geometry_Module */
+typedef Transform<double,2,Affine> Affine2d;
+/** \ingroup Geometry_Module */
+typedef Transform<double,3,Affine> Affine3d;
+
+/** \ingroup Geometry_Module */
+typedef Transform<float,2,AffineCompact> AffineCompact2f;
+/** \ingroup Geometry_Module */
+typedef Transform<float,3,AffineCompact> AffineCompact3f;
+/** \ingroup Geometry_Module */
+typedef Transform<double,2,AffineCompact> AffineCompact2d;
+/** \ingroup Geometry_Module */
+typedef Transform<double,3,AffineCompact> AffineCompact3d;
+
+/** \ingroup Geometry_Module */
+typedef Transform<float,2,Projective> Projective2f;
+/** \ingroup Geometry_Module */
+typedef Transform<float,3,Projective> Projective3f;
+/** \ingroup Geometry_Module */
+typedef Transform<double,2,Projective> Projective2d;
+/** \ingroup Geometry_Module */
+typedef Transform<double,3,Projective> Projective3d;
+
+/**************************
+*** Optional QT support ***
+**************************/
+
+#ifdef EIGEN_QT_SUPPORT
+
+#if (QT_VERSION < QT_VERSION_CHECK(6, 0, 0))
+/** Initializes \c *this from a QMatrix assuming the dimension is 2.
+ *
+ * This function is available only if the token EIGEN_QT_SUPPORT is defined.
+ */
+template<typename Scalar, int Dim, int Mode,int Options>
+Transform<Scalar,Dim,Mode,Options>::Transform(const QMatrix& other)
+{
+ check_template_params();
+ *this = other;
+}
+
+/** Set \c *this from a QMatrix assuming the dimension is 2.
+ *
+ * This function is available only if the token EIGEN_QT_SUPPORT is defined.
+ */
+template<typename Scalar, int Dim, int Mode,int Options>
+Transform<Scalar,Dim,Mode,Options>& Transform<Scalar,Dim,Mode,Options>::operator=(const QMatrix& other)
+{
+ EIGEN_STATIC_ASSERT(Dim==2, YOU_MADE_A_PROGRAMMING_MISTAKE)
+ if (EIGEN_CONST_CONDITIONAL(Mode == int(AffineCompact)))
+ m_matrix << other.m11(), other.m21(), other.dx(),
+ other.m12(), other.m22(), other.dy();
+ else
+ m_matrix << other.m11(), other.m21(), other.dx(),
+ other.m12(), other.m22(), other.dy(),
+ 0, 0, 1;
+ return *this;
+}
+
+/** \returns a QMatrix from \c *this assuming the dimension is 2.
+ *
+ * \warning this conversion might loss data if \c *this is not affine
+ *
+ * This function is available only if the token EIGEN_QT_SUPPORT is defined.
+ */
+template<typename Scalar, int Dim, int Mode, int Options>
+QMatrix Transform<Scalar,Dim,Mode,Options>::toQMatrix(void) const
+{
+ check_template_params();
+ EIGEN_STATIC_ASSERT(Dim==2, YOU_MADE_A_PROGRAMMING_MISTAKE)
+ return QMatrix(m_matrix.coeff(0,0), m_matrix.coeff(1,0),
+ m_matrix.coeff(0,1), m_matrix.coeff(1,1),
+ m_matrix.coeff(0,2), m_matrix.coeff(1,2));
+}
+#endif
+
+/** Initializes \c *this from a QTransform assuming the dimension is 2.
+ *
+ * This function is available only if the token EIGEN_QT_SUPPORT is defined.
+ */
+template<typename Scalar, int Dim, int Mode,int Options>
+Transform<Scalar,Dim,Mode,Options>::Transform(const QTransform& other)
+{
+ check_template_params();
+ *this = other;
+}
+
+/** Set \c *this from a QTransform assuming the dimension is 2.
+ *
+ * This function is available only if the token EIGEN_QT_SUPPORT is defined.
+ */
+template<typename Scalar, int Dim, int Mode, int Options>
+Transform<Scalar,Dim,Mode,Options>& Transform<Scalar,Dim,Mode,Options>::operator=(const QTransform& other)
+{
+ check_template_params();
+ EIGEN_STATIC_ASSERT(Dim==2, YOU_MADE_A_PROGRAMMING_MISTAKE)
+ if (EIGEN_CONST_CONDITIONAL(Mode == int(AffineCompact)))
+ m_matrix << other.m11(), other.m21(), other.dx(),
+ other.m12(), other.m22(), other.dy();
+ else
+ m_matrix << other.m11(), other.m21(), other.dx(),
+ other.m12(), other.m22(), other.dy(),
+ other.m13(), other.m23(), other.m33();
+ return *this;
+}
+
+/** \returns a QTransform from \c *this assuming the dimension is 2.
+ *
+ * This function is available only if the token EIGEN_QT_SUPPORT is defined.
+ */
+template<typename Scalar, int Dim, int Mode, int Options>
+QTransform Transform<Scalar,Dim,Mode,Options>::toQTransform(void) const
+{
+ EIGEN_STATIC_ASSERT(Dim==2, YOU_MADE_A_PROGRAMMING_MISTAKE)
+ if (EIGEN_CONST_CONDITIONAL(Mode == int(AffineCompact)))
+ return QTransform(m_matrix.coeff(0,0), m_matrix.coeff(1,0),
+ m_matrix.coeff(0,1), m_matrix.coeff(1,1),
+ m_matrix.coeff(0,2), m_matrix.coeff(1,2));
+ else
+ return QTransform(m_matrix.coeff(0,0), m_matrix.coeff(1,0), m_matrix.coeff(2,0),
+ m_matrix.coeff(0,1), m_matrix.coeff(1,1), m_matrix.coeff(2,1),
+ m_matrix.coeff(0,2), m_matrix.coeff(1,2), m_matrix.coeff(2,2));
+}
+#endif
+
+/*********************
+*** Procedural API ***
+*********************/
+
+/** Applies on the right the non uniform scale transformation represented
+ * by the vector \a other to \c *this and returns a reference to \c *this.
+ * \sa prescale()
+ */
+template<typename Scalar, int Dim, int Mode, int Options>
+template<typename OtherDerived>
+EIGEN_DEVICE_FUNC Transform<Scalar,Dim,Mode,Options>&
+Transform<Scalar,Dim,Mode,Options>::scale(const MatrixBase<OtherDerived> &other)
+{
+ EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(OtherDerived,int(Dim))
+ EIGEN_STATIC_ASSERT(Mode!=int(Isometry), THIS_METHOD_IS_ONLY_FOR_SPECIFIC_TRANSFORMATIONS)
+ linearExt().noalias() = (linearExt() * other.asDiagonal());
+ return *this;
+}
+
+/** Applies on the right a uniform scale of a factor \a c to \c *this
+ * and returns a reference to \c *this.
+ * \sa prescale(Scalar)
+ */
+template<typename Scalar, int Dim, int Mode, int Options>
+EIGEN_DEVICE_FUNC inline Transform<Scalar,Dim,Mode,Options>& Transform<Scalar,Dim,Mode,Options>::scale(const Scalar& s)
+{
+ EIGEN_STATIC_ASSERT(Mode!=int(Isometry), THIS_METHOD_IS_ONLY_FOR_SPECIFIC_TRANSFORMATIONS)
+ linearExt() *= s;
+ return *this;
+}
+
+/** Applies on the left the non uniform scale transformation represented
+ * by the vector \a other to \c *this and returns a reference to \c *this.
+ * \sa scale()
+ */
+template<typename Scalar, int Dim, int Mode, int Options>
+template<typename OtherDerived>
+EIGEN_DEVICE_FUNC Transform<Scalar,Dim,Mode,Options>&
+Transform<Scalar,Dim,Mode,Options>::prescale(const MatrixBase<OtherDerived> &other)
+{
+ EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(OtherDerived,int(Dim))
+ EIGEN_STATIC_ASSERT(Mode!=int(Isometry), THIS_METHOD_IS_ONLY_FOR_SPECIFIC_TRANSFORMATIONS)
+ affine().noalias() = (other.asDiagonal() * affine());
+ return *this;
+}
+
+/** Applies on the left a uniform scale of a factor \a c to \c *this
+ * and returns a reference to \c *this.
+ * \sa scale(Scalar)
+ */
+template<typename Scalar, int Dim, int Mode, int Options>
+EIGEN_DEVICE_FUNC inline Transform<Scalar,Dim,Mode,Options>& Transform<Scalar,Dim,Mode,Options>::prescale(const Scalar& s)
+{
+ EIGEN_STATIC_ASSERT(Mode!=int(Isometry), THIS_METHOD_IS_ONLY_FOR_SPECIFIC_TRANSFORMATIONS)
+ m_matrix.template topRows<Dim>() *= s;
+ return *this;
+}
+
+/** Applies on the right the translation matrix represented by the vector \a other
+ * to \c *this and returns a reference to \c *this.
+ * \sa pretranslate()
+ */
+template<typename Scalar, int Dim, int Mode, int Options>
+template<typename OtherDerived>
+EIGEN_DEVICE_FUNC Transform<Scalar,Dim,Mode,Options>&
+Transform<Scalar,Dim,Mode,Options>::translate(const MatrixBase<OtherDerived> &other)
+{
+ EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(OtherDerived,int(Dim))
+ translationExt() += linearExt() * other;
+ return *this;
+}
+
+/** Applies on the left the translation matrix represented by the vector \a other
+ * to \c *this and returns a reference to \c *this.
+ * \sa translate()
+ */
+template<typename Scalar, int Dim, int Mode, int Options>
+template<typename OtherDerived>
+EIGEN_DEVICE_FUNC Transform<Scalar,Dim,Mode,Options>&
+Transform<Scalar,Dim,Mode,Options>::pretranslate(const MatrixBase<OtherDerived> &other)
+{
+ EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(OtherDerived,int(Dim))
+ if(EIGEN_CONST_CONDITIONAL(int(Mode)==int(Projective)))
+ affine() += other * m_matrix.row(Dim);
+ else
+ translation() += other;
+ return *this;
+}
+
+/** Applies on the right the rotation represented by the rotation \a rotation
+ * to \c *this and returns a reference to \c *this.
+ *
+ * The template parameter \a RotationType is the type of the rotation which
+ * must be known by internal::toRotationMatrix<>.
+ *
+ * Natively supported types includes:
+ * - any scalar (2D),
+ * - a Dim x Dim matrix expression,
+ * - a Quaternion (3D),
+ * - a AngleAxis (3D)
+ *
+ * This mechanism is easily extendable to support user types such as Euler angles,
+ * or a pair of Quaternion for 4D rotations.
+ *
+ * \sa rotate(Scalar), class Quaternion, class AngleAxis, prerotate(RotationType)
+ */
+template<typename Scalar, int Dim, int Mode, int Options>
+template<typename RotationType>
+EIGEN_DEVICE_FUNC Transform<Scalar,Dim,Mode,Options>&
+Transform<Scalar,Dim,Mode,Options>::rotate(const RotationType& rotation)
+{
+ linearExt() *= internal::toRotationMatrix<Scalar,Dim>(rotation);
+ return *this;
+}
+
+/** Applies on the left the rotation represented by the rotation \a rotation
+ * to \c *this and returns a reference to \c *this.
+ *
+ * See rotate() for further details.
+ *
+ * \sa rotate()
+ */
+template<typename Scalar, int Dim, int Mode, int Options>
+template<typename RotationType>
+EIGEN_DEVICE_FUNC Transform<Scalar,Dim,Mode,Options>&
+Transform<Scalar,Dim,Mode,Options>::prerotate(const RotationType& rotation)
+{
+ m_matrix.template block<Dim,HDim>(0,0) = internal::toRotationMatrix<Scalar,Dim>(rotation)
+ * m_matrix.template block<Dim,HDim>(0,0);
+ return *this;
+}
+
+/** Applies on the right the shear transformation represented
+ * by the vector \a other to \c *this and returns a reference to \c *this.
+ * \warning 2D only.
+ * \sa preshear()
+ */
+template<typename Scalar, int Dim, int Mode, int Options>
+EIGEN_DEVICE_FUNC Transform<Scalar,Dim,Mode,Options>&
+Transform<Scalar,Dim,Mode,Options>::shear(const Scalar& sx, const Scalar& sy)
+{
+ EIGEN_STATIC_ASSERT(int(Dim)==2, YOU_MADE_A_PROGRAMMING_MISTAKE)
+ EIGEN_STATIC_ASSERT(Mode!=int(Isometry), THIS_METHOD_IS_ONLY_FOR_SPECIFIC_TRANSFORMATIONS)
+ VectorType tmp = linear().col(0)*sy + linear().col(1);
+ linear() << linear().col(0) + linear().col(1)*sx, tmp;
+ return *this;
+}
+
+/** Applies on the left the shear transformation represented
+ * by the vector \a other to \c *this and returns a reference to \c *this.
+ * \warning 2D only.
+ * \sa shear()
+ */
+template<typename Scalar, int Dim, int Mode, int Options>
+EIGEN_DEVICE_FUNC Transform<Scalar,Dim,Mode,Options>&
+Transform<Scalar,Dim,Mode,Options>::preshear(const Scalar& sx, const Scalar& sy)
+{
+ EIGEN_STATIC_ASSERT(int(Dim)==2, YOU_MADE_A_PROGRAMMING_MISTAKE)
+ EIGEN_STATIC_ASSERT(Mode!=int(Isometry), THIS_METHOD_IS_ONLY_FOR_SPECIFIC_TRANSFORMATIONS)
+ m_matrix.template block<Dim,HDim>(0,0) = LinearMatrixType(1, sx, sy, 1) * m_matrix.template block<Dim,HDim>(0,0);
+ return *this;
+}
+
+/******************************************************
+*** Scaling, Translation and Rotation compatibility ***
+******************************************************/
+
+template<typename Scalar, int Dim, int Mode, int Options>
+EIGEN_DEVICE_FUNC inline Transform<Scalar,Dim,Mode,Options>& Transform<Scalar,Dim,Mode,Options>::operator=(const TranslationType& t)
+{
+ linear().setIdentity();
+ translation() = t.vector();
+ makeAffine();
+ return *this;
+}
+
+template<typename Scalar, int Dim, int Mode, int Options>
+EIGEN_DEVICE_FUNC inline Transform<Scalar,Dim,Mode,Options> Transform<Scalar,Dim,Mode,Options>::operator*(const TranslationType& t) const
+{
+ Transform res = *this;
+ res.translate(t.vector());
+ return res;
+}
+
+template<typename Scalar, int Dim, int Mode, int Options>
+EIGEN_DEVICE_FUNC inline Transform<Scalar,Dim,Mode,Options>& Transform<Scalar,Dim,Mode,Options>::operator=(const UniformScaling<Scalar>& s)
+{
+ m_matrix.setZero();
+ linear().diagonal().fill(s.factor());
+ makeAffine();
+ return *this;
+}
+
+template<typename Scalar, int Dim, int Mode, int Options>
+template<typename Derived>
+EIGEN_DEVICE_FUNC inline Transform<Scalar,Dim,Mode,Options>& Transform<Scalar,Dim,Mode,Options>::operator=(const RotationBase<Derived,Dim>& r)
+{
+ linear() = internal::toRotationMatrix<Scalar,Dim>(r);
+ translation().setZero();
+ makeAffine();
+ return *this;
+}
+
+template<typename Scalar, int Dim, int Mode, int Options>
+template<typename Derived>
+EIGEN_DEVICE_FUNC inline Transform<Scalar,Dim,Mode,Options> Transform<Scalar,Dim,Mode,Options>::operator*(const RotationBase<Derived,Dim>& r) const
+{
+ Transform res = *this;
+ res.rotate(r.derived());
+ return res;
+}
+
+/************************
+*** Special functions ***
+************************/
+
+namespace internal {
+template<int Mode> struct transform_rotation_impl {
+ template<typename TransformType>
+ EIGEN_DEVICE_FUNC static inline
+ const typename TransformType::LinearMatrixType run(const TransformType& t)
+ {
+ typedef typename TransformType::LinearMatrixType LinearMatrixType;
+ LinearMatrixType result;
+ t.computeRotationScaling(&result, (LinearMatrixType*)0);
+ return result;
+ }
+};
+template<> struct transform_rotation_impl<Isometry> {
+ template<typename TransformType>
+ EIGEN_DEVICE_FUNC static inline
+ typename TransformType::ConstLinearPart run(const TransformType& t)
+ {
+ return t.linear();
+ }
+};
+}
+/** \returns the rotation part of the transformation
+ *
+ * If Mode==Isometry, then this method is an alias for linear(),
+ * otherwise it calls computeRotationScaling() to extract the rotation
+ * through a SVD decomposition.
+ *
+ * \svd_module
+ *
+ * \sa computeRotationScaling(), computeScalingRotation(), class SVD
+ */
+template<typename Scalar, int Dim, int Mode, int Options>
+EIGEN_DEVICE_FUNC
+typename Transform<Scalar,Dim,Mode,Options>::RotationReturnType
+Transform<Scalar,Dim,Mode,Options>::rotation() const
+{
+ return internal::transform_rotation_impl<Mode>::run(*this);
+}
+
+
+/** decomposes the linear part of the transformation as a product rotation x scaling, the scaling being
+ * not necessarily positive.
+ *
+ * If either pointer is zero, the corresponding computation is skipped.
+ *
+ *
+ *
+ * \svd_module
+ *
+ * \sa computeScalingRotation(), rotation(), class SVD
+ */
+template<typename Scalar, int Dim, int Mode, int Options>
+template<typename RotationMatrixType, typename ScalingMatrixType>
+EIGEN_DEVICE_FUNC void Transform<Scalar,Dim,Mode,Options>::computeRotationScaling(RotationMatrixType *rotation, ScalingMatrixType *scaling) const
+{
+ // Note that JacobiSVD is faster than BDCSVD for small matrices.
+ JacobiSVD<LinearMatrixType, ComputeFullU | ComputeFullV> svd(linear());
+
+ Scalar x = (svd.matrixU() * svd.matrixV().adjoint()).determinant() < Scalar(0) ? Scalar(-1) : Scalar(1); // so x has absolute value 1
+ VectorType sv(svd.singularValues());
+ sv.coeffRef(Dim-1) *= x;
+ if(scaling) *scaling = svd.matrixV() * sv.asDiagonal() * svd.matrixV().adjoint();
+ if(rotation)
+ {
+ LinearMatrixType m(svd.matrixU());
+ m.col(Dim-1) *= x;
+ *rotation = m * svd.matrixV().adjoint();
+ }
+}
+
+/** decomposes the linear part of the transformation as a product scaling x rotation, the scaling being
+ * not necessarily positive.
+ *
+ * If either pointer is zero, the corresponding computation is skipped.
+ *
+ *
+ *
+ * \svd_module
+ *
+ * \sa computeRotationScaling(), rotation(), class SVD
+ */
+template<typename Scalar, int Dim, int Mode, int Options>
+template<typename ScalingMatrixType, typename RotationMatrixType>
+EIGEN_DEVICE_FUNC void Transform<Scalar,Dim,Mode,Options>::computeScalingRotation(ScalingMatrixType *scaling, RotationMatrixType *rotation) const
+{
+ // Note that JacobiSVD is faster than BDCSVD for small matrices.
+ JacobiSVD<LinearMatrixType, ComputeFullU | ComputeFullV> svd(linear());
+
+ Scalar x = (svd.matrixU() * svd.matrixV().adjoint()).determinant() < Scalar(0) ? Scalar(-1) : Scalar(1); // so x has absolute value 1
+ VectorType sv(svd.singularValues());
+ sv.coeffRef(Dim-1) *= x;
+ if(scaling) *scaling = svd.matrixU() * sv.asDiagonal() * svd.matrixU().adjoint();
+ if(rotation)
+ {
+ LinearMatrixType m(svd.matrixU());
+ m.col(Dim-1) *= x;
+ *rotation = m * svd.matrixV().adjoint();
+ }
+}
+
+/** Convenient method to set \c *this from a position, orientation and scale
+ * of a 3D object.
+ */
+template<typename Scalar, int Dim, int Mode, int Options>
+template<typename PositionDerived, typename OrientationType, typename ScaleDerived>
+EIGEN_DEVICE_FUNC Transform<Scalar,Dim,Mode,Options>&
+Transform<Scalar,Dim,Mode,Options>::fromPositionOrientationScale(const MatrixBase<PositionDerived> &position,
+ const OrientationType& orientation, const MatrixBase<ScaleDerived> &scale)
+{
+ linear() = internal::toRotationMatrix<Scalar,Dim>(orientation);
+ linear() *= scale.asDiagonal();
+ translation() = position;
+ makeAffine();
+ return *this;
+}
+
+namespace internal {
+
+template<int Mode>
+struct transform_make_affine
+{
+ template<typename MatrixType>
+ EIGEN_DEVICE_FUNC static void run(MatrixType &mat)
+ {
+ static const int Dim = MatrixType::ColsAtCompileTime-1;
+ mat.template block<1,Dim>(Dim,0).setZero();
+ mat.coeffRef(Dim,Dim) = typename MatrixType::Scalar(1);
+ }
+};
+
+template<>
+struct transform_make_affine<AffineCompact>
+{
+ template<typename MatrixType> EIGEN_DEVICE_FUNC static void run(MatrixType &) { }
+};
+
+// selector needed to avoid taking the inverse of a 3x4 matrix
+template<typename TransformType, int Mode=TransformType::Mode>
+struct projective_transform_inverse
+{
+ EIGEN_DEVICE_FUNC static inline void run(const TransformType&, TransformType&)
+ {}
+};
+
+template<typename TransformType>
+struct projective_transform_inverse<TransformType, Projective>
+{
+ EIGEN_DEVICE_FUNC static inline void run(const TransformType& m, TransformType& res)
+ {
+ res.matrix() = m.matrix().inverse();
+ }
+};
+
+} // end namespace internal
+
+
+/**
+ *
+ * \returns the inverse transformation according to some given knowledge
+ * on \c *this.
+ *
+ * \param hint allows to optimize the inversion process when the transformation
+ * is known to be not a general transformation (optional). The possible values are:
+ * - #Projective if the transformation is not necessarily affine, i.e., if the
+ * last row is not guaranteed to be [0 ... 0 1]
+ * - #Affine if the last row can be assumed to be [0 ... 0 1]
+ * - #Isometry if the transformation is only a concatenations of translations
+ * and rotations.
+ * The default is the template class parameter \c Mode.
+ *
+ * \warning unless \a traits is always set to NoShear or NoScaling, this function
+ * requires the generic inverse method of MatrixBase defined in the LU module. If
+ * you forget to include this module, then you will get hard to debug linking errors.
+ *
+ * \sa MatrixBase::inverse()
+ */
+template<typename Scalar, int Dim, int Mode, int Options>
+EIGEN_DEVICE_FUNC Transform<Scalar,Dim,Mode,Options>
+Transform<Scalar,Dim,Mode,Options>::inverse(TransformTraits hint) const
+{
+ Transform res;
+ if (hint == Projective)
+ {
+ internal::projective_transform_inverse<Transform>::run(*this, res);
+ }
+ else
+ {
+ if (hint == Isometry)
+ {
+ res.matrix().template topLeftCorner<Dim,Dim>() = linear().transpose();
+ }
+ else if(hint&Affine)
+ {
+ res.matrix().template topLeftCorner<Dim,Dim>() = linear().inverse();
+ }
+ else
+ {
+ eigen_assert(false && "Invalid transform traits in Transform::Inverse");
+ }
+ // translation and remaining parts
+ res.matrix().template topRightCorner<Dim,1>()
+ = - res.matrix().template topLeftCorner<Dim,Dim>() * translation();
+ res.makeAffine(); // we do need this, because in the beginning res is uninitialized
+ }
+ return res;
+}
+
+namespace internal {
+
+/*****************************************************
+*** Specializations of take affine part ***
+*****************************************************/
+
+template<typename TransformType> struct transform_take_affine_part {
+ typedef typename TransformType::MatrixType MatrixType;
+ typedef typename TransformType::AffinePart AffinePart;
+ typedef typename TransformType::ConstAffinePart ConstAffinePart;
+ static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE AffinePart run(MatrixType& m)
+ { return m.template block<TransformType::Dim,TransformType::HDim>(0,0); }
+ static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE ConstAffinePart run(const MatrixType& m)
+ { return m.template block<TransformType::Dim,TransformType::HDim>(0,0); }
+};
+
+template<typename Scalar, int Dim, int Options>
+struct transform_take_affine_part<Transform<Scalar,Dim,AffineCompact, Options> > {
+ typedef typename Transform<Scalar,Dim,AffineCompact,Options>::MatrixType MatrixType;
+ static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE MatrixType& run(MatrixType& m) { return m; }
+ static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const MatrixType& run(const MatrixType& m) { return m; }
+};
+
+/*****************************************************
+*** Specializations of construct from matrix ***
+*****************************************************/
+
+template<typename Other, int Mode, int Options, int Dim, int HDim>
+struct transform_construct_from_matrix<Other, Mode,Options,Dim,HDim, Dim,Dim>
+{
+ static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void run(Transform<typename Other::Scalar,Dim,Mode,Options> *transform, const Other& other)
+ {
+ transform->linear() = other;
+ transform->translation().setZero();
+ transform->makeAffine();
+ }
+};
+
+template<typename Other, int Mode, int Options, int Dim, int HDim>
+struct transform_construct_from_matrix<Other, Mode,Options,Dim,HDim, Dim,HDim>
+{
+ static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void run(Transform<typename Other::Scalar,Dim,Mode,Options> *transform, const Other& other)
+ {
+ transform->affine() = other;
+ transform->makeAffine();
+ }
+};
+
+template<typename Other, int Mode, int Options, int Dim, int HDim>
+struct transform_construct_from_matrix<Other, Mode,Options,Dim,HDim, HDim,HDim>
+{
+ static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void run(Transform<typename Other::Scalar,Dim,Mode,Options> *transform, const Other& other)
+ { transform->matrix() = other; }
+};
+
+template<typename Other, int Options, int Dim, int HDim>
+struct transform_construct_from_matrix<Other, AffineCompact,Options,Dim,HDim, HDim,HDim>
+{
+ static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void run(Transform<typename Other::Scalar,Dim,AffineCompact,Options> *transform, const Other& other)
+ { transform->matrix() = other.template block<Dim,HDim>(0,0); }
+};
+
+/**********************************************************
+*** Specializations of operator* with rhs EigenBase ***
+**********************************************************/
+
+template<int LhsMode,int RhsMode>
+struct transform_product_result
+{
+ enum
+ {
+ Mode =
+ (LhsMode == (int)Projective || RhsMode == (int)Projective ) ? Projective :
+ (LhsMode == (int)Affine || RhsMode == (int)Affine ) ? Affine :
+ (LhsMode == (int)AffineCompact || RhsMode == (int)AffineCompact ) ? AffineCompact :
+ (LhsMode == (int)Isometry || RhsMode == (int)Isometry ) ? Isometry : Projective
+ };
+};
+
+template< typename TransformType, typename MatrixType, int RhsCols>
+struct transform_right_product_impl< TransformType, MatrixType, 0, RhsCols>
+{
+ typedef typename MatrixType::PlainObject ResultType;
+
+ static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE ResultType run(const TransformType& T, const MatrixType& other)
+ {
+ return T.matrix() * other;
+ }
+};
+
+template< typename TransformType, typename MatrixType, int RhsCols>
+struct transform_right_product_impl< TransformType, MatrixType, 1, RhsCols>
+{
+ enum {
+ Dim = TransformType::Dim,
+ HDim = TransformType::HDim,
+ OtherRows = MatrixType::RowsAtCompileTime,
+ OtherCols = MatrixType::ColsAtCompileTime
+ };
+
+ typedef typename MatrixType::PlainObject ResultType;
+
+ static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE ResultType run(const TransformType& T, const MatrixType& other)
+ {
+ EIGEN_STATIC_ASSERT(OtherRows==HDim, YOU_MIXED_MATRICES_OF_DIFFERENT_SIZES);
+
+ typedef Block<ResultType, Dim, OtherCols, int(MatrixType::RowsAtCompileTime)==Dim> TopLeftLhs;
+
+ ResultType res(other.rows(),other.cols());
+ TopLeftLhs(res, 0, 0, Dim, other.cols()).noalias() = T.affine() * other;
+ res.row(OtherRows-1) = other.row(OtherRows-1);
+
+ return res;
+ }
+};
+
+template< typename TransformType, typename MatrixType, int RhsCols>
+struct transform_right_product_impl< TransformType, MatrixType, 2, RhsCols>
+{
+ enum {
+ Dim = TransformType::Dim,
+ HDim = TransformType::HDim,
+ OtherRows = MatrixType::RowsAtCompileTime,
+ OtherCols = MatrixType::ColsAtCompileTime
+ };
+
+ typedef typename MatrixType::PlainObject ResultType;
+
+ static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE ResultType run(const TransformType& T, const MatrixType& other)
+ {
+ EIGEN_STATIC_ASSERT(OtherRows==Dim, YOU_MIXED_MATRICES_OF_DIFFERENT_SIZES);
+
+ typedef Block<ResultType, Dim, OtherCols, true> TopLeftLhs;
+ ResultType res(Replicate<typename TransformType::ConstTranslationPart, 1, OtherCols>(T.translation(),1,other.cols()));
+ TopLeftLhs(res, 0, 0, Dim, other.cols()).noalias() += T.linear() * other;
+
+ return res;
+ }
+};
+
+template< typename TransformType, typename MatrixType >
+struct transform_right_product_impl< TransformType, MatrixType, 2, 1> // rhs is a vector of size Dim
+{
+ typedef typename TransformType::MatrixType TransformMatrix;
+ enum {
+ Dim = TransformType::Dim,
+ HDim = TransformType::HDim,
+ OtherRows = MatrixType::RowsAtCompileTime,
+ WorkingRows = plain_enum_min(TransformMatrix::RowsAtCompileTime, HDim)
+ };
+
+ typedef typename MatrixType::PlainObject ResultType;
+
+ static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE ResultType run(const TransformType& T, const MatrixType& other)
+ {
+ EIGEN_STATIC_ASSERT(OtherRows==Dim, YOU_MIXED_MATRICES_OF_DIFFERENT_SIZES);
+
+ Matrix<typename ResultType::Scalar, Dim+1, 1> rhs;
+ rhs.template head<Dim>() = other; rhs[Dim] = typename ResultType::Scalar(1);
+ Matrix<typename ResultType::Scalar, WorkingRows, 1> res(T.matrix() * rhs);
+ return res.template head<Dim>();
+ }
+};
+
+/**********************************************************
+*** Specializations of operator* with lhs EigenBase ***
+**********************************************************/
+
+// generic HDim x HDim matrix * T => Projective
+template<typename Other,int Mode, int Options, int Dim, int HDim>
+struct transform_left_product_impl<Other,Mode,Options,Dim,HDim, HDim,HDim>
+{
+ typedef Transform<typename Other::Scalar,Dim,Mode,Options> TransformType;
+ typedef typename TransformType::MatrixType MatrixType;
+ typedef Transform<typename Other::Scalar,Dim,Projective,Options> ResultType;
+ static ResultType run(const Other& other,const TransformType& tr)
+ { return ResultType(other * tr.matrix()); }
+};
+
+// generic HDim x HDim matrix * AffineCompact => Projective
+template<typename Other, int Options, int Dim, int HDim>
+struct transform_left_product_impl<Other,AffineCompact,Options,Dim,HDim, HDim,HDim>
+{
+ typedef Transform<typename Other::Scalar,Dim,AffineCompact,Options> TransformType;
+ typedef typename TransformType::MatrixType MatrixType;
+ typedef Transform<typename Other::Scalar,Dim,Projective,Options> ResultType;
+ static ResultType run(const Other& other,const TransformType& tr)
+ {
+ ResultType res;
+ res.matrix().noalias() = other.template block<HDim,Dim>(0,0) * tr.matrix();
+ res.matrix().col(Dim) += other.col(Dim);
+ return res;
+ }
+};
+
+// affine matrix * T
+template<typename Other,int Mode, int Options, int Dim, int HDim>
+struct transform_left_product_impl<Other,Mode,Options,Dim,HDim, Dim,HDim>
+{
+ typedef Transform<typename Other::Scalar,Dim,Mode,Options> TransformType;
+ typedef typename TransformType::MatrixType MatrixType;
+ typedef TransformType ResultType;
+ static ResultType run(const Other& other,const TransformType& tr)
+ {
+ ResultType res;
+ res.affine().noalias() = other * tr.matrix();
+ res.matrix().row(Dim) = tr.matrix().row(Dim);
+ return res;
+ }
+};
+
+// affine matrix * AffineCompact
+template<typename Other, int Options, int Dim, int HDim>
+struct transform_left_product_impl<Other,AffineCompact,Options,Dim,HDim, Dim,HDim>
+{
+ typedef Transform<typename Other::Scalar,Dim,AffineCompact,Options> TransformType;
+ typedef typename TransformType::MatrixType MatrixType;
+ typedef TransformType ResultType;
+ static ResultType run(const Other& other,const TransformType& tr)
+ {
+ ResultType res;
+ res.matrix().noalias() = other.template block<Dim,Dim>(0,0) * tr.matrix();
+ res.translation() += other.col(Dim);
+ return res;
+ }
+};
+
+// linear matrix * T
+template<typename Other,int Mode, int Options, int Dim, int HDim>
+struct transform_left_product_impl<Other,Mode,Options,Dim,HDim, Dim,Dim>
+{
+ typedef Transform<typename Other::Scalar,Dim,Mode,Options> TransformType;
+ typedef typename TransformType::MatrixType MatrixType;
+ typedef TransformType ResultType;
+ static ResultType run(const Other& other, const TransformType& tr)
+ {
+ TransformType res;
+ if(Mode!=int(AffineCompact))
+ res.matrix().row(Dim) = tr.matrix().row(Dim);
+ res.matrix().template topRows<Dim>().noalias()
+ = other * tr.matrix().template topRows<Dim>();
+ return res;
+ }
+};
+
+/**********************************************************
+*** Specializations of operator* with another Transform ***
+**********************************************************/
+
+template<typename Scalar, int Dim, int LhsMode, int LhsOptions, int RhsMode, int RhsOptions>
+struct transform_transform_product_impl<Transform<Scalar,Dim,LhsMode,LhsOptions>,Transform<Scalar,Dim,RhsMode,RhsOptions>,false >
+{
+ enum { ResultMode = transform_product_result<LhsMode,RhsMode>::Mode };
+ typedef Transform<Scalar,Dim,LhsMode,LhsOptions> Lhs;
+ typedef Transform<Scalar,Dim,RhsMode,RhsOptions> Rhs;
+ typedef Transform<Scalar,Dim,ResultMode,LhsOptions> ResultType;
+ static ResultType run(const Lhs& lhs, const Rhs& rhs)
+ {
+ ResultType res;
+ res.linear() = lhs.linear() * rhs.linear();
+ res.translation() = lhs.linear() * rhs.translation() + lhs.translation();
+ res.makeAffine();
+ return res;
+ }
+};
+
+template<typename Scalar, int Dim, int LhsMode, int LhsOptions, int RhsMode, int RhsOptions>
+struct transform_transform_product_impl<Transform<Scalar,Dim,LhsMode,LhsOptions>,Transform<Scalar,Dim,RhsMode,RhsOptions>,true >
+{
+ typedef Transform<Scalar,Dim,LhsMode,LhsOptions> Lhs;
+ typedef Transform<Scalar,Dim,RhsMode,RhsOptions> Rhs;
+ typedef Transform<Scalar,Dim,Projective> ResultType;
+ static ResultType run(const Lhs& lhs, const Rhs& rhs)
+ {
+ return ResultType( lhs.matrix() * rhs.matrix() );
+ }
+};
+
+template<typename Scalar, int Dim, int LhsOptions, int RhsOptions>
+struct transform_transform_product_impl<Transform<Scalar,Dim,AffineCompact,LhsOptions>,Transform<Scalar,Dim,Projective,RhsOptions>,true >
+{
+ typedef Transform<Scalar,Dim,AffineCompact,LhsOptions> Lhs;
+ typedef Transform<Scalar,Dim,Projective,RhsOptions> Rhs;
+ typedef Transform<Scalar,Dim,Projective> ResultType;
+ static ResultType run(const Lhs& lhs, const Rhs& rhs)
+ {
+ ResultType res;
+ res.matrix().template topRows<Dim>() = lhs.matrix() * rhs.matrix();
+ res.matrix().row(Dim) = rhs.matrix().row(Dim);
+ return res;
+ }
+};
+
+template<typename Scalar, int Dim, int LhsOptions, int RhsOptions>
+struct transform_transform_product_impl<Transform<Scalar,Dim,Projective,LhsOptions>,Transform<Scalar,Dim,AffineCompact,RhsOptions>,true >
+{
+ typedef Transform<Scalar,Dim,Projective,LhsOptions> Lhs;
+ typedef Transform<Scalar,Dim,AffineCompact,RhsOptions> Rhs;
+ typedef Transform<Scalar,Dim,Projective> ResultType;
+ static ResultType run(const Lhs& lhs, const Rhs& rhs)
+ {
+ ResultType res(lhs.matrix().template leftCols<Dim>() * rhs.matrix());
+ res.matrix().col(Dim) += lhs.matrix().col(Dim);
+ return res;
+ }
+};
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_TRANSFORM_H
diff --git a/Eigen/src/Geometry/Translation.h b/Eigen/src/Geometry/Translation.h
new file mode 100644
index 0000000..dd0adba
--- /dev/null
+++ b/Eigen/src/Geometry/Translation.h
@@ -0,0 +1,204 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_TRANSLATION_H
+#define EIGEN_TRANSLATION_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+/** \geometry_module \ingroup Geometry_Module
+ *
+ * \class Translation
+ *
+ * \brief Represents a translation transformation
+ *
+ * \tparam Scalar_ the scalar type, i.e., the type of the coefficients.
+ * \tparam Dim_ the dimension of the space, can be a compile time value or Dynamic
+ *
+ * \note This class is not aimed to be used to store a translation transformation,
+ * but rather to make easier the constructions and updates of Transform objects.
+ *
+ * \sa class Scaling, class Transform
+ */
+template<typename Scalar_, int Dim_>
+class Translation
+{
+public:
+ EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE(Scalar_,Dim_)
+ /** dimension of the space */
+ enum { Dim = Dim_ };
+ /** the scalar type of the coefficients */
+ typedef Scalar_ Scalar;
+ /** corresponding vector type */
+ typedef Matrix<Scalar,Dim,1> VectorType;
+ /** corresponding linear transformation matrix type */
+ typedef Matrix<Scalar,Dim,Dim> LinearMatrixType;
+ /** corresponding affine transformation type */
+ typedef Transform<Scalar,Dim,Affine> AffineTransformType;
+ /** corresponding isometric transformation type */
+ typedef Transform<Scalar,Dim,Isometry> IsometryTransformType;
+
+protected:
+
+ VectorType m_coeffs;
+
+public:
+
+ /** Default constructor without initialization. */
+ EIGEN_DEVICE_FUNC Translation() {}
+ /** */
+ EIGEN_DEVICE_FUNC inline Translation(const Scalar& sx, const Scalar& sy)
+ {
+ eigen_assert(Dim==2);
+ m_coeffs.x() = sx;
+ m_coeffs.y() = sy;
+ }
+ /** */
+ EIGEN_DEVICE_FUNC inline Translation(const Scalar& sx, const Scalar& sy, const Scalar& sz)
+ {
+ eigen_assert(Dim==3);
+ m_coeffs.x() = sx;
+ m_coeffs.y() = sy;
+ m_coeffs.z() = sz;
+ }
+ /** Constructs and initialize the translation transformation from a vector of translation coefficients */
+ EIGEN_DEVICE_FUNC explicit inline Translation(const VectorType& vector) : m_coeffs(vector) {}
+
+ /** \brief Returns the x-translation by value. **/
+ EIGEN_DEVICE_FUNC inline Scalar x() const { return m_coeffs.x(); }
+ /** \brief Returns the y-translation by value. **/
+ EIGEN_DEVICE_FUNC inline Scalar y() const { return m_coeffs.y(); }
+ /** \brief Returns the z-translation by value. **/
+ EIGEN_DEVICE_FUNC inline Scalar z() const { return m_coeffs.z(); }
+
+ /** \brief Returns the x-translation as a reference. **/
+ EIGEN_DEVICE_FUNC inline Scalar& x() { return m_coeffs.x(); }
+ /** \brief Returns the y-translation as a reference. **/
+ EIGEN_DEVICE_FUNC inline Scalar& y() { return m_coeffs.y(); }
+ /** \brief Returns the z-translation as a reference. **/
+ EIGEN_DEVICE_FUNC inline Scalar& z() { return m_coeffs.z(); }
+
+ EIGEN_DEVICE_FUNC const VectorType& vector() const { return m_coeffs; }
+ EIGEN_DEVICE_FUNC VectorType& vector() { return m_coeffs; }
+
+ EIGEN_DEVICE_FUNC const VectorType& translation() const { return m_coeffs; }
+ EIGEN_DEVICE_FUNC VectorType& translation() { return m_coeffs; }
+
+ /** Concatenates two translation */
+ EIGEN_DEVICE_FUNC inline Translation operator* (const Translation& other) const
+ { return Translation(m_coeffs + other.m_coeffs); }
+
+ /** Concatenates a translation and a uniform scaling */
+ EIGEN_DEVICE_FUNC inline AffineTransformType operator* (const UniformScaling<Scalar>& other) const;
+
+ /** Concatenates a translation and a linear transformation */
+ template<typename OtherDerived>
+ EIGEN_DEVICE_FUNC inline AffineTransformType operator* (const EigenBase<OtherDerived>& linear) const;
+
+ /** Concatenates a translation and a rotation */
+ template<typename Derived>
+ EIGEN_DEVICE_FUNC inline IsometryTransformType operator*(const RotationBase<Derived,Dim>& r) const
+ { return *this * IsometryTransformType(r); }
+
+ /** \returns the concatenation of a linear transformation \a l with the translation \a t */
+ // its a nightmare to define a templated friend function outside its declaration
+ template<typename OtherDerived> friend
+ EIGEN_DEVICE_FUNC inline AffineTransformType operator*(const EigenBase<OtherDerived>& linear, const Translation& t)
+ {
+ AffineTransformType res;
+ res.matrix().setZero();
+ res.linear() = linear.derived();
+ res.translation() = linear.derived() * t.m_coeffs;
+ res.matrix().row(Dim).setZero();
+ res(Dim,Dim) = Scalar(1);
+ return res;
+ }
+
+ /** Concatenates a translation and a transformation */
+ template<int Mode, int Options>
+ EIGEN_DEVICE_FUNC inline Transform<Scalar,Dim,Mode> operator* (const Transform<Scalar,Dim,Mode,Options>& t) const
+ {
+ Transform<Scalar,Dim,Mode> res = t;
+ res.pretranslate(m_coeffs);
+ return res;
+ }
+
+ /** Applies translation to vector */
+ template<typename Derived>
+ inline std::enable_if_t<Derived::IsVectorAtCompileTime,VectorType>
+ operator* (const MatrixBase<Derived>& vec) const
+ { return m_coeffs + vec.derived(); }
+
+ /** \returns the inverse translation (opposite) */
+ Translation inverse() const { return Translation(-m_coeffs); }
+
+ static const Translation Identity() { return Translation(VectorType::Zero()); }
+
+ /** \returns \c *this with scalar type casted to \a NewScalarType
+ *
+ * Note that if \a NewScalarType is equal to the current scalar type of \c *this
+ * then this function smartly returns a const reference to \c *this.
+ */
+ template<typename NewScalarType>
+ EIGEN_DEVICE_FUNC inline typename internal::cast_return_type<Translation,Translation<NewScalarType,Dim> >::type cast() const
+ { return typename internal::cast_return_type<Translation,Translation<NewScalarType,Dim> >::type(*this); }
+
+ /** Copy constructor with scalar type conversion */
+ template<typename OtherScalarType>
+ EIGEN_DEVICE_FUNC inline explicit Translation(const Translation<OtherScalarType,Dim>& other)
+ { m_coeffs = other.vector().template cast<Scalar>(); }
+
+ /** \returns \c true if \c *this is approximately equal to \a other, within the precision
+ * determined by \a prec.
+ *
+ * \sa MatrixBase::isApprox() */
+ EIGEN_DEVICE_FUNC bool isApprox(const Translation& other, const typename NumTraits<Scalar>::Real& prec = NumTraits<Scalar>::dummy_precision()) const
+ { return m_coeffs.isApprox(other.m_coeffs, prec); }
+
+};
+
+/** \addtogroup Geometry_Module */
+//@{
+typedef Translation<float, 2> Translation2f;
+typedef Translation<double,2> Translation2d;
+typedef Translation<float, 3> Translation3f;
+typedef Translation<double,3> Translation3d;
+//@}
+
+template<typename Scalar, int Dim>
+EIGEN_DEVICE_FUNC inline typename Translation<Scalar,Dim>::AffineTransformType
+Translation<Scalar,Dim>::operator* (const UniformScaling<Scalar>& other) const
+{
+ AffineTransformType res;
+ res.matrix().setZero();
+ res.linear().diagonal().fill(other.factor());
+ res.translation() = m_coeffs;
+ res(Dim,Dim) = Scalar(1);
+ return res;
+}
+
+template<typename Scalar, int Dim>
+template<typename OtherDerived>
+EIGEN_DEVICE_FUNC inline typename Translation<Scalar,Dim>::AffineTransformType
+Translation<Scalar,Dim>::operator* (const EigenBase<OtherDerived>& linear) const
+{
+ AffineTransformType res;
+ res.matrix().setZero();
+ res.linear() = linear.derived();
+ res.translation() = m_coeffs;
+ res.matrix().row(Dim).setZero();
+ res(Dim,Dim) = Scalar(1);
+ return res;
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_TRANSLATION_H
diff --git a/Eigen/src/Geometry/Umeyama.h b/Eigen/src/Geometry/Umeyama.h
new file mode 100644
index 0000000..be0c1b1
--- /dev/null
+++ b/Eigen/src/Geometry/Umeyama.h
@@ -0,0 +1,170 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009 Hauke Heibel <hauke.heibel@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_UMEYAMA_H
+#define EIGEN_UMEYAMA_H
+
+// This file requires the user to include
+// * Eigen/Core
+// * Eigen/LU
+// * Eigen/SVD
+// * Eigen/Array
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+#ifndef EIGEN_PARSED_BY_DOXYGEN
+
+// These helpers are required since it allows to use mixed types as parameters
+// for the Umeyama. The problem with mixed parameters is that the return type
+// cannot trivially be deduced when float and double types are mixed.
+namespace internal {
+
+// Compile time return type deduction for different MatrixBase types.
+// Different means here different alignment and parameters but the same underlying
+// real scalar type.
+template<typename MatrixType, typename OtherMatrixType>
+struct umeyama_transform_matrix_type
+{
+ enum {
+ MinRowsAtCompileTime = internal::min_size_prefer_dynamic(MatrixType::RowsAtCompileTime, OtherMatrixType::RowsAtCompileTime),
+
+ // When possible we want to choose some small fixed size value since the result
+ // is likely to fit on the stack. So here, min_size_prefer_dynamic is not what we want.
+ HomogeneousDimension = int(MinRowsAtCompileTime) == Dynamic ? Dynamic : int(MinRowsAtCompileTime)+1
+ };
+
+ typedef Matrix<typename traits<MatrixType>::Scalar,
+ HomogeneousDimension,
+ HomogeneousDimension,
+ AutoAlign | (traits<MatrixType>::Flags & RowMajorBit ? RowMajor : ColMajor),
+ HomogeneousDimension,
+ HomogeneousDimension
+ > type;
+};
+
+}
+
+#endif
+
+/**
+* \geometry_module \ingroup Geometry_Module
+*
+* \brief Returns the transformation between two point sets.
+*
+* The algorithm is based on:
+* "Least-squares estimation of transformation parameters between two point patterns",
+* Shinji Umeyama, PAMI 1991, DOI: 10.1109/34.88573
+*
+* It estimates parameters \f$ c, \mathbf{R}, \f$ and \f$ \mathbf{t} \f$ such that
+* \f{align*}
+* \frac{1}{n} \sum_{i=1}^n \vert\vert y_i - (c\mathbf{R}x_i + \mathbf{t}) \vert\vert_2^2
+* \f}
+* is minimized.
+*
+* The algorithm is based on the analysis of the covariance matrix
+* \f$ \Sigma_{\mathbf{x}\mathbf{y}} \in \mathbb{R}^{d \times d} \f$
+* of the input point sets \f$ \mathbf{x} \f$ and \f$ \mathbf{y} \f$ where
+* \f$d\f$ is corresponding to the dimension (which is typically small).
+* The analysis is involving the SVD having a complexity of \f$O(d^3)\f$
+* though the actual computational effort lies in the covariance
+* matrix computation which has an asymptotic lower bound of \f$O(dm)\f$ when
+* the input point sets have dimension \f$d \times m\f$.
+*
+* Currently the method is working only for floating point matrices.
+*
+* \todo Should the return type of umeyama() become a Transform?
+*
+* \param src Source points \f$ \mathbf{x} = \left( x_1, \hdots, x_n \right) \f$.
+* \param dst Destination points \f$ \mathbf{y} = \left( y_1, \hdots, y_n \right) \f$.
+* \param with_scaling Sets \f$ c=1 \f$ when <code>false</code> is passed.
+* \return The homogeneous transformation
+* \f{align*}
+* T = \begin{bmatrix} c\mathbf{R} & \mathbf{t} \\ \mathbf{0} & 1 \end{bmatrix}
+* \f}
+* minimizing the residual above. This transformation is always returned as an
+* Eigen::Matrix.
+*/
+template <typename Derived, typename OtherDerived>
+typename internal::umeyama_transform_matrix_type<Derived, OtherDerived>::type
+umeyama(const MatrixBase<Derived>& src, const MatrixBase<OtherDerived>& dst, bool with_scaling = true)
+{
+ typedef typename internal::umeyama_transform_matrix_type<Derived, OtherDerived>::type TransformationMatrixType;
+ typedef typename internal::traits<TransformationMatrixType>::Scalar Scalar;
+ typedef typename NumTraits<Scalar>::Real RealScalar;
+
+ EIGEN_STATIC_ASSERT(!NumTraits<Scalar>::IsComplex, NUMERIC_TYPE_MUST_BE_REAL)
+ EIGEN_STATIC_ASSERT((internal::is_same<Scalar, typename internal::traits<OtherDerived>::Scalar>::value),
+ YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY)
+
+ enum { Dimension = internal::min_size_prefer_dynamic(Derived::RowsAtCompileTime, OtherDerived::RowsAtCompileTime) };
+
+ typedef Matrix<Scalar, Dimension, 1> VectorType;
+ typedef Matrix<Scalar, Dimension, Dimension> MatrixType;
+ typedef typename internal::plain_matrix_type_row_major<Derived>::type RowMajorMatrixType;
+
+ const Index m = src.rows(); // dimension
+ const Index n = src.cols(); // number of measurements
+
+ // required for demeaning ...
+ const RealScalar one_over_n = RealScalar(1) / static_cast<RealScalar>(n);
+
+ // computation of mean
+ const VectorType src_mean = src.rowwise().sum() * one_over_n;
+ const VectorType dst_mean = dst.rowwise().sum() * one_over_n;
+
+ // demeaning of src and dst points
+ const RowMajorMatrixType src_demean = src.colwise() - src_mean;
+ const RowMajorMatrixType dst_demean = dst.colwise() - dst_mean;
+
+ // Eq. (38)
+ const MatrixType sigma = one_over_n * dst_demean * src_demean.transpose();
+
+ JacobiSVD<MatrixType, ComputeFullU | ComputeFullV> svd(sigma);
+
+ // Initialize the resulting transformation with an identity matrix...
+ TransformationMatrixType Rt = TransformationMatrixType::Identity(m+1,m+1);
+
+ // Eq. (39)
+ VectorType S = VectorType::Ones(m);
+
+ if ( svd.matrixU().determinant() * svd.matrixV().determinant() < 0 ) {
+ Index tmp = m - 1;
+ S(tmp) = -1;
+ }
+
+ // Eq. (40) and (43)
+ Rt.block(0,0,m,m).noalias() = svd.matrixU() * S.asDiagonal() * svd.matrixV().transpose();
+
+ if (with_scaling)
+ {
+ // Eq. (36)-(37)
+ const Scalar src_var = src_demean.rowwise().squaredNorm().sum() * one_over_n;
+
+ // Eq. (42)
+ const Scalar c = Scalar(1)/src_var * svd.singularValues().dot(S);
+
+ // Eq. (41)
+ Rt.col(m).head(m) = dst_mean;
+ Rt.col(m).head(m).noalias() -= c*Rt.topLeftCorner(m,m)*src_mean;
+ Rt.block(0,0,m,m) *= c;
+ }
+ else
+ {
+ Rt.col(m).head(m) = dst_mean;
+ Rt.col(m).head(m).noalias() -= Rt.topLeftCorner(m,m)*src_mean;
+ }
+
+ return Rt;
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_UMEYAMA_H
diff --git a/Eigen/src/Geometry/arch/Geometry_SIMD.h b/Eigen/src/Geometry/arch/Geometry_SIMD.h
new file mode 100644
index 0000000..bd91949
--- /dev/null
+++ b/Eigen/src/Geometry/arch/Geometry_SIMD.h
@@ -0,0 +1,170 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009 Rohit Garg <rpg.314@gmail.com>
+// Copyright (C) 2009-2010 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_GEOMETRY_SIMD_H
+#define EIGEN_GEOMETRY_SIMD_H
+
+#include "../InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+
+template<class Derived, class OtherDerived>
+struct quat_product<Architecture::Target, Derived, OtherDerived, float>
+{
+ enum {
+ AAlignment = traits<Derived>::Alignment,
+ BAlignment = traits<OtherDerived>::Alignment,
+ ResAlignment = traits<Quaternion<float> >::Alignment
+ };
+ static inline Quaternion<float> run(const QuaternionBase<Derived>& _a, const QuaternionBase<OtherDerived>& _b)
+ {
+ evaluator<typename Derived::Coefficients> ae(_a.coeffs());
+ evaluator<typename OtherDerived::Coefficients> be(_b.coeffs());
+ Quaternion<float> res;
+ const float neg_zero = numext::bit_cast<float>(0x80000000u);
+ const float arr[4] = {0.f, 0.f, 0.f, neg_zero};
+ const Packet4f mask = ploadu<Packet4f>(arr);
+ Packet4f a = ae.template packet<AAlignment,Packet4f>(0);
+ Packet4f b = be.template packet<BAlignment,Packet4f>(0);
+ Packet4f s1 = pmul(vec4f_swizzle1(a,1,2,0,2),vec4f_swizzle1(b,2,0,1,2));
+ Packet4f s2 = pmul(vec4f_swizzle1(a,3,3,3,1),vec4f_swizzle1(b,0,1,2,1));
+ pstoret<float,Packet4f,ResAlignment>(
+ &res.x(),
+ padd(psub(pmul(a,vec4f_swizzle1(b,3,3,3,3)),
+ pmul(vec4f_swizzle1(a,2,0,1,0),
+ vec4f_swizzle1(b,1,2,0,0))),
+ pxor(mask,padd(s1,s2))));
+
+ return res;
+ }
+};
+
+template<class Derived>
+struct quat_conj<Architecture::Target, Derived, float>
+{
+ enum {
+ ResAlignment = traits<Quaternion<float> >::Alignment
+ };
+ static inline Quaternion<float> run(const QuaternionBase<Derived>& q)
+ {
+ evaluator<typename Derived::Coefficients> qe(q.coeffs());
+ Quaternion<float> res;
+ const float neg_zero = numext::bit_cast<float>(0x80000000u);
+ const float arr[4] = {neg_zero, neg_zero, neg_zero,0.f};
+ const Packet4f mask = ploadu<Packet4f>(arr);
+ pstoret<float,Packet4f,ResAlignment>(&res.x(), pxor(mask, qe.template packet<traits<Derived>::Alignment,Packet4f>(0)));
+ return res;
+ }
+};
+
+
+template<typename VectorLhs,typename VectorRhs>
+struct cross3_impl<Architecture::Target,VectorLhs,VectorRhs,float,true>
+{
+ enum {
+ ResAlignment = traits<typename plain_matrix_type<VectorLhs>::type>::Alignment
+ };
+ static inline typename plain_matrix_type<VectorLhs>::type
+ run(const VectorLhs& lhs, const VectorRhs& rhs)
+ {
+ evaluator<VectorLhs> lhs_eval(lhs);
+ evaluator<VectorRhs> rhs_eval(rhs);
+ Packet4f a = lhs_eval.template packet<traits<VectorLhs>::Alignment,Packet4f>(0);
+ Packet4f b = rhs_eval.template packet<traits<VectorRhs>::Alignment,Packet4f>(0);
+ Packet4f mul1 = pmul(vec4f_swizzle1(a,1,2,0,3),vec4f_swizzle1(b,2,0,1,3));
+ Packet4f mul2 = pmul(vec4f_swizzle1(a,2,0,1,3),vec4f_swizzle1(b,1,2,0,3));
+ typename plain_matrix_type<VectorLhs>::type res;
+ pstoret<float,Packet4f,ResAlignment>(&res.x(),psub(mul1,mul2));
+ return res;
+ }
+};
+
+
+
+#if (defined EIGEN_VECTORIZE_SSE) || (EIGEN_ARCH_ARM64)
+
+template<class Derived, class OtherDerived>
+struct quat_product<Architecture::Target, Derived, OtherDerived, double>
+{
+ enum {
+ BAlignment = traits<OtherDerived>::Alignment,
+ ResAlignment = traits<Quaternion<double> >::Alignment
+ };
+
+ static inline Quaternion<double> run(const QuaternionBase<Derived>& _a, const QuaternionBase<OtherDerived>& _b)
+ {
+ Quaternion<double> res;
+
+ evaluator<typename Derived::Coefficients> ae(_a.coeffs());
+ evaluator<typename OtherDerived::Coefficients> be(_b.coeffs());
+
+ const double* a = _a.coeffs().data();
+ Packet2d b_xy = be.template packet<BAlignment,Packet2d>(0);
+ Packet2d b_zw = be.template packet<BAlignment,Packet2d>(2);
+ Packet2d a_xx = pset1<Packet2d>(a[0]);
+ Packet2d a_yy = pset1<Packet2d>(a[1]);
+ Packet2d a_zz = pset1<Packet2d>(a[2]);
+ Packet2d a_ww = pset1<Packet2d>(a[3]);
+
+ // two temporaries:
+ Packet2d t1, t2;
+
+ /*
+ * t1 = ww*xy + yy*zw
+ * t2 = zz*xy - xx*zw
+ * res.xy = t1 +/- swap(t2)
+ */
+ t1 = padd(pmul(a_ww, b_xy), pmul(a_yy, b_zw));
+ t2 = psub(pmul(a_zz, b_xy), pmul(a_xx, b_zw));
+ pstoret<double,Packet2d,ResAlignment>(&res.x(), paddsub(t1, preverse(t2)));
+
+ /*
+ * t1 = ww*zw - yy*xy
+ * t2 = zz*zw + xx*xy
+ * res.zw = t1 -/+ swap(t2) = swap( swap(t1) +/- t2)
+ */
+ t1 = psub(pmul(a_ww, b_zw), pmul(a_yy, b_xy));
+ t2 = padd(pmul(a_zz, b_zw), pmul(a_xx, b_xy));
+ pstoret<double,Packet2d,ResAlignment>(&res.z(), preverse(paddsub(preverse(t1), t2)));
+
+ return res;
+}
+};
+
+template<class Derived>
+struct quat_conj<Architecture::Target, Derived, double>
+{
+ enum {
+ ResAlignment = traits<Quaternion<double> >::Alignment
+ };
+ static inline Quaternion<double> run(const QuaternionBase<Derived>& q)
+ {
+ evaluator<typename Derived::Coefficients> qe(q.coeffs());
+ Quaternion<double> res;
+ const double neg_zero = numext::bit_cast<double>(0x8000000000000000ull);
+ const double arr1[2] = {neg_zero, neg_zero};
+ const double arr2[2] = {neg_zero, 0.0};
+ const Packet2d mask0 = ploadu<Packet2d>(arr1);
+ const Packet2d mask2 = ploadu<Packet2d>(arr2);
+ pstoret<double,Packet2d,ResAlignment>(&res.x(), pxor(mask0, qe.template packet<traits<Derived>::Alignment,Packet2d>(0)));
+ pstoret<double,Packet2d,ResAlignment>(&res.z(), pxor(mask2, qe.template packet<traits<Derived>::Alignment,Packet2d>(2)));
+ return res;
+ }
+};
+
+#endif // end EIGEN_VECTORIZE_SSE_OR_EIGEN_ARCH_ARM64
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_GEOMETRY_SIMD_H
diff --git a/Eigen/src/Householder/BlockHouseholder.h b/Eigen/src/Householder/BlockHouseholder.h
new file mode 100644
index 0000000..a5c8095
--- /dev/null
+++ b/Eigen/src/Householder/BlockHouseholder.h
@@ -0,0 +1,112 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2010 Vincent Lejeune
+// Copyright (C) 2010 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_BLOCK_HOUSEHOLDER_H
+#define EIGEN_BLOCK_HOUSEHOLDER_H
+
+// This file contains some helper function to deal with block householder reflectors
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+
+/** \internal */
+// template<typename TriangularFactorType,typename VectorsType,typename CoeffsType>
+// void make_block_householder_triangular_factor(TriangularFactorType& triFactor, const VectorsType& vectors, const CoeffsType& hCoeffs)
+// {
+// typedef typename VectorsType::Scalar Scalar;
+// const Index nbVecs = vectors.cols();
+// eigen_assert(triFactor.rows() == nbVecs && triFactor.cols() == nbVecs && vectors.rows()>=nbVecs);
+//
+// for(Index i = 0; i < nbVecs; i++)
+// {
+// Index rs = vectors.rows() - i;
+// // Warning, note that hCoeffs may alias with vectors.
+// // It is then necessary to copy it before modifying vectors(i,i).
+// typename CoeffsType::Scalar h = hCoeffs(i);
+// // This hack permits to pass trough nested Block<> and Transpose<> expressions.
+// Scalar *Vii_ptr = const_cast<Scalar*>(vectors.data() + vectors.outerStride()*i + vectors.innerStride()*i);
+// Scalar Vii = *Vii_ptr;
+// *Vii_ptr = Scalar(1);
+// triFactor.col(i).head(i).noalias() = -h * vectors.block(i, 0, rs, i).adjoint()
+// * vectors.col(i).tail(rs);
+// *Vii_ptr = Vii;
+// // FIXME add .noalias() once the triangular product can work inplace
+// triFactor.col(i).head(i) = triFactor.block(0,0,i,i).template triangularView<Upper>()
+// * triFactor.col(i).head(i);
+// triFactor(i,i) = hCoeffs(i);
+// }
+// }
+
+/** \internal */
+// This variant avoid modifications in vectors
+template<typename TriangularFactorType,typename VectorsType,typename CoeffsType>
+void make_block_householder_triangular_factor(TriangularFactorType& triFactor, const VectorsType& vectors, const CoeffsType& hCoeffs)
+{
+ const Index nbVecs = vectors.cols();
+ eigen_assert(triFactor.rows() == nbVecs && triFactor.cols() == nbVecs && vectors.rows()>=nbVecs);
+
+ for(Index i = nbVecs-1; i >=0 ; --i)
+ {
+ Index rs = vectors.rows() - i - 1;
+ Index rt = nbVecs-i-1;
+
+ if(rt>0)
+ {
+ triFactor.row(i).tail(rt).noalias() = -hCoeffs(i) * vectors.col(i).tail(rs).adjoint()
+ * vectors.bottomRightCorner(rs, rt).template triangularView<UnitLower>();
+
+ // FIXME use the following line with .noalias() once the triangular product can work inplace
+ // triFactor.row(i).tail(rt) = triFactor.row(i).tail(rt) * triFactor.bottomRightCorner(rt,rt).template triangularView<Upper>();
+ for(Index j=nbVecs-1; j>i; --j)
+ {
+ typename TriangularFactorType::Scalar z = triFactor(i,j);
+ triFactor(i,j) = z * triFactor(j,j);
+ if(nbVecs-j-1>0)
+ triFactor.row(i).tail(nbVecs-j-1) += z * triFactor.row(j).tail(nbVecs-j-1);
+ }
+
+ }
+ triFactor(i,i) = hCoeffs(i);
+ }
+}
+
+/** \internal
+ * if forward then perform mat = H0 * H1 * H2 * mat
+ * otherwise perform mat = H2 * H1 * H0 * mat
+ */
+template<typename MatrixType,typename VectorsType,typename CoeffsType>
+void apply_block_householder_on_the_left(MatrixType& mat, const VectorsType& vectors, const CoeffsType& hCoeffs, bool forward)
+{
+ enum { TFactorSize = VectorsType::ColsAtCompileTime };
+ Index nbVecs = vectors.cols();
+ Matrix<typename MatrixType::Scalar, TFactorSize, TFactorSize, RowMajor> T(nbVecs,nbVecs);
+
+ if(forward) make_block_householder_triangular_factor(T, vectors, hCoeffs);
+ else make_block_householder_triangular_factor(T, vectors, hCoeffs.conjugate());
+ const TriangularView<const VectorsType, UnitLower> V(vectors);
+
+ // A -= V T V^* A
+ Matrix<typename MatrixType::Scalar,VectorsType::ColsAtCompileTime,MatrixType::ColsAtCompileTime,
+ (VectorsType::MaxColsAtCompileTime==1 && MatrixType::MaxColsAtCompileTime!=1)?RowMajor:ColMajor,
+ VectorsType::MaxColsAtCompileTime,MatrixType::MaxColsAtCompileTime> tmp = V.adjoint() * mat;
+ // FIXME add .noalias() once the triangular product can work inplace
+ if(forward) tmp = T.template triangularView<Upper>() * tmp;
+ else tmp = T.template triangularView<Upper>().adjoint() * tmp;
+ mat.noalias() -= V * tmp;
+}
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_BLOCK_HOUSEHOLDER_H
diff --git a/Eigen/src/Householder/Householder.h b/Eigen/src/Householder/Householder.h
new file mode 100644
index 0000000..855b752
--- /dev/null
+++ b/Eigen/src/Householder/Householder.h
@@ -0,0 +1,178 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2010 Benoit Jacob <jacob.benoit.1@gmail.com>
+// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_HOUSEHOLDER_H
+#define EIGEN_HOUSEHOLDER_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+template<int n> struct decrement_size
+{
+ enum {
+ ret = n==Dynamic ? n : n-1
+ };
+};
+}
+
+/** Computes the elementary reflector H such that:
+ * \f$ H *this = [ beta 0 ... 0]^T \f$
+ * where the transformation H is:
+ * \f$ H = I - tau v v^*\f$
+ * and the vector v is:
+ * \f$ v^T = [1 essential^T] \f$
+ *
+ * The essential part of the vector \c v is stored in *this.
+ *
+ * On output:
+ * \param tau the scaling factor of the Householder transformation
+ * \param beta the result of H * \c *this
+ *
+ * \sa MatrixBase::makeHouseholder(), MatrixBase::applyHouseholderOnTheLeft(),
+ * MatrixBase::applyHouseholderOnTheRight()
+ */
+template<typename Derived>
+EIGEN_DEVICE_FUNC
+void MatrixBase<Derived>::makeHouseholderInPlace(Scalar& tau, RealScalar& beta)
+{
+ VectorBlock<Derived, internal::decrement_size<Base::SizeAtCompileTime>::ret> essentialPart(derived(), 1, size()-1);
+ makeHouseholder(essentialPart, tau, beta);
+}
+
+/** Computes the elementary reflector H such that:
+ * \f$ H *this = [ beta 0 ... 0]^T \f$
+ * where the transformation H is:
+ * \f$ H = I - tau v v^*\f$
+ * and the vector v is:
+ * \f$ v^T = [1 essential^T] \f$
+ *
+ * On output:
+ * \param essential the essential part of the vector \c v
+ * \param tau the scaling factor of the Householder transformation
+ * \param beta the result of H * \c *this
+ *
+ * \sa MatrixBase::makeHouseholderInPlace(), MatrixBase::applyHouseholderOnTheLeft(),
+ * MatrixBase::applyHouseholderOnTheRight()
+ */
+template<typename Derived>
+template<typename EssentialPart>
+EIGEN_DEVICE_FUNC
+void MatrixBase<Derived>::makeHouseholder(
+ EssentialPart& essential,
+ Scalar& tau,
+ RealScalar& beta) const
+{
+ using numext::sqrt;
+ using numext::conj;
+
+ EIGEN_STATIC_ASSERT_VECTOR_ONLY(EssentialPart)
+ VectorBlock<const Derived, EssentialPart::SizeAtCompileTime> tail(derived(), 1, size()-1);
+
+ RealScalar tailSqNorm = size()==1 ? RealScalar(0) : tail.squaredNorm();
+ Scalar c0 = coeff(0);
+ const RealScalar tol = (std::numeric_limits<RealScalar>::min)();
+
+ if(tailSqNorm <= tol && numext::abs2(numext::imag(c0))<=tol)
+ {
+ tau = RealScalar(0);
+ beta = numext::real(c0);
+ essential.setZero();
+ }
+ else
+ {
+ beta = sqrt(numext::abs2(c0) + tailSqNorm);
+ if (numext::real(c0)>=RealScalar(0))
+ beta = -beta;
+ essential = tail / (c0 - beta);
+ tau = conj((beta - c0) / beta);
+ }
+}
+
+/** Apply the elementary reflector H given by
+ * \f$ H = I - tau v v^*\f$
+ * with
+ * \f$ v^T = [1 essential^T] \f$
+ * from the left to a vector or matrix.
+ *
+ * On input:
+ * \param essential the essential part of the vector \c v
+ * \param tau the scaling factor of the Householder transformation
+ * \param workspace a pointer to working space with at least
+ * this->cols() entries
+ *
+ * \sa MatrixBase::makeHouseholder(), MatrixBase::makeHouseholderInPlace(),
+ * MatrixBase::applyHouseholderOnTheRight()
+ */
+template<typename Derived>
+template<typename EssentialPart>
+EIGEN_DEVICE_FUNC
+void MatrixBase<Derived>::applyHouseholderOnTheLeft(
+ const EssentialPart& essential,
+ const Scalar& tau,
+ Scalar* workspace)
+{
+ if(rows() == 1)
+ {
+ *this *= Scalar(1)-tau;
+ }
+ else if(!numext::is_exactly_zero(tau))
+ {
+ Map<typename internal::plain_row_type<PlainObject>::type> tmp(workspace,cols());
+ Block<Derived, EssentialPart::SizeAtCompileTime, Derived::ColsAtCompileTime> bottom(derived(), 1, 0, rows()-1, cols());
+ tmp.noalias() = essential.adjoint() * bottom;
+ tmp += this->row(0);
+ this->row(0) -= tau * tmp;
+ bottom.noalias() -= tau * essential * tmp;
+ }
+}
+
+/** Apply the elementary reflector H given by
+ * \f$ H = I - tau v v^*\f$
+ * with
+ * \f$ v^T = [1 essential^T] \f$
+ * from the right to a vector or matrix.
+ *
+ * On input:
+ * \param essential the essential part of the vector \c v
+ * \param tau the scaling factor of the Householder transformation
+ * \param workspace a pointer to working space with at least
+ * this->rows() entries
+ *
+ * \sa MatrixBase::makeHouseholder(), MatrixBase::makeHouseholderInPlace(),
+ * MatrixBase::applyHouseholderOnTheLeft()
+ */
+template<typename Derived>
+template<typename EssentialPart>
+EIGEN_DEVICE_FUNC
+void MatrixBase<Derived>::applyHouseholderOnTheRight(
+ const EssentialPart& essential,
+ const Scalar& tau,
+ Scalar* workspace)
+{
+ if(cols() == 1)
+ {
+ *this *= Scalar(1)-tau;
+ }
+ else if(!numext::is_exactly_zero(tau))
+ {
+ Map<typename internal::plain_col_type<PlainObject>::type> tmp(workspace,rows());
+ Block<Derived, Derived::RowsAtCompileTime, EssentialPart::SizeAtCompileTime> right(derived(), 0, 1, rows(), cols()-1);
+ tmp.noalias() = right * essential;
+ tmp += this->col(0);
+ this->col(0) -= tau * tmp;
+ right.noalias() -= tau * tmp * essential.adjoint();
+ }
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_HOUSEHOLDER_H
diff --git a/Eigen/src/Householder/HouseholderSequence.h b/Eigen/src/Householder/HouseholderSequence.h
new file mode 100644
index 0000000..41fef64
--- /dev/null
+++ b/Eigen/src/Householder/HouseholderSequence.h
@@ -0,0 +1,560 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2010 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_HOUSEHOLDER_SEQUENCE_H
+#define EIGEN_HOUSEHOLDER_SEQUENCE_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+/** \ingroup Householder_Module
+ * \householder_module
+ * \class HouseholderSequence
+ * \brief Sequence of Householder reflections acting on subspaces with decreasing size
+ * \tparam VectorsType type of matrix containing the Householder vectors
+ * \tparam CoeffsType type of vector containing the Householder coefficients
+ * \tparam Side either OnTheLeft (the default) or OnTheRight
+ *
+ * This class represents a product sequence of Householder reflections where the first Householder reflection
+ * acts on the whole space, the second Householder reflection leaves the one-dimensional subspace spanned by
+ * the first unit vector invariant, the third Householder reflection leaves the two-dimensional subspace
+ * spanned by the first two unit vectors invariant, and so on up to the last reflection which leaves all but
+ * one dimensions invariant and acts only on the last dimension. Such sequences of Householder reflections
+ * are used in several algorithms to zero out certain parts of a matrix. Indeed, the methods
+ * HessenbergDecomposition::matrixQ(), Tridiagonalization::matrixQ(), HouseholderQR::householderQ(),
+ * and ColPivHouseholderQR::householderQ() all return a %HouseholderSequence.
+ *
+ * More precisely, the class %HouseholderSequence represents an \f$ n \times n \f$ matrix \f$ H \f$ of the
+ * form \f$ H = \prod_{i=0}^{n-1} H_i \f$ where the i-th Householder reflection is \f$ H_i = I - h_i v_i
+ * v_i^* \f$. The i-th Householder coefficient \f$ h_i \f$ is a scalar and the i-th Householder vector \f$
+ * v_i \f$ is a vector of the form
+ * \f[
+ * v_i = [\underbrace{0, \ldots, 0}_{i-1\mbox{ zeros}}, 1, \underbrace{*, \ldots,*}_{n-i\mbox{ arbitrary entries}} ].
+ * \f]
+ * The last \f$ n-i \f$ entries of \f$ v_i \f$ are called the essential part of the Householder vector.
+ *
+ * Typical usages are listed below, where H is a HouseholderSequence:
+ * \code
+ * A.applyOnTheRight(H); // A = A * H
+ * A.applyOnTheLeft(H); // A = H * A
+ * A.applyOnTheRight(H.adjoint()); // A = A * H^*
+ * A.applyOnTheLeft(H.adjoint()); // A = H^* * A
+ * MatrixXd Q = H; // conversion to a dense matrix
+ * \endcode
+ * In addition to the adjoint, you can also apply the inverse (=adjoint), the transpose, and the conjugate operators.
+ *
+ * See the documentation for HouseholderSequence(const VectorsType&, const CoeffsType&) for an example.
+ *
+ * \sa MatrixBase::applyOnTheLeft(), MatrixBase::applyOnTheRight()
+ */
+
+namespace internal {
+
+template<typename VectorsType, typename CoeffsType, int Side>
+struct traits<HouseholderSequence<VectorsType,CoeffsType,Side> >
+{
+ typedef typename VectorsType::Scalar Scalar;
+ typedef typename VectorsType::StorageIndex StorageIndex;
+ typedef typename VectorsType::StorageKind StorageKind;
+ enum {
+ RowsAtCompileTime = Side==OnTheLeft ? traits<VectorsType>::RowsAtCompileTime
+ : traits<VectorsType>::ColsAtCompileTime,
+ ColsAtCompileTime = RowsAtCompileTime,
+ MaxRowsAtCompileTime = Side==OnTheLeft ? traits<VectorsType>::MaxRowsAtCompileTime
+ : traits<VectorsType>::MaxColsAtCompileTime,
+ MaxColsAtCompileTime = MaxRowsAtCompileTime,
+ Flags = 0
+ };
+};
+
+struct HouseholderSequenceShape {};
+
+template<typename VectorsType, typename CoeffsType, int Side>
+struct evaluator_traits<HouseholderSequence<VectorsType,CoeffsType,Side> >
+ : public evaluator_traits_base<HouseholderSequence<VectorsType,CoeffsType,Side> >
+{
+ typedef HouseholderSequenceShape Shape;
+};
+
+template<typename VectorsType, typename CoeffsType, int Side>
+struct hseq_side_dependent_impl
+{
+ typedef Block<const VectorsType, Dynamic, 1> EssentialVectorType;
+ typedef HouseholderSequence<VectorsType, CoeffsType, OnTheLeft> HouseholderSequenceType;
+ static EIGEN_DEVICE_FUNC inline const EssentialVectorType essentialVector(const HouseholderSequenceType& h, Index k)
+ {
+ Index start = k+1+h.m_shift;
+ return Block<const VectorsType,Dynamic,1>(h.m_vectors, start, k, h.rows()-start, 1);
+ }
+};
+
+template<typename VectorsType, typename CoeffsType>
+struct hseq_side_dependent_impl<VectorsType, CoeffsType, OnTheRight>
+{
+ typedef Transpose<Block<const VectorsType, 1, Dynamic> > EssentialVectorType;
+ typedef HouseholderSequence<VectorsType, CoeffsType, OnTheRight> HouseholderSequenceType;
+ static inline const EssentialVectorType essentialVector(const HouseholderSequenceType& h, Index k)
+ {
+ Index start = k+1+h.m_shift;
+ return Block<const VectorsType,1,Dynamic>(h.m_vectors, k, start, 1, h.rows()-start).transpose();
+ }
+};
+
+template<typename OtherScalarType, typename MatrixType> struct matrix_type_times_scalar_type
+{
+ typedef typename ScalarBinaryOpTraits<OtherScalarType, typename MatrixType::Scalar>::ReturnType
+ ResultScalar;
+ typedef Matrix<ResultScalar, MatrixType::RowsAtCompileTime, MatrixType::ColsAtCompileTime,
+ 0, MatrixType::MaxRowsAtCompileTime, MatrixType::MaxColsAtCompileTime> Type;
+};
+
+} // end namespace internal
+
+template<typename VectorsType, typename CoeffsType, int Side> class HouseholderSequence
+ : public EigenBase<HouseholderSequence<VectorsType,CoeffsType,Side> >
+{
+ typedef typename internal::hseq_side_dependent_impl<VectorsType,CoeffsType,Side>::EssentialVectorType EssentialVectorType;
+
+ public:
+ enum {
+ RowsAtCompileTime = internal::traits<HouseholderSequence>::RowsAtCompileTime,
+ ColsAtCompileTime = internal::traits<HouseholderSequence>::ColsAtCompileTime,
+ MaxRowsAtCompileTime = internal::traits<HouseholderSequence>::MaxRowsAtCompileTime,
+ MaxColsAtCompileTime = internal::traits<HouseholderSequence>::MaxColsAtCompileTime
+ };
+ typedef typename internal::traits<HouseholderSequence>::Scalar Scalar;
+
+ typedef HouseholderSequence<
+ std::conditional_t<NumTraits<Scalar>::IsComplex,
+ internal::remove_all_t<typename VectorsType::ConjugateReturnType>,
+ VectorsType>,
+ std::conditional_t<NumTraits<Scalar>::IsComplex,
+ internal::remove_all_t<typename CoeffsType::ConjugateReturnType>,
+ CoeffsType>,
+ Side
+ > ConjugateReturnType;
+
+ typedef HouseholderSequence<
+ VectorsType,
+ std::conditional_t<NumTraits<Scalar>::IsComplex,
+ internal::remove_all_t<typename CoeffsType::ConjugateReturnType>,
+ CoeffsType>,
+ Side
+ > AdjointReturnType;
+
+ typedef HouseholderSequence<
+ std::conditional_t<NumTraits<Scalar>::IsComplex,
+ internal::remove_all_t<typename VectorsType::ConjugateReturnType>,
+ VectorsType>,
+ CoeffsType,
+ Side
+ > TransposeReturnType;
+
+ typedef HouseholderSequence<
+ std::add_const_t<VectorsType>,
+ std::add_const_t<CoeffsType>,
+ Side
+ > ConstHouseholderSequence;
+
+ /** \brief Constructor.
+ * \param[in] v %Matrix containing the essential parts of the Householder vectors
+ * \param[in] h Vector containing the Householder coefficients
+ *
+ * Constructs the Householder sequence with coefficients given by \p h and vectors given by \p v. The
+ * i-th Householder coefficient \f$ h_i \f$ is given by \p h(i) and the essential part of the i-th
+ * Householder vector \f$ v_i \f$ is given by \p v(k,i) with \p k > \p i (the subdiagonal part of the
+ * i-th column). If \p v has fewer columns than rows, then the Householder sequence contains as many
+ * Householder reflections as there are columns.
+ *
+ * \note The %HouseholderSequence object stores \p v and \p h by reference.
+ *
+ * Example: \include HouseholderSequence_HouseholderSequence.cpp
+ * Output: \verbinclude HouseholderSequence_HouseholderSequence.out
+ *
+ * \sa setLength(), setShift()
+ */
+ EIGEN_DEVICE_FUNC
+ HouseholderSequence(const VectorsType& v, const CoeffsType& h)
+ : m_vectors(v), m_coeffs(h), m_reverse(false), m_length(v.diagonalSize()),
+ m_shift(0)
+ {
+ }
+
+ /** \brief Copy constructor. */
+ EIGEN_DEVICE_FUNC
+ HouseholderSequence(const HouseholderSequence& other)
+ : m_vectors(other.m_vectors),
+ m_coeffs(other.m_coeffs),
+ m_reverse(other.m_reverse),
+ m_length(other.m_length),
+ m_shift(other.m_shift)
+ {
+ }
+
+ /** \brief Number of rows of transformation viewed as a matrix.
+ * \returns Number of rows
+ * \details This equals the dimension of the space that the transformation acts on.
+ */
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
+ Index rows() const EIGEN_NOEXCEPT { return Side==OnTheLeft ? m_vectors.rows() : m_vectors.cols(); }
+
+ /** \brief Number of columns of transformation viewed as a matrix.
+ * \returns Number of columns
+ * \details This equals the dimension of the space that the transformation acts on.
+ */
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
+ Index cols() const EIGEN_NOEXCEPT { return rows(); }
+
+ /** \brief Essential part of a Householder vector.
+ * \param[in] k Index of Householder reflection
+ * \returns Vector containing non-trivial entries of k-th Householder vector
+ *
+ * This function returns the essential part of the Householder vector \f$ v_i \f$. This is a vector of
+ * length \f$ n-i \f$ containing the last \f$ n-i \f$ entries of the vector
+ * \f[
+ * v_i = [\underbrace{0, \ldots, 0}_{i-1\mbox{ zeros}}, 1, \underbrace{*, \ldots,*}_{n-i\mbox{ arbitrary entries}} ].
+ * \f]
+ * The index \f$ i \f$ equals \p k + shift(), corresponding to the k-th column of the matrix \p v
+ * passed to the constructor.
+ *
+ * \sa setShift(), shift()
+ */
+ EIGEN_DEVICE_FUNC
+ const EssentialVectorType essentialVector(Index k) const
+ {
+ eigen_assert(k >= 0 && k < m_length);
+ return internal::hseq_side_dependent_impl<VectorsType,CoeffsType,Side>::essentialVector(*this, k);
+ }
+
+ /** \brief %Transpose of the Householder sequence. */
+ TransposeReturnType transpose() const
+ {
+ return TransposeReturnType(m_vectors.conjugate(), m_coeffs)
+ .setReverseFlag(!m_reverse)
+ .setLength(m_length)
+ .setShift(m_shift);
+ }
+
+ /** \brief Complex conjugate of the Householder sequence. */
+ ConjugateReturnType conjugate() const
+ {
+ return ConjugateReturnType(m_vectors.conjugate(), m_coeffs.conjugate())
+ .setReverseFlag(m_reverse)
+ .setLength(m_length)
+ .setShift(m_shift);
+ }
+
+ /** \returns an expression of the complex conjugate of \c *this if Cond==true,
+ * returns \c *this otherwise.
+ */
+ template<bool Cond>
+ EIGEN_DEVICE_FUNC
+ inline std::conditional_t<Cond,ConjugateReturnType,ConstHouseholderSequence>
+ conjugateIf() const
+ {
+ typedef std::conditional_t<Cond,ConjugateReturnType,ConstHouseholderSequence> ReturnType;
+ return ReturnType(m_vectors.template conjugateIf<Cond>(), m_coeffs.template conjugateIf<Cond>());
+ }
+
+ /** \brief Adjoint (conjugate transpose) of the Householder sequence. */
+ AdjointReturnType adjoint() const
+ {
+ return AdjointReturnType(m_vectors, m_coeffs.conjugate())
+ .setReverseFlag(!m_reverse)
+ .setLength(m_length)
+ .setShift(m_shift);
+ }
+
+ /** \brief Inverse of the Householder sequence (equals the adjoint). */
+ AdjointReturnType inverse() const { return adjoint(); }
+
+ /** \internal */
+ template<typename DestType>
+ inline EIGEN_DEVICE_FUNC
+ void evalTo(DestType& dst) const
+ {
+ Matrix<Scalar, DestType::RowsAtCompileTime, 1,
+ AutoAlign|ColMajor, DestType::MaxRowsAtCompileTime, 1> workspace(rows());
+ evalTo(dst, workspace);
+ }
+
+ /** \internal */
+ template<typename Dest, typename Workspace>
+ EIGEN_DEVICE_FUNC
+ void evalTo(Dest& dst, Workspace& workspace) const
+ {
+ workspace.resize(rows());
+ Index vecs = m_length;
+ if(internal::is_same_dense(dst,m_vectors))
+ {
+ // in-place
+ dst.diagonal().setOnes();
+ dst.template triangularView<StrictlyUpper>().setZero();
+ for(Index k = vecs-1; k >= 0; --k)
+ {
+ Index cornerSize = rows() - k - m_shift;
+ if(m_reverse)
+ dst.bottomRightCorner(cornerSize, cornerSize)
+ .applyHouseholderOnTheRight(essentialVector(k), m_coeffs.coeff(k), workspace.data());
+ else
+ dst.bottomRightCorner(cornerSize, cornerSize)
+ .applyHouseholderOnTheLeft(essentialVector(k), m_coeffs.coeff(k), workspace.data());
+
+ // clear the off diagonal vector
+ dst.col(k).tail(rows()-k-1).setZero();
+ }
+ // clear the remaining columns if needed
+ for(Index k = 0; k<cols()-vecs ; ++k)
+ dst.col(k).tail(rows()-k-1).setZero();
+ }
+ else if(m_length>BlockSize)
+ {
+ dst.setIdentity(rows(), rows());
+ if(m_reverse)
+ applyThisOnTheLeft(dst,workspace,true);
+ else
+ applyThisOnTheLeft(dst,workspace,true);
+ }
+ else
+ {
+ dst.setIdentity(rows(), rows());
+ for(Index k = vecs-1; k >= 0; --k)
+ {
+ Index cornerSize = rows() - k - m_shift;
+ if(m_reverse)
+ dst.bottomRightCorner(cornerSize, cornerSize)
+ .applyHouseholderOnTheRight(essentialVector(k), m_coeffs.coeff(k), workspace.data());
+ else
+ dst.bottomRightCorner(cornerSize, cornerSize)
+ .applyHouseholderOnTheLeft(essentialVector(k), m_coeffs.coeff(k), workspace.data());
+ }
+ }
+ }
+
+ /** \internal */
+ template<typename Dest> inline void applyThisOnTheRight(Dest& dst) const
+ {
+ Matrix<Scalar,1,Dest::RowsAtCompileTime,RowMajor,1,Dest::MaxRowsAtCompileTime> workspace(dst.rows());
+ applyThisOnTheRight(dst, workspace);
+ }
+
+ /** \internal */
+ template<typename Dest, typename Workspace>
+ inline void applyThisOnTheRight(Dest& dst, Workspace& workspace) const
+ {
+ workspace.resize(dst.rows());
+ for(Index k = 0; k < m_length; ++k)
+ {
+ Index actual_k = m_reverse ? m_length-k-1 : k;
+ dst.rightCols(rows()-m_shift-actual_k)
+ .applyHouseholderOnTheRight(essentialVector(actual_k), m_coeffs.coeff(actual_k), workspace.data());
+ }
+ }
+
+ /** \internal */
+ template<typename Dest> inline void applyThisOnTheLeft(Dest& dst, bool inputIsIdentity = false) const
+ {
+ Matrix<Scalar,1,Dest::ColsAtCompileTime,RowMajor,1,Dest::MaxColsAtCompileTime> workspace;
+ applyThisOnTheLeft(dst, workspace, inputIsIdentity);
+ }
+
+ /** \internal */
+ template<typename Dest, typename Workspace>
+ inline void applyThisOnTheLeft(Dest& dst, Workspace& workspace, bool inputIsIdentity = false) const
+ {
+ if(inputIsIdentity && m_reverse)
+ inputIsIdentity = false;
+ // if the entries are large enough, then apply the reflectors by block
+ if(m_length>=BlockSize && dst.cols()>1)
+ {
+ // Make sure we have at least 2 useful blocks, otherwise it is point-less:
+ Index blockSize = m_length<Index(2*BlockSize) ? (m_length+1)/2 : Index(BlockSize);
+ for(Index i = 0; i < m_length; i+=blockSize)
+ {
+ Index end = m_reverse ? (std::min)(m_length,i+blockSize) : m_length-i;
+ Index k = m_reverse ? i : (std::max)(Index(0),end-blockSize);
+ Index bs = end-k;
+ Index start = k + m_shift;
+
+ typedef Block<internal::remove_all_t<VectorsType>,Dynamic,Dynamic> SubVectorsType;
+ SubVectorsType sub_vecs1(m_vectors.const_cast_derived(), Side==OnTheRight ? k : start,
+ Side==OnTheRight ? start : k,
+ Side==OnTheRight ? bs : m_vectors.rows()-start,
+ Side==OnTheRight ? m_vectors.cols()-start : bs);
+ std::conditional_t<Side==OnTheRight, Transpose<SubVectorsType>, SubVectorsType&> sub_vecs(sub_vecs1);
+
+ Index dstRows = rows()-m_shift-k;
+
+ if (inputIsIdentity)
+ {
+ Block<Dest, Dynamic, Dynamic> sub_dst = dst.bottomRightCorner(dstRows, dstRows);
+ apply_block_householder_on_the_left(sub_dst, sub_vecs, m_coeffs.segment(k, bs), !m_reverse);
+ }
+ else
+ {
+ auto sub_dst = dst.bottomRows(dstRows);
+ apply_block_householder_on_the_left(sub_dst, sub_vecs, m_coeffs.segment(k, bs), !m_reverse);
+ }
+ }
+ }
+ else
+ {
+ workspace.resize(dst.cols());
+ for(Index k = 0; k < m_length; ++k)
+ {
+ Index actual_k = m_reverse ? k : m_length-k-1;
+ Index dstRows = rows()-m_shift-actual_k;
+
+ if (inputIsIdentity)
+ {
+ Block<Dest, Dynamic, Dynamic> sub_dst = dst.bottomRightCorner(dstRows, dstRows);
+ sub_dst.applyHouseholderOnTheLeft(essentialVector(actual_k), m_coeffs.coeff(actual_k), workspace.data());
+ }
+ else
+ {
+ auto sub_dst = dst.bottomRows(dstRows);
+ sub_dst.applyHouseholderOnTheLeft(essentialVector(actual_k), m_coeffs.coeff(actual_k), workspace.data());
+ }
+ }
+ }
+ }
+
+ /** \brief Computes the product of a Householder sequence with a matrix.
+ * \param[in] other %Matrix being multiplied.
+ * \returns Expression object representing the product.
+ *
+ * This function computes \f$ HM \f$ where \f$ H \f$ is the Householder sequence represented by \p *this
+ * and \f$ M \f$ is the matrix \p other.
+ */
+ template<typename OtherDerived>
+ typename internal::matrix_type_times_scalar_type<Scalar, OtherDerived>::Type operator*(const MatrixBase<OtherDerived>& other) const
+ {
+ typename internal::matrix_type_times_scalar_type<Scalar, OtherDerived>::Type
+ res(other.template cast<typename internal::matrix_type_times_scalar_type<Scalar,OtherDerived>::ResultScalar>());
+ applyThisOnTheLeft(res, internal::is_identity<OtherDerived>::value && res.rows()==res.cols());
+ return res;
+ }
+
+ template<typename VectorsType_, typename CoeffsType_, int Side_> friend struct internal::hseq_side_dependent_impl;
+
+ /** \brief Sets the length of the Householder sequence.
+ * \param [in] length New value for the length.
+ *
+ * By default, the length \f$ n \f$ of the Householder sequence \f$ H = H_0 H_1 \ldots H_{n-1} \f$ is set
+ * to the number of columns of the matrix \p v passed to the constructor, or the number of rows if that
+ * is smaller. After this function is called, the length equals \p length.
+ *
+ * \sa length()
+ */
+ EIGEN_DEVICE_FUNC
+ HouseholderSequence& setLength(Index length)
+ {
+ m_length = length;
+ return *this;
+ }
+
+ /** \brief Sets the shift of the Householder sequence.
+ * \param [in] shift New value for the shift.
+ *
+ * By default, a %HouseholderSequence object represents \f$ H = H_0 H_1 \ldots H_{n-1} \f$ and the i-th
+ * column of the matrix \p v passed to the constructor corresponds to the i-th Householder
+ * reflection. After this function is called, the object represents \f$ H = H_{\mathrm{shift}}
+ * H_{\mathrm{shift}+1} \ldots H_{n-1} \f$ and the i-th column of \p v corresponds to the (shift+i)-th
+ * Householder reflection.
+ *
+ * \sa shift()
+ */
+ EIGEN_DEVICE_FUNC
+ HouseholderSequence& setShift(Index shift)
+ {
+ m_shift = shift;
+ return *this;
+ }
+
+ EIGEN_DEVICE_FUNC
+ Index length() const { return m_length; } /**< \brief Returns the length of the Householder sequence. */
+
+ EIGEN_DEVICE_FUNC
+ Index shift() const { return m_shift; } /**< \brief Returns the shift of the Householder sequence. */
+
+ /* Necessary for .adjoint() and .conjugate() */
+ template <typename VectorsType2, typename CoeffsType2, int Side2> friend class HouseholderSequence;
+
+ protected:
+
+ /** \internal
+ * \brief Sets the reverse flag.
+ * \param [in] reverse New value of the reverse flag.
+ *
+ * By default, the reverse flag is not set. If the reverse flag is set, then this object represents
+ * \f$ H^r = H_{n-1} \ldots H_1 H_0 \f$ instead of \f$ H = H_0 H_1 \ldots H_{n-1} \f$.
+ * \note For real valued HouseholderSequence this is equivalent to transposing \f$ H \f$.
+ *
+ * \sa reverseFlag(), transpose(), adjoint()
+ */
+ HouseholderSequence& setReverseFlag(bool reverse)
+ {
+ m_reverse = reverse;
+ return *this;
+ }
+
+ bool reverseFlag() const { return m_reverse; } /**< \internal \brief Returns the reverse flag. */
+
+ typename VectorsType::Nested m_vectors;
+ typename CoeffsType::Nested m_coeffs;
+ bool m_reverse;
+ Index m_length;
+ Index m_shift;
+ enum { BlockSize = 48 };
+};
+
+/** \brief Computes the product of a matrix with a Householder sequence.
+ * \param[in] other %Matrix being multiplied.
+ * \param[in] h %HouseholderSequence being multiplied.
+ * \returns Expression object representing the product.
+ *
+ * This function computes \f$ MH \f$ where \f$ M \f$ is the matrix \p other and \f$ H \f$ is the
+ * Householder sequence represented by \p h.
+ */
+template<typename OtherDerived, typename VectorsType, typename CoeffsType, int Side>
+typename internal::matrix_type_times_scalar_type<typename VectorsType::Scalar,OtherDerived>::Type operator*(const MatrixBase<OtherDerived>& other, const HouseholderSequence<VectorsType,CoeffsType,Side>& h)
+{
+ typename internal::matrix_type_times_scalar_type<typename VectorsType::Scalar,OtherDerived>::Type
+ res(other.template cast<typename internal::matrix_type_times_scalar_type<typename VectorsType::Scalar,OtherDerived>::ResultScalar>());
+ h.applyThisOnTheRight(res);
+ return res;
+}
+
+/** \ingroup Householder_Module \householder_module
+ * \brief Convenience function for constructing a Householder sequence.
+ * \returns A HouseholderSequence constructed from the specified arguments.
+ */
+template<typename VectorsType, typename CoeffsType>
+HouseholderSequence<VectorsType,CoeffsType> householderSequence(const VectorsType& v, const CoeffsType& h)
+{
+ return HouseholderSequence<VectorsType,CoeffsType,OnTheLeft>(v, h);
+}
+
+/** \ingroup Householder_Module \householder_module
+ * \brief Convenience function for constructing a Householder sequence.
+ * \returns A HouseholderSequence constructed from the specified arguments.
+ * \details This function differs from householderSequence() in that the template argument \p OnTheSide of
+ * the constructed HouseholderSequence is set to OnTheRight, instead of the default OnTheLeft.
+ */
+template<typename VectorsType, typename CoeffsType>
+HouseholderSequence<VectorsType,CoeffsType,OnTheRight> rightHouseholderSequence(const VectorsType& v, const CoeffsType& h)
+{
+ return HouseholderSequence<VectorsType,CoeffsType,OnTheRight>(v, h);
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_HOUSEHOLDER_SEQUENCE_H
diff --git a/Eigen/src/Householder/InternalHeaderCheck.h b/Eigen/src/Householder/InternalHeaderCheck.h
new file mode 100644
index 0000000..70de89b
--- /dev/null
+++ b/Eigen/src/Householder/InternalHeaderCheck.h
@@ -0,0 +1,3 @@
+#ifndef EIGEN_HOUSEHOLDER_MODULE_H
+#error "Please include Eigen/Householder instead of including headers inside the src directory directly."
+#endif
diff --git a/Eigen/src/IterativeLinearSolvers/BasicPreconditioners.h b/Eigen/src/IterativeLinearSolvers/BasicPreconditioners.h
new file mode 100644
index 0000000..d2d55b7
--- /dev/null
+++ b/Eigen/src/IterativeLinearSolvers/BasicPreconditioners.h
@@ -0,0 +1,228 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2011-2014 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_BASIC_PRECONDITIONERS_H
+#define EIGEN_BASIC_PRECONDITIONERS_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+/** \ingroup IterativeLinearSolvers_Module
+ * \brief A preconditioner based on the digonal entries
+ *
+ * This class allows to approximately solve for A.x = b problems assuming A is a diagonal matrix.
+ * In other words, this preconditioner neglects all off diagonal entries and, in Eigen's language, solves for:
+ \code
+ A.diagonal().asDiagonal() . x = b
+ \endcode
+ *
+ * \tparam Scalar_ the type of the scalar.
+ *
+ * \implsparsesolverconcept
+ *
+ * This preconditioner is suitable for both selfadjoint and general problems.
+ * The diagonal entries are pre-inverted and stored into a dense vector.
+ *
+ * \note A variant that has yet to be implemented would attempt to preserve the norm of each column.
+ *
+ * \sa class LeastSquareDiagonalPreconditioner, class ConjugateGradient
+ */
+template <typename Scalar_>
+class DiagonalPreconditioner
+{
+ typedef Scalar_ Scalar;
+ typedef Matrix<Scalar,Dynamic,1> Vector;
+ public:
+ typedef typename Vector::StorageIndex StorageIndex;
+ enum {
+ ColsAtCompileTime = Dynamic,
+ MaxColsAtCompileTime = Dynamic
+ };
+
+ DiagonalPreconditioner() : m_isInitialized(false) {}
+
+ template<typename MatType>
+ explicit DiagonalPreconditioner(const MatType& mat) : m_invdiag(mat.cols())
+ {
+ compute(mat);
+ }
+
+ EIGEN_CONSTEXPR Index rows() const EIGEN_NOEXCEPT { return m_invdiag.size(); }
+ EIGEN_CONSTEXPR Index cols() const EIGEN_NOEXCEPT { return m_invdiag.size(); }
+
+ template<typename MatType>
+ DiagonalPreconditioner& analyzePattern(const MatType& )
+ {
+ return *this;
+ }
+
+ template<typename MatType>
+ DiagonalPreconditioner& factorize(const MatType& mat)
+ {
+ m_invdiag.resize(mat.cols());
+ for(int j=0; j<mat.outerSize(); ++j)
+ {
+ typename MatType::InnerIterator it(mat,j);
+ while(it && it.index()!=j) ++it;
+ if(it && it.index()==j && it.value()!=Scalar(0))
+ m_invdiag(j) = Scalar(1)/it.value();
+ else
+ m_invdiag(j) = Scalar(1);
+ }
+ m_isInitialized = true;
+ return *this;
+ }
+
+ template<typename MatType>
+ DiagonalPreconditioner& compute(const MatType& mat)
+ {
+ return factorize(mat);
+ }
+
+ /** \internal */
+ template<typename Rhs, typename Dest>
+ void _solve_impl(const Rhs& b, Dest& x) const
+ {
+ x = m_invdiag.array() * b.array() ;
+ }
+
+ template<typename Rhs> inline const Solve<DiagonalPreconditioner, Rhs>
+ solve(const MatrixBase<Rhs>& b) const
+ {
+ eigen_assert(m_isInitialized && "DiagonalPreconditioner is not initialized.");
+ eigen_assert(m_invdiag.size()==b.rows()
+ && "DiagonalPreconditioner::solve(): invalid number of rows of the right hand side matrix b");
+ return Solve<DiagonalPreconditioner, Rhs>(*this, b.derived());
+ }
+
+ ComputationInfo info() { return Success; }
+
+ protected:
+ Vector m_invdiag;
+ bool m_isInitialized;
+};
+
+/** \ingroup IterativeLinearSolvers_Module
+ * \brief Jacobi preconditioner for LeastSquaresConjugateGradient
+ *
+ * This class allows to approximately solve for A' A x = A' b problems assuming A' A is a diagonal matrix.
+ * In other words, this preconditioner neglects all off diagonal entries and, in Eigen's language, solves for:
+ \code
+ (A.adjoint() * A).diagonal().asDiagonal() * x = b
+ \endcode
+ *
+ * \tparam Scalar_ the type of the scalar.
+ *
+ * \implsparsesolverconcept
+ *
+ * The diagonal entries are pre-inverted and stored into a dense vector.
+ *
+ * \sa class LeastSquaresConjugateGradient, class DiagonalPreconditioner
+ */
+template <typename Scalar_>
+class LeastSquareDiagonalPreconditioner : public DiagonalPreconditioner<Scalar_>
+{
+ typedef Scalar_ Scalar;
+ typedef typename NumTraits<Scalar>::Real RealScalar;
+ typedef DiagonalPreconditioner<Scalar_> Base;
+ using Base::m_invdiag;
+ public:
+
+ LeastSquareDiagonalPreconditioner() : Base() {}
+
+ template<typename MatType>
+ explicit LeastSquareDiagonalPreconditioner(const MatType& mat) : Base()
+ {
+ compute(mat);
+ }
+
+ template<typename MatType>
+ LeastSquareDiagonalPreconditioner& analyzePattern(const MatType& )
+ {
+ return *this;
+ }
+
+ template<typename MatType>
+ LeastSquareDiagonalPreconditioner& factorize(const MatType& mat)
+ {
+ // Compute the inverse squared-norm of each column of mat
+ m_invdiag.resize(mat.cols());
+ if(MatType::IsRowMajor)
+ {
+ m_invdiag.setZero();
+ for(Index j=0; j<mat.outerSize(); ++j)
+ {
+ for(typename MatType::InnerIterator it(mat,j); it; ++it)
+ m_invdiag(it.index()) += numext::abs2(it.value());
+ }
+ for(Index j=0; j<mat.cols(); ++j)
+ if(numext::real(m_invdiag(j))>RealScalar(0))
+ m_invdiag(j) = RealScalar(1)/numext::real(m_invdiag(j));
+ }
+ else
+ {
+ for(Index j=0; j<mat.outerSize(); ++j)
+ {
+ RealScalar sum = mat.col(j).squaredNorm();
+ if(sum>RealScalar(0))
+ m_invdiag(j) = RealScalar(1)/sum;
+ else
+ m_invdiag(j) = RealScalar(1);
+ }
+ }
+ Base::m_isInitialized = true;
+ return *this;
+ }
+
+ template<typename MatType>
+ LeastSquareDiagonalPreconditioner& compute(const MatType& mat)
+ {
+ return factorize(mat);
+ }
+
+ ComputationInfo info() { return Success; }
+
+ protected:
+};
+
+/** \ingroup IterativeLinearSolvers_Module
+ * \brief A naive preconditioner which approximates any matrix as the identity matrix
+ *
+ * \implsparsesolverconcept
+ *
+ * \sa class DiagonalPreconditioner
+ */
+class IdentityPreconditioner
+{
+ public:
+
+ IdentityPreconditioner() {}
+
+ template<typename MatrixType>
+ explicit IdentityPreconditioner(const MatrixType& ) {}
+
+ template<typename MatrixType>
+ IdentityPreconditioner& analyzePattern(const MatrixType& ) { return *this; }
+
+ template<typename MatrixType>
+ IdentityPreconditioner& factorize(const MatrixType& ) { return *this; }
+
+ template<typename MatrixType>
+ IdentityPreconditioner& compute(const MatrixType& ) { return *this; }
+
+ template<typename Rhs>
+ inline const Rhs& solve(const Rhs& b) const { return b; }
+
+ ComputationInfo info() { return Success; }
+};
+
+} // end namespace Eigen
+
+#endif // EIGEN_BASIC_PRECONDITIONERS_H
diff --git a/Eigen/src/IterativeLinearSolvers/BiCGSTAB.h b/Eigen/src/IterativeLinearSolvers/BiCGSTAB.h
new file mode 100644
index 0000000..079b22d
--- /dev/null
+++ b/Eigen/src/IterativeLinearSolvers/BiCGSTAB.h
@@ -0,0 +1,214 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2011-2014 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2012 Désiré Nuentsa-Wakam <desire.nuentsa_wakam@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_BICGSTAB_H
+#define EIGEN_BICGSTAB_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+
+/** \internal Low-level bi conjugate gradient stabilized algorithm
+ * \param mat The matrix A
+ * \param rhs The right hand side vector b
+ * \param x On input and initial solution, on output the computed solution.
+ * \param precond A preconditioner being able to efficiently solve for an
+ * approximation of Ax=b (regardless of b)
+ * \param iters On input the max number of iteration, on output the number of performed iterations.
+ * \param tol_error On input the tolerance error, on output an estimation of the relative error.
+ * \return false in the case of numerical issue, for example a break down of BiCGSTAB.
+ */
+template<typename MatrixType, typename Rhs, typename Dest, typename Preconditioner>
+bool bicgstab(const MatrixType& mat, const Rhs& rhs, Dest& x,
+ const Preconditioner& precond, Index& iters,
+ typename Dest::RealScalar& tol_error)
+{
+ using std::sqrt;
+ using std::abs;
+ typedef typename Dest::RealScalar RealScalar;
+ typedef typename Dest::Scalar Scalar;
+ typedef Matrix<Scalar,Dynamic,1> VectorType;
+ RealScalar tol = tol_error;
+ Index maxIters = iters;
+
+ Index n = mat.cols();
+ VectorType r = rhs - mat * x;
+ VectorType r0 = r;
+
+ RealScalar r0_sqnorm = r0.squaredNorm();
+ RealScalar rhs_sqnorm = rhs.squaredNorm();
+ if(rhs_sqnorm == 0)
+ {
+ x.setZero();
+ return true;
+ }
+ Scalar rho = 1;
+ Scalar alpha = 1;
+ Scalar w = 1;
+
+ VectorType v = VectorType::Zero(n), p = VectorType::Zero(n);
+ VectorType y(n), z(n);
+ VectorType kt(n), ks(n);
+
+ VectorType s(n), t(n);
+
+ RealScalar tol2 = tol*tol*rhs_sqnorm;
+ RealScalar eps2 = NumTraits<Scalar>::epsilon()*NumTraits<Scalar>::epsilon();
+ Index i = 0;
+ Index restarts = 0;
+
+ while ( r.squaredNorm() > tol2 && i<maxIters )
+ {
+ Scalar rho_old = rho;
+
+ rho = r0.dot(r);
+ if (abs(rho) < eps2*r0_sqnorm)
+ {
+ // The new residual vector became too orthogonal to the arbitrarily chosen direction r0
+ // Let's restart with a new r0:
+ r = rhs - mat * x;
+ r0 = r;
+ rho = r0_sqnorm = r.squaredNorm();
+ if(restarts++ == 0)
+ i = 0;
+ }
+ Scalar beta = (rho/rho_old) * (alpha / w);
+ p = r + beta * (p - w * v);
+
+ y = precond.solve(p);
+
+ v.noalias() = mat * y;
+
+ alpha = rho / r0.dot(v);
+ s = r - alpha * v;
+
+ z = precond.solve(s);
+ t.noalias() = mat * z;
+
+ RealScalar tmp = t.squaredNorm();
+ if(tmp>RealScalar(0))
+ w = t.dot(s) / tmp;
+ else
+ w = Scalar(0);
+ x += alpha * y + w * z;
+ r = s - w * t;
+ ++i;
+ }
+ tol_error = sqrt(r.squaredNorm()/rhs_sqnorm);
+ iters = i;
+ return true;
+}
+
+}
+
+template< typename MatrixType_,
+ typename Preconditioner_ = DiagonalPreconditioner<typename MatrixType_::Scalar> >
+class BiCGSTAB;
+
+namespace internal {
+
+template< typename MatrixType_, typename Preconditioner_>
+struct traits<BiCGSTAB<MatrixType_,Preconditioner_> >
+{
+ typedef MatrixType_ MatrixType;
+ typedef Preconditioner_ Preconditioner;
+};
+
+}
+
+/** \ingroup IterativeLinearSolvers_Module
+ * \brief A bi conjugate gradient stabilized solver for sparse square problems
+ *
+ * This class allows to solve for A.x = b sparse linear problems using a bi conjugate gradient
+ * stabilized algorithm. The vectors x and b can be either dense or sparse.
+ *
+ * \tparam MatrixType_ the type of the sparse matrix A, can be a dense or a sparse matrix.
+ * \tparam Preconditioner_ the type of the preconditioner. Default is DiagonalPreconditioner
+ *
+ * \implsparsesolverconcept
+ *
+ * The maximal number of iterations and tolerance value can be controlled via the setMaxIterations()
+ * and setTolerance() methods. The defaults are the size of the problem for the maximal number of iterations
+ * and NumTraits<Scalar>::epsilon() for the tolerance.
+ *
+ * The tolerance corresponds to the relative residual error: |Ax-b|/|b|
+ *
+ * \b Performance: when using sparse matrices, best performance is achied for a row-major sparse matrix format.
+ * Moreover, in this case multi-threading can be exploited if the user code is compiled with OpenMP enabled.
+ * See \ref TopicMultiThreading for details.
+ *
+ * This class can be used as the direct solver classes. Here is a typical usage example:
+ * \include BiCGSTAB_simple.cpp
+ *
+ * By default the iterations start with x=0 as an initial guess of the solution.
+ * One can control the start using the solveWithGuess() method.
+ *
+ * BiCGSTAB can also be used in a matrix-free context, see the following \link MatrixfreeSolverExample example \endlink.
+ *
+ * \sa class SimplicialCholesky, DiagonalPreconditioner, IdentityPreconditioner
+ */
+template< typename MatrixType_, typename Preconditioner_>
+class BiCGSTAB : public IterativeSolverBase<BiCGSTAB<MatrixType_,Preconditioner_> >
+{
+ typedef IterativeSolverBase<BiCGSTAB> Base;
+ using Base::matrix;
+ using Base::m_error;
+ using Base::m_iterations;
+ using Base::m_info;
+ using Base::m_isInitialized;
+public:
+ typedef MatrixType_ MatrixType;
+ typedef typename MatrixType::Scalar Scalar;
+ typedef typename MatrixType::RealScalar RealScalar;
+ typedef Preconditioner_ Preconditioner;
+
+public:
+
+ /** Default constructor. */
+ BiCGSTAB() : Base() {}
+
+ /** Initialize the solver with matrix \a A for further \c Ax=b solving.
+ *
+ * This constructor is a shortcut for the default constructor followed
+ * by a call to compute().
+ *
+ * \warning this class stores a reference to the matrix A as well as some
+ * precomputed values that depend on it. Therefore, if \a A is changed
+ * this class becomes invalid. Call compute() to update it with the new
+ * matrix A, or modify a copy of A.
+ */
+ template<typename MatrixDerived>
+ explicit BiCGSTAB(const EigenBase<MatrixDerived>& A) : Base(A.derived()) {}
+
+ ~BiCGSTAB() {}
+
+ /** \internal */
+ template<typename Rhs,typename Dest>
+ void _solve_vector_with_guess_impl(const Rhs& b, Dest& x) const
+ {
+ m_iterations = Base::maxIterations();
+ m_error = Base::m_tolerance;
+
+ bool ret = internal::bicgstab(matrix(), b, x, Base::m_preconditioner, m_iterations, m_error);
+
+ m_info = (!ret) ? NumericalIssue
+ : m_error <= Base::m_tolerance ? Success
+ : NoConvergence;
+ }
+
+protected:
+
+};
+
+} // end namespace Eigen
+
+#endif // EIGEN_BICGSTAB_H
diff --git a/Eigen/src/IterativeLinearSolvers/ConjugateGradient.h b/Eigen/src/IterativeLinearSolvers/ConjugateGradient.h
new file mode 100644
index 0000000..5a7dbc7
--- /dev/null
+++ b/Eigen/src/IterativeLinearSolvers/ConjugateGradient.h
@@ -0,0 +1,229 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2011-2014 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_CONJUGATE_GRADIENT_H
+#define EIGEN_CONJUGATE_GRADIENT_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+
+/** \internal Low-level conjugate gradient algorithm
+ * \param mat The matrix A
+ * \param rhs The right hand side vector b
+ * \param x On input and initial solution, on output the computed solution.
+ * \param precond A preconditioner being able to efficiently solve for an
+ * approximation of Ax=b (regardless of b)
+ * \param iters On input the max number of iteration, on output the number of performed iterations.
+ * \param tol_error On input the tolerance error, on output an estimation of the relative error.
+ */
+template<typename MatrixType, typename Rhs, typename Dest, typename Preconditioner>
+EIGEN_DONT_INLINE
+void conjugate_gradient(const MatrixType& mat, const Rhs& rhs, Dest& x,
+ const Preconditioner& precond, Index& iters,
+ typename Dest::RealScalar& tol_error)
+{
+ typedef typename Dest::RealScalar RealScalar;
+ typedef typename Dest::Scalar Scalar;
+ typedef Matrix<Scalar,Dynamic,1> VectorType;
+
+ RealScalar tol = tol_error;
+ Index maxIters = iters;
+
+ Index n = mat.cols();
+
+ VectorType residual = rhs - mat * x; //initial residual
+
+ RealScalar rhsNorm2 = rhs.squaredNorm();
+ if(rhsNorm2 == 0)
+ {
+ x.setZero();
+ iters = 0;
+ tol_error = 0;
+ return;
+ }
+ const RealScalar considerAsZero = (std::numeric_limits<RealScalar>::min)();
+ RealScalar threshold = numext::maxi(RealScalar(tol*tol*rhsNorm2),considerAsZero);
+ RealScalar residualNorm2 = residual.squaredNorm();
+ if (residualNorm2 < threshold)
+ {
+ iters = 0;
+ tol_error = numext::sqrt(residualNorm2 / rhsNorm2);
+ return;
+ }
+
+ VectorType p(n);
+ p = precond.solve(residual); // initial search direction
+
+ VectorType z(n), tmp(n);
+ RealScalar absNew = numext::real(residual.dot(p)); // the square of the absolute value of r scaled by invM
+ Index i = 0;
+ while(i < maxIters)
+ {
+ tmp.noalias() = mat * p; // the bottleneck of the algorithm
+
+ Scalar alpha = absNew / p.dot(tmp); // the amount we travel on dir
+ x += alpha * p; // update solution
+ residual -= alpha * tmp; // update residual
+
+ residualNorm2 = residual.squaredNorm();
+ if(residualNorm2 < threshold)
+ break;
+
+ z = precond.solve(residual); // approximately solve for "A z = residual"
+
+ RealScalar absOld = absNew;
+ absNew = numext::real(residual.dot(z)); // update the absolute value of r
+ RealScalar beta = absNew / absOld; // calculate the Gram-Schmidt value used to create the new search direction
+ p = z + beta * p; // update search direction
+ i++;
+ }
+ tol_error = numext::sqrt(residualNorm2 / rhsNorm2);
+ iters = i;
+}
+
+}
+
+template< typename MatrixType_, int UpLo_=Lower,
+ typename Preconditioner_ = DiagonalPreconditioner<typename MatrixType_::Scalar> >
+class ConjugateGradient;
+
+namespace internal {
+
+template< typename MatrixType_, int UpLo_, typename Preconditioner_>
+struct traits<ConjugateGradient<MatrixType_,UpLo_,Preconditioner_> >
+{
+ typedef MatrixType_ MatrixType;
+ typedef Preconditioner_ Preconditioner;
+};
+
+}
+
+/** \ingroup IterativeLinearSolvers_Module
+ * \brief A conjugate gradient solver for sparse (or dense) self-adjoint problems
+ *
+ * This class allows to solve for A.x = b linear problems using an iterative conjugate gradient algorithm.
+ * The matrix A must be selfadjoint. The matrix A and the vectors x and b can be either dense or sparse.
+ *
+ * \tparam MatrixType_ the type of the matrix A, can be a dense or a sparse matrix.
+ * \tparam UpLo_ the triangular part that will be used for the computations. It can be Lower,
+ * \c Upper, or \c Lower|Upper in which the full matrix entries will be considered.
+ * Default is \c Lower, best performance is \c Lower|Upper.
+ * \tparam Preconditioner_ the type of the preconditioner. Default is DiagonalPreconditioner
+ *
+ * \implsparsesolverconcept
+ *
+ * The maximal number of iterations and tolerance value can be controlled via the setMaxIterations()
+ * and setTolerance() methods. The defaults are the size of the problem for the maximal number of iterations
+ * and NumTraits<Scalar>::epsilon() for the tolerance.
+ *
+ * The tolerance corresponds to the relative residual error: |Ax-b|/|b|
+ *
+ * \b Performance: Even though the default value of \c UpLo_ is \c Lower, significantly higher performance is
+ * achieved when using a complete matrix and \b Lower|Upper as the \a UpLo_ template parameter. Moreover, in this
+ * case multi-threading can be exploited if the user code is compiled with OpenMP enabled.
+ * See \ref TopicMultiThreading for details.
+ *
+ * This class can be used as the direct solver classes. Here is a typical usage example:
+ \code
+ int n = 10000;
+ VectorXd x(n), b(n);
+ SparseMatrix<double> A(n,n);
+ // fill A and b
+ ConjugateGradient<SparseMatrix<double>, Lower|Upper> cg;
+ cg.compute(A);
+ x = cg.solve(b);
+ std::cout << "#iterations: " << cg.iterations() << std::endl;
+ std::cout << "estimated error: " << cg.error() << std::endl;
+ // update b, and solve again
+ x = cg.solve(b);
+ \endcode
+ *
+ * By default the iterations start with x=0 as an initial guess of the solution.
+ * One can control the start using the solveWithGuess() method.
+ *
+ * ConjugateGradient can also be used in a matrix-free context, see the following \link MatrixfreeSolverExample example \endlink.
+ *
+ * \sa class LeastSquaresConjugateGradient, class SimplicialCholesky, DiagonalPreconditioner, IdentityPreconditioner
+ */
+template< typename MatrixType_, int UpLo_, typename Preconditioner_>
+class ConjugateGradient : public IterativeSolverBase<ConjugateGradient<MatrixType_,UpLo_,Preconditioner_> >
+{
+ typedef IterativeSolverBase<ConjugateGradient> Base;
+ using Base::matrix;
+ using Base::m_error;
+ using Base::m_iterations;
+ using Base::m_info;
+ using Base::m_isInitialized;
+public:
+ typedef MatrixType_ MatrixType;
+ typedef typename MatrixType::Scalar Scalar;
+ typedef typename MatrixType::RealScalar RealScalar;
+ typedef Preconditioner_ Preconditioner;
+
+ enum {
+ UpLo = UpLo_
+ };
+
+public:
+
+ /** Default constructor. */
+ ConjugateGradient() : Base() {}
+
+ /** Initialize the solver with matrix \a A for further \c Ax=b solving.
+ *
+ * This constructor is a shortcut for the default constructor followed
+ * by a call to compute().
+ *
+ * \warning this class stores a reference to the matrix A as well as some
+ * precomputed values that depend on it. Therefore, if \a A is changed
+ * this class becomes invalid. Call compute() to update it with the new
+ * matrix A, or modify a copy of A.
+ */
+ template<typename MatrixDerived>
+ explicit ConjugateGradient(const EigenBase<MatrixDerived>& A) : Base(A.derived()) {}
+
+ ~ConjugateGradient() {}
+
+ /** \internal */
+ template<typename Rhs,typename Dest>
+ void _solve_vector_with_guess_impl(const Rhs& b, Dest& x) const
+ {
+ typedef typename Base::MatrixWrapper MatrixWrapper;
+ typedef typename Base::ActualMatrixType ActualMatrixType;
+ enum {
+ TransposeInput = (!MatrixWrapper::MatrixFree)
+ && (UpLo==(Lower|Upper))
+ && (!MatrixType::IsRowMajor)
+ && (!NumTraits<Scalar>::IsComplex)
+ };
+ typedef std::conditional_t<TransposeInput,Transpose<const ActualMatrixType>, ActualMatrixType const&> RowMajorWrapper;
+ EIGEN_STATIC_ASSERT(internal::check_implication(MatrixWrapper::MatrixFree,UpLo==(Lower|Upper)),MATRIX_FREE_CONJUGATE_GRADIENT_IS_COMPATIBLE_WITH_UPPER_UNION_LOWER_MODE_ONLY);
+ typedef std::conditional_t<UpLo==(Lower|Upper),
+ RowMajorWrapper,
+ typename MatrixWrapper::template ConstSelfAdjointViewReturnType<UpLo>::Type
+ > SelfAdjointWrapper;
+
+ m_iterations = Base::maxIterations();
+ m_error = Base::m_tolerance;
+
+ RowMajorWrapper row_mat(matrix());
+ internal::conjugate_gradient(SelfAdjointWrapper(row_mat), b, x, Base::m_preconditioner, m_iterations, m_error);
+ m_info = m_error <= Base::m_tolerance ? Success : NoConvergence;
+ }
+
+protected:
+
+};
+
+} // end namespace Eigen
+
+#endif // EIGEN_CONJUGATE_GRADIENT_H
diff --git a/Eigen/src/IterativeLinearSolvers/IncompleteCholesky.h b/Eigen/src/IterativeLinearSolvers/IncompleteCholesky.h
new file mode 100644
index 0000000..e697f32
--- /dev/null
+++ b/Eigen/src/IterativeLinearSolvers/IncompleteCholesky.h
@@ -0,0 +1,396 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2012 Désiré Nuentsa-Wakam <desire.nuentsa_wakam@inria.fr>
+// Copyright (C) 2015 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_INCOMPLETE_CHOlESKY_H
+#define EIGEN_INCOMPLETE_CHOlESKY_H
+
+#include <vector>
+#include <list>
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+/**
+ * \brief Modified Incomplete Cholesky with dual threshold
+ *
+ * References : C-J. Lin and J. J. Moré, Incomplete Cholesky Factorizations with
+ * Limited memory, SIAM J. Sci. Comput. 21(1), pp. 24-45, 1999
+ *
+ * \tparam Scalar the scalar type of the input matrices
+ * \tparam UpLo_ The triangular part that will be used for the computations. It can be Lower
+ * or Upper. Default is Lower.
+ * \tparam OrderingType_ The ordering method to use, either AMDOrdering<> or NaturalOrdering<>. Default is AMDOrdering<int>,
+ * unless EIGEN_MPL2_ONLY is defined, in which case the default is NaturalOrdering<int>.
+ *
+ * \implsparsesolverconcept
+ *
+ * It performs the following incomplete factorization: \f$ S P A P' S \approx L L' \f$
+ * where L is a lower triangular factor, S is a diagonal scaling matrix, and P is a
+ * fill-in reducing permutation as computed by the ordering method.
+ *
+ * \b Shifting \b strategy: Let \f$ B = S P A P' S \f$ be the scaled matrix on which the factorization is carried out,
+ * and \f$ \beta \f$ be the minimum value of the diagonal. If \f$ \beta > 0 \f$ then, the factorization is directly performed
+ * on the matrix B. Otherwise, the factorization is performed on the shifted matrix \f$ B + (\sigma+|\beta| I \f$ where
+ * \f$ \sigma \f$ is the initial shift value as returned and set by setInitialShift() method. The default value is \f$ \sigma = 10^{-3} \f$.
+ * If the factorization fails, then the shift in doubled until it succeed or a maximum of ten attempts. If it still fails, as returned by
+ * the info() method, then you can either increase the initial shift, or better use another preconditioning technique.
+ *
+ */
+template <typename Scalar, int UpLo_ = Lower, typename OrderingType_ = AMDOrdering<int> >
+class IncompleteCholesky : public SparseSolverBase<IncompleteCholesky<Scalar,UpLo_,OrderingType_> >
+{
+ protected:
+ typedef SparseSolverBase<IncompleteCholesky<Scalar,UpLo_,OrderingType_> > Base;
+ using Base::m_isInitialized;
+ public:
+ typedef typename NumTraits<Scalar>::Real RealScalar;
+ typedef OrderingType_ OrderingType;
+ typedef typename OrderingType::PermutationType PermutationType;
+ typedef typename PermutationType::StorageIndex StorageIndex;
+ typedef SparseMatrix<Scalar,ColMajor,StorageIndex> FactorType;
+ typedef Matrix<Scalar,Dynamic,1> VectorSx;
+ typedef Matrix<RealScalar,Dynamic,1> VectorRx;
+ typedef Matrix<StorageIndex,Dynamic, 1> VectorIx;
+ typedef std::vector<std::list<StorageIndex> > VectorList;
+ enum { UpLo = UpLo_ };
+ enum {
+ ColsAtCompileTime = Dynamic,
+ MaxColsAtCompileTime = Dynamic
+ };
+ public:
+
+ /** Default constructor leaving the object in a partly non-initialized stage.
+ *
+ * You must call compute() or the pair analyzePattern()/factorize() to make it valid.
+ *
+ * \sa IncompleteCholesky(const MatrixType&)
+ */
+ IncompleteCholesky() : m_initialShift(1e-3),m_analysisIsOk(false),m_factorizationIsOk(false) {}
+
+ /** Constructor computing the incomplete factorization for the given matrix \a matrix.
+ */
+ template<typename MatrixType>
+ IncompleteCholesky(const MatrixType& matrix) : m_initialShift(1e-3),m_analysisIsOk(false),m_factorizationIsOk(false)
+ {
+ compute(matrix);
+ }
+
+ /** \returns number of rows of the factored matrix */
+ EIGEN_CONSTEXPR Index rows() const EIGEN_NOEXCEPT { return m_L.rows(); }
+
+ /** \returns number of columns of the factored matrix */
+ EIGEN_CONSTEXPR Index cols() const EIGEN_NOEXCEPT { return m_L.cols(); }
+
+
+ /** \brief Reports whether previous computation was successful.
+ *
+ * It triggers an assertion if \c *this has not been initialized through the respective constructor,
+ * or a call to compute() or analyzePattern().
+ *
+ * \returns \c Success if computation was successful,
+ * \c NumericalIssue if the matrix appears to be negative.
+ */
+ ComputationInfo info() const
+ {
+ eigen_assert(m_isInitialized && "IncompleteCholesky is not initialized.");
+ return m_info;
+ }
+
+ /** \brief Set the initial shift parameter \f$ \sigma \f$.
+ */
+ void setInitialShift(RealScalar shift) { m_initialShift = shift; }
+
+ /** \brief Computes the fill reducing permutation vector using the sparsity pattern of \a mat
+ */
+ template<typename MatrixType>
+ void analyzePattern(const MatrixType& mat)
+ {
+ OrderingType ord;
+ PermutationType pinv;
+ ord(mat.template selfadjointView<UpLo>(), pinv);
+ if(pinv.size()>0) m_perm = pinv.inverse();
+ else m_perm.resize(0);
+ m_L.resize(mat.rows(), mat.cols());
+ m_analysisIsOk = true;
+ m_isInitialized = true;
+ m_info = Success;
+ }
+
+ /** \brief Performs the numerical factorization of the input matrix \a mat
+ *
+ * The method analyzePattern() or compute() must have been called beforehand
+ * with a matrix having the same pattern.
+ *
+ * \sa compute(), analyzePattern()
+ */
+ template<typename MatrixType>
+ void factorize(const MatrixType& mat);
+
+ /** Computes or re-computes the incomplete Cholesky factorization of the input matrix \a mat
+ *
+ * It is a shortcut for a sequential call to the analyzePattern() and factorize() methods.
+ *
+ * \sa analyzePattern(), factorize()
+ */
+ template<typename MatrixType>
+ void compute(const MatrixType& mat)
+ {
+ analyzePattern(mat);
+ factorize(mat);
+ }
+
+ // internal
+ template<typename Rhs, typename Dest>
+ void _solve_impl(const Rhs& b, Dest& x) const
+ {
+ eigen_assert(m_factorizationIsOk && "factorize() should be called first");
+ if (m_perm.rows() == b.rows()) x = m_perm * b;
+ else x = b;
+ x = m_scale.asDiagonal() * x;
+ x = m_L.template triangularView<Lower>().solve(x);
+ x = m_L.adjoint().template triangularView<Upper>().solve(x);
+ x = m_scale.asDiagonal() * x;
+ if (m_perm.rows() == b.rows())
+ x = m_perm.inverse() * x;
+ }
+
+ /** \returns the sparse lower triangular factor L */
+ const FactorType& matrixL() const { eigen_assert(m_factorizationIsOk && "factorize() should be called first"); return m_L; }
+
+ /** \returns a vector representing the scaling factor S */
+ const VectorRx& scalingS() const { eigen_assert(m_factorizationIsOk && "factorize() should be called first"); return m_scale; }
+
+ /** \returns the fill-in reducing permutation P (can be empty for a natural ordering) */
+ const PermutationType& permutationP() const { eigen_assert(m_analysisIsOk && "analyzePattern() should be called first"); return m_perm; }
+
+ protected:
+ FactorType m_L; // The lower part stored in CSC
+ VectorRx m_scale; // The vector for scaling the matrix
+ RealScalar m_initialShift; // The initial shift parameter
+ bool m_analysisIsOk;
+ bool m_factorizationIsOk;
+ ComputationInfo m_info;
+ PermutationType m_perm;
+
+ private:
+ inline void updateList(Ref<const VectorIx> colPtr, Ref<VectorIx> rowIdx, Ref<VectorSx> vals, const Index& col, const Index& jk, VectorIx& firstElt, VectorList& listCol);
+};
+
+// Based on the following paper:
+// C-J. Lin and J. J. Moré, Incomplete Cholesky Factorizations with
+// Limited memory, SIAM J. Sci. Comput. 21(1), pp. 24-45, 1999
+// http://ftp.mcs.anl.gov/pub/tech_reports/reports/P682.pdf
+template<typename Scalar, int UpLo_, typename OrderingType>
+template<typename MatrixType_>
+void IncompleteCholesky<Scalar,UpLo_, OrderingType>::factorize(const MatrixType_& mat)
+{
+ using std::sqrt;
+ eigen_assert(m_analysisIsOk && "analyzePattern() should be called first");
+
+ // Dropping strategy : Keep only the p largest elements per column, where p is the number of elements in the column of the original matrix. Other strategies will be added
+
+ // Apply the fill-reducing permutation computed in analyzePattern()
+ if (m_perm.rows() == mat.rows() ) // To detect the null permutation
+ {
+ // The temporary is needed to make sure that the diagonal entry is properly sorted
+ FactorType tmp(mat.rows(), mat.cols());
+ tmp = mat.template selfadjointView<UpLo_>().twistedBy(m_perm);
+ m_L.template selfadjointView<Lower>() = tmp.template selfadjointView<Lower>();
+ }
+ else
+ {
+ m_L.template selfadjointView<Lower>() = mat.template selfadjointView<UpLo_>();
+ }
+
+ Index n = m_L.cols();
+ Index nnz = m_L.nonZeros();
+ Map<VectorSx> vals(m_L.valuePtr(), nnz); //values
+ Map<VectorIx> rowIdx(m_L.innerIndexPtr(), nnz); //Row indices
+ Map<VectorIx> colPtr( m_L.outerIndexPtr(), n+1); // Pointer to the beginning of each row
+ VectorIx firstElt(n-1); // for each j, points to the next entry in vals that will be used in the factorization
+ VectorList listCol(n); // listCol(j) is a linked list of columns to update column j
+ VectorSx col_vals(n); // Store a nonzero values in each column
+ VectorIx col_irow(n); // Row indices of nonzero elements in each column
+ VectorIx col_pattern(n);
+ col_pattern.fill(-1);
+ StorageIndex col_nnz;
+
+
+ // Computes the scaling factors
+ m_scale.resize(n);
+ m_scale.setZero();
+ for (Index j = 0; j < n; j++)
+ for (Index k = colPtr[j]; k < colPtr[j+1]; k++)
+ {
+ m_scale(j) += numext::abs2(vals(k));
+ if(rowIdx[k]!=j)
+ m_scale(rowIdx[k]) += numext::abs2(vals(k));
+ }
+
+ m_scale = m_scale.cwiseSqrt().cwiseSqrt();
+
+ for (Index j = 0; j < n; ++j)
+ if(m_scale(j)>(std::numeric_limits<RealScalar>::min)())
+ m_scale(j) = RealScalar(1)/m_scale(j);
+ else
+ m_scale(j) = 1;
+
+ // TODO disable scaling if not needed, i.e., if it is roughly uniform? (this will make solve() faster)
+
+ // Scale and compute the shift for the matrix
+ RealScalar mindiag = NumTraits<RealScalar>::highest();
+ for (Index j = 0; j < n; j++)
+ {
+ for (Index k = colPtr[j]; k < colPtr[j+1]; k++)
+ vals[k] *= (m_scale(j)*m_scale(rowIdx[k]));
+ eigen_internal_assert(rowIdx[colPtr[j]]==j && "IncompleteCholesky: only the lower triangular part must be stored");
+ mindiag = numext::mini(numext::real(vals[colPtr[j]]), mindiag);
+ }
+
+ FactorType L_save = m_L;
+
+ RealScalar shift = 0;
+ if(mindiag <= RealScalar(0.))
+ shift = m_initialShift - mindiag;
+
+ m_info = NumericalIssue;
+
+ // Try to perform the incomplete factorization using the current shift
+ int iter = 0;
+ do
+ {
+ // Apply the shift to the diagonal elements of the matrix
+ for (Index j = 0; j < n; j++)
+ vals[colPtr[j]] += shift;
+
+ // jki version of the Cholesky factorization
+ Index j=0;
+ for (; j < n; ++j)
+ {
+ // Left-looking factorization of the j-th column
+ // First, load the j-th column into col_vals
+ Scalar diag = vals[colPtr[j]]; // It is assumed that only the lower part is stored
+ col_nnz = 0;
+ for (Index i = colPtr[j] + 1; i < colPtr[j+1]; i++)
+ {
+ StorageIndex l = rowIdx[i];
+ col_vals(col_nnz) = vals[i];
+ col_irow(col_nnz) = l;
+ col_pattern(l) = col_nnz;
+ col_nnz++;
+ }
+ {
+ typename std::list<StorageIndex>::iterator k;
+ // Browse all previous columns that will update column j
+ for(k = listCol[j].begin(); k != listCol[j].end(); k++)
+ {
+ Index jk = firstElt(*k); // First element to use in the column
+ eigen_internal_assert(rowIdx[jk]==j);
+ Scalar v_j_jk = numext::conj(vals[jk]);
+
+ jk += 1;
+ for (Index i = jk; i < colPtr[*k+1]; i++)
+ {
+ StorageIndex l = rowIdx[i];
+ if(col_pattern[l]<0)
+ {
+ col_vals(col_nnz) = vals[i] * v_j_jk;
+ col_irow[col_nnz] = l;
+ col_pattern(l) = col_nnz;
+ col_nnz++;
+ }
+ else
+ col_vals(col_pattern[l]) -= vals[i] * v_j_jk;
+ }
+ updateList(colPtr,rowIdx,vals, *k, jk, firstElt, listCol);
+ }
+ }
+
+ // Scale the current column
+ if(numext::real(diag) <= 0)
+ {
+ if(++iter>=10)
+ return;
+
+ // increase shift
+ shift = numext::maxi(m_initialShift,RealScalar(2)*shift);
+ // restore m_L, col_pattern, and listCol
+ vals = Map<const VectorSx>(L_save.valuePtr(), nnz);
+ rowIdx = Map<const VectorIx>(L_save.innerIndexPtr(), nnz);
+ colPtr = Map<const VectorIx>(L_save.outerIndexPtr(), n+1);
+ col_pattern.fill(-1);
+ for(Index i=0; i<n; ++i)
+ listCol[i].clear();
+
+ break;
+ }
+
+ RealScalar rdiag = sqrt(numext::real(diag));
+ vals[colPtr[j]] = rdiag;
+ for (Index k = 0; k<col_nnz; ++k)
+ {
+ Index i = col_irow[k];
+ //Scale
+ col_vals(k) /= rdiag;
+ //Update the remaining diagonals with col_vals
+ vals[colPtr[i]] -= numext::abs2(col_vals(k));
+ }
+ // Select the largest p elements
+ // p is the original number of elements in the column (without the diagonal)
+ Index p = colPtr[j+1] - colPtr[j] - 1 ;
+ Ref<VectorSx> cvals = col_vals.head(col_nnz);
+ Ref<VectorIx> cirow = col_irow.head(col_nnz);
+ internal::QuickSplit(cvals,cirow, p);
+ // Insert the largest p elements in the matrix
+ Index cpt = 0;
+ for (Index i = colPtr[j]+1; i < colPtr[j+1]; i++)
+ {
+ vals[i] = col_vals(cpt);
+ rowIdx[i] = col_irow(cpt);
+ // restore col_pattern:
+ col_pattern(col_irow(cpt)) = -1;
+ cpt++;
+ }
+ // Get the first smallest row index and put it after the diagonal element
+ Index jk = colPtr(j)+1;
+ updateList(colPtr,rowIdx,vals,j,jk,firstElt,listCol);
+ }
+
+ if(j==n)
+ {
+ m_factorizationIsOk = true;
+ m_info = Success;
+ }
+ } while(m_info!=Success);
+}
+
+template<typename Scalar, int UpLo_, typename OrderingType>
+inline void IncompleteCholesky<Scalar,UpLo_, OrderingType>::updateList(Ref<const VectorIx> colPtr, Ref<VectorIx> rowIdx, Ref<VectorSx> vals, const Index& col, const Index& jk, VectorIx& firstElt, VectorList& listCol)
+{
+ if (jk < colPtr(col+1) )
+ {
+ Index p = colPtr(col+1) - jk;
+ Index minpos;
+ rowIdx.segment(jk,p).minCoeff(&minpos);
+ minpos += jk;
+ if (rowIdx(minpos) != rowIdx(jk))
+ {
+ //Swap
+ std::swap(rowIdx(jk),rowIdx(minpos));
+ std::swap(vals(jk),vals(minpos));
+ }
+ firstElt(col) = internal::convert_index<StorageIndex,Index>(jk);
+ listCol[rowIdx(jk)].push_back(internal::convert_index<StorageIndex,Index>(col));
+ }
+}
+
+} // end namespace Eigen
+
+#endif
diff --git a/Eigen/src/IterativeLinearSolvers/IncompleteLUT.h b/Eigen/src/IterativeLinearSolvers/IncompleteLUT.h
new file mode 100644
index 0000000..44f25fc
--- /dev/null
+++ b/Eigen/src/IterativeLinearSolvers/IncompleteLUT.h
@@ -0,0 +1,455 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2012 Désiré Nuentsa-Wakam <desire.nuentsa_wakam@inria.fr>
+// Copyright (C) 2014 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_INCOMPLETE_LUT_H
+#define EIGEN_INCOMPLETE_LUT_H
+
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+
+/** \internal
+ * Compute a quick-sort split of a vector
+ * On output, the vector row is permuted such that its elements satisfy
+ * abs(row(i)) >= abs(row(ncut)) if i<ncut
+ * abs(row(i)) <= abs(row(ncut)) if i>ncut
+ * \param row The vector of values
+ * \param ind The array of index for the elements in @p row
+ * \param ncut The number of largest elements to keep
+ **/
+template <typename VectorV, typename VectorI>
+Index QuickSplit(VectorV &row, VectorI &ind, Index ncut)
+{
+ typedef typename VectorV::RealScalar RealScalar;
+ using std::swap;
+ using std::abs;
+ Index mid;
+ Index n = row.size(); /* length of the vector */
+ Index first, last ;
+
+ ncut--; /* to fit the zero-based indices */
+ first = 0;
+ last = n-1;
+ if (ncut < first || ncut > last ) return 0;
+
+ do {
+ mid = first;
+ RealScalar abskey = abs(row(mid));
+ for (Index j = first + 1; j <= last; j++) {
+ if ( abs(row(j)) > abskey) {
+ ++mid;
+ swap(row(mid), row(j));
+ swap(ind(mid), ind(j));
+ }
+ }
+ /* Interchange for the pivot element */
+ swap(row(mid), row(first));
+ swap(ind(mid), ind(first));
+
+ if (mid > ncut) last = mid - 1;
+ else if (mid < ncut ) first = mid + 1;
+ } while (mid != ncut );
+
+ return 0; /* mid is equal to ncut */
+}
+
+}// end namespace internal
+
+/** \ingroup IterativeLinearSolvers_Module
+ * \class IncompleteLUT
+ * \brief Incomplete LU factorization with dual-threshold strategy
+ *
+ * \implsparsesolverconcept
+ *
+ * During the numerical factorization, two dropping rules are used :
+ * 1) any element whose magnitude is less than some tolerance is dropped.
+ * This tolerance is obtained by multiplying the input tolerance @p droptol
+ * by the average magnitude of all the original elements in the current row.
+ * 2) After the elimination of the row, only the @p fill largest elements in
+ * the L part and the @p fill largest elements in the U part are kept
+ * (in addition to the diagonal element ). Note that @p fill is computed from
+ * the input parameter @p fillfactor which is used the ratio to control the fill_in
+ * relatively to the initial number of nonzero elements.
+ *
+ * The two extreme cases are when @p droptol=0 (to keep all the @p fill*2 largest elements)
+ * and when @p fill=n/2 with @p droptol being different to zero.
+ *
+ * References : Yousef Saad, ILUT: A dual threshold incomplete LU factorization,
+ * Numerical Linear Algebra with Applications, 1(4), pp 387-402, 1994.
+ *
+ * NOTE : The following implementation is derived from the ILUT implementation
+ * in the SPARSKIT package, Copyright (C) 2005, the Regents of the University of Minnesota
+ * released under the terms of the GNU LGPL:
+ * http://www-users.cs.umn.edu/~saad/software/SPARSKIT/README
+ * However, Yousef Saad gave us permission to relicense his ILUT code to MPL2.
+ * See the Eigen mailing list archive, thread: ILUT, date: July 8, 2012:
+ * http://listengine.tuxfamily.org/lists.tuxfamily.org/eigen/2012/07/msg00064.html
+ * alternatively, on GMANE:
+ * http://comments.gmane.org/gmane.comp.lib.eigen/3302
+ */
+template <typename Scalar_, typename StorageIndex_ = int>
+class IncompleteLUT : public SparseSolverBase<IncompleteLUT<Scalar_, StorageIndex_> >
+{
+ protected:
+ typedef SparseSolverBase<IncompleteLUT> Base;
+ using Base::m_isInitialized;
+ public:
+ typedef Scalar_ Scalar;
+ typedef StorageIndex_ StorageIndex;
+ typedef typename NumTraits<Scalar>::Real RealScalar;
+ typedef Matrix<Scalar,Dynamic,1> Vector;
+ typedef Matrix<StorageIndex,Dynamic,1> VectorI;
+ typedef SparseMatrix<Scalar,RowMajor,StorageIndex> FactorType;
+
+ enum {
+ ColsAtCompileTime = Dynamic,
+ MaxColsAtCompileTime = Dynamic
+ };
+
+ public:
+
+ IncompleteLUT()
+ : m_droptol(NumTraits<Scalar>::dummy_precision()), m_fillfactor(10),
+ m_analysisIsOk(false), m_factorizationIsOk(false)
+ {}
+
+ template<typename MatrixType>
+ explicit IncompleteLUT(const MatrixType& mat, const RealScalar& droptol=NumTraits<Scalar>::dummy_precision(), int fillfactor = 10)
+ : m_droptol(droptol),m_fillfactor(fillfactor),
+ m_analysisIsOk(false),m_factorizationIsOk(false)
+ {
+ eigen_assert(fillfactor != 0);
+ compute(mat);
+ }
+
+ EIGEN_CONSTEXPR Index rows() const EIGEN_NOEXCEPT { return m_lu.rows(); }
+
+ EIGEN_CONSTEXPR Index cols() const EIGEN_NOEXCEPT { return m_lu.cols(); }
+
+ /** \brief Reports whether previous computation was successful.
+ *
+ * \returns \c Success if computation was successful,
+ * \c NumericalIssue if the matrix.appears to be negative.
+ */
+ ComputationInfo info() const
+ {
+ eigen_assert(m_isInitialized && "IncompleteLUT is not initialized.");
+ return m_info;
+ }
+
+ template<typename MatrixType>
+ void analyzePattern(const MatrixType& amat);
+
+ template<typename MatrixType>
+ void factorize(const MatrixType& amat);
+
+ /**
+ * Compute an incomplete LU factorization with dual threshold on the matrix mat
+ * No pivoting is done in this version
+ *
+ **/
+ template<typename MatrixType>
+ IncompleteLUT& compute(const MatrixType& amat)
+ {
+ analyzePattern(amat);
+ factorize(amat);
+ return *this;
+ }
+
+ void setDroptol(const RealScalar& droptol);
+ void setFillfactor(int fillfactor);
+
+ template<typename Rhs, typename Dest>
+ void _solve_impl(const Rhs& b, Dest& x) const
+ {
+ x = m_Pinv * b;
+ x = m_lu.template triangularView<UnitLower>().solve(x);
+ x = m_lu.template triangularView<Upper>().solve(x);
+ x = m_P * x;
+ }
+
+protected:
+
+ /** keeps off-diagonal entries; drops diagonal entries */
+ struct keep_diag {
+ inline bool operator() (const Index& row, const Index& col, const Scalar&) const
+ {
+ return row!=col;
+ }
+ };
+
+protected:
+
+ FactorType m_lu;
+ RealScalar m_droptol;
+ int m_fillfactor;
+ bool m_analysisIsOk;
+ bool m_factorizationIsOk;
+ ComputationInfo m_info;
+ PermutationMatrix<Dynamic,Dynamic,StorageIndex> m_P; // Fill-reducing permutation
+ PermutationMatrix<Dynamic,Dynamic,StorageIndex> m_Pinv; // Inverse permutation
+};
+
+/**
+ * Set control parameter droptol
+ * \param droptol Drop any element whose magnitude is less than this tolerance
+ **/
+template<typename Scalar, typename StorageIndex>
+void IncompleteLUT<Scalar,StorageIndex>::setDroptol(const RealScalar& droptol)
+{
+ this->m_droptol = droptol;
+}
+
+/**
+ * Set control parameter fillfactor
+ * \param fillfactor This is used to compute the number @p fill_in of largest elements to keep on each row.
+ **/
+template<typename Scalar, typename StorageIndex>
+void IncompleteLUT<Scalar,StorageIndex>::setFillfactor(int fillfactor)
+{
+ this->m_fillfactor = fillfactor;
+}
+
+template <typename Scalar, typename StorageIndex>
+template<typename MatrixType_>
+void IncompleteLUT<Scalar,StorageIndex>::analyzePattern(const MatrixType_& amat)
+{
+ // Compute the Fill-reducing permutation
+ // Since ILUT does not perform any numerical pivoting,
+ // it is highly preferable to keep the diagonal through symmetric permutations.
+ // To this end, let's symmetrize the pattern and perform AMD on it.
+ SparseMatrix<Scalar,ColMajor, StorageIndex> mat1 = amat;
+ SparseMatrix<Scalar,ColMajor, StorageIndex> mat2 = amat.transpose();
+ // FIXME for a matrix with nearly symmetric pattern, mat2+mat1 is the appropriate choice.
+ // on the other hand for a really non-symmetric pattern, mat2*mat1 should be preferred...
+ SparseMatrix<Scalar,ColMajor, StorageIndex> AtA = mat2 + mat1;
+ AMDOrdering<StorageIndex> ordering;
+ ordering(AtA,m_P);
+ m_Pinv = m_P.inverse(); // cache the inverse permutation
+ m_analysisIsOk = true;
+ m_factorizationIsOk = false;
+ m_isInitialized = true;
+}
+
+template <typename Scalar, typename StorageIndex>
+template<typename MatrixType_>
+void IncompleteLUT<Scalar,StorageIndex>::factorize(const MatrixType_& amat)
+{
+ using std::sqrt;
+ using std::swap;
+ using std::abs;
+ using internal::convert_index;
+
+ eigen_assert((amat.rows() == amat.cols()) && "The factorization should be done on a square matrix");
+ Index n = amat.cols(); // Size of the matrix
+ m_lu.resize(n,n);
+ // Declare Working vectors and variables
+ Vector u(n) ; // real values of the row -- maximum size is n --
+ VectorI ju(n); // column position of the values in u -- maximum size is n
+ VectorI jr(n); // Indicate the position of the nonzero elements in the vector u -- A zero location is indicated by -1
+
+ // Apply the fill-reducing permutation
+ eigen_assert(m_analysisIsOk && "You must first call analyzePattern()");
+ SparseMatrix<Scalar,RowMajor, StorageIndex> mat;
+ mat = amat.twistedBy(m_Pinv);
+
+ // Initialization
+ jr.fill(-1);
+ ju.fill(0);
+ u.fill(0);
+
+ // number of largest elements to keep in each row:
+ Index fill_in = (amat.nonZeros()*m_fillfactor)/n + 1;
+ if (fill_in > n) fill_in = n;
+
+ // number of largest nonzero elements to keep in the L and the U part of the current row:
+ Index nnzL = fill_in/2;
+ Index nnzU = nnzL;
+ m_lu.reserve(n * (nnzL + nnzU + 1));
+
+ // global loop over the rows of the sparse matrix
+ for (Index ii = 0; ii < n; ii++)
+ {
+ // 1 - copy the lower and the upper part of the row i of mat in the working vector u
+
+ Index sizeu = 1; // number of nonzero elements in the upper part of the current row
+ Index sizel = 0; // number of nonzero elements in the lower part of the current row
+ ju(ii) = convert_index<StorageIndex>(ii);
+ u(ii) = 0;
+ jr(ii) = convert_index<StorageIndex>(ii);
+ RealScalar rownorm = 0;
+
+ typename FactorType::InnerIterator j_it(mat, ii); // Iterate through the current row ii
+ for (; j_it; ++j_it)
+ {
+ Index k = j_it.index();
+ if (k < ii)
+ {
+ // copy the lower part
+ ju(sizel) = convert_index<StorageIndex>(k);
+ u(sizel) = j_it.value();
+ jr(k) = convert_index<StorageIndex>(sizel);
+ ++sizel;
+ }
+ else if (k == ii)
+ {
+ u(ii) = j_it.value();
+ }
+ else
+ {
+ // copy the upper part
+ Index jpos = ii + sizeu;
+ ju(jpos) = convert_index<StorageIndex>(k);
+ u(jpos) = j_it.value();
+ jr(k) = convert_index<StorageIndex>(jpos);
+ ++sizeu;
+ }
+ rownorm += numext::abs2(j_it.value());
+ }
+
+ // 2 - detect possible zero row
+ if(rownorm==0)
+ {
+ m_info = NumericalIssue;
+ return;
+ }
+ // Take the 2-norm of the current row as a relative tolerance
+ rownorm = sqrt(rownorm);
+
+ // 3 - eliminate the previous nonzero rows
+ Index jj = 0;
+ Index len = 0;
+ while (jj < sizel)
+ {
+ // In order to eliminate in the correct order,
+ // we must select first the smallest column index among ju(jj:sizel)
+ Index k;
+ Index minrow = ju.segment(jj,sizel-jj).minCoeff(&k); // k is relative to the segment
+ k += jj;
+ if (minrow != ju(jj))
+ {
+ // swap the two locations
+ Index j = ju(jj);
+ swap(ju(jj), ju(k));
+ jr(minrow) = convert_index<StorageIndex>(jj);
+ jr(j) = convert_index<StorageIndex>(k);
+ swap(u(jj), u(k));
+ }
+ // Reset this location
+ jr(minrow) = -1;
+
+ // Start elimination
+ typename FactorType::InnerIterator ki_it(m_lu, minrow);
+ while (ki_it && ki_it.index() < minrow) ++ki_it;
+ eigen_internal_assert(ki_it && ki_it.col()==minrow);
+ Scalar fact = u(jj) / ki_it.value();
+
+ // drop too small elements
+ if(abs(fact) <= m_droptol)
+ {
+ jj++;
+ continue;
+ }
+
+ // linear combination of the current row ii and the row minrow
+ ++ki_it;
+ for (; ki_it; ++ki_it)
+ {
+ Scalar prod = fact * ki_it.value();
+ Index j = ki_it.index();
+ Index jpos = jr(j);
+ if (jpos == -1) // fill-in element
+ {
+ Index newpos;
+ if (j >= ii) // dealing with the upper part
+ {
+ newpos = ii + sizeu;
+ sizeu++;
+ eigen_internal_assert(sizeu<=n);
+ }
+ else // dealing with the lower part
+ {
+ newpos = sizel;
+ sizel++;
+ eigen_internal_assert(sizel<=ii);
+ }
+ ju(newpos) = convert_index<StorageIndex>(j);
+ u(newpos) = -prod;
+ jr(j) = convert_index<StorageIndex>(newpos);
+ }
+ else
+ u(jpos) -= prod;
+ }
+ // store the pivot element
+ u(len) = fact;
+ ju(len) = convert_index<StorageIndex>(minrow);
+ ++len;
+
+ jj++;
+ } // end of the elimination on the row ii
+
+ // reset the upper part of the pointer jr to zero
+ for(Index k = 0; k <sizeu; k++) jr(ju(ii+k)) = -1;
+
+ // 4 - partially sort and insert the elements in the m_lu matrix
+
+ // sort the L-part of the row
+ sizel = len;
+ len = (std::min)(sizel, nnzL);
+ typename Vector::SegmentReturnType ul(u.segment(0, sizel));
+ typename VectorI::SegmentReturnType jul(ju.segment(0, sizel));
+ internal::QuickSplit(ul, jul, len);
+
+ // store the largest m_fill elements of the L part
+ m_lu.startVec(ii);
+ for(Index k = 0; k < len; k++)
+ m_lu.insertBackByOuterInnerUnordered(ii,ju(k)) = u(k);
+
+ // store the diagonal element
+ // apply a shifting rule to avoid zero pivots (we are doing an incomplete factorization)
+ if (u(ii) == Scalar(0))
+ u(ii) = sqrt(m_droptol) * rownorm;
+ m_lu.insertBackByOuterInnerUnordered(ii, ii) = u(ii);
+
+ // sort the U-part of the row
+ // apply the dropping rule first
+ len = 0;
+ for(Index k = 1; k < sizeu; k++)
+ {
+ if(abs(u(ii+k)) > m_droptol * rownorm )
+ {
+ ++len;
+ u(ii + len) = u(ii + k);
+ ju(ii + len) = ju(ii + k);
+ }
+ }
+ sizeu = len + 1; // +1 to take into account the diagonal element
+ len = (std::min)(sizeu, nnzU);
+ typename Vector::SegmentReturnType uu(u.segment(ii+1, sizeu-1));
+ typename VectorI::SegmentReturnType juu(ju.segment(ii+1, sizeu-1));
+ internal::QuickSplit(uu, juu, len);
+
+ // store the largest elements of the U part
+ for(Index k = ii + 1; k < ii + len; k++)
+ m_lu.insertBackByOuterInnerUnordered(ii,ju(k)) = u(k);
+ }
+ m_lu.finalize();
+ m_lu.makeCompressed();
+
+ m_factorizationIsOk = true;
+ m_info = Success;
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_INCOMPLETE_LUT_H
diff --git a/Eigen/src/IterativeLinearSolvers/InternalHeaderCheck.h b/Eigen/src/IterativeLinearSolvers/InternalHeaderCheck.h
new file mode 100644
index 0000000..b657e84
--- /dev/null
+++ b/Eigen/src/IterativeLinearSolvers/InternalHeaderCheck.h
@@ -0,0 +1,3 @@
+#ifndef EIGEN_ITERATIVELINEARSOLVERS_MODULE_H
+#error "Please include Eigen/IterativeLinearSolvers instead of including headers inside the src directory directly."
+#endif
diff --git a/Eigen/src/IterativeLinearSolvers/IterativeSolverBase.h b/Eigen/src/IterativeLinearSolvers/IterativeSolverBase.h
new file mode 100644
index 0000000..49829d0
--- /dev/null
+++ b/Eigen/src/IterativeLinearSolvers/IterativeSolverBase.h
@@ -0,0 +1,449 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2011-2014 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_ITERATIVE_SOLVER_BASE_H
+#define EIGEN_ITERATIVE_SOLVER_BASE_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+
+template<typename MatrixType>
+struct is_ref_compatible_impl
+{
+private:
+ template <typename T0>
+ struct any_conversion
+ {
+ template <typename T> any_conversion(const volatile T&);
+ template <typename T> any_conversion(T&);
+ };
+ struct yes {int a[1];};
+ struct no {int a[2];};
+
+ template<typename T>
+ static yes test(const Ref<const T>&, int);
+ template<typename T>
+ static no test(any_conversion<T>, ...);
+
+public:
+ static MatrixType ms_from;
+ enum { value = sizeof(test<MatrixType>(ms_from, 0))==sizeof(yes) };
+};
+
+template<typename MatrixType>
+struct is_ref_compatible
+{
+ enum { value = is_ref_compatible_impl<remove_all_t<MatrixType>>::value };
+};
+
+template<typename MatrixType, bool MatrixFree = !internal::is_ref_compatible<MatrixType>::value>
+class generic_matrix_wrapper;
+
+// We have an explicit matrix at hand, compatible with Ref<>
+template<typename MatrixType>
+class generic_matrix_wrapper<MatrixType,false>
+{
+public:
+ typedef Ref<const MatrixType> ActualMatrixType;
+ template<int UpLo> struct ConstSelfAdjointViewReturnType {
+ typedef typename ActualMatrixType::template ConstSelfAdjointViewReturnType<UpLo>::Type Type;
+ };
+
+ enum {
+ MatrixFree = false
+ };
+
+ generic_matrix_wrapper()
+ : m_dummy(0,0), m_matrix(m_dummy)
+ {}
+
+ template<typename InputType>
+ generic_matrix_wrapper(const InputType &mat)
+ : m_matrix(mat)
+ {}
+
+ const ActualMatrixType& matrix() const
+ {
+ return m_matrix;
+ }
+
+ template<typename MatrixDerived>
+ void grab(const EigenBase<MatrixDerived> &mat)
+ {
+ internal::destroy_at(&m_matrix);
+ internal::construct_at(&m_matrix, mat.derived());
+ }
+
+ void grab(const Ref<const MatrixType> &mat)
+ {
+ if(&(mat.derived()) != &m_matrix)
+ {
+ internal::destroy_at(&m_matrix);
+ internal::construct_at(&m_matrix, mat);
+ }
+ }
+
+protected:
+ MatrixType m_dummy; // used to default initialize the Ref<> object
+ ActualMatrixType m_matrix;
+};
+
+// MatrixType is not compatible with Ref<> -> matrix-free wrapper
+template<typename MatrixType>
+class generic_matrix_wrapper<MatrixType,true>
+{
+public:
+ typedef MatrixType ActualMatrixType;
+ template<int UpLo> struct ConstSelfAdjointViewReturnType
+ {
+ typedef ActualMatrixType Type;
+ };
+
+ enum {
+ MatrixFree = true
+ };
+
+ generic_matrix_wrapper()
+ : mp_matrix(0)
+ {}
+
+ generic_matrix_wrapper(const MatrixType &mat)
+ : mp_matrix(&mat)
+ {}
+
+ const ActualMatrixType& matrix() const
+ {
+ return *mp_matrix;
+ }
+
+ void grab(const MatrixType &mat)
+ {
+ mp_matrix = &mat;
+ }
+
+protected:
+ const ActualMatrixType *mp_matrix;
+};
+
+}
+
+/** \ingroup IterativeLinearSolvers_Module
+ * \brief Base class for linear iterative solvers
+ *
+ * \sa class SimplicialCholesky, DiagonalPreconditioner, IdentityPreconditioner
+ */
+template< typename Derived>
+class IterativeSolverBase : public SparseSolverBase<Derived>
+{
+protected:
+ typedef SparseSolverBase<Derived> Base;
+ using Base::m_isInitialized;
+
+public:
+ typedef typename internal::traits<Derived>::MatrixType MatrixType;
+ typedef typename internal::traits<Derived>::Preconditioner Preconditioner;
+ typedef typename MatrixType::Scalar Scalar;
+ typedef typename MatrixType::StorageIndex StorageIndex;
+ typedef typename MatrixType::RealScalar RealScalar;
+
+ enum {
+ ColsAtCompileTime = MatrixType::ColsAtCompileTime,
+ MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime
+ };
+
+public:
+
+ using Base::derived;
+
+ /** Default constructor. */
+ IterativeSolverBase()
+ {
+ init();
+ }
+
+ /** Initialize the solver with matrix \a A for further \c Ax=b solving.
+ *
+ * This constructor is a shortcut for the default constructor followed
+ * by a call to compute().
+ *
+ * \warning this class stores a reference to the matrix A as well as some
+ * precomputed values that depend on it. Therefore, if \a A is changed
+ * this class becomes invalid. Call compute() to update it with the new
+ * matrix A, or modify a copy of A.
+ */
+ template<typename MatrixDerived>
+ explicit IterativeSolverBase(const EigenBase<MatrixDerived>& A)
+ : m_matrixWrapper(A.derived())
+ {
+ init();
+ compute(matrix());
+ }
+
+
+ IterativeSolverBase(IterativeSolverBase&&) = default;
+
+ ~IterativeSolverBase() {}
+
+ /** Initializes the iterative solver for the sparsity pattern of the matrix \a A for further solving \c Ax=b problems.
+ *
+ * Currently, this function mostly calls analyzePattern on the preconditioner. In the future
+ * we might, for instance, implement column reordering for faster matrix vector products.
+ */
+ template<typename MatrixDerived>
+ Derived& analyzePattern(const EigenBase<MatrixDerived>& A)
+ {
+ grab(A.derived());
+ m_preconditioner.analyzePattern(matrix());
+ m_isInitialized = true;
+ m_analysisIsOk = true;
+ m_info = m_preconditioner.info();
+ return derived();
+ }
+
+ /** Initializes the iterative solver with the numerical values of the matrix \a A for further solving \c Ax=b problems.
+ *
+ * Currently, this function mostly calls factorize on the preconditioner.
+ *
+ * \warning this class stores a reference to the matrix A as well as some
+ * precomputed values that depend on it. Therefore, if \a A is changed
+ * this class becomes invalid. Call compute() to update it with the new
+ * matrix A, or modify a copy of A.
+ */
+ template<typename MatrixDerived>
+ Derived& factorize(const EigenBase<MatrixDerived>& A)
+ {
+ eigen_assert(m_analysisIsOk && "You must first call analyzePattern()");
+ grab(A.derived());
+ m_preconditioner.factorize(matrix());
+ m_factorizationIsOk = true;
+ m_info = m_preconditioner.info();
+ return derived();
+ }
+
+ /** Initializes the iterative solver with the matrix \a A for further solving \c Ax=b problems.
+ *
+ * Currently, this function mostly initializes/computes the preconditioner. In the future
+ * we might, for instance, implement column reordering for faster matrix vector products.
+ *
+ * \warning this class stores a reference to the matrix A as well as some
+ * precomputed values that depend on it. Therefore, if \a A is changed
+ * this class becomes invalid. Call compute() to update it with the new
+ * matrix A, or modify a copy of A.
+ */
+ template<typename MatrixDerived>
+ Derived& compute(const EigenBase<MatrixDerived>& A)
+ {
+ grab(A.derived());
+ m_preconditioner.compute(matrix());
+ m_isInitialized = true;
+ m_analysisIsOk = true;
+ m_factorizationIsOk = true;
+ m_info = m_preconditioner.info();
+ return derived();
+ }
+
+ /** \internal */
+ EIGEN_CONSTEXPR Index rows() const EIGEN_NOEXCEPT { return matrix().rows(); }
+
+ /** \internal */
+ EIGEN_CONSTEXPR Index cols() const EIGEN_NOEXCEPT { return matrix().cols(); }
+
+ /** \returns the tolerance threshold used by the stopping criteria.
+ * \sa setTolerance()
+ */
+ RealScalar tolerance() const { return m_tolerance; }
+
+ /** Sets the tolerance threshold used by the stopping criteria.
+ *
+ * This value is used as an upper bound to the relative residual error: |Ax-b|/|b|.
+ * The default value is the machine precision given by NumTraits<Scalar>::epsilon()
+ */
+ Derived& setTolerance(const RealScalar& tolerance)
+ {
+ m_tolerance = tolerance;
+ return derived();
+ }
+
+ /** \returns a read-write reference to the preconditioner for custom configuration. */
+ Preconditioner& preconditioner() { return m_preconditioner; }
+
+ /** \returns a read-only reference to the preconditioner. */
+ const Preconditioner& preconditioner() const { return m_preconditioner; }
+
+ /** \returns the max number of iterations.
+ * It is either the value set by setMaxIterations or, by default,
+ * twice the number of columns of the matrix.
+ */
+ Index maxIterations() const
+ {
+ return (m_maxIterations<0) ? 2*matrix().cols() : m_maxIterations;
+ }
+
+ /** Sets the max number of iterations.
+ * Default is twice the number of columns of the matrix.
+ */
+ Derived& setMaxIterations(Index maxIters)
+ {
+ m_maxIterations = maxIters;
+ return derived();
+ }
+
+ /** \returns the number of iterations performed during the last solve */
+ Index iterations() const
+ {
+ eigen_assert(m_isInitialized && "IterativeSolverBase is not initialized.");
+ return m_iterations;
+ }
+
+ /** \returns the tolerance error reached during the last solve.
+ * It is a close approximation of the true relative residual error |Ax-b|/|b|.
+ */
+ RealScalar error() const
+ {
+ eigen_assert(m_isInitialized && "IterativeSolverBase is not initialized.");
+ return m_error;
+ }
+
+ /** \returns the solution x of \f$ A x = b \f$ using the current decomposition of A
+ * and \a x0 as an initial solution.
+ *
+ * \sa solve(), compute()
+ */
+ template<typename Rhs,typename Guess>
+ inline const SolveWithGuess<Derived, Rhs, Guess>
+ solveWithGuess(const MatrixBase<Rhs>& b, const Guess& x0) const
+ {
+ eigen_assert(m_isInitialized && "Solver is not initialized.");
+ eigen_assert(derived().rows()==b.rows() && "solve(): invalid number of rows of the right hand side matrix b");
+ return SolveWithGuess<Derived, Rhs, Guess>(derived(), b.derived(), x0);
+ }
+
+ /** \returns Success if the iterations converged, and NoConvergence otherwise. */
+ ComputationInfo info() const
+ {
+ eigen_assert(m_isInitialized && "IterativeSolverBase is not initialized.");
+ return m_info;
+ }
+
+ /** \internal */
+ template<typename Rhs, typename DestDerived>
+ void _solve_with_guess_impl(const Rhs& b, SparseMatrixBase<DestDerived> &aDest) const
+ {
+ eigen_assert(rows()==b.rows());
+
+ Index rhsCols = b.cols();
+ Index size = b.rows();
+ DestDerived& dest(aDest.derived());
+ typedef typename DestDerived::Scalar DestScalar;
+ Eigen::Matrix<DestScalar,Dynamic,1> tb(size);
+ Eigen::Matrix<DestScalar,Dynamic,1> tx(cols());
+ // We do not directly fill dest because sparse expressions have to be free of aliasing issue.
+ // For non square least-square problems, b and dest might not have the same size whereas they might alias each-other.
+ typename DestDerived::PlainObject tmp(cols(),rhsCols);
+ ComputationInfo global_info = Success;
+ for(Index k=0; k<rhsCols; ++k)
+ {
+ tb = b.col(k);
+ tx = dest.col(k);
+ derived()._solve_vector_with_guess_impl(tb,tx);
+ tmp.col(k) = tx.sparseView(0);
+
+ // The call to _solve_vector_with_guess_impl updates m_info, so if it failed for a previous column
+ // we need to restore it to the worst value.
+ if(m_info==NumericalIssue)
+ global_info = NumericalIssue;
+ else if(m_info==NoConvergence)
+ global_info = NoConvergence;
+ }
+ m_info = global_info;
+ dest.swap(tmp);
+ }
+
+ template<typename Rhs, typename DestDerived>
+ std::enable_if_t<Rhs::ColsAtCompileTime!=1 && DestDerived::ColsAtCompileTime!=1>
+ _solve_with_guess_impl(const Rhs& b, MatrixBase<DestDerived> &aDest) const
+ {
+ eigen_assert(rows()==b.rows());
+
+ Index rhsCols = b.cols();
+ DestDerived& dest(aDest.derived());
+ ComputationInfo global_info = Success;
+ for(Index k=0; k<rhsCols; ++k)
+ {
+ typename DestDerived::ColXpr xk(dest,k);
+ typename Rhs::ConstColXpr bk(b,k);
+ derived()._solve_vector_with_guess_impl(bk,xk);
+
+ // The call to _solve_vector_with_guess updates m_info, so if it failed for a previous column
+ // we need to restore it to the worst value.
+ if(m_info==NumericalIssue)
+ global_info = NumericalIssue;
+ else if(m_info==NoConvergence)
+ global_info = NoConvergence;
+ }
+ m_info = global_info;
+ }
+
+ template<typename Rhs, typename DestDerived>
+ std::enable_if_t<Rhs::ColsAtCompileTime==1 || DestDerived::ColsAtCompileTime==1>
+ _solve_with_guess_impl(const Rhs& b, MatrixBase<DestDerived> &dest) const
+ {
+ derived()._solve_vector_with_guess_impl(b,dest.derived());
+ }
+
+ /** \internal default initial guess = 0 */
+ template<typename Rhs,typename Dest>
+ void _solve_impl(const Rhs& b, Dest& x) const
+ {
+ x.setZero();
+ derived()._solve_with_guess_impl(b,x);
+ }
+
+protected:
+ void init()
+ {
+ m_isInitialized = false;
+ m_analysisIsOk = false;
+ m_factorizationIsOk = false;
+ m_maxIterations = -1;
+ m_tolerance = NumTraits<Scalar>::epsilon();
+ }
+
+ typedef internal::generic_matrix_wrapper<MatrixType> MatrixWrapper;
+ typedef typename MatrixWrapper::ActualMatrixType ActualMatrixType;
+
+ const ActualMatrixType& matrix() const
+ {
+ return m_matrixWrapper.matrix();
+ }
+
+ template<typename InputType>
+ void grab(const InputType &A)
+ {
+ m_matrixWrapper.grab(A);
+ }
+
+ MatrixWrapper m_matrixWrapper;
+ Preconditioner m_preconditioner;
+
+ Index m_maxIterations;
+ RealScalar m_tolerance;
+
+ mutable RealScalar m_error;
+ mutable Index m_iterations;
+ mutable ComputationInfo m_info;
+ mutable bool m_analysisIsOk, m_factorizationIsOk;
+};
+
+} // end namespace Eigen
+
+#endif // EIGEN_ITERATIVE_SOLVER_BASE_H
diff --git a/Eigen/src/IterativeLinearSolvers/LeastSquareConjugateGradient.h b/Eigen/src/IterativeLinearSolvers/LeastSquareConjugateGradient.h
new file mode 100644
index 0000000..a76f3f8
--- /dev/null
+++ b/Eigen/src/IterativeLinearSolvers/LeastSquareConjugateGradient.h
@@ -0,0 +1,200 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2015 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_LEAST_SQUARE_CONJUGATE_GRADIENT_H
+#define EIGEN_LEAST_SQUARE_CONJUGATE_GRADIENT_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+
+/** \internal Low-level conjugate gradient algorithm for least-square problems
+ * \param mat The matrix A
+ * \param rhs The right hand side vector b
+ * \param x On input and initial solution, on output the computed solution.
+ * \param precond A preconditioner being able to efficiently solve for an
+ * approximation of A'Ax=b (regardless of b)
+ * \param iters On input the max number of iteration, on output the number of performed iterations.
+ * \param tol_error On input the tolerance error, on output an estimation of the relative error.
+ */
+template<typename MatrixType, typename Rhs, typename Dest, typename Preconditioner>
+EIGEN_DONT_INLINE
+void least_square_conjugate_gradient(const MatrixType& mat, const Rhs& rhs, Dest& x,
+ const Preconditioner& precond, Index& iters,
+ typename Dest::RealScalar& tol_error)
+{
+ using std::sqrt;
+ using std::abs;
+ typedef typename Dest::RealScalar RealScalar;
+ typedef typename Dest::Scalar Scalar;
+ typedef Matrix<Scalar,Dynamic,1> VectorType;
+
+ RealScalar tol = tol_error;
+ Index maxIters = iters;
+
+ Index m = mat.rows(), n = mat.cols();
+
+ VectorType residual = rhs - mat * x;
+ VectorType normal_residual = mat.adjoint() * residual;
+
+ RealScalar rhsNorm2 = (mat.adjoint()*rhs).squaredNorm();
+ if(rhsNorm2 == 0)
+ {
+ x.setZero();
+ iters = 0;
+ tol_error = 0;
+ return;
+ }
+ RealScalar threshold = tol*tol*rhsNorm2;
+ RealScalar residualNorm2 = normal_residual.squaredNorm();
+ if (residualNorm2 < threshold)
+ {
+ iters = 0;
+ tol_error = sqrt(residualNorm2 / rhsNorm2);
+ return;
+ }
+
+ VectorType p(n);
+ p = precond.solve(normal_residual); // initial search direction
+
+ VectorType z(n), tmp(m);
+ RealScalar absNew = numext::real(normal_residual.dot(p)); // the square of the absolute value of r scaled by invM
+ Index i = 0;
+ while(i < maxIters)
+ {
+ tmp.noalias() = mat * p;
+
+ Scalar alpha = absNew / tmp.squaredNorm(); // the amount we travel on dir
+ x += alpha * p; // update solution
+ residual -= alpha * tmp; // update residual
+ normal_residual.noalias() = mat.adjoint() * residual; // update residual of the normal equation
+
+ residualNorm2 = normal_residual.squaredNorm();
+ if(residualNorm2 < threshold)
+ break;
+
+ z = precond.solve(normal_residual); // approximately solve for "A'A z = normal_residual"
+
+ RealScalar absOld = absNew;
+ absNew = numext::real(normal_residual.dot(z)); // update the absolute value of r
+ RealScalar beta = absNew / absOld; // calculate the Gram-Schmidt value used to create the new search direction
+ p = z + beta * p; // update search direction
+ i++;
+ }
+ tol_error = sqrt(residualNorm2 / rhsNorm2);
+ iters = i;
+}
+
+}
+
+template< typename MatrixType_,
+ typename Preconditioner_ = LeastSquareDiagonalPreconditioner<typename MatrixType_::Scalar> >
+class LeastSquaresConjugateGradient;
+
+namespace internal {
+
+template< typename MatrixType_, typename Preconditioner_>
+struct traits<LeastSquaresConjugateGradient<MatrixType_,Preconditioner_> >
+{
+ typedef MatrixType_ MatrixType;
+ typedef Preconditioner_ Preconditioner;
+};
+
+}
+
+/** \ingroup IterativeLinearSolvers_Module
+ * \brief A conjugate gradient solver for sparse (or dense) least-square problems
+ *
+ * This class solves for the least-squares solution to A x = b using an iterative conjugate gradient algorithm.
+ * The matrix A can be non symmetric and rectangular, but the matrix A' A should be positive-definite to guaranty stability.
+ * Otherwise, the SparseLU or SparseQR classes might be preferable.
+ * The matrix A and the vectors x and b can be either dense or sparse.
+ *
+ * \tparam MatrixType_ the type of the matrix A, can be a dense or a sparse matrix.
+ * \tparam Preconditioner_ the type of the preconditioner. Default is LeastSquareDiagonalPreconditioner
+ *
+ * \implsparsesolverconcept
+ *
+ * The maximal number of iterations and tolerance value can be controlled via the setMaxIterations()
+ * and setTolerance() methods. The defaults are the size of the problem for the maximal number of iterations
+ * and NumTraits<Scalar>::epsilon() for the tolerance.
+ *
+ * This class can be used as the direct solver classes. Here is a typical usage example:
+ \code
+ int m=1000000, n = 10000;
+ VectorXd x(n), b(m);
+ SparseMatrix<double> A(m,n);
+ // fill A and b
+ LeastSquaresConjugateGradient<SparseMatrix<double> > lscg;
+ lscg.compute(A);
+ x = lscg.solve(b);
+ std::cout << "#iterations: " << lscg.iterations() << std::endl;
+ std::cout << "estimated error: " << lscg.error() << std::endl;
+ // update b, and solve again
+ x = lscg.solve(b);
+ \endcode
+ *
+ * By default the iterations start with x=0 as an initial guess of the solution.
+ * One can control the start using the solveWithGuess() method.
+ *
+ * \sa class ConjugateGradient, SparseLU, SparseQR
+ */
+template< typename MatrixType_, typename Preconditioner_>
+class LeastSquaresConjugateGradient : public IterativeSolverBase<LeastSquaresConjugateGradient<MatrixType_,Preconditioner_> >
+{
+ typedef IterativeSolverBase<LeastSquaresConjugateGradient> Base;
+ using Base::matrix;
+ using Base::m_error;
+ using Base::m_iterations;
+ using Base::m_info;
+ using Base::m_isInitialized;
+public:
+ typedef MatrixType_ MatrixType;
+ typedef typename MatrixType::Scalar Scalar;
+ typedef typename MatrixType::RealScalar RealScalar;
+ typedef Preconditioner_ Preconditioner;
+
+public:
+
+ /** Default constructor. */
+ LeastSquaresConjugateGradient() : Base() {}
+
+ /** Initialize the solver with matrix \a A for further \c Ax=b solving.
+ *
+ * This constructor is a shortcut for the default constructor followed
+ * by a call to compute().
+ *
+ * \warning this class stores a reference to the matrix A as well as some
+ * precomputed values that depend on it. Therefore, if \a A is changed
+ * this class becomes invalid. Call compute() to update it with the new
+ * matrix A, or modify a copy of A.
+ */
+ template<typename MatrixDerived>
+ explicit LeastSquaresConjugateGradient(const EigenBase<MatrixDerived>& A) : Base(A.derived()) {}
+
+ ~LeastSquaresConjugateGradient() {}
+
+ /** \internal */
+ template<typename Rhs,typename Dest>
+ void _solve_vector_with_guess_impl(const Rhs& b, Dest& x) const
+ {
+ m_iterations = Base::maxIterations();
+ m_error = Base::m_tolerance;
+
+ internal::least_square_conjugate_gradient(matrix(), b, x, Base::m_preconditioner, m_iterations, m_error);
+ m_info = m_error <= Base::m_tolerance ? Success : NoConvergence;
+ }
+
+};
+
+} // end namespace Eigen
+
+#endif // EIGEN_LEAST_SQUARE_CONJUGATE_GRADIENT_H
diff --git a/Eigen/src/IterativeLinearSolvers/SolveWithGuess.h b/Eigen/src/IterativeLinearSolvers/SolveWithGuess.h
new file mode 100644
index 0000000..bb56db3
--- /dev/null
+++ b/Eigen/src/IterativeLinearSolvers/SolveWithGuess.h
@@ -0,0 +1,119 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2014 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_SOLVEWITHGUESS_H
+#define EIGEN_SOLVEWITHGUESS_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+template<typename Decomposition, typename RhsType, typename GuessType> class SolveWithGuess;
+
+/** \class SolveWithGuess
+ * \ingroup IterativeLinearSolvers_Module
+ *
+ * \brief Pseudo expression representing a solving operation
+ *
+ * \tparam Decomposition the type of the matrix or decomposion object
+ * \tparam Rhstype the type of the right-hand side
+ *
+ * This class represents an expression of A.solve(B)
+ * and most of the time this is the only way it is used.
+ *
+ */
+namespace internal {
+
+
+template<typename Decomposition, typename RhsType, typename GuessType>
+struct traits<SolveWithGuess<Decomposition, RhsType, GuessType> >
+ : traits<Solve<Decomposition,RhsType> >
+{};
+
+}
+
+
+template<typename Decomposition, typename RhsType, typename GuessType>
+class SolveWithGuess : public internal::generic_xpr_base<SolveWithGuess<Decomposition,RhsType,GuessType>, MatrixXpr, typename internal::traits<RhsType>::StorageKind>::type
+{
+public:
+ typedef typename internal::traits<SolveWithGuess>::Scalar Scalar;
+ typedef typename internal::traits<SolveWithGuess>::PlainObject PlainObject;
+ typedef typename internal::generic_xpr_base<SolveWithGuess<Decomposition,RhsType,GuessType>, MatrixXpr, typename internal::traits<RhsType>::StorageKind>::type Base;
+ typedef typename internal::ref_selector<SolveWithGuess>::type Nested;
+
+ SolveWithGuess(const Decomposition &dec, const RhsType &rhs, const GuessType &guess)
+ : m_dec(dec), m_rhs(rhs), m_guess(guess)
+ {}
+
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
+ Index rows() const EIGEN_NOEXCEPT { return m_dec.cols(); }
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
+ Index cols() const EIGEN_NOEXCEPT { return m_rhs.cols(); }
+
+ EIGEN_DEVICE_FUNC const Decomposition& dec() const { return m_dec; }
+ EIGEN_DEVICE_FUNC const RhsType& rhs() const { return m_rhs; }
+ EIGEN_DEVICE_FUNC const GuessType& guess() const { return m_guess; }
+
+protected:
+ const Decomposition &m_dec;
+ const RhsType &m_rhs;
+ const GuessType &m_guess;
+
+private:
+ Scalar coeff(Index row, Index col) const;
+ Scalar coeff(Index i) const;
+};
+
+namespace internal {
+
+// Evaluator of SolveWithGuess -> eval into a temporary
+template<typename Decomposition, typename RhsType, typename GuessType>
+struct evaluator<SolveWithGuess<Decomposition,RhsType, GuessType> >
+ : public evaluator<typename SolveWithGuess<Decomposition,RhsType,GuessType>::PlainObject>
+{
+ typedef SolveWithGuess<Decomposition,RhsType,GuessType> SolveType;
+ typedef typename SolveType::PlainObject PlainObject;
+ typedef evaluator<PlainObject> Base;
+
+ evaluator(const SolveType& solve)
+ : m_result(solve.rows(), solve.cols())
+ {
+ internal::construct_at<Base>(this, m_result);
+ m_result = solve.guess();
+ solve.dec()._solve_with_guess_impl(solve.rhs(), m_result);
+ }
+
+protected:
+ PlainObject m_result;
+};
+
+// Specialization for "dst = dec.solveWithGuess(rhs)"
+// NOTE we need to specialize it for Dense2Dense to avoid ambiguous specialization error and a Sparse2Sparse specialization must exist somewhere
+template<typename DstXprType, typename DecType, typename RhsType, typename GuessType, typename Scalar>
+struct Assignment<DstXprType, SolveWithGuess<DecType,RhsType,GuessType>, internal::assign_op<Scalar,Scalar>, Dense2Dense>
+{
+ typedef SolveWithGuess<DecType,RhsType,GuessType> SrcXprType;
+ static void run(DstXprType &dst, const SrcXprType &src, const internal::assign_op<Scalar,Scalar> &)
+ {
+ Index dstRows = src.rows();
+ Index dstCols = src.cols();
+ if((dst.rows()!=dstRows) || (dst.cols()!=dstCols))
+ dst.resize(dstRows, dstCols);
+
+ dst = src.guess();
+ src.dec()._solve_with_guess_impl(src.rhs(), dst/*, src.guess()*/);
+ }
+};
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_SOLVEWITHGUESS_H
diff --git a/Eigen/src/Jacobi/InternalHeaderCheck.h b/Eigen/src/Jacobi/InternalHeaderCheck.h
new file mode 100644
index 0000000..b17b1f2
--- /dev/null
+++ b/Eigen/src/Jacobi/InternalHeaderCheck.h
@@ -0,0 +1,3 @@
+#ifndef EIGEN_JACOBI_MODULE_H
+#error "Please include Eigen/Jacobi instead of including headers inside the src directory directly."
+#endif
diff --git a/Eigen/src/Jacobi/Jacobi.h b/Eigen/src/Jacobi/Jacobi.h
new file mode 100644
index 0000000..5d96989
--- /dev/null
+++ b/Eigen/src/Jacobi/Jacobi.h
@@ -0,0 +1,488 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009 Benoit Jacob <jacob.benoit.1@gmail.com>
+// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_JACOBI_H
+#define EIGEN_JACOBI_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+/** \ingroup Jacobi_Module
+ * \jacobi_module
+ * \class JacobiRotation
+ * \brief Rotation given by a cosine-sine pair.
+ *
+ * This class represents a Jacobi or Givens rotation.
+ * This is a 2D rotation in the plane \c J of angle \f$ \theta \f$ defined by
+ * its cosine \c c and sine \c s as follow:
+ * \f$ J = \left ( \begin{array}{cc} c & \overline s \\ -s & \overline c \end{array} \right ) \f$
+ *
+ * You can apply the respective counter-clockwise rotation to a column vector \c v by
+ * applying its adjoint on the left: \f$ v = J^* v \f$ that translates to the following Eigen code:
+ * \code
+ * v.applyOnTheLeft(J.adjoint());
+ * \endcode
+ *
+ * \sa MatrixBase::applyOnTheLeft(), MatrixBase::applyOnTheRight()
+ */
+template<typename Scalar> class JacobiRotation
+{
+ public:
+ typedef typename NumTraits<Scalar>::Real RealScalar;
+
+ /** Default constructor without any initialization. */
+ EIGEN_DEVICE_FUNC
+ JacobiRotation() {}
+
+ /** Construct a planar rotation from a cosine-sine pair (\a c, \c s). */
+ EIGEN_DEVICE_FUNC
+ JacobiRotation(const Scalar& c, const Scalar& s) : m_c(c), m_s(s) {}
+
+ EIGEN_DEVICE_FUNC Scalar& c() { return m_c; }
+ EIGEN_DEVICE_FUNC Scalar c() const { return m_c; }
+ EIGEN_DEVICE_FUNC Scalar& s() { return m_s; }
+ EIGEN_DEVICE_FUNC Scalar s() const { return m_s; }
+
+ /** Concatenates two planar rotation */
+ EIGEN_DEVICE_FUNC
+ JacobiRotation operator*(const JacobiRotation& other)
+ {
+ using numext::conj;
+ return JacobiRotation(m_c * other.m_c - conj(m_s) * other.m_s,
+ conj(m_c * conj(other.m_s) + conj(m_s) * conj(other.m_c)));
+ }
+
+ /** Returns the transposed transformation */
+ EIGEN_DEVICE_FUNC
+ JacobiRotation transpose() const { using numext::conj; return JacobiRotation(m_c, -conj(m_s)); }
+
+ /** Returns the adjoint transformation */
+ EIGEN_DEVICE_FUNC
+ JacobiRotation adjoint() const { using numext::conj; return JacobiRotation(conj(m_c), -m_s); }
+
+ template<typename Derived>
+ EIGEN_DEVICE_FUNC
+ bool makeJacobi(const MatrixBase<Derived>&, Index p, Index q);
+ EIGEN_DEVICE_FUNC
+ bool makeJacobi(const RealScalar& x, const Scalar& y, const RealScalar& z);
+
+ EIGEN_DEVICE_FUNC
+ void makeGivens(const Scalar& p, const Scalar& q, Scalar* r=0);
+
+ protected:
+ EIGEN_DEVICE_FUNC
+ void makeGivens(const Scalar& p, const Scalar& q, Scalar* r, internal::true_type);
+ EIGEN_DEVICE_FUNC
+ void makeGivens(const Scalar& p, const Scalar& q, Scalar* r, internal::false_type);
+
+ Scalar m_c, m_s;
+};
+
+/** Makes \c *this as a Jacobi rotation \a J such that applying \a J on both the right and left sides of the selfadjoint 2x2 matrix
+ * \f$ B = \left ( \begin{array}{cc} x & y \\ \overline y & z \end{array} \right )\f$ yields a diagonal matrix \f$ A = J^* B J \f$
+ *
+ * \sa MatrixBase::makeJacobi(const MatrixBase<Derived>&, Index, Index), MatrixBase::applyOnTheLeft(), MatrixBase::applyOnTheRight()
+ */
+template<typename Scalar>
+EIGEN_DEVICE_FUNC
+bool JacobiRotation<Scalar>::makeJacobi(const RealScalar& x, const Scalar& y, const RealScalar& z)
+{
+ using std::sqrt;
+ using std::abs;
+
+ RealScalar deno = RealScalar(2)*abs(y);
+ if(deno < (std::numeric_limits<RealScalar>::min)())
+ {
+ m_c = Scalar(1);
+ m_s = Scalar(0);
+ return false;
+ }
+ else
+ {
+ RealScalar tau = (x-z)/deno;
+ RealScalar w = sqrt(numext::abs2(tau) + RealScalar(1));
+ RealScalar t;
+ if(tau>RealScalar(0))
+ {
+ t = RealScalar(1) / (tau + w);
+ }
+ else
+ {
+ t = RealScalar(1) / (tau - w);
+ }
+ RealScalar sign_t = t > RealScalar(0) ? RealScalar(1) : RealScalar(-1);
+ RealScalar n = RealScalar(1) / sqrt(numext::abs2(t)+RealScalar(1));
+ m_s = - sign_t * (numext::conj(y) / abs(y)) * abs(t) * n;
+ m_c = n;
+ return true;
+ }
+}
+
+/** Makes \c *this as a Jacobi rotation \c J such that applying \a J on both the right and left sides of the 2x2 selfadjoint matrix
+ * \f$ B = \left ( \begin{array}{cc} \text{this}_{pp} & \text{this}_{pq} \\ (\text{this}_{pq})^* & \text{this}_{qq} \end{array} \right )\f$ yields
+ * a diagonal matrix \f$ A = J^* B J \f$
+ *
+ * Example: \include Jacobi_makeJacobi.cpp
+ * Output: \verbinclude Jacobi_makeJacobi.out
+ *
+ * \sa JacobiRotation::makeJacobi(RealScalar, Scalar, RealScalar), MatrixBase::applyOnTheLeft(), MatrixBase::applyOnTheRight()
+ */
+template<typename Scalar>
+template<typename Derived>
+EIGEN_DEVICE_FUNC
+inline bool JacobiRotation<Scalar>::makeJacobi(const MatrixBase<Derived>& m, Index p, Index q)
+{
+ return makeJacobi(numext::real(m.coeff(p,p)), m.coeff(p,q), numext::real(m.coeff(q,q)));
+}
+
+/** Makes \c *this as a Givens rotation \c G such that applying \f$ G^* \f$ to the left of the vector
+ * \f$ V = \left ( \begin{array}{c} p \\ q \end{array} \right )\f$ yields:
+ * \f$ G^* V = \left ( \begin{array}{c} r \\ 0 \end{array} \right )\f$.
+ *
+ * The value of \a r is returned if \a r is not null (the default is null).
+ * Also note that G is built such that the cosine is always real.
+ *
+ * Example: \include Jacobi_makeGivens.cpp
+ * Output: \verbinclude Jacobi_makeGivens.out
+ *
+ * This function implements the continuous Givens rotation generation algorithm
+ * found in Anderson (2000), Discontinuous Plane Rotations and the Symmetric Eigenvalue Problem.
+ * LAPACK Working Note 150, University of Tennessee, UT-CS-00-454, December 4, 2000.
+ *
+ * \sa MatrixBase::applyOnTheLeft(), MatrixBase::applyOnTheRight()
+ */
+template<typename Scalar>
+EIGEN_DEVICE_FUNC
+void JacobiRotation<Scalar>::makeGivens(const Scalar& p, const Scalar& q, Scalar* r)
+{
+ makeGivens(p, q, r, std::conditional_t<NumTraits<Scalar>::IsComplex, internal::true_type, internal::false_type>());
+}
+
+
+// specialization for complexes
+template<typename Scalar>
+EIGEN_DEVICE_FUNC
+void JacobiRotation<Scalar>::makeGivens(const Scalar& p, const Scalar& q, Scalar* r, internal::true_type)
+{
+ using std::sqrt;
+ using std::abs;
+ using numext::conj;
+
+ if(q==Scalar(0))
+ {
+ m_c = numext::real(p)<0 ? Scalar(-1) : Scalar(1);
+ m_s = 0;
+ if(r) *r = m_c * p;
+ }
+ else if(p==Scalar(0))
+ {
+ m_c = 0;
+ m_s = -q/abs(q);
+ if(r) *r = abs(q);
+ }
+ else
+ {
+ RealScalar p1 = numext::norm1(p);
+ RealScalar q1 = numext::norm1(q);
+ if(p1>=q1)
+ {
+ Scalar ps = p / p1;
+ RealScalar p2 = numext::abs2(ps);
+ Scalar qs = q / p1;
+ RealScalar q2 = numext::abs2(qs);
+
+ RealScalar u = sqrt(RealScalar(1) + q2/p2);
+ if(numext::real(p)<RealScalar(0))
+ u = -u;
+
+ m_c = Scalar(1)/u;
+ m_s = -qs*conj(ps)*(m_c/p2);
+ if(r) *r = p * u;
+ }
+ else
+ {
+ Scalar ps = p / q1;
+ RealScalar p2 = numext::abs2(ps);
+ Scalar qs = q / q1;
+ RealScalar q2 = numext::abs2(qs);
+
+ RealScalar u = q1 * sqrt(p2 + q2);
+ if(numext::real(p)<RealScalar(0))
+ u = -u;
+
+ p1 = abs(p);
+ ps = p/p1;
+ m_c = p1/u;
+ m_s = -conj(ps) * (q/u);
+ if(r) *r = ps * u;
+ }
+ }
+}
+
+// specialization for reals
+template<typename Scalar>
+EIGEN_DEVICE_FUNC
+void JacobiRotation<Scalar>::makeGivens(const Scalar& p, const Scalar& q, Scalar* r, internal::false_type)
+{
+ using std::sqrt;
+ using std::abs;
+ if(numext::is_exactly_zero(q))
+ {
+ m_c = p<Scalar(0) ? Scalar(-1) : Scalar(1);
+ m_s = Scalar(0);
+ if(r) *r = abs(p);
+ }
+ else if(numext::is_exactly_zero(p))
+ {
+ m_c = Scalar(0);
+ m_s = q<Scalar(0) ? Scalar(1) : Scalar(-1);
+ if(r) *r = abs(q);
+ }
+ else if(abs(p) > abs(q))
+ {
+ Scalar t = q/p;
+ Scalar u = sqrt(Scalar(1) + numext::abs2(t));
+ if(p<Scalar(0))
+ u = -u;
+ m_c = Scalar(1)/u;
+ m_s = -t * m_c;
+ if(r) *r = p * u;
+ }
+ else
+ {
+ Scalar t = p/q;
+ Scalar u = sqrt(Scalar(1) + numext::abs2(t));
+ if(q<Scalar(0))
+ u = -u;
+ m_s = -Scalar(1)/u;
+ m_c = -t * m_s;
+ if(r) *r = q * u;
+ }
+
+}
+
+/****************************************************************************************
+* Implementation of MatrixBase methods
+****************************************************************************************/
+
+namespace internal {
+/** \jacobi_module
+ * Applies the clock wise 2D rotation \a j to the set of 2D vectors of coordinates \a x and \a y:
+ * \f$ \left ( \begin{array}{cc} x \\ y \end{array} \right ) = J \left ( \begin{array}{cc} x \\ y \end{array} \right ) \f$
+ *
+ * \sa MatrixBase::applyOnTheLeft(), MatrixBase::applyOnTheRight()
+ */
+template<typename VectorX, typename VectorY, typename OtherScalar>
+EIGEN_DEVICE_FUNC
+void apply_rotation_in_the_plane(DenseBase<VectorX>& xpr_x, DenseBase<VectorY>& xpr_y, const JacobiRotation<OtherScalar>& j);
+}
+
+/** \jacobi_module
+ * Applies the rotation in the plane \a j to the rows \a p and \a q of \c *this, i.e., it computes B = J * B,
+ * with \f$ B = \left ( \begin{array}{cc} \text{*this.row}(p) \\ \text{*this.row}(q) \end{array} \right ) \f$.
+ *
+ * \sa class JacobiRotation, MatrixBase::applyOnTheRight(), internal::apply_rotation_in_the_plane()
+ */
+template<typename Derived>
+template<typename OtherScalar>
+EIGEN_DEVICE_FUNC
+inline void MatrixBase<Derived>::applyOnTheLeft(Index p, Index q, const JacobiRotation<OtherScalar>& j)
+{
+ RowXpr x(this->row(p));
+ RowXpr y(this->row(q));
+ internal::apply_rotation_in_the_plane(x, y, j);
+}
+
+/** \ingroup Jacobi_Module
+ * Applies the rotation in the plane \a j to the columns \a p and \a q of \c *this, i.e., it computes B = B * J
+ * with \f$ B = \left ( \begin{array}{cc} \text{*this.col}(p) & \text{*this.col}(q) \end{array} \right ) \f$.
+ *
+ * \sa class JacobiRotation, MatrixBase::applyOnTheLeft(), internal::apply_rotation_in_the_plane()
+ */
+template<typename Derived>
+template<typename OtherScalar>
+EIGEN_DEVICE_FUNC
+inline void MatrixBase<Derived>::applyOnTheRight(Index p, Index q, const JacobiRotation<OtherScalar>& j)
+{
+ ColXpr x(this->col(p));
+ ColXpr y(this->col(q));
+ internal::apply_rotation_in_the_plane(x, y, j.transpose());
+}
+
+namespace internal {
+
+template<typename Scalar, typename OtherScalar,
+ int SizeAtCompileTime, int MinAlignment, bool Vectorizable>
+struct apply_rotation_in_the_plane_selector
+{
+ static EIGEN_DEVICE_FUNC
+ inline void run(Scalar *x, Index incrx, Scalar *y, Index incry, Index size, OtherScalar c, OtherScalar s)
+ {
+ for(Index i=0; i<size; ++i)
+ {
+ Scalar xi = *x;
+ Scalar yi = *y;
+ *x = c * xi + numext::conj(s) * yi;
+ *y = -s * xi + numext::conj(c) * yi;
+ x += incrx;
+ y += incry;
+ }
+ }
+};
+
+template<typename Scalar, typename OtherScalar,
+ int SizeAtCompileTime, int MinAlignment>
+struct apply_rotation_in_the_plane_selector<Scalar,OtherScalar,SizeAtCompileTime,MinAlignment,true /* vectorizable */>
+{
+ static inline void run(Scalar *x, Index incrx, Scalar *y, Index incry, Index size, OtherScalar c, OtherScalar s)
+ {
+ typedef typename packet_traits<Scalar>::type Packet;
+ typedef typename packet_traits<OtherScalar>::type OtherPacket;
+
+ enum {
+ RequiredAlignment = plain_enum_max(unpacket_traits<Packet>::alignment,
+ unpacket_traits<OtherPacket>::alignment),
+ PacketSize = packet_traits<Scalar>::size,
+ OtherPacketSize = packet_traits<OtherScalar>::size
+ };
+
+ /*** dynamic-size vectorized paths ***/
+ if(size >= 2 * PacketSize && SizeAtCompileTime == Dynamic && ((incrx == 1 && incry == 1) || PacketSize == 1))
+ {
+ // both vectors are sequentially stored in memory => vectorization
+ enum { Peeling = 2 };
+
+ Index alignedStart = internal::first_default_aligned(y, size);
+ Index alignedEnd = alignedStart + ((size-alignedStart)/PacketSize)*PacketSize;
+
+ const OtherPacket pc = pset1<OtherPacket>(c);
+ const OtherPacket ps = pset1<OtherPacket>(s);
+ conj_helper<OtherPacket,Packet,NumTraits<OtherScalar>::IsComplex,false> pcj;
+ conj_helper<OtherPacket,Packet,false,false> pm;
+
+ for(Index i=0; i<alignedStart; ++i)
+ {
+ Scalar xi = x[i];
+ Scalar yi = y[i];
+ x[i] = c * xi + numext::conj(s) * yi;
+ y[i] = -s * xi + numext::conj(c) * yi;
+ }
+
+ Scalar* EIGEN_RESTRICT px = x + alignedStart;
+ Scalar* EIGEN_RESTRICT py = y + alignedStart;
+
+ if(internal::first_default_aligned(x, size)==alignedStart)
+ {
+ for(Index i=alignedStart; i<alignedEnd; i+=PacketSize)
+ {
+ Packet xi = pload<Packet>(px);
+ Packet yi = pload<Packet>(py);
+ pstore(px, padd(pm.pmul(pc,xi),pcj.pmul(ps,yi)));
+ pstore(py, psub(pcj.pmul(pc,yi),pm.pmul(ps,xi)));
+ px += PacketSize;
+ py += PacketSize;
+ }
+ }
+ else
+ {
+ Index peelingEnd = alignedStart + ((size-alignedStart)/(Peeling*PacketSize))*(Peeling*PacketSize);
+ for(Index i=alignedStart; i<peelingEnd; i+=Peeling*PacketSize)
+ {
+ Packet xi = ploadu<Packet>(px);
+ Packet xi1 = ploadu<Packet>(px+PacketSize);
+ Packet yi = pload <Packet>(py);
+ Packet yi1 = pload <Packet>(py+PacketSize);
+ pstoreu(px, padd(pm.pmul(pc,xi),pcj.pmul(ps,yi)));
+ pstoreu(px+PacketSize, padd(pm.pmul(pc,xi1),pcj.pmul(ps,yi1)));
+ pstore (py, psub(pcj.pmul(pc,yi),pm.pmul(ps,xi)));
+ pstore (py+PacketSize, psub(pcj.pmul(pc,yi1),pm.pmul(ps,xi1)));
+ px += Peeling*PacketSize;
+ py += Peeling*PacketSize;
+ }
+ if(alignedEnd!=peelingEnd)
+ {
+ Packet xi = ploadu<Packet>(x+peelingEnd);
+ Packet yi = pload <Packet>(y+peelingEnd);
+ pstoreu(x+peelingEnd, padd(pm.pmul(pc,xi),pcj.pmul(ps,yi)));
+ pstore (y+peelingEnd, psub(pcj.pmul(pc,yi),pm.pmul(ps,xi)));
+ }
+ }
+
+ for(Index i=alignedEnd; i<size; ++i)
+ {
+ Scalar xi = x[i];
+ Scalar yi = y[i];
+ x[i] = c * xi + numext::conj(s) * yi;
+ y[i] = -s * xi + numext::conj(c) * yi;
+ }
+ }
+
+ /*** fixed-size vectorized path ***/
+ else if(SizeAtCompileTime != Dynamic && MinAlignment >= RequiredAlignment)
+ {
+ const OtherPacket pc = pset1<OtherPacket>(c);
+ const OtherPacket ps = pset1<OtherPacket>(s);
+ conj_helper<OtherPacket,Packet,NumTraits<OtherScalar>::IsComplex,false> pcj;
+ conj_helper<OtherPacket,Packet,false,false> pm;
+ Scalar* EIGEN_RESTRICT px = x;
+ Scalar* EIGEN_RESTRICT py = y;
+ for(Index i=0; i<size; i+=PacketSize)
+ {
+ Packet xi = pload<Packet>(px);
+ Packet yi = pload<Packet>(py);
+ pstore(px, padd(pm.pmul(pc,xi),pcj.pmul(ps,yi)));
+ pstore(py, psub(pcj.pmul(pc,yi),pm.pmul(ps,xi)));
+ px += PacketSize;
+ py += PacketSize;
+ }
+ }
+
+ /*** non-vectorized path ***/
+ else
+ {
+ apply_rotation_in_the_plane_selector<Scalar,OtherScalar,SizeAtCompileTime,MinAlignment,false>::run(x,incrx,y,incry,size,c,s);
+ }
+ }
+};
+
+template<typename VectorX, typename VectorY, typename OtherScalar>
+EIGEN_DEVICE_FUNC
+void inline apply_rotation_in_the_plane(DenseBase<VectorX>& xpr_x, DenseBase<VectorY>& xpr_y, const JacobiRotation<OtherScalar>& j)
+{
+ typedef typename VectorX::Scalar Scalar;
+ constexpr bool Vectorizable = (int(evaluator<VectorX>::Flags) & int(evaluator<VectorY>::Flags) & PacketAccessBit) &&
+ (int(packet_traits<Scalar>::size) == int(packet_traits<OtherScalar>::size));
+
+ eigen_assert(xpr_x.size() == xpr_y.size());
+ Index size = xpr_x.size();
+ Index incrx = xpr_x.derived().innerStride();
+ Index incry = xpr_y.derived().innerStride();
+
+ Scalar* EIGEN_RESTRICT x = &xpr_x.derived().coeffRef(0);
+ Scalar* EIGEN_RESTRICT y = &xpr_y.derived().coeffRef(0);
+
+ OtherScalar c = j.c();
+ OtherScalar s = j.s();
+ if (numext::is_exactly_one(c) && numext::is_exactly_zero(s))
+ return;
+
+ apply_rotation_in_the_plane_selector<
+ Scalar,OtherScalar,
+ VectorX::SizeAtCompileTime,
+ plain_enum_min(evaluator<VectorX>::Alignment, evaluator<VectorY>::Alignment),
+ Vectorizable>::run(x,incrx,y,incry,size,c,s);
+}
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_JACOBI_H
diff --git a/Eigen/src/KLUSupport/InternalHeaderCheck.h b/Eigen/src/KLUSupport/InternalHeaderCheck.h
new file mode 100644
index 0000000..eb1d671
--- /dev/null
+++ b/Eigen/src/KLUSupport/InternalHeaderCheck.h
@@ -0,0 +1,3 @@
+#ifndef EIGEN_KLUSUPPORT_MODULE_H
+#error "Please include Eigen/KLUSupport instead of including headers inside the src directory directly."
+#endif
diff --git a/Eigen/src/KLUSupport/KLUSupport.h b/Eigen/src/KLUSupport/KLUSupport.h
new file mode 100644
index 0000000..bfe2f66
--- /dev/null
+++ b/Eigen/src/KLUSupport/KLUSupport.h
@@ -0,0 +1,360 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2017 Kyle Macfarlan <kyle.macfarlan@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_KLUSUPPORT_H
+#define EIGEN_KLUSUPPORT_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+/* TODO extract L, extract U, compute det, etc... */
+
+/** \ingroup KLUSupport_Module
+ * \brief A sparse LU factorization and solver based on KLU
+ *
+ * This class allows to solve for A.X = B sparse linear problems via a LU factorization
+ * using the KLU library. The sparse matrix A must be squared and full rank.
+ * The vectors or matrices X and B can be either dense or sparse.
+ *
+ * \warning The input matrix A should be in a \b compressed and \b column-major form.
+ * Otherwise an expensive copy will be made. You can call the inexpensive makeCompressed() to get a compressed matrix.
+ * \tparam MatrixType_ the type of the sparse matrix A, it must be a SparseMatrix<>
+ *
+ * \implsparsesolverconcept
+ *
+ * \sa \ref TutorialSparseSolverConcept, class UmfPackLU, class SparseLU
+ */
+
+
+inline int klu_solve(klu_symbolic *Symbolic, klu_numeric *Numeric, Index ldim, Index nrhs, double B [ ], klu_common *Common, double) {
+ return klu_solve(Symbolic, Numeric, internal::convert_index<int>(ldim), internal::convert_index<int>(nrhs), B, Common);
+}
+
+inline int klu_solve(klu_symbolic *Symbolic, klu_numeric *Numeric, Index ldim, Index nrhs, std::complex<double>B[], klu_common *Common, std::complex<double>) {
+ return klu_z_solve(Symbolic, Numeric, internal::convert_index<int>(ldim), internal::convert_index<int>(nrhs), &numext::real_ref(B[0]), Common);
+}
+
+inline int klu_tsolve(klu_symbolic *Symbolic, klu_numeric *Numeric, Index ldim, Index nrhs, double B[], klu_common *Common, double) {
+ return klu_tsolve(Symbolic, Numeric, internal::convert_index<int>(ldim), internal::convert_index<int>(nrhs), B, Common);
+}
+
+inline int klu_tsolve(klu_symbolic *Symbolic, klu_numeric *Numeric, Index ldim, Index nrhs, std::complex<double>B[], klu_common *Common, std::complex<double>) {
+ return klu_z_tsolve(Symbolic, Numeric, internal::convert_index<int>(ldim), internal::convert_index<int>(nrhs), &numext::real_ref(B[0]), 0, Common);
+}
+
+inline klu_numeric* klu_factor(int Ap [ ], int Ai [ ], double Ax [ ], klu_symbolic *Symbolic, klu_common *Common, double) {
+ return klu_factor(Ap, Ai, Ax, Symbolic, Common);
+}
+
+inline klu_numeric* klu_factor(int Ap[], int Ai[], std::complex<double> Ax[], klu_symbolic *Symbolic, klu_common *Common, std::complex<double>) {
+ return klu_z_factor(Ap, Ai, &numext::real_ref(Ax[0]), Symbolic, Common);
+}
+
+
+template<typename MatrixType_>
+class KLU : public SparseSolverBase<KLU<MatrixType_> >
+{
+ protected:
+ typedef SparseSolverBase<KLU<MatrixType_> > Base;
+ using Base::m_isInitialized;
+ public:
+ using Base::_solve_impl;
+ typedef MatrixType_ MatrixType;
+ typedef typename MatrixType::Scalar Scalar;
+ typedef typename MatrixType::RealScalar RealScalar;
+ typedef typename MatrixType::StorageIndex StorageIndex;
+ typedef Matrix<Scalar,Dynamic,1> Vector;
+ typedef Matrix<int, 1, MatrixType::ColsAtCompileTime> IntRowVectorType;
+ typedef Matrix<int, MatrixType::RowsAtCompileTime, 1> IntColVectorType;
+ typedef SparseMatrix<Scalar> LUMatrixType;
+ typedef SparseMatrix<Scalar,ColMajor,int> KLUMatrixType;
+ typedef Ref<const KLUMatrixType, StandardCompressedFormat> KLUMatrixRef;
+ enum {
+ ColsAtCompileTime = MatrixType::ColsAtCompileTime,
+ MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime
+ };
+
+ public:
+
+ KLU()
+ : m_dummy(0,0), mp_matrix(m_dummy)
+ {
+ init();
+ }
+
+ template<typename InputMatrixType>
+ explicit KLU(const InputMatrixType& matrix)
+ : mp_matrix(matrix)
+ {
+ init();
+ compute(matrix);
+ }
+
+ ~KLU()
+ {
+ if(m_symbolic) klu_free_symbolic(&m_symbolic,&m_common);
+ if(m_numeric) klu_free_numeric(&m_numeric,&m_common);
+ }
+
+ EIGEN_CONSTEXPR inline Index rows() const EIGEN_NOEXCEPT { return mp_matrix.rows(); }
+ EIGEN_CONSTEXPR inline Index cols() const EIGEN_NOEXCEPT { return mp_matrix.cols(); }
+
+ /** \brief Reports whether previous computation was successful.
+ *
+ * \returns \c Success if computation was successful,
+ * \c NumericalIssue if the matrix.appears to be negative.
+ */
+ ComputationInfo info() const
+ {
+ eigen_assert(m_isInitialized && "Decomposition is not initialized.");
+ return m_info;
+ }
+#if 0 // not implemented yet
+ inline const LUMatrixType& matrixL() const
+ {
+ if (m_extractedDataAreDirty) extractData();
+ return m_l;
+ }
+
+ inline const LUMatrixType& matrixU() const
+ {
+ if (m_extractedDataAreDirty) extractData();
+ return m_u;
+ }
+
+ inline const IntColVectorType& permutationP() const
+ {
+ if (m_extractedDataAreDirty) extractData();
+ return m_p;
+ }
+
+ inline const IntRowVectorType& permutationQ() const
+ {
+ if (m_extractedDataAreDirty) extractData();
+ return m_q;
+ }
+#endif
+ /** Computes the sparse Cholesky decomposition of \a matrix
+ * Note that the matrix should be column-major, and in compressed format for best performance.
+ * \sa SparseMatrix::makeCompressed().
+ */
+ template<typename InputMatrixType>
+ void compute(const InputMatrixType& matrix)
+ {
+ if(m_symbolic) klu_free_symbolic(&m_symbolic, &m_common);
+ if(m_numeric) klu_free_numeric(&m_numeric, &m_common);
+ grab(matrix.derived());
+ analyzePattern_impl();
+ factorize_impl();
+ }
+
+ /** Performs a symbolic decomposition on the sparcity of \a matrix.
+ *
+ * This function is particularly useful when solving for several problems having the same structure.
+ *
+ * \sa factorize(), compute()
+ */
+ template<typename InputMatrixType>
+ void analyzePattern(const InputMatrixType& matrix)
+ {
+ if(m_symbolic) klu_free_symbolic(&m_symbolic, &m_common);
+ if(m_numeric) klu_free_numeric(&m_numeric, &m_common);
+
+ grab(matrix.derived());
+
+ analyzePattern_impl();
+ }
+
+
+ /** Provides access to the control settings array used by KLU.
+ *
+ * See KLU documentation for details.
+ */
+ inline const klu_common& kluCommon() const
+ {
+ return m_common;
+ }
+
+ /** Provides access to the control settings array used by UmfPack.
+ *
+ * If this array contains NaN's, the default values are used.
+ *
+ * See KLU documentation for details.
+ */
+ inline klu_common& kluCommon()
+ {
+ return m_common;
+ }
+
+ /** Performs a numeric decomposition of \a matrix
+ *
+ * The given matrix must has the same sparcity than the matrix on which the pattern anylysis has been performed.
+ *
+ * \sa analyzePattern(), compute()
+ */
+ template<typename InputMatrixType>
+ void factorize(const InputMatrixType& matrix)
+ {
+ eigen_assert(m_analysisIsOk && "KLU: you must first call analyzePattern()");
+ if(m_numeric)
+ klu_free_numeric(&m_numeric,&m_common);
+
+ grab(matrix.derived());
+
+ factorize_impl();
+ }
+
+ /** \internal */
+ template<typename BDerived,typename XDerived>
+ bool _solve_impl(const MatrixBase<BDerived> &b, MatrixBase<XDerived> &x) const;
+
+#if 0 // not implemented yet
+ Scalar determinant() const;
+
+ void extractData() const;
+#endif
+
+ protected:
+
+ void init()
+ {
+ m_info = InvalidInput;
+ m_isInitialized = false;
+ m_numeric = 0;
+ m_symbolic = 0;
+ m_extractedDataAreDirty = true;
+
+ klu_defaults(&m_common);
+ }
+
+ void analyzePattern_impl()
+ {
+ m_info = InvalidInput;
+ m_analysisIsOk = false;
+ m_factorizationIsOk = false;
+ m_symbolic = klu_analyze(internal::convert_index<int>(mp_matrix.rows()),
+ const_cast<StorageIndex*>(mp_matrix.outerIndexPtr()), const_cast<StorageIndex*>(mp_matrix.innerIndexPtr()),
+ &m_common);
+ if (m_symbolic) {
+ m_isInitialized = true;
+ m_info = Success;
+ m_analysisIsOk = true;
+ m_extractedDataAreDirty = true;
+ }
+ }
+
+ void factorize_impl()
+ {
+
+ m_numeric = klu_factor(const_cast<StorageIndex*>(mp_matrix.outerIndexPtr()), const_cast<StorageIndex*>(mp_matrix.innerIndexPtr()), const_cast<Scalar*>(mp_matrix.valuePtr()),
+ m_symbolic, &m_common, Scalar());
+
+
+ m_info = m_numeric ? Success : NumericalIssue;
+ m_factorizationIsOk = m_numeric ? 1 : 0;
+ m_extractedDataAreDirty = true;
+ }
+
+ template<typename MatrixDerived>
+ void grab(const EigenBase<MatrixDerived> &A)
+ {
+ internal::destroy_at(&mp_matrix);
+ internal::construct_at(&mp_matrix, A.derived());
+ }
+
+ void grab(const KLUMatrixRef &A)
+ {
+ if(&(A.derived()) != &mp_matrix)
+ {
+ internal::destroy_at(&mp_matrix);
+ internal::construct_at(&mp_matrix, A);
+ }
+ }
+
+ // cached data to reduce reallocation, etc.
+#if 0 // not implemented yet
+ mutable LUMatrixType m_l;
+ mutable LUMatrixType m_u;
+ mutable IntColVectorType m_p;
+ mutable IntRowVectorType m_q;
+#endif
+
+ KLUMatrixType m_dummy;
+ KLUMatrixRef mp_matrix;
+
+ klu_numeric* m_numeric;
+ klu_symbolic* m_symbolic;
+ klu_common m_common;
+ mutable ComputationInfo m_info;
+ int m_factorizationIsOk;
+ int m_analysisIsOk;
+ mutable bool m_extractedDataAreDirty;
+
+ private:
+ KLU(const KLU& ) { }
+};
+
+#if 0 // not implemented yet
+template<typename MatrixType>
+void KLU<MatrixType>::extractData() const
+{
+ if (m_extractedDataAreDirty)
+ {
+ eigen_assert(false && "KLU: extractData Not Yet Implemented");
+
+ // get size of the data
+ int lnz, unz, rows, cols, nz_udiag;
+ umfpack_get_lunz(&lnz, &unz, &rows, &cols, &nz_udiag, m_numeric, Scalar());
+
+ // allocate data
+ m_l.resize(rows,(std::min)(rows,cols));
+ m_l.resizeNonZeros(lnz);
+
+ m_u.resize((std::min)(rows,cols),cols);
+ m_u.resizeNonZeros(unz);
+
+ m_p.resize(rows);
+ m_q.resize(cols);
+
+ // extract
+ umfpack_get_numeric(m_l.outerIndexPtr(), m_l.innerIndexPtr(), m_l.valuePtr(),
+ m_u.outerIndexPtr(), m_u.innerIndexPtr(), m_u.valuePtr(),
+ m_p.data(), m_q.data(), 0, 0, 0, m_numeric);
+
+ m_extractedDataAreDirty = false;
+ }
+}
+
+template<typename MatrixType>
+typename KLU<MatrixType>::Scalar KLU<MatrixType>::determinant() const
+{
+ eigen_assert(false && "KLU: extractData Not Yet Implemented");
+ return Scalar();
+}
+#endif
+
+template<typename MatrixType>
+template<typename BDerived,typename XDerived>
+bool KLU<MatrixType>::_solve_impl(const MatrixBase<BDerived> &b, MatrixBase<XDerived> &x) const
+{
+ Index rhsCols = b.cols();
+ EIGEN_STATIC_ASSERT((XDerived::Flags&RowMajorBit)==0, THIS_METHOD_IS_ONLY_FOR_COLUMN_MAJOR_MATRICES);
+ eigen_assert(m_factorizationIsOk && "The decomposition is not in a valid state for solving, you must first call either compute() or analyzePattern()/factorize()");
+
+ x = b;
+ int info = klu_solve(m_symbolic, m_numeric, b.rows(), rhsCols, x.const_cast_derived().data(), const_cast<klu_common*>(&m_common), Scalar());
+
+ m_info = info!=0 ? Success : NumericalIssue;
+ return true;
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_KLUSUPPORT_H
diff --git a/Eigen/src/LU/Determinant.h b/Eigen/src/LU/Determinant.h
new file mode 100644
index 0000000..80e695d
--- /dev/null
+++ b/Eigen/src/LU/Determinant.h
@@ -0,0 +1,119 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_DETERMINANT_H
+#define EIGEN_DETERMINANT_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+
+template<typename Derived>
+EIGEN_DEVICE_FUNC
+inline const typename Derived::Scalar bruteforce_det3_helper
+(const MatrixBase<Derived>& matrix, int a, int b, int c)
+{
+ return matrix.coeff(0,a)
+ * (matrix.coeff(1,b) * matrix.coeff(2,c) - matrix.coeff(1,c) * matrix.coeff(2,b));
+}
+
+template<typename Derived,
+ int DeterminantType = Derived::RowsAtCompileTime
+> struct determinant_impl
+{
+ static inline typename traits<Derived>::Scalar run(const Derived& m)
+ {
+ if(Derived::ColsAtCompileTime==Dynamic && m.rows()==0)
+ return typename traits<Derived>::Scalar(1);
+ return m.partialPivLu().determinant();
+ }
+};
+
+template<typename Derived> struct determinant_impl<Derived, 1>
+{
+ static inline EIGEN_DEVICE_FUNC
+ typename traits<Derived>::Scalar run(const Derived& m)
+ {
+ return m.coeff(0,0);
+ }
+};
+
+template<typename Derived> struct determinant_impl<Derived, 2>
+{
+ static inline EIGEN_DEVICE_FUNC
+ typename traits<Derived>::Scalar run(const Derived& m)
+ {
+ return m.coeff(0,0) * m.coeff(1,1) - m.coeff(1,0) * m.coeff(0,1);
+ }
+};
+
+template<typename Derived> struct determinant_impl<Derived, 3>
+{
+ static inline EIGEN_DEVICE_FUNC
+ typename traits<Derived>::Scalar run(const Derived& m)
+ {
+ return bruteforce_det3_helper(m,0,1,2)
+ - bruteforce_det3_helper(m,1,0,2)
+ + bruteforce_det3_helper(m,2,0,1);
+ }
+};
+
+template<typename Derived> struct determinant_impl<Derived, 4>
+{
+ typedef typename traits<Derived>::Scalar Scalar;
+ static EIGEN_DEVICE_FUNC
+ Scalar run(const Derived& m)
+ {
+ Scalar d2_01 = det2(m, 0, 1);
+ Scalar d2_02 = det2(m, 0, 2);
+ Scalar d2_03 = det2(m, 0, 3);
+ Scalar d2_12 = det2(m, 1, 2);
+ Scalar d2_13 = det2(m, 1, 3);
+ Scalar d2_23 = det2(m, 2, 3);
+ Scalar d3_0 = det3(m, 1,d2_23, 2,d2_13, 3,d2_12);
+ Scalar d3_1 = det3(m, 0,d2_23, 2,d2_03, 3,d2_02);
+ Scalar d3_2 = det3(m, 0,d2_13, 1,d2_03, 3,d2_01);
+ Scalar d3_3 = det3(m, 0,d2_12, 1,d2_02, 2,d2_01);
+ return internal::pmadd(static_cast<Scalar>(-m(0,3)),d3_0, static_cast<Scalar>(m(1,3)*d3_1)) +
+ internal::pmadd(static_cast<Scalar>(-m(2,3)),d3_2, static_cast<Scalar>(m(3,3)*d3_3));
+ }
+protected:
+ static EIGEN_DEVICE_FUNC
+ Scalar det2(const Derived& m, Index i0, Index i1)
+ {
+ return m(i0,0) * m(i1,1) - m(i1,0) * m(i0,1);
+ }
+
+ static EIGEN_DEVICE_FUNC
+ Scalar det3(const Derived& m, Index i0, const Scalar& d0, Index i1, const Scalar& d1, Index i2, const Scalar& d2)
+ {
+ return internal::pmadd(m(i0,2), d0, internal::pmadd(static_cast<Scalar>(-m(i1,2)), d1, static_cast<Scalar>(m(i2,2)*d2)));
+ }
+};
+
+} // end namespace internal
+
+/** \lu_module
+ *
+ * \returns the determinant of this matrix
+ */
+template<typename Derived>
+EIGEN_DEVICE_FUNC
+inline typename internal::traits<Derived>::Scalar MatrixBase<Derived>::determinant() const
+{
+ eigen_assert(rows() == cols());
+ typedef typename internal::nested_eval<Derived,Base::RowsAtCompileTime>::type Nested;
+ return internal::determinant_impl<internal::remove_all_t<Nested>>::run(derived());
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_DETERMINANT_H
diff --git a/Eigen/src/LU/FullPivLU.h b/Eigen/src/LU/FullPivLU.h
new file mode 100644
index 0000000..259b549
--- /dev/null
+++ b/Eigen/src/LU/FullPivLU.h
@@ -0,0 +1,874 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2006-2009 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_LU_H
+#define EIGEN_LU_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+template<typename MatrixType_> struct traits<FullPivLU<MatrixType_> >
+ : traits<MatrixType_>
+{
+ typedef MatrixXpr XprKind;
+ typedef SolverStorage StorageKind;
+ typedef int StorageIndex;
+ enum { Flags = 0 };
+};
+
+} // end namespace internal
+
+/** \ingroup LU_Module
+ *
+ * \class FullPivLU
+ *
+ * \brief LU decomposition of a matrix with complete pivoting, and related features
+ *
+ * \tparam MatrixType_ the type of the matrix of which we are computing the LU decomposition
+ *
+ * This class represents a LU decomposition of any matrix, with complete pivoting: the matrix A is
+ * decomposed as \f$ A = P^{-1} L U Q^{-1} \f$ where L is unit-lower-triangular, U is
+ * upper-triangular, and P and Q are permutation matrices. This is a rank-revealing LU
+ * decomposition. The eigenvalues (diagonal coefficients) of U are sorted in such a way that any
+ * zeros are at the end.
+ *
+ * This decomposition provides the generic approach to solving systems of linear equations, computing
+ * the rank, invertibility, inverse, kernel, and determinant.
+ *
+ * This LU decomposition is very stable and well tested with large matrices. However there are use cases where the SVD
+ * decomposition is inherently more stable and/or flexible. For example, when computing the kernel of a matrix,
+ * working with the SVD allows to select the smallest singular values of the matrix, something that
+ * the LU decomposition doesn't see.
+ *
+ * The data of the LU decomposition can be directly accessed through the methods matrixLU(),
+ * permutationP(), permutationQ().
+ *
+ * As an example, here is how the original matrix can be retrieved:
+ * \include class_FullPivLU.cpp
+ * Output: \verbinclude class_FullPivLU.out
+ *
+ * This class supports the \link InplaceDecomposition inplace decomposition \endlink mechanism.
+ *
+ * \sa MatrixBase::fullPivLu(), MatrixBase::determinant(), MatrixBase::inverse()
+ */
+template<typename MatrixType_> class FullPivLU
+ : public SolverBase<FullPivLU<MatrixType_> >
+{
+ public:
+ typedef MatrixType_ MatrixType;
+ typedef SolverBase<FullPivLU> Base;
+ friend class SolverBase<FullPivLU>;
+
+ EIGEN_GENERIC_PUBLIC_INTERFACE(FullPivLU)
+ enum {
+ MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime,
+ MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime
+ };
+ typedef typename internal::plain_row_type<MatrixType, StorageIndex>::type IntRowVectorType;
+ typedef typename internal::plain_col_type<MatrixType, StorageIndex>::type IntColVectorType;
+ typedef PermutationMatrix<ColsAtCompileTime, MaxColsAtCompileTime> PermutationQType;
+ typedef PermutationMatrix<RowsAtCompileTime, MaxRowsAtCompileTime> PermutationPType;
+ typedef typename MatrixType::PlainObject PlainObject;
+
+ /**
+ * \brief Default Constructor.
+ *
+ * The default constructor is useful in cases in which the user intends to
+ * perform decompositions via LU::compute(const MatrixType&).
+ */
+ FullPivLU();
+
+ /** \brief Default Constructor with memory preallocation
+ *
+ * Like the default constructor but with preallocation of the internal data
+ * according to the specified problem \a size.
+ * \sa FullPivLU()
+ */
+ FullPivLU(Index rows, Index cols);
+
+ /** Constructor.
+ *
+ * \param matrix the matrix of which to compute the LU decomposition.
+ * It is required to be nonzero.
+ */
+ template<typename InputType>
+ explicit FullPivLU(const EigenBase<InputType>& matrix);
+
+ /** \brief Constructs a LU factorization from a given matrix
+ *
+ * This overloaded constructor is provided for \link InplaceDecomposition inplace decomposition \endlink when \c MatrixType is a Eigen::Ref.
+ *
+ * \sa FullPivLU(const EigenBase&)
+ */
+ template<typename InputType>
+ explicit FullPivLU(EigenBase<InputType>& matrix);
+
+ /** Computes the LU decomposition of the given matrix.
+ *
+ * \param matrix the matrix of which to compute the LU decomposition.
+ * It is required to be nonzero.
+ *
+ * \returns a reference to *this
+ */
+ template<typename InputType>
+ FullPivLU& compute(const EigenBase<InputType>& matrix) {
+ m_lu = matrix.derived();
+ computeInPlace();
+ return *this;
+ }
+
+ /** \returns the LU decomposition matrix: the upper-triangular part is U, the
+ * unit-lower-triangular part is L (at least for square matrices; in the non-square
+ * case, special care is needed, see the documentation of class FullPivLU).
+ *
+ * \sa matrixL(), matrixU()
+ */
+ inline const MatrixType& matrixLU() const
+ {
+ eigen_assert(m_isInitialized && "LU is not initialized.");
+ return m_lu;
+ }
+
+ /** \returns the number of nonzero pivots in the LU decomposition.
+ * Here nonzero is meant in the exact sense, not in a fuzzy sense.
+ * So that notion isn't really intrinsically interesting, but it is
+ * still useful when implementing algorithms.
+ *
+ * \sa rank()
+ */
+ inline Index nonzeroPivots() const
+ {
+ eigen_assert(m_isInitialized && "LU is not initialized.");
+ return m_nonzero_pivots;
+ }
+
+ /** \returns the absolute value of the biggest pivot, i.e. the biggest
+ * diagonal coefficient of U.
+ */
+ RealScalar maxPivot() const { return m_maxpivot; }
+
+ /** \returns the permutation matrix P
+ *
+ * \sa permutationQ()
+ */
+ EIGEN_DEVICE_FUNC inline const PermutationPType& permutationP() const
+ {
+ eigen_assert(m_isInitialized && "LU is not initialized.");
+ return m_p;
+ }
+
+ /** \returns the permutation matrix Q
+ *
+ * \sa permutationP()
+ */
+ inline const PermutationQType& permutationQ() const
+ {
+ eigen_assert(m_isInitialized && "LU is not initialized.");
+ return m_q;
+ }
+
+ /** \returns the kernel of the matrix, also called its null-space. The columns of the returned matrix
+ * will form a basis of the kernel.
+ *
+ * \note If the kernel has dimension zero, then the returned matrix is a column-vector filled with zeros.
+ *
+ * \note This method has to determine which pivots should be considered nonzero.
+ * For that, it uses the threshold value that you can control by calling
+ * setThreshold(const RealScalar&).
+ *
+ * Example: \include FullPivLU_kernel.cpp
+ * Output: \verbinclude FullPivLU_kernel.out
+ *
+ * \sa image()
+ */
+ inline const internal::kernel_retval<FullPivLU> kernel() const
+ {
+ eigen_assert(m_isInitialized && "LU is not initialized.");
+ return internal::kernel_retval<FullPivLU>(*this);
+ }
+
+ /** \returns the image of the matrix, also called its column-space. The columns of the returned matrix
+ * will form a basis of the image (column-space).
+ *
+ * \param originalMatrix the original matrix, of which *this is the LU decomposition.
+ * The reason why it is needed to pass it here, is that this allows
+ * a large optimization, as otherwise this method would need to reconstruct it
+ * from the LU decomposition.
+ *
+ * \note If the image has dimension zero, then the returned matrix is a column-vector filled with zeros.
+ *
+ * \note This method has to determine which pivots should be considered nonzero.
+ * For that, it uses the threshold value that you can control by calling
+ * setThreshold(const RealScalar&).
+ *
+ * Example: \include FullPivLU_image.cpp
+ * Output: \verbinclude FullPivLU_image.out
+ *
+ * \sa kernel()
+ */
+ inline const internal::image_retval<FullPivLU>
+ image(const MatrixType& originalMatrix) const
+ {
+ eigen_assert(m_isInitialized && "LU is not initialized.");
+ return internal::image_retval<FullPivLU>(*this, originalMatrix);
+ }
+
+ #ifdef EIGEN_PARSED_BY_DOXYGEN
+ /** \return a solution x to the equation Ax=b, where A is the matrix of which
+ * *this is the LU decomposition.
+ *
+ * \param b the right-hand-side of the equation to solve. Can be a vector or a matrix,
+ * the only requirement in order for the equation to make sense is that
+ * b.rows()==A.rows(), where A is the matrix of which *this is the LU decomposition.
+ *
+ * \returns a solution.
+ *
+ * \note_about_checking_solutions
+ *
+ * \note_about_arbitrary_choice_of_solution
+ * \note_about_using_kernel_to_study_multiple_solutions
+ *
+ * Example: \include FullPivLU_solve.cpp
+ * Output: \verbinclude FullPivLU_solve.out
+ *
+ * \sa TriangularView::solve(), kernel(), inverse()
+ */
+ template<typename Rhs>
+ inline const Solve<FullPivLU, Rhs>
+ solve(const MatrixBase<Rhs>& b) const;
+ #endif
+
+ /** \returns an estimate of the reciprocal condition number of the matrix of which \c *this is
+ the LU decomposition.
+ */
+ inline RealScalar rcond() const
+ {
+ eigen_assert(m_isInitialized && "PartialPivLU is not initialized.");
+ return internal::rcond_estimate_helper(m_l1_norm, *this);
+ }
+
+ /** \returns the determinant of the matrix of which
+ * *this is the LU decomposition. It has only linear complexity
+ * (that is, O(n) where n is the dimension of the square matrix)
+ * as the LU decomposition has already been computed.
+ *
+ * \note This is only for square matrices.
+ *
+ * \note For fixed-size matrices of size up to 4, MatrixBase::determinant() offers
+ * optimized paths.
+ *
+ * \warning a determinant can be very big or small, so for matrices
+ * of large enough dimension, there is a risk of overflow/underflow.
+ *
+ * \sa MatrixBase::determinant()
+ */
+ typename internal::traits<MatrixType>::Scalar determinant() const;
+
+ /** Allows to prescribe a threshold to be used by certain methods, such as rank(),
+ * who need to determine when pivots are to be considered nonzero. This is not used for the
+ * LU decomposition itself.
+ *
+ * When it needs to get the threshold value, Eigen calls threshold(). By default, this
+ * uses a formula to automatically determine a reasonable threshold.
+ * Once you have called the present method setThreshold(const RealScalar&),
+ * your value is used instead.
+ *
+ * \param threshold The new value to use as the threshold.
+ *
+ * A pivot will be considered nonzero if its absolute value is strictly greater than
+ * \f$ \vert pivot \vert \leqslant threshold \times \vert maxpivot \vert \f$
+ * where maxpivot is the biggest pivot.
+ *
+ * If you want to come back to the default behavior, call setThreshold(Default_t)
+ */
+ FullPivLU& setThreshold(const RealScalar& threshold)
+ {
+ m_usePrescribedThreshold = true;
+ m_prescribedThreshold = threshold;
+ return *this;
+ }
+
+ /** Allows to come back to the default behavior, letting Eigen use its default formula for
+ * determining the threshold.
+ *
+ * You should pass the special object Eigen::Default as parameter here.
+ * \code lu.setThreshold(Eigen::Default); \endcode
+ *
+ * See the documentation of setThreshold(const RealScalar&).
+ */
+ FullPivLU& setThreshold(Default_t)
+ {
+ m_usePrescribedThreshold = false;
+ return *this;
+ }
+
+ /** Returns the threshold that will be used by certain methods such as rank().
+ *
+ * See the documentation of setThreshold(const RealScalar&).
+ */
+ RealScalar threshold() const
+ {
+ eigen_assert(m_isInitialized || m_usePrescribedThreshold);
+ return m_usePrescribedThreshold ? m_prescribedThreshold
+ // this formula comes from experimenting (see "LU precision tuning" thread on the list)
+ // and turns out to be identical to Higham's formula used already in LDLt.
+ : NumTraits<Scalar>::epsilon() * RealScalar(m_lu.diagonalSize());
+ }
+
+ /** \returns the rank of the matrix of which *this is the LU decomposition.
+ *
+ * \note This method has to determine which pivots should be considered nonzero.
+ * For that, it uses the threshold value that you can control by calling
+ * setThreshold(const RealScalar&).
+ */
+ inline Index rank() const
+ {
+ using std::abs;
+ eigen_assert(m_isInitialized && "LU is not initialized.");
+ RealScalar premultiplied_threshold = abs(m_maxpivot) * threshold();
+ Index result = 0;
+ for(Index i = 0; i < m_nonzero_pivots; ++i)
+ result += (abs(m_lu.coeff(i,i)) > premultiplied_threshold);
+ return result;
+ }
+
+ /** \returns the dimension of the kernel of the matrix of which *this is the LU decomposition.
+ *
+ * \note This method has to determine which pivots should be considered nonzero.
+ * For that, it uses the threshold value that you can control by calling
+ * setThreshold(const RealScalar&).
+ */
+ inline Index dimensionOfKernel() const
+ {
+ eigen_assert(m_isInitialized && "LU is not initialized.");
+ return cols() - rank();
+ }
+
+ /** \returns true if the matrix of which *this is the LU decomposition represents an injective
+ * linear map, i.e. has trivial kernel; false otherwise.
+ *
+ * \note This method has to determine which pivots should be considered nonzero.
+ * For that, it uses the threshold value that you can control by calling
+ * setThreshold(const RealScalar&).
+ */
+ inline bool isInjective() const
+ {
+ eigen_assert(m_isInitialized && "LU is not initialized.");
+ return rank() == cols();
+ }
+
+ /** \returns true if the matrix of which *this is the LU decomposition represents a surjective
+ * linear map; false otherwise.
+ *
+ * \note This method has to determine which pivots should be considered nonzero.
+ * For that, it uses the threshold value that you can control by calling
+ * setThreshold(const RealScalar&).
+ */
+ inline bool isSurjective() const
+ {
+ eigen_assert(m_isInitialized && "LU is not initialized.");
+ return rank() == rows();
+ }
+
+ /** \returns true if the matrix of which *this is the LU decomposition is invertible.
+ *
+ * \note This method has to determine which pivots should be considered nonzero.
+ * For that, it uses the threshold value that you can control by calling
+ * setThreshold(const RealScalar&).
+ */
+ inline bool isInvertible() const
+ {
+ eigen_assert(m_isInitialized && "LU is not initialized.");
+ return isInjective() && (m_lu.rows() == m_lu.cols());
+ }
+
+ /** \returns the inverse of the matrix of which *this is the LU decomposition.
+ *
+ * \note If this matrix is not invertible, the returned matrix has undefined coefficients.
+ * Use isInvertible() to first determine whether this matrix is invertible.
+ *
+ * \sa MatrixBase::inverse()
+ */
+ inline const Inverse<FullPivLU> inverse() const
+ {
+ eigen_assert(m_isInitialized && "LU is not initialized.");
+ eigen_assert(m_lu.rows() == m_lu.cols() && "You can't take the inverse of a non-square matrix!");
+ return Inverse<FullPivLU>(*this);
+ }
+
+ MatrixType reconstructedMatrix() const;
+
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
+ inline Index rows() const EIGEN_NOEXCEPT { return m_lu.rows(); }
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
+ inline Index cols() const EIGEN_NOEXCEPT { return m_lu.cols(); }
+
+ #ifndef EIGEN_PARSED_BY_DOXYGEN
+ template<typename RhsType, typename DstType>
+ void _solve_impl(const RhsType &rhs, DstType &dst) const;
+
+ template<bool Conjugate, typename RhsType, typename DstType>
+ void _solve_impl_transposed(const RhsType &rhs, DstType &dst) const;
+ #endif
+
+ protected:
+
+ EIGEN_STATIC_ASSERT_NON_INTEGER(Scalar)
+
+ void computeInPlace();
+
+ MatrixType m_lu;
+ PermutationPType m_p;
+ PermutationQType m_q;
+ IntColVectorType m_rowsTranspositions;
+ IntRowVectorType m_colsTranspositions;
+ Index m_nonzero_pivots;
+ RealScalar m_l1_norm;
+ RealScalar m_maxpivot, m_prescribedThreshold;
+ signed char m_det_pq;
+ bool m_isInitialized, m_usePrescribedThreshold;
+};
+
+template<typename MatrixType>
+FullPivLU<MatrixType>::FullPivLU()
+ : m_isInitialized(false), m_usePrescribedThreshold(false)
+{
+}
+
+template<typename MatrixType>
+FullPivLU<MatrixType>::FullPivLU(Index rows, Index cols)
+ : m_lu(rows, cols),
+ m_p(rows),
+ m_q(cols),
+ m_rowsTranspositions(rows),
+ m_colsTranspositions(cols),
+ m_isInitialized(false),
+ m_usePrescribedThreshold(false)
+{
+}
+
+template<typename MatrixType>
+template<typename InputType>
+FullPivLU<MatrixType>::FullPivLU(const EigenBase<InputType>& matrix)
+ : m_lu(matrix.rows(), matrix.cols()),
+ m_p(matrix.rows()),
+ m_q(matrix.cols()),
+ m_rowsTranspositions(matrix.rows()),
+ m_colsTranspositions(matrix.cols()),
+ m_isInitialized(false),
+ m_usePrescribedThreshold(false)
+{
+ compute(matrix.derived());
+}
+
+template<typename MatrixType>
+template<typename InputType>
+FullPivLU<MatrixType>::FullPivLU(EigenBase<InputType>& matrix)
+ : m_lu(matrix.derived()),
+ m_p(matrix.rows()),
+ m_q(matrix.cols()),
+ m_rowsTranspositions(matrix.rows()),
+ m_colsTranspositions(matrix.cols()),
+ m_isInitialized(false),
+ m_usePrescribedThreshold(false)
+{
+ computeInPlace();
+}
+
+template<typename MatrixType>
+void FullPivLU<MatrixType>::computeInPlace()
+{
+ // the permutations are stored as int indices, so just to be sure:
+ eigen_assert(m_lu.rows()<=NumTraits<int>::highest() && m_lu.cols()<=NumTraits<int>::highest());
+
+ m_l1_norm = m_lu.cwiseAbs().colwise().sum().maxCoeff();
+
+ const Index size = m_lu.diagonalSize();
+ const Index rows = m_lu.rows();
+ const Index cols = m_lu.cols();
+
+ // will store the transpositions, before we accumulate them at the end.
+ // can't accumulate on-the-fly because that will be done in reverse order for the rows.
+ m_rowsTranspositions.resize(m_lu.rows());
+ m_colsTranspositions.resize(m_lu.cols());
+ Index number_of_transpositions = 0; // number of NONTRIVIAL transpositions, i.e. m_rowsTranspositions[i]!=i
+
+ m_nonzero_pivots = size; // the generic case is that in which all pivots are nonzero (invertible case)
+ m_maxpivot = RealScalar(0);
+
+ for(Index k = 0; k < size; ++k)
+ {
+ // First, we need to find the pivot.
+
+ // biggest coefficient in the remaining bottom-right corner (starting at row k, col k)
+ Index row_of_biggest_in_corner, col_of_biggest_in_corner;
+ typedef internal::scalar_score_coeff_op<Scalar> Scoring;
+ typedef typename Scoring::result_type Score;
+ Score biggest_in_corner;
+ biggest_in_corner = m_lu.bottomRightCorner(rows-k, cols-k)
+ .unaryExpr(Scoring())
+ .maxCoeff(&row_of_biggest_in_corner, &col_of_biggest_in_corner);
+ row_of_biggest_in_corner += k; // correct the values! since they were computed in the corner,
+ col_of_biggest_in_corner += k; // need to add k to them.
+
+ if(numext::is_exactly_zero(biggest_in_corner))
+ {
+ // before exiting, make sure to initialize the still uninitialized transpositions
+ // in a sane state without destroying what we already have.
+ m_nonzero_pivots = k;
+ for(Index i = k; i < size; ++i)
+ {
+ m_rowsTranspositions.coeffRef(i) = internal::convert_index<StorageIndex>(i);
+ m_colsTranspositions.coeffRef(i) = internal::convert_index<StorageIndex>(i);
+ }
+ break;
+ }
+
+ RealScalar abs_pivot = internal::abs_knowing_score<Scalar>()(m_lu(row_of_biggest_in_corner, col_of_biggest_in_corner), biggest_in_corner);
+ if(abs_pivot > m_maxpivot) m_maxpivot = abs_pivot;
+
+ // Now that we've found the pivot, we need to apply the row/col swaps to
+ // bring it to the location (k,k).
+
+ m_rowsTranspositions.coeffRef(k) = internal::convert_index<StorageIndex>(row_of_biggest_in_corner);
+ m_colsTranspositions.coeffRef(k) = internal::convert_index<StorageIndex>(col_of_biggest_in_corner);
+ if(k != row_of_biggest_in_corner) {
+ m_lu.row(k).swap(m_lu.row(row_of_biggest_in_corner));
+ ++number_of_transpositions;
+ }
+ if(k != col_of_biggest_in_corner) {
+ m_lu.col(k).swap(m_lu.col(col_of_biggest_in_corner));
+ ++number_of_transpositions;
+ }
+
+ // Now that the pivot is at the right location, we update the remaining
+ // bottom-right corner by Gaussian elimination.
+
+ if(k<rows-1)
+ m_lu.col(k).tail(rows-k-1) /= m_lu.coeff(k,k);
+ if(k<size-1)
+ m_lu.block(k+1,k+1,rows-k-1,cols-k-1).noalias() -= m_lu.col(k).tail(rows-k-1) * m_lu.row(k).tail(cols-k-1);
+ }
+
+ // the main loop is over, we still have to accumulate the transpositions to find the
+ // permutations P and Q
+
+ m_p.setIdentity(rows);
+ for(Index k = size-1; k >= 0; --k)
+ m_p.applyTranspositionOnTheRight(k, m_rowsTranspositions.coeff(k));
+
+ m_q.setIdentity(cols);
+ for(Index k = 0; k < size; ++k)
+ m_q.applyTranspositionOnTheRight(k, m_colsTranspositions.coeff(k));
+
+ m_det_pq = (number_of_transpositions%2) ? -1 : 1;
+
+ m_isInitialized = true;
+}
+
+template<typename MatrixType>
+typename internal::traits<MatrixType>::Scalar FullPivLU<MatrixType>::determinant() const
+{
+ eigen_assert(m_isInitialized && "LU is not initialized.");
+ eigen_assert(m_lu.rows() == m_lu.cols() && "You can't take the determinant of a non-square matrix!");
+ return Scalar(m_det_pq) * Scalar(m_lu.diagonal().prod());
+}
+
+/** \returns the matrix represented by the decomposition,
+ * i.e., it returns the product: \f$ P^{-1} L U Q^{-1} \f$.
+ * This function is provided for debug purposes. */
+template<typename MatrixType>
+MatrixType FullPivLU<MatrixType>::reconstructedMatrix() const
+{
+ eigen_assert(m_isInitialized && "LU is not initialized.");
+ const Index smalldim = (std::min)(m_lu.rows(), m_lu.cols());
+ // LU
+ MatrixType res(m_lu.rows(),m_lu.cols());
+ // FIXME the .toDenseMatrix() should not be needed...
+ res = m_lu.leftCols(smalldim)
+ .template triangularView<UnitLower>().toDenseMatrix()
+ * m_lu.topRows(smalldim)
+ .template triangularView<Upper>().toDenseMatrix();
+
+ // P^{-1}(LU)
+ res = m_p.inverse() * res;
+
+ // (P^{-1}LU)Q^{-1}
+ res = res * m_q.inverse();
+
+ return res;
+}
+
+/********* Implementation of kernel() **************************************************/
+
+namespace internal {
+template<typename MatrixType_>
+struct kernel_retval<FullPivLU<MatrixType_> >
+ : kernel_retval_base<FullPivLU<MatrixType_> >
+{
+ EIGEN_MAKE_KERNEL_HELPERS(FullPivLU<MatrixType_>)
+
+ enum { MaxSmallDimAtCompileTime = min_size_prefer_fixed(
+ MatrixType::MaxColsAtCompileTime,
+ MatrixType::MaxRowsAtCompileTime)
+ };
+
+ template<typename Dest> void evalTo(Dest& dst) const
+ {
+ using std::abs;
+ const Index cols = dec().matrixLU().cols(), dimker = cols - rank();
+ if(dimker == 0)
+ {
+ // The Kernel is just {0}, so it doesn't have a basis properly speaking, but let's
+ // avoid crashing/asserting as that depends on floating point calculations. Let's
+ // just return a single column vector filled with zeros.
+ dst.setZero();
+ return;
+ }
+
+ /* Let us use the following lemma:
+ *
+ * Lemma: If the matrix A has the LU decomposition PAQ = LU,
+ * then Ker A = Q(Ker U).
+ *
+ * Proof: trivial: just keep in mind that P, Q, L are invertible.
+ */
+
+ /* Thus, all we need to do is to compute Ker U, and then apply Q.
+ *
+ * U is upper triangular, with eigenvalues sorted so that any zeros appear at the end.
+ * Thus, the diagonal of U ends with exactly
+ * dimKer zero's. Let us use that to construct dimKer linearly
+ * independent vectors in Ker U.
+ */
+
+ Matrix<Index, Dynamic, 1, 0, MaxSmallDimAtCompileTime, 1> pivots(rank());
+ RealScalar premultiplied_threshold = dec().maxPivot() * dec().threshold();
+ Index p = 0;
+ for(Index i = 0; i < dec().nonzeroPivots(); ++i)
+ if(abs(dec().matrixLU().coeff(i,i)) > premultiplied_threshold)
+ pivots.coeffRef(p++) = i;
+ eigen_internal_assert(p == rank());
+
+ // we construct a temporaty trapezoid matrix m, by taking the U matrix and
+ // permuting the rows and cols to bring the nonnegligible pivots to the top of
+ // the main diagonal. We need that to be able to apply our triangular solvers.
+ // FIXME when we get triangularView-for-rectangular-matrices, this can be simplified
+ Matrix<typename MatrixType::Scalar, Dynamic, Dynamic, MatrixType::Options,
+ MaxSmallDimAtCompileTime, MatrixType::MaxColsAtCompileTime>
+ m(dec().matrixLU().block(0, 0, rank(), cols));
+ for(Index i = 0; i < rank(); ++i)
+ {
+ if(i) m.row(i).head(i).setZero();
+ m.row(i).tail(cols-i) = dec().matrixLU().row(pivots.coeff(i)).tail(cols-i);
+ }
+ m.block(0, 0, rank(), rank());
+ m.block(0, 0, rank(), rank()).template triangularView<StrictlyLower>().setZero();
+ for(Index i = 0; i < rank(); ++i)
+ m.col(i).swap(m.col(pivots.coeff(i)));
+
+ // ok, we have our trapezoid matrix, we can apply the triangular solver.
+ // notice that the math behind this suggests that we should apply this to the
+ // negative of the RHS, but for performance we just put the negative sign elsewhere, see below.
+ m.topLeftCorner(rank(), rank())
+ .template triangularView<Upper>().solveInPlace(
+ m.topRightCorner(rank(), dimker)
+ );
+
+ // now we must undo the column permutation that we had applied!
+ for(Index i = rank()-1; i >= 0; --i)
+ m.col(i).swap(m.col(pivots.coeff(i)));
+
+ // see the negative sign in the next line, that's what we were talking about above.
+ for(Index i = 0; i < rank(); ++i) dst.row(dec().permutationQ().indices().coeff(i)) = -m.row(i).tail(dimker);
+ for(Index i = rank(); i < cols; ++i) dst.row(dec().permutationQ().indices().coeff(i)).setZero();
+ for(Index k = 0; k < dimker; ++k) dst.coeffRef(dec().permutationQ().indices().coeff(rank()+k), k) = Scalar(1);
+ }
+};
+
+/***** Implementation of image() *****************************************************/
+
+template<typename MatrixType_>
+struct image_retval<FullPivLU<MatrixType_> >
+ : image_retval_base<FullPivLU<MatrixType_> >
+{
+ EIGEN_MAKE_IMAGE_HELPERS(FullPivLU<MatrixType_>)
+
+ enum { MaxSmallDimAtCompileTime = min_size_prefer_fixed(
+ MatrixType::MaxColsAtCompileTime,
+ MatrixType::MaxRowsAtCompileTime)
+ };
+
+ template<typename Dest> void evalTo(Dest& dst) const
+ {
+ using std::abs;
+ if(rank() == 0)
+ {
+ // The Image is just {0}, so it doesn't have a basis properly speaking, but let's
+ // avoid crashing/asserting as that depends on floating point calculations. Let's
+ // just return a single column vector filled with zeros.
+ dst.setZero();
+ return;
+ }
+
+ Matrix<Index, Dynamic, 1, 0, MaxSmallDimAtCompileTime, 1> pivots(rank());
+ RealScalar premultiplied_threshold = dec().maxPivot() * dec().threshold();
+ Index p = 0;
+ for(Index i = 0; i < dec().nonzeroPivots(); ++i)
+ if(abs(dec().matrixLU().coeff(i,i)) > premultiplied_threshold)
+ pivots.coeffRef(p++) = i;
+ eigen_internal_assert(p == rank());
+
+ for(Index i = 0; i < rank(); ++i)
+ dst.col(i) = originalMatrix().col(dec().permutationQ().indices().coeff(pivots.coeff(i)));
+ }
+};
+
+/***** Implementation of solve() *****************************************************/
+
+} // end namespace internal
+
+#ifndef EIGEN_PARSED_BY_DOXYGEN
+template<typename MatrixType_>
+template<typename RhsType, typename DstType>
+void FullPivLU<MatrixType_>::_solve_impl(const RhsType &rhs, DstType &dst) const
+{
+ /* The decomposition PAQ = LU can be rewritten as A = P^{-1} L U Q^{-1}.
+ * So we proceed as follows:
+ * Step 1: compute c = P * rhs.
+ * Step 2: replace c by the solution x to Lx = c. Exists because L is invertible.
+ * Step 3: replace c by the solution x to Ux = c. May or may not exist.
+ * Step 4: result = Q * c;
+ */
+
+ const Index rows = this->rows(),
+ cols = this->cols(),
+ nonzero_pivots = this->rank();
+ const Index smalldim = (std::min)(rows, cols);
+
+ if(nonzero_pivots == 0)
+ {
+ dst.setZero();
+ return;
+ }
+
+ typename RhsType::PlainObject c(rhs.rows(), rhs.cols());
+
+ // Step 1
+ c = permutationP() * rhs;
+
+ // Step 2
+ m_lu.topLeftCorner(smalldim,smalldim)
+ .template triangularView<UnitLower>()
+ .solveInPlace(c.topRows(smalldim));
+ if(rows>cols)
+ c.bottomRows(rows-cols) -= m_lu.bottomRows(rows-cols) * c.topRows(cols);
+
+ // Step 3
+ m_lu.topLeftCorner(nonzero_pivots, nonzero_pivots)
+ .template triangularView<Upper>()
+ .solveInPlace(c.topRows(nonzero_pivots));
+
+ // Step 4
+ for(Index i = 0; i < nonzero_pivots; ++i)
+ dst.row(permutationQ().indices().coeff(i)) = c.row(i);
+ for(Index i = nonzero_pivots; i < m_lu.cols(); ++i)
+ dst.row(permutationQ().indices().coeff(i)).setZero();
+}
+
+template<typename MatrixType_>
+template<bool Conjugate, typename RhsType, typename DstType>
+void FullPivLU<MatrixType_>::_solve_impl_transposed(const RhsType &rhs, DstType &dst) const
+{
+ /* The decomposition PAQ = LU can be rewritten as A = P^{-1} L U Q^{-1},
+ * and since permutations are real and unitary, we can write this
+ * as A^T = Q U^T L^T P,
+ * So we proceed as follows:
+ * Step 1: compute c = Q^T rhs.
+ * Step 2: replace c by the solution x to U^T x = c. May or may not exist.
+ * Step 3: replace c by the solution x to L^T x = c.
+ * Step 4: result = P^T c.
+ * If Conjugate is true, replace "^T" by "^*" above.
+ */
+
+ const Index rows = this->rows(), cols = this->cols(),
+ nonzero_pivots = this->rank();
+ const Index smalldim = (std::min)(rows, cols);
+
+ if(nonzero_pivots == 0)
+ {
+ dst.setZero();
+ return;
+ }
+
+ typename RhsType::PlainObject c(rhs.rows(), rhs.cols());
+
+ // Step 1
+ c = permutationQ().inverse() * rhs;
+
+ // Step 2
+ m_lu.topLeftCorner(nonzero_pivots, nonzero_pivots)
+ .template triangularView<Upper>()
+ .transpose()
+ .template conjugateIf<Conjugate>()
+ .solveInPlace(c.topRows(nonzero_pivots));
+
+ // Step 3
+ m_lu.topLeftCorner(smalldim, smalldim)
+ .template triangularView<UnitLower>()
+ .transpose()
+ .template conjugateIf<Conjugate>()
+ .solveInPlace(c.topRows(smalldim));
+
+ // Step 4
+ PermutationPType invp = permutationP().inverse().eval();
+ for(Index i = 0; i < smalldim; ++i)
+ dst.row(invp.indices().coeff(i)) = c.row(i);
+ for(Index i = smalldim; i < rows; ++i)
+ dst.row(invp.indices().coeff(i)).setZero();
+}
+
+#endif
+
+namespace internal {
+
+
+/***** Implementation of inverse() *****************************************************/
+template<typename DstXprType, typename MatrixType>
+struct Assignment<DstXprType, Inverse<FullPivLU<MatrixType> >, internal::assign_op<typename DstXprType::Scalar,typename FullPivLU<MatrixType>::Scalar>, Dense2Dense>
+{
+ typedef FullPivLU<MatrixType> LuType;
+ typedef Inverse<LuType> SrcXprType;
+ static void run(DstXprType &dst, const SrcXprType &src, const internal::assign_op<typename DstXprType::Scalar,typename MatrixType::Scalar> &)
+ {
+ dst = src.nestedExpression().solve(MatrixType::Identity(src.rows(), src.cols()));
+ }
+};
+} // end namespace internal
+
+/******* MatrixBase methods *****************************************************************/
+
+/** \lu_module
+ *
+ * \return the full-pivoting LU decomposition of \c *this.
+ *
+ * \sa class FullPivLU
+ */
+template<typename Derived>
+inline const FullPivLU<typename MatrixBase<Derived>::PlainObject>
+MatrixBase<Derived>::fullPivLu() const
+{
+ return FullPivLU<PlainObject>(eval());
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_LU_H
diff --git a/Eigen/src/LU/InternalHeaderCheck.h b/Eigen/src/LU/InternalHeaderCheck.h
new file mode 100644
index 0000000..f346b17
--- /dev/null
+++ b/Eigen/src/LU/InternalHeaderCheck.h
@@ -0,0 +1,3 @@
+#ifndef EIGEN_LU_MODULE_H
+#error "Please include Eigen/LU instead of including headers inside the src directory directly."
+#endif
diff --git a/Eigen/src/LU/InverseImpl.h b/Eigen/src/LU/InverseImpl.h
new file mode 100644
index 0000000..bcfe703
--- /dev/null
+++ b/Eigen/src/LU/InverseImpl.h
@@ -0,0 +1,434 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2010 Benoit Jacob <jacob.benoit.1@gmail.com>
+// Copyright (C) 2014 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_INVERSE_IMPL_H
+#define EIGEN_INVERSE_IMPL_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+
+/**********************************
+*** General case implementation ***
+**********************************/
+
+template<typename MatrixType, typename ResultType, int Size = MatrixType::RowsAtCompileTime>
+struct compute_inverse
+{
+ EIGEN_DEVICE_FUNC
+ static inline void run(const MatrixType& matrix, ResultType& result)
+ {
+ result = matrix.partialPivLu().inverse();
+ }
+};
+
+template<typename MatrixType, typename ResultType, int Size = MatrixType::RowsAtCompileTime>
+struct compute_inverse_and_det_with_check { /* nothing! general case not supported. */ };
+
+/****************************
+*** Size 1 implementation ***
+****************************/
+
+template<typename MatrixType, typename ResultType>
+struct compute_inverse<MatrixType, ResultType, 1>
+{
+ EIGEN_DEVICE_FUNC
+ static inline void run(const MatrixType& matrix, ResultType& result)
+ {
+ typedef typename MatrixType::Scalar Scalar;
+ internal::evaluator<MatrixType> matrixEval(matrix);
+ result.coeffRef(0,0) = Scalar(1) / matrixEval.coeff(0,0);
+ }
+};
+
+template<typename MatrixType, typename ResultType>
+struct compute_inverse_and_det_with_check<MatrixType, ResultType, 1>
+{
+ EIGEN_DEVICE_FUNC
+ static inline void run(
+ const MatrixType& matrix,
+ const typename MatrixType::RealScalar& absDeterminantThreshold,
+ ResultType& result,
+ typename ResultType::Scalar& determinant,
+ bool& invertible
+ )
+ {
+ using std::abs;
+ determinant = matrix.coeff(0,0);
+ invertible = abs(determinant) > absDeterminantThreshold;
+ if(invertible) result.coeffRef(0,0) = typename ResultType::Scalar(1) / determinant;
+ }
+};
+
+/****************************
+*** Size 2 implementation ***
+****************************/
+
+template<typename MatrixType, typename ResultType>
+EIGEN_DEVICE_FUNC
+inline void compute_inverse_size2_helper(
+ const MatrixType& matrix, const typename ResultType::Scalar& invdet,
+ ResultType& result)
+{
+ typename ResultType::Scalar temp = matrix.coeff(0,0);
+ result.coeffRef(0,0) = matrix.coeff(1,1) * invdet;
+ result.coeffRef(1,0) = -matrix.coeff(1,0) * invdet;
+ result.coeffRef(0,1) = -matrix.coeff(0,1) * invdet;
+ result.coeffRef(1,1) = temp * invdet;
+}
+
+template<typename MatrixType, typename ResultType>
+struct compute_inverse<MatrixType, ResultType, 2>
+{
+ EIGEN_DEVICE_FUNC
+ static inline void run(const MatrixType& matrix, ResultType& result)
+ {
+ typedef typename ResultType::Scalar Scalar;
+ const Scalar invdet = typename MatrixType::Scalar(1) / matrix.determinant();
+ compute_inverse_size2_helper(matrix, invdet, result);
+ }
+};
+
+template<typename MatrixType, typename ResultType>
+struct compute_inverse_and_det_with_check<MatrixType, ResultType, 2>
+{
+ EIGEN_DEVICE_FUNC
+ static inline void run(
+ const MatrixType& matrix,
+ const typename MatrixType::RealScalar& absDeterminantThreshold,
+ ResultType& inverse,
+ typename ResultType::Scalar& determinant,
+ bool& invertible
+ )
+ {
+ using std::abs;
+ typedef typename ResultType::Scalar Scalar;
+ determinant = matrix.determinant();
+ invertible = abs(determinant) > absDeterminantThreshold;
+ if(!invertible) return;
+ const Scalar invdet = Scalar(1) / determinant;
+ compute_inverse_size2_helper(matrix, invdet, inverse);
+ }
+};
+
+/****************************
+*** Size 3 implementation ***
+****************************/
+
+template<typename MatrixType, int i, int j>
+EIGEN_DEVICE_FUNC
+inline typename MatrixType::Scalar cofactor_3x3(const MatrixType& m)
+{
+ enum {
+ i1 = (i+1) % 3,
+ i2 = (i+2) % 3,
+ j1 = (j+1) % 3,
+ j2 = (j+2) % 3
+ };
+ return m.coeff(i1, j1) * m.coeff(i2, j2)
+ - m.coeff(i1, j2) * m.coeff(i2, j1);
+}
+
+template<typename MatrixType, typename ResultType>
+EIGEN_DEVICE_FUNC
+inline void compute_inverse_size3_helper(
+ const MatrixType& matrix,
+ const typename ResultType::Scalar& invdet,
+ const Matrix<typename ResultType::Scalar,3,1>& cofactors_col0,
+ ResultType& result)
+{
+ // Compute cofactors in a way that avoids aliasing issues.
+ typedef typename ResultType::Scalar Scalar;
+ const Scalar c01 = cofactor_3x3<MatrixType,0,1>(matrix) * invdet;
+ const Scalar c11 = cofactor_3x3<MatrixType,1,1>(matrix) * invdet;
+ const Scalar c02 = cofactor_3x3<MatrixType,0,2>(matrix) * invdet;
+ result.coeffRef(1,2) = cofactor_3x3<MatrixType,2,1>(matrix) * invdet;
+ result.coeffRef(2,1) = cofactor_3x3<MatrixType,1,2>(matrix) * invdet;
+ result.coeffRef(2,2) = cofactor_3x3<MatrixType,2,2>(matrix) * invdet;
+ result.coeffRef(1,0) = c01;
+ result.coeffRef(1,1) = c11;
+ result.coeffRef(2,0) = c02;
+ result.row(0) = cofactors_col0 * invdet;
+}
+
+template<typename MatrixType, typename ResultType>
+struct compute_inverse<MatrixType, ResultType, 3>
+{
+ EIGEN_DEVICE_FUNC
+ static inline void run(const MatrixType& matrix, ResultType& result)
+ {
+ typedef typename ResultType::Scalar Scalar;
+ Matrix<typename MatrixType::Scalar,3,1> cofactors_col0;
+ cofactors_col0.coeffRef(0) = cofactor_3x3<MatrixType,0,0>(matrix);
+ cofactors_col0.coeffRef(1) = cofactor_3x3<MatrixType,1,0>(matrix);
+ cofactors_col0.coeffRef(2) = cofactor_3x3<MatrixType,2,0>(matrix);
+ const Scalar det = (cofactors_col0.cwiseProduct(matrix.col(0))).sum();
+ const Scalar invdet = Scalar(1) / det;
+ compute_inverse_size3_helper(matrix, invdet, cofactors_col0, result);
+ }
+};
+
+template<typename MatrixType, typename ResultType>
+struct compute_inverse_and_det_with_check<MatrixType, ResultType, 3>
+{
+ EIGEN_DEVICE_FUNC
+ static inline void run(
+ const MatrixType& matrix,
+ const typename MatrixType::RealScalar& absDeterminantThreshold,
+ ResultType& inverse,
+ typename ResultType::Scalar& determinant,
+ bool& invertible
+ )
+ {
+ typedef typename ResultType::Scalar Scalar;
+ Matrix<Scalar,3,1> cofactors_col0;
+ cofactors_col0.coeffRef(0) = cofactor_3x3<MatrixType,0,0>(matrix);
+ cofactors_col0.coeffRef(1) = cofactor_3x3<MatrixType,1,0>(matrix);
+ cofactors_col0.coeffRef(2) = cofactor_3x3<MatrixType,2,0>(matrix);
+ determinant = (cofactors_col0.cwiseProduct(matrix.col(0))).sum();
+ invertible = Eigen::numext::abs(determinant) > absDeterminantThreshold;
+ if(!invertible) return;
+ const Scalar invdet = Scalar(1) / determinant;
+ compute_inverse_size3_helper(matrix, invdet, cofactors_col0, inverse);
+ }
+};
+
+/****************************
+*** Size 4 implementation ***
+****************************/
+
+template<typename Derived>
+EIGEN_DEVICE_FUNC
+inline const typename Derived::Scalar general_det3_helper
+(const MatrixBase<Derived>& matrix, int i1, int i2, int i3, int j1, int j2, int j3)
+{
+ return matrix.coeff(i1,j1)
+ * (matrix.coeff(i2,j2) * matrix.coeff(i3,j3) - matrix.coeff(i2,j3) * matrix.coeff(i3,j2));
+}
+
+template<typename MatrixType, int i, int j>
+EIGEN_DEVICE_FUNC
+inline typename MatrixType::Scalar cofactor_4x4(const MatrixType& matrix)
+{
+ enum {
+ i1 = (i+1) % 4,
+ i2 = (i+2) % 4,
+ i3 = (i+3) % 4,
+ j1 = (j+1) % 4,
+ j2 = (j+2) % 4,
+ j3 = (j+3) % 4
+ };
+ return general_det3_helper(matrix, i1, i2, i3, j1, j2, j3)
+ + general_det3_helper(matrix, i2, i3, i1, j1, j2, j3)
+ + general_det3_helper(matrix, i3, i1, i2, j1, j2, j3);
+}
+
+template<int Arch, typename Scalar, typename MatrixType, typename ResultType>
+struct compute_inverse_size4
+{
+ EIGEN_DEVICE_FUNC
+ static void run(const MatrixType& matrix, ResultType& result)
+ {
+ result.coeffRef(0,0) = cofactor_4x4<MatrixType,0,0>(matrix);
+ result.coeffRef(1,0) = -cofactor_4x4<MatrixType,0,1>(matrix);
+ result.coeffRef(2,0) = cofactor_4x4<MatrixType,0,2>(matrix);
+ result.coeffRef(3,0) = -cofactor_4x4<MatrixType,0,3>(matrix);
+ result.coeffRef(0,2) = cofactor_4x4<MatrixType,2,0>(matrix);
+ result.coeffRef(1,2) = -cofactor_4x4<MatrixType,2,1>(matrix);
+ result.coeffRef(2,2) = cofactor_4x4<MatrixType,2,2>(matrix);
+ result.coeffRef(3,2) = -cofactor_4x4<MatrixType,2,3>(matrix);
+ result.coeffRef(0,1) = -cofactor_4x4<MatrixType,1,0>(matrix);
+ result.coeffRef(1,1) = cofactor_4x4<MatrixType,1,1>(matrix);
+ result.coeffRef(2,1) = -cofactor_4x4<MatrixType,1,2>(matrix);
+ result.coeffRef(3,1) = cofactor_4x4<MatrixType,1,3>(matrix);
+ result.coeffRef(0,3) = -cofactor_4x4<MatrixType,3,0>(matrix);
+ result.coeffRef(1,3) = cofactor_4x4<MatrixType,3,1>(matrix);
+ result.coeffRef(2,3) = -cofactor_4x4<MatrixType,3,2>(matrix);
+ result.coeffRef(3,3) = cofactor_4x4<MatrixType,3,3>(matrix);
+ result /= (matrix.col(0).cwiseProduct(result.row(0).transpose())).sum();
+ }
+};
+
+template<typename MatrixType, typename ResultType>
+struct compute_inverse<MatrixType, ResultType, 4>
+ : compute_inverse_size4<Architecture::Target, typename MatrixType::Scalar,
+ MatrixType, ResultType>
+{
+};
+
+template<typename MatrixType, typename ResultType>
+struct compute_inverse_and_det_with_check<MatrixType, ResultType, 4>
+{
+ EIGEN_DEVICE_FUNC
+ static inline void run(
+ const MatrixType& matrix,
+ const typename MatrixType::RealScalar& absDeterminantThreshold,
+ ResultType& inverse,
+ typename ResultType::Scalar& determinant,
+ bool& invertible
+ )
+ {
+ using std::abs;
+ determinant = matrix.determinant();
+ invertible = abs(determinant) > absDeterminantThreshold;
+ if(invertible && extract_data(matrix) != extract_data(inverse)) {
+ compute_inverse<MatrixType, ResultType>::run(matrix, inverse);
+ }
+ else if(invertible) {
+ MatrixType matrix_t = matrix;
+ compute_inverse<MatrixType, ResultType>::run(matrix_t, inverse);
+ }
+ }
+};
+
+/*************************
+*** MatrixBase methods ***
+*************************/
+
+} // end namespace internal
+
+namespace internal {
+
+// Specialization for "dense = dense_xpr.inverse()"
+template<typename DstXprType, typename XprType>
+struct Assignment<DstXprType, Inverse<XprType>, internal::assign_op<typename DstXprType::Scalar,typename XprType::Scalar>, Dense2Dense>
+{
+ typedef Inverse<XprType> SrcXprType;
+ EIGEN_DEVICE_FUNC
+ static void run(DstXprType &dst, const SrcXprType &src, const internal::assign_op<typename DstXprType::Scalar,typename XprType::Scalar> &)
+ {
+ Index dstRows = src.rows();
+ Index dstCols = src.cols();
+ if((dst.rows()!=dstRows) || (dst.cols()!=dstCols))
+ dst.resize(dstRows, dstCols);
+
+ const int Size = plain_enum_min(XprType::ColsAtCompileTime, DstXprType::ColsAtCompileTime);
+ EIGEN_ONLY_USED_FOR_DEBUG(Size);
+ eigen_assert(( (Size<=1) || (Size>4) || (extract_data(src.nestedExpression())!=extract_data(dst)))
+ && "Aliasing problem detected in inverse(), you need to do inverse().eval() here.");
+
+ typedef typename internal::nested_eval<XprType,XprType::ColsAtCompileTime>::type ActualXprType;
+ typedef internal::remove_all_t<ActualXprType> ActualXprTypeCleanded;
+
+ ActualXprType actual_xpr(src.nestedExpression());
+
+ compute_inverse<ActualXprTypeCleanded, DstXprType>::run(actual_xpr, dst);
+ }
+};
+
+
+} // end namespace internal
+
+/** \lu_module
+ *
+ * \returns the matrix inverse of this matrix.
+ *
+ * For small fixed sizes up to 4x4, this method uses cofactors.
+ * In the general case, this method uses class PartialPivLU.
+ *
+ * \note This matrix must be invertible, otherwise the result is undefined. If you need an
+ * invertibility check, do the following:
+ * \li for fixed sizes up to 4x4, use computeInverseAndDetWithCheck().
+ * \li for the general case, use class FullPivLU.
+ *
+ * Example: \include MatrixBase_inverse.cpp
+ * Output: \verbinclude MatrixBase_inverse.out
+ *
+ * \sa computeInverseAndDetWithCheck()
+ */
+template<typename Derived>
+EIGEN_DEVICE_FUNC
+inline const Inverse<Derived> MatrixBase<Derived>::inverse() const
+{
+ EIGEN_STATIC_ASSERT(!NumTraits<Scalar>::IsInteger,THIS_FUNCTION_IS_NOT_FOR_INTEGER_NUMERIC_TYPES)
+ eigen_assert(rows() == cols());
+ return Inverse<Derived>(derived());
+}
+
+/** \lu_module
+ *
+ * Computation of matrix inverse and determinant, with invertibility check.
+ *
+ * This is only for fixed-size square matrices of size up to 4x4.
+ *
+ * Notice that it will trigger a copy of input matrix when trying to do the inverse in place.
+ *
+ * \param inverse Reference to the matrix in which to store the inverse.
+ * \param determinant Reference to the variable in which to store the determinant.
+ * \param invertible Reference to the bool variable in which to store whether the matrix is invertible.
+ * \param absDeterminantThreshold Optional parameter controlling the invertibility check.
+ * The matrix will be declared invertible if the absolute value of its
+ * determinant is greater than this threshold.
+ *
+ * Example: \include MatrixBase_computeInverseAndDetWithCheck.cpp
+ * Output: \verbinclude MatrixBase_computeInverseAndDetWithCheck.out
+ *
+ * \sa inverse(), computeInverseWithCheck()
+ */
+template<typename Derived>
+template<typename ResultType>
+inline void MatrixBase<Derived>::computeInverseAndDetWithCheck(
+ ResultType& inverse,
+ typename ResultType::Scalar& determinant,
+ bool& invertible,
+ const RealScalar& absDeterminantThreshold
+ ) const
+{
+ // i'd love to put some static assertions there, but SFINAE means that they have no effect...
+ eigen_assert(rows() == cols());
+ // for 2x2, it's worth giving a chance to avoid evaluating.
+ // for larger sizes, evaluating has negligible cost and limits code size.
+ typedef std::conditional_t<
+ RowsAtCompileTime == 2,
+ internal::remove_all_t<typename internal::nested_eval<Derived, 2>::type>,
+ PlainObject
+ > MatrixType;
+ internal::compute_inverse_and_det_with_check<MatrixType, ResultType>::run
+ (derived(), absDeterminantThreshold, inverse, determinant, invertible);
+}
+
+/** \lu_module
+ *
+ * Computation of matrix inverse, with invertibility check.
+ *
+ * This is only for fixed-size square matrices of size up to 4x4.
+ *
+ * Notice that it will trigger a copy of input matrix when trying to do the inverse in place.
+ *
+ * \param inverse Reference to the matrix in which to store the inverse.
+ * \param invertible Reference to the bool variable in which to store whether the matrix is invertible.
+ * \param absDeterminantThreshold Optional parameter controlling the invertibility check.
+ * The matrix will be declared invertible if the absolute value of its
+ * determinant is greater than this threshold.
+ *
+ * Example: \include MatrixBase_computeInverseWithCheck.cpp
+ * Output: \verbinclude MatrixBase_computeInverseWithCheck.out
+ *
+ * \sa inverse(), computeInverseAndDetWithCheck()
+ */
+template<typename Derived>
+template<typename ResultType>
+inline void MatrixBase<Derived>::computeInverseWithCheck(
+ ResultType& inverse,
+ bool& invertible,
+ const RealScalar& absDeterminantThreshold
+ ) const
+{
+ Scalar determinant;
+ // i'd love to put some static assertions there, but SFINAE means that they have no effect...
+ eigen_assert(rows() == cols());
+ computeInverseAndDetWithCheck(inverse,determinant,invertible,absDeterminantThreshold);
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_INVERSE_IMPL_H
diff --git a/Eigen/src/LU/PartialPivLU.h b/Eigen/src/LU/PartialPivLU.h
new file mode 100644
index 0000000..1377398
--- /dev/null
+++ b/Eigen/src/LU/PartialPivLU.h
@@ -0,0 +1,621 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2006-2009 Benoit Jacob <jacob.benoit.1@gmail.com>
+// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_PARTIALLU_H
+#define EIGEN_PARTIALLU_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+template<typename MatrixType_> struct traits<PartialPivLU<MatrixType_> >
+ : traits<MatrixType_>
+{
+ typedef MatrixXpr XprKind;
+ typedef SolverStorage StorageKind;
+ typedef int StorageIndex;
+ typedef traits<MatrixType_> BaseTraits;
+ enum {
+ Flags = BaseTraits::Flags & RowMajorBit,
+ CoeffReadCost = Dynamic
+ };
+};
+
+template<typename T,typename Derived>
+struct enable_if_ref;
+// {
+// typedef Derived type;
+// };
+
+template<typename T,typename Derived>
+struct enable_if_ref<Ref<T>,Derived> {
+ typedef Derived type;
+};
+
+} // end namespace internal
+
+/** \ingroup LU_Module
+ *
+ * \class PartialPivLU
+ *
+ * \brief LU decomposition of a matrix with partial pivoting, and related features
+ *
+ * \tparam MatrixType_ the type of the matrix of which we are computing the LU decomposition
+ *
+ * This class represents a LU decomposition of a \b square \b invertible matrix, with partial pivoting: the matrix A
+ * is decomposed as A = PLU where L is unit-lower-triangular, U is upper-triangular, and P
+ * is a permutation matrix.
+ *
+ * Typically, partial pivoting LU decomposition is only considered numerically stable for square invertible
+ * matrices. Thus LAPACK's dgesv and dgesvx require the matrix to be square and invertible. The present class
+ * does the same. It will assert that the matrix is square, but it won't (actually it can't) check that the
+ * matrix is invertible: it is your task to check that you only use this decomposition on invertible matrices.
+ *
+ * The guaranteed safe alternative, working for all matrices, is the full pivoting LU decomposition, provided
+ * by class FullPivLU.
+ *
+ * This is \b not a rank-revealing LU decomposition. Many features are intentionally absent from this class,
+ * such as rank computation. If you need these features, use class FullPivLU.
+ *
+ * This LU decomposition is suitable to invert invertible matrices. It is what MatrixBase::inverse() uses
+ * in the general case.
+ * On the other hand, it is \b not suitable to determine whether a given matrix is invertible.
+ *
+ * The data of the LU decomposition can be directly accessed through the methods matrixLU(), permutationP().
+ *
+ * This class supports the \link InplaceDecomposition inplace decomposition \endlink mechanism.
+ *
+ * \sa MatrixBase::partialPivLu(), MatrixBase::determinant(), MatrixBase::inverse(), MatrixBase::computeInverse(), class FullPivLU
+ */
+template<typename MatrixType_> class PartialPivLU
+ : public SolverBase<PartialPivLU<MatrixType_> >
+{
+ public:
+
+ typedef MatrixType_ MatrixType;
+ typedef SolverBase<PartialPivLU> Base;
+ friend class SolverBase<PartialPivLU>;
+
+ EIGEN_GENERIC_PUBLIC_INTERFACE(PartialPivLU)
+ enum {
+ MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime,
+ MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime
+ };
+ typedef PermutationMatrix<RowsAtCompileTime, MaxRowsAtCompileTime> PermutationType;
+ typedef Transpositions<RowsAtCompileTime, MaxRowsAtCompileTime> TranspositionType;
+ typedef typename MatrixType::PlainObject PlainObject;
+
+ /**
+ * \brief Default Constructor.
+ *
+ * The default constructor is useful in cases in which the user intends to
+ * perform decompositions via PartialPivLU::compute(const MatrixType&).
+ */
+ PartialPivLU();
+
+ /** \brief Default Constructor with memory preallocation
+ *
+ * Like the default constructor but with preallocation of the internal data
+ * according to the specified problem \a size.
+ * \sa PartialPivLU()
+ */
+ explicit PartialPivLU(Index size);
+
+ /** Constructor.
+ *
+ * \param matrix the matrix of which to compute the LU decomposition.
+ *
+ * \warning The matrix should have full rank (e.g. if it's square, it should be invertible).
+ * If you need to deal with non-full rank, use class FullPivLU instead.
+ */
+ template<typename InputType>
+ explicit PartialPivLU(const EigenBase<InputType>& matrix);
+
+ /** Constructor for \link InplaceDecomposition inplace decomposition \endlink
+ *
+ * \param matrix the matrix of which to compute the LU decomposition.
+ *
+ * \warning The matrix should have full rank (e.g. if it's square, it should be invertible).
+ * If you need to deal with non-full rank, use class FullPivLU instead.
+ */
+ template<typename InputType>
+ explicit PartialPivLU(EigenBase<InputType>& matrix);
+
+ template<typename InputType>
+ PartialPivLU& compute(const EigenBase<InputType>& matrix) {
+ m_lu = matrix.derived();
+ compute();
+ return *this;
+ }
+
+ /** \returns the LU decomposition matrix: the upper-triangular part is U, the
+ * unit-lower-triangular part is L (at least for square matrices; in the non-square
+ * case, special care is needed, see the documentation of class FullPivLU).
+ *
+ * \sa matrixL(), matrixU()
+ */
+ inline const MatrixType& matrixLU() const
+ {
+ eigen_assert(m_isInitialized && "PartialPivLU is not initialized.");
+ return m_lu;
+ }
+
+ /** \returns the permutation matrix P.
+ */
+ inline const PermutationType& permutationP() const
+ {
+ eigen_assert(m_isInitialized && "PartialPivLU is not initialized.");
+ return m_p;
+ }
+
+ #ifdef EIGEN_PARSED_BY_DOXYGEN
+ /** This method returns the solution x to the equation Ax=b, where A is the matrix of which
+ * *this is the LU decomposition.
+ *
+ * \param b the right-hand-side of the equation to solve. Can be a vector or a matrix,
+ * the only requirement in order for the equation to make sense is that
+ * b.rows()==A.rows(), where A is the matrix of which *this is the LU decomposition.
+ *
+ * \returns the solution.
+ *
+ * Example: \include PartialPivLU_solve.cpp
+ * Output: \verbinclude PartialPivLU_solve.out
+ *
+ * Since this PartialPivLU class assumes anyway that the matrix A is invertible, the solution
+ * theoretically exists and is unique regardless of b.
+ *
+ * \sa TriangularView::solve(), inverse(), computeInverse()
+ */
+ template<typename Rhs>
+ inline const Solve<PartialPivLU, Rhs>
+ solve(const MatrixBase<Rhs>& b) const;
+ #endif
+
+ /** \returns an estimate of the reciprocal condition number of the matrix of which \c *this is
+ the LU decomposition.
+ */
+ inline RealScalar rcond() const
+ {
+ eigen_assert(m_isInitialized && "PartialPivLU is not initialized.");
+ return internal::rcond_estimate_helper(m_l1_norm, *this);
+ }
+
+ /** \returns the inverse of the matrix of which *this is the LU decomposition.
+ *
+ * \warning The matrix being decomposed here is assumed to be invertible. If you need to check for
+ * invertibility, use class FullPivLU instead.
+ *
+ * \sa MatrixBase::inverse(), LU::inverse()
+ */
+ inline const Inverse<PartialPivLU> inverse() const
+ {
+ eigen_assert(m_isInitialized && "PartialPivLU is not initialized.");
+ return Inverse<PartialPivLU>(*this);
+ }
+
+ /** \returns the determinant of the matrix of which
+ * *this is the LU decomposition. It has only linear complexity
+ * (that is, O(n) where n is the dimension of the square matrix)
+ * as the LU decomposition has already been computed.
+ *
+ * \note For fixed-size matrices of size up to 4, MatrixBase::determinant() offers
+ * optimized paths.
+ *
+ * \warning a determinant can be very big or small, so for matrices
+ * of large enough dimension, there is a risk of overflow/underflow.
+ *
+ * \sa MatrixBase::determinant()
+ */
+ Scalar determinant() const;
+
+ MatrixType reconstructedMatrix() const;
+
+ EIGEN_CONSTEXPR inline Index rows() const EIGEN_NOEXCEPT { return m_lu.rows(); }
+ EIGEN_CONSTEXPR inline Index cols() const EIGEN_NOEXCEPT { return m_lu.cols(); }
+
+ #ifndef EIGEN_PARSED_BY_DOXYGEN
+ template<typename RhsType, typename DstType>
+ EIGEN_DEVICE_FUNC
+ void _solve_impl(const RhsType &rhs, DstType &dst) const {
+ /* The decomposition PA = LU can be rewritten as A = P^{-1} L U.
+ * So we proceed as follows:
+ * Step 1: compute c = Pb.
+ * Step 2: replace c by the solution x to Lx = c.
+ * Step 3: replace c by the solution x to Ux = c.
+ */
+
+ // Step 1
+ dst = permutationP() * rhs;
+
+ // Step 2
+ m_lu.template triangularView<UnitLower>().solveInPlace(dst);
+
+ // Step 3
+ m_lu.template triangularView<Upper>().solveInPlace(dst);
+ }
+
+ template<bool Conjugate, typename RhsType, typename DstType>
+ EIGEN_DEVICE_FUNC
+ void _solve_impl_transposed(const RhsType &rhs, DstType &dst) const {
+ /* The decomposition PA = LU can be rewritten as A^T = U^T L^T P.
+ * So we proceed as follows:
+ * Step 1: compute c as the solution to L^T c = b
+ * Step 2: replace c by the solution x to U^T x = c.
+ * Step 3: update c = P^-1 c.
+ */
+
+ eigen_assert(rhs.rows() == m_lu.cols());
+
+ // Step 1
+ dst = m_lu.template triangularView<Upper>().transpose()
+ .template conjugateIf<Conjugate>().solve(rhs);
+ // Step 2
+ m_lu.template triangularView<UnitLower>().transpose()
+ .template conjugateIf<Conjugate>().solveInPlace(dst);
+ // Step 3
+ dst = permutationP().transpose() * dst;
+ }
+ #endif
+
+ protected:
+
+ EIGEN_STATIC_ASSERT_NON_INTEGER(Scalar)
+
+ void compute();
+
+ MatrixType m_lu;
+ PermutationType m_p;
+ TranspositionType m_rowsTranspositions;
+ RealScalar m_l1_norm;
+ signed char m_det_p;
+ bool m_isInitialized;
+};
+
+template<typename MatrixType>
+PartialPivLU<MatrixType>::PartialPivLU()
+ : m_lu(),
+ m_p(),
+ m_rowsTranspositions(),
+ m_l1_norm(0),
+ m_det_p(0),
+ m_isInitialized(false)
+{
+}
+
+template<typename MatrixType>
+PartialPivLU<MatrixType>::PartialPivLU(Index size)
+ : m_lu(size, size),
+ m_p(size),
+ m_rowsTranspositions(size),
+ m_l1_norm(0),
+ m_det_p(0),
+ m_isInitialized(false)
+{
+}
+
+template<typename MatrixType>
+template<typename InputType>
+PartialPivLU<MatrixType>::PartialPivLU(const EigenBase<InputType>& matrix)
+ : m_lu(matrix.rows(),matrix.cols()),
+ m_p(matrix.rows()),
+ m_rowsTranspositions(matrix.rows()),
+ m_l1_norm(0),
+ m_det_p(0),
+ m_isInitialized(false)
+{
+ compute(matrix.derived());
+}
+
+template<typename MatrixType>
+template<typename InputType>
+PartialPivLU<MatrixType>::PartialPivLU(EigenBase<InputType>& matrix)
+ : m_lu(matrix.derived()),
+ m_p(matrix.rows()),
+ m_rowsTranspositions(matrix.rows()),
+ m_l1_norm(0),
+ m_det_p(0),
+ m_isInitialized(false)
+{
+ compute();
+}
+
+namespace internal {
+
+/** \internal This is the blocked version of fullpivlu_unblocked() */
+template<typename Scalar, int StorageOrder, typename PivIndex, int SizeAtCompileTime=Dynamic>
+struct partial_lu_impl
+{
+ static constexpr int UnBlockedBound = 16;
+ static constexpr bool UnBlockedAtCompileTime = SizeAtCompileTime!=Dynamic && SizeAtCompileTime<=UnBlockedBound;
+ static constexpr int ActualSizeAtCompileTime = UnBlockedAtCompileTime ? SizeAtCompileTime : Dynamic;
+ // Remaining rows and columns at compile-time:
+ static constexpr int RRows = SizeAtCompileTime==2 ? 1 : Dynamic;
+ static constexpr int RCols = SizeAtCompileTime==2 ? 1 : Dynamic;
+ typedef Matrix<Scalar, ActualSizeAtCompileTime, ActualSizeAtCompileTime, StorageOrder> MatrixType;
+ typedef Ref<MatrixType> MatrixTypeRef;
+ typedef Ref<Matrix<Scalar, Dynamic, Dynamic, StorageOrder> > BlockType;
+ typedef typename MatrixType::RealScalar RealScalar;
+
+ /** \internal performs the LU decomposition in-place of the matrix \a lu
+ * using an unblocked algorithm.
+ *
+ * In addition, this function returns the row transpositions in the
+ * vector \a row_transpositions which must have a size equal to the number
+ * of columns of the matrix \a lu, and an integer \a nb_transpositions
+ * which returns the actual number of transpositions.
+ *
+ * \returns The index of the first pivot which is exactly zero if any, or a negative number otherwise.
+ */
+ static Index unblocked_lu(MatrixTypeRef& lu, PivIndex* row_transpositions, PivIndex& nb_transpositions)
+ {
+ typedef scalar_score_coeff_op<Scalar> Scoring;
+ typedef typename Scoring::result_type Score;
+ const Index rows = lu.rows();
+ const Index cols = lu.cols();
+ const Index size = (std::min)(rows,cols);
+ // For small compile-time matrices it is worth processing the last row separately:
+ // speedup: +100% for 2x2, +10% for others.
+ const Index endk = UnBlockedAtCompileTime ? size-1 : size;
+ nb_transpositions = 0;
+ Index first_zero_pivot = -1;
+ for(Index k = 0; k < endk; ++k)
+ {
+ int rrows = internal::convert_index<int>(rows-k-1);
+ int rcols = internal::convert_index<int>(cols-k-1);
+
+ Index row_of_biggest_in_col;
+ Score biggest_in_corner
+ = lu.col(k).tail(rows-k).unaryExpr(Scoring()).maxCoeff(&row_of_biggest_in_col);
+ row_of_biggest_in_col += k;
+
+ row_transpositions[k] = PivIndex(row_of_biggest_in_col);
+
+ if(!numext::is_exactly_zero(biggest_in_corner))
+ {
+ if(k != row_of_biggest_in_col)
+ {
+ lu.row(k).swap(lu.row(row_of_biggest_in_col));
+ ++nb_transpositions;
+ }
+
+ lu.col(k).tail(fix<RRows>(rrows)) /= lu.coeff(k,k);
+ }
+ else if(first_zero_pivot==-1)
+ {
+ // the pivot is exactly zero, we record the index of the first pivot which is exactly 0,
+ // and continue the factorization such we still have A = PLU
+ first_zero_pivot = k;
+ }
+
+ if(k<rows-1)
+ lu.bottomRightCorner(fix<RRows>(rrows),fix<RCols>(rcols)).noalias() -= lu.col(k).tail(fix<RRows>(rrows)) * lu.row(k).tail(fix<RCols>(rcols));
+ }
+
+ // special handling of the last entry
+ if(UnBlockedAtCompileTime)
+ {
+ Index k = endk;
+ row_transpositions[k] = PivIndex(k);
+ if (numext::is_exactly_zero(Scoring()(lu(k, k))) && first_zero_pivot == -1)
+ first_zero_pivot = k;
+ }
+
+ return first_zero_pivot;
+ }
+
+ /** \internal performs the LU decomposition in-place of the matrix represented
+ * by the variables \a rows, \a cols, \a lu_data, and \a lu_stride using a
+ * recursive, blocked algorithm.
+ *
+ * In addition, this function returns the row transpositions in the
+ * vector \a row_transpositions which must have a size equal to the number
+ * of columns of the matrix \a lu, and an integer \a nb_transpositions
+ * which returns the actual number of transpositions.
+ *
+ * \returns The index of the first pivot which is exactly zero if any, or a negative number otherwise.
+ *
+ * \note This very low level interface using pointers, etc. is to:
+ * 1 - reduce the number of instantiations to the strict minimum
+ * 2 - avoid infinite recursion of the instantiations with Block<Block<Block<...> > >
+ */
+ static Index blocked_lu(Index rows, Index cols, Scalar* lu_data, Index luStride, PivIndex* row_transpositions, PivIndex& nb_transpositions, Index maxBlockSize=256)
+ {
+ MatrixTypeRef lu = MatrixType::Map(lu_data,rows, cols, OuterStride<>(luStride));
+
+ const Index size = (std::min)(rows,cols);
+
+ // if the matrix is too small, no blocking:
+ if(UnBlockedAtCompileTime || size<=UnBlockedBound)
+ {
+ return unblocked_lu(lu, row_transpositions, nb_transpositions);
+ }
+
+ // automatically adjust the number of subdivisions to the size
+ // of the matrix so that there is enough sub blocks:
+ Index blockSize;
+ {
+ blockSize = size/8;
+ blockSize = (blockSize/16)*16;
+ blockSize = (std::min)((std::max)(blockSize,Index(8)), maxBlockSize);
+ }
+
+ nb_transpositions = 0;
+ Index first_zero_pivot = -1;
+ for(Index k = 0; k < size; k+=blockSize)
+ {
+ Index bs = (std::min)(size-k,blockSize); // actual size of the block
+ Index trows = rows - k - bs; // trailing rows
+ Index tsize = size - k - bs; // trailing size
+
+ // partition the matrix:
+ // A00 | A01 | A02
+ // lu = A_0 | A_1 | A_2 = A10 | A11 | A12
+ // A20 | A21 | A22
+ BlockType A_0 = lu.block(0,0,rows,k);
+ BlockType A_2 = lu.block(0,k+bs,rows,tsize);
+ BlockType A11 = lu.block(k,k,bs,bs);
+ BlockType A12 = lu.block(k,k+bs,bs,tsize);
+ BlockType A21 = lu.block(k+bs,k,trows,bs);
+ BlockType A22 = lu.block(k+bs,k+bs,trows,tsize);
+
+ PivIndex nb_transpositions_in_panel;
+ // recursively call the blocked LU algorithm on [A11^T A21^T]^T
+ // with a very small blocking size:
+ Index ret = blocked_lu(trows+bs, bs, &lu.coeffRef(k,k), luStride,
+ row_transpositions+k, nb_transpositions_in_panel, 16);
+ if(ret>=0 && first_zero_pivot==-1)
+ first_zero_pivot = k+ret;
+
+ nb_transpositions += nb_transpositions_in_panel;
+ // update permutations and apply them to A_0
+ for(Index i=k; i<k+bs; ++i)
+ {
+ Index piv = (row_transpositions[i] += internal::convert_index<PivIndex>(k));
+ A_0.row(i).swap(A_0.row(piv));
+ }
+
+ if(trows)
+ {
+ // apply permutations to A_2
+ for(Index i=k;i<k+bs; ++i)
+ A_2.row(i).swap(A_2.row(row_transpositions[i]));
+
+ // A12 = A11^-1 A12
+ A11.template triangularView<UnitLower>().solveInPlace(A12);
+
+ A22.noalias() -= A21 * A12;
+ }
+ }
+ return first_zero_pivot;
+ }
+};
+
+/** \internal performs the LU decomposition with partial pivoting in-place.
+ */
+template<typename MatrixType, typename TranspositionType>
+void partial_lu_inplace(MatrixType& lu, TranspositionType& row_transpositions, typename TranspositionType::StorageIndex& nb_transpositions)
+{
+ // Special-case of zero matrix.
+ if (lu.rows() == 0 || lu.cols() == 0) {
+ nb_transpositions = 0;
+ return;
+ }
+ eigen_assert(lu.cols() == row_transpositions.size());
+ eigen_assert(row_transpositions.size() < 2 || (&row_transpositions.coeffRef(1)-&row_transpositions.coeffRef(0)) == 1);
+
+ partial_lu_impl
+ < typename MatrixType::Scalar, MatrixType::Flags&RowMajorBit?RowMajor:ColMajor,
+ typename TranspositionType::StorageIndex,
+ internal::min_size_prefer_fixed(MatrixType::RowsAtCompileTime, MatrixType::ColsAtCompileTime)>
+ ::blocked_lu(lu.rows(), lu.cols(), &lu.coeffRef(0,0), lu.outerStride(), &row_transpositions.coeffRef(0), nb_transpositions);
+}
+
+} // end namespace internal
+
+template<typename MatrixType>
+void PartialPivLU<MatrixType>::compute()
+{
+ // the row permutation is stored as int indices, so just to be sure:
+ eigen_assert(m_lu.rows()<NumTraits<int>::highest());
+
+ if(m_lu.cols()>0)
+ m_l1_norm = m_lu.cwiseAbs().colwise().sum().maxCoeff();
+ else
+ m_l1_norm = RealScalar(0);
+
+ eigen_assert(m_lu.rows() == m_lu.cols() && "PartialPivLU is only for square (and moreover invertible) matrices");
+ const Index size = m_lu.rows();
+
+ m_rowsTranspositions.resize(size);
+
+ typename TranspositionType::StorageIndex nb_transpositions;
+ internal::partial_lu_inplace(m_lu, m_rowsTranspositions, nb_transpositions);
+ m_det_p = (nb_transpositions%2) ? -1 : 1;
+
+ m_p = m_rowsTranspositions;
+
+ m_isInitialized = true;
+}
+
+template<typename MatrixType>
+typename PartialPivLU<MatrixType>::Scalar PartialPivLU<MatrixType>::determinant() const
+{
+ eigen_assert(m_isInitialized && "PartialPivLU is not initialized.");
+ return Scalar(m_det_p) * m_lu.diagonal().prod();
+}
+
+/** \returns the matrix represented by the decomposition,
+ * i.e., it returns the product: P^{-1} L U.
+ * This function is provided for debug purpose. */
+template<typename MatrixType>
+MatrixType PartialPivLU<MatrixType>::reconstructedMatrix() const
+{
+ eigen_assert(m_isInitialized && "LU is not initialized.");
+ // LU
+ MatrixType res = m_lu.template triangularView<UnitLower>().toDenseMatrix()
+ * m_lu.template triangularView<Upper>();
+
+ // P^{-1}(LU)
+ res = m_p.inverse() * res;
+
+ return res;
+}
+
+/***** Implementation details *****************************************************/
+
+namespace internal {
+
+/***** Implementation of inverse() *****************************************************/
+template<typename DstXprType, typename MatrixType>
+struct Assignment<DstXprType, Inverse<PartialPivLU<MatrixType> >, internal::assign_op<typename DstXprType::Scalar,typename PartialPivLU<MatrixType>::Scalar>, Dense2Dense>
+{
+ typedef PartialPivLU<MatrixType> LuType;
+ typedef Inverse<LuType> SrcXprType;
+ static void run(DstXprType &dst, const SrcXprType &src, const internal::assign_op<typename DstXprType::Scalar,typename LuType::Scalar> &)
+ {
+ dst = src.nestedExpression().solve(MatrixType::Identity(src.rows(), src.cols()));
+ }
+};
+} // end namespace internal
+
+/******** MatrixBase methods *******/
+
+/** \lu_module
+ *
+ * \return the partial-pivoting LU decomposition of \c *this.
+ *
+ * \sa class PartialPivLU
+ */
+template<typename Derived>
+inline const PartialPivLU<typename MatrixBase<Derived>::PlainObject>
+MatrixBase<Derived>::partialPivLu() const
+{
+ return PartialPivLU<PlainObject>(eval());
+}
+
+/** \lu_module
+ *
+ * Synonym of partialPivLu().
+ *
+ * \return the partial-pivoting LU decomposition of \c *this.
+ *
+ * \sa class PartialPivLU
+ */
+template<typename Derived>
+inline const PartialPivLU<typename MatrixBase<Derived>::PlainObject>
+MatrixBase<Derived>::lu() const
+{
+ return PartialPivLU<PlainObject>(eval());
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_PARTIALLU_H
diff --git a/Eigen/src/LU/PartialPivLU_LAPACKE.h b/Eigen/src/LU/PartialPivLU_LAPACKE.h
new file mode 100644
index 0000000..b636442
--- /dev/null
+++ b/Eigen/src/LU/PartialPivLU_LAPACKE.h
@@ -0,0 +1,96 @@
+/*
+ Copyright (c) 2011, Intel Corporation. All rights reserved.
+
+ Redistribution and use in source and binary forms, with or without modification,
+ are permitted provided that the following conditions are met:
+
+ * Redistributions of source code must retain the above copyright notice, this
+ list of conditions and the following disclaimer.
+ * Redistributions in binary form must reproduce the above copyright notice,
+ this list of conditions and the following disclaimer in the documentation
+ and/or other materials provided with the distribution.
+ * Neither the name of Intel Corporation nor the names of its contributors may
+ be used to endorse or promote products derived from this software without
+ specific prior written permission.
+
+ THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
+ ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
+ WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
+ DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR
+ ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
+ (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
+ LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON
+ ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
+ (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
+ SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+
+ ********************************************************************************
+ * Content : Eigen bindings to LAPACKe
+ * LU decomposition with partial pivoting based on LAPACKE_?getrf function.
+ ********************************************************************************
+*/
+
+#ifndef EIGEN_PARTIALLU_LAPACK_H
+#define EIGEN_PARTIALLU_LAPACK_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+
+namespace lapacke_helpers {
+// -------------------------------------------------------------------------------------------------------------------
+// Generic lapacke partial lu implementation that converts arguments and dispatches to the function above
+// -------------------------------------------------------------------------------------------------------------------
+
+template<typename Scalar, int StorageOrder>
+struct lapacke_partial_lu {
+ /** \internal performs the LU decomposition in-place of the matrix represented */
+ static lapack_int blocked_lu(Index rows, Index cols, Scalar* lu_data, Index luStride, lapack_int* row_transpositions,
+ lapack_int& nb_transpositions, lapack_int maxBlockSize=256)
+ {
+ EIGEN_UNUSED_VARIABLE(maxBlockSize);
+ // Set up parameters for getrf
+ lapack_int matrix_order = StorageOrder==RowMajor ? LAPACK_ROW_MAJOR : LAPACK_COL_MAJOR;
+ lapack_int lda = to_lapack(luStride);
+ Scalar* a = lu_data;
+ lapack_int* ipiv = row_transpositions;
+ lapack_int m = to_lapack(rows);
+ lapack_int n = to_lapack(cols);
+ nb_transpositions = 0;
+
+ lapack_int info = getrf(matrix_order, m, n, to_lapack(a), lda, ipiv );
+ eigen_assert(info >= 0);
+
+ for(int i=0; i<m; i++) {
+ ipiv[i]--;
+ if (ipiv[i] != i) nb_transpositions++;
+ }
+ lapack_int first_zero_pivot = info;
+ return first_zero_pivot;
+ }
+};
+} // end namespace lapacke_helpers
+
+/*
+ * Here, we just put the generic implementation from lapacke_partial_lu into a partial specialization of the partial_lu_impl
+ * type. This specialization is more specialized than the generic implementations that Eigen implements, so if the
+ * Scalar type matches they will be chosen.
+ */
+#define EIGEN_LAPACKE_PARTIAL_LU(EIGTYPE) \
+template<int StorageOrder> \
+struct partial_lu_impl<EIGTYPE, StorageOrder, lapack_int, Dynamic> : public lapacke_helpers::lapacke_partial_lu<EIGTYPE, StorageOrder> {};
+
+EIGEN_LAPACKE_PARTIAL_LU(double)
+EIGEN_LAPACKE_PARTIAL_LU(float)
+EIGEN_LAPACKE_PARTIAL_LU(std::complex<double>)
+EIGEN_LAPACKE_PARTIAL_LU(std::complex<float>)
+
+#undef EIGEN_LAPACKE_PARTIAL_LU
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_PARTIALLU_LAPACK_H
diff --git a/Eigen/src/LU/arch/InverseSize4.h b/Eigen/src/LU/arch/InverseSize4.h
new file mode 100644
index 0000000..2733fbe
--- /dev/null
+++ b/Eigen/src/LU/arch/InverseSize4.h
@@ -0,0 +1,365 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2001 Intel Corporation
+// Copyright (C) 2010 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2009 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+//
+// The algorithm below is a reimplementation of former \src\LU\Inverse_SSE.h using PacketMath.
+// inv(M) = M#/|M|, where inv(M), M# and |M| denote the inverse of M,
+// adjugate of M and determinant of M respectively. M# is computed block-wise
+// using specific formulae. For proof, see:
+// https://lxjk.github.io/2017/09/03/Fast-4x4-Matrix-Inverse-with-SSE-SIMD-Explained.html
+// Variable names are adopted from \src\LU\Inverse_SSE.h.
+//
+// The SSE code for the 4x4 float and double matrix inverse in former (deprecated) \src\LU\Inverse_SSE.h
+// comes from the following Intel's library:
+// http://software.intel.com/en-us/articles/optimized-matrix-library-for-use-with-the-intel-pentiumr-4-processors-sse2-instructions/
+//
+// Here is the respective copyright and license statement:
+//
+// Copyright (c) 2001 Intel Corporation.
+//
+// Permition is granted to use, copy, distribute and prepare derivative works
+// of this library for any purpose and without fee, provided, that the above
+// copyright notice and this statement appear in all copies.
+// Intel makes no representations about the suitability of this software for
+// any purpose, and specifically disclaims all warranties.
+// See LEGAL.TXT for all the legal information.
+//
+// TODO: Unify implementations of different data types (i.e. float and double).
+#ifndef EIGEN_INVERSE_SIZE_4_H
+#define EIGEN_INVERSE_SIZE_4_H
+
+#include "../InternalHeaderCheck.h"
+
+#if !EIGEN_COMP_LLVM
+// These routines requires bit manipulation of the sign, which is not compatible
+// with fastmath.
+#pragma GCC push_options
+#pragma GCC optimize ("no-fast-math")
+#endif
+
+namespace Eigen
+{
+namespace internal
+{
+template <typename MatrixType, typename ResultType>
+struct compute_inverse_size4<Architecture::Target, float, MatrixType, ResultType>
+{
+ enum
+ {
+ MatrixAlignment = traits<MatrixType>::Alignment,
+ ResultAlignment = traits<ResultType>::Alignment,
+ StorageOrdersMatch = (MatrixType::Flags & RowMajorBit) == (ResultType::Flags & RowMajorBit)
+ };
+ typedef std::conditional_t<(MatrixType::Flags & LinearAccessBit), MatrixType const &, typename MatrixType::PlainObject> ActualMatrixType;
+
+ static void run(const MatrixType &mat, ResultType &result)
+ {
+ ActualMatrixType matrix(mat);
+
+ const float* data = matrix.data();
+ const Index stride = matrix.innerStride();
+ Packet4f L1 = ploadt<Packet4f,MatrixAlignment>(data);
+ Packet4f L2 = ploadt<Packet4f,MatrixAlignment>(data + stride*4);
+ Packet4f L3 = ploadt<Packet4f,MatrixAlignment>(data + stride*8);
+ Packet4f L4 = ploadt<Packet4f,MatrixAlignment>(data + stride*12);
+
+ // Four 2x2 sub-matrices of the input matrix
+ // input = [[A, B],
+ // [C, D]]
+ Packet4f A, B, C, D;
+
+ if (!StorageOrdersMatch)
+ {
+ A = vec4f_unpacklo(L1, L2);
+ B = vec4f_unpacklo(L3, L4);
+ C = vec4f_unpackhi(L1, L2);
+ D = vec4f_unpackhi(L3, L4);
+ }
+ else
+ {
+ A = vec4f_movelh(L1, L2);
+ B = vec4f_movehl(L2, L1);
+ C = vec4f_movelh(L3, L4);
+ D = vec4f_movehl(L4, L3);
+ }
+
+ Packet4f AB, DC;
+
+ // AB = A# * B, where A# denotes the adjugate of A, and * denotes matrix product.
+ AB = pmul(vec4f_swizzle2(A, A, 3, 3, 0, 0), B);
+ AB = psub(AB, pmul(vec4f_swizzle2(A, A, 1, 1, 2, 2), vec4f_swizzle2(B, B, 2, 3, 0, 1)));
+
+ // DC = D#*C
+ DC = pmul(vec4f_swizzle2(D, D, 3, 3, 0, 0), C);
+ DC = psub(DC, pmul(vec4f_swizzle2(D, D, 1, 1, 2, 2), vec4f_swizzle2(C, C, 2, 3, 0, 1)));
+
+ // determinants of the sub-matrices
+ Packet4f dA, dB, dC, dD;
+
+ dA = pmul(vec4f_swizzle2(A, A, 3, 3, 1, 1), A);
+ dA = psub(dA, vec4f_movehl(dA, dA));
+
+ dB = pmul(vec4f_swizzle2(B, B, 3, 3, 1, 1), B);
+ dB = psub(dB, vec4f_movehl(dB, dB));
+
+ dC = pmul(vec4f_swizzle2(C, C, 3, 3, 1, 1), C);
+ dC = psub(dC, vec4f_movehl(dC, dC));
+
+ dD = pmul(vec4f_swizzle2(D, D, 3, 3, 1, 1), D);
+ dD = psub(dD, vec4f_movehl(dD, dD));
+
+ Packet4f d, d1, d2;
+
+ d = pmul(vec4f_swizzle2(DC, DC, 0, 2, 1, 3), AB);
+ d = padd(d, vec4f_movehl(d, d));
+ d = padd(d, vec4f_swizzle2(d, d, 1, 0, 0, 0));
+ d1 = pmul(dA, dD);
+ d2 = pmul(dB, dC);
+
+ // determinant of the input matrix, det = |A||D| + |B||C| - trace(A#*B*D#*C)
+ Packet4f det = vec4f_duplane(psub(padd(d1, d2), d), 0);
+
+ // reciprocal of the determinant of the input matrix, rd = 1/det
+ Packet4f rd = preciprocal(det);
+
+ // Four sub-matrices of the inverse
+ Packet4f iA, iB, iC, iD;
+
+ // iD = D*|A| - C*A#*B
+ iD = pmul(vec4f_swizzle2(C, C, 0, 0, 2, 2), vec4f_movelh(AB, AB));
+ iD = padd(iD, pmul(vec4f_swizzle2(C, C, 1, 1, 3, 3), vec4f_movehl(AB, AB)));
+ iD = psub(pmul(D, vec4f_duplane(dA, 0)), iD);
+
+ // iA = A*|D| - B*D#*C
+ iA = pmul(vec4f_swizzle2(B, B, 0, 0, 2, 2), vec4f_movelh(DC, DC));
+ iA = padd(iA, pmul(vec4f_swizzle2(B, B, 1, 1, 3, 3), vec4f_movehl(DC, DC)));
+ iA = psub(pmul(A, vec4f_duplane(dD, 0)), iA);
+
+ // iB = C*|B| - D * (A#B)# = C*|B| - D*B#*A
+ iB = pmul(D, vec4f_swizzle2(AB, AB, 3, 0, 3, 0));
+ iB = psub(iB, pmul(vec4f_swizzle2(D, D, 1, 0, 3, 2), vec4f_swizzle2(AB, AB, 2, 1, 2, 1)));
+ iB = psub(pmul(C, vec4f_duplane(dB, 0)), iB);
+
+ // iC = B*|C| - A * (D#C)# = B*|C| - A*C#*D
+ iC = pmul(A, vec4f_swizzle2(DC, DC, 3, 0, 3, 0));
+ iC = psub(iC, pmul(vec4f_swizzle2(A, A, 1, 0, 3, 2), vec4f_swizzle2(DC, DC, 2, 1, 2, 1)));
+ iC = psub(pmul(B, vec4f_duplane(dC, 0)), iC);
+
+ EIGEN_ALIGN_MAX const float sign_mask[4] = {0.0f, -0.0f, -0.0f, 0.0f};
+ const Packet4f p4f_sign_PNNP = pload<Packet4f>(sign_mask);
+ rd = pxor(rd, p4f_sign_PNNP);
+ iA = pmul(iA, rd);
+ iB = pmul(iB, rd);
+ iC = pmul(iC, rd);
+ iD = pmul(iD, rd);
+
+ Index res_stride = result.outerStride();
+ float *res = result.data();
+
+ pstoret<float, Packet4f, ResultAlignment>(res + 0, vec4f_swizzle2(iA, iB, 3, 1, 3, 1));
+ pstoret<float, Packet4f, ResultAlignment>(res + res_stride, vec4f_swizzle2(iA, iB, 2, 0, 2, 0));
+ pstoret<float, Packet4f, ResultAlignment>(res + 2 * res_stride, vec4f_swizzle2(iC, iD, 3, 1, 3, 1));
+ pstoret<float, Packet4f, ResultAlignment>(res + 3 * res_stride, vec4f_swizzle2(iC, iD, 2, 0, 2, 0));
+ }
+};
+
+#if !(defined EIGEN_VECTORIZE_NEON && !(EIGEN_ARCH_ARM64 && !EIGEN_APPLE_DOUBLE_NEON_BUG))
+// same algorithm as above, except that each operand is split into
+// halves for two registers to hold.
+template <typename MatrixType, typename ResultType>
+struct compute_inverse_size4<Architecture::Target, double, MatrixType, ResultType>
+{
+ enum
+ {
+ MatrixAlignment = traits<MatrixType>::Alignment,
+ ResultAlignment = traits<ResultType>::Alignment,
+ StorageOrdersMatch = (MatrixType::Flags & RowMajorBit) == (ResultType::Flags & RowMajorBit)
+ };
+ typedef std::conditional_t<(MatrixType::Flags & LinearAccessBit),
+ MatrixType const &,
+ typename MatrixType::PlainObject>
+ ActualMatrixType;
+
+ static void run(const MatrixType &mat, ResultType &result)
+ {
+ ActualMatrixType matrix(mat);
+
+ // Four 2x2 sub-matrices of the input matrix, each is further divided into upper and lower
+ // row e.g. A1, upper row of A, A2, lower row of A
+ // input = [[A, B], = [[[A1, [B1,
+ // [C, D]] A2], B2]],
+ // [[C1, [D1,
+ // C2], D2]]]
+
+ Packet2d A1, A2, B1, B2, C1, C2, D1, D2;
+
+ const double* data = matrix.data();
+ const Index stride = matrix.innerStride();
+ if (StorageOrdersMatch)
+ {
+ A1 = ploadt<Packet2d,MatrixAlignment>(data + stride*0);
+ B1 = ploadt<Packet2d,MatrixAlignment>(data + stride*2);
+ A2 = ploadt<Packet2d,MatrixAlignment>(data + stride*4);
+ B2 = ploadt<Packet2d,MatrixAlignment>(data + stride*6);
+ C1 = ploadt<Packet2d,MatrixAlignment>(data + stride*8);
+ D1 = ploadt<Packet2d,MatrixAlignment>(data + stride*10);
+ C2 = ploadt<Packet2d,MatrixAlignment>(data + stride*12);
+ D2 = ploadt<Packet2d,MatrixAlignment>(data + stride*14);
+ }
+ else
+ {
+ Packet2d temp;
+ A1 = ploadt<Packet2d,MatrixAlignment>(data + stride*0);
+ C1 = ploadt<Packet2d,MatrixAlignment>(data + stride*2);
+ A2 = ploadt<Packet2d,MatrixAlignment>(data + stride*4);
+ C2 = ploadt<Packet2d,MatrixAlignment>(data + stride*6);
+ temp = A1;
+ A1 = vec2d_unpacklo(A1, A2);
+ A2 = vec2d_unpackhi(temp, A2);
+
+ temp = C1;
+ C1 = vec2d_unpacklo(C1, C2);
+ C2 = vec2d_unpackhi(temp, C2);
+
+ B1 = ploadt<Packet2d,MatrixAlignment>(data + stride*8);
+ D1 = ploadt<Packet2d,MatrixAlignment>(data + stride*10);
+ B2 = ploadt<Packet2d,MatrixAlignment>(data + stride*12);
+ D2 = ploadt<Packet2d,MatrixAlignment>(data + stride*14);
+
+ temp = B1;
+ B1 = vec2d_unpacklo(B1, B2);
+ B2 = vec2d_unpackhi(temp, B2);
+
+ temp = D1;
+ D1 = vec2d_unpacklo(D1, D2);
+ D2 = vec2d_unpackhi(temp, D2);
+ }
+
+ // determinants of the sub-matrices
+ Packet2d dA, dB, dC, dD;
+
+ dA = vec2d_swizzle2(A2, A2, 1);
+ dA = pmul(A1, dA);
+ dA = psub(dA, vec2d_duplane(dA, 1));
+
+ dB = vec2d_swizzle2(B2, B2, 1);
+ dB = pmul(B1, dB);
+ dB = psub(dB, vec2d_duplane(dB, 1));
+
+ dC = vec2d_swizzle2(C2, C2, 1);
+ dC = pmul(C1, dC);
+ dC = psub(dC, vec2d_duplane(dC, 1));
+
+ dD = vec2d_swizzle2(D2, D2, 1);
+ dD = pmul(D1, dD);
+ dD = psub(dD, vec2d_duplane(dD, 1));
+
+ Packet2d DC1, DC2, AB1, AB2;
+
+ // AB = A# * B, where A# denotes the adjugate of A, and * denotes matrix product.
+ AB1 = pmul(B1, vec2d_duplane(A2, 1));
+ AB2 = pmul(B2, vec2d_duplane(A1, 0));
+ AB1 = psub(AB1, pmul(B2, vec2d_duplane(A1, 1)));
+ AB2 = psub(AB2, pmul(B1, vec2d_duplane(A2, 0)));
+
+ // DC = D#*C
+ DC1 = pmul(C1, vec2d_duplane(D2, 1));
+ DC2 = pmul(C2, vec2d_duplane(D1, 0));
+ DC1 = psub(DC1, pmul(C2, vec2d_duplane(D1, 1)));
+ DC2 = psub(DC2, pmul(C1, vec2d_duplane(D2, 0)));
+
+ Packet2d d1, d2;
+
+ // determinant of the input matrix, det = |A||D| + |B||C| - trace(A#*B*D#*C)
+ Packet2d det;
+
+ // reciprocal of the determinant of the input matrix, rd = 1/det
+ Packet2d rd;
+
+ d1 = pmul(AB1, vec2d_swizzle2(DC1, DC2, 0));
+ d2 = pmul(AB2, vec2d_swizzle2(DC1, DC2, 3));
+ rd = padd(d1, d2);
+ rd = padd(rd, vec2d_duplane(rd, 1));
+
+ d1 = pmul(dA, dD);
+ d2 = pmul(dB, dC);
+
+ det = padd(d1, d2);
+ det = psub(det, rd);
+ det = vec2d_duplane(det, 0);
+ rd = pdiv(pset1<Packet2d>(1.0), det);
+
+ // rows of four sub-matrices of the inverse
+ Packet2d iA1, iA2, iB1, iB2, iC1, iC2, iD1, iD2;
+
+ // iD = D*|A| - C*A#*B
+ iD1 = pmul(AB1, vec2d_duplane(C1, 0));
+ iD2 = pmul(AB1, vec2d_duplane(C2, 0));
+ iD1 = padd(iD1, pmul(AB2, vec2d_duplane(C1, 1)));
+ iD2 = padd(iD2, pmul(AB2, vec2d_duplane(C2, 1)));
+ dA = vec2d_duplane(dA, 0);
+ iD1 = psub(pmul(D1, dA), iD1);
+ iD2 = psub(pmul(D2, dA), iD2);
+
+ // iA = A*|D| - B*D#*C
+ iA1 = pmul(DC1, vec2d_duplane(B1, 0));
+ iA2 = pmul(DC1, vec2d_duplane(B2, 0));
+ iA1 = padd(iA1, pmul(DC2, vec2d_duplane(B1, 1)));
+ iA2 = padd(iA2, pmul(DC2, vec2d_duplane(B2, 1)));
+ dD = vec2d_duplane(dD, 0);
+ iA1 = psub(pmul(A1, dD), iA1);
+ iA2 = psub(pmul(A2, dD), iA2);
+
+ // iB = C*|B| - D * (A#B)# = C*|B| - D*B#*A
+ iB1 = pmul(D1, vec2d_swizzle2(AB2, AB1, 1));
+ iB2 = pmul(D2, vec2d_swizzle2(AB2, AB1, 1));
+ iB1 = psub(iB1, pmul(vec2d_swizzle2(D1, D1, 1), vec2d_swizzle2(AB2, AB1, 2)));
+ iB2 = psub(iB2, pmul(vec2d_swizzle2(D2, D2, 1), vec2d_swizzle2(AB2, AB1, 2)));
+ dB = vec2d_duplane(dB, 0);
+ iB1 = psub(pmul(C1, dB), iB1);
+ iB2 = psub(pmul(C2, dB), iB2);
+
+ // iC = B*|C| - A * (D#C)# = B*|C| - A*C#*D
+ iC1 = pmul(A1, vec2d_swizzle2(DC2, DC1, 1));
+ iC2 = pmul(A2, vec2d_swizzle2(DC2, DC1, 1));
+ iC1 = psub(iC1, pmul(vec2d_swizzle2(A1, A1, 1), vec2d_swizzle2(DC2, DC1, 2)));
+ iC2 = psub(iC2, pmul(vec2d_swizzle2(A2, A2, 1), vec2d_swizzle2(DC2, DC1, 2)));
+ dC = vec2d_duplane(dC, 0);
+ iC1 = psub(pmul(B1, dC), iC1);
+ iC2 = psub(pmul(B2, dC), iC2);
+
+ EIGEN_ALIGN_MAX const double sign_mask1[2] = {0.0, -0.0};
+ EIGEN_ALIGN_MAX const double sign_mask2[2] = {-0.0, 0.0};
+ const Packet2d sign_PN = pload<Packet2d>(sign_mask1);
+ const Packet2d sign_NP = pload<Packet2d>(sign_mask2);
+ d1 = pxor(rd, sign_PN);
+ d2 = pxor(rd, sign_NP);
+
+ Index res_stride = result.outerStride();
+ double *res = result.data();
+ pstoret<double, Packet2d, ResultAlignment>(res + 0, pmul(vec2d_swizzle2(iA2, iA1, 3), d1));
+ pstoret<double, Packet2d, ResultAlignment>(res + res_stride, pmul(vec2d_swizzle2(iA2, iA1, 0), d2));
+ pstoret<double, Packet2d, ResultAlignment>(res + 2, pmul(vec2d_swizzle2(iB2, iB1, 3), d1));
+ pstoret<double, Packet2d, ResultAlignment>(res + res_stride + 2, pmul(vec2d_swizzle2(iB2, iB1, 0), d2));
+ pstoret<double, Packet2d, ResultAlignment>(res + 2 * res_stride, pmul(vec2d_swizzle2(iC2, iC1, 3), d1));
+ pstoret<double, Packet2d, ResultAlignment>(res + 3 * res_stride, pmul(vec2d_swizzle2(iC2, iC1, 0), d2));
+ pstoret<double, Packet2d, ResultAlignment>(res + 2 * res_stride + 2, pmul(vec2d_swizzle2(iD2, iD1, 3), d1));
+ pstoret<double, Packet2d, ResultAlignment>(res + 3 * res_stride + 2, pmul(vec2d_swizzle2(iD2, iD1, 0), d2));
+ }
+};
+#endif
+} // namespace internal
+} // namespace Eigen
+
+#if !EIGEN_COMP_LLVM
+#pragma GCC pop_options
+#endif
+
+#endif
diff --git a/Eigen/src/MetisSupport/InternalHeaderCheck.h b/Eigen/src/MetisSupport/InternalHeaderCheck.h
new file mode 100644
index 0000000..9d34825
--- /dev/null
+++ b/Eigen/src/MetisSupport/InternalHeaderCheck.h
@@ -0,0 +1,3 @@
+#ifndef EIGEN_METISSUPPORT_MODULE_H
+#error "Please include Eigen/MetisSupport instead of including headers inside the src directory directly."
+#endif
diff --git a/Eigen/src/MetisSupport/MetisSupport.h b/Eigen/src/MetisSupport/MetisSupport.h
new file mode 100644
index 0000000..c5e143b
--- /dev/null
+++ b/Eigen/src/MetisSupport/MetisSupport.h
@@ -0,0 +1,139 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2012 Désiré Nuentsa-Wakam <desire.nuentsa_wakam@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+#ifndef METIS_SUPPORT_H
+#define METIS_SUPPORT_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+/**
+ * Get the fill-reducing ordering from the METIS package
+ *
+ * If A is the original matrix and Ap is the permuted matrix,
+ * the fill-reducing permutation is defined as follows :
+ * Row (column) i of A is the matperm(i) row (column) of Ap.
+ * WARNING: As computed by METIS, this corresponds to the vector iperm (instead of perm)
+ */
+template <typename StorageIndex>
+class MetisOrdering
+{
+public:
+ typedef PermutationMatrix<Dynamic,Dynamic,StorageIndex> PermutationType;
+ typedef Matrix<StorageIndex,Dynamic,1> IndexVector;
+
+ template <typename MatrixType>
+ void get_symmetrized_graph(const MatrixType& A)
+ {
+ Index m = A.cols();
+ eigen_assert((A.rows() == A.cols()) && "ONLY FOR SQUARED MATRICES");
+ // Get the transpose of the input matrix
+ MatrixType At = A.transpose();
+ // Get the number of nonzeros elements in each row/col of At+A
+ Index TotNz = 0;
+ IndexVector visited(m);
+ visited.setConstant(-1);
+ for (StorageIndex j = 0; j < m; j++)
+ {
+ // Compute the union structure of of A(j,:) and At(j,:)
+ visited(j) = j; // Do not include the diagonal element
+ // Get the nonzeros in row/column j of A
+ for (typename MatrixType::InnerIterator it(A, j); it; ++it)
+ {
+ Index idx = it.index(); // Get the row index (for column major) or column index (for row major)
+ if (visited(idx) != j )
+ {
+ visited(idx) = j;
+ ++TotNz;
+ }
+ }
+ //Get the nonzeros in row/column j of At
+ for (typename MatrixType::InnerIterator it(At, j); it; ++it)
+ {
+ Index idx = it.index();
+ if(visited(idx) != j)
+ {
+ visited(idx) = j;
+ ++TotNz;
+ }
+ }
+ }
+ // Reserve place for A + At
+ m_indexPtr.resize(m+1);
+ m_innerIndices.resize(TotNz);
+
+ // Now compute the real adjacency list of each column/row
+ visited.setConstant(-1);
+ StorageIndex CurNz = 0;
+ for (StorageIndex j = 0; j < m; j++)
+ {
+ m_indexPtr(j) = CurNz;
+
+ visited(j) = j; // Do not include the diagonal element
+ // Add the pattern of row/column j of A to A+At
+ for (typename MatrixType::InnerIterator it(A,j); it; ++it)
+ {
+ StorageIndex idx = it.index(); // Get the row index (for column major) or column index (for row major)
+ if (visited(idx) != j )
+ {
+ visited(idx) = j;
+ m_innerIndices(CurNz) = idx;
+ CurNz++;
+ }
+ }
+ //Add the pattern of row/column j of At to A+At
+ for (typename MatrixType::InnerIterator it(At, j); it; ++it)
+ {
+ StorageIndex idx = it.index();
+ if(visited(idx) != j)
+ {
+ visited(idx) = j;
+ m_innerIndices(CurNz) = idx;
+ ++CurNz;
+ }
+ }
+ }
+ m_indexPtr(m) = CurNz;
+ }
+
+ template <typename MatrixType>
+ void operator() (const MatrixType& A, PermutationType& matperm)
+ {
+ StorageIndex m = internal::convert_index<StorageIndex>(A.cols()); // must be StorageIndex, because it is passed by address to METIS
+ IndexVector perm(m),iperm(m);
+ // First, symmetrize the matrix graph.
+ get_symmetrized_graph(A);
+ int output_error;
+
+ // Call the fill-reducing routine from METIS
+ output_error = METIS_NodeND(&m, m_indexPtr.data(), m_innerIndices.data(), NULL, NULL, perm.data(), iperm.data());
+
+ if(output_error != METIS_OK)
+ {
+ //FIXME The ordering interface should define a class of possible errors
+ std::cerr << "ERROR WHILE CALLING THE METIS PACKAGE \n";
+ return;
+ }
+
+ // Get the fill-reducing permutation
+ //NOTE: If Ap is the permuted matrix then perm and iperm vectors are defined as follows
+ // Row (column) i of Ap is the perm(i) row(column) of A, and row (column) i of A is the iperm(i) row(column) of Ap
+
+ matperm.resize(m);
+ for (int j = 0; j < m; j++)
+ matperm.indices()(iperm(j)) = j;
+
+ }
+
+ protected:
+ IndexVector m_indexPtr; // Pointer to the adjacenccy list of each row/column
+ IndexVector m_innerIndices; // Adjacency list
+};
+
+}// end namespace eigen
+#endif
diff --git a/Eigen/src/OrderingMethods/Amd.h b/Eigen/src/OrderingMethods/Amd.h
new file mode 100644
index 0000000..5bd531c
--- /dev/null
+++ b/Eigen/src/OrderingMethods/Amd.h
@@ -0,0 +1,437 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2010 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+/*
+NOTE: this routine has been adapted from the CSparse library:
+
+Copyright (c) 2006, Timothy A. Davis.
+http://www.suitesparse.com
+
+The author of CSparse, Timothy A. Davis., has executed a license with Google LLC
+to permit distribution of this code and derivative works as part of Eigen under
+the Mozilla Public License v. 2.0, as stated at the top of this file.
+*/
+
+#ifndef EIGEN_SPARSE_AMD_H
+#define EIGEN_SPARSE_AMD_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+
+template<typename T> inline T amd_flip(const T& i) { return -i-2; }
+template<typename T> inline T amd_unflip(const T& i) { return i<0 ? amd_flip(i) : i; }
+template<typename T0, typename T1> inline bool amd_marked(const T0* w, const T1& j) { return w[j]<0; }
+template<typename T0, typename T1> inline void amd_mark(const T0* w, const T1& j) { return w[j] = amd_flip(w[j]); }
+
+/* clear w */
+template<typename StorageIndex>
+static StorageIndex cs_wclear (StorageIndex mark, StorageIndex lemax, StorageIndex *w, StorageIndex n)
+{
+ StorageIndex k;
+ if(mark < 2 || (mark + lemax < 0))
+ {
+ for(k = 0; k < n; k++)
+ if(w[k] != 0)
+ w[k] = 1;
+ mark = 2;
+ }
+ return (mark); /* at this point, w[0..n-1] < mark holds */
+}
+
+/* depth-first search and postorder of a tree rooted at node j */
+template<typename StorageIndex>
+StorageIndex cs_tdfs(StorageIndex j, StorageIndex k, StorageIndex *head, const StorageIndex *next, StorageIndex *post, StorageIndex *stack)
+{
+ StorageIndex i, p, top = 0;
+ if(!head || !next || !post || !stack) return (-1); /* check inputs */
+ stack[0] = j; /* place j on the stack */
+ while (top >= 0) /* while (stack is not empty) */
+ {
+ p = stack[top]; /* p = top of stack */
+ i = head[p]; /* i = youngest child of p */
+ if(i == -1)
+ {
+ top--; /* p has no unordered children left */
+ post[k++] = p; /* node p is the kth postordered node */
+ }
+ else
+ {
+ head[p] = next[i]; /* remove i from children of p */
+ stack[++top] = i; /* start dfs on child node i */
+ }
+ }
+ return k;
+}
+
+
+/** \internal
+ * \ingroup OrderingMethods_Module
+ * Approximate minimum degree ordering algorithm.
+ *
+ * \param[in] C the input selfadjoint matrix stored in compressed column major format.
+ * \param[out] perm the permutation P reducing the fill-in of the input matrix \a C
+ *
+ * Note that the input matrix \a C must be complete, that is both the upper and lower parts have to be stored, as well as the diagonal entries.
+ * On exit the values of C are destroyed */
+template<typename Scalar, typename StorageIndex>
+void minimum_degree_ordering(SparseMatrix<Scalar,ColMajor,StorageIndex>& C, PermutationMatrix<Dynamic,Dynamic,StorageIndex>& perm)
+{
+ using std::sqrt;
+
+ StorageIndex d, dk, dext, lemax = 0, e, elenk, eln, i, j, k, k1,
+ k2, k3, jlast, ln, dense, nzmax, mindeg = 0, nvi, nvj, nvk, mark, wnvi,
+ ok, nel = 0, p, p1, p2, p3, p4, pj, pk, pk1, pk2, pn, q, t, h;
+
+ StorageIndex n = StorageIndex(C.cols());
+ dense = std::max<StorageIndex> (16, StorageIndex(10 * sqrt(double(n)))); /* find dense threshold */
+ dense = (std::min)(n-2, dense);
+
+ StorageIndex cnz = StorageIndex(C.nonZeros());
+ perm.resize(n+1);
+ t = cnz + cnz/5 + 2*n; /* add elbow room to C */
+ C.resizeNonZeros(t);
+
+ // get workspace
+ ei_declare_aligned_stack_constructed_variable(StorageIndex,W,8*(n+1),0);
+ StorageIndex* len = W;
+ StorageIndex* nv = W + (n+1);
+ StorageIndex* next = W + 2*(n+1);
+ StorageIndex* head = W + 3*(n+1);
+ StorageIndex* elen = W + 4*(n+1);
+ StorageIndex* degree = W + 5*(n+1);
+ StorageIndex* w = W + 6*(n+1);
+ StorageIndex* hhead = W + 7*(n+1);
+ StorageIndex* last = perm.indices().data(); /* use P as workspace for last */
+
+ /* --- Initialize quotient graph ---------------------------------------- */
+ StorageIndex* Cp = C.outerIndexPtr();
+ StorageIndex* Ci = C.innerIndexPtr();
+ for(k = 0; k < n; k++)
+ len[k] = Cp[k+1] - Cp[k];
+ len[n] = 0;
+ nzmax = t;
+
+ for(i = 0; i <= n; i++)
+ {
+ head[i] = -1; // degree list i is empty
+ last[i] = -1;
+ next[i] = -1;
+ hhead[i] = -1; // hash list i is empty
+ nv[i] = 1; // node i is just one node
+ w[i] = 1; // node i is alive
+ elen[i] = 0; // Ek of node i is empty
+ degree[i] = len[i]; // degree of node i
+ }
+ mark = internal::cs_wclear<StorageIndex>(0, 0, w, n); /* clear w */
+
+ /* --- Initialize degree lists ------------------------------------------ */
+ for(i = 0; i < n; i++)
+ {
+ bool has_diag = false;
+ for(p = Cp[i]; p<Cp[i+1]; ++p)
+ if(Ci[p]==i)
+ {
+ has_diag = true;
+ break;
+ }
+
+ d = degree[i];
+ if(d == 1 && has_diag) /* node i is empty */
+ {
+ elen[i] = -2; /* element i is dead */
+ nel++;
+ Cp[i] = -1; /* i is a root of assembly tree */
+ w[i] = 0;
+ }
+ else if(d > dense || !has_diag) /* node i is dense or has no structural diagonal element */
+ {
+ nv[i] = 0; /* absorb i into element n */
+ elen[i] = -1; /* node i is dead */
+ nel++;
+ Cp[i] = amd_flip (n);
+ nv[n]++;
+ }
+ else
+ {
+ if(head[d] != -1) last[head[d]] = i;
+ next[i] = head[d]; /* put node i in degree list d */
+ head[d] = i;
+ }
+ }
+
+ elen[n] = -2; /* n is a dead element */
+ Cp[n] = -1; /* n is a root of assembly tree */
+ w[n] = 0; /* n is a dead element */
+
+ while (nel < n) /* while (selecting pivots) do */
+ {
+ /* --- Select node of minimum approximate degree -------------------- */
+ for(k = -1; mindeg < n && (k = head[mindeg]) == -1; mindeg++) {}
+ if(next[k] != -1) last[next[k]] = -1;
+ head[mindeg] = next[k]; /* remove k from degree list */
+ elenk = elen[k]; /* elenk = |Ek| */
+ nvk = nv[k]; /* # of nodes k represents */
+ nel += nvk; /* nv[k] nodes of A eliminated */
+
+ /* --- Garbage collection ------------------------------------------- */
+ if(elenk > 0 && cnz + mindeg >= nzmax)
+ {
+ for(j = 0; j < n; j++)
+ {
+ if((p = Cp[j]) >= 0) /* j is a live node or element */
+ {
+ Cp[j] = Ci[p]; /* save first entry of object */
+ Ci[p] = amd_flip (j); /* first entry is now amd_flip(j) */
+ }
+ }
+ for(q = 0, p = 0; p < cnz; ) /* scan all of memory */
+ {
+ if((j = amd_flip (Ci[p++])) >= 0) /* found object j */
+ {
+ Ci[q] = Cp[j]; /* restore first entry of object */
+ Cp[j] = q++; /* new pointer to object j */
+ for(k3 = 0; k3 < len[j]-1; k3++) Ci[q++] = Ci[p++];
+ }
+ }
+ cnz = q; /* Ci[cnz...nzmax-1] now free */
+ }
+
+ /* --- Construct new element ---------------------------------------- */
+ dk = 0;
+ nv[k] = -nvk; /* flag k as in Lk */
+ p = Cp[k];
+ pk1 = (elenk == 0) ? p : cnz; /* do in place if elen[k] == 0 */
+ pk2 = pk1;
+ for(k1 = 1; k1 <= elenk + 1; k1++)
+ {
+ if(k1 > elenk)
+ {
+ e = k; /* search the nodes in k */
+ pj = p; /* list of nodes starts at Ci[pj]*/
+ ln = len[k] - elenk; /* length of list of nodes in k */
+ }
+ else
+ {
+ e = Ci[p++]; /* search the nodes in e */
+ pj = Cp[e];
+ ln = len[e]; /* length of list of nodes in e */
+ }
+ for(k2 = 1; k2 <= ln; k2++)
+ {
+ i = Ci[pj++];
+ if((nvi = nv[i]) <= 0) continue; /* node i dead, or seen */
+ dk += nvi; /* degree[Lk] += size of node i */
+ nv[i] = -nvi; /* negate nv[i] to denote i in Lk*/
+ Ci[pk2++] = i; /* place i in Lk */
+ if(next[i] != -1) last[next[i]] = last[i];
+ if(last[i] != -1) /* remove i from degree list */
+ {
+ next[last[i]] = next[i];
+ }
+ else
+ {
+ head[degree[i]] = next[i];
+ }
+ }
+ if(e != k)
+ {
+ Cp[e] = amd_flip (k); /* absorb e into k */
+ w[e] = 0; /* e is now a dead element */
+ }
+ }
+ if(elenk != 0) cnz = pk2; /* Ci[cnz...nzmax] is free */
+ degree[k] = dk; /* external degree of k - |Lk\i| */
+ Cp[k] = pk1; /* element k is in Ci[pk1..pk2-1] */
+ len[k] = pk2 - pk1;
+ elen[k] = -2; /* k is now an element */
+
+ /* --- Find set differences ----------------------------------------- */
+ mark = internal::cs_wclear<StorageIndex>(mark, lemax, w, n); /* clear w if necessary */
+ for(pk = pk1; pk < pk2; pk++) /* scan 1: find |Le\Lk| */
+ {
+ i = Ci[pk];
+ if((eln = elen[i]) <= 0) continue;/* skip if elen[i] empty */
+ nvi = -nv[i]; /* nv[i] was negated */
+ wnvi = mark - nvi;
+ for(p = Cp[i]; p <= Cp[i] + eln - 1; p++) /* scan Ei */
+ {
+ e = Ci[p];
+ if(w[e] >= mark)
+ {
+ w[e] -= nvi; /* decrement |Le\Lk| */
+ }
+ else if(w[e] != 0) /* ensure e is a live element */
+ {
+ w[e] = degree[e] + wnvi; /* 1st time e seen in scan 1 */
+ }
+ }
+ }
+
+ /* --- Degree update ------------------------------------------------ */
+ for(pk = pk1; pk < pk2; pk++) /* scan2: degree update */
+ {
+ i = Ci[pk]; /* consider node i in Lk */
+ p1 = Cp[i];
+ p2 = p1 + elen[i] - 1;
+ pn = p1;
+ for(h = 0, d = 0, p = p1; p <= p2; p++) /* scan Ei */
+ {
+ e = Ci[p];
+ if(w[e] != 0) /* e is an unabsorbed element */
+ {
+ dext = w[e] - mark; /* dext = |Le\Lk| */
+ if(dext > 0)
+ {
+ d += dext; /* sum up the set differences */
+ Ci[pn++] = e; /* keep e in Ei */
+ h += e; /* compute the hash of node i */
+ }
+ else
+ {
+ Cp[e] = amd_flip (k); /* aggressive absorb. e->k */
+ w[e] = 0; /* e is a dead element */
+ }
+ }
+ }
+ elen[i] = pn - p1 + 1; /* elen[i] = |Ei| */
+ p3 = pn;
+ p4 = p1 + len[i];
+ for(p = p2 + 1; p < p4; p++) /* prune edges in Ai */
+ {
+ j = Ci[p];
+ if((nvj = nv[j]) <= 0) continue; /* node j dead or in Lk */
+ d += nvj; /* degree(i) += |j| */
+ Ci[pn++] = j; /* place j in node list of i */
+ h += j; /* compute hash for node i */
+ }
+ if(d == 0) /* check for mass elimination */
+ {
+ Cp[i] = amd_flip (k); /* absorb i into k */
+ nvi = -nv[i];
+ dk -= nvi; /* |Lk| -= |i| */
+ nvk += nvi; /* |k| += nv[i] */
+ nel += nvi;
+ nv[i] = 0;
+ elen[i] = -1; /* node i is dead */
+ }
+ else
+ {
+ degree[i] = std::min<StorageIndex> (degree[i], d); /* update degree(i) */
+ Ci[pn] = Ci[p3]; /* move first node to end */
+ Ci[p3] = Ci[p1]; /* move 1st el. to end of Ei */
+ Ci[p1] = k; /* add k as 1st element in of Ei */
+ len[i] = pn - p1 + 1; /* new len of adj. list of node i */
+ h %= n; /* finalize hash of i */
+ next[i] = hhead[h]; /* place i in hash bucket */
+ hhead[h] = i;
+ last[i] = h; /* save hash of i in last[i] */
+ }
+ } /* scan2 is done */
+ degree[k] = dk; /* finalize |Lk| */
+ lemax = std::max<StorageIndex>(lemax, dk);
+ mark = internal::cs_wclear<StorageIndex>(mark+lemax, lemax, w, n); /* clear w */
+
+ /* --- Supernode detection ------------------------------------------ */
+ for(pk = pk1; pk < pk2; pk++)
+ {
+ i = Ci[pk];
+ if(nv[i] >= 0) continue; /* skip if i is dead */
+ h = last[i]; /* scan hash bucket of node i */
+ i = hhead[h];
+ hhead[h] = -1; /* hash bucket will be empty */
+ for(; i != -1 && next[i] != -1; i = next[i], mark++)
+ {
+ ln = len[i];
+ eln = elen[i];
+ for(p = Cp[i]+1; p <= Cp[i] + ln-1; p++) w[Ci[p]] = mark;
+ jlast = i;
+ for(j = next[i]; j != -1; ) /* compare i with all j */
+ {
+ ok = (len[j] == ln) && (elen[j] == eln);
+ for(p = Cp[j] + 1; ok && p <= Cp[j] + ln - 1; p++)
+ {
+ if(w[Ci[p]] != mark) ok = 0; /* compare i and j*/
+ }
+ if(ok) /* i and j are identical */
+ {
+ Cp[j] = amd_flip (i); /* absorb j into i */
+ nv[i] += nv[j];
+ nv[j] = 0;
+ elen[j] = -1; /* node j is dead */
+ j = next[j]; /* delete j from hash bucket */
+ next[jlast] = j;
+ }
+ else
+ {
+ jlast = j; /* j and i are different */
+ j = next[j];
+ }
+ }
+ }
+ }
+
+ /* --- Finalize new element------------------------------------------ */
+ for(p = pk1, pk = pk1; pk < pk2; pk++) /* finalize Lk */
+ {
+ i = Ci[pk];
+ if((nvi = -nv[i]) <= 0) continue;/* skip if i is dead */
+ nv[i] = nvi; /* restore nv[i] */
+ d = degree[i] + dk - nvi; /* compute external degree(i) */
+ d = std::min<StorageIndex> (d, n - nel - nvi);
+ if(head[d] != -1) last[head[d]] = i;
+ next[i] = head[d]; /* put i back in degree list */
+ last[i] = -1;
+ head[d] = i;
+ mindeg = std::min<StorageIndex> (mindeg, d); /* find new minimum degree */
+ degree[i] = d;
+ Ci[p++] = i; /* place i in Lk */
+ }
+ nv[k] = nvk; /* # nodes absorbed into k */
+ if((len[k] = p-pk1) == 0) /* length of adj list of element k*/
+ {
+ Cp[k] = -1; /* k is a root of the tree */
+ w[k] = 0; /* k is now a dead element */
+ }
+ if(elenk != 0) cnz = p; /* free unused space in Lk */
+ }
+
+ /* --- Postordering ----------------------------------------------------- */
+ for(i = 0; i < n; i++) Cp[i] = amd_flip (Cp[i]);/* fix assembly tree */
+ for(j = 0; j <= n; j++) head[j] = -1;
+ for(j = n; j >= 0; j--) /* place unordered nodes in lists */
+ {
+ if(nv[j] > 0) continue; /* skip if j is an element */
+ next[j] = head[Cp[j]]; /* place j in list of its parent */
+ head[Cp[j]] = j;
+ }
+ for(e = n; e >= 0; e--) /* place elements in lists */
+ {
+ if(nv[e] <= 0) continue; /* skip unless e is an element */
+ if(Cp[e] != -1)
+ {
+ next[e] = head[Cp[e]]; /* place e in list of its parent */
+ head[Cp[e]] = e;
+ }
+ }
+ for(k = 0, i = 0; i <= n; i++) /* postorder the assembly tree */
+ {
+ if(Cp[i] == -1) k = internal::cs_tdfs<StorageIndex>(i, k, head, next, perm.indices().data(), w);
+ }
+
+ perm.indices().conservativeResize(n);
+}
+
+} // namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_SPARSE_AMD_H
diff --git a/Eigen/src/OrderingMethods/Eigen_Colamd.h b/Eigen/src/OrderingMethods/Eigen_Colamd.h
new file mode 100644
index 0000000..8e339a7
--- /dev/null
+++ b/Eigen/src/OrderingMethods/Eigen_Colamd.h
@@ -0,0 +1,1863 @@
+// // This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2012 Desire Nuentsa Wakam <desire.nuentsa_wakam@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+// This file is modified from the colamd/symamd library. The copyright is below
+
+// The authors of the code itself are Stefan I. Larimore and Timothy A.
+// Davis (davis@cise.ufl.edu), University of Florida. The algorithm was
+// developed in collaboration with John Gilbert, Xerox PARC, and Esmond
+// Ng, Oak Ridge National Laboratory.
+//
+// Date:
+//
+// September 8, 2003. Version 2.3.
+//
+// Acknowledgements:
+//
+// This work was supported by the National Science Foundation, under
+// grants DMS-9504974 and DMS-9803599.
+//
+// Notice:
+//
+// Copyright (c) 1998-2003 by the University of Florida.
+// All Rights Reserved.
+//
+// THIS MATERIAL IS PROVIDED AS IS, WITH ABSOLUTELY NO WARRANTY
+// EXPRESSED OR IMPLIED. ANY USE IS AT YOUR OWN RISK.
+//
+// Permission is hereby granted to use, copy, modify, and/or distribute
+// this program, provided that the Copyright, this License, and the
+// Availability of the original version is retained on all copies and made
+// accessible to the end-user of any code or package that includes COLAMD
+// or any modified version of COLAMD.
+//
+// Availability:
+//
+// The colamd/symamd library is available at
+//
+// http://www.suitesparse.com
+
+
+#ifndef EIGEN_COLAMD_H
+#define EIGEN_COLAMD_H
+
+namespace internal {
+
+namespace Colamd {
+
+/* Ensure that debugging is turned off: */
+#ifndef COLAMD_NDEBUG
+#define COLAMD_NDEBUG
+#endif /* NDEBUG */
+
+
+/* ========================================================================== */
+/* === Knob and statistics definitions ====================================== */
+/* ========================================================================== */
+
+/* size of the knobs [ ] array. Only knobs [0..1] are currently used. */
+const int NKnobs = 20;
+
+/* number of output statistics. Only stats [0..6] are currently used. */
+const int NStats = 20;
+
+/* Indices into knobs and stats array. */
+enum KnobsStatsIndex {
+ /* knobs [0] and stats [0]: dense row knob and output statistic. */
+ DenseRow = 0,
+
+ /* knobs [1] and stats [1]: dense column knob and output statistic. */
+ DenseCol = 1,
+
+ /* stats [2]: memory defragmentation count output statistic */
+ DefragCount = 2,
+
+ /* stats [3]: colamd status: zero OK, > 0 warning or notice, < 0 error */
+ Status = 3,
+
+ /* stats [4..6]: error info, or info on jumbled columns */
+ Info1 = 4,
+ Info2 = 5,
+ Info3 = 6
+};
+
+/* error codes returned in stats [3]: */
+enum Status {
+ Ok = 0,
+ OkButJumbled = 1,
+ ErrorANotPresent = -1,
+ ErrorPNotPresent = -2,
+ ErrorNrowNegative = -3,
+ ErrorNcolNegative = -4,
+ ErrorNnzNegative = -5,
+ ErrorP0Nonzero = -6,
+ ErrorATooSmall = -7,
+ ErrorColLengthNegative = -8,
+ ErrorRowIndexOutOfBounds = -9,
+ ErrorOutOfMemory = -10,
+ ErrorInternalError = -999
+};
+/* ========================================================================== */
+/* === Definitions ========================================================== */
+/* ========================================================================== */
+
+template <typename IndexType>
+IndexType ones_complement(const IndexType r) {
+ return (-(r)-1);
+}
+
+/* -------------------------------------------------------------------------- */
+const int Empty = -1;
+
+/* Row and column status */
+enum RowColumnStatus {
+ Alive = 0,
+ Dead = -1
+};
+
+/* Column status */
+enum ColumnStatus {
+ DeadPrincipal = -1,
+ DeadNonPrincipal = -2
+};
+
+/* ========================================================================== */
+/* === Colamd reporting mechanism =========================================== */
+/* ========================================================================== */
+
+// == Row and Column structures ==
+template <typename IndexType>
+struct ColStructure
+{
+ IndexType start ; /* index for A of first row in this column, or Dead */
+ /* if column is dead */
+ IndexType length ; /* number of rows in this column */
+ union
+ {
+ IndexType thickness ; /* number of original columns represented by this */
+ /* col, if the column is alive */
+ IndexType parent ; /* parent in parent tree super-column structure, if */
+ /* the column is dead */
+ } shared1 ;
+ union
+ {
+ IndexType score ; /* the score used to maintain heap, if col is alive */
+ IndexType order ; /* pivot ordering of this column, if col is dead */
+ } shared2 ;
+ union
+ {
+ IndexType headhash ; /* head of a hash bucket, if col is at the head of */
+ /* a degree list */
+ IndexType hash ; /* hash value, if col is not in a degree list */
+ IndexType prev ; /* previous column in degree list, if col is in a */
+ /* degree list (but not at the head of a degree list) */
+ } shared3 ;
+ union
+ {
+ IndexType degree_next ; /* next column, if col is in a degree list */
+ IndexType hash_next ; /* next column, if col is in a hash list */
+ } shared4 ;
+
+ inline bool is_dead() const { return start < Alive; }
+
+ inline bool is_alive() const { return start >= Alive; }
+
+ inline bool is_dead_principal() const { return start == DeadPrincipal; }
+
+ inline void kill_principal() { start = DeadPrincipal; }
+
+ inline void kill_non_principal() { start = DeadNonPrincipal; }
+
+};
+
+template <typename IndexType>
+struct RowStructure
+{
+ IndexType start ; /* index for A of first col in this row */
+ IndexType length ; /* number of principal columns in this row */
+ union
+ {
+ IndexType degree ; /* number of principal & non-principal columns in row */
+ IndexType p ; /* used as a row pointer in init_rows_cols () */
+ } shared1 ;
+ union
+ {
+ IndexType mark ; /* for computing set differences and marking dead rows*/
+ IndexType first_column ;/* first column in row (used in garbage collection) */
+ } shared2 ;
+
+ inline bool is_dead() const { return shared2.mark < Alive; }
+
+ inline bool is_alive() const { return shared2.mark >= Alive; }
+
+ inline void kill() { shared2.mark = Dead; }
+
+};
+
+/* ========================================================================== */
+/* === Colamd recommended memory size ======================================= */
+/* ========================================================================== */
+
+/*
+ The recommended length Alen of the array A passed to colamd is given by
+ the COLAMD_RECOMMENDED (nnz, n_row, n_col) macro. It returns -1 if any
+ argument is negative. 2*nnz space is required for the row and column
+ indices of the matrix. colamd_c (n_col) + colamd_r (n_row) space is
+ required for the Col and Row arrays, respectively, which are internal to
+ colamd. An additional n_col space is the minimal amount of "elbow room",
+ and nnz/5 more space is recommended for run time efficiency.
+
+ This macro is not needed when using symamd.
+
+ Explicit typecast to IndexType added Sept. 23, 2002, COLAMD version 2.2, to avoid
+ gcc -pedantic warning messages.
+*/
+template <typename IndexType>
+inline IndexType colamd_c(IndexType n_col)
+{ return IndexType( ((n_col) + 1) * sizeof (ColStructure<IndexType>) / sizeof (IndexType) ) ; }
+
+template <typename IndexType>
+inline IndexType colamd_r(IndexType n_row)
+{ return IndexType(((n_row) + 1) * sizeof (RowStructure<IndexType>) / sizeof (IndexType)); }
+
+// Prototypes of non-user callable routines
+template <typename IndexType>
+static IndexType init_rows_cols (IndexType n_row, IndexType n_col, RowStructure<IndexType> Row [], ColStructure<IndexType> col [], IndexType A [], IndexType p [], IndexType stats[NStats] );
+
+template <typename IndexType>
+static void init_scoring (IndexType n_row, IndexType n_col, RowStructure<IndexType> Row [], ColStructure<IndexType> Col [], IndexType A [], IndexType head [], double knobs[NKnobs], IndexType *p_n_row2, IndexType *p_n_col2, IndexType *p_max_deg);
+
+template <typename IndexType>
+static IndexType find_ordering (IndexType n_row, IndexType n_col, IndexType Alen, RowStructure<IndexType> Row [], ColStructure<IndexType> Col [], IndexType A [], IndexType head [], IndexType n_col2, IndexType max_deg, IndexType pfree);
+
+template <typename IndexType>
+static void order_children (IndexType n_col, ColStructure<IndexType> Col [], IndexType p []);
+
+template <typename IndexType>
+static void detect_super_cols (ColStructure<IndexType> Col [], IndexType A [], IndexType head [], IndexType row_start, IndexType row_length ) ;
+
+template <typename IndexType>
+static IndexType garbage_collection (IndexType n_row, IndexType n_col, RowStructure<IndexType> Row [], ColStructure<IndexType> Col [], IndexType A [], IndexType *pfree) ;
+
+template <typename IndexType>
+static inline IndexType clear_mark (IndexType n_row, RowStructure<IndexType> Row [] ) ;
+
+/* === No debugging ========================================================= */
+
+#define COLAMD_DEBUG0(params) ;
+#define COLAMD_DEBUG1(params) ;
+#define COLAMD_DEBUG2(params) ;
+#define COLAMD_DEBUG3(params) ;
+#define COLAMD_DEBUG4(params) ;
+
+#define COLAMD_ASSERT(expression) ((void) 0)
+
+
+/**
+ * \brief Returns the recommended value of Alen
+ *
+ * Returns recommended value of Alen for use by colamd.
+ * Returns -1 if any input argument is negative.
+ * The use of this routine or macro is optional.
+ * Note that the macro uses its arguments more than once,
+ * so be careful for side effects, if you pass expressions as arguments to COLAMD_RECOMMENDED.
+ *
+ * \param nnz nonzeros in A
+ * \param n_row number of rows in A
+ * \param n_col number of columns in A
+ * \return recommended value of Alen for use by colamd
+ */
+template <typename IndexType>
+inline IndexType recommended ( IndexType nnz, IndexType n_row, IndexType n_col)
+{
+ if ((nnz) < 0 || (n_row) < 0 || (n_col) < 0)
+ return (-1);
+ else
+ return (2 * (nnz) + colamd_c (n_col) + colamd_r (n_row) + (n_col) + ((nnz) / 5));
+}
+
+/**
+ * \brief set default parameters The use of this routine is optional.
+ *
+ * Colamd: rows with more than (knobs [DenseRow] * n_col)
+ * entries are removed prior to ordering. Columns with more than
+ * (knobs [DenseCol] * n_row) entries are removed prior to
+ * ordering, and placed last in the output column ordering.
+ *
+ * DenseRow and DenseCol are defined as 0 and 1,
+ * respectively, in colamd.h. Default values of these two knobs
+ * are both 0.5. Currently, only knobs [0] and knobs [1] are
+ * used, but future versions may use more knobs. If so, they will
+ * be properly set to their defaults by the future version of
+ * colamd_set_defaults, so that the code that calls colamd will
+ * not need to change, assuming that you either use
+ * colamd_set_defaults, or pass a (double *) NULL pointer as the
+ * knobs array to colamd or symamd.
+ *
+ * \param knobs parameter settings for colamd
+ */
+
+static inline void set_defaults(double knobs[NKnobs])
+{
+ /* === Local variables ================================================== */
+
+ int i ;
+
+ if (!knobs)
+ {
+ return ; /* no knobs to initialize */
+ }
+ for (i = 0 ; i < NKnobs ; i++)
+ {
+ knobs [i] = 0 ;
+ }
+ knobs [Colamd::DenseRow] = 0.5 ; /* ignore rows over 50% dense */
+ knobs [Colamd::DenseCol] = 0.5 ; /* ignore columns over 50% dense */
+}
+
+/**
+ * \brief Computes a column ordering using the column approximate minimum degree ordering
+ *
+ * Computes a column ordering (Q) of A such that P(AQ)=LU or
+ * (AQ)'AQ=LL' have less fill-in and require fewer floating point
+ * operations than factorizing the unpermuted matrix A or A'A,
+ * respectively.
+ *
+ *
+ * \param n_row number of rows in A
+ * \param n_col number of columns in A
+ * \param Alen, size of the array A
+ * \param A row indices of the matrix, of size ALen
+ * \param p column pointers of A, of size n_col+1
+ * \param knobs parameter settings for colamd
+ * \param stats colamd output statistics and error codes
+ */
+template <typename IndexType>
+static bool compute_ordering(IndexType n_row, IndexType n_col, IndexType Alen, IndexType *A, IndexType *p, double knobs[NKnobs], IndexType stats[NStats])
+{
+ /* === Local variables ================================================== */
+
+ IndexType i ; /* loop index */
+ IndexType nnz ; /* nonzeros in A */
+ IndexType Row_size ; /* size of Row [], in integers */
+ IndexType Col_size ; /* size of Col [], in integers */
+ IndexType need ; /* minimum required length of A */
+ Colamd::RowStructure<IndexType> *Row ; /* pointer into A of Row [0..n_row] array */
+ Colamd::ColStructure<IndexType> *Col ; /* pointer into A of Col [0..n_col] array */
+ IndexType n_col2 ; /* number of non-dense, non-empty columns */
+ IndexType n_row2 ; /* number of non-dense, non-empty rows */
+ IndexType ngarbage ; /* number of garbage collections performed */
+ IndexType max_deg ; /* maximum row degree */
+ double default_knobs [NKnobs] ; /* default knobs array */
+
+
+ /* === Check the input arguments ======================================== */
+
+ if (!stats)
+ {
+ COLAMD_DEBUG0 (("colamd: stats not present\n")) ;
+ return (false) ;
+ }
+ for (i = 0 ; i < NStats ; i++)
+ {
+ stats [i] = 0 ;
+ }
+ stats [Colamd::Status] = Colamd::Ok ;
+ stats [Colamd::Info1] = -1 ;
+ stats [Colamd::Info2] = -1 ;
+
+ if (!A) /* A is not present */
+ {
+ stats [Colamd::Status] = Colamd::ErrorANotPresent ;
+ COLAMD_DEBUG0 (("colamd: A not present\n")) ;
+ return (false) ;
+ }
+
+ if (!p) /* p is not present */
+ {
+ stats [Colamd::Status] = Colamd::ErrorPNotPresent ;
+ COLAMD_DEBUG0 (("colamd: p not present\n")) ;
+ return (false) ;
+ }
+
+ if (n_row < 0) /* n_row must be >= 0 */
+ {
+ stats [Colamd::Status] = Colamd::ErrorNrowNegative ;
+ stats [Colamd::Info1] = n_row ;
+ COLAMD_DEBUG0 (("colamd: nrow negative %d\n", n_row)) ;
+ return (false) ;
+ }
+
+ if (n_col < 0) /* n_col must be >= 0 */
+ {
+ stats [Colamd::Status] = Colamd::ErrorNcolNegative ;
+ stats [Colamd::Info1] = n_col ;
+ COLAMD_DEBUG0 (("colamd: ncol negative %d\n", n_col)) ;
+ return (false) ;
+ }
+
+ nnz = p [n_col] ;
+ if (nnz < 0) /* nnz must be >= 0 */
+ {
+ stats [Colamd::Status] = Colamd::ErrorNnzNegative ;
+ stats [Colamd::Info1] = nnz ;
+ COLAMD_DEBUG0 (("colamd: number of entries negative %d\n", nnz)) ;
+ return (false) ;
+ }
+
+ if (p [0] != 0)
+ {
+ stats [Colamd::Status] = Colamd::ErrorP0Nonzero ;
+ stats [Colamd::Info1] = p [0] ;
+ COLAMD_DEBUG0 (("colamd: p[0] not zero %d\n", p [0])) ;
+ return (false) ;
+ }
+
+ /* === If no knobs, set default knobs =================================== */
+
+ if (!knobs)
+ {
+ set_defaults (default_knobs) ;
+ knobs = default_knobs ;
+ }
+
+ /* === Allocate the Row and Col arrays from array A ===================== */
+
+ Col_size = colamd_c (n_col) ;
+ Row_size = colamd_r (n_row) ;
+ need = 2*nnz + n_col + Col_size + Row_size ;
+
+ if (need > Alen)
+ {
+ /* not enough space in array A to perform the ordering */
+ stats [Colamd::Status] = Colamd::ErrorATooSmall ;
+ stats [Colamd::Info1] = need ;
+ stats [Colamd::Info2] = Alen ;
+ COLAMD_DEBUG0 (("colamd: Need Alen >= %d, given only Alen = %d\n", need,Alen));
+ return (false) ;
+ }
+
+ Alen -= Col_size + Row_size ;
+ Col = (ColStructure<IndexType> *) &A [Alen] ;
+ Row = (RowStructure<IndexType> *) &A [Alen + Col_size] ;
+
+ /* === Construct the row and column data structures ===================== */
+
+ if (!Colamd::init_rows_cols (n_row, n_col, Row, Col, A, p, stats))
+ {
+ /* input matrix is invalid */
+ COLAMD_DEBUG0 (("colamd: Matrix invalid\n")) ;
+ return (false) ;
+ }
+
+ /* === Initialize scores, kill dense rows/columns ======================= */
+
+ Colamd::init_scoring (n_row, n_col, Row, Col, A, p, knobs,
+ &n_row2, &n_col2, &max_deg) ;
+
+ /* === Order the supercolumns =========================================== */
+
+ ngarbage = Colamd::find_ordering (n_row, n_col, Alen, Row, Col, A, p,
+ n_col2, max_deg, 2*nnz) ;
+
+ /* === Order the non-principal columns ================================== */
+
+ Colamd::order_children (n_col, Col, p) ;
+
+ /* === Return statistics in stats ======================================= */
+
+ stats [Colamd::DenseRow] = n_row - n_row2 ;
+ stats [Colamd::DenseCol] = n_col - n_col2 ;
+ stats [Colamd::DefragCount] = ngarbage ;
+ COLAMD_DEBUG0 (("colamd: done.\n")) ;
+ return (true) ;
+}
+
+/* ========================================================================== */
+/* === NON-USER-CALLABLE ROUTINES: ========================================== */
+/* ========================================================================== */
+
+/* There are no user-callable routines beyond this point in the file */
+
+/* ========================================================================== */
+/* === init_rows_cols ======================================================= */
+/* ========================================================================== */
+
+/*
+ Takes the column form of the matrix in A and creates the row form of the
+ matrix. Also, row and column attributes are stored in the Col and Row
+ structs. If the columns are un-sorted or contain duplicate row indices,
+ this routine will also sort and remove duplicate row indices from the
+ column form of the matrix. Returns false if the matrix is invalid,
+ true otherwise. Not user-callable.
+*/
+template <typename IndexType>
+static IndexType init_rows_cols /* returns true if OK, or false otherwise */
+ (
+ /* === Parameters ======================================================= */
+
+ IndexType n_row, /* number of rows of A */
+ IndexType n_col, /* number of columns of A */
+ RowStructure<IndexType> Row [], /* of size n_row+1 */
+ ColStructure<IndexType> Col [], /* of size n_col+1 */
+ IndexType A [], /* row indices of A, of size Alen */
+ IndexType p [], /* pointers to columns in A, of size n_col+1 */
+ IndexType stats [NStats] /* colamd statistics */
+ )
+{
+ /* === Local variables ================================================== */
+
+ IndexType col ; /* a column index */
+ IndexType row ; /* a row index */
+ IndexType *cp ; /* a column pointer */
+ IndexType *cp_end ; /* a pointer to the end of a column */
+ IndexType *rp ; /* a row pointer */
+ IndexType *rp_end ; /* a pointer to the end of a row */
+ IndexType last_row ; /* previous row */
+
+ /* === Initialize columns, and check column pointers ==================== */
+
+ for (col = 0 ; col < n_col ; col++)
+ {
+ Col [col].start = p [col] ;
+ Col [col].length = p [col+1] - p [col] ;
+
+ if ((Col [col].length) < 0) // extra parentheses to work-around gcc bug 10200
+ {
+ /* column pointers must be non-decreasing */
+ stats [Colamd::Status] = Colamd::ErrorColLengthNegative ;
+ stats [Colamd::Info1] = col ;
+ stats [Colamd::Info2] = Col [col].length ;
+ COLAMD_DEBUG0 (("colamd: col %d length %d < 0\n", col, Col [col].length)) ;
+ return (false) ;
+ }
+
+ Col [col].shared1.thickness = 1 ;
+ Col [col].shared2.score = 0 ;
+ Col [col].shared3.prev = Empty ;
+ Col [col].shared4.degree_next = Empty ;
+ }
+
+ /* p [0..n_col] no longer needed, used as "head" in subsequent routines */
+
+ /* === Scan columns, compute row degrees, and check row indices ========= */
+
+ stats [Info3] = 0 ; /* number of duplicate or unsorted row indices*/
+
+ for (row = 0 ; row < n_row ; row++)
+ {
+ Row [row].length = 0 ;
+ Row [row].shared2.mark = -1 ;
+ }
+
+ for (col = 0 ; col < n_col ; col++)
+ {
+ last_row = -1 ;
+
+ cp = &A [p [col]] ;
+ cp_end = &A [p [col+1]] ;
+
+ while (cp < cp_end)
+ {
+ row = *cp++ ;
+
+ /* make sure row indices within range */
+ if (row < 0 || row >= n_row)
+ {
+ stats [Colamd::Status] = Colamd::ErrorRowIndexOutOfBounds ;
+ stats [Colamd::Info1] = col ;
+ stats [Colamd::Info2] = row ;
+ stats [Colamd::Info3] = n_row ;
+ COLAMD_DEBUG0 (("colamd: row %d col %d out of bounds\n", row, col)) ;
+ return (false) ;
+ }
+
+ if (row <= last_row || Row [row].shared2.mark == col)
+ {
+ /* row index are unsorted or repeated (or both), thus col */
+ /* is jumbled. This is a notice, not an error condition. */
+ stats [Colamd::Status] = Colamd::OkButJumbled ;
+ stats [Colamd::Info1] = col ;
+ stats [Colamd::Info2] = row ;
+ (stats [Colamd::Info3]) ++ ;
+ COLAMD_DEBUG1 (("colamd: row %d col %d unsorted/duplicate\n",row,col));
+ }
+
+ if (Row [row].shared2.mark != col)
+ {
+ Row [row].length++ ;
+ }
+ else
+ {
+ /* this is a repeated entry in the column, */
+ /* it will be removed */
+ Col [col].length-- ;
+ }
+
+ /* mark the row as having been seen in this column */
+ Row [row].shared2.mark = col ;
+
+ last_row = row ;
+ }
+ }
+
+ /* === Compute row pointers ============================================= */
+
+ /* row form of the matrix starts directly after the column */
+ /* form of matrix in A */
+ Row [0].start = p [n_col] ;
+ Row [0].shared1.p = Row [0].start ;
+ Row [0].shared2.mark = -1 ;
+ for (row = 1 ; row < n_row ; row++)
+ {
+ Row [row].start = Row [row-1].start + Row [row-1].length ;
+ Row [row].shared1.p = Row [row].start ;
+ Row [row].shared2.mark = -1 ;
+ }
+
+ /* === Create row form ================================================== */
+
+ if (stats [Status] == OkButJumbled)
+ {
+ /* if cols jumbled, watch for repeated row indices */
+ for (col = 0 ; col < n_col ; col++)
+ {
+ cp = &A [p [col]] ;
+ cp_end = &A [p [col+1]] ;
+ while (cp < cp_end)
+ {
+ row = *cp++ ;
+ if (Row [row].shared2.mark != col)
+ {
+ A [(Row [row].shared1.p)++] = col ;
+ Row [row].shared2.mark = col ;
+ }
+ }
+ }
+ }
+ else
+ {
+ /* if cols not jumbled, we don't need the mark (this is faster) */
+ for (col = 0 ; col < n_col ; col++)
+ {
+ cp = &A [p [col]] ;
+ cp_end = &A [p [col+1]] ;
+ while (cp < cp_end)
+ {
+ A [(Row [*cp++].shared1.p)++] = col ;
+ }
+ }
+ }
+
+ /* === Clear the row marks and set row degrees ========================== */
+
+ for (row = 0 ; row < n_row ; row++)
+ {
+ Row [row].shared2.mark = 0 ;
+ Row [row].shared1.degree = Row [row].length ;
+ }
+
+ /* === See if we need to re-create columns ============================== */
+
+ if (stats [Status] == OkButJumbled)
+ {
+ COLAMD_DEBUG0 (("colamd: reconstructing column form, matrix jumbled\n")) ;
+
+
+ /* === Compute col pointers ========================================= */
+
+ /* col form of the matrix starts at A [0]. */
+ /* Note, we may have a gap between the col form and the row */
+ /* form if there were duplicate entries, if so, it will be */
+ /* removed upon the first garbage collection */
+ Col [0].start = 0 ;
+ p [0] = Col [0].start ;
+ for (col = 1 ; col < n_col ; col++)
+ {
+ /* note that the lengths here are for pruned columns, i.e. */
+ /* no duplicate row indices will exist for these columns */
+ Col [col].start = Col [col-1].start + Col [col-1].length ;
+ p [col] = Col [col].start ;
+ }
+
+ /* === Re-create col form =========================================== */
+
+ for (row = 0 ; row < n_row ; row++)
+ {
+ rp = &A [Row [row].start] ;
+ rp_end = rp + Row [row].length ;
+ while (rp < rp_end)
+ {
+ A [(p [*rp++])++] = row ;
+ }
+ }
+ }
+
+ /* === Done. Matrix is not (or no longer) jumbled ====================== */
+
+ return (true) ;
+}
+
+
+/* ========================================================================== */
+/* === init_scoring ========================================================= */
+/* ========================================================================== */
+
+/*
+ Kills dense or empty columns and rows, calculates an initial score for
+ each column, and places all columns in the degree lists. Not user-callable.
+*/
+template <typename IndexType>
+static void init_scoring
+ (
+ /* === Parameters ======================================================= */
+
+ IndexType n_row, /* number of rows of A */
+ IndexType n_col, /* number of columns of A */
+ RowStructure<IndexType> Row [], /* of size n_row+1 */
+ ColStructure<IndexType> Col [], /* of size n_col+1 */
+ IndexType A [], /* column form and row form of A */
+ IndexType head [], /* of size n_col+1 */
+ double knobs [NKnobs],/* parameters */
+ IndexType *p_n_row2, /* number of non-dense, non-empty rows */
+ IndexType *p_n_col2, /* number of non-dense, non-empty columns */
+ IndexType *p_max_deg /* maximum row degree */
+ )
+{
+ /* === Local variables ================================================== */
+
+ IndexType c ; /* a column index */
+ IndexType r, row ; /* a row index */
+ IndexType *cp ; /* a column pointer */
+ IndexType deg ; /* degree of a row or column */
+ IndexType *cp_end ; /* a pointer to the end of a column */
+ IndexType *new_cp ; /* new column pointer */
+ IndexType col_length ; /* length of pruned column */
+ IndexType score ; /* current column score */
+ IndexType n_col2 ; /* number of non-dense, non-empty columns */
+ IndexType n_row2 ; /* number of non-dense, non-empty rows */
+ IndexType dense_row_count ; /* remove rows with more entries than this */
+ IndexType dense_col_count ; /* remove cols with more entries than this */
+ IndexType min_score ; /* smallest column score */
+ IndexType max_deg ; /* maximum row degree */
+ IndexType next_col ; /* Used to add to degree list.*/
+
+
+ /* === Extract knobs ==================================================== */
+
+ dense_row_count = numext::maxi(IndexType(0), numext::mini(IndexType(knobs [Colamd::DenseRow] * n_col), n_col)) ;
+ dense_col_count = numext::maxi(IndexType(0), numext::mini(IndexType(knobs [Colamd::DenseCol] * n_row), n_row)) ;
+ COLAMD_DEBUG1 (("colamd: densecount: %d %d\n", dense_row_count, dense_col_count)) ;
+ max_deg = 0 ;
+ n_col2 = n_col ;
+ n_row2 = n_row ;
+
+ /* === Kill empty columns =============================================== */
+
+ /* Put the empty columns at the end in their natural order, so that LU */
+ /* factorization can proceed as far as possible. */
+ for (c = n_col-1 ; c >= 0 ; c--)
+ {
+ deg = Col [c].length ;
+ if (deg == 0)
+ {
+ /* this is a empty column, kill and order it last */
+ Col [c].shared2.order = --n_col2 ;
+ Col[c].kill_principal() ;
+ }
+ }
+ COLAMD_DEBUG1 (("colamd: null columns killed: %d\n", n_col - n_col2)) ;
+
+ /* === Kill dense columns =============================================== */
+
+ /* Put the dense columns at the end, in their natural order */
+ for (c = n_col-1 ; c >= 0 ; c--)
+ {
+ /* skip any dead columns */
+ if (Col[c].is_dead())
+ {
+ continue ;
+ }
+ deg = Col [c].length ;
+ if (deg > dense_col_count)
+ {
+ /* this is a dense column, kill and order it last */
+ Col [c].shared2.order = --n_col2 ;
+ /* decrement the row degrees */
+ cp = &A [Col [c].start] ;
+ cp_end = cp + Col [c].length ;
+ while (cp < cp_end)
+ {
+ Row [*cp++].shared1.degree-- ;
+ }
+ Col[c].kill_principal() ;
+ }
+ }
+ COLAMD_DEBUG1 (("colamd: Dense and null columns killed: %d\n", n_col - n_col2)) ;
+
+ /* === Kill dense and empty rows ======================================== */
+
+ for (r = 0 ; r < n_row ; r++)
+ {
+ deg = Row [r].shared1.degree ;
+ COLAMD_ASSERT (deg >= 0 && deg <= n_col) ;
+ if (deg > dense_row_count || deg == 0)
+ {
+ /* kill a dense or empty row */
+ Row[r].kill() ;
+ --n_row2 ;
+ }
+ else
+ {
+ /* keep track of max degree of remaining rows */
+ max_deg = numext::maxi(max_deg, deg) ;
+ }
+ }
+ COLAMD_DEBUG1 (("colamd: Dense and null rows killed: %d\n", n_row - n_row2)) ;
+
+ /* === Compute initial column scores ==================================== */
+
+ /* At this point the row degrees are accurate. They reflect the number */
+ /* of "live" (non-dense) columns in each row. No empty rows exist. */
+ /* Some "live" columns may contain only dead rows, however. These are */
+ /* pruned in the code below. */
+
+ /* now find the initial matlab score for each column */
+ for (c = n_col-1 ; c >= 0 ; c--)
+ {
+ /* skip dead column */
+ if (Col[c].is_dead())
+ {
+ continue ;
+ }
+ score = 0 ;
+ cp = &A [Col [c].start] ;
+ new_cp = cp ;
+ cp_end = cp + Col [c].length ;
+ while (cp < cp_end)
+ {
+ /* get a row */
+ row = *cp++ ;
+ /* skip if dead */
+ if (Row[row].is_dead())
+ {
+ continue ;
+ }
+ /* compact the column */
+ *new_cp++ = row ;
+ /* add row's external degree */
+ score += Row [row].shared1.degree - 1 ;
+ /* guard against integer overflow */
+ score = numext::mini(score, n_col) ;
+ }
+ /* determine pruned column length */
+ col_length = (IndexType) (new_cp - &A [Col [c].start]) ;
+ if (col_length == 0)
+ {
+ /* a newly-made null column (all rows in this col are "dense" */
+ /* and have already been killed) */
+ COLAMD_DEBUG2 (("Newly null killed: %d\n", c)) ;
+ Col [c].shared2.order = --n_col2 ;
+ Col[c].kill_principal() ;
+ }
+ else
+ {
+ /* set column length and set score */
+ COLAMD_ASSERT (score >= 0) ;
+ COLAMD_ASSERT (score <= n_col) ;
+ Col [c].length = col_length ;
+ Col [c].shared2.score = score ;
+ }
+ }
+ COLAMD_DEBUG1 (("colamd: Dense, null, and newly-null columns killed: %d\n",
+ n_col-n_col2)) ;
+
+ /* At this point, all empty rows and columns are dead. All live columns */
+ /* are "clean" (containing no dead rows) and simplicial (no supercolumns */
+ /* yet). Rows may contain dead columns, but all live rows contain at */
+ /* least one live column. */
+
+ /* === Initialize degree lists ========================================== */
+
+
+ /* clear the hash buckets */
+ for (c = 0 ; c <= n_col ; c++)
+ {
+ head [c] = Empty ;
+ }
+ min_score = n_col ;
+ /* place in reverse order, so low column indices are at the front */
+ /* of the lists. This is to encourage natural tie-breaking */
+ for (c = n_col-1 ; c >= 0 ; c--)
+ {
+ /* only add principal columns to degree lists */
+ if (Col[c].is_alive())
+ {
+ COLAMD_DEBUG4 (("place %d score %d minscore %d ncol %d\n",
+ c, Col [c].shared2.score, min_score, n_col)) ;
+
+ /* === Add columns score to DList =============================== */
+
+ score = Col [c].shared2.score ;
+
+ COLAMD_ASSERT (min_score >= 0) ;
+ COLAMD_ASSERT (min_score <= n_col) ;
+ COLAMD_ASSERT (score >= 0) ;
+ COLAMD_ASSERT (score <= n_col) ;
+ COLAMD_ASSERT (head [score] >= Empty) ;
+
+ /* now add this column to dList at proper score location */
+ next_col = head [score] ;
+ Col [c].shared3.prev = Empty ;
+ Col [c].shared4.degree_next = next_col ;
+
+ /* if there already was a column with the same score, set its */
+ /* previous pointer to this new column */
+ if (next_col != Empty)
+ {
+ Col [next_col].shared3.prev = c ;
+ }
+ head [score] = c ;
+
+ /* see if this score is less than current min */
+ min_score = numext::mini(min_score, score) ;
+
+
+ }
+ }
+
+
+ /* === Return number of remaining columns, and max row degree =========== */
+
+ *p_n_col2 = n_col2 ;
+ *p_n_row2 = n_row2 ;
+ *p_max_deg = max_deg ;
+}
+
+
+/* ========================================================================== */
+/* === find_ordering ======================================================== */
+/* ========================================================================== */
+
+/*
+ Order the principal columns of the supercolumn form of the matrix
+ (no supercolumns on input). Uses a minimum approximate column minimum
+ degree ordering method. Not user-callable.
+*/
+template <typename IndexType>
+static IndexType find_ordering /* return the number of garbage collections */
+ (
+ /* === Parameters ======================================================= */
+
+ IndexType n_row, /* number of rows of A */
+ IndexType n_col, /* number of columns of A */
+ IndexType Alen, /* size of A, 2*nnz + n_col or larger */
+ RowStructure<IndexType> Row [], /* of size n_row+1 */
+ ColStructure<IndexType> Col [], /* of size n_col+1 */
+ IndexType A [], /* column form and row form of A */
+ IndexType head [], /* of size n_col+1 */
+ IndexType n_col2, /* Remaining columns to order */
+ IndexType max_deg, /* Maximum row degree */
+ IndexType pfree /* index of first free slot (2*nnz on entry) */
+ )
+{
+ /* === Local variables ================================================== */
+
+ IndexType k ; /* current pivot ordering step */
+ IndexType pivot_col ; /* current pivot column */
+ IndexType *cp ; /* a column pointer */
+ IndexType *rp ; /* a row pointer */
+ IndexType pivot_row ; /* current pivot row */
+ IndexType *new_cp ; /* modified column pointer */
+ IndexType *new_rp ; /* modified row pointer */
+ IndexType pivot_row_start ; /* pointer to start of pivot row */
+ IndexType pivot_row_degree ; /* number of columns in pivot row */
+ IndexType pivot_row_length ; /* number of supercolumns in pivot row */
+ IndexType pivot_col_score ; /* score of pivot column */
+ IndexType needed_memory ; /* free space needed for pivot row */
+ IndexType *cp_end ; /* pointer to the end of a column */
+ IndexType *rp_end ; /* pointer to the end of a row */
+ IndexType row ; /* a row index */
+ IndexType col ; /* a column index */
+ IndexType max_score ; /* maximum possible score */
+ IndexType cur_score ; /* score of current column */
+ unsigned int hash ; /* hash value for supernode detection */
+ IndexType head_column ; /* head of hash bucket */
+ IndexType first_col ; /* first column in hash bucket */
+ IndexType tag_mark ; /* marker value for mark array */
+ IndexType row_mark ; /* Row [row].shared2.mark */
+ IndexType set_difference ; /* set difference size of row with pivot row */
+ IndexType min_score ; /* smallest column score */
+ IndexType col_thickness ; /* "thickness" (no. of columns in a supercol) */
+ IndexType max_mark ; /* maximum value of tag_mark */
+ IndexType pivot_col_thickness ; /* number of columns represented by pivot col */
+ IndexType prev_col ; /* Used by Dlist operations. */
+ IndexType next_col ; /* Used by Dlist operations. */
+ IndexType ngarbage ; /* number of garbage collections performed */
+
+
+ /* === Initialization and clear mark ==================================== */
+
+ max_mark = INT_MAX - n_col ; /* INT_MAX defined in <limits.h> */
+ tag_mark = Colamd::clear_mark (n_row, Row) ;
+ min_score = 0 ;
+ ngarbage = 0 ;
+ COLAMD_DEBUG1 (("colamd: Ordering, n_col2=%d\n", n_col2)) ;
+
+ /* === Order the columns ================================================ */
+
+ for (k = 0 ; k < n_col2 ; /* 'k' is incremented below */)
+ {
+
+ /* === Select pivot column, and order it ============================ */
+
+ /* make sure degree list isn't empty */
+ COLAMD_ASSERT (min_score >= 0) ;
+ COLAMD_ASSERT (min_score <= n_col) ;
+ COLAMD_ASSERT (head [min_score] >= Empty) ;
+
+ /* get pivot column from head of minimum degree list */
+ while (min_score < n_col && head [min_score] == Empty)
+ {
+ min_score++ ;
+ }
+ pivot_col = head [min_score] ;
+ COLAMD_ASSERT (pivot_col >= 0 && pivot_col <= n_col) ;
+ next_col = Col [pivot_col].shared4.degree_next ;
+ head [min_score] = next_col ;
+ if (next_col != Empty)
+ {
+ Col [next_col].shared3.prev = Empty ;
+ }
+
+ COLAMD_ASSERT (Col[pivot_col].is_alive()) ;
+ COLAMD_DEBUG3 (("Pivot col: %d\n", pivot_col)) ;
+
+ /* remember score for defrag check */
+ pivot_col_score = Col [pivot_col].shared2.score ;
+
+ /* the pivot column is the kth column in the pivot order */
+ Col [pivot_col].shared2.order = k ;
+
+ /* increment order count by column thickness */
+ pivot_col_thickness = Col [pivot_col].shared1.thickness ;
+ k += pivot_col_thickness ;
+ COLAMD_ASSERT (pivot_col_thickness > 0) ;
+
+ /* === Garbage_collection, if necessary ============================= */
+
+ needed_memory = numext::mini(pivot_col_score, n_col - k) ;
+ if (pfree + needed_memory >= Alen)
+ {
+ pfree = Colamd::garbage_collection (n_row, n_col, Row, Col, A, &A [pfree]) ;
+ ngarbage++ ;
+ /* after garbage collection we will have enough */
+ COLAMD_ASSERT (pfree + needed_memory < Alen) ;
+ /* garbage collection has wiped out the Row[].shared2.mark array */
+ tag_mark = Colamd::clear_mark (n_row, Row) ;
+
+ }
+
+ /* === Compute pivot row pattern ==================================== */
+
+ /* get starting location for this new merged row */
+ pivot_row_start = pfree ;
+
+ /* initialize new row counts to zero */
+ pivot_row_degree = 0 ;
+
+ /* tag pivot column as having been visited so it isn't included */
+ /* in merged pivot row */
+ Col [pivot_col].shared1.thickness = -pivot_col_thickness ;
+
+ /* pivot row is the union of all rows in the pivot column pattern */
+ cp = &A [Col [pivot_col].start] ;
+ cp_end = cp + Col [pivot_col].length ;
+ while (cp < cp_end)
+ {
+ /* get a row */
+ row = *cp++ ;
+ COLAMD_DEBUG4 (("Pivot col pattern %d %d\n", Row[row].is_alive(), row)) ;
+ /* skip if row is dead */
+ if (Row[row].is_dead())
+ {
+ continue ;
+ }
+ rp = &A [Row [row].start] ;
+ rp_end = rp + Row [row].length ;
+ while (rp < rp_end)
+ {
+ /* get a column */
+ col = *rp++ ;
+ /* add the column, if alive and untagged */
+ col_thickness = Col [col].shared1.thickness ;
+ if (col_thickness > 0 && Col[col].is_alive())
+ {
+ /* tag column in pivot row */
+ Col [col].shared1.thickness = -col_thickness ;
+ COLAMD_ASSERT (pfree < Alen) ;
+ /* place column in pivot row */
+ A [pfree++] = col ;
+ pivot_row_degree += col_thickness ;
+ }
+ }
+ }
+
+ /* clear tag on pivot column */
+ Col [pivot_col].shared1.thickness = pivot_col_thickness ;
+ max_deg = numext::maxi(max_deg, pivot_row_degree) ;
+
+
+ /* === Kill all rows used to construct pivot row ==================== */
+
+ /* also kill pivot row, temporarily */
+ cp = &A [Col [pivot_col].start] ;
+ cp_end = cp + Col [pivot_col].length ;
+ while (cp < cp_end)
+ {
+ /* may be killing an already dead row */
+ row = *cp++ ;
+ COLAMD_DEBUG3 (("Kill row in pivot col: %d\n", row)) ;
+ Row[row].kill() ;
+ }
+
+ /* === Select a row index to use as the new pivot row =============== */
+
+ pivot_row_length = pfree - pivot_row_start ;
+ if (pivot_row_length > 0)
+ {
+ /* pick the "pivot" row arbitrarily (first row in col) */
+ pivot_row = A [Col [pivot_col].start] ;
+ COLAMD_DEBUG3 (("Pivotal row is %d\n", pivot_row)) ;
+ }
+ else
+ {
+ /* there is no pivot row, since it is of zero length */
+ pivot_row = Empty ;
+ COLAMD_ASSERT (pivot_row_length == 0) ;
+ }
+ COLAMD_ASSERT (Col [pivot_col].length > 0 || pivot_row_length == 0) ;
+
+ /* === Approximate degree computation =============================== */
+
+ /* Here begins the computation of the approximate degree. The column */
+ /* score is the sum of the pivot row "length", plus the size of the */
+ /* set differences of each row in the column minus the pattern of the */
+ /* pivot row itself. The column ("thickness") itself is also */
+ /* excluded from the column score (we thus use an approximate */
+ /* external degree). */
+
+ /* The time taken by the following code (compute set differences, and */
+ /* add them up) is proportional to the size of the data structure */
+ /* being scanned - that is, the sum of the sizes of each column in */
+ /* the pivot row. Thus, the amortized time to compute a column score */
+ /* is proportional to the size of that column (where size, in this */
+ /* context, is the column "length", or the number of row indices */
+ /* in that column). The number of row indices in a column is */
+ /* monotonically non-decreasing, from the length of the original */
+ /* column on input to colamd. */
+
+ /* === Compute set differences ====================================== */
+
+ COLAMD_DEBUG3 (("** Computing set differences phase. **\n")) ;
+
+ /* pivot row is currently dead - it will be revived later. */
+
+ COLAMD_DEBUG3 (("Pivot row: ")) ;
+ /* for each column in pivot row */
+ rp = &A [pivot_row_start] ;
+ rp_end = rp + pivot_row_length ;
+ while (rp < rp_end)
+ {
+ col = *rp++ ;
+ COLAMD_ASSERT (Col[col].is_alive() && col != pivot_col) ;
+ COLAMD_DEBUG3 (("Col: %d\n", col)) ;
+
+ /* clear tags used to construct pivot row pattern */
+ col_thickness = -Col [col].shared1.thickness ;
+ COLAMD_ASSERT (col_thickness > 0) ;
+ Col [col].shared1.thickness = col_thickness ;
+
+ /* === Remove column from degree list =========================== */
+
+ cur_score = Col [col].shared2.score ;
+ prev_col = Col [col].shared3.prev ;
+ next_col = Col [col].shared4.degree_next ;
+ COLAMD_ASSERT (cur_score >= 0) ;
+ COLAMD_ASSERT (cur_score <= n_col) ;
+ COLAMD_ASSERT (cur_score >= Empty) ;
+ if (prev_col == Empty)
+ {
+ head [cur_score] = next_col ;
+ }
+ else
+ {
+ Col [prev_col].shared4.degree_next = next_col ;
+ }
+ if (next_col != Empty)
+ {
+ Col [next_col].shared3.prev = prev_col ;
+ }
+
+ /* === Scan the column ========================================== */
+
+ cp = &A [Col [col].start] ;
+ cp_end = cp + Col [col].length ;
+ while (cp < cp_end)
+ {
+ /* get a row */
+ row = *cp++ ;
+ /* skip if dead */
+ if (Row[row].is_dead())
+ {
+ continue ;
+ }
+ row_mark = Row [row].shared2.mark ;
+ COLAMD_ASSERT (row != pivot_row) ;
+ set_difference = row_mark - tag_mark ;
+ /* check if the row has been seen yet */
+ if (set_difference < 0)
+ {
+ COLAMD_ASSERT (Row [row].shared1.degree <= max_deg) ;
+ set_difference = Row [row].shared1.degree ;
+ }
+ /* subtract column thickness from this row's set difference */
+ set_difference -= col_thickness ;
+ COLAMD_ASSERT (set_difference >= 0) ;
+ /* absorb this row if the set difference becomes zero */
+ if (set_difference == 0)
+ {
+ COLAMD_DEBUG3 (("aggressive absorption. Row: %d\n", row)) ;
+ Row[row].kill() ;
+ }
+ else
+ {
+ /* save the new mark */
+ Row [row].shared2.mark = set_difference + tag_mark ;
+ }
+ }
+ }
+
+
+ /* === Add up set differences for each column ======================= */
+
+ COLAMD_DEBUG3 (("** Adding set differences phase. **\n")) ;
+
+ /* for each column in pivot row */
+ rp = &A [pivot_row_start] ;
+ rp_end = rp + pivot_row_length ;
+ while (rp < rp_end)
+ {
+ /* get a column */
+ col = *rp++ ;
+ COLAMD_ASSERT (Col[col].is_alive() && col != pivot_col) ;
+ hash = 0 ;
+ cur_score = 0 ;
+ cp = &A [Col [col].start] ;
+ /* compact the column */
+ new_cp = cp ;
+ cp_end = cp + Col [col].length ;
+
+ COLAMD_DEBUG4 (("Adding set diffs for Col: %d.\n", col)) ;
+
+ while (cp < cp_end)
+ {
+ /* get a row */
+ row = *cp++ ;
+ COLAMD_ASSERT(row >= 0 && row < n_row) ;
+ /* skip if dead */
+ if (Row [row].is_dead())
+ {
+ continue ;
+ }
+ row_mark = Row [row].shared2.mark ;
+ COLAMD_ASSERT (row_mark > tag_mark) ;
+ /* compact the column */
+ *new_cp++ = row ;
+ /* compute hash function */
+ hash += row ;
+ /* add set difference */
+ cur_score += row_mark - tag_mark ;
+ /* integer overflow... */
+ cur_score = numext::mini(cur_score, n_col) ;
+ }
+
+ /* recompute the column's length */
+ Col [col].length = (IndexType) (new_cp - &A [Col [col].start]) ;
+
+ /* === Further mass elimination ================================= */
+
+ if (Col [col].length == 0)
+ {
+ COLAMD_DEBUG4 (("further mass elimination. Col: %d\n", col)) ;
+ /* nothing left but the pivot row in this column */
+ Col[col].kill_principal() ;
+ pivot_row_degree -= Col [col].shared1.thickness ;
+ COLAMD_ASSERT (pivot_row_degree >= 0) ;
+ /* order it */
+ Col [col].shared2.order = k ;
+ /* increment order count by column thickness */
+ k += Col [col].shared1.thickness ;
+ }
+ else
+ {
+ /* === Prepare for supercolumn detection ==================== */
+
+ COLAMD_DEBUG4 (("Preparing supercol detection for Col: %d.\n", col)) ;
+
+ /* save score so far */
+ Col [col].shared2.score = cur_score ;
+
+ /* add column to hash table, for supercolumn detection */
+ hash %= n_col + 1 ;
+
+ COLAMD_DEBUG4 ((" Hash = %d, n_col = %d.\n", hash, n_col)) ;
+ COLAMD_ASSERT (hash <= n_col) ;
+
+ head_column = head [hash] ;
+ if (head_column > Empty)
+ {
+ /* degree list "hash" is non-empty, use prev (shared3) of */
+ /* first column in degree list as head of hash bucket */
+ first_col = Col [head_column].shared3.headhash ;
+ Col [head_column].shared3.headhash = col ;
+ }
+ else
+ {
+ /* degree list "hash" is empty, use head as hash bucket */
+ first_col = - (head_column + 2) ;
+ head [hash] = - (col + 2) ;
+ }
+ Col [col].shared4.hash_next = first_col ;
+
+ /* save hash function in Col [col].shared3.hash */
+ Col [col].shared3.hash = (IndexType) hash ;
+ COLAMD_ASSERT (Col[col].is_alive()) ;
+ }
+ }
+
+ /* The approximate external column degree is now computed. */
+
+ /* === Supercolumn detection ======================================== */
+
+ COLAMD_DEBUG3 (("** Supercolumn detection phase. **\n")) ;
+
+ Colamd::detect_super_cols (Col, A, head, pivot_row_start, pivot_row_length) ;
+
+ /* === Kill the pivotal column ====================================== */
+
+ Col[pivot_col].kill_principal() ;
+
+ /* === Clear mark =================================================== */
+
+ tag_mark += (max_deg + 1) ;
+ if (tag_mark >= max_mark)
+ {
+ COLAMD_DEBUG2 (("clearing tag_mark\n")) ;
+ tag_mark = Colamd::clear_mark (n_row, Row) ;
+ }
+
+ /* === Finalize the new pivot row, and column scores ================ */
+
+ COLAMD_DEBUG3 (("** Finalize scores phase. **\n")) ;
+
+ /* for each column in pivot row */
+ rp = &A [pivot_row_start] ;
+ /* compact the pivot row */
+ new_rp = rp ;
+ rp_end = rp + pivot_row_length ;
+ while (rp < rp_end)
+ {
+ col = *rp++ ;
+ /* skip dead columns */
+ if (Col[col].is_dead())
+ {
+ continue ;
+ }
+ *new_rp++ = col ;
+ /* add new pivot row to column */
+ A [Col [col].start + (Col [col].length++)] = pivot_row ;
+
+ /* retrieve score so far and add on pivot row's degree. */
+ /* (we wait until here for this in case the pivot */
+ /* row's degree was reduced due to mass elimination). */
+ cur_score = Col [col].shared2.score + pivot_row_degree ;
+
+ /* calculate the max possible score as the number of */
+ /* external columns minus the 'k' value minus the */
+ /* columns thickness */
+ max_score = n_col - k - Col [col].shared1.thickness ;
+
+ /* make the score the external degree of the union-of-rows */
+ cur_score -= Col [col].shared1.thickness ;
+
+ /* make sure score is less or equal than the max score */
+ cur_score = numext::mini(cur_score, max_score) ;
+ COLAMD_ASSERT (cur_score >= 0) ;
+
+ /* store updated score */
+ Col [col].shared2.score = cur_score ;
+
+ /* === Place column back in degree list ========================= */
+
+ COLAMD_ASSERT (min_score >= 0) ;
+ COLAMD_ASSERT (min_score <= n_col) ;
+ COLAMD_ASSERT (cur_score >= 0) ;
+ COLAMD_ASSERT (cur_score <= n_col) ;
+ COLAMD_ASSERT (head [cur_score] >= Empty) ;
+ next_col = head [cur_score] ;
+ Col [col].shared4.degree_next = next_col ;
+ Col [col].shared3.prev = Empty ;
+ if (next_col != Empty)
+ {
+ Col [next_col].shared3.prev = col ;
+ }
+ head [cur_score] = col ;
+
+ /* see if this score is less than current min */
+ min_score = numext::mini(min_score, cur_score) ;
+
+ }
+
+ /* === Resurrect the new pivot row ================================== */
+
+ if (pivot_row_degree > 0)
+ {
+ /* update pivot row length to reflect any cols that were killed */
+ /* during super-col detection and mass elimination */
+ Row [pivot_row].start = pivot_row_start ;
+ Row [pivot_row].length = (IndexType) (new_rp - &A[pivot_row_start]) ;
+ Row [pivot_row].shared1.degree = pivot_row_degree ;
+ Row [pivot_row].shared2.mark = 0 ;
+ /* pivot row is no longer dead */
+ }
+ }
+
+ /* === All principal columns have now been ordered ====================== */
+
+ return (ngarbage) ;
+}
+
+
+/* ========================================================================== */
+/* === order_children ======================================================= */
+/* ========================================================================== */
+
+/*
+ The find_ordering routine has ordered all of the principal columns (the
+ representatives of the supercolumns). The non-principal columns have not
+ yet been ordered. This routine orders those columns by walking up the
+ parent tree (a column is a child of the column which absorbed it). The
+ final permutation vector is then placed in p [0 ... n_col-1], with p [0]
+ being the first column, and p [n_col-1] being the last. It doesn't look
+ like it at first glance, but be assured that this routine takes time linear
+ in the number of columns. Although not immediately obvious, the time
+ taken by this routine is O (n_col), that is, linear in the number of
+ columns. Not user-callable.
+*/
+template <typename IndexType>
+static inline void order_children
+(
+ /* === Parameters ======================================================= */
+
+ IndexType n_col, /* number of columns of A */
+ ColStructure<IndexType> Col [], /* of size n_col+1 */
+ IndexType p [] /* p [0 ... n_col-1] is the column permutation*/
+ )
+{
+ /* === Local variables ================================================== */
+
+ IndexType i ; /* loop counter for all columns */
+ IndexType c ; /* column index */
+ IndexType parent ; /* index of column's parent */
+ IndexType order ; /* column's order */
+
+ /* === Order each non-principal column ================================== */
+
+ for (i = 0 ; i < n_col ; i++)
+ {
+ /* find an un-ordered non-principal column */
+ COLAMD_ASSERT (col_is_dead(Col, i)) ;
+ if (!Col[i].is_dead_principal() && Col [i].shared2.order == Empty)
+ {
+ parent = i ;
+ /* once found, find its principal parent */
+ do
+ {
+ parent = Col [parent].shared1.parent ;
+ } while (!Col[parent].is_dead_principal()) ;
+
+ /* now, order all un-ordered non-principal columns along path */
+ /* to this parent. collapse tree at the same time */
+ c = i ;
+ /* get order of parent */
+ order = Col [parent].shared2.order ;
+
+ do
+ {
+ COLAMD_ASSERT (Col [c].shared2.order == Empty) ;
+
+ /* order this column */
+ Col [c].shared2.order = order++ ;
+ /* collaps tree */
+ Col [c].shared1.parent = parent ;
+
+ /* get immediate parent of this column */
+ c = Col [c].shared1.parent ;
+
+ /* continue until we hit an ordered column. There are */
+ /* guaranteed not to be anymore unordered columns */
+ /* above an ordered column */
+ } while (Col [c].shared2.order == Empty) ;
+
+ /* re-order the super_col parent to largest order for this group */
+ Col [parent].shared2.order = order ;
+ }
+ }
+
+ /* === Generate the permutation ========================================= */
+
+ for (c = 0 ; c < n_col ; c++)
+ {
+ p [Col [c].shared2.order] = c ;
+ }
+}
+
+
+/* ========================================================================== */
+/* === detect_super_cols ==================================================== */
+/* ========================================================================== */
+
+/*
+ Detects supercolumns by finding matches between columns in the hash buckets.
+ Check amongst columns in the set A [row_start ... row_start + row_length-1].
+ The columns under consideration are currently *not* in the degree lists,
+ and have already been placed in the hash buckets.
+
+ The hash bucket for columns whose hash function is equal to h is stored
+ as follows:
+
+ if head [h] is >= 0, then head [h] contains a degree list, so:
+
+ head [h] is the first column in degree bucket h.
+ Col [head [h]].headhash gives the first column in hash bucket h.
+
+ otherwise, the degree list is empty, and:
+
+ -(head [h] + 2) is the first column in hash bucket h.
+
+ For a column c in a hash bucket, Col [c].shared3.prev is NOT a "previous
+ column" pointer. Col [c].shared3.hash is used instead as the hash number
+ for that column. The value of Col [c].shared4.hash_next is the next column
+ in the same hash bucket.
+
+ Assuming no, or "few" hash collisions, the time taken by this routine is
+ linear in the sum of the sizes (lengths) of each column whose score has
+ just been computed in the approximate degree computation.
+ Not user-callable.
+*/
+template <typename IndexType>
+static void detect_super_cols
+(
+ /* === Parameters ======================================================= */
+
+ ColStructure<IndexType> Col [], /* of size n_col+1 */
+ IndexType A [], /* row indices of A */
+ IndexType head [], /* head of degree lists and hash buckets */
+ IndexType row_start, /* pointer to set of columns to check */
+ IndexType row_length /* number of columns to check */
+)
+{
+ /* === Local variables ================================================== */
+
+ IndexType hash ; /* hash value for a column */
+ IndexType *rp ; /* pointer to a row */
+ IndexType c ; /* a column index */
+ IndexType super_c ; /* column index of the column to absorb into */
+ IndexType *cp1 ; /* column pointer for column super_c */
+ IndexType *cp2 ; /* column pointer for column c */
+ IndexType length ; /* length of column super_c */
+ IndexType prev_c ; /* column preceding c in hash bucket */
+ IndexType i ; /* loop counter */
+ IndexType *rp_end ; /* pointer to the end of the row */
+ IndexType col ; /* a column index in the row to check */
+ IndexType head_column ; /* first column in hash bucket or degree list */
+ IndexType first_col ; /* first column in hash bucket */
+
+ /* === Consider each column in the row ================================== */
+
+ rp = &A [row_start] ;
+ rp_end = rp + row_length ;
+ while (rp < rp_end)
+ {
+ col = *rp++ ;
+ if (Col[col].is_dead())
+ {
+ continue ;
+ }
+
+ /* get hash number for this column */
+ hash = Col [col].shared3.hash ;
+ COLAMD_ASSERT (hash <= n_col) ;
+
+ /* === Get the first column in this hash bucket ===================== */
+
+ head_column = head [hash] ;
+ if (head_column > Empty)
+ {
+ first_col = Col [head_column].shared3.headhash ;
+ }
+ else
+ {
+ first_col = - (head_column + 2) ;
+ }
+
+ /* === Consider each column in the hash bucket ====================== */
+
+ for (super_c = first_col ; super_c != Empty ;
+ super_c = Col [super_c].shared4.hash_next)
+ {
+ COLAMD_ASSERT (Col [super_c].is_alive()) ;
+ COLAMD_ASSERT (Col [super_c].shared3.hash == hash) ;
+ length = Col [super_c].length ;
+
+ /* prev_c is the column preceding column c in the hash bucket */
+ prev_c = super_c ;
+
+ /* === Compare super_c with all columns after it ================ */
+
+ for (c = Col [super_c].shared4.hash_next ;
+ c != Empty ; c = Col [c].shared4.hash_next)
+ {
+ COLAMD_ASSERT (c != super_c) ;
+ COLAMD_ASSERT (Col[c].is_alive()) ;
+ COLAMD_ASSERT (Col [c].shared3.hash == hash) ;
+
+ /* not identical if lengths or scores are different */
+ if (Col [c].length != length ||
+ Col [c].shared2.score != Col [super_c].shared2.score)
+ {
+ prev_c = c ;
+ continue ;
+ }
+
+ /* compare the two columns */
+ cp1 = &A [Col [super_c].start] ;
+ cp2 = &A [Col [c].start] ;
+
+ for (i = 0 ; i < length ; i++)
+ {
+ /* the columns are "clean" (no dead rows) */
+ COLAMD_ASSERT ( cp1->is_alive() );
+ COLAMD_ASSERT ( cp2->is_alive() );
+ /* row indices will same order for both supercols, */
+ /* no gather scatter necessary */
+ if (*cp1++ != *cp2++)
+ {
+ break ;
+ }
+ }
+
+ /* the two columns are different if the for-loop "broke" */
+ if (i != length)
+ {
+ prev_c = c ;
+ continue ;
+ }
+
+ /* === Got it! two columns are identical =================== */
+
+ COLAMD_ASSERT (Col [c].shared2.score == Col [super_c].shared2.score) ;
+
+ Col [super_c].shared1.thickness += Col [c].shared1.thickness ;
+ Col [c].shared1.parent = super_c ;
+ Col[c].kill_non_principal() ;
+ /* order c later, in order_children() */
+ Col [c].shared2.order = Empty ;
+ /* remove c from hash bucket */
+ Col [prev_c].shared4.hash_next = Col [c].shared4.hash_next ;
+ }
+ }
+
+ /* === Empty this hash bucket ======================================= */
+
+ if (head_column > Empty)
+ {
+ /* corresponding degree list "hash" is not empty */
+ Col [head_column].shared3.headhash = Empty ;
+ }
+ else
+ {
+ /* corresponding degree list "hash" is empty */
+ head [hash] = Empty ;
+ }
+ }
+}
+
+
+/* ========================================================================== */
+/* === garbage_collection =================================================== */
+/* ========================================================================== */
+
+/*
+ Defragments and compacts columns and rows in the workspace A. Used when
+ all available memory has been used while performing row merging. Returns
+ the index of the first free position in A, after garbage collection. The
+ time taken by this routine is linear is the size of the array A, which is
+ itself linear in the number of nonzeros in the input matrix.
+ Not user-callable.
+*/
+template <typename IndexType>
+static IndexType garbage_collection /* returns the new value of pfree */
+ (
+ /* === Parameters ======================================================= */
+
+ IndexType n_row, /* number of rows */
+ IndexType n_col, /* number of columns */
+ RowStructure<IndexType> Row [], /* row info */
+ ColStructure<IndexType> Col [], /* column info */
+ IndexType A [], /* A [0 ... Alen-1] holds the matrix */
+ IndexType *pfree /* &A [0] ... pfree is in use */
+ )
+{
+ /* === Local variables ================================================== */
+
+ IndexType *psrc ; /* source pointer */
+ IndexType *pdest ; /* destination pointer */
+ IndexType j ; /* counter */
+ IndexType r ; /* a row index */
+ IndexType c ; /* a column index */
+ IndexType length ; /* length of a row or column */
+
+ /* === Defragment the columns =========================================== */
+
+ pdest = &A[0] ;
+ for (c = 0 ; c < n_col ; c++)
+ {
+ if (Col[c].is_alive())
+ {
+ psrc = &A [Col [c].start] ;
+
+ /* move and compact the column */
+ COLAMD_ASSERT (pdest <= psrc) ;
+ Col [c].start = (IndexType) (pdest - &A [0]) ;
+ length = Col [c].length ;
+ for (j = 0 ; j < length ; j++)
+ {
+ r = *psrc++ ;
+ if (Row[r].is_alive())
+ {
+ *pdest++ = r ;
+ }
+ }
+ Col [c].length = (IndexType) (pdest - &A [Col [c].start]) ;
+ }
+ }
+
+ /* === Prepare to defragment the rows =================================== */
+
+ for (r = 0 ; r < n_row ; r++)
+ {
+ if (Row[r].is_alive())
+ {
+ if (Row [r].length == 0)
+ {
+ /* this row is of zero length. cannot compact it, so kill it */
+ COLAMD_DEBUG3 (("Defrag row kill\n")) ;
+ Row[r].kill() ;
+ }
+ else
+ {
+ /* save first column index in Row [r].shared2.first_column */
+ psrc = &A [Row [r].start] ;
+ Row [r].shared2.first_column = *psrc ;
+ COLAMD_ASSERT (Row[r].is_alive()) ;
+ /* flag the start of the row with the one's complement of row */
+ *psrc = ones_complement(r) ;
+
+ }
+ }
+ }
+
+ /* === Defragment the rows ============================================== */
+
+ psrc = pdest ;
+ while (psrc < pfree)
+ {
+ /* find a negative number ... the start of a row */
+ if (*psrc++ < 0)
+ {
+ psrc-- ;
+ /* get the row index */
+ r = ones_complement(*psrc) ;
+ COLAMD_ASSERT (r >= 0 && r < n_row) ;
+ /* restore first column index */
+ *psrc = Row [r].shared2.first_column ;
+ COLAMD_ASSERT (Row[r].is_alive()) ;
+
+ /* move and compact the row */
+ COLAMD_ASSERT (pdest <= psrc) ;
+ Row [r].start = (IndexType) (pdest - &A [0]) ;
+ length = Row [r].length ;
+ for (j = 0 ; j < length ; j++)
+ {
+ c = *psrc++ ;
+ if (Col[c].is_alive())
+ {
+ *pdest++ = c ;
+ }
+ }
+ Row [r].length = (IndexType) (pdest - &A [Row [r].start]) ;
+
+ }
+ }
+ /* ensure we found all the rows */
+ COLAMD_ASSERT (debug_rows == 0) ;
+
+ /* === Return the new value of pfree ==================================== */
+
+ return ((IndexType) (pdest - &A [0])) ;
+}
+
+
+/* ========================================================================== */
+/* === clear_mark =========================================================== */
+/* ========================================================================== */
+
+/*
+ Clears the Row [].shared2.mark array, and returns the new tag_mark.
+ Return value is the new tag_mark. Not user-callable.
+*/
+template <typename IndexType>
+static inline IndexType clear_mark /* return the new value for tag_mark */
+ (
+ /* === Parameters ======================================================= */
+
+ IndexType n_row, /* number of rows in A */
+ RowStructure<IndexType> Row [] /* Row [0 ... n_row-1].shared2.mark is set to zero */
+ )
+{
+ /* === Local variables ================================================== */
+
+ IndexType r ;
+
+ for (r = 0 ; r < n_row ; r++)
+ {
+ if (Row[r].is_alive())
+ {
+ Row [r].shared2.mark = 0 ;
+ }
+ }
+ return (1) ;
+}
+
+} // namespace Colamd
+
+} // namespace internal
+#endif
diff --git a/Eigen/src/OrderingMethods/InternalHeaderCheck.h b/Eigen/src/OrderingMethods/InternalHeaderCheck.h
new file mode 100644
index 0000000..713c447
--- /dev/null
+++ b/Eigen/src/OrderingMethods/InternalHeaderCheck.h
@@ -0,0 +1,3 @@
+#ifndef EIGEN_ORDERINGMETHODS_MODULE_H
+#error "Please include Eigen/OrderingMethods instead of including headers inside the src directory directly."
+#endif
diff --git a/Eigen/src/OrderingMethods/Ordering.h b/Eigen/src/OrderingMethods/Ordering.h
new file mode 100644
index 0000000..5cc4a85
--- /dev/null
+++ b/Eigen/src/OrderingMethods/Ordering.h
@@ -0,0 +1,155 @@
+
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2012 Désiré Nuentsa-Wakam <desire.nuentsa_wakam@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_ORDERING_H
+#define EIGEN_ORDERING_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+#include "Eigen_Colamd.h"
+
+namespace internal {
+
+/** \internal
+ * \ingroup OrderingMethods_Module
+ * \param[in] A the input non-symmetric matrix
+ * \param[out] symmat the symmetric pattern A^T+A from the input matrix \a A.
+ * FIXME: The values should not be considered here
+ */
+template<typename MatrixType>
+void ordering_helper_at_plus_a(const MatrixType& A, MatrixType& symmat)
+{
+ MatrixType C;
+ C = A.transpose(); // NOTE: Could be costly
+ for (int i = 0; i < C.rows(); i++)
+ {
+ for (typename MatrixType::InnerIterator it(C, i); it; ++it)
+ it.valueRef() = typename MatrixType::Scalar(0);
+ }
+ symmat = C + A;
+}
+
+}
+
+/** \ingroup OrderingMethods_Module
+ * \class AMDOrdering
+ *
+ * Functor computing the \em approximate \em minimum \em degree ordering
+ * If the matrix is not structurally symmetric, an ordering of A^T+A is computed
+ * \tparam StorageIndex The type of indices of the matrix
+ * \sa COLAMDOrdering
+ */
+template <typename StorageIndex>
+class AMDOrdering
+{
+ public:
+ typedef PermutationMatrix<Dynamic, Dynamic, StorageIndex> PermutationType;
+
+ /** Compute the permutation vector from a sparse matrix
+ * This routine is much faster if the input matrix is column-major
+ */
+ template <typename MatrixType>
+ void operator()(const MatrixType& mat, PermutationType& perm)
+ {
+ // Compute the symmetric pattern
+ SparseMatrix<typename MatrixType::Scalar, ColMajor, StorageIndex> symm;
+ internal::ordering_helper_at_plus_a(mat,symm);
+
+ // Call the AMD routine
+ //m_mat.prune(keep_diag());
+ internal::minimum_degree_ordering(symm, perm);
+ }
+
+ /** Compute the permutation with a selfadjoint matrix */
+ template <typename SrcType, unsigned int SrcUpLo>
+ void operator()(const SparseSelfAdjointView<SrcType, SrcUpLo>& mat, PermutationType& perm)
+ {
+ SparseMatrix<typename SrcType::Scalar, ColMajor, StorageIndex> C; C = mat;
+
+ // Call the AMD routine
+ // m_mat.prune(keep_diag()); //Remove the diagonal elements
+ internal::minimum_degree_ordering(C, perm);
+ }
+};
+
+/** \ingroup OrderingMethods_Module
+ * \class NaturalOrdering
+ *
+ * Functor computing the natural ordering (identity)
+ *
+ * \note Returns an empty permutation matrix
+ * \tparam StorageIndex The type of indices of the matrix
+ */
+template <typename StorageIndex>
+class NaturalOrdering
+{
+ public:
+ typedef PermutationMatrix<Dynamic, Dynamic, StorageIndex> PermutationType;
+
+ /** Compute the permutation vector from a column-major sparse matrix */
+ template <typename MatrixType>
+ void operator()(const MatrixType& /*mat*/, PermutationType& perm)
+ {
+ perm.resize(0);
+ }
+
+};
+
+/** \ingroup OrderingMethods_Module
+ * \class COLAMDOrdering
+ *
+ * \tparam StorageIndex The type of indices of the matrix
+ *
+ * Functor computing the \em column \em approximate \em minimum \em degree ordering
+ * The matrix should be in column-major and \b compressed format (see SparseMatrix::makeCompressed()).
+ */
+template<typename StorageIndex>
+class COLAMDOrdering
+{
+ public:
+ typedef PermutationMatrix<Dynamic, Dynamic, StorageIndex> PermutationType;
+ typedef Matrix<StorageIndex, Dynamic, 1> IndexVector;
+
+ /** Compute the permutation vector \a perm form the sparse matrix \a mat
+ * \warning The input sparse matrix \a mat must be in compressed mode (see SparseMatrix::makeCompressed()).
+ */
+ template <typename MatrixType>
+ void operator() (const MatrixType& mat, PermutationType& perm)
+ {
+ eigen_assert(mat.isCompressed() && "COLAMDOrdering requires a sparse matrix in compressed mode. Call .makeCompressed() before passing it to COLAMDOrdering");
+
+ StorageIndex m = StorageIndex(mat.rows());
+ StorageIndex n = StorageIndex(mat.cols());
+ StorageIndex nnz = StorageIndex(mat.nonZeros());
+ // Get the recommended value of Alen to be used by colamd
+ StorageIndex Alen = internal::Colamd::recommended(nnz, m, n);
+ // Set the default parameters
+ double knobs [internal::Colamd::NKnobs];
+ StorageIndex stats [internal::Colamd::NStats];
+ internal::Colamd::set_defaults(knobs);
+
+ IndexVector p(n+1), A(Alen);
+ for(StorageIndex i=0; i <= n; i++) p(i) = mat.outerIndexPtr()[i];
+ for(StorageIndex i=0; i < nnz; i++) A(i) = mat.innerIndexPtr()[i];
+ // Call Colamd routine to compute the ordering
+ StorageIndex info = internal::Colamd::compute_ordering(m, n, Alen, A.data(), p.data(), knobs, stats);
+ EIGEN_UNUSED_VARIABLE(info);
+ eigen_assert( info && "COLAMD failed " );
+
+ perm.resize(n);
+ for (StorageIndex i = 0; i < n; i++) perm.indices()(p(i)) = i;
+ }
+};
+
+} // end namespace Eigen
+
+#endif
diff --git a/Eigen/src/PaStiXSupport/InternalHeaderCheck.h b/Eigen/src/PaStiXSupport/InternalHeaderCheck.h
new file mode 100644
index 0000000..f588e50
--- /dev/null
+++ b/Eigen/src/PaStiXSupport/InternalHeaderCheck.h
@@ -0,0 +1,3 @@
+#ifndef EIGEN_PASTIXSUPPORT_MODULE_H
+#error "Please include Eigen/PaStiXSupport instead of including headers inside the src directory directly."
+#endif
diff --git a/Eigen/src/PaStiXSupport/PaStiXSupport.h b/Eigen/src/PaStiXSupport/PaStiXSupport.h
new file mode 100644
index 0000000..d3126b1
--- /dev/null
+++ b/Eigen/src/PaStiXSupport/PaStiXSupport.h
@@ -0,0 +1,680 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2012 Désiré Nuentsa-Wakam <desire.nuentsa_wakam@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_PASTIXSUPPORT_H
+#define EIGEN_PASTIXSUPPORT_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+#if defined(DCOMPLEX)
+ #define PASTIX_COMPLEX COMPLEX
+ #define PASTIX_DCOMPLEX DCOMPLEX
+#else
+ #define PASTIX_COMPLEX std::complex<float>
+ #define PASTIX_DCOMPLEX std::complex<double>
+#endif
+
+/** \ingroup PaStiXSupport_Module
+ * \brief Interface to the PaStix solver
+ *
+ * This class is used to solve the linear systems A.X = B via the PaStix library.
+ * The matrix can be either real or complex, symmetric or not.
+ *
+ * \sa TutorialSparseDirectSolvers
+ */
+template<typename MatrixType_, bool IsStrSym = false> class PastixLU;
+template<typename MatrixType_, int Options> class PastixLLT;
+template<typename MatrixType_, int Options> class PastixLDLT;
+
+namespace internal
+{
+
+ template<class Pastix> struct pastix_traits;
+
+ template<typename MatrixType_>
+ struct pastix_traits< PastixLU<MatrixType_> >
+ {
+ typedef MatrixType_ MatrixType;
+ typedef typename MatrixType_::Scalar Scalar;
+ typedef typename MatrixType_::RealScalar RealScalar;
+ typedef typename MatrixType_::StorageIndex StorageIndex;
+ };
+
+ template<typename MatrixType_, int Options>
+ struct pastix_traits< PastixLLT<MatrixType_,Options> >
+ {
+ typedef MatrixType_ MatrixType;
+ typedef typename MatrixType_::Scalar Scalar;
+ typedef typename MatrixType_::RealScalar RealScalar;
+ typedef typename MatrixType_::StorageIndex StorageIndex;
+ };
+
+ template<typename MatrixType_, int Options>
+ struct pastix_traits< PastixLDLT<MatrixType_,Options> >
+ {
+ typedef MatrixType_ MatrixType;
+ typedef typename MatrixType_::Scalar Scalar;
+ typedef typename MatrixType_::RealScalar RealScalar;
+ typedef typename MatrixType_::StorageIndex StorageIndex;
+ };
+
+ inline void eigen_pastix(pastix_data_t **pastix_data, int pastix_comm, int n, int *ptr, int *idx, float *vals, int *perm, int * invp, float *x, int nbrhs, int *iparm, double *dparm)
+ {
+ if (n == 0) { ptr = NULL; idx = NULL; vals = NULL; }
+ if (nbrhs == 0) {x = NULL; nbrhs=1;}
+ s_pastix(pastix_data, pastix_comm, n, ptr, idx, vals, perm, invp, x, nbrhs, iparm, dparm);
+ }
+
+ inline void eigen_pastix(pastix_data_t **pastix_data, int pastix_comm, int n, int *ptr, int *idx, double *vals, int *perm, int * invp, double *x, int nbrhs, int *iparm, double *dparm)
+ {
+ if (n == 0) { ptr = NULL; idx = NULL; vals = NULL; }
+ if (nbrhs == 0) {x = NULL; nbrhs=1;}
+ d_pastix(pastix_data, pastix_comm, n, ptr, idx, vals, perm, invp, x, nbrhs, iparm, dparm);
+ }
+
+ inline void eigen_pastix(pastix_data_t **pastix_data, int pastix_comm, int n, int *ptr, int *idx, std::complex<float> *vals, int *perm, int * invp, std::complex<float> *x, int nbrhs, int *iparm, double *dparm)
+ {
+ if (n == 0) { ptr = NULL; idx = NULL; vals = NULL; }
+ if (nbrhs == 0) {x = NULL; nbrhs=1;}
+ c_pastix(pastix_data, pastix_comm, n, ptr, idx, reinterpret_cast<PASTIX_COMPLEX*>(vals), perm, invp, reinterpret_cast<PASTIX_COMPLEX*>(x), nbrhs, iparm, dparm);
+ }
+
+ inline void eigen_pastix(pastix_data_t **pastix_data, int pastix_comm, int n, int *ptr, int *idx, std::complex<double> *vals, int *perm, int * invp, std::complex<double> *x, int nbrhs, int *iparm, double *dparm)
+ {
+ if (n == 0) { ptr = NULL; idx = NULL; vals = NULL; }
+ if (nbrhs == 0) {x = NULL; nbrhs=1;}
+ z_pastix(pastix_data, pastix_comm, n, ptr, idx, reinterpret_cast<PASTIX_DCOMPLEX*>(vals), perm, invp, reinterpret_cast<PASTIX_DCOMPLEX*>(x), nbrhs, iparm, dparm);
+ }
+
+ // Convert the matrix to Fortran-style Numbering
+ template <typename MatrixType>
+ void c_to_fortran_numbering (MatrixType& mat)
+ {
+ if ( !(mat.outerIndexPtr()[0]) )
+ {
+ int i;
+ for(i = 0; i <= mat.rows(); ++i)
+ ++mat.outerIndexPtr()[i];
+ for(i = 0; i < mat.nonZeros(); ++i)
+ ++mat.innerIndexPtr()[i];
+ }
+ }
+
+ // Convert to C-style Numbering
+ template <typename MatrixType>
+ void fortran_to_c_numbering (MatrixType& mat)
+ {
+ // Check the Numbering
+ if ( mat.outerIndexPtr()[0] == 1 )
+ { // Convert to C-style numbering
+ int i;
+ for(i = 0; i <= mat.rows(); ++i)
+ --mat.outerIndexPtr()[i];
+ for(i = 0; i < mat.nonZeros(); ++i)
+ --mat.innerIndexPtr()[i];
+ }
+ }
+}
+
+// This is the base class to interface with PaStiX functions.
+// Users should not used this class directly.
+template <class Derived>
+class PastixBase : public SparseSolverBase<Derived>
+{
+ protected:
+ typedef SparseSolverBase<Derived> Base;
+ using Base::derived;
+ using Base::m_isInitialized;
+ public:
+ using Base::_solve_impl;
+
+ typedef typename internal::pastix_traits<Derived>::MatrixType MatrixType_;
+ typedef MatrixType_ MatrixType;
+ typedef typename MatrixType::Scalar Scalar;
+ typedef typename MatrixType::RealScalar RealScalar;
+ typedef typename MatrixType::StorageIndex StorageIndex;
+ typedef Matrix<Scalar,Dynamic,1> Vector;
+ typedef SparseMatrix<Scalar, ColMajor> ColSpMatrix;
+ enum {
+ ColsAtCompileTime = MatrixType::ColsAtCompileTime,
+ MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime
+ };
+
+ public:
+
+ PastixBase() : m_initisOk(false), m_analysisIsOk(false), m_factorizationIsOk(false), m_pastixdata(0), m_size(0)
+ {
+ init();
+ }
+
+ ~PastixBase()
+ {
+ clean();
+ }
+
+ template<typename Rhs,typename Dest>
+ bool _solve_impl(const MatrixBase<Rhs> &b, MatrixBase<Dest> &x) const;
+
+ /** Returns a reference to the integer vector IPARM of PaStiX parameters
+ * to modify the default parameters.
+ * The statistics related to the different phases of factorization and solve are saved here as well
+ * \sa analyzePattern() factorize()
+ */
+ Array<StorageIndex,IPARM_SIZE,1>& iparm()
+ {
+ return m_iparm;
+ }
+
+ /** Return a reference to a particular index parameter of the IPARM vector
+ * \sa iparm()
+ */
+
+ int& iparm(int idxparam)
+ {
+ return m_iparm(idxparam);
+ }
+
+ /** Returns a reference to the double vector DPARM of PaStiX parameters
+ * The statistics related to the different phases of factorization and solve are saved here as well
+ * \sa analyzePattern() factorize()
+ */
+ Array<double,DPARM_SIZE,1>& dparm()
+ {
+ return m_dparm;
+ }
+
+
+ /** Return a reference to a particular index parameter of the DPARM vector
+ * \sa dparm()
+ */
+ double& dparm(int idxparam)
+ {
+ return m_dparm(idxparam);
+ }
+
+ inline Index cols() const { return m_size; }
+ inline Index rows() const { return m_size; }
+
+ /** \brief Reports whether previous computation was successful.
+ *
+ * \returns \c Success if computation was successful,
+ * \c NumericalIssue if the PaStiX reports a problem
+ * \c InvalidInput if the input matrix is invalid
+ *
+ * \sa iparm()
+ */
+ ComputationInfo info() const
+ {
+ eigen_assert(m_isInitialized && "Decomposition is not initialized.");
+ return m_info;
+ }
+
+ protected:
+
+ // Initialize the Pastix data structure, check the matrix
+ void init();
+
+ // Compute the ordering and the symbolic factorization
+ void analyzePattern(ColSpMatrix& mat);
+
+ // Compute the numerical factorization
+ void factorize(ColSpMatrix& mat);
+
+ // Free all the data allocated by Pastix
+ void clean()
+ {
+ eigen_assert(m_initisOk && "The Pastix structure should be allocated first");
+ m_iparm(IPARM_START_TASK) = API_TASK_CLEAN;
+ m_iparm(IPARM_END_TASK) = API_TASK_CLEAN;
+ internal::eigen_pastix(&m_pastixdata, MPI_COMM_WORLD, 0, 0, 0, (Scalar*)0,
+ m_perm.data(), m_invp.data(), 0, 0, m_iparm.data(), m_dparm.data());
+ }
+
+ void compute(ColSpMatrix& mat);
+
+ int m_initisOk;
+ int m_analysisIsOk;
+ int m_factorizationIsOk;
+ mutable ComputationInfo m_info;
+ mutable pastix_data_t *m_pastixdata; // Data structure for pastix
+ mutable int m_comm; // The MPI communicator identifier
+ mutable Array<int,IPARM_SIZE,1> m_iparm; // integer vector for the input parameters
+ mutable Array<double,DPARM_SIZE,1> m_dparm; // Scalar vector for the input parameters
+ mutable Matrix<StorageIndex,Dynamic,1> m_perm; // Permutation vector
+ mutable Matrix<StorageIndex,Dynamic,1> m_invp; // Inverse permutation vector
+ mutable int m_size; // Size of the matrix
+};
+
+ /** Initialize the PaStiX data structure.
+ *A first call to this function fills iparm and dparm with the default PaStiX parameters
+ * \sa iparm() dparm()
+ */
+template <class Derived>
+void PastixBase<Derived>::init()
+{
+ m_size = 0;
+ m_iparm.setZero(IPARM_SIZE);
+ m_dparm.setZero(DPARM_SIZE);
+
+ m_iparm(IPARM_MODIFY_PARAMETER) = API_NO;
+ pastix(&m_pastixdata, MPI_COMM_WORLD,
+ 0, 0, 0, 0,
+ 0, 0, 0, 1, m_iparm.data(), m_dparm.data());
+
+ m_iparm[IPARM_MATRIX_VERIFICATION] = API_NO;
+ m_iparm[IPARM_VERBOSE] = API_VERBOSE_NOT;
+ m_iparm[IPARM_ORDERING] = API_ORDER_SCOTCH;
+ m_iparm[IPARM_INCOMPLETE] = API_NO;
+ m_iparm[IPARM_OOC_LIMIT] = 2000;
+ m_iparm[IPARM_RHS_MAKING] = API_RHS_B;
+ m_iparm(IPARM_MATRIX_VERIFICATION) = API_NO;
+
+ m_iparm(IPARM_START_TASK) = API_TASK_INIT;
+ m_iparm(IPARM_END_TASK) = API_TASK_INIT;
+ internal::eigen_pastix(&m_pastixdata, MPI_COMM_WORLD, 0, 0, 0, (Scalar*)0,
+ 0, 0, 0, 0, m_iparm.data(), m_dparm.data());
+
+ // Check the returned error
+ if(m_iparm(IPARM_ERROR_NUMBER)) {
+ m_info = InvalidInput;
+ m_initisOk = false;
+ }
+ else {
+ m_info = Success;
+ m_initisOk = true;
+ }
+}
+
+template <class Derived>
+void PastixBase<Derived>::compute(ColSpMatrix& mat)
+{
+ eigen_assert(mat.rows() == mat.cols() && "The input matrix should be squared");
+
+ analyzePattern(mat);
+ factorize(mat);
+
+ m_iparm(IPARM_MATRIX_VERIFICATION) = API_NO;
+}
+
+
+template <class Derived>
+void PastixBase<Derived>::analyzePattern(ColSpMatrix& mat)
+{
+ eigen_assert(m_initisOk && "The initialization of PaSTiX failed");
+
+ // clean previous calls
+ if(m_size>0)
+ clean();
+
+ m_size = internal::convert_index<int>(mat.rows());
+ m_perm.resize(m_size);
+ m_invp.resize(m_size);
+
+ m_iparm(IPARM_START_TASK) = API_TASK_ORDERING;
+ m_iparm(IPARM_END_TASK) = API_TASK_ANALYSE;
+ internal::eigen_pastix(&m_pastixdata, MPI_COMM_WORLD, m_size, mat.outerIndexPtr(), mat.innerIndexPtr(),
+ mat.valuePtr(), m_perm.data(), m_invp.data(), 0, 0, m_iparm.data(), m_dparm.data());
+
+ // Check the returned error
+ if(m_iparm(IPARM_ERROR_NUMBER))
+ {
+ m_info = NumericalIssue;
+ m_analysisIsOk = false;
+ }
+ else
+ {
+ m_info = Success;
+ m_analysisIsOk = true;
+ }
+}
+
+template <class Derived>
+void PastixBase<Derived>::factorize(ColSpMatrix& mat)
+{
+// if(&m_cpyMat != &mat) m_cpyMat = mat;
+ eigen_assert(m_analysisIsOk && "The analysis phase should be called before the factorization phase");
+ m_iparm(IPARM_START_TASK) = API_TASK_NUMFACT;
+ m_iparm(IPARM_END_TASK) = API_TASK_NUMFACT;
+ m_size = internal::convert_index<int>(mat.rows());
+
+ internal::eigen_pastix(&m_pastixdata, MPI_COMM_WORLD, m_size, mat.outerIndexPtr(), mat.innerIndexPtr(),
+ mat.valuePtr(), m_perm.data(), m_invp.data(), 0, 0, m_iparm.data(), m_dparm.data());
+
+ // Check the returned error
+ if(m_iparm(IPARM_ERROR_NUMBER))
+ {
+ m_info = NumericalIssue;
+ m_factorizationIsOk = false;
+ m_isInitialized = false;
+ }
+ else
+ {
+ m_info = Success;
+ m_factorizationIsOk = true;
+ m_isInitialized = true;
+ }
+}
+
+/* Solve the system */
+template<typename Base>
+template<typename Rhs,typename Dest>
+bool PastixBase<Base>::_solve_impl(const MatrixBase<Rhs> &b, MatrixBase<Dest> &x) const
+{
+ eigen_assert(m_isInitialized && "The matrix should be factorized first");
+ EIGEN_STATIC_ASSERT((Dest::Flags&RowMajorBit)==0,
+ THIS_METHOD_IS_ONLY_FOR_COLUMN_MAJOR_MATRICES);
+ int rhs = 1;
+
+ x = b; /* on return, x is overwritten by the computed solution */
+
+ for (int i = 0; i < b.cols(); i++){
+ m_iparm[IPARM_START_TASK] = API_TASK_SOLVE;
+ m_iparm[IPARM_END_TASK] = API_TASK_REFINE;
+
+ internal::eigen_pastix(&m_pastixdata, MPI_COMM_WORLD, internal::convert_index<int>(x.rows()), 0, 0, 0,
+ m_perm.data(), m_invp.data(), &x(0, i), rhs, m_iparm.data(), m_dparm.data());
+ }
+
+ // Check the returned error
+ m_info = m_iparm(IPARM_ERROR_NUMBER)==0 ? Success : NumericalIssue;
+
+ return m_iparm(IPARM_ERROR_NUMBER)==0;
+}
+
+/** \ingroup PaStiXSupport_Module
+ * \class PastixLU
+ * \brief Sparse direct LU solver based on PaStiX library
+ *
+ * This class is used to solve the linear systems A.X = B with a supernodal LU
+ * factorization in the PaStiX library. The matrix A should be squared and nonsingular
+ * PaStiX requires that the matrix A has a symmetric structural pattern.
+ * This interface can symmetrize the input matrix otherwise.
+ * The vectors or matrices X and B can be either dense or sparse.
+ *
+ * \tparam MatrixType_ the type of the sparse matrix A, it must be a SparseMatrix<>
+ * \tparam IsStrSym Indicates if the input matrix has a symmetric pattern, default is false
+ * NOTE : Note that if the analysis and factorization phase are called separately,
+ * the input matrix will be symmetrized at each call, hence it is advised to
+ * symmetrize the matrix in a end-user program and set \p IsStrSym to true
+ *
+ * \implsparsesolverconcept
+ *
+ * \sa \ref TutorialSparseSolverConcept, class SparseLU
+ *
+ */
+template<typename MatrixType_, bool IsStrSym>
+class PastixLU : public PastixBase< PastixLU<MatrixType_> >
+{
+ public:
+ typedef MatrixType_ MatrixType;
+ typedef PastixBase<PastixLU<MatrixType> > Base;
+ typedef typename Base::ColSpMatrix ColSpMatrix;
+ typedef typename MatrixType::StorageIndex StorageIndex;
+
+ public:
+ PastixLU() : Base()
+ {
+ init();
+ }
+
+ explicit PastixLU(const MatrixType& matrix):Base()
+ {
+ init();
+ compute(matrix);
+ }
+ /** Compute the LU supernodal factorization of \p matrix.
+ * iparm and dparm can be used to tune the PaStiX parameters.
+ * see the PaStiX user's manual
+ * \sa analyzePattern() factorize()
+ */
+ void compute (const MatrixType& matrix)
+ {
+ m_structureIsUptodate = false;
+ ColSpMatrix temp;
+ grabMatrix(matrix, temp);
+ Base::compute(temp);
+ }
+ /** Compute the LU symbolic factorization of \p matrix using its sparsity pattern.
+ * Several ordering methods can be used at this step. See the PaStiX user's manual.
+ * The result of this operation can be used with successive matrices having the same pattern as \p matrix
+ * \sa factorize()
+ */
+ void analyzePattern(const MatrixType& matrix)
+ {
+ m_structureIsUptodate = false;
+ ColSpMatrix temp;
+ grabMatrix(matrix, temp);
+ Base::analyzePattern(temp);
+ }
+
+ /** Compute the LU supernodal factorization of \p matrix
+ * WARNING The matrix \p matrix should have the same structural pattern
+ * as the same used in the analysis phase.
+ * \sa analyzePattern()
+ */
+ void factorize(const MatrixType& matrix)
+ {
+ ColSpMatrix temp;
+ grabMatrix(matrix, temp);
+ Base::factorize(temp);
+ }
+ protected:
+
+ void init()
+ {
+ m_structureIsUptodate = false;
+ m_iparm(IPARM_SYM) = API_SYM_NO;
+ m_iparm(IPARM_FACTORIZATION) = API_FACT_LU;
+ }
+
+ void grabMatrix(const MatrixType& matrix, ColSpMatrix& out)
+ {
+ if(IsStrSym)
+ out = matrix;
+ else
+ {
+ if(!m_structureIsUptodate)
+ {
+ // update the transposed structure
+ m_transposedStructure = matrix.transpose();
+
+ // Set the elements of the matrix to zero
+ for (Index j=0; j<m_transposedStructure.outerSize(); ++j)
+ for(typename ColSpMatrix::InnerIterator it(m_transposedStructure, j); it; ++it)
+ it.valueRef() = 0.0;
+
+ m_structureIsUptodate = true;
+ }
+
+ out = m_transposedStructure + matrix;
+ }
+ internal::c_to_fortran_numbering(out);
+ }
+
+ using Base::m_iparm;
+ using Base::m_dparm;
+
+ ColSpMatrix m_transposedStructure;
+ bool m_structureIsUptodate;
+};
+
+/** \ingroup PaStiXSupport_Module
+ * \class PastixLLT
+ * \brief A sparse direct supernodal Cholesky (LLT) factorization and solver based on the PaStiX library
+ *
+ * This class is used to solve the linear systems A.X = B via a LL^T supernodal Cholesky factorization
+ * available in the PaStiX library. The matrix A should be symmetric and positive definite
+ * WARNING Selfadjoint complex matrices are not supported in the current version of PaStiX
+ * The vectors or matrices X and B can be either dense or sparse
+ *
+ * \tparam MatrixType the type of the sparse matrix A, it must be a SparseMatrix<>
+ * \tparam UpLo The part of the matrix to use : Lower or Upper. The default is Lower as required by PaStiX
+ *
+ * \implsparsesolverconcept
+ *
+ * \sa \ref TutorialSparseSolverConcept, class SimplicialLLT
+ */
+template<typename MatrixType_, int UpLo_>
+class PastixLLT : public PastixBase< PastixLLT<MatrixType_, UpLo_> >
+{
+ public:
+ typedef MatrixType_ MatrixType;
+ typedef PastixBase<PastixLLT<MatrixType, UpLo_> > Base;
+ typedef typename Base::ColSpMatrix ColSpMatrix;
+
+ public:
+ enum { UpLo = UpLo_ };
+ PastixLLT() : Base()
+ {
+ init();
+ }
+
+ explicit PastixLLT(const MatrixType& matrix):Base()
+ {
+ init();
+ compute(matrix);
+ }
+
+ /** Compute the L factor of the LL^T supernodal factorization of \p matrix
+ * \sa analyzePattern() factorize()
+ */
+ void compute (const MatrixType& matrix)
+ {
+ ColSpMatrix temp;
+ grabMatrix(matrix, temp);
+ Base::compute(temp);
+ }
+
+ /** Compute the LL^T symbolic factorization of \p matrix using its sparsity pattern
+ * The result of this operation can be used with successive matrices having the same pattern as \p matrix
+ * \sa factorize()
+ */
+ void analyzePattern(const MatrixType& matrix)
+ {
+ ColSpMatrix temp;
+ grabMatrix(matrix, temp);
+ Base::analyzePattern(temp);
+ }
+ /** Compute the LL^T supernodal numerical factorization of \p matrix
+ * \sa analyzePattern()
+ */
+ void factorize(const MatrixType& matrix)
+ {
+ ColSpMatrix temp;
+ grabMatrix(matrix, temp);
+ Base::factorize(temp);
+ }
+ protected:
+ using Base::m_iparm;
+
+ void init()
+ {
+ m_iparm(IPARM_SYM) = API_SYM_YES;
+ m_iparm(IPARM_FACTORIZATION) = API_FACT_LLT;
+ }
+
+ void grabMatrix(const MatrixType& matrix, ColSpMatrix& out)
+ {
+ out.resize(matrix.rows(), matrix.cols());
+ // Pastix supports only lower, column-major matrices
+ out.template selfadjointView<Lower>() = matrix.template selfadjointView<UpLo>();
+ internal::c_to_fortran_numbering(out);
+ }
+};
+
+/** \ingroup PaStiXSupport_Module
+ * \class PastixLDLT
+ * \brief A sparse direct supernodal Cholesky (LLT) factorization and solver based on the PaStiX library
+ *
+ * This class is used to solve the linear systems A.X = B via a LDL^T supernodal Cholesky factorization
+ * available in the PaStiX library. The matrix A should be symmetric and positive definite
+ * WARNING Selfadjoint complex matrices are not supported in the current version of PaStiX
+ * The vectors or matrices X and B can be either dense or sparse
+ *
+ * \tparam MatrixType the type of the sparse matrix A, it must be a SparseMatrix<>
+ * \tparam UpLo The part of the matrix to use : Lower or Upper. The default is Lower as required by PaStiX
+ *
+ * \implsparsesolverconcept
+ *
+ * \sa \ref TutorialSparseSolverConcept, class SimplicialLDLT
+ */
+template<typename MatrixType_, int UpLo_>
+class PastixLDLT : public PastixBase< PastixLDLT<MatrixType_, UpLo_> >
+{
+ public:
+ typedef MatrixType_ MatrixType;
+ typedef PastixBase<PastixLDLT<MatrixType, UpLo_> > Base;
+ typedef typename Base::ColSpMatrix ColSpMatrix;
+
+ public:
+ enum { UpLo = UpLo_ };
+ PastixLDLT():Base()
+ {
+ init();
+ }
+
+ explicit PastixLDLT(const MatrixType& matrix):Base()
+ {
+ init();
+ compute(matrix);
+ }
+
+ /** Compute the L and D factors of the LDL^T factorization of \p matrix
+ * \sa analyzePattern() factorize()
+ */
+ void compute (const MatrixType& matrix)
+ {
+ ColSpMatrix temp;
+ grabMatrix(matrix, temp);
+ Base::compute(temp);
+ }
+
+ /** Compute the LDL^T symbolic factorization of \p matrix using its sparsity pattern
+ * The result of this operation can be used with successive matrices having the same pattern as \p matrix
+ * \sa factorize()
+ */
+ void analyzePattern(const MatrixType& matrix)
+ {
+ ColSpMatrix temp;
+ grabMatrix(matrix, temp);
+ Base::analyzePattern(temp);
+ }
+ /** Compute the LDL^T supernodal numerical factorization of \p matrix
+ *
+ */
+ void factorize(const MatrixType& matrix)
+ {
+ ColSpMatrix temp;
+ grabMatrix(matrix, temp);
+ Base::factorize(temp);
+ }
+
+ protected:
+ using Base::m_iparm;
+
+ void init()
+ {
+ m_iparm(IPARM_SYM) = API_SYM_YES;
+ m_iparm(IPARM_FACTORIZATION) = API_FACT_LDLT;
+ }
+
+ void grabMatrix(const MatrixType& matrix, ColSpMatrix& out)
+ {
+ // Pastix supports only lower, column-major matrices
+ out.resize(matrix.rows(), matrix.cols());
+ out.template selfadjointView<Lower>() = matrix.template selfadjointView<UpLo>();
+ internal::c_to_fortran_numbering(out);
+ }
+};
+
+} // end namespace Eigen
+
+#endif
diff --git a/Eigen/src/PardisoSupport/InternalHeaderCheck.h b/Eigen/src/PardisoSupport/InternalHeaderCheck.h
new file mode 100644
index 0000000..8ef33f0
--- /dev/null
+++ b/Eigen/src/PardisoSupport/InternalHeaderCheck.h
@@ -0,0 +1,3 @@
+#ifndef EIGEN_PARDISOSUPPORT_MODULE_H
+#error "Please include Eigen/PardisoSupport instead of including headers inside the src directory directly."
+#endif
diff --git a/Eigen/src/PardisoSupport/PardisoSupport.h b/Eigen/src/PardisoSupport/PardisoSupport.h
new file mode 100644
index 0000000..e9815e6
--- /dev/null
+++ b/Eigen/src/PardisoSupport/PardisoSupport.h
@@ -0,0 +1,547 @@
+/*
+ Copyright (c) 2011, Intel Corporation. All rights reserved.
+
+ Redistribution and use in source and binary forms, with or without modification,
+ are permitted provided that the following conditions are met:
+
+ * Redistributions of source code must retain the above copyright notice, this
+ list of conditions and the following disclaimer.
+ * Redistributions in binary form must reproduce the above copyright notice,
+ this list of conditions and the following disclaimer in the documentation
+ and/or other materials provided with the distribution.
+ * Neither the name of Intel Corporation nor the names of its contributors may
+ be used to endorse or promote products derived from this software without
+ specific prior written permission.
+
+ THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
+ ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
+ WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
+ DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR
+ ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
+ (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
+ LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON
+ ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
+ (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
+ SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+
+ ********************************************************************************
+ * Content : Eigen bindings to Intel(R) MKL PARDISO
+ ********************************************************************************
+*/
+
+#ifndef EIGEN_PARDISOSUPPORT_H
+#define EIGEN_PARDISOSUPPORT_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+template<typename MatrixType_> class PardisoLU;
+template<typename MatrixType_, int Options=Upper> class PardisoLLT;
+template<typename MatrixType_, int Options=Upper> class PardisoLDLT;
+
+namespace internal
+{
+ template<typename IndexType>
+ struct pardiso_run_selector
+ {
+ static IndexType run( _MKL_DSS_HANDLE_t pt, IndexType maxfct, IndexType mnum, IndexType type, IndexType phase, IndexType n, void *a,
+ IndexType *ia, IndexType *ja, IndexType *perm, IndexType nrhs, IndexType *iparm, IndexType msglvl, void *b, void *x)
+ {
+ IndexType error = 0;
+ ::pardiso(pt, &maxfct, &mnum, &type, &phase, &n, a, ia, ja, perm, &nrhs, iparm, &msglvl, b, x, &error);
+ return error;
+ }
+ };
+ template<>
+ struct pardiso_run_selector<long long int>
+ {
+ typedef long long int IndexType;
+ static IndexType run( _MKL_DSS_HANDLE_t pt, IndexType maxfct, IndexType mnum, IndexType type, IndexType phase, IndexType n, void *a,
+ IndexType *ia, IndexType *ja, IndexType *perm, IndexType nrhs, IndexType *iparm, IndexType msglvl, void *b, void *x)
+ {
+ IndexType error = 0;
+ ::pardiso_64(pt, &maxfct, &mnum, &type, &phase, &n, a, ia, ja, perm, &nrhs, iparm, &msglvl, b, x, &error);
+ return error;
+ }
+ };
+
+ template<class Pardiso> struct pardiso_traits;
+
+ template<typename MatrixType_>
+ struct pardiso_traits< PardisoLU<MatrixType_> >
+ {
+ typedef MatrixType_ MatrixType;
+ typedef typename MatrixType_::Scalar Scalar;
+ typedef typename MatrixType_::RealScalar RealScalar;
+ typedef typename MatrixType_::StorageIndex StorageIndex;
+ };
+
+ template<typename MatrixType_, int Options>
+ struct pardiso_traits< PardisoLLT<MatrixType_, Options> >
+ {
+ typedef MatrixType_ MatrixType;
+ typedef typename MatrixType_::Scalar Scalar;
+ typedef typename MatrixType_::RealScalar RealScalar;
+ typedef typename MatrixType_::StorageIndex StorageIndex;
+ };
+
+ template<typename MatrixType_, int Options>
+ struct pardiso_traits< PardisoLDLT<MatrixType_, Options> >
+ {
+ typedef MatrixType_ MatrixType;
+ typedef typename MatrixType_::Scalar Scalar;
+ typedef typename MatrixType_::RealScalar RealScalar;
+ typedef typename MatrixType_::StorageIndex StorageIndex;
+ };
+
+} // end namespace internal
+
+template<class Derived>
+class PardisoImpl : public SparseSolverBase<Derived>
+{
+ protected:
+ typedef SparseSolverBase<Derived> Base;
+ using Base::derived;
+ using Base::m_isInitialized;
+
+ typedef internal::pardiso_traits<Derived> Traits;
+ public:
+ using Base::_solve_impl;
+
+ typedef typename Traits::MatrixType MatrixType;
+ typedef typename Traits::Scalar Scalar;
+ typedef typename Traits::RealScalar RealScalar;
+ typedef typename Traits::StorageIndex StorageIndex;
+ typedef SparseMatrix<Scalar,RowMajor,StorageIndex> SparseMatrixType;
+ typedef Matrix<Scalar,Dynamic,1> VectorType;
+ typedef Matrix<StorageIndex, 1, MatrixType::ColsAtCompileTime> IntRowVectorType;
+ typedef Matrix<StorageIndex, MatrixType::RowsAtCompileTime, 1> IntColVectorType;
+ typedef Array<StorageIndex,64,1,DontAlign> ParameterType;
+ enum {
+ ScalarIsComplex = NumTraits<Scalar>::IsComplex,
+ ColsAtCompileTime = Dynamic,
+ MaxColsAtCompileTime = Dynamic
+ };
+
+ PardisoImpl()
+ : m_analysisIsOk(false), m_factorizationIsOk(false)
+ {
+ eigen_assert((sizeof(StorageIndex) >= sizeof(_INTEGER_t) && sizeof(StorageIndex) <= 8) && "Non-supported index type");
+ m_iparm.setZero();
+ m_msglvl = 0; // No output
+ m_isInitialized = false;
+ }
+
+ ~PardisoImpl()
+ {
+ pardisoRelease();
+ }
+
+ inline Index cols() const { return m_size; }
+ inline Index rows() const { return m_size; }
+
+ /** \brief Reports whether previous computation was successful.
+ *
+ * \returns \c Success if computation was successful,
+ * \c NumericalIssue if the matrix appears to be negative.
+ */
+ ComputationInfo info() const
+ {
+ eigen_assert(m_isInitialized && "Decomposition is not initialized.");
+ return m_info;
+ }
+
+ /** \warning for advanced usage only.
+ * \returns a reference to the parameter array controlling PARDISO.
+ * See the PARDISO manual to know how to use it. */
+ ParameterType& pardisoParameterArray()
+ {
+ return m_iparm;
+ }
+
+ /** Performs a symbolic decomposition on the sparcity of \a matrix.
+ *
+ * This function is particularly useful when solving for several problems having the same structure.
+ *
+ * \sa factorize()
+ */
+ Derived& analyzePattern(const MatrixType& matrix);
+
+ /** Performs a numeric decomposition of \a matrix
+ *
+ * The given matrix must has the same sparcity than the matrix on which the symbolic decomposition has been performed.
+ *
+ * \sa analyzePattern()
+ */
+ Derived& factorize(const MatrixType& matrix);
+
+ Derived& compute(const MatrixType& matrix);
+
+ template<typename Rhs,typename Dest>
+ void _solve_impl(const MatrixBase<Rhs> &b, MatrixBase<Dest> &dest) const;
+
+ protected:
+ void pardisoRelease()
+ {
+ if(m_isInitialized) // Factorization ran at least once
+ {
+ internal::pardiso_run_selector<StorageIndex>::run(m_pt, 1, 1, m_type, -1, internal::convert_index<StorageIndex>(m_size),0, 0, 0, m_perm.data(), 0,
+ m_iparm.data(), m_msglvl, NULL, NULL);
+ m_isInitialized = false;
+ }
+ }
+
+ void pardisoInit(int type)
+ {
+ m_type = type;
+ bool symmetric = std::abs(m_type) < 10;
+ m_iparm[0] = 1; // No solver default
+ m_iparm[1] = 2; // use Metis for the ordering
+ m_iparm[2] = 0; // Reserved. Set to zero. (??Numbers of processors, value of OMP_NUM_THREADS??)
+ m_iparm[3] = 0; // No iterative-direct algorithm
+ m_iparm[4] = 0; // No user fill-in reducing permutation
+ m_iparm[5] = 0; // Write solution into x, b is left unchanged
+ m_iparm[6] = 0; // Not in use
+ m_iparm[7] = 2; // Max numbers of iterative refinement steps
+ m_iparm[8] = 0; // Not in use
+ m_iparm[9] = 13; // Perturb the pivot elements with 1E-13
+ m_iparm[10] = symmetric ? 0 : 1; // Use nonsymmetric permutation and scaling MPS
+ m_iparm[11] = 0; // Not in use
+ m_iparm[12] = symmetric ? 0 : 1; // Maximum weighted matching algorithm is switched-off (default for symmetric).
+ // Try m_iparm[12] = 1 in case of inappropriate accuracy
+ m_iparm[13] = 0; // Output: Number of perturbed pivots
+ m_iparm[14] = 0; // Not in use
+ m_iparm[15] = 0; // Not in use
+ m_iparm[16] = 0; // Not in use
+ m_iparm[17] = -1; // Output: Number of nonzeros in the factor LU
+ m_iparm[18] = -1; // Output: Mflops for LU factorization
+ m_iparm[19] = 0; // Output: Numbers of CG Iterations
+
+ m_iparm[20] = 0; // 1x1 pivoting
+ m_iparm[26] = 0; // No matrix checker
+ m_iparm[27] = (sizeof(RealScalar) == 4) ? 1 : 0;
+ m_iparm[34] = 1; // C indexing
+ m_iparm[36] = 0; // CSR
+ m_iparm[59] = 0; // 0 - In-Core ; 1 - Automatic switch between In-Core and Out-of-Core modes ; 2 - Out-of-Core
+
+ memset(m_pt, 0, sizeof(m_pt));
+ }
+
+ protected:
+ // cached data to reduce reallocation, etc.
+
+ void manageErrorCode(Index error) const
+ {
+ switch(error)
+ {
+ case 0:
+ m_info = Success;
+ break;
+ case -4:
+ case -7:
+ m_info = NumericalIssue;
+ break;
+ default:
+ m_info = InvalidInput;
+ }
+ }
+
+ mutable SparseMatrixType m_matrix;
+ mutable ComputationInfo m_info;
+ bool m_analysisIsOk, m_factorizationIsOk;
+ StorageIndex m_type, m_msglvl;
+ mutable void *m_pt[64];
+ mutable ParameterType m_iparm;
+ mutable IntColVectorType m_perm;
+ Index m_size;
+
+};
+
+template<class Derived>
+Derived& PardisoImpl<Derived>::compute(const MatrixType& a)
+{
+ m_size = a.rows();
+ eigen_assert(a.rows() == a.cols());
+
+ pardisoRelease();
+ m_perm.setZero(m_size);
+ derived().getMatrix(a);
+
+ Index error;
+ error = internal::pardiso_run_selector<StorageIndex>::run(m_pt, 1, 1, m_type, 12, internal::convert_index<StorageIndex>(m_size),
+ m_matrix.valuePtr(), m_matrix.outerIndexPtr(), m_matrix.innerIndexPtr(),
+ m_perm.data(), 0, m_iparm.data(), m_msglvl, NULL, NULL);
+ manageErrorCode(error);
+ m_analysisIsOk = true;
+ m_factorizationIsOk = true;
+ m_isInitialized = true;
+ return derived();
+}
+
+template<class Derived>
+Derived& PardisoImpl<Derived>::analyzePattern(const MatrixType& a)
+{
+ m_size = a.rows();
+ eigen_assert(m_size == a.cols());
+
+ pardisoRelease();
+ m_perm.setZero(m_size);
+ derived().getMatrix(a);
+
+ Index error;
+ error = internal::pardiso_run_selector<StorageIndex>::run(m_pt, 1, 1, m_type, 11, internal::convert_index<StorageIndex>(m_size),
+ m_matrix.valuePtr(), m_matrix.outerIndexPtr(), m_matrix.innerIndexPtr(),
+ m_perm.data(), 0, m_iparm.data(), m_msglvl, NULL, NULL);
+
+ manageErrorCode(error);
+ m_analysisIsOk = true;
+ m_factorizationIsOk = false;
+ m_isInitialized = true;
+ return derived();
+}
+
+template<class Derived>
+Derived& PardisoImpl<Derived>::factorize(const MatrixType& a)
+{
+ eigen_assert(m_analysisIsOk && "You must first call analyzePattern()");
+ eigen_assert(m_size == a.rows() && m_size == a.cols());
+
+ derived().getMatrix(a);
+
+ Index error;
+ error = internal::pardiso_run_selector<StorageIndex>::run(m_pt, 1, 1, m_type, 22, internal::convert_index<StorageIndex>(m_size),
+ m_matrix.valuePtr(), m_matrix.outerIndexPtr(), m_matrix.innerIndexPtr(),
+ m_perm.data(), 0, m_iparm.data(), m_msglvl, NULL, NULL);
+
+ manageErrorCode(error);
+ m_factorizationIsOk = true;
+ return derived();
+}
+
+template<class Derived>
+template<typename BDerived,typename XDerived>
+void PardisoImpl<Derived>::_solve_impl(const MatrixBase<BDerived> &b, MatrixBase<XDerived>& x) const
+{
+ if(m_iparm[0] == 0) // Factorization was not computed
+ {
+ m_info = InvalidInput;
+ return;
+ }
+
+ //Index n = m_matrix.rows();
+ Index nrhs = Index(b.cols());
+ eigen_assert(m_size==b.rows());
+ eigen_assert(((MatrixBase<BDerived>::Flags & RowMajorBit) == 0 || nrhs == 1) && "Row-major right hand sides are not supported");
+ eigen_assert(((MatrixBase<XDerived>::Flags & RowMajorBit) == 0 || nrhs == 1) && "Row-major matrices of unknowns are not supported");
+ eigen_assert(((nrhs == 1) || b.outerStride() == b.rows()));
+
+
+// switch (transposed) {
+// case SvNoTrans : m_iparm[11] = 0 ; break;
+// case SvTranspose : m_iparm[11] = 2 ; break;
+// case SvAdjoint : m_iparm[11] = 1 ; break;
+// default:
+// //std::cerr << "Eigen: transposition option \"" << transposed << "\" not supported by the PARDISO backend\n";
+// m_iparm[11] = 0;
+// }
+
+ Scalar* rhs_ptr = const_cast<Scalar*>(b.derived().data());
+ Matrix<Scalar,Dynamic,Dynamic,ColMajor> tmp;
+
+ // Pardiso cannot solve in-place
+ if(rhs_ptr == x.derived().data())
+ {
+ tmp = b;
+ rhs_ptr = tmp.data();
+ }
+
+ Index error;
+ error = internal::pardiso_run_selector<StorageIndex>::run(m_pt, 1, 1, m_type, 33, internal::convert_index<StorageIndex>(m_size),
+ m_matrix.valuePtr(), m_matrix.outerIndexPtr(), m_matrix.innerIndexPtr(),
+ m_perm.data(), internal::convert_index<StorageIndex>(nrhs), m_iparm.data(), m_msglvl,
+ rhs_ptr, x.derived().data());
+
+ manageErrorCode(error);
+}
+
+
+/** \ingroup PardisoSupport_Module
+ * \class PardisoLU
+ * \brief A sparse direct LU factorization and solver based on the PARDISO library
+ *
+ * This class allows to solve for A.X = B sparse linear problems via a direct LU factorization
+ * using the Intel MKL PARDISO library. The sparse matrix A must be squared and invertible.
+ * The vectors or matrices X and B can be either dense or sparse.
+ *
+ * By default, it runs in in-core mode. To enable PARDISO's out-of-core feature, set:
+ * \code solver.pardisoParameterArray()[59] = 1; \endcode
+ *
+ * \tparam MatrixType_ the type of the sparse matrix A, it must be a SparseMatrix<>
+ *
+ * \implsparsesolverconcept
+ *
+ * \sa \ref TutorialSparseSolverConcept, class SparseLU
+ */
+template<typename MatrixType>
+class PardisoLU : public PardisoImpl< PardisoLU<MatrixType> >
+{
+ protected:
+ typedef PardisoImpl<PardisoLU> Base;
+ using Base::pardisoInit;
+ using Base::m_matrix;
+ friend class PardisoImpl< PardisoLU<MatrixType> >;
+
+ public:
+
+ typedef typename Base::Scalar Scalar;
+ typedef typename Base::RealScalar RealScalar;
+
+ using Base::compute;
+ using Base::solve;
+
+ PardisoLU()
+ : Base()
+ {
+ pardisoInit(Base::ScalarIsComplex ? 13 : 11);
+ }
+
+ explicit PardisoLU(const MatrixType& matrix)
+ : Base()
+ {
+ pardisoInit(Base::ScalarIsComplex ? 13 : 11);
+ compute(matrix);
+ }
+ protected:
+ void getMatrix(const MatrixType& matrix)
+ {
+ m_matrix = matrix;
+ m_matrix.makeCompressed();
+ }
+};
+
+/** \ingroup PardisoSupport_Module
+ * \class PardisoLLT
+ * \brief A sparse direct Cholesky (LLT) factorization and solver based on the PARDISO library
+ *
+ * This class allows to solve for A.X = B sparse linear problems via a LL^T Cholesky factorization
+ * using the Intel MKL PARDISO library. The sparse matrix A must be selfajoint and positive definite.
+ * The vectors or matrices X and B can be either dense or sparse.
+ *
+ * By default, it runs in in-core mode. To enable PARDISO's out-of-core feature, set:
+ * \code solver.pardisoParameterArray()[59] = 1; \endcode
+ *
+ * \tparam MatrixType the type of the sparse matrix A, it must be a SparseMatrix<>
+ * \tparam UpLo can be any bitwise combination of Upper, Lower. The default is Upper, meaning only the upper triangular part has to be used.
+ * Upper|Lower can be used to tell both triangular parts can be used as input.
+ *
+ * \implsparsesolverconcept
+ *
+ * \sa \ref TutorialSparseSolverConcept, class SimplicialLLT
+ */
+template<typename MatrixType, int UpLo_>
+class PardisoLLT : public PardisoImpl< PardisoLLT<MatrixType,UpLo_> >
+{
+ protected:
+ typedef PardisoImpl< PardisoLLT<MatrixType,UpLo_> > Base;
+ using Base::pardisoInit;
+ using Base::m_matrix;
+ friend class PardisoImpl< PardisoLLT<MatrixType,UpLo_> >;
+
+ public:
+
+ typedef typename Base::Scalar Scalar;
+ typedef typename Base::RealScalar RealScalar;
+ typedef typename Base::StorageIndex StorageIndex;
+ enum { UpLo = UpLo_ };
+ using Base::compute;
+
+ PardisoLLT()
+ : Base()
+ {
+ pardisoInit(Base::ScalarIsComplex ? 4 : 2);
+ }
+
+ explicit PardisoLLT(const MatrixType& matrix)
+ : Base()
+ {
+ pardisoInit(Base::ScalarIsComplex ? 4 : 2);
+ compute(matrix);
+ }
+
+ protected:
+
+ void getMatrix(const MatrixType& matrix)
+ {
+ // PARDISO supports only upper, row-major matrices
+ PermutationMatrix<Dynamic,Dynamic,StorageIndex> p_null;
+ m_matrix.resize(matrix.rows(), matrix.cols());
+ m_matrix.template selfadjointView<Upper>() = matrix.template selfadjointView<UpLo>().twistedBy(p_null);
+ m_matrix.makeCompressed();
+ }
+};
+
+/** \ingroup PardisoSupport_Module
+ * \class PardisoLDLT
+ * \brief A sparse direct Cholesky (LDLT) factorization and solver based on the PARDISO library
+ *
+ * This class allows to solve for A.X = B sparse linear problems via a LDL^T Cholesky factorization
+ * using the Intel MKL PARDISO library. The sparse matrix A is assumed to be selfajoint and positive definite.
+ * For complex matrices, A can also be symmetric only, see the \a Options template parameter.
+ * The vectors or matrices X and B can be either dense or sparse.
+ *
+ * By default, it runs in in-core mode. To enable PARDISO's out-of-core feature, set:
+ * \code solver.pardisoParameterArray()[59] = 1; \endcode
+ *
+ * \tparam MatrixType the type of the sparse matrix A, it must be a SparseMatrix<>
+ * \tparam Options can be any bitwise combination of Upper, Lower, and Symmetric. The default is Upper, meaning only the upper triangular part has to be used.
+ * Symmetric can be used for symmetric, non-selfadjoint complex matrices, the default being to assume a selfadjoint matrix.
+ * Upper|Lower can be used to tell both triangular parts can be used as input.
+ *
+ * \implsparsesolverconcept
+ *
+ * \sa \ref TutorialSparseSolverConcept, class SimplicialLDLT
+ */
+template<typename MatrixType, int Options>
+class PardisoLDLT : public PardisoImpl< PardisoLDLT<MatrixType,Options> >
+{
+ protected:
+ typedef PardisoImpl< PardisoLDLT<MatrixType,Options> > Base;
+ using Base::pardisoInit;
+ using Base::m_matrix;
+ friend class PardisoImpl< PardisoLDLT<MatrixType,Options> >;
+
+ public:
+
+ typedef typename Base::Scalar Scalar;
+ typedef typename Base::RealScalar RealScalar;
+ typedef typename Base::StorageIndex StorageIndex;
+ using Base::compute;
+ enum { UpLo = Options&(Upper|Lower) };
+
+ PardisoLDLT()
+ : Base()
+ {
+ pardisoInit(Base::ScalarIsComplex ? ( bool(Options&Symmetric) ? 6 : -4 ) : -2);
+ }
+
+ explicit PardisoLDLT(const MatrixType& matrix)
+ : Base()
+ {
+ pardisoInit(Base::ScalarIsComplex ? ( bool(Options&Symmetric) ? 6 : -4 ) : -2);
+ compute(matrix);
+ }
+
+ void getMatrix(const MatrixType& matrix)
+ {
+ // PARDISO supports only upper, row-major matrices
+ PermutationMatrix<Dynamic,Dynamic,StorageIndex> p_null;
+ m_matrix.resize(matrix.rows(), matrix.cols());
+ m_matrix.template selfadjointView<Upper>() = matrix.template selfadjointView<UpLo>().twistedBy(p_null);
+ m_matrix.makeCompressed();
+ }
+};
+
+} // end namespace Eigen
+
+#endif // EIGEN_PARDISOSUPPORT_H
diff --git a/Eigen/src/QR/ColPivHouseholderQR.h b/Eigen/src/QR/ColPivHouseholderQR.h
new file mode 100644
index 0000000..c906997
--- /dev/null
+++ b/Eigen/src/QR/ColPivHouseholderQR.h
@@ -0,0 +1,696 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2009 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_COLPIVOTINGHOUSEHOLDERQR_H
+#define EIGEN_COLPIVOTINGHOUSEHOLDERQR_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+template<typename MatrixType_> struct traits<ColPivHouseholderQR<MatrixType_> >
+ : traits<MatrixType_>
+{
+ typedef MatrixXpr XprKind;
+ typedef SolverStorage StorageKind;
+ typedef int StorageIndex;
+ enum { Flags = 0 };
+};
+
+} // end namespace internal
+
+/** \ingroup QR_Module
+ *
+ * \class ColPivHouseholderQR
+ *
+ * \brief Householder rank-revealing QR decomposition of a matrix with column-pivoting
+ *
+ * \tparam MatrixType_ the type of the matrix of which we are computing the QR decomposition
+ *
+ * This class performs a rank-revealing QR decomposition of a matrix \b A into matrices \b P, \b Q and \b R
+ * such that
+ * \f[
+ * \mathbf{A} \, \mathbf{P} = \mathbf{Q} \, \mathbf{R}
+ * \f]
+ * by using Householder transformations. Here, \b P is a permutation matrix, \b Q a unitary matrix and \b R an
+ * upper triangular matrix.
+ *
+ * This decomposition performs column pivoting in order to be rank-revealing and improve
+ * numerical stability. It is slower than HouseholderQR, and faster than FullPivHouseholderQR.
+ *
+ * This class supports the \link InplaceDecomposition inplace decomposition \endlink mechanism.
+ *
+ * \sa MatrixBase::colPivHouseholderQr()
+ */
+template<typename MatrixType_> class ColPivHouseholderQR
+ : public SolverBase<ColPivHouseholderQR<MatrixType_> >
+{
+ public:
+
+ typedef MatrixType_ MatrixType;
+ typedef SolverBase<ColPivHouseholderQR> Base;
+ friend class SolverBase<ColPivHouseholderQR>;
+
+ EIGEN_GENERIC_PUBLIC_INTERFACE(ColPivHouseholderQR)
+ enum {
+ MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime,
+ MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime
+ };
+ typedef typename internal::plain_diag_type<MatrixType>::type HCoeffsType;
+ typedef PermutationMatrix<ColsAtCompileTime, MaxColsAtCompileTime> PermutationType;
+ typedef typename internal::plain_row_type<MatrixType, Index>::type IntRowVectorType;
+ typedef typename internal::plain_row_type<MatrixType>::type RowVectorType;
+ typedef typename internal::plain_row_type<MatrixType, RealScalar>::type RealRowVectorType;
+ typedef HouseholderSequence<MatrixType,internal::remove_all_t<typename HCoeffsType::ConjugateReturnType>> HouseholderSequenceType;
+ typedef typename MatrixType::PlainObject PlainObject;
+
+ private:
+
+ typedef typename PermutationType::StorageIndex PermIndexType;
+
+ public:
+
+ /**
+ * \brief Default Constructor.
+ *
+ * The default constructor is useful in cases in which the user intends to
+ * perform decompositions via ColPivHouseholderQR::compute(const MatrixType&).
+ */
+ ColPivHouseholderQR()
+ : m_qr(),
+ m_hCoeffs(),
+ m_colsPermutation(),
+ m_colsTranspositions(),
+ m_temp(),
+ m_colNormsUpdated(),
+ m_colNormsDirect(),
+ m_isInitialized(false),
+ m_usePrescribedThreshold(false) {}
+
+ /** \brief Default Constructor with memory preallocation
+ *
+ * Like the default constructor but with preallocation of the internal data
+ * according to the specified problem \a size.
+ * \sa ColPivHouseholderQR()
+ */
+ ColPivHouseholderQR(Index rows, Index cols)
+ : m_qr(rows, cols),
+ m_hCoeffs((std::min)(rows,cols)),
+ m_colsPermutation(PermIndexType(cols)),
+ m_colsTranspositions(cols),
+ m_temp(cols),
+ m_colNormsUpdated(cols),
+ m_colNormsDirect(cols),
+ m_isInitialized(false),
+ m_usePrescribedThreshold(false) {}
+
+ /** \brief Constructs a QR factorization from a given matrix
+ *
+ * This constructor computes the QR factorization of the matrix \a matrix by calling
+ * the method compute(). It is a short cut for:
+ *
+ * \code
+ * ColPivHouseholderQR<MatrixType> qr(matrix.rows(), matrix.cols());
+ * qr.compute(matrix);
+ * \endcode
+ *
+ * \sa compute()
+ */
+ template<typename InputType>
+ explicit ColPivHouseholderQR(const EigenBase<InputType>& matrix)
+ : m_qr(matrix.rows(), matrix.cols()),
+ m_hCoeffs((std::min)(matrix.rows(),matrix.cols())),
+ m_colsPermutation(PermIndexType(matrix.cols())),
+ m_colsTranspositions(matrix.cols()),
+ m_temp(matrix.cols()),
+ m_colNormsUpdated(matrix.cols()),
+ m_colNormsDirect(matrix.cols()),
+ m_isInitialized(false),
+ m_usePrescribedThreshold(false)
+ {
+ compute(matrix.derived());
+ }
+
+ /** \brief Constructs a QR factorization from a given matrix
+ *
+ * This overloaded constructor is provided for \link InplaceDecomposition inplace decomposition \endlink when \c MatrixType is a Eigen::Ref.
+ *
+ * \sa ColPivHouseholderQR(const EigenBase&)
+ */
+ template<typename InputType>
+ explicit ColPivHouseholderQR(EigenBase<InputType>& matrix)
+ : m_qr(matrix.derived()),
+ m_hCoeffs((std::min)(matrix.rows(),matrix.cols())),
+ m_colsPermutation(PermIndexType(matrix.cols())),
+ m_colsTranspositions(matrix.cols()),
+ m_temp(matrix.cols()),
+ m_colNormsUpdated(matrix.cols()),
+ m_colNormsDirect(matrix.cols()),
+ m_isInitialized(false),
+ m_usePrescribedThreshold(false)
+ {
+ computeInPlace();
+ }
+
+ #ifdef EIGEN_PARSED_BY_DOXYGEN
+ /** This method finds a solution x to the equation Ax=b, where A is the matrix of which
+ * *this is the QR decomposition, if any exists.
+ *
+ * \param b the right-hand-side of the equation to solve.
+ *
+ * \returns a solution.
+ *
+ * \note_about_checking_solutions
+ *
+ * \note_about_arbitrary_choice_of_solution
+ *
+ * Example: \include ColPivHouseholderQR_solve.cpp
+ * Output: \verbinclude ColPivHouseholderQR_solve.out
+ */
+ template<typename Rhs>
+ inline const Solve<ColPivHouseholderQR, Rhs>
+ solve(const MatrixBase<Rhs>& b) const;
+ #endif
+
+ HouseholderSequenceType householderQ() const;
+ HouseholderSequenceType matrixQ() const
+ {
+ return householderQ();
+ }
+
+ /** \returns a reference to the matrix where the Householder QR decomposition is stored
+ */
+ const MatrixType& matrixQR() const
+ {
+ eigen_assert(m_isInitialized && "ColPivHouseholderQR is not initialized.");
+ return m_qr;
+ }
+
+ /** \returns a reference to the matrix where the result Householder QR is stored
+ * \warning The strict lower part of this matrix contains internal values.
+ * Only the upper triangular part should be referenced. To get it, use
+ * \code matrixR().template triangularView<Upper>() \endcode
+ * For rank-deficient matrices, use
+ * \code
+ * matrixR().topLeftCorner(rank(), rank()).template triangularView<Upper>()
+ * \endcode
+ */
+ const MatrixType& matrixR() const
+ {
+ eigen_assert(m_isInitialized && "ColPivHouseholderQR is not initialized.");
+ return m_qr;
+ }
+
+ template<typename InputType>
+ ColPivHouseholderQR& compute(const EigenBase<InputType>& matrix);
+
+ /** \returns a const reference to the column permutation matrix */
+ const PermutationType& colsPermutation() const
+ {
+ eigen_assert(m_isInitialized && "ColPivHouseholderQR is not initialized.");
+ return m_colsPermutation;
+ }
+
+ /** \returns the determinant of the matrix of which
+ * *this is the QR decomposition. It has only linear complexity
+ * (that is, O(n) where n is the dimension of the square matrix)
+ * as the QR decomposition has already been computed.
+ *
+ * \note This is only for square matrices.
+ *
+ * \warning a determinant can be very big or small, so for matrices
+ * of large enough dimension, there is a risk of overflow/underflow.
+ * One way to work around that is to use logAbsDeterminant() instead.
+ *
+ * \sa absDeterminant(), logAbsDeterminant(), MatrixBase::determinant()
+ */
+ typename MatrixType::Scalar determinant() const;
+
+ /** \returns the absolute value of the determinant of the matrix of which
+ * *this is the QR decomposition. It has only linear complexity
+ * (that is, O(n) where n is the dimension of the square matrix)
+ * as the QR decomposition has already been computed.
+ *
+ * \note This is only for square matrices.
+ *
+ * \warning a determinant can be very big or small, so for matrices
+ * of large enough dimension, there is a risk of overflow/underflow.
+ * One way to work around that is to use logAbsDeterminant() instead.
+ *
+ * \sa determinant(), logAbsDeterminant(), MatrixBase::determinant()
+ */
+ typename MatrixType::RealScalar absDeterminant() const;
+
+ /** \returns the natural log of the absolute value of the determinant of the matrix of which
+ * *this is the QR decomposition. It has only linear complexity
+ * (that is, O(n) where n is the dimension of the square matrix)
+ * as the QR decomposition has already been computed.
+ *
+ * \note This is only for square matrices.
+ *
+ * \note This method is useful to work around the risk of overflow/underflow that's inherent
+ * to determinant computation.
+ *
+ * \sa determinant(), absDeterminant(), MatrixBase::determinant()
+ */
+ typename MatrixType::RealScalar logAbsDeterminant() const;
+
+ /** \returns the rank of the matrix of which *this is the QR decomposition.
+ *
+ * \note This method has to determine which pivots should be considered nonzero.
+ * For that, it uses the threshold value that you can control by calling
+ * setThreshold(const RealScalar&).
+ */
+ inline Index rank() const
+ {
+ using std::abs;
+ eigen_assert(m_isInitialized && "ColPivHouseholderQR is not initialized.");
+ RealScalar premultiplied_threshold = abs(m_maxpivot) * threshold();
+ Index result = 0;
+ for(Index i = 0; i < m_nonzero_pivots; ++i)
+ result += (abs(m_qr.coeff(i,i)) > premultiplied_threshold);
+ return result;
+ }
+
+ /** \returns the dimension of the kernel of the matrix of which *this is the QR decomposition.
+ *
+ * \note This method has to determine which pivots should be considered nonzero.
+ * For that, it uses the threshold value that you can control by calling
+ * setThreshold(const RealScalar&).
+ */
+ inline Index dimensionOfKernel() const
+ {
+ eigen_assert(m_isInitialized && "ColPivHouseholderQR is not initialized.");
+ return cols() - rank();
+ }
+
+ /** \returns true if the matrix of which *this is the QR decomposition represents an injective
+ * linear map, i.e. has trivial kernel; false otherwise.
+ *
+ * \note This method has to determine which pivots should be considered nonzero.
+ * For that, it uses the threshold value that you can control by calling
+ * setThreshold(const RealScalar&).
+ */
+ inline bool isInjective() const
+ {
+ eigen_assert(m_isInitialized && "ColPivHouseholderQR is not initialized.");
+ return rank() == cols();
+ }
+
+ /** \returns true if the matrix of which *this is the QR decomposition represents a surjective
+ * linear map; false otherwise.
+ *
+ * \note This method has to determine which pivots should be considered nonzero.
+ * For that, it uses the threshold value that you can control by calling
+ * setThreshold(const RealScalar&).
+ */
+ inline bool isSurjective() const
+ {
+ eigen_assert(m_isInitialized && "ColPivHouseholderQR is not initialized.");
+ return rank() == rows();
+ }
+
+ /** \returns true if the matrix of which *this is the QR decomposition is invertible.
+ *
+ * \note This method has to determine which pivots should be considered nonzero.
+ * For that, it uses the threshold value that you can control by calling
+ * setThreshold(const RealScalar&).
+ */
+ inline bool isInvertible() const
+ {
+ eigen_assert(m_isInitialized && "ColPivHouseholderQR is not initialized.");
+ return isInjective() && isSurjective();
+ }
+
+ /** \returns the inverse of the matrix of which *this is the QR decomposition.
+ *
+ * \note If this matrix is not invertible, the returned matrix has undefined coefficients.
+ * Use isInvertible() to first determine whether this matrix is invertible.
+ */
+ inline const Inverse<ColPivHouseholderQR> inverse() const
+ {
+ eigen_assert(m_isInitialized && "ColPivHouseholderQR is not initialized.");
+ return Inverse<ColPivHouseholderQR>(*this);
+ }
+
+ inline Index rows() const { return m_qr.rows(); }
+ inline Index cols() const { return m_qr.cols(); }
+
+ /** \returns a const reference to the vector of Householder coefficients used to represent the factor \c Q.
+ *
+ * For advanced uses only.
+ */
+ const HCoeffsType& hCoeffs() const { return m_hCoeffs; }
+
+ /** Allows to prescribe a threshold to be used by certain methods, such as rank(),
+ * who need to determine when pivots are to be considered nonzero. This is not used for the
+ * QR decomposition itself.
+ *
+ * When it needs to get the threshold value, Eigen calls threshold(). By default, this
+ * uses a formula to automatically determine a reasonable threshold.
+ * Once you have called the present method setThreshold(const RealScalar&),
+ * your value is used instead.
+ *
+ * \param threshold The new value to use as the threshold.
+ *
+ * A pivot will be considered nonzero if its absolute value is strictly greater than
+ * \f$ \vert pivot \vert \leqslant threshold \times \vert maxpivot \vert \f$
+ * where maxpivot is the biggest pivot.
+ *
+ * If you want to come back to the default behavior, call setThreshold(Default_t)
+ */
+ ColPivHouseholderQR& setThreshold(const RealScalar& threshold)
+ {
+ m_usePrescribedThreshold = true;
+ m_prescribedThreshold = threshold;
+ return *this;
+ }
+
+ /** Allows to come back to the default behavior, letting Eigen use its default formula for
+ * determining the threshold.
+ *
+ * You should pass the special object Eigen::Default as parameter here.
+ * \code qr.setThreshold(Eigen::Default); \endcode
+ *
+ * See the documentation of setThreshold(const RealScalar&).
+ */
+ ColPivHouseholderQR& setThreshold(Default_t)
+ {
+ m_usePrescribedThreshold = false;
+ return *this;
+ }
+
+ /** Returns the threshold that will be used by certain methods such as rank().
+ *
+ * See the documentation of setThreshold(const RealScalar&).
+ */
+ RealScalar threshold() const
+ {
+ eigen_assert(m_isInitialized || m_usePrescribedThreshold);
+ return m_usePrescribedThreshold ? m_prescribedThreshold
+ // this formula comes from experimenting (see "LU precision tuning" thread on the list)
+ // and turns out to be identical to Higham's formula used already in LDLt.
+ : NumTraits<Scalar>::epsilon() * RealScalar(m_qr.diagonalSize());
+ }
+
+ /** \returns the number of nonzero pivots in the QR decomposition.
+ * Here nonzero is meant in the exact sense, not in a fuzzy sense.
+ * So that notion isn't really intrinsically interesting, but it is
+ * still useful when implementing algorithms.
+ *
+ * \sa rank()
+ */
+ inline Index nonzeroPivots() const
+ {
+ eigen_assert(m_isInitialized && "ColPivHouseholderQR is not initialized.");
+ return m_nonzero_pivots;
+ }
+
+ /** \returns the absolute value of the biggest pivot, i.e. the biggest
+ * diagonal coefficient of R.
+ */
+ RealScalar maxPivot() const { return m_maxpivot; }
+
+ /** \brief Reports whether the QR factorization was successful.
+ *
+ * \note This function always returns \c Success. It is provided for compatibility
+ * with other factorization routines.
+ * \returns \c Success
+ */
+ ComputationInfo info() const
+ {
+ eigen_assert(m_isInitialized && "Decomposition is not initialized.");
+ return Success;
+ }
+
+ #ifndef EIGEN_PARSED_BY_DOXYGEN
+ template<typename RhsType, typename DstType>
+ void _solve_impl(const RhsType &rhs, DstType &dst) const;
+
+ template<bool Conjugate, typename RhsType, typename DstType>
+ void _solve_impl_transposed(const RhsType &rhs, DstType &dst) const;
+ #endif
+
+ protected:
+
+ friend class CompleteOrthogonalDecomposition<MatrixType>;
+
+ EIGEN_STATIC_ASSERT_NON_INTEGER(Scalar)
+
+ void computeInPlace();
+
+ MatrixType m_qr;
+ HCoeffsType m_hCoeffs;
+ PermutationType m_colsPermutation;
+ IntRowVectorType m_colsTranspositions;
+ RowVectorType m_temp;
+ RealRowVectorType m_colNormsUpdated;
+ RealRowVectorType m_colNormsDirect;
+ bool m_isInitialized, m_usePrescribedThreshold;
+ RealScalar m_prescribedThreshold, m_maxpivot;
+ Index m_nonzero_pivots;
+ Index m_det_p;
+};
+
+template<typename MatrixType>
+typename MatrixType::Scalar ColPivHouseholderQR<MatrixType>::determinant() const
+{
+ eigen_assert(m_isInitialized && "HouseholderQR is not initialized.");
+ eigen_assert(m_qr.rows() == m_qr.cols() && "You can't take the determinant of a non-square matrix!");
+ Scalar detQ;
+ internal::householder_determinant<HCoeffsType, Scalar, NumTraits<Scalar>::IsComplex>::run(m_hCoeffs, detQ);
+ return m_qr.diagonal().prod() * detQ * Scalar(m_det_p);
+}
+
+template<typename MatrixType>
+typename MatrixType::RealScalar ColPivHouseholderQR<MatrixType>::absDeterminant() const
+{
+ using std::abs;
+ eigen_assert(m_isInitialized && "ColPivHouseholderQR is not initialized.");
+ eigen_assert(m_qr.rows() == m_qr.cols() && "You can't take the determinant of a non-square matrix!");
+ return abs(m_qr.diagonal().prod());
+}
+
+template<typename MatrixType>
+typename MatrixType::RealScalar ColPivHouseholderQR<MatrixType>::logAbsDeterminant() const
+{
+ eigen_assert(m_isInitialized && "ColPivHouseholderQR is not initialized.");
+ eigen_assert(m_qr.rows() == m_qr.cols() && "You can't take the determinant of a non-square matrix!");
+ return m_qr.diagonal().cwiseAbs().array().log().sum();
+}
+
+/** Performs the QR factorization of the given matrix \a matrix. The result of
+ * the factorization is stored into \c *this, and a reference to \c *this
+ * is returned.
+ *
+ * \sa class ColPivHouseholderQR, ColPivHouseholderQR(const MatrixType&)
+ */
+template<typename MatrixType>
+template<typename InputType>
+ColPivHouseholderQR<MatrixType>& ColPivHouseholderQR<MatrixType>::compute(const EigenBase<InputType>& matrix)
+{
+ m_qr = matrix.derived();
+ computeInPlace();
+ return *this;
+}
+
+template<typename MatrixType>
+void ColPivHouseholderQR<MatrixType>::computeInPlace()
+{
+ // the column permutation is stored as int indices, so just to be sure:
+ eigen_assert(m_qr.cols()<=NumTraits<int>::highest());
+
+ using std::abs;
+
+ Index rows = m_qr.rows();
+ Index cols = m_qr.cols();
+ Index size = m_qr.diagonalSize();
+
+ m_hCoeffs.resize(size);
+
+ m_temp.resize(cols);
+
+ m_colsTranspositions.resize(m_qr.cols());
+ Index number_of_transpositions = 0;
+
+ m_colNormsUpdated.resize(cols);
+ m_colNormsDirect.resize(cols);
+ for (Index k = 0; k < cols; ++k) {
+ // colNormsDirect(k) caches the most recent directly computed norm of
+ // column k.
+ m_colNormsDirect.coeffRef(k) = m_qr.col(k).norm();
+ m_colNormsUpdated.coeffRef(k) = m_colNormsDirect.coeffRef(k);
+ }
+
+ RealScalar threshold_helper = numext::abs2<RealScalar>(m_colNormsUpdated.maxCoeff() * NumTraits<RealScalar>::epsilon()) / RealScalar(rows);
+ RealScalar norm_downdate_threshold = numext::sqrt(NumTraits<RealScalar>::epsilon());
+
+ m_nonzero_pivots = size; // the generic case is that in which all pivots are nonzero (invertible case)
+ m_maxpivot = RealScalar(0);
+
+ for(Index k = 0; k < size; ++k)
+ {
+ // first, we look up in our table m_colNormsUpdated which column has the biggest norm
+ Index biggest_col_index;
+ RealScalar biggest_col_sq_norm = numext::abs2(m_colNormsUpdated.tail(cols-k).maxCoeff(&biggest_col_index));
+ biggest_col_index += k;
+
+ // Track the number of meaningful pivots but do not stop the decomposition to make
+ // sure that the initial matrix is properly reproduced. See bug 941.
+ if(m_nonzero_pivots==size && biggest_col_sq_norm < threshold_helper * RealScalar(rows-k))
+ m_nonzero_pivots = k;
+
+ // apply the transposition to the columns
+ m_colsTranspositions.coeffRef(k) = biggest_col_index;
+ if(k != biggest_col_index) {
+ m_qr.col(k).swap(m_qr.col(biggest_col_index));
+ std::swap(m_colNormsUpdated.coeffRef(k), m_colNormsUpdated.coeffRef(biggest_col_index));
+ std::swap(m_colNormsDirect.coeffRef(k), m_colNormsDirect.coeffRef(biggest_col_index));
+ ++number_of_transpositions;
+ }
+
+ // generate the householder vector, store it below the diagonal
+ RealScalar beta;
+ m_qr.col(k).tail(rows-k).makeHouseholderInPlace(m_hCoeffs.coeffRef(k), beta);
+
+ // apply the householder transformation to the diagonal coefficient
+ m_qr.coeffRef(k,k) = beta;
+
+ // remember the maximum absolute value of diagonal coefficients
+ if(abs(beta) > m_maxpivot) m_maxpivot = abs(beta);
+
+ // apply the householder transformation
+ m_qr.bottomRightCorner(rows-k, cols-k-1)
+ .applyHouseholderOnTheLeft(m_qr.col(k).tail(rows-k-1), m_hCoeffs.coeffRef(k), &m_temp.coeffRef(k+1));
+
+ // update our table of norms of the columns
+ for (Index j = k + 1; j < cols; ++j) {
+ // The following implements the stable norm downgrade step discussed in
+ // http://www.netlib.org/lapack/lawnspdf/lawn176.pdf
+ // and used in LAPACK routines xGEQPF and xGEQP3.
+ // See lines 278-297 in http://www.netlib.org/lapack/explore-html/dc/df4/sgeqpf_8f_source.html
+ if (!numext::is_exactly_zero(m_colNormsUpdated.coeffRef(j))) {
+ RealScalar temp = abs(m_qr.coeffRef(k, j)) / m_colNormsUpdated.coeffRef(j);
+ temp = (RealScalar(1) + temp) * (RealScalar(1) - temp);
+ temp = temp < RealScalar(0) ? RealScalar(0) : temp;
+ RealScalar temp2 = temp * numext::abs2<RealScalar>(m_colNormsUpdated.coeffRef(j) /
+ m_colNormsDirect.coeffRef(j));
+ if (temp2 <= norm_downdate_threshold) {
+ // The updated norm has become too inaccurate so re-compute the column
+ // norm directly.
+ m_colNormsDirect.coeffRef(j) = m_qr.col(j).tail(rows - k - 1).norm();
+ m_colNormsUpdated.coeffRef(j) = m_colNormsDirect.coeffRef(j);
+ } else {
+ m_colNormsUpdated.coeffRef(j) *= numext::sqrt(temp);
+ }
+ }
+ }
+ }
+
+ m_colsPermutation.setIdentity(PermIndexType(cols));
+ for(PermIndexType k = 0; k < size/*m_nonzero_pivots*/; ++k)
+ m_colsPermutation.applyTranspositionOnTheRight(k, PermIndexType(m_colsTranspositions.coeff(k)));
+
+ m_det_p = (number_of_transpositions%2) ? -1 : 1;
+ m_isInitialized = true;
+}
+
+#ifndef EIGEN_PARSED_BY_DOXYGEN
+template<typename MatrixType_>
+template<typename RhsType, typename DstType>
+void ColPivHouseholderQR<MatrixType_>::_solve_impl(const RhsType &rhs, DstType &dst) const
+{
+ const Index nonzero_pivots = nonzeroPivots();
+
+ if(nonzero_pivots == 0)
+ {
+ dst.setZero();
+ return;
+ }
+
+ typename RhsType::PlainObject c(rhs);
+
+ c.applyOnTheLeft(householderQ().setLength(nonzero_pivots).adjoint() );
+
+ m_qr.topLeftCorner(nonzero_pivots, nonzero_pivots)
+ .template triangularView<Upper>()
+ .solveInPlace(c.topRows(nonzero_pivots));
+
+ for(Index i = 0; i < nonzero_pivots; ++i) dst.row(m_colsPermutation.indices().coeff(i)) = c.row(i);
+ for(Index i = nonzero_pivots; i < cols(); ++i) dst.row(m_colsPermutation.indices().coeff(i)).setZero();
+}
+
+template<typename MatrixType_>
+template<bool Conjugate, typename RhsType, typename DstType>
+void ColPivHouseholderQR<MatrixType_>::_solve_impl_transposed(const RhsType &rhs, DstType &dst) const
+{
+ const Index nonzero_pivots = nonzeroPivots();
+
+ if(nonzero_pivots == 0)
+ {
+ dst.setZero();
+ return;
+ }
+
+ typename RhsType::PlainObject c(m_colsPermutation.transpose()*rhs);
+
+ m_qr.topLeftCorner(nonzero_pivots, nonzero_pivots)
+ .template triangularView<Upper>()
+ .transpose().template conjugateIf<Conjugate>()
+ .solveInPlace(c.topRows(nonzero_pivots));
+
+ dst.topRows(nonzero_pivots) = c.topRows(nonzero_pivots);
+ dst.bottomRows(rows()-nonzero_pivots).setZero();
+
+ dst.applyOnTheLeft(householderQ().setLength(nonzero_pivots).template conjugateIf<!Conjugate>() );
+}
+#endif
+
+namespace internal {
+
+template<typename DstXprType, typename MatrixType>
+struct Assignment<DstXprType, Inverse<ColPivHouseholderQR<MatrixType> >, internal::assign_op<typename DstXprType::Scalar,typename ColPivHouseholderQR<MatrixType>::Scalar>, Dense2Dense>
+{
+ typedef ColPivHouseholderQR<MatrixType> QrType;
+ typedef Inverse<QrType> SrcXprType;
+ static void run(DstXprType &dst, const SrcXprType &src, const internal::assign_op<typename DstXprType::Scalar,typename QrType::Scalar> &)
+ {
+ dst = src.nestedExpression().solve(MatrixType::Identity(src.rows(), src.cols()));
+ }
+};
+
+} // end namespace internal
+
+/** \returns the matrix Q as a sequence of householder transformations.
+ * You can extract the meaningful part only by using:
+ * \code qr.householderQ().setLength(qr.nonzeroPivots()) \endcode*/
+template<typename MatrixType>
+typename ColPivHouseholderQR<MatrixType>::HouseholderSequenceType ColPivHouseholderQR<MatrixType>
+ ::householderQ() const
+{
+ eigen_assert(m_isInitialized && "ColPivHouseholderQR is not initialized.");
+ return HouseholderSequenceType(m_qr, m_hCoeffs.conjugate());
+}
+
+/** \return the column-pivoting Householder QR decomposition of \c *this.
+ *
+ * \sa class ColPivHouseholderQR
+ */
+template<typename Derived>
+const ColPivHouseholderQR<typename MatrixBase<Derived>::PlainObject>
+MatrixBase<Derived>::colPivHouseholderQr() const
+{
+ return ColPivHouseholderQR<PlainObject>(eval());
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_COLPIVOTINGHOUSEHOLDERQR_H
diff --git a/Eigen/src/QR/ColPivHouseholderQR_LAPACKE.h b/Eigen/src/QR/ColPivHouseholderQR_LAPACKE.h
new file mode 100644
index 0000000..7652d31
--- /dev/null
+++ b/Eigen/src/QR/ColPivHouseholderQR_LAPACKE.h
@@ -0,0 +1,99 @@
+/*
+ Copyright (c) 2011, Intel Corporation. All rights reserved.
+
+ Redistribution and use in source and binary forms, with or without modification,
+ are permitted provided that the following conditions are met:
+
+ * Redistributions of source code must retain the above copyright notice, this
+ list of conditions and the following disclaimer.
+ * Redistributions in binary form must reproduce the above copyright notice,
+ this list of conditions and the following disclaimer in the documentation
+ and/or other materials provided with the distribution.
+ * Neither the name of Intel Corporation nor the names of its contributors may
+ be used to endorse or promote products derived from this software without
+ specific prior written permission.
+
+ THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
+ ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
+ WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
+ DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR
+ ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
+ (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
+ LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON
+ ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
+ (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
+ SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+
+ ********************************************************************************
+ * Content : Eigen bindings to LAPACKe
+ * Householder QR decomposition of a matrix with column pivoting based on
+ * LAPACKE_?geqp3 function.
+ ********************************************************************************
+*/
+
+#ifndef EIGEN_COLPIVOTINGHOUSEHOLDERQR_LAPACKE_H
+#define EIGEN_COLPIVOTINGHOUSEHOLDERQR_LAPACKE_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+/** \internal Specialization for the data types supported by LAPACKe */
+
+#define EIGEN_LAPACKE_QR_COLPIV(EIGTYPE, LAPACKE_TYPE, LAPACKE_PREFIX, EIGCOLROW, LAPACKE_COLROW) \
+template<> template<typename InputType> inline \
+ColPivHouseholderQR<Matrix<EIGTYPE, Dynamic, Dynamic, EIGCOLROW, Dynamic, Dynamic> >& \
+ColPivHouseholderQR<Matrix<EIGTYPE, Dynamic, Dynamic, EIGCOLROW, Dynamic, Dynamic> >::compute( \
+ const EigenBase<InputType>& matrix) \
+\
+{ \
+ using std::abs; \
+ typedef Matrix<EIGTYPE, Dynamic, Dynamic, EIGCOLROW, Dynamic, Dynamic> MatrixType; \
+ typedef MatrixType::RealScalar RealScalar; \
+ Index rows = matrix.rows();\
+ Index cols = matrix.cols();\
+\
+ m_qr = matrix;\
+ Index size = m_qr.diagonalSize();\
+ m_hCoeffs.resize(size);\
+\
+ m_colsTranspositions.resize(cols);\
+ /*Index number_of_transpositions = 0;*/ \
+\
+ m_nonzero_pivots = 0; \
+ m_maxpivot = RealScalar(0);\
+ m_colsPermutation.resize(cols); \
+ m_colsPermutation.indices().setZero(); \
+\
+ lapack_int lda = internal::convert_index<lapack_int,Index>(m_qr.outerStride()); \
+ lapack_int matrix_order = LAPACKE_COLROW; \
+ LAPACKE_##LAPACKE_PREFIX##geqp3( matrix_order, internal::convert_index<lapack_int,Index>(rows), internal::convert_index<lapack_int,Index>(cols), \
+ (LAPACKE_TYPE*)m_qr.data(), lda, (lapack_int*)m_colsPermutation.indices().data(), (LAPACKE_TYPE*)m_hCoeffs.data()); \
+ m_isInitialized = true; \
+ m_maxpivot=m_qr.diagonal().cwiseAbs().maxCoeff(); \
+ m_hCoeffs.adjointInPlace(); \
+ RealScalar premultiplied_threshold = abs(m_maxpivot) * threshold(); \
+ lapack_int *perm = m_colsPermutation.indices().data(); \
+ for(Index i=0;i<size;i++) { \
+ m_nonzero_pivots += (abs(m_qr.coeff(i,i)) > premultiplied_threshold);\
+ } \
+ for(Index i=0;i<cols;i++) perm[i]--;\
+\
+ /*m_det_pq = (number_of_transpositions%2) ? -1 : 1; // TODO: It's not needed now; fix upon availability in Eigen */ \
+\
+ return *this; \
+}
+
+EIGEN_LAPACKE_QR_COLPIV(double, double, d, ColMajor, LAPACK_COL_MAJOR)
+EIGEN_LAPACKE_QR_COLPIV(float, float, s, ColMajor, LAPACK_COL_MAJOR)
+EIGEN_LAPACKE_QR_COLPIV(dcomplex, lapack_complex_double, z, ColMajor, LAPACK_COL_MAJOR)
+EIGEN_LAPACKE_QR_COLPIV(scomplex, lapack_complex_float, c, ColMajor, LAPACK_COL_MAJOR)
+
+EIGEN_LAPACKE_QR_COLPIV(double, double, d, RowMajor, LAPACK_ROW_MAJOR)
+EIGEN_LAPACKE_QR_COLPIV(float, float, s, RowMajor, LAPACK_ROW_MAJOR)
+EIGEN_LAPACKE_QR_COLPIV(dcomplex, lapack_complex_double, z, RowMajor, LAPACK_ROW_MAJOR)
+EIGEN_LAPACKE_QR_COLPIV(scomplex, lapack_complex_float, c, RowMajor, LAPACK_ROW_MAJOR)
+
+} // end namespace Eigen
+
+#endif // EIGEN_COLPIVOTINGHOUSEHOLDERQR_LAPACKE_H
diff --git a/Eigen/src/QR/CompleteOrthogonalDecomposition.h b/Eigen/src/QR/CompleteOrthogonalDecomposition.h
new file mode 100644
index 0000000..02583a2
--- /dev/null
+++ b/Eigen/src/QR/CompleteOrthogonalDecomposition.h
@@ -0,0 +1,654 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2016 Rasmus Munk Larsen <rmlarsen@google.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_COMPLETEORTHOGONALDECOMPOSITION_H
+#define EIGEN_COMPLETEORTHOGONALDECOMPOSITION_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+template <typename MatrixType_>
+struct traits<CompleteOrthogonalDecomposition<MatrixType_> >
+ : traits<MatrixType_> {
+ typedef MatrixXpr XprKind;
+ typedef SolverStorage StorageKind;
+ typedef int StorageIndex;
+ enum { Flags = 0 };
+};
+
+} // end namespace internal
+
+/** \ingroup QR_Module
+ *
+ * \class CompleteOrthogonalDecomposition
+ *
+ * \brief Complete orthogonal decomposition (COD) of a matrix.
+ *
+ * \tparam MatrixType_ the type of the matrix of which we are computing the COD.
+ *
+ * This class performs a rank-revealing complete orthogonal decomposition of a
+ * matrix \b A into matrices \b P, \b Q, \b T, and \b Z such that
+ * \f[
+ * \mathbf{A} \, \mathbf{P} = \mathbf{Q} \,
+ * \begin{bmatrix} \mathbf{T} & \mathbf{0} \\
+ * \mathbf{0} & \mathbf{0} \end{bmatrix} \, \mathbf{Z}
+ * \f]
+ * by using Householder transformations. Here, \b P is a permutation matrix,
+ * \b Q and \b Z are unitary matrices and \b T an upper triangular matrix of
+ * size rank-by-rank. \b A may be rank deficient.
+ *
+ * This class supports the \link InplaceDecomposition inplace decomposition \endlink mechanism.
+ *
+ * \sa MatrixBase::completeOrthogonalDecomposition()
+ */
+template <typename MatrixType_> class CompleteOrthogonalDecomposition
+ : public SolverBase<CompleteOrthogonalDecomposition<MatrixType_> >
+{
+ public:
+ typedef MatrixType_ MatrixType;
+ typedef SolverBase<CompleteOrthogonalDecomposition> Base;
+
+ template<typename Derived>
+ friend struct internal::solve_assertion;
+
+ EIGEN_GENERIC_PUBLIC_INTERFACE(CompleteOrthogonalDecomposition)
+ enum {
+ MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime,
+ MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime
+ };
+ typedef typename internal::plain_diag_type<MatrixType>::type HCoeffsType;
+ typedef PermutationMatrix<ColsAtCompileTime, MaxColsAtCompileTime>
+ PermutationType;
+ typedef typename internal::plain_row_type<MatrixType, Index>::type
+ IntRowVectorType;
+ typedef typename internal::plain_row_type<MatrixType>::type RowVectorType;
+ typedef typename internal::plain_row_type<MatrixType, RealScalar>::type
+ RealRowVectorType;
+ typedef HouseholderSequence<
+ MatrixType, internal::remove_all_t<
+ typename HCoeffsType::ConjugateReturnType>>
+ HouseholderSequenceType;
+ typedef typename MatrixType::PlainObject PlainObject;
+
+ private:
+ typedef typename PermutationType::Index PermIndexType;
+
+ public:
+ /**
+ * \brief Default Constructor.
+ *
+ * The default constructor is useful in cases in which the user intends to
+ * perform decompositions via
+ * \c CompleteOrthogonalDecomposition::compute(const* MatrixType&).
+ */
+ CompleteOrthogonalDecomposition() : m_cpqr(), m_zCoeffs(), m_temp() {}
+
+ /** \brief Default Constructor with memory preallocation
+ *
+ * Like the default constructor but with preallocation of the internal data
+ * according to the specified problem \a size.
+ * \sa CompleteOrthogonalDecomposition()
+ */
+ CompleteOrthogonalDecomposition(Index rows, Index cols)
+ : m_cpqr(rows, cols), m_zCoeffs((std::min)(rows, cols)), m_temp(cols) {}
+
+ /** \brief Constructs a complete orthogonal decomposition from a given
+ * matrix.
+ *
+ * This constructor computes the complete orthogonal decomposition of the
+ * matrix \a matrix by calling the method compute(). The default
+ * threshold for rank determination will be used. It is a short cut for:
+ *
+ * \code
+ * CompleteOrthogonalDecomposition<MatrixType> cod(matrix.rows(),
+ * matrix.cols());
+ * cod.setThreshold(Default);
+ * cod.compute(matrix);
+ * \endcode
+ *
+ * \sa compute()
+ */
+ template <typename InputType>
+ explicit CompleteOrthogonalDecomposition(const EigenBase<InputType>& matrix)
+ : m_cpqr(matrix.rows(), matrix.cols()),
+ m_zCoeffs((std::min)(matrix.rows(), matrix.cols())),
+ m_temp(matrix.cols())
+ {
+ compute(matrix.derived());
+ }
+
+ /** \brief Constructs a complete orthogonal decomposition from a given matrix
+ *
+ * This overloaded constructor is provided for \link InplaceDecomposition inplace decomposition \endlink when \c MatrixType is a Eigen::Ref.
+ *
+ * \sa CompleteOrthogonalDecomposition(const EigenBase&)
+ */
+ template<typename InputType>
+ explicit CompleteOrthogonalDecomposition(EigenBase<InputType>& matrix)
+ : m_cpqr(matrix.derived()),
+ m_zCoeffs((std::min)(matrix.rows(), matrix.cols())),
+ m_temp(matrix.cols())
+ {
+ computeInPlace();
+ }
+
+ #ifdef EIGEN_PARSED_BY_DOXYGEN
+ /** This method computes the minimum-norm solution X to a least squares
+ * problem \f[\mathrm{minimize} \|A X - B\|, \f] where \b A is the matrix of
+ * which \c *this is the complete orthogonal decomposition.
+ *
+ * \param b the right-hand sides of the problem to solve.
+ *
+ * \returns a solution.
+ *
+ */
+ template <typename Rhs>
+ inline const Solve<CompleteOrthogonalDecomposition, Rhs> solve(
+ const MatrixBase<Rhs>& b) const;
+ #endif
+
+ HouseholderSequenceType householderQ(void) const;
+ HouseholderSequenceType matrixQ(void) const { return m_cpqr.householderQ(); }
+
+ /** \returns the matrix \b Z.
+ */
+ MatrixType matrixZ() const {
+ MatrixType Z = MatrixType::Identity(m_cpqr.cols(), m_cpqr.cols());
+ applyZOnTheLeftInPlace<false>(Z);
+ return Z;
+ }
+
+ /** \returns a reference to the matrix where the complete orthogonal
+ * decomposition is stored
+ */
+ const MatrixType& matrixQTZ() const { return m_cpqr.matrixQR(); }
+
+ /** \returns a reference to the matrix where the complete orthogonal
+ * decomposition is stored.
+ * \warning The strict lower part and \code cols() - rank() \endcode right
+ * columns of this matrix contains internal values.
+ * Only the upper triangular part should be referenced. To get it, use
+ * \code matrixT().template triangularView<Upper>() \endcode
+ * For rank-deficient matrices, use
+ * \code
+ * matrixT().topLeftCorner(rank(), rank()).template triangularView<Upper>()
+ * \endcode
+ */
+ const MatrixType& matrixT() const { return m_cpqr.matrixQR(); }
+
+ template <typename InputType>
+ CompleteOrthogonalDecomposition& compute(const EigenBase<InputType>& matrix) {
+ // Compute the column pivoted QR factorization A P = Q R.
+ m_cpqr.compute(matrix);
+ computeInPlace();
+ return *this;
+ }
+
+ /** \returns a const reference to the column permutation matrix */
+ const PermutationType& colsPermutation() const {
+ return m_cpqr.colsPermutation();
+ }
+
+ /** \returns the determinant of the matrix of which
+ * *this is the complete orthogonal decomposition. It has only linear
+ * complexity (that is, O(n) where n is the dimension of the square matrix)
+ * as the complete orthogonal decomposition has already been computed.
+ *
+ * \note This is only for square matrices.
+ *
+ * \warning a determinant can be very big or small, so for matrices
+ * of large enough dimension, there is a risk of overflow/underflow.
+ * One way to work around that is to use logAbsDeterminant() instead.
+ *
+ * \sa absDeterminant(), logAbsDeterminant(), MatrixBase::determinant()
+ */
+ typename MatrixType::Scalar determinant() const;
+
+ /** \returns the absolute value of the determinant of the matrix of which
+ * *this is the complete orthogonal decomposition. It has only linear
+ * complexity (that is, O(n) where n is the dimension of the square matrix)
+ * as the complete orthogonal decomposition has already been computed.
+ *
+ * \note This is only for square matrices.
+ *
+ * \warning a determinant can be very big or small, so for matrices
+ * of large enough dimension, there is a risk of overflow/underflow.
+ * One way to work around that is to use logAbsDeterminant() instead.
+ *
+ * \sa determinant(), logAbsDeterminant(), MatrixBase::determinant()
+ */
+ typename MatrixType::RealScalar absDeterminant() const;
+
+ /** \returns the natural log of the absolute value of the determinant of the
+ * matrix of which *this is the complete orthogonal decomposition. It has
+ * only linear complexity (that is, O(n) where n is the dimension of the
+ * square matrix) as the complete orthogonal decomposition has already been
+ * computed.
+ *
+ * \note This is only for square matrices.
+ *
+ * \note This method is useful to work around the risk of overflow/underflow
+ * that's inherent to determinant computation.
+ *
+ * \sa determinant(), absDeterminant(), MatrixBase::determinant()
+ */
+ typename MatrixType::RealScalar logAbsDeterminant() const;
+
+ /** \returns the rank of the matrix of which *this is the complete orthogonal
+ * decomposition.
+ *
+ * \note This method has to determine which pivots should be considered
+ * nonzero. For that, it uses the threshold value that you can control by
+ * calling setThreshold(const RealScalar&).
+ */
+ inline Index rank() const { return m_cpqr.rank(); }
+
+ /** \returns the dimension of the kernel of the matrix of which *this is the
+ * complete orthogonal decomposition.
+ *
+ * \note This method has to determine which pivots should be considered
+ * nonzero. For that, it uses the threshold value that you can control by
+ * calling setThreshold(const RealScalar&).
+ */
+ inline Index dimensionOfKernel() const { return m_cpqr.dimensionOfKernel(); }
+
+ /** \returns true if the matrix of which *this is the decomposition represents
+ * an injective linear map, i.e. has trivial kernel; false otherwise.
+ *
+ * \note This method has to determine which pivots should be considered
+ * nonzero. For that, it uses the threshold value that you can control by
+ * calling setThreshold(const RealScalar&).
+ */
+ inline bool isInjective() const { return m_cpqr.isInjective(); }
+
+ /** \returns true if the matrix of which *this is the decomposition represents
+ * a surjective linear map; false otherwise.
+ *
+ * \note This method has to determine which pivots should be considered
+ * nonzero. For that, it uses the threshold value that you can control by
+ * calling setThreshold(const RealScalar&).
+ */
+ inline bool isSurjective() const { return m_cpqr.isSurjective(); }
+
+ /** \returns true if the matrix of which *this is the complete orthogonal
+ * decomposition is invertible.
+ *
+ * \note This method has to determine which pivots should be considered
+ * nonzero. For that, it uses the threshold value that you can control by
+ * calling setThreshold(const RealScalar&).
+ */
+ inline bool isInvertible() const { return m_cpqr.isInvertible(); }
+
+ /** \returns the pseudo-inverse of the matrix of which *this is the complete
+ * orthogonal decomposition.
+ * \warning: Do not compute \c this->pseudoInverse()*rhs to solve a linear systems.
+ * It is more efficient and numerically stable to call \c this->solve(rhs).
+ */
+ inline const Inverse<CompleteOrthogonalDecomposition> pseudoInverse() const
+ {
+ eigen_assert(m_cpqr.m_isInitialized && "CompleteOrthogonalDecomposition is not initialized.");
+ return Inverse<CompleteOrthogonalDecomposition>(*this);
+ }
+
+ inline Index rows() const { return m_cpqr.rows(); }
+ inline Index cols() const { return m_cpqr.cols(); }
+
+ /** \returns a const reference to the vector of Householder coefficients used
+ * to represent the factor \c Q.
+ *
+ * For advanced uses only.
+ */
+ inline const HCoeffsType& hCoeffs() const { return m_cpqr.hCoeffs(); }
+
+ /** \returns a const reference to the vector of Householder coefficients
+ * used to represent the factor \c Z.
+ *
+ * For advanced uses only.
+ */
+ const HCoeffsType& zCoeffs() const { return m_zCoeffs; }
+
+ /** Allows to prescribe a threshold to be used by certain methods, such as
+ * rank(), who need to determine when pivots are to be considered nonzero.
+ * Most be called before calling compute().
+ *
+ * When it needs to get the threshold value, Eigen calls threshold(). By
+ * default, this uses a formula to automatically determine a reasonable
+ * threshold. Once you have called the present method
+ * setThreshold(const RealScalar&), your value is used instead.
+ *
+ * \param threshold The new value to use as the threshold.
+ *
+ * A pivot will be considered nonzero if its absolute value is strictly
+ * greater than
+ * \f$ \vert pivot \vert \leqslant threshold \times \vert maxpivot \vert \f$
+ * where maxpivot is the biggest pivot.
+ *
+ * If you want to come back to the default behavior, call
+ * setThreshold(Default_t)
+ */
+ CompleteOrthogonalDecomposition& setThreshold(const RealScalar& threshold) {
+ m_cpqr.setThreshold(threshold);
+ return *this;
+ }
+
+ /** Allows to come back to the default behavior, letting Eigen use its default
+ * formula for determining the threshold.
+ *
+ * You should pass the special object Eigen::Default as parameter here.
+ * \code qr.setThreshold(Eigen::Default); \endcode
+ *
+ * See the documentation of setThreshold(const RealScalar&).
+ */
+ CompleteOrthogonalDecomposition& setThreshold(Default_t) {
+ m_cpqr.setThreshold(Default);
+ return *this;
+ }
+
+ /** Returns the threshold that will be used by certain methods such as rank().
+ *
+ * See the documentation of setThreshold(const RealScalar&).
+ */
+ RealScalar threshold() const { return m_cpqr.threshold(); }
+
+ /** \returns the number of nonzero pivots in the complete orthogonal
+ * decomposition. Here nonzero is meant in the exact sense, not in a
+ * fuzzy sense. So that notion isn't really intrinsically interesting,
+ * but it is still useful when implementing algorithms.
+ *
+ * \sa rank()
+ */
+ inline Index nonzeroPivots() const { return m_cpqr.nonzeroPivots(); }
+
+ /** \returns the absolute value of the biggest pivot, i.e. the biggest
+ * diagonal coefficient of R.
+ */
+ inline RealScalar maxPivot() const { return m_cpqr.maxPivot(); }
+
+ /** \brief Reports whether the complete orthogonal decomposition was
+ * successful.
+ *
+ * \note This function always returns \c Success. It is provided for
+ * compatibility
+ * with other factorization routines.
+ * \returns \c Success
+ */
+ ComputationInfo info() const {
+ eigen_assert(m_cpqr.m_isInitialized && "Decomposition is not initialized.");
+ return Success;
+ }
+
+#ifndef EIGEN_PARSED_BY_DOXYGEN
+ template <typename RhsType, typename DstType>
+ void _solve_impl(const RhsType& rhs, DstType& dst) const;
+
+ template<bool Conjugate, typename RhsType, typename DstType>
+ void _solve_impl_transposed(const RhsType &rhs, DstType &dst) const;
+#endif
+
+ protected:
+ EIGEN_STATIC_ASSERT_NON_INTEGER(Scalar)
+
+ template<bool Transpose_, typename Rhs>
+ void _check_solve_assertion(const Rhs& b) const {
+ EIGEN_ONLY_USED_FOR_DEBUG(b);
+ eigen_assert(m_cpqr.m_isInitialized && "CompleteOrthogonalDecomposition is not initialized.");
+ eigen_assert((Transpose_?derived().cols():derived().rows())==b.rows() && "CompleteOrthogonalDecomposition::solve(): invalid number of rows of the right hand side matrix b");
+ }
+
+ void computeInPlace();
+
+ /** Overwrites \b rhs with \f$ \mathbf{Z} * \mathbf{rhs} \f$ or
+ * \f$ \mathbf{\overline Z} * \mathbf{rhs} \f$ if \c Conjugate
+ * is set to \c true.
+ */
+ template <bool Conjugate, typename Rhs>
+ void applyZOnTheLeftInPlace(Rhs& rhs) const;
+
+ /** Overwrites \b rhs with \f$ \mathbf{Z}^* * \mathbf{rhs} \f$.
+ */
+ template <typename Rhs>
+ void applyZAdjointOnTheLeftInPlace(Rhs& rhs) const;
+
+ ColPivHouseholderQR<MatrixType> m_cpqr;
+ HCoeffsType m_zCoeffs;
+ RowVectorType m_temp;
+};
+
+template <typename MatrixType>
+typename MatrixType::Scalar
+CompleteOrthogonalDecomposition<MatrixType>::determinant() const {
+ return m_cpqr.determinant();
+}
+
+template <typename MatrixType>
+typename MatrixType::RealScalar
+CompleteOrthogonalDecomposition<MatrixType>::absDeterminant() const {
+ return m_cpqr.absDeterminant();
+}
+
+template <typename MatrixType>
+typename MatrixType::RealScalar
+CompleteOrthogonalDecomposition<MatrixType>::logAbsDeterminant() const {
+ return m_cpqr.logAbsDeterminant();
+}
+
+/** Performs the complete orthogonal decomposition of the given matrix \a
+ * matrix. The result of the factorization is stored into \c *this, and a
+ * reference to \c *this is returned.
+ *
+ * \sa class CompleteOrthogonalDecomposition,
+ * CompleteOrthogonalDecomposition(const MatrixType&)
+ */
+template <typename MatrixType>
+void CompleteOrthogonalDecomposition<MatrixType>::computeInPlace()
+{
+ // the column permutation is stored as int indices, so just to be sure:
+ eigen_assert(m_cpqr.cols() <= NumTraits<int>::highest());
+
+ const Index rank = m_cpqr.rank();
+ const Index cols = m_cpqr.cols();
+ const Index rows = m_cpqr.rows();
+ m_zCoeffs.resize((std::min)(rows, cols));
+ m_temp.resize(cols);
+
+ if (rank < cols) {
+ // We have reduced the (permuted) matrix to the form
+ // [R11 R12]
+ // [ 0 R22]
+ // where R11 is r-by-r (r = rank) upper triangular, R12 is
+ // r-by-(n-r), and R22 is empty or the norm of R22 is negligible.
+ // We now compute the complete orthogonal decomposition by applying
+ // Householder transformations from the right to the upper trapezoidal
+ // matrix X = [R11 R12] to zero out R12 and obtain the factorization
+ // [R11 R12] = [T11 0] * Z, where T11 is r-by-r upper triangular and
+ // Z = Z(0) * Z(1) ... Z(r-1) is an n-by-n orthogonal matrix.
+ // We store the data representing Z in R12 and m_zCoeffs.
+ for (Index k = rank - 1; k >= 0; --k) {
+ if (k != rank - 1) {
+ // Given the API for Householder reflectors, it is more convenient if
+ // we swap the leading parts of columns k and r-1 (zero-based) to form
+ // the matrix X_k = [X(0:k, k), X(0:k, r:n)]
+ m_cpqr.m_qr.col(k).head(k + 1).swap(
+ m_cpqr.m_qr.col(rank - 1).head(k + 1));
+ }
+ // Construct Householder reflector Z(k) to zero out the last row of X_k,
+ // i.e. choose Z(k) such that
+ // [X(k, k), X(k, r:n)] * Z(k) = [beta, 0, .., 0].
+ RealScalar beta;
+ m_cpqr.m_qr.row(k)
+ .tail(cols - rank + 1)
+ .makeHouseholderInPlace(m_zCoeffs(k), beta);
+ m_cpqr.m_qr(k, rank - 1) = beta;
+ if (k > 0) {
+ // Apply Z(k) to the first k rows of X_k
+ m_cpqr.m_qr.topRightCorner(k, cols - rank + 1)
+ .applyHouseholderOnTheRight(
+ m_cpqr.m_qr.row(k).tail(cols - rank).adjoint(), m_zCoeffs(k),
+ &m_temp(0));
+ }
+ if (k != rank - 1) {
+ // Swap X(0:k,k) back to its proper location.
+ m_cpqr.m_qr.col(k).head(k + 1).swap(
+ m_cpqr.m_qr.col(rank - 1).head(k + 1));
+ }
+ }
+ }
+}
+
+template <typename MatrixType>
+template <bool Conjugate, typename Rhs>
+void CompleteOrthogonalDecomposition<MatrixType>::applyZOnTheLeftInPlace(
+ Rhs& rhs) const {
+ const Index cols = this->cols();
+ const Index nrhs = rhs.cols();
+ const Index rank = this->rank();
+ Matrix<typename Rhs::Scalar, Dynamic, 1> temp((std::max)(cols, nrhs));
+ for (Index k = rank-1; k >= 0; --k) {
+ if (k != rank - 1) {
+ rhs.row(k).swap(rhs.row(rank - 1));
+ }
+ rhs.middleRows(rank - 1, cols - rank + 1)
+ .applyHouseholderOnTheLeft(
+ matrixQTZ().row(k).tail(cols - rank).transpose().template conjugateIf<!Conjugate>(), zCoeffs().template conjugateIf<Conjugate>()(k),
+ &temp(0));
+ if (k != rank - 1) {
+ rhs.row(k).swap(rhs.row(rank - 1));
+ }
+ }
+}
+
+template <typename MatrixType>
+template <typename Rhs>
+void CompleteOrthogonalDecomposition<MatrixType>::applyZAdjointOnTheLeftInPlace(
+ Rhs& rhs) const {
+ const Index cols = this->cols();
+ const Index nrhs = rhs.cols();
+ const Index rank = this->rank();
+ Matrix<typename Rhs::Scalar, Dynamic, 1> temp((std::max)(cols, nrhs));
+ for (Index k = 0; k < rank; ++k) {
+ if (k != rank - 1) {
+ rhs.row(k).swap(rhs.row(rank - 1));
+ }
+ rhs.middleRows(rank - 1, cols - rank + 1)
+ .applyHouseholderOnTheLeft(
+ matrixQTZ().row(k).tail(cols - rank).adjoint(), zCoeffs()(k),
+ &temp(0));
+ if (k != rank - 1) {
+ rhs.row(k).swap(rhs.row(rank - 1));
+ }
+ }
+}
+
+#ifndef EIGEN_PARSED_BY_DOXYGEN
+template <typename MatrixType_>
+template <typename RhsType, typename DstType>
+void CompleteOrthogonalDecomposition<MatrixType_>::_solve_impl(
+ const RhsType& rhs, DstType& dst) const {
+ const Index rank = this->rank();
+ if (rank == 0) {
+ dst.setZero();
+ return;
+ }
+
+ // Compute c = Q^* * rhs
+ typename RhsType::PlainObject c(rhs);
+ c.applyOnTheLeft(matrixQ().setLength(rank).adjoint());
+
+ // Solve T z = c(1:rank, :)
+ dst.topRows(rank) = matrixT()
+ .topLeftCorner(rank, rank)
+ .template triangularView<Upper>()
+ .solve(c.topRows(rank));
+
+ const Index cols = this->cols();
+ if (rank < cols) {
+ // Compute y = Z^* * [ z ]
+ // [ 0 ]
+ dst.bottomRows(cols - rank).setZero();
+ applyZAdjointOnTheLeftInPlace(dst);
+ }
+
+ // Undo permutation to get x = P^{-1} * y.
+ dst = colsPermutation() * dst;
+}
+
+template<typename MatrixType_>
+template<bool Conjugate, typename RhsType, typename DstType>
+void CompleteOrthogonalDecomposition<MatrixType_>::_solve_impl_transposed(const RhsType &rhs, DstType &dst) const
+{
+ const Index rank = this->rank();
+
+ if (rank == 0) {
+ dst.setZero();
+ return;
+ }
+
+ typename RhsType::PlainObject c(colsPermutation().transpose()*rhs);
+
+ if (rank < cols()) {
+ applyZOnTheLeftInPlace<!Conjugate>(c);
+ }
+
+ matrixT().topLeftCorner(rank, rank)
+ .template triangularView<Upper>()
+ .transpose().template conjugateIf<Conjugate>()
+ .solveInPlace(c.topRows(rank));
+
+ dst.topRows(rank) = c.topRows(rank);
+ dst.bottomRows(rows()-rank).setZero();
+
+ dst.applyOnTheLeft(householderQ().setLength(rank).template conjugateIf<!Conjugate>() );
+}
+#endif
+
+namespace internal {
+
+template<typename MatrixType>
+struct traits<Inverse<CompleteOrthogonalDecomposition<MatrixType> > >
+ : traits<typename Transpose<typename MatrixType::PlainObject>::PlainObject>
+{
+ enum { Flags = 0 };
+};
+
+template<typename DstXprType, typename MatrixType>
+struct Assignment<DstXprType, Inverse<CompleteOrthogonalDecomposition<MatrixType> >, internal::assign_op<typename DstXprType::Scalar,typename CompleteOrthogonalDecomposition<MatrixType>::Scalar>, Dense2Dense>
+{
+ typedef CompleteOrthogonalDecomposition<MatrixType> CodType;
+ typedef Inverse<CodType> SrcXprType;
+ static void run(DstXprType &dst, const SrcXprType &src, const internal::assign_op<typename DstXprType::Scalar,typename CodType::Scalar> &)
+ {
+ typedef Matrix<typename CodType::Scalar, CodType::RowsAtCompileTime, CodType::RowsAtCompileTime, 0, CodType::MaxRowsAtCompileTime, CodType::MaxRowsAtCompileTime> IdentityMatrixType;
+ dst = src.nestedExpression().solve(IdentityMatrixType::Identity(src.cols(), src.cols()));
+ }
+};
+
+} // end namespace internal
+
+/** \returns the matrix Q as a sequence of householder transformations */
+template <typename MatrixType>
+typename CompleteOrthogonalDecomposition<MatrixType>::HouseholderSequenceType
+CompleteOrthogonalDecomposition<MatrixType>::householderQ() const {
+ return m_cpqr.householderQ();
+}
+
+/** \return the complete orthogonal decomposition of \c *this.
+ *
+ * \sa class CompleteOrthogonalDecomposition
+ */
+template <typename Derived>
+const CompleteOrthogonalDecomposition<typename MatrixBase<Derived>::PlainObject>
+MatrixBase<Derived>::completeOrthogonalDecomposition() const {
+ return CompleteOrthogonalDecomposition<PlainObject>(eval());
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_COMPLETEORTHOGONALDECOMPOSITION_H
diff --git a/Eigen/src/QR/FullPivHouseholderQR.h b/Eigen/src/QR/FullPivHouseholderQR.h
new file mode 100644
index 0000000..ec7e19b
--- /dev/null
+++ b/Eigen/src/QR/FullPivHouseholderQR.h
@@ -0,0 +1,735 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2009 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_FULLPIVOTINGHOUSEHOLDERQR_H
+#define EIGEN_FULLPIVOTINGHOUSEHOLDERQR_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+
+template<typename MatrixType_> struct traits<FullPivHouseholderQR<MatrixType_> >
+ : traits<MatrixType_>
+{
+ typedef MatrixXpr XprKind;
+ typedef SolverStorage StorageKind;
+ typedef int StorageIndex;
+ enum { Flags = 0 };
+};
+
+template<typename MatrixType> struct FullPivHouseholderQRMatrixQReturnType;
+
+template<typename MatrixType>
+struct traits<FullPivHouseholderQRMatrixQReturnType<MatrixType> >
+{
+ typedef typename MatrixType::PlainObject ReturnType;
+};
+
+} // end namespace internal
+
+/** \ingroup QR_Module
+ *
+ * \class FullPivHouseholderQR
+ *
+ * \brief Householder rank-revealing QR decomposition of a matrix with full pivoting
+ *
+ * \tparam MatrixType_ the type of the matrix of which we are computing the QR decomposition
+ *
+ * This class performs a rank-revealing QR decomposition of a matrix \b A into matrices \b P, \b P', \b Q and \b R
+ * such that
+ * \f[
+ * \mathbf{P} \, \mathbf{A} \, \mathbf{P}' = \mathbf{Q} \, \mathbf{R}
+ * \f]
+ * by using Householder transformations. Here, \b P and \b P' are permutation matrices, \b Q a unitary matrix
+ * and \b R an upper triangular matrix.
+ *
+ * This decomposition performs a very prudent full pivoting in order to be rank-revealing and achieve optimal
+ * numerical stability. The trade-off is that it is slower than HouseholderQR and ColPivHouseholderQR.
+ *
+ * This class supports the \link InplaceDecomposition inplace decomposition \endlink mechanism.
+ *
+ * \sa MatrixBase::fullPivHouseholderQr()
+ */
+template<typename MatrixType_> class FullPivHouseholderQR
+ : public SolverBase<FullPivHouseholderQR<MatrixType_> >
+{
+ public:
+
+ typedef MatrixType_ MatrixType;
+ typedef SolverBase<FullPivHouseholderQR> Base;
+ friend class SolverBase<FullPivHouseholderQR>;
+
+ EIGEN_GENERIC_PUBLIC_INTERFACE(FullPivHouseholderQR)
+ enum {
+ MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime,
+ MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime
+ };
+ typedef internal::FullPivHouseholderQRMatrixQReturnType<MatrixType> MatrixQReturnType;
+ typedef typename internal::plain_diag_type<MatrixType>::type HCoeffsType;
+ typedef Matrix<StorageIndex, 1,
+ internal::min_size_prefer_dynamic(ColsAtCompileTime,RowsAtCompileTime), RowMajor, 1,
+ internal::min_size_prefer_fixed(MaxColsAtCompileTime, MaxRowsAtCompileTime)> IntDiagSizeVectorType;
+ typedef PermutationMatrix<ColsAtCompileTime, MaxColsAtCompileTime> PermutationType;
+ typedef typename internal::plain_row_type<MatrixType>::type RowVectorType;
+ typedef typename internal::plain_col_type<MatrixType>::type ColVectorType;
+ typedef typename MatrixType::PlainObject PlainObject;
+
+ /** \brief Default Constructor.
+ *
+ * The default constructor is useful in cases in which the user intends to
+ * perform decompositions via FullPivHouseholderQR::compute(const MatrixType&).
+ */
+ FullPivHouseholderQR()
+ : m_qr(),
+ m_hCoeffs(),
+ m_rows_transpositions(),
+ m_cols_transpositions(),
+ m_cols_permutation(),
+ m_temp(),
+ m_isInitialized(false),
+ m_usePrescribedThreshold(false) {}
+
+ /** \brief Default Constructor with memory preallocation
+ *
+ * Like the default constructor but with preallocation of the internal data
+ * according to the specified problem \a size.
+ * \sa FullPivHouseholderQR()
+ */
+ FullPivHouseholderQR(Index rows, Index cols)
+ : m_qr(rows, cols),
+ m_hCoeffs((std::min)(rows,cols)),
+ m_rows_transpositions((std::min)(rows,cols)),
+ m_cols_transpositions((std::min)(rows,cols)),
+ m_cols_permutation(cols),
+ m_temp(cols),
+ m_isInitialized(false),
+ m_usePrescribedThreshold(false) {}
+
+ /** \brief Constructs a QR factorization from a given matrix
+ *
+ * This constructor computes the QR factorization of the matrix \a matrix by calling
+ * the method compute(). It is a short cut for:
+ *
+ * \code
+ * FullPivHouseholderQR<MatrixType> qr(matrix.rows(), matrix.cols());
+ * qr.compute(matrix);
+ * \endcode
+ *
+ * \sa compute()
+ */
+ template<typename InputType>
+ explicit FullPivHouseholderQR(const EigenBase<InputType>& matrix)
+ : m_qr(matrix.rows(), matrix.cols()),
+ m_hCoeffs((std::min)(matrix.rows(), matrix.cols())),
+ m_rows_transpositions((std::min)(matrix.rows(), matrix.cols())),
+ m_cols_transpositions((std::min)(matrix.rows(), matrix.cols())),
+ m_cols_permutation(matrix.cols()),
+ m_temp(matrix.cols()),
+ m_isInitialized(false),
+ m_usePrescribedThreshold(false)
+ {
+ compute(matrix.derived());
+ }
+
+ /** \brief Constructs a QR factorization from a given matrix
+ *
+ * This overloaded constructor is provided for \link InplaceDecomposition inplace decomposition \endlink when \c MatrixType is a Eigen::Ref.
+ *
+ * \sa FullPivHouseholderQR(const EigenBase&)
+ */
+ template<typename InputType>
+ explicit FullPivHouseholderQR(EigenBase<InputType>& matrix)
+ : m_qr(matrix.derived()),
+ m_hCoeffs((std::min)(matrix.rows(), matrix.cols())),
+ m_rows_transpositions((std::min)(matrix.rows(), matrix.cols())),
+ m_cols_transpositions((std::min)(matrix.rows(), matrix.cols())),
+ m_cols_permutation(matrix.cols()),
+ m_temp(matrix.cols()),
+ m_isInitialized(false),
+ m_usePrescribedThreshold(false)
+ {
+ computeInPlace();
+ }
+
+ #ifdef EIGEN_PARSED_BY_DOXYGEN
+ /** This method finds a solution x to the equation Ax=b, where A is the matrix of which
+ * \c *this is the QR decomposition.
+ *
+ * \param b the right-hand-side of the equation to solve.
+ *
+ * \returns the exact or least-square solution if the rank is greater or equal to the number of columns of A,
+ * and an arbitrary solution otherwise.
+ *
+ * \note_about_checking_solutions
+ *
+ * \note_about_arbitrary_choice_of_solution
+ *
+ * Example: \include FullPivHouseholderQR_solve.cpp
+ * Output: \verbinclude FullPivHouseholderQR_solve.out
+ */
+ template<typename Rhs>
+ inline const Solve<FullPivHouseholderQR, Rhs>
+ solve(const MatrixBase<Rhs>& b) const;
+ #endif
+
+ /** \returns Expression object representing the matrix Q
+ */
+ MatrixQReturnType matrixQ(void) const;
+
+ /** \returns a reference to the matrix where the Householder QR decomposition is stored
+ */
+ const MatrixType& matrixQR() const
+ {
+ eigen_assert(m_isInitialized && "FullPivHouseholderQR is not initialized.");
+ return m_qr;
+ }
+
+ template<typename InputType>
+ FullPivHouseholderQR& compute(const EigenBase<InputType>& matrix);
+
+ /** \returns a const reference to the column permutation matrix */
+ const PermutationType& colsPermutation() const
+ {
+ eigen_assert(m_isInitialized && "FullPivHouseholderQR is not initialized.");
+ return m_cols_permutation;
+ }
+
+ /** \returns a const reference to the vector of indices representing the rows transpositions */
+ const IntDiagSizeVectorType& rowsTranspositions() const
+ {
+ eigen_assert(m_isInitialized && "FullPivHouseholderQR is not initialized.");
+ return m_rows_transpositions;
+ }
+
+ /** \returns the determinant of the matrix of which
+ * *this is the QR decomposition. It has only linear complexity
+ * (that is, O(n) where n is the dimension of the square matrix)
+ * as the QR decomposition has already been computed.
+ *
+ * \note This is only for square matrices.
+ *
+ * \warning a determinant can be very big or small, so for matrices
+ * of large enough dimension, there is a risk of overflow/underflow.
+ * One way to work around that is to use logAbsDeterminant() instead.
+ *
+ * \sa absDeterminant(), logAbsDeterminant(), MatrixBase::determinant()
+ */
+ typename MatrixType::Scalar determinant() const;
+
+ /** \returns the absolute value of the determinant of the matrix of which
+ * *this is the QR decomposition. It has only linear complexity
+ * (that is, O(n) where n is the dimension of the square matrix)
+ * as the QR decomposition has already been computed.
+ *
+ * \note This is only for square matrices.
+ *
+ * \warning a determinant can be very big or small, so for matrices
+ * of large enough dimension, there is a risk of overflow/underflow.
+ * One way to work around that is to use logAbsDeterminant() instead.
+ *
+ * \sa determinant(), logAbsDeterminant(), MatrixBase::determinant()
+ */
+ typename MatrixType::RealScalar absDeterminant() const;
+
+ /** \returns the natural log of the absolute value of the determinant of the matrix of which
+ * *this is the QR decomposition. It has only linear complexity
+ * (that is, O(n) where n is the dimension of the square matrix)
+ * as the QR decomposition has already been computed.
+ *
+ * \note This is only for square matrices.
+ *
+ * \note This method is useful to work around the risk of overflow/underflow that's inherent
+ * to determinant computation.
+ *
+ * \sa determinant(), absDeterminant(), MatrixBase::determinant()
+ */
+ typename MatrixType::RealScalar logAbsDeterminant() const;
+
+ /** \returns the rank of the matrix of which *this is the QR decomposition.
+ *
+ * \note This method has to determine which pivots should be considered nonzero.
+ * For that, it uses the threshold value that you can control by calling
+ * setThreshold(const RealScalar&).
+ */
+ inline Index rank() const
+ {
+ using std::abs;
+ eigen_assert(m_isInitialized && "FullPivHouseholderQR is not initialized.");
+ RealScalar premultiplied_threshold = abs(m_maxpivot) * threshold();
+ Index result = 0;
+ for(Index i = 0; i < m_nonzero_pivots; ++i)
+ result += (abs(m_qr.coeff(i,i)) > premultiplied_threshold);
+ return result;
+ }
+
+ /** \returns the dimension of the kernel of the matrix of which *this is the QR decomposition.
+ *
+ * \note This method has to determine which pivots should be considered nonzero.
+ * For that, it uses the threshold value that you can control by calling
+ * setThreshold(const RealScalar&).
+ */
+ inline Index dimensionOfKernel() const
+ {
+ eigen_assert(m_isInitialized && "FullPivHouseholderQR is not initialized.");
+ return cols() - rank();
+ }
+
+ /** \returns true if the matrix of which *this is the QR decomposition represents an injective
+ * linear map, i.e. has trivial kernel; false otherwise.
+ *
+ * \note This method has to determine which pivots should be considered nonzero.
+ * For that, it uses the threshold value that you can control by calling
+ * setThreshold(const RealScalar&).
+ */
+ inline bool isInjective() const
+ {
+ eigen_assert(m_isInitialized && "FullPivHouseholderQR is not initialized.");
+ return rank() == cols();
+ }
+
+ /** \returns true if the matrix of which *this is the QR decomposition represents a surjective
+ * linear map; false otherwise.
+ *
+ * \note This method has to determine which pivots should be considered nonzero.
+ * For that, it uses the threshold value that you can control by calling
+ * setThreshold(const RealScalar&).
+ */
+ inline bool isSurjective() const
+ {
+ eigen_assert(m_isInitialized && "FullPivHouseholderQR is not initialized.");
+ return rank() == rows();
+ }
+
+ /** \returns true if the matrix of which *this is the QR decomposition is invertible.
+ *
+ * \note This method has to determine which pivots should be considered nonzero.
+ * For that, it uses the threshold value that you can control by calling
+ * setThreshold(const RealScalar&).
+ */
+ inline bool isInvertible() const
+ {
+ eigen_assert(m_isInitialized && "FullPivHouseholderQR is not initialized.");
+ return isInjective() && isSurjective();
+ }
+
+ /** \returns the inverse of the matrix of which *this is the QR decomposition.
+ *
+ * \note If this matrix is not invertible, the returned matrix has undefined coefficients.
+ * Use isInvertible() to first determine whether this matrix is invertible.
+ */
+ inline const Inverse<FullPivHouseholderQR> inverse() const
+ {
+ eigen_assert(m_isInitialized && "FullPivHouseholderQR is not initialized.");
+ return Inverse<FullPivHouseholderQR>(*this);
+ }
+
+ inline Index rows() const { return m_qr.rows(); }
+ inline Index cols() const { return m_qr.cols(); }
+
+ /** \returns a const reference to the vector of Householder coefficients used to represent the factor \c Q.
+ *
+ * For advanced uses only.
+ */
+ const HCoeffsType& hCoeffs() const { return m_hCoeffs; }
+
+ /** Allows to prescribe a threshold to be used by certain methods, such as rank(),
+ * who need to determine when pivots are to be considered nonzero. This is not used for the
+ * QR decomposition itself.
+ *
+ * When it needs to get the threshold value, Eigen calls threshold(). By default, this
+ * uses a formula to automatically determine a reasonable threshold.
+ * Once you have called the present method setThreshold(const RealScalar&),
+ * your value is used instead.
+ *
+ * \param threshold The new value to use as the threshold.
+ *
+ * A pivot will be considered nonzero if its absolute value is strictly greater than
+ * \f$ \vert pivot \vert \leqslant threshold \times \vert maxpivot \vert \f$
+ * where maxpivot is the biggest pivot.
+ *
+ * If you want to come back to the default behavior, call setThreshold(Default_t)
+ */
+ FullPivHouseholderQR& setThreshold(const RealScalar& threshold)
+ {
+ m_usePrescribedThreshold = true;
+ m_prescribedThreshold = threshold;
+ return *this;
+ }
+
+ /** Allows to come back to the default behavior, letting Eigen use its default formula for
+ * determining the threshold.
+ *
+ * You should pass the special object Eigen::Default as parameter here.
+ * \code qr.setThreshold(Eigen::Default); \endcode
+ *
+ * See the documentation of setThreshold(const RealScalar&).
+ */
+ FullPivHouseholderQR& setThreshold(Default_t)
+ {
+ m_usePrescribedThreshold = false;
+ return *this;
+ }
+
+ /** Returns the threshold that will be used by certain methods such as rank().
+ *
+ * See the documentation of setThreshold(const RealScalar&).
+ */
+ RealScalar threshold() const
+ {
+ eigen_assert(m_isInitialized || m_usePrescribedThreshold);
+ return m_usePrescribedThreshold ? m_prescribedThreshold
+ // this formula comes from experimenting (see "LU precision tuning" thread on the list)
+ // and turns out to be identical to Higham's formula used already in LDLt.
+ : NumTraits<Scalar>::epsilon() * RealScalar(m_qr.diagonalSize());
+ }
+
+ /** \returns the number of nonzero pivots in the QR decomposition.
+ * Here nonzero is meant in the exact sense, not in a fuzzy sense.
+ * So that notion isn't really intrinsically interesting, but it is
+ * still useful when implementing algorithms.
+ *
+ * \sa rank()
+ */
+ inline Index nonzeroPivots() const
+ {
+ eigen_assert(m_isInitialized && "LU is not initialized.");
+ return m_nonzero_pivots;
+ }
+
+ /** \returns the absolute value of the biggest pivot, i.e. the biggest
+ * diagonal coefficient of U.
+ */
+ RealScalar maxPivot() const { return m_maxpivot; }
+
+ #ifndef EIGEN_PARSED_BY_DOXYGEN
+ template<typename RhsType, typename DstType>
+ void _solve_impl(const RhsType &rhs, DstType &dst) const;
+
+ template<bool Conjugate, typename RhsType, typename DstType>
+ void _solve_impl_transposed(const RhsType &rhs, DstType &dst) const;
+ #endif
+
+ protected:
+
+ EIGEN_STATIC_ASSERT_NON_INTEGER(Scalar)
+
+ void computeInPlace();
+
+ MatrixType m_qr;
+ HCoeffsType m_hCoeffs;
+ IntDiagSizeVectorType m_rows_transpositions;
+ IntDiagSizeVectorType m_cols_transpositions;
+ PermutationType m_cols_permutation;
+ RowVectorType m_temp;
+ bool m_isInitialized, m_usePrescribedThreshold;
+ RealScalar m_prescribedThreshold, m_maxpivot;
+ Index m_nonzero_pivots;
+ RealScalar m_precision;
+ Index m_det_p;
+};
+
+template<typename MatrixType>
+typename MatrixType::Scalar FullPivHouseholderQR<MatrixType>::determinant() const
+{
+ eigen_assert(m_isInitialized && "HouseholderQR is not initialized.");
+ eigen_assert(m_qr.rows() == m_qr.cols() && "You can't take the determinant of a non-square matrix!");
+ Scalar detQ;
+ internal::householder_determinant<HCoeffsType, Scalar, NumTraits<Scalar>::IsComplex>::run(m_hCoeffs, detQ);
+ return m_qr.diagonal().prod() * detQ * Scalar(m_det_p);
+}
+
+template<typename MatrixType>
+typename MatrixType::RealScalar FullPivHouseholderQR<MatrixType>::absDeterminant() const
+{
+ using std::abs;
+ eigen_assert(m_isInitialized && "FullPivHouseholderQR is not initialized.");
+ eigen_assert(m_qr.rows() == m_qr.cols() && "You can't take the determinant of a non-square matrix!");
+ return abs(m_qr.diagonal().prod());
+}
+
+template<typename MatrixType>
+typename MatrixType::RealScalar FullPivHouseholderQR<MatrixType>::logAbsDeterminant() const
+{
+ eigen_assert(m_isInitialized && "FullPivHouseholderQR is not initialized.");
+ eigen_assert(m_qr.rows() == m_qr.cols() && "You can't take the determinant of a non-square matrix!");
+ return m_qr.diagonal().cwiseAbs().array().log().sum();
+}
+
+/** Performs the QR factorization of the given matrix \a matrix. The result of
+ * the factorization is stored into \c *this, and a reference to \c *this
+ * is returned.
+ *
+ * \sa class FullPivHouseholderQR, FullPivHouseholderQR(const MatrixType&)
+ */
+template<typename MatrixType>
+template<typename InputType>
+FullPivHouseholderQR<MatrixType>& FullPivHouseholderQR<MatrixType>::compute(const EigenBase<InputType>& matrix)
+{
+ m_qr = matrix.derived();
+ computeInPlace();
+ return *this;
+}
+
+template<typename MatrixType>
+void FullPivHouseholderQR<MatrixType>::computeInPlace()
+{
+ using std::abs;
+ Index rows = m_qr.rows();
+ Index cols = m_qr.cols();
+ Index size = (std::min)(rows,cols);
+
+
+ m_hCoeffs.resize(size);
+
+ m_temp.resize(cols);
+
+ m_precision = NumTraits<Scalar>::epsilon() * RealScalar(size);
+
+ m_rows_transpositions.resize(size);
+ m_cols_transpositions.resize(size);
+ Index number_of_transpositions = 0;
+
+ RealScalar biggest(0);
+
+ m_nonzero_pivots = size; // the generic case is that in which all pivots are nonzero (invertible case)
+ m_maxpivot = RealScalar(0);
+
+ for (Index k = 0; k < size; ++k)
+ {
+ Index row_of_biggest_in_corner, col_of_biggest_in_corner;
+ typedef internal::scalar_score_coeff_op<Scalar> Scoring;
+ typedef typename Scoring::result_type Score;
+
+ Score score = m_qr.bottomRightCorner(rows-k, cols-k)
+ .unaryExpr(Scoring())
+ .maxCoeff(&row_of_biggest_in_corner, &col_of_biggest_in_corner);
+ row_of_biggest_in_corner += k;
+ col_of_biggest_in_corner += k;
+ RealScalar biggest_in_corner = internal::abs_knowing_score<Scalar>()(m_qr(row_of_biggest_in_corner, col_of_biggest_in_corner), score);
+ if(k==0) biggest = biggest_in_corner;
+
+ // if the corner is negligible, then we have less than full rank, and we can finish early
+ if(internal::isMuchSmallerThan(biggest_in_corner, biggest, m_precision))
+ {
+ m_nonzero_pivots = k;
+ for(Index i = k; i < size; i++)
+ {
+ m_rows_transpositions.coeffRef(i) = internal::convert_index<StorageIndex>(i);
+ m_cols_transpositions.coeffRef(i) = internal::convert_index<StorageIndex>(i);
+ m_hCoeffs.coeffRef(i) = Scalar(0);
+ }
+ break;
+ }
+
+ m_rows_transpositions.coeffRef(k) = internal::convert_index<StorageIndex>(row_of_biggest_in_corner);
+ m_cols_transpositions.coeffRef(k) = internal::convert_index<StorageIndex>(col_of_biggest_in_corner);
+ if(k != row_of_biggest_in_corner) {
+ m_qr.row(k).tail(cols-k).swap(m_qr.row(row_of_biggest_in_corner).tail(cols-k));
+ ++number_of_transpositions;
+ }
+ if(k != col_of_biggest_in_corner) {
+ m_qr.col(k).swap(m_qr.col(col_of_biggest_in_corner));
+ ++number_of_transpositions;
+ }
+
+ RealScalar beta;
+ m_qr.col(k).tail(rows-k).makeHouseholderInPlace(m_hCoeffs.coeffRef(k), beta);
+ m_qr.coeffRef(k,k) = beta;
+
+ // remember the maximum absolute value of diagonal coefficients
+ if(abs(beta) > m_maxpivot) m_maxpivot = abs(beta);
+
+ m_qr.bottomRightCorner(rows-k, cols-k-1)
+ .applyHouseholderOnTheLeft(m_qr.col(k).tail(rows-k-1), m_hCoeffs.coeffRef(k), &m_temp.coeffRef(k+1));
+ }
+
+ m_cols_permutation.setIdentity(cols);
+ for(Index k = 0; k < size; ++k)
+ m_cols_permutation.applyTranspositionOnTheRight(k, m_cols_transpositions.coeff(k));
+
+ m_det_p = (number_of_transpositions%2) ? -1 : 1;
+ m_isInitialized = true;
+}
+
+#ifndef EIGEN_PARSED_BY_DOXYGEN
+template<typename MatrixType_>
+template<typename RhsType, typename DstType>
+void FullPivHouseholderQR<MatrixType_>::_solve_impl(const RhsType &rhs, DstType &dst) const
+{
+ const Index l_rank = rank();
+
+ // FIXME introduce nonzeroPivots() and use it here. and more generally,
+ // make the same improvements in this dec as in FullPivLU.
+ if(l_rank==0)
+ {
+ dst.setZero();
+ return;
+ }
+
+ typename RhsType::PlainObject c(rhs);
+
+ Matrix<typename RhsType::Scalar,1,RhsType::ColsAtCompileTime> temp(rhs.cols());
+ for (Index k = 0; k < l_rank; ++k)
+ {
+ Index remainingSize = rows()-k;
+ c.row(k).swap(c.row(m_rows_transpositions.coeff(k)));
+ c.bottomRightCorner(remainingSize, rhs.cols())
+ .applyHouseholderOnTheLeft(m_qr.col(k).tail(remainingSize-1),
+ m_hCoeffs.coeff(k), &temp.coeffRef(0));
+ }
+
+ m_qr.topLeftCorner(l_rank, l_rank)
+ .template triangularView<Upper>()
+ .solveInPlace(c.topRows(l_rank));
+
+ for(Index i = 0; i < l_rank; ++i) dst.row(m_cols_permutation.indices().coeff(i)) = c.row(i);
+ for(Index i = l_rank; i < cols(); ++i) dst.row(m_cols_permutation.indices().coeff(i)).setZero();
+}
+
+template<typename MatrixType_>
+template<bool Conjugate, typename RhsType, typename DstType>
+void FullPivHouseholderQR<MatrixType_>::_solve_impl_transposed(const RhsType &rhs, DstType &dst) const
+{
+ const Index l_rank = rank();
+
+ if(l_rank == 0)
+ {
+ dst.setZero();
+ return;
+ }
+
+ typename RhsType::PlainObject c(m_cols_permutation.transpose()*rhs);
+
+ m_qr.topLeftCorner(l_rank, l_rank)
+ .template triangularView<Upper>()
+ .transpose().template conjugateIf<Conjugate>()
+ .solveInPlace(c.topRows(l_rank));
+
+ dst.topRows(l_rank) = c.topRows(l_rank);
+ dst.bottomRows(rows()-l_rank).setZero();
+
+ Matrix<Scalar, 1, DstType::ColsAtCompileTime> temp(dst.cols());
+ const Index size = (std::min)(rows(), cols());
+ for (Index k = size-1; k >= 0; --k)
+ {
+ Index remainingSize = rows()-k;
+
+ dst.bottomRightCorner(remainingSize, dst.cols())
+ .applyHouseholderOnTheLeft(m_qr.col(k).tail(remainingSize-1).template conjugateIf<!Conjugate>(),
+ m_hCoeffs.template conjugateIf<Conjugate>().coeff(k), &temp.coeffRef(0));
+
+ dst.row(k).swap(dst.row(m_rows_transpositions.coeff(k)));
+ }
+}
+#endif
+
+namespace internal {
+
+template<typename DstXprType, typename MatrixType>
+struct Assignment<DstXprType, Inverse<FullPivHouseholderQR<MatrixType> >, internal::assign_op<typename DstXprType::Scalar,typename FullPivHouseholderQR<MatrixType>::Scalar>, Dense2Dense>
+{
+ typedef FullPivHouseholderQR<MatrixType> QrType;
+ typedef Inverse<QrType> SrcXprType;
+ static void run(DstXprType &dst, const SrcXprType &src, const internal::assign_op<typename DstXprType::Scalar,typename QrType::Scalar> &)
+ {
+ dst = src.nestedExpression().solve(MatrixType::Identity(src.rows(), src.cols()));
+ }
+};
+
+/** \ingroup QR_Module
+ *
+ * \brief Expression type for return value of FullPivHouseholderQR::matrixQ()
+ *
+ * \tparam MatrixType type of underlying dense matrix
+ */
+template<typename MatrixType> struct FullPivHouseholderQRMatrixQReturnType
+ : public ReturnByValue<FullPivHouseholderQRMatrixQReturnType<MatrixType> >
+{
+public:
+ typedef typename FullPivHouseholderQR<MatrixType>::IntDiagSizeVectorType IntDiagSizeVectorType;
+ typedef typename internal::plain_diag_type<MatrixType>::type HCoeffsType;
+ typedef Matrix<typename MatrixType::Scalar, 1, MatrixType::RowsAtCompileTime, RowMajor, 1,
+ MatrixType::MaxRowsAtCompileTime> WorkVectorType;
+
+ FullPivHouseholderQRMatrixQReturnType(const MatrixType& qr,
+ const HCoeffsType& hCoeffs,
+ const IntDiagSizeVectorType& rowsTranspositions)
+ : m_qr(qr),
+ m_hCoeffs(hCoeffs),
+ m_rowsTranspositions(rowsTranspositions)
+ {}
+
+ template <typename ResultType>
+ void evalTo(ResultType& result) const
+ {
+ const Index rows = m_qr.rows();
+ WorkVectorType workspace(rows);
+ evalTo(result, workspace);
+ }
+
+ template <typename ResultType>
+ void evalTo(ResultType& result, WorkVectorType& workspace) const
+ {
+ using numext::conj;
+ // compute the product H'_0 H'_1 ... H'_n-1,
+ // where H_k is the k-th Householder transformation I - h_k v_k v_k'
+ // and v_k is the k-th Householder vector [1,m_qr(k+1,k), m_qr(k+2,k), ...]
+ const Index rows = m_qr.rows();
+ const Index cols = m_qr.cols();
+ const Index size = (std::min)(rows, cols);
+ workspace.resize(rows);
+ result.setIdentity(rows, rows);
+ for (Index k = size-1; k >= 0; k--)
+ {
+ result.block(k, k, rows-k, rows-k)
+ .applyHouseholderOnTheLeft(m_qr.col(k).tail(rows-k-1), conj(m_hCoeffs.coeff(k)), &workspace.coeffRef(k));
+ result.row(k).swap(result.row(m_rowsTranspositions.coeff(k)));
+ }
+ }
+
+ Index rows() const { return m_qr.rows(); }
+ Index cols() const { return m_qr.rows(); }
+
+protected:
+ typename MatrixType::Nested m_qr;
+ typename HCoeffsType::Nested m_hCoeffs;
+ typename IntDiagSizeVectorType::Nested m_rowsTranspositions;
+};
+
+// template<typename MatrixType>
+// struct evaluator<FullPivHouseholderQRMatrixQReturnType<MatrixType> >
+// : public evaluator<ReturnByValue<FullPivHouseholderQRMatrixQReturnType<MatrixType> > >
+// {};
+
+} // end namespace internal
+
+template<typename MatrixType>
+inline typename FullPivHouseholderQR<MatrixType>::MatrixQReturnType FullPivHouseholderQR<MatrixType>::matrixQ() const
+{
+ eigen_assert(m_isInitialized && "FullPivHouseholderQR is not initialized.");
+ return MatrixQReturnType(m_qr, m_hCoeffs, m_rows_transpositions);
+}
+
+/** \return the full-pivoting Householder QR decomposition of \c *this.
+ *
+ * \sa class FullPivHouseholderQR
+ */
+template<typename Derived>
+const FullPivHouseholderQR<typename MatrixBase<Derived>::PlainObject>
+MatrixBase<Derived>::fullPivHouseholderQr() const
+{
+ return FullPivHouseholderQR<PlainObject>(eval());
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_FULLPIVOTINGHOUSEHOLDERQR_H
diff --git a/Eigen/src/QR/HouseholderQR.h b/Eigen/src/QR/HouseholderQR.h
new file mode 100644
index 0000000..abfefd1
--- /dev/null
+++ b/Eigen/src/QR/HouseholderQR.h
@@ -0,0 +1,534 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2010 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2009 Benoit Jacob <jacob.benoit.1@gmail.com>
+// Copyright (C) 2010 Vincent Lejeune
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_QR_H
+#define EIGEN_QR_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+template<typename MatrixType_> struct traits<HouseholderQR<MatrixType_> >
+ : traits<MatrixType_>
+{
+ typedef MatrixXpr XprKind;
+ typedef SolverStorage StorageKind;
+ typedef int StorageIndex;
+ enum { Flags = 0 };
+};
+
+} // end namespace internal
+
+/** \ingroup QR_Module
+ *
+ *
+ * \class HouseholderQR
+ *
+ * \brief Householder QR decomposition of a matrix
+ *
+ * \tparam MatrixType_ the type of the matrix of which we are computing the QR decomposition
+ *
+ * This class performs a QR decomposition of a matrix \b A into matrices \b Q and \b R
+ * such that
+ * \f[
+ * \mathbf{A} = \mathbf{Q} \, \mathbf{R}
+ * \f]
+ * by using Householder transformations. Here, \b Q a unitary matrix and \b R an upper triangular matrix.
+ * The result is stored in a compact way compatible with LAPACK.
+ *
+ * Note that no pivoting is performed. This is \b not a rank-revealing decomposition.
+ * If you want that feature, use FullPivHouseholderQR or ColPivHouseholderQR instead.
+ *
+ * This Householder QR decomposition is faster, but less numerically stable and less feature-full than
+ * FullPivHouseholderQR or ColPivHouseholderQR.
+ *
+ * This class supports the \link InplaceDecomposition inplace decomposition \endlink mechanism.
+ *
+ * \sa MatrixBase::householderQr()
+ */
+template<typename MatrixType_> class HouseholderQR
+ : public SolverBase<HouseholderQR<MatrixType_> >
+{
+ public:
+
+ typedef MatrixType_ MatrixType;
+ typedef SolverBase<HouseholderQR> Base;
+ friend class SolverBase<HouseholderQR>;
+
+ EIGEN_GENERIC_PUBLIC_INTERFACE(HouseholderQR)
+ enum {
+ MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime,
+ MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime
+ };
+ typedef Matrix<Scalar, RowsAtCompileTime, RowsAtCompileTime, (MatrixType::Flags&RowMajorBit) ? RowMajor : ColMajor, MaxRowsAtCompileTime, MaxRowsAtCompileTime> MatrixQType;
+ typedef typename internal::plain_diag_type<MatrixType>::type HCoeffsType;
+ typedef typename internal::plain_row_type<MatrixType>::type RowVectorType;
+ typedef HouseholderSequence<MatrixType,internal::remove_all_t<typename HCoeffsType::ConjugateReturnType>> HouseholderSequenceType;
+
+ /**
+ * \brief Default Constructor.
+ *
+ * The default constructor is useful in cases in which the user intends to
+ * perform decompositions via HouseholderQR::compute(const MatrixType&).
+ */
+ HouseholderQR() : m_qr(), m_hCoeffs(), m_temp(), m_isInitialized(false) {}
+
+ /** \brief Default Constructor with memory preallocation
+ *
+ * Like the default constructor but with preallocation of the internal data
+ * according to the specified problem \a size.
+ * \sa HouseholderQR()
+ */
+ HouseholderQR(Index rows, Index cols)
+ : m_qr(rows, cols),
+ m_hCoeffs((std::min)(rows,cols)),
+ m_temp(cols),
+ m_isInitialized(false) {}
+
+ /** \brief Constructs a QR factorization from a given matrix
+ *
+ * This constructor computes the QR factorization of the matrix \a matrix by calling
+ * the method compute(). It is a short cut for:
+ *
+ * \code
+ * HouseholderQR<MatrixType> qr(matrix.rows(), matrix.cols());
+ * qr.compute(matrix);
+ * \endcode
+ *
+ * \sa compute()
+ */
+ template<typename InputType>
+ explicit HouseholderQR(const EigenBase<InputType>& matrix)
+ : m_qr(matrix.rows(), matrix.cols()),
+ m_hCoeffs((std::min)(matrix.rows(),matrix.cols())),
+ m_temp(matrix.cols()),
+ m_isInitialized(false)
+ {
+ compute(matrix.derived());
+ }
+
+
+ /** \brief Constructs a QR factorization from a given matrix
+ *
+ * This overloaded constructor is provided for \link InplaceDecomposition inplace decomposition \endlink when
+ * \c MatrixType is a Eigen::Ref.
+ *
+ * \sa HouseholderQR(const EigenBase&)
+ */
+ template<typename InputType>
+ explicit HouseholderQR(EigenBase<InputType>& matrix)
+ : m_qr(matrix.derived()),
+ m_hCoeffs((std::min)(matrix.rows(),matrix.cols())),
+ m_temp(matrix.cols()),
+ m_isInitialized(false)
+ {
+ computeInPlace();
+ }
+
+ #ifdef EIGEN_PARSED_BY_DOXYGEN
+ /** This method finds a solution x to the equation Ax=b, where A is the matrix of which
+ * *this is the QR decomposition, if any exists.
+ *
+ * \param b the right-hand-side of the equation to solve.
+ *
+ * \returns a solution.
+ *
+ * \note_about_checking_solutions
+ *
+ * \note_about_arbitrary_choice_of_solution
+ *
+ * Example: \include HouseholderQR_solve.cpp
+ * Output: \verbinclude HouseholderQR_solve.out
+ */
+ template<typename Rhs>
+ inline const Solve<HouseholderQR, Rhs>
+ solve(const MatrixBase<Rhs>& b) const;
+ #endif
+
+ /** This method returns an expression of the unitary matrix Q as a sequence of Householder transformations.
+ *
+ * The returned expression can directly be used to perform matrix products. It can also be assigned to a dense Matrix object.
+ * Here is an example showing how to recover the full or thin matrix Q, as well as how to perform matrix products using operator*:
+ *
+ * Example: \include HouseholderQR_householderQ.cpp
+ * Output: \verbinclude HouseholderQR_householderQ.out
+ */
+ HouseholderSequenceType householderQ() const
+ {
+ eigen_assert(m_isInitialized && "HouseholderQR is not initialized.");
+ return HouseholderSequenceType(m_qr, m_hCoeffs.conjugate());
+ }
+
+ /** \returns a reference to the matrix where the Householder QR decomposition is stored
+ * in a LAPACK-compatible way.
+ */
+ const MatrixType& matrixQR() const
+ {
+ eigen_assert(m_isInitialized && "HouseholderQR is not initialized.");
+ return m_qr;
+ }
+
+ template<typename InputType>
+ HouseholderQR& compute(const EigenBase<InputType>& matrix) {
+ m_qr = matrix.derived();
+ computeInPlace();
+ return *this;
+ }
+
+ /** \returns the determinant of the matrix of which
+ * *this is the QR decomposition. It has only linear complexity
+ * (that is, O(n) where n is the dimension of the square matrix)
+ * as the QR decomposition has already been computed.
+ *
+ * \note This is only for square matrices.
+ *
+ * \warning a determinant can be very big or small, so for matrices
+ * of large enough dimension, there is a risk of overflow/underflow.
+ * One way to work around that is to use logAbsDeterminant() instead.
+ *
+ * \sa absDeterminant(), logAbsDeterminant(), MatrixBase::determinant()
+ */
+ typename MatrixType::Scalar determinant() const;
+
+ /** \returns the absolute value of the determinant of the matrix of which
+ * *this is the QR decomposition. It has only linear complexity
+ * (that is, O(n) where n is the dimension of the square matrix)
+ * as the QR decomposition has already been computed.
+ *
+ * \note This is only for square matrices.
+ *
+ * \warning a determinant can be very big or small, so for matrices
+ * of large enough dimension, there is a risk of overflow/underflow.
+ * One way to work around that is to use logAbsDeterminant() instead.
+ *
+ * \sa determinant(), logAbsDeterminant(), MatrixBase::determinant()
+ */
+ typename MatrixType::RealScalar absDeterminant() const;
+
+ /** \returns the natural log of the absolute value of the determinant of the matrix of which
+ * *this is the QR decomposition. It has only linear complexity
+ * (that is, O(n) where n is the dimension of the square matrix)
+ * as the QR decomposition has already been computed.
+ *
+ * \note This is only for square matrices.
+ *
+ * \note This method is useful to work around the risk of overflow/underflow that's inherent
+ * to determinant computation.
+ *
+ * \sa determinant(), absDeterminant(), MatrixBase::determinant()
+ */
+ typename MatrixType::RealScalar logAbsDeterminant() const;
+
+ inline Index rows() const { return m_qr.rows(); }
+ inline Index cols() const { return m_qr.cols(); }
+
+ /** \returns a const reference to the vector of Householder coefficients used to represent the factor \c Q.
+ *
+ * For advanced uses only.
+ */
+ const HCoeffsType& hCoeffs() const { return m_hCoeffs; }
+
+ #ifndef EIGEN_PARSED_BY_DOXYGEN
+ template<typename RhsType, typename DstType>
+ void _solve_impl(const RhsType &rhs, DstType &dst) const;
+
+ template<bool Conjugate, typename RhsType, typename DstType>
+ void _solve_impl_transposed(const RhsType &rhs, DstType &dst) const;
+ #endif
+
+ protected:
+
+ EIGEN_STATIC_ASSERT_NON_INTEGER(Scalar)
+
+ void computeInPlace();
+
+ MatrixType m_qr;
+ HCoeffsType m_hCoeffs;
+ RowVectorType m_temp;
+ bool m_isInitialized;
+};
+
+namespace internal {
+
+/** \internal */
+template<typename HCoeffs, typename Scalar, bool IsComplex>
+struct householder_determinant
+{
+ static void run(const HCoeffs& hCoeffs, Scalar& out_det)
+ {
+ out_det = Scalar(1);
+ Index size = hCoeffs.rows();
+ for (Index i = 0; i < size; i ++)
+ {
+ // For each valid reflection Q_n,
+ // det(Q_n) = - conj(h_n) / h_n
+ // where h_n is the Householder coefficient.
+ if (hCoeffs(i) != Scalar(0))
+ out_det *= - numext::conj(hCoeffs(i)) / hCoeffs(i);
+ }
+ }
+};
+
+/** \internal */
+template<typename HCoeffs, typename Scalar>
+struct householder_determinant<HCoeffs, Scalar, false>
+{
+ static void run(const HCoeffs& hCoeffs, Scalar& out_det)
+ {
+ bool negated = false;
+ Index size = hCoeffs.rows();
+ for (Index i = 0; i < size; i ++)
+ {
+ // Each valid reflection negates the determinant.
+ if (hCoeffs(i) != Scalar(0))
+ negated ^= true;
+ }
+ out_det = negated ? Scalar(-1) : Scalar(1);
+ }
+};
+
+} // end namespace internal
+
+template<typename MatrixType>
+typename MatrixType::Scalar HouseholderQR<MatrixType>::determinant() const
+{
+ eigen_assert(m_isInitialized && "HouseholderQR is not initialized.");
+ eigen_assert(m_qr.rows() == m_qr.cols() && "You can't take the determinant of a non-square matrix!");
+ Scalar detQ;
+ internal::householder_determinant<HCoeffsType, Scalar, NumTraits<Scalar>::IsComplex>::run(m_hCoeffs, detQ);
+ return m_qr.diagonal().prod() * detQ;
+}
+
+template<typename MatrixType>
+typename MatrixType::RealScalar HouseholderQR<MatrixType>::absDeterminant() const
+{
+ using std::abs;
+ eigen_assert(m_isInitialized && "HouseholderQR is not initialized.");
+ eigen_assert(m_qr.rows() == m_qr.cols() && "You can't take the determinant of a non-square matrix!");
+ return abs(m_qr.diagonal().prod());
+}
+
+template<typename MatrixType>
+typename MatrixType::RealScalar HouseholderQR<MatrixType>::logAbsDeterminant() const
+{
+ eigen_assert(m_isInitialized && "HouseholderQR is not initialized.");
+ eigen_assert(m_qr.rows() == m_qr.cols() && "You can't take the determinant of a non-square matrix!");
+ return m_qr.diagonal().cwiseAbs().array().log().sum();
+}
+
+namespace internal {
+
+/** \internal */
+template<typename MatrixQR, typename HCoeffs>
+void householder_qr_inplace_unblocked(MatrixQR& mat, HCoeffs& hCoeffs, typename MatrixQR::Scalar* tempData = 0)
+{
+ typedef typename MatrixQR::Scalar Scalar;
+ typedef typename MatrixQR::RealScalar RealScalar;
+ Index rows = mat.rows();
+ Index cols = mat.cols();
+ Index size = (std::min)(rows,cols);
+
+ eigen_assert(hCoeffs.size() == size);
+
+ typedef Matrix<Scalar,MatrixQR::ColsAtCompileTime,1> TempType;
+ TempType tempVector;
+ if(tempData==0)
+ {
+ tempVector.resize(cols);
+ tempData = tempVector.data();
+ }
+
+ for(Index k = 0; k < size; ++k)
+ {
+ Index remainingRows = rows - k;
+ Index remainingCols = cols - k - 1;
+
+ RealScalar beta;
+ mat.col(k).tail(remainingRows).makeHouseholderInPlace(hCoeffs.coeffRef(k), beta);
+ mat.coeffRef(k,k) = beta;
+
+ // apply H to remaining part of m_qr from the left
+ mat.bottomRightCorner(remainingRows, remainingCols)
+ .applyHouseholderOnTheLeft(mat.col(k).tail(remainingRows-1), hCoeffs.coeffRef(k), tempData+k+1);
+ }
+}
+
+// TODO: add a corresponding public API for updating a QR factorization
+/** \internal
+ * Basically a modified copy of @c Eigen::internal::householder_qr_inplace_unblocked that
+ * performs a rank-1 update of the QR matrix in compact storage. This function assumes, that
+ * the first @c k-1 columns of the matrix @c mat contain the QR decomposition of \f$A^N\f$ up to
+ * column k-1. Then the QR decomposition of the k-th column (given by @c newColumn) is computed by
+ * applying the k-1 Householder projectors on it and finally compute the projector \f$H_k\f$ of
+ * it. On exit the matrix @c mat and the vector @c hCoeffs contain the QR decomposition of the
+ * first k columns of \f$A^N\f$. The \a tempData argument must point to at least mat.cols() scalars. */
+template <typename MatrixQR, typename HCoeffs, typename VectorQR>
+void householder_qr_inplace_update(MatrixQR& mat, HCoeffs& hCoeffs, const VectorQR& newColumn,
+ typename MatrixQR::Index k, typename MatrixQR::Scalar* tempData) {
+ typedef typename MatrixQR::Index Index;
+ typedef typename MatrixQR::RealScalar RealScalar;
+ Index rows = mat.rows();
+
+ eigen_assert(k < mat.cols());
+ eigen_assert(k < rows);
+ eigen_assert(hCoeffs.size() == mat.cols());
+ eigen_assert(newColumn.size() == rows);
+ eigen_assert(tempData);
+
+ // Store new column in mat at column k
+ mat.col(k) = newColumn;
+ // Apply H = H_1...H_{k-1} on newColumn (skip if k=0)
+ for (Index i = 0; i < k; ++i) {
+ Index remainingRows = rows - i;
+ mat.col(k)
+ .tail(remainingRows)
+ .applyHouseholderOnTheLeft(mat.col(i).tail(remainingRows - 1), hCoeffs.coeffRef(i), tempData + i + 1);
+ }
+ // Construct Householder projector in-place in column k
+ RealScalar beta;
+ mat.col(k).tail(rows - k).makeHouseholderInPlace(hCoeffs.coeffRef(k), beta);
+ mat.coeffRef(k, k) = beta;
+}
+
+/** \internal */
+template<typename MatrixQR, typename HCoeffs,
+ typename MatrixQRScalar = typename MatrixQR::Scalar,
+ bool InnerStrideIsOne = (MatrixQR::InnerStrideAtCompileTime == 1 && HCoeffs::InnerStrideAtCompileTime == 1)>
+struct householder_qr_inplace_blocked
+{
+ // This is specialized for LAPACK-supported Scalar types in HouseholderQR_LAPACKE.h
+ static void run(MatrixQR& mat, HCoeffs& hCoeffs, Index maxBlockSize=32,
+ typename MatrixQR::Scalar* tempData = 0)
+ {
+ typedef typename MatrixQR::Scalar Scalar;
+ typedef Block<MatrixQR,Dynamic,Dynamic> BlockType;
+
+ Index rows = mat.rows();
+ Index cols = mat.cols();
+ Index size = (std::min)(rows, cols);
+
+ typedef Matrix<Scalar,Dynamic,1,ColMajor,MatrixQR::MaxColsAtCompileTime,1> TempType;
+ TempType tempVector;
+ if(tempData==0)
+ {
+ tempVector.resize(cols);
+ tempData = tempVector.data();
+ }
+
+ Index blockSize = (std::min)(maxBlockSize,size);
+
+ Index k = 0;
+ for (k = 0; k < size; k += blockSize)
+ {
+ Index bs = (std::min)(size-k,blockSize); // actual size of the block
+ Index tcols = cols - k - bs; // trailing columns
+ Index brows = rows-k; // rows of the block
+
+ // partition the matrix:
+ // A00 | A01 | A02
+ // mat = A10 | A11 | A12
+ // A20 | A21 | A22
+ // and performs the qr dec of [A11^T A12^T]^T
+ // and update [A21^T A22^T]^T using level 3 operations.
+ // Finally, the algorithm continue on A22
+
+ BlockType A11_21 = mat.block(k,k,brows,bs);
+ Block<HCoeffs,Dynamic,1> hCoeffsSegment = hCoeffs.segment(k,bs);
+
+ householder_qr_inplace_unblocked(A11_21, hCoeffsSegment, tempData);
+
+ if(tcols)
+ {
+ BlockType A21_22 = mat.block(k,k+bs,brows,tcols);
+ apply_block_householder_on_the_left(A21_22,A11_21,hCoeffsSegment, false); // false == backward
+ }
+ }
+ }
+};
+
+} // end namespace internal
+
+#ifndef EIGEN_PARSED_BY_DOXYGEN
+template<typename MatrixType_>
+template<typename RhsType, typename DstType>
+void HouseholderQR<MatrixType_>::_solve_impl(const RhsType &rhs, DstType &dst) const
+{
+ const Index rank = (std::min)(rows(), cols());
+
+ typename RhsType::PlainObject c(rhs);
+
+ c.applyOnTheLeft(householderQ().setLength(rank).adjoint() );
+
+ m_qr.topLeftCorner(rank, rank)
+ .template triangularView<Upper>()
+ .solveInPlace(c.topRows(rank));
+
+ dst.topRows(rank) = c.topRows(rank);
+ dst.bottomRows(cols()-rank).setZero();
+}
+
+template<typename MatrixType_>
+template<bool Conjugate, typename RhsType, typename DstType>
+void HouseholderQR<MatrixType_>::_solve_impl_transposed(const RhsType &rhs, DstType &dst) const
+{
+ const Index rank = (std::min)(rows(), cols());
+
+ typename RhsType::PlainObject c(rhs);
+
+ m_qr.topLeftCorner(rank, rank)
+ .template triangularView<Upper>()
+ .transpose().template conjugateIf<Conjugate>()
+ .solveInPlace(c.topRows(rank));
+
+ dst.topRows(rank) = c.topRows(rank);
+ dst.bottomRows(rows()-rank).setZero();
+
+ dst.applyOnTheLeft(householderQ().setLength(rank).template conjugateIf<!Conjugate>() );
+}
+#endif
+
+/** Performs the QR factorization of the given matrix \a matrix. The result of
+ * the factorization is stored into \c *this, and a reference to \c *this
+ * is returned.
+ *
+ * \sa class HouseholderQR, HouseholderQR(const MatrixType&)
+ */
+template<typename MatrixType>
+void HouseholderQR<MatrixType>::computeInPlace()
+{
+ Index rows = m_qr.rows();
+ Index cols = m_qr.cols();
+ Index size = (std::min)(rows,cols);
+
+ m_hCoeffs.resize(size);
+
+ m_temp.resize(cols);
+
+ internal::householder_qr_inplace_blocked<MatrixType, HCoeffsType>::run(m_qr, m_hCoeffs, 48, m_temp.data());
+
+ m_isInitialized = true;
+}
+
+/** \return the Householder QR decomposition of \c *this.
+ *
+ * \sa class HouseholderQR
+ */
+template<typename Derived>
+const HouseholderQR<typename MatrixBase<Derived>::PlainObject>
+MatrixBase<Derived>::householderQr() const
+{
+ return HouseholderQR<PlainObject>(eval());
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_QR_H
diff --git a/Eigen/src/QR/HouseholderQR_LAPACKE.h b/Eigen/src/QR/HouseholderQR_LAPACKE.h
new file mode 100644
index 0000000..57c2f6a
--- /dev/null
+++ b/Eigen/src/QR/HouseholderQR_LAPACKE.h
@@ -0,0 +1,77 @@
+/*
+ Copyright (c) 2011, Intel Corporation. All rights reserved.
+
+ Redistribution and use in source and binary forms, with or without modification,
+ are permitted provided that the following conditions are met:
+
+ * Redistributions of source code must retain the above copyright notice, this
+ list of conditions and the following disclaimer.
+ * Redistributions in binary form must reproduce the above copyright notice,
+ this list of conditions and the following disclaimer in the documentation
+ and/or other materials provided with the distribution.
+ * Neither the name of Intel Corporation nor the names of its contributors may
+ be used to endorse or promote products derived from this software without
+ specific prior written permission.
+
+ THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
+ ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
+ WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
+ DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR
+ ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
+ (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
+ LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON
+ ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
+ (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
+ SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+
+ ********************************************************************************
+ * Content : Eigen bindings to LAPACKe
+ * Householder QR decomposition of a matrix w/o pivoting based on
+ * LAPACKE_?geqrf function.
+ ********************************************************************************
+*/
+
+#ifndef EIGEN_QR_LAPACKE_H
+#define EIGEN_QR_LAPACKE_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+
+namespace lapacke_helpers {
+
+template<typename MatrixQR, typename HCoeffs>
+struct lapacke_hqr
+{
+ static void run(MatrixQR& mat, HCoeffs& hCoeffs, Index = 32, typename MatrixQR::Scalar* = 0)
+ {
+ lapack_int m = to_lapack(mat.rows());
+ lapack_int n = to_lapack(mat.cols());
+ lapack_int lda = to_lapack(mat.outerStride());
+ lapack_int matrix_order = lapack_storage_of(mat);
+ geqrf(matrix_order, m, n, to_lapack(mat.data()), lda, to_lapack(hCoeffs.data()));
+ hCoeffs.adjointInPlace();
+ }
+};
+
+}
+
+/** \internal Specialization for the data types supported by LAPACKe */
+#define EIGEN_LAPACKE_HH_QR(EIGTYPE) \
+template<typename MatrixQR, typename HCoeffs> \
+struct householder_qr_inplace_blocked<MatrixQR, HCoeffs, EIGTYPE, true> : public lapacke_helpers::lapacke_hqr<MatrixQR, HCoeffs> {};
+
+EIGEN_LAPACKE_HH_QR(double)
+EIGEN_LAPACKE_HH_QR(float)
+EIGEN_LAPACKE_HH_QR(std::complex<double>)
+EIGEN_LAPACKE_HH_QR(std::complex<float>)
+
+#undef EIGEN_LAPACKE_HH_QR
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_QR_LAPACKE_H
diff --git a/Eigen/src/QR/InternalHeaderCheck.h b/Eigen/src/QR/InternalHeaderCheck.h
new file mode 100644
index 0000000..bf8df01
--- /dev/null
+++ b/Eigen/src/QR/InternalHeaderCheck.h
@@ -0,0 +1,3 @@
+#ifndef EIGEN_QR_MODULE_H
+#error "Please include Eigen/QR instead of including headers inside the src directory directly."
+#endif
diff --git a/Eigen/src/SPQRSupport/InternalHeaderCheck.h b/Eigen/src/SPQRSupport/InternalHeaderCheck.h
new file mode 100644
index 0000000..8d94ba4
--- /dev/null
+++ b/Eigen/src/SPQRSupport/InternalHeaderCheck.h
@@ -0,0 +1,3 @@
+#ifndef EIGEN_SPQRSUPPORT_MODULE_H
+#error "Please include Eigen/SPQRSupport instead of including headers inside the src directory directly."
+#endif
diff --git a/Eigen/src/SPQRSupport/SuiteSparseQRSupport.h b/Eigen/src/SPQRSupport/SuiteSparseQRSupport.h
new file mode 100644
index 0000000..36e8ead
--- /dev/null
+++ b/Eigen/src/SPQRSupport/SuiteSparseQRSupport.h
@@ -0,0 +1,337 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2012 Desire Nuentsa <desire.nuentsa_wakam@inria.fr>
+// Copyright (C) 2014 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_SUITESPARSEQRSUPPORT_H
+#define EIGEN_SUITESPARSEQRSUPPORT_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+ template<typename MatrixType> class SPQR;
+ template<typename SPQRType> struct SPQRMatrixQReturnType;
+ template<typename SPQRType> struct SPQRMatrixQTransposeReturnType;
+ template <typename SPQRType, typename Derived> struct SPQR_QProduct;
+ namespace internal {
+ template <typename SPQRType> struct traits<SPQRMatrixQReturnType<SPQRType> >
+ {
+ typedef typename SPQRType::MatrixType ReturnType;
+ };
+ template <typename SPQRType> struct traits<SPQRMatrixQTransposeReturnType<SPQRType> >
+ {
+ typedef typename SPQRType::MatrixType ReturnType;
+ };
+ template <typename SPQRType, typename Derived> struct traits<SPQR_QProduct<SPQRType, Derived> >
+ {
+ typedef typename Derived::PlainObject ReturnType;
+ };
+ } // End namespace internal
+
+/**
+ * \ingroup SPQRSupport_Module
+ * \class SPQR
+ * \brief Sparse QR factorization based on SuiteSparseQR library
+ *
+ * This class is used to perform a multithreaded and multifrontal rank-revealing QR decomposition
+ * of sparse matrices. The result is then used to solve linear leasts_square systems.
+ * Clearly, a QR factorization is returned such that A*P = Q*R where :
+ *
+ * P is the column permutation. Use colsPermutation() to get it.
+ *
+ * Q is the orthogonal matrix represented as Householder reflectors.
+ * Use matrixQ() to get an expression and matrixQ().transpose() to get the transpose.
+ * You can then apply it to a vector.
+ *
+ * R is the sparse triangular factor. Use matrixQR() to get it as SparseMatrix.
+ * NOTE : The Index type of R is always SuiteSparse_long. You can get it with SPQR::Index
+ *
+ * \tparam MatrixType_ The type of the sparse matrix A, must be a column-major SparseMatrix<>
+ *
+ * \implsparsesolverconcept
+ *
+ *
+ */
+template<typename MatrixType_>
+class SPQR : public SparseSolverBase<SPQR<MatrixType_> >
+{
+ protected:
+ typedef SparseSolverBase<SPQR<MatrixType_> > Base;
+ using Base::m_isInitialized;
+ public:
+ typedef typename MatrixType_::Scalar Scalar;
+ typedef typename MatrixType_::RealScalar RealScalar;
+ typedef SuiteSparse_long StorageIndex ;
+ typedef SparseMatrix<Scalar, ColMajor, StorageIndex> MatrixType;
+ typedef Map<PermutationMatrix<Dynamic, Dynamic, StorageIndex> > PermutationType;
+ enum {
+ ColsAtCompileTime = Dynamic,
+ MaxColsAtCompileTime = Dynamic
+ };
+ public:
+ SPQR()
+ : m_analysisIsOk(false),
+ m_factorizationIsOk(false),
+ m_isRUpToDate(false),
+ m_ordering(SPQR_ORDERING_DEFAULT),
+ m_allow_tol(SPQR_DEFAULT_TOL),
+ m_tolerance (NumTraits<Scalar>::epsilon()),
+ m_cR(0),
+ m_E(0),
+ m_H(0),
+ m_HPinv(0),
+ m_HTau(0),
+ m_useDefaultThreshold(true)
+ {
+ cholmod_l_start(&m_cc);
+ }
+
+ explicit SPQR(const MatrixType_& matrix)
+ : m_analysisIsOk(false),
+ m_factorizationIsOk(false),
+ m_isRUpToDate(false),
+ m_ordering(SPQR_ORDERING_DEFAULT),
+ m_allow_tol(SPQR_DEFAULT_TOL),
+ m_tolerance (NumTraits<Scalar>::epsilon()),
+ m_cR(0),
+ m_E(0),
+ m_H(0),
+ m_HPinv(0),
+ m_HTau(0),
+ m_useDefaultThreshold(true)
+ {
+ cholmod_l_start(&m_cc);
+ compute(matrix);
+ }
+
+ ~SPQR()
+ {
+ SPQR_free();
+ cholmod_l_finish(&m_cc);
+ }
+ void SPQR_free()
+ {
+ cholmod_l_free_sparse(&m_H, &m_cc);
+ cholmod_l_free_sparse(&m_cR, &m_cc);
+ cholmod_l_free_dense(&m_HTau, &m_cc);
+ std::free(m_E);
+ std::free(m_HPinv);
+ }
+
+ void compute(const MatrixType_& matrix)
+ {
+ if(m_isInitialized) SPQR_free();
+
+ MatrixType mat(matrix);
+
+ /* Compute the default threshold as in MatLab, see:
+ * Tim Davis, "Algorithm 915, SuiteSparseQR: Multifrontal Multithreaded Rank-Revealing
+ * Sparse QR Factorization, ACM Trans. on Math. Soft. 38(1), 2011, Page 8:3
+ */
+ RealScalar pivotThreshold = m_tolerance;
+ if(m_useDefaultThreshold)
+ {
+ RealScalar max2Norm = 0.0;
+ for (int j = 0; j < mat.cols(); j++) max2Norm = numext::maxi(max2Norm, mat.col(j).norm());
+ if(numext::is_exactly_zero(max2Norm))
+ max2Norm = RealScalar(1);
+ pivotThreshold = 20 * (mat.rows() + mat.cols()) * max2Norm * NumTraits<RealScalar>::epsilon();
+ }
+ cholmod_sparse A;
+ A = viewAsCholmod(mat);
+ m_rows = matrix.rows();
+ Index col = matrix.cols();
+ m_rank = SuiteSparseQR<Scalar>(m_ordering, pivotThreshold, col, &A,
+ &m_cR, &m_E, &m_H, &m_HPinv, &m_HTau, &m_cc);
+
+ if (!m_cR)
+ {
+ m_info = NumericalIssue;
+ m_isInitialized = false;
+ return;
+ }
+ m_info = Success;
+ m_isInitialized = true;
+ m_isRUpToDate = false;
+ }
+ /**
+ * Get the number of rows of the input matrix and the Q matrix
+ */
+ inline Index rows() const {return m_rows; }
+
+ /**
+ * Get the number of columns of the input matrix.
+ */
+ inline Index cols() const { return m_cR->ncol; }
+
+ template<typename Rhs, typename Dest>
+ void _solve_impl(const MatrixBase<Rhs> &b, MatrixBase<Dest> &dest) const
+ {
+ eigen_assert(m_isInitialized && " The QR factorization should be computed first, call compute()");
+ eigen_assert(b.cols()==1 && "This method is for vectors only");
+
+ //Compute Q^T * b
+ typename Dest::PlainObject y, y2;
+ y = matrixQ().transpose() * b;
+
+ // Solves with the triangular matrix R
+ Index rk = this->rank();
+ y2 = y;
+ y.resize((std::max)(cols(),Index(y.rows())),y.cols());
+ y.topRows(rk) = this->matrixR().topLeftCorner(rk, rk).template triangularView<Upper>().solve(y2.topRows(rk));
+
+ // Apply the column permutation
+ // colsPermutation() performs a copy of the permutation,
+ // so let's apply it manually:
+ for(Index i = 0; i < rk; ++i) dest.row(m_E[i]) = y.row(i);
+ for(Index i = rk; i < cols(); ++i) dest.row(m_E[i]).setZero();
+
+// y.bottomRows(y.rows()-rk).setZero();
+// dest = colsPermutation() * y.topRows(cols());
+
+ m_info = Success;
+ }
+
+ /** \returns the sparse triangular factor R. It is a sparse matrix
+ */
+ const MatrixType matrixR() const
+ {
+ eigen_assert(m_isInitialized && " The QR factorization should be computed first, call compute()");
+ if(!m_isRUpToDate) {
+ m_R = viewAsEigen<Scalar,ColMajor, typename MatrixType::StorageIndex>(*m_cR);
+ m_isRUpToDate = true;
+ }
+ return m_R;
+ }
+ /// Get an expression of the matrix Q
+ SPQRMatrixQReturnType<SPQR> matrixQ() const
+ {
+ return SPQRMatrixQReturnType<SPQR>(*this);
+ }
+ /// Get the permutation that was applied to columns of A
+ PermutationType colsPermutation() const
+ {
+ eigen_assert(m_isInitialized && "Decomposition is not initialized.");
+ return PermutationType(m_E, m_cR->ncol);
+ }
+ /**
+ * Gets the rank of the matrix.
+ * It should be equal to matrixQR().cols if the matrix is full-rank
+ */
+ Index rank() const
+ {
+ eigen_assert(m_isInitialized && "Decomposition is not initialized.");
+ return m_cc.SPQR_istat[4];
+ }
+ /// Set the fill-reducing ordering method to be used
+ void setSPQROrdering(int ord) { m_ordering = ord;}
+ /// Set the tolerance tol to treat columns with 2-norm < =tol as zero
+ void setPivotThreshold(const RealScalar& tol)
+ {
+ m_useDefaultThreshold = false;
+ m_tolerance = tol;
+ }
+
+ /** \returns a pointer to the SPQR workspace */
+ cholmod_common *cholmodCommon() const { return &m_cc; }
+
+
+ /** \brief Reports whether previous computation was successful.
+ *
+ * \returns \c Success if computation was successful,
+ * \c NumericalIssue if the sparse QR can not be computed
+ */
+ ComputationInfo info() const
+ {
+ eigen_assert(m_isInitialized && "Decomposition is not initialized.");
+ return m_info;
+ }
+ protected:
+ bool m_analysisIsOk;
+ bool m_factorizationIsOk;
+ mutable bool m_isRUpToDate;
+ mutable ComputationInfo m_info;
+ int m_ordering; // Ordering method to use, see SPQR's manual
+ int m_allow_tol; // Allow to use some tolerance during numerical factorization.
+ RealScalar m_tolerance; // treat columns with 2-norm below this tolerance as zero
+ mutable cholmod_sparse *m_cR = nullptr; // The sparse R factor in cholmod format
+ mutable MatrixType m_R; // The sparse matrix R in Eigen format
+ mutable StorageIndex *m_E = nullptr; // The permutation applied to columns
+ mutable cholmod_sparse *m_H = nullptr; //The householder vectors
+ mutable StorageIndex *m_HPinv = nullptr; // The row permutation of H
+ mutable cholmod_dense *m_HTau = nullptr; // The Householder coefficients
+ mutable Index m_rank; // The rank of the matrix
+ mutable cholmod_common m_cc; // Workspace and parameters
+ bool m_useDefaultThreshold; // Use default threshold
+ Index m_rows;
+ template<typename ,typename > friend struct SPQR_QProduct;
+};
+
+template <typename SPQRType, typename Derived>
+struct SPQR_QProduct : ReturnByValue<SPQR_QProduct<SPQRType,Derived> >
+{
+ typedef typename SPQRType::Scalar Scalar;
+ typedef typename SPQRType::StorageIndex StorageIndex;
+ //Define the constructor to get reference to argument types
+ SPQR_QProduct(const SPQRType& spqr, const Derived& other, bool transpose) : m_spqr(spqr),m_other(other),m_transpose(transpose) {}
+
+ inline Index rows() const { return m_transpose ? m_spqr.rows() : m_spqr.cols(); }
+ inline Index cols() const { return m_other.cols(); }
+ // Assign to a vector
+ template<typename ResType>
+ void evalTo(ResType& res) const
+ {
+ cholmod_dense y_cd;
+ cholmod_dense *x_cd;
+ int method = m_transpose ? SPQR_QTX : SPQR_QX;
+ cholmod_common *cc = m_spqr.cholmodCommon();
+ y_cd = viewAsCholmod(m_other.const_cast_derived());
+ x_cd = SuiteSparseQR_qmult<Scalar>(method, m_spqr.m_H, m_spqr.m_HTau, m_spqr.m_HPinv, &y_cd, cc);
+ res = Matrix<Scalar,ResType::RowsAtCompileTime,ResType::ColsAtCompileTime>::Map(reinterpret_cast<Scalar*>(x_cd->x), x_cd->nrow, x_cd->ncol);
+ cholmod_l_free_dense(&x_cd, cc);
+ }
+ const SPQRType& m_spqr;
+ const Derived& m_other;
+ bool m_transpose;
+
+};
+template<typename SPQRType>
+struct SPQRMatrixQReturnType{
+
+ SPQRMatrixQReturnType(const SPQRType& spqr) : m_spqr(spqr) {}
+ template<typename Derived>
+ SPQR_QProduct<SPQRType, Derived> operator*(const MatrixBase<Derived>& other)
+ {
+ return SPQR_QProduct<SPQRType,Derived>(m_spqr,other.derived(),false);
+ }
+ SPQRMatrixQTransposeReturnType<SPQRType> adjoint() const
+ {
+ return SPQRMatrixQTransposeReturnType<SPQRType>(m_spqr);
+ }
+ // To use for operations with the transpose of Q
+ SPQRMatrixQTransposeReturnType<SPQRType> transpose() const
+ {
+ return SPQRMatrixQTransposeReturnType<SPQRType>(m_spqr);
+ }
+ const SPQRType& m_spqr;
+};
+
+template<typename SPQRType>
+struct SPQRMatrixQTransposeReturnType{
+ SPQRMatrixQTransposeReturnType(const SPQRType& spqr) : m_spqr(spqr) {}
+ template<typename Derived>
+ SPQR_QProduct<SPQRType,Derived> operator*(const MatrixBase<Derived>& other)
+ {
+ return SPQR_QProduct<SPQRType,Derived>(m_spqr,other.derived(), true);
+ }
+ const SPQRType& m_spqr;
+};
+
+}// End namespace Eigen
+#endif
diff --git a/Eigen/src/SVD/BDCSVD.h b/Eigen/src/SVD/BDCSVD.h
new file mode 100644
index 0000000..1b10c0e
--- /dev/null
+++ b/Eigen/src/SVD/BDCSVD.h
@@ -0,0 +1,1494 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// We used the "A Divide-And-Conquer Algorithm for the Bidiagonal SVD"
+// research report written by Ming Gu and Stanley C.Eisenstat
+// The code variable names correspond to the names they used in their
+// report
+//
+// Copyright (C) 2013 Gauthier Brun <brun.gauthier@gmail.com>
+// Copyright (C) 2013 Nicolas Carre <nicolas.carre@ensimag.fr>
+// Copyright (C) 2013 Jean Ceccato <jean.ceccato@ensimag.fr>
+// Copyright (C) 2013 Pierre Zoppitelli <pierre.zoppitelli@ensimag.fr>
+// Copyright (C) 2013 Jitse Niesen <jitse@maths.leeds.ac.uk>
+// Copyright (C) 2014-2017 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_BDCSVD_H
+#define EIGEN_BDCSVD_H
+// #define EIGEN_BDCSVD_DEBUG_VERBOSE
+// #define EIGEN_BDCSVD_SANITY_CHECKS
+
+#ifdef EIGEN_BDCSVD_SANITY_CHECKS
+#undef eigen_internal_assert
+#define eigen_internal_assert(X) assert(X);
+#endif
+
+#include "./InternalHeaderCheck.h"
+
+#ifdef EIGEN_BDCSVD_DEBUG_VERBOSE
+#include <iostream>
+#endif
+
+namespace Eigen {
+
+#ifdef EIGEN_BDCSVD_DEBUG_VERBOSE
+IOFormat bdcsvdfmt(8, 0, ", ", "\n", " [", "]");
+#endif
+
+template <typename MatrixType_, int Options>
+class BDCSVD;
+
+namespace internal {
+
+template <typename MatrixType_, int Options>
+struct traits<BDCSVD<MatrixType_, Options> > : svd_traits<MatrixType_, Options> {
+ typedef MatrixType_ MatrixType;
+};
+
+template <typename MatrixType, int Options>
+struct allocate_small_svd {
+ static void run(JacobiSVD<MatrixType, Options>& smallSvd, Index rows, Index cols, unsigned int computationOptions) {
+ (void)computationOptions;
+ smallSvd = JacobiSVD<MatrixType, Options>(rows, cols);
+ }
+};
+
+EIGEN_DIAGNOSTICS(push)
+EIGEN_DISABLE_DEPRECATED_WARNING
+
+template <typename MatrixType>
+struct allocate_small_svd<MatrixType, 0> {
+ static void run(JacobiSVD<MatrixType>& smallSvd, Index rows, Index cols, unsigned int computationOptions) {
+ smallSvd = JacobiSVD<MatrixType>(rows, cols, computationOptions);
+ }
+};
+
+EIGEN_DIAGNOSTICS(pop)
+
+} // end namespace internal
+
+/** \ingroup SVD_Module
+ *
+ *
+ * \class BDCSVD
+ *
+ * \brief class Bidiagonal Divide and Conquer SVD
+ *
+ * \tparam MatrixType_ the type of the matrix of which we are computing the SVD decomposition
+ *
+ * \tparam Options_ this optional parameter allows one to specify options for computing unitaries \a U and \a V.
+ * Possible values are #ComputeThinU, #ComputeThinV, #ComputeFullU, #ComputeFullV, and
+ * #DisableQRDecomposition. It is not possible to request both the thin and full version of \a U or
+ * \a V. By default, unitaries are not computed. BDCSVD uses R-Bidiagonalization to improve
+ * performance on tall and wide matrices. For backwards compatility, the option
+ * #DisableQRDecomposition can be used to disable this optimization.
+ *
+ * This class first reduces the input matrix to bi-diagonal form using class UpperBidiagonalization,
+ * and then performs a divide-and-conquer diagonalization. Small blocks are diagonalized using class JacobiSVD.
+ * You can control the switching size with the setSwitchSize() method, default is 16.
+ * For small matrice (<16), it is thus preferable to directly use JacobiSVD. For larger ones, BDCSVD is highly
+ * recommended and can several order of magnitude faster.
+ *
+ * \warning this algorithm is unlikely to provide accurate result when compiled with unsafe math optimizations.
+ * For instance, this concerns Intel's compiler (ICC), which performs such optimization by default unless
+ * you compile with the \c -fp-model \c precise option. Likewise, the \c -ffast-math option of GCC or clang will
+ * significantly degrade the accuracy.
+ *
+ * \sa class JacobiSVD
+ */
+template <typename MatrixType_, int Options_>
+class BDCSVD : public SVDBase<BDCSVD<MatrixType_, Options_> > {
+ typedef SVDBase<BDCSVD> Base;
+
+public:
+ using Base::rows;
+ using Base::cols;
+ using Base::computeU;
+ using Base::computeV;
+
+ typedef MatrixType_ MatrixType;
+ typedef typename Base::Scalar Scalar;
+ typedef typename Base::RealScalar RealScalar;
+ typedef typename NumTraits<RealScalar>::Literal Literal;
+ typedef typename Base::Index Index;
+ enum {
+ Options = Options_,
+ QRDecomposition = Options & internal::QRPreconditionerBits,
+ ComputationOptions = Options & internal::ComputationOptionsBits,
+ RowsAtCompileTime = Base::RowsAtCompileTime,
+ ColsAtCompileTime = Base::ColsAtCompileTime,
+ DiagSizeAtCompileTime = Base::DiagSizeAtCompileTime,
+ MaxRowsAtCompileTime = Base::MaxRowsAtCompileTime,
+ MaxColsAtCompileTime = Base::MaxColsAtCompileTime,
+ MaxDiagSizeAtCompileTime = Base::MaxDiagSizeAtCompileTime,
+ MatrixOptions = Base::MatrixOptions
+ };
+
+ typedef typename Base::MatrixUType MatrixUType;
+ typedef typename Base::MatrixVType MatrixVType;
+ typedef typename Base::SingularValuesType SingularValuesType;
+
+ typedef Matrix<Scalar, Dynamic, Dynamic, ColMajor> MatrixX;
+ typedef Matrix<RealScalar, Dynamic, Dynamic, ColMajor> MatrixXr;
+ typedef Matrix<RealScalar, Dynamic, 1> VectorType;
+ typedef Array<RealScalar, Dynamic, 1> ArrayXr;
+ typedef Array<Index,1,Dynamic> ArrayXi;
+ typedef Ref<ArrayXr> ArrayRef;
+ typedef Ref<ArrayXi> IndicesRef;
+
+ /** \brief Default Constructor.
+ *
+ * The default constructor is useful in cases in which the user intends to
+ * perform decompositions via BDCSVD::compute(const MatrixType&).
+ */
+ BDCSVD() : m_algoswap(16), m_isTranspose(false), m_compU(false), m_compV(false), m_numIters(0)
+ {}
+
+ /** \brief Default Constructor with memory preallocation
+ *
+ * Like the default constructor but with preallocation of the internal data
+ * according to the specified problem size and \a Options template parameter.
+ * \sa BDCSVD()
+ */
+ BDCSVD(Index rows, Index cols) : m_algoswap(16), m_numIters(0) {
+ allocate(rows, cols, internal::get_computation_options(Options));
+ }
+
+ /** \brief Default Constructor with memory preallocation
+ *
+ * Like the default constructor but with preallocation of the internal data
+ * according to the specified problem size and the \a computationOptions.
+ *
+ * One \b cannot request unitiaries using both the \a Options template parameter
+ * and the constructor. If possible, prefer using the \a Options template parameter.
+ *
+ * \param computationOptions specifification for computing Thin/Full unitaries U/V
+ * \sa BDCSVD()
+ *
+ * \deprecated Will be removed in the next major Eigen version. Options should
+ * be specified in the \a Options template parameter.
+ */
+ EIGEN_DEPRECATED
+ BDCSVD(Index rows, Index cols, unsigned int computationOptions) : m_algoswap(16), m_numIters(0) {
+ internal::check_svd_options_assertions<MatrixType, Options>(computationOptions, rows, cols);
+ allocate(rows, cols, computationOptions);
+ }
+
+ /** \brief Constructor performing the decomposition of given matrix, using the custom options specified
+ * with the \a Options template paramter.
+ *
+ * \param matrix the matrix to decompose
+ */
+ BDCSVD(const MatrixType& matrix) : m_algoswap(16), m_numIters(0) {
+ compute_impl(matrix, internal::get_computation_options(Options));
+ }
+
+ /** \brief Constructor performing the decomposition of given matrix using specified options
+ * for computing unitaries.
+ *
+ * One \b cannot request unitiaries using both the \a Options template parameter
+ * and the constructor. If possible, prefer using the \a Options template parameter.
+ *
+ * \param matrix the matrix to decompose
+ * \param computationOptions specifification for computing Thin/Full unitaries U/V
+ *
+ * \deprecated Will be removed in the next major Eigen version. Options should
+ * be specified in the \a Options template parameter.
+ */
+ EIGEN_DEPRECATED
+ BDCSVD(const MatrixType& matrix, unsigned int computationOptions) : m_algoswap(16), m_numIters(0) {
+ internal::check_svd_options_assertions<MatrixType, Options>(computationOptions, matrix.rows(), matrix.cols());
+ compute_impl(matrix, computationOptions);
+ }
+
+ ~BDCSVD() {}
+
+ /** \brief Method performing the decomposition of given matrix. Computes Thin/Full unitaries U/V if specified
+ * using the \a Options template parameter or the class constructor.
+ *
+ * \param matrix the matrix to decompose
+ */
+ BDCSVD& compute(const MatrixType& matrix) { return compute_impl(matrix, m_computationOptions); }
+
+ /** \brief Method performing the decomposition of given matrix, as specified by
+ * the `computationOptions` parameter.
+ *
+ * \param matrix the matrix to decompose
+ * \param computationOptions specify whether to compute Thin/Full unitaries U/V
+ *
+ * \deprecated Will be removed in the next major Eigen version. Options should
+ * be specified in the \a Options template parameter.
+ */
+ EIGEN_DEPRECATED
+ BDCSVD& compute(const MatrixType& matrix, unsigned int computationOptions) {
+ internal::check_svd_options_assertions<MatrixType, Options>(computationOptions, matrix.rows(), matrix.cols());
+ return compute_impl(matrix, computationOptions);
+ }
+
+ void setSwitchSize(int s)
+ {
+ eigen_assert(s>=3 && "BDCSVD the size of the algo switch has to be at least 3.");
+ m_algoswap = s;
+ }
+
+private:
+ void allocate(Index rows, Index cols, unsigned int computationOptions);
+ BDCSVD& compute_impl(const MatrixType& matrix, unsigned int computationOptions);
+ void divide(Index firstCol, Index lastCol, Index firstRowW, Index firstColW, Index shift);
+ void computeSVDofM(Index firstCol, Index n, MatrixXr& U, VectorType& singVals, MatrixXr& V);
+ void computeSingVals(const ArrayRef& col0, const ArrayRef& diag, const IndicesRef& perm, VectorType& singVals, ArrayRef shifts, ArrayRef mus);
+ void perturbCol0(const ArrayRef& col0, const ArrayRef& diag, const IndicesRef& perm, const VectorType& singVals, const ArrayRef& shifts, const ArrayRef& mus, ArrayRef zhat);
+ void computeSingVecs(const ArrayRef& zhat, const ArrayRef& diag, const IndicesRef& perm, const VectorType& singVals, const ArrayRef& shifts, const ArrayRef& mus, MatrixXr& U, MatrixXr& V);
+ void deflation43(Index firstCol, Index shift, Index i, Index size);
+ void deflation44(Index firstColu , Index firstColm, Index firstRowW, Index firstColW, Index i, Index j, Index size);
+ void deflation(Index firstCol, Index lastCol, Index k, Index firstRowW, Index firstColW, Index shift);
+ template<typename HouseholderU, typename HouseholderV, typename NaiveU, typename NaiveV>
+ void copyUV(const HouseholderU &householderU, const HouseholderV &householderV, const NaiveU &naiveU, const NaiveV &naivev);
+ void structured_update(Block<MatrixXr,Dynamic,Dynamic> A, const MatrixXr &B, Index n1);
+ static RealScalar secularEq(RealScalar x, const ArrayRef& col0, const ArrayRef& diag, const IndicesRef &perm, const ArrayRef& diagShifted, RealScalar shift);
+ template <typename SVDType>
+ void computeBaseCase(SVDType& svd, Index n, Index firstCol, Index firstRowW, Index firstColW, Index shift);
+
+ protected:
+ MatrixXr m_naiveU, m_naiveV;
+ MatrixXr m_computed;
+ Index m_nRec;
+ ArrayXr m_workspace;
+ ArrayXi m_workspaceI;
+ int m_algoswap;
+ bool m_isTranspose, m_compU, m_compV, m_useQrDecomp;
+ JacobiSVD<MatrixType, ComputationOptions> smallSvd;
+ HouseholderQR<MatrixX> qrDecomp;
+ internal::UpperBidiagonalization<MatrixX> bid;
+ MatrixX copyWorkspace;
+ MatrixX reducedTriangle;
+
+ using Base::m_computationOptions;
+ using Base::m_computeThinU;
+ using Base::m_computeThinV;
+ using Base::m_diagSize;
+ using Base::m_info;
+ using Base::m_isInitialized;
+ using Base::m_matrixU;
+ using Base::m_matrixV;
+ using Base::m_nonzeroSingularValues;
+ using Base::m_singularValues;
+
+ public:
+ int m_numIters;
+}; // end class BDCSVD
+
+// Method to allocate and initialize matrix and attributes
+template <typename MatrixType, int Options>
+void BDCSVD<MatrixType, Options>::allocate(Index rows, Index cols, unsigned int computationOptions) {
+ if (Base::allocate(rows, cols, computationOptions))
+ return;
+
+ if (cols < m_algoswap)
+ internal::allocate_small_svd<MatrixType, ComputationOptions>::run(smallSvd, rows, cols, computationOptions);
+
+ m_computed = MatrixXr::Zero(m_diagSize + 1, m_diagSize );
+ m_compU = computeV();
+ m_compV = computeU();
+ m_isTranspose = (cols > rows);
+ if (m_isTranspose)
+ std::swap(m_compU, m_compV);
+
+ // kMinAspectRatio is the crossover point that determines if we perform R-Bidiagonalization
+ // or bidiagonalize the input matrix directly.
+ // It is based off of LAPACK's dgesdd routine, which uses 11.0/6.0
+ // we use a larger scalar to prevent a regression for relatively square matrices.
+ constexpr Index kMinAspectRatio = 4;
+ constexpr bool disableQrDecomp = static_cast<int>(QRDecomposition) == static_cast<int>(DisableQRDecomposition);
+ m_useQrDecomp = !disableQrDecomp && ((rows / kMinAspectRatio > cols) || (cols / kMinAspectRatio > rows));
+ if (m_useQrDecomp) {
+ qrDecomp = HouseholderQR<MatrixX>((std::max)(rows, cols), (std::min)(rows, cols));
+ reducedTriangle = MatrixX(m_diagSize, m_diagSize);
+ }
+
+ copyWorkspace = MatrixX(m_isTranspose ? cols : rows, m_isTranspose ? rows : cols);
+ bid = internal::UpperBidiagonalization<MatrixX>(m_useQrDecomp ? m_diagSize : copyWorkspace.rows(),
+ m_useQrDecomp ? m_diagSize : copyWorkspace.cols());
+
+ if (m_compU) m_naiveU = MatrixXr::Zero(m_diagSize + 1, m_diagSize + 1 );
+ else m_naiveU = MatrixXr::Zero(2, m_diagSize + 1 );
+
+ if (m_compV) m_naiveV = MatrixXr::Zero(m_diagSize, m_diagSize);
+
+ m_workspace.resize((m_diagSize+1)*(m_diagSize+1)*3);
+ m_workspaceI.resize(3*m_diagSize);
+} // end allocate
+
+template <typename MatrixType, int Options>
+BDCSVD<MatrixType, Options>& BDCSVD<MatrixType, Options>::compute_impl(const MatrixType& matrix,
+ unsigned int computationOptions) {
+#ifdef EIGEN_BDCSVD_DEBUG_VERBOSE
+ std::cout << "\n\n\n======================================================================================================================\n\n\n";
+#endif
+ using std::abs;
+
+ allocate(matrix.rows(), matrix.cols(), computationOptions);
+
+ const RealScalar considerZero = (std::numeric_limits<RealScalar>::min)();
+
+ //**** step -1 - If the problem is too small, directly falls back to JacobiSVD and return
+ if(matrix.cols() < m_algoswap)
+ {
+ smallSvd.compute(matrix);
+ m_isInitialized = true;
+ m_info = smallSvd.info();
+ if (m_info == Success || m_info == NoConvergence) {
+ if (computeU()) m_matrixU = smallSvd.matrixU();
+ if (computeV()) m_matrixV = smallSvd.matrixV();
+ m_singularValues = smallSvd.singularValues();
+ m_nonzeroSingularValues = smallSvd.nonzeroSingularValues();
+ }
+ return *this;
+ }
+
+ //**** step 0 - Copy the input matrix and apply scaling to reduce over/under-flows
+ RealScalar scale = matrix.cwiseAbs().template maxCoeff<PropagateNaN>();
+ if (!(numext::isfinite)(scale)) {
+ m_isInitialized = true;
+ m_info = InvalidInput;
+ return *this;
+ }
+
+ if(numext::is_exactly_zero(scale)) scale = Literal(1);
+
+ if (m_isTranspose) copyWorkspace = matrix.adjoint() / scale;
+ else copyWorkspace = matrix / scale;
+
+ //**** step 1 - Bidiagonalization.
+ // If the problem is sufficiently rectangular, we perform R-Bidiagonalization: compute A = Q(R/0)
+ // and then bidiagonalize R. Otherwise, if the problem is relatively square, we
+ // bidiagonalize the input matrix directly.
+ if (m_useQrDecomp) {
+ qrDecomp.compute(copyWorkspace);
+ reducedTriangle = qrDecomp.matrixQR().topRows(m_diagSize);
+ reducedTriangle.template triangularView<StrictlyLower>().setZero();
+ bid.compute(reducedTriangle);
+ } else {
+ bid.compute(copyWorkspace);
+ }
+
+ //**** step 2 - Divide & Conquer
+ m_naiveU.setZero();
+ m_naiveV.setZero();
+ // FIXME this line involves a temporary matrix
+ m_computed.topRows(m_diagSize) = bid.bidiagonal().toDenseMatrix().transpose();
+ m_computed.template bottomRows<1>().setZero();
+ divide(0, m_diagSize - 1, 0, 0, 0);
+ if (m_info != Success && m_info != NoConvergence) {
+ m_isInitialized = true;
+ return *this;
+ }
+
+ //**** step 3 - Copy singular values and vectors
+ for (int i=0; i<m_diagSize; i++)
+ {
+ RealScalar a = abs(m_computed.coeff(i, i));
+ m_singularValues.coeffRef(i) = a * scale;
+ if (a<considerZero)
+ {
+ m_nonzeroSingularValues = i;
+ m_singularValues.tail(m_diagSize - i - 1).setZero();
+ break;
+ }
+ else if (i == m_diagSize - 1)
+ {
+ m_nonzeroSingularValues = i + 1;
+ break;
+ }
+ }
+
+ //**** step 4 - Finalize unitaries U and V
+ if(m_isTranspose) copyUV(bid.householderV(), bid.householderU(), m_naiveV, m_naiveU);
+ else copyUV(bid.householderU(), bid.householderV(), m_naiveU, m_naiveV);
+
+ if (m_useQrDecomp) {
+ if (m_isTranspose && computeV()) m_matrixV.applyOnTheLeft(qrDecomp.householderQ());
+ else if (!m_isTranspose && computeU()) m_matrixU.applyOnTheLeft(qrDecomp.householderQ());
+ }
+
+ m_isInitialized = true;
+ return *this;
+} // end compute
+
+template <typename MatrixType, int Options>
+template <typename HouseholderU, typename HouseholderV, typename NaiveU, typename NaiveV>
+void BDCSVD<MatrixType, Options>::copyUV(const HouseholderU& householderU, const HouseholderV& householderV,
+ const NaiveU& naiveU, const NaiveV& naiveV) {
+ // Note exchange of U and V: m_matrixU is set from m_naiveV and vice versa
+ if (computeU())
+ {
+ Index Ucols = m_computeThinU ? m_diagSize : rows();
+ m_matrixU = MatrixX::Identity(rows(), Ucols);
+ m_matrixU.topLeftCorner(m_diagSize, m_diagSize) = naiveV.template cast<Scalar>().topLeftCorner(m_diagSize, m_diagSize);
+ // FIXME the following conditionals involve temporary buffers
+ if (m_useQrDecomp) m_matrixU.topLeftCorner(householderU.cols(), m_diagSize).applyOnTheLeft(householderU);
+ else m_matrixU.applyOnTheLeft(householderU);
+ }
+ if (computeV())
+ {
+ Index Vcols = m_computeThinV ? m_diagSize : cols();
+ m_matrixV = MatrixX::Identity(cols(), Vcols);
+ m_matrixV.topLeftCorner(m_diagSize, m_diagSize) = naiveU.template cast<Scalar>().topLeftCorner(m_diagSize, m_diagSize);
+ // FIXME the following conditionals involve temporary buffers
+ if (m_useQrDecomp) m_matrixV.topLeftCorner(householderV.cols(), m_diagSize).applyOnTheLeft(householderV);
+ else m_matrixV.applyOnTheLeft(householderV);
+ }
+}
+
+/** \internal
+ * Performs A = A * B exploiting the special structure of the matrix A. Splitting A as:
+ * A = [A1]
+ * [A2]
+ * such that A1.rows()==n1, then we assume that at least half of the columns of A1 and A2 are zeros.
+ * We can thus pack them prior to the the matrix product. However, this is only worth the effort if the matrix is large
+ * enough.
+ */
+template <typename MatrixType, int Options>
+void BDCSVD<MatrixType, Options>::structured_update(Block<MatrixXr, Dynamic, Dynamic> A, const MatrixXr& B, Index n1) {
+ Index n = A.rows();
+ if(n>100)
+ {
+ // If the matrices are large enough, let's exploit the sparse structure of A by
+ // splitting it in half (wrt n1), and packing the non-zero columns.
+ Index n2 = n - n1;
+ Map<MatrixXr> A1(m_workspace.data() , n1, n);
+ Map<MatrixXr> A2(m_workspace.data()+ n1*n, n2, n);
+ Map<MatrixXr> B1(m_workspace.data()+ n*n, n, n);
+ Map<MatrixXr> B2(m_workspace.data()+2*n*n, n, n);
+ Index k1=0, k2=0;
+ for(Index j=0; j<n; ++j)
+ {
+ if( (A.col(j).head(n1).array()!=Literal(0)).any() )
+ {
+ A1.col(k1) = A.col(j).head(n1);
+ B1.row(k1) = B.row(j);
+ ++k1;
+ }
+ if( (A.col(j).tail(n2).array()!=Literal(0)).any() )
+ {
+ A2.col(k2) = A.col(j).tail(n2);
+ B2.row(k2) = B.row(j);
+ ++k2;
+ }
+ }
+
+ A.topRows(n1).noalias() = A1.leftCols(k1) * B1.topRows(k1);
+ A.bottomRows(n2).noalias() = A2.leftCols(k2) * B2.topRows(k2);
+ }
+ else
+ {
+ Map<MatrixXr,Aligned> tmp(m_workspace.data(),n,n);
+ tmp.noalias() = A*B;
+ A = tmp;
+ }
+}
+
+template <typename MatrixType, int Options>
+template <typename SVDType>
+void BDCSVD<MatrixType, Options>::computeBaseCase(SVDType& svd, Index n, Index firstCol, Index firstRowW,
+ Index firstColW, Index shift) {
+ svd.compute(m_computed.block(firstCol, firstCol, n + 1, n));
+ m_info = svd.info();
+ if (m_info != Success && m_info != NoConvergence) return;
+ if (m_compU)
+ m_naiveU.block(firstCol, firstCol, n + 1, n + 1).real() = svd.matrixU();
+ else {
+ m_naiveU.row(0).segment(firstCol, n + 1).real() = svd.matrixU().row(0);
+ m_naiveU.row(1).segment(firstCol, n + 1).real() = svd.matrixU().row(n);
+ }
+ if (m_compV) m_naiveV.block(firstRowW, firstColW, n, n).real() = svd.matrixV();
+ m_computed.block(firstCol + shift, firstCol + shift, n + 1, n).setZero();
+ m_computed.diagonal().segment(firstCol + shift, n) = svd.singularValues().head(n);
+}
+
+// The divide algorithm is done "in place", we are always working on subsets of the same matrix. The divide methods
+// takes as argument the place of the submatrix we are currently working on.
+
+//@param firstCol : The Index of the first column of the submatrix of m_computed and for m_naiveU;
+//@param lastCol : The Index of the last column of the submatrix of m_computed and for m_naiveU;
+// lastCol + 1 - firstCol is the size of the submatrix.
+//@param firstRowW : The Index of the first row of the matrix W that we are to change. (see the reference paper section 1 for more information on W)
+//@param firstColW : Same as firstRowW with the column.
+//@param shift : Each time one takes the left submatrix, one must add 1 to the shift. Why? Because! We actually want the last column of the U submatrix
+// to become the first column (*coeff) and to shift all the other columns to the right. There are more details on the reference paper.
+template <typename MatrixType, int Options>
+void BDCSVD<MatrixType, Options>::divide(Index firstCol, Index lastCol, Index firstRowW,
+ Index firstColW, Index shift) {
+ // requires rows = cols + 1;
+ using std::pow;
+ using std::sqrt;
+ using std::abs;
+ const Index n = lastCol - firstCol + 1;
+ const Index k = n/2;
+ const RealScalar considerZero = (std::numeric_limits<RealScalar>::min)();
+ RealScalar alphaK;
+ RealScalar betaK;
+ RealScalar r0;
+ RealScalar lambda, phi, c0, s0;
+ VectorType l, f;
+ // We use the other algorithm which is more efficient for small
+ // matrices.
+ if (n < m_algoswap)
+ {
+ // FIXME this block involves temporaries
+ if (m_compV) {
+ JacobiSVD<MatrixXr, ComputeFullU | ComputeFullV> baseSvd;
+ computeBaseCase(baseSvd, n, firstCol, firstRowW, firstColW, shift);
+ } else {
+ JacobiSVD<MatrixXr, ComputeFullU> baseSvd;
+ computeBaseCase(baseSvd, n, firstCol, firstRowW, firstColW, shift);
+ }
+ return;
+ }
+ // We use the divide and conquer algorithm
+ alphaK = m_computed(firstCol + k, firstCol + k);
+ betaK = m_computed(firstCol + k + 1, firstCol + k);
+ // The divide must be done in that order in order to have good results. Divide change the data inside the submatrices
+ // and the divide of the right submatrice reads one column of the left submatrice. That's why we need to treat the
+ // right submatrix before the left one.
+ divide(k + 1 + firstCol, lastCol, k + 1 + firstRowW, k + 1 + firstColW, shift);
+ if (m_info != Success && m_info != NoConvergence) return;
+ divide(firstCol, k - 1 + firstCol, firstRowW, firstColW + 1, shift + 1);
+ if (m_info != Success && m_info != NoConvergence) return;
+
+ if (m_compU)
+ {
+ lambda = m_naiveU(firstCol + k, firstCol + k);
+ phi = m_naiveU(firstCol + k + 1, lastCol + 1);
+ }
+ else
+ {
+ lambda = m_naiveU(1, firstCol + k);
+ phi = m_naiveU(0, lastCol + 1);
+ }
+ r0 = sqrt((abs(alphaK * lambda) * abs(alphaK * lambda)) + abs(betaK * phi) * abs(betaK * phi));
+ if (m_compU)
+ {
+ l = m_naiveU.row(firstCol + k).segment(firstCol, k);
+ f = m_naiveU.row(firstCol + k + 1).segment(firstCol + k + 1, n - k - 1);
+ }
+ else
+ {
+ l = m_naiveU.row(1).segment(firstCol, k);
+ f = m_naiveU.row(0).segment(firstCol + k + 1, n - k - 1);
+ }
+ if (m_compV) m_naiveV(firstRowW+k, firstColW) = Literal(1);
+ if (r0<considerZero)
+ {
+ c0 = Literal(1);
+ s0 = Literal(0);
+ }
+ else
+ {
+ c0 = alphaK * lambda / r0;
+ s0 = betaK * phi / r0;
+ }
+
+#ifdef EIGEN_BDCSVD_SANITY_CHECKS
+ eigen_internal_assert(m_naiveU.allFinite());
+ eigen_internal_assert(m_naiveV.allFinite());
+ eigen_internal_assert(m_computed.allFinite());
+#endif
+
+ if (m_compU)
+ {
+ MatrixXr q1 (m_naiveU.col(firstCol + k).segment(firstCol, k + 1));
+ // we shiftW Q1 to the right
+ for (Index i = firstCol + k - 1; i >= firstCol; i--)
+ m_naiveU.col(i + 1).segment(firstCol, k + 1) = m_naiveU.col(i).segment(firstCol, k + 1);
+ // we shift q1 at the left with a factor c0
+ m_naiveU.col(firstCol).segment( firstCol, k + 1) = (q1 * c0);
+ // last column = q1 * - s0
+ m_naiveU.col(lastCol + 1).segment(firstCol, k + 1) = (q1 * ( - s0));
+ // first column = q2 * s0
+ m_naiveU.col(firstCol).segment(firstCol + k + 1, n - k) = m_naiveU.col(lastCol + 1).segment(firstCol + k + 1, n - k) * s0;
+ // q2 *= c0
+ m_naiveU.col(lastCol + 1).segment(firstCol + k + 1, n - k) *= c0;
+ }
+ else
+ {
+ RealScalar q1 = m_naiveU(0, firstCol + k);
+ // we shift Q1 to the right
+ for (Index i = firstCol + k - 1; i >= firstCol; i--)
+ m_naiveU(0, i + 1) = m_naiveU(0, i);
+ // we shift q1 at the left with a factor c0
+ m_naiveU(0, firstCol) = (q1 * c0);
+ // last column = q1 * - s0
+ m_naiveU(0, lastCol + 1) = (q1 * ( - s0));
+ // first column = q2 * s0
+ m_naiveU(1, firstCol) = m_naiveU(1, lastCol + 1) *s0;
+ // q2 *= c0
+ m_naiveU(1, lastCol + 1) *= c0;
+ m_naiveU.row(1).segment(firstCol + 1, k).setZero();
+ m_naiveU.row(0).segment(firstCol + k + 1, n - k - 1).setZero();
+ }
+
+#ifdef EIGEN_BDCSVD_SANITY_CHECKS
+ eigen_internal_assert(m_naiveU.allFinite());
+ eigen_internal_assert(m_naiveV.allFinite());
+ eigen_internal_assert(m_computed.allFinite());
+#endif
+
+ m_computed(firstCol + shift, firstCol + shift) = r0;
+ m_computed.col(firstCol + shift).segment(firstCol + shift + 1, k) = alphaK * l.transpose().real();
+ m_computed.col(firstCol + shift).segment(firstCol + shift + k + 1, n - k - 1) = betaK * f.transpose().real();
+
+#ifdef EIGEN_BDCSVD_DEBUG_VERBOSE
+ ArrayXr tmp1 = (m_computed.block(firstCol+shift, firstCol+shift, n, n)).jacobiSvd().singularValues();
+#endif
+ // Second part: try to deflate singular values in combined matrix
+ deflation(firstCol, lastCol, k, firstRowW, firstColW, shift);
+#ifdef EIGEN_BDCSVD_DEBUG_VERBOSE
+ ArrayXr tmp2 = (m_computed.block(firstCol+shift, firstCol+shift, n, n)).jacobiSvd().singularValues();
+ std::cout << "\n\nj1 = " << tmp1.transpose().format(bdcsvdfmt) << "\n";
+ std::cout << "j2 = " << tmp2.transpose().format(bdcsvdfmt) << "\n\n";
+ std::cout << "err: " << ((tmp1-tmp2).abs()>1e-12*tmp2.abs()).transpose() << "\n";
+ static int count = 0;
+ std::cout << "# " << ++count << "\n\n";
+ eigen_internal_assert((tmp1-tmp2).matrix().norm() < 1e-14*tmp2.matrix().norm());
+// eigen_internal_assert(count<681);
+// eigen_internal_assert(((tmp1-tmp2).abs()<1e-13*tmp2.abs()).all());
+#endif
+
+ // Third part: compute SVD of combined matrix
+ MatrixXr UofSVD, VofSVD;
+ VectorType singVals;
+ computeSVDofM(firstCol + shift, n, UofSVD, singVals, VofSVD);
+
+#ifdef EIGEN_BDCSVD_SANITY_CHECKS
+ eigen_internal_assert(UofSVD.allFinite());
+ eigen_internal_assert(VofSVD.allFinite());
+#endif
+
+ if (m_compU)
+ structured_update(m_naiveU.block(firstCol, firstCol, n + 1, n + 1), UofSVD, (n+2)/2);
+ else
+ {
+ Map<Matrix<RealScalar,2,Dynamic>,Aligned> tmp(m_workspace.data(),2,n+1);
+ tmp.noalias() = m_naiveU.middleCols(firstCol, n+1) * UofSVD;
+ m_naiveU.middleCols(firstCol, n + 1) = tmp;
+ }
+
+ if (m_compV) structured_update(m_naiveV.block(firstRowW, firstColW, n, n), VofSVD, (n+1)/2);
+
+#ifdef EIGEN_BDCSVD_SANITY_CHECKS
+ eigen_internal_assert(m_naiveU.allFinite());
+ eigen_internal_assert(m_naiveV.allFinite());
+ eigen_internal_assert(m_computed.allFinite());
+#endif
+
+ m_computed.block(firstCol + shift, firstCol + shift, n, n).setZero();
+ m_computed.block(firstCol + shift, firstCol + shift, n, n).diagonal() = singVals;
+} // end divide
+
+// Compute SVD of m_computed.block(firstCol, firstCol, n + 1, n); this block only has non-zeros in
+// the first column and on the diagonal and has undergone deflation, so diagonal is in increasing
+// order except for possibly the (0,0) entry. The computed SVD is stored U, singVals and V, except
+// that if m_compV is false, then V is not computed. Singular values are sorted in decreasing order.
+//
+// TODO Opportunities for optimization: better root finding algo, better stopping criterion, better
+// handling of round-off errors, be consistent in ordering
+// For instance, to solve the secular equation using FMM, see http://www.stat.uchicago.edu/~lekheng/courses/302/classics/greengard-rokhlin.pdf
+template <typename MatrixType, int Options>
+void BDCSVD<MatrixType, Options>::computeSVDofM(Index firstCol, Index n, MatrixXr& U,
+ VectorType& singVals, MatrixXr& V) {
+ const RealScalar considerZero = (std::numeric_limits<RealScalar>::min)();
+ using std::abs;
+ ArrayRef col0 = m_computed.col(firstCol).segment(firstCol, n);
+ m_workspace.head(n) = m_computed.block(firstCol, firstCol, n, n).diagonal();
+ ArrayRef diag = m_workspace.head(n);
+ diag(0) = Literal(0);
+
+ // Allocate space for singular values and vectors
+ singVals.resize(n);
+ U.resize(n+1, n+1);
+ if (m_compV) V.resize(n, n);
+
+#ifdef EIGEN_BDCSVD_DEBUG_VERBOSE
+ if (col0.hasNaN() || diag.hasNaN())
+ std::cout << "\n\nHAS NAN\n\n";
+#endif
+
+ // Many singular values might have been deflated, the zero ones have been moved to the end,
+ // but others are interleaved and we must ignore them at this stage.
+ // To this end, let's compute a permutation skipping them:
+ Index actual_n = n;
+ while(actual_n>1 && numext::is_exactly_zero(diag(actual_n - 1))) {
+ --actual_n;
+ eigen_internal_assert(numext::is_exactly_zero(col0(actual_n)));
+ }
+ Index m = 0; // size of the deflated problem
+ for(Index k=0;k<actual_n;++k)
+ if(abs(col0(k))>considerZero)
+ m_workspaceI(m++) = k;
+ Map<ArrayXi> perm(m_workspaceI.data(),m);
+
+ Map<ArrayXr> shifts(m_workspace.data()+1*n, n);
+ Map<ArrayXr> mus(m_workspace.data()+2*n, n);
+ Map<ArrayXr> zhat(m_workspace.data()+3*n, n);
+
+#ifdef EIGEN_BDCSVD_DEBUG_VERBOSE
+ std::cout << "computeSVDofM using:\n";
+ std::cout << " z: " << col0.transpose() << "\n";
+ std::cout << " d: " << diag.transpose() << "\n";
+#endif
+
+ // Compute singVals, shifts, and mus
+ computeSingVals(col0, diag, perm, singVals, shifts, mus);
+
+#ifdef EIGEN_BDCSVD_DEBUG_VERBOSE
+ std::cout << " j: " << (m_computed.block(firstCol, firstCol, n, n)).jacobiSvd().singularValues().transpose().reverse() << "\n\n";
+ std::cout << " sing-val: " << singVals.transpose() << "\n";
+ std::cout << " mu: " << mus.transpose() << "\n";
+ std::cout << " shift: " << shifts.transpose() << "\n";
+
+ {
+ std::cout << "\n\n mus: " << mus.head(actual_n).transpose() << "\n\n";
+ std::cout << " check1 (expect0) : " << ((singVals.array()-(shifts+mus)) / singVals.array()).head(actual_n).transpose() << "\n\n";
+ eigen_internal_assert((((singVals.array()-(shifts+mus)) / singVals.array()).head(actual_n) >= 0).all());
+ std::cout << " check2 (>0) : " << ((singVals.array()-diag) / singVals.array()).head(actual_n).transpose() << "\n\n";
+ eigen_internal_assert((((singVals.array()-diag) / singVals.array()).head(actual_n) >= 0).all());
+ }
+#endif
+
+#ifdef EIGEN_BDCSVD_SANITY_CHECKS
+ eigen_internal_assert(singVals.allFinite());
+ eigen_internal_assert(mus.allFinite());
+ eigen_internal_assert(shifts.allFinite());
+#endif
+
+ // Compute zhat
+ perturbCol0(col0, diag, perm, singVals, shifts, mus, zhat);
+#ifdef EIGEN_BDCSVD_DEBUG_VERBOSE
+ std::cout << " zhat: " << zhat.transpose() << "\n";
+#endif
+
+#ifdef EIGEN_BDCSVD_SANITY_CHECKS
+ eigen_internal_assert(zhat.allFinite());
+#endif
+
+ computeSingVecs(zhat, diag, perm, singVals, shifts, mus, U, V);
+
+#ifdef EIGEN_BDCSVD_DEBUG_VERBOSE
+ std::cout << "U^T U: " << (U.transpose() * U - MatrixXr(MatrixXr::Identity(U.cols(),U.cols()))).norm() << "\n";
+ std::cout << "V^T V: " << (V.transpose() * V - MatrixXr(MatrixXr::Identity(V.cols(),V.cols()))).norm() << "\n";
+#endif
+
+#ifdef EIGEN_BDCSVD_SANITY_CHECKS
+ eigen_internal_assert(m_naiveU.allFinite());
+ eigen_internal_assert(m_naiveV.allFinite());
+ eigen_internal_assert(m_computed.allFinite());
+ eigen_internal_assert(U.allFinite());
+ eigen_internal_assert(V.allFinite());
+// eigen_internal_assert((U.transpose() * U - MatrixXr(MatrixXr::Identity(U.cols(),U.cols()))).norm() < 100*NumTraits<RealScalar>::epsilon() * n);
+// eigen_internal_assert((V.transpose() * V - MatrixXr(MatrixXr::Identity(V.cols(),V.cols()))).norm() < 100*NumTraits<RealScalar>::epsilon() * n);
+#endif
+
+ // Because of deflation, the singular values might not be completely sorted.
+ // Fortunately, reordering them is a O(n) problem
+ for(Index i=0; i<actual_n-1; ++i)
+ {
+ if(singVals(i)>singVals(i+1))
+ {
+ using std::swap;
+ swap(singVals(i),singVals(i+1));
+ U.col(i).swap(U.col(i+1));
+ if(m_compV) V.col(i).swap(V.col(i+1));
+ }
+ }
+
+#ifdef EIGEN_BDCSVD_SANITY_CHECKS
+ {
+ bool singular_values_sorted = (((singVals.segment(1,actual_n-1)-singVals.head(actual_n-1))).array() >= 0).all();
+ if(!singular_values_sorted)
+ std::cout << "Singular values are not sorted: " << singVals.segment(1,actual_n).transpose() << "\n";
+ eigen_internal_assert(singular_values_sorted);
+ }
+#endif
+
+ // Reverse order so that singular values in increased order
+ // Because of deflation, the zeros singular-values are already at the end
+ singVals.head(actual_n).reverseInPlace();
+ U.leftCols(actual_n).rowwise().reverseInPlace();
+ if (m_compV) V.leftCols(actual_n).rowwise().reverseInPlace();
+
+#ifdef EIGEN_BDCSVD_DEBUG_VERBOSE
+ JacobiSVD<MatrixXr> jsvd(m_computed.block(firstCol, firstCol, n, n) );
+ std::cout << " * j: " << jsvd.singularValues().transpose() << "\n\n";
+ std::cout << " * sing-val: " << singVals.transpose() << "\n";
+// std::cout << " * err: " << ((jsvd.singularValues()-singVals)>1e-13*singVals.norm()).transpose() << "\n";
+#endif
+}
+
+template <typename MatrixType, int Options>
+typename BDCSVD<MatrixType, Options>::RealScalar BDCSVD<MatrixType, Options>::secularEq(
+ RealScalar mu, const ArrayRef& col0, const ArrayRef& diag, const IndicesRef& perm, const ArrayRef& diagShifted,
+ RealScalar shift) {
+ Index m = perm.size();
+ RealScalar res = Literal(1);
+ for(Index i=0; i<m; ++i)
+ {
+ Index j = perm(i);
+ // The following expression could be rewritten to involve only a single division,
+ // but this would make the expression more sensitive to overflow.
+ res += (col0(j) / (diagShifted(j) - mu)) * (col0(j) / (diag(j) + shift + mu));
+ }
+ return res;
+}
+
+template <typename MatrixType, int Options>
+void BDCSVD<MatrixType, Options>::computeSingVals(const ArrayRef& col0, const ArrayRef& diag, const IndicesRef& perm,
+ VectorType& singVals, ArrayRef shifts, ArrayRef mus) {
+ using std::abs;
+ using std::swap;
+ using std::sqrt;
+
+ Index n = col0.size();
+ Index actual_n = n;
+ // Note that here actual_n is computed based on col0(i)==0 instead of diag(i)==0 as above
+ // because 1) we have diag(i)==0 => col0(i)==0 and 2) if col0(i)==0, then diag(i) is already a singular value.
+ while(actual_n>1 && numext::is_exactly_zero(col0(actual_n - 1))) --actual_n;
+
+ for (Index k = 0; k < n; ++k)
+ {
+ if (numext::is_exactly_zero(col0(k)) || actual_n == 1)
+ {
+ // if col0(k) == 0, then entry is deflated, so singular value is on diagonal
+ // if actual_n==1, then the deflated problem is already diagonalized
+ singVals(k) = k==0 ? col0(0) : diag(k);
+ mus(k) = Literal(0);
+ shifts(k) = k==0 ? col0(0) : diag(k);
+ continue;
+ }
+
+ // otherwise, use secular equation to find singular value
+ RealScalar left = diag(k);
+ RealScalar right; // was: = (k != actual_n-1) ? diag(k+1) : (diag(actual_n-1) + col0.matrix().norm());
+ if(k==actual_n-1)
+ right = (diag(actual_n-1) + col0.matrix().norm());
+ else
+ {
+ // Skip deflated singular values,
+ // recall that at this stage we assume that z[j]!=0 and all entries for which z[j]==0 have been put aside.
+ // This should be equivalent to using perm[]
+ Index l = k+1;
+ while(numext::is_exactly_zero(col0(l))) { ++l; eigen_internal_assert(l < actual_n); }
+ right = diag(l);
+ }
+
+ // first decide whether it's closer to the left end or the right end
+ RealScalar mid = left + (right-left) / Literal(2);
+ RealScalar fMid = secularEq(mid, col0, diag, perm, diag, Literal(0));
+#ifdef EIGEN_BDCSVD_DEBUG_VERBOSE
+ std::cout << "right-left = " << right-left << "\n";
+// std::cout << "fMid = " << fMid << " " << secularEq(mid-left, col0, diag, perm, ArrayXr(diag-left), left)
+// << " " << secularEq(mid-right, col0, diag, perm, ArrayXr(diag-right), right) << "\n";
+ std::cout << " = " << secularEq(left+RealScalar(0.000001)*(right-left), col0, diag, perm, diag, 0)
+ << " " << secularEq(left+RealScalar(0.1) *(right-left), col0, diag, perm, diag, 0)
+ << " " << secularEq(left+RealScalar(0.2) *(right-left), col0, diag, perm, diag, 0)
+ << " " << secularEq(left+RealScalar(0.3) *(right-left), col0, diag, perm, diag, 0)
+ << " " << secularEq(left+RealScalar(0.4) *(right-left), col0, diag, perm, diag, 0)
+ << " " << secularEq(left+RealScalar(0.49) *(right-left), col0, diag, perm, diag, 0)
+ << " " << secularEq(left+RealScalar(0.5) *(right-left), col0, diag, perm, diag, 0)
+ << " " << secularEq(left+RealScalar(0.51) *(right-left), col0, diag, perm, diag, 0)
+ << " " << secularEq(left+RealScalar(0.6) *(right-left), col0, diag, perm, diag, 0)
+ << " " << secularEq(left+RealScalar(0.7) *(right-left), col0, diag, perm, diag, 0)
+ << " " << secularEq(left+RealScalar(0.8) *(right-left), col0, diag, perm, diag, 0)
+ << " " << secularEq(left+RealScalar(0.9) *(right-left), col0, diag, perm, diag, 0)
+ << " " << secularEq(left+RealScalar(0.999999)*(right-left), col0, diag, perm, diag, 0) << "\n";
+#endif
+ RealScalar shift = (k == actual_n-1 || fMid > Literal(0)) ? left : right;
+
+ // measure everything relative to shift
+ Map<ArrayXr> diagShifted(m_workspace.data()+4*n, n);
+ diagShifted = diag - shift;
+
+ if(k!=actual_n-1)
+ {
+ // check that after the shift, f(mid) is still negative:
+ RealScalar midShifted = (right - left) / RealScalar(2);
+ // we can test exact equality here, because shift comes from `... ? left : right`
+ if(numext::equal_strict(shift, right))
+ midShifted = -midShifted;
+ RealScalar fMidShifted = secularEq(midShifted, col0, diag, perm, diagShifted, shift);
+ if(fMidShifted>0)
+ {
+ // fMid was erroneous, fix it:
+ shift = fMidShifted > Literal(0) ? left : right;
+ diagShifted = diag - shift;
+ }
+ }
+
+ // initial guess
+ RealScalar muPrev, muCur;
+ // we can test exact equality here, because shift comes from `... ? left : right`
+ if (numext::equal_strict(shift, left))
+ {
+ muPrev = (right - left) * RealScalar(0.1);
+ if (k == actual_n-1) muCur = right - left;
+ else muCur = (right - left) * RealScalar(0.5);
+ }
+ else
+ {
+ muPrev = -(right - left) * RealScalar(0.1);
+ muCur = -(right - left) * RealScalar(0.5);
+ }
+
+ RealScalar fPrev = secularEq(muPrev, col0, diag, perm, diagShifted, shift);
+ RealScalar fCur = secularEq(muCur, col0, diag, perm, diagShifted, shift);
+ if (abs(fPrev) < abs(fCur))
+ {
+ swap(fPrev, fCur);
+ swap(muPrev, muCur);
+ }
+
+ // rational interpolation: fit a function of the form a / mu + b through the two previous
+ // iterates and use its zero to compute the next iterate
+ bool useBisection = fPrev*fCur>Literal(0);
+ while (!numext::is_exactly_zero(fCur) && abs(muCur - muPrev) > Literal(8) * NumTraits<RealScalar>::epsilon() * numext::maxi<RealScalar>(abs(muCur), abs(muPrev)) && abs(fCur - fPrev) > NumTraits<RealScalar>::epsilon() && !useBisection)
+ {
+ ++m_numIters;
+
+ // Find a and b such that the function f(mu) = a / mu + b matches the current and previous samples.
+ RealScalar a = (fCur - fPrev) / (Literal(1)/muCur - Literal(1)/muPrev);
+ RealScalar b = fCur - a / muCur;
+ // And find mu such that f(mu)==0:
+ RealScalar muZero = -a/b;
+ RealScalar fZero = secularEq(muZero, col0, diag, perm, diagShifted, shift);
+
+#ifdef EIGEN_BDCSVD_SANITY_CHECKS
+ eigen_internal_assert((numext::isfinite)(fZero));
+#endif
+
+ muPrev = muCur;
+ fPrev = fCur;
+ muCur = muZero;
+ fCur = fZero;
+
+ // we can test exact equality here, because shift comes from `... ? left : right`
+ if (numext::equal_strict(shift, left) && (muCur < Literal(0) || muCur > right - left)) useBisection = true;
+ if (numext::equal_strict(shift, right) && (muCur < -(right - left) || muCur > Literal(0))) useBisection = true;
+ if (abs(fCur)>abs(fPrev)) useBisection = true;
+ }
+
+ // fall back on bisection method if rational interpolation did not work
+ if (useBisection)
+ {
+#ifdef EIGEN_BDCSVD_DEBUG_VERBOSE
+ std::cout << "useBisection for k = " << k << ", actual_n = " << actual_n << "\n";
+#endif
+ RealScalar leftShifted, rightShifted;
+ // we can test exact equality here, because shift comes from `... ? left : right`
+ if (numext::equal_strict(shift, left))
+ {
+ // to avoid overflow, we must have mu > max(real_min, |z(k)|/sqrt(real_max)),
+ // the factor 2 is to be more conservative
+ leftShifted = numext::maxi<RealScalar>( (std::numeric_limits<RealScalar>::min)(), Literal(2) * abs(col0(k)) / sqrt((std::numeric_limits<RealScalar>::max)()) );
+
+ // check that we did it right:
+ eigen_internal_assert( (numext::isfinite)( (col0(k)/leftShifted)*(col0(k)/(diag(k)+shift+leftShifted)) ) );
+ // I don't understand why the case k==0 would be special there:
+ // if (k == 0) rightShifted = right - left; else
+ rightShifted = (k==actual_n-1) ? right : ((right - left) * RealScalar(0.51)); // theoretically we can take 0.5, but let's be safe
+ }
+ else
+ {
+ leftShifted = -(right - left) * RealScalar(0.51);
+ if(k+1<n)
+ rightShifted = -numext::maxi<RealScalar>( (std::numeric_limits<RealScalar>::min)(), abs(col0(k+1)) / sqrt((std::numeric_limits<RealScalar>::max)()) );
+ else
+ rightShifted = -(std::numeric_limits<RealScalar>::min)();
+ }
+
+ RealScalar fLeft = secularEq(leftShifted, col0, diag, perm, diagShifted, shift);
+ eigen_internal_assert(fLeft<Literal(0));
+
+#if defined EIGEN_BDCSVD_DEBUG_VERBOSE || defined EIGEN_BDCSVD_SANITY_CHECKS || defined EIGEN_INTERNAL_DEBUGGING
+ RealScalar fRight = secularEq(rightShifted, col0, diag, perm, diagShifted, shift);
+#endif
+
+#ifdef EIGEN_BDCSVD_SANITY_CHECKS
+ if(!(numext::isfinite)(fLeft))
+ std::cout << "f(" << leftShifted << ") =" << fLeft << " ; " << left << " " << shift << " " << right << "\n";
+ eigen_internal_assert((numext::isfinite)(fLeft));
+
+ if(!(numext::isfinite)(fRight))
+ std::cout << "f(" << rightShifted << ") =" << fRight << " ; " << left << " " << shift << " " << right << "\n";
+ // eigen_internal_assert((numext::isfinite)(fRight));
+#endif
+
+#ifdef EIGEN_BDCSVD_DEBUG_VERBOSE
+ if(!(fLeft * fRight<0))
+ {
+ std::cout << "f(leftShifted) using leftShifted=" << leftShifted << " ; diagShifted(1:10):" << diagShifted.head(10).transpose() << "\n ; "
+ << "left==shift=" << bool(left==shift) << " ; left-shift = " << (left-shift) << "\n";
+ std::cout << "k=" << k << ", " << fLeft << " * " << fRight << " == " << fLeft * fRight << " ; "
+ << "[" << left << " .. " << right << "] -> [" << leftShifted << " " << rightShifted << "], shift=" << shift
+ << " , f(right)=" << secularEq(0, col0, diag, perm, diagShifted, shift)
+ << " == " << secularEq(right, col0, diag, perm, diag, 0) << " == " << fRight << "\n";
+ }
+#endif
+ eigen_internal_assert(fLeft * fRight < Literal(0));
+
+ if(fLeft<Literal(0))
+ {
+ while (rightShifted - leftShifted > Literal(2) * NumTraits<RealScalar>::epsilon() * numext::maxi<RealScalar>(abs(leftShifted), abs(rightShifted)))
+ {
+ RealScalar midShifted = (leftShifted + rightShifted) / Literal(2);
+ fMid = secularEq(midShifted, col0, diag, perm, diagShifted, shift);
+ eigen_internal_assert((numext::isfinite)(fMid));
+
+ if (fLeft * fMid < Literal(0))
+ {
+ rightShifted = midShifted;
+ }
+ else
+ {
+ leftShifted = midShifted;
+ fLeft = fMid;
+ }
+ }
+ muCur = (leftShifted + rightShifted) / Literal(2);
+ }
+ else
+ {
+ // We have a problem as shifting on the left or right give either a positive or negative value
+ // at the middle of [left,right]...
+ // Instead fo abbording or entering an infinite loop,
+ // let's just use the middle as the estimated zero-crossing:
+ muCur = (right - left) * RealScalar(0.5);
+ // we can test exact equality here, because shift comes from `... ? left : right`
+ if(numext::equal_strict(shift, right))
+ muCur = -muCur;
+ }
+ }
+
+ singVals[k] = shift + muCur;
+ shifts[k] = shift;
+ mus[k] = muCur;
+
+#ifdef EIGEN_BDCSVD_DEBUG_VERBOSE
+ if(k+1<n)
+ std::cout << "found " << singVals[k] << " == " << shift << " + " << muCur << " from " << diag(k) << " .. " << diag(k+1) << "\n";
+#endif
+#ifdef EIGEN_BDCSVD_SANITY_CHECKS
+ eigen_internal_assert(k==0 || singVals[k]>=singVals[k-1]);
+ eigen_internal_assert(singVals[k]>=diag(k));
+#endif
+
+ // perturb singular value slightly if it equals diagonal entry to avoid division by zero later
+ // (deflation is supposed to avoid this from happening)
+ // - this does no seem to be necessary anymore -
+ // if (singVals[k] == left) singVals[k] *= 1 + NumTraits<RealScalar>::epsilon();
+ // if (singVals[k] == right) singVals[k] *= 1 - NumTraits<RealScalar>::epsilon();
+ }
+}
+
+// zhat is perturbation of col0 for which singular vectors can be computed stably (see Section 3.1)
+template <typename MatrixType, int Options>
+void BDCSVD<MatrixType, Options>::perturbCol0(const ArrayRef& col0, const ArrayRef& diag, const IndicesRef& perm,
+ const VectorType& singVals, const ArrayRef& shifts, const ArrayRef& mus,
+ ArrayRef zhat) {
+ using std::sqrt;
+ Index n = col0.size();
+ Index m = perm.size();
+ if(m==0)
+ {
+ zhat.setZero();
+ return;
+ }
+ Index lastIdx = perm(m-1);
+ // The offset permits to skip deflated entries while computing zhat
+ for (Index k = 0; k < n; ++k)
+ {
+ if (numext::is_exactly_zero(col0(k))) // deflated
+ zhat(k) = Literal(0);
+ else
+ {
+ // see equation (3.6)
+ RealScalar dk = diag(k);
+ RealScalar prod = (singVals(lastIdx) + dk) * (mus(lastIdx) + (shifts(lastIdx) - dk));
+#ifdef EIGEN_BDCSVD_SANITY_CHECKS
+ if(prod<0) {
+ std::cout << "k = " << k << " ; z(k)=" << col0(k) << ", diag(k)=" << dk << "\n";
+ std::cout << "prod = " << "(" << singVals(lastIdx) << " + " << dk << ") * (" << mus(lastIdx) << " + (" << shifts(lastIdx) << " - " << dk << "))" << "\n";
+ std::cout << " = " << singVals(lastIdx) + dk << " * " << mus(lastIdx) + (shifts(lastIdx) - dk) << "\n";
+ }
+ eigen_internal_assert(prod>=0);
+#endif
+
+ for(Index l = 0; l<m; ++l)
+ {
+ Index i = perm(l);
+ if(i!=k)
+ {
+#ifdef EIGEN_BDCSVD_SANITY_CHECKS
+ if(i>=k && (l==0 || l-1>=m))
+ {
+ std::cout << "Error in perturbCol0\n";
+ std::cout << " " << k << "/" << n << " " << l << "/" << m << " " << i << "/" << n << " ; " << col0(k) << " " << diag(k) << " " << "\n";
+ std::cout << " " <<diag(i) << "\n";
+ Index j = (i<k /*|| l==0*/) ? i : perm(l-1);
+ std::cout << " " << "j=" << j << "\n";
+ }
+#endif
+ // Avoid index out of bounds.
+ // Will end up setting zhat(k) = 0.
+ if (i >= k && l == 0) {
+ m_info = NumericalIssue;
+ prod = 0;
+ break;
+ }
+ Index j = i<k ? i : l > 0 ? perm(l-1) : i;
+#ifdef EIGEN_BDCSVD_SANITY_CHECKS
+ if(!(dk!=Literal(0) || diag(i)!=Literal(0)))
+ {
+ std::cout << "k=" << k << ", i=" << i << ", l=" << l << ", perm.size()=" << perm.size() << "\n";
+ }
+ eigen_internal_assert(dk!=Literal(0) || diag(i)!=Literal(0));
+#endif
+ prod *= ((singVals(j)+dk) / ((diag(i)+dk))) * ((mus(j)+(shifts(j)-dk)) / ((diag(i)-dk)));
+#ifdef EIGEN_BDCSVD_SANITY_CHECKS
+ eigen_internal_assert(prod>=0);
+#endif
+#ifdef EIGEN_BDCSVD_DEBUG_VERBOSE
+ if(i!=k && numext::abs(((singVals(j)+dk)*(mus(j)+(shifts(j)-dk)))/((diag(i)+dk)*(diag(i)-dk)) - 1) > 0.9 )
+ std::cout << " " << ((singVals(j)+dk)*(mus(j)+(shifts(j)-dk)))/((diag(i)+dk)*(diag(i)-dk)) << " == (" << (singVals(j)+dk) << " * " << (mus(j)+(shifts(j)-dk))
+ << ") / (" << (diag(i)+dk) << " * " << (diag(i)-dk) << ")\n";
+#endif
+ }
+ }
+#ifdef EIGEN_BDCSVD_DEBUG_VERBOSE
+ std::cout << "zhat(" << k << ") = sqrt( " << prod << ") ; " << (singVals(lastIdx) + dk) << " * " << mus(lastIdx) + shifts(lastIdx) << " - " << dk << "\n";
+#endif
+ RealScalar tmp = sqrt(prod);
+#ifdef EIGEN_BDCSVD_SANITY_CHECKS
+ eigen_internal_assert((numext::isfinite)(tmp));
+#endif
+ zhat(k) = col0(k) > Literal(0) ? RealScalar(tmp) : RealScalar(-tmp);
+ }
+ }
+}
+
+// compute singular vectors
+template <typename MatrixType, int Options>
+void BDCSVD<MatrixType, Options>::computeSingVecs(const ArrayRef& zhat, const ArrayRef& diag, const IndicesRef& perm,
+ const VectorType& singVals, const ArrayRef& shifts,
+ const ArrayRef& mus, MatrixXr& U, MatrixXr& V) {
+ Index n = zhat.size();
+ Index m = perm.size();
+
+ for (Index k = 0; k < n; ++k)
+ {
+ if (numext::is_exactly_zero(zhat(k)))
+ {
+ U.col(k) = VectorType::Unit(n+1, k);
+ if (m_compV) V.col(k) = VectorType::Unit(n, k);
+ }
+ else
+ {
+ U.col(k).setZero();
+ for(Index l=0;l<m;++l)
+ {
+ Index i = perm(l);
+ U(i,k) = zhat(i)/(((diag(i) - shifts(k)) - mus(k)) )/( (diag(i) + singVals[k]));
+ }
+ U(n,k) = Literal(0);
+ U.col(k).normalize();
+
+ if (m_compV)
+ {
+ V.col(k).setZero();
+ for(Index l=1;l<m;++l)
+ {
+ Index i = perm(l);
+ V(i,k) = diag(i) * zhat(i) / (((diag(i) - shifts(k)) - mus(k)) )/( (diag(i) + singVals[k]));
+ }
+ V(0,k) = Literal(-1);
+ V.col(k).normalize();
+ }
+ }
+ }
+ U.col(n) = VectorType::Unit(n+1, n);
+}
+
+// page 12_13
+// i >= 1, di almost null and zi non null.
+// We use a rotation to zero out zi applied to the left of M
+template <typename MatrixType, int Options>
+void BDCSVD<MatrixType, Options>::deflation43(Index firstCol, Index shift, Index i,
+ Index size) {
+ using std::abs;
+ using std::sqrt;
+ using std::pow;
+ Index start = firstCol + shift;
+ RealScalar c = m_computed(start, start);
+ RealScalar s = m_computed(start+i, start);
+ RealScalar r = numext::hypot(c,s);
+ if (numext::is_exactly_zero(r))
+ {
+ m_computed(start+i, start+i) = Literal(0);
+ return;
+ }
+ m_computed(start,start) = r;
+ m_computed(start+i, start) = Literal(0);
+ m_computed(start+i, start+i) = Literal(0);
+
+ JacobiRotation<RealScalar> J(c/r,-s/r);
+ if (m_compU) m_naiveU.middleRows(firstCol, size+1).applyOnTheRight(firstCol, firstCol+i, J);
+ else m_naiveU.applyOnTheRight(firstCol, firstCol+i, J);
+} // end deflation 43
+
+// page 13
+// i,j >= 1, i!=j and |di - dj| < epsilon * norm2(M)
+// We apply two rotations to have zj = 0;
+// TODO deflation44 is still broken and not properly tested
+template <typename MatrixType, int Options>
+void BDCSVD<MatrixType, Options>::deflation44(Index firstColu, Index firstColm, Index firstRowW,
+ Index firstColW, Index i, Index j,
+ Index size) {
+ using std::abs;
+ using std::sqrt;
+ using std::conj;
+ using std::pow;
+ RealScalar c = m_computed(firstColm+i, firstColm);
+ RealScalar s = m_computed(firstColm+j, firstColm);
+ RealScalar r = sqrt(numext::abs2(c) + numext::abs2(s));
+#ifdef EIGEN_BDCSVD_DEBUG_VERBOSE
+ std::cout << "deflation 4.4: " << i << "," << j << " -> " << c << " " << s << " " << r << " ; "
+ << m_computed(firstColm + i-1, firstColm) << " "
+ << m_computed(firstColm + i, firstColm) << " "
+ << m_computed(firstColm + i+1, firstColm) << " "
+ << m_computed(firstColm + i+2, firstColm) << "\n";
+ std::cout << m_computed(firstColm + i-1, firstColm + i-1) << " "
+ << m_computed(firstColm + i, firstColm+i) << " "
+ << m_computed(firstColm + i+1, firstColm+i+1) << " "
+ << m_computed(firstColm + i+2, firstColm+i+2) << "\n";
+#endif
+ if (numext::is_exactly_zero(r))
+ {
+ m_computed(firstColm + i, firstColm + i) = m_computed(firstColm + j, firstColm + j);
+ return;
+ }
+ c/=r;
+ s/=r;
+ m_computed(firstColm + i, firstColm) = r;
+ m_computed(firstColm + j, firstColm + j) = m_computed(firstColm + i, firstColm + i);
+ m_computed(firstColm + j, firstColm) = Literal(0);
+
+ JacobiRotation<RealScalar> J(c,-s);
+ if (m_compU) m_naiveU.middleRows(firstColu, size+1).applyOnTheRight(firstColu + i, firstColu + j, J);
+ else m_naiveU.applyOnTheRight(firstColu+i, firstColu+j, J);
+ if (m_compV) m_naiveV.middleRows(firstRowW, size).applyOnTheRight(firstColW + i, firstColW + j, J);
+} // end deflation 44
+
+// acts on block from (firstCol+shift, firstCol+shift) to (lastCol+shift, lastCol+shift) [inclusive]
+template <typename MatrixType, int Options>
+void BDCSVD<MatrixType, Options>::deflation(Index firstCol, Index lastCol, Index k,
+ Index firstRowW, Index firstColW, Index shift) {
+ using std::sqrt;
+ using std::abs;
+ const Index length = lastCol + 1 - firstCol;
+
+ Block<MatrixXr,Dynamic,1> col0(m_computed, firstCol+shift, firstCol+shift, length, 1);
+ Diagonal<MatrixXr> fulldiag(m_computed);
+ VectorBlock<Diagonal<MatrixXr>,Dynamic> diag(fulldiag, firstCol+shift, length);
+
+ const RealScalar considerZero = (std::numeric_limits<RealScalar>::min)();
+ RealScalar maxDiag = diag.tail((std::max)(Index(1),length-1)).cwiseAbs().maxCoeff();
+ RealScalar epsilon_strict = numext::maxi<RealScalar>(considerZero,NumTraits<RealScalar>::epsilon() * maxDiag);
+ RealScalar epsilon_coarse = Literal(8) * NumTraits<RealScalar>::epsilon() * numext::maxi<RealScalar>(col0.cwiseAbs().maxCoeff(), maxDiag);
+
+#ifdef EIGEN_BDCSVD_SANITY_CHECKS
+ eigen_internal_assert(m_naiveU.allFinite());
+ eigen_internal_assert(m_naiveV.allFinite());
+ eigen_internal_assert(m_computed.allFinite());
+#endif
+
+#ifdef EIGEN_BDCSVD_DEBUG_VERBOSE
+ std::cout << "\ndeflate:" << diag.head(k+1).transpose() << " | " << diag.segment(k+1,length-k-1).transpose() << "\n";
+#endif
+
+ //condition 4.1
+ if (diag(0) < epsilon_coarse)
+ {
+#ifdef EIGEN_BDCSVD_DEBUG_VERBOSE
+ std::cout << "deflation 4.1, because " << diag(0) << " < " << epsilon_coarse << "\n";
+#endif
+ diag(0) = epsilon_coarse;
+ }
+
+ //condition 4.2
+ for (Index i=1;i<length;++i)
+ if (abs(col0(i)) < epsilon_strict)
+ {
+#ifdef EIGEN_BDCSVD_DEBUG_VERBOSE
+ std::cout << "deflation 4.2, set z(" << i << ") to zero because " << abs(col0(i)) << " < " << epsilon_strict << " (diag(" << i << ")=" << diag(i) << ")\n";
+#endif
+ col0(i) = Literal(0);
+ }
+
+ //condition 4.3
+ for (Index i=1;i<length; i++)
+ if (diag(i) < epsilon_coarse)
+ {
+#ifdef EIGEN_BDCSVD_DEBUG_VERBOSE
+ std::cout << "deflation 4.3, cancel z(" << i << ")=" << col0(i) << " because diag(" << i << ")=" << diag(i) << " < " << epsilon_coarse << "\n";
+#endif
+ deflation43(firstCol, shift, i, length);
+ }
+
+#ifdef EIGEN_BDCSVD_SANITY_CHECKS
+ eigen_internal_assert(m_naiveU.allFinite());
+ eigen_internal_assert(m_naiveV.allFinite());
+ eigen_internal_assert(m_computed.allFinite());
+#endif
+#ifdef EIGEN_BDCSVD_DEBUG_VERBOSE
+ std::cout << "to be sorted: " << diag.transpose() << "\n\n";
+ std::cout << " : " << col0.transpose() << "\n\n";
+#endif
+ {
+ // Check for total deflation:
+ // If we have a total deflation, then we have to consider col0(0)==diag(0) as a singular value during sorting.
+ const bool total_deflation = (col0.tail(length-1).array().abs()<considerZero).all();
+
+ // Sort the diagonal entries, since diag(1:k-1) and diag(k:length) are already sorted, let's do a sorted merge.
+ // First, compute the respective permutation.
+ Index *permutation = m_workspaceI.data();
+ {
+ permutation[0] = 0;
+ Index p = 1;
+
+ // Move deflated diagonal entries at the end.
+ for(Index i=1; i<length; ++i)
+ if(abs(diag(i))<considerZero)
+ permutation[p++] = i;
+
+ Index i=1, j=k+1;
+ for( ; p < length; ++p)
+ {
+ if (i > k) permutation[p] = j++;
+ else if (j >= length) permutation[p] = i++;
+ else if (diag(i) < diag(j)) permutation[p] = j++;
+ else permutation[p] = i++;
+ }
+ }
+
+ // If we have a total deflation, then we have to insert diag(0) at the right place
+ if(total_deflation)
+ {
+ for(Index i=1; i<length; ++i)
+ {
+ Index pi = permutation[i];
+ if(abs(diag(pi))<considerZero || diag(0)<diag(pi))
+ permutation[i-1] = permutation[i];
+ else
+ {
+ permutation[i-1] = 0;
+ break;
+ }
+ }
+ }
+
+ // Current index of each col, and current column of each index
+ Index *realInd = m_workspaceI.data()+length;
+ Index *realCol = m_workspaceI.data()+2*length;
+
+ for(int pos = 0; pos< length; pos++)
+ {
+ realCol[pos] = pos;
+ realInd[pos] = pos;
+ }
+
+ for(Index i = total_deflation?0:1; i < length; i++)
+ {
+ const Index pi = permutation[length - (total_deflation ? i+1 : i)];
+ const Index J = realCol[pi];
+
+ using std::swap;
+ // swap diagonal and first column entries:
+ swap(diag(i), diag(J));
+ if(i!=0 && J!=0) swap(col0(i), col0(J));
+
+ // change columns
+ if (m_compU) m_naiveU.col(firstCol+i).segment(firstCol, length + 1).swap(m_naiveU.col(firstCol+J).segment(firstCol, length + 1));
+ else m_naiveU.col(firstCol+i).segment(0, 2) .swap(m_naiveU.col(firstCol+J).segment(0, 2));
+ if (m_compV) m_naiveV.col(firstColW + i).segment(firstRowW, length).swap(m_naiveV.col(firstColW + J).segment(firstRowW, length));
+
+ //update real pos
+ const Index realI = realInd[i];
+ realCol[realI] = J;
+ realCol[pi] = i;
+ realInd[J] = realI;
+ realInd[i] = pi;
+ }
+ }
+#ifdef EIGEN_BDCSVD_DEBUG_VERBOSE
+ std::cout << "sorted: " << diag.transpose().format(bdcsvdfmt) << "\n";
+ std::cout << " : " << col0.transpose() << "\n\n";
+#endif
+
+ //condition 4.4
+ {
+ Index i = length-1;
+ while(i>0 && (abs(diag(i))<considerZero || abs(col0(i))<considerZero)) --i;
+ for(; i>1;--i)
+ if( (diag(i) - diag(i-1)) < NumTraits<RealScalar>::epsilon()*maxDiag )
+ {
+#ifdef EIGEN_BDCSVD_DEBUG_VERBOSE
+ std::cout << "deflation 4.4 with i = " << i << " because " << diag(i) << " - " << diag(i-1) << " == " << (diag(i) - diag(i-1)) << " < " << NumTraits<RealScalar>::epsilon()*/*diag(i)*/maxDiag << "\n";
+#endif
+ eigen_internal_assert(abs(diag(i) - diag(i-1))<epsilon_coarse && " diagonal entries are not properly sorted");
+ deflation44(firstCol, firstCol + shift, firstRowW, firstColW, i-1, i, length);
+ }
+ }
+
+#ifdef EIGEN_BDCSVD_SANITY_CHECKS
+ for(Index j=2;j<length;++j)
+ eigen_internal_assert(diag(j-1)<=diag(j) || abs(diag(j))<considerZero);
+#endif
+
+#ifdef EIGEN_BDCSVD_SANITY_CHECKS
+ eigen_internal_assert(m_naiveU.allFinite());
+ eigen_internal_assert(m_naiveV.allFinite());
+ eigen_internal_assert(m_computed.allFinite());
+#endif
+} // end deflation
+
+/** \svd_module
+ *
+ * \return the singular value decomposition of \c *this computed by Divide & Conquer algorithm
+ *
+ * \sa class BDCSVD
+ */
+template <typename Derived>
+template <int Options>
+BDCSVD<typename MatrixBase<Derived>::PlainObject, Options> MatrixBase<Derived>::bdcSvd() const {
+ return BDCSVD<PlainObject, Options>(*this);
+}
+
+/** \svd_module
+ *
+ * \return the singular value decomposition of \c *this computed by Divide & Conquer algorithm
+ *
+ * \sa class BDCSVD
+ */
+template <typename Derived>
+template <int Options>
+BDCSVD<typename MatrixBase<Derived>::PlainObject, Options> MatrixBase<Derived>::bdcSvd(
+ unsigned int computationOptions) const {
+ return BDCSVD<PlainObject, Options>(*this, computationOptions);
+}
+
+} // end namespace Eigen
+
+#endif
diff --git a/Eigen/src/SVD/InternalHeaderCheck.h b/Eigen/src/SVD/InternalHeaderCheck.h
new file mode 100644
index 0000000..fa67b96
--- /dev/null
+++ b/Eigen/src/SVD/InternalHeaderCheck.h
@@ -0,0 +1,3 @@
+#ifndef EIGEN_SVD_MODULE_H
+#error "Please include Eigen/SVD instead of including headers inside the src directory directly."
+#endif
diff --git a/Eigen/src/SVD/JacobiSVD.h b/Eigen/src/SVD/JacobiSVD.h
new file mode 100644
index 0000000..d7dc209
--- /dev/null
+++ b/Eigen/src/SVD/JacobiSVD.h
@@ -0,0 +1,842 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009-2010 Benoit Jacob <jacob.benoit.1@gmail.com>
+// Copyright (C) 2013-2014 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_JACOBISVD_H
+#define EIGEN_JACOBISVD_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+
+// forward declaration (needed by ICC)
+// the empty body is required by MSVC
+template <typename MatrixType, int Options, bool IsComplex = NumTraits<typename MatrixType::Scalar>::IsComplex>
+struct svd_precondition_2x2_block_to_be_real {};
+
+/*** QR preconditioners (R-SVD)
+ ***
+ *** Their role is to reduce the problem of computing the SVD to the case of a square matrix.
+ *** This approach, known as R-SVD, is an optimization for rectangular-enough matrices, and is a requirement for
+ *** JacobiSVD which by itself is only able to work on square matrices.
+ ***/
+
+enum { PreconditionIfMoreColsThanRows, PreconditionIfMoreRowsThanCols };
+
+template<typename MatrixType, int QRPreconditioner, int Case>
+struct qr_preconditioner_should_do_anything
+{
+ enum { a = MatrixType::RowsAtCompileTime != Dynamic &&
+ MatrixType::ColsAtCompileTime != Dynamic &&
+ MatrixType::ColsAtCompileTime <= MatrixType::RowsAtCompileTime,
+ b = MatrixType::RowsAtCompileTime != Dynamic &&
+ MatrixType::ColsAtCompileTime != Dynamic &&
+ MatrixType::RowsAtCompileTime <= MatrixType::ColsAtCompileTime,
+ ret = !( (QRPreconditioner == NoQRPreconditioner) ||
+ (Case == PreconditionIfMoreColsThanRows && bool(a)) ||
+ (Case == PreconditionIfMoreRowsThanCols && bool(b)) )
+ };
+};
+
+template <typename MatrixType, int Options, int QRPreconditioner, int Case,
+ bool DoAnything = qr_preconditioner_should_do_anything<MatrixType, QRPreconditioner, Case>::ret>
+struct qr_preconditioner_impl {};
+
+template <typename MatrixType, int Options, int QRPreconditioner, int Case>
+class qr_preconditioner_impl<MatrixType, Options, QRPreconditioner, Case, false> {
+ public:
+ void allocate(const JacobiSVD<MatrixType, Options>&) {}
+ bool run(JacobiSVD<MatrixType, Options>&, const MatrixType&) { return false; }
+};
+
+/*** preconditioner using FullPivHouseholderQR ***/
+
+template <typename MatrixType, int Options>
+class qr_preconditioner_impl<MatrixType, Options, FullPivHouseholderQRPreconditioner, PreconditionIfMoreRowsThanCols,
+ true> {
+ public:
+ typedef typename MatrixType::Scalar Scalar;
+ typedef JacobiSVD<MatrixType, Options> SVDType;
+
+ enum { WorkspaceSize = MatrixType::RowsAtCompileTime, MaxWorkspaceSize = MatrixType::MaxRowsAtCompileTime };
+
+ typedef Matrix<Scalar, 1, WorkspaceSize, RowMajor, 1, MaxWorkspaceSize> WorkspaceType;
+
+ void allocate(const SVDType& svd) {
+ if (svd.rows() != m_qr.rows() || svd.cols() != m_qr.cols())
+ {
+ internal::destroy_at(&m_qr);
+ internal::construct_at(&m_qr, svd.rows(), svd.cols());
+ }
+ if (svd.m_computeFullU) m_workspace.resize(svd.rows());
+ }
+
+ bool run(SVDType& svd, const MatrixType& matrix) {
+ if(matrix.rows() > matrix.cols())
+ {
+ m_qr.compute(matrix);
+ svd.m_workMatrix = m_qr.matrixQR().block(0,0,matrix.cols(),matrix.cols()).template triangularView<Upper>();
+ if(svd.m_computeFullU) m_qr.matrixQ().evalTo(svd.m_matrixU, m_workspace);
+ if(svd.computeV()) svd.m_matrixV = m_qr.colsPermutation();
+ return true;
+ }
+ return false;
+ }
+
+private:
+ typedef FullPivHouseholderQR<MatrixType> QRType;
+ QRType m_qr;
+ WorkspaceType m_workspace;
+};
+
+template <typename MatrixType, int Options>
+class qr_preconditioner_impl<MatrixType, Options, FullPivHouseholderQRPreconditioner, PreconditionIfMoreColsThanRows,
+ true> {
+ public:
+ typedef typename MatrixType::Scalar Scalar;
+ typedef JacobiSVD<MatrixType, Options> SVDType;
+
+ enum {
+ RowsAtCompileTime = MatrixType::RowsAtCompileTime,
+ ColsAtCompileTime = MatrixType::ColsAtCompileTime,
+ MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime,
+ MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime,
+ MatrixOptions = MatrixType::Options
+ };
+
+ typedef typename internal::make_proper_matrix_type<Scalar, ColsAtCompileTime, RowsAtCompileTime, MatrixOptions,
+ MaxColsAtCompileTime, MaxRowsAtCompileTime>::type
+ TransposeTypeWithSameStorageOrder;
+
+ void allocate(const SVDType& svd) {
+ if (svd.cols() != m_qr.rows() || svd.rows() != m_qr.cols())
+ {
+ internal::destroy_at(&m_qr);
+ internal::construct_at(&m_qr, svd.cols(), svd.rows());
+ }
+ m_adjoint.resize(svd.cols(), svd.rows());
+ if (svd.m_computeFullV) m_workspace.resize(svd.cols());
+ }
+
+ bool run(SVDType& svd, const MatrixType& matrix) {
+ if(matrix.cols() > matrix.rows())
+ {
+ m_adjoint = matrix.adjoint();
+ m_qr.compute(m_adjoint);
+ svd.m_workMatrix = m_qr.matrixQR().block(0,0,matrix.rows(),matrix.rows()).template triangularView<Upper>().adjoint();
+ if(svd.m_computeFullV) m_qr.matrixQ().evalTo(svd.m_matrixV, m_workspace);
+ if(svd.computeU()) svd.m_matrixU = m_qr.colsPermutation();
+ return true;
+ }
+ else return false;
+ }
+
+private:
+ typedef FullPivHouseholderQR<TransposeTypeWithSameStorageOrder> QRType;
+ QRType m_qr;
+ TransposeTypeWithSameStorageOrder m_adjoint;
+ typename plain_row_type<MatrixType>::type m_workspace;
+};
+
+/*** preconditioner using ColPivHouseholderQR ***/
+
+template <typename MatrixType, int Options>
+class qr_preconditioner_impl<MatrixType, Options, ColPivHouseholderQRPreconditioner, PreconditionIfMoreRowsThanCols,
+ true> {
+ public:
+ typedef typename MatrixType::Scalar Scalar;
+ typedef JacobiSVD<MatrixType, Options> SVDType;
+
+ enum {
+ WorkspaceSize = internal::traits<SVDType>::MatrixUColsAtCompileTime,
+ MaxWorkspaceSize = internal::traits<SVDType>::MatrixUMaxColsAtCompileTime
+ };
+
+ typedef Matrix<Scalar, 1, WorkspaceSize, RowMajor, 1, MaxWorkspaceSize> WorkspaceType;
+
+ void allocate(const SVDType& svd) {
+ if (svd.rows() != m_qr.rows() || svd.cols() != m_qr.cols())
+ {
+ internal::destroy_at(&m_qr);
+ internal::construct_at(&m_qr, svd.rows(), svd.cols());
+ }
+ if (svd.m_computeFullU) m_workspace.resize(svd.rows());
+ else if (svd.m_computeThinU) m_workspace.resize(svd.cols());
+ }
+
+ bool run(SVDType& svd, const MatrixType& matrix) {
+ if(matrix.rows() > matrix.cols())
+ {
+ m_qr.compute(matrix);
+ svd.m_workMatrix = m_qr.matrixQR().block(0,0,matrix.cols(),matrix.cols()).template triangularView<Upper>();
+ if(svd.m_computeFullU) m_qr.householderQ().evalTo(svd.m_matrixU, m_workspace);
+ else if(svd.m_computeThinU)
+ {
+ svd.m_matrixU.setIdentity(matrix.rows(), matrix.cols());
+ m_qr.householderQ().applyThisOnTheLeft(svd.m_matrixU, m_workspace);
+ }
+ if(svd.computeV()) svd.m_matrixV = m_qr.colsPermutation();
+ return true;
+ }
+ return false;
+ }
+
+private:
+ typedef ColPivHouseholderQR<MatrixType> QRType;
+ QRType m_qr;
+ WorkspaceType m_workspace;
+};
+
+template <typename MatrixType, int Options>
+class qr_preconditioner_impl<MatrixType, Options, ColPivHouseholderQRPreconditioner, PreconditionIfMoreColsThanRows,
+ true> {
+ public:
+ typedef typename MatrixType::Scalar Scalar;
+ typedef JacobiSVD<MatrixType, Options> SVDType;
+
+ enum {
+ RowsAtCompileTime = MatrixType::RowsAtCompileTime,
+ ColsAtCompileTime = MatrixType::ColsAtCompileTime,
+ MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime,
+ MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime,
+ MatrixOptions = MatrixType::Options,
+ WorkspaceSize = internal::traits<SVDType>::MatrixVColsAtCompileTime,
+ MaxWorkspaceSize = internal::traits<SVDType>::MatrixVMaxColsAtCompileTime
+ };
+
+ typedef Matrix<Scalar, WorkspaceSize, 1, ColMajor, MaxWorkspaceSize, 1> WorkspaceType;
+
+ typedef typename internal::make_proper_matrix_type<Scalar, ColsAtCompileTime, RowsAtCompileTime, MatrixOptions,
+ MaxColsAtCompileTime, MaxRowsAtCompileTime>::type
+ TransposeTypeWithSameStorageOrder;
+
+ void allocate(const SVDType& svd) {
+ if (svd.cols() != m_qr.rows() || svd.rows() != m_qr.cols())
+ {
+ internal::destroy_at(&m_qr);
+ internal::construct_at(&m_qr, svd.cols(), svd.rows());
+ }
+ if (svd.m_computeFullV) m_workspace.resize(svd.cols());
+ else if (svd.m_computeThinV) m_workspace.resize(svd.rows());
+ m_adjoint.resize(svd.cols(), svd.rows());
+ }
+
+ bool run(SVDType& svd, const MatrixType& matrix) {
+ if(matrix.cols() > matrix.rows())
+ {
+ m_adjoint = matrix.adjoint();
+ m_qr.compute(m_adjoint);
+
+ svd.m_workMatrix = m_qr.matrixQR().block(0,0,matrix.rows(),matrix.rows()).template triangularView<Upper>().adjoint();
+ if(svd.m_computeFullV) m_qr.householderQ().evalTo(svd.m_matrixV, m_workspace);
+ else if(svd.m_computeThinV)
+ {
+ svd.m_matrixV.setIdentity(matrix.cols(), matrix.rows());
+ m_qr.householderQ().applyThisOnTheLeft(svd.m_matrixV, m_workspace);
+ }
+ if(svd.computeU()) svd.m_matrixU = m_qr.colsPermutation();
+ return true;
+ }
+ else return false;
+ }
+
+private:
+ typedef ColPivHouseholderQR<TransposeTypeWithSameStorageOrder> QRType;
+ QRType m_qr;
+ TransposeTypeWithSameStorageOrder m_adjoint;
+ WorkspaceType m_workspace;
+};
+
+/*** preconditioner using HouseholderQR ***/
+
+template <typename MatrixType, int Options>
+class qr_preconditioner_impl<MatrixType, Options, HouseholderQRPreconditioner, PreconditionIfMoreRowsThanCols, true> {
+ public:
+ typedef typename MatrixType::Scalar Scalar;
+ typedef JacobiSVD<MatrixType, Options> SVDType;
+
+ enum {
+ WorkspaceSize = internal::traits<SVDType>::MatrixUColsAtCompileTime,
+ MaxWorkspaceSize = internal::traits<SVDType>::MatrixUMaxColsAtCompileTime
+ };
+
+ typedef Matrix<Scalar, 1, WorkspaceSize, RowMajor, 1, MaxWorkspaceSize> WorkspaceType;
+
+ void allocate(const SVDType& svd) {
+ if (svd.rows() != m_qr.rows() || svd.cols() != m_qr.cols())
+ {
+ internal::destroy_at(&m_qr);
+ internal::construct_at(&m_qr, svd.rows(), svd.cols());
+ }
+ if (svd.m_computeFullU) m_workspace.resize(svd.rows());
+ else if (svd.m_computeThinU) m_workspace.resize(svd.cols());
+ }
+
+ bool run(SVDType& svd, const MatrixType& matrix) {
+ if(matrix.rows() > matrix.cols())
+ {
+ m_qr.compute(matrix);
+ svd.m_workMatrix = m_qr.matrixQR().block(0,0,matrix.cols(),matrix.cols()).template triangularView<Upper>();
+ if(svd.m_computeFullU) m_qr.householderQ().evalTo(svd.m_matrixU, m_workspace);
+ else if(svd.m_computeThinU)
+ {
+ svd.m_matrixU.setIdentity(matrix.rows(), matrix.cols());
+ m_qr.householderQ().applyThisOnTheLeft(svd.m_matrixU, m_workspace);
+ }
+ if(svd.computeV()) svd.m_matrixV.setIdentity(matrix.cols(), matrix.cols());
+ return true;
+ }
+ return false;
+ }
+
+private:
+ typedef HouseholderQR<MatrixType> QRType;
+ QRType m_qr;
+ WorkspaceType m_workspace;
+};
+
+template <typename MatrixType, int Options>
+class qr_preconditioner_impl<MatrixType, Options, HouseholderQRPreconditioner, PreconditionIfMoreColsThanRows, true> {
+ public:
+ typedef typename MatrixType::Scalar Scalar;
+ typedef JacobiSVD<MatrixType, Options> SVDType;
+
+ enum {
+ RowsAtCompileTime = MatrixType::RowsAtCompileTime,
+ ColsAtCompileTime = MatrixType::ColsAtCompileTime,
+ MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime,
+ MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime,
+ MatrixOptions = MatrixType::Options,
+ WorkspaceSize = internal::traits<SVDType>::MatrixVColsAtCompileTime,
+ MaxWorkspaceSize = internal::traits<SVDType>::MatrixVMaxColsAtCompileTime
+ };
+
+ typedef Matrix<Scalar, WorkspaceSize, 1, ColMajor, MaxWorkspaceSize, 1> WorkspaceType;
+
+ typedef typename internal::make_proper_matrix_type<Scalar, ColsAtCompileTime, RowsAtCompileTime, MatrixOptions,
+ MaxColsAtCompileTime, MaxRowsAtCompileTime>::type
+ TransposeTypeWithSameStorageOrder;
+
+ void allocate(const SVDType& svd) {
+ if (svd.cols() != m_qr.rows() || svd.rows() != m_qr.cols())
+ {
+ internal::destroy_at(&m_qr);
+ internal::construct_at(&m_qr, svd.cols(), svd.rows());
+ }
+ if (svd.m_computeFullV) m_workspace.resize(svd.cols());
+ else if (svd.m_computeThinV) m_workspace.resize(svd.rows());
+ m_adjoint.resize(svd.cols(), svd.rows());
+ }
+
+ bool run(SVDType& svd, const MatrixType& matrix) {
+ if(matrix.cols() > matrix.rows())
+ {
+ m_adjoint = matrix.adjoint();
+ m_qr.compute(m_adjoint);
+
+ svd.m_workMatrix = m_qr.matrixQR().block(0,0,matrix.rows(),matrix.rows()).template triangularView<Upper>().adjoint();
+ if(svd.m_computeFullV) m_qr.householderQ().evalTo(svd.m_matrixV, m_workspace);
+ else if(svd.m_computeThinV)
+ {
+ svd.m_matrixV.setIdentity(matrix.cols(), matrix.rows());
+ m_qr.householderQ().applyThisOnTheLeft(svd.m_matrixV, m_workspace);
+ }
+ if(svd.computeU()) svd.m_matrixU.setIdentity(matrix.rows(), matrix.rows());
+ return true;
+ }
+ else return false;
+ }
+
+private:
+ typedef HouseholderQR<TransposeTypeWithSameStorageOrder> QRType;
+ QRType m_qr;
+ TransposeTypeWithSameStorageOrder m_adjoint;
+ WorkspaceType m_workspace;
+};
+
+/*** 2x2 SVD implementation
+ ***
+ *** JacobiSVD consists in performing a series of 2x2 SVD subproblems
+ ***/
+
+template <typename MatrixType, int Options>
+struct svd_precondition_2x2_block_to_be_real<MatrixType, Options, false> {
+ typedef JacobiSVD<MatrixType, Options> SVD;
+ typedef typename MatrixType::RealScalar RealScalar;
+ static bool run(typename SVD::WorkMatrixType&, SVD&, Index, Index, RealScalar&) { return true; }
+};
+
+template <typename MatrixType, int Options>
+struct svd_precondition_2x2_block_to_be_real<MatrixType, Options, true> {
+ typedef JacobiSVD<MatrixType, Options> SVD;
+ typedef typename MatrixType::Scalar Scalar;
+ typedef typename MatrixType::RealScalar RealScalar;
+ static bool run(typename SVD::WorkMatrixType& work_matrix, SVD& svd, Index p, Index q, RealScalar& maxDiagEntry)
+ {
+ using std::sqrt;
+ using std::abs;
+ Scalar z;
+ JacobiRotation<Scalar> rot;
+ RealScalar n = sqrt(numext::abs2(work_matrix.coeff(p,p)) + numext::abs2(work_matrix.coeff(q,p)));
+
+ const RealScalar considerAsZero = (std::numeric_limits<RealScalar>::min)();
+ const RealScalar precision = NumTraits<Scalar>::epsilon();
+
+ if(numext::is_exactly_zero(n))
+ {
+ // make sure first column is zero
+ work_matrix.coeffRef(p,p) = work_matrix.coeffRef(q,p) = Scalar(0);
+
+ if(abs(numext::imag(work_matrix.coeff(p,q)))>considerAsZero)
+ {
+ // work_matrix.coeff(p,q) can be zero if work_matrix.coeff(q,p) is not zero but small enough to underflow when computing n
+ z = abs(work_matrix.coeff(p,q)) / work_matrix.coeff(p,q);
+ work_matrix.row(p) *= z;
+ if(svd.computeU()) svd.m_matrixU.col(p) *= conj(z);
+ }
+ if(abs(numext::imag(work_matrix.coeff(q,q)))>considerAsZero)
+ {
+ z = abs(work_matrix.coeff(q,q)) / work_matrix.coeff(q,q);
+ work_matrix.row(q) *= z;
+ if(svd.computeU()) svd.m_matrixU.col(q) *= conj(z);
+ }
+ // otherwise the second row is already zero, so we have nothing to do.
+ }
+ else
+ {
+ rot.c() = conj(work_matrix.coeff(p,p)) / n;
+ rot.s() = work_matrix.coeff(q,p) / n;
+ work_matrix.applyOnTheLeft(p,q,rot);
+ if(svd.computeU()) svd.m_matrixU.applyOnTheRight(p,q,rot.adjoint());
+ if(abs(numext::imag(work_matrix.coeff(p,q)))>considerAsZero)
+ {
+ z = abs(work_matrix.coeff(p,q)) / work_matrix.coeff(p,q);
+ work_matrix.col(q) *= z;
+ if(svd.computeV()) svd.m_matrixV.col(q) *= z;
+ }
+ if(abs(numext::imag(work_matrix.coeff(q,q)))>considerAsZero)
+ {
+ z = abs(work_matrix.coeff(q,q)) / work_matrix.coeff(q,q);
+ work_matrix.row(q) *= z;
+ if(svd.computeU()) svd.m_matrixU.col(q) *= conj(z);
+ }
+ }
+
+ // update largest diagonal entry
+ maxDiagEntry = numext::maxi<RealScalar>(maxDiagEntry,numext::maxi<RealScalar>(abs(work_matrix.coeff(p,p)), abs(work_matrix.coeff(q,q))));
+ // and check whether the 2x2 block is already diagonal
+ RealScalar threshold = numext::maxi<RealScalar>(considerAsZero, precision * maxDiagEntry);
+ return abs(work_matrix.coeff(p,q))>threshold || abs(work_matrix.coeff(q,p)) > threshold;
+ }
+};
+
+template <typename MatrixType_, int Options>
+struct traits<JacobiSVD<MatrixType_, Options> > : svd_traits<MatrixType_, Options> {
+ typedef MatrixType_ MatrixType;
+};
+
+} // end namespace internal
+
+/** \ingroup SVD_Module
+ *
+ *
+ * \class JacobiSVD
+ *
+ * \brief Two-sided Jacobi SVD decomposition of a rectangular matrix
+ *
+ * \tparam MatrixType_ the type of the matrix of which we are computing the SVD decomposition
+ * \tparam Options this optional parameter allows one to specify the type of QR decomposition that will be used
+ * internally for the R-SVD step for non-square matrices. Additionally, it allows one to specify whether to compute thin
+ * or full unitaries \a U and \a V. See discussion of possible values below.
+ *
+ * SVD decomposition consists in decomposing any n-by-p matrix \a A as a product
+ * \f[ A = U S V^* \f]
+ * where \a U is a n-by-n unitary, \a V is a p-by-p unitary, and \a S is a n-by-p real positive matrix which is zero
+ * outside of its main diagonal; the diagonal entries of S are known as the \em singular \em values of \a A and the
+ * columns of \a U and \a V are known as the left and right \em singular \em vectors of \a A respectively.
+ *
+ * Singular values are always sorted in decreasing order.
+ *
+ * This JacobiSVD decomposition computes only the singular values by default. If you want \a U or \a V, you need to ask
+ * for them explicitly.
+ *
+ * You can ask for only \em thin \a U or \a V to be computed, meaning the following. In case of a rectangular n-by-p
+ * matrix, letting \a m be the smaller value among \a n and \a p, there are only \a m singular vectors; the remaining
+ * columns of \a U and \a V do not correspond to actual singular vectors. Asking for \em thin \a U or \a V means asking
+ * for only their \a m first columns to be formed. So \a U is then a n-by-m matrix, and \a V is then a p-by-m matrix.
+ * Notice that thin \a U and \a V are all you need for (least squares) solving.
+ *
+ * Here's an example demonstrating basic usage:
+ * \include JacobiSVD_basic.cpp
+ * Output: \verbinclude JacobiSVD_basic.out
+ *
+ * This JacobiSVD class is a two-sided Jacobi R-SVD decomposition, ensuring optimal reliability and accuracy. The
+ * downside is that it's slower than bidiagonalizing SVD algorithms for large square matrices; however its complexity is
+ * still \f$ O(n^2p) \f$ where \a n is the smaller dimension and \a p is the greater dimension, meaning that it is still
+ * of the same order of complexity as the faster bidiagonalizing R-SVD algorithms. In particular, like any R-SVD, it
+ * takes advantage of non-squareness in that its complexity is only linear in the greater dimension.
+ *
+ * If the input matrix has inf or nan coefficients, the result of the computation is undefined, but the computation is
+ * guaranteed to terminate in finite (and reasonable) time.
+ *
+ * The possible QR preconditioners that can be set with Options template parameter are:
+ * \li ColPivHouseholderQRPreconditioner is the default. In practice it's very safe. It uses column-pivoting QR.
+ * \li FullPivHouseholderQRPreconditioner, is the safest and slowest. It uses full-pivoting QR.
+ * Contrary to other QRs, it doesn't allow computing thin unitaries.
+ * \li HouseholderQRPreconditioner is the fastest, and less safe and accurate than the pivoting variants. It uses
+ * non-pivoting QR. This is very similar in safety and accuracy to the bidiagonalization process used by bidiagonalizing
+ * SVD algorithms (since bidiagonalization is inherently non-pivoting). However the resulting SVD is still more reliable
+ * than bidiagonalizing SVDs because the Jacobi-based iterarive process is more reliable than the optimized bidiagonal
+ * SVD iterations. \li NoQRPreconditioner allows not to use a QR preconditioner at all. This is useful if you know that
+ * you will only be computing JacobiSVD decompositions of square matrices. Non-square matrices require a QR
+ * preconditioner. Using this option will result in faster compilation and smaller executable code. It won't
+ * significantly speed up computation, since JacobiSVD is always checking if QR preconditioning is needed before
+ * applying it anyway.
+ *
+ * One may also use the Options template parameter to specify how the unitaries should be computed. The options are
+ * #ComputeThinU, #ComputeThinV, #ComputeFullU, #ComputeFullV. It is not possible to request both the thin and full
+ * versions of a unitary. By default, unitaries will not be computed.
+ *
+ * You can set the QRPreconditioner and unitary options together: JacobiSVD<MatrixType,
+ * ColPivHouseholderQRPreconditioner | ComputeThinU | ComputeFullV>
+ *
+ * \sa MatrixBase::jacobiSvd()
+ */
+template <typename MatrixType_, int Options_>
+class JacobiSVD : public SVDBase<JacobiSVD<MatrixType_, Options_> > {
+ typedef SVDBase<JacobiSVD> Base;
+
+ public:
+ typedef MatrixType_ MatrixType;
+ typedef typename Base::Scalar Scalar;
+ typedef typename Base::RealScalar RealScalar;
+ typedef typename Base::Index Index;
+ enum {
+ Options = Options_,
+ QRPreconditioner = internal::get_qr_preconditioner(Options),
+ RowsAtCompileTime = Base::RowsAtCompileTime,
+ ColsAtCompileTime = Base::ColsAtCompileTime,
+ DiagSizeAtCompileTime = Base::DiagSizeAtCompileTime,
+ MaxRowsAtCompileTime = Base::MaxRowsAtCompileTime,
+ MaxColsAtCompileTime = Base::MaxColsAtCompileTime,
+ MaxDiagSizeAtCompileTime = Base::MaxDiagSizeAtCompileTime,
+ MatrixOptions = Base::MatrixOptions
+ };
+
+ typedef typename Base::MatrixUType MatrixUType;
+ typedef typename Base::MatrixVType MatrixVType;
+ typedef typename Base::SingularValuesType SingularValuesType;
+ typedef Matrix<Scalar, DiagSizeAtCompileTime, DiagSizeAtCompileTime, MatrixOptions, MaxDiagSizeAtCompileTime,
+ MaxDiagSizeAtCompileTime>
+ WorkMatrixType;
+
+ /** \brief Default Constructor.
+ *
+ * The default constructor is useful in cases in which the user intends to
+ * perform decompositions via JacobiSVD::compute(const MatrixType&).
+ */
+ JacobiSVD() {}
+
+ /** \brief Default Constructor with memory preallocation
+ *
+ * Like the default constructor but with preallocation of the internal data
+ * according to the specified problem size and \a Options template parameter.
+ *
+ * \sa JacobiSVD()
+ */
+ JacobiSVD(Index rows, Index cols) { allocate(rows, cols, internal::get_computation_options(Options)); }
+
+ /** \brief Default Constructor with memory preallocation
+ *
+ * Like the default constructor but with preallocation of the internal data
+ * according to the specified problem size.
+ *
+ * One \b cannot request unitaries using both the \a Options template parameter
+ * and the constructor. If possible, prefer using the \a Options template parameter.
+ *
+ * \param computationOptions specify whether to compute Thin/Full unitaries U/V
+ * \sa JacobiSVD()
+ *
+ * \deprecated Will be removed in the next major Eigen version. Options should
+ * be specified in the \a Options template parameter.
+ */
+ EIGEN_DEPRECATED
+ JacobiSVD(Index rows, Index cols, unsigned int computationOptions) {
+ internal::check_svd_options_assertions<MatrixType, Options>(computationOptions, rows, cols);
+ allocate(rows, cols, computationOptions);
+ }
+
+ /** \brief Constructor performing the decomposition of given matrix, using the custom options specified
+ * with the \a Options template paramter.
+ *
+ * \param matrix the matrix to decompose
+ */
+ explicit JacobiSVD(const MatrixType& matrix) { compute_impl(matrix, internal::get_computation_options(Options)); }
+
+ /** \brief Constructor performing the decomposition of given matrix using specified options
+ * for computing unitaries.
+ *
+ * One \b cannot request unitiaries using both the \a Options template parameter
+ * and the constructor. If possible, prefer using the \a Options template parameter.
+ *
+ * \param matrix the matrix to decompose
+ * \param computationOptions specify whether to compute Thin/Full unitaries U/V
+ *
+ * \deprecated Will be removed in the next major Eigen version. Options should
+ * be specified in the \a Options template parameter.
+ */
+ // EIGEN_DEPRECATED // TODO(cantonios): re-enable after fixing a few 3p libraries that error on deprecation warnings.
+ JacobiSVD(const MatrixType& matrix, unsigned int computationOptions) {
+ internal::check_svd_options_assertions<MatrixType, Options>(computationOptions, matrix.rows(), matrix.cols());
+ compute_impl(matrix, computationOptions);
+ }
+
+ /** \brief Method performing the decomposition of given matrix. Computes Thin/Full unitaries U/V if specified
+ * using the \a Options template parameter or the class constructor.
+ *
+ * \param matrix the matrix to decompose
+ */
+ JacobiSVD& compute(const MatrixType& matrix) { return compute_impl(matrix, m_computationOptions); }
+
+ /** \brief Method performing the decomposition of given matrix, as specified by
+ * the `computationOptions` parameter.
+ *
+ * \param matrix the matrix to decompose
+ * \param computationOptions specify whether to compute Thin/Full unitaries U/V
+ *
+ * \deprecated Will be removed in the next major Eigen version. Options should
+ * be specified in the \a Options template parameter.
+ */
+ EIGEN_DEPRECATED
+ JacobiSVD& compute(const MatrixType& matrix, unsigned int computationOptions) {
+ internal::check_svd_options_assertions<MatrixType, Options>(m_computationOptions, matrix.rows(), matrix.cols());
+ return compute_impl(matrix, computationOptions);
+ }
+
+ using Base::computeU;
+ using Base::computeV;
+ using Base::rows;
+ using Base::cols;
+ using Base::rank;
+
+ private:
+ void allocate(Index rows, Index cols, unsigned int computationOptions);
+ JacobiSVD& compute_impl(const MatrixType& matrix, unsigned int computationOptions);
+
+ protected:
+ using Base::m_cols;
+ using Base::m_computationOptions;
+ using Base::m_computeFullU;
+ using Base::m_computeFullV;
+ using Base::m_computeThinU;
+ using Base::m_computeThinV;
+ using Base::m_diagSize;
+ using Base::m_info;
+ using Base::m_isAllocated;
+ using Base::m_isInitialized;
+ using Base::m_matrixU;
+ using Base::m_matrixV;
+ using Base::m_nonzeroSingularValues;
+ using Base::m_prescribedThreshold;
+ using Base::m_rows;
+ using Base::m_singularValues;
+ using Base::m_usePrescribedThreshold;
+ using Base::ShouldComputeThinU;
+ using Base::ShouldComputeThinV;
+
+ EIGEN_STATIC_ASSERT(!(ShouldComputeThinU && int(QRPreconditioner) == int(FullPivHouseholderQRPreconditioner)) &&
+ !(ShouldComputeThinU && int(QRPreconditioner) == int(FullPivHouseholderQRPreconditioner)),
+ "JacobiSVD: can't compute thin U or thin V with the FullPivHouseholderQR preconditioner. "
+ "Use the ColPivHouseholderQR preconditioner instead.")
+
+ template <typename MatrixType__, int Options__, bool IsComplex_>
+ friend struct internal::svd_precondition_2x2_block_to_be_real;
+ template <typename MatrixType__, int Options__, int QRPreconditioner_, int Case_, bool DoAnything_>
+ friend struct internal::qr_preconditioner_impl;
+
+ internal::qr_preconditioner_impl<MatrixType, Options, QRPreconditioner, internal::PreconditionIfMoreColsThanRows>
+ m_qr_precond_morecols;
+ internal::qr_preconditioner_impl<MatrixType, Options, QRPreconditioner, internal::PreconditionIfMoreRowsThanCols>
+ m_qr_precond_morerows;
+ WorkMatrixType m_workMatrix;
+ MatrixType m_scaledMatrix;
+};
+
+template <typename MatrixType, int Options>
+void JacobiSVD<MatrixType, Options>::allocate(Index rows, Index cols, unsigned int computationOptions) {
+ if (Base::allocate(rows, cols, computationOptions)) return;
+
+ eigen_assert(!(ShouldComputeThinU && int(QRPreconditioner) == int(FullPivHouseholderQRPreconditioner)) &&
+ !(ShouldComputeThinU && int(QRPreconditioner) == int(FullPivHouseholderQRPreconditioner)) &&
+ "JacobiSVD: can't compute thin U or thin V with the FullPivHouseholderQR preconditioner. "
+ "Use the ColPivHouseholderQR preconditioner instead.");
+
+ m_workMatrix.resize(m_diagSize, m_diagSize);
+ if(m_cols>m_rows) m_qr_precond_morecols.allocate(*this);
+ if(m_rows>m_cols) m_qr_precond_morerows.allocate(*this);
+ if(m_rows!=m_cols) m_scaledMatrix.resize(rows,cols);
+}
+
+template <typename MatrixType, int Options>
+JacobiSVD<MatrixType, Options>& JacobiSVD<MatrixType, Options>::compute_impl(const MatrixType& matrix,
+ unsigned int computationOptions) {
+ using std::abs;
+
+ allocate(matrix.rows(), matrix.cols(), computationOptions);
+
+ // currently we stop when we reach precision 2*epsilon as the last bit of precision can require an unreasonable number of iterations,
+ // only worsening the precision of U and V as we accumulate more rotations
+ const RealScalar precision = RealScalar(2) * NumTraits<Scalar>::epsilon();
+
+ // limit for denormal numbers to be considered zero in order to avoid infinite loops (see bug 286)
+ const RealScalar considerAsZero = (std::numeric_limits<RealScalar>::min)();
+
+ // Scaling factor to reduce over/under-flows
+ RealScalar scale = matrix.cwiseAbs().template maxCoeff<PropagateNaN>();
+ if (!(numext::isfinite)(scale)) {
+ m_isInitialized = true;
+ m_info = InvalidInput;
+ return *this;
+ }
+ if(numext::is_exactly_zero(scale)) scale = RealScalar(1);
+
+ /*** step 1. The R-SVD step: we use a QR decomposition to reduce to the case of a square matrix */
+
+ if(m_rows!=m_cols)
+ {
+ m_scaledMatrix = matrix / scale;
+ m_qr_precond_morecols.run(*this, m_scaledMatrix);
+ m_qr_precond_morerows.run(*this, m_scaledMatrix);
+ }
+ else
+ {
+ m_workMatrix = matrix.block(0,0,m_diagSize,m_diagSize) / scale;
+ if(m_computeFullU) m_matrixU.setIdentity(m_rows,m_rows);
+ if(m_computeThinU) m_matrixU.setIdentity(m_rows,m_diagSize);
+ if(m_computeFullV) m_matrixV.setIdentity(m_cols,m_cols);
+ if(m_computeThinV) m_matrixV.setIdentity(m_cols, m_diagSize);
+ }
+
+ /*** step 2. The main Jacobi SVD iteration. ***/
+ RealScalar maxDiagEntry = m_workMatrix.cwiseAbs().diagonal().maxCoeff();
+
+ bool finished = false;
+ while(!finished)
+ {
+ finished = true;
+
+ // do a sweep: for all index pairs (p,q), perform SVD of the corresponding 2x2 sub-matrix
+
+ for(Index p = 1; p < m_diagSize; ++p)
+ {
+ for(Index q = 0; q < p; ++q)
+ {
+ // if this 2x2 sub-matrix is not diagonal already...
+ // notice that this comparison will evaluate to false if any NaN is involved, ensuring that NaN's don't
+ // keep us iterating forever. Similarly, small denormal numbers are considered zero.
+ RealScalar threshold = numext::maxi<RealScalar>(considerAsZero, precision * maxDiagEntry);
+ if(abs(m_workMatrix.coeff(p,q))>threshold || abs(m_workMatrix.coeff(q,p)) > threshold)
+ {
+ finished = false;
+ // perform SVD decomposition of 2x2 sub-matrix corresponding to indices p,q to make it diagonal
+ // the complex to real operation returns true if the updated 2x2 block is not already diagonal
+ if (internal::svd_precondition_2x2_block_to_be_real<MatrixType, Options>::run(m_workMatrix, *this, p, q,
+ maxDiagEntry)) {
+ JacobiRotation<RealScalar> j_left, j_right;
+ internal::real_2x2_jacobi_svd(m_workMatrix, p, q, &j_left, &j_right);
+
+ // accumulate resulting Jacobi rotations
+ m_workMatrix.applyOnTheLeft(p,q,j_left);
+ if(computeU()) m_matrixU.applyOnTheRight(p,q,j_left.transpose());
+
+ m_workMatrix.applyOnTheRight(p,q,j_right);
+ if(computeV()) m_matrixV.applyOnTheRight(p,q,j_right);
+
+ // keep track of the largest diagonal coefficient
+ maxDiagEntry = numext::maxi<RealScalar>(maxDiagEntry,numext::maxi<RealScalar>(abs(m_workMatrix.coeff(p,p)), abs(m_workMatrix.coeff(q,q))));
+ }
+ }
+ }
+ }
+ }
+
+ /*** step 3. The work matrix is now diagonal, so ensure it's positive so its diagonal entries are the singular values ***/
+
+ for(Index i = 0; i < m_diagSize; ++i)
+ {
+ // For a complex matrix, some diagonal coefficients might note have been
+ // treated by svd_precondition_2x2_block_to_be_real, and the imaginary part
+ // of some diagonal entry might not be null.
+ if(NumTraits<Scalar>::IsComplex && abs(numext::imag(m_workMatrix.coeff(i,i)))>considerAsZero)
+ {
+ RealScalar a = abs(m_workMatrix.coeff(i,i));
+ m_singularValues.coeffRef(i) = abs(a);
+ if(computeU()) m_matrixU.col(i) *= m_workMatrix.coeff(i,i)/a;
+ }
+ else
+ {
+ // m_workMatrix.coeff(i,i) is already real, no difficulty:
+ RealScalar a = numext::real(m_workMatrix.coeff(i,i));
+ m_singularValues.coeffRef(i) = abs(a);
+ if(computeU() && (a<RealScalar(0))) m_matrixU.col(i) = -m_matrixU.col(i);
+ }
+ }
+
+ m_singularValues *= scale;
+
+ /*** step 4. Sort singular values in descending order and compute the number of nonzero singular values ***/
+
+ m_nonzeroSingularValues = m_diagSize;
+ for(Index i = 0; i < m_diagSize; i++)
+ {
+ Index pos;
+ RealScalar maxRemainingSingularValue = m_singularValues.tail(m_diagSize-i).maxCoeff(&pos);
+ if(numext::is_exactly_zero(maxRemainingSingularValue))
+ {
+ m_nonzeroSingularValues = i;
+ break;
+ }
+ if(pos)
+ {
+ pos += i;
+ std::swap(m_singularValues.coeffRef(i), m_singularValues.coeffRef(pos));
+ if(computeU()) m_matrixU.col(pos).swap(m_matrixU.col(i));
+ if(computeV()) m_matrixV.col(pos).swap(m_matrixV.col(i));
+ }
+ }
+
+ m_isInitialized = true;
+ return *this;
+}
+
+/** \svd_module
+ *
+ * \return the singular value decomposition of \c *this computed by two-sided
+ * Jacobi transformations.
+ *
+ * \sa class JacobiSVD
+ */
+template <typename Derived>
+template <int Options>
+JacobiSVD<typename MatrixBase<Derived>::PlainObject, Options> MatrixBase<Derived>::jacobiSvd() const {
+ return JacobiSVD<PlainObject, Options>(*this);
+}
+
+template <typename Derived>
+template <int Options>
+JacobiSVD<typename MatrixBase<Derived>::PlainObject, Options> MatrixBase<Derived>::jacobiSvd(
+ unsigned int computationOptions) const {
+ return JacobiSVD<PlainObject, Options>(*this, computationOptions);
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_JACOBISVD_H
diff --git a/Eigen/src/SVD/JacobiSVD_LAPACKE.h b/Eigen/src/SVD/JacobiSVD_LAPACKE.h
new file mode 100644
index 0000000..c5717e9
--- /dev/null
+++ b/Eigen/src/SVD/JacobiSVD_LAPACKE.h
@@ -0,0 +1,105 @@
+/*
+ Copyright (c) 2011, Intel Corporation. All rights reserved.
+
+ Redistribution and use in source and binary forms, with or without modification,
+ are permitted provided that the following conditions are met:
+
+ * Redistributions of source code must retain the above copyright notice, this
+ list of conditions and the following disclaimer.
+ * Redistributions in binary form must reproduce the above copyright notice,
+ this list of conditions and the following disclaimer in the documentation
+ and/or other materials provided with the distribution.
+ * Neither the name of Intel Corporation nor the names of its contributors may
+ be used to endorse or promote products derived from this software without
+ specific prior written permission.
+
+ THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
+ ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
+ WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
+ DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR
+ ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
+ (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
+ LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON
+ ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
+ (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
+ SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+
+ ********************************************************************************
+ * Content : Eigen bindings to LAPACKe
+ * Singular Value Decomposition - SVD.
+ ********************************************************************************
+*/
+
+#ifndef EIGEN_JACOBISVD_LAPACKE_H
+#define EIGEN_JACOBISVD_LAPACKE_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+/** \internal Specialization for the data types supported by LAPACKe */
+
+#define EIGEN_LAPACKE_SVD(EIGTYPE, LAPACKE_TYPE, LAPACKE_RTYPE, LAPACKE_PREFIX, EIGCOLROW, LAPACKE_COLROW, OPTIONS) \
+template<> inline \
+JacobiSVD<Matrix<EIGTYPE, Dynamic, Dynamic, EIGCOLROW, Dynamic, Dynamic>, OPTIONS>& \
+JacobiSVD<Matrix<EIGTYPE, Dynamic, Dynamic, EIGCOLROW, Dynamic, Dynamic>, OPTIONS>::compute_impl(const Matrix<EIGTYPE, Dynamic, Dynamic, EIGCOLROW, Dynamic, Dynamic>& matrix, \
+ unsigned int computationOptions) \
+{ \
+ typedef Matrix<EIGTYPE, Dynamic, Dynamic, EIGCOLROW, Dynamic, Dynamic> MatrixType; \
+ /*typedef MatrixType::Scalar Scalar;*/ \
+ /*typedef MatrixType::RealScalar RealScalar;*/ \
+ allocate(matrix.rows(), matrix.cols(), computationOptions); \
+\
+ /*const RealScalar precision = RealScalar(2) * NumTraits<Scalar>::epsilon();*/ \
+ m_nonzeroSingularValues = m_diagSize; \
+\
+ lapack_int lda = internal::convert_index<lapack_int>(matrix.outerStride()), ldu, ldvt; \
+ lapack_int matrix_order = LAPACKE_COLROW; \
+ char jobu, jobvt; \
+ LAPACKE_TYPE *u, *vt, dummy; \
+ jobu = (m_computeFullU) ? 'A' : (m_computeThinU) ? 'S' : 'N'; \
+ jobvt = (m_computeFullV) ? 'A' : (m_computeThinV) ? 'S' : 'N'; \
+ if (computeU()) { \
+ ldu = internal::convert_index<lapack_int>(m_matrixU.outerStride()); \
+ u = (LAPACKE_TYPE*)m_matrixU.data(); \
+ } else { ldu=1; u=&dummy; }\
+ MatrixType localV; \
+ lapack_int vt_rows = (m_computeFullV) ? internal::convert_index<lapack_int>(m_cols) : (m_computeThinV) ? internal::convert_index<lapack_int>(m_diagSize) : 1; \
+ if (computeV()) { \
+ localV.resize(vt_rows, m_cols); \
+ ldvt = internal::convert_index<lapack_int>(localV.outerStride()); \
+ vt = (LAPACKE_TYPE*)localV.data(); \
+ } else { ldvt=1; vt=&dummy; }\
+ Matrix<LAPACKE_RTYPE, Dynamic, Dynamic> superb; superb.resize(m_diagSize, 1); \
+ MatrixType m_temp; m_temp = matrix; \
+ LAPACKE_##LAPACKE_PREFIX##gesvd( matrix_order, jobu, jobvt, internal::convert_index<lapack_int>(m_rows), internal::convert_index<lapack_int>(m_cols), (LAPACKE_TYPE*)m_temp.data(), lda, (LAPACKE_RTYPE*)m_singularValues.data(), u, ldu, vt, ldvt, superb.data()); \
+ if (computeV()) m_matrixV = localV.adjoint(); \
+ /* for(int i=0;i<m_diagSize;i++) if (m_singularValues.coeffRef(i) < precision) { m_nonzeroSingularValues--; m_singularValues.coeffRef(i)=RealScalar(0);}*/ \
+ m_isInitialized = true; \
+ return *this; \
+}
+
+#define EIGEN_LAPACK_SVD_OPTIONS(OPTIONS) \
+ EIGEN_LAPACKE_SVD(double, double, double, d, ColMajor, LAPACK_COL_MAJOR, OPTIONS) \
+ EIGEN_LAPACKE_SVD(float, float, float , s, ColMajor, LAPACK_COL_MAJOR, OPTIONS) \
+ EIGEN_LAPACKE_SVD(dcomplex, lapack_complex_double, double, z, ColMajor, LAPACK_COL_MAJOR, OPTIONS) \
+ EIGEN_LAPACKE_SVD(scomplex, lapack_complex_float, float , c, ColMajor, LAPACK_COL_MAJOR, OPTIONS) \
+\
+ EIGEN_LAPACKE_SVD(double, double, double, d, RowMajor, LAPACK_ROW_MAJOR, OPTIONS) \
+ EIGEN_LAPACKE_SVD(float, float, float , s, RowMajor, LAPACK_ROW_MAJOR, OPTIONS) \
+ EIGEN_LAPACKE_SVD(dcomplex, lapack_complex_double, double, z, RowMajor, LAPACK_ROW_MAJOR, OPTIONS) \
+ EIGEN_LAPACKE_SVD(scomplex, lapack_complex_float, float , c, RowMajor, LAPACK_ROW_MAJOR, OPTIONS)
+
+EIGEN_LAPACK_SVD_OPTIONS(0)
+EIGEN_LAPACK_SVD_OPTIONS(ComputeThinU)
+EIGEN_LAPACK_SVD_OPTIONS(ComputeThinV)
+EIGEN_LAPACK_SVD_OPTIONS(ComputeFullU)
+EIGEN_LAPACK_SVD_OPTIONS(ComputeFullV)
+EIGEN_LAPACK_SVD_OPTIONS(ComputeThinU | ComputeThinV)
+EIGEN_LAPACK_SVD_OPTIONS(ComputeFullU | ComputeFullV)
+EIGEN_LAPACK_SVD_OPTIONS(ComputeThinU | ComputeFullV)
+EIGEN_LAPACK_SVD_OPTIONS(ComputeFullU | ComputeThinV)
+
+} // end namespace Eigen
+
+#endif // EIGEN_JACOBISVD_LAPACKE_H
diff --git a/Eigen/src/SVD/SVDBase.h b/Eigen/src/SVD/SVDBase.h
new file mode 100644
index 0000000..f01c7a9
--- /dev/null
+++ b/Eigen/src/SVD/SVDBase.h
@@ -0,0 +1,442 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009-2010 Benoit Jacob <jacob.benoit.1@gmail.com>
+// Copyright (C) 2014 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// Copyright (C) 2013 Gauthier Brun <brun.gauthier@gmail.com>
+// Copyright (C) 2013 Nicolas Carre <nicolas.carre@ensimag.fr>
+// Copyright (C) 2013 Jean Ceccato <jean.ceccato@ensimag.fr>
+// Copyright (C) 2013 Pierre Zoppitelli <pierre.zoppitelli@ensimag.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_SVDBASE_H
+#define EIGEN_SVDBASE_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+
+enum OptionsMasks {
+ QRPreconditionerBits = NoQRPreconditioner | HouseholderQRPreconditioner | ColPivHouseholderQRPreconditioner |
+ FullPivHouseholderQRPreconditioner,
+ ComputationOptionsBits = ComputeThinU | ComputeFullU | ComputeThinV | ComputeFullV
+};
+
+constexpr int get_qr_preconditioner(int options) { return options & QRPreconditionerBits; }
+
+constexpr int get_computation_options(int options) { return options & ComputationOptionsBits; }
+
+constexpr bool should_svd_compute_thin_u(int options) { return (options & ComputeThinU) != 0; }
+constexpr bool should_svd_compute_full_u(int options) { return (options & ComputeFullU) != 0; }
+constexpr bool should_svd_compute_thin_v(int options) { return (options & ComputeThinV) != 0; }
+constexpr bool should_svd_compute_full_v(int options) { return (options & ComputeFullV) != 0; }
+
+template<typename MatrixType, int Options>
+void check_svd_options_assertions(unsigned int computationOptions, Index rows, Index cols) {
+ EIGEN_STATIC_ASSERT((Options & ComputationOptionsBits) == 0,
+ "SVDBase: Cannot request U or V using both static and runtime options, even if they match. "
+ "Requesting unitaries at runtime is DEPRECATED: "
+ "Prefer requesting unitaries statically, using the Options template parameter.");
+ eigen_assert(!(should_svd_compute_thin_u(computationOptions) && cols < rows && MatrixType::RowsAtCompileTime != Dynamic) &&
+ !(should_svd_compute_thin_v(computationOptions) && rows < cols && MatrixType::ColsAtCompileTime != Dynamic) &&
+ "SVDBase: If thin U is requested at runtime, your matrix must have more rows than columns or a dynamic number of rows."
+ "Similarly, if thin V is requested at runtime, you matrix must have more columns than rows or a dynamic number of columns.");
+ (void)computationOptions;
+ (void)rows;
+ (void)cols;
+}
+
+template<typename Derived> struct traits<SVDBase<Derived> >
+ : traits<Derived>
+{
+ typedef MatrixXpr XprKind;
+ typedef SolverStorage StorageKind;
+ typedef int StorageIndex;
+ enum { Flags = 0 };
+};
+
+template <typename MatrixType, int Options_>
+struct svd_traits : traits<MatrixType> {
+ static constexpr int Options = Options_;
+ static constexpr bool ShouldComputeFullU = internal::should_svd_compute_full_u(Options);
+ static constexpr bool ShouldComputeThinU = internal::should_svd_compute_thin_u(Options);
+ static constexpr bool ShouldComputeFullV = internal::should_svd_compute_full_v(Options);
+ static constexpr bool ShouldComputeThinV = internal::should_svd_compute_thin_v(Options);
+ enum {
+ DiagSizeAtCompileTime =
+ internal::min_size_prefer_dynamic(MatrixType::RowsAtCompileTime, MatrixType::ColsAtCompileTime),
+ MaxDiagSizeAtCompileTime =
+ internal::min_size_prefer_dynamic(MatrixType::MaxRowsAtCompileTime, MatrixType::MaxColsAtCompileTime),
+ MatrixUColsAtCompileTime = ShouldComputeThinU ? DiagSizeAtCompileTime
+ : MatrixType::RowsAtCompileTime,
+ MatrixVColsAtCompileTime = ShouldComputeThinV ? DiagSizeAtCompileTime
+ : MatrixType::ColsAtCompileTime,
+ MatrixUMaxColsAtCompileTime = ShouldComputeThinU ? MaxDiagSizeAtCompileTime
+ : MatrixType::MaxRowsAtCompileTime,
+ MatrixVMaxColsAtCompileTime = ShouldComputeThinV ? MaxDiagSizeAtCompileTime
+ : MatrixType::MaxColsAtCompileTime
+ };
+};
+}
+
+/** \ingroup SVD_Module
+ *
+ *
+ * \class SVDBase
+ *
+ * \brief Base class of SVD algorithms
+ *
+ * \tparam Derived the type of the actual SVD decomposition
+ *
+ * SVD decomposition consists in decomposing any n-by-p matrix \a A as a product
+ * \f[ A = U S V^* \f]
+ * where \a U is a n-by-n unitary, \a V is a p-by-p unitary, and \a S is a n-by-p real positive matrix which is zero outside of its main diagonal;
+ * the diagonal entries of S are known as the \em singular \em values of \a A and the columns of \a U and \a V are known as the left
+ * and right \em singular \em vectors of \a A respectively.
+ *
+ * Singular values are always sorted in decreasing order.
+ *
+ *
+ * You can ask for only \em thin \a U or \a V to be computed, meaning the following. In case of a rectangular n-by-p matrix, letting \a m be the
+ * smaller value among \a n and \a p, there are only \a m singular vectors; the remaining columns of \a U and \a V do not correspond to actual
+ * singular vectors. Asking for \em thin \a U or \a V means asking for only their \a m first columns to be formed. So \a U is then a n-by-m matrix,
+ * and \a V is then a p-by-m matrix. Notice that thin \a U and \a V are all you need for (least squares) solving.
+ *
+ * The status of the computation can be retrieved using the \a info() method. Unless \a info() returns \a Success, the results should be not
+ * considered well defined.
+ *
+ * If the input matrix has inf or nan coefficients, the result of the computation is undefined, and \a info() will return \a InvalidInput, but the computation is guaranteed to
+ * terminate in finite (and reasonable) time.
+ * \sa class BDCSVD, class JacobiSVD
+ */
+template<typename Derived> class SVDBase
+ : public SolverBase<SVDBase<Derived> >
+{
+public:
+
+ template<typename Derived_>
+ friend struct internal::solve_assertion;
+
+ typedef typename internal::traits<Derived>::MatrixType MatrixType;
+ typedef typename MatrixType::Scalar Scalar;
+ typedef typename NumTraits<typename MatrixType::Scalar>::Real RealScalar;
+ typedef typename Eigen::internal::traits<SVDBase>::StorageIndex StorageIndex;
+ typedef Eigen::Index Index; ///< \deprecated since Eigen 3.3
+
+ static constexpr bool ShouldComputeFullU = internal::traits<Derived>::ShouldComputeFullU;
+ static constexpr bool ShouldComputeThinU = internal::traits<Derived>::ShouldComputeThinU;
+ static constexpr bool ShouldComputeFullV = internal::traits<Derived>::ShouldComputeFullV;
+ static constexpr bool ShouldComputeThinV = internal::traits<Derived>::ShouldComputeThinV;
+
+ enum {
+ RowsAtCompileTime = MatrixType::RowsAtCompileTime,
+ ColsAtCompileTime = MatrixType::ColsAtCompileTime,
+ DiagSizeAtCompileTime = internal::min_size_prefer_dynamic(RowsAtCompileTime, ColsAtCompileTime),
+ MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime,
+ MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime,
+ MaxDiagSizeAtCompileTime = internal::min_size_prefer_fixed(MaxRowsAtCompileTime, MaxColsAtCompileTime),
+ MatrixOptions = MatrixType::Options,
+ MatrixUColsAtCompileTime = internal::traits<Derived>::MatrixUColsAtCompileTime,
+ MatrixVColsAtCompileTime = internal::traits<Derived>::MatrixVColsAtCompileTime,
+ MatrixUMaxColsAtCompileTime = internal::traits<Derived>::MatrixUMaxColsAtCompileTime,
+ MatrixVMaxColsAtCompileTime = internal::traits<Derived>::MatrixVMaxColsAtCompileTime
+ };
+
+ EIGEN_STATIC_ASSERT(!(ShouldComputeFullU && ShouldComputeThinU), "SVDBase: Cannot request both full and thin U")
+ EIGEN_STATIC_ASSERT(!(ShouldComputeFullV && ShouldComputeThinV), "SVDBase: Cannot request both full and thin V")
+
+ typedef
+ typename internal::make_proper_matrix_type<Scalar, RowsAtCompileTime, MatrixUColsAtCompileTime, MatrixOptions,
+ MaxRowsAtCompileTime, MatrixUMaxColsAtCompileTime>::type MatrixUType;
+ typedef
+ typename internal::make_proper_matrix_type<Scalar, ColsAtCompileTime, MatrixVColsAtCompileTime, MatrixOptions,
+ MaxColsAtCompileTime, MatrixVMaxColsAtCompileTime>::type MatrixVType;
+
+ typedef typename internal::plain_diag_type<MatrixType, RealScalar>::type SingularValuesType;
+
+ Derived& derived() { return *static_cast<Derived*>(this); }
+ const Derived& derived() const { return *static_cast<const Derived*>(this); }
+
+ /** \returns the \a U matrix.
+ *
+ * For the SVD decomposition of a n-by-p matrix, letting \a m be the minimum of \a n and \a p,
+ * the U matrix is n-by-n if you asked for \link Eigen::ComputeFullU ComputeFullU \endlink, and is n-by-m if you asked for \link Eigen::ComputeThinU ComputeThinU \endlink.
+ *
+ * The \a m first columns of \a U are the left singular vectors of the matrix being decomposed.
+ *
+ * This method asserts that you asked for \a U to be computed.
+ */
+ const MatrixUType& matrixU() const
+ {
+ _check_compute_assertions();
+ eigen_assert(computeU() && "This SVD decomposition didn't compute U. Did you ask for it?");
+ return m_matrixU;
+ }
+
+ /** \returns the \a V matrix.
+ *
+ * For the SVD decomposition of a n-by-p matrix, letting \a m be the minimum of \a n and \a p,
+ * the V matrix is p-by-p if you asked for \link Eigen::ComputeFullV ComputeFullV \endlink, and is p-by-m if you asked for \link Eigen::ComputeThinV ComputeThinV \endlink.
+ *
+ * The \a m first columns of \a V are the right singular vectors of the matrix being decomposed.
+ *
+ * This method asserts that you asked for \a V to be computed.
+ */
+ const MatrixVType& matrixV() const
+ {
+ _check_compute_assertions();
+ eigen_assert(computeV() && "This SVD decomposition didn't compute V. Did you ask for it?");
+ return m_matrixV;
+ }
+
+ /** \returns the vector of singular values.
+ *
+ * For the SVD decomposition of a n-by-p matrix, letting \a m be the minimum of \a n and \a p, the
+ * returned vector has size \a m. Singular values are always sorted in decreasing order.
+ */
+ const SingularValuesType& singularValues() const
+ {
+ _check_compute_assertions();
+ return m_singularValues;
+ }
+
+ /** \returns the number of singular values that are not exactly 0 */
+ Index nonzeroSingularValues() const
+ {
+ _check_compute_assertions();
+ return m_nonzeroSingularValues;
+ }
+
+ /** \returns the rank of the matrix of which \c *this is the SVD.
+ *
+ * \note This method has to determine which singular values should be considered nonzero.
+ * For that, it uses the threshold value that you can control by calling
+ * setThreshold(const RealScalar&).
+ */
+ inline Index rank() const
+ {
+ using std::abs;
+ _check_compute_assertions();
+ if(m_singularValues.size()==0) return 0;
+ RealScalar premultiplied_threshold = numext::maxi<RealScalar>(m_singularValues.coeff(0) * threshold(), (std::numeric_limits<RealScalar>::min)());
+ Index i = m_nonzeroSingularValues-1;
+ while(i>=0 && m_singularValues.coeff(i) < premultiplied_threshold) --i;
+ return i+1;
+ }
+
+ /** Allows to prescribe a threshold to be used by certain methods, such as rank() and solve(),
+ * which need to determine when singular values are to be considered nonzero.
+ * This is not used for the SVD decomposition itself.
+ *
+ * When it needs to get the threshold value, Eigen calls threshold().
+ * The default is \c NumTraits<Scalar>::epsilon()
+ *
+ * \param threshold The new value to use as the threshold.
+ *
+ * A singular value will be considered nonzero if its value is strictly greater than
+ * \f$ \vert singular value \vert \leqslant threshold \times \vert max singular value \vert \f$.
+ *
+ * If you want to come back to the default behavior, call setThreshold(Default_t)
+ */
+ Derived& setThreshold(const RealScalar& threshold)
+ {
+ m_usePrescribedThreshold = true;
+ m_prescribedThreshold = threshold;
+ return derived();
+ }
+
+ /** Allows to come back to the default behavior, letting Eigen use its default formula for
+ * determining the threshold.
+ *
+ * You should pass the special object Eigen::Default as parameter here.
+ * \code svd.setThreshold(Eigen::Default); \endcode
+ *
+ * See the documentation of setThreshold(const RealScalar&).
+ */
+ Derived& setThreshold(Default_t)
+ {
+ m_usePrescribedThreshold = false;
+ return derived();
+ }
+
+ /** Returns the threshold that will be used by certain methods such as rank().
+ *
+ * See the documentation of setThreshold(const RealScalar&).
+ */
+ RealScalar threshold() const
+ {
+ eigen_assert(m_isInitialized || m_usePrescribedThreshold);
+ // this temporary is needed to workaround a MSVC issue
+ Index diagSize = (std::max<Index>)(1,m_diagSize);
+ return m_usePrescribedThreshold ? m_prescribedThreshold
+ : RealScalar(diagSize)*NumTraits<Scalar>::epsilon();
+ }
+
+ /** \returns true if \a U (full or thin) is asked for in this SVD decomposition */
+ inline bool computeU() const { return m_computeFullU || m_computeThinU; }
+ /** \returns true if \a V (full or thin) is asked for in this SVD decomposition */
+ inline bool computeV() const { return m_computeFullV || m_computeThinV; }
+
+ inline Index rows() const { return m_rows; }
+ inline Index cols() const { return m_cols; }
+
+ #ifdef EIGEN_PARSED_BY_DOXYGEN
+ /** \returns a (least squares) solution of \f$ A x = b \f$ using the current SVD decomposition of A.
+ *
+ * \param b the right-hand-side of the equation to solve.
+ *
+ * \note Solving requires both U and V to be computed. Thin U and V are enough, there is no need for full U or V.
+ *
+ * \note SVD solving is implicitly least-squares. Thus, this method serves both purposes of exact solving and least-squares solving.
+ * In other words, the returned solution is guaranteed to minimize the Euclidean norm \f$ \Vert A x - b \Vert \f$.
+ */
+ template<typename Rhs>
+ inline const Solve<Derived, Rhs>
+ solve(const MatrixBase<Rhs>& b) const;
+ #endif
+
+
+ /** \brief Reports whether previous computation was successful.
+ *
+ * \returns \c Success if computation was successful.
+ */
+ EIGEN_DEVICE_FUNC
+ ComputationInfo info() const
+ {
+ eigen_assert(m_isInitialized && "SVD is not initialized.");
+ return m_info;
+ }
+
+ #ifndef EIGEN_PARSED_BY_DOXYGEN
+ template<typename RhsType, typename DstType>
+ void _solve_impl(const RhsType &rhs, DstType &dst) const;
+
+ template<bool Conjugate, typename RhsType, typename DstType>
+ void _solve_impl_transposed(const RhsType &rhs, DstType &dst) const;
+ #endif
+
+protected:
+
+ EIGEN_STATIC_ASSERT_NON_INTEGER(Scalar)
+
+ void _check_compute_assertions() const {
+ eigen_assert(m_isInitialized && "SVD is not initialized.");
+ }
+
+ template<bool Transpose_, typename Rhs>
+ void _check_solve_assertion(const Rhs& b) const {
+ EIGEN_ONLY_USED_FOR_DEBUG(b);
+ _check_compute_assertions();
+ eigen_assert(computeU() && computeV() && "SVDBase::solve(): Both unitaries U and V are required to be computed (thin unitaries suffice).");
+ eigen_assert((Transpose_?cols():rows())==b.rows() && "SVDBase::solve(): invalid number of rows of the right hand side matrix b");
+ }
+
+ // return true if already allocated
+ bool allocate(Index rows, Index cols, unsigned int computationOptions);
+
+ MatrixUType m_matrixU;
+ MatrixVType m_matrixV;
+ SingularValuesType m_singularValues;
+ ComputationInfo m_info;
+ bool m_isInitialized, m_isAllocated, m_usePrescribedThreshold;
+ bool m_computeFullU, m_computeThinU;
+ bool m_computeFullV, m_computeThinV;
+ unsigned int m_computationOptions;
+ Index m_nonzeroSingularValues, m_rows, m_cols, m_diagSize;
+ RealScalar m_prescribedThreshold;
+
+ /** \brief Default Constructor.
+ *
+ * Default constructor of SVDBase
+ */
+ SVDBase()
+ : m_info(Success),
+ m_isInitialized(false),
+ m_isAllocated(false),
+ m_usePrescribedThreshold(false),
+ m_computeFullU(false),
+ m_computeThinU(false),
+ m_computeFullV(false),
+ m_computeThinV(false),
+ m_computationOptions(0),
+ m_rows(-1),
+ m_cols(-1),
+ m_diagSize(0) {}
+};
+
+#ifndef EIGEN_PARSED_BY_DOXYGEN
+template<typename Derived>
+template<typename RhsType, typename DstType>
+void SVDBase<Derived>::_solve_impl(const RhsType &rhs, DstType &dst) const
+{
+ // A = U S V^*
+ // So A^{-1} = V S^{-1} U^*
+
+ Matrix<typename RhsType::Scalar, Dynamic, RhsType::ColsAtCompileTime, 0, MatrixType::MaxRowsAtCompileTime, RhsType::MaxColsAtCompileTime> tmp;
+ Index l_rank = rank();
+ tmp.noalias() = m_matrixU.leftCols(l_rank).adjoint() * rhs;
+ tmp = m_singularValues.head(l_rank).asDiagonal().inverse() * tmp;
+ dst = m_matrixV.leftCols(l_rank) * tmp;
+}
+
+template<typename Derived>
+template<bool Conjugate, typename RhsType, typename DstType>
+void SVDBase<Derived>::_solve_impl_transposed(const RhsType &rhs, DstType &dst) const
+{
+ // A = U S V^*
+ // So A^{-*} = U S^{-1} V^*
+ // And A^{-T} = U_conj S^{-1} V^T
+ Matrix<typename RhsType::Scalar, Dynamic, RhsType::ColsAtCompileTime, 0, MatrixType::MaxRowsAtCompileTime, RhsType::MaxColsAtCompileTime> tmp;
+ Index l_rank = rank();
+
+ tmp.noalias() = m_matrixV.leftCols(l_rank).transpose().template conjugateIf<Conjugate>() * rhs;
+ tmp = m_singularValues.head(l_rank).asDiagonal().inverse() * tmp;
+ dst = m_matrixU.template conjugateIf<!Conjugate>().leftCols(l_rank) * tmp;
+}
+#endif
+
+template <typename Derived>
+bool SVDBase<Derived>::allocate(Index rows, Index cols, unsigned int computationOptions) {
+ eigen_assert(rows >= 0 && cols >= 0);
+
+ if (m_isAllocated &&
+ rows == m_rows &&
+ cols == m_cols &&
+ computationOptions == m_computationOptions)
+ {
+ return true;
+ }
+
+ m_rows = rows;
+ m_cols = cols;
+ m_info = Success;
+ m_isInitialized = false;
+ m_isAllocated = true;
+ m_computationOptions = computationOptions;
+ m_computeFullU = ShouldComputeFullU || internal::should_svd_compute_full_u(computationOptions);
+ m_computeThinU = ShouldComputeThinU || internal::should_svd_compute_thin_u(computationOptions);
+ m_computeFullV = ShouldComputeFullV || internal::should_svd_compute_full_v(computationOptions);
+ m_computeThinV = ShouldComputeThinV || internal::should_svd_compute_thin_v(computationOptions);
+
+ eigen_assert(!(m_computeFullU && m_computeThinU) && "SVDBase: you can't ask for both full and thin U");
+ eigen_assert(!(m_computeFullV && m_computeThinV) && "SVDBase: you can't ask for both full and thin V");
+
+ m_diagSize = (std::min)(m_rows, m_cols);
+ m_singularValues.resize(m_diagSize);
+ if(RowsAtCompileTime==Dynamic)
+ m_matrixU.resize(m_rows, m_computeFullU ? m_rows : m_computeThinU ? m_diagSize : 0);
+ if(ColsAtCompileTime==Dynamic)
+ m_matrixV.resize(m_cols, m_computeFullV ? m_cols : m_computeThinV ? m_diagSize : 0);
+
+ return false;
+}
+
+}// end namespace
+
+#endif // EIGEN_SVDBASE_H
diff --git a/Eigen/src/SVD/UpperBidiagonalization.h b/Eigen/src/SVD/UpperBidiagonalization.h
new file mode 100644
index 0000000..e6c9097
--- /dev/null
+++ b/Eigen/src/SVD/UpperBidiagonalization.h
@@ -0,0 +1,422 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2010 Benoit Jacob <jacob.benoit.1@gmail.com>
+// Copyright (C) 2013-2014 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_BIDIAGONALIZATION_H
+#define EIGEN_BIDIAGONALIZATION_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+// UpperBidiagonalization will probably be replaced by a Bidiagonalization class, don't want to make it stable API.
+// At the same time, it's useful to keep for now as it's about the only thing that is testing the BandMatrix class.
+
+template<typename MatrixType_> class UpperBidiagonalization
+{
+ public:
+
+ typedef MatrixType_ MatrixType;
+ enum {
+ RowsAtCompileTime = MatrixType::RowsAtCompileTime,
+ ColsAtCompileTime = MatrixType::ColsAtCompileTime,
+ ColsAtCompileTimeMinusOne = internal::decrement_size<ColsAtCompileTime>::ret
+ };
+ typedef typename MatrixType::Scalar Scalar;
+ typedef typename MatrixType::RealScalar RealScalar;
+ typedef Eigen::Index Index; ///< \deprecated since Eigen 3.3
+ typedef Matrix<Scalar, 1, ColsAtCompileTime> RowVectorType;
+ typedef Matrix<Scalar, RowsAtCompileTime, 1> ColVectorType;
+ typedef BandMatrix<RealScalar, ColsAtCompileTime, ColsAtCompileTime, 1, 0, RowMajor> BidiagonalType;
+ typedef Matrix<Scalar, ColsAtCompileTime, 1> DiagVectorType;
+ typedef Matrix<Scalar, ColsAtCompileTimeMinusOne, 1> SuperDiagVectorType;
+ typedef HouseholderSequence<
+ const MatrixType,
+ const internal::remove_all_t<typename Diagonal<const MatrixType,0>::ConjugateReturnType>
+ > HouseholderUSequenceType;
+ typedef HouseholderSequence<
+ const internal::remove_all_t<typename MatrixType::ConjugateReturnType>,
+ Diagonal<const MatrixType,1>,
+ OnTheRight
+ > HouseholderVSequenceType;
+
+ /**
+ * \brief Default Constructor.
+ *
+ * The default constructor is useful in cases in which the user intends to
+ * perform decompositions via Bidiagonalization::compute(const MatrixType&).
+ */
+ UpperBidiagonalization() : m_householder(), m_bidiagonal(0, 0), m_isInitialized(false) {}
+
+ explicit UpperBidiagonalization(const MatrixType& matrix)
+ : m_householder(matrix.rows(), matrix.cols()),
+ m_bidiagonal(matrix.cols(), matrix.cols()),
+ m_isInitialized(false)
+ {
+ compute(matrix);
+ }
+
+ UpperBidiagonalization(Index rows, Index cols)
+ : m_householder(rows, cols),
+ m_bidiagonal(cols, cols),
+ m_isInitialized(false)
+ {}
+
+ UpperBidiagonalization& compute(const MatrixType& matrix);
+ UpperBidiagonalization& computeUnblocked(const MatrixType& matrix);
+
+ const MatrixType& householder() const { return m_householder; }
+ const BidiagonalType& bidiagonal() const { return m_bidiagonal; }
+
+ const HouseholderUSequenceType householderU() const
+ {
+ eigen_assert(m_isInitialized && "UpperBidiagonalization is not initialized.");
+ return HouseholderUSequenceType(m_householder, m_householder.diagonal().conjugate());
+ }
+
+ const HouseholderVSequenceType householderV() // const here gives nasty errors and i'm lazy
+ {
+ eigen_assert(m_isInitialized && "UpperBidiagonalization is not initialized.");
+ return HouseholderVSequenceType(m_householder.conjugate(), m_householder.const_derived().template diagonal<1>())
+ .setLength(m_householder.cols()-1)
+ .setShift(1);
+ }
+
+ protected:
+ MatrixType m_householder;
+ BidiagonalType m_bidiagonal;
+ bool m_isInitialized;
+};
+
+// Standard upper bidiagonalization without fancy optimizations
+// This version should be faster for small matrix size
+template<typename MatrixType>
+void upperbidiagonalization_inplace_unblocked(MatrixType& mat,
+ typename MatrixType::RealScalar *diagonal,
+ typename MatrixType::RealScalar *upper_diagonal,
+ typename MatrixType::Scalar* tempData = 0)
+{
+ typedef typename MatrixType::Scalar Scalar;
+
+ Index rows = mat.rows();
+ Index cols = mat.cols();
+
+ typedef Matrix<Scalar,Dynamic,1,ColMajor,MatrixType::MaxRowsAtCompileTime,1> TempType;
+ TempType tempVector;
+ if(tempData==0)
+ {
+ tempVector.resize(rows);
+ tempData = tempVector.data();
+ }
+
+ for (Index k = 0; /* breaks at k==cols-1 below */ ; ++k)
+ {
+ Index remainingRows = rows - k;
+ Index remainingCols = cols - k - 1;
+
+ // construct left householder transform in-place in A
+ mat.col(k).tail(remainingRows)
+ .makeHouseholderInPlace(mat.coeffRef(k,k), diagonal[k]);
+ // apply householder transform to remaining part of A on the left
+ mat.bottomRightCorner(remainingRows, remainingCols)
+ .applyHouseholderOnTheLeft(mat.col(k).tail(remainingRows-1), mat.coeff(k,k), tempData);
+
+ if(k == cols-1) break;
+
+ // construct right householder transform in-place in mat
+ mat.row(k).tail(remainingCols)
+ .makeHouseholderInPlace(mat.coeffRef(k,k+1), upper_diagonal[k]);
+ // apply householder transform to remaining part of mat on the left
+ mat.bottomRightCorner(remainingRows-1, remainingCols)
+ .applyHouseholderOnTheRight(mat.row(k).tail(remainingCols-1).adjoint(), mat.coeff(k,k+1), tempData);
+ }
+}
+
+/** \internal
+ * Helper routine for the block reduction to upper bidiagonal form.
+ *
+ * Let's partition the matrix A:
+ *
+ * | A00 A01 |
+ * A = | |
+ * | A10 A11 |
+ *
+ * This function reduces to bidiagonal form the left \c rows x \a blockSize vertical panel [A00/A10]
+ * and the \a blockSize x \c cols horizontal panel [A00 A01] of the matrix \a A. The bottom-right block A11
+ * is updated using matrix-matrix products:
+ * A22 -= V * Y^T - X * U^T
+ * where V and U contains the left and right Householder vectors. U and V are stored in A10, and A01
+ * respectively, and the update matrices X and Y are computed during the reduction.
+ *
+ */
+template<typename MatrixType>
+void upperbidiagonalization_blocked_helper(MatrixType& A,
+ typename MatrixType::RealScalar *diagonal,
+ typename MatrixType::RealScalar *upper_diagonal,
+ Index bs,
+ Ref<Matrix<typename MatrixType::Scalar, Dynamic, Dynamic,
+ traits<MatrixType>::Flags & RowMajorBit> > X,
+ Ref<Matrix<typename MatrixType::Scalar, Dynamic, Dynamic,
+ traits<MatrixType>::Flags & RowMajorBit> > Y)
+{
+ typedef typename MatrixType::Scalar Scalar;
+ typedef typename MatrixType::RealScalar RealScalar;
+ typedef typename NumTraits<RealScalar>::Literal Literal;
+ static constexpr int StorageOrder = (traits<MatrixType>::Flags & RowMajorBit) ? RowMajor : ColMajor;
+ typedef InnerStride<StorageOrder == ColMajor ? 1 : Dynamic> ColInnerStride;
+ typedef InnerStride<StorageOrder == ColMajor ? Dynamic : 1> RowInnerStride;
+ typedef Ref<Matrix<Scalar, Dynamic, 1>, 0, ColInnerStride> SubColumnType;
+ typedef Ref<Matrix<Scalar, 1, Dynamic>, 0, RowInnerStride> SubRowType;
+ typedef Ref<Matrix<Scalar, Dynamic, Dynamic, StorageOrder > > SubMatType;
+
+ Index brows = A.rows();
+ Index bcols = A.cols();
+
+ Scalar tau_u, tau_u_prev(0), tau_v;
+
+ for(Index k = 0; k < bs; ++k)
+ {
+ Index remainingRows = brows - k;
+ Index remainingCols = bcols - k - 1;
+
+ SubMatType X_k1( X.block(k,0, remainingRows,k) );
+ SubMatType V_k1( A.block(k,0, remainingRows,k) );
+
+ // 1 - update the k-th column of A
+ SubColumnType v_k = A.col(k).tail(remainingRows);
+ v_k -= V_k1 * Y.row(k).head(k).adjoint();
+ if(k) v_k -= X_k1 * A.col(k).head(k);
+
+ // 2 - construct left Householder transform in-place
+ v_k.makeHouseholderInPlace(tau_v, diagonal[k]);
+
+ if(k+1<bcols)
+ {
+ SubMatType Y_k ( Y.block(k+1,0, remainingCols, k+1) );
+ SubMatType U_k1 ( A.block(0,k+1, k,remainingCols) );
+
+ // this eases the application of Householder transforAions
+ // A(k,k) will store tau_v later
+ A(k,k) = Scalar(1);
+
+ // 3 - Compute y_k^T = tau_v * ( A^T*v_k - Y_k-1*V_k-1^T*v_k - U_k-1*X_k-1^T*v_k )
+ {
+ SubColumnType y_k( Y.col(k).tail(remainingCols) );
+
+ // let's use the beginning of column k of Y as a temporary vector
+ SubColumnType tmp( Y.col(k).head(k) );
+ y_k.noalias() = A.block(k,k+1, remainingRows,remainingCols).adjoint() * v_k; // bottleneck
+ tmp.noalias() = V_k1.adjoint() * v_k;
+ y_k.noalias() -= Y_k.leftCols(k) * tmp;
+ tmp.noalias() = X_k1.adjoint() * v_k;
+ y_k.noalias() -= U_k1.adjoint() * tmp;
+ y_k *= numext::conj(tau_v);
+ }
+
+ // 4 - update k-th row of A (it will become u_k)
+ SubRowType u_k( A.row(k).tail(remainingCols) );
+ u_k = u_k.conjugate();
+ {
+ u_k -= Y_k * A.row(k).head(k+1).adjoint();
+ if(k) u_k -= U_k1.adjoint() * X.row(k).head(k).adjoint();
+ }
+
+ // 5 - construct right Householder transform in-place
+ u_k.makeHouseholderInPlace(tau_u, upper_diagonal[k]);
+
+ // this eases the application of Householder transformations
+ // A(k,k+1) will store tau_u later
+ A(k,k+1) = Scalar(1);
+
+ // 6 - Compute x_k = tau_u * ( A*u_k - X_k-1*U_k-1^T*u_k - V_k*Y_k^T*u_k )
+ {
+ SubColumnType x_k ( X.col(k).tail(remainingRows-1) );
+
+ // let's use the beginning of column k of X as a temporary vectors
+ // note that tmp0 and tmp1 overlaps
+ SubColumnType tmp0 ( X.col(k).head(k) ),
+ tmp1 ( X.col(k).head(k+1) );
+
+ x_k.noalias() = A.block(k+1,k+1, remainingRows-1,remainingCols) * u_k.transpose(); // bottleneck
+ tmp0.noalias() = U_k1 * u_k.transpose();
+ x_k.noalias() -= X_k1.bottomRows(remainingRows-1) * tmp0;
+ tmp1.noalias() = Y_k.adjoint() * u_k.transpose();
+ x_k.noalias() -= A.block(k+1,0, remainingRows-1,k+1) * tmp1;
+ x_k *= numext::conj(tau_u);
+ tau_u = numext::conj(tau_u);
+ u_k = u_k.conjugate();
+ }
+
+ if(k>0) A.coeffRef(k-1,k) = tau_u_prev;
+ tau_u_prev = tau_u;
+ }
+ else
+ A.coeffRef(k-1,k) = tau_u_prev;
+
+ A.coeffRef(k,k) = tau_v;
+ }
+
+ if(bs<bcols)
+ A.coeffRef(bs-1,bs) = tau_u_prev;
+
+ // update A22
+ if(bcols>bs && brows>bs)
+ {
+ SubMatType A11( A.bottomRightCorner(brows-bs,bcols-bs) );
+ SubMatType A10( A.block(bs,0, brows-bs,bs) );
+ SubMatType A01( A.block(0,bs, bs,bcols-bs) );
+ Scalar tmp = A01(bs-1,0);
+ A01(bs-1,0) = Literal(1);
+ A11.noalias() -= A10 * Y.topLeftCorner(bcols,bs).bottomRows(bcols-bs).adjoint();
+ A11.noalias() -= X.topLeftCorner(brows,bs).bottomRows(brows-bs) * A01;
+ A01(bs-1,0) = tmp;
+ }
+}
+
+/** \internal
+ *
+ * Implementation of a block-bidiagonal reduction.
+ * It is based on the following paper:
+ * The Design of a Parallel Dense Linear Algebra Software Library: Reduction to Hessenberg, Tridiagonal, and Bidiagonal Form.
+ * by Jaeyoung Choi, Jack J. Dongarra, David W. Walker. (1995)
+ * section 3.3
+ */
+template<typename MatrixType, typename BidiagType>
+void upperbidiagonalization_inplace_blocked(MatrixType& A, BidiagType& bidiagonal,
+ Index maxBlockSize=32,
+ typename MatrixType::Scalar* /*tempData*/ = 0)
+{
+ typedef typename MatrixType::Scalar Scalar;
+ typedef Block<MatrixType,Dynamic,Dynamic> BlockType;
+
+ Index rows = A.rows();
+ Index cols = A.cols();
+ Index size = (std::min)(rows, cols);
+
+ // X and Y are work space
+ static constexpr int StorageOrder = (traits<MatrixType>::Flags & RowMajorBit) ? RowMajor : ColMajor;
+ Matrix<Scalar,
+ MatrixType::RowsAtCompileTime,
+ Dynamic,
+ StorageOrder,
+ MatrixType::MaxRowsAtCompileTime> X(rows,maxBlockSize);
+ Matrix<Scalar,
+ MatrixType::ColsAtCompileTime,
+ Dynamic,
+ StorageOrder,
+ MatrixType::MaxColsAtCompileTime> Y(cols,maxBlockSize);
+ Index blockSize = (std::min)(maxBlockSize,size);
+
+ Index k = 0;
+ for(k = 0; k < size; k += blockSize)
+ {
+ Index bs = (std::min)(size-k,blockSize); // actual size of the block
+ Index brows = rows - k; // rows of the block
+ Index bcols = cols - k; // columns of the block
+
+ // partition the matrix A:
+ //
+ // | A00 A01 A02 |
+ // | |
+ // A = | A10 A11 A12 |
+ // | |
+ // | A20 A21 A22 |
+ //
+ // where A11 is a bs x bs diagonal block,
+ // and let:
+ // | A11 A12 |
+ // B = | |
+ // | A21 A22 |
+
+ BlockType B = A.block(k,k,brows,bcols);
+
+ // This stage performs the bidiagonalization of A11, A21, A12, and updating of A22.
+ // Finally, the algorithm continue on the updated A22.
+ //
+ // However, if B is too small, or A22 empty, then let's use an unblocked strategy
+ if(k+bs==cols || bcols<48) // somewhat arbitrary threshold
+ {
+ upperbidiagonalization_inplace_unblocked(B,
+ &(bidiagonal.template diagonal<0>().coeffRef(k)),
+ &(bidiagonal.template diagonal<1>().coeffRef(k)),
+ X.data()
+ );
+ break; // We're done
+ }
+ else
+ {
+ upperbidiagonalization_blocked_helper<BlockType>( B,
+ &(bidiagonal.template diagonal<0>().coeffRef(k)),
+ &(bidiagonal.template diagonal<1>().coeffRef(k)),
+ bs,
+ X.topLeftCorner(brows,bs),
+ Y.topLeftCorner(bcols,bs)
+ );
+ }
+ }
+}
+
+template<typename MatrixType_>
+UpperBidiagonalization<MatrixType_>& UpperBidiagonalization<MatrixType_>::computeUnblocked(const MatrixType_& matrix)
+{
+ Index rows = matrix.rows();
+ Index cols = matrix.cols();
+ EIGEN_ONLY_USED_FOR_DEBUG(cols);
+
+ eigen_assert(rows >= cols && "UpperBidiagonalization is only for Arices satisfying rows>=cols.");
+
+ m_householder = matrix;
+
+ ColVectorType temp(rows);
+
+ upperbidiagonalization_inplace_unblocked(m_householder,
+ &(m_bidiagonal.template diagonal<0>().coeffRef(0)),
+ &(m_bidiagonal.template diagonal<1>().coeffRef(0)),
+ temp.data());
+
+ m_isInitialized = true;
+ return *this;
+}
+
+template<typename MatrixType_>
+UpperBidiagonalization<MatrixType_>& UpperBidiagonalization<MatrixType_>::compute(const MatrixType_& matrix)
+{
+ Index rows = matrix.rows();
+ Index cols = matrix.cols();
+ EIGEN_ONLY_USED_FOR_DEBUG(rows);
+ EIGEN_ONLY_USED_FOR_DEBUG(cols);
+
+ eigen_assert(rows >= cols && "UpperBidiagonalization is only for Arices satisfying rows>=cols.");
+
+ m_householder = matrix;
+ upperbidiagonalization_inplace_blocked(m_householder, m_bidiagonal);
+
+ m_isInitialized = true;
+ return *this;
+}
+
+#if 0
+/** \return the Householder QR decomposition of \c *this.
+ *
+ * \sa class Bidiagonalization
+ */
+template<typename Derived>
+const UpperBidiagonalization<typename MatrixBase<Derived>::PlainObject>
+MatrixBase<Derived>::bidiagonalization() const
+{
+ return UpperBidiagonalization<PlainObject>(eval());
+}
+#endif
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_BIDIAGONALIZATION_H
diff --git a/Eigen/src/SparseCholesky/InternalHeaderCheck.h b/Eigen/src/SparseCholesky/InternalHeaderCheck.h
new file mode 100644
index 0000000..f8d8762
--- /dev/null
+++ b/Eigen/src/SparseCholesky/InternalHeaderCheck.h
@@ -0,0 +1,3 @@
+#ifndef EIGEN_SPARSECHOLESKY_MODULE_H
+#error "Please include Eigen/SparseCholesky instead of including headers inside the src directory directly."
+#endif
diff --git a/Eigen/src/SparseCholesky/SimplicialCholesky.h b/Eigen/src/SparseCholesky/SimplicialCholesky.h
new file mode 100644
index 0000000..d90ca13
--- /dev/null
+++ b/Eigen/src/SparseCholesky/SimplicialCholesky.h
@@ -0,0 +1,699 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2012 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_SIMPLICIAL_CHOLESKY_H
+#define EIGEN_SIMPLICIAL_CHOLESKY_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+enum SimplicialCholeskyMode {
+ SimplicialCholeskyLLT,
+ SimplicialCholeskyLDLT
+};
+
+namespace internal {
+ template<typename CholMatrixType, typename InputMatrixType>
+ struct simplicial_cholesky_grab_input {
+ typedef CholMatrixType const * ConstCholMatrixPtr;
+ static void run(const InputMatrixType& input, ConstCholMatrixPtr &pmat, CholMatrixType &tmp)
+ {
+ tmp = input;
+ pmat = &tmp;
+ }
+ };
+
+ template<typename MatrixType>
+ struct simplicial_cholesky_grab_input<MatrixType,MatrixType> {
+ typedef MatrixType const * ConstMatrixPtr;
+ static void run(const MatrixType& input, ConstMatrixPtr &pmat, MatrixType &/*tmp*/)
+ {
+ pmat = &input;
+ }
+ };
+} // end namespace internal
+
+/** \ingroup SparseCholesky_Module
+ * \brief A base class for direct sparse Cholesky factorizations
+ *
+ * This is a base class for LL^T and LDL^T Cholesky factorizations of sparse matrices that are
+ * selfadjoint and positive definite. These factorizations allow for solving A.X = B where
+ * X and B can be either dense or sparse.
+ *
+ * In order to reduce the fill-in, a symmetric permutation P is applied prior to the factorization
+ * such that the factorized matrix is P A P^-1.
+ *
+ * \tparam Derived the type of the derived class, that is the actual factorization type.
+ *
+ */
+template<typename Derived>
+class SimplicialCholeskyBase : public SparseSolverBase<Derived>
+{
+ typedef SparseSolverBase<Derived> Base;
+ using Base::m_isInitialized;
+
+ public:
+ typedef typename internal::traits<Derived>::MatrixType MatrixType;
+ typedef typename internal::traits<Derived>::OrderingType OrderingType;
+ enum { UpLo = internal::traits<Derived>::UpLo };
+ typedef typename MatrixType::Scalar Scalar;
+ typedef typename MatrixType::RealScalar RealScalar;
+ typedef typename MatrixType::StorageIndex StorageIndex;
+ typedef SparseMatrix<Scalar,ColMajor,StorageIndex> CholMatrixType;
+ typedef CholMatrixType const * ConstCholMatrixPtr;
+ typedef Matrix<Scalar,Dynamic,1> VectorType;
+ typedef Matrix<StorageIndex,Dynamic,1> VectorI;
+
+ enum {
+ ColsAtCompileTime = MatrixType::ColsAtCompileTime,
+ MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime
+ };
+
+ public:
+
+ using Base::derived;
+
+ /** Default constructor */
+ SimplicialCholeskyBase()
+ : m_info(Success),
+ m_factorizationIsOk(false),
+ m_analysisIsOk(false),
+ m_shiftOffset(0),
+ m_shiftScale(1)
+ {}
+
+ explicit SimplicialCholeskyBase(const MatrixType& matrix)
+ : m_info(Success),
+ m_factorizationIsOk(false),
+ m_analysisIsOk(false),
+ m_shiftOffset(0),
+ m_shiftScale(1)
+ {
+ derived().compute(matrix);
+ }
+
+ ~SimplicialCholeskyBase()
+ {
+ }
+
+ Derived& derived() { return *static_cast<Derived*>(this); }
+ const Derived& derived() const { return *static_cast<const Derived*>(this); }
+
+ inline Index cols() const { return m_matrix.cols(); }
+ inline Index rows() const { return m_matrix.rows(); }
+
+ /** \brief Reports whether previous computation was successful.
+ *
+ * \returns \c Success if computation was successful,
+ * \c NumericalIssue if the matrix.appears to be negative.
+ */
+ ComputationInfo info() const
+ {
+ eigen_assert(m_isInitialized && "Decomposition is not initialized.");
+ return m_info;
+ }
+
+ /** \returns the permutation P
+ * \sa permutationPinv() */
+ const PermutationMatrix<Dynamic,Dynamic,StorageIndex>& permutationP() const
+ { return m_P; }
+
+ /** \returns the inverse P^-1 of the permutation P
+ * \sa permutationP() */
+ const PermutationMatrix<Dynamic,Dynamic,StorageIndex>& permutationPinv() const
+ { return m_Pinv; }
+
+ /** Sets the shift parameters that will be used to adjust the diagonal coefficients during the numerical factorization.
+ *
+ * During the numerical factorization, the diagonal coefficients are transformed by the following linear model:\n
+ * \c d_ii = \a offset + \a scale * \c d_ii
+ *
+ * The default is the identity transformation with \a offset=0, and \a scale=1.
+ *
+ * \returns a reference to \c *this.
+ */
+ Derived& setShift(const RealScalar& offset, const RealScalar& scale = 1)
+ {
+ m_shiftOffset = offset;
+ m_shiftScale = scale;
+ return derived();
+ }
+
+#ifndef EIGEN_PARSED_BY_DOXYGEN
+ /** \internal */
+ template<typename Stream>
+ void dumpMemory(Stream& s)
+ {
+ int total = 0;
+ s << " L: " << ((total+=(m_matrix.cols()+1) * sizeof(int) + m_matrix.nonZeros()*(sizeof(int)+sizeof(Scalar))) >> 20) << "Mb" << "\n";
+ s << " diag: " << ((total+=m_diag.size() * sizeof(Scalar)) >> 20) << "Mb" << "\n";
+ s << " tree: " << ((total+=m_parent.size() * sizeof(int)) >> 20) << "Mb" << "\n";
+ s << " nonzeros: " << ((total+=m_nonZerosPerCol.size() * sizeof(int)) >> 20) << "Mb" << "\n";
+ s << " perm: " << ((total+=m_P.size() * sizeof(int)) >> 20) << "Mb" << "\n";
+ s << " perm^-1: " << ((total+=m_Pinv.size() * sizeof(int)) >> 20) << "Mb" << "\n";
+ s << " TOTAL: " << (total>> 20) << "Mb" << "\n";
+ }
+
+ /** \internal */
+ template<typename Rhs,typename Dest>
+ void _solve_impl(const MatrixBase<Rhs> &b, MatrixBase<Dest> &dest) const
+ {
+ eigen_assert(m_factorizationIsOk && "The decomposition is not in a valid state for solving, you must first call either compute() or symbolic()/numeric()");
+ eigen_assert(m_matrix.rows()==b.rows());
+
+ if(m_info!=Success)
+ return;
+
+ if(m_P.size()>0)
+ dest = m_P * b;
+ else
+ dest = b;
+
+ if(m_matrix.nonZeros()>0) // otherwise L==I
+ derived().matrixL().solveInPlace(dest);
+
+ if(m_diag.size()>0)
+ dest = m_diag.asDiagonal().inverse() * dest;
+
+ if (m_matrix.nonZeros()>0) // otherwise U==I
+ derived().matrixU().solveInPlace(dest);
+
+ if(m_P.size()>0)
+ dest = m_Pinv * dest;
+ }
+
+ template<typename Rhs,typename Dest>
+ void _solve_impl(const SparseMatrixBase<Rhs> &b, SparseMatrixBase<Dest> &dest) const
+ {
+ internal::solve_sparse_through_dense_panels(derived(), b, dest);
+ }
+
+#endif // EIGEN_PARSED_BY_DOXYGEN
+
+ protected:
+
+ /** Computes the sparse Cholesky decomposition of \a matrix */
+ template<bool DoLDLT>
+ void compute(const MatrixType& matrix)
+ {
+ eigen_assert(matrix.rows()==matrix.cols());
+ Index size = matrix.cols();
+ CholMatrixType tmp(size,size);
+ ConstCholMatrixPtr pmat;
+ ordering(matrix, pmat, tmp);
+ analyzePattern_preordered(*pmat, DoLDLT);
+ factorize_preordered<DoLDLT>(*pmat);
+ }
+
+ template<bool DoLDLT>
+ void factorize(const MatrixType& a)
+ {
+ eigen_assert(a.rows()==a.cols());
+ Index size = a.cols();
+ CholMatrixType tmp(size,size);
+ ConstCholMatrixPtr pmat;
+
+ if(m_P.size() == 0 && (int(UpLo) & int(Upper)) == Upper)
+ {
+ // If there is no ordering, try to directly use the input matrix without any copy
+ internal::simplicial_cholesky_grab_input<CholMatrixType,MatrixType>::run(a, pmat, tmp);
+ }
+ else
+ {
+ tmp.template selfadjointView<Upper>() = a.template selfadjointView<UpLo>().twistedBy(m_P);
+ pmat = &tmp;
+ }
+
+ factorize_preordered<DoLDLT>(*pmat);
+ }
+
+ template<bool DoLDLT>
+ void factorize_preordered(const CholMatrixType& a);
+
+ void analyzePattern(const MatrixType& a, bool doLDLT)
+ {
+ eigen_assert(a.rows()==a.cols());
+ Index size = a.cols();
+ CholMatrixType tmp(size,size);
+ ConstCholMatrixPtr pmat;
+ ordering(a, pmat, tmp);
+ analyzePattern_preordered(*pmat,doLDLT);
+ }
+ void analyzePattern_preordered(const CholMatrixType& a, bool doLDLT);
+
+ void ordering(const MatrixType& a, ConstCholMatrixPtr &pmat, CholMatrixType& ap);
+
+ /** keeps off-diagonal entries; drops diagonal entries */
+ struct keep_diag {
+ inline bool operator() (const Index& row, const Index& col, const Scalar&) const
+ {
+ return row!=col;
+ }
+ };
+
+ mutable ComputationInfo m_info;
+ bool m_factorizationIsOk;
+ bool m_analysisIsOk;
+
+ CholMatrixType m_matrix;
+ VectorType m_diag; // the diagonal coefficients (LDLT mode)
+ VectorI m_parent; // elimination tree
+ VectorI m_nonZerosPerCol;
+ PermutationMatrix<Dynamic,Dynamic,StorageIndex> m_P; // the permutation
+ PermutationMatrix<Dynamic,Dynamic,StorageIndex> m_Pinv; // the inverse permutation
+
+ RealScalar m_shiftOffset;
+ RealScalar m_shiftScale;
+};
+
+template<typename MatrixType_, int UpLo_ = Lower, typename Ordering_ = AMDOrdering<typename MatrixType_::StorageIndex> > class SimplicialLLT;
+template<typename MatrixType_, int UpLo_ = Lower, typename Ordering_ = AMDOrdering<typename MatrixType_::StorageIndex> > class SimplicialLDLT;
+template<typename MatrixType_, int UpLo_ = Lower, typename Ordering_ = AMDOrdering<typename MatrixType_::StorageIndex> > class SimplicialCholesky;
+
+namespace internal {
+
+template<typename MatrixType_, int UpLo_, typename Ordering_> struct traits<SimplicialLLT<MatrixType_,UpLo_,Ordering_> >
+{
+ typedef MatrixType_ MatrixType;
+ typedef Ordering_ OrderingType;
+ enum { UpLo = UpLo_ };
+ typedef typename MatrixType::Scalar Scalar;
+ typedef typename MatrixType::StorageIndex StorageIndex;
+ typedef SparseMatrix<Scalar, ColMajor, StorageIndex> CholMatrixType;
+ typedef TriangularView<const CholMatrixType, Eigen::Lower> MatrixL;
+ typedef TriangularView<const typename CholMatrixType::AdjointReturnType, Eigen::Upper> MatrixU;
+ static inline MatrixL getL(const CholMatrixType& m) { return MatrixL(m); }
+ static inline MatrixU getU(const CholMatrixType& m) { return MatrixU(m.adjoint()); }
+};
+
+template<typename MatrixType_,int UpLo_, typename Ordering_> struct traits<SimplicialLDLT<MatrixType_,UpLo_,Ordering_> >
+{
+ typedef MatrixType_ MatrixType;
+ typedef Ordering_ OrderingType;
+ enum { UpLo = UpLo_ };
+ typedef typename MatrixType::Scalar Scalar;
+ typedef typename MatrixType::StorageIndex StorageIndex;
+ typedef SparseMatrix<Scalar, ColMajor, StorageIndex> CholMatrixType;
+ typedef TriangularView<const CholMatrixType, Eigen::UnitLower> MatrixL;
+ typedef TriangularView<const typename CholMatrixType::AdjointReturnType, Eigen::UnitUpper> MatrixU;
+ static inline MatrixL getL(const CholMatrixType& m) { return MatrixL(m); }
+ static inline MatrixU getU(const CholMatrixType& m) { return MatrixU(m.adjoint()); }
+};
+
+template<typename MatrixType_, int UpLo_, typename Ordering_> struct traits<SimplicialCholesky<MatrixType_,UpLo_,Ordering_> >
+{
+ typedef MatrixType_ MatrixType;
+ typedef Ordering_ OrderingType;
+ enum { UpLo = UpLo_ };
+};
+
+}
+
+/** \ingroup SparseCholesky_Module
+ * \class SimplicialLLT
+ * \brief A direct sparse LLT Cholesky factorizations
+ *
+ * This class provides a LL^T Cholesky factorizations of sparse matrices that are
+ * selfadjoint and positive definite. The factorization allows for solving A.X = B where
+ * X and B can be either dense or sparse.
+ *
+ * In order to reduce the fill-in, a symmetric permutation P is applied prior to the factorization
+ * such that the factorized matrix is P A P^-1.
+ *
+ * \tparam MatrixType_ the type of the sparse matrix A, it must be a SparseMatrix<>
+ * \tparam UpLo_ the triangular part that will be used for the computations. It can be Lower
+ * or Upper. Default is Lower.
+ * \tparam Ordering_ The ordering method to use, either AMDOrdering<> or NaturalOrdering<>. Default is AMDOrdering<>
+ *
+ * \implsparsesolverconcept
+ *
+ * \sa class SimplicialLDLT, class AMDOrdering, class NaturalOrdering
+ */
+template<typename MatrixType_, int UpLo_, typename Ordering_>
+ class SimplicialLLT : public SimplicialCholeskyBase<SimplicialLLT<MatrixType_,UpLo_,Ordering_> >
+{
+public:
+ typedef MatrixType_ MatrixType;
+ enum { UpLo = UpLo_ };
+ typedef SimplicialCholeskyBase<SimplicialLLT> Base;
+ typedef typename MatrixType::Scalar Scalar;
+ typedef typename MatrixType::RealScalar RealScalar;
+ typedef typename MatrixType::StorageIndex StorageIndex;
+ typedef SparseMatrix<Scalar,ColMajor,Index> CholMatrixType;
+ typedef Matrix<Scalar,Dynamic,1> VectorType;
+ typedef internal::traits<SimplicialLLT> Traits;
+ typedef typename Traits::MatrixL MatrixL;
+ typedef typename Traits::MatrixU MatrixU;
+public:
+ /** Default constructor */
+ SimplicialLLT() : Base() {}
+ /** Constructs and performs the LLT factorization of \a matrix */
+ explicit SimplicialLLT(const MatrixType& matrix)
+ : Base(matrix) {}
+
+ /** \returns an expression of the factor L */
+ inline const MatrixL matrixL() const {
+ eigen_assert(Base::m_factorizationIsOk && "Simplicial LLT not factorized");
+ return Traits::getL(Base::m_matrix);
+ }
+
+ /** \returns an expression of the factor U (= L^*) */
+ inline const MatrixU matrixU() const {
+ eigen_assert(Base::m_factorizationIsOk && "Simplicial LLT not factorized");
+ return Traits::getU(Base::m_matrix);
+ }
+
+ /** Computes the sparse Cholesky decomposition of \a matrix */
+ SimplicialLLT& compute(const MatrixType& matrix)
+ {
+ Base::template compute<false>(matrix);
+ return *this;
+ }
+
+ /** Performs a symbolic decomposition on the sparcity of \a matrix.
+ *
+ * This function is particularly useful when solving for several problems having the same structure.
+ *
+ * \sa factorize()
+ */
+ void analyzePattern(const MatrixType& a)
+ {
+ Base::analyzePattern(a, false);
+ }
+
+ /** Performs a numeric decomposition of \a matrix
+ *
+ * The given matrix must has the same sparcity than the matrix on which the symbolic decomposition has been performed.
+ *
+ * \sa analyzePattern()
+ */
+ void factorize(const MatrixType& a)
+ {
+ Base::template factorize<false>(a);
+ }
+
+ /** \returns the determinant of the underlying matrix from the current factorization */
+ Scalar determinant() const
+ {
+ Scalar detL = Base::m_matrix.diagonal().prod();
+ return numext::abs2(detL);
+ }
+};
+
+/** \ingroup SparseCholesky_Module
+ * \class SimplicialLDLT
+ * \brief A direct sparse LDLT Cholesky factorizations without square root.
+ *
+ * This class provides a LDL^T Cholesky factorizations without square root of sparse matrices that are
+ * selfadjoint and positive definite. The factorization allows for solving A.X = B where
+ * X and B can be either dense or sparse.
+ *
+ * In order to reduce the fill-in, a symmetric permutation P is applied prior to the factorization
+ * such that the factorized matrix is P A P^-1.
+ *
+ * \tparam MatrixType_ the type of the sparse matrix A, it must be a SparseMatrix<>
+ * \tparam UpLo_ the triangular part that will be used for the computations. It can be Lower
+ * or Upper. Default is Lower.
+ * \tparam Ordering_ The ordering method to use, either AMDOrdering<> or NaturalOrdering<>. Default is AMDOrdering<>
+ *
+ * \implsparsesolverconcept
+ *
+ * \sa class SimplicialLLT, class AMDOrdering, class NaturalOrdering
+ */
+template<typename MatrixType_, int UpLo_, typename Ordering_>
+ class SimplicialLDLT : public SimplicialCholeskyBase<SimplicialLDLT<MatrixType_,UpLo_,Ordering_> >
+{
+public:
+ typedef MatrixType_ MatrixType;
+ enum { UpLo = UpLo_ };
+ typedef SimplicialCholeskyBase<SimplicialLDLT> Base;
+ typedef typename MatrixType::Scalar Scalar;
+ typedef typename MatrixType::RealScalar RealScalar;
+ typedef typename MatrixType::StorageIndex StorageIndex;
+ typedef SparseMatrix<Scalar,ColMajor,StorageIndex> CholMatrixType;
+ typedef Matrix<Scalar,Dynamic,1> VectorType;
+ typedef internal::traits<SimplicialLDLT> Traits;
+ typedef typename Traits::MatrixL MatrixL;
+ typedef typename Traits::MatrixU MatrixU;
+public:
+ /** Default constructor */
+ SimplicialLDLT() : Base() {}
+
+ /** Constructs and performs the LLT factorization of \a matrix */
+ explicit SimplicialLDLT(const MatrixType& matrix)
+ : Base(matrix) {}
+
+ /** \returns a vector expression of the diagonal D */
+ inline const VectorType vectorD() const {
+ eigen_assert(Base::m_factorizationIsOk && "Simplicial LDLT not factorized");
+ return Base::m_diag;
+ }
+ /** \returns an expression of the factor L */
+ inline const MatrixL matrixL() const {
+ eigen_assert(Base::m_factorizationIsOk && "Simplicial LDLT not factorized");
+ return Traits::getL(Base::m_matrix);
+ }
+
+ /** \returns an expression of the factor U (= L^*) */
+ inline const MatrixU matrixU() const {
+ eigen_assert(Base::m_factorizationIsOk && "Simplicial LDLT not factorized");
+ return Traits::getU(Base::m_matrix);
+ }
+
+ /** Computes the sparse Cholesky decomposition of \a matrix */
+ SimplicialLDLT& compute(const MatrixType& matrix)
+ {
+ Base::template compute<true>(matrix);
+ return *this;
+ }
+
+ /** Performs a symbolic decomposition on the sparcity of \a matrix.
+ *
+ * This function is particularly useful when solving for several problems having the same structure.
+ *
+ * \sa factorize()
+ */
+ void analyzePattern(const MatrixType& a)
+ {
+ Base::analyzePattern(a, true);
+ }
+
+ /** Performs a numeric decomposition of \a matrix
+ *
+ * The given matrix must has the same sparcity than the matrix on which the symbolic decomposition has been performed.
+ *
+ * \sa analyzePattern()
+ */
+ void factorize(const MatrixType& a)
+ {
+ Base::template factorize<true>(a);
+ }
+
+ /** \returns the determinant of the underlying matrix from the current factorization */
+ Scalar determinant() const
+ {
+ return Base::m_diag.prod();
+ }
+};
+
+/** \deprecated use SimplicialLDLT or class SimplicialLLT
+ * \ingroup SparseCholesky_Module
+ * \class SimplicialCholesky
+ *
+ * \sa class SimplicialLDLT, class SimplicialLLT
+ */
+template<typename MatrixType_, int UpLo_, typename Ordering_>
+ class SimplicialCholesky : public SimplicialCholeskyBase<SimplicialCholesky<MatrixType_,UpLo_,Ordering_> >
+{
+public:
+ typedef MatrixType_ MatrixType;
+ enum { UpLo = UpLo_ };
+ typedef SimplicialCholeskyBase<SimplicialCholesky> Base;
+ typedef typename MatrixType::Scalar Scalar;
+ typedef typename MatrixType::RealScalar RealScalar;
+ typedef typename MatrixType::StorageIndex StorageIndex;
+ typedef SparseMatrix<Scalar,ColMajor,StorageIndex> CholMatrixType;
+ typedef Matrix<Scalar,Dynamic,1> VectorType;
+ typedef internal::traits<SimplicialCholesky> Traits;
+ typedef internal::traits<SimplicialLDLT<MatrixType,UpLo> > LDLTTraits;
+ typedef internal::traits<SimplicialLLT<MatrixType,UpLo> > LLTTraits;
+ public:
+ SimplicialCholesky() : Base(), m_LDLT(true) {}
+
+ explicit SimplicialCholesky(const MatrixType& matrix)
+ : Base(), m_LDLT(true)
+ {
+ compute(matrix);
+ }
+
+ SimplicialCholesky& setMode(SimplicialCholeskyMode mode)
+ {
+ switch(mode)
+ {
+ case SimplicialCholeskyLLT:
+ m_LDLT = false;
+ break;
+ case SimplicialCholeskyLDLT:
+ m_LDLT = true;
+ break;
+ default:
+ break;
+ }
+
+ return *this;
+ }
+
+ inline const VectorType vectorD() const {
+ eigen_assert(Base::m_factorizationIsOk && "Simplicial Cholesky not factorized");
+ return Base::m_diag;
+ }
+ inline const CholMatrixType rawMatrix() const {
+ eigen_assert(Base::m_factorizationIsOk && "Simplicial Cholesky not factorized");
+ return Base::m_matrix;
+ }
+
+ /** Computes the sparse Cholesky decomposition of \a matrix */
+ SimplicialCholesky& compute(const MatrixType& matrix)
+ {
+ if(m_LDLT)
+ Base::template compute<true>(matrix);
+ else
+ Base::template compute<false>(matrix);
+ return *this;
+ }
+
+ /** Performs a symbolic decomposition on the sparcity of \a matrix.
+ *
+ * This function is particularly useful when solving for several problems having the same structure.
+ *
+ * \sa factorize()
+ */
+ void analyzePattern(const MatrixType& a)
+ {
+ Base::analyzePattern(a, m_LDLT);
+ }
+
+ /** Performs a numeric decomposition of \a matrix
+ *
+ * The given matrix must has the same sparcity than the matrix on which the symbolic decomposition has been performed.
+ *
+ * \sa analyzePattern()
+ */
+ void factorize(const MatrixType& a)
+ {
+ if(m_LDLT)
+ Base::template factorize<true>(a);
+ else
+ Base::template factorize<false>(a);
+ }
+
+ /** \internal */
+ template<typename Rhs,typename Dest>
+ void _solve_impl(const MatrixBase<Rhs> &b, MatrixBase<Dest> &dest) const
+ {
+ eigen_assert(Base::m_factorizationIsOk && "The decomposition is not in a valid state for solving, you must first call either compute() or symbolic()/numeric()");
+ eigen_assert(Base::m_matrix.rows()==b.rows());
+
+ if(Base::m_info!=Success)
+ return;
+
+ if(Base::m_P.size()>0)
+ dest = Base::m_P * b;
+ else
+ dest = b;
+
+ if(Base::m_matrix.nonZeros()>0) // otherwise L==I
+ {
+ if(m_LDLT)
+ LDLTTraits::getL(Base::m_matrix).solveInPlace(dest);
+ else
+ LLTTraits::getL(Base::m_matrix).solveInPlace(dest);
+ }
+
+ if(Base::m_diag.size()>0)
+ dest = Base::m_diag.real().asDiagonal().inverse() * dest;
+
+ if (Base::m_matrix.nonZeros()>0) // otherwise I==I
+ {
+ if(m_LDLT)
+ LDLTTraits::getU(Base::m_matrix).solveInPlace(dest);
+ else
+ LLTTraits::getU(Base::m_matrix).solveInPlace(dest);
+ }
+
+ if(Base::m_P.size()>0)
+ dest = Base::m_Pinv * dest;
+ }
+
+ /** \internal */
+ template<typename Rhs,typename Dest>
+ void _solve_impl(const SparseMatrixBase<Rhs> &b, SparseMatrixBase<Dest> &dest) const
+ {
+ internal::solve_sparse_through_dense_panels(*this, b, dest);
+ }
+
+ Scalar determinant() const
+ {
+ if(m_LDLT)
+ {
+ return Base::m_diag.prod();
+ }
+ else
+ {
+ Scalar detL = Diagonal<const CholMatrixType>(Base::m_matrix).prod();
+ return numext::abs2(detL);
+ }
+ }
+
+ protected:
+ bool m_LDLT;
+};
+
+template<typename Derived>
+void SimplicialCholeskyBase<Derived>::ordering(const MatrixType& a, ConstCholMatrixPtr &pmat, CholMatrixType& ap)
+{
+ eigen_assert(a.rows()==a.cols());
+ const Index size = a.rows();
+ pmat = ≈
+ // Note that ordering methods compute the inverse permutation
+ if(!internal::is_same<OrderingType,NaturalOrdering<Index> >::value)
+ {
+ {
+ CholMatrixType C;
+ C = a.template selfadjointView<UpLo>();
+
+ OrderingType ordering;
+ ordering(C,m_Pinv);
+ }
+
+ if(m_Pinv.size()>0) m_P = m_Pinv.inverse();
+ else m_P.resize(0);
+
+ ap.resize(size,size);
+ ap.template selfadjointView<Upper>() = a.template selfadjointView<UpLo>().twistedBy(m_P);
+ }
+ else
+ {
+ m_Pinv.resize(0);
+ m_P.resize(0);
+ if(int(UpLo)==int(Lower) || MatrixType::IsRowMajor)
+ {
+ // we have to transpose the lower part to to the upper one
+ ap.resize(size,size);
+ ap.template selfadjointView<Upper>() = a.template selfadjointView<UpLo>();
+ }
+ else
+ internal::simplicial_cholesky_grab_input<CholMatrixType,MatrixType>::run(a, pmat, ap);
+ }
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_SIMPLICIAL_CHOLESKY_H
diff --git a/Eigen/src/SparseCholesky/SimplicialCholesky_impl.h b/Eigen/src/SparseCholesky/SimplicialCholesky_impl.h
new file mode 100644
index 0000000..3106c9b
--- /dev/null
+++ b/Eigen/src/SparseCholesky/SimplicialCholesky_impl.h
@@ -0,0 +1,176 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2012 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+/*
+NOTE: these functions have been adapted from the LDL library:
+
+LDL Copyright (c) 2005 by Timothy A. Davis. All Rights Reserved.
+
+The author of LDL, Timothy A. Davis., has executed a license with Google LLC
+to permit distribution of this code and derivative works as part of Eigen under
+the Mozilla Public License v. 2.0, as stated at the top of this file.
+ */
+
+#ifndef EIGEN_SIMPLICIAL_CHOLESKY_IMPL_H
+#define EIGEN_SIMPLICIAL_CHOLESKY_IMPL_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+template<typename Derived>
+void SimplicialCholeskyBase<Derived>::analyzePattern_preordered(const CholMatrixType& ap, bool doLDLT)
+{
+ const StorageIndex size = StorageIndex(ap.rows());
+ m_matrix.resize(size, size);
+ m_parent.resize(size);
+ m_nonZerosPerCol.resize(size);
+
+ ei_declare_aligned_stack_constructed_variable(StorageIndex, tags, size, 0);
+
+ for(StorageIndex k = 0; k < size; ++k)
+ {
+ /* L(k,:) pattern: all nodes reachable in etree from nz in A(0:k-1,k) */
+ m_parent[k] = -1; /* parent of k is not yet known */
+ tags[k] = k; /* mark node k as visited */
+ m_nonZerosPerCol[k] = 0; /* count of nonzeros in column k of L */
+ for(typename CholMatrixType::InnerIterator it(ap,k); it; ++it)
+ {
+ StorageIndex i = it.index();
+ if(i < k)
+ {
+ /* follow path from i to root of etree, stop at flagged node */
+ for(; tags[i] != k; i = m_parent[i])
+ {
+ /* find parent of i if not yet determined */
+ if (m_parent[i] == -1)
+ m_parent[i] = k;
+ m_nonZerosPerCol[i]++; /* L (k,i) is nonzero */
+ tags[i] = k; /* mark i as visited */
+ }
+ }
+ }
+ }
+
+ /* construct Lp index array from m_nonZerosPerCol column counts */
+ StorageIndex* Lp = m_matrix.outerIndexPtr();
+ Lp[0] = 0;
+ for(StorageIndex k = 0; k < size; ++k)
+ Lp[k+1] = Lp[k] + m_nonZerosPerCol[k] + (doLDLT ? 0 : 1);
+
+ m_matrix.resizeNonZeros(Lp[size]);
+
+ m_isInitialized = true;
+ m_info = Success;
+ m_analysisIsOk = true;
+ m_factorizationIsOk = false;
+}
+
+
+template<typename Derived>
+template<bool DoLDLT>
+void SimplicialCholeskyBase<Derived>::factorize_preordered(const CholMatrixType& ap)
+{
+ using std::sqrt;
+
+ eigen_assert(m_analysisIsOk && "You must first call analyzePattern()");
+ eigen_assert(ap.rows()==ap.cols());
+ eigen_assert(m_parent.size()==ap.rows());
+ eigen_assert(m_nonZerosPerCol.size()==ap.rows());
+
+ const StorageIndex size = StorageIndex(ap.rows());
+ const StorageIndex* Lp = m_matrix.outerIndexPtr();
+ StorageIndex* Li = m_matrix.innerIndexPtr();
+ Scalar* Lx = m_matrix.valuePtr();
+
+ ei_declare_aligned_stack_constructed_variable(Scalar, y, size, 0);
+ ei_declare_aligned_stack_constructed_variable(StorageIndex, pattern, size, 0);
+ ei_declare_aligned_stack_constructed_variable(StorageIndex, tags, size, 0);
+
+ bool ok = true;
+ m_diag.resize(DoLDLT ? size : 0);
+
+ for(StorageIndex k = 0; k < size; ++k)
+ {
+ // compute nonzero pattern of kth row of L, in topological order
+ y[k] = Scalar(0); // Y(0:k) is now all zero
+ StorageIndex top = size; // stack for pattern is empty
+ tags[k] = k; // mark node k as visited
+ m_nonZerosPerCol[k] = 0; // count of nonzeros in column k of L
+ for(typename CholMatrixType::InnerIterator it(ap,k); it; ++it)
+ {
+ StorageIndex i = it.index();
+ if(i <= k)
+ {
+ y[i] += numext::conj(it.value()); /* scatter A(i,k) into Y (sum duplicates) */
+ Index len;
+ for(len = 0; tags[i] != k; i = m_parent[i])
+ {
+ pattern[len++] = i; /* L(k,i) is nonzero */
+ tags[i] = k; /* mark i as visited */
+ }
+ while(len > 0)
+ pattern[--top] = pattern[--len];
+ }
+ }
+
+ /* compute numerical values kth row of L (a sparse triangular solve) */
+
+ RealScalar d = numext::real(y[k]) * m_shiftScale + m_shiftOffset; // get D(k,k), apply the shift function, and clear Y(k)
+ y[k] = Scalar(0);
+ for(; top < size; ++top)
+ {
+ Index i = pattern[top]; /* pattern[top:n-1] is pattern of L(:,k) */
+ Scalar yi = y[i]; /* get and clear Y(i) */
+ y[i] = Scalar(0);
+
+ /* the nonzero entry L(k,i) */
+ Scalar l_ki;
+ if(DoLDLT)
+ l_ki = yi / numext::real(m_diag[i]);
+ else
+ yi = l_ki = yi / Lx[Lp[i]];
+
+ Index p2 = Lp[i] + m_nonZerosPerCol[i];
+ Index p;
+ for(p = Lp[i] + (DoLDLT ? 0 : 1); p < p2; ++p)
+ y[Li[p]] -= numext::conj(Lx[p]) * yi;
+ d -= numext::real(l_ki * numext::conj(yi));
+ Li[p] = k; /* store L(k,i) in column form of L */
+ Lx[p] = l_ki;
+ ++m_nonZerosPerCol[i]; /* increment count of nonzeros in col i */
+ }
+ if(DoLDLT)
+ {
+ m_diag[k] = d;
+ if(d == RealScalar(0))
+ {
+ ok = false; /* failure, D(k,k) is zero */
+ break;
+ }
+ }
+ else
+ {
+ Index p = Lp[k] + m_nonZerosPerCol[k]++;
+ Li[p] = k ; /* store L(k,k) = sqrt (d) in column k */
+ if(d <= RealScalar(0)) {
+ ok = false; /* failure, matrix is not positive definite */
+ break;
+ }
+ Lx[p] = sqrt(d) ;
+ }
+ }
+
+ m_info = ok ? Success : NumericalIssue;
+ m_factorizationIsOk = true;
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_SIMPLICIAL_CHOLESKY_IMPL_H
diff --git a/Eigen/src/SparseCore/AmbiVector.h b/Eigen/src/SparseCore/AmbiVector.h
new file mode 100644
index 0000000..594e91d
--- /dev/null
+++ b/Eigen/src/SparseCore/AmbiVector.h
@@ -0,0 +1,380 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_AMBIVECTOR_H
+#define EIGEN_AMBIVECTOR_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+
+/** \internal
+ * Hybrid sparse/dense vector class designed for intensive read-write operations.
+ *
+ * See BasicSparseLLT and SparseProduct for usage examples.
+ */
+template<typename Scalar_, typename StorageIndex_>
+class AmbiVector
+{
+ public:
+ typedef Scalar_ Scalar;
+ typedef StorageIndex_ StorageIndex;
+ typedef typename NumTraits<Scalar>::Real RealScalar;
+
+ explicit AmbiVector(Index size)
+ : m_buffer(0), m_zero(0), m_size(0), m_end(0), m_allocatedSize(0), m_allocatedElements(0), m_mode(-1)
+ {
+ resize(size);
+ }
+
+ void init(double estimatedDensity);
+ void init(int mode);
+
+ Index nonZeros() const;
+
+ /** Specifies a sub-vector to work on */
+ void setBounds(Index start, Index end) { m_start = convert_index(start); m_end = convert_index(end); }
+
+ void setZero();
+
+ void restart();
+ Scalar& coeffRef(Index i);
+ Scalar& coeff(Index i);
+
+ class Iterator;
+
+ ~AmbiVector() { delete[] m_buffer; }
+
+ void resize(Index size)
+ {
+ if (m_allocatedSize < size)
+ reallocate(size);
+ m_size = convert_index(size);
+ }
+
+ StorageIndex size() const { return m_size; }
+
+ protected:
+ StorageIndex convert_index(Index idx)
+ {
+ return internal::convert_index<StorageIndex>(idx);
+ }
+
+ void reallocate(Index size)
+ {
+ // if the size of the matrix is not too large, let's allocate a bit more than needed such
+ // that we can handle dense vector even in sparse mode.
+ delete[] m_buffer;
+ if (size<1000)
+ {
+ Index allocSize = (size * sizeof(ListEl) + sizeof(Scalar) - 1)/sizeof(Scalar);
+ m_allocatedElements = convert_index((allocSize*sizeof(Scalar))/sizeof(ListEl));
+ m_buffer = new Scalar[allocSize];
+ }
+ else
+ {
+ m_allocatedElements = convert_index((size*sizeof(Scalar))/sizeof(ListEl));
+ m_buffer = new Scalar[size];
+ }
+ m_size = convert_index(size);
+ m_start = 0;
+ m_end = m_size;
+ }
+
+ void reallocateSparse()
+ {
+ Index copyElements = m_allocatedElements;
+ m_allocatedElements = (std::min)(StorageIndex(m_allocatedElements*1.5),m_size);
+ Index allocSize = m_allocatedElements * sizeof(ListEl);
+ allocSize = (allocSize + sizeof(Scalar) - 1)/sizeof(Scalar);
+ Scalar* newBuffer = new Scalar[allocSize];
+ std::memcpy(newBuffer, m_buffer, copyElements * sizeof(ListEl));
+ delete[] m_buffer;
+ m_buffer = newBuffer;
+ }
+
+ protected:
+ // element type of the linked list
+ struct ListEl
+ {
+ StorageIndex next;
+ StorageIndex index;
+ Scalar value;
+ };
+
+ // used to store data in both mode
+ Scalar* m_buffer;
+ Scalar m_zero;
+ StorageIndex m_size;
+ StorageIndex m_start;
+ StorageIndex m_end;
+ StorageIndex m_allocatedSize;
+ StorageIndex m_allocatedElements;
+ StorageIndex m_mode;
+
+ // linked list mode
+ StorageIndex m_llStart;
+ StorageIndex m_llCurrent;
+ StorageIndex m_llSize;
+};
+
+/** \returns the number of non zeros in the current sub vector */
+template<typename Scalar_,typename StorageIndex_>
+Index AmbiVector<Scalar_,StorageIndex_>::nonZeros() const
+{
+ if (m_mode==IsSparse)
+ return m_llSize;
+ else
+ return m_end - m_start;
+}
+
+template<typename Scalar_,typename StorageIndex_>
+void AmbiVector<Scalar_,StorageIndex_>::init(double estimatedDensity)
+{
+ if (estimatedDensity>0.1)
+ init(IsDense);
+ else
+ init(IsSparse);
+}
+
+template<typename Scalar_,typename StorageIndex_>
+void AmbiVector<Scalar_,StorageIndex_>::init(int mode)
+{
+ m_mode = mode;
+ // This is only necessary in sparse mode, but we set these unconditionally to avoid some maybe-uninitialized warnings
+ // if (m_mode==IsSparse)
+ {
+ m_llSize = 0;
+ m_llStart = -1;
+ }
+}
+
+/** Must be called whenever we might perform a write access
+ * with an index smaller than the previous one.
+ *
+ * Don't worry, this function is extremely cheap.
+ */
+template<typename Scalar_,typename StorageIndex_>
+void AmbiVector<Scalar_,StorageIndex_>::restart()
+{
+ m_llCurrent = m_llStart;
+}
+
+/** Set all coefficients of current subvector to zero */
+template<typename Scalar_,typename StorageIndex_>
+void AmbiVector<Scalar_,StorageIndex_>::setZero()
+{
+ if (m_mode==IsDense)
+ {
+ for (Index i=m_start; i<m_end; ++i)
+ m_buffer[i] = Scalar(0);
+ }
+ else
+ {
+ eigen_assert(m_mode==IsSparse);
+ m_llSize = 0;
+ m_llStart = -1;
+ }
+}
+
+template<typename Scalar_,typename StorageIndex_>
+Scalar_& AmbiVector<Scalar_,StorageIndex_>::coeffRef(Index i)
+{
+ if (m_mode==IsDense)
+ return m_buffer[i];
+ else
+ {
+ ListEl* EIGEN_RESTRICT llElements = reinterpret_cast<ListEl*>(m_buffer);
+ // TODO factorize the following code to reduce code generation
+ eigen_assert(m_mode==IsSparse);
+ if (m_llSize==0)
+ {
+ // this is the first element
+ m_llStart = 0;
+ m_llCurrent = 0;
+ ++m_llSize;
+ llElements[0].value = Scalar(0);
+ llElements[0].index = convert_index(i);
+ llElements[0].next = -1;
+ return llElements[0].value;
+ }
+ else if (i<llElements[m_llStart].index)
+ {
+ // this is going to be the new first element of the list
+ ListEl& el = llElements[m_llSize];
+ el.value = Scalar(0);
+ el.index = convert_index(i);
+ el.next = m_llStart;
+ m_llStart = m_llSize;
+ ++m_llSize;
+ m_llCurrent = m_llStart;
+ return el.value;
+ }
+ else
+ {
+ StorageIndex nextel = llElements[m_llCurrent].next;
+ eigen_assert(i>=llElements[m_llCurrent].index && "you must call restart() before inserting an element with lower or equal index");
+ while (nextel >= 0 && llElements[nextel].index<=i)
+ {
+ m_llCurrent = nextel;
+ nextel = llElements[nextel].next;
+ }
+
+ if (llElements[m_llCurrent].index==i)
+ {
+ // the coefficient already exists and we found it !
+ return llElements[m_llCurrent].value;
+ }
+ else
+ {
+ if (m_llSize>=m_allocatedElements)
+ {
+ reallocateSparse();
+ llElements = reinterpret_cast<ListEl*>(m_buffer);
+ }
+ eigen_internal_assert(m_llSize<m_allocatedElements && "internal error: overflow in sparse mode");
+ // let's insert a new coefficient
+ ListEl& el = llElements[m_llSize];
+ el.value = Scalar(0);
+ el.index = convert_index(i);
+ el.next = llElements[m_llCurrent].next;
+ llElements[m_llCurrent].next = m_llSize;
+ ++m_llSize;
+ return el.value;
+ }
+ }
+ }
+}
+
+template<typename Scalar_,typename StorageIndex_>
+Scalar_& AmbiVector<Scalar_,StorageIndex_>::coeff(Index i)
+{
+ if (m_mode==IsDense)
+ return m_buffer[i];
+ else
+ {
+ ListEl* EIGEN_RESTRICT llElements = reinterpret_cast<ListEl*>(m_buffer);
+ eigen_assert(m_mode==IsSparse);
+ if ((m_llSize==0) || (i<llElements[m_llStart].index))
+ {
+ return m_zero;
+ }
+ else
+ {
+ Index elid = m_llStart;
+ while (elid >= 0 && llElements[elid].index<i)
+ elid = llElements[elid].next;
+
+ if (llElements[elid].index==i)
+ return llElements[m_llCurrent].value;
+ else
+ return m_zero;
+ }
+ }
+}
+
+/** Iterator over the nonzero coefficients */
+template<typename Scalar_,typename StorageIndex_>
+class AmbiVector<Scalar_,StorageIndex_>::Iterator
+{
+ public:
+ typedef Scalar_ Scalar;
+ typedef typename NumTraits<Scalar>::Real RealScalar;
+
+ /** Default constructor
+ * \param vec the vector on which we iterate
+ * \param epsilon the minimal value used to prune zero coefficients.
+ * In practice, all coefficients having a magnitude smaller than \a epsilon
+ * are skipped.
+ */
+ explicit Iterator(const AmbiVector& vec, const RealScalar& epsilon = 0)
+ : m_vector(vec)
+ {
+ using std::abs;
+ m_epsilon = epsilon;
+ m_isDense = m_vector.m_mode==IsDense;
+ if (m_isDense)
+ {
+ m_currentEl = 0; // this is to avoid a compilation warning
+ m_cachedValue = 0; // this is to avoid a compilation warning
+ m_cachedIndex = m_vector.m_start-1;
+ ++(*this);
+ }
+ else
+ {
+ ListEl* EIGEN_RESTRICT llElements = reinterpret_cast<ListEl*>(m_vector.m_buffer);
+ m_currentEl = m_vector.m_llStart;
+ while (m_currentEl>=0 && abs(llElements[m_currentEl].value)<=m_epsilon)
+ m_currentEl = llElements[m_currentEl].next;
+ if (m_currentEl<0)
+ {
+ m_cachedValue = 0; // this is to avoid a compilation warning
+ m_cachedIndex = -1;
+ }
+ else
+ {
+ m_cachedIndex = llElements[m_currentEl].index;
+ m_cachedValue = llElements[m_currentEl].value;
+ }
+ }
+ }
+
+ StorageIndex index() const { return m_cachedIndex; }
+ Scalar value() const { return m_cachedValue; }
+
+ operator bool() const { return m_cachedIndex>=0; }
+
+ Iterator& operator++()
+ {
+ using std::abs;
+ if (m_isDense)
+ {
+ do {
+ ++m_cachedIndex;
+ } while (m_cachedIndex<m_vector.m_end && abs(m_vector.m_buffer[m_cachedIndex])<=m_epsilon);
+ if (m_cachedIndex<m_vector.m_end)
+ m_cachedValue = m_vector.m_buffer[m_cachedIndex];
+ else
+ m_cachedIndex=-1;
+ }
+ else
+ {
+ ListEl* EIGEN_RESTRICT llElements = reinterpret_cast<ListEl*>(m_vector.m_buffer);
+ do {
+ m_currentEl = llElements[m_currentEl].next;
+ } while (m_currentEl>=0 && abs(llElements[m_currentEl].value)<=m_epsilon);
+ if (m_currentEl<0)
+ {
+ m_cachedIndex = -1;
+ }
+ else
+ {
+ m_cachedIndex = llElements[m_currentEl].index;
+ m_cachedValue = llElements[m_currentEl].value;
+ }
+ }
+ return *this;
+ }
+
+ protected:
+ const AmbiVector& m_vector; // the target vector
+ StorageIndex m_currentEl; // the current element in sparse/linked-list mode
+ RealScalar m_epsilon; // epsilon used to prune zero coefficients
+ StorageIndex m_cachedIndex; // current coordinate
+ Scalar m_cachedValue; // current value
+ bool m_isDense; // mode of the vector
+};
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_AMBIVECTOR_H
diff --git a/Eigen/src/SparseCore/CompressedStorage.h b/Eigen/src/SparseCore/CompressedStorage.h
new file mode 100644
index 0000000..733b1aa
--- /dev/null
+++ b/Eigen/src/SparseCore/CompressedStorage.h
@@ -0,0 +1,242 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2014 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_COMPRESSED_STORAGE_H
+#define EIGEN_COMPRESSED_STORAGE_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+
+/** \internal
+ * Stores a sparse set of values as a list of values and a list of indices.
+ *
+ */
+template<typename Scalar_,typename StorageIndex_>
+class CompressedStorage
+{
+ public:
+
+ typedef Scalar_ Scalar;
+ typedef StorageIndex_ StorageIndex;
+
+ protected:
+
+ typedef typename NumTraits<Scalar>::Real RealScalar;
+
+ public:
+
+ CompressedStorage()
+ : m_values(0), m_indices(0), m_size(0), m_allocatedSize(0)
+ {}
+
+ explicit CompressedStorage(Index size)
+ : m_values(0), m_indices(0), m_size(0), m_allocatedSize(0)
+ {
+ resize(size);
+ }
+
+ CompressedStorage(const CompressedStorage& other)
+ : m_values(0), m_indices(0), m_size(0), m_allocatedSize(0)
+ {
+ *this = other;
+ }
+
+ CompressedStorage& operator=(const CompressedStorage& other)
+ {
+ resize(other.size());
+ if(other.size()>0)
+ {
+ internal::smart_copy(other.m_values, other.m_values + m_size, m_values);
+ internal::smart_copy(other.m_indices, other.m_indices + m_size, m_indices);
+ }
+ return *this;
+ }
+
+ void swap(CompressedStorage& other)
+ {
+ std::swap(m_values, other.m_values);
+ std::swap(m_indices, other.m_indices);
+ std::swap(m_size, other.m_size);
+ std::swap(m_allocatedSize, other.m_allocatedSize);
+ }
+
+ ~CompressedStorage()
+ {
+ conditional_aligned_delete_auto<Scalar, true>(m_values, m_allocatedSize);
+ conditional_aligned_delete_auto<StorageIndex, true>(m_indices, m_allocatedSize);
+ }
+
+ void reserve(Index size)
+ {
+ Index newAllocatedSize = m_size + size;
+ if (newAllocatedSize > m_allocatedSize)
+ reallocate(newAllocatedSize);
+ }
+
+ void squeeze()
+ {
+ if (m_allocatedSize>m_size)
+ reallocate(m_size);
+ }
+
+ void resize(Index size, double reserveSizeFactor = 0)
+ {
+ if (m_allocatedSize<size)
+ {
+ Index realloc_size = (std::min<Index>)(NumTraits<StorageIndex>::highest(), size + Index(reserveSizeFactor*double(size)));
+ if(realloc_size<size)
+ internal::throw_std_bad_alloc();
+ reallocate(realloc_size);
+ }
+ m_size = size;
+ }
+
+ void append(const Scalar& v, Index i)
+ {
+ Index id = m_size;
+ resize(m_size+1, 1);
+ m_values[id] = v;
+ m_indices[id] = internal::convert_index<StorageIndex>(i);
+ }
+
+ inline Index size() const { return m_size; }
+ inline Index allocatedSize() const { return m_allocatedSize; }
+ inline void clear() { m_size = 0; }
+
+ const Scalar* valuePtr() const { return m_values; }
+ Scalar* valuePtr() { return m_values; }
+ const StorageIndex* indexPtr() const { return m_indices; }
+ StorageIndex* indexPtr() { return m_indices; }
+
+ inline Scalar& value(Index i) { eigen_internal_assert(m_values!=0); return m_values[i]; }
+ inline const Scalar& value(Index i) const { eigen_internal_assert(m_values!=0); return m_values[i]; }
+
+ inline StorageIndex& index(Index i) { eigen_internal_assert(m_indices!=0); return m_indices[i]; }
+ inline const StorageIndex& index(Index i) const { eigen_internal_assert(m_indices!=0); return m_indices[i]; }
+
+ /** \returns the largest \c k such that for all \c j in [0,k) index[\c j]\<\a key */
+ inline Index searchLowerIndex(Index key) const
+ {
+ return searchLowerIndex(0, m_size, key);
+ }
+
+ /** \returns the largest \c k in [start,end) such that for all \c j in [start,k) index[\c j]\<\a key */
+ inline Index searchLowerIndex(Index start, Index end, Index key) const
+ {
+ while(end>start)
+ {
+ Index mid = (end+start)>>1;
+ if (m_indices[mid]<key)
+ start = mid+1;
+ else
+ end = mid;
+ }
+ return start;
+ }
+
+ /** \returns the stored value at index \a key
+ * If the value does not exist, then the value \a defaultValue is returned without any insertion. */
+ inline Scalar at(Index key, const Scalar& defaultValue = Scalar(0)) const
+ {
+ if (m_size==0)
+ return defaultValue;
+ else if (key==m_indices[m_size-1])
+ return m_values[m_size-1];
+ // ^^ optimization: let's first check if it is the last coefficient
+ // (very common in high level algorithms)
+ const Index id = searchLowerIndex(0,m_size-1,key);
+ return ((id<m_size) && (m_indices[id]==key)) ? m_values[id] : defaultValue;
+ }
+
+ /** Like at(), but the search is performed in the range [start,end) */
+ inline Scalar atInRange(Index start, Index end, Index key, const Scalar &defaultValue = Scalar(0)) const
+ {
+ if (start>=end)
+ return defaultValue;
+ else if (end>start && key==m_indices[end-1])
+ return m_values[end-1];
+ // ^^ optimization: let's first check if it is the last coefficient
+ // (very common in high level algorithms)
+ const Index id = searchLowerIndex(start,end-1,key);
+ return ((id<end) && (m_indices[id]==key)) ? m_values[id] : defaultValue;
+ }
+
+ /** \returns a reference to the value at index \a key
+ * If the value does not exist, then the value \a defaultValue is inserted
+ * such that the keys are sorted. */
+ inline Scalar& atWithInsertion(Index key, const Scalar& defaultValue = Scalar(0))
+ {
+ Index id = searchLowerIndex(0,m_size,key);
+ if (id>=m_size || m_indices[id]!=key)
+ {
+ if (m_allocatedSize<m_size+1)
+ {
+ Index newAllocatedSize = 2 * (m_size + 1);
+ m_values = conditional_aligned_realloc_new_auto<Scalar, true>(m_values, newAllocatedSize, m_allocatedSize);
+ m_indices =
+ conditional_aligned_realloc_new_auto<StorageIndex, true>(m_indices, newAllocatedSize, m_allocatedSize);
+ m_allocatedSize = newAllocatedSize;
+ }
+ if(m_size>id)
+ {
+ internal::smart_memmove(m_values +id, m_values +m_size, m_values +id+1);
+ internal::smart_memmove(m_indices+id, m_indices+m_size, m_indices+id+1);
+ }
+ m_size++;
+ m_indices[id] = internal::convert_index<StorageIndex>(key);
+ m_values[id] = defaultValue;
+ }
+ return m_values[id];
+ }
+
+ void moveChunk(Index from, Index to, Index chunkSize)
+ {
+ eigen_internal_assert(to+chunkSize <= m_size);
+ if(to>from && from+chunkSize>to)
+ {
+ // move backward
+ internal::smart_memmove(m_values+from, m_values+from+chunkSize, m_values+to);
+ internal::smart_memmove(m_indices+from, m_indices+from+chunkSize, m_indices+to);
+ }
+ else
+ {
+ internal::smart_copy(m_values+from, m_values+from+chunkSize, m_values+to);
+ internal::smart_copy(m_indices+from, m_indices+from+chunkSize, m_indices+to);
+ }
+ }
+
+ protected:
+
+ inline void reallocate(Index size)
+ {
+ #ifdef EIGEN_SPARSE_COMPRESSED_STORAGE_REALLOCATE_PLUGIN
+ EIGEN_SPARSE_COMPRESSED_STORAGE_REALLOCATE_PLUGIN
+ #endif
+ eigen_internal_assert(size!=m_allocatedSize);
+ m_values = conditional_aligned_realloc_new_auto<Scalar, true>(m_values, size, m_allocatedSize);
+ m_indices = conditional_aligned_realloc_new_auto<StorageIndex, true>(m_indices, size, m_allocatedSize);
+ m_allocatedSize = size;
+ }
+
+ protected:
+ Scalar* m_values;
+ StorageIndex* m_indices;
+ Index m_size;
+ Index m_allocatedSize;
+
+};
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_COMPRESSED_STORAGE_H
diff --git a/Eigen/src/SparseCore/ConservativeSparseSparseProduct.h b/Eigen/src/SparseCore/ConservativeSparseSparseProduct.h
new file mode 100644
index 0000000..f852493
--- /dev/null
+++ b/Eigen/src/SparseCore/ConservativeSparseSparseProduct.h
@@ -0,0 +1,359 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2015 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_CONSERVATIVESPARSESPARSEPRODUCT_H
+#define EIGEN_CONSERVATIVESPARSESPARSEPRODUCT_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+
+template<typename Lhs, typename Rhs, typename ResultType>
+static void conservative_sparse_sparse_product_impl(const Lhs& lhs, const Rhs& rhs, ResultType& res, bool sortedInsertion = false)
+{
+ typedef typename remove_all_t<Lhs>::Scalar LhsScalar;
+ typedef typename remove_all_t<Rhs>::Scalar RhsScalar;
+ typedef typename remove_all_t<ResultType>::Scalar ResScalar;
+
+ // make sure to call innerSize/outerSize since we fake the storage order.
+ Index rows = lhs.innerSize();
+ Index cols = rhs.outerSize();
+ eigen_assert(lhs.outerSize() == rhs.innerSize());
+
+ ei_declare_aligned_stack_constructed_variable(bool, mask, rows, 0);
+ ei_declare_aligned_stack_constructed_variable(ResScalar, values, rows, 0);
+ ei_declare_aligned_stack_constructed_variable(Index, indices, rows, 0);
+
+ std::memset(mask,0,sizeof(bool)*rows);
+
+ evaluator<Lhs> lhsEval(lhs);
+ evaluator<Rhs> rhsEval(rhs);
+
+ // estimate the number of non zero entries
+ // given a rhs column containing Y non zeros, we assume that the respective Y columns
+ // of the lhs differs in average of one non zeros, thus the number of non zeros for
+ // the product of a rhs column with the lhs is X+Y where X is the average number of non zero
+ // per column of the lhs.
+ // Therefore, we have nnz(lhs*rhs) = nnz(lhs) + nnz(rhs)
+ Index estimated_nnz_prod = lhsEval.nonZerosEstimate() + rhsEval.nonZerosEstimate();
+
+ res.setZero();
+ res.reserve(Index(estimated_nnz_prod));
+ // we compute each column of the result, one after the other
+ for (Index j=0; j<cols; ++j)
+ {
+
+ res.startVec(j);
+ Index nnz = 0;
+ for (typename evaluator<Rhs>::InnerIterator rhsIt(rhsEval, j); rhsIt; ++rhsIt)
+ {
+ RhsScalar y = rhsIt.value();
+ Index k = rhsIt.index();
+ for (typename evaluator<Lhs>::InnerIterator lhsIt(lhsEval, k); lhsIt; ++lhsIt)
+ {
+ Index i = lhsIt.index();
+ LhsScalar x = lhsIt.value();
+ if(!mask[i])
+ {
+ mask[i] = true;
+ values[i] = x * y;
+ indices[nnz] = i;
+ ++nnz;
+ }
+ else
+ values[i] += x * y;
+ }
+ }
+ if(!sortedInsertion)
+ {
+ // unordered insertion
+ for(Index k=0; k<nnz; ++k)
+ {
+ Index i = indices[k];
+ res.insertBackByOuterInnerUnordered(j,i) = values[i];
+ mask[i] = false;
+ }
+ }
+ else
+ {
+ // alternative ordered insertion code:
+ const Index t200 = rows/11; // 11 == (log2(200)*1.39)
+ const Index t = (rows*100)/139;
+
+ // FIXME reserve nnz non zeros
+ // FIXME implement faster sorting algorithms for very small nnz
+ // if the result is sparse enough => use a quick sort
+ // otherwise => loop through the entire vector
+ // In order to avoid to perform an expensive log2 when the
+ // result is clearly very sparse we use a linear bound up to 200.
+ if((nnz<200 && nnz<t200) || nnz * numext::log2(int(nnz)) < t)
+ {
+ if(nnz>1) std::sort(indices,indices+nnz);
+ for(Index k=0; k<nnz; ++k)
+ {
+ Index i = indices[k];
+ res.insertBackByOuterInner(j,i) = values[i];
+ mask[i] = false;
+ }
+ }
+ else
+ {
+ // dense path
+ for(Index i=0; i<rows; ++i)
+ {
+ if(mask[i])
+ {
+ mask[i] = false;
+ res.insertBackByOuterInner(j,i) = values[i];
+ }
+ }
+ }
+ }
+ }
+ res.finalize();
+}
+
+
+} // end namespace internal
+
+namespace internal {
+
+
+// Helper template to generate new sparse matrix types
+template<class Source, int Order>
+using WithStorageOrder = SparseMatrix<typename Source::Scalar, Order, typename Source::StorageIndex>;
+
+template<typename Lhs, typename Rhs, typename ResultType,
+ int LhsStorageOrder = (traits<Lhs>::Flags&RowMajorBit) ? RowMajor : ColMajor,
+ int RhsStorageOrder = (traits<Rhs>::Flags&RowMajorBit) ? RowMajor : ColMajor,
+ int ResStorageOrder = (traits<ResultType>::Flags&RowMajorBit) ? RowMajor : ColMajor>
+struct conservative_sparse_sparse_product_selector;
+
+template<typename Lhs, typename Rhs, typename ResultType>
+struct conservative_sparse_sparse_product_selector<Lhs,Rhs,ResultType,ColMajor,ColMajor,ColMajor>
+{
+ typedef remove_all_t<Lhs> LhsCleaned;
+ typedef typename LhsCleaned::Scalar Scalar;
+
+ static void run(const Lhs& lhs, const Rhs& rhs, ResultType& res)
+ {
+ using RowMajorMatrix = WithStorageOrder<ResultType, RowMajor>;
+ using ColMajorMatrixAux = WithStorageOrder<ResultType, ColMajor>;
+
+ // If the result is tall and thin (in the extreme case a column vector)
+ // then it is faster to sort the coefficients inplace instead of transposing twice.
+ // FIXME, the following heuristic is probably not very good.
+ if(lhs.rows()>rhs.cols())
+ {
+ using ColMajorMatrix = typename sparse_eval<ColMajorMatrixAux,ResultType::RowsAtCompileTime,ResultType::ColsAtCompileTime,ColMajorMatrixAux::Flags>::type;
+ ColMajorMatrix resCol(lhs.rows(),rhs.cols());
+ // perform sorted insertion
+ internal::conservative_sparse_sparse_product_impl<Lhs,Rhs,ColMajorMatrix>(lhs, rhs, resCol, true);
+ res = resCol.markAsRValue();
+ }
+ else
+ {
+ ColMajorMatrixAux resCol(lhs.rows(),rhs.cols());
+ // resort to transpose to sort the entries
+ internal::conservative_sparse_sparse_product_impl<Lhs,Rhs,ColMajorMatrixAux>(lhs, rhs, resCol, false);
+ RowMajorMatrix resRow(resCol);
+ res = resRow.markAsRValue();
+ }
+ }
+};
+
+template<typename Lhs, typename Rhs, typename ResultType>
+struct conservative_sparse_sparse_product_selector<Lhs,Rhs,ResultType,RowMajor,ColMajor,ColMajor>
+{
+ static void run(const Lhs& lhs, const Rhs& rhs, ResultType& res)
+ {
+ using RowMajorRhs = WithStorageOrder<Rhs, RowMajor>;
+ using RowMajorRes = WithStorageOrder<ResultType, RowMajor>;
+ RowMajorRhs rhsRow = rhs;
+ RowMajorRes resRow(lhs.rows(), rhs.cols());
+ internal::conservative_sparse_sparse_product_impl<RowMajorRhs,Lhs,RowMajorRes>(rhsRow, lhs, resRow);
+ res = resRow;
+ }
+};
+
+template<typename Lhs, typename Rhs, typename ResultType>
+struct conservative_sparse_sparse_product_selector<Lhs,Rhs,ResultType,ColMajor,RowMajor,ColMajor>
+{
+ static void run(const Lhs& lhs, const Rhs& rhs, ResultType& res)
+ {
+ using RowMajorLhs = WithStorageOrder<Lhs, RowMajor>;
+ using RowMajorRes = WithStorageOrder<ResultType, RowMajor>;
+ RowMajorLhs lhsRow = lhs;
+ RowMajorRes resRow(lhs.rows(), rhs.cols());
+ internal::conservative_sparse_sparse_product_impl<Rhs,RowMajorLhs,RowMajorRes>(rhs, lhsRow, resRow);
+ res = resRow;
+ }
+};
+
+template<typename Lhs, typename Rhs, typename ResultType>
+struct conservative_sparse_sparse_product_selector<Lhs,Rhs,ResultType,RowMajor,RowMajor,ColMajor>
+{
+ static void run(const Lhs& lhs, const Rhs& rhs, ResultType& res)
+ {
+ using RowMajorRes = WithStorageOrder<ResultType, RowMajor>;
+ RowMajorRes resRow(lhs.rows(), rhs.cols());
+ internal::conservative_sparse_sparse_product_impl<Rhs,Lhs,RowMajorRes>(rhs, lhs, resRow);
+ res = resRow;
+ }
+};
+
+
+template<typename Lhs, typename Rhs, typename ResultType>
+struct conservative_sparse_sparse_product_selector<Lhs,Rhs,ResultType,ColMajor,ColMajor,RowMajor>
+{
+ typedef typename traits<remove_all_t<Lhs>>::Scalar Scalar;
+
+ static void run(const Lhs& lhs, const Rhs& rhs, ResultType& res)
+ {
+ using ColMajorRes = WithStorageOrder<ResultType, ColMajor>;
+ ColMajorRes resCol(lhs.rows(), rhs.cols());
+ internal::conservative_sparse_sparse_product_impl<Lhs,Rhs,ColMajorRes>(lhs, rhs, resCol);
+ res = resCol;
+ }
+};
+
+template<typename Lhs, typename Rhs, typename ResultType>
+struct conservative_sparse_sparse_product_selector<Lhs,Rhs,ResultType,RowMajor,ColMajor,RowMajor>
+{
+ static void run(const Lhs& lhs, const Rhs& rhs, ResultType& res)
+ {
+ using ColMajorLhs = WithStorageOrder<Lhs, ColMajor>;
+ using ColMajorRes = WithStorageOrder<ResultType, ColMajor>;
+ ColMajorLhs lhsCol = lhs;
+ ColMajorRes resCol(lhs.rows(), rhs.cols());
+ internal::conservative_sparse_sparse_product_impl<ColMajorLhs,Rhs,ColMajorRes>(lhsCol, rhs, resCol);
+ res = resCol;
+ }
+};
+
+template<typename Lhs, typename Rhs, typename ResultType>
+struct conservative_sparse_sparse_product_selector<Lhs,Rhs,ResultType,ColMajor,RowMajor,RowMajor>
+{
+ static void run(const Lhs& lhs, const Rhs& rhs, ResultType& res)
+ {
+ using ColMajorRhs = WithStorageOrder<Rhs, ColMajor>;
+ using ColMajorRes = WithStorageOrder<ResultType, ColMajor>;
+ ColMajorRhs rhsCol = rhs;
+ ColMajorRes resCol(lhs.rows(), rhs.cols());
+ internal::conservative_sparse_sparse_product_impl<Lhs,ColMajorRhs,ColMajorRes>(lhs, rhsCol, resCol);
+ res = resCol;
+ }
+};
+
+template<typename Lhs, typename Rhs, typename ResultType>
+struct conservative_sparse_sparse_product_selector<Lhs,Rhs,ResultType,RowMajor,RowMajor,RowMajor>
+{
+ static void run(const Lhs& lhs, const Rhs& rhs, ResultType& res)
+ {
+ using ColMajorRes = WithStorageOrder<ResultType, ColMajor>;
+ using RowMajorRes = WithStorageOrder<ResultType, RowMajor>;
+ RowMajorRes resRow(lhs.rows(),rhs.cols());
+ internal::conservative_sparse_sparse_product_impl<Rhs,Lhs,RowMajorRes>(rhs, lhs, resRow);
+ // sort the non zeros:
+ ColMajorRes resCol(resRow);
+ res = resCol;
+ }
+};
+
+} // end namespace internal
+
+
+namespace internal {
+
+template<typename Lhs, typename Rhs, typename ResultType>
+static void sparse_sparse_to_dense_product_impl(const Lhs& lhs, const Rhs& rhs, ResultType& res)
+{
+ typedef typename remove_all_t<Lhs>::Scalar LhsScalar;
+ typedef typename remove_all_t<Rhs>::Scalar RhsScalar;
+ Index cols = rhs.outerSize();
+ eigen_assert(lhs.outerSize() == rhs.innerSize());
+
+ evaluator<Lhs> lhsEval(lhs);
+ evaluator<Rhs> rhsEval(rhs);
+
+ for (Index j=0; j<cols; ++j)
+ {
+ for (typename evaluator<Rhs>::InnerIterator rhsIt(rhsEval, j); rhsIt; ++rhsIt)
+ {
+ RhsScalar y = rhsIt.value();
+ Index k = rhsIt.index();
+ for (typename evaluator<Lhs>::InnerIterator lhsIt(lhsEval, k); lhsIt; ++lhsIt)
+ {
+ Index i = lhsIt.index();
+ LhsScalar x = lhsIt.value();
+ res.coeffRef(i,j) += x * y;
+ }
+ }
+ }
+}
+
+
+} // end namespace internal
+
+namespace internal {
+
+template<typename Lhs, typename Rhs, typename ResultType,
+ int LhsStorageOrder = (traits<Lhs>::Flags&RowMajorBit) ? RowMajor : ColMajor,
+ int RhsStorageOrder = (traits<Rhs>::Flags&RowMajorBit) ? RowMajor : ColMajor>
+struct sparse_sparse_to_dense_product_selector;
+
+template<typename Lhs, typename Rhs, typename ResultType>
+struct sparse_sparse_to_dense_product_selector<Lhs,Rhs,ResultType,ColMajor,ColMajor>
+{
+ static void run(const Lhs& lhs, const Rhs& rhs, ResultType& res)
+ {
+ internal::sparse_sparse_to_dense_product_impl<Lhs,Rhs,ResultType>(lhs, rhs, res);
+ }
+};
+
+template<typename Lhs, typename Rhs, typename ResultType>
+struct sparse_sparse_to_dense_product_selector<Lhs,Rhs,ResultType,RowMajor,ColMajor>
+{
+ static void run(const Lhs& lhs, const Rhs& rhs, ResultType& res)
+ {
+ using ColMajorLhs = WithStorageOrder<Lhs, ColMajor>;
+ ColMajorLhs lhsCol(lhs);
+ internal::sparse_sparse_to_dense_product_impl<ColMajorLhs,Rhs,ResultType>(lhsCol, rhs, res);
+ }
+};
+
+template<typename Lhs, typename Rhs, typename ResultType>
+struct sparse_sparse_to_dense_product_selector<Lhs,Rhs,ResultType,ColMajor,RowMajor>
+{
+ static void run(const Lhs& lhs, const Rhs& rhs, ResultType& res)
+ {
+ using ColMajorRhs = WithStorageOrder<Rhs, ColMajor>;
+ ColMajorRhs rhsCol(rhs);
+ internal::sparse_sparse_to_dense_product_impl<Lhs,ColMajorRhs,ResultType>(lhs, rhsCol, res);
+ }
+};
+
+template<typename Lhs, typename Rhs, typename ResultType>
+struct sparse_sparse_to_dense_product_selector<Lhs,Rhs,ResultType,RowMajor,RowMajor>
+{
+ static void run(const Lhs& lhs, const Rhs& rhs, ResultType& res)
+ {
+ Transpose<ResultType> trRes(res);
+ internal::sparse_sparse_to_dense_product_impl<Rhs,Lhs,Transpose<ResultType> >(rhs, lhs, trRes);
+ }
+};
+
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_CONSERVATIVESPARSESPARSEPRODUCT_H
diff --git a/Eigen/src/SparseCore/InternalHeaderCheck.h b/Eigen/src/SparseCore/InternalHeaderCheck.h
new file mode 100644
index 0000000..9de5936
--- /dev/null
+++ b/Eigen/src/SparseCore/InternalHeaderCheck.h
@@ -0,0 +1,3 @@
+#ifndef EIGEN_SPARSECORE_MODULE_H
+#error "Please include Eigen/SparseCore instead of including headers inside the src directory directly."
+#endif
diff --git a/Eigen/src/SparseCore/SparseAssign.h b/Eigen/src/SparseCore/SparseAssign.h
new file mode 100644
index 0000000..29f6af4
--- /dev/null
+++ b/Eigen/src/SparseCore/SparseAssign.h
@@ -0,0 +1,278 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2014 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_SPARSEASSIGN_H
+#define EIGEN_SPARSEASSIGN_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+template<typename Derived>
+template<typename OtherDerived>
+Derived& SparseMatrixBase<Derived>::operator=(const EigenBase<OtherDerived> &other)
+{
+ internal::call_assignment_no_alias(derived(), other.derived());
+ return derived();
+}
+
+template<typename Derived>
+template<typename OtherDerived>
+Derived& SparseMatrixBase<Derived>::operator=(const ReturnByValue<OtherDerived>& other)
+{
+ // TODO use the evaluator mechanism
+ other.evalTo(derived());
+ return derived();
+}
+
+template<typename Derived>
+template<typename OtherDerived>
+inline Derived& SparseMatrixBase<Derived>::operator=(const SparseMatrixBase<OtherDerived>& other)
+{
+ // by default sparse evaluation do not alias, so we can safely bypass the generic call_assignment routine
+ internal::Assignment<Derived,OtherDerived,internal::assign_op<Scalar,typename OtherDerived::Scalar> >
+ ::run(derived(), other.derived(), internal::assign_op<Scalar,typename OtherDerived::Scalar>());
+ return derived();
+}
+
+template<typename Derived>
+inline Derived& SparseMatrixBase<Derived>::operator=(const Derived& other)
+{
+ internal::call_assignment_no_alias(derived(), other.derived());
+ return derived();
+}
+
+namespace internal {
+
+template<>
+struct storage_kind_to_evaluator_kind<Sparse> {
+ typedef IteratorBased Kind;
+};
+
+template<>
+struct storage_kind_to_shape<Sparse> {
+ typedef SparseShape Shape;
+};
+
+struct Sparse2Sparse {};
+struct Sparse2Dense {};
+
+template<> struct AssignmentKind<SparseShape, SparseShape> { typedef Sparse2Sparse Kind; };
+template<> struct AssignmentKind<SparseShape, SparseTriangularShape> { typedef Sparse2Sparse Kind; };
+template<> struct AssignmentKind<DenseShape, SparseShape> { typedef Sparse2Dense Kind; };
+template<> struct AssignmentKind<DenseShape, SparseTriangularShape> { typedef Sparse2Dense Kind; };
+
+
+template<typename DstXprType, typename SrcXprType>
+void assign_sparse_to_sparse(DstXprType &dst, const SrcXprType &src)
+{
+ typedef typename DstXprType::Scalar Scalar;
+ typedef internal::evaluator<DstXprType> DstEvaluatorType;
+ typedef internal::evaluator<SrcXprType> SrcEvaluatorType;
+
+ SrcEvaluatorType srcEvaluator(src);
+
+ const bool transpose = (DstEvaluatorType::Flags & RowMajorBit) != (SrcEvaluatorType::Flags & RowMajorBit);
+ const Index outerEvaluationSize = (SrcEvaluatorType::Flags&RowMajorBit) ? src.rows() : src.cols();
+
+ Index reserveSize = 0;
+ for (Index j = 0; j < outerEvaluationSize; ++j)
+ for (typename SrcEvaluatorType::InnerIterator it(srcEvaluator, j); it; ++it)
+ reserveSize++;
+
+ if ((!transpose) && src.isRValue())
+ {
+ // eval without temporary
+ dst.resize(src.rows(), src.cols());
+ dst.setZero();
+ dst.reserve(reserveSize);
+ for (Index j=0; j<outerEvaluationSize; ++j)
+ {
+ dst.startVec(j);
+ for (typename SrcEvaluatorType::InnerIterator it(srcEvaluator, j); it; ++it)
+ {
+ Scalar v = it.value();
+ dst.insertBackByOuterInner(j,it.index()) = v;
+ }
+ }
+ dst.finalize();
+ }
+ else
+ {
+ // eval through a temporary
+ eigen_assert(( ((internal::traits<DstXprType>::SupportedAccessPatterns & OuterRandomAccessPattern)==OuterRandomAccessPattern) ||
+ (!((DstEvaluatorType::Flags & RowMajorBit) != (SrcEvaluatorType::Flags & RowMajorBit)))) &&
+ "the transpose operation is supposed to be handled in SparseMatrix::operator=");
+
+ enum { Flip = (DstEvaluatorType::Flags & RowMajorBit) != (SrcEvaluatorType::Flags & RowMajorBit) };
+
+
+ DstXprType temp(src.rows(), src.cols());
+
+ temp.reserve(reserveSize);
+ for (Index j=0; j<outerEvaluationSize; ++j)
+ {
+ temp.startVec(j);
+ for (typename SrcEvaluatorType::InnerIterator it(srcEvaluator, j); it; ++it)
+ {
+ Scalar v = it.value();
+ temp.insertBackByOuterInner(Flip?it.index():j,Flip?j:it.index()) = v;
+ }
+ }
+ temp.finalize();
+
+ dst = temp.markAsRValue();
+ }
+}
+
+// Generic Sparse to Sparse assignment
+template< typename DstXprType, typename SrcXprType, typename Functor>
+struct Assignment<DstXprType, SrcXprType, Functor, Sparse2Sparse>
+{
+ static void run(DstXprType &dst, const SrcXprType &src, const internal::assign_op<typename DstXprType::Scalar,typename SrcXprType::Scalar> &/*func*/)
+ {
+ assign_sparse_to_sparse(dst.derived(), src.derived());
+ }
+};
+
+// Generic Sparse to Dense assignment
+template< typename DstXprType, typename SrcXprType, typename Functor, typename Weak>
+struct Assignment<DstXprType, SrcXprType, Functor, Sparse2Dense, Weak>
+{
+ static void run(DstXprType &dst, const SrcXprType &src, const Functor &func)
+ {
+ if(internal::is_same<Functor,internal::assign_op<typename DstXprType::Scalar,typename SrcXprType::Scalar> >::value)
+ dst.setZero();
+
+ internal::evaluator<SrcXprType> srcEval(src);
+ resize_if_allowed(dst, src, func);
+ internal::evaluator<DstXprType> dstEval(dst);
+
+ const Index outerEvaluationSize = (internal::evaluator<SrcXprType>::Flags&RowMajorBit) ? src.rows() : src.cols();
+ for (Index j=0; j<outerEvaluationSize; ++j)
+ for (typename internal::evaluator<SrcXprType>::InnerIterator i(srcEval,j); i; ++i)
+ func.assignCoeff(dstEval.coeffRef(i.row(),i.col()), i.value());
+ }
+};
+
+// Specialization for dense ?= dense +/- sparse and dense ?= sparse +/- dense
+template<typename DstXprType, typename Func1, typename Func2>
+struct assignment_from_dense_op_sparse
+{
+ template<typename SrcXprType, typename InitialFunc>
+ static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ void run(DstXprType &dst, const SrcXprType &src, const InitialFunc& /*func*/)
+ {
+ #ifdef EIGEN_SPARSE_ASSIGNMENT_FROM_DENSE_OP_SPARSE_PLUGIN
+ EIGEN_SPARSE_ASSIGNMENT_FROM_DENSE_OP_SPARSE_PLUGIN
+ #endif
+
+ call_assignment_no_alias(dst, src.lhs(), Func1());
+ call_assignment_no_alias(dst, src.rhs(), Func2());
+ }
+
+ // Specialization for dense1 = sparse + dense2; -> dense1 = dense2; dense1 += sparse;
+ template<typename Lhs, typename Rhs, typename Scalar>
+ static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ std::enable_if_t<internal::is_same<typename internal::evaluator_traits<Rhs>::Shape,DenseShape>::value>
+ run(DstXprType &dst, const CwiseBinaryOp<internal::scalar_sum_op<Scalar,Scalar>, const Lhs, const Rhs> &src,
+ const internal::assign_op<typename DstXprType::Scalar,Scalar>& /*func*/)
+ {
+ #ifdef EIGEN_SPARSE_ASSIGNMENT_FROM_SPARSE_ADD_DENSE_PLUGIN
+ EIGEN_SPARSE_ASSIGNMENT_FROM_SPARSE_ADD_DENSE_PLUGIN
+ #endif
+
+ // Apply the dense matrix first, then the sparse one.
+ call_assignment_no_alias(dst, src.rhs(), Func1());
+ call_assignment_no_alias(dst, src.lhs(), Func2());
+ }
+
+ // Specialization for dense1 = sparse - dense2; -> dense1 = -dense2; dense1 += sparse;
+ template<typename Lhs, typename Rhs, typename Scalar>
+ static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ std::enable_if_t<internal::is_same<typename internal::evaluator_traits<Rhs>::Shape,DenseShape>::value>
+ run(DstXprType &dst, const CwiseBinaryOp<internal::scalar_difference_op<Scalar,Scalar>, const Lhs, const Rhs> &src,
+ const internal::assign_op<typename DstXprType::Scalar,Scalar>& /*func*/)
+ {
+ #ifdef EIGEN_SPARSE_ASSIGNMENT_FROM_SPARSE_SUB_DENSE_PLUGIN
+ EIGEN_SPARSE_ASSIGNMENT_FROM_SPARSE_SUB_DENSE_PLUGIN
+ #endif
+
+ // Apply the dense matrix first, then the sparse one.
+ call_assignment_no_alias(dst, -src.rhs(), Func1());
+ call_assignment_no_alias(dst, src.lhs(), add_assign_op<typename DstXprType::Scalar,typename Lhs::Scalar>());
+ }
+};
+
+#define EIGEN_CATCH_ASSIGN_DENSE_OP_SPARSE(ASSIGN_OP,BINOP,ASSIGN_OP2) \
+ template< typename DstXprType, typename Lhs, typename Rhs, typename Scalar> \
+ struct Assignment<DstXprType, CwiseBinaryOp<internal::BINOP<Scalar,Scalar>, const Lhs, const Rhs>, internal::ASSIGN_OP<typename DstXprType::Scalar,Scalar>, \
+ Sparse2Dense, \
+ std::enable_if_t< internal::is_same<typename internal::evaluator_traits<Lhs>::Shape,DenseShape>::value \
+ || internal::is_same<typename internal::evaluator_traits<Rhs>::Shape,DenseShape>::value>> \
+ : assignment_from_dense_op_sparse<DstXprType, internal::ASSIGN_OP<typename DstXprType::Scalar,typename Lhs::Scalar>, internal::ASSIGN_OP2<typename DstXprType::Scalar,typename Rhs::Scalar> > \
+ {}
+
+EIGEN_CATCH_ASSIGN_DENSE_OP_SPARSE(assign_op, scalar_sum_op,add_assign_op);
+EIGEN_CATCH_ASSIGN_DENSE_OP_SPARSE(add_assign_op,scalar_sum_op,add_assign_op);
+EIGEN_CATCH_ASSIGN_DENSE_OP_SPARSE(sub_assign_op,scalar_sum_op,sub_assign_op);
+
+EIGEN_CATCH_ASSIGN_DENSE_OP_SPARSE(assign_op, scalar_difference_op,sub_assign_op);
+EIGEN_CATCH_ASSIGN_DENSE_OP_SPARSE(add_assign_op,scalar_difference_op,sub_assign_op);
+EIGEN_CATCH_ASSIGN_DENSE_OP_SPARSE(sub_assign_op,scalar_difference_op,add_assign_op);
+
+
+// Specialization for "dst = dec.solve(rhs)"
+// NOTE we need to specialize it for Sparse2Sparse to avoid ambiguous specialization error
+template<typename DstXprType, typename DecType, typename RhsType, typename Scalar>
+struct Assignment<DstXprType, Solve<DecType,RhsType>, internal::assign_op<Scalar,Scalar>, Sparse2Sparse>
+{
+ typedef Solve<DecType,RhsType> SrcXprType;
+ static void run(DstXprType &dst, const SrcXprType &src, const internal::assign_op<Scalar,Scalar> &)
+ {
+ Index dstRows = src.rows();
+ Index dstCols = src.cols();
+ if((dst.rows()!=dstRows) || (dst.cols()!=dstCols))
+ dst.resize(dstRows, dstCols);
+
+ src.dec()._solve_impl(src.rhs(), dst);
+ }
+};
+
+struct Diagonal2Sparse {};
+
+template<> struct AssignmentKind<SparseShape,DiagonalShape> { typedef Diagonal2Sparse Kind; };
+
+template< typename DstXprType, typename SrcXprType, typename Functor>
+struct Assignment<DstXprType, SrcXprType, Functor, Diagonal2Sparse>
+{
+ typedef typename DstXprType::StorageIndex StorageIndex;
+ typedef typename DstXprType::Scalar Scalar;
+
+ template<int Options, typename AssignFunc>
+ static void run(SparseMatrix<Scalar,Options,StorageIndex> &dst, const SrcXprType &src, const AssignFunc &func)
+ { dst.assignDiagonal(src.diagonal(), func); }
+
+ template<typename DstDerived>
+ static void run(SparseMatrixBase<DstDerived> &dst, const SrcXprType &src, const internal::assign_op<typename DstXprType::Scalar,typename SrcXprType::Scalar> &/*func*/)
+ { dst.derived().diagonal() = src.diagonal(); }
+
+ template<typename DstDerived>
+ static void run(SparseMatrixBase<DstDerived> &dst, const SrcXprType &src, const internal::add_assign_op<typename DstXprType::Scalar,typename SrcXprType::Scalar> &/*func*/)
+ { dst.derived().diagonal() += src.diagonal(); }
+
+ template<typename DstDerived>
+ static void run(SparseMatrixBase<DstDerived> &dst, const SrcXprType &src, const internal::sub_assign_op<typename DstXprType::Scalar,typename SrcXprType::Scalar> &/*func*/)
+ { dst.derived().diagonal() -= src.diagonal(); }
+};
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_SPARSEASSIGN_H
diff --git a/Eigen/src/SparseCore/SparseBlock.h b/Eigen/src/SparseCore/SparseBlock.h
new file mode 100644
index 0000000..b3fc859
--- /dev/null
+++ b/Eigen/src/SparseCore/SparseBlock.h
@@ -0,0 +1,568 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2014 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_SPARSE_BLOCK_H
+#define EIGEN_SPARSE_BLOCK_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+// Subset of columns or rows
+template<typename XprType, int BlockRows, int BlockCols>
+class BlockImpl<XprType,BlockRows,BlockCols,true,Sparse>
+ : public SparseMatrixBase<Block<XprType,BlockRows,BlockCols,true> >
+{
+ typedef internal::remove_all_t<typename XprType::Nested> MatrixTypeNested_;
+ typedef Block<XprType, BlockRows, BlockCols, true> BlockType;
+public:
+ enum { IsRowMajor = internal::traits<BlockType>::IsRowMajor };
+protected:
+ enum { OuterSize = IsRowMajor ? BlockRows : BlockCols };
+ typedef SparseMatrixBase<BlockType> Base;
+ using Base::convert_index;
+public:
+ EIGEN_SPARSE_PUBLIC_INTERFACE(BlockType)
+
+ inline BlockImpl(XprType& xpr, Index i)
+ : m_matrix(xpr), m_outerStart(convert_index(i)), m_outerSize(OuterSize)
+ {}
+
+ inline BlockImpl(XprType& xpr, Index startRow, Index startCol, Index blockRows, Index blockCols)
+ : m_matrix(xpr), m_outerStart(convert_index(IsRowMajor ? startRow : startCol)), m_outerSize(convert_index(IsRowMajor ? blockRows : blockCols))
+ {}
+
+ EIGEN_STRONG_INLINE Index rows() const { return IsRowMajor ? m_outerSize.value() : m_matrix.rows(); }
+ EIGEN_STRONG_INLINE Index cols() const { return IsRowMajor ? m_matrix.cols() : m_outerSize.value(); }
+
+ Index nonZeros() const
+ {
+ typedef internal::evaluator<XprType> EvaluatorType;
+ EvaluatorType matEval(m_matrix);
+ Index nnz = 0;
+ Index end = m_outerStart + m_outerSize.value();
+ for(Index j=m_outerStart; j<end; ++j)
+ for(typename EvaluatorType::InnerIterator it(matEval, j); it; ++it)
+ ++nnz;
+ return nnz;
+ }
+
+ inline const Scalar coeff(Index row, Index col) const
+ {
+ return m_matrix.coeff(row + (IsRowMajor ? m_outerStart : 0), col + (IsRowMajor ? 0 : m_outerStart));
+ }
+
+ inline const Scalar coeff(Index index) const
+ {
+ return m_matrix.coeff(IsRowMajor ? m_outerStart : index, IsRowMajor ? index : m_outerStart);
+ }
+
+ inline const XprType& nestedExpression() const { return m_matrix; }
+ inline XprType& nestedExpression() { return m_matrix; }
+ Index startRow() const { return IsRowMajor ? m_outerStart : 0; }
+ Index startCol() const { return IsRowMajor ? 0 : m_outerStart; }
+ Index blockRows() const { return IsRowMajor ? m_outerSize.value() : m_matrix.rows(); }
+ Index blockCols() const { return IsRowMajor ? m_matrix.cols() : m_outerSize.value(); }
+
+ protected:
+
+ typename internal::ref_selector<XprType>::non_const_type m_matrix;
+ Index m_outerStart;
+ const internal::variable_if_dynamic<Index, OuterSize> m_outerSize;
+
+ protected:
+ // Disable assignment with clear error message.
+ // Note that simply removing operator= yields compilation errors with ICC+MSVC
+ template<typename T>
+ BlockImpl& operator=(const T&)
+ {
+ EIGEN_STATIC_ASSERT(sizeof(T)==0, THIS_SPARSE_BLOCK_SUBEXPRESSION_IS_READ_ONLY);
+ return *this;
+ }
+};
+
+
+/***************************************************************************
+* specialization for SparseMatrix
+***************************************************************************/
+
+namespace internal {
+
+template<typename SparseMatrixType, int BlockRows, int BlockCols>
+class sparse_matrix_block_impl
+ : public SparseCompressedBase<Block<SparseMatrixType,BlockRows,BlockCols,true> >
+{
+ typedef internal::remove_all_t<typename SparseMatrixType::Nested> MatrixTypeNested_;
+ typedef Block<SparseMatrixType, BlockRows, BlockCols, true> BlockType;
+ typedef SparseCompressedBase<Block<SparseMatrixType,BlockRows,BlockCols,true> > Base;
+ using Base::convert_index;
+public:
+ enum { IsRowMajor = internal::traits<BlockType>::IsRowMajor };
+ EIGEN_SPARSE_PUBLIC_INTERFACE(BlockType)
+protected:
+ typedef typename Base::IndexVector IndexVector;
+ enum { OuterSize = IsRowMajor ? BlockRows : BlockCols };
+public:
+
+ inline sparse_matrix_block_impl(SparseMatrixType& xpr, Index i)
+ : m_matrix(xpr), m_outerStart(convert_index(i)), m_outerSize(OuterSize)
+ {}
+
+ inline sparse_matrix_block_impl(SparseMatrixType& xpr, Index startRow, Index startCol, Index blockRows, Index blockCols)
+ : m_matrix(xpr), m_outerStart(convert_index(IsRowMajor ? startRow : startCol)), m_outerSize(convert_index(IsRowMajor ? blockRows : blockCols))
+ {}
+
+ template<typename OtherDerived>
+ inline BlockType& operator=(const SparseMatrixBase<OtherDerived>& other)
+ {
+ typedef internal::remove_all_t<typename SparseMatrixType::Nested> NestedMatrixType_;
+ NestedMatrixType_& matrix = m_matrix;
+ // This assignment is slow if this vector set is not empty
+ // and/or it is not at the end of the nonzeros of the underlying matrix.
+
+ // 1 - eval to a temporary to avoid transposition and/or aliasing issues
+ Ref<const SparseMatrix<Scalar, IsRowMajor ? RowMajor : ColMajor, StorageIndex> > tmp(other.derived());
+ eigen_internal_assert(tmp.outerSize()==m_outerSize.value());
+
+ // 2 - let's check whether there is enough allocated memory
+ Index nnz = tmp.nonZeros();
+ Index start = m_outerStart==0 ? 0 : m_matrix.outerIndexPtr()[m_outerStart]; // starting position of the current block
+ Index end = m_matrix.outerIndexPtr()[m_outerStart+m_outerSize.value()]; // ending position of the current block
+ Index block_size = end - start; // available room in the current block
+ Index tail_size = m_matrix.outerIndexPtr()[m_matrix.outerSize()] - end;
+
+ Index free_size = m_matrix.isCompressed()
+ ? Index(matrix.data().allocatedSize()) + block_size
+ : block_size;
+
+ Index tmp_start = tmp.outerIndexPtr()[0];
+
+ bool update_trailing_pointers = false;
+ if(nnz>free_size)
+ {
+ // realloc manually to reduce copies
+ typename SparseMatrixType::Storage newdata(m_matrix.data().allocatedSize() - block_size + nnz);
+
+ internal::smart_copy(m_matrix.valuePtr(), m_matrix.valuePtr() + start, newdata.valuePtr());
+ internal::smart_copy(m_matrix.innerIndexPtr(), m_matrix.innerIndexPtr() + start, newdata.indexPtr());
+
+ internal::smart_copy(tmp.valuePtr() + tmp_start, tmp.valuePtr() + tmp_start + nnz, newdata.valuePtr() + start);
+ internal::smart_copy(tmp.innerIndexPtr() + tmp_start, tmp.innerIndexPtr() + tmp_start + nnz, newdata.indexPtr() + start);
+
+ internal::smart_copy(matrix.valuePtr()+end, matrix.valuePtr()+end + tail_size, newdata.valuePtr()+start+nnz);
+ internal::smart_copy(matrix.innerIndexPtr()+end, matrix.innerIndexPtr()+end + tail_size, newdata.indexPtr()+start+nnz);
+
+ newdata.resize(m_matrix.outerIndexPtr()[m_matrix.outerSize()] - block_size + nnz);
+
+ matrix.data().swap(newdata);
+
+ update_trailing_pointers = true;
+ }
+ else
+ {
+ if(m_matrix.isCompressed() && nnz!=block_size)
+ {
+ // no need to realloc, simply copy the tail at its respective position and insert tmp
+ matrix.data().resize(start + nnz + tail_size);
+
+ internal::smart_memmove(matrix.valuePtr()+end, matrix.valuePtr() + end+tail_size, matrix.valuePtr() + start+nnz);
+ internal::smart_memmove(matrix.innerIndexPtr()+end, matrix.innerIndexPtr() + end+tail_size, matrix.innerIndexPtr() + start+nnz);
+
+ update_trailing_pointers = true;
+ }
+
+ internal::smart_copy(tmp.valuePtr() + tmp_start, tmp.valuePtr() + tmp_start + nnz, matrix.valuePtr() + start);
+ internal::smart_copy(tmp.innerIndexPtr() + tmp_start, tmp.innerIndexPtr() + tmp_start + nnz, matrix.innerIndexPtr() + start);
+ }
+
+ // update outer index pointers and innerNonZeros
+ if(IsVectorAtCompileTime)
+ {
+ if(!m_matrix.isCompressed())
+ matrix.innerNonZeroPtr()[m_outerStart] = StorageIndex(nnz);
+ matrix.outerIndexPtr()[m_outerStart] = StorageIndex(start);
+ }
+ else
+ {
+ StorageIndex p = StorageIndex(start);
+ for(Index k=0; k<m_outerSize.value(); ++k)
+ {
+ StorageIndex nnz_k = internal::convert_index<StorageIndex>(tmp.innerVector(k).nonZeros());
+ if(!m_matrix.isCompressed())
+ matrix.innerNonZeroPtr()[m_outerStart+k] = nnz_k;
+ matrix.outerIndexPtr()[m_outerStart+k] = p;
+ p += nnz_k;
+ }
+ }
+
+ if(update_trailing_pointers)
+ {
+ StorageIndex offset = internal::convert_index<StorageIndex>(nnz - block_size);
+ for(Index k = m_outerStart + m_outerSize.value(); k<=matrix.outerSize(); ++k)
+ {
+ matrix.outerIndexPtr()[k] += offset;
+ }
+ }
+
+ return derived();
+ }
+
+ inline BlockType& operator=(const BlockType& other)
+ {
+ return operator=<BlockType>(other);
+ }
+
+ inline const Scalar* valuePtr() const
+ { return m_matrix.valuePtr(); }
+ inline Scalar* valuePtr()
+ { return m_matrix.valuePtr(); }
+
+ inline const StorageIndex* innerIndexPtr() const
+ { return m_matrix.innerIndexPtr(); }
+ inline StorageIndex* innerIndexPtr()
+ { return m_matrix.innerIndexPtr(); }
+
+ inline const StorageIndex* outerIndexPtr() const
+ { return m_matrix.outerIndexPtr() + m_outerStart; }
+ inline StorageIndex* outerIndexPtr()
+ { return m_matrix.outerIndexPtr() + m_outerStart; }
+
+ inline const StorageIndex* innerNonZeroPtr() const
+ { return isCompressed() ? 0 : (m_matrix.innerNonZeroPtr()+m_outerStart); }
+ inline StorageIndex* innerNonZeroPtr()
+ { return isCompressed() ? 0 : (m_matrix.innerNonZeroPtr()+m_outerStart); }
+
+ bool isCompressed() const { return m_matrix.innerNonZeroPtr()==0; }
+
+ inline Scalar& coeffRef(Index row, Index col)
+ {
+ return m_matrix.coeffRef(row + (IsRowMajor ? m_outerStart : 0), col + (IsRowMajor ? 0 : m_outerStart));
+ }
+
+ inline const Scalar coeff(Index row, Index col) const
+ {
+ return m_matrix.coeff(row + (IsRowMajor ? m_outerStart : 0), col + (IsRowMajor ? 0 : m_outerStart));
+ }
+
+ inline const Scalar coeff(Index index) const
+ {
+ return m_matrix.coeff(IsRowMajor ? m_outerStart : index, IsRowMajor ? index : m_outerStart);
+ }
+
+ const Scalar& lastCoeff() const
+ {
+ EIGEN_STATIC_ASSERT_VECTOR_ONLY(sparse_matrix_block_impl);
+ eigen_assert(Base::nonZeros()>0);
+ if(m_matrix.isCompressed())
+ return m_matrix.valuePtr()[m_matrix.outerIndexPtr()[m_outerStart+1]-1];
+ else
+ return m_matrix.valuePtr()[m_matrix.outerIndexPtr()[m_outerStart]+m_matrix.innerNonZeroPtr()[m_outerStart]-1];
+ }
+
+ EIGEN_STRONG_INLINE Index rows() const { return IsRowMajor ? m_outerSize.value() : m_matrix.rows(); }
+ EIGEN_STRONG_INLINE Index cols() const { return IsRowMajor ? m_matrix.cols() : m_outerSize.value(); }
+
+ inline const SparseMatrixType& nestedExpression() const { return m_matrix; }
+ inline SparseMatrixType& nestedExpression() { return m_matrix; }
+ Index startRow() const { return IsRowMajor ? m_outerStart : 0; }
+ Index startCol() const { return IsRowMajor ? 0 : m_outerStart; }
+ Index blockRows() const { return IsRowMajor ? m_outerSize.value() : m_matrix.rows(); }
+ Index blockCols() const { return IsRowMajor ? m_matrix.cols() : m_outerSize.value(); }
+
+ protected:
+
+ typename internal::ref_selector<SparseMatrixType>::non_const_type m_matrix;
+ Index m_outerStart;
+ const internal::variable_if_dynamic<Index, OuterSize> m_outerSize;
+
+};
+
+} // namespace internal
+
+template<typename Scalar_, int Options_, typename StorageIndex_, int BlockRows, int BlockCols>
+class BlockImpl<SparseMatrix<Scalar_, Options_, StorageIndex_>,BlockRows,BlockCols,true,Sparse>
+ : public internal::sparse_matrix_block_impl<SparseMatrix<Scalar_, Options_, StorageIndex_>,BlockRows,BlockCols>
+{
+public:
+ typedef StorageIndex_ StorageIndex;
+ typedef SparseMatrix<Scalar_, Options_, StorageIndex_> SparseMatrixType;
+ typedef internal::sparse_matrix_block_impl<SparseMatrixType,BlockRows,BlockCols> Base;
+ inline BlockImpl(SparseMatrixType& xpr, Index i)
+ : Base(xpr, i)
+ {}
+
+ inline BlockImpl(SparseMatrixType& xpr, Index startRow, Index startCol, Index blockRows, Index blockCols)
+ : Base(xpr, startRow, startCol, blockRows, blockCols)
+ {}
+
+ using Base::operator=;
+};
+
+template<typename Scalar_, int Options_, typename StorageIndex_, int BlockRows, int BlockCols>
+class BlockImpl<const SparseMatrix<Scalar_, Options_, StorageIndex_>,BlockRows,BlockCols,true,Sparse>
+ : public internal::sparse_matrix_block_impl<const SparseMatrix<Scalar_, Options_, StorageIndex_>,BlockRows,BlockCols>
+{
+public:
+ typedef StorageIndex_ StorageIndex;
+ typedef const SparseMatrix<Scalar_, Options_, StorageIndex_> SparseMatrixType;
+ typedef internal::sparse_matrix_block_impl<SparseMatrixType,BlockRows,BlockCols> Base;
+ inline BlockImpl(SparseMatrixType& xpr, Index i)
+ : Base(xpr, i)
+ {}
+
+ inline BlockImpl(SparseMatrixType& xpr, Index startRow, Index startCol, Index blockRows, Index blockCols)
+ : Base(xpr, startRow, startCol, blockRows, blockCols)
+ {}
+
+ using Base::operator=;
+private:
+ template<typename Derived> BlockImpl(const SparseMatrixBase<Derived>& xpr, Index i);
+ template<typename Derived> BlockImpl(const SparseMatrixBase<Derived>& xpr);
+};
+
+//----------
+
+/** Generic implementation of sparse Block expression.
+ * Real-only.
+ */
+template<typename XprType, int BlockRows, int BlockCols, bool InnerPanel>
+class BlockImpl<XprType,BlockRows,BlockCols,InnerPanel,Sparse>
+ : public SparseMatrixBase<Block<XprType,BlockRows,BlockCols,InnerPanel> >, internal::no_assignment_operator
+{
+ typedef Block<XprType, BlockRows, BlockCols, InnerPanel> BlockType;
+ typedef SparseMatrixBase<BlockType> Base;
+ using Base::convert_index;
+public:
+ enum { IsRowMajor = internal::traits<BlockType>::IsRowMajor };
+ EIGEN_SPARSE_PUBLIC_INTERFACE(BlockType)
+
+ typedef internal::remove_all_t<typename XprType::Nested> MatrixTypeNested_;
+
+ /** Column or Row constructor
+ */
+ inline BlockImpl(XprType& xpr, Index i)
+ : m_matrix(xpr),
+ m_startRow( (BlockRows==1) && (BlockCols==XprType::ColsAtCompileTime) ? convert_index(i) : 0),
+ m_startCol( (BlockRows==XprType::RowsAtCompileTime) && (BlockCols==1) ? convert_index(i) : 0),
+ m_blockRows(BlockRows==1 ? 1 : xpr.rows()),
+ m_blockCols(BlockCols==1 ? 1 : xpr.cols())
+ {}
+
+ /** Dynamic-size constructor
+ */
+ inline BlockImpl(XprType& xpr, Index startRow, Index startCol, Index blockRows, Index blockCols)
+ : m_matrix(xpr), m_startRow(convert_index(startRow)), m_startCol(convert_index(startCol)), m_blockRows(convert_index(blockRows)), m_blockCols(convert_index(blockCols))
+ {}
+
+ inline Index rows() const { return m_blockRows.value(); }
+ inline Index cols() const { return m_blockCols.value(); }
+
+ inline Scalar& coeffRef(Index row, Index col)
+ {
+ return m_matrix.coeffRef(row + m_startRow.value(), col + m_startCol.value());
+ }
+
+ inline const Scalar coeff(Index row, Index col) const
+ {
+ return m_matrix.coeff(row + m_startRow.value(), col + m_startCol.value());
+ }
+
+ inline Scalar& coeffRef(Index index)
+ {
+ return m_matrix.coeffRef(m_startRow.value() + (RowsAtCompileTime == 1 ? 0 : index),
+ m_startCol.value() + (RowsAtCompileTime == 1 ? index : 0));
+ }
+
+ inline const Scalar coeff(Index index) const
+ {
+ return m_matrix.coeff(m_startRow.value() + (RowsAtCompileTime == 1 ? 0 : index),
+ m_startCol.value() + (RowsAtCompileTime == 1 ? index : 0));
+ }
+
+ inline const XprType& nestedExpression() const { return m_matrix; }
+ inline XprType& nestedExpression() { return m_matrix; }
+ Index startRow() const { return m_startRow.value(); }
+ Index startCol() const { return m_startCol.value(); }
+ Index blockRows() const { return m_blockRows.value(); }
+ Index blockCols() const { return m_blockCols.value(); }
+
+ protected:
+// friend class internal::GenericSparseBlockInnerIteratorImpl<XprType,BlockRows,BlockCols,InnerPanel>;
+ friend struct internal::unary_evaluator<Block<XprType,BlockRows,BlockCols,InnerPanel>, internal::IteratorBased, Scalar >;
+
+ Index nonZeros() const { return Dynamic; }
+
+ typename internal::ref_selector<XprType>::non_const_type m_matrix;
+ const internal::variable_if_dynamic<Index, XprType::RowsAtCompileTime == 1 ? 0 : Dynamic> m_startRow;
+ const internal::variable_if_dynamic<Index, XprType::ColsAtCompileTime == 1 ? 0 : Dynamic> m_startCol;
+ const internal::variable_if_dynamic<Index, RowsAtCompileTime> m_blockRows;
+ const internal::variable_if_dynamic<Index, ColsAtCompileTime> m_blockCols;
+
+ protected:
+ // Disable assignment with clear error message.
+ // Note that simply removing operator= yields compilation errors with ICC+MSVC
+ template<typename T>
+ BlockImpl& operator=(const T&)
+ {
+ EIGEN_STATIC_ASSERT(sizeof(T)==0, THIS_SPARSE_BLOCK_SUBEXPRESSION_IS_READ_ONLY);
+ return *this;
+ }
+
+};
+
+namespace internal {
+
+template<typename ArgType, int BlockRows, int BlockCols, bool InnerPanel>
+struct unary_evaluator<Block<ArgType,BlockRows,BlockCols,InnerPanel>, IteratorBased >
+ : public evaluator_base<Block<ArgType,BlockRows,BlockCols,InnerPanel> >
+{
+ class InnerVectorInnerIterator;
+ class OuterVectorInnerIterator;
+ public:
+ typedef Block<ArgType,BlockRows,BlockCols,InnerPanel> XprType;
+ typedef typename XprType::StorageIndex StorageIndex;
+ typedef typename XprType::Scalar Scalar;
+
+ enum {
+ IsRowMajor = XprType::IsRowMajor,
+ OuterVector = (BlockCols == 1 && ArgType::IsRowMajor) || (BlockRows == 1 && !ArgType::IsRowMajor),
+ CoeffReadCost = evaluator<ArgType>::CoeffReadCost,
+ Flags = XprType::Flags
+ };
+
+ typedef std::conditional_t<OuterVector,OuterVectorInnerIterator,InnerVectorInnerIterator> InnerIterator;
+
+ explicit unary_evaluator(const XprType& op)
+ : m_argImpl(op.nestedExpression()), m_block(op)
+ {}
+
+ inline Index nonZerosEstimate() const {
+ const Index nnz = m_block.nonZeros();
+ if(nnz < 0) {
+ // Scale the non-zero estimate for the underlying expression linearly with block size.
+ // Return zero if the underlying block is empty.
+ const Index nested_sz = m_block.nestedExpression().size();
+ return nested_sz == 0 ? 0 : m_argImpl.nonZerosEstimate() * m_block.size() / nested_sz;
+ }
+ return nnz;
+ }
+
+ protected:
+ typedef typename evaluator<ArgType>::InnerIterator EvalIterator;
+
+ evaluator<ArgType> m_argImpl;
+ const XprType &m_block;
+};
+
+template<typename ArgType, int BlockRows, int BlockCols, bool InnerPanel>
+class unary_evaluator<Block<ArgType,BlockRows,BlockCols,InnerPanel>, IteratorBased>::InnerVectorInnerIterator
+ : public EvalIterator
+{
+ // NOTE MSVC fails to compile if we don't explicitly "import" IsRowMajor from unary_evaluator
+ // because the base class EvalIterator has a private IsRowMajor enum too. (bug #1786)
+ // NOTE We cannot call it IsRowMajor because it would shadow unary_evaluator::IsRowMajor
+ enum { XprIsRowMajor = unary_evaluator::IsRowMajor };
+ const XprType& m_block;
+ Index m_end;
+public:
+
+ EIGEN_STRONG_INLINE InnerVectorInnerIterator(const unary_evaluator& aEval, Index outer)
+ : EvalIterator(aEval.m_argImpl, outer + (XprIsRowMajor ? aEval.m_block.startRow() : aEval.m_block.startCol())),
+ m_block(aEval.m_block),
+ m_end(XprIsRowMajor ? aEval.m_block.startCol()+aEval.m_block.blockCols() : aEval.m_block.startRow()+aEval.m_block.blockRows())
+ {
+ while( (EvalIterator::operator bool()) && (EvalIterator::index() < (XprIsRowMajor ? m_block.startCol() : m_block.startRow())) )
+ EvalIterator::operator++();
+ }
+
+ inline StorageIndex index() const { return EvalIterator::index() - convert_index<StorageIndex>(XprIsRowMajor ? m_block.startCol() : m_block.startRow()); }
+ inline Index outer() const { return EvalIterator::outer() - (XprIsRowMajor ? m_block.startRow() : m_block.startCol()); }
+ inline Index row() const { return EvalIterator::row() - m_block.startRow(); }
+ inline Index col() const { return EvalIterator::col() - m_block.startCol(); }
+
+ inline operator bool() const { return EvalIterator::operator bool() && EvalIterator::index() < m_end; }
+};
+
+template<typename ArgType, int BlockRows, int BlockCols, bool InnerPanel>
+class unary_evaluator<Block<ArgType,BlockRows,BlockCols,InnerPanel>, IteratorBased>::OuterVectorInnerIterator
+{
+ // NOTE see above
+ enum { XprIsRowMajor = unary_evaluator::IsRowMajor };
+ const unary_evaluator& m_eval;
+ Index m_outerPos;
+ const Index m_innerIndex;
+ Index m_end;
+ EvalIterator m_it;
+public:
+
+ EIGEN_STRONG_INLINE OuterVectorInnerIterator(const unary_evaluator& aEval, Index outer)
+ : m_eval(aEval),
+ m_outerPos( (XprIsRowMajor ? aEval.m_block.startCol() : aEval.m_block.startRow()) ),
+ m_innerIndex(XprIsRowMajor ? aEval.m_block.startRow() : aEval.m_block.startCol()),
+ m_end(XprIsRowMajor ? aEval.m_block.startCol()+aEval.m_block.blockCols() : aEval.m_block.startRow()+aEval.m_block.blockRows()),
+ m_it(m_eval.m_argImpl, m_outerPos)
+ {
+ EIGEN_UNUSED_VARIABLE(outer);
+ eigen_assert(outer==0);
+
+ while(m_it && m_it.index() < m_innerIndex) ++m_it;
+ if((!m_it) || (m_it.index()!=m_innerIndex))
+ ++(*this);
+ }
+
+ inline StorageIndex index() const { return convert_index<StorageIndex>(m_outerPos - (XprIsRowMajor ? m_eval.m_block.startCol() : m_eval.m_block.startRow())); }
+ inline Index outer() const { return 0; }
+ inline Index row() const { return XprIsRowMajor ? 0 : index(); }
+ inline Index col() const { return XprIsRowMajor ? index() : 0; }
+
+ inline Scalar value() const { return m_it.value(); }
+ inline Scalar& valueRef() { return m_it.valueRef(); }
+
+ inline OuterVectorInnerIterator& operator++()
+ {
+ // search next non-zero entry
+ while(++m_outerPos<m_end)
+ {
+ // Restart iterator at the next inner-vector:
+ internal::destroy_at(&m_it);
+ internal::construct_at(&m_it, m_eval.m_argImpl, m_outerPos);
+ // search for the key m_innerIndex in the current outer-vector
+ while(m_it && m_it.index() < m_innerIndex) ++m_it;
+ if(m_it && m_it.index()==m_innerIndex) break;
+ }
+ return *this;
+ }
+
+ inline operator bool() const { return m_outerPos < m_end; }
+};
+
+template<typename Scalar_, int Options_, typename StorageIndex_, int BlockRows, int BlockCols>
+struct unary_evaluator<Block<SparseMatrix<Scalar_, Options_, StorageIndex_>,BlockRows,BlockCols,true>, IteratorBased>
+ : evaluator<SparseCompressedBase<Block<SparseMatrix<Scalar_, Options_, StorageIndex_>,BlockRows,BlockCols,true> > >
+{
+ typedef Block<SparseMatrix<Scalar_, Options_, StorageIndex_>,BlockRows,BlockCols,true> XprType;
+ typedef evaluator<SparseCompressedBase<XprType> > Base;
+ explicit unary_evaluator(const XprType &xpr) : Base(xpr) {}
+};
+
+template<typename Scalar_, int Options_, typename StorageIndex_, int BlockRows, int BlockCols>
+struct unary_evaluator<Block<const SparseMatrix<Scalar_, Options_, StorageIndex_>,BlockRows,BlockCols,true>, IteratorBased>
+ : evaluator<SparseCompressedBase<Block<const SparseMatrix<Scalar_, Options_, StorageIndex_>,BlockRows,BlockCols,true> > >
+{
+ typedef Block<const SparseMatrix<Scalar_, Options_, StorageIndex_>,BlockRows,BlockCols,true> XprType;
+ typedef evaluator<SparseCompressedBase<XprType> > Base;
+ explicit unary_evaluator(const XprType &xpr) : Base(xpr) {}
+};
+
+} // end namespace internal
+
+
+} // end namespace Eigen
+
+#endif // EIGEN_SPARSE_BLOCK_H
diff --git a/Eigen/src/SparseCore/SparseColEtree.h b/Eigen/src/SparseCore/SparseColEtree.h
new file mode 100644
index 0000000..ff32458
--- /dev/null
+++ b/Eigen/src/SparseCore/SparseColEtree.h
@@ -0,0 +1,208 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2012 Désiré Nuentsa-Wakam <desire.nuentsa_wakam@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+
+/*
+
+ * NOTE: This file is the modified version of sp_coletree.c file in SuperLU
+
+ * -- SuperLU routine (version 3.1) --
+ * Univ. of California Berkeley, Xerox Palo Alto Research Center,
+ * and Lawrence Berkeley National Lab.
+ * August 1, 2008
+ *
+ * Copyright (c) 1994 by Xerox Corporation. All rights reserved.
+ *
+ * THIS MATERIAL IS PROVIDED AS IS, WITH ABSOLUTELY NO WARRANTY
+ * EXPRESSED OR IMPLIED. ANY USE IS AT YOUR OWN RISK.
+ *
+ * Permission is hereby granted to use or copy this program for any
+ * purpose, provided the above notices are retained on all copies.
+ * Permission to modify the code and to distribute modified code is
+ * granted, provided the above notices are retained, and a notice that
+ * the code was modified is included with the above copyright notice.
+ */
+#ifndef SPARSE_COLETREE_H
+#define SPARSE_COLETREE_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+
+/** Find the root of the tree/set containing the vertex i : Use Path halving */
+template<typename Index, typename IndexVector>
+Index etree_find (Index i, IndexVector& pp)
+{
+ Index p = pp(i); // Parent
+ Index gp = pp(p); // Grand parent
+ while (gp != p)
+ {
+ pp(i) = gp; // Parent pointer on find path is changed to former grand parent
+ i = gp;
+ p = pp(i);
+ gp = pp(p);
+ }
+ return p;
+}
+
+/** Compute the column elimination tree of a sparse matrix
+ * \param mat The matrix in column-major format.
+ * \param parent The elimination tree
+ * \param firstRowElt The column index of the first element in each row
+ * \param perm The permutation to apply to the column of \b mat
+ */
+template <typename MatrixType, typename IndexVector>
+int coletree(const MatrixType& mat, IndexVector& parent, IndexVector& firstRowElt, typename MatrixType::StorageIndex *perm=0)
+{
+ typedef typename MatrixType::StorageIndex StorageIndex;
+ StorageIndex nc = convert_index<StorageIndex>(mat.cols()); // Number of columns
+ StorageIndex m = convert_index<StorageIndex>(mat.rows());
+ StorageIndex diagSize = (std::min)(nc,m);
+ IndexVector root(nc); // root of subtree of etree
+ root.setZero();
+ IndexVector pp(nc); // disjoint sets
+ pp.setZero(); // Initialize disjoint sets
+ parent.resize(mat.cols());
+ //Compute first nonzero column in each row
+ firstRowElt.resize(m);
+ firstRowElt.setConstant(nc);
+ firstRowElt.segment(0, diagSize).setLinSpaced(diagSize, 0, diagSize-1);
+ bool found_diag;
+ for (StorageIndex col = 0; col < nc; col++)
+ {
+ StorageIndex pcol = col;
+ if(perm) pcol = perm[col];
+ for (typename MatrixType::InnerIterator it(mat, pcol); it; ++it)
+ {
+ Index row = it.row();
+ firstRowElt(row) = (std::min)(firstRowElt(row), col);
+ }
+ }
+ /* Compute etree by Liu's algorithm for symmetric matrices,
+ except use (firstRowElt[r],c) in place of an edge (r,c) of A.
+ Thus each row clique in A'*A is replaced by a star
+ centered at its first vertex, which has the same fill. */
+ StorageIndex rset, cset, rroot;
+ for (StorageIndex col = 0; col < nc; col++)
+ {
+ found_diag = col>=m;
+ pp(col) = col;
+ cset = col;
+ root(cset) = col;
+ parent(col) = nc;
+ /* The diagonal element is treated here even if it does not exist in the matrix
+ * hence the loop is executed once more */
+ StorageIndex pcol = col;
+ if(perm) pcol = perm[col];
+ for (typename MatrixType::InnerIterator it(mat, pcol); it||!found_diag; ++it)
+ { // A sequence of interleaved find and union is performed
+ Index i = col;
+ if(it) i = it.index();
+ if (i == col) found_diag = true;
+
+ StorageIndex row = firstRowElt(i);
+ if (row >= col) continue;
+ rset = internal::etree_find(row, pp); // Find the name of the set containing row
+ rroot = root(rset);
+ if (rroot != col)
+ {
+ parent(rroot) = col;
+ pp(cset) = rset;
+ cset = rset;
+ root(cset) = col;
+ }
+ }
+ }
+ return 0;
+}
+
+/**
+ * Depth-first search from vertex n. No recursion.
+ * This routine was contributed by Cédric Doucet, CEDRAT Group, Meylan, France.
+*/
+template <typename IndexVector>
+void nr_etdfs (typename IndexVector::Scalar n, IndexVector& parent, IndexVector& first_kid, IndexVector& next_kid, IndexVector& post, typename IndexVector::Scalar postnum)
+{
+ typedef typename IndexVector::Scalar StorageIndex;
+ StorageIndex current = n, first, next;
+ while (postnum != n)
+ {
+ // No kid for the current node
+ first = first_kid(current);
+
+ // no kid for the current node
+ if (first == -1)
+ {
+ // Numbering this node because it has no kid
+ post(current) = postnum++;
+
+ // looking for the next kid
+ next = next_kid(current);
+ while (next == -1)
+ {
+ // No more kids : back to the parent node
+ current = parent(current);
+ // numbering the parent node
+ post(current) = postnum++;
+
+ // Get the next kid
+ next = next_kid(current);
+ }
+ // stopping criterion
+ if (postnum == n+1) return;
+
+ // Updating current node
+ current = next;
+ }
+ else
+ {
+ current = first;
+ }
+ }
+}
+
+
+/**
+ * \brief Post order a tree
+ * \param n the number of nodes
+ * \param parent Input tree
+ * \param post postordered tree
+ */
+template <typename IndexVector>
+void treePostorder(typename IndexVector::Scalar n, IndexVector& parent, IndexVector& post)
+{
+ typedef typename IndexVector::Scalar StorageIndex;
+ IndexVector first_kid, next_kid; // Linked list of children
+ StorageIndex postnum;
+ // Allocate storage for working arrays and results
+ first_kid.resize(n+1);
+ next_kid.setZero(n+1);
+ post.setZero(n+1);
+
+ // Set up structure describing children
+ first_kid.setConstant(-1);
+ for (StorageIndex v = n-1; v >= 0; v--)
+ {
+ StorageIndex dad = parent(v);
+ next_kid(v) = first_kid(dad);
+ first_kid(dad) = v;
+ }
+
+ // Depth-first search from dummy root vertex #n
+ postnum = 0;
+ internal::nr_etdfs(n, parent, first_kid, next_kid, post, postnum);
+}
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // SPARSE_COLETREE_H
diff --git a/Eigen/src/SparseCore/SparseCompressedBase.h b/Eigen/src/SparseCore/SparseCompressedBase.h
new file mode 100644
index 0000000..ede5766
--- /dev/null
+++ b/Eigen/src/SparseCore/SparseCompressedBase.h
@@ -0,0 +1,371 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2015 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_SPARSE_COMPRESSED_BASE_H
+#define EIGEN_SPARSE_COMPRESSED_BASE_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+template<typename Derived> class SparseCompressedBase;
+
+namespace internal {
+
+template<typename Derived>
+struct traits<SparseCompressedBase<Derived> > : traits<Derived>
+{};
+
+} // end namespace internal
+
+/** \ingroup SparseCore_Module
+ * \class SparseCompressedBase
+ * \brief Common base class for sparse [compressed]-{row|column}-storage format.
+ *
+ * This class defines the common interface for all derived classes implementing the compressed sparse storage format, such as:
+ * - SparseMatrix
+ * - Ref<SparseMatrixType,Options>
+ * - Map<SparseMatrixType>
+ *
+ */
+template<typename Derived>
+class SparseCompressedBase
+ : public SparseMatrixBase<Derived>
+{
+ public:
+ typedef SparseMatrixBase<Derived> Base;
+ EIGEN_SPARSE_PUBLIC_INTERFACE(SparseCompressedBase)
+ using Base::operator=;
+ using Base::IsRowMajor;
+
+ class InnerIterator;
+ class ReverseInnerIterator;
+
+ protected:
+ typedef typename Base::IndexVector IndexVector;
+ Eigen::Map<IndexVector> innerNonZeros() { return Eigen::Map<IndexVector>(innerNonZeroPtr(), isCompressed()?0:derived().outerSize()); }
+ const Eigen::Map<const IndexVector> innerNonZeros() const { return Eigen::Map<const IndexVector>(innerNonZeroPtr(), isCompressed()?0:derived().outerSize()); }
+
+ public:
+
+ /** \returns the number of non zero coefficients */
+ inline Index nonZeros() const
+ {
+ if(Derived::IsVectorAtCompileTime && outerIndexPtr()==0)
+ return derived().nonZeros();
+ else if(isCompressed())
+ return outerIndexPtr()[derived().outerSize()]-outerIndexPtr()[0];
+ else if(derived().outerSize()==0)
+ return 0;
+ else
+ return innerNonZeros().sum();
+ }
+
+ /** \returns a const pointer to the array of values.
+ * This function is aimed at interoperability with other libraries.
+ * \sa innerIndexPtr(), outerIndexPtr() */
+ inline const Scalar* valuePtr() const { return derived().valuePtr(); }
+ /** \returns a non-const pointer to the array of values.
+ * This function is aimed at interoperability with other libraries.
+ * \sa innerIndexPtr(), outerIndexPtr() */
+ inline Scalar* valuePtr() { return derived().valuePtr(); }
+
+ /** \returns a const pointer to the array of inner indices.
+ * This function is aimed at interoperability with other libraries.
+ * \sa valuePtr(), outerIndexPtr() */
+ inline const StorageIndex* innerIndexPtr() const { return derived().innerIndexPtr(); }
+ /** \returns a non-const pointer to the array of inner indices.
+ * This function is aimed at interoperability with other libraries.
+ * \sa valuePtr(), outerIndexPtr() */
+ inline StorageIndex* innerIndexPtr() { return derived().innerIndexPtr(); }
+
+ /** \returns a const pointer to the array of the starting positions of the inner vectors.
+ * This function is aimed at interoperability with other libraries.
+ * \warning it returns the null pointer 0 for SparseVector
+ * \sa valuePtr(), innerIndexPtr() */
+ inline const StorageIndex* outerIndexPtr() const { return derived().outerIndexPtr(); }
+ /** \returns a non-const pointer to the array of the starting positions of the inner vectors.
+ * This function is aimed at interoperability with other libraries.
+ * \warning it returns the null pointer 0 for SparseVector
+ * \sa valuePtr(), innerIndexPtr() */
+ inline StorageIndex* outerIndexPtr() { return derived().outerIndexPtr(); }
+
+ /** \returns a const pointer to the array of the number of non zeros of the inner vectors.
+ * This function is aimed at interoperability with other libraries.
+ * \warning it returns the null pointer 0 in compressed mode */
+ inline const StorageIndex* innerNonZeroPtr() const { return derived().innerNonZeroPtr(); }
+ /** \returns a non-const pointer to the array of the number of non zeros of the inner vectors.
+ * This function is aimed at interoperability with other libraries.
+ * \warning it returns the null pointer 0 in compressed mode */
+ inline StorageIndex* innerNonZeroPtr() { return derived().innerNonZeroPtr(); }
+
+ /** \returns whether \c *this is in compressed form. */
+ inline bool isCompressed() const { return innerNonZeroPtr()==0; }
+
+ /** \returns a read-only view of the stored coefficients as a 1D array expression.
+ *
+ * \warning this method is for \b compressed \b storage \b only, and it will trigger an assertion otherwise.
+ *
+ * \sa valuePtr(), isCompressed() */
+ const Map<const Array<Scalar,Dynamic,1> > coeffs() const { eigen_assert(isCompressed()); return Array<Scalar,Dynamic,1>::Map(valuePtr(),nonZeros()); }
+
+ /** \returns a read-write view of the stored coefficients as a 1D array expression
+ *
+ * \warning this method is for \b compressed \b storage \b only, and it will trigger an assertion otherwise.
+ *
+ * Here is an example:
+ * \include SparseMatrix_coeffs.cpp
+ * and the output is:
+ * \include SparseMatrix_coeffs.out
+ *
+ * \sa valuePtr(), isCompressed() */
+ Map<Array<Scalar,Dynamic,1> > coeffs() { eigen_assert(isCompressed()); return Array<Scalar,Dynamic,1>::Map(valuePtr(),nonZeros()); }
+
+ protected:
+ /** Default constructor. Do nothing. */
+ SparseCompressedBase() {}
+
+ /** \internal return the index of the coeff at (row,col) or just before if it does not exist.
+ * This is an analogue of std::lower_bound.
+ */
+ internal::LowerBoundIndex lower_bound(Index row, Index col) const
+ {
+ eigen_internal_assert(row>=0 && row<this->rows() && col>=0 && col<this->cols());
+
+ const Index outer = Derived::IsRowMajor ? row : col;
+ const Index inner = Derived::IsRowMajor ? col : row;
+
+ Index start = this->outerIndexPtr()[outer];
+ Index end = this->isCompressed() ? this->outerIndexPtr()[outer+1] : this->outerIndexPtr()[outer] + this->innerNonZeroPtr()[outer];
+ eigen_assert(end>=start && "you are using a non finalized sparse matrix or written coefficient does not exist");
+ internal::LowerBoundIndex p;
+ p.value = std::lower_bound(this->innerIndexPtr()+start, this->innerIndexPtr()+end,inner) - this->innerIndexPtr();
+ p.found = (p.value<end) && (this->innerIndexPtr()[p.value]==inner);
+ return p;
+ }
+
+ friend struct internal::evaluator<SparseCompressedBase<Derived> >;
+
+ private:
+ template<typename OtherDerived> explicit SparseCompressedBase(const SparseCompressedBase<OtherDerived>&);
+};
+
+template<typename Derived>
+class SparseCompressedBase<Derived>::InnerIterator
+{
+ public:
+ InnerIterator()
+ : m_values(0), m_indices(0), m_outer(0), m_id(0), m_end(0)
+ {}
+
+ InnerIterator(const InnerIterator& other)
+ : m_values(other.m_values), m_indices(other.m_indices), m_outer(other.m_outer), m_id(other.m_id), m_end(other.m_end)
+ {}
+
+ InnerIterator& operator=(const InnerIterator& other)
+ {
+ m_values = other.m_values;
+ m_indices = other.m_indices;
+ const_cast<OuterType&>(m_outer).setValue(other.m_outer.value());
+ m_id = other.m_id;
+ m_end = other.m_end;
+ return *this;
+ }
+
+ InnerIterator(const SparseCompressedBase& mat, Index outer)
+ : m_values(mat.valuePtr()), m_indices(mat.innerIndexPtr()), m_outer(outer)
+ {
+ if(Derived::IsVectorAtCompileTime && mat.outerIndexPtr()==0)
+ {
+ m_id = 0;
+ m_end = mat.nonZeros();
+ }
+ else
+ {
+ m_id = mat.outerIndexPtr()[outer];
+ if(mat.isCompressed())
+ m_end = mat.outerIndexPtr()[outer+1];
+ else
+ m_end = m_id + mat.innerNonZeroPtr()[outer];
+ }
+ }
+
+ explicit InnerIterator(const SparseCompressedBase& mat) : InnerIterator(mat, Index(0))
+ {
+ EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived);
+ }
+
+ explicit InnerIterator(const internal::CompressedStorage<Scalar,StorageIndex>& data)
+ : m_values(data.valuePtr()), m_indices(data.indexPtr()), m_outer(0), m_id(0), m_end(data.size())
+ {
+ EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived);
+ }
+
+ inline InnerIterator& operator++() { m_id++; return *this; }
+ inline InnerIterator& operator+=(Index i) { m_id += i ; return *this; }
+
+ inline InnerIterator operator+(Index i)
+ {
+ InnerIterator result = *this;
+ result += i;
+ return result;
+ }
+
+ inline const Scalar& value() const { return m_values[m_id]; }
+ inline Scalar& valueRef() { return const_cast<Scalar&>(m_values[m_id]); }
+
+ inline StorageIndex index() const { return m_indices[m_id]; }
+ inline Index outer() const { return m_outer.value(); }
+ inline Index row() const { return IsRowMajor ? m_outer.value() : index(); }
+ inline Index col() const { return IsRowMajor ? index() : m_outer.value(); }
+
+ inline operator bool() const { return (m_id < m_end); }
+
+ protected:
+ const Scalar* m_values;
+ const StorageIndex* m_indices;
+ typedef internal::variable_if_dynamic<Index,Derived::IsVectorAtCompileTime?0:Dynamic> OuterType;
+ const OuterType m_outer;
+ Index m_id;
+ Index m_end;
+ private:
+ // If you get here, then you're not using the right InnerIterator type, e.g.:
+ // SparseMatrix<double,RowMajor> A;
+ // SparseMatrix<double>::InnerIterator it(A,0);
+ template<typename T> InnerIterator(const SparseMatrixBase<T>&, Index outer);
+};
+
+template<typename Derived>
+class SparseCompressedBase<Derived>::ReverseInnerIterator
+{
+ public:
+ ReverseInnerIterator(const SparseCompressedBase& mat, Index outer)
+ : m_values(mat.valuePtr()), m_indices(mat.innerIndexPtr()), m_outer(outer)
+ {
+ if(Derived::IsVectorAtCompileTime && mat.outerIndexPtr()==0)
+ {
+ m_start = 0;
+ m_id = mat.nonZeros();
+ }
+ else
+ {
+ m_start = mat.outerIndexPtr()[outer];
+ if(mat.isCompressed())
+ m_id = mat.outerIndexPtr()[outer+1];
+ else
+ m_id = m_start + mat.innerNonZeroPtr()[outer];
+ }
+ }
+
+ explicit ReverseInnerIterator(const SparseCompressedBase& mat)
+ : m_values(mat.valuePtr()), m_indices(mat.innerIndexPtr()), m_outer(0), m_start(0), m_id(mat.nonZeros())
+ {
+ EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived);
+ }
+
+ explicit ReverseInnerIterator(const internal::CompressedStorage<Scalar,StorageIndex>& data)
+ : m_values(data.valuePtr()), m_indices(data.indexPtr()), m_outer(0), m_start(0), m_id(data.size())
+ {
+ EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived);
+ }
+
+ inline ReverseInnerIterator& operator--() { --m_id; return *this; }
+ inline ReverseInnerIterator& operator-=(Index i) { m_id -= i; return *this; }
+
+ inline ReverseInnerIterator operator-(Index i)
+ {
+ ReverseInnerIterator result = *this;
+ result -= i;
+ return result;
+ }
+
+ inline const Scalar& value() const { return m_values[m_id-1]; }
+ inline Scalar& valueRef() { return const_cast<Scalar&>(m_values[m_id-1]); }
+
+ inline StorageIndex index() const { return m_indices[m_id-1]; }
+ inline Index outer() const { return m_outer.value(); }
+ inline Index row() const { return IsRowMajor ? m_outer.value() : index(); }
+ inline Index col() const { return IsRowMajor ? index() : m_outer.value(); }
+
+ inline operator bool() const { return (m_id > m_start); }
+
+ protected:
+ const Scalar* m_values;
+ const StorageIndex* m_indices;
+ typedef internal::variable_if_dynamic<Index,Derived::IsVectorAtCompileTime?0:Dynamic> OuterType;
+ const OuterType m_outer;
+ Index m_start;
+ Index m_id;
+};
+
+namespace internal {
+
+template<typename Derived>
+struct evaluator<SparseCompressedBase<Derived> >
+ : evaluator_base<Derived>
+{
+ typedef typename Derived::Scalar Scalar;
+ typedef typename Derived::InnerIterator InnerIterator;
+
+ enum {
+ CoeffReadCost = NumTraits<Scalar>::ReadCost,
+ Flags = Derived::Flags
+ };
+
+ evaluator() : m_matrix(0), m_zero(0)
+ {
+ EIGEN_INTERNAL_CHECK_COST_VALUE(CoeffReadCost);
+ }
+ explicit evaluator(const Derived &mat) : m_matrix(&mat), m_zero(0)
+ {
+ EIGEN_INTERNAL_CHECK_COST_VALUE(CoeffReadCost);
+ }
+
+ inline Index nonZerosEstimate() const {
+ return m_matrix->nonZeros();
+ }
+
+ operator Derived&() { return m_matrix->const_cast_derived(); }
+ operator const Derived&() const { return *m_matrix; }
+
+ typedef typename DenseCoeffsBase<Derived,ReadOnlyAccessors>::CoeffReturnType CoeffReturnType;
+ const Scalar& coeff(Index row, Index col) const
+ {
+ Index p = find(row,col);
+
+ if(p==Dynamic)
+ return m_zero;
+ else
+ return m_matrix->const_cast_derived().valuePtr()[p];
+ }
+
+ Scalar& coeffRef(Index row, Index col)
+ {
+ Index p = find(row,col);
+ eigen_assert(p!=Dynamic && "written coefficient does not exist");
+ return m_matrix->const_cast_derived().valuePtr()[p];
+ }
+
+protected:
+
+ Index find(Index row, Index col) const
+ {
+ internal::LowerBoundIndex p = m_matrix->lower_bound(row,col);
+ return p.found ? p.value : Dynamic;
+ }
+
+ const Derived *m_matrix;
+ const Scalar m_zero;
+};
+
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_SPARSE_COMPRESSED_BASE_H
diff --git a/Eigen/src/SparseCore/SparseCwiseBinaryOp.h b/Eigen/src/SparseCore/SparseCwiseBinaryOp.h
new file mode 100644
index 0000000..17cdb8e
--- /dev/null
+++ b/Eigen/src/SparseCore/SparseCwiseBinaryOp.h
@@ -0,0 +1,721 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2014 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_SPARSE_CWISE_BINARY_OP_H
+#define EIGEN_SPARSE_CWISE_BINARY_OP_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+// Here we have to handle 3 cases:
+// 1 - sparse op dense
+// 2 - dense op sparse
+// 3 - sparse op sparse
+// We also need to implement a 4th iterator for:
+// 4 - dense op dense
+// Finally, we also need to distinguish between the product and other operations :
+// configuration returned mode
+// 1 - sparse op dense product sparse
+// generic dense
+// 2 - dense op sparse product sparse
+// generic dense
+// 3 - sparse op sparse product sparse
+// generic sparse
+// 4 - dense op dense product dense
+// generic dense
+//
+// TODO to ease compiler job, we could specialize product/quotient with a scalar
+// and fallback to cwise-unary evaluator using bind1st_op and bind2nd_op.
+
+template<typename BinaryOp, typename Lhs, typename Rhs>
+class CwiseBinaryOpImpl<BinaryOp, Lhs, Rhs, Sparse>
+ : public SparseMatrixBase<CwiseBinaryOp<BinaryOp, Lhs, Rhs> >
+{
+ public:
+ typedef CwiseBinaryOp<BinaryOp, Lhs, Rhs> Derived;
+ typedef SparseMatrixBase<Derived> Base;
+ EIGEN_SPARSE_PUBLIC_INTERFACE(Derived)
+ EIGEN_STATIC_ASSERT((
+ (!internal::is_same<typename internal::traits<Lhs>::StorageKind,
+ typename internal::traits<Rhs>::StorageKind>::value)
+ || ((internal::evaluator<Lhs>::Flags&RowMajorBit) == (internal::evaluator<Rhs>::Flags&RowMajorBit))),
+ THE_STORAGE_ORDER_OF_BOTH_SIDES_MUST_MATCH)
+};
+
+namespace internal {
+
+
+// Generic "sparse OP sparse"
+template<typename XprType> struct binary_sparse_evaluator;
+
+template<typename BinaryOp, typename Lhs, typename Rhs>
+struct binary_evaluator<CwiseBinaryOp<BinaryOp, Lhs, Rhs>, IteratorBased, IteratorBased>
+ : evaluator_base<CwiseBinaryOp<BinaryOp, Lhs, Rhs> >
+{
+protected:
+ typedef typename evaluator<Lhs>::InnerIterator LhsIterator;
+ typedef typename evaluator<Rhs>::InnerIterator RhsIterator;
+ typedef CwiseBinaryOp<BinaryOp, Lhs, Rhs> XprType;
+ typedef typename traits<XprType>::Scalar Scalar;
+ typedef typename XprType::StorageIndex StorageIndex;
+public:
+
+ class InnerIterator
+ {
+ public:
+
+ EIGEN_STRONG_INLINE InnerIterator(const binary_evaluator& aEval, Index outer)
+ : m_lhsIter(aEval.m_lhsImpl,outer), m_rhsIter(aEval.m_rhsImpl,outer), m_functor(aEval.m_functor)
+ {
+ this->operator++();
+ }
+
+ EIGEN_STRONG_INLINE InnerIterator& operator++()
+ {
+ if (m_lhsIter && m_rhsIter && (m_lhsIter.index() == m_rhsIter.index()))
+ {
+ m_id = m_lhsIter.index();
+ m_value = m_functor(m_lhsIter.value(), m_rhsIter.value());
+ ++m_lhsIter;
+ ++m_rhsIter;
+ }
+ else if (m_lhsIter && (!m_rhsIter || (m_lhsIter.index() < m_rhsIter.index())))
+ {
+ m_id = m_lhsIter.index();
+ m_value = m_functor(m_lhsIter.value(), Scalar(0));
+ ++m_lhsIter;
+ }
+ else if (m_rhsIter && (!m_lhsIter || (m_lhsIter.index() > m_rhsIter.index())))
+ {
+ m_id = m_rhsIter.index();
+ m_value = m_functor(Scalar(0), m_rhsIter.value());
+ ++m_rhsIter;
+ }
+ else
+ {
+ m_value = Scalar(0); // this is to avoid a compilation warning
+ m_id = -1;
+ }
+ return *this;
+ }
+
+ EIGEN_STRONG_INLINE Scalar value() const { return m_value; }
+
+ EIGEN_STRONG_INLINE StorageIndex index() const { return m_id; }
+ EIGEN_STRONG_INLINE Index outer() const { return m_lhsIter.outer(); }
+ EIGEN_STRONG_INLINE Index row() const { return Lhs::IsRowMajor ? m_lhsIter.row() : index(); }
+ EIGEN_STRONG_INLINE Index col() const { return Lhs::IsRowMajor ? index() : m_lhsIter.col(); }
+
+ EIGEN_STRONG_INLINE operator bool() const { return m_id>=0; }
+
+ protected:
+ LhsIterator m_lhsIter;
+ RhsIterator m_rhsIter;
+ const BinaryOp& m_functor;
+ Scalar m_value;
+ StorageIndex m_id;
+ };
+
+
+ enum {
+ CoeffReadCost = int(evaluator<Lhs>::CoeffReadCost) + int(evaluator<Rhs>::CoeffReadCost) + int(functor_traits<BinaryOp>::Cost),
+ Flags = XprType::Flags
+ };
+
+ explicit binary_evaluator(const XprType& xpr)
+ : m_functor(xpr.functor()),
+ m_lhsImpl(xpr.lhs()),
+ m_rhsImpl(xpr.rhs())
+ {
+ EIGEN_INTERNAL_CHECK_COST_VALUE(functor_traits<BinaryOp>::Cost);
+ EIGEN_INTERNAL_CHECK_COST_VALUE(CoeffReadCost);
+ }
+
+ inline Index nonZerosEstimate() const {
+ return m_lhsImpl.nonZerosEstimate() + m_rhsImpl.nonZerosEstimate();
+ }
+
+protected:
+ const BinaryOp m_functor;
+ evaluator<Lhs> m_lhsImpl;
+ evaluator<Rhs> m_rhsImpl;
+};
+
+// dense op sparse
+template<typename BinaryOp, typename Lhs, typename Rhs>
+struct binary_evaluator<CwiseBinaryOp<BinaryOp, Lhs, Rhs>, IndexBased, IteratorBased>
+ : evaluator_base<CwiseBinaryOp<BinaryOp, Lhs, Rhs> >
+{
+protected:
+ typedef typename evaluator<Rhs>::InnerIterator RhsIterator;
+ typedef CwiseBinaryOp<BinaryOp, Lhs, Rhs> XprType;
+ typedef typename traits<XprType>::Scalar Scalar;
+ typedef typename XprType::StorageIndex StorageIndex;
+public:
+
+ class InnerIterator
+ {
+ enum { IsRowMajor = (int(Rhs::Flags)&RowMajorBit)==RowMajorBit };
+ public:
+
+ EIGEN_STRONG_INLINE InnerIterator(const binary_evaluator& aEval, Index outer)
+ : m_lhsEval(aEval.m_lhsImpl), m_rhsIter(aEval.m_rhsImpl,outer), m_functor(aEval.m_functor), m_value(0), m_id(-1), m_innerSize(aEval.m_expr.rhs().innerSize())
+ {
+ this->operator++();
+ }
+
+ EIGEN_STRONG_INLINE InnerIterator& operator++()
+ {
+ ++m_id;
+ if(m_id<m_innerSize)
+ {
+ Scalar lhsVal = m_lhsEval.coeff(IsRowMajor?m_rhsIter.outer():m_id,
+ IsRowMajor?m_id:m_rhsIter.outer());
+ if(m_rhsIter && m_rhsIter.index()==m_id)
+ {
+ m_value = m_functor(lhsVal, m_rhsIter.value());
+ ++m_rhsIter;
+ }
+ else
+ m_value = m_functor(lhsVal, Scalar(0));
+ }
+
+ return *this;
+ }
+
+ EIGEN_STRONG_INLINE Scalar value() const { eigen_internal_assert(m_id<m_innerSize); return m_value; }
+
+ EIGEN_STRONG_INLINE StorageIndex index() const { return m_id; }
+ EIGEN_STRONG_INLINE Index outer() const { return m_rhsIter.outer(); }
+ EIGEN_STRONG_INLINE Index row() const { return IsRowMajor ? m_rhsIter.outer() : m_id; }
+ EIGEN_STRONG_INLINE Index col() const { return IsRowMajor ? m_id : m_rhsIter.outer(); }
+
+ EIGEN_STRONG_INLINE operator bool() const { return m_id<m_innerSize; }
+
+ protected:
+ const evaluator<Lhs> &m_lhsEval;
+ RhsIterator m_rhsIter;
+ const BinaryOp& m_functor;
+ Scalar m_value;
+ StorageIndex m_id;
+ StorageIndex m_innerSize;
+ };
+
+
+ enum {
+ CoeffReadCost = int(evaluator<Lhs>::CoeffReadCost) + int(evaluator<Rhs>::CoeffReadCost) + int(functor_traits<BinaryOp>::Cost),
+ Flags = XprType::Flags
+ };
+
+ explicit binary_evaluator(const XprType& xpr)
+ : m_functor(xpr.functor()),
+ m_lhsImpl(xpr.lhs()),
+ m_rhsImpl(xpr.rhs()),
+ m_expr(xpr)
+ {
+ EIGEN_INTERNAL_CHECK_COST_VALUE(functor_traits<BinaryOp>::Cost);
+ EIGEN_INTERNAL_CHECK_COST_VALUE(CoeffReadCost);
+ }
+
+ inline Index nonZerosEstimate() const {
+ return m_expr.size();
+ }
+
+protected:
+ const BinaryOp m_functor;
+ evaluator<Lhs> m_lhsImpl;
+ evaluator<Rhs> m_rhsImpl;
+ const XprType &m_expr;
+};
+
+// sparse op dense
+template<typename BinaryOp, typename Lhs, typename Rhs>
+struct binary_evaluator<CwiseBinaryOp<BinaryOp, Lhs, Rhs>, IteratorBased, IndexBased>
+ : evaluator_base<CwiseBinaryOp<BinaryOp, Lhs, Rhs> >
+{
+protected:
+ typedef typename evaluator<Lhs>::InnerIterator LhsIterator;
+ typedef CwiseBinaryOp<BinaryOp, Lhs, Rhs> XprType;
+ typedef typename traits<XprType>::Scalar Scalar;
+ typedef typename XprType::StorageIndex StorageIndex;
+public:
+
+ class InnerIterator
+ {
+ enum { IsRowMajor = (int(Lhs::Flags)&RowMajorBit)==RowMajorBit };
+ public:
+
+ EIGEN_STRONG_INLINE InnerIterator(const binary_evaluator& aEval, Index outer)
+ : m_lhsIter(aEval.m_lhsImpl,outer), m_rhsEval(aEval.m_rhsImpl), m_functor(aEval.m_functor), m_value(0), m_id(-1), m_innerSize(aEval.m_expr.lhs().innerSize())
+ {
+ this->operator++();
+ }
+
+ EIGEN_STRONG_INLINE InnerIterator& operator++()
+ {
+ ++m_id;
+ if(m_id<m_innerSize)
+ {
+ Scalar rhsVal = m_rhsEval.coeff(IsRowMajor?m_lhsIter.outer():m_id,
+ IsRowMajor?m_id:m_lhsIter.outer());
+ if(m_lhsIter && m_lhsIter.index()==m_id)
+ {
+ m_value = m_functor(m_lhsIter.value(), rhsVal);
+ ++m_lhsIter;
+ }
+ else
+ m_value = m_functor(Scalar(0),rhsVal);
+ }
+
+ return *this;
+ }
+
+ EIGEN_STRONG_INLINE Scalar value() const { eigen_internal_assert(m_id<m_innerSize); return m_value; }
+
+ EIGEN_STRONG_INLINE StorageIndex index() const { return m_id; }
+ EIGEN_STRONG_INLINE Index outer() const { return m_lhsIter.outer(); }
+ EIGEN_STRONG_INLINE Index row() const { return IsRowMajor ? m_lhsIter.outer() : m_id; }
+ EIGEN_STRONG_INLINE Index col() const { return IsRowMajor ? m_id : m_lhsIter.outer(); }
+
+ EIGEN_STRONG_INLINE operator bool() const { return m_id<m_innerSize; }
+
+ protected:
+ LhsIterator m_lhsIter;
+ const evaluator<Rhs> &m_rhsEval;
+ const BinaryOp& m_functor;
+ Scalar m_value;
+ StorageIndex m_id;
+ StorageIndex m_innerSize;
+ };
+
+
+ enum {
+ CoeffReadCost = int(evaluator<Lhs>::CoeffReadCost) + int(evaluator<Rhs>::CoeffReadCost) + int(functor_traits<BinaryOp>::Cost),
+ Flags = XprType::Flags
+ };
+
+ explicit binary_evaluator(const XprType& xpr)
+ : m_functor(xpr.functor()),
+ m_lhsImpl(xpr.lhs()),
+ m_rhsImpl(xpr.rhs()),
+ m_expr(xpr)
+ {
+ EIGEN_INTERNAL_CHECK_COST_VALUE(functor_traits<BinaryOp>::Cost);
+ EIGEN_INTERNAL_CHECK_COST_VALUE(CoeffReadCost);
+ }
+
+ inline Index nonZerosEstimate() const {
+ return m_expr.size();
+ }
+
+protected:
+ const BinaryOp m_functor;
+ evaluator<Lhs> m_lhsImpl;
+ evaluator<Rhs> m_rhsImpl;
+ const XprType &m_expr;
+};
+
+template<typename T,
+ typename LhsKind = typename evaluator_traits<typename T::Lhs>::Kind,
+ typename RhsKind = typename evaluator_traits<typename T::Rhs>::Kind,
+ typename LhsScalar = typename traits<typename T::Lhs>::Scalar,
+ typename RhsScalar = typename traits<typename T::Rhs>::Scalar> struct sparse_conjunction_evaluator;
+
+// "sparse .* sparse"
+template<typename T1, typename T2, typename Lhs, typename Rhs>
+struct binary_evaluator<CwiseBinaryOp<scalar_product_op<T1,T2>, Lhs, Rhs>, IteratorBased, IteratorBased>
+ : sparse_conjunction_evaluator<CwiseBinaryOp<scalar_product_op<T1,T2>, Lhs, Rhs> >
+{
+ typedef CwiseBinaryOp<scalar_product_op<T1,T2>, Lhs, Rhs> XprType;
+ typedef sparse_conjunction_evaluator<XprType> Base;
+ explicit binary_evaluator(const XprType& xpr) : Base(xpr) {}
+};
+// "dense .* sparse"
+template<typename T1, typename T2, typename Lhs, typename Rhs>
+struct binary_evaluator<CwiseBinaryOp<scalar_product_op<T1,T2>, Lhs, Rhs>, IndexBased, IteratorBased>
+ : sparse_conjunction_evaluator<CwiseBinaryOp<scalar_product_op<T1,T2>, Lhs, Rhs> >
+{
+ typedef CwiseBinaryOp<scalar_product_op<T1,T2>, Lhs, Rhs> XprType;
+ typedef sparse_conjunction_evaluator<XprType> Base;
+ explicit binary_evaluator(const XprType& xpr) : Base(xpr) {}
+};
+// "sparse .* dense"
+template<typename T1, typename T2, typename Lhs, typename Rhs>
+struct binary_evaluator<CwiseBinaryOp<scalar_product_op<T1,T2>, Lhs, Rhs>, IteratorBased, IndexBased>
+ : sparse_conjunction_evaluator<CwiseBinaryOp<scalar_product_op<T1,T2>, Lhs, Rhs> >
+{
+ typedef CwiseBinaryOp<scalar_product_op<T1,T2>, Lhs, Rhs> XprType;
+ typedef sparse_conjunction_evaluator<XprType> Base;
+ explicit binary_evaluator(const XprType& xpr) : Base(xpr) {}
+};
+
+// "sparse ./ dense"
+template<typename T1, typename T2, typename Lhs, typename Rhs>
+struct binary_evaluator<CwiseBinaryOp<scalar_quotient_op<T1,T2>, Lhs, Rhs>, IteratorBased, IndexBased>
+ : sparse_conjunction_evaluator<CwiseBinaryOp<scalar_quotient_op<T1,T2>, Lhs, Rhs> >
+{
+ typedef CwiseBinaryOp<scalar_quotient_op<T1,T2>, Lhs, Rhs> XprType;
+ typedef sparse_conjunction_evaluator<XprType> Base;
+ explicit binary_evaluator(const XprType& xpr) : Base(xpr) {}
+};
+
+// "sparse && sparse"
+template<typename Lhs, typename Rhs>
+struct binary_evaluator<CwiseBinaryOp<scalar_boolean_and_op, Lhs, Rhs>, IteratorBased, IteratorBased>
+ : sparse_conjunction_evaluator<CwiseBinaryOp<scalar_boolean_and_op, Lhs, Rhs> >
+{
+ typedef CwiseBinaryOp<scalar_boolean_and_op, Lhs, Rhs> XprType;
+ typedef sparse_conjunction_evaluator<XprType> Base;
+ explicit binary_evaluator(const XprType& xpr) : Base(xpr) {}
+};
+// "dense && sparse"
+template<typename Lhs, typename Rhs>
+struct binary_evaluator<CwiseBinaryOp<scalar_boolean_and_op, Lhs, Rhs>, IndexBased, IteratorBased>
+ : sparse_conjunction_evaluator<CwiseBinaryOp<scalar_boolean_and_op, Lhs, Rhs> >
+{
+ typedef CwiseBinaryOp<scalar_boolean_and_op, Lhs, Rhs> XprType;
+ typedef sparse_conjunction_evaluator<XprType> Base;
+ explicit binary_evaluator(const XprType& xpr) : Base(xpr) {}
+};
+// "sparse && dense"
+template<typename Lhs, typename Rhs>
+struct binary_evaluator<CwiseBinaryOp<scalar_boolean_and_op, Lhs, Rhs>, IteratorBased, IndexBased>
+ : sparse_conjunction_evaluator<CwiseBinaryOp<scalar_boolean_and_op, Lhs, Rhs> >
+{
+ typedef CwiseBinaryOp<scalar_boolean_and_op, Lhs, Rhs> XprType;
+ typedef sparse_conjunction_evaluator<XprType> Base;
+ explicit binary_evaluator(const XprType& xpr) : Base(xpr) {}
+};
+
+// "sparse ^ sparse"
+template<typename XprType>
+struct sparse_conjunction_evaluator<XprType, IteratorBased, IteratorBased>
+ : evaluator_base<XprType>
+{
+protected:
+ typedef typename XprType::Functor BinaryOp;
+ typedef typename XprType::Lhs LhsArg;
+ typedef typename XprType::Rhs RhsArg;
+ typedef typename evaluator<LhsArg>::InnerIterator LhsIterator;
+ typedef typename evaluator<RhsArg>::InnerIterator RhsIterator;
+ typedef typename XprType::StorageIndex StorageIndex;
+ typedef typename traits<XprType>::Scalar Scalar;
+public:
+
+ class InnerIterator
+ {
+ public:
+
+ EIGEN_STRONG_INLINE InnerIterator(const sparse_conjunction_evaluator& aEval, Index outer)
+ : m_lhsIter(aEval.m_lhsImpl,outer), m_rhsIter(aEval.m_rhsImpl,outer), m_functor(aEval.m_functor)
+ {
+ while (m_lhsIter && m_rhsIter && (m_lhsIter.index() != m_rhsIter.index()))
+ {
+ if (m_lhsIter.index() < m_rhsIter.index())
+ ++m_lhsIter;
+ else
+ ++m_rhsIter;
+ }
+ }
+
+ EIGEN_STRONG_INLINE InnerIterator& operator++()
+ {
+ ++m_lhsIter;
+ ++m_rhsIter;
+ while (m_lhsIter && m_rhsIter && (m_lhsIter.index() != m_rhsIter.index()))
+ {
+ if (m_lhsIter.index() < m_rhsIter.index())
+ ++m_lhsIter;
+ else
+ ++m_rhsIter;
+ }
+ return *this;
+ }
+
+ EIGEN_STRONG_INLINE Scalar value() const { return m_functor(m_lhsIter.value(), m_rhsIter.value()); }
+
+ EIGEN_STRONG_INLINE StorageIndex index() const { return m_lhsIter.index(); }
+ EIGEN_STRONG_INLINE Index outer() const { return m_lhsIter.outer(); }
+ EIGEN_STRONG_INLINE Index row() const { return m_lhsIter.row(); }
+ EIGEN_STRONG_INLINE Index col() const { return m_lhsIter.col(); }
+
+ EIGEN_STRONG_INLINE operator bool() const { return (m_lhsIter && m_rhsIter); }
+
+ protected:
+ LhsIterator m_lhsIter;
+ RhsIterator m_rhsIter;
+ const BinaryOp& m_functor;
+ };
+
+
+ enum {
+ CoeffReadCost = int(evaluator<LhsArg>::CoeffReadCost) + int(evaluator<RhsArg>::CoeffReadCost) + int(functor_traits<BinaryOp>::Cost),
+ Flags = XprType::Flags
+ };
+
+ explicit sparse_conjunction_evaluator(const XprType& xpr)
+ : m_functor(xpr.functor()),
+ m_lhsImpl(xpr.lhs()),
+ m_rhsImpl(xpr.rhs())
+ {
+ EIGEN_INTERNAL_CHECK_COST_VALUE(functor_traits<BinaryOp>::Cost);
+ EIGEN_INTERNAL_CHECK_COST_VALUE(CoeffReadCost);
+ }
+
+ inline Index nonZerosEstimate() const {
+ return (std::min)(m_lhsImpl.nonZerosEstimate(), m_rhsImpl.nonZerosEstimate());
+ }
+
+protected:
+ const BinaryOp m_functor;
+ evaluator<LhsArg> m_lhsImpl;
+ evaluator<RhsArg> m_rhsImpl;
+};
+
+// "dense ^ sparse"
+template<typename XprType>
+struct sparse_conjunction_evaluator<XprType, IndexBased, IteratorBased>
+ : evaluator_base<XprType>
+{
+protected:
+ typedef typename XprType::Functor BinaryOp;
+ typedef typename XprType::Lhs LhsArg;
+ typedef typename XprType::Rhs RhsArg;
+ typedef evaluator<LhsArg> LhsEvaluator;
+ typedef typename evaluator<RhsArg>::InnerIterator RhsIterator;
+ typedef typename XprType::StorageIndex StorageIndex;
+ typedef typename traits<XprType>::Scalar Scalar;
+public:
+
+ class InnerIterator
+ {
+ enum { IsRowMajor = (int(RhsArg::Flags)&RowMajorBit)==RowMajorBit };
+
+ public:
+
+ EIGEN_STRONG_INLINE InnerIterator(const sparse_conjunction_evaluator& aEval, Index outer)
+ : m_lhsEval(aEval.m_lhsImpl), m_rhsIter(aEval.m_rhsImpl,outer), m_functor(aEval.m_functor), m_outer(outer)
+ {}
+
+ EIGEN_STRONG_INLINE InnerIterator& operator++()
+ {
+ ++m_rhsIter;
+ return *this;
+ }
+
+ EIGEN_STRONG_INLINE Scalar value() const
+ { return m_functor(m_lhsEval.coeff(IsRowMajor?m_outer:m_rhsIter.index(),IsRowMajor?m_rhsIter.index():m_outer), m_rhsIter.value()); }
+
+ EIGEN_STRONG_INLINE StorageIndex index() const { return m_rhsIter.index(); }
+ EIGEN_STRONG_INLINE Index outer() const { return m_rhsIter.outer(); }
+ EIGEN_STRONG_INLINE Index row() const { return m_rhsIter.row(); }
+ EIGEN_STRONG_INLINE Index col() const { return m_rhsIter.col(); }
+
+ EIGEN_STRONG_INLINE operator bool() const { return m_rhsIter; }
+
+ protected:
+ const LhsEvaluator &m_lhsEval;
+ RhsIterator m_rhsIter;
+ const BinaryOp& m_functor;
+ const Index m_outer;
+ };
+
+
+ enum {
+ CoeffReadCost = int(evaluator<LhsArg>::CoeffReadCost) + int(evaluator<RhsArg>::CoeffReadCost) + int(functor_traits<BinaryOp>::Cost),
+ Flags = XprType::Flags
+ };
+
+ explicit sparse_conjunction_evaluator(const XprType& xpr)
+ : m_functor(xpr.functor()),
+ m_lhsImpl(xpr.lhs()),
+ m_rhsImpl(xpr.rhs())
+ {
+ EIGEN_INTERNAL_CHECK_COST_VALUE(functor_traits<BinaryOp>::Cost);
+ EIGEN_INTERNAL_CHECK_COST_VALUE(CoeffReadCost);
+ }
+
+ inline Index nonZerosEstimate() const {
+ return m_rhsImpl.nonZerosEstimate();
+ }
+
+protected:
+ const BinaryOp m_functor;
+ evaluator<LhsArg> m_lhsImpl;
+ evaluator<RhsArg> m_rhsImpl;
+};
+
+// "sparse ^ dense"
+template<typename XprType>
+struct sparse_conjunction_evaluator<XprType, IteratorBased, IndexBased>
+ : evaluator_base<XprType>
+{
+protected:
+ typedef typename XprType::Functor BinaryOp;
+ typedef typename XprType::Lhs LhsArg;
+ typedef typename XprType::Rhs RhsArg;
+ typedef typename evaluator<LhsArg>::InnerIterator LhsIterator;
+ typedef evaluator<RhsArg> RhsEvaluator;
+ typedef typename XprType::StorageIndex StorageIndex;
+ typedef typename traits<XprType>::Scalar Scalar;
+public:
+
+ class InnerIterator
+ {
+ enum { IsRowMajor = (int(LhsArg::Flags)&RowMajorBit)==RowMajorBit };
+
+ public:
+
+ EIGEN_STRONG_INLINE InnerIterator(const sparse_conjunction_evaluator& aEval, Index outer)
+ : m_lhsIter(aEval.m_lhsImpl,outer), m_rhsEval(aEval.m_rhsImpl), m_functor(aEval.m_functor), m_outer(outer)
+ {}
+
+ EIGEN_STRONG_INLINE InnerIterator& operator++()
+ {
+ ++m_lhsIter;
+ return *this;
+ }
+
+ EIGEN_STRONG_INLINE Scalar value() const
+ { return m_functor(m_lhsIter.value(),
+ m_rhsEval.coeff(IsRowMajor?m_outer:m_lhsIter.index(),IsRowMajor?m_lhsIter.index():m_outer)); }
+
+ EIGEN_STRONG_INLINE StorageIndex index() const { return m_lhsIter.index(); }
+ EIGEN_STRONG_INLINE Index outer() const { return m_lhsIter.outer(); }
+ EIGEN_STRONG_INLINE Index row() const { return m_lhsIter.row(); }
+ EIGEN_STRONG_INLINE Index col() const { return m_lhsIter.col(); }
+
+ EIGEN_STRONG_INLINE operator bool() const { return m_lhsIter; }
+
+ protected:
+ LhsIterator m_lhsIter;
+ const evaluator<RhsArg> &m_rhsEval;
+ const BinaryOp& m_functor;
+ const Index m_outer;
+ };
+
+
+ enum {
+ CoeffReadCost = int(evaluator<LhsArg>::CoeffReadCost) + int(evaluator<RhsArg>::CoeffReadCost) + int(functor_traits<BinaryOp>::Cost),
+ Flags = XprType::Flags
+ };
+
+ explicit sparse_conjunction_evaluator(const XprType& xpr)
+ : m_functor(xpr.functor()),
+ m_lhsImpl(xpr.lhs()),
+ m_rhsImpl(xpr.rhs())
+ {
+ EIGEN_INTERNAL_CHECK_COST_VALUE(functor_traits<BinaryOp>::Cost);
+ EIGEN_INTERNAL_CHECK_COST_VALUE(CoeffReadCost);
+ }
+
+ inline Index nonZerosEstimate() const {
+ return m_lhsImpl.nonZerosEstimate();
+ }
+
+protected:
+ const BinaryOp m_functor;
+ evaluator<LhsArg> m_lhsImpl;
+ evaluator<RhsArg> m_rhsImpl;
+};
+
+}
+
+/***************************************************************************
+* Implementation of SparseMatrixBase and SparseCwise functions/operators
+***************************************************************************/
+
+template<typename Derived>
+template<typename OtherDerived>
+Derived& SparseMatrixBase<Derived>::operator+=(const EigenBase<OtherDerived> &other)
+{
+ call_assignment(derived(), other.derived(), internal::add_assign_op<Scalar,typename OtherDerived::Scalar>());
+ return derived();
+}
+
+template<typename Derived>
+template<typename OtherDerived>
+Derived& SparseMatrixBase<Derived>::operator-=(const EigenBase<OtherDerived> &other)
+{
+ call_assignment(derived(), other.derived(), internal::assign_op<Scalar,typename OtherDerived::Scalar>());
+ return derived();
+}
+
+template<typename Derived>
+template<typename OtherDerived>
+EIGEN_STRONG_INLINE Derived &
+SparseMatrixBase<Derived>::operator-=(const SparseMatrixBase<OtherDerived> &other)
+{
+ return derived() = derived() - other.derived();
+}
+
+template<typename Derived>
+template<typename OtherDerived>
+EIGEN_STRONG_INLINE Derived &
+SparseMatrixBase<Derived>::operator+=(const SparseMatrixBase<OtherDerived>& other)
+{
+ return derived() = derived() + other.derived();
+}
+
+template<typename Derived>
+template<typename OtherDerived>
+Derived& SparseMatrixBase<Derived>::operator+=(const DiagonalBase<OtherDerived>& other)
+{
+ call_assignment_no_alias(derived(), other.derived(), internal::add_assign_op<Scalar,typename OtherDerived::Scalar>());
+ return derived();
+}
+
+template<typename Derived>
+template<typename OtherDerived>
+Derived& SparseMatrixBase<Derived>::operator-=(const DiagonalBase<OtherDerived>& other)
+{
+ call_assignment_no_alias(derived(), other.derived(), internal::sub_assign_op<Scalar,typename OtherDerived::Scalar>());
+ return derived();
+}
+
+template<typename Derived>
+template<typename OtherDerived>
+EIGEN_STRONG_INLINE const typename SparseMatrixBase<Derived>::template CwiseProductDenseReturnType<OtherDerived>::Type
+SparseMatrixBase<Derived>::cwiseProduct(const MatrixBase<OtherDerived> &other) const
+{
+ return typename CwiseProductDenseReturnType<OtherDerived>::Type(derived(), other.derived());
+}
+
+template<typename DenseDerived, typename SparseDerived>
+EIGEN_STRONG_INLINE const CwiseBinaryOp<internal::scalar_sum_op<typename DenseDerived::Scalar,typename SparseDerived::Scalar>, const DenseDerived, const SparseDerived>
+operator+(const MatrixBase<DenseDerived> &a, const SparseMatrixBase<SparseDerived> &b)
+{
+ return CwiseBinaryOp<internal::scalar_sum_op<typename DenseDerived::Scalar,typename SparseDerived::Scalar>, const DenseDerived, const SparseDerived>(a.derived(), b.derived());
+}
+
+template<typename SparseDerived, typename DenseDerived>
+EIGEN_STRONG_INLINE const CwiseBinaryOp<internal::scalar_sum_op<typename SparseDerived::Scalar,typename DenseDerived::Scalar>, const SparseDerived, const DenseDerived>
+operator+(const SparseMatrixBase<SparseDerived> &a, const MatrixBase<DenseDerived> &b)
+{
+ return CwiseBinaryOp<internal::scalar_sum_op<typename SparseDerived::Scalar,typename DenseDerived::Scalar>, const SparseDerived, const DenseDerived>(a.derived(), b.derived());
+}
+
+template<typename DenseDerived, typename SparseDerived>
+EIGEN_STRONG_INLINE const CwiseBinaryOp<internal::scalar_difference_op<typename DenseDerived::Scalar,typename SparseDerived::Scalar>, const DenseDerived, const SparseDerived>
+operator-(const MatrixBase<DenseDerived> &a, const SparseMatrixBase<SparseDerived> &b)
+{
+ return CwiseBinaryOp<internal::scalar_difference_op<typename DenseDerived::Scalar,typename SparseDerived::Scalar>, const DenseDerived, const SparseDerived>(a.derived(), b.derived());
+}
+
+template<typename SparseDerived, typename DenseDerived>
+EIGEN_STRONG_INLINE const CwiseBinaryOp<internal::scalar_difference_op<typename SparseDerived::Scalar,typename DenseDerived::Scalar>, const SparseDerived, const DenseDerived>
+operator-(const SparseMatrixBase<SparseDerived> &a, const MatrixBase<DenseDerived> &b)
+{
+ return CwiseBinaryOp<internal::scalar_difference_op<typename SparseDerived::Scalar,typename DenseDerived::Scalar>, const SparseDerived, const DenseDerived>(a.derived(), b.derived());
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_SPARSE_CWISE_BINARY_OP_H
diff --git a/Eigen/src/SparseCore/SparseCwiseUnaryOp.h b/Eigen/src/SparseCore/SparseCwiseUnaryOp.h
new file mode 100644
index 0000000..6f48fa7
--- /dev/null
+++ b/Eigen/src/SparseCore/SparseCwiseUnaryOp.h
@@ -0,0 +1,152 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2015 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_SPARSE_CWISE_UNARY_OP_H
+#define EIGEN_SPARSE_CWISE_UNARY_OP_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+
+template<typename UnaryOp, typename ArgType>
+struct unary_evaluator<CwiseUnaryOp<UnaryOp,ArgType>, IteratorBased>
+ : public evaluator_base<CwiseUnaryOp<UnaryOp,ArgType> >
+{
+ public:
+ typedef CwiseUnaryOp<UnaryOp, ArgType> XprType;
+
+ class InnerIterator;
+
+ enum {
+ CoeffReadCost = int(evaluator<ArgType>::CoeffReadCost) + int(functor_traits<UnaryOp>::Cost),
+ Flags = XprType::Flags
+ };
+
+ explicit unary_evaluator(const XprType& op) : m_functor(op.functor()), m_argImpl(op.nestedExpression())
+ {
+ EIGEN_INTERNAL_CHECK_COST_VALUE(functor_traits<UnaryOp>::Cost);
+ EIGEN_INTERNAL_CHECK_COST_VALUE(CoeffReadCost);
+ }
+
+ inline Index nonZerosEstimate() const {
+ return m_argImpl.nonZerosEstimate();
+ }
+
+ protected:
+ typedef typename evaluator<ArgType>::InnerIterator EvalIterator;
+
+ const UnaryOp m_functor;
+ evaluator<ArgType> m_argImpl;
+};
+
+template<typename UnaryOp, typename ArgType>
+class unary_evaluator<CwiseUnaryOp<UnaryOp,ArgType>, IteratorBased>::InnerIterator
+ : public unary_evaluator<CwiseUnaryOp<UnaryOp,ArgType>, IteratorBased>::EvalIterator
+{
+ protected:
+ typedef typename XprType::Scalar Scalar;
+ typedef typename unary_evaluator<CwiseUnaryOp<UnaryOp,ArgType>, IteratorBased>::EvalIterator Base;
+ public:
+
+ EIGEN_STRONG_INLINE InnerIterator(const unary_evaluator& unaryOp, Index outer)
+ : Base(unaryOp.m_argImpl,outer), m_functor(unaryOp.m_functor)
+ {}
+
+ EIGEN_STRONG_INLINE InnerIterator& operator++()
+ { Base::operator++(); return *this; }
+
+ EIGEN_STRONG_INLINE Scalar value() const { return m_functor(Base::value()); }
+
+ protected:
+ const UnaryOp m_functor;
+ private:
+ Scalar& valueRef();
+};
+
+template<typename ViewOp, typename ArgType>
+struct unary_evaluator<CwiseUnaryView<ViewOp,ArgType>, IteratorBased>
+ : public evaluator_base<CwiseUnaryView<ViewOp,ArgType> >
+{
+ public:
+ typedef CwiseUnaryView<ViewOp, ArgType> XprType;
+
+ class InnerIterator;
+
+ enum {
+ CoeffReadCost = int(evaluator<ArgType>::CoeffReadCost) + int(functor_traits<ViewOp>::Cost),
+ Flags = XprType::Flags
+ };
+
+ explicit unary_evaluator(const XprType& op) : m_functor(op.functor()), m_argImpl(op.nestedExpression())
+ {
+ EIGEN_INTERNAL_CHECK_COST_VALUE(functor_traits<ViewOp>::Cost);
+ EIGEN_INTERNAL_CHECK_COST_VALUE(CoeffReadCost);
+ }
+
+ protected:
+ typedef typename evaluator<ArgType>::InnerIterator EvalIterator;
+
+ const ViewOp m_functor;
+ evaluator<ArgType> m_argImpl;
+};
+
+template<typename ViewOp, typename ArgType>
+class unary_evaluator<CwiseUnaryView<ViewOp,ArgType>, IteratorBased>::InnerIterator
+ : public unary_evaluator<CwiseUnaryView<ViewOp,ArgType>, IteratorBased>::EvalIterator
+{
+ protected:
+ typedef typename XprType::Scalar Scalar;
+ typedef typename unary_evaluator<CwiseUnaryView<ViewOp,ArgType>, IteratorBased>::EvalIterator Base;
+ public:
+
+ EIGEN_STRONG_INLINE InnerIterator(const unary_evaluator& unaryOp, Index outer)
+ : Base(unaryOp.m_argImpl,outer), m_functor(unaryOp.m_functor)
+ {}
+
+ EIGEN_STRONG_INLINE InnerIterator& operator++()
+ { Base::operator++(); return *this; }
+
+ EIGEN_STRONG_INLINE Scalar value() const { return m_functor(Base::value()); }
+ EIGEN_STRONG_INLINE Scalar& valueRef() { return m_functor(Base::valueRef()); }
+
+ protected:
+ const ViewOp m_functor;
+};
+
+} // end namespace internal
+
+template<typename Derived>
+EIGEN_STRONG_INLINE Derived&
+SparseMatrixBase<Derived>::operator*=(const Scalar& other)
+{
+ typedef typename internal::evaluator<Derived>::InnerIterator EvalIterator;
+ internal::evaluator<Derived> thisEval(derived());
+ for (Index j=0; j<outerSize(); ++j)
+ for (EvalIterator i(thisEval,j); i; ++i)
+ i.valueRef() *= other;
+ return derived();
+}
+
+template<typename Derived>
+EIGEN_STRONG_INLINE Derived&
+SparseMatrixBase<Derived>::operator/=(const Scalar& other)
+{
+ typedef typename internal::evaluator<Derived>::InnerIterator EvalIterator;
+ internal::evaluator<Derived> thisEval(derived());
+ for (Index j=0; j<outerSize(); ++j)
+ for (EvalIterator i(thisEval,j); i; ++i)
+ i.valueRef() /= other;
+ return derived();
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_SPARSE_CWISE_UNARY_OP_H
diff --git a/Eigen/src/SparseCore/SparseDenseProduct.h b/Eigen/src/SparseCore/SparseDenseProduct.h
new file mode 100644
index 0000000..9c0c531
--- /dev/null
+++ b/Eigen/src/SparseCore/SparseDenseProduct.h
@@ -0,0 +1,352 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2015 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_SPARSEDENSEPRODUCT_H
+#define EIGEN_SPARSEDENSEPRODUCT_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+
+template <> struct product_promote_storage_type<Sparse,Dense, OuterProduct> { typedef Sparse ret; };
+template <> struct product_promote_storage_type<Dense,Sparse, OuterProduct> { typedef Sparse ret; };
+
+template<typename SparseLhsType, typename DenseRhsType, typename DenseResType,
+ typename AlphaType,
+ int LhsStorageOrder = ((SparseLhsType::Flags&RowMajorBit)==RowMajorBit) ? RowMajor : ColMajor,
+ bool ColPerCol = ((DenseRhsType::Flags&RowMajorBit)==0) || DenseRhsType::ColsAtCompileTime==1>
+struct sparse_time_dense_product_impl;
+
+template<typename SparseLhsType, typename DenseRhsType, typename DenseResType>
+struct sparse_time_dense_product_impl<SparseLhsType,DenseRhsType,DenseResType, typename DenseResType::Scalar, RowMajor, true>
+{
+ typedef internal::remove_all_t<SparseLhsType> Lhs;
+ typedef internal::remove_all_t<DenseRhsType> Rhs;
+ typedef internal::remove_all_t<DenseResType> Res;
+ typedef typename evaluator<Lhs>::InnerIterator LhsInnerIterator;
+ typedef evaluator<Lhs> LhsEval;
+ static void run(const SparseLhsType& lhs, const DenseRhsType& rhs, DenseResType& res, const typename Res::Scalar& alpha)
+ {
+ LhsEval lhsEval(lhs);
+
+ Index n = lhs.outerSize();
+#ifdef EIGEN_HAS_OPENMP
+ Eigen::initParallel();
+ Index threads = Eigen::nbThreads();
+#endif
+
+ for(Index c=0; c<rhs.cols(); ++c)
+ {
+#ifdef EIGEN_HAS_OPENMP
+ // This 20000 threshold has been found experimentally on 2D and 3D Poisson problems.
+ // It basically represents the minimal amount of work to be done to be worth it.
+ if(threads>1 && lhsEval.nonZerosEstimate() > 20000)
+ {
+ #pragma omp parallel for schedule(dynamic,(n+threads*4-1)/(threads*4)) num_threads(threads)
+ for(Index i=0; i<n; ++i)
+ processRow(lhsEval,rhs,res,alpha,i,c);
+ }
+ else
+#endif
+ {
+ for(Index i=0; i<n; ++i)
+ processRow(lhsEval,rhs,res,alpha,i,c);
+ }
+ }
+ }
+
+ static void processRow(const LhsEval& lhsEval, const DenseRhsType& rhs, DenseResType& res, const typename Res::Scalar& alpha, Index i, Index col)
+ {
+ // Two accumulators, which breaks the dependency chain on the accumulator
+ // and allows more instruction-level parallelism in the following loop
+ typename Res::Scalar tmp_a(0);
+ typename Res::Scalar tmp_b(0);
+ for(LhsInnerIterator it(lhsEval,i); it ;++it) {
+ tmp_a += it.value() * rhs.coeff(it.index(), col);
+ ++it;
+ if(it) {
+ tmp_b += it.value() * rhs.coeff(it.index(), col);
+ }
+ }
+ res.coeffRef(i, col) += alpha * (tmp_a + tmp_b);
+ }
+
+};
+
+// FIXME: what is the purpose of the following specialization? Is it for the BlockedSparse format?
+// -> let's disable it for now as it is conflicting with generic scalar*matrix and matrix*scalar operators
+// template<typename T1, typename T2/*, int Options_, typename StrideType_*/>
+// struct ScalarBinaryOpTraits<T1, Ref<T2/*, Options_, StrideType_*/> >
+// {
+// enum {
+// Defined = 1
+// };
+// typedef typename CwiseUnaryOp<scalar_multiple2_op<T1, typename T2::Scalar>, T2>::PlainObject ReturnType;
+// };
+
+template<typename SparseLhsType, typename DenseRhsType, typename DenseResType, typename AlphaType>
+struct sparse_time_dense_product_impl<SparseLhsType,DenseRhsType,DenseResType, AlphaType, ColMajor, true>
+{
+ typedef internal::remove_all_t<SparseLhsType> Lhs;
+ typedef internal::remove_all_t<DenseRhsType> Rhs;
+ typedef internal::remove_all_t<DenseResType> Res;
+ typedef evaluator<Lhs> LhsEval;
+ typedef typename LhsEval::InnerIterator LhsInnerIterator;
+ static void run(const SparseLhsType& lhs, const DenseRhsType& rhs, DenseResType& res, const AlphaType& alpha)
+ {
+ LhsEval lhsEval(lhs);
+ for(Index c=0; c<rhs.cols(); ++c)
+ {
+ for(Index j=0; j<lhs.outerSize(); ++j)
+ {
+// typename Res::Scalar rhs_j = alpha * rhs.coeff(j,c);
+ typename ScalarBinaryOpTraits<AlphaType, typename Rhs::Scalar>::ReturnType rhs_j(alpha * rhs.coeff(j,c));
+ for(LhsInnerIterator it(lhsEval,j); it ;++it)
+ res.coeffRef(it.index(),c) += it.value() * rhs_j;
+ }
+ }
+ }
+};
+
+template<typename SparseLhsType, typename DenseRhsType, typename DenseResType>
+struct sparse_time_dense_product_impl<SparseLhsType,DenseRhsType,DenseResType, typename DenseResType::Scalar, RowMajor, false>
+{
+ typedef internal::remove_all_t<SparseLhsType> Lhs;
+ typedef internal::remove_all_t<DenseRhsType> Rhs;
+ typedef internal::remove_all_t<DenseResType> Res;
+ typedef evaluator<Lhs> LhsEval;
+ typedef typename LhsEval::InnerIterator LhsInnerIterator;
+ static void run(const SparseLhsType& lhs, const DenseRhsType& rhs, DenseResType& res, const typename Res::Scalar& alpha)
+ {
+ Index n = lhs.rows();
+ LhsEval lhsEval(lhs);
+
+#ifdef EIGEN_HAS_OPENMP
+ Eigen::initParallel();
+ Index threads = Eigen::nbThreads();
+ // This 20000 threshold has been found experimentally on 2D and 3D Poisson problems.
+ // It basically represents the minimal amount of work to be done to be worth it.
+ if(threads>1 && lhsEval.nonZerosEstimate()*rhs.cols() > 20000)
+ {
+ #pragma omp parallel for schedule(dynamic,(n+threads*4-1)/(threads*4)) num_threads(threads)
+ for(Index i=0; i<n; ++i)
+ processRow(lhsEval,rhs,res,alpha,i);
+ }
+ else
+#endif
+ {
+ for(Index i=0; i<n; ++i)
+ processRow(lhsEval, rhs, res, alpha, i);
+ }
+ }
+
+ static void processRow(const LhsEval& lhsEval, const DenseRhsType& rhs, Res& res, const typename Res::Scalar& alpha, Index i)
+ {
+ typename Res::RowXpr res_i(res.row(i));
+ for(LhsInnerIterator it(lhsEval,i); it ;++it)
+ res_i += (alpha*it.value()) * rhs.row(it.index());
+ }
+};
+
+template<typename SparseLhsType, typename DenseRhsType, typename DenseResType>
+struct sparse_time_dense_product_impl<SparseLhsType,DenseRhsType,DenseResType, typename DenseResType::Scalar, ColMajor, false>
+{
+ typedef internal::remove_all_t<SparseLhsType> Lhs;
+ typedef internal::remove_all_t<DenseRhsType> Rhs;
+ typedef internal::remove_all_t<DenseResType> Res;
+ typedef typename evaluator<Lhs>::InnerIterator LhsInnerIterator;
+ static void run(const SparseLhsType& lhs, const DenseRhsType& rhs, DenseResType& res, const typename Res::Scalar& alpha)
+ {
+ evaluator<Lhs> lhsEval(lhs);
+ for(Index j=0; j<lhs.outerSize(); ++j)
+ {
+ typename Rhs::ConstRowXpr rhs_j(rhs.row(j));
+ for(LhsInnerIterator it(lhsEval,j); it ;++it)
+ res.row(it.index()) += (alpha*it.value()) * rhs_j;
+ }
+ }
+};
+
+template<typename SparseLhsType, typename DenseRhsType, typename DenseResType,typename AlphaType>
+inline void sparse_time_dense_product(const SparseLhsType& lhs, const DenseRhsType& rhs, DenseResType& res, const AlphaType& alpha)
+{
+ sparse_time_dense_product_impl<SparseLhsType,DenseRhsType,DenseResType, AlphaType>::run(lhs, rhs, res, alpha);
+}
+
+} // end namespace internal
+
+namespace internal {
+
+template<typename Lhs, typename Rhs, int ProductType>
+struct generic_product_impl<Lhs, Rhs, SparseShape, DenseShape, ProductType>
+ : generic_product_impl_base<Lhs,Rhs,generic_product_impl<Lhs,Rhs,SparseShape,DenseShape,ProductType> >
+{
+ typedef typename Product<Lhs,Rhs>::Scalar Scalar;
+
+ template<typename Dest>
+ static void scaleAndAddTo(Dest& dst, const Lhs& lhs, const Rhs& rhs, const Scalar& alpha)
+ {
+ typedef typename nested_eval<Lhs,((Rhs::Flags&RowMajorBit)==0) ? 1 : Rhs::ColsAtCompileTime>::type LhsNested;
+ typedef typename nested_eval<Rhs,((Lhs::Flags&RowMajorBit)==0) ? 1 : Dynamic>::type RhsNested;
+ LhsNested lhsNested(lhs);
+ RhsNested rhsNested(rhs);
+ internal::sparse_time_dense_product(lhsNested, rhsNested, dst, alpha);
+ }
+};
+
+template<typename Lhs, typename Rhs, int ProductType>
+struct generic_product_impl<Lhs, Rhs, SparseTriangularShape, DenseShape, ProductType>
+ : generic_product_impl<Lhs, Rhs, SparseShape, DenseShape, ProductType>
+{};
+
+template<typename Lhs, typename Rhs, int ProductType>
+struct generic_product_impl<Lhs, Rhs, DenseShape, SparseShape, ProductType>
+ : generic_product_impl_base<Lhs,Rhs,generic_product_impl<Lhs,Rhs,DenseShape,SparseShape,ProductType> >
+{
+ typedef typename Product<Lhs,Rhs>::Scalar Scalar;
+
+ template<typename Dst>
+ static void scaleAndAddTo(Dst& dst, const Lhs& lhs, const Rhs& rhs, const Scalar& alpha)
+ {
+ typedef typename nested_eval<Lhs,((Rhs::Flags&RowMajorBit)==0) ? Dynamic : 1>::type LhsNested;
+ typedef typename nested_eval<Rhs,((Lhs::Flags&RowMajorBit)==RowMajorBit) ? 1 : Lhs::RowsAtCompileTime>::type RhsNested;
+ LhsNested lhsNested(lhs);
+ RhsNested rhsNested(rhs);
+
+ // transpose everything
+ Transpose<Dst> dstT(dst);
+ internal::sparse_time_dense_product(rhsNested.transpose(), lhsNested.transpose(), dstT, alpha);
+ }
+};
+
+template<typename Lhs, typename Rhs, int ProductType>
+struct generic_product_impl<Lhs, Rhs, DenseShape, SparseTriangularShape, ProductType>
+ : generic_product_impl<Lhs, Rhs, DenseShape, SparseShape, ProductType>
+{};
+
+template<typename LhsT, typename RhsT, bool NeedToTranspose>
+struct sparse_dense_outer_product_evaluator
+{
+protected:
+ typedef std::conditional_t<NeedToTranspose,RhsT,LhsT> Lhs1;
+ typedef std::conditional_t<NeedToTranspose,LhsT,RhsT> ActualRhs;
+ typedef Product<LhsT,RhsT,DefaultProduct> ProdXprType;
+
+ // if the actual left-hand side is a dense vector,
+ // then build a sparse-view so that we can seamlessly iterate over it.
+ typedef std::conditional_t<is_same<typename internal::traits<Lhs1>::StorageKind,Sparse>::value,
+ Lhs1, SparseView<Lhs1> > ActualLhs;
+ typedef std::conditional_t<is_same<typename internal::traits<Lhs1>::StorageKind,Sparse>::value,
+ Lhs1 const&, SparseView<Lhs1> > LhsArg;
+
+ typedef evaluator<ActualLhs> LhsEval;
+ typedef evaluator<ActualRhs> RhsEval;
+ typedef typename evaluator<ActualLhs>::InnerIterator LhsIterator;
+ typedef typename ProdXprType::Scalar Scalar;
+
+public:
+ enum {
+ Flags = NeedToTranspose ? RowMajorBit : 0,
+ CoeffReadCost = HugeCost
+ };
+
+ class InnerIterator : public LhsIterator
+ {
+ public:
+ InnerIterator(const sparse_dense_outer_product_evaluator &xprEval, Index outer)
+ : LhsIterator(xprEval.m_lhsXprImpl, 0),
+ m_outer(outer),
+ m_empty(false),
+ m_factor(get(xprEval.m_rhsXprImpl, outer, typename internal::traits<ActualRhs>::StorageKind() ))
+ {}
+
+ EIGEN_STRONG_INLINE Index outer() const { return m_outer; }
+ EIGEN_STRONG_INLINE Index row() const { return NeedToTranspose ? m_outer : LhsIterator::index(); }
+ EIGEN_STRONG_INLINE Index col() const { return NeedToTranspose ? LhsIterator::index() : m_outer; }
+
+ EIGEN_STRONG_INLINE Scalar value() const { return LhsIterator::value() * m_factor; }
+ EIGEN_STRONG_INLINE operator bool() const { return LhsIterator::operator bool() && (!m_empty); }
+
+ protected:
+ Scalar get(const RhsEval &rhs, Index outer, Dense = Dense()) const
+ {
+ return rhs.coeff(outer);
+ }
+
+ Scalar get(const RhsEval &rhs, Index outer, Sparse = Sparse())
+ {
+ typename RhsEval::InnerIterator it(rhs, outer);
+ if (it && it.index()==0 && it.value()!=Scalar(0))
+ return it.value();
+ m_empty = true;
+ return Scalar(0);
+ }
+
+ Index m_outer;
+ bool m_empty;
+ Scalar m_factor;
+ };
+
+ sparse_dense_outer_product_evaluator(const Lhs1 &lhs, const ActualRhs &rhs)
+ : m_lhs(lhs), m_lhsXprImpl(m_lhs), m_rhsXprImpl(rhs)
+ {
+ EIGEN_INTERNAL_CHECK_COST_VALUE(CoeffReadCost);
+ }
+
+ // transpose case
+ sparse_dense_outer_product_evaluator(const ActualRhs &rhs, const Lhs1 &lhs)
+ : m_lhs(lhs), m_lhsXprImpl(m_lhs), m_rhsXprImpl(rhs)
+ {
+ EIGEN_INTERNAL_CHECK_COST_VALUE(CoeffReadCost);
+ }
+
+protected:
+ const LhsArg m_lhs;
+ evaluator<ActualLhs> m_lhsXprImpl;
+ evaluator<ActualRhs> m_rhsXprImpl;
+};
+
+// sparse * dense outer product
+template<typename Lhs, typename Rhs>
+struct product_evaluator<Product<Lhs, Rhs, DefaultProduct>, OuterProduct, SparseShape, DenseShape>
+ : sparse_dense_outer_product_evaluator<Lhs,Rhs, Lhs::IsRowMajor>
+{
+ typedef sparse_dense_outer_product_evaluator<Lhs,Rhs, Lhs::IsRowMajor> Base;
+
+ typedef Product<Lhs, Rhs> XprType;
+ typedef typename XprType::PlainObject PlainObject;
+
+ explicit product_evaluator(const XprType& xpr)
+ : Base(xpr.lhs(), xpr.rhs())
+ {}
+
+};
+
+template<typename Lhs, typename Rhs>
+struct product_evaluator<Product<Lhs, Rhs, DefaultProduct>, OuterProduct, DenseShape, SparseShape>
+ : sparse_dense_outer_product_evaluator<Lhs,Rhs, Rhs::IsRowMajor>
+{
+ typedef sparse_dense_outer_product_evaluator<Lhs,Rhs, Rhs::IsRowMajor> Base;
+
+ typedef Product<Lhs, Rhs> XprType;
+ typedef typename XprType::PlainObject PlainObject;
+
+ explicit product_evaluator(const XprType& xpr)
+ : Base(xpr.lhs(), xpr.rhs())
+ {}
+
+};
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_SPARSEDENSEPRODUCT_H
diff --git a/Eigen/src/SparseCore/SparseDiagonalProduct.h b/Eigen/src/SparseCore/SparseDiagonalProduct.h
new file mode 100644
index 0000000..4dc9502
--- /dev/null
+++ b/Eigen/src/SparseCore/SparseDiagonalProduct.h
@@ -0,0 +1,140 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009-2015 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_SPARSE_DIAGONAL_PRODUCT_H
+#define EIGEN_SPARSE_DIAGONAL_PRODUCT_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+// The product of a diagonal matrix with a sparse matrix can be easily
+// implemented using expression template.
+// We have two consider very different cases:
+// 1 - diag * row-major sparse
+// => each inner vector <=> scalar * sparse vector product
+// => so we can reuse CwiseUnaryOp::InnerIterator
+// 2 - diag * col-major sparse
+// => each inner vector <=> densevector * sparse vector cwise product
+// => again, we can reuse specialization of CwiseBinaryOp::InnerIterator
+// for that particular case
+// The two other cases are symmetric.
+
+namespace internal {
+
+enum {
+ SDP_AsScalarProduct,
+ SDP_AsCwiseProduct
+};
+
+template<typename SparseXprType, typename DiagonalCoeffType, int SDP_Tag>
+struct sparse_diagonal_product_evaluator;
+
+template<typename Lhs, typename Rhs, int ProductTag>
+struct product_evaluator<Product<Lhs, Rhs, DefaultProduct>, ProductTag, DiagonalShape, SparseShape>
+ : public sparse_diagonal_product_evaluator<Rhs, typename Lhs::DiagonalVectorType, Rhs::Flags&RowMajorBit?SDP_AsScalarProduct:SDP_AsCwiseProduct>
+{
+ typedef Product<Lhs, Rhs, DefaultProduct> XprType;
+ enum { CoeffReadCost = HugeCost, Flags = Rhs::Flags&RowMajorBit, Alignment = 0 }; // FIXME CoeffReadCost & Flags
+
+ typedef sparse_diagonal_product_evaluator<Rhs, typename Lhs::DiagonalVectorType, Rhs::Flags&RowMajorBit?SDP_AsScalarProduct:SDP_AsCwiseProduct> Base;
+ explicit product_evaluator(const XprType& xpr) : Base(xpr.rhs(), xpr.lhs().diagonal()) {}
+};
+
+template<typename Lhs, typename Rhs, int ProductTag>
+struct product_evaluator<Product<Lhs, Rhs, DefaultProduct>, ProductTag, SparseShape, DiagonalShape>
+ : public sparse_diagonal_product_evaluator<Lhs, Transpose<const typename Rhs::DiagonalVectorType>, Lhs::Flags&RowMajorBit?SDP_AsCwiseProduct:SDP_AsScalarProduct>
+{
+ typedef Product<Lhs, Rhs, DefaultProduct> XprType;
+ enum { CoeffReadCost = HugeCost, Flags = Lhs::Flags&RowMajorBit, Alignment = 0 }; // FIXME CoeffReadCost & Flags
+
+ typedef sparse_diagonal_product_evaluator<Lhs, Transpose<const typename Rhs::DiagonalVectorType>, Lhs::Flags&RowMajorBit?SDP_AsCwiseProduct:SDP_AsScalarProduct> Base;
+ explicit product_evaluator(const XprType& xpr) : Base(xpr.lhs(), xpr.rhs().diagonal().transpose()) {}
+};
+
+template<typename SparseXprType, typename DiagonalCoeffType>
+struct sparse_diagonal_product_evaluator<SparseXprType, DiagonalCoeffType, SDP_AsScalarProduct>
+{
+protected:
+ typedef typename evaluator<SparseXprType>::InnerIterator SparseXprInnerIterator;
+ typedef typename SparseXprType::Scalar Scalar;
+
+public:
+ class InnerIterator : public SparseXprInnerIterator
+ {
+ public:
+ InnerIterator(const sparse_diagonal_product_evaluator &xprEval, Index outer)
+ : SparseXprInnerIterator(xprEval.m_sparseXprImpl, outer),
+ m_coeff(xprEval.m_diagCoeffImpl.coeff(outer))
+ {}
+
+ EIGEN_STRONG_INLINE Scalar value() const { return m_coeff * SparseXprInnerIterator::value(); }
+ protected:
+ typename DiagonalCoeffType::Scalar m_coeff;
+ };
+
+ sparse_diagonal_product_evaluator(const SparseXprType &sparseXpr, const DiagonalCoeffType &diagCoeff)
+ : m_sparseXprImpl(sparseXpr), m_diagCoeffImpl(diagCoeff)
+ {}
+
+ Index nonZerosEstimate() const { return m_sparseXprImpl.nonZerosEstimate(); }
+
+protected:
+ evaluator<SparseXprType> m_sparseXprImpl;
+ evaluator<DiagonalCoeffType> m_diagCoeffImpl;
+};
+
+
+template<typename SparseXprType, typename DiagCoeffType>
+struct sparse_diagonal_product_evaluator<SparseXprType, DiagCoeffType, SDP_AsCwiseProduct>
+{
+ typedef typename SparseXprType::Scalar Scalar;
+ typedef typename SparseXprType::StorageIndex StorageIndex;
+
+ typedef typename nested_eval<DiagCoeffType,SparseXprType::IsRowMajor ? SparseXprType::RowsAtCompileTime
+ : SparseXprType::ColsAtCompileTime>::type DiagCoeffNested;
+
+ class InnerIterator
+ {
+ typedef typename evaluator<SparseXprType>::InnerIterator SparseXprIter;
+ public:
+ InnerIterator(const sparse_diagonal_product_evaluator &xprEval, Index outer)
+ : m_sparseIter(xprEval.m_sparseXprEval, outer), m_diagCoeffNested(xprEval.m_diagCoeffNested)
+ {}
+
+ inline Scalar value() const { return m_sparseIter.value() * m_diagCoeffNested.coeff(index()); }
+ inline StorageIndex index() const { return m_sparseIter.index(); }
+ inline Index outer() const { return m_sparseIter.outer(); }
+ inline Index col() const { return SparseXprType::IsRowMajor ? m_sparseIter.index() : m_sparseIter.outer(); }
+ inline Index row() const { return SparseXprType::IsRowMajor ? m_sparseIter.outer() : m_sparseIter.index(); }
+
+ EIGEN_STRONG_INLINE InnerIterator& operator++() { ++m_sparseIter; return *this; }
+ inline operator bool() const { return m_sparseIter; }
+
+ protected:
+ SparseXprIter m_sparseIter;
+ DiagCoeffNested m_diagCoeffNested;
+ };
+
+ sparse_diagonal_product_evaluator(const SparseXprType &sparseXpr, const DiagCoeffType &diagCoeff)
+ : m_sparseXprEval(sparseXpr), m_diagCoeffNested(diagCoeff)
+ {}
+
+ Index nonZerosEstimate() const { return m_sparseXprEval.nonZerosEstimate(); }
+
+protected:
+ evaluator<SparseXprType> m_sparseXprEval;
+ DiagCoeffNested m_diagCoeffNested;
+};
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_SPARSE_DIAGONAL_PRODUCT_H
diff --git a/Eigen/src/SparseCore/SparseDot.h b/Eigen/src/SparseCore/SparseDot.h
new file mode 100644
index 0000000..a45ecfa
--- /dev/null
+++ b/Eigen/src/SparseCore/SparseDot.h
@@ -0,0 +1,100 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_SPARSE_DOT_H
+#define EIGEN_SPARSE_DOT_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+template<typename Derived>
+template<typename OtherDerived>
+typename internal::traits<Derived>::Scalar
+SparseMatrixBase<Derived>::dot(const MatrixBase<OtherDerived>& other) const
+{
+ EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
+ EIGEN_STATIC_ASSERT_VECTOR_ONLY(OtherDerived)
+ EIGEN_STATIC_ASSERT_SAME_VECTOR_SIZE(Derived,OtherDerived)
+ EIGEN_STATIC_ASSERT((internal::is_same<Scalar, typename OtherDerived::Scalar>::value),
+ YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY)
+
+ eigen_assert(size() == other.size());
+ eigen_assert(other.size()>0 && "you are using a non initialized vector");
+
+ internal::evaluator<Derived> thisEval(derived());
+ typename internal::evaluator<Derived>::InnerIterator i(thisEval, 0);
+ Scalar res(0);
+ while (i)
+ {
+ res += numext::conj(i.value()) * other.coeff(i.index());
+ ++i;
+ }
+ return res;
+}
+
+template<typename Derived>
+template<typename OtherDerived>
+typename internal::traits<Derived>::Scalar
+SparseMatrixBase<Derived>::dot(const SparseMatrixBase<OtherDerived>& other) const
+{
+ EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
+ EIGEN_STATIC_ASSERT_VECTOR_ONLY(OtherDerived)
+ EIGEN_STATIC_ASSERT_SAME_VECTOR_SIZE(Derived,OtherDerived)
+ EIGEN_STATIC_ASSERT((internal::is_same<Scalar, typename OtherDerived::Scalar>::value),
+ YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY)
+
+ eigen_assert(size() == other.size());
+
+ internal::evaluator<Derived> thisEval(derived());
+ typename internal::evaluator<Derived>::InnerIterator i(thisEval, 0);
+
+ internal::evaluator<OtherDerived> otherEval(other.derived());
+ typename internal::evaluator<OtherDerived>::InnerIterator j(otherEval, 0);
+
+ Scalar res(0);
+ while (i && j)
+ {
+ if (i.index()==j.index())
+ {
+ res += numext::conj(i.value()) * j.value();
+ ++i; ++j;
+ }
+ else if (i.index()<j.index())
+ ++i;
+ else
+ ++j;
+ }
+ return res;
+}
+
+template<typename Derived>
+inline typename NumTraits<typename internal::traits<Derived>::Scalar>::Real
+SparseMatrixBase<Derived>::squaredNorm() const
+{
+ return numext::real((*this).cwiseAbs2().sum());
+}
+
+template<typename Derived>
+inline typename NumTraits<typename internal::traits<Derived>::Scalar>::Real
+SparseMatrixBase<Derived>::norm() const
+{
+ using std::sqrt;
+ return sqrt(squaredNorm());
+}
+
+template<typename Derived>
+inline typename NumTraits<typename internal::traits<Derived>::Scalar>::Real
+SparseMatrixBase<Derived>::blueNorm() const
+{
+ return internal::blueNorm_impl(*this);
+}
+} // end namespace Eigen
+
+#endif // EIGEN_SPARSE_DOT_H
diff --git a/Eigen/src/SparseCore/SparseFuzzy.h b/Eigen/src/SparseCore/SparseFuzzy.h
new file mode 100644
index 0000000..dcfdde9
--- /dev/null
+++ b/Eigen/src/SparseCore/SparseFuzzy.h
@@ -0,0 +1,31 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2014 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_SPARSE_FUZZY_H
+#define EIGEN_SPARSE_FUZZY_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+template<typename Derived>
+template<typename OtherDerived>
+bool SparseMatrixBase<Derived>::isApprox(const SparseMatrixBase<OtherDerived>& other, const RealScalar &prec) const
+{
+ const typename internal::nested_eval<Derived,2,PlainObject>::type actualA(derived());
+ std::conditional_t<bool(IsRowMajor)==bool(OtherDerived::IsRowMajor),
+ const typename internal::nested_eval<OtherDerived,2,PlainObject>::type,
+ const PlainObject> actualB(other.derived());
+
+ return (actualA - actualB).squaredNorm() <= prec * prec * numext::mini(actualA.squaredNorm(), actualB.squaredNorm());
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_SPARSE_FUZZY_H
diff --git a/Eigen/src/SparseCore/SparseMap.h b/Eigen/src/SparseCore/SparseMap.h
new file mode 100644
index 0000000..a74baec
--- /dev/null
+++ b/Eigen/src/SparseCore/SparseMap.h
@@ -0,0 +1,307 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2015 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_SPARSE_MAP_H
+#define EIGEN_SPARSE_MAP_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+
+template<typename MatScalar, int MatOptions, typename MatIndex, int Options, typename StrideType>
+struct traits<Map<SparseMatrix<MatScalar,MatOptions,MatIndex>, Options, StrideType> >
+ : public traits<SparseMatrix<MatScalar,MatOptions,MatIndex> >
+{
+ typedef SparseMatrix<MatScalar,MatOptions,MatIndex> PlainObjectType;
+ typedef traits<PlainObjectType> TraitsBase;
+ enum {
+ Flags = TraitsBase::Flags & (~NestByRefBit)
+ };
+};
+
+template<typename MatScalar, int MatOptions, typename MatIndex, int Options, typename StrideType>
+struct traits<Map<const SparseMatrix<MatScalar,MatOptions,MatIndex>, Options, StrideType> >
+ : public traits<SparseMatrix<MatScalar,MatOptions,MatIndex> >
+{
+ typedef SparseMatrix<MatScalar,MatOptions,MatIndex> PlainObjectType;
+ typedef traits<PlainObjectType> TraitsBase;
+ enum {
+ Flags = TraitsBase::Flags & (~ (NestByRefBit | LvalueBit))
+ };
+};
+
+} // end namespace internal
+
+template<typename Derived,
+ int Level = internal::accessors_level<Derived>::has_write_access ? WriteAccessors : ReadOnlyAccessors
+> class SparseMapBase;
+
+/** \ingroup SparseCore_Module
+ * class SparseMapBase
+ * \brief Common base class for Map and Ref instance of sparse matrix and vector.
+ */
+template<typename Derived>
+class SparseMapBase<Derived,ReadOnlyAccessors>
+ : public SparseCompressedBase<Derived>
+{
+ public:
+ typedef SparseCompressedBase<Derived> Base;
+ typedef typename Base::Scalar Scalar;
+ typedef typename Base::StorageIndex StorageIndex;
+ enum { IsRowMajor = Base::IsRowMajor };
+ using Base::operator=;
+ protected:
+
+ typedef std::conditional_t<
+ bool(internal::is_lvalue<Derived>::value),
+ Scalar *, const Scalar *> ScalarPointer;
+ typedef std::conditional_t<
+ bool(internal::is_lvalue<Derived>::value),
+ StorageIndex *, const StorageIndex *> IndexPointer;
+
+ Index m_outerSize;
+ Index m_innerSize;
+ Array<StorageIndex,2,1> m_zero_nnz;
+ IndexPointer m_outerIndex;
+ IndexPointer m_innerIndices;
+ ScalarPointer m_values;
+ IndexPointer m_innerNonZeros;
+
+ public:
+
+ /** \copydoc SparseMatrixBase::rows() */
+ inline Index rows() const { return IsRowMajor ? m_outerSize : m_innerSize; }
+ /** \copydoc SparseMatrixBase::cols() */
+ inline Index cols() const { return IsRowMajor ? m_innerSize : m_outerSize; }
+ /** \copydoc SparseMatrixBase::innerSize() */
+ inline Index innerSize() const { return m_innerSize; }
+ /** \copydoc SparseMatrixBase::outerSize() */
+ inline Index outerSize() const { return m_outerSize; }
+ /** \copydoc SparseCompressedBase::nonZeros */
+ inline Index nonZeros() const { return m_zero_nnz[1]; }
+
+ /** \copydoc SparseCompressedBase::isCompressed */
+ bool isCompressed() const { return m_innerNonZeros==0; }
+
+ //----------------------------------------
+ // direct access interface
+ /** \copydoc SparseMatrix::valuePtr */
+ inline const Scalar* valuePtr() const { return m_values; }
+ /** \copydoc SparseMatrix::innerIndexPtr */
+ inline const StorageIndex* innerIndexPtr() const { return m_innerIndices; }
+ /** \copydoc SparseMatrix::outerIndexPtr */
+ inline const StorageIndex* outerIndexPtr() const { return m_outerIndex; }
+ /** \copydoc SparseMatrix::innerNonZeroPtr */
+ inline const StorageIndex* innerNonZeroPtr() const { return m_innerNonZeros; }
+ //----------------------------------------
+
+ /** \copydoc SparseMatrix::coeff */
+ inline Scalar coeff(Index row, Index col) const
+ {
+ const Index outer = IsRowMajor ? row : col;
+ const Index inner = IsRowMajor ? col : row;
+
+ Index start = m_outerIndex[outer];
+ Index end = isCompressed() ? m_outerIndex[outer+1] : start + m_innerNonZeros[outer];
+ if (start==end)
+ return Scalar(0);
+ else if (end>0 && inner==m_innerIndices[end-1])
+ return m_values[end-1];
+ // ^^ optimization: let's first check if it is the last coefficient
+ // (very common in high level algorithms)
+
+ const StorageIndex* r = std::lower_bound(&m_innerIndices[start],&m_innerIndices[end-1],inner);
+ const Index id = r-&m_innerIndices[0];
+ return ((*r==inner) && (id<end)) ? m_values[id] : Scalar(0);
+ }
+
+ inline SparseMapBase(Index rows, Index cols, Index nnz, IndexPointer outerIndexPtr, IndexPointer innerIndexPtr,
+ ScalarPointer valuePtr, IndexPointer innerNonZerosPtr = 0)
+ : m_outerSize(IsRowMajor?rows:cols), m_innerSize(IsRowMajor?cols:rows), m_zero_nnz(0,internal::convert_index<StorageIndex>(nnz)), m_outerIndex(outerIndexPtr),
+ m_innerIndices(innerIndexPtr), m_values(valuePtr), m_innerNonZeros(innerNonZerosPtr)
+ {}
+
+ // for vectors
+ inline SparseMapBase(Index size, Index nnz, IndexPointer innerIndexPtr, ScalarPointer valuePtr)
+ : m_outerSize(1), m_innerSize(size), m_zero_nnz(0,internal::convert_index<StorageIndex>(nnz)), m_outerIndex(m_zero_nnz.data()),
+ m_innerIndices(innerIndexPtr), m_values(valuePtr), m_innerNonZeros(0)
+ {}
+
+ /** Empty destructor */
+ inline ~SparseMapBase() {}
+
+ protected:
+ inline SparseMapBase() {}
+};
+
+/** \ingroup SparseCore_Module
+ * class SparseMapBase
+ * \brief Common base class for writable Map and Ref instance of sparse matrix and vector.
+ */
+template<typename Derived>
+class SparseMapBase<Derived,WriteAccessors>
+ : public SparseMapBase<Derived,ReadOnlyAccessors>
+{
+ typedef MapBase<Derived, ReadOnlyAccessors> ReadOnlyMapBase;
+
+ public:
+ typedef SparseMapBase<Derived, ReadOnlyAccessors> Base;
+ typedef typename Base::Scalar Scalar;
+ typedef typename Base::StorageIndex StorageIndex;
+ enum { IsRowMajor = Base::IsRowMajor };
+
+ using Base::operator=;
+
+ public:
+
+ //----------------------------------------
+ // direct access interface
+ using Base::valuePtr;
+ using Base::innerIndexPtr;
+ using Base::outerIndexPtr;
+ using Base::innerNonZeroPtr;
+ /** \copydoc SparseMatrix::valuePtr */
+ inline Scalar* valuePtr() { return Base::m_values; }
+ /** \copydoc SparseMatrix::innerIndexPtr */
+ inline StorageIndex* innerIndexPtr() { return Base::m_innerIndices; }
+ /** \copydoc SparseMatrix::outerIndexPtr */
+ inline StorageIndex* outerIndexPtr() { return Base::m_outerIndex; }
+ /** \copydoc SparseMatrix::innerNonZeroPtr */
+ inline StorageIndex* innerNonZeroPtr() { return Base::m_innerNonZeros; }
+ //----------------------------------------
+
+ /** \copydoc SparseMatrix::coeffRef */
+ inline Scalar& coeffRef(Index row, Index col)
+ {
+ const Index outer = IsRowMajor ? row : col;
+ const Index inner = IsRowMajor ? col : row;
+
+ Index start = Base::m_outerIndex[outer];
+ Index end = Base::isCompressed() ? Base::m_outerIndex[outer+1] : start + Base::m_innerNonZeros[outer];
+ eigen_assert(end>=start && "you probably called coeffRef on a non finalized matrix");
+ eigen_assert(end>start && "coeffRef cannot be called on a zero coefficient");
+ StorageIndex* r = std::lower_bound(&Base::m_innerIndices[start],&Base::m_innerIndices[end],inner);
+ const Index id = r - &Base::m_innerIndices[0];
+ eigen_assert((*r==inner) && (id<end) && "coeffRef cannot be called on a zero coefficient");
+ return const_cast<Scalar*>(Base::m_values)[id];
+ }
+
+ inline SparseMapBase(Index rows, Index cols, Index nnz, StorageIndex* outerIndexPtr, StorageIndex* innerIndexPtr,
+ Scalar* valuePtr, StorageIndex* innerNonZerosPtr = 0)
+ : Base(rows, cols, nnz, outerIndexPtr, innerIndexPtr, valuePtr, innerNonZerosPtr)
+ {}
+
+ // for vectors
+ inline SparseMapBase(Index size, Index nnz, StorageIndex* innerIndexPtr, Scalar* valuePtr)
+ : Base(size, nnz, innerIndexPtr, valuePtr)
+ {}
+
+ /** Empty destructor */
+ inline ~SparseMapBase() {}
+
+ protected:
+ inline SparseMapBase() {}
+};
+
+/** \ingroup SparseCore_Module
+ *
+ * \brief Specialization of class Map for SparseMatrix-like storage.
+ *
+ * \tparam SparseMatrixType the equivalent sparse matrix type of the referenced data, it must be a template instance of class SparseMatrix.
+ *
+ * \sa class Map, class SparseMatrix, class Ref<SparseMatrixType,Options>
+ */
+#ifndef EIGEN_PARSED_BY_DOXYGEN
+template<typename MatScalar, int MatOptions, typename MatIndex, int Options, typename StrideType>
+class Map<SparseMatrix<MatScalar,MatOptions,MatIndex>, Options, StrideType>
+ : public SparseMapBase<Map<SparseMatrix<MatScalar,MatOptions,MatIndex>, Options, StrideType> >
+#else
+template<typename SparseMatrixType>
+class Map<SparseMatrixType>
+ : public SparseMapBase<Derived,WriteAccessors>
+#endif
+{
+ public:
+ typedef SparseMapBase<Map> Base;
+ EIGEN_SPARSE_PUBLIC_INTERFACE(Map)
+ enum { IsRowMajor = Base::IsRowMajor };
+
+ public:
+
+ /** Constructs a read-write Map to a sparse matrix of size \a rows x \a cols, containing \a nnz non-zero coefficients,
+ * stored as a sparse format as defined by the pointers \a outerIndexPtr, \a innerIndexPtr, and \a valuePtr.
+ * If the optional parameter \a innerNonZerosPtr is the null pointer, then a standard compressed format is assumed.
+ *
+ * This constructor is available only if \c SparseMatrixType is non-const.
+ *
+ * More details on the expected storage schemes are given in the \ref TutorialSparse "manual pages".
+ */
+ inline Map(Index rows, Index cols, Index nnz, StorageIndex* outerIndexPtr,
+ StorageIndex* innerIndexPtr, Scalar* valuePtr, StorageIndex* innerNonZerosPtr = 0)
+ : Base(rows, cols, nnz, outerIndexPtr, innerIndexPtr, valuePtr, innerNonZerosPtr)
+ {}
+#ifndef EIGEN_PARSED_BY_DOXYGEN
+ /** Empty destructor */
+ inline ~Map() {}
+};
+
+template<typename MatScalar, int MatOptions, typename MatIndex, int Options, typename StrideType>
+class Map<const SparseMatrix<MatScalar,MatOptions,MatIndex>, Options, StrideType>
+ : public SparseMapBase<Map<const SparseMatrix<MatScalar,MatOptions,MatIndex>, Options, StrideType> >
+{
+ public:
+ typedef SparseMapBase<Map> Base;
+ EIGEN_SPARSE_PUBLIC_INTERFACE(Map)
+ enum { IsRowMajor = Base::IsRowMajor };
+
+ public:
+#endif
+ /** This is the const version of the above constructor.
+ *
+ * This constructor is available only if \c SparseMatrixType is const, e.g.:
+ * \code Map<const SparseMatrix<double> > \endcode
+ */
+ inline Map(Index rows, Index cols, Index nnz, const StorageIndex* outerIndexPtr,
+ const StorageIndex* innerIndexPtr, const Scalar* valuePtr, const StorageIndex* innerNonZerosPtr = 0)
+ : Base(rows, cols, nnz, outerIndexPtr, innerIndexPtr, valuePtr, innerNonZerosPtr)
+ {}
+
+ /** Empty destructor */
+ inline ~Map() {}
+};
+
+namespace internal {
+
+template<typename MatScalar, int MatOptions, typename MatIndex, int Options, typename StrideType>
+struct evaluator<Map<SparseMatrix<MatScalar,MatOptions,MatIndex>, Options, StrideType> >
+ : evaluator<SparseCompressedBase<Map<SparseMatrix<MatScalar,MatOptions,MatIndex>, Options, StrideType> > >
+{
+ typedef evaluator<SparseCompressedBase<Map<SparseMatrix<MatScalar,MatOptions,MatIndex>, Options, StrideType> > > Base;
+ typedef Map<SparseMatrix<MatScalar,MatOptions,MatIndex>, Options, StrideType> XprType;
+ evaluator() : Base() {}
+ explicit evaluator(const XprType &mat) : Base(mat) {}
+};
+
+template<typename MatScalar, int MatOptions, typename MatIndex, int Options, typename StrideType>
+struct evaluator<Map<const SparseMatrix<MatScalar,MatOptions,MatIndex>, Options, StrideType> >
+ : evaluator<SparseCompressedBase<Map<const SparseMatrix<MatScalar,MatOptions,MatIndex>, Options, StrideType> > >
+{
+ typedef evaluator<SparseCompressedBase<Map<const SparseMatrix<MatScalar,MatOptions,MatIndex>, Options, StrideType> > > Base;
+ typedef Map<const SparseMatrix<MatScalar,MatOptions,MatIndex>, Options, StrideType> XprType;
+ evaluator() : Base() {}
+ explicit evaluator(const XprType &mat) : Base(mat) {}
+};
+
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_SPARSE_MAP_H
diff --git a/Eigen/src/SparseCore/SparseMatrix.h b/Eigen/src/SparseCore/SparseMatrix.h
new file mode 100644
index 0000000..fdac443
--- /dev/null
+++ b/Eigen/src/SparseCore/SparseMatrix.h
@@ -0,0 +1,1501 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2014 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_SPARSEMATRIX_H
+#define EIGEN_SPARSEMATRIX_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+/** \ingroup SparseCore_Module
+ *
+ * \class SparseMatrix
+ *
+ * \brief A versatible sparse matrix representation
+ *
+ * This class implements a more versatile variants of the common \em compressed row/column storage format.
+ * Each colmun's (resp. row) non zeros are stored as a pair of value with associated row (resp. colmiun) index.
+ * All the non zeros are stored in a single large buffer. Unlike the \em compressed format, there might be extra
+ * space in between the nonzeros of two successive colmuns (resp. rows) such that insertion of new non-zero
+ * can be done with limited memory reallocation and copies.
+ *
+ * A call to the function makeCompressed() turns the matrix into the standard \em compressed format
+ * compatible with many library.
+ *
+ * More details on this storage sceheme are given in the \ref TutorialSparse "manual pages".
+ *
+ * \tparam Scalar_ the scalar type, i.e. the type of the coefficients
+ * \tparam Options_ Union of bit flags controlling the storage scheme. Currently the only possibility
+ * is ColMajor or RowMajor. The default is 0 which means column-major.
+ * \tparam StorageIndex_ the type of the indices. It has to be a \b signed type (e.g., short, int, std::ptrdiff_t). Default is \c int.
+ *
+ * \warning In %Eigen 3.2, the undocumented type \c SparseMatrix::Index was improperly defined as the storage index type (e.g., int),
+ * whereas it is now (starting from %Eigen 3.3) deprecated and always defined as Eigen::Index.
+ * Codes making use of \c SparseMatrix::Index, might thus likely have to be changed to use \c SparseMatrix::StorageIndex instead.
+ *
+ * This class can be extended with the help of the plugin mechanism described on the page
+ * \ref TopicCustomizing_Plugins by defining the preprocessor symbol \c EIGEN_SPARSEMATRIX_PLUGIN.
+ */
+
+namespace internal {
+template<typename Scalar_, int Options_, typename StorageIndex_>
+struct traits<SparseMatrix<Scalar_, Options_, StorageIndex_> >
+{
+ typedef Scalar_ Scalar;
+ typedef StorageIndex_ StorageIndex;
+ typedef Sparse StorageKind;
+ typedef MatrixXpr XprKind;
+ enum {
+ RowsAtCompileTime = Dynamic,
+ ColsAtCompileTime = Dynamic,
+ MaxRowsAtCompileTime = Dynamic,
+ MaxColsAtCompileTime = Dynamic,
+ Flags = Options_ | NestByRefBit | LvalueBit | CompressedAccessBit,
+ SupportedAccessPatterns = InnerRandomAccessPattern
+ };
+};
+
+template<typename Scalar_, int Options_, typename StorageIndex_, int DiagIndex>
+struct traits<Diagonal<SparseMatrix<Scalar_, Options_, StorageIndex_>, DiagIndex> >
+{
+ typedef SparseMatrix<Scalar_, Options_, StorageIndex_> MatrixType;
+ typedef typename ref_selector<MatrixType>::type MatrixTypeNested;
+ typedef std::remove_reference_t<MatrixTypeNested> MatrixTypeNested_;
+
+ typedef Scalar_ Scalar;
+ typedef Dense StorageKind;
+ typedef StorageIndex_ StorageIndex;
+ typedef MatrixXpr XprKind;
+
+ enum {
+ RowsAtCompileTime = Dynamic,
+ ColsAtCompileTime = 1,
+ MaxRowsAtCompileTime = Dynamic,
+ MaxColsAtCompileTime = 1,
+ Flags = LvalueBit
+ };
+};
+
+template<typename Scalar_, int Options_, typename StorageIndex_, int DiagIndex>
+struct traits<Diagonal<const SparseMatrix<Scalar_, Options_, StorageIndex_>, DiagIndex> >
+ : public traits<Diagonal<SparseMatrix<Scalar_, Options_, StorageIndex_>, DiagIndex> >
+{
+ enum {
+ Flags = 0
+ };
+};
+
+} // end namespace internal
+
+template<typename Scalar_, int Options_, typename StorageIndex_>
+class SparseMatrix
+ : public SparseCompressedBase<SparseMatrix<Scalar_, Options_, StorageIndex_> >
+{
+ typedef SparseCompressedBase<SparseMatrix> Base;
+ using Base::convert_index;
+ friend class SparseVector<Scalar_,0,StorageIndex_>;
+ template<typename, typename, typename, typename, typename>
+ friend struct internal::Assignment;
+ public:
+ using Base::isCompressed;
+ using Base::nonZeros;
+ EIGEN_SPARSE_PUBLIC_INTERFACE(SparseMatrix)
+ using Base::operator+=;
+ using Base::operator-=;
+
+ typedef Eigen::Map<SparseMatrix<Scalar,Flags,StorageIndex>> Map;
+ typedef Diagonal<SparseMatrix> DiagonalReturnType;
+ typedef Diagonal<const SparseMatrix> ConstDiagonalReturnType;
+ typedef typename Base::InnerIterator InnerIterator;
+ typedef typename Base::ReverseInnerIterator ReverseInnerIterator;
+
+
+ using Base::IsRowMajor;
+ typedef internal::CompressedStorage<Scalar,StorageIndex> Storage;
+ enum {
+ Options = Options_
+ };
+
+ typedef typename Base::IndexVector IndexVector;
+ typedef typename Base::ScalarVector ScalarVector;
+ protected:
+ typedef SparseMatrix<Scalar,(Flags&~RowMajorBit)|(IsRowMajor?RowMajorBit:0),StorageIndex> TransposedSparseMatrix;
+
+ Index m_outerSize;
+ Index m_innerSize;
+ StorageIndex* m_outerIndex;
+ StorageIndex* m_innerNonZeros; // optional, if null then the data is compressed
+ Storage m_data;
+
+ public:
+
+ /** \returns the number of rows of the matrix */
+ inline Index rows() const { return IsRowMajor ? m_outerSize : m_innerSize; }
+ /** \returns the number of columns of the matrix */
+ inline Index cols() const { return IsRowMajor ? m_innerSize : m_outerSize; }
+
+ /** \returns the number of rows (resp. columns) of the matrix if the storage order column major (resp. row major) */
+ inline Index innerSize() const { return m_innerSize; }
+ /** \returns the number of columns (resp. rows) of the matrix if the storage order column major (resp. row major) */
+ inline Index outerSize() const { return m_outerSize; }
+
+ /** \returns a const pointer to the array of values.
+ * This function is aimed at interoperability with other libraries.
+ * \sa innerIndexPtr(), outerIndexPtr() */
+ inline const Scalar* valuePtr() const { return m_data.valuePtr(); }
+ /** \returns a non-const pointer to the array of values.
+ * This function is aimed at interoperability with other libraries.
+ * \sa innerIndexPtr(), outerIndexPtr() */
+ inline Scalar* valuePtr() { return m_data.valuePtr(); }
+
+ /** \returns a const pointer to the array of inner indices.
+ * This function is aimed at interoperability with other libraries.
+ * \sa valuePtr(), outerIndexPtr() */
+ inline const StorageIndex* innerIndexPtr() const { return m_data.indexPtr(); }
+ /** \returns a non-const pointer to the array of inner indices.
+ * This function is aimed at interoperability with other libraries.
+ * \sa valuePtr(), outerIndexPtr() */
+ inline StorageIndex* innerIndexPtr() { return m_data.indexPtr(); }
+
+ /** \returns a const pointer to the array of the starting positions of the inner vectors.
+ * This function is aimed at interoperability with other libraries.
+ * \sa valuePtr(), innerIndexPtr() */
+ inline const StorageIndex* outerIndexPtr() const { return m_outerIndex; }
+ /** \returns a non-const pointer to the array of the starting positions of the inner vectors.
+ * This function is aimed at interoperability with other libraries.
+ * \sa valuePtr(), innerIndexPtr() */
+ inline StorageIndex* outerIndexPtr() { return m_outerIndex; }
+
+ /** \returns a const pointer to the array of the number of non zeros of the inner vectors.
+ * This function is aimed at interoperability with other libraries.
+ * \warning it returns the null pointer 0 in compressed mode */
+ inline const StorageIndex* innerNonZeroPtr() const { return m_innerNonZeros; }
+ /** \returns a non-const pointer to the array of the number of non zeros of the inner vectors.
+ * This function is aimed at interoperability with other libraries.
+ * \warning it returns the null pointer 0 in compressed mode */
+ inline StorageIndex* innerNonZeroPtr() { return m_innerNonZeros; }
+
+ /** \internal */
+ inline Storage& data() { return m_data; }
+ /** \internal */
+ inline const Storage& data() const { return m_data; }
+
+ /** \returns the value of the matrix at position \a i, \a j
+ * This function returns Scalar(0) if the element is an explicit \em zero */
+ inline Scalar coeff(Index row, Index col) const
+ {
+ eigen_assert(row>=0 && row<rows() && col>=0 && col<cols());
+
+ const Index outer = IsRowMajor ? row : col;
+ const Index inner = IsRowMajor ? col : row;
+ Index end = m_innerNonZeros ? m_outerIndex[outer] + m_innerNonZeros[outer] : m_outerIndex[outer+1];
+ return m_data.atInRange(m_outerIndex[outer], end, StorageIndex(inner));
+ }
+
+ /** \returns a non-const reference to the value of the matrix at position \a i, \a j
+ *
+ * If the element does not exist then it is inserted via the insert(Index,Index) function
+ * which itself turns the matrix into a non compressed form if that was not the case.
+ *
+ * This is a O(log(nnz_j)) operation (binary search) plus the cost of insert(Index,Index)
+ * function if the element does not already exist.
+ */
+ inline Scalar& coeffRef(Index row, Index col)
+ {
+ eigen_assert(row>=0 && row<rows() && col>=0 && col<cols());
+
+ const Index outer = IsRowMajor ? row : col;
+ const Index inner = IsRowMajor ? col : row;
+
+ Index start = m_outerIndex[outer];
+ Index end = m_innerNonZeros ? m_outerIndex[outer] + m_innerNonZeros[outer] : m_outerIndex[outer+1];
+ eigen_assert(end>=start && "you probably called coeffRef on a non finalized matrix");
+ if(end<=start)
+ return insert(row,col);
+ const Index p = m_data.searchLowerIndex(start,end-1,StorageIndex(inner));
+ if((p<end) && (m_data.index(p)==inner))
+ return m_data.value(p);
+ else
+ return insert(row,col);
+ }
+
+ /** \returns a reference to a novel non zero coefficient with coordinates \a row x \a col.
+ * The non zero coefficient must \b not already exist.
+ *
+ * If the matrix \c *this is in compressed mode, then \c *this is turned into uncompressed
+ * mode while reserving room for 2 x this->innerSize() non zeros if reserve(Index) has not been called earlier.
+ * In this case, the insertion procedure is optimized for a \e sequential insertion mode where elements are assumed to be
+ * inserted by increasing outer-indices.
+ *
+ * If that's not the case, then it is strongly recommended to either use a triplet-list to assemble the matrix, or to first
+ * call reserve(const SizesType &) to reserve the appropriate number of non-zero elements per inner vector.
+ *
+ * Assuming memory has been appropriately reserved, this function performs a sorted insertion in O(1)
+ * if the elements of each inner vector are inserted in increasing inner index order, and in O(nnz_j) for a random insertion.
+ *
+ */
+ Scalar& insert(Index row, Index col);
+
+ public:
+
+ /** Removes all non zeros but keep allocated memory
+ *
+ * This function does not free the currently allocated memory. To release as much as memory as possible,
+ * call \code mat.data().squeeze(); \endcode after resizing it.
+ *
+ * \sa resize(Index,Index), data()
+ */
+ inline void setZero()
+ {
+ m_data.clear();
+ std::fill_n(m_outerIndex, m_outerSize + 1, StorageIndex(0));
+ if(m_innerNonZeros) {
+ std::fill_n(m_innerNonZeros, m_outerSize, StorageIndex(0));
+ }
+ }
+
+ /** Preallocates \a reserveSize non zeros.
+ *
+ * Precondition: the matrix must be in compressed mode. */
+ inline void reserve(Index reserveSize)
+ {
+ eigen_assert(isCompressed() && "This function does not make sense in non compressed mode.");
+ m_data.reserve(reserveSize);
+ }
+
+ #ifdef EIGEN_PARSED_BY_DOXYGEN
+ /** Preallocates \a reserveSize[\c j] non zeros for each column (resp. row) \c j.
+ *
+ * This function turns the matrix in non-compressed mode.
+ *
+ * The type \c SizesType must expose the following interface:
+ \code
+ typedef value_type;
+ const value_type& operator[](i) const;
+ \endcode
+ * for \c i in the [0,this->outerSize()[ range.
+ * Typical choices include std::vector<int>, Eigen::VectorXi, Eigen::VectorXi::Constant, etc.
+ */
+ template<class SizesType>
+ inline void reserve(const SizesType& reserveSizes);
+ #else
+ template<class SizesType>
+ inline void reserve(const SizesType& reserveSizes, const typename SizesType::value_type& enableif =
+ typename SizesType::value_type())
+ {
+ EIGEN_UNUSED_VARIABLE(enableif);
+ reserveInnerVectors(reserveSizes);
+ }
+ #endif // EIGEN_PARSED_BY_DOXYGEN
+ protected:
+ template<class SizesType>
+ inline void reserveInnerVectors(const SizesType& reserveSizes)
+ {
+ if(isCompressed())
+ {
+ Index totalReserveSize = 0;
+ // turn the matrix into non-compressed mode
+ m_innerNonZeros = internal::conditional_aligned_new_auto<StorageIndex, true>(m_outerSize);
+
+ // temporarily use m_innerSizes to hold the new starting points.
+ StorageIndex* newOuterIndex = m_innerNonZeros;
+
+ StorageIndex count = 0;
+ for(Index j=0; j<m_outerSize; ++j)
+ {
+ newOuterIndex[j] = count;
+ count += reserveSizes[j] + (m_outerIndex[j+1]-m_outerIndex[j]);
+ totalReserveSize += reserveSizes[j];
+ }
+ m_data.reserve(totalReserveSize);
+ StorageIndex previousOuterIndex = m_outerIndex[m_outerSize];
+ for(Index j=m_outerSize-1; j>=0; --j)
+ {
+ StorageIndex innerNNZ = previousOuterIndex - m_outerIndex[j];
+ for(Index i=innerNNZ-1; i>=0; --i)
+ {
+ m_data.index(newOuterIndex[j]+i) = m_data.index(m_outerIndex[j]+i);
+ m_data.value(newOuterIndex[j]+i) = m_data.value(m_outerIndex[j]+i);
+ }
+ previousOuterIndex = m_outerIndex[j];
+ m_outerIndex[j] = newOuterIndex[j];
+ m_innerNonZeros[j] = innerNNZ;
+ }
+ if(m_outerSize>0)
+ m_outerIndex[m_outerSize] = m_outerIndex[m_outerSize-1] + m_innerNonZeros[m_outerSize-1] + reserveSizes[m_outerSize-1];
+
+ m_data.resize(m_outerIndex[m_outerSize]);
+ }
+ else
+ {
+ StorageIndex* newOuterIndex = internal::conditional_aligned_new_auto<StorageIndex, true>(m_outerSize + 1);
+
+ StorageIndex count = 0;
+ for(Index j=0; j<m_outerSize; ++j)
+ {
+ newOuterIndex[j] = count;
+ StorageIndex alreadyReserved = (m_outerIndex[j+1]-m_outerIndex[j]) - m_innerNonZeros[j];
+ StorageIndex toReserve = std::max<StorageIndex>(reserveSizes[j], alreadyReserved);
+ count += toReserve + m_innerNonZeros[j];
+ }
+ newOuterIndex[m_outerSize] = count;
+
+ m_data.resize(count);
+ for(Index j=m_outerSize-1; j>=0; --j)
+ {
+ Index offset = newOuterIndex[j] - m_outerIndex[j];
+ if(offset>0)
+ {
+ StorageIndex innerNNZ = m_innerNonZeros[j];
+ for(Index i=innerNNZ-1; i>=0; --i)
+ {
+ m_data.index(newOuterIndex[j]+i) = m_data.index(m_outerIndex[j]+i);
+ m_data.value(newOuterIndex[j]+i) = m_data.value(m_outerIndex[j]+i);
+ }
+ }
+ }
+
+ std::swap(m_outerIndex, newOuterIndex);
+ internal::conditional_aligned_delete_auto<StorageIndex, true>(newOuterIndex, m_outerSize + 1);
+ }
+
+ }
+ public:
+
+ //--- low level purely coherent filling ---
+
+ /** \internal
+ * \returns a reference to the non zero coefficient at position \a row, \a col assuming that:
+ * - the nonzero does not already exist
+ * - the new coefficient is the last one according to the storage order
+ *
+ * Before filling a given inner vector you must call the statVec(Index) function.
+ *
+ * After an insertion session, you should call the finalize() function.
+ *
+ * \sa insert, insertBackByOuterInner, startVec */
+ inline Scalar& insertBack(Index row, Index col)
+ {
+ return insertBackByOuterInner(IsRowMajor?row:col, IsRowMajor?col:row);
+ }
+
+ /** \internal
+ * \sa insertBack, startVec */
+ inline Scalar& insertBackByOuterInner(Index outer, Index inner)
+ {
+ eigen_assert(Index(m_outerIndex[outer+1]) == m_data.size() && "Invalid ordered insertion (invalid outer index)");
+ eigen_assert( (m_outerIndex[outer+1]-m_outerIndex[outer]==0 || m_data.index(m_data.size()-1)<inner) && "Invalid ordered insertion (invalid inner index)");
+ Index p = m_outerIndex[outer+1];
+ ++m_outerIndex[outer+1];
+ m_data.append(Scalar(0), inner);
+ return m_data.value(p);
+ }
+
+ /** \internal
+ * \warning use it only if you know what you are doing */
+ inline Scalar& insertBackByOuterInnerUnordered(Index outer, Index inner)
+ {
+ Index p = m_outerIndex[outer+1];
+ ++m_outerIndex[outer+1];
+ m_data.append(Scalar(0), inner);
+ return m_data.value(p);
+ }
+
+ /** \internal
+ * \sa insertBack, insertBackByOuterInner */
+ inline void startVec(Index outer)
+ {
+ eigen_assert(m_outerIndex[outer]==Index(m_data.size()) && "You must call startVec for each inner vector sequentially");
+ eigen_assert(m_outerIndex[outer+1]==0 && "You must call startVec for each inner vector sequentially");
+ m_outerIndex[outer+1] = m_outerIndex[outer];
+ }
+
+ /** \internal
+ * Must be called after inserting a set of non zero entries using the low level compressed API.
+ */
+ inline void finalize()
+ {
+ if(isCompressed())
+ {
+ StorageIndex size = internal::convert_index<StorageIndex>(m_data.size());
+ Index i = m_outerSize;
+ // find the last filled column
+ while (i>=0 && m_outerIndex[i]==0)
+ --i;
+ ++i;
+ while (i<=m_outerSize)
+ {
+ m_outerIndex[i] = size;
+ ++i;
+ }
+ }
+ }
+
+ //---
+
+ template<typename InputIterators>
+ void setFromTriplets(const InputIterators& begin, const InputIterators& end);
+
+ template<typename InputIterators,typename DupFunctor>
+ void setFromTriplets(const InputIterators& begin, const InputIterators& end, DupFunctor dup_func);
+
+ void sumupDuplicates() { collapseDuplicates(internal::scalar_sum_op<Scalar,Scalar>()); }
+
+ template<typename DupFunctor>
+ void collapseDuplicates(DupFunctor dup_func = DupFunctor());
+
+ //---
+
+ /** \internal
+ * same as insert(Index,Index) except that the indices are given relative to the storage order */
+ Scalar& insertByOuterInner(Index j, Index i)
+ {
+ return insert(IsRowMajor ? j : i, IsRowMajor ? i : j);
+ }
+
+ /** Turns the matrix into the \em compressed format.
+ */
+ void makeCompressed()
+ {
+ if(isCompressed())
+ return;
+
+ eigen_internal_assert(m_outerIndex!=0 && m_outerSize>0);
+
+ Index oldStart = m_outerIndex[1];
+ m_outerIndex[1] = m_innerNonZeros[0];
+ for(Index j=1; j<m_outerSize; ++j)
+ {
+ Index nextOldStart = m_outerIndex[j+1];
+ Index offset = oldStart - m_outerIndex[j];
+ if(offset>0)
+ {
+ for(Index k=0; k<m_innerNonZeros[j]; ++k)
+ {
+ m_data.index(m_outerIndex[j]+k) = m_data.index(oldStart+k);
+ m_data.value(m_outerIndex[j]+k) = m_data.value(oldStart+k);
+ }
+ }
+ m_outerIndex[j+1] = m_outerIndex[j] + m_innerNonZeros[j];
+ oldStart = nextOldStart;
+ }
+ internal::conditional_aligned_delete_auto<StorageIndex, true>(m_innerNonZeros, m_outerSize);
+ m_innerNonZeros = 0;
+ m_data.resize(m_outerIndex[m_outerSize]);
+ m_data.squeeze();
+ }
+
+ /** Turns the matrix into the uncompressed mode */
+ void uncompress()
+ {
+ if(m_innerNonZeros != 0)
+ return;
+ m_innerNonZeros = internal::conditional_aligned_new_auto<StorageIndex, true>(m_outerSize);
+ for (Index i = 0; i < m_outerSize; i++)
+ {
+ m_innerNonZeros[i] = m_outerIndex[i+1] - m_outerIndex[i];
+ }
+ }
+
+ /** Suppresses all nonzeros which are \b much \b smaller \b than \a reference under the tolerance \a epsilon */
+ void prune(const Scalar& reference, const RealScalar& epsilon = NumTraits<RealScalar>::dummy_precision())
+ {
+ prune(default_prunning_func(reference,epsilon));
+ }
+
+ /** Turns the matrix into compressed format, and suppresses all nonzeros which do not satisfy the predicate \a keep.
+ * The functor type \a KeepFunc must implement the following function:
+ * \code
+ * bool operator() (const Index& row, const Index& col, const Scalar& value) const;
+ * \endcode
+ * \sa prune(Scalar,RealScalar)
+ */
+ template<typename KeepFunc>
+ void prune(const KeepFunc& keep = KeepFunc())
+ {
+ // TODO optimize the uncompressed mode to avoid moving and allocating the data twice
+ makeCompressed();
+
+ StorageIndex k = 0;
+ for(Index j=0; j<m_outerSize; ++j)
+ {
+ Index previousStart = m_outerIndex[j];
+ m_outerIndex[j] = k;
+ Index end = m_outerIndex[j+1];
+ for(Index i=previousStart; i<end; ++i)
+ {
+ if(keep(IsRowMajor?j:m_data.index(i), IsRowMajor?m_data.index(i):j, m_data.value(i)))
+ {
+ m_data.value(k) = m_data.value(i);
+ m_data.index(k) = m_data.index(i);
+ ++k;
+ }
+ }
+ }
+ m_outerIndex[m_outerSize] = k;
+ m_data.resize(k,0);
+ }
+
+ /** Resizes the matrix to a \a rows x \a cols matrix leaving old values untouched.
+ *
+ * If the sizes of the matrix are decreased, then the matrix is turned to \b uncompressed-mode
+ * and the storage of the out of bounds coefficients is kept and reserved.
+ * Call makeCompressed() to pack the entries and squeeze extra memory.
+ *
+ * \sa reserve(), setZero(), makeCompressed()
+ */
+ void conservativeResize(Index rows, Index cols)
+ {
+ // No change
+ if (this->rows() == rows && this->cols() == cols) return;
+
+ // If one dimension is null, then there is nothing to be preserved
+ if(rows==0 || cols==0) return resize(rows,cols);
+
+ Index innerChange = IsRowMajor ? cols - this->cols() : rows - this->rows();
+ Index outerChange = IsRowMajor ? rows - this->rows() : cols - this->cols();
+ StorageIndex newInnerSize = convert_index(IsRowMajor ? cols : rows);
+
+ // Deals with inner non zeros
+ if (m_innerNonZeros)
+ {
+ // Resize m_innerNonZeros
+ m_innerNonZeros = internal::conditional_aligned_realloc_new_auto<StorageIndex, true>(
+ m_innerNonZeros, m_outerSize + outerChange, m_outerSize);
+
+ for(Index i=m_outerSize; i<m_outerSize+outerChange; i++)
+ m_innerNonZeros[i] = 0;
+ }
+ else if (innerChange < 0)
+ {
+ // Inner size decreased: allocate a new m_innerNonZeros
+ m_innerNonZeros = internal::conditional_aligned_new_auto<StorageIndex, true>(m_outerSize + outerChange);
+ for(Index i = 0; i < m_outerSize + (std::min)(outerChange, Index(0)); i++)
+ m_innerNonZeros[i] = m_outerIndex[i+1] - m_outerIndex[i];
+ for(Index i = m_outerSize; i < m_outerSize + outerChange; i++)
+ m_innerNonZeros[i] = 0;
+ }
+
+ // Change the m_innerNonZeros in case of a decrease of inner size
+ if (m_innerNonZeros && innerChange < 0)
+ {
+ for(Index i = 0; i < m_outerSize + (std::min)(outerChange, Index(0)); i++)
+ {
+ StorageIndex &n = m_innerNonZeros[i];
+ StorageIndex start = m_outerIndex[i];
+ while (n > 0 && m_data.index(start+n-1) >= newInnerSize) --n;
+ }
+ }
+
+ m_innerSize = newInnerSize;
+
+ // Re-allocate outer index structure if necessary
+ if (outerChange == 0)
+ return;
+
+ m_outerIndex = internal::conditional_aligned_realloc_new_auto<StorageIndex, true>(
+ m_outerIndex, m_outerSize + outerChange + 1, m_outerSize + 1);
+ if (outerChange > 0)
+ {
+ StorageIndex lastIdx = m_outerSize == 0 ? 0 : m_outerIndex[m_outerSize];
+ for(Index i=m_outerSize; i<m_outerSize+outerChange+1; i++)
+ m_outerIndex[i] = lastIdx;
+ }
+ m_outerSize += outerChange;
+ }
+
+ /** Resizes the matrix to a \a rows x \a cols matrix and initializes it to zero.
+ *
+ * This function does not free the currently allocated memory. To release as much as memory as possible,
+ * call \code mat.data().squeeze(); \endcode after resizing it.
+ *
+ * \sa reserve(), setZero()
+ */
+ void resize(Index rows, Index cols)
+ {
+ const Index outerSize = IsRowMajor ? rows : cols;
+ m_innerSize = IsRowMajor ? cols : rows;
+ m_data.clear();
+ if (m_outerSize != outerSize || m_outerSize==0)
+ {
+ m_outerIndex = internal::conditional_aligned_realloc_new_auto<StorageIndex, true>(m_outerIndex, outerSize + 1,
+ m_outerSize + 1);
+ m_outerSize = outerSize;
+ }
+ if(m_innerNonZeros)
+ {
+ internal::conditional_aligned_delete_auto<StorageIndex, true>(m_innerNonZeros, m_outerSize);
+ m_innerNonZeros = 0;
+ }
+ std::fill_n(m_outerIndex, m_outerSize + 1, StorageIndex(0));
+ }
+
+ /** \internal
+ * Resize the nonzero vector to \a size */
+ void resizeNonZeros(Index size)
+ {
+ m_data.resize(size);
+ }
+
+ /** \returns a const expression of the diagonal coefficients. */
+ const ConstDiagonalReturnType diagonal() const { return ConstDiagonalReturnType(*this); }
+
+ /** \returns a read-write expression of the diagonal coefficients.
+ * \warning If the diagonal entries are written, then all diagonal
+ * entries \b must already exist, otherwise an assertion will be raised.
+ */
+ DiagonalReturnType diagonal() { return DiagonalReturnType(*this); }
+
+ /** Default constructor yielding an empty \c 0 \c x \c 0 matrix */
+ inline SparseMatrix()
+ : m_outerSize(-1), m_innerSize(0), m_outerIndex(0), m_innerNonZeros(0)
+ {
+ resize(0, 0);
+ }
+
+ /** Constructs a \a rows \c x \a cols empty matrix */
+ inline SparseMatrix(Index rows, Index cols)
+ : m_outerSize(0), m_innerSize(0), m_outerIndex(0), m_innerNonZeros(0)
+ {
+ resize(rows, cols);
+ }
+
+ /** Constructs a sparse matrix from the sparse expression \a other */
+ template<typename OtherDerived>
+ inline SparseMatrix(const SparseMatrixBase<OtherDerived>& other)
+ : m_outerSize(0), m_innerSize(0), m_outerIndex(0), m_innerNonZeros(0)
+ {
+ EIGEN_STATIC_ASSERT((internal::is_same<Scalar, typename OtherDerived::Scalar>::value),
+ YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY)
+ const bool needToTranspose = (Flags & RowMajorBit) != (internal::evaluator<OtherDerived>::Flags & RowMajorBit);
+ if (needToTranspose)
+ *this = other.derived();
+ else
+ {
+ #ifdef EIGEN_SPARSE_CREATE_TEMPORARY_PLUGIN
+ EIGEN_SPARSE_CREATE_TEMPORARY_PLUGIN
+ #endif
+ internal::call_assignment_no_alias(*this, other.derived());
+ }
+ }
+
+ /** Constructs a sparse matrix from the sparse selfadjoint view \a other */
+ template<typename OtherDerived, unsigned int UpLo>
+ inline SparseMatrix(const SparseSelfAdjointView<OtherDerived, UpLo>& other)
+ : m_outerSize(0), m_innerSize(0), m_outerIndex(0), m_innerNonZeros(0)
+ {
+ Base::operator=(other);
+ }
+
+ /** Copy constructor (it performs a deep copy) */
+ inline SparseMatrix(const SparseMatrix& other)
+ : Base(), m_outerSize(0), m_innerSize(0), m_outerIndex(0), m_innerNonZeros(0)
+ {
+ *this = other.derived();
+ }
+
+ /** \brief Copy constructor with in-place evaluation */
+ template<typename OtherDerived>
+ SparseMatrix(const ReturnByValue<OtherDerived>& other)
+ : Base(), m_outerSize(0), m_innerSize(0), m_outerIndex(0), m_innerNonZeros(0)
+ {
+ initAssignment(other);
+ other.evalTo(*this);
+ }
+
+ /** \brief Copy constructor with in-place evaluation */
+ template<typename OtherDerived>
+ explicit SparseMatrix(const DiagonalBase<OtherDerived>& other)
+ : Base(), m_outerSize(0), m_innerSize(0), m_outerIndex(0), m_innerNonZeros(0)
+ {
+ *this = other.derived();
+ }
+
+ /** Swaps the content of two sparse matrices of the same type.
+ * This is a fast operation that simply swaps the underlying pointers and parameters. */
+ inline void swap(SparseMatrix& other)
+ {
+ //EIGEN_DBG_SPARSE(std::cout << "SparseMatrix:: swap\n");
+ std::swap(m_outerIndex, other.m_outerIndex);
+ std::swap(m_innerSize, other.m_innerSize);
+ std::swap(m_outerSize, other.m_outerSize);
+ std::swap(m_innerNonZeros, other.m_innerNonZeros);
+ m_data.swap(other.m_data);
+ }
+
+ /** Sets *this to the identity matrix.
+ * This function also turns the matrix into compressed mode, and drop any reserved memory. */
+ inline void setIdentity()
+ {
+ eigen_assert(rows() == cols() && "ONLY FOR SQUARED MATRICES");
+ this->m_data.resize(rows());
+ Eigen::Map<IndexVector>(this->m_data.indexPtr(), rows()).setLinSpaced(0, StorageIndex(rows()-1));
+ Eigen::Map<ScalarVector>(this->m_data.valuePtr(), rows()).setOnes();
+ Eigen::Map<IndexVector>(this->m_outerIndex, rows()+1).setLinSpaced(0, StorageIndex(rows()));
+ internal::conditional_aligned_delete_auto<StorageIndex, true>(m_innerNonZeros, m_outerSize);
+ m_innerNonZeros = 0;
+ }
+ inline SparseMatrix& operator=(const SparseMatrix& other)
+ {
+ if (other.isRValue())
+ {
+ swap(other.const_cast_derived());
+ }
+ else if(this!=&other)
+ {
+ #ifdef EIGEN_SPARSE_CREATE_TEMPORARY_PLUGIN
+ EIGEN_SPARSE_CREATE_TEMPORARY_PLUGIN
+ #endif
+ initAssignment(other);
+ if(other.isCompressed())
+ {
+ internal::smart_copy(other.m_outerIndex, other.m_outerIndex + m_outerSize + 1, m_outerIndex);
+ m_data = other.m_data;
+ }
+ else
+ {
+ Base::operator=(other);
+ }
+ }
+ return *this;
+ }
+
+#ifndef EIGEN_PARSED_BY_DOXYGEN
+ template<typename OtherDerived>
+ inline SparseMatrix& operator=(const EigenBase<OtherDerived>& other)
+ { return Base::operator=(other.derived()); }
+
+ template<typename Lhs, typename Rhs>
+ inline SparseMatrix& operator=(const Product<Lhs,Rhs,AliasFreeProduct>& other);
+#endif // EIGEN_PARSED_BY_DOXYGEN
+
+ template<typename OtherDerived>
+ EIGEN_DONT_INLINE SparseMatrix& operator=(const SparseMatrixBase<OtherDerived>& other);
+
+#ifndef EIGEN_NO_IO
+ friend std::ostream & operator << (std::ostream & s, const SparseMatrix& m)
+ {
+ EIGEN_DBG_SPARSE(
+ s << "Nonzero entries:\n";
+ if(m.isCompressed())
+ {
+ for (Index i=0; i<m.nonZeros(); ++i)
+ s << "(" << m.m_data.value(i) << "," << m.m_data.index(i) << ") ";
+ }
+ else
+ {
+ for (Index i=0; i<m.outerSize(); ++i)
+ {
+ Index p = m.m_outerIndex[i];
+ Index pe = m.m_outerIndex[i]+m.m_innerNonZeros[i];
+ Index k=p;
+ for (; k<pe; ++k) {
+ s << "(" << m.m_data.value(k) << "," << m.m_data.index(k) << ") ";
+ }
+ for (; k<m.m_outerIndex[i+1]; ++k) {
+ s << "(_,_) ";
+ }
+ }
+ }
+ s << std::endl;
+ s << std::endl;
+ s << "Outer pointers:\n";
+ for (Index i=0; i<m.outerSize(); ++i) {
+ s << m.m_outerIndex[i] << " ";
+ }
+ s << " $" << std::endl;
+ if(!m.isCompressed())
+ {
+ s << "Inner non zeros:\n";
+ for (Index i=0; i<m.outerSize(); ++i) {
+ s << m.m_innerNonZeros[i] << " ";
+ }
+ s << " $" << std::endl;
+ }
+ s << std::endl;
+ );
+ s << static_cast<const SparseMatrixBase<SparseMatrix>&>(m);
+ return s;
+ }
+#endif
+
+ /** Destructor */
+ inline ~SparseMatrix()
+ {
+ internal::conditional_aligned_delete_auto<StorageIndex, true>(m_outerIndex, m_outerSize + 1);
+ internal::conditional_aligned_delete_auto<StorageIndex, true>(m_innerNonZeros, m_outerSize);
+ }
+
+ /** Overloaded for performance */
+ Scalar sum() const;
+
+# ifdef EIGEN_SPARSEMATRIX_PLUGIN
+# include EIGEN_SPARSEMATRIX_PLUGIN
+# endif
+
+protected:
+
+ template<typename Other>
+ void initAssignment(const Other& other)
+ {
+ resize(other.rows(), other.cols());
+ if(m_innerNonZeros)
+ {
+ internal::conditional_aligned_delete_auto<StorageIndex, true>(m_innerNonZeros, m_outerSize);
+ m_innerNonZeros = 0;
+ }
+ }
+
+ /** \internal
+ * \sa insert(Index,Index) */
+ EIGEN_DONT_INLINE Scalar& insertCompressed(Index row, Index col);
+
+ /** \internal
+ * A vector object that is equal to 0 everywhere but v at the position i */
+ class SingletonVector
+ {
+ StorageIndex m_index;
+ StorageIndex m_value;
+ public:
+ typedef StorageIndex value_type;
+ SingletonVector(Index i, Index v)
+ : m_index(convert_index(i)), m_value(convert_index(v))
+ {}
+
+ StorageIndex operator[](Index i) const { return i==m_index ? m_value : 0; }
+ };
+
+ /** \internal
+ * \sa insert(Index,Index) */
+ EIGEN_DONT_INLINE Scalar& insertUncompressed(Index row, Index col);
+
+public:
+ /** \internal
+ * \sa insert(Index,Index) */
+ EIGEN_STRONG_INLINE Scalar& insertBackUncompressed(Index row, Index col)
+ {
+ const Index outer = IsRowMajor ? row : col;
+ const Index inner = IsRowMajor ? col : row;
+
+ eigen_assert(!isCompressed());
+ eigen_assert(m_innerNonZeros[outer]<=(m_outerIndex[outer+1] - m_outerIndex[outer]));
+
+ Index p = m_outerIndex[outer] + m_innerNonZeros[outer]++;
+ m_data.index(p) = convert_index(inner);
+ return (m_data.value(p) = Scalar(0));
+ }
+protected:
+ struct IndexPosPair {
+ IndexPosPair(Index a_i, Index a_p) : i(a_i), p(a_p) {}
+ Index i;
+ Index p;
+ };
+
+ /** \internal assign \a diagXpr to the diagonal of \c *this
+ * There are different strategies:
+ * 1 - if *this is overwritten (Func==assign_op) or *this is empty, then we can work treat *this as a dense vector expression.
+ * 2 - otherwise, for each diagonal coeff,
+ * 2.a - if it already exists, then we update it,
+ * 2.b - otherwise, if *this is uncompressed and that the current inner-vector has empty room for at least 1 element, then we perform an in-place insertion.
+ * 2.c - otherwise, we'll have to reallocate and copy everything, so instead of doing so for each new element, it is recorded in a std::vector.
+ * 3 - at the end, if some entries failed to be inserted in-place, then we alloc a new buffer, copy each chunk at the right position, and insert the new elements.
+ *
+ * TODO: some piece of code could be isolated and reused for a general in-place update strategy.
+ * TODO: if we start to defer the insertion of some elements (i.e., case 2.c executed once),
+ * then it *might* be better to disable case 2.b since they will have to be copied anyway.
+ */
+ template<typename DiagXpr, typename Func>
+ void assignDiagonal(const DiagXpr diagXpr, const Func& assignFunc)
+ {
+ Index n = diagXpr.size();
+
+ const bool overwrite = internal::is_same<Func, internal::assign_op<Scalar,Scalar> >::value;
+ if(overwrite)
+ {
+ if((this->rows()!=n) || (this->cols()!=n))
+ this->resize(n, n);
+ }
+
+ if(m_data.size()==0 || overwrite)
+ {
+ typedef Array<StorageIndex,Dynamic,1> ArrayXI;
+ this->makeCompressed();
+ this->resizeNonZeros(n);
+ Eigen::Map<ArrayXI>(this->innerIndexPtr(), n).setLinSpaced(0,StorageIndex(n)-1);
+ Eigen::Map<ArrayXI>(this->outerIndexPtr(), n+1).setLinSpaced(0,StorageIndex(n));
+ Eigen::Map<Array<Scalar,Dynamic,1> > values = this->coeffs();
+ values.setZero();
+ internal::call_assignment_no_alias(values, diagXpr, assignFunc);
+ }
+ else
+ {
+ bool isComp = isCompressed();
+ internal::evaluator<DiagXpr> diaEval(diagXpr);
+ std::vector<IndexPosPair> newEntries;
+
+ // 1 - try in-place update and record insertion failures
+ for(Index i = 0; i<n; ++i)
+ {
+ internal::LowerBoundIndex lb = this->lower_bound(i,i);
+ Index p = lb.value;
+ if(lb.found)
+ {
+ // the coeff already exists
+ assignFunc.assignCoeff(m_data.value(p), diaEval.coeff(i));
+ }
+ else if((!isComp) && m_innerNonZeros[i] < (m_outerIndex[i+1]-m_outerIndex[i]))
+ {
+ // non compressed mode with local room for inserting one element
+ m_data.moveChunk(p, p+1, m_outerIndex[i]+m_innerNonZeros[i]-p);
+ m_innerNonZeros[i]++;
+ m_data.value(p) = Scalar(0);
+ m_data.index(p) = StorageIndex(i);
+ assignFunc.assignCoeff(m_data.value(p), diaEval.coeff(i));
+ }
+ else
+ {
+ // defer insertion
+ newEntries.push_back(IndexPosPair(i,p));
+ }
+ }
+ // 2 - insert deferred entries
+ Index n_entries = Index(newEntries.size());
+ if(n_entries>0)
+ {
+ Storage newData(m_data.size()+n_entries);
+ Index prev_p = 0;
+ Index prev_i = 0;
+ for(Index k=0; k<n_entries;++k)
+ {
+ Index i = newEntries[k].i;
+ Index p = newEntries[k].p;
+ internal::smart_copy(m_data.valuePtr()+prev_p, m_data.valuePtr()+p, newData.valuePtr()+prev_p+k);
+ internal::smart_copy(m_data.indexPtr()+prev_p, m_data.indexPtr()+p, newData.indexPtr()+prev_p+k);
+ for(Index j=prev_i;j<i;++j)
+ m_outerIndex[j+1] += k;
+ if(!isComp)
+ m_innerNonZeros[i]++;
+ prev_p = p;
+ prev_i = i;
+ newData.value(p+k) = Scalar(0);
+ newData.index(p+k) = StorageIndex(i);
+ assignFunc.assignCoeff(newData.value(p+k), diaEval.coeff(i));
+ }
+ {
+ internal::smart_copy(m_data.valuePtr()+prev_p, m_data.valuePtr()+m_data.size(), newData.valuePtr()+prev_p+n_entries);
+ internal::smart_copy(m_data.indexPtr()+prev_p, m_data.indexPtr()+m_data.size(), newData.indexPtr()+prev_p+n_entries);
+ for(Index j=prev_i+1;j<=m_outerSize;++j)
+ m_outerIndex[j] += n_entries;
+ }
+ m_data.swap(newData);
+ }
+ }
+ }
+
+private:
+ EIGEN_STATIC_ASSERT(NumTraits<StorageIndex>::IsSigned,THE_INDEX_TYPE_MUST_BE_A_SIGNED_TYPE)
+ EIGEN_STATIC_ASSERT((Options&(ColMajor|RowMajor))==Options,INVALID_MATRIX_TEMPLATE_PARAMETERS)
+
+ struct default_prunning_func {
+ default_prunning_func(const Scalar& ref, const RealScalar& eps) : reference(ref), epsilon(eps) {}
+ inline bool operator() (const Index&, const Index&, const Scalar& value) const
+ {
+ return !internal::isMuchSmallerThan(value, reference, epsilon);
+ }
+ Scalar reference;
+ RealScalar epsilon;
+ };
+};
+
+namespace internal {
+
+template<typename InputIterator, typename SparseMatrixType, typename DupFunctor>
+void set_from_triplets(const InputIterator& begin, const InputIterator& end, SparseMatrixType& mat, DupFunctor dup_func)
+{
+ enum { IsRowMajor = SparseMatrixType::IsRowMajor };
+ typedef typename SparseMatrixType::Scalar Scalar;
+ typedef typename SparseMatrixType::StorageIndex StorageIndex;
+ SparseMatrix<Scalar,IsRowMajor?ColMajor:RowMajor,StorageIndex> trMat(mat.rows(),mat.cols());
+
+ if(begin!=end)
+ {
+ // pass 1: count the nnz per inner-vector
+ typename SparseMatrixType::IndexVector wi(trMat.outerSize());
+ wi.setZero();
+ for(InputIterator it(begin); it!=end; ++it)
+ {
+ eigen_assert(it->row()>=0 && it->row()<mat.rows() && it->col()>=0 && it->col()<mat.cols());
+ wi(IsRowMajor ? it->col() : it->row())++;
+ }
+
+ // pass 2: insert all the elements into trMat
+ trMat.reserve(wi);
+ for(InputIterator it(begin); it!=end; ++it)
+ trMat.insertBackUncompressed(it->row(),it->col()) = it->value();
+
+ // pass 3:
+ trMat.collapseDuplicates(dup_func);
+ }
+
+ // pass 4: transposed copy -> implicit sorting
+ mat = trMat;
+}
+
+}
+
+
+/** Fill the matrix \c *this with the list of \em triplets defined by the iterator range \a begin - \a end.
+ *
+ * A \em triplet is a tuple (i,j,value) defining a non-zero element.
+ * The input list of triplets does not have to be sorted, and can contains duplicated elements.
+ * In any case, the result is a \b sorted and \b compressed sparse matrix where the duplicates have been summed up.
+ * This is a \em O(n) operation, with \em n the number of triplet elements.
+ * The initial contents of \c *this is destroyed.
+ * The matrix \c *this must be properly resized beforehand using the SparseMatrix(Index,Index) constructor,
+ * or the resize(Index,Index) method. The sizes are not extracted from the triplet list.
+ *
+ * The \a InputIterators value_type must provide the following interface:
+ * \code
+ * Scalar value() const; // the value
+ * Scalar row() const; // the row index i
+ * Scalar col() const; // the column index j
+ * \endcode
+ * See for instance the Eigen::Triplet template class.
+ *
+ * Here is a typical usage example:
+ * \code
+ typedef Triplet<double> T;
+ std::vector<T> tripletList;
+ tripletList.reserve(estimation_of_entries);
+ for(...)
+ {
+ // ...
+ tripletList.push_back(T(i,j,v_ij));
+ }
+ SparseMatrixType m(rows,cols);
+ m.setFromTriplets(tripletList.begin(), tripletList.end());
+ // m is ready to go!
+ * \endcode
+ *
+ * \warning The list of triplets is read multiple times (at least twice). Therefore, it is not recommended to define
+ * an abstract iterator over a complex data-structure that would be expensive to evaluate. The triplets should rather
+ * be explicitly stored into a std::vector for instance.
+ */
+template<typename Scalar, int Options_, typename StorageIndex_>
+template<typename InputIterators>
+void SparseMatrix<Scalar,Options_,StorageIndex_>::setFromTriplets(const InputIterators& begin, const InputIterators& end)
+{
+ internal::set_from_triplets<InputIterators, SparseMatrix<Scalar,Options_,StorageIndex_> >(begin, end, *this, internal::scalar_sum_op<Scalar,Scalar>());
+}
+
+/** The same as setFromTriplets but when duplicates are met the functor \a dup_func is applied:
+ * \code
+ * value = dup_func(OldValue, NewValue)
+ * \endcode
+ * Here is a C++11 example keeping the latest entry only:
+ * \code
+ * mat.setFromTriplets(triplets.begin(), triplets.end(), [] (const Scalar&,const Scalar &b) { return b; });
+ * \endcode
+ */
+template<typename Scalar, int Options_, typename StorageIndex_>
+template<typename InputIterators,typename DupFunctor>
+void SparseMatrix<Scalar,Options_,StorageIndex_>::setFromTriplets(const InputIterators& begin, const InputIterators& end, DupFunctor dup_func)
+{
+ internal::set_from_triplets<InputIterators, SparseMatrix<Scalar,Options_,StorageIndex_>, DupFunctor>(begin, end, *this, dup_func);
+}
+
+/** \internal */
+template<typename Scalar, int Options_, typename StorageIndex_>
+template<typename DupFunctor>
+void SparseMatrix<Scalar,Options_,StorageIndex_>::collapseDuplicates(DupFunctor dup_func)
+{
+ eigen_assert(!isCompressed());
+ // TODO, in practice we should be able to use m_innerNonZeros for that task
+ IndexVector wi(innerSize());
+ wi.fill(-1);
+ StorageIndex count = 0;
+ // for each inner-vector, wi[inner_index] will hold the position of first element into the index/value buffers
+ for(Index j=0; j<outerSize(); ++j)
+ {
+ StorageIndex start = count;
+ Index oldEnd = m_outerIndex[j]+m_innerNonZeros[j];
+ for(Index k=m_outerIndex[j]; k<oldEnd; ++k)
+ {
+ Index i = m_data.index(k);
+ if(wi(i)>=start)
+ {
+ // we already meet this entry => accumulate it
+ m_data.value(wi(i)) = dup_func(m_data.value(wi(i)), m_data.value(k));
+ }
+ else
+ {
+ m_data.value(count) = m_data.value(k);
+ m_data.index(count) = m_data.index(k);
+ wi(i) = count;
+ ++count;
+ }
+ }
+ m_outerIndex[j] = start;
+ }
+ m_outerIndex[m_outerSize] = count;
+
+ // turn the matrix into compressed form
+ internal::conditional_aligned_delete_auto<StorageIndex, true>(m_innerNonZeros, m_outerSize);
+ m_innerNonZeros = 0;
+ m_data.resize(m_outerIndex[m_outerSize]);
+}
+
+template<typename Scalar, int Options_, typename StorageIndex_>
+template<typename OtherDerived>
+EIGEN_DONT_INLINE SparseMatrix<Scalar,Options_,StorageIndex_>& SparseMatrix<Scalar,Options_,StorageIndex_>::operator=(const SparseMatrixBase<OtherDerived>& other)
+{
+ EIGEN_STATIC_ASSERT((internal::is_same<Scalar, typename OtherDerived::Scalar>::value),
+ YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY)
+
+ #ifdef EIGEN_SPARSE_CREATE_TEMPORARY_PLUGIN
+ EIGEN_SPARSE_CREATE_TEMPORARY_PLUGIN
+ #endif
+
+ const bool needToTranspose = (Flags & RowMajorBit) != (internal::evaluator<OtherDerived>::Flags & RowMajorBit);
+ if (needToTranspose)
+ {
+ #ifdef EIGEN_SPARSE_TRANSPOSED_COPY_PLUGIN
+ EIGEN_SPARSE_TRANSPOSED_COPY_PLUGIN
+ #endif
+ // two passes algorithm:
+ // 1 - compute the number of coeffs per dest inner vector
+ // 2 - do the actual copy/eval
+ // Since each coeff of the rhs has to be evaluated twice, let's evaluate it if needed
+ typedef typename internal::nested_eval<OtherDerived,2,typename internal::plain_matrix_type<OtherDerived>::type >::type OtherCopy;
+ typedef internal::remove_all_t<OtherCopy> OtherCopy_;
+ typedef internal::evaluator<OtherCopy_> OtherCopyEval;
+ OtherCopy otherCopy(other.derived());
+ OtherCopyEval otherCopyEval(otherCopy);
+
+ SparseMatrix dest(other.rows(),other.cols());
+ Eigen::Map<IndexVector> (dest.m_outerIndex,dest.outerSize()).setZero();
+
+ // pass 1
+ // FIXME the above copy could be merged with that pass
+ for (Index j=0; j<otherCopy.outerSize(); ++j)
+ for (typename OtherCopyEval::InnerIterator it(otherCopyEval, j); it; ++it)
+ ++dest.m_outerIndex[it.index()];
+
+ // prefix sum
+ StorageIndex count = 0;
+ IndexVector positions(dest.outerSize());
+ for (Index j=0; j<dest.outerSize(); ++j)
+ {
+ StorageIndex tmp = dest.m_outerIndex[j];
+ dest.m_outerIndex[j] = count;
+ positions[j] = count;
+ count += tmp;
+ }
+ dest.m_outerIndex[dest.outerSize()] = count;
+ // alloc
+ dest.m_data.resize(count);
+ // pass 2
+ for (StorageIndex j=0; j<otherCopy.outerSize(); ++j)
+ {
+ for (typename OtherCopyEval::InnerIterator it(otherCopyEval, j); it; ++it)
+ {
+ Index pos = positions[it.index()]++;
+ dest.m_data.index(pos) = j;
+ dest.m_data.value(pos) = it.value();
+ }
+ }
+ this->swap(dest);
+ return *this;
+ }
+ else
+ {
+ if(other.isRValue())
+ {
+ initAssignment(other.derived());
+ }
+ // there is no special optimization
+ return Base::operator=(other.derived());
+ }
+}
+
+template<typename Scalar_, int Options_, typename StorageIndex_>
+typename SparseMatrix<Scalar_,Options_,StorageIndex_>::Scalar& SparseMatrix<Scalar_,Options_,StorageIndex_>::insert(Index row, Index col)
+{
+ eigen_assert(row>=0 && row<rows() && col>=0 && col<cols());
+
+ const Index outer = IsRowMajor ? row : col;
+ const Index inner = IsRowMajor ? col : row;
+
+ if(isCompressed())
+ {
+ if(nonZeros()==0)
+ {
+ // reserve space if not already done
+ if(m_data.allocatedSize()==0)
+ m_data.reserve(2*m_innerSize);
+
+ // turn the matrix into non-compressed mode
+ m_innerNonZeros = internal::conditional_aligned_new_auto<StorageIndex, true>(m_outerSize);
+
+ std::fill(m_innerNonZeros, m_innerNonZeros + m_outerSize, StorageIndex(0));
+
+ // pack all inner-vectors to the end of the pre-allocated space
+ // and allocate the entire free-space to the first inner-vector
+ StorageIndex end = convert_index(m_data.allocatedSize());
+ for(Index j=1; j<=m_outerSize; ++j)
+ m_outerIndex[j] = end;
+ }
+ else
+ {
+ // turn the matrix into non-compressed mode
+ m_innerNonZeros = internal::conditional_aligned_new_auto<StorageIndex, true>(m_outerSize);
+ for(Index j=0; j<m_outerSize; ++j)
+ m_innerNonZeros[j] = m_outerIndex[j+1]-m_outerIndex[j];
+ }
+ }
+
+ // check whether we can do a fast "push back" insertion
+ Index data_end = m_data.allocatedSize();
+
+ // First case: we are filling a new inner vector which is packed at the end.
+ // We assume that all remaining inner-vectors are also empty and packed to the end.
+ if(m_outerIndex[outer]==data_end)
+ {
+ eigen_internal_assert(m_innerNonZeros[outer]==0);
+
+ // pack previous empty inner-vectors to end of the used-space
+ // and allocate the entire free-space to the current inner-vector.
+ StorageIndex p = convert_index(m_data.size());
+ Index j = outer;
+ while(j>=0 && m_innerNonZeros[j]==0)
+ m_outerIndex[j--] = p;
+
+ // push back the new element
+ ++m_innerNonZeros[outer];
+ m_data.append(Scalar(0), inner);
+
+ // check for reallocation
+ if(data_end != m_data.allocatedSize())
+ {
+ // m_data has been reallocated
+ // -> move remaining inner-vectors back to the end of the free-space
+ // so that the entire free-space is allocated to the current inner-vector.
+ eigen_internal_assert(data_end < m_data.allocatedSize());
+ StorageIndex new_end = convert_index(m_data.allocatedSize());
+ for(Index k=outer+1; k<=m_outerSize; ++k)
+ if(m_outerIndex[k]==data_end)
+ m_outerIndex[k] = new_end;
+ }
+ return m_data.value(p);
+ }
+
+ // Second case: the next inner-vector is packed to the end
+ // and the current inner-vector end match the used-space.
+ if(m_outerIndex[outer+1]==data_end && m_outerIndex[outer]+m_innerNonZeros[outer]==m_data.size())
+ {
+ eigen_internal_assert(outer+1==m_outerSize || m_innerNonZeros[outer+1]==0);
+
+ // add space for the new element
+ ++m_innerNonZeros[outer];
+ m_data.resize(m_data.size()+1);
+
+ // check for reallocation
+ if(data_end != m_data.allocatedSize())
+ {
+ // m_data has been reallocated
+ // -> move remaining inner-vectors back to the end of the free-space
+ // so that the entire free-space is allocated to the current inner-vector.
+ eigen_internal_assert(data_end < m_data.allocatedSize());
+ StorageIndex new_end = convert_index(m_data.allocatedSize());
+ for(Index k=outer+1; k<=m_outerSize; ++k)
+ if(m_outerIndex[k]==data_end)
+ m_outerIndex[k] = new_end;
+ }
+
+ // and insert it at the right position (sorted insertion)
+ Index startId = m_outerIndex[outer];
+ Index p = m_outerIndex[outer]+m_innerNonZeros[outer]-1;
+ while ( (p > startId) && (m_data.index(p-1) > inner) )
+ {
+ m_data.index(p) = m_data.index(p-1);
+ m_data.value(p) = m_data.value(p-1);
+ --p;
+ }
+
+ m_data.index(p) = convert_index(inner);
+ return (m_data.value(p) = Scalar(0));
+ }
+
+ if(m_data.size() != m_data.allocatedSize())
+ {
+ // make sure the matrix is compatible to random un-compressed insertion:
+ m_data.resize(m_data.allocatedSize());
+ this->reserveInnerVectors(Array<StorageIndex,Dynamic,1>::Constant(m_outerSize, 2));
+ }
+
+ return insertUncompressed(row,col);
+}
+
+template<typename Scalar_, int Options_, typename StorageIndex_>
+EIGEN_DONT_INLINE typename SparseMatrix<Scalar_,Options_,StorageIndex_>::Scalar& SparseMatrix<Scalar_,Options_,StorageIndex_>::insertUncompressed(Index row, Index col)
+{
+ eigen_assert(!isCompressed());
+
+ const Index outer = IsRowMajor ? row : col;
+ const StorageIndex inner = convert_index(IsRowMajor ? col : row);
+
+ Index room = m_outerIndex[outer+1] - m_outerIndex[outer];
+ StorageIndex innerNNZ = m_innerNonZeros[outer];
+ if(innerNNZ>=room)
+ {
+ // this inner vector is full, we need to reallocate the whole buffer :(
+ reserve(SingletonVector(outer,std::max<StorageIndex>(2,innerNNZ)));
+ }
+
+ Index startId = m_outerIndex[outer];
+ Index p = startId + m_innerNonZeros[outer];
+ while ( (p > startId) && (m_data.index(p-1) > inner) )
+ {
+ m_data.index(p) = m_data.index(p-1);
+ m_data.value(p) = m_data.value(p-1);
+ --p;
+ }
+ eigen_assert((p<=startId || m_data.index(p-1)!=inner) && "you cannot insert an element that already exists, you must call coeffRef to this end");
+
+ m_innerNonZeros[outer]++;
+
+ m_data.index(p) = inner;
+ return (m_data.value(p) = Scalar(0));
+}
+
+template<typename Scalar_, int Options_, typename StorageIndex_>
+EIGEN_DONT_INLINE typename SparseMatrix<Scalar_,Options_,StorageIndex_>::Scalar& SparseMatrix<Scalar_,Options_,StorageIndex_>::insertCompressed(Index row, Index col)
+{
+ eigen_assert(isCompressed());
+
+ const Index outer = IsRowMajor ? row : col;
+ const Index inner = IsRowMajor ? col : row;
+
+ Index previousOuter = outer;
+ if (m_outerIndex[outer+1]==0)
+ {
+ // we start a new inner vector
+ while (previousOuter>=0 && m_outerIndex[previousOuter]==0)
+ {
+ m_outerIndex[previousOuter] = convert_index(m_data.size());
+ --previousOuter;
+ }
+ m_outerIndex[outer+1] = m_outerIndex[outer];
+ }
+
+ // here we have to handle the tricky case where the outerIndex array
+ // starts with: [ 0 0 0 0 0 1 ...] and we are inserted in, e.g.,
+ // the 2nd inner vector...
+ bool isLastVec = (!(previousOuter==-1 && m_data.size()!=0))
+ && (std::size_t(m_outerIndex[outer+1]) == m_data.size());
+
+ std::size_t startId = m_outerIndex[outer];
+ // FIXME let's make sure sizeof(long int) == sizeof(std::size_t)
+ std::size_t p = m_outerIndex[outer+1];
+ ++m_outerIndex[outer+1];
+
+ double reallocRatio = 1;
+ if (m_data.allocatedSize()<=m_data.size())
+ {
+ // if there is no preallocated memory, let's reserve a minimum of 32 elements
+ if (m_data.size()==0)
+ {
+ m_data.reserve(32);
+ }
+ else
+ {
+ // we need to reallocate the data, to reduce multiple reallocations
+ // we use a smart resize algorithm based on the current filling ratio
+ // in addition, we use double to avoid integers overflows
+ double nnzEstimate = double(m_outerIndex[outer])*double(m_outerSize)/double(outer+1);
+ reallocRatio = (nnzEstimate-double(m_data.size()))/double(m_data.size());
+ // furthermore we bound the realloc ratio to:
+ // 1) reduce multiple minor realloc when the matrix is almost filled
+ // 2) avoid to allocate too much memory when the matrix is almost empty
+ reallocRatio = (std::min)((std::max)(reallocRatio,1.5),8.);
+ }
+ }
+ m_data.resize(m_data.size()+1,reallocRatio);
+
+ if (!isLastVec)
+ {
+ if (previousOuter==-1)
+ {
+ // oops wrong guess.
+ // let's correct the outer offsets
+ for (Index k=0; k<=(outer+1); ++k)
+ m_outerIndex[k] = 0;
+ Index k=outer+1;
+ while(m_outerIndex[k]==0)
+ m_outerIndex[k++] = 1;
+ while (k<=m_outerSize && m_outerIndex[k]!=0)
+ m_outerIndex[k++]++;
+ p = 0;
+ --k;
+ k = m_outerIndex[k]-1;
+ while (k>0)
+ {
+ m_data.index(k) = m_data.index(k-1);
+ m_data.value(k) = m_data.value(k-1);
+ k--;
+ }
+ }
+ else
+ {
+ // we are not inserting into the last inner vec
+ // update outer indices:
+ Index j = outer+2;
+ while (j<=m_outerSize && m_outerIndex[j]!=0)
+ m_outerIndex[j++]++;
+ --j;
+ // shift data of last vecs:
+ Index k = m_outerIndex[j]-1;
+ while (k>=Index(p))
+ {
+ m_data.index(k) = m_data.index(k-1);
+ m_data.value(k) = m_data.value(k-1);
+ k--;
+ }
+ }
+ }
+
+ while ( (p > startId) && (m_data.index(p-1) > inner) )
+ {
+ m_data.index(p) = m_data.index(p-1);
+ m_data.value(p) = m_data.value(p-1);
+ --p;
+ }
+
+ m_data.index(p) = inner;
+ return (m_data.value(p) = Scalar(0));
+}
+
+namespace internal {
+
+template<typename Scalar_, int Options_, typename StorageIndex_>
+struct evaluator<SparseMatrix<Scalar_,Options_,StorageIndex_> >
+ : evaluator<SparseCompressedBase<SparseMatrix<Scalar_,Options_,StorageIndex_> > >
+{
+ typedef evaluator<SparseCompressedBase<SparseMatrix<Scalar_,Options_,StorageIndex_> > > Base;
+ typedef SparseMatrix<Scalar_,Options_,StorageIndex_> SparseMatrixType;
+ evaluator() : Base() {}
+ explicit evaluator(const SparseMatrixType &mat) : Base(mat) {}
+};
+
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_SPARSEMATRIX_H
diff --git a/Eigen/src/SparseCore/SparseMatrixBase.h b/Eigen/src/SparseCore/SparseMatrixBase.h
new file mode 100644
index 0000000..dc78c2e
--- /dev/null
+++ b/Eigen/src/SparseCore/SparseMatrixBase.h
@@ -0,0 +1,399 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2014 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_SPARSEMATRIXBASE_H
+#define EIGEN_SPARSEMATRIXBASE_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+/** \ingroup SparseCore_Module
+ *
+ * \class SparseMatrixBase
+ *
+ * \brief Base class of any sparse matrices or sparse expressions
+ *
+ * \tparam Derived is the derived type, e.g. a sparse matrix type, or an expression, etc.
+ *
+ * This class can be extended with the help of the plugin mechanism described on the page
+ * \ref TopicCustomizing_Plugins by defining the preprocessor symbol \c EIGEN_SPARSEMATRIXBASE_PLUGIN.
+ */
+template<typename Derived> class SparseMatrixBase
+ : public EigenBase<Derived>
+{
+ public:
+
+ typedef typename internal::traits<Derived>::Scalar Scalar;
+
+ /** The numeric type of the expression' coefficients, e.g. float, double, int or std::complex<float>, etc.
+ *
+ * It is an alias for the Scalar type */
+ typedef Scalar value_type;
+
+ typedef typename internal::packet_traits<Scalar>::type PacketScalar;
+ typedef typename internal::traits<Derived>::StorageKind StorageKind;
+
+ /** The integer type used to \b store indices within a SparseMatrix.
+ * For a \c SparseMatrix<Scalar,Options,IndexType> it an alias of the third template parameter \c IndexType. */
+ typedef typename internal::traits<Derived>::StorageIndex StorageIndex;
+
+ typedef typename internal::add_const_on_value_type_if_arithmetic<
+ typename internal::packet_traits<Scalar>::type
+ >::type PacketReturnType;
+
+ typedef SparseMatrixBase StorageBaseType;
+
+ typedef Matrix<StorageIndex,Dynamic,1> IndexVector;
+ typedef Matrix<Scalar,Dynamic,1> ScalarVector;
+
+ template<typename OtherDerived>
+ Derived& operator=(const EigenBase<OtherDerived> &other);
+
+ enum {
+
+ RowsAtCompileTime = internal::traits<Derived>::RowsAtCompileTime,
+ /**< The number of rows at compile-time. This is just a copy of the value provided
+ * by the \a Derived type. If a value is not known at compile-time,
+ * it is set to the \a Dynamic constant.
+ * \sa MatrixBase::rows(), MatrixBase::cols(), ColsAtCompileTime, SizeAtCompileTime */
+
+ ColsAtCompileTime = internal::traits<Derived>::ColsAtCompileTime,
+ /**< The number of columns at compile-time. This is just a copy of the value provided
+ * by the \a Derived type. If a value is not known at compile-time,
+ * it is set to the \a Dynamic constant.
+ * \sa MatrixBase::rows(), MatrixBase::cols(), RowsAtCompileTime, SizeAtCompileTime */
+
+
+ SizeAtCompileTime = (internal::size_of_xpr_at_compile_time<Derived>::ret),
+ /**< This is equal to the number of coefficients, i.e. the number of
+ * rows times the number of columns, or to \a Dynamic if this is not
+ * known at compile-time. \sa RowsAtCompileTime, ColsAtCompileTime */
+
+ MaxRowsAtCompileTime = RowsAtCompileTime,
+ MaxColsAtCompileTime = ColsAtCompileTime,
+
+ MaxSizeAtCompileTime = internal::size_at_compile_time(MaxRowsAtCompileTime, MaxColsAtCompileTime),
+
+ IsVectorAtCompileTime = RowsAtCompileTime == 1 || ColsAtCompileTime == 1,
+ /**< This is set to true if either the number of rows or the number of
+ * columns is known at compile-time to be equal to 1. Indeed, in that case,
+ * we are dealing with a column-vector (if there is only one column) or with
+ * a row-vector (if there is only one row). */
+
+ NumDimensions = int(MaxSizeAtCompileTime) == 1 ? 0 : bool(IsVectorAtCompileTime) ? 1 : 2,
+ /**< This value is equal to Tensor::NumDimensions, i.e. 0 for scalars, 1 for vectors,
+ * and 2 for matrices.
+ */
+
+ Flags = internal::traits<Derived>::Flags,
+ /**< This stores expression \ref flags flags which may or may not be inherited by new expressions
+ * constructed from this one. See the \ref flags "list of flags".
+ */
+
+ IsRowMajor = Flags&RowMajorBit ? 1 : 0,
+
+ InnerSizeAtCompileTime = int(IsVectorAtCompileTime) ? int(SizeAtCompileTime)
+ : int(IsRowMajor) ? int(ColsAtCompileTime) : int(RowsAtCompileTime),
+
+ #ifndef EIGEN_PARSED_BY_DOXYGEN
+ HasDirectAccess_ = (int(Flags)&DirectAccessBit) ? 1 : 0 // workaround sunCC
+ #endif
+ };
+
+ /** \internal the return type of MatrixBase::adjoint() */
+ typedef std::conditional_t<NumTraits<Scalar>::IsComplex,
+ CwiseUnaryOp<internal::scalar_conjugate_op<Scalar>, Eigen::Transpose<const Derived> >,
+ Transpose<const Derived>
+ > AdjointReturnType;
+ typedef Transpose<Derived> TransposeReturnType;
+ typedef Transpose<const Derived> ConstTransposeReturnType;
+
+ // FIXME storage order do not match evaluator storage order
+ typedef SparseMatrix<Scalar, Flags&RowMajorBit ? RowMajor : ColMajor, StorageIndex> PlainObject;
+
+#ifndef EIGEN_PARSED_BY_DOXYGEN
+ /** This is the "real scalar" type; if the \a Scalar type is already real numbers
+ * (e.g. int, float or double) then \a RealScalar is just the same as \a Scalar. If
+ * \a Scalar is \a std::complex<T> then RealScalar is \a T.
+ *
+ * \sa class NumTraits
+ */
+ typedef typename NumTraits<Scalar>::Real RealScalar;
+
+ /** \internal the return type of coeff()
+ */
+ typedef std::conditional_t<HasDirectAccess_, const Scalar&, Scalar> CoeffReturnType;
+
+ /** \internal Represents a matrix with all coefficients equal to one another*/
+ typedef CwiseNullaryOp<internal::scalar_constant_op<Scalar>,Matrix<Scalar,Dynamic,Dynamic> > ConstantReturnType;
+
+ /** type of the equivalent dense matrix */
+ typedef Matrix<Scalar,RowsAtCompileTime,ColsAtCompileTime> DenseMatrixType;
+ /** type of the equivalent square matrix */
+ typedef Matrix<Scalar, internal::max_size_prefer_dynamic(RowsAtCompileTime, ColsAtCompileTime),
+ internal::max_size_prefer_dynamic(RowsAtCompileTime, ColsAtCompileTime)> SquareMatrixType;
+
+ inline const Derived& derived() const { return *static_cast<const Derived*>(this); }
+ inline Derived& derived() { return *static_cast<Derived*>(this); }
+ inline Derived& const_cast_derived() const
+ { return *static_cast<Derived*>(const_cast<SparseMatrixBase*>(this)); }
+
+ typedef EigenBase<Derived> Base;
+
+#endif // not EIGEN_PARSED_BY_DOXYGEN
+
+#define EIGEN_CURRENT_STORAGE_BASE_CLASS Eigen::SparseMatrixBase
+#ifdef EIGEN_PARSED_BY_DOXYGEN
+#define EIGEN_DOC_UNARY_ADDONS(METHOD,OP) /** <p>This method does not change the sparsity of \c *this: the OP is applied to explicitly stored coefficients only. \sa SparseCompressedBase::coeffs() </p> */
+#define EIGEN_DOC_BLOCK_ADDONS_NOT_INNER_PANEL /** <p> \warning This method returns a read-only expression for any sparse matrices. \sa \ref TutorialSparse_SubMatrices "Sparse block operations" </p> */
+#define EIGEN_DOC_BLOCK_ADDONS_INNER_PANEL_IF(COND) /** <p> \warning This method returns a read-write expression for COND sparse matrices only. Otherwise, the returned expression is read-only. \sa \ref TutorialSparse_SubMatrices "Sparse block operations" </p> */
+#else
+#define EIGEN_DOC_UNARY_ADDONS(X,Y)
+#define EIGEN_DOC_BLOCK_ADDONS_NOT_INNER_PANEL
+#define EIGEN_DOC_BLOCK_ADDONS_INNER_PANEL_IF(COND)
+#endif
+# include "../plugins/CommonCwiseUnaryOps.h"
+# include "../plugins/CommonCwiseBinaryOps.h"
+# include "../plugins/MatrixCwiseUnaryOps.h"
+# include "../plugins/MatrixCwiseBinaryOps.h"
+# include "../plugins/BlockMethods.h"
+# ifdef EIGEN_SPARSEMATRIXBASE_PLUGIN
+# include EIGEN_SPARSEMATRIXBASE_PLUGIN
+# endif
+#undef EIGEN_CURRENT_STORAGE_BASE_CLASS
+#undef EIGEN_DOC_UNARY_ADDONS
+#undef EIGEN_DOC_BLOCK_ADDONS_NOT_INNER_PANEL
+#undef EIGEN_DOC_BLOCK_ADDONS_INNER_PANEL_IF
+
+ /** \returns the number of rows. \sa cols() */
+ inline Index rows() const { return derived().rows(); }
+ /** \returns the number of columns. \sa rows() */
+ inline Index cols() const { return derived().cols(); }
+ /** \returns the number of coefficients, which is \a rows()*cols().
+ * \sa rows(), cols(). */
+ inline Index size() const { return rows() * cols(); }
+ /** \returns true if either the number of rows or the number of columns is equal to 1.
+ * In other words, this function returns
+ * \code rows()==1 || cols()==1 \endcode
+ * \sa rows(), cols(), IsVectorAtCompileTime. */
+ inline bool isVector() const { return rows()==1 || cols()==1; }
+ /** \returns the size of the storage major dimension,
+ * i.e., the number of columns for a columns major matrix, and the number of rows otherwise */
+ Index outerSize() const { return (int(Flags)&RowMajorBit) ? this->rows() : this->cols(); }
+ /** \returns the size of the inner dimension according to the storage order,
+ * i.e., the number of rows for a columns major matrix, and the number of cols otherwise */
+ Index innerSize() const { return (int(Flags)&RowMajorBit) ? this->cols() : this->rows(); }
+
+ bool isRValue() const { return m_isRValue; }
+ Derived& markAsRValue() { m_isRValue = true; return derived(); }
+
+ SparseMatrixBase() : m_isRValue(false) { /* TODO check flags */ }
+
+
+ template<typename OtherDerived>
+ Derived& operator=(const ReturnByValue<OtherDerived>& other);
+
+ template<typename OtherDerived>
+ inline Derived& operator=(const SparseMatrixBase<OtherDerived>& other);
+
+ inline Derived& operator=(const Derived& other);
+
+ protected:
+
+ template<typename OtherDerived>
+ inline Derived& assign(const OtherDerived& other);
+
+ template<typename OtherDerived>
+ inline void assignGeneric(const OtherDerived& other);
+
+ public:
+#ifndef EIGEN_NO_IO
+ friend std::ostream & operator << (std::ostream & s, const SparseMatrixBase& m)
+ {
+ typedef typename Derived::Nested Nested;
+ typedef internal::remove_all_t<Nested> NestedCleaned;
+
+ if (Flags&RowMajorBit)
+ {
+ Nested nm(m.derived());
+ internal::evaluator<NestedCleaned> thisEval(nm);
+ for (Index row=0; row<nm.outerSize(); ++row)
+ {
+ Index col = 0;
+ for (typename internal::evaluator<NestedCleaned>::InnerIterator it(thisEval, row); it; ++it)
+ {
+ for ( ; col<it.index(); ++col)
+ s << "0 ";
+ s << it.value() << " ";
+ ++col;
+ }
+ for ( ; col<m.cols(); ++col)
+ s << "0 ";
+ s << std::endl;
+ }
+ }
+ else
+ {
+ Nested nm(m.derived());
+ internal::evaluator<NestedCleaned> thisEval(nm);
+ if (m.cols() == 1) {
+ Index row = 0;
+ for (typename internal::evaluator<NestedCleaned>::InnerIterator it(thisEval, 0); it; ++it)
+ {
+ for ( ; row<it.index(); ++row)
+ s << "0" << std::endl;
+ s << it.value() << std::endl;
+ ++row;
+ }
+ for ( ; row<m.rows(); ++row)
+ s << "0" << std::endl;
+ }
+ else
+ {
+ SparseMatrix<Scalar, RowMajorBit, StorageIndex> trans = m;
+ s << static_cast<const SparseMatrixBase<SparseMatrix<Scalar, RowMajorBit, StorageIndex> >&>(trans);
+ }
+ }
+ return s;
+ }
+#endif
+
+ template<typename OtherDerived>
+ Derived& operator+=(const SparseMatrixBase<OtherDerived>& other);
+ template<typename OtherDerived>
+ Derived& operator-=(const SparseMatrixBase<OtherDerived>& other);
+
+ template<typename OtherDerived>
+ Derived& operator+=(const DiagonalBase<OtherDerived>& other);
+ template<typename OtherDerived>
+ Derived& operator-=(const DiagonalBase<OtherDerived>& other);
+
+ template<typename OtherDerived>
+ Derived& operator+=(const EigenBase<OtherDerived> &other);
+ template<typename OtherDerived>
+ Derived& operator-=(const EigenBase<OtherDerived> &other);
+
+ Derived& operator*=(const Scalar& other);
+ Derived& operator/=(const Scalar& other);
+
+ template<typename OtherDerived> struct CwiseProductDenseReturnType {
+ typedef CwiseBinaryOp<internal::scalar_product_op<typename ScalarBinaryOpTraits<
+ typename internal::traits<Derived>::Scalar,
+ typename internal::traits<OtherDerived>::Scalar
+ >::ReturnType>,
+ const Derived,
+ const OtherDerived
+ > Type;
+ };
+
+ template<typename OtherDerived>
+ EIGEN_STRONG_INLINE const typename CwiseProductDenseReturnType<OtherDerived>::Type
+ cwiseProduct(const MatrixBase<OtherDerived> &other) const;
+
+ // sparse * diagonal
+ template<typename OtherDerived>
+ const Product<Derived,OtherDerived>
+ operator*(const DiagonalBase<OtherDerived> &other) const
+ { return Product<Derived,OtherDerived>(derived(), other.derived()); }
+
+ // diagonal * sparse
+ template<typename OtherDerived> friend
+ const Product<OtherDerived,Derived>
+ operator*(const DiagonalBase<OtherDerived> &lhs, const SparseMatrixBase& rhs)
+ { return Product<OtherDerived,Derived>(lhs.derived(), rhs.derived()); }
+
+ // sparse * sparse
+ template<typename OtherDerived>
+ const Product<Derived,OtherDerived,AliasFreeProduct>
+ operator*(const SparseMatrixBase<OtherDerived> &other) const;
+
+ // sparse * dense
+ template<typename OtherDerived>
+ const Product<Derived,OtherDerived>
+ operator*(const MatrixBase<OtherDerived> &other) const
+ { return Product<Derived,OtherDerived>(derived(), other.derived()); }
+
+ // dense * sparse
+ template<typename OtherDerived> friend
+ const Product<OtherDerived,Derived>
+ operator*(const MatrixBase<OtherDerived> &lhs, const SparseMatrixBase& rhs)
+ { return Product<OtherDerived,Derived>(lhs.derived(), rhs.derived()); }
+
+ /** \returns an expression of P H P^-1 where H is the matrix represented by \c *this */
+ SparseSymmetricPermutationProduct<Derived,Upper|Lower> twistedBy(const PermutationMatrix<Dynamic,Dynamic,StorageIndex>& perm) const
+ {
+ return SparseSymmetricPermutationProduct<Derived,Upper|Lower>(derived(), perm);
+ }
+
+ template<typename OtherDerived>
+ Derived& operator*=(const SparseMatrixBase<OtherDerived>& other);
+
+ template<int Mode>
+ inline const TriangularView<const Derived, Mode> triangularView() const;
+
+ template<unsigned int UpLo> struct SelfAdjointViewReturnType { typedef SparseSelfAdjointView<Derived, UpLo> Type; };
+ template<unsigned int UpLo> struct ConstSelfAdjointViewReturnType { typedef const SparseSelfAdjointView<const Derived, UpLo> Type; };
+
+ template<unsigned int UpLo> inline
+ typename ConstSelfAdjointViewReturnType<UpLo>::Type selfadjointView() const;
+ template<unsigned int UpLo> inline
+ typename SelfAdjointViewReturnType<UpLo>::Type selfadjointView();
+
+ template<typename OtherDerived> Scalar dot(const MatrixBase<OtherDerived>& other) const;
+ template<typename OtherDerived> Scalar dot(const SparseMatrixBase<OtherDerived>& other) const;
+ RealScalar squaredNorm() const;
+ RealScalar norm() const;
+ RealScalar blueNorm() const;
+
+ TransposeReturnType transpose() { return TransposeReturnType(derived()); }
+ const ConstTransposeReturnType transpose() const { return ConstTransposeReturnType(derived()); }
+ const AdjointReturnType adjoint() const { return AdjointReturnType(transpose()); }
+
+ DenseMatrixType toDense() const
+ {
+ return DenseMatrixType(derived());
+ }
+
+ template<typename OtherDerived>
+ bool isApprox(const SparseMatrixBase<OtherDerived>& other,
+ const RealScalar& prec = NumTraits<Scalar>::dummy_precision()) const;
+
+ template<typename OtherDerived>
+ bool isApprox(const MatrixBase<OtherDerived>& other,
+ const RealScalar& prec = NumTraits<Scalar>::dummy_precision()) const
+ { return toDense().isApprox(other,prec); }
+
+ /** \returns the matrix or vector obtained by evaluating this expression.
+ *
+ * Notice that in the case of a plain matrix or vector (not an expression) this function just returns
+ * a const reference, in order to avoid a useless copy.
+ */
+ inline const typename internal::eval<Derived>::type eval() const
+ { return typename internal::eval<Derived>::type(derived()); }
+
+ Scalar sum() const;
+
+ inline const SparseView<Derived>
+ pruned(const Scalar& reference = Scalar(0), const RealScalar& epsilon = NumTraits<Scalar>::dummy_precision()) const;
+
+ protected:
+
+ bool m_isRValue;
+
+ static inline StorageIndex convert_index(const Index idx) {
+ return internal::convert_index<StorageIndex>(idx);
+ }
+ private:
+ template<typename Dest> void evalTo(Dest &) const;
+};
+
+} // end namespace Eigen
+
+#endif // EIGEN_SPARSEMATRIXBASE_H
diff --git a/Eigen/src/SparseCore/SparsePermutation.h b/Eigen/src/SparseCore/SparsePermutation.h
new file mode 100644
index 0000000..af9a1fe
--- /dev/null
+++ b/Eigen/src/SparseCore/SparsePermutation.h
@@ -0,0 +1,180 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2012 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_SPARSE_PERMUTATION_H
+#define EIGEN_SPARSE_PERMUTATION_H
+
+// This file implements sparse * permutation products
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+
+template<typename ExpressionType, int Side, bool Transposed>
+struct permutation_matrix_product<ExpressionType, Side, Transposed, SparseShape>
+{
+ typedef typename nested_eval<ExpressionType, 1>::type MatrixType;
+ typedef remove_all_t<MatrixType> MatrixTypeCleaned;
+
+ typedef typename MatrixTypeCleaned::Scalar Scalar;
+ typedef typename MatrixTypeCleaned::StorageIndex StorageIndex;
+
+ enum {
+ SrcStorageOrder = MatrixTypeCleaned::Flags&RowMajorBit ? RowMajor : ColMajor,
+ MoveOuter = SrcStorageOrder==RowMajor ? Side==OnTheLeft : Side==OnTheRight
+ };
+
+ typedef std::conditional_t<MoveOuter,
+ SparseMatrix<Scalar,SrcStorageOrder,StorageIndex>,
+ SparseMatrix<Scalar,int(SrcStorageOrder)==RowMajor?ColMajor:RowMajor,StorageIndex> > ReturnType;
+
+ template<typename Dest,typename PermutationType>
+ static inline void run(Dest& dst, const PermutationType& perm, const ExpressionType& xpr)
+ {
+ MatrixType mat(xpr);
+ if(MoveOuter)
+ {
+ SparseMatrix<Scalar,SrcStorageOrder,StorageIndex> tmp(mat.rows(), mat.cols());
+ Matrix<StorageIndex,Dynamic,1> sizes(mat.outerSize());
+ for(Index j=0; j<mat.outerSize(); ++j)
+ {
+ Index jp = perm.indices().coeff(j);
+ sizes[((Side==OnTheLeft) ^ Transposed) ? jp : j] = StorageIndex(mat.innerVector(((Side==OnTheRight) ^ Transposed) ? jp : j).nonZeros());
+ }
+ tmp.reserve(sizes);
+ for(Index j=0; j<mat.outerSize(); ++j)
+ {
+ Index jp = perm.indices().coeff(j);
+ Index jsrc = ((Side==OnTheRight) ^ Transposed) ? jp : j;
+ Index jdst = ((Side==OnTheLeft) ^ Transposed) ? jp : j;
+ for(typename MatrixTypeCleaned::InnerIterator it(mat,jsrc); it; ++it)
+ tmp.insertByOuterInner(jdst,it.index()) = it.value();
+ }
+ dst = tmp;
+ }
+ else
+ {
+ SparseMatrix<Scalar,int(SrcStorageOrder)==RowMajor?ColMajor:RowMajor,StorageIndex> tmp(mat.rows(), mat.cols());
+ Matrix<StorageIndex,Dynamic,1> sizes(tmp.outerSize());
+ sizes.setZero();
+ PermutationMatrix<Dynamic,Dynamic,StorageIndex> perm_cpy;
+ if((Side==OnTheLeft) ^ Transposed)
+ perm_cpy = perm;
+ else
+ perm_cpy = perm.transpose();
+
+ for(Index j=0; j<mat.outerSize(); ++j)
+ for(typename MatrixTypeCleaned::InnerIterator it(mat,j); it; ++it)
+ sizes[perm_cpy.indices().coeff(it.index())]++;
+ tmp.reserve(sizes);
+ for(Index j=0; j<mat.outerSize(); ++j)
+ for(typename MatrixTypeCleaned::InnerIterator it(mat,j); it; ++it)
+ tmp.insertByOuterInner(perm_cpy.indices().coeff(it.index()),j) = it.value();
+ dst = tmp;
+ }
+ }
+};
+
+}
+
+namespace internal {
+
+template <int ProductTag> struct product_promote_storage_type<Sparse, PermutationStorage, ProductTag> { typedef Sparse ret; };
+template <int ProductTag> struct product_promote_storage_type<PermutationStorage, Sparse, ProductTag> { typedef Sparse ret; };
+
+// TODO, the following two overloads are only needed to define the right temporary type through
+// typename traits<permutation_sparse_matrix_product<Rhs,Lhs,OnTheRight,false> >::ReturnType
+// whereas it should be correctly handled by traits<Product<> >::PlainObject
+
+template<typename Lhs, typename Rhs, int ProductTag>
+struct product_evaluator<Product<Lhs, Rhs, AliasFreeProduct>, ProductTag, PermutationShape, SparseShape>
+ : public evaluator<typename permutation_matrix_product<Rhs,OnTheLeft,false,SparseShape>::ReturnType>
+{
+ typedef Product<Lhs, Rhs, AliasFreeProduct> XprType;
+ typedef typename permutation_matrix_product<Rhs,OnTheLeft,false,SparseShape>::ReturnType PlainObject;
+ typedef evaluator<PlainObject> Base;
+
+ enum {
+ Flags = Base::Flags | EvalBeforeNestingBit
+ };
+
+ explicit product_evaluator(const XprType& xpr)
+ : m_result(xpr.rows(), xpr.cols())
+ {
+ internal::construct_at<Base>(this, m_result);
+ generic_product_impl<Lhs, Rhs, PermutationShape, SparseShape, ProductTag>::evalTo(m_result, xpr.lhs(), xpr.rhs());
+ }
+
+protected:
+ PlainObject m_result;
+};
+
+template<typename Lhs, typename Rhs, int ProductTag>
+struct product_evaluator<Product<Lhs, Rhs, AliasFreeProduct>, ProductTag, SparseShape, PermutationShape >
+ : public evaluator<typename permutation_matrix_product<Lhs,OnTheRight,false,SparseShape>::ReturnType>
+{
+ typedef Product<Lhs, Rhs, AliasFreeProduct> XprType;
+ typedef typename permutation_matrix_product<Lhs,OnTheRight,false,SparseShape>::ReturnType PlainObject;
+ typedef evaluator<PlainObject> Base;
+
+ enum {
+ Flags = Base::Flags | EvalBeforeNestingBit
+ };
+
+ explicit product_evaluator(const XprType& xpr)
+ : m_result(xpr.rows(), xpr.cols())
+ {
+ ::new (static_cast<Base*>(this)) Base(m_result);
+ generic_product_impl<Lhs, Rhs, SparseShape, PermutationShape, ProductTag>::evalTo(m_result, xpr.lhs(), xpr.rhs());
+ }
+
+protected:
+ PlainObject m_result;
+};
+
+} // end namespace internal
+
+/** \returns the matrix with the permutation applied to the columns
+ */
+template<typename SparseDerived, typename PermDerived>
+inline const Product<SparseDerived, PermDerived, AliasFreeProduct>
+operator*(const SparseMatrixBase<SparseDerived>& matrix, const PermutationBase<PermDerived>& perm)
+{ return Product<SparseDerived, PermDerived, AliasFreeProduct>(matrix.derived(), perm.derived()); }
+
+/** \returns the matrix with the permutation applied to the rows
+ */
+template<typename SparseDerived, typename PermDerived>
+inline const Product<PermDerived, SparseDerived, AliasFreeProduct>
+operator*( const PermutationBase<PermDerived>& perm, const SparseMatrixBase<SparseDerived>& matrix)
+{ return Product<PermDerived, SparseDerived, AliasFreeProduct>(perm.derived(), matrix.derived()); }
+
+
+/** \returns the matrix with the inverse permutation applied to the columns.
+ */
+template<typename SparseDerived, typename PermutationType>
+inline const Product<SparseDerived, Inverse<PermutationType>, AliasFreeProduct>
+operator*(const SparseMatrixBase<SparseDerived>& matrix, const InverseImpl<PermutationType, PermutationStorage>& tperm)
+{
+ return Product<SparseDerived, Inverse<PermutationType>, AliasFreeProduct>(matrix.derived(), tperm.derived());
+}
+
+/** \returns the matrix with the inverse permutation applied to the rows.
+ */
+template<typename SparseDerived, typename PermutationType>
+inline const Product<Inverse<PermutationType>, SparseDerived, AliasFreeProduct>
+operator*(const InverseImpl<PermutationType,PermutationStorage>& tperm, const SparseMatrixBase<SparseDerived>& matrix)
+{
+ return Product<Inverse<PermutationType>, SparseDerived, AliasFreeProduct>(tperm.derived(), matrix.derived());
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_SPARSE_SELFADJOINTVIEW_H
diff --git a/Eigen/src/SparseCore/SparseProduct.h b/Eigen/src/SparseCore/SparseProduct.h
new file mode 100644
index 0000000..85a8a10
--- /dev/null
+++ b/Eigen/src/SparseCore/SparseProduct.h
@@ -0,0 +1,183 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2015 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_SPARSEPRODUCT_H
+#define EIGEN_SPARSEPRODUCT_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+/** \returns an expression of the product of two sparse matrices.
+ * By default a conservative product preserving the symbolic non zeros is performed.
+ * The automatic pruning of the small values can be achieved by calling the pruned() function
+ * in which case a totally different product algorithm is employed:
+ * \code
+ * C = (A*B).pruned(); // suppress numerical zeros (exact)
+ * C = (A*B).pruned(ref);
+ * C = (A*B).pruned(ref,epsilon);
+ * \endcode
+ * where \c ref is a meaningful non zero reference value.
+ * */
+template<typename Derived>
+template<typename OtherDerived>
+inline const Product<Derived,OtherDerived,AliasFreeProduct>
+SparseMatrixBase<Derived>::operator*(const SparseMatrixBase<OtherDerived> &other) const
+{
+ return Product<Derived,OtherDerived,AliasFreeProduct>(derived(), other.derived());
+}
+
+namespace internal {
+
+// sparse * sparse
+template<typename Lhs, typename Rhs, int ProductType>
+struct generic_product_impl<Lhs, Rhs, SparseShape, SparseShape, ProductType>
+{
+ template<typename Dest>
+ static void evalTo(Dest& dst, const Lhs& lhs, const Rhs& rhs)
+ {
+ evalTo(dst, lhs, rhs, typename evaluator_traits<Dest>::Shape());
+ }
+
+ // dense += sparse * sparse
+ template<typename Dest,typename ActualLhs>
+ static void addTo(Dest& dst, const ActualLhs& lhs, const Rhs& rhs, std::enable_if_t<is_same<typename evaluator_traits<Dest>::Shape,DenseShape>::value,int*>* = 0)
+ {
+ typedef typename nested_eval<ActualLhs,Dynamic>::type LhsNested;
+ typedef typename nested_eval<Rhs,Dynamic>::type RhsNested;
+ LhsNested lhsNested(lhs);
+ RhsNested rhsNested(rhs);
+ internal::sparse_sparse_to_dense_product_selector<remove_all_t<LhsNested>,
+ remove_all_t<RhsNested>, Dest>::run(lhsNested,rhsNested,dst);
+ }
+
+ // dense -= sparse * sparse
+ template<typename Dest>
+ static void subTo(Dest& dst, const Lhs& lhs, const Rhs& rhs, std::enable_if_t<is_same<typename evaluator_traits<Dest>::Shape,DenseShape>::value,int*>* = 0)
+ {
+ addTo(dst, -lhs, rhs);
+ }
+
+protected:
+
+ // sparse = sparse * sparse
+ template<typename Dest>
+ static void evalTo(Dest& dst, const Lhs& lhs, const Rhs& rhs, SparseShape)
+ {
+ typedef typename nested_eval<Lhs,Dynamic>::type LhsNested;
+ typedef typename nested_eval<Rhs,Dynamic>::type RhsNested;
+ LhsNested lhsNested(lhs);
+ RhsNested rhsNested(rhs);
+ internal::conservative_sparse_sparse_product_selector<remove_all_t<LhsNested>,
+ remove_all_t<RhsNested>, Dest>::run(lhsNested,rhsNested,dst);
+ }
+
+ // dense = sparse * sparse
+ template<typename Dest>
+ static void evalTo(Dest& dst, const Lhs& lhs, const Rhs& rhs, DenseShape)
+ {
+ dst.setZero();
+ addTo(dst, lhs, rhs);
+ }
+};
+
+// sparse * sparse-triangular
+template<typename Lhs, typename Rhs, int ProductType>
+struct generic_product_impl<Lhs, Rhs, SparseShape, SparseTriangularShape, ProductType>
+ : public generic_product_impl<Lhs, Rhs, SparseShape, SparseShape, ProductType>
+{};
+
+// sparse-triangular * sparse
+template<typename Lhs, typename Rhs, int ProductType>
+struct generic_product_impl<Lhs, Rhs, SparseTriangularShape, SparseShape, ProductType>
+ : public generic_product_impl<Lhs, Rhs, SparseShape, SparseShape, ProductType>
+{};
+
+// dense = sparse-product (can be sparse*sparse, sparse*perm, etc.)
+template< typename DstXprType, typename Lhs, typename Rhs>
+struct Assignment<DstXprType, Product<Lhs,Rhs,AliasFreeProduct>, internal::assign_op<typename DstXprType::Scalar,typename Product<Lhs,Rhs,AliasFreeProduct>::Scalar>, Sparse2Dense>
+{
+ typedef Product<Lhs,Rhs,AliasFreeProduct> SrcXprType;
+ static void run(DstXprType &dst, const SrcXprType &src, const internal::assign_op<typename DstXprType::Scalar,typename SrcXprType::Scalar> &)
+ {
+ Index dstRows = src.rows();
+ Index dstCols = src.cols();
+ if((dst.rows()!=dstRows) || (dst.cols()!=dstCols))
+ dst.resize(dstRows, dstCols);
+
+ generic_product_impl<Lhs, Rhs>::evalTo(dst,src.lhs(),src.rhs());
+ }
+};
+
+// dense += sparse-product (can be sparse*sparse, sparse*perm, etc.)
+template< typename DstXprType, typename Lhs, typename Rhs>
+struct Assignment<DstXprType, Product<Lhs,Rhs,AliasFreeProduct>, internal::add_assign_op<typename DstXprType::Scalar,typename Product<Lhs,Rhs,AliasFreeProduct>::Scalar>, Sparse2Dense>
+{
+ typedef Product<Lhs,Rhs,AliasFreeProduct> SrcXprType;
+ static void run(DstXprType &dst, const SrcXprType &src, const internal::add_assign_op<typename DstXprType::Scalar,typename SrcXprType::Scalar> &)
+ {
+ generic_product_impl<Lhs, Rhs>::addTo(dst,src.lhs(),src.rhs());
+ }
+};
+
+// dense -= sparse-product (can be sparse*sparse, sparse*perm, etc.)
+template< typename DstXprType, typename Lhs, typename Rhs>
+struct Assignment<DstXprType, Product<Lhs,Rhs,AliasFreeProduct>, internal::sub_assign_op<typename DstXprType::Scalar,typename Product<Lhs,Rhs,AliasFreeProduct>::Scalar>, Sparse2Dense>
+{
+ typedef Product<Lhs,Rhs,AliasFreeProduct> SrcXprType;
+ static void run(DstXprType &dst, const SrcXprType &src, const internal::sub_assign_op<typename DstXprType::Scalar,typename SrcXprType::Scalar> &)
+ {
+ generic_product_impl<Lhs, Rhs>::subTo(dst,src.lhs(),src.rhs());
+ }
+};
+
+template<typename Lhs, typename Rhs, int Options>
+struct unary_evaluator<SparseView<Product<Lhs, Rhs, Options> >, IteratorBased>
+ : public evaluator<typename Product<Lhs, Rhs, DefaultProduct>::PlainObject>
+{
+ typedef SparseView<Product<Lhs, Rhs, Options> > XprType;
+ typedef typename XprType::PlainObject PlainObject;
+ typedef evaluator<PlainObject> Base;
+
+ explicit unary_evaluator(const XprType& xpr)
+ : m_result(xpr.rows(), xpr.cols())
+ {
+ using std::abs;
+ internal::construct_at<Base>(this, m_result);
+ typedef typename nested_eval<Lhs,Dynamic>::type LhsNested;
+ typedef typename nested_eval<Rhs,Dynamic>::type RhsNested;
+ LhsNested lhsNested(xpr.nestedExpression().lhs());
+ RhsNested rhsNested(xpr.nestedExpression().rhs());
+
+ internal::sparse_sparse_product_with_pruning_selector<remove_all_t<LhsNested>,
+ remove_all_t<RhsNested>, PlainObject>::run(lhsNested,rhsNested,m_result,
+ abs(xpr.reference())*xpr.epsilon());
+ }
+
+protected:
+ PlainObject m_result;
+};
+
+} // end namespace internal
+
+// sparse matrix = sparse-product (can be sparse*sparse, sparse*perm, etc.)
+template<typename Scalar, int Options_, typename StorageIndex_>
+template<typename Lhs, typename Rhs>
+SparseMatrix<Scalar,Options_,StorageIndex_>& SparseMatrix<Scalar,Options_,StorageIndex_>::operator=(const Product<Lhs,Rhs,AliasFreeProduct>& src)
+{
+ // std::cout << "in Assignment : " << DstOptions << "\n";
+ SparseMatrix dst(src.rows(),src.cols());
+ internal::generic_product_impl<Lhs, Rhs>::evalTo(dst,src.lhs(),src.rhs());
+ this->swap(dst);
+ return *this;
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_SPARSEPRODUCT_H
diff --git a/Eigen/src/SparseCore/SparseRedux.h b/Eigen/src/SparseCore/SparseRedux.h
new file mode 100644
index 0000000..6b14c58
--- /dev/null
+++ b/Eigen/src/SparseCore/SparseRedux.h
@@ -0,0 +1,51 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2014 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_SPARSEREDUX_H
+#define EIGEN_SPARSEREDUX_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+template<typename Derived>
+typename internal::traits<Derived>::Scalar
+SparseMatrixBase<Derived>::sum() const
+{
+ eigen_assert(rows()>0 && cols()>0 && "you are using a non initialized matrix");
+ Scalar res(0);
+ internal::evaluator<Derived> thisEval(derived());
+ for (Index j=0; j<outerSize(); ++j)
+ for (typename internal::evaluator<Derived>::InnerIterator iter(thisEval,j); iter; ++iter)
+ res += iter.value();
+ return res;
+}
+
+template<typename Scalar_, int Options_, typename Index_>
+typename internal::traits<SparseMatrix<Scalar_,Options_,Index_> >::Scalar
+SparseMatrix<Scalar_,Options_,Index_>::sum() const
+{
+ eigen_assert(rows()>0 && cols()>0 && "you are using a non initialized matrix");
+ if(this->isCompressed())
+ return Matrix<Scalar,1,Dynamic>::Map(m_data.valuePtr(), m_data.size()).sum();
+ else
+ return Base::sum();
+}
+
+template<typename Scalar_, int Options_, typename Index_>
+typename internal::traits<SparseVector<Scalar_,Options_, Index_> >::Scalar
+SparseVector<Scalar_,Options_,Index_>::sum() const
+{
+ eigen_assert(rows()>0 && cols()>0 && "you are using a non initialized matrix");
+ return Matrix<Scalar,1,Dynamic>::Map(m_data.valuePtr(), m_data.size()).sum();
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_SPARSEREDUX_H
diff --git a/Eigen/src/SparseCore/SparseRef.h b/Eigen/src/SparseCore/SparseRef.h
new file mode 100644
index 0000000..9e69d93
--- /dev/null
+++ b/Eigen/src/SparseCore/SparseRef.h
@@ -0,0 +1,394 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2015 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_SPARSE_REF_H
+#define EIGEN_SPARSE_REF_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+enum {
+ StandardCompressedFormat = 2 /**< used by Ref<SparseMatrix> to specify whether the input storage must be in standard compressed form */
+};
+
+namespace internal {
+
+template<typename Derived> class SparseRefBase;
+
+template<typename MatScalar, int MatOptions, typename MatIndex, int Options_, typename StrideType_>
+struct traits<Ref<SparseMatrix<MatScalar,MatOptions,MatIndex>, Options_, StrideType_> >
+ : public traits<SparseMatrix<MatScalar,MatOptions,MatIndex> >
+{
+ typedef SparseMatrix<MatScalar,MatOptions,MatIndex> PlainObjectType;
+ enum {
+ Options = Options_,
+ Flags = traits<PlainObjectType>::Flags | CompressedAccessBit | NestByRefBit
+ };
+
+ template<typename Derived> struct match {
+ enum {
+ StorageOrderMatch = PlainObjectType::IsVectorAtCompileTime || Derived::IsVectorAtCompileTime || ((PlainObjectType::Flags&RowMajorBit)==(Derived::Flags&RowMajorBit)),
+ MatchAtCompileTime = (Derived::Flags&CompressedAccessBit) && StorageOrderMatch
+ };
+ typedef std::conditional_t<MatchAtCompileTime,internal::true_type,internal::false_type> type;
+ };
+
+};
+
+template<typename MatScalar, int MatOptions, typename MatIndex, int Options_, typename StrideType_>
+struct traits<Ref<const SparseMatrix<MatScalar,MatOptions,MatIndex>, Options_, StrideType_> >
+ : public traits<Ref<SparseMatrix<MatScalar,MatOptions,MatIndex>, Options_, StrideType_> >
+{
+ enum {
+ Flags = (traits<SparseMatrix<MatScalar,MatOptions,MatIndex> >::Flags | CompressedAccessBit | NestByRefBit) & ~LvalueBit
+ };
+};
+
+template<typename MatScalar, int MatOptions, typename MatIndex, int Options_, typename StrideType_>
+struct traits<Ref<SparseVector<MatScalar,MatOptions,MatIndex>, Options_, StrideType_> >
+ : public traits<SparseVector<MatScalar,MatOptions,MatIndex> >
+{
+ typedef SparseVector<MatScalar,MatOptions,MatIndex> PlainObjectType;
+ enum {
+ Options = Options_,
+ Flags = traits<PlainObjectType>::Flags | CompressedAccessBit | NestByRefBit
+ };
+
+ template<typename Derived> struct match {
+ enum {
+ MatchAtCompileTime = (Derived::Flags&CompressedAccessBit) && Derived::IsVectorAtCompileTime
+ };
+ typedef std::conditional_t<MatchAtCompileTime,internal::true_type,internal::false_type> type;
+ };
+
+};
+
+template<typename MatScalar, int MatOptions, typename MatIndex, int Options_, typename StrideType_>
+struct traits<Ref<const SparseVector<MatScalar,MatOptions,MatIndex>, Options_, StrideType_> >
+ : public traits<Ref<SparseVector<MatScalar,MatOptions,MatIndex>, Options_, StrideType_> >
+{
+ enum {
+ Flags = (traits<SparseVector<MatScalar,MatOptions,MatIndex> >::Flags | CompressedAccessBit | NestByRefBit) & ~LvalueBit
+ };
+};
+
+template<typename Derived>
+struct traits<SparseRefBase<Derived> > : public traits<Derived> {};
+
+template<typename Derived> class SparseRefBase
+ : public SparseMapBase<Derived>
+{
+public:
+
+ typedef SparseMapBase<Derived> Base;
+ EIGEN_SPARSE_PUBLIC_INTERFACE(SparseRefBase)
+
+ SparseRefBase()
+ : Base(RowsAtCompileTime==Dynamic?0:RowsAtCompileTime,ColsAtCompileTime==Dynamic?0:ColsAtCompileTime, 0, 0, 0, 0, 0)
+ {}
+
+protected:
+
+ template<typename Expression>
+ void construct(Expression& expr)
+ {
+ if(expr.outerIndexPtr()==0)
+ internal::construct_at<Base>(this, expr.size(), expr.nonZeros(), expr.innerIndexPtr(), expr.valuePtr());
+ else
+ internal::construct_at<Base>(this, expr.rows(), expr.cols(), expr.nonZeros(), expr.outerIndexPtr(), expr.innerIndexPtr(), expr.valuePtr(), expr.innerNonZeroPtr());
+ }
+};
+
+} // namespace internal
+
+
+/**
+ * \ingroup SparseCore_Module
+ *
+ * \brief A sparse matrix expression referencing an existing sparse expression
+ *
+ * \tparam SparseMatrixType the equivalent sparse matrix type of the referenced data, it must be a template instance of class SparseMatrix.
+ * \tparam Options specifies whether the a standard compressed format is required \c Options is \c #StandardCompressedFormat, or \c 0.
+ * The default is \c 0.
+ *
+ * \sa class Ref
+ */
+#ifndef EIGEN_PARSED_BY_DOXYGEN
+template<typename MatScalar, int MatOptions, typename MatIndex, int Options, typename StrideType>
+class Ref<SparseMatrix<MatScalar,MatOptions,MatIndex>, Options, StrideType >
+ : public internal::SparseRefBase<Ref<SparseMatrix<MatScalar,MatOptions,MatIndex>, Options, StrideType > >
+#else
+template<typename SparseMatrixType, int Options>
+class Ref<SparseMatrixType, Options>
+ : public SparseMapBase<Derived,WriteAccessors> // yes, that's weird to use Derived here, but that works!
+#endif
+{
+ typedef SparseMatrix<MatScalar,MatOptions,MatIndex> PlainObjectType;
+ typedef internal::traits<Ref> Traits;
+ template<int OtherOptions>
+ inline Ref(const SparseMatrix<MatScalar,OtherOptions,MatIndex>& expr);
+ template<int OtherOptions>
+ inline Ref(const Map<SparseMatrix<MatScalar,OtherOptions,MatIndex>>& expr);
+ public:
+
+ typedef internal::SparseRefBase<Ref> Base;
+ EIGEN_SPARSE_PUBLIC_INTERFACE(Ref)
+
+
+ #ifndef EIGEN_PARSED_BY_DOXYGEN
+ template<int OtherOptions>
+ inline Ref(SparseMatrix<MatScalar,OtherOptions,MatIndex>& expr)
+ {
+ EIGEN_STATIC_ASSERT(bool(Traits::template match<SparseMatrix<MatScalar,OtherOptions,MatIndex> >::MatchAtCompileTime), STORAGE_LAYOUT_DOES_NOT_MATCH);
+ eigen_assert( ((Options & int(StandardCompressedFormat))==0) || (expr.isCompressed()) );
+ Base::construct(expr.derived());
+ }
+
+ template<int OtherOptions>
+ inline Ref(Map<SparseMatrix<MatScalar,OtherOptions,MatIndex> >& expr)
+ {
+ EIGEN_STATIC_ASSERT(bool(Traits::template match<SparseMatrix<MatScalar,OtherOptions,MatIndex> >::MatchAtCompileTime), STORAGE_LAYOUT_DOES_NOT_MATCH);
+ eigen_assert( ((Options & int(StandardCompressedFormat))==0) || (expr.isCompressed()) );
+ Base::construct(expr.derived());
+ }
+
+ template<typename Derived>
+ inline Ref(const SparseCompressedBase<Derived>& expr)
+ #else
+ /** Implicit constructor from any sparse expression (2D matrix or 1D vector) */
+ template<typename Derived>
+ inline Ref(SparseCompressedBase<Derived>& expr)
+ #endif
+ {
+ EIGEN_STATIC_ASSERT(bool(internal::is_lvalue<Derived>::value), THIS_EXPRESSION_IS_NOT_A_LVALUE__IT_IS_READ_ONLY);
+ EIGEN_STATIC_ASSERT(bool(Traits::template match<Derived>::MatchAtCompileTime), STORAGE_LAYOUT_DOES_NOT_MATCH);
+ eigen_assert( ((Options & int(StandardCompressedFormat))==0) || (expr.isCompressed()) );
+ Base::construct(expr.const_cast_derived());
+ }
+};
+
+// this is the const ref version
+template<typename MatScalar, int MatOptions, typename MatIndex, int Options, typename StrideType>
+class Ref<const SparseMatrix<MatScalar,MatOptions,MatIndex>, Options, StrideType>
+ : public internal::SparseRefBase<Ref<const SparseMatrix<MatScalar,MatOptions,MatIndex>, Options, StrideType> >
+{
+ typedef SparseMatrix<MatScalar,MatOptions,MatIndex> TPlainObjectType;
+ typedef internal::traits<Ref> Traits;
+ public:
+
+ typedef internal::SparseRefBase<Ref> Base;
+ EIGEN_SPARSE_PUBLIC_INTERFACE(Ref)
+
+ template<typename Derived>
+ inline Ref(const SparseMatrixBase<Derived>& expr) : m_hasCopy(false)
+ {
+ construct(expr.derived(), typename Traits::template match<Derived>::type());
+ }
+
+ inline Ref(const Ref& other) : Base(other), m_hasCopy(false) {
+ // copy constructor shall not copy the m_object, to avoid unnecessary malloc and copy
+ }
+
+ template<typename OtherRef>
+ inline Ref(const RefBase<OtherRef>& other) : m_hasCopy(false) {
+ construct(other.derived(), typename Traits::template match<OtherRef>::type());
+ }
+
+ ~Ref() {
+ if(m_hasCopy) {
+ internal::destroy_at(reinterpret_cast<TPlainObjectType*>(&m_storage));
+ }
+ }
+
+ protected:
+
+ template<typename Expression>
+ void construct(const Expression& expr,internal::true_type)
+ {
+ if((Options & int(StandardCompressedFormat)) && (!expr.isCompressed()))
+ {
+ TPlainObjectType* obj = internal::construct_at(reinterpret_cast<TPlainObjectType*>(&m_storage), expr);
+ m_hasCopy = true;
+ Base::construct(*obj);
+ }
+ else
+ {
+ Base::construct(expr);
+ }
+ }
+
+ template<typename Expression>
+ void construct(const Expression& expr, internal::false_type)
+ {
+ TPlainObjectType* obj = internal::construct_at(reinterpret_cast<TPlainObjectType*>(&m_storage), expr);
+ m_hasCopy = true;
+ Base::construct(*obj);
+ }
+
+ protected:
+ typename internal::aligned_storage<sizeof(TPlainObjectType), EIGEN_ALIGNOF(TPlainObjectType)>::type m_storage;
+ bool m_hasCopy;
+};
+
+
+
+/**
+ * \ingroup SparseCore_Module
+ *
+ * \brief A sparse vector expression referencing an existing sparse vector expression
+ *
+ * \tparam SparseVectorType the equivalent sparse vector type of the referenced data, it must be a template instance of class SparseVector.
+ *
+ * \sa class Ref
+ */
+#ifndef EIGEN_PARSED_BY_DOXYGEN
+template<typename MatScalar, int MatOptions, typename MatIndex, int Options, typename StrideType>
+class Ref<SparseVector<MatScalar,MatOptions,MatIndex>, Options, StrideType >
+ : public internal::SparseRefBase<Ref<SparseVector<MatScalar,MatOptions,MatIndex>, Options, StrideType > >
+#else
+template<typename SparseVectorType>
+class Ref<SparseVectorType>
+ : public SparseMapBase<Derived,WriteAccessors>
+#endif
+{
+ typedef SparseVector<MatScalar,MatOptions,MatIndex> PlainObjectType;
+ typedef internal::traits<Ref> Traits;
+ template<int OtherOptions>
+ inline Ref(const SparseVector<MatScalar,OtherOptions,MatIndex>& expr);
+ public:
+
+ typedef internal::SparseRefBase<Ref> Base;
+ EIGEN_SPARSE_PUBLIC_INTERFACE(Ref)
+
+ #ifndef EIGEN_PARSED_BY_DOXYGEN
+ template<int OtherOptions>
+ inline Ref(SparseVector<MatScalar,OtherOptions,MatIndex>& expr)
+ {
+ EIGEN_STATIC_ASSERT(bool(Traits::template match<SparseVector<MatScalar,OtherOptions,MatIndex> >::MatchAtCompileTime), STORAGE_LAYOUT_DOES_NOT_MATCH);
+ Base::construct(expr.derived());
+ }
+
+ template<typename Derived>
+ inline Ref(const SparseCompressedBase<Derived>& expr)
+ #else
+ /** Implicit constructor from any 1D sparse vector expression */
+ template<typename Derived>
+ inline Ref(SparseCompressedBase<Derived>& expr)
+ #endif
+ {
+ EIGEN_STATIC_ASSERT(bool(internal::is_lvalue<Derived>::value), THIS_EXPRESSION_IS_NOT_A_LVALUE__IT_IS_READ_ONLY);
+ EIGEN_STATIC_ASSERT(bool(Traits::template match<Derived>::MatchAtCompileTime), STORAGE_LAYOUT_DOES_NOT_MATCH);
+ Base::construct(expr.const_cast_derived());
+ }
+};
+
+// this is the const ref version
+template<typename MatScalar, int MatOptions, typename MatIndex, int Options, typename StrideType>
+class Ref<const SparseVector<MatScalar,MatOptions,MatIndex>, Options, StrideType>
+ : public internal::SparseRefBase<Ref<const SparseVector<MatScalar,MatOptions,MatIndex>, Options, StrideType> >
+{
+ typedef SparseVector<MatScalar,MatOptions,MatIndex> TPlainObjectType;
+ typedef internal::traits<Ref> Traits;
+ public:
+
+ typedef internal::SparseRefBase<Ref> Base;
+ EIGEN_SPARSE_PUBLIC_INTERFACE(Ref)
+
+ template<typename Derived>
+ inline Ref(const SparseMatrixBase<Derived>& expr) : m_hasCopy(false)
+ {
+ construct(expr.derived(), typename Traits::template match<Derived>::type());
+ }
+
+ inline Ref(const Ref& other) : Base(other), m_hasCopy(false) {
+ // copy constructor shall not copy the m_object, to avoid unnecessary malloc and copy
+ }
+
+ template<typename OtherRef>
+ inline Ref(const RefBase<OtherRef>& other) : m_hasCopy(false) {
+ construct(other.derived(), typename Traits::template match<OtherRef>::type());
+ }
+
+ ~Ref() {
+ if(m_hasCopy) {
+ internal::destroy_at(reinterpret_cast<TPlainObjectType*>(&m_storage));
+ }
+ }
+
+ protected:
+
+ template<typename Expression>
+ void construct(const Expression& expr,internal::true_type)
+ {
+ Base::construct(expr);
+ }
+
+ template<typename Expression>
+ void construct(const Expression& expr, internal::false_type)
+ {
+ TPlainObjectType* obj = internal::construct_at(reinterpret_cast<TPlainObjectType*>(&m_storage), expr);
+ m_hasCopy = true;
+ Base::construct(*obj);
+ }
+
+ protected:
+ typename internal::aligned_storage<sizeof(TPlainObjectType), EIGEN_ALIGNOF(TPlainObjectType)>::type m_storage;
+ bool m_hasCopy;
+};
+
+namespace internal {
+
+// FIXME shall we introduce a general evaluatior_ref that we can specialize for any sparse object once, and thus remove this copy-pasta thing...
+
+template<typename MatScalar, int MatOptions, typename MatIndex, int Options, typename StrideType>
+struct evaluator<Ref<SparseMatrix<MatScalar,MatOptions,MatIndex>, Options, StrideType> >
+ : evaluator<SparseCompressedBase<Ref<SparseMatrix<MatScalar,MatOptions,MatIndex>, Options, StrideType> > >
+{
+ typedef evaluator<SparseCompressedBase<Ref<SparseMatrix<MatScalar,MatOptions,MatIndex>, Options, StrideType> > > Base;
+ typedef Ref<SparseMatrix<MatScalar,MatOptions,MatIndex>, Options, StrideType> XprType;
+ evaluator() : Base() {}
+ explicit evaluator(const XprType &mat) : Base(mat) {}
+};
+
+template<typename MatScalar, int MatOptions, typename MatIndex, int Options, typename StrideType>
+struct evaluator<Ref<const SparseMatrix<MatScalar,MatOptions,MatIndex>, Options, StrideType> >
+ : evaluator<SparseCompressedBase<Ref<const SparseMatrix<MatScalar,MatOptions,MatIndex>, Options, StrideType> > >
+{
+ typedef evaluator<SparseCompressedBase<Ref<const SparseMatrix<MatScalar,MatOptions,MatIndex>, Options, StrideType> > > Base;
+ typedef Ref<const SparseMatrix<MatScalar,MatOptions,MatIndex>, Options, StrideType> XprType;
+ evaluator() : Base() {}
+ explicit evaluator(const XprType &mat) : Base(mat) {}
+};
+
+template<typename MatScalar, int MatOptions, typename MatIndex, int Options, typename StrideType>
+struct evaluator<Ref<SparseVector<MatScalar,MatOptions,MatIndex>, Options, StrideType> >
+ : evaluator<SparseCompressedBase<Ref<SparseVector<MatScalar,MatOptions,MatIndex>, Options, StrideType> > >
+{
+ typedef evaluator<SparseCompressedBase<Ref<SparseVector<MatScalar,MatOptions,MatIndex>, Options, StrideType> > > Base;
+ typedef Ref<SparseVector<MatScalar,MatOptions,MatIndex>, Options, StrideType> XprType;
+ evaluator() : Base() {}
+ explicit evaluator(const XprType &mat) : Base(mat) {}
+};
+
+template<typename MatScalar, int MatOptions, typename MatIndex, int Options, typename StrideType>
+struct evaluator<Ref<const SparseVector<MatScalar,MatOptions,MatIndex>, Options, StrideType> >
+ : evaluator<SparseCompressedBase<Ref<const SparseVector<MatScalar,MatOptions,MatIndex>, Options, StrideType> > >
+{
+ typedef evaluator<SparseCompressedBase<Ref<const SparseVector<MatScalar,MatOptions,MatIndex>, Options, StrideType> > > Base;
+ typedef Ref<const SparseVector<MatScalar,MatOptions,MatIndex>, Options, StrideType> XprType;
+ evaluator() : Base() {}
+ explicit evaluator(const XprType &mat) : Base(mat) {}
+};
+
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_SPARSE_REF_H
diff --git a/Eigen/src/SparseCore/SparseSelfAdjointView.h b/Eigen/src/SparseCore/SparseSelfAdjointView.h
new file mode 100644
index 0000000..211506e
--- /dev/null
+++ b/Eigen/src/SparseCore/SparseSelfAdjointView.h
@@ -0,0 +1,652 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009-2014 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_SPARSE_SELFADJOINTVIEW_H
+#define EIGEN_SPARSE_SELFADJOINTVIEW_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+/** \ingroup SparseCore_Module
+ * \class SparseSelfAdjointView
+ *
+ * \brief Pseudo expression to manipulate a triangular sparse matrix as a selfadjoint matrix.
+ *
+ * \param MatrixType the type of the dense matrix storing the coefficients
+ * \param Mode can be either \c #Lower or \c #Upper
+ *
+ * This class is an expression of a sefladjoint matrix from a triangular part of a matrix
+ * with given dense storage of the coefficients. It is the return type of MatrixBase::selfadjointView()
+ * and most of the time this is the only way that it is used.
+ *
+ * \sa SparseMatrixBase::selfadjointView()
+ */
+namespace internal {
+
+template<typename MatrixType, unsigned int Mode>
+struct traits<SparseSelfAdjointView<MatrixType,Mode> > : traits<MatrixType> {
+};
+
+template<int SrcMode,int DstMode,typename MatrixType,int DestOrder>
+void permute_symm_to_symm(const MatrixType& mat, SparseMatrix<typename MatrixType::Scalar,DestOrder,typename MatrixType::StorageIndex>& _dest, const typename MatrixType::StorageIndex* perm = 0);
+
+template<int Mode,typename MatrixType,int DestOrder>
+void permute_symm_to_fullsymm(const MatrixType& mat, SparseMatrix<typename MatrixType::Scalar,DestOrder,typename MatrixType::StorageIndex>& _dest, const typename MatrixType::StorageIndex* perm = 0);
+
+}
+
+template<typename MatrixType, unsigned int Mode_> class SparseSelfAdjointView
+ : public EigenBase<SparseSelfAdjointView<MatrixType,Mode_> >
+{
+ public:
+
+ enum {
+ Mode = Mode_,
+ TransposeMode = ((Mode & Upper) ? Lower : 0) | ((Mode & Lower) ? Upper : 0),
+ RowsAtCompileTime = internal::traits<SparseSelfAdjointView>::RowsAtCompileTime,
+ ColsAtCompileTime = internal::traits<SparseSelfAdjointView>::ColsAtCompileTime
+ };
+
+ typedef EigenBase<SparseSelfAdjointView> Base;
+ typedef typename MatrixType::Scalar Scalar;
+ typedef typename MatrixType::StorageIndex StorageIndex;
+ typedef Matrix<StorageIndex,Dynamic,1> VectorI;
+ typedef typename internal::ref_selector<MatrixType>::non_const_type MatrixTypeNested;
+ typedef internal::remove_all_t<MatrixTypeNested> MatrixTypeNested_;
+
+ explicit inline SparseSelfAdjointView(MatrixType& matrix) : m_matrix(matrix)
+ {
+ eigen_assert(rows()==cols() && "SelfAdjointView is only for squared matrices");
+ }
+
+ inline Index rows() const { return m_matrix.rows(); }
+ inline Index cols() const { return m_matrix.cols(); }
+
+ /** \internal \returns a reference to the nested matrix */
+ const MatrixTypeNested_& matrix() const { return m_matrix; }
+ std::remove_reference_t<MatrixTypeNested>& matrix() { return m_matrix; }
+
+ /** \returns an expression of the matrix product between a sparse self-adjoint matrix \c *this and a sparse matrix \a rhs.
+ *
+ * Note that there is no algorithmic advantage of performing such a product compared to a general sparse-sparse matrix product.
+ * Indeed, the SparseSelfadjointView operand is first copied into a temporary SparseMatrix before computing the product.
+ */
+ template<typename OtherDerived>
+ Product<SparseSelfAdjointView, OtherDerived>
+ operator*(const SparseMatrixBase<OtherDerived>& rhs) const
+ {
+ return Product<SparseSelfAdjointView, OtherDerived>(*this, rhs.derived());
+ }
+
+ /** \returns an expression of the matrix product between a sparse matrix \a lhs and a sparse self-adjoint matrix \a rhs.
+ *
+ * Note that there is no algorithmic advantage of performing such a product compared to a general sparse-sparse matrix product.
+ * Indeed, the SparseSelfadjointView operand is first copied into a temporary SparseMatrix before computing the product.
+ */
+ template<typename OtherDerived> friend
+ Product<OtherDerived, SparseSelfAdjointView>
+ operator*(const SparseMatrixBase<OtherDerived>& lhs, const SparseSelfAdjointView& rhs)
+ {
+ return Product<OtherDerived, SparseSelfAdjointView>(lhs.derived(), rhs);
+ }
+
+ /** Efficient sparse self-adjoint matrix times dense vector/matrix product */
+ template<typename OtherDerived>
+ Product<SparseSelfAdjointView,OtherDerived>
+ operator*(const MatrixBase<OtherDerived>& rhs) const
+ {
+ return Product<SparseSelfAdjointView,OtherDerived>(*this, rhs.derived());
+ }
+
+ /** Efficient dense vector/matrix times sparse self-adjoint matrix product */
+ template<typename OtherDerived> friend
+ Product<OtherDerived,SparseSelfAdjointView>
+ operator*(const MatrixBase<OtherDerived>& lhs, const SparseSelfAdjointView& rhs)
+ {
+ return Product<OtherDerived,SparseSelfAdjointView>(lhs.derived(), rhs);
+ }
+
+ /** Perform a symmetric rank K update of the selfadjoint matrix \c *this:
+ * \f$ this = this + \alpha ( u u^* ) \f$ where \a u is a vector or matrix.
+ *
+ * \returns a reference to \c *this
+ *
+ * To perform \f$ this = this + \alpha ( u^* u ) \f$ you can simply
+ * call this function with u.adjoint().
+ */
+ template<typename DerivedU>
+ SparseSelfAdjointView& rankUpdate(const SparseMatrixBase<DerivedU>& u, const Scalar& alpha = Scalar(1));
+
+ /** \returns an expression of P H P^-1 */
+ // TODO implement twists in a more evaluator friendly fashion
+ SparseSymmetricPermutationProduct<MatrixTypeNested_,Mode> twistedBy(const PermutationMatrix<Dynamic,Dynamic,StorageIndex>& perm) const
+ {
+ return SparseSymmetricPermutationProduct<MatrixTypeNested_,Mode>(m_matrix, perm);
+ }
+
+ template<typename SrcMatrixType,int SrcMode>
+ SparseSelfAdjointView& operator=(const SparseSymmetricPermutationProduct<SrcMatrixType,SrcMode>& permutedMatrix)
+ {
+ internal::call_assignment_no_alias_no_transpose(*this, permutedMatrix);
+ return *this;
+ }
+
+ SparseSelfAdjointView& operator=(const SparseSelfAdjointView& src)
+ {
+ PermutationMatrix<Dynamic,Dynamic,StorageIndex> pnull;
+ return *this = src.twistedBy(pnull);
+ }
+
+ // Since we override the copy-assignment operator, we need to explicitly re-declare the copy-constructor
+ EIGEN_DEFAULT_COPY_CONSTRUCTOR(SparseSelfAdjointView)
+
+ template<typename SrcMatrixType,unsigned int SrcMode>
+ SparseSelfAdjointView& operator=(const SparseSelfAdjointView<SrcMatrixType,SrcMode>& src)
+ {
+ PermutationMatrix<Dynamic,Dynamic,StorageIndex> pnull;
+ return *this = src.twistedBy(pnull);
+ }
+
+ void resize(Index rows, Index cols)
+ {
+ EIGEN_ONLY_USED_FOR_DEBUG(rows);
+ EIGEN_ONLY_USED_FOR_DEBUG(cols);
+ eigen_assert(rows == this->rows() && cols == this->cols()
+ && "SparseSelfadjointView::resize() does not actually allow to resize.");
+ }
+
+ protected:
+
+ MatrixTypeNested m_matrix;
+ //mutable VectorI m_countPerRow;
+ //mutable VectorI m_countPerCol;
+ private:
+ template<typename Dest> void evalTo(Dest &) const;
+};
+
+/***************************************************************************
+* Implementation of SparseMatrixBase methods
+***************************************************************************/
+
+template<typename Derived>
+template<unsigned int UpLo>
+typename SparseMatrixBase<Derived>::template ConstSelfAdjointViewReturnType<UpLo>::Type SparseMatrixBase<Derived>::selfadjointView() const
+{
+ return SparseSelfAdjointView<const Derived, UpLo>(derived());
+}
+
+template<typename Derived>
+template<unsigned int UpLo>
+typename SparseMatrixBase<Derived>::template SelfAdjointViewReturnType<UpLo>::Type SparseMatrixBase<Derived>::selfadjointView()
+{
+ return SparseSelfAdjointView<Derived, UpLo>(derived());
+}
+
+/***************************************************************************
+* Implementation of SparseSelfAdjointView methods
+***************************************************************************/
+
+template<typename MatrixType, unsigned int Mode>
+template<typename DerivedU>
+SparseSelfAdjointView<MatrixType,Mode>&
+SparseSelfAdjointView<MatrixType,Mode>::rankUpdate(const SparseMatrixBase<DerivedU>& u, const Scalar& alpha)
+{
+ SparseMatrix<Scalar,(MatrixType::Flags&RowMajorBit)?RowMajor:ColMajor> tmp = u * u.adjoint();
+ if(alpha==Scalar(0))
+ m_matrix = tmp.template triangularView<Mode>();
+ else
+ m_matrix += alpha * tmp.template triangularView<Mode>();
+
+ return *this;
+}
+
+namespace internal {
+
+// TODO currently a selfadjoint expression has the form SelfAdjointView<.,.>
+// in the future selfadjoint-ness should be defined by the expression traits
+// such that Transpose<SelfAdjointView<.,.> > is valid. (currently TriangularBase::transpose() is overloaded to make it work)
+template<typename MatrixType, unsigned int Mode>
+struct evaluator_traits<SparseSelfAdjointView<MatrixType,Mode> >
+{
+ typedef typename storage_kind_to_evaluator_kind<typename MatrixType::StorageKind>::Kind Kind;
+ typedef SparseSelfAdjointShape Shape;
+};
+
+struct SparseSelfAdjoint2Sparse {};
+
+template<> struct AssignmentKind<SparseShape,SparseSelfAdjointShape> { typedef SparseSelfAdjoint2Sparse Kind; };
+template<> struct AssignmentKind<SparseSelfAdjointShape,SparseShape> { typedef Sparse2Sparse Kind; };
+
+template< typename DstXprType, typename SrcXprType, typename Functor>
+struct Assignment<DstXprType, SrcXprType, Functor, SparseSelfAdjoint2Sparse>
+{
+ typedef typename DstXprType::StorageIndex StorageIndex;
+ typedef internal::assign_op<typename DstXprType::Scalar,typename SrcXprType::Scalar> AssignOpType;
+
+ template<typename DestScalar,int StorageOrder>
+ static void run(SparseMatrix<DestScalar,StorageOrder,StorageIndex> &dst, const SrcXprType &src, const AssignOpType&/*func*/)
+ {
+ internal::permute_symm_to_fullsymm<SrcXprType::Mode>(src.matrix(), dst);
+ }
+
+ // FIXME: the handling of += and -= in sparse matrices should be cleanup so that next two overloads could be reduced to:
+ template<typename DestScalar,int StorageOrder,typename AssignFunc>
+ static void run(SparseMatrix<DestScalar,StorageOrder,StorageIndex> &dst, const SrcXprType &src, const AssignFunc& func)
+ {
+ SparseMatrix<DestScalar,StorageOrder,StorageIndex> tmp(src.rows(),src.cols());
+ run(tmp, src, AssignOpType());
+ call_assignment_no_alias_no_transpose(dst, tmp, func);
+ }
+
+ template<typename DestScalar,int StorageOrder>
+ static void run(SparseMatrix<DestScalar,StorageOrder,StorageIndex> &dst, const SrcXprType &src,
+ const internal::add_assign_op<typename DstXprType::Scalar,typename SrcXprType::Scalar>& /* func */)
+ {
+ SparseMatrix<DestScalar,StorageOrder,StorageIndex> tmp(src.rows(),src.cols());
+ run(tmp, src, AssignOpType());
+ dst += tmp;
+ }
+
+ template<typename DestScalar,int StorageOrder>
+ static void run(SparseMatrix<DestScalar,StorageOrder,StorageIndex> &dst, const SrcXprType &src,
+ const internal::sub_assign_op<typename DstXprType::Scalar,typename SrcXprType::Scalar>& /* func */)
+ {
+ SparseMatrix<DestScalar,StorageOrder,StorageIndex> tmp(src.rows(),src.cols());
+ run(tmp, src, AssignOpType());
+ dst -= tmp;
+ }
+};
+
+} // end namespace internal
+
+/***************************************************************************
+* Implementation of sparse self-adjoint time dense matrix
+***************************************************************************/
+
+namespace internal {
+
+template<int Mode, typename SparseLhsType, typename DenseRhsType, typename DenseResType, typename AlphaType>
+inline void sparse_selfadjoint_time_dense_product(const SparseLhsType& lhs, const DenseRhsType& rhs, DenseResType& res, const AlphaType& alpha)
+{
+ EIGEN_ONLY_USED_FOR_DEBUG(alpha);
+
+ typedef typename internal::nested_eval<SparseLhsType,DenseRhsType::MaxColsAtCompileTime>::type SparseLhsTypeNested;
+ typedef internal::remove_all_t<SparseLhsTypeNested> SparseLhsTypeNestedCleaned;
+ typedef evaluator<SparseLhsTypeNestedCleaned> LhsEval;
+ typedef typename LhsEval::InnerIterator LhsIterator;
+ typedef typename SparseLhsType::Scalar LhsScalar;
+
+ enum {
+ LhsIsRowMajor = (LhsEval::Flags&RowMajorBit)==RowMajorBit,
+ ProcessFirstHalf =
+ ((Mode&(Upper|Lower))==(Upper|Lower))
+ || ( (Mode&Upper) && !LhsIsRowMajor)
+ || ( (Mode&Lower) && LhsIsRowMajor),
+ ProcessSecondHalf = !ProcessFirstHalf
+ };
+
+ SparseLhsTypeNested lhs_nested(lhs);
+ LhsEval lhsEval(lhs_nested);
+
+ // work on one column at once
+ for (Index k=0; k<rhs.cols(); ++k)
+ {
+ for (Index j=0; j<lhs.outerSize(); ++j)
+ {
+ LhsIterator i(lhsEval,j);
+ // handle diagonal coeff
+ if (ProcessSecondHalf)
+ {
+ while (i && i.index()<j) ++i;
+ if(i && i.index()==j)
+ {
+ res.coeffRef(j,k) += alpha * i.value() * rhs.coeff(j,k);
+ ++i;
+ }
+ }
+
+ // premultiplied rhs for scatters
+ typename ScalarBinaryOpTraits<AlphaType, typename DenseRhsType::Scalar>::ReturnType rhs_j(alpha*rhs(j,k));
+ // accumulator for partial scalar product
+ typename DenseResType::Scalar res_j(0);
+ for(; (ProcessFirstHalf ? i && i.index() < j : i) ; ++i)
+ {
+ LhsScalar lhs_ij = i.value();
+ if(!LhsIsRowMajor) lhs_ij = numext::conj(lhs_ij);
+ res_j += lhs_ij * rhs.coeff(i.index(),k);
+ res(i.index(),k) += numext::conj(lhs_ij) * rhs_j;
+ }
+ res.coeffRef(j,k) += alpha * res_j;
+
+ // handle diagonal coeff
+ if (ProcessFirstHalf && i && (i.index()==j))
+ res.coeffRef(j,k) += alpha * i.value() * rhs.coeff(j,k);
+ }
+ }
+}
+
+
+template<typename LhsView, typename Rhs, int ProductType>
+struct generic_product_impl<LhsView, Rhs, SparseSelfAdjointShape, DenseShape, ProductType>
+: generic_product_impl_base<LhsView, Rhs, generic_product_impl<LhsView, Rhs, SparseSelfAdjointShape, DenseShape, ProductType> >
+{
+ template<typename Dest>
+ static void scaleAndAddTo(Dest& dst, const LhsView& lhsView, const Rhs& rhs, const typename Dest::Scalar& alpha)
+ {
+ typedef typename LhsView::MatrixTypeNested_ Lhs;
+ typedef typename nested_eval<Lhs,Dynamic>::type LhsNested;
+ typedef typename nested_eval<Rhs,Dynamic>::type RhsNested;
+ LhsNested lhsNested(lhsView.matrix());
+ RhsNested rhsNested(rhs);
+
+ internal::sparse_selfadjoint_time_dense_product<LhsView::Mode>(lhsNested, rhsNested, dst, alpha);
+ }
+};
+
+template<typename Lhs, typename RhsView, int ProductType>
+struct generic_product_impl<Lhs, RhsView, DenseShape, SparseSelfAdjointShape, ProductType>
+: generic_product_impl_base<Lhs, RhsView, generic_product_impl<Lhs, RhsView, DenseShape, SparseSelfAdjointShape, ProductType> >
+{
+ template<typename Dest>
+ static void scaleAndAddTo(Dest& dst, const Lhs& lhs, const RhsView& rhsView, const typename Dest::Scalar& alpha)
+ {
+ typedef typename RhsView::MatrixTypeNested_ Rhs;
+ typedef typename nested_eval<Lhs,Dynamic>::type LhsNested;
+ typedef typename nested_eval<Rhs,Dynamic>::type RhsNested;
+ LhsNested lhsNested(lhs);
+ RhsNested rhsNested(rhsView.matrix());
+
+ // transpose everything
+ Transpose<Dest> dstT(dst);
+ internal::sparse_selfadjoint_time_dense_product<RhsView::TransposeMode>(rhsNested.transpose(), lhsNested.transpose(), dstT, alpha);
+ }
+};
+
+// NOTE: these two overloads are needed to evaluate the sparse selfadjoint view into a full sparse matrix
+// TODO: maybe the copy could be handled by generic_product_impl so that these overloads would not be needed anymore
+
+template<typename LhsView, typename Rhs, int ProductTag>
+struct product_evaluator<Product<LhsView, Rhs, DefaultProduct>, ProductTag, SparseSelfAdjointShape, SparseShape>
+ : public evaluator<typename Product<typename Rhs::PlainObject, Rhs, DefaultProduct>::PlainObject>
+{
+ typedef Product<LhsView, Rhs, DefaultProduct> XprType;
+ typedef typename XprType::PlainObject PlainObject;
+ typedef evaluator<PlainObject> Base;
+
+ product_evaluator(const XprType& xpr)
+ : m_lhs(xpr.lhs()), m_result(xpr.rows(), xpr.cols())
+ {
+ internal::construct_at<Base>(this, m_result);
+ generic_product_impl<typename Rhs::PlainObject, Rhs, SparseShape, SparseShape, ProductTag>::evalTo(m_result, m_lhs, xpr.rhs());
+ }
+
+protected:
+ typename Rhs::PlainObject m_lhs;
+ PlainObject m_result;
+};
+
+template<typename Lhs, typename RhsView, int ProductTag>
+struct product_evaluator<Product<Lhs, RhsView, DefaultProduct>, ProductTag, SparseShape, SparseSelfAdjointShape>
+ : public evaluator<typename Product<Lhs, typename Lhs::PlainObject, DefaultProduct>::PlainObject>
+{
+ typedef Product<Lhs, RhsView, DefaultProduct> XprType;
+ typedef typename XprType::PlainObject PlainObject;
+ typedef evaluator<PlainObject> Base;
+
+ product_evaluator(const XprType& xpr)
+ : m_rhs(xpr.rhs()), m_result(xpr.rows(), xpr.cols())
+ {
+ ::new (static_cast<Base*>(this)) Base(m_result);
+ generic_product_impl<Lhs, typename Lhs::PlainObject, SparseShape, SparseShape, ProductTag>::evalTo(m_result, xpr.lhs(), m_rhs);
+ }
+
+protected:
+ typename Lhs::PlainObject m_rhs;
+ PlainObject m_result;
+};
+
+} // namespace internal
+
+/***************************************************************************
+* Implementation of symmetric copies and permutations
+***************************************************************************/
+namespace internal {
+
+template<int Mode,typename MatrixType,int DestOrder>
+void permute_symm_to_fullsymm(const MatrixType& mat, SparseMatrix<typename MatrixType::Scalar,DestOrder,typename MatrixType::StorageIndex>& _dest, const typename MatrixType::StorageIndex* perm)
+{
+ typedef typename MatrixType::StorageIndex StorageIndex;
+ typedef typename MatrixType::Scalar Scalar;
+ typedef SparseMatrix<Scalar,DestOrder,StorageIndex> Dest;
+ typedef Matrix<StorageIndex,Dynamic,1> VectorI;
+ typedef evaluator<MatrixType> MatEval;
+ typedef typename evaluator<MatrixType>::InnerIterator MatIterator;
+
+ MatEval matEval(mat);
+ Dest& dest(_dest.derived());
+ enum {
+ StorageOrderMatch = int(Dest::IsRowMajor) == int(MatrixType::IsRowMajor)
+ };
+
+ Index size = mat.rows();
+ VectorI count;
+ count.resize(size);
+ count.setZero();
+ dest.resize(size,size);
+ for(Index j = 0; j<size; ++j)
+ {
+ Index jp = perm ? perm[j] : j;
+ for(MatIterator it(matEval,j); it; ++it)
+ {
+ Index i = it.index();
+ Index r = it.row();
+ Index c = it.col();
+ Index ip = perm ? perm[i] : i;
+ if(Mode==int(Upper|Lower))
+ count[StorageOrderMatch ? jp : ip]++;
+ else if(r==c)
+ count[ip]++;
+ else if(( Mode==Lower && r>c) || ( Mode==Upper && r<c))
+ {
+ count[ip]++;
+ count[jp]++;
+ }
+ }
+ }
+ Index nnz = count.sum();
+
+ // reserve space
+ dest.resizeNonZeros(nnz);
+ dest.outerIndexPtr()[0] = 0;
+ for(Index j=0; j<size; ++j)
+ dest.outerIndexPtr()[j+1] = dest.outerIndexPtr()[j] + count[j];
+ for(Index j=0; j<size; ++j)
+ count[j] = dest.outerIndexPtr()[j];
+
+ // copy data
+ for(StorageIndex j = 0; j<size; ++j)
+ {
+ for(MatIterator it(matEval,j); it; ++it)
+ {
+ StorageIndex i = internal::convert_index<StorageIndex>(it.index());
+ Index r = it.row();
+ Index c = it.col();
+
+ StorageIndex jp = perm ? perm[j] : j;
+ StorageIndex ip = perm ? perm[i] : i;
+
+ if(Mode==int(Upper|Lower))
+ {
+ Index k = count[StorageOrderMatch ? jp : ip]++;
+ dest.innerIndexPtr()[k] = StorageOrderMatch ? ip : jp;
+ dest.valuePtr()[k] = it.value();
+ }
+ else if(r==c)
+ {
+ Index k = count[ip]++;
+ dest.innerIndexPtr()[k] = ip;
+ dest.valuePtr()[k] = it.value();
+ }
+ else if(( (Mode&Lower)==Lower && r>c) || ( (Mode&Upper)==Upper && r<c))
+ {
+ if(!StorageOrderMatch)
+ std::swap(ip,jp);
+ Index k = count[jp]++;
+ dest.innerIndexPtr()[k] = ip;
+ dest.valuePtr()[k] = it.value();
+ k = count[ip]++;
+ dest.innerIndexPtr()[k] = jp;
+ dest.valuePtr()[k] = numext::conj(it.value());
+ }
+ }
+ }
+}
+
+template<int SrcMode_,int DstMode_,typename MatrixType,int DstOrder>
+void permute_symm_to_symm(const MatrixType& mat, SparseMatrix<typename MatrixType::Scalar,DstOrder,typename MatrixType::StorageIndex>& _dest, const typename MatrixType::StorageIndex* perm)
+{
+ typedef typename MatrixType::StorageIndex StorageIndex;
+ typedef typename MatrixType::Scalar Scalar;
+ SparseMatrix<Scalar,DstOrder,StorageIndex>& dest(_dest.derived());
+ typedef Matrix<StorageIndex,Dynamic,1> VectorI;
+ typedef evaluator<MatrixType> MatEval;
+ typedef typename evaluator<MatrixType>::InnerIterator MatIterator;
+
+ enum {
+ SrcOrder = MatrixType::IsRowMajor ? RowMajor : ColMajor,
+ StorageOrderMatch = int(SrcOrder) == int(DstOrder),
+ DstMode = DstOrder==RowMajor ? (DstMode_==Upper ? Lower : Upper) : DstMode_,
+ SrcMode = SrcOrder==RowMajor ? (SrcMode_==Upper ? Lower : Upper) : SrcMode_
+ };
+
+ MatEval matEval(mat);
+
+ Index size = mat.rows();
+ VectorI count(size);
+ count.setZero();
+ dest.resize(size,size);
+ for(StorageIndex j = 0; j<size; ++j)
+ {
+ StorageIndex jp = perm ? perm[j] : j;
+ for(MatIterator it(matEval,j); it; ++it)
+ {
+ StorageIndex i = it.index();
+ if((int(SrcMode)==int(Lower) && i<j) || (int(SrcMode)==int(Upper) && i>j))
+ continue;
+
+ StorageIndex ip = perm ? perm[i] : i;
+ count[int(DstMode)==int(Lower) ? (std::min)(ip,jp) : (std::max)(ip,jp)]++;
+ }
+ }
+ dest.outerIndexPtr()[0] = 0;
+ for(Index j=0; j<size; ++j)
+ dest.outerIndexPtr()[j+1] = dest.outerIndexPtr()[j] + count[j];
+ dest.resizeNonZeros(dest.outerIndexPtr()[size]);
+ for(Index j=0; j<size; ++j)
+ count[j] = dest.outerIndexPtr()[j];
+
+ for(StorageIndex j = 0; j<size; ++j)
+ {
+
+ for(MatIterator it(matEval,j); it; ++it)
+ {
+ StorageIndex i = it.index();
+ if((int(SrcMode)==int(Lower) && i<j) || (int(SrcMode)==int(Upper) && i>j))
+ continue;
+
+ StorageIndex jp = perm ? perm[j] : j;
+ StorageIndex ip = perm? perm[i] : i;
+
+ Index k = count[int(DstMode)==int(Lower) ? (std::min)(ip,jp) : (std::max)(ip,jp)]++;
+ dest.innerIndexPtr()[k] = int(DstMode)==int(Lower) ? (std::max)(ip,jp) : (std::min)(ip,jp);
+
+ if(!StorageOrderMatch) std::swap(ip,jp);
+ if( ((int(DstMode)==int(Lower) && ip<jp) || (int(DstMode)==int(Upper) && ip>jp)))
+ dest.valuePtr()[k] = numext::conj(it.value());
+ else
+ dest.valuePtr()[k] = it.value();
+ }
+ }
+}
+
+}
+
+// TODO implement twists in a more evaluator friendly fashion
+
+namespace internal {
+
+template<typename MatrixType, int Mode>
+struct traits<SparseSymmetricPermutationProduct<MatrixType,Mode> > : traits<MatrixType> {
+};
+
+}
+
+template<typename MatrixType,int Mode>
+class SparseSymmetricPermutationProduct
+ : public EigenBase<SparseSymmetricPermutationProduct<MatrixType,Mode> >
+{
+ public:
+ typedef typename MatrixType::Scalar Scalar;
+ typedef typename MatrixType::StorageIndex StorageIndex;
+ enum {
+ RowsAtCompileTime = internal::traits<SparseSymmetricPermutationProduct>::RowsAtCompileTime,
+ ColsAtCompileTime = internal::traits<SparseSymmetricPermutationProduct>::ColsAtCompileTime
+ };
+ protected:
+ typedef PermutationMatrix<Dynamic,Dynamic,StorageIndex> Perm;
+ public:
+ typedef Matrix<StorageIndex,Dynamic,1> VectorI;
+ typedef typename MatrixType::Nested MatrixTypeNested;
+ typedef internal::remove_all_t<MatrixTypeNested> NestedExpression;
+
+ SparseSymmetricPermutationProduct(const MatrixType& mat, const Perm& perm)
+ : m_matrix(mat), m_perm(perm)
+ {}
+
+ inline Index rows() const { return m_matrix.rows(); }
+ inline Index cols() const { return m_matrix.cols(); }
+
+ const NestedExpression& matrix() const { return m_matrix; }
+ const Perm& perm() const { return m_perm; }
+
+ protected:
+ MatrixTypeNested m_matrix;
+ const Perm& m_perm;
+
+};
+
+namespace internal {
+
+template<typename DstXprType, typename MatrixType, int Mode, typename Scalar>
+struct Assignment<DstXprType, SparseSymmetricPermutationProduct<MatrixType,Mode>, internal::assign_op<Scalar,typename MatrixType::Scalar>, Sparse2Sparse>
+{
+ typedef SparseSymmetricPermutationProduct<MatrixType,Mode> SrcXprType;
+ typedef typename DstXprType::StorageIndex DstIndex;
+ template<int Options>
+ static void run(SparseMatrix<Scalar,Options,DstIndex> &dst, const SrcXprType &src, const internal::assign_op<Scalar,typename MatrixType::Scalar> &)
+ {
+ // internal::permute_symm_to_fullsymm<Mode>(m_matrix,_dest,m_perm.indices().data());
+ SparseMatrix<Scalar,(Options&RowMajor)==RowMajor ? ColMajor : RowMajor, DstIndex> tmp;
+ internal::permute_symm_to_fullsymm<Mode>(src.matrix(),tmp,src.perm().indices().data());
+ dst = tmp;
+ }
+
+ template<typename DestType,unsigned int DestMode>
+ static void run(SparseSelfAdjointView<DestType,DestMode>& dst, const SrcXprType &src, const internal::assign_op<Scalar,typename MatrixType::Scalar> &)
+ {
+ internal::permute_symm_to_symm<Mode,DestMode>(src.matrix(),dst.matrix(),src.perm().indices().data());
+ }
+};
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_SPARSE_SELFADJOINTVIEW_H
diff --git a/Eigen/src/SparseCore/SparseSolverBase.h b/Eigen/src/SparseCore/SparseSolverBase.h
new file mode 100644
index 0000000..8261fb5
--- /dev/null
+++ b/Eigen/src/SparseCore/SparseSolverBase.h
@@ -0,0 +1,128 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2014 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_SPARSESOLVERBASE_H
+#define EIGEN_SPARSESOLVERBASE_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+
+ /** \internal
+ * Helper functions to solve with a sparse right-hand-side and result.
+ * The rhs is decomposed into small vertical panels which are solved through dense temporaries.
+ */
+template<typename Decomposition, typename Rhs, typename Dest>
+std::enable_if_t<Rhs::ColsAtCompileTime!=1 && Dest::ColsAtCompileTime!=1>
+solve_sparse_through_dense_panels(const Decomposition &dec, const Rhs& rhs, Dest &dest)
+{
+ EIGEN_STATIC_ASSERT((Dest::Flags&RowMajorBit)==0,THIS_METHOD_IS_ONLY_FOR_COLUMN_MAJOR_MATRICES);
+ typedef typename Dest::Scalar DestScalar;
+ // we process the sparse rhs per block of NbColsAtOnce columns temporarily stored into a dense matrix.
+ static const Index NbColsAtOnce = 4;
+ Index rhsCols = rhs.cols();
+ Index size = rhs.rows();
+ // the temporary matrices do not need more columns than NbColsAtOnce:
+ Index tmpCols = (std::min)(rhsCols, NbColsAtOnce);
+ Eigen::Matrix<DestScalar,Dynamic,Dynamic> tmp(size,tmpCols);
+ Eigen::Matrix<DestScalar,Dynamic,Dynamic> tmpX(size,tmpCols);
+ for(Index k=0; k<rhsCols; k+=NbColsAtOnce)
+ {
+ Index actualCols = std::min<Index>(rhsCols-k, NbColsAtOnce);
+ tmp.leftCols(actualCols) = rhs.middleCols(k,actualCols);
+ tmpX.leftCols(actualCols) = dec.solve(tmp.leftCols(actualCols));
+ dest.middleCols(k,actualCols) = tmpX.leftCols(actualCols).sparseView();
+ }
+}
+
+// Overload for vector as rhs
+template<typename Decomposition, typename Rhs, typename Dest>
+std::enable_if_t<Rhs::ColsAtCompileTime==1 || Dest::ColsAtCompileTime==1>
+solve_sparse_through_dense_panels(const Decomposition &dec, const Rhs& rhs, Dest &dest)
+{
+ typedef typename Dest::Scalar DestScalar;
+ Index size = rhs.rows();
+ Eigen::Matrix<DestScalar,Dynamic,1> rhs_dense(rhs);
+ Eigen::Matrix<DestScalar,Dynamic,1> dest_dense(size);
+ dest_dense = dec.solve(rhs_dense);
+ dest = dest_dense.sparseView();
+}
+
+} // end namespace internal
+
+/** \class SparseSolverBase
+ * \ingroup SparseCore_Module
+ * \brief A base class for sparse solvers
+ *
+ * \tparam Derived the actual type of the solver.
+ *
+ */
+template<typename Derived>
+class SparseSolverBase : internal::noncopyable
+{
+ public:
+
+ /** Default constructor */
+ SparseSolverBase()
+ : m_isInitialized(false)
+ {}
+
+ SparseSolverBase(SparseSolverBase&&other ) : internal::noncopyable{}, m_isInitialized{other.m_isInitialized} {}
+
+ ~SparseSolverBase()
+ {}
+
+ Derived& derived() { return *static_cast<Derived*>(this); }
+ const Derived& derived() const { return *static_cast<const Derived*>(this); }
+
+ /** \returns an expression of the solution x of \f$ A x = b \f$ using the current decomposition of A.
+ *
+ * \sa compute()
+ */
+ template<typename Rhs>
+ inline const Solve<Derived, Rhs>
+ solve(const MatrixBase<Rhs>& b) const
+ {
+ eigen_assert(m_isInitialized && "Solver is not initialized.");
+ eigen_assert(derived().rows()==b.rows() && "solve(): invalid number of rows of the right hand side matrix b");
+ return Solve<Derived, Rhs>(derived(), b.derived());
+ }
+
+ /** \returns an expression of the solution x of \f$ A x = b \f$ using the current decomposition of A.
+ *
+ * \sa compute()
+ */
+ template<typename Rhs>
+ inline const Solve<Derived, Rhs>
+ solve(const SparseMatrixBase<Rhs>& b) const
+ {
+ eigen_assert(m_isInitialized && "Solver is not initialized.");
+ eigen_assert(derived().rows()==b.rows() && "solve(): invalid number of rows of the right hand side matrix b");
+ return Solve<Derived, Rhs>(derived(), b.derived());
+ }
+
+ #ifndef EIGEN_PARSED_BY_DOXYGEN
+ /** \internal default implementation of solving with a sparse rhs */
+ template<typename Rhs,typename Dest>
+ void _solve_impl(const SparseMatrixBase<Rhs> &b, SparseMatrixBase<Dest> &dest) const
+ {
+ internal::solve_sparse_through_dense_panels(derived(), b.derived(), dest.derived());
+ }
+ #endif // EIGEN_PARSED_BY_DOXYGEN
+
+ protected:
+
+ mutable bool m_isInitialized;
+};
+
+} // end namespace Eigen
+
+#endif // EIGEN_SPARSESOLVERBASE_H
diff --git a/Eigen/src/SparseCore/SparseSparseProductWithPruning.h b/Eigen/src/SparseCore/SparseSparseProductWithPruning.h
new file mode 100644
index 0000000..ee0ec1b
--- /dev/null
+++ b/Eigen/src/SparseCore/SparseSparseProductWithPruning.h
@@ -0,0 +1,200 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2014 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_SPARSESPARSEPRODUCTWITHPRUNING_H
+#define EIGEN_SPARSESPARSEPRODUCTWITHPRUNING_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+
+
+// perform a pseudo in-place sparse * sparse product assuming all matrices are col major
+template<typename Lhs, typename Rhs, typename ResultType>
+static void sparse_sparse_product_with_pruning_impl(const Lhs& lhs, const Rhs& rhs, ResultType& res, const typename ResultType::RealScalar& tolerance)
+{
+ // return sparse_sparse_product_with_pruning_impl2(lhs,rhs,res);
+
+ typedef typename remove_all_t<Rhs>::Scalar RhsScalar;
+ typedef typename remove_all_t<ResultType>::Scalar ResScalar;
+ typedef typename remove_all_t<Lhs>::StorageIndex StorageIndex;
+
+ // make sure to call innerSize/outerSize since we fake the storage order.
+ Index rows = lhs.innerSize();
+ Index cols = rhs.outerSize();
+ //Index size = lhs.outerSize();
+ eigen_assert(lhs.outerSize() == rhs.innerSize());
+
+ // allocate a temporary buffer
+ AmbiVector<ResScalar,StorageIndex> tempVector(rows);
+
+ // mimics a resizeByInnerOuter:
+ if(ResultType::IsRowMajor)
+ res.resize(cols, rows);
+ else
+ res.resize(rows, cols);
+
+ evaluator<Lhs> lhsEval(lhs);
+ evaluator<Rhs> rhsEval(rhs);
+
+ // estimate the number of non zero entries
+ // given a rhs column containing Y non zeros, we assume that the respective Y columns
+ // of the lhs differs in average of one non zeros, thus the number of non zeros for
+ // the product of a rhs column with the lhs is X+Y where X is the average number of non zero
+ // per column of the lhs.
+ // Therefore, we have nnz(lhs*rhs) = nnz(lhs) + nnz(rhs)
+ Index estimated_nnz_prod = lhsEval.nonZerosEstimate() + rhsEval.nonZerosEstimate();
+
+ res.reserve(estimated_nnz_prod);
+ double ratioColRes = double(estimated_nnz_prod)/(double(lhs.rows())*double(rhs.cols()));
+ for (Index j=0; j<cols; ++j)
+ {
+ // FIXME:
+ //double ratioColRes = (double(rhs.innerVector(j).nonZeros()) + double(lhs.nonZeros())/double(lhs.cols()))/double(lhs.rows());
+ // let's do a more accurate determination of the nnz ratio for the current column j of res
+ tempVector.init(ratioColRes);
+ tempVector.setZero();
+ for (typename evaluator<Rhs>::InnerIterator rhsIt(rhsEval, j); rhsIt; ++rhsIt)
+ {
+ // FIXME should be written like this: tmp += rhsIt.value() * lhs.col(rhsIt.index())
+ tempVector.restart();
+ RhsScalar x = rhsIt.value();
+ for (typename evaluator<Lhs>::InnerIterator lhsIt(lhsEval, rhsIt.index()); lhsIt; ++lhsIt)
+ {
+ tempVector.coeffRef(lhsIt.index()) += lhsIt.value() * x;
+ }
+ }
+ res.startVec(j);
+ for (typename AmbiVector<ResScalar,StorageIndex>::Iterator it(tempVector,tolerance); it; ++it)
+ res.insertBackByOuterInner(j,it.index()) = it.value();
+ }
+ res.finalize();
+}
+
+template<typename Lhs, typename Rhs, typename ResultType,
+ int LhsStorageOrder = traits<Lhs>::Flags&RowMajorBit,
+ int RhsStorageOrder = traits<Rhs>::Flags&RowMajorBit,
+ int ResStorageOrder = traits<ResultType>::Flags&RowMajorBit>
+struct sparse_sparse_product_with_pruning_selector;
+
+template<typename Lhs, typename Rhs, typename ResultType>
+struct sparse_sparse_product_with_pruning_selector<Lhs,Rhs,ResultType,ColMajor,ColMajor,ColMajor>
+{
+ typedef typename ResultType::RealScalar RealScalar;
+
+ static void run(const Lhs& lhs, const Rhs& rhs, ResultType& res, const RealScalar& tolerance)
+ {
+ remove_all_t<ResultType> _res(res.rows(), res.cols());
+ internal::sparse_sparse_product_with_pruning_impl<Lhs,Rhs,ResultType>(lhs, rhs, _res, tolerance);
+ res.swap(_res);
+ }
+};
+
+template<typename Lhs, typename Rhs, typename ResultType>
+struct sparse_sparse_product_with_pruning_selector<Lhs,Rhs,ResultType,ColMajor,ColMajor,RowMajor>
+{
+ typedef typename ResultType::RealScalar RealScalar;
+ static void run(const Lhs& lhs, const Rhs& rhs, ResultType& res, const RealScalar& tolerance)
+ {
+ // we need a col-major matrix to hold the result
+ typedef SparseMatrix<typename ResultType::Scalar,ColMajor,typename ResultType::StorageIndex> SparseTemporaryType;
+ SparseTemporaryType _res(res.rows(), res.cols());
+ internal::sparse_sparse_product_with_pruning_impl<Lhs,Rhs,SparseTemporaryType>(lhs, rhs, _res, tolerance);
+ res = _res;
+ }
+};
+
+template<typename Lhs, typename Rhs, typename ResultType>
+struct sparse_sparse_product_with_pruning_selector<Lhs,Rhs,ResultType,RowMajor,RowMajor,RowMajor>
+{
+ typedef typename ResultType::RealScalar RealScalar;
+ static void run(const Lhs& lhs, const Rhs& rhs, ResultType& res, const RealScalar& tolerance)
+ {
+ // let's transpose the product to get a column x column product
+ remove_all_t<ResultType> _res(res.rows(), res.cols());
+ internal::sparse_sparse_product_with_pruning_impl<Rhs,Lhs,ResultType>(rhs, lhs, _res, tolerance);
+ res.swap(_res);
+ }
+};
+
+template<typename Lhs, typename Rhs, typename ResultType>
+struct sparse_sparse_product_with_pruning_selector<Lhs,Rhs,ResultType,RowMajor,RowMajor,ColMajor>
+{
+ typedef typename ResultType::RealScalar RealScalar;
+ static void run(const Lhs& lhs, const Rhs& rhs, ResultType& res, const RealScalar& tolerance)
+ {
+ typedef SparseMatrix<typename Lhs::Scalar,ColMajor,typename Lhs::StorageIndex> ColMajorMatrixLhs;
+ typedef SparseMatrix<typename Rhs::Scalar,ColMajor,typename Lhs::StorageIndex> ColMajorMatrixRhs;
+ ColMajorMatrixLhs colLhs(lhs);
+ ColMajorMatrixRhs colRhs(rhs);
+ internal::sparse_sparse_product_with_pruning_impl<ColMajorMatrixLhs,ColMajorMatrixRhs,ResultType>(colLhs, colRhs, res, tolerance);
+
+ // let's transpose the product to get a column x column product
+// typedef SparseMatrix<typename ResultType::Scalar> SparseTemporaryType;
+// SparseTemporaryType _res(res.cols(), res.rows());
+// sparse_sparse_product_with_pruning_impl<Rhs,Lhs,SparseTemporaryType>(rhs, lhs, _res);
+// res = _res.transpose();
+ }
+};
+
+template<typename Lhs, typename Rhs, typename ResultType>
+struct sparse_sparse_product_with_pruning_selector<Lhs,Rhs,ResultType,ColMajor,RowMajor,RowMajor>
+{
+ typedef typename ResultType::RealScalar RealScalar;
+ static void run(const Lhs& lhs, const Rhs& rhs, ResultType& res, const RealScalar& tolerance)
+ {
+ typedef SparseMatrix<typename Lhs::Scalar,RowMajor,typename Lhs::StorageIndex> RowMajorMatrixLhs;
+ RowMajorMatrixLhs rowLhs(lhs);
+ sparse_sparse_product_with_pruning_selector<RowMajorMatrixLhs,Rhs,ResultType,RowMajor,RowMajor>(rowLhs,rhs,res,tolerance);
+ }
+};
+
+template<typename Lhs, typename Rhs, typename ResultType>
+struct sparse_sparse_product_with_pruning_selector<Lhs,Rhs,ResultType,RowMajor,ColMajor,RowMajor>
+{
+ typedef typename ResultType::RealScalar RealScalar;
+ static void run(const Lhs& lhs, const Rhs& rhs, ResultType& res, const RealScalar& tolerance)
+ {
+ typedef SparseMatrix<typename Rhs::Scalar,RowMajor,typename Lhs::StorageIndex> RowMajorMatrixRhs;
+ RowMajorMatrixRhs rowRhs(rhs);
+ sparse_sparse_product_with_pruning_selector<Lhs,RowMajorMatrixRhs,ResultType,RowMajor,RowMajor,RowMajor>(lhs,rowRhs,res,tolerance);
+ }
+};
+
+template<typename Lhs, typename Rhs, typename ResultType>
+struct sparse_sparse_product_with_pruning_selector<Lhs,Rhs,ResultType,ColMajor,RowMajor,ColMajor>
+{
+ typedef typename ResultType::RealScalar RealScalar;
+ static void run(const Lhs& lhs, const Rhs& rhs, ResultType& res, const RealScalar& tolerance)
+ {
+ typedef SparseMatrix<typename Rhs::Scalar,ColMajor,typename Lhs::StorageIndex> ColMajorMatrixRhs;
+ ColMajorMatrixRhs colRhs(rhs);
+ internal::sparse_sparse_product_with_pruning_impl<Lhs,ColMajorMatrixRhs,ResultType>(lhs, colRhs, res, tolerance);
+ }
+};
+
+template<typename Lhs, typename Rhs, typename ResultType>
+struct sparse_sparse_product_with_pruning_selector<Lhs,Rhs,ResultType,RowMajor,ColMajor,ColMajor>
+{
+ typedef typename ResultType::RealScalar RealScalar;
+ static void run(const Lhs& lhs, const Rhs& rhs, ResultType& res, const RealScalar& tolerance)
+ {
+ typedef SparseMatrix<typename Lhs::Scalar,ColMajor,typename Lhs::StorageIndex> ColMajorMatrixLhs;
+ ColMajorMatrixLhs colLhs(lhs);
+ internal::sparse_sparse_product_with_pruning_impl<ColMajorMatrixLhs,Rhs,ResultType>(colLhs, rhs, res, tolerance);
+ }
+};
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_SPARSESPARSEPRODUCTWITHPRUNING_H
diff --git a/Eigen/src/SparseCore/SparseTranspose.h b/Eigen/src/SparseCore/SparseTranspose.h
new file mode 100644
index 0000000..cce5903
--- /dev/null
+++ b/Eigen/src/SparseCore/SparseTranspose.h
@@ -0,0 +1,94 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2015 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_SPARSETRANSPOSE_H
+#define EIGEN_SPARSETRANSPOSE_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+ template<typename MatrixType,int CompressedAccess=int(MatrixType::Flags&CompressedAccessBit)>
+ class SparseTransposeImpl
+ : public SparseMatrixBase<Transpose<MatrixType> >
+ {};
+
+ template<typename MatrixType>
+ class SparseTransposeImpl<MatrixType,CompressedAccessBit>
+ : public SparseCompressedBase<Transpose<MatrixType> >
+ {
+ typedef SparseCompressedBase<Transpose<MatrixType> > Base;
+ public:
+ using Base::derived;
+ typedef typename Base::Scalar Scalar;
+ typedef typename Base::StorageIndex StorageIndex;
+
+ inline Index nonZeros() const { return derived().nestedExpression().nonZeros(); }
+
+ inline const Scalar* valuePtr() const { return derived().nestedExpression().valuePtr(); }
+ inline const StorageIndex* innerIndexPtr() const { return derived().nestedExpression().innerIndexPtr(); }
+ inline const StorageIndex* outerIndexPtr() const { return derived().nestedExpression().outerIndexPtr(); }
+ inline const StorageIndex* innerNonZeroPtr() const { return derived().nestedExpression().innerNonZeroPtr(); }
+
+ inline Scalar* valuePtr() { return derived().nestedExpression().valuePtr(); }
+ inline StorageIndex* innerIndexPtr() { return derived().nestedExpression().innerIndexPtr(); }
+ inline StorageIndex* outerIndexPtr() { return derived().nestedExpression().outerIndexPtr(); }
+ inline StorageIndex* innerNonZeroPtr() { return derived().nestedExpression().innerNonZeroPtr(); }
+ };
+}
+
+template<typename MatrixType> class TransposeImpl<MatrixType,Sparse>
+ : public internal::SparseTransposeImpl<MatrixType>
+{
+ protected:
+ typedef internal::SparseTransposeImpl<MatrixType> Base;
+};
+
+namespace internal {
+
+template<typename ArgType>
+struct unary_evaluator<Transpose<ArgType>, IteratorBased>
+ : public evaluator_base<Transpose<ArgType> >
+{
+ typedef typename evaluator<ArgType>::InnerIterator EvalIterator;
+ public:
+ typedef Transpose<ArgType> XprType;
+
+ inline Index nonZerosEstimate() const {
+ return m_argImpl.nonZerosEstimate();
+ }
+
+ class InnerIterator : public EvalIterator
+ {
+ public:
+ EIGEN_STRONG_INLINE InnerIterator(const unary_evaluator& unaryOp, Index outer)
+ : EvalIterator(unaryOp.m_argImpl,outer)
+ {}
+
+ Index row() const { return EvalIterator::col(); }
+ Index col() const { return EvalIterator::row(); }
+ };
+
+ enum {
+ CoeffReadCost = evaluator<ArgType>::CoeffReadCost,
+ Flags = XprType::Flags
+ };
+
+ explicit unary_evaluator(const XprType& op) :m_argImpl(op.nestedExpression()) {}
+
+ protected:
+ evaluator<ArgType> m_argImpl;
+};
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_SPARSETRANSPOSE_H
diff --git a/Eigen/src/SparseCore/SparseTriangularView.h b/Eigen/src/SparseCore/SparseTriangularView.h
new file mode 100644
index 0000000..5e7cea7
--- /dev/null
+++ b/Eigen/src/SparseCore/SparseTriangularView.h
@@ -0,0 +1,191 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009-2015 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2012 Désiré Nuentsa-Wakam <desire.nuentsa_wakam@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_SPARSE_TRIANGULARVIEW_H
+#define EIGEN_SPARSE_TRIANGULARVIEW_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+/** \ingroup SparseCore_Module
+ *
+ * \brief Base class for a triangular part in a \b sparse matrix
+ *
+ * This class is an abstract base class of class TriangularView, and objects of type TriangularViewImpl cannot be instantiated.
+ * It extends class TriangularView with additional methods which are available for sparse expressions only.
+ *
+ * \sa class TriangularView, SparseMatrixBase::triangularView()
+ */
+template<typename MatrixType, unsigned int Mode> class TriangularViewImpl<MatrixType,Mode,Sparse>
+ : public SparseMatrixBase<TriangularView<MatrixType,Mode> >
+{
+ enum { SkipFirst = ((Mode&Lower) && !(MatrixType::Flags&RowMajorBit))
+ || ((Mode&Upper) && (MatrixType::Flags&RowMajorBit)),
+ SkipLast = !SkipFirst,
+ SkipDiag = (Mode&ZeroDiag) ? 1 : 0,
+ HasUnitDiag = (Mode&UnitDiag) ? 1 : 0
+ };
+
+ typedef TriangularView<MatrixType,Mode> TriangularViewType;
+
+ protected:
+ // dummy solve function to make TriangularView happy.
+ void solve() const;
+
+ typedef SparseMatrixBase<TriangularViewType> Base;
+ public:
+
+ EIGEN_SPARSE_PUBLIC_INTERFACE(TriangularViewType)
+
+ typedef typename MatrixType::Nested MatrixTypeNested;
+ typedef std::remove_reference_t<MatrixTypeNested> MatrixTypeNestedNonRef;
+ typedef internal::remove_all_t<MatrixTypeNested> MatrixTypeNestedCleaned;
+
+ template<typename RhsType, typename DstType>
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE void _solve_impl(const RhsType &rhs, DstType &dst) const {
+ if(!(internal::is_same<RhsType,DstType>::value && internal::extract_data(dst) == internal::extract_data(rhs)))
+ dst = rhs;
+ this->solveInPlace(dst);
+ }
+
+ /** Applies the inverse of \c *this to the dense vector or matrix \a other, "in-place" */
+ template<typename OtherDerived> void solveInPlace(MatrixBase<OtherDerived>& other) const;
+
+ /** Applies the inverse of \c *this to the sparse vector or matrix \a other, "in-place" */
+ template<typename OtherDerived> void solveInPlace(SparseMatrixBase<OtherDerived>& other) const;
+
+};
+
+namespace internal {
+
+template<typename ArgType, unsigned int Mode>
+struct unary_evaluator<TriangularView<ArgType,Mode>, IteratorBased>
+ : evaluator_base<TriangularView<ArgType,Mode> >
+{
+ typedef TriangularView<ArgType,Mode> XprType;
+
+protected:
+
+ typedef typename XprType::Scalar Scalar;
+ typedef typename XprType::StorageIndex StorageIndex;
+ typedef typename evaluator<ArgType>::InnerIterator EvalIterator;
+
+ enum { SkipFirst = ((Mode&Lower) && !(ArgType::Flags&RowMajorBit))
+ || ((Mode&Upper) && (ArgType::Flags&RowMajorBit)),
+ SkipLast = !SkipFirst,
+ SkipDiag = (Mode&ZeroDiag) ? 1 : 0,
+ HasUnitDiag = (Mode&UnitDiag) ? 1 : 0
+ };
+
+public:
+
+ enum {
+ CoeffReadCost = evaluator<ArgType>::CoeffReadCost,
+ Flags = XprType::Flags
+ };
+
+ explicit unary_evaluator(const XprType &xpr) : m_argImpl(xpr.nestedExpression()), m_arg(xpr.nestedExpression()) {}
+
+ inline Index nonZerosEstimate() const {
+ return m_argImpl.nonZerosEstimate();
+ }
+
+ class InnerIterator : public EvalIterator
+ {
+ typedef EvalIterator Base;
+ public:
+
+ EIGEN_STRONG_INLINE InnerIterator(const unary_evaluator& xprEval, Index outer)
+ : Base(xprEval.m_argImpl,outer), m_returnOne(false), m_containsDiag(Base::outer()<xprEval.m_arg.innerSize())
+ {
+ if(SkipFirst)
+ {
+ while((*this) && ((HasUnitDiag||SkipDiag) ? this->index()<=outer : this->index()<outer))
+ Base::operator++();
+ if(HasUnitDiag)
+ m_returnOne = m_containsDiag;
+ }
+ else if(HasUnitDiag && ((!Base::operator bool()) || Base::index()>=Base::outer()))
+ {
+ if((!SkipFirst) && Base::operator bool())
+ Base::operator++();
+ m_returnOne = m_containsDiag;
+ }
+ }
+
+ EIGEN_STRONG_INLINE InnerIterator& operator++()
+ {
+ if(HasUnitDiag && m_returnOne)
+ m_returnOne = false;
+ else
+ {
+ Base::operator++();
+ if(HasUnitDiag && (!SkipFirst) && ((!Base::operator bool()) || Base::index()>=Base::outer()))
+ {
+ if((!SkipFirst) && Base::operator bool())
+ Base::operator++();
+ m_returnOne = m_containsDiag;
+ }
+ }
+ return *this;
+ }
+
+ EIGEN_STRONG_INLINE operator bool() const
+ {
+ if(HasUnitDiag && m_returnOne)
+ return true;
+ if(SkipFirst) return Base::operator bool();
+ else
+ {
+ if (SkipDiag) return (Base::operator bool() && this->index() < this->outer());
+ else return (Base::operator bool() && this->index() <= this->outer());
+ }
+ }
+
+// inline Index row() const { return (ArgType::Flags&RowMajorBit ? Base::outer() : this->index()); }
+// inline Index col() const { return (ArgType::Flags&RowMajorBit ? this->index() : Base::outer()); }
+ inline StorageIndex index() const
+ {
+ if(HasUnitDiag && m_returnOne) return internal::convert_index<StorageIndex>(Base::outer());
+ else return Base::index();
+ }
+ inline Scalar value() const
+ {
+ if(HasUnitDiag && m_returnOne) return Scalar(1);
+ else return Base::value();
+ }
+
+ protected:
+ bool m_returnOne;
+ bool m_containsDiag;
+ private:
+ Scalar& valueRef();
+ };
+
+protected:
+ evaluator<ArgType> m_argImpl;
+ const ArgType& m_arg;
+};
+
+} // end namespace internal
+
+template<typename Derived>
+template<int Mode>
+inline const TriangularView<const Derived, Mode>
+SparseMatrixBase<Derived>::triangularView() const
+{
+ return TriangularView<const Derived, Mode>(derived());
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_SPARSE_TRIANGULARVIEW_H
diff --git a/Eigen/src/SparseCore/SparseUtil.h b/Eigen/src/SparseCore/SparseUtil.h
new file mode 100644
index 0000000..47f5ef6
--- /dev/null
+++ b/Eigen/src/SparseCore/SparseUtil.h
@@ -0,0 +1,186 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2014 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_SPARSEUTIL_H
+#define EIGEN_SPARSEUTIL_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+#ifdef NDEBUG
+#define EIGEN_DBG_SPARSE(X)
+#else
+#define EIGEN_DBG_SPARSE(X) X
+#endif
+
+#define EIGEN_SPARSE_INHERIT_ASSIGNMENT_OPERATOR(Derived, Op) \
+template<typename OtherDerived> \
+EIGEN_STRONG_INLINE Derived& operator Op(const Eigen::SparseMatrixBase<OtherDerived>& other) \
+{ \
+ return Base::operator Op(other.derived()); \
+} \
+EIGEN_STRONG_INLINE Derived& operator Op(const Derived& other) \
+{ \
+ return Base::operator Op(other); \
+}
+
+#define EIGEN_SPARSE_INHERIT_SCALAR_ASSIGNMENT_OPERATOR(Derived, Op) \
+template<typename Other> \
+EIGEN_STRONG_INLINE Derived& operator Op(const Other& scalar) \
+{ \
+ return Base::operator Op(scalar); \
+}
+
+#define EIGEN_SPARSE_INHERIT_ASSIGNMENT_OPERATORS(Derived) \
+EIGEN_SPARSE_INHERIT_ASSIGNMENT_OPERATOR(Derived, =)
+
+
+#define EIGEN_SPARSE_PUBLIC_INTERFACE(Derived) \
+ EIGEN_GENERIC_PUBLIC_INTERFACE(Derived)
+
+
+const int CoherentAccessPattern = 0x1;
+const int InnerRandomAccessPattern = 0x2 | CoherentAccessPattern;
+const int OuterRandomAccessPattern = 0x4 | CoherentAccessPattern;
+const int RandomAccessPattern = 0x8 | OuterRandomAccessPattern | InnerRandomAccessPattern;
+
+template<typename Scalar_, int Flags_ = 0, typename StorageIndex_ = int> class SparseMatrix;
+template<typename Scalar_, int Flags_ = 0, typename StorageIndex_ = int> class SparseVector;
+
+template<typename MatrixType, unsigned int UpLo> class SparseSelfAdjointView;
+template<typename Lhs, typename Rhs> class SparseDiagonalProduct;
+template<typename MatrixType> class SparseView;
+
+template<typename Lhs, typename Rhs> class SparseSparseProduct;
+template<typename Lhs, typename Rhs> class SparseTimeDenseProduct;
+template<typename Lhs, typename Rhs> class DenseTimeSparseProduct;
+template<typename Lhs, typename Rhs, bool Transpose> class SparseDenseOuterProduct;
+
+template<typename Lhs, typename Rhs> struct SparseSparseProductReturnType;
+template<typename Lhs, typename Rhs,
+ int InnerSize = internal::min_size_prefer_fixed(internal::traits<Lhs>::ColsAtCompileTime, internal::traits<Rhs>::RowsAtCompileTime)> struct DenseSparseProductReturnType;
+
+template<typename Lhs, typename Rhs,
+ int InnerSize = internal::min_size_prefer_fixed(internal::traits<Lhs>::ColsAtCompileTime, internal::traits<Rhs>::RowsAtCompileTime)> struct SparseDenseProductReturnType;
+template<typename MatrixType,int UpLo> class SparseSymmetricPermutationProduct;
+
+namespace internal {
+
+template<typename T,int Rows,int Cols,int Flags> struct sparse_eval;
+
+template<typename T> struct eval<T,Sparse>
+ : sparse_eval<T, traits<T>::RowsAtCompileTime,traits<T>::ColsAtCompileTime,traits<T>::Flags>
+{};
+
+template<typename T,int Cols,int Flags> struct sparse_eval<T,1,Cols,Flags> {
+ typedef typename traits<T>::Scalar Scalar_;
+ typedef typename traits<T>::StorageIndex StorageIndex_;
+ public:
+ typedef SparseVector<Scalar_, RowMajor, StorageIndex_> type;
+};
+
+template<typename T,int Rows,int Flags> struct sparse_eval<T,Rows,1,Flags> {
+ typedef typename traits<T>::Scalar Scalar_;
+ typedef typename traits<T>::StorageIndex StorageIndex_;
+ public:
+ typedef SparseVector<Scalar_, ColMajor, StorageIndex_> type;
+};
+
+// TODO this seems almost identical to plain_matrix_type<T, Sparse>
+template<typename T,int Rows,int Cols,int Flags> struct sparse_eval {
+ typedef typename traits<T>::Scalar Scalar_;
+ typedef typename traits<T>::StorageIndex StorageIndex_;
+ enum { Options_ = ((Flags&RowMajorBit)==RowMajorBit) ? RowMajor : ColMajor };
+ public:
+ typedef SparseMatrix<Scalar_, Options_, StorageIndex_> type;
+};
+
+template<typename T,int Flags> struct sparse_eval<T,1,1,Flags> {
+ typedef typename traits<T>::Scalar Scalar_;
+ public:
+ typedef Matrix<Scalar_, 1, 1> type;
+};
+
+template<typename T> struct plain_matrix_type<T,Sparse>
+{
+ typedef typename traits<T>::Scalar Scalar_;
+ typedef typename traits<T>::StorageIndex StorageIndex_;
+ enum { Options_ = ((evaluator<T>::Flags&RowMajorBit)==RowMajorBit) ? RowMajor : ColMajor };
+ public:
+ typedef SparseMatrix<Scalar_, Options_, StorageIndex_> type;
+};
+
+template<typename T>
+struct plain_object_eval<T,Sparse>
+ : sparse_eval<T, traits<T>::RowsAtCompileTime,traits<T>::ColsAtCompileTime, evaluator<T>::Flags>
+{};
+
+template<typename Decomposition, typename RhsType>
+struct solve_traits<Decomposition,RhsType,Sparse>
+{
+ typedef typename sparse_eval<RhsType, RhsType::RowsAtCompileTime, RhsType::ColsAtCompileTime,traits<RhsType>::Flags>::type PlainObject;
+};
+
+template<typename Derived>
+struct generic_xpr_base<Derived, MatrixXpr, Sparse>
+{
+ typedef SparseMatrixBase<Derived> type;
+};
+
+struct SparseTriangularShape { static std::string debugName() { return "SparseTriangularShape"; } };
+struct SparseSelfAdjointShape { static std::string debugName() { return "SparseSelfAdjointShape"; } };
+
+template<> struct glue_shapes<SparseShape,SelfAdjointShape> { typedef SparseSelfAdjointShape type; };
+template<> struct glue_shapes<SparseShape,TriangularShape > { typedef SparseTriangularShape type; };
+
+// return type of SparseCompressedBase::lower_bound;
+struct LowerBoundIndex {
+ LowerBoundIndex() : value(-1), found(false) {}
+ LowerBoundIndex(Index val, bool ok) : value(val), found(ok) {}
+ Index value;
+ bool found;
+};
+
+} // end namespace internal
+
+/** \ingroup SparseCore_Module
+ *
+ * \class Triplet
+ *
+ * \brief A small structure to hold a non zero as a triplet (i,j,value).
+ *
+ * \sa SparseMatrix::setFromTriplets()
+ */
+template<typename Scalar, typename StorageIndex=typename SparseMatrix<Scalar>::StorageIndex >
+class Triplet
+{
+public:
+ Triplet() : m_row(0), m_col(0), m_value(0) {}
+
+ Triplet(const StorageIndex& i, const StorageIndex& j, const Scalar& v = Scalar(0))
+ : m_row(i), m_col(j), m_value(v)
+ {}
+
+ /** \returns the row index of the element */
+ const StorageIndex& row() const { return m_row; }
+
+ /** \returns the column index of the element */
+ const StorageIndex& col() const { return m_col; }
+
+ /** \returns the value of the element */
+ const Scalar& value() const { return m_value; }
+protected:
+ StorageIndex m_row, m_col;
+ Scalar m_value;
+};
+
+} // end namespace Eigen
+
+#endif // EIGEN_SPARSEUTIL_H
diff --git a/Eigen/src/SparseCore/SparseVector.h b/Eigen/src/SparseCore/SparseVector.h
new file mode 100644
index 0000000..ebbadb5
--- /dev/null
+++ b/Eigen/src/SparseCore/SparseVector.h
@@ -0,0 +1,500 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2015 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_SPARSEVECTOR_H
+#define EIGEN_SPARSEVECTOR_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+/** \ingroup SparseCore_Module
+ * \class SparseVector
+ *
+ * \brief a sparse vector class
+ *
+ * \tparam Scalar_ the scalar type, i.e. the type of the coefficients
+ *
+ * See http://www.netlib.org/linalg/html_templates/node91.html for details on the storage scheme.
+ *
+ * This class can be extended with the help of the plugin mechanism described on the page
+ * \ref TopicCustomizing_Plugins by defining the preprocessor symbol \c EIGEN_SPARSEVECTOR_PLUGIN.
+ */
+
+namespace internal {
+template<typename Scalar_, int Options_, typename StorageIndex_>
+struct traits<SparseVector<Scalar_, Options_, StorageIndex_> >
+{
+ typedef Scalar_ Scalar;
+ typedef StorageIndex_ StorageIndex;
+ typedef Sparse StorageKind;
+ typedef MatrixXpr XprKind;
+ enum {
+ IsColVector = (Options_ & RowMajorBit) ? 0 : 1,
+
+ RowsAtCompileTime = IsColVector ? Dynamic : 1,
+ ColsAtCompileTime = IsColVector ? 1 : Dynamic,
+ MaxRowsAtCompileTime = RowsAtCompileTime,
+ MaxColsAtCompileTime = ColsAtCompileTime,
+ Flags = Options_ | NestByRefBit | LvalueBit | (IsColVector ? 0 : RowMajorBit) | CompressedAccessBit,
+ SupportedAccessPatterns = InnerRandomAccessPattern
+ };
+};
+
+// Sparse-Vector-Assignment kinds:
+enum {
+ SVA_RuntimeSwitch,
+ SVA_Inner,
+ SVA_Outer
+};
+
+template< typename Dest, typename Src,
+ int AssignmentKind = !bool(Src::IsVectorAtCompileTime) ? SVA_RuntimeSwitch
+ : Src::InnerSizeAtCompileTime==1 ? SVA_Outer
+ : SVA_Inner>
+struct sparse_vector_assign_selector;
+
+}
+
+template<typename Scalar_, int Options_, typename StorageIndex_>
+class SparseVector
+ : public SparseCompressedBase<SparseVector<Scalar_, Options_, StorageIndex_> >
+{
+ typedef SparseCompressedBase<SparseVector> Base;
+ using Base::convert_index;
+ public:
+ EIGEN_SPARSE_PUBLIC_INTERFACE(SparseVector)
+ EIGEN_SPARSE_INHERIT_ASSIGNMENT_OPERATOR(SparseVector, +=)
+ EIGEN_SPARSE_INHERIT_ASSIGNMENT_OPERATOR(SparseVector, -=)
+
+ typedef internal::CompressedStorage<Scalar,StorageIndex> Storage;
+ enum { IsColVector = internal::traits<SparseVector>::IsColVector };
+
+ enum {
+ Options = Options_
+ };
+
+ EIGEN_STRONG_INLINE Index rows() const { return IsColVector ? m_size : 1; }
+ EIGEN_STRONG_INLINE Index cols() const { return IsColVector ? 1 : m_size; }
+ EIGEN_STRONG_INLINE Index innerSize() const { return m_size; }
+ EIGEN_STRONG_INLINE Index outerSize() const { return 1; }
+
+ EIGEN_STRONG_INLINE const Scalar* valuePtr() const { return m_data.valuePtr(); }
+ EIGEN_STRONG_INLINE Scalar* valuePtr() { return m_data.valuePtr(); }
+
+ EIGEN_STRONG_INLINE const StorageIndex* innerIndexPtr() const { return m_data.indexPtr(); }
+ EIGEN_STRONG_INLINE StorageIndex* innerIndexPtr() { return m_data.indexPtr(); }
+
+ inline const StorageIndex* outerIndexPtr() const { return 0; }
+ inline StorageIndex* outerIndexPtr() { return 0; }
+ inline const StorageIndex* innerNonZeroPtr() const { return 0; }
+ inline StorageIndex* innerNonZeroPtr() { return 0; }
+
+ /** \internal */
+ inline Storage& data() { return m_data; }
+ /** \internal */
+ inline const Storage& data() const { return m_data; }
+
+ inline Scalar coeff(Index row, Index col) const
+ {
+ eigen_assert(IsColVector ? (col==0 && row>=0 && row<m_size) : (row==0 && col>=0 && col<m_size));
+ return coeff(IsColVector ? row : col);
+ }
+ inline Scalar coeff(Index i) const
+ {
+ eigen_assert(i>=0 && i<m_size);
+ return m_data.at(StorageIndex(i));
+ }
+
+ inline Scalar& coeffRef(Index row, Index col)
+ {
+ eigen_assert(IsColVector ? (col==0 && row>=0 && row<m_size) : (row==0 && col>=0 && col<m_size));
+ return coeffRef(IsColVector ? row : col);
+ }
+
+ /** \returns a reference to the coefficient value at given index \a i
+ * This operation involes a log(rho*size) binary search. If the coefficient does not
+ * exist yet, then a sorted insertion into a sequential buffer is performed.
+ *
+ * This insertion might be very costly if the number of nonzeros above \a i is large.
+ */
+ inline Scalar& coeffRef(Index i)
+ {
+ eigen_assert(i>=0 && i<m_size);
+
+ return m_data.atWithInsertion(StorageIndex(i));
+ }
+
+ public:
+
+ typedef typename Base::InnerIterator InnerIterator;
+ typedef typename Base::ReverseInnerIterator ReverseInnerIterator;
+
+ inline void setZero() { m_data.clear(); }
+
+ /** \returns the number of non zero coefficients */
+ inline Index nonZeros() const { return m_data.size(); }
+
+ inline void startVec(Index outer)
+ {
+ EIGEN_UNUSED_VARIABLE(outer);
+ eigen_assert(outer==0);
+ }
+
+ inline Scalar& insertBackByOuterInner(Index outer, Index inner)
+ {
+ EIGEN_UNUSED_VARIABLE(outer);
+ eigen_assert(outer==0);
+ return insertBack(inner);
+ }
+ inline Scalar& insertBack(Index i)
+ {
+ m_data.append(0, i);
+ return m_data.value(m_data.size()-1);
+ }
+
+ Scalar& insertBackByOuterInnerUnordered(Index outer, Index inner)
+ {
+ EIGEN_UNUSED_VARIABLE(outer);
+ eigen_assert(outer==0);
+ return insertBackUnordered(inner);
+ }
+ inline Scalar& insertBackUnordered(Index i)
+ {
+ m_data.append(0, i);
+ return m_data.value(m_data.size()-1);
+ }
+
+ inline Scalar& insert(Index row, Index col)
+ {
+ eigen_assert(IsColVector ? (col==0 && row>=0 && row<m_size) : (row==0 && col>=0 && col<m_size));
+
+ Index inner = IsColVector ? row : col;
+ Index outer = IsColVector ? col : row;
+ EIGEN_ONLY_USED_FOR_DEBUG(outer);
+ eigen_assert(outer==0);
+ return insert(inner);
+ }
+ Scalar& insert(Index i)
+ {
+ eigen_assert(i>=0 && i<m_size);
+
+ Index startId = 0;
+ Index p = Index(m_data.size()) - 1;
+ // TODO smart realloc
+ m_data.resize(p+2,1);
+
+ while ( (p >= startId) && (m_data.index(p) > i) )
+ {
+ m_data.index(p+1) = m_data.index(p);
+ m_data.value(p+1) = m_data.value(p);
+ --p;
+ }
+ m_data.index(p+1) = convert_index(i);
+ m_data.value(p+1) = 0;
+ return m_data.value(p+1);
+ }
+
+ /**
+ */
+ inline void reserve(Index reserveSize) { m_data.reserve(reserveSize); }
+
+
+ inline void finalize() {}
+
+ /** \copydoc SparseMatrix::prune(const Scalar&,const RealScalar&) */
+ Index prune(const Scalar& reference, const RealScalar& epsilon = NumTraits<RealScalar>::dummy_precision()) {
+ return prune([&](const Scalar& val){ return !internal::isMuchSmallerThan(val, reference, epsilon); });
+ }
+
+ /**
+ * \brief Prunes the entries of the vector based on a `predicate`
+ * \tparam F Type of the predicate.
+ * \param keep_predicate The predicate that is used to test whether a value should be kept. A callable that
+ * gets passed om a `Scalar` value and returns a boolean. If the predicate returns true, the value is kept.
+ * \return The new number of structural non-zeros.
+ */
+ template<class F>
+ Index prune(F&& keep_predicate)
+ {
+ Index k = 0;
+ Index n = m_data.size();
+ for (Index i = 0; i < n; ++i)
+ {
+ if (keep_predicate(m_data.value(i)))
+ {
+ m_data.value(k) = std::move(m_data.value(i));
+ m_data.index(k) = m_data.index(i);
+ ++k;
+ }
+ }
+ m_data.resize(k);
+ return k;
+ }
+
+ /** Resizes the sparse vector to \a rows x \a cols
+ *
+ * This method is provided for compatibility with matrices.
+ * For a column vector, \a cols must be equal to 1.
+ * For a row vector, \a rows must be equal to 1.
+ *
+ * \sa resize(Index)
+ */
+ void resize(Index rows, Index cols)
+ {
+ eigen_assert((IsColVector ? cols : rows)==1 && "Outer dimension must equal 1");
+ resize(IsColVector ? rows : cols);
+ }
+
+ /** Resizes the sparse vector to \a newSize
+ * This method deletes all entries, thus leaving an empty sparse vector
+ *
+ * \sa conservativeResize(), setZero() */
+ void resize(Index newSize)
+ {
+ m_size = newSize;
+ m_data.clear();
+ }
+
+ /** Resizes the sparse vector to \a newSize, while leaving old values untouched.
+ *
+ * If the size of the vector is decreased, then the storage of the out-of bounds coefficients is kept and reserved.
+ * Call .data().squeeze() to free extra memory.
+ *
+ * \sa reserve(), setZero()
+ */
+ void conservativeResize(Index newSize)
+ {
+ if (newSize < m_size)
+ {
+ Index i = 0;
+ while (i<m_data.size() && m_data.index(i)<newSize) ++i;
+ m_data.resize(i);
+ }
+ m_size = newSize;
+ }
+
+ void resizeNonZeros(Index size) { m_data.resize(size); }
+
+ inline SparseVector() : m_size(0) { resize(0); }
+
+ explicit inline SparseVector(Index size) : m_size(0) { resize(size); }
+
+ inline SparseVector(Index rows, Index cols) : m_size(0) { resize(rows,cols); }
+
+ template<typename OtherDerived>
+ inline SparseVector(const SparseMatrixBase<OtherDerived>& other)
+ : m_size(0)
+ {
+ #ifdef EIGEN_SPARSE_CREATE_TEMPORARY_PLUGIN
+ EIGEN_SPARSE_CREATE_TEMPORARY_PLUGIN
+ #endif
+ *this = other.derived();
+ }
+
+ inline SparseVector(const SparseVector& other)
+ : Base(other), m_size(0)
+ {
+ *this = other.derived();
+ }
+
+ /** Swaps the values of \c *this and \a other.
+ * Overloaded for performance: this version performs a \em shallow swap by swapping pointers and attributes only.
+ * \sa SparseMatrixBase::swap()
+ */
+ inline void swap(SparseVector& other)
+ {
+ std::swap(m_size, other.m_size);
+ m_data.swap(other.m_data);
+ }
+
+ template<int OtherOptions>
+ inline void swap(SparseMatrix<Scalar,OtherOptions,StorageIndex>& other)
+ {
+ eigen_assert(other.outerSize()==1);
+ std::swap(m_size, other.m_innerSize);
+ m_data.swap(other.m_data);
+ }
+
+ inline SparseVector& operator=(const SparseVector& other)
+ {
+ if (other.isRValue())
+ {
+ swap(other.const_cast_derived());
+ }
+ else
+ {
+ resize(other.size());
+ m_data = other.m_data;
+ }
+ return *this;
+ }
+
+ template<typename OtherDerived>
+ inline SparseVector& operator=(const SparseMatrixBase<OtherDerived>& other)
+ {
+ SparseVector tmp(other.size());
+ internal::sparse_vector_assign_selector<SparseVector,OtherDerived>::run(tmp,other.derived());
+ this->swap(tmp);
+ return *this;
+ }
+
+ #ifndef EIGEN_PARSED_BY_DOXYGEN
+ template<typename Lhs, typename Rhs>
+ inline SparseVector& operator=(const SparseSparseProduct<Lhs,Rhs>& product)
+ {
+ return Base::operator=(product);
+ }
+ #endif
+
+#ifndef EIGEN_NO_IO
+ friend std::ostream & operator << (std::ostream & s, const SparseVector& m)
+ {
+ for (Index i=0; i<m.nonZeros(); ++i)
+ s << "(" << m.m_data.value(i) << "," << m.m_data.index(i) << ") ";
+ s << std::endl;
+ return s;
+ }
+#endif
+
+ /** Destructor */
+ inline ~SparseVector() {}
+
+ /** Overloaded for performance */
+ Scalar sum() const;
+
+ public:
+
+ /** \internal \deprecated use setZero() and reserve() */
+ EIGEN_DEPRECATED void startFill(Index reserve)
+ {
+ setZero();
+ m_data.reserve(reserve);
+ }
+
+ /** \internal \deprecated use insertBack(Index,Index) */
+ EIGEN_DEPRECATED Scalar& fill(Index r, Index c)
+ {
+ eigen_assert(r==0 || c==0);
+ return fill(IsColVector ? r : c);
+ }
+
+ /** \internal \deprecated use insertBack(Index) */
+ EIGEN_DEPRECATED Scalar& fill(Index i)
+ {
+ m_data.append(0, i);
+ return m_data.value(m_data.size()-1);
+ }
+
+ /** \internal \deprecated use insert(Index,Index) */
+ EIGEN_DEPRECATED Scalar& fillrand(Index r, Index c)
+ {
+ eigen_assert(r==0 || c==0);
+ return fillrand(IsColVector ? r : c);
+ }
+
+ /** \internal \deprecated use insert(Index) */
+ EIGEN_DEPRECATED Scalar& fillrand(Index i)
+ {
+ return insert(i);
+ }
+
+ /** \internal \deprecated use finalize() */
+ EIGEN_DEPRECATED void endFill() {}
+
+ // These two functions were here in the 3.1 release, so let's keep them in case some code rely on them.
+ /** \internal \deprecated use data() */
+ EIGEN_DEPRECATED Storage& _data() { return m_data; }
+ /** \internal \deprecated use data() */
+ EIGEN_DEPRECATED const Storage& _data() const { return m_data; }
+
+# ifdef EIGEN_SPARSEVECTOR_PLUGIN
+# include EIGEN_SPARSEVECTOR_PLUGIN
+# endif
+
+protected:
+ EIGEN_STATIC_ASSERT(NumTraits<StorageIndex>::IsSigned,THE_INDEX_TYPE_MUST_BE_A_SIGNED_TYPE)
+ EIGEN_STATIC_ASSERT((Options_&(ColMajor|RowMajor))==Options,INVALID_MATRIX_TEMPLATE_PARAMETERS)
+
+ Storage m_data;
+ Index m_size;
+};
+
+namespace internal {
+
+template<typename Scalar_, int Options_, typename Index_>
+struct evaluator<SparseVector<Scalar_,Options_,Index_> >
+ : evaluator_base<SparseVector<Scalar_,Options_,Index_> >
+{
+ typedef SparseVector<Scalar_,Options_,Index_> SparseVectorType;
+ typedef evaluator_base<SparseVectorType> Base;
+ typedef typename SparseVectorType::InnerIterator InnerIterator;
+ typedef typename SparseVectorType::ReverseInnerIterator ReverseInnerIterator;
+
+ enum {
+ CoeffReadCost = NumTraits<Scalar_>::ReadCost,
+ Flags = SparseVectorType::Flags
+ };
+
+ evaluator() : Base() {}
+
+ explicit evaluator(const SparseVectorType &mat) : m_matrix(&mat)
+ {
+ EIGEN_INTERNAL_CHECK_COST_VALUE(CoeffReadCost);
+ }
+
+ inline Index nonZerosEstimate() const {
+ return m_matrix->nonZeros();
+ }
+
+ operator SparseVectorType&() { return m_matrix->const_cast_derived(); }
+ operator const SparseVectorType&() const { return *m_matrix; }
+
+ const SparseVectorType *m_matrix;
+};
+
+template< typename Dest, typename Src>
+struct sparse_vector_assign_selector<Dest,Src,SVA_Inner> {
+ static void run(Dest& dst, const Src& src) {
+ eigen_internal_assert(src.innerSize()==src.size());
+ typedef internal::evaluator<Src> SrcEvaluatorType;
+ SrcEvaluatorType srcEval(src);
+ for(typename SrcEvaluatorType::InnerIterator it(srcEval, 0); it; ++it)
+ dst.insert(it.index()) = it.value();
+ }
+};
+
+template< typename Dest, typename Src>
+struct sparse_vector_assign_selector<Dest,Src,SVA_Outer> {
+ static void run(Dest& dst, const Src& src) {
+ eigen_internal_assert(src.outerSize()==src.size());
+ typedef internal::evaluator<Src> SrcEvaluatorType;
+ SrcEvaluatorType srcEval(src);
+ for(Index i=0; i<src.size(); ++i)
+ {
+ typename SrcEvaluatorType::InnerIterator it(srcEval, i);
+ if(it)
+ dst.insert(i) = it.value();
+ }
+ }
+};
+
+template< typename Dest, typename Src>
+struct sparse_vector_assign_selector<Dest,Src,SVA_RuntimeSwitch> {
+ static void run(Dest& dst, const Src& src) {
+ if(src.outerSize()==1) sparse_vector_assign_selector<Dest,Src,SVA_Inner>::run(dst, src);
+ else sparse_vector_assign_selector<Dest,Src,SVA_Outer>::run(dst, src);
+ }
+};
+
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_SPARSEVECTOR_H
diff --git a/Eigen/src/SparseCore/SparseView.h b/Eigen/src/SparseCore/SparseView.h
new file mode 100644
index 0000000..dbb4c43
--- /dev/null
+++ b/Eigen/src/SparseCore/SparseView.h
@@ -0,0 +1,256 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2011-2014 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2010 Daniel Lowengrub <lowdanie@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_SPARSEVIEW_H
+#define EIGEN_SPARSEVIEW_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+
+template<typename MatrixType>
+struct traits<SparseView<MatrixType> > : traits<MatrixType>
+{
+ typedef typename MatrixType::StorageIndex StorageIndex;
+ typedef Sparse StorageKind;
+ enum {
+ Flags = int(traits<MatrixType>::Flags) & (RowMajorBit)
+ };
+};
+
+} // end namespace internal
+
+/** \ingroup SparseCore_Module
+ * \class SparseView
+ *
+ * \brief Expression of a dense or sparse matrix with zero or too small values removed
+ *
+ * \tparam MatrixType the type of the object of which we are removing the small entries
+ *
+ * This class represents an expression of a given dense or sparse matrix with
+ * entries smaller than \c reference * \c epsilon are removed.
+ * It is the return type of MatrixBase::sparseView() and SparseMatrixBase::pruned()
+ * and most of the time this is the only way it is used.
+ *
+ * \sa MatrixBase::sparseView(), SparseMatrixBase::pruned()
+ */
+template<typename MatrixType>
+class SparseView : public SparseMatrixBase<SparseView<MatrixType> >
+{
+ typedef typename MatrixType::Nested MatrixTypeNested;
+ typedef internal::remove_all_t<MatrixTypeNested> MatrixTypeNested_;
+ typedef SparseMatrixBase<SparseView > Base;
+public:
+ EIGEN_SPARSE_PUBLIC_INTERFACE(SparseView)
+ typedef internal::remove_all_t<MatrixType> NestedExpression;
+
+ explicit SparseView(const MatrixType& mat, const Scalar& reference = Scalar(0),
+ const RealScalar &epsilon = NumTraits<Scalar>::dummy_precision())
+ : m_matrix(mat), m_reference(reference), m_epsilon(epsilon) {}
+
+ inline Index rows() const { return m_matrix.rows(); }
+ inline Index cols() const { return m_matrix.cols(); }
+
+ inline Index innerSize() const { return m_matrix.innerSize(); }
+ inline Index outerSize() const { return m_matrix.outerSize(); }
+
+ /** \returns the nested expression */
+ const internal::remove_all_t<MatrixTypeNested>&
+ nestedExpression() const { return m_matrix; }
+
+ Scalar reference() const { return m_reference; }
+ RealScalar epsilon() const { return m_epsilon; }
+
+protected:
+ MatrixTypeNested m_matrix;
+ Scalar m_reference;
+ RealScalar m_epsilon;
+};
+
+namespace internal {
+
+// TODO find a way to unify the two following variants
+// This is tricky because implementing an inner iterator on top of an IndexBased evaluator is
+// not easy because the evaluators do not expose the sizes of the underlying expression.
+
+template<typename ArgType>
+struct unary_evaluator<SparseView<ArgType>, IteratorBased>
+ : public evaluator_base<SparseView<ArgType> >
+{
+ typedef typename evaluator<ArgType>::InnerIterator EvalIterator;
+ public:
+ typedef SparseView<ArgType> XprType;
+
+ class InnerIterator : public EvalIterator
+ {
+ protected:
+ typedef typename XprType::Scalar Scalar;
+ public:
+
+ EIGEN_STRONG_INLINE InnerIterator(const unary_evaluator& sve, Index outer)
+ : EvalIterator(sve.m_argImpl,outer), m_view(sve.m_view)
+ {
+ incrementToNonZero();
+ }
+
+ EIGEN_STRONG_INLINE InnerIterator& operator++()
+ {
+ EvalIterator::operator++();
+ incrementToNonZero();
+ return *this;
+ }
+
+ using EvalIterator::value;
+
+ protected:
+ const XprType &m_view;
+
+ private:
+ void incrementToNonZero()
+ {
+ while((bool(*this)) && internal::isMuchSmallerThan(value(), m_view.reference(), m_view.epsilon()))
+ {
+ EvalIterator::operator++();
+ }
+ }
+ };
+
+ enum {
+ CoeffReadCost = evaluator<ArgType>::CoeffReadCost,
+ Flags = XprType::Flags
+ };
+
+ explicit unary_evaluator(const XprType& xpr) : m_argImpl(xpr.nestedExpression()), m_view(xpr) {}
+
+ protected:
+ evaluator<ArgType> m_argImpl;
+ const XprType &m_view;
+};
+
+template<typename ArgType>
+struct unary_evaluator<SparseView<ArgType>, IndexBased>
+ : public evaluator_base<SparseView<ArgType> >
+{
+ public:
+ typedef SparseView<ArgType> XprType;
+ protected:
+ enum { IsRowMajor = (XprType::Flags&RowMajorBit)==RowMajorBit };
+ typedef typename XprType::Scalar Scalar;
+ typedef typename XprType::StorageIndex StorageIndex;
+ public:
+
+ class InnerIterator
+ {
+ public:
+
+ EIGEN_STRONG_INLINE InnerIterator(const unary_evaluator& sve, Index outer)
+ : m_sve(sve), m_inner(0), m_outer(outer), m_end(sve.m_view.innerSize())
+ {
+ incrementToNonZero();
+ }
+
+ EIGEN_STRONG_INLINE InnerIterator& operator++()
+ {
+ m_inner++;
+ incrementToNonZero();
+ return *this;
+ }
+
+ EIGEN_STRONG_INLINE Scalar value() const
+ {
+ return (IsRowMajor) ? m_sve.m_argImpl.coeff(m_outer, m_inner)
+ : m_sve.m_argImpl.coeff(m_inner, m_outer);
+ }
+
+ EIGEN_STRONG_INLINE StorageIndex index() const { return m_inner; }
+ inline Index row() const { return IsRowMajor ? m_outer : index(); }
+ inline Index col() const { return IsRowMajor ? index() : m_outer; }
+
+ EIGEN_STRONG_INLINE operator bool() const { return m_inner < m_end && m_inner>=0; }
+
+ protected:
+ const unary_evaluator &m_sve;
+ Index m_inner;
+ const Index m_outer;
+ const Index m_end;
+
+ private:
+ void incrementToNonZero()
+ {
+ while((bool(*this)) && internal::isMuchSmallerThan(value(), m_sve.m_view.reference(), m_sve.m_view.epsilon()))
+ {
+ m_inner++;
+ }
+ }
+ };
+
+ enum {
+ CoeffReadCost = evaluator<ArgType>::CoeffReadCost,
+ Flags = XprType::Flags
+ };
+
+ explicit unary_evaluator(const XprType& xpr) : m_argImpl(xpr.nestedExpression()), m_view(xpr) {}
+
+ protected:
+ evaluator<ArgType> m_argImpl;
+ const XprType &m_view;
+};
+
+} // end namespace internal
+
+/** \ingroup SparseCore_Module
+ *
+ * \returns a sparse expression of the dense expression \c *this with values smaller than
+ * \a reference * \a epsilon removed.
+ *
+ * This method is typically used when prototyping to convert a quickly assembled dense Matrix \c D to a SparseMatrix \c S:
+ * \code
+ * MatrixXd D(n,m);
+ * SparseMatrix<double> S;
+ * S = D.sparseView(); // suppress numerical zeros (exact)
+ * S = D.sparseView(reference);
+ * S = D.sparseView(reference,epsilon);
+ * \endcode
+ * where \a reference is a meaningful non zero reference value,
+ * and \a epsilon is a tolerance factor defaulting to NumTraits<Scalar>::dummy_precision().
+ *
+ * \sa SparseMatrixBase::pruned(), class SparseView */
+template<typename Derived>
+const SparseView<Derived> MatrixBase<Derived>::sparseView(const Scalar& reference,
+ const typename NumTraits<Scalar>::Real& epsilon) const
+{
+ return SparseView<Derived>(derived(), reference, epsilon);
+}
+
+/** \returns an expression of \c *this with values smaller than
+ * \a reference * \a epsilon removed.
+ *
+ * This method is typically used in conjunction with the product of two sparse matrices
+ * to automatically prune the smallest values as follows:
+ * \code
+ * C = (A*B).pruned(); // suppress numerical zeros (exact)
+ * C = (A*B).pruned(ref);
+ * C = (A*B).pruned(ref,epsilon);
+ * \endcode
+ * where \c ref is a meaningful non zero reference value.
+ * */
+template<typename Derived>
+const SparseView<Derived>
+SparseMatrixBase<Derived>::pruned(const Scalar& reference,
+ const RealScalar& epsilon) const
+{
+ return SparseView<Derived>(derived(), reference, epsilon);
+}
+
+} // end namespace Eigen
+
+#endif
diff --git a/Eigen/src/SparseCore/TriangularSolver.h b/Eigen/src/SparseCore/TriangularSolver.h
new file mode 100644
index 0000000..a9fbeeb
--- /dev/null
+++ b/Eigen/src/SparseCore/TriangularSolver.h
@@ -0,0 +1,317 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_SPARSETRIANGULARSOLVER_H
+#define EIGEN_SPARSETRIANGULARSOLVER_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+
+template<typename Lhs, typename Rhs, int Mode,
+ int UpLo = (Mode & Lower)
+ ? Lower
+ : (Mode & Upper)
+ ? Upper
+ : -1,
+ int StorageOrder = int(traits<Lhs>::Flags) & RowMajorBit>
+struct sparse_solve_triangular_selector;
+
+// forward substitution, row-major
+template<typename Lhs, typename Rhs, int Mode>
+struct sparse_solve_triangular_selector<Lhs,Rhs,Mode,Lower,RowMajor>
+{
+ typedef typename Rhs::Scalar Scalar;
+ typedef evaluator<Lhs> LhsEval;
+ typedef typename evaluator<Lhs>::InnerIterator LhsIterator;
+ static void run(const Lhs& lhs, Rhs& other)
+ {
+ LhsEval lhsEval(lhs);
+ for(Index col=0 ; col<other.cols() ; ++col)
+ {
+ for(Index i=0; i<lhs.rows(); ++i)
+ {
+ Scalar tmp = other.coeff(i,col);
+ Scalar lastVal(0);
+ Index lastIndex = 0;
+ for(LhsIterator it(lhsEval, i); it; ++it)
+ {
+ lastVal = it.value();
+ lastIndex = it.index();
+ if(lastIndex==i)
+ break;
+ tmp -= lastVal * other.coeff(lastIndex,col);
+ }
+ if (Mode & UnitDiag)
+ other.coeffRef(i,col) = tmp;
+ else
+ {
+ eigen_assert(lastIndex==i);
+ other.coeffRef(i,col) = tmp/lastVal;
+ }
+ }
+ }
+ }
+};
+
+// backward substitution, row-major
+template<typename Lhs, typename Rhs, int Mode>
+struct sparse_solve_triangular_selector<Lhs,Rhs,Mode,Upper,RowMajor>
+{
+ typedef typename Rhs::Scalar Scalar;
+ typedef evaluator<Lhs> LhsEval;
+ typedef typename evaluator<Lhs>::InnerIterator LhsIterator;
+ static void run(const Lhs& lhs, Rhs& other)
+ {
+ LhsEval lhsEval(lhs);
+ for(Index col=0 ; col<other.cols() ; ++col)
+ {
+ for(Index i=lhs.rows()-1 ; i>=0 ; --i)
+ {
+ Scalar tmp = other.coeff(i,col);
+ Scalar l_ii(0);
+ LhsIterator it(lhsEval, i);
+ while(it && it.index()<i)
+ ++it;
+ if(!(Mode & UnitDiag))
+ {
+ eigen_assert(it && it.index()==i);
+ l_ii = it.value();
+ ++it;
+ }
+ else if (it && it.index() == i)
+ ++it;
+ for(; it; ++it)
+ {
+ tmp -= it.value() * other.coeff(it.index(),col);
+ }
+
+ if (Mode & UnitDiag) other.coeffRef(i,col) = tmp;
+ else other.coeffRef(i,col) = tmp/l_ii;
+ }
+ }
+ }
+};
+
+// forward substitution, col-major
+template<typename Lhs, typename Rhs, int Mode>
+struct sparse_solve_triangular_selector<Lhs,Rhs,Mode,Lower,ColMajor>
+{
+ typedef typename Rhs::Scalar Scalar;
+ typedef evaluator<Lhs> LhsEval;
+ typedef typename evaluator<Lhs>::InnerIterator LhsIterator;
+ static void run(const Lhs& lhs, Rhs& other)
+ {
+ LhsEval lhsEval(lhs);
+ for(Index col=0 ; col<other.cols() ; ++col)
+ {
+ for(Index i=0; i<lhs.cols(); ++i)
+ {
+ Scalar& tmp = other.coeffRef(i,col);
+ if (!numext::is_exactly_zero(tmp)) // optimization when other is actually sparse
+ {
+ LhsIterator it(lhsEval, i);
+ while(it && it.index()<i)
+ ++it;
+ if(!(Mode & UnitDiag))
+ {
+ eigen_assert(it && it.index()==i);
+ tmp /= it.value();
+ }
+ if (it && it.index()==i)
+ ++it;
+ for(; it; ++it)
+ other.coeffRef(it.index(), col) -= tmp * it.value();
+ }
+ }
+ }
+ }
+};
+
+// backward substitution, col-major
+template<typename Lhs, typename Rhs, int Mode>
+struct sparse_solve_triangular_selector<Lhs,Rhs,Mode,Upper,ColMajor>
+{
+ typedef typename Rhs::Scalar Scalar;
+ typedef evaluator<Lhs> LhsEval;
+ typedef typename evaluator<Lhs>::InnerIterator LhsIterator;
+ static void run(const Lhs& lhs, Rhs& other)
+ {
+ LhsEval lhsEval(lhs);
+ for(Index col=0 ; col<other.cols() ; ++col)
+ {
+ for(Index i=lhs.cols()-1; i>=0; --i)
+ {
+ Scalar& tmp = other.coeffRef(i,col);
+ if (!numext::is_exactly_zero(tmp)) // optimization when other is actually sparse
+ {
+ if(!(Mode & UnitDiag))
+ {
+ // TODO replace this by a binary search. make sure the binary search is safe for partially sorted elements
+ LhsIterator it(lhsEval, i);
+ while(it && it.index()!=i)
+ ++it;
+ eigen_assert(it && it.index()==i);
+ other.coeffRef(i,col) /= it.value();
+ }
+ LhsIterator it(lhsEval, i);
+ for(; it && it.index()<i; ++it)
+ other.coeffRef(it.index(), col) -= tmp * it.value();
+ }
+ }
+ }
+ }
+};
+
+} // end namespace internal
+
+#ifndef EIGEN_PARSED_BY_DOXYGEN
+
+template<typename ExpressionType,unsigned int Mode>
+template<typename OtherDerived>
+void TriangularViewImpl<ExpressionType,Mode,Sparse>::solveInPlace(MatrixBase<OtherDerived>& other) const
+{
+ eigen_assert(derived().cols() == derived().rows() && derived().cols() == other.rows());
+ eigen_assert((!(Mode & ZeroDiag)) && bool(Mode & (Upper|Lower)));
+
+ enum { copy = internal::traits<OtherDerived>::Flags & RowMajorBit };
+
+ typedef std::conditional_t<copy,
+ typename internal::plain_matrix_type_column_major<OtherDerived>::type, OtherDerived&> OtherCopy;
+ OtherCopy otherCopy(other.derived());
+
+ internal::sparse_solve_triangular_selector<ExpressionType, std::remove_reference_t<OtherCopy>, Mode>::run(derived().nestedExpression(), otherCopy);
+
+ if (copy)
+ other = otherCopy;
+}
+#endif
+
+// pure sparse path
+
+namespace internal {
+
+template<typename Lhs, typename Rhs, int Mode,
+ int UpLo = (Mode & Lower)
+ ? Lower
+ : (Mode & Upper)
+ ? Upper
+ : -1,
+ int StorageOrder = int(Lhs::Flags) & (RowMajorBit)>
+struct sparse_solve_triangular_sparse_selector;
+
+// forward substitution, col-major
+template<typename Lhs, typename Rhs, int Mode, int UpLo>
+struct sparse_solve_triangular_sparse_selector<Lhs,Rhs,Mode,UpLo,ColMajor>
+{
+ typedef typename Rhs::Scalar Scalar;
+ typedef typename promote_index_type<typename traits<Lhs>::StorageIndex,
+ typename traits<Rhs>::StorageIndex>::type StorageIndex;
+ static void run(const Lhs& lhs, Rhs& other)
+ {
+ const bool IsLower = (UpLo==Lower);
+ AmbiVector<Scalar,StorageIndex> tempVector(other.rows()*2);
+ tempVector.setBounds(0,other.rows());
+
+ Rhs res(other.rows(), other.cols());
+ res.reserve(other.nonZeros());
+
+ for(Index col=0 ; col<other.cols() ; ++col)
+ {
+ // FIXME estimate number of non zeros
+ tempVector.init(.99/*float(other.col(col).nonZeros())/float(other.rows())*/);
+ tempVector.setZero();
+ tempVector.restart();
+ for (typename Rhs::InnerIterator rhsIt(other, col); rhsIt; ++rhsIt)
+ {
+ tempVector.coeffRef(rhsIt.index()) = rhsIt.value();
+ }
+
+ for(Index i=IsLower?0:lhs.cols()-1;
+ IsLower?i<lhs.cols():i>=0;
+ i+=IsLower?1:-1)
+ {
+ tempVector.restart();
+ Scalar& ci = tempVector.coeffRef(i);
+ if (!numext::is_exactly_zero(ci))
+ {
+ // find
+ typename Lhs::InnerIterator it(lhs, i);
+ if(!(Mode & UnitDiag))
+ {
+ if (IsLower)
+ {
+ eigen_assert(it.index()==i);
+ ci /= it.value();
+ }
+ else
+ ci /= lhs.coeff(i,i);
+ }
+ tempVector.restart();
+ if (IsLower)
+ {
+ if (it.index()==i)
+ ++it;
+ for(; it; ++it)
+ tempVector.coeffRef(it.index()) -= ci * it.value();
+ }
+ else
+ {
+ for(; it && it.index()<i; ++it)
+ tempVector.coeffRef(it.index()) -= ci * it.value();
+ }
+ }
+ }
+
+
+// Index count = 0;
+ // FIXME compute a reference value to filter zeros
+ for (typename AmbiVector<Scalar,StorageIndex>::Iterator it(tempVector/*,1e-12*/); it; ++it)
+ {
+// ++ count;
+// std::cerr << "fill " << it.index() << ", " << col << "\n";
+// std::cout << it.value() << " ";
+ // FIXME use insertBack
+ res.insert(it.index(), col) = it.value();
+ }
+// std::cout << "tempVector.nonZeros() == " << int(count) << " / " << (other.rows()) << "\n";
+ }
+ res.finalize();
+ other = res.markAsRValue();
+ }
+};
+
+} // end namespace internal
+
+#ifndef EIGEN_PARSED_BY_DOXYGEN
+template<typename ExpressionType,unsigned int Mode>
+template<typename OtherDerived>
+void TriangularViewImpl<ExpressionType,Mode,Sparse>::solveInPlace(SparseMatrixBase<OtherDerived>& other) const
+{
+ eigen_assert(derived().cols() == derived().rows() && derived().cols() == other.rows());
+ eigen_assert( (!(Mode & ZeroDiag)) && bool(Mode & (Upper|Lower)));
+
+// enum { copy = internal::traits<OtherDerived>::Flags & RowMajorBit };
+
+// typedef std::conditional_t<copy,
+// typename internal::plain_matrix_type_column_major<OtherDerived>::type, OtherDerived&> OtherCopy;
+// OtherCopy otherCopy(other.derived());
+
+ internal::sparse_solve_triangular_sparse_selector<ExpressionType, OtherDerived, Mode>::run(derived().nestedExpression(), other.derived());
+
+// if (copy)
+// other = otherCopy;
+}
+#endif
+
+} // end namespace Eigen
+
+#endif // EIGEN_SPARSETRIANGULARSOLVER_H
diff --git a/Eigen/src/SparseLU/InternalHeaderCheck.h b/Eigen/src/SparseLU/InternalHeaderCheck.h
new file mode 100644
index 0000000..78ebfcc
--- /dev/null
+++ b/Eigen/src/SparseLU/InternalHeaderCheck.h
@@ -0,0 +1,3 @@
+#ifndef EIGEN_SPARSELU_MODULE_H
+#error "Please include Eigen/SparseLU instead of including headers inside the src directory directly."
+#endif
diff --git a/Eigen/src/SparseLU/SparseLU.h b/Eigen/src/SparseLU/SparseLU.h
new file mode 100644
index 0000000..9fd7e25
--- /dev/null
+++ b/Eigen/src/SparseLU/SparseLU.h
@@ -0,0 +1,979 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2012 Désiré Nuentsa-Wakam <desire.nuentsa_wakam@inria.fr>
+// Copyright (C) 2012-2014 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+
+#ifndef EIGEN_SPARSE_LU_H
+#define EIGEN_SPARSE_LU_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+template <typename MatrixType_, typename OrderingType_ = COLAMDOrdering<typename MatrixType_::StorageIndex> > class SparseLU;
+template <typename MappedSparseMatrixType> struct SparseLUMatrixLReturnType;
+template <typename MatrixLType, typename MatrixUType> struct SparseLUMatrixUReturnType;
+
+template <bool Conjugate,class SparseLUType>
+class SparseLUTransposeView : public SparseSolverBase<SparseLUTransposeView<Conjugate,SparseLUType> >
+{
+protected:
+ typedef SparseSolverBase<SparseLUTransposeView<Conjugate,SparseLUType> > APIBase;
+ using APIBase::m_isInitialized;
+public:
+ typedef typename SparseLUType::Scalar Scalar;
+ typedef typename SparseLUType::StorageIndex StorageIndex;
+ typedef typename SparseLUType::MatrixType MatrixType;
+ typedef typename SparseLUType::OrderingType OrderingType;
+
+ enum {
+ ColsAtCompileTime = MatrixType::ColsAtCompileTime,
+ MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime
+ };
+
+ SparseLUTransposeView() : m_sparseLU(NULL) {}
+ SparseLUTransposeView(const SparseLUTransposeView& view) {
+ this->m_sparseLU = view.m_sparseLU;
+ }
+ void setIsInitialized(const bool isInitialized) {this->m_isInitialized = isInitialized;}
+ void setSparseLU(SparseLUType* sparseLU) {m_sparseLU = sparseLU;}
+ using APIBase::_solve_impl;
+ template<typename Rhs, typename Dest>
+ bool _solve_impl(const MatrixBase<Rhs> &B, MatrixBase<Dest> &X_base) const
+ {
+ Dest& X(X_base.derived());
+ eigen_assert(m_sparseLU->info() == Success && "The matrix should be factorized first");
+ EIGEN_STATIC_ASSERT((Dest::Flags&RowMajorBit)==0,
+ THIS_METHOD_IS_ONLY_FOR_COLUMN_MAJOR_MATRICES);
+
+
+ // this ugly const_cast_derived() helps to detect aliasing when applying the permutations
+ for(Index j = 0; j < B.cols(); ++j){
+ X.col(j) = m_sparseLU->colsPermutation() * B.const_cast_derived().col(j);
+ }
+ //Forward substitution with transposed or adjoint of U
+ m_sparseLU->matrixU().template solveTransposedInPlace<Conjugate>(X);
+
+ //Backward substitution with transposed or adjoint of L
+ m_sparseLU->matrixL().template solveTransposedInPlace<Conjugate>(X);
+
+ // Permute back the solution
+ for (Index j = 0; j < B.cols(); ++j)
+ X.col(j) = m_sparseLU->rowsPermutation().transpose() * X.col(j);
+ return true;
+ }
+ inline Index rows() const { return m_sparseLU->rows(); }
+ inline Index cols() const { return m_sparseLU->cols(); }
+
+private:
+ SparseLUType *m_sparseLU;
+ SparseLUTransposeView& operator=(const SparseLUTransposeView&);
+};
+
+
+/** \ingroup SparseLU_Module
+ * \class SparseLU
+ *
+ * \brief Sparse supernodal LU factorization for general matrices
+ *
+ * This class implements the supernodal LU factorization for general matrices.
+ * It uses the main techniques from the sequential SuperLU package
+ * (http://crd-legacy.lbl.gov/~xiaoye/SuperLU/). It handles transparently real
+ * and complex arithmetic with single and double precision, depending on the
+ * scalar type of your input matrix.
+ * The code has been optimized to provide BLAS-3 operations during supernode-panel updates.
+ * It benefits directly from the built-in high-performant Eigen BLAS routines.
+ * Moreover, when the size of a supernode is very small, the BLAS calls are avoided to
+ * enable a better optimization from the compiler. For best performance,
+ * you should compile it with NDEBUG flag to avoid the numerous bounds checking on vectors.
+ *
+ * An important parameter of this class is the ordering method. It is used to reorder the columns
+ * (and eventually the rows) of the matrix to reduce the number of new elements that are created during
+ * numerical factorization. The cheapest method available is COLAMD.
+ * See \link OrderingMethods_Module the OrderingMethods module \endlink for the list of
+ * built-in and external ordering methods.
+ *
+ * Simple example with key steps
+ * \code
+ * VectorXd x(n), b(n);
+ * SparseMatrix<double> A;
+ * SparseLU<SparseMatrix<double>, COLAMDOrdering<int> > solver;
+ * // fill A and b;
+ * // Compute the ordering permutation vector from the structural pattern of A
+ * solver.analyzePattern(A);
+ * // Compute the numerical factorization
+ * solver.factorize(A);
+ * //Use the factors to solve the linear system
+ * x = solver.solve(b);
+ * \endcode
+ *
+ * \warning The input matrix A should be in a \b compressed and \b column-major form.
+ * Otherwise an expensive copy will be made. You can call the inexpensive makeCompressed() to get a compressed matrix.
+ *
+ * \note Unlike the initial SuperLU implementation, there is no step to equilibrate the matrix.
+ * For badly scaled matrices, this step can be useful to reduce the pivoting during factorization.
+ * If this is the case for your matrices, you can try the basic scaling method at
+ * "unsupported/Eigen/src/IterativeSolvers/Scaling.h"
+ *
+ * \tparam MatrixType_ The type of the sparse matrix. It must be a column-major SparseMatrix<>
+ * \tparam OrderingType_ The ordering method to use, either AMD, COLAMD or METIS. Default is COLMAD
+ *
+ * \implsparsesolverconcept
+ *
+ * \sa \ref TutorialSparseSolverConcept
+ * \sa \ref OrderingMethods_Module
+ */
+template <typename MatrixType_, typename OrderingType_>
+class SparseLU : public SparseSolverBase<SparseLU<MatrixType_,OrderingType_> >, public internal::SparseLUImpl<typename MatrixType_::Scalar, typename MatrixType_::StorageIndex>
+{
+ protected:
+ typedef SparseSolverBase<SparseLU<MatrixType_,OrderingType_> > APIBase;
+ using APIBase::m_isInitialized;
+ public:
+ using APIBase::_solve_impl;
+
+ typedef MatrixType_ MatrixType;
+ typedef OrderingType_ OrderingType;
+ typedef typename MatrixType::Scalar Scalar;
+ typedef typename MatrixType::RealScalar RealScalar;
+ typedef typename MatrixType::StorageIndex StorageIndex;
+ typedef SparseMatrix<Scalar,ColMajor,StorageIndex> NCMatrix;
+ typedef internal::MappedSuperNodalMatrix<Scalar, StorageIndex> SCMatrix;
+ typedef Matrix<Scalar,Dynamic,1> ScalarVector;
+ typedef Matrix<StorageIndex,Dynamic,1> IndexVector;
+ typedef PermutationMatrix<Dynamic, Dynamic, StorageIndex> PermutationType;
+ typedef internal::SparseLUImpl<Scalar, StorageIndex> Base;
+
+ enum {
+ ColsAtCompileTime = MatrixType::ColsAtCompileTime,
+ MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime
+ };
+
+ public:
+
+ SparseLU():m_lastError(""),m_Ustore(0,0,0,0,0,0),m_symmetricmode(false),m_diagpivotthresh(1.0),m_detPermR(1)
+ {
+ initperfvalues();
+ }
+ explicit SparseLU(const MatrixType& matrix)
+ : m_lastError(""),m_Ustore(0,0,0,0,0,0),m_symmetricmode(false),m_diagpivotthresh(1.0),m_detPermR(1)
+ {
+ initperfvalues();
+ compute(matrix);
+ }
+
+ ~SparseLU()
+ {
+ // Free all explicit dynamic pointers
+ }
+
+ void analyzePattern (const MatrixType& matrix);
+ void factorize (const MatrixType& matrix);
+ void simplicialfactorize(const MatrixType& matrix);
+
+ /**
+ * Compute the symbolic and numeric factorization of the input sparse matrix.
+ * The input matrix should be in column-major storage.
+ */
+ void compute (const MatrixType& matrix)
+ {
+ // Analyze
+ analyzePattern(matrix);
+ //Factorize
+ factorize(matrix);
+ }
+
+ /** \returns an expression of the transposed of the factored matrix.
+ *
+ * A typical usage is to solve for the transposed problem A^T x = b:
+ * \code
+ * solver.compute(A);
+ * x = solver.transpose().solve(b);
+ * \endcode
+ *
+ * \sa adjoint(), solve()
+ */
+ const SparseLUTransposeView<false,SparseLU<MatrixType_,OrderingType_> > transpose()
+ {
+ SparseLUTransposeView<false, SparseLU<MatrixType_,OrderingType_> > transposeView;
+ transposeView.setSparseLU(this);
+ transposeView.setIsInitialized(this->m_isInitialized);
+ return transposeView;
+ }
+
+
+ /** \returns an expression of the adjoint of the factored matrix
+ *
+ * A typical usage is to solve for the adjoint problem A' x = b:
+ * \code
+ * solver.compute(A);
+ * x = solver.adjoint().solve(b);
+ * \endcode
+ *
+ * For real scalar types, this function is equivalent to transpose().
+ *
+ * \sa transpose(), solve()
+ */
+ const SparseLUTransposeView<true, SparseLU<MatrixType_,OrderingType_> > adjoint()
+ {
+ SparseLUTransposeView<true, SparseLU<MatrixType_,OrderingType_> > adjointView;
+ adjointView.setSparseLU(this);
+ adjointView.setIsInitialized(this->m_isInitialized);
+ return adjointView;
+ }
+
+ inline Index rows() const { return m_mat.rows(); }
+ inline Index cols() const { return m_mat.cols(); }
+ /** Indicate that the pattern of the input matrix is symmetric */
+ void isSymmetric(bool sym)
+ {
+ m_symmetricmode = sym;
+ }
+
+ /** \returns an expression of the matrix L, internally stored as supernodes
+ * The only operation available with this expression is the triangular solve
+ * \code
+ * y = b; matrixL().solveInPlace(y);
+ * \endcode
+ */
+ SparseLUMatrixLReturnType<SCMatrix> matrixL() const
+ {
+ return SparseLUMatrixLReturnType<SCMatrix>(m_Lstore);
+ }
+ /** \returns an expression of the matrix U,
+ * The only operation available with this expression is the triangular solve
+ * \code
+ * y = b; matrixU().solveInPlace(y);
+ * \endcode
+ */
+ SparseLUMatrixUReturnType<SCMatrix,Map<SparseMatrix<Scalar,ColMajor,StorageIndex> > > matrixU() const
+ {
+ return SparseLUMatrixUReturnType<SCMatrix, Map<SparseMatrix<Scalar,ColMajor,StorageIndex> > >(m_Lstore, m_Ustore);
+ }
+
+ /**
+ * \returns a reference to the row matrix permutation \f$ P_r \f$ such that \f$P_r A P_c^T = L U\f$
+ * \sa colsPermutation()
+ */
+ inline const PermutationType& rowsPermutation() const
+ {
+ return m_perm_r;
+ }
+ /**
+ * \returns a reference to the column matrix permutation\f$ P_c^T \f$ such that \f$P_r A P_c^T = L U\f$
+ * \sa rowsPermutation()
+ */
+ inline const PermutationType& colsPermutation() const
+ {
+ return m_perm_c;
+ }
+ /** Set the threshold used for a diagonal entry to be an acceptable pivot. */
+ void setPivotThreshold(const RealScalar& thresh)
+ {
+ m_diagpivotthresh = thresh;
+ }
+
+#ifdef EIGEN_PARSED_BY_DOXYGEN
+ /** \returns the solution X of \f$ A X = B \f$ using the current decomposition of A.
+ *
+ * \warning the destination matrix X in X = this->solve(B) must be colmun-major.
+ *
+ * \sa compute()
+ */
+ template<typename Rhs>
+ inline const Solve<SparseLU, Rhs> solve(const MatrixBase<Rhs>& B) const;
+#endif // EIGEN_PARSED_BY_DOXYGEN
+
+ /** \brief Reports whether previous computation was successful.
+ *
+ * \returns \c Success if computation was successful,
+ * \c NumericalIssue if the LU factorization reports a problem, zero diagonal for instance
+ * \c InvalidInput if the input matrix is invalid
+ *
+ * \sa iparm()
+ */
+ ComputationInfo info() const
+ {
+ eigen_assert(m_isInitialized && "Decomposition is not initialized.");
+ return m_info;
+ }
+
+ /**
+ * \returns A string describing the type of error
+ */
+ std::string lastErrorMessage() const
+ {
+ return m_lastError;
+ }
+
+ template<typename Rhs, typename Dest>
+ bool _solve_impl(const MatrixBase<Rhs> &B, MatrixBase<Dest> &X_base) const
+ {
+ Dest& X(X_base.derived());
+ eigen_assert(m_factorizationIsOk && "The matrix should be factorized first");
+ EIGEN_STATIC_ASSERT((Dest::Flags&RowMajorBit)==0,
+ THIS_METHOD_IS_ONLY_FOR_COLUMN_MAJOR_MATRICES);
+
+ // Permute the right hand side to form X = Pr*B
+ // on return, X is overwritten by the computed solution
+ X.resize(B.rows(),B.cols());
+
+ // this ugly const_cast_derived() helps to detect aliasing when applying the permutations
+ for(Index j = 0; j < B.cols(); ++j)
+ X.col(j) = rowsPermutation() * B.const_cast_derived().col(j);
+
+ //Forward substitution with L
+ this->matrixL().solveInPlace(X);
+ this->matrixU().solveInPlace(X);
+
+ // Permute back the solution
+ for (Index j = 0; j < B.cols(); ++j)
+ X.col(j) = colsPermutation().inverse() * X.col(j);
+
+ return true;
+ }
+
+ /**
+ * \returns the absolute value of the determinant of the matrix of which
+ * *this is the QR decomposition.
+ *
+ * \warning a determinant can be very big or small, so for matrices
+ * of large enough dimension, there is a risk of overflow/underflow.
+ * One way to work around that is to use logAbsDeterminant() instead.
+ *
+ * \sa logAbsDeterminant(), signDeterminant()
+ */
+ Scalar absDeterminant()
+ {
+ using std::abs;
+ eigen_assert(m_factorizationIsOk && "The matrix should be factorized first.");
+ // Initialize with the determinant of the row matrix
+ Scalar det = Scalar(1.);
+ // Note that the diagonal blocks of U are stored in supernodes,
+ // which are available in the L part :)
+ for (Index j = 0; j < this->cols(); ++j)
+ {
+ for (typename SCMatrix::InnerIterator it(m_Lstore, j); it; ++it)
+ {
+ if(it.index() == j)
+ {
+ det *= abs(it.value());
+ break;
+ }
+ }
+ }
+ return det;
+ }
+
+ /** \returns the natural log of the absolute value of the determinant of the matrix
+ * of which **this is the QR decomposition
+ *
+ * \note This method is useful to work around the risk of overflow/underflow that's
+ * inherent to the determinant computation.
+ *
+ * \sa absDeterminant(), signDeterminant()
+ */
+ Scalar logAbsDeterminant() const
+ {
+ using std::log;
+ using std::abs;
+
+ eigen_assert(m_factorizationIsOk && "The matrix should be factorized first.");
+ Scalar det = Scalar(0.);
+ for (Index j = 0; j < this->cols(); ++j)
+ {
+ for (typename SCMatrix::InnerIterator it(m_Lstore, j); it; ++it)
+ {
+ if(it.row() < j) continue;
+ if(it.row() == j)
+ {
+ det += log(abs(it.value()));
+ break;
+ }
+ }
+ }
+ return det;
+ }
+
+ /** \returns A number representing the sign of the determinant
+ *
+ * \sa absDeterminant(), logAbsDeterminant()
+ */
+ Scalar signDeterminant()
+ {
+ eigen_assert(m_factorizationIsOk && "The matrix should be factorized first.");
+ // Initialize with the determinant of the row matrix
+ Index det = 1;
+ // Note that the diagonal blocks of U are stored in supernodes,
+ // which are available in the L part :)
+ for (Index j = 0; j < this->cols(); ++j)
+ {
+ for (typename SCMatrix::InnerIterator it(m_Lstore, j); it; ++it)
+ {
+ if(it.index() == j)
+ {
+ if(it.value()<0)
+ det = -det;
+ else if(it.value()==0)
+ return 0;
+ break;
+ }
+ }
+ }
+ return det * m_detPermR * m_detPermC;
+ }
+
+ /** \returns The determinant of the matrix.
+ *
+ * \sa absDeterminant(), logAbsDeterminant()
+ */
+ Scalar determinant()
+ {
+ eigen_assert(m_factorizationIsOk && "The matrix should be factorized first.");
+ // Initialize with the determinant of the row matrix
+ Scalar det = Scalar(1.);
+ // Note that the diagonal blocks of U are stored in supernodes,
+ // which are available in the L part :)
+ for (Index j = 0; j < this->cols(); ++j)
+ {
+ for (typename SCMatrix::InnerIterator it(m_Lstore, j); it; ++it)
+ {
+ if(it.index() == j)
+ {
+ det *= it.value();
+ break;
+ }
+ }
+ }
+ return (m_detPermR * m_detPermC) > 0 ? det : -det;
+ }
+
+ Index nnzL() const { return m_nnzL; }
+ Index nnzU() const { return m_nnzU; }
+
+ protected:
+ // Functions
+ void initperfvalues()
+ {
+ m_perfv.panel_size = 16;
+ m_perfv.relax = 1;
+ m_perfv.maxsuper = 128;
+ m_perfv.rowblk = 16;
+ m_perfv.colblk = 8;
+ m_perfv.fillfactor = 20;
+ }
+
+ // Variables
+ mutable ComputationInfo m_info;
+ bool m_factorizationIsOk;
+ bool m_analysisIsOk;
+ std::string m_lastError;
+ NCMatrix m_mat; // The input (permuted ) matrix
+ SCMatrix m_Lstore; // The lower triangular matrix (supernodal)
+ Map<SparseMatrix<Scalar,ColMajor,StorageIndex>> m_Ustore; // The upper triangular matrix
+ PermutationType m_perm_c; // Column permutation
+ PermutationType m_perm_r ; // Row permutation
+ IndexVector m_etree; // Column elimination tree
+
+ typename Base::GlobalLU_t m_glu;
+
+ // SparseLU options
+ bool m_symmetricmode;
+ // values for performance
+ internal::perfvalues m_perfv;
+ RealScalar m_diagpivotthresh; // Specifies the threshold used for a diagonal entry to be an acceptable pivot
+ Index m_nnzL, m_nnzU; // Nonzeros in L and U factors
+ Index m_detPermR, m_detPermC; // Determinants of the permutation matrices
+ private:
+ // Disable copy constructor
+ SparseLU (const SparseLU& );
+}; // End class SparseLU
+
+
+
+// Functions needed by the anaysis phase
+/**
+ * Compute the column permutation to minimize the fill-in
+ *
+ * - Apply this permutation to the input matrix -
+ *
+ * - Compute the column elimination tree on the permuted matrix
+ *
+ * - Postorder the elimination tree and the column permutation
+ *
+ */
+template <typename MatrixType, typename OrderingType>
+void SparseLU<MatrixType, OrderingType>::analyzePattern(const MatrixType& mat)
+{
+
+ //TODO It is possible as in SuperLU to compute row and columns scaling vectors to equilibrate the matrix mat.
+
+ // Firstly, copy the whole input matrix.
+ m_mat = mat;
+
+ // Compute fill-in ordering
+ OrderingType ord;
+ ord(m_mat,m_perm_c);
+
+ // Apply the permutation to the column of the input matrix
+ if (m_perm_c.size())
+ {
+ m_mat.uncompress(); //NOTE: The effect of this command is only to create the InnerNonzeros pointers. FIXME : This vector is filled but not subsequently used.
+ // Then, permute only the column pointers
+ ei_declare_aligned_stack_constructed_variable(StorageIndex,outerIndexPtr,mat.cols()+1,mat.isCompressed()?const_cast<StorageIndex*>(mat.outerIndexPtr()):0);
+
+ // If the input matrix 'mat' is uncompressed, then the outer-indices do not match the ones of m_mat, and a copy is thus needed.
+ if(!mat.isCompressed())
+ IndexVector::Map(outerIndexPtr, mat.cols()+1) = IndexVector::Map(m_mat.outerIndexPtr(),mat.cols()+1);
+
+ // Apply the permutation and compute the nnz per column.
+ for (Index i = 0; i < mat.cols(); i++)
+ {
+ m_mat.outerIndexPtr()[m_perm_c.indices()(i)] = outerIndexPtr[i];
+ m_mat.innerNonZeroPtr()[m_perm_c.indices()(i)] = outerIndexPtr[i+1] - outerIndexPtr[i];
+ }
+ }
+
+ // Compute the column elimination tree of the permuted matrix
+ IndexVector firstRowElt;
+ internal::coletree(m_mat, m_etree,firstRowElt);
+
+ // In symmetric mode, do not do postorder here
+ if (!m_symmetricmode) {
+ IndexVector post, iwork;
+ // Post order etree
+ internal::treePostorder(StorageIndex(m_mat.cols()), m_etree, post);
+
+
+ // Renumber etree in postorder
+ Index m = m_mat.cols();
+ iwork.resize(m+1);
+ for (Index i = 0; i < m; ++i) iwork(post(i)) = post(m_etree(i));
+ m_etree = iwork;
+
+ // Postmultiply A*Pc by post, i.e reorder the matrix according to the postorder of the etree
+ PermutationType post_perm(m);
+ for (Index i = 0; i < m; i++)
+ post_perm.indices()(i) = post(i);
+
+ // Combine the two permutations : postorder the permutation for future use
+ if(m_perm_c.size()) {
+ m_perm_c = post_perm * m_perm_c;
+ }
+
+ } // end postordering
+
+ m_analysisIsOk = true;
+}
+
+// Functions needed by the numerical factorization phase
+
+
+/**
+ * - Numerical factorization
+ * - Interleaved with the symbolic factorization
+ * On exit, info is
+ *
+ * = 0: successful factorization
+ *
+ * > 0: if info = i, and i is
+ *
+ * <= A->ncol: U(i,i) is exactly zero. The factorization has
+ * been completed, but the factor U is exactly singular,
+ * and division by zero will occur if it is used to solve a
+ * system of equations.
+ *
+ * > A->ncol: number of bytes allocated when memory allocation
+ * failure occurred, plus A->ncol. If lwork = -1, it is
+ * the estimated amount of space needed, plus A->ncol.
+ */
+template <typename MatrixType, typename OrderingType>
+void SparseLU<MatrixType, OrderingType>::factorize(const MatrixType& matrix)
+{
+ using internal::emptyIdxLU;
+ eigen_assert(m_analysisIsOk && "analyzePattern() should be called first");
+ eigen_assert((matrix.rows() == matrix.cols()) && "Only for squared matrices");
+
+ m_isInitialized = true;
+
+ // Apply the column permutation computed in analyzepattern()
+ // m_mat = matrix * m_perm_c.inverse();
+ m_mat = matrix;
+ if (m_perm_c.size())
+ {
+ m_mat.uncompress(); //NOTE: The effect of this command is only to create the InnerNonzeros pointers.
+ //Then, permute only the column pointers
+ const StorageIndex * outerIndexPtr;
+ if (matrix.isCompressed()) outerIndexPtr = matrix.outerIndexPtr();
+ else
+ {
+ StorageIndex* outerIndexPtr_t = new StorageIndex[matrix.cols()+1];
+ for(Index i = 0; i <= matrix.cols(); i++) outerIndexPtr_t[i] = m_mat.outerIndexPtr()[i];
+ outerIndexPtr = outerIndexPtr_t;
+ }
+ for (Index i = 0; i < matrix.cols(); i++)
+ {
+ m_mat.outerIndexPtr()[m_perm_c.indices()(i)] = outerIndexPtr[i];
+ m_mat.innerNonZeroPtr()[m_perm_c.indices()(i)] = outerIndexPtr[i+1] - outerIndexPtr[i];
+ }
+ if(!matrix.isCompressed()) delete[] outerIndexPtr;
+ }
+ else
+ { //FIXME This should not be needed if the empty permutation is handled transparently
+ m_perm_c.resize(matrix.cols());
+ for(StorageIndex i = 0; i < matrix.cols(); ++i) m_perm_c.indices()(i) = i;
+ }
+
+ Index m = m_mat.rows();
+ Index n = m_mat.cols();
+ Index nnz = m_mat.nonZeros();
+ Index maxpanel = m_perfv.panel_size * m;
+ // Allocate working storage common to the factor routines
+ Index lwork = 0;
+ Index info = Base::memInit(m, n, nnz, lwork, m_perfv.fillfactor, m_perfv.panel_size, m_glu);
+ if (info)
+ {
+ m_lastError = "UNABLE TO ALLOCATE WORKING MEMORY\n\n" ;
+ m_factorizationIsOk = false;
+ return ;
+ }
+
+ // Set up pointers for integer working arrays
+ IndexVector segrep(m); segrep.setZero();
+ IndexVector parent(m); parent.setZero();
+ IndexVector xplore(m); xplore.setZero();
+ IndexVector repfnz(maxpanel);
+ IndexVector panel_lsub(maxpanel);
+ IndexVector xprune(n); xprune.setZero();
+ IndexVector marker(m*internal::LUNoMarker); marker.setZero();
+
+ repfnz.setConstant(-1);
+ panel_lsub.setConstant(-1);
+
+ // Set up pointers for scalar working arrays
+ ScalarVector dense;
+ dense.setZero(maxpanel);
+ ScalarVector tempv;
+ tempv.setZero(internal::LUnumTempV(m, m_perfv.panel_size, m_perfv.maxsuper, /*m_perfv.rowblk*/m) );
+
+ // Compute the inverse of perm_c
+ PermutationType iperm_c(m_perm_c.inverse());
+
+ // Identify initial relaxed snodes
+ IndexVector relax_end(n);
+ if ( m_symmetricmode == true )
+ Base::heap_relax_snode(n, m_etree, m_perfv.relax, marker, relax_end);
+ else
+ Base::relax_snode(n, m_etree, m_perfv.relax, marker, relax_end);
+
+
+ m_perm_r.resize(m);
+ m_perm_r.indices().setConstant(-1);
+ marker.setConstant(-1);
+ m_detPermR = 1; // Record the determinant of the row permutation
+
+ m_glu.supno(0) = emptyIdxLU; m_glu.xsup.setConstant(0);
+ m_glu.xsup(0) = m_glu.xlsub(0) = m_glu.xusub(0) = m_glu.xlusup(0) = Index(0);
+
+ // Work on one 'panel' at a time. A panel is one of the following :
+ // (a) a relaxed supernode at the bottom of the etree, or
+ // (b) panel_size contiguous columns, <panel_size> defined by the user
+ Index jcol;
+ Index pivrow; // Pivotal row number in the original row matrix
+ Index nseg1; // Number of segments in U-column above panel row jcol
+ Index nseg; // Number of segments in each U-column
+ Index irep;
+ Index i, k, jj;
+ for (jcol = 0; jcol < n; )
+ {
+ // Adjust panel size so that a panel won't overlap with the next relaxed snode.
+ Index panel_size = m_perfv.panel_size; // upper bound on panel width
+ for (k = jcol + 1; k < (std::min)(jcol+panel_size, n); k++)
+ {
+ if (relax_end(k) != emptyIdxLU)
+ {
+ panel_size = k - jcol;
+ break;
+ }
+ }
+ if (k == n)
+ panel_size = n - jcol;
+
+ // Symbolic outer factorization on a panel of columns
+ Base::panel_dfs(m, panel_size, jcol, m_mat, m_perm_r.indices(), nseg1, dense, panel_lsub, segrep, repfnz, xprune, marker, parent, xplore, m_glu);
+
+ // Numeric sup-panel updates in topological order
+ Base::panel_bmod(m, panel_size, jcol, nseg1, dense, tempv, segrep, repfnz, m_glu);
+
+ // Sparse LU within the panel, and below the panel diagonal
+ for ( jj = jcol; jj< jcol + panel_size; jj++)
+ {
+ k = (jj - jcol) * m; // Column index for w-wide arrays
+
+ nseg = nseg1; // begin after all the panel segments
+ //Depth-first-search for the current column
+ VectorBlock<IndexVector> panel_lsubk(panel_lsub, k, m);
+ VectorBlock<IndexVector> repfnz_k(repfnz, k, m);
+ info = Base::column_dfs(m, jj, m_perm_r.indices(), m_perfv.maxsuper, nseg, panel_lsubk, segrep, repfnz_k, xprune, marker, parent, xplore, m_glu);
+ if ( info )
+ {
+ m_lastError = "UNABLE TO EXPAND MEMORY IN COLUMN_DFS() ";
+ m_info = NumericalIssue;
+ m_factorizationIsOk = false;
+ return;
+ }
+ // Numeric updates to this column
+ VectorBlock<ScalarVector> dense_k(dense, k, m);
+ VectorBlock<IndexVector> segrep_k(segrep, nseg1, m-nseg1);
+ info = Base::column_bmod(jj, (nseg - nseg1), dense_k, tempv, segrep_k, repfnz_k, jcol, m_glu);
+ if ( info )
+ {
+ m_lastError = "UNABLE TO EXPAND MEMORY IN COLUMN_BMOD() ";
+ m_info = NumericalIssue;
+ m_factorizationIsOk = false;
+ return;
+ }
+
+ // Copy the U-segments to ucol(*)
+ info = Base::copy_to_ucol(jj, nseg, segrep, repfnz_k ,m_perm_r.indices(), dense_k, m_glu);
+ if ( info )
+ {
+ m_lastError = "UNABLE TO EXPAND MEMORY IN COPY_TO_UCOL() ";
+ m_info = NumericalIssue;
+ m_factorizationIsOk = false;
+ return;
+ }
+
+ // Form the L-segment
+ info = Base::pivotL(jj, m_diagpivotthresh, m_perm_r.indices(), iperm_c.indices(), pivrow, m_glu);
+ if ( info )
+ {
+ m_lastError = "THE MATRIX IS STRUCTURALLY SINGULAR";
+#ifndef EIGEN_NO_IO
+ std::ostringstream returnInfo;
+ returnInfo << " ... ZERO COLUMN AT ";
+ returnInfo << info;
+ m_lastError += returnInfo.str();
+#endif
+ m_info = NumericalIssue;
+ m_factorizationIsOk = false;
+ return;
+ }
+
+ // Update the determinant of the row permutation matrix
+ // FIXME: the following test is not correct, we should probably take iperm_c into account and pivrow is not directly the row pivot.
+ if (pivrow != jj) m_detPermR = -m_detPermR;
+
+ // Prune columns (0:jj-1) using column jj
+ Base::pruneL(jj, m_perm_r.indices(), pivrow, nseg, segrep, repfnz_k, xprune, m_glu);
+
+ // Reset repfnz for this column
+ for (i = 0; i < nseg; i++)
+ {
+ irep = segrep(i);
+ repfnz_k(irep) = emptyIdxLU;
+ }
+ } // end SparseLU within the panel
+ jcol += panel_size; // Move to the next panel
+ } // end for -- end elimination
+
+ m_detPermR = m_perm_r.determinant();
+ m_detPermC = m_perm_c.determinant();
+
+ // Count the number of nonzeros in factors
+ Base::countnz(n, m_nnzL, m_nnzU, m_glu);
+ // Apply permutation to the L subscripts
+ Base::fixupL(n, m_perm_r.indices(), m_glu);
+
+ // Create supernode matrix L
+ m_Lstore.setInfos(m, n, m_glu.lusup, m_glu.xlusup, m_glu.lsub, m_glu.xlsub, m_glu.supno, m_glu.xsup);
+ // Create the column major upper sparse matrix U;
+ new (&m_Ustore) Map<SparseMatrix<Scalar, ColMajor, StorageIndex>> ( m, n, m_nnzU, m_glu.xusub.data(), m_glu.usub.data(), m_glu.ucol.data() );
+
+ m_info = Success;
+ m_factorizationIsOk = true;
+}
+
+template<typename MappedSupernodalType>
+struct SparseLUMatrixLReturnType : internal::no_assignment_operator
+{
+ typedef typename MappedSupernodalType::Scalar Scalar;
+ explicit SparseLUMatrixLReturnType(const MappedSupernodalType& mapL) : m_mapL(mapL)
+ { }
+ Index rows() const { return m_mapL.rows(); }
+ Index cols() const { return m_mapL.cols(); }
+ template<typename Dest>
+ void solveInPlace( MatrixBase<Dest> &X) const
+ {
+ m_mapL.solveInPlace(X);
+ }
+ template<bool Conjugate, typename Dest>
+ void solveTransposedInPlace( MatrixBase<Dest> &X) const
+ {
+ m_mapL.template solveTransposedInPlace<Conjugate>(X);
+ }
+
+ SparseMatrix<Scalar, ColMajor, Index> toSparse() const {
+ ArrayXi colCount = ArrayXi::Ones(cols());
+ for (Index i = 0; i < cols(); i++) {
+ typename MappedSupernodalType::InnerIterator iter(m_mapL, i);
+ for (; iter; ++iter) {
+ if (iter.row() > iter.col()) {
+ colCount(iter.col())++;
+ }
+ }
+ }
+ SparseMatrix<Scalar, ColMajor, Index> sL(rows(), cols());
+ sL.reserve(colCount);
+ for (Index i = 0; i < cols(); i++) {
+ sL.insert(i, i) = 1.0;
+ typename MappedSupernodalType::InnerIterator iter(m_mapL, i);
+ for (; iter; ++iter) {
+ if (iter.row() > iter.col()) {
+ sL.insert(iter.row(), iter.col()) = iter.value();
+ }
+ }
+ }
+ sL.makeCompressed();
+ return sL;
+ }
+
+ const MappedSupernodalType& m_mapL;
+};
+
+template<typename MatrixLType, typename MatrixUType>
+struct SparseLUMatrixUReturnType : internal::no_assignment_operator
+{
+ typedef typename MatrixLType::Scalar Scalar;
+ SparseLUMatrixUReturnType(const MatrixLType& mapL, const MatrixUType& mapU)
+ : m_mapL(mapL),m_mapU(mapU)
+ { }
+ Index rows() const { return m_mapL.rows(); }
+ Index cols() const { return m_mapL.cols(); }
+
+ template<typename Dest> void solveInPlace(MatrixBase<Dest> &X) const
+ {
+ Index nrhs = X.cols();
+ Index n = X.rows();
+ // Backward solve with U
+ for (Index k = m_mapL.nsuper(); k >= 0; k--)
+ {
+ Index fsupc = m_mapL.supToCol()[k];
+ Index lda = m_mapL.colIndexPtr()[fsupc+1] - m_mapL.colIndexPtr()[fsupc]; // leading dimension
+ Index nsupc = m_mapL.supToCol()[k+1] - fsupc;
+ Index luptr = m_mapL.colIndexPtr()[fsupc];
+
+ if (nsupc == 1)
+ {
+ for (Index j = 0; j < nrhs; j++)
+ {
+ X(fsupc, j) /= m_mapL.valuePtr()[luptr];
+ }
+ }
+ else
+ {
+ // FIXME: the following lines should use Block expressions and not Map!
+ Map<const Matrix<Scalar,Dynamic,Dynamic, ColMajor>, 0, OuterStride<> > A( &(m_mapL.valuePtr()[luptr]), nsupc, nsupc, OuterStride<>(lda) );
+ Map< Matrix<Scalar,Dynamic,Dest::ColsAtCompileTime, ColMajor>, 0, OuterStride<> > U (&(X.coeffRef(fsupc,0)), nsupc, nrhs, OuterStride<>(n) );
+ U = A.template triangularView<Upper>().solve(U);
+ }
+
+ for (Index j = 0; j < nrhs; ++j)
+ {
+ for (Index jcol = fsupc; jcol < fsupc + nsupc; jcol++)
+ {
+ typename MatrixUType::InnerIterator it(m_mapU, jcol);
+ for ( ; it; ++it)
+ {
+ Index irow = it.index();
+ X(irow, j) -= X(jcol, j) * it.value();
+ }
+ }
+ }
+ } // End For U-solve
+ }
+
+ template<bool Conjugate, typename Dest> void solveTransposedInPlace(MatrixBase<Dest> &X) const
+ {
+ using numext::conj;
+ Index nrhs = X.cols();
+ Index n = X.rows();
+ // Forward solve with U
+ for (Index k = 0; k <= m_mapL.nsuper(); k++)
+ {
+ Index fsupc = m_mapL.supToCol()[k];
+ Index lda = m_mapL.colIndexPtr()[fsupc+1] - m_mapL.colIndexPtr()[fsupc]; // leading dimension
+ Index nsupc = m_mapL.supToCol()[k+1] - fsupc;
+ Index luptr = m_mapL.colIndexPtr()[fsupc];
+
+ for (Index j = 0; j < nrhs; ++j)
+ {
+ for (Index jcol = fsupc; jcol < fsupc + nsupc; jcol++)
+ {
+ typename MatrixUType::InnerIterator it(m_mapU, jcol);
+ for ( ; it; ++it)
+ {
+ Index irow = it.index();
+ X(jcol, j) -= X(irow, j) * (Conjugate? conj(it.value()): it.value());
+ }
+ }
+ }
+ if (nsupc == 1)
+ {
+ for (Index j = 0; j < nrhs; j++)
+ {
+ X(fsupc, j) /= (Conjugate? conj(m_mapL.valuePtr()[luptr]) : m_mapL.valuePtr()[luptr]);
+ }
+ }
+ else
+ {
+ Map<const Matrix<Scalar,Dynamic,Dynamic, ColMajor>, 0, OuterStride<> > A( &(m_mapL.valuePtr()[luptr]), nsupc, nsupc, OuterStride<>(lda) );
+ Map< Matrix<Scalar,Dynamic,Dest::ColsAtCompileTime, ColMajor>, 0, OuterStride<> > U (&(X(fsupc,0)), nsupc, nrhs, OuterStride<>(n) );
+ if(Conjugate)
+ U = A.adjoint().template triangularView<Lower>().solve(U);
+ else
+ U = A.transpose().template triangularView<Lower>().solve(U);
+ }
+ }// End For U-solve
+ }
+
+ SparseMatrix<Scalar, RowMajor, Index> toSparse() {
+ ArrayXi rowCount = ArrayXi::Zero(rows());
+ for (Index i = 0; i < cols(); i++) {
+ typename MatrixLType::InnerIterator iter(m_mapL, i);
+ for (; iter; ++iter) {
+ if (iter.row() <= iter.col()) {
+ rowCount(iter.row())++;
+ }
+ }
+ }
+
+ SparseMatrix<Scalar, RowMajor, Index> sU(rows(), cols());
+ sU.reserve(rowCount);
+ for (Index i = 0; i < cols(); i++) {
+ typename MatrixLType::InnerIterator iter(m_mapL, i);
+ for (; iter; ++iter) {
+ if (iter.row() <= iter.col()) {
+ sU.insert(iter.row(), iter.col()) = iter.value();
+ }
+ }
+ }
+ sU.makeCompressed();
+ const SparseMatrix<Scalar, RowMajor, Index> u = m_mapU; // convert to RowMajor
+ sU += u;
+ return sU;
+ }
+
+ const MatrixLType& m_mapL;
+ const MatrixUType& m_mapU;
+};
+
+} // End namespace Eigen
+
+#endif
diff --git a/Eigen/src/SparseLU/SparseLUImpl.h b/Eigen/src/SparseLU/SparseLUImpl.h
new file mode 100644
index 0000000..daec837
--- /dev/null
+++ b/Eigen/src/SparseLU/SparseLUImpl.h
@@ -0,0 +1,68 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2012 Désiré Nuentsa-Wakam <desire.nuentsa_wakam@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+#ifndef SPARSELU_IMPL_H
+#define SPARSELU_IMPL_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+namespace internal {
+
+/** \ingroup SparseLU_Module
+ * \class SparseLUImpl
+ * Base class for sparseLU
+ */
+template <typename Scalar, typename StorageIndex>
+class SparseLUImpl
+{
+ public:
+ typedef Matrix<Scalar,Dynamic,1> ScalarVector;
+ typedef Matrix<StorageIndex,Dynamic,1> IndexVector;
+ typedef Matrix<Scalar,Dynamic,Dynamic,ColMajor> ScalarMatrix;
+ typedef Map<ScalarMatrix, 0, OuterStride<> > MappedMatrixBlock;
+ typedef typename ScalarVector::RealScalar RealScalar;
+ typedef Ref<Matrix<Scalar,Dynamic,1> > BlockScalarVector;
+ typedef Ref<Matrix<StorageIndex,Dynamic,1> > BlockIndexVector;
+ typedef LU_GlobalLU_t<IndexVector, ScalarVector> GlobalLU_t;
+ typedef SparseMatrix<Scalar,ColMajor,StorageIndex> MatrixType;
+
+ protected:
+ template <typename VectorType>
+ Index expand(VectorType& vec, Index& length, Index nbElts, Index keep_prev, Index& num_expansions);
+ Index memInit(Index m, Index n, Index annz, Index lwork, Index fillratio, Index panel_size, GlobalLU_t& glu);
+ template <typename VectorType>
+ Index memXpand(VectorType& vec, Index& maxlen, Index nbElts, MemType memtype, Index& num_expansions);
+ void heap_relax_snode (const Index n, IndexVector& et, const Index relax_columns, IndexVector& descendants, IndexVector& relax_end);
+ void relax_snode (const Index n, IndexVector& et, const Index relax_columns, IndexVector& descendants, IndexVector& relax_end);
+ Index snode_dfs(const Index jcol, const Index kcol,const MatrixType& mat, IndexVector& xprune, IndexVector& marker, GlobalLU_t& glu);
+ Index snode_bmod (const Index jcol, const Index fsupc, ScalarVector& dense, GlobalLU_t& glu);
+ Index pivotL(const Index jcol, const RealScalar& diagpivotthresh, IndexVector& perm_r, IndexVector& iperm_c, Index& pivrow, GlobalLU_t& glu);
+ template <typename Traits>
+ void dfs_kernel(const StorageIndex jj, IndexVector& perm_r,
+ Index& nseg, IndexVector& panel_lsub, IndexVector& segrep,
+ Ref<IndexVector> repfnz_col, IndexVector& xprune, Ref<IndexVector> marker, IndexVector& parent,
+ IndexVector& xplore, GlobalLU_t& glu, Index& nextl_col, Index krow, Traits& traits);
+ void panel_dfs(const Index m, const Index w, const Index jcol, MatrixType& A, IndexVector& perm_r, Index& nseg, ScalarVector& dense, IndexVector& panel_lsub, IndexVector& segrep, IndexVector& repfnz, IndexVector& xprune, IndexVector& marker, IndexVector& parent, IndexVector& xplore, GlobalLU_t& glu);
+
+ void panel_bmod(const Index m, const Index w, const Index jcol, const Index nseg, ScalarVector& dense, ScalarVector& tempv, IndexVector& segrep, IndexVector& repfnz, GlobalLU_t& glu);
+ Index column_dfs(const Index m, const Index jcol, IndexVector& perm_r, Index maxsuper, Index& nseg, BlockIndexVector lsub_col, IndexVector& segrep, BlockIndexVector repfnz, IndexVector& xprune, IndexVector& marker, IndexVector& parent, IndexVector& xplore, GlobalLU_t& glu);
+ Index column_bmod(const Index jcol, const Index nseg, BlockScalarVector dense, ScalarVector& tempv, BlockIndexVector segrep, BlockIndexVector repfnz, Index fpanelc, GlobalLU_t& glu);
+ Index copy_to_ucol(const Index jcol, const Index nseg, IndexVector& segrep, BlockIndexVector repfnz ,IndexVector& perm_r, BlockScalarVector dense, GlobalLU_t& glu);
+ void pruneL(const Index jcol, const IndexVector& perm_r, const Index pivrow, const Index nseg, const IndexVector& segrep, BlockIndexVector repfnz, IndexVector& xprune, GlobalLU_t& glu);
+ void countnz(const Index n, Index& nnzL, Index& nnzU, GlobalLU_t& glu);
+ void fixupL(const Index n, const IndexVector& perm_r, GlobalLU_t& glu);
+
+ template<typename , typename >
+ friend struct column_dfs_traits;
+};
+
+} // end namespace internal
+} // namespace Eigen
+
+#endif
diff --git a/Eigen/src/SparseLU/SparseLU_Memory.h b/Eigen/src/SparseLU/SparseLU_Memory.h
new file mode 100644
index 0000000..798745f
--- /dev/null
+++ b/Eigen/src/SparseLU/SparseLU_Memory.h
@@ -0,0 +1,228 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2012 Désiré Nuentsa-Wakam <desire.nuentsa_wakam@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+/*
+
+ * NOTE: This file is the modified version of [s,d,c,z]memory.c files in SuperLU
+
+ * -- SuperLU routine (version 3.1) --
+ * Univ. of California Berkeley, Xerox Palo Alto Research Center,
+ * and Lawrence Berkeley National Lab.
+ * August 1, 2008
+ *
+ * Copyright (c) 1994 by Xerox Corporation. All rights reserved.
+ *
+ * THIS MATERIAL IS PROVIDED AS IS, WITH ABSOLUTELY NO WARRANTY
+ * EXPRESSED OR IMPLIED. ANY USE IS AT YOUR OWN RISK.
+ *
+ * Permission is hereby granted to use or copy this program for any
+ * purpose, provided the above notices are retained on all copies.
+ * Permission to modify the code and to distribute modified code is
+ * granted, provided the above notices are retained, and a notice that
+ * the code was modified is included with the above copyright notice.
+ */
+
+#ifndef EIGEN_SPARSELU_MEMORY
+#define EIGEN_SPARSELU_MEMORY
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+namespace internal {
+
+enum { LUNoMarker = 3 };
+enum {emptyIdxLU = -1};
+inline Index LUnumTempV(Index& m, Index& w, Index& t, Index& b)
+{
+ return (std::max)(m, (t+b)*w);
+}
+
+template< typename Scalar>
+inline Index LUTempSpace(Index&m, Index& w)
+{
+ return (2*w + 4 + LUNoMarker) * m * sizeof(Index) + (w + 1) * m * sizeof(Scalar);
+}
+
+
+
+
+/**
+ * Expand the existing storage to accommodate more fill-ins
+ * \param vec Valid pointer to the vector to allocate or expand
+ * \param[in,out] length At input, contain the current length of the vector that is to be increased. At output, length of the newly allocated vector
+ * \param[in] nbElts Current number of elements in the factors
+ * \param keep_prev 1: use length and do not expand the vector; 0: compute new_len and expand
+ * \param[in,out] num_expansions Number of times the memory has been expanded
+ */
+template <typename Scalar, typename StorageIndex>
+template <typename VectorType>
+Index SparseLUImpl<Scalar,StorageIndex>::expand(VectorType& vec, Index& length, Index nbElts, Index keep_prev, Index& num_expansions)
+{
+
+ float alpha = 1.5; // Ratio of the memory increase
+ Index new_len; // New size of the allocated memory
+
+ if(num_expansions == 0 || keep_prev)
+ new_len = length ; // First time allocate requested
+ else
+ new_len = (std::max)(length+1,Index(alpha * length));
+
+ VectorType old_vec; // Temporary vector to hold the previous values
+ if (nbElts > 0 )
+ old_vec = vec.segment(0,nbElts);
+
+ //Allocate or expand the current vector
+#ifdef EIGEN_EXCEPTIONS
+ try
+#endif
+ {
+ vec.resize(new_len);
+ }
+#ifdef EIGEN_EXCEPTIONS
+ catch(std::bad_alloc& )
+#else
+ if(!vec.size())
+#endif
+ {
+ if (!num_expansions)
+ {
+ // First time to allocate from LUMemInit()
+ // Let LUMemInit() deals with it.
+ return -1;
+ }
+ if (keep_prev)
+ {
+ // In this case, the memory length should not not be reduced
+ return new_len;
+ }
+ else
+ {
+ // Reduce the size and increase again
+ Index tries = 0; // Number of attempts
+ do
+ {
+ alpha = (alpha + 1)/2;
+ new_len = (std::max)(length+1,Index(alpha * length));
+#ifdef EIGEN_EXCEPTIONS
+ try
+#endif
+ {
+ vec.resize(new_len);
+ }
+#ifdef EIGEN_EXCEPTIONS
+ catch(std::bad_alloc& )
+#else
+ if (!vec.size())
+#endif
+ {
+ tries += 1;
+ if ( tries > 10) return new_len;
+ }
+ } while (!vec.size());
+ }
+ }
+ //Copy the previous values to the newly allocated space
+ if (nbElts > 0)
+ vec.segment(0, nbElts) = old_vec;
+
+
+ length = new_len;
+ if(num_expansions) ++num_expansions;
+ return 0;
+}
+
+/**
+ * \brief Allocate various working space for the numerical factorization phase.
+ * \param m number of rows of the input matrix
+ * \param n number of columns
+ * \param annz number of initial nonzeros in the matrix
+ * \param lwork if lwork=-1, this routine returns an estimated size of the required memory
+ * \param glu persistent data to facilitate multiple factors : will be deleted later ??
+ * \param fillratio estimated ratio of fill in the factors
+ * \param panel_size Size of a panel
+ * \return an estimated size of the required memory if lwork = -1; otherwise, return the size of actually allocated memory when allocation failed, and 0 on success
+ * \note Unlike SuperLU, this routine does not support successive factorization with the same pattern and the same row permutation
+ */
+template <typename Scalar, typename StorageIndex>
+Index SparseLUImpl<Scalar,StorageIndex>::memInit(Index m, Index n, Index annz, Index lwork, Index fillratio, Index panel_size, GlobalLU_t& glu)
+{
+ Index& num_expansions = glu.num_expansions; //No memory expansions so far
+ num_expansions = 0;
+ glu.nzumax = glu.nzlumax = (std::min)(fillratio * (annz+1) / n, m) * n; // estimated number of nonzeros in U
+ glu.nzlmax = (std::max)(Index(4), fillratio) * (annz+1) / 4; // estimated nnz in L factor
+ // Return the estimated size to the user if necessary
+ Index tempSpace;
+ tempSpace = (2*panel_size + 4 + LUNoMarker) * m * sizeof(Index) + (panel_size + 1) * m * sizeof(Scalar);
+ if (lwork == emptyIdxLU)
+ {
+ Index estimated_size;
+ estimated_size = (5 * n + 5) * sizeof(Index) + tempSpace
+ + (glu.nzlmax + glu.nzumax) * sizeof(Index) + (glu.nzlumax+glu.nzumax) * sizeof(Scalar) + n;
+ return estimated_size;
+ }
+
+ // Setup the required space
+
+ // First allocate Integer pointers for L\U factors
+ glu.xsup.resize(n+1);
+ glu.supno.resize(n+1);
+ glu.xlsub.resize(n+1);
+ glu.xlusup.resize(n+1);
+ glu.xusub.resize(n+1);
+
+ // Reserve memory for L/U factors
+ do
+ {
+ if( (expand<ScalarVector>(glu.lusup, glu.nzlumax, 0, 0, num_expansions)<0)
+ || (expand<ScalarVector>(glu.ucol, glu.nzumax, 0, 0, num_expansions)<0)
+ || (expand<IndexVector> (glu.lsub, glu.nzlmax, 0, 0, num_expansions)<0)
+ || (expand<IndexVector> (glu.usub, glu.nzumax, 0, 1, num_expansions)<0) )
+ {
+ //Reduce the estimated size and retry
+ glu.nzlumax /= 2;
+ glu.nzumax /= 2;
+ glu.nzlmax /= 2;
+ if (glu.nzlumax < annz ) return glu.nzlumax;
+ }
+ } while (!glu.lusup.size() || !glu.ucol.size() || !glu.lsub.size() || !glu.usub.size());
+
+ ++num_expansions;
+ return 0;
+
+} // end LuMemInit
+
+/**
+ * \brief Expand the existing storage
+ * \param vec vector to expand
+ * \param[in,out] maxlen On input, previous size of vec (Number of elements to copy ). on output, new size
+ * \param nbElts current number of elements in the vector.
+ * \param memtype Type of the element to expand
+ * \param num_expansions Number of expansions
+ * \return 0 on success, > 0 size of the memory allocated so far
+ */
+template <typename Scalar, typename StorageIndex>
+template <typename VectorType>
+Index SparseLUImpl<Scalar,StorageIndex>::memXpand(VectorType& vec, Index& maxlen, Index nbElts, MemType memtype, Index& num_expansions)
+{
+ Index failed_size;
+ if (memtype == USUB)
+ failed_size = this->expand<VectorType>(vec, maxlen, nbElts, 1, num_expansions);
+ else
+ failed_size = this->expand<VectorType>(vec, maxlen, nbElts, 0, num_expansions);
+
+ if (failed_size)
+ return failed_size;
+
+ return 0 ;
+}
+
+} // end namespace internal
+
+} // end namespace Eigen
+#endif // EIGEN_SPARSELU_MEMORY
diff --git a/Eigen/src/SparseLU/SparseLU_Structs.h b/Eigen/src/SparseLU/SparseLU_Structs.h
new file mode 100644
index 0000000..3ab0c72
--- /dev/null
+++ b/Eigen/src/SparseLU/SparseLU_Structs.h
@@ -0,0 +1,112 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2012 Désiré Nuentsa-Wakam <desire.nuentsa_wakam@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+/*
+ * NOTE: This file comes from a partly modified version of files slu_[s,d,c,z]defs.h
+ * -- SuperLU routine (version 4.1) --
+ * Univ. of California Berkeley, Xerox Palo Alto Research Center,
+ * and Lawrence Berkeley National Lab.
+ * November, 2010
+ *
+ * Global data structures used in LU factorization -
+ *
+ * nsuper: #supernodes = nsuper + 1, numbered [0, nsuper].
+ * (xsup,supno): supno[i] is the supernode no to which i belongs;
+ * xsup(s) points to the beginning of the s-th supernode.
+ * e.g. supno 0 1 2 2 3 3 3 4 4 4 4 4 (n=12)
+ * xsup 0 1 2 4 7 12
+ * Note: dfs will be performed on supernode rep. relative to the new
+ * row pivoting ordering
+ *
+ * (xlsub,lsub): lsub[*] contains the compressed subscript of
+ * rectangular supernodes; xlsub[j] points to the starting
+ * location of the j-th column in lsub[*]. Note that xlsub
+ * is indexed by column.
+ * Storage: original row subscripts
+ *
+ * During the course of sparse LU factorization, we also use
+ * (xlsub,lsub) for the purpose of symmetric pruning. For each
+ * supernode {s,s+1,...,t=s+r} with first column s and last
+ * column t, the subscript set
+ * lsub[j], j=xlsub[s], .., xlsub[s+1]-1
+ * is the structure of column s (i.e. structure of this supernode).
+ * It is used for the storage of numerical values.
+ * Furthermore,
+ * lsub[j], j=xlsub[t], .., xlsub[t+1]-1
+ * is the structure of the last column t of this supernode.
+ * It is for the purpose of symmetric pruning. Therefore, the
+ * structural subscripts can be rearranged without making physical
+ * interchanges among the numerical values.
+ *
+ * However, if the supernode has only one column, then we
+ * only keep one set of subscripts. For any subscript interchange
+ * performed, similar interchange must be done on the numerical
+ * values.
+ *
+ * The last column structures (for pruning) will be removed
+ * after the numercial LU factorization phase.
+ *
+ * (xlusup,lusup): lusup[*] contains the numerical values of the
+ * rectangular supernodes; xlusup[j] points to the starting
+ * location of the j-th column in storage vector lusup[*]
+ * Note: xlusup is indexed by column.
+ * Each rectangular supernode is stored by column-major
+ * scheme, consistent with Fortran 2-dim array storage.
+ *
+ * (xusub,ucol,usub): ucol[*] stores the numerical values of
+ * U-columns outside the rectangular supernodes. The row
+ * subscript of nonzero ucol[k] is stored in usub[k].
+ * xusub[i] points to the starting location of column i in ucol.
+ * Storage: new row subscripts; that is subscripts of PA.
+ */
+
+#ifndef EIGEN_LU_STRUCTS
+#define EIGEN_LU_STRUCTS
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+namespace internal {
+
+enum MemType {LUSUP, UCOL, LSUB, USUB, LLVL, ULVL};
+
+template <typename IndexVector, typename ScalarVector>
+struct LU_GlobalLU_t {
+ typedef typename IndexVector::Scalar StorageIndex;
+ IndexVector xsup; //First supernode column ... xsup(s) points to the beginning of the s-th supernode
+ IndexVector supno; // Supernode number corresponding to this column (column to supernode mapping)
+ ScalarVector lusup; // nonzero values of L ordered by columns
+ IndexVector lsub; // Compressed row indices of L rectangular supernodes.
+ IndexVector xlusup; // pointers to the beginning of each column in lusup
+ IndexVector xlsub; // pointers to the beginning of each column in lsub
+ Index nzlmax; // Current max size of lsub
+ Index nzlumax; // Current max size of lusup
+ ScalarVector ucol; // nonzero values of U ordered by columns
+ IndexVector usub; // row indices of U columns in ucol
+ IndexVector xusub; // Pointers to the beginning of each column of U in ucol
+ Index nzumax; // Current max size of ucol
+ Index n; // Number of columns in the matrix
+ Index num_expansions;
+};
+
+// Values to set for performance
+struct perfvalues {
+ Index panel_size; // a panel consists of at most <panel_size> consecutive columns
+ Index relax; // To control degree of relaxing supernodes. If the number of nodes (columns)
+ // in a subtree of the elimination tree is less than relax, this subtree is considered
+ // as one supernode regardless of the row structures of those columns
+ Index maxsuper; // The maximum size for a supernode in complete LU
+ Index rowblk; // The minimum row dimension for 2-D blocking to be used;
+ Index colblk; // The minimum column dimension for 2-D blocking to be used;
+ Index fillfactor; // The estimated fills factors for L and U, compared with A
+};
+
+} // end namespace internal
+
+} // end namespace Eigen
+#endif // EIGEN_LU_STRUCTS
diff --git a/Eigen/src/SparseLU/SparseLU_SupernodalMatrix.h b/Eigen/src/SparseLU/SparseLU_SupernodalMatrix.h
new file mode 100644
index 0000000..0d59a38
--- /dev/null
+++ b/Eigen/src/SparseLU/SparseLU_SupernodalMatrix.h
@@ -0,0 +1,377 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2012 Désiré Nuentsa-Wakam <desire.nuentsa_wakam@inria.fr>
+// Copyright (C) 2012 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_SPARSELU_SUPERNODAL_MATRIX_H
+#define EIGEN_SPARSELU_SUPERNODAL_MATRIX_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+namespace internal {
+
+/** \ingroup SparseLU_Module
+ * \brief a class to manipulate the L supernodal factor from the SparseLU factorization
+ *
+ * This class contain the data to easily store
+ * and manipulate the supernodes during the factorization and solution phase of Sparse LU.
+ * Only the lower triangular matrix has supernodes.
+ *
+ * NOTE : This class corresponds to the SCformat structure in SuperLU
+ *
+ */
+/* TODO
+ * InnerIterator as for sparsematrix
+ * SuperInnerIterator to iterate through all supernodes
+ * Function for triangular solve
+ */
+template <typename Scalar_, typename StorageIndex_>
+class MappedSuperNodalMatrix
+{
+ public:
+ typedef Scalar_ Scalar;
+ typedef StorageIndex_ StorageIndex;
+ typedef Matrix<StorageIndex,Dynamic,1> IndexVector;
+ typedef Matrix<Scalar,Dynamic,1> ScalarVector;
+ public:
+ MappedSuperNodalMatrix()
+ {
+
+ }
+ MappedSuperNodalMatrix(Index m, Index n, ScalarVector& nzval, IndexVector& nzval_colptr, IndexVector& rowind,
+ IndexVector& rowind_colptr, IndexVector& col_to_sup, IndexVector& sup_to_col )
+ {
+ setInfos(m, n, nzval, nzval_colptr, rowind, rowind_colptr, col_to_sup, sup_to_col);
+ }
+
+ ~MappedSuperNodalMatrix()
+ {
+
+ }
+ /**
+ * Set appropriate pointers for the lower triangular supernodal matrix
+ * These infos are available at the end of the numerical factorization
+ * FIXME This class will be modified such that it can be use in the course
+ * of the factorization.
+ */
+ void setInfos(Index m, Index n, ScalarVector& nzval, IndexVector& nzval_colptr, IndexVector& rowind,
+ IndexVector& rowind_colptr, IndexVector& col_to_sup, IndexVector& sup_to_col )
+ {
+ m_row = m;
+ m_col = n;
+ m_nzval = nzval.data();
+ m_nzval_colptr = nzval_colptr.data();
+ m_rowind = rowind.data();
+ m_rowind_colptr = rowind_colptr.data();
+ m_nsuper = col_to_sup(n);
+ m_col_to_sup = col_to_sup.data();
+ m_sup_to_col = sup_to_col.data();
+ }
+
+ /**
+ * Number of rows
+ */
+ Index rows() const { return m_row; }
+
+ /**
+ * Number of columns
+ */
+ Index cols() const { return m_col; }
+
+ /**
+ * Return the array of nonzero values packed by column
+ *
+ * The size is nnz
+ */
+ Scalar* valuePtr() { return m_nzval; }
+
+ const Scalar* valuePtr() const
+ {
+ return m_nzval;
+ }
+ /**
+ * Return the pointers to the beginning of each column in \ref valuePtr()
+ */
+ StorageIndex* colIndexPtr()
+ {
+ return m_nzval_colptr;
+ }
+
+ const StorageIndex* colIndexPtr() const
+ {
+ return m_nzval_colptr;
+ }
+
+ /**
+ * Return the array of compressed row indices of all supernodes
+ */
+ StorageIndex* rowIndex() { return m_rowind; }
+
+ const StorageIndex* rowIndex() const
+ {
+ return m_rowind;
+ }
+
+ /**
+ * Return the location in \em rowvaluePtr() which starts each column
+ */
+ StorageIndex* rowIndexPtr() { return m_rowind_colptr; }
+
+ const StorageIndex* rowIndexPtr() const
+ {
+ return m_rowind_colptr;
+ }
+
+ /**
+ * Return the array of column-to-supernode mapping
+ */
+ StorageIndex* colToSup() { return m_col_to_sup; }
+
+ const StorageIndex* colToSup() const
+ {
+ return m_col_to_sup;
+ }
+ /**
+ * Return the array of supernode-to-column mapping
+ */
+ StorageIndex* supToCol() { return m_sup_to_col; }
+
+ const StorageIndex* supToCol() const
+ {
+ return m_sup_to_col;
+ }
+
+ /**
+ * Return the number of supernodes
+ */
+ Index nsuper() const
+ {
+ return m_nsuper;
+ }
+
+ class InnerIterator;
+ template<typename Dest>
+ void solveInPlace( MatrixBase<Dest>&X) const;
+ template<bool Conjugate, typename Dest>
+ void solveTransposedInPlace( MatrixBase<Dest>&X) const;
+
+
+
+
+
+ protected:
+ Index m_row; // Number of rows
+ Index m_col; // Number of columns
+ Index m_nsuper; // Number of supernodes
+ Scalar* m_nzval; //array of nonzero values packed by column
+ StorageIndex* m_nzval_colptr; //nzval_colptr[j] Stores the location in nzval[] which starts column j
+ StorageIndex* m_rowind; // Array of compressed row indices of rectangular supernodes
+ StorageIndex* m_rowind_colptr; //rowind_colptr[j] stores the location in rowind[] which starts column j
+ StorageIndex* m_col_to_sup; // col_to_sup[j] is the supernode number to which column j belongs
+ StorageIndex* m_sup_to_col; //sup_to_col[s] points to the starting column of the s-th supernode
+
+ private :
+};
+
+/**
+ * \brief InnerIterator class to iterate over nonzero values of the current column in the supernodal matrix L
+ *
+ */
+template<typename Scalar, typename StorageIndex>
+class MappedSuperNodalMatrix<Scalar,StorageIndex>::InnerIterator
+{
+ public:
+ InnerIterator(const MappedSuperNodalMatrix& mat, Index outer)
+ : m_matrix(mat),
+ m_outer(outer),
+ m_supno(mat.colToSup()[outer]),
+ m_idval(mat.colIndexPtr()[outer]),
+ m_startidval(m_idval),
+ m_endidval(mat.colIndexPtr()[outer+1]),
+ m_idrow(mat.rowIndexPtr()[mat.supToCol()[mat.colToSup()[outer]]]),
+ m_endidrow(mat.rowIndexPtr()[mat.supToCol()[mat.colToSup()[outer]]+1])
+ {}
+ inline InnerIterator& operator++()
+ {
+ m_idval++;
+ m_idrow++;
+ return *this;
+ }
+ inline Scalar value() const { return m_matrix.valuePtr()[m_idval]; }
+
+ inline Scalar& valueRef() { return const_cast<Scalar&>(m_matrix.valuePtr()[m_idval]); }
+
+ inline Index index() const { return m_matrix.rowIndex()[m_idrow]; }
+ inline Index row() const { return index(); }
+ inline Index col() const { return m_outer; }
+
+ inline Index supIndex() const { return m_supno; }
+
+ inline operator bool() const
+ {
+ return ( (m_idval < m_endidval) && (m_idval >= m_startidval)
+ && (m_idrow < m_endidrow) );
+ }
+
+ protected:
+ const MappedSuperNodalMatrix& m_matrix; // Supernodal lower triangular matrix
+ const Index m_outer; // Current column
+ const Index m_supno; // Current SuperNode number
+ Index m_idval; // Index to browse the values in the current column
+ const Index m_startidval; // Start of the column value
+ const Index m_endidval; // End of the column value
+ Index m_idrow; // Index to browse the row indices
+ Index m_endidrow; // End index of row indices of the current column
+};
+
+/**
+ * \brief Solve with the supernode triangular matrix
+ *
+ */
+template<typename Scalar, typename Index_>
+template<typename Dest>
+void MappedSuperNodalMatrix<Scalar,Index_>::solveInPlace( MatrixBase<Dest>&X) const
+{
+ /* Explicit type conversion as the Index type of MatrixBase<Dest> may be wider than Index */
+// eigen_assert(X.rows() <= NumTraits<Index>::highest());
+// eigen_assert(X.cols() <= NumTraits<Index>::highest());
+ Index n = int(X.rows());
+ Index nrhs = Index(X.cols());
+ const Scalar * Lval = valuePtr(); // Nonzero values
+ Matrix<Scalar,Dynamic,Dest::ColsAtCompileTime, ColMajor> work(n, nrhs); // working vector
+ work.setZero();
+ for (Index k = 0; k <= nsuper(); k ++)
+ {
+ Index fsupc = supToCol()[k]; // First column of the current supernode
+ Index istart = rowIndexPtr()[fsupc]; // Pointer index to the subscript of the current column
+ Index nsupr = rowIndexPtr()[fsupc+1] - istart; // Number of rows in the current supernode
+ Index nsupc = supToCol()[k+1] - fsupc; // Number of columns in the current supernode
+ Index nrow = nsupr - nsupc; // Number of rows in the non-diagonal part of the supernode
+ Index irow; //Current index row
+
+ if (nsupc == 1 )
+ {
+ for (Index j = 0; j < nrhs; j++)
+ {
+ InnerIterator it(*this, fsupc);
+ ++it; // Skip the diagonal element
+ for (; it; ++it)
+ {
+ irow = it.row();
+ X(irow, j) -= X(fsupc, j) * it.value();
+ }
+ }
+ }
+ else
+ {
+ // The supernode has more than one column
+ Index luptr = colIndexPtr()[fsupc];
+ Index lda = colIndexPtr()[fsupc+1] - luptr;
+
+ // Triangular solve
+ Map<const Matrix<Scalar,Dynamic,Dynamic, ColMajor>, 0, OuterStride<> > A( &(Lval[luptr]), nsupc, nsupc, OuterStride<>(lda) );
+ Map< Matrix<Scalar,Dynamic,Dest::ColsAtCompileTime, ColMajor>, 0, OuterStride<> > U (&(X(fsupc,0)), nsupc, nrhs, OuterStride<>(n) );
+ U = A.template triangularView<UnitLower>().solve(U);
+
+ // Matrix-vector product
+ new (&A) Map<const Matrix<Scalar,Dynamic,Dynamic, ColMajor>, 0, OuterStride<> > ( &(Lval[luptr+nsupc]), nrow, nsupc, OuterStride<>(lda) );
+ work.topRows(nrow).noalias() = A * U;
+
+ //Begin Scatter
+ for (Index j = 0; j < nrhs; j++)
+ {
+ Index iptr = istart + nsupc;
+ for (Index i = 0; i < nrow; i++)
+ {
+ irow = rowIndex()[iptr];
+ X(irow, j) -= work(i, j); // Scatter operation
+ work(i, j) = Scalar(0);
+ iptr++;
+ }
+ }
+ }
+ }
+}
+
+template<typename Scalar, typename Index_>
+template<bool Conjugate, typename Dest>
+void MappedSuperNodalMatrix<Scalar,Index_>::solveTransposedInPlace( MatrixBase<Dest>&X) const
+{
+ using numext::conj;
+ Index n = int(X.rows());
+ Index nrhs = Index(X.cols());
+ const Scalar * Lval = valuePtr(); // Nonzero values
+ Matrix<Scalar,Dynamic,Dest::ColsAtCompileTime, ColMajor> work(n, nrhs); // working vector
+ work.setZero();
+ for (Index k = nsuper(); k >= 0; k--)
+ {
+ Index fsupc = supToCol()[k]; // First column of the current supernode
+ Index istart = rowIndexPtr()[fsupc]; // Pointer index to the subscript of the current column
+ Index nsupr = rowIndexPtr()[fsupc+1] - istart; // Number of rows in the current supernode
+ Index nsupc = supToCol()[k+1] - fsupc; // Number of columns in the current supernode
+ Index nrow = nsupr - nsupc; // Number of rows in the non-diagonal part of the supernode
+ Index irow; //Current index row
+
+ if (nsupc == 1 )
+ {
+ for (Index j = 0; j < nrhs; j++)
+ {
+ InnerIterator it(*this, fsupc);
+ ++it; // Skip the diagonal element
+ for (; it; ++it)
+ {
+ irow = it.row();
+ X(fsupc,j) -= X(irow, j) * (Conjugate?conj(it.value()):it.value());
+ }
+ }
+ }
+ else
+ {
+ // The supernode has more than one column
+ Index luptr = colIndexPtr()[fsupc];
+ Index lda = colIndexPtr()[fsupc+1] - luptr;
+
+ //Begin Gather
+ for (Index j = 0; j < nrhs; j++)
+ {
+ Index iptr = istart + nsupc;
+ for (Index i = 0; i < nrow; i++)
+ {
+ irow = rowIndex()[iptr];
+ work.topRows(nrow)(i,j)= X(irow,j); // Gather operation
+ iptr++;
+ }
+ }
+
+ // Matrix-vector product with transposed submatrix
+ Map<const Matrix<Scalar,Dynamic,Dynamic, ColMajor>, 0, OuterStride<> > A( &(Lval[luptr+nsupc]), nrow, nsupc, OuterStride<>(lda) );
+ Map< Matrix<Scalar,Dynamic,Dest::ColsAtCompileTime, ColMajor>, 0, OuterStride<> > U (&(X(fsupc,0)), nsupc, nrhs, OuterStride<>(n) );
+ if(Conjugate)
+ U = U - A.adjoint() * work.topRows(nrow);
+ else
+ U = U - A.transpose() * work.topRows(nrow);
+
+ // Triangular solve (of transposed diagonal block)
+ new (&A) Map<const Matrix<Scalar,Dynamic,Dynamic, ColMajor>, 0, OuterStride<> > ( &(Lval[luptr]), nsupc, nsupc, OuterStride<>(lda) );
+ if(Conjugate)
+ U = A.adjoint().template triangularView<UnitUpper>().solve(U);
+ else
+ U = A.transpose().template triangularView<UnitUpper>().solve(U);
+
+ }
+
+ }
+}
+
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_SPARSELU_MATRIX_H
diff --git a/Eigen/src/SparseLU/SparseLU_Utils.h b/Eigen/src/SparseLU/SparseLU_Utils.h
new file mode 100644
index 0000000..e399fed
--- /dev/null
+++ b/Eigen/src/SparseLU/SparseLU_Utils.h
@@ -0,0 +1,82 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2012 Désiré Nuentsa-Wakam <desire.nuentsa_wakam@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+
+#ifndef EIGEN_SPARSELU_UTILS_H
+#define EIGEN_SPARSELU_UTILS_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+namespace internal {
+
+/**
+ * \brief Count Nonzero elements in the factors
+ */
+template <typename Scalar, typename StorageIndex>
+void SparseLUImpl<Scalar,StorageIndex>::countnz(const Index n, Index& nnzL, Index& nnzU, GlobalLU_t& glu)
+{
+ nnzL = 0;
+ nnzU = (glu.xusub)(n);
+ Index nsuper = (glu.supno)(n);
+ Index jlen;
+ Index i, j, fsupc;
+ if (n <= 0 ) return;
+ // For each supernode
+ for (i = 0; i <= nsuper; i++)
+ {
+ fsupc = glu.xsup(i);
+ jlen = glu.xlsub(fsupc+1) - glu.xlsub(fsupc);
+
+ for (j = fsupc; j < glu.xsup(i+1); j++)
+ {
+ nnzL += jlen;
+ nnzU += j - fsupc + 1;
+ jlen--;
+ }
+ }
+}
+
+/**
+ * \brief Fix up the data storage lsub for L-subscripts.
+ *
+ * It removes the subscripts sets for structural pruning,
+ * and applies permutation to the remaining subscripts
+ *
+ */
+template <typename Scalar, typename StorageIndex>
+void SparseLUImpl<Scalar,StorageIndex>::fixupL(const Index n, const IndexVector& perm_r, GlobalLU_t& glu)
+{
+ Index fsupc, i, j, k, jstart;
+
+ StorageIndex nextl = 0;
+ Index nsuper = (glu.supno)(n);
+
+ // For each supernode
+ for (i = 0; i <= nsuper; i++)
+ {
+ fsupc = glu.xsup(i);
+ jstart = glu.xlsub(fsupc);
+ glu.xlsub(fsupc) = nextl;
+ for (j = jstart; j < glu.xlsub(fsupc + 1); j++)
+ {
+ glu.lsub(nextl) = perm_r(glu.lsub(j)); // Now indexed into P*A
+ nextl++;
+ }
+ for (k = fsupc+1; k < glu.xsup(i+1); k++)
+ glu.xlsub(k) = nextl; // other columns in supernode i
+ }
+
+ glu.xlsub(n) = nextl;
+}
+
+} // end namespace internal
+
+} // end namespace Eigen
+#endif // EIGEN_SPARSELU_UTILS_H
diff --git a/Eigen/src/SparseLU/SparseLU_column_bmod.h b/Eigen/src/SparseLU/SparseLU_column_bmod.h
new file mode 100644
index 0000000..d5c29b3
--- /dev/null
+++ b/Eigen/src/SparseLU/SparseLU_column_bmod.h
@@ -0,0 +1,183 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2012 Désiré Nuentsa-Wakam <desire.nuentsa_wakam@inria.fr>
+// Copyright (C) 2012 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+/*
+
+ * NOTE: This file is the modified version of xcolumn_bmod.c file in SuperLU
+
+ * -- SuperLU routine (version 3.0) --
+ * Univ. of California Berkeley, Xerox Palo Alto Research Center,
+ * and Lawrence Berkeley National Lab.
+ * October 15, 2003
+ *
+ * Copyright (c) 1994 by Xerox Corporation. All rights reserved.
+ *
+ * THIS MATERIAL IS PROVIDED AS IS, WITH ABSOLUTELY NO WARRANTY
+ * EXPRESSED OR IMPLIED. ANY USE IS AT YOUR OWN RISK.
+ *
+ * Permission is hereby granted to use or copy this program for any
+ * purpose, provided the above notices are retained on all copies.
+ * Permission to modify the code and to distribute modified code is
+ * granted, provided the above notices are retained, and a notice that
+ * the code was modified is included with the above copyright notice.
+ */
+#ifndef SPARSELU_COLUMN_BMOD_H
+#define SPARSELU_COLUMN_BMOD_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+/**
+ * \brief Performs numeric block updates (sup-col) in topological order
+ *
+ * \param jcol current column to update
+ * \param nseg Number of segments in the U part
+ * \param dense Store the full representation of the column
+ * \param tempv working array
+ * \param segrep segment representative ...
+ * \param repfnz ??? First nonzero column in each row ??? ...
+ * \param fpanelc First column in the current panel
+ * \param glu Global LU data.
+ * \return 0 - successful return
+ * > 0 - number of bytes allocated when run out of space
+ *
+ */
+template <typename Scalar, typename StorageIndex>
+Index SparseLUImpl<Scalar,StorageIndex>::column_bmod(const Index jcol, const Index nseg, BlockScalarVector dense, ScalarVector& tempv,
+ BlockIndexVector segrep, BlockIndexVector repfnz, Index fpanelc, GlobalLU_t& glu)
+{
+ Index jsupno, k, ksub, krep, ksupno;
+ Index lptr, nrow, isub, irow, nextlu, new_next, ufirst;
+ Index fsupc, nsupc, nsupr, luptr, kfnz, no_zeros;
+ /* krep = representative of current k-th supernode
+ * fsupc = first supernodal column
+ * nsupc = number of columns in a supernode
+ * nsupr = number of rows in a supernode
+ * luptr = location of supernodal LU-block in storage
+ * kfnz = first nonz in the k-th supernodal segment
+ * no_zeros = no lf leading zeros in a supernodal U-segment
+ */
+
+ jsupno = glu.supno(jcol);
+ // For each nonzero supernode segment of U[*,j] in topological order
+ k = nseg - 1;
+ Index d_fsupc; // distance between the first column of the current panel and the
+ // first column of the current snode
+ Index fst_col; // First column within small LU update
+ Index segsize;
+ for (ksub = 0; ksub < nseg; ksub++)
+ {
+ krep = segrep(k); k--;
+ ksupno = glu.supno(krep);
+ if (jsupno != ksupno )
+ {
+ // outside the rectangular supernode
+ fsupc = glu.xsup(ksupno);
+ fst_col = (std::max)(fsupc, fpanelc);
+
+ // Distance from the current supernode to the current panel;
+ // d_fsupc = 0 if fsupc > fpanelc
+ d_fsupc = fst_col - fsupc;
+
+ luptr = glu.xlusup(fst_col) + d_fsupc;
+ lptr = glu.xlsub(fsupc) + d_fsupc;
+
+ kfnz = repfnz(krep);
+ kfnz = (std::max)(kfnz, fpanelc);
+
+ segsize = krep - kfnz + 1;
+ nsupc = krep - fst_col + 1;
+ nsupr = glu.xlsub(fsupc+1) - glu.xlsub(fsupc);
+ nrow = nsupr - d_fsupc - nsupc;
+ Index lda = glu.xlusup(fst_col+1) - glu.xlusup(fst_col);
+
+
+ // Perform a triangular solver and block update,
+ // then scatter the result of sup-col update to dense
+ no_zeros = kfnz - fst_col;
+ if(segsize==1)
+ LU_kernel_bmod<1>::run(segsize, dense, tempv, glu.lusup, luptr, lda, nrow, glu.lsub, lptr, no_zeros);
+ else
+ LU_kernel_bmod<Dynamic>::run(segsize, dense, tempv, glu.lusup, luptr, lda, nrow, glu.lsub, lptr, no_zeros);
+ } // end if jsupno
+ } // end for each segment
+
+ // Process the supernodal portion of L\U[*,j]
+ nextlu = glu.xlusup(jcol);
+ fsupc = glu.xsup(jsupno);
+
+ // copy the SPA dense into L\U[*,j]
+ Index mem;
+ new_next = nextlu + glu.xlsub(fsupc + 1) - glu.xlsub(fsupc);
+ Index offset = internal::first_multiple<Index>(new_next, internal::packet_traits<Scalar>::size) - new_next;
+ if(offset)
+ new_next += offset;
+ while (new_next > glu.nzlumax )
+ {
+ mem = memXpand<ScalarVector>(glu.lusup, glu.nzlumax, nextlu, LUSUP, glu.num_expansions);
+ if (mem) return mem;
+ }
+
+ for (isub = glu.xlsub(fsupc); isub < glu.xlsub(fsupc+1); isub++)
+ {
+ irow = glu.lsub(isub);
+ glu.lusup(nextlu) = dense(irow);
+ dense(irow) = Scalar(0.0);
+ ++nextlu;
+ }
+
+ if(offset)
+ {
+ glu.lusup.segment(nextlu,offset).setZero();
+ nextlu += offset;
+ }
+ glu.xlusup(jcol + 1) = StorageIndex(nextlu); // close L\U(*,jcol);
+
+ /* For more updates within the panel (also within the current supernode),
+ * should start from the first column of the panel, or the first column
+ * of the supernode, whichever is bigger. There are two cases:
+ * 1) fsupc < fpanelc, then fst_col <-- fpanelc
+ * 2) fsupc >= fpanelc, then fst_col <-- fsupc
+ */
+ fst_col = (std::max)(fsupc, fpanelc);
+
+ if (fst_col < jcol)
+ {
+ // Distance between the current supernode and the current panel
+ // d_fsupc = 0 if fsupc >= fpanelc
+ d_fsupc = fst_col - fsupc;
+
+ lptr = glu.xlsub(fsupc) + d_fsupc;
+ luptr = glu.xlusup(fst_col) + d_fsupc;
+ nsupr = glu.xlsub(fsupc+1) - glu.xlsub(fsupc); // leading dimension
+ nsupc = jcol - fst_col; // excluding jcol
+ nrow = nsupr - d_fsupc - nsupc;
+
+ // points to the beginning of jcol in snode L\U(jsupno)
+ ufirst = glu.xlusup(jcol) + d_fsupc;
+ Index lda = glu.xlusup(jcol+1) - glu.xlusup(jcol);
+ MappedMatrixBlock A( &(glu.lusup.data()[luptr]), nsupc, nsupc, OuterStride<>(lda) );
+ VectorBlock<ScalarVector> u(glu.lusup, ufirst, nsupc);
+ u = A.template triangularView<UnitLower>().solve(u);
+
+ new (&A) MappedMatrixBlock ( &(glu.lusup.data()[luptr+nsupc]), nrow, nsupc, OuterStride<>(lda) );
+ VectorBlock<ScalarVector> l(glu.lusup, ufirst+nsupc, nrow);
+ l.noalias() -= A * u;
+
+ } // End if fst_col
+ return 0;
+}
+
+} // end namespace internal
+} // end namespace Eigen
+
+#endif // SPARSELU_COLUMN_BMOD_H
diff --git a/Eigen/src/SparseLU/SparseLU_column_dfs.h b/Eigen/src/SparseLU/SparseLU_column_dfs.h
new file mode 100644
index 0000000..be4cfd1
--- /dev/null
+++ b/Eigen/src/SparseLU/SparseLU_column_dfs.h
@@ -0,0 +1,181 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2012 Désiré Nuentsa-Wakam <desire.nuentsa_wakam@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+/*
+
+ * NOTE: This file is the modified version of [s,d,c,z]column_dfs.c file in SuperLU
+
+ * -- SuperLU routine (version 2.0) --
+ * Univ. of California Berkeley, Xerox Palo Alto Research Center,
+ * and Lawrence Berkeley National Lab.
+ * November 15, 1997
+ *
+ * Copyright (c) 1994 by Xerox Corporation. All rights reserved.
+ *
+ * THIS MATERIAL IS PROVIDED AS IS, WITH ABSOLUTELY NO WARRANTY
+ * EXPRESSED OR IMPLIED. ANY USE IS AT YOUR OWN RISK.
+ *
+ * Permission is hereby granted to use or copy this program for any
+ * purpose, provided the above notices are retained on all copies.
+ * Permission to modify the code and to distribute modified code is
+ * granted, provided the above notices are retained, and a notice that
+ * the code was modified is included with the above copyright notice.
+ */
+#ifndef SPARSELU_COLUMN_DFS_H
+#define SPARSELU_COLUMN_DFS_H
+
+template <typename Scalar, typename StorageIndex> class SparseLUImpl;
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+
+template<typename IndexVector, typename ScalarVector>
+struct column_dfs_traits : no_assignment_operator
+{
+ typedef typename ScalarVector::Scalar Scalar;
+ typedef typename IndexVector::Scalar StorageIndex;
+ column_dfs_traits(Index jcol, Index& jsuper, typename SparseLUImpl<Scalar, StorageIndex>::GlobalLU_t& glu, SparseLUImpl<Scalar, StorageIndex>& luImpl)
+ : m_jcol(jcol), m_jsuper_ref(jsuper), m_glu(glu), m_luImpl(luImpl)
+ {}
+ bool update_segrep(Index /*krep*/, Index /*jj*/)
+ {
+ return true;
+ }
+ void mem_expand(IndexVector& lsub, Index& nextl, Index chmark)
+ {
+ if (nextl >= m_glu.nzlmax)
+ m_luImpl.memXpand(lsub, m_glu.nzlmax, nextl, LSUB, m_glu.num_expansions);
+ if (chmark != (m_jcol-1)) m_jsuper_ref = emptyIdxLU;
+ }
+ enum { ExpandMem = true };
+
+ Index m_jcol;
+ Index& m_jsuper_ref;
+ typename SparseLUImpl<Scalar, StorageIndex>::GlobalLU_t& m_glu;
+ SparseLUImpl<Scalar, StorageIndex>& m_luImpl;
+};
+
+
+/**
+ * \brief Performs a symbolic factorization on column jcol and decide the supernode boundary
+ *
+ * A supernode representative is the last column of a supernode.
+ * The nonzeros in U[*,j] are segments that end at supernodes representatives.
+ * The routine returns a list of the supernodal representatives
+ * in topological order of the dfs that generates them.
+ * The location of the first nonzero in each supernodal segment
+ * (supernodal entry location) is also returned.
+ *
+ * \param m number of rows in the matrix
+ * \param jcol Current column
+ * \param perm_r Row permutation
+ * \param maxsuper Maximum number of column allowed in a supernode
+ * \param [in,out] nseg Number of segments in current U[*,j] - new segments appended
+ * \param lsub_col defines the rhs vector to start the dfs
+ * \param [in,out] segrep Segment representatives - new segments appended
+ * \param repfnz First nonzero location in each row
+ * \param xprune
+ * \param marker marker[i] == jj, if i was visited during dfs of current column jj;
+ * \param parent
+ * \param xplore working array
+ * \param glu global LU data
+ * \return 0 success
+ * > 0 number of bytes allocated when run out of space
+ *
+ */
+template <typename Scalar, typename StorageIndex>
+Index SparseLUImpl<Scalar,StorageIndex>::column_dfs(const Index m, const Index jcol, IndexVector& perm_r, Index maxsuper, Index& nseg,
+ BlockIndexVector lsub_col, IndexVector& segrep, BlockIndexVector repfnz, IndexVector& xprune,
+ IndexVector& marker, IndexVector& parent, IndexVector& xplore, GlobalLU_t& glu)
+{
+
+ Index jsuper = glu.supno(jcol);
+ Index nextl = glu.xlsub(jcol);
+ VectorBlock<IndexVector> marker2(marker, 2*m, m);
+
+
+ column_dfs_traits<IndexVector, ScalarVector> traits(jcol, jsuper, glu, *this);
+
+ // For each nonzero in A(*,jcol) do dfs
+ for (Index k = 0; ((k < m) ? lsub_col[k] != emptyIdxLU : false) ; k++)
+ {
+ Index krow = lsub_col(k);
+ lsub_col(k) = emptyIdxLU;
+ Index kmark = marker2(krow);
+
+ // krow was visited before, go to the next nonz;
+ if (kmark == jcol) continue;
+
+ dfs_kernel(StorageIndex(jcol), perm_r, nseg, glu.lsub, segrep, repfnz, xprune, marker2, parent,
+ xplore, glu, nextl, krow, traits);
+ } // for each nonzero ...
+
+ Index fsupc;
+ StorageIndex nsuper = glu.supno(jcol);
+ StorageIndex jcolp1 = StorageIndex(jcol) + 1;
+ Index jcolm1 = jcol - 1;
+
+ // check to see if j belongs in the same supernode as j-1
+ if ( jcol == 0 )
+ { // Do nothing for column 0
+ nsuper = glu.supno(0) = 0 ;
+ }
+ else
+ {
+ fsupc = glu.xsup(nsuper);
+ StorageIndex jptr = glu.xlsub(jcol); // Not yet compressed
+ StorageIndex jm1ptr = glu.xlsub(jcolm1);
+
+ // Use supernodes of type T2 : see SuperLU paper
+ if ( (nextl-jptr != jptr-jm1ptr-1) ) jsuper = emptyIdxLU;
+
+ // Make sure the number of columns in a supernode doesn't
+ // exceed threshold
+ if ( (jcol - fsupc) >= maxsuper) jsuper = emptyIdxLU;
+
+ /* If jcol starts a new supernode, reclaim storage space in
+ * glu.lsub from previous supernode. Note we only store
+ * the subscript set of the first and last columns of
+ * a supernode. (first for num values, last for pruning)
+ */
+ if (jsuper == emptyIdxLU)
+ { // starts a new supernode
+ if ( (fsupc < jcolm1-1) )
+ { // >= 3 columns in nsuper
+ StorageIndex ito = glu.xlsub(fsupc+1);
+ glu.xlsub(jcolm1) = ito;
+ StorageIndex istop = ito + jptr - jm1ptr;
+ xprune(jcolm1) = istop; // initialize xprune(jcol-1)
+ glu.xlsub(jcol) = istop;
+
+ for (StorageIndex ifrom = jm1ptr; ifrom < nextl; ++ifrom, ++ito)
+ glu.lsub(ito) = glu.lsub(ifrom);
+ nextl = ito; // = istop + length(jcol)
+ }
+ nsuper++;
+ glu.supno(jcol) = nsuper;
+ } // if a new supernode
+ } // end else: jcol > 0
+
+ // Tidy up the pointers before exit
+ glu.xsup(nsuper+1) = jcolp1;
+ glu.supno(jcolp1) = nsuper;
+ xprune(jcol) = StorageIndex(nextl); // Initialize upper bound for pruning
+ glu.xlsub(jcolp1) = StorageIndex(nextl);
+
+ return 0;
+}
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif
diff --git a/Eigen/src/SparseLU/SparseLU_copy_to_ucol.h b/Eigen/src/SparseLU/SparseLU_copy_to_ucol.h
new file mode 100644
index 0000000..e06b2a0
--- /dev/null
+++ b/Eigen/src/SparseLU/SparseLU_copy_to_ucol.h
@@ -0,0 +1,109 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2012 Désiré Nuentsa-Wakam <desire.nuentsa_wakam@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+/*
+
+ * NOTE: This file is the modified version of [s,d,c,z]copy_to_ucol.c file in SuperLU
+
+ * -- SuperLU routine (version 2.0) --
+ * Univ. of California Berkeley, Xerox Palo Alto Research Center,
+ * and Lawrence Berkeley National Lab.
+ * November 15, 1997
+ *
+ * Copyright (c) 1994 by Xerox Corporation. All rights reserved.
+ *
+ * THIS MATERIAL IS PROVIDED AS IS, WITH ABSOLUTELY NO WARRANTY
+ * EXPRESSED OR IMPLIED. ANY USE IS AT YOUR OWN RISK.
+ *
+ * Permission is hereby granted to use or copy this program for any
+ * purpose, provided the above notices are retained on all copies.
+ * Permission to modify the code and to distribute modified code is
+ * granted, provided the above notices are retained, and a notice that
+ * the code was modified is included with the above copyright notice.
+ */
+#ifndef SPARSELU_COPY_TO_UCOL_H
+#define SPARSELU_COPY_TO_UCOL_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+namespace internal {
+
+/**
+ * \brief Performs numeric block updates (sup-col) in topological order
+ *
+ * \param jcol current column to update
+ * \param nseg Number of segments in the U part
+ * \param segrep segment representative ...
+ * \param repfnz First nonzero column in each row ...
+ * \param perm_r Row permutation
+ * \param dense Store the full representation of the column
+ * \param glu Global LU data.
+ * \return 0 - successful return
+ * > 0 - number of bytes allocated when run out of space
+ *
+ */
+template <typename Scalar, typename StorageIndex>
+Index SparseLUImpl<Scalar,StorageIndex>::copy_to_ucol(const Index jcol, const Index nseg, IndexVector& segrep,
+ BlockIndexVector repfnz ,IndexVector& perm_r, BlockScalarVector dense, GlobalLU_t& glu)
+{
+ Index ksub, krep, ksupno;
+
+ Index jsupno = glu.supno(jcol);
+
+ // For each nonzero supernode segment of U[*,j] in topological order
+ Index k = nseg - 1, i;
+ StorageIndex nextu = glu.xusub(jcol);
+ Index kfnz, isub, segsize;
+ Index new_next,irow;
+ Index fsupc, mem;
+ for (ksub = 0; ksub < nseg; ksub++)
+ {
+ krep = segrep(k); k--;
+ ksupno = glu.supno(krep);
+ if (jsupno != ksupno ) // should go into ucol();
+ {
+ kfnz = repfnz(krep);
+ if (kfnz != emptyIdxLU)
+ { // Nonzero U-segment
+ fsupc = glu.xsup(ksupno);
+ isub = glu.xlsub(fsupc) + kfnz - fsupc;
+ segsize = krep - kfnz + 1;
+ new_next = nextu + segsize;
+ while (new_next > glu.nzumax)
+ {
+ mem = memXpand<ScalarVector>(glu.ucol, glu.nzumax, nextu, UCOL, glu.num_expansions);
+ if (mem) return mem;
+ mem = memXpand<IndexVector>(glu.usub, glu.nzumax, nextu, USUB, glu.num_expansions);
+ if (mem) return mem;
+
+ }
+
+ for (i = 0; i < segsize; i++)
+ {
+ irow = glu.lsub(isub);
+ glu.usub(nextu) = perm_r(irow); // Unlike the L part, the U part is stored in its final order
+ glu.ucol(nextu) = dense(irow);
+ dense(irow) = Scalar(0.0);
+ nextu++;
+ isub++;
+ }
+
+ } // end nonzero U-segment
+
+ } // end if jsupno
+
+ } // end for each segment
+ glu.xusub(jcol + 1) = nextu; // close U(*,jcol)
+ return 0;
+}
+
+} // namespace internal
+} // end namespace Eigen
+
+#endif // SPARSELU_COPY_TO_UCOL_H
diff --git a/Eigen/src/SparseLU/SparseLU_gemm_kernel.h b/Eigen/src/SparseLU/SparseLU_gemm_kernel.h
new file mode 100644
index 0000000..034d379
--- /dev/null
+++ b/Eigen/src/SparseLU/SparseLU_gemm_kernel.h
@@ -0,0 +1,282 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2012 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_SPARSELU_GEMM_KERNEL_H
+#define EIGEN_SPARSELU_GEMM_KERNEL_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+
+
+/** \internal
+ * A general matrix-matrix product kernel optimized for the SparseLU factorization.
+ * - A, B, and C must be column major
+ * - lda and ldc must be multiples of the respective packet size
+ * - C must have the same alignment as A
+ */
+template<typename Scalar>
+EIGEN_DONT_INLINE
+void sparselu_gemm(Index m, Index n, Index d, const Scalar* A, Index lda, const Scalar* B, Index ldb, Scalar* C, Index ldc)
+{
+ using namespace Eigen::internal;
+
+ typedef typename packet_traits<Scalar>::type Packet;
+ enum {
+ NumberOfRegisters = EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS,
+ PacketSize = packet_traits<Scalar>::size,
+ PM = 8, // peeling in M
+ RN = 2, // register blocking
+ RK = NumberOfRegisters>=16 ? 4 : 2, // register blocking
+ BM = 4096/sizeof(Scalar), // number of rows of A-C per chunk
+ SM = PM*PacketSize // step along M
+ };
+ Index d_end = (d/RK)*RK; // number of columns of A (rows of B) suitable for full register blocking
+ Index n_end = (n/RN)*RN; // number of columns of B-C suitable for processing RN columns at once
+ Index i0 = internal::first_default_aligned(A,m);
+
+ eigen_internal_assert(((lda%PacketSize)==0) && ((ldc%PacketSize)==0) && (i0==internal::first_default_aligned(C,m)));
+
+ // handle the non aligned rows of A and C without any optimization:
+ for(Index i=0; i<i0; ++i)
+ {
+ for(Index j=0; j<n; ++j)
+ {
+ Scalar c = C[i+j*ldc];
+ for(Index k=0; k<d; ++k)
+ c += B[k+j*ldb] * A[i+k*lda];
+ C[i+j*ldc] = c;
+ }
+ }
+ // process the remaining rows per chunk of BM rows
+ for(Index ib=i0; ib<m; ib+=BM)
+ {
+ Index actual_b = std::min<Index>(BM, m-ib); // actual number of rows
+ Index actual_b_end1 = (actual_b/SM)*SM; // actual number of rows suitable for peeling
+ Index actual_b_end2 = (actual_b/PacketSize)*PacketSize; // actual number of rows suitable for vectorization
+
+ // Let's process two columns of B-C at once
+ for(Index j=0; j<n_end; j+=RN)
+ {
+ const Scalar* Bc0 = B+(j+0)*ldb;
+ const Scalar* Bc1 = B+(j+1)*ldb;
+
+ for(Index k=0; k<d_end; k+=RK)
+ {
+
+ // load and expand a RN x RK block of B
+ Packet b00, b10, b20, b30, b01, b11, b21, b31;
+ { b00 = pset1<Packet>(Bc0[0]); }
+ { b10 = pset1<Packet>(Bc0[1]); }
+ if(RK==4) { b20 = pset1<Packet>(Bc0[2]); }
+ if(RK==4) { b30 = pset1<Packet>(Bc0[3]); }
+ { b01 = pset1<Packet>(Bc1[0]); }
+ { b11 = pset1<Packet>(Bc1[1]); }
+ if(RK==4) { b21 = pset1<Packet>(Bc1[2]); }
+ if(RK==4) { b31 = pset1<Packet>(Bc1[3]); }
+
+ Packet a0, a1, a2, a3, c0, c1, t0, t1;
+
+ const Scalar* A0 = A+ib+(k+0)*lda;
+ const Scalar* A1 = A+ib+(k+1)*lda;
+ const Scalar* A2 = A+ib+(k+2)*lda;
+ const Scalar* A3 = A+ib+(k+3)*lda;
+
+ Scalar* C0 = C+ib+(j+0)*ldc;
+ Scalar* C1 = C+ib+(j+1)*ldc;
+
+ a0 = pload<Packet>(A0);
+ a1 = pload<Packet>(A1);
+ if(RK==4)
+ {
+ a2 = pload<Packet>(A2);
+ a3 = pload<Packet>(A3);
+ }
+ else
+ {
+ // workaround "may be used uninitialized in this function" warning
+ a2 = a3 = a0;
+ }
+
+#define KMADD(c, a, b, tmp) {tmp = b; tmp = pmul(a,tmp); c = padd(c,tmp);}
+#define WORK(I) \
+ c0 = pload<Packet>(C0+i+(I)*PacketSize); \
+ c1 = pload<Packet>(C1+i+(I)*PacketSize); \
+ KMADD(c0, a0, b00, t0) \
+ KMADD(c1, a0, b01, t1) \
+ a0 = pload<Packet>(A0+i+(I+1)*PacketSize); \
+ KMADD(c0, a1, b10, t0) \
+ KMADD(c1, a1, b11, t1) \
+ a1 = pload<Packet>(A1+i+(I+1)*PacketSize); \
+ if(RK==4){ KMADD(c0, a2, b20, t0) }\
+ if(RK==4){ KMADD(c1, a2, b21, t1) }\
+ if(RK==4){ a2 = pload<Packet>(A2+i+(I+1)*PacketSize); }\
+ if(RK==4){ KMADD(c0, a3, b30, t0) }\
+ if(RK==4){ KMADD(c1, a3, b31, t1) }\
+ if(RK==4){ a3 = pload<Packet>(A3+i+(I+1)*PacketSize); }\
+ pstore(C0+i+(I)*PacketSize, c0); \
+ pstore(C1+i+(I)*PacketSize, c1)
+
+ // process rows of A' - C' with aggressive vectorization and peeling
+ for(Index i=0; i<actual_b_end1; i+=PacketSize*8)
+ {
+ EIGEN_ASM_COMMENT("SPARSELU_GEMML_KERNEL1");
+ prefetch((A0+i+(5)*PacketSize));
+ prefetch((A1+i+(5)*PacketSize));
+ if(RK==4) prefetch((A2+i+(5)*PacketSize));
+ if(RK==4) prefetch((A3+i+(5)*PacketSize));
+
+ WORK(0);
+ WORK(1);
+ WORK(2);
+ WORK(3);
+ WORK(4);
+ WORK(5);
+ WORK(6);
+ WORK(7);
+ }
+ // process the remaining rows with vectorization only
+ for(Index i=actual_b_end1; i<actual_b_end2; i+=PacketSize)
+ {
+ WORK(0);
+ }
+#undef WORK
+ // process the remaining rows without vectorization
+ for(Index i=actual_b_end2; i<actual_b; ++i)
+ {
+ if(RK==4)
+ {
+ C0[i] += A0[i]*Bc0[0]+A1[i]*Bc0[1]+A2[i]*Bc0[2]+A3[i]*Bc0[3];
+ C1[i] += A0[i]*Bc1[0]+A1[i]*Bc1[1]+A2[i]*Bc1[2]+A3[i]*Bc1[3];
+ }
+ else
+ {
+ C0[i] += A0[i]*Bc0[0]+A1[i]*Bc0[1];
+ C1[i] += A0[i]*Bc1[0]+A1[i]*Bc1[1];
+ }
+ }
+
+ Bc0 += RK;
+ Bc1 += RK;
+ } // peeled loop on k
+ } // peeled loop on the columns j
+ // process the last column (we now perform a matrix-vector product)
+ if((n-n_end)>0)
+ {
+ const Scalar* Bc0 = B+(n-1)*ldb;
+
+ for(Index k=0; k<d_end; k+=RK)
+ {
+
+ // load and expand a 1 x RK block of B
+ Packet b00, b10, b20, b30;
+ b00 = pset1<Packet>(Bc0[0]);
+ b10 = pset1<Packet>(Bc0[1]);
+ if(RK==4) b20 = pset1<Packet>(Bc0[2]);
+ if(RK==4) b30 = pset1<Packet>(Bc0[3]);
+
+ Packet a0, a1, a2, a3, c0, t0/*, t1*/;
+
+ const Scalar* A0 = A+ib+(k+0)*lda;
+ const Scalar* A1 = A+ib+(k+1)*lda;
+ const Scalar* A2 = A+ib+(k+2)*lda;
+ const Scalar* A3 = A+ib+(k+3)*lda;
+
+ Scalar* C0 = C+ib+(n_end)*ldc;
+
+ a0 = pload<Packet>(A0);
+ a1 = pload<Packet>(A1);
+ if(RK==4)
+ {
+ a2 = pload<Packet>(A2);
+ a3 = pload<Packet>(A3);
+ }
+ else
+ {
+ // workaround "may be used uninitialized in this function" warning
+ a2 = a3 = a0;
+ }
+
+#define WORK(I) \
+ c0 = pload<Packet>(C0+i+(I)*PacketSize); \
+ KMADD(c0, a0, b00, t0) \
+ a0 = pload<Packet>(A0+i+(I+1)*PacketSize); \
+ KMADD(c0, a1, b10, t0) \
+ a1 = pload<Packet>(A1+i+(I+1)*PacketSize); \
+ if(RK==4){ KMADD(c0, a2, b20, t0) }\
+ if(RK==4){ a2 = pload<Packet>(A2+i+(I+1)*PacketSize); }\
+ if(RK==4){ KMADD(c0, a3, b30, t0) }\
+ if(RK==4){ a3 = pload<Packet>(A3+i+(I+1)*PacketSize); }\
+ pstore(C0+i+(I)*PacketSize, c0);
+
+ // aggressive vectorization and peeling
+ for(Index i=0; i<actual_b_end1; i+=PacketSize*8)
+ {
+ EIGEN_ASM_COMMENT("SPARSELU_GEMML_KERNEL2");
+ WORK(0);
+ WORK(1);
+ WORK(2);
+ WORK(3);
+ WORK(4);
+ WORK(5);
+ WORK(6);
+ WORK(7);
+ }
+ // vectorization only
+ for(Index i=actual_b_end1; i<actual_b_end2; i+=PacketSize)
+ {
+ WORK(0);
+ }
+ // remaining scalars
+ for(Index i=actual_b_end2; i<actual_b; ++i)
+ {
+ if(RK==4)
+ C0[i] += A0[i]*Bc0[0]+A1[i]*Bc0[1]+A2[i]*Bc0[2]+A3[i]*Bc0[3];
+ else
+ C0[i] += A0[i]*Bc0[0]+A1[i]*Bc0[1];
+ }
+
+ Bc0 += RK;
+#undef WORK
+ }
+ }
+
+ // process the last columns of A, corresponding to the last rows of B
+ Index rd = d-d_end;
+ if(rd>0)
+ {
+ for(Index j=0; j<n; ++j)
+ {
+ enum {
+ Alignment = PacketSize>1 ? Aligned : 0
+ };
+ typedef Map<Matrix<Scalar,Dynamic,1>, Alignment > MapVector;
+ typedef Map<const Matrix<Scalar,Dynamic,1>, Alignment > ConstMapVector;
+ if(rd==1) MapVector(C+j*ldc+ib,actual_b) += B[0+d_end+j*ldb] * ConstMapVector(A+(d_end+0)*lda+ib, actual_b);
+
+ else if(rd==2) MapVector(C+j*ldc+ib,actual_b) += B[0+d_end+j*ldb] * ConstMapVector(A+(d_end+0)*lda+ib, actual_b)
+ + B[1+d_end+j*ldb] * ConstMapVector(A+(d_end+1)*lda+ib, actual_b);
+
+ else MapVector(C+j*ldc+ib,actual_b) += B[0+d_end+j*ldb] * ConstMapVector(A+(d_end+0)*lda+ib, actual_b)
+ + B[1+d_end+j*ldb] * ConstMapVector(A+(d_end+1)*lda+ib, actual_b)
+ + B[2+d_end+j*ldb] * ConstMapVector(A+(d_end+2)*lda+ib, actual_b);
+ }
+ }
+
+ } // blocking on the rows of A and C
+}
+#undef KMADD
+
+} // namespace internal
+
+} // namespace Eigen
+
+#endif // EIGEN_SPARSELU_GEMM_KERNEL_H
diff --git a/Eigen/src/SparseLU/SparseLU_heap_relax_snode.h b/Eigen/src/SparseLU/SparseLU_heap_relax_snode.h
new file mode 100644
index 0000000..2a8d80b
--- /dev/null
+++ b/Eigen/src/SparseLU/SparseLU_heap_relax_snode.h
@@ -0,0 +1,123 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2012 Désiré Nuentsa-Wakam <desire.nuentsa_wakam@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+/* This file is a modified version of heap_relax_snode.c file in SuperLU
+ * -- SuperLU routine (version 3.0) --
+ * Univ. of California Berkeley, Xerox Palo Alto Research Center,
+ * and Lawrence Berkeley National Lab.
+ * October 15, 2003
+ *
+ * Copyright (c) 1994 by Xerox Corporation. All rights reserved.
+ *
+ * THIS MATERIAL IS PROVIDED AS IS, WITH ABSOLUTELY NO WARRANTY
+ * EXPRESSED OR IMPLIED. ANY USE IS AT YOUR OWN RISK.
+ *
+ * Permission is hereby granted to use or copy this program for any
+ * purpose, provided the above notices are retained on all copies.
+ * Permission to modify the code and to distribute modified code is
+ * granted, provided the above notices are retained, and a notice that
+ * the code was modified is included with the above copyright notice.
+ */
+
+#ifndef SPARSELU_HEAP_RELAX_SNODE_H
+#define SPARSELU_HEAP_RELAX_SNODE_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+namespace internal {
+
+/**
+ * \brief Identify the initial relaxed supernodes
+ *
+ * This routine applied to a symmetric elimination tree.
+ * It assumes that the matrix has been reordered according to the postorder of the etree
+ * \param n The number of columns
+ * \param et elimination tree
+ * \param relax_columns Maximum number of columns allowed in a relaxed snode
+ * \param descendants Number of descendants of each node in the etree
+ * \param relax_end last column in a supernode
+ */
+template <typename Scalar, typename StorageIndex>
+void SparseLUImpl<Scalar,StorageIndex>::heap_relax_snode (const Index n, IndexVector& et, const Index relax_columns, IndexVector& descendants, IndexVector& relax_end)
+{
+
+ // The etree may not be postordered, but its heap ordered
+ IndexVector post;
+ internal::treePostorder(StorageIndex(n), et, post); // Post order etree
+ IndexVector inv_post(n+1);
+ for (StorageIndex i = 0; i < n+1; ++i) inv_post(post(i)) = i; // inv_post = post.inverse()???
+
+ // Renumber etree in postorder
+ IndexVector iwork(n);
+ IndexVector et_save(n+1);
+ for (Index i = 0; i < n; ++i)
+ {
+ iwork(post(i)) = post(et(i));
+ }
+ et_save = et; // Save the original etree
+ et = iwork;
+
+ // compute the number of descendants of each node in the etree
+ relax_end.setConstant(emptyIdxLU);
+ Index j, parent;
+ descendants.setZero();
+ for (j = 0; j < n; j++)
+ {
+ parent = et(j);
+ if (parent != n) // not the dummy root
+ descendants(parent) += descendants(j) + 1;
+ }
+ // Identify the relaxed supernodes by postorder traversal of the etree
+ Index snode_start; // beginning of a snode
+ StorageIndex k;
+ StorageIndex l;
+ for (j = 0; j < n; )
+ {
+ parent = et(j);
+ snode_start = j;
+ while ( parent != n && descendants(parent) < relax_columns )
+ {
+ j = parent;
+ parent = et(j);
+ }
+ // Found a supernode in postordered etree, j is the last column
+ k = StorageIndex(n);
+ for (Index i = snode_start; i <= j; ++i)
+ k = (std::min)(k, inv_post(i));
+ l = inv_post(j);
+ if ( (l - k) == (j - snode_start) ) // Same number of columns in the snode
+ {
+ // This is also a supernode in the original etree
+ relax_end(k) = l; // Record last column
+ }
+ else
+ {
+ for (Index i = snode_start; i <= j; ++i)
+ {
+ l = inv_post(i);
+ if (descendants(i) == 0)
+ {
+ relax_end(l) = l;
+ }
+ }
+ }
+ j++;
+ // Search for a new leaf
+ while (descendants(j) != 0 && j < n) j++;
+ } // End postorder traversal of the etree
+
+ // Recover the original etree
+ et = et_save;
+}
+
+} // end namespace internal
+
+} // end namespace Eigen
+#endif // SPARSELU_HEAP_RELAX_SNODE_H
diff --git a/Eigen/src/SparseLU/SparseLU_kernel_bmod.h b/Eigen/src/SparseLU/SparseLU_kernel_bmod.h
new file mode 100644
index 0000000..424f93c
--- /dev/null
+++ b/Eigen/src/SparseLU/SparseLU_kernel_bmod.h
@@ -0,0 +1,132 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2012 Désiré Nuentsa-Wakam <desire.nuentsa_wakam@inria.fr>
+// Copyright (C) 2012 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef SPARSELU_KERNEL_BMOD_H
+#define SPARSELU_KERNEL_BMOD_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+namespace internal {
+
+template <int SegSizeAtCompileTime> struct LU_kernel_bmod
+{
+ /** \internal
+ * \brief Performs numeric block updates from a given supernode to a single column
+ *
+ * \param segsize Size of the segment (and blocks ) to use for updates
+ * \param[in,out] dense Packed values of the original matrix
+ * \param tempv temporary vector to use for updates
+ * \param lusup array containing the supernodes
+ * \param lda Leading dimension in the supernode
+ * \param nrow Number of rows in the rectangular part of the supernode
+ * \param lsub compressed row subscripts of supernodes
+ * \param lptr pointer to the first column of the current supernode in lsub
+ * \param no_zeros Number of nonzeros elements before the diagonal part of the supernode
+ */
+ template <typename BlockScalarVector, typename ScalarVector, typename IndexVector>
+ static EIGEN_DONT_INLINE void run(const Index segsize, BlockScalarVector& dense, ScalarVector& tempv, ScalarVector& lusup, Index& luptr, const Index lda,
+ const Index nrow, IndexVector& lsub, const Index lptr, const Index no_zeros);
+};
+
+template <int SegSizeAtCompileTime>
+template <typename BlockScalarVector, typename ScalarVector, typename IndexVector>
+EIGEN_DONT_INLINE void LU_kernel_bmod<SegSizeAtCompileTime>::run(const Index segsize, BlockScalarVector& dense, ScalarVector& tempv, ScalarVector& lusup, Index& luptr, const Index lda,
+ const Index nrow, IndexVector& lsub, const Index lptr, const Index no_zeros)
+{
+ typedef typename ScalarVector::Scalar Scalar;
+ // First, copy U[*,j] segment from dense(*) to tempv(*)
+ // The result of triangular solve is in tempv[*];
+ // The result of matric-vector update is in dense[*]
+ Index isub = lptr + no_zeros;
+ Index i;
+ Index irow;
+ for (i = 0; i < ((SegSizeAtCompileTime==Dynamic)?segsize:SegSizeAtCompileTime); i++)
+ {
+ irow = lsub(isub);
+ tempv(i) = dense(irow);
+ ++isub;
+ }
+ // Dense triangular solve -- start effective triangle
+ luptr += lda * no_zeros + no_zeros;
+ // Form Eigen matrix and vector
+ Map<Matrix<Scalar,SegSizeAtCompileTime,SegSizeAtCompileTime, ColMajor>, 0, OuterStride<> > A( &(lusup.data()[luptr]), segsize, segsize, OuterStride<>(lda) );
+ Map<Matrix<Scalar,SegSizeAtCompileTime,1> > u(tempv.data(), segsize);
+
+ u = A.template triangularView<UnitLower>().solve(u);
+
+ // Dense matrix-vector product y <-- B*x
+ luptr += segsize;
+ const Index PacketSize = internal::packet_traits<Scalar>::size;
+ Index ldl = internal::first_multiple(nrow, PacketSize);
+ Map<Matrix<Scalar,Dynamic,SegSizeAtCompileTime, ColMajor>, 0, OuterStride<> > B( &(lusup.data()[luptr]), nrow, segsize, OuterStride<>(lda) );
+ Index aligned_offset = internal::first_default_aligned(tempv.data()+segsize, PacketSize);
+ Index aligned_with_B_offset = (PacketSize-internal::first_default_aligned(B.data(), PacketSize))%PacketSize;
+ Map<Matrix<Scalar,Dynamic,1>, 0, OuterStride<> > l(tempv.data()+segsize+aligned_offset+aligned_with_B_offset, nrow, OuterStride<>(ldl) );
+
+ l.setZero();
+ internal::sparselu_gemm<Scalar>(l.rows(), l.cols(), B.cols(), B.data(), B.outerStride(), u.data(), u.outerStride(), l.data(), l.outerStride());
+
+ // Scatter tempv[] into SPA dense[] as a temporary storage
+ isub = lptr + no_zeros;
+ for (i = 0; i < ((SegSizeAtCompileTime==Dynamic)?segsize:SegSizeAtCompileTime); i++)
+ {
+ irow = lsub(isub++);
+ dense(irow) = tempv(i);
+ }
+
+ // Scatter l into SPA dense[]
+ for (i = 0; i < nrow; i++)
+ {
+ irow = lsub(isub++);
+ dense(irow) -= l(i);
+ }
+}
+
+template <> struct LU_kernel_bmod<1>
+{
+ template <typename BlockScalarVector, typename ScalarVector, typename IndexVector>
+ static EIGEN_DONT_INLINE void run(const Index /*segsize*/, BlockScalarVector& dense, ScalarVector& /*tempv*/, ScalarVector& lusup, Index& luptr,
+ const Index lda, const Index nrow, IndexVector& lsub, const Index lptr, const Index no_zeros);
+};
+
+
+template <typename BlockScalarVector, typename ScalarVector, typename IndexVector>
+EIGEN_DONT_INLINE void LU_kernel_bmod<1>::run(const Index /*segsize*/, BlockScalarVector& dense, ScalarVector& /*tempv*/, ScalarVector& lusup, Index& luptr,
+ const Index lda, const Index nrow, IndexVector& lsub, const Index lptr, const Index no_zeros)
+{
+ typedef typename ScalarVector::Scalar Scalar;
+ typedef typename IndexVector::Scalar StorageIndex;
+ Scalar f = dense(lsub(lptr + no_zeros));
+ luptr += lda * no_zeros + no_zeros + 1;
+ const Scalar* a(lusup.data() + luptr);
+ const StorageIndex* irow(lsub.data()+lptr + no_zeros + 1);
+ Index i = 0;
+ for (; i+1 < nrow; i+=2)
+ {
+ Index i0 = *(irow++);
+ Index i1 = *(irow++);
+ Scalar a0 = *(a++);
+ Scalar a1 = *(a++);
+ Scalar d0 = dense.coeff(i0);
+ Scalar d1 = dense.coeff(i1);
+ d0 -= f*a0;
+ d1 -= f*a1;
+ dense.coeffRef(i0) = d0;
+ dense.coeffRef(i1) = d1;
+ }
+ if(i<nrow)
+ dense.coeffRef(*(irow++)) -= f * *(a++);
+}
+
+} // end namespace internal
+
+} // end namespace Eigen
+#endif // SPARSELU_KERNEL_BMOD_H
diff --git a/Eigen/src/SparseLU/SparseLU_panel_bmod.h b/Eigen/src/SparseLU/SparseLU_panel_bmod.h
new file mode 100644
index 0000000..8cd331a
--- /dev/null
+++ b/Eigen/src/SparseLU/SparseLU_panel_bmod.h
@@ -0,0 +1,225 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2012 Désiré Nuentsa-Wakam <desire.nuentsa_wakam@inria.fr>
+// Copyright (C) 2012 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+/*
+
+ * NOTE: This file is the modified version of [s,d,c,z]panel_bmod.c file in SuperLU
+
+ * -- SuperLU routine (version 3.0) --
+ * Univ. of California Berkeley, Xerox Palo Alto Research Center,
+ * and Lawrence Berkeley National Lab.
+ * October 15, 2003
+ *
+ * Copyright (c) 1994 by Xerox Corporation. All rights reserved.
+ *
+ * THIS MATERIAL IS PROVIDED AS IS, WITH ABSOLUTELY NO WARRANTY
+ * EXPRESSED OR IMPLIED. ANY USE IS AT YOUR OWN RISK.
+ *
+ * Permission is hereby granted to use or copy this program for any
+ * purpose, provided the above notices are retained on all copies.
+ * Permission to modify the code and to distribute modified code is
+ * granted, provided the above notices are retained, and a notice that
+ * the code was modified is included with the above copyright notice.
+ */
+#ifndef SPARSELU_PANEL_BMOD_H
+#define SPARSELU_PANEL_BMOD_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+namespace internal {
+
+/**
+ * \brief Performs numeric block updates (sup-panel) in topological order.
+ *
+ * Before entering this routine, the original nonzeros in the panel
+ * were already copied into the spa[m,w]
+ *
+ * \param m number of rows in the matrix
+ * \param w Panel size
+ * \param jcol Starting column of the panel
+ * \param nseg Number of segments in the U part
+ * \param dense Store the full representation of the panel
+ * \param tempv working array
+ * \param segrep segment representative... first row in the segment
+ * \param repfnz First nonzero rows
+ * \param glu Global LU data.
+ *
+ *
+ */
+template <typename Scalar, typename StorageIndex>
+void SparseLUImpl<Scalar,StorageIndex>::panel_bmod(const Index m, const Index w, const Index jcol,
+ const Index nseg, ScalarVector& dense, ScalarVector& tempv,
+ IndexVector& segrep, IndexVector& repfnz, GlobalLU_t& glu)
+{
+
+ Index ksub,jj,nextl_col;
+ Index fsupc, nsupc, nsupr, nrow;
+ Index krep, kfnz;
+ Index lptr; // points to the row subscripts of a supernode
+ Index luptr; // ...
+ Index segsize,no_zeros ;
+ // For each nonz supernode segment of U[*,j] in topological order
+ Index k = nseg - 1;
+ const Index PacketSize = internal::packet_traits<Scalar>::size;
+
+ for (ksub = 0; ksub < nseg; ksub++)
+ { // For each updating supernode
+ /* krep = representative of current k-th supernode
+ * fsupc = first supernodal column
+ * nsupc = number of columns in a supernode
+ * nsupr = number of rows in a supernode
+ */
+ krep = segrep(k); k--;
+ fsupc = glu.xsup(glu.supno(krep));
+ nsupc = krep - fsupc + 1;
+ nsupr = glu.xlsub(fsupc+1) - glu.xlsub(fsupc);
+ nrow = nsupr - nsupc;
+ lptr = glu.xlsub(fsupc);
+
+ // loop over the panel columns to detect the actual number of columns and rows
+ Index u_rows = 0;
+ Index u_cols = 0;
+ for (jj = jcol; jj < jcol + w; jj++)
+ {
+ nextl_col = (jj-jcol) * m;
+ VectorBlock<IndexVector> repfnz_col(repfnz, nextl_col, m); // First nonzero column index for each row
+
+ kfnz = repfnz_col(krep);
+ if ( kfnz == emptyIdxLU )
+ continue; // skip any zero segment
+
+ segsize = krep - kfnz + 1;
+ u_cols++;
+ u_rows = (std::max)(segsize,u_rows);
+ }
+
+ if(nsupc >= 2)
+ {
+ Index ldu = internal::first_multiple<Index>(u_rows, PacketSize);
+ Map<ScalarMatrix, Aligned, OuterStride<> > U(tempv.data(), u_rows, u_cols, OuterStride<>(ldu));
+
+ // gather U
+ Index u_col = 0;
+ for (jj = jcol; jj < jcol + w; jj++)
+ {
+ nextl_col = (jj-jcol) * m;
+ VectorBlock<IndexVector> repfnz_col(repfnz, nextl_col, m); // First nonzero column index for each row
+ VectorBlock<ScalarVector> dense_col(dense, nextl_col, m); // Scatter/gather entire matrix column from/to here
+
+ kfnz = repfnz_col(krep);
+ if ( kfnz == emptyIdxLU )
+ continue; // skip any zero segment
+
+ segsize = krep - kfnz + 1;
+ luptr = glu.xlusup(fsupc);
+ no_zeros = kfnz - fsupc;
+
+ Index isub = lptr + no_zeros;
+ Index off = u_rows-segsize;
+ for (Index i = 0; i < off; i++) U(i,u_col) = 0;
+ for (Index i = 0; i < segsize; i++)
+ {
+ Index irow = glu.lsub(isub);
+ U(i+off,u_col) = dense_col(irow);
+ ++isub;
+ }
+ u_col++;
+ }
+ // solve U = A^-1 U
+ luptr = glu.xlusup(fsupc);
+ Index lda = glu.xlusup(fsupc+1) - glu.xlusup(fsupc);
+ no_zeros = (krep - u_rows + 1) - fsupc;
+ luptr += lda * no_zeros + no_zeros;
+ MappedMatrixBlock A(glu.lusup.data()+luptr, u_rows, u_rows, OuterStride<>(lda) );
+ U = A.template triangularView<UnitLower>().solve(U);
+
+ // update
+ luptr += u_rows;
+ MappedMatrixBlock B(glu.lusup.data()+luptr, nrow, u_rows, OuterStride<>(lda) );
+ eigen_assert(tempv.size()>w*ldu + nrow*w + 1);
+
+ Index ldl = internal::first_multiple<Index>(nrow, PacketSize);
+ Index offset = (PacketSize-internal::first_default_aligned(B.data(), PacketSize)) % PacketSize;
+ MappedMatrixBlock L(tempv.data()+w*ldu+offset, nrow, u_cols, OuterStride<>(ldl));
+
+ L.setZero();
+ internal::sparselu_gemm<Scalar>(L.rows(), L.cols(), B.cols(), B.data(), B.outerStride(), U.data(), U.outerStride(), L.data(), L.outerStride());
+
+ // scatter U and L
+ u_col = 0;
+ for (jj = jcol; jj < jcol + w; jj++)
+ {
+ nextl_col = (jj-jcol) * m;
+ VectorBlock<IndexVector> repfnz_col(repfnz, nextl_col, m); // First nonzero column index for each row
+ VectorBlock<ScalarVector> dense_col(dense, nextl_col, m); // Scatter/gather entire matrix column from/to here
+
+ kfnz = repfnz_col(krep);
+ if ( kfnz == emptyIdxLU )
+ continue; // skip any zero segment
+
+ segsize = krep - kfnz + 1;
+ no_zeros = kfnz - fsupc;
+ Index isub = lptr + no_zeros;
+
+ Index off = u_rows-segsize;
+ for (Index i = 0; i < segsize; i++)
+ {
+ Index irow = glu.lsub(isub++);
+ dense_col(irow) = U.coeff(i+off,u_col);
+ U.coeffRef(i+off,u_col) = 0;
+ }
+
+ // Scatter l into SPA dense[]
+ for (Index i = 0; i < nrow; i++)
+ {
+ Index irow = glu.lsub(isub++);
+ dense_col(irow) -= L.coeff(i,u_col);
+ L.coeffRef(i,u_col) = 0;
+ }
+ u_col++;
+ }
+ }
+ else // level 2 only
+ {
+ // Sequence through each column in the panel
+ for (jj = jcol; jj < jcol + w; jj++)
+ {
+ nextl_col = (jj-jcol) * m;
+ VectorBlock<IndexVector> repfnz_col(repfnz, nextl_col, m); // First nonzero column index for each row
+ VectorBlock<ScalarVector> dense_col(dense, nextl_col, m); // Scatter/gather entire matrix column from/to here
+
+ kfnz = repfnz_col(krep);
+ if ( kfnz == emptyIdxLU )
+ continue; // skip any zero segment
+
+ segsize = krep - kfnz + 1;
+ luptr = glu.xlusup(fsupc);
+
+ Index lda = glu.xlusup(fsupc+1)-glu.xlusup(fsupc);// nsupr
+
+ // Perform a trianglar solve and block update,
+ // then scatter the result of sup-col update to dense[]
+ no_zeros = kfnz - fsupc;
+ if(segsize==1) LU_kernel_bmod<1>::run(segsize, dense_col, tempv, glu.lusup, luptr, lda, nrow, glu.lsub, lptr, no_zeros);
+ else if(segsize==2) LU_kernel_bmod<2>::run(segsize, dense_col, tempv, glu.lusup, luptr, lda, nrow, glu.lsub, lptr, no_zeros);
+ else if(segsize==3) LU_kernel_bmod<3>::run(segsize, dense_col, tempv, glu.lusup, luptr, lda, nrow, glu.lsub, lptr, no_zeros);
+ else LU_kernel_bmod<Dynamic>::run(segsize, dense_col, tempv, glu.lusup, luptr, lda, nrow, glu.lsub, lptr, no_zeros);
+ } // End for each column in the panel
+ }
+
+ } // End for each updating supernode
+} // end panel bmod
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // SPARSELU_PANEL_BMOD_H
diff --git a/Eigen/src/SparseLU/SparseLU_panel_dfs.h b/Eigen/src/SparseLU/SparseLU_panel_dfs.h
new file mode 100644
index 0000000..c3ff013
--- /dev/null
+++ b/Eigen/src/SparseLU/SparseLU_panel_dfs.h
@@ -0,0 +1,260 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2012 Désiré Nuentsa-Wakam <desire.nuentsa_wakam@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+/*
+
+ * NOTE: This file is the modified version of [s,d,c,z]panel_dfs.c file in SuperLU
+
+ * -- SuperLU routine (version 2.0) --
+ * Univ. of California Berkeley, Xerox Palo Alto Research Center,
+ * and Lawrence Berkeley National Lab.
+ * November 15, 1997
+ *
+ * Copyright (c) 1994 by Xerox Corporation. All rights reserved.
+ *
+ * THIS MATERIAL IS PROVIDED AS IS, WITH ABSOLUTELY NO WARRANTY
+ * EXPRESSED OR IMPLIED. ANY USE IS AT YOUR OWN RISK.
+ *
+ * Permission is hereby granted to use or copy this program for any
+ * purpose, provided the above notices are retained on all copies.
+ * Permission to modify the code and to distribute modified code is
+ * granted, provided the above notices are retained, and a notice that
+ * the code was modified is included with the above copyright notice.
+ */
+#ifndef SPARSELU_PANEL_DFS_H
+#define SPARSELU_PANEL_DFS_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+
+template<typename IndexVector>
+struct panel_dfs_traits
+{
+ typedef typename IndexVector::Scalar StorageIndex;
+ panel_dfs_traits(Index jcol, StorageIndex* marker)
+ : m_jcol(jcol), m_marker(marker)
+ {}
+ bool update_segrep(Index krep, StorageIndex jj)
+ {
+ if(m_marker[krep]<m_jcol)
+ {
+ m_marker[krep] = jj;
+ return true;
+ }
+ return false;
+ }
+ void mem_expand(IndexVector& /*glu.lsub*/, Index /*nextl*/, Index /*chmark*/) {}
+ enum { ExpandMem = false };
+ Index m_jcol;
+ StorageIndex* m_marker;
+};
+
+
+template <typename Scalar, typename StorageIndex>
+template <typename Traits>
+void SparseLUImpl<Scalar,StorageIndex>::dfs_kernel(const StorageIndex jj, IndexVector& perm_r,
+ Index& nseg, IndexVector& panel_lsub, IndexVector& segrep,
+ Ref<IndexVector> repfnz_col, IndexVector& xprune, Ref<IndexVector> marker, IndexVector& parent,
+ IndexVector& xplore, GlobalLU_t& glu,
+ Index& nextl_col, Index krow, Traits& traits
+ )
+{
+
+ StorageIndex kmark = marker(krow);
+
+ // For each unmarked krow of jj
+ marker(krow) = jj;
+ StorageIndex kperm = perm_r(krow);
+ if (kperm == emptyIdxLU ) {
+ // krow is in L : place it in structure of L(*, jj)
+ panel_lsub(nextl_col++) = StorageIndex(krow); // krow is indexed into A
+
+ traits.mem_expand(panel_lsub, nextl_col, kmark);
+ }
+ else
+ {
+ // krow is in U : if its supernode-representative krep
+ // has been explored, update repfnz(*)
+ // krep = supernode representative of the current row
+ StorageIndex krep = glu.xsup(glu.supno(kperm)+1) - 1;
+ // First nonzero element in the current column:
+ StorageIndex myfnz = repfnz_col(krep);
+
+ if (myfnz != emptyIdxLU )
+ {
+ // Representative visited before
+ if (myfnz > kperm ) repfnz_col(krep) = kperm;
+
+ }
+ else
+ {
+ // Otherwise, perform dfs starting at krep
+ StorageIndex oldrep = emptyIdxLU;
+ parent(krep) = oldrep;
+ repfnz_col(krep) = kperm;
+ StorageIndex xdfs = glu.xlsub(krep);
+ Index maxdfs = xprune(krep);
+
+ StorageIndex kpar;
+ do
+ {
+ // For each unmarked kchild of krep
+ while (xdfs < maxdfs)
+ {
+ StorageIndex kchild = glu.lsub(xdfs);
+ xdfs++;
+ StorageIndex chmark = marker(kchild);
+
+ if (chmark != jj )
+ {
+ marker(kchild) = jj;
+ StorageIndex chperm = perm_r(kchild);
+
+ if (chperm == emptyIdxLU)
+ {
+ // case kchild is in L: place it in L(*, j)
+ panel_lsub(nextl_col++) = kchild;
+ traits.mem_expand(panel_lsub, nextl_col, chmark);
+ }
+ else
+ {
+ // case kchild is in U :
+ // chrep = its supernode-rep. If its rep has been explored,
+ // update its repfnz(*)
+ StorageIndex chrep = glu.xsup(glu.supno(chperm)+1) - 1;
+ myfnz = repfnz_col(chrep);
+
+ if (myfnz != emptyIdxLU)
+ { // Visited before
+ if (myfnz > chperm)
+ repfnz_col(chrep) = chperm;
+ }
+ else
+ { // Cont. dfs at snode-rep of kchild
+ xplore(krep) = xdfs;
+ oldrep = krep;
+ krep = chrep; // Go deeper down G(L)
+ parent(krep) = oldrep;
+ repfnz_col(krep) = chperm;
+ xdfs = glu.xlsub(krep);
+ maxdfs = xprune(krep);
+
+ } // end if myfnz != -1
+ } // end if chperm == -1
+
+ } // end if chmark !=jj
+ } // end while xdfs < maxdfs
+
+ // krow has no more unexplored nbrs :
+ // Place snode-rep krep in postorder DFS, if this
+ // segment is seen for the first time. (Note that
+ // "repfnz(krep)" may change later.)
+ // Baktrack dfs to its parent
+ if(traits.update_segrep(krep,jj))
+ //if (marker1(krep) < jcol )
+ {
+ segrep(nseg) = krep;
+ ++nseg;
+ //marker1(krep) = jj;
+ }
+
+ kpar = parent(krep); // Pop recursion, mimic recursion
+ if (kpar == emptyIdxLU)
+ break; // dfs done
+ krep = kpar;
+ xdfs = xplore(krep);
+ maxdfs = xprune(krep);
+
+ } while (kpar != emptyIdxLU); // Do until empty stack
+
+ } // end if (myfnz = -1)
+
+ } // end if (kperm == -1)
+}
+
+/**
+ * \brief Performs a symbolic factorization on a panel of columns [jcol, jcol+w)
+ *
+ * A supernode representative is the last column of a supernode.
+ * The nonzeros in U[*,j] are segments that end at supernodes representatives
+ *
+ * The routine returns a list of the supernodal representatives
+ * in topological order of the dfs that generates them. This list is
+ * a superset of the topological order of each individual column within
+ * the panel.
+ * The location of the first nonzero in each supernodal segment
+ * (supernodal entry location) is also returned. Each column has
+ * a separate list for this purpose.
+ *
+ * Two markers arrays are used for dfs :
+ * marker[i] == jj, if i was visited during dfs of current column jj;
+ * marker1[i] >= jcol, if i was visited by earlier columns in this panel;
+ *
+ * \param[in] m number of rows in the matrix
+ * \param[in] w Panel size
+ * \param[in] jcol Starting column of the panel
+ * \param[in] A Input matrix in column-major storage
+ * \param[in] perm_r Row permutation
+ * \param[out] nseg Number of U segments
+ * \param[out] dense Accumulate the column vectors of the panel
+ * \param[out] panel_lsub Subscripts of the row in the panel
+ * \param[out] segrep Segment representative i.e first nonzero row of each segment
+ * \param[out] repfnz First nonzero location in each row
+ * \param[out] xprune The pruned elimination tree
+ * \param[out] marker work vector
+ * \param parent The elimination tree
+ * \param xplore work vector
+ * \param glu The global data structure
+ *
+ */
+
+template <typename Scalar, typename StorageIndex>
+void SparseLUImpl<Scalar,StorageIndex>::panel_dfs(const Index m, const Index w, const Index jcol, MatrixType& A, IndexVector& perm_r, Index& nseg, ScalarVector& dense, IndexVector& panel_lsub, IndexVector& segrep, IndexVector& repfnz, IndexVector& xprune, IndexVector& marker, IndexVector& parent, IndexVector& xplore, GlobalLU_t& glu)
+{
+ Index nextl_col; // Next available position in panel_lsub[*,jj]
+
+ // Initialize pointers
+ VectorBlock<IndexVector> marker1(marker, m, m);
+ nseg = 0;
+
+ panel_dfs_traits<IndexVector> traits(jcol, marker1.data());
+
+ // For each column in the panel
+ for (StorageIndex jj = StorageIndex(jcol); jj < jcol + w; jj++)
+ {
+ nextl_col = (jj - jcol) * m;
+
+ VectorBlock<IndexVector> repfnz_col(repfnz, nextl_col, m); // First nonzero location in each row
+ VectorBlock<ScalarVector> dense_col(dense,nextl_col, m); // Accumulate a column vector here
+
+
+ // For each nnz in A[*, jj] do depth first search
+ for (typename MatrixType::InnerIterator it(A, jj); it; ++it)
+ {
+ Index krow = it.row();
+ dense_col(krow) = it.value();
+
+ StorageIndex kmark = marker(krow);
+ if (kmark == jj)
+ continue; // krow visited before, go to the next nonzero
+
+ dfs_kernel(jj, perm_r, nseg, panel_lsub, segrep, repfnz_col, xprune, marker, parent,
+ xplore, glu, nextl_col, krow, traits);
+ }// end for nonzeros in column jj
+
+ } // end for column jj
+}
+
+} // end namespace internal
+} // end namespace Eigen
+
+#endif // SPARSELU_PANEL_DFS_H
diff --git a/Eigen/src/SparseLU/SparseLU_pivotL.h b/Eigen/src/SparseLU/SparseLU_pivotL.h
new file mode 100644
index 0000000..6daed91
--- /dev/null
+++ b/Eigen/src/SparseLU/SparseLU_pivotL.h
@@ -0,0 +1,139 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2012 Désiré Nuentsa-Wakam <desire.nuentsa_wakam@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+/*
+
+ * NOTE: This file is the modified version of xpivotL.c file in SuperLU
+
+ * -- SuperLU routine (version 3.0) --
+ * Univ. of California Berkeley, Xerox Palo Alto Research Center,
+ * and Lawrence Berkeley National Lab.
+ * October 15, 2003
+ *
+ * Copyright (c) 1994 by Xerox Corporation. All rights reserved.
+ *
+ * THIS MATERIAL IS PROVIDED AS IS, WITH ABSOLUTELY NO WARRANTY
+ * EXPRESSED OR IMPLIED. ANY USE IS AT YOUR OWN RISK.
+ *
+ * Permission is hereby granted to use or copy this program for any
+ * purpose, provided the above notices are retained on all copies.
+ * Permission to modify the code and to distribute modified code is
+ * granted, provided the above notices are retained, and a notice that
+ * the code was modified is included with the above copyright notice.
+ */
+#ifndef SPARSELU_PIVOTL_H
+#define SPARSELU_PIVOTL_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+namespace internal {
+
+/**
+ * \brief Performs the numerical pivotin on the current column of L, and the CDIV operation.
+ *
+ * Pivot policy :
+ * (1) Compute thresh = u * max_(i>=j) abs(A_ij);
+ * (2) IF user specifies pivot row k and abs(A_kj) >= thresh THEN
+ * pivot row = k;
+ * ELSE IF abs(A_jj) >= thresh THEN
+ * pivot row = j;
+ * ELSE
+ * pivot row = m;
+ *
+ * Note: If you absolutely want to use a given pivot order, then set u=0.0.
+ *
+ * \param jcol The current column of L
+ * \param diagpivotthresh diagonal pivoting threshold
+ * \param[in,out] perm_r Row permutation (threshold pivoting)
+ * \param[in] iperm_c column permutation - used to finf diagonal of Pc*A*Pc'
+ * \param[out] pivrow The pivot row
+ * \param glu Global LU data
+ * \return 0 if success, i > 0 if U(i,i) is exactly zero
+ *
+ */
+template <typename Scalar, typename StorageIndex>
+Index SparseLUImpl<Scalar,StorageIndex>::pivotL(const Index jcol, const RealScalar& diagpivotthresh, IndexVector& perm_r, IndexVector& iperm_c, Index& pivrow, GlobalLU_t& glu)
+{
+
+ Index fsupc = (glu.xsup)((glu.supno)(jcol)); // First column in the supernode containing the column jcol
+ Index nsupc = jcol - fsupc; // Number of columns in the supernode portion, excluding jcol; nsupc >=0
+ Index lptr = glu.xlsub(fsupc); // pointer to the starting location of the row subscripts for this supernode portion
+ Index nsupr = glu.xlsub(fsupc+1) - lptr; // Number of rows in the supernode
+ Index lda = glu.xlusup(fsupc+1) - glu.xlusup(fsupc); // leading dimension
+ Scalar* lu_sup_ptr = &(glu.lusup.data()[glu.xlusup(fsupc)]); // Start of the current supernode
+ Scalar* lu_col_ptr = &(glu.lusup.data()[glu.xlusup(jcol)]); // Start of jcol in the supernode
+ StorageIndex* lsub_ptr = &(glu.lsub.data()[lptr]); // Start of row indices of the supernode
+
+ // Determine the largest abs numerical value for partial pivoting
+ Index diagind = iperm_c(jcol); // diagonal index
+ RealScalar pivmax(-1.0);
+ Index pivptr = nsupc;
+ Index diag = emptyIdxLU;
+ RealScalar rtemp;
+ Index isub, icol, itemp, k;
+ for (isub = nsupc; isub < nsupr; ++isub) {
+ using std::abs;
+ rtemp = abs(lu_col_ptr[isub]);
+ if (rtemp > pivmax) {
+ pivmax = rtemp;
+ pivptr = isub;
+ }
+ if (lsub_ptr[isub] == diagind) diag = isub;
+ }
+
+ // Test for singularity
+ if ( pivmax <= RealScalar(0.0) ) {
+ // if pivmax == -1, the column is structurally empty, otherwise it is only numerically zero
+ pivrow = pivmax < RealScalar(0.0) ? diagind : lsub_ptr[pivptr];
+ perm_r(pivrow) = StorageIndex(jcol);
+ return (jcol+1);
+ }
+
+ RealScalar thresh = diagpivotthresh * pivmax;
+
+ // Choose appropriate pivotal element
+
+ {
+ // Test if the diagonal element can be used as a pivot (given the threshold value)
+ if (diag >= 0 )
+ {
+ // Diagonal element exists
+ using std::abs;
+ rtemp = abs(lu_col_ptr[diag]);
+ if (rtemp != RealScalar(0.0) && rtemp >= thresh) pivptr = diag;
+ }
+ pivrow = lsub_ptr[pivptr];
+ }
+
+ // Record pivot row
+ perm_r(pivrow) = StorageIndex(jcol);
+ // Interchange row subscripts
+ if (pivptr != nsupc )
+ {
+ std::swap( lsub_ptr[pivptr], lsub_ptr[nsupc] );
+ // Interchange numerical values as well, for the two rows in the whole snode
+ // such that L is indexed the same way as A
+ for (icol = 0; icol <= nsupc; icol++)
+ {
+ itemp = pivptr + icol * lda;
+ std::swap(lu_sup_ptr[itemp], lu_sup_ptr[nsupc + icol * lda]);
+ }
+ }
+ // cdiv operations
+ Scalar temp = Scalar(1.0) / lu_col_ptr[nsupc];
+ for (k = nsupc+1; k < nsupr; k++)
+ lu_col_ptr[k] *= temp;
+ return 0;
+}
+
+} // end namespace internal
+} // end namespace Eigen
+
+#endif // SPARSELU_PIVOTL_H
diff --git a/Eigen/src/SparseLU/SparseLU_pruneL.h b/Eigen/src/SparseLU/SparseLU_pruneL.h
new file mode 100644
index 0000000..e5da73b
--- /dev/null
+++ b/Eigen/src/SparseLU/SparseLU_pruneL.h
@@ -0,0 +1,138 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2012 Désiré Nuentsa-Wakam <desire.nuentsa_wakam@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+/*
+
+ * NOTE: This file is the modified version of [s,d,c,z]pruneL.c file in SuperLU
+
+ * -- SuperLU routine (version 2.0) --
+ * Univ. of California Berkeley, Xerox Palo Alto Research Center,
+ * and Lawrence Berkeley National Lab.
+ * November 15, 1997
+ *
+ * Copyright (c) 1994 by Xerox Corporation. All rights reserved.
+ *
+ * THIS MATERIAL IS PROVIDED AS IS, WITH ABSOLUTELY NO WARRANTY
+ * EXPRESSED OR IMPLIED. ANY USE IS AT YOUR OWN RISK.
+ *
+ * Permission is hereby granted to use or copy this program for any
+ * purpose, provided the above notices are retained on all copies.
+ * Permission to modify the code and to distribute modified code is
+ * granted, provided the above notices are retained, and a notice that
+ * the code was modified is included with the above copyright notice.
+ */
+#ifndef SPARSELU_PRUNEL_H
+#define SPARSELU_PRUNEL_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+namespace internal {
+
+/**
+ * \brief Prunes the L-structure.
+ *
+ * It prunes the L-structure of supernodes whose L-structure contains the current pivot row "pivrow"
+ *
+ *
+ * \param jcol The current column of L
+ * \param[in] perm_r Row permutation
+ * \param[out] pivrow The pivot row
+ * \param nseg Number of segments
+ * \param segrep
+ * \param repfnz
+ * \param[out] xprune
+ * \param glu Global LU data
+ *
+ */
+template <typename Scalar, typename StorageIndex>
+void SparseLUImpl<Scalar,StorageIndex>::pruneL(const Index jcol, const IndexVector& perm_r, const Index pivrow, const Index nseg,
+ const IndexVector& segrep, BlockIndexVector repfnz, IndexVector& xprune, GlobalLU_t& glu)
+{
+ // For each supernode-rep irep in U(*,j]
+ Index jsupno = glu.supno(jcol);
+ Index i,irep,irep1;
+ bool movnum, do_prune = false;
+ Index kmin = 0, kmax = 0, minloc, maxloc,krow;
+ for (i = 0; i < nseg; i++)
+ {
+ irep = segrep(i);
+ irep1 = irep + 1;
+ do_prune = false;
+
+ // Don't prune with a zero U-segment
+ if (repfnz(irep) == emptyIdxLU) continue;
+
+ // If a snode overlaps with the next panel, then the U-segment
+ // is fragmented into two parts -- irep and irep1. We should let
+ // pruning occur at the rep-column in irep1s snode.
+ if (glu.supno(irep) == glu.supno(irep1) ) continue; // don't prune
+
+ // If it has not been pruned & it has a nonz in row L(pivrow,i)
+ if (glu.supno(irep) != jsupno )
+ {
+ if ( xprune (irep) >= glu.xlsub(irep1) )
+ {
+ kmin = glu.xlsub(irep);
+ kmax = glu.xlsub(irep1) - 1;
+ for (krow = kmin; krow <= kmax; krow++)
+ {
+ if (glu.lsub(krow) == pivrow)
+ {
+ do_prune = true;
+ break;
+ }
+ }
+ }
+
+ if (do_prune)
+ {
+ // do a quicksort-type partition
+ // movnum=true means that the num values have to be exchanged
+ movnum = false;
+ if (irep == glu.xsup(glu.supno(irep)) ) // Snode of size 1
+ movnum = true;
+
+ while (kmin <= kmax)
+ {
+ if (perm_r(glu.lsub(kmax)) == emptyIdxLU)
+ kmax--;
+ else if ( perm_r(glu.lsub(kmin)) != emptyIdxLU)
+ kmin++;
+ else
+ {
+ // kmin below pivrow (not yet pivoted), and kmax
+ // above pivrow: interchange the two suscripts
+ std::swap(glu.lsub(kmin), glu.lsub(kmax));
+
+ // If the supernode has only one column, then we
+ // only keep one set of subscripts. For any subscript
+ // intercnahge performed, similar interchange must be
+ // done on the numerical values.
+ if (movnum)
+ {
+ minloc = glu.xlusup(irep) + ( kmin - glu.xlsub(irep) );
+ maxloc = glu.xlusup(irep) + ( kmax - glu.xlsub(irep) );
+ std::swap(glu.lusup(minloc), glu.lusup(maxloc));
+ }
+ kmin++;
+ kmax--;
+ }
+ } // end while
+
+ xprune(irep) = StorageIndex(kmin); //Pruning
+ } // end if do_prune
+ } // end pruning
+ } // End for each U-segment
+}
+
+} // end namespace internal
+} // end namespace Eigen
+
+#endif // SPARSELU_PRUNEL_H
diff --git a/Eigen/src/SparseLU/SparseLU_relax_snode.h b/Eigen/src/SparseLU/SparseLU_relax_snode.h
new file mode 100644
index 0000000..ed79532
--- /dev/null
+++ b/Eigen/src/SparseLU/SparseLU_relax_snode.h
@@ -0,0 +1,85 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2012 Désiré Nuentsa-Wakam <desire.nuentsa_wakam@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+/* This file is a modified version of heap_relax_snode.c file in SuperLU
+ * -- SuperLU routine (version 3.0) --
+ * Univ. of California Berkeley, Xerox Palo Alto Research Center,
+ * and Lawrence Berkeley National Lab.
+ * October 15, 2003
+ *
+ * Copyright (c) 1994 by Xerox Corporation. All rights reserved.
+ *
+ * THIS MATERIAL IS PROVIDED AS IS, WITH ABSOLUTELY NO WARRANTY
+ * EXPRESSED OR IMPLIED. ANY USE IS AT YOUR OWN RISK.
+ *
+ * Permission is hereby granted to use or copy this program for any
+ * purpose, provided the above notices are retained on all copies.
+ * Permission to modify the code and to distribute modified code is
+ * granted, provided the above notices are retained, and a notice that
+ * the code was modified is included with the above copyright notice.
+ */
+
+#ifndef SPARSELU_RELAX_SNODE_H
+#define SPARSELU_RELAX_SNODE_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+
+/**
+ * \brief Identify the initial relaxed supernodes
+ *
+ * This routine is applied to a column elimination tree.
+ * It assumes that the matrix has been reordered according to the postorder of the etree
+ * \param n the number of columns
+ * \param et elimination tree
+ * \param relax_columns Maximum number of columns allowed in a relaxed snode
+ * \param descendants Number of descendants of each node in the etree
+ * \param relax_end last column in a supernode
+ */
+template <typename Scalar, typename StorageIndex>
+void SparseLUImpl<Scalar,StorageIndex>::relax_snode (const Index n, IndexVector& et, const Index relax_columns, IndexVector& descendants, IndexVector& relax_end)
+{
+
+ // compute the number of descendants of each node in the etree
+ Index parent;
+ relax_end.setConstant(emptyIdxLU);
+ descendants.setZero();
+ for (Index j = 0; j < n; j++)
+ {
+ parent = et(j);
+ if (parent != n) // not the dummy root
+ descendants(parent) += descendants(j) + 1;
+ }
+ // Identify the relaxed supernodes by postorder traversal of the etree
+ Index snode_start; // beginning of a snode
+ for (Index j = 0; j < n; )
+ {
+ parent = et(j);
+ snode_start = j;
+ while ( parent != n && descendants(parent) < relax_columns )
+ {
+ j = parent;
+ parent = et(j);
+ }
+ // Found a supernode in postordered etree, j is the last column
+ relax_end(snode_start) = StorageIndex(j); // Record last column
+ j++;
+ // Search for a new leaf
+ while (descendants(j) != 0 && j < n) j++;
+ } // End postorder traversal of the etree
+
+}
+
+} // end namespace internal
+
+} // end namespace Eigen
+#endif
diff --git a/Eigen/src/SparseQR/InternalHeaderCheck.h b/Eigen/src/SparseQR/InternalHeaderCheck.h
new file mode 100644
index 0000000..0564e93
--- /dev/null
+++ b/Eigen/src/SparseQR/InternalHeaderCheck.h
@@ -0,0 +1,3 @@
+#ifndef EIGEN_SPARSEQR_MODULE_H
+#error "Please include Eigen/SparseQR instead of including headers inside the src directory directly."
+#endif
diff --git a/Eigen/src/SparseQR/SparseQR.h b/Eigen/src/SparseQR/SparseQR.h
new file mode 100644
index 0000000..f825092
--- /dev/null
+++ b/Eigen/src/SparseQR/SparseQR.h
@@ -0,0 +1,760 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2012-2013 Desire Nuentsa <desire.nuentsa_wakam@inria.fr>
+// Copyright (C) 2012-2014 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_SPARSE_QR_H
+#define EIGEN_SPARSE_QR_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+template<typename MatrixType, typename OrderingType> class SparseQR;
+template<typename SparseQRType> struct SparseQRMatrixQReturnType;
+template<typename SparseQRType> struct SparseQRMatrixQTransposeReturnType;
+template<typename SparseQRType, typename Derived> struct SparseQR_QProduct;
+namespace internal {
+ template <typename SparseQRType> struct traits<SparseQRMatrixQReturnType<SparseQRType> >
+ {
+ typedef typename SparseQRType::MatrixType ReturnType;
+ typedef typename ReturnType::StorageIndex StorageIndex;
+ typedef typename ReturnType::StorageKind StorageKind;
+ enum {
+ RowsAtCompileTime = Dynamic,
+ ColsAtCompileTime = Dynamic
+ };
+ };
+ template <typename SparseQRType> struct traits<SparseQRMatrixQTransposeReturnType<SparseQRType> >
+ {
+ typedef typename SparseQRType::MatrixType ReturnType;
+ };
+ template <typename SparseQRType, typename Derived> struct traits<SparseQR_QProduct<SparseQRType, Derived> >
+ {
+ typedef typename Derived::PlainObject ReturnType;
+ };
+} // End namespace internal
+
+/**
+ * \ingroup SparseQR_Module
+ * \class SparseQR
+ * \brief Sparse left-looking QR factorization with numerical column pivoting
+ *
+ * This class implements a left-looking QR decomposition of sparse matrices
+ * with numerical column pivoting.
+ * When a column has a norm less than a given tolerance
+ * it is implicitly permuted to the end. The QR factorization thus obtained is
+ * given by A*P = Q*R where R is upper triangular or trapezoidal.
+ *
+ * P is the column permutation which is the product of the fill-reducing and the
+ * numerical permutations. Use colsPermutation() to get it.
+ *
+ * Q is the orthogonal matrix represented as products of Householder reflectors.
+ * Use matrixQ() to get an expression and matrixQ().adjoint() to get the adjoint.
+ * You can then apply it to a vector.
+ *
+ * R is the sparse triangular or trapezoidal matrix. The later occurs when A is rank-deficient.
+ * matrixR().topLeftCorner(rank(), rank()) always returns a triangular factor of full rank.
+ *
+ * \tparam MatrixType_ The type of the sparse matrix A, must be a column-major SparseMatrix<>
+ * \tparam OrderingType_ The fill-reducing ordering method. See the \link OrderingMethods_Module
+ * OrderingMethods \endlink module for the list of built-in and external ordering methods.
+ *
+ * \implsparsesolverconcept
+ *
+ * The numerical pivoting strategy and default threshold are the same as in SuiteSparse QR, and
+ * detailed in the following paper:
+ * <i>
+ * Tim Davis, "Algorithm 915, SuiteSparseQR: Multifrontal Multithreaded Rank-Revealing
+ * Sparse QR Factorization, ACM Trans. on Math. Soft. 38(1), 2011.
+ * </i>
+ * Even though it is qualified as "rank-revealing", this strategy might fail for some
+ * rank deficient problems. When this class is used to solve linear or least-square problems
+ * it is thus strongly recommended to check the accuracy of the computed solution. If it
+ * failed, it usually helps to increase the threshold with setPivotThreshold.
+ *
+ * \warning The input sparse matrix A must be in compressed mode (see SparseMatrix::makeCompressed()).
+ * \warning For complex matrices matrixQ().transpose() will actually return the adjoint matrix.
+ *
+ */
+template<typename MatrixType_, typename OrderingType_>
+class SparseQR : public SparseSolverBase<SparseQR<MatrixType_,OrderingType_> >
+{
+ protected:
+ typedef SparseSolverBase<SparseQR<MatrixType_,OrderingType_> > Base;
+ using Base::m_isInitialized;
+ public:
+ using Base::_solve_impl;
+ typedef MatrixType_ MatrixType;
+ typedef OrderingType_ OrderingType;
+ typedef typename MatrixType::Scalar Scalar;
+ typedef typename MatrixType::RealScalar RealScalar;
+ typedef typename MatrixType::StorageIndex StorageIndex;
+ typedef SparseMatrix<Scalar,ColMajor,StorageIndex> QRMatrixType;
+ typedef Matrix<StorageIndex, Dynamic, 1> IndexVector;
+ typedef Matrix<Scalar, Dynamic, 1> ScalarVector;
+ typedef PermutationMatrix<Dynamic, Dynamic, StorageIndex> PermutationType;
+
+ enum {
+ ColsAtCompileTime = MatrixType::ColsAtCompileTime,
+ MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime
+ };
+
+ public:
+ SparseQR () : m_analysisIsok(false), m_lastError(""), m_useDefaultThreshold(true),m_isQSorted(false),m_isEtreeOk(false)
+ { }
+
+ /** Construct a QR factorization of the matrix \a mat.
+ *
+ * \warning The matrix \a mat must be in compressed mode (see SparseMatrix::makeCompressed()).
+ *
+ * \sa compute()
+ */
+ explicit SparseQR(const MatrixType& mat) : m_analysisIsok(false), m_lastError(""), m_useDefaultThreshold(true),m_isQSorted(false),m_isEtreeOk(false)
+ {
+ compute(mat);
+ }
+
+ /** Computes the QR factorization of the sparse matrix \a mat.
+ *
+ * \warning The matrix \a mat must be in compressed mode (see SparseMatrix::makeCompressed()).
+ *
+ * \sa analyzePattern(), factorize()
+ */
+ void compute(const MatrixType& mat)
+ {
+ analyzePattern(mat);
+ factorize(mat);
+ }
+ void analyzePattern(const MatrixType& mat);
+ void factorize(const MatrixType& mat);
+
+ /** \returns the number of rows of the represented matrix.
+ */
+ inline Index rows() const { return m_pmat.rows(); }
+
+ /** \returns the number of columns of the represented matrix.
+ */
+ inline Index cols() const { return m_pmat.cols();}
+
+ /** \returns a const reference to the \b sparse upper triangular matrix R of the QR factorization.
+ * \warning The entries of the returned matrix are not sorted. This means that using it in algorithms
+ * expecting sorted entries will fail. This include random coefficient accesses (SpaseMatrix::coeff()),
+ * and coefficient-wise operations. Matrix products and triangular solves are fine though.
+ *
+ * To sort the entries, you can assign it to a row-major matrix, and if a column-major matrix
+ * is required, you can copy it again:
+ * \code
+ * SparseMatrix<double> R = qr.matrixR(); // column-major, not sorted!
+ * SparseMatrix<double,RowMajor> Rr = qr.matrixR(); // row-major, sorted
+ * SparseMatrix<double> Rc = Rr; // column-major, sorted
+ * \endcode
+ */
+ const QRMatrixType& matrixR() const { return m_R; }
+
+ /** \returns the number of non linearly dependent columns as determined by the pivoting threshold.
+ *
+ * \sa setPivotThreshold()
+ */
+ Index rank() const
+ {
+ eigen_assert(m_isInitialized && "The factorization should be called first, use compute()");
+ return m_nonzeropivots;
+ }
+
+ /** \returns an expression of the matrix Q as products of sparse Householder reflectors.
+ * The common usage of this function is to apply it to a dense matrix or vector
+ * \code
+ * VectorXd B1, B2;
+ * // Initialize B1
+ * B2 = matrixQ() * B1;
+ * \endcode
+ *
+ * To get a plain SparseMatrix representation of Q:
+ * \code
+ * SparseMatrix<double> Q;
+ * Q = SparseQR<SparseMatrix<double> >(A).matrixQ();
+ * \endcode
+ * Internally, this call simply performs a sparse product between the matrix Q
+ * and a sparse identity matrix. However, due to the fact that the sparse
+ * reflectors are stored unsorted, two transpositions are needed to sort
+ * them before performing the product.
+ */
+ SparseQRMatrixQReturnType<SparseQR> matrixQ() const
+ { return SparseQRMatrixQReturnType<SparseQR>(*this); }
+
+ /** \returns a const reference to the column permutation P that was applied to A such that A*P = Q*R
+ * It is the combination of the fill-in reducing permutation and numerical column pivoting.
+ */
+ const PermutationType& colsPermutation() const
+ {
+ eigen_assert(m_isInitialized && "Decomposition is not initialized.");
+ return m_outputPerm_c;
+ }
+
+ /** \returns A string describing the type of error.
+ * This method is provided to ease debugging, not to handle errors.
+ */
+ std::string lastErrorMessage() const { return m_lastError; }
+
+ /** \internal */
+ template<typename Rhs, typename Dest>
+ bool _solve_impl(const MatrixBase<Rhs> &B, MatrixBase<Dest> &dest) const
+ {
+ eigen_assert(m_isInitialized && "The factorization should be called first, use compute()");
+ eigen_assert(this->rows() == B.rows() && "SparseQR::solve() : invalid number of rows in the right hand side matrix");
+
+ Index rank = this->rank();
+
+ // Compute Q^* * b;
+ typename Dest::PlainObject y, b;
+ y = this->matrixQ().adjoint() * B;
+ b = y;
+
+ // Solve with the triangular matrix R
+ y.resize((std::max<Index>)(cols(),y.rows()),y.cols());
+ y.topRows(rank) = this->matrixR().topLeftCorner(rank, rank).template triangularView<Upper>().solve(b.topRows(rank));
+ y.bottomRows(y.rows()-rank).setZero();
+
+ // Apply the column permutation
+ if (m_perm_c.size()) dest = colsPermutation() * y.topRows(cols());
+ else dest = y.topRows(cols());
+
+ m_info = Success;
+ return true;
+ }
+
+ /** Sets the threshold that is used to determine linearly dependent columns during the factorization.
+ *
+ * In practice, if during the factorization the norm of the column that has to be eliminated is below
+ * this threshold, then the entire column is treated as zero, and it is moved at the end.
+ */
+ void setPivotThreshold(const RealScalar& threshold)
+ {
+ m_useDefaultThreshold = false;
+ m_threshold = threshold;
+ }
+
+ /** \returns the solution X of \f$ A X = B \f$ using the current decomposition of A.
+ *
+ * \sa compute()
+ */
+ template<typename Rhs>
+ inline const Solve<SparseQR, Rhs> solve(const MatrixBase<Rhs>& B) const
+ {
+ eigen_assert(m_isInitialized && "The factorization should be called first, use compute()");
+ eigen_assert(this->rows() == B.rows() && "SparseQR::solve() : invalid number of rows in the right hand side matrix");
+ return Solve<SparseQR, Rhs>(*this, B.derived());
+ }
+ template<typename Rhs>
+ inline const Solve<SparseQR, Rhs> solve(const SparseMatrixBase<Rhs>& B) const
+ {
+ eigen_assert(m_isInitialized && "The factorization should be called first, use compute()");
+ eigen_assert(this->rows() == B.rows() && "SparseQR::solve() : invalid number of rows in the right hand side matrix");
+ return Solve<SparseQR, Rhs>(*this, B.derived());
+ }
+
+ /** \brief Reports whether previous computation was successful.
+ *
+ * \returns \c Success if computation was successful,
+ * \c NumericalIssue if the QR factorization reports a numerical problem
+ * \c InvalidInput if the input matrix is invalid
+ *
+ * \sa iparm()
+ */
+ ComputationInfo info() const
+ {
+ eigen_assert(m_isInitialized && "Decomposition is not initialized.");
+ return m_info;
+ }
+
+
+ /** \internal */
+ inline void _sort_matrix_Q()
+ {
+ if(this->m_isQSorted) return;
+ // The matrix Q is sorted during the transposition
+ SparseMatrix<Scalar, RowMajor, Index> mQrm(this->m_Q);
+ this->m_Q = mQrm;
+ this->m_isQSorted = true;
+ }
+
+
+ protected:
+ bool m_analysisIsok;
+ bool m_factorizationIsok;
+ mutable ComputationInfo m_info;
+ std::string m_lastError;
+ QRMatrixType m_pmat; // Temporary matrix
+ QRMatrixType m_R; // The triangular factor matrix
+ QRMatrixType m_Q; // The orthogonal reflectors
+ ScalarVector m_hcoeffs; // The Householder coefficients
+ PermutationType m_perm_c; // Fill-reducing Column permutation
+ PermutationType m_pivotperm; // The permutation for rank revealing
+ PermutationType m_outputPerm_c; // The final column permutation
+ RealScalar m_threshold; // Threshold to determine null Householder reflections
+ bool m_useDefaultThreshold; // Use default threshold
+ Index m_nonzeropivots; // Number of non zero pivots found
+ IndexVector m_etree; // Column elimination tree
+ IndexVector m_firstRowElt; // First element in each row
+ bool m_isQSorted; // whether Q is sorted or not
+ bool m_isEtreeOk; // whether the elimination tree match the initial input matrix
+
+ template <typename, typename > friend struct SparseQR_QProduct;
+
+};
+
+/** \brief Preprocessing step of a QR factorization
+ *
+ * \warning The matrix \a mat must be in compressed mode (see SparseMatrix::makeCompressed()).
+ *
+ * In this step, the fill-reducing permutation is computed and applied to the columns of A
+ * and the column elimination tree is computed as well. Only the sparsity pattern of \a mat is exploited.
+ *
+ * \note In this step it is assumed that there is no empty row in the matrix \a mat.
+ */
+template <typename MatrixType, typename OrderingType>
+void SparseQR<MatrixType,OrderingType>::analyzePattern(const MatrixType& mat)
+{
+ eigen_assert(mat.isCompressed() && "SparseQR requires a sparse matrix in compressed mode. Call .makeCompressed() before passing it to SparseQR");
+ // Copy to a column major matrix if the input is rowmajor
+ std::conditional_t<MatrixType::IsRowMajor,QRMatrixType,const MatrixType&> matCpy(mat);
+ // Compute the column fill reducing ordering
+ OrderingType ord;
+ ord(matCpy, m_perm_c);
+ Index n = mat.cols();
+ Index m = mat.rows();
+ Index diagSize = (std::min)(m,n);
+
+ if (!m_perm_c.size())
+ {
+ m_perm_c.resize(n);
+ m_perm_c.indices().setLinSpaced(n, 0,StorageIndex(n-1));
+ }
+
+ // Compute the column elimination tree of the permuted matrix
+ m_outputPerm_c = m_perm_c.inverse();
+ internal::coletree(matCpy, m_etree, m_firstRowElt, m_outputPerm_c.indices().data());
+ m_isEtreeOk = true;
+
+ m_R.resize(m, n);
+ m_Q.resize(m, diagSize);
+
+ // Allocate space for nonzero elements: rough estimation
+ m_R.reserve(2*mat.nonZeros()); //FIXME Get a more accurate estimation through symbolic factorization with the etree
+ m_Q.reserve(2*mat.nonZeros());
+ m_hcoeffs.resize(diagSize);
+ m_analysisIsok = true;
+}
+
+/** \brief Performs the numerical QR factorization of the input matrix
+ *
+ * The function SparseQR::analyzePattern(const MatrixType&) must have been called beforehand with
+ * a matrix having the same sparsity pattern than \a mat.
+ *
+ * \param mat The sparse column-major matrix
+ */
+template <typename MatrixType, typename OrderingType>
+void SparseQR<MatrixType,OrderingType>::factorize(const MatrixType& mat)
+{
+ using std::abs;
+
+ eigen_assert(m_analysisIsok && "analyzePattern() should be called before this step");
+ StorageIndex m = StorageIndex(mat.rows());
+ StorageIndex n = StorageIndex(mat.cols());
+ StorageIndex diagSize = (std::min)(m,n);
+ IndexVector mark((std::max)(m,n)); mark.setConstant(-1); // Record the visited nodes
+ IndexVector Ridx(n), Qidx(m); // Store temporarily the row indexes for the current column of R and Q
+ Index nzcolR, nzcolQ; // Number of nonzero for the current column of R and Q
+ ScalarVector tval(m); // The dense vector used to compute the current column
+ RealScalar pivotThreshold = m_threshold;
+
+ m_R.setZero();
+ m_Q.setZero();
+ m_pmat = mat;
+ if(!m_isEtreeOk)
+ {
+ m_outputPerm_c = m_perm_c.inverse();
+ internal::coletree(m_pmat, m_etree, m_firstRowElt, m_outputPerm_c.indices().data());
+ m_isEtreeOk = true;
+ }
+
+ m_pmat.uncompress(); // To have the innerNonZeroPtr allocated
+
+ // Apply the fill-in reducing permutation lazily:
+ {
+ // If the input is row major, copy the original column indices,
+ // otherwise directly use the input matrix
+ //
+ IndexVector originalOuterIndicesCpy;
+ const StorageIndex *originalOuterIndices = mat.outerIndexPtr();
+ if(MatrixType::IsRowMajor)
+ {
+ originalOuterIndicesCpy = IndexVector::Map(m_pmat.outerIndexPtr(),n+1);
+ originalOuterIndices = originalOuterIndicesCpy.data();
+ }
+
+ for (int i = 0; i < n; i++)
+ {
+ Index p = m_perm_c.size() ? m_perm_c.indices()(i) : i;
+ m_pmat.outerIndexPtr()[p] = originalOuterIndices[i];
+ m_pmat.innerNonZeroPtr()[p] = originalOuterIndices[i+1] - originalOuterIndices[i];
+ }
+ }
+
+ /* Compute the default threshold as in MatLab, see:
+ * Tim Davis, "Algorithm 915, SuiteSparseQR: Multifrontal Multithreaded Rank-Revealing
+ * Sparse QR Factorization, ACM Trans. on Math. Soft. 38(1), 2011, Page 8:3
+ */
+ if(m_useDefaultThreshold)
+ {
+ RealScalar max2Norm = 0.0;
+ for (int j = 0; j < n; j++) max2Norm = numext::maxi(max2Norm, m_pmat.col(j).norm());
+ if(max2Norm==RealScalar(0))
+ max2Norm = RealScalar(1);
+ pivotThreshold = 20 * (m + n) * max2Norm * NumTraits<RealScalar>::epsilon();
+ }
+
+ // Initialize the numerical permutation
+ m_pivotperm.setIdentity(n);
+
+ StorageIndex nonzeroCol = 0; // Record the number of valid pivots
+ m_Q.startVec(0);
+
+ // Left looking rank-revealing QR factorization: compute a column of R and Q at a time
+ for (StorageIndex col = 0; col < n; ++col)
+ {
+ mark.setConstant(-1);
+ m_R.startVec(col);
+ mark(nonzeroCol) = col;
+ Qidx(0) = nonzeroCol;
+ nzcolR = 0; nzcolQ = 1;
+ bool found_diag = nonzeroCol>=m;
+ tval.setZero();
+
+ // Symbolic factorization: find the nonzero locations of the column k of the factors R and Q, i.e.,
+ // all the nodes (with indexes lower than rank) reachable through the column elimination tree (etree) rooted at node k.
+ // Note: if the diagonal entry does not exist, then its contribution must be explicitly added,
+ // thus the trick with found_diag that permits to do one more iteration on the diagonal element if this one has not been found.
+ for (typename QRMatrixType::InnerIterator itp(m_pmat, col); itp || !found_diag; ++itp)
+ {
+ StorageIndex curIdx = nonzeroCol;
+ if(itp) curIdx = StorageIndex(itp.row());
+ if(curIdx == nonzeroCol) found_diag = true;
+
+ // Get the nonzeros indexes of the current column of R
+ StorageIndex st = m_firstRowElt(curIdx); // The traversal of the etree starts here
+ if (st < 0 )
+ {
+ m_lastError = "Empty row found during numerical factorization";
+ m_info = InvalidInput;
+ return;
+ }
+
+ // Traverse the etree
+ Index bi = nzcolR;
+ for (; mark(st) != col; st = m_etree(st))
+ {
+ Ridx(nzcolR) = st; // Add this row to the list,
+ mark(st) = col; // and mark this row as visited
+ nzcolR++;
+ }
+
+ // Reverse the list to get the topological ordering
+ Index nt = nzcolR-bi;
+ for(Index i = 0; i < nt/2; i++) std::swap(Ridx(bi+i), Ridx(nzcolR-i-1));
+
+ // Copy the current (curIdx,pcol) value of the input matrix
+ if(itp) tval(curIdx) = itp.value();
+ else tval(curIdx) = Scalar(0);
+
+ // Compute the pattern of Q(:,k)
+ if(curIdx > nonzeroCol && mark(curIdx) != col )
+ {
+ Qidx(nzcolQ) = curIdx; // Add this row to the pattern of Q,
+ mark(curIdx) = col; // and mark it as visited
+ nzcolQ++;
+ }
+ }
+
+ // Browse all the indexes of R(:,col) in reverse order
+ for (Index i = nzcolR-1; i >= 0; i--)
+ {
+ Index curIdx = Ridx(i);
+
+ // Apply the curIdx-th householder vector to the current column (temporarily stored into tval)
+ Scalar tdot(0);
+
+ // First compute q' * tval
+ tdot = m_Q.col(curIdx).dot(tval);
+
+ tdot *= m_hcoeffs(curIdx);
+
+ // Then update tval = tval - q * tau
+ // FIXME: tval -= tdot * m_Q.col(curIdx) should amount to the same (need to check/add support for efficient "dense ?= sparse")
+ for (typename QRMatrixType::InnerIterator itq(m_Q, curIdx); itq; ++itq)
+ tval(itq.row()) -= itq.value() * tdot;
+
+ // Detect fill-in for the current column of Q
+ if(m_etree(Ridx(i)) == nonzeroCol)
+ {
+ for (typename QRMatrixType::InnerIterator itq(m_Q, curIdx); itq; ++itq)
+ {
+ StorageIndex iQ = StorageIndex(itq.row());
+ if (mark(iQ) != col)
+ {
+ Qidx(nzcolQ++) = iQ; // Add this row to the pattern of Q,
+ mark(iQ) = col; // and mark it as visited
+ }
+ }
+ }
+ } // End update current column
+
+ Scalar tau = RealScalar(0);
+ RealScalar beta = 0;
+
+ if(nonzeroCol < diagSize)
+ {
+ // Compute the Householder reflection that eliminate the current column
+ // FIXME this step should call the Householder module.
+ Scalar c0 = nzcolQ ? tval(Qidx(0)) : Scalar(0);
+
+ // First, the squared norm of Q((col+1):m, col)
+ RealScalar sqrNorm = 0.;
+ for (Index itq = 1; itq < nzcolQ; ++itq) sqrNorm += numext::abs2(tval(Qidx(itq)));
+ if(sqrNorm == RealScalar(0) && numext::imag(c0) == RealScalar(0))
+ {
+ beta = numext::real(c0);
+ tval(Qidx(0)) = 1;
+ }
+ else
+ {
+ using std::sqrt;
+ beta = sqrt(numext::abs2(c0) + sqrNorm);
+ if(numext::real(c0) >= RealScalar(0))
+ beta = -beta;
+ tval(Qidx(0)) = 1;
+ for (Index itq = 1; itq < nzcolQ; ++itq)
+ tval(Qidx(itq)) /= (c0 - beta);
+ tau = numext::conj((beta-c0) / beta);
+
+ }
+ }
+
+ // Insert values in R
+ for (Index i = nzcolR-1; i >= 0; i--)
+ {
+ Index curIdx = Ridx(i);
+ if(curIdx < nonzeroCol)
+ {
+ m_R.insertBackByOuterInnerUnordered(col, curIdx) = tval(curIdx);
+ tval(curIdx) = Scalar(0.);
+ }
+ }
+
+ if(nonzeroCol < diagSize && abs(beta) >= pivotThreshold)
+ {
+ m_R.insertBackByOuterInner(col, nonzeroCol) = beta;
+ // The householder coefficient
+ m_hcoeffs(nonzeroCol) = tau;
+ // Record the householder reflections
+ for (Index itq = 0; itq < nzcolQ; ++itq)
+ {
+ Index iQ = Qidx(itq);
+ m_Q.insertBackByOuterInnerUnordered(nonzeroCol,iQ) = tval(iQ);
+ tval(iQ) = Scalar(0.);
+ }
+ nonzeroCol++;
+ if(nonzeroCol<diagSize)
+ m_Q.startVec(nonzeroCol);
+ }
+ else
+ {
+ // Zero pivot found: move implicitly this column to the end
+ for (Index j = nonzeroCol; j < n-1; j++)
+ std::swap(m_pivotperm.indices()(j), m_pivotperm.indices()[j+1]);
+
+ // Recompute the column elimination tree
+ internal::coletree(m_pmat, m_etree, m_firstRowElt, m_pivotperm.indices().data());
+ m_isEtreeOk = false;
+ }
+ }
+
+ m_hcoeffs.tail(diagSize-nonzeroCol).setZero();
+
+ // Finalize the column pointers of the sparse matrices R and Q
+ m_Q.finalize();
+ m_Q.makeCompressed();
+ m_R.finalize();
+ m_R.makeCompressed();
+ m_isQSorted = false;
+
+ m_nonzeropivots = nonzeroCol;
+
+ if(nonzeroCol<n)
+ {
+ // Permute the triangular factor to put the 'dead' columns to the end
+ QRMatrixType tempR(m_R);
+ m_R = tempR * m_pivotperm;
+
+ // Update the column permutation
+ m_outputPerm_c = m_outputPerm_c * m_pivotperm;
+ }
+
+ m_isInitialized = true;
+ m_factorizationIsok = true;
+ m_info = Success;
+}
+
+template <typename SparseQRType, typename Derived>
+struct SparseQR_QProduct : ReturnByValue<SparseQR_QProduct<SparseQRType, Derived> >
+{
+ typedef typename SparseQRType::QRMatrixType MatrixType;
+ typedef typename SparseQRType::Scalar Scalar;
+ // Get the references
+ SparseQR_QProduct(const SparseQRType& qr, const Derived& other, bool transpose) :
+ m_qr(qr),m_other(other),m_transpose(transpose) {}
+ inline Index rows() const { return m_qr.matrixQ().rows(); }
+ inline Index cols() const { return m_other.cols(); }
+
+ // Assign to a vector
+ template<typename DesType>
+ void evalTo(DesType& res) const
+ {
+ Index m = m_qr.rows();
+ Index n = m_qr.cols();
+ Index diagSize = (std::min)(m,n);
+ res = m_other;
+ if (m_transpose)
+ {
+ eigen_assert(m_qr.m_Q.rows() == m_other.rows() && "Non conforming object sizes");
+ //Compute res = Q' * other column by column
+ for(Index j = 0; j < res.cols(); j++){
+ for (Index k = 0; k < diagSize; k++)
+ {
+ Scalar tau = Scalar(0);
+ tau = m_qr.m_Q.col(k).dot(res.col(j));
+ if(tau==Scalar(0)) continue;
+ tau = tau * m_qr.m_hcoeffs(k);
+ res.col(j) -= tau * m_qr.m_Q.col(k);
+ }
+ }
+ }
+ else
+ {
+ eigen_assert(m_qr.matrixQ().cols() == m_other.rows() && "Non conforming object sizes");
+
+ res.conservativeResize(rows(), cols());
+
+ // Compute res = Q * other column by column
+ for(Index j = 0; j < res.cols(); j++)
+ {
+ Index start_k = internal::is_identity<Derived>::value ? numext::mini(j,diagSize-1) : diagSize-1;
+ for (Index k = start_k; k >=0; k--)
+ {
+ Scalar tau = Scalar(0);
+ tau = m_qr.m_Q.col(k).dot(res.col(j));
+ if(tau==Scalar(0)) continue;
+ tau = tau * numext::conj(m_qr.m_hcoeffs(k));
+ res.col(j) -= tau * m_qr.m_Q.col(k);
+ }
+ }
+ }
+ }
+
+ const SparseQRType& m_qr;
+ const Derived& m_other;
+ bool m_transpose; // TODO this actually means adjoint
+};
+
+template<typename SparseQRType>
+struct SparseQRMatrixQReturnType : public EigenBase<SparseQRMatrixQReturnType<SparseQRType> >
+{
+ typedef typename SparseQRType::Scalar Scalar;
+ typedef Matrix<Scalar,Dynamic,Dynamic> DenseMatrix;
+ enum {
+ RowsAtCompileTime = Dynamic,
+ ColsAtCompileTime = Dynamic
+ };
+ explicit SparseQRMatrixQReturnType(const SparseQRType& qr) : m_qr(qr) {}
+ template<typename Derived>
+ SparseQR_QProduct<SparseQRType, Derived> operator*(const MatrixBase<Derived>& other)
+ {
+ return SparseQR_QProduct<SparseQRType,Derived>(m_qr,other.derived(),false);
+ }
+ // To use for operations with the adjoint of Q
+ SparseQRMatrixQTransposeReturnType<SparseQRType> adjoint() const
+ {
+ return SparseQRMatrixQTransposeReturnType<SparseQRType>(m_qr);
+ }
+ inline Index rows() const { return m_qr.rows(); }
+ inline Index cols() const { return m_qr.rows(); }
+ // To use for operations with the transpose of Q FIXME this is the same as adjoint at the moment
+ SparseQRMatrixQTransposeReturnType<SparseQRType> transpose() const
+ {
+ return SparseQRMatrixQTransposeReturnType<SparseQRType>(m_qr);
+ }
+ const SparseQRType& m_qr;
+};
+
+// TODO this actually represents the adjoint of Q
+template<typename SparseQRType>
+struct SparseQRMatrixQTransposeReturnType
+{
+ explicit SparseQRMatrixQTransposeReturnType(const SparseQRType& qr) : m_qr(qr) {}
+ template<typename Derived>
+ SparseQR_QProduct<SparseQRType,Derived> operator*(const MatrixBase<Derived>& other)
+ {
+ return SparseQR_QProduct<SparseQRType,Derived>(m_qr,other.derived(), true);
+ }
+ const SparseQRType& m_qr;
+};
+
+namespace internal {
+
+template<typename SparseQRType>
+struct evaluator_traits<SparseQRMatrixQReturnType<SparseQRType> >
+{
+ typedef typename SparseQRType::MatrixType MatrixType;
+ typedef typename storage_kind_to_evaluator_kind<typename MatrixType::StorageKind>::Kind Kind;
+ typedef SparseShape Shape;
+};
+
+template< typename DstXprType, typename SparseQRType>
+struct Assignment<DstXprType, SparseQRMatrixQReturnType<SparseQRType>, internal::assign_op<typename DstXprType::Scalar,typename DstXprType::Scalar>, Sparse2Sparse>
+{
+ typedef SparseQRMatrixQReturnType<SparseQRType> SrcXprType;
+ typedef typename DstXprType::Scalar Scalar;
+ typedef typename DstXprType::StorageIndex StorageIndex;
+ static void run(DstXprType &dst, const SrcXprType &src, const internal::assign_op<Scalar,Scalar> &/*func*/)
+ {
+ typename DstXprType::PlainObject idMat(src.rows(), src.cols());
+ idMat.setIdentity();
+ // Sort the sparse householder reflectors if needed
+ const_cast<SparseQRType *>(&src.m_qr)->_sort_matrix_Q();
+ dst = SparseQR_QProduct<SparseQRType, DstXprType>(src.m_qr, idMat, false);
+ }
+};
+
+template< typename DstXprType, typename SparseQRType>
+struct Assignment<DstXprType, SparseQRMatrixQReturnType<SparseQRType>, internal::assign_op<typename DstXprType::Scalar,typename DstXprType::Scalar>, Sparse2Dense>
+{
+ typedef SparseQRMatrixQReturnType<SparseQRType> SrcXprType;
+ typedef typename DstXprType::Scalar Scalar;
+ typedef typename DstXprType::StorageIndex StorageIndex;
+ static void run(DstXprType &dst, const SrcXprType &src, const internal::assign_op<Scalar,Scalar> &/*func*/)
+ {
+ dst = src.m_qr.matrixQ() * DstXprType::Identity(src.m_qr.rows(), src.m_qr.rows());
+ }
+};
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif
diff --git a/Eigen/src/StlSupport/StdDeque.h b/Eigen/src/StlSupport/StdDeque.h
new file mode 100644
index 0000000..1e95182
--- /dev/null
+++ b/Eigen/src/StlSupport/StdDeque.h
@@ -0,0 +1,51 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2009 Hauke Heibel <hauke.heibel@googlemail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_STDDEQUE_H
+#define EIGEN_STDDEQUE_H
+
+#ifndef EIGEN_STDDEQUE_MODULE_H
+#error "Please include Eigen/StdDeque instead of including this file directly."
+#endif
+
+#include "details.h"
+
+/**
+ * This section contains a convenience MACRO which allows an easy specialization of
+ * std::deque such that for data types with alignment issues the correct allocator
+ * is used automatically.
+ */
+#define EIGEN_DEFINE_STL_DEQUE_SPECIALIZATION(...) \
+namespace std \
+{ \
+ template<> \
+ class deque<__VA_ARGS__, std::allocator<__VA_ARGS__> > \
+ : public deque<__VA_ARGS__, EIGEN_ALIGNED_ALLOCATOR<__VA_ARGS__> > \
+ { \
+ typedef deque<__VA_ARGS__, EIGEN_ALIGNED_ALLOCATOR<__VA_ARGS__> > deque_base; \
+ public: \
+ typedef __VA_ARGS__ value_type; \
+ typedef deque_base::allocator_type allocator_type; \
+ typedef deque_base::size_type size_type; \
+ typedef deque_base::iterator iterator; \
+ explicit deque(const allocator_type& a = allocator_type()) : deque_base(a) {} \
+ template<typename InputIterator> \
+ deque(InputIterator first, InputIterator last, const allocator_type& a = allocator_type()) : deque_base(first, last, a) {} \
+ deque(const deque& c) : deque_base(c) {} \
+ explicit deque(size_type num, const value_type& val = value_type()) : deque_base(num, val) {} \
+ deque(iterator start_, iterator end_) : deque_base(start_, end_) {} \
+ deque& operator=(const deque& x) { \
+ deque_base::operator=(x); \
+ return *this; \
+ } \
+ }; \
+}
+
+#endif // EIGEN_STDDEQUE_H
diff --git a/Eigen/src/StlSupport/StdList.h b/Eigen/src/StlSupport/StdList.h
new file mode 100644
index 0000000..da36677
--- /dev/null
+++ b/Eigen/src/StlSupport/StdList.h
@@ -0,0 +1,50 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009 Hauke Heibel <hauke.heibel@googlemail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_STDLIST_H
+#define EIGEN_STDLIST_H
+
+#ifndef EIGEN_STDLIST_MODULE_H
+#error "Please include Eigen/StdList instead of including this file directly."
+#endif
+
+#include "details.h"
+
+/**
+ * This section contains a convenience MACRO which allows an easy specialization of
+ * std::list such that for data types with alignment issues the correct allocator
+ * is used automatically.
+ */
+#define EIGEN_DEFINE_STL_LIST_SPECIALIZATION(...) \
+namespace std \
+{ \
+ template<> \
+ class list<__VA_ARGS__, std::allocator<__VA_ARGS__> > \
+ : public list<__VA_ARGS__, EIGEN_ALIGNED_ALLOCATOR<__VA_ARGS__> > \
+ { \
+ typedef list<__VA_ARGS__, EIGEN_ALIGNED_ALLOCATOR<__VA_ARGS__> > list_base; \
+ public: \
+ typedef __VA_ARGS__ value_type; \
+ typedef list_base::allocator_type allocator_type; \
+ typedef list_base::size_type size_type; \
+ typedef list_base::iterator iterator; \
+ explicit list(const allocator_type& a = allocator_type()) : list_base(a) {} \
+ template<typename InputIterator> \
+ list(InputIterator first, InputIterator last, const allocator_type& a = allocator_type()) : list_base(first, last, a) {} \
+ list(const list& c) : list_base(c) {} \
+ explicit list(size_type num, const value_type& val = value_type()) : list_base(num, val) {} \
+ list(iterator start_, iterator end_) : list_base(start_, end_) {} \
+ list& operator=(const list& x) { \
+ list_base::operator=(x); \
+ return *this; \
+ } \
+ }; \
+}
+
+#endif // EIGEN_STDLIST_H
diff --git a/Eigen/src/StlSupport/StdVector.h b/Eigen/src/StlSupport/StdVector.h
new file mode 100644
index 0000000..02dfb39
--- /dev/null
+++ b/Eigen/src/StlSupport/StdVector.h
@@ -0,0 +1,51 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2009 Hauke Heibel <hauke.heibel@googlemail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_STDVECTOR_H
+#define EIGEN_STDVECTOR_H
+
+#ifndef EIGEN_STDVECTOR_MODULE_H
+#error "Please include Eigen/StdVector instead of including this file directly."
+#endif
+
+#include "details.h"
+
+/**
+ * This section contains a convenience MACRO which allows an easy specialization of
+ * std::vector such that for data types with alignment issues the correct allocator
+ * is used automatically.
+ */
+#define EIGEN_DEFINE_STL_VECTOR_SPECIALIZATION(...) \
+namespace std \
+{ \
+ template<> \
+ class vector<__VA_ARGS__, std::allocator<__VA_ARGS__> > \
+ : public vector<__VA_ARGS__, EIGEN_ALIGNED_ALLOCATOR<__VA_ARGS__> > \
+ { \
+ typedef vector<__VA_ARGS__, EIGEN_ALIGNED_ALLOCATOR<__VA_ARGS__> > vector_base; \
+ public: \
+ typedef __VA_ARGS__ value_type; \
+ typedef vector_base::allocator_type allocator_type; \
+ typedef vector_base::size_type size_type; \
+ typedef vector_base::iterator iterator; \
+ explicit vector(const allocator_type& a = allocator_type()) : vector_base(a) {} \
+ template<typename InputIterator> \
+ vector(InputIterator first, InputIterator last, const allocator_type& a = allocator_type()) : vector_base(first, last, a) {} \
+ vector(const vector& c) : vector_base(c) {} \
+ explicit vector(size_type num, const value_type& val = value_type()) : vector_base(num, val) {} \
+ vector(iterator start_, iterator end_) : vector_base(start_, end_) {} \
+ vector& operator=(const vector& x) { \
+ vector_base::operator=(x); \
+ return *this; \
+ } \
+ }; \
+}
+
+#endif // EIGEN_STDVECTOR_H
diff --git a/Eigen/src/StlSupport/details.h b/Eigen/src/StlSupport/details.h
new file mode 100644
index 0000000..29fd871
--- /dev/null
+++ b/Eigen/src/StlSupport/details.h
@@ -0,0 +1,80 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2009 Hauke Heibel <hauke.heibel@googlemail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_STL_DETAILS_H
+#define EIGEN_STL_DETAILS_H
+
+#ifndef EIGEN_ALIGNED_ALLOCATOR
+ #define EIGEN_ALIGNED_ALLOCATOR Eigen::aligned_allocator
+#endif
+
+namespace Eigen {
+
+ // This one is needed to prevent reimplementing the whole std::vector.
+ template <class T>
+ class aligned_allocator_indirection : public EIGEN_ALIGNED_ALLOCATOR<T>
+ {
+ public:
+ typedef std::size_t size_type;
+ typedef std::ptrdiff_t difference_type;
+ typedef T* pointer;
+ typedef const T* const_pointer;
+ typedef T& reference;
+ typedef const T& const_reference;
+ typedef T value_type;
+
+ template<class U>
+ struct rebind
+ {
+ typedef aligned_allocator_indirection<U> other;
+ };
+
+ aligned_allocator_indirection() {}
+ aligned_allocator_indirection(const aligned_allocator_indirection& ) : EIGEN_ALIGNED_ALLOCATOR<T>() {}
+ aligned_allocator_indirection(const EIGEN_ALIGNED_ALLOCATOR<T>& ) {}
+ template<class U>
+ aligned_allocator_indirection(const aligned_allocator_indirection<U>& ) {}
+ template<class U>
+ aligned_allocator_indirection(const EIGEN_ALIGNED_ALLOCATOR<U>& ) {}
+ ~aligned_allocator_indirection() {}
+ };
+
+#if EIGEN_COMP_MSVC
+
+ // sometimes, MSVC detects, at compile time, that the argument x
+ // in std::vector::resize(size_t s,T x) won't be aligned and generate an error
+ // even if this function is never called. Whence this little wrapper.
+#define EIGEN_WORKAROUND_MSVC_STL_SUPPORT(T) \
+ std::conditional_t<Eigen::internal::is_arithmetic<T>::value, T, Eigen::internal::workaround_msvc_stl_support<T> >
+
+ namespace internal {
+ template<typename T> struct workaround_msvc_stl_support : public T
+ {
+ inline workaround_msvc_stl_support() : T() {}
+ inline workaround_msvc_stl_support(const T& other) : T(other) {}
+ inline operator T& () { return *static_cast<T*>(this); }
+ inline operator const T& () const { return *static_cast<const T*>(this); }
+ template<typename OtherT>
+ inline T& operator=(const OtherT& other)
+ { T::operator=(other); return *this; }
+ inline workaround_msvc_stl_support& operator=(const workaround_msvc_stl_support& other)
+ { T::operator=(other); return *this; }
+ };
+ }
+
+#else
+
+#define EIGEN_WORKAROUND_MSVC_STL_SUPPORT(T) T
+
+#endif
+
+}
+
+#endif // EIGEN_STL_DETAILS_H
diff --git a/Eigen/src/SuperLUSupport/InternalHeaderCheck.h b/Eigen/src/SuperLUSupport/InternalHeaderCheck.h
new file mode 100644
index 0000000..94a62b5
--- /dev/null
+++ b/Eigen/src/SuperLUSupport/InternalHeaderCheck.h
@@ -0,0 +1,3 @@
+#ifndef EIGEN_SUPERLUSUPPORT_MODULE_H
+#error "Please include Eigen/SuperLUSupport instead of including headers inside the src directory directly."
+#endif
diff --git a/Eigen/src/SuperLUSupport/SuperLUSupport.h b/Eigen/src/SuperLUSupport/SuperLUSupport.h
new file mode 100644
index 0000000..4bac22d
--- /dev/null
+++ b/Eigen/src/SuperLUSupport/SuperLUSupport.h
@@ -0,0 +1,1027 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2015 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_SUPERLUSUPPORT_H
+#define EIGEN_SUPERLUSUPPORT_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+#if defined(SUPERLU_MAJOR_VERSION) && (SUPERLU_MAJOR_VERSION >= 5)
+#define DECL_GSSVX(PREFIX,FLOATTYPE,KEYTYPE) \
+ extern "C" { \
+ extern void PREFIX##gssvx(superlu_options_t *, SuperMatrix *, int *, int *, int *, \
+ char *, FLOATTYPE *, FLOATTYPE *, SuperMatrix *, SuperMatrix *, \
+ void *, int, SuperMatrix *, SuperMatrix *, \
+ FLOATTYPE *, FLOATTYPE *, FLOATTYPE *, FLOATTYPE *, \
+ GlobalLU_t *, mem_usage_t *, SuperLUStat_t *, int *); \
+ } \
+ inline float SuperLU_gssvx(superlu_options_t *options, SuperMatrix *A, \
+ int *perm_c, int *perm_r, int *etree, char *equed, \
+ FLOATTYPE *R, FLOATTYPE *C, SuperMatrix *L, \
+ SuperMatrix *U, void *work, int lwork, \
+ SuperMatrix *B, SuperMatrix *X, \
+ FLOATTYPE *recip_pivot_growth, \
+ FLOATTYPE *rcond, FLOATTYPE *ferr, FLOATTYPE *berr, \
+ SuperLUStat_t *stats, int *info, KEYTYPE) { \
+ mem_usage_t mem_usage; \
+ GlobalLU_t gLU; \
+ PREFIX##gssvx(options, A, perm_c, perm_r, etree, equed, R, C, L, \
+ U, work, lwork, B, X, recip_pivot_growth, rcond, \
+ ferr, berr, &gLU, &mem_usage, stats, info); \
+ return mem_usage.for_lu; /* bytes used by the factor storage */ \
+ }
+#else // version < 5.0
+#define DECL_GSSVX(PREFIX,FLOATTYPE,KEYTYPE) \
+ extern "C" { \
+ extern void PREFIX##gssvx(superlu_options_t *, SuperMatrix *, int *, int *, int *, \
+ char *, FLOATTYPE *, FLOATTYPE *, SuperMatrix *, SuperMatrix *, \
+ void *, int, SuperMatrix *, SuperMatrix *, \
+ FLOATTYPE *, FLOATTYPE *, FLOATTYPE *, FLOATTYPE *, \
+ mem_usage_t *, SuperLUStat_t *, int *); \
+ } \
+ inline float SuperLU_gssvx(superlu_options_t *options, SuperMatrix *A, \
+ int *perm_c, int *perm_r, int *etree, char *equed, \
+ FLOATTYPE *R, FLOATTYPE *C, SuperMatrix *L, \
+ SuperMatrix *U, void *work, int lwork, \
+ SuperMatrix *B, SuperMatrix *X, \
+ FLOATTYPE *recip_pivot_growth, \
+ FLOATTYPE *rcond, FLOATTYPE *ferr, FLOATTYPE *berr, \
+ SuperLUStat_t *stats, int *info, KEYTYPE) { \
+ mem_usage_t mem_usage; \
+ PREFIX##gssvx(options, A, perm_c, perm_r, etree, equed, R, C, L, \
+ U, work, lwork, B, X, recip_pivot_growth, rcond, \
+ ferr, berr, &mem_usage, stats, info); \
+ return mem_usage.for_lu; /* bytes used by the factor storage */ \
+ }
+#endif
+
+DECL_GSSVX(s,float,float)
+DECL_GSSVX(c,float,std::complex<float>)
+DECL_GSSVX(d,double,double)
+DECL_GSSVX(z,double,std::complex<double>)
+
+#ifdef MILU_ALPHA
+#define EIGEN_SUPERLU_HAS_ILU
+#endif
+
+#ifdef EIGEN_SUPERLU_HAS_ILU
+
+// similarly for the incomplete factorization using gsisx
+#define DECL_GSISX(PREFIX,FLOATTYPE,KEYTYPE) \
+ extern "C" { \
+ extern void PREFIX##gsisx(superlu_options_t *, SuperMatrix *, int *, int *, int *, \
+ char *, FLOATTYPE *, FLOATTYPE *, SuperMatrix *, SuperMatrix *, \
+ void *, int, SuperMatrix *, SuperMatrix *, FLOATTYPE *, FLOATTYPE *, \
+ mem_usage_t *, SuperLUStat_t *, int *); \
+ } \
+ inline float SuperLU_gsisx(superlu_options_t *options, SuperMatrix *A, \
+ int *perm_c, int *perm_r, int *etree, char *equed, \
+ FLOATTYPE *R, FLOATTYPE *C, SuperMatrix *L, \
+ SuperMatrix *U, void *work, int lwork, \
+ SuperMatrix *B, SuperMatrix *X, \
+ FLOATTYPE *recip_pivot_growth, \
+ FLOATTYPE *rcond, \
+ SuperLUStat_t *stats, int *info, KEYTYPE) { \
+ mem_usage_t mem_usage; \
+ PREFIX##gsisx(options, A, perm_c, perm_r, etree, equed, R, C, L, \
+ U, work, lwork, B, X, recip_pivot_growth, rcond, \
+ &mem_usage, stats, info); \
+ return mem_usage.for_lu; /* bytes used by the factor storage */ \
+ }
+
+DECL_GSISX(s,float,float)
+DECL_GSISX(c,float,std::complex<float>)
+DECL_GSISX(d,double,double)
+DECL_GSISX(z,double,std::complex<double>)
+
+#endif
+
+template<typename MatrixType>
+struct SluMatrixMapHelper;
+
+/** \internal
+ *
+ * A wrapper class for SuperLU matrices. It supports only compressed sparse matrices
+ * and dense matrices. Supernodal and other fancy format are not supported by this wrapper.
+ *
+ * This wrapper class mainly aims to avoids the need of dynamic allocation of the storage structure.
+ */
+struct SluMatrix : SuperMatrix
+{
+ SluMatrix()
+ {
+ Store = &storage;
+ }
+
+ SluMatrix(const SluMatrix& other)
+ : SuperMatrix(other)
+ {
+ Store = &storage;
+ storage = other.storage;
+ }
+
+ SluMatrix& operator=(const SluMatrix& other)
+ {
+ SuperMatrix::operator=(static_cast<const SuperMatrix&>(other));
+ Store = &storage;
+ storage = other.storage;
+ return *this;
+ }
+
+ struct
+ {
+ union {int nnz;int lda;};
+ void *values;
+ int *innerInd;
+ int *outerInd;
+ } storage;
+
+ void setStorageType(Stype_t t)
+ {
+ Stype = t;
+ if (t==SLU_NC || t==SLU_NR || t==SLU_DN)
+ Store = &storage;
+ else
+ {
+ eigen_assert(false && "storage type not supported");
+ Store = 0;
+ }
+ }
+
+ template<typename Scalar>
+ void setScalarType()
+ {
+ if (internal::is_same<Scalar,float>::value)
+ Dtype = SLU_S;
+ else if (internal::is_same<Scalar,double>::value)
+ Dtype = SLU_D;
+ else if (internal::is_same<Scalar,std::complex<float> >::value)
+ Dtype = SLU_C;
+ else if (internal::is_same<Scalar,std::complex<double> >::value)
+ Dtype = SLU_Z;
+ else
+ {
+ eigen_assert(false && "Scalar type not supported by SuperLU");
+ }
+ }
+
+ template<typename MatrixType>
+ static SluMatrix Map(MatrixBase<MatrixType>& _mat)
+ {
+ MatrixType& mat(_mat.derived());
+ eigen_assert( ((MatrixType::Flags&RowMajorBit)!=RowMajorBit) && "row-major dense matrices are not supported by SuperLU");
+ SluMatrix res;
+ res.setStorageType(SLU_DN);
+ res.setScalarType<typename MatrixType::Scalar>();
+ res.Mtype = SLU_GE;
+
+ res.nrow = internal::convert_index<int>(mat.rows());
+ res.ncol = internal::convert_index<int>(mat.cols());
+
+ res.storage.lda = internal::convert_index<int>(MatrixType::IsVectorAtCompileTime ? mat.size() : mat.outerStride());
+ res.storage.values = (void*)(mat.data());
+ return res;
+ }
+
+ template<typename MatrixType>
+ static SluMatrix Map(SparseMatrixBase<MatrixType>& a_mat)
+ {
+ MatrixType &mat(a_mat.derived());
+ SluMatrix res;
+ if ((MatrixType::Flags&RowMajorBit)==RowMajorBit)
+ {
+ res.setStorageType(SLU_NR);
+ res.nrow = internal::convert_index<int>(mat.cols());
+ res.ncol = internal::convert_index<int>(mat.rows());
+ }
+ else
+ {
+ res.setStorageType(SLU_NC);
+ res.nrow = internal::convert_index<int>(mat.rows());
+ res.ncol = internal::convert_index<int>(mat.cols());
+ }
+
+ res.Mtype = SLU_GE;
+
+ res.storage.nnz = internal::convert_index<int>(mat.nonZeros());
+ res.storage.values = mat.valuePtr();
+ res.storage.innerInd = mat.innerIndexPtr();
+ res.storage.outerInd = mat.outerIndexPtr();
+
+ res.setScalarType<typename MatrixType::Scalar>();
+
+ // FIXME the following is not very accurate
+ if (int(MatrixType::Flags) & int(Upper))
+ res.Mtype = SLU_TRU;
+ if (int(MatrixType::Flags) & int(Lower))
+ res.Mtype = SLU_TRL;
+
+ eigen_assert(((int(MatrixType::Flags) & int(SelfAdjoint))==0) && "SelfAdjoint matrix shape not supported by SuperLU");
+
+ return res;
+ }
+};
+
+template<typename Scalar, int Rows, int Cols, int Options, int MRows, int MCols>
+struct SluMatrixMapHelper<Matrix<Scalar,Rows,Cols,Options,MRows,MCols> >
+{
+ typedef Matrix<Scalar,Rows,Cols,Options,MRows,MCols> MatrixType;
+ static void run(MatrixType& mat, SluMatrix& res)
+ {
+ eigen_assert( ((Options&RowMajor)!=RowMajor) && "row-major dense matrices is not supported by SuperLU");
+ res.setStorageType(SLU_DN);
+ res.setScalarType<Scalar>();
+ res.Mtype = SLU_GE;
+
+ res.nrow = mat.rows();
+ res.ncol = mat.cols();
+
+ res.storage.lda = mat.outerStride();
+ res.storage.values = mat.data();
+ }
+};
+
+template<typename Derived>
+struct SluMatrixMapHelper<SparseMatrixBase<Derived> >
+{
+ typedef Derived MatrixType;
+ static void run(MatrixType& mat, SluMatrix& res)
+ {
+ if ((MatrixType::Flags&RowMajorBit)==RowMajorBit)
+ {
+ res.setStorageType(SLU_NR);
+ res.nrow = mat.cols();
+ res.ncol = mat.rows();
+ }
+ else
+ {
+ res.setStorageType(SLU_NC);
+ res.nrow = mat.rows();
+ res.ncol = mat.cols();
+ }
+
+ res.Mtype = SLU_GE;
+
+ res.storage.nnz = mat.nonZeros();
+ res.storage.values = mat.valuePtr();
+ res.storage.innerInd = mat.innerIndexPtr();
+ res.storage.outerInd = mat.outerIndexPtr();
+
+ res.setScalarType<typename MatrixType::Scalar>();
+
+ // FIXME the following is not very accurate
+ if (MatrixType::Flags & Upper)
+ res.Mtype = SLU_TRU;
+ if (MatrixType::Flags & Lower)
+ res.Mtype = SLU_TRL;
+
+ eigen_assert(((MatrixType::Flags & SelfAdjoint)==0) && "SelfAdjoint matrix shape not supported by SuperLU");
+ }
+};
+
+namespace internal {
+
+template<typename MatrixType>
+SluMatrix asSluMatrix(MatrixType& mat)
+{
+ return SluMatrix::Map(mat);
+}
+
+/** View a Super LU matrix as an Eigen expression */
+template<typename Scalar, int Flags, typename Index>
+Map<SparseMatrix<Scalar,Flags,Index> > map_superlu(SluMatrix& sluMat)
+{
+ eigen_assert(((Flags&RowMajor)==RowMajor && sluMat.Stype == SLU_NR)
+ || ((Flags&ColMajor)==ColMajor && sluMat.Stype == SLU_NC));
+
+ Index outerSize = (Flags&RowMajor)==RowMajor ? sluMat.ncol : sluMat.nrow;
+
+ return Map<SparseMatrix<Scalar,Flags,Index> >(
+ sluMat.nrow, sluMat.ncol, sluMat.storage.outerInd[outerSize],
+ sluMat.storage.outerInd, sluMat.storage.innerInd, reinterpret_cast<Scalar*>(sluMat.storage.values) );
+}
+
+} // end namespace internal
+
+/** \ingroup SuperLUSupport_Module
+ * \class SuperLUBase
+ * \brief The base class for the direct and incomplete LU factorization of SuperLU
+ */
+template<typename MatrixType_, typename Derived>
+class SuperLUBase : public SparseSolverBase<Derived>
+{
+ protected:
+ typedef SparseSolverBase<Derived> Base;
+ using Base::derived;
+ using Base::m_isInitialized;
+ public:
+ typedef MatrixType_ MatrixType;
+ typedef typename MatrixType::Scalar Scalar;
+ typedef typename MatrixType::RealScalar RealScalar;
+ typedef typename MatrixType::StorageIndex StorageIndex;
+ typedef Matrix<Scalar,Dynamic,1> Vector;
+ typedef Matrix<int, 1, MatrixType::ColsAtCompileTime> IntRowVectorType;
+ typedef Matrix<int, MatrixType::RowsAtCompileTime, 1> IntColVectorType;
+ typedef Map<PermutationMatrix<Dynamic,Dynamic,int> > PermutationMap;
+ typedef SparseMatrix<Scalar> LUMatrixType;
+ enum {
+ ColsAtCompileTime = MatrixType::ColsAtCompileTime,
+ MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime
+ };
+
+ public:
+
+ SuperLUBase() {}
+
+ ~SuperLUBase()
+ {
+ clearFactors();
+ }
+
+ inline Index rows() const { return m_matrix.rows(); }
+ inline Index cols() const { return m_matrix.cols(); }
+
+ /** \returns a reference to the Super LU option object to configure the Super LU algorithms. */
+ inline superlu_options_t& options() { return m_sluOptions; }
+
+ /** \brief Reports whether previous computation was successful.
+ *
+ * \returns \c Success if computation was successful,
+ * \c NumericalIssue if the matrix.appears to be negative.
+ */
+ ComputationInfo info() const
+ {
+ eigen_assert(m_isInitialized && "Decomposition is not initialized.");
+ return m_info;
+ }
+
+ /** Computes the sparse Cholesky decomposition of \a matrix */
+ void compute(const MatrixType& matrix)
+ {
+ derived().analyzePattern(matrix);
+ derived().factorize(matrix);
+ }
+
+ /** Performs a symbolic decomposition on the sparcity of \a matrix.
+ *
+ * This function is particularly useful when solving for several problems having the same structure.
+ *
+ * \sa factorize()
+ */
+ void analyzePattern(const MatrixType& /*matrix*/)
+ {
+ m_isInitialized = true;
+ m_info = Success;
+ m_analysisIsOk = true;
+ m_factorizationIsOk = false;
+ }
+
+ template<typename Stream>
+ void dumpMemory(Stream& /*s*/)
+ {}
+
+ protected:
+
+ void initFactorization(const MatrixType& a)
+ {
+ set_default_options(&this->m_sluOptions);
+
+ const Index size = a.rows();
+ m_matrix = a;
+
+ m_sluA = internal::asSluMatrix(m_matrix);
+ clearFactors();
+
+ m_p.resize(size);
+ m_q.resize(size);
+ m_sluRscale.resize(size);
+ m_sluCscale.resize(size);
+ m_sluEtree.resize(size);
+
+ // set empty B and X
+ m_sluB.setStorageType(SLU_DN);
+ m_sluB.setScalarType<Scalar>();
+ m_sluB.Mtype = SLU_GE;
+ m_sluB.storage.values = 0;
+ m_sluB.nrow = 0;
+ m_sluB.ncol = 0;
+ m_sluB.storage.lda = internal::convert_index<int>(size);
+ m_sluX = m_sluB;
+
+ m_extractedDataAreDirty = true;
+ }
+
+ void init()
+ {
+ m_info = InvalidInput;
+ m_isInitialized = false;
+ m_sluL.Store = 0;
+ m_sluU.Store = 0;
+ }
+
+ void extractData() const;
+
+ void clearFactors()
+ {
+ if(m_sluL.Store)
+ Destroy_SuperNode_Matrix(&m_sluL);
+ if(m_sluU.Store)
+ Destroy_CompCol_Matrix(&m_sluU);
+
+ m_sluL.Store = 0;
+ m_sluU.Store = 0;
+
+ memset(&m_sluL,0,sizeof m_sluL);
+ memset(&m_sluU,0,sizeof m_sluU);
+ }
+
+ // cached data to reduce reallocation, etc.
+ mutable LUMatrixType m_l;
+ mutable LUMatrixType m_u;
+ mutable IntColVectorType m_p;
+ mutable IntRowVectorType m_q;
+
+ mutable LUMatrixType m_matrix; // copy of the factorized matrix
+ mutable SluMatrix m_sluA;
+ mutable SuperMatrix m_sluL, m_sluU;
+ mutable SluMatrix m_sluB, m_sluX;
+ mutable SuperLUStat_t m_sluStat;
+ mutable superlu_options_t m_sluOptions;
+ mutable std::vector<int> m_sluEtree;
+ mutable Matrix<RealScalar,Dynamic,1> m_sluRscale, m_sluCscale;
+ mutable Matrix<RealScalar,Dynamic,1> m_sluFerr, m_sluBerr;
+ mutable char m_sluEqued;
+
+ mutable ComputationInfo m_info;
+ int m_factorizationIsOk;
+ int m_analysisIsOk;
+ mutable bool m_extractedDataAreDirty;
+
+ private:
+ SuperLUBase(SuperLUBase& ) { }
+};
+
+
+/** \ingroup SuperLUSupport_Module
+ * \class SuperLU
+ * \brief A sparse direct LU factorization and solver based on the SuperLU library
+ *
+ * This class allows to solve for A.X = B sparse linear problems via a direct LU factorization
+ * using the SuperLU library. The sparse matrix A must be squared and invertible. The vectors or matrices
+ * X and B can be either dense or sparse.
+ *
+ * \tparam MatrixType_ the type of the sparse matrix A, it must be a SparseMatrix<>
+ *
+ * \warning This class is only for the 4.x versions of SuperLU. The 3.x and 5.x versions are not supported.
+ *
+ * \implsparsesolverconcept
+ *
+ * \sa \ref TutorialSparseSolverConcept, class SparseLU
+ */
+template<typename MatrixType_>
+class SuperLU : public SuperLUBase<MatrixType_,SuperLU<MatrixType_> >
+{
+ public:
+ typedef SuperLUBase<MatrixType_,SuperLU> Base;
+ typedef MatrixType_ MatrixType;
+ typedef typename Base::Scalar Scalar;
+ typedef typename Base::RealScalar RealScalar;
+ typedef typename Base::StorageIndex StorageIndex;
+ typedef typename Base::IntRowVectorType IntRowVectorType;
+ typedef typename Base::IntColVectorType IntColVectorType;
+ typedef typename Base::PermutationMap PermutationMap;
+ typedef typename Base::LUMatrixType LUMatrixType;
+ typedef TriangularView<LUMatrixType, Lower|UnitDiag> LMatrixType;
+ typedef TriangularView<LUMatrixType, Upper> UMatrixType;
+
+ public:
+ using Base::_solve_impl;
+
+ SuperLU() : Base() { init(); }
+
+ explicit SuperLU(const MatrixType& matrix) : Base()
+ {
+ init();
+ Base::compute(matrix);
+ }
+
+ ~SuperLU()
+ {
+ }
+
+ /** Performs a symbolic decomposition on the sparcity of \a matrix.
+ *
+ * This function is particularly useful when solving for several problems having the same structure.
+ *
+ * \sa factorize()
+ */
+ void analyzePattern(const MatrixType& matrix)
+ {
+ m_info = InvalidInput;
+ m_isInitialized = false;
+ Base::analyzePattern(matrix);
+ }
+
+ /** Performs a numeric decomposition of \a matrix
+ *
+ * The given matrix must has the same sparcity than the matrix on which the symbolic decomposition has been performed.
+ *
+ * \sa analyzePattern()
+ */
+ void factorize(const MatrixType& matrix);
+
+ /** \internal */
+ template<typename Rhs,typename Dest>
+ void _solve_impl(const MatrixBase<Rhs> &b, MatrixBase<Dest> &dest) const;
+
+ inline const LMatrixType& matrixL() const
+ {
+ if (m_extractedDataAreDirty) this->extractData();
+ return m_l;
+ }
+
+ inline const UMatrixType& matrixU() const
+ {
+ if (m_extractedDataAreDirty) this->extractData();
+ return m_u;
+ }
+
+ inline const IntColVectorType& permutationP() const
+ {
+ if (m_extractedDataAreDirty) this->extractData();
+ return m_p;
+ }
+
+ inline const IntRowVectorType& permutationQ() const
+ {
+ if (m_extractedDataAreDirty) this->extractData();
+ return m_q;
+ }
+
+ Scalar determinant() const;
+
+ protected:
+
+ using Base::m_matrix;
+ using Base::m_sluOptions;
+ using Base::m_sluA;
+ using Base::m_sluB;
+ using Base::m_sluX;
+ using Base::m_p;
+ using Base::m_q;
+ using Base::m_sluEtree;
+ using Base::m_sluEqued;
+ using Base::m_sluRscale;
+ using Base::m_sluCscale;
+ using Base::m_sluL;
+ using Base::m_sluU;
+ using Base::m_sluStat;
+ using Base::m_sluFerr;
+ using Base::m_sluBerr;
+ using Base::m_l;
+ using Base::m_u;
+
+ using Base::m_analysisIsOk;
+ using Base::m_factorizationIsOk;
+ using Base::m_extractedDataAreDirty;
+ using Base::m_isInitialized;
+ using Base::m_info;
+
+ void init()
+ {
+ Base::init();
+
+ set_default_options(&this->m_sluOptions);
+ m_sluOptions.PrintStat = NO;
+ m_sluOptions.ConditionNumber = NO;
+ m_sluOptions.Trans = NOTRANS;
+ m_sluOptions.ColPerm = COLAMD;
+ }
+
+
+ private:
+ SuperLU(SuperLU& ) { }
+};
+
+template<typename MatrixType>
+void SuperLU<MatrixType>::factorize(const MatrixType& a)
+{
+ eigen_assert(m_analysisIsOk && "You must first call analyzePattern()");
+ if(!m_analysisIsOk)
+ {
+ m_info = InvalidInput;
+ return;
+ }
+
+ this->initFactorization(a);
+
+ m_sluOptions.ColPerm = COLAMD;
+ int info = 0;
+ RealScalar recip_pivot_growth, rcond;
+ RealScalar ferr, berr;
+
+ StatInit(&m_sluStat);
+ SuperLU_gssvx(&m_sluOptions, &m_sluA, m_q.data(), m_p.data(), &m_sluEtree[0],
+ &m_sluEqued, &m_sluRscale[0], &m_sluCscale[0],
+ &m_sluL, &m_sluU,
+ NULL, 0,
+ &m_sluB, &m_sluX,
+ &recip_pivot_growth, &rcond,
+ &ferr, &berr,
+ &m_sluStat, &info, Scalar());
+ StatFree(&m_sluStat);
+
+ m_extractedDataAreDirty = true;
+
+ // FIXME how to better check for errors ???
+ m_info = info == 0 ? Success : NumericalIssue;
+ m_factorizationIsOk = true;
+}
+
+template<typename MatrixType>
+template<typename Rhs,typename Dest>
+void SuperLU<MatrixType>::_solve_impl(const MatrixBase<Rhs> &b, MatrixBase<Dest>& x) const
+{
+ eigen_assert(m_factorizationIsOk && "The decomposition is not in a valid state for solving, you must first call either compute() or analyzePattern()/factorize()");
+
+ const Index rhsCols = b.cols();
+ eigen_assert(m_matrix.rows()==b.rows());
+
+ m_sluOptions.Trans = NOTRANS;
+ m_sluOptions.Fact = FACTORED;
+ m_sluOptions.IterRefine = NOREFINE;
+
+
+ m_sluFerr.resize(rhsCols);
+ m_sluBerr.resize(rhsCols);
+
+ Ref<const Matrix<typename Rhs::Scalar,Dynamic,Dynamic,ColMajor> > b_ref(b);
+ Ref<const Matrix<typename Dest::Scalar,Dynamic,Dynamic,ColMajor> > x_ref(x);
+
+ m_sluB = SluMatrix::Map(b_ref.const_cast_derived());
+ m_sluX = SluMatrix::Map(x_ref.const_cast_derived());
+
+ typename Rhs::PlainObject b_cpy;
+ if(m_sluEqued!='N')
+ {
+ b_cpy = b;
+ m_sluB = SluMatrix::Map(b_cpy.const_cast_derived());
+ }
+
+ StatInit(&m_sluStat);
+ int info = 0;
+ RealScalar recip_pivot_growth, rcond;
+ SuperLU_gssvx(&m_sluOptions, &m_sluA,
+ m_q.data(), m_p.data(),
+ &m_sluEtree[0], &m_sluEqued,
+ &m_sluRscale[0], &m_sluCscale[0],
+ &m_sluL, &m_sluU,
+ NULL, 0,
+ &m_sluB, &m_sluX,
+ &recip_pivot_growth, &rcond,
+ &m_sluFerr[0], &m_sluBerr[0],
+ &m_sluStat, &info, Scalar());
+ StatFree(&m_sluStat);
+
+ if(x.derived().data() != x_ref.data())
+ x = x_ref;
+
+ m_info = info==0 ? Success : NumericalIssue;
+}
+
+// the code of this extractData() function has been adapted from the SuperLU's Matlab support code,
+//
+// Copyright (c) 1994 by Xerox Corporation. All rights reserved.
+//
+// THIS MATERIAL IS PROVIDED AS IS, WITH ABSOLUTELY NO WARRANTY
+// EXPRESSED OR IMPLIED. ANY USE IS AT YOUR OWN RISK.
+//
+template<typename MatrixType, typename Derived>
+void SuperLUBase<MatrixType,Derived>::extractData() const
+{
+ eigen_assert(m_factorizationIsOk && "The decomposition is not in a valid state for extracting factors, you must first call either compute() or analyzePattern()/factorize()");
+ if (m_extractedDataAreDirty)
+ {
+ int upper;
+ int fsupc, istart, nsupr;
+ int lastl = 0, lastu = 0;
+ SCformat *Lstore = static_cast<SCformat*>(m_sluL.Store);
+ NCformat *Ustore = static_cast<NCformat*>(m_sluU.Store);
+ Scalar *SNptr;
+
+ const Index size = m_matrix.rows();
+ m_l.resize(size,size);
+ m_l.resizeNonZeros(Lstore->nnz);
+ m_u.resize(size,size);
+ m_u.resizeNonZeros(Ustore->nnz);
+
+ int* Lcol = m_l.outerIndexPtr();
+ int* Lrow = m_l.innerIndexPtr();
+ Scalar* Lval = m_l.valuePtr();
+
+ int* Ucol = m_u.outerIndexPtr();
+ int* Urow = m_u.innerIndexPtr();
+ Scalar* Uval = m_u.valuePtr();
+
+ Ucol[0] = 0;
+ Ucol[0] = 0;
+
+ /* for each supernode */
+ for (int k = 0; k <= Lstore->nsuper; ++k)
+ {
+ fsupc = L_FST_SUPC(k);
+ istart = L_SUB_START(fsupc);
+ nsupr = L_SUB_START(fsupc+1) - istart;
+ upper = 1;
+
+ /* for each column in the supernode */
+ for (int j = fsupc; j < L_FST_SUPC(k+1); ++j)
+ {
+ SNptr = &((Scalar*)Lstore->nzval)[L_NZ_START(j)];
+
+ /* Extract U */
+ for (int i = U_NZ_START(j); i < U_NZ_START(j+1); ++i)
+ {
+ Uval[lastu] = ((Scalar*)Ustore->nzval)[i];
+ /* Matlab doesn't like explicit zero. */
+ if (Uval[lastu] != 0.0)
+ Urow[lastu++] = U_SUB(i);
+ }
+ for (int i = 0; i < upper; ++i)
+ {
+ /* upper triangle in the supernode */
+ Uval[lastu] = SNptr[i];
+ /* Matlab doesn't like explicit zero. */
+ if (Uval[lastu] != 0.0)
+ Urow[lastu++] = L_SUB(istart+i);
+ }
+ Ucol[j+1] = lastu;
+
+ /* Extract L */
+ Lval[lastl] = 1.0; /* unit diagonal */
+ Lrow[lastl++] = L_SUB(istart + upper - 1);
+ for (int i = upper; i < nsupr; ++i)
+ {
+ Lval[lastl] = SNptr[i];
+ /* Matlab doesn't like explicit zero. */
+ if (Lval[lastl] != 0.0)
+ Lrow[lastl++] = L_SUB(istart+i);
+ }
+ Lcol[j+1] = lastl;
+
+ ++upper;
+ } /* for j ... */
+
+ } /* for k ... */
+
+ // squeeze the matrices :
+ m_l.resizeNonZeros(lastl);
+ m_u.resizeNonZeros(lastu);
+
+ m_extractedDataAreDirty = false;
+ }
+}
+
+template<typename MatrixType>
+typename SuperLU<MatrixType>::Scalar SuperLU<MatrixType>::determinant() const
+{
+ eigen_assert(m_factorizationIsOk && "The decomposition is not in a valid state for computing the determinant, you must first call either compute() or analyzePattern()/factorize()");
+
+ if (m_extractedDataAreDirty)
+ this->extractData();
+
+ Scalar det = Scalar(1);
+ for (int j=0; j<m_u.cols(); ++j)
+ {
+ if (m_u.outerIndexPtr()[j+1]-m_u.outerIndexPtr()[j] > 0)
+ {
+ int lastId = m_u.outerIndexPtr()[j+1]-1;
+ eigen_assert(m_u.innerIndexPtr()[lastId]<=j);
+ if (m_u.innerIndexPtr()[lastId]==j)
+ det *= m_u.valuePtr()[lastId];
+ }
+ }
+ if(PermutationMap(m_p.data(),m_p.size()).determinant()*PermutationMap(m_q.data(),m_q.size()).determinant()<0)
+ det = -det;
+ if(m_sluEqued!='N')
+ return det/m_sluRscale.prod()/m_sluCscale.prod();
+ else
+ return det;
+}
+
+#ifdef EIGEN_PARSED_BY_DOXYGEN
+#define EIGEN_SUPERLU_HAS_ILU
+#endif
+
+#ifdef EIGEN_SUPERLU_HAS_ILU
+
+/** \ingroup SuperLUSupport_Module
+ * \class SuperILU
+ * \brief A sparse direct \b incomplete LU factorization and solver based on the SuperLU library
+ *
+ * This class allows to solve for an approximate solution of A.X = B sparse linear problems via an incomplete LU factorization
+ * using the SuperLU library. This class is aimed to be used as a preconditioner of the iterative linear solvers.
+ *
+ * \warning This class is only for the 4.x versions of SuperLU. The 3.x and 5.x versions are not supported.
+ *
+ * \tparam MatrixType_ the type of the sparse matrix A, it must be a SparseMatrix<>
+ *
+ * \implsparsesolverconcept
+ *
+ * \sa \ref TutorialSparseSolverConcept, class IncompleteLUT, class ConjugateGradient, class BiCGSTAB
+ */
+
+template<typename MatrixType_>
+class SuperILU : public SuperLUBase<MatrixType_,SuperILU<MatrixType_> >
+{
+ public:
+ typedef SuperLUBase<MatrixType_,SuperILU> Base;
+ typedef MatrixType_ MatrixType;
+ typedef typename Base::Scalar Scalar;
+ typedef typename Base::RealScalar RealScalar;
+
+ public:
+ using Base::_solve_impl;
+
+ SuperILU() : Base() { init(); }
+
+ SuperILU(const MatrixType& matrix) : Base()
+ {
+ init();
+ Base::compute(matrix);
+ }
+
+ ~SuperILU()
+ {
+ }
+
+ /** Performs a symbolic decomposition on the sparcity of \a matrix.
+ *
+ * This function is particularly useful when solving for several problems having the same structure.
+ *
+ * \sa factorize()
+ */
+ void analyzePattern(const MatrixType& matrix)
+ {
+ Base::analyzePattern(matrix);
+ }
+
+ /** Performs a numeric decomposition of \a matrix
+ *
+ * The given matrix must has the same sparcity than the matrix on which the symbolic decomposition has been performed.
+ *
+ * \sa analyzePattern()
+ */
+ void factorize(const MatrixType& matrix);
+
+ #ifndef EIGEN_PARSED_BY_DOXYGEN
+ /** \internal */
+ template<typename Rhs,typename Dest>
+ void _solve_impl(const MatrixBase<Rhs> &b, MatrixBase<Dest> &dest) const;
+ #endif // EIGEN_PARSED_BY_DOXYGEN
+
+ protected:
+
+ using Base::m_matrix;
+ using Base::m_sluOptions;
+ using Base::m_sluA;
+ using Base::m_sluB;
+ using Base::m_sluX;
+ using Base::m_p;
+ using Base::m_q;
+ using Base::m_sluEtree;
+ using Base::m_sluEqued;
+ using Base::m_sluRscale;
+ using Base::m_sluCscale;
+ using Base::m_sluL;
+ using Base::m_sluU;
+ using Base::m_sluStat;
+ using Base::m_sluFerr;
+ using Base::m_sluBerr;
+ using Base::m_l;
+ using Base::m_u;
+
+ using Base::m_analysisIsOk;
+ using Base::m_factorizationIsOk;
+ using Base::m_extractedDataAreDirty;
+ using Base::m_isInitialized;
+ using Base::m_info;
+
+ void init()
+ {
+ Base::init();
+
+ ilu_set_default_options(&m_sluOptions);
+ m_sluOptions.PrintStat = NO;
+ m_sluOptions.ConditionNumber = NO;
+ m_sluOptions.Trans = NOTRANS;
+ m_sluOptions.ColPerm = MMD_AT_PLUS_A;
+
+ // no attempt to preserve column sum
+ m_sluOptions.ILU_MILU = SILU;
+ // only basic ILU(k) support -- no direct control over memory consumption
+ // better to use ILU_DropRule = DROP_BASIC | DROP_AREA
+ // and set ILU_FillFactor to max memory growth
+ m_sluOptions.ILU_DropRule = DROP_BASIC;
+ m_sluOptions.ILU_DropTol = NumTraits<Scalar>::dummy_precision()*10;
+ }
+
+ private:
+ SuperILU(SuperILU& ) { }
+};
+
+template<typename MatrixType>
+void SuperILU<MatrixType>::factorize(const MatrixType& a)
+{
+ eigen_assert(m_analysisIsOk && "You must first call analyzePattern()");
+ if(!m_analysisIsOk)
+ {
+ m_info = InvalidInput;
+ return;
+ }
+
+ this->initFactorization(a);
+
+ int info = 0;
+ RealScalar recip_pivot_growth, rcond;
+
+ StatInit(&m_sluStat);
+ SuperLU_gsisx(&m_sluOptions, &m_sluA, m_q.data(), m_p.data(), &m_sluEtree[0],
+ &m_sluEqued, &m_sluRscale[0], &m_sluCscale[0],
+ &m_sluL, &m_sluU,
+ NULL, 0,
+ &m_sluB, &m_sluX,
+ &recip_pivot_growth, &rcond,
+ &m_sluStat, &info, Scalar());
+ StatFree(&m_sluStat);
+
+ // FIXME how to better check for errors ???
+ m_info = info == 0 ? Success : NumericalIssue;
+ m_factorizationIsOk = true;
+}
+
+#ifndef EIGEN_PARSED_BY_DOXYGEN
+template<typename MatrixType>
+template<typename Rhs,typename Dest>
+void SuperILU<MatrixType>::_solve_impl(const MatrixBase<Rhs> &b, MatrixBase<Dest>& x) const
+{
+ eigen_assert(m_factorizationIsOk && "The decomposition is not in a valid state for solving, you must first call either compute() or analyzePattern()/factorize()");
+
+ const int rhsCols = b.cols();
+ eigen_assert(m_matrix.rows()==b.rows());
+
+ m_sluOptions.Trans = NOTRANS;
+ m_sluOptions.Fact = FACTORED;
+ m_sluOptions.IterRefine = NOREFINE;
+
+ m_sluFerr.resize(rhsCols);
+ m_sluBerr.resize(rhsCols);
+
+ Ref<const Matrix<typename Rhs::Scalar,Dynamic,Dynamic,ColMajor> > b_ref(b);
+ Ref<const Matrix<typename Dest::Scalar,Dynamic,Dynamic,ColMajor> > x_ref(x);
+
+ m_sluB = SluMatrix::Map(b_ref.const_cast_derived());
+ m_sluX = SluMatrix::Map(x_ref.const_cast_derived());
+
+ typename Rhs::PlainObject b_cpy;
+ if(m_sluEqued!='N')
+ {
+ b_cpy = b;
+ m_sluB = SluMatrix::Map(b_cpy.const_cast_derived());
+ }
+
+ int info = 0;
+ RealScalar recip_pivot_growth, rcond;
+
+ StatInit(&m_sluStat);
+ SuperLU_gsisx(&m_sluOptions, &m_sluA,
+ m_q.data(), m_p.data(),
+ &m_sluEtree[0], &m_sluEqued,
+ &m_sluRscale[0], &m_sluCscale[0],
+ &m_sluL, &m_sluU,
+ NULL, 0,
+ &m_sluB, &m_sluX,
+ &recip_pivot_growth, &rcond,
+ &m_sluStat, &info, Scalar());
+ StatFree(&m_sluStat);
+
+ if(x.derived().data() != x_ref.data())
+ x = x_ref;
+
+ m_info = info==0 ? Success : NumericalIssue;
+}
+#endif
+
+#endif
+
+} // end namespace Eigen
+
+#endif // EIGEN_SUPERLUSUPPORT_H
diff --git a/Eigen/src/UmfPackSupport/InternalHeaderCheck.h b/Eigen/src/UmfPackSupport/InternalHeaderCheck.h
new file mode 100644
index 0000000..64112f1
--- /dev/null
+++ b/Eigen/src/UmfPackSupport/InternalHeaderCheck.h
@@ -0,0 +1,3 @@
+#ifndef EIGEN_UMFPACKSUPPORT_MODULE_H
+#error "Please include Eigen/UmfPackSupport instead of including headers inside the src directory directly."
+#endif
diff --git a/Eigen/src/UmfPackSupport/UmfPackSupport.h b/Eigen/src/UmfPackSupport/UmfPackSupport.h
new file mode 100644
index 0000000..d9a8d38
--- /dev/null
+++ b/Eigen/src/UmfPackSupport/UmfPackSupport.h
@@ -0,0 +1,644 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2011 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_UMFPACKSUPPORT_H
+#define EIGEN_UMFPACKSUPPORT_H
+
+// for compatibility with super old version of umfpack,
+// not sure this is really needed, but this is harmless.
+#ifndef SuiteSparse_long
+#ifdef UF_long
+#define SuiteSparse_long UF_long
+#else
+#error neither SuiteSparse_long nor UF_long are defined
+#endif
+#endif
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+/* TODO extract L, extract U, compute det, etc... */
+
+// generic double/complex<double> wrapper functions:
+
+
+ // Defaults
+inline void umfpack_defaults(double control[UMFPACK_CONTROL], double, int)
+{ umfpack_di_defaults(control); }
+
+inline void umfpack_defaults(double control[UMFPACK_CONTROL], std::complex<double>, int)
+{ umfpack_zi_defaults(control); }
+
+inline void umfpack_defaults(double control[UMFPACK_CONTROL], double, SuiteSparse_long)
+{ umfpack_dl_defaults(control); }
+
+inline void umfpack_defaults(double control[UMFPACK_CONTROL], std::complex<double>, SuiteSparse_long)
+{ umfpack_zl_defaults(control); }
+
+// Report info
+inline void umfpack_report_info(double control[UMFPACK_CONTROL], double info[UMFPACK_INFO], double, int)
+{ umfpack_di_report_info(control, info);}
+
+inline void umfpack_report_info(double control[UMFPACK_CONTROL], double info[UMFPACK_INFO], std::complex<double>, int)
+{ umfpack_zi_report_info(control, info);}
+
+inline void umfpack_report_info(double control[UMFPACK_CONTROL], double info[UMFPACK_INFO], double, SuiteSparse_long)
+{ umfpack_dl_report_info(control, info);}
+
+inline void umfpack_report_info(double control[UMFPACK_CONTROL], double info[UMFPACK_INFO], std::complex<double>, SuiteSparse_long)
+{ umfpack_zl_report_info(control, info);}
+
+// Report status
+inline void umfpack_report_status(double control[UMFPACK_CONTROL], int status, double, int)
+{ umfpack_di_report_status(control, status);}
+
+inline void umfpack_report_status(double control[UMFPACK_CONTROL], int status, std::complex<double>, int)
+{ umfpack_zi_report_status(control, status);}
+
+inline void umfpack_report_status(double control[UMFPACK_CONTROL], int status, double, SuiteSparse_long)
+{ umfpack_dl_report_status(control, status);}
+
+inline void umfpack_report_status(double control[UMFPACK_CONTROL], int status, std::complex<double>, SuiteSparse_long)
+{ umfpack_zl_report_status(control, status);}
+
+// report control
+inline void umfpack_report_control(double control[UMFPACK_CONTROL], double, int)
+{ umfpack_di_report_control(control);}
+
+inline void umfpack_report_control(double control[UMFPACK_CONTROL], std::complex<double>, int)
+{ umfpack_zi_report_control(control);}
+
+inline void umfpack_report_control(double control[UMFPACK_CONTROL], double, SuiteSparse_long)
+{ umfpack_dl_report_control(control);}
+
+inline void umfpack_report_control(double control[UMFPACK_CONTROL], std::complex<double>, SuiteSparse_long)
+{ umfpack_zl_report_control(control);}
+
+// Free numeric
+inline void umfpack_free_numeric(void **Numeric, double, int)
+{ umfpack_di_free_numeric(Numeric); *Numeric = 0; }
+
+inline void umfpack_free_numeric(void **Numeric, std::complex<double>, int)
+{ umfpack_zi_free_numeric(Numeric); *Numeric = 0; }
+
+inline void umfpack_free_numeric(void **Numeric, double, SuiteSparse_long)
+{ umfpack_dl_free_numeric(Numeric); *Numeric = 0; }
+
+inline void umfpack_free_numeric(void **Numeric, std::complex<double>, SuiteSparse_long)
+{ umfpack_zl_free_numeric(Numeric); *Numeric = 0; }
+
+// Free symbolic
+inline void umfpack_free_symbolic(void **Symbolic, double, int)
+{ umfpack_di_free_symbolic(Symbolic); *Symbolic = 0; }
+
+inline void umfpack_free_symbolic(void **Symbolic, std::complex<double>, int)
+{ umfpack_zi_free_symbolic(Symbolic); *Symbolic = 0; }
+
+inline void umfpack_free_symbolic(void **Symbolic, double, SuiteSparse_long)
+{ umfpack_dl_free_symbolic(Symbolic); *Symbolic = 0; }
+
+inline void umfpack_free_symbolic(void **Symbolic, std::complex<double>, SuiteSparse_long)
+{ umfpack_zl_free_symbolic(Symbolic); *Symbolic = 0; }
+
+// Symbolic
+inline int umfpack_symbolic(int n_row,int n_col,
+ const int Ap[], const int Ai[], const double Ax[], void **Symbolic,
+ const double Control [UMFPACK_CONTROL], double Info [UMFPACK_INFO])
+{
+ return umfpack_di_symbolic(n_row,n_col,Ap,Ai,Ax,Symbolic,Control,Info);
+}
+
+inline int umfpack_symbolic(int n_row,int n_col,
+ const int Ap[], const int Ai[], const std::complex<double> Ax[], void **Symbolic,
+ const double Control [UMFPACK_CONTROL], double Info [UMFPACK_INFO])
+{
+ return umfpack_zi_symbolic(n_row,n_col,Ap,Ai,&numext::real_ref(Ax[0]),0,Symbolic,Control,Info);
+}
+inline SuiteSparse_long umfpack_symbolic( SuiteSparse_long n_row,SuiteSparse_long n_col,
+ const SuiteSparse_long Ap[], const SuiteSparse_long Ai[], const double Ax[], void **Symbolic,
+ const double Control [UMFPACK_CONTROL], double Info [UMFPACK_INFO])
+{
+ return umfpack_dl_symbolic(n_row,n_col,Ap,Ai,Ax,Symbolic,Control,Info);
+}
+
+inline SuiteSparse_long umfpack_symbolic( SuiteSparse_long n_row,SuiteSparse_long n_col,
+ const SuiteSparse_long Ap[], const SuiteSparse_long Ai[], const std::complex<double> Ax[], void **Symbolic,
+ const double Control [UMFPACK_CONTROL], double Info [UMFPACK_INFO])
+{
+ return umfpack_zl_symbolic(n_row,n_col,Ap,Ai,&numext::real_ref(Ax[0]),0,Symbolic,Control,Info);
+}
+
+// Numeric
+inline int umfpack_numeric( const int Ap[], const int Ai[], const double Ax[],
+ void *Symbolic, void **Numeric,
+ const double Control[UMFPACK_CONTROL],double Info [UMFPACK_INFO])
+{
+ return umfpack_di_numeric(Ap,Ai,Ax,Symbolic,Numeric,Control,Info);
+}
+
+inline int umfpack_numeric( const int Ap[], const int Ai[], const std::complex<double> Ax[],
+ void *Symbolic, void **Numeric,
+ const double Control[UMFPACK_CONTROL],double Info [UMFPACK_INFO])
+{
+ return umfpack_zi_numeric(Ap,Ai,&numext::real_ref(Ax[0]),0,Symbolic,Numeric,Control,Info);
+}
+inline SuiteSparse_long umfpack_numeric(const SuiteSparse_long Ap[], const SuiteSparse_long Ai[], const double Ax[],
+ void *Symbolic, void **Numeric,
+ const double Control[UMFPACK_CONTROL],double Info [UMFPACK_INFO])
+{
+ return umfpack_dl_numeric(Ap,Ai,Ax,Symbolic,Numeric,Control,Info);
+}
+
+inline SuiteSparse_long umfpack_numeric(const SuiteSparse_long Ap[], const SuiteSparse_long Ai[], const std::complex<double> Ax[],
+ void *Symbolic, void **Numeric,
+ const double Control[UMFPACK_CONTROL],double Info [UMFPACK_INFO])
+{
+ return umfpack_zl_numeric(Ap,Ai,&numext::real_ref(Ax[0]),0,Symbolic,Numeric,Control,Info);
+}
+
+// solve
+inline int umfpack_solve( int sys, const int Ap[], const int Ai[], const double Ax[],
+ double X[], const double B[], void *Numeric,
+ const double Control[UMFPACK_CONTROL], double Info[UMFPACK_INFO])
+{
+ return umfpack_di_solve(sys,Ap,Ai,Ax,X,B,Numeric,Control,Info);
+}
+
+inline int umfpack_solve( int sys, const int Ap[], const int Ai[], const std::complex<double> Ax[],
+ std::complex<double> X[], const std::complex<double> B[], void *Numeric,
+ const double Control[UMFPACK_CONTROL], double Info[UMFPACK_INFO])
+{
+ return umfpack_zi_solve(sys,Ap,Ai,&numext::real_ref(Ax[0]),0,&numext::real_ref(X[0]),0,&numext::real_ref(B[0]),0,Numeric,Control,Info);
+}
+
+inline SuiteSparse_long umfpack_solve(int sys, const SuiteSparse_long Ap[], const SuiteSparse_long Ai[], const double Ax[],
+ double X[], const double B[], void *Numeric,
+ const double Control[UMFPACK_CONTROL], double Info[UMFPACK_INFO])
+{
+ return umfpack_dl_solve(sys,Ap,Ai,Ax,X,B,Numeric,Control,Info);
+}
+
+inline SuiteSparse_long umfpack_solve(int sys, const SuiteSparse_long Ap[], const SuiteSparse_long Ai[], const std::complex<double> Ax[],
+ std::complex<double> X[], const std::complex<double> B[], void *Numeric,
+ const double Control[UMFPACK_CONTROL], double Info[UMFPACK_INFO])
+{
+ return umfpack_zl_solve(sys,Ap,Ai,&numext::real_ref(Ax[0]),0,&numext::real_ref(X[0]),0,&numext::real_ref(B[0]),0,Numeric,Control,Info);
+}
+
+// Get Lunz
+inline int umfpack_get_lunz(int *lnz, int *unz, int *n_row, int *n_col, int *nz_udiag, void *Numeric, double)
+{
+ return umfpack_di_get_lunz(lnz,unz,n_row,n_col,nz_udiag,Numeric);
+}
+
+inline int umfpack_get_lunz(int *lnz, int *unz, int *n_row, int *n_col, int *nz_udiag, void *Numeric, std::complex<double>)
+{
+ return umfpack_zi_get_lunz(lnz,unz,n_row,n_col,nz_udiag,Numeric);
+}
+
+inline SuiteSparse_long umfpack_get_lunz( SuiteSparse_long *lnz, SuiteSparse_long *unz, SuiteSparse_long *n_row, SuiteSparse_long *n_col,
+ SuiteSparse_long *nz_udiag, void *Numeric, double)
+{
+ return umfpack_dl_get_lunz(lnz,unz,n_row,n_col,nz_udiag,Numeric);
+}
+
+inline SuiteSparse_long umfpack_get_lunz( SuiteSparse_long *lnz, SuiteSparse_long *unz, SuiteSparse_long *n_row, SuiteSparse_long *n_col,
+ SuiteSparse_long *nz_udiag, void *Numeric, std::complex<double>)
+{
+ return umfpack_zl_get_lunz(lnz,unz,n_row,n_col,nz_udiag,Numeric);
+}
+
+// Get Numeric
+inline int umfpack_get_numeric(int Lp[], int Lj[], double Lx[], int Up[], int Ui[], double Ux[],
+ int P[], int Q[], double Dx[], int *do_recip, double Rs[], void *Numeric)
+{
+ return umfpack_di_get_numeric(Lp,Lj,Lx,Up,Ui,Ux,P,Q,Dx,do_recip,Rs,Numeric);
+}
+
+inline int umfpack_get_numeric(int Lp[], int Lj[], std::complex<double> Lx[], int Up[], int Ui[], std::complex<double> Ux[],
+ int P[], int Q[], std::complex<double> Dx[], int *do_recip, double Rs[], void *Numeric)
+{
+ double& lx0_real = numext::real_ref(Lx[0]);
+ double& ux0_real = numext::real_ref(Ux[0]);
+ double& dx0_real = numext::real_ref(Dx[0]);
+ return umfpack_zi_get_numeric(Lp,Lj,Lx?&lx0_real:0,0,Up,Ui,Ux?&ux0_real:0,0,P,Q,
+ Dx?&dx0_real:0,0,do_recip,Rs,Numeric);
+}
+inline SuiteSparse_long umfpack_get_numeric(SuiteSparse_long Lp[], SuiteSparse_long Lj[], double Lx[], SuiteSparse_long Up[], SuiteSparse_long Ui[], double Ux[],
+ SuiteSparse_long P[], SuiteSparse_long Q[], double Dx[], SuiteSparse_long *do_recip, double Rs[], void *Numeric)
+{
+ return umfpack_dl_get_numeric(Lp,Lj,Lx,Up,Ui,Ux,P,Q,Dx,do_recip,Rs,Numeric);
+}
+
+inline SuiteSparse_long umfpack_get_numeric(SuiteSparse_long Lp[], SuiteSparse_long Lj[], std::complex<double> Lx[], SuiteSparse_long Up[], SuiteSparse_long Ui[], std::complex<double> Ux[],
+ SuiteSparse_long P[], SuiteSparse_long Q[], std::complex<double> Dx[], SuiteSparse_long *do_recip, double Rs[], void *Numeric)
+{
+ double& lx0_real = numext::real_ref(Lx[0]);
+ double& ux0_real = numext::real_ref(Ux[0]);
+ double& dx0_real = numext::real_ref(Dx[0]);
+ return umfpack_zl_get_numeric(Lp,Lj,Lx?&lx0_real:0,0,Up,Ui,Ux?&ux0_real:0,0,P,Q,
+ Dx?&dx0_real:0,0,do_recip,Rs,Numeric);
+}
+
+// Get Determinant
+inline int umfpack_get_determinant(double *Mx, double *Ex, void *NumericHandle, double User_Info [UMFPACK_INFO], int)
+{
+ return umfpack_di_get_determinant(Mx,Ex,NumericHandle,User_Info);
+}
+
+inline int umfpack_get_determinant(std::complex<double> *Mx, double *Ex, void *NumericHandle, double User_Info [UMFPACK_INFO], int)
+{
+ double& mx_real = numext::real_ref(*Mx);
+ return umfpack_zi_get_determinant(&mx_real,0,Ex,NumericHandle,User_Info);
+}
+
+inline SuiteSparse_long umfpack_get_determinant(double *Mx, double *Ex, void *NumericHandle, double User_Info [UMFPACK_INFO], SuiteSparse_long)
+{
+ return umfpack_dl_get_determinant(Mx,Ex,NumericHandle,User_Info);
+}
+
+inline SuiteSparse_long umfpack_get_determinant(std::complex<double> *Mx, double *Ex, void *NumericHandle, double User_Info [UMFPACK_INFO], SuiteSparse_long)
+{
+ double& mx_real = numext::real_ref(*Mx);
+ return umfpack_zl_get_determinant(&mx_real,0,Ex,NumericHandle,User_Info);
+}
+
+
+/** \ingroup UmfPackSupport_Module
+ * \brief A sparse LU factorization and solver based on UmfPack
+ *
+ * This class allows to solve for A.X = B sparse linear problems via a LU factorization
+ * using the UmfPack library. The sparse matrix A must be squared and full rank.
+ * The vectors or matrices X and B can be either dense or sparse.
+ *
+ * \warning The input matrix A should be in a \b compressed and \b column-major form.
+ * Otherwise an expensive copy will be made. You can call the inexpensive makeCompressed() to get a compressed matrix.
+ * \tparam MatrixType_ the type of the sparse matrix A, it must be a SparseMatrix<>
+ *
+ * \implsparsesolverconcept
+ *
+ * \sa \ref TutorialSparseSolverConcept, class SparseLU
+ */
+template<typename MatrixType_>
+class UmfPackLU : public SparseSolverBase<UmfPackLU<MatrixType_> >
+{
+ protected:
+ typedef SparseSolverBase<UmfPackLU<MatrixType_> > Base;
+ using Base::m_isInitialized;
+ public:
+ using Base::_solve_impl;
+ typedef MatrixType_ MatrixType;
+ typedef typename MatrixType::Scalar Scalar;
+ typedef typename MatrixType::RealScalar RealScalar;
+ typedef typename MatrixType::StorageIndex StorageIndex;
+ typedef Matrix<Scalar,Dynamic,1> Vector;
+ typedef Matrix<int, 1, MatrixType::ColsAtCompileTime> IntRowVectorType;
+ typedef Matrix<int, MatrixType::RowsAtCompileTime, 1> IntColVectorType;
+ typedef SparseMatrix<Scalar> LUMatrixType;
+ typedef SparseMatrix<Scalar,ColMajor,StorageIndex> UmfpackMatrixType;
+ typedef Ref<const UmfpackMatrixType, StandardCompressedFormat> UmfpackMatrixRef;
+ enum {
+ ColsAtCompileTime = MatrixType::ColsAtCompileTime,
+ MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime
+ };
+
+ public:
+
+ typedef Array<double, UMFPACK_CONTROL, 1> UmfpackControl;
+ typedef Array<double, UMFPACK_INFO, 1> UmfpackInfo;
+
+ UmfPackLU()
+ : m_dummy(0,0), mp_matrix(m_dummy)
+ {
+ init();
+ }
+
+ template<typename InputMatrixType>
+ explicit UmfPackLU(const InputMatrixType& matrix)
+ : mp_matrix(matrix)
+ {
+ init();
+ compute(matrix);
+ }
+
+ ~UmfPackLU()
+ {
+ if(m_symbolic) umfpack_free_symbolic(&m_symbolic,Scalar(), StorageIndex());
+ if(m_numeric) umfpack_free_numeric(&m_numeric,Scalar(), StorageIndex());
+ }
+
+ inline Index rows() const { return mp_matrix.rows(); }
+ inline Index cols() const { return mp_matrix.cols(); }
+
+ /** \brief Reports whether previous computation was successful.
+ *
+ * \returns \c Success if computation was successful,
+ * \c NumericalIssue if the matrix.appears to be negative.
+ */
+ ComputationInfo info() const
+ {
+ eigen_assert(m_isInitialized && "Decomposition is not initialized.");
+ return m_info;
+ }
+
+ inline const LUMatrixType& matrixL() const
+ {
+ if (m_extractedDataAreDirty) extractData();
+ return m_l;
+ }
+
+ inline const LUMatrixType& matrixU() const
+ {
+ if (m_extractedDataAreDirty) extractData();
+ return m_u;
+ }
+
+ inline const IntColVectorType& permutationP() const
+ {
+ if (m_extractedDataAreDirty) extractData();
+ return m_p;
+ }
+
+ inline const IntRowVectorType& permutationQ() const
+ {
+ if (m_extractedDataAreDirty) extractData();
+ return m_q;
+ }
+
+ /** Computes the sparse Cholesky decomposition of \a matrix
+ * Note that the matrix should be column-major, and in compressed format for best performance.
+ * \sa SparseMatrix::makeCompressed().
+ */
+ template<typename InputMatrixType>
+ void compute(const InputMatrixType& matrix)
+ {
+ if(m_symbolic) umfpack_free_symbolic(&m_symbolic,Scalar(),StorageIndex());
+ if(m_numeric) umfpack_free_numeric(&m_numeric,Scalar(),StorageIndex());
+ grab(matrix.derived());
+ analyzePattern_impl();
+ factorize_impl();
+ }
+
+ /** Performs a symbolic decomposition on the sparcity of \a matrix.
+ *
+ * This function is particularly useful when solving for several problems having the same structure.
+ *
+ * \sa factorize(), compute()
+ */
+ template<typename InputMatrixType>
+ void analyzePattern(const InputMatrixType& matrix)
+ {
+ if(m_symbolic) umfpack_free_symbolic(&m_symbolic,Scalar(),StorageIndex());
+ if(m_numeric) umfpack_free_numeric(&m_numeric,Scalar(),StorageIndex());
+
+ grab(matrix.derived());
+
+ analyzePattern_impl();
+ }
+
+ /** Provides the return status code returned by UmfPack during the numeric
+ * factorization.
+ *
+ * \sa factorize(), compute()
+ */
+ inline int umfpackFactorizeReturncode() const
+ {
+ eigen_assert(m_numeric && "UmfPackLU: you must first call factorize()");
+ return m_fact_errorCode;
+ }
+
+ /** Provides access to the control settings array used by UmfPack.
+ *
+ * If this array contains NaN's, the default values are used.
+ *
+ * See UMFPACK documentation for details.
+ */
+ inline const UmfpackControl& umfpackControl() const
+ {
+ return m_control;
+ }
+
+ /** Provides access to the control settings array used by UmfPack.
+ *
+ * If this array contains NaN's, the default values are used.
+ *
+ * See UMFPACK documentation for details.
+ */
+ inline UmfpackControl& umfpackControl()
+ {
+ return m_control;
+ }
+
+ /** Performs a numeric decomposition of \a matrix
+ *
+ * The given matrix must has the same sparcity than the matrix on which the pattern anylysis has been performed.
+ *
+ * \sa analyzePattern(), compute()
+ */
+ template<typename InputMatrixType>
+ void factorize(const InputMatrixType& matrix)
+ {
+ eigen_assert(m_analysisIsOk && "UmfPackLU: you must first call analyzePattern()");
+ if(m_numeric)
+ umfpack_free_numeric(&m_numeric,Scalar(),StorageIndex());
+
+ grab(matrix.derived());
+
+ factorize_impl();
+ }
+
+ /** Prints the current UmfPack control settings.
+ *
+ * \sa umfpackControl()
+ */
+ void printUmfpackControl()
+ {
+ umfpack_report_control(m_control.data(), Scalar(),StorageIndex());
+ }
+
+ /** Prints statistics collected by UmfPack.
+ *
+ * \sa analyzePattern(), compute()
+ */
+ void printUmfpackInfo()
+ {
+ eigen_assert(m_analysisIsOk && "UmfPackLU: you must first call analyzePattern()");
+ umfpack_report_info(m_control.data(), m_umfpackInfo.data(), Scalar(),StorageIndex());
+ }
+
+ /** Prints the status of the previous factorization operation performed by UmfPack (symbolic or numerical factorization).
+ *
+ * \sa analyzePattern(), compute()
+ */
+ void printUmfpackStatus() {
+ eigen_assert(m_analysisIsOk && "UmfPackLU: you must first call analyzePattern()");
+ umfpack_report_status(m_control.data(), m_fact_errorCode, Scalar(),StorageIndex());
+ }
+
+ /** \internal */
+ template<typename BDerived,typename XDerived>
+ bool _solve_impl(const MatrixBase<BDerived> &b, MatrixBase<XDerived> &x) const;
+
+ Scalar determinant() const;
+
+ void extractData() const;
+
+ protected:
+
+ void init()
+ {
+ m_info = InvalidInput;
+ m_isInitialized = false;
+ m_numeric = 0;
+ m_symbolic = 0;
+ m_extractedDataAreDirty = true;
+
+ umfpack_defaults(m_control.data(), Scalar(),StorageIndex());
+ }
+
+ void analyzePattern_impl()
+ {
+ m_fact_errorCode = umfpack_symbolic(internal::convert_index<StorageIndex>(mp_matrix.rows()),
+ internal::convert_index<StorageIndex>(mp_matrix.cols()),
+ mp_matrix.outerIndexPtr(), mp_matrix.innerIndexPtr(), mp_matrix.valuePtr(),
+ &m_symbolic, m_control.data(), m_umfpackInfo.data());
+
+ m_isInitialized = true;
+ m_info = m_fact_errorCode ? InvalidInput : Success;
+ m_analysisIsOk = true;
+ m_factorizationIsOk = false;
+ m_extractedDataAreDirty = true;
+ }
+
+ void factorize_impl()
+ {
+
+ m_fact_errorCode = umfpack_numeric(mp_matrix.outerIndexPtr(), mp_matrix.innerIndexPtr(), mp_matrix.valuePtr(),
+ m_symbolic, &m_numeric, m_control.data(), m_umfpackInfo.data());
+
+ m_info = m_fact_errorCode == UMFPACK_OK ? Success : NumericalIssue;
+ m_factorizationIsOk = true;
+ m_extractedDataAreDirty = true;
+ }
+
+ template<typename MatrixDerived>
+ void grab(const EigenBase<MatrixDerived> &A)
+ {
+ internal::destroy_at(&mp_matrix);
+ internal::construct_at(&mp_matrix, A.derived());
+ }
+
+ void grab(const UmfpackMatrixRef &A)
+ {
+ if(&(A.derived()) != &mp_matrix)
+ {
+ internal::destroy_at(&mp_matrix);
+ internal::construct_at(&mp_matrix, A);
+ }
+ }
+
+ // cached data to reduce reallocation, etc.
+ mutable LUMatrixType m_l;
+ StorageIndex m_fact_errorCode;
+ UmfpackControl m_control;
+ mutable UmfpackInfo m_umfpackInfo;
+
+ mutable LUMatrixType m_u;
+ mutable IntColVectorType m_p;
+ mutable IntRowVectorType m_q;
+
+ UmfpackMatrixType m_dummy;
+ UmfpackMatrixRef mp_matrix;
+
+ void* m_numeric;
+ void* m_symbolic;
+
+ mutable ComputationInfo m_info;
+ int m_factorizationIsOk;
+ int m_analysisIsOk;
+ mutable bool m_extractedDataAreDirty;
+
+ private:
+ UmfPackLU(const UmfPackLU& ) { }
+};
+
+
+template<typename MatrixType>
+void UmfPackLU<MatrixType>::extractData() const
+{
+ if (m_extractedDataAreDirty)
+ {
+ // get size of the data
+ StorageIndex lnz, unz, rows, cols, nz_udiag;
+ umfpack_get_lunz(&lnz, &unz, &rows, &cols, &nz_udiag, m_numeric, Scalar());
+
+ // allocate data
+ m_l.resize(rows,(std::min)(rows,cols));
+ m_l.resizeNonZeros(lnz);
+
+ m_u.resize((std::min)(rows,cols),cols);
+ m_u.resizeNonZeros(unz);
+
+ m_p.resize(rows);
+ m_q.resize(cols);
+
+ // extract
+ umfpack_get_numeric(m_l.outerIndexPtr(), m_l.innerIndexPtr(), m_l.valuePtr(),
+ m_u.outerIndexPtr(), m_u.innerIndexPtr(), m_u.valuePtr(),
+ m_p.data(), m_q.data(), 0, 0, 0, m_numeric);
+
+ m_extractedDataAreDirty = false;
+ }
+}
+
+template<typename MatrixType>
+typename UmfPackLU<MatrixType>::Scalar UmfPackLU<MatrixType>::determinant() const
+{
+ Scalar det;
+ umfpack_get_determinant(&det, 0, m_numeric, 0, StorageIndex());
+ return det;
+}
+
+template<typename MatrixType>
+template<typename BDerived,typename XDerived>
+bool UmfPackLU<MatrixType>::_solve_impl(const MatrixBase<BDerived> &b, MatrixBase<XDerived> &x) const
+{
+ Index rhsCols = b.cols();
+ eigen_assert((BDerived::Flags&RowMajorBit)==0 && "UmfPackLU backend does not support non col-major rhs yet");
+ eigen_assert((XDerived::Flags&RowMajorBit)==0 && "UmfPackLU backend does not support non col-major result yet");
+ eigen_assert(b.derived().data() != x.derived().data() && " Umfpack does not support inplace solve");
+
+ Scalar* x_ptr = 0;
+ Matrix<Scalar,Dynamic,1> x_tmp;
+ if(x.innerStride()!=1)
+ {
+ x_tmp.resize(x.rows());
+ x_ptr = x_tmp.data();
+ }
+ for (int j=0; j<rhsCols; ++j)
+ {
+ if(x.innerStride()==1)
+ x_ptr = &x.col(j).coeffRef(0);
+ StorageIndex errorCode = umfpack_solve(UMFPACK_A,
+ mp_matrix.outerIndexPtr(), mp_matrix.innerIndexPtr(), mp_matrix.valuePtr(),
+ x_ptr, &b.const_cast_derived().col(j).coeffRef(0),
+ m_numeric, m_control.data(), m_umfpackInfo.data());
+ if(x.innerStride()!=1)
+ x.col(j) = x_tmp;
+ if (errorCode!=0)
+ return false;
+ }
+
+ return true;
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_UMFPACKSUPPORT_H
diff --git a/Eigen/src/misc/Image.h b/Eigen/src/misc/Image.h
new file mode 100644
index 0000000..b500036
--- /dev/null
+++ b/Eigen/src/misc/Image.h
@@ -0,0 +1,84 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_MISC_IMAGE_H
+#define EIGEN_MISC_IMAGE_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+
+/** \class image_retval_base
+ *
+ */
+template<typename DecompositionType>
+struct traits<image_retval_base<DecompositionType> >
+{
+ typedef typename DecompositionType::MatrixType MatrixType;
+ typedef Matrix<
+ typename MatrixType::Scalar,
+ MatrixType::RowsAtCompileTime, // the image is a subspace of the destination space, whose
+ // dimension is the number of rows of the original matrix
+ Dynamic, // we don't know at compile time the dimension of the image (the rank)
+ MatrixType::Options,
+ MatrixType::MaxRowsAtCompileTime, // the image matrix will consist of columns from the original matrix,
+ MatrixType::MaxColsAtCompileTime // so it has the same number of rows and at most as many columns.
+ > ReturnType;
+};
+
+template<typename DecompositionType_> struct image_retval_base
+ : public ReturnByValue<image_retval_base<DecompositionType_> >
+{
+ typedef DecompositionType_ DecompositionType;
+ typedef typename DecompositionType::MatrixType MatrixType;
+ typedef ReturnByValue<image_retval_base> Base;
+
+ image_retval_base(const DecompositionType& dec, const MatrixType& originalMatrix)
+ : m_dec(dec), m_rank(dec.rank()),
+ m_cols(m_rank == 0 ? 1 : m_rank),
+ m_originalMatrix(originalMatrix)
+ {}
+
+ inline Index rows() const { return m_dec.rows(); }
+ inline Index cols() const { return m_cols; }
+ inline Index rank() const { return m_rank; }
+ inline const DecompositionType& dec() const { return m_dec; }
+ inline const MatrixType& originalMatrix() const { return m_originalMatrix; }
+
+ template<typename Dest> inline void evalTo(Dest& dst) const
+ {
+ static_cast<const image_retval<DecompositionType>*>(this)->evalTo(dst);
+ }
+
+ protected:
+ const DecompositionType& m_dec;
+ Index m_rank, m_cols;
+ const MatrixType& m_originalMatrix;
+};
+
+} // end namespace internal
+
+#define EIGEN_MAKE_IMAGE_HELPERS(DecompositionType) \
+ typedef typename DecompositionType::MatrixType MatrixType; \
+ typedef typename MatrixType::Scalar Scalar; \
+ typedef typename MatrixType::RealScalar RealScalar; \
+ typedef Eigen::internal::image_retval_base<DecompositionType> Base; \
+ using Base::dec; \
+ using Base::originalMatrix; \
+ using Base::rank; \
+ using Base::rows; \
+ using Base::cols; \
+ image_retval(const DecompositionType& dec, const MatrixType& originalMatrix) \
+ : Base(dec, originalMatrix) {}
+
+} // end namespace Eigen
+
+#endif // EIGEN_MISC_IMAGE_H
diff --git a/Eigen/src/misc/InternalHeaderCheck.h b/Eigen/src/misc/InternalHeaderCheck.h
new file mode 100644
index 0000000..1cea572
--- /dev/null
+++ b/Eigen/src/misc/InternalHeaderCheck.h
@@ -0,0 +1,3 @@
+#ifndef EIGEN_CORE_MODULE_H
+#error "Please include Eigen/Core instead of including headers inside the src directory directly."
+#endif
diff --git a/Eigen/src/misc/Kernel.h b/Eigen/src/misc/Kernel.h
new file mode 100644
index 0000000..7abfbb7
--- /dev/null
+++ b/Eigen/src/misc/Kernel.h
@@ -0,0 +1,81 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_MISC_KERNEL_H
+#define EIGEN_MISC_KERNEL_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+
+/** \class kernel_retval_base
+ *
+ */
+template<typename DecompositionType>
+struct traits<kernel_retval_base<DecompositionType> >
+{
+ typedef typename DecompositionType::MatrixType MatrixType;
+ typedef Matrix<
+ typename MatrixType::Scalar,
+ MatrixType::ColsAtCompileTime, // the number of rows in the "kernel matrix"
+ // is the number of cols of the original matrix
+ // so that the product "matrix * kernel = zero" makes sense
+ Dynamic, // we don't know at compile-time the dimension of the kernel
+ MatrixType::Options,
+ MatrixType::MaxColsAtCompileTime, // see explanation for 2nd template parameter
+ MatrixType::MaxColsAtCompileTime // the kernel is a subspace of the domain space,
+ // whose dimension is the number of columns of the original matrix
+ > ReturnType;
+};
+
+template<typename DecompositionType_> struct kernel_retval_base
+ : public ReturnByValue<kernel_retval_base<DecompositionType_> >
+{
+ typedef DecompositionType_ DecompositionType;
+ typedef ReturnByValue<kernel_retval_base> Base;
+
+ explicit kernel_retval_base(const DecompositionType& dec)
+ : m_dec(dec),
+ m_rank(dec.rank()),
+ m_cols(m_rank==dec.cols() ? 1 : dec.cols() - m_rank)
+ {}
+
+ inline Index rows() const { return m_dec.cols(); }
+ inline Index cols() const { return m_cols; }
+ inline Index rank() const { return m_rank; }
+ inline const DecompositionType& dec() const { return m_dec; }
+
+ template<typename Dest> inline void evalTo(Dest& dst) const
+ {
+ static_cast<const kernel_retval<DecompositionType>*>(this)->evalTo(dst);
+ }
+
+ protected:
+ const DecompositionType& m_dec;
+ Index m_rank, m_cols;
+};
+
+} // end namespace internal
+
+#define EIGEN_MAKE_KERNEL_HELPERS(DecompositionType) \
+ typedef typename DecompositionType::MatrixType MatrixType; \
+ typedef typename MatrixType::Scalar Scalar; \
+ typedef typename MatrixType::RealScalar RealScalar; \
+ typedef Eigen::internal::kernel_retval_base<DecompositionType> Base; \
+ using Base::dec; \
+ using Base::rank; \
+ using Base::rows; \
+ using Base::cols; \
+ kernel_retval(const DecompositionType& dec) : Base(dec) {}
+
+} // end namespace Eigen
+
+#endif // EIGEN_MISC_KERNEL_H
diff --git a/Eigen/src/misc/RealSvd2x2.h b/Eigen/src/misc/RealSvd2x2.h
new file mode 100644
index 0000000..5dd75f3
--- /dev/null
+++ b/Eigen/src/misc/RealSvd2x2.h
@@ -0,0 +1,57 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009-2010 Benoit Jacob <jacob.benoit.1@gmail.com>
+// Copyright (C) 2013-2016 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_REALSVD2X2_H
+#define EIGEN_REALSVD2X2_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+
+template<typename MatrixType, typename RealScalar, typename Index>
+void real_2x2_jacobi_svd(const MatrixType& matrix, Index p, Index q,
+ JacobiRotation<RealScalar> *j_left,
+ JacobiRotation<RealScalar> *j_right)
+{
+ using std::sqrt;
+ using std::abs;
+ Matrix<RealScalar,2,2> m;
+ m << numext::real(matrix.coeff(p,p)), numext::real(matrix.coeff(p,q)),
+ numext::real(matrix.coeff(q,p)), numext::real(matrix.coeff(q,q));
+ JacobiRotation<RealScalar> rot1;
+ RealScalar t = m.coeff(0,0) + m.coeff(1,1);
+ RealScalar d = m.coeff(1,0) - m.coeff(0,1);
+
+ if(abs(d) < (std::numeric_limits<RealScalar>::min)())
+ {
+ rot1.s() = RealScalar(0);
+ rot1.c() = RealScalar(1);
+ }
+ else
+ {
+ // If d!=0, then t/d cannot overflow because the magnitude of the
+ // entries forming d are not too small compared to the ones forming t.
+ RealScalar u = t / d;
+ RealScalar tmp = sqrt(RealScalar(1) + numext::abs2(u));
+ rot1.s() = RealScalar(1) / tmp;
+ rot1.c() = u / tmp;
+ }
+ m.applyOnTheLeft(0,1,rot1);
+ j_right->makeJacobi(m,0,1);
+ *j_left = rot1 * j_right->transpose();
+}
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_REALSVD2X2_H
diff --git a/Eigen/src/misc/blas.h b/Eigen/src/misc/blas.h
new file mode 100644
index 0000000..25215b1
--- /dev/null
+++ b/Eigen/src/misc/blas.h
@@ -0,0 +1,440 @@
+#ifndef BLAS_H
+#define BLAS_H
+
+#ifdef __cplusplus
+extern "C"
+{
+#endif
+
+#define BLASFUNC(FUNC) FUNC##_
+
+#ifdef __WIN64__
+typedef long long BLASLONG;
+typedef unsigned long long BLASULONG;
+#else
+typedef long BLASLONG;
+typedef unsigned long BLASULONG;
+#endif
+
+int BLASFUNC(xerbla)(const char *, int *info, int);
+
+float BLASFUNC(sdot) (int *, float *, int *, float *, int *);
+float BLASFUNC(sdsdot)(int *, float *, float *, int *, float *, int *);
+
+double BLASFUNC(dsdot) (int *, float *, int *, float *, int *);
+double BLASFUNC(ddot) (int *, double *, int *, double *, int *);
+double BLASFUNC(qdot) (int *, double *, int *, double *, int *);
+
+int BLASFUNC(cdotuw) (int *, float *, int *, float *, int *, float*);
+int BLASFUNC(cdotcw) (int *, float *, int *, float *, int *, float*);
+int BLASFUNC(zdotuw) (int *, double *, int *, double *, int *, double*);
+int BLASFUNC(zdotcw) (int *, double *, int *, double *, int *, double*);
+
+int BLASFUNC(saxpy) (const int *, const float *, const float *, const int *, float *, const int *);
+int BLASFUNC(daxpy) (const int *, const double *, const double *, const int *, double *, const int *);
+int BLASFUNC(qaxpy) (const int *, const double *, const double *, const int *, double *, const int *);
+int BLASFUNC(caxpy) (const int *, const float *, const float *, const int *, float *, const int *);
+int BLASFUNC(zaxpy) (const int *, const double *, const double *, const int *, double *, const int *);
+int BLASFUNC(xaxpy) (const int *, const double *, const double *, const int *, double *, const int *);
+int BLASFUNC(caxpyc)(const int *, const float *, const float *, const int *, float *, const int *);
+int BLASFUNC(zaxpyc)(const int *, const double *, const double *, const int *, double *, const int *);
+int BLASFUNC(xaxpyc)(const int *, const double *, const double *, const int *, double *, const int *);
+
+int BLASFUNC(scopy) (int *, float *, int *, float *, int *);
+int BLASFUNC(dcopy) (int *, double *, int *, double *, int *);
+int BLASFUNC(qcopy) (int *, double *, int *, double *, int *);
+int BLASFUNC(ccopy) (int *, float *, int *, float *, int *);
+int BLASFUNC(zcopy) (int *, double *, int *, double *, int *);
+int BLASFUNC(xcopy) (int *, double *, int *, double *, int *);
+
+int BLASFUNC(sswap) (int *, float *, int *, float *, int *);
+int BLASFUNC(dswap) (int *, double *, int *, double *, int *);
+int BLASFUNC(qswap) (int *, double *, int *, double *, int *);
+int BLASFUNC(cswap) (int *, float *, int *, float *, int *);
+int BLASFUNC(zswap) (int *, double *, int *, double *, int *);
+int BLASFUNC(xswap) (int *, double *, int *, double *, int *);
+
+float BLASFUNC(sasum) (int *, float *, int *);
+float BLASFUNC(scasum)(int *, float *, int *);
+double BLASFUNC(dasum) (int *, double *, int *);
+double BLASFUNC(qasum) (int *, double *, int *);
+double BLASFUNC(dzasum)(int *, double *, int *);
+double BLASFUNC(qxasum)(int *, double *, int *);
+
+int BLASFUNC(isamax)(int *, float *, int *);
+int BLASFUNC(idamax)(int *, double *, int *);
+int BLASFUNC(iqamax)(int *, double *, int *);
+int BLASFUNC(icamax)(int *, float *, int *);
+int BLASFUNC(izamax)(int *, double *, int *);
+int BLASFUNC(ixamax)(int *, double *, int *);
+
+int BLASFUNC(ismax) (int *, float *, int *);
+int BLASFUNC(idmax) (int *, double *, int *);
+int BLASFUNC(iqmax) (int *, double *, int *);
+int BLASFUNC(icmax) (int *, float *, int *);
+int BLASFUNC(izmax) (int *, double *, int *);
+int BLASFUNC(ixmax) (int *, double *, int *);
+
+int BLASFUNC(isamin)(int *, float *, int *);
+int BLASFUNC(idamin)(int *, double *, int *);
+int BLASFUNC(iqamin)(int *, double *, int *);
+int BLASFUNC(icamin)(int *, float *, int *);
+int BLASFUNC(izamin)(int *, double *, int *);
+int BLASFUNC(ixamin)(int *, double *, int *);
+
+int BLASFUNC(ismin)(int *, float *, int *);
+int BLASFUNC(idmin)(int *, double *, int *);
+int BLASFUNC(iqmin)(int *, double *, int *);
+int BLASFUNC(icmin)(int *, float *, int *);
+int BLASFUNC(izmin)(int *, double *, int *);
+int BLASFUNC(ixmin)(int *, double *, int *);
+
+float BLASFUNC(samax) (int *, float *, int *);
+double BLASFUNC(damax) (int *, double *, int *);
+double BLASFUNC(qamax) (int *, double *, int *);
+float BLASFUNC(scamax)(int *, float *, int *);
+double BLASFUNC(dzamax)(int *, double *, int *);
+double BLASFUNC(qxamax)(int *, double *, int *);
+
+float BLASFUNC(samin) (int *, float *, int *);
+double BLASFUNC(damin) (int *, double *, int *);
+double BLASFUNC(qamin) (int *, double *, int *);
+float BLASFUNC(scamin)(int *, float *, int *);
+double BLASFUNC(dzamin)(int *, double *, int *);
+double BLASFUNC(qxamin)(int *, double *, int *);
+
+float BLASFUNC(smax) (int *, float *, int *);
+double BLASFUNC(dmax) (int *, double *, int *);
+double BLASFUNC(qmax) (int *, double *, int *);
+float BLASFUNC(scmax) (int *, float *, int *);
+double BLASFUNC(dzmax) (int *, double *, int *);
+double BLASFUNC(qxmax) (int *, double *, int *);
+
+float BLASFUNC(smin) (int *, float *, int *);
+double BLASFUNC(dmin) (int *, double *, int *);
+double BLASFUNC(qmin) (int *, double *, int *);
+float BLASFUNC(scmin) (int *, float *, int *);
+double BLASFUNC(dzmin) (int *, double *, int *);
+double BLASFUNC(qxmin) (int *, double *, int *);
+
+int BLASFUNC(sscal) (int *, float *, float *, int *);
+int BLASFUNC(dscal) (int *, double *, double *, int *);
+int BLASFUNC(qscal) (int *, double *, double *, int *);
+int BLASFUNC(cscal) (int *, float *, float *, int *);
+int BLASFUNC(zscal) (int *, double *, double *, int *);
+int BLASFUNC(xscal) (int *, double *, double *, int *);
+int BLASFUNC(csscal)(int *, float *, float *, int *);
+int BLASFUNC(zdscal)(int *, double *, double *, int *);
+int BLASFUNC(xqscal)(int *, double *, double *, int *);
+
+float BLASFUNC(snrm2) (int *, float *, int *);
+float BLASFUNC(scnrm2)(int *, float *, int *);
+
+double BLASFUNC(dnrm2) (int *, double *, int *);
+double BLASFUNC(qnrm2) (int *, double *, int *);
+double BLASFUNC(dznrm2)(int *, double *, int *);
+double BLASFUNC(qxnrm2)(int *, double *, int *);
+
+int BLASFUNC(srot) (int *, float *, int *, float *, int *, float *, float *);
+int BLASFUNC(drot) (int *, double *, int *, double *, int *, double *, double *);
+int BLASFUNC(qrot) (int *, double *, int *, double *, int *, double *, double *);
+int BLASFUNC(csrot) (int *, float *, int *, float *, int *, float *, float *);
+int BLASFUNC(zdrot) (int *, double *, int *, double *, int *, double *, double *);
+int BLASFUNC(xqrot) (int *, double *, int *, double *, int *, double *, double *);
+
+int BLASFUNC(srotg) (float *, float *, float *, float *);
+int BLASFUNC(drotg) (double *, double *, double *, double *);
+int BLASFUNC(qrotg) (double *, double *, double *, double *);
+int BLASFUNC(crotg) (float *, float *, float *, float *);
+int BLASFUNC(zrotg) (double *, double *, double *, double *);
+int BLASFUNC(xrotg) (double *, double *, double *, double *);
+
+int BLASFUNC(srotmg)(float *, float *, float *, float *, float *);
+int BLASFUNC(drotmg)(double *, double *, double *, double *, double *);
+
+int BLASFUNC(srotm) (int *, float *, int *, float *, int *, float *);
+int BLASFUNC(drotm) (int *, double *, int *, double *, int *, double *);
+int BLASFUNC(qrotm) (int *, double *, int *, double *, int *, double *);
+
+/* Level 2 routines */
+
+int BLASFUNC(sger)(int *, int *, float *, float *, int *,
+ float *, int *, float *, int *);
+int BLASFUNC(dger)(int *, int *, double *, double *, int *,
+ double *, int *, double *, int *);
+int BLASFUNC(qger)(int *, int *, double *, double *, int *,
+ double *, int *, double *, int *);
+int BLASFUNC(cgeru)(int *, int *, float *, float *, int *,
+ float *, int *, float *, int *);
+int BLASFUNC(cgerc)(int *, int *, float *, float *, int *,
+ float *, int *, float *, int *);
+int BLASFUNC(zgeru)(int *, int *, double *, double *, int *,
+ double *, int *, double *, int *);
+int BLASFUNC(zgerc)(int *, int *, double *, double *, int *,
+ double *, int *, double *, int *);
+int BLASFUNC(xgeru)(int *, int *, double *, double *, int *,
+ double *, int *, double *, int *);
+int BLASFUNC(xgerc)(int *, int *, double *, double *, int *,
+ double *, int *, double *, int *);
+
+int BLASFUNC(sgemv)(const char *, const int *, const int *, const float *, const float *, const int *, const float *, const int *, const float *, float *, const int *);
+int BLASFUNC(dgemv)(const char *, const int *, const int *, const double *, const double *, const int *, const double *, const int *, const double *, double *, const int *);
+int BLASFUNC(qgemv)(const char *, const int *, const int *, const double *, const double *, const int *, const double *, const int *, const double *, double *, const int *);
+int BLASFUNC(cgemv)(const char *, const int *, const int *, const float *, const float *, const int *, const float *, const int *, const float *, float *, const int *);
+int BLASFUNC(zgemv)(const char *, const int *, const int *, const double *, const double *, const int *, const double *, const int *, const double *, double *, const int *);
+int BLASFUNC(xgemv)(const char *, const int *, const int *, const double *, const double *, const int *, const double *, const int *, const double *, double *, const int *);
+
+int BLASFUNC(strsv) (const char *, const char *, const char *, const int *, const float *, const int *, float *, const int *);
+int BLASFUNC(dtrsv) (const char *, const char *, const char *, const int *, const double *, const int *, double *, const int *);
+int BLASFUNC(qtrsv) (const char *, const char *, const char *, const int *, const double *, const int *, double *, const int *);
+int BLASFUNC(ctrsv) (const char *, const char *, const char *, const int *, const float *, const int *, float *, const int *);
+int BLASFUNC(ztrsv) (const char *, const char *, const char *, const int *, const double *, const int *, double *, const int *);
+int BLASFUNC(xtrsv) (const char *, const char *, const char *, const int *, const double *, const int *, double *, const int *);
+
+int BLASFUNC(stpsv) (char *, char *, char *, int *, float *, float *, int *);
+int BLASFUNC(dtpsv) (char *, char *, char *, int *, double *, double *, int *);
+int BLASFUNC(qtpsv) (char *, char *, char *, int *, double *, double *, int *);
+int BLASFUNC(ctpsv) (char *, char *, char *, int *, float *, float *, int *);
+int BLASFUNC(ztpsv) (char *, char *, char *, int *, double *, double *, int *);
+int BLASFUNC(xtpsv) (char *, char *, char *, int *, double *, double *, int *);
+
+int BLASFUNC(strmv) (const char *, const char *, const char *, const int *, const float *, const int *, float *, const int *);
+int BLASFUNC(dtrmv) (const char *, const char *, const char *, const int *, const double *, const int *, double *, const int *);
+int BLASFUNC(qtrmv) (const char *, const char *, const char *, const int *, const double *, const int *, double *, const int *);
+int BLASFUNC(ctrmv) (const char *, const char *, const char *, const int *, const float *, const int *, float *, const int *);
+int BLASFUNC(ztrmv) (const char *, const char *, const char *, const int *, const double *, const int *, double *, const int *);
+int BLASFUNC(xtrmv) (const char *, const char *, const char *, const int *, const double *, const int *, double *, const int *);
+
+int BLASFUNC(stpmv) (char *, char *, char *, int *, float *, float *, int *);
+int BLASFUNC(dtpmv) (char *, char *, char *, int *, double *, double *, int *);
+int BLASFUNC(qtpmv) (char *, char *, char *, int *, double *, double *, int *);
+int BLASFUNC(ctpmv) (char *, char *, char *, int *, float *, float *, int *);
+int BLASFUNC(ztpmv) (char *, char *, char *, int *, double *, double *, int *);
+int BLASFUNC(xtpmv) (char *, char *, char *, int *, double *, double *, int *);
+
+int BLASFUNC(stbmv) (char *, char *, char *, int *, int *, float *, int *, float *, int *);
+int BLASFUNC(dtbmv) (char *, char *, char *, int *, int *, double *, int *, double *, int *);
+int BLASFUNC(qtbmv) (char *, char *, char *, int *, int *, double *, int *, double *, int *);
+int BLASFUNC(ctbmv) (char *, char *, char *, int *, int *, float *, int *, float *, int *);
+int BLASFUNC(ztbmv) (char *, char *, char *, int *, int *, double *, int *, double *, int *);
+int BLASFUNC(xtbmv) (char *, char *, char *, int *, int *, double *, int *, double *, int *);
+
+int BLASFUNC(stbsv) (char *, char *, char *, int *, int *, float *, int *, float *, int *);
+int BLASFUNC(dtbsv) (char *, char *, char *, int *, int *, double *, int *, double *, int *);
+int BLASFUNC(qtbsv) (char *, char *, char *, int *, int *, double *, int *, double *, int *);
+int BLASFUNC(ctbsv) (char *, char *, char *, int *, int *, float *, int *, float *, int *);
+int BLASFUNC(ztbsv) (char *, char *, char *, int *, int *, double *, int *, double *, int *);
+int BLASFUNC(xtbsv) (char *, char *, char *, int *, int *, double *, int *, double *, int *);
+
+int BLASFUNC(ssymv) (const char *, const int *, const float *, const float *, const int *, const float *, const int *, const float *, float *, const int *);
+int BLASFUNC(dsymv) (const char *, const int *, const double *, const double *, const int *, const double *, const int *, const double *, double *, const int *);
+int BLASFUNC(qsymv) (const char *, const int *, const double *, const double *, const int *, const double *, const int *, const double *, double *, const int *);
+
+int BLASFUNC(sspmv) (char *, int *, float *, float *,
+ float *, int *, float *, float *, int *);
+int BLASFUNC(dspmv) (char *, int *, double *, double *,
+ double *, int *, double *, double *, int *);
+int BLASFUNC(qspmv) (char *, int *, double *, double *,
+ double *, int *, double *, double *, int *);
+
+int BLASFUNC(ssyr) (const char *, const int *, const float *, const float *, const int *, float *, const int *);
+int BLASFUNC(dsyr) (const char *, const int *, const double *, const double *, const int *, double *, const int *);
+int BLASFUNC(qsyr) (const char *, const int *, const double *, const double *, const int *, double *, const int *);
+
+int BLASFUNC(ssyr2) (const char *, const int *, const float *, const float *, const int *, const float *, const int *, float *, const int *);
+int BLASFUNC(dsyr2) (const char *, const int *, const double *, const double *, const int *, const double *, const int *, double *, const int *);
+int BLASFUNC(qsyr2) (const char *, const int *, const double *, const double *, const int *, const double *, const int *, double *, const int *);
+int BLASFUNC(csyr2) (const char *, const int *, const float *, const float *, const int *, const float *, const int *, float *, const int *);
+int BLASFUNC(zsyr2) (const char *, const int *, const double *, const double *, const int *, const double *, const int *, double *, const int *);
+int BLASFUNC(xsyr2) (const char *, const int *, const double *, const double *, const int *, const double *, const int *, double *, const int *);
+
+int BLASFUNC(sspr) (char *, int *, float *, float *, int *,
+ float *);
+int BLASFUNC(dspr) (char *, int *, double *, double *, int *,
+ double *);
+int BLASFUNC(qspr) (char *, int *, double *, double *, int *,
+ double *);
+
+int BLASFUNC(sspr2) (char *, int *, float *,
+ float *, int *, float *, int *, float *);
+int BLASFUNC(dspr2) (char *, int *, double *,
+ double *, int *, double *, int *, double *);
+int BLASFUNC(qspr2) (char *, int *, double *,
+ double *, int *, double *, int *, double *);
+int BLASFUNC(cspr2) (char *, int *, float *,
+ float *, int *, float *, int *, float *);
+int BLASFUNC(zspr2) (char *, int *, double *,
+ double *, int *, double *, int *, double *);
+int BLASFUNC(xspr2) (char *, int *, double *,
+ double *, int *, double *, int *, double *);
+
+int BLASFUNC(cher) (char *, int *, float *, float *, int *,
+ float *, int *);
+int BLASFUNC(zher) (char *, int *, double *, double *, int *,
+ double *, int *);
+int BLASFUNC(xher) (char *, int *, double *, double *, int *,
+ double *, int *);
+
+int BLASFUNC(chpr) (char *, int *, float *, float *, int *, float *);
+int BLASFUNC(zhpr) (char *, int *, double *, double *, int *, double *);
+int BLASFUNC(xhpr) (char *, int *, double *, double *, int *, double *);
+
+int BLASFUNC(cher2) (char *, int *, float *,
+ float *, int *, float *, int *, float *, int *);
+int BLASFUNC(zher2) (char *, int *, double *,
+ double *, int *, double *, int *, double *, int *);
+int BLASFUNC(xher2) (char *, int *, double *,
+ double *, int *, double *, int *, double *, int *);
+
+int BLASFUNC(chpr2) (char *, int *, float *,
+ float *, int *, float *, int *, float *);
+int BLASFUNC(zhpr2) (char *, int *, double *,
+ double *, int *, double *, int *, double *);
+int BLASFUNC(xhpr2) (char *, int *, double *,
+ double *, int *, double *, int *, double *);
+
+int BLASFUNC(chemv) (const char *, const int *, const float *, const float *, const int *, const float *, const int *, const float *, float *, const int *);
+int BLASFUNC(zhemv) (const char *, const int *, const double *, const double *, const int *, const double *, const int *, const double *, double *, const int *);
+int BLASFUNC(xhemv) (const char *, const int *, const double *, const double *, const int *, const double *, const int *, const double *, double *, const int *);
+
+int BLASFUNC(chpmv) (char *, int *, float *, float *,
+ float *, int *, float *, float *, int *);
+int BLASFUNC(zhpmv) (char *, int *, double *, double *,
+ double *, int *, double *, double *, int *);
+int BLASFUNC(xhpmv) (char *, int *, double *, double *,
+ double *, int *, double *, double *, int *);
+
+int BLASFUNC(snorm)(char *, int *, int *, float *, int *);
+int BLASFUNC(dnorm)(char *, int *, int *, double *, int *);
+int BLASFUNC(cnorm)(char *, int *, int *, float *, int *);
+int BLASFUNC(znorm)(char *, int *, int *, double *, int *);
+
+int BLASFUNC(sgbmv)(char *, int *, int *, int *, int *, float *, float *, int *,
+ float *, int *, float *, float *, int *);
+int BLASFUNC(dgbmv)(char *, int *, int *, int *, int *, double *, double *, int *,
+ double *, int *, double *, double *, int *);
+int BLASFUNC(qgbmv)(char *, int *, int *, int *, int *, double *, double *, int *,
+ double *, int *, double *, double *, int *);
+int BLASFUNC(cgbmv)(char *, int *, int *, int *, int *, float *, float *, int *,
+ float *, int *, float *, float *, int *);
+int BLASFUNC(zgbmv)(char *, int *, int *, int *, int *, double *, double *, int *,
+ double *, int *, double *, double *, int *);
+int BLASFUNC(xgbmv)(char *, int *, int *, int *, int *, double *, double *, int *,
+ double *, int *, double *, double *, int *);
+
+int BLASFUNC(ssbmv)(char *, int *, int *, float *, float *, int *,
+ float *, int *, float *, float *, int *);
+int BLASFUNC(dsbmv)(char *, int *, int *, double *, double *, int *,
+ double *, int *, double *, double *, int *);
+int BLASFUNC(qsbmv)(char *, int *, int *, double *, double *, int *,
+ double *, int *, double *, double *, int *);
+int BLASFUNC(csbmv)(char *, int *, int *, float *, float *, int *,
+ float *, int *, float *, float *, int *);
+int BLASFUNC(zsbmv)(char *, int *, int *, double *, double *, int *,
+ double *, int *, double *, double *, int *);
+int BLASFUNC(xsbmv)(char *, int *, int *, double *, double *, int *,
+ double *, int *, double *, double *, int *);
+
+int BLASFUNC(chbmv)(char *, int *, int *, float *, float *, int *,
+ float *, int *, float *, float *, int *);
+int BLASFUNC(zhbmv)(char *, int *, int *, double *, double *, int *,
+ double *, int *, double *, double *, int *);
+int BLASFUNC(xhbmv)(char *, int *, int *, double *, double *, int *,
+ double *, int *, double *, double *, int *);
+
+/* Level 3 routines */
+
+int BLASFUNC(sgemm)(const char *, const char *, const int *, const int *, const int *, const float *, const float *, const int *, const float *, const int *, const float *, float *, const int *);
+int BLASFUNC(dgemm)(const char *, const char *, const int *, const int *, const int *, const double *, const double *, const int *, const double *, const int *, const double *, double *, const int *);
+int BLASFUNC(qgemm)(const char *, const char *, const int *, const int *, const int *, const double *, const double *, const int *, const double *, const int *, const double *, double *, const int *);
+int BLASFUNC(cgemm)(const char *, const char *, const int *, const int *, const int *, const float *, const float *, const int *, const float *, const int *, const float *, float *, const int *);
+int BLASFUNC(zgemm)(const char *, const char *, const int *, const int *, const int *, const double *, const double *, const int *, const double *, const int *, const double *, double *, const int *);
+int BLASFUNC(xgemm)(const char *, const char *, const int *, const int *, const int *, const double *, const double *, const int *, const double *, const int *, const double *, double *, const int *);
+
+int BLASFUNC(cgemm3m)(char *, char *, int *, int *, int *, float *,
+ float *, int *, float *, int *, float *, float *, int *);
+int BLASFUNC(zgemm3m)(char *, char *, int *, int *, int *, double *,
+ double *, int *, double *, int *, double *, double *, int *);
+int BLASFUNC(xgemm3m)(char *, char *, int *, int *, int *, double *,
+ double *, int *, double *, int *, double *, double *, int *);
+
+int BLASFUNC(sge2mm)(char *, char *, char *, int *, int *,
+ float *, float *, int *, float *, int *,
+ float *, float *, int *);
+int BLASFUNC(dge2mm)(char *, char *, char *, int *, int *,
+ double *, double *, int *, double *, int *,
+ double *, double *, int *);
+int BLASFUNC(cge2mm)(char *, char *, char *, int *, int *,
+ float *, float *, int *, float *, int *,
+ float *, float *, int *);
+int BLASFUNC(zge2mm)(char *, char *, char *, int *, int *,
+ double *, double *, int *, double *, int *,
+ double *, double *, int *);
+
+int BLASFUNC(strsm)(const char *, const char *, const char *, const char *, const int *, const int *, const float *, const float *, const int *, float *, const int *);
+int BLASFUNC(dtrsm)(const char *, const char *, const char *, const char *, const int *, const int *, const double *, const double *, const int *, double *, const int *);
+int BLASFUNC(qtrsm)(const char *, const char *, const char *, const char *, const int *, const int *, const double *, const double *, const int *, double *, const int *);
+int BLASFUNC(ctrsm)(const char *, const char *, const char *, const char *, const int *, const int *, const float *, const float *, const int *, float *, const int *);
+int BLASFUNC(ztrsm)(const char *, const char *, const char *, const char *, const int *, const int *, const double *, const double *, const int *, double *, const int *);
+int BLASFUNC(xtrsm)(const char *, const char *, const char *, const char *, const int *, const int *, const double *, const double *, const int *, double *, const int *);
+
+int BLASFUNC(strmm)(const char *, const char *, const char *, const char *, const int *, const int *, const float *, const float *, const int *, float *, const int *);
+int BLASFUNC(dtrmm)(const char *, const char *, const char *, const char *, const int *, const int *, const double *, const double *, const int *, double *, const int *);
+int BLASFUNC(qtrmm)(const char *, const char *, const char *, const char *, const int *, const int *, const double *, const double *, const int *, double *, const int *);
+int BLASFUNC(ctrmm)(const char *, const char *, const char *, const char *, const int *, const int *, const float *, const float *, const int *, float *, const int *);
+int BLASFUNC(ztrmm)(const char *, const char *, const char *, const char *, const int *, const int *, const double *, const double *, const int *, double *, const int *);
+int BLASFUNC(xtrmm)(const char *, const char *, const char *, const char *, const int *, const int *, const double *, const double *, const int *, double *, const int *);
+
+int BLASFUNC(ssymm)(const char *, const char *, const int *, const int *, const float *, const float *, const int *, const float *, const int *, const float *, float *, const int *);
+int BLASFUNC(dsymm)(const char *, const char *, const int *, const int *, const double *, const double *, const int *, const double *, const int *, const double *, double *, const int *);
+int BLASFUNC(qsymm)(const char *, const char *, const int *, const int *, const double *, const double *, const int *, const double *, const int *, const double *, double *, const int *);
+int BLASFUNC(csymm)(const char *, const char *, const int *, const int *, const float *, const float *, const int *, const float *, const int *, const float *, float *, const int *);
+int BLASFUNC(zsymm)(const char *, const char *, const int *, const int *, const double *, const double *, const int *, const double *, const int *, const double *, double *, const int *);
+int BLASFUNC(xsymm)(const char *, const char *, const int *, const int *, const double *, const double *, const int *, const double *, const int *, const double *, double *, const int *);
+
+int BLASFUNC(csymm3m)(char *, char *, int *, int *, float *, float *, int *, float *, int *, float *, float *, int *);
+int BLASFUNC(zsymm3m)(char *, char *, int *, int *, double *, double *, int *, double *, int *, double *, double *, int *);
+int BLASFUNC(xsymm3m)(char *, char *, int *, int *, double *, double *, int *, double *, int *, double *, double *, int *);
+
+int BLASFUNC(ssyrk)(const char *, const char *, const int *, const int *, const float *, const float *, const int *, const float *, float *, const int *);
+int BLASFUNC(dsyrk)(const char *, const char *, const int *, const int *, const double *, const double *, const int *, const double *, double *, const int *);
+int BLASFUNC(qsyrk)(const char *, const char *, const int *, const int *, const double *, const double *, const int *, const double *, double *, const int *);
+int BLASFUNC(csyrk)(const char *, const char *, const int *, const int *, const float *, const float *, const int *, const float *, float *, const int *);
+int BLASFUNC(zsyrk)(const char *, const char *, const int *, const int *, const double *, const double *, const int *, const double *, double *, const int *);
+int BLASFUNC(xsyrk)(const char *, const char *, const int *, const int *, const double *, const double *, const int *, const double *, double *, const int *);
+
+int BLASFUNC(ssyr2k)(const char *, const char *, const int *, const int *, const float *, const float *, const int *, const float *, const int *, const float *, float *, const int *);
+int BLASFUNC(dsyr2k)(const char *, const char *, const int *, const int *, const double *, const double *, const int *, const double*, const int *, const double *, double *, const int *);
+int BLASFUNC(qsyr2k)(const char *, const char *, const int *, const int *, const double *, const double *, const int *, const double*, const int *, const double *, double *, const int *);
+int BLASFUNC(csyr2k)(const char *, const char *, const int *, const int *, const float *, const float *, const int *, const float *, const int *, const float *, float *, const int *);
+int BLASFUNC(zsyr2k)(const char *, const char *, const int *, const int *, const double *, const double *, const int *, const double*, const int *, const double *, double *, const int *);
+int BLASFUNC(xsyr2k)(const char *, const char *, const int *, const int *, const double *, const double *, const int *, const double*, const int *, const double *, double *, const int *);
+
+int BLASFUNC(chemm)(const char *, const char *, const int *, const int *, const float *, const float *, const int *, const float *, const int *, const float *, float *, const int *);
+int BLASFUNC(zhemm)(const char *, const char *, const int *, const int *, const double *, const double *, const int *, const double *, const int *, const double *, double *, const int *);
+int BLASFUNC(xhemm)(const char *, const char *, const int *, const int *, const double *, const double *, const int *, const double *, const int *, const double *, double *, const int *);
+
+int BLASFUNC(chemm3m)(char *, char *, int *, int *, float *, float *, int *,
+ float *, int *, float *, float *, int *);
+int BLASFUNC(zhemm3m)(char *, char *, int *, int *, double *, double *, int *,
+ double *, int *, double *, double *, int *);
+int BLASFUNC(xhemm3m)(char *, char *, int *, int *, double *, double *, int *,
+ double *, int *, double *, double *, int *);
+
+int BLASFUNC(cherk)(const char *, const char *, const int *, const int *, const float *, const float *, const int *, const float *, float *, const int *);
+int BLASFUNC(zherk)(const char *, const char *, const int *, const int *, const double *, const double *, const int *, const double *, double *, const int *);
+int BLASFUNC(xherk)(const char *, const char *, const int *, const int *, const double *, const double *, const int *, const double *, double *, const int *);
+
+int BLASFUNC(cher2k)(const char *, const char *, const int *, const int *, const float *, const float *, const int *, const float *, const int *, const float *, float *, const int *);
+int BLASFUNC(zher2k)(const char *, const char *, const int *, const int *, const double *, const double *, const int *, const double *, const int *, const double *, double *, const int *);
+int BLASFUNC(xher2k)(const char *, const char *, const int *, const int *, const double *, const double *, const int *, const double *, const int *, const double *, double *, const int *);
+int BLASFUNC(cher2m)(const char *, const char *, const char *, const int *, const int *, const float *, const float *, const int *, const float *, const int *, const float *, float *, const int *);
+int BLASFUNC(zher2m)(const char *, const char *, const char *, const int *, const int *, const double *, const double *, const int *, const double*, const int *, const double *, double *, const int *);
+int BLASFUNC(xher2m)(const char *, const char *, const char *, const int *, const int *, const double *, const double *, const int *, const double*, const int *, const double *, double *, const int *);
+
+
+#ifdef __cplusplus
+}
+#endif
+
+#endif
diff --git a/Eigen/src/misc/lapack.h b/Eigen/src/misc/lapack.h
new file mode 100644
index 0000000..249f357
--- /dev/null
+++ b/Eigen/src/misc/lapack.h
@@ -0,0 +1,152 @@
+#ifndef LAPACK_H
+#define LAPACK_H
+
+#include "blas.h"
+
+#ifdef __cplusplus
+extern "C"
+{
+#endif
+
+int BLASFUNC(csymv) (const char *, const int *, const float *, const float *, const int *, const float *, const int *, const float *, float *, const int *);
+int BLASFUNC(zsymv) (const char *, const int *, const double *, const double *, const int *, const double *, const int *, const double *, double *, const int *);
+int BLASFUNC(xsymv) (const char *, const int *, const double *, const double *, const int *, const double *, const int *, const double *, double *, const int *);
+
+
+int BLASFUNC(cspmv) (char *, int *, float *, float *,
+ float *, int *, float *, float *, int *);
+int BLASFUNC(zspmv) (char *, int *, double *, double *,
+ double *, int *, double *, double *, int *);
+int BLASFUNC(xspmv) (char *, int *, double *, double *,
+ double *, int *, double *, double *, int *);
+
+int BLASFUNC(csyr) (char *, int *, float *, float *, int *,
+ float *, int *);
+int BLASFUNC(zsyr) (char *, int *, double *, double *, int *,
+ double *, int *);
+int BLASFUNC(xsyr) (char *, int *, double *, double *, int *,
+ double *, int *);
+
+int BLASFUNC(cspr) (char *, int *, float *, float *, int *,
+ float *);
+int BLASFUNC(zspr) (char *, int *, double *, double *, int *,
+ double *);
+int BLASFUNC(xspr) (char *, int *, double *, double *, int *,
+ double *);
+
+int BLASFUNC(sgemt)(char *, int *, int *, float *, float *, int *,
+ float *, int *);
+int BLASFUNC(dgemt)(char *, int *, int *, double *, double *, int *,
+ double *, int *);
+int BLASFUNC(cgemt)(char *, int *, int *, float *, float *, int *,
+ float *, int *);
+int BLASFUNC(zgemt)(char *, int *, int *, double *, double *, int *,
+ double *, int *);
+
+int BLASFUNC(sgema)(char *, char *, int *, int *, float *,
+ float *, int *, float *, float *, int *, float *, int *);
+int BLASFUNC(dgema)(char *, char *, int *, int *, double *,
+ double *, int *, double*, double *, int *, double*, int *);
+int BLASFUNC(cgema)(char *, char *, int *, int *, float *,
+ float *, int *, float *, float *, int *, float *, int *);
+int BLASFUNC(zgema)(char *, char *, int *, int *, double *,
+ double *, int *, double*, double *, int *, double*, int *);
+
+int BLASFUNC(sgems)(char *, char *, int *, int *, float *,
+ float *, int *, float *, float *, int *, float *, int *);
+int BLASFUNC(dgems)(char *, char *, int *, int *, double *,
+ double *, int *, double*, double *, int *, double*, int *);
+int BLASFUNC(cgems)(char *, char *, int *, int *, float *,
+ float *, int *, float *, float *, int *, float *, int *);
+int BLASFUNC(zgems)(char *, char *, int *, int *, double *,
+ double *, int *, double*, double *, int *, double*, int *);
+
+int BLASFUNC(sgetf2)(int *, int *, float *, int *, int *, int *);
+int BLASFUNC(dgetf2)(int *, int *, double *, int *, int *, int *);
+int BLASFUNC(qgetf2)(int *, int *, double *, int *, int *, int *);
+int BLASFUNC(cgetf2)(int *, int *, float *, int *, int *, int *);
+int BLASFUNC(zgetf2)(int *, int *, double *, int *, int *, int *);
+int BLASFUNC(xgetf2)(int *, int *, double *, int *, int *, int *);
+
+int BLASFUNC(sgetrf)(int *, int *, float *, int *, int *, int *);
+int BLASFUNC(dgetrf)(int *, int *, double *, int *, int *, int *);
+int BLASFUNC(qgetrf)(int *, int *, double *, int *, int *, int *);
+int BLASFUNC(cgetrf)(int *, int *, float *, int *, int *, int *);
+int BLASFUNC(zgetrf)(int *, int *, double *, int *, int *, int *);
+int BLASFUNC(xgetrf)(int *, int *, double *, int *, int *, int *);
+
+int BLASFUNC(slaswp)(int *, float *, int *, int *, int *, int *, int *);
+int BLASFUNC(dlaswp)(int *, double *, int *, int *, int *, int *, int *);
+int BLASFUNC(qlaswp)(int *, double *, int *, int *, int *, int *, int *);
+int BLASFUNC(claswp)(int *, float *, int *, int *, int *, int *, int *);
+int BLASFUNC(zlaswp)(int *, double *, int *, int *, int *, int *, int *);
+int BLASFUNC(xlaswp)(int *, double *, int *, int *, int *, int *, int *);
+
+int BLASFUNC(sgetrs)(char *, int *, int *, float *, int *, int *, float *, int *, int *);
+int BLASFUNC(dgetrs)(char *, int *, int *, double *, int *, int *, double *, int *, int *);
+int BLASFUNC(qgetrs)(char *, int *, int *, double *, int *, int *, double *, int *, int *);
+int BLASFUNC(cgetrs)(char *, int *, int *, float *, int *, int *, float *, int *, int *);
+int BLASFUNC(zgetrs)(char *, int *, int *, double *, int *, int *, double *, int *, int *);
+int BLASFUNC(xgetrs)(char *, int *, int *, double *, int *, int *, double *, int *, int *);
+
+int BLASFUNC(sgesv)(int *, int *, float *, int *, int *, float *, int *, int *);
+int BLASFUNC(dgesv)(int *, int *, double *, int *, int *, double*, int *, int *);
+int BLASFUNC(qgesv)(int *, int *, double *, int *, int *, double*, int *, int *);
+int BLASFUNC(cgesv)(int *, int *, float *, int *, int *, float *, int *, int *);
+int BLASFUNC(zgesv)(int *, int *, double *, int *, int *, double*, int *, int *);
+int BLASFUNC(xgesv)(int *, int *, double *, int *, int *, double*, int *, int *);
+
+int BLASFUNC(spotf2)(char *, int *, float *, int *, int *);
+int BLASFUNC(dpotf2)(char *, int *, double *, int *, int *);
+int BLASFUNC(qpotf2)(char *, int *, double *, int *, int *);
+int BLASFUNC(cpotf2)(char *, int *, float *, int *, int *);
+int BLASFUNC(zpotf2)(char *, int *, double *, int *, int *);
+int BLASFUNC(xpotf2)(char *, int *, double *, int *, int *);
+
+int BLASFUNC(spotrf)(char *, int *, float *, int *, int *);
+int BLASFUNC(dpotrf)(char *, int *, double *, int *, int *);
+int BLASFUNC(qpotrf)(char *, int *, double *, int *, int *);
+int BLASFUNC(cpotrf)(char *, int *, float *, int *, int *);
+int BLASFUNC(zpotrf)(char *, int *, double *, int *, int *);
+int BLASFUNC(xpotrf)(char *, int *, double *, int *, int *);
+
+int BLASFUNC(slauu2)(char *, int *, float *, int *, int *);
+int BLASFUNC(dlauu2)(char *, int *, double *, int *, int *);
+int BLASFUNC(qlauu2)(char *, int *, double *, int *, int *);
+int BLASFUNC(clauu2)(char *, int *, float *, int *, int *);
+int BLASFUNC(zlauu2)(char *, int *, double *, int *, int *);
+int BLASFUNC(xlauu2)(char *, int *, double *, int *, int *);
+
+int BLASFUNC(slauum)(char *, int *, float *, int *, int *);
+int BLASFUNC(dlauum)(char *, int *, double *, int *, int *);
+int BLASFUNC(qlauum)(char *, int *, double *, int *, int *);
+int BLASFUNC(clauum)(char *, int *, float *, int *, int *);
+int BLASFUNC(zlauum)(char *, int *, double *, int *, int *);
+int BLASFUNC(xlauum)(char *, int *, double *, int *, int *);
+
+int BLASFUNC(strti2)(char *, char *, int *, float *, int *, int *);
+int BLASFUNC(dtrti2)(char *, char *, int *, double *, int *, int *);
+int BLASFUNC(qtrti2)(char *, char *, int *, double *, int *, int *);
+int BLASFUNC(ctrti2)(char *, char *, int *, float *, int *, int *);
+int BLASFUNC(ztrti2)(char *, char *, int *, double *, int *, int *);
+int BLASFUNC(xtrti2)(char *, char *, int *, double *, int *, int *);
+
+int BLASFUNC(strtri)(char *, char *, int *, float *, int *, int *);
+int BLASFUNC(dtrtri)(char *, char *, int *, double *, int *, int *);
+int BLASFUNC(qtrtri)(char *, char *, int *, double *, int *, int *);
+int BLASFUNC(ctrtri)(char *, char *, int *, float *, int *, int *);
+int BLASFUNC(ztrtri)(char *, char *, int *, double *, int *, int *);
+int BLASFUNC(xtrtri)(char *, char *, int *, double *, int *, int *);
+
+int BLASFUNC(spotri)(char *, int *, float *, int *, int *);
+int BLASFUNC(dpotri)(char *, int *, double *, int *, int *);
+int BLASFUNC(qpotri)(char *, int *, double *, int *, int *);
+int BLASFUNC(cpotri)(char *, int *, float *, int *, int *);
+int BLASFUNC(zpotri)(char *, int *, double *, int *, int *);
+int BLASFUNC(xpotri)(char *, int *, double *, int *, int *);
+
+#ifdef __cplusplus
+}
+#endif
+
+#endif
diff --git a/Eigen/src/misc/lapacke.h b/Eigen/src/misc/lapacke.h
new file mode 100644
index 0000000..3d8e24f
--- /dev/null
+++ b/Eigen/src/misc/lapacke.h
@@ -0,0 +1,16292 @@
+/*****************************************************************************
+ Copyright (c) 2010, Intel Corp.
+ All rights reserved.
+
+ Redistribution and use in source and binary forms, with or without
+ modification, are permitted provided that the following conditions are met:
+
+ * Redistributions of source code must retain the above copyright notice,
+ this list of conditions and the following disclaimer.
+ * Redistributions in binary form must reproduce the above copyright
+ notice, this list of conditions and the following disclaimer in the
+ documentation and/or other materials provided with the distribution.
+ * Neither the name of Intel Corporation nor the names of its contributors
+ may be used to endorse or promote products derived from this software
+ without specific prior written permission.
+
+ THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
+ AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+ IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+ ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE
+ LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
+ CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
+ SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
+ INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
+ CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
+ ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF
+ THE POSSIBILITY OF SUCH DAMAGE.
+******************************************************************************
+* Contents: Native C interface to LAPACK
+* Author: Intel Corporation
+* Generated November, 2011
+*****************************************************************************/
+
+#ifndef _MKL_LAPACKE_H_
+
+#ifndef _LAPACKE_H_
+#define _LAPACKE_H_
+
+/*
+* Turn on HAVE_LAPACK_CONFIG_H to redefine C-LAPACK datatypes
+*/
+#ifdef HAVE_LAPACK_CONFIG_H
+#include "lapacke_config.h"
+#endif
+
+#include <stdlib.h>
+
+#ifndef lapack_int
+#define lapack_int int
+#endif
+
+#ifndef lapack_logical
+#define lapack_logical lapack_int
+#endif
+
+/* Complex types are structures equivalent to the
+* Fortran complex types COMPLEX(4) and COMPLEX(8).
+*
+* One can also redefine the types with his own types
+* for example by including in the code definitions like
+*
+* #define lapack_complex_float std::complex<float>
+* #define lapack_complex_double std::complex<double>
+*
+* or define these types in the command line:
+*
+* -Dlapack_complex_float="std::complex<float>"
+* -Dlapack_complex_double="std::complex<double>"
+*/
+
+#ifndef LAPACK_COMPLEX_CUSTOM
+
+/* Complex type (single precision) */
+#ifndef lapack_complex_float
+#include <complex.h>
+#define lapack_complex_float float _Complex
+#endif
+
+#ifndef lapack_complex_float_real
+#define lapack_complex_float_real(z) (creal(z))
+#endif
+
+#ifndef lapack_complex_float_imag
+#define lapack_complex_float_imag(z) (cimag(z))
+#endif
+
+lapack_complex_float lapack_make_complex_float( float re, float im );
+
+/* Complex type (double precision) */
+#ifndef lapack_complex_double
+#include <complex.h>
+#define lapack_complex_double double _Complex
+#endif
+
+#ifndef lapack_complex_double_real
+#define lapack_complex_double_real(z) (creal(z))
+#endif
+
+#ifndef lapack_complex_double_imag
+#define lapack_complex_double_imag(z) (cimag(z))
+#endif
+
+lapack_complex_double lapack_make_complex_double( double re, double im );
+
+#endif
+
+
+#ifdef __cplusplus
+extern "C" {
+#endif /* __cplusplus */
+
+#ifndef LAPACKE_malloc
+#define LAPACKE_malloc( size ) malloc( size )
+#endif
+#ifndef LAPACKE_free
+#define LAPACKE_free( p ) free( p )
+#endif
+
+#define LAPACK_C2INT( x ) (lapack_int)(*((float*)&x ))
+#define LAPACK_Z2INT( x ) (lapack_int)(*((double*)&x ))
+
+#define LAPACK_ROW_MAJOR 101
+#define LAPACK_COL_MAJOR 102
+
+#define LAPACK_WORK_MEMORY_ERROR -1010
+#define LAPACK_TRANSPOSE_MEMORY_ERROR -1011
+
+/* Callback logical functions of one, two, or three arguments are used
+* to select eigenvalues to sort to the top left of the Schur form.
+* The value is selected if function returns TRUE (non-zero). */
+
+typedef lapack_logical (*LAPACK_S_SELECT2) ( const float*, const float* );
+typedef lapack_logical (*LAPACK_S_SELECT3)
+ ( const float*, const float*, const float* );
+typedef lapack_logical (*LAPACK_D_SELECT2) ( const double*, const double* );
+typedef lapack_logical (*LAPACK_D_SELECT3)
+ ( const double*, const double*, const double* );
+
+typedef lapack_logical (*LAPACK_C_SELECT1) ( const lapack_complex_float* );
+typedef lapack_logical (*LAPACK_C_SELECT2)
+ ( const lapack_complex_float*, const lapack_complex_float* );
+typedef lapack_logical (*LAPACK_Z_SELECT1) ( const lapack_complex_double* );
+typedef lapack_logical (*LAPACK_Z_SELECT2)
+ ( const lapack_complex_double*, const lapack_complex_double* );
+
+#include "lapacke_mangling.h"
+
+#define LAPACK_lsame LAPACK_GLOBAL(lsame,LSAME)
+lapack_logical LAPACK_lsame( char* ca, char* cb,
+ lapack_int lca, lapack_int lcb );
+
+/* C-LAPACK function prototypes */
+
+lapack_int LAPACKE_sbdsdc( int matrix_order, char uplo, char compq,
+ lapack_int n, float* d, float* e, float* u,
+ lapack_int ldu, float* vt, lapack_int ldvt, float* q,
+ lapack_int* iq );
+lapack_int LAPACKE_dbdsdc( int matrix_order, char uplo, char compq,
+ lapack_int n, double* d, double* e, double* u,
+ lapack_int ldu, double* vt, lapack_int ldvt,
+ double* q, lapack_int* iq );
+
+lapack_int LAPACKE_sbdsqr( int matrix_order, char uplo, lapack_int n,
+ lapack_int ncvt, lapack_int nru, lapack_int ncc,
+ float* d, float* e, float* vt, lapack_int ldvt,
+ float* u, lapack_int ldu, float* c, lapack_int ldc );
+lapack_int LAPACKE_dbdsqr( int matrix_order, char uplo, lapack_int n,
+ lapack_int ncvt, lapack_int nru, lapack_int ncc,
+ double* d, double* e, double* vt, lapack_int ldvt,
+ double* u, lapack_int ldu, double* c,
+ lapack_int ldc );
+lapack_int LAPACKE_cbdsqr( int matrix_order, char uplo, lapack_int n,
+ lapack_int ncvt, lapack_int nru, lapack_int ncc,
+ float* d, float* e, lapack_complex_float* vt,
+ lapack_int ldvt, lapack_complex_float* u,
+ lapack_int ldu, lapack_complex_float* c,
+ lapack_int ldc );
+lapack_int LAPACKE_zbdsqr( int matrix_order, char uplo, lapack_int n,
+ lapack_int ncvt, lapack_int nru, lapack_int ncc,
+ double* d, double* e, lapack_complex_double* vt,
+ lapack_int ldvt, lapack_complex_double* u,
+ lapack_int ldu, lapack_complex_double* c,
+ lapack_int ldc );
+
+lapack_int LAPACKE_sdisna( char job, lapack_int m, lapack_int n, const float* d,
+ float* sep );
+lapack_int LAPACKE_ddisna( char job, lapack_int m, lapack_int n,
+ const double* d, double* sep );
+
+lapack_int LAPACKE_sgbbrd( int matrix_order, char vect, lapack_int m,
+ lapack_int n, lapack_int ncc, lapack_int kl,
+ lapack_int ku, float* ab, lapack_int ldab, float* d,
+ float* e, float* q, lapack_int ldq, float* pt,
+ lapack_int ldpt, float* c, lapack_int ldc );
+lapack_int LAPACKE_dgbbrd( int matrix_order, char vect, lapack_int m,
+ lapack_int n, lapack_int ncc, lapack_int kl,
+ lapack_int ku, double* ab, lapack_int ldab,
+ double* d, double* e, double* q, lapack_int ldq,
+ double* pt, lapack_int ldpt, double* c,
+ lapack_int ldc );
+lapack_int LAPACKE_cgbbrd( int matrix_order, char vect, lapack_int m,
+ lapack_int n, lapack_int ncc, lapack_int kl,
+ lapack_int ku, lapack_complex_float* ab,
+ lapack_int ldab, float* d, float* e,
+ lapack_complex_float* q, lapack_int ldq,
+ lapack_complex_float* pt, lapack_int ldpt,
+ lapack_complex_float* c, lapack_int ldc );
+lapack_int LAPACKE_zgbbrd( int matrix_order, char vect, lapack_int m,
+ lapack_int n, lapack_int ncc, lapack_int kl,
+ lapack_int ku, lapack_complex_double* ab,
+ lapack_int ldab, double* d, double* e,
+ lapack_complex_double* q, lapack_int ldq,
+ lapack_complex_double* pt, lapack_int ldpt,
+ lapack_complex_double* c, lapack_int ldc );
+
+lapack_int LAPACKE_sgbcon( int matrix_order, char norm, lapack_int n,
+ lapack_int kl, lapack_int ku, const float* ab,
+ lapack_int ldab, const lapack_int* ipiv, float anorm,
+ float* rcond );
+lapack_int LAPACKE_dgbcon( int matrix_order, char norm, lapack_int n,
+ lapack_int kl, lapack_int ku, const double* ab,
+ lapack_int ldab, const lapack_int* ipiv,
+ double anorm, double* rcond );
+lapack_int LAPACKE_cgbcon( int matrix_order, char norm, lapack_int n,
+ lapack_int kl, lapack_int ku,
+ const lapack_complex_float* ab, lapack_int ldab,
+ const lapack_int* ipiv, float anorm, float* rcond );
+lapack_int LAPACKE_zgbcon( int matrix_order, char norm, lapack_int n,
+ lapack_int kl, lapack_int ku,
+ const lapack_complex_double* ab, lapack_int ldab,
+ const lapack_int* ipiv, double anorm,
+ double* rcond );
+
+lapack_int LAPACKE_sgbequ( int matrix_order, lapack_int m, lapack_int n,
+ lapack_int kl, lapack_int ku, const float* ab,
+ lapack_int ldab, float* r, float* c, float* rowcnd,
+ float* colcnd, float* amax );
+lapack_int LAPACKE_dgbequ( int matrix_order, lapack_int m, lapack_int n,
+ lapack_int kl, lapack_int ku, const double* ab,
+ lapack_int ldab, double* r, double* c,
+ double* rowcnd, double* colcnd, double* amax );
+lapack_int LAPACKE_cgbequ( int matrix_order, lapack_int m, lapack_int n,
+ lapack_int kl, lapack_int ku,
+ const lapack_complex_float* ab, lapack_int ldab,
+ float* r, float* c, float* rowcnd, float* colcnd,
+ float* amax );
+lapack_int LAPACKE_zgbequ( int matrix_order, lapack_int m, lapack_int n,
+ lapack_int kl, lapack_int ku,
+ const lapack_complex_double* ab, lapack_int ldab,
+ double* r, double* c, double* rowcnd, double* colcnd,
+ double* amax );
+
+lapack_int LAPACKE_sgbequb( int matrix_order, lapack_int m, lapack_int n,
+ lapack_int kl, lapack_int ku, const float* ab,
+ lapack_int ldab, float* r, float* c, float* rowcnd,
+ float* colcnd, float* amax );
+lapack_int LAPACKE_dgbequb( int matrix_order, lapack_int m, lapack_int n,
+ lapack_int kl, lapack_int ku, const double* ab,
+ lapack_int ldab, double* r, double* c,
+ double* rowcnd, double* colcnd, double* amax );
+lapack_int LAPACKE_cgbequb( int matrix_order, lapack_int m, lapack_int n,
+ lapack_int kl, lapack_int ku,
+ const lapack_complex_float* ab, lapack_int ldab,
+ float* r, float* c, float* rowcnd, float* colcnd,
+ float* amax );
+lapack_int LAPACKE_zgbequb( int matrix_order, lapack_int m, lapack_int n,
+ lapack_int kl, lapack_int ku,
+ const lapack_complex_double* ab, lapack_int ldab,
+ double* r, double* c, double* rowcnd,
+ double* colcnd, double* amax );
+
+lapack_int LAPACKE_sgbrfs( int matrix_order, char trans, lapack_int n,
+ lapack_int kl, lapack_int ku, lapack_int nrhs,
+ const float* ab, lapack_int ldab, const float* afb,
+ lapack_int ldafb, const lapack_int* ipiv,
+ const float* b, lapack_int ldb, float* x,
+ lapack_int ldx, float* ferr, float* berr );
+lapack_int LAPACKE_dgbrfs( int matrix_order, char trans, lapack_int n,
+ lapack_int kl, lapack_int ku, lapack_int nrhs,
+ const double* ab, lapack_int ldab, const double* afb,
+ lapack_int ldafb, const lapack_int* ipiv,
+ const double* b, lapack_int ldb, double* x,
+ lapack_int ldx, double* ferr, double* berr );
+lapack_int LAPACKE_cgbrfs( int matrix_order, char trans, lapack_int n,
+ lapack_int kl, lapack_int ku, lapack_int nrhs,
+ const lapack_complex_float* ab, lapack_int ldab,
+ const lapack_complex_float* afb, lapack_int ldafb,
+ const lapack_int* ipiv,
+ const lapack_complex_float* b, lapack_int ldb,
+ lapack_complex_float* x, lapack_int ldx, float* ferr,
+ float* berr );
+lapack_int LAPACKE_zgbrfs( int matrix_order, char trans, lapack_int n,
+ lapack_int kl, lapack_int ku, lapack_int nrhs,
+ const lapack_complex_double* ab, lapack_int ldab,
+ const lapack_complex_double* afb, lapack_int ldafb,
+ const lapack_int* ipiv,
+ const lapack_complex_double* b, lapack_int ldb,
+ lapack_complex_double* x, lapack_int ldx,
+ double* ferr, double* berr );
+
+lapack_int LAPACKE_sgbrfsx( int matrix_order, char trans, char equed,
+ lapack_int n, lapack_int kl, lapack_int ku,
+ lapack_int nrhs, const float* ab, lapack_int ldab,
+ const float* afb, lapack_int ldafb,
+ const lapack_int* ipiv, const float* r,
+ const float* c, const float* b, lapack_int ldb,
+ float* x, lapack_int ldx, float* rcond, float* berr,
+ lapack_int n_err_bnds, float* err_bnds_norm,
+ float* err_bnds_comp, lapack_int nparams,
+ float* params );
+lapack_int LAPACKE_dgbrfsx( int matrix_order, char trans, char equed,
+ lapack_int n, lapack_int kl, lapack_int ku,
+ lapack_int nrhs, const double* ab, lapack_int ldab,
+ const double* afb, lapack_int ldafb,
+ const lapack_int* ipiv, const double* r,
+ const double* c, const double* b, lapack_int ldb,
+ double* x, lapack_int ldx, double* rcond,
+ double* berr, lapack_int n_err_bnds,
+ double* err_bnds_norm, double* err_bnds_comp,
+ lapack_int nparams, double* params );
+lapack_int LAPACKE_cgbrfsx( int matrix_order, char trans, char equed,
+ lapack_int n, lapack_int kl, lapack_int ku,
+ lapack_int nrhs, const lapack_complex_float* ab,
+ lapack_int ldab, const lapack_complex_float* afb,
+ lapack_int ldafb, const lapack_int* ipiv,
+ const float* r, const float* c,
+ const lapack_complex_float* b, lapack_int ldb,
+ lapack_complex_float* x, lapack_int ldx,
+ float* rcond, float* berr, lapack_int n_err_bnds,
+ float* err_bnds_norm, float* err_bnds_comp,
+ lapack_int nparams, float* params );
+lapack_int LAPACKE_zgbrfsx( int matrix_order, char trans, char equed,
+ lapack_int n, lapack_int kl, lapack_int ku,
+ lapack_int nrhs, const lapack_complex_double* ab,
+ lapack_int ldab, const lapack_complex_double* afb,
+ lapack_int ldafb, const lapack_int* ipiv,
+ const double* r, const double* c,
+ const lapack_complex_double* b, lapack_int ldb,
+ lapack_complex_double* x, lapack_int ldx,
+ double* rcond, double* berr, lapack_int n_err_bnds,
+ double* err_bnds_norm, double* err_bnds_comp,
+ lapack_int nparams, double* params );
+
+lapack_int LAPACKE_sgbsv( int matrix_order, lapack_int n, lapack_int kl,
+ lapack_int ku, lapack_int nrhs, float* ab,
+ lapack_int ldab, lapack_int* ipiv, float* b,
+ lapack_int ldb );
+lapack_int LAPACKE_dgbsv( int matrix_order, lapack_int n, lapack_int kl,
+ lapack_int ku, lapack_int nrhs, double* ab,
+ lapack_int ldab, lapack_int* ipiv, double* b,
+ lapack_int ldb );
+lapack_int LAPACKE_cgbsv( int matrix_order, lapack_int n, lapack_int kl,
+ lapack_int ku, lapack_int nrhs,
+ lapack_complex_float* ab, lapack_int ldab,
+ lapack_int* ipiv, lapack_complex_float* b,
+ lapack_int ldb );
+lapack_int LAPACKE_zgbsv( int matrix_order, lapack_int n, lapack_int kl,
+ lapack_int ku, lapack_int nrhs,
+ lapack_complex_double* ab, lapack_int ldab,
+ lapack_int* ipiv, lapack_complex_double* b,
+ lapack_int ldb );
+
+lapack_int LAPACKE_sgbsvx( int matrix_order, char fact, char trans,
+ lapack_int n, lapack_int kl, lapack_int ku,
+ lapack_int nrhs, float* ab, lapack_int ldab,
+ float* afb, lapack_int ldafb, lapack_int* ipiv,
+ char* equed, float* r, float* c, float* b,
+ lapack_int ldb, float* x, lapack_int ldx,
+ float* rcond, float* ferr, float* berr,
+ float* rpivot );
+lapack_int LAPACKE_dgbsvx( int matrix_order, char fact, char trans,
+ lapack_int n, lapack_int kl, lapack_int ku,
+ lapack_int nrhs, double* ab, lapack_int ldab,
+ double* afb, lapack_int ldafb, lapack_int* ipiv,
+ char* equed, double* r, double* c, double* b,
+ lapack_int ldb, double* x, lapack_int ldx,
+ double* rcond, double* ferr, double* berr,
+ double* rpivot );
+lapack_int LAPACKE_cgbsvx( int matrix_order, char fact, char trans,
+ lapack_int n, lapack_int kl, lapack_int ku,
+ lapack_int nrhs, lapack_complex_float* ab,
+ lapack_int ldab, lapack_complex_float* afb,
+ lapack_int ldafb, lapack_int* ipiv, char* equed,
+ float* r, float* c, lapack_complex_float* b,
+ lapack_int ldb, lapack_complex_float* x,
+ lapack_int ldx, float* rcond, float* ferr,
+ float* berr, float* rpivot );
+lapack_int LAPACKE_zgbsvx( int matrix_order, char fact, char trans,
+ lapack_int n, lapack_int kl, lapack_int ku,
+ lapack_int nrhs, lapack_complex_double* ab,
+ lapack_int ldab, lapack_complex_double* afb,
+ lapack_int ldafb, lapack_int* ipiv, char* equed,
+ double* r, double* c, lapack_complex_double* b,
+ lapack_int ldb, lapack_complex_double* x,
+ lapack_int ldx, double* rcond, double* ferr,
+ double* berr, double* rpivot );
+
+lapack_int LAPACKE_sgbsvxx( int matrix_order, char fact, char trans,
+ lapack_int n, lapack_int kl, lapack_int ku,
+ lapack_int nrhs, float* ab, lapack_int ldab,
+ float* afb, lapack_int ldafb, lapack_int* ipiv,
+ char* equed, float* r, float* c, float* b,
+ lapack_int ldb, float* x, lapack_int ldx,
+ float* rcond, float* rpvgrw, float* berr,
+ lapack_int n_err_bnds, float* err_bnds_norm,
+ float* err_bnds_comp, lapack_int nparams,
+ float* params );
+lapack_int LAPACKE_dgbsvxx( int matrix_order, char fact, char trans,
+ lapack_int n, lapack_int kl, lapack_int ku,
+ lapack_int nrhs, double* ab, lapack_int ldab,
+ double* afb, lapack_int ldafb, lapack_int* ipiv,
+ char* equed, double* r, double* c, double* b,
+ lapack_int ldb, double* x, lapack_int ldx,
+ double* rcond, double* rpvgrw, double* berr,
+ lapack_int n_err_bnds, double* err_bnds_norm,
+ double* err_bnds_comp, lapack_int nparams,
+ double* params );
+lapack_int LAPACKE_cgbsvxx( int matrix_order, char fact, char trans,
+ lapack_int n, lapack_int kl, lapack_int ku,
+ lapack_int nrhs, lapack_complex_float* ab,
+ lapack_int ldab, lapack_complex_float* afb,
+ lapack_int ldafb, lapack_int* ipiv, char* equed,
+ float* r, float* c, lapack_complex_float* b,
+ lapack_int ldb, lapack_complex_float* x,
+ lapack_int ldx, float* rcond, float* rpvgrw,
+ float* berr, lapack_int n_err_bnds,
+ float* err_bnds_norm, float* err_bnds_comp,
+ lapack_int nparams, float* params );
+lapack_int LAPACKE_zgbsvxx( int matrix_order, char fact, char trans,
+ lapack_int n, lapack_int kl, lapack_int ku,
+ lapack_int nrhs, lapack_complex_double* ab,
+ lapack_int ldab, lapack_complex_double* afb,
+ lapack_int ldafb, lapack_int* ipiv, char* equed,
+ double* r, double* c, lapack_complex_double* b,
+ lapack_int ldb, lapack_complex_double* x,
+ lapack_int ldx, double* rcond, double* rpvgrw,
+ double* berr, lapack_int n_err_bnds,
+ double* err_bnds_norm, double* err_bnds_comp,
+ lapack_int nparams, double* params );
+
+lapack_int LAPACKE_sgbtrf( int matrix_order, lapack_int m, lapack_int n,
+ lapack_int kl, lapack_int ku, float* ab,
+ lapack_int ldab, lapack_int* ipiv );
+lapack_int LAPACKE_dgbtrf( int matrix_order, lapack_int m, lapack_int n,
+ lapack_int kl, lapack_int ku, double* ab,
+ lapack_int ldab, lapack_int* ipiv );
+lapack_int LAPACKE_cgbtrf( int matrix_order, lapack_int m, lapack_int n,
+ lapack_int kl, lapack_int ku,
+ lapack_complex_float* ab, lapack_int ldab,
+ lapack_int* ipiv );
+lapack_int LAPACKE_zgbtrf( int matrix_order, lapack_int m, lapack_int n,
+ lapack_int kl, lapack_int ku,
+ lapack_complex_double* ab, lapack_int ldab,
+ lapack_int* ipiv );
+
+lapack_int LAPACKE_sgbtrs( int matrix_order, char trans, lapack_int n,
+ lapack_int kl, lapack_int ku, lapack_int nrhs,
+ const float* ab, lapack_int ldab,
+ const lapack_int* ipiv, float* b, lapack_int ldb );
+lapack_int LAPACKE_dgbtrs( int matrix_order, char trans, lapack_int n,
+ lapack_int kl, lapack_int ku, lapack_int nrhs,
+ const double* ab, lapack_int ldab,
+ const lapack_int* ipiv, double* b, lapack_int ldb );
+lapack_int LAPACKE_cgbtrs( int matrix_order, char trans, lapack_int n,
+ lapack_int kl, lapack_int ku, lapack_int nrhs,
+ const lapack_complex_float* ab, lapack_int ldab,
+ const lapack_int* ipiv, lapack_complex_float* b,
+ lapack_int ldb );
+lapack_int LAPACKE_zgbtrs( int matrix_order, char trans, lapack_int n,
+ lapack_int kl, lapack_int ku, lapack_int nrhs,
+ const lapack_complex_double* ab, lapack_int ldab,
+ const lapack_int* ipiv, lapack_complex_double* b,
+ lapack_int ldb );
+
+lapack_int LAPACKE_sgebak( int matrix_order, char job, char side, lapack_int n,
+ lapack_int ilo, lapack_int ihi, const float* scale,
+ lapack_int m, float* v, lapack_int ldv );
+lapack_int LAPACKE_dgebak( int matrix_order, char job, char side, lapack_int n,
+ lapack_int ilo, lapack_int ihi, const double* scale,
+ lapack_int m, double* v, lapack_int ldv );
+lapack_int LAPACKE_cgebak( int matrix_order, char job, char side, lapack_int n,
+ lapack_int ilo, lapack_int ihi, const float* scale,
+ lapack_int m, lapack_complex_float* v,
+ lapack_int ldv );
+lapack_int LAPACKE_zgebak( int matrix_order, char job, char side, lapack_int n,
+ lapack_int ilo, lapack_int ihi, const double* scale,
+ lapack_int m, lapack_complex_double* v,
+ lapack_int ldv );
+
+lapack_int LAPACKE_sgebal( int matrix_order, char job, lapack_int n, float* a,
+ lapack_int lda, lapack_int* ilo, lapack_int* ihi,
+ float* scale );
+lapack_int LAPACKE_dgebal( int matrix_order, char job, lapack_int n, double* a,
+ lapack_int lda, lapack_int* ilo, lapack_int* ihi,
+ double* scale );
+lapack_int LAPACKE_cgebal( int matrix_order, char job, lapack_int n,
+ lapack_complex_float* a, lapack_int lda,
+ lapack_int* ilo, lapack_int* ihi, float* scale );
+lapack_int LAPACKE_zgebal( int matrix_order, char job, lapack_int n,
+ lapack_complex_double* a, lapack_int lda,
+ lapack_int* ilo, lapack_int* ihi, double* scale );
+
+lapack_int LAPACKE_sgebrd( int matrix_order, lapack_int m, lapack_int n,
+ float* a, lapack_int lda, float* d, float* e,
+ float* tauq, float* taup );
+lapack_int LAPACKE_dgebrd( int matrix_order, lapack_int m, lapack_int n,
+ double* a, lapack_int lda, double* d, double* e,
+ double* tauq, double* taup );
+lapack_int LAPACKE_cgebrd( int matrix_order, lapack_int m, lapack_int n,
+ lapack_complex_float* a, lapack_int lda, float* d,
+ float* e, lapack_complex_float* tauq,
+ lapack_complex_float* taup );
+lapack_int LAPACKE_zgebrd( int matrix_order, lapack_int m, lapack_int n,
+ lapack_complex_double* a, lapack_int lda, double* d,
+ double* e, lapack_complex_double* tauq,
+ lapack_complex_double* taup );
+
+lapack_int LAPACKE_sgecon( int matrix_order, char norm, lapack_int n,
+ const float* a, lapack_int lda, float anorm,
+ float* rcond );
+lapack_int LAPACKE_dgecon( int matrix_order, char norm, lapack_int n,
+ const double* a, lapack_int lda, double anorm,
+ double* rcond );
+lapack_int LAPACKE_cgecon( int matrix_order, char norm, lapack_int n,
+ const lapack_complex_float* a, lapack_int lda,
+ float anorm, float* rcond );
+lapack_int LAPACKE_zgecon( int matrix_order, char norm, lapack_int n,
+ const lapack_complex_double* a, lapack_int lda,
+ double anorm, double* rcond );
+
+lapack_int LAPACKE_sgeequ( int matrix_order, lapack_int m, lapack_int n,
+ const float* a, lapack_int lda, float* r, float* c,
+ float* rowcnd, float* colcnd, float* amax );
+lapack_int LAPACKE_dgeequ( int matrix_order, lapack_int m, lapack_int n,
+ const double* a, lapack_int lda, double* r,
+ double* c, double* rowcnd, double* colcnd,
+ double* amax );
+lapack_int LAPACKE_cgeequ( int matrix_order, lapack_int m, lapack_int n,
+ const lapack_complex_float* a, lapack_int lda,
+ float* r, float* c, float* rowcnd, float* colcnd,
+ float* amax );
+lapack_int LAPACKE_zgeequ( int matrix_order, lapack_int m, lapack_int n,
+ const lapack_complex_double* a, lapack_int lda,
+ double* r, double* c, double* rowcnd, double* colcnd,
+ double* amax );
+
+lapack_int LAPACKE_sgeequb( int matrix_order, lapack_int m, lapack_int n,
+ const float* a, lapack_int lda, float* r, float* c,
+ float* rowcnd, float* colcnd, float* amax );
+lapack_int LAPACKE_dgeequb( int matrix_order, lapack_int m, lapack_int n,
+ const double* a, lapack_int lda, double* r,
+ double* c, double* rowcnd, double* colcnd,
+ double* amax );
+lapack_int LAPACKE_cgeequb( int matrix_order, lapack_int m, lapack_int n,
+ const lapack_complex_float* a, lapack_int lda,
+ float* r, float* c, float* rowcnd, float* colcnd,
+ float* amax );
+lapack_int LAPACKE_zgeequb( int matrix_order, lapack_int m, lapack_int n,
+ const lapack_complex_double* a, lapack_int lda,
+ double* r, double* c, double* rowcnd,
+ double* colcnd, double* amax );
+
+lapack_int LAPACKE_sgees( int matrix_order, char jobvs, char sort,
+ LAPACK_S_SELECT2 select, lapack_int n, float* a,
+ lapack_int lda, lapack_int* sdim, float* wr,
+ float* wi, float* vs, lapack_int ldvs );
+lapack_int LAPACKE_dgees( int matrix_order, char jobvs, char sort,
+ LAPACK_D_SELECT2 select, lapack_int n, double* a,
+ lapack_int lda, lapack_int* sdim, double* wr,
+ double* wi, double* vs, lapack_int ldvs );
+lapack_int LAPACKE_cgees( int matrix_order, char jobvs, char sort,
+ LAPACK_C_SELECT1 select, lapack_int n,
+ lapack_complex_float* a, lapack_int lda,
+ lapack_int* sdim, lapack_complex_float* w,
+ lapack_complex_float* vs, lapack_int ldvs );
+lapack_int LAPACKE_zgees( int matrix_order, char jobvs, char sort,
+ LAPACK_Z_SELECT1 select, lapack_int n,
+ lapack_complex_double* a, lapack_int lda,
+ lapack_int* sdim, lapack_complex_double* w,
+ lapack_complex_double* vs, lapack_int ldvs );
+
+lapack_int LAPACKE_sgeesx( int matrix_order, char jobvs, char sort,
+ LAPACK_S_SELECT2 select, char sense, lapack_int n,
+ float* a, lapack_int lda, lapack_int* sdim,
+ float* wr, float* wi, float* vs, lapack_int ldvs,
+ float* rconde, float* rcondv );
+lapack_int LAPACKE_dgeesx( int matrix_order, char jobvs, char sort,
+ LAPACK_D_SELECT2 select, char sense, lapack_int n,
+ double* a, lapack_int lda, lapack_int* sdim,
+ double* wr, double* wi, double* vs, lapack_int ldvs,
+ double* rconde, double* rcondv );
+lapack_int LAPACKE_cgeesx( int matrix_order, char jobvs, char sort,
+ LAPACK_C_SELECT1 select, char sense, lapack_int n,
+ lapack_complex_float* a, lapack_int lda,
+ lapack_int* sdim, lapack_complex_float* w,
+ lapack_complex_float* vs, lapack_int ldvs,
+ float* rconde, float* rcondv );
+lapack_int LAPACKE_zgeesx( int matrix_order, char jobvs, char sort,
+ LAPACK_Z_SELECT1 select, char sense, lapack_int n,
+ lapack_complex_double* a, lapack_int lda,
+ lapack_int* sdim, lapack_complex_double* w,
+ lapack_complex_double* vs, lapack_int ldvs,
+ double* rconde, double* rcondv );
+
+lapack_int LAPACKE_sgeev( int matrix_order, char jobvl, char jobvr,
+ lapack_int n, float* a, lapack_int lda, float* wr,
+ float* wi, float* vl, lapack_int ldvl, float* vr,
+ lapack_int ldvr );
+lapack_int LAPACKE_dgeev( int matrix_order, char jobvl, char jobvr,
+ lapack_int n, double* a, lapack_int lda, double* wr,
+ double* wi, double* vl, lapack_int ldvl, double* vr,
+ lapack_int ldvr );
+lapack_int LAPACKE_cgeev( int matrix_order, char jobvl, char jobvr,
+ lapack_int n, lapack_complex_float* a, lapack_int lda,
+ lapack_complex_float* w, lapack_complex_float* vl,
+ lapack_int ldvl, lapack_complex_float* vr,
+ lapack_int ldvr );
+lapack_int LAPACKE_zgeev( int matrix_order, char jobvl, char jobvr,
+ lapack_int n, lapack_complex_double* a,
+ lapack_int lda, lapack_complex_double* w,
+ lapack_complex_double* vl, lapack_int ldvl,
+ lapack_complex_double* vr, lapack_int ldvr );
+
+lapack_int LAPACKE_sgeevx( int matrix_order, char balanc, char jobvl,
+ char jobvr, char sense, lapack_int n, float* a,
+ lapack_int lda, float* wr, float* wi, float* vl,
+ lapack_int ldvl, float* vr, lapack_int ldvr,
+ lapack_int* ilo, lapack_int* ihi, float* scale,
+ float* abnrm, float* rconde, float* rcondv );
+lapack_int LAPACKE_dgeevx( int matrix_order, char balanc, char jobvl,
+ char jobvr, char sense, lapack_int n, double* a,
+ lapack_int lda, double* wr, double* wi, double* vl,
+ lapack_int ldvl, double* vr, lapack_int ldvr,
+ lapack_int* ilo, lapack_int* ihi, double* scale,
+ double* abnrm, double* rconde, double* rcondv );
+lapack_int LAPACKE_cgeevx( int matrix_order, char balanc, char jobvl,
+ char jobvr, char sense, lapack_int n,
+ lapack_complex_float* a, lapack_int lda,
+ lapack_complex_float* w, lapack_complex_float* vl,
+ lapack_int ldvl, lapack_complex_float* vr,
+ lapack_int ldvr, lapack_int* ilo, lapack_int* ihi,
+ float* scale, float* abnrm, float* rconde,
+ float* rcondv );
+lapack_int LAPACKE_zgeevx( int matrix_order, char balanc, char jobvl,
+ char jobvr, char sense, lapack_int n,
+ lapack_complex_double* a, lapack_int lda,
+ lapack_complex_double* w, lapack_complex_double* vl,
+ lapack_int ldvl, lapack_complex_double* vr,
+ lapack_int ldvr, lapack_int* ilo, lapack_int* ihi,
+ double* scale, double* abnrm, double* rconde,
+ double* rcondv );
+
+lapack_int LAPACKE_sgehrd( int matrix_order, lapack_int n, lapack_int ilo,
+ lapack_int ihi, float* a, lapack_int lda,
+ float* tau );
+lapack_int LAPACKE_dgehrd( int matrix_order, lapack_int n, lapack_int ilo,
+ lapack_int ihi, double* a, lapack_int lda,
+ double* tau );
+lapack_int LAPACKE_cgehrd( int matrix_order, lapack_int n, lapack_int ilo,
+ lapack_int ihi, lapack_complex_float* a,
+ lapack_int lda, lapack_complex_float* tau );
+lapack_int LAPACKE_zgehrd( int matrix_order, lapack_int n, lapack_int ilo,
+ lapack_int ihi, lapack_complex_double* a,
+ lapack_int lda, lapack_complex_double* tau );
+
+lapack_int LAPACKE_sgejsv( int matrix_order, char joba, char jobu, char jobv,
+ char jobr, char jobt, char jobp, lapack_int m,
+ lapack_int n, float* a, lapack_int lda, float* sva,
+ float* u, lapack_int ldu, float* v, lapack_int ldv,
+ float* stat, lapack_int* istat );
+lapack_int LAPACKE_dgejsv( int matrix_order, char joba, char jobu, char jobv,
+ char jobr, char jobt, char jobp, lapack_int m,
+ lapack_int n, double* a, lapack_int lda, double* sva,
+ double* u, lapack_int ldu, double* v, lapack_int ldv,
+ double* stat, lapack_int* istat );
+
+lapack_int LAPACKE_sgelq2( int matrix_order, lapack_int m, lapack_int n,
+ float* a, lapack_int lda, float* tau );
+lapack_int LAPACKE_dgelq2( int matrix_order, lapack_int m, lapack_int n,
+ double* a, lapack_int lda, double* tau );
+lapack_int LAPACKE_cgelq2( int matrix_order, lapack_int m, lapack_int n,
+ lapack_complex_float* a, lapack_int lda,
+ lapack_complex_float* tau );
+lapack_int LAPACKE_zgelq2( int matrix_order, lapack_int m, lapack_int n,
+ lapack_complex_double* a, lapack_int lda,
+ lapack_complex_double* tau );
+
+lapack_int LAPACKE_sgelqf( int matrix_order, lapack_int m, lapack_int n,
+ float* a, lapack_int lda, float* tau );
+lapack_int LAPACKE_dgelqf( int matrix_order, lapack_int m, lapack_int n,
+ double* a, lapack_int lda, double* tau );
+lapack_int LAPACKE_cgelqf( int matrix_order, lapack_int m, lapack_int n,
+ lapack_complex_float* a, lapack_int lda,
+ lapack_complex_float* tau );
+lapack_int LAPACKE_zgelqf( int matrix_order, lapack_int m, lapack_int n,
+ lapack_complex_double* a, lapack_int lda,
+ lapack_complex_double* tau );
+
+lapack_int LAPACKE_sgels( int matrix_order, char trans, lapack_int m,
+ lapack_int n, lapack_int nrhs, float* a,
+ lapack_int lda, float* b, lapack_int ldb );
+lapack_int LAPACKE_dgels( int matrix_order, char trans, lapack_int m,
+ lapack_int n, lapack_int nrhs, double* a,
+ lapack_int lda, double* b, lapack_int ldb );
+lapack_int LAPACKE_cgels( int matrix_order, char trans, lapack_int m,
+ lapack_int n, lapack_int nrhs,
+ lapack_complex_float* a, lapack_int lda,
+ lapack_complex_float* b, lapack_int ldb );
+lapack_int LAPACKE_zgels( int matrix_order, char trans, lapack_int m,
+ lapack_int n, lapack_int nrhs,
+ lapack_complex_double* a, lapack_int lda,
+ lapack_complex_double* b, lapack_int ldb );
+
+lapack_int LAPACKE_sgelsd( int matrix_order, lapack_int m, lapack_int n,
+ lapack_int nrhs, float* a, lapack_int lda, float* b,
+ lapack_int ldb, float* s, float rcond,
+ lapack_int* rank );
+lapack_int LAPACKE_dgelsd( int matrix_order, lapack_int m, lapack_int n,
+ lapack_int nrhs, double* a, lapack_int lda,
+ double* b, lapack_int ldb, double* s, double rcond,
+ lapack_int* rank );
+lapack_int LAPACKE_cgelsd( int matrix_order, lapack_int m, lapack_int n,
+ lapack_int nrhs, lapack_complex_float* a,
+ lapack_int lda, lapack_complex_float* b,
+ lapack_int ldb, float* s, float rcond,
+ lapack_int* rank );
+lapack_int LAPACKE_zgelsd( int matrix_order, lapack_int m, lapack_int n,
+ lapack_int nrhs, lapack_complex_double* a,
+ lapack_int lda, lapack_complex_double* b,
+ lapack_int ldb, double* s, double rcond,
+ lapack_int* rank );
+
+lapack_int LAPACKE_sgelss( int matrix_order, lapack_int m, lapack_int n,
+ lapack_int nrhs, float* a, lapack_int lda, float* b,
+ lapack_int ldb, float* s, float rcond,
+ lapack_int* rank );
+lapack_int LAPACKE_dgelss( int matrix_order, lapack_int m, lapack_int n,
+ lapack_int nrhs, double* a, lapack_int lda,
+ double* b, lapack_int ldb, double* s, double rcond,
+ lapack_int* rank );
+lapack_int LAPACKE_cgelss( int matrix_order, lapack_int m, lapack_int n,
+ lapack_int nrhs, lapack_complex_float* a,
+ lapack_int lda, lapack_complex_float* b,
+ lapack_int ldb, float* s, float rcond,
+ lapack_int* rank );
+lapack_int LAPACKE_zgelss( int matrix_order, lapack_int m, lapack_int n,
+ lapack_int nrhs, lapack_complex_double* a,
+ lapack_int lda, lapack_complex_double* b,
+ lapack_int ldb, double* s, double rcond,
+ lapack_int* rank );
+
+lapack_int LAPACKE_sgelsy( int matrix_order, lapack_int m, lapack_int n,
+ lapack_int nrhs, float* a, lapack_int lda, float* b,
+ lapack_int ldb, lapack_int* jpvt, float rcond,
+ lapack_int* rank );
+lapack_int LAPACKE_dgelsy( int matrix_order, lapack_int m, lapack_int n,
+ lapack_int nrhs, double* a, lapack_int lda,
+ double* b, lapack_int ldb, lapack_int* jpvt,
+ double rcond, lapack_int* rank );
+lapack_int LAPACKE_cgelsy( int matrix_order, lapack_int m, lapack_int n,
+ lapack_int nrhs, lapack_complex_float* a,
+ lapack_int lda, lapack_complex_float* b,
+ lapack_int ldb, lapack_int* jpvt, float rcond,
+ lapack_int* rank );
+lapack_int LAPACKE_zgelsy( int matrix_order, lapack_int m, lapack_int n,
+ lapack_int nrhs, lapack_complex_double* a,
+ lapack_int lda, lapack_complex_double* b,
+ lapack_int ldb, lapack_int* jpvt, double rcond,
+ lapack_int* rank );
+
+lapack_int LAPACKE_sgeqlf( int matrix_order, lapack_int m, lapack_int n,
+ float* a, lapack_int lda, float* tau );
+lapack_int LAPACKE_dgeqlf( int matrix_order, lapack_int m, lapack_int n,
+ double* a, lapack_int lda, double* tau );
+lapack_int LAPACKE_cgeqlf( int matrix_order, lapack_int m, lapack_int n,
+ lapack_complex_float* a, lapack_int lda,
+ lapack_complex_float* tau );
+lapack_int LAPACKE_zgeqlf( int matrix_order, lapack_int m, lapack_int n,
+ lapack_complex_double* a, lapack_int lda,
+ lapack_complex_double* tau );
+
+lapack_int LAPACKE_sgeqp3( int matrix_order, lapack_int m, lapack_int n,
+ float* a, lapack_int lda, lapack_int* jpvt,
+ float* tau );
+lapack_int LAPACKE_dgeqp3( int matrix_order, lapack_int m, lapack_int n,
+ double* a, lapack_int lda, lapack_int* jpvt,
+ double* tau );
+lapack_int LAPACKE_cgeqp3( int matrix_order, lapack_int m, lapack_int n,
+ lapack_complex_float* a, lapack_int lda,
+ lapack_int* jpvt, lapack_complex_float* tau );
+lapack_int LAPACKE_zgeqp3( int matrix_order, lapack_int m, lapack_int n,
+ lapack_complex_double* a, lapack_int lda,
+ lapack_int* jpvt, lapack_complex_double* tau );
+
+lapack_int LAPACKE_sgeqpf( int matrix_order, lapack_int m, lapack_int n,
+ float* a, lapack_int lda, lapack_int* jpvt,
+ float* tau );
+lapack_int LAPACKE_dgeqpf( int matrix_order, lapack_int m, lapack_int n,
+ double* a, lapack_int lda, lapack_int* jpvt,
+ double* tau );
+lapack_int LAPACKE_cgeqpf( int matrix_order, lapack_int m, lapack_int n,
+ lapack_complex_float* a, lapack_int lda,
+ lapack_int* jpvt, lapack_complex_float* tau );
+lapack_int LAPACKE_zgeqpf( int matrix_order, lapack_int m, lapack_int n,
+ lapack_complex_double* a, lapack_int lda,
+ lapack_int* jpvt, lapack_complex_double* tau );
+
+lapack_int LAPACKE_sgeqr2( int matrix_order, lapack_int m, lapack_int n,
+ float* a, lapack_int lda, float* tau );
+lapack_int LAPACKE_dgeqr2( int matrix_order, lapack_int m, lapack_int n,
+ double* a, lapack_int lda, double* tau );
+lapack_int LAPACKE_cgeqr2( int matrix_order, lapack_int m, lapack_int n,
+ lapack_complex_float* a, lapack_int lda,
+ lapack_complex_float* tau );
+lapack_int LAPACKE_zgeqr2( int matrix_order, lapack_int m, lapack_int n,
+ lapack_complex_double* a, lapack_int lda,
+ lapack_complex_double* tau );
+
+lapack_int LAPACKE_sgeqrf( int matrix_order, lapack_int m, lapack_int n,
+ float* a, lapack_int lda, float* tau );
+lapack_int LAPACKE_dgeqrf( int matrix_order, lapack_int m, lapack_int n,
+ double* a, lapack_int lda, double* tau );
+lapack_int LAPACKE_cgeqrf( int matrix_order, lapack_int m, lapack_int n,
+ lapack_complex_float* a, lapack_int lda,
+ lapack_complex_float* tau );
+lapack_int LAPACKE_zgeqrf( int matrix_order, lapack_int m, lapack_int n,
+ lapack_complex_double* a, lapack_int lda,
+ lapack_complex_double* tau );
+
+lapack_int LAPACKE_sgeqrfp( int matrix_order, lapack_int m, lapack_int n,
+ float* a, lapack_int lda, float* tau );
+lapack_int LAPACKE_dgeqrfp( int matrix_order, lapack_int m, lapack_int n,
+ double* a, lapack_int lda, double* tau );
+lapack_int LAPACKE_cgeqrfp( int matrix_order, lapack_int m, lapack_int n,
+ lapack_complex_float* a, lapack_int lda,
+ lapack_complex_float* tau );
+lapack_int LAPACKE_zgeqrfp( int matrix_order, lapack_int m, lapack_int n,
+ lapack_complex_double* a, lapack_int lda,
+ lapack_complex_double* tau );
+
+lapack_int LAPACKE_sgerfs( int matrix_order, char trans, lapack_int n,
+ lapack_int nrhs, const float* a, lapack_int lda,
+ const float* af, lapack_int ldaf,
+ const lapack_int* ipiv, const float* b,
+ lapack_int ldb, float* x, lapack_int ldx,
+ float* ferr, float* berr );
+lapack_int LAPACKE_dgerfs( int matrix_order, char trans, lapack_int n,
+ lapack_int nrhs, const double* a, lapack_int lda,
+ const double* af, lapack_int ldaf,
+ const lapack_int* ipiv, const double* b,
+ lapack_int ldb, double* x, lapack_int ldx,
+ double* ferr, double* berr );
+lapack_int LAPACKE_cgerfs( int matrix_order, char trans, lapack_int n,
+ lapack_int nrhs, const lapack_complex_float* a,
+ lapack_int lda, const lapack_complex_float* af,
+ lapack_int ldaf, const lapack_int* ipiv,
+ const lapack_complex_float* b, lapack_int ldb,
+ lapack_complex_float* x, lapack_int ldx, float* ferr,
+ float* berr );
+lapack_int LAPACKE_zgerfs( int matrix_order, char trans, lapack_int n,
+ lapack_int nrhs, const lapack_complex_double* a,
+ lapack_int lda, const lapack_complex_double* af,
+ lapack_int ldaf, const lapack_int* ipiv,
+ const lapack_complex_double* b, lapack_int ldb,
+ lapack_complex_double* x, lapack_int ldx,
+ double* ferr, double* berr );
+
+lapack_int LAPACKE_sgerfsx( int matrix_order, char trans, char equed,
+ lapack_int n, lapack_int nrhs, const float* a,
+ lapack_int lda, const float* af, lapack_int ldaf,
+ const lapack_int* ipiv, const float* r,
+ const float* c, const float* b, lapack_int ldb,
+ float* x, lapack_int ldx, float* rcond, float* berr,
+ lapack_int n_err_bnds, float* err_bnds_norm,
+ float* err_bnds_comp, lapack_int nparams,
+ float* params );
+lapack_int LAPACKE_dgerfsx( int matrix_order, char trans, char equed,
+ lapack_int n, lapack_int nrhs, const double* a,
+ lapack_int lda, const double* af, lapack_int ldaf,
+ const lapack_int* ipiv, const double* r,
+ const double* c, const double* b, lapack_int ldb,
+ double* x, lapack_int ldx, double* rcond,
+ double* berr, lapack_int n_err_bnds,
+ double* err_bnds_norm, double* err_bnds_comp,
+ lapack_int nparams, double* params );
+lapack_int LAPACKE_cgerfsx( int matrix_order, char trans, char equed,
+ lapack_int n, lapack_int nrhs,
+ const lapack_complex_float* a, lapack_int lda,
+ const lapack_complex_float* af, lapack_int ldaf,
+ const lapack_int* ipiv, const float* r,
+ const float* c, const lapack_complex_float* b,
+ lapack_int ldb, lapack_complex_float* x,
+ lapack_int ldx, float* rcond, float* berr,
+ lapack_int n_err_bnds, float* err_bnds_norm,
+ float* err_bnds_comp, lapack_int nparams,
+ float* params );
+lapack_int LAPACKE_zgerfsx( int matrix_order, char trans, char equed,
+ lapack_int n, lapack_int nrhs,
+ const lapack_complex_double* a, lapack_int lda,
+ const lapack_complex_double* af, lapack_int ldaf,
+ const lapack_int* ipiv, const double* r,
+ const double* c, const lapack_complex_double* b,
+ lapack_int ldb, lapack_complex_double* x,
+ lapack_int ldx, double* rcond, double* berr,
+ lapack_int n_err_bnds, double* err_bnds_norm,
+ double* err_bnds_comp, lapack_int nparams,
+ double* params );
+
+lapack_int LAPACKE_sgerqf( int matrix_order, lapack_int m, lapack_int n,
+ float* a, lapack_int lda, float* tau );
+lapack_int LAPACKE_dgerqf( int matrix_order, lapack_int m, lapack_int n,
+ double* a, lapack_int lda, double* tau );
+lapack_int LAPACKE_cgerqf( int matrix_order, lapack_int m, lapack_int n,
+ lapack_complex_float* a, lapack_int lda,
+ lapack_complex_float* tau );
+lapack_int LAPACKE_zgerqf( int matrix_order, lapack_int m, lapack_int n,
+ lapack_complex_double* a, lapack_int lda,
+ lapack_complex_double* tau );
+
+lapack_int LAPACKE_sgesdd( int matrix_order, char jobz, lapack_int m,
+ lapack_int n, float* a, lapack_int lda, float* s,
+ float* u, lapack_int ldu, float* vt,
+ lapack_int ldvt );
+lapack_int LAPACKE_dgesdd( int matrix_order, char jobz, lapack_int m,
+ lapack_int n, double* a, lapack_int lda, double* s,
+ double* u, lapack_int ldu, double* vt,
+ lapack_int ldvt );
+lapack_int LAPACKE_cgesdd( int matrix_order, char jobz, lapack_int m,
+ lapack_int n, lapack_complex_float* a,
+ lapack_int lda, float* s, lapack_complex_float* u,
+ lapack_int ldu, lapack_complex_float* vt,
+ lapack_int ldvt );
+lapack_int LAPACKE_zgesdd( int matrix_order, char jobz, lapack_int m,
+ lapack_int n, lapack_complex_double* a,
+ lapack_int lda, double* s, lapack_complex_double* u,
+ lapack_int ldu, lapack_complex_double* vt,
+ lapack_int ldvt );
+
+lapack_int LAPACKE_sgesv( int matrix_order, lapack_int n, lapack_int nrhs,
+ float* a, lapack_int lda, lapack_int* ipiv, float* b,
+ lapack_int ldb );
+lapack_int LAPACKE_dgesv( int matrix_order, lapack_int n, lapack_int nrhs,
+ double* a, lapack_int lda, lapack_int* ipiv,
+ double* b, lapack_int ldb );
+lapack_int LAPACKE_cgesv( int matrix_order, lapack_int n, lapack_int nrhs,
+ lapack_complex_float* a, lapack_int lda,
+ lapack_int* ipiv, lapack_complex_float* b,
+ lapack_int ldb );
+lapack_int LAPACKE_zgesv( int matrix_order, lapack_int n, lapack_int nrhs,
+ lapack_complex_double* a, lapack_int lda,
+ lapack_int* ipiv, lapack_complex_double* b,
+ lapack_int ldb );
+lapack_int LAPACKE_dsgesv( int matrix_order, lapack_int n, lapack_int nrhs,
+ double* a, lapack_int lda, lapack_int* ipiv,
+ double* b, lapack_int ldb, double* x, lapack_int ldx,
+ lapack_int* iter );
+lapack_int LAPACKE_zcgesv( int matrix_order, lapack_int n, lapack_int nrhs,
+ lapack_complex_double* a, lapack_int lda,
+ lapack_int* ipiv, lapack_complex_double* b,
+ lapack_int ldb, lapack_complex_double* x,
+ lapack_int ldx, lapack_int* iter );
+
+lapack_int LAPACKE_sgesvd( int matrix_order, char jobu, char jobvt,
+ lapack_int m, lapack_int n, float* a, lapack_int lda,
+ float* s, float* u, lapack_int ldu, float* vt,
+ lapack_int ldvt, float* superb );
+lapack_int LAPACKE_dgesvd( int matrix_order, char jobu, char jobvt,
+ lapack_int m, lapack_int n, double* a,
+ lapack_int lda, double* s, double* u, lapack_int ldu,
+ double* vt, lapack_int ldvt, double* superb );
+lapack_int LAPACKE_cgesvd( int matrix_order, char jobu, char jobvt,
+ lapack_int m, lapack_int n, lapack_complex_float* a,
+ lapack_int lda, float* s, lapack_complex_float* u,
+ lapack_int ldu, lapack_complex_float* vt,
+ lapack_int ldvt, float* superb );
+lapack_int LAPACKE_zgesvd( int matrix_order, char jobu, char jobvt,
+ lapack_int m, lapack_int n, lapack_complex_double* a,
+ lapack_int lda, double* s, lapack_complex_double* u,
+ lapack_int ldu, lapack_complex_double* vt,
+ lapack_int ldvt, double* superb );
+
+lapack_int LAPACKE_sgesvj( int matrix_order, char joba, char jobu, char jobv,
+ lapack_int m, lapack_int n, float* a, lapack_int lda,
+ float* sva, lapack_int mv, float* v, lapack_int ldv,
+ float* stat );
+lapack_int LAPACKE_dgesvj( int matrix_order, char joba, char jobu, char jobv,
+ lapack_int m, lapack_int n, double* a,
+ lapack_int lda, double* sva, lapack_int mv,
+ double* v, lapack_int ldv, double* stat );
+
+lapack_int LAPACKE_sgesvx( int matrix_order, char fact, char trans,
+ lapack_int n, lapack_int nrhs, float* a,
+ lapack_int lda, float* af, lapack_int ldaf,
+ lapack_int* ipiv, char* equed, float* r, float* c,
+ float* b, lapack_int ldb, float* x, lapack_int ldx,
+ float* rcond, float* ferr, float* berr,
+ float* rpivot );
+lapack_int LAPACKE_dgesvx( int matrix_order, char fact, char trans,
+ lapack_int n, lapack_int nrhs, double* a,
+ lapack_int lda, double* af, lapack_int ldaf,
+ lapack_int* ipiv, char* equed, double* r, double* c,
+ double* b, lapack_int ldb, double* x, lapack_int ldx,
+ double* rcond, double* ferr, double* berr,
+ double* rpivot );
+lapack_int LAPACKE_cgesvx( int matrix_order, char fact, char trans,
+ lapack_int n, lapack_int nrhs,
+ lapack_complex_float* a, lapack_int lda,
+ lapack_complex_float* af, lapack_int ldaf,
+ lapack_int* ipiv, char* equed, float* r, float* c,
+ lapack_complex_float* b, lapack_int ldb,
+ lapack_complex_float* x, lapack_int ldx,
+ float* rcond, float* ferr, float* berr,
+ float* rpivot );
+lapack_int LAPACKE_zgesvx( int matrix_order, char fact, char trans,
+ lapack_int n, lapack_int nrhs,
+ lapack_complex_double* a, lapack_int lda,
+ lapack_complex_double* af, lapack_int ldaf,
+ lapack_int* ipiv, char* equed, double* r, double* c,
+ lapack_complex_double* b, lapack_int ldb,
+ lapack_complex_double* x, lapack_int ldx,
+ double* rcond, double* ferr, double* berr,
+ double* rpivot );
+
+lapack_int LAPACKE_sgesvxx( int matrix_order, char fact, char trans,
+ lapack_int n, lapack_int nrhs, float* a,
+ lapack_int lda, float* af, lapack_int ldaf,
+ lapack_int* ipiv, char* equed, float* r, float* c,
+ float* b, lapack_int ldb, float* x, lapack_int ldx,
+ float* rcond, float* rpvgrw, float* berr,
+ lapack_int n_err_bnds, float* err_bnds_norm,
+ float* err_bnds_comp, lapack_int nparams,
+ float* params );
+lapack_int LAPACKE_dgesvxx( int matrix_order, char fact, char trans,
+ lapack_int n, lapack_int nrhs, double* a,
+ lapack_int lda, double* af, lapack_int ldaf,
+ lapack_int* ipiv, char* equed, double* r, double* c,
+ double* b, lapack_int ldb, double* x,
+ lapack_int ldx, double* rcond, double* rpvgrw,
+ double* berr, lapack_int n_err_bnds,
+ double* err_bnds_norm, double* err_bnds_comp,
+ lapack_int nparams, double* params );
+lapack_int LAPACKE_cgesvxx( int matrix_order, char fact, char trans,
+ lapack_int n, lapack_int nrhs,
+ lapack_complex_float* a, lapack_int lda,
+ lapack_complex_float* af, lapack_int ldaf,
+ lapack_int* ipiv, char* equed, float* r, float* c,
+ lapack_complex_float* b, lapack_int ldb,
+ lapack_complex_float* x, lapack_int ldx,
+ float* rcond, float* rpvgrw, float* berr,
+ lapack_int n_err_bnds, float* err_bnds_norm,
+ float* err_bnds_comp, lapack_int nparams,
+ float* params );
+lapack_int LAPACKE_zgesvxx( int matrix_order, char fact, char trans,
+ lapack_int n, lapack_int nrhs,
+ lapack_complex_double* a, lapack_int lda,
+ lapack_complex_double* af, lapack_int ldaf,
+ lapack_int* ipiv, char* equed, double* r, double* c,
+ lapack_complex_double* b, lapack_int ldb,
+ lapack_complex_double* x, lapack_int ldx,
+ double* rcond, double* rpvgrw, double* berr,
+ lapack_int n_err_bnds, double* err_bnds_norm,
+ double* err_bnds_comp, lapack_int nparams,
+ double* params );
+
+lapack_int LAPACKE_sgetf2( int matrix_order, lapack_int m, lapack_int n,
+ float* a, lapack_int lda, lapack_int* ipiv );
+lapack_int LAPACKE_dgetf2( int matrix_order, lapack_int m, lapack_int n,
+ double* a, lapack_int lda, lapack_int* ipiv );
+lapack_int LAPACKE_cgetf2( int matrix_order, lapack_int m, lapack_int n,
+ lapack_complex_float* a, lapack_int lda,
+ lapack_int* ipiv );
+lapack_int LAPACKE_zgetf2( int matrix_order, lapack_int m, lapack_int n,
+ lapack_complex_double* a, lapack_int lda,
+ lapack_int* ipiv );
+
+lapack_int LAPACKE_sgetrf( int matrix_order, lapack_int m, lapack_int n,
+ float* a, lapack_int lda, lapack_int* ipiv );
+lapack_int LAPACKE_dgetrf( int matrix_order, lapack_int m, lapack_int n,
+ double* a, lapack_int lda, lapack_int* ipiv );
+lapack_int LAPACKE_cgetrf( int matrix_order, lapack_int m, lapack_int n,
+ lapack_complex_float* a, lapack_int lda,
+ lapack_int* ipiv );
+lapack_int LAPACKE_zgetrf( int matrix_order, lapack_int m, lapack_int n,
+ lapack_complex_double* a, lapack_int lda,
+ lapack_int* ipiv );
+
+lapack_int LAPACKE_sgetri( int matrix_order, lapack_int n, float* a,
+ lapack_int lda, const lapack_int* ipiv );
+lapack_int LAPACKE_dgetri( int matrix_order, lapack_int n, double* a,
+ lapack_int lda, const lapack_int* ipiv );
+lapack_int LAPACKE_cgetri( int matrix_order, lapack_int n,
+ lapack_complex_float* a, lapack_int lda,
+ const lapack_int* ipiv );
+lapack_int LAPACKE_zgetri( int matrix_order, lapack_int n,
+ lapack_complex_double* a, lapack_int lda,
+ const lapack_int* ipiv );
+
+lapack_int LAPACKE_sgetrs( int matrix_order, char trans, lapack_int n,
+ lapack_int nrhs, const float* a, lapack_int lda,
+ const lapack_int* ipiv, float* b, lapack_int ldb );
+lapack_int LAPACKE_dgetrs( int matrix_order, char trans, lapack_int n,
+ lapack_int nrhs, const double* a, lapack_int lda,
+ const lapack_int* ipiv, double* b, lapack_int ldb );
+lapack_int LAPACKE_cgetrs( int matrix_order, char trans, lapack_int n,
+ lapack_int nrhs, const lapack_complex_float* a,
+ lapack_int lda, const lapack_int* ipiv,
+ lapack_complex_float* b, lapack_int ldb );
+lapack_int LAPACKE_zgetrs( int matrix_order, char trans, lapack_int n,
+ lapack_int nrhs, const lapack_complex_double* a,
+ lapack_int lda, const lapack_int* ipiv,
+ lapack_complex_double* b, lapack_int ldb );
+
+lapack_int LAPACKE_sggbak( int matrix_order, char job, char side, lapack_int n,
+ lapack_int ilo, lapack_int ihi, const float* lscale,
+ const float* rscale, lapack_int m, float* v,
+ lapack_int ldv );
+lapack_int LAPACKE_dggbak( int matrix_order, char job, char side, lapack_int n,
+ lapack_int ilo, lapack_int ihi, const double* lscale,
+ const double* rscale, lapack_int m, double* v,
+ lapack_int ldv );
+lapack_int LAPACKE_cggbak( int matrix_order, char job, char side, lapack_int n,
+ lapack_int ilo, lapack_int ihi, const float* lscale,
+ const float* rscale, lapack_int m,
+ lapack_complex_float* v, lapack_int ldv );
+lapack_int LAPACKE_zggbak( int matrix_order, char job, char side, lapack_int n,
+ lapack_int ilo, lapack_int ihi, const double* lscale,
+ const double* rscale, lapack_int m,
+ lapack_complex_double* v, lapack_int ldv );
+
+lapack_int LAPACKE_sggbal( int matrix_order, char job, lapack_int n, float* a,
+ lapack_int lda, float* b, lapack_int ldb,
+ lapack_int* ilo, lapack_int* ihi, float* lscale,
+ float* rscale );
+lapack_int LAPACKE_dggbal( int matrix_order, char job, lapack_int n, double* a,
+ lapack_int lda, double* b, lapack_int ldb,
+ lapack_int* ilo, lapack_int* ihi, double* lscale,
+ double* rscale );
+lapack_int LAPACKE_cggbal( int matrix_order, char job, lapack_int n,
+ lapack_complex_float* a, lapack_int lda,
+ lapack_complex_float* b, lapack_int ldb,
+ lapack_int* ilo, lapack_int* ihi, float* lscale,
+ float* rscale );
+lapack_int LAPACKE_zggbal( int matrix_order, char job, lapack_int n,
+ lapack_complex_double* a, lapack_int lda,
+ lapack_complex_double* b, lapack_int ldb,
+ lapack_int* ilo, lapack_int* ihi, double* lscale,
+ double* rscale );
+
+lapack_int LAPACKE_sgges( int matrix_order, char jobvsl, char jobvsr, char sort,
+ LAPACK_S_SELECT3 selctg, lapack_int n, float* a,
+ lapack_int lda, float* b, lapack_int ldb,
+ lapack_int* sdim, float* alphar, float* alphai,
+ float* beta, float* vsl, lapack_int ldvsl, float* vsr,
+ lapack_int ldvsr );
+lapack_int LAPACKE_dgges( int matrix_order, char jobvsl, char jobvsr, char sort,
+ LAPACK_D_SELECT3 selctg, lapack_int n, double* a,
+ lapack_int lda, double* b, lapack_int ldb,
+ lapack_int* sdim, double* alphar, double* alphai,
+ double* beta, double* vsl, lapack_int ldvsl,
+ double* vsr, lapack_int ldvsr );
+lapack_int LAPACKE_cgges( int matrix_order, char jobvsl, char jobvsr, char sort,
+ LAPACK_C_SELECT2 selctg, lapack_int n,
+ lapack_complex_float* a, lapack_int lda,
+ lapack_complex_float* b, lapack_int ldb,
+ lapack_int* sdim, lapack_complex_float* alpha,
+ lapack_complex_float* beta, lapack_complex_float* vsl,
+ lapack_int ldvsl, lapack_complex_float* vsr,
+ lapack_int ldvsr );
+lapack_int LAPACKE_zgges( int matrix_order, char jobvsl, char jobvsr, char sort,
+ LAPACK_Z_SELECT2 selctg, lapack_int n,
+ lapack_complex_double* a, lapack_int lda,
+ lapack_complex_double* b, lapack_int ldb,
+ lapack_int* sdim, lapack_complex_double* alpha,
+ lapack_complex_double* beta,
+ lapack_complex_double* vsl, lapack_int ldvsl,
+ lapack_complex_double* vsr, lapack_int ldvsr );
+
+lapack_int LAPACKE_sggesx( int matrix_order, char jobvsl, char jobvsr,
+ char sort, LAPACK_S_SELECT3 selctg, char sense,
+ lapack_int n, float* a, lapack_int lda, float* b,
+ lapack_int ldb, lapack_int* sdim, float* alphar,
+ float* alphai, float* beta, float* vsl,
+ lapack_int ldvsl, float* vsr, lapack_int ldvsr,
+ float* rconde, float* rcondv );
+lapack_int LAPACKE_dggesx( int matrix_order, char jobvsl, char jobvsr,
+ char sort, LAPACK_D_SELECT3 selctg, char sense,
+ lapack_int n, double* a, lapack_int lda, double* b,
+ lapack_int ldb, lapack_int* sdim, double* alphar,
+ double* alphai, double* beta, double* vsl,
+ lapack_int ldvsl, double* vsr, lapack_int ldvsr,
+ double* rconde, double* rcondv );
+lapack_int LAPACKE_cggesx( int matrix_order, char jobvsl, char jobvsr,
+ char sort, LAPACK_C_SELECT2 selctg, char sense,
+ lapack_int n, lapack_complex_float* a,
+ lapack_int lda, lapack_complex_float* b,
+ lapack_int ldb, lapack_int* sdim,
+ lapack_complex_float* alpha,
+ lapack_complex_float* beta,
+ lapack_complex_float* vsl, lapack_int ldvsl,
+ lapack_complex_float* vsr, lapack_int ldvsr,
+ float* rconde, float* rcondv );
+lapack_int LAPACKE_zggesx( int matrix_order, char jobvsl, char jobvsr,
+ char sort, LAPACK_Z_SELECT2 selctg, char sense,
+ lapack_int n, lapack_complex_double* a,
+ lapack_int lda, lapack_complex_double* b,
+ lapack_int ldb, lapack_int* sdim,
+ lapack_complex_double* alpha,
+ lapack_complex_double* beta,
+ lapack_complex_double* vsl, lapack_int ldvsl,
+ lapack_complex_double* vsr, lapack_int ldvsr,
+ double* rconde, double* rcondv );
+
+lapack_int LAPACKE_sggev( int matrix_order, char jobvl, char jobvr,
+ lapack_int n, float* a, lapack_int lda, float* b,
+ lapack_int ldb, float* alphar, float* alphai,
+ float* beta, float* vl, lapack_int ldvl, float* vr,
+ lapack_int ldvr );
+lapack_int LAPACKE_dggev( int matrix_order, char jobvl, char jobvr,
+ lapack_int n, double* a, lapack_int lda, double* b,
+ lapack_int ldb, double* alphar, double* alphai,
+ double* beta, double* vl, lapack_int ldvl, double* vr,
+ lapack_int ldvr );
+lapack_int LAPACKE_cggev( int matrix_order, char jobvl, char jobvr,
+ lapack_int n, lapack_complex_float* a, lapack_int lda,
+ lapack_complex_float* b, lapack_int ldb,
+ lapack_complex_float* alpha,
+ lapack_complex_float* beta, lapack_complex_float* vl,
+ lapack_int ldvl, lapack_complex_float* vr,
+ lapack_int ldvr );
+lapack_int LAPACKE_zggev( int matrix_order, char jobvl, char jobvr,
+ lapack_int n, lapack_complex_double* a,
+ lapack_int lda, lapack_complex_double* b,
+ lapack_int ldb, lapack_complex_double* alpha,
+ lapack_complex_double* beta,
+ lapack_complex_double* vl, lapack_int ldvl,
+ lapack_complex_double* vr, lapack_int ldvr );
+
+lapack_int LAPACKE_sggevx( int matrix_order, char balanc, char jobvl,
+ char jobvr, char sense, lapack_int n, float* a,
+ lapack_int lda, float* b, lapack_int ldb,
+ float* alphar, float* alphai, float* beta, float* vl,
+ lapack_int ldvl, float* vr, lapack_int ldvr,
+ lapack_int* ilo, lapack_int* ihi, float* lscale,
+ float* rscale, float* abnrm, float* bbnrm,
+ float* rconde, float* rcondv );
+lapack_int LAPACKE_dggevx( int matrix_order, char balanc, char jobvl,
+ char jobvr, char sense, lapack_int n, double* a,
+ lapack_int lda, double* b, lapack_int ldb,
+ double* alphar, double* alphai, double* beta,
+ double* vl, lapack_int ldvl, double* vr,
+ lapack_int ldvr, lapack_int* ilo, lapack_int* ihi,
+ double* lscale, double* rscale, double* abnrm,
+ double* bbnrm, double* rconde, double* rcondv );
+lapack_int LAPACKE_cggevx( int matrix_order, char balanc, char jobvl,
+ char jobvr, char sense, lapack_int n,
+ lapack_complex_float* a, lapack_int lda,
+ lapack_complex_float* b, lapack_int ldb,
+ lapack_complex_float* alpha,
+ lapack_complex_float* beta, lapack_complex_float* vl,
+ lapack_int ldvl, lapack_complex_float* vr,
+ lapack_int ldvr, lapack_int* ilo, lapack_int* ihi,
+ float* lscale, float* rscale, float* abnrm,
+ float* bbnrm, float* rconde, float* rcondv );
+lapack_int LAPACKE_zggevx( int matrix_order, char balanc, char jobvl,
+ char jobvr, char sense, lapack_int n,
+ lapack_complex_double* a, lapack_int lda,
+ lapack_complex_double* b, lapack_int ldb,
+ lapack_complex_double* alpha,
+ lapack_complex_double* beta,
+ lapack_complex_double* vl, lapack_int ldvl,
+ lapack_complex_double* vr, lapack_int ldvr,
+ lapack_int* ilo, lapack_int* ihi, double* lscale,
+ double* rscale, double* abnrm, double* bbnrm,
+ double* rconde, double* rcondv );
+
+lapack_int LAPACKE_sggglm( int matrix_order, lapack_int n, lapack_int m,
+ lapack_int p, float* a, lapack_int lda, float* b,
+ lapack_int ldb, float* d, float* x, float* y );
+lapack_int LAPACKE_dggglm( int matrix_order, lapack_int n, lapack_int m,
+ lapack_int p, double* a, lapack_int lda, double* b,
+ lapack_int ldb, double* d, double* x, double* y );
+lapack_int LAPACKE_cggglm( int matrix_order, lapack_int n, lapack_int m,
+ lapack_int p, lapack_complex_float* a,
+ lapack_int lda, lapack_complex_float* b,
+ lapack_int ldb, lapack_complex_float* d,
+ lapack_complex_float* x, lapack_complex_float* y );
+lapack_int LAPACKE_zggglm( int matrix_order, lapack_int n, lapack_int m,
+ lapack_int p, lapack_complex_double* a,
+ lapack_int lda, lapack_complex_double* b,
+ lapack_int ldb, lapack_complex_double* d,
+ lapack_complex_double* x, lapack_complex_double* y );
+
+lapack_int LAPACKE_sgghrd( int matrix_order, char compq, char compz,
+ lapack_int n, lapack_int ilo, lapack_int ihi,
+ float* a, lapack_int lda, float* b, lapack_int ldb,
+ float* q, lapack_int ldq, float* z, lapack_int ldz );
+lapack_int LAPACKE_dgghrd( int matrix_order, char compq, char compz,
+ lapack_int n, lapack_int ilo, lapack_int ihi,
+ double* a, lapack_int lda, double* b, lapack_int ldb,
+ double* q, lapack_int ldq, double* z,
+ lapack_int ldz );
+lapack_int LAPACKE_cgghrd( int matrix_order, char compq, char compz,
+ lapack_int n, lapack_int ilo, lapack_int ihi,
+ lapack_complex_float* a, lapack_int lda,
+ lapack_complex_float* b, lapack_int ldb,
+ lapack_complex_float* q, lapack_int ldq,
+ lapack_complex_float* z, lapack_int ldz );
+lapack_int LAPACKE_zgghrd( int matrix_order, char compq, char compz,
+ lapack_int n, lapack_int ilo, lapack_int ihi,
+ lapack_complex_double* a, lapack_int lda,
+ lapack_complex_double* b, lapack_int ldb,
+ lapack_complex_double* q, lapack_int ldq,
+ lapack_complex_double* z, lapack_int ldz );
+
+lapack_int LAPACKE_sgglse( int matrix_order, lapack_int m, lapack_int n,
+ lapack_int p, float* a, lapack_int lda, float* b,
+ lapack_int ldb, float* c, float* d, float* x );
+lapack_int LAPACKE_dgglse( int matrix_order, lapack_int m, lapack_int n,
+ lapack_int p, double* a, lapack_int lda, double* b,
+ lapack_int ldb, double* c, double* d, double* x );
+lapack_int LAPACKE_cgglse( int matrix_order, lapack_int m, lapack_int n,
+ lapack_int p, lapack_complex_float* a,
+ lapack_int lda, lapack_complex_float* b,
+ lapack_int ldb, lapack_complex_float* c,
+ lapack_complex_float* d, lapack_complex_float* x );
+lapack_int LAPACKE_zgglse( int matrix_order, lapack_int m, lapack_int n,
+ lapack_int p, lapack_complex_double* a,
+ lapack_int lda, lapack_complex_double* b,
+ lapack_int ldb, lapack_complex_double* c,
+ lapack_complex_double* d, lapack_complex_double* x );
+
+lapack_int LAPACKE_sggqrf( int matrix_order, lapack_int n, lapack_int m,
+ lapack_int p, float* a, lapack_int lda, float* taua,
+ float* b, lapack_int ldb, float* taub );
+lapack_int LAPACKE_dggqrf( int matrix_order, lapack_int n, lapack_int m,
+ lapack_int p, double* a, lapack_int lda,
+ double* taua, double* b, lapack_int ldb,
+ double* taub );
+lapack_int LAPACKE_cggqrf( int matrix_order, lapack_int n, lapack_int m,
+ lapack_int p, lapack_complex_float* a,
+ lapack_int lda, lapack_complex_float* taua,
+ lapack_complex_float* b, lapack_int ldb,
+ lapack_complex_float* taub );
+lapack_int LAPACKE_zggqrf( int matrix_order, lapack_int n, lapack_int m,
+ lapack_int p, lapack_complex_double* a,
+ lapack_int lda, lapack_complex_double* taua,
+ lapack_complex_double* b, lapack_int ldb,
+ lapack_complex_double* taub );
+
+lapack_int LAPACKE_sggrqf( int matrix_order, lapack_int m, lapack_int p,
+ lapack_int n, float* a, lapack_int lda, float* taua,
+ float* b, lapack_int ldb, float* taub );
+lapack_int LAPACKE_dggrqf( int matrix_order, lapack_int m, lapack_int p,
+ lapack_int n, double* a, lapack_int lda,
+ double* taua, double* b, lapack_int ldb,
+ double* taub );
+lapack_int LAPACKE_cggrqf( int matrix_order, lapack_int m, lapack_int p,
+ lapack_int n, lapack_complex_float* a,
+ lapack_int lda, lapack_complex_float* taua,
+ lapack_complex_float* b, lapack_int ldb,
+ lapack_complex_float* taub );
+lapack_int LAPACKE_zggrqf( int matrix_order, lapack_int m, lapack_int p,
+ lapack_int n, lapack_complex_double* a,
+ lapack_int lda, lapack_complex_double* taua,
+ lapack_complex_double* b, lapack_int ldb,
+ lapack_complex_double* taub );
+
+lapack_int LAPACKE_sggsvd( int matrix_order, char jobu, char jobv, char jobq,
+ lapack_int m, lapack_int n, lapack_int p,
+ lapack_int* k, lapack_int* l, float* a,
+ lapack_int lda, float* b, lapack_int ldb,
+ float* alpha, float* beta, float* u, lapack_int ldu,
+ float* v, lapack_int ldv, float* q, lapack_int ldq,
+ lapack_int* iwork );
+lapack_int LAPACKE_dggsvd( int matrix_order, char jobu, char jobv, char jobq,
+ lapack_int m, lapack_int n, lapack_int p,
+ lapack_int* k, lapack_int* l, double* a,
+ lapack_int lda, double* b, lapack_int ldb,
+ double* alpha, double* beta, double* u,
+ lapack_int ldu, double* v, lapack_int ldv, double* q,
+ lapack_int ldq, lapack_int* iwork );
+lapack_int LAPACKE_cggsvd( int matrix_order, char jobu, char jobv, char jobq,
+ lapack_int m, lapack_int n, lapack_int p,
+ lapack_int* k, lapack_int* l,
+ lapack_complex_float* a, lapack_int lda,
+ lapack_complex_float* b, lapack_int ldb,
+ float* alpha, float* beta, lapack_complex_float* u,
+ lapack_int ldu, lapack_complex_float* v,
+ lapack_int ldv, lapack_complex_float* q,
+ lapack_int ldq, lapack_int* iwork );
+lapack_int LAPACKE_zggsvd( int matrix_order, char jobu, char jobv, char jobq,
+ lapack_int m, lapack_int n, lapack_int p,
+ lapack_int* k, lapack_int* l,
+ lapack_complex_double* a, lapack_int lda,
+ lapack_complex_double* b, lapack_int ldb,
+ double* alpha, double* beta,
+ lapack_complex_double* u, lapack_int ldu,
+ lapack_complex_double* v, lapack_int ldv,
+ lapack_complex_double* q, lapack_int ldq,
+ lapack_int* iwork );
+
+lapack_int LAPACKE_sggsvp( int matrix_order, char jobu, char jobv, char jobq,
+ lapack_int m, lapack_int p, lapack_int n, float* a,
+ lapack_int lda, float* b, lapack_int ldb, float tola,
+ float tolb, lapack_int* k, lapack_int* l, float* u,
+ lapack_int ldu, float* v, lapack_int ldv, float* q,
+ lapack_int ldq );
+lapack_int LAPACKE_dggsvp( int matrix_order, char jobu, char jobv, char jobq,
+ lapack_int m, lapack_int p, lapack_int n, double* a,
+ lapack_int lda, double* b, lapack_int ldb,
+ double tola, double tolb, lapack_int* k,
+ lapack_int* l, double* u, lapack_int ldu, double* v,
+ lapack_int ldv, double* q, lapack_int ldq );
+lapack_int LAPACKE_cggsvp( int matrix_order, char jobu, char jobv, char jobq,
+ lapack_int m, lapack_int p, lapack_int n,
+ lapack_complex_float* a, lapack_int lda,
+ lapack_complex_float* b, lapack_int ldb, float tola,
+ float tolb, lapack_int* k, lapack_int* l,
+ lapack_complex_float* u, lapack_int ldu,
+ lapack_complex_float* v, lapack_int ldv,
+ lapack_complex_float* q, lapack_int ldq );
+lapack_int LAPACKE_zggsvp( int matrix_order, char jobu, char jobv, char jobq,
+ lapack_int m, lapack_int p, lapack_int n,
+ lapack_complex_double* a, lapack_int lda,
+ lapack_complex_double* b, lapack_int ldb,
+ double tola, double tolb, lapack_int* k,
+ lapack_int* l, lapack_complex_double* u,
+ lapack_int ldu, lapack_complex_double* v,
+ lapack_int ldv, lapack_complex_double* q,
+ lapack_int ldq );
+
+lapack_int LAPACKE_sgtcon( char norm, lapack_int n, const float* dl,
+ const float* d, const float* du, const float* du2,
+ const lapack_int* ipiv, float anorm, float* rcond );
+lapack_int LAPACKE_dgtcon( char norm, lapack_int n, const double* dl,
+ const double* d, const double* du, const double* du2,
+ const lapack_int* ipiv, double anorm,
+ double* rcond );
+lapack_int LAPACKE_cgtcon( char norm, lapack_int n,
+ const lapack_complex_float* dl,
+ const lapack_complex_float* d,
+ const lapack_complex_float* du,
+ const lapack_complex_float* du2,
+ const lapack_int* ipiv, float anorm, float* rcond );
+lapack_int LAPACKE_zgtcon( char norm, lapack_int n,
+ const lapack_complex_double* dl,
+ const lapack_complex_double* d,
+ const lapack_complex_double* du,
+ const lapack_complex_double* du2,
+ const lapack_int* ipiv, double anorm,
+ double* rcond );
+
+lapack_int LAPACKE_sgtrfs( int matrix_order, char trans, lapack_int n,
+ lapack_int nrhs, const float* dl, const float* d,
+ const float* du, const float* dlf, const float* df,
+ const float* duf, const float* du2,
+ const lapack_int* ipiv, const float* b,
+ lapack_int ldb, float* x, lapack_int ldx,
+ float* ferr, float* berr );
+lapack_int LAPACKE_dgtrfs( int matrix_order, char trans, lapack_int n,
+ lapack_int nrhs, const double* dl, const double* d,
+ const double* du, const double* dlf,
+ const double* df, const double* duf,
+ const double* du2, const lapack_int* ipiv,
+ const double* b, lapack_int ldb, double* x,
+ lapack_int ldx, double* ferr, double* berr );
+lapack_int LAPACKE_cgtrfs( int matrix_order, char trans, lapack_int n,
+ lapack_int nrhs, const lapack_complex_float* dl,
+ const lapack_complex_float* d,
+ const lapack_complex_float* du,
+ const lapack_complex_float* dlf,
+ const lapack_complex_float* df,
+ const lapack_complex_float* duf,
+ const lapack_complex_float* du2,
+ const lapack_int* ipiv,
+ const lapack_complex_float* b, lapack_int ldb,
+ lapack_complex_float* x, lapack_int ldx, float* ferr,
+ float* berr );
+lapack_int LAPACKE_zgtrfs( int matrix_order, char trans, lapack_int n,
+ lapack_int nrhs, const lapack_complex_double* dl,
+ const lapack_complex_double* d,
+ const lapack_complex_double* du,
+ const lapack_complex_double* dlf,
+ const lapack_complex_double* df,
+ const lapack_complex_double* duf,
+ const lapack_complex_double* du2,
+ const lapack_int* ipiv,
+ const lapack_complex_double* b, lapack_int ldb,
+ lapack_complex_double* x, lapack_int ldx,
+ double* ferr, double* berr );
+
+lapack_int LAPACKE_sgtsv( int matrix_order, lapack_int n, lapack_int nrhs,
+ float* dl, float* d, float* du, float* b,
+ lapack_int ldb );
+lapack_int LAPACKE_dgtsv( int matrix_order, lapack_int n, lapack_int nrhs,
+ double* dl, double* d, double* du, double* b,
+ lapack_int ldb );
+lapack_int LAPACKE_cgtsv( int matrix_order, lapack_int n, lapack_int nrhs,
+ lapack_complex_float* dl, lapack_complex_float* d,
+ lapack_complex_float* du, lapack_complex_float* b,
+ lapack_int ldb );
+lapack_int LAPACKE_zgtsv( int matrix_order, lapack_int n, lapack_int nrhs,
+ lapack_complex_double* dl, lapack_complex_double* d,
+ lapack_complex_double* du, lapack_complex_double* b,
+ lapack_int ldb );
+
+lapack_int LAPACKE_sgtsvx( int matrix_order, char fact, char trans,
+ lapack_int n, lapack_int nrhs, const float* dl,
+ const float* d, const float* du, float* dlf,
+ float* df, float* duf, float* du2, lapack_int* ipiv,
+ const float* b, lapack_int ldb, float* x,
+ lapack_int ldx, float* rcond, float* ferr,
+ float* berr );
+lapack_int LAPACKE_dgtsvx( int matrix_order, char fact, char trans,
+ lapack_int n, lapack_int nrhs, const double* dl,
+ const double* d, const double* du, double* dlf,
+ double* df, double* duf, double* du2,
+ lapack_int* ipiv, const double* b, lapack_int ldb,
+ double* x, lapack_int ldx, double* rcond,
+ double* ferr, double* berr );
+lapack_int LAPACKE_cgtsvx( int matrix_order, char fact, char trans,
+ lapack_int n, lapack_int nrhs,
+ const lapack_complex_float* dl,
+ const lapack_complex_float* d,
+ const lapack_complex_float* du,
+ lapack_complex_float* dlf, lapack_complex_float* df,
+ lapack_complex_float* duf, lapack_complex_float* du2,
+ lapack_int* ipiv, const lapack_complex_float* b,
+ lapack_int ldb, lapack_complex_float* x,
+ lapack_int ldx, float* rcond, float* ferr,
+ float* berr );
+lapack_int LAPACKE_zgtsvx( int matrix_order, char fact, char trans,
+ lapack_int n, lapack_int nrhs,
+ const lapack_complex_double* dl,
+ const lapack_complex_double* d,
+ const lapack_complex_double* du,
+ lapack_complex_double* dlf,
+ lapack_complex_double* df,
+ lapack_complex_double* duf,
+ lapack_complex_double* du2, lapack_int* ipiv,
+ const lapack_complex_double* b, lapack_int ldb,
+ lapack_complex_double* x, lapack_int ldx,
+ double* rcond, double* ferr, double* berr );
+
+lapack_int LAPACKE_sgttrf( lapack_int n, float* dl, float* d, float* du,
+ float* du2, lapack_int* ipiv );
+lapack_int LAPACKE_dgttrf( lapack_int n, double* dl, double* d, double* du,
+ double* du2, lapack_int* ipiv );
+lapack_int LAPACKE_cgttrf( lapack_int n, lapack_complex_float* dl,
+ lapack_complex_float* d, lapack_complex_float* du,
+ lapack_complex_float* du2, lapack_int* ipiv );
+lapack_int LAPACKE_zgttrf( lapack_int n, lapack_complex_double* dl,
+ lapack_complex_double* d, lapack_complex_double* du,
+ lapack_complex_double* du2, lapack_int* ipiv );
+
+lapack_int LAPACKE_sgttrs( int matrix_order, char trans, lapack_int n,
+ lapack_int nrhs, const float* dl, const float* d,
+ const float* du, const float* du2,
+ const lapack_int* ipiv, float* b, lapack_int ldb );
+lapack_int LAPACKE_dgttrs( int matrix_order, char trans, lapack_int n,
+ lapack_int nrhs, const double* dl, const double* d,
+ const double* du, const double* du2,
+ const lapack_int* ipiv, double* b, lapack_int ldb );
+lapack_int LAPACKE_cgttrs( int matrix_order, char trans, lapack_int n,
+ lapack_int nrhs, const lapack_complex_float* dl,
+ const lapack_complex_float* d,
+ const lapack_complex_float* du,
+ const lapack_complex_float* du2,
+ const lapack_int* ipiv, lapack_complex_float* b,
+ lapack_int ldb );
+lapack_int LAPACKE_zgttrs( int matrix_order, char trans, lapack_int n,
+ lapack_int nrhs, const lapack_complex_double* dl,
+ const lapack_complex_double* d,
+ const lapack_complex_double* du,
+ const lapack_complex_double* du2,
+ const lapack_int* ipiv, lapack_complex_double* b,
+ lapack_int ldb );
+
+lapack_int LAPACKE_chbev( int matrix_order, char jobz, char uplo, lapack_int n,
+ lapack_int kd, lapack_complex_float* ab,
+ lapack_int ldab, float* w, lapack_complex_float* z,
+ lapack_int ldz );
+lapack_int LAPACKE_zhbev( int matrix_order, char jobz, char uplo, lapack_int n,
+ lapack_int kd, lapack_complex_double* ab,
+ lapack_int ldab, double* w, lapack_complex_double* z,
+ lapack_int ldz );
+
+lapack_int LAPACKE_chbevd( int matrix_order, char jobz, char uplo, lapack_int n,
+ lapack_int kd, lapack_complex_float* ab,
+ lapack_int ldab, float* w, lapack_complex_float* z,
+ lapack_int ldz );
+lapack_int LAPACKE_zhbevd( int matrix_order, char jobz, char uplo, lapack_int n,
+ lapack_int kd, lapack_complex_double* ab,
+ lapack_int ldab, double* w, lapack_complex_double* z,
+ lapack_int ldz );
+
+lapack_int LAPACKE_chbevx( int matrix_order, char jobz, char range, char uplo,
+ lapack_int n, lapack_int kd,
+ lapack_complex_float* ab, lapack_int ldab,
+ lapack_complex_float* q, lapack_int ldq, float vl,
+ float vu, lapack_int il, lapack_int iu, float abstol,
+ lapack_int* m, float* w, lapack_complex_float* z,
+ lapack_int ldz, lapack_int* ifail );
+lapack_int LAPACKE_zhbevx( int matrix_order, char jobz, char range, char uplo,
+ lapack_int n, lapack_int kd,
+ lapack_complex_double* ab, lapack_int ldab,
+ lapack_complex_double* q, lapack_int ldq, double vl,
+ double vu, lapack_int il, lapack_int iu,
+ double abstol, lapack_int* m, double* w,
+ lapack_complex_double* z, lapack_int ldz,
+ lapack_int* ifail );
+
+lapack_int LAPACKE_chbgst( int matrix_order, char vect, char uplo, lapack_int n,
+ lapack_int ka, lapack_int kb,
+ lapack_complex_float* ab, lapack_int ldab,
+ const lapack_complex_float* bb, lapack_int ldbb,
+ lapack_complex_float* x, lapack_int ldx );
+lapack_int LAPACKE_zhbgst( int matrix_order, char vect, char uplo, lapack_int n,
+ lapack_int ka, lapack_int kb,
+ lapack_complex_double* ab, lapack_int ldab,
+ const lapack_complex_double* bb, lapack_int ldbb,
+ lapack_complex_double* x, lapack_int ldx );
+
+lapack_int LAPACKE_chbgv( int matrix_order, char jobz, char uplo, lapack_int n,
+ lapack_int ka, lapack_int kb,
+ lapack_complex_float* ab, lapack_int ldab,
+ lapack_complex_float* bb, lapack_int ldbb, float* w,
+ lapack_complex_float* z, lapack_int ldz );
+lapack_int LAPACKE_zhbgv( int matrix_order, char jobz, char uplo, lapack_int n,
+ lapack_int ka, lapack_int kb,
+ lapack_complex_double* ab, lapack_int ldab,
+ lapack_complex_double* bb, lapack_int ldbb, double* w,
+ lapack_complex_double* z, lapack_int ldz );
+
+lapack_int LAPACKE_chbgvd( int matrix_order, char jobz, char uplo, lapack_int n,
+ lapack_int ka, lapack_int kb,
+ lapack_complex_float* ab, lapack_int ldab,
+ lapack_complex_float* bb, lapack_int ldbb, float* w,
+ lapack_complex_float* z, lapack_int ldz );
+lapack_int LAPACKE_zhbgvd( int matrix_order, char jobz, char uplo, lapack_int n,
+ lapack_int ka, lapack_int kb,
+ lapack_complex_double* ab, lapack_int ldab,
+ lapack_complex_double* bb, lapack_int ldbb,
+ double* w, lapack_complex_double* z,
+ lapack_int ldz );
+
+lapack_int LAPACKE_chbgvx( int matrix_order, char jobz, char range, char uplo,
+ lapack_int n, lapack_int ka, lapack_int kb,
+ lapack_complex_float* ab, lapack_int ldab,
+ lapack_complex_float* bb, lapack_int ldbb,
+ lapack_complex_float* q, lapack_int ldq, float vl,
+ float vu, lapack_int il, lapack_int iu, float abstol,
+ lapack_int* m, float* w, lapack_complex_float* z,
+ lapack_int ldz, lapack_int* ifail );
+lapack_int LAPACKE_zhbgvx( int matrix_order, char jobz, char range, char uplo,
+ lapack_int n, lapack_int ka, lapack_int kb,
+ lapack_complex_double* ab, lapack_int ldab,
+ lapack_complex_double* bb, lapack_int ldbb,
+ lapack_complex_double* q, lapack_int ldq, double vl,
+ double vu, lapack_int il, lapack_int iu,
+ double abstol, lapack_int* m, double* w,
+ lapack_complex_double* z, lapack_int ldz,
+ lapack_int* ifail );
+
+lapack_int LAPACKE_chbtrd( int matrix_order, char vect, char uplo, lapack_int n,
+ lapack_int kd, lapack_complex_float* ab,
+ lapack_int ldab, float* d, float* e,
+ lapack_complex_float* q, lapack_int ldq );
+lapack_int LAPACKE_zhbtrd( int matrix_order, char vect, char uplo, lapack_int n,
+ lapack_int kd, lapack_complex_double* ab,
+ lapack_int ldab, double* d, double* e,
+ lapack_complex_double* q, lapack_int ldq );
+
+lapack_int LAPACKE_checon( int matrix_order, char uplo, lapack_int n,
+ const lapack_complex_float* a, lapack_int lda,
+ const lapack_int* ipiv, float anorm, float* rcond );
+lapack_int LAPACKE_zhecon( int matrix_order, char uplo, lapack_int n,
+ const lapack_complex_double* a, lapack_int lda,
+ const lapack_int* ipiv, double anorm,
+ double* rcond );
+
+lapack_int LAPACKE_cheequb( int matrix_order, char uplo, lapack_int n,
+ const lapack_complex_float* a, lapack_int lda,
+ float* s, float* scond, float* amax );
+lapack_int LAPACKE_zheequb( int matrix_order, char uplo, lapack_int n,
+ const lapack_complex_double* a, lapack_int lda,
+ double* s, double* scond, double* amax );
+
+lapack_int LAPACKE_cheev( int matrix_order, char jobz, char uplo, lapack_int n,
+ lapack_complex_float* a, lapack_int lda, float* w );
+lapack_int LAPACKE_zheev( int matrix_order, char jobz, char uplo, lapack_int n,
+ lapack_complex_double* a, lapack_int lda, double* w );
+
+lapack_int LAPACKE_cheevd( int matrix_order, char jobz, char uplo, lapack_int n,
+ lapack_complex_float* a, lapack_int lda, float* w );
+lapack_int LAPACKE_zheevd( int matrix_order, char jobz, char uplo, lapack_int n,
+ lapack_complex_double* a, lapack_int lda,
+ double* w );
+
+lapack_int LAPACKE_cheevr( int matrix_order, char jobz, char range, char uplo,
+ lapack_int n, lapack_complex_float* a,
+ lapack_int lda, float vl, float vu, lapack_int il,
+ lapack_int iu, float abstol, lapack_int* m, float* w,
+ lapack_complex_float* z, lapack_int ldz,
+ lapack_int* isuppz );
+lapack_int LAPACKE_zheevr( int matrix_order, char jobz, char range, char uplo,
+ lapack_int n, lapack_complex_double* a,
+ lapack_int lda, double vl, double vu, lapack_int il,
+ lapack_int iu, double abstol, lapack_int* m,
+ double* w, lapack_complex_double* z, lapack_int ldz,
+ lapack_int* isuppz );
+
+lapack_int LAPACKE_cheevx( int matrix_order, char jobz, char range, char uplo,
+ lapack_int n, lapack_complex_float* a,
+ lapack_int lda, float vl, float vu, lapack_int il,
+ lapack_int iu, float abstol, lapack_int* m, float* w,
+ lapack_complex_float* z, lapack_int ldz,
+ lapack_int* ifail );
+lapack_int LAPACKE_zheevx( int matrix_order, char jobz, char range, char uplo,
+ lapack_int n, lapack_complex_double* a,
+ lapack_int lda, double vl, double vu, lapack_int il,
+ lapack_int iu, double abstol, lapack_int* m,
+ double* w, lapack_complex_double* z, lapack_int ldz,
+ lapack_int* ifail );
+
+lapack_int LAPACKE_chegst( int matrix_order, lapack_int itype, char uplo,
+ lapack_int n, lapack_complex_float* a,
+ lapack_int lda, const lapack_complex_float* b,
+ lapack_int ldb );
+lapack_int LAPACKE_zhegst( int matrix_order, lapack_int itype, char uplo,
+ lapack_int n, lapack_complex_double* a,
+ lapack_int lda, const lapack_complex_double* b,
+ lapack_int ldb );
+
+lapack_int LAPACKE_chegv( int matrix_order, lapack_int itype, char jobz,
+ char uplo, lapack_int n, lapack_complex_float* a,
+ lapack_int lda, lapack_complex_float* b,
+ lapack_int ldb, float* w );
+lapack_int LAPACKE_zhegv( int matrix_order, lapack_int itype, char jobz,
+ char uplo, lapack_int n, lapack_complex_double* a,
+ lapack_int lda, lapack_complex_double* b,
+ lapack_int ldb, double* w );
+
+lapack_int LAPACKE_chegvd( int matrix_order, lapack_int itype, char jobz,
+ char uplo, lapack_int n, lapack_complex_float* a,
+ lapack_int lda, lapack_complex_float* b,
+ lapack_int ldb, float* w );
+lapack_int LAPACKE_zhegvd( int matrix_order, lapack_int itype, char jobz,
+ char uplo, lapack_int n, lapack_complex_double* a,
+ lapack_int lda, lapack_complex_double* b,
+ lapack_int ldb, double* w );
+
+lapack_int LAPACKE_chegvx( int matrix_order, lapack_int itype, char jobz,
+ char range, char uplo, lapack_int n,
+ lapack_complex_float* a, lapack_int lda,
+ lapack_complex_float* b, lapack_int ldb, float vl,
+ float vu, lapack_int il, lapack_int iu, float abstol,
+ lapack_int* m, float* w, lapack_complex_float* z,
+ lapack_int ldz, lapack_int* ifail );
+lapack_int LAPACKE_zhegvx( int matrix_order, lapack_int itype, char jobz,
+ char range, char uplo, lapack_int n,
+ lapack_complex_double* a, lapack_int lda,
+ lapack_complex_double* b, lapack_int ldb, double vl,
+ double vu, lapack_int il, lapack_int iu,
+ double abstol, lapack_int* m, double* w,
+ lapack_complex_double* z, lapack_int ldz,
+ lapack_int* ifail );
+
+lapack_int LAPACKE_cherfs( int matrix_order, char uplo, lapack_int n,
+ lapack_int nrhs, const lapack_complex_float* a,
+ lapack_int lda, const lapack_complex_float* af,
+ lapack_int ldaf, const lapack_int* ipiv,
+ const lapack_complex_float* b, lapack_int ldb,
+ lapack_complex_float* x, lapack_int ldx, float* ferr,
+ float* berr );
+lapack_int LAPACKE_zherfs( int matrix_order, char uplo, lapack_int n,
+ lapack_int nrhs, const lapack_complex_double* a,
+ lapack_int lda, const lapack_complex_double* af,
+ lapack_int ldaf, const lapack_int* ipiv,
+ const lapack_complex_double* b, lapack_int ldb,
+ lapack_complex_double* x, lapack_int ldx,
+ double* ferr, double* berr );
+
+lapack_int LAPACKE_cherfsx( int matrix_order, char uplo, char equed,
+ lapack_int n, lapack_int nrhs,
+ const lapack_complex_float* a, lapack_int lda,
+ const lapack_complex_float* af, lapack_int ldaf,
+ const lapack_int* ipiv, const float* s,
+ const lapack_complex_float* b, lapack_int ldb,
+ lapack_complex_float* x, lapack_int ldx,
+ float* rcond, float* berr, lapack_int n_err_bnds,
+ float* err_bnds_norm, float* err_bnds_comp,
+ lapack_int nparams, float* params );
+lapack_int LAPACKE_zherfsx( int matrix_order, char uplo, char equed,
+ lapack_int n, lapack_int nrhs,
+ const lapack_complex_double* a, lapack_int lda,
+ const lapack_complex_double* af, lapack_int ldaf,
+ const lapack_int* ipiv, const double* s,
+ const lapack_complex_double* b, lapack_int ldb,
+ lapack_complex_double* x, lapack_int ldx,
+ double* rcond, double* berr, lapack_int n_err_bnds,
+ double* err_bnds_norm, double* err_bnds_comp,
+ lapack_int nparams, double* params );
+
+lapack_int LAPACKE_chesv( int matrix_order, char uplo, lapack_int n,
+ lapack_int nrhs, lapack_complex_float* a,
+ lapack_int lda, lapack_int* ipiv,
+ lapack_complex_float* b, lapack_int ldb );
+lapack_int LAPACKE_zhesv( int matrix_order, char uplo, lapack_int n,
+ lapack_int nrhs, lapack_complex_double* a,
+ lapack_int lda, lapack_int* ipiv,
+ lapack_complex_double* b, lapack_int ldb );
+
+lapack_int LAPACKE_chesvx( int matrix_order, char fact, char uplo, lapack_int n,
+ lapack_int nrhs, const lapack_complex_float* a,
+ lapack_int lda, lapack_complex_float* af,
+ lapack_int ldaf, lapack_int* ipiv,
+ const lapack_complex_float* b, lapack_int ldb,
+ lapack_complex_float* x, lapack_int ldx,
+ float* rcond, float* ferr, float* berr );
+lapack_int LAPACKE_zhesvx( int matrix_order, char fact, char uplo, lapack_int n,
+ lapack_int nrhs, const lapack_complex_double* a,
+ lapack_int lda, lapack_complex_double* af,
+ lapack_int ldaf, lapack_int* ipiv,
+ const lapack_complex_double* b, lapack_int ldb,
+ lapack_complex_double* x, lapack_int ldx,
+ double* rcond, double* ferr, double* berr );
+
+lapack_int LAPACKE_chesvxx( int matrix_order, char fact, char uplo,
+ lapack_int n, lapack_int nrhs,
+ lapack_complex_float* a, lapack_int lda,
+ lapack_complex_float* af, lapack_int ldaf,
+ lapack_int* ipiv, char* equed, float* s,
+ lapack_complex_float* b, lapack_int ldb,
+ lapack_complex_float* x, lapack_int ldx,
+ float* rcond, float* rpvgrw, float* berr,
+ lapack_int n_err_bnds, float* err_bnds_norm,
+ float* err_bnds_comp, lapack_int nparams,
+ float* params );
+lapack_int LAPACKE_zhesvxx( int matrix_order, char fact, char uplo,
+ lapack_int n, lapack_int nrhs,
+ lapack_complex_double* a, lapack_int lda,
+ lapack_complex_double* af, lapack_int ldaf,
+ lapack_int* ipiv, char* equed, double* s,
+ lapack_complex_double* b, lapack_int ldb,
+ lapack_complex_double* x, lapack_int ldx,
+ double* rcond, double* rpvgrw, double* berr,
+ lapack_int n_err_bnds, double* err_bnds_norm,
+ double* err_bnds_comp, lapack_int nparams,
+ double* params );
+
+lapack_int LAPACKE_chetrd( int matrix_order, char uplo, lapack_int n,
+ lapack_complex_float* a, lapack_int lda, float* d,
+ float* e, lapack_complex_float* tau );
+lapack_int LAPACKE_zhetrd( int matrix_order, char uplo, lapack_int n,
+ lapack_complex_double* a, lapack_int lda, double* d,
+ double* e, lapack_complex_double* tau );
+
+lapack_int LAPACKE_chetrf( int matrix_order, char uplo, lapack_int n,
+ lapack_complex_float* a, lapack_int lda,
+ lapack_int* ipiv );
+lapack_int LAPACKE_zhetrf( int matrix_order, char uplo, lapack_int n,
+ lapack_complex_double* a, lapack_int lda,
+ lapack_int* ipiv );
+
+lapack_int LAPACKE_chetri( int matrix_order, char uplo, lapack_int n,
+ lapack_complex_float* a, lapack_int lda,
+ const lapack_int* ipiv );
+lapack_int LAPACKE_zhetri( int matrix_order, char uplo, lapack_int n,
+ lapack_complex_double* a, lapack_int lda,
+ const lapack_int* ipiv );
+
+lapack_int LAPACKE_chetrs( int matrix_order, char uplo, lapack_int n,
+ lapack_int nrhs, const lapack_complex_float* a,
+ lapack_int lda, const lapack_int* ipiv,
+ lapack_complex_float* b, lapack_int ldb );
+lapack_int LAPACKE_zhetrs( int matrix_order, char uplo, lapack_int n,
+ lapack_int nrhs, const lapack_complex_double* a,
+ lapack_int lda, const lapack_int* ipiv,
+ lapack_complex_double* b, lapack_int ldb );
+
+lapack_int LAPACKE_chfrk( int matrix_order, char transr, char uplo, char trans,
+ lapack_int n, lapack_int k, float alpha,
+ const lapack_complex_float* a, lapack_int lda,
+ float beta, lapack_complex_float* c );
+lapack_int LAPACKE_zhfrk( int matrix_order, char transr, char uplo, char trans,
+ lapack_int n, lapack_int k, double alpha,
+ const lapack_complex_double* a, lapack_int lda,
+ double beta, lapack_complex_double* c );
+
+lapack_int LAPACKE_shgeqz( int matrix_order, char job, char compq, char compz,
+ lapack_int n, lapack_int ilo, lapack_int ihi,
+ float* h, lapack_int ldh, float* t, lapack_int ldt,
+ float* alphar, float* alphai, float* beta, float* q,
+ lapack_int ldq, float* z, lapack_int ldz );
+lapack_int LAPACKE_dhgeqz( int matrix_order, char job, char compq, char compz,
+ lapack_int n, lapack_int ilo, lapack_int ihi,
+ double* h, lapack_int ldh, double* t, lapack_int ldt,
+ double* alphar, double* alphai, double* beta,
+ double* q, lapack_int ldq, double* z,
+ lapack_int ldz );
+lapack_int LAPACKE_chgeqz( int matrix_order, char job, char compq, char compz,
+ lapack_int n, lapack_int ilo, lapack_int ihi,
+ lapack_complex_float* h, lapack_int ldh,
+ lapack_complex_float* t, lapack_int ldt,
+ lapack_complex_float* alpha,
+ lapack_complex_float* beta, lapack_complex_float* q,
+ lapack_int ldq, lapack_complex_float* z,
+ lapack_int ldz );
+lapack_int LAPACKE_zhgeqz( int matrix_order, char job, char compq, char compz,
+ lapack_int n, lapack_int ilo, lapack_int ihi,
+ lapack_complex_double* h, lapack_int ldh,
+ lapack_complex_double* t, lapack_int ldt,
+ lapack_complex_double* alpha,
+ lapack_complex_double* beta,
+ lapack_complex_double* q, lapack_int ldq,
+ lapack_complex_double* z, lapack_int ldz );
+
+lapack_int LAPACKE_chpcon( int matrix_order, char uplo, lapack_int n,
+ const lapack_complex_float* ap,
+ const lapack_int* ipiv, float anorm, float* rcond );
+lapack_int LAPACKE_zhpcon( int matrix_order, char uplo, lapack_int n,
+ const lapack_complex_double* ap,
+ const lapack_int* ipiv, double anorm,
+ double* rcond );
+
+lapack_int LAPACKE_chpev( int matrix_order, char jobz, char uplo, lapack_int n,
+ lapack_complex_float* ap, float* w,
+ lapack_complex_float* z, lapack_int ldz );
+lapack_int LAPACKE_zhpev( int matrix_order, char jobz, char uplo, lapack_int n,
+ lapack_complex_double* ap, double* w,
+ lapack_complex_double* z, lapack_int ldz );
+
+lapack_int LAPACKE_chpevd( int matrix_order, char jobz, char uplo, lapack_int n,
+ lapack_complex_float* ap, float* w,
+ lapack_complex_float* z, lapack_int ldz );
+lapack_int LAPACKE_zhpevd( int matrix_order, char jobz, char uplo, lapack_int n,
+ lapack_complex_double* ap, double* w,
+ lapack_complex_double* z, lapack_int ldz );
+
+lapack_int LAPACKE_chpevx( int matrix_order, char jobz, char range, char uplo,
+ lapack_int n, lapack_complex_float* ap, float vl,
+ float vu, lapack_int il, lapack_int iu, float abstol,
+ lapack_int* m, float* w, lapack_complex_float* z,
+ lapack_int ldz, lapack_int* ifail );
+lapack_int LAPACKE_zhpevx( int matrix_order, char jobz, char range, char uplo,
+ lapack_int n, lapack_complex_double* ap, double vl,
+ double vu, lapack_int il, lapack_int iu,
+ double abstol, lapack_int* m, double* w,
+ lapack_complex_double* z, lapack_int ldz,
+ lapack_int* ifail );
+
+lapack_int LAPACKE_chpgst( int matrix_order, lapack_int itype, char uplo,
+ lapack_int n, lapack_complex_float* ap,
+ const lapack_complex_float* bp );
+lapack_int LAPACKE_zhpgst( int matrix_order, lapack_int itype, char uplo,
+ lapack_int n, lapack_complex_double* ap,
+ const lapack_complex_double* bp );
+
+lapack_int LAPACKE_chpgv( int matrix_order, lapack_int itype, char jobz,
+ char uplo, lapack_int n, lapack_complex_float* ap,
+ lapack_complex_float* bp, float* w,
+ lapack_complex_float* z, lapack_int ldz );
+lapack_int LAPACKE_zhpgv( int matrix_order, lapack_int itype, char jobz,
+ char uplo, lapack_int n, lapack_complex_double* ap,
+ lapack_complex_double* bp, double* w,
+ lapack_complex_double* z, lapack_int ldz );
+
+lapack_int LAPACKE_chpgvd( int matrix_order, lapack_int itype, char jobz,
+ char uplo, lapack_int n, lapack_complex_float* ap,
+ lapack_complex_float* bp, float* w,
+ lapack_complex_float* z, lapack_int ldz );
+lapack_int LAPACKE_zhpgvd( int matrix_order, lapack_int itype, char jobz,
+ char uplo, lapack_int n, lapack_complex_double* ap,
+ lapack_complex_double* bp, double* w,
+ lapack_complex_double* z, lapack_int ldz );
+
+lapack_int LAPACKE_chpgvx( int matrix_order, lapack_int itype, char jobz,
+ char range, char uplo, lapack_int n,
+ lapack_complex_float* ap, lapack_complex_float* bp,
+ float vl, float vu, lapack_int il, lapack_int iu,
+ float abstol, lapack_int* m, float* w,
+ lapack_complex_float* z, lapack_int ldz,
+ lapack_int* ifail );
+lapack_int LAPACKE_zhpgvx( int matrix_order, lapack_int itype, char jobz,
+ char range, char uplo, lapack_int n,
+ lapack_complex_double* ap, lapack_complex_double* bp,
+ double vl, double vu, lapack_int il, lapack_int iu,
+ double abstol, lapack_int* m, double* w,
+ lapack_complex_double* z, lapack_int ldz,
+ lapack_int* ifail );
+
+lapack_int LAPACKE_chprfs( int matrix_order, char uplo, lapack_int n,
+ lapack_int nrhs, const lapack_complex_float* ap,
+ const lapack_complex_float* afp,
+ const lapack_int* ipiv,
+ const lapack_complex_float* b, lapack_int ldb,
+ lapack_complex_float* x, lapack_int ldx, float* ferr,
+ float* berr );
+lapack_int LAPACKE_zhprfs( int matrix_order, char uplo, lapack_int n,
+ lapack_int nrhs, const lapack_complex_double* ap,
+ const lapack_complex_double* afp,
+ const lapack_int* ipiv,
+ const lapack_complex_double* b, lapack_int ldb,
+ lapack_complex_double* x, lapack_int ldx,
+ double* ferr, double* berr );
+
+lapack_int LAPACKE_chpsv( int matrix_order, char uplo, lapack_int n,
+ lapack_int nrhs, lapack_complex_float* ap,
+ lapack_int* ipiv, lapack_complex_float* b,
+ lapack_int ldb );
+lapack_int LAPACKE_zhpsv( int matrix_order, char uplo, lapack_int n,
+ lapack_int nrhs, lapack_complex_double* ap,
+ lapack_int* ipiv, lapack_complex_double* b,
+ lapack_int ldb );
+
+lapack_int LAPACKE_chpsvx( int matrix_order, char fact, char uplo, lapack_int n,
+ lapack_int nrhs, const lapack_complex_float* ap,
+ lapack_complex_float* afp, lapack_int* ipiv,
+ const lapack_complex_float* b, lapack_int ldb,
+ lapack_complex_float* x, lapack_int ldx,
+ float* rcond, float* ferr, float* berr );
+lapack_int LAPACKE_zhpsvx( int matrix_order, char fact, char uplo, lapack_int n,
+ lapack_int nrhs, const lapack_complex_double* ap,
+ lapack_complex_double* afp, lapack_int* ipiv,
+ const lapack_complex_double* b, lapack_int ldb,
+ lapack_complex_double* x, lapack_int ldx,
+ double* rcond, double* ferr, double* berr );
+
+lapack_int LAPACKE_chptrd( int matrix_order, char uplo, lapack_int n,
+ lapack_complex_float* ap, float* d, float* e,
+ lapack_complex_float* tau );
+lapack_int LAPACKE_zhptrd( int matrix_order, char uplo, lapack_int n,
+ lapack_complex_double* ap, double* d, double* e,
+ lapack_complex_double* tau );
+
+lapack_int LAPACKE_chptrf( int matrix_order, char uplo, lapack_int n,
+ lapack_complex_float* ap, lapack_int* ipiv );
+lapack_int LAPACKE_zhptrf( int matrix_order, char uplo, lapack_int n,
+ lapack_complex_double* ap, lapack_int* ipiv );
+
+lapack_int LAPACKE_chptri( int matrix_order, char uplo, lapack_int n,
+ lapack_complex_float* ap, const lapack_int* ipiv );
+lapack_int LAPACKE_zhptri( int matrix_order, char uplo, lapack_int n,
+ lapack_complex_double* ap, const lapack_int* ipiv );
+
+lapack_int LAPACKE_chptrs( int matrix_order, char uplo, lapack_int n,
+ lapack_int nrhs, const lapack_complex_float* ap,
+ const lapack_int* ipiv, lapack_complex_float* b,
+ lapack_int ldb );
+lapack_int LAPACKE_zhptrs( int matrix_order, char uplo, lapack_int n,
+ lapack_int nrhs, const lapack_complex_double* ap,
+ const lapack_int* ipiv, lapack_complex_double* b,
+ lapack_int ldb );
+
+lapack_int LAPACKE_shsein( int matrix_order, char job, char eigsrc, char initv,
+ lapack_logical* select, lapack_int n, const float* h,
+ lapack_int ldh, float* wr, const float* wi,
+ float* vl, lapack_int ldvl, float* vr,
+ lapack_int ldvr, lapack_int mm, lapack_int* m,
+ lapack_int* ifaill, lapack_int* ifailr );
+lapack_int LAPACKE_dhsein( int matrix_order, char job, char eigsrc, char initv,
+ lapack_logical* select, lapack_int n,
+ const double* h, lapack_int ldh, double* wr,
+ const double* wi, double* vl, lapack_int ldvl,
+ double* vr, lapack_int ldvr, lapack_int mm,
+ lapack_int* m, lapack_int* ifaill,
+ lapack_int* ifailr );
+lapack_int LAPACKE_chsein( int matrix_order, char job, char eigsrc, char initv,
+ const lapack_logical* select, lapack_int n,
+ const lapack_complex_float* h, lapack_int ldh,
+ lapack_complex_float* w, lapack_complex_float* vl,
+ lapack_int ldvl, lapack_complex_float* vr,
+ lapack_int ldvr, lapack_int mm, lapack_int* m,
+ lapack_int* ifaill, lapack_int* ifailr );
+lapack_int LAPACKE_zhsein( int matrix_order, char job, char eigsrc, char initv,
+ const lapack_logical* select, lapack_int n,
+ const lapack_complex_double* h, lapack_int ldh,
+ lapack_complex_double* w, lapack_complex_double* vl,
+ lapack_int ldvl, lapack_complex_double* vr,
+ lapack_int ldvr, lapack_int mm, lapack_int* m,
+ lapack_int* ifaill, lapack_int* ifailr );
+
+lapack_int LAPACKE_shseqr( int matrix_order, char job, char compz, lapack_int n,
+ lapack_int ilo, lapack_int ihi, float* h,
+ lapack_int ldh, float* wr, float* wi, float* z,
+ lapack_int ldz );
+lapack_int LAPACKE_dhseqr( int matrix_order, char job, char compz, lapack_int n,
+ lapack_int ilo, lapack_int ihi, double* h,
+ lapack_int ldh, double* wr, double* wi, double* z,
+ lapack_int ldz );
+lapack_int LAPACKE_chseqr( int matrix_order, char job, char compz, lapack_int n,
+ lapack_int ilo, lapack_int ihi,
+ lapack_complex_float* h, lapack_int ldh,
+ lapack_complex_float* w, lapack_complex_float* z,
+ lapack_int ldz );
+lapack_int LAPACKE_zhseqr( int matrix_order, char job, char compz, lapack_int n,
+ lapack_int ilo, lapack_int ihi,
+ lapack_complex_double* h, lapack_int ldh,
+ lapack_complex_double* w, lapack_complex_double* z,
+ lapack_int ldz );
+
+lapack_int LAPACKE_clacgv( lapack_int n, lapack_complex_float* x,
+ lapack_int incx );
+lapack_int LAPACKE_zlacgv( lapack_int n, lapack_complex_double* x,
+ lapack_int incx );
+
+lapack_int LAPACKE_slacpy( int matrix_order, char uplo, lapack_int m,
+ lapack_int n, const float* a, lapack_int lda, float* b,
+ lapack_int ldb );
+lapack_int LAPACKE_dlacpy( int matrix_order, char uplo, lapack_int m,
+ lapack_int n, const double* a, lapack_int lda, double* b,
+ lapack_int ldb );
+lapack_int LAPACKE_clacpy( int matrix_order, char uplo, lapack_int m,
+ lapack_int n, const lapack_complex_float* a,
+ lapack_int lda, lapack_complex_float* b,
+ lapack_int ldb );
+lapack_int LAPACKE_zlacpy( int matrix_order, char uplo, lapack_int m,
+ lapack_int n, const lapack_complex_double* a,
+ lapack_int lda, lapack_complex_double* b,
+ lapack_int ldb );
+
+lapack_int LAPACKE_zlag2c( int matrix_order, lapack_int m, lapack_int n,
+ const lapack_complex_double* a, lapack_int lda,
+ lapack_complex_float* sa, lapack_int ldsa );
+
+lapack_int LAPACKE_slag2d( int matrix_order, lapack_int m, lapack_int n,
+ const float* sa, lapack_int ldsa, double* a,
+ lapack_int lda );
+
+lapack_int LAPACKE_dlag2s( int matrix_order, lapack_int m, lapack_int n,
+ const double* a, lapack_int lda, float* sa,
+ lapack_int ldsa );
+
+lapack_int LAPACKE_clag2z( int matrix_order, lapack_int m, lapack_int n,
+ const lapack_complex_float* sa, lapack_int ldsa,
+ lapack_complex_double* a, lapack_int lda );
+
+lapack_int LAPACKE_slagge( int matrix_order, lapack_int m, lapack_int n,
+ lapack_int kl, lapack_int ku, const float* d,
+ float* a, lapack_int lda, lapack_int* iseed );
+lapack_int LAPACKE_dlagge( int matrix_order, lapack_int m, lapack_int n,
+ lapack_int kl, lapack_int ku, const double* d,
+ double* a, lapack_int lda, lapack_int* iseed );
+lapack_int LAPACKE_clagge( int matrix_order, lapack_int m, lapack_int n,
+ lapack_int kl, lapack_int ku, const float* d,
+ lapack_complex_float* a, lapack_int lda,
+ lapack_int* iseed );
+lapack_int LAPACKE_zlagge( int matrix_order, lapack_int m, lapack_int n,
+ lapack_int kl, lapack_int ku, const double* d,
+ lapack_complex_double* a, lapack_int lda,
+ lapack_int* iseed );
+
+float LAPACKE_slamch( char cmach );
+double LAPACKE_dlamch( char cmach );
+
+float LAPACKE_slange( int matrix_order, char norm, lapack_int m,
+ lapack_int n, const float* a, lapack_int lda );
+double LAPACKE_dlange( int matrix_order, char norm, lapack_int m,
+ lapack_int n, const double* a, lapack_int lda );
+float LAPACKE_clange( int matrix_order, char norm, lapack_int m,
+ lapack_int n, const lapack_complex_float* a,
+ lapack_int lda );
+double LAPACKE_zlange( int matrix_order, char norm, lapack_int m,
+ lapack_int n, const lapack_complex_double* a,
+ lapack_int lda );
+
+float LAPACKE_clanhe( int matrix_order, char norm, char uplo, lapack_int n,
+ const lapack_complex_float* a, lapack_int lda );
+double LAPACKE_zlanhe( int matrix_order, char norm, char uplo, lapack_int n,
+ const lapack_complex_double* a, lapack_int lda );
+
+float LAPACKE_slansy( int matrix_order, char norm, char uplo, lapack_int n,
+ const float* a, lapack_int lda );
+double LAPACKE_dlansy( int matrix_order, char norm, char uplo, lapack_int n,
+ const double* a, lapack_int lda );
+float LAPACKE_clansy( int matrix_order, char norm, char uplo, lapack_int n,
+ const lapack_complex_float* a, lapack_int lda );
+double LAPACKE_zlansy( int matrix_order, char norm, char uplo, lapack_int n,
+ const lapack_complex_double* a, lapack_int lda );
+
+float LAPACKE_slantr( int matrix_order, char norm, char uplo, char diag,
+ lapack_int m, lapack_int n, const float* a,
+ lapack_int lda );
+double LAPACKE_dlantr( int matrix_order, char norm, char uplo, char diag,
+ lapack_int m, lapack_int n, const double* a,
+ lapack_int lda );
+float LAPACKE_clantr( int matrix_order, char norm, char uplo, char diag,
+ lapack_int m, lapack_int n, const lapack_complex_float* a,
+ lapack_int lda );
+double LAPACKE_zlantr( int matrix_order, char norm, char uplo, char diag,
+ lapack_int m, lapack_int n, const lapack_complex_double* a,
+ lapack_int lda );
+
+
+lapack_int LAPACKE_slarfb( int matrix_order, char side, char trans, char direct,
+ char storev, lapack_int m, lapack_int n,
+ lapack_int k, const float* v, lapack_int ldv,
+ const float* t, lapack_int ldt, float* c,
+ lapack_int ldc );
+lapack_int LAPACKE_dlarfb( int matrix_order, char side, char trans, char direct,
+ char storev, lapack_int m, lapack_int n,
+ lapack_int k, const double* v, lapack_int ldv,
+ const double* t, lapack_int ldt, double* c,
+ lapack_int ldc );
+lapack_int LAPACKE_clarfb( int matrix_order, char side, char trans, char direct,
+ char storev, lapack_int m, lapack_int n,
+ lapack_int k, const lapack_complex_float* v,
+ lapack_int ldv, const lapack_complex_float* t,
+ lapack_int ldt, lapack_complex_float* c,
+ lapack_int ldc );
+lapack_int LAPACKE_zlarfb( int matrix_order, char side, char trans, char direct,
+ char storev, lapack_int m, lapack_int n,
+ lapack_int k, const lapack_complex_double* v,
+ lapack_int ldv, const lapack_complex_double* t,
+ lapack_int ldt, lapack_complex_double* c,
+ lapack_int ldc );
+
+lapack_int LAPACKE_slarfg( lapack_int n, float* alpha, float* x,
+ lapack_int incx, float* tau );
+lapack_int LAPACKE_dlarfg( lapack_int n, double* alpha, double* x,
+ lapack_int incx, double* tau );
+lapack_int LAPACKE_clarfg( lapack_int n, lapack_complex_float* alpha,
+ lapack_complex_float* x, lapack_int incx,
+ lapack_complex_float* tau );
+lapack_int LAPACKE_zlarfg( lapack_int n, lapack_complex_double* alpha,
+ lapack_complex_double* x, lapack_int incx,
+ lapack_complex_double* tau );
+
+lapack_int LAPACKE_slarft( int matrix_order, char direct, char storev,
+ lapack_int n, lapack_int k, const float* v,
+ lapack_int ldv, const float* tau, float* t,
+ lapack_int ldt );
+lapack_int LAPACKE_dlarft( int matrix_order, char direct, char storev,
+ lapack_int n, lapack_int k, const double* v,
+ lapack_int ldv, const double* tau, double* t,
+ lapack_int ldt );
+lapack_int LAPACKE_clarft( int matrix_order, char direct, char storev,
+ lapack_int n, lapack_int k,
+ const lapack_complex_float* v, lapack_int ldv,
+ const lapack_complex_float* tau,
+ lapack_complex_float* t, lapack_int ldt );
+lapack_int LAPACKE_zlarft( int matrix_order, char direct, char storev,
+ lapack_int n, lapack_int k,
+ const lapack_complex_double* v, lapack_int ldv,
+ const lapack_complex_double* tau,
+ lapack_complex_double* t, lapack_int ldt );
+
+lapack_int LAPACKE_slarfx( int matrix_order, char side, lapack_int m,
+ lapack_int n, const float* v, float tau, float* c,
+ lapack_int ldc, float* work );
+lapack_int LAPACKE_dlarfx( int matrix_order, char side, lapack_int m,
+ lapack_int n, const double* v, double tau, double* c,
+ lapack_int ldc, double* work );
+lapack_int LAPACKE_clarfx( int matrix_order, char side, lapack_int m,
+ lapack_int n, const lapack_complex_float* v,
+ lapack_complex_float tau, lapack_complex_float* c,
+ lapack_int ldc, lapack_complex_float* work );
+lapack_int LAPACKE_zlarfx( int matrix_order, char side, lapack_int m,
+ lapack_int n, const lapack_complex_double* v,
+ lapack_complex_double tau, lapack_complex_double* c,
+ lapack_int ldc, lapack_complex_double* work );
+
+lapack_int LAPACKE_slarnv( lapack_int idist, lapack_int* iseed, lapack_int n,
+ float* x );
+lapack_int LAPACKE_dlarnv( lapack_int idist, lapack_int* iseed, lapack_int n,
+ double* x );
+lapack_int LAPACKE_clarnv( lapack_int idist, lapack_int* iseed, lapack_int n,
+ lapack_complex_float* x );
+lapack_int LAPACKE_zlarnv( lapack_int idist, lapack_int* iseed, lapack_int n,
+ lapack_complex_double* x );
+
+lapack_int LAPACKE_slaset( int matrix_order, char uplo, lapack_int m,
+ lapack_int n, float alpha, float beta, float* a,
+ lapack_int lda );
+lapack_int LAPACKE_dlaset( int matrix_order, char uplo, lapack_int m,
+ lapack_int n, double alpha, double beta, double* a,
+ lapack_int lda );
+lapack_int LAPACKE_claset( int matrix_order, char uplo, lapack_int m,
+ lapack_int n, lapack_complex_float alpha,
+ lapack_complex_float beta, lapack_complex_float* a,
+ lapack_int lda );
+lapack_int LAPACKE_zlaset( int matrix_order, char uplo, lapack_int m,
+ lapack_int n, lapack_complex_double alpha,
+ lapack_complex_double beta, lapack_complex_double* a,
+ lapack_int lda );
+
+lapack_int LAPACKE_slasrt( char id, lapack_int n, float* d );
+lapack_int LAPACKE_dlasrt( char id, lapack_int n, double* d );
+
+lapack_int LAPACKE_slaswp( int matrix_order, lapack_int n, float* a,
+ lapack_int lda, lapack_int k1, lapack_int k2,
+ const lapack_int* ipiv, lapack_int incx );
+lapack_int LAPACKE_dlaswp( int matrix_order, lapack_int n, double* a,
+ lapack_int lda, lapack_int k1, lapack_int k2,
+ const lapack_int* ipiv, lapack_int incx );
+lapack_int LAPACKE_claswp( int matrix_order, lapack_int n,
+ lapack_complex_float* a, lapack_int lda,
+ lapack_int k1, lapack_int k2, const lapack_int* ipiv,
+ lapack_int incx );
+lapack_int LAPACKE_zlaswp( int matrix_order, lapack_int n,
+ lapack_complex_double* a, lapack_int lda,
+ lapack_int k1, lapack_int k2, const lapack_int* ipiv,
+ lapack_int incx );
+
+lapack_int LAPACKE_slatms( int matrix_order, lapack_int m, lapack_int n,
+ char dist, lapack_int* iseed, char sym, float* d,
+ lapack_int mode, float cond, float dmax,
+ lapack_int kl, lapack_int ku, char pack, float* a,
+ lapack_int lda );
+lapack_int LAPACKE_dlatms( int matrix_order, lapack_int m, lapack_int n,
+ char dist, lapack_int* iseed, char sym, double* d,
+ lapack_int mode, double cond, double dmax,
+ lapack_int kl, lapack_int ku, char pack, double* a,
+ lapack_int lda );
+lapack_int LAPACKE_clatms( int matrix_order, lapack_int m, lapack_int n,
+ char dist, lapack_int* iseed, char sym, float* d,
+ lapack_int mode, float cond, float dmax,
+ lapack_int kl, lapack_int ku, char pack,
+ lapack_complex_float* a, lapack_int lda );
+lapack_int LAPACKE_zlatms( int matrix_order, lapack_int m, lapack_int n,
+ char dist, lapack_int* iseed, char sym, double* d,
+ lapack_int mode, double cond, double dmax,
+ lapack_int kl, lapack_int ku, char pack,
+ lapack_complex_double* a, lapack_int lda );
+
+lapack_int LAPACKE_slauum( int matrix_order, char uplo, lapack_int n, float* a,
+ lapack_int lda );
+lapack_int LAPACKE_dlauum( int matrix_order, char uplo, lapack_int n, double* a,
+ lapack_int lda );
+lapack_int LAPACKE_clauum( int matrix_order, char uplo, lapack_int n,
+ lapack_complex_float* a, lapack_int lda );
+lapack_int LAPACKE_zlauum( int matrix_order, char uplo, lapack_int n,
+ lapack_complex_double* a, lapack_int lda );
+
+lapack_int LAPACKE_sopgtr( int matrix_order, char uplo, lapack_int n,
+ const float* ap, const float* tau, float* q,
+ lapack_int ldq );
+lapack_int LAPACKE_dopgtr( int matrix_order, char uplo, lapack_int n,
+ const double* ap, const double* tau, double* q,
+ lapack_int ldq );
+
+lapack_int LAPACKE_sopmtr( int matrix_order, char side, char uplo, char trans,
+ lapack_int m, lapack_int n, const float* ap,
+ const float* tau, float* c, lapack_int ldc );
+lapack_int LAPACKE_dopmtr( int matrix_order, char side, char uplo, char trans,
+ lapack_int m, lapack_int n, const double* ap,
+ const double* tau, double* c, lapack_int ldc );
+
+lapack_int LAPACKE_sorgbr( int matrix_order, char vect, lapack_int m,
+ lapack_int n, lapack_int k, float* a, lapack_int lda,
+ const float* tau );
+lapack_int LAPACKE_dorgbr( int matrix_order, char vect, lapack_int m,
+ lapack_int n, lapack_int k, double* a,
+ lapack_int lda, const double* tau );
+
+lapack_int LAPACKE_sorghr( int matrix_order, lapack_int n, lapack_int ilo,
+ lapack_int ihi, float* a, lapack_int lda,
+ const float* tau );
+lapack_int LAPACKE_dorghr( int matrix_order, lapack_int n, lapack_int ilo,
+ lapack_int ihi, double* a, lapack_int lda,
+ const double* tau );
+
+lapack_int LAPACKE_sorglq( int matrix_order, lapack_int m, lapack_int n,
+ lapack_int k, float* a, lapack_int lda,
+ const float* tau );
+lapack_int LAPACKE_dorglq( int matrix_order, lapack_int m, lapack_int n,
+ lapack_int k, double* a, lapack_int lda,
+ const double* tau );
+
+lapack_int LAPACKE_sorgql( int matrix_order, lapack_int m, lapack_int n,
+ lapack_int k, float* a, lapack_int lda,
+ const float* tau );
+lapack_int LAPACKE_dorgql( int matrix_order, lapack_int m, lapack_int n,
+ lapack_int k, double* a, lapack_int lda,
+ const double* tau );
+
+lapack_int LAPACKE_sorgqr( int matrix_order, lapack_int m, lapack_int n,
+ lapack_int k, float* a, lapack_int lda,
+ const float* tau );
+lapack_int LAPACKE_dorgqr( int matrix_order, lapack_int m, lapack_int n,
+ lapack_int k, double* a, lapack_int lda,
+ const double* tau );
+
+lapack_int LAPACKE_sorgrq( int matrix_order, lapack_int m, lapack_int n,
+ lapack_int k, float* a, lapack_int lda,
+ const float* tau );
+lapack_int LAPACKE_dorgrq( int matrix_order, lapack_int m, lapack_int n,
+ lapack_int k, double* a, lapack_int lda,
+ const double* tau );
+
+lapack_int LAPACKE_sorgtr( int matrix_order, char uplo, lapack_int n, float* a,
+ lapack_int lda, const float* tau );
+lapack_int LAPACKE_dorgtr( int matrix_order, char uplo, lapack_int n, double* a,
+ lapack_int lda, const double* tau );
+
+lapack_int LAPACKE_sormbr( int matrix_order, char vect, char side, char trans,
+ lapack_int m, lapack_int n, lapack_int k,
+ const float* a, lapack_int lda, const float* tau,
+ float* c, lapack_int ldc );
+lapack_int LAPACKE_dormbr( int matrix_order, char vect, char side, char trans,
+ lapack_int m, lapack_int n, lapack_int k,
+ const double* a, lapack_int lda, const double* tau,
+ double* c, lapack_int ldc );
+
+lapack_int LAPACKE_sormhr( int matrix_order, char side, char trans,
+ lapack_int m, lapack_int n, lapack_int ilo,
+ lapack_int ihi, const float* a, lapack_int lda,
+ const float* tau, float* c, lapack_int ldc );
+lapack_int LAPACKE_dormhr( int matrix_order, char side, char trans,
+ lapack_int m, lapack_int n, lapack_int ilo,
+ lapack_int ihi, const double* a, lapack_int lda,
+ const double* tau, double* c, lapack_int ldc );
+
+lapack_int LAPACKE_sormlq( int matrix_order, char side, char trans,
+ lapack_int m, lapack_int n, lapack_int k,
+ const float* a, lapack_int lda, const float* tau,
+ float* c, lapack_int ldc );
+lapack_int LAPACKE_dormlq( int matrix_order, char side, char trans,
+ lapack_int m, lapack_int n, lapack_int k,
+ const double* a, lapack_int lda, const double* tau,
+ double* c, lapack_int ldc );
+
+lapack_int LAPACKE_sormql( int matrix_order, char side, char trans,
+ lapack_int m, lapack_int n, lapack_int k,
+ const float* a, lapack_int lda, const float* tau,
+ float* c, lapack_int ldc );
+lapack_int LAPACKE_dormql( int matrix_order, char side, char trans,
+ lapack_int m, lapack_int n, lapack_int k,
+ const double* a, lapack_int lda, const double* tau,
+ double* c, lapack_int ldc );
+
+lapack_int LAPACKE_sormqr( int matrix_order, char side, char trans,
+ lapack_int m, lapack_int n, lapack_int k,
+ const float* a, lapack_int lda, const float* tau,
+ float* c, lapack_int ldc );
+lapack_int LAPACKE_dormqr( int matrix_order, char side, char trans,
+ lapack_int m, lapack_int n, lapack_int k,
+ const double* a, lapack_int lda, const double* tau,
+ double* c, lapack_int ldc );
+
+lapack_int LAPACKE_sormrq( int matrix_order, char side, char trans,
+ lapack_int m, lapack_int n, lapack_int k,
+ const float* a, lapack_int lda, const float* tau,
+ float* c, lapack_int ldc );
+lapack_int LAPACKE_dormrq( int matrix_order, char side, char trans,
+ lapack_int m, lapack_int n, lapack_int k,
+ const double* a, lapack_int lda, const double* tau,
+ double* c, lapack_int ldc );
+
+lapack_int LAPACKE_sormrz( int matrix_order, char side, char trans,
+ lapack_int m, lapack_int n, lapack_int k,
+ lapack_int l, const float* a, lapack_int lda,
+ const float* tau, float* c, lapack_int ldc );
+lapack_int LAPACKE_dormrz( int matrix_order, char side, char trans,
+ lapack_int m, lapack_int n, lapack_int k,
+ lapack_int l, const double* a, lapack_int lda,
+ const double* tau, double* c, lapack_int ldc );
+
+lapack_int LAPACKE_sormtr( int matrix_order, char side, char uplo, char trans,
+ lapack_int m, lapack_int n, const float* a,
+ lapack_int lda, const float* tau, float* c,
+ lapack_int ldc );
+lapack_int LAPACKE_dormtr( int matrix_order, char side, char uplo, char trans,
+ lapack_int m, lapack_int n, const double* a,
+ lapack_int lda, const double* tau, double* c,
+ lapack_int ldc );
+
+lapack_int LAPACKE_spbcon( int matrix_order, char uplo, lapack_int n,
+ lapack_int kd, const float* ab, lapack_int ldab,
+ float anorm, float* rcond );
+lapack_int LAPACKE_dpbcon( int matrix_order, char uplo, lapack_int n,
+ lapack_int kd, const double* ab, lapack_int ldab,
+ double anorm, double* rcond );
+lapack_int LAPACKE_cpbcon( int matrix_order, char uplo, lapack_int n,
+ lapack_int kd, const lapack_complex_float* ab,
+ lapack_int ldab, float anorm, float* rcond );
+lapack_int LAPACKE_zpbcon( int matrix_order, char uplo, lapack_int n,
+ lapack_int kd, const lapack_complex_double* ab,
+ lapack_int ldab, double anorm, double* rcond );
+
+lapack_int LAPACKE_spbequ( int matrix_order, char uplo, lapack_int n,
+ lapack_int kd, const float* ab, lapack_int ldab,
+ float* s, float* scond, float* amax );
+lapack_int LAPACKE_dpbequ( int matrix_order, char uplo, lapack_int n,
+ lapack_int kd, const double* ab, lapack_int ldab,
+ double* s, double* scond, double* amax );
+lapack_int LAPACKE_cpbequ( int matrix_order, char uplo, lapack_int n,
+ lapack_int kd, const lapack_complex_float* ab,
+ lapack_int ldab, float* s, float* scond,
+ float* amax );
+lapack_int LAPACKE_zpbequ( int matrix_order, char uplo, lapack_int n,
+ lapack_int kd, const lapack_complex_double* ab,
+ lapack_int ldab, double* s, double* scond,
+ double* amax );
+
+lapack_int LAPACKE_spbrfs( int matrix_order, char uplo, lapack_int n,
+ lapack_int kd, lapack_int nrhs, const float* ab,
+ lapack_int ldab, const float* afb, lapack_int ldafb,
+ const float* b, lapack_int ldb, float* x,
+ lapack_int ldx, float* ferr, float* berr );
+lapack_int LAPACKE_dpbrfs( int matrix_order, char uplo, lapack_int n,
+ lapack_int kd, lapack_int nrhs, const double* ab,
+ lapack_int ldab, const double* afb, lapack_int ldafb,
+ const double* b, lapack_int ldb, double* x,
+ lapack_int ldx, double* ferr, double* berr );
+lapack_int LAPACKE_cpbrfs( int matrix_order, char uplo, lapack_int n,
+ lapack_int kd, lapack_int nrhs,
+ const lapack_complex_float* ab, lapack_int ldab,
+ const lapack_complex_float* afb, lapack_int ldafb,
+ const lapack_complex_float* b, lapack_int ldb,
+ lapack_complex_float* x, lapack_int ldx, float* ferr,
+ float* berr );
+lapack_int LAPACKE_zpbrfs( int matrix_order, char uplo, lapack_int n,
+ lapack_int kd, lapack_int nrhs,
+ const lapack_complex_double* ab, lapack_int ldab,
+ const lapack_complex_double* afb, lapack_int ldafb,
+ const lapack_complex_double* b, lapack_int ldb,
+ lapack_complex_double* x, lapack_int ldx,
+ double* ferr, double* berr );
+
+lapack_int LAPACKE_spbstf( int matrix_order, char uplo, lapack_int n,
+ lapack_int kb, float* bb, lapack_int ldbb );
+lapack_int LAPACKE_dpbstf( int matrix_order, char uplo, lapack_int n,
+ lapack_int kb, double* bb, lapack_int ldbb );
+lapack_int LAPACKE_cpbstf( int matrix_order, char uplo, lapack_int n,
+ lapack_int kb, lapack_complex_float* bb,
+ lapack_int ldbb );
+lapack_int LAPACKE_zpbstf( int matrix_order, char uplo, lapack_int n,
+ lapack_int kb, lapack_complex_double* bb,
+ lapack_int ldbb );
+
+lapack_int LAPACKE_spbsv( int matrix_order, char uplo, lapack_int n,
+ lapack_int kd, lapack_int nrhs, float* ab,
+ lapack_int ldab, float* b, lapack_int ldb );
+lapack_int LAPACKE_dpbsv( int matrix_order, char uplo, lapack_int n,
+ lapack_int kd, lapack_int nrhs, double* ab,
+ lapack_int ldab, double* b, lapack_int ldb );
+lapack_int LAPACKE_cpbsv( int matrix_order, char uplo, lapack_int n,
+ lapack_int kd, lapack_int nrhs,
+ lapack_complex_float* ab, lapack_int ldab,
+ lapack_complex_float* b, lapack_int ldb );
+lapack_int LAPACKE_zpbsv( int matrix_order, char uplo, lapack_int n,
+ lapack_int kd, lapack_int nrhs,
+ lapack_complex_double* ab, lapack_int ldab,
+ lapack_complex_double* b, lapack_int ldb );
+
+lapack_int LAPACKE_spbsvx( int matrix_order, char fact, char uplo, lapack_int n,
+ lapack_int kd, lapack_int nrhs, float* ab,
+ lapack_int ldab, float* afb, lapack_int ldafb,
+ char* equed, float* s, float* b, lapack_int ldb,
+ float* x, lapack_int ldx, float* rcond, float* ferr,
+ float* berr );
+lapack_int LAPACKE_dpbsvx( int matrix_order, char fact, char uplo, lapack_int n,
+ lapack_int kd, lapack_int nrhs, double* ab,
+ lapack_int ldab, double* afb, lapack_int ldafb,
+ char* equed, double* s, double* b, lapack_int ldb,
+ double* x, lapack_int ldx, double* rcond,
+ double* ferr, double* berr );
+lapack_int LAPACKE_cpbsvx( int matrix_order, char fact, char uplo, lapack_int n,
+ lapack_int kd, lapack_int nrhs,
+ lapack_complex_float* ab, lapack_int ldab,
+ lapack_complex_float* afb, lapack_int ldafb,
+ char* equed, float* s, lapack_complex_float* b,
+ lapack_int ldb, lapack_complex_float* x,
+ lapack_int ldx, float* rcond, float* ferr,
+ float* berr );
+lapack_int LAPACKE_zpbsvx( int matrix_order, char fact, char uplo, lapack_int n,
+ lapack_int kd, lapack_int nrhs,
+ lapack_complex_double* ab, lapack_int ldab,
+ lapack_complex_double* afb, lapack_int ldafb,
+ char* equed, double* s, lapack_complex_double* b,
+ lapack_int ldb, lapack_complex_double* x,
+ lapack_int ldx, double* rcond, double* ferr,
+ double* berr );
+
+lapack_int LAPACKE_spbtrf( int matrix_order, char uplo, lapack_int n,
+ lapack_int kd, float* ab, lapack_int ldab );
+lapack_int LAPACKE_dpbtrf( int matrix_order, char uplo, lapack_int n,
+ lapack_int kd, double* ab, lapack_int ldab );
+lapack_int LAPACKE_cpbtrf( int matrix_order, char uplo, lapack_int n,
+ lapack_int kd, lapack_complex_float* ab,
+ lapack_int ldab );
+lapack_int LAPACKE_zpbtrf( int matrix_order, char uplo, lapack_int n,
+ lapack_int kd, lapack_complex_double* ab,
+ lapack_int ldab );
+
+lapack_int LAPACKE_spbtrs( int matrix_order, char uplo, lapack_int n,
+ lapack_int kd, lapack_int nrhs, const float* ab,
+ lapack_int ldab, float* b, lapack_int ldb );
+lapack_int LAPACKE_dpbtrs( int matrix_order, char uplo, lapack_int n,
+ lapack_int kd, lapack_int nrhs, const double* ab,
+ lapack_int ldab, double* b, lapack_int ldb );
+lapack_int LAPACKE_cpbtrs( int matrix_order, char uplo, lapack_int n,
+ lapack_int kd, lapack_int nrhs,
+ const lapack_complex_float* ab, lapack_int ldab,
+ lapack_complex_float* b, lapack_int ldb );
+lapack_int LAPACKE_zpbtrs( int matrix_order, char uplo, lapack_int n,
+ lapack_int kd, lapack_int nrhs,
+ const lapack_complex_double* ab, lapack_int ldab,
+ lapack_complex_double* b, lapack_int ldb );
+
+lapack_int LAPACKE_spftrf( int matrix_order, char transr, char uplo,
+ lapack_int n, float* a );
+lapack_int LAPACKE_dpftrf( int matrix_order, char transr, char uplo,
+ lapack_int n, double* a );
+lapack_int LAPACKE_cpftrf( int matrix_order, char transr, char uplo,
+ lapack_int n, lapack_complex_float* a );
+lapack_int LAPACKE_zpftrf( int matrix_order, char transr, char uplo,
+ lapack_int n, lapack_complex_double* a );
+
+lapack_int LAPACKE_spftri( int matrix_order, char transr, char uplo,
+ lapack_int n, float* a );
+lapack_int LAPACKE_dpftri( int matrix_order, char transr, char uplo,
+ lapack_int n, double* a );
+lapack_int LAPACKE_cpftri( int matrix_order, char transr, char uplo,
+ lapack_int n, lapack_complex_float* a );
+lapack_int LAPACKE_zpftri( int matrix_order, char transr, char uplo,
+ lapack_int n, lapack_complex_double* a );
+
+lapack_int LAPACKE_spftrs( int matrix_order, char transr, char uplo,
+ lapack_int n, lapack_int nrhs, const float* a,
+ float* b, lapack_int ldb );
+lapack_int LAPACKE_dpftrs( int matrix_order, char transr, char uplo,
+ lapack_int n, lapack_int nrhs, const double* a,
+ double* b, lapack_int ldb );
+lapack_int LAPACKE_cpftrs( int matrix_order, char transr, char uplo,
+ lapack_int n, lapack_int nrhs,
+ const lapack_complex_float* a,
+ lapack_complex_float* b, lapack_int ldb );
+lapack_int LAPACKE_zpftrs( int matrix_order, char transr, char uplo,
+ lapack_int n, lapack_int nrhs,
+ const lapack_complex_double* a,
+ lapack_complex_double* b, lapack_int ldb );
+
+lapack_int LAPACKE_spocon( int matrix_order, char uplo, lapack_int n,
+ const float* a, lapack_int lda, float anorm,
+ float* rcond );
+lapack_int LAPACKE_dpocon( int matrix_order, char uplo, lapack_int n,
+ const double* a, lapack_int lda, double anorm,
+ double* rcond );
+lapack_int LAPACKE_cpocon( int matrix_order, char uplo, lapack_int n,
+ const lapack_complex_float* a, lapack_int lda,
+ float anorm, float* rcond );
+lapack_int LAPACKE_zpocon( int matrix_order, char uplo, lapack_int n,
+ const lapack_complex_double* a, lapack_int lda,
+ double anorm, double* rcond );
+
+lapack_int LAPACKE_spoequ( int matrix_order, lapack_int n, const float* a,
+ lapack_int lda, float* s, float* scond,
+ float* amax );
+lapack_int LAPACKE_dpoequ( int matrix_order, lapack_int n, const double* a,
+ lapack_int lda, double* s, double* scond,
+ double* amax );
+lapack_int LAPACKE_cpoequ( int matrix_order, lapack_int n,
+ const lapack_complex_float* a, lapack_int lda,
+ float* s, float* scond, float* amax );
+lapack_int LAPACKE_zpoequ( int matrix_order, lapack_int n,
+ const lapack_complex_double* a, lapack_int lda,
+ double* s, double* scond, double* amax );
+
+lapack_int LAPACKE_spoequb( int matrix_order, lapack_int n, const float* a,
+ lapack_int lda, float* s, float* scond,
+ float* amax );
+lapack_int LAPACKE_dpoequb( int matrix_order, lapack_int n, const double* a,
+ lapack_int lda, double* s, double* scond,
+ double* amax );
+lapack_int LAPACKE_cpoequb( int matrix_order, lapack_int n,
+ const lapack_complex_float* a, lapack_int lda,
+ float* s, float* scond, float* amax );
+lapack_int LAPACKE_zpoequb( int matrix_order, lapack_int n,
+ const lapack_complex_double* a, lapack_int lda,
+ double* s, double* scond, double* amax );
+
+lapack_int LAPACKE_sporfs( int matrix_order, char uplo, lapack_int n,
+ lapack_int nrhs, const float* a, lapack_int lda,
+ const float* af, lapack_int ldaf, const float* b,
+ lapack_int ldb, float* x, lapack_int ldx,
+ float* ferr, float* berr );
+lapack_int LAPACKE_dporfs( int matrix_order, char uplo, lapack_int n,
+ lapack_int nrhs, const double* a, lapack_int lda,
+ const double* af, lapack_int ldaf, const double* b,
+ lapack_int ldb, double* x, lapack_int ldx,
+ double* ferr, double* berr );
+lapack_int LAPACKE_cporfs( int matrix_order, char uplo, lapack_int n,
+ lapack_int nrhs, const lapack_complex_float* a,
+ lapack_int lda, const lapack_complex_float* af,
+ lapack_int ldaf, const lapack_complex_float* b,
+ lapack_int ldb, lapack_complex_float* x,
+ lapack_int ldx, float* ferr, float* berr );
+lapack_int LAPACKE_zporfs( int matrix_order, char uplo, lapack_int n,
+ lapack_int nrhs, const lapack_complex_double* a,
+ lapack_int lda, const lapack_complex_double* af,
+ lapack_int ldaf, const lapack_complex_double* b,
+ lapack_int ldb, lapack_complex_double* x,
+ lapack_int ldx, double* ferr, double* berr );
+
+lapack_int LAPACKE_sporfsx( int matrix_order, char uplo, char equed,
+ lapack_int n, lapack_int nrhs, const float* a,
+ lapack_int lda, const float* af, lapack_int ldaf,
+ const float* s, const float* b, lapack_int ldb,
+ float* x, lapack_int ldx, float* rcond, float* berr,
+ lapack_int n_err_bnds, float* err_bnds_norm,
+ float* err_bnds_comp, lapack_int nparams,
+ float* params );
+lapack_int LAPACKE_dporfsx( int matrix_order, char uplo, char equed,
+ lapack_int n, lapack_int nrhs, const double* a,
+ lapack_int lda, const double* af, lapack_int ldaf,
+ const double* s, const double* b, lapack_int ldb,
+ double* x, lapack_int ldx, double* rcond,
+ double* berr, lapack_int n_err_bnds,
+ double* err_bnds_norm, double* err_bnds_comp,
+ lapack_int nparams, double* params );
+lapack_int LAPACKE_cporfsx( int matrix_order, char uplo, char equed,
+ lapack_int n, lapack_int nrhs,
+ const lapack_complex_float* a, lapack_int lda,
+ const lapack_complex_float* af, lapack_int ldaf,
+ const float* s, const lapack_complex_float* b,
+ lapack_int ldb, lapack_complex_float* x,
+ lapack_int ldx, float* rcond, float* berr,
+ lapack_int n_err_bnds, float* err_bnds_norm,
+ float* err_bnds_comp, lapack_int nparams,
+ float* params );
+lapack_int LAPACKE_zporfsx( int matrix_order, char uplo, char equed,
+ lapack_int n, lapack_int nrhs,
+ const lapack_complex_double* a, lapack_int lda,
+ const lapack_complex_double* af, lapack_int ldaf,
+ const double* s, const lapack_complex_double* b,
+ lapack_int ldb, lapack_complex_double* x,
+ lapack_int ldx, double* rcond, double* berr,
+ lapack_int n_err_bnds, double* err_bnds_norm,
+ double* err_bnds_comp, lapack_int nparams,
+ double* params );
+
+lapack_int LAPACKE_sposv( int matrix_order, char uplo, lapack_int n,
+ lapack_int nrhs, float* a, lapack_int lda, float* b,
+ lapack_int ldb );
+lapack_int LAPACKE_dposv( int matrix_order, char uplo, lapack_int n,
+ lapack_int nrhs, double* a, lapack_int lda, double* b,
+ lapack_int ldb );
+lapack_int LAPACKE_cposv( int matrix_order, char uplo, lapack_int n,
+ lapack_int nrhs, lapack_complex_float* a,
+ lapack_int lda, lapack_complex_float* b,
+ lapack_int ldb );
+lapack_int LAPACKE_zposv( int matrix_order, char uplo, lapack_int n,
+ lapack_int nrhs, lapack_complex_double* a,
+ lapack_int lda, lapack_complex_double* b,
+ lapack_int ldb );
+lapack_int LAPACKE_dsposv( int matrix_order, char uplo, lapack_int n,
+ lapack_int nrhs, double* a, lapack_int lda,
+ double* b, lapack_int ldb, double* x, lapack_int ldx,
+ lapack_int* iter );
+lapack_int LAPACKE_zcposv( int matrix_order, char uplo, lapack_int n,
+ lapack_int nrhs, lapack_complex_double* a,
+ lapack_int lda, lapack_complex_double* b,
+ lapack_int ldb, lapack_complex_double* x,
+ lapack_int ldx, lapack_int* iter );
+
+lapack_int LAPACKE_sposvx( int matrix_order, char fact, char uplo, lapack_int n,
+ lapack_int nrhs, float* a, lapack_int lda, float* af,
+ lapack_int ldaf, char* equed, float* s, float* b,
+ lapack_int ldb, float* x, lapack_int ldx,
+ float* rcond, float* ferr, float* berr );
+lapack_int LAPACKE_dposvx( int matrix_order, char fact, char uplo, lapack_int n,
+ lapack_int nrhs, double* a, lapack_int lda,
+ double* af, lapack_int ldaf, char* equed, double* s,
+ double* b, lapack_int ldb, double* x, lapack_int ldx,
+ double* rcond, double* ferr, double* berr );
+lapack_int LAPACKE_cposvx( int matrix_order, char fact, char uplo, lapack_int n,
+ lapack_int nrhs, lapack_complex_float* a,
+ lapack_int lda, lapack_complex_float* af,
+ lapack_int ldaf, char* equed, float* s,
+ lapack_complex_float* b, lapack_int ldb,
+ lapack_complex_float* x, lapack_int ldx,
+ float* rcond, float* ferr, float* berr );
+lapack_int LAPACKE_zposvx( int matrix_order, char fact, char uplo, lapack_int n,
+ lapack_int nrhs, lapack_complex_double* a,
+ lapack_int lda, lapack_complex_double* af,
+ lapack_int ldaf, char* equed, double* s,
+ lapack_complex_double* b, lapack_int ldb,
+ lapack_complex_double* x, lapack_int ldx,
+ double* rcond, double* ferr, double* berr );
+
+lapack_int LAPACKE_sposvxx( int matrix_order, char fact, char uplo,
+ lapack_int n, lapack_int nrhs, float* a,
+ lapack_int lda, float* af, lapack_int ldaf,
+ char* equed, float* s, float* b, lapack_int ldb,
+ float* x, lapack_int ldx, float* rcond,
+ float* rpvgrw, float* berr, lapack_int n_err_bnds,
+ float* err_bnds_norm, float* err_bnds_comp,
+ lapack_int nparams, float* params );
+lapack_int LAPACKE_dposvxx( int matrix_order, char fact, char uplo,
+ lapack_int n, lapack_int nrhs, double* a,
+ lapack_int lda, double* af, lapack_int ldaf,
+ char* equed, double* s, double* b, lapack_int ldb,
+ double* x, lapack_int ldx, double* rcond,
+ double* rpvgrw, double* berr, lapack_int n_err_bnds,
+ double* err_bnds_norm, double* err_bnds_comp,
+ lapack_int nparams, double* params );
+lapack_int LAPACKE_cposvxx( int matrix_order, char fact, char uplo,
+ lapack_int n, lapack_int nrhs,
+ lapack_complex_float* a, lapack_int lda,
+ lapack_complex_float* af, lapack_int ldaf,
+ char* equed, float* s, lapack_complex_float* b,
+ lapack_int ldb, lapack_complex_float* x,
+ lapack_int ldx, float* rcond, float* rpvgrw,
+ float* berr, lapack_int n_err_bnds,
+ float* err_bnds_norm, float* err_bnds_comp,
+ lapack_int nparams, float* params );
+lapack_int LAPACKE_zposvxx( int matrix_order, char fact, char uplo,
+ lapack_int n, lapack_int nrhs,
+ lapack_complex_double* a, lapack_int lda,
+ lapack_complex_double* af, lapack_int ldaf,
+ char* equed, double* s, lapack_complex_double* b,
+ lapack_int ldb, lapack_complex_double* x,
+ lapack_int ldx, double* rcond, double* rpvgrw,
+ double* berr, lapack_int n_err_bnds,
+ double* err_bnds_norm, double* err_bnds_comp,
+ lapack_int nparams, double* params );
+
+lapack_int LAPACKE_spotrf( int matrix_order, char uplo, lapack_int n, float* a,
+ lapack_int lda );
+lapack_int LAPACKE_dpotrf( int matrix_order, char uplo, lapack_int n, double* a,
+ lapack_int lda );
+lapack_int LAPACKE_cpotrf( int matrix_order, char uplo, lapack_int n,
+ lapack_complex_float* a, lapack_int lda );
+lapack_int LAPACKE_zpotrf( int matrix_order, char uplo, lapack_int n,
+ lapack_complex_double* a, lapack_int lda );
+
+lapack_int LAPACKE_spotri( int matrix_order, char uplo, lapack_int n, float* a,
+ lapack_int lda );
+lapack_int LAPACKE_dpotri( int matrix_order, char uplo, lapack_int n, double* a,
+ lapack_int lda );
+lapack_int LAPACKE_cpotri( int matrix_order, char uplo, lapack_int n,
+ lapack_complex_float* a, lapack_int lda );
+lapack_int LAPACKE_zpotri( int matrix_order, char uplo, lapack_int n,
+ lapack_complex_double* a, lapack_int lda );
+
+lapack_int LAPACKE_spotrs( int matrix_order, char uplo, lapack_int n,
+ lapack_int nrhs, const float* a, lapack_int lda,
+ float* b, lapack_int ldb );
+lapack_int LAPACKE_dpotrs( int matrix_order, char uplo, lapack_int n,
+ lapack_int nrhs, const double* a, lapack_int lda,
+ double* b, lapack_int ldb );
+lapack_int LAPACKE_cpotrs( int matrix_order, char uplo, lapack_int n,
+ lapack_int nrhs, const lapack_complex_float* a,
+ lapack_int lda, lapack_complex_float* b,
+ lapack_int ldb );
+lapack_int LAPACKE_zpotrs( int matrix_order, char uplo, lapack_int n,
+ lapack_int nrhs, const lapack_complex_double* a,
+ lapack_int lda, lapack_complex_double* b,
+ lapack_int ldb );
+
+lapack_int LAPACKE_sppcon( int matrix_order, char uplo, lapack_int n,
+ const float* ap, float anorm, float* rcond );
+lapack_int LAPACKE_dppcon( int matrix_order, char uplo, lapack_int n,
+ const double* ap, double anorm, double* rcond );
+lapack_int LAPACKE_cppcon( int matrix_order, char uplo, lapack_int n,
+ const lapack_complex_float* ap, float anorm,
+ float* rcond );
+lapack_int LAPACKE_zppcon( int matrix_order, char uplo, lapack_int n,
+ const lapack_complex_double* ap, double anorm,
+ double* rcond );
+
+lapack_int LAPACKE_sppequ( int matrix_order, char uplo, lapack_int n,
+ const float* ap, float* s, float* scond,
+ float* amax );
+lapack_int LAPACKE_dppequ( int matrix_order, char uplo, lapack_int n,
+ const double* ap, double* s, double* scond,
+ double* amax );
+lapack_int LAPACKE_cppequ( int matrix_order, char uplo, lapack_int n,
+ const lapack_complex_float* ap, float* s,
+ float* scond, float* amax );
+lapack_int LAPACKE_zppequ( int matrix_order, char uplo, lapack_int n,
+ const lapack_complex_double* ap, double* s,
+ double* scond, double* amax );
+
+lapack_int LAPACKE_spprfs( int matrix_order, char uplo, lapack_int n,
+ lapack_int nrhs, const float* ap, const float* afp,
+ const float* b, lapack_int ldb, float* x,
+ lapack_int ldx, float* ferr, float* berr );
+lapack_int LAPACKE_dpprfs( int matrix_order, char uplo, lapack_int n,
+ lapack_int nrhs, const double* ap, const double* afp,
+ const double* b, lapack_int ldb, double* x,
+ lapack_int ldx, double* ferr, double* berr );
+lapack_int LAPACKE_cpprfs( int matrix_order, char uplo, lapack_int n,
+ lapack_int nrhs, const lapack_complex_float* ap,
+ const lapack_complex_float* afp,
+ const lapack_complex_float* b, lapack_int ldb,
+ lapack_complex_float* x, lapack_int ldx, float* ferr,
+ float* berr );
+lapack_int LAPACKE_zpprfs( int matrix_order, char uplo, lapack_int n,
+ lapack_int nrhs, const lapack_complex_double* ap,
+ const lapack_complex_double* afp,
+ const lapack_complex_double* b, lapack_int ldb,
+ lapack_complex_double* x, lapack_int ldx,
+ double* ferr, double* berr );
+
+lapack_int LAPACKE_sppsv( int matrix_order, char uplo, lapack_int n,
+ lapack_int nrhs, float* ap, float* b,
+ lapack_int ldb );
+lapack_int LAPACKE_dppsv( int matrix_order, char uplo, lapack_int n,
+ lapack_int nrhs, double* ap, double* b,
+ lapack_int ldb );
+lapack_int LAPACKE_cppsv( int matrix_order, char uplo, lapack_int n,
+ lapack_int nrhs, lapack_complex_float* ap,
+ lapack_complex_float* b, lapack_int ldb );
+lapack_int LAPACKE_zppsv( int matrix_order, char uplo, lapack_int n,
+ lapack_int nrhs, lapack_complex_double* ap,
+ lapack_complex_double* b, lapack_int ldb );
+
+lapack_int LAPACKE_sppsvx( int matrix_order, char fact, char uplo, lapack_int n,
+ lapack_int nrhs, float* ap, float* afp, char* equed,
+ float* s, float* b, lapack_int ldb, float* x,
+ lapack_int ldx, float* rcond, float* ferr,
+ float* berr );
+lapack_int LAPACKE_dppsvx( int matrix_order, char fact, char uplo, lapack_int n,
+ lapack_int nrhs, double* ap, double* afp,
+ char* equed, double* s, double* b, lapack_int ldb,
+ double* x, lapack_int ldx, double* rcond,
+ double* ferr, double* berr );
+lapack_int LAPACKE_cppsvx( int matrix_order, char fact, char uplo, lapack_int n,
+ lapack_int nrhs, lapack_complex_float* ap,
+ lapack_complex_float* afp, char* equed, float* s,
+ lapack_complex_float* b, lapack_int ldb,
+ lapack_complex_float* x, lapack_int ldx,
+ float* rcond, float* ferr, float* berr );
+lapack_int LAPACKE_zppsvx( int matrix_order, char fact, char uplo, lapack_int n,
+ lapack_int nrhs, lapack_complex_double* ap,
+ lapack_complex_double* afp, char* equed, double* s,
+ lapack_complex_double* b, lapack_int ldb,
+ lapack_complex_double* x, lapack_int ldx,
+ double* rcond, double* ferr, double* berr );
+
+lapack_int LAPACKE_spptrf( int matrix_order, char uplo, lapack_int n,
+ float* ap );
+lapack_int LAPACKE_dpptrf( int matrix_order, char uplo, lapack_int n,
+ double* ap );
+lapack_int LAPACKE_cpptrf( int matrix_order, char uplo, lapack_int n,
+ lapack_complex_float* ap );
+lapack_int LAPACKE_zpptrf( int matrix_order, char uplo, lapack_int n,
+ lapack_complex_double* ap );
+
+lapack_int LAPACKE_spptri( int matrix_order, char uplo, lapack_int n,
+ float* ap );
+lapack_int LAPACKE_dpptri( int matrix_order, char uplo, lapack_int n,
+ double* ap );
+lapack_int LAPACKE_cpptri( int matrix_order, char uplo, lapack_int n,
+ lapack_complex_float* ap );
+lapack_int LAPACKE_zpptri( int matrix_order, char uplo, lapack_int n,
+ lapack_complex_double* ap );
+
+lapack_int LAPACKE_spptrs( int matrix_order, char uplo, lapack_int n,
+ lapack_int nrhs, const float* ap, float* b,
+ lapack_int ldb );
+lapack_int LAPACKE_dpptrs( int matrix_order, char uplo, lapack_int n,
+ lapack_int nrhs, const double* ap, double* b,
+ lapack_int ldb );
+lapack_int LAPACKE_cpptrs( int matrix_order, char uplo, lapack_int n,
+ lapack_int nrhs, const lapack_complex_float* ap,
+ lapack_complex_float* b, lapack_int ldb );
+lapack_int LAPACKE_zpptrs( int matrix_order, char uplo, lapack_int n,
+ lapack_int nrhs, const lapack_complex_double* ap,
+ lapack_complex_double* b, lapack_int ldb );
+
+lapack_int LAPACKE_spstrf( int matrix_order, char uplo, lapack_int n, float* a,
+ lapack_int lda, lapack_int* piv, lapack_int* rank,
+ float tol );
+lapack_int LAPACKE_dpstrf( int matrix_order, char uplo, lapack_int n, double* a,
+ lapack_int lda, lapack_int* piv, lapack_int* rank,
+ double tol );
+lapack_int LAPACKE_cpstrf( int matrix_order, char uplo, lapack_int n,
+ lapack_complex_float* a, lapack_int lda,
+ lapack_int* piv, lapack_int* rank, float tol );
+lapack_int LAPACKE_zpstrf( int matrix_order, char uplo, lapack_int n,
+ lapack_complex_double* a, lapack_int lda,
+ lapack_int* piv, lapack_int* rank, double tol );
+
+lapack_int LAPACKE_sptcon( lapack_int n, const float* d, const float* e,
+ float anorm, float* rcond );
+lapack_int LAPACKE_dptcon( lapack_int n, const double* d, const double* e,
+ double anorm, double* rcond );
+lapack_int LAPACKE_cptcon( lapack_int n, const float* d,
+ const lapack_complex_float* e, float anorm,
+ float* rcond );
+lapack_int LAPACKE_zptcon( lapack_int n, const double* d,
+ const lapack_complex_double* e, double anorm,
+ double* rcond );
+
+lapack_int LAPACKE_spteqr( int matrix_order, char compz, lapack_int n, float* d,
+ float* e, float* z, lapack_int ldz );
+lapack_int LAPACKE_dpteqr( int matrix_order, char compz, lapack_int n,
+ double* d, double* e, double* z, lapack_int ldz );
+lapack_int LAPACKE_cpteqr( int matrix_order, char compz, lapack_int n, float* d,
+ float* e, lapack_complex_float* z, lapack_int ldz );
+lapack_int LAPACKE_zpteqr( int matrix_order, char compz, lapack_int n,
+ double* d, double* e, lapack_complex_double* z,
+ lapack_int ldz );
+
+lapack_int LAPACKE_sptrfs( int matrix_order, lapack_int n, lapack_int nrhs,
+ const float* d, const float* e, const float* df,
+ const float* ef, const float* b, lapack_int ldb,
+ float* x, lapack_int ldx, float* ferr, float* berr );
+lapack_int LAPACKE_dptrfs( int matrix_order, lapack_int n, lapack_int nrhs,
+ const double* d, const double* e, const double* df,
+ const double* ef, const double* b, lapack_int ldb,
+ double* x, lapack_int ldx, double* ferr,
+ double* berr );
+lapack_int LAPACKE_cptrfs( int matrix_order, char uplo, lapack_int n,
+ lapack_int nrhs, const float* d,
+ const lapack_complex_float* e, const float* df,
+ const lapack_complex_float* ef,
+ const lapack_complex_float* b, lapack_int ldb,
+ lapack_complex_float* x, lapack_int ldx, float* ferr,
+ float* berr );
+lapack_int LAPACKE_zptrfs( int matrix_order, char uplo, lapack_int n,
+ lapack_int nrhs, const double* d,
+ const lapack_complex_double* e, const double* df,
+ const lapack_complex_double* ef,
+ const lapack_complex_double* b, lapack_int ldb,
+ lapack_complex_double* x, lapack_int ldx,
+ double* ferr, double* berr );
+
+lapack_int LAPACKE_sptsv( int matrix_order, lapack_int n, lapack_int nrhs,
+ float* d, float* e, float* b, lapack_int ldb );
+lapack_int LAPACKE_dptsv( int matrix_order, lapack_int n, lapack_int nrhs,
+ double* d, double* e, double* b, lapack_int ldb );
+lapack_int LAPACKE_cptsv( int matrix_order, lapack_int n, lapack_int nrhs,
+ float* d, lapack_complex_float* e,
+ lapack_complex_float* b, lapack_int ldb );
+lapack_int LAPACKE_zptsv( int matrix_order, lapack_int n, lapack_int nrhs,
+ double* d, lapack_complex_double* e,
+ lapack_complex_double* b, lapack_int ldb );
+
+lapack_int LAPACKE_sptsvx( int matrix_order, char fact, lapack_int n,
+ lapack_int nrhs, const float* d, const float* e,
+ float* df, float* ef, const float* b, lapack_int ldb,
+ float* x, lapack_int ldx, float* rcond, float* ferr,
+ float* berr );
+lapack_int LAPACKE_dptsvx( int matrix_order, char fact, lapack_int n,
+ lapack_int nrhs, const double* d, const double* e,
+ double* df, double* ef, const double* b,
+ lapack_int ldb, double* x, lapack_int ldx,
+ double* rcond, double* ferr, double* berr );
+lapack_int LAPACKE_cptsvx( int matrix_order, char fact, lapack_int n,
+ lapack_int nrhs, const float* d,
+ const lapack_complex_float* e, float* df,
+ lapack_complex_float* ef,
+ const lapack_complex_float* b, lapack_int ldb,
+ lapack_complex_float* x, lapack_int ldx,
+ float* rcond, float* ferr, float* berr );
+lapack_int LAPACKE_zptsvx( int matrix_order, char fact, lapack_int n,
+ lapack_int nrhs, const double* d,
+ const lapack_complex_double* e, double* df,
+ lapack_complex_double* ef,
+ const lapack_complex_double* b, lapack_int ldb,
+ lapack_complex_double* x, lapack_int ldx,
+ double* rcond, double* ferr, double* berr );
+
+lapack_int LAPACKE_spttrf( lapack_int n, float* d, float* e );
+lapack_int LAPACKE_dpttrf( lapack_int n, double* d, double* e );
+lapack_int LAPACKE_cpttrf( lapack_int n, float* d, lapack_complex_float* e );
+lapack_int LAPACKE_zpttrf( lapack_int n, double* d, lapack_complex_double* e );
+
+lapack_int LAPACKE_spttrs( int matrix_order, lapack_int n, lapack_int nrhs,
+ const float* d, const float* e, float* b,
+ lapack_int ldb );
+lapack_int LAPACKE_dpttrs( int matrix_order, lapack_int n, lapack_int nrhs,
+ const double* d, const double* e, double* b,
+ lapack_int ldb );
+lapack_int LAPACKE_cpttrs( int matrix_order, char uplo, lapack_int n,
+ lapack_int nrhs, const float* d,
+ const lapack_complex_float* e,
+ lapack_complex_float* b, lapack_int ldb );
+lapack_int LAPACKE_zpttrs( int matrix_order, char uplo, lapack_int n,
+ lapack_int nrhs, const double* d,
+ const lapack_complex_double* e,
+ lapack_complex_double* b, lapack_int ldb );
+
+lapack_int LAPACKE_ssbev( int matrix_order, char jobz, char uplo, lapack_int n,
+ lapack_int kd, float* ab, lapack_int ldab, float* w,
+ float* z, lapack_int ldz );
+lapack_int LAPACKE_dsbev( int matrix_order, char jobz, char uplo, lapack_int n,
+ lapack_int kd, double* ab, lapack_int ldab, double* w,
+ double* z, lapack_int ldz );
+
+lapack_int LAPACKE_ssbevd( int matrix_order, char jobz, char uplo, lapack_int n,
+ lapack_int kd, float* ab, lapack_int ldab, float* w,
+ float* z, lapack_int ldz );
+lapack_int LAPACKE_dsbevd( int matrix_order, char jobz, char uplo, lapack_int n,
+ lapack_int kd, double* ab, lapack_int ldab,
+ double* w, double* z, lapack_int ldz );
+
+lapack_int LAPACKE_ssbevx( int matrix_order, char jobz, char range, char uplo,
+ lapack_int n, lapack_int kd, float* ab,
+ lapack_int ldab, float* q, lapack_int ldq, float vl,
+ float vu, lapack_int il, lapack_int iu, float abstol,
+ lapack_int* m, float* w, float* z, lapack_int ldz,
+ lapack_int* ifail );
+lapack_int LAPACKE_dsbevx( int matrix_order, char jobz, char range, char uplo,
+ lapack_int n, lapack_int kd, double* ab,
+ lapack_int ldab, double* q, lapack_int ldq,
+ double vl, double vu, lapack_int il, lapack_int iu,
+ double abstol, lapack_int* m, double* w, double* z,
+ lapack_int ldz, lapack_int* ifail );
+
+lapack_int LAPACKE_ssbgst( int matrix_order, char vect, char uplo, lapack_int n,
+ lapack_int ka, lapack_int kb, float* ab,
+ lapack_int ldab, const float* bb, lapack_int ldbb,
+ float* x, lapack_int ldx );
+lapack_int LAPACKE_dsbgst( int matrix_order, char vect, char uplo, lapack_int n,
+ lapack_int ka, lapack_int kb, double* ab,
+ lapack_int ldab, const double* bb, lapack_int ldbb,
+ double* x, lapack_int ldx );
+
+lapack_int LAPACKE_ssbgv( int matrix_order, char jobz, char uplo, lapack_int n,
+ lapack_int ka, lapack_int kb, float* ab,
+ lapack_int ldab, float* bb, lapack_int ldbb, float* w,
+ float* z, lapack_int ldz );
+lapack_int LAPACKE_dsbgv( int matrix_order, char jobz, char uplo, lapack_int n,
+ lapack_int ka, lapack_int kb, double* ab,
+ lapack_int ldab, double* bb, lapack_int ldbb,
+ double* w, double* z, lapack_int ldz );
+
+lapack_int LAPACKE_ssbgvd( int matrix_order, char jobz, char uplo, lapack_int n,
+ lapack_int ka, lapack_int kb, float* ab,
+ lapack_int ldab, float* bb, lapack_int ldbb,
+ float* w, float* z, lapack_int ldz );
+lapack_int LAPACKE_dsbgvd( int matrix_order, char jobz, char uplo, lapack_int n,
+ lapack_int ka, lapack_int kb, double* ab,
+ lapack_int ldab, double* bb, lapack_int ldbb,
+ double* w, double* z, lapack_int ldz );
+
+lapack_int LAPACKE_ssbgvx( int matrix_order, char jobz, char range, char uplo,
+ lapack_int n, lapack_int ka, lapack_int kb,
+ float* ab, lapack_int ldab, float* bb,
+ lapack_int ldbb, float* q, lapack_int ldq, float vl,
+ float vu, lapack_int il, lapack_int iu, float abstol,
+ lapack_int* m, float* w, float* z, lapack_int ldz,
+ lapack_int* ifail );
+lapack_int LAPACKE_dsbgvx( int matrix_order, char jobz, char range, char uplo,
+ lapack_int n, lapack_int ka, lapack_int kb,
+ double* ab, lapack_int ldab, double* bb,
+ lapack_int ldbb, double* q, lapack_int ldq,
+ double vl, double vu, lapack_int il, lapack_int iu,
+ double abstol, lapack_int* m, double* w, double* z,
+ lapack_int ldz, lapack_int* ifail );
+
+lapack_int LAPACKE_ssbtrd( int matrix_order, char vect, char uplo, lapack_int n,
+ lapack_int kd, float* ab, lapack_int ldab, float* d,
+ float* e, float* q, lapack_int ldq );
+lapack_int LAPACKE_dsbtrd( int matrix_order, char vect, char uplo, lapack_int n,
+ lapack_int kd, double* ab, lapack_int ldab,
+ double* d, double* e, double* q, lapack_int ldq );
+
+lapack_int LAPACKE_ssfrk( int matrix_order, char transr, char uplo, char trans,
+ lapack_int n, lapack_int k, float alpha,
+ const float* a, lapack_int lda, float beta,
+ float* c );
+lapack_int LAPACKE_dsfrk( int matrix_order, char transr, char uplo, char trans,
+ lapack_int n, lapack_int k, double alpha,
+ const double* a, lapack_int lda, double beta,
+ double* c );
+
+lapack_int LAPACKE_sspcon( int matrix_order, char uplo, lapack_int n,
+ const float* ap, const lapack_int* ipiv, float anorm,
+ float* rcond );
+lapack_int LAPACKE_dspcon( int matrix_order, char uplo, lapack_int n,
+ const double* ap, const lapack_int* ipiv,
+ double anorm, double* rcond );
+lapack_int LAPACKE_cspcon( int matrix_order, char uplo, lapack_int n,
+ const lapack_complex_float* ap,
+ const lapack_int* ipiv, float anorm, float* rcond );
+lapack_int LAPACKE_zspcon( int matrix_order, char uplo, lapack_int n,
+ const lapack_complex_double* ap,
+ const lapack_int* ipiv, double anorm,
+ double* rcond );
+
+lapack_int LAPACKE_sspev( int matrix_order, char jobz, char uplo, lapack_int n,
+ float* ap, float* w, float* z, lapack_int ldz );
+lapack_int LAPACKE_dspev( int matrix_order, char jobz, char uplo, lapack_int n,
+ double* ap, double* w, double* z, lapack_int ldz );
+
+lapack_int LAPACKE_sspevd( int matrix_order, char jobz, char uplo, lapack_int n,
+ float* ap, float* w, float* z, lapack_int ldz );
+lapack_int LAPACKE_dspevd( int matrix_order, char jobz, char uplo, lapack_int n,
+ double* ap, double* w, double* z, lapack_int ldz );
+
+lapack_int LAPACKE_sspevx( int matrix_order, char jobz, char range, char uplo,
+ lapack_int n, float* ap, float vl, float vu,
+ lapack_int il, lapack_int iu, float abstol,
+ lapack_int* m, float* w, float* z, lapack_int ldz,
+ lapack_int* ifail );
+lapack_int LAPACKE_dspevx( int matrix_order, char jobz, char range, char uplo,
+ lapack_int n, double* ap, double vl, double vu,
+ lapack_int il, lapack_int iu, double abstol,
+ lapack_int* m, double* w, double* z, lapack_int ldz,
+ lapack_int* ifail );
+
+lapack_int LAPACKE_sspgst( int matrix_order, lapack_int itype, char uplo,
+ lapack_int n, float* ap, const float* bp );
+lapack_int LAPACKE_dspgst( int matrix_order, lapack_int itype, char uplo,
+ lapack_int n, double* ap, const double* bp );
+
+lapack_int LAPACKE_sspgv( int matrix_order, lapack_int itype, char jobz,
+ char uplo, lapack_int n, float* ap, float* bp,
+ float* w, float* z, lapack_int ldz );
+lapack_int LAPACKE_dspgv( int matrix_order, lapack_int itype, char jobz,
+ char uplo, lapack_int n, double* ap, double* bp,
+ double* w, double* z, lapack_int ldz );
+
+lapack_int LAPACKE_sspgvd( int matrix_order, lapack_int itype, char jobz,
+ char uplo, lapack_int n, float* ap, float* bp,
+ float* w, float* z, lapack_int ldz );
+lapack_int LAPACKE_dspgvd( int matrix_order, lapack_int itype, char jobz,
+ char uplo, lapack_int n, double* ap, double* bp,
+ double* w, double* z, lapack_int ldz );
+
+lapack_int LAPACKE_sspgvx( int matrix_order, lapack_int itype, char jobz,
+ char range, char uplo, lapack_int n, float* ap,
+ float* bp, float vl, float vu, lapack_int il,
+ lapack_int iu, float abstol, lapack_int* m, float* w,
+ float* z, lapack_int ldz, lapack_int* ifail );
+lapack_int LAPACKE_dspgvx( int matrix_order, lapack_int itype, char jobz,
+ char range, char uplo, lapack_int n, double* ap,
+ double* bp, double vl, double vu, lapack_int il,
+ lapack_int iu, double abstol, lapack_int* m,
+ double* w, double* z, lapack_int ldz,
+ lapack_int* ifail );
+
+lapack_int LAPACKE_ssprfs( int matrix_order, char uplo, lapack_int n,
+ lapack_int nrhs, const float* ap, const float* afp,
+ const lapack_int* ipiv, const float* b,
+ lapack_int ldb, float* x, lapack_int ldx,
+ float* ferr, float* berr );
+lapack_int LAPACKE_dsprfs( int matrix_order, char uplo, lapack_int n,
+ lapack_int nrhs, const double* ap, const double* afp,
+ const lapack_int* ipiv, const double* b,
+ lapack_int ldb, double* x, lapack_int ldx,
+ double* ferr, double* berr );
+lapack_int LAPACKE_csprfs( int matrix_order, char uplo, lapack_int n,
+ lapack_int nrhs, const lapack_complex_float* ap,
+ const lapack_complex_float* afp,
+ const lapack_int* ipiv,
+ const lapack_complex_float* b, lapack_int ldb,
+ lapack_complex_float* x, lapack_int ldx, float* ferr,
+ float* berr );
+lapack_int LAPACKE_zsprfs( int matrix_order, char uplo, lapack_int n,
+ lapack_int nrhs, const lapack_complex_double* ap,
+ const lapack_complex_double* afp,
+ const lapack_int* ipiv,
+ const lapack_complex_double* b, lapack_int ldb,
+ lapack_complex_double* x, lapack_int ldx,
+ double* ferr, double* berr );
+
+lapack_int LAPACKE_sspsv( int matrix_order, char uplo, lapack_int n,
+ lapack_int nrhs, float* ap, lapack_int* ipiv,
+ float* b, lapack_int ldb );
+lapack_int LAPACKE_dspsv( int matrix_order, char uplo, lapack_int n,
+ lapack_int nrhs, double* ap, lapack_int* ipiv,
+ double* b, lapack_int ldb );
+lapack_int LAPACKE_cspsv( int matrix_order, char uplo, lapack_int n,
+ lapack_int nrhs, lapack_complex_float* ap,
+ lapack_int* ipiv, lapack_complex_float* b,
+ lapack_int ldb );
+lapack_int LAPACKE_zspsv( int matrix_order, char uplo, lapack_int n,
+ lapack_int nrhs, lapack_complex_double* ap,
+ lapack_int* ipiv, lapack_complex_double* b,
+ lapack_int ldb );
+
+lapack_int LAPACKE_sspsvx( int matrix_order, char fact, char uplo, lapack_int n,
+ lapack_int nrhs, const float* ap, float* afp,
+ lapack_int* ipiv, const float* b, lapack_int ldb,
+ float* x, lapack_int ldx, float* rcond, float* ferr,
+ float* berr );
+lapack_int LAPACKE_dspsvx( int matrix_order, char fact, char uplo, lapack_int n,
+ lapack_int nrhs, const double* ap, double* afp,
+ lapack_int* ipiv, const double* b, lapack_int ldb,
+ double* x, lapack_int ldx, double* rcond,
+ double* ferr, double* berr );
+lapack_int LAPACKE_cspsvx( int matrix_order, char fact, char uplo, lapack_int n,
+ lapack_int nrhs, const lapack_complex_float* ap,
+ lapack_complex_float* afp, lapack_int* ipiv,
+ const lapack_complex_float* b, lapack_int ldb,
+ lapack_complex_float* x, lapack_int ldx,
+ float* rcond, float* ferr, float* berr );
+lapack_int LAPACKE_zspsvx( int matrix_order, char fact, char uplo, lapack_int n,
+ lapack_int nrhs, const lapack_complex_double* ap,
+ lapack_complex_double* afp, lapack_int* ipiv,
+ const lapack_complex_double* b, lapack_int ldb,
+ lapack_complex_double* x, lapack_int ldx,
+ double* rcond, double* ferr, double* berr );
+
+lapack_int LAPACKE_ssptrd( int matrix_order, char uplo, lapack_int n, float* ap,
+ float* d, float* e, float* tau );
+lapack_int LAPACKE_dsptrd( int matrix_order, char uplo, lapack_int n,
+ double* ap, double* d, double* e, double* tau );
+
+lapack_int LAPACKE_ssptrf( int matrix_order, char uplo, lapack_int n, float* ap,
+ lapack_int* ipiv );
+lapack_int LAPACKE_dsptrf( int matrix_order, char uplo, lapack_int n,
+ double* ap, lapack_int* ipiv );
+lapack_int LAPACKE_csptrf( int matrix_order, char uplo, lapack_int n,
+ lapack_complex_float* ap, lapack_int* ipiv );
+lapack_int LAPACKE_zsptrf( int matrix_order, char uplo, lapack_int n,
+ lapack_complex_double* ap, lapack_int* ipiv );
+
+lapack_int LAPACKE_ssptri( int matrix_order, char uplo, lapack_int n, float* ap,
+ const lapack_int* ipiv );
+lapack_int LAPACKE_dsptri( int matrix_order, char uplo, lapack_int n,
+ double* ap, const lapack_int* ipiv );
+lapack_int LAPACKE_csptri( int matrix_order, char uplo, lapack_int n,
+ lapack_complex_float* ap, const lapack_int* ipiv );
+lapack_int LAPACKE_zsptri( int matrix_order, char uplo, lapack_int n,
+ lapack_complex_double* ap, const lapack_int* ipiv );
+
+lapack_int LAPACKE_ssptrs( int matrix_order, char uplo, lapack_int n,
+ lapack_int nrhs, const float* ap,
+ const lapack_int* ipiv, float* b, lapack_int ldb );
+lapack_int LAPACKE_dsptrs( int matrix_order, char uplo, lapack_int n,
+ lapack_int nrhs, const double* ap,
+ const lapack_int* ipiv, double* b, lapack_int ldb );
+lapack_int LAPACKE_csptrs( int matrix_order, char uplo, lapack_int n,
+ lapack_int nrhs, const lapack_complex_float* ap,
+ const lapack_int* ipiv, lapack_complex_float* b,
+ lapack_int ldb );
+lapack_int LAPACKE_zsptrs( int matrix_order, char uplo, lapack_int n,
+ lapack_int nrhs, const lapack_complex_double* ap,
+ const lapack_int* ipiv, lapack_complex_double* b,
+ lapack_int ldb );
+
+lapack_int LAPACKE_sstebz( char range, char order, lapack_int n, float vl,
+ float vu, lapack_int il, lapack_int iu, float abstol,
+ const float* d, const float* e, lapack_int* m,
+ lapack_int* nsplit, float* w, lapack_int* iblock,
+ lapack_int* isplit );
+lapack_int LAPACKE_dstebz( char range, char order, lapack_int n, double vl,
+ double vu, lapack_int il, lapack_int iu,
+ double abstol, const double* d, const double* e,
+ lapack_int* m, lapack_int* nsplit, double* w,
+ lapack_int* iblock, lapack_int* isplit );
+
+lapack_int LAPACKE_sstedc( int matrix_order, char compz, lapack_int n, float* d,
+ float* e, float* z, lapack_int ldz );
+lapack_int LAPACKE_dstedc( int matrix_order, char compz, lapack_int n,
+ double* d, double* e, double* z, lapack_int ldz );
+lapack_int LAPACKE_cstedc( int matrix_order, char compz, lapack_int n, float* d,
+ float* e, lapack_complex_float* z, lapack_int ldz );
+lapack_int LAPACKE_zstedc( int matrix_order, char compz, lapack_int n,
+ double* d, double* e, lapack_complex_double* z,
+ lapack_int ldz );
+
+lapack_int LAPACKE_sstegr( int matrix_order, char jobz, char range,
+ lapack_int n, float* d, float* e, float vl, float vu,
+ lapack_int il, lapack_int iu, float abstol,
+ lapack_int* m, float* w, float* z, lapack_int ldz,
+ lapack_int* isuppz );
+lapack_int LAPACKE_dstegr( int matrix_order, char jobz, char range,
+ lapack_int n, double* d, double* e, double vl,
+ double vu, lapack_int il, lapack_int iu,
+ double abstol, lapack_int* m, double* w, double* z,
+ lapack_int ldz, lapack_int* isuppz );
+lapack_int LAPACKE_cstegr( int matrix_order, char jobz, char range,
+ lapack_int n, float* d, float* e, float vl, float vu,
+ lapack_int il, lapack_int iu, float abstol,
+ lapack_int* m, float* w, lapack_complex_float* z,
+ lapack_int ldz, lapack_int* isuppz );
+lapack_int LAPACKE_zstegr( int matrix_order, char jobz, char range,
+ lapack_int n, double* d, double* e, double vl,
+ double vu, lapack_int il, lapack_int iu,
+ double abstol, lapack_int* m, double* w,
+ lapack_complex_double* z, lapack_int ldz,
+ lapack_int* isuppz );
+
+lapack_int LAPACKE_sstein( int matrix_order, lapack_int n, const float* d,
+ const float* e, lapack_int m, const float* w,
+ const lapack_int* iblock, const lapack_int* isplit,
+ float* z, lapack_int ldz, lapack_int* ifailv );
+lapack_int LAPACKE_dstein( int matrix_order, lapack_int n, const double* d,
+ const double* e, lapack_int m, const double* w,
+ const lapack_int* iblock, const lapack_int* isplit,
+ double* z, lapack_int ldz, lapack_int* ifailv );
+lapack_int LAPACKE_cstein( int matrix_order, lapack_int n, const float* d,
+ const float* e, lapack_int m, const float* w,
+ const lapack_int* iblock, const lapack_int* isplit,
+ lapack_complex_float* z, lapack_int ldz,
+ lapack_int* ifailv );
+lapack_int LAPACKE_zstein( int matrix_order, lapack_int n, const double* d,
+ const double* e, lapack_int m, const double* w,
+ const lapack_int* iblock, const lapack_int* isplit,
+ lapack_complex_double* z, lapack_int ldz,
+ lapack_int* ifailv );
+
+lapack_int LAPACKE_sstemr( int matrix_order, char jobz, char range,
+ lapack_int n, float* d, float* e, float vl, float vu,
+ lapack_int il, lapack_int iu, lapack_int* m,
+ float* w, float* z, lapack_int ldz, lapack_int nzc,
+ lapack_int* isuppz, lapack_logical* tryrac );
+lapack_int LAPACKE_dstemr( int matrix_order, char jobz, char range,
+ lapack_int n, double* d, double* e, double vl,
+ double vu, lapack_int il, lapack_int iu,
+ lapack_int* m, double* w, double* z, lapack_int ldz,
+ lapack_int nzc, lapack_int* isuppz,
+ lapack_logical* tryrac );
+lapack_int LAPACKE_cstemr( int matrix_order, char jobz, char range,
+ lapack_int n, float* d, float* e, float vl, float vu,
+ lapack_int il, lapack_int iu, lapack_int* m,
+ float* w, lapack_complex_float* z, lapack_int ldz,
+ lapack_int nzc, lapack_int* isuppz,
+ lapack_logical* tryrac );
+lapack_int LAPACKE_zstemr( int matrix_order, char jobz, char range,
+ lapack_int n, double* d, double* e, double vl,
+ double vu, lapack_int il, lapack_int iu,
+ lapack_int* m, double* w, lapack_complex_double* z,
+ lapack_int ldz, lapack_int nzc, lapack_int* isuppz,
+ lapack_logical* tryrac );
+
+lapack_int LAPACKE_ssteqr( int matrix_order, char compz, lapack_int n, float* d,
+ float* e, float* z, lapack_int ldz );
+lapack_int LAPACKE_dsteqr( int matrix_order, char compz, lapack_int n,
+ double* d, double* e, double* z, lapack_int ldz );
+lapack_int LAPACKE_csteqr( int matrix_order, char compz, lapack_int n, float* d,
+ float* e, lapack_complex_float* z, lapack_int ldz );
+lapack_int LAPACKE_zsteqr( int matrix_order, char compz, lapack_int n,
+ double* d, double* e, lapack_complex_double* z,
+ lapack_int ldz );
+
+lapack_int LAPACKE_ssterf( lapack_int n, float* d, float* e );
+lapack_int LAPACKE_dsterf( lapack_int n, double* d, double* e );
+
+lapack_int LAPACKE_sstev( int matrix_order, char jobz, lapack_int n, float* d,
+ float* e, float* z, lapack_int ldz );
+lapack_int LAPACKE_dstev( int matrix_order, char jobz, lapack_int n, double* d,
+ double* e, double* z, lapack_int ldz );
+
+lapack_int LAPACKE_sstevd( int matrix_order, char jobz, lapack_int n, float* d,
+ float* e, float* z, lapack_int ldz );
+lapack_int LAPACKE_dstevd( int matrix_order, char jobz, lapack_int n, double* d,
+ double* e, double* z, lapack_int ldz );
+
+lapack_int LAPACKE_sstevr( int matrix_order, char jobz, char range,
+ lapack_int n, float* d, float* e, float vl, float vu,
+ lapack_int il, lapack_int iu, float abstol,
+ lapack_int* m, float* w, float* z, lapack_int ldz,
+ lapack_int* isuppz );
+lapack_int LAPACKE_dstevr( int matrix_order, char jobz, char range,
+ lapack_int n, double* d, double* e, double vl,
+ double vu, lapack_int il, lapack_int iu,
+ double abstol, lapack_int* m, double* w, double* z,
+ lapack_int ldz, lapack_int* isuppz );
+
+lapack_int LAPACKE_sstevx( int matrix_order, char jobz, char range,
+ lapack_int n, float* d, float* e, float vl, float vu,
+ lapack_int il, lapack_int iu, float abstol,
+ lapack_int* m, float* w, float* z, lapack_int ldz,
+ lapack_int* ifail );
+lapack_int LAPACKE_dstevx( int matrix_order, char jobz, char range,
+ lapack_int n, double* d, double* e, double vl,
+ double vu, lapack_int il, lapack_int iu,
+ double abstol, lapack_int* m, double* w, double* z,
+ lapack_int ldz, lapack_int* ifail );
+
+lapack_int LAPACKE_ssycon( int matrix_order, char uplo, lapack_int n,
+ const float* a, lapack_int lda,
+ const lapack_int* ipiv, float anorm, float* rcond );
+lapack_int LAPACKE_dsycon( int matrix_order, char uplo, lapack_int n,
+ const double* a, lapack_int lda,
+ const lapack_int* ipiv, double anorm,
+ double* rcond );
+lapack_int LAPACKE_csycon( int matrix_order, char uplo, lapack_int n,
+ const lapack_complex_float* a, lapack_int lda,
+ const lapack_int* ipiv, float anorm, float* rcond );
+lapack_int LAPACKE_zsycon( int matrix_order, char uplo, lapack_int n,
+ const lapack_complex_double* a, lapack_int lda,
+ const lapack_int* ipiv, double anorm,
+ double* rcond );
+
+lapack_int LAPACKE_ssyequb( int matrix_order, char uplo, lapack_int n,
+ const float* a, lapack_int lda, float* s,
+ float* scond, float* amax );
+lapack_int LAPACKE_dsyequb( int matrix_order, char uplo, lapack_int n,
+ const double* a, lapack_int lda, double* s,
+ double* scond, double* amax );
+lapack_int LAPACKE_csyequb( int matrix_order, char uplo, lapack_int n,
+ const lapack_complex_float* a, lapack_int lda,
+ float* s, float* scond, float* amax );
+lapack_int LAPACKE_zsyequb( int matrix_order, char uplo, lapack_int n,
+ const lapack_complex_double* a, lapack_int lda,
+ double* s, double* scond, double* amax );
+
+lapack_int LAPACKE_ssyev( int matrix_order, char jobz, char uplo, lapack_int n,
+ float* a, lapack_int lda, float* w );
+lapack_int LAPACKE_dsyev( int matrix_order, char jobz, char uplo, lapack_int n,
+ double* a, lapack_int lda, double* w );
+
+lapack_int LAPACKE_ssyevd( int matrix_order, char jobz, char uplo, lapack_int n,
+ float* a, lapack_int lda, float* w );
+lapack_int LAPACKE_dsyevd( int matrix_order, char jobz, char uplo, lapack_int n,
+ double* a, lapack_int lda, double* w );
+
+lapack_int LAPACKE_ssyevr( int matrix_order, char jobz, char range, char uplo,
+ lapack_int n, float* a, lapack_int lda, float vl,
+ float vu, lapack_int il, lapack_int iu, float abstol,
+ lapack_int* m, float* w, float* z, lapack_int ldz,
+ lapack_int* isuppz );
+lapack_int LAPACKE_dsyevr( int matrix_order, char jobz, char range, char uplo,
+ lapack_int n, double* a, lapack_int lda, double vl,
+ double vu, lapack_int il, lapack_int iu,
+ double abstol, lapack_int* m, double* w, double* z,
+ lapack_int ldz, lapack_int* isuppz );
+
+lapack_int LAPACKE_ssyevx( int matrix_order, char jobz, char range, char uplo,
+ lapack_int n, float* a, lapack_int lda, float vl,
+ float vu, lapack_int il, lapack_int iu, float abstol,
+ lapack_int* m, float* w, float* z, lapack_int ldz,
+ lapack_int* ifail );
+lapack_int LAPACKE_dsyevx( int matrix_order, char jobz, char range, char uplo,
+ lapack_int n, double* a, lapack_int lda, double vl,
+ double vu, lapack_int il, lapack_int iu,
+ double abstol, lapack_int* m, double* w, double* z,
+ lapack_int ldz, lapack_int* ifail );
+
+lapack_int LAPACKE_ssygst( int matrix_order, lapack_int itype, char uplo,
+ lapack_int n, float* a, lapack_int lda,
+ const float* b, lapack_int ldb );
+lapack_int LAPACKE_dsygst( int matrix_order, lapack_int itype, char uplo,
+ lapack_int n, double* a, lapack_int lda,
+ const double* b, lapack_int ldb );
+
+lapack_int LAPACKE_ssygv( int matrix_order, lapack_int itype, char jobz,
+ char uplo, lapack_int n, float* a, lapack_int lda,
+ float* b, lapack_int ldb, float* w );
+lapack_int LAPACKE_dsygv( int matrix_order, lapack_int itype, char jobz,
+ char uplo, lapack_int n, double* a, lapack_int lda,
+ double* b, lapack_int ldb, double* w );
+
+lapack_int LAPACKE_ssygvd( int matrix_order, lapack_int itype, char jobz,
+ char uplo, lapack_int n, float* a, lapack_int lda,
+ float* b, lapack_int ldb, float* w );
+lapack_int LAPACKE_dsygvd( int matrix_order, lapack_int itype, char jobz,
+ char uplo, lapack_int n, double* a, lapack_int lda,
+ double* b, lapack_int ldb, double* w );
+
+lapack_int LAPACKE_ssygvx( int matrix_order, lapack_int itype, char jobz,
+ char range, char uplo, lapack_int n, float* a,
+ lapack_int lda, float* b, lapack_int ldb, float vl,
+ float vu, lapack_int il, lapack_int iu, float abstol,
+ lapack_int* m, float* w, float* z, lapack_int ldz,
+ lapack_int* ifail );
+lapack_int LAPACKE_dsygvx( int matrix_order, lapack_int itype, char jobz,
+ char range, char uplo, lapack_int n, double* a,
+ lapack_int lda, double* b, lapack_int ldb, double vl,
+ double vu, lapack_int il, lapack_int iu,
+ double abstol, lapack_int* m, double* w, double* z,
+ lapack_int ldz, lapack_int* ifail );
+
+lapack_int LAPACKE_ssyrfs( int matrix_order, char uplo, lapack_int n,
+ lapack_int nrhs, const float* a, lapack_int lda,
+ const float* af, lapack_int ldaf,
+ const lapack_int* ipiv, const float* b,
+ lapack_int ldb, float* x, lapack_int ldx,
+ float* ferr, float* berr );
+lapack_int LAPACKE_dsyrfs( int matrix_order, char uplo, lapack_int n,
+ lapack_int nrhs, const double* a, lapack_int lda,
+ const double* af, lapack_int ldaf,
+ const lapack_int* ipiv, const double* b,
+ lapack_int ldb, double* x, lapack_int ldx,
+ double* ferr, double* berr );
+lapack_int LAPACKE_csyrfs( int matrix_order, char uplo, lapack_int n,
+ lapack_int nrhs, const lapack_complex_float* a,
+ lapack_int lda, const lapack_complex_float* af,
+ lapack_int ldaf, const lapack_int* ipiv,
+ const lapack_complex_float* b, lapack_int ldb,
+ lapack_complex_float* x, lapack_int ldx, float* ferr,
+ float* berr );
+lapack_int LAPACKE_zsyrfs( int matrix_order, char uplo, lapack_int n,
+ lapack_int nrhs, const lapack_complex_double* a,
+ lapack_int lda, const lapack_complex_double* af,
+ lapack_int ldaf, const lapack_int* ipiv,
+ const lapack_complex_double* b, lapack_int ldb,
+ lapack_complex_double* x, lapack_int ldx,
+ double* ferr, double* berr );
+
+lapack_int LAPACKE_ssyrfsx( int matrix_order, char uplo, char equed,
+ lapack_int n, lapack_int nrhs, const float* a,
+ lapack_int lda, const float* af, lapack_int ldaf,
+ const lapack_int* ipiv, const float* s,
+ const float* b, lapack_int ldb, float* x,
+ lapack_int ldx, float* rcond, float* berr,
+ lapack_int n_err_bnds, float* err_bnds_norm,
+ float* err_bnds_comp, lapack_int nparams,
+ float* params );
+lapack_int LAPACKE_dsyrfsx( int matrix_order, char uplo, char equed,
+ lapack_int n, lapack_int nrhs, const double* a,
+ lapack_int lda, const double* af, lapack_int ldaf,
+ const lapack_int* ipiv, const double* s,
+ const double* b, lapack_int ldb, double* x,
+ lapack_int ldx, double* rcond, double* berr,
+ lapack_int n_err_bnds, double* err_bnds_norm,
+ double* err_bnds_comp, lapack_int nparams,
+ double* params );
+lapack_int LAPACKE_csyrfsx( int matrix_order, char uplo, char equed,
+ lapack_int n, lapack_int nrhs,
+ const lapack_complex_float* a, lapack_int lda,
+ const lapack_complex_float* af, lapack_int ldaf,
+ const lapack_int* ipiv, const float* s,
+ const lapack_complex_float* b, lapack_int ldb,
+ lapack_complex_float* x, lapack_int ldx,
+ float* rcond, float* berr, lapack_int n_err_bnds,
+ float* err_bnds_norm, float* err_bnds_comp,
+ lapack_int nparams, float* params );
+lapack_int LAPACKE_zsyrfsx( int matrix_order, char uplo, char equed,
+ lapack_int n, lapack_int nrhs,
+ const lapack_complex_double* a, lapack_int lda,
+ const lapack_complex_double* af, lapack_int ldaf,
+ const lapack_int* ipiv, const double* s,
+ const lapack_complex_double* b, lapack_int ldb,
+ lapack_complex_double* x, lapack_int ldx,
+ double* rcond, double* berr, lapack_int n_err_bnds,
+ double* err_bnds_norm, double* err_bnds_comp,
+ lapack_int nparams, double* params );
+
+lapack_int LAPACKE_ssysv( int matrix_order, char uplo, lapack_int n,
+ lapack_int nrhs, float* a, lapack_int lda,
+ lapack_int* ipiv, float* b, lapack_int ldb );
+lapack_int LAPACKE_dsysv( int matrix_order, char uplo, lapack_int n,
+ lapack_int nrhs, double* a, lapack_int lda,
+ lapack_int* ipiv, double* b, lapack_int ldb );
+lapack_int LAPACKE_csysv( int matrix_order, char uplo, lapack_int n,
+ lapack_int nrhs, lapack_complex_float* a,
+ lapack_int lda, lapack_int* ipiv,
+ lapack_complex_float* b, lapack_int ldb );
+lapack_int LAPACKE_zsysv( int matrix_order, char uplo, lapack_int n,
+ lapack_int nrhs, lapack_complex_double* a,
+ lapack_int lda, lapack_int* ipiv,
+ lapack_complex_double* b, lapack_int ldb );
+
+lapack_int LAPACKE_ssysvx( int matrix_order, char fact, char uplo, lapack_int n,
+ lapack_int nrhs, const float* a, lapack_int lda,
+ float* af, lapack_int ldaf, lapack_int* ipiv,
+ const float* b, lapack_int ldb, float* x,
+ lapack_int ldx, float* rcond, float* ferr,
+ float* berr );
+lapack_int LAPACKE_dsysvx( int matrix_order, char fact, char uplo, lapack_int n,
+ lapack_int nrhs, const double* a, lapack_int lda,
+ double* af, lapack_int ldaf, lapack_int* ipiv,
+ const double* b, lapack_int ldb, double* x,
+ lapack_int ldx, double* rcond, double* ferr,
+ double* berr );
+lapack_int LAPACKE_csysvx( int matrix_order, char fact, char uplo, lapack_int n,
+ lapack_int nrhs, const lapack_complex_float* a,
+ lapack_int lda, lapack_complex_float* af,
+ lapack_int ldaf, lapack_int* ipiv,
+ const lapack_complex_float* b, lapack_int ldb,
+ lapack_complex_float* x, lapack_int ldx,
+ float* rcond, float* ferr, float* berr );
+lapack_int LAPACKE_zsysvx( int matrix_order, char fact, char uplo, lapack_int n,
+ lapack_int nrhs, const lapack_complex_double* a,
+ lapack_int lda, lapack_complex_double* af,
+ lapack_int ldaf, lapack_int* ipiv,
+ const lapack_complex_double* b, lapack_int ldb,
+ lapack_complex_double* x, lapack_int ldx,
+ double* rcond, double* ferr, double* berr );
+
+lapack_int LAPACKE_ssysvxx( int matrix_order, char fact, char uplo,
+ lapack_int n, lapack_int nrhs, float* a,
+ lapack_int lda, float* af, lapack_int ldaf,
+ lapack_int* ipiv, char* equed, float* s, float* b,
+ lapack_int ldb, float* x, lapack_int ldx,
+ float* rcond, float* rpvgrw, float* berr,
+ lapack_int n_err_bnds, float* err_bnds_norm,
+ float* err_bnds_comp, lapack_int nparams,
+ float* params );
+lapack_int LAPACKE_dsysvxx( int matrix_order, char fact, char uplo,
+ lapack_int n, lapack_int nrhs, double* a,
+ lapack_int lda, double* af, lapack_int ldaf,
+ lapack_int* ipiv, char* equed, double* s, double* b,
+ lapack_int ldb, double* x, lapack_int ldx,
+ double* rcond, double* rpvgrw, double* berr,
+ lapack_int n_err_bnds, double* err_bnds_norm,
+ double* err_bnds_comp, lapack_int nparams,
+ double* params );
+lapack_int LAPACKE_csysvxx( int matrix_order, char fact, char uplo,
+ lapack_int n, lapack_int nrhs,
+ lapack_complex_float* a, lapack_int lda,
+ lapack_complex_float* af, lapack_int ldaf,
+ lapack_int* ipiv, char* equed, float* s,
+ lapack_complex_float* b, lapack_int ldb,
+ lapack_complex_float* x, lapack_int ldx,
+ float* rcond, float* rpvgrw, float* berr,
+ lapack_int n_err_bnds, float* err_bnds_norm,
+ float* err_bnds_comp, lapack_int nparams,
+ float* params );
+lapack_int LAPACKE_zsysvxx( int matrix_order, char fact, char uplo,
+ lapack_int n, lapack_int nrhs,
+ lapack_complex_double* a, lapack_int lda,
+ lapack_complex_double* af, lapack_int ldaf,
+ lapack_int* ipiv, char* equed, double* s,
+ lapack_complex_double* b, lapack_int ldb,
+ lapack_complex_double* x, lapack_int ldx,
+ double* rcond, double* rpvgrw, double* berr,
+ lapack_int n_err_bnds, double* err_bnds_norm,
+ double* err_bnds_comp, lapack_int nparams,
+ double* params );
+
+lapack_int LAPACKE_ssytrd( int matrix_order, char uplo, lapack_int n, float* a,
+ lapack_int lda, float* d, float* e, float* tau );
+lapack_int LAPACKE_dsytrd( int matrix_order, char uplo, lapack_int n, double* a,
+ lapack_int lda, double* d, double* e, double* tau );
+
+lapack_int LAPACKE_ssytrf( int matrix_order, char uplo, lapack_int n, float* a,
+ lapack_int lda, lapack_int* ipiv );
+lapack_int LAPACKE_dsytrf( int matrix_order, char uplo, lapack_int n, double* a,
+ lapack_int lda, lapack_int* ipiv );
+lapack_int LAPACKE_csytrf( int matrix_order, char uplo, lapack_int n,
+ lapack_complex_float* a, lapack_int lda,
+ lapack_int* ipiv );
+lapack_int LAPACKE_zsytrf( int matrix_order, char uplo, lapack_int n,
+ lapack_complex_double* a, lapack_int lda,
+ lapack_int* ipiv );
+
+lapack_int LAPACKE_ssytri( int matrix_order, char uplo, lapack_int n, float* a,
+ lapack_int lda, const lapack_int* ipiv );
+lapack_int LAPACKE_dsytri( int matrix_order, char uplo, lapack_int n, double* a,
+ lapack_int lda, const lapack_int* ipiv );
+lapack_int LAPACKE_csytri( int matrix_order, char uplo, lapack_int n,
+ lapack_complex_float* a, lapack_int lda,
+ const lapack_int* ipiv );
+lapack_int LAPACKE_zsytri( int matrix_order, char uplo, lapack_int n,
+ lapack_complex_double* a, lapack_int lda,
+ const lapack_int* ipiv );
+
+lapack_int LAPACKE_ssytrs( int matrix_order, char uplo, lapack_int n,
+ lapack_int nrhs, const float* a, lapack_int lda,
+ const lapack_int* ipiv, float* b, lapack_int ldb );
+lapack_int LAPACKE_dsytrs( int matrix_order, char uplo, lapack_int n,
+ lapack_int nrhs, const double* a, lapack_int lda,
+ const lapack_int* ipiv, double* b, lapack_int ldb );
+lapack_int LAPACKE_csytrs( int matrix_order, char uplo, lapack_int n,
+ lapack_int nrhs, const lapack_complex_float* a,
+ lapack_int lda, const lapack_int* ipiv,
+ lapack_complex_float* b, lapack_int ldb );
+lapack_int LAPACKE_zsytrs( int matrix_order, char uplo, lapack_int n,
+ lapack_int nrhs, const lapack_complex_double* a,
+ lapack_int lda, const lapack_int* ipiv,
+ lapack_complex_double* b, lapack_int ldb );
+
+lapack_int LAPACKE_stbcon( int matrix_order, char norm, char uplo, char diag,
+ lapack_int n, lapack_int kd, const float* ab,
+ lapack_int ldab, float* rcond );
+lapack_int LAPACKE_dtbcon( int matrix_order, char norm, char uplo, char diag,
+ lapack_int n, lapack_int kd, const double* ab,
+ lapack_int ldab, double* rcond );
+lapack_int LAPACKE_ctbcon( int matrix_order, char norm, char uplo, char diag,
+ lapack_int n, lapack_int kd,
+ const lapack_complex_float* ab, lapack_int ldab,
+ float* rcond );
+lapack_int LAPACKE_ztbcon( int matrix_order, char norm, char uplo, char diag,
+ lapack_int n, lapack_int kd,
+ const lapack_complex_double* ab, lapack_int ldab,
+ double* rcond );
+
+lapack_int LAPACKE_stbrfs( int matrix_order, char uplo, char trans, char diag,
+ lapack_int n, lapack_int kd, lapack_int nrhs,
+ const float* ab, lapack_int ldab, const float* b,
+ lapack_int ldb, const float* x, lapack_int ldx,
+ float* ferr, float* berr );
+lapack_int LAPACKE_dtbrfs( int matrix_order, char uplo, char trans, char diag,
+ lapack_int n, lapack_int kd, lapack_int nrhs,
+ const double* ab, lapack_int ldab, const double* b,
+ lapack_int ldb, const double* x, lapack_int ldx,
+ double* ferr, double* berr );
+lapack_int LAPACKE_ctbrfs( int matrix_order, char uplo, char trans, char diag,
+ lapack_int n, lapack_int kd, lapack_int nrhs,
+ const lapack_complex_float* ab, lapack_int ldab,
+ const lapack_complex_float* b, lapack_int ldb,
+ const lapack_complex_float* x, lapack_int ldx,
+ float* ferr, float* berr );
+lapack_int LAPACKE_ztbrfs( int matrix_order, char uplo, char trans, char diag,
+ lapack_int n, lapack_int kd, lapack_int nrhs,
+ const lapack_complex_double* ab, lapack_int ldab,
+ const lapack_complex_double* b, lapack_int ldb,
+ const lapack_complex_double* x, lapack_int ldx,
+ double* ferr, double* berr );
+
+lapack_int LAPACKE_stbtrs( int matrix_order, char uplo, char trans, char diag,
+ lapack_int n, lapack_int kd, lapack_int nrhs,
+ const float* ab, lapack_int ldab, float* b,
+ lapack_int ldb );
+lapack_int LAPACKE_dtbtrs( int matrix_order, char uplo, char trans, char diag,
+ lapack_int n, lapack_int kd, lapack_int nrhs,
+ const double* ab, lapack_int ldab, double* b,
+ lapack_int ldb );
+lapack_int LAPACKE_ctbtrs( int matrix_order, char uplo, char trans, char diag,
+ lapack_int n, lapack_int kd, lapack_int nrhs,
+ const lapack_complex_float* ab, lapack_int ldab,
+ lapack_complex_float* b, lapack_int ldb );
+lapack_int LAPACKE_ztbtrs( int matrix_order, char uplo, char trans, char diag,
+ lapack_int n, lapack_int kd, lapack_int nrhs,
+ const lapack_complex_double* ab, lapack_int ldab,
+ lapack_complex_double* b, lapack_int ldb );
+
+lapack_int LAPACKE_stfsm( int matrix_order, char transr, char side, char uplo,
+ char trans, char diag, lapack_int m, lapack_int n,
+ float alpha, const float* a, float* b,
+ lapack_int ldb );
+lapack_int LAPACKE_dtfsm( int matrix_order, char transr, char side, char uplo,
+ char trans, char diag, lapack_int m, lapack_int n,
+ double alpha, const double* a, double* b,
+ lapack_int ldb );
+lapack_int LAPACKE_ctfsm( int matrix_order, char transr, char side, char uplo,
+ char trans, char diag, lapack_int m, lapack_int n,
+ lapack_complex_float alpha,
+ const lapack_complex_float* a,
+ lapack_complex_float* b, lapack_int ldb );
+lapack_int LAPACKE_ztfsm( int matrix_order, char transr, char side, char uplo,
+ char trans, char diag, lapack_int m, lapack_int n,
+ lapack_complex_double alpha,
+ const lapack_complex_double* a,
+ lapack_complex_double* b, lapack_int ldb );
+
+lapack_int LAPACKE_stftri( int matrix_order, char transr, char uplo, char diag,
+ lapack_int n, float* a );
+lapack_int LAPACKE_dtftri( int matrix_order, char transr, char uplo, char diag,
+ lapack_int n, double* a );
+lapack_int LAPACKE_ctftri( int matrix_order, char transr, char uplo, char diag,
+ lapack_int n, lapack_complex_float* a );
+lapack_int LAPACKE_ztftri( int matrix_order, char transr, char uplo, char diag,
+ lapack_int n, lapack_complex_double* a );
+
+lapack_int LAPACKE_stfttp( int matrix_order, char transr, char uplo,
+ lapack_int n, const float* arf, float* ap );
+lapack_int LAPACKE_dtfttp( int matrix_order, char transr, char uplo,
+ lapack_int n, const double* arf, double* ap );
+lapack_int LAPACKE_ctfttp( int matrix_order, char transr, char uplo,
+ lapack_int n, const lapack_complex_float* arf,
+ lapack_complex_float* ap );
+lapack_int LAPACKE_ztfttp( int matrix_order, char transr, char uplo,
+ lapack_int n, const lapack_complex_double* arf,
+ lapack_complex_double* ap );
+
+lapack_int LAPACKE_stfttr( int matrix_order, char transr, char uplo,
+ lapack_int n, const float* arf, float* a,
+ lapack_int lda );
+lapack_int LAPACKE_dtfttr( int matrix_order, char transr, char uplo,
+ lapack_int n, const double* arf, double* a,
+ lapack_int lda );
+lapack_int LAPACKE_ctfttr( int matrix_order, char transr, char uplo,
+ lapack_int n, const lapack_complex_float* arf,
+ lapack_complex_float* a, lapack_int lda );
+lapack_int LAPACKE_ztfttr( int matrix_order, char transr, char uplo,
+ lapack_int n, const lapack_complex_double* arf,
+ lapack_complex_double* a, lapack_int lda );
+
+lapack_int LAPACKE_stgevc( int matrix_order, char side, char howmny,
+ const lapack_logical* select, lapack_int n,
+ const float* s, lapack_int lds, const float* p,
+ lapack_int ldp, float* vl, lapack_int ldvl,
+ float* vr, lapack_int ldvr, lapack_int mm,
+ lapack_int* m );
+lapack_int LAPACKE_dtgevc( int matrix_order, char side, char howmny,
+ const lapack_logical* select, lapack_int n,
+ const double* s, lapack_int lds, const double* p,
+ lapack_int ldp, double* vl, lapack_int ldvl,
+ double* vr, lapack_int ldvr, lapack_int mm,
+ lapack_int* m );
+lapack_int LAPACKE_ctgevc( int matrix_order, char side, char howmny,
+ const lapack_logical* select, lapack_int n,
+ const lapack_complex_float* s, lapack_int lds,
+ const lapack_complex_float* p, lapack_int ldp,
+ lapack_complex_float* vl, lapack_int ldvl,
+ lapack_complex_float* vr, lapack_int ldvr,
+ lapack_int mm, lapack_int* m );
+lapack_int LAPACKE_ztgevc( int matrix_order, char side, char howmny,
+ const lapack_logical* select, lapack_int n,
+ const lapack_complex_double* s, lapack_int lds,
+ const lapack_complex_double* p, lapack_int ldp,
+ lapack_complex_double* vl, lapack_int ldvl,
+ lapack_complex_double* vr, lapack_int ldvr,
+ lapack_int mm, lapack_int* m );
+
+lapack_int LAPACKE_stgexc( int matrix_order, lapack_logical wantq,
+ lapack_logical wantz, lapack_int n, float* a,
+ lapack_int lda, float* b, lapack_int ldb, float* q,
+ lapack_int ldq, float* z, lapack_int ldz,
+ lapack_int* ifst, lapack_int* ilst );
+lapack_int LAPACKE_dtgexc( int matrix_order, lapack_logical wantq,
+ lapack_logical wantz, lapack_int n, double* a,
+ lapack_int lda, double* b, lapack_int ldb, double* q,
+ lapack_int ldq, double* z, lapack_int ldz,
+ lapack_int* ifst, lapack_int* ilst );
+lapack_int LAPACKE_ctgexc( int matrix_order, lapack_logical wantq,
+ lapack_logical wantz, lapack_int n,
+ lapack_complex_float* a, lapack_int lda,
+ lapack_complex_float* b, lapack_int ldb,
+ lapack_complex_float* q, lapack_int ldq,
+ lapack_complex_float* z, lapack_int ldz,
+ lapack_int ifst, lapack_int ilst );
+lapack_int LAPACKE_ztgexc( int matrix_order, lapack_logical wantq,
+ lapack_logical wantz, lapack_int n,
+ lapack_complex_double* a, lapack_int lda,
+ lapack_complex_double* b, lapack_int ldb,
+ lapack_complex_double* q, lapack_int ldq,
+ lapack_complex_double* z, lapack_int ldz,
+ lapack_int ifst, lapack_int ilst );
+
+lapack_int LAPACKE_stgsen( int matrix_order, lapack_int ijob,
+ lapack_logical wantq, lapack_logical wantz,
+ const lapack_logical* select, lapack_int n, float* a,
+ lapack_int lda, float* b, lapack_int ldb,
+ float* alphar, float* alphai, float* beta, float* q,
+ lapack_int ldq, float* z, lapack_int ldz,
+ lapack_int* m, float* pl, float* pr, float* dif );
+lapack_int LAPACKE_dtgsen( int matrix_order, lapack_int ijob,
+ lapack_logical wantq, lapack_logical wantz,
+ const lapack_logical* select, lapack_int n,
+ double* a, lapack_int lda, double* b, lapack_int ldb,
+ double* alphar, double* alphai, double* beta,
+ double* q, lapack_int ldq, double* z, lapack_int ldz,
+ lapack_int* m, double* pl, double* pr, double* dif );
+lapack_int LAPACKE_ctgsen( int matrix_order, lapack_int ijob,
+ lapack_logical wantq, lapack_logical wantz,
+ const lapack_logical* select, lapack_int n,
+ lapack_complex_float* a, lapack_int lda,
+ lapack_complex_float* b, lapack_int ldb,
+ lapack_complex_float* alpha,
+ lapack_complex_float* beta, lapack_complex_float* q,
+ lapack_int ldq, lapack_complex_float* z,
+ lapack_int ldz, lapack_int* m, float* pl, float* pr,
+ float* dif );
+lapack_int LAPACKE_ztgsen( int matrix_order, lapack_int ijob,
+ lapack_logical wantq, lapack_logical wantz,
+ const lapack_logical* select, lapack_int n,
+ lapack_complex_double* a, lapack_int lda,
+ lapack_complex_double* b, lapack_int ldb,
+ lapack_complex_double* alpha,
+ lapack_complex_double* beta,
+ lapack_complex_double* q, lapack_int ldq,
+ lapack_complex_double* z, lapack_int ldz,
+ lapack_int* m, double* pl, double* pr, double* dif );
+
+lapack_int LAPACKE_stgsja( int matrix_order, char jobu, char jobv, char jobq,
+ lapack_int m, lapack_int p, lapack_int n,
+ lapack_int k, lapack_int l, float* a, lapack_int lda,
+ float* b, lapack_int ldb, float tola, float tolb,
+ float* alpha, float* beta, float* u, lapack_int ldu,
+ float* v, lapack_int ldv, float* q, lapack_int ldq,
+ lapack_int* ncycle );
+lapack_int LAPACKE_dtgsja( int matrix_order, char jobu, char jobv, char jobq,
+ lapack_int m, lapack_int p, lapack_int n,
+ lapack_int k, lapack_int l, double* a,
+ lapack_int lda, double* b, lapack_int ldb,
+ double tola, double tolb, double* alpha,
+ double* beta, double* u, lapack_int ldu, double* v,
+ lapack_int ldv, double* q, lapack_int ldq,
+ lapack_int* ncycle );
+lapack_int LAPACKE_ctgsja( int matrix_order, char jobu, char jobv, char jobq,
+ lapack_int m, lapack_int p, lapack_int n,
+ lapack_int k, lapack_int l, lapack_complex_float* a,
+ lapack_int lda, lapack_complex_float* b,
+ lapack_int ldb, float tola, float tolb, float* alpha,
+ float* beta, lapack_complex_float* u, lapack_int ldu,
+ lapack_complex_float* v, lapack_int ldv,
+ lapack_complex_float* q, lapack_int ldq,
+ lapack_int* ncycle );
+lapack_int LAPACKE_ztgsja( int matrix_order, char jobu, char jobv, char jobq,
+ lapack_int m, lapack_int p, lapack_int n,
+ lapack_int k, lapack_int l, lapack_complex_double* a,
+ lapack_int lda, lapack_complex_double* b,
+ lapack_int ldb, double tola, double tolb,
+ double* alpha, double* beta,
+ lapack_complex_double* u, lapack_int ldu,
+ lapack_complex_double* v, lapack_int ldv,
+ lapack_complex_double* q, lapack_int ldq,
+ lapack_int* ncycle );
+
+lapack_int LAPACKE_stgsna( int matrix_order, char job, char howmny,
+ const lapack_logical* select, lapack_int n,
+ const float* a, lapack_int lda, const float* b,
+ lapack_int ldb, const float* vl, lapack_int ldvl,
+ const float* vr, lapack_int ldvr, float* s,
+ float* dif, lapack_int mm, lapack_int* m );
+lapack_int LAPACKE_dtgsna( int matrix_order, char job, char howmny,
+ const lapack_logical* select, lapack_int n,
+ const double* a, lapack_int lda, const double* b,
+ lapack_int ldb, const double* vl, lapack_int ldvl,
+ const double* vr, lapack_int ldvr, double* s,
+ double* dif, lapack_int mm, lapack_int* m );
+lapack_int LAPACKE_ctgsna( int matrix_order, char job, char howmny,
+ const lapack_logical* select, lapack_int n,
+ const lapack_complex_float* a, lapack_int lda,
+ const lapack_complex_float* b, lapack_int ldb,
+ const lapack_complex_float* vl, lapack_int ldvl,
+ const lapack_complex_float* vr, lapack_int ldvr,
+ float* s, float* dif, lapack_int mm, lapack_int* m );
+lapack_int LAPACKE_ztgsna( int matrix_order, char job, char howmny,
+ const lapack_logical* select, lapack_int n,
+ const lapack_complex_double* a, lapack_int lda,
+ const lapack_complex_double* b, lapack_int ldb,
+ const lapack_complex_double* vl, lapack_int ldvl,
+ const lapack_complex_double* vr, lapack_int ldvr,
+ double* s, double* dif, lapack_int mm,
+ lapack_int* m );
+
+lapack_int LAPACKE_stgsyl( int matrix_order, char trans, lapack_int ijob,
+ lapack_int m, lapack_int n, const float* a,
+ lapack_int lda, const float* b, lapack_int ldb,
+ float* c, lapack_int ldc, const float* d,
+ lapack_int ldd, const float* e, lapack_int lde,
+ float* f, lapack_int ldf, float* scale, float* dif );
+lapack_int LAPACKE_dtgsyl( int matrix_order, char trans, lapack_int ijob,
+ lapack_int m, lapack_int n, const double* a,
+ lapack_int lda, const double* b, lapack_int ldb,
+ double* c, lapack_int ldc, const double* d,
+ lapack_int ldd, const double* e, lapack_int lde,
+ double* f, lapack_int ldf, double* scale,
+ double* dif );
+lapack_int LAPACKE_ctgsyl( int matrix_order, char trans, lapack_int ijob,
+ lapack_int m, lapack_int n,
+ const lapack_complex_float* a, lapack_int lda,
+ const lapack_complex_float* b, lapack_int ldb,
+ lapack_complex_float* c, lapack_int ldc,
+ const lapack_complex_float* d, lapack_int ldd,
+ const lapack_complex_float* e, lapack_int lde,
+ lapack_complex_float* f, lapack_int ldf,
+ float* scale, float* dif );
+lapack_int LAPACKE_ztgsyl( int matrix_order, char trans, lapack_int ijob,
+ lapack_int m, lapack_int n,
+ const lapack_complex_double* a, lapack_int lda,
+ const lapack_complex_double* b, lapack_int ldb,
+ lapack_complex_double* c, lapack_int ldc,
+ const lapack_complex_double* d, lapack_int ldd,
+ const lapack_complex_double* e, lapack_int lde,
+ lapack_complex_double* f, lapack_int ldf,
+ double* scale, double* dif );
+
+lapack_int LAPACKE_stpcon( int matrix_order, char norm, char uplo, char diag,
+ lapack_int n, const float* ap, float* rcond );
+lapack_int LAPACKE_dtpcon( int matrix_order, char norm, char uplo, char diag,
+ lapack_int n, const double* ap, double* rcond );
+lapack_int LAPACKE_ctpcon( int matrix_order, char norm, char uplo, char diag,
+ lapack_int n, const lapack_complex_float* ap,
+ float* rcond );
+lapack_int LAPACKE_ztpcon( int matrix_order, char norm, char uplo, char diag,
+ lapack_int n, const lapack_complex_double* ap,
+ double* rcond );
+
+lapack_int LAPACKE_stprfs( int matrix_order, char uplo, char trans, char diag,
+ lapack_int n, lapack_int nrhs, const float* ap,
+ const float* b, lapack_int ldb, const float* x,
+ lapack_int ldx, float* ferr, float* berr );
+lapack_int LAPACKE_dtprfs( int matrix_order, char uplo, char trans, char diag,
+ lapack_int n, lapack_int nrhs, const double* ap,
+ const double* b, lapack_int ldb, const double* x,
+ lapack_int ldx, double* ferr, double* berr );
+lapack_int LAPACKE_ctprfs( int matrix_order, char uplo, char trans, char diag,
+ lapack_int n, lapack_int nrhs,
+ const lapack_complex_float* ap,
+ const lapack_complex_float* b, lapack_int ldb,
+ const lapack_complex_float* x, lapack_int ldx,
+ float* ferr, float* berr );
+lapack_int LAPACKE_ztprfs( int matrix_order, char uplo, char trans, char diag,
+ lapack_int n, lapack_int nrhs,
+ const lapack_complex_double* ap,
+ const lapack_complex_double* b, lapack_int ldb,
+ const lapack_complex_double* x, lapack_int ldx,
+ double* ferr, double* berr );
+
+lapack_int LAPACKE_stptri( int matrix_order, char uplo, char diag, lapack_int n,
+ float* ap );
+lapack_int LAPACKE_dtptri( int matrix_order, char uplo, char diag, lapack_int n,
+ double* ap );
+lapack_int LAPACKE_ctptri( int matrix_order, char uplo, char diag, lapack_int n,
+ lapack_complex_float* ap );
+lapack_int LAPACKE_ztptri( int matrix_order, char uplo, char diag, lapack_int n,
+ lapack_complex_double* ap );
+
+lapack_int LAPACKE_stptrs( int matrix_order, char uplo, char trans, char diag,
+ lapack_int n, lapack_int nrhs, const float* ap,
+ float* b, lapack_int ldb );
+lapack_int LAPACKE_dtptrs( int matrix_order, char uplo, char trans, char diag,
+ lapack_int n, lapack_int nrhs, const double* ap,
+ double* b, lapack_int ldb );
+lapack_int LAPACKE_ctptrs( int matrix_order, char uplo, char trans, char diag,
+ lapack_int n, lapack_int nrhs,
+ const lapack_complex_float* ap,
+ lapack_complex_float* b, lapack_int ldb );
+lapack_int LAPACKE_ztptrs( int matrix_order, char uplo, char trans, char diag,
+ lapack_int n, lapack_int nrhs,
+ const lapack_complex_double* ap,
+ lapack_complex_double* b, lapack_int ldb );
+
+lapack_int LAPACKE_stpttf( int matrix_order, char transr, char uplo,
+ lapack_int n, const float* ap, float* arf );
+lapack_int LAPACKE_dtpttf( int matrix_order, char transr, char uplo,
+ lapack_int n, const double* ap, double* arf );
+lapack_int LAPACKE_ctpttf( int matrix_order, char transr, char uplo,
+ lapack_int n, const lapack_complex_float* ap,
+ lapack_complex_float* arf );
+lapack_int LAPACKE_ztpttf( int matrix_order, char transr, char uplo,
+ lapack_int n, const lapack_complex_double* ap,
+ lapack_complex_double* arf );
+
+lapack_int LAPACKE_stpttr( int matrix_order, char uplo, lapack_int n,
+ const float* ap, float* a, lapack_int lda );
+lapack_int LAPACKE_dtpttr( int matrix_order, char uplo, lapack_int n,
+ const double* ap, double* a, lapack_int lda );
+lapack_int LAPACKE_ctpttr( int matrix_order, char uplo, lapack_int n,
+ const lapack_complex_float* ap,
+ lapack_complex_float* a, lapack_int lda );
+lapack_int LAPACKE_ztpttr( int matrix_order, char uplo, lapack_int n,
+ const lapack_complex_double* ap,
+ lapack_complex_double* a, lapack_int lda );
+
+lapack_int LAPACKE_strcon( int matrix_order, char norm, char uplo, char diag,
+ lapack_int n, const float* a, lapack_int lda,
+ float* rcond );
+lapack_int LAPACKE_dtrcon( int matrix_order, char norm, char uplo, char diag,
+ lapack_int n, const double* a, lapack_int lda,
+ double* rcond );
+lapack_int LAPACKE_ctrcon( int matrix_order, char norm, char uplo, char diag,
+ lapack_int n, const lapack_complex_float* a,
+ lapack_int lda, float* rcond );
+lapack_int LAPACKE_ztrcon( int matrix_order, char norm, char uplo, char diag,
+ lapack_int n, const lapack_complex_double* a,
+ lapack_int lda, double* rcond );
+
+lapack_int LAPACKE_strevc( int matrix_order, char side, char howmny,
+ lapack_logical* select, lapack_int n, const float* t,
+ lapack_int ldt, float* vl, lapack_int ldvl,
+ float* vr, lapack_int ldvr, lapack_int mm,
+ lapack_int* m );
+lapack_int LAPACKE_dtrevc( int matrix_order, char side, char howmny,
+ lapack_logical* select, lapack_int n,
+ const double* t, lapack_int ldt, double* vl,
+ lapack_int ldvl, double* vr, lapack_int ldvr,
+ lapack_int mm, lapack_int* m );
+lapack_int LAPACKE_ctrevc( int matrix_order, char side, char howmny,
+ const lapack_logical* select, lapack_int n,
+ lapack_complex_float* t, lapack_int ldt,
+ lapack_complex_float* vl, lapack_int ldvl,
+ lapack_complex_float* vr, lapack_int ldvr,
+ lapack_int mm, lapack_int* m );
+lapack_int LAPACKE_ztrevc( int matrix_order, char side, char howmny,
+ const lapack_logical* select, lapack_int n,
+ lapack_complex_double* t, lapack_int ldt,
+ lapack_complex_double* vl, lapack_int ldvl,
+ lapack_complex_double* vr, lapack_int ldvr,
+ lapack_int mm, lapack_int* m );
+
+lapack_int LAPACKE_strexc( int matrix_order, char compq, lapack_int n, float* t,
+ lapack_int ldt, float* q, lapack_int ldq,
+ lapack_int* ifst, lapack_int* ilst );
+lapack_int LAPACKE_dtrexc( int matrix_order, char compq, lapack_int n,
+ double* t, lapack_int ldt, double* q, lapack_int ldq,
+ lapack_int* ifst, lapack_int* ilst );
+lapack_int LAPACKE_ctrexc( int matrix_order, char compq, lapack_int n,
+ lapack_complex_float* t, lapack_int ldt,
+ lapack_complex_float* q, lapack_int ldq,
+ lapack_int ifst, lapack_int ilst );
+lapack_int LAPACKE_ztrexc( int matrix_order, char compq, lapack_int n,
+ lapack_complex_double* t, lapack_int ldt,
+ lapack_complex_double* q, lapack_int ldq,
+ lapack_int ifst, lapack_int ilst );
+
+lapack_int LAPACKE_strrfs( int matrix_order, char uplo, char trans, char diag,
+ lapack_int n, lapack_int nrhs, const float* a,
+ lapack_int lda, const float* b, lapack_int ldb,
+ const float* x, lapack_int ldx, float* ferr,
+ float* berr );
+lapack_int LAPACKE_dtrrfs( int matrix_order, char uplo, char trans, char diag,
+ lapack_int n, lapack_int nrhs, const double* a,
+ lapack_int lda, const double* b, lapack_int ldb,
+ const double* x, lapack_int ldx, double* ferr,
+ double* berr );
+lapack_int LAPACKE_ctrrfs( int matrix_order, char uplo, char trans, char diag,
+ lapack_int n, lapack_int nrhs,
+ const lapack_complex_float* a, lapack_int lda,
+ const lapack_complex_float* b, lapack_int ldb,
+ const lapack_complex_float* x, lapack_int ldx,
+ float* ferr, float* berr );
+lapack_int LAPACKE_ztrrfs( int matrix_order, char uplo, char trans, char diag,
+ lapack_int n, lapack_int nrhs,
+ const lapack_complex_double* a, lapack_int lda,
+ const lapack_complex_double* b, lapack_int ldb,
+ const lapack_complex_double* x, lapack_int ldx,
+ double* ferr, double* berr );
+
+lapack_int LAPACKE_strsen( int matrix_order, char job, char compq,
+ const lapack_logical* select, lapack_int n, float* t,
+ lapack_int ldt, float* q, lapack_int ldq, float* wr,
+ float* wi, lapack_int* m, float* s, float* sep );
+lapack_int LAPACKE_dtrsen( int matrix_order, char job, char compq,
+ const lapack_logical* select, lapack_int n,
+ double* t, lapack_int ldt, double* q, lapack_int ldq,
+ double* wr, double* wi, lapack_int* m, double* s,
+ double* sep );
+lapack_int LAPACKE_ctrsen( int matrix_order, char job, char compq,
+ const lapack_logical* select, lapack_int n,
+ lapack_complex_float* t, lapack_int ldt,
+ lapack_complex_float* q, lapack_int ldq,
+ lapack_complex_float* w, lapack_int* m, float* s,
+ float* sep );
+lapack_int LAPACKE_ztrsen( int matrix_order, char job, char compq,
+ const lapack_logical* select, lapack_int n,
+ lapack_complex_double* t, lapack_int ldt,
+ lapack_complex_double* q, lapack_int ldq,
+ lapack_complex_double* w, lapack_int* m, double* s,
+ double* sep );
+
+lapack_int LAPACKE_strsna( int matrix_order, char job, char howmny,
+ const lapack_logical* select, lapack_int n,
+ const float* t, lapack_int ldt, const float* vl,
+ lapack_int ldvl, const float* vr, lapack_int ldvr,
+ float* s, float* sep, lapack_int mm, lapack_int* m );
+lapack_int LAPACKE_dtrsna( int matrix_order, char job, char howmny,
+ const lapack_logical* select, lapack_int n,
+ const double* t, lapack_int ldt, const double* vl,
+ lapack_int ldvl, const double* vr, lapack_int ldvr,
+ double* s, double* sep, lapack_int mm,
+ lapack_int* m );
+lapack_int LAPACKE_ctrsna( int matrix_order, char job, char howmny,
+ const lapack_logical* select, lapack_int n,
+ const lapack_complex_float* t, lapack_int ldt,
+ const lapack_complex_float* vl, lapack_int ldvl,
+ const lapack_complex_float* vr, lapack_int ldvr,
+ float* s, float* sep, lapack_int mm, lapack_int* m );
+lapack_int LAPACKE_ztrsna( int matrix_order, char job, char howmny,
+ const lapack_logical* select, lapack_int n,
+ const lapack_complex_double* t, lapack_int ldt,
+ const lapack_complex_double* vl, lapack_int ldvl,
+ const lapack_complex_double* vr, lapack_int ldvr,
+ double* s, double* sep, lapack_int mm,
+ lapack_int* m );
+
+lapack_int LAPACKE_strsyl( int matrix_order, char trana, char tranb,
+ lapack_int isgn, lapack_int m, lapack_int n,
+ const float* a, lapack_int lda, const float* b,
+ lapack_int ldb, float* c, lapack_int ldc,
+ float* scale );
+lapack_int LAPACKE_dtrsyl( int matrix_order, char trana, char tranb,
+ lapack_int isgn, lapack_int m, lapack_int n,
+ const double* a, lapack_int lda, const double* b,
+ lapack_int ldb, double* c, lapack_int ldc,
+ double* scale );
+lapack_int LAPACKE_ctrsyl( int matrix_order, char trana, char tranb,
+ lapack_int isgn, lapack_int m, lapack_int n,
+ const lapack_complex_float* a, lapack_int lda,
+ const lapack_complex_float* b, lapack_int ldb,
+ lapack_complex_float* c, lapack_int ldc,
+ float* scale );
+lapack_int LAPACKE_ztrsyl( int matrix_order, char trana, char tranb,
+ lapack_int isgn, lapack_int m, lapack_int n,
+ const lapack_complex_double* a, lapack_int lda,
+ const lapack_complex_double* b, lapack_int ldb,
+ lapack_complex_double* c, lapack_int ldc,
+ double* scale );
+
+lapack_int LAPACKE_strtri( int matrix_order, char uplo, char diag, lapack_int n,
+ float* a, lapack_int lda );
+lapack_int LAPACKE_dtrtri( int matrix_order, char uplo, char diag, lapack_int n,
+ double* a, lapack_int lda );
+lapack_int LAPACKE_ctrtri( int matrix_order, char uplo, char diag, lapack_int n,
+ lapack_complex_float* a, lapack_int lda );
+lapack_int LAPACKE_ztrtri( int matrix_order, char uplo, char diag, lapack_int n,
+ lapack_complex_double* a, lapack_int lda );
+
+lapack_int LAPACKE_strtrs( int matrix_order, char uplo, char trans, char diag,
+ lapack_int n, lapack_int nrhs, const float* a,
+ lapack_int lda, float* b, lapack_int ldb );
+lapack_int LAPACKE_dtrtrs( int matrix_order, char uplo, char trans, char diag,
+ lapack_int n, lapack_int nrhs, const double* a,
+ lapack_int lda, double* b, lapack_int ldb );
+lapack_int LAPACKE_ctrtrs( int matrix_order, char uplo, char trans, char diag,
+ lapack_int n, lapack_int nrhs,
+ const lapack_complex_float* a, lapack_int lda,
+ lapack_complex_float* b, lapack_int ldb );
+lapack_int LAPACKE_ztrtrs( int matrix_order, char uplo, char trans, char diag,
+ lapack_int n, lapack_int nrhs,
+ const lapack_complex_double* a, lapack_int lda,
+ lapack_complex_double* b, lapack_int ldb );
+
+lapack_int LAPACKE_strttf( int matrix_order, char transr, char uplo,
+ lapack_int n, const float* a, lapack_int lda,
+ float* arf );
+lapack_int LAPACKE_dtrttf( int matrix_order, char transr, char uplo,
+ lapack_int n, const double* a, lapack_int lda,
+ double* arf );
+lapack_int LAPACKE_ctrttf( int matrix_order, char transr, char uplo,
+ lapack_int n, const lapack_complex_float* a,
+ lapack_int lda, lapack_complex_float* arf );
+lapack_int LAPACKE_ztrttf( int matrix_order, char transr, char uplo,
+ lapack_int n, const lapack_complex_double* a,
+ lapack_int lda, lapack_complex_double* arf );
+
+lapack_int LAPACKE_strttp( int matrix_order, char uplo, lapack_int n,
+ const float* a, lapack_int lda, float* ap );
+lapack_int LAPACKE_dtrttp( int matrix_order, char uplo, lapack_int n,
+ const double* a, lapack_int lda, double* ap );
+lapack_int LAPACKE_ctrttp( int matrix_order, char uplo, lapack_int n,
+ const lapack_complex_float* a, lapack_int lda,
+ lapack_complex_float* ap );
+lapack_int LAPACKE_ztrttp( int matrix_order, char uplo, lapack_int n,
+ const lapack_complex_double* a, lapack_int lda,
+ lapack_complex_double* ap );
+
+lapack_int LAPACKE_stzrzf( int matrix_order, lapack_int m, lapack_int n,
+ float* a, lapack_int lda, float* tau );
+lapack_int LAPACKE_dtzrzf( int matrix_order, lapack_int m, lapack_int n,
+ double* a, lapack_int lda, double* tau );
+lapack_int LAPACKE_ctzrzf( int matrix_order, lapack_int m, lapack_int n,
+ lapack_complex_float* a, lapack_int lda,
+ lapack_complex_float* tau );
+lapack_int LAPACKE_ztzrzf( int matrix_order, lapack_int m, lapack_int n,
+ lapack_complex_double* a, lapack_int lda,
+ lapack_complex_double* tau );
+
+lapack_int LAPACKE_cungbr( int matrix_order, char vect, lapack_int m,
+ lapack_int n, lapack_int k, lapack_complex_float* a,
+ lapack_int lda, const lapack_complex_float* tau );
+lapack_int LAPACKE_zungbr( int matrix_order, char vect, lapack_int m,
+ lapack_int n, lapack_int k, lapack_complex_double* a,
+ lapack_int lda, const lapack_complex_double* tau );
+
+lapack_int LAPACKE_cunghr( int matrix_order, lapack_int n, lapack_int ilo,
+ lapack_int ihi, lapack_complex_float* a,
+ lapack_int lda, const lapack_complex_float* tau );
+lapack_int LAPACKE_zunghr( int matrix_order, lapack_int n, lapack_int ilo,
+ lapack_int ihi, lapack_complex_double* a,
+ lapack_int lda, const lapack_complex_double* tau );
+
+lapack_int LAPACKE_cunglq( int matrix_order, lapack_int m, lapack_int n,
+ lapack_int k, lapack_complex_float* a,
+ lapack_int lda, const lapack_complex_float* tau );
+lapack_int LAPACKE_zunglq( int matrix_order, lapack_int m, lapack_int n,
+ lapack_int k, lapack_complex_double* a,
+ lapack_int lda, const lapack_complex_double* tau );
+
+lapack_int LAPACKE_cungql( int matrix_order, lapack_int m, lapack_int n,
+ lapack_int k, lapack_complex_float* a,
+ lapack_int lda, const lapack_complex_float* tau );
+lapack_int LAPACKE_zungql( int matrix_order, lapack_int m, lapack_int n,
+ lapack_int k, lapack_complex_double* a,
+ lapack_int lda, const lapack_complex_double* tau );
+
+lapack_int LAPACKE_cungqr( int matrix_order, lapack_int m, lapack_int n,
+ lapack_int k, lapack_complex_float* a,
+ lapack_int lda, const lapack_complex_float* tau );
+lapack_int LAPACKE_zungqr( int matrix_order, lapack_int m, lapack_int n,
+ lapack_int k, lapack_complex_double* a,
+ lapack_int lda, const lapack_complex_double* tau );
+
+lapack_int LAPACKE_cungrq( int matrix_order, lapack_int m, lapack_int n,
+ lapack_int k, lapack_complex_float* a,
+ lapack_int lda, const lapack_complex_float* tau );
+lapack_int LAPACKE_zungrq( int matrix_order, lapack_int m, lapack_int n,
+ lapack_int k, lapack_complex_double* a,
+ lapack_int lda, const lapack_complex_double* tau );
+
+lapack_int LAPACKE_cungtr( int matrix_order, char uplo, lapack_int n,
+ lapack_complex_float* a, lapack_int lda,
+ const lapack_complex_float* tau );
+lapack_int LAPACKE_zungtr( int matrix_order, char uplo, lapack_int n,
+ lapack_complex_double* a, lapack_int lda,
+ const lapack_complex_double* tau );
+
+lapack_int LAPACKE_cunmbr( int matrix_order, char vect, char side, char trans,
+ lapack_int m, lapack_int n, lapack_int k,
+ const lapack_complex_float* a, lapack_int lda,
+ const lapack_complex_float* tau,
+ lapack_complex_float* c, lapack_int ldc );
+lapack_int LAPACKE_zunmbr( int matrix_order, char vect, char side, char trans,
+ lapack_int m, lapack_int n, lapack_int k,
+ const lapack_complex_double* a, lapack_int lda,
+ const lapack_complex_double* tau,
+ lapack_complex_double* c, lapack_int ldc );
+
+lapack_int LAPACKE_cunmhr( int matrix_order, char side, char trans,
+ lapack_int m, lapack_int n, lapack_int ilo,
+ lapack_int ihi, const lapack_complex_float* a,
+ lapack_int lda, const lapack_complex_float* tau,
+ lapack_complex_float* c, lapack_int ldc );
+lapack_int LAPACKE_zunmhr( int matrix_order, char side, char trans,
+ lapack_int m, lapack_int n, lapack_int ilo,
+ lapack_int ihi, const lapack_complex_double* a,
+ lapack_int lda, const lapack_complex_double* tau,
+ lapack_complex_double* c, lapack_int ldc );
+
+lapack_int LAPACKE_cunmlq( int matrix_order, char side, char trans,
+ lapack_int m, lapack_int n, lapack_int k,
+ const lapack_complex_float* a, lapack_int lda,
+ const lapack_complex_float* tau,
+ lapack_complex_float* c, lapack_int ldc );
+lapack_int LAPACKE_zunmlq( int matrix_order, char side, char trans,
+ lapack_int m, lapack_int n, lapack_int k,
+ const lapack_complex_double* a, lapack_int lda,
+ const lapack_complex_double* tau,
+ lapack_complex_double* c, lapack_int ldc );
+
+lapack_int LAPACKE_cunmql( int matrix_order, char side, char trans,
+ lapack_int m, lapack_int n, lapack_int k,
+ const lapack_complex_float* a, lapack_int lda,
+ const lapack_complex_float* tau,
+ lapack_complex_float* c, lapack_int ldc );
+lapack_int LAPACKE_zunmql( int matrix_order, char side, char trans,
+ lapack_int m, lapack_int n, lapack_int k,
+ const lapack_complex_double* a, lapack_int lda,
+ const lapack_complex_double* tau,
+ lapack_complex_double* c, lapack_int ldc );
+
+lapack_int LAPACKE_cunmqr( int matrix_order, char side, char trans,
+ lapack_int m, lapack_int n, lapack_int k,
+ const lapack_complex_float* a, lapack_int lda,
+ const lapack_complex_float* tau,
+ lapack_complex_float* c, lapack_int ldc );
+lapack_int LAPACKE_zunmqr( int matrix_order, char side, char trans,
+ lapack_int m, lapack_int n, lapack_int k,
+ const lapack_complex_double* a, lapack_int lda,
+ const lapack_complex_double* tau,
+ lapack_complex_double* c, lapack_int ldc );
+
+lapack_int LAPACKE_cunmrq( int matrix_order, char side, char trans,
+ lapack_int m, lapack_int n, lapack_int k,
+ const lapack_complex_float* a, lapack_int lda,
+ const lapack_complex_float* tau,
+ lapack_complex_float* c, lapack_int ldc );
+lapack_int LAPACKE_zunmrq( int matrix_order, char side, char trans,
+ lapack_int m, lapack_int n, lapack_int k,
+ const lapack_complex_double* a, lapack_int lda,
+ const lapack_complex_double* tau,
+ lapack_complex_double* c, lapack_int ldc );
+
+lapack_int LAPACKE_cunmrz( int matrix_order, char side, char trans,
+ lapack_int m, lapack_int n, lapack_int k,
+ lapack_int l, const lapack_complex_float* a,
+ lapack_int lda, const lapack_complex_float* tau,
+ lapack_complex_float* c, lapack_int ldc );
+lapack_int LAPACKE_zunmrz( int matrix_order, char side, char trans,
+ lapack_int m, lapack_int n, lapack_int k,
+ lapack_int l, const lapack_complex_double* a,
+ lapack_int lda, const lapack_complex_double* tau,
+ lapack_complex_double* c, lapack_int ldc );
+
+lapack_int LAPACKE_cunmtr( int matrix_order, char side, char uplo, char trans,
+ lapack_int m, lapack_int n,
+ const lapack_complex_float* a, lapack_int lda,
+ const lapack_complex_float* tau,
+ lapack_complex_float* c, lapack_int ldc );
+lapack_int LAPACKE_zunmtr( int matrix_order, char side, char uplo, char trans,
+ lapack_int m, lapack_int n,
+ const lapack_complex_double* a, lapack_int lda,
+ const lapack_complex_double* tau,
+ lapack_complex_double* c, lapack_int ldc );
+
+lapack_int LAPACKE_cupgtr( int matrix_order, char uplo, lapack_int n,
+ const lapack_complex_float* ap,
+ const lapack_complex_float* tau,
+ lapack_complex_float* q, lapack_int ldq );
+lapack_int LAPACKE_zupgtr( int matrix_order, char uplo, lapack_int n,
+ const lapack_complex_double* ap,
+ const lapack_complex_double* tau,
+ lapack_complex_double* q, lapack_int ldq );
+
+lapack_int LAPACKE_cupmtr( int matrix_order, char side, char uplo, char trans,
+ lapack_int m, lapack_int n,
+ const lapack_complex_float* ap,
+ const lapack_complex_float* tau,
+ lapack_complex_float* c, lapack_int ldc );
+lapack_int LAPACKE_zupmtr( int matrix_order, char side, char uplo, char trans,
+ lapack_int m, lapack_int n,
+ const lapack_complex_double* ap,
+ const lapack_complex_double* tau,
+ lapack_complex_double* c, lapack_int ldc );
+
+lapack_int LAPACKE_sbdsdc_work( int matrix_order, char uplo, char compq,
+ lapack_int n, float* d, float* e, float* u,
+ lapack_int ldu, float* vt, lapack_int ldvt,
+ float* q, lapack_int* iq, float* work,
+ lapack_int* iwork );
+lapack_int LAPACKE_dbdsdc_work( int matrix_order, char uplo, char compq,
+ lapack_int n, double* d, double* e, double* u,
+ lapack_int ldu, double* vt, lapack_int ldvt,
+ double* q, lapack_int* iq, double* work,
+ lapack_int* iwork );
+
+lapack_int LAPACKE_sbdsqr_work( int matrix_order, char uplo, lapack_int n,
+ lapack_int ncvt, lapack_int nru, lapack_int ncc,
+ float* d, float* e, float* vt, lapack_int ldvt,
+ float* u, lapack_int ldu, float* c,
+ lapack_int ldc, float* work );
+lapack_int LAPACKE_dbdsqr_work( int matrix_order, char uplo, lapack_int n,
+ lapack_int ncvt, lapack_int nru, lapack_int ncc,
+ double* d, double* e, double* vt,
+ lapack_int ldvt, double* u, lapack_int ldu,
+ double* c, lapack_int ldc, double* work );
+lapack_int LAPACKE_cbdsqr_work( int matrix_order, char uplo, lapack_int n,
+ lapack_int ncvt, lapack_int nru, lapack_int ncc,
+ float* d, float* e, lapack_complex_float* vt,
+ lapack_int ldvt, lapack_complex_float* u,
+ lapack_int ldu, lapack_complex_float* c,
+ lapack_int ldc, float* work );
+lapack_int LAPACKE_zbdsqr_work( int matrix_order, char uplo, lapack_int n,
+ lapack_int ncvt, lapack_int nru, lapack_int ncc,
+ double* d, double* e, lapack_complex_double* vt,
+ lapack_int ldvt, lapack_complex_double* u,
+ lapack_int ldu, lapack_complex_double* c,
+ lapack_int ldc, double* work );
+
+lapack_int LAPACKE_sdisna_work( char job, lapack_int m, lapack_int n,
+ const float* d, float* sep );
+lapack_int LAPACKE_ddisna_work( char job, lapack_int m, lapack_int n,
+ const double* d, double* sep );
+
+lapack_int LAPACKE_sgbbrd_work( int matrix_order, char vect, lapack_int m,
+ lapack_int n, lapack_int ncc, lapack_int kl,
+ lapack_int ku, float* ab, lapack_int ldab,
+ float* d, float* e, float* q, lapack_int ldq,
+ float* pt, lapack_int ldpt, float* c,
+ lapack_int ldc, float* work );
+lapack_int LAPACKE_dgbbrd_work( int matrix_order, char vect, lapack_int m,
+ lapack_int n, lapack_int ncc, lapack_int kl,
+ lapack_int ku, double* ab, lapack_int ldab,
+ double* d, double* e, double* q, lapack_int ldq,
+ double* pt, lapack_int ldpt, double* c,
+ lapack_int ldc, double* work );
+lapack_int LAPACKE_cgbbrd_work( int matrix_order, char vect, lapack_int m,
+ lapack_int n, lapack_int ncc, lapack_int kl,
+ lapack_int ku, lapack_complex_float* ab,
+ lapack_int ldab, float* d, float* e,
+ lapack_complex_float* q, lapack_int ldq,
+ lapack_complex_float* pt, lapack_int ldpt,
+ lapack_complex_float* c, lapack_int ldc,
+ lapack_complex_float* work, float* rwork );
+lapack_int LAPACKE_zgbbrd_work( int matrix_order, char vect, lapack_int m,
+ lapack_int n, lapack_int ncc, lapack_int kl,
+ lapack_int ku, lapack_complex_double* ab,
+ lapack_int ldab, double* d, double* e,
+ lapack_complex_double* q, lapack_int ldq,
+ lapack_complex_double* pt, lapack_int ldpt,
+ lapack_complex_double* c, lapack_int ldc,
+ lapack_complex_double* work, double* rwork );
+
+lapack_int LAPACKE_sgbcon_work( int matrix_order, char norm, lapack_int n,
+ lapack_int kl, lapack_int ku, const float* ab,
+ lapack_int ldab, const lapack_int* ipiv,
+ float anorm, float* rcond, float* work,
+ lapack_int* iwork );
+lapack_int LAPACKE_dgbcon_work( int matrix_order, char norm, lapack_int n,
+ lapack_int kl, lapack_int ku, const double* ab,
+ lapack_int ldab, const lapack_int* ipiv,
+ double anorm, double* rcond, double* work,
+ lapack_int* iwork );
+lapack_int LAPACKE_cgbcon_work( int matrix_order, char norm, lapack_int n,
+ lapack_int kl, lapack_int ku,
+ const lapack_complex_float* ab, lapack_int ldab,
+ const lapack_int* ipiv, float anorm,
+ float* rcond, lapack_complex_float* work,
+ float* rwork );
+lapack_int LAPACKE_zgbcon_work( int matrix_order, char norm, lapack_int n,
+ lapack_int kl, lapack_int ku,
+ const lapack_complex_double* ab,
+ lapack_int ldab, const lapack_int* ipiv,
+ double anorm, double* rcond,
+ lapack_complex_double* work, double* rwork );
+
+lapack_int LAPACKE_sgbequ_work( int matrix_order, lapack_int m, lapack_int n,
+ lapack_int kl, lapack_int ku, const float* ab,
+ lapack_int ldab, float* r, float* c,
+ float* rowcnd, float* colcnd, float* amax );
+lapack_int LAPACKE_dgbequ_work( int matrix_order, lapack_int m, lapack_int n,
+ lapack_int kl, lapack_int ku, const double* ab,
+ lapack_int ldab, double* r, double* c,
+ double* rowcnd, double* colcnd, double* amax );
+lapack_int LAPACKE_cgbequ_work( int matrix_order, lapack_int m, lapack_int n,
+ lapack_int kl, lapack_int ku,
+ const lapack_complex_float* ab, lapack_int ldab,
+ float* r, float* c, float* rowcnd,
+ float* colcnd, float* amax );
+lapack_int LAPACKE_zgbequ_work( int matrix_order, lapack_int m, lapack_int n,
+ lapack_int kl, lapack_int ku,
+ const lapack_complex_double* ab,
+ lapack_int ldab, double* r, double* c,
+ double* rowcnd, double* colcnd, double* amax );
+
+lapack_int LAPACKE_sgbequb_work( int matrix_order, lapack_int m, lapack_int n,
+ lapack_int kl, lapack_int ku, const float* ab,
+ lapack_int ldab, float* r, float* c,
+ float* rowcnd, float* colcnd, float* amax );
+lapack_int LAPACKE_dgbequb_work( int matrix_order, lapack_int m, lapack_int n,
+ lapack_int kl, lapack_int ku, const double* ab,
+ lapack_int ldab, double* r, double* c,
+ double* rowcnd, double* colcnd, double* amax );
+lapack_int LAPACKE_cgbequb_work( int matrix_order, lapack_int m, lapack_int n,
+ lapack_int kl, lapack_int ku,
+ const lapack_complex_float* ab,
+ lapack_int ldab, float* r, float* c,
+ float* rowcnd, float* colcnd, float* amax );
+lapack_int LAPACKE_zgbequb_work( int matrix_order, lapack_int m, lapack_int n,
+ lapack_int kl, lapack_int ku,
+ const lapack_complex_double* ab,
+ lapack_int ldab, double* r, double* c,
+ double* rowcnd, double* colcnd, double* amax );
+
+lapack_int LAPACKE_sgbrfs_work( int matrix_order, char trans, lapack_int n,
+ lapack_int kl, lapack_int ku, lapack_int nrhs,
+ const float* ab, lapack_int ldab,
+ const float* afb, lapack_int ldafb,
+ const lapack_int* ipiv, const float* b,
+ lapack_int ldb, float* x, lapack_int ldx,
+ float* ferr, float* berr, float* work,
+ lapack_int* iwork );
+lapack_int LAPACKE_dgbrfs_work( int matrix_order, char trans, lapack_int n,
+ lapack_int kl, lapack_int ku, lapack_int nrhs,
+ const double* ab, lapack_int ldab,
+ const double* afb, lapack_int ldafb,
+ const lapack_int* ipiv, const double* b,
+ lapack_int ldb, double* x, lapack_int ldx,
+ double* ferr, double* berr, double* work,
+ lapack_int* iwork );
+lapack_int LAPACKE_cgbrfs_work( int matrix_order, char trans, lapack_int n,
+ lapack_int kl, lapack_int ku, lapack_int nrhs,
+ const lapack_complex_float* ab, lapack_int ldab,
+ const lapack_complex_float* afb,
+ lapack_int ldafb, const lapack_int* ipiv,
+ const lapack_complex_float* b, lapack_int ldb,
+ lapack_complex_float* x, lapack_int ldx,
+ float* ferr, float* berr,
+ lapack_complex_float* work, float* rwork );
+lapack_int LAPACKE_zgbrfs_work( int matrix_order, char trans, lapack_int n,
+ lapack_int kl, lapack_int ku, lapack_int nrhs,
+ const lapack_complex_double* ab,
+ lapack_int ldab,
+ const lapack_complex_double* afb,
+ lapack_int ldafb, const lapack_int* ipiv,
+ const lapack_complex_double* b, lapack_int ldb,
+ lapack_complex_double* x, lapack_int ldx,
+ double* ferr, double* berr,
+ lapack_complex_double* work, double* rwork );
+
+lapack_int LAPACKE_sgbrfsx_work( int matrix_order, char trans, char equed,
+ lapack_int n, lapack_int kl, lapack_int ku,
+ lapack_int nrhs, const float* ab,
+ lapack_int ldab, const float* afb,
+ lapack_int ldafb, const lapack_int* ipiv,
+ const float* r, const float* c, const float* b,
+ lapack_int ldb, float* x, lapack_int ldx,
+ float* rcond, float* berr,
+ lapack_int n_err_bnds, float* err_bnds_norm,
+ float* err_bnds_comp, lapack_int nparams,
+ float* params, float* work,
+ lapack_int* iwork );
+lapack_int LAPACKE_dgbrfsx_work( int matrix_order, char trans, char equed,
+ lapack_int n, lapack_int kl, lapack_int ku,
+ lapack_int nrhs, const double* ab,
+ lapack_int ldab, const double* afb,
+ lapack_int ldafb, const lapack_int* ipiv,
+ const double* r, const double* c,
+ const double* b, lapack_int ldb, double* x,
+ lapack_int ldx, double* rcond, double* berr,
+ lapack_int n_err_bnds, double* err_bnds_norm,
+ double* err_bnds_comp, lapack_int nparams,
+ double* params, double* work,
+ lapack_int* iwork );
+lapack_int LAPACKE_cgbrfsx_work( int matrix_order, char trans, char equed,
+ lapack_int n, lapack_int kl, lapack_int ku,
+ lapack_int nrhs,
+ const lapack_complex_float* ab,
+ lapack_int ldab,
+ const lapack_complex_float* afb,
+ lapack_int ldafb, const lapack_int* ipiv,
+ const float* r, const float* c,
+ const lapack_complex_float* b, lapack_int ldb,
+ lapack_complex_float* x, lapack_int ldx,
+ float* rcond, float* berr,
+ lapack_int n_err_bnds, float* err_bnds_norm,
+ float* err_bnds_comp, lapack_int nparams,
+ float* params, lapack_complex_float* work,
+ float* rwork );
+lapack_int LAPACKE_zgbrfsx_work( int matrix_order, char trans, char equed,
+ lapack_int n, lapack_int kl, lapack_int ku,
+ lapack_int nrhs,
+ const lapack_complex_double* ab,
+ lapack_int ldab,
+ const lapack_complex_double* afb,
+ lapack_int ldafb, const lapack_int* ipiv,
+ const double* r, const double* c,
+ const lapack_complex_double* b, lapack_int ldb,
+ lapack_complex_double* x, lapack_int ldx,
+ double* rcond, double* berr,
+ lapack_int n_err_bnds, double* err_bnds_norm,
+ double* err_bnds_comp, lapack_int nparams,
+ double* params, lapack_complex_double* work,
+ double* rwork );
+
+lapack_int LAPACKE_sgbsv_work( int matrix_order, lapack_int n, lapack_int kl,
+ lapack_int ku, lapack_int nrhs, float* ab,
+ lapack_int ldab, lapack_int* ipiv, float* b,
+ lapack_int ldb );
+lapack_int LAPACKE_dgbsv_work( int matrix_order, lapack_int n, lapack_int kl,
+ lapack_int ku, lapack_int nrhs, double* ab,
+ lapack_int ldab, lapack_int* ipiv, double* b,
+ lapack_int ldb );
+lapack_int LAPACKE_cgbsv_work( int matrix_order, lapack_int n, lapack_int kl,
+ lapack_int ku, lapack_int nrhs,
+ lapack_complex_float* ab, lapack_int ldab,
+ lapack_int* ipiv, lapack_complex_float* b,
+ lapack_int ldb );
+lapack_int LAPACKE_zgbsv_work( int matrix_order, lapack_int n, lapack_int kl,
+ lapack_int ku, lapack_int nrhs,
+ lapack_complex_double* ab, lapack_int ldab,
+ lapack_int* ipiv, lapack_complex_double* b,
+ lapack_int ldb );
+
+lapack_int LAPACKE_sgbsvx_work( int matrix_order, char fact, char trans,
+ lapack_int n, lapack_int kl, lapack_int ku,
+ lapack_int nrhs, float* ab, lapack_int ldab,
+ float* afb, lapack_int ldafb, lapack_int* ipiv,
+ char* equed, float* r, float* c, float* b,
+ lapack_int ldb, float* x, lapack_int ldx,
+ float* rcond, float* ferr, float* berr,
+ float* work, lapack_int* iwork );
+lapack_int LAPACKE_dgbsvx_work( int matrix_order, char fact, char trans,
+ lapack_int n, lapack_int kl, lapack_int ku,
+ lapack_int nrhs, double* ab, lapack_int ldab,
+ double* afb, lapack_int ldafb, lapack_int* ipiv,
+ char* equed, double* r, double* c, double* b,
+ lapack_int ldb, double* x, lapack_int ldx,
+ double* rcond, double* ferr, double* berr,
+ double* work, lapack_int* iwork );
+lapack_int LAPACKE_cgbsvx_work( int matrix_order, char fact, char trans,
+ lapack_int n, lapack_int kl, lapack_int ku,
+ lapack_int nrhs, lapack_complex_float* ab,
+ lapack_int ldab, lapack_complex_float* afb,
+ lapack_int ldafb, lapack_int* ipiv, char* equed,
+ float* r, float* c, lapack_complex_float* b,
+ lapack_int ldb, lapack_complex_float* x,
+ lapack_int ldx, float* rcond, float* ferr,
+ float* berr, lapack_complex_float* work,
+ float* rwork );
+lapack_int LAPACKE_zgbsvx_work( int matrix_order, char fact, char trans,
+ lapack_int n, lapack_int kl, lapack_int ku,
+ lapack_int nrhs, lapack_complex_double* ab,
+ lapack_int ldab, lapack_complex_double* afb,
+ lapack_int ldafb, lapack_int* ipiv, char* equed,
+ double* r, double* c, lapack_complex_double* b,
+ lapack_int ldb, lapack_complex_double* x,
+ lapack_int ldx, double* rcond, double* ferr,
+ double* berr, lapack_complex_double* work,
+ double* rwork );
+
+lapack_int LAPACKE_sgbsvxx_work( int matrix_order, char fact, char trans,
+ lapack_int n, lapack_int kl, lapack_int ku,
+ lapack_int nrhs, float* ab, lapack_int ldab,
+ float* afb, lapack_int ldafb, lapack_int* ipiv,
+ char* equed, float* r, float* c, float* b,
+ lapack_int ldb, float* x, lapack_int ldx,
+ float* rcond, float* rpvgrw, float* berr,
+ lapack_int n_err_bnds, float* err_bnds_norm,
+ float* err_bnds_comp, lapack_int nparams,
+ float* params, float* work,
+ lapack_int* iwork );
+lapack_int LAPACKE_dgbsvxx_work( int matrix_order, char fact, char trans,
+ lapack_int n, lapack_int kl, lapack_int ku,
+ lapack_int nrhs, double* ab, lapack_int ldab,
+ double* afb, lapack_int ldafb,
+ lapack_int* ipiv, char* equed, double* r,
+ double* c, double* b, lapack_int ldb,
+ double* x, lapack_int ldx, double* rcond,
+ double* rpvgrw, double* berr,
+ lapack_int n_err_bnds, double* err_bnds_norm,
+ double* err_bnds_comp, lapack_int nparams,
+ double* params, double* work,
+ lapack_int* iwork );
+lapack_int LAPACKE_cgbsvxx_work( int matrix_order, char fact, char trans,
+ lapack_int n, lapack_int kl, lapack_int ku,
+ lapack_int nrhs, lapack_complex_float* ab,
+ lapack_int ldab, lapack_complex_float* afb,
+ lapack_int ldafb, lapack_int* ipiv,
+ char* equed, float* r, float* c,
+ lapack_complex_float* b, lapack_int ldb,
+ lapack_complex_float* x, lapack_int ldx,
+ float* rcond, float* rpvgrw, float* berr,
+ lapack_int n_err_bnds, float* err_bnds_norm,
+ float* err_bnds_comp, lapack_int nparams,
+ float* params, lapack_complex_float* work,
+ float* rwork );
+lapack_int LAPACKE_zgbsvxx_work( int matrix_order, char fact, char trans,
+ lapack_int n, lapack_int kl, lapack_int ku,
+ lapack_int nrhs, lapack_complex_double* ab,
+ lapack_int ldab, lapack_complex_double* afb,
+ lapack_int ldafb, lapack_int* ipiv,
+ char* equed, double* r, double* c,
+ lapack_complex_double* b, lapack_int ldb,
+ lapack_complex_double* x, lapack_int ldx,
+ double* rcond, double* rpvgrw, double* berr,
+ lapack_int n_err_bnds, double* err_bnds_norm,
+ double* err_bnds_comp, lapack_int nparams,
+ double* params, lapack_complex_double* work,
+ double* rwork );
+
+lapack_int LAPACKE_sgbtrf_work( int matrix_order, lapack_int m, lapack_int n,
+ lapack_int kl, lapack_int ku, float* ab,
+ lapack_int ldab, lapack_int* ipiv );
+lapack_int LAPACKE_dgbtrf_work( int matrix_order, lapack_int m, lapack_int n,
+ lapack_int kl, lapack_int ku, double* ab,
+ lapack_int ldab, lapack_int* ipiv );
+lapack_int LAPACKE_cgbtrf_work( int matrix_order, lapack_int m, lapack_int n,
+ lapack_int kl, lapack_int ku,
+ lapack_complex_float* ab, lapack_int ldab,
+ lapack_int* ipiv );
+lapack_int LAPACKE_zgbtrf_work( int matrix_order, lapack_int m, lapack_int n,
+ lapack_int kl, lapack_int ku,
+ lapack_complex_double* ab, lapack_int ldab,
+ lapack_int* ipiv );
+
+lapack_int LAPACKE_sgbtrs_work( int matrix_order, char trans, lapack_int n,
+ lapack_int kl, lapack_int ku, lapack_int nrhs,
+ const float* ab, lapack_int ldab,
+ const lapack_int* ipiv, float* b,
+ lapack_int ldb );
+lapack_int LAPACKE_dgbtrs_work( int matrix_order, char trans, lapack_int n,
+ lapack_int kl, lapack_int ku, lapack_int nrhs,
+ const double* ab, lapack_int ldab,
+ const lapack_int* ipiv, double* b,
+ lapack_int ldb );
+lapack_int LAPACKE_cgbtrs_work( int matrix_order, char trans, lapack_int n,
+ lapack_int kl, lapack_int ku, lapack_int nrhs,
+ const lapack_complex_float* ab, lapack_int ldab,
+ const lapack_int* ipiv, lapack_complex_float* b,
+ lapack_int ldb );
+lapack_int LAPACKE_zgbtrs_work( int matrix_order, char trans, lapack_int n,
+ lapack_int kl, lapack_int ku, lapack_int nrhs,
+ const lapack_complex_double* ab,
+ lapack_int ldab, const lapack_int* ipiv,
+ lapack_complex_double* b, lapack_int ldb );
+
+lapack_int LAPACKE_sgebak_work( int matrix_order, char job, char side,
+ lapack_int n, lapack_int ilo, lapack_int ihi,
+ const float* scale, lapack_int m, float* v,
+ lapack_int ldv );
+lapack_int LAPACKE_dgebak_work( int matrix_order, char job, char side,
+ lapack_int n, lapack_int ilo, lapack_int ihi,
+ const double* scale, lapack_int m, double* v,
+ lapack_int ldv );
+lapack_int LAPACKE_cgebak_work( int matrix_order, char job, char side,
+ lapack_int n, lapack_int ilo, lapack_int ihi,
+ const float* scale, lapack_int m,
+ lapack_complex_float* v, lapack_int ldv );
+lapack_int LAPACKE_zgebak_work( int matrix_order, char job, char side,
+ lapack_int n, lapack_int ilo, lapack_int ihi,
+ const double* scale, lapack_int m,
+ lapack_complex_double* v, lapack_int ldv );
+
+lapack_int LAPACKE_sgebal_work( int matrix_order, char job, lapack_int n,
+ float* a, lapack_int lda, lapack_int* ilo,
+ lapack_int* ihi, float* scale );
+lapack_int LAPACKE_dgebal_work( int matrix_order, char job, lapack_int n,
+ double* a, lapack_int lda, lapack_int* ilo,
+ lapack_int* ihi, double* scale );
+lapack_int LAPACKE_cgebal_work( int matrix_order, char job, lapack_int n,
+ lapack_complex_float* a, lapack_int lda,
+ lapack_int* ilo, lapack_int* ihi,
+ float* scale );
+lapack_int LAPACKE_zgebal_work( int matrix_order, char job, lapack_int n,
+ lapack_complex_double* a, lapack_int lda,
+ lapack_int* ilo, lapack_int* ihi,
+ double* scale );
+
+lapack_int LAPACKE_sgebrd_work( int matrix_order, lapack_int m, lapack_int n,
+ float* a, lapack_int lda, float* d, float* e,
+ float* tauq, float* taup, float* work,
+ lapack_int lwork );
+lapack_int LAPACKE_dgebrd_work( int matrix_order, lapack_int m, lapack_int n,
+ double* a, lapack_int lda, double* d, double* e,
+ double* tauq, double* taup, double* work,
+ lapack_int lwork );
+lapack_int LAPACKE_cgebrd_work( int matrix_order, lapack_int m, lapack_int n,
+ lapack_complex_float* a, lapack_int lda,
+ float* d, float* e, lapack_complex_float* tauq,
+ lapack_complex_float* taup,
+ lapack_complex_float* work, lapack_int lwork );
+lapack_int LAPACKE_zgebrd_work( int matrix_order, lapack_int m, lapack_int n,
+ lapack_complex_double* a, lapack_int lda,
+ double* d, double* e,
+ lapack_complex_double* tauq,
+ lapack_complex_double* taup,
+ lapack_complex_double* work, lapack_int lwork );
+
+lapack_int LAPACKE_sgecon_work( int matrix_order, char norm, lapack_int n,
+ const float* a, lapack_int lda, float anorm,
+ float* rcond, float* work, lapack_int* iwork );
+lapack_int LAPACKE_dgecon_work( int matrix_order, char norm, lapack_int n,
+ const double* a, lapack_int lda, double anorm,
+ double* rcond, double* work,
+ lapack_int* iwork );
+lapack_int LAPACKE_cgecon_work( int matrix_order, char norm, lapack_int n,
+ const lapack_complex_float* a, lapack_int lda,
+ float anorm, float* rcond,
+ lapack_complex_float* work, float* rwork );
+lapack_int LAPACKE_zgecon_work( int matrix_order, char norm, lapack_int n,
+ const lapack_complex_double* a, lapack_int lda,
+ double anorm, double* rcond,
+ lapack_complex_double* work, double* rwork );
+
+lapack_int LAPACKE_sgeequ_work( int matrix_order, lapack_int m, lapack_int n,
+ const float* a, lapack_int lda, float* r,
+ float* c, float* rowcnd, float* colcnd,
+ float* amax );
+lapack_int LAPACKE_dgeequ_work( int matrix_order, lapack_int m, lapack_int n,
+ const double* a, lapack_int lda, double* r,
+ double* c, double* rowcnd, double* colcnd,
+ double* amax );
+lapack_int LAPACKE_cgeequ_work( int matrix_order, lapack_int m, lapack_int n,
+ const lapack_complex_float* a, lapack_int lda,
+ float* r, float* c, float* rowcnd,
+ float* colcnd, float* amax );
+lapack_int LAPACKE_zgeequ_work( int matrix_order, lapack_int m, lapack_int n,
+ const lapack_complex_double* a, lapack_int lda,
+ double* r, double* c, double* rowcnd,
+ double* colcnd, double* amax );
+
+lapack_int LAPACKE_sgeequb_work( int matrix_order, lapack_int m, lapack_int n,
+ const float* a, lapack_int lda, float* r,
+ float* c, float* rowcnd, float* colcnd,
+ float* amax );
+lapack_int LAPACKE_dgeequb_work( int matrix_order, lapack_int m, lapack_int n,
+ const double* a, lapack_int lda, double* r,
+ double* c, double* rowcnd, double* colcnd,
+ double* amax );
+lapack_int LAPACKE_cgeequb_work( int matrix_order, lapack_int m, lapack_int n,
+ const lapack_complex_float* a, lapack_int lda,
+ float* r, float* c, float* rowcnd,
+ float* colcnd, float* amax );
+lapack_int LAPACKE_zgeequb_work( int matrix_order, lapack_int m, lapack_int n,
+ const lapack_complex_double* a, lapack_int lda,
+ double* r, double* c, double* rowcnd,
+ double* colcnd, double* amax );
+
+lapack_int LAPACKE_sgees_work( int matrix_order, char jobvs, char sort,
+ LAPACK_S_SELECT2 select, lapack_int n, float* a,
+ lapack_int lda, lapack_int* sdim, float* wr,
+ float* wi, float* vs, lapack_int ldvs,
+ float* work, lapack_int lwork,
+ lapack_logical* bwork );
+lapack_int LAPACKE_dgees_work( int matrix_order, char jobvs, char sort,
+ LAPACK_D_SELECT2 select, lapack_int n, double* a,
+ lapack_int lda, lapack_int* sdim, double* wr,
+ double* wi, double* vs, lapack_int ldvs,
+ double* work, lapack_int lwork,
+ lapack_logical* bwork );
+lapack_int LAPACKE_cgees_work( int matrix_order, char jobvs, char sort,
+ LAPACK_C_SELECT1 select, lapack_int n,
+ lapack_complex_float* a, lapack_int lda,
+ lapack_int* sdim, lapack_complex_float* w,
+ lapack_complex_float* vs, lapack_int ldvs,
+ lapack_complex_float* work, lapack_int lwork,
+ float* rwork, lapack_logical* bwork );
+lapack_int LAPACKE_zgees_work( int matrix_order, char jobvs, char sort,
+ LAPACK_Z_SELECT1 select, lapack_int n,
+ lapack_complex_double* a, lapack_int lda,
+ lapack_int* sdim, lapack_complex_double* w,
+ lapack_complex_double* vs, lapack_int ldvs,
+ lapack_complex_double* work, lapack_int lwork,
+ double* rwork, lapack_logical* bwork );
+
+lapack_int LAPACKE_sgeesx_work( int matrix_order, char jobvs, char sort,
+ LAPACK_S_SELECT2 select, char sense,
+ lapack_int n, float* a, lapack_int lda,
+ lapack_int* sdim, float* wr, float* wi,
+ float* vs, lapack_int ldvs, float* rconde,
+ float* rcondv, float* work, lapack_int lwork,
+ lapack_int* iwork, lapack_int liwork,
+ lapack_logical* bwork );
+lapack_int LAPACKE_dgeesx_work( int matrix_order, char jobvs, char sort,
+ LAPACK_D_SELECT2 select, char sense,
+ lapack_int n, double* a, lapack_int lda,
+ lapack_int* sdim, double* wr, double* wi,
+ double* vs, lapack_int ldvs, double* rconde,
+ double* rcondv, double* work, lapack_int lwork,
+ lapack_int* iwork, lapack_int liwork,
+ lapack_logical* bwork );
+lapack_int LAPACKE_cgeesx_work( int matrix_order, char jobvs, char sort,
+ LAPACK_C_SELECT1 select, char sense,
+ lapack_int n, lapack_complex_float* a,
+ lapack_int lda, lapack_int* sdim,
+ lapack_complex_float* w,
+ lapack_complex_float* vs, lapack_int ldvs,
+ float* rconde, float* rcondv,
+ lapack_complex_float* work, lapack_int lwork,
+ float* rwork, lapack_logical* bwork );
+lapack_int LAPACKE_zgeesx_work( int matrix_order, char jobvs, char sort,
+ LAPACK_Z_SELECT1 select, char sense,
+ lapack_int n, lapack_complex_double* a,
+ lapack_int lda, lapack_int* sdim,
+ lapack_complex_double* w,
+ lapack_complex_double* vs, lapack_int ldvs,
+ double* rconde, double* rcondv,
+ lapack_complex_double* work, lapack_int lwork,
+ double* rwork, lapack_logical* bwork );
+
+lapack_int LAPACKE_sgeev_work( int matrix_order, char jobvl, char jobvr,
+ lapack_int n, float* a, lapack_int lda,
+ float* wr, float* wi, float* vl, lapack_int ldvl,
+ float* vr, lapack_int ldvr, float* work,
+ lapack_int lwork );
+lapack_int LAPACKE_dgeev_work( int matrix_order, char jobvl, char jobvr,
+ lapack_int n, double* a, lapack_int lda,
+ double* wr, double* wi, double* vl,
+ lapack_int ldvl, double* vr, lapack_int ldvr,
+ double* work, lapack_int lwork );
+lapack_int LAPACKE_cgeev_work( int matrix_order, char jobvl, char jobvr,
+ lapack_int n, lapack_complex_float* a,
+ lapack_int lda, lapack_complex_float* w,
+ lapack_complex_float* vl, lapack_int ldvl,
+ lapack_complex_float* vr, lapack_int ldvr,
+ lapack_complex_float* work, lapack_int lwork,
+ float* rwork );
+lapack_int LAPACKE_zgeev_work( int matrix_order, char jobvl, char jobvr,
+ lapack_int n, lapack_complex_double* a,
+ lapack_int lda, lapack_complex_double* w,
+ lapack_complex_double* vl, lapack_int ldvl,
+ lapack_complex_double* vr, lapack_int ldvr,
+ lapack_complex_double* work, lapack_int lwork,
+ double* rwork );
+
+lapack_int LAPACKE_sgeevx_work( int matrix_order, char balanc, char jobvl,
+ char jobvr, char sense, lapack_int n, float* a,
+ lapack_int lda, float* wr, float* wi, float* vl,
+ lapack_int ldvl, float* vr, lapack_int ldvr,
+ lapack_int* ilo, lapack_int* ihi, float* scale,
+ float* abnrm, float* rconde, float* rcondv,
+ float* work, lapack_int lwork,
+ lapack_int* iwork );
+lapack_int LAPACKE_dgeevx_work( int matrix_order, char balanc, char jobvl,
+ char jobvr, char sense, lapack_int n, double* a,
+ lapack_int lda, double* wr, double* wi,
+ double* vl, lapack_int ldvl, double* vr,
+ lapack_int ldvr, lapack_int* ilo,
+ lapack_int* ihi, double* scale, double* abnrm,
+ double* rconde, double* rcondv, double* work,
+ lapack_int lwork, lapack_int* iwork );
+lapack_int LAPACKE_cgeevx_work( int matrix_order, char balanc, char jobvl,
+ char jobvr, char sense, lapack_int n,
+ lapack_complex_float* a, lapack_int lda,
+ lapack_complex_float* w,
+ lapack_complex_float* vl, lapack_int ldvl,
+ lapack_complex_float* vr, lapack_int ldvr,
+ lapack_int* ilo, lapack_int* ihi, float* scale,
+ float* abnrm, float* rconde, float* rcondv,
+ lapack_complex_float* work, lapack_int lwork,
+ float* rwork );
+lapack_int LAPACKE_zgeevx_work( int matrix_order, char balanc, char jobvl,
+ char jobvr, char sense, lapack_int n,
+ lapack_complex_double* a, lapack_int lda,
+ lapack_complex_double* w,
+ lapack_complex_double* vl, lapack_int ldvl,
+ lapack_complex_double* vr, lapack_int ldvr,
+ lapack_int* ilo, lapack_int* ihi, double* scale,
+ double* abnrm, double* rconde, double* rcondv,
+ lapack_complex_double* work, lapack_int lwork,
+ double* rwork );
+
+lapack_int LAPACKE_sgehrd_work( int matrix_order, lapack_int n, lapack_int ilo,
+ lapack_int ihi, float* a, lapack_int lda,
+ float* tau, float* work, lapack_int lwork );
+lapack_int LAPACKE_dgehrd_work( int matrix_order, lapack_int n, lapack_int ilo,
+ lapack_int ihi, double* a, lapack_int lda,
+ double* tau, double* work, lapack_int lwork );
+lapack_int LAPACKE_cgehrd_work( int matrix_order, lapack_int n, lapack_int ilo,
+ lapack_int ihi, lapack_complex_float* a,
+ lapack_int lda, lapack_complex_float* tau,
+ lapack_complex_float* work, lapack_int lwork );
+lapack_int LAPACKE_zgehrd_work( int matrix_order, lapack_int n, lapack_int ilo,
+ lapack_int ihi, lapack_complex_double* a,
+ lapack_int lda, lapack_complex_double* tau,
+ lapack_complex_double* work, lapack_int lwork );
+
+lapack_int LAPACKE_sgejsv_work( int matrix_order, char joba, char jobu,
+ char jobv, char jobr, char jobt, char jobp,
+ lapack_int m, lapack_int n, float* a,
+ lapack_int lda, float* sva, float* u,
+ lapack_int ldu, float* v, lapack_int ldv,
+ float* work, lapack_int lwork,
+ lapack_int* iwork );
+lapack_int LAPACKE_dgejsv_work( int matrix_order, char joba, char jobu,
+ char jobv, char jobr, char jobt, char jobp,
+ lapack_int m, lapack_int n, double* a,
+ lapack_int lda, double* sva, double* u,
+ lapack_int ldu, double* v, lapack_int ldv,
+ double* work, lapack_int lwork,
+ lapack_int* iwork );
+
+lapack_int LAPACKE_sgelq2_work( int matrix_order, lapack_int m, lapack_int n,
+ float* a, lapack_int lda, float* tau,
+ float* work );
+lapack_int LAPACKE_dgelq2_work( int matrix_order, lapack_int m, lapack_int n,
+ double* a, lapack_int lda, double* tau,
+ double* work );
+lapack_int LAPACKE_cgelq2_work( int matrix_order, lapack_int m, lapack_int n,
+ lapack_complex_float* a, lapack_int lda,
+ lapack_complex_float* tau,
+ lapack_complex_float* work );
+lapack_int LAPACKE_zgelq2_work( int matrix_order, lapack_int m, lapack_int n,
+ lapack_complex_double* a, lapack_int lda,
+ lapack_complex_double* tau,
+ lapack_complex_double* work );
+
+lapack_int LAPACKE_sgelqf_work( int matrix_order, lapack_int m, lapack_int n,
+ float* a, lapack_int lda, float* tau,
+ float* work, lapack_int lwork );
+lapack_int LAPACKE_dgelqf_work( int matrix_order, lapack_int m, lapack_int n,
+ double* a, lapack_int lda, double* tau,
+ double* work, lapack_int lwork );
+lapack_int LAPACKE_cgelqf_work( int matrix_order, lapack_int m, lapack_int n,
+ lapack_complex_float* a, lapack_int lda,
+ lapack_complex_float* tau,
+ lapack_complex_float* work, lapack_int lwork );
+lapack_int LAPACKE_zgelqf_work( int matrix_order, lapack_int m, lapack_int n,
+ lapack_complex_double* a, lapack_int lda,
+ lapack_complex_double* tau,
+ lapack_complex_double* work, lapack_int lwork );
+
+lapack_int LAPACKE_sgels_work( int matrix_order, char trans, lapack_int m,
+ lapack_int n, lapack_int nrhs, float* a,
+ lapack_int lda, float* b, lapack_int ldb,
+ float* work, lapack_int lwork );
+lapack_int LAPACKE_dgels_work( int matrix_order, char trans, lapack_int m,
+ lapack_int n, lapack_int nrhs, double* a,
+ lapack_int lda, double* b, lapack_int ldb,
+ double* work, lapack_int lwork );
+lapack_int LAPACKE_cgels_work( int matrix_order, char trans, lapack_int m,
+ lapack_int n, lapack_int nrhs,
+ lapack_complex_float* a, lapack_int lda,
+ lapack_complex_float* b, lapack_int ldb,
+ lapack_complex_float* work, lapack_int lwork );
+lapack_int LAPACKE_zgels_work( int matrix_order, char trans, lapack_int m,
+ lapack_int n, lapack_int nrhs,
+ lapack_complex_double* a, lapack_int lda,
+ lapack_complex_double* b, lapack_int ldb,
+ lapack_complex_double* work, lapack_int lwork );
+
+lapack_int LAPACKE_sgelsd_work( int matrix_order, lapack_int m, lapack_int n,
+ lapack_int nrhs, float* a, lapack_int lda,
+ float* b, lapack_int ldb, float* s, float rcond,
+ lapack_int* rank, float* work, lapack_int lwork,
+ lapack_int* iwork );
+lapack_int LAPACKE_dgelsd_work( int matrix_order, lapack_int m, lapack_int n,
+ lapack_int nrhs, double* a, lapack_int lda,
+ double* b, lapack_int ldb, double* s,
+ double rcond, lapack_int* rank, double* work,
+ lapack_int lwork, lapack_int* iwork );
+lapack_int LAPACKE_cgelsd_work( int matrix_order, lapack_int m, lapack_int n,
+ lapack_int nrhs, lapack_complex_float* a,
+ lapack_int lda, lapack_complex_float* b,
+ lapack_int ldb, float* s, float rcond,
+ lapack_int* rank, lapack_complex_float* work,
+ lapack_int lwork, float* rwork,
+ lapack_int* iwork );
+lapack_int LAPACKE_zgelsd_work( int matrix_order, lapack_int m, lapack_int n,
+ lapack_int nrhs, lapack_complex_double* a,
+ lapack_int lda, lapack_complex_double* b,
+ lapack_int ldb, double* s, double rcond,
+ lapack_int* rank, lapack_complex_double* work,
+ lapack_int lwork, double* rwork,
+ lapack_int* iwork );
+
+lapack_int LAPACKE_sgelss_work( int matrix_order, lapack_int m, lapack_int n,
+ lapack_int nrhs, float* a, lapack_int lda,
+ float* b, lapack_int ldb, float* s, float rcond,
+ lapack_int* rank, float* work,
+ lapack_int lwork );
+lapack_int LAPACKE_dgelss_work( int matrix_order, lapack_int m, lapack_int n,
+ lapack_int nrhs, double* a, lapack_int lda,
+ double* b, lapack_int ldb, double* s,
+ double rcond, lapack_int* rank, double* work,
+ lapack_int lwork );
+lapack_int LAPACKE_cgelss_work( int matrix_order, lapack_int m, lapack_int n,
+ lapack_int nrhs, lapack_complex_float* a,
+ lapack_int lda, lapack_complex_float* b,
+ lapack_int ldb, float* s, float rcond,
+ lapack_int* rank, lapack_complex_float* work,
+ lapack_int lwork, float* rwork );
+lapack_int LAPACKE_zgelss_work( int matrix_order, lapack_int m, lapack_int n,
+ lapack_int nrhs, lapack_complex_double* a,
+ lapack_int lda, lapack_complex_double* b,
+ lapack_int ldb, double* s, double rcond,
+ lapack_int* rank, lapack_complex_double* work,
+ lapack_int lwork, double* rwork );
+
+lapack_int LAPACKE_sgelsy_work( int matrix_order, lapack_int m, lapack_int n,
+ lapack_int nrhs, float* a, lapack_int lda,
+ float* b, lapack_int ldb, lapack_int* jpvt,
+ float rcond, lapack_int* rank, float* work,
+ lapack_int lwork );
+lapack_int LAPACKE_dgelsy_work( int matrix_order, lapack_int m, lapack_int n,
+ lapack_int nrhs, double* a, lapack_int lda,
+ double* b, lapack_int ldb, lapack_int* jpvt,
+ double rcond, lapack_int* rank, double* work,
+ lapack_int lwork );
+lapack_int LAPACKE_cgelsy_work( int matrix_order, lapack_int m, lapack_int n,
+ lapack_int nrhs, lapack_complex_float* a,
+ lapack_int lda, lapack_complex_float* b,
+ lapack_int ldb, lapack_int* jpvt, float rcond,
+ lapack_int* rank, lapack_complex_float* work,
+ lapack_int lwork, float* rwork );
+lapack_int LAPACKE_zgelsy_work( int matrix_order, lapack_int m, lapack_int n,
+ lapack_int nrhs, lapack_complex_double* a,
+ lapack_int lda, lapack_complex_double* b,
+ lapack_int ldb, lapack_int* jpvt, double rcond,
+ lapack_int* rank, lapack_complex_double* work,
+ lapack_int lwork, double* rwork );
+
+lapack_int LAPACKE_sgeqlf_work( int matrix_order, lapack_int m, lapack_int n,
+ float* a, lapack_int lda, float* tau,
+ float* work, lapack_int lwork );
+lapack_int LAPACKE_dgeqlf_work( int matrix_order, lapack_int m, lapack_int n,
+ double* a, lapack_int lda, double* tau,
+ double* work, lapack_int lwork );
+lapack_int LAPACKE_cgeqlf_work( int matrix_order, lapack_int m, lapack_int n,
+ lapack_complex_float* a, lapack_int lda,
+ lapack_complex_float* tau,
+ lapack_complex_float* work, lapack_int lwork );
+lapack_int LAPACKE_zgeqlf_work( int matrix_order, lapack_int m, lapack_int n,
+ lapack_complex_double* a, lapack_int lda,
+ lapack_complex_double* tau,
+ lapack_complex_double* work, lapack_int lwork );
+
+lapack_int LAPACKE_sgeqp3_work( int matrix_order, lapack_int m, lapack_int n,
+ float* a, lapack_int lda, lapack_int* jpvt,
+ float* tau, float* work, lapack_int lwork );
+lapack_int LAPACKE_dgeqp3_work( int matrix_order, lapack_int m, lapack_int n,
+ double* a, lapack_int lda, lapack_int* jpvt,
+ double* tau, double* work, lapack_int lwork );
+lapack_int LAPACKE_cgeqp3_work( int matrix_order, lapack_int m, lapack_int n,
+ lapack_complex_float* a, lapack_int lda,
+ lapack_int* jpvt, lapack_complex_float* tau,
+ lapack_complex_float* work, lapack_int lwork,
+ float* rwork );
+lapack_int LAPACKE_zgeqp3_work( int matrix_order, lapack_int m, lapack_int n,
+ lapack_complex_double* a, lapack_int lda,
+ lapack_int* jpvt, lapack_complex_double* tau,
+ lapack_complex_double* work, lapack_int lwork,
+ double* rwork );
+
+lapack_int LAPACKE_sgeqpf_work( int matrix_order, lapack_int m, lapack_int n,
+ float* a, lapack_int lda, lapack_int* jpvt,
+ float* tau, float* work );
+lapack_int LAPACKE_dgeqpf_work( int matrix_order, lapack_int m, lapack_int n,
+ double* a, lapack_int lda, lapack_int* jpvt,
+ double* tau, double* work );
+lapack_int LAPACKE_cgeqpf_work( int matrix_order, lapack_int m, lapack_int n,
+ lapack_complex_float* a, lapack_int lda,
+ lapack_int* jpvt, lapack_complex_float* tau,
+ lapack_complex_float* work, float* rwork );
+lapack_int LAPACKE_zgeqpf_work( int matrix_order, lapack_int m, lapack_int n,
+ lapack_complex_double* a, lapack_int lda,
+ lapack_int* jpvt, lapack_complex_double* tau,
+ lapack_complex_double* work, double* rwork );
+
+lapack_int LAPACKE_sgeqr2_work( int matrix_order, lapack_int m, lapack_int n,
+ float* a, lapack_int lda, float* tau,
+ float* work );
+lapack_int LAPACKE_dgeqr2_work( int matrix_order, lapack_int m, lapack_int n,
+ double* a, lapack_int lda, double* tau,
+ double* work );
+lapack_int LAPACKE_cgeqr2_work( int matrix_order, lapack_int m, lapack_int n,
+ lapack_complex_float* a, lapack_int lda,
+ lapack_complex_float* tau,
+ lapack_complex_float* work );
+lapack_int LAPACKE_zgeqr2_work( int matrix_order, lapack_int m, lapack_int n,
+ lapack_complex_double* a, lapack_int lda,
+ lapack_complex_double* tau,
+ lapack_complex_double* work );
+
+lapack_int LAPACKE_sgeqrf_work( int matrix_order, lapack_int m, lapack_int n,
+ float* a, lapack_int lda, float* tau,
+ float* work, lapack_int lwork );
+lapack_int LAPACKE_dgeqrf_work( int matrix_order, lapack_int m, lapack_int n,
+ double* a, lapack_int lda, double* tau,
+ double* work, lapack_int lwork );
+lapack_int LAPACKE_cgeqrf_work( int matrix_order, lapack_int m, lapack_int n,
+ lapack_complex_float* a, lapack_int lda,
+ lapack_complex_float* tau,
+ lapack_complex_float* work, lapack_int lwork );
+lapack_int LAPACKE_zgeqrf_work( int matrix_order, lapack_int m, lapack_int n,
+ lapack_complex_double* a, lapack_int lda,
+ lapack_complex_double* tau,
+ lapack_complex_double* work, lapack_int lwork );
+
+lapack_int LAPACKE_sgeqrfp_work( int matrix_order, lapack_int m, lapack_int n,
+ float* a, lapack_int lda, float* tau,
+ float* work, lapack_int lwork );
+lapack_int LAPACKE_dgeqrfp_work( int matrix_order, lapack_int m, lapack_int n,
+ double* a, lapack_int lda, double* tau,
+ double* work, lapack_int lwork );
+lapack_int LAPACKE_cgeqrfp_work( int matrix_order, lapack_int m, lapack_int n,
+ lapack_complex_float* a, lapack_int lda,
+ lapack_complex_float* tau,
+ lapack_complex_float* work, lapack_int lwork );
+lapack_int LAPACKE_zgeqrfp_work( int matrix_order, lapack_int m, lapack_int n,
+ lapack_complex_double* a, lapack_int lda,
+ lapack_complex_double* tau,
+ lapack_complex_double* work,
+ lapack_int lwork );
+
+lapack_int LAPACKE_sgerfs_work( int matrix_order, char trans, lapack_int n,
+ lapack_int nrhs, const float* a, lapack_int lda,
+ const float* af, lapack_int ldaf,
+ const lapack_int* ipiv, const float* b,
+ lapack_int ldb, float* x, lapack_int ldx,
+ float* ferr, float* berr, float* work,
+ lapack_int* iwork );
+lapack_int LAPACKE_dgerfs_work( int matrix_order, char trans, lapack_int n,
+ lapack_int nrhs, const double* a,
+ lapack_int lda, const double* af,
+ lapack_int ldaf, const lapack_int* ipiv,
+ const double* b, lapack_int ldb, double* x,
+ lapack_int ldx, double* ferr, double* berr,
+ double* work, lapack_int* iwork );
+lapack_int LAPACKE_cgerfs_work( int matrix_order, char trans, lapack_int n,
+ lapack_int nrhs, const lapack_complex_float* a,
+ lapack_int lda, const lapack_complex_float* af,
+ lapack_int ldaf, const lapack_int* ipiv,
+ const lapack_complex_float* b, lapack_int ldb,
+ lapack_complex_float* x, lapack_int ldx,
+ float* ferr, float* berr,
+ lapack_complex_float* work, float* rwork );
+lapack_int LAPACKE_zgerfs_work( int matrix_order, char trans, lapack_int n,
+ lapack_int nrhs, const lapack_complex_double* a,
+ lapack_int lda, const lapack_complex_double* af,
+ lapack_int ldaf, const lapack_int* ipiv,
+ const lapack_complex_double* b, lapack_int ldb,
+ lapack_complex_double* x, lapack_int ldx,
+ double* ferr, double* berr,
+ lapack_complex_double* work, double* rwork );
+
+lapack_int LAPACKE_sgerfsx_work( int matrix_order, char trans, char equed,
+ lapack_int n, lapack_int nrhs, const float* a,
+ lapack_int lda, const float* af,
+ lapack_int ldaf, const lapack_int* ipiv,
+ const float* r, const float* c, const float* b,
+ lapack_int ldb, float* x, lapack_int ldx,
+ float* rcond, float* berr,
+ lapack_int n_err_bnds, float* err_bnds_norm,
+ float* err_bnds_comp, lapack_int nparams,
+ float* params, float* work,
+ lapack_int* iwork );
+lapack_int LAPACKE_dgerfsx_work( int matrix_order, char trans, char equed,
+ lapack_int n, lapack_int nrhs, const double* a,
+ lapack_int lda, const double* af,
+ lapack_int ldaf, const lapack_int* ipiv,
+ const double* r, const double* c,
+ const double* b, lapack_int ldb, double* x,
+ lapack_int ldx, double* rcond, double* berr,
+ lapack_int n_err_bnds, double* err_bnds_norm,
+ double* err_bnds_comp, lapack_int nparams,
+ double* params, double* work,
+ lapack_int* iwork );
+lapack_int LAPACKE_cgerfsx_work( int matrix_order, char trans, char equed,
+ lapack_int n, lapack_int nrhs,
+ const lapack_complex_float* a, lapack_int lda,
+ const lapack_complex_float* af,
+ lapack_int ldaf, const lapack_int* ipiv,
+ const float* r, const float* c,
+ const lapack_complex_float* b, lapack_int ldb,
+ lapack_complex_float* x, lapack_int ldx,
+ float* rcond, float* berr,
+ lapack_int n_err_bnds, float* err_bnds_norm,
+ float* err_bnds_comp, lapack_int nparams,
+ float* params, lapack_complex_float* work,
+ float* rwork );
+lapack_int LAPACKE_zgerfsx_work( int matrix_order, char trans, char equed,
+ lapack_int n, lapack_int nrhs,
+ const lapack_complex_double* a, lapack_int lda,
+ const lapack_complex_double* af,
+ lapack_int ldaf, const lapack_int* ipiv,
+ const double* r, const double* c,
+ const lapack_complex_double* b, lapack_int ldb,
+ lapack_complex_double* x, lapack_int ldx,
+ double* rcond, double* berr,
+ lapack_int n_err_bnds, double* err_bnds_norm,
+ double* err_bnds_comp, lapack_int nparams,
+ double* params, lapack_complex_double* work,
+ double* rwork );
+
+lapack_int LAPACKE_sgerqf_work( int matrix_order, lapack_int m, lapack_int n,
+ float* a, lapack_int lda, float* tau,
+ float* work, lapack_int lwork );
+lapack_int LAPACKE_dgerqf_work( int matrix_order, lapack_int m, lapack_int n,
+ double* a, lapack_int lda, double* tau,
+ double* work, lapack_int lwork );
+lapack_int LAPACKE_cgerqf_work( int matrix_order, lapack_int m, lapack_int n,
+ lapack_complex_float* a, lapack_int lda,
+ lapack_complex_float* tau,
+ lapack_complex_float* work, lapack_int lwork );
+lapack_int LAPACKE_zgerqf_work( int matrix_order, lapack_int m, lapack_int n,
+ lapack_complex_double* a, lapack_int lda,
+ lapack_complex_double* tau,
+ lapack_complex_double* work, lapack_int lwork );
+
+lapack_int LAPACKE_sgesdd_work( int matrix_order, char jobz, lapack_int m,
+ lapack_int n, float* a, lapack_int lda,
+ float* s, float* u, lapack_int ldu, float* vt,
+ lapack_int ldvt, float* work, lapack_int lwork,
+ lapack_int* iwork );
+lapack_int LAPACKE_dgesdd_work( int matrix_order, char jobz, lapack_int m,
+ lapack_int n, double* a, lapack_int lda,
+ double* s, double* u, lapack_int ldu,
+ double* vt, lapack_int ldvt, double* work,
+ lapack_int lwork, lapack_int* iwork );
+lapack_int LAPACKE_cgesdd_work( int matrix_order, char jobz, lapack_int m,
+ lapack_int n, lapack_complex_float* a,
+ lapack_int lda, float* s,
+ lapack_complex_float* u, lapack_int ldu,
+ lapack_complex_float* vt, lapack_int ldvt,
+ lapack_complex_float* work, lapack_int lwork,
+ float* rwork, lapack_int* iwork );
+lapack_int LAPACKE_zgesdd_work( int matrix_order, char jobz, lapack_int m,
+ lapack_int n, lapack_complex_double* a,
+ lapack_int lda, double* s,
+ lapack_complex_double* u, lapack_int ldu,
+ lapack_complex_double* vt, lapack_int ldvt,
+ lapack_complex_double* work, lapack_int lwork,
+ double* rwork, lapack_int* iwork );
+
+lapack_int LAPACKE_sgesv_work( int matrix_order, lapack_int n, lapack_int nrhs,
+ float* a, lapack_int lda, lapack_int* ipiv,
+ float* b, lapack_int ldb );
+lapack_int LAPACKE_dgesv_work( int matrix_order, lapack_int n, lapack_int nrhs,
+ double* a, lapack_int lda, lapack_int* ipiv,
+ double* b, lapack_int ldb );
+lapack_int LAPACKE_cgesv_work( int matrix_order, lapack_int n, lapack_int nrhs,
+ lapack_complex_float* a, lapack_int lda,
+ lapack_int* ipiv, lapack_complex_float* b,
+ lapack_int ldb );
+lapack_int LAPACKE_zgesv_work( int matrix_order, lapack_int n, lapack_int nrhs,
+ lapack_complex_double* a, lapack_int lda,
+ lapack_int* ipiv, lapack_complex_double* b,
+ lapack_int ldb );
+lapack_int LAPACKE_dsgesv_work( int matrix_order, lapack_int n, lapack_int nrhs,
+ double* a, lapack_int lda, lapack_int* ipiv,
+ double* b, lapack_int ldb, double* x,
+ lapack_int ldx, double* work, float* swork,
+ lapack_int* iter );
+lapack_int LAPACKE_zcgesv_work( int matrix_order, lapack_int n, lapack_int nrhs,
+ lapack_complex_double* a, lapack_int lda,
+ lapack_int* ipiv, lapack_complex_double* b,
+ lapack_int ldb, lapack_complex_double* x,
+ lapack_int ldx, lapack_complex_double* work,
+ lapack_complex_float* swork, double* rwork,
+ lapack_int* iter );
+
+lapack_int LAPACKE_sgesvd_work( int matrix_order, char jobu, char jobvt,
+ lapack_int m, lapack_int n, float* a,
+ lapack_int lda, float* s, float* u,
+ lapack_int ldu, float* vt, lapack_int ldvt,
+ float* work, lapack_int lwork );
+lapack_int LAPACKE_dgesvd_work( int matrix_order, char jobu, char jobvt,
+ lapack_int m, lapack_int n, double* a,
+ lapack_int lda, double* s, double* u,
+ lapack_int ldu, double* vt, lapack_int ldvt,
+ double* work, lapack_int lwork );
+lapack_int LAPACKE_cgesvd_work( int matrix_order, char jobu, char jobvt,
+ lapack_int m, lapack_int n,
+ lapack_complex_float* a, lapack_int lda,
+ float* s, lapack_complex_float* u,
+ lapack_int ldu, lapack_complex_float* vt,
+ lapack_int ldvt, lapack_complex_float* work,
+ lapack_int lwork, float* rwork );
+lapack_int LAPACKE_zgesvd_work( int matrix_order, char jobu, char jobvt,
+ lapack_int m, lapack_int n,
+ lapack_complex_double* a, lapack_int lda,
+ double* s, lapack_complex_double* u,
+ lapack_int ldu, lapack_complex_double* vt,
+ lapack_int ldvt, lapack_complex_double* work,
+ lapack_int lwork, double* rwork );
+
+lapack_int LAPACKE_sgesvj_work( int matrix_order, char joba, char jobu,
+ char jobv, lapack_int m, lapack_int n, float* a,
+ lapack_int lda, float* sva, lapack_int mv,
+ float* v, lapack_int ldv, float* work,
+ lapack_int lwork );
+lapack_int LAPACKE_dgesvj_work( int matrix_order, char joba, char jobu,
+ char jobv, lapack_int m, lapack_int n,
+ double* a, lapack_int lda, double* sva,
+ lapack_int mv, double* v, lapack_int ldv,
+ double* work, lapack_int lwork );
+
+lapack_int LAPACKE_sgesvx_work( int matrix_order, char fact, char trans,
+ lapack_int n, lapack_int nrhs, float* a,
+ lapack_int lda, float* af, lapack_int ldaf,
+ lapack_int* ipiv, char* equed, float* r,
+ float* c, float* b, lapack_int ldb, float* x,
+ lapack_int ldx, float* rcond, float* ferr,
+ float* berr, float* work, lapack_int* iwork );
+lapack_int LAPACKE_dgesvx_work( int matrix_order, char fact, char trans,
+ lapack_int n, lapack_int nrhs, double* a,
+ lapack_int lda, double* af, lapack_int ldaf,
+ lapack_int* ipiv, char* equed, double* r,
+ double* c, double* b, lapack_int ldb, double* x,
+ lapack_int ldx, double* rcond, double* ferr,
+ double* berr, double* work, lapack_int* iwork );
+lapack_int LAPACKE_cgesvx_work( int matrix_order, char fact, char trans,
+ lapack_int n, lapack_int nrhs,
+ lapack_complex_float* a, lapack_int lda,
+ lapack_complex_float* af, lapack_int ldaf,
+ lapack_int* ipiv, char* equed, float* r,
+ float* c, lapack_complex_float* b,
+ lapack_int ldb, lapack_complex_float* x,
+ lapack_int ldx, float* rcond, float* ferr,
+ float* berr, lapack_complex_float* work,
+ float* rwork );
+lapack_int LAPACKE_zgesvx_work( int matrix_order, char fact, char trans,
+ lapack_int n, lapack_int nrhs,
+ lapack_complex_double* a, lapack_int lda,
+ lapack_complex_double* af, lapack_int ldaf,
+ lapack_int* ipiv, char* equed, double* r,
+ double* c, lapack_complex_double* b,
+ lapack_int ldb, lapack_complex_double* x,
+ lapack_int ldx, double* rcond, double* ferr,
+ double* berr, lapack_complex_double* work,
+ double* rwork );
+
+lapack_int LAPACKE_sgesvxx_work( int matrix_order, char fact, char trans,
+ lapack_int n, lapack_int nrhs, float* a,
+ lapack_int lda, float* af, lapack_int ldaf,
+ lapack_int* ipiv, char* equed, float* r,
+ float* c, float* b, lapack_int ldb, float* x,
+ lapack_int ldx, float* rcond, float* rpvgrw,
+ float* berr, lapack_int n_err_bnds,
+ float* err_bnds_norm, float* err_bnds_comp,
+ lapack_int nparams, float* params, float* work,
+ lapack_int* iwork );
+lapack_int LAPACKE_dgesvxx_work( int matrix_order, char fact, char trans,
+ lapack_int n, lapack_int nrhs, double* a,
+ lapack_int lda, double* af, lapack_int ldaf,
+ lapack_int* ipiv, char* equed, double* r,
+ double* c, double* b, lapack_int ldb,
+ double* x, lapack_int ldx, double* rcond,
+ double* rpvgrw, double* berr,
+ lapack_int n_err_bnds, double* err_bnds_norm,
+ double* err_bnds_comp, lapack_int nparams,
+ double* params, double* work,
+ lapack_int* iwork );
+lapack_int LAPACKE_cgesvxx_work( int matrix_order, char fact, char trans,
+ lapack_int n, lapack_int nrhs,
+ lapack_complex_float* a, lapack_int lda,
+ lapack_complex_float* af, lapack_int ldaf,
+ lapack_int* ipiv, char* equed, float* r,
+ float* c, lapack_complex_float* b,
+ lapack_int ldb, lapack_complex_float* x,
+ lapack_int ldx, float* rcond, float* rpvgrw,
+ float* berr, lapack_int n_err_bnds,
+ float* err_bnds_norm, float* err_bnds_comp,
+ lapack_int nparams, float* params,
+ lapack_complex_float* work, float* rwork );
+lapack_int LAPACKE_zgesvxx_work( int matrix_order, char fact, char trans,
+ lapack_int n, lapack_int nrhs,
+ lapack_complex_double* a, lapack_int lda,
+ lapack_complex_double* af, lapack_int ldaf,
+ lapack_int* ipiv, char* equed, double* r,
+ double* c, lapack_complex_double* b,
+ lapack_int ldb, lapack_complex_double* x,
+ lapack_int ldx, double* rcond, double* rpvgrw,
+ double* berr, lapack_int n_err_bnds,
+ double* err_bnds_norm, double* err_bnds_comp,
+ lapack_int nparams, double* params,
+ lapack_complex_double* work, double* rwork );
+
+lapack_int LAPACKE_sgetf2_work( int matrix_order, lapack_int m, lapack_int n,
+ float* a, lapack_int lda, lapack_int* ipiv );
+lapack_int LAPACKE_dgetf2_work( int matrix_order, lapack_int m, lapack_int n,
+ double* a, lapack_int lda, lapack_int* ipiv );
+lapack_int LAPACKE_cgetf2_work( int matrix_order, lapack_int m, lapack_int n,
+ lapack_complex_float* a, lapack_int lda,
+ lapack_int* ipiv );
+lapack_int LAPACKE_zgetf2_work( int matrix_order, lapack_int m, lapack_int n,
+ lapack_complex_double* a, lapack_int lda,
+ lapack_int* ipiv );
+
+lapack_int LAPACKE_sgetrf_work( int matrix_order, lapack_int m, lapack_int n,
+ float* a, lapack_int lda, lapack_int* ipiv );
+lapack_int LAPACKE_dgetrf_work( int matrix_order, lapack_int m, lapack_int n,
+ double* a, lapack_int lda, lapack_int* ipiv );
+lapack_int LAPACKE_cgetrf_work( int matrix_order, lapack_int m, lapack_int n,
+ lapack_complex_float* a, lapack_int lda,
+ lapack_int* ipiv );
+lapack_int LAPACKE_zgetrf_work( int matrix_order, lapack_int m, lapack_int n,
+ lapack_complex_double* a, lapack_int lda,
+ lapack_int* ipiv );
+
+lapack_int LAPACKE_sgetri_work( int matrix_order, lapack_int n, float* a,
+ lapack_int lda, const lapack_int* ipiv,
+ float* work, lapack_int lwork );
+lapack_int LAPACKE_dgetri_work( int matrix_order, lapack_int n, double* a,
+ lapack_int lda, const lapack_int* ipiv,
+ double* work, lapack_int lwork );
+lapack_int LAPACKE_cgetri_work( int matrix_order, lapack_int n,
+ lapack_complex_float* a, lapack_int lda,
+ const lapack_int* ipiv,
+ lapack_complex_float* work, lapack_int lwork );
+lapack_int LAPACKE_zgetri_work( int matrix_order, lapack_int n,
+ lapack_complex_double* a, lapack_int lda,
+ const lapack_int* ipiv,
+ lapack_complex_double* work, lapack_int lwork );
+
+lapack_int LAPACKE_sgetrs_work( int matrix_order, char trans, lapack_int n,
+ lapack_int nrhs, const float* a, lapack_int lda,
+ const lapack_int* ipiv, float* b,
+ lapack_int ldb );
+lapack_int LAPACKE_dgetrs_work( int matrix_order, char trans, lapack_int n,
+ lapack_int nrhs, const double* a,
+ lapack_int lda, const lapack_int* ipiv,
+ double* b, lapack_int ldb );
+lapack_int LAPACKE_cgetrs_work( int matrix_order, char trans, lapack_int n,
+ lapack_int nrhs, const lapack_complex_float* a,
+ lapack_int lda, const lapack_int* ipiv,
+ lapack_complex_float* b, lapack_int ldb );
+lapack_int LAPACKE_zgetrs_work( int matrix_order, char trans, lapack_int n,
+ lapack_int nrhs, const lapack_complex_double* a,
+ lapack_int lda, const lapack_int* ipiv,
+ lapack_complex_double* b, lapack_int ldb );
+
+lapack_int LAPACKE_sggbak_work( int matrix_order, char job, char side,
+ lapack_int n, lapack_int ilo, lapack_int ihi,
+ const float* lscale, const float* rscale,
+ lapack_int m, float* v, lapack_int ldv );
+lapack_int LAPACKE_dggbak_work( int matrix_order, char job, char side,
+ lapack_int n, lapack_int ilo, lapack_int ihi,
+ const double* lscale, const double* rscale,
+ lapack_int m, double* v, lapack_int ldv );
+lapack_int LAPACKE_cggbak_work( int matrix_order, char job, char side,
+ lapack_int n, lapack_int ilo, lapack_int ihi,
+ const float* lscale, const float* rscale,
+ lapack_int m, lapack_complex_float* v,
+ lapack_int ldv );
+lapack_int LAPACKE_zggbak_work( int matrix_order, char job, char side,
+ lapack_int n, lapack_int ilo, lapack_int ihi,
+ const double* lscale, const double* rscale,
+ lapack_int m, lapack_complex_double* v,
+ lapack_int ldv );
+
+lapack_int LAPACKE_sggbal_work( int matrix_order, char job, lapack_int n,
+ float* a, lapack_int lda, float* b,
+ lapack_int ldb, lapack_int* ilo,
+ lapack_int* ihi, float* lscale, float* rscale,
+ float* work );
+lapack_int LAPACKE_dggbal_work( int matrix_order, char job, lapack_int n,
+ double* a, lapack_int lda, double* b,
+ lapack_int ldb, lapack_int* ilo,
+ lapack_int* ihi, double* lscale, double* rscale,
+ double* work );
+lapack_int LAPACKE_cggbal_work( int matrix_order, char job, lapack_int n,
+ lapack_complex_float* a, lapack_int lda,
+ lapack_complex_float* b, lapack_int ldb,
+ lapack_int* ilo, lapack_int* ihi, float* lscale,
+ float* rscale, float* work );
+lapack_int LAPACKE_zggbal_work( int matrix_order, char job, lapack_int n,
+ lapack_complex_double* a, lapack_int lda,
+ lapack_complex_double* b, lapack_int ldb,
+ lapack_int* ilo, lapack_int* ihi,
+ double* lscale, double* rscale, double* work );
+
+lapack_int LAPACKE_sgges_work( int matrix_order, char jobvsl, char jobvsr,
+ char sort, LAPACK_S_SELECT3 selctg, lapack_int n,
+ float* a, lapack_int lda, float* b,
+ lapack_int ldb, lapack_int* sdim, float* alphar,
+ float* alphai, float* beta, float* vsl,
+ lapack_int ldvsl, float* vsr, lapack_int ldvsr,
+ float* work, lapack_int lwork,
+ lapack_logical* bwork );
+lapack_int LAPACKE_dgges_work( int matrix_order, char jobvsl, char jobvsr,
+ char sort, LAPACK_D_SELECT3 selctg, lapack_int n,
+ double* a, lapack_int lda, double* b,
+ lapack_int ldb, lapack_int* sdim, double* alphar,
+ double* alphai, double* beta, double* vsl,
+ lapack_int ldvsl, double* vsr, lapack_int ldvsr,
+ double* work, lapack_int lwork,
+ lapack_logical* bwork );
+lapack_int LAPACKE_cgges_work( int matrix_order, char jobvsl, char jobvsr,
+ char sort, LAPACK_C_SELECT2 selctg, lapack_int n,
+ lapack_complex_float* a, lapack_int lda,
+ lapack_complex_float* b, lapack_int ldb,
+ lapack_int* sdim, lapack_complex_float* alpha,
+ lapack_complex_float* beta,
+ lapack_complex_float* vsl, lapack_int ldvsl,
+ lapack_complex_float* vsr, lapack_int ldvsr,
+ lapack_complex_float* work, lapack_int lwork,
+ float* rwork, lapack_logical* bwork );
+lapack_int LAPACKE_zgges_work( int matrix_order, char jobvsl, char jobvsr,
+ char sort, LAPACK_Z_SELECT2 selctg, lapack_int n,
+ lapack_complex_double* a, lapack_int lda,
+ lapack_complex_double* b, lapack_int ldb,
+ lapack_int* sdim, lapack_complex_double* alpha,
+ lapack_complex_double* beta,
+ lapack_complex_double* vsl, lapack_int ldvsl,
+ lapack_complex_double* vsr, lapack_int ldvsr,
+ lapack_complex_double* work, lapack_int lwork,
+ double* rwork, lapack_logical* bwork );
+
+lapack_int LAPACKE_sggesx_work( int matrix_order, char jobvsl, char jobvsr,
+ char sort, LAPACK_S_SELECT3 selctg, char sense,
+ lapack_int n, float* a, lapack_int lda,
+ float* b, lapack_int ldb, lapack_int* sdim,
+ float* alphar, float* alphai, float* beta,
+ float* vsl, lapack_int ldvsl, float* vsr,
+ lapack_int ldvsr, float* rconde, float* rcondv,
+ float* work, lapack_int lwork,
+ lapack_int* iwork, lapack_int liwork,
+ lapack_logical* bwork );
+lapack_int LAPACKE_dggesx_work( int matrix_order, char jobvsl, char jobvsr,
+ char sort, LAPACK_D_SELECT3 selctg, char sense,
+ lapack_int n, double* a, lapack_int lda,
+ double* b, lapack_int ldb, lapack_int* sdim,
+ double* alphar, double* alphai, double* beta,
+ double* vsl, lapack_int ldvsl, double* vsr,
+ lapack_int ldvsr, double* rconde,
+ double* rcondv, double* work, lapack_int lwork,
+ lapack_int* iwork, lapack_int liwork,
+ lapack_logical* bwork );
+lapack_int LAPACKE_cggesx_work( int matrix_order, char jobvsl, char jobvsr,
+ char sort, LAPACK_C_SELECT2 selctg, char sense,
+ lapack_int n, lapack_complex_float* a,
+ lapack_int lda, lapack_complex_float* b,
+ lapack_int ldb, lapack_int* sdim,
+ lapack_complex_float* alpha,
+ lapack_complex_float* beta,
+ lapack_complex_float* vsl, lapack_int ldvsl,
+ lapack_complex_float* vsr, lapack_int ldvsr,
+ float* rconde, float* rcondv,
+ lapack_complex_float* work, lapack_int lwork,
+ float* rwork, lapack_int* iwork,
+ lapack_int liwork, lapack_logical* bwork );
+lapack_int LAPACKE_zggesx_work( int matrix_order, char jobvsl, char jobvsr,
+ char sort, LAPACK_Z_SELECT2 selctg, char sense,
+ lapack_int n, lapack_complex_double* a,
+ lapack_int lda, lapack_complex_double* b,
+ lapack_int ldb, lapack_int* sdim,
+ lapack_complex_double* alpha,
+ lapack_complex_double* beta,
+ lapack_complex_double* vsl, lapack_int ldvsl,
+ lapack_complex_double* vsr, lapack_int ldvsr,
+ double* rconde, double* rcondv,
+ lapack_complex_double* work, lapack_int lwork,
+ double* rwork, lapack_int* iwork,
+ lapack_int liwork, lapack_logical* bwork );
+
+lapack_int LAPACKE_sggev_work( int matrix_order, char jobvl, char jobvr,
+ lapack_int n, float* a, lapack_int lda, float* b,
+ lapack_int ldb, float* alphar, float* alphai,
+ float* beta, float* vl, lapack_int ldvl,
+ float* vr, lapack_int ldvr, float* work,
+ lapack_int lwork );
+lapack_int LAPACKE_dggev_work( int matrix_order, char jobvl, char jobvr,
+ lapack_int n, double* a, lapack_int lda,
+ double* b, lapack_int ldb, double* alphar,
+ double* alphai, double* beta, double* vl,
+ lapack_int ldvl, double* vr, lapack_int ldvr,
+ double* work, lapack_int lwork );
+lapack_int LAPACKE_cggev_work( int matrix_order, char jobvl, char jobvr,
+ lapack_int n, lapack_complex_float* a,
+ lapack_int lda, lapack_complex_float* b,
+ lapack_int ldb, lapack_complex_float* alpha,
+ lapack_complex_float* beta,
+ lapack_complex_float* vl, lapack_int ldvl,
+ lapack_complex_float* vr, lapack_int ldvr,
+ lapack_complex_float* work, lapack_int lwork,
+ float* rwork );
+lapack_int LAPACKE_zggev_work( int matrix_order, char jobvl, char jobvr,
+ lapack_int n, lapack_complex_double* a,
+ lapack_int lda, lapack_complex_double* b,
+ lapack_int ldb, lapack_complex_double* alpha,
+ lapack_complex_double* beta,
+ lapack_complex_double* vl, lapack_int ldvl,
+ lapack_complex_double* vr, lapack_int ldvr,
+ lapack_complex_double* work, lapack_int lwork,
+ double* rwork );
+
+lapack_int LAPACKE_sggevx_work( int matrix_order, char balanc, char jobvl,
+ char jobvr, char sense, lapack_int n, float* a,
+ lapack_int lda, float* b, lapack_int ldb,
+ float* alphar, float* alphai, float* beta,
+ float* vl, lapack_int ldvl, float* vr,
+ lapack_int ldvr, lapack_int* ilo,
+ lapack_int* ihi, float* lscale, float* rscale,
+ float* abnrm, float* bbnrm, float* rconde,
+ float* rcondv, float* work, lapack_int lwork,
+ lapack_int* iwork, lapack_logical* bwork );
+lapack_int LAPACKE_dggevx_work( int matrix_order, char balanc, char jobvl,
+ char jobvr, char sense, lapack_int n, double* a,
+ lapack_int lda, double* b, lapack_int ldb,
+ double* alphar, double* alphai, double* beta,
+ double* vl, lapack_int ldvl, double* vr,
+ lapack_int ldvr, lapack_int* ilo,
+ lapack_int* ihi, double* lscale, double* rscale,
+ double* abnrm, double* bbnrm, double* rconde,
+ double* rcondv, double* work, lapack_int lwork,
+ lapack_int* iwork, lapack_logical* bwork );
+lapack_int LAPACKE_cggevx_work( int matrix_order, char balanc, char jobvl,
+ char jobvr, char sense, lapack_int n,
+ lapack_complex_float* a, lapack_int lda,
+ lapack_complex_float* b, lapack_int ldb,
+ lapack_complex_float* alpha,
+ lapack_complex_float* beta,
+ lapack_complex_float* vl, lapack_int ldvl,
+ lapack_complex_float* vr, lapack_int ldvr,
+ lapack_int* ilo, lapack_int* ihi, float* lscale,
+ float* rscale, float* abnrm, float* bbnrm,
+ float* rconde, float* rcondv,
+ lapack_complex_float* work, lapack_int lwork,
+ float* rwork, lapack_int* iwork,
+ lapack_logical* bwork );
+lapack_int LAPACKE_zggevx_work( int matrix_order, char balanc, char jobvl,
+ char jobvr, char sense, lapack_int n,
+ lapack_complex_double* a, lapack_int lda,
+ lapack_complex_double* b, lapack_int ldb,
+ lapack_complex_double* alpha,
+ lapack_complex_double* beta,
+ lapack_complex_double* vl, lapack_int ldvl,
+ lapack_complex_double* vr, lapack_int ldvr,
+ lapack_int* ilo, lapack_int* ihi,
+ double* lscale, double* rscale, double* abnrm,
+ double* bbnrm, double* rconde, double* rcondv,
+ lapack_complex_double* work, lapack_int lwork,
+ double* rwork, lapack_int* iwork,
+ lapack_logical* bwork );
+
+lapack_int LAPACKE_sggglm_work( int matrix_order, lapack_int n, lapack_int m,
+ lapack_int p, float* a, lapack_int lda,
+ float* b, lapack_int ldb, float* d, float* x,
+ float* y, float* work, lapack_int lwork );
+lapack_int LAPACKE_dggglm_work( int matrix_order, lapack_int n, lapack_int m,
+ lapack_int p, double* a, lapack_int lda,
+ double* b, lapack_int ldb, double* d, double* x,
+ double* y, double* work, lapack_int lwork );
+lapack_int LAPACKE_cggglm_work( int matrix_order, lapack_int n, lapack_int m,
+ lapack_int p, lapack_complex_float* a,
+ lapack_int lda, lapack_complex_float* b,
+ lapack_int ldb, lapack_complex_float* d,
+ lapack_complex_float* x,
+ lapack_complex_float* y,
+ lapack_complex_float* work, lapack_int lwork );
+lapack_int LAPACKE_zggglm_work( int matrix_order, lapack_int n, lapack_int m,
+ lapack_int p, lapack_complex_double* a,
+ lapack_int lda, lapack_complex_double* b,
+ lapack_int ldb, lapack_complex_double* d,
+ lapack_complex_double* x,
+ lapack_complex_double* y,
+ lapack_complex_double* work, lapack_int lwork );
+
+lapack_int LAPACKE_sgghrd_work( int matrix_order, char compq, char compz,
+ lapack_int n, lapack_int ilo, lapack_int ihi,
+ float* a, lapack_int lda, float* b,
+ lapack_int ldb, float* q, lapack_int ldq,
+ float* z, lapack_int ldz );
+lapack_int LAPACKE_dgghrd_work( int matrix_order, char compq, char compz,
+ lapack_int n, lapack_int ilo, lapack_int ihi,
+ double* a, lapack_int lda, double* b,
+ lapack_int ldb, double* q, lapack_int ldq,
+ double* z, lapack_int ldz );
+lapack_int LAPACKE_cgghrd_work( int matrix_order, char compq, char compz,
+ lapack_int n, lapack_int ilo, lapack_int ihi,
+ lapack_complex_float* a, lapack_int lda,
+ lapack_complex_float* b, lapack_int ldb,
+ lapack_complex_float* q, lapack_int ldq,
+ lapack_complex_float* z, lapack_int ldz );
+lapack_int LAPACKE_zgghrd_work( int matrix_order, char compq, char compz,
+ lapack_int n, lapack_int ilo, lapack_int ihi,
+ lapack_complex_double* a, lapack_int lda,
+ lapack_complex_double* b, lapack_int ldb,
+ lapack_complex_double* q, lapack_int ldq,
+ lapack_complex_double* z, lapack_int ldz );
+
+lapack_int LAPACKE_sgglse_work( int matrix_order, lapack_int m, lapack_int n,
+ lapack_int p, float* a, lapack_int lda,
+ float* b, lapack_int ldb, float* c, float* d,
+ float* x, float* work, lapack_int lwork );
+lapack_int LAPACKE_dgglse_work( int matrix_order, lapack_int m, lapack_int n,
+ lapack_int p, double* a, lapack_int lda,
+ double* b, lapack_int ldb, double* c, double* d,
+ double* x, double* work, lapack_int lwork );
+lapack_int LAPACKE_cgglse_work( int matrix_order, lapack_int m, lapack_int n,
+ lapack_int p, lapack_complex_float* a,
+ lapack_int lda, lapack_complex_float* b,
+ lapack_int ldb, lapack_complex_float* c,
+ lapack_complex_float* d,
+ lapack_complex_float* x,
+ lapack_complex_float* work, lapack_int lwork );
+lapack_int LAPACKE_zgglse_work( int matrix_order, lapack_int m, lapack_int n,
+ lapack_int p, lapack_complex_double* a,
+ lapack_int lda, lapack_complex_double* b,
+ lapack_int ldb, lapack_complex_double* c,
+ lapack_complex_double* d,
+ lapack_complex_double* x,
+ lapack_complex_double* work, lapack_int lwork );
+
+lapack_int LAPACKE_sggqrf_work( int matrix_order, lapack_int n, lapack_int m,
+ lapack_int p, float* a, lapack_int lda,
+ float* taua, float* b, lapack_int ldb,
+ float* taub, float* work, lapack_int lwork );
+lapack_int LAPACKE_dggqrf_work( int matrix_order, lapack_int n, lapack_int m,
+ lapack_int p, double* a, lapack_int lda,
+ double* taua, double* b, lapack_int ldb,
+ double* taub, double* work, lapack_int lwork );
+lapack_int LAPACKE_cggqrf_work( int matrix_order, lapack_int n, lapack_int m,
+ lapack_int p, lapack_complex_float* a,
+ lapack_int lda, lapack_complex_float* taua,
+ lapack_complex_float* b, lapack_int ldb,
+ lapack_complex_float* taub,
+ lapack_complex_float* work, lapack_int lwork );
+lapack_int LAPACKE_zggqrf_work( int matrix_order, lapack_int n, lapack_int m,
+ lapack_int p, lapack_complex_double* a,
+ lapack_int lda, lapack_complex_double* taua,
+ lapack_complex_double* b, lapack_int ldb,
+ lapack_complex_double* taub,
+ lapack_complex_double* work, lapack_int lwork );
+
+lapack_int LAPACKE_sggrqf_work( int matrix_order, lapack_int m, lapack_int p,
+ lapack_int n, float* a, lapack_int lda,
+ float* taua, float* b, lapack_int ldb,
+ float* taub, float* work, lapack_int lwork );
+lapack_int LAPACKE_dggrqf_work( int matrix_order, lapack_int m, lapack_int p,
+ lapack_int n, double* a, lapack_int lda,
+ double* taua, double* b, lapack_int ldb,
+ double* taub, double* work, lapack_int lwork );
+lapack_int LAPACKE_cggrqf_work( int matrix_order, lapack_int m, lapack_int p,
+ lapack_int n, lapack_complex_float* a,
+ lapack_int lda, lapack_complex_float* taua,
+ lapack_complex_float* b, lapack_int ldb,
+ lapack_complex_float* taub,
+ lapack_complex_float* work, lapack_int lwork );
+lapack_int LAPACKE_zggrqf_work( int matrix_order, lapack_int m, lapack_int p,
+ lapack_int n, lapack_complex_double* a,
+ lapack_int lda, lapack_complex_double* taua,
+ lapack_complex_double* b, lapack_int ldb,
+ lapack_complex_double* taub,
+ lapack_complex_double* work, lapack_int lwork );
+
+lapack_int LAPACKE_sggsvd_work( int matrix_order, char jobu, char jobv,
+ char jobq, lapack_int m, lapack_int n,
+ lapack_int p, lapack_int* k, lapack_int* l,
+ float* a, lapack_int lda, float* b,
+ lapack_int ldb, float* alpha, float* beta,
+ float* u, lapack_int ldu, float* v,
+ lapack_int ldv, float* q, lapack_int ldq,
+ float* work, lapack_int* iwork );
+lapack_int LAPACKE_dggsvd_work( int matrix_order, char jobu, char jobv,
+ char jobq, lapack_int m, lapack_int n,
+ lapack_int p, lapack_int* k, lapack_int* l,
+ double* a, lapack_int lda, double* b,
+ lapack_int ldb, double* alpha, double* beta,
+ double* u, lapack_int ldu, double* v,
+ lapack_int ldv, double* q, lapack_int ldq,
+ double* work, lapack_int* iwork );
+lapack_int LAPACKE_cggsvd_work( int matrix_order, char jobu, char jobv,
+ char jobq, lapack_int m, lapack_int n,
+ lapack_int p, lapack_int* k, lapack_int* l,
+ lapack_complex_float* a, lapack_int lda,
+ lapack_complex_float* b, lapack_int ldb,
+ float* alpha, float* beta,
+ lapack_complex_float* u, lapack_int ldu,
+ lapack_complex_float* v, lapack_int ldv,
+ lapack_complex_float* q, lapack_int ldq,
+ lapack_complex_float* work, float* rwork,
+ lapack_int* iwork );
+lapack_int LAPACKE_zggsvd_work( int matrix_order, char jobu, char jobv,
+ char jobq, lapack_int m, lapack_int n,
+ lapack_int p, lapack_int* k, lapack_int* l,
+ lapack_complex_double* a, lapack_int lda,
+ lapack_complex_double* b, lapack_int ldb,
+ double* alpha, double* beta,
+ lapack_complex_double* u, lapack_int ldu,
+ lapack_complex_double* v, lapack_int ldv,
+ lapack_complex_double* q, lapack_int ldq,
+ lapack_complex_double* work, double* rwork,
+ lapack_int* iwork );
+
+lapack_int LAPACKE_sggsvp_work( int matrix_order, char jobu, char jobv,
+ char jobq, lapack_int m, lapack_int p,
+ lapack_int n, float* a, lapack_int lda,
+ float* b, lapack_int ldb, float tola,
+ float tolb, lapack_int* k, lapack_int* l,
+ float* u, lapack_int ldu, float* v,
+ lapack_int ldv, float* q, lapack_int ldq,
+ lapack_int* iwork, float* tau, float* work );
+lapack_int LAPACKE_dggsvp_work( int matrix_order, char jobu, char jobv,
+ char jobq, lapack_int m, lapack_int p,
+ lapack_int n, double* a, lapack_int lda,
+ double* b, lapack_int ldb, double tola,
+ double tolb, lapack_int* k, lapack_int* l,
+ double* u, lapack_int ldu, double* v,
+ lapack_int ldv, double* q, lapack_int ldq,
+ lapack_int* iwork, double* tau, double* work );
+lapack_int LAPACKE_cggsvp_work( int matrix_order, char jobu, char jobv,
+ char jobq, lapack_int m, lapack_int p,
+ lapack_int n, lapack_complex_float* a,
+ lapack_int lda, lapack_complex_float* b,
+ lapack_int ldb, float tola, float tolb,
+ lapack_int* k, lapack_int* l,
+ lapack_complex_float* u, lapack_int ldu,
+ lapack_complex_float* v, lapack_int ldv,
+ lapack_complex_float* q, lapack_int ldq,
+ lapack_int* iwork, float* rwork,
+ lapack_complex_float* tau,
+ lapack_complex_float* work );
+lapack_int LAPACKE_zggsvp_work( int matrix_order, char jobu, char jobv,
+ char jobq, lapack_int m, lapack_int p,
+ lapack_int n, lapack_complex_double* a,
+ lapack_int lda, lapack_complex_double* b,
+ lapack_int ldb, double tola, double tolb,
+ lapack_int* k, lapack_int* l,
+ lapack_complex_double* u, lapack_int ldu,
+ lapack_complex_double* v, lapack_int ldv,
+ lapack_complex_double* q, lapack_int ldq,
+ lapack_int* iwork, double* rwork,
+ lapack_complex_double* tau,
+ lapack_complex_double* work );
+
+lapack_int LAPACKE_sgtcon_work( char norm, lapack_int n, const float* dl,
+ const float* d, const float* du,
+ const float* du2, const lapack_int* ipiv,
+ float anorm, float* rcond, float* work,
+ lapack_int* iwork );
+lapack_int LAPACKE_dgtcon_work( char norm, lapack_int n, const double* dl,
+ const double* d, const double* du,
+ const double* du2, const lapack_int* ipiv,
+ double anorm, double* rcond, double* work,
+ lapack_int* iwork );
+lapack_int LAPACKE_cgtcon_work( char norm, lapack_int n,
+ const lapack_complex_float* dl,
+ const lapack_complex_float* d,
+ const lapack_complex_float* du,
+ const lapack_complex_float* du2,
+ const lapack_int* ipiv, float anorm,
+ float* rcond, lapack_complex_float* work );
+lapack_int LAPACKE_zgtcon_work( char norm, lapack_int n,
+ const lapack_complex_double* dl,
+ const lapack_complex_double* d,
+ const lapack_complex_double* du,
+ const lapack_complex_double* du2,
+ const lapack_int* ipiv, double anorm,
+ double* rcond, lapack_complex_double* work );
+
+lapack_int LAPACKE_sgtrfs_work( int matrix_order, char trans, lapack_int n,
+ lapack_int nrhs, const float* dl,
+ const float* d, const float* du,
+ const float* dlf, const float* df,
+ const float* duf, const float* du2,
+ const lapack_int* ipiv, const float* b,
+ lapack_int ldb, float* x, lapack_int ldx,
+ float* ferr, float* berr, float* work,
+ lapack_int* iwork );
+lapack_int LAPACKE_dgtrfs_work( int matrix_order, char trans, lapack_int n,
+ lapack_int nrhs, const double* dl,
+ const double* d, const double* du,
+ const double* dlf, const double* df,
+ const double* duf, const double* du2,
+ const lapack_int* ipiv, const double* b,
+ lapack_int ldb, double* x, lapack_int ldx,
+ double* ferr, double* berr, double* work,
+ lapack_int* iwork );
+lapack_int LAPACKE_cgtrfs_work( int matrix_order, char trans, lapack_int n,
+ lapack_int nrhs, const lapack_complex_float* dl,
+ const lapack_complex_float* d,
+ const lapack_complex_float* du,
+ const lapack_complex_float* dlf,
+ const lapack_complex_float* df,
+ const lapack_complex_float* duf,
+ const lapack_complex_float* du2,
+ const lapack_int* ipiv,
+ const lapack_complex_float* b, lapack_int ldb,
+ lapack_complex_float* x, lapack_int ldx,
+ float* ferr, float* berr,
+ lapack_complex_float* work, float* rwork );
+lapack_int LAPACKE_zgtrfs_work( int matrix_order, char trans, lapack_int n,
+ lapack_int nrhs,
+ const lapack_complex_double* dl,
+ const lapack_complex_double* d,
+ const lapack_complex_double* du,
+ const lapack_complex_double* dlf,
+ const lapack_complex_double* df,
+ const lapack_complex_double* duf,
+ const lapack_complex_double* du2,
+ const lapack_int* ipiv,
+ const lapack_complex_double* b, lapack_int ldb,
+ lapack_complex_double* x, lapack_int ldx,
+ double* ferr, double* berr,
+ lapack_complex_double* work, double* rwork );
+
+lapack_int LAPACKE_sgtsv_work( int matrix_order, lapack_int n, lapack_int nrhs,
+ float* dl, float* d, float* du, float* b,
+ lapack_int ldb );
+lapack_int LAPACKE_dgtsv_work( int matrix_order, lapack_int n, lapack_int nrhs,
+ double* dl, double* d, double* du, double* b,
+ lapack_int ldb );
+lapack_int LAPACKE_cgtsv_work( int matrix_order, lapack_int n, lapack_int nrhs,
+ lapack_complex_float* dl,
+ lapack_complex_float* d,
+ lapack_complex_float* du,
+ lapack_complex_float* b, lapack_int ldb );
+lapack_int LAPACKE_zgtsv_work( int matrix_order, lapack_int n, lapack_int nrhs,
+ lapack_complex_double* dl,
+ lapack_complex_double* d,
+ lapack_complex_double* du,
+ lapack_complex_double* b, lapack_int ldb );
+
+lapack_int LAPACKE_sgtsvx_work( int matrix_order, char fact, char trans,
+ lapack_int n, lapack_int nrhs, const float* dl,
+ const float* d, const float* du, float* dlf,
+ float* df, float* duf, float* du2,
+ lapack_int* ipiv, const float* b,
+ lapack_int ldb, float* x, lapack_int ldx,
+ float* rcond, float* ferr, float* berr,
+ float* work, lapack_int* iwork );
+lapack_int LAPACKE_dgtsvx_work( int matrix_order, char fact, char trans,
+ lapack_int n, lapack_int nrhs, const double* dl,
+ const double* d, const double* du, double* dlf,
+ double* df, double* duf, double* du2,
+ lapack_int* ipiv, const double* b,
+ lapack_int ldb, double* x, lapack_int ldx,
+ double* rcond, double* ferr, double* berr,
+ double* work, lapack_int* iwork );
+lapack_int LAPACKE_cgtsvx_work( int matrix_order, char fact, char trans,
+ lapack_int n, lapack_int nrhs,
+ const lapack_complex_float* dl,
+ const lapack_complex_float* d,
+ const lapack_complex_float* du,
+ lapack_complex_float* dlf,
+ lapack_complex_float* df,
+ lapack_complex_float* duf,
+ lapack_complex_float* du2, lapack_int* ipiv,
+ const lapack_complex_float* b, lapack_int ldb,
+ lapack_complex_float* x, lapack_int ldx,
+ float* rcond, float* ferr, float* berr,
+ lapack_complex_float* work, float* rwork );
+lapack_int LAPACKE_zgtsvx_work( int matrix_order, char fact, char trans,
+ lapack_int n, lapack_int nrhs,
+ const lapack_complex_double* dl,
+ const lapack_complex_double* d,
+ const lapack_complex_double* du,
+ lapack_complex_double* dlf,
+ lapack_complex_double* df,
+ lapack_complex_double* duf,
+ lapack_complex_double* du2, lapack_int* ipiv,
+ const lapack_complex_double* b, lapack_int ldb,
+ lapack_complex_double* x, lapack_int ldx,
+ double* rcond, double* ferr, double* berr,
+ lapack_complex_double* work, double* rwork );
+
+lapack_int LAPACKE_sgttrf_work( lapack_int n, float* dl, float* d, float* du,
+ float* du2, lapack_int* ipiv );
+lapack_int LAPACKE_dgttrf_work( lapack_int n, double* dl, double* d, double* du,
+ double* du2, lapack_int* ipiv );
+lapack_int LAPACKE_cgttrf_work( lapack_int n, lapack_complex_float* dl,
+ lapack_complex_float* d,
+ lapack_complex_float* du,
+ lapack_complex_float* du2, lapack_int* ipiv );
+lapack_int LAPACKE_zgttrf_work( lapack_int n, lapack_complex_double* dl,
+ lapack_complex_double* d,
+ lapack_complex_double* du,
+ lapack_complex_double* du2, lapack_int* ipiv );
+
+lapack_int LAPACKE_sgttrs_work( int matrix_order, char trans, lapack_int n,
+ lapack_int nrhs, const float* dl,
+ const float* d, const float* du,
+ const float* du2, const lapack_int* ipiv,
+ float* b, lapack_int ldb );
+lapack_int LAPACKE_dgttrs_work( int matrix_order, char trans, lapack_int n,
+ lapack_int nrhs, const double* dl,
+ const double* d, const double* du,
+ const double* du2, const lapack_int* ipiv,
+ double* b, lapack_int ldb );
+lapack_int LAPACKE_cgttrs_work( int matrix_order, char trans, lapack_int n,
+ lapack_int nrhs, const lapack_complex_float* dl,
+ const lapack_complex_float* d,
+ const lapack_complex_float* du,
+ const lapack_complex_float* du2,
+ const lapack_int* ipiv, lapack_complex_float* b,
+ lapack_int ldb );
+lapack_int LAPACKE_zgttrs_work( int matrix_order, char trans, lapack_int n,
+ lapack_int nrhs,
+ const lapack_complex_double* dl,
+ const lapack_complex_double* d,
+ const lapack_complex_double* du,
+ const lapack_complex_double* du2,
+ const lapack_int* ipiv,
+ lapack_complex_double* b, lapack_int ldb );
+
+lapack_int LAPACKE_chbev_work( int matrix_order, char jobz, char uplo,
+ lapack_int n, lapack_int kd,
+ lapack_complex_float* ab, lapack_int ldab,
+ float* w, lapack_complex_float* z,
+ lapack_int ldz, lapack_complex_float* work,
+ float* rwork );
+lapack_int LAPACKE_zhbev_work( int matrix_order, char jobz, char uplo,
+ lapack_int n, lapack_int kd,
+ lapack_complex_double* ab, lapack_int ldab,
+ double* w, lapack_complex_double* z,
+ lapack_int ldz, lapack_complex_double* work,
+ double* rwork );
+
+lapack_int LAPACKE_chbevd_work( int matrix_order, char jobz, char uplo,
+ lapack_int n, lapack_int kd,
+ lapack_complex_float* ab, lapack_int ldab,
+ float* w, lapack_complex_float* z,
+ lapack_int ldz, lapack_complex_float* work,
+ lapack_int lwork, float* rwork,
+ lapack_int lrwork, lapack_int* iwork,
+ lapack_int liwork );
+lapack_int LAPACKE_zhbevd_work( int matrix_order, char jobz, char uplo,
+ lapack_int n, lapack_int kd,
+ lapack_complex_double* ab, lapack_int ldab,
+ double* w, lapack_complex_double* z,
+ lapack_int ldz, lapack_complex_double* work,
+ lapack_int lwork, double* rwork,
+ lapack_int lrwork, lapack_int* iwork,
+ lapack_int liwork );
+
+lapack_int LAPACKE_chbevx_work( int matrix_order, char jobz, char range,
+ char uplo, lapack_int n, lapack_int kd,
+ lapack_complex_float* ab, lapack_int ldab,
+ lapack_complex_float* q, lapack_int ldq,
+ float vl, float vu, lapack_int il,
+ lapack_int iu, float abstol, lapack_int* m,
+ float* w, lapack_complex_float* z,
+ lapack_int ldz, lapack_complex_float* work,
+ float* rwork, lapack_int* iwork,
+ lapack_int* ifail );
+lapack_int LAPACKE_zhbevx_work( int matrix_order, char jobz, char range,
+ char uplo, lapack_int n, lapack_int kd,
+ lapack_complex_double* ab, lapack_int ldab,
+ lapack_complex_double* q, lapack_int ldq,
+ double vl, double vu, lapack_int il,
+ lapack_int iu, double abstol, lapack_int* m,
+ double* w, lapack_complex_double* z,
+ lapack_int ldz, lapack_complex_double* work,
+ double* rwork, lapack_int* iwork,
+ lapack_int* ifail );
+
+lapack_int LAPACKE_chbgst_work( int matrix_order, char vect, char uplo,
+ lapack_int n, lapack_int ka, lapack_int kb,
+ lapack_complex_float* ab, lapack_int ldab,
+ const lapack_complex_float* bb, lapack_int ldbb,
+ lapack_complex_float* x, lapack_int ldx,
+ lapack_complex_float* work, float* rwork );
+lapack_int LAPACKE_zhbgst_work( int matrix_order, char vect, char uplo,
+ lapack_int n, lapack_int ka, lapack_int kb,
+ lapack_complex_double* ab, lapack_int ldab,
+ const lapack_complex_double* bb,
+ lapack_int ldbb, lapack_complex_double* x,
+ lapack_int ldx, lapack_complex_double* work,
+ double* rwork );
+
+lapack_int LAPACKE_chbgv_work( int matrix_order, char jobz, char uplo,
+ lapack_int n, lapack_int ka, lapack_int kb,
+ lapack_complex_float* ab, lapack_int ldab,
+ lapack_complex_float* bb, lapack_int ldbb,
+ float* w, lapack_complex_float* z,
+ lapack_int ldz, lapack_complex_float* work,
+ float* rwork );
+lapack_int LAPACKE_zhbgv_work( int matrix_order, char jobz, char uplo,
+ lapack_int n, lapack_int ka, lapack_int kb,
+ lapack_complex_double* ab, lapack_int ldab,
+ lapack_complex_double* bb, lapack_int ldbb,
+ double* w, lapack_complex_double* z,
+ lapack_int ldz, lapack_complex_double* work,
+ double* rwork );
+
+lapack_int LAPACKE_chbgvd_work( int matrix_order, char jobz, char uplo,
+ lapack_int n, lapack_int ka, lapack_int kb,
+ lapack_complex_float* ab, lapack_int ldab,
+ lapack_complex_float* bb, lapack_int ldbb,
+ float* w, lapack_complex_float* z,
+ lapack_int ldz, lapack_complex_float* work,
+ lapack_int lwork, float* rwork,
+ lapack_int lrwork, lapack_int* iwork,
+ lapack_int liwork );
+lapack_int LAPACKE_zhbgvd_work( int matrix_order, char jobz, char uplo,
+ lapack_int n, lapack_int ka, lapack_int kb,
+ lapack_complex_double* ab, lapack_int ldab,
+ lapack_complex_double* bb, lapack_int ldbb,
+ double* w, lapack_complex_double* z,
+ lapack_int ldz, lapack_complex_double* work,
+ lapack_int lwork, double* rwork,
+ lapack_int lrwork, lapack_int* iwork,
+ lapack_int liwork );
+
+lapack_int LAPACKE_chbgvx_work( int matrix_order, char jobz, char range,
+ char uplo, lapack_int n, lapack_int ka,
+ lapack_int kb, lapack_complex_float* ab,
+ lapack_int ldab, lapack_complex_float* bb,
+ lapack_int ldbb, lapack_complex_float* q,
+ lapack_int ldq, float vl, float vu,
+ lapack_int il, lapack_int iu, float abstol,
+ lapack_int* m, float* w,
+ lapack_complex_float* z, lapack_int ldz,
+ lapack_complex_float* work, float* rwork,
+ lapack_int* iwork, lapack_int* ifail );
+lapack_int LAPACKE_zhbgvx_work( int matrix_order, char jobz, char range,
+ char uplo, lapack_int n, lapack_int ka,
+ lapack_int kb, lapack_complex_double* ab,
+ lapack_int ldab, lapack_complex_double* bb,
+ lapack_int ldbb, lapack_complex_double* q,
+ lapack_int ldq, double vl, double vu,
+ lapack_int il, lapack_int iu, double abstol,
+ lapack_int* m, double* w,
+ lapack_complex_double* z, lapack_int ldz,
+ lapack_complex_double* work, double* rwork,
+ lapack_int* iwork, lapack_int* ifail );
+
+lapack_int LAPACKE_chbtrd_work( int matrix_order, char vect, char uplo,
+ lapack_int n, lapack_int kd,
+ lapack_complex_float* ab, lapack_int ldab,
+ float* d, float* e, lapack_complex_float* q,
+ lapack_int ldq, lapack_complex_float* work );
+lapack_int LAPACKE_zhbtrd_work( int matrix_order, char vect, char uplo,
+ lapack_int n, lapack_int kd,
+ lapack_complex_double* ab, lapack_int ldab,
+ double* d, double* e, lapack_complex_double* q,
+ lapack_int ldq, lapack_complex_double* work );
+
+lapack_int LAPACKE_checon_work( int matrix_order, char uplo, lapack_int n,
+ const lapack_complex_float* a, lapack_int lda,
+ const lapack_int* ipiv, float anorm,
+ float* rcond, lapack_complex_float* work );
+lapack_int LAPACKE_zhecon_work( int matrix_order, char uplo, lapack_int n,
+ const lapack_complex_double* a, lapack_int lda,
+ const lapack_int* ipiv, double anorm,
+ double* rcond, lapack_complex_double* work );
+
+lapack_int LAPACKE_cheequb_work( int matrix_order, char uplo, lapack_int n,
+ const lapack_complex_float* a, lapack_int lda,
+ float* s, float* scond, float* amax,
+ lapack_complex_float* work );
+lapack_int LAPACKE_zheequb_work( int matrix_order, char uplo, lapack_int n,
+ const lapack_complex_double* a, lapack_int lda,
+ double* s, double* scond, double* amax,
+ lapack_complex_double* work );
+
+lapack_int LAPACKE_cheev_work( int matrix_order, char jobz, char uplo,
+ lapack_int n, lapack_complex_float* a,
+ lapack_int lda, float* w,
+ lapack_complex_float* work, lapack_int lwork,
+ float* rwork );
+lapack_int LAPACKE_zheev_work( int matrix_order, char jobz, char uplo,
+ lapack_int n, lapack_complex_double* a,
+ lapack_int lda, double* w,
+ lapack_complex_double* work, lapack_int lwork,
+ double* rwork );
+
+lapack_int LAPACKE_cheevd_work( int matrix_order, char jobz, char uplo,
+ lapack_int n, lapack_complex_float* a,
+ lapack_int lda, float* w,
+ lapack_complex_float* work, lapack_int lwork,
+ float* rwork, lapack_int lrwork,
+ lapack_int* iwork, lapack_int liwork );
+lapack_int LAPACKE_zheevd_work( int matrix_order, char jobz, char uplo,
+ lapack_int n, lapack_complex_double* a,
+ lapack_int lda, double* w,
+ lapack_complex_double* work, lapack_int lwork,
+ double* rwork, lapack_int lrwork,
+ lapack_int* iwork, lapack_int liwork );
+
+lapack_int LAPACKE_cheevr_work( int matrix_order, char jobz, char range,
+ char uplo, lapack_int n,
+ lapack_complex_float* a, lapack_int lda,
+ float vl, float vu, lapack_int il,
+ lapack_int iu, float abstol, lapack_int* m,
+ float* w, lapack_complex_float* z,
+ lapack_int ldz, lapack_int* isuppz,
+ lapack_complex_float* work, lapack_int lwork,
+ float* rwork, lapack_int lrwork,
+ lapack_int* iwork, lapack_int liwork );
+lapack_int LAPACKE_zheevr_work( int matrix_order, char jobz, char range,
+ char uplo, lapack_int n,
+ lapack_complex_double* a, lapack_int lda,
+ double vl, double vu, lapack_int il,
+ lapack_int iu, double abstol, lapack_int* m,
+ double* w, lapack_complex_double* z,
+ lapack_int ldz, lapack_int* isuppz,
+ lapack_complex_double* work, lapack_int lwork,
+ double* rwork, lapack_int lrwork,
+ lapack_int* iwork, lapack_int liwork );
+
+lapack_int LAPACKE_cheevx_work( int matrix_order, char jobz, char range,
+ char uplo, lapack_int n,
+ lapack_complex_float* a, lapack_int lda,
+ float vl, float vu, lapack_int il,
+ lapack_int iu, float abstol, lapack_int* m,
+ float* w, lapack_complex_float* z,
+ lapack_int ldz, lapack_complex_float* work,
+ lapack_int lwork, float* rwork,
+ lapack_int* iwork, lapack_int* ifail );
+lapack_int LAPACKE_zheevx_work( int matrix_order, char jobz, char range,
+ char uplo, lapack_int n,
+ lapack_complex_double* a, lapack_int lda,
+ double vl, double vu, lapack_int il,
+ lapack_int iu, double abstol, lapack_int* m,
+ double* w, lapack_complex_double* z,
+ lapack_int ldz, lapack_complex_double* work,
+ lapack_int lwork, double* rwork,
+ lapack_int* iwork, lapack_int* ifail );
+
+lapack_int LAPACKE_chegst_work( int matrix_order, lapack_int itype, char uplo,
+ lapack_int n, lapack_complex_float* a,
+ lapack_int lda, const lapack_complex_float* b,
+ lapack_int ldb );
+lapack_int LAPACKE_zhegst_work( int matrix_order, lapack_int itype, char uplo,
+ lapack_int n, lapack_complex_double* a,
+ lapack_int lda, const lapack_complex_double* b,
+ lapack_int ldb );
+
+lapack_int LAPACKE_chegv_work( int matrix_order, lapack_int itype, char jobz,
+ char uplo, lapack_int n, lapack_complex_float* a,
+ lapack_int lda, lapack_complex_float* b,
+ lapack_int ldb, float* w,
+ lapack_complex_float* work, lapack_int lwork,
+ float* rwork );
+lapack_int LAPACKE_zhegv_work( int matrix_order, lapack_int itype, char jobz,
+ char uplo, lapack_int n,
+ lapack_complex_double* a, lapack_int lda,
+ lapack_complex_double* b, lapack_int ldb,
+ double* w, lapack_complex_double* work,
+ lapack_int lwork, double* rwork );
+
+lapack_int LAPACKE_chegvd_work( int matrix_order, lapack_int itype, char jobz,
+ char uplo, lapack_int n,
+ lapack_complex_float* a, lapack_int lda,
+ lapack_complex_float* b, lapack_int ldb,
+ float* w, lapack_complex_float* work,
+ lapack_int lwork, float* rwork,
+ lapack_int lrwork, lapack_int* iwork,
+ lapack_int liwork );
+lapack_int LAPACKE_zhegvd_work( int matrix_order, lapack_int itype, char jobz,
+ char uplo, lapack_int n,
+ lapack_complex_double* a, lapack_int lda,
+ lapack_complex_double* b, lapack_int ldb,
+ double* w, lapack_complex_double* work,
+ lapack_int lwork, double* rwork,
+ lapack_int lrwork, lapack_int* iwork,
+ lapack_int liwork );
+
+lapack_int LAPACKE_chegvx_work( int matrix_order, lapack_int itype, char jobz,
+ char range, char uplo, lapack_int n,
+ lapack_complex_float* a, lapack_int lda,
+ lapack_complex_float* b, lapack_int ldb,
+ float vl, float vu, lapack_int il,
+ lapack_int iu, float abstol, lapack_int* m,
+ float* w, lapack_complex_float* z,
+ lapack_int ldz, lapack_complex_float* work,
+ lapack_int lwork, float* rwork,
+ lapack_int* iwork, lapack_int* ifail );
+lapack_int LAPACKE_zhegvx_work( int matrix_order, lapack_int itype, char jobz,
+ char range, char uplo, lapack_int n,
+ lapack_complex_double* a, lapack_int lda,
+ lapack_complex_double* b, lapack_int ldb,
+ double vl, double vu, lapack_int il,
+ lapack_int iu, double abstol, lapack_int* m,
+ double* w, lapack_complex_double* z,
+ lapack_int ldz, lapack_complex_double* work,
+ lapack_int lwork, double* rwork,
+ lapack_int* iwork, lapack_int* ifail );
+
+lapack_int LAPACKE_cherfs_work( int matrix_order, char uplo, lapack_int n,
+ lapack_int nrhs, const lapack_complex_float* a,
+ lapack_int lda, const lapack_complex_float* af,
+ lapack_int ldaf, const lapack_int* ipiv,
+ const lapack_complex_float* b, lapack_int ldb,
+ lapack_complex_float* x, lapack_int ldx,
+ float* ferr, float* berr,
+ lapack_complex_float* work, float* rwork );
+lapack_int LAPACKE_zherfs_work( int matrix_order, char uplo, lapack_int n,
+ lapack_int nrhs, const lapack_complex_double* a,
+ lapack_int lda, const lapack_complex_double* af,
+ lapack_int ldaf, const lapack_int* ipiv,
+ const lapack_complex_double* b, lapack_int ldb,
+ lapack_complex_double* x, lapack_int ldx,
+ double* ferr, double* berr,
+ lapack_complex_double* work, double* rwork );
+
+lapack_int LAPACKE_cherfsx_work( int matrix_order, char uplo, char equed,
+ lapack_int n, lapack_int nrhs,
+ const lapack_complex_float* a, lapack_int lda,
+ const lapack_complex_float* af,
+ lapack_int ldaf, const lapack_int* ipiv,
+ const float* s, const lapack_complex_float* b,
+ lapack_int ldb, lapack_complex_float* x,
+ lapack_int ldx, float* rcond, float* berr,
+ lapack_int n_err_bnds, float* err_bnds_norm,
+ float* err_bnds_comp, lapack_int nparams,
+ float* params, lapack_complex_float* work,
+ float* rwork );
+lapack_int LAPACKE_zherfsx_work( int matrix_order, char uplo, char equed,
+ lapack_int n, lapack_int nrhs,
+ const lapack_complex_double* a, lapack_int lda,
+ const lapack_complex_double* af,
+ lapack_int ldaf, const lapack_int* ipiv,
+ const double* s,
+ const lapack_complex_double* b, lapack_int ldb,
+ lapack_complex_double* x, lapack_int ldx,
+ double* rcond, double* berr,
+ lapack_int n_err_bnds, double* err_bnds_norm,
+ double* err_bnds_comp, lapack_int nparams,
+ double* params, lapack_complex_double* work,
+ double* rwork );
+
+lapack_int LAPACKE_chesv_work( int matrix_order, char uplo, lapack_int n,
+ lapack_int nrhs, lapack_complex_float* a,
+ lapack_int lda, lapack_int* ipiv,
+ lapack_complex_float* b, lapack_int ldb,
+ lapack_complex_float* work, lapack_int lwork );
+lapack_int LAPACKE_zhesv_work( int matrix_order, char uplo, lapack_int n,
+ lapack_int nrhs, lapack_complex_double* a,
+ lapack_int lda, lapack_int* ipiv,
+ lapack_complex_double* b, lapack_int ldb,
+ lapack_complex_double* work, lapack_int lwork );
+
+lapack_int LAPACKE_chesvx_work( int matrix_order, char fact, char uplo,
+ lapack_int n, lapack_int nrhs,
+ const lapack_complex_float* a, lapack_int lda,
+ lapack_complex_float* af, lapack_int ldaf,
+ lapack_int* ipiv, const lapack_complex_float* b,
+ lapack_int ldb, lapack_complex_float* x,
+ lapack_int ldx, float* rcond, float* ferr,
+ float* berr, lapack_complex_float* work,
+ lapack_int lwork, float* rwork );
+lapack_int LAPACKE_zhesvx_work( int matrix_order, char fact, char uplo,
+ lapack_int n, lapack_int nrhs,
+ const lapack_complex_double* a, lapack_int lda,
+ lapack_complex_double* af, lapack_int ldaf,
+ lapack_int* ipiv,
+ const lapack_complex_double* b, lapack_int ldb,
+ lapack_complex_double* x, lapack_int ldx,
+ double* rcond, double* ferr, double* berr,
+ lapack_complex_double* work, lapack_int lwork,
+ double* rwork );
+
+lapack_int LAPACKE_chesvxx_work( int matrix_order, char fact, char uplo,
+ lapack_int n, lapack_int nrhs,
+ lapack_complex_float* a, lapack_int lda,
+ lapack_complex_float* af, lapack_int ldaf,
+ lapack_int* ipiv, char* equed, float* s,
+ lapack_complex_float* b, lapack_int ldb,
+ lapack_complex_float* x, lapack_int ldx,
+ float* rcond, float* rpvgrw, float* berr,
+ lapack_int n_err_bnds, float* err_bnds_norm,
+ float* err_bnds_comp, lapack_int nparams,
+ float* params, lapack_complex_float* work,
+ float* rwork );
+lapack_int LAPACKE_zhesvxx_work( int matrix_order, char fact, char uplo,
+ lapack_int n, lapack_int nrhs,
+ lapack_complex_double* a, lapack_int lda,
+ lapack_complex_double* af, lapack_int ldaf,
+ lapack_int* ipiv, char* equed, double* s,
+ lapack_complex_double* b, lapack_int ldb,
+ lapack_complex_double* x, lapack_int ldx,
+ double* rcond, double* rpvgrw, double* berr,
+ lapack_int n_err_bnds, double* err_bnds_norm,
+ double* err_bnds_comp, lapack_int nparams,
+ double* params, lapack_complex_double* work,
+ double* rwork );
+
+lapack_int LAPACKE_chetrd_work( int matrix_order, char uplo, lapack_int n,
+ lapack_complex_float* a, lapack_int lda,
+ float* d, float* e, lapack_complex_float* tau,
+ lapack_complex_float* work, lapack_int lwork );
+lapack_int LAPACKE_zhetrd_work( int matrix_order, char uplo, lapack_int n,
+ lapack_complex_double* a, lapack_int lda,
+ double* d, double* e,
+ lapack_complex_double* tau,
+ lapack_complex_double* work, lapack_int lwork );
+
+lapack_int LAPACKE_chetrf_work( int matrix_order, char uplo, lapack_int n,
+ lapack_complex_float* a, lapack_int lda,
+ lapack_int* ipiv, lapack_complex_float* work,
+ lapack_int lwork );
+lapack_int LAPACKE_zhetrf_work( int matrix_order, char uplo, lapack_int n,
+ lapack_complex_double* a, lapack_int lda,
+ lapack_int* ipiv, lapack_complex_double* work,
+ lapack_int lwork );
+
+lapack_int LAPACKE_chetri_work( int matrix_order, char uplo, lapack_int n,
+ lapack_complex_float* a, lapack_int lda,
+ const lapack_int* ipiv,
+ lapack_complex_float* work );
+lapack_int LAPACKE_zhetri_work( int matrix_order, char uplo, lapack_int n,
+ lapack_complex_double* a, lapack_int lda,
+ const lapack_int* ipiv,
+ lapack_complex_double* work );
+
+lapack_int LAPACKE_chetrs_work( int matrix_order, char uplo, lapack_int n,
+ lapack_int nrhs, const lapack_complex_float* a,
+ lapack_int lda, const lapack_int* ipiv,
+ lapack_complex_float* b, lapack_int ldb );
+lapack_int LAPACKE_zhetrs_work( int matrix_order, char uplo, lapack_int n,
+ lapack_int nrhs, const lapack_complex_double* a,
+ lapack_int lda, const lapack_int* ipiv,
+ lapack_complex_double* b, lapack_int ldb );
+
+lapack_int LAPACKE_chfrk_work( int matrix_order, char transr, char uplo,
+ char trans, lapack_int n, lapack_int k,
+ float alpha, const lapack_complex_float* a,
+ lapack_int lda, float beta,
+ lapack_complex_float* c );
+lapack_int LAPACKE_zhfrk_work( int matrix_order, char transr, char uplo,
+ char trans, lapack_int n, lapack_int k,
+ double alpha, const lapack_complex_double* a,
+ lapack_int lda, double beta,
+ lapack_complex_double* c );
+
+lapack_int LAPACKE_shgeqz_work( int matrix_order, char job, char compq,
+ char compz, lapack_int n, lapack_int ilo,
+ lapack_int ihi, float* h, lapack_int ldh,
+ float* t, lapack_int ldt, float* alphar,
+ float* alphai, float* beta, float* q,
+ lapack_int ldq, float* z, lapack_int ldz,
+ float* work, lapack_int lwork );
+lapack_int LAPACKE_dhgeqz_work( int matrix_order, char job, char compq,
+ char compz, lapack_int n, lapack_int ilo,
+ lapack_int ihi, double* h, lapack_int ldh,
+ double* t, lapack_int ldt, double* alphar,
+ double* alphai, double* beta, double* q,
+ lapack_int ldq, double* z, lapack_int ldz,
+ double* work, lapack_int lwork );
+lapack_int LAPACKE_chgeqz_work( int matrix_order, char job, char compq,
+ char compz, lapack_int n, lapack_int ilo,
+ lapack_int ihi, lapack_complex_float* h,
+ lapack_int ldh, lapack_complex_float* t,
+ lapack_int ldt, lapack_complex_float* alpha,
+ lapack_complex_float* beta,
+ lapack_complex_float* q, lapack_int ldq,
+ lapack_complex_float* z, lapack_int ldz,
+ lapack_complex_float* work, lapack_int lwork,
+ float* rwork );
+lapack_int LAPACKE_zhgeqz_work( int matrix_order, char job, char compq,
+ char compz, lapack_int n, lapack_int ilo,
+ lapack_int ihi, lapack_complex_double* h,
+ lapack_int ldh, lapack_complex_double* t,
+ lapack_int ldt, lapack_complex_double* alpha,
+ lapack_complex_double* beta,
+ lapack_complex_double* q, lapack_int ldq,
+ lapack_complex_double* z, lapack_int ldz,
+ lapack_complex_double* work, lapack_int lwork,
+ double* rwork );
+
+lapack_int LAPACKE_chpcon_work( int matrix_order, char uplo, lapack_int n,
+ const lapack_complex_float* ap,
+ const lapack_int* ipiv, float anorm,
+ float* rcond, lapack_complex_float* work );
+lapack_int LAPACKE_zhpcon_work( int matrix_order, char uplo, lapack_int n,
+ const lapack_complex_double* ap,
+ const lapack_int* ipiv, double anorm,
+ double* rcond, lapack_complex_double* work );
+
+lapack_int LAPACKE_chpev_work( int matrix_order, char jobz, char uplo,
+ lapack_int n, lapack_complex_float* ap, float* w,
+ lapack_complex_float* z, lapack_int ldz,
+ lapack_complex_float* work, float* rwork );
+lapack_int LAPACKE_zhpev_work( int matrix_order, char jobz, char uplo,
+ lapack_int n, lapack_complex_double* ap,
+ double* w, lapack_complex_double* z,
+ lapack_int ldz, lapack_complex_double* work,
+ double* rwork );
+
+lapack_int LAPACKE_chpevd_work( int matrix_order, char jobz, char uplo,
+ lapack_int n, lapack_complex_float* ap,
+ float* w, lapack_complex_float* z,
+ lapack_int ldz, lapack_complex_float* work,
+ lapack_int lwork, float* rwork,
+ lapack_int lrwork, lapack_int* iwork,
+ lapack_int liwork );
+lapack_int LAPACKE_zhpevd_work( int matrix_order, char jobz, char uplo,
+ lapack_int n, lapack_complex_double* ap,
+ double* w, lapack_complex_double* z,
+ lapack_int ldz, lapack_complex_double* work,
+ lapack_int lwork, double* rwork,
+ lapack_int lrwork, lapack_int* iwork,
+ lapack_int liwork );
+
+lapack_int LAPACKE_chpevx_work( int matrix_order, char jobz, char range,
+ char uplo, lapack_int n,
+ lapack_complex_float* ap, float vl, float vu,
+ lapack_int il, lapack_int iu, float abstol,
+ lapack_int* m, float* w,
+ lapack_complex_float* z, lapack_int ldz,
+ lapack_complex_float* work, float* rwork,
+ lapack_int* iwork, lapack_int* ifail );
+lapack_int LAPACKE_zhpevx_work( int matrix_order, char jobz, char range,
+ char uplo, lapack_int n,
+ lapack_complex_double* ap, double vl, double vu,
+ lapack_int il, lapack_int iu, double abstol,
+ lapack_int* m, double* w,
+ lapack_complex_double* z, lapack_int ldz,
+ lapack_complex_double* work, double* rwork,
+ lapack_int* iwork, lapack_int* ifail );
+
+lapack_int LAPACKE_chpgst_work( int matrix_order, lapack_int itype, char uplo,
+ lapack_int n, lapack_complex_float* ap,
+ const lapack_complex_float* bp );
+lapack_int LAPACKE_zhpgst_work( int matrix_order, lapack_int itype, char uplo,
+ lapack_int n, lapack_complex_double* ap,
+ const lapack_complex_double* bp );
+
+lapack_int LAPACKE_chpgv_work( int matrix_order, lapack_int itype, char jobz,
+ char uplo, lapack_int n,
+ lapack_complex_float* ap,
+ lapack_complex_float* bp, float* w,
+ lapack_complex_float* z, lapack_int ldz,
+ lapack_complex_float* work, float* rwork );
+lapack_int LAPACKE_zhpgv_work( int matrix_order, lapack_int itype, char jobz,
+ char uplo, lapack_int n,
+ lapack_complex_double* ap,
+ lapack_complex_double* bp, double* w,
+ lapack_complex_double* z, lapack_int ldz,
+ lapack_complex_double* work, double* rwork );
+
+lapack_int LAPACKE_chpgvd_work( int matrix_order, lapack_int itype, char jobz,
+ char uplo, lapack_int n,
+ lapack_complex_float* ap,
+ lapack_complex_float* bp, float* w,
+ lapack_complex_float* z, lapack_int ldz,
+ lapack_complex_float* work, lapack_int lwork,
+ float* rwork, lapack_int lrwork,
+ lapack_int* iwork, lapack_int liwork );
+lapack_int LAPACKE_zhpgvd_work( int matrix_order, lapack_int itype, char jobz,
+ char uplo, lapack_int n,
+ lapack_complex_double* ap,
+ lapack_complex_double* bp, double* w,
+ lapack_complex_double* z, lapack_int ldz,
+ lapack_complex_double* work, lapack_int lwork,
+ double* rwork, lapack_int lrwork,
+ lapack_int* iwork, lapack_int liwork );
+
+lapack_int LAPACKE_chpgvx_work( int matrix_order, lapack_int itype, char jobz,
+ char range, char uplo, lapack_int n,
+ lapack_complex_float* ap,
+ lapack_complex_float* bp, float vl, float vu,
+ lapack_int il, lapack_int iu, float abstol,
+ lapack_int* m, float* w,
+ lapack_complex_float* z, lapack_int ldz,
+ lapack_complex_float* work, float* rwork,
+ lapack_int* iwork, lapack_int* ifail );
+lapack_int LAPACKE_zhpgvx_work( int matrix_order, lapack_int itype, char jobz,
+ char range, char uplo, lapack_int n,
+ lapack_complex_double* ap,
+ lapack_complex_double* bp, double vl, double vu,
+ lapack_int il, lapack_int iu, double abstol,
+ lapack_int* m, double* w,
+ lapack_complex_double* z, lapack_int ldz,
+ lapack_complex_double* work, double* rwork,
+ lapack_int* iwork, lapack_int* ifail );
+
+lapack_int LAPACKE_chprfs_work( int matrix_order, char uplo, lapack_int n,
+ lapack_int nrhs, const lapack_complex_float* ap,
+ const lapack_complex_float* afp,
+ const lapack_int* ipiv,
+ const lapack_complex_float* b, lapack_int ldb,
+ lapack_complex_float* x, lapack_int ldx,
+ float* ferr, float* berr,
+ lapack_complex_float* work, float* rwork );
+lapack_int LAPACKE_zhprfs_work( int matrix_order, char uplo, lapack_int n,
+ lapack_int nrhs,
+ const lapack_complex_double* ap,
+ const lapack_complex_double* afp,
+ const lapack_int* ipiv,
+ const lapack_complex_double* b, lapack_int ldb,
+ lapack_complex_double* x, lapack_int ldx,
+ double* ferr, double* berr,
+ lapack_complex_double* work, double* rwork );
+
+lapack_int LAPACKE_chpsv_work( int matrix_order, char uplo, lapack_int n,
+ lapack_int nrhs, lapack_complex_float* ap,
+ lapack_int* ipiv, lapack_complex_float* b,
+ lapack_int ldb );
+lapack_int LAPACKE_zhpsv_work( int matrix_order, char uplo, lapack_int n,
+ lapack_int nrhs, lapack_complex_double* ap,
+ lapack_int* ipiv, lapack_complex_double* b,
+ lapack_int ldb );
+
+lapack_int LAPACKE_chpsvx_work( int matrix_order, char fact, char uplo,
+ lapack_int n, lapack_int nrhs,
+ const lapack_complex_float* ap,
+ lapack_complex_float* afp, lapack_int* ipiv,
+ const lapack_complex_float* b, lapack_int ldb,
+ lapack_complex_float* x, lapack_int ldx,
+ float* rcond, float* ferr, float* berr,
+ lapack_complex_float* work, float* rwork );
+lapack_int LAPACKE_zhpsvx_work( int matrix_order, char fact, char uplo,
+ lapack_int n, lapack_int nrhs,
+ const lapack_complex_double* ap,
+ lapack_complex_double* afp, lapack_int* ipiv,
+ const lapack_complex_double* b, lapack_int ldb,
+ lapack_complex_double* x, lapack_int ldx,
+ double* rcond, double* ferr, double* berr,
+ lapack_complex_double* work, double* rwork );
+
+lapack_int LAPACKE_chptrd_work( int matrix_order, char uplo, lapack_int n,
+ lapack_complex_float* ap, float* d, float* e,
+ lapack_complex_float* tau );
+lapack_int LAPACKE_zhptrd_work( int matrix_order, char uplo, lapack_int n,
+ lapack_complex_double* ap, double* d, double* e,
+ lapack_complex_double* tau );
+
+lapack_int LAPACKE_chptrf_work( int matrix_order, char uplo, lapack_int n,
+ lapack_complex_float* ap, lapack_int* ipiv );
+lapack_int LAPACKE_zhptrf_work( int matrix_order, char uplo, lapack_int n,
+ lapack_complex_double* ap, lapack_int* ipiv );
+
+lapack_int LAPACKE_chptri_work( int matrix_order, char uplo, lapack_int n,
+ lapack_complex_float* ap,
+ const lapack_int* ipiv,
+ lapack_complex_float* work );
+lapack_int LAPACKE_zhptri_work( int matrix_order, char uplo, lapack_int n,
+ lapack_complex_double* ap,
+ const lapack_int* ipiv,
+ lapack_complex_double* work );
+
+lapack_int LAPACKE_chptrs_work( int matrix_order, char uplo, lapack_int n,
+ lapack_int nrhs, const lapack_complex_float* ap,
+ const lapack_int* ipiv, lapack_complex_float* b,
+ lapack_int ldb );
+lapack_int LAPACKE_zhptrs_work( int matrix_order, char uplo, lapack_int n,
+ lapack_int nrhs,
+ const lapack_complex_double* ap,
+ const lapack_int* ipiv,
+ lapack_complex_double* b, lapack_int ldb );
+
+lapack_int LAPACKE_shsein_work( int matrix_order, char job, char eigsrc,
+ char initv, lapack_logical* select,
+ lapack_int n, const float* h, lapack_int ldh,
+ float* wr, const float* wi, float* vl,
+ lapack_int ldvl, float* vr, lapack_int ldvr,
+ lapack_int mm, lapack_int* m, float* work,
+ lapack_int* ifaill, lapack_int* ifailr );
+lapack_int LAPACKE_dhsein_work( int matrix_order, char job, char eigsrc,
+ char initv, lapack_logical* select,
+ lapack_int n, const double* h, lapack_int ldh,
+ double* wr, const double* wi, double* vl,
+ lapack_int ldvl, double* vr, lapack_int ldvr,
+ lapack_int mm, lapack_int* m, double* work,
+ lapack_int* ifaill, lapack_int* ifailr );
+lapack_int LAPACKE_chsein_work( int matrix_order, char job, char eigsrc,
+ char initv, const lapack_logical* select,
+ lapack_int n, const lapack_complex_float* h,
+ lapack_int ldh, lapack_complex_float* w,
+ lapack_complex_float* vl, lapack_int ldvl,
+ lapack_complex_float* vr, lapack_int ldvr,
+ lapack_int mm, lapack_int* m,
+ lapack_complex_float* work, float* rwork,
+ lapack_int* ifaill, lapack_int* ifailr );
+lapack_int LAPACKE_zhsein_work( int matrix_order, char job, char eigsrc,
+ char initv, const lapack_logical* select,
+ lapack_int n, const lapack_complex_double* h,
+ lapack_int ldh, lapack_complex_double* w,
+ lapack_complex_double* vl, lapack_int ldvl,
+ lapack_complex_double* vr, lapack_int ldvr,
+ lapack_int mm, lapack_int* m,
+ lapack_complex_double* work, double* rwork,
+ lapack_int* ifaill, lapack_int* ifailr );
+
+lapack_int LAPACKE_shseqr_work( int matrix_order, char job, char compz,
+ lapack_int n, lapack_int ilo, lapack_int ihi,
+ float* h, lapack_int ldh, float* wr, float* wi,
+ float* z, lapack_int ldz, float* work,
+ lapack_int lwork );
+lapack_int LAPACKE_dhseqr_work( int matrix_order, char job, char compz,
+ lapack_int n, lapack_int ilo, lapack_int ihi,
+ double* h, lapack_int ldh, double* wr,
+ double* wi, double* z, lapack_int ldz,
+ double* work, lapack_int lwork );
+lapack_int LAPACKE_chseqr_work( int matrix_order, char job, char compz,
+ lapack_int n, lapack_int ilo, lapack_int ihi,
+ lapack_complex_float* h, lapack_int ldh,
+ lapack_complex_float* w,
+ lapack_complex_float* z, lapack_int ldz,
+ lapack_complex_float* work, lapack_int lwork );
+lapack_int LAPACKE_zhseqr_work( int matrix_order, char job, char compz,
+ lapack_int n, lapack_int ilo, lapack_int ihi,
+ lapack_complex_double* h, lapack_int ldh,
+ lapack_complex_double* w,
+ lapack_complex_double* z, lapack_int ldz,
+ lapack_complex_double* work, lapack_int lwork );
+
+lapack_int LAPACKE_clacgv_work( lapack_int n, lapack_complex_float* x,
+ lapack_int incx );
+lapack_int LAPACKE_zlacgv_work( lapack_int n, lapack_complex_double* x,
+ lapack_int incx );
+
+lapack_int LAPACKE_slacpy_work( int matrix_order, char uplo, lapack_int m,
+ lapack_int n, const float* a, lapack_int lda,
+ float* b, lapack_int ldb );
+lapack_int LAPACKE_dlacpy_work( int matrix_order, char uplo, lapack_int m,
+ lapack_int n, const double* a, lapack_int lda,
+ double* b, lapack_int ldb );
+lapack_int LAPACKE_clacpy_work( int matrix_order, char uplo, lapack_int m,
+ lapack_int n, const lapack_complex_float* a,
+ lapack_int lda, lapack_complex_float* b,
+ lapack_int ldb );
+lapack_int LAPACKE_zlacpy_work( int matrix_order, char uplo, lapack_int m,
+ lapack_int n, const lapack_complex_double* a,
+ lapack_int lda, lapack_complex_double* b,
+ lapack_int ldb );
+
+lapack_int LAPACKE_zlag2c_work( int matrix_order, lapack_int m, lapack_int n,
+ const lapack_complex_double* a, lapack_int lda,
+ lapack_complex_float* sa, lapack_int ldsa );
+
+lapack_int LAPACKE_slag2d_work( int matrix_order, lapack_int m, lapack_int n,
+ const float* sa, lapack_int ldsa, double* a,
+ lapack_int lda );
+
+lapack_int LAPACKE_dlag2s_work( int matrix_order, lapack_int m, lapack_int n,
+ const double* a, lapack_int lda, float* sa,
+ lapack_int ldsa );
+
+lapack_int LAPACKE_clag2z_work( int matrix_order, lapack_int m, lapack_int n,
+ const lapack_complex_float* sa, lapack_int ldsa,
+ lapack_complex_double* a, lapack_int lda );
+
+lapack_int LAPACKE_slagge_work( int matrix_order, lapack_int m, lapack_int n,
+ lapack_int kl, lapack_int ku, const float* d,
+ float* a, lapack_int lda, lapack_int* iseed,
+ float* work );
+lapack_int LAPACKE_dlagge_work( int matrix_order, lapack_int m, lapack_int n,
+ lapack_int kl, lapack_int ku, const double* d,
+ double* a, lapack_int lda, lapack_int* iseed,
+ double* work );
+lapack_int LAPACKE_clagge_work( int matrix_order, lapack_int m, lapack_int n,
+ lapack_int kl, lapack_int ku, const float* d,
+ lapack_complex_float* a, lapack_int lda,
+ lapack_int* iseed, lapack_complex_float* work );
+lapack_int LAPACKE_zlagge_work( int matrix_order, lapack_int m, lapack_int n,
+ lapack_int kl, lapack_int ku, const double* d,
+ lapack_complex_double* a, lapack_int lda,
+ lapack_int* iseed,
+ lapack_complex_double* work );
+
+lapack_int LAPACKE_claghe_work( int matrix_order, lapack_int n, lapack_int k,
+ const float* d, lapack_complex_float* a,
+ lapack_int lda, lapack_int* iseed,
+ lapack_complex_float* work );
+lapack_int LAPACKE_zlaghe_work( int matrix_order, lapack_int n, lapack_int k,
+ const double* d, lapack_complex_double* a,
+ lapack_int lda, lapack_int* iseed,
+ lapack_complex_double* work );
+
+lapack_int LAPACKE_slagsy_work( int matrix_order, lapack_int n, lapack_int k,
+ const float* d, float* a, lapack_int lda,
+ lapack_int* iseed, float* work );
+lapack_int LAPACKE_dlagsy_work( int matrix_order, lapack_int n, lapack_int k,
+ const double* d, double* a, lapack_int lda,
+ lapack_int* iseed, double* work );
+lapack_int LAPACKE_clagsy_work( int matrix_order, lapack_int n, lapack_int k,
+ const float* d, lapack_complex_float* a,
+ lapack_int lda, lapack_int* iseed,
+ lapack_complex_float* work );
+lapack_int LAPACKE_zlagsy_work( int matrix_order, lapack_int n, lapack_int k,
+ const double* d, lapack_complex_double* a,
+ lapack_int lda, lapack_int* iseed,
+ lapack_complex_double* work );
+
+lapack_int LAPACKE_slapmr_work( int matrix_order, lapack_logical forwrd,
+ lapack_int m, lapack_int n, float* x,
+ lapack_int ldx, lapack_int* k );
+lapack_int LAPACKE_dlapmr_work( int matrix_order, lapack_logical forwrd,
+ lapack_int m, lapack_int n, double* x,
+ lapack_int ldx, lapack_int* k );
+lapack_int LAPACKE_clapmr_work( int matrix_order, lapack_logical forwrd,
+ lapack_int m, lapack_int n,
+ lapack_complex_float* x, lapack_int ldx,
+ lapack_int* k );
+lapack_int LAPACKE_zlapmr_work( int matrix_order, lapack_logical forwrd,
+ lapack_int m, lapack_int n,
+ lapack_complex_double* x, lapack_int ldx,
+ lapack_int* k );
+
+lapack_int LAPACKE_slartgp_work( float f, float g, float* cs, float* sn,
+ float* r );
+lapack_int LAPACKE_dlartgp_work( double f, double g, double* cs, double* sn,
+ double* r );
+
+lapack_int LAPACKE_slartgs_work( float x, float y, float sigma, float* cs,
+ float* sn );
+lapack_int LAPACKE_dlartgs_work( double x, double y, double sigma, double* cs,
+ double* sn );
+
+float LAPACKE_slapy2_work( float x, float y );
+double LAPACKE_dlapy2_work( double x, double y );
+
+float LAPACKE_slapy3_work( float x, float y, float z );
+double LAPACKE_dlapy3_work( double x, double y, double z );
+
+float LAPACKE_slamch_work( char cmach );
+double LAPACKE_dlamch_work( char cmach );
+
+float LAPACKE_slange_work( int matrix_order, char norm, lapack_int m,
+ lapack_int n, const float* a, lapack_int lda,
+ float* work );
+double LAPACKE_dlange_work( int matrix_order, char norm, lapack_int m,
+ lapack_int n, const double* a, lapack_int lda,
+ double* work );
+float LAPACKE_clange_work( int matrix_order, char norm, lapack_int m,
+ lapack_int n, const lapack_complex_float* a,
+ lapack_int lda, float* work );
+double LAPACKE_zlange_work( int matrix_order, char norm, lapack_int m,
+ lapack_int n, const lapack_complex_double* a,
+ lapack_int lda, double* work );
+
+float LAPACKE_clanhe_work( int matrix_order, char norm, char uplo,
+ lapack_int n, const lapack_complex_float* a,
+ lapack_int lda, float* work );
+double LAPACKE_zlanhe_work( int matrix_order, char norm, char uplo,
+ lapack_int n, const lapack_complex_double* a,
+ lapack_int lda, double* work );
+
+float LAPACKE_slansy_work( int matrix_order, char norm, char uplo,
+ lapack_int n, const float* a, lapack_int lda,
+ float* work );
+double LAPACKE_dlansy_work( int matrix_order, char norm, char uplo,
+ lapack_int n, const double* a, lapack_int lda,
+ double* work );
+float LAPACKE_clansy_work( int matrix_order, char norm, char uplo,
+ lapack_int n, const lapack_complex_float* a,
+ lapack_int lda, float* work );
+double LAPACKE_zlansy_work( int matrix_order, char norm, char uplo,
+ lapack_int n, const lapack_complex_double* a,
+ lapack_int lda, double* work );
+
+float LAPACKE_slantr_work( int matrix_order, char norm, char uplo,
+ char diag, lapack_int m, lapack_int n, const float* a,
+ lapack_int lda, float* work );
+double LAPACKE_dlantr_work( int matrix_order, char norm, char uplo,
+ char diag, lapack_int m, lapack_int n,
+ const double* a, lapack_int lda, double* work );
+float LAPACKE_clantr_work( int matrix_order, char norm, char uplo,
+ char diag, lapack_int m, lapack_int n,
+ const lapack_complex_float* a, lapack_int lda,
+ float* work );
+double LAPACKE_zlantr_work( int matrix_order, char norm, char uplo,
+ char diag, lapack_int m, lapack_int n,
+ const lapack_complex_double* a, lapack_int lda,
+ double* work );
+
+lapack_int LAPACKE_slarfb_work( int matrix_order, char side, char trans,
+ char direct, char storev, lapack_int m,
+ lapack_int n, lapack_int k, const float* v,
+ lapack_int ldv, const float* t, lapack_int ldt,
+ float* c, lapack_int ldc, float* work,
+ lapack_int ldwork );
+lapack_int LAPACKE_dlarfb_work( int matrix_order, char side, char trans,
+ char direct, char storev, lapack_int m,
+ lapack_int n, lapack_int k, const double* v,
+ lapack_int ldv, const double* t, lapack_int ldt,
+ double* c, lapack_int ldc, double* work,
+ lapack_int ldwork );
+lapack_int LAPACKE_clarfb_work( int matrix_order, char side, char trans,
+ char direct, char storev, lapack_int m,
+ lapack_int n, lapack_int k,
+ const lapack_complex_float* v, lapack_int ldv,
+ const lapack_complex_float* t, lapack_int ldt,
+ lapack_complex_float* c, lapack_int ldc,
+ lapack_complex_float* work, lapack_int ldwork );
+lapack_int LAPACKE_zlarfb_work( int matrix_order, char side, char trans,
+ char direct, char storev, lapack_int m,
+ lapack_int n, lapack_int k,
+ const lapack_complex_double* v, lapack_int ldv,
+ const lapack_complex_double* t, lapack_int ldt,
+ lapack_complex_double* c, lapack_int ldc,
+ lapack_complex_double* work,
+ lapack_int ldwork );
+
+lapack_int LAPACKE_slarfg_work( lapack_int n, float* alpha, float* x,
+ lapack_int incx, float* tau );
+lapack_int LAPACKE_dlarfg_work( lapack_int n, double* alpha, double* x,
+ lapack_int incx, double* tau );
+lapack_int LAPACKE_clarfg_work( lapack_int n, lapack_complex_float* alpha,
+ lapack_complex_float* x, lapack_int incx,
+ lapack_complex_float* tau );
+lapack_int LAPACKE_zlarfg_work( lapack_int n, lapack_complex_double* alpha,
+ lapack_complex_double* x, lapack_int incx,
+ lapack_complex_double* tau );
+
+lapack_int LAPACKE_slarft_work( int matrix_order, char direct, char storev,
+ lapack_int n, lapack_int k, const float* v,
+ lapack_int ldv, const float* tau, float* t,
+ lapack_int ldt );
+lapack_int LAPACKE_dlarft_work( int matrix_order, char direct, char storev,
+ lapack_int n, lapack_int k, const double* v,
+ lapack_int ldv, const double* tau, double* t,
+ lapack_int ldt );
+lapack_int LAPACKE_clarft_work( int matrix_order, char direct, char storev,
+ lapack_int n, lapack_int k,
+ const lapack_complex_float* v, lapack_int ldv,
+ const lapack_complex_float* tau,
+ lapack_complex_float* t, lapack_int ldt );
+lapack_int LAPACKE_zlarft_work( int matrix_order, char direct, char storev,
+ lapack_int n, lapack_int k,
+ const lapack_complex_double* v, lapack_int ldv,
+ const lapack_complex_double* tau,
+ lapack_complex_double* t, lapack_int ldt );
+
+lapack_int LAPACKE_slarfx_work( int matrix_order, char side, lapack_int m,
+ lapack_int n, const float* v, float tau,
+ float* c, lapack_int ldc, float* work );
+lapack_int LAPACKE_dlarfx_work( int matrix_order, char side, lapack_int m,
+ lapack_int n, const double* v, double tau,
+ double* c, lapack_int ldc, double* work );
+lapack_int LAPACKE_clarfx_work( int matrix_order, char side, lapack_int m,
+ lapack_int n, const lapack_complex_float* v,
+ lapack_complex_float tau,
+ lapack_complex_float* c, lapack_int ldc,
+ lapack_complex_float* work );
+lapack_int LAPACKE_zlarfx_work( int matrix_order, char side, lapack_int m,
+ lapack_int n, const lapack_complex_double* v,
+ lapack_complex_double tau,
+ lapack_complex_double* c, lapack_int ldc,
+ lapack_complex_double* work );
+
+lapack_int LAPACKE_slarnv_work( lapack_int idist, lapack_int* iseed,
+ lapack_int n, float* x );
+lapack_int LAPACKE_dlarnv_work( lapack_int idist, lapack_int* iseed,
+ lapack_int n, double* x );
+lapack_int LAPACKE_clarnv_work( lapack_int idist, lapack_int* iseed,
+ lapack_int n, lapack_complex_float* x );
+lapack_int LAPACKE_zlarnv_work( lapack_int idist, lapack_int* iseed,
+ lapack_int n, lapack_complex_double* x );
+
+lapack_int LAPACKE_slaset_work( int matrix_order, char uplo, lapack_int m,
+ lapack_int n, float alpha, float beta, float* a,
+ lapack_int lda );
+lapack_int LAPACKE_dlaset_work( int matrix_order, char uplo, lapack_int m,
+ lapack_int n, double alpha, double beta,
+ double* a, lapack_int lda );
+lapack_int LAPACKE_claset_work( int matrix_order, char uplo, lapack_int m,
+ lapack_int n, lapack_complex_float alpha,
+ lapack_complex_float beta,
+ lapack_complex_float* a, lapack_int lda );
+lapack_int LAPACKE_zlaset_work( int matrix_order, char uplo, lapack_int m,
+ lapack_int n, lapack_complex_double alpha,
+ lapack_complex_double beta,
+ lapack_complex_double* a, lapack_int lda );
+
+lapack_int LAPACKE_slasrt_work( char id, lapack_int n, float* d );
+lapack_int LAPACKE_dlasrt_work( char id, lapack_int n, double* d );
+
+lapack_int LAPACKE_slaswp_work( int matrix_order, lapack_int n, float* a,
+ lapack_int lda, lapack_int k1, lapack_int k2,
+ const lapack_int* ipiv, lapack_int incx );
+lapack_int LAPACKE_dlaswp_work( int matrix_order, lapack_int n, double* a,
+ lapack_int lda, lapack_int k1, lapack_int k2,
+ const lapack_int* ipiv, lapack_int incx );
+lapack_int LAPACKE_claswp_work( int matrix_order, lapack_int n,
+ lapack_complex_float* a, lapack_int lda,
+ lapack_int k1, lapack_int k2,
+ const lapack_int* ipiv, lapack_int incx );
+lapack_int LAPACKE_zlaswp_work( int matrix_order, lapack_int n,
+ lapack_complex_double* a, lapack_int lda,
+ lapack_int k1, lapack_int k2,
+ const lapack_int* ipiv, lapack_int incx );
+
+lapack_int LAPACKE_slatms_work( int matrix_order, lapack_int m, lapack_int n,
+ char dist, lapack_int* iseed, char sym,
+ float* d, lapack_int mode, float cond,
+ float dmax, lapack_int kl, lapack_int ku,
+ char pack, float* a, lapack_int lda,
+ float* work );
+lapack_int LAPACKE_dlatms_work( int matrix_order, lapack_int m, lapack_int n,
+ char dist, lapack_int* iseed, char sym,
+ double* d, lapack_int mode, double cond,
+ double dmax, lapack_int kl, lapack_int ku,
+ char pack, double* a, lapack_int lda,
+ double* work );
+lapack_int LAPACKE_clatms_work( int matrix_order, lapack_int m, lapack_int n,
+ char dist, lapack_int* iseed, char sym,
+ float* d, lapack_int mode, float cond,
+ float dmax, lapack_int kl, lapack_int ku,
+ char pack, lapack_complex_float* a,
+ lapack_int lda, lapack_complex_float* work );
+lapack_int LAPACKE_zlatms_work( int matrix_order, lapack_int m, lapack_int n,
+ char dist, lapack_int* iseed, char sym,
+ double* d, lapack_int mode, double cond,
+ double dmax, lapack_int kl, lapack_int ku,
+ char pack, lapack_complex_double* a,
+ lapack_int lda, lapack_complex_double* work );
+
+lapack_int LAPACKE_slauum_work( int matrix_order, char uplo, lapack_int n,
+ float* a, lapack_int lda );
+lapack_int LAPACKE_dlauum_work( int matrix_order, char uplo, lapack_int n,
+ double* a, lapack_int lda );
+lapack_int LAPACKE_clauum_work( int matrix_order, char uplo, lapack_int n,
+ lapack_complex_float* a, lapack_int lda );
+lapack_int LAPACKE_zlauum_work( int matrix_order, char uplo, lapack_int n,
+ lapack_complex_double* a, lapack_int lda );
+
+lapack_int LAPACKE_sopgtr_work( int matrix_order, char uplo, lapack_int n,
+ const float* ap, const float* tau, float* q,
+ lapack_int ldq, float* work );
+lapack_int LAPACKE_dopgtr_work( int matrix_order, char uplo, lapack_int n,
+ const double* ap, const double* tau, double* q,
+ lapack_int ldq, double* work );
+
+lapack_int LAPACKE_sopmtr_work( int matrix_order, char side, char uplo,
+ char trans, lapack_int m, lapack_int n,
+ const float* ap, const float* tau, float* c,
+ lapack_int ldc, float* work );
+lapack_int LAPACKE_dopmtr_work( int matrix_order, char side, char uplo,
+ char trans, lapack_int m, lapack_int n,
+ const double* ap, const double* tau, double* c,
+ lapack_int ldc, double* work );
+
+lapack_int LAPACKE_sorgbr_work( int matrix_order, char vect, lapack_int m,
+ lapack_int n, lapack_int k, float* a,
+ lapack_int lda, const float* tau, float* work,
+ lapack_int lwork );
+lapack_int LAPACKE_dorgbr_work( int matrix_order, char vect, lapack_int m,
+ lapack_int n, lapack_int k, double* a,
+ lapack_int lda, const double* tau, double* work,
+ lapack_int lwork );
+
+lapack_int LAPACKE_sorghr_work( int matrix_order, lapack_int n, lapack_int ilo,
+ lapack_int ihi, float* a, lapack_int lda,
+ const float* tau, float* work,
+ lapack_int lwork );
+lapack_int LAPACKE_dorghr_work( int matrix_order, lapack_int n, lapack_int ilo,
+ lapack_int ihi, double* a, lapack_int lda,
+ const double* tau, double* work,
+ lapack_int lwork );
+
+lapack_int LAPACKE_sorglq_work( int matrix_order, lapack_int m, lapack_int n,
+ lapack_int k, float* a, lapack_int lda,
+ const float* tau, float* work,
+ lapack_int lwork );
+lapack_int LAPACKE_dorglq_work( int matrix_order, lapack_int m, lapack_int n,
+ lapack_int k, double* a, lapack_int lda,
+ const double* tau, double* work,
+ lapack_int lwork );
+
+lapack_int LAPACKE_sorgql_work( int matrix_order, lapack_int m, lapack_int n,
+ lapack_int k, float* a, lapack_int lda,
+ const float* tau, float* work,
+ lapack_int lwork );
+lapack_int LAPACKE_dorgql_work( int matrix_order, lapack_int m, lapack_int n,
+ lapack_int k, double* a, lapack_int lda,
+ const double* tau, double* work,
+ lapack_int lwork );
+
+lapack_int LAPACKE_sorgqr_work( int matrix_order, lapack_int m, lapack_int n,
+ lapack_int k, float* a, lapack_int lda,
+ const float* tau, float* work,
+ lapack_int lwork );
+lapack_int LAPACKE_dorgqr_work( int matrix_order, lapack_int m, lapack_int n,
+ lapack_int k, double* a, lapack_int lda,
+ const double* tau, double* work,
+ lapack_int lwork );
+
+lapack_int LAPACKE_sorgrq_work( int matrix_order, lapack_int m, lapack_int n,
+ lapack_int k, float* a, lapack_int lda,
+ const float* tau, float* work,
+ lapack_int lwork );
+lapack_int LAPACKE_dorgrq_work( int matrix_order, lapack_int m, lapack_int n,
+ lapack_int k, double* a, lapack_int lda,
+ const double* tau, double* work,
+ lapack_int lwork );
+
+lapack_int LAPACKE_sorgtr_work( int matrix_order, char uplo, lapack_int n,
+ float* a, lapack_int lda, const float* tau,
+ float* work, lapack_int lwork );
+lapack_int LAPACKE_dorgtr_work( int matrix_order, char uplo, lapack_int n,
+ double* a, lapack_int lda, const double* tau,
+ double* work, lapack_int lwork );
+
+lapack_int LAPACKE_sormbr_work( int matrix_order, char vect, char side,
+ char trans, lapack_int m, lapack_int n,
+ lapack_int k, const float* a, lapack_int lda,
+ const float* tau, float* c, lapack_int ldc,
+ float* work, lapack_int lwork );
+lapack_int LAPACKE_dormbr_work( int matrix_order, char vect, char side,
+ char trans, lapack_int m, lapack_int n,
+ lapack_int k, const double* a, lapack_int lda,
+ const double* tau, double* c, lapack_int ldc,
+ double* work, lapack_int lwork );
+
+lapack_int LAPACKE_sormhr_work( int matrix_order, char side, char trans,
+ lapack_int m, lapack_int n, lapack_int ilo,
+ lapack_int ihi, const float* a, lapack_int lda,
+ const float* tau, float* c, lapack_int ldc,
+ float* work, lapack_int lwork );
+lapack_int LAPACKE_dormhr_work( int matrix_order, char side, char trans,
+ lapack_int m, lapack_int n, lapack_int ilo,
+ lapack_int ihi, const double* a, lapack_int lda,
+ const double* tau, double* c, lapack_int ldc,
+ double* work, lapack_int lwork );
+
+lapack_int LAPACKE_sormlq_work( int matrix_order, char side, char trans,
+ lapack_int m, lapack_int n, lapack_int k,
+ const float* a, lapack_int lda,
+ const float* tau, float* c, lapack_int ldc,
+ float* work, lapack_int lwork );
+lapack_int LAPACKE_dormlq_work( int matrix_order, char side, char trans,
+ lapack_int m, lapack_int n, lapack_int k,
+ const double* a, lapack_int lda,
+ const double* tau, double* c, lapack_int ldc,
+ double* work, lapack_int lwork );
+
+lapack_int LAPACKE_sormql_work( int matrix_order, char side, char trans,
+ lapack_int m, lapack_int n, lapack_int k,
+ const float* a, lapack_int lda,
+ const float* tau, float* c, lapack_int ldc,
+ float* work, lapack_int lwork );
+lapack_int LAPACKE_dormql_work( int matrix_order, char side, char trans,
+ lapack_int m, lapack_int n, lapack_int k,
+ const double* a, lapack_int lda,
+ const double* tau, double* c, lapack_int ldc,
+ double* work, lapack_int lwork );
+
+lapack_int LAPACKE_sormqr_work( int matrix_order, char side, char trans,
+ lapack_int m, lapack_int n, lapack_int k,
+ const float* a, lapack_int lda,
+ const float* tau, float* c, lapack_int ldc,
+ float* work, lapack_int lwork );
+lapack_int LAPACKE_dormqr_work( int matrix_order, char side, char trans,
+ lapack_int m, lapack_int n, lapack_int k,
+ const double* a, lapack_int lda,
+ const double* tau, double* c, lapack_int ldc,
+ double* work, lapack_int lwork );
+
+lapack_int LAPACKE_sormrq_work( int matrix_order, char side, char trans,
+ lapack_int m, lapack_int n, lapack_int k,
+ const float* a, lapack_int lda,
+ const float* tau, float* c, lapack_int ldc,
+ float* work, lapack_int lwork );
+lapack_int LAPACKE_dormrq_work( int matrix_order, char side, char trans,
+ lapack_int m, lapack_int n, lapack_int k,
+ const double* a, lapack_int lda,
+ const double* tau, double* c, lapack_int ldc,
+ double* work, lapack_int lwork );
+
+lapack_int LAPACKE_sormrz_work( int matrix_order, char side, char trans,
+ lapack_int m, lapack_int n, lapack_int k,
+ lapack_int l, const float* a, lapack_int lda,
+ const float* tau, float* c, lapack_int ldc,
+ float* work, lapack_int lwork );
+lapack_int LAPACKE_dormrz_work( int matrix_order, char side, char trans,
+ lapack_int m, lapack_int n, lapack_int k,
+ lapack_int l, const double* a, lapack_int lda,
+ const double* tau, double* c, lapack_int ldc,
+ double* work, lapack_int lwork );
+
+lapack_int LAPACKE_sormtr_work( int matrix_order, char side, char uplo,
+ char trans, lapack_int m, lapack_int n,
+ const float* a, lapack_int lda,
+ const float* tau, float* c, lapack_int ldc,
+ float* work, lapack_int lwork );
+lapack_int LAPACKE_dormtr_work( int matrix_order, char side, char uplo,
+ char trans, lapack_int m, lapack_int n,
+ const double* a, lapack_int lda,
+ const double* tau, double* c, lapack_int ldc,
+ double* work, lapack_int lwork );
+
+lapack_int LAPACKE_spbcon_work( int matrix_order, char uplo, lapack_int n,
+ lapack_int kd, const float* ab, lapack_int ldab,
+ float anorm, float* rcond, float* work,
+ lapack_int* iwork );
+lapack_int LAPACKE_dpbcon_work( int matrix_order, char uplo, lapack_int n,
+ lapack_int kd, const double* ab,
+ lapack_int ldab, double anorm, double* rcond,
+ double* work, lapack_int* iwork );
+lapack_int LAPACKE_cpbcon_work( int matrix_order, char uplo, lapack_int n,
+ lapack_int kd, const lapack_complex_float* ab,
+ lapack_int ldab, float anorm, float* rcond,
+ lapack_complex_float* work, float* rwork );
+lapack_int LAPACKE_zpbcon_work( int matrix_order, char uplo, lapack_int n,
+ lapack_int kd, const lapack_complex_double* ab,
+ lapack_int ldab, double anorm, double* rcond,
+ lapack_complex_double* work, double* rwork );
+
+lapack_int LAPACKE_spbequ_work( int matrix_order, char uplo, lapack_int n,
+ lapack_int kd, const float* ab, lapack_int ldab,
+ float* s, float* scond, float* amax );
+lapack_int LAPACKE_dpbequ_work( int matrix_order, char uplo, lapack_int n,
+ lapack_int kd, const double* ab,
+ lapack_int ldab, double* s, double* scond,
+ double* amax );
+lapack_int LAPACKE_cpbequ_work( int matrix_order, char uplo, lapack_int n,
+ lapack_int kd, const lapack_complex_float* ab,
+ lapack_int ldab, float* s, float* scond,
+ float* amax );
+lapack_int LAPACKE_zpbequ_work( int matrix_order, char uplo, lapack_int n,
+ lapack_int kd, const lapack_complex_double* ab,
+ lapack_int ldab, double* s, double* scond,
+ double* amax );
+
+lapack_int LAPACKE_spbrfs_work( int matrix_order, char uplo, lapack_int n,
+ lapack_int kd, lapack_int nrhs, const float* ab,
+ lapack_int ldab, const float* afb,
+ lapack_int ldafb, const float* b,
+ lapack_int ldb, float* x, lapack_int ldx,
+ float* ferr, float* berr, float* work,
+ lapack_int* iwork );
+lapack_int LAPACKE_dpbrfs_work( int matrix_order, char uplo, lapack_int n,
+ lapack_int kd, lapack_int nrhs,
+ const double* ab, lapack_int ldab,
+ const double* afb, lapack_int ldafb,
+ const double* b, lapack_int ldb, double* x,
+ lapack_int ldx, double* ferr, double* berr,
+ double* work, lapack_int* iwork );
+lapack_int LAPACKE_cpbrfs_work( int matrix_order, char uplo, lapack_int n,
+ lapack_int kd, lapack_int nrhs,
+ const lapack_complex_float* ab, lapack_int ldab,
+ const lapack_complex_float* afb,
+ lapack_int ldafb, const lapack_complex_float* b,
+ lapack_int ldb, lapack_complex_float* x,
+ lapack_int ldx, float* ferr, float* berr,
+ lapack_complex_float* work, float* rwork );
+lapack_int LAPACKE_zpbrfs_work( int matrix_order, char uplo, lapack_int n,
+ lapack_int kd, lapack_int nrhs,
+ const lapack_complex_double* ab,
+ lapack_int ldab,
+ const lapack_complex_double* afb,
+ lapack_int ldafb,
+ const lapack_complex_double* b, lapack_int ldb,
+ lapack_complex_double* x, lapack_int ldx,
+ double* ferr, double* berr,
+ lapack_complex_double* work, double* rwork );
+
+lapack_int LAPACKE_spbstf_work( int matrix_order, char uplo, lapack_int n,
+ lapack_int kb, float* bb, lapack_int ldbb );
+lapack_int LAPACKE_dpbstf_work( int matrix_order, char uplo, lapack_int n,
+ lapack_int kb, double* bb, lapack_int ldbb );
+lapack_int LAPACKE_cpbstf_work( int matrix_order, char uplo, lapack_int n,
+ lapack_int kb, lapack_complex_float* bb,
+ lapack_int ldbb );
+lapack_int LAPACKE_zpbstf_work( int matrix_order, char uplo, lapack_int n,
+ lapack_int kb, lapack_complex_double* bb,
+ lapack_int ldbb );
+
+lapack_int LAPACKE_spbsv_work( int matrix_order, char uplo, lapack_int n,
+ lapack_int kd, lapack_int nrhs, float* ab,
+ lapack_int ldab, float* b, lapack_int ldb );
+lapack_int LAPACKE_dpbsv_work( int matrix_order, char uplo, lapack_int n,
+ lapack_int kd, lapack_int nrhs, double* ab,
+ lapack_int ldab, double* b, lapack_int ldb );
+lapack_int LAPACKE_cpbsv_work( int matrix_order, char uplo, lapack_int n,
+ lapack_int kd, lapack_int nrhs,
+ lapack_complex_float* ab, lapack_int ldab,
+ lapack_complex_float* b, lapack_int ldb );
+lapack_int LAPACKE_zpbsv_work( int matrix_order, char uplo, lapack_int n,
+ lapack_int kd, lapack_int nrhs,
+ lapack_complex_double* ab, lapack_int ldab,
+ lapack_complex_double* b, lapack_int ldb );
+
+lapack_int LAPACKE_spbsvx_work( int matrix_order, char fact, char uplo,
+ lapack_int n, lapack_int kd, lapack_int nrhs,
+ float* ab, lapack_int ldab, float* afb,
+ lapack_int ldafb, char* equed, float* s,
+ float* b, lapack_int ldb, float* x,
+ lapack_int ldx, float* rcond, float* ferr,
+ float* berr, float* work, lapack_int* iwork );
+lapack_int LAPACKE_dpbsvx_work( int matrix_order, char fact, char uplo,
+ lapack_int n, lapack_int kd, lapack_int nrhs,
+ double* ab, lapack_int ldab, double* afb,
+ lapack_int ldafb, char* equed, double* s,
+ double* b, lapack_int ldb, double* x,
+ lapack_int ldx, double* rcond, double* ferr,
+ double* berr, double* work, lapack_int* iwork );
+lapack_int LAPACKE_cpbsvx_work( int matrix_order, char fact, char uplo,
+ lapack_int n, lapack_int kd, lapack_int nrhs,
+ lapack_complex_float* ab, lapack_int ldab,
+ lapack_complex_float* afb, lapack_int ldafb,
+ char* equed, float* s, lapack_complex_float* b,
+ lapack_int ldb, lapack_complex_float* x,
+ lapack_int ldx, float* rcond, float* ferr,
+ float* berr, lapack_complex_float* work,
+ float* rwork );
+lapack_int LAPACKE_zpbsvx_work( int matrix_order, char fact, char uplo,
+ lapack_int n, lapack_int kd, lapack_int nrhs,
+ lapack_complex_double* ab, lapack_int ldab,
+ lapack_complex_double* afb, lapack_int ldafb,
+ char* equed, double* s,
+ lapack_complex_double* b, lapack_int ldb,
+ lapack_complex_double* x, lapack_int ldx,
+ double* rcond, double* ferr, double* berr,
+ lapack_complex_double* work, double* rwork );
+
+lapack_int LAPACKE_spbtrf_work( int matrix_order, char uplo, lapack_int n,
+ lapack_int kd, float* ab, lapack_int ldab );
+lapack_int LAPACKE_dpbtrf_work( int matrix_order, char uplo, lapack_int n,
+ lapack_int kd, double* ab, lapack_int ldab );
+lapack_int LAPACKE_cpbtrf_work( int matrix_order, char uplo, lapack_int n,
+ lapack_int kd, lapack_complex_float* ab,
+ lapack_int ldab );
+lapack_int LAPACKE_zpbtrf_work( int matrix_order, char uplo, lapack_int n,
+ lapack_int kd, lapack_complex_double* ab,
+ lapack_int ldab );
+
+lapack_int LAPACKE_spbtrs_work( int matrix_order, char uplo, lapack_int n,
+ lapack_int kd, lapack_int nrhs, const float* ab,
+ lapack_int ldab, float* b, lapack_int ldb );
+lapack_int LAPACKE_dpbtrs_work( int matrix_order, char uplo, lapack_int n,
+ lapack_int kd, lapack_int nrhs,
+ const double* ab, lapack_int ldab, double* b,
+ lapack_int ldb );
+lapack_int LAPACKE_cpbtrs_work( int matrix_order, char uplo, lapack_int n,
+ lapack_int kd, lapack_int nrhs,
+ const lapack_complex_float* ab, lapack_int ldab,
+ lapack_complex_float* b, lapack_int ldb );
+lapack_int LAPACKE_zpbtrs_work( int matrix_order, char uplo, lapack_int n,
+ lapack_int kd, lapack_int nrhs,
+ const lapack_complex_double* ab,
+ lapack_int ldab, lapack_complex_double* b,
+ lapack_int ldb );
+
+lapack_int LAPACKE_spftrf_work( int matrix_order, char transr, char uplo,
+ lapack_int n, float* a );
+lapack_int LAPACKE_dpftrf_work( int matrix_order, char transr, char uplo,
+ lapack_int n, double* a );
+lapack_int LAPACKE_cpftrf_work( int matrix_order, char transr, char uplo,
+ lapack_int n, lapack_complex_float* a );
+lapack_int LAPACKE_zpftrf_work( int matrix_order, char transr, char uplo,
+ lapack_int n, lapack_complex_double* a );
+
+lapack_int LAPACKE_spftri_work( int matrix_order, char transr, char uplo,
+ lapack_int n, float* a );
+lapack_int LAPACKE_dpftri_work( int matrix_order, char transr, char uplo,
+ lapack_int n, double* a );
+lapack_int LAPACKE_cpftri_work( int matrix_order, char transr, char uplo,
+ lapack_int n, lapack_complex_float* a );
+lapack_int LAPACKE_zpftri_work( int matrix_order, char transr, char uplo,
+ lapack_int n, lapack_complex_double* a );
+
+lapack_int LAPACKE_spftrs_work( int matrix_order, char transr, char uplo,
+ lapack_int n, lapack_int nrhs, const float* a,
+ float* b, lapack_int ldb );
+lapack_int LAPACKE_dpftrs_work( int matrix_order, char transr, char uplo,
+ lapack_int n, lapack_int nrhs, const double* a,
+ double* b, lapack_int ldb );
+lapack_int LAPACKE_cpftrs_work( int matrix_order, char transr, char uplo,
+ lapack_int n, lapack_int nrhs,
+ const lapack_complex_float* a,
+ lapack_complex_float* b, lapack_int ldb );
+lapack_int LAPACKE_zpftrs_work( int matrix_order, char transr, char uplo,
+ lapack_int n, lapack_int nrhs,
+ const lapack_complex_double* a,
+ lapack_complex_double* b, lapack_int ldb );
+
+lapack_int LAPACKE_spocon_work( int matrix_order, char uplo, lapack_int n,
+ const float* a, lapack_int lda, float anorm,
+ float* rcond, float* work, lapack_int* iwork );
+lapack_int LAPACKE_dpocon_work( int matrix_order, char uplo, lapack_int n,
+ const double* a, lapack_int lda, double anorm,
+ double* rcond, double* work,
+ lapack_int* iwork );
+lapack_int LAPACKE_cpocon_work( int matrix_order, char uplo, lapack_int n,
+ const lapack_complex_float* a, lapack_int lda,
+ float anorm, float* rcond,
+ lapack_complex_float* work, float* rwork );
+lapack_int LAPACKE_zpocon_work( int matrix_order, char uplo, lapack_int n,
+ const lapack_complex_double* a, lapack_int lda,
+ double anorm, double* rcond,
+ lapack_complex_double* work, double* rwork );
+
+lapack_int LAPACKE_spoequ_work( int matrix_order, lapack_int n, const float* a,
+ lapack_int lda, float* s, float* scond,
+ float* amax );
+lapack_int LAPACKE_dpoequ_work( int matrix_order, lapack_int n, const double* a,
+ lapack_int lda, double* s, double* scond,
+ double* amax );
+lapack_int LAPACKE_cpoequ_work( int matrix_order, lapack_int n,
+ const lapack_complex_float* a, lapack_int lda,
+ float* s, float* scond, float* amax );
+lapack_int LAPACKE_zpoequ_work( int matrix_order, lapack_int n,
+ const lapack_complex_double* a, lapack_int lda,
+ double* s, double* scond, double* amax );
+
+lapack_int LAPACKE_spoequb_work( int matrix_order, lapack_int n, const float* a,
+ lapack_int lda, float* s, float* scond,
+ float* amax );
+lapack_int LAPACKE_dpoequb_work( int matrix_order, lapack_int n,
+ const double* a, lapack_int lda, double* s,
+ double* scond, double* amax );
+lapack_int LAPACKE_cpoequb_work( int matrix_order, lapack_int n,
+ const lapack_complex_float* a, lapack_int lda,
+ float* s, float* scond, float* amax );
+lapack_int LAPACKE_zpoequb_work( int matrix_order, lapack_int n,
+ const lapack_complex_double* a, lapack_int lda,
+ double* s, double* scond, double* amax );
+
+lapack_int LAPACKE_sporfs_work( int matrix_order, char uplo, lapack_int n,
+ lapack_int nrhs, const float* a, lapack_int lda,
+ const float* af, lapack_int ldaf,
+ const float* b, lapack_int ldb, float* x,
+ lapack_int ldx, float* ferr, float* berr,
+ float* work, lapack_int* iwork );
+lapack_int LAPACKE_dporfs_work( int matrix_order, char uplo, lapack_int n,
+ lapack_int nrhs, const double* a,
+ lapack_int lda, const double* af,
+ lapack_int ldaf, const double* b,
+ lapack_int ldb, double* x, lapack_int ldx,
+ double* ferr, double* berr, double* work,
+ lapack_int* iwork );
+lapack_int LAPACKE_cporfs_work( int matrix_order, char uplo, lapack_int n,
+ lapack_int nrhs, const lapack_complex_float* a,
+ lapack_int lda, const lapack_complex_float* af,
+ lapack_int ldaf, const lapack_complex_float* b,
+ lapack_int ldb, lapack_complex_float* x,
+ lapack_int ldx, float* ferr, float* berr,
+ lapack_complex_float* work, float* rwork );
+lapack_int LAPACKE_zporfs_work( int matrix_order, char uplo, lapack_int n,
+ lapack_int nrhs, const lapack_complex_double* a,
+ lapack_int lda, const lapack_complex_double* af,
+ lapack_int ldaf, const lapack_complex_double* b,
+ lapack_int ldb, lapack_complex_double* x,
+ lapack_int ldx, double* ferr, double* berr,
+ lapack_complex_double* work, double* rwork );
+
+lapack_int LAPACKE_sporfsx_work( int matrix_order, char uplo, char equed,
+ lapack_int n, lapack_int nrhs, const float* a,
+ lapack_int lda, const float* af,
+ lapack_int ldaf, const float* s,
+ const float* b, lapack_int ldb, float* x,
+ lapack_int ldx, float* rcond, float* berr,
+ lapack_int n_err_bnds, float* err_bnds_norm,
+ float* err_bnds_comp, lapack_int nparams,
+ float* params, float* work,
+ lapack_int* iwork );
+lapack_int LAPACKE_dporfsx_work( int matrix_order, char uplo, char equed,
+ lapack_int n, lapack_int nrhs, const double* a,
+ lapack_int lda, const double* af,
+ lapack_int ldaf, const double* s,
+ const double* b, lapack_int ldb, double* x,
+ lapack_int ldx, double* rcond, double* berr,
+ lapack_int n_err_bnds, double* err_bnds_norm,
+ double* err_bnds_comp, lapack_int nparams,
+ double* params, double* work,
+ lapack_int* iwork );
+lapack_int LAPACKE_cporfsx_work( int matrix_order, char uplo, char equed,
+ lapack_int n, lapack_int nrhs,
+ const lapack_complex_float* a, lapack_int lda,
+ const lapack_complex_float* af,
+ lapack_int ldaf, const float* s,
+ const lapack_complex_float* b, lapack_int ldb,
+ lapack_complex_float* x, lapack_int ldx,
+ float* rcond, float* berr,
+ lapack_int n_err_bnds, float* err_bnds_norm,
+ float* err_bnds_comp, lapack_int nparams,
+ float* params, lapack_complex_float* work,
+ float* rwork );
+lapack_int LAPACKE_zporfsx_work( int matrix_order, char uplo, char equed,
+ lapack_int n, lapack_int nrhs,
+ const lapack_complex_double* a, lapack_int lda,
+ const lapack_complex_double* af,
+ lapack_int ldaf, const double* s,
+ const lapack_complex_double* b, lapack_int ldb,
+ lapack_complex_double* x, lapack_int ldx,
+ double* rcond, double* berr,
+ lapack_int n_err_bnds, double* err_bnds_norm,
+ double* err_bnds_comp, lapack_int nparams,
+ double* params, lapack_complex_double* work,
+ double* rwork );
+
+lapack_int LAPACKE_sposv_work( int matrix_order, char uplo, lapack_int n,
+ lapack_int nrhs, float* a, lapack_int lda,
+ float* b, lapack_int ldb );
+lapack_int LAPACKE_dposv_work( int matrix_order, char uplo, lapack_int n,
+ lapack_int nrhs, double* a, lapack_int lda,
+ double* b, lapack_int ldb );
+lapack_int LAPACKE_cposv_work( int matrix_order, char uplo, lapack_int n,
+ lapack_int nrhs, lapack_complex_float* a,
+ lapack_int lda, lapack_complex_float* b,
+ lapack_int ldb );
+lapack_int LAPACKE_zposv_work( int matrix_order, char uplo, lapack_int n,
+ lapack_int nrhs, lapack_complex_double* a,
+ lapack_int lda, lapack_complex_double* b,
+ lapack_int ldb );
+lapack_int LAPACKE_dsposv_work( int matrix_order, char uplo, lapack_int n,
+ lapack_int nrhs, double* a, lapack_int lda,
+ double* b, lapack_int ldb, double* x,
+ lapack_int ldx, double* work, float* swork,
+ lapack_int* iter );
+lapack_int LAPACKE_zcposv_work( int matrix_order, char uplo, lapack_int n,
+ lapack_int nrhs, lapack_complex_double* a,
+ lapack_int lda, lapack_complex_double* b,
+ lapack_int ldb, lapack_complex_double* x,
+ lapack_int ldx, lapack_complex_double* work,
+ lapack_complex_float* swork, double* rwork,
+ lapack_int* iter );
+
+lapack_int LAPACKE_sposvx_work( int matrix_order, char fact, char uplo,
+ lapack_int n, lapack_int nrhs, float* a,
+ lapack_int lda, float* af, lapack_int ldaf,
+ char* equed, float* s, float* b, lapack_int ldb,
+ float* x, lapack_int ldx, float* rcond,
+ float* ferr, float* berr, float* work,
+ lapack_int* iwork );
+lapack_int LAPACKE_dposvx_work( int matrix_order, char fact, char uplo,
+ lapack_int n, lapack_int nrhs, double* a,
+ lapack_int lda, double* af, lapack_int ldaf,
+ char* equed, double* s, double* b,
+ lapack_int ldb, double* x, lapack_int ldx,
+ double* rcond, double* ferr, double* berr,
+ double* work, lapack_int* iwork );
+lapack_int LAPACKE_cposvx_work( int matrix_order, char fact, char uplo,
+ lapack_int n, lapack_int nrhs,
+ lapack_complex_float* a, lapack_int lda,
+ lapack_complex_float* af, lapack_int ldaf,
+ char* equed, float* s, lapack_complex_float* b,
+ lapack_int ldb, lapack_complex_float* x,
+ lapack_int ldx, float* rcond, float* ferr,
+ float* berr, lapack_complex_float* work,
+ float* rwork );
+lapack_int LAPACKE_zposvx_work( int matrix_order, char fact, char uplo,
+ lapack_int n, lapack_int nrhs,
+ lapack_complex_double* a, lapack_int lda,
+ lapack_complex_double* af, lapack_int ldaf,
+ char* equed, double* s,
+ lapack_complex_double* b, lapack_int ldb,
+ lapack_complex_double* x, lapack_int ldx,
+ double* rcond, double* ferr, double* berr,
+ lapack_complex_double* work, double* rwork );
+
+lapack_int LAPACKE_sposvxx_work( int matrix_order, char fact, char uplo,
+ lapack_int n, lapack_int nrhs, float* a,
+ lapack_int lda, float* af, lapack_int ldaf,
+ char* equed, float* s, float* b,
+ lapack_int ldb, float* x, lapack_int ldx,
+ float* rcond, float* rpvgrw, float* berr,
+ lapack_int n_err_bnds, float* err_bnds_norm,
+ float* err_bnds_comp, lapack_int nparams,
+ float* params, float* work,
+ lapack_int* iwork );
+lapack_int LAPACKE_dposvxx_work( int matrix_order, char fact, char uplo,
+ lapack_int n, lapack_int nrhs, double* a,
+ lapack_int lda, double* af, lapack_int ldaf,
+ char* equed, double* s, double* b,
+ lapack_int ldb, double* x, lapack_int ldx,
+ double* rcond, double* rpvgrw, double* berr,
+ lapack_int n_err_bnds, double* err_bnds_norm,
+ double* err_bnds_comp, lapack_int nparams,
+ double* params, double* work,
+ lapack_int* iwork );
+lapack_int LAPACKE_cposvxx_work( int matrix_order, char fact, char uplo,
+ lapack_int n, lapack_int nrhs,
+ lapack_complex_float* a, lapack_int lda,
+ lapack_complex_float* af, lapack_int ldaf,
+ char* equed, float* s, lapack_complex_float* b,
+ lapack_int ldb, lapack_complex_float* x,
+ lapack_int ldx, float* rcond, float* rpvgrw,
+ float* berr, lapack_int n_err_bnds,
+ float* err_bnds_norm, float* err_bnds_comp,
+ lapack_int nparams, float* params,
+ lapack_complex_float* work, float* rwork );
+lapack_int LAPACKE_zposvxx_work( int matrix_order, char fact, char uplo,
+ lapack_int n, lapack_int nrhs,
+ lapack_complex_double* a, lapack_int lda,
+ lapack_complex_double* af, lapack_int ldaf,
+ char* equed, double* s,
+ lapack_complex_double* b, lapack_int ldb,
+ lapack_complex_double* x, lapack_int ldx,
+ double* rcond, double* rpvgrw, double* berr,
+ lapack_int n_err_bnds, double* err_bnds_norm,
+ double* err_bnds_comp, lapack_int nparams,
+ double* params, lapack_complex_double* work,
+ double* rwork );
+
+lapack_int LAPACKE_spotrf_work( int matrix_order, char uplo, lapack_int n,
+ float* a, lapack_int lda );
+lapack_int LAPACKE_dpotrf_work( int matrix_order, char uplo, lapack_int n,
+ double* a, lapack_int lda );
+lapack_int LAPACKE_cpotrf_work( int matrix_order, char uplo, lapack_int n,
+ lapack_complex_float* a, lapack_int lda );
+lapack_int LAPACKE_zpotrf_work( int matrix_order, char uplo, lapack_int n,
+ lapack_complex_double* a, lapack_int lda );
+
+lapack_int LAPACKE_spotri_work( int matrix_order, char uplo, lapack_int n,
+ float* a, lapack_int lda );
+lapack_int LAPACKE_dpotri_work( int matrix_order, char uplo, lapack_int n,
+ double* a, lapack_int lda );
+lapack_int LAPACKE_cpotri_work( int matrix_order, char uplo, lapack_int n,
+ lapack_complex_float* a, lapack_int lda );
+lapack_int LAPACKE_zpotri_work( int matrix_order, char uplo, lapack_int n,
+ lapack_complex_double* a, lapack_int lda );
+
+lapack_int LAPACKE_spotrs_work( int matrix_order, char uplo, lapack_int n,
+ lapack_int nrhs, const float* a, lapack_int lda,
+ float* b, lapack_int ldb );
+lapack_int LAPACKE_dpotrs_work( int matrix_order, char uplo, lapack_int n,
+ lapack_int nrhs, const double* a,
+ lapack_int lda, double* b, lapack_int ldb );
+lapack_int LAPACKE_cpotrs_work( int matrix_order, char uplo, lapack_int n,
+ lapack_int nrhs, const lapack_complex_float* a,
+ lapack_int lda, lapack_complex_float* b,
+ lapack_int ldb );
+lapack_int LAPACKE_zpotrs_work( int matrix_order, char uplo, lapack_int n,
+ lapack_int nrhs, const lapack_complex_double* a,
+ lapack_int lda, lapack_complex_double* b,
+ lapack_int ldb );
+
+lapack_int LAPACKE_sppcon_work( int matrix_order, char uplo, lapack_int n,
+ const float* ap, float anorm, float* rcond,
+ float* work, lapack_int* iwork );
+lapack_int LAPACKE_dppcon_work( int matrix_order, char uplo, lapack_int n,
+ const double* ap, double anorm, double* rcond,
+ double* work, lapack_int* iwork );
+lapack_int LAPACKE_cppcon_work( int matrix_order, char uplo, lapack_int n,
+ const lapack_complex_float* ap, float anorm,
+ float* rcond, lapack_complex_float* work,
+ float* rwork );
+lapack_int LAPACKE_zppcon_work( int matrix_order, char uplo, lapack_int n,
+ const lapack_complex_double* ap, double anorm,
+ double* rcond, lapack_complex_double* work,
+ double* rwork );
+
+lapack_int LAPACKE_sppequ_work( int matrix_order, char uplo, lapack_int n,
+ const float* ap, float* s, float* scond,
+ float* amax );
+lapack_int LAPACKE_dppequ_work( int matrix_order, char uplo, lapack_int n,
+ const double* ap, double* s, double* scond,
+ double* amax );
+lapack_int LAPACKE_cppequ_work( int matrix_order, char uplo, lapack_int n,
+ const lapack_complex_float* ap, float* s,
+ float* scond, float* amax );
+lapack_int LAPACKE_zppequ_work( int matrix_order, char uplo, lapack_int n,
+ const lapack_complex_double* ap, double* s,
+ double* scond, double* amax );
+
+lapack_int LAPACKE_spprfs_work( int matrix_order, char uplo, lapack_int n,
+ lapack_int nrhs, const float* ap,
+ const float* afp, const float* b,
+ lapack_int ldb, float* x, lapack_int ldx,
+ float* ferr, float* berr, float* work,
+ lapack_int* iwork );
+lapack_int LAPACKE_dpprfs_work( int matrix_order, char uplo, lapack_int n,
+ lapack_int nrhs, const double* ap,
+ const double* afp, const double* b,
+ lapack_int ldb, double* x, lapack_int ldx,
+ double* ferr, double* berr, double* work,
+ lapack_int* iwork );
+lapack_int LAPACKE_cpprfs_work( int matrix_order, char uplo, lapack_int n,
+ lapack_int nrhs, const lapack_complex_float* ap,
+ const lapack_complex_float* afp,
+ const lapack_complex_float* b, lapack_int ldb,
+ lapack_complex_float* x, lapack_int ldx,
+ float* ferr, float* berr,
+ lapack_complex_float* work, float* rwork );
+lapack_int LAPACKE_zpprfs_work( int matrix_order, char uplo, lapack_int n,
+ lapack_int nrhs,
+ const lapack_complex_double* ap,
+ const lapack_complex_double* afp,
+ const lapack_complex_double* b, lapack_int ldb,
+ lapack_complex_double* x, lapack_int ldx,
+ double* ferr, double* berr,
+ lapack_complex_double* work, double* rwork );
+
+lapack_int LAPACKE_sppsv_work( int matrix_order, char uplo, lapack_int n,
+ lapack_int nrhs, float* ap, float* b,
+ lapack_int ldb );
+lapack_int LAPACKE_dppsv_work( int matrix_order, char uplo, lapack_int n,
+ lapack_int nrhs, double* ap, double* b,
+ lapack_int ldb );
+lapack_int LAPACKE_cppsv_work( int matrix_order, char uplo, lapack_int n,
+ lapack_int nrhs, lapack_complex_float* ap,
+ lapack_complex_float* b, lapack_int ldb );
+lapack_int LAPACKE_zppsv_work( int matrix_order, char uplo, lapack_int n,
+ lapack_int nrhs, lapack_complex_double* ap,
+ lapack_complex_double* b, lapack_int ldb );
+
+lapack_int LAPACKE_sppsvx_work( int matrix_order, char fact, char uplo,
+ lapack_int n, lapack_int nrhs, float* ap,
+ float* afp, char* equed, float* s, float* b,
+ lapack_int ldb, float* x, lapack_int ldx,
+ float* rcond, float* ferr, float* berr,
+ float* work, lapack_int* iwork );
+lapack_int LAPACKE_dppsvx_work( int matrix_order, char fact, char uplo,
+ lapack_int n, lapack_int nrhs, double* ap,
+ double* afp, char* equed, double* s, double* b,
+ lapack_int ldb, double* x, lapack_int ldx,
+ double* rcond, double* ferr, double* berr,
+ double* work, lapack_int* iwork );
+lapack_int LAPACKE_cppsvx_work( int matrix_order, char fact, char uplo,
+ lapack_int n, lapack_int nrhs,
+ lapack_complex_float* ap,
+ lapack_complex_float* afp, char* equed,
+ float* s, lapack_complex_float* b,
+ lapack_int ldb, lapack_complex_float* x,
+ lapack_int ldx, float* rcond, float* ferr,
+ float* berr, lapack_complex_float* work,
+ float* rwork );
+lapack_int LAPACKE_zppsvx_work( int matrix_order, char fact, char uplo,
+ lapack_int n, lapack_int nrhs,
+ lapack_complex_double* ap,
+ lapack_complex_double* afp, char* equed,
+ double* s, lapack_complex_double* b,
+ lapack_int ldb, lapack_complex_double* x,
+ lapack_int ldx, double* rcond, double* ferr,
+ double* berr, lapack_complex_double* work,
+ double* rwork );
+
+lapack_int LAPACKE_spptrf_work( int matrix_order, char uplo, lapack_int n,
+ float* ap );
+lapack_int LAPACKE_dpptrf_work( int matrix_order, char uplo, lapack_int n,
+ double* ap );
+lapack_int LAPACKE_cpptrf_work( int matrix_order, char uplo, lapack_int n,
+ lapack_complex_float* ap );
+lapack_int LAPACKE_zpptrf_work( int matrix_order, char uplo, lapack_int n,
+ lapack_complex_double* ap );
+
+lapack_int LAPACKE_spptri_work( int matrix_order, char uplo, lapack_int n,
+ float* ap );
+lapack_int LAPACKE_dpptri_work( int matrix_order, char uplo, lapack_int n,
+ double* ap );
+lapack_int LAPACKE_cpptri_work( int matrix_order, char uplo, lapack_int n,
+ lapack_complex_float* ap );
+lapack_int LAPACKE_zpptri_work( int matrix_order, char uplo, lapack_int n,
+ lapack_complex_double* ap );
+
+lapack_int LAPACKE_spptrs_work( int matrix_order, char uplo, lapack_int n,
+ lapack_int nrhs, const float* ap, float* b,
+ lapack_int ldb );
+lapack_int LAPACKE_dpptrs_work( int matrix_order, char uplo, lapack_int n,
+ lapack_int nrhs, const double* ap, double* b,
+ lapack_int ldb );
+lapack_int LAPACKE_cpptrs_work( int matrix_order, char uplo, lapack_int n,
+ lapack_int nrhs, const lapack_complex_float* ap,
+ lapack_complex_float* b, lapack_int ldb );
+lapack_int LAPACKE_zpptrs_work( int matrix_order, char uplo, lapack_int n,
+ lapack_int nrhs,
+ const lapack_complex_double* ap,
+ lapack_complex_double* b, lapack_int ldb );
+
+lapack_int LAPACKE_spstrf_work( int matrix_order, char uplo, lapack_int n,
+ float* a, lapack_int lda, lapack_int* piv,
+ lapack_int* rank, float tol, float* work );
+lapack_int LAPACKE_dpstrf_work( int matrix_order, char uplo, lapack_int n,
+ double* a, lapack_int lda, lapack_int* piv,
+ lapack_int* rank, double tol, double* work );
+lapack_int LAPACKE_cpstrf_work( int matrix_order, char uplo, lapack_int n,
+ lapack_complex_float* a, lapack_int lda,
+ lapack_int* piv, lapack_int* rank, float tol,
+ float* work );
+lapack_int LAPACKE_zpstrf_work( int matrix_order, char uplo, lapack_int n,
+ lapack_complex_double* a, lapack_int lda,
+ lapack_int* piv, lapack_int* rank, double tol,
+ double* work );
+
+lapack_int LAPACKE_sptcon_work( lapack_int n, const float* d, const float* e,
+ float anorm, float* rcond, float* work );
+lapack_int LAPACKE_dptcon_work( lapack_int n, const double* d, const double* e,
+ double anorm, double* rcond, double* work );
+lapack_int LAPACKE_cptcon_work( lapack_int n, const float* d,
+ const lapack_complex_float* e, float anorm,
+ float* rcond, float* work );
+lapack_int LAPACKE_zptcon_work( lapack_int n, const double* d,
+ const lapack_complex_double* e, double anorm,
+ double* rcond, double* work );
+
+lapack_int LAPACKE_spteqr_work( int matrix_order, char compz, lapack_int n,
+ float* d, float* e, float* z, lapack_int ldz,
+ float* work );
+lapack_int LAPACKE_dpteqr_work( int matrix_order, char compz, lapack_int n,
+ double* d, double* e, double* z, lapack_int ldz,
+ double* work );
+lapack_int LAPACKE_cpteqr_work( int matrix_order, char compz, lapack_int n,
+ float* d, float* e, lapack_complex_float* z,
+ lapack_int ldz, float* work );
+lapack_int LAPACKE_zpteqr_work( int matrix_order, char compz, lapack_int n,
+ double* d, double* e, lapack_complex_double* z,
+ lapack_int ldz, double* work );
+
+lapack_int LAPACKE_sptrfs_work( int matrix_order, lapack_int n, lapack_int nrhs,
+ const float* d, const float* e, const float* df,
+ const float* ef, const float* b, lapack_int ldb,
+ float* x, lapack_int ldx, float* ferr,
+ float* berr, float* work );
+lapack_int LAPACKE_dptrfs_work( int matrix_order, lapack_int n, lapack_int nrhs,
+ const double* d, const double* e,
+ const double* df, const double* ef,
+ const double* b, lapack_int ldb, double* x,
+ lapack_int ldx, double* ferr, double* berr,
+ double* work );
+lapack_int LAPACKE_cptrfs_work( int matrix_order, char uplo, lapack_int n,
+ lapack_int nrhs, const float* d,
+ const lapack_complex_float* e, const float* df,
+ const lapack_complex_float* ef,
+ const lapack_complex_float* b, lapack_int ldb,
+ lapack_complex_float* x, lapack_int ldx,
+ float* ferr, float* berr,
+ lapack_complex_float* work, float* rwork );
+lapack_int LAPACKE_zptrfs_work( int matrix_order, char uplo, lapack_int n,
+ lapack_int nrhs, const double* d,
+ const lapack_complex_double* e,
+ const double* df,
+ const lapack_complex_double* ef,
+ const lapack_complex_double* b, lapack_int ldb,
+ lapack_complex_double* x, lapack_int ldx,
+ double* ferr, double* berr,
+ lapack_complex_double* work, double* rwork );
+
+lapack_int LAPACKE_sptsv_work( int matrix_order, lapack_int n, lapack_int nrhs,
+ float* d, float* e, float* b, lapack_int ldb );
+lapack_int LAPACKE_dptsv_work( int matrix_order, lapack_int n, lapack_int nrhs,
+ double* d, double* e, double* b,
+ lapack_int ldb );
+lapack_int LAPACKE_cptsv_work( int matrix_order, lapack_int n, lapack_int nrhs,
+ float* d, lapack_complex_float* e,
+ lapack_complex_float* b, lapack_int ldb );
+lapack_int LAPACKE_zptsv_work( int matrix_order, lapack_int n, lapack_int nrhs,
+ double* d, lapack_complex_double* e,
+ lapack_complex_double* b, lapack_int ldb );
+
+lapack_int LAPACKE_sptsvx_work( int matrix_order, char fact, lapack_int n,
+ lapack_int nrhs, const float* d, const float* e,
+ float* df, float* ef, const float* b,
+ lapack_int ldb, float* x, lapack_int ldx,
+ float* rcond, float* ferr, float* berr,
+ float* work );
+lapack_int LAPACKE_dptsvx_work( int matrix_order, char fact, lapack_int n,
+ lapack_int nrhs, const double* d,
+ const double* e, double* df, double* ef,
+ const double* b, lapack_int ldb, double* x,
+ lapack_int ldx, double* rcond, double* ferr,
+ double* berr, double* work );
+lapack_int LAPACKE_cptsvx_work( int matrix_order, char fact, lapack_int n,
+ lapack_int nrhs, const float* d,
+ const lapack_complex_float* e, float* df,
+ lapack_complex_float* ef,
+ const lapack_complex_float* b, lapack_int ldb,
+ lapack_complex_float* x, lapack_int ldx,
+ float* rcond, float* ferr, float* berr,
+ lapack_complex_float* work, float* rwork );
+lapack_int LAPACKE_zptsvx_work( int matrix_order, char fact, lapack_int n,
+ lapack_int nrhs, const double* d,
+ const lapack_complex_double* e, double* df,
+ lapack_complex_double* ef,
+ const lapack_complex_double* b, lapack_int ldb,
+ lapack_complex_double* x, lapack_int ldx,
+ double* rcond, double* ferr, double* berr,
+ lapack_complex_double* work, double* rwork );
+
+lapack_int LAPACKE_spttrf_work( lapack_int n, float* d, float* e );
+lapack_int LAPACKE_dpttrf_work( lapack_int n, double* d, double* e );
+lapack_int LAPACKE_cpttrf_work( lapack_int n, float* d,
+ lapack_complex_float* e );
+lapack_int LAPACKE_zpttrf_work( lapack_int n, double* d,
+ lapack_complex_double* e );
+
+lapack_int LAPACKE_spttrs_work( int matrix_order, lapack_int n, lapack_int nrhs,
+ const float* d, const float* e, float* b,
+ lapack_int ldb );
+lapack_int LAPACKE_dpttrs_work( int matrix_order, lapack_int n, lapack_int nrhs,
+ const double* d, const double* e, double* b,
+ lapack_int ldb );
+lapack_int LAPACKE_cpttrs_work( int matrix_order, char uplo, lapack_int n,
+ lapack_int nrhs, const float* d,
+ const lapack_complex_float* e,
+ lapack_complex_float* b, lapack_int ldb );
+lapack_int LAPACKE_zpttrs_work( int matrix_order, char uplo, lapack_int n,
+ lapack_int nrhs, const double* d,
+ const lapack_complex_double* e,
+ lapack_complex_double* b, lapack_int ldb );
+
+lapack_int LAPACKE_ssbev_work( int matrix_order, char jobz, char uplo,
+ lapack_int n, lapack_int kd, float* ab,
+ lapack_int ldab, float* w, float* z,
+ lapack_int ldz, float* work );
+lapack_int LAPACKE_dsbev_work( int matrix_order, char jobz, char uplo,
+ lapack_int n, lapack_int kd, double* ab,
+ lapack_int ldab, double* w, double* z,
+ lapack_int ldz, double* work );
+
+lapack_int LAPACKE_ssbevd_work( int matrix_order, char jobz, char uplo,
+ lapack_int n, lapack_int kd, float* ab,
+ lapack_int ldab, float* w, float* z,
+ lapack_int ldz, float* work, lapack_int lwork,
+ lapack_int* iwork, lapack_int liwork );
+lapack_int LAPACKE_dsbevd_work( int matrix_order, char jobz, char uplo,
+ lapack_int n, lapack_int kd, double* ab,
+ lapack_int ldab, double* w, double* z,
+ lapack_int ldz, double* work, lapack_int lwork,
+ lapack_int* iwork, lapack_int liwork );
+
+lapack_int LAPACKE_ssbevx_work( int matrix_order, char jobz, char range,
+ char uplo, lapack_int n, lapack_int kd,
+ float* ab, lapack_int ldab, float* q,
+ lapack_int ldq, float vl, float vu,
+ lapack_int il, lapack_int iu, float abstol,
+ lapack_int* m, float* w, float* z,
+ lapack_int ldz, float* work, lapack_int* iwork,
+ lapack_int* ifail );
+lapack_int LAPACKE_dsbevx_work( int matrix_order, char jobz, char range,
+ char uplo, lapack_int n, lapack_int kd,
+ double* ab, lapack_int ldab, double* q,
+ lapack_int ldq, double vl, double vu,
+ lapack_int il, lapack_int iu, double abstol,
+ lapack_int* m, double* w, double* z,
+ lapack_int ldz, double* work, lapack_int* iwork,
+ lapack_int* ifail );
+
+lapack_int LAPACKE_ssbgst_work( int matrix_order, char vect, char uplo,
+ lapack_int n, lapack_int ka, lapack_int kb,
+ float* ab, lapack_int ldab, const float* bb,
+ lapack_int ldbb, float* x, lapack_int ldx,
+ float* work );
+lapack_int LAPACKE_dsbgst_work( int matrix_order, char vect, char uplo,
+ lapack_int n, lapack_int ka, lapack_int kb,
+ double* ab, lapack_int ldab, const double* bb,
+ lapack_int ldbb, double* x, lapack_int ldx,
+ double* work );
+
+lapack_int LAPACKE_ssbgv_work( int matrix_order, char jobz, char uplo,
+ lapack_int n, lapack_int ka, lapack_int kb,
+ float* ab, lapack_int ldab, float* bb,
+ lapack_int ldbb, float* w, float* z,
+ lapack_int ldz, float* work );
+lapack_int LAPACKE_dsbgv_work( int matrix_order, char jobz, char uplo,
+ lapack_int n, lapack_int ka, lapack_int kb,
+ double* ab, lapack_int ldab, double* bb,
+ lapack_int ldbb, double* w, double* z,
+ lapack_int ldz, double* work );
+
+lapack_int LAPACKE_ssbgvd_work( int matrix_order, char jobz, char uplo,
+ lapack_int n, lapack_int ka, lapack_int kb,
+ float* ab, lapack_int ldab, float* bb,
+ lapack_int ldbb, float* w, float* z,
+ lapack_int ldz, float* work, lapack_int lwork,
+ lapack_int* iwork, lapack_int liwork );
+lapack_int LAPACKE_dsbgvd_work( int matrix_order, char jobz, char uplo,
+ lapack_int n, lapack_int ka, lapack_int kb,
+ double* ab, lapack_int ldab, double* bb,
+ lapack_int ldbb, double* w, double* z,
+ lapack_int ldz, double* work, lapack_int lwork,
+ lapack_int* iwork, lapack_int liwork );
+
+lapack_int LAPACKE_ssbgvx_work( int matrix_order, char jobz, char range,
+ char uplo, lapack_int n, lapack_int ka,
+ lapack_int kb, float* ab, lapack_int ldab,
+ float* bb, lapack_int ldbb, float* q,
+ lapack_int ldq, float vl, float vu,
+ lapack_int il, lapack_int iu, float abstol,
+ lapack_int* m, float* w, float* z,
+ lapack_int ldz, float* work, lapack_int* iwork,
+ lapack_int* ifail );
+lapack_int LAPACKE_dsbgvx_work( int matrix_order, char jobz, char range,
+ char uplo, lapack_int n, lapack_int ka,
+ lapack_int kb, double* ab, lapack_int ldab,
+ double* bb, lapack_int ldbb, double* q,
+ lapack_int ldq, double vl, double vu,
+ lapack_int il, lapack_int iu, double abstol,
+ lapack_int* m, double* w, double* z,
+ lapack_int ldz, double* work, lapack_int* iwork,
+ lapack_int* ifail );
+
+lapack_int LAPACKE_ssbtrd_work( int matrix_order, char vect, char uplo,
+ lapack_int n, lapack_int kd, float* ab,
+ lapack_int ldab, float* d, float* e, float* q,
+ lapack_int ldq, float* work );
+lapack_int LAPACKE_dsbtrd_work( int matrix_order, char vect, char uplo,
+ lapack_int n, lapack_int kd, double* ab,
+ lapack_int ldab, double* d, double* e,
+ double* q, lapack_int ldq, double* work );
+
+lapack_int LAPACKE_ssfrk_work( int matrix_order, char transr, char uplo,
+ char trans, lapack_int n, lapack_int k,
+ float alpha, const float* a, lapack_int lda,
+ float beta, float* c );
+lapack_int LAPACKE_dsfrk_work( int matrix_order, char transr, char uplo,
+ char trans, lapack_int n, lapack_int k,
+ double alpha, const double* a, lapack_int lda,
+ double beta, double* c );
+
+lapack_int LAPACKE_sspcon_work( int matrix_order, char uplo, lapack_int n,
+ const float* ap, const lapack_int* ipiv,
+ float anorm, float* rcond, float* work,
+ lapack_int* iwork );
+lapack_int LAPACKE_dspcon_work( int matrix_order, char uplo, lapack_int n,
+ const double* ap, const lapack_int* ipiv,
+ double anorm, double* rcond, double* work,
+ lapack_int* iwork );
+lapack_int LAPACKE_cspcon_work( int matrix_order, char uplo, lapack_int n,
+ const lapack_complex_float* ap,
+ const lapack_int* ipiv, float anorm,
+ float* rcond, lapack_complex_float* work );
+lapack_int LAPACKE_zspcon_work( int matrix_order, char uplo, lapack_int n,
+ const lapack_complex_double* ap,
+ const lapack_int* ipiv, double anorm,
+ double* rcond, lapack_complex_double* work );
+
+lapack_int LAPACKE_sspev_work( int matrix_order, char jobz, char uplo,
+ lapack_int n, float* ap, float* w, float* z,
+ lapack_int ldz, float* work );
+lapack_int LAPACKE_dspev_work( int matrix_order, char jobz, char uplo,
+ lapack_int n, double* ap, double* w, double* z,
+ lapack_int ldz, double* work );
+
+lapack_int LAPACKE_sspevd_work( int matrix_order, char jobz, char uplo,
+ lapack_int n, float* ap, float* w, float* z,
+ lapack_int ldz, float* work, lapack_int lwork,
+ lapack_int* iwork, lapack_int liwork );
+lapack_int LAPACKE_dspevd_work( int matrix_order, char jobz, char uplo,
+ lapack_int n, double* ap, double* w, double* z,
+ lapack_int ldz, double* work, lapack_int lwork,
+ lapack_int* iwork, lapack_int liwork );
+
+lapack_int LAPACKE_sspevx_work( int matrix_order, char jobz, char range,
+ char uplo, lapack_int n, float* ap, float vl,
+ float vu, lapack_int il, lapack_int iu,
+ float abstol, lapack_int* m, float* w, float* z,
+ lapack_int ldz, float* work, lapack_int* iwork,
+ lapack_int* ifail );
+lapack_int LAPACKE_dspevx_work( int matrix_order, char jobz, char range,
+ char uplo, lapack_int n, double* ap, double vl,
+ double vu, lapack_int il, lapack_int iu,
+ double abstol, lapack_int* m, double* w,
+ double* z, lapack_int ldz, double* work,
+ lapack_int* iwork, lapack_int* ifail );
+
+lapack_int LAPACKE_sspgst_work( int matrix_order, lapack_int itype, char uplo,
+ lapack_int n, float* ap, const float* bp );
+lapack_int LAPACKE_dspgst_work( int matrix_order, lapack_int itype, char uplo,
+ lapack_int n, double* ap, const double* bp );
+
+lapack_int LAPACKE_sspgv_work( int matrix_order, lapack_int itype, char jobz,
+ char uplo, lapack_int n, float* ap, float* bp,
+ float* w, float* z, lapack_int ldz,
+ float* work );
+lapack_int LAPACKE_dspgv_work( int matrix_order, lapack_int itype, char jobz,
+ char uplo, lapack_int n, double* ap, double* bp,
+ double* w, double* z, lapack_int ldz,
+ double* work );
+
+lapack_int LAPACKE_sspgvd_work( int matrix_order, lapack_int itype, char jobz,
+ char uplo, lapack_int n, float* ap, float* bp,
+ float* w, float* z, lapack_int ldz, float* work,
+ lapack_int lwork, lapack_int* iwork,
+ lapack_int liwork );
+lapack_int LAPACKE_dspgvd_work( int matrix_order, lapack_int itype, char jobz,
+ char uplo, lapack_int n, double* ap, double* bp,
+ double* w, double* z, lapack_int ldz,
+ double* work, lapack_int lwork,
+ lapack_int* iwork, lapack_int liwork );
+
+lapack_int LAPACKE_sspgvx_work( int matrix_order, lapack_int itype, char jobz,
+ char range, char uplo, lapack_int n, float* ap,
+ float* bp, float vl, float vu, lapack_int il,
+ lapack_int iu, float abstol, lapack_int* m,
+ float* w, float* z, lapack_int ldz, float* work,
+ lapack_int* iwork, lapack_int* ifail );
+lapack_int LAPACKE_dspgvx_work( int matrix_order, lapack_int itype, char jobz,
+ char range, char uplo, lapack_int n, double* ap,
+ double* bp, double vl, double vu, lapack_int il,
+ lapack_int iu, double abstol, lapack_int* m,
+ double* w, double* z, lapack_int ldz,
+ double* work, lapack_int* iwork,
+ lapack_int* ifail );
+
+lapack_int LAPACKE_ssprfs_work( int matrix_order, char uplo, lapack_int n,
+ lapack_int nrhs, const float* ap,
+ const float* afp, const lapack_int* ipiv,
+ const float* b, lapack_int ldb, float* x,
+ lapack_int ldx, float* ferr, float* berr,
+ float* work, lapack_int* iwork );
+lapack_int LAPACKE_dsprfs_work( int matrix_order, char uplo, lapack_int n,
+ lapack_int nrhs, const double* ap,
+ const double* afp, const lapack_int* ipiv,
+ const double* b, lapack_int ldb, double* x,
+ lapack_int ldx, double* ferr, double* berr,
+ double* work, lapack_int* iwork );
+lapack_int LAPACKE_csprfs_work( int matrix_order, char uplo, lapack_int n,
+ lapack_int nrhs, const lapack_complex_float* ap,
+ const lapack_complex_float* afp,
+ const lapack_int* ipiv,
+ const lapack_complex_float* b, lapack_int ldb,
+ lapack_complex_float* x, lapack_int ldx,
+ float* ferr, float* berr,
+ lapack_complex_float* work, float* rwork );
+lapack_int LAPACKE_zsprfs_work( int matrix_order, char uplo, lapack_int n,
+ lapack_int nrhs,
+ const lapack_complex_double* ap,
+ const lapack_complex_double* afp,
+ const lapack_int* ipiv,
+ const lapack_complex_double* b, lapack_int ldb,
+ lapack_complex_double* x, lapack_int ldx,
+ double* ferr, double* berr,
+ lapack_complex_double* work, double* rwork );
+
+lapack_int LAPACKE_sspsv_work( int matrix_order, char uplo, lapack_int n,
+ lapack_int nrhs, float* ap, lapack_int* ipiv,
+ float* b, lapack_int ldb );
+lapack_int LAPACKE_dspsv_work( int matrix_order, char uplo, lapack_int n,
+ lapack_int nrhs, double* ap, lapack_int* ipiv,
+ double* b, lapack_int ldb );
+lapack_int LAPACKE_cspsv_work( int matrix_order, char uplo, lapack_int n,
+ lapack_int nrhs, lapack_complex_float* ap,
+ lapack_int* ipiv, lapack_complex_float* b,
+ lapack_int ldb );
+lapack_int LAPACKE_zspsv_work( int matrix_order, char uplo, lapack_int n,
+ lapack_int nrhs, lapack_complex_double* ap,
+ lapack_int* ipiv, lapack_complex_double* b,
+ lapack_int ldb );
+
+lapack_int LAPACKE_sspsvx_work( int matrix_order, char fact, char uplo,
+ lapack_int n, lapack_int nrhs, const float* ap,
+ float* afp, lapack_int* ipiv, const float* b,
+ lapack_int ldb, float* x, lapack_int ldx,
+ float* rcond, float* ferr, float* berr,
+ float* work, lapack_int* iwork );
+lapack_int LAPACKE_dspsvx_work( int matrix_order, char fact, char uplo,
+ lapack_int n, lapack_int nrhs, const double* ap,
+ double* afp, lapack_int* ipiv, const double* b,
+ lapack_int ldb, double* x, lapack_int ldx,
+ double* rcond, double* ferr, double* berr,
+ double* work, lapack_int* iwork );
+lapack_int LAPACKE_cspsvx_work( int matrix_order, char fact, char uplo,
+ lapack_int n, lapack_int nrhs,
+ const lapack_complex_float* ap,
+ lapack_complex_float* afp, lapack_int* ipiv,
+ const lapack_complex_float* b, lapack_int ldb,
+ lapack_complex_float* x, lapack_int ldx,
+ float* rcond, float* ferr, float* berr,
+ lapack_complex_float* work, float* rwork );
+lapack_int LAPACKE_zspsvx_work( int matrix_order, char fact, char uplo,
+ lapack_int n, lapack_int nrhs,
+ const lapack_complex_double* ap,
+ lapack_complex_double* afp, lapack_int* ipiv,
+ const lapack_complex_double* b, lapack_int ldb,
+ lapack_complex_double* x, lapack_int ldx,
+ double* rcond, double* ferr, double* berr,
+ lapack_complex_double* work, double* rwork );
+
+lapack_int LAPACKE_ssptrd_work( int matrix_order, char uplo, lapack_int n,
+ float* ap, float* d, float* e, float* tau );
+lapack_int LAPACKE_dsptrd_work( int matrix_order, char uplo, lapack_int n,
+ double* ap, double* d, double* e, double* tau );
+
+lapack_int LAPACKE_ssptrf_work( int matrix_order, char uplo, lapack_int n,
+ float* ap, lapack_int* ipiv );
+lapack_int LAPACKE_dsptrf_work( int matrix_order, char uplo, lapack_int n,
+ double* ap, lapack_int* ipiv );
+lapack_int LAPACKE_csptrf_work( int matrix_order, char uplo, lapack_int n,
+ lapack_complex_float* ap, lapack_int* ipiv );
+lapack_int LAPACKE_zsptrf_work( int matrix_order, char uplo, lapack_int n,
+ lapack_complex_double* ap, lapack_int* ipiv );
+
+lapack_int LAPACKE_ssptri_work( int matrix_order, char uplo, lapack_int n,
+ float* ap, const lapack_int* ipiv,
+ float* work );
+lapack_int LAPACKE_dsptri_work( int matrix_order, char uplo, lapack_int n,
+ double* ap, const lapack_int* ipiv,
+ double* work );
+lapack_int LAPACKE_csptri_work( int matrix_order, char uplo, lapack_int n,
+ lapack_complex_float* ap,
+ const lapack_int* ipiv,
+ lapack_complex_float* work );
+lapack_int LAPACKE_zsptri_work( int matrix_order, char uplo, lapack_int n,
+ lapack_complex_double* ap,
+ const lapack_int* ipiv,
+ lapack_complex_double* work );
+
+lapack_int LAPACKE_ssptrs_work( int matrix_order, char uplo, lapack_int n,
+ lapack_int nrhs, const float* ap,
+ const lapack_int* ipiv, float* b,
+ lapack_int ldb );
+lapack_int LAPACKE_dsptrs_work( int matrix_order, char uplo, lapack_int n,
+ lapack_int nrhs, const double* ap,
+ const lapack_int* ipiv, double* b,
+ lapack_int ldb );
+lapack_int LAPACKE_csptrs_work( int matrix_order, char uplo, lapack_int n,
+ lapack_int nrhs, const lapack_complex_float* ap,
+ const lapack_int* ipiv, lapack_complex_float* b,
+ lapack_int ldb );
+lapack_int LAPACKE_zsptrs_work( int matrix_order, char uplo, lapack_int n,
+ lapack_int nrhs,
+ const lapack_complex_double* ap,
+ const lapack_int* ipiv,
+ lapack_complex_double* b, lapack_int ldb );
+
+lapack_int LAPACKE_sstebz_work( char range, char order, lapack_int n, float vl,
+ float vu, lapack_int il, lapack_int iu,
+ float abstol, const float* d, const float* e,
+ lapack_int* m, lapack_int* nsplit, float* w,
+ lapack_int* iblock, lapack_int* isplit,
+ float* work, lapack_int* iwork );
+lapack_int LAPACKE_dstebz_work( char range, char order, lapack_int n, double vl,
+ double vu, lapack_int il, lapack_int iu,
+ double abstol, const double* d, const double* e,
+ lapack_int* m, lapack_int* nsplit, double* w,
+ lapack_int* iblock, lapack_int* isplit,
+ double* work, lapack_int* iwork );
+
+lapack_int LAPACKE_sstedc_work( int matrix_order, char compz, lapack_int n,
+ float* d, float* e, float* z, lapack_int ldz,
+ float* work, lapack_int lwork,
+ lapack_int* iwork, lapack_int liwork );
+lapack_int LAPACKE_dstedc_work( int matrix_order, char compz, lapack_int n,
+ double* d, double* e, double* z, lapack_int ldz,
+ double* work, lapack_int lwork,
+ lapack_int* iwork, lapack_int liwork );
+lapack_int LAPACKE_cstedc_work( int matrix_order, char compz, lapack_int n,
+ float* d, float* e, lapack_complex_float* z,
+ lapack_int ldz, lapack_complex_float* work,
+ lapack_int lwork, float* rwork,
+ lapack_int lrwork, lapack_int* iwork,
+ lapack_int liwork );
+lapack_int LAPACKE_zstedc_work( int matrix_order, char compz, lapack_int n,
+ double* d, double* e, lapack_complex_double* z,
+ lapack_int ldz, lapack_complex_double* work,
+ lapack_int lwork, double* rwork,
+ lapack_int lrwork, lapack_int* iwork,
+ lapack_int liwork );
+
+lapack_int LAPACKE_sstegr_work( int matrix_order, char jobz, char range,
+ lapack_int n, float* d, float* e, float vl,
+ float vu, lapack_int il, lapack_int iu,
+ float abstol, lapack_int* m, float* w, float* z,
+ lapack_int ldz, lapack_int* isuppz, float* work,
+ lapack_int lwork, lapack_int* iwork,
+ lapack_int liwork );
+lapack_int LAPACKE_dstegr_work( int matrix_order, char jobz, char range,
+ lapack_int n, double* d, double* e, double vl,
+ double vu, lapack_int il, lapack_int iu,
+ double abstol, lapack_int* m, double* w,
+ double* z, lapack_int ldz, lapack_int* isuppz,
+ double* work, lapack_int lwork,
+ lapack_int* iwork, lapack_int liwork );
+lapack_int LAPACKE_cstegr_work( int matrix_order, char jobz, char range,
+ lapack_int n, float* d, float* e, float vl,
+ float vu, lapack_int il, lapack_int iu,
+ float abstol, lapack_int* m, float* w,
+ lapack_complex_float* z, lapack_int ldz,
+ lapack_int* isuppz, float* work,
+ lapack_int lwork, lapack_int* iwork,
+ lapack_int liwork );
+lapack_int LAPACKE_zstegr_work( int matrix_order, char jobz, char range,
+ lapack_int n, double* d, double* e, double vl,
+ double vu, lapack_int il, lapack_int iu,
+ double abstol, lapack_int* m, double* w,
+ lapack_complex_double* z, lapack_int ldz,
+ lapack_int* isuppz, double* work,
+ lapack_int lwork, lapack_int* iwork,
+ lapack_int liwork );
+
+lapack_int LAPACKE_sstein_work( int matrix_order, lapack_int n, const float* d,
+ const float* e, lapack_int m, const float* w,
+ const lapack_int* iblock,
+ const lapack_int* isplit, float* z,
+ lapack_int ldz, float* work, lapack_int* iwork,
+ lapack_int* ifailv );
+lapack_int LAPACKE_dstein_work( int matrix_order, lapack_int n, const double* d,
+ const double* e, lapack_int m, const double* w,
+ const lapack_int* iblock,
+ const lapack_int* isplit, double* z,
+ lapack_int ldz, double* work, lapack_int* iwork,
+ lapack_int* ifailv );
+lapack_int LAPACKE_cstein_work( int matrix_order, lapack_int n, const float* d,
+ const float* e, lapack_int m, const float* w,
+ const lapack_int* iblock,
+ const lapack_int* isplit,
+ lapack_complex_float* z, lapack_int ldz,
+ float* work, lapack_int* iwork,
+ lapack_int* ifailv );
+lapack_int LAPACKE_zstein_work( int matrix_order, lapack_int n, const double* d,
+ const double* e, lapack_int m, const double* w,
+ const lapack_int* iblock,
+ const lapack_int* isplit,
+ lapack_complex_double* z, lapack_int ldz,
+ double* work, lapack_int* iwork,
+ lapack_int* ifailv );
+
+lapack_int LAPACKE_sstemr_work( int matrix_order, char jobz, char range,
+ lapack_int n, float* d, float* e, float vl,
+ float vu, lapack_int il, lapack_int iu,
+ lapack_int* m, float* w, float* z,
+ lapack_int ldz, lapack_int nzc,
+ lapack_int* isuppz, lapack_logical* tryrac,
+ float* work, lapack_int lwork,
+ lapack_int* iwork, lapack_int liwork );
+lapack_int LAPACKE_dstemr_work( int matrix_order, char jobz, char range,
+ lapack_int n, double* d, double* e, double vl,
+ double vu, lapack_int il, lapack_int iu,
+ lapack_int* m, double* w, double* z,
+ lapack_int ldz, lapack_int nzc,
+ lapack_int* isuppz, lapack_logical* tryrac,
+ double* work, lapack_int lwork,
+ lapack_int* iwork, lapack_int liwork );
+lapack_int LAPACKE_cstemr_work( int matrix_order, char jobz, char range,
+ lapack_int n, float* d, float* e, float vl,
+ float vu, lapack_int il, lapack_int iu,
+ lapack_int* m, float* w,
+ lapack_complex_float* z, lapack_int ldz,
+ lapack_int nzc, lapack_int* isuppz,
+ lapack_logical* tryrac, float* work,
+ lapack_int lwork, lapack_int* iwork,
+ lapack_int liwork );
+lapack_int LAPACKE_zstemr_work( int matrix_order, char jobz, char range,
+ lapack_int n, double* d, double* e, double vl,
+ double vu, lapack_int il, lapack_int iu,
+ lapack_int* m, double* w,
+ lapack_complex_double* z, lapack_int ldz,
+ lapack_int nzc, lapack_int* isuppz,
+ lapack_logical* tryrac, double* work,
+ lapack_int lwork, lapack_int* iwork,
+ lapack_int liwork );
+
+lapack_int LAPACKE_ssteqr_work( int matrix_order, char compz, lapack_int n,
+ float* d, float* e, float* z, lapack_int ldz,
+ float* work );
+lapack_int LAPACKE_dsteqr_work( int matrix_order, char compz, lapack_int n,
+ double* d, double* e, double* z, lapack_int ldz,
+ double* work );
+lapack_int LAPACKE_csteqr_work( int matrix_order, char compz, lapack_int n,
+ float* d, float* e, lapack_complex_float* z,
+ lapack_int ldz, float* work );
+lapack_int LAPACKE_zsteqr_work( int matrix_order, char compz, lapack_int n,
+ double* d, double* e, lapack_complex_double* z,
+ lapack_int ldz, double* work );
+
+lapack_int LAPACKE_ssterf_work( lapack_int n, float* d, float* e );
+lapack_int LAPACKE_dsterf_work( lapack_int n, double* d, double* e );
+
+lapack_int LAPACKE_sstev_work( int matrix_order, char jobz, lapack_int n,
+ float* d, float* e, float* z, lapack_int ldz,
+ float* work );
+lapack_int LAPACKE_dstev_work( int matrix_order, char jobz, lapack_int n,
+ double* d, double* e, double* z, lapack_int ldz,
+ double* work );
+
+lapack_int LAPACKE_sstevd_work( int matrix_order, char jobz, lapack_int n,
+ float* d, float* e, float* z, lapack_int ldz,
+ float* work, lapack_int lwork,
+ lapack_int* iwork, lapack_int liwork );
+lapack_int LAPACKE_dstevd_work( int matrix_order, char jobz, lapack_int n,
+ double* d, double* e, double* z, lapack_int ldz,
+ double* work, lapack_int lwork,
+ lapack_int* iwork, lapack_int liwork );
+
+lapack_int LAPACKE_sstevr_work( int matrix_order, char jobz, char range,
+ lapack_int n, float* d, float* e, float vl,
+ float vu, lapack_int il, lapack_int iu,
+ float abstol, lapack_int* m, float* w, float* z,
+ lapack_int ldz, lapack_int* isuppz, float* work,
+ lapack_int lwork, lapack_int* iwork,
+ lapack_int liwork );
+lapack_int LAPACKE_dstevr_work( int matrix_order, char jobz, char range,
+ lapack_int n, double* d, double* e, double vl,
+ double vu, lapack_int il, lapack_int iu,
+ double abstol, lapack_int* m, double* w,
+ double* z, lapack_int ldz, lapack_int* isuppz,
+ double* work, lapack_int lwork,
+ lapack_int* iwork, lapack_int liwork );
+
+lapack_int LAPACKE_sstevx_work( int matrix_order, char jobz, char range,
+ lapack_int n, float* d, float* e, float vl,
+ float vu, lapack_int il, lapack_int iu,
+ float abstol, lapack_int* m, float* w, float* z,
+ lapack_int ldz, float* work, lapack_int* iwork,
+ lapack_int* ifail );
+lapack_int LAPACKE_dstevx_work( int matrix_order, char jobz, char range,
+ lapack_int n, double* d, double* e, double vl,
+ double vu, lapack_int il, lapack_int iu,
+ double abstol, lapack_int* m, double* w,
+ double* z, lapack_int ldz, double* work,
+ lapack_int* iwork, lapack_int* ifail );
+
+lapack_int LAPACKE_ssycon_work( int matrix_order, char uplo, lapack_int n,
+ const float* a, lapack_int lda,
+ const lapack_int* ipiv, float anorm,
+ float* rcond, float* work, lapack_int* iwork );
+lapack_int LAPACKE_dsycon_work( int matrix_order, char uplo, lapack_int n,
+ const double* a, lapack_int lda,
+ const lapack_int* ipiv, double anorm,
+ double* rcond, double* work,
+ lapack_int* iwork );
+lapack_int LAPACKE_csycon_work( int matrix_order, char uplo, lapack_int n,
+ const lapack_complex_float* a, lapack_int lda,
+ const lapack_int* ipiv, float anorm,
+ float* rcond, lapack_complex_float* work );
+lapack_int LAPACKE_zsycon_work( int matrix_order, char uplo, lapack_int n,
+ const lapack_complex_double* a, lapack_int lda,
+ const lapack_int* ipiv, double anorm,
+ double* rcond, lapack_complex_double* work );
+
+lapack_int LAPACKE_ssyequb_work( int matrix_order, char uplo, lapack_int n,
+ const float* a, lapack_int lda, float* s,
+ float* scond, float* amax, float* work );
+lapack_int LAPACKE_dsyequb_work( int matrix_order, char uplo, lapack_int n,
+ const double* a, lapack_int lda, double* s,
+ double* scond, double* amax, double* work );
+lapack_int LAPACKE_csyequb_work( int matrix_order, char uplo, lapack_int n,
+ const lapack_complex_float* a, lapack_int lda,
+ float* s, float* scond, float* amax,
+ lapack_complex_float* work );
+lapack_int LAPACKE_zsyequb_work( int matrix_order, char uplo, lapack_int n,
+ const lapack_complex_double* a, lapack_int lda,
+ double* s, double* scond, double* amax,
+ lapack_complex_double* work );
+
+lapack_int LAPACKE_ssyev_work( int matrix_order, char jobz, char uplo,
+ lapack_int n, float* a, lapack_int lda, float* w,
+ float* work, lapack_int lwork );
+lapack_int LAPACKE_dsyev_work( int matrix_order, char jobz, char uplo,
+ lapack_int n, double* a, lapack_int lda,
+ double* w, double* work, lapack_int lwork );
+
+lapack_int LAPACKE_ssyevd_work( int matrix_order, char jobz, char uplo,
+ lapack_int n, float* a, lapack_int lda,
+ float* w, float* work, lapack_int lwork,
+ lapack_int* iwork, lapack_int liwork );
+lapack_int LAPACKE_dsyevd_work( int matrix_order, char jobz, char uplo,
+ lapack_int n, double* a, lapack_int lda,
+ double* w, double* work, lapack_int lwork,
+ lapack_int* iwork, lapack_int liwork );
+
+lapack_int LAPACKE_ssyevr_work( int matrix_order, char jobz, char range,
+ char uplo, lapack_int n, float* a,
+ lapack_int lda, float vl, float vu,
+ lapack_int il, lapack_int iu, float abstol,
+ lapack_int* m, float* w, float* z,
+ lapack_int ldz, lapack_int* isuppz, float* work,
+ lapack_int lwork, lapack_int* iwork,
+ lapack_int liwork );
+lapack_int LAPACKE_dsyevr_work( int matrix_order, char jobz, char range,
+ char uplo, lapack_int n, double* a,
+ lapack_int lda, double vl, double vu,
+ lapack_int il, lapack_int iu, double abstol,
+ lapack_int* m, double* w, double* z,
+ lapack_int ldz, lapack_int* isuppz,
+ double* work, lapack_int lwork,
+ lapack_int* iwork, lapack_int liwork );
+
+lapack_int LAPACKE_ssyevx_work( int matrix_order, char jobz, char range,
+ char uplo, lapack_int n, float* a,
+ lapack_int lda, float vl, float vu,
+ lapack_int il, lapack_int iu, float abstol,
+ lapack_int* m, float* w, float* z,
+ lapack_int ldz, float* work, lapack_int lwork,
+ lapack_int* iwork, lapack_int* ifail );
+lapack_int LAPACKE_dsyevx_work( int matrix_order, char jobz, char range,
+ char uplo, lapack_int n, double* a,
+ lapack_int lda, double vl, double vu,
+ lapack_int il, lapack_int iu, double abstol,
+ lapack_int* m, double* w, double* z,
+ lapack_int ldz, double* work, lapack_int lwork,
+ lapack_int* iwork, lapack_int* ifail );
+
+lapack_int LAPACKE_ssygst_work( int matrix_order, lapack_int itype, char uplo,
+ lapack_int n, float* a, lapack_int lda,
+ const float* b, lapack_int ldb );
+lapack_int LAPACKE_dsygst_work( int matrix_order, lapack_int itype, char uplo,
+ lapack_int n, double* a, lapack_int lda,
+ const double* b, lapack_int ldb );
+
+lapack_int LAPACKE_ssygv_work( int matrix_order, lapack_int itype, char jobz,
+ char uplo, lapack_int n, float* a,
+ lapack_int lda, float* b, lapack_int ldb,
+ float* w, float* work, lapack_int lwork );
+lapack_int LAPACKE_dsygv_work( int matrix_order, lapack_int itype, char jobz,
+ char uplo, lapack_int n, double* a,
+ lapack_int lda, double* b, lapack_int ldb,
+ double* w, double* work, lapack_int lwork );
+
+lapack_int LAPACKE_ssygvd_work( int matrix_order, lapack_int itype, char jobz,
+ char uplo, lapack_int n, float* a,
+ lapack_int lda, float* b, lapack_int ldb,
+ float* w, float* work, lapack_int lwork,
+ lapack_int* iwork, lapack_int liwork );
+lapack_int LAPACKE_dsygvd_work( int matrix_order, lapack_int itype, char jobz,
+ char uplo, lapack_int n, double* a,
+ lapack_int lda, double* b, lapack_int ldb,
+ double* w, double* work, lapack_int lwork,
+ lapack_int* iwork, lapack_int liwork );
+
+lapack_int LAPACKE_ssygvx_work( int matrix_order, lapack_int itype, char jobz,
+ char range, char uplo, lapack_int n, float* a,
+ lapack_int lda, float* b, lapack_int ldb,
+ float vl, float vu, lapack_int il,
+ lapack_int iu, float abstol, lapack_int* m,
+ float* w, float* z, lapack_int ldz, float* work,
+ lapack_int lwork, lapack_int* iwork,
+ lapack_int* ifail );
+lapack_int LAPACKE_dsygvx_work( int matrix_order, lapack_int itype, char jobz,
+ char range, char uplo, lapack_int n, double* a,
+ lapack_int lda, double* b, lapack_int ldb,
+ double vl, double vu, lapack_int il,
+ lapack_int iu, double abstol, lapack_int* m,
+ double* w, double* z, lapack_int ldz,
+ double* work, lapack_int lwork,
+ lapack_int* iwork, lapack_int* ifail );
+
+lapack_int LAPACKE_ssyrfs_work( int matrix_order, char uplo, lapack_int n,
+ lapack_int nrhs, const float* a, lapack_int lda,
+ const float* af, lapack_int ldaf,
+ const lapack_int* ipiv, const float* b,
+ lapack_int ldb, float* x, lapack_int ldx,
+ float* ferr, float* berr, float* work,
+ lapack_int* iwork );
+lapack_int LAPACKE_dsyrfs_work( int matrix_order, char uplo, lapack_int n,
+ lapack_int nrhs, const double* a,
+ lapack_int lda, const double* af,
+ lapack_int ldaf, const lapack_int* ipiv,
+ const double* b, lapack_int ldb, double* x,
+ lapack_int ldx, double* ferr, double* berr,
+ double* work, lapack_int* iwork );
+lapack_int LAPACKE_csyrfs_work( int matrix_order, char uplo, lapack_int n,
+ lapack_int nrhs, const lapack_complex_float* a,
+ lapack_int lda, const lapack_complex_float* af,
+ lapack_int ldaf, const lapack_int* ipiv,
+ const lapack_complex_float* b, lapack_int ldb,
+ lapack_complex_float* x, lapack_int ldx,
+ float* ferr, float* berr,
+ lapack_complex_float* work, float* rwork );
+lapack_int LAPACKE_zsyrfs_work( int matrix_order, char uplo, lapack_int n,
+ lapack_int nrhs, const lapack_complex_double* a,
+ lapack_int lda, const lapack_complex_double* af,
+ lapack_int ldaf, const lapack_int* ipiv,
+ const lapack_complex_double* b, lapack_int ldb,
+ lapack_complex_double* x, lapack_int ldx,
+ double* ferr, double* berr,
+ lapack_complex_double* work, double* rwork );
+
+lapack_int LAPACKE_ssyrfsx_work( int matrix_order, char uplo, char equed,
+ lapack_int n, lapack_int nrhs, const float* a,
+ lapack_int lda, const float* af,
+ lapack_int ldaf, const lapack_int* ipiv,
+ const float* s, const float* b, lapack_int ldb,
+ float* x, lapack_int ldx, float* rcond,
+ float* berr, lapack_int n_err_bnds,
+ float* err_bnds_norm, float* err_bnds_comp,
+ lapack_int nparams, float* params, float* work,
+ lapack_int* iwork );
+lapack_int LAPACKE_dsyrfsx_work( int matrix_order, char uplo, char equed,
+ lapack_int n, lapack_int nrhs, const double* a,
+ lapack_int lda, const double* af,
+ lapack_int ldaf, const lapack_int* ipiv,
+ const double* s, const double* b,
+ lapack_int ldb, double* x, lapack_int ldx,
+ double* rcond, double* berr,
+ lapack_int n_err_bnds, double* err_bnds_norm,
+ double* err_bnds_comp, lapack_int nparams,
+ double* params, double* work,
+ lapack_int* iwork );
+lapack_int LAPACKE_csyrfsx_work( int matrix_order, char uplo, char equed,
+ lapack_int n, lapack_int nrhs,
+ const lapack_complex_float* a, lapack_int lda,
+ const lapack_complex_float* af,
+ lapack_int ldaf, const lapack_int* ipiv,
+ const float* s, const lapack_complex_float* b,
+ lapack_int ldb, lapack_complex_float* x,
+ lapack_int ldx, float* rcond, float* berr,
+ lapack_int n_err_bnds, float* err_bnds_norm,
+ float* err_bnds_comp, lapack_int nparams,
+ float* params, lapack_complex_float* work,
+ float* rwork );
+lapack_int LAPACKE_zsyrfsx_work( int matrix_order, char uplo, char equed,
+ lapack_int n, lapack_int nrhs,
+ const lapack_complex_double* a, lapack_int lda,
+ const lapack_complex_double* af,
+ lapack_int ldaf, const lapack_int* ipiv,
+ const double* s,
+ const lapack_complex_double* b, lapack_int ldb,
+ lapack_complex_double* x, lapack_int ldx,
+ double* rcond, double* berr,
+ lapack_int n_err_bnds, double* err_bnds_norm,
+ double* err_bnds_comp, lapack_int nparams,
+ double* params, lapack_complex_double* work,
+ double* rwork );
+
+lapack_int LAPACKE_ssysv_work( int matrix_order, char uplo, lapack_int n,
+ lapack_int nrhs, float* a, lapack_int lda,
+ lapack_int* ipiv, float* b, lapack_int ldb,
+ float* work, lapack_int lwork );
+lapack_int LAPACKE_dsysv_work( int matrix_order, char uplo, lapack_int n,
+ lapack_int nrhs, double* a, lapack_int lda,
+ lapack_int* ipiv, double* b, lapack_int ldb,
+ double* work, lapack_int lwork );
+lapack_int LAPACKE_csysv_work( int matrix_order, char uplo, lapack_int n,
+ lapack_int nrhs, lapack_complex_float* a,
+ lapack_int lda, lapack_int* ipiv,
+ lapack_complex_float* b, lapack_int ldb,
+ lapack_complex_float* work, lapack_int lwork );
+lapack_int LAPACKE_zsysv_work( int matrix_order, char uplo, lapack_int n,
+ lapack_int nrhs, lapack_complex_double* a,
+ lapack_int lda, lapack_int* ipiv,
+ lapack_complex_double* b, lapack_int ldb,
+ lapack_complex_double* work, lapack_int lwork );
+
+lapack_int LAPACKE_ssysvx_work( int matrix_order, char fact, char uplo,
+ lapack_int n, lapack_int nrhs, const float* a,
+ lapack_int lda, float* af, lapack_int ldaf,
+ lapack_int* ipiv, const float* b,
+ lapack_int ldb, float* x, lapack_int ldx,
+ float* rcond, float* ferr, float* berr,
+ float* work, lapack_int lwork,
+ lapack_int* iwork );
+lapack_int LAPACKE_dsysvx_work( int matrix_order, char fact, char uplo,
+ lapack_int n, lapack_int nrhs, const double* a,
+ lapack_int lda, double* af, lapack_int ldaf,
+ lapack_int* ipiv, const double* b,
+ lapack_int ldb, double* x, lapack_int ldx,
+ double* rcond, double* ferr, double* berr,
+ double* work, lapack_int lwork,
+ lapack_int* iwork );
+lapack_int LAPACKE_csysvx_work( int matrix_order, char fact, char uplo,
+ lapack_int n, lapack_int nrhs,
+ const lapack_complex_float* a, lapack_int lda,
+ lapack_complex_float* af, lapack_int ldaf,
+ lapack_int* ipiv, const lapack_complex_float* b,
+ lapack_int ldb, lapack_complex_float* x,
+ lapack_int ldx, float* rcond, float* ferr,
+ float* berr, lapack_complex_float* work,
+ lapack_int lwork, float* rwork );
+lapack_int LAPACKE_zsysvx_work( int matrix_order, char fact, char uplo,
+ lapack_int n, lapack_int nrhs,
+ const lapack_complex_double* a, lapack_int lda,
+ lapack_complex_double* af, lapack_int ldaf,
+ lapack_int* ipiv,
+ const lapack_complex_double* b, lapack_int ldb,
+ lapack_complex_double* x, lapack_int ldx,
+ double* rcond, double* ferr, double* berr,
+ lapack_complex_double* work, lapack_int lwork,
+ double* rwork );
+
+lapack_int LAPACKE_ssysvxx_work( int matrix_order, char fact, char uplo,
+ lapack_int n, lapack_int nrhs, float* a,
+ lapack_int lda, float* af, lapack_int ldaf,
+ lapack_int* ipiv, char* equed, float* s,
+ float* b, lapack_int ldb, float* x,
+ lapack_int ldx, float* rcond, float* rpvgrw,
+ float* berr, lapack_int n_err_bnds,
+ float* err_bnds_norm, float* err_bnds_comp,
+ lapack_int nparams, float* params, float* work,
+ lapack_int* iwork );
+lapack_int LAPACKE_dsysvxx_work( int matrix_order, char fact, char uplo,
+ lapack_int n, lapack_int nrhs, double* a,
+ lapack_int lda, double* af, lapack_int ldaf,
+ lapack_int* ipiv, char* equed, double* s,
+ double* b, lapack_int ldb, double* x,
+ lapack_int ldx, double* rcond, double* rpvgrw,
+ double* berr, lapack_int n_err_bnds,
+ double* err_bnds_norm, double* err_bnds_comp,
+ lapack_int nparams, double* params,
+ double* work, lapack_int* iwork );
+lapack_int LAPACKE_csysvxx_work( int matrix_order, char fact, char uplo,
+ lapack_int n, lapack_int nrhs,
+ lapack_complex_float* a, lapack_int lda,
+ lapack_complex_float* af, lapack_int ldaf,
+ lapack_int* ipiv, char* equed, float* s,
+ lapack_complex_float* b, lapack_int ldb,
+ lapack_complex_float* x, lapack_int ldx,
+ float* rcond, float* rpvgrw, float* berr,
+ lapack_int n_err_bnds, float* err_bnds_norm,
+ float* err_bnds_comp, lapack_int nparams,
+ float* params, lapack_complex_float* work,
+ float* rwork );
+lapack_int LAPACKE_zsysvxx_work( int matrix_order, char fact, char uplo,
+ lapack_int n, lapack_int nrhs,
+ lapack_complex_double* a, lapack_int lda,
+ lapack_complex_double* af, lapack_int ldaf,
+ lapack_int* ipiv, char* equed, double* s,
+ lapack_complex_double* b, lapack_int ldb,
+ lapack_complex_double* x, lapack_int ldx,
+ double* rcond, double* rpvgrw, double* berr,
+ lapack_int n_err_bnds, double* err_bnds_norm,
+ double* err_bnds_comp, lapack_int nparams,
+ double* params, lapack_complex_double* work,
+ double* rwork );
+
+lapack_int LAPACKE_ssytrd_work( int matrix_order, char uplo, lapack_int n,
+ float* a, lapack_int lda, float* d, float* e,
+ float* tau, float* work, lapack_int lwork );
+lapack_int LAPACKE_dsytrd_work( int matrix_order, char uplo, lapack_int n,
+ double* a, lapack_int lda, double* d, double* e,
+ double* tau, double* work, lapack_int lwork );
+
+lapack_int LAPACKE_ssytrf_work( int matrix_order, char uplo, lapack_int n,
+ float* a, lapack_int lda, lapack_int* ipiv,
+ float* work, lapack_int lwork );
+lapack_int LAPACKE_dsytrf_work( int matrix_order, char uplo, lapack_int n,
+ double* a, lapack_int lda, lapack_int* ipiv,
+ double* work, lapack_int lwork );
+lapack_int LAPACKE_csytrf_work( int matrix_order, char uplo, lapack_int n,
+ lapack_complex_float* a, lapack_int lda,
+ lapack_int* ipiv, lapack_complex_float* work,
+ lapack_int lwork );
+lapack_int LAPACKE_zsytrf_work( int matrix_order, char uplo, lapack_int n,
+ lapack_complex_double* a, lapack_int lda,
+ lapack_int* ipiv, lapack_complex_double* work,
+ lapack_int lwork );
+
+lapack_int LAPACKE_ssytri_work( int matrix_order, char uplo, lapack_int n,
+ float* a, lapack_int lda,
+ const lapack_int* ipiv, float* work );
+lapack_int LAPACKE_dsytri_work( int matrix_order, char uplo, lapack_int n,
+ double* a, lapack_int lda,
+ const lapack_int* ipiv, double* work );
+lapack_int LAPACKE_csytri_work( int matrix_order, char uplo, lapack_int n,
+ lapack_complex_float* a, lapack_int lda,
+ const lapack_int* ipiv,
+ lapack_complex_float* work );
+lapack_int LAPACKE_zsytri_work( int matrix_order, char uplo, lapack_int n,
+ lapack_complex_double* a, lapack_int lda,
+ const lapack_int* ipiv,
+ lapack_complex_double* work );
+
+lapack_int LAPACKE_ssytrs_work( int matrix_order, char uplo, lapack_int n,
+ lapack_int nrhs, const float* a, lapack_int lda,
+ const lapack_int* ipiv, float* b,
+ lapack_int ldb );
+lapack_int LAPACKE_dsytrs_work( int matrix_order, char uplo, lapack_int n,
+ lapack_int nrhs, const double* a,
+ lapack_int lda, const lapack_int* ipiv,
+ double* b, lapack_int ldb );
+lapack_int LAPACKE_csytrs_work( int matrix_order, char uplo, lapack_int n,
+ lapack_int nrhs, const lapack_complex_float* a,
+ lapack_int lda, const lapack_int* ipiv,
+ lapack_complex_float* b, lapack_int ldb );
+lapack_int LAPACKE_zsytrs_work( int matrix_order, char uplo, lapack_int n,
+ lapack_int nrhs, const lapack_complex_double* a,
+ lapack_int lda, const lapack_int* ipiv,
+ lapack_complex_double* b, lapack_int ldb );
+
+lapack_int LAPACKE_stbcon_work( int matrix_order, char norm, char uplo,
+ char diag, lapack_int n, lapack_int kd,
+ const float* ab, lapack_int ldab, float* rcond,
+ float* work, lapack_int* iwork );
+lapack_int LAPACKE_dtbcon_work( int matrix_order, char norm, char uplo,
+ char diag, lapack_int n, lapack_int kd,
+ const double* ab, lapack_int ldab,
+ double* rcond, double* work,
+ lapack_int* iwork );
+lapack_int LAPACKE_ctbcon_work( int matrix_order, char norm, char uplo,
+ char diag, lapack_int n, lapack_int kd,
+ const lapack_complex_float* ab, lapack_int ldab,
+ float* rcond, lapack_complex_float* work,
+ float* rwork );
+lapack_int LAPACKE_ztbcon_work( int matrix_order, char norm, char uplo,
+ char diag, lapack_int n, lapack_int kd,
+ const lapack_complex_double* ab,
+ lapack_int ldab, double* rcond,
+ lapack_complex_double* work, double* rwork );
+
+lapack_int LAPACKE_stbrfs_work( int matrix_order, char uplo, char trans,
+ char diag, lapack_int n, lapack_int kd,
+ lapack_int nrhs, const float* ab,
+ lapack_int ldab, const float* b, lapack_int ldb,
+ const float* x, lapack_int ldx, float* ferr,
+ float* berr, float* work, lapack_int* iwork );
+lapack_int LAPACKE_dtbrfs_work( int matrix_order, char uplo, char trans,
+ char diag, lapack_int n, lapack_int kd,
+ lapack_int nrhs, const double* ab,
+ lapack_int ldab, const double* b,
+ lapack_int ldb, const double* x, lapack_int ldx,
+ double* ferr, double* berr, double* work,
+ lapack_int* iwork );
+lapack_int LAPACKE_ctbrfs_work( int matrix_order, char uplo, char trans,
+ char diag, lapack_int n, lapack_int kd,
+ lapack_int nrhs, const lapack_complex_float* ab,
+ lapack_int ldab, const lapack_complex_float* b,
+ lapack_int ldb, const lapack_complex_float* x,
+ lapack_int ldx, float* ferr, float* berr,
+ lapack_complex_float* work, float* rwork );
+lapack_int LAPACKE_ztbrfs_work( int matrix_order, char uplo, char trans,
+ char diag, lapack_int n, lapack_int kd,
+ lapack_int nrhs,
+ const lapack_complex_double* ab,
+ lapack_int ldab, const lapack_complex_double* b,
+ lapack_int ldb, const lapack_complex_double* x,
+ lapack_int ldx, double* ferr, double* berr,
+ lapack_complex_double* work, double* rwork );
+
+lapack_int LAPACKE_stbtrs_work( int matrix_order, char uplo, char trans,
+ char diag, lapack_int n, lapack_int kd,
+ lapack_int nrhs, const float* ab,
+ lapack_int ldab, float* b, lapack_int ldb );
+lapack_int LAPACKE_dtbtrs_work( int matrix_order, char uplo, char trans,
+ char diag, lapack_int n, lapack_int kd,
+ lapack_int nrhs, const double* ab,
+ lapack_int ldab, double* b, lapack_int ldb );
+lapack_int LAPACKE_ctbtrs_work( int matrix_order, char uplo, char trans,
+ char diag, lapack_int n, lapack_int kd,
+ lapack_int nrhs, const lapack_complex_float* ab,
+ lapack_int ldab, lapack_complex_float* b,
+ lapack_int ldb );
+lapack_int LAPACKE_ztbtrs_work( int matrix_order, char uplo, char trans,
+ char diag, lapack_int n, lapack_int kd,
+ lapack_int nrhs,
+ const lapack_complex_double* ab,
+ lapack_int ldab, lapack_complex_double* b,
+ lapack_int ldb );
+
+lapack_int LAPACKE_stfsm_work( int matrix_order, char transr, char side,
+ char uplo, char trans, char diag, lapack_int m,
+ lapack_int n, float alpha, const float* a,
+ float* b, lapack_int ldb );
+lapack_int LAPACKE_dtfsm_work( int matrix_order, char transr, char side,
+ char uplo, char trans, char diag, lapack_int m,
+ lapack_int n, double alpha, const double* a,
+ double* b, lapack_int ldb );
+lapack_int LAPACKE_ctfsm_work( int matrix_order, char transr, char side,
+ char uplo, char trans, char diag, lapack_int m,
+ lapack_int n, lapack_complex_float alpha,
+ const lapack_complex_float* a,
+ lapack_complex_float* b, lapack_int ldb );
+lapack_int LAPACKE_ztfsm_work( int matrix_order, char transr, char side,
+ char uplo, char trans, char diag, lapack_int m,
+ lapack_int n, lapack_complex_double alpha,
+ const lapack_complex_double* a,
+ lapack_complex_double* b, lapack_int ldb );
+
+lapack_int LAPACKE_stftri_work( int matrix_order, char transr, char uplo,
+ char diag, lapack_int n, float* a );
+lapack_int LAPACKE_dtftri_work( int matrix_order, char transr, char uplo,
+ char diag, lapack_int n, double* a );
+lapack_int LAPACKE_ctftri_work( int matrix_order, char transr, char uplo,
+ char diag, lapack_int n,
+ lapack_complex_float* a );
+lapack_int LAPACKE_ztftri_work( int matrix_order, char transr, char uplo,
+ char diag, lapack_int n,
+ lapack_complex_double* a );
+
+lapack_int LAPACKE_stfttp_work( int matrix_order, char transr, char uplo,
+ lapack_int n, const float* arf, float* ap );
+lapack_int LAPACKE_dtfttp_work( int matrix_order, char transr, char uplo,
+ lapack_int n, const double* arf, double* ap );
+lapack_int LAPACKE_ctfttp_work( int matrix_order, char transr, char uplo,
+ lapack_int n, const lapack_complex_float* arf,
+ lapack_complex_float* ap );
+lapack_int LAPACKE_ztfttp_work( int matrix_order, char transr, char uplo,
+ lapack_int n, const lapack_complex_double* arf,
+ lapack_complex_double* ap );
+
+lapack_int LAPACKE_stfttr_work( int matrix_order, char transr, char uplo,
+ lapack_int n, const float* arf, float* a,
+ lapack_int lda );
+lapack_int LAPACKE_dtfttr_work( int matrix_order, char transr, char uplo,
+ lapack_int n, const double* arf, double* a,
+ lapack_int lda );
+lapack_int LAPACKE_ctfttr_work( int matrix_order, char transr, char uplo,
+ lapack_int n, const lapack_complex_float* arf,
+ lapack_complex_float* a, lapack_int lda );
+lapack_int LAPACKE_ztfttr_work( int matrix_order, char transr, char uplo,
+ lapack_int n, const lapack_complex_double* arf,
+ lapack_complex_double* a, lapack_int lda );
+
+lapack_int LAPACKE_stgevc_work( int matrix_order, char side, char howmny,
+ const lapack_logical* select, lapack_int n,
+ const float* s, lapack_int lds, const float* p,
+ lapack_int ldp, float* vl, lapack_int ldvl,
+ float* vr, lapack_int ldvr, lapack_int mm,
+ lapack_int* m, float* work );
+lapack_int LAPACKE_dtgevc_work( int matrix_order, char side, char howmny,
+ const lapack_logical* select, lapack_int n,
+ const double* s, lapack_int lds,
+ const double* p, lapack_int ldp, double* vl,
+ lapack_int ldvl, double* vr, lapack_int ldvr,
+ lapack_int mm, lapack_int* m, double* work );
+lapack_int LAPACKE_ctgevc_work( int matrix_order, char side, char howmny,
+ const lapack_logical* select, lapack_int n,
+ const lapack_complex_float* s, lapack_int lds,
+ const lapack_complex_float* p, lapack_int ldp,
+ lapack_complex_float* vl, lapack_int ldvl,
+ lapack_complex_float* vr, lapack_int ldvr,
+ lapack_int mm, lapack_int* m,
+ lapack_complex_float* work, float* rwork );
+lapack_int LAPACKE_ztgevc_work( int matrix_order, char side, char howmny,
+ const lapack_logical* select, lapack_int n,
+ const lapack_complex_double* s, lapack_int lds,
+ const lapack_complex_double* p, lapack_int ldp,
+ lapack_complex_double* vl, lapack_int ldvl,
+ lapack_complex_double* vr, lapack_int ldvr,
+ lapack_int mm, lapack_int* m,
+ lapack_complex_double* work, double* rwork );
+
+lapack_int LAPACKE_stgexc_work( int matrix_order, lapack_logical wantq,
+ lapack_logical wantz, lapack_int n, float* a,
+ lapack_int lda, float* b, lapack_int ldb,
+ float* q, lapack_int ldq, float* z,
+ lapack_int ldz, lapack_int* ifst,
+ lapack_int* ilst, float* work,
+ lapack_int lwork );
+lapack_int LAPACKE_dtgexc_work( int matrix_order, lapack_logical wantq,
+ lapack_logical wantz, lapack_int n, double* a,
+ lapack_int lda, double* b, lapack_int ldb,
+ double* q, lapack_int ldq, double* z,
+ lapack_int ldz, lapack_int* ifst,
+ lapack_int* ilst, double* work,
+ lapack_int lwork );
+lapack_int LAPACKE_ctgexc_work( int matrix_order, lapack_logical wantq,
+ lapack_logical wantz, lapack_int n,
+ lapack_complex_float* a, lapack_int lda,
+ lapack_complex_float* b, lapack_int ldb,
+ lapack_complex_float* q, lapack_int ldq,
+ lapack_complex_float* z, lapack_int ldz,
+ lapack_int ifst, lapack_int ilst );
+lapack_int LAPACKE_ztgexc_work( int matrix_order, lapack_logical wantq,
+ lapack_logical wantz, lapack_int n,
+ lapack_complex_double* a, lapack_int lda,
+ lapack_complex_double* b, lapack_int ldb,
+ lapack_complex_double* q, lapack_int ldq,
+ lapack_complex_double* z, lapack_int ldz,
+ lapack_int ifst, lapack_int ilst );
+
+lapack_int LAPACKE_stgsen_work( int matrix_order, lapack_int ijob,
+ lapack_logical wantq, lapack_logical wantz,
+ const lapack_logical* select, lapack_int n,
+ float* a, lapack_int lda, float* b,
+ lapack_int ldb, float* alphar, float* alphai,
+ float* beta, float* q, lapack_int ldq, float* z,
+ lapack_int ldz, lapack_int* m, float* pl,
+ float* pr, float* dif, float* work,
+ lapack_int lwork, lapack_int* iwork,
+ lapack_int liwork );
+lapack_int LAPACKE_dtgsen_work( int matrix_order, lapack_int ijob,
+ lapack_logical wantq, lapack_logical wantz,
+ const lapack_logical* select, lapack_int n,
+ double* a, lapack_int lda, double* b,
+ lapack_int ldb, double* alphar, double* alphai,
+ double* beta, double* q, lapack_int ldq,
+ double* z, lapack_int ldz, lapack_int* m,
+ double* pl, double* pr, double* dif,
+ double* work, lapack_int lwork,
+ lapack_int* iwork, lapack_int liwork );
+lapack_int LAPACKE_ctgsen_work( int matrix_order, lapack_int ijob,
+ lapack_logical wantq, lapack_logical wantz,
+ const lapack_logical* select, lapack_int n,
+ lapack_complex_float* a, lapack_int lda,
+ lapack_complex_float* b, lapack_int ldb,
+ lapack_complex_float* alpha,
+ lapack_complex_float* beta,
+ lapack_complex_float* q, lapack_int ldq,
+ lapack_complex_float* z, lapack_int ldz,
+ lapack_int* m, float* pl, float* pr, float* dif,
+ lapack_complex_float* work, lapack_int lwork,
+ lapack_int* iwork, lapack_int liwork );
+lapack_int LAPACKE_ztgsen_work( int matrix_order, lapack_int ijob,
+ lapack_logical wantq, lapack_logical wantz,
+ const lapack_logical* select, lapack_int n,
+ lapack_complex_double* a, lapack_int lda,
+ lapack_complex_double* b, lapack_int ldb,
+ lapack_complex_double* alpha,
+ lapack_complex_double* beta,
+ lapack_complex_double* q, lapack_int ldq,
+ lapack_complex_double* z, lapack_int ldz,
+ lapack_int* m, double* pl, double* pr,
+ double* dif, lapack_complex_double* work,
+ lapack_int lwork, lapack_int* iwork,
+ lapack_int liwork );
+
+lapack_int LAPACKE_stgsja_work( int matrix_order, char jobu, char jobv,
+ char jobq, lapack_int m, lapack_int p,
+ lapack_int n, lapack_int k, lapack_int l,
+ float* a, lapack_int lda, float* b,
+ lapack_int ldb, float tola, float tolb,
+ float* alpha, float* beta, float* u,
+ lapack_int ldu, float* v, lapack_int ldv,
+ float* q, lapack_int ldq, float* work,
+ lapack_int* ncycle );
+lapack_int LAPACKE_dtgsja_work( int matrix_order, char jobu, char jobv,
+ char jobq, lapack_int m, lapack_int p,
+ lapack_int n, lapack_int k, lapack_int l,
+ double* a, lapack_int lda, double* b,
+ lapack_int ldb, double tola, double tolb,
+ double* alpha, double* beta, double* u,
+ lapack_int ldu, double* v, lapack_int ldv,
+ double* q, lapack_int ldq, double* work,
+ lapack_int* ncycle );
+lapack_int LAPACKE_ctgsja_work( int matrix_order, char jobu, char jobv,
+ char jobq, lapack_int m, lapack_int p,
+ lapack_int n, lapack_int k, lapack_int l,
+ lapack_complex_float* a, lapack_int lda,
+ lapack_complex_float* b, lapack_int ldb,
+ float tola, float tolb, float* alpha,
+ float* beta, lapack_complex_float* u,
+ lapack_int ldu, lapack_complex_float* v,
+ lapack_int ldv, lapack_complex_float* q,
+ lapack_int ldq, lapack_complex_float* work,
+ lapack_int* ncycle );
+lapack_int LAPACKE_ztgsja_work( int matrix_order, char jobu, char jobv,
+ char jobq, lapack_int m, lapack_int p,
+ lapack_int n, lapack_int k, lapack_int l,
+ lapack_complex_double* a, lapack_int lda,
+ lapack_complex_double* b, lapack_int ldb,
+ double tola, double tolb, double* alpha,
+ double* beta, lapack_complex_double* u,
+ lapack_int ldu, lapack_complex_double* v,
+ lapack_int ldv, lapack_complex_double* q,
+ lapack_int ldq, lapack_complex_double* work,
+ lapack_int* ncycle );
+
+lapack_int LAPACKE_stgsna_work( int matrix_order, char job, char howmny,
+ const lapack_logical* select, lapack_int n,
+ const float* a, lapack_int lda, const float* b,
+ lapack_int ldb, const float* vl,
+ lapack_int ldvl, const float* vr,
+ lapack_int ldvr, float* s, float* dif,
+ lapack_int mm, lapack_int* m, float* work,
+ lapack_int lwork, lapack_int* iwork );
+lapack_int LAPACKE_dtgsna_work( int matrix_order, char job, char howmny,
+ const lapack_logical* select, lapack_int n,
+ const double* a, lapack_int lda,
+ const double* b, lapack_int ldb,
+ const double* vl, lapack_int ldvl,
+ const double* vr, lapack_int ldvr, double* s,
+ double* dif, lapack_int mm, lapack_int* m,
+ double* work, lapack_int lwork,
+ lapack_int* iwork );
+lapack_int LAPACKE_ctgsna_work( int matrix_order, char job, char howmny,
+ const lapack_logical* select, lapack_int n,
+ const lapack_complex_float* a, lapack_int lda,
+ const lapack_complex_float* b, lapack_int ldb,
+ const lapack_complex_float* vl, lapack_int ldvl,
+ const lapack_complex_float* vr, lapack_int ldvr,
+ float* s, float* dif, lapack_int mm,
+ lapack_int* m, lapack_complex_float* work,
+ lapack_int lwork, lapack_int* iwork );
+lapack_int LAPACKE_ztgsna_work( int matrix_order, char job, char howmny,
+ const lapack_logical* select, lapack_int n,
+ const lapack_complex_double* a, lapack_int lda,
+ const lapack_complex_double* b, lapack_int ldb,
+ const lapack_complex_double* vl,
+ lapack_int ldvl,
+ const lapack_complex_double* vr,
+ lapack_int ldvr, double* s, double* dif,
+ lapack_int mm, lapack_int* m,
+ lapack_complex_double* work, lapack_int lwork,
+ lapack_int* iwork );
+
+lapack_int LAPACKE_stgsyl_work( int matrix_order, char trans, lapack_int ijob,
+ lapack_int m, lapack_int n, const float* a,
+ lapack_int lda, const float* b, lapack_int ldb,
+ float* c, lapack_int ldc, const float* d,
+ lapack_int ldd, const float* e, lapack_int lde,
+ float* f, lapack_int ldf, float* scale,
+ float* dif, float* work, lapack_int lwork,
+ lapack_int* iwork );
+lapack_int LAPACKE_dtgsyl_work( int matrix_order, char trans, lapack_int ijob,
+ lapack_int m, lapack_int n, const double* a,
+ lapack_int lda, const double* b, lapack_int ldb,
+ double* c, lapack_int ldc, const double* d,
+ lapack_int ldd, const double* e, lapack_int lde,
+ double* f, lapack_int ldf, double* scale,
+ double* dif, double* work, lapack_int lwork,
+ lapack_int* iwork );
+lapack_int LAPACKE_ctgsyl_work( int matrix_order, char trans, lapack_int ijob,
+ lapack_int m, lapack_int n,
+ const lapack_complex_float* a, lapack_int lda,
+ const lapack_complex_float* b, lapack_int ldb,
+ lapack_complex_float* c, lapack_int ldc,
+ const lapack_complex_float* d, lapack_int ldd,
+ const lapack_complex_float* e, lapack_int lde,
+ lapack_complex_float* f, lapack_int ldf,
+ float* scale, float* dif,
+ lapack_complex_float* work, lapack_int lwork,
+ lapack_int* iwork );
+lapack_int LAPACKE_ztgsyl_work( int matrix_order, char trans, lapack_int ijob,
+ lapack_int m, lapack_int n,
+ const lapack_complex_double* a, lapack_int lda,
+ const lapack_complex_double* b, lapack_int ldb,
+ lapack_complex_double* c, lapack_int ldc,
+ const lapack_complex_double* d, lapack_int ldd,
+ const lapack_complex_double* e, lapack_int lde,
+ lapack_complex_double* f, lapack_int ldf,
+ double* scale, double* dif,
+ lapack_complex_double* work, lapack_int lwork,
+ lapack_int* iwork );
+
+lapack_int LAPACKE_stpcon_work( int matrix_order, char norm, char uplo,
+ char diag, lapack_int n, const float* ap,
+ float* rcond, float* work, lapack_int* iwork );
+lapack_int LAPACKE_dtpcon_work( int matrix_order, char norm, char uplo,
+ char diag, lapack_int n, const double* ap,
+ double* rcond, double* work,
+ lapack_int* iwork );
+lapack_int LAPACKE_ctpcon_work( int matrix_order, char norm, char uplo,
+ char diag, lapack_int n,
+ const lapack_complex_float* ap, float* rcond,
+ lapack_complex_float* work, float* rwork );
+lapack_int LAPACKE_ztpcon_work( int matrix_order, char norm, char uplo,
+ char diag, lapack_int n,
+ const lapack_complex_double* ap, double* rcond,
+ lapack_complex_double* work, double* rwork );
+
+lapack_int LAPACKE_stprfs_work( int matrix_order, char uplo, char trans,
+ char diag, lapack_int n, lapack_int nrhs,
+ const float* ap, const float* b, lapack_int ldb,
+ const float* x, lapack_int ldx, float* ferr,
+ float* berr, float* work, lapack_int* iwork );
+lapack_int LAPACKE_dtprfs_work( int matrix_order, char uplo, char trans,
+ char diag, lapack_int n, lapack_int nrhs,
+ const double* ap, const double* b,
+ lapack_int ldb, const double* x, lapack_int ldx,
+ double* ferr, double* berr, double* work,
+ lapack_int* iwork );
+lapack_int LAPACKE_ctprfs_work( int matrix_order, char uplo, char trans,
+ char diag, lapack_int n, lapack_int nrhs,
+ const lapack_complex_float* ap,
+ const lapack_complex_float* b, lapack_int ldb,
+ const lapack_complex_float* x, lapack_int ldx,
+ float* ferr, float* berr,
+ lapack_complex_float* work, float* rwork );
+lapack_int LAPACKE_ztprfs_work( int matrix_order, char uplo, char trans,
+ char diag, lapack_int n, lapack_int nrhs,
+ const lapack_complex_double* ap,
+ const lapack_complex_double* b, lapack_int ldb,
+ const lapack_complex_double* x, lapack_int ldx,
+ double* ferr, double* berr,
+ lapack_complex_double* work, double* rwork );
+
+lapack_int LAPACKE_stptri_work( int matrix_order, char uplo, char diag,
+ lapack_int n, float* ap );
+lapack_int LAPACKE_dtptri_work( int matrix_order, char uplo, char diag,
+ lapack_int n, double* ap );
+lapack_int LAPACKE_ctptri_work( int matrix_order, char uplo, char diag,
+ lapack_int n, lapack_complex_float* ap );
+lapack_int LAPACKE_ztptri_work( int matrix_order, char uplo, char diag,
+ lapack_int n, lapack_complex_double* ap );
+
+lapack_int LAPACKE_stptrs_work( int matrix_order, char uplo, char trans,
+ char diag, lapack_int n, lapack_int nrhs,
+ const float* ap, float* b, lapack_int ldb );
+lapack_int LAPACKE_dtptrs_work( int matrix_order, char uplo, char trans,
+ char diag, lapack_int n, lapack_int nrhs,
+ const double* ap, double* b, lapack_int ldb );
+lapack_int LAPACKE_ctptrs_work( int matrix_order, char uplo, char trans,
+ char diag, lapack_int n, lapack_int nrhs,
+ const lapack_complex_float* ap,
+ lapack_complex_float* b, lapack_int ldb );
+lapack_int LAPACKE_ztptrs_work( int matrix_order, char uplo, char trans,
+ char diag, lapack_int n, lapack_int nrhs,
+ const lapack_complex_double* ap,
+ lapack_complex_double* b, lapack_int ldb );
+
+lapack_int LAPACKE_stpttf_work( int matrix_order, char transr, char uplo,
+ lapack_int n, const float* ap, float* arf );
+lapack_int LAPACKE_dtpttf_work( int matrix_order, char transr, char uplo,
+ lapack_int n, const double* ap, double* arf );
+lapack_int LAPACKE_ctpttf_work( int matrix_order, char transr, char uplo,
+ lapack_int n, const lapack_complex_float* ap,
+ lapack_complex_float* arf );
+lapack_int LAPACKE_ztpttf_work( int matrix_order, char transr, char uplo,
+ lapack_int n, const lapack_complex_double* ap,
+ lapack_complex_double* arf );
+
+lapack_int LAPACKE_stpttr_work( int matrix_order, char uplo, lapack_int n,
+ const float* ap, float* a, lapack_int lda );
+lapack_int LAPACKE_dtpttr_work( int matrix_order, char uplo, lapack_int n,
+ const double* ap, double* a, lapack_int lda );
+lapack_int LAPACKE_ctpttr_work( int matrix_order, char uplo, lapack_int n,
+ const lapack_complex_float* ap,
+ lapack_complex_float* a, lapack_int lda );
+lapack_int LAPACKE_ztpttr_work( int matrix_order, char uplo, lapack_int n,
+ const lapack_complex_double* ap,
+ lapack_complex_double* a, lapack_int lda );
+
+lapack_int LAPACKE_strcon_work( int matrix_order, char norm, char uplo,
+ char diag, lapack_int n, const float* a,
+ lapack_int lda, float* rcond, float* work,
+ lapack_int* iwork );
+lapack_int LAPACKE_dtrcon_work( int matrix_order, char norm, char uplo,
+ char diag, lapack_int n, const double* a,
+ lapack_int lda, double* rcond, double* work,
+ lapack_int* iwork );
+lapack_int LAPACKE_ctrcon_work( int matrix_order, char norm, char uplo,
+ char diag, lapack_int n,
+ const lapack_complex_float* a, lapack_int lda,
+ float* rcond, lapack_complex_float* work,
+ float* rwork );
+lapack_int LAPACKE_ztrcon_work( int matrix_order, char norm, char uplo,
+ char diag, lapack_int n,
+ const lapack_complex_double* a, lapack_int lda,
+ double* rcond, lapack_complex_double* work,
+ double* rwork );
+
+lapack_int LAPACKE_strevc_work( int matrix_order, char side, char howmny,
+ lapack_logical* select, lapack_int n,
+ const float* t, lapack_int ldt, float* vl,
+ lapack_int ldvl, float* vr, lapack_int ldvr,
+ lapack_int mm, lapack_int* m, float* work );
+lapack_int LAPACKE_dtrevc_work( int matrix_order, char side, char howmny,
+ lapack_logical* select, lapack_int n,
+ const double* t, lapack_int ldt, double* vl,
+ lapack_int ldvl, double* vr, lapack_int ldvr,
+ lapack_int mm, lapack_int* m, double* work );
+lapack_int LAPACKE_ctrevc_work( int matrix_order, char side, char howmny,
+ const lapack_logical* select, lapack_int n,
+ lapack_complex_float* t, lapack_int ldt,
+ lapack_complex_float* vl, lapack_int ldvl,
+ lapack_complex_float* vr, lapack_int ldvr,
+ lapack_int mm, lapack_int* m,
+ lapack_complex_float* work, float* rwork );
+lapack_int LAPACKE_ztrevc_work( int matrix_order, char side, char howmny,
+ const lapack_logical* select, lapack_int n,
+ lapack_complex_double* t, lapack_int ldt,
+ lapack_complex_double* vl, lapack_int ldvl,
+ lapack_complex_double* vr, lapack_int ldvr,
+ lapack_int mm, lapack_int* m,
+ lapack_complex_double* work, double* rwork );
+
+lapack_int LAPACKE_strexc_work( int matrix_order, char compq, lapack_int n,
+ float* t, lapack_int ldt, float* q,
+ lapack_int ldq, lapack_int* ifst,
+ lapack_int* ilst, float* work );
+lapack_int LAPACKE_dtrexc_work( int matrix_order, char compq, lapack_int n,
+ double* t, lapack_int ldt, double* q,
+ lapack_int ldq, lapack_int* ifst,
+ lapack_int* ilst, double* work );
+lapack_int LAPACKE_ctrexc_work( int matrix_order, char compq, lapack_int n,
+ lapack_complex_float* t, lapack_int ldt,
+ lapack_complex_float* q, lapack_int ldq,
+ lapack_int ifst, lapack_int ilst );
+lapack_int LAPACKE_ztrexc_work( int matrix_order, char compq, lapack_int n,
+ lapack_complex_double* t, lapack_int ldt,
+ lapack_complex_double* q, lapack_int ldq,
+ lapack_int ifst, lapack_int ilst );
+
+lapack_int LAPACKE_strrfs_work( int matrix_order, char uplo, char trans,
+ char diag, lapack_int n, lapack_int nrhs,
+ const float* a, lapack_int lda, const float* b,
+ lapack_int ldb, const float* x, lapack_int ldx,
+ float* ferr, float* berr, float* work,
+ lapack_int* iwork );
+lapack_int LAPACKE_dtrrfs_work( int matrix_order, char uplo, char trans,
+ char diag, lapack_int n, lapack_int nrhs,
+ const double* a, lapack_int lda,
+ const double* b, lapack_int ldb,
+ const double* x, lapack_int ldx, double* ferr,
+ double* berr, double* work, lapack_int* iwork );
+lapack_int LAPACKE_ctrrfs_work( int matrix_order, char uplo, char trans,
+ char diag, lapack_int n, lapack_int nrhs,
+ const lapack_complex_float* a, lapack_int lda,
+ const lapack_complex_float* b, lapack_int ldb,
+ const lapack_complex_float* x, lapack_int ldx,
+ float* ferr, float* berr,
+ lapack_complex_float* work, float* rwork );
+lapack_int LAPACKE_ztrrfs_work( int matrix_order, char uplo, char trans,
+ char diag, lapack_int n, lapack_int nrhs,
+ const lapack_complex_double* a, lapack_int lda,
+ const lapack_complex_double* b, lapack_int ldb,
+ const lapack_complex_double* x, lapack_int ldx,
+ double* ferr, double* berr,
+ lapack_complex_double* work, double* rwork );
+
+lapack_int LAPACKE_strsen_work( int matrix_order, char job, char compq,
+ const lapack_logical* select, lapack_int n,
+ float* t, lapack_int ldt, float* q,
+ lapack_int ldq, float* wr, float* wi,
+ lapack_int* m, float* s, float* sep,
+ float* work, lapack_int lwork,
+ lapack_int* iwork, lapack_int liwork );
+lapack_int LAPACKE_dtrsen_work( int matrix_order, char job, char compq,
+ const lapack_logical* select, lapack_int n,
+ double* t, lapack_int ldt, double* q,
+ lapack_int ldq, double* wr, double* wi,
+ lapack_int* m, double* s, double* sep,
+ double* work, lapack_int lwork,
+ lapack_int* iwork, lapack_int liwork );
+lapack_int LAPACKE_ctrsen_work( int matrix_order, char job, char compq,
+ const lapack_logical* select, lapack_int n,
+ lapack_complex_float* t, lapack_int ldt,
+ lapack_complex_float* q, lapack_int ldq,
+ lapack_complex_float* w, lapack_int* m,
+ float* s, float* sep,
+ lapack_complex_float* work, lapack_int lwork );
+lapack_int LAPACKE_ztrsen_work( int matrix_order, char job, char compq,
+ const lapack_logical* select, lapack_int n,
+ lapack_complex_double* t, lapack_int ldt,
+ lapack_complex_double* q, lapack_int ldq,
+ lapack_complex_double* w, lapack_int* m,
+ double* s, double* sep,
+ lapack_complex_double* work, lapack_int lwork );
+
+lapack_int LAPACKE_strsna_work( int matrix_order, char job, char howmny,
+ const lapack_logical* select, lapack_int n,
+ const float* t, lapack_int ldt, const float* vl,
+ lapack_int ldvl, const float* vr,
+ lapack_int ldvr, float* s, float* sep,
+ lapack_int mm, lapack_int* m, float* work,
+ lapack_int ldwork, lapack_int* iwork );
+lapack_int LAPACKE_dtrsna_work( int matrix_order, char job, char howmny,
+ const lapack_logical* select, lapack_int n,
+ const double* t, lapack_int ldt,
+ const double* vl, lapack_int ldvl,
+ const double* vr, lapack_int ldvr, double* s,
+ double* sep, lapack_int mm, lapack_int* m,
+ double* work, lapack_int ldwork,
+ lapack_int* iwork );
+lapack_int LAPACKE_ctrsna_work( int matrix_order, char job, char howmny,
+ const lapack_logical* select, lapack_int n,
+ const lapack_complex_float* t, lapack_int ldt,
+ const lapack_complex_float* vl, lapack_int ldvl,
+ const lapack_complex_float* vr, lapack_int ldvr,
+ float* s, float* sep, lapack_int mm,
+ lapack_int* m, lapack_complex_float* work,
+ lapack_int ldwork, float* rwork );
+lapack_int LAPACKE_ztrsna_work( int matrix_order, char job, char howmny,
+ const lapack_logical* select, lapack_int n,
+ const lapack_complex_double* t, lapack_int ldt,
+ const lapack_complex_double* vl,
+ lapack_int ldvl,
+ const lapack_complex_double* vr,
+ lapack_int ldvr, double* s, double* sep,
+ lapack_int mm, lapack_int* m,
+ lapack_complex_double* work, lapack_int ldwork,
+ double* rwork );
+
+lapack_int LAPACKE_strsyl_work( int matrix_order, char trana, char tranb,
+ lapack_int isgn, lapack_int m, lapack_int n,
+ const float* a, lapack_int lda, const float* b,
+ lapack_int ldb, float* c, lapack_int ldc,
+ float* scale );
+lapack_int LAPACKE_dtrsyl_work( int matrix_order, char trana, char tranb,
+ lapack_int isgn, lapack_int m, lapack_int n,
+ const double* a, lapack_int lda,
+ const double* b, lapack_int ldb, double* c,
+ lapack_int ldc, double* scale );
+lapack_int LAPACKE_ctrsyl_work( int matrix_order, char trana, char tranb,
+ lapack_int isgn, lapack_int m, lapack_int n,
+ const lapack_complex_float* a, lapack_int lda,
+ const lapack_complex_float* b, lapack_int ldb,
+ lapack_complex_float* c, lapack_int ldc,
+ float* scale );
+lapack_int LAPACKE_ztrsyl_work( int matrix_order, char trana, char tranb,
+ lapack_int isgn, lapack_int m, lapack_int n,
+ const lapack_complex_double* a, lapack_int lda,
+ const lapack_complex_double* b, lapack_int ldb,
+ lapack_complex_double* c, lapack_int ldc,
+ double* scale );
+
+lapack_int LAPACKE_strtri_work( int matrix_order, char uplo, char diag,
+ lapack_int n, float* a, lapack_int lda );
+lapack_int LAPACKE_dtrtri_work( int matrix_order, char uplo, char diag,
+ lapack_int n, double* a, lapack_int lda );
+lapack_int LAPACKE_ctrtri_work( int matrix_order, char uplo, char diag,
+ lapack_int n, lapack_complex_float* a,
+ lapack_int lda );
+lapack_int LAPACKE_ztrtri_work( int matrix_order, char uplo, char diag,
+ lapack_int n, lapack_complex_double* a,
+ lapack_int lda );
+
+lapack_int LAPACKE_strtrs_work( int matrix_order, char uplo, char trans,
+ char diag, lapack_int n, lapack_int nrhs,
+ const float* a, lapack_int lda, float* b,
+ lapack_int ldb );
+lapack_int LAPACKE_dtrtrs_work( int matrix_order, char uplo, char trans,
+ char diag, lapack_int n, lapack_int nrhs,
+ const double* a, lapack_int lda, double* b,
+ lapack_int ldb );
+lapack_int LAPACKE_ctrtrs_work( int matrix_order, char uplo, char trans,
+ char diag, lapack_int n, lapack_int nrhs,
+ const lapack_complex_float* a, lapack_int lda,
+ lapack_complex_float* b, lapack_int ldb );
+lapack_int LAPACKE_ztrtrs_work( int matrix_order, char uplo, char trans,
+ char diag, lapack_int n, lapack_int nrhs,
+ const lapack_complex_double* a, lapack_int lda,
+ lapack_complex_double* b, lapack_int ldb );
+
+lapack_int LAPACKE_strttf_work( int matrix_order, char transr, char uplo,
+ lapack_int n, const float* a, lapack_int lda,
+ float* arf );
+lapack_int LAPACKE_dtrttf_work( int matrix_order, char transr, char uplo,
+ lapack_int n, const double* a, lapack_int lda,
+ double* arf );
+lapack_int LAPACKE_ctrttf_work( int matrix_order, char transr, char uplo,
+ lapack_int n, const lapack_complex_float* a,
+ lapack_int lda, lapack_complex_float* arf );
+lapack_int LAPACKE_ztrttf_work( int matrix_order, char transr, char uplo,
+ lapack_int n, const lapack_complex_double* a,
+ lapack_int lda, lapack_complex_double* arf );
+
+lapack_int LAPACKE_strttp_work( int matrix_order, char uplo, lapack_int n,
+ const float* a, lapack_int lda, float* ap );
+lapack_int LAPACKE_dtrttp_work( int matrix_order, char uplo, lapack_int n,
+ const double* a, lapack_int lda, double* ap );
+lapack_int LAPACKE_ctrttp_work( int matrix_order, char uplo, lapack_int n,
+ const lapack_complex_float* a, lapack_int lda,
+ lapack_complex_float* ap );
+lapack_int LAPACKE_ztrttp_work( int matrix_order, char uplo, lapack_int n,
+ const lapack_complex_double* a, lapack_int lda,
+ lapack_complex_double* ap );
+
+lapack_int LAPACKE_stzrzf_work( int matrix_order, lapack_int m, lapack_int n,
+ float* a, lapack_int lda, float* tau,
+ float* work, lapack_int lwork );
+lapack_int LAPACKE_dtzrzf_work( int matrix_order, lapack_int m, lapack_int n,
+ double* a, lapack_int lda, double* tau,
+ double* work, lapack_int lwork );
+lapack_int LAPACKE_ctzrzf_work( int matrix_order, lapack_int m, lapack_int n,
+ lapack_complex_float* a, lapack_int lda,
+ lapack_complex_float* tau,
+ lapack_complex_float* work, lapack_int lwork );
+lapack_int LAPACKE_ztzrzf_work( int matrix_order, lapack_int m, lapack_int n,
+ lapack_complex_double* a, lapack_int lda,
+ lapack_complex_double* tau,
+ lapack_complex_double* work, lapack_int lwork );
+
+lapack_int LAPACKE_cungbr_work( int matrix_order, char vect, lapack_int m,
+ lapack_int n, lapack_int k,
+ lapack_complex_float* a, lapack_int lda,
+ const lapack_complex_float* tau,
+ lapack_complex_float* work, lapack_int lwork );
+lapack_int LAPACKE_zungbr_work( int matrix_order, char vect, lapack_int m,
+ lapack_int n, lapack_int k,
+ lapack_complex_double* a, lapack_int lda,
+ const lapack_complex_double* tau,
+ lapack_complex_double* work, lapack_int lwork );
+
+lapack_int LAPACKE_cunghr_work( int matrix_order, lapack_int n, lapack_int ilo,
+ lapack_int ihi, lapack_complex_float* a,
+ lapack_int lda, const lapack_complex_float* tau,
+ lapack_complex_float* work, lapack_int lwork );
+lapack_int LAPACKE_zunghr_work( int matrix_order, lapack_int n, lapack_int ilo,
+ lapack_int ihi, lapack_complex_double* a,
+ lapack_int lda,
+ const lapack_complex_double* tau,
+ lapack_complex_double* work, lapack_int lwork );
+
+lapack_int LAPACKE_cunglq_work( int matrix_order, lapack_int m, lapack_int n,
+ lapack_int k, lapack_complex_float* a,
+ lapack_int lda, const lapack_complex_float* tau,
+ lapack_complex_float* work, lapack_int lwork );
+lapack_int LAPACKE_zunglq_work( int matrix_order, lapack_int m, lapack_int n,
+ lapack_int k, lapack_complex_double* a,
+ lapack_int lda,
+ const lapack_complex_double* tau,
+ lapack_complex_double* work, lapack_int lwork );
+
+lapack_int LAPACKE_cungql_work( int matrix_order, lapack_int m, lapack_int n,
+ lapack_int k, lapack_complex_float* a,
+ lapack_int lda, const lapack_complex_float* tau,
+ lapack_complex_float* work, lapack_int lwork );
+lapack_int LAPACKE_zungql_work( int matrix_order, lapack_int m, lapack_int n,
+ lapack_int k, lapack_complex_double* a,
+ lapack_int lda,
+ const lapack_complex_double* tau,
+ lapack_complex_double* work, lapack_int lwork );
+
+lapack_int LAPACKE_cungqr_work( int matrix_order, lapack_int m, lapack_int n,
+ lapack_int k, lapack_complex_float* a,
+ lapack_int lda, const lapack_complex_float* tau,
+ lapack_complex_float* work, lapack_int lwork );
+lapack_int LAPACKE_zungqr_work( int matrix_order, lapack_int m, lapack_int n,
+ lapack_int k, lapack_complex_double* a,
+ lapack_int lda,
+ const lapack_complex_double* tau,
+ lapack_complex_double* work, lapack_int lwork );
+
+lapack_int LAPACKE_cungrq_work( int matrix_order, lapack_int m, lapack_int n,
+ lapack_int k, lapack_complex_float* a,
+ lapack_int lda, const lapack_complex_float* tau,
+ lapack_complex_float* work, lapack_int lwork );
+lapack_int LAPACKE_zungrq_work( int matrix_order, lapack_int m, lapack_int n,
+ lapack_int k, lapack_complex_double* a,
+ lapack_int lda,
+ const lapack_complex_double* tau,
+ lapack_complex_double* work, lapack_int lwork );
+
+lapack_int LAPACKE_cungtr_work( int matrix_order, char uplo, lapack_int n,
+ lapack_complex_float* a, lapack_int lda,
+ const lapack_complex_float* tau,
+ lapack_complex_float* work, lapack_int lwork );
+lapack_int LAPACKE_zungtr_work( int matrix_order, char uplo, lapack_int n,
+ lapack_complex_double* a, lapack_int lda,
+ const lapack_complex_double* tau,
+ lapack_complex_double* work, lapack_int lwork );
+
+lapack_int LAPACKE_cunmbr_work( int matrix_order, char vect, char side,
+ char trans, lapack_int m, lapack_int n,
+ lapack_int k, const lapack_complex_float* a,
+ lapack_int lda, const lapack_complex_float* tau,
+ lapack_complex_float* c, lapack_int ldc,
+ lapack_complex_float* work, lapack_int lwork );
+lapack_int LAPACKE_zunmbr_work( int matrix_order, char vect, char side,
+ char trans, lapack_int m, lapack_int n,
+ lapack_int k, const lapack_complex_double* a,
+ lapack_int lda,
+ const lapack_complex_double* tau,
+ lapack_complex_double* c, lapack_int ldc,
+ lapack_complex_double* work, lapack_int lwork );
+
+lapack_int LAPACKE_cunmhr_work( int matrix_order, char side, char trans,
+ lapack_int m, lapack_int n, lapack_int ilo,
+ lapack_int ihi, const lapack_complex_float* a,
+ lapack_int lda, const lapack_complex_float* tau,
+ lapack_complex_float* c, lapack_int ldc,
+ lapack_complex_float* work, lapack_int lwork );
+lapack_int LAPACKE_zunmhr_work( int matrix_order, char side, char trans,
+ lapack_int m, lapack_int n, lapack_int ilo,
+ lapack_int ihi, const lapack_complex_double* a,
+ lapack_int lda,
+ const lapack_complex_double* tau,
+ lapack_complex_double* c, lapack_int ldc,
+ lapack_complex_double* work, lapack_int lwork );
+
+lapack_int LAPACKE_cunmlq_work( int matrix_order, char side, char trans,
+ lapack_int m, lapack_int n, lapack_int k,
+ const lapack_complex_float* a, lapack_int lda,
+ const lapack_complex_float* tau,
+ lapack_complex_float* c, lapack_int ldc,
+ lapack_complex_float* work, lapack_int lwork );
+lapack_int LAPACKE_zunmlq_work( int matrix_order, char side, char trans,
+ lapack_int m, lapack_int n, lapack_int k,
+ const lapack_complex_double* a, lapack_int lda,
+ const lapack_complex_double* tau,
+ lapack_complex_double* c, lapack_int ldc,
+ lapack_complex_double* work, lapack_int lwork );
+
+lapack_int LAPACKE_cunmql_work( int matrix_order, char side, char trans,
+ lapack_int m, lapack_int n, lapack_int k,
+ const lapack_complex_float* a, lapack_int lda,
+ const lapack_complex_float* tau,
+ lapack_complex_float* c, lapack_int ldc,
+ lapack_complex_float* work, lapack_int lwork );
+lapack_int LAPACKE_zunmql_work( int matrix_order, char side, char trans,
+ lapack_int m, lapack_int n, lapack_int k,
+ const lapack_complex_double* a, lapack_int lda,
+ const lapack_complex_double* tau,
+ lapack_complex_double* c, lapack_int ldc,
+ lapack_complex_double* work, lapack_int lwork );
+
+lapack_int LAPACKE_cunmqr_work( int matrix_order, char side, char trans,
+ lapack_int m, lapack_int n, lapack_int k,
+ const lapack_complex_float* a, lapack_int lda,
+ const lapack_complex_float* tau,
+ lapack_complex_float* c, lapack_int ldc,
+ lapack_complex_float* work, lapack_int lwork );
+lapack_int LAPACKE_zunmqr_work( int matrix_order, char side, char trans,
+ lapack_int m, lapack_int n, lapack_int k,
+ const lapack_complex_double* a, lapack_int lda,
+ const lapack_complex_double* tau,
+ lapack_complex_double* c, lapack_int ldc,
+ lapack_complex_double* work, lapack_int lwork );
+
+lapack_int LAPACKE_cunmrq_work( int matrix_order, char side, char trans,
+ lapack_int m, lapack_int n, lapack_int k,
+ const lapack_complex_float* a, lapack_int lda,
+ const lapack_complex_float* tau,
+ lapack_complex_float* c, lapack_int ldc,
+ lapack_complex_float* work, lapack_int lwork );
+lapack_int LAPACKE_zunmrq_work( int matrix_order, char side, char trans,
+ lapack_int m, lapack_int n, lapack_int k,
+ const lapack_complex_double* a, lapack_int lda,
+ const lapack_complex_double* tau,
+ lapack_complex_double* c, lapack_int ldc,
+ lapack_complex_double* work, lapack_int lwork );
+
+lapack_int LAPACKE_cunmrz_work( int matrix_order, char side, char trans,
+ lapack_int m, lapack_int n, lapack_int k,
+ lapack_int l, const lapack_complex_float* a,
+ lapack_int lda, const lapack_complex_float* tau,
+ lapack_complex_float* c, lapack_int ldc,
+ lapack_complex_float* work, lapack_int lwork );
+lapack_int LAPACKE_zunmrz_work( int matrix_order, char side, char trans,
+ lapack_int m, lapack_int n, lapack_int k,
+ lapack_int l, const lapack_complex_double* a,
+ lapack_int lda,
+ const lapack_complex_double* tau,
+ lapack_complex_double* c, lapack_int ldc,
+ lapack_complex_double* work, lapack_int lwork );
+
+lapack_int LAPACKE_cunmtr_work( int matrix_order, char side, char uplo,
+ char trans, lapack_int m, lapack_int n,
+ const lapack_complex_float* a, lapack_int lda,
+ const lapack_complex_float* tau,
+ lapack_complex_float* c, lapack_int ldc,
+ lapack_complex_float* work, lapack_int lwork );
+lapack_int LAPACKE_zunmtr_work( int matrix_order, char side, char uplo,
+ char trans, lapack_int m, lapack_int n,
+ const lapack_complex_double* a, lapack_int lda,
+ const lapack_complex_double* tau,
+ lapack_complex_double* c, lapack_int ldc,
+ lapack_complex_double* work, lapack_int lwork );
+
+lapack_int LAPACKE_cupgtr_work( int matrix_order, char uplo, lapack_int n,
+ const lapack_complex_float* ap,
+ const lapack_complex_float* tau,
+ lapack_complex_float* q, lapack_int ldq,
+ lapack_complex_float* work );
+lapack_int LAPACKE_zupgtr_work( int matrix_order, char uplo, lapack_int n,
+ const lapack_complex_double* ap,
+ const lapack_complex_double* tau,
+ lapack_complex_double* q, lapack_int ldq,
+ lapack_complex_double* work );
+
+lapack_int LAPACKE_cupmtr_work( int matrix_order, char side, char uplo,
+ char trans, lapack_int m, lapack_int n,
+ const lapack_complex_float* ap,
+ const lapack_complex_float* tau,
+ lapack_complex_float* c, lapack_int ldc,
+ lapack_complex_float* work );
+lapack_int LAPACKE_zupmtr_work( int matrix_order, char side, char uplo,
+ char trans, lapack_int m, lapack_int n,
+ const lapack_complex_double* ap,
+ const lapack_complex_double* tau,
+ lapack_complex_double* c, lapack_int ldc,
+ lapack_complex_double* work );
+
+lapack_int LAPACKE_claghe( int matrix_order, lapack_int n, lapack_int k,
+ const float* d, lapack_complex_float* a,
+ lapack_int lda, lapack_int* iseed );
+lapack_int LAPACKE_zlaghe( int matrix_order, lapack_int n, lapack_int k,
+ const double* d, lapack_complex_double* a,
+ lapack_int lda, lapack_int* iseed );
+
+lapack_int LAPACKE_slagsy( int matrix_order, lapack_int n, lapack_int k,
+ const float* d, float* a, lapack_int lda,
+ lapack_int* iseed );
+lapack_int LAPACKE_dlagsy( int matrix_order, lapack_int n, lapack_int k,
+ const double* d, double* a, lapack_int lda,
+ lapack_int* iseed );
+lapack_int LAPACKE_clagsy( int matrix_order, lapack_int n, lapack_int k,
+ const float* d, lapack_complex_float* a,
+ lapack_int lda, lapack_int* iseed );
+lapack_int LAPACKE_zlagsy( int matrix_order, lapack_int n, lapack_int k,
+ const double* d, lapack_complex_double* a,
+ lapack_int lda, lapack_int* iseed );
+
+lapack_int LAPACKE_slapmr( int matrix_order, lapack_logical forwrd,
+ lapack_int m, lapack_int n, float* x, lapack_int ldx,
+ lapack_int* k );
+lapack_int LAPACKE_dlapmr( int matrix_order, lapack_logical forwrd,
+ lapack_int m, lapack_int n, double* x,
+ lapack_int ldx, lapack_int* k );
+lapack_int LAPACKE_clapmr( int matrix_order, lapack_logical forwrd,
+ lapack_int m, lapack_int n, lapack_complex_float* x,
+ lapack_int ldx, lapack_int* k );
+lapack_int LAPACKE_zlapmr( int matrix_order, lapack_logical forwrd,
+ lapack_int m, lapack_int n, lapack_complex_double* x,
+ lapack_int ldx, lapack_int* k );
+
+
+float LAPACKE_slapy2( float x, float y );
+double LAPACKE_dlapy2( double x, double y );
+
+float LAPACKE_slapy3( float x, float y, float z );
+double LAPACKE_dlapy3( double x, double y, double z );
+
+lapack_int LAPACKE_slartgp( float f, float g, float* cs, float* sn, float* r );
+lapack_int LAPACKE_dlartgp( double f, double g, double* cs, double* sn,
+ double* r );
+
+lapack_int LAPACKE_slartgs( float x, float y, float sigma, float* cs,
+ float* sn );
+lapack_int LAPACKE_dlartgs( double x, double y, double sigma, double* cs,
+ double* sn );
+
+
+//LAPACK 3.3.0
+lapack_int LAPACKE_cbbcsd( int matrix_order, char jobu1, char jobu2,
+ char jobv1t, char jobv2t, char trans, lapack_int m,
+ lapack_int p, lapack_int q, float* theta, float* phi,
+ lapack_complex_float* u1, lapack_int ldu1,
+ lapack_complex_float* u2, lapack_int ldu2,
+ lapack_complex_float* v1t, lapack_int ldv1t,
+ lapack_complex_float* v2t, lapack_int ldv2t,
+ float* b11d, float* b11e, float* b12d, float* b12e,
+ float* b21d, float* b21e, float* b22d, float* b22e );
+lapack_int LAPACKE_cbbcsd_work( int matrix_order, char jobu1, char jobu2,
+ char jobv1t, char jobv2t, char trans,
+ lapack_int m, lapack_int p, lapack_int q,
+ float* theta, float* phi,
+ lapack_complex_float* u1, lapack_int ldu1,
+ lapack_complex_float* u2, lapack_int ldu2,
+ lapack_complex_float* v1t, lapack_int ldv1t,
+ lapack_complex_float* v2t, lapack_int ldv2t,
+ float* b11d, float* b11e, float* b12d,
+ float* b12e, float* b21d, float* b21e,
+ float* b22d, float* b22e, float* rwork,
+ lapack_int lrwork );
+lapack_int LAPACKE_cheswapr( int matrix_order, char uplo, lapack_int n,
+ lapack_complex_float* a, lapack_int i1,
+ lapack_int i2 );
+lapack_int LAPACKE_cheswapr_work( int matrix_order, char uplo, lapack_int n,
+ lapack_complex_float* a, lapack_int i1,
+ lapack_int i2 );
+lapack_int LAPACKE_chetri2( int matrix_order, char uplo, lapack_int n,
+ lapack_complex_float* a, lapack_int lda,
+ const lapack_int* ipiv );
+lapack_int LAPACKE_chetri2_work( int matrix_order, char uplo, lapack_int n,
+ lapack_complex_float* a, lapack_int lda,
+ const lapack_int* ipiv,
+ lapack_complex_float* work, lapack_int lwork );
+lapack_int LAPACKE_chetri2x( int matrix_order, char uplo, lapack_int n,
+ lapack_complex_float* a, lapack_int lda,
+ const lapack_int* ipiv, lapack_int nb );
+lapack_int LAPACKE_chetri2x_work( int matrix_order, char uplo, lapack_int n,
+ lapack_complex_float* a, lapack_int lda,
+ const lapack_int* ipiv,
+ lapack_complex_float* work, lapack_int nb );
+lapack_int LAPACKE_chetrs2( int matrix_order, char uplo, lapack_int n,
+ lapack_int nrhs, const lapack_complex_float* a,
+ lapack_int lda, const lapack_int* ipiv,
+ lapack_complex_float* b, lapack_int ldb );
+lapack_int LAPACKE_chetrs2_work( int matrix_order, char uplo, lapack_int n,
+ lapack_int nrhs, const lapack_complex_float* a,
+ lapack_int lda, const lapack_int* ipiv,
+ lapack_complex_float* b, lapack_int ldb,
+ lapack_complex_float* work );
+lapack_int LAPACKE_csyconv( int matrix_order, char uplo, char way, lapack_int n,
+ lapack_complex_float* a, lapack_int lda,
+ const lapack_int* ipiv );
+lapack_int LAPACKE_csyconv_work( int matrix_order, char uplo, char way,
+ lapack_int n, lapack_complex_float* a,
+ lapack_int lda, const lapack_int* ipiv,
+ lapack_complex_float* work );
+lapack_int LAPACKE_csyswapr( int matrix_order, char uplo, lapack_int n,
+ lapack_complex_float* a, lapack_int i1,
+ lapack_int i2 );
+lapack_int LAPACKE_csyswapr_work( int matrix_order, char uplo, lapack_int n,
+ lapack_complex_float* a, lapack_int i1,
+ lapack_int i2 );
+lapack_int LAPACKE_csytri2( int matrix_order, char uplo, lapack_int n,
+ lapack_complex_float* a, lapack_int lda,
+ const lapack_int* ipiv );
+lapack_int LAPACKE_csytri2_work( int matrix_order, char uplo, lapack_int n,
+ lapack_complex_float* a, lapack_int lda,
+ const lapack_int* ipiv,
+ lapack_complex_float* work, lapack_int lwork );
+lapack_int LAPACKE_csytri2x( int matrix_order, char uplo, lapack_int n,
+ lapack_complex_float* a, lapack_int lda,
+ const lapack_int* ipiv, lapack_int nb );
+lapack_int LAPACKE_csytri2x_work( int matrix_order, char uplo, lapack_int n,
+ lapack_complex_float* a, lapack_int lda,
+ const lapack_int* ipiv,
+ lapack_complex_float* work, lapack_int nb );
+lapack_int LAPACKE_csytrs2( int matrix_order, char uplo, lapack_int n,
+ lapack_int nrhs, const lapack_complex_float* a,
+ lapack_int lda, const lapack_int* ipiv,
+ lapack_complex_float* b, lapack_int ldb );
+lapack_int LAPACKE_csytrs2_work( int matrix_order, char uplo, lapack_int n,
+ lapack_int nrhs, const lapack_complex_float* a,
+ lapack_int lda, const lapack_int* ipiv,
+ lapack_complex_float* b, lapack_int ldb,
+ lapack_complex_float* work );
+lapack_int LAPACKE_cunbdb( int matrix_order, char trans, char signs,
+ lapack_int m, lapack_int p, lapack_int q,
+ lapack_complex_float* x11, lapack_int ldx11,
+ lapack_complex_float* x12, lapack_int ldx12,
+ lapack_complex_float* x21, lapack_int ldx21,
+ lapack_complex_float* x22, lapack_int ldx22,
+ float* theta, float* phi,
+ lapack_complex_float* taup1,
+ lapack_complex_float* taup2,
+ lapack_complex_float* tauq1,
+ lapack_complex_float* tauq2 );
+lapack_int LAPACKE_cunbdb_work( int matrix_order, char trans, char signs,
+ lapack_int m, lapack_int p, lapack_int q,
+ lapack_complex_float* x11, lapack_int ldx11,
+ lapack_complex_float* x12, lapack_int ldx12,
+ lapack_complex_float* x21, lapack_int ldx21,
+ lapack_complex_float* x22, lapack_int ldx22,
+ float* theta, float* phi,
+ lapack_complex_float* taup1,
+ lapack_complex_float* taup2,
+ lapack_complex_float* tauq1,
+ lapack_complex_float* tauq2,
+ lapack_complex_float* work, lapack_int lwork );
+lapack_int LAPACKE_cuncsd( int matrix_order, char jobu1, char jobu2,
+ char jobv1t, char jobv2t, char trans, char signs,
+ lapack_int m, lapack_int p, lapack_int q,
+ lapack_complex_float* x11, lapack_int ldx11,
+ lapack_complex_float* x12, lapack_int ldx12,
+ lapack_complex_float* x21, lapack_int ldx21,
+ lapack_complex_float* x22, lapack_int ldx22,
+ float* theta, lapack_complex_float* u1,
+ lapack_int ldu1, lapack_complex_float* u2,
+ lapack_int ldu2, lapack_complex_float* v1t,
+ lapack_int ldv1t, lapack_complex_float* v2t,
+ lapack_int ldv2t );
+lapack_int LAPACKE_cuncsd_work( int matrix_order, char jobu1, char jobu2,
+ char jobv1t, char jobv2t, char trans,
+ char signs, lapack_int m, lapack_int p,
+ lapack_int q, lapack_complex_float* x11,
+ lapack_int ldx11, lapack_complex_float* x12,
+ lapack_int ldx12, lapack_complex_float* x21,
+ lapack_int ldx21, lapack_complex_float* x22,
+ lapack_int ldx22, float* theta,
+ lapack_complex_float* u1, lapack_int ldu1,
+ lapack_complex_float* u2, lapack_int ldu2,
+ lapack_complex_float* v1t, lapack_int ldv1t,
+ lapack_complex_float* v2t, lapack_int ldv2t,
+ lapack_complex_float* work, lapack_int lwork,
+ float* rwork, lapack_int lrwork,
+ lapack_int* iwork );
+lapack_int LAPACKE_dbbcsd( int matrix_order, char jobu1, char jobu2,
+ char jobv1t, char jobv2t, char trans, lapack_int m,
+ lapack_int p, lapack_int q, double* theta,
+ double* phi, double* u1, lapack_int ldu1, double* u2,
+ lapack_int ldu2, double* v1t, lapack_int ldv1t,
+ double* v2t, lapack_int ldv2t, double* b11d,
+ double* b11e, double* b12d, double* b12e,
+ double* b21d, double* b21e, double* b22d,
+ double* b22e );
+lapack_int LAPACKE_dbbcsd_work( int matrix_order, char jobu1, char jobu2,
+ char jobv1t, char jobv2t, char trans,
+ lapack_int m, lapack_int p, lapack_int q,
+ double* theta, double* phi, double* u1,
+ lapack_int ldu1, double* u2, lapack_int ldu2,
+ double* v1t, lapack_int ldv1t, double* v2t,
+ lapack_int ldv2t, double* b11d, double* b11e,
+ double* b12d, double* b12e, double* b21d,
+ double* b21e, double* b22d, double* b22e,
+ double* work, lapack_int lwork );
+lapack_int LAPACKE_dorbdb( int matrix_order, char trans, char signs,
+ lapack_int m, lapack_int p, lapack_int q,
+ double* x11, lapack_int ldx11, double* x12,
+ lapack_int ldx12, double* x21, lapack_int ldx21,
+ double* x22, lapack_int ldx22, double* theta,
+ double* phi, double* taup1, double* taup2,
+ double* tauq1, double* tauq2 );
+lapack_int LAPACKE_dorbdb_work( int matrix_order, char trans, char signs,
+ lapack_int m, lapack_int p, lapack_int q,
+ double* x11, lapack_int ldx11, double* x12,
+ lapack_int ldx12, double* x21, lapack_int ldx21,
+ double* x22, lapack_int ldx22, double* theta,
+ double* phi, double* taup1, double* taup2,
+ double* tauq1, double* tauq2, double* work,
+ lapack_int lwork );
+lapack_int LAPACKE_dorcsd( int matrix_order, char jobu1, char jobu2,
+ char jobv1t, char jobv2t, char trans, char signs,
+ lapack_int m, lapack_int p, lapack_int q,
+ double* x11, lapack_int ldx11, double* x12,
+ lapack_int ldx12, double* x21, lapack_int ldx21,
+ double* x22, lapack_int ldx22, double* theta,
+ double* u1, lapack_int ldu1, double* u2,
+ lapack_int ldu2, double* v1t, lapack_int ldv1t,
+ double* v2t, lapack_int ldv2t );
+lapack_int LAPACKE_dorcsd_work( int matrix_order, char jobu1, char jobu2,
+ char jobv1t, char jobv2t, char trans,
+ char signs, lapack_int m, lapack_int p,
+ lapack_int q, double* x11, lapack_int ldx11,
+ double* x12, lapack_int ldx12, double* x21,
+ lapack_int ldx21, double* x22, lapack_int ldx22,
+ double* theta, double* u1, lapack_int ldu1,
+ double* u2, lapack_int ldu2, double* v1t,
+ lapack_int ldv1t, double* v2t, lapack_int ldv2t,
+ double* work, lapack_int lwork,
+ lapack_int* iwork );
+lapack_int LAPACKE_dsyconv( int matrix_order, char uplo, char way, lapack_int n,
+ double* a, lapack_int lda, const lapack_int* ipiv );
+lapack_int LAPACKE_dsyconv_work( int matrix_order, char uplo, char way,
+ lapack_int n, double* a, lapack_int lda,
+ const lapack_int* ipiv, double* work );
+lapack_int LAPACKE_dsyswapr( int matrix_order, char uplo, lapack_int n,
+ double* a, lapack_int i1, lapack_int i2 );
+lapack_int LAPACKE_dsyswapr_work( int matrix_order, char uplo, lapack_int n,
+ double* a, lapack_int i1, lapack_int i2 );
+lapack_int LAPACKE_dsytri2( int matrix_order, char uplo, lapack_int n,
+ double* a, lapack_int lda, const lapack_int* ipiv );
+lapack_int LAPACKE_dsytri2_work( int matrix_order, char uplo, lapack_int n,
+ double* a, lapack_int lda,
+ const lapack_int* ipiv,
+ lapack_complex_double* work, lapack_int lwork );
+lapack_int LAPACKE_dsytri2x( int matrix_order, char uplo, lapack_int n,
+ double* a, lapack_int lda, const lapack_int* ipiv,
+ lapack_int nb );
+lapack_int LAPACKE_dsytri2x_work( int matrix_order, char uplo, lapack_int n,
+ double* a, lapack_int lda,
+ const lapack_int* ipiv, double* work,
+ lapack_int nb );
+lapack_int LAPACKE_dsytrs2( int matrix_order, char uplo, lapack_int n,
+ lapack_int nrhs, const double* a, lapack_int lda,
+ const lapack_int* ipiv, double* b, lapack_int ldb );
+lapack_int LAPACKE_dsytrs2_work( int matrix_order, char uplo, lapack_int n,
+ lapack_int nrhs, const double* a,
+ lapack_int lda, const lapack_int* ipiv,
+ double* b, lapack_int ldb, double* work );
+lapack_int LAPACKE_sbbcsd( int matrix_order, char jobu1, char jobu2,
+ char jobv1t, char jobv2t, char trans, lapack_int m,
+ lapack_int p, lapack_int q, float* theta, float* phi,
+ float* u1, lapack_int ldu1, float* u2,
+ lapack_int ldu2, float* v1t, lapack_int ldv1t,
+ float* v2t, lapack_int ldv2t, float* b11d,
+ float* b11e, float* b12d, float* b12e, float* b21d,
+ float* b21e, float* b22d, float* b22e );
+lapack_int LAPACKE_sbbcsd_work( int matrix_order, char jobu1, char jobu2,
+ char jobv1t, char jobv2t, char trans,
+ lapack_int m, lapack_int p, lapack_int q,
+ float* theta, float* phi, float* u1,
+ lapack_int ldu1, float* u2, lapack_int ldu2,
+ float* v1t, lapack_int ldv1t, float* v2t,
+ lapack_int ldv2t, float* b11d, float* b11e,
+ float* b12d, float* b12e, float* b21d,
+ float* b21e, float* b22d, float* b22e,
+ float* work, lapack_int lwork );
+lapack_int LAPACKE_sorbdb( int matrix_order, char trans, char signs,
+ lapack_int m, lapack_int p, lapack_int q, float* x11,
+ lapack_int ldx11, float* x12, lapack_int ldx12,
+ float* x21, lapack_int ldx21, float* x22,
+ lapack_int ldx22, float* theta, float* phi,
+ float* taup1, float* taup2, float* tauq1,
+ float* tauq2 );
+lapack_int LAPACKE_sorbdb_work( int matrix_order, char trans, char signs,
+ lapack_int m, lapack_int p, lapack_int q,
+ float* x11, lapack_int ldx11, float* x12,
+ lapack_int ldx12, float* x21, lapack_int ldx21,
+ float* x22, lapack_int ldx22, float* theta,
+ float* phi, float* taup1, float* taup2,
+ float* tauq1, float* tauq2, float* work,
+ lapack_int lwork );
+lapack_int LAPACKE_sorcsd( int matrix_order, char jobu1, char jobu2,
+ char jobv1t, char jobv2t, char trans, char signs,
+ lapack_int m, lapack_int p, lapack_int q, float* x11,
+ lapack_int ldx11, float* x12, lapack_int ldx12,
+ float* x21, lapack_int ldx21, float* x22,
+ lapack_int ldx22, float* theta, float* u1,
+ lapack_int ldu1, float* u2, lapack_int ldu2,
+ float* v1t, lapack_int ldv1t, float* v2t,
+ lapack_int ldv2t );
+lapack_int LAPACKE_sorcsd_work( int matrix_order, char jobu1, char jobu2,
+ char jobv1t, char jobv2t, char trans,
+ char signs, lapack_int m, lapack_int p,
+ lapack_int q, float* x11, lapack_int ldx11,
+ float* x12, lapack_int ldx12, float* x21,
+ lapack_int ldx21, float* x22, lapack_int ldx22,
+ float* theta, float* u1, lapack_int ldu1,
+ float* u2, lapack_int ldu2, float* v1t,
+ lapack_int ldv1t, float* v2t, lapack_int ldv2t,
+ float* work, lapack_int lwork,
+ lapack_int* iwork );
+lapack_int LAPACKE_ssyconv( int matrix_order, char uplo, char way, lapack_int n,
+ float* a, lapack_int lda, const lapack_int* ipiv );
+lapack_int LAPACKE_ssyconv_work( int matrix_order, char uplo, char way,
+ lapack_int n, float* a, lapack_int lda,
+ const lapack_int* ipiv, float* work );
+lapack_int LAPACKE_ssyswapr( int matrix_order, char uplo, lapack_int n,
+ float* a, lapack_int i1, lapack_int i2 );
+lapack_int LAPACKE_ssyswapr_work( int matrix_order, char uplo, lapack_int n,
+ float* a, lapack_int i1, lapack_int i2 );
+lapack_int LAPACKE_ssytri2( int matrix_order, char uplo, lapack_int n, float* a,
+ lapack_int lda, const lapack_int* ipiv );
+lapack_int LAPACKE_ssytri2_work( int matrix_order, char uplo, lapack_int n,
+ float* a, lapack_int lda,
+ const lapack_int* ipiv,
+ lapack_complex_float* work, lapack_int lwork );
+lapack_int LAPACKE_ssytri2x( int matrix_order, char uplo, lapack_int n,
+ float* a, lapack_int lda, const lapack_int* ipiv,
+ lapack_int nb );
+lapack_int LAPACKE_ssytri2x_work( int matrix_order, char uplo, lapack_int n,
+ float* a, lapack_int lda,
+ const lapack_int* ipiv, float* work,
+ lapack_int nb );
+lapack_int LAPACKE_ssytrs2( int matrix_order, char uplo, lapack_int n,
+ lapack_int nrhs, const float* a, lapack_int lda,
+ const lapack_int* ipiv, float* b, lapack_int ldb );
+lapack_int LAPACKE_ssytrs2_work( int matrix_order, char uplo, lapack_int n,
+ lapack_int nrhs, const float* a,
+ lapack_int lda, const lapack_int* ipiv,
+ float* b, lapack_int ldb, float* work );
+lapack_int LAPACKE_zbbcsd( int matrix_order, char jobu1, char jobu2,
+ char jobv1t, char jobv2t, char trans, lapack_int m,
+ lapack_int p, lapack_int q, double* theta,
+ double* phi, lapack_complex_double* u1,
+ lapack_int ldu1, lapack_complex_double* u2,
+ lapack_int ldu2, lapack_complex_double* v1t,
+ lapack_int ldv1t, lapack_complex_double* v2t,
+ lapack_int ldv2t, double* b11d, double* b11e,
+ double* b12d, double* b12e, double* b21d,
+ double* b21e, double* b22d, double* b22e );
+lapack_int LAPACKE_zbbcsd_work( int matrix_order, char jobu1, char jobu2,
+ char jobv1t, char jobv2t, char trans,
+ lapack_int m, lapack_int p, lapack_int q,
+ double* theta, double* phi,
+ lapack_complex_double* u1, lapack_int ldu1,
+ lapack_complex_double* u2, lapack_int ldu2,
+ lapack_complex_double* v1t, lapack_int ldv1t,
+ lapack_complex_double* v2t, lapack_int ldv2t,
+ double* b11d, double* b11e, double* b12d,
+ double* b12e, double* b21d, double* b21e,
+ double* b22d, double* b22e, double* rwork,
+ lapack_int lrwork );
+lapack_int LAPACKE_zheswapr( int matrix_order, char uplo, lapack_int n,
+ lapack_complex_double* a, lapack_int i1,
+ lapack_int i2 );
+lapack_int LAPACKE_zheswapr_work( int matrix_order, char uplo, lapack_int n,
+ lapack_complex_double* a, lapack_int i1,
+ lapack_int i2 );
+lapack_int LAPACKE_zhetri2( int matrix_order, char uplo, lapack_int n,
+ lapack_complex_double* a, lapack_int lda,
+ const lapack_int* ipiv );
+lapack_int LAPACKE_zhetri2_work( int matrix_order, char uplo, lapack_int n,
+ lapack_complex_double* a, lapack_int lda,
+ const lapack_int* ipiv,
+ lapack_complex_double* work, lapack_int lwork );
+lapack_int LAPACKE_zhetri2x( int matrix_order, char uplo, lapack_int n,
+ lapack_complex_double* a, lapack_int lda,
+ const lapack_int* ipiv, lapack_int nb );
+lapack_int LAPACKE_zhetri2x_work( int matrix_order, char uplo, lapack_int n,
+ lapack_complex_double* a, lapack_int lda,
+ const lapack_int* ipiv,
+ lapack_complex_double* work, lapack_int nb );
+lapack_int LAPACKE_zhetrs2( int matrix_order, char uplo, lapack_int n,
+ lapack_int nrhs, const lapack_complex_double* a,
+ lapack_int lda, const lapack_int* ipiv,
+ lapack_complex_double* b, lapack_int ldb );
+lapack_int LAPACKE_zhetrs2_work( int matrix_order, char uplo, lapack_int n,
+ lapack_int nrhs, const lapack_complex_double* a,
+ lapack_int lda, const lapack_int* ipiv,
+ lapack_complex_double* b, lapack_int ldb,
+ lapack_complex_double* work );
+lapack_int LAPACKE_zsyconv( int matrix_order, char uplo, char way, lapack_int n,
+ lapack_complex_double* a, lapack_int lda,
+ const lapack_int* ipiv );
+lapack_int LAPACKE_zsyconv_work( int matrix_order, char uplo, char way,
+ lapack_int n, lapack_complex_double* a,
+ lapack_int lda, const lapack_int* ipiv,
+ lapack_complex_double* work );
+lapack_int LAPACKE_zsyswapr( int matrix_order, char uplo, lapack_int n,
+ lapack_complex_double* a, lapack_int i1,
+ lapack_int i2 );
+lapack_int LAPACKE_zsyswapr_work( int matrix_order, char uplo, lapack_int n,
+ lapack_complex_double* a, lapack_int i1,
+ lapack_int i2 );
+lapack_int LAPACKE_zsytri2( int matrix_order, char uplo, lapack_int n,
+ lapack_complex_double* a, lapack_int lda,
+ const lapack_int* ipiv );
+lapack_int LAPACKE_zsytri2_work( int matrix_order, char uplo, lapack_int n,
+ lapack_complex_double* a, lapack_int lda,
+ const lapack_int* ipiv,
+ lapack_complex_double* work, lapack_int lwork );
+lapack_int LAPACKE_zsytri2x( int matrix_order, char uplo, lapack_int n,
+ lapack_complex_double* a, lapack_int lda,
+ const lapack_int* ipiv, lapack_int nb );
+lapack_int LAPACKE_zsytri2x_work( int matrix_order, char uplo, lapack_int n,
+ lapack_complex_double* a, lapack_int lda,
+ const lapack_int* ipiv,
+ lapack_complex_double* work, lapack_int nb );
+lapack_int LAPACKE_zsytrs2( int matrix_order, char uplo, lapack_int n,
+ lapack_int nrhs, const lapack_complex_double* a,
+ lapack_int lda, const lapack_int* ipiv,
+ lapack_complex_double* b, lapack_int ldb );
+lapack_int LAPACKE_zsytrs2_work( int matrix_order, char uplo, lapack_int n,
+ lapack_int nrhs, const lapack_complex_double* a,
+ lapack_int lda, const lapack_int* ipiv,
+ lapack_complex_double* b, lapack_int ldb,
+ lapack_complex_double* work );
+lapack_int LAPACKE_zunbdb( int matrix_order, char trans, char signs,
+ lapack_int m, lapack_int p, lapack_int q,
+ lapack_complex_double* x11, lapack_int ldx11,
+ lapack_complex_double* x12, lapack_int ldx12,
+ lapack_complex_double* x21, lapack_int ldx21,
+ lapack_complex_double* x22, lapack_int ldx22,
+ double* theta, double* phi,
+ lapack_complex_double* taup1,
+ lapack_complex_double* taup2,
+ lapack_complex_double* tauq1,
+ lapack_complex_double* tauq2 );
+lapack_int LAPACKE_zunbdb_work( int matrix_order, char trans, char signs,
+ lapack_int m, lapack_int p, lapack_int q,
+ lapack_complex_double* x11, lapack_int ldx11,
+ lapack_complex_double* x12, lapack_int ldx12,
+ lapack_complex_double* x21, lapack_int ldx21,
+ lapack_complex_double* x22, lapack_int ldx22,
+ double* theta, double* phi,
+ lapack_complex_double* taup1,
+ lapack_complex_double* taup2,
+ lapack_complex_double* tauq1,
+ lapack_complex_double* tauq2,
+ lapack_complex_double* work, lapack_int lwork );
+lapack_int LAPACKE_zuncsd( int matrix_order, char jobu1, char jobu2,
+ char jobv1t, char jobv2t, char trans, char signs,
+ lapack_int m, lapack_int p, lapack_int q,
+ lapack_complex_double* x11, lapack_int ldx11,
+ lapack_complex_double* x12, lapack_int ldx12,
+ lapack_complex_double* x21, lapack_int ldx21,
+ lapack_complex_double* x22, lapack_int ldx22,
+ double* theta, lapack_complex_double* u1,
+ lapack_int ldu1, lapack_complex_double* u2,
+ lapack_int ldu2, lapack_complex_double* v1t,
+ lapack_int ldv1t, lapack_complex_double* v2t,
+ lapack_int ldv2t );
+lapack_int LAPACKE_zuncsd_work( int matrix_order, char jobu1, char jobu2,
+ char jobv1t, char jobv2t, char trans,
+ char signs, lapack_int m, lapack_int p,
+ lapack_int q, lapack_complex_double* x11,
+ lapack_int ldx11, lapack_complex_double* x12,
+ lapack_int ldx12, lapack_complex_double* x21,
+ lapack_int ldx21, lapack_complex_double* x22,
+ lapack_int ldx22, double* theta,
+ lapack_complex_double* u1, lapack_int ldu1,
+ lapack_complex_double* u2, lapack_int ldu2,
+ lapack_complex_double* v1t, lapack_int ldv1t,
+ lapack_complex_double* v2t, lapack_int ldv2t,
+ lapack_complex_double* work, lapack_int lwork,
+ double* rwork, lapack_int lrwork,
+ lapack_int* iwork );
+//LAPACK 3.4.0
+lapack_int LAPACKE_sgemqrt( int matrix_order, char side, char trans,
+ lapack_int m, lapack_int n, lapack_int k,
+ lapack_int nb, const float* v, lapack_int ldv,
+ const float* t, lapack_int ldt, float* c,
+ lapack_int ldc );
+lapack_int LAPACKE_dgemqrt( int matrix_order, char side, char trans,
+ lapack_int m, lapack_int n, lapack_int k,
+ lapack_int nb, const double* v, lapack_int ldv,
+ const double* t, lapack_int ldt, double* c,
+ lapack_int ldc );
+lapack_int LAPACKE_cgemqrt( int matrix_order, char side, char trans,
+ lapack_int m, lapack_int n, lapack_int k,
+ lapack_int nb, const lapack_complex_float* v,
+ lapack_int ldv, const lapack_complex_float* t,
+ lapack_int ldt, lapack_complex_float* c,
+ lapack_int ldc );
+lapack_int LAPACKE_zgemqrt( int matrix_order, char side, char trans,
+ lapack_int m, lapack_int n, lapack_int k,
+ lapack_int nb, const lapack_complex_double* v,
+ lapack_int ldv, const lapack_complex_double* t,
+ lapack_int ldt, lapack_complex_double* c,
+ lapack_int ldc );
+
+lapack_int LAPACKE_sgeqrt( int matrix_order, lapack_int m, lapack_int n,
+ lapack_int nb, float* a, lapack_int lda, float* t,
+ lapack_int ldt );
+lapack_int LAPACKE_dgeqrt( int matrix_order, lapack_int m, lapack_int n,
+ lapack_int nb, double* a, lapack_int lda, double* t,
+ lapack_int ldt );
+lapack_int LAPACKE_cgeqrt( int matrix_order, lapack_int m, lapack_int n,
+ lapack_int nb, lapack_complex_float* a,
+ lapack_int lda, lapack_complex_float* t,
+ lapack_int ldt );
+lapack_int LAPACKE_zgeqrt( int matrix_order, lapack_int m, lapack_int n,
+ lapack_int nb, lapack_complex_double* a,
+ lapack_int lda, lapack_complex_double* t,
+ lapack_int ldt );
+
+lapack_int LAPACKE_sgeqrt2( int matrix_order, lapack_int m, lapack_int n,
+ float* a, lapack_int lda, float* t,
+ lapack_int ldt );
+lapack_int LAPACKE_dgeqrt2( int matrix_order, lapack_int m, lapack_int n,
+ double* a, lapack_int lda, double* t,
+ lapack_int ldt );
+lapack_int LAPACKE_cgeqrt2( int matrix_order, lapack_int m, lapack_int n,
+ lapack_complex_float* a, lapack_int lda,
+ lapack_complex_float* t, lapack_int ldt );
+lapack_int LAPACKE_zgeqrt2( int matrix_order, lapack_int m, lapack_int n,
+ lapack_complex_double* a, lapack_int lda,
+ lapack_complex_double* t, lapack_int ldt );
+
+lapack_int LAPACKE_sgeqrt3( int matrix_order, lapack_int m, lapack_int n,
+ float* a, lapack_int lda, float* t,
+ lapack_int ldt );
+lapack_int LAPACKE_dgeqrt3( int matrix_order, lapack_int m, lapack_int n,
+ double* a, lapack_int lda, double* t,
+ lapack_int ldt );
+lapack_int LAPACKE_cgeqrt3( int matrix_order, lapack_int m, lapack_int n,
+ lapack_complex_float* a, lapack_int lda,
+ lapack_complex_float* t, lapack_int ldt );
+lapack_int LAPACKE_zgeqrt3( int matrix_order, lapack_int m, lapack_int n,
+ lapack_complex_double* a, lapack_int lda,
+ lapack_complex_double* t, lapack_int ldt );
+
+lapack_int LAPACKE_stpmqrt( int matrix_order, char side, char trans,
+ lapack_int m, lapack_int n, lapack_int k,
+ lapack_int l, lapack_int nb, const float* v,
+ lapack_int ldv, const float* t, lapack_int ldt,
+ float* a, lapack_int lda, float* b,
+ lapack_int ldb );
+lapack_int LAPACKE_dtpmqrt( int matrix_order, char side, char trans,
+ lapack_int m, lapack_int n, lapack_int k,
+ lapack_int l, lapack_int nb, const double* v,
+ lapack_int ldv, const double* t, lapack_int ldt,
+ double* a, lapack_int lda, double* b,
+ lapack_int ldb );
+lapack_int LAPACKE_ctpmqrt( int matrix_order, char side, char trans,
+ lapack_int m, lapack_int n, lapack_int k,
+ lapack_int l, lapack_int nb,
+ const lapack_complex_float* v, lapack_int ldv,
+ const lapack_complex_float* t, lapack_int ldt,
+ lapack_complex_float* a, lapack_int lda,
+ lapack_complex_float* b, lapack_int ldb );
+lapack_int LAPACKE_ztpmqrt( int matrix_order, char side, char trans,
+ lapack_int m, lapack_int n, lapack_int k,
+ lapack_int l, lapack_int nb,
+ const lapack_complex_double* v, lapack_int ldv,
+ const lapack_complex_double* t, lapack_int ldt,
+ lapack_complex_double* a, lapack_int lda,
+ lapack_complex_double* b, lapack_int ldb );
+
+lapack_int LAPACKE_dtpqrt( int matrix_order, lapack_int m, lapack_int n,
+ lapack_int l, lapack_int nb, double* a,
+ lapack_int lda, double* b, lapack_int ldb, double* t,
+ lapack_int ldt );
+lapack_int LAPACKE_ctpqrt( int matrix_order, lapack_int m, lapack_int n,
+ lapack_int l, lapack_int nb, lapack_complex_float* a,
+ lapack_int lda, lapack_complex_float* t,
+ lapack_complex_float* b, lapack_int ldb,
+ lapack_int ldt );
+lapack_int LAPACKE_ztpqrt( int matrix_order, lapack_int m, lapack_int n,
+ lapack_int l, lapack_int nb,
+ lapack_complex_double* a, lapack_int lda,
+ lapack_complex_double* b, lapack_int ldb,
+ lapack_complex_double* t, lapack_int ldt );
+
+lapack_int LAPACKE_stpqrt2( int matrix_order, lapack_int m, lapack_int n,
+ float* a, lapack_int lda, float* b, lapack_int ldb,
+ float* t, lapack_int ldt );
+lapack_int LAPACKE_dtpqrt2( int matrix_order, lapack_int m, lapack_int n,
+ double* a, lapack_int lda, double* b,
+ lapack_int ldb, double* t, lapack_int ldt );
+lapack_int LAPACKE_ctpqrt2( int matrix_order, lapack_int m, lapack_int n,
+ lapack_complex_float* a, lapack_int lda,
+ lapack_complex_float* b, lapack_int ldb,
+ lapack_complex_float* t, lapack_int ldt );
+lapack_int LAPACKE_ztpqrt2( int matrix_order, lapack_int m, lapack_int n,
+ lapack_complex_double* a, lapack_int lda,
+ lapack_complex_double* b, lapack_int ldb,
+ lapack_complex_double* t, lapack_int ldt );
+
+lapack_int LAPACKE_stprfb( int matrix_order, char side, char trans, char direct,
+ char storev, lapack_int m, lapack_int n,
+ lapack_int k, lapack_int l, const float* v,
+ lapack_int ldv, const float* t, lapack_int ldt,
+ float* a, lapack_int lda, float* b, lapack_int ldb,
+ lapack_int myldwork );
+lapack_int LAPACKE_dtprfb( int matrix_order, char side, char trans, char direct,
+ char storev, lapack_int m, lapack_int n,
+ lapack_int k, lapack_int l, const double* v,
+ lapack_int ldv, const double* t, lapack_int ldt,
+ double* a, lapack_int lda, double* b, lapack_int ldb,
+ lapack_int myldwork );
+lapack_int LAPACKE_ctprfb( int matrix_order, char side, char trans, char direct,
+ char storev, lapack_int m, lapack_int n,
+ lapack_int k, lapack_int l,
+ const lapack_complex_float* v, lapack_int ldv,
+ const lapack_complex_float* t, lapack_int ldt,
+ lapack_complex_float* a, lapack_int lda,
+ lapack_complex_float* b, lapack_int ldb,
+ lapack_int myldwork );
+lapack_int LAPACKE_ztprfb( int matrix_order, char side, char trans, char direct,
+ char storev, lapack_int m, lapack_int n,
+ lapack_int k, lapack_int l,
+ const lapack_complex_double* v, lapack_int ldv,
+ const lapack_complex_double* t, lapack_int ldt,
+ lapack_complex_double* a, lapack_int lda,
+ lapack_complex_double* b, lapack_int ldb,
+ lapack_int myldwork );
+
+lapack_int LAPACKE_sgemqrt_work( int matrix_order, char side, char trans,
+ lapack_int m, lapack_int n, lapack_int k,
+ lapack_int nb, const float* v, lapack_int ldv,
+ const float* t, lapack_int ldt, float* c,
+ lapack_int ldc, float* work );
+lapack_int LAPACKE_dgemqrt_work( int matrix_order, char side, char trans,
+ lapack_int m, lapack_int n, lapack_int k,
+ lapack_int nb, const double* v, lapack_int ldv,
+ const double* t, lapack_int ldt, double* c,
+ lapack_int ldc, double* work );
+lapack_int LAPACKE_cgemqrt_work( int matrix_order, char side, char trans,
+ lapack_int m, lapack_int n, lapack_int k,
+ lapack_int nb, const lapack_complex_float* v,
+ lapack_int ldv, const lapack_complex_float* t,
+ lapack_int ldt, lapack_complex_float* c,
+ lapack_int ldc, lapack_complex_float* work );
+lapack_int LAPACKE_zgemqrt_work( int matrix_order, char side, char trans,
+ lapack_int m, lapack_int n, lapack_int k,
+ lapack_int nb, const lapack_complex_double* v,
+ lapack_int ldv, const lapack_complex_double* t,
+ lapack_int ldt, lapack_complex_double* c,
+ lapack_int ldc, lapack_complex_double* work );
+
+lapack_int LAPACKE_sgeqrt_work( int matrix_order, lapack_int m, lapack_int n,
+ lapack_int nb, float* a, lapack_int lda,
+ float* t, lapack_int ldt, float* work );
+lapack_int LAPACKE_dgeqrt_work( int matrix_order, lapack_int m, lapack_int n,
+ lapack_int nb, double* a, lapack_int lda,
+ double* t, lapack_int ldt, double* work );
+lapack_int LAPACKE_cgeqrt_work( int matrix_order, lapack_int m, lapack_int n,
+ lapack_int nb, lapack_complex_float* a,
+ lapack_int lda, lapack_complex_float* t,
+ lapack_int ldt, lapack_complex_float* work );
+lapack_int LAPACKE_zgeqrt_work( int matrix_order, lapack_int m, lapack_int n,
+ lapack_int nb, lapack_complex_double* a,
+ lapack_int lda, lapack_complex_double* t,
+ lapack_int ldt, lapack_complex_double* work );
+
+lapack_int LAPACKE_sgeqrt2_work( int matrix_order, lapack_int m, lapack_int n,
+ float* a, lapack_int lda, float* t,
+ lapack_int ldt );
+lapack_int LAPACKE_dgeqrt2_work( int matrix_order, lapack_int m, lapack_int n,
+ double* a, lapack_int lda, double* t,
+ lapack_int ldt );
+lapack_int LAPACKE_cgeqrt2_work( int matrix_order, lapack_int m, lapack_int n,
+ lapack_complex_float* a, lapack_int lda,
+ lapack_complex_float* t, lapack_int ldt );
+lapack_int LAPACKE_zgeqrt2_work( int matrix_order, lapack_int m, lapack_int n,
+ lapack_complex_double* a, lapack_int lda,
+ lapack_complex_double* t, lapack_int ldt );
+
+lapack_int LAPACKE_sgeqrt3_work( int matrix_order, lapack_int m, lapack_int n,
+ float* a, lapack_int lda, float* t,
+ lapack_int ldt );
+lapack_int LAPACKE_dgeqrt3_work( int matrix_order, lapack_int m, lapack_int n,
+ double* a, lapack_int lda, double* t,
+ lapack_int ldt );
+lapack_int LAPACKE_cgeqrt3_work( int matrix_order, lapack_int m, lapack_int n,
+ lapack_complex_float* a, lapack_int lda,
+ lapack_complex_float* t, lapack_int ldt );
+lapack_int LAPACKE_zgeqrt3_work( int matrix_order, lapack_int m, lapack_int n,
+ lapack_complex_double* a, lapack_int lda,
+ lapack_complex_double* t, lapack_int ldt );
+
+lapack_int LAPACKE_stpmqrt_work( int matrix_order, char side, char trans,
+ lapack_int m, lapack_int n, lapack_int k,
+ lapack_int l, lapack_int nb, const float* v,
+ lapack_int ldv, const float* t, lapack_int ldt,
+ float* a, lapack_int lda, float* b,
+ lapack_int ldb, float* work );
+lapack_int LAPACKE_dtpmqrt_work( int matrix_order, char side, char trans,
+ lapack_int m, lapack_int n, lapack_int k,
+ lapack_int l, lapack_int nb, const double* v,
+ lapack_int ldv, const double* t,
+ lapack_int ldt, double* a, lapack_int lda,
+ double* b, lapack_int ldb, double* work );
+lapack_int LAPACKE_ctpmqrt_work( int matrix_order, char side, char trans,
+ lapack_int m, lapack_int n, lapack_int k,
+ lapack_int l, lapack_int nb,
+ const lapack_complex_float* v, lapack_int ldv,
+ const lapack_complex_float* t, lapack_int ldt,
+ lapack_complex_float* a, lapack_int lda,
+ lapack_complex_float* b, lapack_int ldb,
+ lapack_complex_float* work );
+lapack_int LAPACKE_ztpmqrt_work( int matrix_order, char side, char trans,
+ lapack_int m, lapack_int n, lapack_int k,
+ lapack_int l, lapack_int nb,
+ const lapack_complex_double* v, lapack_int ldv,
+ const lapack_complex_double* t, lapack_int ldt,
+ lapack_complex_double* a, lapack_int lda,
+ lapack_complex_double* b, lapack_int ldb,
+ lapack_complex_double* work );
+
+lapack_int LAPACKE_dtpqrt_work( int matrix_order, lapack_int m, lapack_int n,
+ lapack_int l, lapack_int nb, double* a,
+ lapack_int lda, double* b, lapack_int ldb,
+ double* t, lapack_int ldt, double* work );
+lapack_int LAPACKE_ctpqrt_work( int matrix_order, lapack_int m, lapack_int n,
+ lapack_int l, lapack_int nb,
+ lapack_complex_float* a, lapack_int lda,
+ lapack_complex_float* t,
+ lapack_complex_float* b, lapack_int ldb,
+ lapack_int ldt, lapack_complex_float* work );
+lapack_int LAPACKE_ztpqrt_work( int matrix_order, lapack_int m, lapack_int n,
+ lapack_int l, lapack_int nb,
+ lapack_complex_double* a, lapack_int lda,
+ lapack_complex_double* b, lapack_int ldb,
+ lapack_complex_double* t, lapack_int ldt,
+ lapack_complex_double* work );
+
+lapack_int LAPACKE_stpqrt2_work( int matrix_order, lapack_int m, lapack_int n,
+ float* a, lapack_int lda, float* b,
+ lapack_int ldb, float* t, lapack_int ldt );
+lapack_int LAPACKE_dtpqrt2_work( int matrix_order, lapack_int m, lapack_int n,
+ double* a, lapack_int lda, double* b,
+ lapack_int ldb, double* t, lapack_int ldt );
+lapack_int LAPACKE_ctpqrt2_work( int matrix_order, lapack_int m, lapack_int n,
+ lapack_complex_float* a, lapack_int lda,
+ lapack_complex_float* b, lapack_int ldb,
+ lapack_complex_float* t, lapack_int ldt );
+lapack_int LAPACKE_ztpqrt2_work( int matrix_order, lapack_int m, lapack_int n,
+ lapack_complex_double* a, lapack_int lda,
+ lapack_complex_double* b, lapack_int ldb,
+ lapack_complex_double* t, lapack_int ldt );
+
+lapack_int LAPACKE_stprfb_work( int matrix_order, char side, char trans,
+ char direct, char storev, lapack_int m,
+ lapack_int n, lapack_int k, lapack_int l,
+ const float* v, lapack_int ldv, const float* t,
+ lapack_int ldt, float* a, lapack_int lda,
+ float* b, lapack_int ldb, const float* mywork,
+ lapack_int myldwork );
+lapack_int LAPACKE_dtprfb_work( int matrix_order, char side, char trans,
+ char direct, char storev, lapack_int m,
+ lapack_int n, lapack_int k, lapack_int l,
+ const double* v, lapack_int ldv,
+ const double* t, lapack_int ldt, double* a,
+ lapack_int lda, double* b, lapack_int ldb,
+ const double* mywork, lapack_int myldwork );
+lapack_int LAPACKE_ctprfb_work( int matrix_order, char side, char trans,
+ char direct, char storev, lapack_int m,
+ lapack_int n, lapack_int k, lapack_int l,
+ const lapack_complex_float* v, lapack_int ldv,
+ const lapack_complex_float* t, lapack_int ldt,
+ lapack_complex_float* a, lapack_int lda,
+ lapack_complex_float* b, lapack_int ldb,
+ const float* mywork, lapack_int myldwork );
+lapack_int LAPACKE_ztprfb_work( int matrix_order, char side, char trans,
+ char direct, char storev, lapack_int m,
+ lapack_int n, lapack_int k, lapack_int l,
+ const lapack_complex_double* v, lapack_int ldv,
+ const lapack_complex_double* t, lapack_int ldt,
+ lapack_complex_double* a, lapack_int lda,
+ lapack_complex_double* b, lapack_int ldb,
+ const double* mywork, lapack_int myldwork );
+//LAPACK 3.X.X
+lapack_int LAPACKE_csyr( int matrix_order, char uplo, lapack_int n,
+ lapack_complex_float alpha,
+ const lapack_complex_float* x, lapack_int incx,
+ lapack_complex_float* a, lapack_int lda );
+lapack_int LAPACKE_zsyr( int matrix_order, char uplo, lapack_int n,
+ lapack_complex_double alpha,
+ const lapack_complex_double* x, lapack_int incx,
+ lapack_complex_double* a, lapack_int lda );
+
+lapack_int LAPACKE_csyr_work( int matrix_order, char uplo, lapack_int n,
+ lapack_complex_float alpha,
+ const lapack_complex_float* x,
+ lapack_int incx, lapack_complex_float* a,
+ lapack_int lda );
+lapack_int LAPACKE_zsyr_work( int matrix_order, char uplo, lapack_int n,
+ lapack_complex_double alpha,
+ const lapack_complex_double* x,
+ lapack_int incx, lapack_complex_double* a,
+ lapack_int lda );
+
+
+
+#define LAPACK_sgetrf LAPACK_GLOBAL(sgetrf,SGETRF)
+#define LAPACK_dgetrf LAPACK_GLOBAL(dgetrf,DGETRF)
+#define LAPACK_cgetrf LAPACK_GLOBAL(cgetrf,CGETRF)
+#define LAPACK_zgetrf LAPACK_GLOBAL(zgetrf,ZGETRF)
+#define LAPACK_sgbtrf LAPACK_GLOBAL(sgbtrf,SGBTRF)
+#define LAPACK_dgbtrf LAPACK_GLOBAL(dgbtrf,DGBTRF)
+#define LAPACK_cgbtrf LAPACK_GLOBAL(cgbtrf,CGBTRF)
+#define LAPACK_zgbtrf LAPACK_GLOBAL(zgbtrf,ZGBTRF)
+#define LAPACK_sgttrf LAPACK_GLOBAL(sgttrf,SGTTRF)
+#define LAPACK_dgttrf LAPACK_GLOBAL(dgttrf,DGTTRF)
+#define LAPACK_cgttrf LAPACK_GLOBAL(cgttrf,CGTTRF)
+#define LAPACK_zgttrf LAPACK_GLOBAL(zgttrf,ZGTTRF)
+#define LAPACK_spotrf LAPACK_GLOBAL(spotrf,SPOTRF)
+#define LAPACK_dpotrf LAPACK_GLOBAL(dpotrf,DPOTRF)
+#define LAPACK_cpotrf LAPACK_GLOBAL(cpotrf,CPOTRF)
+#define LAPACK_zpotrf LAPACK_GLOBAL(zpotrf,ZPOTRF)
+#define LAPACK_dpstrf LAPACK_GLOBAL(dpstrf,DPSTRF)
+#define LAPACK_spstrf LAPACK_GLOBAL(spstrf,SPSTRF)
+#define LAPACK_zpstrf LAPACK_GLOBAL(zpstrf,ZPSTRF)
+#define LAPACK_cpstrf LAPACK_GLOBAL(cpstrf,CPSTRF)
+#define LAPACK_dpftrf LAPACK_GLOBAL(dpftrf,DPFTRF)
+#define LAPACK_spftrf LAPACK_GLOBAL(spftrf,SPFTRF)
+#define LAPACK_zpftrf LAPACK_GLOBAL(zpftrf,ZPFTRF)
+#define LAPACK_cpftrf LAPACK_GLOBAL(cpftrf,CPFTRF)
+#define LAPACK_spptrf LAPACK_GLOBAL(spptrf,SPPTRF)
+#define LAPACK_dpptrf LAPACK_GLOBAL(dpptrf,DPPTRF)
+#define LAPACK_cpptrf LAPACK_GLOBAL(cpptrf,CPPTRF)
+#define LAPACK_zpptrf LAPACK_GLOBAL(zpptrf,ZPPTRF)
+#define LAPACK_spbtrf LAPACK_GLOBAL(spbtrf,SPBTRF)
+#define LAPACK_dpbtrf LAPACK_GLOBAL(dpbtrf,DPBTRF)
+#define LAPACK_cpbtrf LAPACK_GLOBAL(cpbtrf,CPBTRF)
+#define LAPACK_zpbtrf LAPACK_GLOBAL(zpbtrf,ZPBTRF)
+#define LAPACK_spttrf LAPACK_GLOBAL(spttrf,SPTTRF)
+#define LAPACK_dpttrf LAPACK_GLOBAL(dpttrf,DPTTRF)
+#define LAPACK_cpttrf LAPACK_GLOBAL(cpttrf,CPTTRF)
+#define LAPACK_zpttrf LAPACK_GLOBAL(zpttrf,ZPTTRF)
+#define LAPACK_ssytrf LAPACK_GLOBAL(ssytrf,SSYTRF)
+#define LAPACK_dsytrf LAPACK_GLOBAL(dsytrf,DSYTRF)
+#define LAPACK_csytrf LAPACK_GLOBAL(csytrf,CSYTRF)
+#define LAPACK_zsytrf LAPACK_GLOBAL(zsytrf,ZSYTRF)
+#define LAPACK_chetrf LAPACK_GLOBAL(chetrf,CHETRF)
+#define LAPACK_zhetrf LAPACK_GLOBAL(zhetrf,ZHETRF)
+#define LAPACK_ssptrf LAPACK_GLOBAL(ssptrf,SSPTRF)
+#define LAPACK_dsptrf LAPACK_GLOBAL(dsptrf,DSPTRF)
+#define LAPACK_csptrf LAPACK_GLOBAL(csptrf,CSPTRF)
+#define LAPACK_zsptrf LAPACK_GLOBAL(zsptrf,ZSPTRF)
+#define LAPACK_chptrf LAPACK_GLOBAL(chptrf,CHPTRF)
+#define LAPACK_zhptrf LAPACK_GLOBAL(zhptrf,ZHPTRF)
+#define LAPACK_sgetrs LAPACK_GLOBAL(sgetrs,SGETRS)
+#define LAPACK_dgetrs LAPACK_GLOBAL(dgetrs,DGETRS)
+#define LAPACK_cgetrs LAPACK_GLOBAL(cgetrs,CGETRS)
+#define LAPACK_zgetrs LAPACK_GLOBAL(zgetrs,ZGETRS)
+#define LAPACK_sgbtrs LAPACK_GLOBAL(sgbtrs,SGBTRS)
+#define LAPACK_dgbtrs LAPACK_GLOBAL(dgbtrs,DGBTRS)
+#define LAPACK_cgbtrs LAPACK_GLOBAL(cgbtrs,CGBTRS)
+#define LAPACK_zgbtrs LAPACK_GLOBAL(zgbtrs,ZGBTRS)
+#define LAPACK_sgttrs LAPACK_GLOBAL(sgttrs,SGTTRS)
+#define LAPACK_dgttrs LAPACK_GLOBAL(dgttrs,DGTTRS)
+#define LAPACK_cgttrs LAPACK_GLOBAL(cgttrs,CGTTRS)
+#define LAPACK_zgttrs LAPACK_GLOBAL(zgttrs,ZGTTRS)
+#define LAPACK_spotrs LAPACK_GLOBAL(spotrs,SPOTRS)
+#define LAPACK_dpotrs LAPACK_GLOBAL(dpotrs,DPOTRS)
+#define LAPACK_cpotrs LAPACK_GLOBAL(cpotrs,CPOTRS)
+#define LAPACK_zpotrs LAPACK_GLOBAL(zpotrs,ZPOTRS)
+#define LAPACK_dpftrs LAPACK_GLOBAL(dpftrs,DPFTRS)
+#define LAPACK_spftrs LAPACK_GLOBAL(spftrs,SPFTRS)
+#define LAPACK_zpftrs LAPACK_GLOBAL(zpftrs,ZPFTRS)
+#define LAPACK_cpftrs LAPACK_GLOBAL(cpftrs,CPFTRS)
+#define LAPACK_spptrs LAPACK_GLOBAL(spptrs,SPPTRS)
+#define LAPACK_dpptrs LAPACK_GLOBAL(dpptrs,DPPTRS)
+#define LAPACK_cpptrs LAPACK_GLOBAL(cpptrs,CPPTRS)
+#define LAPACK_zpptrs LAPACK_GLOBAL(zpptrs,ZPPTRS)
+#define LAPACK_spbtrs LAPACK_GLOBAL(spbtrs,SPBTRS)
+#define LAPACK_dpbtrs LAPACK_GLOBAL(dpbtrs,DPBTRS)
+#define LAPACK_cpbtrs LAPACK_GLOBAL(cpbtrs,CPBTRS)
+#define LAPACK_zpbtrs LAPACK_GLOBAL(zpbtrs,ZPBTRS)
+#define LAPACK_spttrs LAPACK_GLOBAL(spttrs,SPTTRS)
+#define LAPACK_dpttrs LAPACK_GLOBAL(dpttrs,DPTTRS)
+#define LAPACK_cpttrs LAPACK_GLOBAL(cpttrs,CPTTRS)
+#define LAPACK_zpttrs LAPACK_GLOBAL(zpttrs,ZPTTRS)
+#define LAPACK_ssytrs LAPACK_GLOBAL(ssytrs,SSYTRS)
+#define LAPACK_dsytrs LAPACK_GLOBAL(dsytrs,DSYTRS)
+#define LAPACK_csytrs LAPACK_GLOBAL(csytrs,CSYTRS)
+#define LAPACK_zsytrs LAPACK_GLOBAL(zsytrs,ZSYTRS)
+#define LAPACK_chetrs LAPACK_GLOBAL(chetrs,CHETRS)
+#define LAPACK_zhetrs LAPACK_GLOBAL(zhetrs,ZHETRS)
+#define LAPACK_ssptrs LAPACK_GLOBAL(ssptrs,SSPTRS)
+#define LAPACK_dsptrs LAPACK_GLOBAL(dsptrs,DSPTRS)
+#define LAPACK_csptrs LAPACK_GLOBAL(csptrs,CSPTRS)
+#define LAPACK_zsptrs LAPACK_GLOBAL(zsptrs,ZSPTRS)
+#define LAPACK_chptrs LAPACK_GLOBAL(chptrs,CHPTRS)
+#define LAPACK_zhptrs LAPACK_GLOBAL(zhptrs,ZHPTRS)
+#define LAPACK_strtrs LAPACK_GLOBAL(strtrs,STRTRS)
+#define LAPACK_dtrtrs LAPACK_GLOBAL(dtrtrs,DTRTRS)
+#define LAPACK_ctrtrs LAPACK_GLOBAL(ctrtrs,CTRTRS)
+#define LAPACK_ztrtrs LAPACK_GLOBAL(ztrtrs,ZTRTRS)
+#define LAPACK_stptrs LAPACK_GLOBAL(stptrs,STPTRS)
+#define LAPACK_dtptrs LAPACK_GLOBAL(dtptrs,DTPTRS)
+#define LAPACK_ctptrs LAPACK_GLOBAL(ctptrs,CTPTRS)
+#define LAPACK_ztptrs LAPACK_GLOBAL(ztptrs,ZTPTRS)
+#define LAPACK_stbtrs LAPACK_GLOBAL(stbtrs,STBTRS)
+#define LAPACK_dtbtrs LAPACK_GLOBAL(dtbtrs,DTBTRS)
+#define LAPACK_ctbtrs LAPACK_GLOBAL(ctbtrs,CTBTRS)
+#define LAPACK_ztbtrs LAPACK_GLOBAL(ztbtrs,ZTBTRS)
+#define LAPACK_sgecon LAPACK_GLOBAL(sgecon,SGECON)
+#define LAPACK_dgecon LAPACK_GLOBAL(dgecon,DGECON)
+#define LAPACK_cgecon LAPACK_GLOBAL(cgecon,CGECON)
+#define LAPACK_zgecon LAPACK_GLOBAL(zgecon,ZGECON)
+#define LAPACK_sgbcon LAPACK_GLOBAL(sgbcon,SGBCON)
+#define LAPACK_dgbcon LAPACK_GLOBAL(dgbcon,DGBCON)
+#define LAPACK_cgbcon LAPACK_GLOBAL(cgbcon,CGBCON)
+#define LAPACK_zgbcon LAPACK_GLOBAL(zgbcon,ZGBCON)
+#define LAPACK_sgtcon LAPACK_GLOBAL(sgtcon,SGTCON)
+#define LAPACK_dgtcon LAPACK_GLOBAL(dgtcon,DGTCON)
+#define LAPACK_cgtcon LAPACK_GLOBAL(cgtcon,CGTCON)
+#define LAPACK_zgtcon LAPACK_GLOBAL(zgtcon,ZGTCON)
+#define LAPACK_spocon LAPACK_GLOBAL(spocon,SPOCON)
+#define LAPACK_dpocon LAPACK_GLOBAL(dpocon,DPOCON)
+#define LAPACK_cpocon LAPACK_GLOBAL(cpocon,CPOCON)
+#define LAPACK_zpocon LAPACK_GLOBAL(zpocon,ZPOCON)
+#define LAPACK_sppcon LAPACK_GLOBAL(sppcon,SPPCON)
+#define LAPACK_dppcon LAPACK_GLOBAL(dppcon,DPPCON)
+#define LAPACK_cppcon LAPACK_GLOBAL(cppcon,CPPCON)
+#define LAPACK_zppcon LAPACK_GLOBAL(zppcon,ZPPCON)
+#define LAPACK_spbcon LAPACK_GLOBAL(spbcon,SPBCON)
+#define LAPACK_dpbcon LAPACK_GLOBAL(dpbcon,DPBCON)
+#define LAPACK_cpbcon LAPACK_GLOBAL(cpbcon,CPBCON)
+#define LAPACK_zpbcon LAPACK_GLOBAL(zpbcon,ZPBCON)
+#define LAPACK_sptcon LAPACK_GLOBAL(sptcon,SPTCON)
+#define LAPACK_dptcon LAPACK_GLOBAL(dptcon,DPTCON)
+#define LAPACK_cptcon LAPACK_GLOBAL(cptcon,CPTCON)
+#define LAPACK_zptcon LAPACK_GLOBAL(zptcon,ZPTCON)
+#define LAPACK_ssycon LAPACK_GLOBAL(ssycon,SSYCON)
+#define LAPACK_dsycon LAPACK_GLOBAL(dsycon,DSYCON)
+#define LAPACK_csycon LAPACK_GLOBAL(csycon,CSYCON)
+#define LAPACK_zsycon LAPACK_GLOBAL(zsycon,ZSYCON)
+#define LAPACK_checon LAPACK_GLOBAL(checon,CHECON)
+#define LAPACK_zhecon LAPACK_GLOBAL(zhecon,ZHECON)
+#define LAPACK_sspcon LAPACK_GLOBAL(sspcon,SSPCON)
+#define LAPACK_dspcon LAPACK_GLOBAL(dspcon,DSPCON)
+#define LAPACK_cspcon LAPACK_GLOBAL(cspcon,CSPCON)
+#define LAPACK_zspcon LAPACK_GLOBAL(zspcon,ZSPCON)
+#define LAPACK_chpcon LAPACK_GLOBAL(chpcon,CHPCON)
+#define LAPACK_zhpcon LAPACK_GLOBAL(zhpcon,ZHPCON)
+#define LAPACK_strcon LAPACK_GLOBAL(strcon,STRCON)
+#define LAPACK_dtrcon LAPACK_GLOBAL(dtrcon,DTRCON)
+#define LAPACK_ctrcon LAPACK_GLOBAL(ctrcon,CTRCON)
+#define LAPACK_ztrcon LAPACK_GLOBAL(ztrcon,ZTRCON)
+#define LAPACK_stpcon LAPACK_GLOBAL(stpcon,STPCON)
+#define LAPACK_dtpcon LAPACK_GLOBAL(dtpcon,DTPCON)
+#define LAPACK_ctpcon LAPACK_GLOBAL(ctpcon,CTPCON)
+#define LAPACK_ztpcon LAPACK_GLOBAL(ztpcon,ZTPCON)
+#define LAPACK_stbcon LAPACK_GLOBAL(stbcon,STBCON)
+#define LAPACK_dtbcon LAPACK_GLOBAL(dtbcon,DTBCON)
+#define LAPACK_ctbcon LAPACK_GLOBAL(ctbcon,CTBCON)
+#define LAPACK_ztbcon LAPACK_GLOBAL(ztbcon,ZTBCON)
+#define LAPACK_sgerfs LAPACK_GLOBAL(sgerfs,SGERFS)
+#define LAPACK_dgerfs LAPACK_GLOBAL(dgerfs,DGERFS)
+#define LAPACK_cgerfs LAPACK_GLOBAL(cgerfs,CGERFS)
+#define LAPACK_zgerfs LAPACK_GLOBAL(zgerfs,ZGERFS)
+#define LAPACK_dgerfsx LAPACK_GLOBAL(dgerfsx,DGERFSX)
+#define LAPACK_sgerfsx LAPACK_GLOBAL(sgerfsx,SGERFSX)
+#define LAPACK_zgerfsx LAPACK_GLOBAL(zgerfsx,ZGERFSX)
+#define LAPACK_cgerfsx LAPACK_GLOBAL(cgerfsx,CGERFSX)
+#define LAPACK_sgbrfs LAPACK_GLOBAL(sgbrfs,SGBRFS)
+#define LAPACK_dgbrfs LAPACK_GLOBAL(dgbrfs,DGBRFS)
+#define LAPACK_cgbrfs LAPACK_GLOBAL(cgbrfs,CGBRFS)
+#define LAPACK_zgbrfs LAPACK_GLOBAL(zgbrfs,ZGBRFS)
+#define LAPACK_dgbrfsx LAPACK_GLOBAL(dgbrfsx,DGBRFSX)
+#define LAPACK_sgbrfsx LAPACK_GLOBAL(sgbrfsx,SGBRFSX)
+#define LAPACK_zgbrfsx LAPACK_GLOBAL(zgbrfsx,ZGBRFSX)
+#define LAPACK_cgbrfsx LAPACK_GLOBAL(cgbrfsx,CGBRFSX)
+#define LAPACK_sgtrfs LAPACK_GLOBAL(sgtrfs,SGTRFS)
+#define LAPACK_dgtrfs LAPACK_GLOBAL(dgtrfs,DGTRFS)
+#define LAPACK_cgtrfs LAPACK_GLOBAL(cgtrfs,CGTRFS)
+#define LAPACK_zgtrfs LAPACK_GLOBAL(zgtrfs,ZGTRFS)
+#define LAPACK_sporfs LAPACK_GLOBAL(sporfs,SPORFS)
+#define LAPACK_dporfs LAPACK_GLOBAL(dporfs,DPORFS)
+#define LAPACK_cporfs LAPACK_GLOBAL(cporfs,CPORFS)
+#define LAPACK_zporfs LAPACK_GLOBAL(zporfs,ZPORFS)
+#define LAPACK_dporfsx LAPACK_GLOBAL(dporfsx,DPORFSX)
+#define LAPACK_sporfsx LAPACK_GLOBAL(sporfsx,SPORFSX)
+#define LAPACK_zporfsx LAPACK_GLOBAL(zporfsx,ZPORFSX)
+#define LAPACK_cporfsx LAPACK_GLOBAL(cporfsx,CPORFSX)
+#define LAPACK_spprfs LAPACK_GLOBAL(spprfs,SPPRFS)
+#define LAPACK_dpprfs LAPACK_GLOBAL(dpprfs,DPPRFS)
+#define LAPACK_cpprfs LAPACK_GLOBAL(cpprfs,CPPRFS)
+#define LAPACK_zpprfs LAPACK_GLOBAL(zpprfs,ZPPRFS)
+#define LAPACK_spbrfs LAPACK_GLOBAL(spbrfs,SPBRFS)
+#define LAPACK_dpbrfs LAPACK_GLOBAL(dpbrfs,DPBRFS)
+#define LAPACK_cpbrfs LAPACK_GLOBAL(cpbrfs,CPBRFS)
+#define LAPACK_zpbrfs LAPACK_GLOBAL(zpbrfs,ZPBRFS)
+#define LAPACK_sptrfs LAPACK_GLOBAL(sptrfs,SPTRFS)
+#define LAPACK_dptrfs LAPACK_GLOBAL(dptrfs,DPTRFS)
+#define LAPACK_cptrfs LAPACK_GLOBAL(cptrfs,CPTRFS)
+#define LAPACK_zptrfs LAPACK_GLOBAL(zptrfs,ZPTRFS)
+#define LAPACK_ssyrfs LAPACK_GLOBAL(ssyrfs,SSYRFS)
+#define LAPACK_dsyrfs LAPACK_GLOBAL(dsyrfs,DSYRFS)
+#define LAPACK_csyrfs LAPACK_GLOBAL(csyrfs,CSYRFS)
+#define LAPACK_zsyrfs LAPACK_GLOBAL(zsyrfs,ZSYRFS)
+#define LAPACK_dsyrfsx LAPACK_GLOBAL(dsyrfsx,DSYRFSX)
+#define LAPACK_ssyrfsx LAPACK_GLOBAL(ssyrfsx,SSYRFSX)
+#define LAPACK_zsyrfsx LAPACK_GLOBAL(zsyrfsx,ZSYRFSX)
+#define LAPACK_csyrfsx LAPACK_GLOBAL(csyrfsx,CSYRFSX)
+#define LAPACK_cherfs LAPACK_GLOBAL(cherfs,CHERFS)
+#define LAPACK_zherfs LAPACK_GLOBAL(zherfs,ZHERFS)
+#define LAPACK_zherfsx LAPACK_GLOBAL(zherfsx,ZHERFSX)
+#define LAPACK_cherfsx LAPACK_GLOBAL(cherfsx,CHERFSX)
+#define LAPACK_ssprfs LAPACK_GLOBAL(ssprfs,SSPRFS)
+#define LAPACK_dsprfs LAPACK_GLOBAL(dsprfs,DSPRFS)
+#define LAPACK_csprfs LAPACK_GLOBAL(csprfs,CSPRFS)
+#define LAPACK_zsprfs LAPACK_GLOBAL(zsprfs,ZSPRFS)
+#define LAPACK_chprfs LAPACK_GLOBAL(chprfs,CHPRFS)
+#define LAPACK_zhprfs LAPACK_GLOBAL(zhprfs,ZHPRFS)
+#define LAPACK_strrfs LAPACK_GLOBAL(strrfs,STRRFS)
+#define LAPACK_dtrrfs LAPACK_GLOBAL(dtrrfs,DTRRFS)
+#define LAPACK_ctrrfs LAPACK_GLOBAL(ctrrfs,CTRRFS)
+#define LAPACK_ztrrfs LAPACK_GLOBAL(ztrrfs,ZTRRFS)
+#define LAPACK_stprfs LAPACK_GLOBAL(stprfs,STPRFS)
+#define LAPACK_dtprfs LAPACK_GLOBAL(dtprfs,DTPRFS)
+#define LAPACK_ctprfs LAPACK_GLOBAL(ctprfs,CTPRFS)
+#define LAPACK_ztprfs LAPACK_GLOBAL(ztprfs,ZTPRFS)
+#define LAPACK_stbrfs LAPACK_GLOBAL(stbrfs,STBRFS)
+#define LAPACK_dtbrfs LAPACK_GLOBAL(dtbrfs,DTBRFS)
+#define LAPACK_ctbrfs LAPACK_GLOBAL(ctbrfs,CTBRFS)
+#define LAPACK_ztbrfs LAPACK_GLOBAL(ztbrfs,ZTBRFS)
+#define LAPACK_sgetri LAPACK_GLOBAL(sgetri,SGETRI)
+#define LAPACK_dgetri LAPACK_GLOBAL(dgetri,DGETRI)
+#define LAPACK_cgetri LAPACK_GLOBAL(cgetri,CGETRI)
+#define LAPACK_zgetri LAPACK_GLOBAL(zgetri,ZGETRI)
+#define LAPACK_spotri LAPACK_GLOBAL(spotri,SPOTRI)
+#define LAPACK_dpotri LAPACK_GLOBAL(dpotri,DPOTRI)
+#define LAPACK_cpotri LAPACK_GLOBAL(cpotri,CPOTRI)
+#define LAPACK_zpotri LAPACK_GLOBAL(zpotri,ZPOTRI)
+#define LAPACK_dpftri LAPACK_GLOBAL(dpftri,DPFTRI)
+#define LAPACK_spftri LAPACK_GLOBAL(spftri,SPFTRI)
+#define LAPACK_zpftri LAPACK_GLOBAL(zpftri,ZPFTRI)
+#define LAPACK_cpftri LAPACK_GLOBAL(cpftri,CPFTRI)
+#define LAPACK_spptri LAPACK_GLOBAL(spptri,SPPTRI)
+#define LAPACK_dpptri LAPACK_GLOBAL(dpptri,DPPTRI)
+#define LAPACK_cpptri LAPACK_GLOBAL(cpptri,CPPTRI)
+#define LAPACK_zpptri LAPACK_GLOBAL(zpptri,ZPPTRI)
+#define LAPACK_ssytri LAPACK_GLOBAL(ssytri,SSYTRI)
+#define LAPACK_dsytri LAPACK_GLOBAL(dsytri,DSYTRI)
+#define LAPACK_csytri LAPACK_GLOBAL(csytri,CSYTRI)
+#define LAPACK_zsytri LAPACK_GLOBAL(zsytri,ZSYTRI)
+#define LAPACK_chetri LAPACK_GLOBAL(chetri,CHETRI)
+#define LAPACK_zhetri LAPACK_GLOBAL(zhetri,ZHETRI)
+#define LAPACK_ssptri LAPACK_GLOBAL(ssptri,SSPTRI)
+#define LAPACK_dsptri LAPACK_GLOBAL(dsptri,DSPTRI)
+#define LAPACK_csptri LAPACK_GLOBAL(csptri,CSPTRI)
+#define LAPACK_zsptri LAPACK_GLOBAL(zsptri,ZSPTRI)
+#define LAPACK_chptri LAPACK_GLOBAL(chptri,CHPTRI)
+#define LAPACK_zhptri LAPACK_GLOBAL(zhptri,ZHPTRI)
+#define LAPACK_strtri LAPACK_GLOBAL(strtri,STRTRI)
+#define LAPACK_dtrtri LAPACK_GLOBAL(dtrtri,DTRTRI)
+#define LAPACK_ctrtri LAPACK_GLOBAL(ctrtri,CTRTRI)
+#define LAPACK_ztrtri LAPACK_GLOBAL(ztrtri,ZTRTRI)
+#define LAPACK_dtftri LAPACK_GLOBAL(dtftri,DTFTRI)
+#define LAPACK_stftri LAPACK_GLOBAL(stftri,STFTRI)
+#define LAPACK_ztftri LAPACK_GLOBAL(ztftri,ZTFTRI)
+#define LAPACK_ctftri LAPACK_GLOBAL(ctftri,CTFTRI)
+#define LAPACK_stptri LAPACK_GLOBAL(stptri,STPTRI)
+#define LAPACK_dtptri LAPACK_GLOBAL(dtptri,DTPTRI)
+#define LAPACK_ctptri LAPACK_GLOBAL(ctptri,CTPTRI)
+#define LAPACK_ztptri LAPACK_GLOBAL(ztptri,ZTPTRI)
+#define LAPACK_sgeequ LAPACK_GLOBAL(sgeequ,SGEEQU)
+#define LAPACK_dgeequ LAPACK_GLOBAL(dgeequ,DGEEQU)
+#define LAPACK_cgeequ LAPACK_GLOBAL(cgeequ,CGEEQU)
+#define LAPACK_zgeequ LAPACK_GLOBAL(zgeequ,ZGEEQU)
+#define LAPACK_dgeequb LAPACK_GLOBAL(dgeequb,DGEEQUB)
+#define LAPACK_sgeequb LAPACK_GLOBAL(sgeequb,SGEEQUB)
+#define LAPACK_zgeequb LAPACK_GLOBAL(zgeequb,ZGEEQUB)
+#define LAPACK_cgeequb LAPACK_GLOBAL(cgeequb,CGEEQUB)
+#define LAPACK_sgbequ LAPACK_GLOBAL(sgbequ,SGBEQU)
+#define LAPACK_dgbequ LAPACK_GLOBAL(dgbequ,DGBEQU)
+#define LAPACK_cgbequ LAPACK_GLOBAL(cgbequ,CGBEQU)
+#define LAPACK_zgbequ LAPACK_GLOBAL(zgbequ,ZGBEQU)
+#define LAPACK_dgbequb LAPACK_GLOBAL(dgbequb,DGBEQUB)
+#define LAPACK_sgbequb LAPACK_GLOBAL(sgbequb,SGBEQUB)
+#define LAPACK_zgbequb LAPACK_GLOBAL(zgbequb,ZGBEQUB)
+#define LAPACK_cgbequb LAPACK_GLOBAL(cgbequb,CGBEQUB)
+#define LAPACK_spoequ LAPACK_GLOBAL(spoequ,SPOEQU)
+#define LAPACK_dpoequ LAPACK_GLOBAL(dpoequ,DPOEQU)
+#define LAPACK_cpoequ LAPACK_GLOBAL(cpoequ,CPOEQU)
+#define LAPACK_zpoequ LAPACK_GLOBAL(zpoequ,ZPOEQU)
+#define LAPACK_dpoequb LAPACK_GLOBAL(dpoequb,DPOEQUB)
+#define LAPACK_spoequb LAPACK_GLOBAL(spoequb,SPOEQUB)
+#define LAPACK_zpoequb LAPACK_GLOBAL(zpoequb,ZPOEQUB)
+#define LAPACK_cpoequb LAPACK_GLOBAL(cpoequb,CPOEQUB)
+#define LAPACK_sppequ LAPACK_GLOBAL(sppequ,SPPEQU)
+#define LAPACK_dppequ LAPACK_GLOBAL(dppequ,DPPEQU)
+#define LAPACK_cppequ LAPACK_GLOBAL(cppequ,CPPEQU)
+#define LAPACK_zppequ LAPACK_GLOBAL(zppequ,ZPPEQU)
+#define LAPACK_spbequ LAPACK_GLOBAL(spbequ,SPBEQU)
+#define LAPACK_dpbequ LAPACK_GLOBAL(dpbequ,DPBEQU)
+#define LAPACK_cpbequ LAPACK_GLOBAL(cpbequ,CPBEQU)
+#define LAPACK_zpbequ LAPACK_GLOBAL(zpbequ,ZPBEQU)
+#define LAPACK_dsyequb LAPACK_GLOBAL(dsyequb,DSYEQUB)
+#define LAPACK_ssyequb LAPACK_GLOBAL(ssyequb,SSYEQUB)
+#define LAPACK_zsyequb LAPACK_GLOBAL(zsyequb,ZSYEQUB)
+#define LAPACK_csyequb LAPACK_GLOBAL(csyequb,CSYEQUB)
+#define LAPACK_zheequb LAPACK_GLOBAL(zheequb,ZHEEQUB)
+#define LAPACK_cheequb LAPACK_GLOBAL(cheequb,CHEEQUB)
+#define LAPACK_sgesv LAPACK_GLOBAL(sgesv,SGESV)
+#define LAPACK_dgesv LAPACK_GLOBAL(dgesv,DGESV)
+#define LAPACK_cgesv LAPACK_GLOBAL(cgesv,CGESV)
+#define LAPACK_zgesv LAPACK_GLOBAL(zgesv,ZGESV)
+#define LAPACK_dsgesv LAPACK_GLOBAL(dsgesv,DSGESV)
+#define LAPACK_zcgesv LAPACK_GLOBAL(zcgesv,ZCGESV)
+#define LAPACK_sgesvx LAPACK_GLOBAL(sgesvx,SGESVX)
+#define LAPACK_dgesvx LAPACK_GLOBAL(dgesvx,DGESVX)
+#define LAPACK_cgesvx LAPACK_GLOBAL(cgesvx,CGESVX)
+#define LAPACK_zgesvx LAPACK_GLOBAL(zgesvx,ZGESVX)
+#define LAPACK_dgesvxx LAPACK_GLOBAL(dgesvxx,DGESVXX)
+#define LAPACK_sgesvxx LAPACK_GLOBAL(sgesvxx,SGESVXX)
+#define LAPACK_zgesvxx LAPACK_GLOBAL(zgesvxx,ZGESVXX)
+#define LAPACK_cgesvxx LAPACK_GLOBAL(cgesvxx,CGESVXX)
+#define LAPACK_sgbsv LAPACK_GLOBAL(sgbsv,SGBSV)
+#define LAPACK_dgbsv LAPACK_GLOBAL(dgbsv,DGBSV)
+#define LAPACK_cgbsv LAPACK_GLOBAL(cgbsv,CGBSV)
+#define LAPACK_zgbsv LAPACK_GLOBAL(zgbsv,ZGBSV)
+#define LAPACK_sgbsvx LAPACK_GLOBAL(sgbsvx,SGBSVX)
+#define LAPACK_dgbsvx LAPACK_GLOBAL(dgbsvx,DGBSVX)
+#define LAPACK_cgbsvx LAPACK_GLOBAL(cgbsvx,CGBSVX)
+#define LAPACK_zgbsvx LAPACK_GLOBAL(zgbsvx,ZGBSVX)
+#define LAPACK_dgbsvxx LAPACK_GLOBAL(dgbsvxx,DGBSVXX)
+#define LAPACK_sgbsvxx LAPACK_GLOBAL(sgbsvxx,SGBSVXX)
+#define LAPACK_zgbsvxx LAPACK_GLOBAL(zgbsvxx,ZGBSVXX)
+#define LAPACK_cgbsvxx LAPACK_GLOBAL(cgbsvxx,CGBSVXX)
+#define LAPACK_sgtsv LAPACK_GLOBAL(sgtsv,SGTSV)
+#define LAPACK_dgtsv LAPACK_GLOBAL(dgtsv,DGTSV)
+#define LAPACK_cgtsv LAPACK_GLOBAL(cgtsv,CGTSV)
+#define LAPACK_zgtsv LAPACK_GLOBAL(zgtsv,ZGTSV)
+#define LAPACK_sgtsvx LAPACK_GLOBAL(sgtsvx,SGTSVX)
+#define LAPACK_dgtsvx LAPACK_GLOBAL(dgtsvx,DGTSVX)
+#define LAPACK_cgtsvx LAPACK_GLOBAL(cgtsvx,CGTSVX)
+#define LAPACK_zgtsvx LAPACK_GLOBAL(zgtsvx,ZGTSVX)
+#define LAPACK_sposv LAPACK_GLOBAL(sposv,SPOSV)
+#define LAPACK_dposv LAPACK_GLOBAL(dposv,DPOSV)
+#define LAPACK_cposv LAPACK_GLOBAL(cposv,CPOSV)
+#define LAPACK_zposv LAPACK_GLOBAL(zposv,ZPOSV)
+#define LAPACK_dsposv LAPACK_GLOBAL(dsposv,DSPOSV)
+#define LAPACK_zcposv LAPACK_GLOBAL(zcposv,ZCPOSV)
+#define LAPACK_sposvx LAPACK_GLOBAL(sposvx,SPOSVX)
+#define LAPACK_dposvx LAPACK_GLOBAL(dposvx,DPOSVX)
+#define LAPACK_cposvx LAPACK_GLOBAL(cposvx,CPOSVX)
+#define LAPACK_zposvx LAPACK_GLOBAL(zposvx,ZPOSVX)
+#define LAPACK_dposvxx LAPACK_GLOBAL(dposvxx,DPOSVXX)
+#define LAPACK_sposvxx LAPACK_GLOBAL(sposvxx,SPOSVXX)
+#define LAPACK_zposvxx LAPACK_GLOBAL(zposvxx,ZPOSVXX)
+#define LAPACK_cposvxx LAPACK_GLOBAL(cposvxx,CPOSVXX)
+#define LAPACK_sppsv LAPACK_GLOBAL(sppsv,SPPSV)
+#define LAPACK_dppsv LAPACK_GLOBAL(dppsv,DPPSV)
+#define LAPACK_cppsv LAPACK_GLOBAL(cppsv,CPPSV)
+#define LAPACK_zppsv LAPACK_GLOBAL(zppsv,ZPPSV)
+#define LAPACK_sppsvx LAPACK_GLOBAL(sppsvx,SPPSVX)
+#define LAPACK_dppsvx LAPACK_GLOBAL(dppsvx,DPPSVX)
+#define LAPACK_cppsvx LAPACK_GLOBAL(cppsvx,CPPSVX)
+#define LAPACK_zppsvx LAPACK_GLOBAL(zppsvx,ZPPSVX)
+#define LAPACK_spbsv LAPACK_GLOBAL(spbsv,SPBSV)
+#define LAPACK_dpbsv LAPACK_GLOBAL(dpbsv,DPBSV)
+#define LAPACK_cpbsv LAPACK_GLOBAL(cpbsv,CPBSV)
+#define LAPACK_zpbsv LAPACK_GLOBAL(zpbsv,ZPBSV)
+#define LAPACK_spbsvx LAPACK_GLOBAL(spbsvx,SPBSVX)
+#define LAPACK_dpbsvx LAPACK_GLOBAL(dpbsvx,DPBSVX)
+#define LAPACK_cpbsvx LAPACK_GLOBAL(cpbsvx,CPBSVX)
+#define LAPACK_zpbsvx LAPACK_GLOBAL(zpbsvx,ZPBSVX)
+#define LAPACK_sptsv LAPACK_GLOBAL(sptsv,SPTSV)
+#define LAPACK_dptsv LAPACK_GLOBAL(dptsv,DPTSV)
+#define LAPACK_cptsv LAPACK_GLOBAL(cptsv,CPTSV)
+#define LAPACK_zptsv LAPACK_GLOBAL(zptsv,ZPTSV)
+#define LAPACK_sptsvx LAPACK_GLOBAL(sptsvx,SPTSVX)
+#define LAPACK_dptsvx LAPACK_GLOBAL(dptsvx,DPTSVX)
+#define LAPACK_cptsvx LAPACK_GLOBAL(cptsvx,CPTSVX)
+#define LAPACK_zptsvx LAPACK_GLOBAL(zptsvx,ZPTSVX)
+#define LAPACK_ssysv LAPACK_GLOBAL(ssysv,SSYSV)
+#define LAPACK_dsysv LAPACK_GLOBAL(dsysv,DSYSV)
+#define LAPACK_csysv LAPACK_GLOBAL(csysv,CSYSV)
+#define LAPACK_zsysv LAPACK_GLOBAL(zsysv,ZSYSV)
+#define LAPACK_ssysvx LAPACK_GLOBAL(ssysvx,SSYSVX)
+#define LAPACK_dsysvx LAPACK_GLOBAL(dsysvx,DSYSVX)
+#define LAPACK_csysvx LAPACK_GLOBAL(csysvx,CSYSVX)
+#define LAPACK_zsysvx LAPACK_GLOBAL(zsysvx,ZSYSVX)
+#define LAPACK_dsysvxx LAPACK_GLOBAL(dsysvxx,DSYSVXX)
+#define LAPACK_ssysvxx LAPACK_GLOBAL(ssysvxx,SSYSVXX)
+#define LAPACK_zsysvxx LAPACK_GLOBAL(zsysvxx,ZSYSVXX)
+#define LAPACK_csysvxx LAPACK_GLOBAL(csysvxx,CSYSVXX)
+#define LAPACK_chesv LAPACK_GLOBAL(chesv,CHESV)
+#define LAPACK_zhesv LAPACK_GLOBAL(zhesv,ZHESV)
+#define LAPACK_chesvx LAPACK_GLOBAL(chesvx,CHESVX)
+#define LAPACK_zhesvx LAPACK_GLOBAL(zhesvx,ZHESVX)
+#define LAPACK_zhesvxx LAPACK_GLOBAL(zhesvxx,ZHESVXX)
+#define LAPACK_chesvxx LAPACK_GLOBAL(chesvxx,CHESVXX)
+#define LAPACK_sspsv LAPACK_GLOBAL(sspsv,SSPSV)
+#define LAPACK_dspsv LAPACK_GLOBAL(dspsv,DSPSV)
+#define LAPACK_cspsv LAPACK_GLOBAL(cspsv,CSPSV)
+#define LAPACK_zspsv LAPACK_GLOBAL(zspsv,ZSPSV)
+#define LAPACK_sspsvx LAPACK_GLOBAL(sspsvx,SSPSVX)
+#define LAPACK_dspsvx LAPACK_GLOBAL(dspsvx,DSPSVX)
+#define LAPACK_cspsvx LAPACK_GLOBAL(cspsvx,CSPSVX)
+#define LAPACK_zspsvx LAPACK_GLOBAL(zspsvx,ZSPSVX)
+#define LAPACK_chpsv LAPACK_GLOBAL(chpsv,CHPSV)
+#define LAPACK_zhpsv LAPACK_GLOBAL(zhpsv,ZHPSV)
+#define LAPACK_chpsvx LAPACK_GLOBAL(chpsvx,CHPSVX)
+#define LAPACK_zhpsvx LAPACK_GLOBAL(zhpsvx,ZHPSVX)
+#define LAPACK_sgeqrf LAPACK_GLOBAL(sgeqrf,SGEQRF)
+#define LAPACK_dgeqrf LAPACK_GLOBAL(dgeqrf,DGEQRF)
+#define LAPACK_cgeqrf LAPACK_GLOBAL(cgeqrf,CGEQRF)
+#define LAPACK_zgeqrf LAPACK_GLOBAL(zgeqrf,ZGEQRF)
+#define LAPACK_sgeqpf LAPACK_GLOBAL(sgeqpf,SGEQPF)
+#define LAPACK_dgeqpf LAPACK_GLOBAL(dgeqpf,DGEQPF)
+#define LAPACK_cgeqpf LAPACK_GLOBAL(cgeqpf,CGEQPF)
+#define LAPACK_zgeqpf LAPACK_GLOBAL(zgeqpf,ZGEQPF)
+#define LAPACK_sgeqp3 LAPACK_GLOBAL(sgeqp3,SGEQP3)
+#define LAPACK_dgeqp3 LAPACK_GLOBAL(dgeqp3,DGEQP3)
+#define LAPACK_cgeqp3 LAPACK_GLOBAL(cgeqp3,CGEQP3)
+#define LAPACK_zgeqp3 LAPACK_GLOBAL(zgeqp3,ZGEQP3)
+#define LAPACK_sorgqr LAPACK_GLOBAL(sorgqr,SORGQR)
+#define LAPACK_dorgqr LAPACK_GLOBAL(dorgqr,DORGQR)
+#define LAPACK_sormqr LAPACK_GLOBAL(sormqr,SORMQR)
+#define LAPACK_dormqr LAPACK_GLOBAL(dormqr,DORMQR)
+#define LAPACK_cungqr LAPACK_GLOBAL(cungqr,CUNGQR)
+#define LAPACK_zungqr LAPACK_GLOBAL(zungqr,ZUNGQR)
+#define LAPACK_cunmqr LAPACK_GLOBAL(cunmqr,CUNMQR)
+#define LAPACK_zunmqr LAPACK_GLOBAL(zunmqr,ZUNMQR)
+#define LAPACK_sgelqf LAPACK_GLOBAL(sgelqf,SGELQF)
+#define LAPACK_dgelqf LAPACK_GLOBAL(dgelqf,DGELQF)
+#define LAPACK_cgelqf LAPACK_GLOBAL(cgelqf,CGELQF)
+#define LAPACK_zgelqf LAPACK_GLOBAL(zgelqf,ZGELQF)
+#define LAPACK_sorglq LAPACK_GLOBAL(sorglq,SORGLQ)
+#define LAPACK_dorglq LAPACK_GLOBAL(dorglq,DORGLQ)
+#define LAPACK_sormlq LAPACK_GLOBAL(sormlq,SORMLQ)
+#define LAPACK_dormlq LAPACK_GLOBAL(dormlq,DORMLQ)
+#define LAPACK_cunglq LAPACK_GLOBAL(cunglq,CUNGLQ)
+#define LAPACK_zunglq LAPACK_GLOBAL(zunglq,ZUNGLQ)
+#define LAPACK_cunmlq LAPACK_GLOBAL(cunmlq,CUNMLQ)
+#define LAPACK_zunmlq LAPACK_GLOBAL(zunmlq,ZUNMLQ)
+#define LAPACK_sgeqlf LAPACK_GLOBAL(sgeqlf,SGEQLF)
+#define LAPACK_dgeqlf LAPACK_GLOBAL(dgeqlf,DGEQLF)
+#define LAPACK_cgeqlf LAPACK_GLOBAL(cgeqlf,CGEQLF)
+#define LAPACK_zgeqlf LAPACK_GLOBAL(zgeqlf,ZGEQLF)
+#define LAPACK_sorgql LAPACK_GLOBAL(sorgql,SORGQL)
+#define LAPACK_dorgql LAPACK_GLOBAL(dorgql,DORGQL)
+#define LAPACK_cungql LAPACK_GLOBAL(cungql,CUNGQL)
+#define LAPACK_zungql LAPACK_GLOBAL(zungql,ZUNGQL)
+#define LAPACK_sormql LAPACK_GLOBAL(sormql,SORMQL)
+#define LAPACK_dormql LAPACK_GLOBAL(dormql,DORMQL)
+#define LAPACK_cunmql LAPACK_GLOBAL(cunmql,CUNMQL)
+#define LAPACK_zunmql LAPACK_GLOBAL(zunmql,ZUNMQL)
+#define LAPACK_sgerqf LAPACK_GLOBAL(sgerqf,SGERQF)
+#define LAPACK_dgerqf LAPACK_GLOBAL(dgerqf,DGERQF)
+#define LAPACK_cgerqf LAPACK_GLOBAL(cgerqf,CGERQF)
+#define LAPACK_zgerqf LAPACK_GLOBAL(zgerqf,ZGERQF)
+#define LAPACK_sorgrq LAPACK_GLOBAL(sorgrq,SORGRQ)
+#define LAPACK_dorgrq LAPACK_GLOBAL(dorgrq,DORGRQ)
+#define LAPACK_cungrq LAPACK_GLOBAL(cungrq,CUNGRQ)
+#define LAPACK_zungrq LAPACK_GLOBAL(zungrq,ZUNGRQ)
+#define LAPACK_sormrq LAPACK_GLOBAL(sormrq,SORMRQ)
+#define LAPACK_dormrq LAPACK_GLOBAL(dormrq,DORMRQ)
+#define LAPACK_cunmrq LAPACK_GLOBAL(cunmrq,CUNMRQ)
+#define LAPACK_zunmrq LAPACK_GLOBAL(zunmrq,ZUNMRQ)
+#define LAPACK_stzrzf LAPACK_GLOBAL(stzrzf,STZRZF)
+#define LAPACK_dtzrzf LAPACK_GLOBAL(dtzrzf,DTZRZF)
+#define LAPACK_ctzrzf LAPACK_GLOBAL(ctzrzf,CTZRZF)
+#define LAPACK_ztzrzf LAPACK_GLOBAL(ztzrzf,ZTZRZF)
+#define LAPACK_sormrz LAPACK_GLOBAL(sormrz,SORMRZ)
+#define LAPACK_dormrz LAPACK_GLOBAL(dormrz,DORMRZ)
+#define LAPACK_cunmrz LAPACK_GLOBAL(cunmrz,CUNMRZ)
+#define LAPACK_zunmrz LAPACK_GLOBAL(zunmrz,ZUNMRZ)
+#define LAPACK_sggqrf LAPACK_GLOBAL(sggqrf,SGGQRF)
+#define LAPACK_dggqrf LAPACK_GLOBAL(dggqrf,DGGQRF)
+#define LAPACK_cggqrf LAPACK_GLOBAL(cggqrf,CGGQRF)
+#define LAPACK_zggqrf LAPACK_GLOBAL(zggqrf,ZGGQRF)
+#define LAPACK_sggrqf LAPACK_GLOBAL(sggrqf,SGGRQF)
+#define LAPACK_dggrqf LAPACK_GLOBAL(dggrqf,DGGRQF)
+#define LAPACK_cggrqf LAPACK_GLOBAL(cggrqf,CGGRQF)
+#define LAPACK_zggrqf LAPACK_GLOBAL(zggrqf,ZGGRQF)
+#define LAPACK_sgebrd LAPACK_GLOBAL(sgebrd,SGEBRD)
+#define LAPACK_dgebrd LAPACK_GLOBAL(dgebrd,DGEBRD)
+#define LAPACK_cgebrd LAPACK_GLOBAL(cgebrd,CGEBRD)
+#define LAPACK_zgebrd LAPACK_GLOBAL(zgebrd,ZGEBRD)
+#define LAPACK_sgbbrd LAPACK_GLOBAL(sgbbrd,SGBBRD)
+#define LAPACK_dgbbrd LAPACK_GLOBAL(dgbbrd,DGBBRD)
+#define LAPACK_cgbbrd LAPACK_GLOBAL(cgbbrd,CGBBRD)
+#define LAPACK_zgbbrd LAPACK_GLOBAL(zgbbrd,ZGBBRD)
+#define LAPACK_sorgbr LAPACK_GLOBAL(sorgbr,SORGBR)
+#define LAPACK_dorgbr LAPACK_GLOBAL(dorgbr,DORGBR)
+#define LAPACK_sormbr LAPACK_GLOBAL(sormbr,SORMBR)
+#define LAPACK_dormbr LAPACK_GLOBAL(dormbr,DORMBR)
+#define LAPACK_cungbr LAPACK_GLOBAL(cungbr,CUNGBR)
+#define LAPACK_zungbr LAPACK_GLOBAL(zungbr,ZUNGBR)
+#define LAPACK_cunmbr LAPACK_GLOBAL(cunmbr,CUNMBR)
+#define LAPACK_zunmbr LAPACK_GLOBAL(zunmbr,ZUNMBR)
+#define LAPACK_sbdsqr LAPACK_GLOBAL(sbdsqr,SBDSQR)
+#define LAPACK_dbdsqr LAPACK_GLOBAL(dbdsqr,DBDSQR)
+#define LAPACK_cbdsqr LAPACK_GLOBAL(cbdsqr,CBDSQR)
+#define LAPACK_zbdsqr LAPACK_GLOBAL(zbdsqr,ZBDSQR)
+#define LAPACK_sbdsdc LAPACK_GLOBAL(sbdsdc,SBDSDC)
+#define LAPACK_dbdsdc LAPACK_GLOBAL(dbdsdc,DBDSDC)
+#define LAPACK_ssytrd LAPACK_GLOBAL(ssytrd,SSYTRD)
+#define LAPACK_dsytrd LAPACK_GLOBAL(dsytrd,DSYTRD)
+#define LAPACK_sorgtr LAPACK_GLOBAL(sorgtr,SORGTR)
+#define LAPACK_dorgtr LAPACK_GLOBAL(dorgtr,DORGTR)
+#define LAPACK_sormtr LAPACK_GLOBAL(sormtr,SORMTR)
+#define LAPACK_dormtr LAPACK_GLOBAL(dormtr,DORMTR)
+#define LAPACK_chetrd LAPACK_GLOBAL(chetrd,CHETRD)
+#define LAPACK_zhetrd LAPACK_GLOBAL(zhetrd,ZHETRD)
+#define LAPACK_cungtr LAPACK_GLOBAL(cungtr,CUNGTR)
+#define LAPACK_zungtr LAPACK_GLOBAL(zungtr,ZUNGTR)
+#define LAPACK_cunmtr LAPACK_GLOBAL(cunmtr,CUNMTR)
+#define LAPACK_zunmtr LAPACK_GLOBAL(zunmtr,ZUNMTR)
+#define LAPACK_ssptrd LAPACK_GLOBAL(ssptrd,SSPTRD)
+#define LAPACK_dsptrd LAPACK_GLOBAL(dsptrd,DSPTRD)
+#define LAPACK_sopgtr LAPACK_GLOBAL(sopgtr,SOPGTR)
+#define LAPACK_dopgtr LAPACK_GLOBAL(dopgtr,DOPGTR)
+#define LAPACK_sopmtr LAPACK_GLOBAL(sopmtr,SOPMTR)
+#define LAPACK_dopmtr LAPACK_GLOBAL(dopmtr,DOPMTR)
+#define LAPACK_chptrd LAPACK_GLOBAL(chptrd,CHPTRD)
+#define LAPACK_zhptrd LAPACK_GLOBAL(zhptrd,ZHPTRD)
+#define LAPACK_cupgtr LAPACK_GLOBAL(cupgtr,CUPGTR)
+#define LAPACK_zupgtr LAPACK_GLOBAL(zupgtr,ZUPGTR)
+#define LAPACK_cupmtr LAPACK_GLOBAL(cupmtr,CUPMTR)
+#define LAPACK_zupmtr LAPACK_GLOBAL(zupmtr,ZUPMTR)
+#define LAPACK_ssbtrd LAPACK_GLOBAL(ssbtrd,SSBTRD)
+#define LAPACK_dsbtrd LAPACK_GLOBAL(dsbtrd,DSBTRD)
+#define LAPACK_chbtrd LAPACK_GLOBAL(chbtrd,CHBTRD)
+#define LAPACK_zhbtrd LAPACK_GLOBAL(zhbtrd,ZHBTRD)
+#define LAPACK_ssterf LAPACK_GLOBAL(ssterf,SSTERF)
+#define LAPACK_dsterf LAPACK_GLOBAL(dsterf,DSTERF)
+#define LAPACK_ssteqr LAPACK_GLOBAL(ssteqr,SSTEQR)
+#define LAPACK_dsteqr LAPACK_GLOBAL(dsteqr,DSTEQR)
+#define LAPACK_csteqr LAPACK_GLOBAL(csteqr,CSTEQR)
+#define LAPACK_zsteqr LAPACK_GLOBAL(zsteqr,ZSTEQR)
+#define LAPACK_sstemr LAPACK_GLOBAL(sstemr,SSTEMR)
+#define LAPACK_dstemr LAPACK_GLOBAL(dstemr,DSTEMR)
+#define LAPACK_cstemr LAPACK_GLOBAL(cstemr,CSTEMR)
+#define LAPACK_zstemr LAPACK_GLOBAL(zstemr,ZSTEMR)
+#define LAPACK_sstedc LAPACK_GLOBAL(sstedc,SSTEDC)
+#define LAPACK_dstedc LAPACK_GLOBAL(dstedc,DSTEDC)
+#define LAPACK_cstedc LAPACK_GLOBAL(cstedc,CSTEDC)
+#define LAPACK_zstedc LAPACK_GLOBAL(zstedc,ZSTEDC)
+#define LAPACK_sstegr LAPACK_GLOBAL(sstegr,SSTEGR)
+#define LAPACK_dstegr LAPACK_GLOBAL(dstegr,DSTEGR)
+#define LAPACK_cstegr LAPACK_GLOBAL(cstegr,CSTEGR)
+#define LAPACK_zstegr LAPACK_GLOBAL(zstegr,ZSTEGR)
+#define LAPACK_spteqr LAPACK_GLOBAL(spteqr,SPTEQR)
+#define LAPACK_dpteqr LAPACK_GLOBAL(dpteqr,DPTEQR)
+#define LAPACK_cpteqr LAPACK_GLOBAL(cpteqr,CPTEQR)
+#define LAPACK_zpteqr LAPACK_GLOBAL(zpteqr,ZPTEQR)
+#define LAPACK_sstebz LAPACK_GLOBAL(sstebz,SSTEBZ)
+#define LAPACK_dstebz LAPACK_GLOBAL(dstebz,DSTEBZ)
+#define LAPACK_sstein LAPACK_GLOBAL(sstein,SSTEIN)
+#define LAPACK_dstein LAPACK_GLOBAL(dstein,DSTEIN)
+#define LAPACK_cstein LAPACK_GLOBAL(cstein,CSTEIN)
+#define LAPACK_zstein LAPACK_GLOBAL(zstein,ZSTEIN)
+#define LAPACK_sdisna LAPACK_GLOBAL(sdisna,SDISNA)
+#define LAPACK_ddisna LAPACK_GLOBAL(ddisna,DDISNA)
+#define LAPACK_ssygst LAPACK_GLOBAL(ssygst,SSYGST)
+#define LAPACK_dsygst LAPACK_GLOBAL(dsygst,DSYGST)
+#define LAPACK_chegst LAPACK_GLOBAL(chegst,CHEGST)
+#define LAPACK_zhegst LAPACK_GLOBAL(zhegst,ZHEGST)
+#define LAPACK_sspgst LAPACK_GLOBAL(sspgst,SSPGST)
+#define LAPACK_dspgst LAPACK_GLOBAL(dspgst,DSPGST)
+#define LAPACK_chpgst LAPACK_GLOBAL(chpgst,CHPGST)
+#define LAPACK_zhpgst LAPACK_GLOBAL(zhpgst,ZHPGST)
+#define LAPACK_ssbgst LAPACK_GLOBAL(ssbgst,SSBGST)
+#define LAPACK_dsbgst LAPACK_GLOBAL(dsbgst,DSBGST)
+#define LAPACK_chbgst LAPACK_GLOBAL(chbgst,CHBGST)
+#define LAPACK_zhbgst LAPACK_GLOBAL(zhbgst,ZHBGST)
+#define LAPACK_spbstf LAPACK_GLOBAL(spbstf,SPBSTF)
+#define LAPACK_dpbstf LAPACK_GLOBAL(dpbstf,DPBSTF)
+#define LAPACK_cpbstf LAPACK_GLOBAL(cpbstf,CPBSTF)
+#define LAPACK_zpbstf LAPACK_GLOBAL(zpbstf,ZPBSTF)
+#define LAPACK_sgehrd LAPACK_GLOBAL(sgehrd,SGEHRD)
+#define LAPACK_dgehrd LAPACK_GLOBAL(dgehrd,DGEHRD)
+#define LAPACK_cgehrd LAPACK_GLOBAL(cgehrd,CGEHRD)
+#define LAPACK_zgehrd LAPACK_GLOBAL(zgehrd,ZGEHRD)
+#define LAPACK_sorghr LAPACK_GLOBAL(sorghr,SORGHR)
+#define LAPACK_dorghr LAPACK_GLOBAL(dorghr,DORGHR)
+#define LAPACK_sormhr LAPACK_GLOBAL(sormhr,SORMHR)
+#define LAPACK_dormhr LAPACK_GLOBAL(dormhr,DORMHR)
+#define LAPACK_cunghr LAPACK_GLOBAL(cunghr,CUNGHR)
+#define LAPACK_zunghr LAPACK_GLOBAL(zunghr,ZUNGHR)
+#define LAPACK_cunmhr LAPACK_GLOBAL(cunmhr,CUNMHR)
+#define LAPACK_zunmhr LAPACK_GLOBAL(zunmhr,ZUNMHR)
+#define LAPACK_sgebal LAPACK_GLOBAL(sgebal,SGEBAL)
+#define LAPACK_dgebal LAPACK_GLOBAL(dgebal,DGEBAL)
+#define LAPACK_cgebal LAPACK_GLOBAL(cgebal,CGEBAL)
+#define LAPACK_zgebal LAPACK_GLOBAL(zgebal,ZGEBAL)
+#define LAPACK_sgebak LAPACK_GLOBAL(sgebak,SGEBAK)
+#define LAPACK_dgebak LAPACK_GLOBAL(dgebak,DGEBAK)
+#define LAPACK_cgebak LAPACK_GLOBAL(cgebak,CGEBAK)
+#define LAPACK_zgebak LAPACK_GLOBAL(zgebak,ZGEBAK)
+#define LAPACK_shseqr LAPACK_GLOBAL(shseqr,SHSEQR)
+#define LAPACK_dhseqr LAPACK_GLOBAL(dhseqr,DHSEQR)
+#define LAPACK_chseqr LAPACK_GLOBAL(chseqr,CHSEQR)
+#define LAPACK_zhseqr LAPACK_GLOBAL(zhseqr,ZHSEQR)
+#define LAPACK_shsein LAPACK_GLOBAL(shsein,SHSEIN)
+#define LAPACK_dhsein LAPACK_GLOBAL(dhsein,DHSEIN)
+#define LAPACK_chsein LAPACK_GLOBAL(chsein,CHSEIN)
+#define LAPACK_zhsein LAPACK_GLOBAL(zhsein,ZHSEIN)
+#define LAPACK_strevc LAPACK_GLOBAL(strevc,STREVC)
+#define LAPACK_dtrevc LAPACK_GLOBAL(dtrevc,DTREVC)
+#define LAPACK_ctrevc LAPACK_GLOBAL(ctrevc,CTREVC)
+#define LAPACK_ztrevc LAPACK_GLOBAL(ztrevc,ZTREVC)
+#define LAPACK_strsna LAPACK_GLOBAL(strsna,STRSNA)
+#define LAPACK_dtrsna LAPACK_GLOBAL(dtrsna,DTRSNA)
+#define LAPACK_ctrsna LAPACK_GLOBAL(ctrsna,CTRSNA)
+#define LAPACK_ztrsna LAPACK_GLOBAL(ztrsna,ZTRSNA)
+#define LAPACK_strexc LAPACK_GLOBAL(strexc,STREXC)
+#define LAPACK_dtrexc LAPACK_GLOBAL(dtrexc,DTREXC)
+#define LAPACK_ctrexc LAPACK_GLOBAL(ctrexc,CTREXC)
+#define LAPACK_ztrexc LAPACK_GLOBAL(ztrexc,ZTREXC)
+#define LAPACK_strsen LAPACK_GLOBAL(strsen,STRSEN)
+#define LAPACK_dtrsen LAPACK_GLOBAL(dtrsen,DTRSEN)
+#define LAPACK_ctrsen LAPACK_GLOBAL(ctrsen,CTRSEN)
+#define LAPACK_ztrsen LAPACK_GLOBAL(ztrsen,ZTRSEN)
+#define LAPACK_strsyl LAPACK_GLOBAL(strsyl,STRSYL)
+#define LAPACK_dtrsyl LAPACK_GLOBAL(dtrsyl,DTRSYL)
+#define LAPACK_ctrsyl LAPACK_GLOBAL(ctrsyl,CTRSYL)
+#define LAPACK_ztrsyl LAPACK_GLOBAL(ztrsyl,ZTRSYL)
+#define LAPACK_sgghrd LAPACK_GLOBAL(sgghrd,SGGHRD)
+#define LAPACK_dgghrd LAPACK_GLOBAL(dgghrd,DGGHRD)
+#define LAPACK_cgghrd LAPACK_GLOBAL(cgghrd,CGGHRD)
+#define LAPACK_zgghrd LAPACK_GLOBAL(zgghrd,ZGGHRD)
+#define LAPACK_sggbal LAPACK_GLOBAL(sggbal,SGGBAL)
+#define LAPACK_dggbal LAPACK_GLOBAL(dggbal,DGGBAL)
+#define LAPACK_cggbal LAPACK_GLOBAL(cggbal,CGGBAL)
+#define LAPACK_zggbal LAPACK_GLOBAL(zggbal,ZGGBAL)
+#define LAPACK_sggbak LAPACK_GLOBAL(sggbak,SGGBAK)
+#define LAPACK_dggbak LAPACK_GLOBAL(dggbak,DGGBAK)
+#define LAPACK_cggbak LAPACK_GLOBAL(cggbak,CGGBAK)
+#define LAPACK_zggbak LAPACK_GLOBAL(zggbak,ZGGBAK)
+#define LAPACK_shgeqz LAPACK_GLOBAL(shgeqz,SHGEQZ)
+#define LAPACK_dhgeqz LAPACK_GLOBAL(dhgeqz,DHGEQZ)
+#define LAPACK_chgeqz LAPACK_GLOBAL(chgeqz,CHGEQZ)
+#define LAPACK_zhgeqz LAPACK_GLOBAL(zhgeqz,ZHGEQZ)
+#define LAPACK_stgevc LAPACK_GLOBAL(stgevc,STGEVC)
+#define LAPACK_dtgevc LAPACK_GLOBAL(dtgevc,DTGEVC)
+#define LAPACK_ctgevc LAPACK_GLOBAL(ctgevc,CTGEVC)
+#define LAPACK_ztgevc LAPACK_GLOBAL(ztgevc,ZTGEVC)
+#define LAPACK_stgexc LAPACK_GLOBAL(stgexc,STGEXC)
+#define LAPACK_dtgexc LAPACK_GLOBAL(dtgexc,DTGEXC)
+#define LAPACK_ctgexc LAPACK_GLOBAL(ctgexc,CTGEXC)
+#define LAPACK_ztgexc LAPACK_GLOBAL(ztgexc,ZTGEXC)
+#define LAPACK_stgsen LAPACK_GLOBAL(stgsen,STGSEN)
+#define LAPACK_dtgsen LAPACK_GLOBAL(dtgsen,DTGSEN)
+#define LAPACK_ctgsen LAPACK_GLOBAL(ctgsen,CTGSEN)
+#define LAPACK_ztgsen LAPACK_GLOBAL(ztgsen,ZTGSEN)
+#define LAPACK_stgsyl LAPACK_GLOBAL(stgsyl,STGSYL)
+#define LAPACK_dtgsyl LAPACK_GLOBAL(dtgsyl,DTGSYL)
+#define LAPACK_ctgsyl LAPACK_GLOBAL(ctgsyl,CTGSYL)
+#define LAPACK_ztgsyl LAPACK_GLOBAL(ztgsyl,ZTGSYL)
+#define LAPACK_stgsna LAPACK_GLOBAL(stgsna,STGSNA)
+#define LAPACK_dtgsna LAPACK_GLOBAL(dtgsna,DTGSNA)
+#define LAPACK_ctgsna LAPACK_GLOBAL(ctgsna,CTGSNA)
+#define LAPACK_ztgsna LAPACK_GLOBAL(ztgsna,ZTGSNA)
+#define LAPACK_sggsvp LAPACK_GLOBAL(sggsvp,SGGSVP)
+#define LAPACK_dggsvp LAPACK_GLOBAL(dggsvp,DGGSVP)
+#define LAPACK_cggsvp LAPACK_GLOBAL(cggsvp,CGGSVP)
+#define LAPACK_zggsvp LAPACK_GLOBAL(zggsvp,ZGGSVP)
+#define LAPACK_stgsja LAPACK_GLOBAL(stgsja,STGSJA)
+#define LAPACK_dtgsja LAPACK_GLOBAL(dtgsja,DTGSJA)
+#define LAPACK_ctgsja LAPACK_GLOBAL(ctgsja,CTGSJA)
+#define LAPACK_ztgsja LAPACK_GLOBAL(ztgsja,ZTGSJA)
+#define LAPACK_sgels LAPACK_GLOBAL(sgels,SGELS)
+#define LAPACK_dgels LAPACK_GLOBAL(dgels,DGELS)
+#define LAPACK_cgels LAPACK_GLOBAL(cgels,CGELS)
+#define LAPACK_zgels LAPACK_GLOBAL(zgels,ZGELS)
+#define LAPACK_sgelsy LAPACK_GLOBAL(sgelsy,SGELSY)
+#define LAPACK_dgelsy LAPACK_GLOBAL(dgelsy,DGELSY)
+#define LAPACK_cgelsy LAPACK_GLOBAL(cgelsy,CGELSY)
+#define LAPACK_zgelsy LAPACK_GLOBAL(zgelsy,ZGELSY)
+#define LAPACK_sgelss LAPACK_GLOBAL(sgelss,SGELSS)
+#define LAPACK_dgelss LAPACK_GLOBAL(dgelss,DGELSS)
+#define LAPACK_cgelss LAPACK_GLOBAL(cgelss,CGELSS)
+#define LAPACK_zgelss LAPACK_GLOBAL(zgelss,ZGELSS)
+#define LAPACK_sgelsd LAPACK_GLOBAL(sgelsd,SGELSD)
+#define LAPACK_dgelsd LAPACK_GLOBAL(dgelsd,DGELSD)
+#define LAPACK_cgelsd LAPACK_GLOBAL(cgelsd,CGELSD)
+#define LAPACK_zgelsd LAPACK_GLOBAL(zgelsd,ZGELSD)
+#define LAPACK_sgglse LAPACK_GLOBAL(sgglse,SGGLSE)
+#define LAPACK_dgglse LAPACK_GLOBAL(dgglse,DGGLSE)
+#define LAPACK_cgglse LAPACK_GLOBAL(cgglse,CGGLSE)
+#define LAPACK_zgglse LAPACK_GLOBAL(zgglse,ZGGLSE)
+#define LAPACK_sggglm LAPACK_GLOBAL(sggglm,SGGGLM)
+#define LAPACK_dggglm LAPACK_GLOBAL(dggglm,DGGGLM)
+#define LAPACK_cggglm LAPACK_GLOBAL(cggglm,CGGGLM)
+#define LAPACK_zggglm LAPACK_GLOBAL(zggglm,ZGGGLM)
+#define LAPACK_ssyev LAPACK_GLOBAL(ssyev,SSYEV)
+#define LAPACK_dsyev LAPACK_GLOBAL(dsyev,DSYEV)
+#define LAPACK_cheev LAPACK_GLOBAL(cheev,CHEEV)
+#define LAPACK_zheev LAPACK_GLOBAL(zheev,ZHEEV)
+#define LAPACK_ssyevd LAPACK_GLOBAL(ssyevd,SSYEVD)
+#define LAPACK_dsyevd LAPACK_GLOBAL(dsyevd,DSYEVD)
+#define LAPACK_cheevd LAPACK_GLOBAL(cheevd,CHEEVD)
+#define LAPACK_zheevd LAPACK_GLOBAL(zheevd,ZHEEVD)
+#define LAPACK_ssyevx LAPACK_GLOBAL(ssyevx,SSYEVX)
+#define LAPACK_dsyevx LAPACK_GLOBAL(dsyevx,DSYEVX)
+#define LAPACK_cheevx LAPACK_GLOBAL(cheevx,CHEEVX)
+#define LAPACK_zheevx LAPACK_GLOBAL(zheevx,ZHEEVX)
+#define LAPACK_ssyevr LAPACK_GLOBAL(ssyevr,SSYEVR)
+#define LAPACK_dsyevr LAPACK_GLOBAL(dsyevr,DSYEVR)
+#define LAPACK_cheevr LAPACK_GLOBAL(cheevr,CHEEVR)
+#define LAPACK_zheevr LAPACK_GLOBAL(zheevr,ZHEEVR)
+#define LAPACK_sspev LAPACK_GLOBAL(sspev,SSPEV)
+#define LAPACK_dspev LAPACK_GLOBAL(dspev,DSPEV)
+#define LAPACK_chpev LAPACK_GLOBAL(chpev,CHPEV)
+#define LAPACK_zhpev LAPACK_GLOBAL(zhpev,ZHPEV)
+#define LAPACK_sspevd LAPACK_GLOBAL(sspevd,SSPEVD)
+#define LAPACK_dspevd LAPACK_GLOBAL(dspevd,DSPEVD)
+#define LAPACK_chpevd LAPACK_GLOBAL(chpevd,CHPEVD)
+#define LAPACK_zhpevd LAPACK_GLOBAL(zhpevd,ZHPEVD)
+#define LAPACK_sspevx LAPACK_GLOBAL(sspevx,SSPEVX)
+#define LAPACK_dspevx LAPACK_GLOBAL(dspevx,DSPEVX)
+#define LAPACK_chpevx LAPACK_GLOBAL(chpevx,CHPEVX)
+#define LAPACK_zhpevx LAPACK_GLOBAL(zhpevx,ZHPEVX)
+#define LAPACK_ssbev LAPACK_GLOBAL(ssbev,SSBEV)
+#define LAPACK_dsbev LAPACK_GLOBAL(dsbev,DSBEV)
+#define LAPACK_chbev LAPACK_GLOBAL(chbev,CHBEV)
+#define LAPACK_zhbev LAPACK_GLOBAL(zhbev,ZHBEV)
+#define LAPACK_ssbevd LAPACK_GLOBAL(ssbevd,SSBEVD)
+#define LAPACK_dsbevd LAPACK_GLOBAL(dsbevd,DSBEVD)
+#define LAPACK_chbevd LAPACK_GLOBAL(chbevd,CHBEVD)
+#define LAPACK_zhbevd LAPACK_GLOBAL(zhbevd,ZHBEVD)
+#define LAPACK_ssbevx LAPACK_GLOBAL(ssbevx,SSBEVX)
+#define LAPACK_dsbevx LAPACK_GLOBAL(dsbevx,DSBEVX)
+#define LAPACK_chbevx LAPACK_GLOBAL(chbevx,CHBEVX)
+#define LAPACK_zhbevx LAPACK_GLOBAL(zhbevx,ZHBEVX)
+#define LAPACK_sstev LAPACK_GLOBAL(sstev,SSTEV)
+#define LAPACK_dstev LAPACK_GLOBAL(dstev,DSTEV)
+#define LAPACK_sstevd LAPACK_GLOBAL(sstevd,SSTEVD)
+#define LAPACK_dstevd LAPACK_GLOBAL(dstevd,DSTEVD)
+#define LAPACK_sstevx LAPACK_GLOBAL(sstevx,SSTEVX)
+#define LAPACK_dstevx LAPACK_GLOBAL(dstevx,DSTEVX)
+#define LAPACK_sstevr LAPACK_GLOBAL(sstevr,SSTEVR)
+#define LAPACK_dstevr LAPACK_GLOBAL(dstevr,DSTEVR)
+#define LAPACK_sgees LAPACK_GLOBAL(sgees,SGEES)
+#define LAPACK_dgees LAPACK_GLOBAL(dgees,DGEES)
+#define LAPACK_cgees LAPACK_GLOBAL(cgees,CGEES)
+#define LAPACK_zgees LAPACK_GLOBAL(zgees,ZGEES)
+#define LAPACK_sgeesx LAPACK_GLOBAL(sgeesx,SGEESX)
+#define LAPACK_dgeesx LAPACK_GLOBAL(dgeesx,DGEESX)
+#define LAPACK_cgeesx LAPACK_GLOBAL(cgeesx,CGEESX)
+#define LAPACK_zgeesx LAPACK_GLOBAL(zgeesx,ZGEESX)
+#define LAPACK_sgeev LAPACK_GLOBAL(sgeev,SGEEV)
+#define LAPACK_dgeev LAPACK_GLOBAL(dgeev,DGEEV)
+#define LAPACK_cgeev LAPACK_GLOBAL(cgeev,CGEEV)
+#define LAPACK_zgeev LAPACK_GLOBAL(zgeev,ZGEEV)
+#define LAPACK_sgeevx LAPACK_GLOBAL(sgeevx,SGEEVX)
+#define LAPACK_dgeevx LAPACK_GLOBAL(dgeevx,DGEEVX)
+#define LAPACK_cgeevx LAPACK_GLOBAL(cgeevx,CGEEVX)
+#define LAPACK_zgeevx LAPACK_GLOBAL(zgeevx,ZGEEVX)
+#define LAPACK_sgesvd LAPACK_GLOBAL(sgesvd,SGESVD)
+#define LAPACK_dgesvd LAPACK_GLOBAL(dgesvd,DGESVD)
+#define LAPACK_cgesvd LAPACK_GLOBAL(cgesvd,CGESVD)
+#define LAPACK_zgesvd LAPACK_GLOBAL(zgesvd,ZGESVD)
+#define LAPACK_sgesdd LAPACK_GLOBAL(sgesdd,SGESDD)
+#define LAPACK_dgesdd LAPACK_GLOBAL(dgesdd,DGESDD)
+#define LAPACK_cgesdd LAPACK_GLOBAL(cgesdd,CGESDD)
+#define LAPACK_zgesdd LAPACK_GLOBAL(zgesdd,ZGESDD)
+#define LAPACK_dgejsv LAPACK_GLOBAL(dgejsv,DGEJSV)
+#define LAPACK_sgejsv LAPACK_GLOBAL(sgejsv,SGEJSV)
+#define LAPACK_dgesvj LAPACK_GLOBAL(dgesvj,DGESVJ)
+#define LAPACK_sgesvj LAPACK_GLOBAL(sgesvj,SGESVJ)
+#define LAPACK_sggsvd LAPACK_GLOBAL(sggsvd,SGGSVD)
+#define LAPACK_dggsvd LAPACK_GLOBAL(dggsvd,DGGSVD)
+#define LAPACK_cggsvd LAPACK_GLOBAL(cggsvd,CGGSVD)
+#define LAPACK_zggsvd LAPACK_GLOBAL(zggsvd,ZGGSVD)
+#define LAPACK_ssygv LAPACK_GLOBAL(ssygv,SSYGV)
+#define LAPACK_dsygv LAPACK_GLOBAL(dsygv,DSYGV)
+#define LAPACK_chegv LAPACK_GLOBAL(chegv,CHEGV)
+#define LAPACK_zhegv LAPACK_GLOBAL(zhegv,ZHEGV)
+#define LAPACK_ssygvd LAPACK_GLOBAL(ssygvd,SSYGVD)
+#define LAPACK_dsygvd LAPACK_GLOBAL(dsygvd,DSYGVD)
+#define LAPACK_chegvd LAPACK_GLOBAL(chegvd,CHEGVD)
+#define LAPACK_zhegvd LAPACK_GLOBAL(zhegvd,ZHEGVD)
+#define LAPACK_ssygvx LAPACK_GLOBAL(ssygvx,SSYGVX)
+#define LAPACK_dsygvx LAPACK_GLOBAL(dsygvx,DSYGVX)
+#define LAPACK_chegvx LAPACK_GLOBAL(chegvx,CHEGVX)
+#define LAPACK_zhegvx LAPACK_GLOBAL(zhegvx,ZHEGVX)
+#define LAPACK_sspgv LAPACK_GLOBAL(sspgv,SSPGV)
+#define LAPACK_dspgv LAPACK_GLOBAL(dspgv,DSPGV)
+#define LAPACK_chpgv LAPACK_GLOBAL(chpgv,CHPGV)
+#define LAPACK_zhpgv LAPACK_GLOBAL(zhpgv,ZHPGV)
+#define LAPACK_sspgvd LAPACK_GLOBAL(sspgvd,SSPGVD)
+#define LAPACK_dspgvd LAPACK_GLOBAL(dspgvd,DSPGVD)
+#define LAPACK_chpgvd LAPACK_GLOBAL(chpgvd,CHPGVD)
+#define LAPACK_zhpgvd LAPACK_GLOBAL(zhpgvd,ZHPGVD)
+#define LAPACK_sspgvx LAPACK_GLOBAL(sspgvx,SSPGVX)
+#define LAPACK_dspgvx LAPACK_GLOBAL(dspgvx,DSPGVX)
+#define LAPACK_chpgvx LAPACK_GLOBAL(chpgvx,CHPGVX)
+#define LAPACK_zhpgvx LAPACK_GLOBAL(zhpgvx,ZHPGVX)
+#define LAPACK_ssbgv LAPACK_GLOBAL(ssbgv,SSBGV)
+#define LAPACK_dsbgv LAPACK_GLOBAL(dsbgv,DSBGV)
+#define LAPACK_chbgv LAPACK_GLOBAL(chbgv,CHBGV)
+#define LAPACK_zhbgv LAPACK_GLOBAL(zhbgv,ZHBGV)
+#define LAPACK_ssbgvd LAPACK_GLOBAL(ssbgvd,SSBGVD)
+#define LAPACK_dsbgvd LAPACK_GLOBAL(dsbgvd,DSBGVD)
+#define LAPACK_chbgvd LAPACK_GLOBAL(chbgvd,CHBGVD)
+#define LAPACK_zhbgvd LAPACK_GLOBAL(zhbgvd,ZHBGVD)
+#define LAPACK_ssbgvx LAPACK_GLOBAL(ssbgvx,SSBGVX)
+#define LAPACK_dsbgvx LAPACK_GLOBAL(dsbgvx,DSBGVX)
+#define LAPACK_chbgvx LAPACK_GLOBAL(chbgvx,CHBGVX)
+#define LAPACK_zhbgvx LAPACK_GLOBAL(zhbgvx,ZHBGVX)
+#define LAPACK_sgges LAPACK_GLOBAL(sgges,SGGES)
+#define LAPACK_dgges LAPACK_GLOBAL(dgges,DGGES)
+#define LAPACK_cgges LAPACK_GLOBAL(cgges,CGGES)
+#define LAPACK_zgges LAPACK_GLOBAL(zgges,ZGGES)
+#define LAPACK_sggesx LAPACK_GLOBAL(sggesx,SGGESX)
+#define LAPACK_dggesx LAPACK_GLOBAL(dggesx,DGGESX)
+#define LAPACK_cggesx LAPACK_GLOBAL(cggesx,CGGESX)
+#define LAPACK_zggesx LAPACK_GLOBAL(zggesx,ZGGESX)
+#define LAPACK_sggev LAPACK_GLOBAL(sggev,SGGEV)
+#define LAPACK_dggev LAPACK_GLOBAL(dggev,DGGEV)
+#define LAPACK_cggev LAPACK_GLOBAL(cggev,CGGEV)
+#define LAPACK_zggev LAPACK_GLOBAL(zggev,ZGGEV)
+#define LAPACK_sggevx LAPACK_GLOBAL(sggevx,SGGEVX)
+#define LAPACK_dggevx LAPACK_GLOBAL(dggevx,DGGEVX)
+#define LAPACK_cggevx LAPACK_GLOBAL(cggevx,CGGEVX)
+#define LAPACK_zggevx LAPACK_GLOBAL(zggevx,ZGGEVX)
+#define LAPACK_dsfrk LAPACK_GLOBAL(dsfrk,DSFRK)
+#define LAPACK_ssfrk LAPACK_GLOBAL(ssfrk,SSFRK)
+#define LAPACK_zhfrk LAPACK_GLOBAL(zhfrk,ZHFRK)
+#define LAPACK_chfrk LAPACK_GLOBAL(chfrk,CHFRK)
+#define LAPACK_dtfsm LAPACK_GLOBAL(dtfsm,DTFSM)
+#define LAPACK_stfsm LAPACK_GLOBAL(stfsm,STFSM)
+#define LAPACK_ztfsm LAPACK_GLOBAL(ztfsm,ZTFSM)
+#define LAPACK_ctfsm LAPACK_GLOBAL(ctfsm,CTFSM)
+#define LAPACK_dtfttp LAPACK_GLOBAL(dtfttp,DTFTTP)
+#define LAPACK_stfttp LAPACK_GLOBAL(stfttp,STFTTP)
+#define LAPACK_ztfttp LAPACK_GLOBAL(ztfttp,ZTFTTP)
+#define LAPACK_ctfttp LAPACK_GLOBAL(ctfttp,CTFTTP)
+#define LAPACK_dtfttr LAPACK_GLOBAL(dtfttr,DTFTTR)
+#define LAPACK_stfttr LAPACK_GLOBAL(stfttr,STFTTR)
+#define LAPACK_ztfttr LAPACK_GLOBAL(ztfttr,ZTFTTR)
+#define LAPACK_ctfttr LAPACK_GLOBAL(ctfttr,CTFTTR)
+#define LAPACK_dtpttf LAPACK_GLOBAL(dtpttf,DTPTTF)
+#define LAPACK_stpttf LAPACK_GLOBAL(stpttf,STPTTF)
+#define LAPACK_ztpttf LAPACK_GLOBAL(ztpttf,ZTPTTF)
+#define LAPACK_ctpttf LAPACK_GLOBAL(ctpttf,CTPTTF)
+#define LAPACK_dtpttr LAPACK_GLOBAL(dtpttr,DTPTTR)
+#define LAPACK_stpttr LAPACK_GLOBAL(stpttr,STPTTR)
+#define LAPACK_ztpttr LAPACK_GLOBAL(ztpttr,ZTPTTR)
+#define LAPACK_ctpttr LAPACK_GLOBAL(ctpttr,CTPTTR)
+#define LAPACK_dtrttf LAPACK_GLOBAL(dtrttf,DTRTTF)
+#define LAPACK_strttf LAPACK_GLOBAL(strttf,STRTTF)
+#define LAPACK_ztrttf LAPACK_GLOBAL(ztrttf,ZTRTTF)
+#define LAPACK_ctrttf LAPACK_GLOBAL(ctrttf,CTRTTF)
+#define LAPACK_dtrttp LAPACK_GLOBAL(dtrttp,DTRTTP)
+#define LAPACK_strttp LAPACK_GLOBAL(strttp,STRTTP)
+#define LAPACK_ztrttp LAPACK_GLOBAL(ztrttp,ZTRTTP)
+#define LAPACK_ctrttp LAPACK_GLOBAL(ctrttp,CTRTTP)
+#define LAPACK_sgeqrfp LAPACK_GLOBAL(sgeqrfp,SGEQRFP)
+#define LAPACK_dgeqrfp LAPACK_GLOBAL(dgeqrfp,DGEQRFP)
+#define LAPACK_cgeqrfp LAPACK_GLOBAL(cgeqrfp,CGEQRFP)
+#define LAPACK_zgeqrfp LAPACK_GLOBAL(zgeqrfp,ZGEQRFP)
+#define LAPACK_clacgv LAPACK_GLOBAL(clacgv,CLACGV)
+#define LAPACK_zlacgv LAPACK_GLOBAL(zlacgv,ZLACGV)
+#define LAPACK_slarnv LAPACK_GLOBAL(slarnv,SLARNV)
+#define LAPACK_dlarnv LAPACK_GLOBAL(dlarnv,DLARNV)
+#define LAPACK_clarnv LAPACK_GLOBAL(clarnv,CLARNV)
+#define LAPACK_zlarnv LAPACK_GLOBAL(zlarnv,ZLARNV)
+#define LAPACK_sgeqr2 LAPACK_GLOBAL(sgeqr2,SGEQR2)
+#define LAPACK_dgeqr2 LAPACK_GLOBAL(dgeqr2,DGEQR2)
+#define LAPACK_cgeqr2 LAPACK_GLOBAL(cgeqr2,CGEQR2)
+#define LAPACK_zgeqr2 LAPACK_GLOBAL(zgeqr2,ZGEQR2)
+#define LAPACK_slacpy LAPACK_GLOBAL(slacpy,SLACPY)
+#define LAPACK_dlacpy LAPACK_GLOBAL(dlacpy,DLACPY)
+#define LAPACK_clacpy LAPACK_GLOBAL(clacpy,CLACPY)
+#define LAPACK_zlacpy LAPACK_GLOBAL(zlacpy,ZLACPY)
+#define LAPACK_sgetf2 LAPACK_GLOBAL(sgetf2,SGETF2)
+#define LAPACK_dgetf2 LAPACK_GLOBAL(dgetf2,DGETF2)
+#define LAPACK_cgetf2 LAPACK_GLOBAL(cgetf2,CGETF2)
+#define LAPACK_zgetf2 LAPACK_GLOBAL(zgetf2,ZGETF2)
+#define LAPACK_slaswp LAPACK_GLOBAL(slaswp,SLASWP)
+#define LAPACK_dlaswp LAPACK_GLOBAL(dlaswp,DLASWP)
+#define LAPACK_claswp LAPACK_GLOBAL(claswp,CLASWP)
+#define LAPACK_zlaswp LAPACK_GLOBAL(zlaswp,ZLASWP)
+#define LAPACK_slange LAPACK_GLOBAL(slange,SLANGE)
+#define LAPACK_dlange LAPACK_GLOBAL(dlange,DLANGE)
+#define LAPACK_clange LAPACK_GLOBAL(clange,CLANGE)
+#define LAPACK_zlange LAPACK_GLOBAL(zlange,ZLANGE)
+#define LAPACK_clanhe LAPACK_GLOBAL(clanhe,CLANHE)
+#define LAPACK_zlanhe LAPACK_GLOBAL(zlanhe,ZLANHE)
+#define LAPACK_slansy LAPACK_GLOBAL(slansy,SLANSY)
+#define LAPACK_dlansy LAPACK_GLOBAL(dlansy,DLANSY)
+#define LAPACK_clansy LAPACK_GLOBAL(clansy,CLANSY)
+#define LAPACK_zlansy LAPACK_GLOBAL(zlansy,ZLANSY)
+#define LAPACK_slantr LAPACK_GLOBAL(slantr,SLANTR)
+#define LAPACK_dlantr LAPACK_GLOBAL(dlantr,DLANTR)
+#define LAPACK_clantr LAPACK_GLOBAL(clantr,CLANTR)
+#define LAPACK_zlantr LAPACK_GLOBAL(zlantr,ZLANTR)
+#define LAPACK_slamch LAPACK_GLOBAL(slamch,SLAMCH)
+#define LAPACK_dlamch LAPACK_GLOBAL(dlamch,DLAMCH)
+#define LAPACK_sgelq2 LAPACK_GLOBAL(sgelq2,SGELQ2)
+#define LAPACK_dgelq2 LAPACK_GLOBAL(dgelq2,DGELQ2)
+#define LAPACK_cgelq2 LAPACK_GLOBAL(cgelq2,CGELQ2)
+#define LAPACK_zgelq2 LAPACK_GLOBAL(zgelq2,ZGELQ2)
+#define LAPACK_slarfb LAPACK_GLOBAL(slarfb,SLARFB)
+#define LAPACK_dlarfb LAPACK_GLOBAL(dlarfb,DLARFB)
+#define LAPACK_clarfb LAPACK_GLOBAL(clarfb,CLARFB)
+#define LAPACK_zlarfb LAPACK_GLOBAL(zlarfb,ZLARFB)
+#define LAPACK_slarfg LAPACK_GLOBAL(slarfg,SLARFG)
+#define LAPACK_dlarfg LAPACK_GLOBAL(dlarfg,DLARFG)
+#define LAPACK_clarfg LAPACK_GLOBAL(clarfg,CLARFG)
+#define LAPACK_zlarfg LAPACK_GLOBAL(zlarfg,ZLARFG)
+#define LAPACK_slarft LAPACK_GLOBAL(slarft,SLARFT)
+#define LAPACK_dlarft LAPACK_GLOBAL(dlarft,DLARFT)
+#define LAPACK_clarft LAPACK_GLOBAL(clarft,CLARFT)
+#define LAPACK_zlarft LAPACK_GLOBAL(zlarft,ZLARFT)
+#define LAPACK_slarfx LAPACK_GLOBAL(slarfx,SLARFX)
+#define LAPACK_dlarfx LAPACK_GLOBAL(dlarfx,DLARFX)
+#define LAPACK_clarfx LAPACK_GLOBAL(clarfx,CLARFX)
+#define LAPACK_zlarfx LAPACK_GLOBAL(zlarfx,ZLARFX)
+#define LAPACK_slatms LAPACK_GLOBAL(slatms,SLATMS)
+#define LAPACK_dlatms LAPACK_GLOBAL(dlatms,DLATMS)
+#define LAPACK_clatms LAPACK_GLOBAL(clatms,CLATMS)
+#define LAPACK_zlatms LAPACK_GLOBAL(zlatms,ZLATMS)
+#define LAPACK_slag2d LAPACK_GLOBAL(slag2d,SLAG2D)
+#define LAPACK_dlag2s LAPACK_GLOBAL(dlag2s,DLAG2S)
+#define LAPACK_clag2z LAPACK_GLOBAL(clag2z,CLAG2Z)
+#define LAPACK_zlag2c LAPACK_GLOBAL(zlag2c,ZLAG2C)
+#define LAPACK_slauum LAPACK_GLOBAL(slauum,SLAUUM)
+#define LAPACK_dlauum LAPACK_GLOBAL(dlauum,DLAUUM)
+#define LAPACK_clauum LAPACK_GLOBAL(clauum,CLAUUM)
+#define LAPACK_zlauum LAPACK_GLOBAL(zlauum,ZLAUUM)
+#define LAPACK_slagge LAPACK_GLOBAL(slagge,SLAGGE)
+#define LAPACK_dlagge LAPACK_GLOBAL(dlagge,DLAGGE)
+#define LAPACK_clagge LAPACK_GLOBAL(clagge,CLAGGE)
+#define LAPACK_zlagge LAPACK_GLOBAL(zlagge,ZLAGGE)
+#define LAPACK_slaset LAPACK_GLOBAL(slaset,SLASET)
+#define LAPACK_dlaset LAPACK_GLOBAL(dlaset,DLASET)
+#define LAPACK_claset LAPACK_GLOBAL(claset,CLASET)
+#define LAPACK_zlaset LAPACK_GLOBAL(zlaset,ZLASET)
+#define LAPACK_slasrt LAPACK_GLOBAL(slasrt,SLASRT)
+#define LAPACK_dlasrt LAPACK_GLOBAL(dlasrt,DLASRT)
+#define LAPACK_slagsy LAPACK_GLOBAL(slagsy,SLAGSY)
+#define LAPACK_dlagsy LAPACK_GLOBAL(dlagsy,DLAGSY)
+#define LAPACK_clagsy LAPACK_GLOBAL(clagsy,CLAGSY)
+#define LAPACK_zlagsy LAPACK_GLOBAL(zlagsy,ZLAGSY)
+#define LAPACK_claghe LAPACK_GLOBAL(claghe,CLAGHE)
+#define LAPACK_zlaghe LAPACK_GLOBAL(zlaghe,ZLAGHE)
+#define LAPACK_slapmr LAPACK_GLOBAL(slapmr,SLAPMR)
+#define LAPACK_dlapmr LAPACK_GLOBAL(dlapmr,DLAPMR)
+#define LAPACK_clapmr LAPACK_GLOBAL(clapmr,CLAPMR)
+#define LAPACK_zlapmr LAPACK_GLOBAL(zlapmr,ZLAPMR)
+#define LAPACK_slapy2 LAPACK_GLOBAL(slapy2,SLAPY2)
+#define LAPACK_dlapy2 LAPACK_GLOBAL(dlapy2,DLAPY2)
+#define LAPACK_slapy3 LAPACK_GLOBAL(slapy3,SLAPY3)
+#define LAPACK_dlapy3 LAPACK_GLOBAL(dlapy3,DLAPY3)
+#define LAPACK_slartgp LAPACK_GLOBAL(slartgp,SLARTGP)
+#define LAPACK_dlartgp LAPACK_GLOBAL(dlartgp,DLARTGP)
+#define LAPACK_slartgs LAPACK_GLOBAL(slartgs,SLARTGS)
+#define LAPACK_dlartgs LAPACK_GLOBAL(dlartgs,DLARTGS)
+// LAPACK 3.3.0
+#define LAPACK_cbbcsd LAPACK_GLOBAL(cbbcsd,CBBCSD)
+#define LAPACK_cheswapr LAPACK_GLOBAL(cheswapr,CHESWAPR)
+#define LAPACK_chetri2 LAPACK_GLOBAL(chetri2,CHETRI2)
+#define LAPACK_chetri2x LAPACK_GLOBAL(chetri2x,CHETRI2X)
+#define LAPACK_chetrs2 LAPACK_GLOBAL(chetrs2,CHETRS2)
+#define LAPACK_csyconv LAPACK_GLOBAL(csyconv,CSYCONV)
+#define LAPACK_csyswapr LAPACK_GLOBAL(csyswapr,CSYSWAPR)
+#define LAPACK_csytri2 LAPACK_GLOBAL(csytri2,CSYTRI2)
+#define LAPACK_csytri2x LAPACK_GLOBAL(csytri2x,CSYTRI2X)
+#define LAPACK_csytrs2 LAPACK_GLOBAL(csytrs2,CSYTRS2)
+#define LAPACK_cunbdb LAPACK_GLOBAL(cunbdb,CUNBDB)
+#define LAPACK_cuncsd LAPACK_GLOBAL(cuncsd,CUNCSD)
+#define LAPACK_dbbcsd LAPACK_GLOBAL(dbbcsd,DBBCSD)
+#define LAPACK_dorbdb LAPACK_GLOBAL(dorbdb,DORBDB)
+#define LAPACK_dorcsd LAPACK_GLOBAL(dorcsd,DORCSD)
+#define LAPACK_dsyconv LAPACK_GLOBAL(dsyconv,DSYCONV)
+#define LAPACK_dsyswapr LAPACK_GLOBAL(dsyswapr,DSYSWAPR)
+#define LAPACK_dsytri2 LAPACK_GLOBAL(dsytri2,DSYTRI2)
+#define LAPACK_dsytri2x LAPACK_GLOBAL(dsytri2x,DSYTRI2X)
+#define LAPACK_dsytrs2 LAPACK_GLOBAL(dsytrs2,DSYTRS2)
+#define LAPACK_sbbcsd LAPACK_GLOBAL(sbbcsd,SBBCSD)
+#define LAPACK_sorbdb LAPACK_GLOBAL(sorbdb,SORBDB)
+#define LAPACK_sorcsd LAPACK_GLOBAL(sorcsd,SORCSD)
+#define LAPACK_ssyconv LAPACK_GLOBAL(ssyconv,SSYCONV)
+#define LAPACK_ssyswapr LAPACK_GLOBAL(ssyswapr,SSYSWAPR)
+#define LAPACK_ssytri2 LAPACK_GLOBAL(ssytri2,SSYTRI2)
+#define LAPACK_ssytri2x LAPACK_GLOBAL(ssytri2x,SSYTRI2X)
+#define LAPACK_ssytrs2 LAPACK_GLOBAL(ssytrs2,SSYTRS2)
+#define LAPACK_zbbcsd LAPACK_GLOBAL(zbbcsd,ZBBCSD)
+#define LAPACK_zheswapr LAPACK_GLOBAL(zheswapr,ZHESWAPR)
+#define LAPACK_zhetri2 LAPACK_GLOBAL(zhetri2,ZHETRI2)
+#define LAPACK_zhetri2x LAPACK_GLOBAL(zhetri2x,ZHETRI2X)
+#define LAPACK_zhetrs2 LAPACK_GLOBAL(zhetrs2,ZHETRS2)
+#define LAPACK_zsyconv LAPACK_GLOBAL(zsyconv,ZSYCONV)
+#define LAPACK_zsyswapr LAPACK_GLOBAL(zsyswapr,ZSYSWAPR)
+#define LAPACK_zsytri2 LAPACK_GLOBAL(zsytri2,ZSYTRI2)
+#define LAPACK_zsytri2x LAPACK_GLOBAL(zsytri2x,ZSYTRI2X)
+#define LAPACK_zsytrs2 LAPACK_GLOBAL(zsytrs2,ZSYTRS2)
+#define LAPACK_zunbdb LAPACK_GLOBAL(zunbdb,ZUNBDB)
+#define LAPACK_zuncsd LAPACK_GLOBAL(zuncsd,ZUNCSD)
+// LAPACK 3.4.0
+#define LAPACK_sgemqrt LAPACK_GLOBAL(sgemqrt,SGEMQRT)
+#define LAPACK_dgemqrt LAPACK_GLOBAL(dgemqrt,DGEMQRT)
+#define LAPACK_cgemqrt LAPACK_GLOBAL(cgemqrt,CGEMQRT)
+#define LAPACK_zgemqrt LAPACK_GLOBAL(zgemqrt,ZGEMQRT)
+#define LAPACK_sgeqrt LAPACK_GLOBAL(sgeqrt,SGEQRT)
+#define LAPACK_dgeqrt LAPACK_GLOBAL(dgeqrt,DGEQRT)
+#define LAPACK_cgeqrt LAPACK_GLOBAL(cgeqrt,CGEQRT)
+#define LAPACK_zgeqrt LAPACK_GLOBAL(zgeqrt,ZGEQRT)
+#define LAPACK_sgeqrt2 LAPACK_GLOBAL(sgeqrt2,SGEQRT2)
+#define LAPACK_dgeqrt2 LAPACK_GLOBAL(dgeqrt2,DGEQRT2)
+#define LAPACK_cgeqrt2 LAPACK_GLOBAL(cgeqrt2,CGEQRT2)
+#define LAPACK_zgeqrt2 LAPACK_GLOBAL(zgeqrt2,ZGEQRT2)
+#define LAPACK_sgeqrt3 LAPACK_GLOBAL(sgeqrt3,SGEQRT3)
+#define LAPACK_dgeqrt3 LAPACK_GLOBAL(dgeqrt3,DGEQRT3)
+#define LAPACK_cgeqrt3 LAPACK_GLOBAL(cgeqrt3,CGEQRT3)
+#define LAPACK_zgeqrt3 LAPACK_GLOBAL(zgeqrt3,ZGEQRT3)
+#define LAPACK_stpmqrt LAPACK_GLOBAL(stpmqrt,STPMQRT)
+#define LAPACK_dtpmqrt LAPACK_GLOBAL(dtpmqrt,DTPMQRT)
+#define LAPACK_ctpmqrt LAPACK_GLOBAL(ctpmqrt,CTPMQRT)
+#define LAPACK_ztpmqrt LAPACK_GLOBAL(ztpmqrt,ZTPMQRT)
+#define LAPACK_dtpqrt LAPACK_GLOBAL(dtpqrt,DTPQRT)
+#define LAPACK_ctpqrt LAPACK_GLOBAL(ctpqrt,CTPQRT)
+#define LAPACK_ztpqrt LAPACK_GLOBAL(ztpqrt,ZTPQRT)
+#define LAPACK_stpqrt2 LAPACK_GLOBAL(stpqrt2,STPQRT2)
+#define LAPACK_dtpqrt2 LAPACK_GLOBAL(dtpqrt2,DTPQRT2)
+#define LAPACK_ctpqrt2 LAPACK_GLOBAL(ctpqrt2,CTPQRT2)
+#define LAPACK_ztpqrt2 LAPACK_GLOBAL(ztpqrt2,ZTPQRT2)
+#define LAPACK_stprfb LAPACK_GLOBAL(stprfb,STPRFB)
+#define LAPACK_dtprfb LAPACK_GLOBAL(dtprfb,DTPRFB)
+#define LAPACK_ctprfb LAPACK_GLOBAL(ctprfb,CTPRFB)
+#define LAPACK_ztprfb LAPACK_GLOBAL(ztprfb,ZTPRFB)
+// LAPACK 3.X.X
+#define LAPACK_csyr LAPACK_GLOBAL(csyr,CSYR)
+#define LAPACK_zsyr LAPACK_GLOBAL(zsyr,ZSYR)
+
+
+void LAPACK_sgetrf( lapack_int* m, lapack_int* n, float* a, lapack_int* lda,
+ lapack_int* ipiv, lapack_int *info );
+void LAPACK_dgetrf( lapack_int* m, lapack_int* n, double* a, lapack_int* lda,
+ lapack_int* ipiv, lapack_int *info );
+void LAPACK_cgetrf( lapack_int* m, lapack_int* n, lapack_complex_float* a,
+ lapack_int* lda, lapack_int* ipiv, lapack_int *info );
+void LAPACK_zgetrf( lapack_int* m, lapack_int* n, lapack_complex_double* a,
+ lapack_int* lda, lapack_int* ipiv, lapack_int *info );
+void LAPACK_sgbtrf( lapack_int* m, lapack_int* n, lapack_int* kl,
+ lapack_int* ku, float* ab, lapack_int* ldab,
+ lapack_int* ipiv, lapack_int *info );
+void LAPACK_dgbtrf( lapack_int* m, lapack_int* n, lapack_int* kl,
+ lapack_int* ku, double* ab, lapack_int* ldab,
+ lapack_int* ipiv, lapack_int *info );
+void LAPACK_cgbtrf( lapack_int* m, lapack_int* n, lapack_int* kl,
+ lapack_int* ku, lapack_complex_float* ab, lapack_int* ldab,
+ lapack_int* ipiv, lapack_int *info );
+void LAPACK_zgbtrf( lapack_int* m, lapack_int* n, lapack_int* kl,
+ lapack_int* ku, lapack_complex_double* ab, lapack_int* ldab,
+ lapack_int* ipiv, lapack_int *info );
+void LAPACK_sgttrf( lapack_int* n, float* dl, float* d, float* du, float* du2,
+ lapack_int* ipiv, lapack_int *info );
+void LAPACK_dgttrf( lapack_int* n, double* dl, double* d, double* du,
+ double* du2, lapack_int* ipiv, lapack_int *info );
+void LAPACK_cgttrf( lapack_int* n, lapack_complex_float* dl,
+ lapack_complex_float* d, lapack_complex_float* du,
+ lapack_complex_float* du2, lapack_int* ipiv,
+ lapack_int *info );
+void LAPACK_zgttrf( lapack_int* n, lapack_complex_double* dl,
+ lapack_complex_double* d, lapack_complex_double* du,
+ lapack_complex_double* du2, lapack_int* ipiv,
+ lapack_int *info );
+void LAPACK_spotrf( char* uplo, lapack_int* n, float* a, lapack_int* lda,
+ lapack_int *info );
+void LAPACK_dpotrf( char* uplo, lapack_int* n, double* a, lapack_int* lda,
+ lapack_int *info );
+void LAPACK_cpotrf( char* uplo, lapack_int* n, lapack_complex_float* a,
+ lapack_int* lda, lapack_int *info );
+void LAPACK_zpotrf( char* uplo, lapack_int* n, lapack_complex_double* a,
+ lapack_int* lda, lapack_int *info );
+void LAPACK_dpstrf( char* uplo, lapack_int* n, double* a, lapack_int* lda,
+ lapack_int* piv, lapack_int* rank, double* tol,
+ double* work, lapack_int *info );
+void LAPACK_spstrf( char* uplo, lapack_int* n, float* a, lapack_int* lda,
+ lapack_int* piv, lapack_int* rank, float* tol, float* work,
+ lapack_int *info );
+void LAPACK_zpstrf( char* uplo, lapack_int* n, lapack_complex_double* a,
+ lapack_int* lda, lapack_int* piv, lapack_int* rank,
+ double* tol, double* work, lapack_int *info );
+void LAPACK_cpstrf( char* uplo, lapack_int* n, lapack_complex_float* a,
+ lapack_int* lda, lapack_int* piv, lapack_int* rank,
+ float* tol, float* work, lapack_int *info );
+void LAPACK_dpftrf( char* transr, char* uplo, lapack_int* n, double* a,
+ lapack_int *info );
+void LAPACK_spftrf( char* transr, char* uplo, lapack_int* n, float* a,
+ lapack_int *info );
+void LAPACK_zpftrf( char* transr, char* uplo, lapack_int* n,
+ lapack_complex_double* a, lapack_int *info );
+void LAPACK_cpftrf( char* transr, char* uplo, lapack_int* n,
+ lapack_complex_float* a, lapack_int *info );
+void LAPACK_spptrf( char* uplo, lapack_int* n, float* ap, lapack_int *info );
+void LAPACK_dpptrf( char* uplo, lapack_int* n, double* ap, lapack_int *info );
+void LAPACK_cpptrf( char* uplo, lapack_int* n, lapack_complex_float* ap,
+ lapack_int *info );
+void LAPACK_zpptrf( char* uplo, lapack_int* n, lapack_complex_double* ap,
+ lapack_int *info );
+void LAPACK_spbtrf( char* uplo, lapack_int* n, lapack_int* kd, float* ab,
+ lapack_int* ldab, lapack_int *info );
+void LAPACK_dpbtrf( char* uplo, lapack_int* n, lapack_int* kd, double* ab,
+ lapack_int* ldab, lapack_int *info );
+void LAPACK_cpbtrf( char* uplo, lapack_int* n, lapack_int* kd,
+ lapack_complex_float* ab, lapack_int* ldab,
+ lapack_int *info );
+void LAPACK_zpbtrf( char* uplo, lapack_int* n, lapack_int* kd,
+ lapack_complex_double* ab, lapack_int* ldab,
+ lapack_int *info );
+void LAPACK_spttrf( lapack_int* n, float* d, float* e, lapack_int *info );
+void LAPACK_dpttrf( lapack_int* n, double* d, double* e, lapack_int *info );
+void LAPACK_cpttrf( lapack_int* n, float* d, lapack_complex_float* e,
+ lapack_int *info );
+void LAPACK_zpttrf( lapack_int* n, double* d, lapack_complex_double* e,
+ lapack_int *info );
+void LAPACK_ssytrf( char* uplo, lapack_int* n, float* a, lapack_int* lda,
+ lapack_int* ipiv, float* work, lapack_int* lwork,
+ lapack_int *info );
+void LAPACK_dsytrf( char* uplo, lapack_int* n, double* a, lapack_int* lda,
+ lapack_int* ipiv, double* work, lapack_int* lwork,
+ lapack_int *info );
+void LAPACK_csytrf( char* uplo, lapack_int* n, lapack_complex_float* a,
+ lapack_int* lda, lapack_int* ipiv,
+ lapack_complex_float* work, lapack_int* lwork,
+ lapack_int *info );
+void LAPACK_zsytrf( char* uplo, lapack_int* n, lapack_complex_double* a,
+ lapack_int* lda, lapack_int* ipiv,
+ lapack_complex_double* work, lapack_int* lwork,
+ lapack_int *info );
+void LAPACK_chetrf( char* uplo, lapack_int* n, lapack_complex_float* a,
+ lapack_int* lda, lapack_int* ipiv,
+ lapack_complex_float* work, lapack_int* lwork,
+ lapack_int *info );
+void LAPACK_zhetrf( char* uplo, lapack_int* n, lapack_complex_double* a,
+ lapack_int* lda, lapack_int* ipiv,
+ lapack_complex_double* work, lapack_int* lwork,
+ lapack_int *info );
+void LAPACK_ssptrf( char* uplo, lapack_int* n, float* ap, lapack_int* ipiv,
+ lapack_int *info );
+void LAPACK_dsptrf( char* uplo, lapack_int* n, double* ap, lapack_int* ipiv,
+ lapack_int *info );
+void LAPACK_csptrf( char* uplo, lapack_int* n, lapack_complex_float* ap,
+ lapack_int* ipiv, lapack_int *info );
+void LAPACK_zsptrf( char* uplo, lapack_int* n, lapack_complex_double* ap,
+ lapack_int* ipiv, lapack_int *info );
+void LAPACK_chptrf( char* uplo, lapack_int* n, lapack_complex_float* ap,
+ lapack_int* ipiv, lapack_int *info );
+void LAPACK_zhptrf( char* uplo, lapack_int* n, lapack_complex_double* ap,
+ lapack_int* ipiv, lapack_int *info );
+void LAPACK_sgetrs( char* trans, lapack_int* n, lapack_int* nrhs,
+ const float* a, lapack_int* lda, const lapack_int* ipiv,
+ float* b, lapack_int* ldb, lapack_int *info );
+void LAPACK_dgetrs( char* trans, lapack_int* n, lapack_int* nrhs,
+ const double* a, lapack_int* lda, const lapack_int* ipiv,
+ double* b, lapack_int* ldb, lapack_int *info );
+void LAPACK_cgetrs( char* trans, lapack_int* n, lapack_int* nrhs,
+ const lapack_complex_float* a, lapack_int* lda,
+ const lapack_int* ipiv, lapack_complex_float* b,
+ lapack_int* ldb, lapack_int *info );
+void LAPACK_zgetrs( char* trans, lapack_int* n, lapack_int* nrhs,
+ const lapack_complex_double* a, lapack_int* lda,
+ const lapack_int* ipiv, lapack_complex_double* b,
+ lapack_int* ldb, lapack_int *info );
+void LAPACK_sgbtrs( char* trans, lapack_int* n, lapack_int* kl, lapack_int* ku,
+ lapack_int* nrhs, const float* ab, lapack_int* ldab,
+ const lapack_int* ipiv, float* b, lapack_int* ldb,
+ lapack_int *info );
+void LAPACK_dgbtrs( char* trans, lapack_int* n, lapack_int* kl, lapack_int* ku,
+ lapack_int* nrhs, const double* ab, lapack_int* ldab,
+ const lapack_int* ipiv, double* b, lapack_int* ldb,
+ lapack_int *info );
+void LAPACK_cgbtrs( char* trans, lapack_int* n, lapack_int* kl, lapack_int* ku,
+ lapack_int* nrhs, const lapack_complex_float* ab,
+ lapack_int* ldab, const lapack_int* ipiv,
+ lapack_complex_float* b, lapack_int* ldb,
+ lapack_int *info );
+void LAPACK_zgbtrs( char* trans, lapack_int* n, lapack_int* kl, lapack_int* ku,
+ lapack_int* nrhs, const lapack_complex_double* ab,
+ lapack_int* ldab, const lapack_int* ipiv,
+ lapack_complex_double* b, lapack_int* ldb,
+ lapack_int *info );
+void LAPACK_sgttrs( char* trans, lapack_int* n, lapack_int* nrhs,
+ const float* dl, const float* d, const float* du,
+ const float* du2, const lapack_int* ipiv, float* b,
+ lapack_int* ldb, lapack_int *info );
+void LAPACK_dgttrs( char* trans, lapack_int* n, lapack_int* nrhs,
+ const double* dl, const double* d, const double* du,
+ const double* du2, const lapack_int* ipiv, double* b,
+ lapack_int* ldb, lapack_int *info );
+void LAPACK_cgttrs( char* trans, lapack_int* n, lapack_int* nrhs,
+ const lapack_complex_float* dl,
+ const lapack_complex_float* d,
+ const lapack_complex_float* du,
+ const lapack_complex_float* du2, const lapack_int* ipiv,
+ lapack_complex_float* b, lapack_int* ldb,
+ lapack_int *info );
+void LAPACK_zgttrs( char* trans, lapack_int* n, lapack_int* nrhs,
+ const lapack_complex_double* dl,
+ const lapack_complex_double* d,
+ const lapack_complex_double* du,
+ const lapack_complex_double* du2, const lapack_int* ipiv,
+ lapack_complex_double* b, lapack_int* ldb,
+ lapack_int *info );
+void LAPACK_spotrs( char* uplo, lapack_int* n, lapack_int* nrhs, const float* a,
+ lapack_int* lda, float* b, lapack_int* ldb,
+ lapack_int *info );
+void LAPACK_dpotrs( char* uplo, lapack_int* n, lapack_int* nrhs,
+ const double* a, lapack_int* lda, double* b,
+ lapack_int* ldb, lapack_int *info );
+void LAPACK_cpotrs( char* uplo, lapack_int* n, lapack_int* nrhs,
+ const lapack_complex_float* a, lapack_int* lda,
+ lapack_complex_float* b, lapack_int* ldb,
+ lapack_int *info );
+void LAPACK_zpotrs( char* uplo, lapack_int* n, lapack_int* nrhs,
+ const lapack_complex_double* a, lapack_int* lda,
+ lapack_complex_double* b, lapack_int* ldb,
+ lapack_int *info );
+void LAPACK_dpftrs( char* transr, char* uplo, lapack_int* n, lapack_int* nrhs,
+ const double* a, double* b, lapack_int* ldb,
+ lapack_int *info );
+void LAPACK_spftrs( char* transr, char* uplo, lapack_int* n, lapack_int* nrhs,
+ const float* a, float* b, lapack_int* ldb,
+ lapack_int *info );
+void LAPACK_zpftrs( char* transr, char* uplo, lapack_int* n, lapack_int* nrhs,
+ const lapack_complex_double* a, lapack_complex_double* b,
+ lapack_int* ldb, lapack_int *info );
+void LAPACK_cpftrs( char* transr, char* uplo, lapack_int* n, lapack_int* nrhs,
+ const lapack_complex_float* a, lapack_complex_float* b,
+ lapack_int* ldb, lapack_int *info );
+void LAPACK_spptrs( char* uplo, lapack_int* n, lapack_int* nrhs,
+ const float* ap, float* b, lapack_int* ldb,
+ lapack_int *info );
+void LAPACK_dpptrs( char* uplo, lapack_int* n, lapack_int* nrhs,
+ const double* ap, double* b, lapack_int* ldb,
+ lapack_int *info );
+void LAPACK_cpptrs( char* uplo, lapack_int* n, lapack_int* nrhs,
+ const lapack_complex_float* ap, lapack_complex_float* b,
+ lapack_int* ldb, lapack_int *info );
+void LAPACK_zpptrs( char* uplo, lapack_int* n, lapack_int* nrhs,
+ const lapack_complex_double* ap, lapack_complex_double* b,
+ lapack_int* ldb, lapack_int *info );
+void LAPACK_spbtrs( char* uplo, lapack_int* n, lapack_int* kd, lapack_int* nrhs,
+ const float* ab, lapack_int* ldab, float* b,
+ lapack_int* ldb, lapack_int *info );
+void LAPACK_dpbtrs( char* uplo, lapack_int* n, lapack_int* kd, lapack_int* nrhs,
+ const double* ab, lapack_int* ldab, double* b,
+ lapack_int* ldb, lapack_int *info );
+void LAPACK_cpbtrs( char* uplo, lapack_int* n, lapack_int* kd, lapack_int* nrhs,
+ const lapack_complex_float* ab, lapack_int* ldab,
+ lapack_complex_float* b, lapack_int* ldb,
+ lapack_int *info );
+void LAPACK_zpbtrs( char* uplo, lapack_int* n, lapack_int* kd, lapack_int* nrhs,
+ const lapack_complex_double* ab, lapack_int* ldab,
+ lapack_complex_double* b, lapack_int* ldb,
+ lapack_int *info );
+void LAPACK_spttrs( lapack_int* n, lapack_int* nrhs, const float* d,
+ const float* e, float* b, lapack_int* ldb,
+ lapack_int *info );
+void LAPACK_dpttrs( lapack_int* n, lapack_int* nrhs, const double* d,
+ const double* e, double* b, lapack_int* ldb,
+ lapack_int *info );
+void LAPACK_cpttrs( char* uplo, lapack_int* n, lapack_int* nrhs, const float* d,
+ const lapack_complex_float* e, lapack_complex_float* b,
+ lapack_int* ldb, lapack_int *info );
+void LAPACK_zpttrs( char* uplo, lapack_int* n, lapack_int* nrhs,
+ const double* d, const lapack_complex_double* e,
+ lapack_complex_double* b, lapack_int* ldb,
+ lapack_int *info );
+void LAPACK_ssytrs( char* uplo, lapack_int* n, lapack_int* nrhs, const float* a,
+ lapack_int* lda, const lapack_int* ipiv, float* b,
+ lapack_int* ldb, lapack_int *info );
+void LAPACK_dsytrs( char* uplo, lapack_int* n, lapack_int* nrhs,
+ const double* a, lapack_int* lda, const lapack_int* ipiv,
+ double* b, lapack_int* ldb, lapack_int *info );
+void LAPACK_csytrs( char* uplo, lapack_int* n, lapack_int* nrhs,
+ const lapack_complex_float* a, lapack_int* lda,
+ const lapack_int* ipiv, lapack_complex_float* b,
+ lapack_int* ldb, lapack_int *info );
+void LAPACK_zsytrs( char* uplo, lapack_int* n, lapack_int* nrhs,
+ const lapack_complex_double* a, lapack_int* lda,
+ const lapack_int* ipiv, lapack_complex_double* b,
+ lapack_int* ldb, lapack_int *info );
+void LAPACK_chetrs( char* uplo, lapack_int* n, lapack_int* nrhs,
+ const lapack_complex_float* a, lapack_int* lda,
+ const lapack_int* ipiv, lapack_complex_float* b,
+ lapack_int* ldb, lapack_int *info );
+void LAPACK_zhetrs( char* uplo, lapack_int* n, lapack_int* nrhs,
+ const lapack_complex_double* a, lapack_int* lda,
+ const lapack_int* ipiv, lapack_complex_double* b,
+ lapack_int* ldb, lapack_int *info );
+void LAPACK_ssptrs( char* uplo, lapack_int* n, lapack_int* nrhs,
+ const float* ap, const lapack_int* ipiv, float* b,
+ lapack_int* ldb, lapack_int *info );
+void LAPACK_dsptrs( char* uplo, lapack_int* n, lapack_int* nrhs,
+ const double* ap, const lapack_int* ipiv, double* b,
+ lapack_int* ldb, lapack_int *info );
+void LAPACK_csptrs( char* uplo, lapack_int* n, lapack_int* nrhs,
+ const lapack_complex_float* ap, const lapack_int* ipiv,
+ lapack_complex_float* b, lapack_int* ldb,
+ lapack_int *info );
+void LAPACK_zsptrs( char* uplo, lapack_int* n, lapack_int* nrhs,
+ const lapack_complex_double* ap, const lapack_int* ipiv,
+ lapack_complex_double* b, lapack_int* ldb,
+ lapack_int *info );
+void LAPACK_chptrs( char* uplo, lapack_int* n, lapack_int* nrhs,
+ const lapack_complex_float* ap, const lapack_int* ipiv,
+ lapack_complex_float* b, lapack_int* ldb,
+ lapack_int *info );
+void LAPACK_zhptrs( char* uplo, lapack_int* n, lapack_int* nrhs,
+ const lapack_complex_double* ap, const lapack_int* ipiv,
+ lapack_complex_double* b, lapack_int* ldb,
+ lapack_int *info );
+void LAPACK_strtrs( char* uplo, char* trans, char* diag, lapack_int* n,
+ lapack_int* nrhs, const float* a, lapack_int* lda, float* b,
+ lapack_int* ldb, lapack_int *info );
+void LAPACK_dtrtrs( char* uplo, char* trans, char* diag, lapack_int* n,
+ lapack_int* nrhs, const double* a, lapack_int* lda,
+ double* b, lapack_int* ldb, lapack_int *info );
+void LAPACK_ctrtrs( char* uplo, char* trans, char* diag, lapack_int* n,
+ lapack_int* nrhs, const lapack_complex_float* a,
+ lapack_int* lda, lapack_complex_float* b, lapack_int* ldb,
+ lapack_int *info );
+void LAPACK_ztrtrs( char* uplo, char* trans, char* diag, lapack_int* n,
+ lapack_int* nrhs, const lapack_complex_double* a,
+ lapack_int* lda, lapack_complex_double* b, lapack_int* ldb,
+ lapack_int *info );
+void LAPACK_stptrs( char* uplo, char* trans, char* diag, lapack_int* n,
+ lapack_int* nrhs, const float* ap, float* b,
+ lapack_int* ldb, lapack_int *info );
+void LAPACK_dtptrs( char* uplo, char* trans, char* diag, lapack_int* n,
+ lapack_int* nrhs, const double* ap, double* b,
+ lapack_int* ldb, lapack_int *info );
+void LAPACK_ctptrs( char* uplo, char* trans, char* diag, lapack_int* n,
+ lapack_int* nrhs, const lapack_complex_float* ap,
+ lapack_complex_float* b, lapack_int* ldb,
+ lapack_int *info );
+void LAPACK_ztptrs( char* uplo, char* trans, char* diag, lapack_int* n,
+ lapack_int* nrhs, const lapack_complex_double* ap,
+ lapack_complex_double* b, lapack_int* ldb,
+ lapack_int *info );
+void LAPACK_stbtrs( char* uplo, char* trans, char* diag, lapack_int* n,
+ lapack_int* kd, lapack_int* nrhs, const float* ab,
+ lapack_int* ldab, float* b, lapack_int* ldb,
+ lapack_int *info );
+void LAPACK_dtbtrs( char* uplo, char* trans, char* diag, lapack_int* n,
+ lapack_int* kd, lapack_int* nrhs, const double* ab,
+ lapack_int* ldab, double* b, lapack_int* ldb,
+ lapack_int *info );
+void LAPACK_ctbtrs( char* uplo, char* trans, char* diag, lapack_int* n,
+ lapack_int* kd, lapack_int* nrhs,
+ const lapack_complex_float* ab, lapack_int* ldab,
+ lapack_complex_float* b, lapack_int* ldb,
+ lapack_int *info );
+void LAPACK_ztbtrs( char* uplo, char* trans, char* diag, lapack_int* n,
+ lapack_int* kd, lapack_int* nrhs,
+ const lapack_complex_double* ab, lapack_int* ldab,
+ lapack_complex_double* b, lapack_int* ldb,
+ lapack_int *info );
+void LAPACK_sgecon( char* norm, lapack_int* n, const float* a, lapack_int* lda,
+ float* anorm, float* rcond, float* work, lapack_int* iwork,
+ lapack_int *info );
+void LAPACK_dgecon( char* norm, lapack_int* n, const double* a, lapack_int* lda,
+ double* anorm, double* rcond, double* work,
+ lapack_int* iwork, lapack_int *info );
+void LAPACK_cgecon( char* norm, lapack_int* n, const lapack_complex_float* a,
+ lapack_int* lda, float* anorm, float* rcond,
+ lapack_complex_float* work, float* rwork,
+ lapack_int *info );
+void LAPACK_zgecon( char* norm, lapack_int* n, const lapack_complex_double* a,
+ lapack_int* lda, double* anorm, double* rcond,
+ lapack_complex_double* work, double* rwork,
+ lapack_int *info );
+void LAPACK_sgbcon( char* norm, lapack_int* n, lapack_int* kl, lapack_int* ku,
+ const float* ab, lapack_int* ldab, const lapack_int* ipiv,
+ float* anorm, float* rcond, float* work, lapack_int* iwork,
+ lapack_int *info );
+void LAPACK_dgbcon( char* norm, lapack_int* n, lapack_int* kl, lapack_int* ku,
+ const double* ab, lapack_int* ldab, const lapack_int* ipiv,
+ double* anorm, double* rcond, double* work,
+ lapack_int* iwork, lapack_int *info );
+void LAPACK_cgbcon( char* norm, lapack_int* n, lapack_int* kl, lapack_int* ku,
+ const lapack_complex_float* ab, lapack_int* ldab,
+ const lapack_int* ipiv, float* anorm, float* rcond,
+ lapack_complex_float* work, float* rwork,
+ lapack_int *info );
+void LAPACK_zgbcon( char* norm, lapack_int* n, lapack_int* kl, lapack_int* ku,
+ const lapack_complex_double* ab, lapack_int* ldab,
+ const lapack_int* ipiv, double* anorm, double* rcond,
+ lapack_complex_double* work, double* rwork,
+ lapack_int *info );
+void LAPACK_sgtcon( char* norm, lapack_int* n, const float* dl, const float* d,
+ const float* du, const float* du2, const lapack_int* ipiv,
+ float* anorm, float* rcond, float* work, lapack_int* iwork,
+ lapack_int *info );
+void LAPACK_dgtcon( char* norm, lapack_int* n, const double* dl,
+ const double* d, const double* du, const double* du2,
+ const lapack_int* ipiv, double* anorm, double* rcond,
+ double* work, lapack_int* iwork, lapack_int *info );
+void LAPACK_cgtcon( char* norm, lapack_int* n, const lapack_complex_float* dl,
+ const lapack_complex_float* d,
+ const lapack_complex_float* du,
+ const lapack_complex_float* du2, const lapack_int* ipiv,
+ float* anorm, float* rcond, lapack_complex_float* work,
+ lapack_int *info );
+void LAPACK_zgtcon( char* norm, lapack_int* n, const lapack_complex_double* dl,
+ const lapack_complex_double* d,
+ const lapack_complex_double* du,
+ const lapack_complex_double* du2, const lapack_int* ipiv,
+ double* anorm, double* rcond, lapack_complex_double* work,
+ lapack_int *info );
+void LAPACK_spocon( char* uplo, lapack_int* n, const float* a, lapack_int* lda,
+ float* anorm, float* rcond, float* work, lapack_int* iwork,
+ lapack_int *info );
+void LAPACK_dpocon( char* uplo, lapack_int* n, const double* a, lapack_int* lda,
+ double* anorm, double* rcond, double* work,
+ lapack_int* iwork, lapack_int *info );
+void LAPACK_cpocon( char* uplo, lapack_int* n, const lapack_complex_float* a,
+ lapack_int* lda, float* anorm, float* rcond,
+ lapack_complex_float* work, float* rwork,
+ lapack_int *info );
+void LAPACK_zpocon( char* uplo, lapack_int* n, const lapack_complex_double* a,
+ lapack_int* lda, double* anorm, double* rcond,
+ lapack_complex_double* work, double* rwork,
+ lapack_int *info );
+void LAPACK_sppcon( char* uplo, lapack_int* n, const float* ap, float* anorm,
+ float* rcond, float* work, lapack_int* iwork,
+ lapack_int *info );
+void LAPACK_dppcon( char* uplo, lapack_int* n, const double* ap, double* anorm,
+ double* rcond, double* work, lapack_int* iwork,
+ lapack_int *info );
+void LAPACK_cppcon( char* uplo, lapack_int* n, const lapack_complex_float* ap,
+ float* anorm, float* rcond, lapack_complex_float* work,
+ float* rwork, lapack_int *info );
+void LAPACK_zppcon( char* uplo, lapack_int* n, const lapack_complex_double* ap,
+ double* anorm, double* rcond, lapack_complex_double* work,
+ double* rwork, lapack_int *info );
+void LAPACK_spbcon( char* uplo, lapack_int* n, lapack_int* kd, const float* ab,
+ lapack_int* ldab, float* anorm, float* rcond, float* work,
+ lapack_int* iwork, lapack_int *info );
+void LAPACK_dpbcon( char* uplo, lapack_int* n, lapack_int* kd, const double* ab,
+ lapack_int* ldab, double* anorm, double* rcond,
+ double* work, lapack_int* iwork, lapack_int *info );
+void LAPACK_cpbcon( char* uplo, lapack_int* n, lapack_int* kd,
+ const lapack_complex_float* ab, lapack_int* ldab,
+ float* anorm, float* rcond, lapack_complex_float* work,
+ float* rwork, lapack_int *info );
+void LAPACK_zpbcon( char* uplo, lapack_int* n, lapack_int* kd,
+ const lapack_complex_double* ab, lapack_int* ldab,
+ double* anorm, double* rcond, lapack_complex_double* work,
+ double* rwork, lapack_int *info );
+void LAPACK_sptcon( lapack_int* n, const float* d, const float* e, float* anorm,
+ float* rcond, float* work, lapack_int *info );
+void LAPACK_dptcon( lapack_int* n, const double* d, const double* e,
+ double* anorm, double* rcond, double* work,
+ lapack_int *info );
+void LAPACK_cptcon( lapack_int* n, const float* d,
+ const lapack_complex_float* e, float* anorm, float* rcond,
+ float* work, lapack_int *info );
+void LAPACK_zptcon( lapack_int* n, const double* d,
+ const lapack_complex_double* e, double* anorm,
+ double* rcond, double* work, lapack_int *info );
+void LAPACK_ssycon( char* uplo, lapack_int* n, const float* a, lapack_int* lda,
+ const lapack_int* ipiv, float* anorm, float* rcond,
+ float* work, lapack_int* iwork, lapack_int *info );
+void LAPACK_dsycon( char* uplo, lapack_int* n, const double* a, lapack_int* lda,
+ const lapack_int* ipiv, double* anorm, double* rcond,
+ double* work, lapack_int* iwork, lapack_int *info );
+void LAPACK_csycon( char* uplo, lapack_int* n, const lapack_complex_float* a,
+ lapack_int* lda, const lapack_int* ipiv, float* anorm,
+ float* rcond, lapack_complex_float* work,
+ lapack_int *info );
+void LAPACK_zsycon( char* uplo, lapack_int* n, const lapack_complex_double* a,
+ lapack_int* lda, const lapack_int* ipiv, double* anorm,
+ double* rcond, lapack_complex_double* work,
+ lapack_int *info );
+void LAPACK_checon( char* uplo, lapack_int* n, const lapack_complex_float* a,
+ lapack_int* lda, const lapack_int* ipiv, float* anorm,
+ float* rcond, lapack_complex_float* work,
+ lapack_int *info );
+void LAPACK_zhecon( char* uplo, lapack_int* n, const lapack_complex_double* a,
+ lapack_int* lda, const lapack_int* ipiv, double* anorm,
+ double* rcond, lapack_complex_double* work,
+ lapack_int *info );
+void LAPACK_sspcon( char* uplo, lapack_int* n, const float* ap,
+ const lapack_int* ipiv, float* anorm, float* rcond,
+ float* work, lapack_int* iwork, lapack_int *info );
+void LAPACK_dspcon( char* uplo, lapack_int* n, const double* ap,
+ const lapack_int* ipiv, double* anorm, double* rcond,
+ double* work, lapack_int* iwork, lapack_int *info );
+void LAPACK_cspcon( char* uplo, lapack_int* n, const lapack_complex_float* ap,
+ const lapack_int* ipiv, float* anorm, float* rcond,
+ lapack_complex_float* work, lapack_int *info );
+void LAPACK_zspcon( char* uplo, lapack_int* n, const lapack_complex_double* ap,
+ const lapack_int* ipiv, double* anorm, double* rcond,
+ lapack_complex_double* work, lapack_int *info );
+void LAPACK_chpcon( char* uplo, lapack_int* n, const lapack_complex_float* ap,
+ const lapack_int* ipiv, float* anorm, float* rcond,
+ lapack_complex_float* work, lapack_int *info );
+void LAPACK_zhpcon( char* uplo, lapack_int* n, const lapack_complex_double* ap,
+ const lapack_int* ipiv, double* anorm, double* rcond,
+ lapack_complex_double* work, lapack_int *info );
+void LAPACK_strcon( char* norm, char* uplo, char* diag, lapack_int* n,
+ const float* a, lapack_int* lda, float* rcond, float* work,
+ lapack_int* iwork, lapack_int *info );
+void LAPACK_dtrcon( char* norm, char* uplo, char* diag, lapack_int* n,
+ const double* a, lapack_int* lda, double* rcond,
+ double* work, lapack_int* iwork, lapack_int *info );
+void LAPACK_ctrcon( char* norm, char* uplo, char* diag, lapack_int* n,
+ const lapack_complex_float* a, lapack_int* lda,
+ float* rcond, lapack_complex_float* work, float* rwork,
+ lapack_int *info );
+void LAPACK_ztrcon( char* norm, char* uplo, char* diag, lapack_int* n,
+ const lapack_complex_double* a, lapack_int* lda,
+ double* rcond, lapack_complex_double* work, double* rwork,
+ lapack_int *info );
+void LAPACK_stpcon( char* norm, char* uplo, char* diag, lapack_int* n,
+ const float* ap, float* rcond, float* work,
+ lapack_int* iwork, lapack_int *info );
+void LAPACK_dtpcon( char* norm, char* uplo, char* diag, lapack_int* n,
+ const double* ap, double* rcond, double* work,
+ lapack_int* iwork, lapack_int *info );
+void LAPACK_ctpcon( char* norm, char* uplo, char* diag, lapack_int* n,
+ const lapack_complex_float* ap, float* rcond,
+ lapack_complex_float* work, float* rwork,
+ lapack_int *info );
+void LAPACK_ztpcon( char* norm, char* uplo, char* diag, lapack_int* n,
+ const lapack_complex_double* ap, double* rcond,
+ lapack_complex_double* work, double* rwork,
+ lapack_int *info );
+void LAPACK_stbcon( char* norm, char* uplo, char* diag, lapack_int* n,
+ lapack_int* kd, const float* ab, lapack_int* ldab,
+ float* rcond, float* work, lapack_int* iwork,
+ lapack_int *info );
+void LAPACK_dtbcon( char* norm, char* uplo, char* diag, lapack_int* n,
+ lapack_int* kd, const double* ab, lapack_int* ldab,
+ double* rcond, double* work, lapack_int* iwork,
+ lapack_int *info );
+void LAPACK_ctbcon( char* norm, char* uplo, char* diag, lapack_int* n,
+ lapack_int* kd, const lapack_complex_float* ab,
+ lapack_int* ldab, float* rcond, lapack_complex_float* work,
+ float* rwork, lapack_int *info );
+void LAPACK_ztbcon( char* norm, char* uplo, char* diag, lapack_int* n,
+ lapack_int* kd, const lapack_complex_double* ab,
+ lapack_int* ldab, double* rcond,
+ lapack_complex_double* work, double* rwork,
+ lapack_int *info );
+void LAPACK_sgerfs( char* trans, lapack_int* n, lapack_int* nrhs,
+ const float* a, lapack_int* lda, const float* af,
+ lapack_int* ldaf, const lapack_int* ipiv, const float* b,
+ lapack_int* ldb, float* x, lapack_int* ldx, float* ferr,
+ float* berr, float* work, lapack_int* iwork,
+ lapack_int *info );
+void LAPACK_dgerfs( char* trans, lapack_int* n, lapack_int* nrhs,
+ const double* a, lapack_int* lda, const double* af,
+ lapack_int* ldaf, const lapack_int* ipiv, const double* b,
+ lapack_int* ldb, double* x, lapack_int* ldx, double* ferr,
+ double* berr, double* work, lapack_int* iwork,
+ lapack_int *info );
+void LAPACK_cgerfs( char* trans, lapack_int* n, lapack_int* nrhs,
+ const lapack_complex_float* a, lapack_int* lda,
+ const lapack_complex_float* af, lapack_int* ldaf,
+ const lapack_int* ipiv, const lapack_complex_float* b,
+ lapack_int* ldb, lapack_complex_float* x, lapack_int* ldx,
+ float* ferr, float* berr, lapack_complex_float* work,
+ float* rwork, lapack_int *info );
+void LAPACK_zgerfs( char* trans, lapack_int* n, lapack_int* nrhs,
+ const lapack_complex_double* a, lapack_int* lda,
+ const lapack_complex_double* af, lapack_int* ldaf,
+ const lapack_int* ipiv, const lapack_complex_double* b,
+ lapack_int* ldb, lapack_complex_double* x, lapack_int* ldx,
+ double* ferr, double* berr, lapack_complex_double* work,
+ double* rwork, lapack_int *info );
+void LAPACK_dgerfsx( char* trans, char* equed, lapack_int* n, lapack_int* nrhs,
+ const double* a, lapack_int* lda, const double* af,
+ lapack_int* ldaf, const lapack_int* ipiv, const double* r,
+ const double* c, const double* b, lapack_int* ldb,
+ double* x, lapack_int* ldx, double* rcond, double* berr,
+ lapack_int* n_err_bnds, double* err_bnds_norm,
+ double* err_bnds_comp, lapack_int* nparams, double* params,
+ double* work, lapack_int* iwork, lapack_int *info );
+void LAPACK_sgerfsx( char* trans, char* equed, lapack_int* n, lapack_int* nrhs,
+ const float* a, lapack_int* lda, const float* af,
+ lapack_int* ldaf, const lapack_int* ipiv, const float* r,
+ const float* c, const float* b, lapack_int* ldb, float* x,
+ lapack_int* ldx, float* rcond, float* berr,
+ lapack_int* n_err_bnds, float* err_bnds_norm,
+ float* err_bnds_comp, lapack_int* nparams, float* params,
+ float* work, lapack_int* iwork, lapack_int *info );
+void LAPACK_zgerfsx( char* trans, char* equed, lapack_int* n, lapack_int* nrhs,
+ const lapack_complex_double* a, lapack_int* lda,
+ const lapack_complex_double* af, lapack_int* ldaf,
+ const lapack_int* ipiv, const double* r, const double* c,
+ const lapack_complex_double* b, lapack_int* ldb,
+ lapack_complex_double* x, lapack_int* ldx, double* rcond,
+ double* berr, lapack_int* n_err_bnds,
+ double* err_bnds_norm, double* err_bnds_comp,
+ lapack_int* nparams, double* params,
+ lapack_complex_double* work, double* rwork,
+ lapack_int *info );
+void LAPACK_cgerfsx( char* trans, char* equed, lapack_int* n, lapack_int* nrhs,
+ const lapack_complex_float* a, lapack_int* lda,
+ const lapack_complex_float* af, lapack_int* ldaf,
+ const lapack_int* ipiv, const float* r, const float* c,
+ const lapack_complex_float* b, lapack_int* ldb,
+ lapack_complex_float* x, lapack_int* ldx, float* rcond,
+ float* berr, lapack_int* n_err_bnds, float* err_bnds_norm,
+ float* err_bnds_comp, lapack_int* nparams, float* params,
+ lapack_complex_float* work, float* rwork,
+ lapack_int *info );
+void LAPACK_sgbrfs( char* trans, lapack_int* n, lapack_int* kl, lapack_int* ku,
+ lapack_int* nrhs, const float* ab, lapack_int* ldab,
+ const float* afb, lapack_int* ldafb, const lapack_int* ipiv,
+ const float* b, lapack_int* ldb, float* x, lapack_int* ldx,
+ float* ferr, float* berr, float* work, lapack_int* iwork,
+ lapack_int *info );
+void LAPACK_dgbrfs( char* trans, lapack_int* n, lapack_int* kl, lapack_int* ku,
+ lapack_int* nrhs, const double* ab, lapack_int* ldab,
+ const double* afb, lapack_int* ldafb,
+ const lapack_int* ipiv, const double* b, lapack_int* ldb,
+ double* x, lapack_int* ldx, double* ferr, double* berr,
+ double* work, lapack_int* iwork, lapack_int *info );
+void LAPACK_cgbrfs( char* trans, lapack_int* n, lapack_int* kl, lapack_int* ku,
+ lapack_int* nrhs, const lapack_complex_float* ab,
+ lapack_int* ldab, const lapack_complex_float* afb,
+ lapack_int* ldafb, const lapack_int* ipiv,
+ const lapack_complex_float* b, lapack_int* ldb,
+ lapack_complex_float* x, lapack_int* ldx, float* ferr,
+ float* berr, lapack_complex_float* work, float* rwork,
+ lapack_int *info );
+void LAPACK_zgbrfs( char* trans, lapack_int* n, lapack_int* kl, lapack_int* ku,
+ lapack_int* nrhs, const lapack_complex_double* ab,
+ lapack_int* ldab, const lapack_complex_double* afb,
+ lapack_int* ldafb, const lapack_int* ipiv,
+ const lapack_complex_double* b, lapack_int* ldb,
+ lapack_complex_double* x, lapack_int* ldx, double* ferr,
+ double* berr, lapack_complex_double* work, double* rwork,
+ lapack_int *info );
+void LAPACK_dgbrfsx( char* trans, char* equed, lapack_int* n, lapack_int* kl,
+ lapack_int* ku, lapack_int* nrhs, const double* ab,
+ lapack_int* ldab, const double* afb, lapack_int* ldafb,
+ const lapack_int* ipiv, const double* r, const double* c,
+ const double* b, lapack_int* ldb, double* x,
+ lapack_int* ldx, double* rcond, double* berr,
+ lapack_int* n_err_bnds, double* err_bnds_norm,
+ double* err_bnds_comp, lapack_int* nparams, double* params,
+ double* work, lapack_int* iwork, lapack_int *info );
+void LAPACK_sgbrfsx( char* trans, char* equed, lapack_int* n, lapack_int* kl,
+ lapack_int* ku, lapack_int* nrhs, const float* ab,
+ lapack_int* ldab, const float* afb, lapack_int* ldafb,
+ const lapack_int* ipiv, const float* r, const float* c,
+ const float* b, lapack_int* ldb, float* x, lapack_int* ldx,
+ float* rcond, float* berr, lapack_int* n_err_bnds,
+ float* err_bnds_norm, float* err_bnds_comp,
+ lapack_int* nparams, float* params, float* work,
+ lapack_int* iwork, lapack_int *info );
+void LAPACK_zgbrfsx( char* trans, char* equed, lapack_int* n, lapack_int* kl,
+ lapack_int* ku, lapack_int* nrhs,
+ const lapack_complex_double* ab, lapack_int* ldab,
+ const lapack_complex_double* afb, lapack_int* ldafb,
+ const lapack_int* ipiv, const double* r, const double* c,
+ const lapack_complex_double* b, lapack_int* ldb,
+ lapack_complex_double* x, lapack_int* ldx, double* rcond,
+ double* berr, lapack_int* n_err_bnds,
+ double* err_bnds_norm, double* err_bnds_comp,
+ lapack_int* nparams, double* params,
+ lapack_complex_double* work, double* rwork,
+ lapack_int *info );
+void LAPACK_cgbrfsx( char* trans, char* equed, lapack_int* n, lapack_int* kl,
+ lapack_int* ku, lapack_int* nrhs,
+ const lapack_complex_float* ab, lapack_int* ldab,
+ const lapack_complex_float* afb, lapack_int* ldafb,
+ const lapack_int* ipiv, const float* r, const float* c,
+ const lapack_complex_float* b, lapack_int* ldb,
+ lapack_complex_float* x, lapack_int* ldx, float* rcond,
+ float* berr, lapack_int* n_err_bnds, float* err_bnds_norm,
+ float* err_bnds_comp, lapack_int* nparams, float* params,
+ lapack_complex_float* work, float* rwork,
+ lapack_int *info );
+void LAPACK_sgtrfs( char* trans, lapack_int* n, lapack_int* nrhs,
+ const float* dl, const float* d, const float* du,
+ const float* dlf, const float* df, const float* duf,
+ const float* du2, const lapack_int* ipiv, const float* b,
+ lapack_int* ldb, float* x, lapack_int* ldx, float* ferr,
+ float* berr, float* work, lapack_int* iwork,
+ lapack_int *info );
+void LAPACK_dgtrfs( char* trans, lapack_int* n, lapack_int* nrhs,
+ const double* dl, const double* d, const double* du,
+ const double* dlf, const double* df, const double* duf,
+ const double* du2, const lapack_int* ipiv, const double* b,
+ lapack_int* ldb, double* x, lapack_int* ldx, double* ferr,
+ double* berr, double* work, lapack_int* iwork,
+ lapack_int *info );
+void LAPACK_cgtrfs( char* trans, lapack_int* n, lapack_int* nrhs,
+ const lapack_complex_float* dl,
+ const lapack_complex_float* d,
+ const lapack_complex_float* du,
+ const lapack_complex_float* dlf,
+ const lapack_complex_float* df,
+ const lapack_complex_float* duf,
+ const lapack_complex_float* du2, const lapack_int* ipiv,
+ const lapack_complex_float* b, lapack_int* ldb,
+ lapack_complex_float* x, lapack_int* ldx, float* ferr,
+ float* berr, lapack_complex_float* work, float* rwork,
+ lapack_int *info );
+void LAPACK_zgtrfs( char* trans, lapack_int* n, lapack_int* nrhs,
+ const lapack_complex_double* dl,
+ const lapack_complex_double* d,
+ const lapack_complex_double* du,
+ const lapack_complex_double* dlf,
+ const lapack_complex_double* df,
+ const lapack_complex_double* duf,
+ const lapack_complex_double* du2, const lapack_int* ipiv,
+ const lapack_complex_double* b, lapack_int* ldb,
+ lapack_complex_double* x, lapack_int* ldx, double* ferr,
+ double* berr, lapack_complex_double* work, double* rwork,
+ lapack_int *info );
+void LAPACK_sporfs( char* uplo, lapack_int* n, lapack_int* nrhs, const float* a,
+ lapack_int* lda, const float* af, lapack_int* ldaf,
+ const float* b, lapack_int* ldb, float* x, lapack_int* ldx,
+ float* ferr, float* berr, float* work, lapack_int* iwork,
+ lapack_int *info );
+void LAPACK_dporfs( char* uplo, lapack_int* n, lapack_int* nrhs,
+ const double* a, lapack_int* lda, const double* af,
+ lapack_int* ldaf, const double* b, lapack_int* ldb,
+ double* x, lapack_int* ldx, double* ferr, double* berr,
+ double* work, lapack_int* iwork, lapack_int *info );
+void LAPACK_cporfs( char* uplo, lapack_int* n, lapack_int* nrhs,
+ const lapack_complex_float* a, lapack_int* lda,
+ const lapack_complex_float* af, lapack_int* ldaf,
+ const lapack_complex_float* b, lapack_int* ldb,
+ lapack_complex_float* x, lapack_int* ldx, float* ferr,
+ float* berr, lapack_complex_float* work, float* rwork,
+ lapack_int *info );
+void LAPACK_zporfs( char* uplo, lapack_int* n, lapack_int* nrhs,
+ const lapack_complex_double* a, lapack_int* lda,
+ const lapack_complex_double* af, lapack_int* ldaf,
+ const lapack_complex_double* b, lapack_int* ldb,
+ lapack_complex_double* x, lapack_int* ldx, double* ferr,
+ double* berr, lapack_complex_double* work, double* rwork,
+ lapack_int *info );
+void LAPACK_dporfsx( char* uplo, char* equed, lapack_int* n, lapack_int* nrhs,
+ const double* a, lapack_int* lda, const double* af,
+ lapack_int* ldaf, const double* s, const double* b,
+ lapack_int* ldb, double* x, lapack_int* ldx, double* rcond,
+ double* berr, lapack_int* n_err_bnds,
+ double* err_bnds_norm, double* err_bnds_comp,
+ lapack_int* nparams, double* params, double* work,
+ lapack_int* iwork, lapack_int *info );
+void LAPACK_sporfsx( char* uplo, char* equed, lapack_int* n, lapack_int* nrhs,
+ const float* a, lapack_int* lda, const float* af,
+ lapack_int* ldaf, const float* s, const float* b,
+ lapack_int* ldb, float* x, lapack_int* ldx, float* rcond,
+ float* berr, lapack_int* n_err_bnds, float* err_bnds_norm,
+ float* err_bnds_comp, lapack_int* nparams, float* params,
+ float* work, lapack_int* iwork, lapack_int *info );
+void LAPACK_zporfsx( char* uplo, char* equed, lapack_int* n, lapack_int* nrhs,
+ const lapack_complex_double* a, lapack_int* lda,
+ const lapack_complex_double* af, lapack_int* ldaf,
+ const double* s, const lapack_complex_double* b,
+ lapack_int* ldb, lapack_complex_double* x, lapack_int* ldx,
+ double* rcond, double* berr, lapack_int* n_err_bnds,
+ double* err_bnds_norm, double* err_bnds_comp,
+ lapack_int* nparams, double* params,
+ lapack_complex_double* work, double* rwork,
+ lapack_int *info );
+void LAPACK_cporfsx( char* uplo, char* equed, lapack_int* n, lapack_int* nrhs,
+ const lapack_complex_float* a, lapack_int* lda,
+ const lapack_complex_float* af, lapack_int* ldaf,
+ const float* s, const lapack_complex_float* b,
+ lapack_int* ldb, lapack_complex_float* x, lapack_int* ldx,
+ float* rcond, float* berr, lapack_int* n_err_bnds,
+ float* err_bnds_norm, float* err_bnds_comp,
+ lapack_int* nparams, float* params,
+ lapack_complex_float* work, float* rwork,
+ lapack_int *info );
+void LAPACK_spprfs( char* uplo, lapack_int* n, lapack_int* nrhs,
+ const float* ap, const float* afp, const float* b,
+ lapack_int* ldb, float* x, lapack_int* ldx, float* ferr,
+ float* berr, float* work, lapack_int* iwork,
+ lapack_int *info );
+void LAPACK_dpprfs( char* uplo, lapack_int* n, lapack_int* nrhs,
+ const double* ap, const double* afp, const double* b,
+ lapack_int* ldb, double* x, lapack_int* ldx, double* ferr,
+ double* berr, double* work, lapack_int* iwork,
+ lapack_int *info );
+void LAPACK_cpprfs( char* uplo, lapack_int* n, lapack_int* nrhs,
+ const lapack_complex_float* ap,
+ const lapack_complex_float* afp,
+ const lapack_complex_float* b, lapack_int* ldb,
+ lapack_complex_float* x, lapack_int* ldx, float* ferr,
+ float* berr, lapack_complex_float* work, float* rwork,
+ lapack_int *info );
+void LAPACK_zpprfs( char* uplo, lapack_int* n, lapack_int* nrhs,
+ const lapack_complex_double* ap,
+ const lapack_complex_double* afp,
+ const lapack_complex_double* b, lapack_int* ldb,
+ lapack_complex_double* x, lapack_int* ldx, double* ferr,
+ double* berr, lapack_complex_double* work, double* rwork,
+ lapack_int *info );
+void LAPACK_spbrfs( char* uplo, lapack_int* n, lapack_int* kd, lapack_int* nrhs,
+ const float* ab, lapack_int* ldab, const float* afb,
+ lapack_int* ldafb, const float* b, lapack_int* ldb,
+ float* x, lapack_int* ldx, float* ferr, float* berr,
+ float* work, lapack_int* iwork, lapack_int *info );
+void LAPACK_dpbrfs( char* uplo, lapack_int* n, lapack_int* kd, lapack_int* nrhs,
+ const double* ab, lapack_int* ldab, const double* afb,
+ lapack_int* ldafb, const double* b, lapack_int* ldb,
+ double* x, lapack_int* ldx, double* ferr, double* berr,
+ double* work, lapack_int* iwork, lapack_int *info );
+void LAPACK_cpbrfs( char* uplo, lapack_int* n, lapack_int* kd, lapack_int* nrhs,
+ const lapack_complex_float* ab, lapack_int* ldab,
+ const lapack_complex_float* afb, lapack_int* ldafb,
+ const lapack_complex_float* b, lapack_int* ldb,
+ lapack_complex_float* x, lapack_int* ldx, float* ferr,
+ float* berr, lapack_complex_float* work, float* rwork,
+ lapack_int *info );
+void LAPACK_zpbrfs( char* uplo, lapack_int* n, lapack_int* kd, lapack_int* nrhs,
+ const lapack_complex_double* ab, lapack_int* ldab,
+ const lapack_complex_double* afb, lapack_int* ldafb,
+ const lapack_complex_double* b, lapack_int* ldb,
+ lapack_complex_double* x, lapack_int* ldx, double* ferr,
+ double* berr, lapack_complex_double* work, double* rwork,
+ lapack_int *info );
+void LAPACK_sptrfs( lapack_int* n, lapack_int* nrhs, const float* d,
+ const float* e, const float* df, const float* ef,
+ const float* b, lapack_int* ldb, float* x, lapack_int* ldx,
+ float* ferr, float* berr, float* work, lapack_int *info );
+void LAPACK_dptrfs( lapack_int* n, lapack_int* nrhs, const double* d,
+ const double* e, const double* df, const double* ef,
+ const double* b, lapack_int* ldb, double* x,
+ lapack_int* ldx, double* ferr, double* berr, double* work,
+ lapack_int *info );
+void LAPACK_cptrfs( char* uplo, lapack_int* n, lapack_int* nrhs, const float* d,
+ const lapack_complex_float* e, const float* df,
+ const lapack_complex_float* ef,
+ const lapack_complex_float* b, lapack_int* ldb,
+ lapack_complex_float* x, lapack_int* ldx, float* ferr,
+ float* berr, lapack_complex_float* work, float* rwork,
+ lapack_int *info );
+void LAPACK_zptrfs( char* uplo, lapack_int* n, lapack_int* nrhs,
+ const double* d, const lapack_complex_double* e,
+ const double* df, const lapack_complex_double* ef,
+ const lapack_complex_double* b, lapack_int* ldb,
+ lapack_complex_double* x, lapack_int* ldx, double* ferr,
+ double* berr, lapack_complex_double* work, double* rwork,
+ lapack_int *info );
+void LAPACK_ssyrfs( char* uplo, lapack_int* n, lapack_int* nrhs, const float* a,
+ lapack_int* lda, const float* af, lapack_int* ldaf,
+ const lapack_int* ipiv, const float* b, lapack_int* ldb,
+ float* x, lapack_int* ldx, float* ferr, float* berr,
+ float* work, lapack_int* iwork, lapack_int *info );
+void LAPACK_dsyrfs( char* uplo, lapack_int* n, lapack_int* nrhs,
+ const double* a, lapack_int* lda, const double* af,
+ lapack_int* ldaf, const lapack_int* ipiv, const double* b,
+ lapack_int* ldb, double* x, lapack_int* ldx, double* ferr,
+ double* berr, double* work, lapack_int* iwork,
+ lapack_int *info );
+void LAPACK_csyrfs( char* uplo, lapack_int* n, lapack_int* nrhs,
+ const lapack_complex_float* a, lapack_int* lda,
+ const lapack_complex_float* af, lapack_int* ldaf,
+ const lapack_int* ipiv, const lapack_complex_float* b,
+ lapack_int* ldb, lapack_complex_float* x, lapack_int* ldx,
+ float* ferr, float* berr, lapack_complex_float* work,
+ float* rwork, lapack_int *info );
+void LAPACK_zsyrfs( char* uplo, lapack_int* n, lapack_int* nrhs,
+ const lapack_complex_double* a, lapack_int* lda,
+ const lapack_complex_double* af, lapack_int* ldaf,
+ const lapack_int* ipiv, const lapack_complex_double* b,
+ lapack_int* ldb, lapack_complex_double* x, lapack_int* ldx,
+ double* ferr, double* berr, lapack_complex_double* work,
+ double* rwork, lapack_int *info );
+void LAPACK_dsyrfsx( char* uplo, char* equed, lapack_int* n, lapack_int* nrhs,
+ const double* a, lapack_int* lda, const double* af,
+ lapack_int* ldaf, const lapack_int* ipiv, const double* s,
+ const double* b, lapack_int* ldb, double* x,
+ lapack_int* ldx, double* rcond, double* berr,
+ lapack_int* n_err_bnds, double* err_bnds_norm,
+ double* err_bnds_comp, lapack_int* nparams, double* params,
+ double* work, lapack_int* iwork, lapack_int *info );
+void LAPACK_ssyrfsx( char* uplo, char* equed, lapack_int* n, lapack_int* nrhs,
+ const float* a, lapack_int* lda, const float* af,
+ lapack_int* ldaf, const lapack_int* ipiv, const float* s,
+ const float* b, lapack_int* ldb, float* x, lapack_int* ldx,
+ float* rcond, float* berr, lapack_int* n_err_bnds,
+ float* err_bnds_norm, float* err_bnds_comp,
+ lapack_int* nparams, float* params, float* work,
+ lapack_int* iwork, lapack_int *info );
+void LAPACK_zsyrfsx( char* uplo, char* equed, lapack_int* n, lapack_int* nrhs,
+ const lapack_complex_double* a, lapack_int* lda,
+ const lapack_complex_double* af, lapack_int* ldaf,
+ const lapack_int* ipiv, const double* s,
+ const lapack_complex_double* b, lapack_int* ldb,
+ lapack_complex_double* x, lapack_int* ldx, double* rcond,
+ double* berr, lapack_int* n_err_bnds,
+ double* err_bnds_norm, double* err_bnds_comp,
+ lapack_int* nparams, double* params,
+ lapack_complex_double* work, double* rwork,
+ lapack_int *info );
+void LAPACK_csyrfsx( char* uplo, char* equed, lapack_int* n, lapack_int* nrhs,
+ const lapack_complex_float* a, lapack_int* lda,
+ const lapack_complex_float* af, lapack_int* ldaf,
+ const lapack_int* ipiv, const float* s,
+ const lapack_complex_float* b, lapack_int* ldb,
+ lapack_complex_float* x, lapack_int* ldx, float* rcond,
+ float* berr, lapack_int* n_err_bnds, float* err_bnds_norm,
+ float* err_bnds_comp, lapack_int* nparams, float* params,
+ lapack_complex_float* work, float* rwork,
+ lapack_int *info );
+void LAPACK_cherfs( char* uplo, lapack_int* n, lapack_int* nrhs,
+ const lapack_complex_float* a, lapack_int* lda,
+ const lapack_complex_float* af, lapack_int* ldaf,
+ const lapack_int* ipiv, const lapack_complex_float* b,
+ lapack_int* ldb, lapack_complex_float* x, lapack_int* ldx,
+ float* ferr, float* berr, lapack_complex_float* work,
+ float* rwork, lapack_int *info );
+void LAPACK_zherfs( char* uplo, lapack_int* n, lapack_int* nrhs,
+ const lapack_complex_double* a, lapack_int* lda,
+ const lapack_complex_double* af, lapack_int* ldaf,
+ const lapack_int* ipiv, const lapack_complex_double* b,
+ lapack_int* ldb, lapack_complex_double* x, lapack_int* ldx,
+ double* ferr, double* berr, lapack_complex_double* work,
+ double* rwork, lapack_int *info );
+void LAPACK_zherfsx( char* uplo, char* equed, lapack_int* n, lapack_int* nrhs,
+ const lapack_complex_double* a, lapack_int* lda,
+ const lapack_complex_double* af, lapack_int* ldaf,
+ const lapack_int* ipiv, const double* s,
+ const lapack_complex_double* b, lapack_int* ldb,
+ lapack_complex_double* x, lapack_int* ldx, double* rcond,
+ double* berr, lapack_int* n_err_bnds,
+ double* err_bnds_norm, double* err_bnds_comp,
+ lapack_int* nparams, double* params,
+ lapack_complex_double* work, double* rwork,
+ lapack_int *info );
+void LAPACK_cherfsx( char* uplo, char* equed, lapack_int* n, lapack_int* nrhs,
+ const lapack_complex_float* a, lapack_int* lda,
+ const lapack_complex_float* af, lapack_int* ldaf,
+ const lapack_int* ipiv, const float* s,
+ const lapack_complex_float* b, lapack_int* ldb,
+ lapack_complex_float* x, lapack_int* ldx, float* rcond,
+ float* berr, lapack_int* n_err_bnds, float* err_bnds_norm,
+ float* err_bnds_comp, lapack_int* nparams, float* params,
+ lapack_complex_float* work, float* rwork,
+ lapack_int *info );
+void LAPACK_ssprfs( char* uplo, lapack_int* n, lapack_int* nrhs,
+ const float* ap, const float* afp, const lapack_int* ipiv,
+ const float* b, lapack_int* ldb, float* x, lapack_int* ldx,
+ float* ferr, float* berr, float* work, lapack_int* iwork,
+ lapack_int *info );
+void LAPACK_dsprfs( char* uplo, lapack_int* n, lapack_int* nrhs,
+ const double* ap, const double* afp, const lapack_int* ipiv,
+ const double* b, lapack_int* ldb, double* x,
+ lapack_int* ldx, double* ferr, double* berr, double* work,
+ lapack_int* iwork, lapack_int *info );
+void LAPACK_csprfs( char* uplo, lapack_int* n, lapack_int* nrhs,
+ const lapack_complex_float* ap,
+ const lapack_complex_float* afp, const lapack_int* ipiv,
+ const lapack_complex_float* b, lapack_int* ldb,
+ lapack_complex_float* x, lapack_int* ldx, float* ferr,
+ float* berr, lapack_complex_float* work, float* rwork,
+ lapack_int *info );
+void LAPACK_zsprfs( char* uplo, lapack_int* n, lapack_int* nrhs,
+ const lapack_complex_double* ap,
+ const lapack_complex_double* afp, const lapack_int* ipiv,
+ const lapack_complex_double* b, lapack_int* ldb,
+ lapack_complex_double* x, lapack_int* ldx, double* ferr,
+ double* berr, lapack_complex_double* work, double* rwork,
+ lapack_int *info );
+void LAPACK_chprfs( char* uplo, lapack_int* n, lapack_int* nrhs,
+ const lapack_complex_float* ap,
+ const lapack_complex_float* afp, const lapack_int* ipiv,
+ const lapack_complex_float* b, lapack_int* ldb,
+ lapack_complex_float* x, lapack_int* ldx, float* ferr,
+ float* berr, lapack_complex_float* work, float* rwork,
+ lapack_int *info );
+void LAPACK_zhprfs( char* uplo, lapack_int* n, lapack_int* nrhs,
+ const lapack_complex_double* ap,
+ const lapack_complex_double* afp, const lapack_int* ipiv,
+ const lapack_complex_double* b, lapack_int* ldb,
+ lapack_complex_double* x, lapack_int* ldx, double* ferr,
+ double* berr, lapack_complex_double* work, double* rwork,
+ lapack_int *info );
+void LAPACK_strrfs( char* uplo, char* trans, char* diag, lapack_int* n,
+ lapack_int* nrhs, const float* a, lapack_int* lda,
+ const float* b, lapack_int* ldb, const float* x,
+ lapack_int* ldx, float* ferr, float* berr, float* work,
+ lapack_int* iwork, lapack_int *info );
+void LAPACK_dtrrfs( char* uplo, char* trans, char* diag, lapack_int* n,
+ lapack_int* nrhs, const double* a, lapack_int* lda,
+ const double* b, lapack_int* ldb, const double* x,
+ lapack_int* ldx, double* ferr, double* berr, double* work,
+ lapack_int* iwork, lapack_int *info );
+void LAPACK_ctrrfs( char* uplo, char* trans, char* diag, lapack_int* n,
+ lapack_int* nrhs, const lapack_complex_float* a,
+ lapack_int* lda, const lapack_complex_float* b,
+ lapack_int* ldb, const lapack_complex_float* x,
+ lapack_int* ldx, float* ferr, float* berr,
+ lapack_complex_float* work, float* rwork,
+ lapack_int *info );
+void LAPACK_ztrrfs( char* uplo, char* trans, char* diag, lapack_int* n,
+ lapack_int* nrhs, const lapack_complex_double* a,
+ lapack_int* lda, const lapack_complex_double* b,
+ lapack_int* ldb, const lapack_complex_double* x,
+ lapack_int* ldx, double* ferr, double* berr,
+ lapack_complex_double* work, double* rwork,
+ lapack_int *info );
+void LAPACK_stprfs( char* uplo, char* trans, char* diag, lapack_int* n,
+ lapack_int* nrhs, const float* ap, const float* b,
+ lapack_int* ldb, const float* x, lapack_int* ldx,
+ float* ferr, float* berr, float* work, lapack_int* iwork,
+ lapack_int *info );
+void LAPACK_dtprfs( char* uplo, char* trans, char* diag, lapack_int* n,
+ lapack_int* nrhs, const double* ap, const double* b,
+ lapack_int* ldb, const double* x, lapack_int* ldx,
+ double* ferr, double* berr, double* work, lapack_int* iwork,
+ lapack_int *info );
+void LAPACK_ctprfs( char* uplo, char* trans, char* diag, lapack_int* n,
+ lapack_int* nrhs, const lapack_complex_float* ap,
+ const lapack_complex_float* b, lapack_int* ldb,
+ const lapack_complex_float* x, lapack_int* ldx, float* ferr,
+ float* berr, lapack_complex_float* work, float* rwork,
+ lapack_int *info );
+void LAPACK_ztprfs( char* uplo, char* trans, char* diag, lapack_int* n,
+ lapack_int* nrhs, const lapack_complex_double* ap,
+ const lapack_complex_double* b, lapack_int* ldb,
+ const lapack_complex_double* x, lapack_int* ldx,
+ double* ferr, double* berr, lapack_complex_double* work,
+ double* rwork, lapack_int *info );
+void LAPACK_stbrfs( char* uplo, char* trans, char* diag, lapack_int* n,
+ lapack_int* kd, lapack_int* nrhs, const float* ab,
+ lapack_int* ldab, const float* b, lapack_int* ldb,
+ const float* x, lapack_int* ldx, float* ferr, float* berr,
+ float* work, lapack_int* iwork, lapack_int *info );
+void LAPACK_dtbrfs( char* uplo, char* trans, char* diag, lapack_int* n,
+ lapack_int* kd, lapack_int* nrhs, const double* ab,
+ lapack_int* ldab, const double* b, lapack_int* ldb,
+ const double* x, lapack_int* ldx, double* ferr,
+ double* berr, double* work, lapack_int* iwork,
+ lapack_int *info );
+void LAPACK_ctbrfs( char* uplo, char* trans, char* diag, lapack_int* n,
+ lapack_int* kd, lapack_int* nrhs,
+ const lapack_complex_float* ab, lapack_int* ldab,
+ const lapack_complex_float* b, lapack_int* ldb,
+ const lapack_complex_float* x, lapack_int* ldx, float* ferr,
+ float* berr, lapack_complex_float* work, float* rwork,
+ lapack_int *info );
+void LAPACK_ztbrfs( char* uplo, char* trans, char* diag, lapack_int* n,
+ lapack_int* kd, lapack_int* nrhs,
+ const lapack_complex_double* ab, lapack_int* ldab,
+ const lapack_complex_double* b, lapack_int* ldb,
+ const lapack_complex_double* x, lapack_int* ldx,
+ double* ferr, double* berr, lapack_complex_double* work,
+ double* rwork, lapack_int *info );
+void LAPACK_sgetri( lapack_int* n, float* a, lapack_int* lda,
+ const lapack_int* ipiv, float* work, lapack_int* lwork,
+ lapack_int *info );
+void LAPACK_dgetri( lapack_int* n, double* a, lapack_int* lda,
+ const lapack_int* ipiv, double* work, lapack_int* lwork,
+ lapack_int *info );
+void LAPACK_cgetri( lapack_int* n, lapack_complex_float* a, lapack_int* lda,
+ const lapack_int* ipiv, lapack_complex_float* work,
+ lapack_int* lwork, lapack_int *info );
+void LAPACK_zgetri( lapack_int* n, lapack_complex_double* a, lapack_int* lda,
+ const lapack_int* ipiv, lapack_complex_double* work,
+ lapack_int* lwork, lapack_int *info );
+void LAPACK_spotri( char* uplo, lapack_int* n, float* a, lapack_int* lda,
+ lapack_int *info );
+void LAPACK_dpotri( char* uplo, lapack_int* n, double* a, lapack_int* lda,
+ lapack_int *info );
+void LAPACK_cpotri( char* uplo, lapack_int* n, lapack_complex_float* a,
+ lapack_int* lda, lapack_int *info );
+void LAPACK_zpotri( char* uplo, lapack_int* n, lapack_complex_double* a,
+ lapack_int* lda, lapack_int *info );
+void LAPACK_dpftri( char* transr, char* uplo, lapack_int* n, double* a,
+ lapack_int *info );
+void LAPACK_spftri( char* transr, char* uplo, lapack_int* n, float* a,
+ lapack_int *info );
+void LAPACK_zpftri( char* transr, char* uplo, lapack_int* n,
+ lapack_complex_double* a, lapack_int *info );
+void LAPACK_cpftri( char* transr, char* uplo, lapack_int* n,
+ lapack_complex_float* a, lapack_int *info );
+void LAPACK_spptri( char* uplo, lapack_int* n, float* ap, lapack_int *info );
+void LAPACK_dpptri( char* uplo, lapack_int* n, double* ap, lapack_int *info );
+void LAPACK_cpptri( char* uplo, lapack_int* n, lapack_complex_float* ap,
+ lapack_int *info );
+void LAPACK_zpptri( char* uplo, lapack_int* n, lapack_complex_double* ap,
+ lapack_int *info );
+void LAPACK_ssytri( char* uplo, lapack_int* n, float* a, lapack_int* lda,
+ const lapack_int* ipiv, float* work, lapack_int *info );
+void LAPACK_dsytri( char* uplo, lapack_int* n, double* a, lapack_int* lda,
+ const lapack_int* ipiv, double* work, lapack_int *info );
+void LAPACK_csytri( char* uplo, lapack_int* n, lapack_complex_float* a,
+ lapack_int* lda, const lapack_int* ipiv,
+ lapack_complex_float* work, lapack_int *info );
+void LAPACK_zsytri( char* uplo, lapack_int* n, lapack_complex_double* a,
+ lapack_int* lda, const lapack_int* ipiv,
+ lapack_complex_double* work, lapack_int *info );
+void LAPACK_chetri( char* uplo, lapack_int* n, lapack_complex_float* a,
+ lapack_int* lda, const lapack_int* ipiv,
+ lapack_complex_float* work, lapack_int *info );
+void LAPACK_zhetri( char* uplo, lapack_int* n, lapack_complex_double* a,
+ lapack_int* lda, const lapack_int* ipiv,
+ lapack_complex_double* work, lapack_int *info );
+void LAPACK_ssptri( char* uplo, lapack_int* n, float* ap,
+ const lapack_int* ipiv, float* work, lapack_int *info );
+void LAPACK_dsptri( char* uplo, lapack_int* n, double* ap,
+ const lapack_int* ipiv, double* work, lapack_int *info );
+void LAPACK_csptri( char* uplo, lapack_int* n, lapack_complex_float* ap,
+ const lapack_int* ipiv, lapack_complex_float* work,
+ lapack_int *info );
+void LAPACK_zsptri( char* uplo, lapack_int* n, lapack_complex_double* ap,
+ const lapack_int* ipiv, lapack_complex_double* work,
+ lapack_int *info );
+void LAPACK_chptri( char* uplo, lapack_int* n, lapack_complex_float* ap,
+ const lapack_int* ipiv, lapack_complex_float* work,
+ lapack_int *info );
+void LAPACK_zhptri( char* uplo, lapack_int* n, lapack_complex_double* ap,
+ const lapack_int* ipiv, lapack_complex_double* work,
+ lapack_int *info );
+void LAPACK_strtri( char* uplo, char* diag, lapack_int* n, float* a,
+ lapack_int* lda, lapack_int *info );
+void LAPACK_dtrtri( char* uplo, char* diag, lapack_int* n, double* a,
+ lapack_int* lda, lapack_int *info );
+void LAPACK_ctrtri( char* uplo, char* diag, lapack_int* n,
+ lapack_complex_float* a, lapack_int* lda,
+ lapack_int *info );
+void LAPACK_ztrtri( char* uplo, char* diag, lapack_int* n,
+ lapack_complex_double* a, lapack_int* lda,
+ lapack_int *info );
+void LAPACK_dtftri( char* transr, char* uplo, char* diag, lapack_int* n,
+ double* a, lapack_int *info );
+void LAPACK_stftri( char* transr, char* uplo, char* diag, lapack_int* n,
+ float* a, lapack_int *info );
+void LAPACK_ztftri( char* transr, char* uplo, char* diag, lapack_int* n,
+ lapack_complex_double* a, lapack_int *info );
+void LAPACK_ctftri( char* transr, char* uplo, char* diag, lapack_int* n,
+ lapack_complex_float* a, lapack_int *info );
+void LAPACK_stptri( char* uplo, char* diag, lapack_int* n, float* ap,
+ lapack_int *info );
+void LAPACK_dtptri( char* uplo, char* diag, lapack_int* n, double* ap,
+ lapack_int *info );
+void LAPACK_ctptri( char* uplo, char* diag, lapack_int* n,
+ lapack_complex_float* ap, lapack_int *info );
+void LAPACK_ztptri( char* uplo, char* diag, lapack_int* n,
+ lapack_complex_double* ap, lapack_int *info );
+void LAPACK_sgeequ( lapack_int* m, lapack_int* n, const float* a,
+ lapack_int* lda, float* r, float* c, float* rowcnd,
+ float* colcnd, float* amax, lapack_int *info );
+void LAPACK_dgeequ( lapack_int* m, lapack_int* n, const double* a,
+ lapack_int* lda, double* r, double* c, double* rowcnd,
+ double* colcnd, double* amax, lapack_int *info );
+void LAPACK_cgeequ( lapack_int* m, lapack_int* n, const lapack_complex_float* a,
+ lapack_int* lda, float* r, float* c, float* rowcnd,
+ float* colcnd, float* amax, lapack_int *info );
+void LAPACK_zgeequ( lapack_int* m, lapack_int* n,
+ const lapack_complex_double* a, lapack_int* lda, double* r,
+ double* c, double* rowcnd, double* colcnd, double* amax,
+ lapack_int *info );
+void LAPACK_dgeequb( lapack_int* m, lapack_int* n, const double* a,
+ lapack_int* lda, double* r, double* c, double* rowcnd,
+ double* colcnd, double* amax, lapack_int *info );
+void LAPACK_sgeequb( lapack_int* m, lapack_int* n, const float* a,
+ lapack_int* lda, float* r, float* c, float* rowcnd,
+ float* colcnd, float* amax, lapack_int *info );
+void LAPACK_zgeequb( lapack_int* m, lapack_int* n,
+ const lapack_complex_double* a, lapack_int* lda, double* r,
+ double* c, double* rowcnd, double* colcnd, double* amax,
+ lapack_int *info );
+void LAPACK_cgeequb( lapack_int* m, lapack_int* n,
+ const lapack_complex_float* a, lapack_int* lda, float* r,
+ float* c, float* rowcnd, float* colcnd, float* amax,
+ lapack_int *info );
+void LAPACK_sgbequ( lapack_int* m, lapack_int* n, lapack_int* kl,
+ lapack_int* ku, const float* ab, lapack_int* ldab, float* r,
+ float* c, float* rowcnd, float* colcnd, float* amax,
+ lapack_int *info );
+void LAPACK_dgbequ( lapack_int* m, lapack_int* n, lapack_int* kl,
+ lapack_int* ku, const double* ab, lapack_int* ldab,
+ double* r, double* c, double* rowcnd, double* colcnd,
+ double* amax, lapack_int *info );
+void LAPACK_cgbequ( lapack_int* m, lapack_int* n, lapack_int* kl,
+ lapack_int* ku, const lapack_complex_float* ab,
+ lapack_int* ldab, float* r, float* c, float* rowcnd,
+ float* colcnd, float* amax, lapack_int *info );
+void LAPACK_zgbequ( lapack_int* m, lapack_int* n, lapack_int* kl,
+ lapack_int* ku, const lapack_complex_double* ab,
+ lapack_int* ldab, double* r, double* c, double* rowcnd,
+ double* colcnd, double* amax, lapack_int *info );
+void LAPACK_dgbequb( lapack_int* m, lapack_int* n, lapack_int* kl,
+ lapack_int* ku, const double* ab, lapack_int* ldab,
+ double* r, double* c, double* rowcnd, double* colcnd,
+ double* amax, lapack_int *info );
+void LAPACK_sgbequb( lapack_int* m, lapack_int* n, lapack_int* kl,
+ lapack_int* ku, const float* ab, lapack_int* ldab,
+ float* r, float* c, float* rowcnd, float* colcnd,
+ float* amax, lapack_int *info );
+void LAPACK_zgbequb( lapack_int* m, lapack_int* n, lapack_int* kl,
+ lapack_int* ku, const lapack_complex_double* ab,
+ lapack_int* ldab, double* r, double* c, double* rowcnd,
+ double* colcnd, double* amax, lapack_int *info );
+void LAPACK_cgbequb( lapack_int* m, lapack_int* n, lapack_int* kl,
+ lapack_int* ku, const lapack_complex_float* ab,
+ lapack_int* ldab, float* r, float* c, float* rowcnd,
+ float* colcnd, float* amax, lapack_int *info );
+void LAPACK_spoequ( lapack_int* n, const float* a, lapack_int* lda, float* s,
+ float* scond, float* amax, lapack_int *info );
+void LAPACK_dpoequ( lapack_int* n, const double* a, lapack_int* lda, double* s,
+ double* scond, double* amax, lapack_int *info );
+void LAPACK_cpoequ( lapack_int* n, const lapack_complex_float* a,
+ lapack_int* lda, float* s, float* scond, float* amax,
+ lapack_int *info );
+void LAPACK_zpoequ( lapack_int* n, const lapack_complex_double* a,
+ lapack_int* lda, double* s, double* scond, double* amax,
+ lapack_int *info );
+void LAPACK_dpoequb( lapack_int* n, const double* a, lapack_int* lda, double* s,
+ double* scond, double* amax, lapack_int *info );
+void LAPACK_spoequb( lapack_int* n, const float* a, lapack_int* lda, float* s,
+ float* scond, float* amax, lapack_int *info );
+void LAPACK_zpoequb( lapack_int* n, const lapack_complex_double* a,
+ lapack_int* lda, double* s, double* scond, double* amax,
+ lapack_int *info );
+void LAPACK_cpoequb( lapack_int* n, const lapack_complex_float* a,
+ lapack_int* lda, float* s, float* scond, float* amax,
+ lapack_int *info );
+void LAPACK_sppequ( char* uplo, lapack_int* n, const float* ap, float* s,
+ float* scond, float* amax, lapack_int *info );
+void LAPACK_dppequ( char* uplo, lapack_int* n, const double* ap, double* s,
+ double* scond, double* amax, lapack_int *info );
+void LAPACK_cppequ( char* uplo, lapack_int* n, const lapack_complex_float* ap,
+ float* s, float* scond, float* amax, lapack_int *info );
+void LAPACK_zppequ( char* uplo, lapack_int* n, const lapack_complex_double* ap,
+ double* s, double* scond, double* amax, lapack_int *info );
+void LAPACK_spbequ( char* uplo, lapack_int* n, lapack_int* kd, const float* ab,
+ lapack_int* ldab, float* s, float* scond, float* amax,
+ lapack_int *info );
+void LAPACK_dpbequ( char* uplo, lapack_int* n, lapack_int* kd, const double* ab,
+ lapack_int* ldab, double* s, double* scond, double* amax,
+ lapack_int *info );
+void LAPACK_cpbequ( char* uplo, lapack_int* n, lapack_int* kd,
+ const lapack_complex_float* ab, lapack_int* ldab, float* s,
+ float* scond, float* amax, lapack_int *info );
+void LAPACK_zpbequ( char* uplo, lapack_int* n, lapack_int* kd,
+ const lapack_complex_double* ab, lapack_int* ldab,
+ double* s, double* scond, double* amax, lapack_int *info );
+void LAPACK_dsyequb( char* uplo, lapack_int* n, const double* a,
+ lapack_int* lda, double* s, double* scond, double* amax,
+ double* work, lapack_int *info );
+void LAPACK_ssyequb( char* uplo, lapack_int* n, const float* a, lapack_int* lda,
+ float* s, float* scond, float* amax, float* work,
+ lapack_int *info );
+void LAPACK_zsyequb( char* uplo, lapack_int* n, const lapack_complex_double* a,
+ lapack_int* lda, double* s, double* scond, double* amax,
+ lapack_complex_double* work, lapack_int *info );
+void LAPACK_csyequb( char* uplo, lapack_int* n, const lapack_complex_float* a,
+ lapack_int* lda, float* s, float* scond, float* amax,
+ lapack_complex_float* work, lapack_int *info );
+void LAPACK_zheequb( char* uplo, lapack_int* n, const lapack_complex_double* a,
+ lapack_int* lda, double* s, double* scond, double* amax,
+ lapack_complex_double* work, lapack_int *info );
+void LAPACK_cheequb( char* uplo, lapack_int* n, const lapack_complex_float* a,
+ lapack_int* lda, float* s, float* scond, float* amax,
+ lapack_complex_float* work, lapack_int *info );
+void LAPACK_sgesv( lapack_int* n, lapack_int* nrhs, float* a, lapack_int* lda,
+ lapack_int* ipiv, float* b, lapack_int* ldb,
+ lapack_int *info );
+void LAPACK_dgesv( lapack_int* n, lapack_int* nrhs, double* a, lapack_int* lda,
+ lapack_int* ipiv, double* b, lapack_int* ldb,
+ lapack_int *info );
+void LAPACK_cgesv( lapack_int* n, lapack_int* nrhs, lapack_complex_float* a,
+ lapack_int* lda, lapack_int* ipiv, lapack_complex_float* b,
+ lapack_int* ldb, lapack_int *info );
+void LAPACK_zgesv( lapack_int* n, lapack_int* nrhs, lapack_complex_double* a,
+ lapack_int* lda, lapack_int* ipiv, lapack_complex_double* b,
+ lapack_int* ldb, lapack_int *info );
+void LAPACK_dsgesv( lapack_int* n, lapack_int* nrhs, double* a, lapack_int* lda,
+ lapack_int* ipiv, double* b, lapack_int* ldb, double* x,
+ lapack_int* ldx, double* work, float* swork,
+ lapack_int* iter, lapack_int *info );
+void LAPACK_zcgesv( lapack_int* n, lapack_int* nrhs, lapack_complex_double* a,
+ lapack_int* lda, lapack_int* ipiv, lapack_complex_double* b,
+ lapack_int* ldb, lapack_complex_double* x, lapack_int* ldx,
+ lapack_complex_double* work, lapack_complex_float* swork,
+ double* rwork, lapack_int* iter, lapack_int *info );
+void LAPACK_sgesvx( char* fact, char* trans, lapack_int* n, lapack_int* nrhs,
+ float* a, lapack_int* lda, float* af, lapack_int* ldaf,
+ lapack_int* ipiv, char* equed, float* r, float* c, float* b,
+ lapack_int* ldb, float* x, lapack_int* ldx, float* rcond,
+ float* ferr, float* berr, float* work, lapack_int* iwork,
+ lapack_int *info );
+void LAPACK_dgesvx( char* fact, char* trans, lapack_int* n, lapack_int* nrhs,
+ double* a, lapack_int* lda, double* af, lapack_int* ldaf,
+ lapack_int* ipiv, char* equed, double* r, double* c,
+ double* b, lapack_int* ldb, double* x, lapack_int* ldx,
+ double* rcond, double* ferr, double* berr, double* work,
+ lapack_int* iwork, lapack_int *info );
+void LAPACK_cgesvx( char* fact, char* trans, lapack_int* n, lapack_int* nrhs,
+ lapack_complex_float* a, lapack_int* lda,
+ lapack_complex_float* af, lapack_int* ldaf,
+ lapack_int* ipiv, char* equed, float* r, float* c,
+ lapack_complex_float* b, lapack_int* ldb,
+ lapack_complex_float* x, lapack_int* ldx, float* rcond,
+ float* ferr, float* berr, lapack_complex_float* work,
+ float* rwork, lapack_int *info );
+void LAPACK_zgesvx( char* fact, char* trans, lapack_int* n, lapack_int* nrhs,
+ lapack_complex_double* a, lapack_int* lda,
+ lapack_complex_double* af, lapack_int* ldaf,
+ lapack_int* ipiv, char* equed, double* r, double* c,
+ lapack_complex_double* b, lapack_int* ldb,
+ lapack_complex_double* x, lapack_int* ldx, double* rcond,
+ double* ferr, double* berr, lapack_complex_double* work,
+ double* rwork, lapack_int *info );
+void LAPACK_dgesvxx( char* fact, char* trans, lapack_int* n, lapack_int* nrhs,
+ double* a, lapack_int* lda, double* af, lapack_int* ldaf,
+ lapack_int* ipiv, char* equed, double* r, double* c,
+ double* b, lapack_int* ldb, double* x, lapack_int* ldx,
+ double* rcond, double* rpvgrw, double* berr,
+ lapack_int* n_err_bnds, double* err_bnds_norm,
+ double* err_bnds_comp, lapack_int* nparams, double* params,
+ double* work, lapack_int* iwork, lapack_int *info );
+void LAPACK_sgesvxx( char* fact, char* trans, lapack_int* n, lapack_int* nrhs,
+ float* a, lapack_int* lda, float* af, lapack_int* ldaf,
+ lapack_int* ipiv, char* equed, float* r, float* c,
+ float* b, lapack_int* ldb, float* x, lapack_int* ldx,
+ float* rcond, float* rpvgrw, float* berr,
+ lapack_int* n_err_bnds, float* err_bnds_norm,
+ float* err_bnds_comp, lapack_int* nparams, float* params,
+ float* work, lapack_int* iwork, lapack_int *info );
+void LAPACK_zgesvxx( char* fact, char* trans, lapack_int* n, lapack_int* nrhs,
+ lapack_complex_double* a, lapack_int* lda,
+ lapack_complex_double* af, lapack_int* ldaf,
+ lapack_int* ipiv, char* equed, double* r, double* c,
+ lapack_complex_double* b, lapack_int* ldb,
+ lapack_complex_double* x, lapack_int* ldx, double* rcond,
+ double* rpvgrw, double* berr, lapack_int* n_err_bnds,
+ double* err_bnds_norm, double* err_bnds_comp,
+ lapack_int* nparams, double* params,
+ lapack_complex_double* work, double* rwork,
+ lapack_int *info );
+void LAPACK_cgesvxx( char* fact, char* trans, lapack_int* n, lapack_int* nrhs,
+ lapack_complex_float* a, lapack_int* lda,
+ lapack_complex_float* af, lapack_int* ldaf,
+ lapack_int* ipiv, char* equed, float* r, float* c,
+ lapack_complex_float* b, lapack_int* ldb,
+ lapack_complex_float* x, lapack_int* ldx, float* rcond,
+ float* rpvgrw, float* berr, lapack_int* n_err_bnds,
+ float* err_bnds_norm, float* err_bnds_comp,
+ lapack_int* nparams, float* params,
+ lapack_complex_float* work, float* rwork,
+ lapack_int *info );
+void LAPACK_sgbsv( lapack_int* n, lapack_int* kl, lapack_int* ku,
+ lapack_int* nrhs, float* ab, lapack_int* ldab,
+ lapack_int* ipiv, float* b, lapack_int* ldb,
+ lapack_int *info );
+void LAPACK_dgbsv( lapack_int* n, lapack_int* kl, lapack_int* ku,
+ lapack_int* nrhs, double* ab, lapack_int* ldab,
+ lapack_int* ipiv, double* b, lapack_int* ldb,
+ lapack_int *info );
+void LAPACK_cgbsv( lapack_int* n, lapack_int* kl, lapack_int* ku,
+ lapack_int* nrhs, lapack_complex_float* ab, lapack_int* ldab,
+ lapack_int* ipiv, lapack_complex_float* b, lapack_int* ldb,
+ lapack_int *info );
+void LAPACK_zgbsv( lapack_int* n, lapack_int* kl, lapack_int* ku,
+ lapack_int* nrhs, lapack_complex_double* ab,
+ lapack_int* ldab, lapack_int* ipiv, lapack_complex_double* b,
+ lapack_int* ldb, lapack_int *info );
+void LAPACK_sgbsvx( char* fact, char* trans, lapack_int* n, lapack_int* kl,
+ lapack_int* ku, lapack_int* nrhs, float* ab,
+ lapack_int* ldab, float* afb, lapack_int* ldafb,
+ lapack_int* ipiv, char* equed, float* r, float* c, float* b,
+ lapack_int* ldb, float* x, lapack_int* ldx, float* rcond,
+ float* ferr, float* berr, float* work, lapack_int* iwork,
+ lapack_int *info );
+void LAPACK_dgbsvx( char* fact, char* trans, lapack_int* n, lapack_int* kl,
+ lapack_int* ku, lapack_int* nrhs, double* ab,
+ lapack_int* ldab, double* afb, lapack_int* ldafb,
+ lapack_int* ipiv, char* equed, double* r, double* c,
+ double* b, lapack_int* ldb, double* x, lapack_int* ldx,
+ double* rcond, double* ferr, double* berr, double* work,
+ lapack_int* iwork, lapack_int *info );
+void LAPACK_cgbsvx( char* fact, char* trans, lapack_int* n, lapack_int* kl,
+ lapack_int* ku, lapack_int* nrhs, lapack_complex_float* ab,
+ lapack_int* ldab, lapack_complex_float* afb,
+ lapack_int* ldafb, lapack_int* ipiv, char* equed, float* r,
+ float* c, lapack_complex_float* b, lapack_int* ldb,
+ lapack_complex_float* x, lapack_int* ldx, float* rcond,
+ float* ferr, float* berr, lapack_complex_float* work,
+ float* rwork, lapack_int *info );
+void LAPACK_zgbsvx( char* fact, char* trans, lapack_int* n, lapack_int* kl,
+ lapack_int* ku, lapack_int* nrhs, lapack_complex_double* ab,
+ lapack_int* ldab, lapack_complex_double* afb,
+ lapack_int* ldafb, lapack_int* ipiv, char* equed, double* r,
+ double* c, lapack_complex_double* b, lapack_int* ldb,
+ lapack_complex_double* x, lapack_int* ldx, double* rcond,
+ double* ferr, double* berr, lapack_complex_double* work,
+ double* rwork, lapack_int *info );
+void LAPACK_dgbsvxx( char* fact, char* trans, lapack_int* n, lapack_int* kl,
+ lapack_int* ku, lapack_int* nrhs, double* ab,
+ lapack_int* ldab, double* afb, lapack_int* ldafb,
+ lapack_int* ipiv, char* equed, double* r, double* c,
+ double* b, lapack_int* ldb, double* x, lapack_int* ldx,
+ double* rcond, double* rpvgrw, double* berr,
+ lapack_int* n_err_bnds, double* err_bnds_norm,
+ double* err_bnds_comp, lapack_int* nparams, double* params,
+ double* work, lapack_int* iwork, lapack_int *info );
+void LAPACK_sgbsvxx( char* fact, char* trans, lapack_int* n, lapack_int* kl,
+ lapack_int* ku, lapack_int* nrhs, float* ab,
+ lapack_int* ldab, float* afb, lapack_int* ldafb,
+ lapack_int* ipiv, char* equed, float* r, float* c,
+ float* b, lapack_int* ldb, float* x, lapack_int* ldx,
+ float* rcond, float* rpvgrw, float* berr,
+ lapack_int* n_err_bnds, float* err_bnds_norm,
+ float* err_bnds_comp, lapack_int* nparams, float* params,
+ float* work, lapack_int* iwork, lapack_int *info );
+void LAPACK_zgbsvxx( char* fact, char* trans, lapack_int* n, lapack_int* kl,
+ lapack_int* ku, lapack_int* nrhs,
+ lapack_complex_double* ab, lapack_int* ldab,
+ lapack_complex_double* afb, lapack_int* ldafb,
+ lapack_int* ipiv, char* equed, double* r, double* c,
+ lapack_complex_double* b, lapack_int* ldb,
+ lapack_complex_double* x, lapack_int* ldx, double* rcond,
+ double* rpvgrw, double* berr, lapack_int* n_err_bnds,
+ double* err_bnds_norm, double* err_bnds_comp,
+ lapack_int* nparams, double* params,
+ lapack_complex_double* work, double* rwork,
+ lapack_int *info );
+void LAPACK_cgbsvxx( char* fact, char* trans, lapack_int* n, lapack_int* kl,
+ lapack_int* ku, lapack_int* nrhs, lapack_complex_float* ab,
+ lapack_int* ldab, lapack_complex_float* afb,
+ lapack_int* ldafb, lapack_int* ipiv, char* equed, float* r,
+ float* c, lapack_complex_float* b, lapack_int* ldb,
+ lapack_complex_float* x, lapack_int* ldx, float* rcond,
+ float* rpvgrw, float* berr, lapack_int* n_err_bnds,
+ float* err_bnds_norm, float* err_bnds_comp,
+ lapack_int* nparams, float* params,
+ lapack_complex_float* work, float* rwork,
+ lapack_int *info );
+void LAPACK_sgtsv( lapack_int* n, lapack_int* nrhs, float* dl, float* d,
+ float* du, float* b, lapack_int* ldb, lapack_int *info );
+void LAPACK_dgtsv( lapack_int* n, lapack_int* nrhs, double* dl, double* d,
+ double* du, double* b, lapack_int* ldb, lapack_int *info );
+void LAPACK_cgtsv( lapack_int* n, lapack_int* nrhs, lapack_complex_float* dl,
+ lapack_complex_float* d, lapack_complex_float* du,
+ lapack_complex_float* b, lapack_int* ldb, lapack_int *info );
+void LAPACK_zgtsv( lapack_int* n, lapack_int* nrhs, lapack_complex_double* dl,
+ lapack_complex_double* d, lapack_complex_double* du,
+ lapack_complex_double* b, lapack_int* ldb,
+ lapack_int *info );
+void LAPACK_sgtsvx( char* fact, char* trans, lapack_int* n, lapack_int* nrhs,
+ const float* dl, const float* d, const float* du,
+ float* dlf, float* df, float* duf, float* du2,
+ lapack_int* ipiv, const float* b, lapack_int* ldb, float* x,
+ lapack_int* ldx, float* rcond, float* ferr, float* berr,
+ float* work, lapack_int* iwork, lapack_int *info );
+void LAPACK_dgtsvx( char* fact, char* trans, lapack_int* n, lapack_int* nrhs,
+ const double* dl, const double* d, const double* du,
+ double* dlf, double* df, double* duf, double* du2,
+ lapack_int* ipiv, const double* b, lapack_int* ldb,
+ double* x, lapack_int* ldx, double* rcond, double* ferr,
+ double* berr, double* work, lapack_int* iwork,
+ lapack_int *info );
+void LAPACK_cgtsvx( char* fact, char* trans, lapack_int* n, lapack_int* nrhs,
+ const lapack_complex_float* dl,
+ const lapack_complex_float* d,
+ const lapack_complex_float* du, lapack_complex_float* dlf,
+ lapack_complex_float* df, lapack_complex_float* duf,
+ lapack_complex_float* du2, lapack_int* ipiv,
+ const lapack_complex_float* b, lapack_int* ldb,
+ lapack_complex_float* x, lapack_int* ldx, float* rcond,
+ float* ferr, float* berr, lapack_complex_float* work,
+ float* rwork, lapack_int *info );
+void LAPACK_zgtsvx( char* fact, char* trans, lapack_int* n, lapack_int* nrhs,
+ const lapack_complex_double* dl,
+ const lapack_complex_double* d,
+ const lapack_complex_double* du, lapack_complex_double* dlf,
+ lapack_complex_double* df, lapack_complex_double* duf,
+ lapack_complex_double* du2, lapack_int* ipiv,
+ const lapack_complex_double* b, lapack_int* ldb,
+ lapack_complex_double* x, lapack_int* ldx, double* rcond,
+ double* ferr, double* berr, lapack_complex_double* work,
+ double* rwork, lapack_int *info );
+void LAPACK_sposv( char* uplo, lapack_int* n, lapack_int* nrhs, float* a,
+ lapack_int* lda, float* b, lapack_int* ldb,
+ lapack_int *info );
+void LAPACK_dposv( char* uplo, lapack_int* n, lapack_int* nrhs, double* a,
+ lapack_int* lda, double* b, lapack_int* ldb,
+ lapack_int *info );
+void LAPACK_cposv( char* uplo, lapack_int* n, lapack_int* nrhs,
+ lapack_complex_float* a, lapack_int* lda,
+ lapack_complex_float* b, lapack_int* ldb, lapack_int *info );
+void LAPACK_zposv( char* uplo, lapack_int* n, lapack_int* nrhs,
+ lapack_complex_double* a, lapack_int* lda,
+ lapack_complex_double* b, lapack_int* ldb,
+ lapack_int *info );
+void LAPACK_dsposv( char* uplo, lapack_int* n, lapack_int* nrhs, double* a,
+ lapack_int* lda, double* b, lapack_int* ldb, double* x,
+ lapack_int* ldx, double* work, float* swork,
+ lapack_int* iter, lapack_int *info );
+void LAPACK_zcposv( char* uplo, lapack_int* n, lapack_int* nrhs,
+ lapack_complex_double* a, lapack_int* lda,
+ lapack_complex_double* b, lapack_int* ldb,
+ lapack_complex_double* x, lapack_int* ldx,
+ lapack_complex_double* work, lapack_complex_float* swork,
+ double* rwork, lapack_int* iter, lapack_int *info );
+void LAPACK_sposvx( char* fact, char* uplo, lapack_int* n, lapack_int* nrhs,
+ float* a, lapack_int* lda, float* af, lapack_int* ldaf,
+ char* equed, float* s, float* b, lapack_int* ldb, float* x,
+ lapack_int* ldx, float* rcond, float* ferr, float* berr,
+ float* work, lapack_int* iwork, lapack_int *info );
+void LAPACK_dposvx( char* fact, char* uplo, lapack_int* n, lapack_int* nrhs,
+ double* a, lapack_int* lda, double* af, lapack_int* ldaf,
+ char* equed, double* s, double* b, lapack_int* ldb,
+ double* x, lapack_int* ldx, double* rcond, double* ferr,
+ double* berr, double* work, lapack_int* iwork,
+ lapack_int *info );
+void LAPACK_cposvx( char* fact, char* uplo, lapack_int* n, lapack_int* nrhs,
+ lapack_complex_float* a, lapack_int* lda,
+ lapack_complex_float* af, lapack_int* ldaf, char* equed,
+ float* s, lapack_complex_float* b, lapack_int* ldb,
+ lapack_complex_float* x, lapack_int* ldx, float* rcond,
+ float* ferr, float* berr, lapack_complex_float* work,
+ float* rwork, lapack_int *info );
+void LAPACK_zposvx( char* fact, char* uplo, lapack_int* n, lapack_int* nrhs,
+ lapack_complex_double* a, lapack_int* lda,
+ lapack_complex_double* af, lapack_int* ldaf, char* equed,
+ double* s, lapack_complex_double* b, lapack_int* ldb,
+ lapack_complex_double* x, lapack_int* ldx, double* rcond,
+ double* ferr, double* berr, lapack_complex_double* work,
+ double* rwork, lapack_int *info );
+void LAPACK_dposvxx( char* fact, char* uplo, lapack_int* n, lapack_int* nrhs,
+ double* a, lapack_int* lda, double* af, lapack_int* ldaf,
+ char* equed, double* s, double* b, lapack_int* ldb,
+ double* x, lapack_int* ldx, double* rcond, double* rpvgrw,
+ double* berr, lapack_int* n_err_bnds,
+ double* err_bnds_norm, double* err_bnds_comp,
+ lapack_int* nparams, double* params, double* work,
+ lapack_int* iwork, lapack_int *info );
+void LAPACK_sposvxx( char* fact, char* uplo, lapack_int* n, lapack_int* nrhs,
+ float* a, lapack_int* lda, float* af, lapack_int* ldaf,
+ char* equed, float* s, float* b, lapack_int* ldb, float* x,
+ lapack_int* ldx, float* rcond, float* rpvgrw, float* berr,
+ lapack_int* n_err_bnds, float* err_bnds_norm,
+ float* err_bnds_comp, lapack_int* nparams, float* params,
+ float* work, lapack_int* iwork, lapack_int *info );
+void LAPACK_zposvxx( char* fact, char* uplo, lapack_int* n, lapack_int* nrhs,
+ lapack_complex_double* a, lapack_int* lda,
+ lapack_complex_double* af, lapack_int* ldaf, char* equed,
+ double* s, lapack_complex_double* b, lapack_int* ldb,
+ lapack_complex_double* x, lapack_int* ldx, double* rcond,
+ double* rpvgrw, double* berr, lapack_int* n_err_bnds,
+ double* err_bnds_norm, double* err_bnds_comp,
+ lapack_int* nparams, double* params,
+ lapack_complex_double* work, double* rwork,
+ lapack_int *info );
+void LAPACK_cposvxx( char* fact, char* uplo, lapack_int* n, lapack_int* nrhs,
+ lapack_complex_float* a, lapack_int* lda,
+ lapack_complex_float* af, lapack_int* ldaf, char* equed,
+ float* s, lapack_complex_float* b, lapack_int* ldb,
+ lapack_complex_float* x, lapack_int* ldx, float* rcond,
+ float* rpvgrw, float* berr, lapack_int* n_err_bnds,
+ float* err_bnds_norm, float* err_bnds_comp,
+ lapack_int* nparams, float* params,
+ lapack_complex_float* work, float* rwork,
+ lapack_int *info );
+void LAPACK_sppsv( char* uplo, lapack_int* n, lapack_int* nrhs, float* ap,
+ float* b, lapack_int* ldb, lapack_int *info );
+void LAPACK_dppsv( char* uplo, lapack_int* n, lapack_int* nrhs, double* ap,
+ double* b, lapack_int* ldb, lapack_int *info );
+void LAPACK_cppsv( char* uplo, lapack_int* n, lapack_int* nrhs,
+ lapack_complex_float* ap, lapack_complex_float* b,
+ lapack_int* ldb, lapack_int *info );
+void LAPACK_zppsv( char* uplo, lapack_int* n, lapack_int* nrhs,
+ lapack_complex_double* ap, lapack_complex_double* b,
+ lapack_int* ldb, lapack_int *info );
+void LAPACK_sppsvx( char* fact, char* uplo, lapack_int* n, lapack_int* nrhs,
+ float* ap, float* afp, char* equed, float* s, float* b,
+ lapack_int* ldb, float* x, lapack_int* ldx, float* rcond,
+ float* ferr, float* berr, float* work, lapack_int* iwork,
+ lapack_int *info );
+void LAPACK_dppsvx( char* fact, char* uplo, lapack_int* n, lapack_int* nrhs,
+ double* ap, double* afp, char* equed, double* s, double* b,
+ lapack_int* ldb, double* x, lapack_int* ldx, double* rcond,
+ double* ferr, double* berr, double* work, lapack_int* iwork,
+ lapack_int *info );
+void LAPACK_cppsvx( char* fact, char* uplo, lapack_int* n, lapack_int* nrhs,
+ lapack_complex_float* ap, lapack_complex_float* afp,
+ char* equed, float* s, lapack_complex_float* b,
+ lapack_int* ldb, lapack_complex_float* x, lapack_int* ldx,
+ float* rcond, float* ferr, float* berr,
+ lapack_complex_float* work, float* rwork,
+ lapack_int *info );
+void LAPACK_zppsvx( char* fact, char* uplo, lapack_int* n, lapack_int* nrhs,
+ lapack_complex_double* ap, lapack_complex_double* afp,
+ char* equed, double* s, lapack_complex_double* b,
+ lapack_int* ldb, lapack_complex_double* x, lapack_int* ldx,
+ double* rcond, double* ferr, double* berr,
+ lapack_complex_double* work, double* rwork,
+ lapack_int *info );
+void LAPACK_spbsv( char* uplo, lapack_int* n, lapack_int* kd, lapack_int* nrhs,
+ float* ab, lapack_int* ldab, float* b, lapack_int* ldb,
+ lapack_int *info );
+void LAPACK_dpbsv( char* uplo, lapack_int* n, lapack_int* kd, lapack_int* nrhs,
+ double* ab, lapack_int* ldab, double* b, lapack_int* ldb,
+ lapack_int *info );
+void LAPACK_cpbsv( char* uplo, lapack_int* n, lapack_int* kd, lapack_int* nrhs,
+ lapack_complex_float* ab, lapack_int* ldab,
+ lapack_complex_float* b, lapack_int* ldb, lapack_int *info );
+void LAPACK_zpbsv( char* uplo, lapack_int* n, lapack_int* kd, lapack_int* nrhs,
+ lapack_complex_double* ab, lapack_int* ldab,
+ lapack_complex_double* b, lapack_int* ldb,
+ lapack_int *info );
+void LAPACK_spbsvx( char* fact, char* uplo, lapack_int* n, lapack_int* kd,
+ lapack_int* nrhs, float* ab, lapack_int* ldab, float* afb,
+ lapack_int* ldafb, char* equed, float* s, float* b,
+ lapack_int* ldb, float* x, lapack_int* ldx, float* rcond,
+ float* ferr, float* berr, float* work, lapack_int* iwork,
+ lapack_int *info );
+void LAPACK_dpbsvx( char* fact, char* uplo, lapack_int* n, lapack_int* kd,
+ lapack_int* nrhs, double* ab, lapack_int* ldab, double* afb,
+ lapack_int* ldafb, char* equed, double* s, double* b,
+ lapack_int* ldb, double* x, lapack_int* ldx, double* rcond,
+ double* ferr, double* berr, double* work, lapack_int* iwork,
+ lapack_int *info );
+void LAPACK_cpbsvx( char* fact, char* uplo, lapack_int* n, lapack_int* kd,
+ lapack_int* nrhs, lapack_complex_float* ab,
+ lapack_int* ldab, lapack_complex_float* afb,
+ lapack_int* ldafb, char* equed, float* s,
+ lapack_complex_float* b, lapack_int* ldb,
+ lapack_complex_float* x, lapack_int* ldx, float* rcond,
+ float* ferr, float* berr, lapack_complex_float* work,
+ float* rwork, lapack_int *info );
+void LAPACK_zpbsvx( char* fact, char* uplo, lapack_int* n, lapack_int* kd,
+ lapack_int* nrhs, lapack_complex_double* ab,
+ lapack_int* ldab, lapack_complex_double* afb,
+ lapack_int* ldafb, char* equed, double* s,
+ lapack_complex_double* b, lapack_int* ldb,
+ lapack_complex_double* x, lapack_int* ldx, double* rcond,
+ double* ferr, double* berr, lapack_complex_double* work,
+ double* rwork, lapack_int *info );
+void LAPACK_sptsv( lapack_int* n, lapack_int* nrhs, float* d, float* e,
+ float* b, lapack_int* ldb, lapack_int *info );
+void LAPACK_dptsv( lapack_int* n, lapack_int* nrhs, double* d, double* e,
+ double* b, lapack_int* ldb, lapack_int *info );
+void LAPACK_cptsv( lapack_int* n, lapack_int* nrhs, float* d,
+ lapack_complex_float* e, lapack_complex_float* b,
+ lapack_int* ldb, lapack_int *info );
+void LAPACK_zptsv( lapack_int* n, lapack_int* nrhs, double* d,
+ lapack_complex_double* e, lapack_complex_double* b,
+ lapack_int* ldb, lapack_int *info );
+void LAPACK_sptsvx( char* fact, lapack_int* n, lapack_int* nrhs, const float* d,
+ const float* e, float* df, float* ef, const float* b,
+ lapack_int* ldb, float* x, lapack_int* ldx, float* rcond,
+ float* ferr, float* berr, float* work, lapack_int *info );
+void LAPACK_dptsvx( char* fact, lapack_int* n, lapack_int* nrhs,
+ const double* d, const double* e, double* df, double* ef,
+ const double* b, lapack_int* ldb, double* x,
+ lapack_int* ldx, double* rcond, double* ferr, double* berr,
+ double* work, lapack_int *info );
+void LAPACK_cptsvx( char* fact, lapack_int* n, lapack_int* nrhs, const float* d,
+ const lapack_complex_float* e, float* df,
+ lapack_complex_float* ef, const lapack_complex_float* b,
+ lapack_int* ldb, lapack_complex_float* x, lapack_int* ldx,
+ float* rcond, float* ferr, float* berr,
+ lapack_complex_float* work, float* rwork,
+ lapack_int *info );
+void LAPACK_zptsvx( char* fact, lapack_int* n, lapack_int* nrhs,
+ const double* d, const lapack_complex_double* e, double* df,
+ lapack_complex_double* ef, const lapack_complex_double* b,
+ lapack_int* ldb, lapack_complex_double* x, lapack_int* ldx,
+ double* rcond, double* ferr, double* berr,
+ lapack_complex_double* work, double* rwork,
+ lapack_int *info );
+void LAPACK_ssysv( char* uplo, lapack_int* n, lapack_int* nrhs, float* a,
+ lapack_int* lda, lapack_int* ipiv, float* b, lapack_int* ldb,
+ float* work, lapack_int* lwork, lapack_int *info );
+void LAPACK_dsysv( char* uplo, lapack_int* n, lapack_int* nrhs, double* a,
+ lapack_int* lda, lapack_int* ipiv, double* b,
+ lapack_int* ldb, double* work, lapack_int* lwork,
+ lapack_int *info );
+void LAPACK_csysv( char* uplo, lapack_int* n, lapack_int* nrhs,
+ lapack_complex_float* a, lapack_int* lda, lapack_int* ipiv,
+ lapack_complex_float* b, lapack_int* ldb,
+ lapack_complex_float* work, lapack_int* lwork,
+ lapack_int *info );
+void LAPACK_zsysv( char* uplo, lapack_int* n, lapack_int* nrhs,
+ lapack_complex_double* a, lapack_int* lda, lapack_int* ipiv,
+ lapack_complex_double* b, lapack_int* ldb,
+ lapack_complex_double* work, lapack_int* lwork,
+ lapack_int *info );
+void LAPACK_ssysvx( char* fact, char* uplo, lapack_int* n, lapack_int* nrhs,
+ const float* a, lapack_int* lda, float* af,
+ lapack_int* ldaf, lapack_int* ipiv, const float* b,
+ lapack_int* ldb, float* x, lapack_int* ldx, float* rcond,
+ float* ferr, float* berr, float* work, lapack_int* lwork,
+ lapack_int* iwork, lapack_int *info );
+void LAPACK_dsysvx( char* fact, char* uplo, lapack_int* n, lapack_int* nrhs,
+ const double* a, lapack_int* lda, double* af,
+ lapack_int* ldaf, lapack_int* ipiv, const double* b,
+ lapack_int* ldb, double* x, lapack_int* ldx, double* rcond,
+ double* ferr, double* berr, double* work, lapack_int* lwork,
+ lapack_int* iwork, lapack_int *info );
+void LAPACK_csysvx( char* fact, char* uplo, lapack_int* n, lapack_int* nrhs,
+ const lapack_complex_float* a, lapack_int* lda,
+ lapack_complex_float* af, lapack_int* ldaf,
+ lapack_int* ipiv, const lapack_complex_float* b,
+ lapack_int* ldb, lapack_complex_float* x, lapack_int* ldx,
+ float* rcond, float* ferr, float* berr,
+ lapack_complex_float* work, lapack_int* lwork, float* rwork,
+ lapack_int *info );
+void LAPACK_zsysvx( char* fact, char* uplo, lapack_int* n, lapack_int* nrhs,
+ const lapack_complex_double* a, lapack_int* lda,
+ lapack_complex_double* af, lapack_int* ldaf,
+ lapack_int* ipiv, const lapack_complex_double* b,
+ lapack_int* ldb, lapack_complex_double* x, lapack_int* ldx,
+ double* rcond, double* ferr, double* berr,
+ lapack_complex_double* work, lapack_int* lwork,
+ double* rwork, lapack_int *info );
+void LAPACK_dsysvxx( char* fact, char* uplo, lapack_int* n, lapack_int* nrhs,
+ double* a, lapack_int* lda, double* af, lapack_int* ldaf,
+ lapack_int* ipiv, char* equed, double* s, double* b,
+ lapack_int* ldb, double* x, lapack_int* ldx, double* rcond,
+ double* rpvgrw, double* berr, lapack_int* n_err_bnds,
+ double* err_bnds_norm, double* err_bnds_comp,
+ lapack_int* nparams, double* params, double* work,
+ lapack_int* iwork, lapack_int *info );
+void LAPACK_ssysvxx( char* fact, char* uplo, lapack_int* n, lapack_int* nrhs,
+ float* a, lapack_int* lda, float* af, lapack_int* ldaf,
+ lapack_int* ipiv, char* equed, float* s, float* b,
+ lapack_int* ldb, float* x, lapack_int* ldx, float* rcond,
+ float* rpvgrw, float* berr, lapack_int* n_err_bnds,
+ float* err_bnds_norm, float* err_bnds_comp,
+ lapack_int* nparams, float* params, float* work,
+ lapack_int* iwork, lapack_int *info );
+void LAPACK_zsysvxx( char* fact, char* uplo, lapack_int* n, lapack_int* nrhs,
+ lapack_complex_double* a, lapack_int* lda,
+ lapack_complex_double* af, lapack_int* ldaf,
+ lapack_int* ipiv, char* equed, double* s,
+ lapack_complex_double* b, lapack_int* ldb,
+ lapack_complex_double* x, lapack_int* ldx, double* rcond,
+ double* rpvgrw, double* berr, lapack_int* n_err_bnds,
+ double* err_bnds_norm, double* err_bnds_comp,
+ lapack_int* nparams, double* params,
+ lapack_complex_double* work, double* rwork,
+ lapack_int *info );
+void LAPACK_csysvxx( char* fact, char* uplo, lapack_int* n, lapack_int* nrhs,
+ lapack_complex_float* a, lapack_int* lda,
+ lapack_complex_float* af, lapack_int* ldaf,
+ lapack_int* ipiv, char* equed, float* s,
+ lapack_complex_float* b, lapack_int* ldb,
+ lapack_complex_float* x, lapack_int* ldx, float* rcond,
+ float* rpvgrw, float* berr, lapack_int* n_err_bnds,
+ float* err_bnds_norm, float* err_bnds_comp,
+ lapack_int* nparams, float* params,
+ lapack_complex_float* work, float* rwork,
+ lapack_int *info );
+void LAPACK_chesv( char* uplo, lapack_int* n, lapack_int* nrhs,
+ lapack_complex_float* a, lapack_int* lda, lapack_int* ipiv,
+ lapack_complex_float* b, lapack_int* ldb,
+ lapack_complex_float* work, lapack_int* lwork,
+ lapack_int *info );
+void LAPACK_zhesv( char* uplo, lapack_int* n, lapack_int* nrhs,
+ lapack_complex_double* a, lapack_int* lda, lapack_int* ipiv,
+ lapack_complex_double* b, lapack_int* ldb,
+ lapack_complex_double* work, lapack_int* lwork,
+ lapack_int *info );
+void LAPACK_chesvx( char* fact, char* uplo, lapack_int* n, lapack_int* nrhs,
+ const lapack_complex_float* a, lapack_int* lda,
+ lapack_complex_float* af, lapack_int* ldaf,
+ lapack_int* ipiv, const lapack_complex_float* b,
+ lapack_int* ldb, lapack_complex_float* x, lapack_int* ldx,
+ float* rcond, float* ferr, float* berr,
+ lapack_complex_float* work, lapack_int* lwork, float* rwork,
+ lapack_int *info );
+void LAPACK_zhesvx( char* fact, char* uplo, lapack_int* n, lapack_int* nrhs,
+ const lapack_complex_double* a, lapack_int* lda,
+ lapack_complex_double* af, lapack_int* ldaf,
+ lapack_int* ipiv, const lapack_complex_double* b,
+ lapack_int* ldb, lapack_complex_double* x, lapack_int* ldx,
+ double* rcond, double* ferr, double* berr,
+ lapack_complex_double* work, lapack_int* lwork,
+ double* rwork, lapack_int *info );
+void LAPACK_zhesvxx( char* fact, char* uplo, lapack_int* n, lapack_int* nrhs,
+ lapack_complex_double* a, lapack_int* lda,
+ lapack_complex_double* af, lapack_int* ldaf,
+ lapack_int* ipiv, char* equed, double* s,
+ lapack_complex_double* b, lapack_int* ldb,
+ lapack_complex_double* x, lapack_int* ldx, double* rcond,
+ double* rpvgrw, double* berr, lapack_int* n_err_bnds,
+ double* err_bnds_norm, double* err_bnds_comp,
+ lapack_int* nparams, double* params,
+ lapack_complex_double* work, double* rwork,
+ lapack_int *info );
+void LAPACK_chesvxx( char* fact, char* uplo, lapack_int* n, lapack_int* nrhs,
+ lapack_complex_float* a, lapack_int* lda,
+ lapack_complex_float* af, lapack_int* ldaf,
+ lapack_int* ipiv, char* equed, float* s,
+ lapack_complex_float* b, lapack_int* ldb,
+ lapack_complex_float* x, lapack_int* ldx, float* rcond,
+ float* rpvgrw, float* berr, lapack_int* n_err_bnds,
+ float* err_bnds_norm, float* err_bnds_comp,
+ lapack_int* nparams, float* params,
+ lapack_complex_float* work, float* rwork,
+ lapack_int *info );
+void LAPACK_sspsv( char* uplo, lapack_int* n, lapack_int* nrhs, float* ap,
+ lapack_int* ipiv, float* b, lapack_int* ldb,
+ lapack_int *info );
+void LAPACK_dspsv( char* uplo, lapack_int* n, lapack_int* nrhs, double* ap,
+ lapack_int* ipiv, double* b, lapack_int* ldb,
+ lapack_int *info );
+void LAPACK_cspsv( char* uplo, lapack_int* n, lapack_int* nrhs,
+ lapack_complex_float* ap, lapack_int* ipiv,
+ lapack_complex_float* b, lapack_int* ldb, lapack_int *info );
+void LAPACK_zspsv( char* uplo, lapack_int* n, lapack_int* nrhs,
+ lapack_complex_double* ap, lapack_int* ipiv,
+ lapack_complex_double* b, lapack_int* ldb,
+ lapack_int *info );
+void LAPACK_sspsvx( char* fact, char* uplo, lapack_int* n, lapack_int* nrhs,
+ const float* ap, float* afp, lapack_int* ipiv,
+ const float* b, lapack_int* ldb, float* x, lapack_int* ldx,
+ float* rcond, float* ferr, float* berr, float* work,
+ lapack_int* iwork, lapack_int *info );
+void LAPACK_dspsvx( char* fact, char* uplo, lapack_int* n, lapack_int* nrhs,
+ const double* ap, double* afp, lapack_int* ipiv,
+ const double* b, lapack_int* ldb, double* x,
+ lapack_int* ldx, double* rcond, double* ferr, double* berr,
+ double* work, lapack_int* iwork, lapack_int *info );
+void LAPACK_cspsvx( char* fact, char* uplo, lapack_int* n, lapack_int* nrhs,
+ const lapack_complex_float* ap, lapack_complex_float* afp,
+ lapack_int* ipiv, const lapack_complex_float* b,
+ lapack_int* ldb, lapack_complex_float* x, lapack_int* ldx,
+ float* rcond, float* ferr, float* berr,
+ lapack_complex_float* work, float* rwork,
+ lapack_int *info );
+void LAPACK_zspsvx( char* fact, char* uplo, lapack_int* n, lapack_int* nrhs,
+ const lapack_complex_double* ap, lapack_complex_double* afp,
+ lapack_int* ipiv, const lapack_complex_double* b,
+ lapack_int* ldb, lapack_complex_double* x, lapack_int* ldx,
+ double* rcond, double* ferr, double* berr,
+ lapack_complex_double* work, double* rwork,
+ lapack_int *info );
+void LAPACK_chpsv( char* uplo, lapack_int* n, lapack_int* nrhs,
+ lapack_complex_float* ap, lapack_int* ipiv,
+ lapack_complex_float* b, lapack_int* ldb, lapack_int *info );
+void LAPACK_zhpsv( char* uplo, lapack_int* n, lapack_int* nrhs,
+ lapack_complex_double* ap, lapack_int* ipiv,
+ lapack_complex_double* b, lapack_int* ldb,
+ lapack_int *info );
+void LAPACK_chpsvx( char* fact, char* uplo, lapack_int* n, lapack_int* nrhs,
+ const lapack_complex_float* ap, lapack_complex_float* afp,
+ lapack_int* ipiv, const lapack_complex_float* b,
+ lapack_int* ldb, lapack_complex_float* x, lapack_int* ldx,
+ float* rcond, float* ferr, float* berr,
+ lapack_complex_float* work, float* rwork,
+ lapack_int *info );
+void LAPACK_zhpsvx( char* fact, char* uplo, lapack_int* n, lapack_int* nrhs,
+ const lapack_complex_double* ap, lapack_complex_double* afp,
+ lapack_int* ipiv, const lapack_complex_double* b,
+ lapack_int* ldb, lapack_complex_double* x, lapack_int* ldx,
+ double* rcond, double* ferr, double* berr,
+ lapack_complex_double* work, double* rwork,
+ lapack_int *info );
+void LAPACK_sgeqrf( lapack_int* m, lapack_int* n, float* a, lapack_int* lda,
+ float* tau, float* work, lapack_int* lwork,
+ lapack_int *info );
+void LAPACK_dgeqrf( lapack_int* m, lapack_int* n, double* a, lapack_int* lda,
+ double* tau, double* work, lapack_int* lwork,
+ lapack_int *info );
+void LAPACK_cgeqrf( lapack_int* m, lapack_int* n, lapack_complex_float* a,
+ lapack_int* lda, lapack_complex_float* tau,
+ lapack_complex_float* work, lapack_int* lwork,
+ lapack_int *info );
+void LAPACK_zgeqrf( lapack_int* m, lapack_int* n, lapack_complex_double* a,
+ lapack_int* lda, lapack_complex_double* tau,
+ lapack_complex_double* work, lapack_int* lwork,
+ lapack_int *info );
+void LAPACK_sgeqpf( lapack_int* m, lapack_int* n, float* a, lapack_int* lda,
+ lapack_int* jpvt, float* tau, float* work,
+ lapack_int *info );
+void LAPACK_dgeqpf( lapack_int* m, lapack_int* n, double* a, lapack_int* lda,
+ lapack_int* jpvt, double* tau, double* work,
+ lapack_int *info );
+void LAPACK_cgeqpf( lapack_int* m, lapack_int* n, lapack_complex_float* a,
+ lapack_int* lda, lapack_int* jpvt,
+ lapack_complex_float* tau, lapack_complex_float* work,
+ float* rwork, lapack_int *info );
+void LAPACK_zgeqpf( lapack_int* m, lapack_int* n, lapack_complex_double* a,
+ lapack_int* lda, lapack_int* jpvt,
+ lapack_complex_double* tau, lapack_complex_double* work,
+ double* rwork, lapack_int *info );
+void LAPACK_sgeqp3( lapack_int* m, lapack_int* n, float* a, lapack_int* lda,
+ lapack_int* jpvt, float* tau, float* work,
+ lapack_int* lwork, lapack_int *info );
+void LAPACK_dgeqp3( lapack_int* m, lapack_int* n, double* a, lapack_int* lda,
+ lapack_int* jpvt, double* tau, double* work,
+ lapack_int* lwork, lapack_int *info );
+void LAPACK_cgeqp3( lapack_int* m, lapack_int* n, lapack_complex_float* a,
+ lapack_int* lda, lapack_int* jpvt,
+ lapack_complex_float* tau, lapack_complex_float* work,
+ lapack_int* lwork, float* rwork, lapack_int *info );
+void LAPACK_zgeqp3( lapack_int* m, lapack_int* n, lapack_complex_double* a,
+ lapack_int* lda, lapack_int* jpvt,
+ lapack_complex_double* tau, lapack_complex_double* work,
+ lapack_int* lwork, double* rwork, lapack_int *info );
+void LAPACK_sorgqr( lapack_int* m, lapack_int* n, lapack_int* k, float* a,
+ lapack_int* lda, const float* tau, float* work,
+ lapack_int* lwork, lapack_int *info );
+void LAPACK_dorgqr( lapack_int* m, lapack_int* n, lapack_int* k, double* a,
+ lapack_int* lda, const double* tau, double* work,
+ lapack_int* lwork, lapack_int *info );
+void LAPACK_sormqr( char* side, char* trans, lapack_int* m, lapack_int* n,
+ lapack_int* k, const float* a, lapack_int* lda,
+ const float* tau, float* c, lapack_int* ldc, float* work,
+ lapack_int* lwork, lapack_int *info );
+void LAPACK_dormqr( char* side, char* trans, lapack_int* m, lapack_int* n,
+ lapack_int* k, const double* a, lapack_int* lda,
+ const double* tau, double* c, lapack_int* ldc, double* work,
+ lapack_int* lwork, lapack_int *info );
+void LAPACK_cungqr( lapack_int* m, lapack_int* n, lapack_int* k,
+ lapack_complex_float* a, lapack_int* lda,
+ const lapack_complex_float* tau, lapack_complex_float* work,
+ lapack_int* lwork, lapack_int *info );
+void LAPACK_zungqr( lapack_int* m, lapack_int* n, lapack_int* k,
+ lapack_complex_double* a, lapack_int* lda,
+ const lapack_complex_double* tau,
+ lapack_complex_double* work, lapack_int* lwork,
+ lapack_int *info );
+void LAPACK_cunmqr( char* side, char* trans, lapack_int* m, lapack_int* n,
+ lapack_int* k, const lapack_complex_float* a,
+ lapack_int* lda, const lapack_complex_float* tau,
+ lapack_complex_float* c, lapack_int* ldc,
+ lapack_complex_float* work, lapack_int* lwork,
+ lapack_int *info );
+void LAPACK_zunmqr( char* side, char* trans, lapack_int* m, lapack_int* n,
+ lapack_int* k, const lapack_complex_double* a,
+ lapack_int* lda, const lapack_complex_double* tau,
+ lapack_complex_double* c, lapack_int* ldc,
+ lapack_complex_double* work, lapack_int* lwork,
+ lapack_int *info );
+void LAPACK_sgelqf( lapack_int* m, lapack_int* n, float* a, lapack_int* lda,
+ float* tau, float* work, lapack_int* lwork,
+ lapack_int *info );
+void LAPACK_dgelqf( lapack_int* m, lapack_int* n, double* a, lapack_int* lda,
+ double* tau, double* work, lapack_int* lwork,
+ lapack_int *info );
+void LAPACK_cgelqf( lapack_int* m, lapack_int* n, lapack_complex_float* a,
+ lapack_int* lda, lapack_complex_float* tau,
+ lapack_complex_float* work, lapack_int* lwork,
+ lapack_int *info );
+void LAPACK_zgelqf( lapack_int* m, lapack_int* n, lapack_complex_double* a,
+ lapack_int* lda, lapack_complex_double* tau,
+ lapack_complex_double* work, lapack_int* lwork,
+ lapack_int *info );
+void LAPACK_sorglq( lapack_int* m, lapack_int* n, lapack_int* k, float* a,
+ lapack_int* lda, const float* tau, float* work,
+ lapack_int* lwork, lapack_int *info );
+void LAPACK_dorglq( lapack_int* m, lapack_int* n, lapack_int* k, double* a,
+ lapack_int* lda, const double* tau, double* work,
+ lapack_int* lwork, lapack_int *info );
+void LAPACK_sormlq( char* side, char* trans, lapack_int* m, lapack_int* n,
+ lapack_int* k, const float* a, lapack_int* lda,
+ const float* tau, float* c, lapack_int* ldc, float* work,
+ lapack_int* lwork, lapack_int *info );
+void LAPACK_dormlq( char* side, char* trans, lapack_int* m, lapack_int* n,
+ lapack_int* k, const double* a, lapack_int* lda,
+ const double* tau, double* c, lapack_int* ldc, double* work,
+ lapack_int* lwork, lapack_int *info );
+void LAPACK_cunglq( lapack_int* m, lapack_int* n, lapack_int* k,
+ lapack_complex_float* a, lapack_int* lda,
+ const lapack_complex_float* tau, lapack_complex_float* work,
+ lapack_int* lwork, lapack_int *info );
+void LAPACK_zunglq( lapack_int* m, lapack_int* n, lapack_int* k,
+ lapack_complex_double* a, lapack_int* lda,
+ const lapack_complex_double* tau,
+ lapack_complex_double* work, lapack_int* lwork,
+ lapack_int *info );
+void LAPACK_cunmlq( char* side, char* trans, lapack_int* m, lapack_int* n,
+ lapack_int* k, const lapack_complex_float* a,
+ lapack_int* lda, const lapack_complex_float* tau,
+ lapack_complex_float* c, lapack_int* ldc,
+ lapack_complex_float* work, lapack_int* lwork,
+ lapack_int *info );
+void LAPACK_zunmlq( char* side, char* trans, lapack_int* m, lapack_int* n,
+ lapack_int* k, const lapack_complex_double* a,
+ lapack_int* lda, const lapack_complex_double* tau,
+ lapack_complex_double* c, lapack_int* ldc,
+ lapack_complex_double* work, lapack_int* lwork,
+ lapack_int *info );
+void LAPACK_sgeqlf( lapack_int* m, lapack_int* n, float* a, lapack_int* lda,
+ float* tau, float* work, lapack_int* lwork,
+ lapack_int *info );
+void LAPACK_dgeqlf( lapack_int* m, lapack_int* n, double* a, lapack_int* lda,
+ double* tau, double* work, lapack_int* lwork,
+ lapack_int *info );
+void LAPACK_cgeqlf( lapack_int* m, lapack_int* n, lapack_complex_float* a,
+ lapack_int* lda, lapack_complex_float* tau,
+ lapack_complex_float* work, lapack_int* lwork,
+ lapack_int *info );
+void LAPACK_zgeqlf( lapack_int* m, lapack_int* n, lapack_complex_double* a,
+ lapack_int* lda, lapack_complex_double* tau,
+ lapack_complex_double* work, lapack_int* lwork,
+ lapack_int *info );
+void LAPACK_sorgql( lapack_int* m, lapack_int* n, lapack_int* k, float* a,
+ lapack_int* lda, const float* tau, float* work,
+ lapack_int* lwork, lapack_int *info );
+void LAPACK_dorgql( lapack_int* m, lapack_int* n, lapack_int* k, double* a,
+ lapack_int* lda, const double* tau, double* work,
+ lapack_int* lwork, lapack_int *info );
+void LAPACK_cungql( lapack_int* m, lapack_int* n, lapack_int* k,
+ lapack_complex_float* a, lapack_int* lda,
+ const lapack_complex_float* tau, lapack_complex_float* work,
+ lapack_int* lwork, lapack_int *info );
+void LAPACK_zungql( lapack_int* m, lapack_int* n, lapack_int* k,
+ lapack_complex_double* a, lapack_int* lda,
+ const lapack_complex_double* tau,
+ lapack_complex_double* work, lapack_int* lwork,
+ lapack_int *info );
+void LAPACK_sormql( char* side, char* trans, lapack_int* m, lapack_int* n,
+ lapack_int* k, const float* a, lapack_int* lda,
+ const float* tau, float* c, lapack_int* ldc, float* work,
+ lapack_int* lwork, lapack_int *info );
+void LAPACK_dormql( char* side, char* trans, lapack_int* m, lapack_int* n,
+ lapack_int* k, const double* a, lapack_int* lda,
+ const double* tau, double* c, lapack_int* ldc, double* work,
+ lapack_int* lwork, lapack_int *info );
+void LAPACK_cunmql( char* side, char* trans, lapack_int* m, lapack_int* n,
+ lapack_int* k, const lapack_complex_float* a,
+ lapack_int* lda, const lapack_complex_float* tau,
+ lapack_complex_float* c, lapack_int* ldc,
+ lapack_complex_float* work, lapack_int* lwork,
+ lapack_int *info );
+void LAPACK_zunmql( char* side, char* trans, lapack_int* m, lapack_int* n,
+ lapack_int* k, const lapack_complex_double* a,
+ lapack_int* lda, const lapack_complex_double* tau,
+ lapack_complex_double* c, lapack_int* ldc,
+ lapack_complex_double* work, lapack_int* lwork,
+ lapack_int *info );
+void LAPACK_sgerqf( lapack_int* m, lapack_int* n, float* a, lapack_int* lda,
+ float* tau, float* work, lapack_int* lwork,
+ lapack_int *info );
+void LAPACK_dgerqf( lapack_int* m, lapack_int* n, double* a, lapack_int* lda,
+ double* tau, double* work, lapack_int* lwork,
+ lapack_int *info );
+void LAPACK_cgerqf( lapack_int* m, lapack_int* n, lapack_complex_float* a,
+ lapack_int* lda, lapack_complex_float* tau,
+ lapack_complex_float* work, lapack_int* lwork,
+ lapack_int *info );
+void LAPACK_zgerqf( lapack_int* m, lapack_int* n, lapack_complex_double* a,
+ lapack_int* lda, lapack_complex_double* tau,
+ lapack_complex_double* work, lapack_int* lwork,
+ lapack_int *info );
+void LAPACK_sorgrq( lapack_int* m, lapack_int* n, lapack_int* k, float* a,
+ lapack_int* lda, const float* tau, float* work,
+ lapack_int* lwork, lapack_int *info );
+void LAPACK_dorgrq( lapack_int* m, lapack_int* n, lapack_int* k, double* a,
+ lapack_int* lda, const double* tau, double* work,
+ lapack_int* lwork, lapack_int *info );
+void LAPACK_cungrq( lapack_int* m, lapack_int* n, lapack_int* k,
+ lapack_complex_float* a, lapack_int* lda,
+ const lapack_complex_float* tau, lapack_complex_float* work,
+ lapack_int* lwork, lapack_int *info );
+void LAPACK_zungrq( lapack_int* m, lapack_int* n, lapack_int* k,
+ lapack_complex_double* a, lapack_int* lda,
+ const lapack_complex_double* tau,
+ lapack_complex_double* work, lapack_int* lwork,
+ lapack_int *info );
+void LAPACK_sormrq( char* side, char* trans, lapack_int* m, lapack_int* n,
+ lapack_int* k, const float* a, lapack_int* lda,
+ const float* tau, float* c, lapack_int* ldc, float* work,
+ lapack_int* lwork, lapack_int *info );
+void LAPACK_dormrq( char* side, char* trans, lapack_int* m, lapack_int* n,
+ lapack_int* k, const double* a, lapack_int* lda,
+ const double* tau, double* c, lapack_int* ldc, double* work,
+ lapack_int* lwork, lapack_int *info );
+void LAPACK_cunmrq( char* side, char* trans, lapack_int* m, lapack_int* n,
+ lapack_int* k, const lapack_complex_float* a,
+ lapack_int* lda, const lapack_complex_float* tau,
+ lapack_complex_float* c, lapack_int* ldc,
+ lapack_complex_float* work, lapack_int* lwork,
+ lapack_int *info );
+void LAPACK_zunmrq( char* side, char* trans, lapack_int* m, lapack_int* n,
+ lapack_int* k, const lapack_complex_double* a,
+ lapack_int* lda, const lapack_complex_double* tau,
+ lapack_complex_double* c, lapack_int* ldc,
+ lapack_complex_double* work, lapack_int* lwork,
+ lapack_int *info );
+void LAPACK_stzrzf( lapack_int* m, lapack_int* n, float* a, lapack_int* lda,
+ float* tau, float* work, lapack_int* lwork,
+ lapack_int *info );
+void LAPACK_dtzrzf( lapack_int* m, lapack_int* n, double* a, lapack_int* lda,
+ double* tau, double* work, lapack_int* lwork,
+ lapack_int *info );
+void LAPACK_ctzrzf( lapack_int* m, lapack_int* n, lapack_complex_float* a,
+ lapack_int* lda, lapack_complex_float* tau,
+ lapack_complex_float* work, lapack_int* lwork,
+ lapack_int *info );
+void LAPACK_ztzrzf( lapack_int* m, lapack_int* n, lapack_complex_double* a,
+ lapack_int* lda, lapack_complex_double* tau,
+ lapack_complex_double* work, lapack_int* lwork,
+ lapack_int *info );
+void LAPACK_sormrz( char* side, char* trans, lapack_int* m, lapack_int* n,
+ lapack_int* k, lapack_int* l, const float* a,
+ lapack_int* lda, const float* tau, float* c,
+ lapack_int* ldc, float* work, lapack_int* lwork,
+ lapack_int *info );
+void LAPACK_dormrz( char* side, char* trans, lapack_int* m, lapack_int* n,
+ lapack_int* k, lapack_int* l, const double* a,
+ lapack_int* lda, const double* tau, double* c,
+ lapack_int* ldc, double* work, lapack_int* lwork,
+ lapack_int *info );
+void LAPACK_cunmrz( char* side, char* trans, lapack_int* m, lapack_int* n,
+ lapack_int* k, lapack_int* l, const lapack_complex_float* a,
+ lapack_int* lda, const lapack_complex_float* tau,
+ lapack_complex_float* c, lapack_int* ldc,
+ lapack_complex_float* work, lapack_int* lwork,
+ lapack_int *info );
+void LAPACK_zunmrz( char* side, char* trans, lapack_int* m, lapack_int* n,
+ lapack_int* k, lapack_int* l,
+ const lapack_complex_double* a, lapack_int* lda,
+ const lapack_complex_double* tau, lapack_complex_double* c,
+ lapack_int* ldc, lapack_complex_double* work,
+ lapack_int* lwork, lapack_int *info );
+void LAPACK_sggqrf( lapack_int* n, lapack_int* m, lapack_int* p, float* a,
+ lapack_int* lda, float* taua, float* b, lapack_int* ldb,
+ float* taub, float* work, lapack_int* lwork,
+ lapack_int *info );
+void LAPACK_dggqrf( lapack_int* n, lapack_int* m, lapack_int* p, double* a,
+ lapack_int* lda, double* taua, double* b, lapack_int* ldb,
+ double* taub, double* work, lapack_int* lwork,
+ lapack_int *info );
+void LAPACK_cggqrf( lapack_int* n, lapack_int* m, lapack_int* p,
+ lapack_complex_float* a, lapack_int* lda,
+ lapack_complex_float* taua, lapack_complex_float* b,
+ lapack_int* ldb, lapack_complex_float* taub,
+ lapack_complex_float* work, lapack_int* lwork,
+ lapack_int *info );
+void LAPACK_zggqrf( lapack_int* n, lapack_int* m, lapack_int* p,
+ lapack_complex_double* a, lapack_int* lda,
+ lapack_complex_double* taua, lapack_complex_double* b,
+ lapack_int* ldb, lapack_complex_double* taub,
+ lapack_complex_double* work, lapack_int* lwork,
+ lapack_int *info );
+void LAPACK_sggrqf( lapack_int* m, lapack_int* p, lapack_int* n, float* a,
+ lapack_int* lda, float* taua, float* b, lapack_int* ldb,
+ float* taub, float* work, lapack_int* lwork,
+ lapack_int *info );
+void LAPACK_dggrqf( lapack_int* m, lapack_int* p, lapack_int* n, double* a,
+ lapack_int* lda, double* taua, double* b, lapack_int* ldb,
+ double* taub, double* work, lapack_int* lwork,
+ lapack_int *info );
+void LAPACK_cggrqf( lapack_int* m, lapack_int* p, lapack_int* n,
+ lapack_complex_float* a, lapack_int* lda,
+ lapack_complex_float* taua, lapack_complex_float* b,
+ lapack_int* ldb, lapack_complex_float* taub,
+ lapack_complex_float* work, lapack_int* lwork,
+ lapack_int *info );
+void LAPACK_zggrqf( lapack_int* m, lapack_int* p, lapack_int* n,
+ lapack_complex_double* a, lapack_int* lda,
+ lapack_complex_double* taua, lapack_complex_double* b,
+ lapack_int* ldb, lapack_complex_double* taub,
+ lapack_complex_double* work, lapack_int* lwork,
+ lapack_int *info );
+void LAPACK_sgebrd( lapack_int* m, lapack_int* n, float* a, lapack_int* lda,
+ float* d, float* e, float* tauq, float* taup, float* work,
+ lapack_int* lwork, lapack_int *info );
+void LAPACK_dgebrd( lapack_int* m, lapack_int* n, double* a, lapack_int* lda,
+ double* d, double* e, double* tauq, double* taup,
+ double* work, lapack_int* lwork, lapack_int *info );
+void LAPACK_cgebrd( lapack_int* m, lapack_int* n, lapack_complex_float* a,
+ lapack_int* lda, float* d, float* e,
+ lapack_complex_float* tauq, lapack_complex_float* taup,
+ lapack_complex_float* work, lapack_int* lwork,
+ lapack_int *info );
+void LAPACK_zgebrd( lapack_int* m, lapack_int* n, lapack_complex_double* a,
+ lapack_int* lda, double* d, double* e,
+ lapack_complex_double* tauq, lapack_complex_double* taup,
+ lapack_complex_double* work, lapack_int* lwork,
+ lapack_int *info );
+void LAPACK_sgbbrd( char* vect, lapack_int* m, lapack_int* n, lapack_int* ncc,
+ lapack_int* kl, lapack_int* ku, float* ab, lapack_int* ldab,
+ float* d, float* e, float* q, lapack_int* ldq, float* pt,
+ lapack_int* ldpt, float* c, lapack_int* ldc, float* work,
+ lapack_int *info );
+void LAPACK_dgbbrd( char* vect, lapack_int* m, lapack_int* n, lapack_int* ncc,
+ lapack_int* kl, lapack_int* ku, double* ab,
+ lapack_int* ldab, double* d, double* e, double* q,
+ lapack_int* ldq, double* pt, lapack_int* ldpt, double* c,
+ lapack_int* ldc, double* work, lapack_int *info );
+void LAPACK_cgbbrd( char* vect, lapack_int* m, lapack_int* n, lapack_int* ncc,
+ lapack_int* kl, lapack_int* ku, lapack_complex_float* ab,
+ lapack_int* ldab, float* d, float* e,
+ lapack_complex_float* q, lapack_int* ldq,
+ lapack_complex_float* pt, lapack_int* ldpt,
+ lapack_complex_float* c, lapack_int* ldc,
+ lapack_complex_float* work, float* rwork,
+ lapack_int *info );
+void LAPACK_zgbbrd( char* vect, lapack_int* m, lapack_int* n, lapack_int* ncc,
+ lapack_int* kl, lapack_int* ku, lapack_complex_double* ab,
+ lapack_int* ldab, double* d, double* e,
+ lapack_complex_double* q, lapack_int* ldq,
+ lapack_complex_double* pt, lapack_int* ldpt,
+ lapack_complex_double* c, lapack_int* ldc,
+ lapack_complex_double* work, double* rwork,
+ lapack_int *info );
+void LAPACK_sorgbr( char* vect, lapack_int* m, lapack_int* n, lapack_int* k,
+ float* a, lapack_int* lda, const float* tau, float* work,
+ lapack_int* lwork, lapack_int *info );
+void LAPACK_dorgbr( char* vect, lapack_int* m, lapack_int* n, lapack_int* k,
+ double* a, lapack_int* lda, const double* tau, double* work,
+ lapack_int* lwork, lapack_int *info );
+void LAPACK_sormbr( char* vect, char* side, char* trans, lapack_int* m,
+ lapack_int* n, lapack_int* k, const float* a,
+ lapack_int* lda, const float* tau, float* c,
+ lapack_int* ldc, float* work, lapack_int* lwork,
+ lapack_int *info );
+void LAPACK_dormbr( char* vect, char* side, char* trans, lapack_int* m,
+ lapack_int* n, lapack_int* k, const double* a,
+ lapack_int* lda, const double* tau, double* c,
+ lapack_int* ldc, double* work, lapack_int* lwork,
+ lapack_int *info );
+void LAPACK_cungbr( char* vect, lapack_int* m, lapack_int* n, lapack_int* k,
+ lapack_complex_float* a, lapack_int* lda,
+ const lapack_complex_float* tau, lapack_complex_float* work,
+ lapack_int* lwork, lapack_int *info );
+void LAPACK_zungbr( char* vect, lapack_int* m, lapack_int* n, lapack_int* k,
+ lapack_complex_double* a, lapack_int* lda,
+ const lapack_complex_double* tau,
+ lapack_complex_double* work, lapack_int* lwork,
+ lapack_int *info );
+void LAPACK_cunmbr( char* vect, char* side, char* trans, lapack_int* m,
+ lapack_int* n, lapack_int* k, const lapack_complex_float* a,
+ lapack_int* lda, const lapack_complex_float* tau,
+ lapack_complex_float* c, lapack_int* ldc,
+ lapack_complex_float* work, lapack_int* lwork,
+ lapack_int *info );
+void LAPACK_zunmbr( char* vect, char* side, char* trans, lapack_int* m,
+ lapack_int* n, lapack_int* k,
+ const lapack_complex_double* a, lapack_int* lda,
+ const lapack_complex_double* tau, lapack_complex_double* c,
+ lapack_int* ldc, lapack_complex_double* work,
+ lapack_int* lwork, lapack_int *info );
+void LAPACK_sbdsqr( char* uplo, lapack_int* n, lapack_int* ncvt,
+ lapack_int* nru, lapack_int* ncc, float* d, float* e,
+ float* vt, lapack_int* ldvt, float* u, lapack_int* ldu,
+ float* c, lapack_int* ldc, float* work, lapack_int *info );
+void LAPACK_dbdsqr( char* uplo, lapack_int* n, lapack_int* ncvt,
+ lapack_int* nru, lapack_int* ncc, double* d, double* e,
+ double* vt, lapack_int* ldvt, double* u, lapack_int* ldu,
+ double* c, lapack_int* ldc, double* work,
+ lapack_int *info );
+void LAPACK_cbdsqr( char* uplo, lapack_int* n, lapack_int* ncvt,
+ lapack_int* nru, lapack_int* ncc, float* d, float* e,
+ lapack_complex_float* vt, lapack_int* ldvt,
+ lapack_complex_float* u, lapack_int* ldu,
+ lapack_complex_float* c, lapack_int* ldc, float* work,
+ lapack_int *info );
+void LAPACK_zbdsqr( char* uplo, lapack_int* n, lapack_int* ncvt,
+ lapack_int* nru, lapack_int* ncc, double* d, double* e,
+ lapack_complex_double* vt, lapack_int* ldvt,
+ lapack_complex_double* u, lapack_int* ldu,
+ lapack_complex_double* c, lapack_int* ldc, double* work,
+ lapack_int *info );
+void LAPACK_sbdsdc( char* uplo, char* compq, lapack_int* n, float* d, float* e,
+ float* u, lapack_int* ldu, float* vt, lapack_int* ldvt,
+ float* q, lapack_int* iq, float* work, lapack_int* iwork,
+ lapack_int *info );
+void LAPACK_dbdsdc( char* uplo, char* compq, lapack_int* n, double* d,
+ double* e, double* u, lapack_int* ldu, double* vt,
+ lapack_int* ldvt, double* q, lapack_int* iq, double* work,
+ lapack_int* iwork, lapack_int *info );
+void LAPACK_ssytrd( char* uplo, lapack_int* n, float* a, lapack_int* lda,
+ float* d, float* e, float* tau, float* work,
+ lapack_int* lwork, lapack_int *info );
+void LAPACK_dsytrd( char* uplo, lapack_int* n, double* a, lapack_int* lda,
+ double* d, double* e, double* tau, double* work,
+ lapack_int* lwork, lapack_int *info );
+void LAPACK_sorgtr( char* uplo, lapack_int* n, float* a, lapack_int* lda,
+ const float* tau, float* work, lapack_int* lwork,
+ lapack_int *info );
+void LAPACK_dorgtr( char* uplo, lapack_int* n, double* a, lapack_int* lda,
+ const double* tau, double* work, lapack_int* lwork,
+ lapack_int *info );
+void LAPACK_sormtr( char* side, char* uplo, char* trans, lapack_int* m,
+ lapack_int* n, const float* a, lapack_int* lda,
+ const float* tau, float* c, lapack_int* ldc, float* work,
+ lapack_int* lwork, lapack_int *info );
+void LAPACK_dormtr( char* side, char* uplo, char* trans, lapack_int* m,
+ lapack_int* n, const double* a, lapack_int* lda,
+ const double* tau, double* c, lapack_int* ldc, double* work,
+ lapack_int* lwork, lapack_int *info );
+void LAPACK_chetrd( char* uplo, lapack_int* n, lapack_complex_float* a,
+ lapack_int* lda, float* d, float* e,
+ lapack_complex_float* tau, lapack_complex_float* work,
+ lapack_int* lwork, lapack_int *info );
+void LAPACK_zhetrd( char* uplo, lapack_int* n, lapack_complex_double* a,
+ lapack_int* lda, double* d, double* e,
+ lapack_complex_double* tau, lapack_complex_double* work,
+ lapack_int* lwork, lapack_int *info );
+void LAPACK_cungtr( char* uplo, lapack_int* n, lapack_complex_float* a,
+ lapack_int* lda, const lapack_complex_float* tau,
+ lapack_complex_float* work, lapack_int* lwork,
+ lapack_int *info );
+void LAPACK_zungtr( char* uplo, lapack_int* n, lapack_complex_double* a,
+ lapack_int* lda, const lapack_complex_double* tau,
+ lapack_complex_double* work, lapack_int* lwork,
+ lapack_int *info );
+void LAPACK_cunmtr( char* side, char* uplo, char* trans, lapack_int* m,
+ lapack_int* n, const lapack_complex_float* a,
+ lapack_int* lda, const lapack_complex_float* tau,
+ lapack_complex_float* c, lapack_int* ldc,
+ lapack_complex_float* work, lapack_int* lwork,
+ lapack_int *info );
+void LAPACK_zunmtr( char* side, char* uplo, char* trans, lapack_int* m,
+ lapack_int* n, const lapack_complex_double* a,
+ lapack_int* lda, const lapack_complex_double* tau,
+ lapack_complex_double* c, lapack_int* ldc,
+ lapack_complex_double* work, lapack_int* lwork,
+ lapack_int *info );
+void LAPACK_ssptrd( char* uplo, lapack_int* n, float* ap, float* d, float* e,
+ float* tau, lapack_int *info );
+void LAPACK_dsptrd( char* uplo, lapack_int* n, double* ap, double* d, double* e,
+ double* tau, lapack_int *info );
+void LAPACK_sopgtr( char* uplo, lapack_int* n, const float* ap,
+ const float* tau, float* q, lapack_int* ldq, float* work,
+ lapack_int *info );
+void LAPACK_dopgtr( char* uplo, lapack_int* n, const double* ap,
+ const double* tau, double* q, lapack_int* ldq, double* work,
+ lapack_int *info );
+void LAPACK_sopmtr( char* side, char* uplo, char* trans, lapack_int* m,
+ lapack_int* n, const float* ap, const float* tau, float* c,
+ lapack_int* ldc, float* work, lapack_int *info );
+void LAPACK_dopmtr( char* side, char* uplo, char* trans, lapack_int* m,
+ lapack_int* n, const double* ap, const double* tau,
+ double* c, lapack_int* ldc, double* work,
+ lapack_int *info );
+void LAPACK_chptrd( char* uplo, lapack_int* n, lapack_complex_float* ap,
+ float* d, float* e, lapack_complex_float* tau,
+ lapack_int *info );
+void LAPACK_zhptrd( char* uplo, lapack_int* n, lapack_complex_double* ap,
+ double* d, double* e, lapack_complex_double* tau,
+ lapack_int *info );
+void LAPACK_cupgtr( char* uplo, lapack_int* n, const lapack_complex_float* ap,
+ const lapack_complex_float* tau, lapack_complex_float* q,
+ lapack_int* ldq, lapack_complex_float* work,
+ lapack_int *info );
+void LAPACK_zupgtr( char* uplo, lapack_int* n, const lapack_complex_double* ap,
+ const lapack_complex_double* tau, lapack_complex_double* q,
+ lapack_int* ldq, lapack_complex_double* work,
+ lapack_int *info );
+void LAPACK_cupmtr( char* side, char* uplo, char* trans, lapack_int* m,
+ lapack_int* n, const lapack_complex_float* ap,
+ const lapack_complex_float* tau, lapack_complex_float* c,
+ lapack_int* ldc, lapack_complex_float* work,
+ lapack_int *info );
+void LAPACK_zupmtr( char* side, char* uplo, char* trans, lapack_int* m,
+ lapack_int* n, const lapack_complex_double* ap,
+ const lapack_complex_double* tau, lapack_complex_double* c,
+ lapack_int* ldc, lapack_complex_double* work,
+ lapack_int *info );
+void LAPACK_ssbtrd( char* vect, char* uplo, lapack_int* n, lapack_int* kd,
+ float* ab, lapack_int* ldab, float* d, float* e, float* q,
+ lapack_int* ldq, float* work, lapack_int *info );
+void LAPACK_dsbtrd( char* vect, char* uplo, lapack_int* n, lapack_int* kd,
+ double* ab, lapack_int* ldab, double* d, double* e,
+ double* q, lapack_int* ldq, double* work,
+ lapack_int *info );
+void LAPACK_chbtrd( char* vect, char* uplo, lapack_int* n, lapack_int* kd,
+ lapack_complex_float* ab, lapack_int* ldab, float* d,
+ float* e, lapack_complex_float* q, lapack_int* ldq,
+ lapack_complex_float* work, lapack_int *info );
+void LAPACK_zhbtrd( char* vect, char* uplo, lapack_int* n, lapack_int* kd,
+ lapack_complex_double* ab, lapack_int* ldab, double* d,
+ double* e, lapack_complex_double* q, lapack_int* ldq,
+ lapack_complex_double* work, lapack_int *info );
+void LAPACK_ssterf( lapack_int* n, float* d, float* e, lapack_int *info );
+void LAPACK_dsterf( lapack_int* n, double* d, double* e, lapack_int *info );
+void LAPACK_ssteqr( char* compz, lapack_int* n, float* d, float* e, float* z,
+ lapack_int* ldz, float* work, lapack_int *info );
+void LAPACK_dsteqr( char* compz, lapack_int* n, double* d, double* e, double* z,
+ lapack_int* ldz, double* work, lapack_int *info );
+void LAPACK_csteqr( char* compz, lapack_int* n, float* d, float* e,
+ lapack_complex_float* z, lapack_int* ldz, float* work,
+ lapack_int *info );
+void LAPACK_zsteqr( char* compz, lapack_int* n, double* d, double* e,
+ lapack_complex_double* z, lapack_int* ldz, double* work,
+ lapack_int *info );
+void LAPACK_sstemr( char* jobz, char* range, lapack_int* n, float* d, float* e,
+ float* vl, float* vu, lapack_int* il, lapack_int* iu,
+ lapack_int* m, float* w, float* z, lapack_int* ldz,
+ lapack_int* nzc, lapack_int* isuppz, lapack_logical* tryrac,
+ float* work, lapack_int* lwork, lapack_int* iwork,
+ lapack_int* liwork, lapack_int *info );
+void LAPACK_dstemr( char* jobz, char* range, lapack_int* n, double* d,
+ double* e, double* vl, double* vu, lapack_int* il,
+ lapack_int* iu, lapack_int* m, double* w, double* z,
+ lapack_int* ldz, lapack_int* nzc, lapack_int* isuppz,
+ lapack_logical* tryrac, double* work, lapack_int* lwork,
+ lapack_int* iwork, lapack_int* liwork, lapack_int *info );
+void LAPACK_cstemr( char* jobz, char* range, lapack_int* n, float* d, float* e,
+ float* vl, float* vu, lapack_int* il, lapack_int* iu,
+ lapack_int* m, float* w, lapack_complex_float* z,
+ lapack_int* ldz, lapack_int* nzc, lapack_int* isuppz,
+ lapack_logical* tryrac, float* work, lapack_int* lwork,
+ lapack_int* iwork, lapack_int* liwork, lapack_int *info );
+void LAPACK_zstemr( char* jobz, char* range, lapack_int* n, double* d,
+ double* e, double* vl, double* vu, lapack_int* il,
+ lapack_int* iu, lapack_int* m, double* w,
+ lapack_complex_double* z, lapack_int* ldz, lapack_int* nzc,
+ lapack_int* isuppz, lapack_logical* tryrac, double* work,
+ lapack_int* lwork, lapack_int* iwork, lapack_int* liwork,
+ lapack_int *info );
+void LAPACK_sstedc( char* compz, lapack_int* n, float* d, float* e, float* z,
+ lapack_int* ldz, float* work, lapack_int* lwork,
+ lapack_int* iwork, lapack_int* liwork, lapack_int *info );
+void LAPACK_dstedc( char* compz, lapack_int* n, double* d, double* e, double* z,
+ lapack_int* ldz, double* work, lapack_int* lwork,
+ lapack_int* iwork, lapack_int* liwork, lapack_int *info );
+void LAPACK_cstedc( char* compz, lapack_int* n, float* d, float* e,
+ lapack_complex_float* z, lapack_int* ldz,
+ lapack_complex_float* work, lapack_int* lwork, float* rwork,
+ lapack_int* lrwork, lapack_int* iwork, lapack_int* liwork,
+ lapack_int *info );
+void LAPACK_zstedc( char* compz, lapack_int* n, double* d, double* e,
+ lapack_complex_double* z, lapack_int* ldz,
+ lapack_complex_double* work, lapack_int* lwork,
+ double* rwork, lapack_int* lrwork, lapack_int* iwork,
+ lapack_int* liwork, lapack_int *info );
+void LAPACK_sstegr( char* jobz, char* range, lapack_int* n, float* d, float* e,
+ float* vl, float* vu, lapack_int* il, lapack_int* iu,
+ float* abstol, lapack_int* m, float* w, float* z,
+ lapack_int* ldz, lapack_int* isuppz, float* work,
+ lapack_int* lwork, lapack_int* iwork, lapack_int* liwork,
+ lapack_int *info );
+void LAPACK_dstegr( char* jobz, char* range, lapack_int* n, double* d,
+ double* e, double* vl, double* vu, lapack_int* il,
+ lapack_int* iu, double* abstol, lapack_int* m, double* w,
+ double* z, lapack_int* ldz, lapack_int* isuppz,
+ double* work, lapack_int* lwork, lapack_int* iwork,
+ lapack_int* liwork, lapack_int *info );
+void LAPACK_cstegr( char* jobz, char* range, lapack_int* n, float* d, float* e,
+ float* vl, float* vu, lapack_int* il, lapack_int* iu,
+ float* abstol, lapack_int* m, float* w,
+ lapack_complex_float* z, lapack_int* ldz,
+ lapack_int* isuppz, float* work, lapack_int* lwork,
+ lapack_int* iwork, lapack_int* liwork, lapack_int *info );
+void LAPACK_zstegr( char* jobz, char* range, lapack_int* n, double* d,
+ double* e, double* vl, double* vu, lapack_int* il,
+ lapack_int* iu, double* abstol, lapack_int* m, double* w,
+ lapack_complex_double* z, lapack_int* ldz,
+ lapack_int* isuppz, double* work, lapack_int* lwork,
+ lapack_int* iwork, lapack_int* liwork, lapack_int *info );
+void LAPACK_spteqr( char* compz, lapack_int* n, float* d, float* e, float* z,
+ lapack_int* ldz, float* work, lapack_int *info );
+void LAPACK_dpteqr( char* compz, lapack_int* n, double* d, double* e, double* z,
+ lapack_int* ldz, double* work, lapack_int *info );
+void LAPACK_cpteqr( char* compz, lapack_int* n, float* d, float* e,
+ lapack_complex_float* z, lapack_int* ldz, float* work,
+ lapack_int *info );
+void LAPACK_zpteqr( char* compz, lapack_int* n, double* d, double* e,
+ lapack_complex_double* z, lapack_int* ldz, double* work,
+ lapack_int *info );
+void LAPACK_sstebz( char* range, char* order, lapack_int* n, float* vl,
+ float* vu, lapack_int* il, lapack_int* iu, float* abstol,
+ const float* d, const float* e, lapack_int* m,
+ lapack_int* nsplit, float* w, lapack_int* iblock,
+ lapack_int* isplit, float* work, lapack_int* iwork,
+ lapack_int *info );
+void LAPACK_dstebz( char* range, char* order, lapack_int* n, double* vl,
+ double* vu, lapack_int* il, lapack_int* iu, double* abstol,
+ const double* d, const double* e, lapack_int* m,
+ lapack_int* nsplit, double* w, lapack_int* iblock,
+ lapack_int* isplit, double* work, lapack_int* iwork,
+ lapack_int *info );
+void LAPACK_sstein( lapack_int* n, const float* d, const float* e,
+ lapack_int* m, const float* w, const lapack_int* iblock,
+ const lapack_int* isplit, float* z, lapack_int* ldz,
+ float* work, lapack_int* iwork, lapack_int* ifailv,
+ lapack_int *info );
+void LAPACK_dstein( lapack_int* n, const double* d, const double* e,
+ lapack_int* m, const double* w, const lapack_int* iblock,
+ const lapack_int* isplit, double* z, lapack_int* ldz,
+ double* work, lapack_int* iwork, lapack_int* ifailv,
+ lapack_int *info );
+void LAPACK_cstein( lapack_int* n, const float* d, const float* e,
+ lapack_int* m, const float* w, const lapack_int* iblock,
+ const lapack_int* isplit, lapack_complex_float* z,
+ lapack_int* ldz, float* work, lapack_int* iwork,
+ lapack_int* ifailv, lapack_int *info );
+void LAPACK_zstein( lapack_int* n, const double* d, const double* e,
+ lapack_int* m, const double* w, const lapack_int* iblock,
+ const lapack_int* isplit, lapack_complex_double* z,
+ lapack_int* ldz, double* work, lapack_int* iwork,
+ lapack_int* ifailv, lapack_int *info );
+void LAPACK_sdisna( char* job, lapack_int* m, lapack_int* n, const float* d,
+ float* sep, lapack_int *info );
+void LAPACK_ddisna( char* job, lapack_int* m, lapack_int* n, const double* d,
+ double* sep, lapack_int *info );
+void LAPACK_ssygst( lapack_int* itype, char* uplo, lapack_int* n, float* a,
+ lapack_int* lda, const float* b, lapack_int* ldb,
+ lapack_int *info );
+void LAPACK_dsygst( lapack_int* itype, char* uplo, lapack_int* n, double* a,
+ lapack_int* lda, const double* b, lapack_int* ldb,
+ lapack_int *info );
+void LAPACK_chegst( lapack_int* itype, char* uplo, lapack_int* n,
+ lapack_complex_float* a, lapack_int* lda,
+ const lapack_complex_float* b, lapack_int* ldb,
+ lapack_int *info );
+void LAPACK_zhegst( lapack_int* itype, char* uplo, lapack_int* n,
+ lapack_complex_double* a, lapack_int* lda,
+ const lapack_complex_double* b, lapack_int* ldb,
+ lapack_int *info );
+void LAPACK_sspgst( lapack_int* itype, char* uplo, lapack_int* n, float* ap,
+ const float* bp, lapack_int *info );
+void LAPACK_dspgst( lapack_int* itype, char* uplo, lapack_int* n, double* ap,
+ const double* bp, lapack_int *info );
+void LAPACK_chpgst( lapack_int* itype, char* uplo, lapack_int* n,
+ lapack_complex_float* ap, const lapack_complex_float* bp,
+ lapack_int *info );
+void LAPACK_zhpgst( lapack_int* itype, char* uplo, lapack_int* n,
+ lapack_complex_double* ap, const lapack_complex_double* bp,
+ lapack_int *info );
+void LAPACK_ssbgst( char* vect, char* uplo, lapack_int* n, lapack_int* ka,
+ lapack_int* kb, float* ab, lapack_int* ldab,
+ const float* bb, lapack_int* ldbb, float* x,
+ lapack_int* ldx, float* work, lapack_int *info );
+void LAPACK_dsbgst( char* vect, char* uplo, lapack_int* n, lapack_int* ka,
+ lapack_int* kb, double* ab, lapack_int* ldab,
+ const double* bb, lapack_int* ldbb, double* x,
+ lapack_int* ldx, double* work, lapack_int *info );
+void LAPACK_chbgst( char* vect, char* uplo, lapack_int* n, lapack_int* ka,
+ lapack_int* kb, lapack_complex_float* ab, lapack_int* ldab,
+ const lapack_complex_float* bb, lapack_int* ldbb,
+ lapack_complex_float* x, lapack_int* ldx,
+ lapack_complex_float* work, float* rwork,
+ lapack_int *info );
+void LAPACK_zhbgst( char* vect, char* uplo, lapack_int* n, lapack_int* ka,
+ lapack_int* kb, lapack_complex_double* ab, lapack_int* ldab,
+ const lapack_complex_double* bb, lapack_int* ldbb,
+ lapack_complex_double* x, lapack_int* ldx,
+ lapack_complex_double* work, double* rwork,
+ lapack_int *info );
+void LAPACK_spbstf( char* uplo, lapack_int* n, lapack_int* kb, float* bb,
+ lapack_int* ldbb, lapack_int *info );
+void LAPACK_dpbstf( char* uplo, lapack_int* n, lapack_int* kb, double* bb,
+ lapack_int* ldbb, lapack_int *info );
+void LAPACK_cpbstf( char* uplo, lapack_int* n, lapack_int* kb,
+ lapack_complex_float* bb, lapack_int* ldbb,
+ lapack_int *info );
+void LAPACK_zpbstf( char* uplo, lapack_int* n, lapack_int* kb,
+ lapack_complex_double* bb, lapack_int* ldbb,
+ lapack_int *info );
+void LAPACK_sgehrd( lapack_int* n, lapack_int* ilo, lapack_int* ihi, float* a,
+ lapack_int* lda, float* tau, float* work, lapack_int* lwork,
+ lapack_int *info );
+void LAPACK_dgehrd( lapack_int* n, lapack_int* ilo, lapack_int* ihi, double* a,
+ lapack_int* lda, double* tau, double* work,
+ lapack_int* lwork, lapack_int *info );
+void LAPACK_cgehrd( lapack_int* n, lapack_int* ilo, lapack_int* ihi,
+ lapack_complex_float* a, lapack_int* lda,
+ lapack_complex_float* tau, lapack_complex_float* work,
+ lapack_int* lwork, lapack_int *info );
+void LAPACK_zgehrd( lapack_int* n, lapack_int* ilo, lapack_int* ihi,
+ lapack_complex_double* a, lapack_int* lda,
+ lapack_complex_double* tau, lapack_complex_double* work,
+ lapack_int* lwork, lapack_int *info );
+void LAPACK_sorghr( lapack_int* n, lapack_int* ilo, lapack_int* ihi, float* a,
+ lapack_int* lda, const float* tau, float* work,
+ lapack_int* lwork, lapack_int *info );
+void LAPACK_dorghr( lapack_int* n, lapack_int* ilo, lapack_int* ihi, double* a,
+ lapack_int* lda, const double* tau, double* work,
+ lapack_int* lwork, lapack_int *info );
+void LAPACK_sormhr( char* side, char* trans, lapack_int* m, lapack_int* n,
+ lapack_int* ilo, lapack_int* ihi, const float* a,
+ lapack_int* lda, const float* tau, float* c,
+ lapack_int* ldc, float* work, lapack_int* lwork,
+ lapack_int *info );
+void LAPACK_dormhr( char* side, char* trans, lapack_int* m, lapack_int* n,
+ lapack_int* ilo, lapack_int* ihi, const double* a,
+ lapack_int* lda, const double* tau, double* c,
+ lapack_int* ldc, double* work, lapack_int* lwork,
+ lapack_int *info );
+void LAPACK_cunghr( lapack_int* n, lapack_int* ilo, lapack_int* ihi,
+ lapack_complex_float* a, lapack_int* lda,
+ const lapack_complex_float* tau, lapack_complex_float* work,
+ lapack_int* lwork, lapack_int *info );
+void LAPACK_zunghr( lapack_int* n, lapack_int* ilo, lapack_int* ihi,
+ lapack_complex_double* a, lapack_int* lda,
+ const lapack_complex_double* tau,
+ lapack_complex_double* work, lapack_int* lwork,
+ lapack_int *info );
+void LAPACK_cunmhr( char* side, char* trans, lapack_int* m, lapack_int* n,
+ lapack_int* ilo, lapack_int* ihi,
+ const lapack_complex_float* a, lapack_int* lda,
+ const lapack_complex_float* tau, lapack_complex_float* c,
+ lapack_int* ldc, lapack_complex_float* work,
+ lapack_int* lwork, lapack_int *info );
+void LAPACK_zunmhr( char* side, char* trans, lapack_int* m, lapack_int* n,
+ lapack_int* ilo, lapack_int* ihi,
+ const lapack_complex_double* a, lapack_int* lda,
+ const lapack_complex_double* tau, lapack_complex_double* c,
+ lapack_int* ldc, lapack_complex_double* work,
+ lapack_int* lwork, lapack_int *info );
+void LAPACK_sgebal( char* job, lapack_int* n, float* a, lapack_int* lda,
+ lapack_int* ilo, lapack_int* ihi, float* scale,
+ lapack_int *info );
+void LAPACK_dgebal( char* job, lapack_int* n, double* a, lapack_int* lda,
+ lapack_int* ilo, lapack_int* ihi, double* scale,
+ lapack_int *info );
+void LAPACK_cgebal( char* job, lapack_int* n, lapack_complex_float* a,
+ lapack_int* lda, lapack_int* ilo, lapack_int* ihi,
+ float* scale, lapack_int *info );
+void LAPACK_zgebal( char* job, lapack_int* n, lapack_complex_double* a,
+ lapack_int* lda, lapack_int* ilo, lapack_int* ihi,
+ double* scale, lapack_int *info );
+void LAPACK_sgebak( char* job, char* side, lapack_int* n, lapack_int* ilo,
+ lapack_int* ihi, const float* scale, lapack_int* m,
+ float* v, lapack_int* ldv, lapack_int *info );
+void LAPACK_dgebak( char* job, char* side, lapack_int* n, lapack_int* ilo,
+ lapack_int* ihi, const double* scale, lapack_int* m,
+ double* v, lapack_int* ldv, lapack_int *info );
+void LAPACK_cgebak( char* job, char* side, lapack_int* n, lapack_int* ilo,
+ lapack_int* ihi, const float* scale, lapack_int* m,
+ lapack_complex_float* v, lapack_int* ldv,
+ lapack_int *info );
+void LAPACK_zgebak( char* job, char* side, lapack_int* n, lapack_int* ilo,
+ lapack_int* ihi, const double* scale, lapack_int* m,
+ lapack_complex_double* v, lapack_int* ldv,
+ lapack_int *info );
+void LAPACK_shseqr( char* job, char* compz, lapack_int* n, lapack_int* ilo,
+ lapack_int* ihi, float* h, lapack_int* ldh, float* wr,
+ float* wi, float* z, lapack_int* ldz, float* work,
+ lapack_int* lwork, lapack_int *info );
+void LAPACK_dhseqr( char* job, char* compz, lapack_int* n, lapack_int* ilo,
+ lapack_int* ihi, double* h, lapack_int* ldh, double* wr,
+ double* wi, double* z, lapack_int* ldz, double* work,
+ lapack_int* lwork, lapack_int *info );
+void LAPACK_chseqr( char* job, char* compz, lapack_int* n, lapack_int* ilo,
+ lapack_int* ihi, lapack_complex_float* h, lapack_int* ldh,
+ lapack_complex_float* w, lapack_complex_float* z,
+ lapack_int* ldz, lapack_complex_float* work,
+ lapack_int* lwork, lapack_int *info );
+void LAPACK_zhseqr( char* job, char* compz, lapack_int* n, lapack_int* ilo,
+ lapack_int* ihi, lapack_complex_double* h, lapack_int* ldh,
+ lapack_complex_double* w, lapack_complex_double* z,
+ lapack_int* ldz, lapack_complex_double* work,
+ lapack_int* lwork, lapack_int *info );
+void LAPACK_shsein( char* job, char* eigsrc, char* initv,
+ lapack_logical* select, lapack_int* n, const float* h,
+ lapack_int* ldh, float* wr, const float* wi, float* vl,
+ lapack_int* ldvl, float* vr, lapack_int* ldvr,
+ lapack_int* mm, lapack_int* m, float* work,
+ lapack_int* ifaill, lapack_int* ifailr, lapack_int *info );
+void LAPACK_dhsein( char* job, char* eigsrc, char* initv,
+ lapack_logical* select, lapack_int* n, const double* h,
+ lapack_int* ldh, double* wr, const double* wi, double* vl,
+ lapack_int* ldvl, double* vr, lapack_int* ldvr,
+ lapack_int* mm, lapack_int* m, double* work,
+ lapack_int* ifaill, lapack_int* ifailr, lapack_int *info );
+void LAPACK_chsein( char* job, char* eigsrc, char* initv,
+ const lapack_logical* select, lapack_int* n,
+ const lapack_complex_float* h, lapack_int* ldh,
+ lapack_complex_float* w, lapack_complex_float* vl,
+ lapack_int* ldvl, lapack_complex_float* vr,
+ lapack_int* ldvr, lapack_int* mm, lapack_int* m,
+ lapack_complex_float* work, float* rwork,
+ lapack_int* ifaill, lapack_int* ifailr, lapack_int *info );
+void LAPACK_zhsein( char* job, char* eigsrc, char* initv,
+ const lapack_logical* select, lapack_int* n,
+ const lapack_complex_double* h, lapack_int* ldh,
+ lapack_complex_double* w, lapack_complex_double* vl,
+ lapack_int* ldvl, lapack_complex_double* vr,
+ lapack_int* ldvr, lapack_int* mm, lapack_int* m,
+ lapack_complex_double* work, double* rwork,
+ lapack_int* ifaill, lapack_int* ifailr, lapack_int *info );
+void LAPACK_strevc( char* side, char* howmny, lapack_logical* select,
+ lapack_int* n, const float* t, lapack_int* ldt, float* vl,
+ lapack_int* ldvl, float* vr, lapack_int* ldvr,
+ lapack_int* mm, lapack_int* m, float* work,
+ lapack_int *info );
+void LAPACK_dtrevc( char* side, char* howmny, lapack_logical* select,
+ lapack_int* n, const double* t, lapack_int* ldt, double* vl,
+ lapack_int* ldvl, double* vr, lapack_int* ldvr,
+ lapack_int* mm, lapack_int* m, double* work,
+ lapack_int *info );
+void LAPACK_ctrevc( char* side, char* howmny, const lapack_logical* select,
+ lapack_int* n, lapack_complex_float* t, lapack_int* ldt,
+ lapack_complex_float* vl, lapack_int* ldvl,
+ lapack_complex_float* vr, lapack_int* ldvr, lapack_int* mm,
+ lapack_int* m, lapack_complex_float* work, float* rwork,
+ lapack_int *info );
+void LAPACK_ztrevc( char* side, char* howmny, const lapack_logical* select,
+ lapack_int* n, lapack_complex_double* t, lapack_int* ldt,
+ lapack_complex_double* vl, lapack_int* ldvl,
+ lapack_complex_double* vr, lapack_int* ldvr, lapack_int* mm,
+ lapack_int* m, lapack_complex_double* work, double* rwork,
+ lapack_int *info );
+void LAPACK_strsna( char* job, char* howmny, const lapack_logical* select,
+ lapack_int* n, const float* t, lapack_int* ldt,
+ const float* vl, lapack_int* ldvl, const float* vr,
+ lapack_int* ldvr, float* s, float* sep, lapack_int* mm,
+ lapack_int* m, float* work, lapack_int* ldwork,
+ lapack_int* iwork, lapack_int *info );
+void LAPACK_dtrsna( char* job, char* howmny, const lapack_logical* select,
+ lapack_int* n, const double* t, lapack_int* ldt,
+ const double* vl, lapack_int* ldvl, const double* vr,
+ lapack_int* ldvr, double* s, double* sep, lapack_int* mm,
+ lapack_int* m, double* work, lapack_int* ldwork,
+ lapack_int* iwork, lapack_int *info );
+void LAPACK_ctrsna( char* job, char* howmny, const lapack_logical* select,
+ lapack_int* n, const lapack_complex_float* t,
+ lapack_int* ldt, const lapack_complex_float* vl,
+ lapack_int* ldvl, const lapack_complex_float* vr,
+ lapack_int* ldvr, float* s, float* sep, lapack_int* mm,
+ lapack_int* m, lapack_complex_float* work,
+ lapack_int* ldwork, float* rwork, lapack_int *info );
+void LAPACK_ztrsna( char* job, char* howmny, const lapack_logical* select,
+ lapack_int* n, const lapack_complex_double* t,
+ lapack_int* ldt, const lapack_complex_double* vl,
+ lapack_int* ldvl, const lapack_complex_double* vr,
+ lapack_int* ldvr, double* s, double* sep, lapack_int* mm,
+ lapack_int* m, lapack_complex_double* work,
+ lapack_int* ldwork, double* rwork, lapack_int *info );
+void LAPACK_strexc( char* compq, lapack_int* n, float* t, lapack_int* ldt,
+ float* q, lapack_int* ldq, lapack_int* ifst,
+ lapack_int* ilst, float* work, lapack_int *info );
+void LAPACK_dtrexc( char* compq, lapack_int* n, double* t, lapack_int* ldt,
+ double* q, lapack_int* ldq, lapack_int* ifst,
+ lapack_int* ilst, double* work, lapack_int *info );
+void LAPACK_ctrexc( char* compq, lapack_int* n, lapack_complex_float* t,
+ lapack_int* ldt, lapack_complex_float* q, lapack_int* ldq,
+ lapack_int* ifst, lapack_int* ilst, lapack_int *info );
+void LAPACK_ztrexc( char* compq, lapack_int* n, lapack_complex_double* t,
+ lapack_int* ldt, lapack_complex_double* q, lapack_int* ldq,
+ lapack_int* ifst, lapack_int* ilst, lapack_int *info );
+void LAPACK_strsen( char* job, char* compq, const lapack_logical* select,
+ lapack_int* n, float* t, lapack_int* ldt, float* q,
+ lapack_int* ldq, float* wr, float* wi, lapack_int* m,
+ float* s, float* sep, float* work, lapack_int* lwork,
+ lapack_int* iwork, lapack_int* liwork, lapack_int *info );
+void LAPACK_dtrsen( char* job, char* compq, const lapack_logical* select,
+ lapack_int* n, double* t, lapack_int* ldt, double* q,
+ lapack_int* ldq, double* wr, double* wi, lapack_int* m,
+ double* s, double* sep, double* work, lapack_int* lwork,
+ lapack_int* iwork, lapack_int* liwork, lapack_int *info );
+void LAPACK_ctrsen( char* job, char* compq, const lapack_logical* select,
+ lapack_int* n, lapack_complex_float* t, lapack_int* ldt,
+ lapack_complex_float* q, lapack_int* ldq,
+ lapack_complex_float* w, lapack_int* m, float* s,
+ float* sep, lapack_complex_float* work, lapack_int* lwork,
+ lapack_int *info );
+void LAPACK_ztrsen( char* job, char* compq, const lapack_logical* select,
+ lapack_int* n, lapack_complex_double* t, lapack_int* ldt,
+ lapack_complex_double* q, lapack_int* ldq,
+ lapack_complex_double* w, lapack_int* m, double* s,
+ double* sep, lapack_complex_double* work, lapack_int* lwork,
+ lapack_int *info );
+void LAPACK_strsyl( char* trana, char* tranb, lapack_int* isgn, lapack_int* m,
+ lapack_int* n, const float* a, lapack_int* lda,
+ const float* b, lapack_int* ldb, float* c, lapack_int* ldc,
+ float* scale, lapack_int *info );
+void LAPACK_dtrsyl( char* trana, char* tranb, lapack_int* isgn, lapack_int* m,
+ lapack_int* n, const double* a, lapack_int* lda,
+ const double* b, lapack_int* ldb, double* c,
+ lapack_int* ldc, double* scale, lapack_int *info );
+void LAPACK_ctrsyl( char* trana, char* tranb, lapack_int* isgn, lapack_int* m,
+ lapack_int* n, const lapack_complex_float* a,
+ lapack_int* lda, const lapack_complex_float* b,
+ lapack_int* ldb, lapack_complex_float* c, lapack_int* ldc,
+ float* scale, lapack_int *info );
+void LAPACK_ztrsyl( char* trana, char* tranb, lapack_int* isgn, lapack_int* m,
+ lapack_int* n, const lapack_complex_double* a,
+ lapack_int* lda, const lapack_complex_double* b,
+ lapack_int* ldb, lapack_complex_double* c, lapack_int* ldc,
+ double* scale, lapack_int *info );
+void LAPACK_sgghrd( char* compq, char* compz, lapack_int* n, lapack_int* ilo,
+ lapack_int* ihi, float* a, lapack_int* lda, float* b,
+ lapack_int* ldb, float* q, lapack_int* ldq, float* z,
+ lapack_int* ldz, lapack_int *info );
+void LAPACK_dgghrd( char* compq, char* compz, lapack_int* n, lapack_int* ilo,
+ lapack_int* ihi, double* a, lapack_int* lda, double* b,
+ lapack_int* ldb, double* q, lapack_int* ldq, double* z,
+ lapack_int* ldz, lapack_int *info );
+void LAPACK_cgghrd( char* compq, char* compz, lapack_int* n, lapack_int* ilo,
+ lapack_int* ihi, lapack_complex_float* a, lapack_int* lda,
+ lapack_complex_float* b, lapack_int* ldb,
+ lapack_complex_float* q, lapack_int* ldq,
+ lapack_complex_float* z, lapack_int* ldz,
+ lapack_int *info );
+void LAPACK_zgghrd( char* compq, char* compz, lapack_int* n, lapack_int* ilo,
+ lapack_int* ihi, lapack_complex_double* a, lapack_int* lda,
+ lapack_complex_double* b, lapack_int* ldb,
+ lapack_complex_double* q, lapack_int* ldq,
+ lapack_complex_double* z, lapack_int* ldz,
+ lapack_int *info );
+void LAPACK_sggbal( char* job, lapack_int* n, float* a, lapack_int* lda,
+ float* b, lapack_int* ldb, lapack_int* ilo, lapack_int* ihi,
+ float* lscale, float* rscale, float* work,
+ lapack_int *info );
+void LAPACK_dggbal( char* job, lapack_int* n, double* a, lapack_int* lda,
+ double* b, lapack_int* ldb, lapack_int* ilo,
+ lapack_int* ihi, double* lscale, double* rscale,
+ double* work, lapack_int *info );
+void LAPACK_cggbal( char* job, lapack_int* n, lapack_complex_float* a,
+ lapack_int* lda, lapack_complex_float* b, lapack_int* ldb,
+ lapack_int* ilo, lapack_int* ihi, float* lscale,
+ float* rscale, float* work, lapack_int *info );
+void LAPACK_zggbal( char* job, lapack_int* n, lapack_complex_double* a,
+ lapack_int* lda, lapack_complex_double* b, lapack_int* ldb,
+ lapack_int* ilo, lapack_int* ihi, double* lscale,
+ double* rscale, double* work, lapack_int *info );
+void LAPACK_sggbak( char* job, char* side, lapack_int* n, lapack_int* ilo,
+ lapack_int* ihi, const float* lscale, const float* rscale,
+ lapack_int* m, float* v, lapack_int* ldv,
+ lapack_int *info );
+void LAPACK_dggbak( char* job, char* side, lapack_int* n, lapack_int* ilo,
+ lapack_int* ihi, const double* lscale, const double* rscale,
+ lapack_int* m, double* v, lapack_int* ldv,
+ lapack_int *info );
+void LAPACK_cggbak( char* job, char* side, lapack_int* n, lapack_int* ilo,
+ lapack_int* ihi, const float* lscale, const float* rscale,
+ lapack_int* m, lapack_complex_float* v, lapack_int* ldv,
+ lapack_int *info );
+void LAPACK_zggbak( char* job, char* side, lapack_int* n, lapack_int* ilo,
+ lapack_int* ihi, const double* lscale, const double* rscale,
+ lapack_int* m, lapack_complex_double* v, lapack_int* ldv,
+ lapack_int *info );
+void LAPACK_shgeqz( char* job, char* compq, char* compz, lapack_int* n,
+ lapack_int* ilo, lapack_int* ihi, float* h, lapack_int* ldh,
+ float* t, lapack_int* ldt, float* alphar, float* alphai,
+ float* beta, float* q, lapack_int* ldq, float* z,
+ lapack_int* ldz, float* work, lapack_int* lwork,
+ lapack_int *info );
+void LAPACK_dhgeqz( char* job, char* compq, char* compz, lapack_int* n,
+ lapack_int* ilo, lapack_int* ihi, double* h,
+ lapack_int* ldh, double* t, lapack_int* ldt, double* alphar,
+ double* alphai, double* beta, double* q, lapack_int* ldq,
+ double* z, lapack_int* ldz, double* work, lapack_int* lwork,
+ lapack_int *info );
+void LAPACK_chgeqz( char* job, char* compq, char* compz, lapack_int* n,
+ lapack_int* ilo, lapack_int* ihi, lapack_complex_float* h,
+ lapack_int* ldh, lapack_complex_float* t, lapack_int* ldt,
+ lapack_complex_float* alpha, lapack_complex_float* beta,
+ lapack_complex_float* q, lapack_int* ldq,
+ lapack_complex_float* z, lapack_int* ldz,
+ lapack_complex_float* work, lapack_int* lwork, float* rwork,
+ lapack_int *info );
+void LAPACK_zhgeqz( char* job, char* compq, char* compz, lapack_int* n,
+ lapack_int* ilo, lapack_int* ihi, lapack_complex_double* h,
+ lapack_int* ldh, lapack_complex_double* t, lapack_int* ldt,
+ lapack_complex_double* alpha, lapack_complex_double* beta,
+ lapack_complex_double* q, lapack_int* ldq,
+ lapack_complex_double* z, lapack_int* ldz,
+ lapack_complex_double* work, lapack_int* lwork,
+ double* rwork, lapack_int *info );
+void LAPACK_stgevc( char* side, char* howmny, const lapack_logical* select,
+ lapack_int* n, const float* s, lapack_int* lds,
+ const float* p, lapack_int* ldp, float* vl,
+ lapack_int* ldvl, float* vr, lapack_int* ldvr,
+ lapack_int* mm, lapack_int* m, float* work,
+ lapack_int *info );
+void LAPACK_dtgevc( char* side, char* howmny, const lapack_logical* select,
+ lapack_int* n, const double* s, lapack_int* lds,
+ const double* p, lapack_int* ldp, double* vl,
+ lapack_int* ldvl, double* vr, lapack_int* ldvr,
+ lapack_int* mm, lapack_int* m, double* work,
+ lapack_int *info );
+void LAPACK_ctgevc( char* side, char* howmny, const lapack_logical* select,
+ lapack_int* n, const lapack_complex_float* s,
+ lapack_int* lds, const lapack_complex_float* p,
+ lapack_int* ldp, lapack_complex_float* vl, lapack_int* ldvl,
+ lapack_complex_float* vr, lapack_int* ldvr, lapack_int* mm,
+ lapack_int* m, lapack_complex_float* work, float* rwork,
+ lapack_int *info );
+void LAPACK_ztgevc( char* side, char* howmny, const lapack_logical* select,
+ lapack_int* n, const lapack_complex_double* s,
+ lapack_int* lds, const lapack_complex_double* p,
+ lapack_int* ldp, lapack_complex_double* vl,
+ lapack_int* ldvl, lapack_complex_double* vr,
+ lapack_int* ldvr, lapack_int* mm, lapack_int* m,
+ lapack_complex_double* work, double* rwork,
+ lapack_int *info );
+void LAPACK_stgexc( lapack_logical* wantq, lapack_logical* wantz, lapack_int* n,
+ float* a, lapack_int* lda, float* b, lapack_int* ldb,
+ float* q, lapack_int* ldq, float* z, lapack_int* ldz,
+ lapack_int* ifst, lapack_int* ilst, float* work,
+ lapack_int* lwork, lapack_int *info );
+void LAPACK_dtgexc( lapack_logical* wantq, lapack_logical* wantz, lapack_int* n,
+ double* a, lapack_int* lda, double* b, lapack_int* ldb,
+ double* q, lapack_int* ldq, double* z, lapack_int* ldz,
+ lapack_int* ifst, lapack_int* ilst, double* work,
+ lapack_int* lwork, lapack_int *info );
+void LAPACK_ctgexc( lapack_logical* wantq, lapack_logical* wantz, lapack_int* n,
+ lapack_complex_float* a, lapack_int* lda,
+ lapack_complex_float* b, lapack_int* ldb,
+ lapack_complex_float* q, lapack_int* ldq,
+ lapack_complex_float* z, lapack_int* ldz, lapack_int* ifst,
+ lapack_int* ilst, lapack_int *info );
+void LAPACK_ztgexc( lapack_logical* wantq, lapack_logical* wantz, lapack_int* n,
+ lapack_complex_double* a, lapack_int* lda,
+ lapack_complex_double* b, lapack_int* ldb,
+ lapack_complex_double* q, lapack_int* ldq,
+ lapack_complex_double* z, lapack_int* ldz, lapack_int* ifst,
+ lapack_int* ilst, lapack_int *info );
+void LAPACK_stgsen( lapack_int* ijob, lapack_logical* wantq,
+ lapack_logical* wantz, const lapack_logical* select,
+ lapack_int* n, float* a, lapack_int* lda, float* b,
+ lapack_int* ldb, float* alphar, float* alphai, float* beta,
+ float* q, lapack_int* ldq, float* z, lapack_int* ldz,
+ lapack_int* m, float* pl, float* pr, float* dif,
+ float* work, lapack_int* lwork, lapack_int* iwork,
+ lapack_int* liwork, lapack_int *info );
+void LAPACK_dtgsen( lapack_int* ijob, lapack_logical* wantq,
+ lapack_logical* wantz, const lapack_logical* select,
+ lapack_int* n, double* a, lapack_int* lda, double* b,
+ lapack_int* ldb, double* alphar, double* alphai,
+ double* beta, double* q, lapack_int* ldq, double* z,
+ lapack_int* ldz, lapack_int* m, double* pl, double* pr,
+ double* dif, double* work, lapack_int* lwork,
+ lapack_int* iwork, lapack_int* liwork, lapack_int *info );
+void LAPACK_ctgsen( lapack_int* ijob, lapack_logical* wantq,
+ lapack_logical* wantz, const lapack_logical* select,
+ lapack_int* n, lapack_complex_float* a, lapack_int* lda,
+ lapack_complex_float* b, lapack_int* ldb,
+ lapack_complex_float* alpha, lapack_complex_float* beta,
+ lapack_complex_float* q, lapack_int* ldq,
+ lapack_complex_float* z, lapack_int* ldz, lapack_int* m,
+ float* pl, float* pr, float* dif,
+ lapack_complex_float* work, lapack_int* lwork,
+ lapack_int* iwork, lapack_int* liwork, lapack_int *info );
+void LAPACK_ztgsen( lapack_int* ijob, lapack_logical* wantq,
+ lapack_logical* wantz, const lapack_logical* select,
+ lapack_int* n, lapack_complex_double* a, lapack_int* lda,
+ lapack_complex_double* b, lapack_int* ldb,
+ lapack_complex_double* alpha, lapack_complex_double* beta,
+ lapack_complex_double* q, lapack_int* ldq,
+ lapack_complex_double* z, lapack_int* ldz, lapack_int* m,
+ double* pl, double* pr, double* dif,
+ lapack_complex_double* work, lapack_int* lwork,
+ lapack_int* iwork, lapack_int* liwork, lapack_int *info );
+void LAPACK_stgsyl( char* trans, lapack_int* ijob, lapack_int* m, lapack_int* n,
+ const float* a, lapack_int* lda, const float* b,
+ lapack_int* ldb, float* c, lapack_int* ldc, const float* d,
+ lapack_int* ldd, const float* e, lapack_int* lde, float* f,
+ lapack_int* ldf, float* scale, float* dif, float* work,
+ lapack_int* lwork, lapack_int* iwork, lapack_int *info );
+void LAPACK_dtgsyl( char* trans, lapack_int* ijob, lapack_int* m, lapack_int* n,
+ const double* a, lapack_int* lda, const double* b,
+ lapack_int* ldb, double* c, lapack_int* ldc,
+ const double* d, lapack_int* ldd, const double* e,
+ lapack_int* lde, double* f, lapack_int* ldf, double* scale,
+ double* dif, double* work, lapack_int* lwork,
+ lapack_int* iwork, lapack_int *info );
+void LAPACK_ctgsyl( char* trans, lapack_int* ijob, lapack_int* m, lapack_int* n,
+ const lapack_complex_float* a, lapack_int* lda,
+ const lapack_complex_float* b, lapack_int* ldb,
+ lapack_complex_float* c, lapack_int* ldc,
+ const lapack_complex_float* d, lapack_int* ldd,
+ const lapack_complex_float* e, lapack_int* lde,
+ lapack_complex_float* f, lapack_int* ldf, float* scale,
+ float* dif, lapack_complex_float* work, lapack_int* lwork,
+ lapack_int* iwork, lapack_int *info );
+void LAPACK_ztgsyl( char* trans, lapack_int* ijob, lapack_int* m, lapack_int* n,
+ const lapack_complex_double* a, lapack_int* lda,
+ const lapack_complex_double* b, lapack_int* ldb,
+ lapack_complex_double* c, lapack_int* ldc,
+ const lapack_complex_double* d, lapack_int* ldd,
+ const lapack_complex_double* e, lapack_int* lde,
+ lapack_complex_double* f, lapack_int* ldf, double* scale,
+ double* dif, lapack_complex_double* work, lapack_int* lwork,
+ lapack_int* iwork, lapack_int *info );
+void LAPACK_stgsna( char* job, char* howmny, const lapack_logical* select,
+ lapack_int* n, const float* a, lapack_int* lda,
+ const float* b, lapack_int* ldb, const float* vl,
+ lapack_int* ldvl, const float* vr, lapack_int* ldvr,
+ float* s, float* dif, lapack_int* mm, lapack_int* m,
+ float* work, lapack_int* lwork, lapack_int* iwork,
+ lapack_int *info );
+void LAPACK_dtgsna( char* job, char* howmny, const lapack_logical* select,
+ lapack_int* n, const double* a, lapack_int* lda,
+ const double* b, lapack_int* ldb, const double* vl,
+ lapack_int* ldvl, const double* vr, lapack_int* ldvr,
+ double* s, double* dif, lapack_int* mm, lapack_int* m,
+ double* work, lapack_int* lwork, lapack_int* iwork,
+ lapack_int *info );
+void LAPACK_ctgsna( char* job, char* howmny, const lapack_logical* select,
+ lapack_int* n, const lapack_complex_float* a,
+ lapack_int* lda, const lapack_complex_float* b,
+ lapack_int* ldb, const lapack_complex_float* vl,
+ lapack_int* ldvl, const lapack_complex_float* vr,
+ lapack_int* ldvr, float* s, float* dif, lapack_int* mm,
+ lapack_int* m, lapack_complex_float* work,
+ lapack_int* lwork, lapack_int* iwork, lapack_int *info );
+void LAPACK_ztgsna( char* job, char* howmny, const lapack_logical* select,
+ lapack_int* n, const lapack_complex_double* a,
+ lapack_int* lda, const lapack_complex_double* b,
+ lapack_int* ldb, const lapack_complex_double* vl,
+ lapack_int* ldvl, const lapack_complex_double* vr,
+ lapack_int* ldvr, double* s, double* dif, lapack_int* mm,
+ lapack_int* m, lapack_complex_double* work,
+ lapack_int* lwork, lapack_int* iwork, lapack_int *info );
+void LAPACK_sggsvp( char* jobu, char* jobv, char* jobq, lapack_int* m,
+ lapack_int* p, lapack_int* n, float* a, lapack_int* lda,
+ float* b, lapack_int* ldb, float* tola, float* tolb,
+ lapack_int* k, lapack_int* l, float* u, lapack_int* ldu,
+ float* v, lapack_int* ldv, float* q, lapack_int* ldq,
+ lapack_int* iwork, float* tau, float* work,
+ lapack_int *info );
+void LAPACK_dggsvp( char* jobu, char* jobv, char* jobq, lapack_int* m,
+ lapack_int* p, lapack_int* n, double* a, lapack_int* lda,
+ double* b, lapack_int* ldb, double* tola, double* tolb,
+ lapack_int* k, lapack_int* l, double* u, lapack_int* ldu,
+ double* v, lapack_int* ldv, double* q, lapack_int* ldq,
+ lapack_int* iwork, double* tau, double* work,
+ lapack_int *info );
+void LAPACK_cggsvp( char* jobu, char* jobv, char* jobq, lapack_int* m,
+ lapack_int* p, lapack_int* n, lapack_complex_float* a,
+ lapack_int* lda, lapack_complex_float* b, lapack_int* ldb,
+ float* tola, float* tolb, lapack_int* k, lapack_int* l,
+ lapack_complex_float* u, lapack_int* ldu,
+ lapack_complex_float* v, lapack_int* ldv,
+ lapack_complex_float* q, lapack_int* ldq, lapack_int* iwork,
+ float* rwork, lapack_complex_float* tau,
+ lapack_complex_float* work, lapack_int *info );
+void LAPACK_zggsvp( char* jobu, char* jobv, char* jobq, lapack_int* m,
+ lapack_int* p, lapack_int* n, lapack_complex_double* a,
+ lapack_int* lda, lapack_complex_double* b, lapack_int* ldb,
+ double* tola, double* tolb, lapack_int* k, lapack_int* l,
+ lapack_complex_double* u, lapack_int* ldu,
+ lapack_complex_double* v, lapack_int* ldv,
+ lapack_complex_double* q, lapack_int* ldq,
+ lapack_int* iwork, double* rwork,
+ lapack_complex_double* tau, lapack_complex_double* work,
+ lapack_int *info );
+void LAPACK_stgsja( char* jobu, char* jobv, char* jobq, lapack_int* m,
+ lapack_int* p, lapack_int* n, lapack_int* k, lapack_int* l,
+ float* a, lapack_int* lda, float* b, lapack_int* ldb,
+ float* tola, float* tolb, float* alpha, float* beta,
+ float* u, lapack_int* ldu, float* v, lapack_int* ldv,
+ float* q, lapack_int* ldq, float* work, lapack_int* ncycle,
+ lapack_int *info );
+void LAPACK_dtgsja( char* jobu, char* jobv, char* jobq, lapack_int* m,
+ lapack_int* p, lapack_int* n, lapack_int* k, lapack_int* l,
+ double* a, lapack_int* lda, double* b, lapack_int* ldb,
+ double* tola, double* tolb, double* alpha, double* beta,
+ double* u, lapack_int* ldu, double* v, lapack_int* ldv,
+ double* q, lapack_int* ldq, double* work,
+ lapack_int* ncycle, lapack_int *info );
+void LAPACK_ctgsja( char* jobu, char* jobv, char* jobq, lapack_int* m,
+ lapack_int* p, lapack_int* n, lapack_int* k, lapack_int* l,
+ lapack_complex_float* a, lapack_int* lda,
+ lapack_complex_float* b, lapack_int* ldb, float* tola,
+ float* tolb, float* alpha, float* beta,
+ lapack_complex_float* u, lapack_int* ldu,
+ lapack_complex_float* v, lapack_int* ldv,
+ lapack_complex_float* q, lapack_int* ldq,
+ lapack_complex_float* work, lapack_int* ncycle,
+ lapack_int *info );
+void LAPACK_ztgsja( char* jobu, char* jobv, char* jobq, lapack_int* m,
+ lapack_int* p, lapack_int* n, lapack_int* k, lapack_int* l,
+ lapack_complex_double* a, lapack_int* lda,
+ lapack_complex_double* b, lapack_int* ldb, double* tola,
+ double* tolb, double* alpha, double* beta,
+ lapack_complex_double* u, lapack_int* ldu,
+ lapack_complex_double* v, lapack_int* ldv,
+ lapack_complex_double* q, lapack_int* ldq,
+ lapack_complex_double* work, lapack_int* ncycle,
+ lapack_int *info );
+void LAPACK_sgels( char* trans, lapack_int* m, lapack_int* n, lapack_int* nrhs,
+ float* a, lapack_int* lda, float* b, lapack_int* ldb,
+ float* work, lapack_int* lwork, lapack_int *info );
+void LAPACK_dgels( char* trans, lapack_int* m, lapack_int* n, lapack_int* nrhs,
+ double* a, lapack_int* lda, double* b, lapack_int* ldb,
+ double* work, lapack_int* lwork, lapack_int *info );
+void LAPACK_cgels( char* trans, lapack_int* m, lapack_int* n, lapack_int* nrhs,
+ lapack_complex_float* a, lapack_int* lda,
+ lapack_complex_float* b, lapack_int* ldb,
+ lapack_complex_float* work, lapack_int* lwork,
+ lapack_int *info );
+void LAPACK_zgels( char* trans, lapack_int* m, lapack_int* n, lapack_int* nrhs,
+ lapack_complex_double* a, lapack_int* lda,
+ lapack_complex_double* b, lapack_int* ldb,
+ lapack_complex_double* work, lapack_int* lwork,
+ lapack_int *info );
+void LAPACK_sgelsy( lapack_int* m, lapack_int* n, lapack_int* nrhs, float* a,
+ lapack_int* lda, float* b, lapack_int* ldb,
+ lapack_int* jpvt, float* rcond, lapack_int* rank,
+ float* work, lapack_int* lwork, lapack_int *info );
+void LAPACK_dgelsy( lapack_int* m, lapack_int* n, lapack_int* nrhs, double* a,
+ lapack_int* lda, double* b, lapack_int* ldb,
+ lapack_int* jpvt, double* rcond, lapack_int* rank,
+ double* work, lapack_int* lwork, lapack_int *info );
+void LAPACK_cgelsy( lapack_int* m, lapack_int* n, lapack_int* nrhs,
+ lapack_complex_float* a, lapack_int* lda,
+ lapack_complex_float* b, lapack_int* ldb, lapack_int* jpvt,
+ float* rcond, lapack_int* rank, lapack_complex_float* work,
+ lapack_int* lwork, float* rwork, lapack_int *info );
+void LAPACK_zgelsy( lapack_int* m, lapack_int* n, lapack_int* nrhs,
+ lapack_complex_double* a, lapack_int* lda,
+ lapack_complex_double* b, lapack_int* ldb, lapack_int* jpvt,
+ double* rcond, lapack_int* rank,
+ lapack_complex_double* work, lapack_int* lwork,
+ double* rwork, lapack_int *info );
+void LAPACK_sgelss( lapack_int* m, lapack_int* n, lapack_int* nrhs, float* a,
+ lapack_int* lda, float* b, lapack_int* ldb, float* s,
+ float* rcond, lapack_int* rank, float* work,
+ lapack_int* lwork, lapack_int *info );
+void LAPACK_dgelss( lapack_int* m, lapack_int* n, lapack_int* nrhs, double* a,
+ lapack_int* lda, double* b, lapack_int* ldb, double* s,
+ double* rcond, lapack_int* rank, double* work,
+ lapack_int* lwork, lapack_int *info );
+void LAPACK_cgelss( lapack_int* m, lapack_int* n, lapack_int* nrhs,
+ lapack_complex_float* a, lapack_int* lda,
+ lapack_complex_float* b, lapack_int* ldb, float* s,
+ float* rcond, lapack_int* rank, lapack_complex_float* work,
+ lapack_int* lwork, float* rwork, lapack_int *info );
+void LAPACK_zgelss( lapack_int* m, lapack_int* n, lapack_int* nrhs,
+ lapack_complex_double* a, lapack_int* lda,
+ lapack_complex_double* b, lapack_int* ldb, double* s,
+ double* rcond, lapack_int* rank,
+ lapack_complex_double* work, lapack_int* lwork,
+ double* rwork, lapack_int *info );
+void LAPACK_sgelsd( lapack_int* m, lapack_int* n, lapack_int* nrhs, float* a,
+ lapack_int* lda, float* b, lapack_int* ldb, float* s,
+ float* rcond, lapack_int* rank, float* work,
+ lapack_int* lwork, lapack_int* iwork, lapack_int *info );
+void LAPACK_dgelsd( lapack_int* m, lapack_int* n, lapack_int* nrhs, double* a,
+ lapack_int* lda, double* b, lapack_int* ldb, double* s,
+ double* rcond, lapack_int* rank, double* work,
+ lapack_int* lwork, lapack_int* iwork, lapack_int *info );
+void LAPACK_cgelsd( lapack_int* m, lapack_int* n, lapack_int* nrhs,
+ lapack_complex_float* a, lapack_int* lda,
+ lapack_complex_float* b, lapack_int* ldb, float* s,
+ float* rcond, lapack_int* rank, lapack_complex_float* work,
+ lapack_int* lwork, float* rwork, lapack_int* iwork,
+ lapack_int *info );
+void LAPACK_zgelsd( lapack_int* m, lapack_int* n, lapack_int* nrhs,
+ lapack_complex_double* a, lapack_int* lda,
+ lapack_complex_double* b, lapack_int* ldb, double* s,
+ double* rcond, lapack_int* rank,
+ lapack_complex_double* work, lapack_int* lwork,
+ double* rwork, lapack_int* iwork, lapack_int *info );
+void LAPACK_sgglse( lapack_int* m, lapack_int* n, lapack_int* p, float* a,
+ lapack_int* lda, float* b, lapack_int* ldb, float* c,
+ float* d, float* x, float* work, lapack_int* lwork,
+ lapack_int *info );
+void LAPACK_dgglse( lapack_int* m, lapack_int* n, lapack_int* p, double* a,
+ lapack_int* lda, double* b, lapack_int* ldb, double* c,
+ double* d, double* x, double* work, lapack_int* lwork,
+ lapack_int *info );
+void LAPACK_cgglse( lapack_int* m, lapack_int* n, lapack_int* p,
+ lapack_complex_float* a, lapack_int* lda,
+ lapack_complex_float* b, lapack_int* ldb,
+ lapack_complex_float* c, lapack_complex_float* d,
+ lapack_complex_float* x, lapack_complex_float* work,
+ lapack_int* lwork, lapack_int *info );
+void LAPACK_zgglse( lapack_int* m, lapack_int* n, lapack_int* p,
+ lapack_complex_double* a, lapack_int* lda,
+ lapack_complex_double* b, lapack_int* ldb,
+ lapack_complex_double* c, lapack_complex_double* d,
+ lapack_complex_double* x, lapack_complex_double* work,
+ lapack_int* lwork, lapack_int *info );
+void LAPACK_sggglm( lapack_int* n, lapack_int* m, lapack_int* p, float* a,
+ lapack_int* lda, float* b, lapack_int* ldb, float* d,
+ float* x, float* y, float* work, lapack_int* lwork,
+ lapack_int *info );
+void LAPACK_dggglm( lapack_int* n, lapack_int* m, lapack_int* p, double* a,
+ lapack_int* lda, double* b, lapack_int* ldb, double* d,
+ double* x, double* y, double* work, lapack_int* lwork,
+ lapack_int *info );
+void LAPACK_cggglm( lapack_int* n, lapack_int* m, lapack_int* p,
+ lapack_complex_float* a, lapack_int* lda,
+ lapack_complex_float* b, lapack_int* ldb,
+ lapack_complex_float* d, lapack_complex_float* x,
+ lapack_complex_float* y, lapack_complex_float* work,
+ lapack_int* lwork, lapack_int *info );
+void LAPACK_zggglm( lapack_int* n, lapack_int* m, lapack_int* p,
+ lapack_complex_double* a, lapack_int* lda,
+ lapack_complex_double* b, lapack_int* ldb,
+ lapack_complex_double* d, lapack_complex_double* x,
+ lapack_complex_double* y, lapack_complex_double* work,
+ lapack_int* lwork, lapack_int *info );
+void LAPACK_ssyev( char* jobz, char* uplo, lapack_int* n, float* a,
+ lapack_int* lda, float* w, float* work, lapack_int* lwork,
+ lapack_int *info );
+void LAPACK_dsyev( char* jobz, char* uplo, lapack_int* n, double* a,
+ lapack_int* lda, double* w, double* work, lapack_int* lwork,
+ lapack_int *info );
+void LAPACK_cheev( char* jobz, char* uplo, lapack_int* n,
+ lapack_complex_float* a, lapack_int* lda, float* w,
+ lapack_complex_float* work, lapack_int* lwork, float* rwork,
+ lapack_int *info );
+void LAPACK_zheev( char* jobz, char* uplo, lapack_int* n,
+ lapack_complex_double* a, lapack_int* lda, double* w,
+ lapack_complex_double* work, lapack_int* lwork,
+ double* rwork, lapack_int *info );
+void LAPACK_ssyevd( char* jobz, char* uplo, lapack_int* n, float* a,
+ lapack_int* lda, float* w, float* work, lapack_int* lwork,
+ lapack_int* iwork, lapack_int* liwork, lapack_int *info );
+void LAPACK_dsyevd( char* jobz, char* uplo, lapack_int* n, double* a,
+ lapack_int* lda, double* w, double* work, lapack_int* lwork,
+ lapack_int* iwork, lapack_int* liwork, lapack_int *info );
+void LAPACK_cheevd( char* jobz, char* uplo, lapack_int* n,
+ lapack_complex_float* a, lapack_int* lda, float* w,
+ lapack_complex_float* work, lapack_int* lwork, float* rwork,
+ lapack_int* lrwork, lapack_int* iwork, lapack_int* liwork,
+ lapack_int *info );
+void LAPACK_zheevd( char* jobz, char* uplo, lapack_int* n,
+ lapack_complex_double* a, lapack_int* lda, double* w,
+ lapack_complex_double* work, lapack_int* lwork,
+ double* rwork, lapack_int* lrwork, lapack_int* iwork,
+ lapack_int* liwork, lapack_int *info );
+void LAPACK_ssyevx( char* jobz, char* range, char* uplo, lapack_int* n,
+ float* a, lapack_int* lda, float* vl, float* vu,
+ lapack_int* il, lapack_int* iu, float* abstol,
+ lapack_int* m, float* w, float* z, lapack_int* ldz,
+ float* work, lapack_int* lwork, lapack_int* iwork,
+ lapack_int* ifail, lapack_int *info );
+void LAPACK_dsyevx( char* jobz, char* range, char* uplo, lapack_int* n,
+ double* a, lapack_int* lda, double* vl, double* vu,
+ lapack_int* il, lapack_int* iu, double* abstol,
+ lapack_int* m, double* w, double* z, lapack_int* ldz,
+ double* work, lapack_int* lwork, lapack_int* iwork,
+ lapack_int* ifail, lapack_int *info );
+void LAPACK_cheevx( char* jobz, char* range, char* uplo, lapack_int* n,
+ lapack_complex_float* a, lapack_int* lda, float* vl,
+ float* vu, lapack_int* il, lapack_int* iu, float* abstol,
+ lapack_int* m, float* w, lapack_complex_float* z,
+ lapack_int* ldz, lapack_complex_float* work,
+ lapack_int* lwork, float* rwork, lapack_int* iwork,
+ lapack_int* ifail, lapack_int *info );
+void LAPACK_zheevx( char* jobz, char* range, char* uplo, lapack_int* n,
+ lapack_complex_double* a, lapack_int* lda, double* vl,
+ double* vu, lapack_int* il, lapack_int* iu, double* abstol,
+ lapack_int* m, double* w, lapack_complex_double* z,
+ lapack_int* ldz, lapack_complex_double* work,
+ lapack_int* lwork, double* rwork, lapack_int* iwork,
+ lapack_int* ifail, lapack_int *info );
+void LAPACK_ssyevr( char* jobz, char* range, char* uplo, lapack_int* n,
+ float* a, lapack_int* lda, float* vl, float* vu,
+ lapack_int* il, lapack_int* iu, float* abstol,
+ lapack_int* m, float* w, float* z, lapack_int* ldz,
+ lapack_int* isuppz, float* work, lapack_int* lwork,
+ lapack_int* iwork, lapack_int* liwork, lapack_int *info );
+void LAPACK_dsyevr( char* jobz, char* range, char* uplo, lapack_int* n,
+ double* a, lapack_int* lda, double* vl, double* vu,
+ lapack_int* il, lapack_int* iu, double* abstol,
+ lapack_int* m, double* w, double* z, lapack_int* ldz,
+ lapack_int* isuppz, double* work, lapack_int* lwork,
+ lapack_int* iwork, lapack_int* liwork, lapack_int *info );
+void LAPACK_cheevr( char* jobz, char* range, char* uplo, lapack_int* n,
+ lapack_complex_float* a, lapack_int* lda, float* vl,
+ float* vu, lapack_int* il, lapack_int* iu, float* abstol,
+ lapack_int* m, float* w, lapack_complex_float* z,
+ lapack_int* ldz, lapack_int* isuppz,
+ lapack_complex_float* work, lapack_int* lwork, float* rwork,
+ lapack_int* lrwork, lapack_int* iwork, lapack_int* liwork,
+ lapack_int *info );
+void LAPACK_zheevr( char* jobz, char* range, char* uplo, lapack_int* n,
+ lapack_complex_double* a, lapack_int* lda, double* vl,
+ double* vu, lapack_int* il, lapack_int* iu, double* abstol,
+ lapack_int* m, double* w, lapack_complex_double* z,
+ lapack_int* ldz, lapack_int* isuppz,
+ lapack_complex_double* work, lapack_int* lwork,
+ double* rwork, lapack_int* lrwork, lapack_int* iwork,
+ lapack_int* liwork, lapack_int *info );
+void LAPACK_sspev( char* jobz, char* uplo, lapack_int* n, float* ap, float* w,
+ float* z, lapack_int* ldz, float* work, lapack_int *info );
+void LAPACK_dspev( char* jobz, char* uplo, lapack_int* n, double* ap, double* w,
+ double* z, lapack_int* ldz, double* work, lapack_int *info );
+void LAPACK_chpev( char* jobz, char* uplo, lapack_int* n,
+ lapack_complex_float* ap, float* w, lapack_complex_float* z,
+ lapack_int* ldz, lapack_complex_float* work, float* rwork,
+ lapack_int *info );
+void LAPACK_zhpev( char* jobz, char* uplo, lapack_int* n,
+ lapack_complex_double* ap, double* w,
+ lapack_complex_double* z, lapack_int* ldz,
+ lapack_complex_double* work, double* rwork,
+ lapack_int *info );
+void LAPACK_sspevd( char* jobz, char* uplo, lapack_int* n, float* ap, float* w,
+ float* z, lapack_int* ldz, float* work, lapack_int* lwork,
+ lapack_int* iwork, lapack_int* liwork, lapack_int *info );
+void LAPACK_dspevd( char* jobz, char* uplo, lapack_int* n, double* ap,
+ double* w, double* z, lapack_int* ldz, double* work,
+ lapack_int* lwork, lapack_int* iwork, lapack_int* liwork,
+ lapack_int *info );
+void LAPACK_chpevd( char* jobz, char* uplo, lapack_int* n,
+ lapack_complex_float* ap, float* w, lapack_complex_float* z,
+ lapack_int* ldz, lapack_complex_float* work,
+ lapack_int* lwork, float* rwork, lapack_int* lrwork,
+ lapack_int* iwork, lapack_int* liwork, lapack_int *info );
+void LAPACK_zhpevd( char* jobz, char* uplo, lapack_int* n,
+ lapack_complex_double* ap, double* w,
+ lapack_complex_double* z, lapack_int* ldz,
+ lapack_complex_double* work, lapack_int* lwork,
+ double* rwork, lapack_int* lrwork, lapack_int* iwork,
+ lapack_int* liwork, lapack_int *info );
+void LAPACK_sspevx( char* jobz, char* range, char* uplo, lapack_int* n,
+ float* ap, float* vl, float* vu, lapack_int* il,
+ lapack_int* iu, float* abstol, lapack_int* m, float* w,
+ float* z, lapack_int* ldz, float* work, lapack_int* iwork,
+ lapack_int* ifail, lapack_int *info );
+void LAPACK_dspevx( char* jobz, char* range, char* uplo, lapack_int* n,
+ double* ap, double* vl, double* vu, lapack_int* il,
+ lapack_int* iu, double* abstol, lapack_int* m, double* w,
+ double* z, lapack_int* ldz, double* work, lapack_int* iwork,
+ lapack_int* ifail, lapack_int *info );
+void LAPACK_chpevx( char* jobz, char* range, char* uplo, lapack_int* n,
+ lapack_complex_float* ap, float* vl, float* vu,
+ lapack_int* il, lapack_int* iu, float* abstol,
+ lapack_int* m, float* w, lapack_complex_float* z,
+ lapack_int* ldz, lapack_complex_float* work, float* rwork,
+ lapack_int* iwork, lapack_int* ifail, lapack_int *info );
+void LAPACK_zhpevx( char* jobz, char* range, char* uplo, lapack_int* n,
+ lapack_complex_double* ap, double* vl, double* vu,
+ lapack_int* il, lapack_int* iu, double* abstol,
+ lapack_int* m, double* w, lapack_complex_double* z,
+ lapack_int* ldz, lapack_complex_double* work, double* rwork,
+ lapack_int* iwork, lapack_int* ifail, lapack_int *info );
+void LAPACK_ssbev( char* jobz, char* uplo, lapack_int* n, lapack_int* kd,
+ float* ab, lapack_int* ldab, float* w, float* z,
+ lapack_int* ldz, float* work, lapack_int *info );
+void LAPACK_dsbev( char* jobz, char* uplo, lapack_int* n, lapack_int* kd,
+ double* ab, lapack_int* ldab, double* w, double* z,
+ lapack_int* ldz, double* work, lapack_int *info );
+void LAPACK_chbev( char* jobz, char* uplo, lapack_int* n, lapack_int* kd,
+ lapack_complex_float* ab, lapack_int* ldab, float* w,
+ lapack_complex_float* z, lapack_int* ldz,
+ lapack_complex_float* work, float* rwork, lapack_int *info );
+void LAPACK_zhbev( char* jobz, char* uplo, lapack_int* n, lapack_int* kd,
+ lapack_complex_double* ab, lapack_int* ldab, double* w,
+ lapack_complex_double* z, lapack_int* ldz,
+ lapack_complex_double* work, double* rwork,
+ lapack_int *info );
+void LAPACK_ssbevd( char* jobz, char* uplo, lapack_int* n, lapack_int* kd,
+ float* ab, lapack_int* ldab, float* w, float* z,
+ lapack_int* ldz, float* work, lapack_int* lwork,
+ lapack_int* iwork, lapack_int* liwork, lapack_int *info );
+void LAPACK_dsbevd( char* jobz, char* uplo, lapack_int* n, lapack_int* kd,
+ double* ab, lapack_int* ldab, double* w, double* z,
+ lapack_int* ldz, double* work, lapack_int* lwork,
+ lapack_int* iwork, lapack_int* liwork, lapack_int *info );
+void LAPACK_chbevd( char* jobz, char* uplo, lapack_int* n, lapack_int* kd,
+ lapack_complex_float* ab, lapack_int* ldab, float* w,
+ lapack_complex_float* z, lapack_int* ldz,
+ lapack_complex_float* work, lapack_int* lwork, float* rwork,
+ lapack_int* lrwork, lapack_int* iwork, lapack_int* liwork,
+ lapack_int *info );
+void LAPACK_zhbevd( char* jobz, char* uplo, lapack_int* n, lapack_int* kd,
+ lapack_complex_double* ab, lapack_int* ldab, double* w,
+ lapack_complex_double* z, lapack_int* ldz,
+ lapack_complex_double* work, lapack_int* lwork,
+ double* rwork, lapack_int* lrwork, lapack_int* iwork,
+ lapack_int* liwork, lapack_int *info );
+void LAPACK_ssbevx( char* jobz, char* range, char* uplo, lapack_int* n,
+ lapack_int* kd, float* ab, lapack_int* ldab, float* q,
+ lapack_int* ldq, float* vl, float* vu, lapack_int* il,
+ lapack_int* iu, float* abstol, lapack_int* m, float* w,
+ float* z, lapack_int* ldz, float* work, lapack_int* iwork,
+ lapack_int* ifail, lapack_int *info );
+void LAPACK_dsbevx( char* jobz, char* range, char* uplo, lapack_int* n,
+ lapack_int* kd, double* ab, lapack_int* ldab, double* q,
+ lapack_int* ldq, double* vl, double* vu, lapack_int* il,
+ lapack_int* iu, double* abstol, lapack_int* m, double* w,
+ double* z, lapack_int* ldz, double* work, lapack_int* iwork,
+ lapack_int* ifail, lapack_int *info );
+void LAPACK_chbevx( char* jobz, char* range, char* uplo, lapack_int* n,
+ lapack_int* kd, lapack_complex_float* ab, lapack_int* ldab,
+ lapack_complex_float* q, lapack_int* ldq, float* vl,
+ float* vu, lapack_int* il, lapack_int* iu, float* abstol,
+ lapack_int* m, float* w, lapack_complex_float* z,
+ lapack_int* ldz, lapack_complex_float* work, float* rwork,
+ lapack_int* iwork, lapack_int* ifail, lapack_int *info );
+void LAPACK_zhbevx( char* jobz, char* range, char* uplo, lapack_int* n,
+ lapack_int* kd, lapack_complex_double* ab, lapack_int* ldab,
+ lapack_complex_double* q, lapack_int* ldq, double* vl,
+ double* vu, lapack_int* il, lapack_int* iu, double* abstol,
+ lapack_int* m, double* w, lapack_complex_double* z,
+ lapack_int* ldz, lapack_complex_double* work, double* rwork,
+ lapack_int* iwork, lapack_int* ifail, lapack_int *info );
+void LAPACK_sstev( char* jobz, lapack_int* n, float* d, float* e, float* z,
+ lapack_int* ldz, float* work, lapack_int *info );
+void LAPACK_dstev( char* jobz, lapack_int* n, double* d, double* e, double* z,
+ lapack_int* ldz, double* work, lapack_int *info );
+void LAPACK_sstevd( char* jobz, lapack_int* n, float* d, float* e, float* z,
+ lapack_int* ldz, float* work, lapack_int* lwork,
+ lapack_int* iwork, lapack_int* liwork, lapack_int *info );
+void LAPACK_dstevd( char* jobz, lapack_int* n, double* d, double* e, double* z,
+ lapack_int* ldz, double* work, lapack_int* lwork,
+ lapack_int* iwork, lapack_int* liwork, lapack_int *info );
+void LAPACK_sstevx( char* jobz, char* range, lapack_int* n, float* d, float* e,
+ float* vl, float* vu, lapack_int* il, lapack_int* iu,
+ float* abstol, lapack_int* m, float* w, float* z,
+ lapack_int* ldz, float* work, lapack_int* iwork,
+ lapack_int* ifail, lapack_int *info );
+void LAPACK_dstevx( char* jobz, char* range, lapack_int* n, double* d,
+ double* e, double* vl, double* vu, lapack_int* il,
+ lapack_int* iu, double* abstol, lapack_int* m, double* w,
+ double* z, lapack_int* ldz, double* work, lapack_int* iwork,
+ lapack_int* ifail, lapack_int *info );
+void LAPACK_sstevr( char* jobz, char* range, lapack_int* n, float* d, float* e,
+ float* vl, float* vu, lapack_int* il, lapack_int* iu,
+ float* abstol, lapack_int* m, float* w, float* z,
+ lapack_int* ldz, lapack_int* isuppz, float* work,
+ lapack_int* lwork, lapack_int* iwork, lapack_int* liwork,
+ lapack_int *info );
+void LAPACK_dstevr( char* jobz, char* range, lapack_int* n, double* d,
+ double* e, double* vl, double* vu, lapack_int* il,
+ lapack_int* iu, double* abstol, lapack_int* m, double* w,
+ double* z, lapack_int* ldz, lapack_int* isuppz,
+ double* work, lapack_int* lwork, lapack_int* iwork,
+ lapack_int* liwork, lapack_int *info );
+void LAPACK_sgees( char* jobvs, char* sort, LAPACK_S_SELECT2 select,
+ lapack_int* n, float* a, lapack_int* lda, lapack_int* sdim,
+ float* wr, float* wi, float* vs, lapack_int* ldvs,
+ float* work, lapack_int* lwork, lapack_logical* bwork,
+ lapack_int *info );
+void LAPACK_dgees( char* jobvs, char* sort, LAPACK_D_SELECT2 select,
+ lapack_int* n, double* a, lapack_int* lda, lapack_int* sdim,
+ double* wr, double* wi, double* vs, lapack_int* ldvs,
+ double* work, lapack_int* lwork, lapack_logical* bwork,
+ lapack_int *info );
+void LAPACK_cgees( char* jobvs, char* sort, LAPACK_C_SELECT1 select,
+ lapack_int* n, lapack_complex_float* a, lapack_int* lda,
+ lapack_int* sdim, lapack_complex_float* w,
+ lapack_complex_float* vs, lapack_int* ldvs,
+ lapack_complex_float* work, lapack_int* lwork, float* rwork,
+ lapack_logical* bwork, lapack_int *info );
+void LAPACK_zgees( char* jobvs, char* sort, LAPACK_Z_SELECT1 select,
+ lapack_int* n, lapack_complex_double* a, lapack_int* lda,
+ lapack_int* sdim, lapack_complex_double* w,
+ lapack_complex_double* vs, lapack_int* ldvs,
+ lapack_complex_double* work, lapack_int* lwork,
+ double* rwork, lapack_logical* bwork, lapack_int *info );
+void LAPACK_sgeesx( char* jobvs, char* sort, LAPACK_S_SELECT2 select,
+ char* sense, lapack_int* n, float* a, lapack_int* lda,
+ lapack_int* sdim, float* wr, float* wi, float* vs,
+ lapack_int* ldvs, float* rconde, float* rcondv, float* work,
+ lapack_int* lwork, lapack_int* iwork, lapack_int* liwork,
+ lapack_logical* bwork, lapack_int *info );
+void LAPACK_dgeesx( char* jobvs, char* sort, LAPACK_D_SELECT2 select,
+ char* sense, lapack_int* n, double* a, lapack_int* lda,
+ lapack_int* sdim, double* wr, double* wi, double* vs,
+ lapack_int* ldvs, double* rconde, double* rcondv,
+ double* work, lapack_int* lwork, lapack_int* iwork,
+ lapack_int* liwork, lapack_logical* bwork,
+ lapack_int *info );
+void LAPACK_cgeesx( char* jobvs, char* sort, LAPACK_C_SELECT1 select,
+ char* sense, lapack_int* n, lapack_complex_float* a,
+ lapack_int* lda, lapack_int* sdim, lapack_complex_float* w,
+ lapack_complex_float* vs, lapack_int* ldvs, float* rconde,
+ float* rcondv, lapack_complex_float* work,
+ lapack_int* lwork, float* rwork, lapack_logical* bwork,
+ lapack_int *info );
+void LAPACK_zgeesx( char* jobvs, char* sort, LAPACK_Z_SELECT1 select,
+ char* sense, lapack_int* n, lapack_complex_double* a,
+ lapack_int* lda, lapack_int* sdim, lapack_complex_double* w,
+ lapack_complex_double* vs, lapack_int* ldvs, double* rconde,
+ double* rcondv, lapack_complex_double* work,
+ lapack_int* lwork, double* rwork, lapack_logical* bwork,
+ lapack_int *info );
+void LAPACK_sgeev( char* jobvl, char* jobvr, lapack_int* n, float* a,
+ lapack_int* lda, float* wr, float* wi, float* vl,
+ lapack_int* ldvl, float* vr, lapack_int* ldvr, float* work,
+ lapack_int* lwork, lapack_int *info );
+void LAPACK_dgeev( char* jobvl, char* jobvr, lapack_int* n, double* a,
+ lapack_int* lda, double* wr, double* wi, double* vl,
+ lapack_int* ldvl, double* vr, lapack_int* ldvr, double* work,
+ lapack_int* lwork, lapack_int *info );
+void LAPACK_cgeev( char* jobvl, char* jobvr, lapack_int* n,
+ lapack_complex_float* a, lapack_int* lda,
+ lapack_complex_float* w, lapack_complex_float* vl,
+ lapack_int* ldvl, lapack_complex_float* vr, lapack_int* ldvr,
+ lapack_complex_float* work, lapack_int* lwork, float* rwork,
+ lapack_int *info );
+void LAPACK_zgeev( char* jobvl, char* jobvr, lapack_int* n,
+ lapack_complex_double* a, lapack_int* lda,
+ lapack_complex_double* w, lapack_complex_double* vl,
+ lapack_int* ldvl, lapack_complex_double* vr,
+ lapack_int* ldvr, lapack_complex_double* work,
+ lapack_int* lwork, double* rwork, lapack_int *info );
+void LAPACK_sgeevx( char* balanc, char* jobvl, char* jobvr, char* sense,
+ lapack_int* n, float* a, lapack_int* lda, float* wr,
+ float* wi, float* vl, lapack_int* ldvl, float* vr,
+ lapack_int* ldvr, lapack_int* ilo, lapack_int* ihi,
+ float* scale, float* abnrm, float* rconde, float* rcondv,
+ float* work, lapack_int* lwork, lapack_int* iwork,
+ lapack_int *info );
+void LAPACK_dgeevx( char* balanc, char* jobvl, char* jobvr, char* sense,
+ lapack_int* n, double* a, lapack_int* lda, double* wr,
+ double* wi, double* vl, lapack_int* ldvl, double* vr,
+ lapack_int* ldvr, lapack_int* ilo, lapack_int* ihi,
+ double* scale, double* abnrm, double* rconde,
+ double* rcondv, double* work, lapack_int* lwork,
+ lapack_int* iwork, lapack_int *info );
+void LAPACK_cgeevx( char* balanc, char* jobvl, char* jobvr, char* sense,
+ lapack_int* n, lapack_complex_float* a, lapack_int* lda,
+ lapack_complex_float* w, lapack_complex_float* vl,
+ lapack_int* ldvl, lapack_complex_float* vr,
+ lapack_int* ldvr, lapack_int* ilo, lapack_int* ihi,
+ float* scale, float* abnrm, float* rconde, float* rcondv,
+ lapack_complex_float* work, lapack_int* lwork, float* rwork,
+ lapack_int *info );
+void LAPACK_zgeevx( char* balanc, char* jobvl, char* jobvr, char* sense,
+ lapack_int* n, lapack_complex_double* a, lapack_int* lda,
+ lapack_complex_double* w, lapack_complex_double* vl,
+ lapack_int* ldvl, lapack_complex_double* vr,
+ lapack_int* ldvr, lapack_int* ilo, lapack_int* ihi,
+ double* scale, double* abnrm, double* rconde,
+ double* rcondv, lapack_complex_double* work,
+ lapack_int* lwork, double* rwork, lapack_int *info );
+void LAPACK_sgesvd( char* jobu, char* jobvt, lapack_int* m, lapack_int* n,
+ float* a, lapack_int* lda, float* s, float* u,
+ lapack_int* ldu, float* vt, lapack_int* ldvt, float* work,
+ lapack_int* lwork, lapack_int *info );
+void LAPACK_dgesvd( char* jobu, char* jobvt, lapack_int* m, lapack_int* n,
+ double* a, lapack_int* lda, double* s, double* u,
+ lapack_int* ldu, double* vt, lapack_int* ldvt, double* work,
+ lapack_int* lwork, lapack_int *info );
+void LAPACK_cgesvd( char* jobu, char* jobvt, lapack_int* m, lapack_int* n,
+ lapack_complex_float* a, lapack_int* lda, float* s,
+ lapack_complex_float* u, lapack_int* ldu,
+ lapack_complex_float* vt, lapack_int* ldvt,
+ lapack_complex_float* work, lapack_int* lwork, float* rwork,
+ lapack_int *info );
+void LAPACK_zgesvd( char* jobu, char* jobvt, lapack_int* m, lapack_int* n,
+ lapack_complex_double* a, lapack_int* lda, double* s,
+ lapack_complex_double* u, lapack_int* ldu,
+ lapack_complex_double* vt, lapack_int* ldvt,
+ lapack_complex_double* work, lapack_int* lwork,
+ double* rwork, lapack_int *info );
+void LAPACK_sgesdd( char* jobz, lapack_int* m, lapack_int* n, float* a,
+ lapack_int* lda, float* s, float* u, lapack_int* ldu,
+ float* vt, lapack_int* ldvt, float* work, lapack_int* lwork,
+ lapack_int* iwork, lapack_int *info );
+void LAPACK_dgesdd( char* jobz, lapack_int* m, lapack_int* n, double* a,
+ lapack_int* lda, double* s, double* u, lapack_int* ldu,
+ double* vt, lapack_int* ldvt, double* work,
+ lapack_int* lwork, lapack_int* iwork, lapack_int *info );
+void LAPACK_cgesdd( char* jobz, lapack_int* m, lapack_int* n,
+ lapack_complex_float* a, lapack_int* lda, float* s,
+ lapack_complex_float* u, lapack_int* ldu,
+ lapack_complex_float* vt, lapack_int* ldvt,
+ lapack_complex_float* work, lapack_int* lwork, float* rwork,
+ lapack_int* iwork, lapack_int *info );
+void LAPACK_zgesdd( char* jobz, lapack_int* m, lapack_int* n,
+ lapack_complex_double* a, lapack_int* lda, double* s,
+ lapack_complex_double* u, lapack_int* ldu,
+ lapack_complex_double* vt, lapack_int* ldvt,
+ lapack_complex_double* work, lapack_int* lwork,
+ double* rwork, lapack_int* iwork, lapack_int *info );
+void LAPACK_dgejsv( char* joba, char* jobu, char* jobv, char* jobr, char* jobt,
+ char* jobp, lapack_int* m, lapack_int* n, double* a,
+ lapack_int* lda, double* sva, double* u, lapack_int* ldu,
+ double* v, lapack_int* ldv, double* work, lapack_int* lwork,
+ lapack_int* iwork, lapack_int *info );
+void LAPACK_sgejsv( char* joba, char* jobu, char* jobv, char* jobr, char* jobt,
+ char* jobp, lapack_int* m, lapack_int* n, float* a,
+ lapack_int* lda, float* sva, float* u, lapack_int* ldu,
+ float* v, lapack_int* ldv, float* work, lapack_int* lwork,
+ lapack_int* iwork, lapack_int *info );
+void LAPACK_dgesvj( char* joba, char* jobu, char* jobv, lapack_int* m,
+ lapack_int* n, double* a, lapack_int* lda, double* sva,
+ lapack_int* mv, double* v, lapack_int* ldv, double* work,
+ lapack_int* lwork, lapack_int *info );
+void LAPACK_sgesvj( char* joba, char* jobu, char* jobv, lapack_int* m,
+ lapack_int* n, float* a, lapack_int* lda, float* sva,
+ lapack_int* mv, float* v, lapack_int* ldv, float* work,
+ lapack_int* lwork, lapack_int *info );
+void LAPACK_sggsvd( char* jobu, char* jobv, char* jobq, lapack_int* m,
+ lapack_int* n, lapack_int* p, lapack_int* k, lapack_int* l,
+ float* a, lapack_int* lda, float* b, lapack_int* ldb,
+ float* alpha, float* beta, float* u, lapack_int* ldu,
+ float* v, lapack_int* ldv, float* q, lapack_int* ldq,
+ float* work, lapack_int* iwork, lapack_int *info );
+void LAPACK_dggsvd( char* jobu, char* jobv, char* jobq, lapack_int* m,
+ lapack_int* n, lapack_int* p, lapack_int* k, lapack_int* l,
+ double* a, lapack_int* lda, double* b, lapack_int* ldb,
+ double* alpha, double* beta, double* u, lapack_int* ldu,
+ double* v, lapack_int* ldv, double* q, lapack_int* ldq,
+ double* work, lapack_int* iwork, lapack_int *info );
+void LAPACK_cggsvd( char* jobu, char* jobv, char* jobq, lapack_int* m,
+ lapack_int* n, lapack_int* p, lapack_int* k, lapack_int* l,
+ lapack_complex_float* a, lapack_int* lda,
+ lapack_complex_float* b, lapack_int* ldb, float* alpha,
+ float* beta, lapack_complex_float* u, lapack_int* ldu,
+ lapack_complex_float* v, lapack_int* ldv,
+ lapack_complex_float* q, lapack_int* ldq,
+ lapack_complex_float* work, float* rwork, lapack_int* iwork,
+ lapack_int *info );
+void LAPACK_zggsvd( char* jobu, char* jobv, char* jobq, lapack_int* m,
+ lapack_int* n, lapack_int* p, lapack_int* k, lapack_int* l,
+ lapack_complex_double* a, lapack_int* lda,
+ lapack_complex_double* b, lapack_int* ldb, double* alpha,
+ double* beta, lapack_complex_double* u, lapack_int* ldu,
+ lapack_complex_double* v, lapack_int* ldv,
+ lapack_complex_double* q, lapack_int* ldq,
+ lapack_complex_double* work, double* rwork,
+ lapack_int* iwork, lapack_int *info );
+void LAPACK_ssygv( lapack_int* itype, char* jobz, char* uplo, lapack_int* n,
+ float* a, lapack_int* lda, float* b, lapack_int* ldb,
+ float* w, float* work, lapack_int* lwork, lapack_int *info );
+void LAPACK_dsygv( lapack_int* itype, char* jobz, char* uplo, lapack_int* n,
+ double* a, lapack_int* lda, double* b, lapack_int* ldb,
+ double* w, double* work, lapack_int* lwork,
+ lapack_int *info );
+void LAPACK_chegv( lapack_int* itype, char* jobz, char* uplo, lapack_int* n,
+ lapack_complex_float* a, lapack_int* lda,
+ lapack_complex_float* b, lapack_int* ldb, float* w,
+ lapack_complex_float* work, lapack_int* lwork, float* rwork,
+ lapack_int *info );
+void LAPACK_zhegv( lapack_int* itype, char* jobz, char* uplo, lapack_int* n,
+ lapack_complex_double* a, lapack_int* lda,
+ lapack_complex_double* b, lapack_int* ldb, double* w,
+ lapack_complex_double* work, lapack_int* lwork,
+ double* rwork, lapack_int *info );
+void LAPACK_ssygvd( lapack_int* itype, char* jobz, char* uplo, lapack_int* n,
+ float* a, lapack_int* lda, float* b, lapack_int* ldb,
+ float* w, float* work, lapack_int* lwork, lapack_int* iwork,
+ lapack_int* liwork, lapack_int *info );
+void LAPACK_dsygvd( lapack_int* itype, char* jobz, char* uplo, lapack_int* n,
+ double* a, lapack_int* lda, double* b, lapack_int* ldb,
+ double* w, double* work, lapack_int* lwork,
+ lapack_int* iwork, lapack_int* liwork, lapack_int *info );
+void LAPACK_chegvd( lapack_int* itype, char* jobz, char* uplo, lapack_int* n,
+ lapack_complex_float* a, lapack_int* lda,
+ lapack_complex_float* b, lapack_int* ldb, float* w,
+ lapack_complex_float* work, lapack_int* lwork, float* rwork,
+ lapack_int* lrwork, lapack_int* iwork, lapack_int* liwork,
+ lapack_int *info );
+void LAPACK_zhegvd( lapack_int* itype, char* jobz, char* uplo, lapack_int* n,
+ lapack_complex_double* a, lapack_int* lda,
+ lapack_complex_double* b, lapack_int* ldb, double* w,
+ lapack_complex_double* work, lapack_int* lwork,
+ double* rwork, lapack_int* lrwork, lapack_int* iwork,
+ lapack_int* liwork, lapack_int *info );
+void LAPACK_ssygvx( lapack_int* itype, char* jobz, char* range, char* uplo,
+ lapack_int* n, float* a, lapack_int* lda, float* b,
+ lapack_int* ldb, float* vl, float* vu, lapack_int* il,
+ lapack_int* iu, float* abstol, lapack_int* m, float* w,
+ float* z, lapack_int* ldz, float* work, lapack_int* lwork,
+ lapack_int* iwork, lapack_int* ifail, lapack_int *info );
+void LAPACK_dsygvx( lapack_int* itype, char* jobz, char* range, char* uplo,
+ lapack_int* n, double* a, lapack_int* lda, double* b,
+ lapack_int* ldb, double* vl, double* vu, lapack_int* il,
+ lapack_int* iu, double* abstol, lapack_int* m, double* w,
+ double* z, lapack_int* ldz, double* work, lapack_int* lwork,
+ lapack_int* iwork, lapack_int* ifail, lapack_int *info );
+void LAPACK_chegvx( lapack_int* itype, char* jobz, char* range, char* uplo,
+ lapack_int* n, lapack_complex_float* a, lapack_int* lda,
+ lapack_complex_float* b, lapack_int* ldb, float* vl,
+ float* vu, lapack_int* il, lapack_int* iu, float* abstol,
+ lapack_int* m, float* w, lapack_complex_float* z,
+ lapack_int* ldz, lapack_complex_float* work,
+ lapack_int* lwork, float* rwork, lapack_int* iwork,
+ lapack_int* ifail, lapack_int *info );
+void LAPACK_zhegvx( lapack_int* itype, char* jobz, char* range, char* uplo,
+ lapack_int* n, lapack_complex_double* a, lapack_int* lda,
+ lapack_complex_double* b, lapack_int* ldb, double* vl,
+ double* vu, lapack_int* il, lapack_int* iu, double* abstol,
+ lapack_int* m, double* w, lapack_complex_double* z,
+ lapack_int* ldz, lapack_complex_double* work,
+ lapack_int* lwork, double* rwork, lapack_int* iwork,
+ lapack_int* ifail, lapack_int *info );
+void LAPACK_sspgv( lapack_int* itype, char* jobz, char* uplo, lapack_int* n,
+ float* ap, float* bp, float* w, float* z, lapack_int* ldz,
+ float* work, lapack_int *info );
+void LAPACK_dspgv( lapack_int* itype, char* jobz, char* uplo, lapack_int* n,
+ double* ap, double* bp, double* w, double* z,
+ lapack_int* ldz, double* work, lapack_int *info );
+void LAPACK_chpgv( lapack_int* itype, char* jobz, char* uplo, lapack_int* n,
+ lapack_complex_float* ap, lapack_complex_float* bp, float* w,
+ lapack_complex_float* z, lapack_int* ldz,
+ lapack_complex_float* work, float* rwork, lapack_int *info );
+void LAPACK_zhpgv( lapack_int* itype, char* jobz, char* uplo, lapack_int* n,
+ lapack_complex_double* ap, lapack_complex_double* bp,
+ double* w, lapack_complex_double* z, lapack_int* ldz,
+ lapack_complex_double* work, double* rwork,
+ lapack_int *info );
+void LAPACK_sspgvd( lapack_int* itype, char* jobz, char* uplo, lapack_int* n,
+ float* ap, float* bp, float* w, float* z, lapack_int* ldz,
+ float* work, lapack_int* lwork, lapack_int* iwork,
+ lapack_int* liwork, lapack_int *info );
+void LAPACK_dspgvd( lapack_int* itype, char* jobz, char* uplo, lapack_int* n,
+ double* ap, double* bp, double* w, double* z,
+ lapack_int* ldz, double* work, lapack_int* lwork,
+ lapack_int* iwork, lapack_int* liwork, lapack_int *info );
+void LAPACK_chpgvd( lapack_int* itype, char* jobz, char* uplo, lapack_int* n,
+ lapack_complex_float* ap, lapack_complex_float* bp,
+ float* w, lapack_complex_float* z, lapack_int* ldz,
+ lapack_complex_float* work, lapack_int* lwork, float* rwork,
+ lapack_int* lrwork, lapack_int* iwork, lapack_int* liwork,
+ lapack_int *info );
+void LAPACK_zhpgvd( lapack_int* itype, char* jobz, char* uplo, lapack_int* n,
+ lapack_complex_double* ap, lapack_complex_double* bp,
+ double* w, lapack_complex_double* z, lapack_int* ldz,
+ lapack_complex_double* work, lapack_int* lwork,
+ double* rwork, lapack_int* lrwork, lapack_int* iwork,
+ lapack_int* liwork, lapack_int *info );
+void LAPACK_sspgvx( lapack_int* itype, char* jobz, char* range, char* uplo,
+ lapack_int* n, float* ap, float* bp, float* vl, float* vu,
+ lapack_int* il, lapack_int* iu, float* abstol,
+ lapack_int* m, float* w, float* z, lapack_int* ldz,
+ float* work, lapack_int* iwork, lapack_int* ifail,
+ lapack_int *info );
+void LAPACK_dspgvx( lapack_int* itype, char* jobz, char* range, char* uplo,
+ lapack_int* n, double* ap, double* bp, double* vl,
+ double* vu, lapack_int* il, lapack_int* iu, double* abstol,
+ lapack_int* m, double* w, double* z, lapack_int* ldz,
+ double* work, lapack_int* iwork, lapack_int* ifail,
+ lapack_int *info );
+void LAPACK_chpgvx( lapack_int* itype, char* jobz, char* range, char* uplo,
+ lapack_int* n, lapack_complex_float* ap,
+ lapack_complex_float* bp, float* vl, float* vu,
+ lapack_int* il, lapack_int* iu, float* abstol,
+ lapack_int* m, float* w, lapack_complex_float* z,
+ lapack_int* ldz, lapack_complex_float* work, float* rwork,
+ lapack_int* iwork, lapack_int* ifail, lapack_int *info );
+void LAPACK_zhpgvx( lapack_int* itype, char* jobz, char* range, char* uplo,
+ lapack_int* n, lapack_complex_double* ap,
+ lapack_complex_double* bp, double* vl, double* vu,
+ lapack_int* il, lapack_int* iu, double* abstol,
+ lapack_int* m, double* w, lapack_complex_double* z,
+ lapack_int* ldz, lapack_complex_double* work, double* rwork,
+ lapack_int* iwork, lapack_int* ifail, lapack_int *info );
+void LAPACK_ssbgv( char* jobz, char* uplo, lapack_int* n, lapack_int* ka,
+ lapack_int* kb, float* ab, lapack_int* ldab, float* bb,
+ lapack_int* ldbb, float* w, float* z, lapack_int* ldz,
+ float* work, lapack_int *info );
+void LAPACK_dsbgv( char* jobz, char* uplo, lapack_int* n, lapack_int* ka,
+ lapack_int* kb, double* ab, lapack_int* ldab, double* bb,
+ lapack_int* ldbb, double* w, double* z, lapack_int* ldz,
+ double* work, lapack_int *info );
+void LAPACK_chbgv( char* jobz, char* uplo, lapack_int* n, lapack_int* ka,
+ lapack_int* kb, lapack_complex_float* ab, lapack_int* ldab,
+ lapack_complex_float* bb, lapack_int* ldbb, float* w,
+ lapack_complex_float* z, lapack_int* ldz,
+ lapack_complex_float* work, float* rwork, lapack_int *info );
+void LAPACK_zhbgv( char* jobz, char* uplo, lapack_int* n, lapack_int* ka,
+ lapack_int* kb, lapack_complex_double* ab, lapack_int* ldab,
+ lapack_complex_double* bb, lapack_int* ldbb, double* w,
+ lapack_complex_double* z, lapack_int* ldz,
+ lapack_complex_double* work, double* rwork,
+ lapack_int *info );
+void LAPACK_ssbgvd( char* jobz, char* uplo, lapack_int* n, lapack_int* ka,
+ lapack_int* kb, float* ab, lapack_int* ldab, float* bb,
+ lapack_int* ldbb, float* w, float* z, lapack_int* ldz,
+ float* work, lapack_int* lwork, lapack_int* iwork,
+ lapack_int* liwork, lapack_int *info );
+void LAPACK_dsbgvd( char* jobz, char* uplo, lapack_int* n, lapack_int* ka,
+ lapack_int* kb, double* ab, lapack_int* ldab, double* bb,
+ lapack_int* ldbb, double* w, double* z, lapack_int* ldz,
+ double* work, lapack_int* lwork, lapack_int* iwork,
+ lapack_int* liwork, lapack_int *info );
+void LAPACK_chbgvd( char* jobz, char* uplo, lapack_int* n, lapack_int* ka,
+ lapack_int* kb, lapack_complex_float* ab, lapack_int* ldab,
+ lapack_complex_float* bb, lapack_int* ldbb, float* w,
+ lapack_complex_float* z, lapack_int* ldz,
+ lapack_complex_float* work, lapack_int* lwork, float* rwork,
+ lapack_int* lrwork, lapack_int* iwork, lapack_int* liwork,
+ lapack_int *info );
+void LAPACK_zhbgvd( char* jobz, char* uplo, lapack_int* n, lapack_int* ka,
+ lapack_int* kb, lapack_complex_double* ab, lapack_int* ldab,
+ lapack_complex_double* bb, lapack_int* ldbb, double* w,
+ lapack_complex_double* z, lapack_int* ldz,
+ lapack_complex_double* work, lapack_int* lwork,
+ double* rwork, lapack_int* lrwork, lapack_int* iwork,
+ lapack_int* liwork, lapack_int *info );
+void LAPACK_ssbgvx( char* jobz, char* range, char* uplo, lapack_int* n,
+ lapack_int* ka, lapack_int* kb, float* ab, lapack_int* ldab,
+ float* bb, lapack_int* ldbb, float* q, lapack_int* ldq,
+ float* vl, float* vu, lapack_int* il, lapack_int* iu,
+ float* abstol, lapack_int* m, float* w, float* z,
+ lapack_int* ldz, float* work, lapack_int* iwork,
+ lapack_int* ifail, lapack_int *info );
+void LAPACK_dsbgvx( char* jobz, char* range, char* uplo, lapack_int* n,
+ lapack_int* ka, lapack_int* kb, double* ab,
+ lapack_int* ldab, double* bb, lapack_int* ldbb, double* q,
+ lapack_int* ldq, double* vl, double* vu, lapack_int* il,
+ lapack_int* iu, double* abstol, lapack_int* m, double* w,
+ double* z, lapack_int* ldz, double* work, lapack_int* iwork,
+ lapack_int* ifail, lapack_int *info );
+void LAPACK_chbgvx( char* jobz, char* range, char* uplo, lapack_int* n,
+ lapack_int* ka, lapack_int* kb, lapack_complex_float* ab,
+ lapack_int* ldab, lapack_complex_float* bb,
+ lapack_int* ldbb, lapack_complex_float* q, lapack_int* ldq,
+ float* vl, float* vu, lapack_int* il, lapack_int* iu,
+ float* abstol, lapack_int* m, float* w,
+ lapack_complex_float* z, lapack_int* ldz,
+ lapack_complex_float* work, float* rwork, lapack_int* iwork,
+ lapack_int* ifail, lapack_int *info );
+void LAPACK_zhbgvx( char* jobz, char* range, char* uplo, lapack_int* n,
+ lapack_int* ka, lapack_int* kb, lapack_complex_double* ab,
+ lapack_int* ldab, lapack_complex_double* bb,
+ lapack_int* ldbb, lapack_complex_double* q, lapack_int* ldq,
+ double* vl, double* vu, lapack_int* il, lapack_int* iu,
+ double* abstol, lapack_int* m, double* w,
+ lapack_complex_double* z, lapack_int* ldz,
+ lapack_complex_double* work, double* rwork,
+ lapack_int* iwork, lapack_int* ifail, lapack_int *info );
+void LAPACK_sgges( char* jobvsl, char* jobvsr, char* sort,
+ LAPACK_S_SELECT3 selctg, lapack_int* n, float* a,
+ lapack_int* lda, float* b, lapack_int* ldb, lapack_int* sdim,
+ float* alphar, float* alphai, float* beta, float* vsl,
+ lapack_int* ldvsl, float* vsr, lapack_int* ldvsr,
+ float* work, lapack_int* lwork, lapack_logical* bwork,
+ lapack_int *info );
+void LAPACK_dgges( char* jobvsl, char* jobvsr, char* sort,
+ LAPACK_D_SELECT3 selctg, lapack_int* n, double* a,
+ lapack_int* lda, double* b, lapack_int* ldb,
+ lapack_int* sdim, double* alphar, double* alphai,
+ double* beta, double* vsl, lapack_int* ldvsl, double* vsr,
+ lapack_int* ldvsr, double* work, lapack_int* lwork,
+ lapack_logical* bwork, lapack_int *info );
+void LAPACK_cgges( char* jobvsl, char* jobvsr, char* sort,
+ LAPACK_C_SELECT2 selctg, lapack_int* n,
+ lapack_complex_float* a, lapack_int* lda,
+ lapack_complex_float* b, lapack_int* ldb, lapack_int* sdim,
+ lapack_complex_float* alpha, lapack_complex_float* beta,
+ lapack_complex_float* vsl, lapack_int* ldvsl,
+ lapack_complex_float* vsr, lapack_int* ldvsr,
+ lapack_complex_float* work, lapack_int* lwork, float* rwork,
+ lapack_logical* bwork, lapack_int *info );
+void LAPACK_zgges( char* jobvsl, char* jobvsr, char* sort,
+ LAPACK_Z_SELECT2 selctg, lapack_int* n,
+ lapack_complex_double* a, lapack_int* lda,
+ lapack_complex_double* b, lapack_int* ldb, lapack_int* sdim,
+ lapack_complex_double* alpha, lapack_complex_double* beta,
+ lapack_complex_double* vsl, lapack_int* ldvsl,
+ lapack_complex_double* vsr, lapack_int* ldvsr,
+ lapack_complex_double* work, lapack_int* lwork,
+ double* rwork, lapack_logical* bwork, lapack_int *info );
+void LAPACK_sggesx( char* jobvsl, char* jobvsr, char* sort,
+ LAPACK_S_SELECT3 selctg, char* sense, lapack_int* n,
+ float* a, lapack_int* lda, float* b, lapack_int* ldb,
+ lapack_int* sdim, float* alphar, float* alphai, float* beta,
+ float* vsl, lapack_int* ldvsl, float* vsr,
+ lapack_int* ldvsr, float* rconde, float* rcondv,
+ float* work, lapack_int* lwork, lapack_int* iwork,
+ lapack_int* liwork, lapack_logical* bwork,
+ lapack_int *info );
+void LAPACK_dggesx( char* jobvsl, char* jobvsr, char* sort,
+ LAPACK_D_SELECT3 selctg, char* sense, lapack_int* n,
+ double* a, lapack_int* lda, double* b, lapack_int* ldb,
+ lapack_int* sdim, double* alphar, double* alphai,
+ double* beta, double* vsl, lapack_int* ldvsl, double* vsr,
+ lapack_int* ldvsr, double* rconde, double* rcondv,
+ double* work, lapack_int* lwork, lapack_int* iwork,
+ lapack_int* liwork, lapack_logical* bwork,
+ lapack_int *info );
+void LAPACK_cggesx( char* jobvsl, char* jobvsr, char* sort,
+ LAPACK_C_SELECT2 selctg, char* sense, lapack_int* n,
+ lapack_complex_float* a, lapack_int* lda,
+ lapack_complex_float* b, lapack_int* ldb, lapack_int* sdim,
+ lapack_complex_float* alpha, lapack_complex_float* beta,
+ lapack_complex_float* vsl, lapack_int* ldvsl,
+ lapack_complex_float* vsr, lapack_int* ldvsr, float* rconde,
+ float* rcondv, lapack_complex_float* work,
+ lapack_int* lwork, float* rwork, lapack_int* iwork,
+ lapack_int* liwork, lapack_logical* bwork,
+ lapack_int *info );
+void LAPACK_zggesx( char* jobvsl, char* jobvsr, char* sort,
+ LAPACK_Z_SELECT2 selctg, char* sense, lapack_int* n,
+ lapack_complex_double* a, lapack_int* lda,
+ lapack_complex_double* b, lapack_int* ldb, lapack_int* sdim,
+ lapack_complex_double* alpha, lapack_complex_double* beta,
+ lapack_complex_double* vsl, lapack_int* ldvsl,
+ lapack_complex_double* vsr, lapack_int* ldvsr,
+ double* rconde, double* rcondv, lapack_complex_double* work,
+ lapack_int* lwork, double* rwork, lapack_int* iwork,
+ lapack_int* liwork, lapack_logical* bwork,
+ lapack_int *info );
+void LAPACK_sggev( char* jobvl, char* jobvr, lapack_int* n, float* a,
+ lapack_int* lda, float* b, lapack_int* ldb, float* alphar,
+ float* alphai, float* beta, float* vl, lapack_int* ldvl,
+ float* vr, lapack_int* ldvr, float* work, lapack_int* lwork,
+ lapack_int *info );
+void LAPACK_dggev( char* jobvl, char* jobvr, lapack_int* n, double* a,
+ lapack_int* lda, double* b, lapack_int* ldb, double* alphar,
+ double* alphai, double* beta, double* vl, lapack_int* ldvl,
+ double* vr, lapack_int* ldvr, double* work,
+ lapack_int* lwork, lapack_int *info );
+void LAPACK_cggev( char* jobvl, char* jobvr, lapack_int* n,
+ lapack_complex_float* a, lapack_int* lda,
+ lapack_complex_float* b, lapack_int* ldb,
+ lapack_complex_float* alpha, lapack_complex_float* beta,
+ lapack_complex_float* vl, lapack_int* ldvl,
+ lapack_complex_float* vr, lapack_int* ldvr,
+ lapack_complex_float* work, lapack_int* lwork, float* rwork,
+ lapack_int *info );
+void LAPACK_zggev( char* jobvl, char* jobvr, lapack_int* n,
+ lapack_complex_double* a, lapack_int* lda,
+ lapack_complex_double* b, lapack_int* ldb,
+ lapack_complex_double* alpha, lapack_complex_double* beta,
+ lapack_complex_double* vl, lapack_int* ldvl,
+ lapack_complex_double* vr, lapack_int* ldvr,
+ lapack_complex_double* work, lapack_int* lwork,
+ double* rwork, lapack_int *info );
+void LAPACK_sggevx( char* balanc, char* jobvl, char* jobvr, char* sense,
+ lapack_int* n, float* a, lapack_int* lda, float* b,
+ lapack_int* ldb, float* alphar, float* alphai, float* beta,
+ float* vl, lapack_int* ldvl, float* vr, lapack_int* ldvr,
+ lapack_int* ilo, lapack_int* ihi, float* lscale,
+ float* rscale, float* abnrm, float* bbnrm, float* rconde,
+ float* rcondv, float* work, lapack_int* lwork,
+ lapack_int* iwork, lapack_logical* bwork,
+ lapack_int *info );
+void LAPACK_dggevx( char* balanc, char* jobvl, char* jobvr, char* sense,
+ lapack_int* n, double* a, lapack_int* lda, double* b,
+ lapack_int* ldb, double* alphar, double* alphai,
+ double* beta, double* vl, lapack_int* ldvl, double* vr,
+ lapack_int* ldvr, lapack_int* ilo, lapack_int* ihi,
+ double* lscale, double* rscale, double* abnrm,
+ double* bbnrm, double* rconde, double* rcondv, double* work,
+ lapack_int* lwork, lapack_int* iwork, lapack_logical* bwork,
+ lapack_int *info );
+void LAPACK_cggevx( char* balanc, char* jobvl, char* jobvr, char* sense,
+ lapack_int* n, lapack_complex_float* a, lapack_int* lda,
+ lapack_complex_float* b, lapack_int* ldb,
+ lapack_complex_float* alpha, lapack_complex_float* beta,
+ lapack_complex_float* vl, lapack_int* ldvl,
+ lapack_complex_float* vr, lapack_int* ldvr, lapack_int* ilo,
+ lapack_int* ihi, float* lscale, float* rscale, float* abnrm,
+ float* bbnrm, float* rconde, float* rcondv,
+ lapack_complex_float* work, lapack_int* lwork, float* rwork,
+ lapack_int* iwork, lapack_logical* bwork,
+ lapack_int *info );
+void LAPACK_zggevx( char* balanc, char* jobvl, char* jobvr, char* sense,
+ lapack_int* n, lapack_complex_double* a, lapack_int* lda,
+ lapack_complex_double* b, lapack_int* ldb,
+ lapack_complex_double* alpha, lapack_complex_double* beta,
+ lapack_complex_double* vl, lapack_int* ldvl,
+ lapack_complex_double* vr, lapack_int* ldvr,
+ lapack_int* ilo, lapack_int* ihi, double* lscale,
+ double* rscale, double* abnrm, double* bbnrm,
+ double* rconde, double* rcondv, lapack_complex_double* work,
+ lapack_int* lwork, double* rwork, lapack_int* iwork,
+ lapack_logical* bwork, lapack_int *info );
+void LAPACK_dsfrk( char* transr, char* uplo, char* trans, lapack_int* n,
+ lapack_int* k, double* alpha, const double* a,
+ lapack_int* lda, double* beta, double* c );
+void LAPACK_ssfrk( char* transr, char* uplo, char* trans, lapack_int* n,
+ lapack_int* k, float* alpha, const float* a, lapack_int* lda,
+ float* beta, float* c );
+void LAPACK_zhfrk( char* transr, char* uplo, char* trans, lapack_int* n,
+ lapack_int* k, double* alpha, const lapack_complex_double* a,
+ lapack_int* lda, double* beta, lapack_complex_double* c );
+void LAPACK_chfrk( char* transr, char* uplo, char* trans, lapack_int* n,
+ lapack_int* k, float* alpha, const lapack_complex_float* a,
+ lapack_int* lda, float* beta, lapack_complex_float* c );
+void LAPACK_dtfsm( char* transr, char* side, char* uplo, char* trans,
+ char* diag, lapack_int* m, lapack_int* n, double* alpha,
+ const double* a, double* b, lapack_int* ldb );
+void LAPACK_stfsm( char* transr, char* side, char* uplo, char* trans,
+ char* diag, lapack_int* m, lapack_int* n, float* alpha,
+ const float* a, float* b, lapack_int* ldb );
+void LAPACK_ztfsm( char* transr, char* side, char* uplo, char* trans,
+ char* diag, lapack_int* m, lapack_int* n,
+ lapack_complex_double* alpha, const lapack_complex_double* a,
+ lapack_complex_double* b, lapack_int* ldb );
+void LAPACK_ctfsm( char* transr, char* side, char* uplo, char* trans,
+ char* diag, lapack_int* m, lapack_int* n,
+ lapack_complex_float* alpha, const lapack_complex_float* a,
+ lapack_complex_float* b, lapack_int* ldb );
+void LAPACK_dtfttp( char* transr, char* uplo, lapack_int* n, const double* arf,
+ double* ap, lapack_int *info );
+void LAPACK_stfttp( char* transr, char* uplo, lapack_int* n, const float* arf,
+ float* ap, lapack_int *info );
+void LAPACK_ztfttp( char* transr, char* uplo, lapack_int* n,
+ const lapack_complex_double* arf, lapack_complex_double* ap,
+ lapack_int *info );
+void LAPACK_ctfttp( char* transr, char* uplo, lapack_int* n,
+ const lapack_complex_float* arf, lapack_complex_float* ap,
+ lapack_int *info );
+void LAPACK_dtfttr( char* transr, char* uplo, lapack_int* n, const double* arf,
+ double* a, lapack_int* lda, lapack_int *info );
+void LAPACK_stfttr( char* transr, char* uplo, lapack_int* n, const float* arf,
+ float* a, lapack_int* lda, lapack_int *info );
+void LAPACK_ztfttr( char* transr, char* uplo, lapack_int* n,
+ const lapack_complex_double* arf, lapack_complex_double* a,
+ lapack_int* lda, lapack_int *info );
+void LAPACK_ctfttr( char* transr, char* uplo, lapack_int* n,
+ const lapack_complex_float* arf, lapack_complex_float* a,
+ lapack_int* lda, lapack_int *info );
+void LAPACK_dtpttf( char* transr, char* uplo, lapack_int* n, const double* ap,
+ double* arf, lapack_int *info );
+void LAPACK_stpttf( char* transr, char* uplo, lapack_int* n, const float* ap,
+ float* arf, lapack_int *info );
+void LAPACK_ztpttf( char* transr, char* uplo, lapack_int* n,
+ const lapack_complex_double* ap, lapack_complex_double* arf,
+ lapack_int *info );
+void LAPACK_ctpttf( char* transr, char* uplo, lapack_int* n,
+ const lapack_complex_float* ap, lapack_complex_float* arf,
+ lapack_int *info );
+void LAPACK_dtpttr( char* uplo, lapack_int* n, const double* ap, double* a,
+ lapack_int* lda, lapack_int *info );
+void LAPACK_stpttr( char* uplo, lapack_int* n, const float* ap, float* a,
+ lapack_int* lda, lapack_int *info );
+void LAPACK_ztpttr( char* uplo, lapack_int* n, const lapack_complex_double* ap,
+ lapack_complex_double* a, lapack_int* lda,
+ lapack_int *info );
+void LAPACK_ctpttr( char* uplo, lapack_int* n, const lapack_complex_float* ap,
+ lapack_complex_float* a, lapack_int* lda,
+ lapack_int *info );
+void LAPACK_dtrttf( char* transr, char* uplo, lapack_int* n, const double* a,
+ lapack_int* lda, double* arf, lapack_int *info );
+void LAPACK_strttf( char* transr, char* uplo, lapack_int* n, const float* a,
+ lapack_int* lda, float* arf, lapack_int *info );
+void LAPACK_ztrttf( char* transr, char* uplo, lapack_int* n,
+ const lapack_complex_double* a, lapack_int* lda,
+ lapack_complex_double* arf, lapack_int *info );
+void LAPACK_ctrttf( char* transr, char* uplo, lapack_int* n,
+ const lapack_complex_float* a, lapack_int* lda,
+ lapack_complex_float* arf, lapack_int *info );
+void LAPACK_dtrttp( char* uplo, lapack_int* n, const double* a, lapack_int* lda,
+ double* ap, lapack_int *info );
+void LAPACK_strttp( char* uplo, lapack_int* n, const float* a, lapack_int* lda,
+ float* ap, lapack_int *info );
+void LAPACK_ztrttp( char* uplo, lapack_int* n, const lapack_complex_double* a,
+ lapack_int* lda, lapack_complex_double* ap,
+ lapack_int *info );
+void LAPACK_ctrttp( char* uplo, lapack_int* n, const lapack_complex_float* a,
+ lapack_int* lda, lapack_complex_float* ap,
+ lapack_int *info );
+void LAPACK_sgeqrfp( lapack_int* m, lapack_int* n, float* a, lapack_int* lda,
+ float* tau, float* work, lapack_int* lwork,
+ lapack_int *info );
+void LAPACK_dgeqrfp( lapack_int* m, lapack_int* n, double* a, lapack_int* lda,
+ double* tau, double* work, lapack_int* lwork,
+ lapack_int *info );
+void LAPACK_cgeqrfp( lapack_int* m, lapack_int* n, lapack_complex_float* a,
+ lapack_int* lda, lapack_complex_float* tau,
+ lapack_complex_float* work, lapack_int* lwork,
+ lapack_int *info );
+void LAPACK_zgeqrfp( lapack_int* m, lapack_int* n, lapack_complex_double* a,
+ lapack_int* lda, lapack_complex_double* tau,
+ lapack_complex_double* work, lapack_int* lwork,
+ lapack_int *info );
+void LAPACK_clacgv( lapack_int* n, lapack_complex_float* x, lapack_int* incx );
+void LAPACK_zlacgv( lapack_int* n, lapack_complex_double* x, lapack_int* incx );
+void LAPACK_slarnv( lapack_int* idist, lapack_int* iseed, lapack_int* n,
+ float* x );
+void LAPACK_dlarnv( lapack_int* idist, lapack_int* iseed, lapack_int* n,
+ double* x );
+void LAPACK_clarnv( lapack_int* idist, lapack_int* iseed, lapack_int* n,
+ lapack_complex_float* x );
+void LAPACK_zlarnv( lapack_int* idist, lapack_int* iseed, lapack_int* n,
+ lapack_complex_double* x );
+void LAPACK_sgeqr2( lapack_int* m, lapack_int* n, float* a, lapack_int* lda,
+ float* tau, float* work, lapack_int *info );
+void LAPACK_dgeqr2( lapack_int* m, lapack_int* n, double* a, lapack_int* lda,
+ double* tau, double* work, lapack_int *info );
+void LAPACK_cgeqr2( lapack_int* m, lapack_int* n, lapack_complex_float* a,
+ lapack_int* lda, lapack_complex_float* tau,
+ lapack_complex_float* work, lapack_int *info );
+void LAPACK_zgeqr2( lapack_int* m, lapack_int* n, lapack_complex_double* a,
+ lapack_int* lda, lapack_complex_double* tau,
+ lapack_complex_double* work, lapack_int *info );
+void LAPACK_slacpy( char* uplo, lapack_int* m, lapack_int* n, const float* a,
+ lapack_int* lda, float* b, lapack_int* ldb );
+void LAPACK_dlacpy( char* uplo, lapack_int* m, lapack_int* n, const double* a,
+ lapack_int* lda, double* b, lapack_int* ldb );
+void LAPACK_clacpy( char* uplo, lapack_int* m, lapack_int* n,
+ const lapack_complex_float* a, lapack_int* lda,
+ lapack_complex_float* b, lapack_int* ldb );
+void LAPACK_zlacpy( char* uplo, lapack_int* m, lapack_int* n,
+ const lapack_complex_double* a, lapack_int* lda,
+ lapack_complex_double* b, lapack_int* ldb );
+void LAPACK_sgetf2( lapack_int* m, lapack_int* n, float* a, lapack_int* lda,
+ lapack_int* ipiv, lapack_int *info );
+void LAPACK_dgetf2( lapack_int* m, lapack_int* n, double* a, lapack_int* lda,
+ lapack_int* ipiv, lapack_int *info );
+void LAPACK_cgetf2( lapack_int* m, lapack_int* n, lapack_complex_float* a,
+ lapack_int* lda, lapack_int* ipiv, lapack_int *info );
+void LAPACK_zgetf2( lapack_int* m, lapack_int* n, lapack_complex_double* a,
+ lapack_int* lda, lapack_int* ipiv, lapack_int *info );
+void LAPACK_slaswp( lapack_int* n, float* a, lapack_int* lda, lapack_int* k1,
+ lapack_int* k2, const lapack_int* ipiv, lapack_int* incx );
+void LAPACK_dlaswp( lapack_int* n, double* a, lapack_int* lda, lapack_int* k1,
+ lapack_int* k2, const lapack_int* ipiv, lapack_int* incx );
+void LAPACK_claswp( lapack_int* n, lapack_complex_float* a, lapack_int* lda,
+ lapack_int* k1, lapack_int* k2, const lapack_int* ipiv,
+ lapack_int* incx );
+void LAPACK_zlaswp( lapack_int* n, lapack_complex_double* a, lapack_int* lda,
+ lapack_int* k1, lapack_int* k2, const lapack_int* ipiv,
+ lapack_int* incx );
+float LAPACK_slange( char* norm, lapack_int* m, lapack_int* n, const float* a,
+ lapack_int* lda, float* work );
+double LAPACK_dlange( char* norm, lapack_int* m, lapack_int* n, const double* a,
+ lapack_int* lda, double* work );
+float LAPACK_clange( char* norm, lapack_int* m, lapack_int* n,
+ const lapack_complex_float* a, lapack_int* lda, float* work );
+double LAPACK_zlange( char* norm, lapack_int* m, lapack_int* n,
+ const lapack_complex_double* a, lapack_int* lda, double* work );
+float LAPACK_clanhe( char* norm, char* uplo, lapack_int* n,
+ const lapack_complex_float* a, lapack_int* lda, float* work );
+double LAPACK_zlanhe( char* norm, char* uplo, lapack_int* n,
+ const lapack_complex_double* a, lapack_int* lda, double* work );
+float LAPACK_slansy( char* norm, char* uplo, lapack_int* n, const float* a,
+ lapack_int* lda, float* work );
+double LAPACK_dlansy( char* norm, char* uplo, lapack_int* n, const double* a,
+ lapack_int* lda, double* work );
+float LAPACK_clansy( char* norm, char* uplo, lapack_int* n,
+ const lapack_complex_float* a, lapack_int* lda, float* work );
+double LAPACK_zlansy( char* norm, char* uplo, lapack_int* n,
+ const lapack_complex_double* a, lapack_int* lda, double* work );
+float LAPACK_slantr( char* norm, char* uplo, char* diag, lapack_int* m,
+ lapack_int* n, const float* a, lapack_int* lda, float* work );
+double LAPACK_dlantr( char* norm, char* uplo, char* diag, lapack_int* m,
+ lapack_int* n, const double* a, lapack_int* lda, double* work );
+float LAPACK_clantr( char* norm, char* uplo, char* diag, lapack_int* m,
+ lapack_int* n, const lapack_complex_float* a, lapack_int* lda,
+ float* work );
+double LAPACK_zlantr( char* norm, char* uplo, char* diag, lapack_int* m,
+ lapack_int* n, const lapack_complex_double* a, lapack_int* lda,
+ double* work );
+float LAPACK_slamch( char* cmach );
+double LAPACK_dlamch( char* cmach );
+void LAPACK_sgelq2( lapack_int* m, lapack_int* n, float* a, lapack_int* lda,
+ float* tau, float* work, lapack_int *info );
+void LAPACK_dgelq2( lapack_int* m, lapack_int* n, double* a, lapack_int* lda,
+ double* tau, double* work, lapack_int *info );
+void LAPACK_cgelq2( lapack_int* m, lapack_int* n, lapack_complex_float* a,
+ lapack_int* lda, lapack_complex_float* tau,
+ lapack_complex_float* work, lapack_int *info );
+void LAPACK_zgelq2( lapack_int* m, lapack_int* n, lapack_complex_double* a,
+ lapack_int* lda, lapack_complex_double* tau,
+ lapack_complex_double* work, lapack_int *info );
+void LAPACK_slarfb( char* side, char* trans, char* direct, char* storev,
+ lapack_int* m, lapack_int* n, lapack_int* k, const float* v,
+ lapack_int* ldv, const float* t, lapack_int* ldt, float* c,
+ lapack_int* ldc, float* work, lapack_int* ldwork );
+void LAPACK_dlarfb( char* side, char* trans, char* direct, char* storev,
+ lapack_int* m, lapack_int* n, lapack_int* k,
+ const double* v, lapack_int* ldv, const double* t,
+ lapack_int* ldt, double* c, lapack_int* ldc, double* work,
+ lapack_int* ldwork );
+void LAPACK_clarfb( char* side, char* trans, char* direct, char* storev,
+ lapack_int* m, lapack_int* n, lapack_int* k,
+ const lapack_complex_float* v, lapack_int* ldv,
+ const lapack_complex_float* t, lapack_int* ldt,
+ lapack_complex_float* c, lapack_int* ldc,
+ lapack_complex_float* work, lapack_int* ldwork );
+void LAPACK_zlarfb( char* side, char* trans, char* direct, char* storev,
+ lapack_int* m, lapack_int* n, lapack_int* k,
+ const lapack_complex_double* v, lapack_int* ldv,
+ const lapack_complex_double* t, lapack_int* ldt,
+ lapack_complex_double* c, lapack_int* ldc,
+ lapack_complex_double* work, lapack_int* ldwork );
+void LAPACK_slarfg( lapack_int* n, float* alpha, float* x, lapack_int* incx,
+ float* tau );
+void LAPACK_dlarfg( lapack_int* n, double* alpha, double* x, lapack_int* incx,
+ double* tau );
+void LAPACK_clarfg( lapack_int* n, lapack_complex_float* alpha,
+ lapack_complex_float* x, lapack_int* incx,
+ lapack_complex_float* tau );
+void LAPACK_zlarfg( lapack_int* n, lapack_complex_double* alpha,
+ lapack_complex_double* x, lapack_int* incx,
+ lapack_complex_double* tau );
+void LAPACK_slarft( char* direct, char* storev, lapack_int* n, lapack_int* k,
+ const float* v, lapack_int* ldv, const float* tau, float* t,
+ lapack_int* ldt );
+void LAPACK_dlarft( char* direct, char* storev, lapack_int* n, lapack_int* k,
+ const double* v, lapack_int* ldv, const double* tau,
+ double* t, lapack_int* ldt );
+void LAPACK_clarft( char* direct, char* storev, lapack_int* n, lapack_int* k,
+ const lapack_complex_float* v, lapack_int* ldv,
+ const lapack_complex_float* tau, lapack_complex_float* t,
+ lapack_int* ldt );
+void LAPACK_zlarft( char* direct, char* storev, lapack_int* n, lapack_int* k,
+ const lapack_complex_double* v, lapack_int* ldv,
+ const lapack_complex_double* tau, lapack_complex_double* t,
+ lapack_int* ldt );
+void LAPACK_slarfx( char* side, lapack_int* m, lapack_int* n, const float* v,
+ float* tau, float* c, lapack_int* ldc, float* work );
+void LAPACK_dlarfx( char* side, lapack_int* m, lapack_int* n, const double* v,
+ double* tau, double* c, lapack_int* ldc, double* work );
+void LAPACK_clarfx( char* side, lapack_int* m, lapack_int* n,
+ const lapack_complex_float* v, lapack_complex_float* tau,
+ lapack_complex_float* c, lapack_int* ldc,
+ lapack_complex_float* work );
+void LAPACK_zlarfx( char* side, lapack_int* m, lapack_int* n,
+ const lapack_complex_double* v, lapack_complex_double* tau,
+ lapack_complex_double* c, lapack_int* ldc,
+ lapack_complex_double* work );
+void LAPACK_slatms( lapack_int* m, lapack_int* n, char* dist, lapack_int* iseed,
+ char* sym, float* d, lapack_int* mode, float* cond,
+ float* dmax, lapack_int* kl, lapack_int* ku, char* pack,
+ float* a, lapack_int* lda, float* work, lapack_int *info );
+void LAPACK_dlatms( lapack_int* m, lapack_int* n, char* dist, lapack_int* iseed,
+ char* sym, double* d, lapack_int* mode, double* cond,
+ double* dmax, lapack_int* kl, lapack_int* ku, char* pack,
+ double* a, lapack_int* lda, double* work,
+ lapack_int *info );
+void LAPACK_clatms( lapack_int* m, lapack_int* n, char* dist, lapack_int* iseed,
+ char* sym, float* d, lapack_int* mode, float* cond,
+ float* dmax, lapack_int* kl, lapack_int* ku, char* pack,
+ lapack_complex_float* a, lapack_int* lda,
+ lapack_complex_float* work, lapack_int *info );
+void LAPACK_zlatms( lapack_int* m, lapack_int* n, char* dist, lapack_int* iseed,
+ char* sym, double* d, lapack_int* mode, double* cond,
+ double* dmax, lapack_int* kl, lapack_int* ku, char* pack,
+ lapack_complex_double* a, lapack_int* lda,
+ lapack_complex_double* work, lapack_int *info );
+void LAPACK_slag2d( lapack_int* m, lapack_int* n, const float* sa,
+ lapack_int* ldsa, double* a, lapack_int* lda,
+ lapack_int *info );
+void LAPACK_dlag2s( lapack_int* m, lapack_int* n, const double* a,
+ lapack_int* lda, float* sa, lapack_int* ldsa,
+ lapack_int *info );
+void LAPACK_clag2z( lapack_int* m, lapack_int* n,
+ const lapack_complex_float* sa, lapack_int* ldsa,
+ lapack_complex_double* a, lapack_int* lda,
+ lapack_int *info );
+void LAPACK_zlag2c( lapack_int* m, lapack_int* n,
+ const lapack_complex_double* a, lapack_int* lda,
+ lapack_complex_float* sa, lapack_int* ldsa,
+ lapack_int *info );
+void LAPACK_slauum( char* uplo, lapack_int* n, float* a, lapack_int* lda,
+ lapack_int *info );
+void LAPACK_dlauum( char* uplo, lapack_int* n, double* a, lapack_int* lda,
+ lapack_int *info );
+void LAPACK_clauum( char* uplo, lapack_int* n, lapack_complex_float* a,
+ lapack_int* lda, lapack_int *info );
+void LAPACK_zlauum( char* uplo, lapack_int* n, lapack_complex_double* a,
+ lapack_int* lda, lapack_int *info );
+void LAPACK_slagge( lapack_int* m, lapack_int* n, lapack_int* kl,
+ lapack_int* ku, const float* d, float* a, lapack_int* lda,
+ lapack_int* iseed, float* work, lapack_int *info );
+void LAPACK_dlagge( lapack_int* m, lapack_int* n, lapack_int* kl,
+ lapack_int* ku, const double* d, double* a, lapack_int* lda,
+ lapack_int* iseed, double* work, lapack_int *info );
+void LAPACK_clagge( lapack_int* m, lapack_int* n, lapack_int* kl,
+ lapack_int* ku, const float* d, lapack_complex_float* a,
+ lapack_int* lda, lapack_int* iseed,
+ lapack_complex_float* work, lapack_int *info );
+void LAPACK_zlagge( lapack_int* m, lapack_int* n, lapack_int* kl,
+ lapack_int* ku, const double* d, lapack_complex_double* a,
+ lapack_int* lda, lapack_int* iseed,
+ lapack_complex_double* work, lapack_int *info );
+void LAPACK_slaset( char* uplo, lapack_int* m, lapack_int* n, float* alpha,
+ float* beta, float* a, lapack_int* lda );
+void LAPACK_dlaset( char* uplo, lapack_int* m, lapack_int* n, double* alpha,
+ double* beta, double* a, lapack_int* lda );
+void LAPACK_claset( char* uplo, lapack_int* m, lapack_int* n,
+ lapack_complex_float* alpha, lapack_complex_float* beta,
+ lapack_complex_float* a, lapack_int* lda );
+void LAPACK_zlaset( char* uplo, lapack_int* m, lapack_int* n,
+ lapack_complex_double* alpha, lapack_complex_double* beta,
+ lapack_complex_double* a, lapack_int* lda );
+void LAPACK_slasrt( char* id, lapack_int* n, float* d, lapack_int *info );
+void LAPACK_dlasrt( char* id, lapack_int* n, double* d, lapack_int *info );
+void LAPACK_claghe( lapack_int* n, lapack_int* k, const float* d,
+ lapack_complex_float* a, lapack_int* lda, lapack_int* iseed,
+ lapack_complex_float* work, lapack_int *info );
+void LAPACK_zlaghe( lapack_int* n, lapack_int* k, const double* d,
+ lapack_complex_double* a, lapack_int* lda,
+ lapack_int* iseed, lapack_complex_double* work,
+ lapack_int *info );
+void LAPACK_slagsy( lapack_int* n, lapack_int* k, const float* d, float* a,
+ lapack_int* lda, lapack_int* iseed, float* work,
+ lapack_int *info );
+void LAPACK_dlagsy( lapack_int* n, lapack_int* k, const double* d, double* a,
+ lapack_int* lda, lapack_int* iseed, double* work,
+ lapack_int *info );
+void LAPACK_clagsy( lapack_int* n, lapack_int* k, const float* d,
+ lapack_complex_float* a, lapack_int* lda, lapack_int* iseed,
+ lapack_complex_float* work, lapack_int *info );
+void LAPACK_zlagsy( lapack_int* n, lapack_int* k, const double* d,
+ lapack_complex_double* a, lapack_int* lda,
+ lapack_int* iseed, lapack_complex_double* work,
+ lapack_int *info );
+void LAPACK_slapmr( lapack_logical* forwrd, lapack_int* m, lapack_int* n,
+ float* x, lapack_int* ldx, lapack_int* k );
+void LAPACK_dlapmr( lapack_logical* forwrd, lapack_int* m, lapack_int* n,
+ double* x, lapack_int* ldx, lapack_int* k );
+void LAPACK_clapmr( lapack_logical* forwrd, lapack_int* m, lapack_int* n,
+ lapack_complex_float* x, lapack_int* ldx, lapack_int* k );
+void LAPACK_zlapmr( lapack_logical* forwrd, lapack_int* m, lapack_int* n,
+ lapack_complex_double* x, lapack_int* ldx, lapack_int* k );
+float LAPACK_slapy2( float* x, float* y );
+double LAPACK_dlapy2( double* x, double* y );
+float LAPACK_slapy3( float* x, float* y, float* z );
+double LAPACK_dlapy3( double* x, double* y, double* z );
+void LAPACK_slartgp( float* f, float* g, float* cs, float* sn, float* r );
+void LAPACK_dlartgp( double* f, double* g, double* cs, double* sn, double* r );
+void LAPACK_slartgs( float* x, float* y, float* sigma, float* cs, float* sn );
+void LAPACK_dlartgs( double* x, double* y, double* sigma, double* cs,
+ double* sn );
+// LAPACK 3.3.0
+void LAPACK_cbbcsd( char* jobu1, char* jobu2,
+ char* jobv1t, char* jobv2t, char* trans,
+ lapack_int* m, lapack_int* p, lapack_int* q,
+ float* theta, float* phi,
+ lapack_complex_float* u1, lapack_int* ldu1,
+ lapack_complex_float* u2, lapack_int* ldu2,
+ lapack_complex_float* v1t, lapack_int* ldv1t,
+ lapack_complex_float* v2t, lapack_int* ldv2t,
+ float* b11d, float* b11e, float* b12d,
+ float* b12e, float* b21d, float* b21e,
+ float* b22d, float* b22e, float* rwork,
+ lapack_int* lrwork , lapack_int *info );
+void LAPACK_cheswapr( char* uplo, lapack_int* n,
+ lapack_complex_float* a, lapack_int* i1,
+ lapack_int* i2 );
+void LAPACK_chetri2( char* uplo, lapack_int* n,
+ lapack_complex_float* a, lapack_int* lda,
+ const lapack_int* ipiv,
+ lapack_complex_float* work, lapack_int* lwork , lapack_int *info );
+void LAPACK_chetri2x( char* uplo, lapack_int* n,
+ lapack_complex_float* a, lapack_int* lda,
+ const lapack_int* ipiv,
+ lapack_complex_float* work, lapack_int* nb , lapack_int *info );
+void LAPACK_chetrs2( char* uplo, lapack_int* n,
+ lapack_int* nrhs, const lapack_complex_float* a,
+ lapack_int* lda, const lapack_int* ipiv,
+ lapack_complex_float* b, lapack_int* ldb,
+ lapack_complex_float* work , lapack_int *info );
+void LAPACK_csyconv( char* uplo, char* way,
+ lapack_int* n, lapack_complex_float* a,
+ lapack_int* lda, const lapack_int* ipiv,
+ lapack_complex_float* work , lapack_int *info );
+void LAPACK_csyswapr( char* uplo, lapack_int* n,
+ lapack_complex_float* a, lapack_int* i1,
+ lapack_int* i2 );
+void LAPACK_csytri2( char* uplo, lapack_int* n,
+ lapack_complex_float* a, lapack_int* lda,
+ const lapack_int* ipiv,
+ lapack_complex_float* work, lapack_int* lwork , lapack_int *info );
+void LAPACK_csytri2x( char* uplo, lapack_int* n,
+ lapack_complex_float* a, lapack_int* lda,
+ const lapack_int* ipiv,
+ lapack_complex_float* work, lapack_int* nb , lapack_int *info );
+void LAPACK_csytrs2( char* uplo, lapack_int* n,
+ lapack_int* nrhs, const lapack_complex_float* a,
+ lapack_int* lda, const lapack_int* ipiv,
+ lapack_complex_float* b, lapack_int* ldb,
+ lapack_complex_float* work , lapack_int *info );
+void LAPACK_cunbdb( char* trans, char* signs,
+ lapack_int* m, lapack_int* p, lapack_int* q,
+ lapack_complex_float* x11, lapack_int* ldx11,
+ lapack_complex_float* x12, lapack_int* ldx12,
+ lapack_complex_float* x21, lapack_int* ldx21,
+ lapack_complex_float* x22, lapack_int* ldx22,
+ float* theta, float* phi,
+ lapack_complex_float* taup1,
+ lapack_complex_float* taup2,
+ lapack_complex_float* tauq1,
+ lapack_complex_float* tauq2,
+ lapack_complex_float* work, lapack_int* lwork , lapack_int *info );
+void LAPACK_cuncsd( char* jobu1, char* jobu2,
+ char* jobv1t, char* jobv2t, char* trans,
+ char* signs, lapack_int* m, lapack_int* p,
+ lapack_int* q, lapack_complex_float* x11,
+ lapack_int* ldx11, lapack_complex_float* x12,
+ lapack_int* ldx12, lapack_complex_float* x21,
+ lapack_int* ldx21, lapack_complex_float* x22,
+ lapack_int* ldx22, float* theta,
+ lapack_complex_float* u1, lapack_int* ldu1,
+ lapack_complex_float* u2, lapack_int* ldu2,
+ lapack_complex_float* v1t, lapack_int* ldv1t,
+ lapack_complex_float* v2t, lapack_int* ldv2t,
+ lapack_complex_float* work, lapack_int* lwork,
+ float* rwork, lapack_int* lrwork,
+ lapack_int* iwork , lapack_int *info );
+void LAPACK_dbbcsd( char* jobu1, char* jobu2,
+ char* jobv1t, char* jobv2t, char* trans,
+ lapack_int* m, lapack_int* p, lapack_int* q,
+ double* theta, double* phi, double* u1,
+ lapack_int* ldu1, double* u2, lapack_int* ldu2,
+ double* v1t, lapack_int* ldv1t, double* v2t,
+ lapack_int* ldv2t, double* b11d, double* b11e,
+ double* b12d, double* b12e, double* b21d,
+ double* b21e, double* b22d, double* b22e,
+ double* work, lapack_int* lwork , lapack_int *info );
+void LAPACK_dorbdb( char* trans, char* signs,
+ lapack_int* m, lapack_int* p, lapack_int* q,
+ double* x11, lapack_int* ldx11, double* x12,
+ lapack_int* ldx12, double* x21, lapack_int* ldx21,
+ double* x22, lapack_int* ldx22, double* theta,
+ double* phi, double* taup1, double* taup2,
+ double* tauq1, double* tauq2, double* work,
+ lapack_int* lwork , lapack_int *info );
+void LAPACK_dorcsd( char* jobu1, char* jobu2,
+ char* jobv1t, char* jobv2t, char* trans,
+ char* signs, lapack_int* m, lapack_int* p,
+ lapack_int* q, double* x11, lapack_int* ldx11,
+ double* x12, lapack_int* ldx12, double* x21,
+ lapack_int* ldx21, double* x22, lapack_int* ldx22,
+ double* theta, double* u1, lapack_int* ldu1,
+ double* u2, lapack_int* ldu2, double* v1t,
+ lapack_int* ldv1t, double* v2t, lapack_int* ldv2t,
+ double* work, lapack_int* lwork,
+ lapack_int* iwork , lapack_int *info );
+void LAPACK_dsyconv( char* uplo, char* way,
+ lapack_int* n, double* a, lapack_int* lda,
+ const lapack_int* ipiv, double* work , lapack_int *info );
+void LAPACK_dsyswapr( char* uplo, lapack_int* n,
+ double* a, lapack_int* i1, lapack_int* i2 );
+void LAPACK_dsytri2( char* uplo, lapack_int* n,
+ double* a, lapack_int* lda,
+ const lapack_int* ipiv,
+ lapack_complex_double* work, lapack_int* lwork , lapack_int *info );
+void LAPACK_dsytri2x( char* uplo, lapack_int* n,
+ double* a, lapack_int* lda,
+ const lapack_int* ipiv, double* work,
+ lapack_int* nb , lapack_int *info );
+void LAPACK_dsytrs2( char* uplo, lapack_int* n,
+ lapack_int* nrhs, const double* a,
+ lapack_int* lda, const lapack_int* ipiv,
+ double* b, lapack_int* ldb, double* work , lapack_int *info );
+void LAPACK_sbbcsd( char* jobu1, char* jobu2,
+ char* jobv1t, char* jobv2t, char* trans,
+ lapack_int* m, lapack_int* p, lapack_int* q,
+ float* theta, float* phi, float* u1,
+ lapack_int* ldu1, float* u2, lapack_int* ldu2,
+ float* v1t, lapack_int* ldv1t, float* v2t,
+ lapack_int* ldv2t, float* b11d, float* b11e,
+ float* b12d, float* b12e, float* b21d,
+ float* b21e, float* b22d, float* b22e,
+ float* work, lapack_int* lwork , lapack_int *info );
+void LAPACK_sorbdb( char* trans, char* signs,
+ lapack_int* m, lapack_int* p, lapack_int* q,
+ float* x11, lapack_int* ldx11, float* x12,
+ lapack_int* ldx12, float* x21, lapack_int* ldx21,
+ float* x22, lapack_int* ldx22, float* theta,
+ float* phi, float* taup1, float* taup2,
+ float* tauq1, float* tauq2, float* work,
+ lapack_int* lwork , lapack_int *info );
+void LAPACK_sorcsd( char* jobu1, char* jobu2,
+ char* jobv1t, char* jobv2t, char* trans,
+ char* signs, lapack_int* m, lapack_int* p,
+ lapack_int* q, float* x11, lapack_int* ldx11,
+ float* x12, lapack_int* ldx12, float* x21,
+ lapack_int* ldx21, float* x22, lapack_int* ldx22,
+ float* theta, float* u1, lapack_int* ldu1,
+ float* u2, lapack_int* ldu2, float* v1t,
+ lapack_int* ldv1t, float* v2t, lapack_int* ldv2t,
+ float* work, lapack_int* lwork,
+ lapack_int* iwork , lapack_int *info );
+void LAPACK_ssyconv( char* uplo, char* way,
+ lapack_int* n, float* a, lapack_int* lda,
+ const lapack_int* ipiv, float* work , lapack_int *info );
+void LAPACK_ssyswapr( char* uplo, lapack_int* n,
+ float* a, lapack_int* i1, lapack_int* i2 );
+void LAPACK_ssytri2( char* uplo, lapack_int* n,
+ float* a, lapack_int* lda,
+ const lapack_int* ipiv,
+ lapack_complex_float* work, lapack_int* lwork , lapack_int *info );
+void LAPACK_ssytri2x( char* uplo, lapack_int* n,
+ float* a, lapack_int* lda,
+ const lapack_int* ipiv, float* work,
+ lapack_int* nb , lapack_int *info );
+void LAPACK_ssytrs2( char* uplo, lapack_int* n,
+ lapack_int* nrhs, const float* a,
+ lapack_int* lda, const lapack_int* ipiv,
+ float* b, lapack_int* ldb, float* work , lapack_int *info );
+void LAPACK_zbbcsd( char* jobu1, char* jobu2,
+ char* jobv1t, char* jobv2t, char* trans,
+ lapack_int* m, lapack_int* p, lapack_int* q,
+ double* theta, double* phi,
+ lapack_complex_double* u1, lapack_int* ldu1,
+ lapack_complex_double* u2, lapack_int* ldu2,
+ lapack_complex_double* v1t, lapack_int* ldv1t,
+ lapack_complex_double* v2t, lapack_int* ldv2t,
+ double* b11d, double* b11e, double* b12d,
+ double* b12e, double* b21d, double* b21e,
+ double* b22d, double* b22e, double* rwork,
+ lapack_int* lrwork , lapack_int *info );
+void LAPACK_zheswapr( char* uplo, lapack_int* n,
+ lapack_complex_double* a, lapack_int* i1,
+ lapack_int* i2 );
+void LAPACK_zhetri2( char* uplo, lapack_int* n,
+ lapack_complex_double* a, lapack_int* lda,
+ const lapack_int* ipiv,
+ lapack_complex_double* work, lapack_int* lwork , lapack_int *info );
+void LAPACK_zhetri2x( char* uplo, lapack_int* n,
+ lapack_complex_double* a, lapack_int* lda,
+ const lapack_int* ipiv,
+ lapack_complex_double* work, lapack_int* nb , lapack_int *info );
+void LAPACK_zhetrs2( char* uplo, lapack_int* n,
+ lapack_int* nrhs,
+ const lapack_complex_double* a, lapack_int* lda,
+ const lapack_int* ipiv,
+ lapack_complex_double* b, lapack_int* ldb,
+ lapack_complex_double* work , lapack_int *info );
+void LAPACK_zsyconv( char* uplo, char* way,
+ lapack_int* n, lapack_complex_double* a,
+ lapack_int* lda, const lapack_int* ipiv,
+ lapack_complex_double* work , lapack_int *info );
+void LAPACK_zsyswapr( char* uplo, lapack_int* n,
+ lapack_complex_double* a, lapack_int* i1,
+ lapack_int* i2 );
+void LAPACK_zsytri2( char* uplo, lapack_int* n,
+ lapack_complex_double* a, lapack_int* lda,
+ const lapack_int* ipiv,
+ lapack_complex_double* work, lapack_int* lwork , lapack_int *info );
+void LAPACK_zsytri2x( char* uplo, lapack_int* n,
+ lapack_complex_double* a, lapack_int* lda,
+ const lapack_int* ipiv,
+ lapack_complex_double* work, lapack_int* nb , lapack_int *info );
+void LAPACK_zsytrs2( char* uplo, lapack_int* n,
+ lapack_int* nrhs,
+ const lapack_complex_double* a, lapack_int* lda,
+ const lapack_int* ipiv,
+ lapack_complex_double* b, lapack_int* ldb,
+ lapack_complex_double* work , lapack_int *info );
+void LAPACK_zunbdb( char* trans, char* signs,
+ lapack_int* m, lapack_int* p, lapack_int* q,
+ lapack_complex_double* x11, lapack_int* ldx11,
+ lapack_complex_double* x12, lapack_int* ldx12,
+ lapack_complex_double* x21, lapack_int* ldx21,
+ lapack_complex_double* x22, lapack_int* ldx22,
+ double* theta, double* phi,
+ lapack_complex_double* taup1,
+ lapack_complex_double* taup2,
+ lapack_complex_double* tauq1,
+ lapack_complex_double* tauq2,
+ lapack_complex_double* work, lapack_int* lwork , lapack_int *info );
+void LAPACK_zuncsd( char* jobu1, char* jobu2,
+ char* jobv1t, char* jobv2t, char* trans,
+ char* signs, lapack_int* m, lapack_int* p,
+ lapack_int* q, lapack_complex_double* x11,
+ lapack_int* ldx11, lapack_complex_double* x12,
+ lapack_int* ldx12, lapack_complex_double* x21,
+ lapack_int* ldx21, lapack_complex_double* x22,
+ lapack_int* ldx22, double* theta,
+ lapack_complex_double* u1, lapack_int* ldu1,
+ lapack_complex_double* u2, lapack_int* ldu2,
+ lapack_complex_double* v1t, lapack_int* ldv1t,
+ lapack_complex_double* v2t, lapack_int* ldv2t,
+ lapack_complex_double* work, lapack_int* lwork,
+ double* rwork, lapack_int* lrwork,
+ lapack_int* iwork , lapack_int *info );
+// LAPACK 3.4.0
+void LAPACK_sgemqrt( char* side, char* trans, lapack_int* m, lapack_int* n,
+ lapack_int* k, lapack_int* nb, const float* v,
+ lapack_int* ldv, const float* t, lapack_int* ldt, float* c,
+ lapack_int* ldc, float* work, lapack_int *info );
+void LAPACK_dgemqrt( char* side, char* trans, lapack_int* m, lapack_int* n,
+ lapack_int* k, lapack_int* nb, const double* v,
+ lapack_int* ldv, const double* t, lapack_int* ldt,
+ double* c, lapack_int* ldc, double* work,
+ lapack_int *info );
+void LAPACK_cgemqrt( char* side, char* trans, lapack_int* m, lapack_int* n,
+ lapack_int* k, lapack_int* nb,
+ const lapack_complex_float* v, lapack_int* ldv,
+ const lapack_complex_float* t, lapack_int* ldt,
+ lapack_complex_float* c, lapack_int* ldc,
+ lapack_complex_float* work, lapack_int *info );
+void LAPACK_zgemqrt( char* side, char* trans, lapack_int* m, lapack_int* n,
+ lapack_int* k, lapack_int* nb,
+ const lapack_complex_double* v, lapack_int* ldv,
+ const lapack_complex_double* t, lapack_int* ldt,
+ lapack_complex_double* c, lapack_int* ldc,
+ lapack_complex_double* work, lapack_int *info );
+void LAPACK_sgeqrt( lapack_int* m, lapack_int* n, lapack_int* nb, float* a,
+ lapack_int* lda, float* t, lapack_int* ldt, float* work,
+ lapack_int *info );
+void LAPACK_dgeqrt( lapack_int* m, lapack_int* n, lapack_int* nb, double* a,
+ lapack_int* lda, double* t, lapack_int* ldt, double* work,
+ lapack_int *info );
+void LAPACK_cgeqrt( lapack_int* m, lapack_int* n, lapack_int* nb,
+ lapack_complex_float* a, lapack_int* lda,
+ lapack_complex_float* t, lapack_int* ldt,
+ lapack_complex_float* work, lapack_int *info );
+void LAPACK_zgeqrt( lapack_int* m, lapack_int* n, lapack_int* nb,
+ lapack_complex_double* a, lapack_int* lda,
+ lapack_complex_double* t, lapack_int* ldt,
+ lapack_complex_double* work, lapack_int *info );
+void LAPACK_sgeqrt2( lapack_int* m, lapack_int* n, float* a, lapack_int* lda,
+ float* t, lapack_int* ldt, lapack_int *info );
+void LAPACK_dgeqrt2( lapack_int* m, lapack_int* n, double* a, lapack_int* lda,
+ double* t, lapack_int* ldt, lapack_int *info );
+void LAPACK_cgeqrt2( lapack_int* m, lapack_int* n, lapack_complex_float* a,
+ lapack_int* lda, lapack_complex_float* t, lapack_int* ldt,
+ lapack_int *info );
+void LAPACK_zgeqrt2( lapack_int* m, lapack_int* n, lapack_complex_double* a,
+ lapack_int* lda, lapack_complex_double* t, lapack_int* ldt,
+ lapack_int *info );
+void LAPACK_sgeqrt3( lapack_int* m, lapack_int* n, float* a, lapack_int* lda,
+ float* t, lapack_int* ldt, lapack_int *info );
+void LAPACK_dgeqrt3( lapack_int* m, lapack_int* n, double* a, lapack_int* lda,
+ double* t, lapack_int* ldt, lapack_int *info );
+void LAPACK_cgeqrt3( lapack_int* m, lapack_int* n, lapack_complex_float* a,
+ lapack_int* lda, lapack_complex_float* t, lapack_int* ldt,
+ lapack_int *info );
+void LAPACK_zgeqrt3( lapack_int* m, lapack_int* n, lapack_complex_double* a,
+ lapack_int* lda, lapack_complex_double* t, lapack_int* ldt,
+ lapack_int *info );
+void LAPACK_stpmqrt( char* side, char* trans, lapack_int* m, lapack_int* n,
+ lapack_int* k, lapack_int* l, lapack_int* nb,
+ const float* v, lapack_int* ldv, const float* t,
+ lapack_int* ldt, float* a, lapack_int* lda, float* b,
+ lapack_int* ldb, float* work, lapack_int *info );
+void LAPACK_dtpmqrt( char* side, char* trans, lapack_int* m, lapack_int* n,
+ lapack_int* k, lapack_int* l, lapack_int* nb,
+ const double* v, lapack_int* ldv, const double* t,
+ lapack_int* ldt, double* a, lapack_int* lda, double* b,
+ lapack_int* ldb, double* work, lapack_int *info );
+void LAPACK_ctpmqrt( char* side, char* trans, lapack_int* m, lapack_int* n,
+ lapack_int* k, lapack_int* l, lapack_int* nb,
+ const lapack_complex_float* v, lapack_int* ldv,
+ const lapack_complex_float* t, lapack_int* ldt,
+ lapack_complex_float* a, lapack_int* lda,
+ lapack_complex_float* b, lapack_int* ldb,
+ lapack_complex_float* work, lapack_int *info );
+void LAPACK_ztpmqrt( char* side, char* trans, lapack_int* m, lapack_int* n,
+ lapack_int* k, lapack_int* l, lapack_int* nb,
+ const lapack_complex_double* v, lapack_int* ldv,
+ const lapack_complex_double* t, lapack_int* ldt,
+ lapack_complex_double* a, lapack_int* lda,
+ lapack_complex_double* b, lapack_int* ldb,
+ lapack_complex_double* work, lapack_int *info );
+void LAPACK_dtpqrt( lapack_int* m, lapack_int* n, lapack_int* l, lapack_int* nb,
+ double* a, lapack_int* lda, double* b, lapack_int* ldb,
+ double* t, lapack_int* ldt, double* work,
+ lapack_int *info );
+void LAPACK_ctpqrt( lapack_int* m, lapack_int* n, lapack_int* l, lapack_int* nb,
+ lapack_complex_float* a, lapack_int* lda,
+ lapack_complex_float* t, lapack_complex_float* b,
+ lapack_int* ldb, lapack_int* ldt,
+ lapack_complex_float* work, lapack_int *info );
+void LAPACK_ztpqrt( lapack_int* m, lapack_int* n, lapack_int* l, lapack_int* nb,
+ lapack_complex_double* a, lapack_int* lda,
+ lapack_complex_double* b, lapack_int* ldb,
+ lapack_complex_double* t, lapack_int* ldt,
+ lapack_complex_double* work, lapack_int *info );
+void LAPACK_stpqrt2( lapack_int* m, lapack_int* n, float* a, lapack_int* lda,
+ float* b, lapack_int* ldb, float* t, lapack_int* ldt,
+ lapack_int *info );
+void LAPACK_dtpqrt2( lapack_int* m, lapack_int* n, double* a, lapack_int* lda,
+ double* b, lapack_int* ldb, double* t, lapack_int* ldt,
+ lapack_int *info );
+void LAPACK_ctpqrt2( lapack_int* m, lapack_int* n, lapack_complex_float* a,
+ lapack_int* lda, lapack_complex_float* b, lapack_int* ldb,
+ lapack_complex_float* t, lapack_int* ldt,
+ lapack_int *info );
+void LAPACK_ztpqrt2( lapack_int* m, lapack_int* n, lapack_complex_double* a,
+ lapack_int* lda, lapack_complex_double* b, lapack_int* ldb,
+ lapack_complex_double* t, lapack_int* ldt,
+ lapack_int *info );
+void LAPACK_stprfb( char* side, char* trans, char* direct, char* storev,
+ lapack_int* m, lapack_int* n, lapack_int* k, lapack_int* l,
+ const float* v, lapack_int* ldv, const float* t,
+ lapack_int* ldt, float* a, lapack_int* lda, float* b,
+ lapack_int* ldb, const float* mywork,
+ lapack_int* myldwork );
+void LAPACK_dtprfb( char* side, char* trans, char* direct, char* storev,
+ lapack_int* m, lapack_int* n, lapack_int* k, lapack_int* l,
+ const double* v, lapack_int* ldv, const double* t,
+ lapack_int* ldt, double* a, lapack_int* lda, double* b,
+ lapack_int* ldb, const double* mywork,
+ lapack_int* myldwork );
+void LAPACK_ctprfb( char* side, char* trans, char* direct, char* storev,
+ lapack_int* m, lapack_int* n, lapack_int* k, lapack_int* l,
+ const lapack_complex_float* v, lapack_int* ldv,
+ const lapack_complex_float* t, lapack_int* ldt,
+ lapack_complex_float* a, lapack_int* lda,
+ lapack_complex_float* b, lapack_int* ldb,
+ const float* mywork, lapack_int* myldwork );
+void LAPACK_ztprfb( char* side, char* trans, char* direct, char* storev,
+ lapack_int* m, lapack_int* n, lapack_int* k, lapack_int* l,
+ const lapack_complex_double* v, lapack_int* ldv,
+ const lapack_complex_double* t, lapack_int* ldt,
+ lapack_complex_double* a, lapack_int* lda,
+ lapack_complex_double* b, lapack_int* ldb,
+ const double* mywork, lapack_int* myldwork );
+// LAPACK 3.X.X
+void LAPACK_csyr( char* uplo, lapack_int* n, lapack_complex_float* alpha,
+ const lapack_complex_float* x, lapack_int* incx,
+ lapack_complex_float* a, lapack_int* lda );
+void LAPACK_zsyr( char* uplo, lapack_int* n, lapack_complex_double* alpha,
+ const lapack_complex_double* x, lapack_int* incx,
+ lapack_complex_double* a, lapack_int* lda );
+
+#ifdef __cplusplus
+}
+#endif /* __cplusplus */
+
+#endif /* _LAPACKE_H_ */
+
+#endif /* _MKL_LAPACKE_H_ */
diff --git a/Eigen/src/misc/lapacke_helpers.h b/Eigen/src/misc/lapacke_helpers.h
new file mode 100644
index 0000000..e5d7ca0
--- /dev/null
+++ b/Eigen/src/misc/lapacke_helpers.h
@@ -0,0 +1,159 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2021 Erik Schultheis <erik.schultheis@aalto.fi>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_LAPACKE_HELPERS_H
+#define EIGEN_LAPACKE_HELPERS_H
+
+#include "./InternalHeaderCheck.h"
+
+#ifdef EIGEN_USE_MKL
+#include "mkl_lapacke.h"
+#else
+#include "lapacke.h"
+#endif
+
+namespace Eigen {
+namespace internal {
+/**
+ * \internal
+ * \brief Implementation details and helper functions for the lapacke glue code.
+ */
+namespace lapacke_helpers {
+
+// ---------------------------------------------------------------------------------------------------------------------
+// Translation from Eigen to Lapacke for types and constants
+// ---------------------------------------------------------------------------------------------------------------------
+
+// For complex numbers, the types in Eigen and Lapacke are different, but layout compatible.
+template<typename Scalar>
+struct translate_type_imp;
+template<>
+struct translate_type_imp<float> {
+ using type = float;
+};
+template<>
+struct translate_type_imp<double> {
+ using type = double;
+};
+template<>
+struct translate_type_imp<std::complex<double>> {
+ using type = lapack_complex_double;
+};
+template<>
+struct translate_type_imp<std::complex<float>> {
+ using type = lapack_complex_float;
+};
+
+/// Given an Eigen types, this is defined to be the corresponding, layout-compatible lapack type
+template<typename Scalar>
+using translated_type = typename translate_type_imp<Scalar>::type;
+
+/// These functions convert their arguments from Eigen to Lapack types
+/// This function performs conversion for any of the translations defined above.
+template<typename Source, typename Target=translated_type<Source>>
+EIGEN_ALWAYS_INLINE auto to_lapack(Source value) { return static_cast<Target>(value); }
+
+/// This function performs conversions for pointer types corresponding to the translations abovce.
+/// This is valid because the translations are between layout-compatible types.
+template<typename Source, typename Target=translated_type<Source>>
+EIGEN_ALWAYS_INLINE auto to_lapack(Source *value) { return reinterpret_cast<Target*>(value); }
+
+/// This function converts the Eigen Index to a lapack index, with possible range checks
+/// \sa internal::convert_index
+EIGEN_ALWAYS_INLINE lapack_int to_lapack(Index index) {
+ return convert_index<lapack_int>(index);
+}
+
+/// translates storage order of the given Eigen object to the corresponding lapack constant
+template<typename Derived>
+EIGEN_ALWAYS_INLINE EIGEN_CONSTEXPR lapack_int lapack_storage_of(const EigenBase<Derived> &) {
+ return Derived::IsRowMajor ? LAPACK_ROW_MAJOR : LAPACK_COL_MAJOR;
+}
+
+/// translate UpLo type to the corresponding letter code
+template<UpLoType mode> char translate_mode;
+template<> constexpr char translate_mode<Lower> = 'L';
+template<> constexpr char translate_mode<Upper> = 'U';
+
+
+// ---------------------------------------------------------------------------------------------------------------------
+// Automatic generation of low-level wrappers
+// ---------------------------------------------------------------------------------------------------------------------
+
+/*!
+ * \internal
+ * \brief Helper type to facilitate the wrapping of raw LAPACKE functions for different types into a single, overloaded C++ function.
+ * This is achieved in combination with \r EIGEN_MAKE_LAPACKE_WRAPPER
+ * \details This implementation works by providing an overloaded call function that just forwards its arguments to the
+ * underlying lapack function. Each of these overloads is enabled only if the call is actually well formed.
+ * Because these lapack functions take pointers to the underlying scalar type as arguments, even though the actual Scalars
+ * would be implicitly convertible, the pointers are not and therefore only a single overload can be valid at the same time.
+ * Thus, despite all functions taking fully generic `Args&&... args` as arguments, there is never any ambiguity.
+ */
+template<typename DoubleFn, typename SingleFn, typename DoubleCpxFn, typename SingleCpxFn>
+struct WrappingHelper {
+ // The naming of double, single, double complex and single complex is purely for readability
+ // and doesn't actually affect the workings of this class. In principle, the arguments can
+ // be supplied in any permuted order.
+ DoubleFn double_; SingleFn single_; DoubleCpxFn double_cpx_; SingleCpxFn single_cpx_;
+
+ template<typename... Args>
+ auto call(Args&&... args) -> decltype(double_(std::forward<Args>(args)...)) {
+ return double_(std::forward<Args>(args)...);
+ }
+
+ template<typename... Args>
+ auto call(Args&&... args) -> decltype(single_(std::forward<Args>(args)...)){
+ return single_(std::forward<Args>(args)...);
+ }
+
+ template<typename... Args>
+ auto call(Args&&... args) -> decltype(double_cpx_(std::forward<Args>(args)...)){
+ return double_cpx_(std::forward<Args>(args)...);
+ }
+
+ template<typename... Args>
+ auto call(Args&&... args) -> decltype(single_cpx_(std::forward<Args>(args)...)){
+ return single_cpx_(std::forward<Args>(args)...);
+ }
+};
+
+/** \internal Helper function that generates a `WrappingHelper` object with the given function pointers and
+ * invokes its `call` method, thus selecting one of the overloads.
+ * \sa EIGEN_MAKE_LAPACKE_WRAPPER
+ */
+template<typename DoubleFn, typename SingleFn, typename DoubleCpxFn, typename SingleCpxFn, typename... Args>
+EIGEN_ALWAYS_INLINE auto call_wrapper(DoubleFn df, SingleFn sf, DoubleCpxFn dcf, SingleCpxFn scf, Args&&... args) {
+ WrappingHelper<DoubleFn, SingleFn, DoubleCpxFn, SingleCpxFn> helper{df, sf, dcf, scf};
+ return helper.call(std::forward<Args>(args)...);
+}
+
+/**
+ * \internal
+ * Generates a new function `Function` that dispatches to the corresponding LAPACKE_? prefixed functions.
+ * \sa WrappingHelper
+ */
+#define EIGEN_MAKE_LAPACKE_WRAPPER(FUNCTION) \
+template<typename... Args> \
+EIGEN_ALWAYS_INLINE auto FUNCTION(Args&&... args) { return call_wrapper(LAPACKE_d##FUNCTION, LAPACKE_s##FUNCTION, LAPACKE_z##FUNCTION, LAPACKE_c##FUNCTION, std::forward<Args>(args)...); }
+
+// Now with this macro and the helper wrappers, we can generate the dispatch for all the lapacke functions that are
+// used in Eigen.
+// We define these here instead of in the files where they are used because this allows us to #undef the macro again
+// right here
+EIGEN_MAKE_LAPACKE_WRAPPER(potrf)
+EIGEN_MAKE_LAPACKE_WRAPPER(getrf)
+EIGEN_MAKE_LAPACKE_WRAPPER(geqrf)
+
+#undef EIGEN_MAKE_LAPACKE_WRAPPER
+}
+}
+}
+
+#endif // EIGEN_LAPACKE_HELPERS_H
diff --git a/Eigen/src/misc/lapacke_mangling.h b/Eigen/src/misc/lapacke_mangling.h
new file mode 100644
index 0000000..6211fd1
--- /dev/null
+++ b/Eigen/src/misc/lapacke_mangling.h
@@ -0,0 +1,17 @@
+#ifndef LAPACK_HEADER_INCLUDED
+#define LAPACK_HEADER_INCLUDED
+
+#ifndef LAPACK_GLOBAL
+#if defined(LAPACK_GLOBAL_PATTERN_LC) || defined(ADD_)
+#define LAPACK_GLOBAL(lcname,UCNAME) lcname##_
+#elif defined(LAPACK_GLOBAL_PATTERN_UC) || defined(UPPER)
+#define LAPACK_GLOBAL(lcname,UCNAME) UCNAME
+#elif defined(LAPACK_GLOBAL_PATTERN_MC) || defined(NOCHANGE)
+#define LAPACK_GLOBAL(lcname,UCNAME) lcname
+#else
+#define LAPACK_GLOBAL(lcname,UCNAME) lcname##_
+#endif
+#endif
+
+#endif
+
diff --git a/Eigen/src/plugins/ArrayCwiseBinaryOps.h b/Eigen/src/plugins/ArrayCwiseBinaryOps.h
new file mode 100644
index 0000000..30e3ee1
--- /dev/null
+++ b/Eigen/src/plugins/ArrayCwiseBinaryOps.h
@@ -0,0 +1,370 @@
+
+/** \returns an expression of the coefficient wise product of \c *this and \a other
+ *
+ * \sa MatrixBase::cwiseProduct
+ */
+template<typename OtherDerived>
+EIGEN_DEVICE_FUNC
+EIGEN_STRONG_INLINE const EIGEN_CWISE_BINARY_RETURN_TYPE(Derived,OtherDerived,product)
+operator*(const EIGEN_CURRENT_STORAGE_BASE_CLASS<OtherDerived> &other) const
+{
+ return EIGEN_CWISE_BINARY_RETURN_TYPE(Derived,OtherDerived,product)(derived(), other.derived());
+}
+
+/** \returns an expression of the coefficient wise quotient of \c *this and \a other
+ *
+ * \sa MatrixBase::cwiseQuotient
+ */
+template<typename OtherDerived>
+EIGEN_DEVICE_FUNC
+EIGEN_STRONG_INLINE const CwiseBinaryOp<internal::scalar_quotient_op<Scalar,typename OtherDerived::Scalar>, const Derived, const OtherDerived>
+operator/(const EIGEN_CURRENT_STORAGE_BASE_CLASS<OtherDerived> &other) const
+{
+ return CwiseBinaryOp<internal::scalar_quotient_op<Scalar,typename OtherDerived::Scalar>, const Derived, const OtherDerived>(derived(), other.derived());
+}
+
+/** \returns an expression of the coefficient-wise min of \c *this and \a other
+ *
+ * Example: \include Cwise_min.cpp
+ * Output: \verbinclude Cwise_min.out
+ *
+ * \sa max()
+ */
+template <int NaNPropagation=PropagateFast, typename OtherDerived>
+EIGEN_DEVICE_FUNC
+EIGEN_STRONG_INLINE const CwiseBinaryOp<internal::scalar_min_op<Scalar,Scalar,NaNPropagation>, const Derived, const OtherDerived>
+#ifdef EIGEN_PARSED_BY_DOXYGEN
+min
+#else
+(min)
+#endif
+(const EIGEN_CURRENT_STORAGE_BASE_CLASS<OtherDerived> &other) const
+{
+ return CwiseBinaryOp<internal::scalar_min_op<Scalar,Scalar,NaNPropagation>, const Derived, const OtherDerived>(derived(), other.derived());
+}
+
+/** \returns an expression of the coefficient-wise min of \c *this and scalar \a other
+ *
+ * \sa max()
+ */
+template <int NaNPropagation=PropagateFast>
+EIGEN_DEVICE_FUNC
+EIGEN_STRONG_INLINE const CwiseBinaryOp<internal::scalar_min_op<Scalar,Scalar,NaNPropagation>, const Derived,
+ const CwiseNullaryOp<internal::scalar_constant_op<Scalar>, PlainObject> >
+#ifdef EIGEN_PARSED_BY_DOXYGEN
+min
+#else
+(min)
+#endif
+(const Scalar &other) const
+{
+ return (min<NaNPropagation>)(Derived::PlainObject::Constant(rows(), cols(), other));
+}
+
+/** \returns an expression of the coefficient-wise max of \c *this and \a other
+ *
+ * Example: \include Cwise_max.cpp
+ * Output: \verbinclude Cwise_max.out
+ *
+ * \sa min()
+ */
+template <int NaNPropagation=PropagateFast, typename OtherDerived>
+EIGEN_DEVICE_FUNC
+EIGEN_STRONG_INLINE const CwiseBinaryOp<internal::scalar_max_op<Scalar,Scalar,NaNPropagation>, const Derived, const OtherDerived>
+#ifdef EIGEN_PARSED_BY_DOXYGEN
+max
+#else
+(max)
+#endif
+(const EIGEN_CURRENT_STORAGE_BASE_CLASS<OtherDerived> &other) const
+{
+ return CwiseBinaryOp<internal::scalar_max_op<Scalar,Scalar,NaNPropagation>, const Derived, const OtherDerived>(derived(), other.derived());
+}
+
+/** \returns an expression of the coefficient-wise max of \c *this and scalar \a other
+ *
+ * \sa min()
+ */
+template <int NaNPropagation=PropagateFast>
+EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE const CwiseBinaryOp<internal::scalar_max_op<Scalar,Scalar,NaNPropagation>, const Derived,
+ const CwiseNullaryOp<internal::scalar_constant_op<Scalar>, PlainObject> >
+#ifdef EIGEN_PARSED_BY_DOXYGEN
+max
+#else
+(max)
+#endif
+(const Scalar &other) const
+{
+ return (max<NaNPropagation>)(Derived::PlainObject::Constant(rows(), cols(), other));
+}
+
+/** \returns an expression of the coefficient-wise absdiff of \c *this and \a other
+ *
+ * Example: \include Cwise_absolute_difference.cpp
+ * Output: \verbinclude Cwise_absolute_difference.out
+ *
+ * \sa absolute_difference()
+ */
+EIGEN_MAKE_CWISE_BINARY_OP(absolute_difference,absolute_difference)
+
+/** \returns an expression of the coefficient-wise absolute_difference of \c *this and scalar \a other
+ *
+ * \sa absolute_difference()
+ */
+EIGEN_DEVICE_FUNC
+EIGEN_STRONG_INLINE const CwiseBinaryOp<internal::scalar_absolute_difference_op<Scalar,Scalar>, const Derived,
+ const CwiseNullaryOp<internal::scalar_constant_op<Scalar>, PlainObject> >
+#ifdef EIGEN_PARSED_BY_DOXYGEN
+absolute_difference
+#else
+(absolute_difference)
+#endif
+(const Scalar &other) const
+{
+ return (absolute_difference)(Derived::PlainObject::Constant(rows(), cols(), other));
+}
+
+/** \returns an expression of the coefficient-wise power of \c *this to the given array of \a exponents.
+ *
+ * This function computes the coefficient-wise power.
+ *
+ * Example: \include Cwise_array_power_array.cpp
+ * Output: \verbinclude Cwise_array_power_array.out
+ */
+EIGEN_MAKE_CWISE_BINARY_OP(pow,pow)
+
+/** \returns an expression of the coefficient-wise atan2(\c *this, \a y), where \a y is the given array argument.
+ *
+ * This function computes the coefficient-wise atan2.
+ *
+ */
+EIGEN_MAKE_CWISE_BINARY_OP(atan2,atan2)
+
+
+// TODO code generating macros could be moved to Macros.h and could include generation of documentation
+#define EIGEN_MAKE_CWISE_COMP_OP(OP, COMPARATOR) \
+template<typename OtherDerived> \
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const CwiseBinaryOp<internal::scalar_cmp_op<Scalar, typename OtherDerived::Scalar, internal::cmp_ ## COMPARATOR>, const Derived, const OtherDerived> \
+OP(const EIGEN_CURRENT_STORAGE_BASE_CLASS<OtherDerived> &other) const \
+{ \
+ return CwiseBinaryOp<internal::scalar_cmp_op<Scalar, typename OtherDerived::Scalar, internal::cmp_ ## COMPARATOR>, const Derived, const OtherDerived>(derived(), other.derived()); \
+}\
+typedef CwiseBinaryOp<internal::scalar_cmp_op<Scalar,Scalar, internal::cmp_ ## COMPARATOR>, const Derived, const CwiseNullaryOp<internal::scalar_constant_op<Scalar>, PlainObject> > Cmp ## COMPARATOR ## ReturnType; \
+typedef CwiseBinaryOp<internal::scalar_cmp_op<Scalar,Scalar, internal::cmp_ ## COMPARATOR>, const CwiseNullaryOp<internal::scalar_constant_op<Scalar>, PlainObject>, const Derived > RCmp ## COMPARATOR ## ReturnType; \
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Cmp ## COMPARATOR ## ReturnType \
+OP(const Scalar& s) const { \
+ return this->OP(Derived::PlainObject::Constant(rows(), cols(), s)); \
+} \
+EIGEN_DEVICE_FUNC friend EIGEN_STRONG_INLINE const RCmp ## COMPARATOR ## ReturnType \
+OP(const Scalar& s, const EIGEN_CURRENT_STORAGE_BASE_CLASS<Derived>& d) { \
+ return Derived::PlainObject::Constant(d.rows(), d.cols(), s).OP(d); \
+}
+
+#define EIGEN_MAKE_CWISE_COMP_R_OP(OP, R_OP, RCOMPARATOR) \
+template<typename OtherDerived> \
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const CwiseBinaryOp<internal::scalar_cmp_op<typename OtherDerived::Scalar, Scalar, internal::cmp_##RCOMPARATOR>, const OtherDerived, const Derived> \
+OP(const EIGEN_CURRENT_STORAGE_BASE_CLASS<OtherDerived> &other) const \
+{ \
+ return CwiseBinaryOp<internal::scalar_cmp_op<typename OtherDerived::Scalar, Scalar, internal::cmp_##RCOMPARATOR>, const OtherDerived, const Derived>(other.derived(), derived()); \
+} \
+EIGEN_DEVICE_FUNC \
+inline const RCmp ## RCOMPARATOR ## ReturnType \
+OP(const Scalar& s) const { \
+ return Derived::PlainObject::Constant(rows(), cols(), s).R_OP(*this); \
+} \
+friend inline const Cmp ## RCOMPARATOR ## ReturnType \
+OP(const Scalar& s, const Derived& d) { \
+ return d.R_OP(Derived::PlainObject::Constant(d.rows(), d.cols(), s)); \
+}
+
+
+
+/** \returns an expression of the coefficient-wise \< operator of *this and \a other
+ *
+ * Example: \include Cwise_less.cpp
+ * Output: \verbinclude Cwise_less.out
+ *
+ * \sa all(), any(), operator>(), operator<=()
+ */
+EIGEN_MAKE_CWISE_COMP_OP(operator<, LT)
+
+/** \returns an expression of the coefficient-wise \<= operator of *this and \a other
+ *
+ * Example: \include Cwise_less_equal.cpp
+ * Output: \verbinclude Cwise_less_equal.out
+ *
+ * \sa all(), any(), operator>=(), operator<()
+ */
+EIGEN_MAKE_CWISE_COMP_OP(operator<=, LE)
+
+/** \returns an expression of the coefficient-wise \> operator of *this and \a other
+ *
+ * Example: \include Cwise_greater.cpp
+ * Output: \verbinclude Cwise_greater.out
+ *
+ * \sa all(), any(), operator>=(), operator<()
+ */
+EIGEN_MAKE_CWISE_COMP_R_OP(operator>, operator<, LT)
+
+/** \returns an expression of the coefficient-wise \>= operator of *this and \a other
+ *
+ * Example: \include Cwise_greater_equal.cpp
+ * Output: \verbinclude Cwise_greater_equal.out
+ *
+ * \sa all(), any(), operator>(), operator<=()
+ */
+EIGEN_MAKE_CWISE_COMP_R_OP(operator>=, operator<=, LE)
+
+/** \returns an expression of the coefficient-wise == operator of *this and \a other
+ *
+ * \warning this performs an exact comparison, which is generally a bad idea with floating-point types.
+ * In order to check for equality between two vectors or matrices with floating-point coefficients, it is
+ * generally a far better idea to use a fuzzy comparison as provided by isApprox() and
+ * isMuchSmallerThan().
+ *
+ * Example: \include Cwise_equal_equal.cpp
+ * Output: \verbinclude Cwise_equal_equal.out
+ *
+ * \sa all(), any(), isApprox(), isMuchSmallerThan()
+ */
+EIGEN_MAKE_CWISE_COMP_OP(operator==, EQ)
+
+/** \returns an expression of the coefficient-wise != operator of *this and \a other
+ *
+ * \warning this performs an exact comparison, which is generally a bad idea with floating-point types.
+ * In order to check for equality between two vectors or matrices with floating-point coefficients, it is
+ * generally a far better idea to use a fuzzy comparison as provided by isApprox() and
+ * isMuchSmallerThan().
+ *
+ * Example: \include Cwise_not_equal.cpp
+ * Output: \verbinclude Cwise_not_equal.out
+ *
+ * \sa all(), any(), isApprox(), isMuchSmallerThan()
+ */
+EIGEN_MAKE_CWISE_COMP_OP(operator!=, NEQ)
+
+
+#undef EIGEN_MAKE_CWISE_COMP_OP
+#undef EIGEN_MAKE_CWISE_COMP_R_OP
+
+// scalar addition
+#ifndef EIGEN_PARSED_BY_DOXYGEN
+EIGEN_MAKE_SCALAR_BINARY_OP(operator+,sum)
+#else
+/** \returns an expression of \c *this with each coeff incremented by the constant \a scalar
+ *
+ * \tparam T is the scalar type of \a scalar. It must be compatible with the scalar type of the given expression.
+ *
+ * Example: \include Cwise_plus.cpp
+ * Output: \verbinclude Cwise_plus.out
+ *
+ * \sa operator+=(), operator-()
+ */
+template<typename T>
+const CwiseBinaryOp<internal::scalar_sum_op<Scalar,T>,Derived,Constant<T> > operator+(const T& scalar) const;
+/** \returns an expression of \a expr with each coeff incremented by the constant \a scalar
+ *
+ * \tparam T is the scalar type of \a scalar. It must be compatible with the scalar type of the given expression.
+ */
+template<typename T> friend
+const CwiseBinaryOp<internal::scalar_sum_op<T,Scalar>,Constant<T>,Derived> operator+(const T& scalar, const StorageBaseType& expr);
+#endif
+
+#ifndef EIGEN_PARSED_BY_DOXYGEN
+EIGEN_MAKE_SCALAR_BINARY_OP(operator-,difference)
+#else
+/** \returns an expression of \c *this with each coeff decremented by the constant \a scalar
+ *
+ * \tparam T is the scalar type of \a scalar. It must be compatible with the scalar type of the given expression.
+ *
+ * Example: \include Cwise_minus.cpp
+ * Output: \verbinclude Cwise_minus.out
+ *
+ * \sa operator+=(), operator-()
+ */
+template<typename T>
+const CwiseBinaryOp<internal::scalar_difference_op<Scalar,T>,Derived,Constant<T> > operator-(const T& scalar) const;
+/** \returns an expression of the constant matrix of value \a scalar decremented by the coefficients of \a expr
+ *
+ * \tparam T is the scalar type of \a scalar. It must be compatible with the scalar type of the given expression.
+ */
+template<typename T> friend
+const CwiseBinaryOp<internal::scalar_difference_op<T,Scalar>,Constant<T>,Derived> operator-(const T& scalar, const StorageBaseType& expr);
+#endif
+
+
+#ifndef EIGEN_PARSED_BY_DOXYGEN
+ EIGEN_MAKE_SCALAR_BINARY_OP_ONTHELEFT(operator/,quotient)
+#else
+ /**
+ * \brief Component-wise division of the scalar \a s by array elements of \a a.
+ *
+ * \tparam Scalar is the scalar type of \a x. It must be compatible with the scalar type of the given array expression (\c Derived::Scalar).
+ */
+ template<typename T> friend
+ inline const CwiseBinaryOp<internal::scalar_quotient_op<T,Scalar>,Constant<T>,Derived>
+ operator/(const T& s,const StorageBaseType& a);
+#endif
+
+/** \returns an expression of the coefficient-wise ^ operator of *this and \a other
+ *
+ * \warning this operator is for expression of bool only.
+ *
+ * Example: \include Cwise_boolean_xor.cpp
+ * Output: \verbinclude Cwise_boolean_xor.out
+ *
+ * \sa operator&&(), select()
+ */
+template<typename OtherDerived>
+EIGEN_DEVICE_FUNC
+inline const CwiseBinaryOp<internal::scalar_boolean_xor_op, const Derived, const OtherDerived>
+operator^(const EIGEN_CURRENT_STORAGE_BASE_CLASS<OtherDerived> &other) const
+{
+ EIGEN_STATIC_ASSERT((internal::is_same<bool,Scalar>::value && internal::is_same<bool,typename OtherDerived::Scalar>::value),
+ THIS_METHOD_IS_ONLY_FOR_EXPRESSIONS_OF_BOOL);
+ return CwiseBinaryOp<internal::scalar_boolean_xor_op, const Derived, const OtherDerived>(derived(),other.derived());
+}
+
+// NOTE disabled until we agree on argument order
+#if 0
+/** \cpp11 \returns an expression of the coefficient-wise polygamma function.
+ *
+ * \specialfunctions_module
+ *
+ * It returns the \a n -th derivative of the digamma(psi) evaluated at \c *this.
+ *
+ * \warning Be careful with the order of the parameters: x.polygamma(n) is equivalent to polygamma(n,x)
+ *
+ * \sa Eigen::polygamma()
+ */
+template<typename DerivedN>
+inline const CwiseBinaryOp<internal::scalar_polygamma_op<Scalar>, const DerivedN, const Derived>
+polygamma(const EIGEN_CURRENT_STORAGE_BASE_CLASS<DerivedN> &n) const
+{
+ return CwiseBinaryOp<internal::scalar_polygamma_op<Scalar>, const DerivedN, const Derived>(n.derived(), this->derived());
+}
+#endif
+
+/** \returns an expression of the coefficient-wise zeta function.
+ *
+ * \specialfunctions_module
+ *
+ * It returns the Riemann zeta function of two arguments \c *this and \a q:
+ *
+ * \param q is the shift, it must be > 0
+ *
+ * \note *this is the exponent, it must be > 1.
+ * \note This function supports only float and double scalar types. To support other scalar types, the user has
+ * to provide implementations of zeta(T,T) for any scalar type T to be supported.
+ *
+ * This method is an alias for zeta(*this,q);
+ *
+ * \sa Eigen::zeta()
+ */
+template<typename DerivedQ>
+inline const CwiseBinaryOp<internal::scalar_zeta_op<Scalar>, const Derived, const DerivedQ>
+zeta(const EIGEN_CURRENT_STORAGE_BASE_CLASS<DerivedQ> &q) const
+{
+ return CwiseBinaryOp<internal::scalar_zeta_op<Scalar>, const Derived, const DerivedQ>(this->derived(), q.derived());
+}
diff --git a/Eigen/src/plugins/ArrayCwiseUnaryOps.h b/Eigen/src/plugins/ArrayCwiseUnaryOps.h
new file mode 100644
index 0000000..d8c1a84
--- /dev/null
+++ b/Eigen/src/plugins/ArrayCwiseUnaryOps.h
@@ -0,0 +1,721 @@
+
+
+typedef CwiseUnaryOp<internal::scalar_abs_op<Scalar>, const Derived> AbsReturnType;
+typedef CwiseUnaryOp<internal::scalar_arg_op<Scalar>, const Derived> ArgReturnType;
+typedef CwiseUnaryOp<internal::scalar_abs2_op<Scalar>, const Derived> Abs2ReturnType;
+typedef CwiseUnaryOp<internal::scalar_sqrt_op<Scalar>, const Derived> SqrtReturnType;
+typedef CwiseUnaryOp<internal::scalar_rsqrt_op<Scalar>, const Derived> RsqrtReturnType;
+typedef CwiseUnaryOp<internal::scalar_sign_op<Scalar>, const Derived> SignReturnType;
+typedef CwiseUnaryOp<internal::scalar_inverse_op<Scalar>, const Derived> InverseReturnType;
+typedef CwiseUnaryOp<internal::scalar_boolean_not_op<Scalar>, const Derived> BooleanNotReturnType;
+
+typedef CwiseUnaryOp<internal::scalar_exp_op<Scalar>, const Derived> ExpReturnType;
+typedef CwiseUnaryOp<internal::scalar_expm1_op<Scalar>, const Derived> Expm1ReturnType;
+typedef CwiseUnaryOp<internal::scalar_log_op<Scalar>, const Derived> LogReturnType;
+typedef CwiseUnaryOp<internal::scalar_log1p_op<Scalar>, const Derived> Log1pReturnType;
+typedef CwiseUnaryOp<internal::scalar_log10_op<Scalar>, const Derived> Log10ReturnType;
+typedef CwiseUnaryOp<internal::scalar_log2_op<Scalar>, const Derived> Log2ReturnType;
+typedef CwiseUnaryOp<internal::scalar_cos_op<Scalar>, const Derived> CosReturnType;
+typedef CwiseUnaryOp<internal::scalar_sin_op<Scalar>, const Derived> SinReturnType;
+typedef CwiseUnaryOp<internal::scalar_tan_op<Scalar>, const Derived> TanReturnType;
+typedef CwiseUnaryOp<internal::scalar_acos_op<Scalar>, const Derived> AcosReturnType;
+typedef CwiseUnaryOp<internal::scalar_asin_op<Scalar>, const Derived> AsinReturnType;
+typedef CwiseUnaryOp<internal::scalar_atan_op<Scalar>, const Derived> AtanReturnType;
+typedef CwiseUnaryOp<internal::scalar_tanh_op<Scalar>, const Derived> TanhReturnType;
+typedef CwiseUnaryOp<internal::scalar_logistic_op<Scalar>, const Derived> LogisticReturnType;
+typedef CwiseUnaryOp<internal::scalar_sinh_op<Scalar>, const Derived> SinhReturnType;
+typedef CwiseUnaryOp<internal::scalar_atanh_op<Scalar>, const Derived> AtanhReturnType;
+typedef CwiseUnaryOp<internal::scalar_asinh_op<Scalar>, const Derived> AsinhReturnType;
+typedef CwiseUnaryOp<internal::scalar_acosh_op<Scalar>, const Derived> AcoshReturnType;
+typedef CwiseUnaryOp<internal::scalar_cosh_op<Scalar>, const Derived> CoshReturnType;
+typedef CwiseUnaryOp<internal::scalar_square_op<Scalar>, const Derived> SquareReturnType;
+typedef CwiseUnaryOp<internal::scalar_cube_op<Scalar>, const Derived> CubeReturnType;
+typedef CwiseUnaryOp<internal::scalar_round_op<Scalar>, const Derived> RoundReturnType;
+typedef CwiseUnaryOp<internal::scalar_rint_op<Scalar>, const Derived> RintReturnType;
+typedef CwiseUnaryOp<internal::scalar_floor_op<Scalar>, const Derived> FloorReturnType;
+typedef CwiseUnaryOp<internal::scalar_ceil_op<Scalar>, const Derived> CeilReturnType;
+typedef CwiseUnaryOp<internal::scalar_isnan_op<Scalar>, const Derived> IsNaNReturnType;
+typedef CwiseUnaryOp<internal::scalar_isinf_op<Scalar>, const Derived> IsInfReturnType;
+typedef CwiseUnaryOp<internal::scalar_isfinite_op<Scalar>, const Derived> IsFiniteReturnType;
+
+/** \returns an expression of the coefficient-wise absolute value of \c *this
+ *
+ * Example: \include Cwise_abs.cpp
+ * Output: \verbinclude Cwise_abs.out
+ *
+ * \sa <a href="group__CoeffwiseMathFunctions.html#cwisetable_abs">Math functions</a>, abs2()
+ */
+EIGEN_DEVICE_FUNC
+EIGEN_STRONG_INLINE const AbsReturnType
+abs() const
+{
+ return AbsReturnType(derived());
+}
+
+/** \returns an expression of the coefficient-wise phase angle of \c *this
+ *
+ * Example: \include Cwise_arg.cpp
+ * Output: \verbinclude Cwise_arg.out
+ *
+ * \sa abs()
+ */
+EIGEN_DEVICE_FUNC
+EIGEN_STRONG_INLINE const ArgReturnType
+arg() const
+{
+ return ArgReturnType(derived());
+}
+
+/** \returns an expression of the coefficient-wise squared absolute value of \c *this
+ *
+ * Example: \include Cwise_abs2.cpp
+ * Output: \verbinclude Cwise_abs2.out
+ *
+ * \sa <a href="group__CoeffwiseMathFunctions.html#cwisetable_abs2">Math functions</a>, abs(), square()
+ */
+EIGEN_DEVICE_FUNC
+EIGEN_STRONG_INLINE const Abs2ReturnType
+abs2() const
+{
+ return Abs2ReturnType(derived());
+}
+
+/** \returns an expression of the coefficient-wise exponential of *this.
+ *
+ * This function computes the coefficient-wise exponential. The function MatrixBase::exp() in the
+ * unsupported module MatrixFunctions computes the matrix exponential.
+ *
+ * Example: \include Cwise_exp.cpp
+ * Output: \verbinclude Cwise_exp.out
+ *
+ * \sa <a href="group__CoeffwiseMathFunctions.html#cwisetable_exp">Math functions</a>, pow(), log(), sin(), cos()
+ */
+EIGEN_DEVICE_FUNC
+inline const ExpReturnType
+exp() const
+{
+ return ExpReturnType(derived());
+}
+
+/** \returns an expression of the coefficient-wise exponential of *this minus 1.
+ *
+ * In exact arithmetic, \c x.expm1() is equivalent to \c x.exp() - 1,
+ * however, with finite precision, this function is much more accurate when \c x is close to zero.
+ *
+ * \sa <a href="group__CoeffwiseMathFunctions.html#cwisetable_expm1">Math functions</a>, exp()
+ */
+EIGEN_DEVICE_FUNC
+inline const Expm1ReturnType
+expm1() const
+{
+ return Expm1ReturnType(derived());
+}
+
+/** \returns an expression of the coefficient-wise logarithm of *this.
+ *
+ * This function computes the coefficient-wise logarithm. The function MatrixBase::log() in the
+ * unsupported module MatrixFunctions computes the matrix logarithm.
+ *
+ * Example: \include Cwise_log.cpp
+ * Output: \verbinclude Cwise_log.out
+ *
+ * \sa <a href="group__CoeffwiseMathFunctions.html#cwisetable_log">Math functions</a>, log()
+ */
+EIGEN_DEVICE_FUNC
+inline const LogReturnType
+log() const
+{
+ return LogReturnType(derived());
+}
+
+/** \returns an expression of the coefficient-wise logarithm of 1 plus \c *this.
+ *
+ * In exact arithmetic, \c x.log() is equivalent to \c (x+1).log(),
+ * however, with finite precision, this function is much more accurate when \c x is close to zero.
+ *
+ * \sa <a href="group__CoeffwiseMathFunctions.html#cwisetable_log1p">Math functions</a>, log()
+ */
+EIGEN_DEVICE_FUNC
+inline const Log1pReturnType
+log1p() const
+{
+ return Log1pReturnType(derived());
+}
+
+/** \returns an expression of the coefficient-wise base-10 logarithm of *this.
+ *
+ * This function computes the coefficient-wise base-10 logarithm.
+ *
+ * Example: \include Cwise_log10.cpp
+ * Output: \verbinclude Cwise_log10.out
+ *
+ * \sa <a href="group__CoeffwiseMathFunctions.html#cwisetable_log10">Math functions</a>, log()
+ */
+EIGEN_DEVICE_FUNC
+inline const Log10ReturnType
+log10() const
+{
+ return Log10ReturnType(derived());
+}
+
+/** \returns an expression of the coefficient-wise base-2 logarithm of *this.
+ *
+ * This function computes the coefficient-wise base-2 logarithm.
+ *
+ */
+EIGEN_DEVICE_FUNC
+inline const Log2ReturnType
+log2() const
+{
+ return Log2ReturnType(derived());
+}
+
+/** \returns an expression of the coefficient-wise square root of *this.
+ *
+ * This function computes the coefficient-wise square root. The function MatrixBase::sqrt() in the
+ * unsupported module MatrixFunctions computes the matrix square root.
+ *
+ * Example: \include Cwise_sqrt.cpp
+ * Output: \verbinclude Cwise_sqrt.out
+ *
+ * \sa <a href="group__CoeffwiseMathFunctions.html#cwisetable_sqrt">Math functions</a>, pow(), square()
+ */
+EIGEN_DEVICE_FUNC
+inline const SqrtReturnType
+sqrt() const
+{
+ return SqrtReturnType(derived());
+}
+
+/** \returns an expression of the coefficient-wise inverse square root of *this.
+ *
+ * This function computes the coefficient-wise inverse square root.
+ *
+ * Example: \include Cwise_sqrt.cpp
+ * Output: \verbinclude Cwise_sqrt.out
+ *
+ * \sa pow(), square()
+ */
+EIGEN_DEVICE_FUNC
+inline const RsqrtReturnType
+rsqrt() const
+{
+ return RsqrtReturnType(derived());
+}
+
+/** \returns an expression of the coefficient-wise signum of *this.
+ *
+ * This function computes the coefficient-wise signum.
+ *
+ * Example: \include Cwise_sign.cpp
+ * Output: \verbinclude Cwise_sign.out
+ *
+ * \sa pow(), square()
+ */
+EIGEN_DEVICE_FUNC
+inline const SignReturnType
+sign() const
+{
+ return SignReturnType(derived());
+}
+
+
+/** \returns an expression of the coefficient-wise cosine of *this.
+ *
+ * This function computes the coefficient-wise cosine. The function MatrixBase::cos() in the
+ * unsupported module MatrixFunctions computes the matrix cosine.
+ *
+ * Example: \include Cwise_cos.cpp
+ * Output: \verbinclude Cwise_cos.out
+ *
+ * \sa <a href="group__CoeffwiseMathFunctions.html#cwisetable_cos">Math functions</a>, sin(), acos()
+ */
+EIGEN_DEVICE_FUNC
+inline const CosReturnType
+cos() const
+{
+ return CosReturnType(derived());
+}
+
+
+/** \returns an expression of the coefficient-wise sine of *this.
+ *
+ * This function computes the coefficient-wise sine. The function MatrixBase::sin() in the
+ * unsupported module MatrixFunctions computes the matrix sine.
+ *
+ * Example: \include Cwise_sin.cpp
+ * Output: \verbinclude Cwise_sin.out
+ *
+ * \sa <a href="group__CoeffwiseMathFunctions.html#cwisetable_sin">Math functions</a>, cos(), asin()
+ */
+EIGEN_DEVICE_FUNC
+inline const SinReturnType
+sin() const
+{
+ return SinReturnType(derived());
+}
+
+/** \returns an expression of the coefficient-wise tan of *this.
+ *
+ * Example: \include Cwise_tan.cpp
+ * Output: \verbinclude Cwise_tan.out
+ *
+ * \sa <a href="group__CoeffwiseMathFunctions.html#cwisetable_tan">Math functions</a>, cos(), sin()
+ */
+EIGEN_DEVICE_FUNC
+inline const TanReturnType
+tan() const
+{
+ return TanReturnType(derived());
+}
+
+/** \returns an expression of the coefficient-wise arc tan of *this.
+ *
+ * Example: \include Cwise_atan.cpp
+ * Output: \verbinclude Cwise_atan.out
+ *
+ * \sa <a href="group__CoeffwiseMathFunctions.html#cwisetable_atan">Math functions</a>, tan(), asin(), acos()
+ */
+EIGEN_DEVICE_FUNC
+inline const AtanReturnType
+atan() const
+{
+ return AtanReturnType(derived());
+}
+
+/** \returns an expression of the coefficient-wise arc cosine of *this.
+ *
+ * Example: \include Cwise_acos.cpp
+ * Output: \verbinclude Cwise_acos.out
+ *
+ * \sa <a href="group__CoeffwiseMathFunctions.html#cwisetable_acos">Math functions</a>, cos(), asin()
+ */
+EIGEN_DEVICE_FUNC
+inline const AcosReturnType
+acos() const
+{
+ return AcosReturnType(derived());
+}
+
+/** \returns an expression of the coefficient-wise arc sine of *this.
+ *
+ * Example: \include Cwise_asin.cpp
+ * Output: \verbinclude Cwise_asin.out
+ *
+ * \sa <a href="group__CoeffwiseMathFunctions.html#cwisetable_asin">Math functions</a>, sin(), acos()
+ */
+EIGEN_DEVICE_FUNC
+inline const AsinReturnType
+asin() const
+{
+ return AsinReturnType(derived());
+}
+
+/** \returns an expression of the coefficient-wise hyperbolic tan of *this.
+ *
+ * Example: \include Cwise_tanh.cpp
+ * Output: \verbinclude Cwise_tanh.out
+ *
+ * \sa <a href="group__CoeffwiseMathFunctions.html#cwisetable_tanh">Math functions</a>, tan(), sinh(), cosh()
+ */
+EIGEN_DEVICE_FUNC
+inline const TanhReturnType
+tanh() const
+{
+ return TanhReturnType(derived());
+}
+
+/** \returns an expression of the coefficient-wise hyperbolic sin of *this.
+ *
+ * Example: \include Cwise_sinh.cpp
+ * Output: \verbinclude Cwise_sinh.out
+ *
+ * \sa <a href="group__CoeffwiseMathFunctions.html#cwisetable_sinh">Math functions</a>, sin(), tanh(), cosh()
+ */
+EIGEN_DEVICE_FUNC
+inline const SinhReturnType
+sinh() const
+{
+ return SinhReturnType(derived());
+}
+
+/** \returns an expression of the coefficient-wise hyperbolic cos of *this.
+ *
+ * Example: \include Cwise_cosh.cpp
+ * Output: \verbinclude Cwise_cosh.out
+ *
+ * \sa <a href="group__CoeffwiseMathFunctions.html#cwisetable_cosh">Math functions</a>, tanh(), sinh(), cosh()
+ */
+EIGEN_DEVICE_FUNC
+inline const CoshReturnType
+cosh() const
+{
+ return CoshReturnType(derived());
+}
+
+/** \returns an expression of the coefficient-wise inverse hyperbolic tan of *this.
+ *
+ * \sa <a href="group__CoeffwiseMathFunctions.html#cwisetable_atanh">Math functions</a>, atanh(), asinh(), acosh()
+ */
+EIGEN_DEVICE_FUNC
+inline const AtanhReturnType
+atanh() const
+{
+ return AtanhReturnType(derived());
+}
+
+/** \returns an expression of the coefficient-wise inverse hyperbolic sin of *this.
+ *
+ * \sa <a href="group__CoeffwiseMathFunctions.html#cwisetable_asinh">Math functions</a>, atanh(), asinh(), acosh()
+ */
+EIGEN_DEVICE_FUNC
+inline const AsinhReturnType
+asinh() const
+{
+ return AsinhReturnType(derived());
+}
+
+/** \returns an expression of the coefficient-wise inverse hyperbolic cos of *this.
+ *
+ * \sa <a href="group__CoeffwiseMathFunctions.html#cwisetable_acosh">Math functions</a>, atanh(), asinh(), acosh()
+ */
+EIGEN_DEVICE_FUNC
+inline const AcoshReturnType
+acosh() const
+{
+ return AcoshReturnType(derived());
+}
+
+/** \returns an expression of the coefficient-wise logistic of *this.
+ */
+EIGEN_DEVICE_FUNC
+inline const LogisticReturnType
+logistic() const
+{
+ return LogisticReturnType(derived());
+}
+
+/** \returns an expression of the coefficient-wise inverse of *this.
+ *
+ * Example: \include Cwise_inverse.cpp
+ * Output: \verbinclude Cwise_inverse.out
+ *
+ * \sa operator/(), operator*()
+ */
+EIGEN_DEVICE_FUNC
+inline const InverseReturnType
+inverse() const
+{
+ return InverseReturnType(derived());
+}
+
+/** \returns an expression of the coefficient-wise square of *this.
+ *
+ * Example: \include Cwise_square.cpp
+ * Output: \verbinclude Cwise_square.out
+ *
+ * \sa <a href="group__CoeffwiseMathFunctions.html#cwisetable_squareE">Math functions</a>, abs2(), cube(), pow()
+ */
+EIGEN_DEVICE_FUNC
+inline const SquareReturnType
+square() const
+{
+ return SquareReturnType(derived());
+}
+
+/** \returns an expression of the coefficient-wise cube of *this.
+ *
+ * Example: \include Cwise_cube.cpp
+ * Output: \verbinclude Cwise_cube.out
+ *
+ * \sa <a href="group__CoeffwiseMathFunctions.html#cwisetable_cube">Math functions</a>, square(), pow()
+ */
+EIGEN_DEVICE_FUNC
+inline const CubeReturnType
+cube() const
+{
+ return CubeReturnType(derived());
+}
+
+/** \returns an expression of the coefficient-wise rint of *this.
+ *
+ * Example: \include Cwise_rint.cpp
+ * Output: \verbinclude Cwise_rint.out
+ *
+ * \sa <a href="group__CoeffwiseMathFunctions.html#cwisetable_rint">Math functions</a>, ceil(), floor()
+ */
+EIGEN_DEVICE_FUNC
+inline const RintReturnType
+rint() const
+{
+ return RintReturnType(derived());
+}
+
+/** \returns an expression of the coefficient-wise round of *this.
+ *
+ * Example: \include Cwise_round.cpp
+ * Output: \verbinclude Cwise_round.out
+ *
+ * \sa <a href="group__CoeffwiseMathFunctions.html#cwisetable_round">Math functions</a>, ceil(), floor()
+ */
+EIGEN_DEVICE_FUNC
+inline const RoundReturnType
+round() const
+{
+ return RoundReturnType(derived());
+}
+
+/** \returns an expression of the coefficient-wise floor of *this.
+ *
+ * Example: \include Cwise_floor.cpp
+ * Output: \verbinclude Cwise_floor.out
+ *
+ * \sa <a href="group__CoeffwiseMathFunctions.html#cwisetable_floor">Math functions</a>, ceil(), round()
+ */
+EIGEN_DEVICE_FUNC
+inline const FloorReturnType
+floor() const
+{
+ return FloorReturnType(derived());
+}
+
+/** \returns an expression of the coefficient-wise ceil of *this.
+ *
+ * Example: \include Cwise_ceil.cpp
+ * Output: \verbinclude Cwise_ceil.out
+ *
+ * \sa <a href="group__CoeffwiseMathFunctions.html#cwisetable_ceil">Math functions</a>, floor(), round()
+ */
+EIGEN_DEVICE_FUNC
+inline const CeilReturnType
+ceil() const
+{
+ return CeilReturnType(derived());
+}
+
+template<int N> struct ShiftRightXpr {
+ typedef CwiseUnaryOp<internal::scalar_shift_right_op<Scalar, N>, const Derived> Type;
+};
+
+/** \returns an expression of \c *this with the \a Scalar type arithmetically
+ * shifted right by \a N bit positions.
+ *
+ * The template parameter \a N specifies the number of bit positions to shift.
+ *
+ * \sa shiftLeft()
+ */
+template<int N>
+EIGEN_DEVICE_FUNC
+typename ShiftRightXpr<N>::Type
+shiftRight() const
+{
+ return typename ShiftRightXpr<N>::Type(derived());
+}
+
+
+template<int N> struct ShiftLeftXpr {
+ typedef CwiseUnaryOp<internal::scalar_shift_left_op<Scalar, N>, const Derived> Type;
+};
+
+/** \returns an expression of \c *this with the \a Scalar type logically
+ * shifted left by \a N bit positions.
+ *
+ * The template parameter \a N specifies the number of bit positions to shift.
+ *
+ * \sa shiftRight()
+ */
+template<int N>
+EIGEN_DEVICE_FUNC
+typename ShiftLeftXpr<N>::Type
+shiftLeft() const
+{
+ return typename ShiftLeftXpr<N>::Type(derived());
+}
+
+/** \returns an expression of the coefficient-wise isnan of *this.
+ *
+ * Example: \include Cwise_isNaN.cpp
+ * Output: \verbinclude Cwise_isNaN.out
+ *
+ * \sa isfinite(), isinf()
+ */
+EIGEN_DEVICE_FUNC
+inline const IsNaNReturnType
+isNaN() const
+{
+ return IsNaNReturnType(derived());
+}
+
+/** \returns an expression of the coefficient-wise isinf of *this.
+ *
+ * Example: \include Cwise_isInf.cpp
+ * Output: \verbinclude Cwise_isInf.out
+ *
+ * \sa isnan(), isfinite()
+ */
+EIGEN_DEVICE_FUNC
+inline const IsInfReturnType
+isInf() const
+{
+ return IsInfReturnType(derived());
+}
+
+/** \returns an expression of the coefficient-wise isfinite of *this.
+ *
+ * Example: \include Cwise_isFinite.cpp
+ * Output: \verbinclude Cwise_isFinite.out
+ *
+ * \sa isnan(), isinf()
+ */
+EIGEN_DEVICE_FUNC
+inline const IsFiniteReturnType
+isFinite() const
+{
+ return IsFiniteReturnType(derived());
+}
+
+/** \returns an expression of the coefficient-wise ! operator of *this
+ *
+ * \warning this operator is for expression of bool only.
+ *
+ * Example: \include Cwise_boolean_not.cpp
+ * Output: \verbinclude Cwise_boolean_not.out
+ *
+ * \sa operator!=()
+ */
+EIGEN_DEVICE_FUNC
+inline const BooleanNotReturnType
+operator!() const
+{
+ EIGEN_STATIC_ASSERT((internal::is_same<bool,Scalar>::value),
+ THIS_METHOD_IS_ONLY_FOR_EXPRESSIONS_OF_BOOL);
+ return BooleanNotReturnType(derived());
+}
+
+
+// --- SpecialFunctions module ---
+
+typedef CwiseUnaryOp<internal::scalar_lgamma_op<Scalar>, const Derived> LgammaReturnType;
+typedef CwiseUnaryOp<internal::scalar_digamma_op<Scalar>, const Derived> DigammaReturnType;
+typedef CwiseUnaryOp<internal::scalar_erf_op<Scalar>, const Derived> ErfReturnType;
+typedef CwiseUnaryOp<internal::scalar_erfc_op<Scalar>, const Derived> ErfcReturnType;
+typedef CwiseUnaryOp<internal::scalar_ndtri_op<Scalar>, const Derived> NdtriReturnType;
+
+/** \cpp11 \returns an expression of the coefficient-wise ln(|gamma(*this)|).
+ *
+ * \specialfunctions_module
+ *
+ * \note This function supports only float and double scalar types in c++11 mode. To support other scalar types,
+ * or float/double in non c++11 mode, the user has to provide implementations of lgamma(T) for any scalar
+ * type T to be supported.
+ *
+ * \sa <a href="group__CoeffwiseMathFunctions.html#cwisetable_lgamma">Math functions</a>, digamma()
+ */
+EIGEN_DEVICE_FUNC
+inline const LgammaReturnType
+lgamma() const
+{
+ return LgammaReturnType(derived());
+}
+
+/** \returns an expression of the coefficient-wise digamma (psi, derivative of lgamma).
+ *
+ * \specialfunctions_module
+ *
+ * \note This function supports only float and double scalar types. To support other scalar types,
+ * the user has to provide implementations of digamma(T) for any scalar
+ * type T to be supported.
+ *
+ * \sa <a href="group__CoeffwiseMathFunctions.html#cwisetable_digamma">Math functions</a>, Eigen::digamma(), Eigen::polygamma(), lgamma()
+ */
+EIGEN_DEVICE_FUNC
+inline const DigammaReturnType
+digamma() const
+{
+ return DigammaReturnType(derived());
+}
+
+/** \cpp11 \returns an expression of the coefficient-wise Gauss error
+ * function of *this.
+ *
+ * \specialfunctions_module
+ *
+ * \note This function supports only float and double scalar types in c++11 mode. To support other scalar types,
+ * or float/double in non c++11 mode, the user has to provide implementations of erf(T) for any scalar
+ * type T to be supported.
+ *
+ * \sa <a href="group__CoeffwiseMathFunctions.html#cwisetable_erf">Math functions</a>, erfc()
+ */
+EIGEN_DEVICE_FUNC
+inline const ErfReturnType
+erf() const
+{
+ return ErfReturnType(derived());
+}
+
+/** \cpp11 \returns an expression of the coefficient-wise Complementary error
+ * function of *this.
+ *
+ * \specialfunctions_module
+ *
+ * \note This function supports only float and double scalar types in c++11 mode. To support other scalar types,
+ * or float/double in non c++11 mode, the user has to provide implementations of erfc(T) for any scalar
+ * type T to be supported.
+ *
+ * \sa <a href="group__CoeffwiseMathFunctions.html#cwisetable_erfc">Math functions</a>, erf()
+ */
+EIGEN_DEVICE_FUNC
+inline const ErfcReturnType
+erfc() const
+{
+ return ErfcReturnType(derived());
+}
+
+/** \returns an expression of the coefficient-wise inverse of the CDF of the Normal distribution function
+ * function of *this.
+ *
+ * \specialfunctions_module
+ *
+ * In other words, considering `x = ndtri(y)`, it returns the argument, x, for which the area under the
+ * Gaussian probability density function (integrated from minus infinity to x) is equal to y.
+ *
+ * \note This function supports only float and double scalar types. To support other scalar types,
+ * the user has to provide implementations of ndtri(T) for any scalar type T to be supported.
+ *
+ * \sa <a href="group__CoeffwiseMathFunctions.html#cwisetable_ndtri">Math functions</a>
+ */
+EIGEN_DEVICE_FUNC
+inline const NdtriReturnType
+ndtri() const
+{
+ return NdtriReturnType(derived());
+}
+
+template <typename ScalarExponent>
+using UnaryPowReturnType =
+ std::enable_if_t<internal::is_arithmetic<typename NumTraits<ScalarExponent>::Real>::value,
+ CwiseUnaryOp<internal::scalar_unary_pow_op<Scalar, ScalarExponent>, const Derived>>;
+
+#ifndef EIGEN_PARSED_BY_DOXYGEN
+template <typename ScalarExponent>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const UnaryPowReturnType<ScalarExponent> pow(
+ const ScalarExponent& exponent) const {
+ return UnaryPowReturnType<ScalarExponent>(derived(), internal::scalar_unary_pow_op<Scalar, ScalarExponent>(exponent));
+#else
+/** \returns an expression of the coefficients of \c *this rasied to the constant power \a exponent
+ *
+ * \tparam T is the scalar type of \a exponent. It must be compatible with the scalar type of the given expression.
+ *
+ * This function computes the coefficient-wise power. The function MatrixBase::pow() in the
+ * unsupported module MatrixFunctions computes the matrix power.
+ *
+ * Example: \include Cwise_pow.cpp
+ * Output: \verbinclude Cwise_pow.out
+ *
+ * \sa ArrayBase::pow(ArrayBase), square(), cube(), exp(), log()
+ */
+template <typename ScalarExponent>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const UnaryPowReturnType<ScalarExponent> pow(
+ const ScalarExponent& exponent) const;
+#endif
+}
diff --git a/Eigen/src/plugins/BlockMethods.h b/Eigen/src/plugins/BlockMethods.h
new file mode 100644
index 0000000..68b9413
--- /dev/null
+++ b/Eigen/src/plugins/BlockMethods.h
@@ -0,0 +1,1442 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2010 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2006-2010 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_PARSED_BY_DOXYGEN
+
+/// \internal expression type of a column */
+typedef Block<Derived, internal::traits<Derived>::RowsAtCompileTime, 1, !IsRowMajor> ColXpr;
+typedef const Block<const Derived, internal::traits<Derived>::RowsAtCompileTime, 1, !IsRowMajor> ConstColXpr;
+/// \internal expression type of a row */
+typedef Block<Derived, 1, internal::traits<Derived>::ColsAtCompileTime, IsRowMajor> RowXpr;
+typedef const Block<const Derived, 1, internal::traits<Derived>::ColsAtCompileTime, IsRowMajor> ConstRowXpr;
+/// \internal expression type of a block of whole columns */
+typedef Block<Derived, internal::traits<Derived>::RowsAtCompileTime, Dynamic, !IsRowMajor> ColsBlockXpr;
+typedef const Block<const Derived, internal::traits<Derived>::RowsAtCompileTime, Dynamic, !IsRowMajor> ConstColsBlockXpr;
+/// \internal expression type of a block of whole rows */
+typedef Block<Derived, Dynamic, internal::traits<Derived>::ColsAtCompileTime, IsRowMajor> RowsBlockXpr;
+typedef const Block<const Derived, Dynamic, internal::traits<Derived>::ColsAtCompileTime, IsRowMajor> ConstRowsBlockXpr;
+/// \internal expression type of a block of whole columns */
+template<int N> struct NColsBlockXpr { typedef Block<Derived, internal::traits<Derived>::RowsAtCompileTime, N, !IsRowMajor> Type; };
+template<int N> struct ConstNColsBlockXpr { typedef const Block<const Derived, internal::traits<Derived>::RowsAtCompileTime, N, !IsRowMajor> Type; };
+/// \internal expression type of a block of whole rows */
+template<int N> struct NRowsBlockXpr { typedef Block<Derived, N, internal::traits<Derived>::ColsAtCompileTime, IsRowMajor> Type; };
+template<int N> struct ConstNRowsBlockXpr { typedef const Block<const Derived, N, internal::traits<Derived>::ColsAtCompileTime, IsRowMajor> Type; };
+/// \internal expression of a block */
+typedef Block<Derived> BlockXpr;
+typedef const Block<const Derived> ConstBlockXpr;
+/// \internal expression of a block of fixed sizes */
+template<int Rows, int Cols> struct FixedBlockXpr { typedef Block<Derived,Rows,Cols> Type; };
+template<int Rows, int Cols> struct ConstFixedBlockXpr { typedef Block<const Derived,Rows,Cols> Type; };
+
+typedef VectorBlock<Derived> SegmentReturnType;
+typedef const VectorBlock<const Derived> ConstSegmentReturnType;
+template<int Size> struct FixedSegmentReturnType { typedef VectorBlock<Derived, Size> Type; };
+template<int Size> struct ConstFixedSegmentReturnType { typedef const VectorBlock<const Derived, Size> Type; };
+
+/// \internal inner-vector
+typedef Block<Derived,IsRowMajor?1:Dynamic,IsRowMajor?Dynamic:1,true> InnerVectorReturnType;
+typedef Block<const Derived,IsRowMajor?1:Dynamic,IsRowMajor?Dynamic:1,true> ConstInnerVectorReturnType;
+
+/// \internal set of inner-vectors
+typedef Block<Derived,Dynamic,Dynamic,true> InnerVectorsReturnType;
+typedef Block<const Derived,Dynamic,Dynamic,true> ConstInnerVectorsReturnType;
+
+#endif // not EIGEN_PARSED_BY_DOXYGEN
+
+/// \returns an expression of a block in \c *this with either dynamic or fixed sizes.
+///
+/// \param startRow the first row in the block
+/// \param startCol the first column in the block
+/// \param blockRows number of rows in the block, specified at either run-time or compile-time
+/// \param blockCols number of columns in the block, specified at either run-time or compile-time
+/// \tparam NRowsType the type of the value handling the number of rows in the block, typically Index.
+/// \tparam NColsType the type of the value handling the number of columns in the block, typically Index.
+///
+/// Example using runtime (aka dynamic) sizes: \include MatrixBase_block_int_int_int_int.cpp
+/// Output: \verbinclude MatrixBase_block_int_int_int_int.out
+///
+/// \newin{3.4}:
+///
+/// The number of rows \a blockRows and columns \a blockCols can also be specified at compile-time by passing Eigen::fix<N>,
+/// or Eigen::fix<N>(n) as arguments. In the later case, \c n plays the role of a runtime fallback value in case \c N equals Eigen::Dynamic.
+/// Here is an example with a fixed number of rows \c NRows and dynamic number of columns \c cols:
+/// \code
+/// mat.block(i,j,fix<NRows>,cols)
+/// \endcode
+///
+/// This function thus fully covers the features offered by the following overloads block<NRows,NCols>(Index, Index),
+/// and block<NRows,NCols>(Index, Index, Index, Index) that are thus obsolete. Indeed, this generic version avoids
+/// redundancy, it preserves the argument order, and prevents the need to rely on the template keyword in templated code.
+///
+/// but with less redundancy and more consistency as it does not modify the argument order
+/// and seamlessly enable hybrid fixed/dynamic sizes.
+///
+/// \note Even in the case that the returned expression has dynamic size, in the case
+/// when it is applied to a fixed-size matrix, it inherits a fixed maximal size,
+/// which means that evaluating it does not cause a dynamic memory allocation.
+///
+EIGEN_DOC_BLOCK_ADDONS_NOT_INNER_PANEL
+///
+/// \sa class Block, fix, fix<N>(int)
+///
+template<typename NRowsType, typename NColsType>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+#ifndef EIGEN_PARSED_BY_DOXYGEN
+typename FixedBlockXpr<internal::get_fixed_value<NRowsType>::value,internal::get_fixed_value<NColsType>::value>::Type
+#else
+typename FixedBlockXpr<...,...>::Type
+#endif
+block(Index startRow, Index startCol, NRowsType blockRows, NColsType blockCols)
+{
+ return typename FixedBlockXpr<internal::get_fixed_value<NRowsType>::value,internal::get_fixed_value<NColsType>::value>::Type(
+ derived(), startRow, startCol, internal::get_runtime_value(blockRows), internal::get_runtime_value(blockCols));
+}
+
+/// This is the const version of block(Index,Index,NRowsType,NColsType)
+template<typename NRowsType, typename NColsType>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+#ifndef EIGEN_PARSED_BY_DOXYGEN
+const typename ConstFixedBlockXpr<internal::get_fixed_value<NRowsType>::value,internal::get_fixed_value<NColsType>::value>::Type
+#else
+const typename ConstFixedBlockXpr<...,...>::Type
+#endif
+block(Index startRow, Index startCol, NRowsType blockRows, NColsType blockCols) const
+{
+ return typename ConstFixedBlockXpr<internal::get_fixed_value<NRowsType>::value,internal::get_fixed_value<NColsType>::value>::Type(
+ derived(), startRow, startCol, internal::get_runtime_value(blockRows), internal::get_runtime_value(blockCols));
+}
+
+
+
+/// \returns a expression of a top-right corner of \c *this with either dynamic or fixed sizes.
+///
+/// \param cRows the number of rows in the corner
+/// \param cCols the number of columns in the corner
+/// \tparam NRowsType the type of the value handling the number of rows in the block, typically Index.
+/// \tparam NColsType the type of the value handling the number of columns in the block, typically Index.
+///
+/// Example with dynamic sizes: \include MatrixBase_topRightCorner_int_int.cpp
+/// Output: \verbinclude MatrixBase_topRightCorner_int_int.out
+///
+/// The number of rows \a blockRows and columns \a blockCols can also be specified at compile-time by passing Eigen::fix<N>,
+/// or Eigen::fix<N>(n) as arguments. See \link block(Index,Index,NRowsType,NColsType) block() \endlink for the details.
+///
+EIGEN_DOC_BLOCK_ADDONS_NOT_INNER_PANEL
+///
+/// \sa block(Index,Index,NRowsType,NColsType), class Block
+///
+template<typename NRowsType, typename NColsType>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+#ifndef EIGEN_PARSED_BY_DOXYGEN
+typename FixedBlockXpr<internal::get_fixed_value<NRowsType>::value,internal::get_fixed_value<NColsType>::value>::Type
+#else
+typename FixedBlockXpr<...,...>::Type
+#endif
+topRightCorner(NRowsType cRows, NColsType cCols)
+{
+ return typename FixedBlockXpr<internal::get_fixed_value<NRowsType>::value,internal::get_fixed_value<NColsType>::value>::Type
+ (derived(), 0, cols() - internal::get_runtime_value(cCols), internal::get_runtime_value(cRows), internal::get_runtime_value(cCols));
+}
+
+/// This is the const version of topRightCorner(NRowsType, NColsType).
+template<typename NRowsType, typename NColsType>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+#ifndef EIGEN_PARSED_BY_DOXYGEN
+const typename ConstFixedBlockXpr<internal::get_fixed_value<NRowsType>::value,internal::get_fixed_value<NColsType>::value>::Type
+#else
+const typename ConstFixedBlockXpr<...,...>::Type
+#endif
+topRightCorner(NRowsType cRows, NColsType cCols) const
+{
+ return typename ConstFixedBlockXpr<internal::get_fixed_value<NRowsType>::value,internal::get_fixed_value<NColsType>::value>::Type
+ (derived(), 0, cols() - internal::get_runtime_value(cCols), internal::get_runtime_value(cRows), internal::get_runtime_value(cCols));
+}
+
+/// \returns an expression of a fixed-size top-right corner of \c *this.
+///
+/// \tparam CRows the number of rows in the corner
+/// \tparam CCols the number of columns in the corner
+///
+/// Example: \include MatrixBase_template_int_int_topRightCorner.cpp
+/// Output: \verbinclude MatrixBase_template_int_int_topRightCorner.out
+///
+EIGEN_DOC_BLOCK_ADDONS_NOT_INNER_PANEL
+///
+/// \sa class Block, block<int,int>(Index,Index)
+///
+template<int CRows, int CCols>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+typename FixedBlockXpr<CRows,CCols>::Type topRightCorner()
+{
+ return typename FixedBlockXpr<CRows,CCols>::Type(derived(), 0, cols() - CCols);
+}
+
+/// This is the const version of topRightCorner<int, int>().
+template<int CRows, int CCols>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+const typename ConstFixedBlockXpr<CRows,CCols>::Type topRightCorner() const
+{
+ return typename ConstFixedBlockXpr<CRows,CCols>::Type(derived(), 0, cols() - CCols);
+}
+
+/// \returns an expression of a top-right corner of \c *this.
+///
+/// \tparam CRows number of rows in corner as specified at compile-time
+/// \tparam CCols number of columns in corner as specified at compile-time
+/// \param cRows number of rows in corner as specified at run-time
+/// \param cCols number of columns in corner as specified at run-time
+///
+/// This function is mainly useful for corners where the number of rows is specified at compile-time
+/// and the number of columns is specified at run-time, or vice versa. The compile-time and run-time
+/// information should not contradict. In other words, \a cRows should equal \a CRows unless
+/// \a CRows is \a Dynamic, and the same for the number of columns.
+///
+/// Example: \include MatrixBase_template_int_int_topRightCorner_int_int.cpp
+/// Output: \verbinclude MatrixBase_template_int_int_topRightCorner_int_int.out
+///
+EIGEN_DOC_BLOCK_ADDONS_NOT_INNER_PANEL
+///
+/// \sa class Block
+///
+template<int CRows, int CCols>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+typename FixedBlockXpr<CRows,CCols>::Type topRightCorner(Index cRows, Index cCols)
+{
+ return typename FixedBlockXpr<CRows,CCols>::Type(derived(), 0, cols() - cCols, cRows, cCols);
+}
+
+/// This is the const version of topRightCorner<int, int>(Index, Index).
+template<int CRows, int CCols>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+const typename ConstFixedBlockXpr<CRows,CCols>::Type topRightCorner(Index cRows, Index cCols) const
+{
+ return typename ConstFixedBlockXpr<CRows,CCols>::Type(derived(), 0, cols() - cCols, cRows, cCols);
+}
+
+
+
+/// \returns an expression of a top-left corner of \c *this with either dynamic or fixed sizes.
+///
+/// \param cRows the number of rows in the corner
+/// \param cCols the number of columns in the corner
+/// \tparam NRowsType the type of the value handling the number of rows in the block, typically Index.
+/// \tparam NColsType the type of the value handling the number of columns in the block, typically Index.
+///
+/// Example: \include MatrixBase_topLeftCorner_int_int.cpp
+/// Output: \verbinclude MatrixBase_topLeftCorner_int_int.out
+///
+/// The number of rows \a blockRows and columns \a blockCols can also be specified at compile-time by passing Eigen::fix<N>,
+/// or Eigen::fix<N>(n) as arguments. See \link block(Index,Index,NRowsType,NColsType) block() \endlink for the details.
+///
+EIGEN_DOC_BLOCK_ADDONS_NOT_INNER_PANEL
+///
+/// \sa block(Index,Index,NRowsType,NColsType), class Block
+///
+template<typename NRowsType, typename NColsType>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+#ifndef EIGEN_PARSED_BY_DOXYGEN
+typename FixedBlockXpr<internal::get_fixed_value<NRowsType>::value,internal::get_fixed_value<NColsType>::value>::Type
+#else
+typename FixedBlockXpr<...,...>::Type
+#endif
+topLeftCorner(NRowsType cRows, NColsType cCols)
+{
+ return typename FixedBlockXpr<internal::get_fixed_value<NRowsType>::value,internal::get_fixed_value<NColsType>::value>::Type
+ (derived(), 0, 0, internal::get_runtime_value(cRows), internal::get_runtime_value(cCols));
+}
+
+/// This is the const version of topLeftCorner(Index, Index).
+template<typename NRowsType, typename NColsType>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+#ifndef EIGEN_PARSED_BY_DOXYGEN
+const typename ConstFixedBlockXpr<internal::get_fixed_value<NRowsType>::value,internal::get_fixed_value<NColsType>::value>::Type
+#else
+const typename ConstFixedBlockXpr<...,...>::Type
+#endif
+topLeftCorner(NRowsType cRows, NColsType cCols) const
+{
+ return typename ConstFixedBlockXpr<internal::get_fixed_value<NRowsType>::value,internal::get_fixed_value<NColsType>::value>::Type
+ (derived(), 0, 0, internal::get_runtime_value(cRows), internal::get_runtime_value(cCols));
+}
+
+/// \returns an expression of a fixed-size top-left corner of \c *this.
+///
+/// The template parameters CRows and CCols are the number of rows and columns in the corner.
+///
+/// Example: \include MatrixBase_template_int_int_topLeftCorner.cpp
+/// Output: \verbinclude MatrixBase_template_int_int_topLeftCorner.out
+///
+EIGEN_DOC_BLOCK_ADDONS_NOT_INNER_PANEL
+///
+/// \sa block(Index,Index,NRowsType,NColsType), class Block
+///
+template<int CRows, int CCols>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+typename FixedBlockXpr<CRows,CCols>::Type topLeftCorner()
+{
+ return typename FixedBlockXpr<CRows,CCols>::Type(derived(), 0, 0);
+}
+
+/// This is the const version of topLeftCorner<int, int>().
+template<int CRows, int CCols>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+const typename ConstFixedBlockXpr<CRows,CCols>::Type topLeftCorner() const
+{
+ return typename ConstFixedBlockXpr<CRows,CCols>::Type(derived(), 0, 0);
+}
+
+/// \returns an expression of a top-left corner of \c *this.
+///
+/// \tparam CRows number of rows in corner as specified at compile-time
+/// \tparam CCols number of columns in corner as specified at compile-time
+/// \param cRows number of rows in corner as specified at run-time
+/// \param cCols number of columns in corner as specified at run-time
+///
+/// This function is mainly useful for corners where the number of rows is specified at compile-time
+/// and the number of columns is specified at run-time, or vice versa. The compile-time and run-time
+/// information should not contradict. In other words, \a cRows should equal \a CRows unless
+/// \a CRows is \a Dynamic, and the same for the number of columns.
+///
+/// Example: \include MatrixBase_template_int_int_topLeftCorner_int_int.cpp
+/// Output: \verbinclude MatrixBase_template_int_int_topLeftCorner_int_int.out
+///
+EIGEN_DOC_BLOCK_ADDONS_NOT_INNER_PANEL
+///
+/// \sa class Block
+///
+template<int CRows, int CCols>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+typename FixedBlockXpr<CRows,CCols>::Type topLeftCorner(Index cRows, Index cCols)
+{
+ return typename FixedBlockXpr<CRows,CCols>::Type(derived(), 0, 0, cRows, cCols);
+}
+
+/// This is the const version of topLeftCorner<int, int>(Index, Index).
+template<int CRows, int CCols>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+const typename ConstFixedBlockXpr<CRows,CCols>::Type topLeftCorner(Index cRows, Index cCols) const
+{
+ return typename ConstFixedBlockXpr<CRows,CCols>::Type(derived(), 0, 0, cRows, cCols);
+}
+
+
+
+/// \returns an expression of a bottom-right corner of \c *this with either dynamic or fixed sizes.
+///
+/// \param cRows the number of rows in the corner
+/// \param cCols the number of columns in the corner
+/// \tparam NRowsType the type of the value handling the number of rows in the block, typically Index.
+/// \tparam NColsType the type of the value handling the number of columns in the block, typically Index.
+///
+/// Example: \include MatrixBase_bottomRightCorner_int_int.cpp
+/// Output: \verbinclude MatrixBase_bottomRightCorner_int_int.out
+///
+/// The number of rows \a blockRows and columns \a blockCols can also be specified at compile-time by passing Eigen::fix<N>,
+/// or Eigen::fix<N>(n) as arguments. See \link block(Index,Index,NRowsType,NColsType) block() \endlink for the details.
+///
+EIGEN_DOC_BLOCK_ADDONS_NOT_INNER_PANEL
+///
+/// \sa block(Index,Index,NRowsType,NColsType), class Block
+///
+template<typename NRowsType, typename NColsType>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+#ifndef EIGEN_PARSED_BY_DOXYGEN
+typename FixedBlockXpr<internal::get_fixed_value<NRowsType>::value,internal::get_fixed_value<NColsType>::value>::Type
+#else
+typename FixedBlockXpr<...,...>::Type
+#endif
+bottomRightCorner(NRowsType cRows, NColsType cCols)
+{
+ return typename FixedBlockXpr<internal::get_fixed_value<NRowsType>::value,internal::get_fixed_value<NColsType>::value>::Type
+ (derived(), rows() - internal::get_runtime_value(cRows), cols() - internal::get_runtime_value(cCols),
+ internal::get_runtime_value(cRows), internal::get_runtime_value(cCols));
+}
+
+/// This is the const version of bottomRightCorner(NRowsType, NColsType).
+template<typename NRowsType, typename NColsType>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+#ifndef EIGEN_PARSED_BY_DOXYGEN
+const typename ConstFixedBlockXpr<internal::get_fixed_value<NRowsType>::value,internal::get_fixed_value<NColsType>::value>::Type
+#else
+const typename ConstFixedBlockXpr<...,...>::Type
+#endif
+bottomRightCorner(NRowsType cRows, NColsType cCols) const
+{
+ return typename ConstFixedBlockXpr<internal::get_fixed_value<NRowsType>::value,internal::get_fixed_value<NColsType>::value>::Type
+ (derived(), rows() - internal::get_runtime_value(cRows), cols() - internal::get_runtime_value(cCols),
+ internal::get_runtime_value(cRows), internal::get_runtime_value(cCols));
+}
+
+/// \returns an expression of a fixed-size bottom-right corner of \c *this.
+///
+/// The template parameters CRows and CCols are the number of rows and columns in the corner.
+///
+/// Example: \include MatrixBase_template_int_int_bottomRightCorner.cpp
+/// Output: \verbinclude MatrixBase_template_int_int_bottomRightCorner.out
+///
+EIGEN_DOC_BLOCK_ADDONS_NOT_INNER_PANEL
+///
+/// \sa block(Index,Index,NRowsType,NColsType), class Block
+///
+template<int CRows, int CCols>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+typename FixedBlockXpr<CRows,CCols>::Type bottomRightCorner()
+{
+ return typename FixedBlockXpr<CRows,CCols>::Type(derived(), rows() - CRows, cols() - CCols);
+}
+
+/// This is the const version of bottomRightCorner<int, int>().
+template<int CRows, int CCols>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+const typename ConstFixedBlockXpr<CRows,CCols>::Type bottomRightCorner() const
+{
+ return typename ConstFixedBlockXpr<CRows,CCols>::Type(derived(), rows() - CRows, cols() - CCols);
+}
+
+/// \returns an expression of a bottom-right corner of \c *this.
+///
+/// \tparam CRows number of rows in corner as specified at compile-time
+/// \tparam CCols number of columns in corner as specified at compile-time
+/// \param cRows number of rows in corner as specified at run-time
+/// \param cCols number of columns in corner as specified at run-time
+///
+/// This function is mainly useful for corners where the number of rows is specified at compile-time
+/// and the number of columns is specified at run-time, or vice versa. The compile-time and run-time
+/// information should not contradict. In other words, \a cRows should equal \a CRows unless
+/// \a CRows is \a Dynamic, and the same for the number of columns.
+///
+/// Example: \include MatrixBase_template_int_int_bottomRightCorner_int_int.cpp
+/// Output: \verbinclude MatrixBase_template_int_int_bottomRightCorner_int_int.out
+///
+EIGEN_DOC_BLOCK_ADDONS_NOT_INNER_PANEL
+///
+/// \sa class Block
+///
+template<int CRows, int CCols>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+typename FixedBlockXpr<CRows,CCols>::Type bottomRightCorner(Index cRows, Index cCols)
+{
+ return typename FixedBlockXpr<CRows,CCols>::Type(derived(), rows() - cRows, cols() - cCols, cRows, cCols);
+}
+
+/// This is the const version of bottomRightCorner<int, int>(Index, Index).
+template<int CRows, int CCols>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+const typename ConstFixedBlockXpr<CRows,CCols>::Type bottomRightCorner(Index cRows, Index cCols) const
+{
+ return typename ConstFixedBlockXpr<CRows,CCols>::Type(derived(), rows() - cRows, cols() - cCols, cRows, cCols);
+}
+
+
+
+/// \returns an expression of a bottom-left corner of \c *this with either dynamic or fixed sizes.
+///
+/// \param cRows the number of rows in the corner
+/// \param cCols the number of columns in the corner
+/// \tparam NRowsType the type of the value handling the number of rows in the block, typically Index.
+/// \tparam NColsType the type of the value handling the number of columns in the block, typically Index.
+///
+/// Example: \include MatrixBase_bottomLeftCorner_int_int.cpp
+/// Output: \verbinclude MatrixBase_bottomLeftCorner_int_int.out
+///
+/// The number of rows \a blockRows and columns \a blockCols can also be specified at compile-time by passing Eigen::fix<N>,
+/// or Eigen::fix<N>(n) as arguments. See \link block(Index,Index,NRowsType,NColsType) block() \endlink for the details.
+///
+EIGEN_DOC_BLOCK_ADDONS_NOT_INNER_PANEL
+///
+/// \sa block(Index,Index,NRowsType,NColsType), class Block
+///
+template<typename NRowsType, typename NColsType>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+#ifndef EIGEN_PARSED_BY_DOXYGEN
+typename FixedBlockXpr<internal::get_fixed_value<NRowsType>::value,internal::get_fixed_value<NColsType>::value>::Type
+#else
+typename FixedBlockXpr<...,...>::Type
+#endif
+bottomLeftCorner(NRowsType cRows, NColsType cCols)
+{
+ return typename FixedBlockXpr<internal::get_fixed_value<NRowsType>::value,internal::get_fixed_value<NColsType>::value>::Type
+ (derived(), rows() - internal::get_runtime_value(cRows), 0,
+ internal::get_runtime_value(cRows), internal::get_runtime_value(cCols));
+}
+
+/// This is the const version of bottomLeftCorner(NRowsType, NColsType).
+template<typename NRowsType, typename NColsType>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+#ifndef EIGEN_PARSED_BY_DOXYGEN
+typename ConstFixedBlockXpr<internal::get_fixed_value<NRowsType>::value,internal::get_fixed_value<NColsType>::value>::Type
+#else
+typename ConstFixedBlockXpr<...,...>::Type
+#endif
+bottomLeftCorner(NRowsType cRows, NColsType cCols) const
+{
+ return typename ConstFixedBlockXpr<internal::get_fixed_value<NRowsType>::value,internal::get_fixed_value<NColsType>::value>::Type
+ (derived(), rows() - internal::get_runtime_value(cRows), 0,
+ internal::get_runtime_value(cRows), internal::get_runtime_value(cCols));
+}
+
+/// \returns an expression of a fixed-size bottom-left corner of \c *this.
+///
+/// The template parameters CRows and CCols are the number of rows and columns in the corner.
+///
+/// Example: \include MatrixBase_template_int_int_bottomLeftCorner.cpp
+/// Output: \verbinclude MatrixBase_template_int_int_bottomLeftCorner.out
+///
+EIGEN_DOC_BLOCK_ADDONS_NOT_INNER_PANEL
+///
+/// \sa block(Index,Index,NRowsType,NColsType), class Block
+///
+template<int CRows, int CCols>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+typename FixedBlockXpr<CRows,CCols>::Type bottomLeftCorner()
+{
+ return typename FixedBlockXpr<CRows,CCols>::Type(derived(), rows() - CRows, 0);
+}
+
+/// This is the const version of bottomLeftCorner<int, int>().
+template<int CRows, int CCols>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+const typename ConstFixedBlockXpr<CRows,CCols>::Type bottomLeftCorner() const
+{
+ return typename ConstFixedBlockXpr<CRows,CCols>::Type(derived(), rows() - CRows, 0);
+}
+
+/// \returns an expression of a bottom-left corner of \c *this.
+///
+/// \tparam CRows number of rows in corner as specified at compile-time
+/// \tparam CCols number of columns in corner as specified at compile-time
+/// \param cRows number of rows in corner as specified at run-time
+/// \param cCols number of columns in corner as specified at run-time
+///
+/// This function is mainly useful for corners where the number of rows is specified at compile-time
+/// and the number of columns is specified at run-time, or vice versa. The compile-time and run-time
+/// information should not contradict. In other words, \a cRows should equal \a CRows unless
+/// \a CRows is \a Dynamic, and the same for the number of columns.
+///
+/// Example: \include MatrixBase_template_int_int_bottomLeftCorner_int_int.cpp
+/// Output: \verbinclude MatrixBase_template_int_int_bottomLeftCorner_int_int.out
+///
+EIGEN_DOC_BLOCK_ADDONS_NOT_INNER_PANEL
+///
+/// \sa class Block
+///
+template<int CRows, int CCols>
+EIGEN_STRONG_INLINE
+typename FixedBlockXpr<CRows,CCols>::Type bottomLeftCorner(Index cRows, Index cCols)
+{
+ return typename FixedBlockXpr<CRows,CCols>::Type(derived(), rows() - cRows, 0, cRows, cCols);
+}
+
+/// This is the const version of bottomLeftCorner<int, int>(Index, Index).
+template<int CRows, int CCols>
+EIGEN_STRONG_INLINE
+const typename ConstFixedBlockXpr<CRows,CCols>::Type bottomLeftCorner(Index cRows, Index cCols) const
+{
+ return typename ConstFixedBlockXpr<CRows,CCols>::Type(derived(), rows() - cRows, 0, cRows, cCols);
+}
+
+
+
+/// \returns a block consisting of the top rows of \c *this.
+///
+/// \param n the number of rows in the block
+/// \tparam NRowsType the type of the value handling the number of rows in the block, typically Index.
+///
+/// Example: \include MatrixBase_topRows_int.cpp
+/// Output: \verbinclude MatrixBase_topRows_int.out
+///
+/// The number of rows \a n can also be specified at compile-time by passing Eigen::fix<N>,
+/// or Eigen::fix<N>(n) as arguments.
+/// See \link block(Index,Index,NRowsType,NColsType) block() \endlink for the details.
+///
+EIGEN_DOC_BLOCK_ADDONS_INNER_PANEL_IF(row-major)
+///
+/// \sa block(Index,Index,NRowsType,NColsType), class Block
+///
+template<typename NRowsType>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+#ifndef EIGEN_PARSED_BY_DOXYGEN
+typename NRowsBlockXpr<internal::get_fixed_value<NRowsType>::value>::Type
+#else
+typename NRowsBlockXpr<...>::Type
+#endif
+topRows(NRowsType n)
+{
+ return typename NRowsBlockXpr<internal::get_fixed_value<NRowsType>::value>::Type
+ (derived(), 0, 0, internal::get_runtime_value(n), cols());
+}
+
+/// This is the const version of topRows(NRowsType).
+template<typename NRowsType>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+#ifndef EIGEN_PARSED_BY_DOXYGEN
+const typename ConstNRowsBlockXpr<internal::get_fixed_value<NRowsType>::value>::Type
+#else
+const typename ConstNRowsBlockXpr<...>::Type
+#endif
+topRows(NRowsType n) const
+{
+ return typename ConstNRowsBlockXpr<internal::get_fixed_value<NRowsType>::value>::Type
+ (derived(), 0, 0, internal::get_runtime_value(n), cols());
+}
+
+/// \returns a block consisting of the top rows of \c *this.
+///
+/// \tparam N the number of rows in the block as specified at compile-time
+/// \param n the number of rows in the block as specified at run-time
+///
+/// The compile-time and run-time information should not contradict. In other words,
+/// \a n should equal \a N unless \a N is \a Dynamic.
+///
+/// Example: \include MatrixBase_template_int_topRows.cpp
+/// Output: \verbinclude MatrixBase_template_int_topRows.out
+///
+EIGEN_DOC_BLOCK_ADDONS_INNER_PANEL_IF(row-major)
+///
+/// \sa block(Index,Index,NRowsType,NColsType), class Block
+///
+template<int N>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+typename NRowsBlockXpr<N>::Type topRows(Index n = N)
+{
+ return typename NRowsBlockXpr<N>::Type(derived(), 0, 0, n, cols());
+}
+
+/// This is the const version of topRows<int>().
+template<int N>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+typename ConstNRowsBlockXpr<N>::Type topRows(Index n = N) const
+{
+ return typename ConstNRowsBlockXpr<N>::Type(derived(), 0, 0, n, cols());
+}
+
+
+
+/// \returns a block consisting of the bottom rows of \c *this.
+///
+/// \param n the number of rows in the block
+/// \tparam NRowsType the type of the value handling the number of rows in the block, typically Index.
+///
+/// Example: \include MatrixBase_bottomRows_int.cpp
+/// Output: \verbinclude MatrixBase_bottomRows_int.out
+///
+/// The number of rows \a n can also be specified at compile-time by passing Eigen::fix<N>,
+/// or Eigen::fix<N>(n) as arguments.
+/// See \link block(Index,Index,NRowsType,NColsType) block() \endlink for the details.
+///
+EIGEN_DOC_BLOCK_ADDONS_INNER_PANEL_IF(row-major)
+///
+/// \sa block(Index,Index,NRowsType,NColsType), class Block
+///
+template<typename NRowsType>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+#ifndef EIGEN_PARSED_BY_DOXYGEN
+typename NRowsBlockXpr<internal::get_fixed_value<NRowsType>::value>::Type
+#else
+typename NRowsBlockXpr<...>::Type
+#endif
+bottomRows(NRowsType n)
+{
+ return typename NRowsBlockXpr<internal::get_fixed_value<NRowsType>::value>::Type
+ (derived(), rows() - internal::get_runtime_value(n), 0, internal::get_runtime_value(n), cols());
+}
+
+/// This is the const version of bottomRows(NRowsType).
+template<typename NRowsType>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+#ifndef EIGEN_PARSED_BY_DOXYGEN
+const typename ConstNRowsBlockXpr<internal::get_fixed_value<NRowsType>::value>::Type
+#else
+const typename ConstNRowsBlockXpr<...>::Type
+#endif
+bottomRows(NRowsType n) const
+{
+ return typename ConstNRowsBlockXpr<internal::get_fixed_value<NRowsType>::value>::Type
+ (derived(), rows() - internal::get_runtime_value(n), 0, internal::get_runtime_value(n), cols());
+}
+
+/// \returns a block consisting of the bottom rows of \c *this.
+///
+/// \tparam N the number of rows in the block as specified at compile-time
+/// \param n the number of rows in the block as specified at run-time
+///
+/// The compile-time and run-time information should not contradict. In other words,
+/// \a n should equal \a N unless \a N is \a Dynamic.
+///
+/// Example: \include MatrixBase_template_int_bottomRows.cpp
+/// Output: \verbinclude MatrixBase_template_int_bottomRows.out
+///
+EIGEN_DOC_BLOCK_ADDONS_INNER_PANEL_IF(row-major)
+///
+/// \sa block(Index,Index,NRowsType,NColsType), class Block
+///
+template<int N>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+typename NRowsBlockXpr<N>::Type bottomRows(Index n = N)
+{
+ return typename NRowsBlockXpr<N>::Type(derived(), rows() - n, 0, n, cols());
+}
+
+/// This is the const version of bottomRows<int>().
+template<int N>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+typename ConstNRowsBlockXpr<N>::Type bottomRows(Index n = N) const
+{
+ return typename ConstNRowsBlockXpr<N>::Type(derived(), rows() - n, 0, n, cols());
+}
+
+
+
+/// \returns a block consisting of a range of rows of \c *this.
+///
+/// \param startRow the index of the first row in the block
+/// \param n the number of rows in the block
+/// \tparam NRowsType the type of the value handling the number of rows in the block, typically Index.
+///
+/// Example: \include DenseBase_middleRows_int.cpp
+/// Output: \verbinclude DenseBase_middleRows_int.out
+///
+/// The number of rows \a n can also be specified at compile-time by passing Eigen::fix<N>,
+/// or Eigen::fix<N>(n) as arguments.
+/// See \link block(Index,Index,NRowsType,NColsType) block() \endlink for the details.
+///
+EIGEN_DOC_BLOCK_ADDONS_INNER_PANEL_IF(row-major)
+///
+/// \sa block(Index,Index,NRowsType,NColsType), class Block
+///
+template<typename NRowsType>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+#ifndef EIGEN_PARSED_BY_DOXYGEN
+typename NRowsBlockXpr<internal::get_fixed_value<NRowsType>::value>::Type
+#else
+typename NRowsBlockXpr<...>::Type
+#endif
+middleRows(Index startRow, NRowsType n)
+{
+ return typename NRowsBlockXpr<internal::get_fixed_value<NRowsType>::value>::Type
+ (derived(), startRow, 0, internal::get_runtime_value(n), cols());
+}
+
+/// This is the const version of middleRows(Index,NRowsType).
+template<typename NRowsType>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+#ifndef EIGEN_PARSED_BY_DOXYGEN
+const typename ConstNRowsBlockXpr<internal::get_fixed_value<NRowsType>::value>::Type
+#else
+const typename ConstNRowsBlockXpr<...>::Type
+#endif
+middleRows(Index startRow, NRowsType n) const
+{
+ return typename ConstNRowsBlockXpr<internal::get_fixed_value<NRowsType>::value>::Type
+ (derived(), startRow, 0, internal::get_runtime_value(n), cols());
+}
+
+/// \returns a block consisting of a range of rows of \c *this.
+///
+/// \tparam N the number of rows in the block as specified at compile-time
+/// \param startRow the index of the first row in the block
+/// \param n the number of rows in the block as specified at run-time
+///
+/// The compile-time and run-time information should not contradict. In other words,
+/// \a n should equal \a N unless \a N is \a Dynamic.
+///
+/// Example: \include DenseBase_template_int_middleRows.cpp
+/// Output: \verbinclude DenseBase_template_int_middleRows.out
+///
+EIGEN_DOC_BLOCK_ADDONS_INNER_PANEL_IF(row-major)
+///
+/// \sa block(Index,Index,NRowsType,NColsType), class Block
+///
+template<int N>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+typename NRowsBlockXpr<N>::Type middleRows(Index startRow, Index n = N)
+{
+ return typename NRowsBlockXpr<N>::Type(derived(), startRow, 0, n, cols());
+}
+
+/// This is the const version of middleRows<int>().
+template<int N>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+typename ConstNRowsBlockXpr<N>::Type middleRows(Index startRow, Index n = N) const
+{
+ return typename ConstNRowsBlockXpr<N>::Type(derived(), startRow, 0, n, cols());
+}
+
+
+
+/// \returns a block consisting of the left columns of \c *this.
+///
+/// \param n the number of columns in the block
+/// \tparam NColsType the type of the value handling the number of columns in the block, typically Index.
+///
+/// Example: \include MatrixBase_leftCols_int.cpp
+/// Output: \verbinclude MatrixBase_leftCols_int.out
+///
+/// The number of columns \a n can also be specified at compile-time by passing Eigen::fix<N>,
+/// or Eigen::fix<N>(n) as arguments.
+/// See \link block(Index,Index,NRowsType,NColsType) block() \endlink for the details.
+///
+EIGEN_DOC_BLOCK_ADDONS_INNER_PANEL_IF(column-major)
+///
+/// \sa block(Index,Index,NRowsType,NColsType), class Block
+///
+template<typename NColsType>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+#ifndef EIGEN_PARSED_BY_DOXYGEN
+typename NColsBlockXpr<internal::get_fixed_value<NColsType>::value>::Type
+#else
+typename NColsBlockXpr<...>::Type
+#endif
+leftCols(NColsType n)
+{
+ return typename NColsBlockXpr<internal::get_fixed_value<NColsType>::value>::Type
+ (derived(), 0, 0, rows(), internal::get_runtime_value(n));
+}
+
+/// This is the const version of leftCols(NColsType).
+template<typename NColsType>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+#ifndef EIGEN_PARSED_BY_DOXYGEN
+const typename ConstNColsBlockXpr<internal::get_fixed_value<NColsType>::value>::Type
+#else
+const typename ConstNColsBlockXpr<...>::Type
+#endif
+leftCols(NColsType n) const
+{
+ return typename ConstNColsBlockXpr<internal::get_fixed_value<NColsType>::value>::Type
+ (derived(), 0, 0, rows(), internal::get_runtime_value(n));
+}
+
+/// \returns a block consisting of the left columns of \c *this.
+///
+/// \tparam N the number of columns in the block as specified at compile-time
+/// \param n the number of columns in the block as specified at run-time
+///
+/// The compile-time and run-time information should not contradict. In other words,
+/// \a n should equal \a N unless \a N is \a Dynamic.
+///
+/// Example: \include MatrixBase_template_int_leftCols.cpp
+/// Output: \verbinclude MatrixBase_template_int_leftCols.out
+///
+EIGEN_DOC_BLOCK_ADDONS_INNER_PANEL_IF(column-major)
+///
+/// \sa block(Index,Index,NRowsType,NColsType), class Block
+///
+template<int N>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+typename NColsBlockXpr<N>::Type leftCols(Index n = N)
+{
+ return typename NColsBlockXpr<N>::Type(derived(), 0, 0, rows(), n);
+}
+
+/// This is the const version of leftCols<int>().
+template<int N>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+typename ConstNColsBlockXpr<N>::Type leftCols(Index n = N) const
+{
+ return typename ConstNColsBlockXpr<N>::Type(derived(), 0, 0, rows(), n);
+}
+
+
+
+/// \returns a block consisting of the right columns of \c *this.
+///
+/// \param n the number of columns in the block
+/// \tparam NColsType the type of the value handling the number of columns in the block, typically Index.
+///
+/// Example: \include MatrixBase_rightCols_int.cpp
+/// Output: \verbinclude MatrixBase_rightCols_int.out
+///
+/// The number of columns \a n can also be specified at compile-time by passing Eigen::fix<N>,
+/// or Eigen::fix<N>(n) as arguments.
+/// See \link block(Index,Index,NRowsType,NColsType) block() \endlink for the details.
+///
+EIGEN_DOC_BLOCK_ADDONS_INNER_PANEL_IF(column-major)
+///
+/// \sa block(Index,Index,NRowsType,NColsType), class Block
+///
+template<typename NColsType>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+#ifndef EIGEN_PARSED_BY_DOXYGEN
+typename NColsBlockXpr<internal::get_fixed_value<NColsType>::value>::Type
+#else
+typename NColsBlockXpr<...>::Type
+#endif
+rightCols(NColsType n)
+{
+ return typename NColsBlockXpr<internal::get_fixed_value<NColsType>::value>::Type
+ (derived(), 0, cols() - internal::get_runtime_value(n), rows(), internal::get_runtime_value(n));
+}
+
+/// This is the const version of rightCols(NColsType).
+template<typename NColsType>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+#ifndef EIGEN_PARSED_BY_DOXYGEN
+const typename ConstNColsBlockXpr<internal::get_fixed_value<NColsType>::value>::Type
+#else
+const typename ConstNColsBlockXpr<...>::Type
+#endif
+rightCols(NColsType n) const
+{
+ return typename ConstNColsBlockXpr<internal::get_fixed_value<NColsType>::value>::Type
+ (derived(), 0, cols() - internal::get_runtime_value(n), rows(), internal::get_runtime_value(n));
+}
+
+/// \returns a block consisting of the right columns of \c *this.
+///
+/// \tparam N the number of columns in the block as specified at compile-time
+/// \param n the number of columns in the block as specified at run-time
+///
+/// The compile-time and run-time information should not contradict. In other words,
+/// \a n should equal \a N unless \a N is \a Dynamic.
+///
+/// Example: \include MatrixBase_template_int_rightCols.cpp
+/// Output: \verbinclude MatrixBase_template_int_rightCols.out
+///
+EIGEN_DOC_BLOCK_ADDONS_INNER_PANEL_IF(column-major)
+///
+/// \sa block(Index,Index,NRowsType,NColsType), class Block
+///
+template<int N>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+typename NColsBlockXpr<N>::Type rightCols(Index n = N)
+{
+ return typename NColsBlockXpr<N>::Type(derived(), 0, cols() - n, rows(), n);
+}
+
+/// This is the const version of rightCols<int>().
+template<int N>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+typename ConstNColsBlockXpr<N>::Type rightCols(Index n = N) const
+{
+ return typename ConstNColsBlockXpr<N>::Type(derived(), 0, cols() - n, rows(), n);
+}
+
+
+
+/// \returns a block consisting of a range of columns of \c *this.
+///
+/// \param startCol the index of the first column in the block
+/// \param numCols the number of columns in the block
+/// \tparam NColsType the type of the value handling the number of columns in the block, typically Index.
+///
+/// Example: \include DenseBase_middleCols_int.cpp
+/// Output: \verbinclude DenseBase_middleCols_int.out
+///
+/// The number of columns \a n can also be specified at compile-time by passing Eigen::fix<N>,
+/// or Eigen::fix<N>(n) as arguments.
+/// See \link block(Index,Index,NRowsType,NColsType) block() \endlink for the details.
+///
+EIGEN_DOC_BLOCK_ADDONS_INNER_PANEL_IF(column-major)
+///
+/// \sa block(Index,Index,NRowsType,NColsType), class Block
+///
+template<typename NColsType>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+#ifndef EIGEN_PARSED_BY_DOXYGEN
+typename NColsBlockXpr<internal::get_fixed_value<NColsType>::value>::Type
+#else
+typename NColsBlockXpr<...>::Type
+#endif
+middleCols(Index startCol, NColsType numCols)
+{
+ return typename NColsBlockXpr<internal::get_fixed_value<NColsType>::value>::Type
+ (derived(), 0, startCol, rows(), internal::get_runtime_value(numCols));
+}
+
+/// This is the const version of middleCols(Index,NColsType).
+template<typename NColsType>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+#ifndef EIGEN_PARSED_BY_DOXYGEN
+const typename ConstNColsBlockXpr<internal::get_fixed_value<NColsType>::value>::Type
+#else
+const typename ConstNColsBlockXpr<...>::Type
+#endif
+middleCols(Index startCol, NColsType numCols) const
+{
+ return typename ConstNColsBlockXpr<internal::get_fixed_value<NColsType>::value>::Type
+ (derived(), 0, startCol, rows(), internal::get_runtime_value(numCols));
+}
+
+/// \returns a block consisting of a range of columns of \c *this.
+///
+/// \tparam N the number of columns in the block as specified at compile-time
+/// \param startCol the index of the first column in the block
+/// \param n the number of columns in the block as specified at run-time
+///
+/// The compile-time and run-time information should not contradict. In other words,
+/// \a n should equal \a N unless \a N is \a Dynamic.
+///
+/// Example: \include DenseBase_template_int_middleCols.cpp
+/// Output: \verbinclude DenseBase_template_int_middleCols.out
+///
+EIGEN_DOC_BLOCK_ADDONS_INNER_PANEL_IF(column-major)
+///
+/// \sa block(Index,Index,NRowsType,NColsType), class Block
+///
+template<int N>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+typename NColsBlockXpr<N>::Type middleCols(Index startCol, Index n = N)
+{
+ return typename NColsBlockXpr<N>::Type(derived(), 0, startCol, rows(), n);
+}
+
+/// This is the const version of middleCols<int>().
+template<int N>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+typename ConstNColsBlockXpr<N>::Type middleCols(Index startCol, Index n = N) const
+{
+ return typename ConstNColsBlockXpr<N>::Type(derived(), 0, startCol, rows(), n);
+}
+
+
+
+/// \returns a fixed-size expression of a block of \c *this.
+///
+/// The template parameters \a NRows and \a NCols are the number of
+/// rows and columns in the block.
+///
+/// \param startRow the first row in the block
+/// \param startCol the first column in the block
+///
+/// Example: \include MatrixBase_block_int_int.cpp
+/// Output: \verbinclude MatrixBase_block_int_int.out
+///
+/// \note The usage of of this overload is discouraged from %Eigen 3.4, better used the generic
+/// block(Index,Index,NRowsType,NColsType), here is the one-to-one equivalence:
+/// \code
+/// mat.template block<NRows,NCols>(i,j) <--> mat.block(i,j,fix<NRows>,fix<NCols>)
+/// \endcode
+///
+/// \note since block is a templated member, the keyword template has to be used
+/// if the matrix type is also a template parameter: \code m.template block<3,3>(1,1); \endcode
+///
+EIGEN_DOC_BLOCK_ADDONS_NOT_INNER_PANEL
+///
+/// \sa block(Index,Index,NRowsType,NColsType), class Block
+///
+template<int NRows, int NCols>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+typename FixedBlockXpr<NRows,NCols>::Type block(Index startRow, Index startCol)
+{
+ return typename FixedBlockXpr<NRows,NCols>::Type(derived(), startRow, startCol);
+}
+
+/// This is the const version of block<>(Index, Index). */
+template<int NRows, int NCols>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+const typename ConstFixedBlockXpr<NRows,NCols>::Type block(Index startRow, Index startCol) const
+{
+ return typename ConstFixedBlockXpr<NRows,NCols>::Type(derived(), startRow, startCol);
+}
+
+/// \returns an expression of a block of \c *this.
+///
+/// \tparam NRows number of rows in block as specified at compile-time
+/// \tparam NCols number of columns in block as specified at compile-time
+/// \param startRow the first row in the block
+/// \param startCol the first column in the block
+/// \param blockRows number of rows in block as specified at run-time
+/// \param blockCols number of columns in block as specified at run-time
+///
+/// This function is mainly useful for blocks where the number of rows is specified at compile-time
+/// and the number of columns is specified at run-time, or vice versa. The compile-time and run-time
+/// information should not contradict. In other words, \a blockRows should equal \a NRows unless
+/// \a NRows is \a Dynamic, and the same for the number of columns.
+///
+/// Example: \include MatrixBase_template_int_int_block_int_int_int_int.cpp
+/// Output: \verbinclude MatrixBase_template_int_int_block_int_int_int_int.out
+///
+/// \note The usage of of this overload is discouraged from %Eigen 3.4, better used the generic
+/// block(Index,Index,NRowsType,NColsType), here is the one-to-one complete equivalence:
+/// \code
+/// mat.template block<NRows,NCols>(i,j,rows,cols) <--> mat.block(i,j,fix<NRows>(rows),fix<NCols>(cols))
+/// \endcode
+/// If we known that, e.g., NRows==Dynamic and NCols!=Dynamic, then the equivalence becomes:
+/// \code
+/// mat.template block<Dynamic,NCols>(i,j,rows,NCols) <--> mat.block(i,j,rows,fix<NCols>)
+/// \endcode
+///
+EIGEN_DOC_BLOCK_ADDONS_NOT_INNER_PANEL
+///
+/// \sa block(Index,Index,NRowsType,NColsType), class Block
+///
+template<int NRows, int NCols>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+typename FixedBlockXpr<NRows,NCols>::Type block(Index startRow, Index startCol,
+ Index blockRows, Index blockCols)
+{
+ return typename FixedBlockXpr<NRows,NCols>::Type(derived(), startRow, startCol, blockRows, blockCols);
+}
+
+/// This is the const version of block<>(Index, Index, Index, Index).
+template<int NRows, int NCols>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+const typename ConstFixedBlockXpr<NRows,NCols>::Type block(Index startRow, Index startCol,
+ Index blockRows, Index blockCols) const
+{
+ return typename ConstFixedBlockXpr<NRows,NCols>::Type(derived(), startRow, startCol, blockRows, blockCols);
+}
+
+/// \returns an expression of the \a i-th column of \c *this. Note that the numbering starts at 0.
+///
+/// Example: \include MatrixBase_col.cpp
+/// Output: \verbinclude MatrixBase_col.out
+///
+EIGEN_DOC_BLOCK_ADDONS_INNER_PANEL_IF(column-major)
+/**
+ * \sa row(), class Block */
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ColXpr col(Index i)
+{
+ return ColXpr(derived(), i);
+}
+
+/// This is the const version of col().
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ConstColXpr col(Index i) const
+{
+ return ConstColXpr(derived(), i);
+}
+
+/// \returns an expression of the \a i-th row of \c *this. Note that the numbering starts at 0.
+///
+/// Example: \include MatrixBase_row.cpp
+/// Output: \verbinclude MatrixBase_row.out
+///
+EIGEN_DOC_BLOCK_ADDONS_INNER_PANEL_IF(row-major)
+/**
+ * \sa col(), class Block */
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+RowXpr row(Index i)
+{
+ return RowXpr(derived(), i);
+}
+
+/// This is the const version of row(). */
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ConstRowXpr row(Index i) const
+{
+ return ConstRowXpr(derived(), i);
+}
+
+/// \returns an expression of a segment (i.e. a vector block) in \c *this with either dynamic or fixed sizes.
+///
+/// \only_for_vectors
+///
+/// \param start the first coefficient in the segment
+/// \param n the number of coefficients in the segment
+/// \tparam NType the type of the value handling the number of coefficients in the segment, typically Index.
+///
+/// Example: \include MatrixBase_segment_int_int.cpp
+/// Output: \verbinclude MatrixBase_segment_int_int.out
+///
+/// The number of coefficients \a n can also be specified at compile-time by passing Eigen::fix<N>,
+/// or Eigen::fix<N>(n) as arguments.
+/// See \link block(Index,Index,NRowsType,NColsType) block() \endlink for the details.
+///
+/// \note Even in the case that the returned expression has dynamic size, in the case
+/// when it is applied to a fixed-size vector, it inherits a fixed maximal size,
+/// which means that evaluating it does not cause a dynamic memory allocation.
+///
+/// \sa block(Index,Index,NRowsType,NColsType), fix<N>, fix<N>(int), class Block
+///
+template<typename NType>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+#ifndef EIGEN_PARSED_BY_DOXYGEN
+typename FixedSegmentReturnType<internal::get_fixed_value<NType>::value>::Type
+#else
+typename FixedSegmentReturnType<...>::Type
+#endif
+segment(Index start, NType n)
+{
+ EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
+ return typename FixedSegmentReturnType<internal::get_fixed_value<NType>::value>::Type
+ (derived(), start, internal::get_runtime_value(n));
+}
+
+
+/// This is the const version of segment(Index,NType).
+template<typename NType>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+#ifndef EIGEN_PARSED_BY_DOXYGEN
+const typename ConstFixedSegmentReturnType<internal::get_fixed_value<NType>::value>::Type
+#else
+const typename ConstFixedSegmentReturnType<...>::Type
+#endif
+segment(Index start, NType n) const
+{
+ EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
+ return typename ConstFixedSegmentReturnType<internal::get_fixed_value<NType>::value>::Type
+ (derived(), start, internal::get_runtime_value(n));
+}
+
+/// \returns an expression of the first coefficients of \c *this with either dynamic or fixed sizes.
+///
+/// \only_for_vectors
+///
+/// \param n the number of coefficients in the segment
+/// \tparam NType the type of the value handling the number of coefficients in the segment, typically Index.
+///
+/// Example: \include MatrixBase_start_int.cpp
+/// Output: \verbinclude MatrixBase_start_int.out
+///
+/// The number of coefficients \a n can also be specified at compile-time by passing Eigen::fix<N>,
+/// or Eigen::fix<N>(n) as arguments.
+/// See \link block(Index,Index,NRowsType,NColsType) block() \endlink for the details.
+///
+/// \note Even in the case that the returned expression has dynamic size, in the case
+/// when it is applied to a fixed-size vector, it inherits a fixed maximal size,
+/// which means that evaluating it does not cause a dynamic memory allocation.
+///
+/// \sa class Block, block(Index,Index)
+///
+template<typename NType>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+#ifndef EIGEN_PARSED_BY_DOXYGEN
+typename FixedSegmentReturnType<internal::get_fixed_value<NType>::value>::Type
+#else
+typename FixedSegmentReturnType<...>::Type
+#endif
+head(NType n)
+{
+ EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
+ return typename FixedSegmentReturnType<internal::get_fixed_value<NType>::value>::Type
+ (derived(), 0, internal::get_runtime_value(n));
+}
+
+/// This is the const version of head(NType).
+template<typename NType>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+#ifndef EIGEN_PARSED_BY_DOXYGEN
+const typename ConstFixedSegmentReturnType<internal::get_fixed_value<NType>::value>::Type
+#else
+const typename ConstFixedSegmentReturnType<...>::Type
+#endif
+head(NType n) const
+{
+ EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
+ return typename ConstFixedSegmentReturnType<internal::get_fixed_value<NType>::value>::Type
+ (derived(), 0, internal::get_runtime_value(n));
+}
+
+/// \returns an expression of a last coefficients of \c *this with either dynamic or fixed sizes.
+///
+/// \only_for_vectors
+///
+/// \param n the number of coefficients in the segment
+/// \tparam NType the type of the value handling the number of coefficients in the segment, typically Index.
+///
+/// Example: \include MatrixBase_end_int.cpp
+/// Output: \verbinclude MatrixBase_end_int.out
+///
+/// The number of coefficients \a n can also be specified at compile-time by passing Eigen::fix<N>,
+/// or Eigen::fix<N>(n) as arguments.
+/// See \link block(Index,Index,NRowsType,NColsType) block() \endlink for the details.
+///
+/// \note Even in the case that the returned expression has dynamic size, in the case
+/// when it is applied to a fixed-size vector, it inherits a fixed maximal size,
+/// which means that evaluating it does not cause a dynamic memory allocation.
+///
+/// \sa class Block, block(Index,Index)
+///
+template<typename NType>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+#ifndef EIGEN_PARSED_BY_DOXYGEN
+typename FixedSegmentReturnType<internal::get_fixed_value<NType>::value>::Type
+#else
+typename FixedSegmentReturnType<...>::Type
+#endif
+tail(NType n)
+{
+ EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
+ return typename FixedSegmentReturnType<internal::get_fixed_value<NType>::value>::Type
+ (derived(), this->size() - internal::get_runtime_value(n), internal::get_runtime_value(n));
+}
+
+/// This is the const version of tail(Index).
+template<typename NType>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+#ifndef EIGEN_PARSED_BY_DOXYGEN
+const typename ConstFixedSegmentReturnType<internal::get_fixed_value<NType>::value>::Type
+#else
+const typename ConstFixedSegmentReturnType<...>::Type
+#endif
+tail(NType n) const
+{
+ EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
+ return typename ConstFixedSegmentReturnType<internal::get_fixed_value<NType>::value>::Type
+ (derived(), this->size() - internal::get_runtime_value(n), internal::get_runtime_value(n));
+}
+
+/// \returns a fixed-size expression of a segment (i.e. a vector block) in \c *this
+///
+/// \only_for_vectors
+///
+/// \tparam N the number of coefficients in the segment as specified at compile-time
+/// \param start the index of the first element in the segment
+/// \param n the number of coefficients in the segment as specified at compile-time
+///
+/// The compile-time and run-time information should not contradict. In other words,
+/// \a n should equal \a N unless \a N is \a Dynamic.
+///
+/// Example: \include MatrixBase_template_int_segment.cpp
+/// Output: \verbinclude MatrixBase_template_int_segment.out
+///
+/// \sa segment(Index,NType), class Block
+///
+template<int N>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+typename FixedSegmentReturnType<N>::Type segment(Index start, Index n = N)
+{
+ EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
+ return typename FixedSegmentReturnType<N>::Type(derived(), start, n);
+}
+
+/// This is the const version of segment<int>(Index).
+template<int N>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+typename ConstFixedSegmentReturnType<N>::Type segment(Index start, Index n = N) const
+{
+ EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
+ return typename ConstFixedSegmentReturnType<N>::Type(derived(), start, n);
+}
+
+/// \returns a fixed-size expression of the first coefficients of \c *this.
+///
+/// \only_for_vectors
+///
+/// \tparam N the number of coefficients in the segment as specified at compile-time
+/// \param n the number of coefficients in the segment as specified at run-time
+///
+/// The compile-time and run-time information should not contradict. In other words,
+/// \a n should equal \a N unless \a N is \a Dynamic.
+///
+/// Example: \include MatrixBase_template_int_start.cpp
+/// Output: \verbinclude MatrixBase_template_int_start.out
+///
+/// \sa head(NType), class Block
+///
+template<int N>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+typename FixedSegmentReturnType<N>::Type head(Index n = N)
+{
+ EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
+ return typename FixedSegmentReturnType<N>::Type(derived(), 0, n);
+}
+
+/// This is the const version of head<int>().
+template<int N>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+typename ConstFixedSegmentReturnType<N>::Type head(Index n = N) const
+{
+ EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
+ return typename ConstFixedSegmentReturnType<N>::Type(derived(), 0, n);
+}
+
+/// \returns a fixed-size expression of the last coefficients of \c *this.
+///
+/// \only_for_vectors
+///
+/// \tparam N the number of coefficients in the segment as specified at compile-time
+/// \param n the number of coefficients in the segment as specified at run-time
+///
+/// The compile-time and run-time information should not contradict. In other words,
+/// \a n should equal \a N unless \a N is \a Dynamic.
+///
+/// Example: \include MatrixBase_template_int_end.cpp
+/// Output: \verbinclude MatrixBase_template_int_end.out
+///
+/// \sa tail(NType), class Block
+///
+template<int N>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+typename FixedSegmentReturnType<N>::Type tail(Index n = N)
+{
+ EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
+ return typename FixedSegmentReturnType<N>::Type(derived(), size() - n);
+}
+
+/// This is the const version of tail<int>.
+template<int N>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+typename ConstFixedSegmentReturnType<N>::Type tail(Index n = N) const
+{
+ EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
+ return typename ConstFixedSegmentReturnType<N>::Type(derived(), size() - n);
+}
+
+/// \returns the \a outer -th column (resp. row) of the matrix \c *this if \c *this
+/// is col-major (resp. row-major).
+///
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+InnerVectorReturnType innerVector(Index outer)
+{ return InnerVectorReturnType(derived(), outer); }
+
+/// \returns the \a outer -th column (resp. row) of the matrix \c *this if \c *this
+/// is col-major (resp. row-major). Read-only.
+///
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+const ConstInnerVectorReturnType innerVector(Index outer) const
+{ return ConstInnerVectorReturnType(derived(), outer); }
+
+/// \returns the \a outer -th column (resp. row) of the matrix \c *this if \c *this
+/// is col-major (resp. row-major).
+///
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+InnerVectorsReturnType
+innerVectors(Index outerStart, Index outerSize)
+{
+ return Block<Derived,Dynamic,Dynamic,true>(derived(),
+ IsRowMajor ? outerStart : 0, IsRowMajor ? 0 : outerStart,
+ IsRowMajor ? outerSize : rows(), IsRowMajor ? cols() : outerSize);
+
+}
+
+/// \returns the \a outer -th column (resp. row) of the matrix \c *this if \c *this
+/// is col-major (resp. row-major). Read-only.
+///
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+const ConstInnerVectorsReturnType
+innerVectors(Index outerStart, Index outerSize) const
+{
+ return Block<const Derived,Dynamic,Dynamic,true>(derived(),
+ IsRowMajor ? outerStart : 0, IsRowMajor ? 0 : outerStart,
+ IsRowMajor ? outerSize : rows(), IsRowMajor ? cols() : outerSize);
+
+}
+
+/** \returns the i-th subvector (column or vector) according to the \c Direction
+ * \sa subVectors()
+ */
+template<DirectionType Direction>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+std::conditional_t<Direction==Vertical,ColXpr,RowXpr>
+subVector(Index i)
+{
+ return std::conditional_t<Direction==Vertical,ColXpr,RowXpr>(derived(),i);
+}
+
+/** This is the const version of subVector(Index) */
+template<DirectionType Direction>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+std::conditional_t<Direction==Vertical,ConstColXpr,ConstRowXpr>
+subVector(Index i) const
+{
+ return std::conditional_t<Direction==Vertical,ConstColXpr,ConstRowXpr>(derived(),i);
+}
+
+/** \returns the number of subvectors (rows or columns) in the direction \c Direction
+ * \sa subVector(Index)
+ */
+template<DirectionType Direction>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE EIGEN_CONSTEXPR
+Index subVectors() const
+{ return (Direction==Vertical)?cols():rows(); }
diff --git a/Eigen/src/plugins/CommonCwiseBinaryOps.h b/Eigen/src/plugins/CommonCwiseBinaryOps.h
new file mode 100644
index 0000000..2f50329
--- /dev/null
+++ b/Eigen/src/plugins/CommonCwiseBinaryOps.h
@@ -0,0 +1,115 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2016 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+// This file is a base class plugin containing common coefficient wise functions.
+
+/** \returns an expression of the difference of \c *this and \a other
+ *
+ * \note If you want to subtract a given scalar from all coefficients, see Cwise::operator-().
+ *
+ * \sa class CwiseBinaryOp, operator-=()
+ */
+EIGEN_MAKE_CWISE_BINARY_OP(operator-,difference)
+
+/** \returns an expression of the sum of \c *this and \a other
+ *
+ * \note If you want to add a given scalar to all coefficients, see Cwise::operator+().
+ *
+ * \sa class CwiseBinaryOp, operator+=()
+ */
+EIGEN_MAKE_CWISE_BINARY_OP(operator+,sum)
+
+/** \returns an expression of a custom coefficient-wise operator \a func of *this and \a other
+ *
+ * The template parameter \a CustomBinaryOp is the type of the functor
+ * of the custom operator (see class CwiseBinaryOp for an example)
+ *
+ * Here is an example illustrating the use of custom functors:
+ * \include class_CwiseBinaryOp.cpp
+ * Output: \verbinclude class_CwiseBinaryOp.out
+ *
+ * \sa class CwiseBinaryOp, operator+(), operator-(), cwiseProduct()
+ */
+template<typename CustomBinaryOp, typename OtherDerived>
+EIGEN_DEVICE_FUNC
+EIGEN_STRONG_INLINE const CwiseBinaryOp<CustomBinaryOp, const Derived, const OtherDerived>
+binaryExpr(const EIGEN_CURRENT_STORAGE_BASE_CLASS<OtherDerived> &other, const CustomBinaryOp& func = CustomBinaryOp()) const
+{
+ return CwiseBinaryOp<CustomBinaryOp, const Derived, const OtherDerived>(derived(), other.derived(), func);
+}
+
+
+#ifndef EIGEN_PARSED_BY_DOXYGEN
+EIGEN_MAKE_SCALAR_BINARY_OP(operator*,product)
+#else
+/** \returns an expression of \c *this scaled by the scalar factor \a scalar
+ *
+ * \tparam T is the scalar type of \a scalar. It must be compatible with the scalar type of the given expression.
+ */
+template<typename T>
+const CwiseBinaryOp<internal::scalar_product_op<Scalar,T>,Derived,Constant<T> > operator*(const T& scalar) const;
+/** \returns an expression of \a expr scaled by the scalar factor \a scalar
+ *
+ * \tparam T is the scalar type of \a scalar. It must be compatible with the scalar type of the given expression.
+ */
+template<typename T> friend
+const CwiseBinaryOp<internal::scalar_product_op<T,Scalar>,Constant<T>,Derived> operator*(const T& scalar, const StorageBaseType& expr);
+#endif
+
+
+
+#ifndef EIGEN_PARSED_BY_DOXYGEN
+EIGEN_MAKE_SCALAR_BINARY_OP_ONTHERIGHT(operator/,quotient)
+#else
+/** \returns an expression of \c *this divided by the scalar value \a scalar
+ *
+ * \tparam T is the scalar type of \a scalar. It must be compatible with the scalar type of the given expression.
+ */
+template<typename T>
+const CwiseBinaryOp<internal::scalar_quotient_op<Scalar,T>,Derived,Constant<T> > operator/(const T& scalar) const;
+#endif
+
+/** \returns an expression of the coefficient-wise boolean \b and operator of \c *this and \a other
+ *
+ * \warning this operator is for expression of bool only.
+ *
+ * Example: \include Cwise_boolean_and.cpp
+ * Output: \verbinclude Cwise_boolean_and.out
+ *
+ * \sa operator||(), select()
+ */
+template<typename OtherDerived>
+EIGEN_DEVICE_FUNC
+inline const CwiseBinaryOp<internal::scalar_boolean_and_op, const Derived, const OtherDerived>
+operator&&(const EIGEN_CURRENT_STORAGE_BASE_CLASS<OtherDerived> &other) const
+{
+ EIGEN_STATIC_ASSERT((internal::is_same<bool,Scalar>::value && internal::is_same<bool,typename OtherDerived::Scalar>::value),
+ THIS_METHOD_IS_ONLY_FOR_EXPRESSIONS_OF_BOOL);
+ return CwiseBinaryOp<internal::scalar_boolean_and_op, const Derived, const OtherDerived>(derived(),other.derived());
+}
+
+/** \returns an expression of the coefficient-wise boolean \b or operator of \c *this and \a other
+ *
+ * \warning this operator is for expression of bool only.
+ *
+ * Example: \include Cwise_boolean_or.cpp
+ * Output: \verbinclude Cwise_boolean_or.out
+ *
+ * \sa operator&&(), select()
+ */
+template<typename OtherDerived>
+EIGEN_DEVICE_FUNC
+inline const CwiseBinaryOp<internal::scalar_boolean_or_op, const Derived, const OtherDerived>
+operator||(const EIGEN_CURRENT_STORAGE_BASE_CLASS<OtherDerived> &other) const
+{
+ EIGEN_STATIC_ASSERT((internal::is_same<bool,Scalar>::value && internal::is_same<bool,typename OtherDerived::Scalar>::value),
+ THIS_METHOD_IS_ONLY_FOR_EXPRESSIONS_OF_BOOL);
+ return CwiseBinaryOp<internal::scalar_boolean_or_op, const Derived, const OtherDerived>(derived(),other.derived());
+}
diff --git a/Eigen/src/plugins/CommonCwiseUnaryOps.h b/Eigen/src/plugins/CommonCwiseUnaryOps.h
new file mode 100644
index 0000000..390759c
--- /dev/null
+++ b/Eigen/src/plugins/CommonCwiseUnaryOps.h
@@ -0,0 +1,177 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+// This file is a base class plugin containing common coefficient wise functions.
+
+#ifndef EIGEN_PARSED_BY_DOXYGEN
+
+/** \internal the return type of conjugate() */
+typedef std::conditional_t<NumTraits<Scalar>::IsComplex,
+ const CwiseUnaryOp<internal::scalar_conjugate_op<Scalar>, const Derived>,
+ const Derived&
+ > ConjugateReturnType;
+/** \internal the return type of real() const */
+typedef std::conditional_t<NumTraits<Scalar>::IsComplex,
+ const CwiseUnaryOp<internal::scalar_real_op<Scalar>, const Derived>,
+ const Derived&
+ > RealReturnType;
+/** \internal the return type of real() */
+typedef std::conditional_t<NumTraits<Scalar>::IsComplex,
+ CwiseUnaryView<internal::scalar_real_ref_op<Scalar>, Derived>,
+ Derived&
+ > NonConstRealReturnType;
+/** \internal the return type of imag() const */
+typedef CwiseUnaryOp<internal::scalar_imag_op<Scalar>, const Derived> ImagReturnType;
+/** \internal the return type of imag() */
+typedef CwiseUnaryView<internal::scalar_imag_ref_op<Scalar>, Derived> NonConstImagReturnType;
+
+typedef CwiseUnaryOp<internal::scalar_opposite_op<Scalar>, const Derived> NegativeReturnType;
+
+#endif // not EIGEN_PARSED_BY_DOXYGEN
+
+/// \returns an expression of the opposite of \c *this
+///
+EIGEN_DOC_UNARY_ADDONS(operator-,opposite)
+///
+EIGEN_DEVICE_FUNC
+inline const NegativeReturnType
+operator-() const { return NegativeReturnType(derived()); }
+
+
+template<class NewType> struct CastXpr { typedef typename internal::cast_return_type<Derived,const CwiseUnaryOp<internal::scalar_cast_op<Scalar, NewType>, const Derived> >::type Type; };
+
+/// \returns an expression of \c *this with the \a Scalar type casted to
+/// \a NewScalar.
+///
+/// The template parameter \a NewScalar is the type we are casting the scalars to.
+///
+EIGEN_DOC_UNARY_ADDONS(cast,conversion function)
+///
+/// \sa class CwiseUnaryOp
+///
+template<typename NewType>
+EIGEN_DEVICE_FUNC
+typename CastXpr<NewType>::Type
+cast() const
+{
+ return typename CastXpr<NewType>::Type(derived());
+}
+
+/// \returns an expression of the complex conjugate of \c *this.
+///
+EIGEN_DOC_UNARY_ADDONS(conjugate,complex conjugate)
+///
+/// \sa <a href="group__CoeffwiseMathFunctions.html#cwisetable_conj">Math functions</a>, MatrixBase::adjoint()
+EIGEN_DEVICE_FUNC
+inline ConjugateReturnType
+conjugate() const
+{
+ return ConjugateReturnType(derived());
+}
+
+/// \returns an expression of the complex conjugate of \c *this if Cond==true, returns derived() otherwise.
+///
+EIGEN_DOC_UNARY_ADDONS(conjugate,complex conjugate)
+///
+/// \sa conjugate()
+template<bool Cond>
+EIGEN_DEVICE_FUNC
+inline std::conditional_t<Cond,ConjugateReturnType,const Derived&>
+conjugateIf() const
+{
+ typedef std::conditional_t<Cond,ConjugateReturnType,const Derived&> ReturnType;
+ return ReturnType(derived());
+}
+
+/// \returns a read-only expression of the real part of \c *this.
+///
+EIGEN_DOC_UNARY_ADDONS(real,real part function)
+///
+/// \sa imag()
+EIGEN_DEVICE_FUNC
+inline RealReturnType
+real() const { return RealReturnType(derived()); }
+
+/// \returns an read-only expression of the imaginary part of \c *this.
+///
+EIGEN_DOC_UNARY_ADDONS(imag,imaginary part function)
+///
+/// \sa real()
+EIGEN_DEVICE_FUNC
+inline const ImagReturnType
+imag() const { return ImagReturnType(derived()); }
+
+/// \brief Apply a unary operator coefficient-wise
+/// \param[in] func Functor implementing the unary operator
+/// \tparam CustomUnaryOp Type of \a func
+/// \returns An expression of a custom coefficient-wise unary operator \a func of *this
+///
+/// The function \c ptr_fun() from the C++ standard library can be used to make functors out of normal functions.
+///
+/// Example:
+/// \include class_CwiseUnaryOp_ptrfun.cpp
+/// Output: \verbinclude class_CwiseUnaryOp_ptrfun.out
+///
+/// Genuine functors allow for more possibilities, for instance it may contain a state.
+///
+/// Example:
+/// \include class_CwiseUnaryOp.cpp
+/// Output: \verbinclude class_CwiseUnaryOp.out
+///
+EIGEN_DOC_UNARY_ADDONS(unaryExpr,unary function)
+///
+/// \sa unaryViewExpr, binaryExpr, class CwiseUnaryOp
+///
+template<typename CustomUnaryOp>
+EIGEN_DEVICE_FUNC
+inline const CwiseUnaryOp<CustomUnaryOp, const Derived>
+unaryExpr(const CustomUnaryOp& func = CustomUnaryOp()) const
+{
+ return CwiseUnaryOp<CustomUnaryOp, const Derived>(derived(), func);
+}
+
+/// \returns an expression of a custom coefficient-wise unary operator \a func of *this
+///
+/// The template parameter \a CustomUnaryOp is the type of the functor
+/// of the custom unary operator.
+///
+/// Example:
+/// \include class_CwiseUnaryOp.cpp
+/// Output: \verbinclude class_CwiseUnaryOp.out
+///
+EIGEN_DOC_UNARY_ADDONS(unaryViewExpr,unary function)
+///
+/// \sa unaryExpr, binaryExpr class CwiseUnaryOp
+///
+template<typename CustomViewOp>
+EIGEN_DEVICE_FUNC
+inline const CwiseUnaryView<CustomViewOp, const Derived>
+unaryViewExpr(const CustomViewOp& func = CustomViewOp()) const
+{
+ return CwiseUnaryView<CustomViewOp, const Derived>(derived(), func);
+}
+
+/// \returns a non const expression of the real part of \c *this.
+///
+EIGEN_DOC_UNARY_ADDONS(real,real part function)
+///
+/// \sa imag()
+EIGEN_DEVICE_FUNC
+inline NonConstRealReturnType
+real() { return NonConstRealReturnType(derived()); }
+
+/// \returns a non const expression of the imaginary part of \c *this.
+///
+EIGEN_DOC_UNARY_ADDONS(imag,imaginary part function)
+///
+/// \sa real()
+EIGEN_DEVICE_FUNC
+inline NonConstImagReturnType
+imag() { return NonConstImagReturnType(derived()); }
diff --git a/Eigen/src/plugins/IndexedViewMethods.h b/Eigen/src/plugins/IndexedViewMethods.h
new file mode 100644
index 0000000..011fcbe
--- /dev/null
+++ b/Eigen/src/plugins/IndexedViewMethods.h
@@ -0,0 +1,255 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2017 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#if !defined(EIGEN_PARSED_BY_DOXYGEN)
+
+// This file is automatically included twice to generate const and non-const versions
+
+#ifndef EIGEN_INDEXED_VIEW_METHOD_2ND_PASS
+#define EIGEN_INDEXED_VIEW_METHOD_CONST const
+#define EIGEN_INDEXED_VIEW_METHOD_TYPE ConstIndexedViewType
+#else
+#define EIGEN_INDEXED_VIEW_METHOD_CONST
+#define EIGEN_INDEXED_VIEW_METHOD_TYPE IndexedViewType
+#endif
+
+#ifndef EIGEN_INDEXED_VIEW_METHOD_2ND_PASS
+protected:
+
+// define some aliases to ease readability
+
+template<typename Indices>
+struct IvcRowType : public internal::IndexedViewCompatibleType<Indices,RowsAtCompileTime> {};
+
+template<typename Indices>
+struct IvcColType : public internal::IndexedViewCompatibleType<Indices,ColsAtCompileTime> {};
+
+template<typename Indices>
+struct IvcType : public internal::IndexedViewCompatibleType<Indices,SizeAtCompileTime> {};
+
+typedef typename internal::IndexedViewCompatibleType<Index,1>::type IvcIndex;
+
+template<typename Indices>
+typename IvcRowType<Indices>::type
+ivcRow(const Indices& indices) const {
+ return internal::makeIndexedViewCompatible(indices, internal::variable_if_dynamic<Index,RowsAtCompileTime>(derived().rows()),Specialized);
+}
+
+template<typename Indices>
+typename IvcColType<Indices>::type
+ivcCol(const Indices& indices) const {
+ return internal::makeIndexedViewCompatible(indices, internal::variable_if_dynamic<Index,ColsAtCompileTime>(derived().cols()),Specialized);
+}
+
+template<typename Indices>
+typename IvcColType<Indices>::type
+ivcSize(const Indices& indices) const {
+ return internal::makeIndexedViewCompatible(indices, internal::variable_if_dynamic<Index,SizeAtCompileTime>(derived().size()),Specialized);
+}
+
+public:
+
+#endif
+
+template<typename RowIndices, typename ColIndices>
+struct EIGEN_INDEXED_VIEW_METHOD_TYPE {
+ typedef IndexedView<EIGEN_INDEXED_VIEW_METHOD_CONST Derived,
+ typename IvcRowType<RowIndices>::type,
+ typename IvcColType<ColIndices>::type> type;
+};
+
+// This is the generic version
+
+template<typename RowIndices, typename ColIndices>
+std::enable_if_t<internal::valid_indexed_view_overload<RowIndices,ColIndices>::value
+ && internal::traits<typename EIGEN_INDEXED_VIEW_METHOD_TYPE<RowIndices,ColIndices>::type>::ReturnAsIndexedView,
+ typename EIGEN_INDEXED_VIEW_METHOD_TYPE<RowIndices,ColIndices>::type>
+operator()(const RowIndices& rowIndices, const ColIndices& colIndices) EIGEN_INDEXED_VIEW_METHOD_CONST
+{
+ return typename EIGEN_INDEXED_VIEW_METHOD_TYPE<RowIndices,ColIndices>::type
+ (derived(), ivcRow(rowIndices), ivcCol(colIndices));
+}
+
+// The following overload returns a Block<> object
+
+template<typename RowIndices, typename ColIndices>
+std::enable_if_t<internal::valid_indexed_view_overload<RowIndices,ColIndices>::value
+ && internal::traits<typename EIGEN_INDEXED_VIEW_METHOD_TYPE<RowIndices,ColIndices>::type>::ReturnAsBlock,
+ typename internal::traits<typename EIGEN_INDEXED_VIEW_METHOD_TYPE<RowIndices,ColIndices>::type>::BlockType>
+operator()(const RowIndices& rowIndices, const ColIndices& colIndices) EIGEN_INDEXED_VIEW_METHOD_CONST
+{
+ typedef typename internal::traits<typename EIGEN_INDEXED_VIEW_METHOD_TYPE<RowIndices,ColIndices>::type>::BlockType BlockType;
+ typename IvcRowType<RowIndices>::type actualRowIndices = ivcRow(rowIndices);
+ typename IvcColType<ColIndices>::type actualColIndices = ivcCol(colIndices);
+ return BlockType(derived(),
+ internal::first(actualRowIndices),
+ internal::first(actualColIndices),
+ internal::index_list_size(actualRowIndices),
+ internal::index_list_size(actualColIndices));
+}
+
+// The following overload returns a Scalar
+
+template<typename RowIndices, typename ColIndices>
+std::enable_if_t<internal::valid_indexed_view_overload<RowIndices,ColIndices>::value
+ && internal::traits<typename EIGEN_INDEXED_VIEW_METHOD_TYPE<RowIndices,ColIndices>::type>::ReturnAsScalar,
+ CoeffReturnType >
+operator()(const RowIndices& rowIndices, const ColIndices& colIndices) EIGEN_INDEXED_VIEW_METHOD_CONST
+{
+ return Base::operator()(internal::eval_expr_given_size(rowIndices,rows()),internal::eval_expr_given_size(colIndices,cols()));
+}
+
+// The following three overloads are needed to handle raw Index[N] arrays.
+
+template<typename RowIndicesT, std::size_t RowIndicesN, typename ColIndices>
+IndexedView<EIGEN_INDEXED_VIEW_METHOD_CONST Derived,const RowIndicesT (&)[RowIndicesN],typename IvcColType<ColIndices>::type>
+operator()(const RowIndicesT (&rowIndices)[RowIndicesN], const ColIndices& colIndices) EIGEN_INDEXED_VIEW_METHOD_CONST
+{
+ return IndexedView<EIGEN_INDEXED_VIEW_METHOD_CONST Derived,const RowIndicesT (&)[RowIndicesN],typename IvcColType<ColIndices>::type>
+ (derived(), rowIndices, ivcCol(colIndices));
+}
+
+template<typename RowIndices, typename ColIndicesT, std::size_t ColIndicesN>
+IndexedView<EIGEN_INDEXED_VIEW_METHOD_CONST Derived,typename IvcRowType<RowIndices>::type, const ColIndicesT (&)[ColIndicesN]>
+operator()(const RowIndices& rowIndices, const ColIndicesT (&colIndices)[ColIndicesN]) EIGEN_INDEXED_VIEW_METHOD_CONST
+{
+ return IndexedView<EIGEN_INDEXED_VIEW_METHOD_CONST Derived,typename IvcRowType<RowIndices>::type,const ColIndicesT (&)[ColIndicesN]>
+ (derived(), ivcRow(rowIndices), colIndices);
+}
+
+template<typename RowIndicesT, std::size_t RowIndicesN, typename ColIndicesT, std::size_t ColIndicesN>
+IndexedView<EIGEN_INDEXED_VIEW_METHOD_CONST Derived,const RowIndicesT (&)[RowIndicesN], const ColIndicesT (&)[ColIndicesN]>
+operator()(const RowIndicesT (&rowIndices)[RowIndicesN], const ColIndicesT (&colIndices)[ColIndicesN]) EIGEN_INDEXED_VIEW_METHOD_CONST
+{
+ return IndexedView<EIGEN_INDEXED_VIEW_METHOD_CONST Derived,const RowIndicesT (&)[RowIndicesN],const ColIndicesT (&)[ColIndicesN]>
+ (derived(), rowIndices, colIndices);
+}
+
+
+// Overloads for 1D vectors/arrays
+
+template<typename Indices>
+std::enable_if_t<
+ IsRowMajor && (!(internal::get_compile_time_incr<typename IvcType<Indices>::type>::value==1 || internal::is_valid_index_type<Indices>::value)),
+ IndexedView<EIGEN_INDEXED_VIEW_METHOD_CONST Derived,IvcIndex,typename IvcType<Indices>::type> >
+operator()(const Indices& indices) EIGEN_INDEXED_VIEW_METHOD_CONST
+{
+ EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
+ return IndexedView<EIGEN_INDEXED_VIEW_METHOD_CONST Derived,IvcIndex,typename IvcType<Indices>::type>
+ (derived(), IvcIndex(0), ivcCol(indices));
+}
+
+template<typename Indices>
+std::enable_if_t<
+ (!IsRowMajor) && (!(internal::get_compile_time_incr<typename IvcType<Indices>::type>::value==1 || internal::is_valid_index_type<Indices>::value)),
+ IndexedView<EIGEN_INDEXED_VIEW_METHOD_CONST Derived,typename IvcType<Indices>::type,IvcIndex> >
+operator()(const Indices& indices) EIGEN_INDEXED_VIEW_METHOD_CONST
+{
+ EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
+ return IndexedView<EIGEN_INDEXED_VIEW_METHOD_CONST Derived,typename IvcType<Indices>::type,IvcIndex>
+ (derived(), ivcRow(indices), IvcIndex(0));
+}
+
+template<typename Indices>
+std::enable_if_t<
+ (internal::get_compile_time_incr<typename IvcType<Indices>::type>::value==1) && (!internal::is_valid_index_type<Indices>::value) && (!symbolic::is_symbolic<Indices>::value),
+ VectorBlock<EIGEN_INDEXED_VIEW_METHOD_CONST Derived,internal::array_size<Indices>::value> >
+operator()(const Indices& indices) EIGEN_INDEXED_VIEW_METHOD_CONST
+{
+ EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
+ typename IvcType<Indices>::type actualIndices = ivcSize(indices);
+ return VectorBlock<EIGEN_INDEXED_VIEW_METHOD_CONST Derived,internal::array_size<Indices>::value>
+ (derived(), internal::first(actualIndices), internal::index_list_size(actualIndices));
+}
+
+template<typename IndexType>
+std::enable_if_t<symbolic::is_symbolic<IndexType>::value, CoeffReturnType >
+operator()(const IndexType& id) EIGEN_INDEXED_VIEW_METHOD_CONST
+{
+ return Base::operator()(internal::eval_expr_given_size(id,size()));
+}
+
+template<typename IndicesT, std::size_t IndicesN>
+std::enable_if_t<IsRowMajor,
+ IndexedView<EIGEN_INDEXED_VIEW_METHOD_CONST Derived,IvcIndex,const IndicesT (&)[IndicesN]> >
+operator()(const IndicesT (&indices)[IndicesN]) EIGEN_INDEXED_VIEW_METHOD_CONST
+{
+ EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
+ return IndexedView<EIGEN_INDEXED_VIEW_METHOD_CONST Derived,IvcIndex,const IndicesT (&)[IndicesN]>
+ (derived(), IvcIndex(0), indices);
+}
+
+template<typename IndicesT, std::size_t IndicesN>
+std::enable_if_t<!IsRowMajor,
+ IndexedView<EIGEN_INDEXED_VIEW_METHOD_CONST Derived,const IndicesT (&)[IndicesN],IvcIndex> >
+operator()(const IndicesT (&indices)[IndicesN]) EIGEN_INDEXED_VIEW_METHOD_CONST
+{
+ EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
+ return IndexedView<EIGEN_INDEXED_VIEW_METHOD_CONST Derived,const IndicesT (&)[IndicesN],IvcIndex>
+ (derived(), indices, IvcIndex(0));
+}
+
+#undef EIGEN_INDEXED_VIEW_METHOD_CONST
+#undef EIGEN_INDEXED_VIEW_METHOD_TYPE
+
+#ifndef EIGEN_INDEXED_VIEW_METHOD_2ND_PASS
+#define EIGEN_INDEXED_VIEW_METHOD_2ND_PASS
+#include "IndexedViewMethods.h"
+#undef EIGEN_INDEXED_VIEW_METHOD_2ND_PASS
+#endif
+
+#else // EIGEN_PARSED_BY_DOXYGEN
+
+/**
+ * \returns a generic submatrix view defined by the rows and columns indexed \a rowIndices and \a colIndices respectively.
+ *
+ * Each parameter must either be:
+ * - An integer indexing a single row or column
+ * - Eigen::placeholders::all indexing the full set of respective rows or columns in increasing order
+ * - An ArithmeticSequence as returned by the Eigen::seq and Eigen::seqN functions
+ * - Any %Eigen's vector/array of integers or expressions
+ * - Plain C arrays: \c int[N]
+ * - And more generally any type exposing the following two member functions:
+ * \code
+ * <integral type> operator[](<integral type>) const;
+ * <integral type> size() const;
+ * \endcode
+ * where \c <integral \c type> stands for any integer type compatible with Eigen::Index (i.e. \c std::ptrdiff_t).
+ *
+ * The last statement implies compatibility with \c std::vector, \c std::valarray, \c std::array, many of the Range-v3's ranges, etc.
+ *
+ * If the submatrix can be represented using a starting position \c (i,j) and positive sizes \c (rows,columns), then this
+ * method will returns a Block object after extraction of the relevant information from the passed arguments. This is the case
+ * when all arguments are either:
+ * - An integer
+ * - Eigen::placeholders::all
+ * - An ArithmeticSequence with compile-time increment strictly equal to 1, as returned by Eigen::seq(a,b), and Eigen::seqN(a,N).
+ *
+ * Otherwise a more general IndexedView<Derived,RowIndices',ColIndices'> object will be returned, after conversion of the inputs
+ * to more suitable types \c RowIndices' and \c ColIndices'.
+ *
+ * For 1D vectors and arrays, you better use the operator()(const Indices&) overload, which behave the same way but taking a single parameter.
+ *
+ * See also this <a href="https://stackoverflow.com/questions/46110917/eigen-replicate-items-along-one-dimension-without-useless-allocations">question</a> and its answer for an example of how to duplicate coefficients.
+ *
+ * \sa operator()(const Indices&), class Block, class IndexedView, DenseBase::block(Index,Index,Index,Index)
+ */
+template<typename RowIndices, typename ColIndices>
+IndexedView_or_Block
+operator()(const RowIndices& rowIndices, const ColIndices& colIndices);
+
+/** This is an overload of operator()(const RowIndices&, const ColIndices&) for 1D vectors or arrays
+ *
+ * \only_for_vectors
+ */
+template<typename Indices>
+IndexedView_or_VectorBlock
+operator()(const Indices& indices);
+
+#endif // EIGEN_PARSED_BY_DOXYGEN
diff --git a/Eigen/src/plugins/InternalHeaderCheck.h b/Eigen/src/plugins/InternalHeaderCheck.h
new file mode 100644
index 0000000..ac6821d
--- /dev/null
+++ b/Eigen/src/plugins/InternalHeaderCheck.h
@@ -0,0 +1,3 @@
+#ifndef EIGEN_CORE_MODULE_H
+#error "Please include Eigen/plugins instead of including headers inside the src directory directly."
+#endif
diff --git a/Eigen/src/plugins/MatrixCwiseBinaryOps.h b/Eigen/src/plugins/MatrixCwiseBinaryOps.h
new file mode 100644
index 0000000..46fe08c
--- /dev/null
+++ b/Eigen/src/plugins/MatrixCwiseBinaryOps.h
@@ -0,0 +1,154 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+// This file is a base class plugin containing matrix specifics coefficient wise functions.
+
+/** \returns an expression of the Schur product (coefficient wise product) of *this and \a other
+ *
+ * Example: \include MatrixBase_cwiseProduct.cpp
+ * Output: \verbinclude MatrixBase_cwiseProduct.out
+ *
+ * \sa class CwiseBinaryOp, cwiseAbs2
+ */
+template<typename OtherDerived>
+EIGEN_DEVICE_FUNC
+EIGEN_STRONG_INLINE const EIGEN_CWISE_BINARY_RETURN_TYPE(Derived,OtherDerived,product)
+cwiseProduct(const EIGEN_CURRENT_STORAGE_BASE_CLASS<OtherDerived> &other) const
+{
+ return EIGEN_CWISE_BINARY_RETURN_TYPE(Derived,OtherDerived,product)(derived(), other.derived());
+}
+
+/** \returns an expression of the coefficient-wise == operator of *this and \a other
+ *
+ * \warning this performs an exact comparison, which is generally a bad idea with floating-point types.
+ * In order to check for equality between two vectors or matrices with floating-point coefficients, it is
+ * generally a far better idea to use a fuzzy comparison as provided by isApprox() and
+ * isMuchSmallerThan().
+ *
+ * Example: \include MatrixBase_cwiseEqual.cpp
+ * Output: \verbinclude MatrixBase_cwiseEqual.out
+ *
+ * \sa cwiseNotEqual(), isApprox(), isMuchSmallerThan()
+ */
+template<typename OtherDerived>
+EIGEN_DEVICE_FUNC
+inline const CwiseBinaryOp<numext::equal_to<Scalar>, const Derived, const OtherDerived>
+cwiseEqual(const EIGEN_CURRENT_STORAGE_BASE_CLASS<OtherDerived> &other) const
+{
+ return CwiseBinaryOp<numext::equal_to<Scalar>, const Derived, const OtherDerived>(derived(), other.derived());
+}
+
+/** \returns an expression of the coefficient-wise != operator of *this and \a other
+ *
+ * \warning this performs an exact comparison, which is generally a bad idea with floating-point types.
+ * In order to check for equality between two vectors or matrices with floating-point coefficients, it is
+ * generally a far better idea to use a fuzzy comparison as provided by isApprox() and
+ * isMuchSmallerThan().
+ *
+ * Example: \include MatrixBase_cwiseNotEqual.cpp
+ * Output: \verbinclude MatrixBase_cwiseNotEqual.out
+ *
+ * \sa cwiseEqual(), isApprox(), isMuchSmallerThan()
+ */
+template<typename OtherDerived>
+EIGEN_DEVICE_FUNC
+inline const CwiseBinaryOp<numext::not_equal_to<Scalar>, const Derived, const OtherDerived>
+cwiseNotEqual(const EIGEN_CURRENT_STORAGE_BASE_CLASS<OtherDerived> &other) const
+{
+ return CwiseBinaryOp<numext::not_equal_to<Scalar>, const Derived, const OtherDerived>(derived(), other.derived());
+}
+
+/** \returns an expression of the coefficient-wise min of *this and \a other
+ *
+ * Example: \include MatrixBase_cwiseMin.cpp
+ * Output: \verbinclude MatrixBase_cwiseMin.out
+ *
+ * \sa class CwiseBinaryOp, max()
+ */
+template<int NaNPropagation=PropagateFast, typename OtherDerived>
+EIGEN_DEVICE_FUNC
+EIGEN_STRONG_INLINE const CwiseBinaryOp<internal::scalar_min_op<Scalar,Scalar,NaNPropagation>, const Derived, const OtherDerived>
+cwiseMin(const EIGEN_CURRENT_STORAGE_BASE_CLASS<OtherDerived> &other) const
+{
+ return CwiseBinaryOp<internal::scalar_min_op<Scalar,Scalar,NaNPropagation>, const Derived, const OtherDerived>(derived(), other.derived());
+}
+
+/** \returns an expression of the coefficient-wise min of *this and scalar \a other
+ *
+ * \sa class CwiseBinaryOp, min()
+ */
+template<int NaNPropagation=PropagateFast>
+EIGEN_DEVICE_FUNC
+EIGEN_STRONG_INLINE const CwiseBinaryOp<internal::scalar_min_op<Scalar,Scalar,NaNPropagation>, const Derived, const ConstantReturnType>
+cwiseMin(const Scalar &other) const
+{
+ return cwiseMin<NaNPropagation>(Derived::Constant(rows(), cols(), other));
+}
+
+/** \returns an expression of the coefficient-wise max of *this and \a other
+ *
+ * Example: \include MatrixBase_cwiseMax.cpp
+ * Output: \verbinclude MatrixBase_cwiseMax.out
+ *
+ * \sa class CwiseBinaryOp, min()
+ */
+template<int NaNPropagation=PropagateFast, typename OtherDerived>
+EIGEN_DEVICE_FUNC
+EIGEN_STRONG_INLINE const CwiseBinaryOp<internal::scalar_max_op<Scalar,Scalar,NaNPropagation>, const Derived, const OtherDerived>
+cwiseMax(const EIGEN_CURRENT_STORAGE_BASE_CLASS<OtherDerived> &other) const
+{
+ return CwiseBinaryOp<internal::scalar_max_op<Scalar,Scalar,NaNPropagation>, const Derived, const OtherDerived>(derived(), other.derived());
+}
+
+/** \returns an expression of the coefficient-wise max of *this and scalar \a other
+ *
+ * \sa class CwiseBinaryOp, min()
+ */
+template<int NaNPropagation=PropagateFast>
+EIGEN_DEVICE_FUNC
+EIGEN_STRONG_INLINE const CwiseBinaryOp<internal::scalar_max_op<Scalar,Scalar,NaNPropagation>, const Derived, const ConstantReturnType>
+cwiseMax(const Scalar &other) const
+{
+ return cwiseMax<NaNPropagation>(Derived::Constant(rows(), cols(), other));
+}
+
+
+/** \returns an expression of the coefficient-wise quotient of *this and \a other
+ *
+ * Example: \include MatrixBase_cwiseQuotient.cpp
+ * Output: \verbinclude MatrixBase_cwiseQuotient.out
+ *
+ * \sa class CwiseBinaryOp, cwiseProduct(), cwiseInverse()
+ */
+template<typename OtherDerived>
+EIGEN_DEVICE_FUNC
+EIGEN_STRONG_INLINE const CwiseBinaryOp<internal::scalar_quotient_op<Scalar>, const Derived, const OtherDerived>
+cwiseQuotient(const EIGEN_CURRENT_STORAGE_BASE_CLASS<OtherDerived> &other) const
+{
+ return CwiseBinaryOp<internal::scalar_quotient_op<Scalar>, const Derived, const OtherDerived>(derived(), other.derived());
+}
+
+typedef CwiseBinaryOp<internal::scalar_cmp_op<Scalar,Scalar,internal::cmp_EQ>, const Derived, const ConstantReturnType> CwiseScalarEqualReturnType;
+
+/** \returns an expression of the coefficient-wise == operator of \c *this and a scalar \a s
+ *
+ * \warning this performs an exact comparison, which is generally a bad idea with floating-point types.
+ * In order to check for equality between two vectors or matrices with floating-point coefficients, it is
+ * generally a far better idea to use a fuzzy comparison as provided by isApprox() and
+ * isMuchSmallerThan().
+ *
+ * \sa cwiseEqual(const MatrixBase<OtherDerived> &) const
+ */
+EIGEN_DEVICE_FUNC
+inline const CwiseScalarEqualReturnType
+cwiseEqual(const Scalar& s) const
+{
+ return CwiseScalarEqualReturnType(derived(), Derived::Constant(rows(), cols(), s), internal::scalar_cmp_op<Scalar,Scalar,internal::cmp_EQ>());
+}
diff --git a/Eigen/src/plugins/MatrixCwiseUnaryOps.h b/Eigen/src/plugins/MatrixCwiseUnaryOps.h
new file mode 100644
index 0000000..98d925d
--- /dev/null
+++ b/Eigen/src/plugins/MatrixCwiseUnaryOps.h
@@ -0,0 +1,105 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+// This file is included into the body of the base classes supporting matrix specific coefficient-wise functions.
+// This include MatrixBase and SparseMatrixBase.
+
+
+typedef CwiseUnaryOp<internal::scalar_abs_op<Scalar>, const Derived> CwiseAbsReturnType;
+typedef CwiseUnaryOp<internal::scalar_abs2_op<Scalar>, const Derived> CwiseAbs2ReturnType;
+typedef CwiseUnaryOp<internal::scalar_arg_op<Scalar>, const Derived> CwiseArgReturnType;
+typedef CwiseUnaryOp<internal::scalar_sqrt_op<Scalar>, const Derived> CwiseSqrtReturnType;
+typedef CwiseUnaryOp<internal::scalar_sign_op<Scalar>, const Derived> CwiseSignReturnType;
+typedef CwiseUnaryOp<internal::scalar_inverse_op<Scalar>, const Derived> CwiseInverseReturnType;
+
+/// \returns an expression of the coefficient-wise absolute value of \c *this
+///
+/// Example: \include MatrixBase_cwiseAbs.cpp
+/// Output: \verbinclude MatrixBase_cwiseAbs.out
+///
+EIGEN_DOC_UNARY_ADDONS(cwiseAbs,absolute value)
+///
+/// \sa cwiseAbs2()
+///
+EIGEN_DEVICE_FUNC
+EIGEN_STRONG_INLINE const CwiseAbsReturnType
+cwiseAbs() const { return CwiseAbsReturnType(derived()); }
+
+/// \returns an expression of the coefficient-wise squared absolute value of \c *this
+///
+/// Example: \include MatrixBase_cwiseAbs2.cpp
+/// Output: \verbinclude MatrixBase_cwiseAbs2.out
+///
+EIGEN_DOC_UNARY_ADDONS(cwiseAbs2,squared absolute value)
+///
+/// \sa cwiseAbs()
+///
+EIGEN_DEVICE_FUNC
+EIGEN_STRONG_INLINE const CwiseAbs2ReturnType
+cwiseAbs2() const { return CwiseAbs2ReturnType(derived()); }
+
+/// \returns an expression of the coefficient-wise square root of *this.
+///
+/// Example: \include MatrixBase_cwiseSqrt.cpp
+/// Output: \verbinclude MatrixBase_cwiseSqrt.out
+///
+EIGEN_DOC_UNARY_ADDONS(cwiseSqrt,square-root)
+///
+/// \sa cwisePow(), cwiseSquare()
+///
+EIGEN_DEVICE_FUNC
+inline const CwiseSqrtReturnType
+cwiseSqrt() const { return CwiseSqrtReturnType(derived()); }
+
+/// \returns an expression of the coefficient-wise signum of *this.
+///
+/// Example: \include MatrixBase_cwiseSign.cpp
+/// Output: \verbinclude MatrixBase_cwiseSign.out
+///
+EIGEN_DOC_UNARY_ADDONS(cwiseSign,sign function)
+///
+EIGEN_DEVICE_FUNC
+inline const CwiseSignReturnType
+cwiseSign() const { return CwiseSignReturnType(derived()); }
+
+
+/// \returns an expression of the coefficient-wise inverse of *this.
+///
+/// Example: \include MatrixBase_cwiseInverse.cpp
+/// Output: \verbinclude MatrixBase_cwiseInverse.out
+///
+EIGEN_DOC_UNARY_ADDONS(cwiseInverse,inverse)
+///
+/// \sa cwiseProduct()
+///
+EIGEN_DEVICE_FUNC
+inline const CwiseInverseReturnType
+cwiseInverse() const { return CwiseInverseReturnType(derived()); }
+
+/// \returns an expression of the coefficient-wise phase angle of \c *this
+///
+/// Example: \include MatrixBase_cwiseArg.cpp
+/// Output: \verbinclude MatrixBase_cwiseArg.out
+///
+EIGEN_DOC_UNARY_ADDONS(cwiseArg,arg)
+
+EIGEN_DEVICE_FUNC
+inline const CwiseArgReturnType
+cwiseArg() const { return CwiseArgReturnType(derived()); }
+
+template <typename ScalarExponent>
+using CwisePowReturnType =
+ std::enable_if_t<internal::is_arithmetic<typename NumTraits<ScalarExponent>::Real>::value,
+ CwiseUnaryOp<internal::scalar_unary_pow_op<Scalar, ScalarExponent>, const Derived>>;
+
+template <typename ScalarExponent>
+EIGEN_DEVICE_FUNC inline const CwisePowReturnType<ScalarExponent> cwisePow(const ScalarExponent& exponent) const {
+ return CwisePowReturnType<ScalarExponent>(derived(), internal::scalar_unary_pow_op<Scalar, ScalarExponent>(exponent));
+}
diff --git a/Eigen/src/plugins/ReshapedMethods.h b/Eigen/src/plugins/ReshapedMethods.h
new file mode 100644
index 0000000..2cb1cf6
--- /dev/null
+++ b/Eigen/src/plugins/ReshapedMethods.h
@@ -0,0 +1,149 @@
+
+#ifdef EIGEN_PARSED_BY_DOXYGEN
+
+/// \returns an expression of \c *this with reshaped sizes.
+///
+/// \param nRows the number of rows in the reshaped expression, specified at either run-time or compile-time, or AutoSize
+/// \param nCols the number of columns in the reshaped expression, specified at either run-time or compile-time, or AutoSize
+/// \tparam Order specifies whether the coefficients should be processed in column-major-order (ColMajor), in row-major-order (RowMajor),
+/// or follows the \em natural order of the nested expression (AutoOrder). The default is ColMajor.
+/// \tparam NRowsType the type of the value handling the number of rows, typically Index.
+/// \tparam NColsType the type of the value handling the number of columns, typically Index.
+///
+/// Dynamic size example: \include MatrixBase_reshaped_int_int.cpp
+/// Output: \verbinclude MatrixBase_reshaped_int_int.out
+///
+/// The number of rows \a nRows and columns \a nCols can also be specified at compile-time by passing Eigen::fix<N>,
+/// or Eigen::fix<N>(n) as arguments. In the later case, \c n plays the role of a runtime fallback value in case \c N equals Eigen::Dynamic.
+/// Here is an example with a fixed number of rows and columns:
+/// \include MatrixBase_reshaped_fixed.cpp
+/// Output: \verbinclude MatrixBase_reshaped_fixed.out
+///
+/// Finally, one of the sizes parameter can be automatically deduced from the other one by passing AutoSize as in the following example:
+/// \include MatrixBase_reshaped_auto.cpp
+/// Output: \verbinclude MatrixBase_reshaped_auto.out
+/// AutoSize does preserve compile-time sizes when possible, i.e., when the sizes of the input are known at compile time \b and
+/// that the other size is passed at compile-time using Eigen::fix<N> as above.
+///
+/// \sa class Reshaped, fix, fix<N>(int)
+///
+template<int Order = ColMajor, typename NRowsType, typename NColsType>
+EIGEN_DEVICE_FUNC
+inline Reshaped<Derived,...>
+reshaped(NRowsType nRows, NColsType nCols);
+
+/// This is the const version of reshaped(NRowsType,NColsType).
+template<int Order = ColMajor, typename NRowsType, typename NColsType>
+EIGEN_DEVICE_FUNC
+inline const Reshaped<const Derived,...>
+reshaped(NRowsType nRows, NColsType nCols) const;
+
+/// \returns an expression of \c *this with columns (or rows) stacked to a linear column vector
+///
+/// \tparam Order specifies whether the coefficients should be processed in column-major-order (ColMajor), in row-major-order (RowMajor),
+/// or follows the \em natural order of the nested expression (AutoOrder). The default is ColMajor.
+///
+/// This overloads is essentially a shortcut for `A.reshaped<Order>(AutoSize,fix<1>)`.
+///
+/// - If `Order==ColMajor` (the default), then it returns a column-vector from the stacked columns of \c *this.
+/// - If `Order==RowMajor`, then it returns a column-vector from the stacked rows of \c *this.
+/// - If `Order==AutoOrder`, then it returns a column-vector with elements stacked following the storage order of \c *this.
+/// This mode is the recommended one when the particular ordering of the element is not relevant.
+///
+/// Example:
+/// \include MatrixBase_reshaped_to_vector.cpp
+/// Output: \verbinclude MatrixBase_reshaped_to_vector.out
+///
+/// If you want more control, you can still fall back to reshaped(NRowsType,NColsType).
+///
+/// \sa reshaped(NRowsType,NColsType), class Reshaped
+///
+template<int Order = ColMajor>
+EIGEN_DEVICE_FUNC
+inline Reshaped<Derived,...>
+reshaped();
+
+/// This is the const version of reshaped().
+template<int Order = ColMajor>
+EIGEN_DEVICE_FUNC
+inline const Reshaped<const Derived,...>
+reshaped() const;
+
+#else
+
+// This file is automatically included twice to generate const and non-const versions
+
+#ifndef EIGEN_RESHAPED_METHOD_2ND_PASS
+#define EIGEN_RESHAPED_METHOD_CONST const
+#else
+#define EIGEN_RESHAPED_METHOD_CONST
+#endif
+
+#ifndef EIGEN_RESHAPED_METHOD_2ND_PASS
+
+// This part is included once
+
+#endif
+
+template<typename NRowsType, typename NColsType>
+EIGEN_DEVICE_FUNC
+inline Reshaped<EIGEN_RESHAPED_METHOD_CONST Derived,
+ internal::get_compiletime_reshape_size<NRowsType,NColsType,SizeAtCompileTime>::value,
+ internal::get_compiletime_reshape_size<NColsType,NRowsType,SizeAtCompileTime>::value>
+reshaped(NRowsType nRows, NColsType nCols) EIGEN_RESHAPED_METHOD_CONST
+{
+ return Reshaped<EIGEN_RESHAPED_METHOD_CONST Derived,
+ internal::get_compiletime_reshape_size<NRowsType,NColsType,SizeAtCompileTime>::value,
+ internal::get_compiletime_reshape_size<NColsType,NRowsType,SizeAtCompileTime>::value>
+ (derived(),
+ internal::get_runtime_reshape_size(nRows,internal::get_runtime_value(nCols),size()),
+ internal::get_runtime_reshape_size(nCols,internal::get_runtime_value(nRows),size()));
+}
+
+template<int Order, typename NRowsType, typename NColsType>
+EIGEN_DEVICE_FUNC
+inline Reshaped<EIGEN_RESHAPED_METHOD_CONST Derived,
+ internal::get_compiletime_reshape_size<NRowsType,NColsType,SizeAtCompileTime>::value,
+ internal::get_compiletime_reshape_size<NColsType,NRowsType,SizeAtCompileTime>::value,
+ internal::get_compiletime_reshape_order(Flags, Order)>
+reshaped(NRowsType nRows, NColsType nCols) EIGEN_RESHAPED_METHOD_CONST
+{
+ return Reshaped<EIGEN_RESHAPED_METHOD_CONST Derived,
+ internal::get_compiletime_reshape_size<NRowsType,NColsType,SizeAtCompileTime>::value,
+ internal::get_compiletime_reshape_size<NColsType,NRowsType,SizeAtCompileTime>::value,
+ internal::get_compiletime_reshape_order(Flags, Order)>
+ (derived(),
+ internal::get_runtime_reshape_size(nRows,internal::get_runtime_value(nCols),size()),
+ internal::get_runtime_reshape_size(nCols,internal::get_runtime_value(nRows),size()));
+}
+
+// Views as linear vectors
+
+EIGEN_DEVICE_FUNC
+inline Reshaped<EIGEN_RESHAPED_METHOD_CONST Derived,SizeAtCompileTime,1>
+reshaped() EIGEN_RESHAPED_METHOD_CONST
+{
+ return Reshaped<EIGEN_RESHAPED_METHOD_CONST Derived,SizeAtCompileTime,1>(derived(),size(),1);
+}
+
+template<int Order>
+EIGEN_DEVICE_FUNC
+inline Reshaped<EIGEN_RESHAPED_METHOD_CONST Derived, SizeAtCompileTime, 1,
+ internal::get_compiletime_reshape_order(Flags, Order)>
+reshaped() EIGEN_RESHAPED_METHOD_CONST
+{
+ EIGEN_STATIC_ASSERT(Order==RowMajor || Order==ColMajor || Order==AutoOrder, INVALID_TEMPLATE_PARAMETER);
+ return Reshaped<EIGEN_RESHAPED_METHOD_CONST Derived, SizeAtCompileTime, 1,
+ internal::get_compiletime_reshape_order(Flags, Order)>
+ (derived(), size(), 1);
+}
+
+#undef EIGEN_RESHAPED_METHOD_CONST
+
+#ifndef EIGEN_RESHAPED_METHOD_2ND_PASS
+#define EIGEN_RESHAPED_METHOD_2ND_PASS
+#include "ReshapedMethods.h"
+#undef EIGEN_RESHAPED_METHOD_2ND_PASS
+#endif
+
+#endif // EIGEN_PARSED_BY_DOXYGEN
diff --git a/INSTALL b/INSTALL
new file mode 100644
index 0000000..4f717e9
--- /dev/null
+++ b/INSTALL
@@ -0,0 +1,35 @@
+Installation instructions for Eigen
+***********************************
+
+Explanation before starting
+***************************
+
+Eigen consists only of header files, hence there is nothing to compile
+before you can use it. Moreover, these header files do not depend on your
+platform, they are the same for everybody.
+
+Method 1. Installing without using CMake
+****************************************
+
+You can use right away the headers in the Eigen/ subdirectory. In order
+to install, just copy this Eigen/ subdirectory to your favorite location.
+If you also want the unsupported features, copy the unsupported/
+subdirectory too.
+
+Method 2. Installing using CMake
+********************************
+
+Let's call this directory 'source_dir' (where this INSTALL file is).
+Before starting, create another directory which we will call 'build_dir'.
+
+Do:
+
+ cd build_dir
+ cmake source_dir
+ make install
+
+The "make install" step may require administrator privileges.
+
+You can adjust the installation destination (the "prefix")
+by passing the -DCMAKE_INSTALL_PREFIX=myprefix option to cmake, as is
+explained in the message that cmake prints at the end.
diff --git a/bench/BenchSparseUtil.h b/bench/BenchSparseUtil.h
new file mode 100644
index 0000000..13981f6
--- /dev/null
+++ b/bench/BenchSparseUtil.h
@@ -0,0 +1,149 @@
+
+#include <Eigen/Sparse>
+#include <bench/BenchTimer.h>
+#include <set>
+
+using namespace std;
+using namespace Eigen;
+using namespace Eigen;
+
+#ifndef SIZE
+#define SIZE 1024
+#endif
+
+#ifndef DENSITY
+#define DENSITY 0.01
+#endif
+
+#ifndef SCALAR
+#define SCALAR double
+#endif
+
+typedef SCALAR Scalar;
+typedef Matrix<Scalar,Dynamic,Dynamic> DenseMatrix;
+typedef Matrix<Scalar,Dynamic,1> DenseVector;
+typedef SparseMatrix<Scalar> EigenSparseMatrix;
+
+void fillMatrix(float density, int rows, int cols, EigenSparseMatrix& dst)
+{
+ dst.reserve(double(rows)*cols*density);
+ for(int j = 0; j < cols; j++)
+ {
+ for(int i = 0; i < rows; i++)
+ {
+ Scalar v = (internal::random<float>(0,1) < density) ? internal::random<Scalar>() : 0;
+ if (v!=0)
+ dst.insert(i,j) = v;
+ }
+ }
+ dst.finalize();
+}
+
+void fillMatrix2(int nnzPerCol, int rows, int cols, EigenSparseMatrix& dst)
+{
+// std::cout << "alloc " << nnzPerCol*cols << "\n";
+ dst.reserve(nnzPerCol*cols);
+ for(int j = 0; j < cols; j++)
+ {
+ std::set<int> aux;
+ for(int i = 0; i < nnzPerCol; i++)
+ {
+ int k = internal::random<int>(0,rows-1);
+ while (aux.find(k)!=aux.end())
+ k = internal::random<int>(0,rows-1);
+ aux.insert(k);
+
+ dst.insert(k,j) = internal::random<Scalar>();
+ }
+ }
+ dst.finalize();
+}
+
+void eiToDense(const EigenSparseMatrix& src, DenseMatrix& dst)
+{
+ dst.setZero();
+ for (int j=0; j<src.cols(); ++j)
+ for (EigenSparseMatrix::InnerIterator it(src.derived(), j); it; ++it)
+ dst(it.index(),j) = it.value();
+}
+
+#ifndef NOGMM
+#include "gmm/gmm.h"
+typedef gmm::csc_matrix<Scalar> GmmSparse;
+typedef gmm::col_matrix< gmm::wsvector<Scalar> > GmmDynSparse;
+void eiToGmm(const EigenSparseMatrix& src, GmmSparse& dst)
+{
+ GmmDynSparse tmp(src.rows(), src.cols());
+ for (int j=0; j<src.cols(); ++j)
+ for (EigenSparseMatrix::InnerIterator it(src.derived(), j); it; ++it)
+ tmp(it.index(),j) = it.value();
+ gmm::copy(tmp, dst);
+}
+#endif
+
+#ifndef NOMTL
+#include <boost/numeric/mtl/mtl.hpp>
+typedef mtl::compressed2D<Scalar, mtl::matrix::parameters<mtl::tag::col_major> > MtlSparse;
+typedef mtl::compressed2D<Scalar, mtl::matrix::parameters<mtl::tag::row_major> > MtlSparseRowMajor;
+void eiToMtl(const EigenSparseMatrix& src, MtlSparse& dst)
+{
+ mtl::matrix::inserter<MtlSparse> ins(dst);
+ for (int j=0; j<src.cols(); ++j)
+ for (EigenSparseMatrix::InnerIterator it(src.derived(), j); it; ++it)
+ ins[it.index()][j] = it.value();
+}
+#endif
+
+#ifdef CSPARSE
+extern "C" {
+#include "cs.h"
+}
+void eiToCSparse(const EigenSparseMatrix& src, cs* &dst)
+{
+ cs* aux = cs_spalloc (0, 0, 1, 1, 1);
+ for (int j=0; j<src.cols(); ++j)
+ for (EigenSparseMatrix::InnerIterator it(src.derived(), j); it; ++it)
+ if (!cs_entry(aux, it.index(), j, it.value()))
+ {
+ std::cout << "cs_entry error\n";
+ exit(2);
+ }
+ dst = cs_compress(aux);
+// cs_spfree(aux);
+}
+#endif // CSPARSE
+
+#ifndef NOUBLAS
+#include <boost/numeric/ublas/vector.hpp>
+#include <boost/numeric/ublas/matrix.hpp>
+#include <boost/numeric/ublas/io.hpp>
+#include <boost/numeric/ublas/triangular.hpp>
+#include <boost/numeric/ublas/vector_sparse.hpp>
+#include <boost/numeric/ublas/matrix_sparse.hpp>
+#include <boost/numeric/ublas/vector_of_vector.hpp>
+#include <boost/numeric/ublas/operation.hpp>
+
+typedef boost::numeric::ublas::compressed_matrix<Scalar,boost::numeric::ublas::column_major> UBlasSparse;
+
+void eiToUblas(const EigenSparseMatrix& src, UBlasSparse& dst)
+{
+ dst.resize(src.rows(), src.cols(), false);
+ for (int j=0; j<src.cols(); ++j)
+ for (EigenSparseMatrix::InnerIterator it(src.derived(), j); it; ++it)
+ dst(it.index(),j) = it.value();
+}
+
+template <typename EigenType, typename UblasType>
+void eiToUblasVec(const EigenType& src, UblasType& dst)
+{
+ dst.resize(src.size());
+ for (int j=0; j<src.size(); ++j)
+ dst[j] = src.coeff(j);
+}
+#endif
+
+#ifdef OSKI
+extern "C" {
+#include <oski/oski.h>
+}
+#endif
diff --git a/bench/BenchTimer.h b/bench/BenchTimer.h
new file mode 100644
index 0000000..8a0dbbe
--- /dev/null
+++ b/bench/BenchTimer.h
@@ -0,0 +1,199 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2010 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2009 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_BENCH_TIMERR_H
+#define EIGEN_BENCH_TIMERR_H
+
+#if defined(_WIN32) || defined(__CYGWIN__)
+# ifndef NOMINMAX
+# define NOMINMAX
+# define EIGEN_BT_UNDEF_NOMINMAX
+# endif
+# ifndef WIN32_LEAN_AND_MEAN
+# define WIN32_LEAN_AND_MEAN
+# define EIGEN_BT_UNDEF_WIN32_LEAN_AND_MEAN
+# endif
+# include <windows.h>
+#elif defined(__APPLE__)
+#include <mach/mach_time.h>
+#else
+# include <unistd.h>
+#endif
+
+static void escape(void *p) {
+#if EIGEN_COMP_GNUC || EIGEN_COMP_CLANG
+ asm volatile("" : : "g"(p) : "memory");
+#endif
+}
+
+static void clobber() {
+#if EIGEN_COMP_GNUC || EIGEN_COMP_CLANG
+ asm volatile("" : : : "memory");
+#endif
+}
+
+#include <Eigen/Core>
+
+namespace Eigen
+{
+
+enum {
+ CPU_TIMER = 0,
+ REAL_TIMER = 1
+};
+
+/** Elapsed time timer keeping the best try.
+ *
+ * On POSIX platforms we use clock_gettime with CLOCK_PROCESS_CPUTIME_ID.
+ * On Windows we use QueryPerformanceCounter
+ *
+ * Important: on linux, you must link with -lrt
+ */
+class BenchTimer
+{
+public:
+
+ BenchTimer()
+ {
+#if defined(_WIN32) || defined(__CYGWIN__)
+ LARGE_INTEGER freq;
+ QueryPerformanceFrequency(&freq);
+ m_frequency = (double)freq.QuadPart;
+#endif
+ reset();
+ }
+
+ ~BenchTimer() {}
+
+ inline void reset()
+ {
+ m_bests.fill(1e9);
+ m_worsts.fill(0);
+ m_totals.setZero();
+ }
+ inline void start()
+ {
+ m_starts[CPU_TIMER] = getCpuTime();
+ m_starts[REAL_TIMER] = getRealTime();
+ }
+ inline void stop()
+ {
+ m_times[CPU_TIMER] = getCpuTime() - m_starts[CPU_TIMER];
+ m_times[REAL_TIMER] = getRealTime() - m_starts[REAL_TIMER];
+ #if EIGEN_VERSION_AT_LEAST(2,90,0)
+ m_bests = m_bests.cwiseMin(m_times);
+ m_worsts = m_worsts.cwiseMax(m_times);
+ #else
+ m_bests(0) = std::min(m_bests(0),m_times(0));
+ m_bests(1) = std::min(m_bests(1),m_times(1));
+ m_worsts(0) = std::max(m_worsts(0),m_times(0));
+ m_worsts(1) = std::max(m_worsts(1),m_times(1));
+ #endif
+ m_totals += m_times;
+ }
+
+ /** Return the elapsed time in seconds between the last start/stop pair
+ */
+ inline double value(int TIMER = CPU_TIMER) const
+ {
+ return m_times[TIMER];
+ }
+
+ /** Return the best elapsed time in seconds
+ */
+ inline double best(int TIMER = CPU_TIMER) const
+ {
+ return m_bests[TIMER];
+ }
+
+ /** Return the worst elapsed time in seconds
+ */
+ inline double worst(int TIMER = CPU_TIMER) const
+ {
+ return m_worsts[TIMER];
+ }
+
+ /** Return the total elapsed time in seconds.
+ */
+ inline double total(int TIMER = CPU_TIMER) const
+ {
+ return m_totals[TIMER];
+ }
+
+ inline double getCpuTime() const
+ {
+#ifdef _WIN32
+ LARGE_INTEGER query_ticks;
+ QueryPerformanceCounter(&query_ticks);
+ return query_ticks.QuadPart/m_frequency;
+#elif __APPLE__
+ return double(mach_absolute_time())*1e-9;
+#else
+ timespec ts;
+ clock_gettime(CLOCK_PROCESS_CPUTIME_ID, &ts);
+ return double(ts.tv_sec) + 1e-9 * double(ts.tv_nsec);
+#endif
+ }
+
+ inline double getRealTime() const
+ {
+#ifdef _WIN32
+ SYSTEMTIME st;
+ GetSystemTime(&st);
+ return (double)st.wSecond + 1.e-3 * (double)st.wMilliseconds;
+#elif __APPLE__
+ return double(mach_absolute_time())*1e-9;
+#else
+ timespec ts;
+ clock_gettime(CLOCK_REALTIME, &ts);
+ return double(ts.tv_sec) + 1e-9 * double(ts.tv_nsec);
+#endif
+ }
+
+protected:
+#if defined(_WIN32) || defined(__CYGWIN__)
+ double m_frequency;
+#endif
+ Vector2d m_starts;
+ Vector2d m_times;
+ Vector2d m_bests;
+ Vector2d m_worsts;
+ Vector2d m_totals;
+
+public:
+ EIGEN_MAKE_ALIGNED_OPERATOR_NEW
+};
+
+#define BENCH(TIMER,TRIES,REP,CODE) { \
+ TIMER.reset(); \
+ for(int uglyvarname1=0; uglyvarname1<TRIES; ++uglyvarname1){ \
+ TIMER.start(); \
+ for(int uglyvarname2=0; uglyvarname2<REP; ++uglyvarname2){ \
+ CODE; \
+ } \
+ TIMER.stop(); \
+ clobber(); \
+ } \
+ }
+
+}
+
+// clean #defined tokens
+#ifdef EIGEN_BT_UNDEF_NOMINMAX
+# undef EIGEN_BT_UNDEF_NOMINMAX
+# undef NOMINMAX
+#endif
+
+#ifdef EIGEN_BT_UNDEF_WIN32_LEAN_AND_MEAN
+# undef EIGEN_BT_UNDEF_WIN32_LEAN_AND_MEAN
+# undef WIN32_LEAN_AND_MEAN
+#endif
+
+#endif // EIGEN_BENCH_TIMERR_H
diff --git a/bench/BenchUtil.h b/bench/BenchUtil.h
new file mode 100644
index 0000000..8883a13
--- /dev/null
+++ b/bench/BenchUtil.h
@@ -0,0 +1,92 @@
+
+#ifndef EIGEN_BENCH_UTIL_H
+#define EIGEN_BENCH_UTIL_H
+
+#include <Eigen/Core>
+#include "BenchTimer.h"
+
+using namespace std;
+using namespace Eigen;
+
+#include <boost/preprocessor/repetition/enum_params.hpp>
+#include <boost/preprocessor/repetition.hpp>
+#include <boost/preprocessor/seq.hpp>
+#include <boost/preprocessor/array.hpp>
+#include <boost/preprocessor/arithmetic.hpp>
+#include <boost/preprocessor/comparison.hpp>
+#include <boost/preprocessor/punctuation.hpp>
+#include <boost/preprocessor/punctuation/comma.hpp>
+#include <boost/preprocessor/stringize.hpp>
+
+template<typename MatrixType> void initMatrix_random(MatrixType& mat) __attribute__((noinline));
+template<typename MatrixType> void initMatrix_random(MatrixType& mat)
+{
+ mat.setRandom();// = MatrixType::random(mat.rows(), mat.cols());
+}
+
+template<typename MatrixType> void initMatrix_identity(MatrixType& mat) __attribute__((noinline));
+template<typename MatrixType> void initMatrix_identity(MatrixType& mat)
+{
+ mat.setIdentity();
+}
+
+#ifndef __INTEL_COMPILER
+#define DISABLE_SSE_EXCEPTIONS() { \
+ int aux; \
+ asm( \
+ "stmxcsr %[aux] \n\t" \
+ "orl $32832, %[aux] \n\t" \
+ "ldmxcsr %[aux] \n\t" \
+ : : [aux] "m" (aux)); \
+}
+#else
+#define DISABLE_SSE_EXCEPTIONS()
+#endif
+
+#ifdef BENCH_GMM
+#include <gmm/gmm.h>
+template <typename EigenMatrixType, typename GmmMatrixType>
+void eiToGmm(const EigenMatrixType& src, GmmMatrixType& dst)
+{
+ dst.resize(src.rows(),src.cols());
+ for (int j=0; j<src.cols(); ++j)
+ for (int i=0; i<src.rows(); ++i)
+ dst(i,j) = src.coeff(i,j);
+}
+#endif
+
+
+#ifdef BENCH_GSL
+#include <gsl/gsl_matrix.h>
+#include <gsl/gsl_linalg.h>
+#include <gsl/gsl_eigen.h>
+template <typename EigenMatrixType>
+void eiToGsl(const EigenMatrixType& src, gsl_matrix** dst)
+{
+ for (int j=0; j<src.cols(); ++j)
+ for (int i=0; i<src.rows(); ++i)
+ gsl_matrix_set(*dst, i, j, src.coeff(i,j));
+}
+#endif
+
+#ifdef BENCH_UBLAS
+#include <boost/numeric/ublas/matrix.hpp>
+#include <boost/numeric/ublas/vector.hpp>
+template <typename EigenMatrixType, typename UblasMatrixType>
+void eiToUblas(const EigenMatrixType& src, UblasMatrixType& dst)
+{
+ dst.resize(src.rows(),src.cols());
+ for (int j=0; j<src.cols(); ++j)
+ for (int i=0; i<src.rows(); ++i)
+ dst(i,j) = src.coeff(i,j);
+}
+template <typename EigenType, typename UblasType>
+void eiToUblasVec(const EigenType& src, UblasType& dst)
+{
+ dst.resize(src.size());
+ for (int j=0; j<src.size(); ++j)
+ dst[j] = src.coeff(j);
+}
+#endif
+
+#endif // EIGEN_BENCH_UTIL_H
diff --git a/bench/README.txt b/bench/README.txt
new file mode 100644
index 0000000..39831ae
--- /dev/null
+++ b/bench/README.txt
@@ -0,0 +1,55 @@
+
+This folder contains a couple of benchmark utities and Eigen benchmarks.
+
+****************************
+* bench_multi_compilers.sh *
+****************************
+
+This script allows to run a benchmark on a set of different compilers/compiler options.
+It takes two arguments:
+ - a file defining the list of the compilers with their options
+ - the .cpp file of the benchmark
+
+Examples:
+
+$ ./bench_multi_compilers.sh basicbench.cxxlist basicbenchmark.cpp
+
+ g++-4.1 -O3 -DNDEBUG -finline-limit=10000
+ 3d-3x3 / 4d-4x4 / Xd-4x4 / Xd-20x20 /
+ 0.271102 0.131416 0.422322 0.198633
+ 0.201658 0.102436 0.397566 0.207282
+
+ g++-4.2 -O3 -DNDEBUG -finline-limit=10000
+ 3d-3x3 / 4d-4x4 / Xd-4x4 / Xd-20x20 /
+ 0.107805 0.0890579 0.30265 0.161843
+ 0.127157 0.0712581 0.278341 0.191029
+
+ g++-4.3 -O3 -DNDEBUG -finline-limit=10000
+ 3d-3x3 / 4d-4x4 / Xd-4x4 / Xd-20x20 /
+ 0.134318 0.105291 0.3704 0.180966
+ 0.137703 0.0732472 0.31225 0.202204
+
+ icpc -fast -DNDEBUG -fno-exceptions -no-inline-max-size
+ 3d-3x3 / 4d-4x4 / Xd-4x4 / Xd-20x20 /
+ 0.226145 0.0941319 0.371873 0.159433
+ 0.109302 0.0837538 0.328102 0.173891
+
+
+$ ./bench_multi_compilers.sh ompbench.cxxlist ompbenchmark.cpp
+
+ g++-4.2 -O3 -DNDEBUG -finline-limit=10000 -fopenmp
+ double, fixed-size 4x4: 0.00165105s 0.0778739s
+ double, 32x32: 0.0654769s 0.075289s => x0.869674 (2)
+ double, 128x128: 0.054148s 0.0419669s => x1.29025 (2)
+ double, 512x512: 0.913799s 0.428533s => x2.13239 (2)
+ double, 1024x1024: 14.5972s 9.3542s => x1.5605 (2)
+
+ icpc -fast -DNDEBUG -fno-exceptions -no-inline-max-size -openmp
+ double, fixed-size 4x4: 0.000589848s 0.019949s
+ double, 32x32: 0.0682781s 0.0449722s => x1.51823 (2)
+ double, 128x128: 0.0547509s 0.0435519s => x1.25714 (2)
+ double, 512x512: 0.829436s 0.424438s => x1.9542 (2)
+ double, 1024x1024: 14.5243s 10.7735s => x1.34815 (2)
+
+
+
diff --git a/bench/analyze-blocking-sizes.cpp b/bench/analyze-blocking-sizes.cpp
new file mode 100644
index 0000000..6bc4aca
--- /dev/null
+++ b/bench/analyze-blocking-sizes.cpp
@@ -0,0 +1,876 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2015 Benoit Jacob <benoitjacob@google.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include <iostream>
+#include <cstdint>
+#include <cstdlib>
+#include <vector>
+#include <algorithm>
+#include <fstream>
+#include <string>
+#include <cmath>
+#include <cassert>
+#include <cstring>
+#include <memory>
+
+#include <Eigen/Core>
+
+using namespace std;
+
+const int default_precision = 4;
+
+// see --only-cubic-sizes
+bool only_cubic_sizes = false;
+
+// see --dump-tables
+bool dump_tables = false;
+
+uint8_t log2_pot(size_t x) {
+ size_t l = 0;
+ while (x >>= 1) l++;
+ return l;
+}
+
+uint16_t compact_size_triple(size_t k, size_t m, size_t n)
+{
+ return (log2_pot(k) << 8) | (log2_pot(m) << 4) | log2_pot(n);
+}
+
+// just a helper to store a triple of K,M,N sizes for matrix product
+struct size_triple_t
+{
+ uint16_t k, m, n;
+ size_triple_t() : k(0), m(0), n(0) {}
+ size_triple_t(size_t _k, size_t _m, size_t _n) : k(_k), m(_m), n(_n) {}
+ size_triple_t(const size_triple_t& o) : k(o.k), m(o.m), n(o.n) {}
+ size_triple_t(uint16_t compact)
+ {
+ k = 1 << ((compact & 0xf00) >> 8);
+ m = 1 << ((compact & 0x0f0) >> 4);
+ n = 1 << ((compact & 0x00f) >> 0);
+ }
+ bool is_cubic() const { return k == m && m == n; }
+};
+
+ostream& operator<<(ostream& s, const size_triple_t& t)
+{
+ return s << "(" << t.k << ", " << t.m << ", " << t.n << ")";
+}
+
+struct inputfile_entry_t
+{
+ uint16_t product_size;
+ uint16_t pot_block_size;
+ size_triple_t nonpot_block_size;
+ float gflops;
+};
+
+struct inputfile_t
+{
+ enum class type_t {
+ unknown,
+ all_pot_sizes,
+ default_sizes
+ };
+
+ string filename;
+ vector<inputfile_entry_t> entries;
+ type_t type;
+
+ inputfile_t(const string& fname)
+ : filename(fname)
+ , type(type_t::unknown)
+ {
+ ifstream stream(filename);
+ if (!stream.is_open()) {
+ cerr << "couldn't open input file: " << filename << endl;
+ exit(1);
+ }
+ string line;
+ while (getline(stream, line)) {
+ if (line.empty()) continue;
+ if (line.find("BEGIN MEASUREMENTS ALL POT SIZES") == 0) {
+ if (type != type_t::unknown) {
+ cerr << "Input file " << filename << " contains redundant BEGIN MEASUREMENTS lines";
+ exit(1);
+ }
+ type = type_t::all_pot_sizes;
+ continue;
+ }
+ if (line.find("BEGIN MEASUREMENTS DEFAULT SIZES") == 0) {
+ if (type != type_t::unknown) {
+ cerr << "Input file " << filename << " contains redundant BEGIN MEASUREMENTS lines";
+ exit(1);
+ }
+ type = type_t::default_sizes;
+ continue;
+ }
+
+
+ if (type == type_t::unknown) {
+ continue;
+ }
+ switch(type) {
+ case type_t::all_pot_sizes: {
+ unsigned int product_size, block_size;
+ float gflops;
+ int sscanf_result =
+ sscanf(line.c_str(), "%x %x %f",
+ &product_size,
+ &block_size,
+ &gflops);
+ if (3 != sscanf_result ||
+ !product_size ||
+ product_size > 0xfff ||
+ !block_size ||
+ block_size > 0xfff ||
+ !isfinite(gflops))
+ {
+ cerr << "ill-formed input file: " << filename << endl;
+ cerr << "offending line:" << endl << line << endl;
+ exit(1);
+ }
+ if (only_cubic_sizes && !size_triple_t(product_size).is_cubic()) {
+ continue;
+ }
+ inputfile_entry_t entry;
+ entry.product_size = uint16_t(product_size);
+ entry.pot_block_size = uint16_t(block_size);
+ entry.gflops = gflops;
+ entries.push_back(entry);
+ break;
+ }
+ case type_t::default_sizes: {
+ unsigned int product_size;
+ float gflops;
+ int bk, bm, bn;
+ int sscanf_result =
+ sscanf(line.c_str(), "%x default(%d, %d, %d) %f",
+ &product_size,
+ &bk, &bm, &bn,
+ &gflops);
+ if (5 != sscanf_result ||
+ !product_size ||
+ product_size > 0xfff ||
+ !isfinite(gflops))
+ {
+ cerr << "ill-formed input file: " << filename << endl;
+ cerr << "offending line:" << endl << line << endl;
+ exit(1);
+ }
+ if (only_cubic_sizes && !size_triple_t(product_size).is_cubic()) {
+ continue;
+ }
+ inputfile_entry_t entry;
+ entry.product_size = uint16_t(product_size);
+ entry.pot_block_size = 0;
+ entry.nonpot_block_size = size_triple_t(bk, bm, bn);
+ entry.gflops = gflops;
+ entries.push_back(entry);
+ break;
+ }
+
+ default:
+ break;
+ }
+ }
+ stream.close();
+ if (type == type_t::unknown) {
+ cerr << "Unrecognized input file " << filename << endl;
+ exit(1);
+ }
+ if (entries.empty()) {
+ cerr << "didn't find any measurements in input file: " << filename << endl;
+ exit(1);
+ }
+ }
+};
+
+struct preprocessed_inputfile_entry_t
+{
+ uint16_t product_size;
+ uint16_t block_size;
+
+ float efficiency;
+};
+
+bool lower_efficiency(const preprocessed_inputfile_entry_t& e1, const preprocessed_inputfile_entry_t& e2)
+{
+ return e1.efficiency < e2.efficiency;
+}
+
+struct preprocessed_inputfile_t
+{
+ string filename;
+ vector<preprocessed_inputfile_entry_t> entries;
+
+ preprocessed_inputfile_t(const inputfile_t& inputfile)
+ : filename(inputfile.filename)
+ {
+ if (inputfile.type != inputfile_t::type_t::all_pot_sizes) {
+ abort();
+ }
+ auto it = inputfile.entries.begin();
+ auto it_first_with_given_product_size = it;
+ while (it != inputfile.entries.end()) {
+ ++it;
+ if (it == inputfile.entries.end() ||
+ it->product_size != it_first_with_given_product_size->product_size)
+ {
+ import_input_file_range_one_product_size(it_first_with_given_product_size, it);
+ it_first_with_given_product_size = it;
+ }
+ }
+ }
+
+private:
+ void import_input_file_range_one_product_size(
+ const vector<inputfile_entry_t>::const_iterator& begin,
+ const vector<inputfile_entry_t>::const_iterator& end)
+ {
+ uint16_t product_size = begin->product_size;
+ float max_gflops = 0.0f;
+ for (auto it = begin; it != end; ++it) {
+ if (it->product_size != product_size) {
+ cerr << "Unexpected ordering of entries in " << filename << endl;
+ cerr << "(Expected all entries for product size " << hex << product_size << dec << " to be grouped)" << endl;
+ exit(1);
+ }
+ max_gflops = max(max_gflops, it->gflops);
+ }
+ for (auto it = begin; it != end; ++it) {
+ preprocessed_inputfile_entry_t entry;
+ entry.product_size = it->product_size;
+ entry.block_size = it->pot_block_size;
+ entry.efficiency = it->gflops / max_gflops;
+ entries.push_back(entry);
+ }
+ }
+};
+
+void check_all_files_in_same_exact_order(
+ const vector<preprocessed_inputfile_t>& preprocessed_inputfiles)
+{
+ if (preprocessed_inputfiles.empty()) {
+ return;
+ }
+
+ const preprocessed_inputfile_t& first_file = preprocessed_inputfiles[0];
+ const size_t num_entries = first_file.entries.size();
+
+ for (size_t i = 0; i < preprocessed_inputfiles.size(); i++) {
+ if (preprocessed_inputfiles[i].entries.size() != num_entries) {
+ cerr << "these files have different number of entries: "
+ << preprocessed_inputfiles[i].filename
+ << " and "
+ << first_file.filename
+ << endl;
+ exit(1);
+ }
+ }
+
+ for (size_t entry_index = 0; entry_index < num_entries; entry_index++) {
+ const uint16_t entry_product_size = first_file.entries[entry_index].product_size;
+ const uint16_t entry_block_size = first_file.entries[entry_index].block_size;
+ for (size_t file_index = 0; file_index < preprocessed_inputfiles.size(); file_index++) {
+ const preprocessed_inputfile_t& cur_file = preprocessed_inputfiles[file_index];
+ if (cur_file.entries[entry_index].product_size != entry_product_size ||
+ cur_file.entries[entry_index].block_size != entry_block_size)
+ {
+ cerr << "entries not in same order between these files: "
+ << first_file.filename
+ << " and "
+ << cur_file.filename
+ << endl;
+ exit(1);
+ }
+ }
+ }
+}
+
+float efficiency_of_subset(
+ const vector<preprocessed_inputfile_t>& preprocessed_inputfiles,
+ const vector<size_t>& subset)
+{
+ if (subset.size() <= 1) {
+ return 1.0f;
+ }
+ const preprocessed_inputfile_t& first_file = preprocessed_inputfiles[subset[0]];
+ const size_t num_entries = first_file.entries.size();
+ float efficiency = 1.0f;
+ size_t entry_index = 0;
+ size_t first_entry_index_with_this_product_size = 0;
+ uint16_t product_size = first_file.entries[0].product_size;
+ while (entry_index < num_entries) {
+ ++entry_index;
+ if (entry_index == num_entries ||
+ first_file.entries[entry_index].product_size != product_size)
+ {
+ float efficiency_this_product_size = 0.0f;
+ for (size_t e = first_entry_index_with_this_product_size; e < entry_index; e++) {
+ float efficiency_this_entry = 1.0f;
+ for (auto i = subset.begin(); i != subset.end(); ++i) {
+ efficiency_this_entry = min(efficiency_this_entry, preprocessed_inputfiles[*i].entries[e].efficiency);
+ }
+ efficiency_this_product_size = max(efficiency_this_product_size, efficiency_this_entry);
+ }
+ efficiency = min(efficiency, efficiency_this_product_size);
+ if (entry_index < num_entries) {
+ first_entry_index_with_this_product_size = entry_index;
+ product_size = first_file.entries[entry_index].product_size;
+ }
+ }
+ }
+
+ return efficiency;
+}
+
+void dump_table_for_subset(
+ const vector<preprocessed_inputfile_t>& preprocessed_inputfiles,
+ const vector<size_t>& subset)
+{
+ const preprocessed_inputfile_t& first_file = preprocessed_inputfiles[subset[0]];
+ const size_t num_entries = first_file.entries.size();
+ size_t entry_index = 0;
+ size_t first_entry_index_with_this_product_size = 0;
+ uint16_t product_size = first_file.entries[0].product_size;
+ size_t i = 0;
+ size_triple_t min_product_size(first_file.entries.front().product_size);
+ size_triple_t max_product_size(first_file.entries.back().product_size);
+ if (!min_product_size.is_cubic() || !max_product_size.is_cubic()) {
+ abort();
+ }
+ if (only_cubic_sizes) {
+ cerr << "Can't generate tables with --only-cubic-sizes." << endl;
+ abort();
+ }
+ cout << "struct LookupTable {" << endl;
+ cout << " static const size_t BaseSize = " << min_product_size.k << ";" << endl;
+ const size_t NumSizes = log2_pot(max_product_size.k / min_product_size.k) + 1;
+ const size_t TableSize = NumSizes * NumSizes * NumSizes;
+ cout << " static const size_t NumSizes = " << NumSizes << ";" << endl;
+ cout << " static const unsigned short* Data() {" << endl;
+ cout << " static const unsigned short data[" << TableSize << "] = {";
+ while (entry_index < num_entries) {
+ ++entry_index;
+ if (entry_index == num_entries ||
+ first_file.entries[entry_index].product_size != product_size)
+ {
+ float best_efficiency_this_product_size = 0.0f;
+ uint16_t best_block_size_this_product_size = 0;
+ for (size_t e = first_entry_index_with_this_product_size; e < entry_index; e++) {
+ float efficiency_this_entry = 1.0f;
+ for (auto i = subset.begin(); i != subset.end(); ++i) {
+ efficiency_this_entry = min(efficiency_this_entry, preprocessed_inputfiles[*i].entries[e].efficiency);
+ }
+ if (efficiency_this_entry > best_efficiency_this_product_size) {
+ best_efficiency_this_product_size = efficiency_this_entry;
+ best_block_size_this_product_size = first_file.entries[e].block_size;
+ }
+ }
+ if ((i++) % NumSizes) {
+ cout << " ";
+ } else {
+ cout << endl << " ";
+ }
+ cout << "0x" << hex << best_block_size_this_product_size << dec;
+ if (entry_index < num_entries) {
+ cout << ",";
+ first_entry_index_with_this_product_size = entry_index;
+ product_size = first_file.entries[entry_index].product_size;
+ }
+ }
+ }
+ if (i != TableSize) {
+ cerr << endl << "Wrote " << i << " table entries, expected " << TableSize << endl;
+ abort();
+ }
+ cout << endl << " };" << endl;
+ cout << " return data;" << endl;
+ cout << " }" << endl;
+ cout << "};" << endl;
+}
+
+float efficiency_of_partition(
+ const vector<preprocessed_inputfile_t>& preprocessed_inputfiles,
+ const vector<vector<size_t>>& partition)
+{
+ float efficiency = 1.0f;
+ for (auto s = partition.begin(); s != partition.end(); ++s) {
+ efficiency = min(efficiency, efficiency_of_subset(preprocessed_inputfiles, *s));
+ }
+ return efficiency;
+}
+
+void make_first_subset(size_t subset_size, vector<size_t>& out_subset, size_t set_size)
+{
+ assert(subset_size >= 1 && subset_size <= set_size);
+ out_subset.resize(subset_size);
+ for (size_t i = 0; i < subset_size; i++) {
+ out_subset[i] = i;
+ }
+}
+
+bool is_last_subset(const vector<size_t>& subset, size_t set_size)
+{
+ return subset[0] == set_size - subset.size();
+}
+
+void next_subset(vector<size_t>& inout_subset, size_t set_size)
+{
+ if (is_last_subset(inout_subset, set_size)) {
+ cerr << "iterating past the last subset" << endl;
+ abort();
+ }
+ size_t i = 1;
+ while (inout_subset[inout_subset.size() - i] == set_size - i) {
+ i++;
+ assert(i <= inout_subset.size());
+ }
+ size_t first_index_to_change = inout_subset.size() - i;
+ inout_subset[first_index_to_change]++;
+ size_t p = inout_subset[first_index_to_change];
+ for (size_t j = first_index_to_change + 1; j < inout_subset.size(); j++) {
+ inout_subset[j] = ++p;
+ }
+}
+
+const size_t number_of_subsets_limit = 100;
+const size_t always_search_subsets_of_size_at_least = 2;
+
+bool is_number_of_subsets_feasible(size_t n, size_t p)
+{
+ assert(n>0 && p>0 && p<=n);
+ uint64_t numerator = 1, denominator = 1;
+ for (size_t i = 0; i < p; i++) {
+ numerator *= n - i;
+ denominator *= i + 1;
+ if (numerator > denominator * number_of_subsets_limit) {
+ return false;
+ }
+ }
+ return true;
+}
+
+size_t max_feasible_subset_size(size_t n)
+{
+ assert(n > 0);
+ const size_t minresult = min<size_t>(n-1, always_search_subsets_of_size_at_least);
+ for (size_t p = 1; p <= n - 1; p++) {
+ if (!is_number_of_subsets_feasible(n, p+1)) {
+ return max(p, minresult);
+ }
+ }
+ return n - 1;
+}
+
+void find_subset_with_efficiency_higher_than(
+ const vector<preprocessed_inputfile_t>& preprocessed_inputfiles,
+ float required_efficiency_to_beat,
+ vector<size_t>& inout_remainder,
+ vector<size_t>& out_subset)
+{
+ out_subset.resize(0);
+
+ if (required_efficiency_to_beat >= 1.0f) {
+ cerr << "can't beat efficiency 1." << endl;
+ abort();
+ }
+
+ while (!inout_remainder.empty()) {
+
+ vector<size_t> candidate_indices(inout_remainder.size());
+ for (size_t i = 0; i < candidate_indices.size(); i++) {
+ candidate_indices[i] = i;
+ }
+
+ size_t candidate_indices_subset_size = max_feasible_subset_size(candidate_indices.size());
+ while (candidate_indices_subset_size >= 1) {
+ vector<size_t> candidate_indices_subset;
+ make_first_subset(candidate_indices_subset_size,
+ candidate_indices_subset,
+ candidate_indices.size());
+
+ vector<size_t> best_candidate_indices_subset;
+ float best_efficiency = 0.0f;
+ vector<size_t> trial_subset = out_subset;
+ trial_subset.resize(out_subset.size() + candidate_indices_subset_size);
+ while (true)
+ {
+ for (size_t i = 0; i < candidate_indices_subset_size; i++) {
+ trial_subset[out_subset.size() + i] = inout_remainder[candidate_indices_subset[i]];
+ }
+
+ float trial_efficiency = efficiency_of_subset(preprocessed_inputfiles, trial_subset);
+ if (trial_efficiency > best_efficiency) {
+ best_efficiency = trial_efficiency;
+ best_candidate_indices_subset = candidate_indices_subset;
+ }
+ if (is_last_subset(candidate_indices_subset, candidate_indices.size())) {
+ break;
+ }
+ next_subset(candidate_indices_subset, candidate_indices.size());
+ }
+
+ if (best_efficiency > required_efficiency_to_beat) {
+ for (size_t i = 0; i < best_candidate_indices_subset.size(); i++) {
+ candidate_indices[i] = candidate_indices[best_candidate_indices_subset[i]];
+ }
+ candidate_indices.resize(best_candidate_indices_subset.size());
+ }
+ candidate_indices_subset_size--;
+ }
+
+ size_t candidate_index = candidate_indices[0];
+ auto candidate_iterator = inout_remainder.begin() + candidate_index;
+ vector<size_t> trial_subset = out_subset;
+
+ trial_subset.push_back(*candidate_iterator);
+ float trial_efficiency = efficiency_of_subset(preprocessed_inputfiles, trial_subset);
+ if (trial_efficiency > required_efficiency_to_beat) {
+ out_subset.push_back(*candidate_iterator);
+ inout_remainder.erase(candidate_iterator);
+ } else {
+ break;
+ }
+ }
+}
+
+void find_partition_with_efficiency_higher_than(
+ const vector<preprocessed_inputfile_t>& preprocessed_inputfiles,
+ float required_efficiency_to_beat,
+ vector<vector<size_t>>& out_partition)
+{
+ out_partition.resize(0);
+
+ vector<size_t> remainder;
+ for (size_t i = 0; i < preprocessed_inputfiles.size(); i++) {
+ remainder.push_back(i);
+ }
+
+ while (!remainder.empty()) {
+ vector<size_t> new_subset;
+ find_subset_with_efficiency_higher_than(
+ preprocessed_inputfiles,
+ required_efficiency_to_beat,
+ remainder,
+ new_subset);
+ out_partition.push_back(new_subset);
+ }
+}
+
+void print_partition(
+ const vector<preprocessed_inputfile_t>& preprocessed_inputfiles,
+ const vector<vector<size_t>>& partition)
+{
+ float efficiency = efficiency_of_partition(preprocessed_inputfiles, partition);
+ cout << "Partition into " << partition.size() << " subsets for " << efficiency * 100.0f << "% efficiency" << endl;
+ for (auto subset = partition.begin(); subset != partition.end(); ++subset) {
+ cout << " Subset " << (subset - partition.begin())
+ << ", efficiency " << efficiency_of_subset(preprocessed_inputfiles, *subset) * 100.0f << "%:"
+ << endl;
+ for (auto file = subset->begin(); file != subset->end(); ++file) {
+ cout << " " << preprocessed_inputfiles[*file].filename << endl;
+ }
+ if (dump_tables) {
+ cout << " Table:" << endl;
+ dump_table_for_subset(preprocessed_inputfiles, *subset);
+ }
+ }
+ cout << endl;
+}
+
+struct action_t
+{
+ virtual const char* invokation_name() const { abort(); return nullptr; }
+ virtual void run(const vector<string>&) const { abort(); }
+ virtual ~action_t() {}
+};
+
+struct partition_action_t : action_t
+{
+ virtual const char* invokation_name() const override { return "partition"; }
+ virtual void run(const vector<string>& input_filenames) const override
+ {
+ vector<preprocessed_inputfile_t> preprocessed_inputfiles;
+
+ if (input_filenames.empty()) {
+ cerr << "The " << invokation_name() << " action needs a list of input files." << endl;
+ exit(1);
+ }
+
+ for (auto it = input_filenames.begin(); it != input_filenames.end(); ++it) {
+ inputfile_t inputfile(*it);
+ switch (inputfile.type) {
+ case inputfile_t::type_t::all_pot_sizes:
+ preprocessed_inputfiles.emplace_back(inputfile);
+ break;
+ case inputfile_t::type_t::default_sizes:
+ cerr << "The " << invokation_name() << " action only uses measurements for all pot sizes, and "
+ << "has no use for " << *it << " which contains measurements for default sizes." << endl;
+ exit(1);
+ break;
+ default:
+ cerr << "Unrecognized input file: " << *it << endl;
+ exit(1);
+ }
+ }
+
+ check_all_files_in_same_exact_order(preprocessed_inputfiles);
+
+ float required_efficiency_to_beat = 0.0f;
+ vector<vector<vector<size_t>>> partitions;
+ cerr << "searching for partitions...\r" << flush;
+ while (true)
+ {
+ vector<vector<size_t>> partition;
+ find_partition_with_efficiency_higher_than(
+ preprocessed_inputfiles,
+ required_efficiency_to_beat,
+ partition);
+ float actual_efficiency = efficiency_of_partition(preprocessed_inputfiles, partition);
+ cerr << "partition " << preprocessed_inputfiles.size() << " files into " << partition.size()
+ << " subsets for " << 100.0f * actual_efficiency
+ << " % efficiency"
+ << " \r" << flush;
+ partitions.push_back(partition);
+ if (partition.size() == preprocessed_inputfiles.size() || actual_efficiency == 1.0f) {
+ break;
+ }
+ required_efficiency_to_beat = actual_efficiency;
+ }
+ cerr << " " << endl;
+ while (true) {
+ bool repeat = false;
+ for (size_t i = 0; i < partitions.size() - 1; i++) {
+ if (partitions[i].size() >= partitions[i+1].size()) {
+ partitions.erase(partitions.begin() + i);
+ repeat = true;
+ break;
+ }
+ }
+ if (!repeat) {
+ break;
+ }
+ }
+ for (auto it = partitions.begin(); it != partitions.end(); ++it) {
+ print_partition(preprocessed_inputfiles, *it);
+ }
+ }
+};
+
+struct evaluate_defaults_action_t : action_t
+{
+ struct results_entry_t {
+ uint16_t product_size;
+ size_triple_t default_block_size;
+ uint16_t best_pot_block_size;
+ float default_gflops;
+ float best_pot_gflops;
+ float default_efficiency;
+ };
+ friend ostream& operator<<(ostream& s, const results_entry_t& entry)
+ {
+ return s
+ << "Product size " << size_triple_t(entry.product_size)
+ << ": default block size " << entry.default_block_size
+ << " -> " << entry.default_gflops
+ << " GFlop/s = " << entry.default_efficiency * 100.0f << " %"
+ << " of best POT block size " << size_triple_t(entry.best_pot_block_size)
+ << " -> " << entry.best_pot_gflops
+ << " GFlop/s" << dec;
+ }
+ static bool lower_efficiency(const results_entry_t& e1, const results_entry_t& e2) {
+ return e1.default_efficiency < e2.default_efficiency;
+ }
+ virtual const char* invokation_name() const override { return "evaluate-defaults"; }
+ void show_usage_and_exit() const
+ {
+ cerr << "usage: " << invokation_name() << " default-sizes-data all-pot-sizes-data" << endl;
+ cerr << "checks how well the performance with default sizes compares to the best "
+ << "performance measured over all POT sizes." << endl;
+ exit(1);
+ }
+ virtual void run(const vector<string>& input_filenames) const override
+ {
+ if (input_filenames.size() != 2) {
+ show_usage_and_exit();
+ }
+ inputfile_t inputfile_default_sizes(input_filenames[0]);
+ inputfile_t inputfile_all_pot_sizes(input_filenames[1]);
+ if (inputfile_default_sizes.type != inputfile_t::type_t::default_sizes) {
+ cerr << inputfile_default_sizes.filename << " is not an input file with default sizes." << endl;
+ show_usage_and_exit();
+ }
+ if (inputfile_all_pot_sizes.type != inputfile_t::type_t::all_pot_sizes) {
+ cerr << inputfile_all_pot_sizes.filename << " is not an input file with all POT sizes." << endl;
+ show_usage_and_exit();
+ }
+ vector<results_entry_t> results;
+ vector<results_entry_t> cubic_results;
+
+ uint16_t product_size = 0;
+ auto it_all_pot_sizes = inputfile_all_pot_sizes.entries.begin();
+ for (auto it_default_sizes = inputfile_default_sizes.entries.begin();
+ it_default_sizes != inputfile_default_sizes.entries.end();
+ ++it_default_sizes)
+ {
+ if (it_default_sizes->product_size == product_size) {
+ continue;
+ }
+ product_size = it_default_sizes->product_size;
+ while (it_all_pot_sizes != inputfile_all_pot_sizes.entries.end() &&
+ it_all_pot_sizes->product_size != product_size)
+ {
+ ++it_all_pot_sizes;
+ }
+ if (it_all_pot_sizes == inputfile_all_pot_sizes.entries.end()) {
+ break;
+ }
+ uint16_t best_pot_block_size = 0;
+ float best_pot_gflops = 0;
+ for (auto it = it_all_pot_sizes;
+ it != inputfile_all_pot_sizes.entries.end() && it->product_size == product_size;
+ ++it)
+ {
+ if (it->gflops > best_pot_gflops) {
+ best_pot_gflops = it->gflops;
+ best_pot_block_size = it->pot_block_size;
+ }
+ }
+ results_entry_t entry;
+ entry.product_size = product_size;
+ entry.default_block_size = it_default_sizes->nonpot_block_size;
+ entry.best_pot_block_size = best_pot_block_size;
+ entry.default_gflops = it_default_sizes->gflops;
+ entry.best_pot_gflops = best_pot_gflops;
+ entry.default_efficiency = entry.default_gflops / entry.best_pot_gflops;
+ results.push_back(entry);
+
+ size_triple_t t(product_size);
+ if (t.k == t.m && t.m == t.n) {
+ cubic_results.push_back(entry);
+ }
+ }
+
+ cout << "All results:" << endl;
+ for (auto it = results.begin(); it != results.end(); ++it) {
+ cout << *it << endl;
+ }
+ cout << endl;
+
+ sort(results.begin(), results.end(), lower_efficiency);
+
+ const size_t n = min<size_t>(20, results.size());
+ cout << n << " worst results:" << endl;
+ for (size_t i = 0; i < n; i++) {
+ cout << results[i] << endl;
+ }
+ cout << endl;
+
+ cout << "cubic results:" << endl;
+ for (auto it = cubic_results.begin(); it != cubic_results.end(); ++it) {
+ cout << *it << endl;
+ }
+ cout << endl;
+
+ sort(cubic_results.begin(), cubic_results.end(), lower_efficiency);
+
+ cout.precision(2);
+ vector<float> a = {0.5f, 0.20f, 0.10f, 0.05f, 0.02f, 0.01f};
+ for (auto it = a.begin(); it != a.end(); ++it) {
+ size_t n = min(results.size() - 1, size_t(*it * results.size()));
+ cout << (100.0f * n / (results.size() - 1))
+ << " % of product sizes have default efficiency <= "
+ << 100.0f * results[n].default_efficiency << " %" << endl;
+ }
+ cout.precision(default_precision);
+ }
+};
+
+
+void show_usage_and_exit(int argc, char* argv[],
+ const vector<unique_ptr<action_t>>& available_actions)
+{
+ cerr << "usage: " << argv[0] << " <action> [options...] <input files...>" << endl;
+ cerr << "available actions:" << endl;
+ for (auto it = available_actions.begin(); it != available_actions.end(); ++it) {
+ cerr << " " << (*it)->invokation_name() << endl;
+ }
+ cerr << "the input files should each contain an output of benchmark-blocking-sizes" << endl;
+ exit(1);
+}
+
+int main(int argc, char* argv[])
+{
+ cout.precision(default_precision);
+ cerr.precision(default_precision);
+
+ vector<unique_ptr<action_t>> available_actions;
+ available_actions.emplace_back(new partition_action_t);
+ available_actions.emplace_back(new evaluate_defaults_action_t);
+
+ vector<string> input_filenames;
+
+ action_t* action = nullptr;
+
+ if (argc < 2) {
+ show_usage_and_exit(argc, argv, available_actions);
+ }
+ for (int i = 1; i < argc; i++) {
+ bool arg_handled = false;
+ // Step 1. Try to match action invocation names.
+ for (auto it = available_actions.begin(); it != available_actions.end(); ++it) {
+ if (!strcmp(argv[i], (*it)->invokation_name())) {
+ if (!action) {
+ action = it->get();
+ arg_handled = true;
+ break;
+ } else {
+ cerr << "can't specify more than one action!" << endl;
+ show_usage_and_exit(argc, argv, available_actions);
+ }
+ }
+ }
+ if (arg_handled) {
+ continue;
+ }
+ // Step 2. Try to match option names.
+ if (argv[i][0] == '-') {
+ if (!strcmp(argv[i], "--only-cubic-sizes")) {
+ only_cubic_sizes = true;
+ arg_handled = true;
+ }
+ if (!strcmp(argv[i], "--dump-tables")) {
+ dump_tables = true;
+ arg_handled = true;
+ }
+ if (!arg_handled) {
+ cerr << "Unrecognized option: " << argv[i] << endl;
+ show_usage_and_exit(argc, argv, available_actions);
+ }
+ }
+ if (arg_handled) {
+ continue;
+ }
+ // Step 3. Default to interpreting args as input filenames.
+ input_filenames.emplace_back(argv[i]);
+ }
+
+ if (dump_tables && only_cubic_sizes) {
+ cerr << "Incompatible options: --only-cubic-sizes and --dump-tables." << endl;
+ show_usage_and_exit(argc, argv, available_actions);
+ }
+
+ if (!action) {
+ show_usage_and_exit(argc, argv, available_actions);
+ }
+
+ action->run(input_filenames);
+}
diff --git a/bench/basicbench.cxxlist b/bench/basicbench.cxxlist
new file mode 100644
index 0000000..a8ab34e
--- /dev/null
+++ b/bench/basicbench.cxxlist
@@ -0,0 +1,28 @@
+#!/bin/bash
+
+# CLIST[((g++))]="g++-3.4 -O3 -DNDEBUG"
+# CLIST[((g++))]="g++-3.4 -O3 -DNDEBUG -finline-limit=20000"
+
+# CLIST[((g++))]="g++-4.1 -O3 -DNDEBUG"
+#CLIST[((g++))]="g++-4.1 -O3 -DNDEBUG -finline-limit=20000"
+
+# CLIST[((g++))]="g++-4.2 -O3 -DNDEBUG"
+#CLIST[((g++))]="g++-4.2 -O3 -DNDEBUG -finline-limit=20000"
+# CLIST[((g++))]="g++-4.2 -O3 -DNDEBUG -finline-limit=20000 -fprofile-generate"
+# CLIST[((g++))]="g++-4.2 -O3 -DNDEBUG -finline-limit=20000 -fprofile-use"
+
+# CLIST[((g++))]="g++-4.3 -O3 -DNDEBUG"
+#CLIST[((g++))]="g++-4.3 -O3 -DNDEBUG -finline-limit=20000"
+# CLIST[((g++))]="g++-4.3 -O3 -DNDEBUG -finline-limit=20000 -fprofile-generate"
+# CLIST[((g++))]="g++-4.3 -O3 -DNDEBUG -finline-limit=20000 -fprofile-use"
+
+# CLIST[((g++))]="icpc -fast -DNDEBUG -fno-exceptions -no-inline-max-size -prof-genx"
+# CLIST[((g++))]="icpc -fast -DNDEBUG -fno-exceptions -no-inline-max-size -prof-use"
+
+#CLIST[((g++))]="/opt/intel/Compiler/11.1/072/bin/intel64/icpc -fast -DNDEBUG -fno-exceptions -no-inline-max-size -lrt"
+CLIST[((g++))]="/home/orzel/svn/llvm/Release/bin/clang++ -O3 -DNDEBUG -DEIGEN_DONT_VECTORIZE -lrt"
+CLIST[((g++))]="/home/orzel/svn/llvm/Release/bin/clang++ -O3 -DNDEBUG -lrt"
+CLIST[((g++))]="g++-4.4.4 -O3 -DNDEBUG -DEIGEN_DONT_VECTORIZE -lrt"
+CLIST[((g++))]="g++-4.4.4 -O3 -DNDEBUG -lrt"
+CLIST[((g++))]="g++-4.5.0 -O3 -DNDEBUG -DEIGEN_DONT_VECTORIZE -lrt"
+CLIST[((g++))]="g++-4.5.0 -O3 -DNDEBUG -lrt"
diff --git a/bench/basicbenchmark.cpp b/bench/basicbenchmark.cpp
new file mode 100644
index 0000000..a26ea85
--- /dev/null
+++ b/bench/basicbenchmark.cpp
@@ -0,0 +1,35 @@
+
+#include <iostream>
+#include "BenchUtil.h"
+#include "basicbenchmark.h"
+
+int main(int argc, char *argv[])
+{
+ DISABLE_SSE_EXCEPTIONS();
+
+ // this is the list of matrix type and size we want to bench:
+ // ((suffix) (matrix size) (number of iterations))
+ #define MODES ((3d)(3)(4000000)) ((4d)(4)(1000000)) ((Xd)(4)(1000000)) ((Xd)(20)(10000))
+// #define MODES ((Xd)(20)(10000))
+
+ #define _GENERATE_HEADER(R,ARG,EL) << BOOST_PP_STRINGIZE(BOOST_PP_SEQ_HEAD(EL)) << "-" \
+ << BOOST_PP_STRINGIZE(BOOST_PP_SEQ_ELEM(1,EL)) << "x" \
+ << BOOST_PP_STRINGIZE(BOOST_PP_SEQ_ELEM(1,EL)) << " / "
+
+ std::cout BOOST_PP_SEQ_FOR_EACH(_GENERATE_HEADER, ~, MODES ) << endl;
+
+ const int tries = 10;
+
+ #define _RUN_BENCH(R,ARG,EL) \
+ std::cout << ARG( \
+ BOOST_PP_CAT(Matrix, BOOST_PP_SEQ_HEAD(EL)) (\
+ BOOST_PP_SEQ_ELEM(1,EL),BOOST_PP_SEQ_ELEM(1,EL)), BOOST_PP_SEQ_ELEM(2,EL), tries) \
+ << " ";
+
+ BOOST_PP_SEQ_FOR_EACH(_RUN_BENCH, benchBasic<LazyEval>, MODES );
+ std::cout << endl;
+ BOOST_PP_SEQ_FOR_EACH(_RUN_BENCH, benchBasic<EarlyEval>, MODES );
+ std::cout << endl;
+
+ return 0;
+}
diff --git a/bench/basicbenchmark.h b/bench/basicbenchmark.h
new file mode 100644
index 0000000..8059375
--- /dev/null
+++ b/bench/basicbenchmark.h
@@ -0,0 +1,63 @@
+
+#ifndef EIGEN_BENCH_BASICBENCH_H
+#define EIGEN_BENCH_BASICBENCH_H
+
+enum {LazyEval, EarlyEval, OmpEval};
+
+template<int Mode, typename MatrixType>
+void benchBasic_loop(const MatrixType& I, MatrixType& m, int iterations) __attribute__((noinline));
+
+template<int Mode, typename MatrixType>
+void benchBasic_loop(const MatrixType& I, MatrixType& m, int iterations)
+{
+ for(int a = 0; a < iterations; a++)
+ {
+ if (Mode==LazyEval)
+ {
+ asm("#begin_bench_loop LazyEval");
+ if (MatrixType::SizeAtCompileTime!=Eigen::Dynamic) asm("#fixedsize");
+ m = (I + 0.00005 * (m + m.lazyProduct(m))).eval();
+ }
+ else if (Mode==OmpEval)
+ {
+ asm("#begin_bench_loop OmpEval");
+ if (MatrixType::SizeAtCompileTime!=Eigen::Dynamic) asm("#fixedsize");
+ m = (I + 0.00005 * (m + m.lazyProduct(m))).eval();
+ }
+ else
+ {
+ asm("#begin_bench_loop EarlyEval");
+ if (MatrixType::SizeAtCompileTime!=Eigen::Dynamic) asm("#fixedsize");
+ m = I + 0.00005 * (m + m * m);
+ }
+ asm("#end_bench_loop");
+ }
+}
+
+template<int Mode, typename MatrixType>
+double benchBasic(const MatrixType& mat, int size, int tries) __attribute__((noinline));
+
+template<int Mode, typename MatrixType>
+double benchBasic(const MatrixType& mat, int iterations, int tries)
+{
+ const int rows = mat.rows();
+ const int cols = mat.cols();
+
+ MatrixType I(rows,cols);
+ MatrixType m(rows,cols);
+
+ initMatrix_identity(I);
+
+ Eigen::BenchTimer timer;
+ for(uint t=0; t<tries; ++t)
+ {
+ initMatrix_random(m);
+ timer.start();
+ benchBasic_loop<Mode>(I, m, iterations);
+ timer.stop();
+ cerr << m;
+ }
+ return timer.value();
+};
+
+#endif // EIGEN_BENCH_BASICBENCH_H
diff --git a/bench/benchBlasGemm.cpp b/bench/benchBlasGemm.cpp
new file mode 100644
index 0000000..cb086a5
--- /dev/null
+++ b/bench/benchBlasGemm.cpp
@@ -0,0 +1,219 @@
+// g++ -O3 -DNDEBUG -I.. -L /usr/lib64/atlas/ benchBlasGemm.cpp -o benchBlasGemm -lrt -lcblas
+// possible options:
+// -DEIGEN_DONT_VECTORIZE
+// -msse2
+
+// #define EIGEN_DEFAULT_TO_ROW_MAJOR
+#define _FLOAT
+
+#include <iostream>
+
+#include <Eigen/Core>
+#include "BenchTimer.h"
+
+// include the BLAS headers
+extern "C" {
+#include <cblas.h>
+}
+#include <string>
+
+#ifdef _FLOAT
+typedef float Scalar;
+#define CBLAS_GEMM cblas_sgemm
+#else
+typedef double Scalar;
+#define CBLAS_GEMM cblas_dgemm
+#endif
+
+
+typedef Eigen::Matrix<Scalar,Eigen::Dynamic,Eigen::Dynamic> MyMatrix;
+void bench_eigengemm(MyMatrix& mc, const MyMatrix& ma, const MyMatrix& mb, int nbloops);
+void check_product(int M, int N, int K);
+void check_product(void);
+
+int main(int argc, char *argv[])
+{
+ // disable SSE exceptions
+ #ifdef __GNUC__
+ {
+ int aux;
+ asm(
+ "stmxcsr %[aux] \n\t"
+ "orl $32832, %[aux] \n\t"
+ "ldmxcsr %[aux] \n\t"
+ : : [aux] "m" (aux));
+ }
+ #endif
+
+ int nbtries=1, nbloops=1, M, N, K;
+
+ if (argc==2)
+ {
+ if (std::string(argv[1])=="check")
+ check_product();
+ else
+ M = N = K = atoi(argv[1]);
+ }
+ else if ((argc==3) && (std::string(argv[1])=="auto"))
+ {
+ M = N = K = atoi(argv[2]);
+ nbloops = 1000000000/(M*M*M);
+ if (nbloops<1)
+ nbloops = 1;
+ nbtries = 6;
+ }
+ else if (argc==4)
+ {
+ M = N = K = atoi(argv[1]);
+ nbloops = atoi(argv[2]);
+ nbtries = atoi(argv[3]);
+ }
+ else if (argc==6)
+ {
+ M = atoi(argv[1]);
+ N = atoi(argv[2]);
+ K = atoi(argv[3]);
+ nbloops = atoi(argv[4]);
+ nbtries = atoi(argv[5]);
+ }
+ else
+ {
+ std::cout << "Usage: " << argv[0] << " size \n";
+ std::cout << "Usage: " << argv[0] << " auto size\n";
+ std::cout << "Usage: " << argv[0] << " size nbloops nbtries\n";
+ std::cout << "Usage: " << argv[0] << " M N K nbloops nbtries\n";
+ std::cout << "Usage: " << argv[0] << " check\n";
+ std::cout << "Options:\n";
+ std::cout << " size unique size of the 2 matrices (integer)\n";
+ std::cout << " auto automatically set the number of repetitions and tries\n";
+ std::cout << " nbloops number of times the GEMM routines is executed\n";
+ std::cout << " nbtries number of times the loop is benched (return the best try)\n";
+ std::cout << " M N K sizes of the matrices: MxN = MxK * KxN (integers)\n";
+ std::cout << " check check eigen product using cblas as a reference\n";
+ exit(1);
+ }
+
+ double nbmad = double(M) * double(N) * double(K) * double(nbloops);
+
+ if (!(std::string(argv[1])=="auto"))
+ std::cout << M << " x " << N << " x " << K << "\n";
+
+ Scalar alpha, beta;
+ MyMatrix ma(M,K), mb(K,N), mc(M,N);
+ ma = MyMatrix::Random(M,K);
+ mb = MyMatrix::Random(K,N);
+ mc = MyMatrix::Random(M,N);
+
+ Eigen::BenchTimer timer;
+
+ // we simply compute c += a*b, so:
+ alpha = 1;
+ beta = 1;
+
+ // bench cblas
+ // ROWS_A, COLS_B, COLS_A, 1.0, A, COLS_A, B, COLS_B, 0.0, C, COLS_B);
+ if (!(std::string(argv[1])=="auto"))
+ {
+ timer.reset();
+ for (uint k=0 ; k<nbtries ; ++k)
+ {
+ timer.start();
+ for (uint j=0 ; j<nbloops ; ++j)
+ #ifdef EIGEN_DEFAULT_TO_ROW_MAJOR
+ CBLAS_GEMM(CblasRowMajor, CblasNoTrans, CblasNoTrans, M, N, K, alpha, ma.data(), K, mb.data(), N, beta, mc.data(), N);
+ #else
+ CBLAS_GEMM(CblasColMajor, CblasNoTrans, CblasNoTrans, M, N, K, alpha, ma.data(), M, mb.data(), K, beta, mc.data(), M);
+ #endif
+ timer.stop();
+ }
+ if (!(std::string(argv[1])=="auto"))
+ std::cout << "cblas: " << timer.value() << " (" << 1e-3*floor(1e-6*nbmad/timer.value()) << " GFlops/s)\n";
+ else
+ std::cout << M << " : " << timer.value() << " ; " << 1e-3*floor(1e-6*nbmad/timer.value()) << "\n";
+ }
+
+ // clear
+ ma = MyMatrix::Random(M,K);
+ mb = MyMatrix::Random(K,N);
+ mc = MyMatrix::Random(M,N);
+
+ // eigen
+// if (!(std::string(argv[1])=="auto"))
+ {
+ timer.reset();
+ for (uint k=0 ; k<nbtries ; ++k)
+ {
+ timer.start();
+ bench_eigengemm(mc, ma, mb, nbloops);
+ timer.stop();
+ }
+ if (!(std::string(argv[1])=="auto"))
+ std::cout << "eigen : " << timer.value() << " (" << 1e-3*floor(1e-6*nbmad/timer.value()) << " GFlops/s)\n";
+ else
+ std::cout << M << " : " << timer.value() << " ; " << 1e-3*floor(1e-6*nbmad/timer.value()) << "\n";
+ }
+
+ std::cout << "l1: " << Eigen::l1CacheSize() << std::endl;
+ std::cout << "l2: " << Eigen::l2CacheSize() << std::endl;
+
+
+ return 0;
+}
+
+using namespace Eigen;
+
+void bench_eigengemm(MyMatrix& mc, const MyMatrix& ma, const MyMatrix& mb, int nbloops)
+{
+ for (uint j=0 ; j<nbloops ; ++j)
+ mc.noalias() += ma * mb;
+}
+
+#define MYVERIFY(A,M) if (!(A)) { \
+ std::cout << "FAIL: " << M << "\n"; \
+ }
+void check_product(int M, int N, int K)
+{
+ MyMatrix ma(M,K), mb(K,N), mc(M,N), maT(K,M), mbT(N,K), meigen(M,N), mref(M,N);
+ ma = MyMatrix::Random(M,K);
+ mb = MyMatrix::Random(K,N);
+ maT = ma.transpose();
+ mbT = mb.transpose();
+ mc = MyMatrix::Random(M,N);
+
+ MyMatrix::Scalar eps = 1e-4;
+
+ meigen = mref = mc;
+ CBLAS_GEMM(CblasColMajor, CblasNoTrans, CblasNoTrans, M, N, K, 1, ma.data(), M, mb.data(), K, 1, mref.data(), M);
+ meigen += ma * mb;
+ MYVERIFY(meigen.isApprox(mref, eps),". * .");
+
+ meigen = mref = mc;
+ CBLAS_GEMM(CblasColMajor, CblasTrans, CblasNoTrans, M, N, K, 1, maT.data(), K, mb.data(), K, 1, mref.data(), M);
+ meigen += maT.transpose() * mb;
+ MYVERIFY(meigen.isApprox(mref, eps),"T * .");
+
+ meigen = mref = mc;
+ CBLAS_GEMM(CblasColMajor, CblasTrans, CblasTrans, M, N, K, 1, maT.data(), K, mbT.data(), N, 1, mref.data(), M);
+ meigen += (maT.transpose()) * (mbT.transpose());
+ MYVERIFY(meigen.isApprox(mref, eps),"T * T");
+
+ meigen = mref = mc;
+ CBLAS_GEMM(CblasColMajor, CblasNoTrans, CblasTrans, M, N, K, 1, ma.data(), M, mbT.data(), N, 1, mref.data(), M);
+ meigen += ma * mbT.transpose();
+ MYVERIFY(meigen.isApprox(mref, eps),". * T");
+}
+
+void check_product(void)
+{
+ int M, N, K;
+ for (uint i=0; i<1000; ++i)
+ {
+ M = internal::random<int>(1,64);
+ N = internal::random<int>(1,768);
+ K = internal::random<int>(1,768);
+ M = (0 + M) * 1;
+ std::cout << M << " x " << N << " x " << K << "\n";
+ check_product(M, N, K);
+ }
+}
+
diff --git a/bench/benchCholesky.cpp b/bench/benchCholesky.cpp
new file mode 100644
index 0000000..0dc94e5
--- /dev/null
+++ b/bench/benchCholesky.cpp
@@ -0,0 +1,141 @@
+// g++ -DNDEBUG -O3 -I.. benchCholesky.cpp -o benchCholesky && ./benchCholesky
+// options:
+// -DBENCH_GSL -lgsl /usr/lib/libcblas.so.3
+// -DEIGEN_DONT_VECTORIZE
+// -msse2
+// -DREPEAT=100
+// -DTRIES=10
+// -DSCALAR=double
+
+#include <iostream>
+
+#include <Eigen/Core>
+#include <Eigen/Cholesky>
+#include <bench/BenchUtil.h>
+using namespace Eigen;
+
+#ifndef REPEAT
+#define REPEAT 10000
+#endif
+
+#ifndef TRIES
+#define TRIES 10
+#endif
+
+typedef float Scalar;
+
+template <typename MatrixType>
+__attribute__ ((noinline)) void benchLLT(const MatrixType& m)
+{
+ int rows = m.rows();
+ int cols = m.cols();
+
+ double cost = 0;
+ for (int j=0; j<rows; ++j)
+ {
+ int r = std::max(rows - j -1,0);
+ cost += 2*(r*j+r+j);
+ }
+
+ int repeats = (REPEAT*1000)/(rows*rows);
+
+ typedef typename MatrixType::Scalar Scalar;
+ typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime> SquareMatrixType;
+
+ MatrixType a = MatrixType::Random(rows,cols);
+ SquareMatrixType covMat = a * a.adjoint();
+
+ BenchTimer timerNoSqrt, timerSqrt;
+
+ Scalar acc = 0;
+ int r = internal::random<int>(0,covMat.rows()-1);
+ int c = internal::random<int>(0,covMat.cols()-1);
+ for (int t=0; t<TRIES; ++t)
+ {
+ timerNoSqrt.start();
+ for (int k=0; k<repeats; ++k)
+ {
+ LDLT<SquareMatrixType> cholnosqrt(covMat);
+ acc += cholnosqrt.matrixL().coeff(r,c);
+ }
+ timerNoSqrt.stop();
+ }
+
+ for (int t=0; t<TRIES; ++t)
+ {
+ timerSqrt.start();
+ for (int k=0; k<repeats; ++k)
+ {
+ LLT<SquareMatrixType> chol(covMat);
+ acc += chol.matrixL().coeff(r,c);
+ }
+ timerSqrt.stop();
+ }
+
+ if (MatrixType::RowsAtCompileTime==Dynamic)
+ std::cout << "dyn ";
+ else
+ std::cout << "fixed ";
+ std::cout << covMat.rows() << " \t"
+ << (timerNoSqrt.best()) / repeats << "s "
+ << "(" << 1e-9 * cost*repeats/timerNoSqrt.best() << " GFLOPS)\t"
+ << (timerSqrt.best()) / repeats << "s "
+ << "(" << 1e-9 * cost*repeats/timerSqrt.best() << " GFLOPS)\n";
+
+
+ #ifdef BENCH_GSL
+ if (MatrixType::RowsAtCompileTime==Dynamic)
+ {
+ timerSqrt.reset();
+
+ gsl_matrix* gslCovMat = gsl_matrix_alloc(covMat.rows(),covMat.cols());
+ gsl_matrix* gslCopy = gsl_matrix_alloc(covMat.rows(),covMat.cols());
+
+ eiToGsl(covMat, &gslCovMat);
+ for (int t=0; t<TRIES; ++t)
+ {
+ timerSqrt.start();
+ for (int k=0; k<repeats; ++k)
+ {
+ gsl_matrix_memcpy(gslCopy,gslCovMat);
+ gsl_linalg_cholesky_decomp(gslCopy);
+ acc += gsl_matrix_get(gslCopy,r,c);
+ }
+ timerSqrt.stop();
+ }
+
+ std::cout << " | \t"
+ << timerSqrt.value() * REPEAT / repeats << "s";
+
+ gsl_matrix_free(gslCovMat);
+ }
+ #endif
+ std::cout << "\n";
+ // make sure the compiler does not optimize too much
+ if (acc==123)
+ std::cout << acc;
+}
+
+int main(int argc, char* argv[])
+{
+ const int dynsizes[] = {4,6,8,16,24,32,49,64,128,256,512,900,1500,0};
+ std::cout << "size LDLT LLT";
+// #ifdef BENCH_GSL
+// std::cout << " GSL (standard + double + ATLAS) ";
+// #endif
+ std::cout << "\n";
+ for (int i=0; dynsizes[i]>0; ++i)
+ benchLLT(Matrix<Scalar,Dynamic,Dynamic>(dynsizes[i],dynsizes[i]));
+
+ benchLLT(Matrix<Scalar,2,2>());
+ benchLLT(Matrix<Scalar,3,3>());
+ benchLLT(Matrix<Scalar,4,4>());
+ benchLLT(Matrix<Scalar,5,5>());
+ benchLLT(Matrix<Scalar,6,6>());
+ benchLLT(Matrix<Scalar,7,7>());
+ benchLLT(Matrix<Scalar,8,8>());
+ benchLLT(Matrix<Scalar,12,12>());
+ benchLLT(Matrix<Scalar,16,16>());
+ return 0;
+}
+
diff --git a/bench/benchEigenSolver.cpp b/bench/benchEigenSolver.cpp
new file mode 100644
index 0000000..dd78c7e
--- /dev/null
+++ b/bench/benchEigenSolver.cpp
@@ -0,0 +1,212 @@
+
+// g++ -DNDEBUG -O3 -I.. benchEigenSolver.cpp -o benchEigenSolver && ./benchEigenSolver
+// options:
+// -DBENCH_GMM
+// -DBENCH_GSL -lgsl /usr/lib/libcblas.so.3
+// -DEIGEN_DONT_VECTORIZE
+// -msse2
+// -DREPEAT=100
+// -DTRIES=10
+// -DSCALAR=double
+
+#include <iostream>
+
+#include <Eigen/Core>
+#include <Eigen/QR>
+#include <bench/BenchUtil.h>
+using namespace Eigen;
+
+#ifndef REPEAT
+#define REPEAT 1000
+#endif
+
+#ifndef TRIES
+#define TRIES 4
+#endif
+
+#ifndef SCALAR
+#define SCALAR float
+#endif
+
+typedef SCALAR Scalar;
+
+template <typename MatrixType>
+__attribute__ ((noinline)) void benchEigenSolver(const MatrixType& m)
+{
+ int rows = m.rows();
+ int cols = m.cols();
+
+ int stdRepeats = std::max(1,int((REPEAT*1000)/(rows*rows*sqrt(rows))));
+ int saRepeats = stdRepeats * 4;
+
+ typedef typename MatrixType::Scalar Scalar;
+ typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime> SquareMatrixType;
+
+ MatrixType a = MatrixType::Random(rows,cols);
+ SquareMatrixType covMat = a * a.adjoint();
+
+ BenchTimer timerSa, timerStd;
+
+ Scalar acc = 0;
+ int r = internal::random<int>(0,covMat.rows()-1);
+ int c = internal::random<int>(0,covMat.cols()-1);
+ {
+ SelfAdjointEigenSolver<SquareMatrixType> ei(covMat);
+ for (int t=0; t<TRIES; ++t)
+ {
+ timerSa.start();
+ for (int k=0; k<saRepeats; ++k)
+ {
+ ei.compute(covMat);
+ acc += ei.eigenvectors().coeff(r,c);
+ }
+ timerSa.stop();
+ }
+ }
+
+ {
+ EigenSolver<SquareMatrixType> ei(covMat);
+ for (int t=0; t<TRIES; ++t)
+ {
+ timerStd.start();
+ for (int k=0; k<stdRepeats; ++k)
+ {
+ ei.compute(covMat);
+ acc += ei.eigenvectors().coeff(r,c);
+ }
+ timerStd.stop();
+ }
+ }
+
+ if (MatrixType::RowsAtCompileTime==Dynamic)
+ std::cout << "dyn ";
+ else
+ std::cout << "fixed ";
+ std::cout << covMat.rows() << " \t"
+ << timerSa.value() * REPEAT / saRepeats << "s \t"
+ << timerStd.value() * REPEAT / stdRepeats << "s";
+
+ #ifdef BENCH_GMM
+ if (MatrixType::RowsAtCompileTime==Dynamic)
+ {
+ timerSa.reset();
+ timerStd.reset();
+
+ gmm::dense_matrix<Scalar> gmmCovMat(covMat.rows(),covMat.cols());
+ gmm::dense_matrix<Scalar> eigvect(covMat.rows(),covMat.cols());
+ std::vector<Scalar> eigval(covMat.rows());
+ eiToGmm(covMat, gmmCovMat);
+ for (int t=0; t<TRIES; ++t)
+ {
+ timerSa.start();
+ for (int k=0; k<saRepeats; ++k)
+ {
+ gmm::symmetric_qr_algorithm(gmmCovMat, eigval, eigvect);
+ acc += eigvect(r,c);
+ }
+ timerSa.stop();
+ }
+ // the non-selfadjoint solver does not compute the eigen vectors
+// for (int t=0; t<TRIES; ++t)
+// {
+// timerStd.start();
+// for (int k=0; k<stdRepeats; ++k)
+// {
+// gmm::implicit_qr_algorithm(gmmCovMat, eigval, eigvect);
+// acc += eigvect(r,c);
+// }
+// timerStd.stop();
+// }
+
+ std::cout << " | \t"
+ << timerSa.value() * REPEAT / saRepeats << "s"
+ << /*timerStd.value() * REPEAT / stdRepeats << "s"*/ " na ";
+ }
+ #endif
+
+ #ifdef BENCH_GSL
+ if (MatrixType::RowsAtCompileTime==Dynamic)
+ {
+ timerSa.reset();
+ timerStd.reset();
+
+ gsl_matrix* gslCovMat = gsl_matrix_alloc(covMat.rows(),covMat.cols());
+ gsl_matrix* gslCopy = gsl_matrix_alloc(covMat.rows(),covMat.cols());
+ gsl_matrix* eigvect = gsl_matrix_alloc(covMat.rows(),covMat.cols());
+ gsl_vector* eigval = gsl_vector_alloc(covMat.rows());
+ gsl_eigen_symmv_workspace* eisymm = gsl_eigen_symmv_alloc(covMat.rows());
+
+ gsl_matrix_complex* eigvectz = gsl_matrix_complex_alloc(covMat.rows(),covMat.cols());
+ gsl_vector_complex* eigvalz = gsl_vector_complex_alloc(covMat.rows());
+ gsl_eigen_nonsymmv_workspace* einonsymm = gsl_eigen_nonsymmv_alloc(covMat.rows());
+
+ eiToGsl(covMat, &gslCovMat);
+ for (int t=0; t<TRIES; ++t)
+ {
+ timerSa.start();
+ for (int k=0; k<saRepeats; ++k)
+ {
+ gsl_matrix_memcpy(gslCopy,gslCovMat);
+ gsl_eigen_symmv(gslCopy, eigval, eigvect, eisymm);
+ acc += gsl_matrix_get(eigvect,r,c);
+ }
+ timerSa.stop();
+ }
+ for (int t=0; t<TRIES; ++t)
+ {
+ timerStd.start();
+ for (int k=0; k<stdRepeats; ++k)
+ {
+ gsl_matrix_memcpy(gslCopy,gslCovMat);
+ gsl_eigen_nonsymmv(gslCopy, eigvalz, eigvectz, einonsymm);
+ acc += GSL_REAL(gsl_matrix_complex_get(eigvectz,r,c));
+ }
+ timerStd.stop();
+ }
+
+ std::cout << " | \t"
+ << timerSa.value() * REPEAT / saRepeats << "s \t"
+ << timerStd.value() * REPEAT / stdRepeats << "s";
+
+ gsl_matrix_free(gslCovMat);
+ gsl_vector_free(gslCopy);
+ gsl_matrix_free(eigvect);
+ gsl_vector_free(eigval);
+ gsl_matrix_complex_free(eigvectz);
+ gsl_vector_complex_free(eigvalz);
+ gsl_eigen_symmv_free(eisymm);
+ gsl_eigen_nonsymmv_free(einonsymm);
+ }
+ #endif
+
+ std::cout << "\n";
+
+ // make sure the compiler does not optimize too much
+ if (acc==123)
+ std::cout << acc;
+}
+
+int main(int argc, char* argv[])
+{
+ const int dynsizes[] = {4,6,8,12,16,24,32,64,128,256,512,0};
+ std::cout << "size selfadjoint generic";
+ #ifdef BENCH_GMM
+ std::cout << " GMM++ ";
+ #endif
+ #ifdef BENCH_GSL
+ std::cout << " GSL (double + ATLAS) ";
+ #endif
+ std::cout << "\n";
+ for (uint i=0; dynsizes[i]>0; ++i)
+ benchEigenSolver(Matrix<Scalar,Dynamic,Dynamic>(dynsizes[i],dynsizes[i]));
+
+ benchEigenSolver(Matrix<Scalar,2,2>());
+ benchEigenSolver(Matrix<Scalar,3,3>());
+ benchEigenSolver(Matrix<Scalar,4,4>());
+ benchEigenSolver(Matrix<Scalar,6,6>());
+ benchEigenSolver(Matrix<Scalar,8,8>());
+ benchEigenSolver(Matrix<Scalar,12,12>());
+ benchEigenSolver(Matrix<Scalar,16,16>());
+ return 0;
+}
+
diff --git a/bench/benchFFT.cpp b/bench/benchFFT.cpp
new file mode 100644
index 0000000..3eb1a1a
--- /dev/null
+++ b/bench/benchFFT.cpp
@@ -0,0 +1,115 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009 Mark Borgerding mark a borgerding net
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include <iostream>
+
+#include <bench/BenchUtil.h>
+#include <complex>
+#include <vector>
+#include <Eigen/Core>
+
+#include <unsupported/Eigen/FFT>
+
+using namespace Eigen;
+using namespace std;
+
+
+template <typename T>
+string nameof();
+
+template <> string nameof<float>() {return "float";}
+template <> string nameof<double>() {return "double";}
+template <> string nameof<long double>() {return "long double";}
+
+#ifndef TYPE
+#define TYPE float
+#endif
+
+#ifndef NFFT
+#define NFFT 1024
+#endif
+#ifndef NDATA
+#define NDATA 1000000
+#endif
+
+using namespace Eigen;
+
+template <typename T>
+void bench(int nfft,bool fwd,bool unscaled=false, bool halfspec=false)
+{
+ typedef typename NumTraits<T>::Real Scalar;
+ typedef typename std::complex<Scalar> Complex;
+ int nits = NDATA/nfft;
+ vector<T> inbuf(nfft);
+ vector<Complex > outbuf(nfft);
+ FFT< Scalar > fft;
+
+ if (unscaled) {
+ fft.SetFlag(fft.Unscaled);
+ cout << "unscaled ";
+ }
+ if (halfspec) {
+ fft.SetFlag(fft.HalfSpectrum);
+ cout << "halfspec ";
+ }
+
+
+ std::fill(inbuf.begin(),inbuf.end(),0);
+ fft.fwd( outbuf , inbuf);
+
+ BenchTimer timer;
+ timer.reset();
+ for (int k=0;k<8;++k) {
+ timer.start();
+ if (fwd)
+ for(int i = 0; i < nits; i++)
+ fft.fwd( outbuf , inbuf);
+ else
+ for(int i = 0; i < nits; i++)
+ fft.inv(inbuf,outbuf);
+ timer.stop();
+ }
+
+ cout << nameof<Scalar>() << " ";
+ double mflops = 5.*nfft*log2((double)nfft) / (1e6 * timer.value() / (double)nits );
+ if ( NumTraits<T>::IsComplex ) {
+ cout << "complex";
+ }else{
+ cout << "real ";
+ mflops /= 2;
+ }
+
+
+ if (fwd)
+ cout << " fwd";
+ else
+ cout << " inv";
+
+ cout << " NFFT=" << nfft << " " << (double(1e-6*nfft*nits)/timer.value()) << " MS/s " << mflops << "MFLOPS\n";
+}
+
+int main(int argc,char ** argv)
+{
+ bench<complex<float> >(NFFT,true);
+ bench<complex<float> >(NFFT,false);
+ bench<float>(NFFT,true);
+ bench<float>(NFFT,false);
+ bench<float>(NFFT,false,true);
+ bench<float>(NFFT,false,true,true);
+
+ bench<complex<double> >(NFFT,true);
+ bench<complex<double> >(NFFT,false);
+ bench<double>(NFFT,true);
+ bench<double>(NFFT,false);
+ bench<complex<long double> >(NFFT,true);
+ bench<complex<long double> >(NFFT,false);
+ bench<long double>(NFFT,true);
+ bench<long double>(NFFT,false);
+ return 0;
+}
diff --git a/bench/benchGeometry.cpp b/bench/benchGeometry.cpp
new file mode 100644
index 0000000..6e16c03
--- /dev/null
+++ b/bench/benchGeometry.cpp
@@ -0,0 +1,134 @@
+#include <iostream>
+#include <iomanip>
+#include <Eigen/Core>
+#include <Eigen/Geometry>
+#include <bench/BenchTimer.h>
+
+using namespace Eigen;
+using namespace std;
+
+#ifndef REPEAT
+#define REPEAT 1000000
+#endif
+
+enum func_opt
+{
+ TV,
+ TMATV,
+ TMATVMAT,
+};
+
+
+template <class res, class arg1, class arg2, int opt>
+struct func;
+
+template <class res, class arg1, class arg2>
+struct func<res, arg1, arg2, TV>
+{
+ static EIGEN_DONT_INLINE res run( arg1& a1, arg2& a2 )
+ {
+ asm ("");
+ return a1 * a2;
+ }
+};
+
+template <class res, class arg1, class arg2>
+struct func<res, arg1, arg2, TMATV>
+{
+ static EIGEN_DONT_INLINE res run( arg1& a1, arg2& a2 )
+ {
+ asm ("");
+ return a1.matrix() * a2;
+ }
+};
+
+template <class res, class arg1, class arg2>
+struct func<res, arg1, arg2, TMATVMAT>
+{
+ static EIGEN_DONT_INLINE res run( arg1& a1, arg2& a2 )
+ {
+ asm ("");
+ return res(a1.matrix() * a2.matrix());
+ }
+};
+
+template <class func, class arg1, class arg2>
+struct test_transform
+{
+ static void run()
+ {
+ arg1 a1;
+ a1.setIdentity();
+ arg2 a2;
+ a2.setIdentity();
+
+ BenchTimer timer;
+ timer.reset();
+ for (int k=0; k<10; ++k)
+ {
+ timer.start();
+ for (int k=0; k<REPEAT; ++k)
+ a2 = func::run( a1, a2 );
+ timer.stop();
+ }
+ cout << setprecision(4) << fixed << timer.value() << "s " << endl;;
+ }
+};
+
+
+#define run_vec( op, scalar, mode, option, vsize ) \
+ std::cout << #scalar << "\t " << #mode << "\t " << #option << " " << #vsize " "; \
+ {\
+ typedef Transform<scalar, 3, mode, option> Trans;\
+ typedef Matrix<scalar, vsize, 1, option> Vec;\
+ typedef func<Vec,Trans,Vec,op> Func;\
+ test_transform< Func, Trans, Vec >::run();\
+ }
+
+#define run_trans( op, scalar, mode, option ) \
+ std::cout << #scalar << "\t " << #mode << "\t " << #option << " "; \
+ {\
+ typedef Transform<scalar, 3, mode, option> Trans;\
+ typedef func<Trans,Trans,Trans,op> Func;\
+ test_transform< Func, Trans, Trans >::run();\
+ }
+
+int main(int argc, char* argv[])
+{
+ cout << "vec = trans * vec" << endl;
+ run_vec(TV, float, Isometry, AutoAlign, 3);
+ run_vec(TV, float, Isometry, DontAlign, 3);
+ run_vec(TV, float, Isometry, AutoAlign, 4);
+ run_vec(TV, float, Isometry, DontAlign, 4);
+ run_vec(TV, float, Projective, AutoAlign, 4);
+ run_vec(TV, float, Projective, DontAlign, 4);
+ run_vec(TV, double, Isometry, AutoAlign, 3);
+ run_vec(TV, double, Isometry, DontAlign, 3);
+ run_vec(TV, double, Isometry, AutoAlign, 4);
+ run_vec(TV, double, Isometry, DontAlign, 4);
+ run_vec(TV, double, Projective, AutoAlign, 4);
+ run_vec(TV, double, Projective, DontAlign, 4);
+
+ cout << "vec = trans.matrix() * vec" << endl;
+ run_vec(TMATV, float, Isometry, AutoAlign, 4);
+ run_vec(TMATV, float, Isometry, DontAlign, 4);
+ run_vec(TMATV, double, Isometry, AutoAlign, 4);
+ run_vec(TMATV, double, Isometry, DontAlign, 4);
+
+ cout << "trans = trans1 * trans" << endl;
+ run_trans(TV, float, Isometry, AutoAlign);
+ run_trans(TV, float, Isometry, DontAlign);
+ run_trans(TV, double, Isometry, AutoAlign);
+ run_trans(TV, double, Isometry, DontAlign);
+ run_trans(TV, float, Projective, AutoAlign);
+ run_trans(TV, float, Projective, DontAlign);
+ run_trans(TV, double, Projective, AutoAlign);
+ run_trans(TV, double, Projective, DontAlign);
+
+ cout << "trans = trans1.matrix() * trans.matrix()" << endl;
+ run_trans(TMATVMAT, float, Isometry, AutoAlign);
+ run_trans(TMATVMAT, float, Isometry, DontAlign);
+ run_trans(TMATVMAT, double, Isometry, AutoAlign);
+ run_trans(TMATVMAT, double, Isometry, DontAlign);
+}
+
diff --git a/bench/benchVecAdd.cpp b/bench/benchVecAdd.cpp
new file mode 100644
index 0000000..ce8e1e9
--- /dev/null
+++ b/bench/benchVecAdd.cpp
@@ -0,0 +1,135 @@
+
+#include <iostream>
+#include <Eigen/Core>
+#include <bench/BenchTimer.h>
+using namespace Eigen;
+
+#ifndef SIZE
+#define SIZE 50
+#endif
+
+#ifndef REPEAT
+#define REPEAT 10000
+#endif
+
+typedef float Scalar;
+
+__attribute__ ((noinline)) void benchVec(Scalar* a, Scalar* b, Scalar* c, int size);
+__attribute__ ((noinline)) void benchVec(MatrixXf& a, MatrixXf& b, MatrixXf& c);
+__attribute__ ((noinline)) void benchVec(VectorXf& a, VectorXf& b, VectorXf& c);
+
+int main(int argc, char* argv[])
+{
+ int size = SIZE * 8;
+ int size2 = size * size;
+ Scalar* a = internal::aligned_new<Scalar>(size2);
+ Scalar* b = internal::aligned_new<Scalar>(size2+4)+1;
+ Scalar* c = internal::aligned_new<Scalar>(size2);
+
+ for (int i=0; i<size; ++i)
+ {
+ a[i] = b[i] = c[i] = 0;
+ }
+
+ BenchTimer timer;
+
+ timer.reset();
+ for (int k=0; k<10; ++k)
+ {
+ timer.start();
+ benchVec(a, b, c, size2);
+ timer.stop();
+ }
+ std::cout << timer.value() << "s " << (double(size2*REPEAT)/timer.value())/(1024.*1024.*1024.) << " GFlops\n";
+ return 0;
+ for (int innersize = size; innersize>2 ; --innersize)
+ {
+ if (size2%innersize==0)
+ {
+ int outersize = size2/innersize;
+ MatrixXf ma = Map<MatrixXf>(a, innersize, outersize );
+ MatrixXf mb = Map<MatrixXf>(b, innersize, outersize );
+ MatrixXf mc = Map<MatrixXf>(c, innersize, outersize );
+ timer.reset();
+ for (int k=0; k<3; ++k)
+ {
+ timer.start();
+ benchVec(ma, mb, mc);
+ timer.stop();
+ }
+ std::cout << innersize << " x " << outersize << " " << timer.value() << "s " << (double(size2*REPEAT)/timer.value())/(1024.*1024.*1024.) << " GFlops\n";
+ }
+ }
+
+ VectorXf va = Map<VectorXf>(a, size2);
+ VectorXf vb = Map<VectorXf>(b, size2);
+ VectorXf vc = Map<VectorXf>(c, size2);
+ timer.reset();
+ for (int k=0; k<3; ++k)
+ {
+ timer.start();
+ benchVec(va, vb, vc);
+ timer.stop();
+ }
+ std::cout << timer.value() << "s " << (double(size2*REPEAT)/timer.value())/(1024.*1024.*1024.) << " GFlops\n";
+
+ return 0;
+}
+
+void benchVec(MatrixXf& a, MatrixXf& b, MatrixXf& c)
+{
+ for (int k=0; k<REPEAT; ++k)
+ a = a + b;
+}
+
+void benchVec(VectorXf& a, VectorXf& b, VectorXf& c)
+{
+ for (int k=0; k<REPEAT; ++k)
+ a = a + b;
+}
+
+void benchVec(Scalar* a, Scalar* b, Scalar* c, int size)
+{
+ typedef internal::packet_traits<Scalar>::type PacketScalar;
+ const int PacketSize = internal::packet_traits<Scalar>::size;
+ PacketScalar a0, a1, a2, a3, b0, b1, b2, b3;
+ for (int k=0; k<REPEAT; ++k)
+ for (int i=0; i<size; i+=PacketSize*8)
+ {
+// a0 = internal::pload(&a[i]);
+// b0 = internal::pload(&b[i]);
+// a1 = internal::pload(&a[i+1*PacketSize]);
+// b1 = internal::pload(&b[i+1*PacketSize]);
+// a2 = internal::pload(&a[i+2*PacketSize]);
+// b2 = internal::pload(&b[i+2*PacketSize]);
+// a3 = internal::pload(&a[i+3*PacketSize]);
+// b3 = internal::pload(&b[i+3*PacketSize]);
+// internal::pstore(&a[i], internal::padd(a0, b0));
+// a0 = internal::pload(&a[i+4*PacketSize]);
+// b0 = internal::pload(&b[i+4*PacketSize]);
+//
+// internal::pstore(&a[i+1*PacketSize], internal::padd(a1, b1));
+// a1 = internal::pload(&a[i+5*PacketSize]);
+// b1 = internal::pload(&b[i+5*PacketSize]);
+//
+// internal::pstore(&a[i+2*PacketSize], internal::padd(a2, b2));
+// a2 = internal::pload(&a[i+6*PacketSize]);
+// b2 = internal::pload(&b[i+6*PacketSize]);
+//
+// internal::pstore(&a[i+3*PacketSize], internal::padd(a3, b3));
+// a3 = internal::pload(&a[i+7*PacketSize]);
+// b3 = internal::pload(&b[i+7*PacketSize]);
+//
+// internal::pstore(&a[i+4*PacketSize], internal::padd(a0, b0));
+// internal::pstore(&a[i+5*PacketSize], internal::padd(a1, b1));
+// internal::pstore(&a[i+6*PacketSize], internal::padd(a2, b2));
+// internal::pstore(&a[i+7*PacketSize], internal::padd(a3, b3));
+
+ internal::pstore(&a[i+2*PacketSize], internal::padd(internal::ploadu(&a[i+2*PacketSize]), internal::ploadu(&b[i+2*PacketSize])));
+ internal::pstore(&a[i+3*PacketSize], internal::padd(internal::ploadu(&a[i+3*PacketSize]), internal::ploadu(&b[i+3*PacketSize])));
+ internal::pstore(&a[i+4*PacketSize], internal::padd(internal::ploadu(&a[i+4*PacketSize]), internal::ploadu(&b[i+4*PacketSize])));
+ internal::pstore(&a[i+5*PacketSize], internal::padd(internal::ploadu(&a[i+5*PacketSize]), internal::ploadu(&b[i+5*PacketSize])));
+ internal::pstore(&a[i+6*PacketSize], internal::padd(internal::ploadu(&a[i+6*PacketSize]), internal::ploadu(&b[i+6*PacketSize])));
+ internal::pstore(&a[i+7*PacketSize], internal::padd(internal::ploadu(&a[i+7*PacketSize]), internal::ploadu(&b[i+7*PacketSize])));
+ }
+}
diff --git a/bench/bench_gemm.cpp b/bench/bench_gemm.cpp
new file mode 100644
index 0000000..78ca1cd
--- /dev/null
+++ b/bench/bench_gemm.cpp
@@ -0,0 +1,375 @@
+
+// g++-4.4 bench_gemm.cpp -I .. -O2 -DNDEBUG -lrt -fopenmp && OMP_NUM_THREADS=2 ./a.out
+// icpc bench_gemm.cpp -I .. -O3 -DNDEBUG -lrt -openmp && OMP_NUM_THREADS=2 ./a.out
+
+// Compilation options:
+//
+// -DSCALAR=std::complex<double>
+// -DSCALARA=double or -DSCALARB=double
+// -DHAVE_BLAS
+// -DDECOUPLED
+//
+
+#include <iostream>
+#include <bench/BenchTimer.h>
+#include <Eigen/Core>
+
+
+using namespace std;
+using namespace Eigen;
+
+#ifndef SCALAR
+// #define SCALAR std::complex<float>
+#define SCALAR float
+#endif
+
+#ifndef SCALARA
+#define SCALARA SCALAR
+#endif
+
+#ifndef SCALARB
+#define SCALARB SCALAR
+#endif
+
+#ifdef ROWMAJ_A
+const int opt_A = RowMajor;
+#else
+const int opt_A = ColMajor;
+#endif
+
+#ifdef ROWMAJ_B
+const int opt_B = RowMajor;
+#else
+const int opt_B = ColMajor;
+#endif
+
+typedef SCALAR Scalar;
+typedef NumTraits<Scalar>::Real RealScalar;
+typedef Matrix<SCALARA,Dynamic,Dynamic,opt_A> A;
+typedef Matrix<SCALARB,Dynamic,Dynamic,opt_B> B;
+typedef Matrix<Scalar,Dynamic,Dynamic> C;
+typedef Matrix<RealScalar,Dynamic,Dynamic> M;
+
+#ifdef HAVE_BLAS
+
+extern "C" {
+ #include <Eigen/src/misc/blas.h>
+}
+
+static float fone = 1;
+static float fzero = 0;
+static double done = 1;
+static double szero = 0;
+static std::complex<float> cfone = 1;
+static std::complex<float> cfzero = 0;
+static std::complex<double> cdone = 1;
+static std::complex<double> cdzero = 0;
+static char notrans = 'N';
+static char trans = 'T';
+static char nonunit = 'N';
+static char lower = 'L';
+static char right = 'R';
+static int intone = 1;
+
+#ifdef ROWMAJ_A
+const char transA = trans;
+#else
+const char transA = notrans;
+#endif
+
+#ifdef ROWMAJ_B
+const char transB = trans;
+#else
+const char transB = notrans;
+#endif
+
+template<typename A,typename B>
+void blas_gemm(const A& a, const B& b, MatrixXf& c)
+{
+ int M = c.rows(); int N = c.cols(); int K = a.cols();
+ int lda = a.outerStride(); int ldb = b.outerStride(); int ldc = c.rows();
+
+ sgemm_(&transA,&transB,&M,&N,&K,&fone,
+ const_cast<float*>(a.data()),&lda,
+ const_cast<float*>(b.data()),&ldb,&fone,
+ c.data(),&ldc);
+}
+
+template<typename A,typename B>
+void blas_gemm(const A& a, const B& b, MatrixXd& c)
+{
+ int M = c.rows(); int N = c.cols(); int K = a.cols();
+ int lda = a.outerStride(); int ldb = b.outerStride(); int ldc = c.rows();
+
+ dgemm_(&transA,&transB,&M,&N,&K,&done,
+ const_cast<double*>(a.data()),&lda,
+ const_cast<double*>(b.data()),&ldb,&done,
+ c.data(),&ldc);
+}
+
+template<typename A,typename B>
+void blas_gemm(const A& a, const B& b, MatrixXcf& c)
+{
+ int M = c.rows(); int N = c.cols(); int K = a.cols();
+ int lda = a.outerStride(); int ldb = b.outerStride(); int ldc = c.rows();
+
+ cgemm_(&transA,&transB,&M,&N,&K,(float*)&cfone,
+ const_cast<float*>((const float*)a.data()),&lda,
+ const_cast<float*>((const float*)b.data()),&ldb,(float*)&cfone,
+ (float*)c.data(),&ldc);
+}
+
+template<typename A,typename B>
+void blas_gemm(const A& a, const B& b, MatrixXcd& c)
+{
+ int M = c.rows(); int N = c.cols(); int K = a.cols();
+ int lda = a.outerStride(); int ldb = b.outerStride(); int ldc = c.rows();
+
+ zgemm_(&transA,&transB,&M,&N,&K,(double*)&cdone,
+ const_cast<double*>((const double*)a.data()),&lda,
+ const_cast<double*>((const double*)b.data()),&ldb,(double*)&cdone,
+ (double*)c.data(),&ldc);
+}
+
+
+
+#endif
+
+void matlab_cplx_cplx(const M& ar, const M& ai, const M& br, const M& bi, M& cr, M& ci)
+{
+ cr.noalias() += ar * br;
+ cr.noalias() -= ai * bi;
+ ci.noalias() += ar * bi;
+ ci.noalias() += ai * br;
+ // [cr ci] += [ar ai] * br + [-ai ar] * bi
+}
+
+void matlab_real_cplx(const M& a, const M& br, const M& bi, M& cr, M& ci)
+{
+ cr.noalias() += a * br;
+ ci.noalias() += a * bi;
+}
+
+void matlab_cplx_real(const M& ar, const M& ai, const M& b, M& cr, M& ci)
+{
+ cr.noalias() += ar * b;
+ ci.noalias() += ai * b;
+}
+
+
+
+template<typename A, typename B, typename C>
+EIGEN_DONT_INLINE void gemm(const A& a, const B& b, C& c)
+{
+ c.noalias() += a * b;
+}
+
+int main(int argc, char ** argv)
+{
+ std::ptrdiff_t l1 = internal::queryL1CacheSize();
+ std::ptrdiff_t l2 = internal::queryTopLevelCacheSize();
+ std::cout << "L1 cache size = " << (l1>0 ? l1/1024 : -1) << " KB\n";
+ std::cout << "L2/L3 cache size = " << (l2>0 ? l2/1024 : -1) << " KB\n";
+ typedef internal::gebp_traits<Scalar,Scalar> Traits;
+ std::cout << "Register blocking = " << Traits::mr << " x " << Traits::nr << "\n";
+
+ int rep = 1; // number of repetitions per try
+ int tries = 2; // number of tries, we keep the best
+
+ int s = 2048;
+ int m = s;
+ int n = s;
+ int p = s;
+ int cache_size1=-1, cache_size2=l2, cache_size3 = 0;
+
+ bool need_help = false;
+ for (int i=1; i<argc;)
+ {
+ if(argv[i][0]=='-')
+ {
+ if(argv[i][1]=='s')
+ {
+ ++i;
+ s = atoi(argv[i++]);
+ m = n = p = s;
+ if(argv[i][0]!='-')
+ {
+ n = atoi(argv[i++]);
+ p = atoi(argv[i++]);
+ }
+ }
+ else if(argv[i][1]=='c')
+ {
+ ++i;
+ cache_size1 = atoi(argv[i++]);
+ if(argv[i][0]!='-')
+ {
+ cache_size2 = atoi(argv[i++]);
+ if(argv[i][0]!='-')
+ cache_size3 = atoi(argv[i++]);
+ }
+ }
+ else if(argv[i][1]=='t')
+ {
+ tries = atoi(argv[++i]);
+ ++i;
+ }
+ else if(argv[i][1]=='p')
+ {
+ ++i;
+ rep = atoi(argv[i++]);
+ }
+ }
+ else
+ {
+ need_help = true;
+ break;
+ }
+ }
+
+ if(need_help)
+ {
+ std::cout << argv[0] << " -s <matrix sizes> -c <cache sizes> -t <nb tries> -p <nb repeats>\n";
+ std::cout << " <matrix sizes> : size\n";
+ std::cout << " <matrix sizes> : rows columns depth\n";
+ return 1;
+ }
+
+#if EIGEN_VERSION_AT_LEAST(3,2,90)
+ if(cache_size1>0)
+ setCpuCacheSizes(cache_size1,cache_size2,cache_size3);
+#endif
+
+ A a(m,p); a.setRandom();
+ B b(p,n); b.setRandom();
+ C c(m,n); c.setOnes();
+ C rc = c;
+
+ std::cout << "Matrix sizes = " << m << "x" << p << " * " << p << "x" << n << "\n";
+ std::ptrdiff_t mc(m), nc(n), kc(p);
+ internal::computeProductBlockingSizes<Scalar,Scalar>(kc, mc, nc);
+ std::cout << "blocking size (mc x kc) = " << mc << " x " << kc << " x " << nc << "\n";
+
+ C r = c;
+
+ // check the parallel product is correct
+ #if defined EIGEN_HAS_OPENMP
+ Eigen::initParallel();
+ int procs = omp_get_max_threads();
+ if(procs>1)
+ {
+ #ifdef HAVE_BLAS
+ blas_gemm(a,b,r);
+ #else
+ omp_set_num_threads(1);
+ r.noalias() += a * b;
+ omp_set_num_threads(procs);
+ #endif
+ c.noalias() += a * b;
+ if(!r.isApprox(c)) std::cerr << "Warning, your parallel product is crap!\n\n";
+ }
+ #elif defined HAVE_BLAS
+ blas_gemm(a,b,r);
+ c.noalias() += a * b;
+ if(!r.isApprox(c)) {
+ std::cout << (r - c).norm()/r.norm() << "\n";
+ std::cerr << "Warning, your product is crap!\n\n";
+ }
+ #else
+ if(1.*m*n*p<2000.*2000*2000)
+ {
+ gemm(a,b,c);
+ r.noalias() += a.cast<Scalar>() .lazyProduct( b.cast<Scalar>() );
+ if(!r.isApprox(c)) {
+ std::cout << (r - c).norm()/r.norm() << "\n";
+ std::cerr << "Warning, your product is crap!\n\n";
+ }
+ }
+ #endif
+
+ #ifdef HAVE_BLAS
+ BenchTimer tblas;
+ c = rc;
+ BENCH(tblas, tries, rep, blas_gemm(a,b,c));
+ std::cout << "blas cpu " << tblas.best(CPU_TIMER)/rep << "s \t" << (double(m)*n*p*rep*2/tblas.best(CPU_TIMER))*1e-9 << " GFLOPS \t(" << tblas.total(CPU_TIMER) << "s)\n";
+ std::cout << "blas real " << tblas.best(REAL_TIMER)/rep << "s \t" << (double(m)*n*p*rep*2/tblas.best(REAL_TIMER))*1e-9 << " GFLOPS \t(" << tblas.total(REAL_TIMER) << "s)\n";
+ #endif
+
+ // warm start
+ if(b.norm()+a.norm()==123.554) std::cout << "\n";
+
+ BenchTimer tmt;
+ c = rc;
+ BENCH(tmt, tries, rep, gemm(a,b,c));
+ std::cout << "eigen cpu " << tmt.best(CPU_TIMER)/rep << "s \t" << (double(m)*n*p*rep*2/tmt.best(CPU_TIMER))*1e-9 << " GFLOPS \t(" << tmt.total(CPU_TIMER) << "s)\n";
+ std::cout << "eigen real " << tmt.best(REAL_TIMER)/rep << "s \t" << (double(m)*n*p*rep*2/tmt.best(REAL_TIMER))*1e-9 << " GFLOPS \t(" << tmt.total(REAL_TIMER) << "s)\n";
+
+ #ifdef EIGEN_HAS_OPENMP
+ if(procs>1)
+ {
+ BenchTimer tmono;
+ omp_set_num_threads(1);
+ Eigen::setNbThreads(1);
+ c = rc;
+ BENCH(tmono, tries, rep, gemm(a,b,c));
+ std::cout << "eigen mono cpu " << tmono.best(CPU_TIMER)/rep << "s \t" << (double(m)*n*p*rep*2/tmono.best(CPU_TIMER))*1e-9 << " GFLOPS \t(" << tmono.total(CPU_TIMER) << "s)\n";
+ std::cout << "eigen mono real " << tmono.best(REAL_TIMER)/rep << "s \t" << (double(m)*n*p*rep*2/tmono.best(REAL_TIMER))*1e-9 << " GFLOPS \t(" << tmono.total(REAL_TIMER) << "s)\n";
+ std::cout << "mt speed up x" << tmono.best(CPU_TIMER) / tmt.best(REAL_TIMER) << " => " << (100.0*tmono.best(CPU_TIMER) / tmt.best(REAL_TIMER))/procs << "%\n";
+ }
+ #endif
+
+ if(1.*m*n*p<30*30*30)
+ {
+ BenchTimer tmt;
+ c = rc;
+ BENCH(tmt, tries, rep, c.noalias()+=a.lazyProduct(b));
+ std::cout << "lazy cpu " << tmt.best(CPU_TIMER)/rep << "s \t" << (double(m)*n*p*rep*2/tmt.best(CPU_TIMER))*1e-9 << " GFLOPS \t(" << tmt.total(CPU_TIMER) << "s)\n";
+ std::cout << "lazy real " << tmt.best(REAL_TIMER)/rep << "s \t" << (double(m)*n*p*rep*2/tmt.best(REAL_TIMER))*1e-9 << " GFLOPS \t(" << tmt.total(REAL_TIMER) << "s)\n";
+ }
+
+ #ifdef DECOUPLED
+ if((NumTraits<A::Scalar>::IsComplex) && (NumTraits<B::Scalar>::IsComplex))
+ {
+ M ar(m,p); ar.setRandom();
+ M ai(m,p); ai.setRandom();
+ M br(p,n); br.setRandom();
+ M bi(p,n); bi.setRandom();
+ M cr(m,n); cr.setRandom();
+ M ci(m,n); ci.setRandom();
+
+ BenchTimer t;
+ BENCH(t, tries, rep, matlab_cplx_cplx(ar,ai,br,bi,cr,ci));
+ std::cout << "\"matlab\" cpu " << t.best(CPU_TIMER)/rep << "s \t" << (double(m)*n*p*rep*2/t.best(CPU_TIMER))*1e-9 << " GFLOPS \t(" << t.total(CPU_TIMER) << "s)\n";
+ std::cout << "\"matlab\" real " << t.best(REAL_TIMER)/rep << "s \t" << (double(m)*n*p*rep*2/t.best(REAL_TIMER))*1e-9 << " GFLOPS \t(" << t.total(REAL_TIMER) << "s)\n";
+ }
+ if((!NumTraits<A::Scalar>::IsComplex) && (NumTraits<B::Scalar>::IsComplex))
+ {
+ M a(m,p); a.setRandom();
+ M br(p,n); br.setRandom();
+ M bi(p,n); bi.setRandom();
+ M cr(m,n); cr.setRandom();
+ M ci(m,n); ci.setRandom();
+
+ BenchTimer t;
+ BENCH(t, tries, rep, matlab_real_cplx(a,br,bi,cr,ci));
+ std::cout << "\"matlab\" cpu " << t.best(CPU_TIMER)/rep << "s \t" << (double(m)*n*p*rep*2/t.best(CPU_TIMER))*1e-9 << " GFLOPS \t(" << t.total(CPU_TIMER) << "s)\n";
+ std::cout << "\"matlab\" real " << t.best(REAL_TIMER)/rep << "s \t" << (double(m)*n*p*rep*2/t.best(REAL_TIMER))*1e-9 << " GFLOPS \t(" << t.total(REAL_TIMER) << "s)\n";
+ }
+ if((NumTraits<A::Scalar>::IsComplex) && (!NumTraits<B::Scalar>::IsComplex))
+ {
+ M ar(m,p); ar.setRandom();
+ M ai(m,p); ai.setRandom();
+ M b(p,n); b.setRandom();
+ M cr(m,n); cr.setRandom();
+ M ci(m,n); ci.setRandom();
+
+ BenchTimer t;
+ BENCH(t, tries, rep, matlab_cplx_real(ar,ai,b,cr,ci));
+ std::cout << "\"matlab\" cpu " << t.best(CPU_TIMER)/rep << "s \t" << (double(m)*n*p*rep*2/t.best(CPU_TIMER))*1e-9 << " GFLOPS \t(" << t.total(CPU_TIMER) << "s)\n";
+ std::cout << "\"matlab\" real " << t.best(REAL_TIMER)/rep << "s \t" << (double(m)*n*p*rep*2/t.best(REAL_TIMER))*1e-9 << " GFLOPS \t(" << t.total(REAL_TIMER) << "s)\n";
+ }
+ #endif
+
+ return 0;
+}
+
diff --git a/bench/bench_move_semantics.cpp b/bench/bench_move_semantics.cpp
new file mode 100644
index 0000000..323d804
--- /dev/null
+++ b/bench/bench_move_semantics.cpp
@@ -0,0 +1,57 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2020 Sebastien Boisvert <seb@boisvert.info>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "BenchTimer.h"
+#include "../test/MovableScalar.h"
+
+#include <Eigen/Core>
+
+#include <iostream>
+#include <utility>
+
+template <typename MatrixType>
+void copy_matrix(MatrixType& m)
+{
+ MatrixType tmp(m);
+ m = tmp;
+}
+
+template <typename MatrixType>
+void move_matrix(MatrixType&& m)
+{
+ MatrixType tmp(std::move(m));
+ m = std::move(tmp);
+}
+
+template<typename Scalar>
+void bench(const std::string& label)
+{
+ using MatrixType = Eigen::Matrix<Eigen::MovableScalar<Scalar>,1,10>;
+ Eigen::BenchTimer t;
+
+ int tries = 10;
+ int rep = 1000000;
+
+ MatrixType data = MatrixType::Random().eval();
+ MatrixType dest;
+
+ BENCH(t, tries, rep, copy_matrix(data));
+ std::cout << label << " copy semantics: " << 1e3*t.best(Eigen::CPU_TIMER) << " ms" << std::endl;
+
+ BENCH(t, tries, rep, move_matrix(std::move(data)));
+ std::cout << label << " move semantics: " << 1e3*t.best(Eigen::CPU_TIMER) << " ms" << std::endl;
+}
+
+int main()
+{
+ bench<float>("float");
+ bench<double>("double");
+ return 0;
+}
+
diff --git a/bench/bench_norm.cpp b/bench/bench_norm.cpp
new file mode 100644
index 0000000..592f25d
--- /dev/null
+++ b/bench/bench_norm.cpp
@@ -0,0 +1,360 @@
+#include <typeinfo>
+#include <iostream>
+#include <Eigen/Core>
+#include "BenchTimer.h"
+using namespace Eigen;
+using namespace std;
+
+template<typename T>
+EIGEN_DONT_INLINE typename T::Scalar sqsumNorm(T& v)
+{
+ return v.norm();
+}
+
+template<typename T>
+EIGEN_DONT_INLINE typename T::Scalar stableNorm(T& v)
+{
+ return v.stableNorm();
+}
+
+template<typename T>
+EIGEN_DONT_INLINE typename T::Scalar hypotNorm(T& v)
+{
+ return v.hypotNorm();
+}
+
+template<typename T>
+EIGEN_DONT_INLINE typename T::Scalar blueNorm(T& v)
+{
+ return v.blueNorm();
+}
+
+template<typename T>
+EIGEN_DONT_INLINE typename T::Scalar lapackNorm(T& v)
+{
+ typedef typename T::Scalar Scalar;
+ int n = v.size();
+ Scalar scale = 0;
+ Scalar ssq = 1;
+ for (int i=0;i<n;++i)
+ {
+ Scalar ax = std::abs(v.coeff(i));
+ if (scale >= ax)
+ {
+ ssq += numext::abs2(ax/scale);
+ }
+ else
+ {
+ ssq = Scalar(1) + ssq * numext::abs2(scale/ax);
+ scale = ax;
+ }
+ }
+ return scale * std::sqrt(ssq);
+}
+
+template<typename T>
+EIGEN_DONT_INLINE typename T::Scalar twopassNorm(T& v)
+{
+ typedef typename T::Scalar Scalar;
+ Scalar s = v.array().abs().maxCoeff();
+ return s*(v/s).norm();
+}
+
+template<typename T>
+EIGEN_DONT_INLINE typename T::Scalar bl2passNorm(T& v)
+{
+ return v.stableNorm();
+}
+
+template<typename T>
+EIGEN_DONT_INLINE typename T::Scalar divacNorm(T& v)
+{
+ int n =v.size() / 2;
+ for (int i=0;i<n;++i)
+ v(i) = v(2*i)*v(2*i) + v(2*i+1)*v(2*i+1);
+ n = n/2;
+ while (n>0)
+ {
+ for (int i=0;i<n;++i)
+ v(i) = v(2*i) + v(2*i+1);
+ n = n/2;
+ }
+ return std::sqrt(v(0));
+}
+
+namespace Eigen {
+namespace internal {
+#ifdef EIGEN_VECTORIZE
+Packet4f plt(const Packet4f& a, Packet4f& b) { return _mm_cmplt_ps(a,b); }
+Packet2d plt(const Packet2d& a, Packet2d& b) { return _mm_cmplt_pd(a,b); }
+
+Packet4f pandnot(const Packet4f& a, Packet4f& b) { return _mm_andnot_ps(a,b); }
+Packet2d pandnot(const Packet2d& a, Packet2d& b) { return _mm_andnot_pd(a,b); }
+#endif
+}
+}
+
+template<typename T>
+EIGEN_DONT_INLINE typename T::Scalar pblueNorm(const T& v)
+{
+ #ifndef EIGEN_VECTORIZE
+ return v.blueNorm();
+ #else
+ typedef typename T::Scalar Scalar;
+
+ static int nmax = 0;
+ static Scalar b1, b2, s1m, s2m, overfl, rbig, relerr;
+ int n;
+
+ if(nmax <= 0)
+ {
+ int nbig, ibeta, it, iemin, iemax, iexp;
+ Scalar abig, eps;
+
+ nbig = NumTraits<int>::highest(); // largest integer
+ ibeta = std::numeric_limits<Scalar>::radix; // NumTraits<Scalar>::Base; // base for floating-point numbers
+ it = NumTraits<Scalar>::digits(); // NumTraits<Scalar>::Mantissa; // number of base-beta digits in mantissa
+ iemin = NumTraits<Scalar>::min_exponent(); // minimum exponent
+ iemax = NumTraits<Scalar>::max_exponent(); // maximum exponent
+ rbig = NumTraits<Scalar>::highest(); // largest floating-point number
+
+ // Check the basic machine-dependent constants.
+ if(iemin > 1 - 2*it || 1+it>iemax || (it==2 && ibeta<5)
+ || (it<=4 && ibeta <= 3 ) || it<2)
+ {
+ eigen_assert(false && "the algorithm cannot be guaranteed on this computer");
+ }
+ iexp = -((1-iemin)/2);
+ b1 = std::pow(ibeta, iexp); // lower boundary of midrange
+ iexp = (iemax + 1 - it)/2;
+ b2 = std::pow(ibeta,iexp); // upper boundary of midrange
+
+ iexp = (2-iemin)/2;
+ s1m = std::pow(ibeta,iexp); // scaling factor for lower range
+ iexp = - ((iemax+it)/2);
+ s2m = std::pow(ibeta,iexp); // scaling factor for upper range
+
+ overfl = rbig*s2m; // overflow boundary for abig
+ eps = std::pow(ibeta, 1-it);
+ relerr = std::sqrt(eps); // tolerance for neglecting asml
+ abig = 1.0/eps - 1.0;
+ if (Scalar(nbig)>abig) nmax = abig; // largest safe n
+ else nmax = nbig;
+ }
+
+ typedef typename internal::packet_traits<Scalar>::type Packet;
+ const int ps = internal::packet_traits<Scalar>::size;
+ Packet pasml = internal::pset1<Packet>(Scalar(0));
+ Packet pamed = internal::pset1<Packet>(Scalar(0));
+ Packet pabig = internal::pset1<Packet>(Scalar(0));
+ Packet ps2m = internal::pset1<Packet>(s2m);
+ Packet ps1m = internal::pset1<Packet>(s1m);
+ Packet pb2 = internal::pset1<Packet>(b2);
+ Packet pb1 = internal::pset1<Packet>(b1);
+ for(int j=0; j<v.size(); j+=ps)
+ {
+ Packet ax = internal::pabs(v.template packet<Aligned>(j));
+ Packet ax_s2m = internal::pmul(ax,ps2m);
+ Packet ax_s1m = internal::pmul(ax,ps1m);
+ Packet maskBig = internal::plt(pb2,ax);
+ Packet maskSml = internal::plt(ax,pb1);
+
+// Packet maskMed = internal::pand(maskSml,maskBig);
+// Packet scale = internal::pset1(Scalar(0));
+// scale = internal::por(scale, internal::pand(maskBig,ps2m));
+// scale = internal::por(scale, internal::pand(maskSml,ps1m));
+// scale = internal::por(scale, internal::pandnot(internal::pset1(Scalar(1)),maskMed));
+// ax = internal::pmul(ax,scale);
+// ax = internal::pmul(ax,ax);
+// pabig = internal::padd(pabig, internal::pand(maskBig, ax));
+// pasml = internal::padd(pasml, internal::pand(maskSml, ax));
+// pamed = internal::padd(pamed, internal::pandnot(ax,maskMed));
+
+
+ pabig = internal::padd(pabig, internal::pand(maskBig, internal::pmul(ax_s2m,ax_s2m)));
+ pasml = internal::padd(pasml, internal::pand(maskSml, internal::pmul(ax_s1m,ax_s1m)));
+ pamed = internal::padd(pamed, internal::pandnot(internal::pmul(ax,ax),internal::pand(maskSml,maskBig)));
+ }
+ Scalar abig = internal::predux(pabig);
+ Scalar asml = internal::predux(pasml);
+ Scalar amed = internal::predux(pamed);
+ if(abig > Scalar(0))
+ {
+ abig = std::sqrt(abig);
+ if(abig > overfl)
+ {
+ eigen_assert(false && "overflow");
+ return rbig;
+ }
+ if(amed > Scalar(0))
+ {
+ abig = abig/s2m;
+ amed = std::sqrt(amed);
+ }
+ else
+ {
+ return abig/s2m;
+ }
+
+ }
+ else if(asml > Scalar(0))
+ {
+ if (amed > Scalar(0))
+ {
+ abig = std::sqrt(amed);
+ amed = std::sqrt(asml) / s1m;
+ }
+ else
+ {
+ return std::sqrt(asml)/s1m;
+ }
+ }
+ else
+ {
+ return std::sqrt(amed);
+ }
+ asml = std::min(abig, amed);
+ abig = std::max(abig, amed);
+ if(asml <= abig*relerr)
+ return abig;
+ else
+ return abig * std::sqrt(Scalar(1) + numext::abs2(asml/abig));
+ #endif
+}
+
+#define BENCH_PERF(NRM) { \
+ float af = 0; double ad = 0; std::complex<float> ac = 0; \
+ Eigen::BenchTimer tf, td, tcf; tf.reset(); td.reset(); tcf.reset();\
+ for (int k=0; k<tries; ++k) { \
+ tf.start(); \
+ for (int i=0; i<iters; ++i) { af += NRM(vf); } \
+ tf.stop(); \
+ } \
+ for (int k=0; k<tries; ++k) { \
+ td.start(); \
+ for (int i=0; i<iters; ++i) { ad += NRM(vd); } \
+ td.stop(); \
+ } \
+ /*for (int k=0; k<std::max(1,tries/3); ++k) { \
+ tcf.start(); \
+ for (int i=0; i<iters; ++i) { ac += NRM(vcf); } \
+ tcf.stop(); \
+ } */\
+ std::cout << #NRM << "\t" << tf.value() << " " << td.value() << " " << tcf.value() << "\n"; \
+}
+
+void check_accuracy(double basef, double based, int s)
+{
+ double yf = basef * std::abs(internal::random<double>());
+ double yd = based * std::abs(internal::random<double>());
+ VectorXf vf = VectorXf::Ones(s) * yf;
+ VectorXd vd = VectorXd::Ones(s) * yd;
+
+ std::cout << "reference\t" << std::sqrt(double(s))*yf << "\t" << std::sqrt(double(s))*yd << "\n";
+ std::cout << "sqsumNorm\t" << sqsumNorm(vf) << "\t" << sqsumNorm(vd) << "\n";
+ std::cout << "hypotNorm\t" << hypotNorm(vf) << "\t" << hypotNorm(vd) << "\n";
+ std::cout << "blueNorm\t" << blueNorm(vf) << "\t" << blueNorm(vd) << "\n";
+ std::cout << "pblueNorm\t" << pblueNorm(vf) << "\t" << pblueNorm(vd) << "\n";
+ std::cout << "lapackNorm\t" << lapackNorm(vf) << "\t" << lapackNorm(vd) << "\n";
+ std::cout << "twopassNorm\t" << twopassNorm(vf) << "\t" << twopassNorm(vd) << "\n";
+ std::cout << "bl2passNorm\t" << bl2passNorm(vf) << "\t" << bl2passNorm(vd) << "\n";
+}
+
+void check_accuracy_var(int ef0, int ef1, int ed0, int ed1, int s)
+{
+ VectorXf vf(s);
+ VectorXd vd(s);
+ for (int i=0; i<s; ++i)
+ {
+ vf[i] = std::abs(internal::random<double>()) * std::pow(double(10), internal::random<int>(ef0,ef1));
+ vd[i] = std::abs(internal::random<double>()) * std::pow(double(10), internal::random<int>(ed0,ed1));
+ }
+
+ //std::cout << "reference\t" << internal::sqrt(double(s))*yf << "\t" << internal::sqrt(double(s))*yd << "\n";
+ std::cout << "sqsumNorm\t" << sqsumNorm(vf) << "\t" << sqsumNorm(vd) << "\t" << sqsumNorm(vf.cast<long double>()) << "\t" << sqsumNorm(vd.cast<long double>()) << "\n";
+ std::cout << "hypotNorm\t" << hypotNorm(vf) << "\t" << hypotNorm(vd) << "\t" << hypotNorm(vf.cast<long double>()) << "\t" << hypotNorm(vd.cast<long double>()) << "\n";
+ std::cout << "blueNorm\t" << blueNorm(vf) << "\t" << blueNorm(vd) << "\t" << blueNorm(vf.cast<long double>()) << "\t" << blueNorm(vd.cast<long double>()) << "\n";
+ std::cout << "pblueNorm\t" << pblueNorm(vf) << "\t" << pblueNorm(vd) << "\t" << blueNorm(vf.cast<long double>()) << "\t" << blueNorm(vd.cast<long double>()) << "\n";
+ std::cout << "lapackNorm\t" << lapackNorm(vf) << "\t" << lapackNorm(vd) << "\t" << lapackNorm(vf.cast<long double>()) << "\t" << lapackNorm(vd.cast<long double>()) << "\n";
+ std::cout << "twopassNorm\t" << twopassNorm(vf) << "\t" << twopassNorm(vd) << "\t" << twopassNorm(vf.cast<long double>()) << "\t" << twopassNorm(vd.cast<long double>()) << "\n";
+// std::cout << "bl2passNorm\t" << bl2passNorm(vf) << "\t" << bl2passNorm(vd) << "\t" << bl2passNorm(vf.cast<long double>()) << "\t" << bl2passNorm(vd.cast<long double>()) << "\n";
+}
+
+int main(int argc, char** argv)
+{
+ int tries = 10;
+ int iters = 100000;
+ double y = 1.1345743233455785456788e12 * internal::random<double>();
+ VectorXf v = VectorXf::Ones(1024) * y;
+
+// return 0;
+ int s = 10000;
+ double basef_ok = 1.1345743233455785456788e15;
+ double based_ok = 1.1345743233455785456788e95;
+
+ double basef_under = 1.1345743233455785456788e-27;
+ double based_under = 1.1345743233455785456788e-303;
+
+ double basef_over = 1.1345743233455785456788e+27;
+ double based_over = 1.1345743233455785456788e+302;
+
+ std::cout.precision(20);
+
+ std::cerr << "\nNo under/overflow:\n";
+ check_accuracy(basef_ok, based_ok, s);
+
+ std::cerr << "\nUnderflow:\n";
+ check_accuracy(basef_under, based_under, s);
+
+ std::cerr << "\nOverflow:\n";
+ check_accuracy(basef_over, based_over, s);
+
+ std::cerr << "\nVarying (over):\n";
+ for (int k=0; k<1; ++k)
+ {
+ check_accuracy_var(20,27,190,302,s);
+ std::cout << "\n";
+ }
+
+ std::cerr << "\nVarying (under):\n";
+ for (int k=0; k<1; ++k)
+ {
+ check_accuracy_var(-27,20,-302,-190,s);
+ std::cout << "\n";
+ }
+
+ y = 1;
+ std::cout.precision(4);
+ int s1 = 1024*1024*32;
+ std::cerr << "Performance (out of cache, " << s1 << "):\n";
+ {
+ int iters = 1;
+ VectorXf vf = VectorXf::Random(s1) * y;
+ VectorXd vd = VectorXd::Random(s1) * y;
+ VectorXcf vcf = VectorXcf::Random(s1) * y;
+ BENCH_PERF(sqsumNorm);
+ BENCH_PERF(stableNorm);
+ BENCH_PERF(blueNorm);
+ BENCH_PERF(pblueNorm);
+ BENCH_PERF(lapackNorm);
+ BENCH_PERF(hypotNorm);
+ BENCH_PERF(twopassNorm);
+ BENCH_PERF(bl2passNorm);
+ }
+
+ std::cerr << "\nPerformance (in cache, " << 512 << "):\n";
+ {
+ int iters = 100000;
+ VectorXf vf = VectorXf::Random(512) * y;
+ VectorXd vd = VectorXd::Random(512) * y;
+ VectorXcf vcf = VectorXcf::Random(512) * y;
+ BENCH_PERF(sqsumNorm);
+ BENCH_PERF(stableNorm);
+ BENCH_PERF(blueNorm);
+ BENCH_PERF(pblueNorm);
+ BENCH_PERF(lapackNorm);
+ BENCH_PERF(hypotNorm);
+ BENCH_PERF(twopassNorm);
+ BENCH_PERF(bl2passNorm);
+ }
+}
diff --git a/bench/bench_reverse.cpp b/bench/bench_reverse.cpp
new file mode 100644
index 0000000..1e69ca1
--- /dev/null
+++ b/bench/bench_reverse.cpp
@@ -0,0 +1,84 @@
+
+#include <iostream>
+#include <Eigen/Core>
+#include <bench/BenchUtil.h>
+using namespace Eigen;
+
+#ifndef REPEAT
+#define REPEAT 100000
+#endif
+
+#ifndef TRIES
+#define TRIES 20
+#endif
+
+typedef double Scalar;
+
+template <typename MatrixType>
+__attribute__ ((noinline)) void bench_reverse(const MatrixType& m)
+{
+ int rows = m.rows();
+ int cols = m.cols();
+ int size = m.size();
+
+ int repeats = (REPEAT*1000)/size;
+ MatrixType a = MatrixType::Random(rows,cols);
+ MatrixType b = MatrixType::Random(rows,cols);
+
+ BenchTimer timerB, timerH, timerV;
+
+ Scalar acc = 0;
+ int r = internal::random<int>(0,rows-1);
+ int c = internal::random<int>(0,cols-1);
+ for (int t=0; t<TRIES; ++t)
+ {
+ timerB.start();
+ for (int k=0; k<repeats; ++k)
+ {
+ asm("#begin foo");
+ b = a.reverse();
+ asm("#end foo");
+ acc += b.coeff(r,c);
+ }
+ timerB.stop();
+ }
+
+ if (MatrixType::RowsAtCompileTime==Dynamic)
+ std::cout << "dyn ";
+ else
+ std::cout << "fixed ";
+ std::cout << rows << " x " << cols << " \t"
+ << (timerB.value() * REPEAT) / repeats << "s "
+ << "(" << 1e-6 * size*repeats/timerB.value() << " MFLOPS)\t";
+
+ std::cout << "\n";
+ // make sure the compiler does not optimize too much
+ if (acc==123)
+ std::cout << acc;
+}
+
+int main(int argc, char* argv[])
+{
+ const int dynsizes[] = {4,6,8,16,24,32,49,64,128,256,512,900,0};
+ std::cout << "size no sqrt standard";
+// #ifdef BENCH_GSL
+// std::cout << " GSL (standard + double + ATLAS) ";
+// #endif
+ std::cout << "\n";
+ for (uint i=0; dynsizes[i]>0; ++i)
+ {
+ bench_reverse(Matrix<Scalar,Dynamic,Dynamic>(dynsizes[i],dynsizes[i]));
+ bench_reverse(Matrix<Scalar,Dynamic,1>(dynsizes[i]*dynsizes[i]));
+ }
+// bench_reverse(Matrix<Scalar,2,2>());
+// bench_reverse(Matrix<Scalar,3,3>());
+// bench_reverse(Matrix<Scalar,4,4>());
+// bench_reverse(Matrix<Scalar,5,5>());
+// bench_reverse(Matrix<Scalar,6,6>());
+// bench_reverse(Matrix<Scalar,7,7>());
+// bench_reverse(Matrix<Scalar,8,8>());
+// bench_reverse(Matrix<Scalar,12,12>());
+// bench_reverse(Matrix<Scalar,16,16>());
+ return 0;
+}
+
diff --git a/bench/bench_sum.cpp b/bench/bench_sum.cpp
new file mode 100644
index 0000000..a3d925e
--- /dev/null
+++ b/bench/bench_sum.cpp
@@ -0,0 +1,18 @@
+#include <iostream>
+#include <Eigen/Core>
+using namespace Eigen;
+using namespace std;
+
+int main()
+{
+ typedef Matrix<SCALAR,Eigen::Dynamic,1> Vec;
+ Vec v(SIZE);
+ v.setZero();
+ v[0] = 1;
+ v[1] = 2;
+ for(int i = 0; i < 1000000; i++)
+ {
+ v.coeffRef(0) += v.sum() * SCALAR(1e-20);
+ }
+ cout << v.sum() << endl;
+}
diff --git a/bench/bench_unrolling b/bench/bench_unrolling
new file mode 100755
index 0000000..8264438
--- /dev/null
+++ b/bench/bench_unrolling
@@ -0,0 +1,12 @@
+#!/bin/bash
+
+# gcc : CXX="g++ -finline-limit=10000 -ftemplate-depth-2000 --param max-inline-recursive-depth=2000"
+# icc : CXX="icpc -fast -no-inline-max-size -fno-exceptions"
+CXX=${CXX-g++ -finline-limit=10000 -ftemplate-depth-2000 --param max-inline-recursive-depth=2000} # default value
+
+for ((i=1; i<16; ++i)); do
+ echo "Matrix size: $i x $i :"
+ $CXX -O3 -I.. -DNDEBUG benchmark.cpp -DMATSIZE=$i -DEIGEN_UNROLLING_LIMIT=400 -o benchmark && time ./benchmark >/dev/null
+ $CXX -O3 -I.. -DNDEBUG -finline-limit=10000 benchmark.cpp -DMATSIZE=$i -DEIGEN_DONT_USE_UNROLLED_LOOPS=1 -o benchmark && time ./benchmark >/dev/null
+ echo " "
+done
diff --git a/bench/benchmark-blocking-sizes.cpp b/bench/benchmark-blocking-sizes.cpp
new file mode 100644
index 0000000..827be28
--- /dev/null
+++ b/bench/benchmark-blocking-sizes.cpp
@@ -0,0 +1,677 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2015 Benoit Jacob <benoitjacob@google.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include <iostream>
+#include <cstdint>
+#include <cstdlib>
+#include <vector>
+#include <fstream>
+#include <memory>
+#include <cstdio>
+
+bool eigen_use_specific_block_size;
+int eigen_block_size_k, eigen_block_size_m, eigen_block_size_n;
+#define EIGEN_TEST_SPECIFIC_BLOCKING_SIZES eigen_use_specific_block_size
+#define EIGEN_TEST_SPECIFIC_BLOCKING_SIZE_K eigen_block_size_k
+#define EIGEN_TEST_SPECIFIC_BLOCKING_SIZE_M eigen_block_size_m
+#define EIGEN_TEST_SPECIFIC_BLOCKING_SIZE_N eigen_block_size_n
+#include <Eigen/Core>
+
+#include <bench/BenchTimer.h>
+
+using namespace Eigen;
+using namespace std;
+
+static BenchTimer timer;
+
+// how many times we repeat each measurement.
+// measurements are randomly shuffled - we're not doing
+// all N identical measurements in a row.
+const int measurement_repetitions = 3;
+
+// Timings below this value are too short to be accurate,
+// we'll repeat measurements with more iterations until
+// we get a timing above that threshold.
+const float min_accurate_time = 1e-2f;
+
+// See --min-working-set-size command line parameter.
+size_t min_working_set_size = 0;
+
+float max_clock_speed = 0.0f;
+
+// range of sizes that we will benchmark (in all 3 K,M,N dimensions)
+const size_t maxsize = 2048;
+const size_t minsize = 16;
+
+typedef MatrixXf MatrixType;
+typedef MatrixType::Scalar Scalar;
+typedef internal::packet_traits<Scalar>::type Packet;
+
+static_assert((maxsize & (maxsize - 1)) == 0, "maxsize must be a power of two");
+static_assert((minsize & (minsize - 1)) == 0, "minsize must be a power of two");
+static_assert(maxsize > minsize, "maxsize must be larger than minsize");
+static_assert(maxsize < (minsize << 16), "maxsize must be less than (minsize<<16)");
+
+// just a helper to store a triple of K,M,N sizes for matrix product
+struct size_triple_t
+{
+ size_t k, m, n;
+ size_triple_t() : k(0), m(0), n(0) {}
+ size_triple_t(size_t _k, size_t _m, size_t _n) : k(_k), m(_m), n(_n) {}
+ size_triple_t(const size_triple_t& o) : k(o.k), m(o.m), n(o.n) {}
+ size_triple_t(uint16_t compact)
+ {
+ k = 1 << ((compact & 0xf00) >> 8);
+ m = 1 << ((compact & 0x0f0) >> 4);
+ n = 1 << ((compact & 0x00f) >> 0);
+ }
+};
+
+uint8_t log2_pot(size_t x) {
+ size_t l = 0;
+ while (x >>= 1) l++;
+ return l;
+}
+
+// Convert between size tripes and a compact form fitting in 12 bits
+// where each size, which must be a POT, is encoded as its log2, on 4 bits
+// so the largest representable size is 2^15 == 32k ... big enough.
+uint16_t compact_size_triple(size_t k, size_t m, size_t n)
+{
+ return (log2_pot(k) << 8) | (log2_pot(m) << 4) | log2_pot(n);
+}
+
+uint16_t compact_size_triple(const size_triple_t& t)
+{
+ return compact_size_triple(t.k, t.m, t.n);
+}
+
+// A single benchmark. Initially only contains benchmark params.
+// Then call run(), which stores the result in the gflops field.
+struct benchmark_t
+{
+ uint16_t compact_product_size;
+ uint16_t compact_block_size;
+ bool use_default_block_size;
+ float gflops;
+ benchmark_t()
+ : compact_product_size(0)
+ , compact_block_size(0)
+ , use_default_block_size(false)
+ , gflops(0)
+ {
+ }
+ benchmark_t(size_t pk, size_t pm, size_t pn,
+ size_t bk, size_t bm, size_t bn)
+ : compact_product_size(compact_size_triple(pk, pm, pn))
+ , compact_block_size(compact_size_triple(bk, bm, bn))
+ , use_default_block_size(false)
+ , gflops(0)
+ {}
+ benchmark_t(size_t pk, size_t pm, size_t pn)
+ : compact_product_size(compact_size_triple(pk, pm, pn))
+ , compact_block_size(0)
+ , use_default_block_size(true)
+ , gflops(0)
+ {}
+
+ void run();
+};
+
+ostream& operator<<(ostream& s, const benchmark_t& b)
+{
+ s << hex << b.compact_product_size << dec;
+ if (b.use_default_block_size) {
+ size_triple_t t(b.compact_product_size);
+ Index k = t.k, m = t.m, n = t.n;
+ internal::computeProductBlockingSizes<Scalar, Scalar>(k, m, n);
+ s << " default(" << k << ", " << m << ", " << n << ")";
+ } else {
+ s << " " << hex << b.compact_block_size << dec;
+ }
+ s << " " << b.gflops;
+ return s;
+}
+
+// We sort first by increasing benchmark parameters,
+// then by decreasing performance.
+bool operator<(const benchmark_t& b1, const benchmark_t& b2)
+{
+ return b1.compact_product_size < b2.compact_product_size ||
+ (b1.compact_product_size == b2.compact_product_size && (
+ (b1.compact_block_size < b2.compact_block_size || (
+ b1.compact_block_size == b2.compact_block_size &&
+ b1.gflops > b2.gflops))));
+}
+
+void benchmark_t::run()
+{
+ size_triple_t productsizes(compact_product_size);
+
+ if (use_default_block_size) {
+ eigen_use_specific_block_size = false;
+ } else {
+ // feed eigen with our custom blocking params
+ eigen_use_specific_block_size = true;
+ size_triple_t blocksizes(compact_block_size);
+ eigen_block_size_k = blocksizes.k;
+ eigen_block_size_m = blocksizes.m;
+ eigen_block_size_n = blocksizes.n;
+ }
+
+ // set up the matrix pool
+
+ const size_t combined_three_matrices_sizes =
+ sizeof(Scalar) *
+ (productsizes.k * productsizes.m +
+ productsizes.k * productsizes.n +
+ productsizes.m * productsizes.n);
+
+ // 64 M is large enough that nobody has a cache bigger than that,
+ // while still being small enough that everybody has this much RAM,
+ // so conveniently we don't need to special-case platforms here.
+ const size_t unlikely_large_cache_size = 64 << 20;
+
+ const size_t working_set_size =
+ min_working_set_size ? min_working_set_size : unlikely_large_cache_size;
+
+ const size_t matrix_pool_size =
+ 1 + working_set_size / combined_three_matrices_sizes;
+
+ MatrixType *lhs = new MatrixType[matrix_pool_size];
+ MatrixType *rhs = new MatrixType[matrix_pool_size];
+ MatrixType *dst = new MatrixType[matrix_pool_size];
+
+ for (size_t i = 0; i < matrix_pool_size; i++) {
+ lhs[i] = MatrixType::Zero(productsizes.m, productsizes.k);
+ rhs[i] = MatrixType::Zero(productsizes.k, productsizes.n);
+ dst[i] = MatrixType::Zero(productsizes.m, productsizes.n);
+ }
+
+ // main benchmark loop
+
+ int iters_at_a_time = 1;
+ float time_per_iter = 0.0f;
+ size_t matrix_index = 0;
+ while (true) {
+
+ double starttime = timer.getCpuTime();
+ for (int i = 0; i < iters_at_a_time; i++) {
+ dst[matrix_index].noalias() = lhs[matrix_index] * rhs[matrix_index];
+ matrix_index++;
+ if (matrix_index == matrix_pool_size) {
+ matrix_index = 0;
+ }
+ }
+ double endtime = timer.getCpuTime();
+
+ const float timing = float(endtime - starttime);
+
+ if (timing >= min_accurate_time) {
+ time_per_iter = timing / iters_at_a_time;
+ break;
+ }
+
+ iters_at_a_time *= 2;
+ }
+
+ delete[] lhs;
+ delete[] rhs;
+ delete[] dst;
+
+ gflops = 2e-9 * productsizes.k * productsizes.m * productsizes.n / time_per_iter;
+}
+
+void print_cpuinfo()
+{
+#ifdef __linux__
+ cout << "contents of /proc/cpuinfo:" << endl;
+ string line;
+ ifstream cpuinfo("/proc/cpuinfo");
+ if (cpuinfo.is_open()) {
+ while (getline(cpuinfo, line)) {
+ cout << line << endl;
+ }
+ cpuinfo.close();
+ }
+ cout << endl;
+#elif defined __APPLE__
+ cout << "output of sysctl hw:" << endl;
+ system("sysctl hw");
+ cout << endl;
+#endif
+}
+
+template <typename T>
+string type_name()
+{
+ return "unknown";
+}
+
+template<>
+string type_name<float>()
+{
+ return "float";
+}
+
+template<>
+string type_name<double>()
+{
+ return "double";
+}
+
+struct action_t
+{
+ virtual const char* invokation_name() const { abort(); return nullptr; }
+ virtual void run() const { abort(); }
+ virtual ~action_t() {}
+};
+
+void show_usage_and_exit(int /*argc*/, char* argv[],
+ const vector<unique_ptr<action_t>>& available_actions)
+{
+ cerr << "usage: " << argv[0] << " <action> [options...]" << endl << endl;
+ cerr << "available actions:" << endl << endl;
+ for (auto it = available_actions.begin(); it != available_actions.end(); ++it) {
+ cerr << " " << (*it)->invokation_name() << endl;
+ }
+ cerr << endl;
+ cerr << "options:" << endl << endl;
+ cerr << " --min-working-set-size=N:" << endl;
+ cerr << " Set the minimum working set size to N bytes." << endl;
+ cerr << " This is rounded up as needed to a multiple of matrix size." << endl;
+ cerr << " A larger working set lowers the chance of a warm cache." << endl;
+ cerr << " The default value 0 means use a large enough working" << endl;
+ cerr << " set to likely outsize caches." << endl;
+ cerr << " A value of 1 (that is, 1 byte) would mean don't do anything to" << endl;
+ cerr << " avoid warm caches." << endl;
+ exit(1);
+}
+
+float measure_clock_speed()
+{
+ cerr << "Measuring clock speed... \r" << flush;
+
+ vector<float> all_gflops;
+ for (int i = 0; i < 8; i++) {
+ benchmark_t b(1024, 1024, 1024);
+ b.run();
+ all_gflops.push_back(b.gflops);
+ }
+
+ sort(all_gflops.begin(), all_gflops.end());
+ float stable_estimate = all_gflops[2] + all_gflops[3] + all_gflops[4] + all_gflops[5];
+
+ // multiply by an arbitrary constant to discourage trying doing anything with the
+ // returned values besides just comparing them with each other.
+ float result = stable_estimate * 123.456f;
+
+ return result;
+}
+
+struct human_duration_t
+{
+ int seconds;
+ human_duration_t(int s) : seconds(s) {}
+};
+
+ostream& operator<<(ostream& s, const human_duration_t& d)
+{
+ int remainder = d.seconds;
+ if (remainder > 3600) {
+ int hours = remainder / 3600;
+ s << hours << " h ";
+ remainder -= hours * 3600;
+ }
+ if (remainder > 60) {
+ int minutes = remainder / 60;
+ s << minutes << " min ";
+ remainder -= minutes * 60;
+ }
+ if (d.seconds < 600) {
+ s << remainder << " s";
+ }
+ return s;
+}
+
+const char session_filename[] = "/data/local/tmp/benchmark-blocking-sizes-session.data";
+
+void serialize_benchmarks(const char* filename, const vector<benchmark_t>& benchmarks, size_t first_benchmark_to_run)
+{
+ FILE* file = fopen(filename, "w");
+ if (!file) {
+ cerr << "Could not open file " << filename << " for writing." << endl;
+ cerr << "Do you have write permissions on the current working directory?" << endl;
+ exit(1);
+ }
+ size_t benchmarks_vector_size = benchmarks.size();
+ fwrite(&max_clock_speed, sizeof(max_clock_speed), 1, file);
+ fwrite(&benchmarks_vector_size, sizeof(benchmarks_vector_size), 1, file);
+ fwrite(&first_benchmark_to_run, sizeof(first_benchmark_to_run), 1, file);
+ fwrite(benchmarks.data(), sizeof(benchmark_t), benchmarks.size(), file);
+ fclose(file);
+}
+
+bool deserialize_benchmarks(const char* filename, vector<benchmark_t>& benchmarks, size_t& first_benchmark_to_run)
+{
+ FILE* file = fopen(filename, "r");
+ if (!file) {
+ return false;
+ }
+ if (1 != fread(&max_clock_speed, sizeof(max_clock_speed), 1, file)) {
+ return false;
+ }
+ size_t benchmarks_vector_size = 0;
+ if (1 != fread(&benchmarks_vector_size, sizeof(benchmarks_vector_size), 1, file)) {
+ return false;
+ }
+ if (1 != fread(&first_benchmark_to_run, sizeof(first_benchmark_to_run), 1, file)) {
+ return false;
+ }
+ benchmarks.resize(benchmarks_vector_size);
+ if (benchmarks.size() != fread(benchmarks.data(), sizeof(benchmark_t), benchmarks.size(), file)) {
+ return false;
+ }
+ unlink(filename);
+ return true;
+}
+
+void try_run_some_benchmarks(
+ vector<benchmark_t>& benchmarks,
+ double time_start,
+ size_t& first_benchmark_to_run)
+{
+ if (first_benchmark_to_run == benchmarks.size()) {
+ return;
+ }
+
+ double time_last_progress_update = 0;
+ double time_last_clock_speed_measurement = 0;
+ double time_now = 0;
+
+ size_t benchmark_index = first_benchmark_to_run;
+
+ while (true) {
+ float ratio_done = float(benchmark_index) / benchmarks.size();
+ time_now = timer.getRealTime();
+
+ // We check clock speed every minute and at the end.
+ if (benchmark_index == benchmarks.size() ||
+ time_now > time_last_clock_speed_measurement + 60.0f)
+ {
+ time_last_clock_speed_measurement = time_now;
+
+ // Ensure that clock speed is as expected
+ float current_clock_speed = measure_clock_speed();
+
+ // The tolerance needs to be smaller than the relative difference between
+ // clock speeds that a device could operate under.
+ // It seems unlikely that a device would be throttling clock speeds by
+ // amounts smaller than 2%.
+ // With a value of 1%, I was getting within noise on a Sandy Bridge.
+ const float clock_speed_tolerance = 0.02f;
+
+ if (current_clock_speed > (1 + clock_speed_tolerance) * max_clock_speed) {
+ // Clock speed is now higher than we previously measured.
+ // Either our initial measurement was inaccurate, which won't happen
+ // too many times as we are keeping the best clock speed value and
+ // and allowing some tolerance; or something really weird happened,
+ // which invalidates all benchmark results collected so far.
+ // Either way, we better restart all over again now.
+ if (benchmark_index) {
+ cerr << "Restarting at " << 100.0f * ratio_done
+ << " % because clock speed increased. " << endl;
+ }
+ max_clock_speed = current_clock_speed;
+ first_benchmark_to_run = 0;
+ return;
+ }
+
+ bool rerun_last_tests = false;
+
+ if (current_clock_speed < (1 - clock_speed_tolerance) * max_clock_speed) {
+ cerr << "Measurements completed so far: "
+ << 100.0f * ratio_done
+ << " % " << endl;
+ cerr << "Clock speed seems to be only "
+ << current_clock_speed/max_clock_speed
+ << " times what it used to be." << endl;
+
+ unsigned int seconds_to_sleep_if_lower_clock_speed = 1;
+
+ while (current_clock_speed < (1 - clock_speed_tolerance) * max_clock_speed) {
+ if (seconds_to_sleep_if_lower_clock_speed > 32) {
+ cerr << "Sleeping longer probably won't make a difference." << endl;
+ cerr << "Serializing benchmarks to " << session_filename << endl;
+ serialize_benchmarks(session_filename, benchmarks, first_benchmark_to_run);
+ cerr << "Now restart this benchmark, and it should pick up where we left." << endl;
+ exit(2);
+ }
+ rerun_last_tests = true;
+ cerr << "Sleeping "
+ << seconds_to_sleep_if_lower_clock_speed
+ << " s... \r" << endl;
+ sleep(seconds_to_sleep_if_lower_clock_speed);
+ current_clock_speed = measure_clock_speed();
+ seconds_to_sleep_if_lower_clock_speed *= 2;
+ }
+ }
+
+ if (rerun_last_tests) {
+ cerr << "Redoing the last "
+ << 100.0f * float(benchmark_index - first_benchmark_to_run) / benchmarks.size()
+ << " % because clock speed had been low. " << endl;
+ return;
+ }
+
+ // nothing wrong with the clock speed so far, so there won't be a need to rerun
+ // benchmarks run so far in case we later encounter a lower clock speed.
+ first_benchmark_to_run = benchmark_index;
+ }
+
+ if (benchmark_index == benchmarks.size()) {
+ // We're done!
+ first_benchmark_to_run = benchmarks.size();
+ // Erase progress info
+ cerr << " " << endl;
+ return;
+ }
+
+ // Display progress info on stderr
+ if (time_now > time_last_progress_update + 1.0f) {
+ time_last_progress_update = time_now;
+ cerr << "Measurements... " << 100.0f * ratio_done
+ << " %, ETA "
+ << human_duration_t(float(time_now - time_start) * (1.0f - ratio_done) / ratio_done)
+ << " \r" << flush;
+ }
+
+ // This is where we actually run a benchmark!
+ benchmarks[benchmark_index].run();
+ benchmark_index++;
+ }
+}
+
+void run_benchmarks(vector<benchmark_t>& benchmarks)
+{
+ size_t first_benchmark_to_run;
+ vector<benchmark_t> deserialized_benchmarks;
+ bool use_deserialized_benchmarks = false;
+ if (deserialize_benchmarks(session_filename, deserialized_benchmarks, first_benchmark_to_run)) {
+ cerr << "Found serialized session with "
+ << 100.0f * first_benchmark_to_run / deserialized_benchmarks.size()
+ << " % already done" << endl;
+ if (deserialized_benchmarks.size() == benchmarks.size() &&
+ first_benchmark_to_run > 0 &&
+ first_benchmark_to_run < benchmarks.size())
+ {
+ use_deserialized_benchmarks = true;
+ }
+ }
+
+ if (use_deserialized_benchmarks) {
+ benchmarks = deserialized_benchmarks;
+ } else {
+ // not using deserialized benchmarks, starting from scratch
+ first_benchmark_to_run = 0;
+
+ // Randomly shuffling benchmarks allows us to get accurate enough progress info,
+ // as now the cheap/expensive benchmarks are randomly mixed so they average out.
+ // It also means that if data is corrupted for some time span, the odds are that
+ // not all repetitions of a given benchmark will be corrupted.
+ random_shuffle(benchmarks.begin(), benchmarks.end());
+ }
+
+ for (int i = 0; i < 4; i++) {
+ max_clock_speed = max(max_clock_speed, measure_clock_speed());
+ }
+
+ double time_start = 0.0;
+ while (first_benchmark_to_run < benchmarks.size()) {
+ if (first_benchmark_to_run == 0) {
+ time_start = timer.getRealTime();
+ }
+ try_run_some_benchmarks(benchmarks,
+ time_start,
+ first_benchmark_to_run);
+ }
+
+ // Sort timings by increasing benchmark parameters, and decreasing gflops.
+ // The latter is very important. It means that we can ignore all but the first
+ // benchmark with given parameters.
+ sort(benchmarks.begin(), benchmarks.end());
+
+ // Collect best (i.e. now first) results for each parameter values.
+ vector<benchmark_t> best_benchmarks;
+ for (auto it = benchmarks.begin(); it != benchmarks.end(); ++it) {
+ if (best_benchmarks.empty() ||
+ best_benchmarks.back().compact_product_size != it->compact_product_size ||
+ best_benchmarks.back().compact_block_size != it->compact_block_size)
+ {
+ best_benchmarks.push_back(*it);
+ }
+ }
+
+ // keep and return only the best benchmarks
+ benchmarks = best_benchmarks;
+}
+
+struct measure_all_pot_sizes_action_t : action_t
+{
+ virtual const char* invokation_name() const { return "all-pot-sizes"; }
+ virtual void run() const
+ {
+ vector<benchmark_t> benchmarks;
+ for (int repetition = 0; repetition < measurement_repetitions; repetition++) {
+ for (size_t ksize = minsize; ksize <= maxsize; ksize *= 2) {
+ for (size_t msize = minsize; msize <= maxsize; msize *= 2) {
+ for (size_t nsize = minsize; nsize <= maxsize; nsize *= 2) {
+ for (size_t kblock = minsize; kblock <= ksize; kblock *= 2) {
+ for (size_t mblock = minsize; mblock <= msize; mblock *= 2) {
+ for (size_t nblock = minsize; nblock <= nsize; nblock *= 2) {
+ benchmarks.emplace_back(ksize, msize, nsize, kblock, mblock, nblock);
+ }
+ }
+ }
+ }
+ }
+ }
+ }
+
+ run_benchmarks(benchmarks);
+
+ cout << "BEGIN MEASUREMENTS ALL POT SIZES" << endl;
+ for (auto it = benchmarks.begin(); it != benchmarks.end(); ++it) {
+ cout << *it << endl;
+ }
+ }
+};
+
+struct measure_default_sizes_action_t : action_t
+{
+ virtual const char* invokation_name() const { return "default-sizes"; }
+ virtual void run() const
+ {
+ vector<benchmark_t> benchmarks;
+ for (int repetition = 0; repetition < measurement_repetitions; repetition++) {
+ for (size_t ksize = minsize; ksize <= maxsize; ksize *= 2) {
+ for (size_t msize = minsize; msize <= maxsize; msize *= 2) {
+ for (size_t nsize = minsize; nsize <= maxsize; nsize *= 2) {
+ benchmarks.emplace_back(ksize, msize, nsize);
+ }
+ }
+ }
+ }
+
+ run_benchmarks(benchmarks);
+
+ cout << "BEGIN MEASUREMENTS DEFAULT SIZES" << endl;
+ for (auto it = benchmarks.begin(); it != benchmarks.end(); ++it) {
+ cout << *it << endl;
+ }
+ }
+};
+
+int main(int argc, char* argv[])
+{
+ double time_start = timer.getRealTime();
+ cout.precision(4);
+ cerr.precision(4);
+
+ vector<unique_ptr<action_t>> available_actions;
+ available_actions.emplace_back(new measure_all_pot_sizes_action_t);
+ available_actions.emplace_back(new measure_default_sizes_action_t);
+
+ auto action = available_actions.end();
+
+ if (argc <= 1) {
+ show_usage_and_exit(argc, argv, available_actions);
+ }
+ for (auto it = available_actions.begin(); it != available_actions.end(); ++it) {
+ if (!strcmp(argv[1], (*it)->invokation_name())) {
+ action = it;
+ break;
+ }
+ }
+
+ if (action == available_actions.end()) {
+ show_usage_and_exit(argc, argv, available_actions);
+ }
+
+ for (int i = 2; i < argc; i++) {
+ if (argv[i] == strstr(argv[i], "--min-working-set-size=")) {
+ const char* equals_sign = strchr(argv[i], '=');
+ min_working_set_size = strtoul(equals_sign+1, nullptr, 10);
+ } else {
+ cerr << "unrecognized option: " << argv[i] << endl << endl;
+ show_usage_and_exit(argc, argv, available_actions);
+ }
+ }
+
+ print_cpuinfo();
+
+ cout << "benchmark parameters:" << endl;
+ cout << "pointer size: " << 8*sizeof(void*) << " bits" << endl;
+ cout << "scalar type: " << type_name<Scalar>() << endl;
+ cout << "packet size: " << internal::packet_traits<MatrixType::Scalar>::size << endl;
+ cout << "minsize = " << minsize << endl;
+ cout << "maxsize = " << maxsize << endl;
+ cout << "measurement_repetitions = " << measurement_repetitions << endl;
+ cout << "min_accurate_time = " << min_accurate_time << endl;
+ cout << "min_working_set_size = " << min_working_set_size;
+ if (min_working_set_size == 0) {
+ cout << " (try to outsize caches)";
+ }
+ cout << endl << endl;
+
+ (*action)->run();
+
+ double time_end = timer.getRealTime();
+ cerr << "Finished in " << human_duration_t(time_end - time_start) << endl;
+}
diff --git a/bench/benchmark.cpp b/bench/benchmark.cpp
new file mode 100644
index 0000000..c721b90
--- /dev/null
+++ b/bench/benchmark.cpp
@@ -0,0 +1,39 @@
+// g++ -O3 -DNDEBUG -DMATSIZE=<x> benchmark.cpp -o benchmark && time ./benchmark
+
+#include <iostream>
+
+#include <Eigen/Core>
+
+#ifndef MATSIZE
+#define MATSIZE 3
+#endif
+
+using namespace std;
+using namespace Eigen;
+
+#ifndef REPEAT
+#define REPEAT 40000000
+#endif
+
+#ifndef SCALAR
+#define SCALAR double
+#endif
+
+int main(int argc, char *argv[])
+{
+ Matrix<SCALAR,MATSIZE,MATSIZE> I = Matrix<SCALAR,MATSIZE,MATSIZE>::Ones();
+ Matrix<SCALAR,MATSIZE,MATSIZE> m;
+ for(int i = 0; i < MATSIZE; i++)
+ for(int j = 0; j < MATSIZE; j++)
+ {
+ m(i,j) = (i+MATSIZE*j);
+ }
+ asm("#begin");
+ for(int a = 0; a < REPEAT; a++)
+ {
+ m = Matrix<SCALAR,MATSIZE,MATSIZE>::Ones() + 0.00005 * (m + (m*m));
+ }
+ asm("#end");
+ cout << m << endl;
+ return 0;
+}
diff --git a/bench/benchmarkSlice.cpp b/bench/benchmarkSlice.cpp
new file mode 100644
index 0000000..c5b89c5
--- /dev/null
+++ b/bench/benchmarkSlice.cpp
@@ -0,0 +1,38 @@
+// g++ -O3 -DNDEBUG benchmarkX.cpp -o benchmarkX && time ./benchmarkX
+
+#include <iostream>
+
+#include <Eigen/Core>
+
+using namespace std;
+using namespace Eigen;
+
+#ifndef REPEAT
+#define REPEAT 10000
+#endif
+
+#ifndef SCALAR
+#define SCALAR float
+#endif
+
+int main(int argc, char *argv[])
+{
+ typedef Matrix<SCALAR, Eigen::Dynamic, Eigen::Dynamic> Mat;
+ Mat m(100, 100);
+ m.setRandom();
+
+ for(int a = 0; a < REPEAT; a++)
+ {
+ int r, c, nr, nc;
+ r = Eigen::internal::random<int>(0,10);
+ c = Eigen::internal::random<int>(0,10);
+ nr = Eigen::internal::random<int>(50,80);
+ nc = Eigen::internal::random<int>(50,80);
+ m.block(r,c,nr,nc) += Mat::Ones(nr,nc);
+ m.block(r,c,nr,nc) *= SCALAR(10);
+ m.block(r,c,nr,nc) -= Mat::constant(nr,nc,10);
+ m.block(r,c,nr,nc) /= SCALAR(10);
+ }
+ cout << m[0] << endl;
+ return 0;
+}
diff --git a/bench/benchmarkX.cpp b/bench/benchmarkX.cpp
new file mode 100644
index 0000000..8e4b60c
--- /dev/null
+++ b/bench/benchmarkX.cpp
@@ -0,0 +1,36 @@
+// g++ -fopenmp -I .. -O3 -DNDEBUG -finline-limit=1000 benchmarkX.cpp -o b && time ./b
+
+#include <iostream>
+
+#include <Eigen/Core>
+
+using namespace std;
+using namespace Eigen;
+
+#ifndef MATTYPE
+#define MATTYPE MatrixXLd
+#endif
+
+#ifndef MATSIZE
+#define MATSIZE 400
+#endif
+
+#ifndef REPEAT
+#define REPEAT 100
+#endif
+
+int main(int argc, char *argv[])
+{
+ MATTYPE I = MATTYPE::Ones(MATSIZE,MATSIZE);
+ MATTYPE m(MATSIZE,MATSIZE);
+ for(int i = 0; i < MATSIZE; i++) for(int j = 0; j < MATSIZE; j++)
+ {
+ m(i,j) = (i+j+1)/(MATSIZE*MATSIZE);
+ }
+ for(int a = 0; a < REPEAT; a++)
+ {
+ m = I + 0.0001 * (m + m*m);
+ }
+ cout << m(0,0) << endl;
+ return 0;
+}
diff --git a/bench/benchmarkXcwise.cpp b/bench/benchmarkXcwise.cpp
new file mode 100644
index 0000000..6243743
--- /dev/null
+++ b/bench/benchmarkXcwise.cpp
@@ -0,0 +1,35 @@
+// g++ -O3 -DNDEBUG benchmarkX.cpp -o benchmarkX && time ./benchmarkX
+
+#include <iostream>
+#include <Eigen/Core>
+
+using namespace std;
+using namespace Eigen;
+
+#ifndef VECTYPE
+#define VECTYPE VectorXLd
+#endif
+
+#ifndef VECSIZE
+#define VECSIZE 1000000
+#endif
+
+#ifndef REPEAT
+#define REPEAT 1000
+#endif
+
+int main(int argc, char *argv[])
+{
+ VECTYPE I = VECTYPE::Ones(VECSIZE);
+ VECTYPE m(VECSIZE,1);
+ for(int i = 0; i < VECSIZE; i++)
+ {
+ m[i] = 0.1 * i/VECSIZE;
+ }
+ for(int a = 0; a < REPEAT; a++)
+ {
+ m = VECTYPE::Ones(VECSIZE) + 0.00005 * (m.cwise().square() + m/4);
+ }
+ cout << m[0] << endl;
+ return 0;
+}
diff --git a/bench/benchmark_suite b/bench/benchmark_suite
new file mode 100755
index 0000000..3f21d36
--- /dev/null
+++ b/bench/benchmark_suite
@@ -0,0 +1,18 @@
+#!/bin/bash
+CXX=${CXX-g++} # default value unless caller has defined CXX
+echo "Fixed size 3x3, column-major, -DNDEBUG"
+$CXX -O3 -I .. -DNDEBUG benchmark.cpp -o benchmark && time ./benchmark >/dev/null
+echo "Fixed size 3x3, column-major, with asserts"
+$CXX -O3 -I .. benchmark.cpp -o benchmark && time ./benchmark >/dev/null
+echo "Fixed size 3x3, row-major, -DNDEBUG"
+$CXX -O3 -I .. -DEIGEN_DEFAULT_TO_ROW_MAJOR -DNDEBUG benchmark.cpp -o benchmark && time ./benchmark >/dev/null
+echo "Fixed size 3x3, row-major, with asserts"
+$CXX -O3 -I .. -DEIGEN_DEFAULT_TO_ROW_MAJOR benchmark.cpp -o benchmark && time ./benchmark >/dev/null
+echo "Dynamic size 20x20, column-major, -DNDEBUG"
+$CXX -O3 -I .. -DNDEBUG benchmarkX.cpp -o benchmarkX && time ./benchmarkX >/dev/null
+echo "Dynamic size 20x20, column-major, with asserts"
+$CXX -O3 -I .. benchmarkX.cpp -o benchmarkX && time ./benchmarkX >/dev/null
+echo "Dynamic size 20x20, row-major, -DNDEBUG"
+$CXX -O3 -I .. -DEIGEN_DEFAULT_TO_ROW_MAJOR -DNDEBUG benchmarkX.cpp -o benchmarkX && time ./benchmarkX >/dev/null
+echo "Dynamic size 20x20, row-major, with asserts"
+$CXX -O3 -I .. -DEIGEN_DEFAULT_TO_ROW_MAJOR benchmarkX.cpp -o benchmarkX && time ./benchmarkX >/dev/null
diff --git a/bench/check_cache_queries.cpp b/bench/check_cache_queries.cpp
new file mode 100644
index 0000000..029d44c
--- /dev/null
+++ b/bench/check_cache_queries.cpp
@@ -0,0 +1,101 @@
+
+#define EIGEN_INTERNAL_DEBUG_CACHE_QUERY
+#include <iostream>
+#include "../Eigen/Core"
+
+using namespace Eigen;
+using namespace std;
+
+#define DUMP_CPUID(CODE) {\
+ int abcd[4]; \
+ abcd[0] = abcd[1] = abcd[2] = abcd[3] = 0;\
+ EIGEN_CPUID(abcd, CODE, 0); \
+ std::cout << "The code " << CODE << " gives " \
+ << (int*)(abcd[0]) << " " << (int*)(abcd[1]) << " " \
+ << (int*)(abcd[2]) << " " << (int*)(abcd[3]) << " " << std::endl; \
+ }
+
+int main()
+{
+ cout << "Eigen's L1 = " << internal::queryL1CacheSize() << endl;
+ cout << "Eigen's L2/L3 = " << internal::queryTopLevelCacheSize() << endl;
+ int l1, l2, l3;
+ internal::queryCacheSizes(l1, l2, l3);
+ cout << "Eigen's L1, L2, L3 = " << l1 << " " << l2 << " " << l3 << endl;
+
+ #ifdef EIGEN_CPUID
+
+ int abcd[4];
+ int string[8];
+ char* string_char = (char*)(string);
+
+ // vendor ID
+ EIGEN_CPUID(abcd,0x0,0);
+ string[0] = abcd[1];
+ string[1] = abcd[3];
+ string[2] = abcd[2];
+ string[3] = 0;
+ cout << endl;
+ cout << "vendor id = " << string_char << endl;
+ cout << endl;
+ int max_funcs = abcd[0];
+
+ internal::queryCacheSizes_intel_codes(l1, l2, l3);
+ cout << "Eigen's intel codes L1, L2, L3 = " << l1 << " " << l2 << " " << l3 << endl;
+ if(max_funcs>=4)
+ {
+ internal::queryCacheSizes_intel_direct(l1, l2, l3);
+ cout << "Eigen's intel direct L1, L2, L3 = " << l1 << " " << l2 << " " << l3 << endl;
+ }
+ internal::queryCacheSizes_amd(l1, l2, l3);
+ cout << "Eigen's amd L1, L2, L3 = " << l1 << " " << l2 << " " << l3 << endl;
+ cout << endl;
+
+ // dump Intel direct method
+ if(max_funcs>=4)
+ {
+ l1 = l2 = l3 = 0;
+ int cache_id = 0;
+ int cache_type = 0;
+ do {
+ abcd[0] = abcd[1] = abcd[2] = abcd[3] = 0;
+ EIGEN_CPUID(abcd,0x4,cache_id);
+ cache_type = (abcd[0] & 0x0F) >> 0;
+ int cache_level = (abcd[0] & 0xE0) >> 5; // A[7:5]
+ int ways = (abcd[1] & 0xFFC00000) >> 22; // B[31:22]
+ int partitions = (abcd[1] & 0x003FF000) >> 12; // B[21:12]
+ int line_size = (abcd[1] & 0x00000FFF) >> 0; // B[11:0]
+ int sets = (abcd[2]); // C[31:0]
+ int cache_size = (ways+1) * (partitions+1) * (line_size+1) * (sets+1);
+
+ cout << "cache[" << cache_id << "].type = " << cache_type << "\n";
+ cout << "cache[" << cache_id << "].level = " << cache_level << "\n";
+ cout << "cache[" << cache_id << "].ways = " << ways << "\n";
+ cout << "cache[" << cache_id << "].partitions = " << partitions << "\n";
+ cout << "cache[" << cache_id << "].line_size = " << line_size << "\n";
+ cout << "cache[" << cache_id << "].sets = " << sets << "\n";
+ cout << "cache[" << cache_id << "].size = " << cache_size << "\n";
+
+ cache_id++;
+ } while(cache_type>0 && cache_id<16);
+ }
+
+ // dump everything
+ std::cout << endl <<"Raw dump:" << endl;
+ for(int i=0; i<max_funcs; ++i)
+ DUMP_CPUID(i);
+
+ DUMP_CPUID(0x80000000);
+ DUMP_CPUID(0x80000001);
+ DUMP_CPUID(0x80000002);
+ DUMP_CPUID(0x80000003);
+ DUMP_CPUID(0x80000004);
+ DUMP_CPUID(0x80000005);
+ DUMP_CPUID(0x80000006);
+ DUMP_CPUID(0x80000007);
+ DUMP_CPUID(0x80000008);
+ #else
+ cout << "EIGEN_CPUID is not defined" << endl;
+ #endif
+ return 0;
+}
diff --git a/bench/dense_solvers.cpp b/bench/dense_solvers.cpp
new file mode 100644
index 0000000..11c755b
--- /dev/null
+++ b/bench/dense_solvers.cpp
@@ -0,0 +1,184 @@
+#include <iostream>
+#include "BenchTimer.h"
+#include <Eigen/Dense>
+#include <map>
+#include <vector>
+#include <string>
+#include <sstream>
+using namespace Eigen;
+
+std::map<std::string,Array<float,1,8,DontAlign|RowMajor> > results;
+std::vector<std::string> labels;
+std::vector<Array2i> sizes;
+
+template<typename Solver,typename MatrixType>
+EIGEN_DONT_INLINE
+void compute_norm_equation(Solver &solver, const MatrixType &A) {
+ if(A.rows()!=A.cols())
+ solver.compute(A.transpose()*A);
+ else
+ solver.compute(A);
+}
+
+template<typename Solver,typename MatrixType>
+EIGEN_DONT_INLINE
+void compute(Solver &solver, const MatrixType &A) {
+ solver.compute(A);
+}
+
+template<typename Scalar,int Size>
+void bench(int id, int rows, int size = Size)
+{
+ typedef Matrix<Scalar,Dynamic,Size> Mat;
+ typedef Matrix<Scalar,Dynamic,Dynamic> MatDyn;
+ typedef Matrix<Scalar,Size,Size> MatSquare;
+ Mat A(rows,size);
+ A.setRandom();
+ if(rows==size)
+ A = A*A.adjoint();
+ BenchTimer t_llt, t_ldlt, t_lu, t_fplu, t_qr, t_cpqr, t_cod, t_fpqr, t_jsvd, t_bdcsvd;
+
+ int tries = 5;
+ int rep = 1000/size;
+ if(rep==0) rep = 1;
+// rep = rep*rep;
+
+ LLT<MatSquare> llt(size);
+ LDLT<MatSquare> ldlt(size);
+ PartialPivLU<MatSquare> lu(size);
+ FullPivLU<MatSquare> fplu(size,size);
+ HouseholderQR<Mat> qr(A.rows(),A.cols());
+ ColPivHouseholderQR<Mat> cpqr(A.rows(),A.cols());
+ CompleteOrthogonalDecomposition<Mat> cod(A.rows(),A.cols());
+ FullPivHouseholderQR<Mat> fpqr(A.rows(),A.cols());
+ JacobiSVD<MatDyn, ComputeThinU|ComputeThinV> jsvd(A.rows(),A.cols());
+ BDCSVD<MatDyn, ComputeThinU|ComputeThinV> bdcsvd(A.rows(),A.cols());
+
+ BENCH(t_llt, tries, rep, compute_norm_equation(llt,A));
+ BENCH(t_ldlt, tries, rep, compute_norm_equation(ldlt,A));
+ BENCH(t_lu, tries, rep, compute_norm_equation(lu,A));
+ if(size<=1000)
+ BENCH(t_fplu, tries, rep, compute_norm_equation(fplu,A));
+ BENCH(t_qr, tries, rep, compute(qr,A));
+ BENCH(t_cpqr, tries, rep, compute(cpqr,A));
+ BENCH(t_cod, tries, rep, compute(cod,A));
+ if(size*rows<=10000000)
+ BENCH(t_fpqr, tries, rep, compute(fpqr,A));
+ if(size<500) // JacobiSVD is really too slow for too large matrices
+ BENCH(t_jsvd, tries, rep, jsvd.compute(A));
+// if(size*rows<=20000000)
+ BENCH(t_bdcsvd, tries, rep, bdcsvd.compute(A));
+
+ results["LLT"][id] = t_llt.best();
+ results["LDLT"][id] = t_ldlt.best();
+ results["PartialPivLU"][id] = t_lu.best();
+ results["FullPivLU"][id] = t_fplu.best();
+ results["HouseholderQR"][id] = t_qr.best();
+ results["ColPivHouseholderQR"][id] = t_cpqr.best();
+ results["CompleteOrthogonalDecomposition"][id] = t_cod.best();
+ results["FullPivHouseholderQR"][id] = t_fpqr.best();
+ results["JacobiSVD"][id] = t_jsvd.best();
+ results["BDCSVD"][id] = t_bdcsvd.best();
+}
+
+
+int main()
+{
+ labels.push_back("LLT");
+ labels.push_back("LDLT");
+ labels.push_back("PartialPivLU");
+ labels.push_back("FullPivLU");
+ labels.push_back("HouseholderQR");
+ labels.push_back("ColPivHouseholderQR");
+ labels.push_back("CompleteOrthogonalDecomposition");
+ labels.push_back("FullPivHouseholderQR");
+ labels.push_back("JacobiSVD");
+ labels.push_back("BDCSVD");
+
+ for(int i=0; i<labels.size(); ++i)
+ results[labels[i]].fill(-1);
+
+ const int small = 8;
+ sizes.push_back(Array2i(small,small));
+ sizes.push_back(Array2i(100,100));
+ sizes.push_back(Array2i(1000,1000));
+ sizes.push_back(Array2i(4000,4000));
+ sizes.push_back(Array2i(10000,small));
+ sizes.push_back(Array2i(10000,100));
+ sizes.push_back(Array2i(10000,1000));
+ sizes.push_back(Array2i(10000,4000));
+
+ using namespace std;
+
+ for(int k=0; k<sizes.size(); ++k)
+ {
+ cout << sizes[k](0) << "x" << sizes[k](1) << "...\n";
+ bench<float,Dynamic>(k,sizes[k](0),sizes[k](1));
+ }
+
+ cout.width(32);
+ cout << "solver/size";
+ cout << " ";
+ for(int k=0; k<sizes.size(); ++k)
+ {
+ std::stringstream ss;
+ ss << sizes[k](0) << "x" << sizes[k](1);
+ cout.width(10); cout << ss.str(); cout << " ";
+ }
+ cout << endl;
+
+
+ for(int i=0; i<labels.size(); ++i)
+ {
+ cout.width(32); cout << labels[i]; cout << " ";
+ ArrayXf r = (results[labels[i]]*100000.f).floor()/100.f;
+ for(int k=0; k<sizes.size(); ++k)
+ {
+ cout.width(10);
+ if(r(k)>=1e6) cout << "-";
+ else cout << r(k);
+ cout << " ";
+ }
+ cout << endl;
+ }
+
+ // HTML output
+ cout << "<table class=\"manual\">" << endl;
+ cout << "<tr><th>solver/size</th>" << endl;
+ for(int k=0; k<sizes.size(); ++k)
+ cout << " <th>" << sizes[k](0) << "x" << sizes[k](1) << "</th>";
+ cout << "</tr>" << endl;
+ for(int i=0; i<labels.size(); ++i)
+ {
+ cout << "<tr";
+ if(i%2==1) cout << " class=\"alt\"";
+ cout << "><td>" << labels[i] << "</td>";
+ ArrayXf r = (results[labels[i]]*100000.f).floor()/100.f;
+ for(int k=0; k<sizes.size(); ++k)
+ {
+ if(r(k)>=1e6) cout << "<td>-</td>";
+ else
+ {
+ cout << "<td>" << r(k);
+ if(i>0)
+ cout << " (x" << numext::round(10.f*results[labels[i]](k)/results["LLT"](k))/10.f << ")";
+ if(i<4 && sizes[k](0)!=sizes[k](1))
+ cout << " <sup><a href=\"#note_ls\">*</a></sup>";
+ cout << "</td>";
+ }
+ }
+ cout << "</tr>" << endl;
+ }
+ cout << "</table>" << endl;
+
+// cout << "LLT (ms) " << (results["LLT"]*1000.).format(fmt) << "\n";
+// cout << "LDLT (%) " << (results["LDLT"]/results["LLT"]).format(fmt) << "\n";
+// cout << "PartialPivLU (%) " << (results["PartialPivLU"]/results["LLT"]).format(fmt) << "\n";
+// cout << "FullPivLU (%) " << (results["FullPivLU"]/results["LLT"]).format(fmt) << "\n";
+// cout << "HouseholderQR (%) " << (results["HouseholderQR"]/results["LLT"]).format(fmt) << "\n";
+// cout << "ColPivHouseholderQR (%) " << (results["ColPivHouseholderQR"]/results["LLT"]).format(fmt) << "\n";
+// cout << "CompleteOrthogonalDecomposition (%) " << (results["CompleteOrthogonalDecomposition"]/results["LLT"]).format(fmt) << "\n";
+// cout << "FullPivHouseholderQR (%) " << (results["FullPivHouseholderQR"]/results["LLT"]).format(fmt) << "\n";
+// cout << "JacobiSVD (%) " << (results["JacobiSVD"]/results["LLT"]).format(fmt) << "\n";
+// cout << "BDCSVD (%) " << (results["BDCSVD"]/results["LLT"]).format(fmt) << "\n";
+}
diff --git a/bench/eig33.cpp b/bench/eig33.cpp
new file mode 100644
index 0000000..f003d8a
--- /dev/null
+++ b/bench/eig33.cpp
@@ -0,0 +1,195 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2010 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+// The computeRoots function included in this is based on materials
+// covered by the following copyright and license:
+//
+// Geometric Tools, LLC
+// Copyright (c) 1998-2010
+// Distributed under the Boost Software License, Version 1.0.
+//
+// Permission is hereby granted, free of charge, to any person or organization
+// obtaining a copy of the software and accompanying documentation covered by
+// this license (the "Software") to use, reproduce, display, distribute,
+// execute, and transmit the Software, and to prepare derivative works of the
+// Software, and to permit third-parties to whom the Software is furnished to
+// do so, all subject to the following:
+//
+// The copyright notices in the Software and this entire statement, including
+// the above license grant, this restriction and the following disclaimer,
+// must be included in all copies of the Software, in whole or in part, and
+// all derivative works of the Software, unless such copies or derivative
+// works are solely in the form of machine-executable object code generated by
+// a source language processor.
+//
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+// FITNESS FOR A PARTICULAR PURPOSE, TITLE AND NON-INFRINGEMENT. IN NO EVENT
+// SHALL THE COPYRIGHT HOLDERS OR ANYONE DISTRIBUTING THE SOFTWARE BE LIABLE
+// FOR ANY DAMAGES OR OTHER LIABILITY, WHETHER IN CONTRACT, TORT OR OTHERWISE,
+// ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
+// DEALINGS IN THE SOFTWARE.
+
+#include <iostream>
+#include <Eigen/Core>
+#include <Eigen/Eigenvalues>
+#include <Eigen/Geometry>
+#include <bench/BenchTimer.h>
+
+using namespace Eigen;
+using namespace std;
+
+template<typename Matrix, typename Roots>
+inline void computeRoots(const Matrix& m, Roots& roots)
+{
+ typedef typename Matrix::Scalar Scalar;
+ const Scalar s_inv3 = 1.0/3.0;
+ const Scalar s_sqrt3 = std::sqrt(Scalar(3.0));
+
+ // The characteristic equation is x^3 - c2*x^2 + c1*x - c0 = 0. The
+ // eigenvalues are the roots to this equation, all guaranteed to be
+ // real-valued, because the matrix is symmetric.
+ Scalar c0 = m(0,0)*m(1,1)*m(2,2) + Scalar(2)*m(0,1)*m(0,2)*m(1,2) - m(0,0)*m(1,2)*m(1,2) - m(1,1)*m(0,2)*m(0,2) - m(2,2)*m(0,1)*m(0,1);
+ Scalar c1 = m(0,0)*m(1,1) - m(0,1)*m(0,1) + m(0,0)*m(2,2) - m(0,2)*m(0,2) + m(1,1)*m(2,2) - m(1,2)*m(1,2);
+ Scalar c2 = m(0,0) + m(1,1) + m(2,2);
+
+ // Construct the parameters used in classifying the roots of the equation
+ // and in solving the equation for the roots in closed form.
+ Scalar c2_over_3 = c2*s_inv3;
+ Scalar a_over_3 = (c1 - c2*c2_over_3)*s_inv3;
+ if (a_over_3 > Scalar(0))
+ a_over_3 = Scalar(0);
+
+ Scalar half_b = Scalar(0.5)*(c0 + c2_over_3*(Scalar(2)*c2_over_3*c2_over_3 - c1));
+
+ Scalar q = half_b*half_b + a_over_3*a_over_3*a_over_3;
+ if (q > Scalar(0))
+ q = Scalar(0);
+
+ // Compute the eigenvalues by solving for the roots of the polynomial.
+ Scalar rho = std::sqrt(-a_over_3);
+ Scalar theta = std::atan2(std::sqrt(-q),half_b)*s_inv3;
+ Scalar cos_theta = std::cos(theta);
+ Scalar sin_theta = std::sin(theta);
+ roots(2) = c2_over_3 + Scalar(2)*rho*cos_theta;
+ roots(0) = c2_over_3 - rho*(cos_theta + s_sqrt3*sin_theta);
+ roots(1) = c2_over_3 - rho*(cos_theta - s_sqrt3*sin_theta);
+}
+
+template<typename Matrix, typename Vector>
+void eigen33(const Matrix& mat, Matrix& evecs, Vector& evals)
+{
+ typedef typename Matrix::Scalar Scalar;
+ // Scale the matrix so its entries are in [-1,1]. The scaling is applied
+ // only when at least one matrix entry has magnitude larger than 1.
+
+ Scalar shift = mat.trace()/3;
+ Matrix scaledMat = mat;
+ scaledMat.diagonal().array() -= shift;
+ Scalar scale = scaledMat.cwiseAbs()/*.template triangularView<Lower>()*/.maxCoeff();
+ scale = std::max(scale,Scalar(1));
+ scaledMat/=scale;
+
+ // Compute the eigenvalues
+// scaledMat.setZero();
+ computeRoots(scaledMat,evals);
+
+ // compute the eigen vectors
+ // **here we assume 3 different eigenvalues**
+
+ // "optimized version" which appears to be slower with gcc!
+// Vector base;
+// Scalar alpha, beta;
+// base << scaledMat(1,0) * scaledMat(2,1),
+// scaledMat(1,0) * scaledMat(2,0),
+// -scaledMat(1,0) * scaledMat(1,0);
+// for(int k=0; k<2; ++k)
+// {
+// alpha = scaledMat(0,0) - evals(k);
+// beta = scaledMat(1,1) - evals(k);
+// evecs.col(k) = (base + Vector(-beta*scaledMat(2,0), -alpha*scaledMat(2,1), alpha*beta)).normalized();
+// }
+// evecs.col(2) = evecs.col(0).cross(evecs.col(1)).normalized();
+
+// // naive version
+// Matrix tmp;
+// tmp = scaledMat;
+// tmp.diagonal().array() -= evals(0);
+// evecs.col(0) = tmp.row(0).cross(tmp.row(1)).normalized();
+//
+// tmp = scaledMat;
+// tmp.diagonal().array() -= evals(1);
+// evecs.col(1) = tmp.row(0).cross(tmp.row(1)).normalized();
+//
+// tmp = scaledMat;
+// tmp.diagonal().array() -= evals(2);
+// evecs.col(2) = tmp.row(0).cross(tmp.row(1)).normalized();
+
+ // a more stable version:
+ if((evals(2)-evals(0))<=Eigen::NumTraits<Scalar>::epsilon())
+ {
+ evecs.setIdentity();
+ }
+ else
+ {
+ Matrix tmp;
+ tmp = scaledMat;
+ tmp.diagonal ().array () -= evals (2);
+ evecs.col (2) = tmp.row (0).cross (tmp.row (1)).normalized ();
+
+ tmp = scaledMat;
+ tmp.diagonal ().array () -= evals (1);
+ evecs.col(1) = tmp.row (0).cross(tmp.row (1));
+ Scalar n1 = evecs.col(1).norm();
+ if(n1<=Eigen::NumTraits<Scalar>::epsilon())
+ evecs.col(1) = evecs.col(2).unitOrthogonal();
+ else
+ evecs.col(1) /= n1;
+
+ // make sure that evecs[1] is orthogonal to evecs[2]
+ evecs.col(1) = evecs.col(2).cross(evecs.col(1).cross(evecs.col(2))).normalized();
+ evecs.col(0) = evecs.col(2).cross(evecs.col(1));
+ }
+
+ // Rescale back to the original size.
+ evals *= scale;
+ evals.array()+=shift;
+}
+
+int main()
+{
+ BenchTimer t;
+ int tries = 10;
+ int rep = 400000;
+ typedef Matrix3d Mat;
+ typedef Vector3d Vec;
+ Mat A = Mat::Random(3,3);
+ A = A.adjoint() * A;
+// Mat Q = A.householderQr().householderQ();
+// A = Q * Vec(2.2424567,2.2424566,7.454353).asDiagonal() * Q.transpose();
+
+ SelfAdjointEigenSolver<Mat> eig(A);
+ BENCH(t, tries, rep, eig.compute(A));
+ std::cout << "Eigen iterative: " << t.best() << "s\n";
+
+ BENCH(t, tries, rep, eig.computeDirect(A));
+ std::cout << "Eigen direct : " << t.best() << "s\n";
+
+ Mat evecs;
+ Vec evals;
+ BENCH(t, tries, rep, eigen33(A,evecs,evals));
+ std::cout << "Direct: " << t.best() << "s\n\n";
+
+// std::cerr << "Eigenvalue/eigenvector diffs:\n";
+// std::cerr << (evals - eig.eigenvalues()).transpose() << "\n";
+// for(int k=0;k<3;++k)
+// if(evecs.col(k).dot(eig.eigenvectors().col(k))<0)
+// evecs.col(k) = -evecs.col(k);
+// std::cerr << evecs - eig.eigenvectors() << "\n\n";
+}
diff --git a/bench/geometry.cpp b/bench/geometry.cpp
new file mode 100644
index 0000000..b187a51
--- /dev/null
+++ b/bench/geometry.cpp
@@ -0,0 +1,126 @@
+
+#include <iostream>
+#include <Eigen/Geometry>
+#include <bench/BenchTimer.h>
+
+using namespace std;
+using namespace Eigen;
+
+#ifndef SCALAR
+#define SCALAR float
+#endif
+
+#ifndef SIZE
+#define SIZE 8
+#endif
+
+typedef SCALAR Scalar;
+typedef NumTraits<Scalar>::Real RealScalar;
+typedef Matrix<RealScalar,Dynamic,Dynamic> A;
+typedef Matrix</*Real*/Scalar,Dynamic,Dynamic> B;
+typedef Matrix<Scalar,Dynamic,Dynamic> C;
+typedef Matrix<RealScalar,Dynamic,Dynamic> M;
+
+template<typename Transformation, typename Data>
+EIGEN_DONT_INLINE void transform(const Transformation& t, Data& data)
+{
+ EIGEN_ASM_COMMENT("begin");
+ data = t * data;
+ EIGEN_ASM_COMMENT("end");
+}
+
+template<typename Scalar, typename Data>
+EIGEN_DONT_INLINE void transform(const Quaternion<Scalar>& t, Data& data)
+{
+ EIGEN_ASM_COMMENT("begin quat");
+ for(int i=0;i<data.cols();++i)
+ data.col(i) = t * data.col(i);
+ EIGEN_ASM_COMMENT("end quat");
+}
+
+template<typename T> struct ToRotationMatrixWrapper
+{
+ enum {Dim = T::Dim};
+ typedef typename T::Scalar Scalar;
+ ToRotationMatrixWrapper(const T& o) : object(o) {}
+ T object;
+};
+
+template<typename QType, typename Data>
+EIGEN_DONT_INLINE void transform(const ToRotationMatrixWrapper<QType>& t, Data& data)
+{
+ EIGEN_ASM_COMMENT("begin quat via mat");
+ data = t.object.toRotationMatrix() * data;
+ EIGEN_ASM_COMMENT("end quat via mat");
+}
+
+template<typename Scalar, int Dim, typename Data>
+EIGEN_DONT_INLINE void transform(const Transform<Scalar,Dim,Projective>& t, Data& data)
+{
+ data = (t * data.colwise().homogeneous()).template block<Dim,Data::ColsAtCompileTime>(0,0);
+}
+
+template<typename T> struct get_dim { enum { Dim = T::Dim }; };
+template<typename S, int R, int C, int O, int MR, int MC>
+struct get_dim<Matrix<S,R,C,O,MR,MC> > { enum { Dim = R }; };
+
+template<typename Transformation, int N>
+struct bench_impl
+{
+ static EIGEN_DONT_INLINE void run(const Transformation& t)
+ {
+ Matrix<typename Transformation::Scalar,get_dim<Transformation>::Dim,N> data;
+ data.setRandom();
+ bench_impl<Transformation,N-1>::run(t);
+ BenchTimer timer;
+ BENCH(timer,10,100000,transform(t,data));
+ cout.width(9);
+ cout << timer.best() << " ";
+ }
+};
+
+
+template<typename Transformation>
+struct bench_impl<Transformation,0>
+{
+ static EIGEN_DONT_INLINE void run(const Transformation&) {}
+};
+
+template<typename Transformation>
+EIGEN_DONT_INLINE void bench(const std::string& msg, const Transformation& t)
+{
+ cout << msg << " ";
+ bench_impl<Transformation,SIZE>::run(t);
+ std::cout << "\n";
+}
+
+int main(int argc, char ** argv)
+{
+ Matrix<Scalar,3,4> mat34; mat34.setRandom();
+ Transform<Scalar,3,Isometry> iso3(mat34);
+ Transform<Scalar,3,Affine> aff3(mat34);
+ Transform<Scalar,3,AffineCompact> caff3(mat34);
+ Transform<Scalar,3,Projective> proj3(mat34);
+ Quaternion<Scalar> quat;quat.setIdentity();
+ ToRotationMatrixWrapper<Quaternion<Scalar> > quatmat(quat);
+ Matrix<Scalar,3,3> mat33; mat33.setRandom();
+
+ cout.precision(4);
+ std::cout
+ << "N ";
+ for(int i=0;i<SIZE;++i)
+ {
+ cout.width(9);
+ cout << i+1 << " ";
+ }
+ cout << "\n";
+
+ bench("matrix 3x3", mat33);
+ bench("quaternion", quat);
+ bench("quat-mat ", quatmat);
+ bench("isometry3 ", iso3);
+ bench("affine3 ", aff3);
+ bench("c affine3 ", caff3);
+ bench("proj3 ", proj3);
+}
+
diff --git a/bench/perf_monitoring/changesets.txt b/bench/perf_monitoring/changesets.txt
new file mode 100644
index 0000000..efdd9a0
--- /dev/null
+++ b/bench/perf_monitoring/changesets.txt
@@ -0,0 +1,95 @@
+Load hg-to-git hash maps from ./eigen_git/.git/
+#3.0.1
+#3.1.1
+#3.2.0
+3.2.4
+#574a7621809fe
+58964a85800bd # introduce AVX
+#589cbd7e98174 # merge
+589db7d49efbb # introduce FMA
+#590a078f442a3 # complex and AVX
+590a419cea4a0 # improve packing with ptranspose
+#59251e85c936d # merge
+#592e497a27ddc
+593d5a795f673 # New gebp kernel: up to 3 packets x 4 register-level blocks
+#5942c3c95990d # merge
+#596c9788d55b9 # Disable 3pX4 kernel on Altivec
+#5999aa3dc4e21 # merge
+6209452eb38f8 # before-evaluators
+#6333eba5e1101 # Implement evaluator for sparse outer products
+#663b9d314ae19
+#6655ef95fabee # Properly detect FMA support on ARM
+#667fe25f3b8e3 # FMA has been wrongly disabled
+#668409547a0c8
+#6694304c73542 # merge default to tensors
+#67216047c8d4a # merge default to tensors
+#67410a79ca3a3 # merge default to tensors
+#674b7271dffb5 # Generalized the gebp apis
+676bfdd9f3ac9 # Made the blocking computation aware of the l3 cache;<br/> Also optimized the blocking parameters to take<br/> into account the number of threads used for a computation.
+6782dde63499c # generalized gemv
+6799f98650d0a # ensured that contractions that can be reduced to a matrix vector product
+#6840918c51e60 # merge tensor
+684e972b55ec4 # change prefetching in gebp
+#68598604576d1 # merge index conversion
+68963eb0f6fe6 # clean blocking size computation
+689db05f2d01e # rotating kernel for ARM only
+#6901b7e12847d # result_of
+69226275b250a # fix prefetching change for ARM
+692692136350b # prefetching
+693a8ad8887bf # blocking size strategy
+693bcf9bb5c1f # avoid redundant pack_rhs
+6987550107028 # dynamic loop swapping
+69858740ce4c6 # rm dynamic loop swapping,<br/> adjust lhs's micro panel height to fully exploit L1 cache
+698cd3bbffa73 # blocking heuristic:<br/> block on the rhs in L1 if the lhs fit in L1.
+701488c15615a # organize a little our default cache sizes,<br/> and use a saner default L1 outside of x86 (10% faster on Nexus 5)
+701e56aabf205 # Refactor computeProductBlockingSizes to make room<br/> for the possibility of using lookup tables
+701ca5c12587b # Polish lookup tables generation
+7013589a9c115 # actual_panel_rows computation should always be resilient<br/> to parameters not consistent with the known L1 cache size, see comment
+70102babb9c0f # Provide a empirical lookup table for blocking sizes measured on a Nexus 5.<br/> Only for float, only for Android on ARM 32bit for now.
+7088481dc21ea # Bug 986: add support for coefficient-based<br/> product with 0 depth.
+709d7f51feb07 # Bug 992: don't select a 3p GEMM path with non-SIMD scalar types.
+759f9303cc7c5 # 3.3-alpha1
+765aba1eda71e # help clang inlining
+770fe630c9873 # Improve numerical accuracy in LLT and triangular solve<br/> by using true scalar divisions (instead of x * (1/y))
+#8741d23430628 # Improved the matrix multiplication blocking in the case<br/> where mr is not a power of 2 (e.g on Haswell CPUs)
+878f629fe95c8 # Made the index type a template parameter to evaluateProductBlockingSizes.<br/> Use numext::mini and numext::maxi instead of <br/> std::min/std::max to compute blocking sizes.
+8975d51a7f12c # Don't optimize the processing of the last rows of<br/> a matrix matrix product in cases that violate<br/> the assumptions made by the optimized code path.
+8986136f4fdd4 # Remove the rotating kernel.
+898e68e165a23 # Bug 256: enable vectorization with unaligned loads/stores.
+91466e99ab6a1 # Relax mixing-type constraints for binary coeff-wise operators
+91776236cdea4 # merge
+917101ea26f5e # Include the cost of stores in unrolling
+921672076db5d # Fix perf regression introduced in changeset e56aabf205
+9210fa9e4a15c # Fix perf regression in dgemm introduced by changeset 5d51a7f12c
+936f6b3cf8de9 # 3.3-beta2
+944504a4404f1 # Optimize expression matching 'd?=a-b*c' as 'd?=a; d?=b*c;'
+95877e27fbeee # 3.3-rc1
+959779774f98c # Bug 1311: fix alignment logic in some cases<br/> of (scalar*small).lazyProduct(small)
+9729f9d8d2f62 # Disabled part of the matrix matrix peeling code<br/> that's incompatible with 512 bit registers
+979eeac81b8c0 # 3.3.0
+989c927af60ed # Fix a performance regression in (mat*mat)*vec<br/> for which mat*mat was evaluated multiple times.
+994fe696022ec # Operators += and -= do not resize!
+99466f65ccc36 # Ease compiler generating clean and efficient code in mat*vec
+9946a5fe86098 # Complete rewrite of column-major-matrix * vector product<br/> to deliver higher performance of modern CPU.
+99591003f3b86 # Improve performance of row-major-dense-matrix * vector products<br/> for recent CPUs.
+997eb621413c1 # Revert vec/y to vec*(1/y) in row-major TRSM
+10444bbc320468 # Bug 1435: fix aliasing issue in exressions like: A = C - B*A;
+1073624df50945 # Adds missing EIGEN_STRONG_INLINE to support MSVC<br/> properly inlining small vector calculations
+1094d428a199ab # Bug 1562: optimize evaluation of small products<br/> of the form s*A*B by rewriting them as: s*(A.lazyProduct(B))<br/> to save a costly temporary.<br/> Measured speedup from 2x to 5x.
+1096de9e31a06d # Introduce the macro ei_declare_local_nested_eval to<br/> help allocating on the stack local temporaries via alloca,<br/> and let outer-products makes a good use of it.
+11087b91c11207 # Bug 1578: Improve prefetching in matrix multiplication on MIPS.
+1153aa110e681b # PR 526: Speed up multiplication of small, dynamically sized matrices
+11544ad359237a # Vectorize row-by-row gebp loop iterations on 16 packets as well
+1157a476054879 # Bug 1624: improve matrix-matrix product on ARM 64, 20% speedup
+1160a4159dba08 # do not read buffers out of bounds
+1163c53eececb0 # Implement AVX512 vectorization of std::complex<float/double>
+11644e7746fe22 # Bug 1636: fix gemm performance issue with gcc>=6 and no FMA
+1164956678a4ef # Bug 1515: disable gebp's 3pX4 micro kernel<br/> for MSVC<=19.14 because of register spilling.
+1165426bce7529 # fix EIGEN_GEBP_2PX4_SPILLING_WORKAROUND<br/> for non vectorized type, and non x86/64 target
+11660d90637838 # enable spilling workaround on architectures with SSE/AVX
+1166f159cf3d75 # Artificially increase l1-blocking size for AVX512.<br/> +10% speedup with current kernels.
+11686dd93f7e3b # Make code compile again for older compilers.
+1175dbfcceabf5 # Bug: 1633: refactor gebp kernel and optimize for neon
+117670e133333d # Bug 1661: fix regression in GEBP and AVX512
+11760f028f61cb # GEBP: cleanup logic to choose between<br/> a 4 packets of 1 packet (=e118ce86fd+fix)
+1180de77bf5d6c # gebp: Add new ½ and ¼ packet rows per (peeling) round on the lhs
diff --git a/bench/perf_monitoring/gemm.cpp b/bench/perf_monitoring/gemm.cpp
new file mode 100644
index 0000000..804139d
--- /dev/null
+++ b/bench/perf_monitoring/gemm.cpp
@@ -0,0 +1,12 @@
+#include "gemm_common.h"
+
+EIGEN_DONT_INLINE
+void gemm(const Mat &A, const Mat &B, Mat &C)
+{
+ C.noalias() += A * B;
+}
+
+int main(int argc, char **argv)
+{
+ return main_gemm(argc, argv, gemm);
+}
diff --git a/bench/perf_monitoring/gemm_common.h b/bench/perf_monitoring/gemm_common.h
new file mode 100644
index 0000000..30dbc0d
--- /dev/null
+++ b/bench/perf_monitoring/gemm_common.h
@@ -0,0 +1,67 @@
+#include <iostream>
+#include <fstream>
+#include <vector>
+#include <string>
+#include "eigen_src/Eigen/Core"
+#include "../BenchTimer.h"
+using namespace Eigen;
+
+#ifndef SCALAR
+#error SCALAR must be defined
+#endif
+
+typedef SCALAR Scalar;
+
+typedef Matrix<Scalar,Dynamic,Dynamic> Mat;
+
+template<typename Func>
+EIGEN_DONT_INLINE
+double bench(long m, long n, long k, const Func& f)
+{
+ Mat A(m,k);
+ Mat B(k,n);
+ Mat C(m,n);
+ A.setRandom();
+ B.setRandom();
+ C.setZero();
+
+ BenchTimer t;
+
+ double up = 1e8*4/sizeof(Scalar);
+ double tm0 = 4, tm1 = 10;
+ if(NumTraits<Scalar>::IsComplex)
+ {
+ up /= 4;
+ tm0 = 2;
+ tm1 = 4;
+ }
+
+ double flops = 2. * m * n * k;
+ long rep = std::max(1., std::min(100., up/flops) );
+ long tries = std::max(tm0, std::min(tm1, up/flops) );
+
+ BENCH(t, tries, rep, f(A,B,C));
+
+ return 1e-9 * rep * flops / t.best();
+}
+
+template<typename Func>
+int main_gemm(int argc, char **argv, const Func& f)
+{
+ std::vector<double> results;
+
+ std::string filename = std::string("gemm_settings.txt");
+ if(argc>1)
+ filename = std::string(argv[1]);
+ std::ifstream settings(filename);
+ long m, n, k;
+ while(settings >> m >> n >> k)
+ {
+ //std::cerr << " Testing " << m << " " << n << " " << k << std::endl;
+ results.push_back( bench(m, n, k, f) );
+ }
+
+ std::cout << RowVectorXd::Map(results.data(), results.size());
+
+ return 0;
+}
diff --git a/bench/perf_monitoring/gemm_settings.txt b/bench/perf_monitoring/gemm_settings.txt
new file mode 100644
index 0000000..5c43e1c
--- /dev/null
+++ b/bench/perf_monitoring/gemm_settings.txt
@@ -0,0 +1,15 @@
+8 8 8
+9 9 9
+24 24 24
+239 239 239
+240 240 240
+2400 24 24
+24 2400 24
+24 24 2400
+24 2400 2400
+2400 24 2400
+2400 2400 24
+2400 2400 64
+4800 23 160
+23 4800 160
+2400 2400 2400
diff --git a/bench/perf_monitoring/gemm_square_settings.txt b/bench/perf_monitoring/gemm_square_settings.txt
new file mode 100644
index 0000000..98474d1
--- /dev/null
+++ b/bench/perf_monitoring/gemm_square_settings.txt
@@ -0,0 +1,11 @@
+8 8 8
+9 9 9
+12 12 12
+15 15 15
+16 16 16
+24 24 24
+102 102 102
+239 239 239
+240 240 240
+2400 2400 2400
+2463 2463 2463
diff --git a/bench/perf_monitoring/gemv.cpp b/bench/perf_monitoring/gemv.cpp
new file mode 100644
index 0000000..82e5ab9
--- /dev/null
+++ b/bench/perf_monitoring/gemv.cpp
@@ -0,0 +1,12 @@
+#include "gemv_common.h"
+
+EIGEN_DONT_INLINE
+void gemv(const Mat &A, const Vec &B, Vec &C)
+{
+ C.noalias() += A * B;
+}
+
+int main(int argc, char **argv)
+{
+ return main_gemv(argc, argv, gemv);
+}
diff --git a/bench/perf_monitoring/gemv_common.h b/bench/perf_monitoring/gemv_common.h
new file mode 100644
index 0000000..cc32577
--- /dev/null
+++ b/bench/perf_monitoring/gemv_common.h
@@ -0,0 +1,69 @@
+#include <iostream>
+#include <fstream>
+#include <vector>
+#include <string>
+#include <functional>
+#include "eigen_src/Eigen/Core"
+#include "../BenchTimer.h"
+using namespace Eigen;
+
+#ifndef SCALAR
+#error SCALAR must be defined
+#endif
+
+typedef SCALAR Scalar;
+
+typedef Matrix<Scalar,Dynamic,Dynamic> Mat;
+typedef Matrix<Scalar,Dynamic,1> Vec;
+
+template<typename Func>
+EIGEN_DONT_INLINE
+double bench(long m, long n, Func &f)
+{
+ Mat A(m,n);
+ Vec B(n);
+ Vec C(m);
+ A.setRandom();
+ B.setRandom();
+ C.setRandom();
+
+ BenchTimer t;
+
+ double up = 1e8/sizeof(Scalar);
+ double tm0 = 4, tm1 = 10;
+ if(NumTraits<Scalar>::IsComplex)
+ {
+ up /= 4;
+ tm0 = 2;
+ tm1 = 4;
+ }
+
+ double flops = 2. * m * n;
+ long rep = std::max(1., std::min(100., up/flops) );
+ long tries = std::max(tm0, std::min(tm1, up/flops) );
+
+ BENCH(t, tries, rep, f(A,B,C));
+
+ return 1e-9 * rep * flops / t.best();
+}
+
+template<typename Func>
+int main_gemv(int argc, char **argv, Func& f)
+{
+ std::vector<double> results;
+
+ std::string filename = std::string("gemv_settings.txt");
+ if(argc>1)
+ filename = std::string(argv[1]);
+ std::ifstream settings(filename);
+ long m, n;
+ while(settings >> m >> n)
+ {
+ //std::cerr << " Testing " << m << " " << n << std::endl;
+ results.push_back( bench(m, n, f) );
+ }
+
+ std::cout << RowVectorXd::Map(results.data(), results.size());
+
+ return 0;
+}
diff --git a/bench/perf_monitoring/gemv_settings.txt b/bench/perf_monitoring/gemv_settings.txt
new file mode 100644
index 0000000..21a5ee0
--- /dev/null
+++ b/bench/perf_monitoring/gemv_settings.txt
@@ -0,0 +1,11 @@
+8 8
+9 9
+24 24
+239 239
+240 240
+2400 24
+24 2400
+24 240
+2400 2400
+4800 23
+23 4800
diff --git a/bench/perf_monitoring/gemv_square_settings.txt b/bench/perf_monitoring/gemv_square_settings.txt
new file mode 100644
index 0000000..5165759
--- /dev/null
+++ b/bench/perf_monitoring/gemv_square_settings.txt
@@ -0,0 +1,13 @@
+8 8
+9 9
+12 12
+15 15
+16 16
+24 24
+53 53
+74 74
+102 102
+239 239
+240 240
+2400 2400
+2463 2463
diff --git a/bench/perf_monitoring/gemvt.cpp b/bench/perf_monitoring/gemvt.cpp
new file mode 100644
index 0000000..fe94576
--- /dev/null
+++ b/bench/perf_monitoring/gemvt.cpp
@@ -0,0 +1,12 @@
+#include "gemv_common.h"
+
+EIGEN_DONT_INLINE
+void gemv(const Mat &A, Vec &B, const Vec &C)
+{
+ B.noalias() += A.transpose() * C;
+}
+
+int main(int argc, char **argv)
+{
+ return main_gemv(argc, argv, gemv);
+}
diff --git a/bench/perf_monitoring/lazy_gemm.cpp b/bench/perf_monitoring/lazy_gemm.cpp
new file mode 100644
index 0000000..7733060
--- /dev/null
+++ b/bench/perf_monitoring/lazy_gemm.cpp
@@ -0,0 +1,101 @@
+#include <iostream>
+#include <fstream>
+#include <vector>
+#include <Eigen/Core>
+#include "../../BenchTimer.h"
+using namespace Eigen;
+
+#ifndef SCALAR
+#error SCALAR must be defined
+#endif
+
+typedef SCALAR Scalar;
+
+template<typename MatA, typename MatB, typename MatC>
+EIGEN_DONT_INLINE
+void lazy_gemm(const MatA &A, const MatB &B, MatC &C)
+{
+// escape((void*)A.data());
+// escape((void*)B.data());
+ C.noalias() += A.lazyProduct(B);
+// escape((void*)C.data());
+}
+
+template<int m, int n, int k, int TA>
+EIGEN_DONT_INLINE
+double bench()
+{
+ typedef Matrix<Scalar,m,k,TA> MatA;
+ typedef Matrix<Scalar,k,n> MatB;
+ typedef Matrix<Scalar,m,n> MatC;
+
+ MatA A(m,k);
+ MatB B(k,n);
+ MatC C(m,n);
+ A.setRandom();
+ B.setRandom();
+ C.setZero();
+
+ BenchTimer t;
+
+ double up = 1e7*4/sizeof(Scalar);
+ double tm0 = 10, tm1 = 20;
+
+ double flops = 2. * m * n * k;
+ long rep = std::max(10., std::min(10000., up/flops) );
+ long tries = std::max(tm0, std::min(tm1, up/flops) );
+
+ BENCH(t, tries, rep, lazy_gemm(A,B,C));
+
+ return 1e-9 * rep * flops / t.best();
+}
+
+template<int m, int n, int k>
+double bench_t(int t)
+{
+ if(t)
+ return bench<m,n,k,RowMajor>();
+ else
+ return bench<m,n,k,0>();
+}
+
+EIGEN_DONT_INLINE
+double bench_mnk(int m, int n, int k, int t)
+{
+ int id = m*10000 + n*100 + k;
+ switch(id) {
+ case 10101 : return bench_t< 1, 1, 1>(t); break;
+ case 20202 : return bench_t< 2, 2, 2>(t); break;
+ case 30303 : return bench_t< 3, 3, 3>(t); break;
+ case 40404 : return bench_t< 4, 4, 4>(t); break;
+ case 50505 : return bench_t< 5, 5, 5>(t); break;
+ case 60606 : return bench_t< 6, 6, 6>(t); break;
+ case 70707 : return bench_t< 7, 7, 7>(t); break;
+ case 80808 : return bench_t< 8, 8, 8>(t); break;
+ case 90909 : return bench_t< 9, 9, 9>(t); break;
+ case 101010 : return bench_t<10,10,10>(t); break;
+ case 111111 : return bench_t<11,11,11>(t); break;
+ case 121212 : return bench_t<12,12,12>(t); break;
+ }
+ return 0;
+}
+
+int main(int argc, char **argv)
+{
+ std::vector<double> results;
+
+ std::string filename = std::string("lazy_gemm_settings.txt");
+ if(argc>1)
+ filename = std::string(argv[1]);
+ std::ifstream settings(filename);
+ long m, n, k, t;
+ while(settings >> m >> n >> k >> t)
+ {
+ //std::cerr << " Testing " << m << " " << n << " " << k << std::endl;
+ results.push_back( bench_mnk(m, n, k, t) );
+ }
+
+ std::cout << RowVectorXd::Map(results.data(), results.size());
+
+ return 0;
+}
diff --git a/bench/perf_monitoring/lazy_gemm_settings.txt b/bench/perf_monitoring/lazy_gemm_settings.txt
new file mode 100644
index 0000000..407d5d4
--- /dev/null
+++ b/bench/perf_monitoring/lazy_gemm_settings.txt
@@ -0,0 +1,15 @@
+1 1 1 0
+2 2 2 0
+3 3 3 0
+4 4 4 0
+4 4 4 1
+5 5 5 0
+6 6 6 0
+7 7 7 0
+7 7 7 1
+8 8 8 0
+9 9 9 0
+10 10 10 0
+11 11 11 0
+12 12 12 0
+12 12 12 1
diff --git a/bench/perf_monitoring/llt.cpp b/bench/perf_monitoring/llt.cpp
new file mode 100644
index 0000000..d55b7d8
--- /dev/null
+++ b/bench/perf_monitoring/llt.cpp
@@ -0,0 +1,15 @@
+#include "gemm_common.h"
+#include <Eigen/Cholesky>
+
+EIGEN_DONT_INLINE
+void llt(const Mat &A, const Mat &B, Mat &C)
+{
+ C = A;
+ C.diagonal().array() += 1000;
+ Eigen::internal::llt_inplace<Mat::Scalar, Lower>::blocked(C);
+}
+
+int main(int argc, char **argv)
+{
+ return main_gemm(argc, argv, llt);
+}
diff --git a/bench/perf_monitoring/resources/chart_footer.html b/bench/perf_monitoring/resources/chart_footer.html
new file mode 100644
index 0000000..a96cdb8
--- /dev/null
+++ b/bench/perf_monitoring/resources/chart_footer.html
@@ -0,0 +1,41 @@
+ /* setup the chart and its options */
+ var chart = nv.models.lineChart()
+ .color(d3.scale.category10().range())
+ .margin({left: 75, bottom: 100})
+ .forceX([0]).forceY([0]);
+
+ chart.x(function(datum){ return datum.r; })
+ .xAxis.options({
+ axisLabel: customSettings.XLABEL || 'Changeset',
+ tickFormat: d3.format('.0f')
+ });
+ chart.xAxis
+ .tickValues(changesets_count)
+ .tickFormat(function(d){return changesets[d]})
+ .rotateLabels(-90);
+
+ chart.y(function(datum){ return datum.v; })
+ .yAxis.options({
+ axisLabel: customSettings.YLABEL || 'GFlops'/*,
+ tickFormat: function(val){ return d3.format('.0f')(val) + ' GFlops'; }*/
+ });
+
+ chart.tooltip.headerFormatter(function(d) { return changesets[d]
+ + ' <p style="font-weight:normal;text-align: left;">'
+ + changesets_details[d] + "</p>"; });
+
+ //chart.useInteractiveGuideline(true);
+ d3.select('#chart').datum(data).call(chart);
+ var plot = d3.select('#chart > g');
+
+ /* setup the title */
+ plot.append('text')
+ .style('font-size', '24px')
+ .attr('text-anchor', 'middle').attr('x', '50%').attr('y', '20px')
+ .text(customSettings.TITLE || '');
+
+ /* ensure the chart is responsive */
+ nv.utils.windowResize(chart.update);
+ </script>
+ </body>
+</html>
diff --git a/bench/perf_monitoring/resources/chart_header.html b/bench/perf_monitoring/resources/chart_header.html
new file mode 100644
index 0000000..27eb02e
--- /dev/null
+++ b/bench/perf_monitoring/resources/chart_header.html
@@ -0,0 +1,45 @@
+
+<!DOCTYPE html>
+<html>
+ <head>
+ <meta charset='utf-8'>
+ <style>.nvd3 .nv-axis line,.nvd3 .nv-axis path{fill:none;shape-rendering:crispEdges}.nv-brush .extent,.nvd3 .background path,.nvd3 .nv-axis line,.nvd3 .nv-axis path{shape-rendering:crispEdges}.nv-distx,.nv-disty,.nv-noninteractive,.nvd3 .nv-axis,.nvd3.nv-pie .nv-label,.nvd3.nv-sparklineplus g.nv-hoverValue{pointer-events:none}.nvtooltip,svg.nvd3-svg{display:block;-webkit-touch-callout:none;-khtml-user-select:none}.nvd3 .nv-axis{opacity:1}.nvd3 .nv-axis.nv-disabled,.nvd3 .nv-controlsWrap .nv-legend .nv-check-box .nv-check{opacity:0}.nvd3 .nv-axis path{stroke:#000;stroke-opacity:.75}.nvd3 .nv-axis path.domain{stroke-opacity:.75}.nvd3 .nv-axis.nv-x path.domain{stroke-opacity:0}.nvd3 .nv-axis line{stroke:#e5e5e5}.nvd3 .nv-axis .zero line, .nvd3 .nv-axis line.zero{stroke-opacity:.75}.nvd3 .nv-axis .nv-axisMaxMin text{font-weight:700}.nvd3 .x .nv-axis .nv-axisMaxMin text,.nvd3 .x2 .nv-axis .nv-axisMaxMin text,.nvd3 .x3 .nv-axis .nv-axisMaxMin text{text-anchor:middle}.nvd3 .nv-bars 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+ <style>
+ * {
+ box-sizing: border-box;
+ }
+ html, body {
+ position: relative;
+ height: 100%;
+ width: 100%;
+ border: 0;
+ margin: 0;
+ padding: 0;
+ font-size: 0;
+ }
+ svg g {
+ clip-path: none;
+ }
+ svg text {
+ fill: #333;
+ }
+ .nv-axislabel {
+ font-size: 16px !important;
+ }
+ .control {
+ cursor: pointer;
+ visibility: hidden;
+ pointer-events: visible;
+ }
+ @media (min-width: 768px) {
+ .control {
+ visibility: visible;
+ }
+ }
+ </style>
+ <script src="s1.js"></script>
+ <script src="s2.js"></script>
+ </head>
+ <body>
+ <svg id='chart'></svg>
+ <script type='text/javascript'>
diff --git a/bench/perf_monitoring/resources/footer.html b/bench/perf_monitoring/resources/footer.html
new file mode 100644
index 0000000..81d8c88
--- /dev/null
+++ b/bench/perf_monitoring/resources/footer.html
@@ -0,0 +1,3 @@
+</table>
+</body>
+</html>
diff --git a/bench/perf_monitoring/resources/header.html b/bench/perf_monitoring/resources/header.html
new file mode 100644
index 0000000..1f22309
--- /dev/null
+++ b/bench/perf_monitoring/resources/header.html
@@ -0,0 +1,42 @@
+<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
+<html xmlns="http://www.w3.org/1999/xhtml">
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
+<title>Eigen performance monitoring</title>
+<style type="text/css">
+
+body
+{
+ background:#fff;
+}
+th {
+
+}
+img
+{
+ width:auto;
+ box-shadow:0px 0px 20px #cecece;
+ margin: 20px 20px 20px 20px;
+ -moz-transform: scale(1);
+ -moz-transition-duration: 0.4s;
+ -webkit-transition-duration: 0.4s;
+ -webkit-transform: scale(1);
+
+ -ms-transform: scale(1);
+ -ms-transition-duration: 0.4s;
+}
+img:hover
+{
+box-shadow: 5px 5px 20px #dcdcdc;
+ -moz-transform: scale(1.1);
+ -moz-transition-duration: 0.4s;
+ -webkit-transition-duration: 0.4s;
+ -webkit-transform: scale(1.1);
+
+ -ms-transform: scale(1.1);
+ -ms-transition-duration: 0.4s;
+
+}
+</style>
+</head>
+<body>
diff --git a/bench/perf_monitoring/resources/s1.js b/bench/perf_monitoring/resources/s1.js
new file mode 100644
index 0000000..cfff2d3
--- /dev/null
+++ b/bench/perf_monitoring/resources/s1.js
@@ -0,0 +1 @@
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diff --git a/bench/perf_monitoring/resources/s2.js b/bench/perf_monitoring/resources/s2.js
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t},set:function(a){t=a,g.orient(t?"right":"left")}},useInteractiveGuideline:{get:function(){return u},set:function(a){u=a,u&&(e.interactive(!1),e.useVoronoi(!1))}}}),a.utils.inheritOptions(b,e),a.utils.initOptions(b),b},a.models.lineWithFocusChart=function(){return a.models.lineChart().margin({bottom:30}).focusEnable(!0)},a.models.linePlusBarChart=function(){"use strict";function b(v){return v.each(function(v){function J(a){var b=+("e"==a),c=b?1:-1,d=Z/3;return"M"+.5*c+","+d+"A6,6 0 0 "+b+" "+6.5*c+","+(d+6)+"V"+(2*d-6)+"A6,6 0 0 "+b+" "+.5*c+","+2*d+"ZM"+2.5*c+","+(d+8)+"V"+(2*d-8)+"M"+4.5*c+","+(d+8)+"V"+(2*d-8)}function R(){u.empty()||u.extent(I),ma.data([u.empty()?e.domain():I]).each(function(a,b){var c=e(a[0])-e.range()[0],d=e.range()[1]-e(a[1]);d3.select(this).select(".left").attr("width",0>c?0:c),d3.select(this).select(".right").attr("x",e(a[1])).attr("width",0>d?0:d)})}function 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diff --git a/bench/perf_monitoring/trmv_lo.cpp b/bench/perf_monitoring/trmv_lo.cpp
new file mode 100644
index 0000000..3fabb6e
--- /dev/null
+++ b/bench/perf_monitoring/trmv_lo.cpp
@@ -0,0 +1,12 @@
+#include "gemv_common.h"
+
+EIGEN_DONT_INLINE
+void trmv(const Mat &A, const Vec &B, Vec &C)
+{
+ C.noalias() += A.triangularView<Lower>() * B;
+}
+
+int main(int argc, char **argv)
+{
+ return main_gemv(argc, argv, trmv);
+}
diff --git a/bench/perf_monitoring/trmv_lot.cpp b/bench/perf_monitoring/trmv_lot.cpp
new file mode 100644
index 0000000..32e085a
--- /dev/null
+++ b/bench/perf_monitoring/trmv_lot.cpp
@@ -0,0 +1,12 @@
+#include "gemv_common.h"
+
+EIGEN_DONT_INLINE
+void trmv(const Mat &A, Vec &B, const Vec &C)
+{
+ B.noalias() += A.transpose().triangularView<Lower>() * C;
+}
+
+int main(int argc, char **argv)
+{
+ return main_gemv(argc, argv, trmv);
+}
diff --git a/bench/perf_monitoring/trmv_up.cpp b/bench/perf_monitoring/trmv_up.cpp
new file mode 100644
index 0000000..c58e471
--- /dev/null
+++ b/bench/perf_monitoring/trmv_up.cpp
@@ -0,0 +1,12 @@
+#include "gemv_common.h"
+
+EIGEN_DONT_INLINE
+void trmv(const Mat &A, const Vec &B, Vec &C)
+{
+ C.noalias() += A.triangularView<Upper>() * B;
+}
+
+int main(int argc, char **argv)
+{
+ return main_gemv(argc, argv, trmv);
+}
diff --git a/bench/perf_monitoring/trmv_upt.cpp b/bench/perf_monitoring/trmv_upt.cpp
new file mode 100644
index 0000000..511e008
--- /dev/null
+++ b/bench/perf_monitoring/trmv_upt.cpp
@@ -0,0 +1,12 @@
+#include "gemv_common.h"
+
+EIGEN_DONT_INLINE
+void trmv(const Mat &A, Vec &B, const Vec &C)
+{
+ B.noalias() += A.transpose().triangularView<Upper>() * C;
+}
+
+int main(int argc, char **argv)
+{
+ return main_gemv(argc, argv, trmv);
+}
diff --git a/bench/product_threshold.cpp b/bench/product_threshold.cpp
new file mode 100644
index 0000000..dd6d15a
--- /dev/null
+++ b/bench/product_threshold.cpp
@@ -0,0 +1,143 @@
+
+#include <iostream>
+#include <Eigen/Core>
+#include <bench/BenchTimer.h>
+
+using namespace Eigen;
+using namespace std;
+
+#define END 9
+
+template<int S> struct map_size { enum { ret = S }; };
+template<> struct map_size<10> { enum { ret = 20 }; };
+template<> struct map_size<11> { enum { ret = 50 }; };
+template<> struct map_size<12> { enum { ret = 100 }; };
+template<> struct map_size<13> { enum { ret = 300 }; };
+
+template<int M, int N,int K> struct alt_prod
+{
+ enum {
+ ret = M==1 && N==1 ? InnerProduct
+ : K==1 ? OuterProduct
+ : M==1 ? GemvProduct
+ : N==1 ? GemvProduct
+ : GemmProduct
+ };
+};
+
+void print_mode(int mode)
+{
+ if(mode==InnerProduct) std::cout << "i";
+ if(mode==OuterProduct) std::cout << "o";
+ if(mode==CoeffBasedProductMode) std::cout << "c";
+ if(mode==LazyCoeffBasedProductMode) std::cout << "l";
+ if(mode==GemvProduct) std::cout << "v";
+ if(mode==GemmProduct) std::cout << "m";
+}
+
+template<int Mode, typename Lhs, typename Rhs, typename Res>
+EIGEN_DONT_INLINE void prod(const Lhs& a, const Rhs& b, Res& c)
+{
+ c.noalias() += typename ProductReturnType<Lhs,Rhs,Mode>::Type(a,b);
+}
+
+template<int M, int N, int K, typename Scalar, int Mode>
+EIGEN_DONT_INLINE void bench_prod()
+{
+ typedef Matrix<Scalar,M,K> Lhs; Lhs a; a.setRandom();
+ typedef Matrix<Scalar,K,N> Rhs; Rhs b; b.setRandom();
+ typedef Matrix<Scalar,M,N> Res; Res c; c.setRandom();
+
+ BenchTimer t;
+ double n = 2.*double(M)*double(N)*double(K);
+ int rep = 100000./n;
+ rep /= 2;
+ if(rep<1) rep = 1;
+ do {
+ rep *= 2;
+ t.reset();
+ BENCH(t,1,rep,prod<CoeffBasedProductMode>(a,b,c));
+ } while(t.best()<0.1);
+
+ t.reset();
+ BENCH(t,5,rep,prod<Mode>(a,b,c));
+
+ print_mode(Mode);
+ std::cout << int(1e-6*n*rep/t.best()) << "\t";
+}
+
+template<int N> struct print_n;
+template<int M, int N, int K> struct loop_on_m;
+template<int M, int N, int K, typename Scalar, int Mode> struct loop_on_n;
+
+template<int M, int N, int K>
+struct loop_on_k
+{
+ static void run()
+ {
+ std::cout << "K=" << K << "\t";
+ print_n<N>::run();
+ std::cout << "\n";
+
+ loop_on_m<M,N,K>::run();
+ std::cout << "\n\n";
+
+ loop_on_k<M,N,K+1>::run();
+ }
+};
+
+template<int M, int N>
+struct loop_on_k<M,N,END> { static void run(){} };
+
+
+template<int M, int N, int K>
+struct loop_on_m
+{
+ static void run()
+ {
+ std::cout << M << "f\t";
+ loop_on_n<M,N,K,float,CoeffBasedProductMode>::run();
+ std::cout << "\n";
+
+ std::cout << M << "f\t";
+ loop_on_n<M,N,K,float,-1>::run();
+ std::cout << "\n";
+
+ loop_on_m<M+1,N,K>::run();
+ }
+};
+
+template<int N, int K>
+struct loop_on_m<END,N,K> { static void run(){} };
+
+template<int M, int N, int K, typename Scalar, int Mode>
+struct loop_on_n
+{
+ static void run()
+ {
+ bench_prod<M,N,K,Scalar,Mode==-1? alt_prod<M,N,K>::ret : Mode>();
+
+ loop_on_n<M,N+1,K,Scalar,Mode>::run();
+ }
+};
+
+template<int M, int K, typename Scalar, int Mode>
+struct loop_on_n<M,END,K,Scalar,Mode> { static void run(){} };
+
+template<int N> struct print_n
+{
+ static void run()
+ {
+ std::cout << map_size<N>::ret << "\t";
+ print_n<N+1>::run();
+ }
+};
+
+template<> struct print_n<END> { static void run(){} };
+
+int main()
+{
+ loop_on_k<1,1,1>::run();
+
+ return 0;
+}
diff --git a/bench/quat_slerp.cpp b/bench/quat_slerp.cpp
new file mode 100644
index 0000000..bffb3bf
--- /dev/null
+++ b/bench/quat_slerp.cpp
@@ -0,0 +1,247 @@
+
+#include <iostream>
+#include <Eigen/Geometry>
+#include <bench/BenchTimer.h>
+using namespace Eigen;
+using namespace std;
+
+
+
+template<typename Q>
+EIGEN_DONT_INLINE Q nlerp(const Q& a, const Q& b, typename Q::Scalar t)
+{
+ return Q((a.coeffs() * (1.0-t) + b.coeffs() * t).normalized());
+}
+
+template<typename Q>
+EIGEN_DONT_INLINE Q slerp_eigen(const Q& a, const Q& b, typename Q::Scalar t)
+{
+ return a.slerp(t,b);
+}
+
+template<typename Q>
+EIGEN_DONT_INLINE Q slerp_legacy(const Q& a, const Q& b, typename Q::Scalar t)
+{
+ typedef typename Q::Scalar Scalar;
+ static const Scalar one = Scalar(1) - dummy_precision<Scalar>();
+ Scalar d = a.dot(b);
+ Scalar absD = internal::abs(d);
+ if (absD>=one)
+ return a;
+
+ // theta is the angle between the 2 quaternions
+ Scalar theta = std::acos(absD);
+ Scalar sinTheta = internal::sin(theta);
+
+ Scalar scale0 = internal::sin( ( Scalar(1) - t ) * theta) / sinTheta;
+ Scalar scale1 = internal::sin( ( t * theta) ) / sinTheta;
+ if (d<0)
+ scale1 = -scale1;
+
+ return Q(scale0 * a.coeffs() + scale1 * b.coeffs());
+}
+
+template<typename Q>
+EIGEN_DONT_INLINE Q slerp_legacy_nlerp(const Q& a, const Q& b, typename Q::Scalar t)
+{
+ typedef typename Q::Scalar Scalar;
+ static const Scalar one = Scalar(1) - epsilon<Scalar>();
+ Scalar d = a.dot(b);
+ Scalar absD = internal::abs(d);
+
+ Scalar scale0;
+ Scalar scale1;
+
+ if (absD>=one)
+ {
+ scale0 = Scalar(1) - t;
+ scale1 = t;
+ }
+ else
+ {
+ // theta is the angle between the 2 quaternions
+ Scalar theta = std::acos(absD);
+ Scalar sinTheta = internal::sin(theta);
+
+ scale0 = internal::sin( ( Scalar(1) - t ) * theta) / sinTheta;
+ scale1 = internal::sin( ( t * theta) ) / sinTheta;
+ if (d<0)
+ scale1 = -scale1;
+ }
+
+ return Q(scale0 * a.coeffs() + scale1 * b.coeffs());
+}
+
+template<typename T>
+inline T sin_over_x(T x)
+{
+ if (T(1) + x*x == T(1))
+ return T(1);
+ else
+ return std::sin(x)/x;
+}
+
+template<typename Q>
+EIGEN_DONT_INLINE Q slerp_rw(const Q& a, const Q& b, typename Q::Scalar t)
+{
+ typedef typename Q::Scalar Scalar;
+
+ Scalar d = a.dot(b);
+ Scalar theta;
+ if (d<0.0)
+ theta = /*M_PI -*/ Scalar(2)*std::asin( (a.coeffs()+b.coeffs()).norm()/2 );
+ else
+ theta = Scalar(2)*std::asin( (a.coeffs()-b.coeffs()).norm()/2 );
+
+ // theta is the angle between the 2 quaternions
+// Scalar theta = std::acos(absD);
+ Scalar sinOverTheta = sin_over_x(theta);
+
+ Scalar scale0 = (Scalar(1)-t)*sin_over_x( ( Scalar(1) - t ) * theta) / sinOverTheta;
+ Scalar scale1 = t * sin_over_x( ( t * theta) ) / sinOverTheta;
+ if (d<0)
+ scale1 = -scale1;
+
+ return Quaternion<Scalar>(scale0 * a.coeffs() + scale1 * b.coeffs());
+}
+
+template<typename Q>
+EIGEN_DONT_INLINE Q slerp_gael(const Q& a, const Q& b, typename Q::Scalar t)
+{
+ typedef typename Q::Scalar Scalar;
+
+ Scalar d = a.dot(b);
+ Scalar theta;
+// theta = Scalar(2) * atan2((a.coeffs()-b.coeffs()).norm(),(a.coeffs()+b.coeffs()).norm());
+// if (d<0.0)
+// theta = M_PI-theta;
+
+ if (d<0.0)
+ theta = /*M_PI -*/ Scalar(2)*std::asin( (-a.coeffs()-b.coeffs()).norm()/2 );
+ else
+ theta = Scalar(2)*std::asin( (a.coeffs()-b.coeffs()).norm()/2 );
+
+
+ Scalar scale0;
+ Scalar scale1;
+ if(theta*theta-Scalar(6)==-Scalar(6))
+ {
+ scale0 = Scalar(1) - t;
+ scale1 = t;
+ }
+ else
+ {
+ Scalar sinTheta = std::sin(theta);
+ scale0 = internal::sin( ( Scalar(1) - t ) * theta) / sinTheta;
+ scale1 = internal::sin( ( t * theta) ) / sinTheta;
+ if (d<0)
+ scale1 = -scale1;
+ }
+
+ return Quaternion<Scalar>(scale0 * a.coeffs() + scale1 * b.coeffs());
+}
+
+int main()
+{
+ typedef double RefScalar;
+ typedef float TestScalar;
+
+ typedef Quaternion<RefScalar> Qd;
+ typedef Quaternion<TestScalar> Qf;
+
+ unsigned int g_seed = (unsigned int) time(NULL);
+ std::cout << g_seed << "\n";
+// g_seed = 1259932496;
+ srand(g_seed);
+
+ Matrix<RefScalar,Dynamic,1> maxerr(7);
+ maxerr.setZero();
+
+ Matrix<RefScalar,Dynamic,1> avgerr(7);
+ avgerr.setZero();
+
+ cout << "double=>float=>double nlerp eigen legacy(snap) legacy(nlerp) rightway gael's criteria\n";
+
+ int rep = 100;
+ int iters = 40;
+ for (int w=0; w<rep; ++w)
+ {
+ Qf a, b;
+ a.coeffs().setRandom();
+ a.normalize();
+ b.coeffs().setRandom();
+ b.normalize();
+
+ Qf c[6];
+
+ Qd ar(a.cast<RefScalar>());
+ Qd br(b.cast<RefScalar>());
+ Qd cr;
+
+
+
+ cout.precision(8);
+ cout << std::scientific;
+ for (int i=0; i<iters; ++i)
+ {
+ RefScalar t = 0.65;
+ cr = slerp_rw(ar,br,t);
+
+ Qf refc = cr.cast<TestScalar>();
+ c[0] = nlerp(a,b,t);
+ c[1] = slerp_eigen(a,b,t);
+ c[2] = slerp_legacy(a,b,t);
+ c[3] = slerp_legacy_nlerp(a,b,t);
+ c[4] = slerp_rw(a,b,t);
+ c[5] = slerp_gael(a,b,t);
+
+ VectorXd err(7);
+ err[0] = (cr.coeffs()-refc.cast<RefScalar>().coeffs()).norm();
+// std::cout << err[0] << " ";
+ for (int k=0; k<6; ++k)
+ {
+ err[k+1] = (c[k].coeffs()-refc.coeffs()).norm();
+// std::cout << err[k+1] << " ";
+ }
+ maxerr = maxerr.cwise().max(err);
+ avgerr += err;
+// std::cout << "\n";
+ b = cr.cast<TestScalar>();
+ br = cr;
+ }
+// std::cout << "\n";
+ }
+ avgerr /= RefScalar(rep*iters);
+ cout << "\n\nAccuracy:\n"
+ << " max: " << maxerr.transpose() << "\n";
+ cout << " avg: " << avgerr.transpose() << "\n";
+
+ // perf bench
+ Quaternionf a,b;
+ a.coeffs().setRandom();
+ a.normalize();
+ b.coeffs().setRandom();
+ b.normalize();
+ //b = a;
+ float s = 0.65;
+
+ #define BENCH(FUNC) {\
+ BenchTimer t; \
+ for(int k=0; k<2; ++k) {\
+ t.start(); \
+ for(int i=0; i<1000000; ++i) \
+ FUNC(a,b,s); \
+ t.stop(); \
+ } \
+ cout << " " << #FUNC << " => \t " << t.value() << "s\n"; \
+ }
+
+ cout << "\nSpeed:\n" << std::fixed;
+ BENCH(nlerp);
+ BENCH(slerp_eigen);
+ BENCH(slerp_legacy);
+ BENCH(slerp_legacy_nlerp);
+ BENCH(slerp_rw);
+ BENCH(slerp_gael);
+}
+
diff --git a/bench/quatmul.cpp b/bench/quatmul.cpp
new file mode 100644
index 0000000..8d9d792
--- /dev/null
+++ b/bench/quatmul.cpp
@@ -0,0 +1,47 @@
+#include <iostream>
+#include <Eigen/Core>
+#include <Eigen/Geometry>
+#include <bench/BenchTimer.h>
+
+using namespace Eigen;
+
+template<typename Quat>
+EIGEN_DONT_INLINE void quatmul_default(const Quat& a, const Quat& b, Quat& c)
+{
+ c = a * b;
+}
+
+template<typename Quat>
+EIGEN_DONT_INLINE void quatmul_novec(const Quat& a, const Quat& b, Quat& c)
+{
+ c = internal::quat_product<0, Quat, Quat, typename Quat::Scalar, Aligned>::run(a,b);
+}
+
+template<typename Quat> void bench(const std::string& label)
+{
+ int tries = 10;
+ int rep = 1000000;
+ BenchTimer t;
+
+ Quat a(4, 1, 2, 3);
+ Quat b(2, 3, 4, 5);
+ Quat c;
+
+ std::cout.precision(3);
+
+ BENCH(t, tries, rep, quatmul_default(a,b,c));
+ std::cout << label << " default " << 1e3*t.best(CPU_TIMER) << "ms \t" << 1e-6*double(rep)/(t.best(CPU_TIMER)) << " M mul/s\n";
+
+ BENCH(t, tries, rep, quatmul_novec(a,b,c));
+ std::cout << label << " novec " << 1e3*t.best(CPU_TIMER) << "ms \t" << 1e-6*double(rep)/(t.best(CPU_TIMER)) << " M mul/s\n";
+}
+
+int main()
+{
+ bench<Quaternionf>("float ");
+ bench<Quaterniond>("double");
+
+ return 0;
+
+}
+
diff --git a/bench/sparse_cholesky.cpp b/bench/sparse_cholesky.cpp
new file mode 100644
index 0000000..ecb2267
--- /dev/null
+++ b/bench/sparse_cholesky.cpp
@@ -0,0 +1,216 @@
+// #define EIGEN_TAUCS_SUPPORT
+// #define EIGEN_CHOLMOD_SUPPORT
+#include <iostream>
+#include <Eigen/Sparse>
+
+// g++ -DSIZE=10000 -DDENSITY=0.001 sparse_cholesky.cpp -I.. -DDENSEMATRI -O3 -g0 -DNDEBUG -DNBTRIES=1 -I /home/gael/Coding/LinearAlgebra/taucs_full/src/ -I/home/gael/Coding/LinearAlgebra/taucs_full/build/linux/ -L/home/gael/Coding/LinearAlgebra/taucs_full/lib/linux/ -ltaucs /home/gael/Coding/LinearAlgebra/GotoBLAS/libgoto.a -lpthread -I /home/gael/Coding/LinearAlgebra/SuiteSparse/CHOLMOD/Include/ $CHOLLIB -I /home/gael/Coding/LinearAlgebra/SuiteSparse/UFconfig/ /home/gael/Coding/LinearAlgebra/SuiteSparse/CCOLAMD/Lib/libccolamd.a /home/gael/Coding/LinearAlgebra/SuiteSparse/CHOLMOD/Lib/libcholmod.a -lmetis /home/gael/Coding/LinearAlgebra/SuiteSparse/AMD/Lib/libamd.a /home/gael/Coding/LinearAlgebra/SuiteSparse/CAMD/Lib/libcamd.a /home/gael/Coding/LinearAlgebra/SuiteSparse/CCOLAMD/Lib/libccolamd.a /home/gael/Coding/LinearAlgebra/SuiteSparse/COLAMD/Lib/libcolamd.a -llapack && ./a.out
+
+#define NOGMM
+#define NOMTL
+
+#ifndef SIZE
+#define SIZE 10
+#endif
+
+#ifndef DENSITY
+#define DENSITY 0.01
+#endif
+
+#ifndef REPEAT
+#define REPEAT 1
+#endif
+
+#include "BenchSparseUtil.h"
+
+#ifndef MINDENSITY
+#define MINDENSITY 0.0004
+#endif
+
+#ifndef NBTRIES
+#define NBTRIES 10
+#endif
+
+#define BENCH(X) \
+ timer.reset(); \
+ for (int _j=0; _j<NBTRIES; ++_j) { \
+ timer.start(); \
+ for (int _k=0; _k<REPEAT; ++_k) { \
+ X \
+ } timer.stop(); }
+
+// typedef SparseMatrix<Scalar,UpperTriangular> EigenSparseTriMatrix;
+typedef SparseMatrix<Scalar,SelfAdjoint|LowerTriangular> EigenSparseSelfAdjointMatrix;
+
+void fillSpdMatrix(float density, int rows, int cols, EigenSparseSelfAdjointMatrix& dst)
+{
+ dst.startFill(rows*cols*density);
+ for(int j = 0; j < cols; j++)
+ {
+ dst.fill(j,j) = internal::random<Scalar>(10,20);
+ for(int i = j+1; i < rows; i++)
+ {
+ Scalar v = (internal::random<float>(0,1) < density) ? internal::random<Scalar>() : 0;
+ if (v!=0)
+ dst.fill(i,j) = v;
+ }
+
+ }
+ dst.endFill();
+}
+
+#include <Eigen/Cholesky>
+
+template<int Backend>
+void doEigen(const char* name, const EigenSparseSelfAdjointMatrix& sm1, int flags = 0)
+{
+ std::cout << name << "..." << std::flush;
+ BenchTimer timer;
+ timer.start();
+ SparseLLT<EigenSparseSelfAdjointMatrix,Backend> chol(sm1, flags);
+ timer.stop();
+ std::cout << ":\t" << timer.value() << endl;
+
+ std::cout << " nnz: " << sm1.nonZeros() << " => " << chol.matrixL().nonZeros() << "\n";
+// std::cout << "sparse\n" << chol.matrixL() << "%\n";
+}
+
+int main(int argc, char *argv[])
+{
+ int rows = SIZE;
+ int cols = SIZE;
+ float density = DENSITY;
+ BenchTimer timer;
+
+ VectorXf b = VectorXf::Random(cols);
+ VectorXf x = VectorXf::Random(cols);
+
+ bool densedone = false;
+
+ //for (float density = DENSITY; density>=MINDENSITY; density*=0.5)
+// float density = 0.5;
+ {
+ EigenSparseSelfAdjointMatrix sm1(rows, cols);
+ std::cout << "Generate sparse matrix (might take a while)...\n";
+ fillSpdMatrix(density, rows, cols, sm1);
+ std::cout << "DONE\n\n";
+
+ // dense matrices
+ #ifdef DENSEMATRIX
+ if (!densedone)
+ {
+ densedone = true;
+ std::cout << "Eigen Dense\t" << density*100 << "%\n";
+ DenseMatrix m1(rows,cols);
+ eiToDense(sm1, m1);
+ m1 = (m1 + m1.transpose()).eval();
+ m1.diagonal() *= 0.5;
+
+// BENCH(LLT<DenseMatrix> chol(m1);)
+// std::cout << "dense:\t" << timer.value() << endl;
+
+ BenchTimer timer;
+ timer.start();
+ LLT<DenseMatrix> chol(m1);
+ timer.stop();
+ std::cout << "dense:\t" << timer.value() << endl;
+ int count = 0;
+ for (int j=0; j<cols; ++j)
+ for (int i=j; i<rows; ++i)
+ if (!internal::isMuchSmallerThan(internal::abs(chol.matrixL()(i,j)), 0.1))
+ count++;
+ std::cout << "dense: " << "nnz = " << count << "\n";
+// std::cout << "dense:\n" << m1 << "\n\n" << chol.matrixL() << endl;
+ }
+ #endif
+
+ // eigen sparse matrices
+ doEigen<Eigen::DefaultBackend>("Eigen/Sparse", sm1, Eigen::IncompleteFactorization);
+
+ #ifdef EIGEN_CHOLMOD_SUPPORT
+ doEigen<Eigen::Cholmod>("Eigen/Cholmod", sm1, Eigen::IncompleteFactorization);
+ #endif
+
+ #ifdef EIGEN_TAUCS_SUPPORT
+ doEigen<Eigen::Taucs>("Eigen/Taucs", sm1, Eigen::IncompleteFactorization);
+ #endif
+
+ #if 0
+ // TAUCS
+ {
+ taucs_ccs_matrix A = sm1.asTaucsMatrix();
+
+ //BENCH(taucs_ccs_matrix* chol = taucs_ccs_factor_llt(&A, 0, 0);)
+// BENCH(taucs_supernodal_factor_to_ccs(taucs_ccs_factor_llt_ll(&A));)
+// std::cout << "taucs:\t" << timer.value() << endl;
+
+ taucs_ccs_matrix* chol = taucs_ccs_factor_llt(&A, 0, 0);
+
+ for (int j=0; j<cols; ++j)
+ {
+ for (int i=chol->colptr[j]; i<chol->colptr[j+1]; ++i)
+ std::cout << chol->values.d[i] << " ";
+ }
+ }
+
+ // CHOLMOD
+ #ifdef EIGEN_CHOLMOD_SUPPORT
+ {
+ cholmod_common c;
+ cholmod_start (&c);
+ cholmod_sparse A;
+ cholmod_factor *L;
+
+ A = sm1.asCholmodMatrix();
+ BenchTimer timer;
+// timer.reset();
+ timer.start();
+ std::vector<int> perm(cols);
+// std::vector<int> set(ncols);
+ for (int i=0; i<cols; ++i)
+ perm[i] = i;
+// c.nmethods = 1;
+// c.method[0] = 1;
+
+ c.nmethods = 1;
+ c.method [0].ordering = CHOLMOD_NATURAL;
+ c.postorder = 0;
+ c.final_ll = 1;
+
+ L = cholmod_analyze_p(&A, &perm[0], &perm[0], cols, &c);
+ timer.stop();
+ std::cout << "cholmod/analyze:\t" << timer.value() << endl;
+ timer.reset();
+ timer.start();
+ cholmod_factorize(&A, L, &c);
+ timer.stop();
+ std::cout << "cholmod/factorize:\t" << timer.value() << endl;
+
+ cholmod_sparse* cholmat = cholmod_factor_to_sparse(L, &c);
+
+ cholmod_print_factor(L, "Factors", &c);
+
+ cholmod_print_sparse(cholmat, "Chol", &c);
+ cholmod_write_sparse(stdout, cholmat, 0, 0, &c);
+//
+// cholmod_print_sparse(&A, "A", &c);
+// cholmod_write_sparse(stdout, &A, 0, 0, &c);
+
+
+// for (int j=0; j<cols; ++j)
+// {
+// for (int i=chol->colptr[j]; i<chol->colptr[j+1]; ++i)
+// std::cout << chol->values.s[i] << " ";
+// }
+ }
+ #endif
+
+ #endif
+
+
+
+ }
+
+
+ return 0;
+}
+
diff --git a/bench/sparse_dense_product.cpp b/bench/sparse_dense_product.cpp
new file mode 100644
index 0000000..f3f5194
--- /dev/null
+++ b/bench/sparse_dense_product.cpp
@@ -0,0 +1,187 @@
+
+//g++ -O3 -g0 -DNDEBUG sparse_product.cpp -I.. -I/home/gael/Coding/LinearAlgebra/mtl4/ -DDENSITY=0.005 -DSIZE=10000 && ./a.out
+//g++ -O3 -g0 -DNDEBUG sparse_product.cpp -I.. -I/home/gael/Coding/LinearAlgebra/mtl4/ -DDENSITY=0.05 -DSIZE=2000 && ./a.out
+// -DNOGMM -DNOMTL -DCSPARSE
+// -I /home/gael/Coding/LinearAlgebra/CSparse/Include/ /home/gael/Coding/LinearAlgebra/CSparse/Lib/libcsparse.a
+#ifndef SIZE
+#define SIZE 650000
+#endif
+
+#ifndef DENSITY
+#define DENSITY 0.01
+#endif
+
+#ifndef REPEAT
+#define REPEAT 1
+#endif
+
+#include "BenchSparseUtil.h"
+
+#ifndef MINDENSITY
+#define MINDENSITY 0.0004
+#endif
+
+#ifndef NBTRIES
+#define NBTRIES 10
+#endif
+
+#define BENCH(X) \
+ timer.reset(); \
+ for (int _j=0; _j<NBTRIES; ++_j) { \
+ timer.start(); \
+ for (int _k=0; _k<REPEAT; ++_k) { \
+ X \
+ } timer.stop(); }
+
+
+#ifdef CSPARSE
+cs* cs_sorted_multiply(const cs* a, const cs* b)
+{
+ cs* A = cs_transpose (a, 1) ;
+ cs* B = cs_transpose (b, 1) ;
+ cs* D = cs_multiply (B,A) ; /* D = B'*A' */
+ cs_spfree (A) ;
+ cs_spfree (B) ;
+ cs_dropzeros (D) ; /* drop zeros from D */
+ cs* C = cs_transpose (D, 1) ; /* C = D', so that C is sorted */
+ cs_spfree (D) ;
+ return C;
+}
+#endif
+
+int main(int argc, char *argv[])
+{
+ int rows = SIZE;
+ int cols = SIZE;
+ float density = DENSITY;
+
+ EigenSparseMatrix sm1(rows,cols);
+ DenseVector v1(cols), v2(cols);
+ v1.setRandom();
+
+ BenchTimer timer;
+ for (float density = DENSITY; density>=MINDENSITY; density*=0.5)
+ {
+ //fillMatrix(density, rows, cols, sm1);
+ fillMatrix2(7, rows, cols, sm1);
+
+ // dense matrices
+ #ifdef DENSEMATRIX
+ {
+ std::cout << "Eigen Dense\t" << density*100 << "%\n";
+ DenseMatrix m1(rows,cols);
+ eiToDense(sm1, m1);
+
+ timer.reset();
+ timer.start();
+ for (int k=0; k<REPEAT; ++k)
+ v2 = m1 * v1;
+ timer.stop();
+ std::cout << " a * v:\t" << timer.best() << " " << double(REPEAT)/timer.best() << " * / sec " << endl;
+
+ timer.reset();
+ timer.start();
+ for (int k=0; k<REPEAT; ++k)
+ v2 = m1.transpose() * v1;
+ timer.stop();
+ std::cout << " a' * v:\t" << timer.best() << endl;
+ }
+ #endif
+
+ // eigen sparse matrices
+ {
+ std::cout << "Eigen sparse\t" << sm1.nonZeros()/float(sm1.rows()*sm1.cols())*100 << "%\n";
+
+ BENCH(asm("#myc"); v2 = sm1 * v1; asm("#myd");)
+ std::cout << " a * v:\t" << timer.best()/REPEAT << " " << double(REPEAT)/timer.best(REAL_TIMER) << " * / sec " << endl;
+
+
+ BENCH( { asm("#mya"); v2 = sm1.transpose() * v1; asm("#myb"); })
+
+ std::cout << " a' * v:\t" << timer.best()/REPEAT << endl;
+ }
+
+// {
+// DynamicSparseMatrix<Scalar> m1(sm1);
+// std::cout << "Eigen dyn-sparse\t" << m1.nonZeros()/float(m1.rows()*m1.cols())*100 << "%\n";
+//
+// BENCH(for (int k=0; k<REPEAT; ++k) v2 = m1 * v1;)
+// std::cout << " a * v:\t" << timer.value() << endl;
+//
+// BENCH(for (int k=0; k<REPEAT; ++k) v2 = m1.transpose() * v1;)
+// std::cout << " a' * v:\t" << timer.value() << endl;
+// }
+
+ // GMM++
+ #ifndef NOGMM
+ {
+ std::cout << "GMM++ sparse\t" << density*100 << "%\n";
+ //GmmDynSparse gmmT3(rows,cols);
+ GmmSparse m1(rows,cols);
+ eiToGmm(sm1, m1);
+
+ std::vector<Scalar> gmmV1(cols), gmmV2(cols);
+ Map<Matrix<Scalar,Dynamic,1> >(&gmmV1[0], cols) = v1;
+ Map<Matrix<Scalar,Dynamic,1> >(&gmmV2[0], cols) = v2;
+
+ BENCH( asm("#myx"); gmm::mult(m1, gmmV1, gmmV2); asm("#myy"); )
+ std::cout << " a * v:\t" << timer.value() << endl;
+
+ BENCH( gmm::mult(gmm::transposed(m1), gmmV1, gmmV2); )
+ std::cout << " a' * v:\t" << timer.value() << endl;
+ }
+ #endif
+
+ #ifndef NOUBLAS
+ {
+ std::cout << "ublas sparse\t" << density*100 << "%\n";
+ UBlasSparse m1(rows,cols);
+ eiToUblas(sm1, m1);
+
+ boost::numeric::ublas::vector<Scalar> uv1, uv2;
+ eiToUblasVec(v1,uv1);
+ eiToUblasVec(v2,uv2);
+
+// std::vector<Scalar> gmmV1(cols), gmmV2(cols);
+// Map<Matrix<Scalar,Dynamic,1> >(&gmmV1[0], cols) = v1;
+// Map<Matrix<Scalar,Dynamic,1> >(&gmmV2[0], cols) = v2;
+
+ BENCH( uv2 = boost::numeric::ublas::prod(m1, uv1); )
+ std::cout << " a * v:\t" << timer.value() << endl;
+
+// BENCH( boost::ublas::prod(gmm::transposed(m1), gmmV1, gmmV2); )
+// std::cout << " a' * v:\t" << timer.value() << endl;
+ }
+ #endif
+
+ // MTL4
+ #ifndef NOMTL
+ {
+ std::cout << "MTL4\t" << density*100 << "%\n";
+ MtlSparse m1(rows,cols);
+ eiToMtl(sm1, m1);
+ mtl::dense_vector<Scalar> mtlV1(cols, 1.0);
+ mtl::dense_vector<Scalar> mtlV2(cols, 1.0);
+
+ timer.reset();
+ timer.start();
+ for (int k=0; k<REPEAT; ++k)
+ mtlV2 = m1 * mtlV1;
+ timer.stop();
+ std::cout << " a * v:\t" << timer.value() << endl;
+
+ timer.reset();
+ timer.start();
+ for (int k=0; k<REPEAT; ++k)
+ mtlV2 = trans(m1) * mtlV1;
+ timer.stop();
+ std::cout << " a' * v:\t" << timer.value() << endl;
+ }
+ #endif
+
+ std::cout << "\n\n";
+ }
+
+ return 0;
+}
+
diff --git a/bench/sparse_lu.cpp b/bench/sparse_lu.cpp
new file mode 100644
index 0000000..5c75001
--- /dev/null
+++ b/bench/sparse_lu.cpp
@@ -0,0 +1,132 @@
+
+// g++ -I.. sparse_lu.cpp -O3 -g0 -I /usr/include/superlu/ -lsuperlu -lgfortran -DSIZE=1000 -DDENSITY=.05 && ./a.out
+
+#define EIGEN_SUPERLU_SUPPORT
+#define EIGEN_UMFPACK_SUPPORT
+#include <Eigen/Sparse>
+
+#define NOGMM
+#define NOMTL
+
+#ifndef SIZE
+#define SIZE 10
+#endif
+
+#ifndef DENSITY
+#define DENSITY 0.01
+#endif
+
+#ifndef REPEAT
+#define REPEAT 1
+#endif
+
+#include "BenchSparseUtil.h"
+
+#ifndef MINDENSITY
+#define MINDENSITY 0.0004
+#endif
+
+#ifndef NBTRIES
+#define NBTRIES 10
+#endif
+
+#define BENCH(X) \
+ timer.reset(); \
+ for (int _j=0; _j<NBTRIES; ++_j) { \
+ timer.start(); \
+ for (int _k=0; _k<REPEAT; ++_k) { \
+ X \
+ } timer.stop(); }
+
+typedef Matrix<Scalar,Dynamic,1> VectorX;
+
+#include <Eigen/LU>
+
+template<int Backend>
+void doEigen(const char* name, const EigenSparseMatrix& sm1, const VectorX& b, VectorX& x, int flags = 0)
+{
+ std::cout << name << "..." << std::flush;
+ BenchTimer timer; timer.start();
+ SparseLU<EigenSparseMatrix,Backend> lu(sm1, flags);
+ timer.stop();
+ if (lu.succeeded())
+ std::cout << ":\t" << timer.value() << endl;
+ else
+ {
+ std::cout << ":\t FAILED" << endl;
+ return;
+ }
+
+ bool ok;
+ timer.reset(); timer.start();
+ ok = lu.solve(b,&x);
+ timer.stop();
+ if (ok)
+ std::cout << " solve:\t" << timer.value() << endl;
+ else
+ std::cout << " solve:\t" << " FAILED" << endl;
+
+ //std::cout << x.transpose() << "\n";
+}
+
+int main(int argc, char *argv[])
+{
+ int rows = SIZE;
+ int cols = SIZE;
+ float density = DENSITY;
+ BenchTimer timer;
+
+ VectorX b = VectorX::Random(cols);
+ VectorX x = VectorX::Random(cols);
+
+ bool densedone = false;
+
+ //for (float density = DENSITY; density>=MINDENSITY; density*=0.5)
+// float density = 0.5;
+ {
+ EigenSparseMatrix sm1(rows, cols);
+ fillMatrix(density, rows, cols, sm1);
+
+ // dense matrices
+ #ifdef DENSEMATRIX
+ if (!densedone)
+ {
+ densedone = true;
+ std::cout << "Eigen Dense\t" << density*100 << "%\n";
+ DenseMatrix m1(rows,cols);
+ eiToDense(sm1, m1);
+
+ BenchTimer timer;
+ timer.start();
+ FullPivLU<DenseMatrix> lu(m1);
+ timer.stop();
+ std::cout << "Eigen/dense:\t" << timer.value() << endl;
+
+ timer.reset();
+ timer.start();
+ lu.solve(b,&x);
+ timer.stop();
+ std::cout << " solve:\t" << timer.value() << endl;
+// std::cout << b.transpose() << "\n";
+// std::cout << x.transpose() << "\n";
+ }
+ #endif
+
+ #ifdef EIGEN_UMFPACK_SUPPORT
+ x.setZero();
+ doEigen<Eigen::UmfPack>("Eigen/UmfPack (auto)", sm1, b, x, 0);
+ #endif
+
+ #ifdef EIGEN_SUPERLU_SUPPORT
+ x.setZero();
+ doEigen<Eigen::SuperLU>("Eigen/SuperLU (nat)", sm1, b, x, Eigen::NaturalOrdering);
+// doEigen<Eigen::SuperLU>("Eigen/SuperLU (MD AT+A)", sm1, b, x, Eigen::MinimumDegree_AT_PLUS_A);
+// doEigen<Eigen::SuperLU>("Eigen/SuperLU (MD ATA)", sm1, b, x, Eigen::MinimumDegree_ATA);
+ doEigen<Eigen::SuperLU>("Eigen/SuperLU (COLAMD)", sm1, b, x, Eigen::ColApproxMinimumDegree);
+ #endif
+
+ }
+
+ return 0;
+}
+
diff --git a/bench/sparse_product.cpp b/bench/sparse_product.cpp
new file mode 100644
index 0000000..d2fc44f
--- /dev/null
+++ b/bench/sparse_product.cpp
@@ -0,0 +1,323 @@
+
+//g++ -O3 -g0 -DNDEBUG sparse_product.cpp -I.. -I/home/gael/Coding/LinearAlgebra/mtl4/ -DDENSITY=0.005 -DSIZE=10000 && ./a.out
+//g++ -O3 -g0 -DNDEBUG sparse_product.cpp -I.. -I/home/gael/Coding/LinearAlgebra/mtl4/ -DDENSITY=0.05 -DSIZE=2000 && ./a.out
+// -DNOGMM -DNOMTL -DCSPARSE
+// -I /home/gael/Coding/LinearAlgebra/CSparse/Include/ /home/gael/Coding/LinearAlgebra/CSparse/Lib/libcsparse.a
+
+#include <typeinfo>
+
+#ifndef SIZE
+#define SIZE 1000000
+#endif
+
+#ifndef NNZPERCOL
+#define NNZPERCOL 6
+#endif
+
+#ifndef REPEAT
+#define REPEAT 1
+#endif
+
+#include <algorithm>
+#include "BenchTimer.h"
+#include "BenchUtil.h"
+#include "BenchSparseUtil.h"
+
+#ifndef NBTRIES
+#define NBTRIES 1
+#endif
+
+#define BENCH(X) \
+ timer.reset(); \
+ for (int _j=0; _j<NBTRIES; ++_j) { \
+ timer.start(); \
+ for (int _k=0; _k<REPEAT; ++_k) { \
+ X \
+ } timer.stop(); }
+
+// #ifdef MKL
+//
+// #include "mkl_types.h"
+// #include "mkl_spblas.h"
+//
+// template<typename Lhs,typename Rhs,typename Res>
+// void mkl_multiply(const Lhs& lhs, const Rhs& rhs, Res& res)
+// {
+// char n = 'N';
+// float alpha = 1;
+// char matdescra[6];
+// matdescra[0] = 'G';
+// matdescra[1] = 0;
+// matdescra[2] = 0;
+// matdescra[3] = 'C';
+// mkl_scscmm(&n, lhs.rows(), rhs.cols(), lhs.cols(), &alpha, matdescra,
+// lhs._valuePtr(), lhs._innerIndexPtr(), lhs.outerIndexPtr(),
+// pntre, b, &ldb, &beta, c, &ldc);
+// // mkl_somatcopy('C', 'T', lhs.rows(), lhs.cols(), 1,
+// // lhs._valuePtr(), lhs.rows(), DST, dst_stride);
+// }
+//
+// #endif
+
+
+#ifdef CSPARSE
+cs* cs_sorted_multiply(const cs* a, const cs* b)
+{
+// return cs_multiply(a,b);
+
+ cs* A = cs_transpose(a, 1);
+ cs* B = cs_transpose(b, 1);
+ cs* D = cs_multiply(B,A); /* D = B'*A' */
+ cs_spfree (A) ;
+ cs_spfree (B) ;
+ cs_dropzeros (D) ; /* drop zeros from D */
+ cs* C = cs_transpose (D, 1) ; /* C = D', so that C is sorted */
+ cs_spfree (D) ;
+ return C;
+
+// cs* A = cs_transpose(a, 1);
+// cs* C = cs_transpose(A, 1);
+// return C;
+}
+
+cs* cs_sorted_multiply2(const cs* a, const cs* b)
+{
+ cs* D = cs_multiply(a,b);
+ cs* E = cs_transpose(D,1);
+ cs_spfree(D);
+ cs* C = cs_transpose(E,1);
+ cs_spfree(E);
+ return C;
+}
+#endif
+
+void bench_sort();
+
+int main(int argc, char *argv[])
+{
+// bench_sort();
+
+ int rows = SIZE;
+ int cols = SIZE;
+ float density = DENSITY;
+
+ EigenSparseMatrix sm1(rows,cols), sm2(rows,cols), sm3(rows,cols), sm4(rows,cols);
+
+ BenchTimer timer;
+ for (int nnzPerCol = NNZPERCOL; nnzPerCol>1; nnzPerCol/=1.1)
+ {
+ sm1.setZero();
+ sm2.setZero();
+ fillMatrix2(nnzPerCol, rows, cols, sm1);
+ fillMatrix2(nnzPerCol, rows, cols, sm2);
+// std::cerr << "filling OK\n";
+
+ // dense matrices
+ #ifdef DENSEMATRIX
+ {
+ std::cout << "Eigen Dense\t" << nnzPerCol << "%\n";
+ DenseMatrix m1(rows,cols), m2(rows,cols), m3(rows,cols);
+ eiToDense(sm1, m1);
+ eiToDense(sm2, m2);
+
+ timer.reset();
+ timer.start();
+ for (int k=0; k<REPEAT; ++k)
+ m3 = m1 * m2;
+ timer.stop();
+ std::cout << " a * b:\t" << timer.value() << endl;
+
+ timer.reset();
+ timer.start();
+ for (int k=0; k<REPEAT; ++k)
+ m3 = m1.transpose() * m2;
+ timer.stop();
+ std::cout << " a' * b:\t" << timer.value() << endl;
+
+ timer.reset();
+ timer.start();
+ for (int k=0; k<REPEAT; ++k)
+ m3 = m1.transpose() * m2.transpose();
+ timer.stop();
+ std::cout << " a' * b':\t" << timer.value() << endl;
+
+ timer.reset();
+ timer.start();
+ for (int k=0; k<REPEAT; ++k)
+ m3 = m1 * m2.transpose();
+ timer.stop();
+ std::cout << " a * b':\t" << timer.value() << endl;
+ }
+ #endif
+
+ // eigen sparse matrices
+ {
+ std::cout << "Eigen sparse\t" << sm1.nonZeros()/(float(sm1.rows())*float(sm1.cols()))*100 << "% * "
+ << sm2.nonZeros()/(float(sm2.rows())*float(sm2.cols()))*100 << "%\n";
+
+ BENCH(sm3 = sm1 * sm2; )
+ std::cout << " a * b:\t" << timer.value() << endl;
+
+// BENCH(sm3 = sm1.transpose() * sm2; )
+// std::cout << " a' * b:\t" << timer.value() << endl;
+// //
+// BENCH(sm3 = sm1.transpose() * sm2.transpose(); )
+// std::cout << " a' * b':\t" << timer.value() << endl;
+// //
+// BENCH(sm3 = sm1 * sm2.transpose(); )
+// std::cout << " a * b' :\t" << timer.value() << endl;
+
+
+// std::cout << "\n";
+//
+// BENCH( sm3._experimentalNewProduct(sm1, sm2); )
+// std::cout << " a * b:\t" << timer.value() << endl;
+//
+// BENCH(sm3._experimentalNewProduct(sm1.transpose(),sm2); )
+// std::cout << " a' * b:\t" << timer.value() << endl;
+// //
+// BENCH(sm3._experimentalNewProduct(sm1.transpose(),sm2.transpose()); )
+// std::cout << " a' * b':\t" << timer.value() << endl;
+// //
+// BENCH(sm3._experimentalNewProduct(sm1, sm2.transpose());)
+// std::cout << " a * b' :\t" << timer.value() << endl;
+ }
+
+ // eigen dyn-sparse matrices
+ /*{
+ DynamicSparseMatrix<Scalar> m1(sm1), m2(sm2), m3(sm3);
+ std::cout << "Eigen dyn-sparse\t" << m1.nonZeros()/(float(m1.rows())*float(m1.cols()))*100 << "% * "
+ << m2.nonZeros()/(float(m2.rows())*float(m2.cols()))*100 << "%\n";
+
+// timer.reset();
+// timer.start();
+ BENCH(for (int k=0; k<REPEAT; ++k) m3 = m1 * m2;)
+// timer.stop();
+ std::cout << " a * b:\t" << timer.value() << endl;
+// std::cout << sm3 << "\n";
+
+ timer.reset();
+ timer.start();
+// std::cerr << "transpose...\n";
+// EigenSparseMatrix sm4 = sm1.transpose();
+// std::cout << sm4.nonZeros() << " == " << sm1.nonZeros() << "\n";
+// exit(1);
+// std::cerr << "transpose OK\n";
+// std::cout << sm1 << "\n\n" << sm1.transpose() << "\n\n" << sm4.transpose() << "\n\n";
+ BENCH(for (int k=0; k<REPEAT; ++k) m3 = m1.transpose() * m2;)
+// timer.stop();
+ std::cout << " a' * b:\t" << timer.value() << endl;
+
+// timer.reset();
+// timer.start();
+ BENCH( for (int k=0; k<REPEAT; ++k) m3 = m1.transpose() * m2.transpose(); )
+// timer.stop();
+ std::cout << " a' * b':\t" << timer.value() << endl;
+
+// timer.reset();
+// timer.start();
+ BENCH( for (int k=0; k<REPEAT; ++k) m3 = m1 * m2.transpose(); )
+// timer.stop();
+ std::cout << " a * b' :\t" << timer.value() << endl;
+ }*/
+
+ // CSparse
+ #ifdef CSPARSE
+ {
+ std::cout << "CSparse \t" << nnzPerCol << "%\n";
+ cs *m1, *m2, *m3;
+ eiToCSparse(sm1, m1);
+ eiToCSparse(sm2, m2);
+
+ BENCH(
+ {
+ m3 = cs_sorted_multiply(m1, m2);
+ if (!m3)
+ {
+ std::cerr << "cs_multiply failed\n";
+ }
+// cs_print(m3, 0);
+ cs_spfree(m3);
+ }
+ );
+// timer.stop();
+ std::cout << " a * b:\t" << timer.value() << endl;
+
+// BENCH( { m3 = cs_sorted_multiply2(m1, m2); cs_spfree(m3); } );
+// std::cout << " a * b:\t" << timer.value() << endl;
+ }
+ #endif
+
+ #ifndef NOUBLAS
+ {
+ std::cout << "ublas\t" << nnzPerCol << "%\n";
+ UBlasSparse m1(rows,cols), m2(rows,cols), m3(rows,cols);
+ eiToUblas(sm1, m1);
+ eiToUblas(sm2, m2);
+
+ BENCH(boost::numeric::ublas::prod(m1, m2, m3););
+ std::cout << " a * b:\t" << timer.value() << endl;
+ }
+ #endif
+
+ // GMM++
+ #ifndef NOGMM
+ {
+ std::cout << "GMM++ sparse\t" << nnzPerCol << "%\n";
+ GmmDynSparse gmmT3(rows,cols);
+ GmmSparse m1(rows,cols), m2(rows,cols), m3(rows,cols);
+ eiToGmm(sm1, m1);
+ eiToGmm(sm2, m2);
+
+ BENCH(gmm::mult(m1, m2, gmmT3););
+ std::cout << " a * b:\t" << timer.value() << endl;
+
+// BENCH(gmm::mult(gmm::transposed(m1), m2, gmmT3););
+// std::cout << " a' * b:\t" << timer.value() << endl;
+//
+// if (rows<500)
+// {
+// BENCH(gmm::mult(gmm::transposed(m1), gmm::transposed(m2), gmmT3););
+// std::cout << " a' * b':\t" << timer.value() << endl;
+//
+// BENCH(gmm::mult(m1, gmm::transposed(m2), gmmT3););
+// std::cout << " a * b':\t" << timer.value() << endl;
+// }
+// else
+// {
+// std::cout << " a' * b':\t" << "forever" << endl;
+// std::cout << " a * b':\t" << "forever" << endl;
+// }
+ }
+ #endif
+
+ // MTL4
+ #ifndef NOMTL
+ {
+ std::cout << "MTL4\t" << nnzPerCol << "%\n";
+ MtlSparse m1(rows,cols), m2(rows,cols), m3(rows,cols);
+ eiToMtl(sm1, m1);
+ eiToMtl(sm2, m2);
+
+ BENCH(m3 = m1 * m2;);
+ std::cout << " a * b:\t" << timer.value() << endl;
+
+// BENCH(m3 = trans(m1) * m2;);
+// std::cout << " a' * b:\t" << timer.value() << endl;
+//
+// BENCH(m3 = trans(m1) * trans(m2););
+// std::cout << " a' * b':\t" << timer.value() << endl;
+//
+// BENCH(m3 = m1 * trans(m2););
+// std::cout << " a * b' :\t" << timer.value() << endl;
+ }
+ #endif
+
+ std::cout << "\n\n";
+ }
+
+ return 0;
+}
+
+
+
diff --git a/bench/sparse_randomsetter.cpp b/bench/sparse_randomsetter.cpp
new file mode 100644
index 0000000..c433742
--- /dev/null
+++ b/bench/sparse_randomsetter.cpp
@@ -0,0 +1,126 @@
+
+#define NOGMM
+#define NOMTL
+#define EIGEN_GOOGLEHASH_SUPPORT 1
+
+#include <map>
+#include <ext/hash_map>
+#include <google/dense_hash_map>
+#include <google/sparse_hash_map>
+
+#ifndef SIZE
+#define SIZE 10000
+#endif
+
+#ifndef DENSITY
+#define DENSITY 0.01
+#endif
+
+#ifndef REPEAT
+#define REPEAT 1
+#endif
+
+#include "BenchSparseUtil.h"
+
+#ifndef MINDENSITY
+#define MINDENSITY 0.0004
+#endif
+
+#ifndef NBTRIES
+#define NBTRIES 10
+#endif
+
+#define BENCH(X) \
+ timer.reset(); \
+ for (int _j=0; _j<NBTRIES; ++_j) { \
+ timer.start(); \
+ for (int _k=0; _k<REPEAT; ++_k) { \
+ X \
+ } timer.stop(); }
+
+
+static double rtime;
+static double nentries;
+
+template<typename SetterType>
+void dostuff(const char* name, EigenSparseMatrix& sm1)
+{
+ int rows = sm1.rows();
+ int cols = sm1.cols();
+ sm1.setZero();
+ BenchTimer t;
+ SetterType* set1 = new SetterType(sm1);
+ t.reset(); t.start();
+ for (int k=0; k<nentries; ++k)
+ (*set1)(internal::random<int>(0,rows-1),internal::random<int>(0,cols-1)) += 1;
+ t.stop();
+ std::cout << "std::map => \t" << t.value()-rtime
+ << " nnz=" << set1->nonZeros() << std::flush;
+
+ // getchar();
+
+ t.reset(); t.start(); delete set1; t.stop();
+ std::cout << " back: \t" << t.value() << "\n";
+}
+
+int main(int argc, char *argv[])
+{
+ int rows = SIZE;
+ int cols = SIZE;
+ float density = DENSITY;
+
+ EigenSparseMatrix sm1(rows,cols), sm2(rows,cols);
+
+
+ nentries = rows*cols*density;
+ std::cout << "n = " << nentries << "\n";
+ int dummy;
+ BenchTimer t;
+
+ t.reset(); t.start();
+ for (int k=0; k<nentries; ++k)
+ dummy = internal::random<int>(0,rows-1) + internal::random<int>(0,cols-1);
+ t.stop();
+ rtime = t.value();
+ std::cout << "rtime = " << rtime << " (" << dummy << ")\n\n";
+ const int Bits = 6;
+ for (;;)
+ {
+ dostuff<RandomSetter<EigenSparseMatrix,StdMapTraits,Bits> >("std::map ", sm1);
+ dostuff<RandomSetter<EigenSparseMatrix,GnuHashMapTraits,Bits> >("gnu::hash_map", sm1);
+ dostuff<RandomSetter<EigenSparseMatrix,GoogleDenseHashMapTraits,Bits> >("google::dense", sm1);
+ dostuff<RandomSetter<EigenSparseMatrix,GoogleSparseHashMapTraits,Bits> >("google::sparse", sm1);
+
+// {
+// RandomSetter<EigenSparseMatrix,GnuHashMapTraits,Bits> set1(sm1);
+// t.reset(); t.start();
+// for (int k=0; k<n; ++k)
+// set1(internal::random<int>(0,rows-1),internal::random<int>(0,cols-1)) += 1;
+// t.stop();
+// std::cout << "gnu::hash_map => \t" << t.value()-rtime
+// << " nnz=" << set1.nonZeros() << "\n";getchar();
+// }
+// {
+// RandomSetter<EigenSparseMatrix,GoogleDenseHashMapTraits,Bits> set1(sm1);
+// t.reset(); t.start();
+// for (int k=0; k<n; ++k)
+// set1(internal::random<int>(0,rows-1),internal::random<int>(0,cols-1)) += 1;
+// t.stop();
+// std::cout << "google::dense => \t" << t.value()-rtime
+// << " nnz=" << set1.nonZeros() << "\n";getchar();
+// }
+// {
+// RandomSetter<EigenSparseMatrix,GoogleSparseHashMapTraits,Bits> set1(sm1);
+// t.reset(); t.start();
+// for (int k=0; k<n; ++k)
+// set1(internal::random<int>(0,rows-1),internal::random<int>(0,cols-1)) += 1;
+// t.stop();
+// std::cout << "google::sparse => \t" << t.value()-rtime
+// << " nnz=" << set1.nonZeros() << "\n";getchar();
+// }
+ std::cout << "\n\n";
+ }
+
+ return 0;
+}
+
diff --git a/bench/sparse_setter.cpp b/bench/sparse_setter.cpp
new file mode 100644
index 0000000..a9f0b11
--- /dev/null
+++ b/bench/sparse_setter.cpp
@@ -0,0 +1,485 @@
+
+//g++ -O3 -g0 -DNDEBUG sparse_product.cpp -I.. -I/home/gael/Coding/LinearAlgebra/mtl4/ -DDENSITY=0.005 -DSIZE=10000 && ./a.out
+//g++ -O3 -g0 -DNDEBUG sparse_product.cpp -I.. -I/home/gael/Coding/LinearAlgebra/mtl4/ -DDENSITY=0.05 -DSIZE=2000 && ./a.out
+// -DNOGMM -DNOMTL -DCSPARSE
+// -I /home/gael/Coding/LinearAlgebra/CSparse/Include/ /home/gael/Coding/LinearAlgebra/CSparse/Lib/libcsparse.a
+#ifndef SIZE
+#define SIZE 100000
+#endif
+
+#ifndef NBPERROW
+#define NBPERROW 24
+#endif
+
+#ifndef REPEAT
+#define REPEAT 2
+#endif
+
+#ifndef NBTRIES
+#define NBTRIES 2
+#endif
+
+#ifndef KK
+#define KK 10
+#endif
+
+#ifndef NOGOOGLE
+#define EIGEN_GOOGLEHASH_SUPPORT
+#include <google/sparse_hash_map>
+#endif
+
+#include "BenchSparseUtil.h"
+
+#define CHECK_MEM
+// #define CHECK_MEM std/**/::cout << "check mem\n"; getchar();
+
+#define BENCH(X) \
+ timer.reset(); \
+ for (int _j=0; _j<NBTRIES; ++_j) { \
+ timer.start(); \
+ for (int _k=0; _k<REPEAT; ++_k) { \
+ X \
+ } timer.stop(); }
+
+typedef std::vector<Vector2i> Coordinates;
+typedef std::vector<float> Values;
+
+EIGEN_DONT_INLINE Scalar* setinnerrand_eigen(const Coordinates& coords, const Values& vals);
+EIGEN_DONT_INLINE Scalar* setrand_eigen_dynamic(const Coordinates& coords, const Values& vals);
+EIGEN_DONT_INLINE Scalar* setrand_eigen_compact(const Coordinates& coords, const Values& vals);
+EIGEN_DONT_INLINE Scalar* setrand_eigen_sumeq(const Coordinates& coords, const Values& vals);
+EIGEN_DONT_INLINE Scalar* setrand_eigen_gnu_hash(const Coordinates& coords, const Values& vals);
+EIGEN_DONT_INLINE Scalar* setrand_eigen_google_dense(const Coordinates& coords, const Values& vals);
+EIGEN_DONT_INLINE Scalar* setrand_eigen_google_sparse(const Coordinates& coords, const Values& vals);
+EIGEN_DONT_INLINE Scalar* setrand_scipy(const Coordinates& coords, const Values& vals);
+EIGEN_DONT_INLINE Scalar* setrand_ublas_mapped(const Coordinates& coords, const Values& vals);
+EIGEN_DONT_INLINE Scalar* setrand_ublas_coord(const Coordinates& coords, const Values& vals);
+EIGEN_DONT_INLINE Scalar* setrand_ublas_compressed(const Coordinates& coords, const Values& vals);
+EIGEN_DONT_INLINE Scalar* setrand_ublas_genvec(const Coordinates& coords, const Values& vals);
+EIGEN_DONT_INLINE Scalar* setrand_mtl(const Coordinates& coords, const Values& vals);
+
+int main(int argc, char *argv[])
+{
+ int rows = SIZE;
+ int cols = SIZE;
+ bool fullyrand = true;
+
+ BenchTimer timer;
+ Coordinates coords;
+ Values values;
+ if(fullyrand)
+ {
+ Coordinates pool;
+ pool.reserve(cols*NBPERROW);
+ std::cerr << "fill pool" << "\n";
+ for (int i=0; i<cols*NBPERROW; )
+ {
+// DynamicSparseMatrix<int> stencil(SIZE,SIZE);
+ Vector2i ij(internal::random<int>(0,rows-1),internal::random<int>(0,cols-1));
+// if(stencil.coeffRef(ij.x(), ij.y())==0)
+ {
+// stencil.coeffRef(ij.x(), ij.y()) = 1;
+ pool.push_back(ij);
+
+ }
+ ++i;
+ }
+ std::cerr << "pool ok" << "\n";
+ int n = cols*NBPERROW*KK;
+ coords.reserve(n);
+ values.reserve(n);
+ for (int i=0; i<n; ++i)
+ {
+ int i = internal::random<int>(0,pool.size());
+ coords.push_back(pool[i]);
+ values.push_back(internal::random<Scalar>());
+ }
+ }
+ else
+ {
+ for (int j=0; j<cols; ++j)
+ for (int i=0; i<NBPERROW; ++i)
+ {
+ coords.push_back(Vector2i(internal::random<int>(0,rows-1),j));
+ values.push_back(internal::random<Scalar>());
+ }
+ }
+ std::cout << "nnz = " << coords.size() << "\n";
+ CHECK_MEM
+
+ // dense matrices
+ #ifdef DENSEMATRIX
+ {
+ BENCH(setrand_eigen_dense(coords,values);)
+ std::cout << "Eigen Dense\t" << timer.value() << "\n";
+ }
+ #endif
+
+ // eigen sparse matrices
+// if (!fullyrand)
+// {
+// BENCH(setinnerrand_eigen(coords,values);)
+// std::cout << "Eigen fillrand\t" << timer.value() << "\n";
+// }
+ {
+ BENCH(setrand_eigen_dynamic(coords,values);)
+ std::cout << "Eigen dynamic\t" << timer.value() << "\n";
+ }
+// {
+// BENCH(setrand_eigen_compact(coords,values);)
+// std::cout << "Eigen compact\t" << timer.value() << "\n";
+// }
+ {
+ BENCH(setrand_eigen_sumeq(coords,values);)
+ std::cout << "Eigen sumeq\t" << timer.value() << "\n";
+ }
+ {
+// BENCH(setrand_eigen_gnu_hash(coords,values);)
+// std::cout << "Eigen std::map\t" << timer.value() << "\n";
+ }
+ {
+ BENCH(setrand_scipy(coords,values);)
+ std::cout << "scipy\t" << timer.value() << "\n";
+ }
+ #ifndef NOGOOGLE
+ {
+ BENCH(setrand_eigen_google_dense(coords,values);)
+ std::cout << "Eigen google dense\t" << timer.value() << "\n";
+ }
+ {
+ BENCH(setrand_eigen_google_sparse(coords,values);)
+ std::cout << "Eigen google sparse\t" << timer.value() << "\n";
+ }
+ #endif
+
+ #ifndef NOUBLAS
+ {
+// BENCH(setrand_ublas_mapped(coords,values);)
+// std::cout << "ublas mapped\t" << timer.value() << "\n";
+ }
+ {
+ BENCH(setrand_ublas_genvec(coords,values);)
+ std::cout << "ublas vecofvec\t" << timer.value() << "\n";
+ }
+ /*{
+ timer.reset();
+ timer.start();
+ for (int k=0; k<REPEAT; ++k)
+ setrand_ublas_compressed(coords,values);
+ timer.stop();
+ std::cout << "ublas comp\t" << timer.value() << "\n";
+ }
+ {
+ timer.reset();
+ timer.start();
+ for (int k=0; k<REPEAT; ++k)
+ setrand_ublas_coord(coords,values);
+ timer.stop();
+ std::cout << "ublas coord\t" << timer.value() << "\n";
+ }*/
+ #endif
+
+
+ // MTL4
+ #ifndef NOMTL
+ {
+ BENCH(setrand_mtl(coords,values));
+ std::cout << "MTL\t" << timer.value() << "\n";
+ }
+ #endif
+
+ return 0;
+}
+
+EIGEN_DONT_INLINE Scalar* setinnerrand_eigen(const Coordinates& coords, const Values& vals)
+{
+ using namespace Eigen;
+ SparseMatrix<Scalar> mat(SIZE,SIZE);
+ //mat.startFill(2000000/*coords.size()*/);
+ for (int i=0; i<coords.size(); ++i)
+ {
+ mat.insert(coords[i].x(), coords[i].y()) = vals[i];
+ }
+ mat.finalize();
+ CHECK_MEM;
+ return 0;
+}
+
+EIGEN_DONT_INLINE Scalar* setrand_eigen_dynamic(const Coordinates& coords, const Values& vals)
+{
+ using namespace Eigen;
+ DynamicSparseMatrix<Scalar> mat(SIZE,SIZE);
+ mat.reserve(coords.size()/10);
+ for (int i=0; i<coords.size(); ++i)
+ {
+ mat.coeffRef(coords[i].x(), coords[i].y()) += vals[i];
+ }
+ mat.finalize();
+ CHECK_MEM;
+ return &mat.coeffRef(coords[0].x(), coords[0].y());
+}
+
+EIGEN_DONT_INLINE Scalar* setrand_eigen_sumeq(const Coordinates& coords, const Values& vals)
+{
+ using namespace Eigen;
+ int n = coords.size()/KK;
+ DynamicSparseMatrix<Scalar> mat(SIZE,SIZE);
+ for (int j=0; j<KK; ++j)
+ {
+ DynamicSparseMatrix<Scalar> aux(SIZE,SIZE);
+ mat.reserve(n);
+ for (int i=j*n; i<(j+1)*n; ++i)
+ {
+ aux.insert(coords[i].x(), coords[i].y()) += vals[i];
+ }
+ aux.finalize();
+ mat += aux;
+ }
+ return &mat.coeffRef(coords[0].x(), coords[0].y());
+}
+
+EIGEN_DONT_INLINE Scalar* setrand_eigen_compact(const Coordinates& coords, const Values& vals)
+{
+ using namespace Eigen;
+ DynamicSparseMatrix<Scalar> setter(SIZE,SIZE);
+ setter.reserve(coords.size()/10);
+ for (int i=0; i<coords.size(); ++i)
+ {
+ setter.coeffRef(coords[i].x(), coords[i].y()) += vals[i];
+ }
+ SparseMatrix<Scalar> mat = setter;
+ CHECK_MEM;
+ return &mat.coeffRef(coords[0].x(), coords[0].y());
+}
+
+EIGEN_DONT_INLINE Scalar* setrand_eigen_gnu_hash(const Coordinates& coords, const Values& vals)
+{
+ using namespace Eigen;
+ SparseMatrix<Scalar> mat(SIZE,SIZE);
+ {
+ RandomSetter<SparseMatrix<Scalar>, StdMapTraits > setter(mat);
+ for (int i=0; i<coords.size(); ++i)
+ {
+ setter(coords[i].x(), coords[i].y()) += vals[i];
+ }
+ CHECK_MEM;
+ }
+ return &mat.coeffRef(coords[0].x(), coords[0].y());
+}
+
+#ifndef NOGOOGLE
+EIGEN_DONT_INLINE Scalar* setrand_eigen_google_dense(const Coordinates& coords, const Values& vals)
+{
+ using namespace Eigen;
+ SparseMatrix<Scalar> mat(SIZE,SIZE);
+ {
+ RandomSetter<SparseMatrix<Scalar>, GoogleDenseHashMapTraits> setter(mat);
+ for (int i=0; i<coords.size(); ++i)
+ setter(coords[i].x(), coords[i].y()) += vals[i];
+ CHECK_MEM;
+ }
+ return &mat.coeffRef(coords[0].x(), coords[0].y());
+}
+
+EIGEN_DONT_INLINE Scalar* setrand_eigen_google_sparse(const Coordinates& coords, const Values& vals)
+{
+ using namespace Eigen;
+ SparseMatrix<Scalar> mat(SIZE,SIZE);
+ {
+ RandomSetter<SparseMatrix<Scalar>, GoogleSparseHashMapTraits> setter(mat);
+ for (int i=0; i<coords.size(); ++i)
+ setter(coords[i].x(), coords[i].y()) += vals[i];
+ CHECK_MEM;
+ }
+ return &mat.coeffRef(coords[0].x(), coords[0].y());
+}
+#endif
+
+
+template <class T>
+void coo_tocsr(const int n_row,
+ const int n_col,
+ const int nnz,
+ const Coordinates Aij,
+ const Values Ax,
+ int Bp[],
+ int Bj[],
+ T Bx[])
+{
+ //compute number of non-zero entries per row of A coo_tocsr
+ std::fill(Bp, Bp + n_row, 0);
+
+ for (int n = 0; n < nnz; n++){
+ Bp[Aij[n].x()]++;
+ }
+
+ //cumsum the nnz per row to get Bp[]
+ for(int i = 0, cumsum = 0; i < n_row; i++){
+ int temp = Bp[i];
+ Bp[i] = cumsum;
+ cumsum += temp;
+ }
+ Bp[n_row] = nnz;
+
+ //write Aj,Ax into Bj,Bx
+ for(int n = 0; n < nnz; n++){
+ int row = Aij[n].x();
+ int dest = Bp[row];
+
+ Bj[dest] = Aij[n].y();
+ Bx[dest] = Ax[n];
+
+ Bp[row]++;
+ }
+
+ for(int i = 0, last = 0; i <= n_row; i++){
+ int temp = Bp[i];
+ Bp[i] = last;
+ last = temp;
+ }
+
+ //now Bp,Bj,Bx form a CSR representation (with possible duplicates)
+}
+
+template< class T1, class T2 >
+bool kv_pair_less(const std::pair<T1,T2>& x, const std::pair<T1,T2>& y){
+ return x.first < y.first;
+}
+
+
+template<class I, class T>
+void csr_sort_indices(const I n_row,
+ const I Ap[],
+ I Aj[],
+ T Ax[])
+{
+ std::vector< std::pair<I,T> > temp;
+
+ for(I i = 0; i < n_row; i++){
+ I row_start = Ap[i];
+ I row_end = Ap[i+1];
+
+ temp.clear();
+
+ for(I jj = row_start; jj < row_end; jj++){
+ temp.push_back(std::make_pair(Aj[jj],Ax[jj]));
+ }
+
+ std::sort(temp.begin(),temp.end(),kv_pair_less<I,T>);
+
+ for(I jj = row_start, n = 0; jj < row_end; jj++, n++){
+ Aj[jj] = temp[n].first;
+ Ax[jj] = temp[n].second;
+ }
+ }
+}
+
+template <class I, class T>
+void csr_sum_duplicates(const I n_row,
+ const I n_col,
+ I Ap[],
+ I Aj[],
+ T Ax[])
+{
+ I nnz = 0;
+ I row_end = 0;
+ for(I i = 0; i < n_row; i++){
+ I jj = row_end;
+ row_end = Ap[i+1];
+ while( jj < row_end ){
+ I j = Aj[jj];
+ T x = Ax[jj];
+ jj++;
+ while( jj < row_end && Aj[jj] == j ){
+ x += Ax[jj];
+ jj++;
+ }
+ Aj[nnz] = j;
+ Ax[nnz] = x;
+ nnz++;
+ }
+ Ap[i+1] = nnz;
+ }
+}
+
+EIGEN_DONT_INLINE Scalar* setrand_scipy(const Coordinates& coords, const Values& vals)
+{
+ using namespace Eigen;
+ SparseMatrix<Scalar> mat(SIZE,SIZE);
+ mat.resizeNonZeros(coords.size());
+// std::cerr << "setrand_scipy...\n";
+ coo_tocsr<Scalar>(SIZE,SIZE, coords.size(), coords, vals, mat._outerIndexPtr(), mat._innerIndexPtr(), mat._valuePtr());
+// std::cerr << "coo_tocsr ok\n";
+
+ csr_sort_indices(SIZE, mat._outerIndexPtr(), mat._innerIndexPtr(), mat._valuePtr());
+
+ csr_sum_duplicates(SIZE, SIZE, mat._outerIndexPtr(), mat._innerIndexPtr(), mat._valuePtr());
+
+ mat.resizeNonZeros(mat._outerIndexPtr()[SIZE]);
+
+ return &mat.coeffRef(coords[0].x(), coords[0].y());
+}
+
+
+#ifndef NOUBLAS
+EIGEN_DONT_INLINE Scalar* setrand_ublas_mapped(const Coordinates& coords, const Values& vals)
+{
+ using namespace boost;
+ using namespace boost::numeric;
+ using namespace boost::numeric::ublas;
+ mapped_matrix<Scalar> aux(SIZE,SIZE);
+ for (int i=0; i<coords.size(); ++i)
+ {
+ aux(coords[i].x(), coords[i].y()) += vals[i];
+ }
+ CHECK_MEM;
+ compressed_matrix<Scalar> mat(aux);
+ return 0;// &mat(coords[0].x(), coords[0].y());
+}
+/*EIGEN_DONT_INLINE Scalar* setrand_ublas_coord(const Coordinates& coords, const Values& vals)
+{
+ using namespace boost;
+ using namespace boost::numeric;
+ using namespace boost::numeric::ublas;
+ coordinate_matrix<Scalar> aux(SIZE,SIZE);
+ for (int i=0; i<coords.size(); ++i)
+ {
+ aux(coords[i].x(), coords[i].y()) = vals[i];
+ }
+ compressed_matrix<Scalar> mat(aux);
+ return 0;//&mat(coords[0].x(), coords[0].y());
+}
+EIGEN_DONT_INLINE Scalar* setrand_ublas_compressed(const Coordinates& coords, const Values& vals)
+{
+ using namespace boost;
+ using namespace boost::numeric;
+ using namespace boost::numeric::ublas;
+ compressed_matrix<Scalar> mat(SIZE,SIZE);
+ for (int i=0; i<coords.size(); ++i)
+ {
+ mat(coords[i].x(), coords[i].y()) = vals[i];
+ }
+ return 0;//&mat(coords[0].x(), coords[0].y());
+}*/
+EIGEN_DONT_INLINE Scalar* setrand_ublas_genvec(const Coordinates& coords, const Values& vals)
+{
+ using namespace boost;
+ using namespace boost::numeric;
+ using namespace boost::numeric::ublas;
+
+// ublas::vector<coordinate_vector<Scalar> > foo;
+ generalized_vector_of_vector<Scalar, row_major, ublas::vector<coordinate_vector<Scalar> > > aux(SIZE,SIZE);
+ for (int i=0; i<coords.size(); ++i)
+ {
+ aux(coords[i].x(), coords[i].y()) += vals[i];
+ }
+ CHECK_MEM;
+ compressed_matrix<Scalar,row_major> mat(aux);
+ return 0;//&mat(coords[0].x(), coords[0].y());
+}
+#endif
+
+#ifndef NOMTL
+EIGEN_DONT_INLINE void setrand_mtl(const Coordinates& coords, const Values& vals);
+#endif
+
diff --git a/bench/sparse_transpose.cpp b/bench/sparse_transpose.cpp
new file mode 100644
index 0000000..c9aacf5
--- /dev/null
+++ b/bench/sparse_transpose.cpp
@@ -0,0 +1,104 @@
+
+//g++ -O3 -g0 -DNDEBUG sparse_transpose.cpp -I.. -I/home/gael/Coding/LinearAlgebra/mtl4/ -DDENSITY=0.005 -DSIZE=10000 && ./a.out
+// -DNOGMM -DNOMTL
+// -DCSPARSE -I /home/gael/Coding/LinearAlgebra/CSparse/Include/ /home/gael/Coding/LinearAlgebra/CSparse/Lib/libcsparse.a
+
+#ifndef SIZE
+#define SIZE 10000
+#endif
+
+#ifndef DENSITY
+#define DENSITY 0.01
+#endif
+
+#ifndef REPEAT
+#define REPEAT 1
+#endif
+
+#include "BenchSparseUtil.h"
+
+#ifndef MINDENSITY
+#define MINDENSITY 0.0004
+#endif
+
+#ifndef NBTRIES
+#define NBTRIES 10
+#endif
+
+#define BENCH(X) \
+ timer.reset(); \
+ for (int _j=0; _j<NBTRIES; ++_j) { \
+ timer.start(); \
+ for (int _k=0; _k<REPEAT; ++_k) { \
+ X \
+ } timer.stop(); }
+
+int main(int argc, char *argv[])
+{
+ int rows = SIZE;
+ int cols = SIZE;
+ float density = DENSITY;
+
+ EigenSparseMatrix sm1(rows,cols), sm3(rows,cols);
+
+ BenchTimer timer;
+ for (float density = DENSITY; density>=MINDENSITY; density*=0.5)
+ {
+ fillMatrix(density, rows, cols, sm1);
+
+ // dense matrices
+ #ifdef DENSEMATRIX
+ {
+ DenseMatrix m1(rows,cols), m3(rows,cols);
+ eiToDense(sm1, m1);
+ BENCH(for (int k=0; k<REPEAT; ++k) m3 = m1.transpose();)
+ std::cout << " Eigen dense:\t" << timer.value() << endl;
+ }
+ #endif
+
+ std::cout << "Non zeros: " << sm1.nonZeros()/float(sm1.rows()*sm1.cols())*100 << "%\n";
+
+ // eigen sparse matrices
+ {
+ BENCH(for (int k=0; k<REPEAT; ++k) sm3 = sm1.transpose();)
+ std::cout << " Eigen:\t" << timer.value() << endl;
+ }
+
+ // CSparse
+ #ifdef CSPARSE
+ {
+ cs *m1, *m3;
+ eiToCSparse(sm1, m1);
+
+ BENCH(for (int k=0; k<REPEAT; ++k) { m3 = cs_transpose(m1,1); cs_spfree(m3);})
+ std::cout << " CSparse:\t" << timer.value() << endl;
+ }
+ #endif
+
+ // GMM++
+ #ifndef NOGMM
+ {
+ GmmDynSparse gmmT3(rows,cols);
+ GmmSparse m1(rows,cols), m3(rows,cols);
+ eiToGmm(sm1, m1);
+ BENCH(for (int k=0; k<REPEAT; ++k) gmm::copy(gmm::transposed(m1),m3);)
+ std::cout << " GMM:\t\t" << timer.value() << endl;
+ }
+ #endif
+
+ // MTL4
+ #ifndef NOMTL
+ {
+ MtlSparse m1(rows,cols), m3(rows,cols);
+ eiToMtl(sm1, m1);
+ BENCH(for (int k=0; k<REPEAT; ++k) m3 = trans(m1);)
+ std::cout << " MTL4:\t\t" << timer.value() << endl;
+ }
+ #endif
+
+ std::cout << "\n\n";
+ }
+
+ return 0;
+}
+
diff --git a/bench/sparse_trisolver.cpp b/bench/sparse_trisolver.cpp
new file mode 100644
index 0000000..13f4f0a
--- /dev/null
+++ b/bench/sparse_trisolver.cpp
@@ -0,0 +1,220 @@
+
+//g++ -O3 -g0 -DNDEBUG sparse_product.cpp -I.. -I/home/gael/Coding/LinearAlgebra/mtl4/ -DDENSITY=0.005 -DSIZE=10000 && ./a.out
+//g++ -O3 -g0 -DNDEBUG sparse_product.cpp -I.. -I/home/gael/Coding/LinearAlgebra/mtl4/ -DDENSITY=0.05 -DSIZE=2000 && ./a.out
+// -DNOGMM -DNOMTL
+// -I /home/gael/Coding/LinearAlgebra/CSparse/Include/ /home/gael/Coding/LinearAlgebra/CSparse/Lib/libcsparse.a
+
+#ifndef SIZE
+#define SIZE 10000
+#endif
+
+#ifndef DENSITY
+#define DENSITY 0.01
+#endif
+
+#ifndef REPEAT
+#define REPEAT 1
+#endif
+
+#include "BenchSparseUtil.h"
+
+#ifndef MINDENSITY
+#define MINDENSITY 0.0004
+#endif
+
+#ifndef NBTRIES
+#define NBTRIES 10
+#endif
+
+#define BENCH(X) \
+ timer.reset(); \
+ for (int _j=0; _j<NBTRIES; ++_j) { \
+ timer.start(); \
+ for (int _k=0; _k<REPEAT; ++_k) { \
+ X \
+ } timer.stop(); }
+
+typedef SparseMatrix<Scalar,UpperTriangular> EigenSparseTriMatrix;
+typedef SparseMatrix<Scalar,RowMajorBit|UpperTriangular> EigenSparseTriMatrixRow;
+
+void fillMatrix(float density, int rows, int cols, EigenSparseTriMatrix& dst)
+{
+ dst.startFill(rows*cols*density);
+ for(int j = 0; j < cols; j++)
+ {
+ for(int i = 0; i < j; i++)
+ {
+ Scalar v = (internal::random<float>(0,1) < density) ? internal::random<Scalar>() : 0;
+ if (v!=0)
+ dst.fill(i,j) = v;
+ }
+ dst.fill(j,j) = internal::random<Scalar>();
+ }
+ dst.endFill();
+}
+
+int main(int argc, char *argv[])
+{
+ int rows = SIZE;
+ int cols = SIZE;
+ float density = DENSITY;
+ BenchTimer timer;
+ #if 1
+ EigenSparseTriMatrix sm1(rows,cols);
+ typedef Matrix<Scalar,Dynamic,1> DenseVector;
+ DenseVector b = DenseVector::Random(cols);
+ DenseVector x = DenseVector::Random(cols);
+
+ bool densedone = false;
+
+ for (float density = DENSITY; density>=MINDENSITY; density*=0.5)
+ {
+ EigenSparseTriMatrix sm1(rows, cols);
+ fillMatrix(density, rows, cols, sm1);
+
+ // dense matrices
+ #ifdef DENSEMATRIX
+ if (!densedone)
+ {
+ densedone = true;
+ std::cout << "Eigen Dense\t" << density*100 << "%\n";
+ DenseMatrix m1(rows,cols);
+ Matrix<Scalar,Dynamic,Dynamic,Dynamic,Dynamic,RowMajorBit> m2(rows,cols);
+ eiToDense(sm1, m1);
+ m2 = m1;
+
+ BENCH(x = m1.marked<UpperTriangular>().solveTriangular(b);)
+ std::cout << " colmajor^-1 * b:\t" << timer.value() << endl;
+// std::cerr << x.transpose() << "\n";
+
+ BENCH(x = m2.marked<UpperTriangular>().solveTriangular(b);)
+ std::cout << " rowmajor^-1 * b:\t" << timer.value() << endl;
+// std::cerr << x.transpose() << "\n";
+ }
+ #endif
+
+ // eigen sparse matrices
+ {
+ std::cout << "Eigen sparse\t" << density*100 << "%\n";
+ EigenSparseTriMatrixRow sm2 = sm1;
+
+ BENCH(x = sm1.solveTriangular(b);)
+ std::cout << " colmajor^-1 * b:\t" << timer.value() << endl;
+// std::cerr << x.transpose() << "\n";
+
+ BENCH(x = sm2.solveTriangular(b);)
+ std::cout << " rowmajor^-1 * b:\t" << timer.value() << endl;
+// std::cerr << x.transpose() << "\n";
+
+// x = b;
+// BENCH(sm1.inverseProductInPlace(x);)
+// std::cout << " colmajor^-1 * b:\t" << timer.value() << " (inplace)" << endl;
+// std::cerr << x.transpose() << "\n";
+//
+// x = b;
+// BENCH(sm2.inverseProductInPlace(x);)
+// std::cout << " rowmajor^-1 * b:\t" << timer.value() << " (inplace)" << endl;
+// std::cerr << x.transpose() << "\n";
+ }
+
+
+
+ // CSparse
+ #ifdef CSPARSE
+ {
+ std::cout << "CSparse \t" << density*100 << "%\n";
+ cs *m1;
+ eiToCSparse(sm1, m1);
+
+ BENCH(x = b; if (!cs_lsolve (m1, x.data())){std::cerr << "cs_lsolve failed\n"; break;}; )
+ std::cout << " colmajor^-1 * b:\t" << timer.value() << endl;
+ }
+ #endif
+
+ // GMM++
+ #ifndef NOGMM
+ {
+ std::cout << "GMM++ sparse\t" << density*100 << "%\n";
+ GmmSparse m1(rows,cols);
+ gmm::csr_matrix<Scalar> m2;
+ eiToGmm(sm1, m1);
+ gmm::copy(m1,m2);
+ std::vector<Scalar> gmmX(cols), gmmB(cols);
+ Map<Matrix<Scalar,Dynamic,1> >(&gmmX[0], cols) = x;
+ Map<Matrix<Scalar,Dynamic,1> >(&gmmB[0], cols) = b;
+
+ gmmX = gmmB;
+ BENCH(gmm::upper_tri_solve(m1, gmmX, false);)
+ std::cout << " colmajor^-1 * b:\t" << timer.value() << endl;
+// std::cerr << Map<Matrix<Scalar,Dynamic,1> >(&gmmX[0], cols).transpose() << "\n";
+
+ gmmX = gmmB;
+ BENCH(gmm::upper_tri_solve(m2, gmmX, false);)
+ timer.stop();
+ std::cout << " rowmajor^-1 * b:\t" << timer.value() << endl;
+// std::cerr << Map<Matrix<Scalar,Dynamic,1> >(&gmmX[0], cols).transpose() << "\n";
+ }
+ #endif
+
+ // MTL4
+ #ifndef NOMTL
+ {
+ std::cout << "MTL4\t" << density*100 << "%\n";
+ MtlSparse m1(rows,cols);
+ MtlSparseRowMajor m2(rows,cols);
+ eiToMtl(sm1, m1);
+ m2 = m1;
+ mtl::dense_vector<Scalar> x(rows, 1.0);
+ mtl::dense_vector<Scalar> b(rows, 1.0);
+
+ BENCH(x = mtl::upper_trisolve(m1,b);)
+ std::cout << " colmajor^-1 * b:\t" << timer.value() << endl;
+// std::cerr << x << "\n";
+
+ BENCH(x = mtl::upper_trisolve(m2,b);)
+ std::cout << " rowmajor^-1 * b:\t" << timer.value() << endl;
+// std::cerr << x << "\n";
+ }
+ #endif
+
+
+ std::cout << "\n\n";
+ }
+ #endif
+
+ #if 0
+ // bench small matrices (in-place versus return bye value)
+ {
+ timer.reset();
+ for (int _j=0; _j<10; ++_j) {
+ Matrix4f m = Matrix4f::Random();
+ Vector4f b = Vector4f::Random();
+ Vector4f x = Vector4f::Random();
+ timer.start();
+ for (int _k=0; _k<1000000; ++_k) {
+ b = m.inverseProduct(b);
+ }
+ timer.stop();
+ }
+ std::cout << "4x4 :\t" << timer.value() << endl;
+ }
+
+ {
+ timer.reset();
+ for (int _j=0; _j<10; ++_j) {
+ Matrix4f m = Matrix4f::Random();
+ Vector4f b = Vector4f::Random();
+ Vector4f x = Vector4f::Random();
+ timer.start();
+ for (int _k=0; _k<1000000; ++_k) {
+ m.inverseProductInPlace(x);
+ }
+ timer.stop();
+ }
+ std::cout << "4x4 IP :\t" << timer.value() << endl;
+ }
+ #endif
+
+ return 0;
+}
+
diff --git a/bench/spbench/CMakeLists.txt b/bench/spbench/CMakeLists.txt
new file mode 100644
index 0000000..75c36b0
--- /dev/null
+++ b/bench/spbench/CMakeLists.txt
@@ -0,0 +1,92 @@
+
+
+set(BLAS_FOUND EIGEN_BUILD_BLAS)
+set(LAPACK_FOUND EIGEN_BUILD_LAPACK)
+set(BLAS_LIBRARIES eigen_blas_static)
+set(LAPACK_LIBRARIES eigen_lapack_static)
+
+set(SPARSE_LIBS "")
+
+# find_library(PARDISO_LIBRARIES pardiso412-GNU450-X86-64)
+# if(PARDISO_LIBRARIES)
+# add_definitions("-DEIGEN_PARDISO_SUPPORT")
+# set(SPARSE_LIBS ${SPARSE_LIBS} ${PARDISO_LIBRARIES})
+# endif()
+
+find_package(CHOLMOD)
+if(CHOLMOD_FOUND AND BLAS_FOUND AND LAPACK_FOUND)
+ add_definitions("-DEIGEN_CHOLMOD_SUPPORT")
+ include_directories(${CHOLMOD_INCLUDES})
+ set(SPARSE_LIBS ${SPARSE_LIBS} ${CHOLMOD_LIBRARIES} ${BLAS_LIBRARIES} ${LAPACK_LIBRARIES})
+ set(CHOLMOD_ALL_LIBS ${CHOLMOD_LIBRARIES} ${BLAS_LIBRARIES} ${LAPACK_LIBRARIES})
+endif()
+
+find_package(UMFPACK)
+if(UMFPACK_FOUND AND BLAS_FOUND)
+ add_definitions("-DEIGEN_UMFPACK_SUPPORT")
+ include_directories(${UMFPACK_INCLUDES})
+ set(SPARSE_LIBS ${SPARSE_LIBS} ${UMFPACK_LIBRARIES} ${BLAS_LIBRARIES})
+ set(UMFPACK_ALL_LIBS ${UMFPACK_LIBRARIES} ${BLAS_LIBRARIES})
+endif()
+
+find_package(KLU)
+if(KLU_FOUND)
+ add_definitions("-DEIGEN_KLU_SUPPORT")
+ include_directories(${KLU_INCLUDES})
+ set(SPARSE_LIBS ${SPARSE_LIBS} ${KLU_LIBRARIES})
+endif()
+
+find_package(SuperLU 4.0)
+if(SuperLU_FOUND AND BLAS_FOUND)
+ add_definitions("-DEIGEN_SUPERLU_SUPPORT")
+ include_directories(${SUPERLU_INCLUDES})
+ set(SPARSE_LIBS ${SPARSE_LIBS} ${SUPERLU_LIBRARIES} ${BLAS_LIBRARIES})
+ set(SUPERLU_ALL_LIBS ${SUPERLU_LIBRARIES} ${BLAS_LIBRARIES})
+endif()
+
+
+find_package(PASTIX QUIET COMPONENTS METIS SCOTCH)
+# check that the PASTIX found is a version without MPI
+find_path(PASTIX_pastix_nompi.h_INCLUDE_DIRS
+ NAMES pastix_nompi.h
+ HINTS ${PASTIX_INCLUDE_DIRS}
+)
+if (NOT PASTIX_pastix_nompi.h_INCLUDE_DIRS)
+ message(STATUS "A version of Pastix has been found but pastix_nompi.h does not exist in the include directory."
+ " Because Eigen tests require a version without MPI, we disable the Pastix backend.")
+endif()
+if(PASTIX_FOUND AND PASTIX_pastix_nompi.h_INCLUDE_DIRS AND BLAS_FOUND)
+ add_definitions("-DEIGEN_PASTIX_SUPPORT")
+ include_directories(${PASTIX_INCLUDE_DIRS_DEP})
+ if(SCOTCH_FOUND)
+ include_directories(${SCOTCH_INCLUDE_DIRS})
+ set(PASTIX_LIBRARIES ${PASTIX_LIBRARIES} ${SCOTCH_LIBRARIES})
+ elseif(METIS_FOUND)
+ include_directories(${METIS_INCLUDE_DIRS})
+ set(PASTIX_LIBRARIES ${PASTIX_LIBRARIES} ${METIS_LIBRARIES})
+ endif()
+ set(SPARSE_LIBS ${SPARSE_LIBS} ${PASTIX_LIBRARIES_DEP} ${ORDERING_LIBRARIES})
+ set(PASTIX_ALL_LIBS ${PASTIX_LIBRARIES_DEP})
+endif()
+
+if(METIS_FOUND)
+ include_directories(${METIS_INCLUDE_DIRS})
+ set (SPARSE_LIBS ${SPARSE_LIBS} ${METIS_LIBRARIES})
+ add_definitions("-DEIGEN_METIS_SUPPORT")
+endif()
+
+find_library(RT_LIBRARY rt)
+if(RT_LIBRARY)
+ set(SPARSE_LIBS ${SPARSE_LIBS} ${RT_LIBRARY})
+endif()
+
+add_executable(spbenchsolver spbenchsolver.cpp)
+target_link_libraries (spbenchsolver ${SPARSE_LIBS})
+
+add_executable(spsolver sp_solver.cpp)
+target_link_libraries (spsolver ${SPARSE_LIBS})
+
+
+add_executable(test_sparseLU test_sparseLU.cpp)
+target_link_libraries (test_sparseLU ${SPARSE_LIBS})
+
diff --git a/bench/spbench/sp_solver.cpp b/bench/spbench/sp_solver.cpp
new file mode 100644
index 0000000..75821a6
--- /dev/null
+++ b/bench/spbench/sp_solver.cpp
@@ -0,0 +1,125 @@
+// Small bench routine for Eigen available in Eigen
+// (C) Desire NUENTSA WAKAM, INRIA
+
+#include <iostream>
+#include <fstream>
+#include <iomanip>
+#include <Eigen/Jacobi>
+#include <Eigen/Householder>
+#include <Eigen/IterativeLinearSolvers>
+#include <Eigen/LU>
+#include <unsupported/Eigen/SparseExtra>
+//#include <Eigen/SparseLU>
+#include <Eigen/SuperLUSupport>
+// #include <unsupported/Eigen/src/IterativeSolvers/Scaling.h>
+#include <bench/BenchTimer.h>
+#include <unsupported/Eigen/IterativeSolvers>
+using namespace std;
+using namespace Eigen;
+
+int main(int argc, char **args)
+{
+ SparseMatrix<double, ColMajor> A;
+ typedef SparseMatrix<double, ColMajor>::Index Index;
+ typedef Matrix<double, Dynamic, Dynamic> DenseMatrix;
+ typedef Matrix<double, Dynamic, 1> DenseRhs;
+ VectorXd b, x, tmp;
+ BenchTimer timer,totaltime;
+ //SparseLU<SparseMatrix<double, ColMajor> > solver;
+// SuperLU<SparseMatrix<double, ColMajor> > solver;
+ ConjugateGradient<SparseMatrix<double, ColMajor>, Lower,IncompleteCholesky<double,Lower> > solver;
+ ifstream matrix_file;
+ string line;
+ int n;
+ // Set parameters
+// solver.iparm(IPARM_THREAD_NBR) = 4;
+ /* Fill the matrix with sparse matrix stored in Matrix-Market coordinate column-oriented format */
+ if (argc < 2) assert(false && "please, give the matrix market file ");
+
+ timer.start();
+ totaltime.start();
+ loadMarket(A, args[1]);
+ cout << "End charging matrix " << endl;
+ bool iscomplex=false, isvector=false;
+ int sym;
+ getMarketHeader(args[1], sym, iscomplex, isvector);
+ if (iscomplex) { cout<< " Not for complex matrices \n"; return -1; }
+ if (isvector) { cout << "The provided file is not a matrix file\n"; return -1;}
+ if (sym != 0) { // symmetric matrices, only the lower part is stored
+ SparseMatrix<double, ColMajor> temp;
+ temp = A;
+ A = temp.selfadjointView<Lower>();
+ }
+ timer.stop();
+
+ n = A.cols();
+ // ====== TESTS FOR SPARSE TUTORIAL ======
+// cout<< "OuterSize " << A.outerSize() << " inner " << A.innerSize() << endl;
+// SparseMatrix<double, RowMajor> mat1(A);
+// SparseMatrix<double, RowMajor> mat2;
+// cout << " norm of A " << mat1.norm() << endl; ;
+// PermutationMatrix<Dynamic, Dynamic, int> perm(n);
+// perm.resize(n,1);
+// perm.indices().setLinSpaced(n, 0, n-1);
+// mat2 = perm * mat1;
+// mat.subrows();
+// mat2.resize(n,n);
+// mat2.reserve(10);
+// mat2.setConstant();
+// std::cout<< "NORM " << mat1.squaredNorm()<< endl;
+
+ cout<< "Time to load the matrix " << timer.value() <<endl;
+ /* Fill the right hand side */
+
+// solver.set_restart(374);
+ if (argc > 2)
+ loadMarketVector(b, args[2]);
+ else
+ {
+ b.resize(n);
+ tmp.resize(n);
+// tmp.setRandom();
+ for (int i = 0; i < n; i++) tmp(i) = i;
+ b = A * tmp ;
+ }
+// Scaling<SparseMatrix<double> > scal;
+// scal.computeRef(A);
+// b = scal.LeftScaling().cwiseProduct(b);
+
+ /* Compute the factorization */
+ cout<< "Starting the factorization "<< endl;
+ timer.reset();
+ timer.start();
+ cout<< "Size of Input Matrix "<< b.size()<<"\n\n";
+ cout<< "Rows and columns "<< A.rows() <<" " <<A.cols() <<"\n";
+ solver.compute(A);
+// solver.analyzePattern(A);
+// solver.factorize(A);
+ if (solver.info() != Success) {
+ std::cout<< "The solver failed \n";
+ return -1;
+ }
+ timer.stop();
+ float time_comp = timer.value();
+ cout <<" Compute Time " << time_comp<< endl;
+
+ timer.reset();
+ timer.start();
+ x = solver.solve(b);
+// x = scal.RightScaling().cwiseProduct(x);
+ timer.stop();
+ float time_solve = timer.value();
+ cout<< " Time to solve " << time_solve << endl;
+
+ /* Check the accuracy */
+ VectorXd tmp2 = b - A*x;
+ double tempNorm = tmp2.norm()/b.norm();
+ cout << "Relative norm of the computed solution : " << tempNorm <<"\n";
+// cout << "Iterations : " << solver.iterations() << "\n";
+
+ totaltime.stop();
+ cout << "Total time " << totaltime.value() << "\n";
+// std::cout<<x.transpose()<<"\n";
+
+ return 0;
+}
diff --git a/bench/spbench/spbench.dtd b/bench/spbench/spbench.dtd
new file mode 100644
index 0000000..0fb51b8
--- /dev/null
+++ b/bench/spbench/spbench.dtd
@@ -0,0 +1,31 @@
+<!ELEMENT BENCH (AVAILSOLVER+,LINEARSYSTEM+)>
+ <!ELEMENT AVAILSOLVER (SOLVER+)>
+ <!ELEMENT SOLVER (TYPE,PACKAGE)>
+ <!ELEMENT TYPE (#PCDATA)> <!-- One of LU, LLT, LDLT, ITER -->
+ <!ELEMENT PACKAGE (#PCDATA)> <!-- Derived from a library -->
+ <!ELEMENT LINEARSYSTEM (MATRIX,SOLVER_STAT+,BEST_SOLVER,GLOBAL_PARAMS*)>
+ <!ELEMENT MATRIX (NAME,SIZE,ENTRIES,PATTERN?,SYMMETRY,POSDEF?,ARITHMETIC,RHS*)>
+ <!ELEMENT NAME (#PCDATA)>
+ <!ELEMENT SIZE (#PCDATA)>
+ <!ELEMENT ENTRIES (#PCDATA)> <!-- The number of nonzeros elements -->
+ <!ELEMENT PATTERN (#PCDATA)> <!-- Is structural pattern symmetric or not -->
+ <!ELEMENT SYMMETRY (#PCDATA)> <!-- symmmetry with numerical values -->
+ <!ELEMENT POSDEF (#PCDATA)> <!-- Is the matrix positive definite or not -->
+ <!ELEMENT ARITHMETIC (#PCDATA)>
+ <!ELEMENT RHS (SOURCE)> <!-- A matrix can have one or more right hand side associated. -->
+ <!ELEMENT SOURCE (#PCDATA)> <!-- Source of the right hand side, either generated or provided -->
+ <!ELEMENT SOLVER_STAT (PARAMS*,TIME,ERROR,ITER?)>
+ <!ELEMENT PARAMS (#PCDATA)>
+ <!ELEMENT TIME (COMPUTE,SOLVE,TOTAL)>
+ <!ELEMENT COMPUTE (#PCDATA)> <!-- Time to analyze,to factorize, or to setup the preconditioner-->
+ <!ELEMENT SOLVE (#PCDATA)> <!-- Time to solve with all the available rhs -->
+ <!ELEMENT TOTAL (#PCDATA)>
+ <!ELEMENT ERROR (#PCDATA)> <!-- Either the relative error or the relative residual norm -->
+ <!ELEMENT ITER (#PCDATA)> <!-- Number of iterations -->
+ <!ELEMENT BEST_SOLVER CDATA> <!-- Id of the best solver -->
+ <!ELEMENT GLOBAL_PARAMS (#PCDATA)> <!-- Parameters shared by all solvers -->
+
+<!ATTLIST SOLVER ID CDATA #REQUIRED>
+<!ATTLIST SOLVER_STAT ID CDATA #REQUIRED>
+<!ATTLIST BEST_SOLVER ID CDATA #REQUIRED>
+<!ATTLIST RHS ID CDATA #IMPLIED>
\ No newline at end of file
diff --git a/bench/spbench/spbenchsolver.cpp b/bench/spbench/spbenchsolver.cpp
new file mode 100644
index 0000000..2a73511
--- /dev/null
+++ b/bench/spbench/spbenchsolver.cpp
@@ -0,0 +1,87 @@
+#include <bench/spbench/spbenchsolver.h>
+
+void bench_printhelp()
+{
+ cout<< " \nbenchsolver : performs a benchmark of all the solvers available in Eigen \n\n";
+ cout<< " MATRIX FOLDER : \n";
+ cout<< " The matrices for the benchmark should be collected in a folder specified with an environment variable EIGEN_MATRIXDIR \n";
+ cout<< " The matrices are stored using the matrix market coordinate format \n";
+ cout<< " The matrix and associated right-hand side (rhs) files are named respectively \n";
+ cout<< " as MatrixName.mtx and MatrixName_b.mtx. If the rhs does not exist, a random one is generated. \n";
+ cout<< " If a matrix is SPD, the matrix should be named as MatrixName_SPD.mtx \n";
+ cout<< " If a true solution exists, it should be named as MatrixName_x.mtx; \n" ;
+ cout<< " it will be used to compute the norm of the error relative to the computed solutions\n\n";
+ cout<< " OPTIONS : \n";
+ cout<< " -h or --help \n print this help and return\n\n";
+ cout<< " -d matrixdir \n Use matrixdir as the matrix folder instead of the one specified in the environment variable EIGEN_MATRIXDIR\n\n";
+ cout<< " -o outputfile.xml \n Output the statistics to a xml file \n\n";
+ cout<< " --eps <RelErr> Sets the relative tolerance for iterative solvers (default 1e-08) \n\n";
+ cout<< " --maxits <MaxIts> Sets the maximum number of iterations (default 1000) \n\n";
+
+}
+int main(int argc, char ** args)
+{
+
+ bool help = ( get_options(argc, args, "-h") || get_options(argc, args, "--help") );
+ if(help) {
+ bench_printhelp();
+ return 0;
+ }
+
+ // Get the location of the test matrices
+ string matrix_dir;
+ if (!get_options(argc, args, "-d", &matrix_dir))
+ {
+ if(getenv("EIGEN_MATRIXDIR") == NULL){
+ std::cerr << "Please, specify the location of the matrices with -d mat_folder or the environment variable EIGEN_MATRIXDIR \n";
+ std::cerr << " Run with --help to see the list of all the available options \n";
+ return -1;
+ }
+ matrix_dir = getenv("EIGEN_MATRIXDIR");
+ }
+
+ std::ofstream statbuf;
+ string statFile ;
+
+ // Get the file to write the statistics
+ bool statFileExists = get_options(argc, args, "-o", &statFile);
+ if(statFileExists)
+ {
+ statbuf.open(statFile.c_str(), std::ios::out);
+ if(statbuf.good()){
+ statFileExists = true;
+ printStatheader(statbuf);
+ statbuf.close();
+ }
+ else
+ std::cerr << "Unable to open the provided file for writing... \n";
+ }
+
+ // Get the maximum number of iterations and the tolerance
+ int maxiters = 1000;
+ double tol = 1e-08;
+ string inval;
+ if (get_options(argc, args, "--eps", &inval))
+ tol = atof(inval.c_str());
+ if(get_options(argc, args, "--maxits", &inval))
+ maxiters = atoi(inval.c_str());
+
+ string current_dir;
+ // Test the real-arithmetics matrices
+ Browse_Matrices<double>(matrix_dir, statFileExists, statFile,maxiters, tol);
+
+ // Test the complex-arithmetics matrices
+ Browse_Matrices<std::complex<double> >(matrix_dir, statFileExists, statFile, maxiters, tol);
+
+ if(statFileExists)
+ {
+ statbuf.open(statFile.c_str(), std::ios::app);
+ statbuf << "</BENCH> \n";
+ cout << "\n Output written in " << statFile << " ...\n";
+ statbuf.close();
+ }
+
+ return 0;
+}
+
+
diff --git a/bench/spbench/spbenchsolver.h b/bench/spbench/spbenchsolver.h
new file mode 100644
index 0000000..8f59d10
--- /dev/null
+++ b/bench/spbench/spbenchsolver.h
@@ -0,0 +1,573 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2012 Désiré Nuentsa-Wakam <desire.nuentsa_wakam@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+
+#include <iostream>
+#include <fstream>
+#include <Eigen/SparseCore>
+#include <bench/BenchTimer.h>
+#include <cstdlib>
+#include <string>
+#include <Eigen/Cholesky>
+#include <Eigen/Jacobi>
+#include <Eigen/Householder>
+#include <Eigen/IterativeLinearSolvers>
+#include <unsupported/Eigen/IterativeSolvers>
+#include <Eigen/LU>
+#include <unsupported/Eigen/SparseExtra>
+#include <Eigen/SparseLU>
+
+#include "spbenchstyle.h"
+
+#ifdef EIGEN_METIS_SUPPORT
+#include <Eigen/MetisSupport>
+#endif
+
+#ifdef EIGEN_CHOLMOD_SUPPORT
+#include <Eigen/CholmodSupport>
+#endif
+
+#ifdef EIGEN_UMFPACK_SUPPORT
+#include <Eigen/UmfPackSupport>
+#endif
+
+#ifdef EIGEN_KLU_SUPPORT
+#include <Eigen/KLUSupport>
+#endif
+
+#ifdef EIGEN_PARDISO_SUPPORT
+#include <Eigen/PardisoSupport>
+#endif
+
+#ifdef EIGEN_SUPERLU_SUPPORT
+#include <Eigen/SuperLUSupport>
+#endif
+
+#ifdef EIGEN_PASTIX_SUPPORT
+#include <Eigen/PaStiXSupport>
+#endif
+
+// CONSTANTS
+#define EIGEN_UMFPACK 10
+#define EIGEN_KLU 11
+#define EIGEN_SUPERLU 20
+#define EIGEN_PASTIX 30
+#define EIGEN_PARDISO 40
+#define EIGEN_SPARSELU_COLAMD 50
+#define EIGEN_SPARSELU_METIS 51
+#define EIGEN_BICGSTAB 60
+#define EIGEN_BICGSTAB_ILUT 61
+#define EIGEN_GMRES 70
+#define EIGEN_GMRES_ILUT 71
+#define EIGEN_SIMPLICIAL_LDLT 80
+#define EIGEN_CHOLMOD_LDLT 90
+#define EIGEN_PASTIX_LDLT 100
+#define EIGEN_PARDISO_LDLT 110
+#define EIGEN_SIMPLICIAL_LLT 120
+#define EIGEN_CHOLMOD_SUPERNODAL_LLT 130
+#define EIGEN_CHOLMOD_SIMPLICIAL_LLT 140
+#define EIGEN_PASTIX_LLT 150
+#define EIGEN_PARDISO_LLT 160
+#define EIGEN_CG 170
+#define EIGEN_CG_PRECOND 180
+
+using namespace Eigen;
+using namespace std;
+
+
+// Global variables for input parameters
+int MaximumIters; // Maximum number of iterations
+double RelErr; // Relative error of the computed solution
+double best_time_val; // Current best time overall solvers
+int best_time_id; // id of the best solver for the current system
+
+template<typename T> inline typename NumTraits<T>::Real test_precision() { return NumTraits<T>::dummy_precision(); }
+template<> inline float test_precision<float>() { return 1e-3f; }
+template<> inline double test_precision<double>() { return 1e-6; }
+template<> inline float test_precision<std::complex<float> >() { return test_precision<float>(); }
+template<> inline double test_precision<std::complex<double> >() { return test_precision<double>(); }
+
+void printStatheader(std::ofstream& out)
+{
+ // Print XML header
+ // NOTE It would have been much easier to write these XML documents using external libraries like tinyXML or Xerces-C++.
+
+ out << "<?xml version='1.0' encoding='UTF-8'?> \n";
+ out << "<?xml-stylesheet type='text/xsl' href='#stylesheet' ?> \n";
+ out << "<!DOCTYPE BENCH [\n<!ATTLIST xsl:stylesheet\n id\t ID #REQUIRED>\n]>";
+ out << "\n\n<!-- Generated by the Eigen library -->\n";
+
+ out << "\n<BENCH> \n" ; //root XML element
+ // Print the xsl style section
+ printBenchStyle(out);
+ // List all available solvers
+ out << " <AVAILSOLVER> \n";
+#ifdef EIGEN_UMFPACK_SUPPORT
+ out <<" <SOLVER ID='" << EIGEN_UMFPACK << "'>\n";
+ out << " <TYPE> LU </TYPE> \n";
+ out << " <PACKAGE> UMFPACK </PACKAGE> \n";
+ out << " </SOLVER> \n";
+#endif
+#ifdef EIGEN_KLU_SUPPORT
+ out <<" <SOLVER ID='" << EIGEN_KLU << "'>\n";
+ out << " <TYPE> LU </TYPE> \n";
+ out << " <PACKAGE> KLU </PACKAGE> \n";
+ out << " </SOLVER> \n";
+#endif
+#ifdef EIGEN_SUPERLU_SUPPORT
+ out <<" <SOLVER ID='" << EIGEN_SUPERLU << "'>\n";
+ out << " <TYPE> LU </TYPE> \n";
+ out << " <PACKAGE> SUPERLU </PACKAGE> \n";
+ out << " </SOLVER> \n";
+#endif
+#ifdef EIGEN_CHOLMOD_SUPPORT
+ out <<" <SOLVER ID='" << EIGEN_CHOLMOD_SIMPLICIAL_LLT << "'>\n";
+ out << " <TYPE> LLT SP</TYPE> \n";
+ out << " <PACKAGE> CHOLMOD </PACKAGE> \n";
+ out << " </SOLVER> \n";
+
+ out <<" <SOLVER ID='" << EIGEN_CHOLMOD_SUPERNODAL_LLT << "'>\n";
+ out << " <TYPE> LLT</TYPE> \n";
+ out << " <PACKAGE> CHOLMOD </PACKAGE> \n";
+ out << " </SOLVER> \n";
+
+ out <<" <SOLVER ID='" << EIGEN_CHOLMOD_LDLT << "'>\n";
+ out << " <TYPE> LDLT </TYPE> \n";
+ out << " <PACKAGE> CHOLMOD </PACKAGE> \n";
+ out << " </SOLVER> \n";
+#endif
+#ifdef EIGEN_PARDISO_SUPPORT
+ out <<" <SOLVER ID='" << EIGEN_PARDISO << "'>\n";
+ out << " <TYPE> LU </TYPE> \n";
+ out << " <PACKAGE> PARDISO </PACKAGE> \n";
+ out << " </SOLVER> \n";
+
+ out <<" <SOLVER ID='" << EIGEN_PARDISO_LLT << "'>\n";
+ out << " <TYPE> LLT </TYPE> \n";
+ out << " <PACKAGE> PARDISO </PACKAGE> \n";
+ out << " </SOLVER> \n";
+
+ out <<" <SOLVER ID='" << EIGEN_PARDISO_LDLT << "'>\n";
+ out << " <TYPE> LDLT </TYPE> \n";
+ out << " <PACKAGE> PARDISO </PACKAGE> \n";
+ out << " </SOLVER> \n";
+#endif
+#ifdef EIGEN_PASTIX_SUPPORT
+ out <<" <SOLVER ID='" << EIGEN_PASTIX << "'>\n";
+ out << " <TYPE> LU </TYPE> \n";
+ out << " <PACKAGE> PASTIX </PACKAGE> \n";
+ out << " </SOLVER> \n";
+
+ out <<" <SOLVER ID='" << EIGEN_PASTIX_LLT << "'>\n";
+ out << " <TYPE> LLT </TYPE> \n";
+ out << " <PACKAGE> PASTIX </PACKAGE> \n";
+ out << " </SOLVER> \n";
+
+ out <<" <SOLVER ID='" << EIGEN_PASTIX_LDLT << "'>\n";
+ out << " <TYPE> LDLT </TYPE> \n";
+ out << " <PACKAGE> PASTIX </PACKAGE> \n";
+ out << " </SOLVER> \n";
+#endif
+
+ out <<" <SOLVER ID='" << EIGEN_BICGSTAB << "'>\n";
+ out << " <TYPE> BICGSTAB </TYPE> \n";
+ out << " <PACKAGE> EIGEN </PACKAGE> \n";
+ out << " </SOLVER> \n";
+
+ out <<" <SOLVER ID='" << EIGEN_BICGSTAB_ILUT << "'>\n";
+ out << " <TYPE> BICGSTAB_ILUT </TYPE> \n";
+ out << " <PACKAGE> EIGEN </PACKAGE> \n";
+ out << " </SOLVER> \n";
+
+ out <<" <SOLVER ID='" << EIGEN_GMRES_ILUT << "'>\n";
+ out << " <TYPE> GMRES_ILUT </TYPE> \n";
+ out << " <PACKAGE> EIGEN </PACKAGE> \n";
+ out << " </SOLVER> \n";
+
+ out <<" <SOLVER ID='" << EIGEN_SIMPLICIAL_LDLT << "'>\n";
+ out << " <TYPE> LDLT </TYPE> \n";
+ out << " <PACKAGE> EIGEN </PACKAGE> \n";
+ out << " </SOLVER> \n";
+
+ out <<" <SOLVER ID='" << EIGEN_SIMPLICIAL_LLT << "'>\n";
+ out << " <TYPE> LLT </TYPE> \n";
+ out << " <PACKAGE> EIGEN </PACKAGE> \n";
+ out << " </SOLVER> \n";
+
+ out <<" <SOLVER ID='" << EIGEN_CG << "'>\n";
+ out << " <TYPE> CG </TYPE> \n";
+ out << " <PACKAGE> EIGEN </PACKAGE> \n";
+ out << " </SOLVER> \n";
+
+ out <<" <SOLVER ID='" << EIGEN_SPARSELU_COLAMD << "'>\n";
+ out << " <TYPE> LU_COLAMD </TYPE> \n";
+ out << " <PACKAGE> EIGEN </PACKAGE> \n";
+ out << " </SOLVER> \n";
+
+#ifdef EIGEN_METIS_SUPPORT
+ out <<" <SOLVER ID='" << EIGEN_SPARSELU_METIS << "'>\n";
+ out << " <TYPE> LU_METIS </TYPE> \n";
+ out << " <PACKAGE> EIGEN </PACKAGE> \n";
+ out << " </SOLVER> \n";
+#endif
+ out << " </AVAILSOLVER> \n";
+
+}
+
+
+template<typename Solver, typename Scalar>
+void call_solver(Solver &solver, const int solver_id, const typename Solver::MatrixType& A, const Matrix<Scalar, Dynamic, 1>& b, const Matrix<Scalar, Dynamic, 1>& refX,std::ofstream& statbuf)
+{
+
+ double total_time;
+ double compute_time;
+ double solve_time;
+ double rel_error;
+ Matrix<Scalar, Dynamic, 1> x;
+ BenchTimer timer;
+ timer.reset();
+ timer.start();
+ solver.compute(A);
+ if (solver.info() != Success)
+ {
+ std::cerr << "Solver failed ... \n";
+ return;
+ }
+ timer.stop();
+ compute_time = timer.value();
+ statbuf << " <TIME>\n";
+ statbuf << " <COMPUTE> " << timer.value() << "</COMPUTE>\n";
+ std::cout<< "COMPUTE TIME : " << timer.value() <<std::endl;
+
+ timer.reset();
+ timer.start();
+ x = solver.solve(b);
+ if (solver.info() == NumericalIssue)
+ {
+ std::cerr << "Solver failed ... \n";
+ return;
+ }
+ timer.stop();
+ solve_time = timer.value();
+ statbuf << " <SOLVE> " << timer.value() << "</SOLVE>\n";
+ std::cout<< "SOLVE TIME : " << timer.value() <<std::endl;
+
+ total_time = solve_time + compute_time;
+ statbuf << " <TOTAL> " << total_time << "</TOTAL>\n";
+ std::cout<< "TOTAL TIME : " << total_time <<std::endl;
+ statbuf << " </TIME>\n";
+
+ // Verify the relative error
+ if(refX.size() != 0)
+ rel_error = (refX - x).norm()/refX.norm();
+ else
+ {
+ // Compute the relative residual norm
+ Matrix<Scalar, Dynamic, 1> temp;
+ temp = A * x;
+ rel_error = (b-temp).norm()/b.norm();
+ }
+ statbuf << " <ERROR> " << rel_error << "</ERROR>\n";
+ std::cout<< "REL. ERROR : " << rel_error << "\n\n" ;
+ if ( rel_error <= RelErr )
+ {
+ // check the best time if convergence
+ if(!best_time_val || (best_time_val > total_time))
+ {
+ best_time_val = total_time;
+ best_time_id = solver_id;
+ }
+ }
+}
+
+template<typename Solver, typename Scalar>
+void call_directsolver(Solver& solver, const int solver_id, const typename Solver::MatrixType& A, const Matrix<Scalar, Dynamic, 1>& b, const Matrix<Scalar, Dynamic, 1>& refX, std::string& statFile)
+{
+ std::ofstream statbuf(statFile.c_str(), std::ios::app);
+ statbuf << " <SOLVER_STAT ID='" << solver_id <<"'>\n";
+ call_solver(solver, solver_id, A, b, refX,statbuf);
+ statbuf << " </SOLVER_STAT>\n";
+ statbuf.close();
+}
+
+template<typename Solver, typename Scalar>
+void call_itersolver(Solver &solver, const int solver_id, const typename Solver::MatrixType& A, const Matrix<Scalar, Dynamic, 1>& b, const Matrix<Scalar, Dynamic, 1>& refX, std::string& statFile)
+{
+ solver.setTolerance(RelErr);
+ solver.setMaxIterations(MaximumIters);
+
+ std::ofstream statbuf(statFile.c_str(), std::ios::app);
+ statbuf << " <SOLVER_STAT ID='" << solver_id <<"'>\n";
+ call_solver(solver, solver_id, A, b, refX,statbuf);
+ statbuf << " <ITER> "<< solver.iterations() << "</ITER>\n";
+ statbuf << " </SOLVER_STAT>\n";
+ std::cout << "ITERATIONS : " << solver.iterations() <<"\n\n\n";
+
+}
+
+
+template <typename Scalar>
+void SelectSolvers(const SparseMatrix<Scalar>&A, unsigned int sym, Matrix<Scalar, Dynamic, 1>& b, const Matrix<Scalar, Dynamic, 1>& refX, std::string& statFile)
+{
+ typedef SparseMatrix<Scalar, ColMajor> SpMat;
+ // First, deal with Nonsymmetric and symmetric matrices
+ best_time_id = 0;
+ best_time_val = 0.0;
+ //UMFPACK
+ #ifdef EIGEN_UMFPACK_SUPPORT
+ {
+ cout << "Solving with UMFPACK LU ... \n";
+ UmfPackLU<SpMat> solver;
+ call_directsolver(solver, EIGEN_UMFPACK, A, b, refX,statFile);
+ }
+ #endif
+ //KLU
+ #ifdef EIGEN_KLU_SUPPORT
+ {
+ cout << "Solving with KLU LU ... \n";
+ KLU<SpMat> solver;
+ call_directsolver(solver, EIGEN_KLU, A, b, refX,statFile);
+ }
+ #endif
+ //SuperLU
+ #ifdef EIGEN_SUPERLU_SUPPORT
+ {
+ cout << "\nSolving with SUPERLU ... \n";
+ SuperLU<SpMat> solver;
+ call_directsolver(solver, EIGEN_SUPERLU, A, b, refX,statFile);
+ }
+ #endif
+
+ // PaStix LU
+ #ifdef EIGEN_PASTIX_SUPPORT
+ {
+ cout << "\nSolving with PASTIX LU ... \n";
+ PastixLU<SpMat> solver;
+ call_directsolver(solver, EIGEN_PASTIX, A, b, refX,statFile) ;
+ }
+ #endif
+
+ //PARDISO LU
+ #ifdef EIGEN_PARDISO_SUPPORT
+ {
+ cout << "\nSolving with PARDISO LU ... \n";
+ PardisoLU<SpMat> solver;
+ call_directsolver(solver, EIGEN_PARDISO, A, b, refX,statFile);
+ }
+ #endif
+
+ // Eigen SparseLU METIS
+ cout << "\n Solving with Sparse LU AND COLAMD ... \n";
+ SparseLU<SpMat, COLAMDOrdering<int> > solver;
+ call_directsolver(solver, EIGEN_SPARSELU_COLAMD, A, b, refX, statFile);
+ // Eigen SparseLU METIS
+ #ifdef EIGEN_METIS_SUPPORT
+ {
+ cout << "\n Solving with Sparse LU AND METIS ... \n";
+ SparseLU<SpMat, MetisOrdering<int> > solver;
+ call_directsolver(solver, EIGEN_SPARSELU_METIS, A, b, refX, statFile);
+ }
+ #endif
+
+ //BiCGSTAB
+ {
+ cout << "\nSolving with BiCGSTAB ... \n";
+ BiCGSTAB<SpMat> solver;
+ call_itersolver(solver, EIGEN_BICGSTAB, A, b, refX,statFile);
+ }
+ //BiCGSTAB+ILUT
+ {
+ cout << "\nSolving with BiCGSTAB and ILUT ... \n";
+ BiCGSTAB<SpMat, IncompleteLUT<Scalar> > solver;
+ call_itersolver(solver, EIGEN_BICGSTAB_ILUT, A, b, refX,statFile);
+ }
+
+
+ //GMRES
+// {
+// cout << "\nSolving with GMRES ... \n";
+// GMRES<SpMat> solver;
+// call_itersolver(solver, EIGEN_GMRES, A, b, refX,statFile);
+// }
+ //GMRES+ILUT
+ {
+ cout << "\nSolving with GMRES and ILUT ... \n";
+ GMRES<SpMat, IncompleteLUT<Scalar> > solver;
+ call_itersolver(solver, EIGEN_GMRES_ILUT, A, b, refX,statFile);
+ }
+
+ // Hermitian and not necessarily positive-definites
+ if (sym != NonSymmetric)
+ {
+ // Internal Cholesky
+ {
+ cout << "\nSolving with Simplicial LDLT ... \n";
+ SimplicialLDLT<SpMat, Lower> solver;
+ call_directsolver(solver, EIGEN_SIMPLICIAL_LDLT, A, b, refX,statFile);
+ }
+
+ // CHOLMOD
+ #ifdef EIGEN_CHOLMOD_SUPPORT
+ {
+ cout << "\nSolving with CHOLMOD LDLT ... \n";
+ CholmodDecomposition<SpMat, Lower> solver;
+ solver.setMode(CholmodLDLt);
+ call_directsolver(solver,EIGEN_CHOLMOD_LDLT, A, b, refX,statFile);
+ }
+ #endif
+
+ //PASTIX LLT
+ #ifdef EIGEN_PASTIX_SUPPORT
+ {
+ cout << "\nSolving with PASTIX LDLT ... \n";
+ PastixLDLT<SpMat, Lower> solver;
+ call_directsolver(solver,EIGEN_PASTIX_LDLT, A, b, refX,statFile);
+ }
+ #endif
+
+ //PARDISO LLT
+ #ifdef EIGEN_PARDISO_SUPPORT
+ {
+ cout << "\nSolving with PARDISO LDLT ... \n";
+ PardisoLDLT<SpMat, Lower> solver;
+ call_directsolver(solver,EIGEN_PARDISO_LDLT, A, b, refX,statFile);
+ }
+ #endif
+ }
+
+ // Now, symmetric POSITIVE DEFINITE matrices
+ if (sym == SPD)
+ {
+
+ //Internal Sparse Cholesky
+ {
+ cout << "\nSolving with SIMPLICIAL LLT ... \n";
+ SimplicialLLT<SpMat, Lower> solver;
+ call_directsolver(solver,EIGEN_SIMPLICIAL_LLT, A, b, refX,statFile);
+ }
+
+ // CHOLMOD
+ #ifdef EIGEN_CHOLMOD_SUPPORT
+ {
+ // CholMOD SuperNodal LLT
+ cout << "\nSolving with CHOLMOD LLT (Supernodal)... \n";
+ CholmodDecomposition<SpMat, Lower> solver;
+ solver.setMode(CholmodSupernodalLLt);
+ call_directsolver(solver,EIGEN_CHOLMOD_SUPERNODAL_LLT, A, b, refX,statFile);
+ // CholMod Simplicial LLT
+ cout << "\nSolving with CHOLMOD LLT (Simplicial) ... \n";
+ solver.setMode(CholmodSimplicialLLt);
+ call_directsolver(solver,EIGEN_CHOLMOD_SIMPLICIAL_LLT, A, b, refX,statFile);
+ }
+ #endif
+
+ //PASTIX LLT
+ #ifdef EIGEN_PASTIX_SUPPORT
+ {
+ cout << "\nSolving with PASTIX LLT ... \n";
+ PastixLLT<SpMat, Lower> solver;
+ call_directsolver(solver,EIGEN_PASTIX_LLT, A, b, refX,statFile);
+ }
+ #endif
+
+ //PARDISO LLT
+ #ifdef EIGEN_PARDISO_SUPPORT
+ {
+ cout << "\nSolving with PARDISO LLT ... \n";
+ PardisoLLT<SpMat, Lower> solver;
+ call_directsolver(solver,EIGEN_PARDISO_LLT, A, b, refX,statFile);
+ }
+ #endif
+
+ // Internal CG
+ {
+ cout << "\nSolving with CG ... \n";
+ ConjugateGradient<SpMat, Lower> solver;
+ call_itersolver(solver,EIGEN_CG, A, b, refX,statFile);
+ }
+ //CG+IdentityPreconditioner
+// {
+// cout << "\nSolving with CG and IdentityPreconditioner ... \n";
+// ConjugateGradient<SpMat, Lower, IdentityPreconditioner> solver;
+// call_itersolver(solver,EIGEN_CG_PRECOND, A, b, refX,statFile);
+// }
+ } // End SPD matrices
+}
+
+/* Browse all the matrices available in the specified folder
+ * and solve the associated linear system.
+ * The results of each solve are printed in the standard output
+ * and optionally in the provided html file
+ */
+template <typename Scalar>
+void Browse_Matrices(const string folder, bool statFileExists, std::string& statFile, int maxiters, double tol)
+{
+ MaximumIters = maxiters; // Maximum number of iterations, global variable
+ RelErr = tol; //Relative residual error as stopping criterion for iterative solvers
+ MatrixMarketIterator<Scalar> it(folder);
+ for ( ; it; ++it)
+ {
+ //print the infos for this linear system
+ if(statFileExists)
+ {
+ std::ofstream statbuf(statFile.c_str(), std::ios::app);
+ statbuf << "<LINEARSYSTEM> \n";
+ statbuf << " <MATRIX> \n";
+ statbuf << " <NAME> " << it.matname() << " </NAME>\n";
+ statbuf << " <SIZE> " << it.matrix().rows() << " </SIZE>\n";
+ statbuf << " <ENTRIES> " << it.matrix().nonZeros() << "</ENTRIES>\n";
+ if (it.sym()!=NonSymmetric)
+ {
+ statbuf << " <SYMMETRY> Symmetric </SYMMETRY>\n" ;
+ if (it.sym() == SPD)
+ statbuf << " <POSDEF> YES </POSDEF>\n";
+ else
+ statbuf << " <POSDEF> NO </POSDEF>\n";
+
+ }
+ else
+ {
+ statbuf << " <SYMMETRY> NonSymmetric </SYMMETRY>\n" ;
+ statbuf << " <POSDEF> NO </POSDEF>\n";
+ }
+ statbuf << " </MATRIX> \n";
+ statbuf.close();
+ }
+
+ cout<< "\n\n===================================================== \n";
+ cout<< " ====== SOLVING WITH MATRIX " << it.matname() << " ====\n";
+ cout<< " =================================================== \n\n";
+ Matrix<Scalar, Dynamic, 1> refX;
+ if(it.hasrefX()) refX = it.refX();
+ // Call all suitable solvers for this linear system
+ SelectSolvers<Scalar>(it.matrix(), it.sym(), it.rhs(), refX, statFile);
+
+ if(statFileExists)
+ {
+ std::ofstream statbuf(statFile.c_str(), std::ios::app);
+ statbuf << " <BEST_SOLVER ID='"<< best_time_id
+ << "'></BEST_SOLVER>\n";
+ statbuf << " </LINEARSYSTEM> \n";
+ statbuf.close();
+ }
+ }
+}
+
+bool get_options(int argc, char **args, string option, string* value=0)
+{
+ int idx = 1, found=false;
+ while (idx<argc && !found){
+ if (option.compare(args[idx]) == 0){
+ found = true;
+ if(value) *value = args[idx+1];
+ }
+ idx+=2;
+ }
+ return found;
+}
diff --git a/bench/spbench/spbenchstyle.h b/bench/spbench/spbenchstyle.h
new file mode 100644
index 0000000..f6a9817
--- /dev/null
+++ b/bench/spbench/spbenchstyle.h
@@ -0,0 +1,95 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2012 Désiré Nuentsa-Wakam <desire.nuentsa_wakam@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef SPBENCHSTYLE_H
+#define SPBENCHSTYLE_H
+
+void printBenchStyle(std::ofstream& out)
+{
+ out << "<xsl:stylesheet id='stylesheet' version='1.0' \
+ xmlns:xsl='http://www.w3.org/1999/XSL/Transform' >\n \
+ <xsl:template match='xsl:stylesheet' />\n \
+ <xsl:template match='/'> <!-- Root of the document -->\n \
+ <html>\n \
+ <head> \n \
+ <style type='text/css'> \n \
+ td { white-space: nowrap;}\n \
+ </style>\n \
+ </head>\n \
+ <body>";
+ out<<"<table border='1' width='100%' height='100%'>\n \
+ <TR> <!-- Write the table header -->\n \
+ <TH>Matrix</TH> <TH>N</TH> <TH> NNZ</TH> <TH> Sym</TH> <TH> SPD</TH> <TH> </TH>\n \
+ <xsl:for-each select='BENCH/AVAILSOLVER/SOLVER'>\n \
+ <xsl:sort select='@ID' data-type='number'/>\n \
+ <TH>\n \
+ <xsl:value-of select='TYPE' />\n \
+ <xsl:text></xsl:text>\n \
+ <xsl:value-of select='PACKAGE' />\n \
+ <xsl:text></xsl:text>\n \
+ </TH>\n \
+ </xsl:for-each>\n \
+ </TR>";
+
+ out<<" <xsl:for-each select='BENCH/LINEARSYSTEM'>\n \
+ <TR> <!-- print statistics for one linear system-->\n \
+ <TH rowspan='4'> <xsl:value-of select='MATRIX/NAME' /> </TH>\n \
+ <TD rowspan='4'> <xsl:value-of select='MATRIX/SIZE' /> </TD>\n \
+ <TD rowspan='4'> <xsl:value-of select='MATRIX/ENTRIES' /> </TD>\n \
+ <TD rowspan='4'> <xsl:value-of select='MATRIX/SYMMETRY' /> </TD>\n \
+ <TD rowspan='4'> <xsl:value-of select='MATRIX/POSDEF' /> </TD>\n \
+ <TH> Compute Time </TH>\n \
+ <xsl:for-each select='SOLVER_STAT'>\n \
+ <xsl:sort select='@ID' data-type='number'/>\n \
+ <TD> <xsl:value-of select='TIME/COMPUTE' /> </TD>\n \
+ </xsl:for-each>\n \
+ </TR>";
+ out<<" <TR>\n \
+ <TH> Solve Time </TH>\n \
+ <xsl:for-each select='SOLVER_STAT'>\n \
+ <xsl:sort select='@ID' data-type='number'/>\n \
+ <TD> <xsl:value-of select='TIME/SOLVE' /> </TD>\n \
+ </xsl:for-each>\n \
+ </TR>\n \
+ <TR>\n \
+ <TH> Total Time </TH>\n \
+ <xsl:for-each select='SOLVER_STAT'>\n \
+ <xsl:sort select='@ID' data-type='number'/>\n \
+ <xsl:choose>\n \
+ <xsl:when test='@ID=../BEST_SOLVER/@ID'>\n \
+ <TD style='background-color:red'> <xsl:value-of select='TIME/TOTAL' /> </TD>\n \
+ </xsl:when>\n \
+ <xsl:otherwise>\n \
+ <TD> <xsl:value-of select='TIME/TOTAL' /></TD>\n \
+ </xsl:otherwise>\n \
+ </xsl:choose>\n \
+ </xsl:for-each>\n \
+ </TR>";
+ out<<" <TR>\n \
+ <TH> Error </TH>\n \
+ <xsl:for-each select='SOLVER_STAT'>\n \
+ <xsl:sort select='@ID' data-type='number'/>\n \
+ <TD> <xsl:value-of select='ERROR' />\n \
+ <xsl:if test='ITER'>\n \
+ <xsl:text>(</xsl:text>\n \
+ <xsl:value-of select='ITER' />\n \
+ <xsl:text>)</xsl:text>\n \
+ </xsl:if> </TD>\n \
+ </xsl:for-each>\n \
+ </TR>\n \
+ </xsl:for-each>\n \
+ </table>\n \
+ </body>\n \
+ </html>\n \
+ </xsl:template>\n \
+ </xsl:stylesheet>\n\n";
+
+}
+
+#endif
diff --git a/bench/spbench/test_sparseLU.cpp b/bench/spbench/test_sparseLU.cpp
new file mode 100644
index 0000000..a4cade6
--- /dev/null
+++ b/bench/spbench/test_sparseLU.cpp
@@ -0,0 +1,93 @@
+// Small bench routine for Eigen available in Eigen
+// (C) Desire NUENTSA WAKAM, INRIA
+
+#include <iostream>
+#include <fstream>
+#include <iomanip>
+#include <unsupported/Eigen/SparseExtra>
+#include <Eigen/SparseLU>
+#include <bench/BenchTimer.h>
+#ifdef EIGEN_METIS_SUPPORT
+#include <Eigen/MetisSupport>
+#endif
+
+using namespace std;
+using namespace Eigen;
+
+int main(int argc, char **args)
+{
+// typedef complex<double> scalar;
+ typedef double scalar;
+ SparseMatrix<scalar, ColMajor> A;
+ typedef SparseMatrix<scalar, ColMajor>::Index Index;
+ typedef Matrix<scalar, Dynamic, Dynamic> DenseMatrix;
+ typedef Matrix<scalar, Dynamic, 1> DenseRhs;
+ Matrix<scalar, Dynamic, 1> b, x, tmp;
+// SparseLU<SparseMatrix<scalar, ColMajor>, AMDOrdering<int> > solver;
+// #ifdef EIGEN_METIS_SUPPORT
+// SparseLU<SparseMatrix<scalar, ColMajor>, MetisOrdering<int> > solver;
+// std::cout<< "ORDERING : METIS\n";
+// #else
+ SparseLU<SparseMatrix<scalar, ColMajor>, COLAMDOrdering<int> > solver;
+ std::cout<< "ORDERING : COLAMD\n";
+// #endif
+
+ ifstream matrix_file;
+ string line;
+ int n;
+ BenchTimer timer;
+
+ // Set parameters
+ /* Fill the matrix with sparse matrix stored in Matrix-Market coordinate column-oriented format */
+ if (argc < 2) assert(false && "please, give the matrix market file ");
+ loadMarket(A, args[1]);
+ cout << "End charging matrix " << endl;
+ bool iscomplex=false, isvector=false;
+ int sym;
+ getMarketHeader(args[1], sym, iscomplex, isvector);
+// if (iscomplex) { cout<< " Not for complex matrices \n"; return -1; }
+ if (isvector) { cout << "The provided file is not a matrix file\n"; return -1;}
+ if (sym != 0) { // symmetric matrices, only the lower part is stored
+ SparseMatrix<scalar, ColMajor> temp;
+ temp = A;
+ A = temp.selfadjointView<Lower>();
+ }
+ n = A.cols();
+ /* Fill the right hand side */
+
+ if (argc > 2)
+ loadMarketVector(b, args[2]);
+ else
+ {
+ b.resize(n);
+ tmp.resize(n);
+// tmp.setRandom();
+ for (int i = 0; i < n; i++) tmp(i) = i;
+ b = A * tmp ;
+ }
+
+ /* Compute the factorization */
+// solver.isSymmetric(true);
+ timer.start();
+// solver.compute(A);
+ solver.analyzePattern(A);
+ timer.stop();
+ cout << "Time to analyze " << timer.value() << std::endl;
+ timer.reset();
+ timer.start();
+ solver.factorize(A);
+ timer.stop();
+ cout << "Factorize Time " << timer.value() << std::endl;
+ timer.reset();
+ timer.start();
+ x = solver.solve(b);
+ timer.stop();
+ cout << "solve time " << timer.value() << std::endl;
+ /* Check the accuracy */
+ Matrix<scalar, Dynamic, 1> tmp2 = b - A*x;
+ scalar tempNorm = tmp2.norm()/b.norm();
+ cout << "Relative norm of the computed solution : " << tempNorm <<"\n";
+ cout << "Number of nonzeros in the factor : " << solver.nnzL() + solver.nnzU() << std::endl;
+
+ return 0;
+}
diff --git a/bench/spmv.cpp b/bench/spmv.cpp
new file mode 100644
index 0000000..959bab0
--- /dev/null
+++ b/bench/spmv.cpp
@@ -0,0 +1,233 @@
+
+//g++-4.4 -DNOMTL -Wl,-rpath /usr/local/lib/oski -L /usr/local/lib/oski/ -l oski -l oski_util -l oski_util_Tid -DOSKI -I ~/Coding/LinearAlgebra/mtl4/ spmv.cpp -I .. -O2 -DNDEBUG -lrt -lm -l oski_mat_CSC_Tid -loskilt && ./a.out r200000 c200000 n100 t1 p1
+
+#define SCALAR double
+
+#include <iostream>
+#include <algorithm>
+#include "BenchTimer.h"
+#include "BenchSparseUtil.h"
+
+#define SPMV_BENCH(CODE) BENCH(t,tries,repeats,CODE);
+
+// #ifdef MKL
+//
+// #include "mkl_types.h"
+// #include "mkl_spblas.h"
+//
+// template<typename Lhs,typename Rhs,typename Res>
+// void mkl_multiply(const Lhs& lhs, const Rhs& rhs, Res& res)
+// {
+// char n = 'N';
+// float alpha = 1;
+// char matdescra[6];
+// matdescra[0] = 'G';
+// matdescra[1] = 0;
+// matdescra[2] = 0;
+// matdescra[3] = 'C';
+// mkl_scscmm(&n, lhs.rows(), rhs.cols(), lhs.cols(), &alpha, matdescra,
+// lhs._valuePtr(), lhs._innerIndexPtr(), lhs.outerIndexPtr(),
+// pntre, b, &ldb, &beta, c, &ldc);
+// // mkl_somatcopy('C', 'T', lhs.rows(), lhs.cols(), 1,
+// // lhs._valuePtr(), lhs.rows(), DST, dst_stride);
+// }
+//
+// #endif
+
+int main(int argc, char *argv[])
+{
+ int size = 10000;
+ int rows = size;
+ int cols = size;
+ int nnzPerCol = 40;
+ int tries = 2;
+ int repeats = 2;
+
+ bool need_help = false;
+ for(int i = 1; i < argc; i++)
+ {
+ if(argv[i][0] == 'r')
+ {
+ rows = atoi(argv[i]+1);
+ }
+ else if(argv[i][0] == 'c')
+ {
+ cols = atoi(argv[i]+1);
+ }
+ else if(argv[i][0] == 'n')
+ {
+ nnzPerCol = atoi(argv[i]+1);
+ }
+ else if(argv[i][0] == 't')
+ {
+ tries = atoi(argv[i]+1);
+ }
+ else if(argv[i][0] == 'p')
+ {
+ repeats = atoi(argv[i]+1);
+ }
+ else
+ {
+ need_help = true;
+ }
+ }
+ if(need_help)
+ {
+ std::cout << argv[0] << " r<nb rows> c<nb columns> n<non zeros per column> t<nb tries> p<nb repeats>\n";
+ return 1;
+ }
+
+ std::cout << "SpMV " << rows << " x " << cols << " with " << nnzPerCol << " non zeros per column. (" << repeats << " repeats, and " << tries << " tries)\n\n";
+
+ EigenSparseMatrix sm(rows,cols);
+ DenseVector dv(cols), res(rows);
+ dv.setRandom();
+
+ BenchTimer t;
+ while (nnzPerCol>=4)
+ {
+ std::cout << "nnz: " << nnzPerCol << "\n";
+ sm.setZero();
+ fillMatrix2(nnzPerCol, rows, cols, sm);
+
+ // dense matrices
+ #ifdef DENSEMATRIX
+ {
+ DenseMatrix dm(rows,cols), (rows,cols);
+ eiToDense(sm, dm);
+
+ SPMV_BENCH(res = dm * sm);
+ std::cout << "Dense " << t.value()/repeats << "\t";
+
+ SPMV_BENCH(res = dm.transpose() * sm);
+ std::cout << t.value()/repeats << endl;
+ }
+ #endif
+
+ // eigen sparse matrices
+ {
+ SPMV_BENCH(res.noalias() += sm * dv; )
+ std::cout << "Eigen " << t.value()/repeats << "\t";
+
+ SPMV_BENCH(res.noalias() += sm.transpose() * dv; )
+ std::cout << t.value()/repeats << endl;
+ }
+
+ // CSparse
+ #ifdef CSPARSE
+ {
+ std::cout << "CSparse \n";
+ cs *csm;
+ eiToCSparse(sm, csm);
+
+// BENCH();
+// timer.stop();
+// std::cout << " a * b:\t" << timer.value() << endl;
+
+// BENCH( { m3 = cs_sorted_multiply2(m1, m2); cs_spfree(m3); } );
+// std::cout << " a * b:\t" << timer.value() << endl;
+ }
+ #endif
+
+ #ifdef OSKI
+ {
+ oski_matrix_t om;
+ oski_vecview_t ov, ores;
+ oski_Init();
+ om = oski_CreateMatCSC(sm._outerIndexPtr(), sm._innerIndexPtr(), sm._valuePtr(), rows, cols,
+ SHARE_INPUTMAT, 1, INDEX_ZERO_BASED);
+ ov = oski_CreateVecView(dv.data(), cols, STRIDE_UNIT);
+ ores = oski_CreateVecView(res.data(), rows, STRIDE_UNIT);
+
+ SPMV_BENCH( oski_MatMult(om, OP_NORMAL, 1, ov, 0, ores) );
+ std::cout << "OSKI " << t.value()/repeats << "\t";
+
+ SPMV_BENCH( oski_MatMult(om, OP_TRANS, 1, ov, 0, ores) );
+ std::cout << t.value()/repeats << "\n";
+
+ // tune
+ t.reset();
+ t.start();
+ oski_SetHintMatMult(om, OP_NORMAL, 1.0, SYMBOLIC_VEC, 0.0, SYMBOLIC_VEC, ALWAYS_TUNE_AGGRESSIVELY);
+ oski_TuneMat(om);
+ t.stop();
+ double tuning = t.value();
+
+ SPMV_BENCH( oski_MatMult(om, OP_NORMAL, 1, ov, 0, ores) );
+ std::cout << "OSKI tuned " << t.value()/repeats << "\t";
+
+ SPMV_BENCH( oski_MatMult(om, OP_TRANS, 1, ov, 0, ores) );
+ std::cout << t.value()/repeats << "\t(" << tuning << ")\n";
+
+
+ oski_DestroyMat(om);
+ oski_DestroyVecView(ov);
+ oski_DestroyVecView(ores);
+ oski_Close();
+ }
+ #endif
+
+ #ifndef NOUBLAS
+ {
+ using namespace boost::numeric;
+ UblasMatrix um(rows,cols);
+ eiToUblas(sm, um);
+
+ boost::numeric::ublas::vector<Scalar> uv(cols), ures(rows);
+ Map<Matrix<Scalar,Dynamic,1> >(&uv[0], cols) = dv;
+ Map<Matrix<Scalar,Dynamic,1> >(&ures[0], rows) = res;
+
+ SPMV_BENCH(ublas::axpy_prod(um, uv, ures, true));
+ std::cout << "ublas " << t.value()/repeats << "\t";
+
+ SPMV_BENCH(ublas::axpy_prod(boost::numeric::ublas::trans(um), uv, ures, true));
+ std::cout << t.value()/repeats << endl;
+ }
+ #endif
+
+ // GMM++
+ #ifndef NOGMM
+ {
+ GmmSparse gm(rows,cols);
+ eiToGmm(sm, gm);
+
+ std::vector<Scalar> gv(cols), gres(rows);
+ Map<Matrix<Scalar,Dynamic,1> >(&gv[0], cols) = dv;
+ Map<Matrix<Scalar,Dynamic,1> >(&gres[0], rows) = res;
+
+ SPMV_BENCH(gmm::mult(gm, gv, gres));
+ std::cout << "GMM++ " << t.value()/repeats << "\t";
+
+ SPMV_BENCH(gmm::mult(gmm::transposed(gm), gv, gres));
+ std::cout << t.value()/repeats << endl;
+ }
+ #endif
+
+ // MTL4
+ #ifndef NOMTL
+ {
+ MtlSparse mm(rows,cols);
+ eiToMtl(sm, mm);
+ mtl::dense_vector<Scalar> mv(cols, 1.0);
+ mtl::dense_vector<Scalar> mres(rows, 1.0);
+
+ SPMV_BENCH(mres = mm * mv);
+ std::cout << "MTL4 " << t.value()/repeats << "\t";
+
+ SPMV_BENCH(mres = trans(mm) * mv);
+ std::cout << t.value()/repeats << endl;
+ }
+ #endif
+
+ std::cout << "\n";
+
+ if(nnzPerCol==1)
+ break;
+ nnzPerCol -= nnzPerCol/2;
+ }
+
+ return 0;
+}
+
+
+
diff --git a/bench/tensors/README b/bench/tensors/README
new file mode 100644
index 0000000..dcbf021
--- /dev/null
+++ b/bench/tensors/README
@@ -0,0 +1,20 @@
+The tensor benchmark suite is made of several parts.
+
+The first part is a generic suite, in which each benchmark comes in 2 flavors: one that runs on CPU, and one that runs on GPU.
+
+To compile the floating point CPU benchmarks, simply call:
+g++ tensor_benchmarks_cpu.cc benchmark_main.cc -I ../../ -std=c++11 -O3 -DNDEBUG -pthread -mavx -o benchmarks_cpu
+
+To compile the floating point GPU benchmarks, simply call:
+nvcc tensor_benchmarks_gpu.cu benchmark_main.cc -I ../../ -std=c++11 -O2 -DNDEBUG -use_fast_math -ftz=true -arch compute_35 -o benchmarks_gpu
+
+We also provide a version of the generic GPU tensor benchmarks that uses half floats (aka fp16) instead of regular floats. To compile these benchmarks, simply call the command line below. You'll need a recent GPU that supports compute capability 5.3 or higher to run them and nvcc 7.5 or higher to compile the code.
+nvcc tensor_benchmarks_fp16_gpu.cu benchmark_main.cc -I ../../ -std=c++11 -O2 -DNDEBUG -use_fast_math -ftz=true -arch compute_53 -o benchmarks_fp16_gpu
+
+To compile and run the benchmark for SYCL, using ComputeCpp, simply run the
+following commands:
+1. export COMPUTECPP_PACKAGE_ROOT_DIR={PATH TO COMPUTECPP ROOT DIRECTORY}
+2. bash eigen_sycl_bench.sh
+
+Last but not least, we also provide a suite of benchmarks to measure the scalability of the contraction code on CPU. To compile these benchmarks, call
+g++ contraction_benchmarks_cpu.cc benchmark_main.cc -I ../../ -std=c++11 -O3 -DNDEBUG -pthread -mavx -o benchmarks_cpu
diff --git a/bench/tensors/benchmark.h b/bench/tensors/benchmark.h
new file mode 100644
index 0000000..f115b54
--- /dev/null
+++ b/bench/tensors/benchmark.h
@@ -0,0 +1,49 @@
+/*
+ * Copyright (C) 2012 The Android Open Source Project
+ *
+ * Licensed under the Apache License, Version 2.0 (the "License");
+ * you may not use this file except in compliance with the License.
+ * You may obtain a copy of the License at
+ *
+ * http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+#include <stddef.h>
+#include <stdint.h>
+#include <vector>
+
+namespace testing {
+class Benchmark {
+ public:
+ Benchmark(const char* name, void (*fn)(int)) {
+ Register(name, fn, NULL);
+ }
+ Benchmark(const char* name, void (*fn_range)(int, int)) {
+ Register(name, NULL, fn_range);
+ }
+ Benchmark* Arg(int x);
+ Benchmark* Range(int lo, int hi);
+ const char* Name();
+ bool ShouldRun(int argc, char* argv[]);
+ void Run();
+ private:
+ const char* name_;
+ void (*fn_)(int);
+ void (*fn_range_)(int, int);
+ std::vector<int> args_;
+ void Register(const char* name, void (*fn)(int), void (*fn_range)(int, int));
+ void RunRepeatedlyWithArg(int iterations, int arg);
+ void RunWithArg(int arg);
+};
+} // namespace testing
+void SetBenchmarkFlopsProcessed(int64_t);
+void StopBenchmarkTiming();
+void StartBenchmarkTiming();
+#define BENCHMARK(f) \
+ static ::testing::Benchmark* _benchmark_##f __attribute__((unused)) = \
+ (new ::testing::Benchmark(#f, f))
diff --git a/bench/tensors/tensor_benchmarks.h b/bench/tensors/tensor_benchmarks.h
new file mode 100644
index 0000000..1a7a0fe
--- /dev/null
+++ b/bench/tensors/tensor_benchmarks.h
@@ -0,0 +1,566 @@
+#ifndef THIRD_PARTY_EIGEN3_TENSOR_BENCHMARKS_H_
+#define THIRD_PARTY_EIGEN3_TENSOR_BENCHMARKS_H_
+
+typedef int TensorIndex;
+#define EIGEN_DEFAULT_DENSE_INDEX_TYPE int
+
+#include "unsupported/Eigen/CXX11/Tensor"
+#include "benchmark.h"
+
+#define BENCHMARK_RANGE(bench, lo, hi) \
+ BENCHMARK(bench)->Range(lo, hi)
+
+using Eigen::Tensor;
+using Eigen::TensorMap;
+
+// TODO(bsteiner): also templatize on the input type since we have users
+// for int8 as well as floats.
+template <typename Device, typename T> class BenchmarkSuite {
+ public:
+ BenchmarkSuite(const Device& device, size_t m, size_t k, size_t n)
+ : m_(m), k_(k), n_(n), device_(device) {
+ initialize();
+ }
+
+ BenchmarkSuite(const Device& device, size_t m)
+ : m_(m), k_(m), n_(m), device_(device) {
+ initialize();
+ }
+
+ BenchmarkSuite(const Device& device, size_t m, size_t k)
+ : m_(1), k_(k), n_(m), device_(device) {
+ initialize();
+ }
+
+ ~BenchmarkSuite() {
+ device_.deallocate(a_);
+ device_.deallocate(b_);
+ device_.deallocate(c_);
+ }
+
+ void memcpy(int num_iters) {
+ eigen_assert(m_ == k_ && k_ == n_);
+#ifdef EIGEN_USE_SYCL // warmup for sycl
+ for (int iter = 0; iter < 10; ++iter) {
+ device_.memcpy(c_, a_, m_ * m_ * sizeof(T));
+ }
+#endif
+ StartBenchmarkTiming();
+ for (int iter = 0; iter < num_iters; ++iter) {
+ device_.memcpy(c_, a_, m_ * m_ * sizeof(T));
+ }
+ // Record the number of values copied per second
+ finalizeBenchmark(static_cast<int64_t>(m_) * m_ * num_iters);
+ }
+
+ void typeCasting(int num_iters) {
+ eigen_assert(m_ == n_);
+ Eigen::array<TensorIndex, 2> sizes;
+ if (sizeof(T) >= sizeof(int)) {
+ sizes[0] = m_;
+ sizes[1] = k_;
+ } else {
+ sizes[0] = m_ * sizeof(T) / sizeof(int);
+ sizes[1] = k_ * sizeof(T) / sizeof(int);
+ }
+ const TensorMap<Tensor<int, 2, 0, TensorIndex>, Eigen::Aligned> A((int*)a_, sizes);
+ TensorMap<Tensor<T, 2, 0, TensorIndex>, Eigen::Aligned> B(b_, sizes);
+#ifdef EIGEN_USE_SYCL // warmup for sycl
+ for (int iter = 0; iter < 10; ++iter) {
+ B.device(device_) = A.template cast<T>();
+ }
+#endif
+ StartBenchmarkTiming();
+ for (int iter = 0; iter < num_iters; ++iter) {
+ B.device(device_) = A.template cast<T>();
+ }
+ // Record the number of values copied per second
+ finalizeBenchmark(static_cast<int64_t>(m_) * k_ * num_iters);
+ }
+
+ void random(int num_iters) {
+ eigen_assert(m_ == k_ && k_ == n_);
+ Eigen::array<TensorIndex, 2> sizes;
+ sizes[0] = m_;
+ sizes[1] = m_;
+ TensorMap<Tensor<T, 2>, Eigen::Aligned> C(c_, sizes);
+#ifdef EIGEN_USE_SYCL // warmup for sycl
+ for (int iter = 0; iter < 10; ++iter) {
+ C.device(device_) = C.random();
+ }
+#endif
+ StartBenchmarkTiming();
+ for (int iter = 0; iter < num_iters; ++iter) {
+ C.device(device_) = C.random();
+ }
+ // Record the number of random numbers generated per second
+ finalizeBenchmark(static_cast<int64_t>(m_) * m_ * num_iters);
+ }
+
+ void slicing(int num_iters) {
+ eigen_assert(m_ == k_ && k_ == n_);
+ Eigen::array<TensorIndex, 2> sizes;
+ sizes[0] = m_;
+ sizes[1] = m_;
+ const TensorMap<Tensor<T, 2>, Eigen::Aligned> A(a_, sizes);
+ const TensorMap<Tensor<T, 2>, Eigen::Aligned> B(b_, sizes);
+ TensorMap<Tensor<T, 2>, Eigen::Aligned> C(c_, sizes);
+
+ const Eigen::DSizes<TensorIndex, 2> quarter_sizes(m_/2, m_/2);
+ const Eigen::DSizes<TensorIndex, 2> first_quadrant(0, 0);
+ const Eigen::DSizes<TensorIndex, 2> second_quadrant(0, m_/2);
+ const Eigen::DSizes<TensorIndex, 2> third_quadrant(m_/2, 0);
+ const Eigen::DSizes<TensorIndex, 2> fourth_quadrant(m_/2, m_/2);
+#ifdef EIGEN_USE_SYCL // warmup for sycl
+ for (int iter = 0; iter < 10; ++iter) {
+ C.slice(first_quadrant, quarter_sizes).device(device_) =
+ A.slice(first_quadrant, quarter_sizes);
+ C.slice(second_quadrant, quarter_sizes).device(device_) =
+ B.slice(second_quadrant, quarter_sizes);
+ C.slice(third_quadrant, quarter_sizes).device(device_) =
+ A.slice(third_quadrant, quarter_sizes);
+ C.slice(fourth_quadrant, quarter_sizes).device(device_) =
+ B.slice(fourth_quadrant, quarter_sizes);
+ }
+#endif
+ StartBenchmarkTiming();
+ for (int iter = 0; iter < num_iters; ++iter) {
+ C.slice(first_quadrant, quarter_sizes).device(device_) =
+ A.slice(first_quadrant, quarter_sizes);
+ C.slice(second_quadrant, quarter_sizes).device(device_) =
+ B.slice(second_quadrant, quarter_sizes);
+ C.slice(third_quadrant, quarter_sizes).device(device_) =
+ A.slice(third_quadrant, quarter_sizes);
+ C.slice(fourth_quadrant, quarter_sizes).device(device_) =
+ B.slice(fourth_quadrant, quarter_sizes);
+ }
+ // Record the number of values copied from the rhs slice to the lhs slice
+ // each second
+ finalizeBenchmark(static_cast<int64_t>(m_) * m_ * num_iters);
+ }
+
+ void rowChip(int num_iters) {
+ Eigen::array<TensorIndex, 2> input_size;
+ input_size[0] = k_;
+ input_size[1] = n_;
+ const TensorMap<Tensor<T, 2, 0, TensorIndex>, Eigen::Aligned> B(b_, input_size);
+ Eigen::array<TensorIndex, 1> output_size;
+ output_size[0] = n_;
+ TensorMap<Tensor<T, 1, 0, TensorIndex>, Eigen::Aligned> C(c_, output_size);
+#ifdef EIGEN_USE_SYCL // warmup for sycl
+ for (int iter = 0; iter < 10; ++iter) {
+ C.device(device_) = B.chip(iter % k_, 0);
+ }
+#endif
+ StartBenchmarkTiming();
+ for (int iter = 0; iter < num_iters; ++iter) {
+ C.device(device_) = B.chip(iter % k_, 0);
+ }
+ // Record the number of values copied from the rhs chip to the lhs.
+ finalizeBenchmark(static_cast<int64_t>(n_) * num_iters);
+ }
+
+ void colChip(int num_iters) {
+ Eigen::array<TensorIndex, 2> input_size;
+ input_size[0] = k_;
+ input_size[1] = n_;
+ const TensorMap<Tensor<T, 2, 0, TensorIndex>, Eigen::Aligned> B(b_, input_size);
+ Eigen::array<TensorIndex, 1> output_size;
+ output_size[0] = n_;
+ TensorMap<Tensor<T, 1, 0, TensorIndex>, Eigen::Aligned> C(c_, output_size);
+#ifdef EIGEN_USE_SYCL // warmup for sycl
+ for (int iter = 0; iter < 10; ++iter) {
+ C.device(device_) = B.chip(iter % n_, 1);
+ }
+#endif
+ StartBenchmarkTiming();
+ for (int iter = 0; iter < num_iters; ++iter) {
+ C.device(device_) = B.chip(iter % n_, 1);
+ }
+ // Record the number of values copied from the rhs chip to the lhs.
+ finalizeBenchmark(static_cast<int64_t>(n_) * num_iters);
+ }
+
+ void shuffling(int num_iters) {
+ eigen_assert(m_ == n_);
+ Eigen::array<TensorIndex, 2> size_a;
+ size_a[0] = m_;
+ size_a[1] = k_;
+ const TensorMap<Tensor<T, 2>, Eigen::Aligned> A(a_, size_a);
+ Eigen::array<TensorIndex, 2> size_b;
+ size_b[0] = k_;
+ size_b[1] = m_;
+ TensorMap<Tensor<T, 2>, Eigen::Aligned> B(b_, size_b);
+
+ Eigen::array<int, 2> shuffle;
+ shuffle[0] = 1;
+ shuffle[1] = 0;
+#ifdef EIGEN_USE_SYCL // warmup for sycl
+ for (int iter = 0; iter < 10; ++iter) {
+ B.device(device_) = A.shuffle(shuffle);
+ }
+#endif
+ StartBenchmarkTiming();
+ for (int iter = 0; iter < num_iters; ++iter) {
+ B.device(device_) = A.shuffle(shuffle);
+ }
+ // Record the number of values shuffled from A and copied to B each second
+ finalizeBenchmark(static_cast<int64_t>(m_) * k_ * num_iters);
+ }
+
+ void padding(int num_iters) {
+ eigen_assert(m_ == k_);
+ Eigen::array<TensorIndex, 2> size_a;
+ size_a[0] = m_;
+ size_a[1] = k_-3;
+ const TensorMap<Tensor<T, 2>, Eigen::Aligned> A(a_, size_a);
+ Eigen::array<TensorIndex, 2> size_b;
+ size_b[0] = k_;
+ size_b[1] = m_;
+ TensorMap<Tensor<T, 2>, Eigen::Aligned> B(b_, size_b);
+
+ Eigen::IndexPairList<Eigen::type2indexpair<0, 0>,
+ Eigen::type2indexpair<2, 1> > paddings;
+#ifdef EIGEN_USE_SYCL // warmup for sycl
+ for (int iter = 0; iter < 10; ++iter) {
+ B.device(device_) = A.pad(paddings);
+ }
+#endif
+ StartBenchmarkTiming();
+ for (int iter = 0; iter < num_iters; ++iter) {
+ B.device(device_) = A.pad(paddings);
+ }
+ // Record the number of values copied from the padded tensor A each second
+ finalizeBenchmark(static_cast<int64_t>(m_) * k_ * num_iters);
+ }
+
+ void striding(int num_iters) {
+ eigen_assert(m_ == k_);
+ Eigen::array<TensorIndex, 2> size_a;
+ size_a[0] = m_;
+ size_a[1] = k_;
+ const TensorMap<Tensor<T, 2>, Eigen::Aligned> A(a_, size_a);
+ Eigen::array<TensorIndex, 2> size_b;
+ size_b[0] = m_;
+ size_b[1] = k_/2;
+ TensorMap<Tensor<T, 2>, Eigen::Aligned> B(b_, size_b);
+
+ Eigen::IndexList<Eigen::type2index<1>, Eigen::type2index<2> > strides;
+
+#ifdef EIGEN_USE_SYCL // warmup for sycl
+ for (int iter = 0; iter < 10; ++iter) {
+ B.device(device_) = A.stride(strides);
+ }
+#endif
+ StartBenchmarkTiming();
+ for (int iter = 0; iter < num_iters; ++iter) {
+ B.device(device_) = A.stride(strides);
+ }
+ // Record the number of values copied from the padded tensor A each second
+ finalizeBenchmark(static_cast<int64_t>(m_) * k_ * num_iters);
+ }
+
+
+ void broadcasting(int num_iters) {
+ Eigen::array<TensorIndex, 2> size_a;
+ size_a[0] = m_;
+ size_a[1] = 1;
+ const TensorMap<Tensor<T, 2>, Eigen::Aligned> A(a_, size_a);
+ Eigen::array<TensorIndex, 2> size_c;
+ size_c[0] = m_;
+ size_c[1] = n_;
+ TensorMap<Tensor<T, 2>, Eigen::Aligned> C(c_, size_c);
+ Eigen::IndexList<Eigen::type2index<1>, int> broadcast;
+ broadcast.set(1, n_);
+
+#ifdef EIGEN_USE_SYCL // warmup for sycl
+ for (int iter = 0; iter < 10; ++iter) {
+ C.device(device_) = A.broadcast(broadcast);
+ }
+#endif
+ StartBenchmarkTiming();
+ for (int iter = 0; iter < num_iters; ++iter) {
+ C.device(device_) = A.broadcast(broadcast);
+ }
+ // Record the number of values broadcasted from A and copied to C each second
+ finalizeBenchmark(static_cast<int64_t>(m_) * n_ * num_iters);
+ }
+
+ void coeffWiseOp(int num_iters) {
+ eigen_assert(m_ == k_ && k_ == n_);
+ Eigen::array<TensorIndex, 2> sizes;
+ sizes[0] = m_;
+ sizes[1] = m_;
+ const TensorMap<Tensor<T, 2>, Eigen::Aligned> A(a_, sizes);
+ const TensorMap<Tensor<T, 2>, Eigen::Aligned> B(b_, sizes);
+ TensorMap<Tensor<T, 2>, Eigen::Aligned> C(c_, sizes);
+#ifdef EIGEN_USE_SYCL // warmup for sycl
+ for (int iter = 0; iter < 10; ++iter) {
+ C.device(device_) = A * A.constant(static_cast<T>(3.14)) + B * B.constant(static_cast<T>(2.7));
+ }
+#endif
+ StartBenchmarkTiming();
+ for (int iter = 0; iter < num_iters; ++iter) {
+ C.device(device_) = A * A.constant(static_cast<T>(3.14)) + B * B.constant(static_cast<T>(2.7));
+ }
+ // Record the number of FLOP executed per second (2 multiplications and
+ // 1 addition per value)
+ finalizeBenchmark(static_cast<int64_t>(3) * m_ * m_ * num_iters);
+ }
+
+ void algebraicFunc(int num_iters) {
+ eigen_assert(m_ == k_ && k_ == n_);
+ Eigen::array<TensorIndex, 2> sizes;
+ sizes[0] = m_;
+ sizes[1] = m_;
+ const TensorMap<Tensor<T, 2>, Eigen::Aligned> A(a_, sizes);
+ const TensorMap<Tensor<T, 2>, Eigen::Aligned> B(b_, sizes);
+ TensorMap<Tensor<T, 2>, Eigen::Aligned> C(c_, sizes);
+
+#ifdef EIGEN_USE_SYCL // warmup for sycl
+for (int iter = 0; iter < 10; ++iter) {
+ C.device(device_) = A.rsqrt() + B.sqrt() * B.square();
+}
+#endif
+ StartBenchmarkTiming();
+ for (int iter = 0; iter < num_iters; ++iter) {
+ C.device(device_) = A.rsqrt() + B.sqrt() * B.square();
+ }
+ // Record the number of FLOP executed per second (assuming one operation
+ // per value)
+ finalizeBenchmark(static_cast<int64_t>(m_) * m_ * num_iters);
+ }
+
+ void transcendentalFunc(int num_iters) {
+ eigen_assert(m_ == k_ && k_ == n_);
+ Eigen::array<TensorIndex, 2> sizes;
+ sizes[0] = m_;
+ sizes[1] = m_;
+ const TensorMap<Tensor<T, 2>, Eigen::Aligned> A(a_, sizes);
+ const TensorMap<Tensor<T, 2>, Eigen::Aligned> B(b_, sizes);
+ TensorMap<Tensor<T, 2>, Eigen::Aligned> C(c_, sizes);
+#ifdef EIGEN_USE_SYCL // warmup for sycl
+ for (int iter = 0; iter < 10; ++iter) {
+ C.device(device_) = A.exp() + B.log();
+ }
+#endif
+ StartBenchmarkTiming();
+ for (int iter = 0; iter < num_iters; ++iter) {
+ C.device(device_) = A.exp() + B.log();
+ }
+ // Record the number of FLOP executed per second (assuming one operation
+ // per value)
+ finalizeBenchmark(static_cast<int64_t>(m_) * m_ * num_iters);
+ }
+
+ // Row reduction
+ void rowReduction(int num_iters) {
+ Eigen::array<TensorIndex, 2> input_size;
+ input_size[0] = k_;
+ input_size[1] = n_;
+ const TensorMap<Tensor<T, 2, 0, TensorIndex>, Eigen::Aligned> B(b_, input_size);
+ Eigen::array<TensorIndex, 1> output_size;
+ output_size[0] = n_;
+ TensorMap<Tensor<T, 1, 0, TensorIndex>, Eigen::Aligned> C(c_, output_size);
+ Eigen::IndexList<Eigen::type2index<0>> sum_along_dim;
+#ifdef EIGEN_USE_SYCL // warmup for sycl
+ for (int iter = 0; iter < 10; ++iter) {
+ C.device(device_) = B.sum(sum_along_dim);
+ }
+#endif
+ StartBenchmarkTiming();
+ for (int iter = 0; iter < num_iters; ++iter) {
+ C.device(device_) = B.sum(sum_along_dim);
+ }
+ // Record the number of FLOP executed per second (assuming one operation
+ // per value)
+ finalizeBenchmark(static_cast<int64_t>(k_) * n_ * num_iters);
+ }
+
+ // Column reduction
+ void colReduction(int num_iters) {
+ Eigen::array<TensorIndex, 2> input_size;
+ input_size[0] = k_;
+ input_size[1] = n_;
+ const TensorMap<Tensor<T, 2, 0, TensorIndex>, Eigen::Aligned> B(
+ b_, input_size);
+ Eigen::array<TensorIndex, 1> output_size;
+ output_size[0] = k_;
+ TensorMap<Tensor<T, 1, 0, TensorIndex>, Eigen::Aligned> A(
+ a_, output_size);
+
+#ifndef EIGEN_HAS_INDEX_LIST
+ Eigen::array<TensorIndex, 1> sum_along_dim;
+ sum_along_dim[0] = 1;
+#else
+ // Take advantage of cxx11 to give the compiler information it can use to
+ // optimize the code.
+ Eigen::IndexList<Eigen::type2index<1>> sum_along_dim;
+#endif
+#ifdef EIGEN_USE_SYCL // warmup for sycl
+ for (int iter = 0; iter < 10; ++iter) {
+ A.device(device_) = B.sum(sum_along_dim);
+ }
+#endif
+ StartBenchmarkTiming();
+ for (int iter = 0; iter < num_iters; ++iter) {
+ A.device(device_) = B.sum(sum_along_dim);
+ }
+ // Record the number of FLOP executed per second (assuming one operation
+ // per value)
+ finalizeBenchmark(static_cast<int64_t>(k_) * n_ * num_iters);
+ }
+
+ // Full reduction
+ void fullReduction(int num_iters) {
+ Eigen::array<TensorIndex, 2> input_size;
+ input_size[0] = k_;
+ input_size[1] = n_;
+ const TensorMap<Tensor<T, 2, 0, TensorIndex>, Eigen::Aligned> B(
+ b_, input_size);
+ Eigen::array<TensorIndex, 0> output_size;
+ TensorMap<Tensor<T, 0, 0, TensorIndex>, Eigen::Aligned> C(
+ c_, output_size);
+#ifdef EIGEN_USE_SYCL // warmup for sycl
+ for (int iter = 0; iter < 10; ++iter) {
+ C.device(device_) = B.sum();
+ }
+#endif
+ StartBenchmarkTiming();
+ for (int iter = 0; iter < num_iters; ++iter) {
+ C.device(device_) = B.sum();
+ }
+ // Record the number of FLOP executed per second (assuming one operation
+ // per value)
+ finalizeBenchmark(static_cast<int64_t>(k_) * n_ * num_iters);
+ }
+
+
+
+ // do a contraction which is equivalent to a matrix multiplication
+ void contraction(int num_iters) {
+ contraction<static_cast<int>(Eigen::ColMajor)>(num_iters, false, false);
+ }
+
+ void contractionRowMajor(int num_iters) {
+ contraction<static_cast<int>(Eigen::RowMajor)>(num_iters, false, false);
+ }
+
+ void contractionRowMajorAT(int num_iters) {
+ contraction<static_cast<int>(Eigen::RowMajor)>(num_iters, true, false);
+ }
+
+ void contractionRowMajorBT(int num_iters) {
+ contraction<static_cast<int>(Eigen::RowMajor)>(num_iters, false, true);
+ }
+
+ void contractionRowMajorABT(int num_iters) {
+ contraction<static_cast<int>(Eigen::RowMajor)>(num_iters, true, true);
+ }
+
+ void convolution(int num_iters, int kernel_x, int kernel_y) {
+ Eigen::array<TensorIndex, 2> input_sizes;
+ input_sizes[0] = m_;
+ input_sizes[1] = n_;
+ TensorMap<Tensor<T, 2>, Eigen::Aligned> A(a_, input_sizes);
+ Eigen::array<TensorIndex, 2> kernel_sizes;
+ kernel_sizes[0] = kernel_x;
+ kernel_sizes[1] = kernel_y;
+ TensorMap<Tensor<T, 2>, Eigen::Aligned> B(b_, kernel_sizes);
+ Eigen::array<TensorIndex, 2> result_sizes;
+ result_sizes[0] = m_ - kernel_x + 1;
+ result_sizes[1] = n_ - kernel_y + 1;
+ TensorMap<Tensor<T, 2>, Eigen::Aligned> C(c_, result_sizes);
+ Eigen::array<TensorIndex, 2> dims;
+ dims[0] = 0;
+ dims[1] = 1;
+#ifdef EIGEN_USE_SYCL // warmup for sycl
+ for (int iter = 0; iter < 10; ++iter) {
+ C.device(device_) = A.convolve(B, dims);
+ }
+#endif
+ StartBenchmarkTiming();
+ for (int iter = 0; iter < num_iters; ++iter) {
+ C.device(device_) = A.convolve(B, dims);
+ }
+ // Record the number of FLOPs executed per second (kernel_size
+ // multiplications and additions for each value in the resulting tensor)
+ finalizeBenchmark(static_cast<int64_t>(2) *
+ (m_ - kernel_x + 1) * (n_ - kernel_y + 1) * kernel_x * kernel_y * num_iters);
+ }
+
+ private:
+ // do a contraction which is equivalent to a matrix multiplication
+ template<int Layout>
+ void contraction(int num_iters, bool trans_a, bool trans_b) {
+ Eigen::array<TensorIndex, 2> sizeA;
+ sizeA[0] = (trans_a ? k_: m_);
+ sizeA[1] = (trans_a ? m_: k_);
+ Eigen::array<TensorIndex, 2> sizeB;
+ sizeB[0] = (trans_b ? n_: k_);
+ sizeB[1] = (trans_b ? k_: n_);
+ Eigen::array<TensorIndex, 2> sizeC;
+ sizeC[0] = m_;
+ sizeC[1] = n_;
+
+ const TensorMap<Tensor<T, 2, Layout>, Eigen::Aligned> A(a_, sizeA);
+ const TensorMap<Tensor<T, 2, Layout>, Eigen::Aligned> B(b_, sizeB);
+ TensorMap<Tensor<T, 2, Layout>, Eigen::Aligned> C(c_, sizeC);
+
+ typedef typename Tensor<T, 2, Layout>::DimensionPair DimPair;
+ Eigen::array<DimPair, 1> dims;
+ TensorIndex a_contract_dim = (trans_a ? 0 : 1);
+ TensorIndex b_contract_dim = (trans_b ? 1 : 0);
+ dims[0] = DimPair(a_contract_dim, b_contract_dim);
+#ifdef EIGEN_USE_SYCL // warmup for sycl
+ for (int iter = 0; iter < 10; ++iter) {
+ C.device(device_) = A.contract(B, dims);
+ }
+#endif
+ StartBenchmarkTiming();
+ for (int iter = 0; iter < num_iters; ++iter) {
+ C.device(device_) = A.contract(B, dims);
+ }
+ // Record the number of FLOP executed per second (size_ multiplications and
+ // additions for each value in the resulting tensor)
+ finalizeBenchmark(static_cast<int64_t>(2) * m_ * n_ * k_ * num_iters);
+ }
+
+ void initialize() {
+ a_ = (T *) device_.allocate(m_ * k_ * sizeof(T));
+ b_ = (T *) device_.allocate(k_ * n_ * sizeof(T));
+ c_ = (T *) device_.allocate(m_ * n_ * sizeof(T));
+
+ // Initialize the content of the memory pools to prevent asan from
+ // complaining.
+ device_.fill(a_, a_ + m_ * k_, T(12));
+ device_.fill(b_, b_ + k_ * n_, T(23));
+ device_.fill(c_, c_ + m_ * n_, T(31));
+
+ }
+
+ inline void finalizeBenchmark(int64_t num_items) {
+#if defined(EIGEN_USE_GPU) && defined(__CUDACC__)
+ if (Eigen::internal::is_same<Device, Eigen::GpuDevice>::value) {
+ device_.synchronize();
+ }
+#elif defined(EIGEN_USE_SYCL)
+ if (Eigen::internal::is_same<Device, Eigen::SyclDevice>::value) {
+ device_.synchronize();
+ }
+
+#endif
+ StopBenchmarkTiming();
+ SetBenchmarkFlopsProcessed(num_items);
+ }
+
+
+ TensorIndex m_;
+ TensorIndex k_;
+ TensorIndex n_;
+ T* a_;
+ T* b_;
+ T* c_;
+ Device device_;
+};
+#endif // THIRD_PARTY_EIGEN3_TENSOR_BENCHMARKS_H_
diff --git a/bench/tensors/tensor_benchmarks_fp16_gpu.cu b/bench/tensors/tensor_benchmarks_fp16_gpu.cu
new file mode 100644
index 0000000..65784d0
--- /dev/null
+++ b/bench/tensors/tensor_benchmarks_fp16_gpu.cu
@@ -0,0 +1,77 @@
+#define EIGEN_USE_GPU
+
+#include <cuda.h>
+#include <cuda_runtime.h>
+#include <iostream>
+
+#include "tensor_benchmarks.h"
+
+// Simple functions
+#define BM_FuncGPU(FUNC) \
+ static void BM_##FUNC(int iters, int N) { \
+ StopBenchmarkTiming(); \
+ Eigen::CudaStreamDevice stream; \
+ Eigen::GpuDevice device(&stream); \
+ BenchmarkSuite<Eigen::GpuDevice, Eigen::half> suite(device, N); \
+ cudaDeviceSynchronize(); \
+ suite.FUNC(iters); \
+ } \
+ BENCHMARK_RANGE(BM_##FUNC, 10, 5000);
+
+BM_FuncGPU(memcpy);
+BM_FuncGPU(typeCasting);
+//BM_FuncGPU(random);
+BM_FuncGPU(slicing);
+BM_FuncGPU(rowChip);
+BM_FuncGPU(colChip);
+BM_FuncGPU(shuffling);
+BM_FuncGPU(padding);
+BM_FuncGPU(striding);
+BM_FuncGPU(broadcasting);
+BM_FuncGPU(coeffWiseOp);
+BM_FuncGPU(algebraicFunc);
+BM_FuncGPU(transcendentalFunc);
+BM_FuncGPU(rowReduction);
+BM_FuncGPU(colReduction);
+BM_FuncGPU(fullReduction);
+
+
+// Contractions
+#define BM_FuncWithInputDimsGPU(FUNC, D1, D2, D3) \
+ static void BM_##FUNC##_##D1##x##D2##x##D3(int iters, int N) { \
+ StopBenchmarkTiming(); \
+ Eigen::CudaStreamDevice stream; \
+ Eigen::GpuDevice device(&stream); \
+ BenchmarkSuite<Eigen::GpuDevice, Eigen::half> suite(device, D1, D2, D3); \
+ cudaDeviceSynchronize(); \
+ suite.FUNC(iters); \
+ } \
+ BENCHMARK_RANGE(BM_##FUNC##_##D1##x##D2##x##D3, 10, 5000);
+
+
+BM_FuncWithInputDimsGPU(contraction, N, N, N);
+BM_FuncWithInputDimsGPU(contraction, 64, N, N);
+BM_FuncWithInputDimsGPU(contraction, N, 64, N);
+BM_FuncWithInputDimsGPU(contraction, N, N, 64);
+
+
+// Convolutions
+#define BM_FuncWithKernelDimsGPU(FUNC, DIM1, DIM2) \
+ static void BM_##FUNC##_##DIM1##x##DIM2(int iters, int N) { \
+ StopBenchmarkTiming(); \
+ Eigen::CudaStreamDevice stream; \
+ Eigen::GpuDevice device(&stream); \
+ BenchmarkSuite<Eigen::GpuDevice, Eigen::half> suite(device, N); \
+ cudaDeviceSynchronize(); \
+ suite.FUNC(iters, DIM1, DIM2); \
+ } \
+ BENCHMARK_RANGE(BM_##FUNC##_##DIM1##x##DIM2, 128, 5000);
+
+/*
+BM_FuncWithKernelDimsGPU(convolution, 7, 1);
+BM_FuncWithKernelDimsGPU(convolution, 1, 7);
+BM_FuncWithKernelDimsGPU(convolution, 7, 4);
+BM_FuncWithKernelDimsGPU(convolution, 4, 7);
+BM_FuncWithKernelDimsGPU(convolution, 7, 64);
+BM_FuncWithKernelDimsGPU(convolution, 64, 7);
+*/
diff --git a/bench/tensors/tensor_benchmarks_gpu.cu b/bench/tensors/tensor_benchmarks_gpu.cu
new file mode 100644
index 0000000..76d68c5
--- /dev/null
+++ b/bench/tensors/tensor_benchmarks_gpu.cu
@@ -0,0 +1,75 @@
+#define EIGEN_USE_GPU
+
+#include <cuda.h>
+#include <cuda_runtime.h>
+#include <iostream>
+
+#include "tensor_benchmarks.h"
+
+// Simple functions
+#define BM_FuncGPU(FUNC) \
+ static void BM_##FUNC(int iters, int N) { \
+ StopBenchmarkTiming(); \
+ Eigen::CudaStreamDevice stream; \
+ Eigen::GpuDevice device(&stream); \
+ BenchmarkSuite<Eigen::GpuDevice, float> suite(device, N); \
+ cudaDeviceSynchronize(); \
+ suite.FUNC(iters); \
+ } \
+ BENCHMARK_RANGE(BM_##FUNC, 10, 5000);
+
+BM_FuncGPU(memcpy);
+BM_FuncGPU(typeCasting);
+BM_FuncGPU(random);
+BM_FuncGPU(slicing);
+BM_FuncGPU(rowChip);
+BM_FuncGPU(colChip);
+BM_FuncGPU(shuffling);
+BM_FuncGPU(padding);
+BM_FuncGPU(striding);
+BM_FuncGPU(broadcasting);
+BM_FuncGPU(coeffWiseOp);
+BM_FuncGPU(algebraicFunc);
+BM_FuncGPU(transcendentalFunc);
+BM_FuncGPU(rowReduction);
+BM_FuncGPU(colReduction);
+BM_FuncGPU(fullReduction);
+
+
+// Contractions
+#define BM_FuncWithInputDimsGPU(FUNC, D1, D2, D3) \
+ static void BM_##FUNC##_##D1##x##D2##x##D3(int iters, int N) { \
+ StopBenchmarkTiming(); \
+ Eigen::CudaStreamDevice stream; \
+ Eigen::GpuDevice device(&stream); \
+ BenchmarkSuite<Eigen::GpuDevice, float> suite(device, D1, D2, D3); \
+ cudaDeviceSynchronize(); \
+ suite.FUNC(iters); \
+ } \
+ BENCHMARK_RANGE(BM_##FUNC##_##D1##x##D2##x##D3, 10, 5000);
+
+
+BM_FuncWithInputDimsGPU(contraction, N, N, N);
+BM_FuncWithInputDimsGPU(contraction, 64, N, N);
+BM_FuncWithInputDimsGPU(contraction, N, 64, N);
+BM_FuncWithInputDimsGPU(contraction, N, N, 64);
+
+
+// Convolutions
+#define BM_FuncWithKernelDimsGPU(FUNC, DIM1, DIM2) \
+ static void BM_##FUNC##_##DIM1##x##DIM2(int iters, int N) { \
+ StopBenchmarkTiming(); \
+ Eigen::CudaStreamDevice stream; \
+ Eigen::GpuDevice device(&stream); \
+ BenchmarkSuite<Eigen::GpuDevice, float> suite(device, N); \
+ cudaDeviceSynchronize(); \
+ suite.FUNC(iters, DIM1, DIM2); \
+ } \
+ BENCHMARK_RANGE(BM_##FUNC##_##DIM1##x##DIM2, 128, 5000);
+
+BM_FuncWithKernelDimsGPU(convolution, 7, 1);
+BM_FuncWithKernelDimsGPU(convolution, 1, 7);
+BM_FuncWithKernelDimsGPU(convolution, 7, 4);
+BM_FuncWithKernelDimsGPU(convolution, 4, 7);
+BM_FuncWithKernelDimsGPU(convolution, 7, 64);
+BM_FuncWithKernelDimsGPU(convolution, 64, 7);
diff --git a/bench/vdw_new.cpp b/bench/vdw_new.cpp
new file mode 100644
index 0000000..d260404
--- /dev/null
+++ b/bench/vdw_new.cpp
@@ -0,0 +1,56 @@
+#include <iostream>
+#include <Eigen/Core>
+
+using namespace Eigen;
+
+#ifndef SCALAR
+#define SCALAR float
+#endif
+
+#ifndef SIZE
+#define SIZE 10000
+#endif
+
+#ifndef REPEAT
+#define REPEAT 10000
+#endif
+
+typedef Matrix<SCALAR, Eigen::Dynamic, 1> Vec;
+
+using namespace std;
+
+SCALAR E_VDW(const Vec &interactions1, const Vec &interactions2)
+{
+ return (interactions2.cwise()/interactions1)
+ .cwise().cube()
+ .cwise().square()
+ .cwise().square()
+ .sum();
+}
+
+int main()
+{
+ //
+ // 1 2 3 4 ... (interactions)
+ // ka . . . . ...
+ // rab . . . . ...
+ // energy . . . . ...
+ // ... ... ... ... ... ...
+ // (variables
+ // for
+ // interaction)
+ //
+ Vec interactions1(SIZE), interactions2(SIZE); // SIZE is the number of vdw interactions in our system
+ // SetupCalculations()
+ SCALAR rab = 1.0;
+ interactions1.setConstant(2.4);
+ interactions2.setConstant(rab);
+
+ // Energy()
+ SCALAR energy = 0.0;
+ for (unsigned int i = 0; i<REPEAT; ++i) {
+ energy += E_VDW(interactions1, interactions2);
+ energy *= 1 + 1e-20 * i; // prevent compiler from optimizing the loop
+ }
+ cout << "energy = " << energy << endl;
+}
diff --git a/blas/BandTriangularSolver.h b/blas/BandTriangularSolver.h
new file mode 100644
index 0000000..e8551cd
--- /dev/null
+++ b/blas/BandTriangularSolver.h
@@ -0,0 +1,93 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2011 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_BAND_TRIANGULARSOLVER_H
+#define EIGEN_BAND_TRIANGULARSOLVER_H
+
+namespace internal {
+
+ /* \internal
+ * Solve Ax=b with A a band triangular matrix
+ * TODO: extend it to matrices for x abd b */
+template<typename Index, int Mode, typename LhsScalar, bool ConjLhs, typename RhsScalar, int StorageOrder>
+struct band_solve_triangular_selector;
+
+
+template<typename Index, int Mode, typename LhsScalar, bool ConjLhs, typename RhsScalar>
+struct band_solve_triangular_selector<Index,Mode,LhsScalar,ConjLhs,RhsScalar,RowMajor>
+{
+ typedef Map<const Matrix<LhsScalar,Dynamic,Dynamic,RowMajor>, 0, OuterStride<> > LhsMap;
+ typedef Map<Matrix<RhsScalar,Dynamic,1> > RhsMap;
+ enum { IsLower = (Mode&Lower) ? 1 : 0 };
+ static void run(Index size, Index k, const LhsScalar* _lhs, Index lhsStride, RhsScalar* _other)
+ {
+ const LhsMap lhs(_lhs,size,k+1,OuterStride<>(lhsStride));
+ RhsMap other(_other,size,1);
+ std::conditional_t<ConjLhs,
+ const CwiseUnaryOp<typename internal::scalar_conjugate_op<LhsScalar>,LhsMap>,
+ const LhsMap&> cjLhs(lhs);
+
+ for(int col=0 ; col<other.cols() ; ++col)
+ {
+ for(int ii=0; ii<size; ++ii)
+ {
+ int i = IsLower ? ii : size-ii-1;
+ int actual_k = (std::min)(k,ii);
+ int actual_start = IsLower ? k-actual_k : 1;
+
+ if(actual_k>0)
+ other.coeffRef(i,col) -= cjLhs.row(i).segment(actual_start,actual_k).transpose()
+ .cwiseProduct(other.col(col).segment(IsLower ? i-actual_k : i+1,actual_k)).sum();
+
+ if((Mode&UnitDiag)==0)
+ other.coeffRef(i,col) /= cjLhs(i,IsLower ? k : 0);
+ }
+ }
+ }
+
+};
+
+template<typename Index, int Mode, typename LhsScalar, bool ConjLhs, typename RhsScalar>
+struct band_solve_triangular_selector<Index,Mode,LhsScalar,ConjLhs,RhsScalar,ColMajor>
+{
+ typedef Map<const Matrix<LhsScalar,Dynamic,Dynamic,ColMajor>, 0, OuterStride<> > LhsMap;
+ typedef Map<Matrix<RhsScalar,Dynamic,1> > RhsMap;
+ enum { IsLower = (Mode&Lower) ? 1 : 0 };
+ static void run(Index size, Index k, const LhsScalar* _lhs, Index lhsStride, RhsScalar* _other)
+ {
+ const LhsMap lhs(_lhs,k+1,size,OuterStride<>(lhsStride));
+ RhsMap other(_other,size,1);
+ std::conditional_t<ConjLhs,
+ const CwiseUnaryOp<typename internal::scalar_conjugate_op<LhsScalar>,LhsMap>,
+ const LhsMap&> cjLhs(lhs);
+
+ for(int col=0 ; col<other.cols() ; ++col)
+ {
+ for(int ii=0; ii<size; ++ii)
+ {
+ int i = IsLower ? ii : size-ii-1;
+ int actual_k = (std::min)(k,size-ii-1);
+ int actual_start = IsLower ? 1 : k-actual_k;
+
+ if((Mode&UnitDiag)==0)
+ other.coeffRef(i,col) /= cjLhs(IsLower ? 0 : k, i);
+
+ if(actual_k>0)
+ other.col(col).segment(IsLower ? i+1 : i-actual_k, actual_k)
+ -= other.coeff(i,col) * cjLhs.col(i).segment(actual_start,actual_k);
+
+ }
+ }
+ }
+};
+
+
+} // end namespace internal
+
+#endif // EIGEN_BAND_TRIANGULARSOLVER_H
diff --git a/blas/CMakeLists.txt b/blas/CMakeLists.txt
new file mode 100644
index 0000000..c530957
--- /dev/null
+++ b/blas/CMakeLists.txt
@@ -0,0 +1,63 @@
+
+project(EigenBlas CXX)
+
+if(EIGEN_BUILD_BLAS)
+include(CheckLanguage)
+check_language(Fortran)
+if(CMAKE_Fortran_COMPILER)
+ enable_language(Fortran)
+ set(EIGEN_Fortran_COMPILER_WORKS ON)
+else()
+ set(EIGEN_Fortran_COMPILER_WORKS OFF)
+endif()
+
+add_custom_target(blas)
+
+set(EigenBlas_SRCS single.cpp double.cpp complex_single.cpp complex_double.cpp xerbla.cpp
+ f2c/srotm.c f2c/srotmg.c f2c/drotm.c f2c/drotmg.c
+ f2c/lsame.c f2c/dspmv.c f2c/ssbmv.c f2c/chbmv.c
+ f2c/sspmv.c f2c/zhbmv.c f2c/chpmv.c f2c/dsbmv.c
+ f2c/zhpmv.c f2c/dtbmv.c f2c/stbmv.c f2c/ctbmv.c
+ f2c/ztbmv.c f2c/d_cnjg.c f2c/r_cnjg.c
+ )
+
+if (EIGEN_Fortran_COMPILER_WORKS)
+ set(EigenBlas_SRCS ${EigenBlas_SRCS} fortran/complexdots.f)
+else()
+ set(EigenBlas_SRCS ${EigenBlas_SRCS} f2c/complexdots.c)
+endif()
+
+set(EIGEN_BLAS_TARGETS "")
+
+add_library(eigen_blas_static ${EigenBlas_SRCS})
+list(APPEND EIGEN_BLAS_TARGETS eigen_blas_static)
+
+if (EIGEN_BUILD_SHARED_LIBS)
+ add_library(eigen_blas SHARED ${EigenBlas_SRCS})
+ list(APPEND EIGEN_BLAS_TARGETS eigen_blas)
+endif()
+
+foreach(target IN LISTS EIGEN_BLAS_TARGETS)
+ if(EIGEN_STANDARD_LIBRARIES_TO_LINK_TO)
+ target_link_libraries(${target} ${EIGEN_STANDARD_LIBRARIES_TO_LINK_TO})
+ endif()
+
+ add_dependencies(blas ${target})
+ install(TARGETS ${target}
+ RUNTIME DESTINATION bin
+ LIBRARY DESTINATION lib
+ ARCHIVE DESTINATION lib)
+endforeach()
+
+if(EIGEN_Fortran_COMPILER_WORKS)
+
+if(EIGEN_BUILD_TESTING)
+ if(EIGEN_LEAVE_TEST_IN_ALL_TARGET)
+ add_subdirectory(testing) # can't do EXCLUDE_FROM_ALL here, breaks CTest
+ else()
+ add_subdirectory(testing EXCLUDE_FROM_ALL)
+ endif()
+endif()
+
+endif()
+endif()
diff --git a/blas/GeneralRank1Update.h b/blas/GeneralRank1Update.h
new file mode 100644
index 0000000..07d388c
--- /dev/null
+++ b/blas/GeneralRank1Update.h
@@ -0,0 +1,44 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2012 Chen-Pang He <jdh8@ms63.hinet.net>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_GENERAL_RANK1UPDATE_H
+#define EIGEN_GENERAL_RANK1UPDATE_H
+
+namespace internal {
+
+/* Optimized matrix += alpha * uv' */
+template<typename Scalar, typename Index, int StorageOrder, bool ConjLhs, bool ConjRhs>
+struct general_rank1_update;
+
+template<typename Scalar, typename Index, bool ConjLhs, bool ConjRhs>
+struct general_rank1_update<Scalar,Index,ColMajor,ConjLhs,ConjRhs>
+{
+ static void run(Index rows, Index cols, Scalar* mat, Index stride, const Scalar* u, const Scalar* v, Scalar alpha)
+ {
+ typedef Map<const Matrix<Scalar,Dynamic,1> > OtherMap;
+ typedef typename conj_expr_if<ConjLhs,OtherMap>::type ConjRhsType;
+ conj_if<ConjRhs> cj;
+
+ for (Index i=0; i<cols; ++i)
+ Map<Matrix<Scalar,Dynamic,1> >(mat+stride*i,rows) += alpha * cj(v[i]) * ConjRhsType(OtherMap(u,rows));
+ }
+};
+
+template<typename Scalar, typename Index, bool ConjLhs, bool ConjRhs>
+struct general_rank1_update<Scalar,Index,RowMajor,ConjLhs,ConjRhs>
+{
+ static void run(Index rows, Index cols, Scalar* mat, Index stride, const Scalar* u, const Scalar* v, Scalar alpha)
+ {
+ general_rank1_update<Scalar,Index,ColMajor,ConjRhs,ConjRhs>::run(rows,cols,mat,stride,u,v,alpha);
+ }
+};
+
+} // end namespace internal
+
+#endif // EIGEN_GENERAL_RANK1UPDATE_H
diff --git a/blas/PackedSelfadjointProduct.h b/blas/PackedSelfadjointProduct.h
new file mode 100644
index 0000000..07327a2
--- /dev/null
+++ b/blas/PackedSelfadjointProduct.h
@@ -0,0 +1,53 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2012 Chen-Pang He <jdh8@ms63.hinet.net>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_SELFADJOINT_PACKED_PRODUCT_H
+#define EIGEN_SELFADJOINT_PACKED_PRODUCT_H
+
+namespace internal {
+
+/* Optimized matrix += alpha * uv'
+ * The matrix is in packed form.
+ */
+template<typename Scalar, typename Index, int StorageOrder, int UpLo, bool ConjLhs, bool ConjRhs>
+struct selfadjoint_packed_rank1_update;
+
+template<typename Scalar, typename Index, int UpLo, bool ConjLhs, bool ConjRhs>
+struct selfadjoint_packed_rank1_update<Scalar,Index,ColMajor,UpLo,ConjLhs,ConjRhs>
+{
+ typedef typename NumTraits<Scalar>::Real RealScalar;
+ static void run(Index size, Scalar* mat, const Scalar* vec, RealScalar alpha)
+ {
+ typedef Map<const Matrix<Scalar,Dynamic,1> > OtherMap;
+ typedef typename conj_expr_if<ConjLhs,OtherMap>::type ConjRhsType;
+ conj_if<ConjRhs> cj;
+
+ for (Index i=0; i<size; ++i)
+ {
+ Map<Matrix<Scalar,Dynamic,1> >(mat, UpLo==Lower ? size-i : (i+1)) += alpha * cj(vec[i]) * ConjRhsType(OtherMap(vec+(UpLo==Lower ? i : 0), UpLo==Lower ? size-i : (i+1)));
+ //FIXME This should be handled outside.
+ mat[UpLo==Lower ? 0 : i] = numext::real(mat[UpLo==Lower ? 0 : i]);
+ mat += UpLo==Lower ? size-i : (i+1);
+ }
+ }
+};
+
+template<typename Scalar, typename Index, int UpLo, bool ConjLhs, bool ConjRhs>
+struct selfadjoint_packed_rank1_update<Scalar,Index,RowMajor,UpLo,ConjLhs,ConjRhs>
+{
+ typedef typename NumTraits<Scalar>::Real RealScalar;
+ static void run(Index size, Scalar* mat, const Scalar* vec, RealScalar alpha)
+ {
+ selfadjoint_packed_rank1_update<Scalar,Index,ColMajor,UpLo==Lower?Upper:Lower,ConjRhs,ConjLhs>::run(size,mat,vec,alpha);
+ }
+};
+
+} // end namespace internal
+
+#endif // EIGEN_SELFADJOINT_PACKED_PRODUCT_H
diff --git a/blas/PackedTriangularMatrixVector.h b/blas/PackedTriangularMatrixVector.h
new file mode 100644
index 0000000..cc2a9b8
--- /dev/null
+++ b/blas/PackedTriangularMatrixVector.h
@@ -0,0 +1,81 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2012 Chen-Pang He <jdh8@ms63.hinet.net>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_PACKED_TRIANGULAR_MATRIX_VECTOR_H
+#define EIGEN_PACKED_TRIANGULAR_MATRIX_VECTOR_H
+
+namespace internal {
+
+template<typename Index, int Mode, typename LhsScalar, bool ConjLhs, typename RhsScalar, bool ConjRhs, int StorageOrder>
+struct packed_triangular_matrix_vector_product;
+
+template<typename Index, int Mode, typename LhsScalar, bool ConjLhs, typename RhsScalar, bool ConjRhs>
+struct packed_triangular_matrix_vector_product<Index,Mode,LhsScalar,ConjLhs,RhsScalar,ConjRhs,ColMajor>
+{
+ typedef typename ScalarBinaryOpTraits<LhsScalar, RhsScalar>::ReturnType ResScalar;
+ enum {
+ IsLower = (Mode & Lower) ==Lower,
+ HasUnitDiag = (Mode & UnitDiag)==UnitDiag,
+ HasZeroDiag = (Mode & ZeroDiag)==ZeroDiag
+ };
+ static void run(Index size, const LhsScalar* lhs, const RhsScalar* rhs, ResScalar* res, ResScalar alpha)
+ {
+ internal::conj_if<ConjRhs> cj;
+ typedef Map<const Matrix<LhsScalar,Dynamic,1> > LhsMap;
+ typedef typename conj_expr_if<ConjLhs,LhsMap>::type ConjLhsType;
+ typedef Map<Matrix<ResScalar,Dynamic,1> > ResMap;
+
+ for (Index i = 0; i < size; ++i) {
+ Index s = IsLower && (HasUnitDiag || HasZeroDiag) ? 1 : 0;
+ Index r = IsLower ? size - i : i + 1;
+ if (!(HasUnitDiag || HasZeroDiag) || (--r > 0)) {
+ ResMap(res + (IsLower ? s + i : 0), r) += alpha * cj(rhs[i]) * ConjLhsType(LhsMap(lhs + s, r));
+ }
+ if (HasUnitDiag) {
+ res[i] += alpha * cj(rhs[i]);
+ }
+ lhs += IsLower ? size - i : i + 1;
+ }
+ };
+};
+
+template<typename Index, int Mode, typename LhsScalar, bool ConjLhs, typename RhsScalar, bool ConjRhs>
+struct packed_triangular_matrix_vector_product<Index,Mode,LhsScalar,ConjLhs,RhsScalar,ConjRhs,RowMajor>
+{
+ typedef typename ScalarBinaryOpTraits<LhsScalar, RhsScalar>::ReturnType ResScalar;
+ enum {
+ IsLower = (Mode & Lower) ==Lower,
+ HasUnitDiag = (Mode & UnitDiag)==UnitDiag,
+ HasZeroDiag = (Mode & ZeroDiag)==ZeroDiag
+ };
+ static void run(Index size, const LhsScalar* lhs, const RhsScalar* rhs, ResScalar* res, ResScalar alpha)
+ {
+ internal::conj_if<ConjRhs> cj;
+ typedef Map<const Matrix<LhsScalar,Dynamic,1> > LhsMap;
+ typedef typename conj_expr_if<ConjLhs,LhsMap>::type ConjLhsType;
+ typedef Map<const Matrix<RhsScalar,Dynamic,1> > RhsMap;
+ typedef typename conj_expr_if<ConjRhs,RhsMap>::type ConjRhsType;
+
+ for (Index i = 0; i < size; ++i) {
+ Index s = !IsLower && (HasUnitDiag || HasZeroDiag) ? 1 : 0;
+ Index r = IsLower ? i + 1 : size - i;
+ if (!(HasUnitDiag || HasZeroDiag) || (--r > 0)) {
+ res[i] += alpha * (ConjLhsType(LhsMap(lhs + s, r)).cwiseProduct(ConjRhsType(RhsMap(rhs + (IsLower ? 0 : s + i), r)))).sum();
+ }
+ if (HasUnitDiag) {
+ res[i] += alpha * cj(rhs[i]);
+ }
+ lhs += IsLower ? i + 1 : size - i;
+ }
+ };
+};
+
+} // end namespace internal
+
+#endif // EIGEN_PACKED_TRIANGULAR_MATRIX_VECTOR_H
diff --git a/blas/PackedTriangularSolverVector.h b/blas/PackedTriangularSolverVector.h
new file mode 100644
index 0000000..5c0bb4b
--- /dev/null
+++ b/blas/PackedTriangularSolverVector.h
@@ -0,0 +1,88 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2012 Chen-Pang He <jdh8@ms63.hinet.net>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_PACKED_TRIANGULAR_SOLVER_VECTOR_H
+#define EIGEN_PACKED_TRIANGULAR_SOLVER_VECTOR_H
+
+namespace internal {
+
+template<typename LhsScalar, typename RhsScalar, typename Index, int Side, int Mode, bool Conjugate, int StorageOrder>
+struct packed_triangular_solve_vector;
+
+// forward and backward substitution, row-major, rhs is a vector
+template<typename LhsScalar, typename RhsScalar, typename Index, int Mode, bool Conjugate>
+struct packed_triangular_solve_vector<LhsScalar, RhsScalar, Index, OnTheLeft, Mode, Conjugate, RowMajor>
+{
+ enum {
+ IsLower = (Mode&Lower)==Lower
+ };
+ static void run(Index size, const LhsScalar* lhs, RhsScalar* rhs)
+ {
+ internal::conj_if<Conjugate> cj;
+ typedef Map<const Matrix<LhsScalar,Dynamic,1> > LhsMap;
+ typedef typename conj_expr_if<Conjugate,LhsMap>::type ConjLhsType;
+
+ lhs += IsLower ? 0 : (size*(size+1)>>1)-1;
+ for(Index pi=0; pi<size; ++pi)
+ {
+ Index i = IsLower ? pi : size-pi-1;
+ Index s = IsLower ? 0 : 1;
+ if (pi>0)
+ rhs[i] -= (ConjLhsType(LhsMap(lhs+s,pi))
+ .cwiseProduct(Map<const Matrix<RhsScalar,Dynamic,1> >(rhs+(IsLower ? 0 : i+1),pi))).sum();
+ if (!(Mode & UnitDiag))
+ rhs[i] /= cj(lhs[IsLower ? i : 0]);
+ IsLower ? lhs += pi+1 : lhs -= pi+2;
+ }
+ }
+};
+
+// forward and backward substitution, column-major, rhs is a vector
+template<typename LhsScalar, typename RhsScalar, typename Index, int Mode, bool Conjugate>
+struct packed_triangular_solve_vector<LhsScalar, RhsScalar, Index, OnTheLeft, Mode, Conjugate, ColMajor>
+{
+ enum {
+ IsLower = (Mode&Lower)==Lower
+ };
+ static void run(Index size, const LhsScalar* lhs, RhsScalar* rhs)
+ {
+ internal::conj_if<Conjugate> cj;
+ typedef Map<const Matrix<LhsScalar,Dynamic,1> > LhsMap;
+ typedef typename conj_expr_if<Conjugate,LhsMap>::type ConjLhsType;
+
+ lhs += IsLower ? 0 : size*(size-1)>>1;
+ for(Index pi=0; pi<size; ++pi)
+ {
+ Index i = IsLower ? pi : size-pi-1;
+ Index r = size - pi - 1;
+ if (!(Mode & UnitDiag))
+ rhs[i] /= cj(lhs[IsLower ? 0 : i]);
+ if (r>0)
+ Map<Matrix<RhsScalar,Dynamic,1> >(rhs+(IsLower? i+1 : 0),r) -=
+ rhs[i] * ConjLhsType(LhsMap(lhs+(IsLower? 1 : 0),r));
+ IsLower ? lhs += size-pi : lhs -= r;
+ }
+ }
+};
+
+template<typename LhsScalar, typename RhsScalar, typename Index, int Mode, bool Conjugate, int StorageOrder>
+struct packed_triangular_solve_vector<LhsScalar, RhsScalar, Index, OnTheRight, Mode, Conjugate, StorageOrder>
+{
+ static void run(Index size, const LhsScalar* lhs, RhsScalar* rhs)
+ {
+ packed_triangular_solve_vector<LhsScalar,RhsScalar,Index,OnTheLeft,
+ ((Mode&Upper)==Upper ? Lower : Upper) | (Mode&UnitDiag),
+ Conjugate,StorageOrder==RowMajor?ColMajor:RowMajor
+ >::run(size, lhs, rhs);
+ }
+};
+
+} // end namespace internal
+
+#endif // EIGEN_PACKED_TRIANGULAR_SOLVER_VECTOR_H
diff --git a/blas/README.txt b/blas/README.txt
new file mode 100644
index 0000000..63a5203
--- /dev/null
+++ b/blas/README.txt
@@ -0,0 +1,6 @@
+
+This directory contains a BLAS library built on top of Eigen.
+
+This module is not built by default. In order to compile it, you need to
+type 'make blas' from within your build dir.
+
diff --git a/blas/Rank2Update.h b/blas/Rank2Update.h
new file mode 100644
index 0000000..138d70f
--- /dev/null
+++ b/blas/Rank2Update.h
@@ -0,0 +1,57 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2012 Chen-Pang He <jdh8@ms63.hinet.net>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_RANK2UPDATE_H
+#define EIGEN_RANK2UPDATE_H
+
+namespace internal {
+
+/* Optimized selfadjoint matrix += alpha * uv' + conj(alpha)*vu'
+ * This is the low-level version of SelfadjointRank2Update.h
+ */
+template<typename Scalar, typename Index, int UpLo>
+struct rank2_update_selector
+{
+ static void run(Index size, Scalar* mat, Index stride, const Scalar* u, const Scalar* v, Scalar alpha)
+ {
+ typedef Map<const Matrix<Scalar,Dynamic,1> > OtherMap;
+ for (Index i=0; i<size; ++i)
+ {
+ Map<Matrix<Scalar,Dynamic,1> >(mat+stride*i+(UpLo==Lower ? i : 0), UpLo==Lower ? size-i : (i+1)) +=
+ numext::conj(alpha) * numext::conj(u[i]) * OtherMap(v+(UpLo==Lower ? i : 0), UpLo==Lower ? size-i : (i+1))
+ + alpha * numext::conj(v[i]) * OtherMap(u+(UpLo==Lower ? i : 0), UpLo==Lower ? size-i : (i+1));
+ }
+ }
+};
+
+/* Optimized selfadjoint matrix += alpha * uv' + conj(alpha)*vu'
+ * The matrix is in packed form.
+ */
+template<typename Scalar, typename Index, int UpLo>
+struct packed_rank2_update_selector
+{
+ static void run(Index size, Scalar* mat, const Scalar* u, const Scalar* v, Scalar alpha)
+ {
+ typedef Map<const Matrix<Scalar,Dynamic,1> > OtherMap;
+ Index offset = 0;
+ for (Index i=0; i<size; ++i)
+ {
+ Map<Matrix<Scalar,Dynamic,1> >(mat+offset, UpLo==Lower ? size-i : (i+1)) +=
+ numext::conj(alpha) * numext::conj(u[i]) * OtherMap(v+(UpLo==Lower ? i : 0), UpLo==Lower ? size-i : (i+1))
+ + alpha * numext::conj(v[i]) * OtherMap(u+(UpLo==Lower ? i : 0), UpLo==Lower ? size-i : (i+1));
+ //FIXME This should be handled outside.
+ mat[offset+(UpLo==Lower ? 0 : i)] = numext::real(mat[offset+(UpLo==Lower ? 0 : i)]);
+ offset += UpLo==Lower ? size-i : (i+1);
+ }
+ }
+};
+
+} // end namespace internal
+
+#endif // EIGEN_RANK2UPDATE_H
diff --git a/blas/common.h b/blas/common.h
new file mode 100644
index 0000000..a938cb1
--- /dev/null
+++ b/blas/common.h
@@ -0,0 +1,175 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009-2015 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_BLAS_COMMON_H
+#define EIGEN_BLAS_COMMON_H
+
+#ifdef __GNUC__
+# if __GNUC__<5
+// GCC < 5.0 does not like the global Scalar typedef
+// we just keep shadow-warnings disabled permanently
+# define EIGEN_PERMANENTLY_DISABLE_STUPID_WARNINGS
+# endif
+#endif
+
+#include "../Eigen/Core"
+#include "../Eigen/Jacobi"
+
+#include <complex>
+
+#ifndef SCALAR
+#error the token SCALAR must be defined to compile this file
+#endif
+
+#include "../Eigen/src/misc/blas.h"
+
+#define NOTR 0
+#define TR 1
+#define ADJ 2
+
+#define LEFT 0
+#define RIGHT 1
+
+#define UP 0
+#define LO 1
+
+#define NUNIT 0
+#define UNIT 1
+
+#define INVALID 0xff
+
+#define OP(X) ( ((X)=='N' || (X)=='n') ? NOTR \
+ : ((X)=='T' || (X)=='t') ? TR \
+ : ((X)=='C' || (X)=='c') ? ADJ \
+ : INVALID)
+
+#define SIDE(X) ( ((X)=='L' || (X)=='l') ? LEFT \
+ : ((X)=='R' || (X)=='r') ? RIGHT \
+ : INVALID)
+
+#define UPLO(X) ( ((X)=='U' || (X)=='u') ? UP \
+ : ((X)=='L' || (X)=='l') ? LO \
+ : INVALID)
+
+#define DIAG(X) ( ((X)=='N' || (X)=='n') ? NUNIT \
+ : ((X)=='U' || (X)=='u') ? UNIT \
+ : INVALID)
+
+
+inline bool check_op(const char* op)
+{
+ return OP(*op)!=0xff;
+}
+
+inline bool check_side(const char* side)
+{
+ return SIDE(*side)!=0xff;
+}
+
+inline bool check_uplo(const char* uplo)
+{
+ return UPLO(*uplo)!=0xff;
+}
+
+
+namespace Eigen {
+#include "BandTriangularSolver.h"
+#include "GeneralRank1Update.h"
+#include "PackedSelfadjointProduct.h"
+#include "PackedTriangularMatrixVector.h"
+#include "PackedTriangularSolverVector.h"
+#include "Rank2Update.h"
+}
+
+using namespace Eigen;
+
+typedef SCALAR Scalar;
+typedef NumTraits<Scalar>::Real RealScalar;
+typedef std::complex<RealScalar> Complex;
+
+enum
+{
+ IsComplex = Eigen::NumTraits<SCALAR>::IsComplex,
+ Conj = IsComplex
+};
+
+typedef Matrix<Scalar,Dynamic,Dynamic,ColMajor> PlainMatrixType;
+typedef Map<Matrix<Scalar,Dynamic,Dynamic,ColMajor>, 0, OuterStride<> > MatrixType;
+typedef Map<const Matrix<Scalar,Dynamic,Dynamic,ColMajor>, 0, OuterStride<> > ConstMatrixType;
+typedef Map<Matrix<Scalar,Dynamic,1>, 0, InnerStride<Dynamic> > StridedVectorType;
+typedef Map<Matrix<Scalar,Dynamic,1> > CompactVectorType;
+
+template<typename T>
+Map<Matrix<T,Dynamic,Dynamic,ColMajor>, 0, OuterStride<> >
+matrix(T* data, int rows, int cols, int stride)
+{
+ return Map<Matrix<T,Dynamic,Dynamic,ColMajor>, 0, OuterStride<> >(data, rows, cols, OuterStride<>(stride));
+}
+
+template<typename T>
+Map<const Matrix<T,Dynamic,Dynamic,ColMajor>, 0, OuterStride<> >
+matrix(const T* data, int rows, int cols, int stride)
+{
+ return Map<const Matrix<T,Dynamic,Dynamic,ColMajor>, 0, OuterStride<> >(data, rows, cols, OuterStride<>(stride));
+}
+
+template<typename T>
+Map<Matrix<T,Dynamic,1>, 0, InnerStride<Dynamic> > make_vector(T* data, int size, int incr)
+{
+ return Map<Matrix<T,Dynamic,1>, 0, InnerStride<Dynamic> >(data, size, InnerStride<Dynamic>(incr));
+}
+
+template<typename T>
+Map<const Matrix<T,Dynamic,1>, 0, InnerStride<Dynamic> > make_vector(const T* data, int size, int incr)
+{
+ return Map<const Matrix<T,Dynamic,1>, 0, InnerStride<Dynamic> >(data, size, InnerStride<Dynamic>(incr));
+}
+
+template<typename T>
+Map<Matrix<T,Dynamic,1> > make_vector(T* data, int size)
+{
+ return Map<Matrix<T,Dynamic,1> >(data, size);
+}
+
+template<typename T>
+Map<const Matrix<T,Dynamic,1> > make_vector(const T* data, int size)
+{
+ return Map<const Matrix<T,Dynamic,1> >(data, size);
+}
+
+template<typename T>
+T* get_compact_vector(T* x, int n, int incx)
+{
+ if(incx==1)
+ return x;
+
+ std::remove_const_t<T>* ret = new Scalar[n];
+ if(incx<0) make_vector(ret,n) = make_vector(x,n,-incx).reverse();
+ else make_vector(ret,n) = make_vector(x,n, incx);
+ return ret;
+}
+
+template<typename T>
+T* copy_back(T* x_cpy, T* x, int n, int incx)
+{
+ if(x_cpy==x)
+ return 0;
+
+ if(incx<0) make_vector(x,n,-incx).reverse() = make_vector(x_cpy,n);
+ else make_vector(x,n, incx) = make_vector(x_cpy,n);
+ return x_cpy;
+}
+
+#ifndef EIGEN_BLAS_FUNC_SUFFIX
+#define EIGEN_BLAS_FUNC_SUFFIX _
+#endif
+
+#define EIGEN_BLAS_FUNC(X) EIGEN_CAT(SCALAR_SUFFIX, EIGEN_CAT(X, EIGEN_BLAS_FUNC_SUFFIX))
+
+#endif // EIGEN_BLAS_COMMON_H
diff --git a/blas/complex_double.cpp b/blas/complex_double.cpp
new file mode 100644
index 0000000..648c6d4
--- /dev/null
+++ b/blas/complex_double.cpp
@@ -0,0 +1,20 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#define SCALAR std::complex<double>
+#define SCALAR_SUFFIX z
+#define SCALAR_SUFFIX_UP "Z"
+#define REAL_SCALAR_SUFFIX d
+#define ISCOMPLEX 1
+
+#include "level1_impl.h"
+#include "level1_cplx_impl.h"
+#include "level2_impl.h"
+#include "level2_cplx_impl.h"
+#include "level3_impl.h"
diff --git a/blas/complex_single.cpp b/blas/complex_single.cpp
new file mode 100644
index 0000000..7786519
--- /dev/null
+++ b/blas/complex_single.cpp
@@ -0,0 +1,20 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#define SCALAR std::complex<float>
+#define SCALAR_SUFFIX c
+#define SCALAR_SUFFIX_UP "C"
+#define REAL_SCALAR_SUFFIX s
+#define ISCOMPLEX 1
+
+#include "level1_impl.h"
+#include "level1_cplx_impl.h"
+#include "level2_impl.h"
+#include "level2_cplx_impl.h"
+#include "level3_impl.h"
diff --git a/blas/double.cpp b/blas/double.cpp
new file mode 100644
index 0000000..eb2e573
--- /dev/null
+++ b/blas/double.cpp
@@ -0,0 +1,32 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2012 Chen-Pang He <jdh8@ms63.hinet.net>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#define SCALAR double
+#define SCALAR_SUFFIX d
+#define SCALAR_SUFFIX_UP "D"
+#define ISCOMPLEX 0
+
+#include "level1_impl.h"
+#include "level1_real_impl.h"
+#include "level2_impl.h"
+#include "level2_real_impl.h"
+#include "level3_impl.h"
+
+double EIGEN_BLAS_FUNC(sdot)(int* n, float* x, int* incx, float* y, int* incy)
+{
+ if(*n<=0) return 0;
+
+ if(*incx==1 && *incy==1) return (make_vector(x,*n).cast<double>().cwiseProduct(make_vector(y,*n).cast<double>())).sum();
+ else if(*incx>0 && *incy>0) return (make_vector(x,*n,*incx).cast<double>().cwiseProduct(make_vector(y,*n,*incy).cast<double>())).sum();
+ else if(*incx<0 && *incy>0) return (make_vector(x,*n,-*incx).reverse().cast<double>().cwiseProduct(make_vector(y,*n,*incy).cast<double>())).sum();
+ else if(*incx>0 && *incy<0) return (make_vector(x,*n,*incx).cast<double>().cwiseProduct(make_vector(y,*n,-*incy).reverse().cast<double>())).sum();
+ else if(*incx<0 && *incy<0) return (make_vector(x,*n,-*incx).reverse().cast<double>().cwiseProduct(make_vector(y,*n,-*incy).reverse().cast<double>())).sum();
+ else return 0;
+}
diff --git a/blas/f2c/chbmv.c b/blas/f2c/chbmv.c
new file mode 100644
index 0000000..f218fe3
--- /dev/null
+++ b/blas/f2c/chbmv.c
@@ -0,0 +1,487 @@
+/* chbmv.f -- translated by f2c (version 20100827).
+ You must link the resulting object file with libf2c:
+ on Microsoft Windows system, link with libf2c.lib;
+ on Linux or Unix systems, link with .../path/to/libf2c.a -lm
+ or, if you install libf2c.a in a standard place, with -lf2c -lm
+ -- in that order, at the end of the command line, as in
+ cc *.o -lf2c -lm
+ Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
+
+ http://www.netlib.org/f2c/libf2c.zip
+*/
+
+#include "datatypes.h"
+
+/* Subroutine */ int chbmv_(char *uplo, integer *n, integer *k, complex *
+ alpha, complex *a, integer *lda, complex *x, integer *incx, complex *
+ beta, complex *y, integer *incy, ftnlen uplo_len)
+{
+ /* System generated locals */
+ integer a_dim1, a_offset, i__1, i__2, i__3, i__4, i__5;
+ real r__1;
+ complex q__1, q__2, q__3, q__4;
+
+ /* Builtin functions */
+ void r_cnjg(complex *, complex *);
+
+ /* Local variables */
+ integer i__, j, l, ix, iy, jx, jy, kx, ky, info;
+ complex temp1, temp2;
+ extern logical lsame_(char *, char *, ftnlen, ftnlen);
+ integer kplus1;
+ extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
+
+/* .. Scalar Arguments .. */
+/* .. */
+/* .. Array Arguments .. */
+/* .. */
+
+/* Purpose */
+/* ======= */
+
+/* CHBMV performs the matrix-vector operation */
+
+/* y := alpha*A*x + beta*y, */
+
+/* where alpha and beta are scalars, x and y are n element vectors and */
+/* A is an n by n hermitian band matrix, with k super-diagonals. */
+
+/* Arguments */
+/* ========== */
+
+/* UPLO - CHARACTER*1. */
+/* On entry, UPLO specifies whether the upper or lower */
+/* triangular part of the band matrix A is being supplied as */
+/* follows: */
+
+/* UPLO = 'U' or 'u' The upper triangular part of A is */
+/* being supplied. */
+
+/* UPLO = 'L' or 'l' The lower triangular part of A is */
+/* being supplied. */
+
+/* Unchanged on exit. */
+
+/* N - INTEGER. */
+/* On entry, N specifies the order of the matrix A. */
+/* N must be at least zero. */
+/* Unchanged on exit. */
+
+/* K - INTEGER. */
+/* On entry, K specifies the number of super-diagonals of the */
+/* matrix A. K must satisfy 0 .le. K. */
+/* Unchanged on exit. */
+
+/* ALPHA - COMPLEX . */
+/* On entry, ALPHA specifies the scalar alpha. */
+/* Unchanged on exit. */
+
+/* A - COMPLEX array of DIMENSION ( LDA, n ). */
+/* Before entry with UPLO = 'U' or 'u', the leading ( k + 1 ) */
+/* by n part of the array A must contain the upper triangular */
+/* band part of the hermitian matrix, supplied column by */
+/* column, with the leading diagonal of the matrix in row */
+/* ( k + 1 ) of the array, the first super-diagonal starting at */
+/* position 2 in row k, and so on. The top left k by k triangle */
+/* of the array A is not referenced. */
+/* The following program segment will transfer the upper */
+/* triangular part of a hermitian band matrix from conventional */
+/* full matrix storage to band storage: */
+
+/* DO 20, J = 1, N */
+/* M = K + 1 - J */
+/* DO 10, I = MAX( 1, J - K ), J */
+/* A( M + I, J ) = matrix( I, J ) */
+/* 10 CONTINUE */
+/* 20 CONTINUE */
+
+/* Before entry with UPLO = 'L' or 'l', the leading ( k + 1 ) */
+/* by n part of the array A must contain the lower triangular */
+/* band part of the hermitian matrix, supplied column by */
+/* column, with the leading diagonal of the matrix in row 1 of */
+/* the array, the first sub-diagonal starting at position 1 in */
+/* row 2, and so on. The bottom right k by k triangle of the */
+/* array A is not referenced. */
+/* The following program segment will transfer the lower */
+/* triangular part of a hermitian band matrix from conventional */
+/* full matrix storage to band storage: */
+
+/* DO 20, J = 1, N */
+/* M = 1 - J */
+/* DO 10, I = J, MIN( N, J + K ) */
+/* A( M + I, J ) = matrix( I, J ) */
+/* 10 CONTINUE */
+/* 20 CONTINUE */
+
+/* Note that the imaginary parts of the diagonal elements need */
+/* not be set and are assumed to be zero. */
+/* Unchanged on exit. */
+
+/* LDA - INTEGER. */
+/* On entry, LDA specifies the first dimension of A as declared */
+/* in the calling (sub) program. LDA must be at least */
+/* ( k + 1 ). */
+/* Unchanged on exit. */
+
+/* X - COMPLEX array of DIMENSION at least */
+/* ( 1 + ( n - 1 )*abs( INCX ) ). */
+/* Before entry, the incremented array X must contain the */
+/* vector x. */
+/* Unchanged on exit. */
+
+/* INCX - INTEGER. */
+/* On entry, INCX specifies the increment for the elements of */
+/* X. INCX must not be zero. */
+/* Unchanged on exit. */
+
+/* BETA - COMPLEX . */
+/* On entry, BETA specifies the scalar beta. */
+/* Unchanged on exit. */
+
+/* Y - COMPLEX array of DIMENSION at least */
+/* ( 1 + ( n - 1 )*abs( INCY ) ). */
+/* Before entry, the incremented array Y must contain the */
+/* vector y. On exit, Y is overwritten by the updated vector y. */
+
+/* INCY - INTEGER. */
+/* On entry, INCY specifies the increment for the elements of */
+/* Y. INCY must not be zero. */
+/* Unchanged on exit. */
+
+/* Further Details */
+/* =============== */
+
+/* Level 2 Blas routine. */
+
+/* -- Written on 22-October-1986. */
+/* Jack Dongarra, Argonne National Lab. */
+/* Jeremy Du Croz, Nag Central Office. */
+/* Sven Hammarling, Nag Central Office. */
+/* Richard Hanson, Sandia National Labs. */
+
+/* ===================================================================== */
+
+/* .. Parameters .. */
+/* .. */
+/* .. Local Scalars .. */
+/* .. */
+/* .. External Functions .. */
+/* .. */
+/* .. External Subroutines .. */
+/* .. */
+/* .. Intrinsic Functions .. */
+/* .. */
+
+/* Test the input parameters. */
+
+ /* Parameter adjustments */
+ a_dim1 = *lda;
+ a_offset = 1 + a_dim1;
+ a -= a_offset;
+ --x;
+ --y;
+
+ /* Function Body */
+ info = 0;
+ if (! lsame_(uplo, "U", (ftnlen)1, (ftnlen)1) && ! lsame_(uplo, "L", (
+ ftnlen)1, (ftnlen)1)) {
+ info = 1;
+ } else if (*n < 0) {
+ info = 2;
+ } else if (*k < 0) {
+ info = 3;
+ } else if (*lda < *k + 1) {
+ info = 6;
+ } else if (*incx == 0) {
+ info = 8;
+ } else if (*incy == 0) {
+ info = 11;
+ }
+ if (info != 0) {
+ xerbla_("CHBMV ", &info, (ftnlen)6);
+ return 0;
+ }
+
+/* Quick return if possible. */
+
+ if (*n == 0 || (alpha->r == 0.f && alpha->i == 0.f && (beta->r == 1.f &&
+ beta->i == 0.f))) {
+ return 0;
+ }
+
+/* Set up the start points in X and Y. */
+
+ if (*incx > 0) {
+ kx = 1;
+ } else {
+ kx = 1 - (*n - 1) * *incx;
+ }
+ if (*incy > 0) {
+ ky = 1;
+ } else {
+ ky = 1 - (*n - 1) * *incy;
+ }
+
+/* Start the operations. In this version the elements of the array A */
+/* are accessed sequentially with one pass through A. */
+
+/* First form y := beta*y. */
+
+ if (beta->r != 1.f || beta->i != 0.f) {
+ if (*incy == 1) {
+ if (beta->r == 0.f && beta->i == 0.f) {
+ i__1 = *n;
+ for (i__ = 1; i__ <= i__1; ++i__) {
+ i__2 = i__;
+ y[i__2].r = 0.f, y[i__2].i = 0.f;
+/* L10: */
+ }
+ } else {
+ i__1 = *n;
+ for (i__ = 1; i__ <= i__1; ++i__) {
+ i__2 = i__;
+ i__3 = i__;
+ q__1.r = beta->r * y[i__3].r - beta->i * y[i__3].i,
+ q__1.i = beta->r * y[i__3].i + beta->i * y[i__3]
+ .r;
+ y[i__2].r = q__1.r, y[i__2].i = q__1.i;
+/* L20: */
+ }
+ }
+ } else {
+ iy = ky;
+ if (beta->r == 0.f && beta->i == 0.f) {
+ i__1 = *n;
+ for (i__ = 1; i__ <= i__1; ++i__) {
+ i__2 = iy;
+ y[i__2].r = 0.f, y[i__2].i = 0.f;
+ iy += *incy;
+/* L30: */
+ }
+ } else {
+ i__1 = *n;
+ for (i__ = 1; i__ <= i__1; ++i__) {
+ i__2 = iy;
+ i__3 = iy;
+ q__1.r = beta->r * y[i__3].r - beta->i * y[i__3].i,
+ q__1.i = beta->r * y[i__3].i + beta->i * y[i__3]
+ .r;
+ y[i__2].r = q__1.r, y[i__2].i = q__1.i;
+ iy += *incy;
+/* L40: */
+ }
+ }
+ }
+ }
+ if (alpha->r == 0.f && alpha->i == 0.f) {
+ return 0;
+ }
+ if (lsame_(uplo, "U", (ftnlen)1, (ftnlen)1)) {
+
+/* Form y when upper triangle of A is stored. */
+
+ kplus1 = *k + 1;
+ if (*incx == 1 && *incy == 1) {
+ i__1 = *n;
+ for (j = 1; j <= i__1; ++j) {
+ i__2 = j;
+ q__1.r = alpha->r * x[i__2].r - alpha->i * x[i__2].i, q__1.i =
+ alpha->r * x[i__2].i + alpha->i * x[i__2].r;
+ temp1.r = q__1.r, temp1.i = q__1.i;
+ temp2.r = 0.f, temp2.i = 0.f;
+ l = kplus1 - j;
+/* Computing MAX */
+ i__2 = 1, i__3 = j - *k;
+ i__4 = j - 1;
+ for (i__ = max(i__2,i__3); i__ <= i__4; ++i__) {
+ i__2 = i__;
+ i__3 = i__;
+ i__5 = l + i__ + j * a_dim1;
+ q__2.r = temp1.r * a[i__5].r - temp1.i * a[i__5].i,
+ q__2.i = temp1.r * a[i__5].i + temp1.i * a[i__5]
+ .r;
+ q__1.r = y[i__3].r + q__2.r, q__1.i = y[i__3].i + q__2.i;
+ y[i__2].r = q__1.r, y[i__2].i = q__1.i;
+ r_cnjg(&q__3, &a[l + i__ + j * a_dim1]);
+ i__2 = i__;
+ q__2.r = q__3.r * x[i__2].r - q__3.i * x[i__2].i, q__2.i =
+ q__3.r * x[i__2].i + q__3.i * x[i__2].r;
+ q__1.r = temp2.r + q__2.r, q__1.i = temp2.i + q__2.i;
+ temp2.r = q__1.r, temp2.i = q__1.i;
+/* L50: */
+ }
+ i__4 = j;
+ i__2 = j;
+ i__3 = kplus1 + j * a_dim1;
+ r__1 = a[i__3].r;
+ q__3.r = r__1 * temp1.r, q__3.i = r__1 * temp1.i;
+ q__2.r = y[i__2].r + q__3.r, q__2.i = y[i__2].i + q__3.i;
+ q__4.r = alpha->r * temp2.r - alpha->i * temp2.i, q__4.i =
+ alpha->r * temp2.i + alpha->i * temp2.r;
+ q__1.r = q__2.r + q__4.r, q__1.i = q__2.i + q__4.i;
+ y[i__4].r = q__1.r, y[i__4].i = q__1.i;
+/* L60: */
+ }
+ } else {
+ jx = kx;
+ jy = ky;
+ i__1 = *n;
+ for (j = 1; j <= i__1; ++j) {
+ i__4 = jx;
+ q__1.r = alpha->r * x[i__4].r - alpha->i * x[i__4].i, q__1.i =
+ alpha->r * x[i__4].i + alpha->i * x[i__4].r;
+ temp1.r = q__1.r, temp1.i = q__1.i;
+ temp2.r = 0.f, temp2.i = 0.f;
+ ix = kx;
+ iy = ky;
+ l = kplus1 - j;
+/* Computing MAX */
+ i__4 = 1, i__2 = j - *k;
+ i__3 = j - 1;
+ for (i__ = max(i__4,i__2); i__ <= i__3; ++i__) {
+ i__4 = iy;
+ i__2 = iy;
+ i__5 = l + i__ + j * a_dim1;
+ q__2.r = temp1.r * a[i__5].r - temp1.i * a[i__5].i,
+ q__2.i = temp1.r * a[i__5].i + temp1.i * a[i__5]
+ .r;
+ q__1.r = y[i__2].r + q__2.r, q__1.i = y[i__2].i + q__2.i;
+ y[i__4].r = q__1.r, y[i__4].i = q__1.i;
+ r_cnjg(&q__3, &a[l + i__ + j * a_dim1]);
+ i__4 = ix;
+ q__2.r = q__3.r * x[i__4].r - q__3.i * x[i__4].i, q__2.i =
+ q__3.r * x[i__4].i + q__3.i * x[i__4].r;
+ q__1.r = temp2.r + q__2.r, q__1.i = temp2.i + q__2.i;
+ temp2.r = q__1.r, temp2.i = q__1.i;
+ ix += *incx;
+ iy += *incy;
+/* L70: */
+ }
+ i__3 = jy;
+ i__4 = jy;
+ i__2 = kplus1 + j * a_dim1;
+ r__1 = a[i__2].r;
+ q__3.r = r__1 * temp1.r, q__3.i = r__1 * temp1.i;
+ q__2.r = y[i__4].r + q__3.r, q__2.i = y[i__4].i + q__3.i;
+ q__4.r = alpha->r * temp2.r - alpha->i * temp2.i, q__4.i =
+ alpha->r * temp2.i + alpha->i * temp2.r;
+ q__1.r = q__2.r + q__4.r, q__1.i = q__2.i + q__4.i;
+ y[i__3].r = q__1.r, y[i__3].i = q__1.i;
+ jx += *incx;
+ jy += *incy;
+ if (j > *k) {
+ kx += *incx;
+ ky += *incy;
+ }
+/* L80: */
+ }
+ }
+ } else {
+
+/* Form y when lower triangle of A is stored. */
+
+ if (*incx == 1 && *incy == 1) {
+ i__1 = *n;
+ for (j = 1; j <= i__1; ++j) {
+ i__3 = j;
+ q__1.r = alpha->r * x[i__3].r - alpha->i * x[i__3].i, q__1.i =
+ alpha->r * x[i__3].i + alpha->i * x[i__3].r;
+ temp1.r = q__1.r, temp1.i = q__1.i;
+ temp2.r = 0.f, temp2.i = 0.f;
+ i__3 = j;
+ i__4 = j;
+ i__2 = j * a_dim1 + 1;
+ r__1 = a[i__2].r;
+ q__2.r = r__1 * temp1.r, q__2.i = r__1 * temp1.i;
+ q__1.r = y[i__4].r + q__2.r, q__1.i = y[i__4].i + q__2.i;
+ y[i__3].r = q__1.r, y[i__3].i = q__1.i;
+ l = 1 - j;
+/* Computing MIN */
+ i__4 = *n, i__2 = j + *k;
+ i__3 = min(i__4,i__2);
+ for (i__ = j + 1; i__ <= i__3; ++i__) {
+ i__4 = i__;
+ i__2 = i__;
+ i__5 = l + i__ + j * a_dim1;
+ q__2.r = temp1.r * a[i__5].r - temp1.i * a[i__5].i,
+ q__2.i = temp1.r * a[i__5].i + temp1.i * a[i__5]
+ .r;
+ q__1.r = y[i__2].r + q__2.r, q__1.i = y[i__2].i + q__2.i;
+ y[i__4].r = q__1.r, y[i__4].i = q__1.i;
+ r_cnjg(&q__3, &a[l + i__ + j * a_dim1]);
+ i__4 = i__;
+ q__2.r = q__3.r * x[i__4].r - q__3.i * x[i__4].i, q__2.i =
+ q__3.r * x[i__4].i + q__3.i * x[i__4].r;
+ q__1.r = temp2.r + q__2.r, q__1.i = temp2.i + q__2.i;
+ temp2.r = q__1.r, temp2.i = q__1.i;
+/* L90: */
+ }
+ i__3 = j;
+ i__4 = j;
+ q__2.r = alpha->r * temp2.r - alpha->i * temp2.i, q__2.i =
+ alpha->r * temp2.i + alpha->i * temp2.r;
+ q__1.r = y[i__4].r + q__2.r, q__1.i = y[i__4].i + q__2.i;
+ y[i__3].r = q__1.r, y[i__3].i = q__1.i;
+/* L100: */
+ }
+ } else {
+ jx = kx;
+ jy = ky;
+ i__1 = *n;
+ for (j = 1; j <= i__1; ++j) {
+ i__3 = jx;
+ q__1.r = alpha->r * x[i__3].r - alpha->i * x[i__3].i, q__1.i =
+ alpha->r * x[i__3].i + alpha->i * x[i__3].r;
+ temp1.r = q__1.r, temp1.i = q__1.i;
+ temp2.r = 0.f, temp2.i = 0.f;
+ i__3 = jy;
+ i__4 = jy;
+ i__2 = j * a_dim1 + 1;
+ r__1 = a[i__2].r;
+ q__2.r = r__1 * temp1.r, q__2.i = r__1 * temp1.i;
+ q__1.r = y[i__4].r + q__2.r, q__1.i = y[i__4].i + q__2.i;
+ y[i__3].r = q__1.r, y[i__3].i = q__1.i;
+ l = 1 - j;
+ ix = jx;
+ iy = jy;
+/* Computing MIN */
+ i__4 = *n, i__2 = j + *k;
+ i__3 = min(i__4,i__2);
+ for (i__ = j + 1; i__ <= i__3; ++i__) {
+ ix += *incx;
+ iy += *incy;
+ i__4 = iy;
+ i__2 = iy;
+ i__5 = l + i__ + j * a_dim1;
+ q__2.r = temp1.r * a[i__5].r - temp1.i * a[i__5].i,
+ q__2.i = temp1.r * a[i__5].i + temp1.i * a[i__5]
+ .r;
+ q__1.r = y[i__2].r + q__2.r, q__1.i = y[i__2].i + q__2.i;
+ y[i__4].r = q__1.r, y[i__4].i = q__1.i;
+ r_cnjg(&q__3, &a[l + i__ + j * a_dim1]);
+ i__4 = ix;
+ q__2.r = q__3.r * x[i__4].r - q__3.i * x[i__4].i, q__2.i =
+ q__3.r * x[i__4].i + q__3.i * x[i__4].r;
+ q__1.r = temp2.r + q__2.r, q__1.i = temp2.i + q__2.i;
+ temp2.r = q__1.r, temp2.i = q__1.i;
+/* L110: */
+ }
+ i__3 = jy;
+ i__4 = jy;
+ q__2.r = alpha->r * temp2.r - alpha->i * temp2.i, q__2.i =
+ alpha->r * temp2.i + alpha->i * temp2.r;
+ q__1.r = y[i__4].r + q__2.r, q__1.i = y[i__4].i + q__2.i;
+ y[i__3].r = q__1.r, y[i__3].i = q__1.i;
+ jx += *incx;
+ jy += *incy;
+/* L120: */
+ }
+ }
+ }
+
+ return 0;
+
+/* End of CHBMV . */
+
+} /* chbmv_ */
+
diff --git a/blas/f2c/chpmv.c b/blas/f2c/chpmv.c
new file mode 100644
index 0000000..65bab1c
--- /dev/null
+++ b/blas/f2c/chpmv.c
@@ -0,0 +1,438 @@
+/* chpmv.f -- translated by f2c (version 20100827).
+ You must link the resulting object file with libf2c:
+ on Microsoft Windows system, link with libf2c.lib;
+ on Linux or Unix systems, link with .../path/to/libf2c.a -lm
+ or, if you install libf2c.a in a standard place, with -lf2c -lm
+ -- in that order, at the end of the command line, as in
+ cc *.o -lf2c -lm
+ Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
+
+ http://www.netlib.org/f2c/libf2c.zip
+*/
+
+#include "datatypes.h"
+
+/* Subroutine */ int chpmv_(char *uplo, integer *n, complex *alpha, complex *
+ ap, complex *x, integer *incx, complex *beta, complex *y, integer *
+ incy, ftnlen uplo_len)
+{
+ /* System generated locals */
+ integer i__1, i__2, i__3, i__4, i__5;
+ real r__1;
+ complex q__1, q__2, q__3, q__4;
+
+ /* Builtin functions */
+ void r_cnjg(complex *, complex *);
+
+ /* Local variables */
+ integer i__, j, k, kk, ix, iy, jx, jy, kx, ky, info;
+ complex temp1, temp2;
+ extern logical lsame_(char *, char *, ftnlen, ftnlen);
+ extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
+
+/* .. Scalar Arguments .. */
+/* .. */
+/* .. Array Arguments .. */
+/* .. */
+
+/* Purpose */
+/* ======= */
+
+/* CHPMV performs the matrix-vector operation */
+
+/* y := alpha*A*x + beta*y, */
+
+/* where alpha and beta are scalars, x and y are n element vectors and */
+/* A is an n by n hermitian matrix, supplied in packed form. */
+
+/* Arguments */
+/* ========== */
+
+/* UPLO - CHARACTER*1. */
+/* On entry, UPLO specifies whether the upper or lower */
+/* triangular part of the matrix A is supplied in the packed */
+/* array AP as follows: */
+
+/* UPLO = 'U' or 'u' The upper triangular part of A is */
+/* supplied in AP. */
+
+/* UPLO = 'L' or 'l' The lower triangular part of A is */
+/* supplied in AP. */
+
+/* Unchanged on exit. */
+
+/* N - INTEGER. */
+/* On entry, N specifies the order of the matrix A. */
+/* N must be at least zero. */
+/* Unchanged on exit. */
+
+/* ALPHA - COMPLEX . */
+/* On entry, ALPHA specifies the scalar alpha. */
+/* Unchanged on exit. */
+
+/* AP - COMPLEX array of DIMENSION at least */
+/* ( ( n*( n + 1 ) )/2 ). */
+/* Before entry with UPLO = 'U' or 'u', the array AP must */
+/* contain the upper triangular part of the hermitian matrix */
+/* packed sequentially, column by column, so that AP( 1 ) */
+/* contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 ) */
+/* and a( 2, 2 ) respectively, and so on. */
+/* Before entry with UPLO = 'L' or 'l', the array AP must */
+/* contain the lower triangular part of the hermitian matrix */
+/* packed sequentially, column by column, so that AP( 1 ) */
+/* contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 ) */
+/* and a( 3, 1 ) respectively, and so on. */
+/* Note that the imaginary parts of the diagonal elements need */
+/* not be set and are assumed to be zero. */
+/* Unchanged on exit. */
+
+/* X - COMPLEX array of dimension at least */
+/* ( 1 + ( n - 1 )*abs( INCX ) ). */
+/* Before entry, the incremented array X must contain the n */
+/* element vector x. */
+/* Unchanged on exit. */
+
+/* INCX - INTEGER. */
+/* On entry, INCX specifies the increment for the elements of */
+/* X. INCX must not be zero. */
+/* Unchanged on exit. */
+
+/* BETA - COMPLEX . */
+/* On entry, BETA specifies the scalar beta. When BETA is */
+/* supplied as zero then Y need not be set on input. */
+/* Unchanged on exit. */
+
+/* Y - COMPLEX array of dimension at least */
+/* ( 1 + ( n - 1 )*abs( INCY ) ). */
+/* Before entry, the incremented array Y must contain the n */
+/* element vector y. On exit, Y is overwritten by the updated */
+/* vector y. */
+
+/* INCY - INTEGER. */
+/* On entry, INCY specifies the increment for the elements of */
+/* Y. INCY must not be zero. */
+/* Unchanged on exit. */
+
+/* Further Details */
+/* =============== */
+
+/* Level 2 Blas routine. */
+
+/* -- Written on 22-October-1986. */
+/* Jack Dongarra, Argonne National Lab. */
+/* Jeremy Du Croz, Nag Central Office. */
+/* Sven Hammarling, Nag Central Office. */
+/* Richard Hanson, Sandia National Labs. */
+
+/* ===================================================================== */
+
+/* .. Parameters .. */
+/* .. */
+/* .. Local Scalars .. */
+/* .. */
+/* .. External Functions .. */
+/* .. */
+/* .. External Subroutines .. */
+/* .. */
+/* .. Intrinsic Functions .. */
+/* .. */
+
+/* Test the input parameters. */
+
+ /* Parameter adjustments */
+ --y;
+ --x;
+ --ap;
+
+ /* Function Body */
+ info = 0;
+ if (! lsame_(uplo, "U", (ftnlen)1, (ftnlen)1) && ! lsame_(uplo, "L", (
+ ftnlen)1, (ftnlen)1)) {
+ info = 1;
+ } else if (*n < 0) {
+ info = 2;
+ } else if (*incx == 0) {
+ info = 6;
+ } else if (*incy == 0) {
+ info = 9;
+ }
+ if (info != 0) {
+ xerbla_("CHPMV ", &info, (ftnlen)6);
+ return 0;
+ }
+
+/* Quick return if possible. */
+
+ if (*n == 0 || (alpha->r == 0.f && alpha->i == 0.f && (beta->r == 1.f &&
+ beta->i == 0.f))) {
+ return 0;
+ }
+
+/* Set up the start points in X and Y. */
+
+ if (*incx > 0) {
+ kx = 1;
+ } else {
+ kx = 1 - (*n - 1) * *incx;
+ }
+ if (*incy > 0) {
+ ky = 1;
+ } else {
+ ky = 1 - (*n - 1) * *incy;
+ }
+
+/* Start the operations. In this version the elements of the array AP */
+/* are accessed sequentially with one pass through AP. */
+
+/* First form y := beta*y. */
+
+ if (beta->r != 1.f || beta->i != 0.f) {
+ if (*incy == 1) {
+ if (beta->r == 0.f && beta->i == 0.f) {
+ i__1 = *n;
+ for (i__ = 1; i__ <= i__1; ++i__) {
+ i__2 = i__;
+ y[i__2].r = 0.f, y[i__2].i = 0.f;
+/* L10: */
+ }
+ } else {
+ i__1 = *n;
+ for (i__ = 1; i__ <= i__1; ++i__) {
+ i__2 = i__;
+ i__3 = i__;
+ q__1.r = beta->r * y[i__3].r - beta->i * y[i__3].i,
+ q__1.i = beta->r * y[i__3].i + beta->i * y[i__3]
+ .r;
+ y[i__2].r = q__1.r, y[i__2].i = q__1.i;
+/* L20: */
+ }
+ }
+ } else {
+ iy = ky;
+ if (beta->r == 0.f && beta->i == 0.f) {
+ i__1 = *n;
+ for (i__ = 1; i__ <= i__1; ++i__) {
+ i__2 = iy;
+ y[i__2].r = 0.f, y[i__2].i = 0.f;
+ iy += *incy;
+/* L30: */
+ }
+ } else {
+ i__1 = *n;
+ for (i__ = 1; i__ <= i__1; ++i__) {
+ i__2 = iy;
+ i__3 = iy;
+ q__1.r = beta->r * y[i__3].r - beta->i * y[i__3].i,
+ q__1.i = beta->r * y[i__3].i + beta->i * y[i__3]
+ .r;
+ y[i__2].r = q__1.r, y[i__2].i = q__1.i;
+ iy += *incy;
+/* L40: */
+ }
+ }
+ }
+ }
+ if (alpha->r == 0.f && alpha->i == 0.f) {
+ return 0;
+ }
+ kk = 1;
+ if (lsame_(uplo, "U", (ftnlen)1, (ftnlen)1)) {
+
+/* Form y when AP contains the upper triangle. */
+
+ if (*incx == 1 && *incy == 1) {
+ i__1 = *n;
+ for (j = 1; j <= i__1; ++j) {
+ i__2 = j;
+ q__1.r = alpha->r * x[i__2].r - alpha->i * x[i__2].i, q__1.i =
+ alpha->r * x[i__2].i + alpha->i * x[i__2].r;
+ temp1.r = q__1.r, temp1.i = q__1.i;
+ temp2.r = 0.f, temp2.i = 0.f;
+ k = kk;
+ i__2 = j - 1;
+ for (i__ = 1; i__ <= i__2; ++i__) {
+ i__3 = i__;
+ i__4 = i__;
+ i__5 = k;
+ q__2.r = temp1.r * ap[i__5].r - temp1.i * ap[i__5].i,
+ q__2.i = temp1.r * ap[i__5].i + temp1.i * ap[i__5]
+ .r;
+ q__1.r = y[i__4].r + q__2.r, q__1.i = y[i__4].i + q__2.i;
+ y[i__3].r = q__1.r, y[i__3].i = q__1.i;
+ r_cnjg(&q__3, &ap[k]);
+ i__3 = i__;
+ q__2.r = q__3.r * x[i__3].r - q__3.i * x[i__3].i, q__2.i =
+ q__3.r * x[i__3].i + q__3.i * x[i__3].r;
+ q__1.r = temp2.r + q__2.r, q__1.i = temp2.i + q__2.i;
+ temp2.r = q__1.r, temp2.i = q__1.i;
+ ++k;
+/* L50: */
+ }
+ i__2 = j;
+ i__3 = j;
+ i__4 = kk + j - 1;
+ r__1 = ap[i__4].r;
+ q__3.r = r__1 * temp1.r, q__3.i = r__1 * temp1.i;
+ q__2.r = y[i__3].r + q__3.r, q__2.i = y[i__3].i + q__3.i;
+ q__4.r = alpha->r * temp2.r - alpha->i * temp2.i, q__4.i =
+ alpha->r * temp2.i + alpha->i * temp2.r;
+ q__1.r = q__2.r + q__4.r, q__1.i = q__2.i + q__4.i;
+ y[i__2].r = q__1.r, y[i__2].i = q__1.i;
+ kk += j;
+/* L60: */
+ }
+ } else {
+ jx = kx;
+ jy = ky;
+ i__1 = *n;
+ for (j = 1; j <= i__1; ++j) {
+ i__2 = jx;
+ q__1.r = alpha->r * x[i__2].r - alpha->i * x[i__2].i, q__1.i =
+ alpha->r * x[i__2].i + alpha->i * x[i__2].r;
+ temp1.r = q__1.r, temp1.i = q__1.i;
+ temp2.r = 0.f, temp2.i = 0.f;
+ ix = kx;
+ iy = ky;
+ i__2 = kk + j - 2;
+ for (k = kk; k <= i__2; ++k) {
+ i__3 = iy;
+ i__4 = iy;
+ i__5 = k;
+ q__2.r = temp1.r * ap[i__5].r - temp1.i * ap[i__5].i,
+ q__2.i = temp1.r * ap[i__5].i + temp1.i * ap[i__5]
+ .r;
+ q__1.r = y[i__4].r + q__2.r, q__1.i = y[i__4].i + q__2.i;
+ y[i__3].r = q__1.r, y[i__3].i = q__1.i;
+ r_cnjg(&q__3, &ap[k]);
+ i__3 = ix;
+ q__2.r = q__3.r * x[i__3].r - q__3.i * x[i__3].i, q__2.i =
+ q__3.r * x[i__3].i + q__3.i * x[i__3].r;
+ q__1.r = temp2.r + q__2.r, q__1.i = temp2.i + q__2.i;
+ temp2.r = q__1.r, temp2.i = q__1.i;
+ ix += *incx;
+ iy += *incy;
+/* L70: */
+ }
+ i__2 = jy;
+ i__3 = jy;
+ i__4 = kk + j - 1;
+ r__1 = ap[i__4].r;
+ q__3.r = r__1 * temp1.r, q__3.i = r__1 * temp1.i;
+ q__2.r = y[i__3].r + q__3.r, q__2.i = y[i__3].i + q__3.i;
+ q__4.r = alpha->r * temp2.r - alpha->i * temp2.i, q__4.i =
+ alpha->r * temp2.i + alpha->i * temp2.r;
+ q__1.r = q__2.r + q__4.r, q__1.i = q__2.i + q__4.i;
+ y[i__2].r = q__1.r, y[i__2].i = q__1.i;
+ jx += *incx;
+ jy += *incy;
+ kk += j;
+/* L80: */
+ }
+ }
+ } else {
+
+/* Form y when AP contains the lower triangle. */
+
+ if (*incx == 1 && *incy == 1) {
+ i__1 = *n;
+ for (j = 1; j <= i__1; ++j) {
+ i__2 = j;
+ q__1.r = alpha->r * x[i__2].r - alpha->i * x[i__2].i, q__1.i =
+ alpha->r * x[i__2].i + alpha->i * x[i__2].r;
+ temp1.r = q__1.r, temp1.i = q__1.i;
+ temp2.r = 0.f, temp2.i = 0.f;
+ i__2 = j;
+ i__3 = j;
+ i__4 = kk;
+ r__1 = ap[i__4].r;
+ q__2.r = r__1 * temp1.r, q__2.i = r__1 * temp1.i;
+ q__1.r = y[i__3].r + q__2.r, q__1.i = y[i__3].i + q__2.i;
+ y[i__2].r = q__1.r, y[i__2].i = q__1.i;
+ k = kk + 1;
+ i__2 = *n;
+ for (i__ = j + 1; i__ <= i__2; ++i__) {
+ i__3 = i__;
+ i__4 = i__;
+ i__5 = k;
+ q__2.r = temp1.r * ap[i__5].r - temp1.i * ap[i__5].i,
+ q__2.i = temp1.r * ap[i__5].i + temp1.i * ap[i__5]
+ .r;
+ q__1.r = y[i__4].r + q__2.r, q__1.i = y[i__4].i + q__2.i;
+ y[i__3].r = q__1.r, y[i__3].i = q__1.i;
+ r_cnjg(&q__3, &ap[k]);
+ i__3 = i__;
+ q__2.r = q__3.r * x[i__3].r - q__3.i * x[i__3].i, q__2.i =
+ q__3.r * x[i__3].i + q__3.i * x[i__3].r;
+ q__1.r = temp2.r + q__2.r, q__1.i = temp2.i + q__2.i;
+ temp2.r = q__1.r, temp2.i = q__1.i;
+ ++k;
+/* L90: */
+ }
+ i__2 = j;
+ i__3 = j;
+ q__2.r = alpha->r * temp2.r - alpha->i * temp2.i, q__2.i =
+ alpha->r * temp2.i + alpha->i * temp2.r;
+ q__1.r = y[i__3].r + q__2.r, q__1.i = y[i__3].i + q__2.i;
+ y[i__2].r = q__1.r, y[i__2].i = q__1.i;
+ kk += *n - j + 1;
+/* L100: */
+ }
+ } else {
+ jx = kx;
+ jy = ky;
+ i__1 = *n;
+ for (j = 1; j <= i__1; ++j) {
+ i__2 = jx;
+ q__1.r = alpha->r * x[i__2].r - alpha->i * x[i__2].i, q__1.i =
+ alpha->r * x[i__2].i + alpha->i * x[i__2].r;
+ temp1.r = q__1.r, temp1.i = q__1.i;
+ temp2.r = 0.f, temp2.i = 0.f;
+ i__2 = jy;
+ i__3 = jy;
+ i__4 = kk;
+ r__1 = ap[i__4].r;
+ q__2.r = r__1 * temp1.r, q__2.i = r__1 * temp1.i;
+ q__1.r = y[i__3].r + q__2.r, q__1.i = y[i__3].i + q__2.i;
+ y[i__2].r = q__1.r, y[i__2].i = q__1.i;
+ ix = jx;
+ iy = jy;
+ i__2 = kk + *n - j;
+ for (k = kk + 1; k <= i__2; ++k) {
+ ix += *incx;
+ iy += *incy;
+ i__3 = iy;
+ i__4 = iy;
+ i__5 = k;
+ q__2.r = temp1.r * ap[i__5].r - temp1.i * ap[i__5].i,
+ q__2.i = temp1.r * ap[i__5].i + temp1.i * ap[i__5]
+ .r;
+ q__1.r = y[i__4].r + q__2.r, q__1.i = y[i__4].i + q__2.i;
+ y[i__3].r = q__1.r, y[i__3].i = q__1.i;
+ r_cnjg(&q__3, &ap[k]);
+ i__3 = ix;
+ q__2.r = q__3.r * x[i__3].r - q__3.i * x[i__3].i, q__2.i =
+ q__3.r * x[i__3].i + q__3.i * x[i__3].r;
+ q__1.r = temp2.r + q__2.r, q__1.i = temp2.i + q__2.i;
+ temp2.r = q__1.r, temp2.i = q__1.i;
+/* L110: */
+ }
+ i__2 = jy;
+ i__3 = jy;
+ q__2.r = alpha->r * temp2.r - alpha->i * temp2.i, q__2.i =
+ alpha->r * temp2.i + alpha->i * temp2.r;
+ q__1.r = y[i__3].r + q__2.r, q__1.i = y[i__3].i + q__2.i;
+ y[i__2].r = q__1.r, y[i__2].i = q__1.i;
+ jx += *incx;
+ jy += *incy;
+ kk += *n - j + 1;
+/* L120: */
+ }
+ }
+ }
+
+ return 0;
+
+/* End of CHPMV . */
+
+} /* chpmv_ */
+
diff --git a/blas/f2c/complexdots.c b/blas/f2c/complexdots.c
new file mode 100644
index 0000000..a856a23
--- /dev/null
+++ b/blas/f2c/complexdots.c
@@ -0,0 +1,84 @@
+/* This file has been modified to use the standard gfortran calling
+ convention, rather than the f2c calling convention.
+
+ It does not require -ff2c when compiled with gfortran.
+*/
+
+/* complexdots.f -- translated by f2c (version 20100827).
+ You must link the resulting object file with libf2c:
+ on Microsoft Windows system, link with libf2c.lib;
+ on Linux or Unix systems, link with .../path/to/libf2c.a -lm
+ or, if you install libf2c.a in a standard place, with -lf2c -lm
+ -- in that order, at the end of the command line, as in
+ cc *.o -lf2c -lm
+ Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
+
+ http://www.netlib.org/f2c/libf2c.zip
+*/
+
+#include "datatypes.h"
+
+complex cdotc_(integer *n, complex *cx, integer
+ *incx, complex *cy, integer *incy)
+{
+ complex res;
+ extern /* Subroutine */ int cdotcw_(integer *, complex *, integer *,
+ complex *, integer *, complex *);
+
+ /* Parameter adjustments */
+ --cy;
+ --cx;
+
+ /* Function Body */
+ cdotcw_(n, &cx[1], incx, &cy[1], incy, &res);
+ return res;
+} /* cdotc_ */
+
+complex cdotu_(integer *n, complex *cx, integer
+ *incx, complex *cy, integer *incy)
+{
+ complex res;
+ extern /* Subroutine */ int cdotuw_(integer *, complex *, integer *,
+ complex *, integer *, complex *);
+
+ /* Parameter adjustments */
+ --cy;
+ --cx;
+
+ /* Function Body */
+ cdotuw_(n, &cx[1], incx, &cy[1], incy, &res);
+ return res;
+} /* cdotu_ */
+
+doublecomplex zdotc_(integer *n, doublecomplex *cx, integer *incx,
+ doublecomplex *cy, integer *incy)
+{
+ doublecomplex res;
+ extern /* Subroutine */ int zdotcw_(integer *, doublecomplex *, integer *,
+ doublecomplex *, integer *, doublecomplex *);
+
+ /* Parameter adjustments */
+ --cy;
+ --cx;
+
+ /* Function Body */
+ zdotcw_(n, &cx[1], incx, &cy[1], incy, &res);
+ return res;
+} /* zdotc_ */
+
+doublecomplex zdotu_(integer *n, doublecomplex *cx, integer *incx,
+ doublecomplex *cy, integer *incy)
+{
+ doublecomplex res;
+ extern /* Subroutine */ int zdotuw_(integer *, doublecomplex *, integer *,
+ doublecomplex *, integer *, doublecomplex *);
+
+ /* Parameter adjustments */
+ --cy;
+ --cx;
+
+ /* Function Body */
+ zdotuw_(n, &cx[1], incx, &cy[1], incy, &res);
+ return res;
+} /* zdotu_ */
+
diff --git a/blas/f2c/ctbmv.c b/blas/f2c/ctbmv.c
new file mode 100644
index 0000000..a6e0dae
--- /dev/null
+++ b/blas/f2c/ctbmv.c
@@ -0,0 +1,647 @@
+/* ctbmv.f -- translated by f2c (version 20100827).
+ You must link the resulting object file with libf2c:
+ on Microsoft Windows system, link with libf2c.lib;
+ on Linux or Unix systems, link with .../path/to/libf2c.a -lm
+ or, if you install libf2c.a in a standard place, with -lf2c -lm
+ -- in that order, at the end of the command line, as in
+ cc *.o -lf2c -lm
+ Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
+
+ http://www.netlib.org/f2c/libf2c.zip
+*/
+
+#include "datatypes.h"
+
+/* Subroutine */ int ctbmv_(char *uplo, char *trans, char *diag, integer *n,
+ integer *k, complex *a, integer *lda, complex *x, integer *incx,
+ ftnlen uplo_len, ftnlen trans_len, ftnlen diag_len)
+{
+ /* System generated locals */
+ integer a_dim1, a_offset, i__1, i__2, i__3, i__4, i__5;
+ complex q__1, q__2, q__3;
+
+ /* Builtin functions */
+ void r_cnjg(complex *, complex *);
+
+ /* Local variables */
+ integer i__, j, l, ix, jx, kx, info;
+ complex temp;
+ extern logical lsame_(char *, char *, ftnlen, ftnlen);
+ integer kplus1;
+ extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
+ logical noconj, nounit;
+
+/* .. Scalar Arguments .. */
+/* .. */
+/* .. Array Arguments .. */
+/* .. */
+
+/* Purpose */
+/* ======= */
+
+/* CTBMV performs one of the matrix-vector operations */
+
+/* x := A*x, or x := A'*x, or x := conjg( A' )*x, */
+
+/* where x is an n element vector and A is an n by n unit, or non-unit, */
+/* upper or lower triangular band matrix, with ( k + 1 ) diagonals. */
+
+/* Arguments */
+/* ========== */
+
+/* UPLO - CHARACTER*1. */
+/* On entry, UPLO specifies whether the matrix is an upper or */
+/* lower triangular matrix as follows: */
+
+/* UPLO = 'U' or 'u' A is an upper triangular matrix. */
+
+/* UPLO = 'L' or 'l' A is a lower triangular matrix. */
+
+/* Unchanged on exit. */
+
+/* TRANS - CHARACTER*1. */
+/* On entry, TRANS specifies the operation to be performed as */
+/* follows: */
+
+/* TRANS = 'N' or 'n' x := A*x. */
+
+/* TRANS = 'T' or 't' x := A'*x. */
+
+/* TRANS = 'C' or 'c' x := conjg( A' )*x. */
+
+/* Unchanged on exit. */
+
+/* DIAG - CHARACTER*1. */
+/* On entry, DIAG specifies whether or not A is unit */
+/* triangular as follows: */
+
+/* DIAG = 'U' or 'u' A is assumed to be unit triangular. */
+
+/* DIAG = 'N' or 'n' A is not assumed to be unit */
+/* triangular. */
+
+/* Unchanged on exit. */
+
+/* N - INTEGER. */
+/* On entry, N specifies the order of the matrix A. */
+/* N must be at least zero. */
+/* Unchanged on exit. */
+
+/* K - INTEGER. */
+/* On entry with UPLO = 'U' or 'u', K specifies the number of */
+/* super-diagonals of the matrix A. */
+/* On entry with UPLO = 'L' or 'l', K specifies the number of */
+/* sub-diagonals of the matrix A. */
+/* K must satisfy 0 .le. K. */
+/* Unchanged on exit. */
+
+/* A - COMPLEX array of DIMENSION ( LDA, n ). */
+/* Before entry with UPLO = 'U' or 'u', the leading ( k + 1 ) */
+/* by n part of the array A must contain the upper triangular */
+/* band part of the matrix of coefficients, supplied column by */
+/* column, with the leading diagonal of the matrix in row */
+/* ( k + 1 ) of the array, the first super-diagonal starting at */
+/* position 2 in row k, and so on. The top left k by k triangle */
+/* of the array A is not referenced. */
+/* The following program segment will transfer an upper */
+/* triangular band matrix from conventional full matrix storage */
+/* to band storage: */
+
+/* DO 20, J = 1, N */
+/* M = K + 1 - J */
+/* DO 10, I = MAX( 1, J - K ), J */
+/* A( M + I, J ) = matrix( I, J ) */
+/* 10 CONTINUE */
+/* 20 CONTINUE */
+
+/* Before entry with UPLO = 'L' or 'l', the leading ( k + 1 ) */
+/* by n part of the array A must contain the lower triangular */
+/* band part of the matrix of coefficients, supplied column by */
+/* column, with the leading diagonal of the matrix in row 1 of */
+/* the array, the first sub-diagonal starting at position 1 in */
+/* row 2, and so on. The bottom right k by k triangle of the */
+/* array A is not referenced. */
+/* The following program segment will transfer a lower */
+/* triangular band matrix from conventional full matrix storage */
+/* to band storage: */
+
+/* DO 20, J = 1, N */
+/* M = 1 - J */
+/* DO 10, I = J, MIN( N, J + K ) */
+/* A( M + I, J ) = matrix( I, J ) */
+/* 10 CONTINUE */
+/* 20 CONTINUE */
+
+/* Note that when DIAG = 'U' or 'u' the elements of the array A */
+/* corresponding to the diagonal elements of the matrix are not */
+/* referenced, but are assumed to be unity. */
+/* Unchanged on exit. */
+
+/* LDA - INTEGER. */
+/* On entry, LDA specifies the first dimension of A as declared */
+/* in the calling (sub) program. LDA must be at least */
+/* ( k + 1 ). */
+/* Unchanged on exit. */
+
+/* X - COMPLEX array of dimension at least */
+/* ( 1 + ( n - 1 )*abs( INCX ) ). */
+/* Before entry, the incremented array X must contain the n */
+/* element vector x. On exit, X is overwritten with the */
+/* transformed vector x. */
+
+/* INCX - INTEGER. */
+/* On entry, INCX specifies the increment for the elements of */
+/* X. INCX must not be zero. */
+/* Unchanged on exit. */
+
+/* Further Details */
+/* =============== */
+
+/* Level 2 Blas routine. */
+
+/* -- Written on 22-October-1986. */
+/* Jack Dongarra, Argonne National Lab. */
+/* Jeremy Du Croz, Nag Central Office. */
+/* Sven Hammarling, Nag Central Office. */
+/* Richard Hanson, Sandia National Labs. */
+
+/* ===================================================================== */
+
+/* .. Parameters .. */
+/* .. */
+/* .. Local Scalars .. */
+/* .. */
+/* .. External Functions .. */
+/* .. */
+/* .. External Subroutines .. */
+/* .. */
+/* .. Intrinsic Functions .. */
+/* .. */
+
+/* Test the input parameters. */
+
+ /* Parameter adjustments */
+ a_dim1 = *lda;
+ a_offset = 1 + a_dim1;
+ a -= a_offset;
+ --x;
+
+ /* Function Body */
+ info = 0;
+ if (! lsame_(uplo, "U", (ftnlen)1, (ftnlen)1) && ! lsame_(uplo, "L", (
+ ftnlen)1, (ftnlen)1)) {
+ info = 1;
+ } else if (! lsame_(trans, "N", (ftnlen)1, (ftnlen)1) && ! lsame_(trans,
+ "T", (ftnlen)1, (ftnlen)1) && ! lsame_(trans, "C", (ftnlen)1, (
+ ftnlen)1)) {
+ info = 2;
+ } else if (! lsame_(diag, "U", (ftnlen)1, (ftnlen)1) && ! lsame_(diag,
+ "N", (ftnlen)1, (ftnlen)1)) {
+ info = 3;
+ } else if (*n < 0) {
+ info = 4;
+ } else if (*k < 0) {
+ info = 5;
+ } else if (*lda < *k + 1) {
+ info = 7;
+ } else if (*incx == 0) {
+ info = 9;
+ }
+ if (info != 0) {
+ xerbla_("CTBMV ", &info, (ftnlen)6);
+ return 0;
+ }
+
+/* Quick return if possible. */
+
+ if (*n == 0) {
+ return 0;
+ }
+
+ noconj = lsame_(trans, "T", (ftnlen)1, (ftnlen)1);
+ nounit = lsame_(diag, "N", (ftnlen)1, (ftnlen)1);
+
+/* Set up the start point in X if the increment is not unity. This */
+/* will be ( N - 1 )*INCX too small for descending loops. */
+
+ if (*incx <= 0) {
+ kx = 1 - (*n - 1) * *incx;
+ } else if (*incx != 1) {
+ kx = 1;
+ }
+
+/* Start the operations. In this version the elements of A are */
+/* accessed sequentially with one pass through A. */
+
+ if (lsame_(trans, "N", (ftnlen)1, (ftnlen)1)) {
+
+/* Form x := A*x. */
+
+ if (lsame_(uplo, "U", (ftnlen)1, (ftnlen)1)) {
+ kplus1 = *k + 1;
+ if (*incx == 1) {
+ i__1 = *n;
+ for (j = 1; j <= i__1; ++j) {
+ i__2 = j;
+ if (x[i__2].r != 0.f || x[i__2].i != 0.f) {
+ i__2 = j;
+ temp.r = x[i__2].r, temp.i = x[i__2].i;
+ l = kplus1 - j;
+/* Computing MAX */
+ i__2 = 1, i__3 = j - *k;
+ i__4 = j - 1;
+ for (i__ = max(i__2,i__3); i__ <= i__4; ++i__) {
+ i__2 = i__;
+ i__3 = i__;
+ i__5 = l + i__ + j * a_dim1;
+ q__2.r = temp.r * a[i__5].r - temp.i * a[i__5].i,
+ q__2.i = temp.r * a[i__5].i + temp.i * a[
+ i__5].r;
+ q__1.r = x[i__3].r + q__2.r, q__1.i = x[i__3].i +
+ q__2.i;
+ x[i__2].r = q__1.r, x[i__2].i = q__1.i;
+/* L10: */
+ }
+ if (nounit) {
+ i__4 = j;
+ i__2 = j;
+ i__3 = kplus1 + j * a_dim1;
+ q__1.r = x[i__2].r * a[i__3].r - x[i__2].i * a[
+ i__3].i, q__1.i = x[i__2].r * a[i__3].i +
+ x[i__2].i * a[i__3].r;
+ x[i__4].r = q__1.r, x[i__4].i = q__1.i;
+ }
+ }
+/* L20: */
+ }
+ } else {
+ jx = kx;
+ i__1 = *n;
+ for (j = 1; j <= i__1; ++j) {
+ i__4 = jx;
+ if (x[i__4].r != 0.f || x[i__4].i != 0.f) {
+ i__4 = jx;
+ temp.r = x[i__4].r, temp.i = x[i__4].i;
+ ix = kx;
+ l = kplus1 - j;
+/* Computing MAX */
+ i__4 = 1, i__2 = j - *k;
+ i__3 = j - 1;
+ for (i__ = max(i__4,i__2); i__ <= i__3; ++i__) {
+ i__4 = ix;
+ i__2 = ix;
+ i__5 = l + i__ + j * a_dim1;
+ q__2.r = temp.r * a[i__5].r - temp.i * a[i__5].i,
+ q__2.i = temp.r * a[i__5].i + temp.i * a[
+ i__5].r;
+ q__1.r = x[i__2].r + q__2.r, q__1.i = x[i__2].i +
+ q__2.i;
+ x[i__4].r = q__1.r, x[i__4].i = q__1.i;
+ ix += *incx;
+/* L30: */
+ }
+ if (nounit) {
+ i__3 = jx;
+ i__4 = jx;
+ i__2 = kplus1 + j * a_dim1;
+ q__1.r = x[i__4].r * a[i__2].r - x[i__4].i * a[
+ i__2].i, q__1.i = x[i__4].r * a[i__2].i +
+ x[i__4].i * a[i__2].r;
+ x[i__3].r = q__1.r, x[i__3].i = q__1.i;
+ }
+ }
+ jx += *incx;
+ if (j > *k) {
+ kx += *incx;
+ }
+/* L40: */
+ }
+ }
+ } else {
+ if (*incx == 1) {
+ for (j = *n; j >= 1; --j) {
+ i__1 = j;
+ if (x[i__1].r != 0.f || x[i__1].i != 0.f) {
+ i__1 = j;
+ temp.r = x[i__1].r, temp.i = x[i__1].i;
+ l = 1 - j;
+/* Computing MIN */
+ i__1 = *n, i__3 = j + *k;
+ i__4 = j + 1;
+ for (i__ = min(i__1,i__3); i__ >= i__4; --i__) {
+ i__1 = i__;
+ i__3 = i__;
+ i__2 = l + i__ + j * a_dim1;
+ q__2.r = temp.r * a[i__2].r - temp.i * a[i__2].i,
+ q__2.i = temp.r * a[i__2].i + temp.i * a[
+ i__2].r;
+ q__1.r = x[i__3].r + q__2.r, q__1.i = x[i__3].i +
+ q__2.i;
+ x[i__1].r = q__1.r, x[i__1].i = q__1.i;
+/* L50: */
+ }
+ if (nounit) {
+ i__4 = j;
+ i__1 = j;
+ i__3 = j * a_dim1 + 1;
+ q__1.r = x[i__1].r * a[i__3].r - x[i__1].i * a[
+ i__3].i, q__1.i = x[i__1].r * a[i__3].i +
+ x[i__1].i * a[i__3].r;
+ x[i__4].r = q__1.r, x[i__4].i = q__1.i;
+ }
+ }
+/* L60: */
+ }
+ } else {
+ kx += (*n - 1) * *incx;
+ jx = kx;
+ for (j = *n; j >= 1; --j) {
+ i__4 = jx;
+ if (x[i__4].r != 0.f || x[i__4].i != 0.f) {
+ i__4 = jx;
+ temp.r = x[i__4].r, temp.i = x[i__4].i;
+ ix = kx;
+ l = 1 - j;
+/* Computing MIN */
+ i__4 = *n, i__1 = j + *k;
+ i__3 = j + 1;
+ for (i__ = min(i__4,i__1); i__ >= i__3; --i__) {
+ i__4 = ix;
+ i__1 = ix;
+ i__2 = l + i__ + j * a_dim1;
+ q__2.r = temp.r * a[i__2].r - temp.i * a[i__2].i,
+ q__2.i = temp.r * a[i__2].i + temp.i * a[
+ i__2].r;
+ q__1.r = x[i__1].r + q__2.r, q__1.i = x[i__1].i +
+ q__2.i;
+ x[i__4].r = q__1.r, x[i__4].i = q__1.i;
+ ix -= *incx;
+/* L70: */
+ }
+ if (nounit) {
+ i__3 = jx;
+ i__4 = jx;
+ i__1 = j * a_dim1 + 1;
+ q__1.r = x[i__4].r * a[i__1].r - x[i__4].i * a[
+ i__1].i, q__1.i = x[i__4].r * a[i__1].i +
+ x[i__4].i * a[i__1].r;
+ x[i__3].r = q__1.r, x[i__3].i = q__1.i;
+ }
+ }
+ jx -= *incx;
+ if (*n - j >= *k) {
+ kx -= *incx;
+ }
+/* L80: */
+ }
+ }
+ }
+ } else {
+
+/* Form x := A'*x or x := conjg( A' )*x. */
+
+ if (lsame_(uplo, "U", (ftnlen)1, (ftnlen)1)) {
+ kplus1 = *k + 1;
+ if (*incx == 1) {
+ for (j = *n; j >= 1; --j) {
+ i__3 = j;
+ temp.r = x[i__3].r, temp.i = x[i__3].i;
+ l = kplus1 - j;
+ if (noconj) {
+ if (nounit) {
+ i__3 = kplus1 + j * a_dim1;
+ q__1.r = temp.r * a[i__3].r - temp.i * a[i__3].i,
+ q__1.i = temp.r * a[i__3].i + temp.i * a[
+ i__3].r;
+ temp.r = q__1.r, temp.i = q__1.i;
+ }
+/* Computing MAX */
+ i__4 = 1, i__1 = j - *k;
+ i__3 = max(i__4,i__1);
+ for (i__ = j - 1; i__ >= i__3; --i__) {
+ i__4 = l + i__ + j * a_dim1;
+ i__1 = i__;
+ q__2.r = a[i__4].r * x[i__1].r - a[i__4].i * x[
+ i__1].i, q__2.i = a[i__4].r * x[i__1].i +
+ a[i__4].i * x[i__1].r;
+ q__1.r = temp.r + q__2.r, q__1.i = temp.i +
+ q__2.i;
+ temp.r = q__1.r, temp.i = q__1.i;
+/* L90: */
+ }
+ } else {
+ if (nounit) {
+ r_cnjg(&q__2, &a[kplus1 + j * a_dim1]);
+ q__1.r = temp.r * q__2.r - temp.i * q__2.i,
+ q__1.i = temp.r * q__2.i + temp.i *
+ q__2.r;
+ temp.r = q__1.r, temp.i = q__1.i;
+ }
+/* Computing MAX */
+ i__4 = 1, i__1 = j - *k;
+ i__3 = max(i__4,i__1);
+ for (i__ = j - 1; i__ >= i__3; --i__) {
+ r_cnjg(&q__3, &a[l + i__ + j * a_dim1]);
+ i__4 = i__;
+ q__2.r = q__3.r * x[i__4].r - q__3.i * x[i__4].i,
+ q__2.i = q__3.r * x[i__4].i + q__3.i * x[
+ i__4].r;
+ q__1.r = temp.r + q__2.r, q__1.i = temp.i +
+ q__2.i;
+ temp.r = q__1.r, temp.i = q__1.i;
+/* L100: */
+ }
+ }
+ i__3 = j;
+ x[i__3].r = temp.r, x[i__3].i = temp.i;
+/* L110: */
+ }
+ } else {
+ kx += (*n - 1) * *incx;
+ jx = kx;
+ for (j = *n; j >= 1; --j) {
+ i__3 = jx;
+ temp.r = x[i__3].r, temp.i = x[i__3].i;
+ kx -= *incx;
+ ix = kx;
+ l = kplus1 - j;
+ if (noconj) {
+ if (nounit) {
+ i__3 = kplus1 + j * a_dim1;
+ q__1.r = temp.r * a[i__3].r - temp.i * a[i__3].i,
+ q__1.i = temp.r * a[i__3].i + temp.i * a[
+ i__3].r;
+ temp.r = q__1.r, temp.i = q__1.i;
+ }
+/* Computing MAX */
+ i__4 = 1, i__1 = j - *k;
+ i__3 = max(i__4,i__1);
+ for (i__ = j - 1; i__ >= i__3; --i__) {
+ i__4 = l + i__ + j * a_dim1;
+ i__1 = ix;
+ q__2.r = a[i__4].r * x[i__1].r - a[i__4].i * x[
+ i__1].i, q__2.i = a[i__4].r * x[i__1].i +
+ a[i__4].i * x[i__1].r;
+ q__1.r = temp.r + q__2.r, q__1.i = temp.i +
+ q__2.i;
+ temp.r = q__1.r, temp.i = q__1.i;
+ ix -= *incx;
+/* L120: */
+ }
+ } else {
+ if (nounit) {
+ r_cnjg(&q__2, &a[kplus1 + j * a_dim1]);
+ q__1.r = temp.r * q__2.r - temp.i * q__2.i,
+ q__1.i = temp.r * q__2.i + temp.i *
+ q__2.r;
+ temp.r = q__1.r, temp.i = q__1.i;
+ }
+/* Computing MAX */
+ i__4 = 1, i__1 = j - *k;
+ i__3 = max(i__4,i__1);
+ for (i__ = j - 1; i__ >= i__3; --i__) {
+ r_cnjg(&q__3, &a[l + i__ + j * a_dim1]);
+ i__4 = ix;
+ q__2.r = q__3.r * x[i__4].r - q__3.i * x[i__4].i,
+ q__2.i = q__3.r * x[i__4].i + q__3.i * x[
+ i__4].r;
+ q__1.r = temp.r + q__2.r, q__1.i = temp.i +
+ q__2.i;
+ temp.r = q__1.r, temp.i = q__1.i;
+ ix -= *incx;
+/* L130: */
+ }
+ }
+ i__3 = jx;
+ x[i__3].r = temp.r, x[i__3].i = temp.i;
+ jx -= *incx;
+/* L140: */
+ }
+ }
+ } else {
+ if (*incx == 1) {
+ i__3 = *n;
+ for (j = 1; j <= i__3; ++j) {
+ i__4 = j;
+ temp.r = x[i__4].r, temp.i = x[i__4].i;
+ l = 1 - j;
+ if (noconj) {
+ if (nounit) {
+ i__4 = j * a_dim1 + 1;
+ q__1.r = temp.r * a[i__4].r - temp.i * a[i__4].i,
+ q__1.i = temp.r * a[i__4].i + temp.i * a[
+ i__4].r;
+ temp.r = q__1.r, temp.i = q__1.i;
+ }
+/* Computing MIN */
+ i__1 = *n, i__2 = j + *k;
+ i__4 = min(i__1,i__2);
+ for (i__ = j + 1; i__ <= i__4; ++i__) {
+ i__1 = l + i__ + j * a_dim1;
+ i__2 = i__;
+ q__2.r = a[i__1].r * x[i__2].r - a[i__1].i * x[
+ i__2].i, q__2.i = a[i__1].r * x[i__2].i +
+ a[i__1].i * x[i__2].r;
+ q__1.r = temp.r + q__2.r, q__1.i = temp.i +
+ q__2.i;
+ temp.r = q__1.r, temp.i = q__1.i;
+/* L150: */
+ }
+ } else {
+ if (nounit) {
+ r_cnjg(&q__2, &a[j * a_dim1 + 1]);
+ q__1.r = temp.r * q__2.r - temp.i * q__2.i,
+ q__1.i = temp.r * q__2.i + temp.i *
+ q__2.r;
+ temp.r = q__1.r, temp.i = q__1.i;
+ }
+/* Computing MIN */
+ i__1 = *n, i__2 = j + *k;
+ i__4 = min(i__1,i__2);
+ for (i__ = j + 1; i__ <= i__4; ++i__) {
+ r_cnjg(&q__3, &a[l + i__ + j * a_dim1]);
+ i__1 = i__;
+ q__2.r = q__3.r * x[i__1].r - q__3.i * x[i__1].i,
+ q__2.i = q__3.r * x[i__1].i + q__3.i * x[
+ i__1].r;
+ q__1.r = temp.r + q__2.r, q__1.i = temp.i +
+ q__2.i;
+ temp.r = q__1.r, temp.i = q__1.i;
+/* L160: */
+ }
+ }
+ i__4 = j;
+ x[i__4].r = temp.r, x[i__4].i = temp.i;
+/* L170: */
+ }
+ } else {
+ jx = kx;
+ i__3 = *n;
+ for (j = 1; j <= i__3; ++j) {
+ i__4 = jx;
+ temp.r = x[i__4].r, temp.i = x[i__4].i;
+ kx += *incx;
+ ix = kx;
+ l = 1 - j;
+ if (noconj) {
+ if (nounit) {
+ i__4 = j * a_dim1 + 1;
+ q__1.r = temp.r * a[i__4].r - temp.i * a[i__4].i,
+ q__1.i = temp.r * a[i__4].i + temp.i * a[
+ i__4].r;
+ temp.r = q__1.r, temp.i = q__1.i;
+ }
+/* Computing MIN */
+ i__1 = *n, i__2 = j + *k;
+ i__4 = min(i__1,i__2);
+ for (i__ = j + 1; i__ <= i__4; ++i__) {
+ i__1 = l + i__ + j * a_dim1;
+ i__2 = ix;
+ q__2.r = a[i__1].r * x[i__2].r - a[i__1].i * x[
+ i__2].i, q__2.i = a[i__1].r * x[i__2].i +
+ a[i__1].i * x[i__2].r;
+ q__1.r = temp.r + q__2.r, q__1.i = temp.i +
+ q__2.i;
+ temp.r = q__1.r, temp.i = q__1.i;
+ ix += *incx;
+/* L180: */
+ }
+ } else {
+ if (nounit) {
+ r_cnjg(&q__2, &a[j * a_dim1 + 1]);
+ q__1.r = temp.r * q__2.r - temp.i * q__2.i,
+ q__1.i = temp.r * q__2.i + temp.i *
+ q__2.r;
+ temp.r = q__1.r, temp.i = q__1.i;
+ }
+/* Computing MIN */
+ i__1 = *n, i__2 = j + *k;
+ i__4 = min(i__1,i__2);
+ for (i__ = j + 1; i__ <= i__4; ++i__) {
+ r_cnjg(&q__3, &a[l + i__ + j * a_dim1]);
+ i__1 = ix;
+ q__2.r = q__3.r * x[i__1].r - q__3.i * x[i__1].i,
+ q__2.i = q__3.r * x[i__1].i + q__3.i * x[
+ i__1].r;
+ q__1.r = temp.r + q__2.r, q__1.i = temp.i +
+ q__2.i;
+ temp.r = q__1.r, temp.i = q__1.i;
+ ix += *incx;
+/* L190: */
+ }
+ }
+ i__4 = jx;
+ x[i__4].r = temp.r, x[i__4].i = temp.i;
+ jx += *incx;
+/* L200: */
+ }
+ }
+ }
+ }
+
+ return 0;
+
+/* End of CTBMV . */
+
+} /* ctbmv_ */
+
diff --git a/blas/f2c/d_cnjg.c b/blas/f2c/d_cnjg.c
new file mode 100644
index 0000000..623090c
--- /dev/null
+++ b/blas/f2c/d_cnjg.c
@@ -0,0 +1,6 @@
+#include "datatypes.h"
+
+void d_cnjg(doublecomplex *r, doublecomplex *z) {
+ r->r = z->r;
+ r->i = -(z->i);
+}
diff --git a/blas/f2c/datatypes.h b/blas/f2c/datatypes.h
new file mode 100644
index 0000000..63232b2
--- /dev/null
+++ b/blas/f2c/datatypes.h
@@ -0,0 +1,24 @@
+/* This contains a limited subset of the typedefs exposed by f2c
+ for use by the Eigen BLAS C-only implementation.
+*/
+
+#ifndef __EIGEN_DATATYPES_H__
+#define __EIGEN_DATATYPES_H__
+
+typedef int integer;
+typedef unsigned int uinteger;
+typedef float real;
+typedef double doublereal;
+typedef struct { real r, i; } complex;
+typedef struct { doublereal r, i; } doublecomplex;
+typedef int ftnlen;
+typedef int logical;
+
+#define abs(x) ((x) >= 0 ? (x) : -(x))
+#define dabs(x) (doublereal)abs(x)
+#define min(a,b) ((a) <= (b) ? (a) : (b))
+#define max(a,b) ((a) >= (b) ? (a) : (b))
+#define dmin(a,b) (doublereal)min(a,b)
+#define dmax(a,b) (doublereal)max(a,b)
+
+#endif
diff --git a/blas/f2c/dcabs1.c b/blas/f2c/dcabs1.c
new file mode 100644
index 0000000..9eaea8f
--- /dev/null
+++ b/blas/f2c/dcabs1.c
@@ -0,0 +1,21 @@
+#include "datatypes.h"
+
+doublereal dcabs1_(doublecomplex *z)
+{
+/* >>Start of File<<
+
+ System generated locals */
+ doublereal ret_val;
+ static doublecomplex equiv_0[1];
+
+ /* Local variables */
+#define t ((doublereal *)equiv_0)
+#define zz (equiv_0)
+
+ zz->r = z->r, zz->i = z->i;
+ ret_val = abs(t[0]) + abs(t[1]);
+ return ret_val;
+} /* dcabs1_ */
+
+#undef zz
+#undef t
diff --git a/blas/f2c/drotm.c b/blas/f2c/drotm.c
new file mode 100644
index 0000000..17a779b
--- /dev/null
+++ b/blas/f2c/drotm.c
@@ -0,0 +1,215 @@
+/* drotm.f -- translated by f2c (version 20100827).
+ You must link the resulting object file with libf2c:
+ on Microsoft Windows system, link with libf2c.lib;
+ on Linux or Unix systems, link with .../path/to/libf2c.a -lm
+ or, if you install libf2c.a in a standard place, with -lf2c -lm
+ -- in that order, at the end of the command line, as in
+ cc *.o -lf2c -lm
+ Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
+
+ http://www.netlib.org/f2c/libf2c.zip
+*/
+
+#include "datatypes.h"
+
+/* Subroutine */ int drotm_(integer *n, doublereal *dx, integer *incx,
+ doublereal *dy, integer *incy, doublereal *dparam)
+{
+ /* Initialized data */
+
+ static doublereal zero = 0.;
+ static doublereal two = 2.;
+
+ /* System generated locals */
+ integer i__1, i__2;
+
+ /* Local variables */
+ integer i__;
+ doublereal w, z__;
+ integer kx, ky;
+ doublereal dh11, dh12, dh21, dh22, dflag;
+ integer nsteps;
+
+/* .. Scalar Arguments .. */
+/* .. */
+/* .. Array Arguments .. */
+/* .. */
+
+/* Purpose */
+/* ======= */
+
+/* APPLY THE MODIFIED GIVENS TRANSFORMATION, H, TO THE 2 BY N MATRIX */
+
+/* (DX**T) , WHERE **T INDICATES TRANSPOSE. THE ELEMENTS OF DX ARE IN */
+/* (DY**T) */
+
+/* DX(LX+I*INCX), I = 0 TO N-1, WHERE LX = 1 IF INCX .GE. 0, ELSE */
+/* LX = (-INCX)*N, AND SIMILARLY FOR SY USING LY AND INCY. */
+/* WITH DPARAM(1)=DFLAG, H HAS ONE OF THE FOLLOWING FORMS.. */
+
+/* DFLAG=-1.D0 DFLAG=0.D0 DFLAG=1.D0 DFLAG=-2.D0 */
+
+/* (DH11 DH12) (1.D0 DH12) (DH11 1.D0) (1.D0 0.D0) */
+/* H=( ) ( ) ( ) ( ) */
+/* (DH21 DH22), (DH21 1.D0), (-1.D0 DH22), (0.D0 1.D0). */
+/* SEE DROTMG FOR A DESCRIPTION OF DATA STORAGE IN DPARAM. */
+
+/* Arguments */
+/* ========= */
+
+/* N (input) INTEGER */
+/* number of elements in input vector(s) */
+
+/* DX (input/output) DOUBLE PRECISION array, dimension N */
+/* double precision vector with N elements */
+
+/* INCX (input) INTEGER */
+/* storage spacing between elements of DX */
+
+/* DY (input/output) DOUBLE PRECISION array, dimension N */
+/* double precision vector with N elements */
+
+/* INCY (input) INTEGER */
+/* storage spacing between elements of DY */
+
+/* DPARAM (input/output) DOUBLE PRECISION array, dimension 5 */
+/* DPARAM(1)=DFLAG */
+/* DPARAM(2)=DH11 */
+/* DPARAM(3)=DH21 */
+/* DPARAM(4)=DH12 */
+/* DPARAM(5)=DH22 */
+
+/* ===================================================================== */
+
+/* .. Local Scalars .. */
+/* .. */
+/* .. Data statements .. */
+ /* Parameter adjustments */
+ --dparam;
+ --dy;
+ --dx;
+
+ /* Function Body */
+/* .. */
+
+ dflag = dparam[1];
+ if (*n <= 0 || dflag + two == zero) {
+ goto L140;
+ }
+ if (! (*incx == *incy && *incx > 0)) {
+ goto L70;
+ }
+
+ nsteps = *n * *incx;
+ if (dflag < 0.) {
+ goto L50;
+ } else if (dflag == 0) {
+ goto L10;
+ } else {
+ goto L30;
+ }
+L10:
+ dh12 = dparam[4];
+ dh21 = dparam[3];
+ i__1 = nsteps;
+ i__2 = *incx;
+ for (i__ = 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) {
+ w = dx[i__];
+ z__ = dy[i__];
+ dx[i__] = w + z__ * dh12;
+ dy[i__] = w * dh21 + z__;
+/* L20: */
+ }
+ goto L140;
+L30:
+ dh11 = dparam[2];
+ dh22 = dparam[5];
+ i__2 = nsteps;
+ i__1 = *incx;
+ for (i__ = 1; i__1 < 0 ? i__ >= i__2 : i__ <= i__2; i__ += i__1) {
+ w = dx[i__];
+ z__ = dy[i__];
+ dx[i__] = w * dh11 + z__;
+ dy[i__] = -w + dh22 * z__;
+/* L40: */
+ }
+ goto L140;
+L50:
+ dh11 = dparam[2];
+ dh12 = dparam[4];
+ dh21 = dparam[3];
+ dh22 = dparam[5];
+ i__1 = nsteps;
+ i__2 = *incx;
+ for (i__ = 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) {
+ w = dx[i__];
+ z__ = dy[i__];
+ dx[i__] = w * dh11 + z__ * dh12;
+ dy[i__] = w * dh21 + z__ * dh22;
+/* L60: */
+ }
+ goto L140;
+L70:
+ kx = 1;
+ ky = 1;
+ if (*incx < 0) {
+ kx = (1 - *n) * *incx + 1;
+ }
+ if (*incy < 0) {
+ ky = (1 - *n) * *incy + 1;
+ }
+
+ if (dflag < 0.) {
+ goto L120;
+ } else if (dflag == 0) {
+ goto L80;
+ } else {
+ goto L100;
+ }
+L80:
+ dh12 = dparam[4];
+ dh21 = dparam[3];
+ i__2 = *n;
+ for (i__ = 1; i__ <= i__2; ++i__) {
+ w = dx[kx];
+ z__ = dy[ky];
+ dx[kx] = w + z__ * dh12;
+ dy[ky] = w * dh21 + z__;
+ kx += *incx;
+ ky += *incy;
+/* L90: */
+ }
+ goto L140;
+L100:
+ dh11 = dparam[2];
+ dh22 = dparam[5];
+ i__2 = *n;
+ for (i__ = 1; i__ <= i__2; ++i__) {
+ w = dx[kx];
+ z__ = dy[ky];
+ dx[kx] = w * dh11 + z__;
+ dy[ky] = -w + dh22 * z__;
+ kx += *incx;
+ ky += *incy;
+/* L110: */
+ }
+ goto L140;
+L120:
+ dh11 = dparam[2];
+ dh12 = dparam[4];
+ dh21 = dparam[3];
+ dh22 = dparam[5];
+ i__2 = *n;
+ for (i__ = 1; i__ <= i__2; ++i__) {
+ w = dx[kx];
+ z__ = dy[ky];
+ dx[kx] = w * dh11 + z__ * dh12;
+ dy[ky] = w * dh21 + z__ * dh22;
+ kx += *incx;
+ ky += *incy;
+/* L130: */
+ }
+L140:
+ return 0;
+} /* drotm_ */
+
diff --git a/blas/f2c/drotmg.c b/blas/f2c/drotmg.c
new file mode 100644
index 0000000..a63eb10
--- /dev/null
+++ b/blas/f2c/drotmg.c
@@ -0,0 +1,293 @@
+/* drotmg.f -- translated by f2c (version 20100827).
+ You must link the resulting object file with libf2c:
+ on Microsoft Windows system, link with libf2c.lib;
+ on Linux or Unix systems, link with .../path/to/libf2c.a -lm
+ or, if you install libf2c.a in a standard place, with -lf2c -lm
+ -- in that order, at the end of the command line, as in
+ cc *.o -lf2c -lm
+ Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
+
+ http://www.netlib.org/f2c/libf2c.zip
+*/
+
+#include "datatypes.h"
+
+/* Subroutine */ int drotmg_(doublereal *dd1, doublereal *dd2, doublereal *
+ dx1, doublereal *dy1, doublereal *dparam)
+{
+ /* Initialized data */
+
+ static doublereal zero = 0.;
+ static doublereal one = 1.;
+ static doublereal two = 2.;
+ static doublereal gam = 4096.;
+ static doublereal gamsq = 16777216.;
+ static doublereal rgamsq = 5.9604645e-8;
+
+ /* Format strings */
+ static char fmt_120[] = "";
+ static char fmt_150[] = "";
+ static char fmt_180[] = "";
+ static char fmt_210[] = "";
+
+ /* System generated locals */
+ doublereal d__1;
+
+ /* Local variables */
+ doublereal du, dp1, dp2, dq1, dq2, dh11, dh12, dh21, dh22;
+ integer igo;
+ doublereal dflag, dtemp;
+
+ /* Assigned format variables */
+ static char *igo_fmt;
+
+/* .. Scalar Arguments .. */
+/* .. */
+/* .. Array Arguments .. */
+/* .. */
+
+/* Purpose */
+/* ======= */
+
+/* CONSTRUCT THE MODIFIED GIVENS TRANSFORMATION MATRIX H WHICH ZEROS */
+/* THE SECOND COMPONENT OF THE 2-VECTOR (DSQRT(DD1)*DX1,DSQRT(DD2)* */
+/* DY2)**T. */
+/* WITH DPARAM(1)=DFLAG, H HAS ONE OF THE FOLLOWING FORMS.. */
+
+/* DFLAG=-1.D0 DFLAG=0.D0 DFLAG=1.D0 DFLAG=-2.D0 */
+
+/* (DH11 DH12) (1.D0 DH12) (DH11 1.D0) (1.D0 0.D0) */
+/* H=( ) ( ) ( ) ( ) */
+/* (DH21 DH22), (DH21 1.D0), (-1.D0 DH22), (0.D0 1.D0). */
+/* LOCATIONS 2-4 OF DPARAM CONTAIN DH11, DH21, DH12, AND DH22 */
+/* RESPECTIVELY. (VALUES OF 1.D0, -1.D0, OR 0.D0 IMPLIED BY THE */
+/* VALUE OF DPARAM(1) ARE NOT STORED IN DPARAM.) */
+
+/* THE VALUES OF GAMSQ AND RGAMSQ SET IN THE DATA STATEMENT MAY BE */
+/* INEXACT. THIS IS OK AS THEY ARE ONLY USED FOR TESTING THE SIZE */
+/* OF DD1 AND DD2. ALL ACTUAL SCALING OF DATA IS DONE USING GAM. */
+
+
+/* Arguments */
+/* ========= */
+
+/* DD1 (input/output) DOUBLE PRECISION */
+
+/* DD2 (input/output) DOUBLE PRECISION */
+
+/* DX1 (input/output) DOUBLE PRECISION */
+
+/* DY1 (input) DOUBLE PRECISION */
+
+/* DPARAM (input/output) DOUBLE PRECISION array, dimension 5 */
+/* DPARAM(1)=DFLAG */
+/* DPARAM(2)=DH11 */
+/* DPARAM(3)=DH21 */
+/* DPARAM(4)=DH12 */
+/* DPARAM(5)=DH22 */
+
+/* ===================================================================== */
+
+/* .. Local Scalars .. */
+/* .. */
+/* .. Intrinsic Functions .. */
+/* .. */
+/* .. Data statements .. */
+
+ /* Parameter adjustments */
+ --dparam;
+
+ /* Function Body */
+/* .. */
+ if (! (*dd1 < zero)) {
+ goto L10;
+ }
+/* GO ZERO-H-D-AND-DX1.. */
+ goto L60;
+L10:
+/* CASE-DD1-NONNEGATIVE */
+ dp2 = *dd2 * *dy1;
+ if (! (dp2 == zero)) {
+ goto L20;
+ }
+ dflag = -two;
+ goto L260;
+/* REGULAR-CASE.. */
+L20:
+ dp1 = *dd1 * *dx1;
+ dq2 = dp2 * *dy1;
+ dq1 = dp1 * *dx1;
+
+ if (! (abs(dq1) > abs(dq2))) {
+ goto L40;
+ }
+ dh21 = -(*dy1) / *dx1;
+ dh12 = dp2 / dp1;
+
+ du = one - dh12 * dh21;
+
+ if (! (du <= zero)) {
+ goto L30;
+ }
+/* GO ZERO-H-D-AND-DX1.. */
+ goto L60;
+L30:
+ dflag = zero;
+ *dd1 /= du;
+ *dd2 /= du;
+ *dx1 *= du;
+/* GO SCALE-CHECK.. */
+ goto L100;
+L40:
+ if (! (dq2 < zero)) {
+ goto L50;
+ }
+/* GO ZERO-H-D-AND-DX1.. */
+ goto L60;
+L50:
+ dflag = one;
+ dh11 = dp1 / dp2;
+ dh22 = *dx1 / *dy1;
+ du = one + dh11 * dh22;
+ dtemp = *dd2 / du;
+ *dd2 = *dd1 / du;
+ *dd1 = dtemp;
+ *dx1 = *dy1 * du;
+/* GO SCALE-CHECK */
+ goto L100;
+/* PROCEDURE..ZERO-H-D-AND-DX1.. */
+L60:
+ dflag = -one;
+ dh11 = zero;
+ dh12 = zero;
+ dh21 = zero;
+ dh22 = zero;
+
+ *dd1 = zero;
+ *dd2 = zero;
+ *dx1 = zero;
+/* RETURN.. */
+ goto L220;
+/* PROCEDURE..FIX-H.. */
+L70:
+ if (! (dflag >= zero)) {
+ goto L90;
+ }
+
+ if (! (dflag == zero)) {
+ goto L80;
+ }
+ dh11 = one;
+ dh22 = one;
+ dflag = -one;
+ goto L90;
+L80:
+ dh21 = -one;
+ dh12 = one;
+ dflag = -one;
+L90:
+ switch (igo) {
+ case 0: goto L120;
+ case 1: goto L150;
+ case 2: goto L180;
+ case 3: goto L210;
+ }
+/* PROCEDURE..SCALE-CHECK */
+L100:
+L110:
+ if (! (*dd1 <= rgamsq)) {
+ goto L130;
+ }
+ if (*dd1 == zero) {
+ goto L160;
+ }
+ igo = 0;
+ igo_fmt = fmt_120;
+/* FIX-H.. */
+ goto L70;
+L120:
+/* Computing 2nd power */
+ d__1 = gam;
+ *dd1 *= d__1 * d__1;
+ *dx1 /= gam;
+ dh11 /= gam;
+ dh12 /= gam;
+ goto L110;
+L130:
+L140:
+ if (! (*dd1 >= gamsq)) {
+ goto L160;
+ }
+ igo = 1;
+ igo_fmt = fmt_150;
+/* FIX-H.. */
+ goto L70;
+L150:
+/* Computing 2nd power */
+ d__1 = gam;
+ *dd1 /= d__1 * d__1;
+ *dx1 *= gam;
+ dh11 *= gam;
+ dh12 *= gam;
+ goto L140;
+L160:
+L170:
+ if (! (abs(*dd2) <= rgamsq)) {
+ goto L190;
+ }
+ if (*dd2 == zero) {
+ goto L220;
+ }
+ igo = 2;
+ igo_fmt = fmt_180;
+/* FIX-H.. */
+ goto L70;
+L180:
+/* Computing 2nd power */
+ d__1 = gam;
+ *dd2 *= d__1 * d__1;
+ dh21 /= gam;
+ dh22 /= gam;
+ goto L170;
+L190:
+L200:
+ if (! (abs(*dd2) >= gamsq)) {
+ goto L220;
+ }
+ igo = 3;
+ igo_fmt = fmt_210;
+/* FIX-H.. */
+ goto L70;
+L210:
+/* Computing 2nd power */
+ d__1 = gam;
+ *dd2 /= d__1 * d__1;
+ dh21 *= gam;
+ dh22 *= gam;
+ goto L200;
+L220:
+ if (dflag < 0.) {
+ goto L250;
+ } else if (dflag == 0) {
+ goto L230;
+ } else {
+ goto L240;
+ }
+L230:
+ dparam[3] = dh21;
+ dparam[4] = dh12;
+ goto L260;
+L240:
+ dparam[2] = dh11;
+ dparam[5] = dh22;
+ goto L260;
+L250:
+ dparam[2] = dh11;
+ dparam[3] = dh21;
+ dparam[4] = dh12;
+ dparam[5] = dh22;
+L260:
+ dparam[1] = dflag;
+ return 0;
+} /* drotmg_ */
+
diff --git a/blas/f2c/dsbmv.c b/blas/f2c/dsbmv.c
new file mode 100644
index 0000000..c6b4b21
--- /dev/null
+++ b/blas/f2c/dsbmv.c
@@ -0,0 +1,366 @@
+/* dsbmv.f -- translated by f2c (version 20100827).
+ You must link the resulting object file with libf2c:
+ on Microsoft Windows system, link with libf2c.lib;
+ on Linux or Unix systems, link with .../path/to/libf2c.a -lm
+ or, if you install libf2c.a in a standard place, with -lf2c -lm
+ -- in that order, at the end of the command line, as in
+ cc *.o -lf2c -lm
+ Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
+
+ http://www.netlib.org/f2c/libf2c.zip
+*/
+
+#include "datatypes.h"
+
+/* Subroutine */ int dsbmv_(char *uplo, integer *n, integer *k, doublereal *
+ alpha, doublereal *a, integer *lda, doublereal *x, integer *incx,
+ doublereal *beta, doublereal *y, integer *incy, ftnlen uplo_len)
+{
+ /* System generated locals */
+ integer a_dim1, a_offset, i__1, i__2, i__3, i__4;
+
+ /* Local variables */
+ integer i__, j, l, ix, iy, jx, jy, kx, ky, info;
+ doublereal temp1, temp2;
+ extern logical lsame_(char *, char *, ftnlen, ftnlen);
+ integer kplus1;
+ extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
+
+/* .. Scalar Arguments .. */
+/* .. */
+/* .. Array Arguments .. */
+/* .. */
+
+/* Purpose */
+/* ======= */
+
+/* DSBMV performs the matrix-vector operation */
+
+/* y := alpha*A*x + beta*y, */
+
+/* where alpha and beta are scalars, x and y are n element vectors and */
+/* A is an n by n symmetric band matrix, with k super-diagonals. */
+
+/* Arguments */
+/* ========== */
+
+/* UPLO - CHARACTER*1. */
+/* On entry, UPLO specifies whether the upper or lower */
+/* triangular part of the band matrix A is being supplied as */
+/* follows: */
+
+/* UPLO = 'U' or 'u' The upper triangular part of A is */
+/* being supplied. */
+
+/* UPLO = 'L' or 'l' The lower triangular part of A is */
+/* being supplied. */
+
+/* Unchanged on exit. */
+
+/* N - INTEGER. */
+/* On entry, N specifies the order of the matrix A. */
+/* N must be at least zero. */
+/* Unchanged on exit. */
+
+/* K - INTEGER. */
+/* On entry, K specifies the number of super-diagonals of the */
+/* matrix A. K must satisfy 0 .le. K. */
+/* Unchanged on exit. */
+
+/* ALPHA - DOUBLE PRECISION. */
+/* On entry, ALPHA specifies the scalar alpha. */
+/* Unchanged on exit. */
+
+/* A - DOUBLE PRECISION array of DIMENSION ( LDA, n ). */
+/* Before entry with UPLO = 'U' or 'u', the leading ( k + 1 ) */
+/* by n part of the array A must contain the upper triangular */
+/* band part of the symmetric matrix, supplied column by */
+/* column, with the leading diagonal of the matrix in row */
+/* ( k + 1 ) of the array, the first super-diagonal starting at */
+/* position 2 in row k, and so on. The top left k by k triangle */
+/* of the array A is not referenced. */
+/* The following program segment will transfer the upper */
+/* triangular part of a symmetric band matrix from conventional */
+/* full matrix storage to band storage: */
+
+/* DO 20, J = 1, N */
+/* M = K + 1 - J */
+/* DO 10, I = MAX( 1, J - K ), J */
+/* A( M + I, J ) = matrix( I, J ) */
+/* 10 CONTINUE */
+/* 20 CONTINUE */
+
+/* Before entry with UPLO = 'L' or 'l', the leading ( k + 1 ) */
+/* by n part of the array A must contain the lower triangular */
+/* band part of the symmetric matrix, supplied column by */
+/* column, with the leading diagonal of the matrix in row 1 of */
+/* the array, the first sub-diagonal starting at position 1 in */
+/* row 2, and so on. The bottom right k by k triangle of the */
+/* array A is not referenced. */
+/* The following program segment will transfer the lower */
+/* triangular part of a symmetric band matrix from conventional */
+/* full matrix storage to band storage: */
+
+/* DO 20, J = 1, N */
+/* M = 1 - J */
+/* DO 10, I = J, MIN( N, J + K ) */
+/* A( M + I, J ) = matrix( I, J ) */
+/* 10 CONTINUE */
+/* 20 CONTINUE */
+
+/* Unchanged on exit. */
+
+/* LDA - INTEGER. */
+/* On entry, LDA specifies the first dimension of A as declared */
+/* in the calling (sub) program. LDA must be at least */
+/* ( k + 1 ). */
+/* Unchanged on exit. */
+
+/* X - DOUBLE PRECISION array of DIMENSION at least */
+/* ( 1 + ( n - 1 )*abs( INCX ) ). */
+/* Before entry, the incremented array X must contain the */
+/* vector x. */
+/* Unchanged on exit. */
+
+/* INCX - INTEGER. */
+/* On entry, INCX specifies the increment for the elements of */
+/* X. INCX must not be zero. */
+/* Unchanged on exit. */
+
+/* BETA - DOUBLE PRECISION. */
+/* On entry, BETA specifies the scalar beta. */
+/* Unchanged on exit. */
+
+/* Y - DOUBLE PRECISION array of DIMENSION at least */
+/* ( 1 + ( n - 1 )*abs( INCY ) ). */
+/* Before entry, the incremented array Y must contain the */
+/* vector y. On exit, Y is overwritten by the updated vector y. */
+
+/* INCY - INTEGER. */
+/* On entry, INCY specifies the increment for the elements of */
+/* Y. INCY must not be zero. */
+/* Unchanged on exit. */
+
+
+/* Level 2 Blas routine. */
+
+/* -- Written on 22-October-1986. */
+/* Jack Dongarra, Argonne National Lab. */
+/* Jeremy Du Croz, Nag Central Office. */
+/* Sven Hammarling, Nag Central Office. */
+/* Richard Hanson, Sandia National Labs. */
+
+/* ===================================================================== */
+
+/* .. Parameters .. */
+/* .. */
+/* .. Local Scalars .. */
+/* .. */
+/* .. External Functions .. */
+/* .. */
+/* .. External Subroutines .. */
+/* .. */
+/* .. Intrinsic Functions .. */
+/* .. */
+
+/* Test the input parameters. */
+
+ /* Parameter adjustments */
+ a_dim1 = *lda;
+ a_offset = 1 + a_dim1;
+ a -= a_offset;
+ --x;
+ --y;
+
+ /* Function Body */
+ info = 0;
+ if (! lsame_(uplo, "U", (ftnlen)1, (ftnlen)1) && ! lsame_(uplo, "L", (
+ ftnlen)1, (ftnlen)1)) {
+ info = 1;
+ } else if (*n < 0) {
+ info = 2;
+ } else if (*k < 0) {
+ info = 3;
+ } else if (*lda < *k + 1) {
+ info = 6;
+ } else if (*incx == 0) {
+ info = 8;
+ } else if (*incy == 0) {
+ info = 11;
+ }
+ if (info != 0) {
+ xerbla_("DSBMV ", &info, (ftnlen)6);
+ return 0;
+ }
+
+/* Quick return if possible. */
+
+ if (*n == 0 || (*alpha == 0. && *beta == 1.)) {
+ return 0;
+ }
+
+/* Set up the start points in X and Y. */
+
+ if (*incx > 0) {
+ kx = 1;
+ } else {
+ kx = 1 - (*n - 1) * *incx;
+ }
+ if (*incy > 0) {
+ ky = 1;
+ } else {
+ ky = 1 - (*n - 1) * *incy;
+ }
+
+/* Start the operations. In this version the elements of the array A */
+/* are accessed sequentially with one pass through A. */
+
+/* First form y := beta*y. */
+
+ if (*beta != 1.) {
+ if (*incy == 1) {
+ if (*beta == 0.) {
+ i__1 = *n;
+ for (i__ = 1; i__ <= i__1; ++i__) {
+ y[i__] = 0.;
+/* L10: */
+ }
+ } else {
+ i__1 = *n;
+ for (i__ = 1; i__ <= i__1; ++i__) {
+ y[i__] = *beta * y[i__];
+/* L20: */
+ }
+ }
+ } else {
+ iy = ky;
+ if (*beta == 0.) {
+ i__1 = *n;
+ for (i__ = 1; i__ <= i__1; ++i__) {
+ y[iy] = 0.;
+ iy += *incy;
+/* L30: */
+ }
+ } else {
+ i__1 = *n;
+ for (i__ = 1; i__ <= i__1; ++i__) {
+ y[iy] = *beta * y[iy];
+ iy += *incy;
+/* L40: */
+ }
+ }
+ }
+ }
+ if (*alpha == 0.) {
+ return 0;
+ }
+ if (lsame_(uplo, "U", (ftnlen)1, (ftnlen)1)) {
+
+/* Form y when upper triangle of A is stored. */
+
+ kplus1 = *k + 1;
+ if (*incx == 1 && *incy == 1) {
+ i__1 = *n;
+ for (j = 1; j <= i__1; ++j) {
+ temp1 = *alpha * x[j];
+ temp2 = 0.;
+ l = kplus1 - j;
+/* Computing MAX */
+ i__2 = 1, i__3 = j - *k;
+ i__4 = j - 1;
+ for (i__ = max(i__2,i__3); i__ <= i__4; ++i__) {
+ y[i__] += temp1 * a[l + i__ + j * a_dim1];
+ temp2 += a[l + i__ + j * a_dim1] * x[i__];
+/* L50: */
+ }
+ y[j] = y[j] + temp1 * a[kplus1 + j * a_dim1] + *alpha * temp2;
+/* L60: */
+ }
+ } else {
+ jx = kx;
+ jy = ky;
+ i__1 = *n;
+ for (j = 1; j <= i__1; ++j) {
+ temp1 = *alpha * x[jx];
+ temp2 = 0.;
+ ix = kx;
+ iy = ky;
+ l = kplus1 - j;
+/* Computing MAX */
+ i__4 = 1, i__2 = j - *k;
+ i__3 = j - 1;
+ for (i__ = max(i__4,i__2); i__ <= i__3; ++i__) {
+ y[iy] += temp1 * a[l + i__ + j * a_dim1];
+ temp2 += a[l + i__ + j * a_dim1] * x[ix];
+ ix += *incx;
+ iy += *incy;
+/* L70: */
+ }
+ y[jy] = y[jy] + temp1 * a[kplus1 + j * a_dim1] + *alpha *
+ temp2;
+ jx += *incx;
+ jy += *incy;
+ if (j > *k) {
+ kx += *incx;
+ ky += *incy;
+ }
+/* L80: */
+ }
+ }
+ } else {
+
+/* Form y when lower triangle of A is stored. */
+
+ if (*incx == 1 && *incy == 1) {
+ i__1 = *n;
+ for (j = 1; j <= i__1; ++j) {
+ temp1 = *alpha * x[j];
+ temp2 = 0.;
+ y[j] += temp1 * a[j * a_dim1 + 1];
+ l = 1 - j;
+/* Computing MIN */
+ i__4 = *n, i__2 = j + *k;
+ i__3 = min(i__4,i__2);
+ for (i__ = j + 1; i__ <= i__3; ++i__) {
+ y[i__] += temp1 * a[l + i__ + j * a_dim1];
+ temp2 += a[l + i__ + j * a_dim1] * x[i__];
+/* L90: */
+ }
+ y[j] += *alpha * temp2;
+/* L100: */
+ }
+ } else {
+ jx = kx;
+ jy = ky;
+ i__1 = *n;
+ for (j = 1; j <= i__1; ++j) {
+ temp1 = *alpha * x[jx];
+ temp2 = 0.;
+ y[jy] += temp1 * a[j * a_dim1 + 1];
+ l = 1 - j;
+ ix = jx;
+ iy = jy;
+/* Computing MIN */
+ i__4 = *n, i__2 = j + *k;
+ i__3 = min(i__4,i__2);
+ for (i__ = j + 1; i__ <= i__3; ++i__) {
+ ix += *incx;
+ iy += *incy;
+ y[iy] += temp1 * a[l + i__ + j * a_dim1];
+ temp2 += a[l + i__ + j * a_dim1] * x[ix];
+/* L110: */
+ }
+ y[jy] += *alpha * temp2;
+ jx += *incx;
+ jy += *incy;
+/* L120: */
+ }
+ }
+ }
+
+ return 0;
+
+/* End of DSBMV . */
+
+} /* dsbmv_ */
+
diff --git a/blas/f2c/dspmv.c b/blas/f2c/dspmv.c
new file mode 100644
index 0000000..0b4e92d
--- /dev/null
+++ b/blas/f2c/dspmv.c
@@ -0,0 +1,316 @@
+/* dspmv.f -- translated by f2c (version 20100827).
+ You must link the resulting object file with libf2c:
+ on Microsoft Windows system, link with libf2c.lib;
+ on Linux or Unix systems, link with .../path/to/libf2c.a -lm
+ or, if you install libf2c.a in a standard place, with -lf2c -lm
+ -- in that order, at the end of the command line, as in
+ cc *.o -lf2c -lm
+ Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
+
+ http://www.netlib.org/f2c/libf2c.zip
+*/
+
+#include "datatypes.h"
+
+/* Subroutine */ int dspmv_(char *uplo, integer *n, doublereal *alpha,
+ doublereal *ap, doublereal *x, integer *incx, doublereal *beta,
+ doublereal *y, integer *incy, ftnlen uplo_len)
+{
+ /* System generated locals */
+ integer i__1, i__2;
+
+ /* Local variables */
+ integer i__, j, k, kk, ix, iy, jx, jy, kx, ky, info;
+ doublereal temp1, temp2;
+ extern logical lsame_(char *, char *, ftnlen, ftnlen);
+ extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
+
+/* .. Scalar Arguments .. */
+/* .. */
+/* .. Array Arguments .. */
+/* .. */
+
+/* Purpose */
+/* ======= */
+
+/* DSPMV performs the matrix-vector operation */
+
+/* y := alpha*A*x + beta*y, */
+
+/* where alpha and beta are scalars, x and y are n element vectors and */
+/* A is an n by n symmetric matrix, supplied in packed form. */
+
+/* Arguments */
+/* ========== */
+
+/* UPLO - CHARACTER*1. */
+/* On entry, UPLO specifies whether the upper or lower */
+/* triangular part of the matrix A is supplied in the packed */
+/* array AP as follows: */
+
+/* UPLO = 'U' or 'u' The upper triangular part of A is */
+/* supplied in AP. */
+
+/* UPLO = 'L' or 'l' The lower triangular part of A is */
+/* supplied in AP. */
+
+/* Unchanged on exit. */
+
+/* N - INTEGER. */
+/* On entry, N specifies the order of the matrix A. */
+/* N must be at least zero. */
+/* Unchanged on exit. */
+
+/* ALPHA - DOUBLE PRECISION. */
+/* On entry, ALPHA specifies the scalar alpha. */
+/* Unchanged on exit. */
+
+/* AP - DOUBLE PRECISION array of DIMENSION at least */
+/* ( ( n*( n + 1 ) )/2 ). */
+/* Before entry with UPLO = 'U' or 'u', the array AP must */
+/* contain the upper triangular part of the symmetric matrix */
+/* packed sequentially, column by column, so that AP( 1 ) */
+/* contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 ) */
+/* and a( 2, 2 ) respectively, and so on. */
+/* Before entry with UPLO = 'L' or 'l', the array AP must */
+/* contain the lower triangular part of the symmetric matrix */
+/* packed sequentially, column by column, so that AP( 1 ) */
+/* contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 ) */
+/* and a( 3, 1 ) respectively, and so on. */
+/* Unchanged on exit. */
+
+/* X - DOUBLE PRECISION array of dimension at least */
+/* ( 1 + ( n - 1 )*abs( INCX ) ). */
+/* Before entry, the incremented array X must contain the n */
+/* element vector x. */
+/* Unchanged on exit. */
+
+/* INCX - INTEGER. */
+/* On entry, INCX specifies the increment for the elements of */
+/* X. INCX must not be zero. */
+/* Unchanged on exit. */
+
+/* BETA - DOUBLE PRECISION. */
+/* On entry, BETA specifies the scalar beta. When BETA is */
+/* supplied as zero then Y need not be set on input. */
+/* Unchanged on exit. */
+
+/* Y - DOUBLE PRECISION array of dimension at least */
+/* ( 1 + ( n - 1 )*abs( INCY ) ). */
+/* Before entry, the incremented array Y must contain the n */
+/* element vector y. On exit, Y is overwritten by the updated */
+/* vector y. */
+
+/* INCY - INTEGER. */
+/* On entry, INCY specifies the increment for the elements of */
+/* Y. INCY must not be zero. */
+/* Unchanged on exit. */
+
+/* Further Details */
+/* =============== */
+
+/* Level 2 Blas routine. */
+
+/* -- Written on 22-October-1986. */
+/* Jack Dongarra, Argonne National Lab. */
+/* Jeremy Du Croz, Nag Central Office. */
+/* Sven Hammarling, Nag Central Office. */
+/* Richard Hanson, Sandia National Labs. */
+
+/* ===================================================================== */
+
+/* .. Parameters .. */
+/* .. */
+/* .. Local Scalars .. */
+/* .. */
+/* .. External Functions .. */
+/* .. */
+/* .. External Subroutines .. */
+/* .. */
+
+/* Test the input parameters. */
+
+ /* Parameter adjustments */
+ --y;
+ --x;
+ --ap;
+
+ /* Function Body */
+ info = 0;
+ if (! lsame_(uplo, "U", (ftnlen)1, (ftnlen)1) && ! lsame_(uplo, "L", (
+ ftnlen)1, (ftnlen)1)) {
+ info = 1;
+ } else if (*n < 0) {
+ info = 2;
+ } else if (*incx == 0) {
+ info = 6;
+ } else if (*incy == 0) {
+ info = 9;
+ }
+ if (info != 0) {
+ xerbla_("DSPMV ", &info, (ftnlen)6);
+ return 0;
+ }
+
+/* Quick return if possible. */
+
+ if (*n == 0 || (*alpha == 0. && *beta == 1.)) {
+ return 0;
+ }
+
+/* Set up the start points in X and Y. */
+
+ if (*incx > 0) {
+ kx = 1;
+ } else {
+ kx = 1 - (*n - 1) * *incx;
+ }
+ if (*incy > 0) {
+ ky = 1;
+ } else {
+ ky = 1 - (*n - 1) * *incy;
+ }
+
+/* Start the operations. In this version the elements of the array AP */
+/* are accessed sequentially with one pass through AP. */
+
+/* First form y := beta*y. */
+
+ if (*beta != 1.) {
+ if (*incy == 1) {
+ if (*beta == 0.) {
+ i__1 = *n;
+ for (i__ = 1; i__ <= i__1; ++i__) {
+ y[i__] = 0.;
+/* L10: */
+ }
+ } else {
+ i__1 = *n;
+ for (i__ = 1; i__ <= i__1; ++i__) {
+ y[i__] = *beta * y[i__];
+/* L20: */
+ }
+ }
+ } else {
+ iy = ky;
+ if (*beta == 0.) {
+ i__1 = *n;
+ for (i__ = 1; i__ <= i__1; ++i__) {
+ y[iy] = 0.;
+ iy += *incy;
+/* L30: */
+ }
+ } else {
+ i__1 = *n;
+ for (i__ = 1; i__ <= i__1; ++i__) {
+ y[iy] = *beta * y[iy];
+ iy += *incy;
+/* L40: */
+ }
+ }
+ }
+ }
+ if (*alpha == 0.) {
+ return 0;
+ }
+ kk = 1;
+ if (lsame_(uplo, "U", (ftnlen)1, (ftnlen)1)) {
+
+/* Form y when AP contains the upper triangle. */
+
+ if (*incx == 1 && *incy == 1) {
+ i__1 = *n;
+ for (j = 1; j <= i__1; ++j) {
+ temp1 = *alpha * x[j];
+ temp2 = 0.;
+ k = kk;
+ i__2 = j - 1;
+ for (i__ = 1; i__ <= i__2; ++i__) {
+ y[i__] += temp1 * ap[k];
+ temp2 += ap[k] * x[i__];
+ ++k;
+/* L50: */
+ }
+ y[j] = y[j] + temp1 * ap[kk + j - 1] + *alpha * temp2;
+ kk += j;
+/* L60: */
+ }
+ } else {
+ jx = kx;
+ jy = ky;
+ i__1 = *n;
+ for (j = 1; j <= i__1; ++j) {
+ temp1 = *alpha * x[jx];
+ temp2 = 0.;
+ ix = kx;
+ iy = ky;
+ i__2 = kk + j - 2;
+ for (k = kk; k <= i__2; ++k) {
+ y[iy] += temp1 * ap[k];
+ temp2 += ap[k] * x[ix];
+ ix += *incx;
+ iy += *incy;
+/* L70: */
+ }
+ y[jy] = y[jy] + temp1 * ap[kk + j - 1] + *alpha * temp2;
+ jx += *incx;
+ jy += *incy;
+ kk += j;
+/* L80: */
+ }
+ }
+ } else {
+
+/* Form y when AP contains the lower triangle. */
+
+ if (*incx == 1 && *incy == 1) {
+ i__1 = *n;
+ for (j = 1; j <= i__1; ++j) {
+ temp1 = *alpha * x[j];
+ temp2 = 0.;
+ y[j] += temp1 * ap[kk];
+ k = kk + 1;
+ i__2 = *n;
+ for (i__ = j + 1; i__ <= i__2; ++i__) {
+ y[i__] += temp1 * ap[k];
+ temp2 += ap[k] * x[i__];
+ ++k;
+/* L90: */
+ }
+ y[j] += *alpha * temp2;
+ kk += *n - j + 1;
+/* L100: */
+ }
+ } else {
+ jx = kx;
+ jy = ky;
+ i__1 = *n;
+ for (j = 1; j <= i__1; ++j) {
+ temp1 = *alpha * x[jx];
+ temp2 = 0.;
+ y[jy] += temp1 * ap[kk];
+ ix = jx;
+ iy = jy;
+ i__2 = kk + *n - j;
+ for (k = kk + 1; k <= i__2; ++k) {
+ ix += *incx;
+ iy += *incy;
+ y[iy] += temp1 * ap[k];
+ temp2 += ap[k] * x[ix];
+/* L110: */
+ }
+ y[jy] += *alpha * temp2;
+ jx += *incx;
+ jy += *incy;
+ kk += *n - j + 1;
+/* L120: */
+ }
+ }
+ }
+
+ return 0;
+
+/* End of DSPMV . */
+
+} /* dspmv_ */
+
diff --git a/blas/f2c/dtbmv.c b/blas/f2c/dtbmv.c
new file mode 100644
index 0000000..aa67d19
--- /dev/null
+++ b/blas/f2c/dtbmv.c
@@ -0,0 +1,428 @@
+/* dtbmv.f -- translated by f2c (version 20100827).
+ You must link the resulting object file with libf2c:
+ on Microsoft Windows system, link with libf2c.lib;
+ on Linux or Unix systems, link with .../path/to/libf2c.a -lm
+ or, if you install libf2c.a in a standard place, with -lf2c -lm
+ -- in that order, at the end of the command line, as in
+ cc *.o -lf2c -lm
+ Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
+
+ http://www.netlib.org/f2c/libf2c.zip
+*/
+
+#include "datatypes.h"
+
+/* Subroutine */ int dtbmv_(char *uplo, char *trans, char *diag, integer *n,
+ integer *k, doublereal *a, integer *lda, doublereal *x, integer *incx,
+ ftnlen uplo_len, ftnlen trans_len, ftnlen diag_len)
+{
+ /* System generated locals */
+ integer a_dim1, a_offset, i__1, i__2, i__3, i__4;
+
+ /* Local variables */
+ integer i__, j, l, ix, jx, kx, info;
+ doublereal temp;
+ extern logical lsame_(char *, char *, ftnlen, ftnlen);
+ integer kplus1;
+ extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
+ logical nounit;
+
+/* .. Scalar Arguments .. */
+/* .. */
+/* .. Array Arguments .. */
+/* .. */
+
+/* Purpose */
+/* ======= */
+
+/* DTBMV performs one of the matrix-vector operations */
+
+/* x := A*x, or x := A'*x, */
+
+/* where x is an n element vector and A is an n by n unit, or non-unit, */
+/* upper or lower triangular band matrix, with ( k + 1 ) diagonals. */
+
+/* Arguments */
+/* ========== */
+
+/* UPLO - CHARACTER*1. */
+/* On entry, UPLO specifies whether the matrix is an upper or */
+/* lower triangular matrix as follows: */
+
+/* UPLO = 'U' or 'u' A is an upper triangular matrix. */
+
+/* UPLO = 'L' or 'l' A is a lower triangular matrix. */
+
+/* Unchanged on exit. */
+
+/* TRANS - CHARACTER*1. */
+/* On entry, TRANS specifies the operation to be performed as */
+/* follows: */
+
+/* TRANS = 'N' or 'n' x := A*x. */
+
+/* TRANS = 'T' or 't' x := A'*x. */
+
+/* TRANS = 'C' or 'c' x := A'*x. */
+
+/* Unchanged on exit. */
+
+/* DIAG - CHARACTER*1. */
+/* On entry, DIAG specifies whether or not A is unit */
+/* triangular as follows: */
+
+/* DIAG = 'U' or 'u' A is assumed to be unit triangular. */
+
+/* DIAG = 'N' or 'n' A is not assumed to be unit */
+/* triangular. */
+
+/* Unchanged on exit. */
+
+/* N - INTEGER. */
+/* On entry, N specifies the order of the matrix A. */
+/* N must be at least zero. */
+/* Unchanged on exit. */
+
+/* K - INTEGER. */
+/* On entry with UPLO = 'U' or 'u', K specifies the number of */
+/* super-diagonals of the matrix A. */
+/* On entry with UPLO = 'L' or 'l', K specifies the number of */
+/* sub-diagonals of the matrix A. */
+/* K must satisfy 0 .le. K. */
+/* Unchanged on exit. */
+
+/* A - DOUBLE PRECISION array of DIMENSION ( LDA, n ). */
+/* Before entry with UPLO = 'U' or 'u', the leading ( k + 1 ) */
+/* by n part of the array A must contain the upper triangular */
+/* band part of the matrix of coefficients, supplied column by */
+/* column, with the leading diagonal of the matrix in row */
+/* ( k + 1 ) of the array, the first super-diagonal starting at */
+/* position 2 in row k, and so on. The top left k by k triangle */
+/* of the array A is not referenced. */
+/* The following program segment will transfer an upper */
+/* triangular band matrix from conventional full matrix storage */
+/* to band storage: */
+
+/* DO 20, J = 1, N */
+/* M = K + 1 - J */
+/* DO 10, I = MAX( 1, J - K ), J */
+/* A( M + I, J ) = matrix( I, J ) */
+/* 10 CONTINUE */
+/* 20 CONTINUE */
+
+/* Before entry with UPLO = 'L' or 'l', the leading ( k + 1 ) */
+/* by n part of the array A must contain the lower triangular */
+/* band part of the matrix of coefficients, supplied column by */
+/* column, with the leading diagonal of the matrix in row 1 of */
+/* the array, the first sub-diagonal starting at position 1 in */
+/* row 2, and so on. The bottom right k by k triangle of the */
+/* array A is not referenced. */
+/* The following program segment will transfer a lower */
+/* triangular band matrix from conventional full matrix storage */
+/* to band storage: */
+
+/* DO 20, J = 1, N */
+/* M = 1 - J */
+/* DO 10, I = J, MIN( N, J + K ) */
+/* A( M + I, J ) = matrix( I, J ) */
+/* 10 CONTINUE */
+/* 20 CONTINUE */
+
+/* Note that when DIAG = 'U' or 'u' the elements of the array A */
+/* corresponding to the diagonal elements of the matrix are not */
+/* referenced, but are assumed to be unity. */
+/* Unchanged on exit. */
+
+/* LDA - INTEGER. */
+/* On entry, LDA specifies the first dimension of A as declared */
+/* in the calling (sub) program. LDA must be at least */
+/* ( k + 1 ). */
+/* Unchanged on exit. */
+
+/* X - DOUBLE PRECISION array of dimension at least */
+/* ( 1 + ( n - 1 )*abs( INCX ) ). */
+/* Before entry, the incremented array X must contain the n */
+/* element vector x. On exit, X is overwritten with the */
+/* transformed vector x. */
+
+/* INCX - INTEGER. */
+/* On entry, INCX specifies the increment for the elements of */
+/* X. INCX must not be zero. */
+/* Unchanged on exit. */
+
+/* Further Details */
+/* =============== */
+
+/* Level 2 Blas routine. */
+
+/* -- Written on 22-October-1986. */
+/* Jack Dongarra, Argonne National Lab. */
+/* Jeremy Du Croz, Nag Central Office. */
+/* Sven Hammarling, Nag Central Office. */
+/* Richard Hanson, Sandia National Labs. */
+
+/* ===================================================================== */
+
+/* .. Parameters .. */
+/* .. */
+/* .. Local Scalars .. */
+/* .. */
+/* .. External Functions .. */
+/* .. */
+/* .. External Subroutines .. */
+/* .. */
+/* .. Intrinsic Functions .. */
+/* .. */
+
+/* Test the input parameters. */
+
+ /* Parameter adjustments */
+ a_dim1 = *lda;
+ a_offset = 1 + a_dim1;
+ a -= a_offset;
+ --x;
+
+ /* Function Body */
+ info = 0;
+ if (! lsame_(uplo, "U", (ftnlen)1, (ftnlen)1) && ! lsame_(uplo, "L", (
+ ftnlen)1, (ftnlen)1)) {
+ info = 1;
+ } else if (! lsame_(trans, "N", (ftnlen)1, (ftnlen)1) && ! lsame_(trans,
+ "T", (ftnlen)1, (ftnlen)1) && ! lsame_(trans, "C", (ftnlen)1, (
+ ftnlen)1)) {
+ info = 2;
+ } else if (! lsame_(diag, "U", (ftnlen)1, (ftnlen)1) && ! lsame_(diag,
+ "N", (ftnlen)1, (ftnlen)1)) {
+ info = 3;
+ } else if (*n < 0) {
+ info = 4;
+ } else if (*k < 0) {
+ info = 5;
+ } else if (*lda < *k + 1) {
+ info = 7;
+ } else if (*incx == 0) {
+ info = 9;
+ }
+ if (info != 0) {
+ xerbla_("DTBMV ", &info, (ftnlen)6);
+ return 0;
+ }
+
+/* Quick return if possible. */
+
+ if (*n == 0) {
+ return 0;
+ }
+
+ nounit = lsame_(diag, "N", (ftnlen)1, (ftnlen)1);
+
+/* Set up the start point in X if the increment is not unity. This */
+/* will be ( N - 1 )*INCX too small for descending loops. */
+
+ if (*incx <= 0) {
+ kx = 1 - (*n - 1) * *incx;
+ } else if (*incx != 1) {
+ kx = 1;
+ }
+
+/* Start the operations. In this version the elements of A are */
+/* accessed sequentially with one pass through A. */
+
+ if (lsame_(trans, "N", (ftnlen)1, (ftnlen)1)) {
+
+/* Form x := A*x. */
+
+ if (lsame_(uplo, "U", (ftnlen)1, (ftnlen)1)) {
+ kplus1 = *k + 1;
+ if (*incx == 1) {
+ i__1 = *n;
+ for (j = 1; j <= i__1; ++j) {
+ if (x[j] != 0.) {
+ temp = x[j];
+ l = kplus1 - j;
+/* Computing MAX */
+ i__2 = 1, i__3 = j - *k;
+ i__4 = j - 1;
+ for (i__ = max(i__2,i__3); i__ <= i__4; ++i__) {
+ x[i__] += temp * a[l + i__ + j * a_dim1];
+/* L10: */
+ }
+ if (nounit) {
+ x[j] *= a[kplus1 + j * a_dim1];
+ }
+ }
+/* L20: */
+ }
+ } else {
+ jx = kx;
+ i__1 = *n;
+ for (j = 1; j <= i__1; ++j) {
+ if (x[jx] != 0.) {
+ temp = x[jx];
+ ix = kx;
+ l = kplus1 - j;
+/* Computing MAX */
+ i__4 = 1, i__2 = j - *k;
+ i__3 = j - 1;
+ for (i__ = max(i__4,i__2); i__ <= i__3; ++i__) {
+ x[ix] += temp * a[l + i__ + j * a_dim1];
+ ix += *incx;
+/* L30: */
+ }
+ if (nounit) {
+ x[jx] *= a[kplus1 + j * a_dim1];
+ }
+ }
+ jx += *incx;
+ if (j > *k) {
+ kx += *incx;
+ }
+/* L40: */
+ }
+ }
+ } else {
+ if (*incx == 1) {
+ for (j = *n; j >= 1; --j) {
+ if (x[j] != 0.) {
+ temp = x[j];
+ l = 1 - j;
+/* Computing MIN */
+ i__1 = *n, i__3 = j + *k;
+ i__4 = j + 1;
+ for (i__ = min(i__1,i__3); i__ >= i__4; --i__) {
+ x[i__] += temp * a[l + i__ + j * a_dim1];
+/* L50: */
+ }
+ if (nounit) {
+ x[j] *= a[j * a_dim1 + 1];
+ }
+ }
+/* L60: */
+ }
+ } else {
+ kx += (*n - 1) * *incx;
+ jx = kx;
+ for (j = *n; j >= 1; --j) {
+ if (x[jx] != 0.) {
+ temp = x[jx];
+ ix = kx;
+ l = 1 - j;
+/* Computing MIN */
+ i__4 = *n, i__1 = j + *k;
+ i__3 = j + 1;
+ for (i__ = min(i__4,i__1); i__ >= i__3; --i__) {
+ x[ix] += temp * a[l + i__ + j * a_dim1];
+ ix -= *incx;
+/* L70: */
+ }
+ if (nounit) {
+ x[jx] *= a[j * a_dim1 + 1];
+ }
+ }
+ jx -= *incx;
+ if (*n - j >= *k) {
+ kx -= *incx;
+ }
+/* L80: */
+ }
+ }
+ }
+ } else {
+
+/* Form x := A'*x. */
+
+ if (lsame_(uplo, "U", (ftnlen)1, (ftnlen)1)) {
+ kplus1 = *k + 1;
+ if (*incx == 1) {
+ for (j = *n; j >= 1; --j) {
+ temp = x[j];
+ l = kplus1 - j;
+ if (nounit) {
+ temp *= a[kplus1 + j * a_dim1];
+ }
+/* Computing MAX */
+ i__4 = 1, i__1 = j - *k;
+ i__3 = max(i__4,i__1);
+ for (i__ = j - 1; i__ >= i__3; --i__) {
+ temp += a[l + i__ + j * a_dim1] * x[i__];
+/* L90: */
+ }
+ x[j] = temp;
+/* L100: */
+ }
+ } else {
+ kx += (*n - 1) * *incx;
+ jx = kx;
+ for (j = *n; j >= 1; --j) {
+ temp = x[jx];
+ kx -= *incx;
+ ix = kx;
+ l = kplus1 - j;
+ if (nounit) {
+ temp *= a[kplus1 + j * a_dim1];
+ }
+/* Computing MAX */
+ i__4 = 1, i__1 = j - *k;
+ i__3 = max(i__4,i__1);
+ for (i__ = j - 1; i__ >= i__3; --i__) {
+ temp += a[l + i__ + j * a_dim1] * x[ix];
+ ix -= *incx;
+/* L110: */
+ }
+ x[jx] = temp;
+ jx -= *incx;
+/* L120: */
+ }
+ }
+ } else {
+ if (*incx == 1) {
+ i__3 = *n;
+ for (j = 1; j <= i__3; ++j) {
+ temp = x[j];
+ l = 1 - j;
+ if (nounit) {
+ temp *= a[j * a_dim1 + 1];
+ }
+/* Computing MIN */
+ i__1 = *n, i__2 = j + *k;
+ i__4 = min(i__1,i__2);
+ for (i__ = j + 1; i__ <= i__4; ++i__) {
+ temp += a[l + i__ + j * a_dim1] * x[i__];
+/* L130: */
+ }
+ x[j] = temp;
+/* L140: */
+ }
+ } else {
+ jx = kx;
+ i__3 = *n;
+ for (j = 1; j <= i__3; ++j) {
+ temp = x[jx];
+ kx += *incx;
+ ix = kx;
+ l = 1 - j;
+ if (nounit) {
+ temp *= a[j * a_dim1 + 1];
+ }
+/* Computing MIN */
+ i__1 = *n, i__2 = j + *k;
+ i__4 = min(i__1,i__2);
+ for (i__ = j + 1; i__ <= i__4; ++i__) {
+ temp += a[l + i__ + j * a_dim1] * x[ix];
+ ix += *incx;
+/* L150: */
+ }
+ x[jx] = temp;
+ jx += *incx;
+/* L160: */
+ }
+ }
+ }
+ }
+
+ return 0;
+
+/* End of DTBMV . */
+
+} /* dtbmv_ */
+
diff --git a/blas/f2c/lsame.c b/blas/f2c/lsame.c
new file mode 100644
index 0000000..46324d9
--- /dev/null
+++ b/blas/f2c/lsame.c
@@ -0,0 +1,117 @@
+/* lsame.f -- translated by f2c (version 20100827).
+ You must link the resulting object file with libf2c:
+ on Microsoft Windows system, link with libf2c.lib;
+ on Linux or Unix systems, link with .../path/to/libf2c.a -lm
+ or, if you install libf2c.a in a standard place, with -lf2c -lm
+ -- in that order, at the end of the command line, as in
+ cc *.o -lf2c -lm
+ Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
+
+ http://www.netlib.org/f2c/libf2c.zip
+*/
+
+#include "datatypes.h"
+
+logical lsame_(char *ca, char *cb, ftnlen ca_len, ftnlen cb_len)
+{
+ /* System generated locals */
+ logical ret_val;
+
+ /* Local variables */
+ integer inta, intb, zcode;
+
+
+/* -- LAPACK auxiliary routine (version 3.1) -- */
+/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
+/* November 2006 */
+
+/* .. Scalar Arguments .. */
+/* .. */
+
+/* Purpose */
+/* ======= */
+
+/* LSAME returns .TRUE. if CA is the same letter as CB regardless of */
+/* case. */
+
+/* Arguments */
+/* ========= */
+
+/* CA (input) CHARACTER*1 */
+
+/* CB (input) CHARACTER*1 */
+/* CA and CB specify the single characters to be compared. */
+
+/* ===================================================================== */
+
+/* .. Intrinsic Functions .. */
+/* .. */
+/* .. Local Scalars .. */
+/* .. */
+
+/* Test if the characters are equal */
+
+ ret_val = *(unsigned char *)ca == *(unsigned char *)cb;
+ if (ret_val) {
+ return ret_val;
+ }
+
+/* Now test for equivalence if both characters are alphabetic. */
+
+ zcode = 'Z';
+
+/* Use 'Z' rather than 'A' so that ASCII can be detected on Prime */
+/* machines, on which ICHAR returns a value with bit 8 set. */
+/* ICHAR('A') on Prime machines returns 193 which is the same as */
+/* ICHAR('A') on an EBCDIC machine. */
+
+ inta = *(unsigned char *)ca;
+ intb = *(unsigned char *)cb;
+
+ if (zcode == 90 || zcode == 122) {
+
+/* ASCII is assumed - ZCODE is the ASCII code of either lower or */
+/* upper case 'Z'. */
+
+ if (inta >= 97 && inta <= 122) {
+ inta += -32;
+ }
+ if (intb >= 97 && intb <= 122) {
+ intb += -32;
+ }
+
+ } else if (zcode == 233 || zcode == 169) {
+
+/* EBCDIC is assumed - ZCODE is the EBCDIC code of either lower or */
+/* upper case 'Z'. */
+
+ if ((inta >= 129 && inta <= 137) || (inta >= 145 && inta <= 153) ||
+ (inta >= 162 && inta <= 169)) {
+ inta += 64;
+ }
+ if ((intb >= 129 && intb <= 137) || (intb >= 145 && intb <= 153) ||
+ (intb >= 162 && intb <= 169)) {
+ intb += 64;
+ }
+
+ } else if (zcode == 218 || zcode == 250) {
+
+/* ASCII is assumed, on Prime machines - ZCODE is the ASCII code */
+/* plus 128 of either lower or upper case 'Z'. */
+
+ if (inta >= 225 && inta <= 250) {
+ inta += -32;
+ }
+ if (intb >= 225 && intb <= 250) {
+ intb += -32;
+ }
+ }
+ ret_val = inta == intb;
+
+/* RETURN */
+
+/* End of LSAME */
+
+ return ret_val;
+} /* lsame_ */
+
diff --git a/blas/f2c/r_cnjg.c b/blas/f2c/r_cnjg.c
new file mode 100644
index 0000000..c08182f
--- /dev/null
+++ b/blas/f2c/r_cnjg.c
@@ -0,0 +1,6 @@
+#include "datatypes.h"
+
+void r_cnjg(complex *r, complex *z) {
+ r->r = z->r;
+ r->i = -(z->i);
+}
diff --git a/blas/f2c/scabs1.c b/blas/f2c/scabs1.c
new file mode 100644
index 0000000..61e4ac8
--- /dev/null
+++ b/blas/f2c/scabs1.c
@@ -0,0 +1,15 @@
+#include "datatypes.h"
+
+doublereal scabs1_(complex *z__)
+{
+ /* System generated locals */
+ real ret_val, r__1, r__2;
+ /* Builtin functions */
+ double r_imag(complex *);
+/* Purpose
+ =======
+ SCABS1 computes absolute value of a complex number */
+ ret_val = (r__1 = z__->r, dabs(r__1)) + (r__2 = r_imag(z__), dabs(r__2));
+ return ret_val;
+} /* scabs1_ */
+
diff --git a/blas/f2c/srotm.c b/blas/f2c/srotm.c
new file mode 100644
index 0000000..bd5944a
--- /dev/null
+++ b/blas/f2c/srotm.c
@@ -0,0 +1,216 @@
+/* srotm.f -- translated by f2c (version 20100827).
+ You must link the resulting object file with libf2c:
+ on Microsoft Windows system, link with libf2c.lib;
+ on Linux or Unix systems, link with .../path/to/libf2c.a -lm
+ or, if you install libf2c.a in a standard place, with -lf2c -lm
+ -- in that order, at the end of the command line, as in
+ cc *.o -lf2c -lm
+ Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
+
+ http://www.netlib.org/f2c/libf2c.zip
+*/
+
+#include "datatypes.h"
+
+/* Subroutine */ int srotm_(integer *n, real *sx, integer *incx, real *sy,
+ integer *incy, real *sparam)
+{
+ /* Initialized data */
+
+ static real zero = 0.f;
+ static real two = 2.f;
+
+ /* System generated locals */
+ integer i__1, i__2;
+
+ /* Local variables */
+ integer i__;
+ real w, z__;
+ integer kx, ky;
+ real sh11, sh12, sh21, sh22, sflag;
+ integer nsteps;
+
+/* .. Scalar Arguments .. */
+/* .. */
+/* .. Array Arguments .. */
+/* .. */
+
+/* Purpose */
+/* ======= */
+
+/* APPLY THE MODIFIED GIVENS TRANSFORMATION, H, TO THE 2 BY N MATRIX */
+
+/* (SX**T) , WHERE **T INDICATES TRANSPOSE. THE ELEMENTS OF SX ARE IN */
+/* (DX**T) */
+
+/* SX(LX+I*INCX), I = 0 TO N-1, WHERE LX = 1 IF INCX .GE. 0, ELSE */
+/* LX = (-INCX)*N, AND SIMILARLY FOR SY USING USING LY AND INCY. */
+/* WITH SPARAM(1)=SFLAG, H HAS ONE OF THE FOLLOWING FORMS.. */
+
+/* SFLAG=-1.E0 SFLAG=0.E0 SFLAG=1.E0 SFLAG=-2.E0 */
+
+/* (SH11 SH12) (1.E0 SH12) (SH11 1.E0) (1.E0 0.E0) */
+/* H=( ) ( ) ( ) ( ) */
+/* (SH21 SH22), (SH21 1.E0), (-1.E0 SH22), (0.E0 1.E0). */
+/* SEE SROTMG FOR A DESCRIPTION OF DATA STORAGE IN SPARAM. */
+
+
+/* Arguments */
+/* ========= */
+
+/* N (input) INTEGER */
+/* number of elements in input vector(s) */
+
+/* SX (input/output) REAL array, dimension N */
+/* double precision vector with N elements */
+
+/* INCX (input) INTEGER */
+/* storage spacing between elements of SX */
+
+/* SY (input/output) REAL array, dimension N */
+/* double precision vector with N elements */
+
+/* INCY (input) INTEGER */
+/* storage spacing between elements of SY */
+
+/* SPARAM (input/output) REAL array, dimension 5 */
+/* SPARAM(1)=SFLAG */
+/* SPARAM(2)=SH11 */
+/* SPARAM(3)=SH21 */
+/* SPARAM(4)=SH12 */
+/* SPARAM(5)=SH22 */
+
+/* ===================================================================== */
+
+/* .. Local Scalars .. */
+/* .. */
+/* .. Data statements .. */
+ /* Parameter adjustments */
+ --sparam;
+ --sy;
+ --sx;
+
+ /* Function Body */
+/* .. */
+
+ sflag = sparam[1];
+ if (*n <= 0 || sflag + two == zero) {
+ goto L140;
+ }
+ if (! (*incx == *incy && *incx > 0)) {
+ goto L70;
+ }
+
+ nsteps = *n * *incx;
+ if (sflag < 0.f) {
+ goto L50;
+ } else if (sflag == 0) {
+ goto L10;
+ } else {
+ goto L30;
+ }
+L10:
+ sh12 = sparam[4];
+ sh21 = sparam[3];
+ i__1 = nsteps;
+ i__2 = *incx;
+ for (i__ = 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) {
+ w = sx[i__];
+ z__ = sy[i__];
+ sx[i__] = w + z__ * sh12;
+ sy[i__] = w * sh21 + z__;
+/* L20: */
+ }
+ goto L140;
+L30:
+ sh11 = sparam[2];
+ sh22 = sparam[5];
+ i__2 = nsteps;
+ i__1 = *incx;
+ for (i__ = 1; i__1 < 0 ? i__ >= i__2 : i__ <= i__2; i__ += i__1) {
+ w = sx[i__];
+ z__ = sy[i__];
+ sx[i__] = w * sh11 + z__;
+ sy[i__] = -w + sh22 * z__;
+/* L40: */
+ }
+ goto L140;
+L50:
+ sh11 = sparam[2];
+ sh12 = sparam[4];
+ sh21 = sparam[3];
+ sh22 = sparam[5];
+ i__1 = nsteps;
+ i__2 = *incx;
+ for (i__ = 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) {
+ w = sx[i__];
+ z__ = sy[i__];
+ sx[i__] = w * sh11 + z__ * sh12;
+ sy[i__] = w * sh21 + z__ * sh22;
+/* L60: */
+ }
+ goto L140;
+L70:
+ kx = 1;
+ ky = 1;
+ if (*incx < 0) {
+ kx = (1 - *n) * *incx + 1;
+ }
+ if (*incy < 0) {
+ ky = (1 - *n) * *incy + 1;
+ }
+
+ if (sflag < 0.f) {
+ goto L120;
+ } else if (sflag == 0) {
+ goto L80;
+ } else {
+ goto L100;
+ }
+L80:
+ sh12 = sparam[4];
+ sh21 = sparam[3];
+ i__2 = *n;
+ for (i__ = 1; i__ <= i__2; ++i__) {
+ w = sx[kx];
+ z__ = sy[ky];
+ sx[kx] = w + z__ * sh12;
+ sy[ky] = w * sh21 + z__;
+ kx += *incx;
+ ky += *incy;
+/* L90: */
+ }
+ goto L140;
+L100:
+ sh11 = sparam[2];
+ sh22 = sparam[5];
+ i__2 = *n;
+ for (i__ = 1; i__ <= i__2; ++i__) {
+ w = sx[kx];
+ z__ = sy[ky];
+ sx[kx] = w * sh11 + z__;
+ sy[ky] = -w + sh22 * z__;
+ kx += *incx;
+ ky += *incy;
+/* L110: */
+ }
+ goto L140;
+L120:
+ sh11 = sparam[2];
+ sh12 = sparam[4];
+ sh21 = sparam[3];
+ sh22 = sparam[5];
+ i__2 = *n;
+ for (i__ = 1; i__ <= i__2; ++i__) {
+ w = sx[kx];
+ z__ = sy[ky];
+ sx[kx] = w * sh11 + z__ * sh12;
+ sy[ky] = w * sh21 + z__ * sh22;
+ kx += *incx;
+ ky += *incy;
+/* L130: */
+ }
+L140:
+ return 0;
+} /* srotm_ */
+
diff --git a/blas/f2c/srotmg.c b/blas/f2c/srotmg.c
new file mode 100644
index 0000000..75f789f
--- /dev/null
+++ b/blas/f2c/srotmg.c
@@ -0,0 +1,295 @@
+/* srotmg.f -- translated by f2c (version 20100827).
+ You must link the resulting object file with libf2c:
+ on Microsoft Windows system, link with libf2c.lib;
+ on Linux or Unix systems, link with .../path/to/libf2c.a -lm
+ or, if you install libf2c.a in a standard place, with -lf2c -lm
+ -- in that order, at the end of the command line, as in
+ cc *.o -lf2c -lm
+ Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
+
+ http://www.netlib.org/f2c/libf2c.zip
+*/
+
+#include "datatypes.h"
+
+/* Subroutine */ int srotmg_(real *sd1, real *sd2, real *sx1, real *sy1, real
+ *sparam)
+{
+ /* Initialized data */
+
+ static real zero = 0.f;
+ static real one = 1.f;
+ static real two = 2.f;
+ static real gam = 4096.f;
+ static real gamsq = 16777200.f;
+ static real rgamsq = 5.96046e-8f;
+
+ /* Format strings */
+ static char fmt_120[] = "";
+ static char fmt_150[] = "";
+ static char fmt_180[] = "";
+ static char fmt_210[] = "";
+
+ /* System generated locals */
+ real r__1;
+
+ /* Local variables */
+ real su, sp1, sp2, sq1, sq2, sh11, sh12, sh21, sh22;
+ integer igo;
+ real sflag, stemp;
+
+ /* Assigned format variables */
+ static char *igo_fmt;
+
+/* .. Scalar Arguments .. */
+/* .. */
+/* .. Array Arguments .. */
+/* .. */
+
+/* Purpose */
+/* ======= */
+
+/* CONSTRUCT THE MODIFIED GIVENS TRANSFORMATION MATRIX H WHICH ZEROS */
+/* THE SECOND COMPONENT OF THE 2-VECTOR (SQRT(SD1)*SX1,SQRT(SD2)* */
+/* SY2)**T. */
+/* WITH SPARAM(1)=SFLAG, H HAS ONE OF THE FOLLOWING FORMS.. */
+
+/* SFLAG=-1.E0 SFLAG=0.E0 SFLAG=1.E0 SFLAG=-2.E0 */
+
+/* (SH11 SH12) (1.E0 SH12) (SH11 1.E0) (1.E0 0.E0) */
+/* H=( ) ( ) ( ) ( ) */
+/* (SH21 SH22), (SH21 1.E0), (-1.E0 SH22), (0.E0 1.E0). */
+/* LOCATIONS 2-4 OF SPARAM CONTAIN SH11,SH21,SH12, AND SH22 */
+/* RESPECTIVELY. (VALUES OF 1.E0, -1.E0, OR 0.E0 IMPLIED BY THE */
+/* VALUE OF SPARAM(1) ARE NOT STORED IN SPARAM.) */
+
+/* THE VALUES OF GAMSQ AND RGAMSQ SET IN THE DATA STATEMENT MAY BE */
+/* INEXACT. THIS IS OK AS THEY ARE ONLY USED FOR TESTING THE SIZE */
+/* OF SD1 AND SD2. ALL ACTUAL SCALING OF DATA IS DONE USING GAM. */
+
+
+/* Arguments */
+/* ========= */
+
+
+/* SD1 (input/output) REAL */
+
+/* SD2 (input/output) REAL */
+
+/* SX1 (input/output) REAL */
+
+/* SY1 (input) REAL */
+
+
+/* SPARAM (input/output) REAL array, dimension 5 */
+/* SPARAM(1)=SFLAG */
+/* SPARAM(2)=SH11 */
+/* SPARAM(3)=SH21 */
+/* SPARAM(4)=SH12 */
+/* SPARAM(5)=SH22 */
+
+/* ===================================================================== */
+
+/* .. Local Scalars .. */
+/* .. */
+/* .. Intrinsic Functions .. */
+/* .. */
+/* .. Data statements .. */
+
+ /* Parameter adjustments */
+ --sparam;
+
+ /* Function Body */
+/* .. */
+ if (! (*sd1 < zero)) {
+ goto L10;
+ }
+/* GO ZERO-H-D-AND-SX1.. */
+ goto L60;
+L10:
+/* CASE-SD1-NONNEGATIVE */
+ sp2 = *sd2 * *sy1;
+ if (! (sp2 == zero)) {
+ goto L20;
+ }
+ sflag = -two;
+ goto L260;
+/* REGULAR-CASE.. */
+L20:
+ sp1 = *sd1 * *sx1;
+ sq2 = sp2 * *sy1;
+ sq1 = sp1 * *sx1;
+
+ if (! (dabs(sq1) > dabs(sq2))) {
+ goto L40;
+ }
+ sh21 = -(*sy1) / *sx1;
+ sh12 = sp2 / sp1;
+
+ su = one - sh12 * sh21;
+
+ if (! (su <= zero)) {
+ goto L30;
+ }
+/* GO ZERO-H-D-AND-SX1.. */
+ goto L60;
+L30:
+ sflag = zero;
+ *sd1 /= su;
+ *sd2 /= su;
+ *sx1 *= su;
+/* GO SCALE-CHECK.. */
+ goto L100;
+L40:
+ if (! (sq2 < zero)) {
+ goto L50;
+ }
+/* GO ZERO-H-D-AND-SX1.. */
+ goto L60;
+L50:
+ sflag = one;
+ sh11 = sp1 / sp2;
+ sh22 = *sx1 / *sy1;
+ su = one + sh11 * sh22;
+ stemp = *sd2 / su;
+ *sd2 = *sd1 / su;
+ *sd1 = stemp;
+ *sx1 = *sy1 * su;
+/* GO SCALE-CHECK */
+ goto L100;
+/* PROCEDURE..ZERO-H-D-AND-SX1.. */
+L60:
+ sflag = -one;
+ sh11 = zero;
+ sh12 = zero;
+ sh21 = zero;
+ sh22 = zero;
+
+ *sd1 = zero;
+ *sd2 = zero;
+ *sx1 = zero;
+/* RETURN.. */
+ goto L220;
+/* PROCEDURE..FIX-H.. */
+L70:
+ if (! (sflag >= zero)) {
+ goto L90;
+ }
+
+ if (! (sflag == zero)) {
+ goto L80;
+ }
+ sh11 = one;
+ sh22 = one;
+ sflag = -one;
+ goto L90;
+L80:
+ sh21 = -one;
+ sh12 = one;
+ sflag = -one;
+L90:
+ switch (igo) {
+ case 0: goto L120;
+ case 1: goto L150;
+ case 2: goto L180;
+ case 3: goto L210;
+ }
+/* PROCEDURE..SCALE-CHECK */
+L100:
+L110:
+ if (! (*sd1 <= rgamsq)) {
+ goto L130;
+ }
+ if (*sd1 == zero) {
+ goto L160;
+ }
+ igo = 0;
+ igo_fmt = fmt_120;
+/* FIX-H.. */
+ goto L70;
+L120:
+/* Computing 2nd power */
+ r__1 = gam;
+ *sd1 *= r__1 * r__1;
+ *sx1 /= gam;
+ sh11 /= gam;
+ sh12 /= gam;
+ goto L110;
+L130:
+L140:
+ if (! (*sd1 >= gamsq)) {
+ goto L160;
+ }
+ igo = 1;
+ igo_fmt = fmt_150;
+/* FIX-H.. */
+ goto L70;
+L150:
+/* Computing 2nd power */
+ r__1 = gam;
+ *sd1 /= r__1 * r__1;
+ *sx1 *= gam;
+ sh11 *= gam;
+ sh12 *= gam;
+ goto L140;
+L160:
+L170:
+ if (! (dabs(*sd2) <= rgamsq)) {
+ goto L190;
+ }
+ if (*sd2 == zero) {
+ goto L220;
+ }
+ igo = 2;
+ igo_fmt = fmt_180;
+/* FIX-H.. */
+ goto L70;
+L180:
+/* Computing 2nd power */
+ r__1 = gam;
+ *sd2 *= r__1 * r__1;
+ sh21 /= gam;
+ sh22 /= gam;
+ goto L170;
+L190:
+L200:
+ if (! (dabs(*sd2) >= gamsq)) {
+ goto L220;
+ }
+ igo = 3;
+ igo_fmt = fmt_210;
+/* FIX-H.. */
+ goto L70;
+L210:
+/* Computing 2nd power */
+ r__1 = gam;
+ *sd2 /= r__1 * r__1;
+ sh21 *= gam;
+ sh22 *= gam;
+ goto L200;
+L220:
+ if (sflag < 0.f) {
+ goto L250;
+ } else if (sflag == 0) {
+ goto L230;
+ } else {
+ goto L240;
+ }
+L230:
+ sparam[3] = sh21;
+ sparam[4] = sh12;
+ goto L260;
+L240:
+ sparam[2] = sh11;
+ sparam[5] = sh22;
+ goto L260;
+L250:
+ sparam[2] = sh11;
+ sparam[3] = sh21;
+ sparam[4] = sh12;
+ sparam[5] = sh22;
+L260:
+ sparam[1] = sflag;
+ return 0;
+} /* srotmg_ */
+
diff --git a/blas/f2c/ssbmv.c b/blas/f2c/ssbmv.c
new file mode 100644
index 0000000..8599325
--- /dev/null
+++ b/blas/f2c/ssbmv.c
@@ -0,0 +1,368 @@
+/* ssbmv.f -- translated by f2c (version 20100827).
+ You must link the resulting object file with libf2c:
+ on Microsoft Windows system, link with libf2c.lib;
+ on Linux or Unix systems, link with .../path/to/libf2c.a -lm
+ or, if you install libf2c.a in a standard place, with -lf2c -lm
+ -- in that order, at the end of the command line, as in
+ cc *.o -lf2c -lm
+ Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
+
+ http://www.netlib.org/f2c/libf2c.zip
+*/
+
+#include "datatypes.h"
+
+/* Subroutine */ int ssbmv_(char *uplo, integer *n, integer *k, real *alpha,
+ real *a, integer *lda, real *x, integer *incx, real *beta, real *y,
+ integer *incy, ftnlen uplo_len)
+{
+ /* System generated locals */
+ integer a_dim1, a_offset, i__1, i__2, i__3, i__4;
+
+ /* Local variables */
+ integer i__, j, l, ix, iy, jx, jy, kx, ky, info;
+ real temp1, temp2;
+ extern logical lsame_(char *, char *, ftnlen, ftnlen);
+ integer kplus1;
+ extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
+
+/* .. Scalar Arguments .. */
+/* .. */
+/* .. Array Arguments .. */
+/* .. */
+
+/* Purpose */
+/* ======= */
+
+/* SSBMV performs the matrix-vector operation */
+
+/* y := alpha*A*x + beta*y, */
+
+/* where alpha and beta are scalars, x and y are n element vectors and */
+/* A is an n by n symmetric band matrix, with k super-diagonals. */
+
+/* Arguments */
+/* ========== */
+
+/* UPLO - CHARACTER*1. */
+/* On entry, UPLO specifies whether the upper or lower */
+/* triangular part of the band matrix A is being supplied as */
+/* follows: */
+
+/* UPLO = 'U' or 'u' The upper triangular part of A is */
+/* being supplied. */
+
+/* UPLO = 'L' or 'l' The lower triangular part of A is */
+/* being supplied. */
+
+/* Unchanged on exit. */
+
+/* N - INTEGER. */
+/* On entry, N specifies the order of the matrix A. */
+/* N must be at least zero. */
+/* Unchanged on exit. */
+
+/* K - INTEGER. */
+/* On entry, K specifies the number of super-diagonals of the */
+/* matrix A. K must satisfy 0 .le. K. */
+/* Unchanged on exit. */
+
+/* ALPHA - REAL . */
+/* On entry, ALPHA specifies the scalar alpha. */
+/* Unchanged on exit. */
+
+/* A - REAL array of DIMENSION ( LDA, n ). */
+/* Before entry with UPLO = 'U' or 'u', the leading ( k + 1 ) */
+/* by n part of the array A must contain the upper triangular */
+/* band part of the symmetric matrix, supplied column by */
+/* column, with the leading diagonal of the matrix in row */
+/* ( k + 1 ) of the array, the first super-diagonal starting at */
+/* position 2 in row k, and so on. The top left k by k triangle */
+/* of the array A is not referenced. */
+/* The following program segment will transfer the upper */
+/* triangular part of a symmetric band matrix from conventional */
+/* full matrix storage to band storage: */
+
+/* DO 20, J = 1, N */
+/* M = K + 1 - J */
+/* DO 10, I = MAX( 1, J - K ), J */
+/* A( M + I, J ) = matrix( I, J ) */
+/* 10 CONTINUE */
+/* 20 CONTINUE */
+
+/* Before entry with UPLO = 'L' or 'l', the leading ( k + 1 ) */
+/* by n part of the array A must contain the lower triangular */
+/* band part of the symmetric matrix, supplied column by */
+/* column, with the leading diagonal of the matrix in row 1 of */
+/* the array, the first sub-diagonal starting at position 1 in */
+/* row 2, and so on. The bottom right k by k triangle of the */
+/* array A is not referenced. */
+/* The following program segment will transfer the lower */
+/* triangular part of a symmetric band matrix from conventional */
+/* full matrix storage to band storage: */
+
+/* DO 20, J = 1, N */
+/* M = 1 - J */
+/* DO 10, I = J, MIN( N, J + K ) */
+/* A( M + I, J ) = matrix( I, J ) */
+/* 10 CONTINUE */
+/* 20 CONTINUE */
+
+/* Unchanged on exit. */
+
+/* LDA - INTEGER. */
+/* On entry, LDA specifies the first dimension of A as declared */
+/* in the calling (sub) program. LDA must be at least */
+/* ( k + 1 ). */
+/* Unchanged on exit. */
+
+/* X - REAL array of DIMENSION at least */
+/* ( 1 + ( n - 1 )*abs( INCX ) ). */
+/* Before entry, the incremented array X must contain the */
+/* vector x. */
+/* Unchanged on exit. */
+
+/* INCX - INTEGER. */
+/* On entry, INCX specifies the increment for the elements of */
+/* X. INCX must not be zero. */
+/* Unchanged on exit. */
+
+/* BETA - REAL . */
+/* On entry, BETA specifies the scalar beta. */
+/* Unchanged on exit. */
+
+/* Y - REAL array of DIMENSION at least */
+/* ( 1 + ( n - 1 )*abs( INCY ) ). */
+/* Before entry, the incremented array Y must contain the */
+/* vector y. On exit, Y is overwritten by the updated vector y. */
+
+/* INCY - INTEGER. */
+/* On entry, INCY specifies the increment for the elements of */
+/* Y. INCY must not be zero. */
+/* Unchanged on exit. */
+
+/* Further Details */
+/* =============== */
+
+/* Level 2 Blas routine. */
+
+/* -- Written on 22-October-1986. */
+/* Jack Dongarra, Argonne National Lab. */
+/* Jeremy Du Croz, Nag Central Office. */
+/* Sven Hammarling, Nag Central Office. */
+/* Richard Hanson, Sandia National Labs. */
+
+/* ===================================================================== */
+
+/* .. Parameters .. */
+/* .. */
+/* .. Local Scalars .. */
+/* .. */
+/* .. External Functions .. */
+/* .. */
+/* .. External Subroutines .. */
+/* .. */
+/* .. Intrinsic Functions .. */
+/* .. */
+
+/* Test the input parameters. */
+
+ /* Parameter adjustments */
+ a_dim1 = *lda;
+ a_offset = 1 + a_dim1;
+ a -= a_offset;
+ --x;
+ --y;
+
+ /* Function Body */
+ info = 0;
+ if (! lsame_(uplo, "U", (ftnlen)1, (ftnlen)1) && ! lsame_(uplo, "L", (
+ ftnlen)1, (ftnlen)1)) {
+ info = 1;
+ } else if (*n < 0) {
+ info = 2;
+ } else if (*k < 0) {
+ info = 3;
+ } else if (*lda < *k + 1) {
+ info = 6;
+ } else if (*incx == 0) {
+ info = 8;
+ } else if (*incy == 0) {
+ info = 11;
+ }
+ if (info != 0) {
+ xerbla_("SSBMV ", &info, (ftnlen)6);
+ return 0;
+ }
+
+/* Quick return if possible. */
+
+ if (*n == 0 || (*alpha == 0.f && *beta == 1.f)) {
+ return 0;
+ }
+
+/* Set up the start points in X and Y. */
+
+ if (*incx > 0) {
+ kx = 1;
+ } else {
+ kx = 1 - (*n - 1) * *incx;
+ }
+ if (*incy > 0) {
+ ky = 1;
+ } else {
+ ky = 1 - (*n - 1) * *incy;
+ }
+
+/* Start the operations. In this version the elements of the array A */
+/* are accessed sequentially with one pass through A. */
+
+/* First form y := beta*y. */
+
+ if (*beta != 1.f) {
+ if (*incy == 1) {
+ if (*beta == 0.f) {
+ i__1 = *n;
+ for (i__ = 1; i__ <= i__1; ++i__) {
+ y[i__] = 0.f;
+/* L10: */
+ }
+ } else {
+ i__1 = *n;
+ for (i__ = 1; i__ <= i__1; ++i__) {
+ y[i__] = *beta * y[i__];
+/* L20: */
+ }
+ }
+ } else {
+ iy = ky;
+ if (*beta == 0.f) {
+ i__1 = *n;
+ for (i__ = 1; i__ <= i__1; ++i__) {
+ y[iy] = 0.f;
+ iy += *incy;
+/* L30: */
+ }
+ } else {
+ i__1 = *n;
+ for (i__ = 1; i__ <= i__1; ++i__) {
+ y[iy] = *beta * y[iy];
+ iy += *incy;
+/* L40: */
+ }
+ }
+ }
+ }
+ if (*alpha == 0.f) {
+ return 0;
+ }
+ if (lsame_(uplo, "U", (ftnlen)1, (ftnlen)1)) {
+
+/* Form y when upper triangle of A is stored. */
+
+ kplus1 = *k + 1;
+ if (*incx == 1 && *incy == 1) {
+ i__1 = *n;
+ for (j = 1; j <= i__1; ++j) {
+ temp1 = *alpha * x[j];
+ temp2 = 0.f;
+ l = kplus1 - j;
+/* Computing MAX */
+ i__2 = 1, i__3 = j - *k;
+ i__4 = j - 1;
+ for (i__ = max(i__2,i__3); i__ <= i__4; ++i__) {
+ y[i__] += temp1 * a[l + i__ + j * a_dim1];
+ temp2 += a[l + i__ + j * a_dim1] * x[i__];
+/* L50: */
+ }
+ y[j] = y[j] + temp1 * a[kplus1 + j * a_dim1] + *alpha * temp2;
+/* L60: */
+ }
+ } else {
+ jx = kx;
+ jy = ky;
+ i__1 = *n;
+ for (j = 1; j <= i__1; ++j) {
+ temp1 = *alpha * x[jx];
+ temp2 = 0.f;
+ ix = kx;
+ iy = ky;
+ l = kplus1 - j;
+/* Computing MAX */
+ i__4 = 1, i__2 = j - *k;
+ i__3 = j - 1;
+ for (i__ = max(i__4,i__2); i__ <= i__3; ++i__) {
+ y[iy] += temp1 * a[l + i__ + j * a_dim1];
+ temp2 += a[l + i__ + j * a_dim1] * x[ix];
+ ix += *incx;
+ iy += *incy;
+/* L70: */
+ }
+ y[jy] = y[jy] + temp1 * a[kplus1 + j * a_dim1] + *alpha *
+ temp2;
+ jx += *incx;
+ jy += *incy;
+ if (j > *k) {
+ kx += *incx;
+ ky += *incy;
+ }
+/* L80: */
+ }
+ }
+ } else {
+
+/* Form y when lower triangle of A is stored. */
+
+ if (*incx == 1 && *incy == 1) {
+ i__1 = *n;
+ for (j = 1; j <= i__1; ++j) {
+ temp1 = *alpha * x[j];
+ temp2 = 0.f;
+ y[j] += temp1 * a[j * a_dim1 + 1];
+ l = 1 - j;
+/* Computing MIN */
+ i__4 = *n, i__2 = j + *k;
+ i__3 = min(i__4,i__2);
+ for (i__ = j + 1; i__ <= i__3; ++i__) {
+ y[i__] += temp1 * a[l + i__ + j * a_dim1];
+ temp2 += a[l + i__ + j * a_dim1] * x[i__];
+/* L90: */
+ }
+ y[j] += *alpha * temp2;
+/* L100: */
+ }
+ } else {
+ jx = kx;
+ jy = ky;
+ i__1 = *n;
+ for (j = 1; j <= i__1; ++j) {
+ temp1 = *alpha * x[jx];
+ temp2 = 0.f;
+ y[jy] += temp1 * a[j * a_dim1 + 1];
+ l = 1 - j;
+ ix = jx;
+ iy = jy;
+/* Computing MIN */
+ i__4 = *n, i__2 = j + *k;
+ i__3 = min(i__4,i__2);
+ for (i__ = j + 1; i__ <= i__3; ++i__) {
+ ix += *incx;
+ iy += *incy;
+ y[iy] += temp1 * a[l + i__ + j * a_dim1];
+ temp2 += a[l + i__ + j * a_dim1] * x[ix];
+/* L110: */
+ }
+ y[jy] += *alpha * temp2;
+ jx += *incx;
+ jy += *incy;
+/* L120: */
+ }
+ }
+ }
+
+ return 0;
+
+/* End of SSBMV . */
+
+} /* ssbmv_ */
+
diff --git a/blas/f2c/sspmv.c b/blas/f2c/sspmv.c
new file mode 100644
index 0000000..47858ec
--- /dev/null
+++ b/blas/f2c/sspmv.c
@@ -0,0 +1,316 @@
+/* sspmv.f -- translated by f2c (version 20100827).
+ You must link the resulting object file with libf2c:
+ on Microsoft Windows system, link with libf2c.lib;
+ on Linux or Unix systems, link with .../path/to/libf2c.a -lm
+ or, if you install libf2c.a in a standard place, with -lf2c -lm
+ -- in that order, at the end of the command line, as in
+ cc *.o -lf2c -lm
+ Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
+
+ http://www.netlib.org/f2c/libf2c.zip
+*/
+
+#include "datatypes.h"
+
+/* Subroutine */ int sspmv_(char *uplo, integer *n, real *alpha, real *ap,
+ real *x, integer *incx, real *beta, real *y, integer *incy, ftnlen
+ uplo_len)
+{
+ /* System generated locals */
+ integer i__1, i__2;
+
+ /* Local variables */
+ integer i__, j, k, kk, ix, iy, jx, jy, kx, ky, info;
+ real temp1, temp2;
+ extern logical lsame_(char *, char *, ftnlen, ftnlen);
+ extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
+
+/* .. Scalar Arguments .. */
+/* .. */
+/* .. Array Arguments .. */
+/* .. */
+
+/* Purpose */
+/* ======= */
+
+/* SSPMV performs the matrix-vector operation */
+
+/* y := alpha*A*x + beta*y, */
+
+/* where alpha and beta are scalars, x and y are n element vectors and */
+/* A is an n by n symmetric matrix, supplied in packed form. */
+
+/* Arguments */
+/* ========== */
+
+/* UPLO - CHARACTER*1. */
+/* On entry, UPLO specifies whether the upper or lower */
+/* triangular part of the matrix A is supplied in the packed */
+/* array AP as follows: */
+
+/* UPLO = 'U' or 'u' The upper triangular part of A is */
+/* supplied in AP. */
+
+/* UPLO = 'L' or 'l' The lower triangular part of A is */
+/* supplied in AP. */
+
+/* Unchanged on exit. */
+
+/* N - INTEGER. */
+/* On entry, N specifies the order of the matrix A. */
+/* N must be at least zero. */
+/* Unchanged on exit. */
+
+/* ALPHA - REAL . */
+/* On entry, ALPHA specifies the scalar alpha. */
+/* Unchanged on exit. */
+
+/* AP - REAL array of DIMENSION at least */
+/* ( ( n*( n + 1 ) )/2 ). */
+/* Before entry with UPLO = 'U' or 'u', the array AP must */
+/* contain the upper triangular part of the symmetric matrix */
+/* packed sequentially, column by column, so that AP( 1 ) */
+/* contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 ) */
+/* and a( 2, 2 ) respectively, and so on. */
+/* Before entry with UPLO = 'L' or 'l', the array AP must */
+/* contain the lower triangular part of the symmetric matrix */
+/* packed sequentially, column by column, so that AP( 1 ) */
+/* contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 ) */
+/* and a( 3, 1 ) respectively, and so on. */
+/* Unchanged on exit. */
+
+/* X - REAL array of dimension at least */
+/* ( 1 + ( n - 1 )*abs( INCX ) ). */
+/* Before entry, the incremented array X must contain the n */
+/* element vector x. */
+/* Unchanged on exit. */
+
+/* INCX - INTEGER. */
+/* On entry, INCX specifies the increment for the elements of */
+/* X. INCX must not be zero. */
+/* Unchanged on exit. */
+
+/* BETA - REAL . */
+/* On entry, BETA specifies the scalar beta. When BETA is */
+/* supplied as zero then Y need not be set on input. */
+/* Unchanged on exit. */
+
+/* Y - REAL array of dimension at least */
+/* ( 1 + ( n - 1 )*abs( INCY ) ). */
+/* Before entry, the incremented array Y must contain the n */
+/* element vector y. On exit, Y is overwritten by the updated */
+/* vector y. */
+
+/* INCY - INTEGER. */
+/* On entry, INCY specifies the increment for the elements of */
+/* Y. INCY must not be zero. */
+/* Unchanged on exit. */
+
+/* Further Details */
+/* =============== */
+
+/* Level 2 Blas routine. */
+
+/* -- Written on 22-October-1986. */
+/* Jack Dongarra, Argonne National Lab. */
+/* Jeremy Du Croz, Nag Central Office. */
+/* Sven Hammarling, Nag Central Office. */
+/* Richard Hanson, Sandia National Labs. */
+
+/* ===================================================================== */
+
+/* .. Parameters .. */
+/* .. */
+/* .. Local Scalars .. */
+/* .. */
+/* .. External Functions .. */
+/* .. */
+/* .. External Subroutines .. */
+/* .. */
+
+/* Test the input parameters. */
+
+ /* Parameter adjustments */
+ --y;
+ --x;
+ --ap;
+
+ /* Function Body */
+ info = 0;
+ if (! lsame_(uplo, "U", (ftnlen)1, (ftnlen)1) && ! lsame_(uplo, "L", (
+ ftnlen)1, (ftnlen)1)) {
+ info = 1;
+ } else if (*n < 0) {
+ info = 2;
+ } else if (*incx == 0) {
+ info = 6;
+ } else if (*incy == 0) {
+ info = 9;
+ }
+ if (info != 0) {
+ xerbla_("SSPMV ", &info, (ftnlen)6);
+ return 0;
+ }
+
+/* Quick return if possible. */
+
+ if (*n == 0 || (*alpha == 0.f && *beta == 1.f)) {
+ return 0;
+ }
+
+/* Set up the start points in X and Y. */
+
+ if (*incx > 0) {
+ kx = 1;
+ } else {
+ kx = 1 - (*n - 1) * *incx;
+ }
+ if (*incy > 0) {
+ ky = 1;
+ } else {
+ ky = 1 - (*n - 1) * *incy;
+ }
+
+/* Start the operations. In this version the elements of the array AP */
+/* are accessed sequentially with one pass through AP. */
+
+/* First form y := beta*y. */
+
+ if (*beta != 1.f) {
+ if (*incy == 1) {
+ if (*beta == 0.f) {
+ i__1 = *n;
+ for (i__ = 1; i__ <= i__1; ++i__) {
+ y[i__] = 0.f;
+/* L10: */
+ }
+ } else {
+ i__1 = *n;
+ for (i__ = 1; i__ <= i__1; ++i__) {
+ y[i__] = *beta * y[i__];
+/* L20: */
+ }
+ }
+ } else {
+ iy = ky;
+ if (*beta == 0.f) {
+ i__1 = *n;
+ for (i__ = 1; i__ <= i__1; ++i__) {
+ y[iy] = 0.f;
+ iy += *incy;
+/* L30: */
+ }
+ } else {
+ i__1 = *n;
+ for (i__ = 1; i__ <= i__1; ++i__) {
+ y[iy] = *beta * y[iy];
+ iy += *incy;
+/* L40: */
+ }
+ }
+ }
+ }
+ if (*alpha == 0.f) {
+ return 0;
+ }
+ kk = 1;
+ if (lsame_(uplo, "U", (ftnlen)1, (ftnlen)1)) {
+
+/* Form y when AP contains the upper triangle. */
+
+ if (*incx == 1 && *incy == 1) {
+ i__1 = *n;
+ for (j = 1; j <= i__1; ++j) {
+ temp1 = *alpha * x[j];
+ temp2 = 0.f;
+ k = kk;
+ i__2 = j - 1;
+ for (i__ = 1; i__ <= i__2; ++i__) {
+ y[i__] += temp1 * ap[k];
+ temp2 += ap[k] * x[i__];
+ ++k;
+/* L50: */
+ }
+ y[j] = y[j] + temp1 * ap[kk + j - 1] + *alpha * temp2;
+ kk += j;
+/* L60: */
+ }
+ } else {
+ jx = kx;
+ jy = ky;
+ i__1 = *n;
+ for (j = 1; j <= i__1; ++j) {
+ temp1 = *alpha * x[jx];
+ temp2 = 0.f;
+ ix = kx;
+ iy = ky;
+ i__2 = kk + j - 2;
+ for (k = kk; k <= i__2; ++k) {
+ y[iy] += temp1 * ap[k];
+ temp2 += ap[k] * x[ix];
+ ix += *incx;
+ iy += *incy;
+/* L70: */
+ }
+ y[jy] = y[jy] + temp1 * ap[kk + j - 1] + *alpha * temp2;
+ jx += *incx;
+ jy += *incy;
+ kk += j;
+/* L80: */
+ }
+ }
+ } else {
+
+/* Form y when AP contains the lower triangle. */
+
+ if (*incx == 1 && *incy == 1) {
+ i__1 = *n;
+ for (j = 1; j <= i__1; ++j) {
+ temp1 = *alpha * x[j];
+ temp2 = 0.f;
+ y[j] += temp1 * ap[kk];
+ k = kk + 1;
+ i__2 = *n;
+ for (i__ = j + 1; i__ <= i__2; ++i__) {
+ y[i__] += temp1 * ap[k];
+ temp2 += ap[k] * x[i__];
+ ++k;
+/* L90: */
+ }
+ y[j] += *alpha * temp2;
+ kk += *n - j + 1;
+/* L100: */
+ }
+ } else {
+ jx = kx;
+ jy = ky;
+ i__1 = *n;
+ for (j = 1; j <= i__1; ++j) {
+ temp1 = *alpha * x[jx];
+ temp2 = 0.f;
+ y[jy] += temp1 * ap[kk];
+ ix = jx;
+ iy = jy;
+ i__2 = kk + *n - j;
+ for (k = kk + 1; k <= i__2; ++k) {
+ ix += *incx;
+ iy += *incy;
+ y[iy] += temp1 * ap[k];
+ temp2 += ap[k] * x[ix];
+/* L110: */
+ }
+ y[jy] += *alpha * temp2;
+ jx += *incx;
+ jy += *incy;
+ kk += *n - j + 1;
+/* L120: */
+ }
+ }
+ }
+
+ return 0;
+
+/* End of SSPMV . */
+
+} /* sspmv_ */
+
diff --git a/blas/f2c/stbmv.c b/blas/f2c/stbmv.c
new file mode 100644
index 0000000..b5a68b5
--- /dev/null
+++ b/blas/f2c/stbmv.c
@@ -0,0 +1,428 @@
+/* stbmv.f -- translated by f2c (version 20100827).
+ You must link the resulting object file with libf2c:
+ on Microsoft Windows system, link with libf2c.lib;
+ on Linux or Unix systems, link with .../path/to/libf2c.a -lm
+ or, if you install libf2c.a in a standard place, with -lf2c -lm
+ -- in that order, at the end of the command line, as in
+ cc *.o -lf2c -lm
+ Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
+
+ http://www.netlib.org/f2c/libf2c.zip
+*/
+
+#include "datatypes.h"
+
+/* Subroutine */ int stbmv_(char *uplo, char *trans, char *diag, integer *n,
+ integer *k, real *a, integer *lda, real *x, integer *incx, ftnlen
+ uplo_len, ftnlen trans_len, ftnlen diag_len)
+{
+ /* System generated locals */
+ integer a_dim1, a_offset, i__1, i__2, i__3, i__4;
+
+ /* Local variables */
+ integer i__, j, l, ix, jx, kx, info;
+ real temp;
+ extern logical lsame_(char *, char *, ftnlen, ftnlen);
+ integer kplus1;
+ extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
+ logical nounit;
+
+/* .. Scalar Arguments .. */
+/* .. */
+/* .. Array Arguments .. */
+/* .. */
+
+/* Purpose */
+/* ======= */
+
+/* STBMV performs one of the matrix-vector operations */
+
+/* x := A*x, or x := A'*x, */
+
+/* where x is an n element vector and A is an n by n unit, or non-unit, */
+/* upper or lower triangular band matrix, with ( k + 1 ) diagonals. */
+
+/* Arguments */
+/* ========== */
+
+/* UPLO - CHARACTER*1. */
+/* On entry, UPLO specifies whether the matrix is an upper or */
+/* lower triangular matrix as follows: */
+
+/* UPLO = 'U' or 'u' A is an upper triangular matrix. */
+
+/* UPLO = 'L' or 'l' A is a lower triangular matrix. */
+
+/* Unchanged on exit. */
+
+/* TRANS - CHARACTER*1. */
+/* On entry, TRANS specifies the operation to be performed as */
+/* follows: */
+
+/* TRANS = 'N' or 'n' x := A*x. */
+
+/* TRANS = 'T' or 't' x := A'*x. */
+
+/* TRANS = 'C' or 'c' x := A'*x. */
+
+/* Unchanged on exit. */
+
+/* DIAG - CHARACTER*1. */
+/* On entry, DIAG specifies whether or not A is unit */
+/* triangular as follows: */
+
+/* DIAG = 'U' or 'u' A is assumed to be unit triangular. */
+
+/* DIAG = 'N' or 'n' A is not assumed to be unit */
+/* triangular. */
+
+/* Unchanged on exit. */
+
+/* N - INTEGER. */
+/* On entry, N specifies the order of the matrix A. */
+/* N must be at least zero. */
+/* Unchanged on exit. */
+
+/* K - INTEGER. */
+/* On entry with UPLO = 'U' or 'u', K specifies the number of */
+/* super-diagonals of the matrix A. */
+/* On entry with UPLO = 'L' or 'l', K specifies the number of */
+/* sub-diagonals of the matrix A. */
+/* K must satisfy 0 .le. K. */
+/* Unchanged on exit. */
+
+/* A - REAL array of DIMENSION ( LDA, n ). */
+/* Before entry with UPLO = 'U' or 'u', the leading ( k + 1 ) */
+/* by n part of the array A must contain the upper triangular */
+/* band part of the matrix of coefficients, supplied column by */
+/* column, with the leading diagonal of the matrix in row */
+/* ( k + 1 ) of the array, the first super-diagonal starting at */
+/* position 2 in row k, and so on. The top left k by k triangle */
+/* of the array A is not referenced. */
+/* The following program segment will transfer an upper */
+/* triangular band matrix from conventional full matrix storage */
+/* to band storage: */
+
+/* DO 20, J = 1, N */
+/* M = K + 1 - J */
+/* DO 10, I = MAX( 1, J - K ), J */
+/* A( M + I, J ) = matrix( I, J ) */
+/* 10 CONTINUE */
+/* 20 CONTINUE */
+
+/* Before entry with UPLO = 'L' or 'l', the leading ( k + 1 ) */
+/* by n part of the array A must contain the lower triangular */
+/* band part of the matrix of coefficients, supplied column by */
+/* column, with the leading diagonal of the matrix in row 1 of */
+/* the array, the first sub-diagonal starting at position 1 in */
+/* row 2, and so on. The bottom right k by k triangle of the */
+/* array A is not referenced. */
+/* The following program segment will transfer a lower */
+/* triangular band matrix from conventional full matrix storage */
+/* to band storage: */
+
+/* DO 20, J = 1, N */
+/* M = 1 - J */
+/* DO 10, I = J, MIN( N, J + K ) */
+/* A( M + I, J ) = matrix( I, J ) */
+/* 10 CONTINUE */
+/* 20 CONTINUE */
+
+/* Note that when DIAG = 'U' or 'u' the elements of the array A */
+/* corresponding to the diagonal elements of the matrix are not */
+/* referenced, but are assumed to be unity. */
+/* Unchanged on exit. */
+
+/* LDA - INTEGER. */
+/* On entry, LDA specifies the first dimension of A as declared */
+/* in the calling (sub) program. LDA must be at least */
+/* ( k + 1 ). */
+/* Unchanged on exit. */
+
+/* X - REAL array of dimension at least */
+/* ( 1 + ( n - 1 )*abs( INCX ) ). */
+/* Before entry, the incremented array X must contain the n */
+/* element vector x. On exit, X is overwritten with the */
+/* transformed vector x. */
+
+/* INCX - INTEGER. */
+/* On entry, INCX specifies the increment for the elements of */
+/* X. INCX must not be zero. */
+/* Unchanged on exit. */
+
+/* Further Details */
+/* =============== */
+
+/* Level 2 Blas routine. */
+
+/* -- Written on 22-October-1986. */
+/* Jack Dongarra, Argonne National Lab. */
+/* Jeremy Du Croz, Nag Central Office. */
+/* Sven Hammarling, Nag Central Office. */
+/* Richard Hanson, Sandia National Labs. */
+
+/* ===================================================================== */
+
+/* .. Parameters .. */
+/* .. */
+/* .. Local Scalars .. */
+/* .. */
+/* .. External Functions .. */
+/* .. */
+/* .. External Subroutines .. */
+/* .. */
+/* .. Intrinsic Functions .. */
+/* .. */
+
+/* Test the input parameters. */
+
+ /* Parameter adjustments */
+ a_dim1 = *lda;
+ a_offset = 1 + a_dim1;
+ a -= a_offset;
+ --x;
+
+ /* Function Body */
+ info = 0;
+ if (! lsame_(uplo, "U", (ftnlen)1, (ftnlen)1) && ! lsame_(uplo, "L", (
+ ftnlen)1, (ftnlen)1)) {
+ info = 1;
+ } else if (! lsame_(trans, "N", (ftnlen)1, (ftnlen)1) && ! lsame_(trans,
+ "T", (ftnlen)1, (ftnlen)1) && ! lsame_(trans, "C", (ftnlen)1, (
+ ftnlen)1)) {
+ info = 2;
+ } else if (! lsame_(diag, "U", (ftnlen)1, (ftnlen)1) && ! lsame_(diag,
+ "N", (ftnlen)1, (ftnlen)1)) {
+ info = 3;
+ } else if (*n < 0) {
+ info = 4;
+ } else if (*k < 0) {
+ info = 5;
+ } else if (*lda < *k + 1) {
+ info = 7;
+ } else if (*incx == 0) {
+ info = 9;
+ }
+ if (info != 0) {
+ xerbla_("STBMV ", &info, (ftnlen)6);
+ return 0;
+ }
+
+/* Quick return if possible. */
+
+ if (*n == 0) {
+ return 0;
+ }
+
+ nounit = lsame_(diag, "N", (ftnlen)1, (ftnlen)1);
+
+/* Set up the start point in X if the increment is not unity. This */
+/* will be ( N - 1 )*INCX too small for descending loops. */
+
+ if (*incx <= 0) {
+ kx = 1 - (*n - 1) * *incx;
+ } else if (*incx != 1) {
+ kx = 1;
+ }
+
+/* Start the operations. In this version the elements of A are */
+/* accessed sequentially with one pass through A. */
+
+ if (lsame_(trans, "N", (ftnlen)1, (ftnlen)1)) {
+
+/* Form x := A*x. */
+
+ if (lsame_(uplo, "U", (ftnlen)1, (ftnlen)1)) {
+ kplus1 = *k + 1;
+ if (*incx == 1) {
+ i__1 = *n;
+ for (j = 1; j <= i__1; ++j) {
+ if (x[j] != 0.f) {
+ temp = x[j];
+ l = kplus1 - j;
+/* Computing MAX */
+ i__2 = 1, i__3 = j - *k;
+ i__4 = j - 1;
+ for (i__ = max(i__2,i__3); i__ <= i__4; ++i__) {
+ x[i__] += temp * a[l + i__ + j * a_dim1];
+/* L10: */
+ }
+ if (nounit) {
+ x[j] *= a[kplus1 + j * a_dim1];
+ }
+ }
+/* L20: */
+ }
+ } else {
+ jx = kx;
+ i__1 = *n;
+ for (j = 1; j <= i__1; ++j) {
+ if (x[jx] != 0.f) {
+ temp = x[jx];
+ ix = kx;
+ l = kplus1 - j;
+/* Computing MAX */
+ i__4 = 1, i__2 = j - *k;
+ i__3 = j - 1;
+ for (i__ = max(i__4,i__2); i__ <= i__3; ++i__) {
+ x[ix] += temp * a[l + i__ + j * a_dim1];
+ ix += *incx;
+/* L30: */
+ }
+ if (nounit) {
+ x[jx] *= a[kplus1 + j * a_dim1];
+ }
+ }
+ jx += *incx;
+ if (j > *k) {
+ kx += *incx;
+ }
+/* L40: */
+ }
+ }
+ } else {
+ if (*incx == 1) {
+ for (j = *n; j >= 1; --j) {
+ if (x[j] != 0.f) {
+ temp = x[j];
+ l = 1 - j;
+/* Computing MIN */
+ i__1 = *n, i__3 = j + *k;
+ i__4 = j + 1;
+ for (i__ = min(i__1,i__3); i__ >= i__4; --i__) {
+ x[i__] += temp * a[l + i__ + j * a_dim1];
+/* L50: */
+ }
+ if (nounit) {
+ x[j] *= a[j * a_dim1 + 1];
+ }
+ }
+/* L60: */
+ }
+ } else {
+ kx += (*n - 1) * *incx;
+ jx = kx;
+ for (j = *n; j >= 1; --j) {
+ if (x[jx] != 0.f) {
+ temp = x[jx];
+ ix = kx;
+ l = 1 - j;
+/* Computing MIN */
+ i__4 = *n, i__1 = j + *k;
+ i__3 = j + 1;
+ for (i__ = min(i__4,i__1); i__ >= i__3; --i__) {
+ x[ix] += temp * a[l + i__ + j * a_dim1];
+ ix -= *incx;
+/* L70: */
+ }
+ if (nounit) {
+ x[jx] *= a[j * a_dim1 + 1];
+ }
+ }
+ jx -= *incx;
+ if (*n - j >= *k) {
+ kx -= *incx;
+ }
+/* L80: */
+ }
+ }
+ }
+ } else {
+
+/* Form x := A'*x. */
+
+ if (lsame_(uplo, "U", (ftnlen)1, (ftnlen)1)) {
+ kplus1 = *k + 1;
+ if (*incx == 1) {
+ for (j = *n; j >= 1; --j) {
+ temp = x[j];
+ l = kplus1 - j;
+ if (nounit) {
+ temp *= a[kplus1 + j * a_dim1];
+ }
+/* Computing MAX */
+ i__4 = 1, i__1 = j - *k;
+ i__3 = max(i__4,i__1);
+ for (i__ = j - 1; i__ >= i__3; --i__) {
+ temp += a[l + i__ + j * a_dim1] * x[i__];
+/* L90: */
+ }
+ x[j] = temp;
+/* L100: */
+ }
+ } else {
+ kx += (*n - 1) * *incx;
+ jx = kx;
+ for (j = *n; j >= 1; --j) {
+ temp = x[jx];
+ kx -= *incx;
+ ix = kx;
+ l = kplus1 - j;
+ if (nounit) {
+ temp *= a[kplus1 + j * a_dim1];
+ }
+/* Computing MAX */
+ i__4 = 1, i__1 = j - *k;
+ i__3 = max(i__4,i__1);
+ for (i__ = j - 1; i__ >= i__3; --i__) {
+ temp += a[l + i__ + j * a_dim1] * x[ix];
+ ix -= *incx;
+/* L110: */
+ }
+ x[jx] = temp;
+ jx -= *incx;
+/* L120: */
+ }
+ }
+ } else {
+ if (*incx == 1) {
+ i__3 = *n;
+ for (j = 1; j <= i__3; ++j) {
+ temp = x[j];
+ l = 1 - j;
+ if (nounit) {
+ temp *= a[j * a_dim1 + 1];
+ }
+/* Computing MIN */
+ i__1 = *n, i__2 = j + *k;
+ i__4 = min(i__1,i__2);
+ for (i__ = j + 1; i__ <= i__4; ++i__) {
+ temp += a[l + i__ + j * a_dim1] * x[i__];
+/* L130: */
+ }
+ x[j] = temp;
+/* L140: */
+ }
+ } else {
+ jx = kx;
+ i__3 = *n;
+ for (j = 1; j <= i__3; ++j) {
+ temp = x[jx];
+ kx += *incx;
+ ix = kx;
+ l = 1 - j;
+ if (nounit) {
+ temp *= a[j * a_dim1 + 1];
+ }
+/* Computing MIN */
+ i__1 = *n, i__2 = j + *k;
+ i__4 = min(i__1,i__2);
+ for (i__ = j + 1; i__ <= i__4; ++i__) {
+ temp += a[l + i__ + j * a_dim1] * x[ix];
+ ix += *incx;
+/* L150: */
+ }
+ x[jx] = temp;
+ jx += *incx;
+/* L160: */
+ }
+ }
+ }
+ }
+
+ return 0;
+
+/* End of STBMV . */
+
+} /* stbmv_ */
+
diff --git a/blas/f2c/zhbmv.c b/blas/f2c/zhbmv.c
new file mode 100644
index 0000000..42da13d
--- /dev/null
+++ b/blas/f2c/zhbmv.c
@@ -0,0 +1,488 @@
+/* zhbmv.f -- translated by f2c (version 20100827).
+ You must link the resulting object file with libf2c:
+ on Microsoft Windows system, link with libf2c.lib;
+ on Linux or Unix systems, link with .../path/to/libf2c.a -lm
+ or, if you install libf2c.a in a standard place, with -lf2c -lm
+ -- in that order, at the end of the command line, as in
+ cc *.o -lf2c -lm
+ Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
+
+ http://www.netlib.org/f2c/libf2c.zip
+*/
+
+#include "datatypes.h"
+
+/* Subroutine */ int zhbmv_(char *uplo, integer *n, integer *k, doublecomplex
+ *alpha, doublecomplex *a, integer *lda, doublecomplex *x, integer *
+ incx, doublecomplex *beta, doublecomplex *y, integer *incy, ftnlen
+ uplo_len)
+{
+ /* System generated locals */
+ integer a_dim1, a_offset, i__1, i__2, i__3, i__4, i__5;
+ doublereal d__1;
+ doublecomplex z__1, z__2, z__3, z__4;
+
+ /* Builtin functions */
+ void d_cnjg(doublecomplex *, doublecomplex *);
+
+ /* Local variables */
+ integer i__, j, l, ix, iy, jx, jy, kx, ky, info;
+ doublecomplex temp1, temp2;
+ extern logical lsame_(char *, char *, ftnlen, ftnlen);
+ integer kplus1;
+ extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
+
+/* .. Scalar Arguments .. */
+/* .. */
+/* .. Array Arguments .. */
+/* .. */
+
+/* Purpose */
+/* ======= */
+
+/* ZHBMV performs the matrix-vector operation */
+
+/* y := alpha*A*x + beta*y, */
+
+/* where alpha and beta are scalars, x and y are n element vectors and */
+/* A is an n by n hermitian band matrix, with k super-diagonals. */
+
+/* Arguments */
+/* ========== */
+
+/* UPLO - CHARACTER*1. */
+/* On entry, UPLO specifies whether the upper or lower */
+/* triangular part of the band matrix A is being supplied as */
+/* follows: */
+
+/* UPLO = 'U' or 'u' The upper triangular part of A is */
+/* being supplied. */
+
+/* UPLO = 'L' or 'l' The lower triangular part of A is */
+/* being supplied. */
+
+/* Unchanged on exit. */
+
+/* N - INTEGER. */
+/* On entry, N specifies the order of the matrix A. */
+/* N must be at least zero. */
+/* Unchanged on exit. */
+
+/* K - INTEGER. */
+/* On entry, K specifies the number of super-diagonals of the */
+/* matrix A. K must satisfy 0 .le. K. */
+/* Unchanged on exit. */
+
+/* ALPHA - COMPLEX*16 . */
+/* On entry, ALPHA specifies the scalar alpha. */
+/* Unchanged on exit. */
+
+/* A - COMPLEX*16 array of DIMENSION ( LDA, n ). */
+/* Before entry with UPLO = 'U' or 'u', the leading ( k + 1 ) */
+/* by n part of the array A must contain the upper triangular */
+/* band part of the hermitian matrix, supplied column by */
+/* column, with the leading diagonal of the matrix in row */
+/* ( k + 1 ) of the array, the first super-diagonal starting at */
+/* position 2 in row k, and so on. The top left k by k triangle */
+/* of the array A is not referenced. */
+/* The following program segment will transfer the upper */
+/* triangular part of a hermitian band matrix from conventional */
+/* full matrix storage to band storage: */
+
+/* DO 20, J = 1, N */
+/* M = K + 1 - J */
+/* DO 10, I = MAX( 1, J - K ), J */
+/* A( M + I, J ) = matrix( I, J ) */
+/* 10 CONTINUE */
+/* 20 CONTINUE */
+
+/* Before entry with UPLO = 'L' or 'l', the leading ( k + 1 ) */
+/* by n part of the array A must contain the lower triangular */
+/* band part of the hermitian matrix, supplied column by */
+/* column, with the leading diagonal of the matrix in row 1 of */
+/* the array, the first sub-diagonal starting at position 1 in */
+/* row 2, and so on. The bottom right k by k triangle of the */
+/* array A is not referenced. */
+/* The following program segment will transfer the lower */
+/* triangular part of a hermitian band matrix from conventional */
+/* full matrix storage to band storage: */
+
+/* DO 20, J = 1, N */
+/* M = 1 - J */
+/* DO 10, I = J, MIN( N, J + K ) */
+/* A( M + I, J ) = matrix( I, J ) */
+/* 10 CONTINUE */
+/* 20 CONTINUE */
+
+/* Note that the imaginary parts of the diagonal elements need */
+/* not be set and are assumed to be zero. */
+/* Unchanged on exit. */
+
+/* LDA - INTEGER. */
+/* On entry, LDA specifies the first dimension of A as declared */
+/* in the calling (sub) program. LDA must be at least */
+/* ( k + 1 ). */
+/* Unchanged on exit. */
+
+/* X - COMPLEX*16 array of DIMENSION at least */
+/* ( 1 + ( n - 1 )*abs( INCX ) ). */
+/* Before entry, the incremented array X must contain the */
+/* vector x. */
+/* Unchanged on exit. */
+
+/* INCX - INTEGER. */
+/* On entry, INCX specifies the increment for the elements of */
+/* X. INCX must not be zero. */
+/* Unchanged on exit. */
+
+/* BETA - COMPLEX*16 . */
+/* On entry, BETA specifies the scalar beta. */
+/* Unchanged on exit. */
+
+/* Y - COMPLEX*16 array of DIMENSION at least */
+/* ( 1 + ( n - 1 )*abs( INCY ) ). */
+/* Before entry, the incremented array Y must contain the */
+/* vector y. On exit, Y is overwritten by the updated vector y. */
+
+/* INCY - INTEGER. */
+/* On entry, INCY specifies the increment for the elements of */
+/* Y. INCY must not be zero. */
+/* Unchanged on exit. */
+
+/* Further Details */
+/* =============== */
+
+/* Level 2 Blas routine. */
+
+/* -- Written on 22-October-1986. */
+/* Jack Dongarra, Argonne National Lab. */
+/* Jeremy Du Croz, Nag Central Office. */
+/* Sven Hammarling, Nag Central Office. */
+/* Richard Hanson, Sandia National Labs. */
+
+/* ===================================================================== */
+
+/* .. Parameters .. */
+/* .. */
+/* .. Local Scalars .. */
+/* .. */
+/* .. External Functions .. */
+/* .. */
+/* .. External Subroutines .. */
+/* .. */
+/* .. Intrinsic Functions .. */
+/* .. */
+
+/* Test the input parameters. */
+
+ /* Parameter adjustments */
+ a_dim1 = *lda;
+ a_offset = 1 + a_dim1;
+ a -= a_offset;
+ --x;
+ --y;
+
+ /* Function Body */
+ info = 0;
+ if (! lsame_(uplo, "U", (ftnlen)1, (ftnlen)1) && ! lsame_(uplo, "L", (
+ ftnlen)1, (ftnlen)1)) {
+ info = 1;
+ } else if (*n < 0) {
+ info = 2;
+ } else if (*k < 0) {
+ info = 3;
+ } else if (*lda < *k + 1) {
+ info = 6;
+ } else if (*incx == 0) {
+ info = 8;
+ } else if (*incy == 0) {
+ info = 11;
+ }
+ if (info != 0) {
+ xerbla_("ZHBMV ", &info, (ftnlen)6);
+ return 0;
+ }
+
+/* Quick return if possible. */
+
+ if (*n == 0 || (alpha->r == 0. && alpha->i == 0. && (beta->r == 1. &&
+ beta->i == 0.))) {
+ return 0;
+ }
+
+/* Set up the start points in X and Y. */
+
+ if (*incx > 0) {
+ kx = 1;
+ } else {
+ kx = 1 - (*n - 1) * *incx;
+ }
+ if (*incy > 0) {
+ ky = 1;
+ } else {
+ ky = 1 - (*n - 1) * *incy;
+ }
+
+/* Start the operations. In this version the elements of the array A */
+/* are accessed sequentially with one pass through A. */
+
+/* First form y := beta*y. */
+
+ if (beta->r != 1. || beta->i != 0.) {
+ if (*incy == 1) {
+ if (beta->r == 0. && beta->i == 0.) {
+ i__1 = *n;
+ for (i__ = 1; i__ <= i__1; ++i__) {
+ i__2 = i__;
+ y[i__2].r = 0., y[i__2].i = 0.;
+/* L10: */
+ }
+ } else {
+ i__1 = *n;
+ for (i__ = 1; i__ <= i__1; ++i__) {
+ i__2 = i__;
+ i__3 = i__;
+ z__1.r = beta->r * y[i__3].r - beta->i * y[i__3].i,
+ z__1.i = beta->r * y[i__3].i + beta->i * y[i__3]
+ .r;
+ y[i__2].r = z__1.r, y[i__2].i = z__1.i;
+/* L20: */
+ }
+ }
+ } else {
+ iy = ky;
+ if (beta->r == 0. && beta->i == 0.) {
+ i__1 = *n;
+ for (i__ = 1; i__ <= i__1; ++i__) {
+ i__2 = iy;
+ y[i__2].r = 0., y[i__2].i = 0.;
+ iy += *incy;
+/* L30: */
+ }
+ } else {
+ i__1 = *n;
+ for (i__ = 1; i__ <= i__1; ++i__) {
+ i__2 = iy;
+ i__3 = iy;
+ z__1.r = beta->r * y[i__3].r - beta->i * y[i__3].i,
+ z__1.i = beta->r * y[i__3].i + beta->i * y[i__3]
+ .r;
+ y[i__2].r = z__1.r, y[i__2].i = z__1.i;
+ iy += *incy;
+/* L40: */
+ }
+ }
+ }
+ }
+ if (alpha->r == 0. && alpha->i == 0.) {
+ return 0;
+ }
+ if (lsame_(uplo, "U", (ftnlen)1, (ftnlen)1)) {
+
+/* Form y when upper triangle of A is stored. */
+
+ kplus1 = *k + 1;
+ if (*incx == 1 && *incy == 1) {
+ i__1 = *n;
+ for (j = 1; j <= i__1; ++j) {
+ i__2 = j;
+ z__1.r = alpha->r * x[i__2].r - alpha->i * x[i__2].i, z__1.i =
+ alpha->r * x[i__2].i + alpha->i * x[i__2].r;
+ temp1.r = z__1.r, temp1.i = z__1.i;
+ temp2.r = 0., temp2.i = 0.;
+ l = kplus1 - j;
+/* Computing MAX */
+ i__2 = 1, i__3 = j - *k;
+ i__4 = j - 1;
+ for (i__ = max(i__2,i__3); i__ <= i__4; ++i__) {
+ i__2 = i__;
+ i__3 = i__;
+ i__5 = l + i__ + j * a_dim1;
+ z__2.r = temp1.r * a[i__5].r - temp1.i * a[i__5].i,
+ z__2.i = temp1.r * a[i__5].i + temp1.i * a[i__5]
+ .r;
+ z__1.r = y[i__3].r + z__2.r, z__1.i = y[i__3].i + z__2.i;
+ y[i__2].r = z__1.r, y[i__2].i = z__1.i;
+ d_cnjg(&z__3, &a[l + i__ + j * a_dim1]);
+ i__2 = i__;
+ z__2.r = z__3.r * x[i__2].r - z__3.i * x[i__2].i, z__2.i =
+ z__3.r * x[i__2].i + z__3.i * x[i__2].r;
+ z__1.r = temp2.r + z__2.r, z__1.i = temp2.i + z__2.i;
+ temp2.r = z__1.r, temp2.i = z__1.i;
+/* L50: */
+ }
+ i__4 = j;
+ i__2 = j;
+ i__3 = kplus1 + j * a_dim1;
+ d__1 = a[i__3].r;
+ z__3.r = d__1 * temp1.r, z__3.i = d__1 * temp1.i;
+ z__2.r = y[i__2].r + z__3.r, z__2.i = y[i__2].i + z__3.i;
+ z__4.r = alpha->r * temp2.r - alpha->i * temp2.i, z__4.i =
+ alpha->r * temp2.i + alpha->i * temp2.r;
+ z__1.r = z__2.r + z__4.r, z__1.i = z__2.i + z__4.i;
+ y[i__4].r = z__1.r, y[i__4].i = z__1.i;
+/* L60: */
+ }
+ } else {
+ jx = kx;
+ jy = ky;
+ i__1 = *n;
+ for (j = 1; j <= i__1; ++j) {
+ i__4 = jx;
+ z__1.r = alpha->r * x[i__4].r - alpha->i * x[i__4].i, z__1.i =
+ alpha->r * x[i__4].i + alpha->i * x[i__4].r;
+ temp1.r = z__1.r, temp1.i = z__1.i;
+ temp2.r = 0., temp2.i = 0.;
+ ix = kx;
+ iy = ky;
+ l = kplus1 - j;
+/* Computing MAX */
+ i__4 = 1, i__2 = j - *k;
+ i__3 = j - 1;
+ for (i__ = max(i__4,i__2); i__ <= i__3; ++i__) {
+ i__4 = iy;
+ i__2 = iy;
+ i__5 = l + i__ + j * a_dim1;
+ z__2.r = temp1.r * a[i__5].r - temp1.i * a[i__5].i,
+ z__2.i = temp1.r * a[i__5].i + temp1.i * a[i__5]
+ .r;
+ z__1.r = y[i__2].r + z__2.r, z__1.i = y[i__2].i + z__2.i;
+ y[i__4].r = z__1.r, y[i__4].i = z__1.i;
+ d_cnjg(&z__3, &a[l + i__ + j * a_dim1]);
+ i__4 = ix;
+ z__2.r = z__3.r * x[i__4].r - z__3.i * x[i__4].i, z__2.i =
+ z__3.r * x[i__4].i + z__3.i * x[i__4].r;
+ z__1.r = temp2.r + z__2.r, z__1.i = temp2.i + z__2.i;
+ temp2.r = z__1.r, temp2.i = z__1.i;
+ ix += *incx;
+ iy += *incy;
+/* L70: */
+ }
+ i__3 = jy;
+ i__4 = jy;
+ i__2 = kplus1 + j * a_dim1;
+ d__1 = a[i__2].r;
+ z__3.r = d__1 * temp1.r, z__3.i = d__1 * temp1.i;
+ z__2.r = y[i__4].r + z__3.r, z__2.i = y[i__4].i + z__3.i;
+ z__4.r = alpha->r * temp2.r - alpha->i * temp2.i, z__4.i =
+ alpha->r * temp2.i + alpha->i * temp2.r;
+ z__1.r = z__2.r + z__4.r, z__1.i = z__2.i + z__4.i;
+ y[i__3].r = z__1.r, y[i__3].i = z__1.i;
+ jx += *incx;
+ jy += *incy;
+ if (j > *k) {
+ kx += *incx;
+ ky += *incy;
+ }
+/* L80: */
+ }
+ }
+ } else {
+
+/* Form y when lower triangle of A is stored. */
+
+ if (*incx == 1 && *incy == 1) {
+ i__1 = *n;
+ for (j = 1; j <= i__1; ++j) {
+ i__3 = j;
+ z__1.r = alpha->r * x[i__3].r - alpha->i * x[i__3].i, z__1.i =
+ alpha->r * x[i__3].i + alpha->i * x[i__3].r;
+ temp1.r = z__1.r, temp1.i = z__1.i;
+ temp2.r = 0., temp2.i = 0.;
+ i__3 = j;
+ i__4 = j;
+ i__2 = j * a_dim1 + 1;
+ d__1 = a[i__2].r;
+ z__2.r = d__1 * temp1.r, z__2.i = d__1 * temp1.i;
+ z__1.r = y[i__4].r + z__2.r, z__1.i = y[i__4].i + z__2.i;
+ y[i__3].r = z__1.r, y[i__3].i = z__1.i;
+ l = 1 - j;
+/* Computing MIN */
+ i__4 = *n, i__2 = j + *k;
+ i__3 = min(i__4,i__2);
+ for (i__ = j + 1; i__ <= i__3; ++i__) {
+ i__4 = i__;
+ i__2 = i__;
+ i__5 = l + i__ + j * a_dim1;
+ z__2.r = temp1.r * a[i__5].r - temp1.i * a[i__5].i,
+ z__2.i = temp1.r * a[i__5].i + temp1.i * a[i__5]
+ .r;
+ z__1.r = y[i__2].r + z__2.r, z__1.i = y[i__2].i + z__2.i;
+ y[i__4].r = z__1.r, y[i__4].i = z__1.i;
+ d_cnjg(&z__3, &a[l + i__ + j * a_dim1]);
+ i__4 = i__;
+ z__2.r = z__3.r * x[i__4].r - z__3.i * x[i__4].i, z__2.i =
+ z__3.r * x[i__4].i + z__3.i * x[i__4].r;
+ z__1.r = temp2.r + z__2.r, z__1.i = temp2.i + z__2.i;
+ temp2.r = z__1.r, temp2.i = z__1.i;
+/* L90: */
+ }
+ i__3 = j;
+ i__4 = j;
+ z__2.r = alpha->r * temp2.r - alpha->i * temp2.i, z__2.i =
+ alpha->r * temp2.i + alpha->i * temp2.r;
+ z__1.r = y[i__4].r + z__2.r, z__1.i = y[i__4].i + z__2.i;
+ y[i__3].r = z__1.r, y[i__3].i = z__1.i;
+/* L100: */
+ }
+ } else {
+ jx = kx;
+ jy = ky;
+ i__1 = *n;
+ for (j = 1; j <= i__1; ++j) {
+ i__3 = jx;
+ z__1.r = alpha->r * x[i__3].r - alpha->i * x[i__3].i, z__1.i =
+ alpha->r * x[i__3].i + alpha->i * x[i__3].r;
+ temp1.r = z__1.r, temp1.i = z__1.i;
+ temp2.r = 0., temp2.i = 0.;
+ i__3 = jy;
+ i__4 = jy;
+ i__2 = j * a_dim1 + 1;
+ d__1 = a[i__2].r;
+ z__2.r = d__1 * temp1.r, z__2.i = d__1 * temp1.i;
+ z__1.r = y[i__4].r + z__2.r, z__1.i = y[i__4].i + z__2.i;
+ y[i__3].r = z__1.r, y[i__3].i = z__1.i;
+ l = 1 - j;
+ ix = jx;
+ iy = jy;
+/* Computing MIN */
+ i__4 = *n, i__2 = j + *k;
+ i__3 = min(i__4,i__2);
+ for (i__ = j + 1; i__ <= i__3; ++i__) {
+ ix += *incx;
+ iy += *incy;
+ i__4 = iy;
+ i__2 = iy;
+ i__5 = l + i__ + j * a_dim1;
+ z__2.r = temp1.r * a[i__5].r - temp1.i * a[i__5].i,
+ z__2.i = temp1.r * a[i__5].i + temp1.i * a[i__5]
+ .r;
+ z__1.r = y[i__2].r + z__2.r, z__1.i = y[i__2].i + z__2.i;
+ y[i__4].r = z__1.r, y[i__4].i = z__1.i;
+ d_cnjg(&z__3, &a[l + i__ + j * a_dim1]);
+ i__4 = ix;
+ z__2.r = z__3.r * x[i__4].r - z__3.i * x[i__4].i, z__2.i =
+ z__3.r * x[i__4].i + z__3.i * x[i__4].r;
+ z__1.r = temp2.r + z__2.r, z__1.i = temp2.i + z__2.i;
+ temp2.r = z__1.r, temp2.i = z__1.i;
+/* L110: */
+ }
+ i__3 = jy;
+ i__4 = jy;
+ z__2.r = alpha->r * temp2.r - alpha->i * temp2.i, z__2.i =
+ alpha->r * temp2.i + alpha->i * temp2.r;
+ z__1.r = y[i__4].r + z__2.r, z__1.i = y[i__4].i + z__2.i;
+ y[i__3].r = z__1.r, y[i__3].i = z__1.i;
+ jx += *incx;
+ jy += *incy;
+/* L120: */
+ }
+ }
+ }
+
+ return 0;
+
+/* End of ZHBMV . */
+
+} /* zhbmv_ */
+
diff --git a/blas/f2c/zhpmv.c b/blas/f2c/zhpmv.c
new file mode 100644
index 0000000..fbe2f42
--- /dev/null
+++ b/blas/f2c/zhpmv.c
@@ -0,0 +1,438 @@
+/* zhpmv.f -- translated by f2c (version 20100827).
+ You must link the resulting object file with libf2c:
+ on Microsoft Windows system, link with libf2c.lib;
+ on Linux or Unix systems, link with .../path/to/libf2c.a -lm
+ or, if you install libf2c.a in a standard place, with -lf2c -lm
+ -- in that order, at the end of the command line, as in
+ cc *.o -lf2c -lm
+ Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
+
+ http://www.netlib.org/f2c/libf2c.zip
+*/
+
+#include "datatypes.h"
+
+/* Subroutine */ int zhpmv_(char *uplo, integer *n, doublecomplex *alpha,
+ doublecomplex *ap, doublecomplex *x, integer *incx, doublecomplex *
+ beta, doublecomplex *y, integer *incy, ftnlen uplo_len)
+{
+ /* System generated locals */
+ integer i__1, i__2, i__3, i__4, i__5;
+ doublereal d__1;
+ doublecomplex z__1, z__2, z__3, z__4;
+
+ /* Builtin functions */
+ void d_cnjg(doublecomplex *, doublecomplex *);
+
+ /* Local variables */
+ integer i__, j, k, kk, ix, iy, jx, jy, kx, ky, info;
+ doublecomplex temp1, temp2;
+ extern logical lsame_(char *, char *, ftnlen, ftnlen);
+ extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
+
+/* .. Scalar Arguments .. */
+/* .. */
+/* .. Array Arguments .. */
+/* .. */
+
+/* Purpose */
+/* ======= */
+
+/* ZHPMV performs the matrix-vector operation */
+
+/* y := alpha*A*x + beta*y, */
+
+/* where alpha and beta are scalars, x and y are n element vectors and */
+/* A is an n by n hermitian matrix, supplied in packed form. */
+
+/* Arguments */
+/* ========== */
+
+/* UPLO - CHARACTER*1. */
+/* On entry, UPLO specifies whether the upper or lower */
+/* triangular part of the matrix A is supplied in the packed */
+/* array AP as follows: */
+
+/* UPLO = 'U' or 'u' The upper triangular part of A is */
+/* supplied in AP. */
+
+/* UPLO = 'L' or 'l' The lower triangular part of A is */
+/* supplied in AP. */
+
+/* Unchanged on exit. */
+
+/* N - INTEGER. */
+/* On entry, N specifies the order of the matrix A. */
+/* N must be at least zero. */
+/* Unchanged on exit. */
+
+/* ALPHA - COMPLEX*16 . */
+/* On entry, ALPHA specifies the scalar alpha. */
+/* Unchanged on exit. */
+
+/* AP - COMPLEX*16 array of DIMENSION at least */
+/* ( ( n*( n + 1 ) )/2 ). */
+/* Before entry with UPLO = 'U' or 'u', the array AP must */
+/* contain the upper triangular part of the hermitian matrix */
+/* packed sequentially, column by column, so that AP( 1 ) */
+/* contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 ) */
+/* and a( 2, 2 ) respectively, and so on. */
+/* Before entry with UPLO = 'L' or 'l', the array AP must */
+/* contain the lower triangular part of the hermitian matrix */
+/* packed sequentially, column by column, so that AP( 1 ) */
+/* contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 ) */
+/* and a( 3, 1 ) respectively, and so on. */
+/* Note that the imaginary parts of the diagonal elements need */
+/* not be set and are assumed to be zero. */
+/* Unchanged on exit. */
+
+/* X - COMPLEX*16 array of dimension at least */
+/* ( 1 + ( n - 1 )*abs( INCX ) ). */
+/* Before entry, the incremented array X must contain the n */
+/* element vector x. */
+/* Unchanged on exit. */
+
+/* INCX - INTEGER. */
+/* On entry, INCX specifies the increment for the elements of */
+/* X. INCX must not be zero. */
+/* Unchanged on exit. */
+
+/* BETA - COMPLEX*16 . */
+/* On entry, BETA specifies the scalar beta. When BETA is */
+/* supplied as zero then Y need not be set on input. */
+/* Unchanged on exit. */
+
+/* Y - COMPLEX*16 array of dimension at least */
+/* ( 1 + ( n - 1 )*abs( INCY ) ). */
+/* Before entry, the incremented array Y must contain the n */
+/* element vector y. On exit, Y is overwritten by the updated */
+/* vector y. */
+
+/* INCY - INTEGER. */
+/* On entry, INCY specifies the increment for the elements of */
+/* Y. INCY must not be zero. */
+/* Unchanged on exit. */
+
+/* Further Details */
+/* =============== */
+
+/* Level 2 Blas routine. */
+
+/* -- Written on 22-October-1986. */
+/* Jack Dongarra, Argonne National Lab. */
+/* Jeremy Du Croz, Nag Central Office. */
+/* Sven Hammarling, Nag Central Office. */
+/* Richard Hanson, Sandia National Labs. */
+
+/* ===================================================================== */
+
+/* .. Parameters .. */
+/* .. */
+/* .. Local Scalars .. */
+/* .. */
+/* .. External Functions .. */
+/* .. */
+/* .. External Subroutines .. */
+/* .. */
+/* .. Intrinsic Functions .. */
+/* .. */
+
+/* Test the input parameters. */
+
+ /* Parameter adjustments */
+ --y;
+ --x;
+ --ap;
+
+ /* Function Body */
+ info = 0;
+ if (! lsame_(uplo, "U", (ftnlen)1, (ftnlen)1) && ! lsame_(uplo, "L", (
+ ftnlen)1, (ftnlen)1)) {
+ info = 1;
+ } else if (*n < 0) {
+ info = 2;
+ } else if (*incx == 0) {
+ info = 6;
+ } else if (*incy == 0) {
+ info = 9;
+ }
+ if (info != 0) {
+ xerbla_("ZHPMV ", &info, (ftnlen)6);
+ return 0;
+ }
+
+/* Quick return if possible. */
+
+ if (*n == 0 || (alpha->r == 0. && alpha->i == 0. && (beta->r == 1. &&
+ beta->i == 0.))) {
+ return 0;
+ }
+
+/* Set up the start points in X and Y. */
+
+ if (*incx > 0) {
+ kx = 1;
+ } else {
+ kx = 1 - (*n - 1) * *incx;
+ }
+ if (*incy > 0) {
+ ky = 1;
+ } else {
+ ky = 1 - (*n - 1) * *incy;
+ }
+
+/* Start the operations. In this version the elements of the array AP */
+/* are accessed sequentially with one pass through AP. */
+
+/* First form y := beta*y. */
+
+ if (beta->r != 1. || beta->i != 0.) {
+ if (*incy == 1) {
+ if (beta->r == 0. && beta->i == 0.) {
+ i__1 = *n;
+ for (i__ = 1; i__ <= i__1; ++i__) {
+ i__2 = i__;
+ y[i__2].r = 0., y[i__2].i = 0.;
+/* L10: */
+ }
+ } else {
+ i__1 = *n;
+ for (i__ = 1; i__ <= i__1; ++i__) {
+ i__2 = i__;
+ i__3 = i__;
+ z__1.r = beta->r * y[i__3].r - beta->i * y[i__3].i,
+ z__1.i = beta->r * y[i__3].i + beta->i * y[i__3]
+ .r;
+ y[i__2].r = z__1.r, y[i__2].i = z__1.i;
+/* L20: */
+ }
+ }
+ } else {
+ iy = ky;
+ if (beta->r == 0. && beta->i == 0.) {
+ i__1 = *n;
+ for (i__ = 1; i__ <= i__1; ++i__) {
+ i__2 = iy;
+ y[i__2].r = 0., y[i__2].i = 0.;
+ iy += *incy;
+/* L30: */
+ }
+ } else {
+ i__1 = *n;
+ for (i__ = 1; i__ <= i__1; ++i__) {
+ i__2 = iy;
+ i__3 = iy;
+ z__1.r = beta->r * y[i__3].r - beta->i * y[i__3].i,
+ z__1.i = beta->r * y[i__3].i + beta->i * y[i__3]
+ .r;
+ y[i__2].r = z__1.r, y[i__2].i = z__1.i;
+ iy += *incy;
+/* L40: */
+ }
+ }
+ }
+ }
+ if (alpha->r == 0. && alpha->i == 0.) {
+ return 0;
+ }
+ kk = 1;
+ if (lsame_(uplo, "U", (ftnlen)1, (ftnlen)1)) {
+
+/* Form y when AP contains the upper triangle. */
+
+ if (*incx == 1 && *incy == 1) {
+ i__1 = *n;
+ for (j = 1; j <= i__1; ++j) {
+ i__2 = j;
+ z__1.r = alpha->r * x[i__2].r - alpha->i * x[i__2].i, z__1.i =
+ alpha->r * x[i__2].i + alpha->i * x[i__2].r;
+ temp1.r = z__1.r, temp1.i = z__1.i;
+ temp2.r = 0., temp2.i = 0.;
+ k = kk;
+ i__2 = j - 1;
+ for (i__ = 1; i__ <= i__2; ++i__) {
+ i__3 = i__;
+ i__4 = i__;
+ i__5 = k;
+ z__2.r = temp1.r * ap[i__5].r - temp1.i * ap[i__5].i,
+ z__2.i = temp1.r * ap[i__5].i + temp1.i * ap[i__5]
+ .r;
+ z__1.r = y[i__4].r + z__2.r, z__1.i = y[i__4].i + z__2.i;
+ y[i__3].r = z__1.r, y[i__3].i = z__1.i;
+ d_cnjg(&z__3, &ap[k]);
+ i__3 = i__;
+ z__2.r = z__3.r * x[i__3].r - z__3.i * x[i__3].i, z__2.i =
+ z__3.r * x[i__3].i + z__3.i * x[i__3].r;
+ z__1.r = temp2.r + z__2.r, z__1.i = temp2.i + z__2.i;
+ temp2.r = z__1.r, temp2.i = z__1.i;
+ ++k;
+/* L50: */
+ }
+ i__2 = j;
+ i__3 = j;
+ i__4 = kk + j - 1;
+ d__1 = ap[i__4].r;
+ z__3.r = d__1 * temp1.r, z__3.i = d__1 * temp1.i;
+ z__2.r = y[i__3].r + z__3.r, z__2.i = y[i__3].i + z__3.i;
+ z__4.r = alpha->r * temp2.r - alpha->i * temp2.i, z__4.i =
+ alpha->r * temp2.i + alpha->i * temp2.r;
+ z__1.r = z__2.r + z__4.r, z__1.i = z__2.i + z__4.i;
+ y[i__2].r = z__1.r, y[i__2].i = z__1.i;
+ kk += j;
+/* L60: */
+ }
+ } else {
+ jx = kx;
+ jy = ky;
+ i__1 = *n;
+ for (j = 1; j <= i__1; ++j) {
+ i__2 = jx;
+ z__1.r = alpha->r * x[i__2].r - alpha->i * x[i__2].i, z__1.i =
+ alpha->r * x[i__2].i + alpha->i * x[i__2].r;
+ temp1.r = z__1.r, temp1.i = z__1.i;
+ temp2.r = 0., temp2.i = 0.;
+ ix = kx;
+ iy = ky;
+ i__2 = kk + j - 2;
+ for (k = kk; k <= i__2; ++k) {
+ i__3 = iy;
+ i__4 = iy;
+ i__5 = k;
+ z__2.r = temp1.r * ap[i__5].r - temp1.i * ap[i__5].i,
+ z__2.i = temp1.r * ap[i__5].i + temp1.i * ap[i__5]
+ .r;
+ z__1.r = y[i__4].r + z__2.r, z__1.i = y[i__4].i + z__2.i;
+ y[i__3].r = z__1.r, y[i__3].i = z__1.i;
+ d_cnjg(&z__3, &ap[k]);
+ i__3 = ix;
+ z__2.r = z__3.r * x[i__3].r - z__3.i * x[i__3].i, z__2.i =
+ z__3.r * x[i__3].i + z__3.i * x[i__3].r;
+ z__1.r = temp2.r + z__2.r, z__1.i = temp2.i + z__2.i;
+ temp2.r = z__1.r, temp2.i = z__1.i;
+ ix += *incx;
+ iy += *incy;
+/* L70: */
+ }
+ i__2 = jy;
+ i__3 = jy;
+ i__4 = kk + j - 1;
+ d__1 = ap[i__4].r;
+ z__3.r = d__1 * temp1.r, z__3.i = d__1 * temp1.i;
+ z__2.r = y[i__3].r + z__3.r, z__2.i = y[i__3].i + z__3.i;
+ z__4.r = alpha->r * temp2.r - alpha->i * temp2.i, z__4.i =
+ alpha->r * temp2.i + alpha->i * temp2.r;
+ z__1.r = z__2.r + z__4.r, z__1.i = z__2.i + z__4.i;
+ y[i__2].r = z__1.r, y[i__2].i = z__1.i;
+ jx += *incx;
+ jy += *incy;
+ kk += j;
+/* L80: */
+ }
+ }
+ } else {
+
+/* Form y when AP contains the lower triangle. */
+
+ if (*incx == 1 && *incy == 1) {
+ i__1 = *n;
+ for (j = 1; j <= i__1; ++j) {
+ i__2 = j;
+ z__1.r = alpha->r * x[i__2].r - alpha->i * x[i__2].i, z__1.i =
+ alpha->r * x[i__2].i + alpha->i * x[i__2].r;
+ temp1.r = z__1.r, temp1.i = z__1.i;
+ temp2.r = 0., temp2.i = 0.;
+ i__2 = j;
+ i__3 = j;
+ i__4 = kk;
+ d__1 = ap[i__4].r;
+ z__2.r = d__1 * temp1.r, z__2.i = d__1 * temp1.i;
+ z__1.r = y[i__3].r + z__2.r, z__1.i = y[i__3].i + z__2.i;
+ y[i__2].r = z__1.r, y[i__2].i = z__1.i;
+ k = kk + 1;
+ i__2 = *n;
+ for (i__ = j + 1; i__ <= i__2; ++i__) {
+ i__3 = i__;
+ i__4 = i__;
+ i__5 = k;
+ z__2.r = temp1.r * ap[i__5].r - temp1.i * ap[i__5].i,
+ z__2.i = temp1.r * ap[i__5].i + temp1.i * ap[i__5]
+ .r;
+ z__1.r = y[i__4].r + z__2.r, z__1.i = y[i__4].i + z__2.i;
+ y[i__3].r = z__1.r, y[i__3].i = z__1.i;
+ d_cnjg(&z__3, &ap[k]);
+ i__3 = i__;
+ z__2.r = z__3.r * x[i__3].r - z__3.i * x[i__3].i, z__2.i =
+ z__3.r * x[i__3].i + z__3.i * x[i__3].r;
+ z__1.r = temp2.r + z__2.r, z__1.i = temp2.i + z__2.i;
+ temp2.r = z__1.r, temp2.i = z__1.i;
+ ++k;
+/* L90: */
+ }
+ i__2 = j;
+ i__3 = j;
+ z__2.r = alpha->r * temp2.r - alpha->i * temp2.i, z__2.i =
+ alpha->r * temp2.i + alpha->i * temp2.r;
+ z__1.r = y[i__3].r + z__2.r, z__1.i = y[i__3].i + z__2.i;
+ y[i__2].r = z__1.r, y[i__2].i = z__1.i;
+ kk += *n - j + 1;
+/* L100: */
+ }
+ } else {
+ jx = kx;
+ jy = ky;
+ i__1 = *n;
+ for (j = 1; j <= i__1; ++j) {
+ i__2 = jx;
+ z__1.r = alpha->r * x[i__2].r - alpha->i * x[i__2].i, z__1.i =
+ alpha->r * x[i__2].i + alpha->i * x[i__2].r;
+ temp1.r = z__1.r, temp1.i = z__1.i;
+ temp2.r = 0., temp2.i = 0.;
+ i__2 = jy;
+ i__3 = jy;
+ i__4 = kk;
+ d__1 = ap[i__4].r;
+ z__2.r = d__1 * temp1.r, z__2.i = d__1 * temp1.i;
+ z__1.r = y[i__3].r + z__2.r, z__1.i = y[i__3].i + z__2.i;
+ y[i__2].r = z__1.r, y[i__2].i = z__1.i;
+ ix = jx;
+ iy = jy;
+ i__2 = kk + *n - j;
+ for (k = kk + 1; k <= i__2; ++k) {
+ ix += *incx;
+ iy += *incy;
+ i__3 = iy;
+ i__4 = iy;
+ i__5 = k;
+ z__2.r = temp1.r * ap[i__5].r - temp1.i * ap[i__5].i,
+ z__2.i = temp1.r * ap[i__5].i + temp1.i * ap[i__5]
+ .r;
+ z__1.r = y[i__4].r + z__2.r, z__1.i = y[i__4].i + z__2.i;
+ y[i__3].r = z__1.r, y[i__3].i = z__1.i;
+ d_cnjg(&z__3, &ap[k]);
+ i__3 = ix;
+ z__2.r = z__3.r * x[i__3].r - z__3.i * x[i__3].i, z__2.i =
+ z__3.r * x[i__3].i + z__3.i * x[i__3].r;
+ z__1.r = temp2.r + z__2.r, z__1.i = temp2.i + z__2.i;
+ temp2.r = z__1.r, temp2.i = z__1.i;
+/* L110: */
+ }
+ i__2 = jy;
+ i__3 = jy;
+ z__2.r = alpha->r * temp2.r - alpha->i * temp2.i, z__2.i =
+ alpha->r * temp2.i + alpha->i * temp2.r;
+ z__1.r = y[i__3].r + z__2.r, z__1.i = y[i__3].i + z__2.i;
+ y[i__2].r = z__1.r, y[i__2].i = z__1.i;
+ jx += *incx;
+ jy += *incy;
+ kk += *n - j + 1;
+/* L120: */
+ }
+ }
+ }
+
+ return 0;
+
+/* End of ZHPMV . */
+
+} /* zhpmv_ */
+
diff --git a/blas/f2c/ztbmv.c b/blas/f2c/ztbmv.c
new file mode 100644
index 0000000..3bf0beb
--- /dev/null
+++ b/blas/f2c/ztbmv.c
@@ -0,0 +1,647 @@
+/* ztbmv.f -- translated by f2c (version 20100827).
+ You must link the resulting object file with libf2c:
+ on Microsoft Windows system, link with libf2c.lib;
+ on Linux or Unix systems, link with .../path/to/libf2c.a -lm
+ or, if you install libf2c.a in a standard place, with -lf2c -lm
+ -- in that order, at the end of the command line, as in
+ cc *.o -lf2c -lm
+ Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
+
+ http://www.netlib.org/f2c/libf2c.zip
+*/
+
+#include "datatypes.h"
+
+/* Subroutine */ int ztbmv_(char *uplo, char *trans, char *diag, integer *n,
+ integer *k, doublecomplex *a, integer *lda, doublecomplex *x, integer
+ *incx, ftnlen uplo_len, ftnlen trans_len, ftnlen diag_len)
+{
+ /* System generated locals */
+ integer a_dim1, a_offset, i__1, i__2, i__3, i__4, i__5;
+ doublecomplex z__1, z__2, z__3;
+
+ /* Builtin functions */
+ void d_cnjg(doublecomplex *, doublecomplex *);
+
+ /* Local variables */
+ integer i__, j, l, ix, jx, kx, info;
+ doublecomplex temp;
+ extern logical lsame_(char *, char *, ftnlen, ftnlen);
+ integer kplus1;
+ extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
+ logical noconj, nounit;
+
+/* .. Scalar Arguments .. */
+/* .. */
+/* .. Array Arguments .. */
+/* .. */
+
+/* Purpose */
+/* ======= */
+
+/* ZTBMV performs one of the matrix-vector operations */
+
+/* x := A*x, or x := A'*x, or x := conjg( A' )*x, */
+
+/* where x is an n element vector and A is an n by n unit, or non-unit, */
+/* upper or lower triangular band matrix, with ( k + 1 ) diagonals. */
+
+/* Arguments */
+/* ========== */
+
+/* UPLO - CHARACTER*1. */
+/* On entry, UPLO specifies whether the matrix is an upper or */
+/* lower triangular matrix as follows: */
+
+/* UPLO = 'U' or 'u' A is an upper triangular matrix. */
+
+/* UPLO = 'L' or 'l' A is a lower triangular matrix. */
+
+/* Unchanged on exit. */
+
+/* TRANS - CHARACTER*1. */
+/* On entry, TRANS specifies the operation to be performed as */
+/* follows: */
+
+/* TRANS = 'N' or 'n' x := A*x. */
+
+/* TRANS = 'T' or 't' x := A'*x. */
+
+/* TRANS = 'C' or 'c' x := conjg( A' )*x. */
+
+/* Unchanged on exit. */
+
+/* DIAG - CHARACTER*1. */
+/* On entry, DIAG specifies whether or not A is unit */
+/* triangular as follows: */
+
+/* DIAG = 'U' or 'u' A is assumed to be unit triangular. */
+
+/* DIAG = 'N' or 'n' A is not assumed to be unit */
+/* triangular. */
+
+/* Unchanged on exit. */
+
+/* N - INTEGER. */
+/* On entry, N specifies the order of the matrix A. */
+/* N must be at least zero. */
+/* Unchanged on exit. */
+
+/* K - INTEGER. */
+/* On entry with UPLO = 'U' or 'u', K specifies the number of */
+/* super-diagonals of the matrix A. */
+/* On entry with UPLO = 'L' or 'l', K specifies the number of */
+/* sub-diagonals of the matrix A. */
+/* K must satisfy 0 .le. K. */
+/* Unchanged on exit. */
+
+/* A - COMPLEX*16 array of DIMENSION ( LDA, n ). */
+/* Before entry with UPLO = 'U' or 'u', the leading ( k + 1 ) */
+/* by n part of the array A must contain the upper triangular */
+/* band part of the matrix of coefficients, supplied column by */
+/* column, with the leading diagonal of the matrix in row */
+/* ( k + 1 ) of the array, the first super-diagonal starting at */
+/* position 2 in row k, and so on. The top left k by k triangle */
+/* of the array A is not referenced. */
+/* The following program segment will transfer an upper */
+/* triangular band matrix from conventional full matrix storage */
+/* to band storage: */
+
+/* DO 20, J = 1, N */
+/* M = K + 1 - J */
+/* DO 10, I = MAX( 1, J - K ), J */
+/* A( M + I, J ) = matrix( I, J ) */
+/* 10 CONTINUE */
+/* 20 CONTINUE */
+
+/* Before entry with UPLO = 'L' or 'l', the leading ( k + 1 ) */
+/* by n part of the array A must contain the lower triangular */
+/* band part of the matrix of coefficients, supplied column by */
+/* column, with the leading diagonal of the matrix in row 1 of */
+/* the array, the first sub-diagonal starting at position 1 in */
+/* row 2, and so on. The bottom right k by k triangle of the */
+/* array A is not referenced. */
+/* The following program segment will transfer a lower */
+/* triangular band matrix from conventional full matrix storage */
+/* to band storage: */
+
+/* DO 20, J = 1, N */
+/* M = 1 - J */
+/* DO 10, I = J, MIN( N, J + K ) */
+/* A( M + I, J ) = matrix( I, J ) */
+/* 10 CONTINUE */
+/* 20 CONTINUE */
+
+/* Note that when DIAG = 'U' or 'u' the elements of the array A */
+/* corresponding to the diagonal elements of the matrix are not */
+/* referenced, but are assumed to be unity. */
+/* Unchanged on exit. */
+
+/* LDA - INTEGER. */
+/* On entry, LDA specifies the first dimension of A as declared */
+/* in the calling (sub) program. LDA must be at least */
+/* ( k + 1 ). */
+/* Unchanged on exit. */
+
+/* X - COMPLEX*16 array of dimension at least */
+/* ( 1 + ( n - 1 )*abs( INCX ) ). */
+/* Before entry, the incremented array X must contain the n */
+/* element vector x. On exit, X is overwritten with the */
+/* transformed vector x. */
+
+/* INCX - INTEGER. */
+/* On entry, INCX specifies the increment for the elements of */
+/* X. INCX must not be zero. */
+/* Unchanged on exit. */
+
+/* Further Details */
+/* =============== */
+
+/* Level 2 Blas routine. */
+
+/* -- Written on 22-October-1986. */
+/* Jack Dongarra, Argonne National Lab. */
+/* Jeremy Du Croz, Nag Central Office. */
+/* Sven Hammarling, Nag Central Office. */
+/* Richard Hanson, Sandia National Labs. */
+
+/* ===================================================================== */
+
+/* .. Parameters .. */
+/* .. */
+/* .. Local Scalars .. */
+/* .. */
+/* .. External Functions .. */
+/* .. */
+/* .. External Subroutines .. */
+/* .. */
+/* .. Intrinsic Functions .. */
+/* .. */
+
+/* Test the input parameters. */
+
+ /* Parameter adjustments */
+ a_dim1 = *lda;
+ a_offset = 1 + a_dim1;
+ a -= a_offset;
+ --x;
+
+ /* Function Body */
+ info = 0;
+ if (! lsame_(uplo, "U", (ftnlen)1, (ftnlen)1) && ! lsame_(uplo, "L", (
+ ftnlen)1, (ftnlen)1)) {
+ info = 1;
+ } else if (! lsame_(trans, "N", (ftnlen)1, (ftnlen)1) && ! lsame_(trans,
+ "T", (ftnlen)1, (ftnlen)1) && ! lsame_(trans, "C", (ftnlen)1, (
+ ftnlen)1)) {
+ info = 2;
+ } else if (! lsame_(diag, "U", (ftnlen)1, (ftnlen)1) && ! lsame_(diag,
+ "N", (ftnlen)1, (ftnlen)1)) {
+ info = 3;
+ } else if (*n < 0) {
+ info = 4;
+ } else if (*k < 0) {
+ info = 5;
+ } else if (*lda < *k + 1) {
+ info = 7;
+ } else if (*incx == 0) {
+ info = 9;
+ }
+ if (info != 0) {
+ xerbla_("ZTBMV ", &info, (ftnlen)6);
+ return 0;
+ }
+
+/* Quick return if possible. */
+
+ if (*n == 0) {
+ return 0;
+ }
+
+ noconj = lsame_(trans, "T", (ftnlen)1, (ftnlen)1);
+ nounit = lsame_(diag, "N", (ftnlen)1, (ftnlen)1);
+
+/* Set up the start point in X if the increment is not unity. This */
+/* will be ( N - 1 )*INCX too small for descending loops. */
+
+ if (*incx <= 0) {
+ kx = 1 - (*n - 1) * *incx;
+ } else if (*incx != 1) {
+ kx = 1;
+ }
+
+/* Start the operations. In this version the elements of A are */
+/* accessed sequentially with one pass through A. */
+
+ if (lsame_(trans, "N", (ftnlen)1, (ftnlen)1)) {
+
+/* Form x := A*x. */
+
+ if (lsame_(uplo, "U", (ftnlen)1, (ftnlen)1)) {
+ kplus1 = *k + 1;
+ if (*incx == 1) {
+ i__1 = *n;
+ for (j = 1; j <= i__1; ++j) {
+ i__2 = j;
+ if (x[i__2].r != 0. || x[i__2].i != 0.) {
+ i__2 = j;
+ temp.r = x[i__2].r, temp.i = x[i__2].i;
+ l = kplus1 - j;
+/* Computing MAX */
+ i__2 = 1, i__3 = j - *k;
+ i__4 = j - 1;
+ for (i__ = max(i__2,i__3); i__ <= i__4; ++i__) {
+ i__2 = i__;
+ i__3 = i__;
+ i__5 = l + i__ + j * a_dim1;
+ z__2.r = temp.r * a[i__5].r - temp.i * a[i__5].i,
+ z__2.i = temp.r * a[i__5].i + temp.i * a[
+ i__5].r;
+ z__1.r = x[i__3].r + z__2.r, z__1.i = x[i__3].i +
+ z__2.i;
+ x[i__2].r = z__1.r, x[i__2].i = z__1.i;
+/* L10: */
+ }
+ if (nounit) {
+ i__4 = j;
+ i__2 = j;
+ i__3 = kplus1 + j * a_dim1;
+ z__1.r = x[i__2].r * a[i__3].r - x[i__2].i * a[
+ i__3].i, z__1.i = x[i__2].r * a[i__3].i +
+ x[i__2].i * a[i__3].r;
+ x[i__4].r = z__1.r, x[i__4].i = z__1.i;
+ }
+ }
+/* L20: */
+ }
+ } else {
+ jx = kx;
+ i__1 = *n;
+ for (j = 1; j <= i__1; ++j) {
+ i__4 = jx;
+ if (x[i__4].r != 0. || x[i__4].i != 0.) {
+ i__4 = jx;
+ temp.r = x[i__4].r, temp.i = x[i__4].i;
+ ix = kx;
+ l = kplus1 - j;
+/* Computing MAX */
+ i__4 = 1, i__2 = j - *k;
+ i__3 = j - 1;
+ for (i__ = max(i__4,i__2); i__ <= i__3; ++i__) {
+ i__4 = ix;
+ i__2 = ix;
+ i__5 = l + i__ + j * a_dim1;
+ z__2.r = temp.r * a[i__5].r - temp.i * a[i__5].i,
+ z__2.i = temp.r * a[i__5].i + temp.i * a[
+ i__5].r;
+ z__1.r = x[i__2].r + z__2.r, z__1.i = x[i__2].i +
+ z__2.i;
+ x[i__4].r = z__1.r, x[i__4].i = z__1.i;
+ ix += *incx;
+/* L30: */
+ }
+ if (nounit) {
+ i__3 = jx;
+ i__4 = jx;
+ i__2 = kplus1 + j * a_dim1;
+ z__1.r = x[i__4].r * a[i__2].r - x[i__4].i * a[
+ i__2].i, z__1.i = x[i__4].r * a[i__2].i +
+ x[i__4].i * a[i__2].r;
+ x[i__3].r = z__1.r, x[i__3].i = z__1.i;
+ }
+ }
+ jx += *incx;
+ if (j > *k) {
+ kx += *incx;
+ }
+/* L40: */
+ }
+ }
+ } else {
+ if (*incx == 1) {
+ for (j = *n; j >= 1; --j) {
+ i__1 = j;
+ if (x[i__1].r != 0. || x[i__1].i != 0.) {
+ i__1 = j;
+ temp.r = x[i__1].r, temp.i = x[i__1].i;
+ l = 1 - j;
+/* Computing MIN */
+ i__1 = *n, i__3 = j + *k;
+ i__4 = j + 1;
+ for (i__ = min(i__1,i__3); i__ >= i__4; --i__) {
+ i__1 = i__;
+ i__3 = i__;
+ i__2 = l + i__ + j * a_dim1;
+ z__2.r = temp.r * a[i__2].r - temp.i * a[i__2].i,
+ z__2.i = temp.r * a[i__2].i + temp.i * a[
+ i__2].r;
+ z__1.r = x[i__3].r + z__2.r, z__1.i = x[i__3].i +
+ z__2.i;
+ x[i__1].r = z__1.r, x[i__1].i = z__1.i;
+/* L50: */
+ }
+ if (nounit) {
+ i__4 = j;
+ i__1 = j;
+ i__3 = j * a_dim1 + 1;
+ z__1.r = x[i__1].r * a[i__3].r - x[i__1].i * a[
+ i__3].i, z__1.i = x[i__1].r * a[i__3].i +
+ x[i__1].i * a[i__3].r;
+ x[i__4].r = z__1.r, x[i__4].i = z__1.i;
+ }
+ }
+/* L60: */
+ }
+ } else {
+ kx += (*n - 1) * *incx;
+ jx = kx;
+ for (j = *n; j >= 1; --j) {
+ i__4 = jx;
+ if (x[i__4].r != 0. || x[i__4].i != 0.) {
+ i__4 = jx;
+ temp.r = x[i__4].r, temp.i = x[i__4].i;
+ ix = kx;
+ l = 1 - j;
+/* Computing MIN */
+ i__4 = *n, i__1 = j + *k;
+ i__3 = j + 1;
+ for (i__ = min(i__4,i__1); i__ >= i__3; --i__) {
+ i__4 = ix;
+ i__1 = ix;
+ i__2 = l + i__ + j * a_dim1;
+ z__2.r = temp.r * a[i__2].r - temp.i * a[i__2].i,
+ z__2.i = temp.r * a[i__2].i + temp.i * a[
+ i__2].r;
+ z__1.r = x[i__1].r + z__2.r, z__1.i = x[i__1].i +
+ z__2.i;
+ x[i__4].r = z__1.r, x[i__4].i = z__1.i;
+ ix -= *incx;
+/* L70: */
+ }
+ if (nounit) {
+ i__3 = jx;
+ i__4 = jx;
+ i__1 = j * a_dim1 + 1;
+ z__1.r = x[i__4].r * a[i__1].r - x[i__4].i * a[
+ i__1].i, z__1.i = x[i__4].r * a[i__1].i +
+ x[i__4].i * a[i__1].r;
+ x[i__3].r = z__1.r, x[i__3].i = z__1.i;
+ }
+ }
+ jx -= *incx;
+ if (*n - j >= *k) {
+ kx -= *incx;
+ }
+/* L80: */
+ }
+ }
+ }
+ } else {
+
+/* Form x := A'*x or x := conjg( A' )*x. */
+
+ if (lsame_(uplo, "U", (ftnlen)1, (ftnlen)1)) {
+ kplus1 = *k + 1;
+ if (*incx == 1) {
+ for (j = *n; j >= 1; --j) {
+ i__3 = j;
+ temp.r = x[i__3].r, temp.i = x[i__3].i;
+ l = kplus1 - j;
+ if (noconj) {
+ if (nounit) {
+ i__3 = kplus1 + j * a_dim1;
+ z__1.r = temp.r * a[i__3].r - temp.i * a[i__3].i,
+ z__1.i = temp.r * a[i__3].i + temp.i * a[
+ i__3].r;
+ temp.r = z__1.r, temp.i = z__1.i;
+ }
+/* Computing MAX */
+ i__4 = 1, i__1 = j - *k;
+ i__3 = max(i__4,i__1);
+ for (i__ = j - 1; i__ >= i__3; --i__) {
+ i__4 = l + i__ + j * a_dim1;
+ i__1 = i__;
+ z__2.r = a[i__4].r * x[i__1].r - a[i__4].i * x[
+ i__1].i, z__2.i = a[i__4].r * x[i__1].i +
+ a[i__4].i * x[i__1].r;
+ z__1.r = temp.r + z__2.r, z__1.i = temp.i +
+ z__2.i;
+ temp.r = z__1.r, temp.i = z__1.i;
+/* L90: */
+ }
+ } else {
+ if (nounit) {
+ d_cnjg(&z__2, &a[kplus1 + j * a_dim1]);
+ z__1.r = temp.r * z__2.r - temp.i * z__2.i,
+ z__1.i = temp.r * z__2.i + temp.i *
+ z__2.r;
+ temp.r = z__1.r, temp.i = z__1.i;
+ }
+/* Computing MAX */
+ i__4 = 1, i__1 = j - *k;
+ i__3 = max(i__4,i__1);
+ for (i__ = j - 1; i__ >= i__3; --i__) {
+ d_cnjg(&z__3, &a[l + i__ + j * a_dim1]);
+ i__4 = i__;
+ z__2.r = z__3.r * x[i__4].r - z__3.i * x[i__4].i,
+ z__2.i = z__3.r * x[i__4].i + z__3.i * x[
+ i__4].r;
+ z__1.r = temp.r + z__2.r, z__1.i = temp.i +
+ z__2.i;
+ temp.r = z__1.r, temp.i = z__1.i;
+/* L100: */
+ }
+ }
+ i__3 = j;
+ x[i__3].r = temp.r, x[i__3].i = temp.i;
+/* L110: */
+ }
+ } else {
+ kx += (*n - 1) * *incx;
+ jx = kx;
+ for (j = *n; j >= 1; --j) {
+ i__3 = jx;
+ temp.r = x[i__3].r, temp.i = x[i__3].i;
+ kx -= *incx;
+ ix = kx;
+ l = kplus1 - j;
+ if (noconj) {
+ if (nounit) {
+ i__3 = kplus1 + j * a_dim1;
+ z__1.r = temp.r * a[i__3].r - temp.i * a[i__3].i,
+ z__1.i = temp.r * a[i__3].i + temp.i * a[
+ i__3].r;
+ temp.r = z__1.r, temp.i = z__1.i;
+ }
+/* Computing MAX */
+ i__4 = 1, i__1 = j - *k;
+ i__3 = max(i__4,i__1);
+ for (i__ = j - 1; i__ >= i__3; --i__) {
+ i__4 = l + i__ + j * a_dim1;
+ i__1 = ix;
+ z__2.r = a[i__4].r * x[i__1].r - a[i__4].i * x[
+ i__1].i, z__2.i = a[i__4].r * x[i__1].i +
+ a[i__4].i * x[i__1].r;
+ z__1.r = temp.r + z__2.r, z__1.i = temp.i +
+ z__2.i;
+ temp.r = z__1.r, temp.i = z__1.i;
+ ix -= *incx;
+/* L120: */
+ }
+ } else {
+ if (nounit) {
+ d_cnjg(&z__2, &a[kplus1 + j * a_dim1]);
+ z__1.r = temp.r * z__2.r - temp.i * z__2.i,
+ z__1.i = temp.r * z__2.i + temp.i *
+ z__2.r;
+ temp.r = z__1.r, temp.i = z__1.i;
+ }
+/* Computing MAX */
+ i__4 = 1, i__1 = j - *k;
+ i__3 = max(i__4,i__1);
+ for (i__ = j - 1; i__ >= i__3; --i__) {
+ d_cnjg(&z__3, &a[l + i__ + j * a_dim1]);
+ i__4 = ix;
+ z__2.r = z__3.r * x[i__4].r - z__3.i * x[i__4].i,
+ z__2.i = z__3.r * x[i__4].i + z__3.i * x[
+ i__4].r;
+ z__1.r = temp.r + z__2.r, z__1.i = temp.i +
+ z__2.i;
+ temp.r = z__1.r, temp.i = z__1.i;
+ ix -= *incx;
+/* L130: */
+ }
+ }
+ i__3 = jx;
+ x[i__3].r = temp.r, x[i__3].i = temp.i;
+ jx -= *incx;
+/* L140: */
+ }
+ }
+ } else {
+ if (*incx == 1) {
+ i__3 = *n;
+ for (j = 1; j <= i__3; ++j) {
+ i__4 = j;
+ temp.r = x[i__4].r, temp.i = x[i__4].i;
+ l = 1 - j;
+ if (noconj) {
+ if (nounit) {
+ i__4 = j * a_dim1 + 1;
+ z__1.r = temp.r * a[i__4].r - temp.i * a[i__4].i,
+ z__1.i = temp.r * a[i__4].i + temp.i * a[
+ i__4].r;
+ temp.r = z__1.r, temp.i = z__1.i;
+ }
+/* Computing MIN */
+ i__1 = *n, i__2 = j + *k;
+ i__4 = min(i__1,i__2);
+ for (i__ = j + 1; i__ <= i__4; ++i__) {
+ i__1 = l + i__ + j * a_dim1;
+ i__2 = i__;
+ z__2.r = a[i__1].r * x[i__2].r - a[i__1].i * x[
+ i__2].i, z__2.i = a[i__1].r * x[i__2].i +
+ a[i__1].i * x[i__2].r;
+ z__1.r = temp.r + z__2.r, z__1.i = temp.i +
+ z__2.i;
+ temp.r = z__1.r, temp.i = z__1.i;
+/* L150: */
+ }
+ } else {
+ if (nounit) {
+ d_cnjg(&z__2, &a[j * a_dim1 + 1]);
+ z__1.r = temp.r * z__2.r - temp.i * z__2.i,
+ z__1.i = temp.r * z__2.i + temp.i *
+ z__2.r;
+ temp.r = z__1.r, temp.i = z__1.i;
+ }
+/* Computing MIN */
+ i__1 = *n, i__2 = j + *k;
+ i__4 = min(i__1,i__2);
+ for (i__ = j + 1; i__ <= i__4; ++i__) {
+ d_cnjg(&z__3, &a[l + i__ + j * a_dim1]);
+ i__1 = i__;
+ z__2.r = z__3.r * x[i__1].r - z__3.i * x[i__1].i,
+ z__2.i = z__3.r * x[i__1].i + z__3.i * x[
+ i__1].r;
+ z__1.r = temp.r + z__2.r, z__1.i = temp.i +
+ z__2.i;
+ temp.r = z__1.r, temp.i = z__1.i;
+/* L160: */
+ }
+ }
+ i__4 = j;
+ x[i__4].r = temp.r, x[i__4].i = temp.i;
+/* L170: */
+ }
+ } else {
+ jx = kx;
+ i__3 = *n;
+ for (j = 1; j <= i__3; ++j) {
+ i__4 = jx;
+ temp.r = x[i__4].r, temp.i = x[i__4].i;
+ kx += *incx;
+ ix = kx;
+ l = 1 - j;
+ if (noconj) {
+ if (nounit) {
+ i__4 = j * a_dim1 + 1;
+ z__1.r = temp.r * a[i__4].r - temp.i * a[i__4].i,
+ z__1.i = temp.r * a[i__4].i + temp.i * a[
+ i__4].r;
+ temp.r = z__1.r, temp.i = z__1.i;
+ }
+/* Computing MIN */
+ i__1 = *n, i__2 = j + *k;
+ i__4 = min(i__1,i__2);
+ for (i__ = j + 1; i__ <= i__4; ++i__) {
+ i__1 = l + i__ + j * a_dim1;
+ i__2 = ix;
+ z__2.r = a[i__1].r * x[i__2].r - a[i__1].i * x[
+ i__2].i, z__2.i = a[i__1].r * x[i__2].i +
+ a[i__1].i * x[i__2].r;
+ z__1.r = temp.r + z__2.r, z__1.i = temp.i +
+ z__2.i;
+ temp.r = z__1.r, temp.i = z__1.i;
+ ix += *incx;
+/* L180: */
+ }
+ } else {
+ if (nounit) {
+ d_cnjg(&z__2, &a[j * a_dim1 + 1]);
+ z__1.r = temp.r * z__2.r - temp.i * z__2.i,
+ z__1.i = temp.r * z__2.i + temp.i *
+ z__2.r;
+ temp.r = z__1.r, temp.i = z__1.i;
+ }
+/* Computing MIN */
+ i__1 = *n, i__2 = j + *k;
+ i__4 = min(i__1,i__2);
+ for (i__ = j + 1; i__ <= i__4; ++i__) {
+ d_cnjg(&z__3, &a[l + i__ + j * a_dim1]);
+ i__1 = ix;
+ z__2.r = z__3.r * x[i__1].r - z__3.i * x[i__1].i,
+ z__2.i = z__3.r * x[i__1].i + z__3.i * x[
+ i__1].r;
+ z__1.r = temp.r + z__2.r, z__1.i = temp.i +
+ z__2.i;
+ temp.r = z__1.r, temp.i = z__1.i;
+ ix += *incx;
+/* L190: */
+ }
+ }
+ i__4 = jx;
+ x[i__4].r = temp.r, x[i__4].i = temp.i;
+ jx += *incx;
+/* L200: */
+ }
+ }
+ }
+ }
+
+ return 0;
+
+/* End of ZTBMV . */
+
+} /* ztbmv_ */
+
diff --git a/blas/fortran/complexdots.f b/blas/fortran/complexdots.f
new file mode 100644
index 0000000..a7da51d
--- /dev/null
+++ b/blas/fortran/complexdots.f
@@ -0,0 +1,43 @@
+ COMPLEX FUNCTION CDOTC(N,CX,INCX,CY,INCY)
+ INTEGER INCX,INCY,N
+ COMPLEX CX(*),CY(*)
+ COMPLEX RES
+ EXTERNAL CDOTCW
+
+ CALL CDOTCW(N,CX,INCX,CY,INCY,RES)
+ CDOTC = RES
+ RETURN
+ END
+
+ COMPLEX FUNCTION CDOTU(N,CX,INCX,CY,INCY)
+ INTEGER INCX,INCY,N
+ COMPLEX CX(*),CY(*)
+ COMPLEX RES
+ EXTERNAL CDOTUW
+
+ CALL CDOTUW(N,CX,INCX,CY,INCY,RES)
+ CDOTU = RES
+ RETURN
+ END
+
+ DOUBLE COMPLEX FUNCTION ZDOTC(N,CX,INCX,CY,INCY)
+ INTEGER INCX,INCY,N
+ DOUBLE COMPLEX CX(*),CY(*)
+ DOUBLE COMPLEX RES
+ EXTERNAL ZDOTCW
+
+ CALL ZDOTCW(N,CX,INCX,CY,INCY,RES)
+ ZDOTC = RES
+ RETURN
+ END
+
+ DOUBLE COMPLEX FUNCTION ZDOTU(N,CX,INCX,CY,INCY)
+ INTEGER INCX,INCY,N
+ DOUBLE COMPLEX CX(*),CY(*)
+ DOUBLE COMPLEX RES
+ EXTERNAL ZDOTUW
+
+ CALL ZDOTUW(N,CX,INCX,CY,INCY,RES)
+ ZDOTU = RES
+ RETURN
+ END
diff --git a/blas/level1_cplx_impl.h b/blas/level1_cplx_impl.h
new file mode 100644
index 0000000..aa46784
--- /dev/null
+++ b/blas/level1_cplx_impl.h
@@ -0,0 +1,154 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009-2010 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "common.h"
+
+struct scalar_norm1_op {
+ typedef RealScalar result_type;
+ inline RealScalar operator() (const Scalar& a) const { return numext::norm1(a); }
+};
+namespace Eigen {
+ namespace internal {
+ template<> struct functor_traits<scalar_norm1_op >
+ {
+ enum { Cost = 3 * NumTraits<Scalar>::AddCost, PacketAccess = 0 };
+ };
+ }
+}
+
+// computes the sum of magnitudes of all vector elements or, for a complex vector x, the sum
+// res = |Rex1| + |Imx1| + |Rex2| + |Imx2| + ... + |Rexn| + |Imxn|, where x is a vector of order n
+RealScalar EIGEN_CAT(REAL_SCALAR_SUFFIX, EIGEN_BLAS_FUNC(asum))(int *n, RealScalar *px, int *incx)
+{
+// std::cerr << "__asum " << *n << " " << *incx << "\n";
+ Complex* x = reinterpret_cast<Complex*>(px);
+
+ if(*n<=0) return 0;
+
+ if(*incx==1) return make_vector(x,*n).unaryExpr<scalar_norm1_op>().sum();
+ else return make_vector(x,*n,std::abs(*incx)).unaryExpr<scalar_norm1_op>().sum();
+}
+
+int EIGEN_CAT(i, EIGEN_BLAS_FUNC(amax))(int *n, RealScalar *px, int *incx)
+{
+ if(*n<=0) return 0;
+ Scalar* x = reinterpret_cast<Scalar*>(px);
+
+ DenseIndex ret;
+ if(*incx==1) make_vector(x,*n).unaryExpr<scalar_norm1_op>().maxCoeff(&ret);
+ else make_vector(x,*n,std::abs(*incx)).unaryExpr<scalar_norm1_op>().maxCoeff(&ret);
+ return int(ret)+1;
+}
+
+int EIGEN_CAT(i, EIGEN_BLAS_FUNC(amin))(int *n, RealScalar *px, int *incx)
+{
+ if(*n<=0) return 0;
+ Scalar* x = reinterpret_cast<Scalar*>(px);
+
+ DenseIndex ret;
+ if(*incx==1) make_vector(x,*n).unaryExpr<scalar_norm1_op>().minCoeff(&ret);
+ else make_vector(x,*n,std::abs(*incx)).unaryExpr<scalar_norm1_op>().minCoeff(&ret);
+ return int(ret)+1;
+}
+
+// computes a dot product of a conjugated vector with another vector.
+int EIGEN_BLAS_FUNC(dotcw)(int *n, RealScalar *px, int *incx, RealScalar *py, int *incy, RealScalar* pres)
+{
+// std::cerr << "_dotc " << *n << " " << *incx << " " << *incy << "\n";
+ Scalar* res = reinterpret_cast<Scalar*>(pres);
+
+ if(*n<=0)
+ {
+ *res = Scalar(0);
+ return 0;
+ }
+
+ Scalar* x = reinterpret_cast<Scalar*>(px);
+ Scalar* y = reinterpret_cast<Scalar*>(py);
+
+ if(*incx==1 && *incy==1) *res = (make_vector(x,*n).dot(make_vector(y,*n)));
+ else if(*incx>0 && *incy>0) *res = (make_vector(x,*n,*incx).dot(make_vector(y,*n,*incy)));
+ else if(*incx<0 && *incy>0) *res = (make_vector(x,*n,-*incx).reverse().dot(make_vector(y,*n,*incy)));
+ else if(*incx>0 && *incy<0) *res = (make_vector(x,*n,*incx).dot(make_vector(y,*n,-*incy).reverse()));
+ else if(*incx<0 && *incy<0) *res = (make_vector(x,*n,-*incx).reverse().dot(make_vector(y,*n,-*incy).reverse()));
+ return 0;
+}
+
+// computes a vector-vector dot product without complex conjugation.
+int EIGEN_BLAS_FUNC(dotuw)(int *n, RealScalar *px, int *incx, RealScalar *py, int *incy, RealScalar* pres)
+{
+ Scalar* res = reinterpret_cast<Scalar*>(pres);
+
+ if(*n<=0)
+ {
+ *res = Scalar(0);
+ return 0;
+ }
+
+ Scalar* x = reinterpret_cast<Scalar*>(px);
+ Scalar* y = reinterpret_cast<Scalar*>(py);
+
+ if(*incx==1 && *incy==1) *res = (make_vector(x,*n).cwiseProduct(make_vector(y,*n))).sum();
+ else if(*incx>0 && *incy>0) *res = (make_vector(x,*n,*incx).cwiseProduct(make_vector(y,*n,*incy))).sum();
+ else if(*incx<0 && *incy>0) *res = (make_vector(x,*n,-*incx).reverse().cwiseProduct(make_vector(y,*n,*incy))).sum();
+ else if(*incx>0 && *incy<0) *res = (make_vector(x,*n,*incx).cwiseProduct(make_vector(y,*n,-*incy).reverse())).sum();
+ else if(*incx<0 && *incy<0) *res = (make_vector(x,*n,-*incx).reverse().cwiseProduct(make_vector(y,*n,-*incy).reverse())).sum();
+ return 0;
+}
+
+RealScalar EIGEN_CAT(REAL_SCALAR_SUFFIX, EIGEN_BLAS_FUNC(nrm2))(int *n, RealScalar *px, int *incx)
+{
+// std::cerr << "__nrm2 " << *n << " " << *incx << "\n";
+ if(*n<=0) return 0;
+
+ Scalar* x = reinterpret_cast<Scalar*>(px);
+
+ if(*incx==1)
+ return make_vector(x,*n).stableNorm();
+
+ return make_vector(x,*n,*incx).stableNorm();
+}
+
+int EIGEN_BLAS_FUNC(EIGEN_CAT(REAL_SCALAR_SUFFIX, rot))(int *n, RealScalar *px, int *incx, RealScalar *py, int *incy, RealScalar *pc, RealScalar *ps)
+{
+ if(*n<=0) return 0;
+
+ Scalar* x = reinterpret_cast<Scalar*>(px);
+ Scalar* y = reinterpret_cast<Scalar*>(py);
+ RealScalar c = *pc;
+ RealScalar s = *ps;
+
+ StridedVectorType vx(make_vector(x,*n,std::abs(*incx)));
+ StridedVectorType vy(make_vector(y,*n,std::abs(*incy)));
+
+ Reverse<StridedVectorType> rvx(vx);
+ Reverse<StridedVectorType> rvy(vy);
+
+ // TODO implement mixed real-scalar rotations
+ if(*incx<0 && *incy>0) internal::apply_rotation_in_the_plane(rvx, vy, JacobiRotation<Scalar>(c,s));
+ else if(*incx>0 && *incy<0) internal::apply_rotation_in_the_plane(vx, rvy, JacobiRotation<Scalar>(c,s));
+ else internal::apply_rotation_in_the_plane(vx, vy, JacobiRotation<Scalar>(c,s));
+
+ return 0;
+}
+
+int EIGEN_BLAS_FUNC(EIGEN_CAT(REAL_SCALAR_SUFFIX, scal))(int *n, RealScalar *palpha, RealScalar *px, int *incx)
+{
+ if(*n<=0) return 0;
+
+ Scalar* x = reinterpret_cast<Scalar*>(px);
+ RealScalar alpha = *palpha;
+
+// std::cerr << "__scal " << *n << " " << alpha << " " << *incx << "\n";
+
+ if(*incx==1) make_vector(x,*n) *= alpha;
+ else make_vector(x,*n,std::abs(*incx)) *= alpha;
+
+ return 0;
+}
diff --git a/blas/level1_impl.h b/blas/level1_impl.h
new file mode 100644
index 0000000..71bd534
--- /dev/null
+++ b/blas/level1_impl.h
@@ -0,0 +1,144 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009-2010 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "common.h"
+
+int EIGEN_BLAS_FUNC(axpy)(const int *n, const RealScalar *palpha, const RealScalar *px, const int *incx, RealScalar *py, const int *incy)
+{
+ const Scalar* x = reinterpret_cast<const Scalar*>(px);
+ Scalar* y = reinterpret_cast<Scalar*>(py);
+ Scalar alpha = *reinterpret_cast<const Scalar*>(palpha);
+
+ if(*n<=0) return 0;
+
+ if(*incx==1 && *incy==1) make_vector(y,*n) += alpha * make_vector(x,*n);
+ else if(*incx>0 && *incy>0) make_vector(y,*n,*incy) += alpha * make_vector(x,*n,*incx);
+ else if(*incx>0 && *incy<0) make_vector(y,*n,-*incy).reverse() += alpha * make_vector(x,*n,*incx);
+ else if(*incx<0 && *incy>0) make_vector(y,*n,*incy) += alpha * make_vector(x,*n,-*incx).reverse();
+ else if(*incx<0 && *incy<0) make_vector(y,*n,-*incy).reverse() += alpha * make_vector(x,*n,-*incx).reverse();
+
+ return 0;
+}
+
+int EIGEN_BLAS_FUNC(copy)(int *n, RealScalar *px, int *incx, RealScalar *py, int *incy)
+{
+ if(*n<=0) return 0;
+
+ Scalar* x = reinterpret_cast<Scalar*>(px);
+ Scalar* y = reinterpret_cast<Scalar*>(py);
+
+ // be careful, *incx==0 is allowed !!
+ if(*incx==1 && *incy==1)
+ make_vector(y,*n) = make_vector(x,*n);
+ else
+ {
+ if(*incx<0) x = x - (*n-1)*(*incx);
+ if(*incy<0) y = y - (*n-1)*(*incy);
+ for(int i=0;i<*n;++i)
+ {
+ *y = *x;
+ x += *incx;
+ y += *incy;
+ }
+ }
+
+ return 0;
+}
+
+int EIGEN_BLAS_FUNC(rotg)(RealScalar *pa, RealScalar *pb, RealScalar *pc, RealScalar *ps)
+{
+ using std::sqrt;
+ using std::abs;
+
+ Scalar& a = *reinterpret_cast<Scalar*>(pa);
+ Scalar& b = *reinterpret_cast<Scalar*>(pb);
+ RealScalar* c = pc;
+ Scalar* s = reinterpret_cast<Scalar*>(ps);
+
+ #if !ISCOMPLEX
+ Scalar r,z;
+ Scalar aa = abs(a);
+ Scalar ab = abs(b);
+ if((aa+ab)==Scalar(0))
+ {
+ *c = 1;
+ *s = 0;
+ r = 0;
+ z = 0;
+ }
+ else
+ {
+ r = sqrt(a*a + b*b);
+ Scalar amax = aa>ab ? a : b;
+ r = amax>0 ? r : -r;
+ *c = a/r;
+ *s = b/r;
+ z = 1;
+ if (aa > ab) z = *s;
+ if (ab > aa && *c!=RealScalar(0))
+ z = Scalar(1)/ *c;
+ }
+ *pa = r;
+ *pb = z;
+ #else
+ Scalar alpha;
+ RealScalar norm,scale;
+ if(abs(a)==RealScalar(0))
+ {
+ *c = RealScalar(0);
+ *s = Scalar(1);
+ a = b;
+ }
+ else
+ {
+ scale = abs(a) + abs(b);
+ norm = scale*sqrt((numext::abs2(a/scale)) + (numext::abs2(b/scale)));
+ alpha = a/abs(a);
+ *c = abs(a)/norm;
+ *s = alpha*numext::conj(b)/norm;
+ a = alpha*norm;
+ }
+ #endif
+
+// JacobiRotation<Scalar> r;
+// r.makeGivens(a,b);
+// *c = r.c();
+// *s = r.s();
+
+ return 0;
+}
+
+int EIGEN_BLAS_FUNC(scal)(int *n, RealScalar *palpha, RealScalar *px, int *incx)
+{
+ if(*n<=0) return 0;
+
+ Scalar* x = reinterpret_cast<Scalar*>(px);
+ Scalar alpha = *reinterpret_cast<Scalar*>(palpha);
+
+ if(*incx==1) make_vector(x,*n) *= alpha;
+ else make_vector(x,*n,std::abs(*incx)) *= alpha;
+
+ return 0;
+}
+
+int EIGEN_BLAS_FUNC(swap)(int *n, RealScalar *px, int *incx, RealScalar *py, int *incy)
+{
+ if(*n<=0) return 0;
+
+ Scalar* x = reinterpret_cast<Scalar*>(px);
+ Scalar* y = reinterpret_cast<Scalar*>(py);
+
+ if(*incx==1 && *incy==1) make_vector(y,*n).swap(make_vector(x,*n));
+ else if(*incx>0 && *incy>0) make_vector(y,*n,*incy).swap(make_vector(x,*n,*incx));
+ else if(*incx>0 && *incy<0) make_vector(y,*n,-*incy).reverse().swap(make_vector(x,*n,*incx));
+ else if(*incx<0 && *incy>0) make_vector(y,*n,*incy).swap(make_vector(x,*n,-*incx).reverse());
+ else if(*incx<0 && *incy<0) make_vector(y,*n,-*incy).reverse().swap(make_vector(x,*n,-*incx).reverse());
+
+ return 1;
+}
diff --git a/blas/level1_real_impl.h b/blas/level1_real_impl.h
new file mode 100644
index 0000000..c587711
--- /dev/null
+++ b/blas/level1_real_impl.h
@@ -0,0 +1,122 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009-2010 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "common.h"
+
+// computes the sum of magnitudes of all vector elements or, for a complex vector x, the sum
+// res = |Rex1| + |Imx1| + |Rex2| + |Imx2| + ... + |Rexn| + |Imxn|, where x is a vector of order n
+RealScalar EIGEN_BLAS_FUNC(asum)(int *n, RealScalar *px, int *incx)
+{
+// std::cerr << "_asum " << *n << " " << *incx << "\n";
+
+ Scalar* x = reinterpret_cast<Scalar*>(px);
+
+ if(*n<=0) return 0;
+
+ if(*incx==1) return make_vector(x,*n).cwiseAbs().sum();
+ else return make_vector(x,*n,std::abs(*incx)).cwiseAbs().sum();
+}
+
+int EIGEN_CAT(i, EIGEN_BLAS_FUNC(amax))(int *n, RealScalar *px, int *incx)
+{
+ if(*n<=0) return 0;
+ Scalar* x = reinterpret_cast<Scalar*>(px);
+
+ DenseIndex ret;
+ if(*incx==1) make_vector(x,*n).cwiseAbs().maxCoeff(&ret);
+ else make_vector(x,*n,std::abs(*incx)).cwiseAbs().maxCoeff(&ret);
+ return int(ret)+1;
+}
+
+int EIGEN_CAT(i, EIGEN_BLAS_FUNC(amin))(int *n, RealScalar *px, int *incx)
+{
+ if(*n<=0) return 0;
+ Scalar* x = reinterpret_cast<Scalar*>(px);
+
+ DenseIndex ret;
+ if(*incx==1) make_vector(x,*n).cwiseAbs().minCoeff(&ret);
+ else make_vector(x,*n,std::abs(*incx)).cwiseAbs().minCoeff(&ret);
+ return int(ret)+1;
+}
+
+// computes a vector-vector dot product.
+Scalar EIGEN_BLAS_FUNC(dot)(int *n, RealScalar *px, int *incx, RealScalar *py, int *incy)
+{
+// std::cerr << "_dot " << *n << " " << *incx << " " << *incy << "\n";
+
+ if(*n<=0) return 0;
+
+ Scalar* x = reinterpret_cast<Scalar*>(px);
+ Scalar* y = reinterpret_cast<Scalar*>(py);
+
+ if(*incx==1 && *incy==1) return (make_vector(x,*n).cwiseProduct(make_vector(y,*n))).sum();
+ else if(*incx>0 && *incy>0) return (make_vector(x,*n,*incx).cwiseProduct(make_vector(y,*n,*incy))).sum();
+ else if(*incx<0 && *incy>0) return (make_vector(x,*n,-*incx).reverse().cwiseProduct(make_vector(y,*n,*incy))).sum();
+ else if(*incx>0 && *incy<0) return (make_vector(x,*n,*incx).cwiseProduct(make_vector(y,*n,-*incy).reverse())).sum();
+ else if(*incx<0 && *incy<0) return (make_vector(x,*n,-*incx).reverse().cwiseProduct(make_vector(y,*n,-*incy).reverse())).sum();
+ else return 0;
+}
+
+// computes the Euclidean norm of a vector.
+// FIXME
+Scalar EIGEN_BLAS_FUNC(nrm2)(int *n, RealScalar *px, int *incx)
+{
+// std::cerr << "_nrm2 " << *n << " " << *incx << "\n";
+ if(*n<=0) return 0;
+
+ Scalar* x = reinterpret_cast<Scalar*>(px);
+
+ if(*incx==1) return make_vector(x,*n).stableNorm();
+ else return make_vector(x,*n,std::abs(*incx)).stableNorm();
+}
+
+int EIGEN_BLAS_FUNC(rot)(int *n, RealScalar *px, int *incx, RealScalar *py, int *incy, RealScalar *pc, RealScalar *ps)
+{
+// std::cerr << "_rot " << *n << " " << *incx << " " << *incy << "\n";
+ if(*n<=0) return 0;
+
+ Scalar* x = reinterpret_cast<Scalar*>(px);
+ Scalar* y = reinterpret_cast<Scalar*>(py);
+ Scalar c = *reinterpret_cast<Scalar*>(pc);
+ Scalar s = *reinterpret_cast<Scalar*>(ps);
+
+ StridedVectorType vx(make_vector(x,*n,std::abs(*incx)));
+ StridedVectorType vy(make_vector(y,*n,std::abs(*incy)));
+
+ Reverse<StridedVectorType> rvx(vx);
+ Reverse<StridedVectorType> rvy(vy);
+
+ if(*incx<0 && *incy>0) internal::apply_rotation_in_the_plane(rvx, vy, JacobiRotation<Scalar>(c,s));
+ else if(*incx>0 && *incy<0) internal::apply_rotation_in_the_plane(vx, rvy, JacobiRotation<Scalar>(c,s));
+ else internal::apply_rotation_in_the_plane(vx, vy, JacobiRotation<Scalar>(c,s));
+
+
+ return 0;
+}
+
+/*
+// performs rotation of points in the modified plane.
+int EIGEN_BLAS_FUNC(rotm)(int *n, RealScalar *px, int *incx, RealScalar *py, int *incy, RealScalar *param)
+{
+ Scalar* x = reinterpret_cast<Scalar*>(px);
+ Scalar* y = reinterpret_cast<Scalar*>(py);
+
+ // TODO
+
+ return 0;
+}
+
+// computes the modified parameters for a Givens rotation.
+int EIGEN_BLAS_FUNC(rotmg)(RealScalar *d1, RealScalar *d2, RealScalar *x1, RealScalar *x2, RealScalar *param)
+{
+ // TODO
+
+ return 0;
+}
+*/
diff --git a/blas/level2_cplx_impl.h b/blas/level2_cplx_impl.h
new file mode 100644
index 0000000..e3ce614
--- /dev/null
+++ b/blas/level2_cplx_impl.h
@@ -0,0 +1,360 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009-2010 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "common.h"
+
+/** ZHEMV performs the matrix-vector operation
+ *
+ * y := alpha*A*x + beta*y,
+ *
+ * where alpha and beta are scalars, x and y are n element vectors and
+ * A is an n by n hermitian matrix.
+ */
+int EIGEN_BLAS_FUNC(hemv)(const char *uplo, const int *n, const RealScalar *palpha, const RealScalar *pa, const int *lda,
+ const RealScalar *px, const int *incx, const RealScalar *pbeta, RealScalar *py, const int *incy)
+{
+ typedef void (*functype)(int, const Scalar*, int, const Scalar*, Scalar*, Scalar);
+ static const functype func[2] = {
+ // array index: UP
+ (internal::selfadjoint_matrix_vector_product<Scalar,int,ColMajor,Upper,false,false>::run),
+ // array index: LO
+ (internal::selfadjoint_matrix_vector_product<Scalar,int,ColMajor,Lower,false,false>::run),
+ };
+
+ const Scalar* a = reinterpret_cast<const Scalar*>(pa);
+ const Scalar* x = reinterpret_cast<const Scalar*>(px);
+ Scalar* y = reinterpret_cast<Scalar*>(py);
+ Scalar alpha = *reinterpret_cast<const Scalar*>(palpha);
+ Scalar beta = *reinterpret_cast<const Scalar*>(pbeta);
+
+ // check arguments
+ int info = 0;
+ if(UPLO(*uplo)==INVALID) info = 1;
+ else if(*n<0) info = 2;
+ else if(*lda<std::max(1,*n)) info = 5;
+ else if(*incx==0) info = 7;
+ else if(*incy==0) info = 10;
+ if(info)
+ return xerbla_(SCALAR_SUFFIX_UP"HEMV ",&info,6);
+
+ if(*n==0)
+ return 1;
+
+ const Scalar* actual_x = get_compact_vector(x,*n,*incx);
+ Scalar* actual_y = get_compact_vector(y,*n,*incy);
+
+ if(beta!=Scalar(1))
+ {
+ if(beta==Scalar(0)) make_vector(actual_y, *n).setZero();
+ else make_vector(actual_y, *n) *= beta;
+ }
+
+ if(alpha!=Scalar(0))
+ {
+ int code = UPLO(*uplo);
+ if(code>=2 || func[code]==0)
+ return 0;
+
+ func[code](*n, a, *lda, actual_x, actual_y, alpha);
+ }
+
+ if(actual_x!=x) delete[] actual_x;
+ if(actual_y!=y) delete[] copy_back(actual_y,y,*n,*incy);
+
+ return 1;
+}
+
+/** ZHBMV performs the matrix-vector operation
+ *
+ * y := alpha*A*x + beta*y,
+ *
+ * where alpha and beta are scalars, x and y are n element vectors and
+ * A is an n by n hermitian band matrix, with k super-diagonals.
+ */
+// int EIGEN_BLAS_FUNC(hbmv)(char *uplo, int *n, int *k, RealScalar *alpha, RealScalar *a, int *lda,
+// RealScalar *x, int *incx, RealScalar *beta, RealScalar *y, int *incy)
+// {
+// return 1;
+// }
+
+/** ZHPMV performs the matrix-vector operation
+ *
+ * y := alpha*A*x + beta*y,
+ *
+ * where alpha and beta are scalars, x and y are n element vectors and
+ * A is an n by n hermitian matrix, supplied in packed form.
+ */
+// int EIGEN_BLAS_FUNC(hpmv)(char *uplo, int *n, RealScalar *alpha, RealScalar *ap, RealScalar *x, int *incx, RealScalar *beta, RealScalar *y, int *incy)
+// {
+// return 1;
+// }
+
+/** ZHPR performs the hermitian rank 1 operation
+ *
+ * A := alpha*x*conjg( x' ) + A,
+ *
+ * where alpha is a real scalar, x is an n element vector and A is an
+ * n by n hermitian matrix, supplied in packed form.
+ */
+int EIGEN_BLAS_FUNC(hpr)(char *uplo, int *n, RealScalar *palpha, RealScalar *px, int *incx, RealScalar *pap)
+{
+ typedef void (*functype)(int, Scalar*, const Scalar*, RealScalar);
+ static const functype func[2] = {
+ // array index: UP
+ (internal::selfadjoint_packed_rank1_update<Scalar,int,ColMajor,Upper,false,Conj>::run),
+ // array index: LO
+ (internal::selfadjoint_packed_rank1_update<Scalar,int,ColMajor,Lower,false,Conj>::run),
+ };
+
+ Scalar* x = reinterpret_cast<Scalar*>(px);
+ Scalar* ap = reinterpret_cast<Scalar*>(pap);
+ RealScalar alpha = *palpha;
+
+ int info = 0;
+ if(UPLO(*uplo)==INVALID) info = 1;
+ else if(*n<0) info = 2;
+ else if(*incx==0) info = 5;
+ if(info)
+ return xerbla_(SCALAR_SUFFIX_UP"HPR ",&info,6);
+
+ if(alpha==Scalar(0))
+ return 1;
+
+ Scalar* x_cpy = get_compact_vector(x, *n, *incx);
+
+ int code = UPLO(*uplo);
+ if(code>=2 || func[code]==0)
+ return 0;
+
+ func[code](*n, ap, x_cpy, alpha);
+
+ if(x_cpy!=x) delete[] x_cpy;
+
+ return 1;
+}
+
+/** ZHPR2 performs the hermitian rank 2 operation
+ *
+ * A := alpha*x*conjg( y' ) + conjg( alpha )*y*conjg( x' ) + A,
+ *
+ * where alpha is a scalar, x and y are n element vectors and A is an
+ * n by n hermitian matrix, supplied in packed form.
+ */
+int EIGEN_BLAS_FUNC(hpr2)(char *uplo, int *n, RealScalar *palpha, RealScalar *px, int *incx, RealScalar *py, int *incy, RealScalar *pap)
+{
+ typedef void (*functype)(int, Scalar*, const Scalar*, const Scalar*, Scalar);
+ static const functype func[2] = {
+ // array index: UP
+ (internal::packed_rank2_update_selector<Scalar,int,Upper>::run),
+ // array index: LO
+ (internal::packed_rank2_update_selector<Scalar,int,Lower>::run),
+ };
+
+ Scalar* x = reinterpret_cast<Scalar*>(px);
+ Scalar* y = reinterpret_cast<Scalar*>(py);
+ Scalar* ap = reinterpret_cast<Scalar*>(pap);
+ Scalar alpha = *reinterpret_cast<Scalar*>(palpha);
+
+ int info = 0;
+ if(UPLO(*uplo)==INVALID) info = 1;
+ else if(*n<0) info = 2;
+ else if(*incx==0) info = 5;
+ else if(*incy==0) info = 7;
+ if(info)
+ return xerbla_(SCALAR_SUFFIX_UP"HPR2 ",&info,6);
+
+ if(alpha==Scalar(0))
+ return 1;
+
+ Scalar* x_cpy = get_compact_vector(x, *n, *incx);
+ Scalar* y_cpy = get_compact_vector(y, *n, *incy);
+
+ int code = UPLO(*uplo);
+ if(code>=2 || func[code]==0)
+ return 0;
+
+ func[code](*n, ap, x_cpy, y_cpy, alpha);
+
+ if(x_cpy!=x) delete[] x_cpy;
+ if(y_cpy!=y) delete[] y_cpy;
+
+ return 1;
+}
+
+/** ZHER performs the hermitian rank 1 operation
+ *
+ * A := alpha*x*conjg( x' ) + A,
+ *
+ * where alpha is a real scalar, x is an n element vector and A is an
+ * n by n hermitian matrix.
+ */
+int EIGEN_BLAS_FUNC(her)(char *uplo, int *n, RealScalar *palpha, RealScalar *px, int *incx, RealScalar *pa, int *lda)
+{
+ typedef void (*functype)(int, Scalar*, int, const Scalar*, const Scalar*, const Scalar&);
+ static const functype func[2] = {
+ // array index: UP
+ (selfadjoint_rank1_update<Scalar,int,ColMajor,Upper,false,Conj>::run),
+ // array index: LO
+ (selfadjoint_rank1_update<Scalar,int,ColMajor,Lower,false,Conj>::run),
+ };
+
+ Scalar* x = reinterpret_cast<Scalar*>(px);
+ Scalar* a = reinterpret_cast<Scalar*>(pa);
+ RealScalar alpha = *reinterpret_cast<RealScalar*>(palpha);
+
+ int info = 0;
+ if(UPLO(*uplo)==INVALID) info = 1;
+ else if(*n<0) info = 2;
+ else if(*incx==0) info = 5;
+ else if(*lda<std::max(1,*n)) info = 7;
+ if(info)
+ return xerbla_(SCALAR_SUFFIX_UP"HER ",&info,6);
+
+ if(alpha==RealScalar(0))
+ return 1;
+
+ Scalar* x_cpy = get_compact_vector(x, *n, *incx);
+
+ int code = UPLO(*uplo);
+ if(code>=2 || func[code]==0)
+ return 0;
+
+ func[code](*n, a, *lda, x_cpy, x_cpy, alpha);
+
+ matrix(a,*n,*n,*lda).diagonal().imag().setZero();
+
+ if(x_cpy!=x) delete[] x_cpy;
+
+ return 1;
+}
+
+/** ZHER2 performs the hermitian rank 2 operation
+ *
+ * A := alpha*x*conjg( y' ) + conjg( alpha )*y*conjg( x' ) + A,
+ *
+ * where alpha is a scalar, x and y are n element vectors and A is an n
+ * by n hermitian matrix.
+ */
+int EIGEN_BLAS_FUNC(her2)(char *uplo, int *n, RealScalar *palpha, RealScalar *px, int *incx, RealScalar *py, int *incy, RealScalar *pa, int *lda)
+{
+ typedef void (*functype)(int, Scalar*, int, const Scalar*, const Scalar*, Scalar);
+ static const functype func[2] = {
+ // array index: UP
+ (internal::rank2_update_selector<Scalar,int,Upper>::run),
+ // array index: LO
+ (internal::rank2_update_selector<Scalar,int,Lower>::run),
+ };
+
+ Scalar* x = reinterpret_cast<Scalar*>(px);
+ Scalar* y = reinterpret_cast<Scalar*>(py);
+ Scalar* a = reinterpret_cast<Scalar*>(pa);
+ Scalar alpha = *reinterpret_cast<Scalar*>(palpha);
+
+ int info = 0;
+ if(UPLO(*uplo)==INVALID) info = 1;
+ else if(*n<0) info = 2;
+ else if(*incx==0) info = 5;
+ else if(*incy==0) info = 7;
+ else if(*lda<std::max(1,*n)) info = 9;
+ if(info)
+ return xerbla_(SCALAR_SUFFIX_UP"HER2 ",&info,6);
+
+ if(alpha==Scalar(0))
+ return 1;
+
+ Scalar* x_cpy = get_compact_vector(x, *n, *incx);
+ Scalar* y_cpy = get_compact_vector(y, *n, *incy);
+
+ int code = UPLO(*uplo);
+ if(code>=2 || func[code]==0)
+ return 0;
+
+ func[code](*n, a, *lda, x_cpy, y_cpy, alpha);
+
+ matrix(a,*n,*n,*lda).diagonal().imag().setZero();
+
+ if(x_cpy!=x) delete[] x_cpy;
+ if(y_cpy!=y) delete[] y_cpy;
+
+ return 1;
+}
+
+/** ZGERU performs the rank 1 operation
+ *
+ * A := alpha*x*y' + A,
+ *
+ * where alpha is a scalar, x is an m element vector, y is an n element
+ * vector and A is an m by n matrix.
+ */
+int EIGEN_BLAS_FUNC(geru)(int *m, int *n, RealScalar *palpha, RealScalar *px, int *incx, RealScalar *py, int *incy, RealScalar *pa, int *lda)
+{
+ Scalar* x = reinterpret_cast<Scalar*>(px);
+ Scalar* y = reinterpret_cast<Scalar*>(py);
+ Scalar* a = reinterpret_cast<Scalar*>(pa);
+ Scalar alpha = *reinterpret_cast<Scalar*>(palpha);
+
+ int info = 0;
+ if(*m<0) info = 1;
+ else if(*n<0) info = 2;
+ else if(*incx==0) info = 5;
+ else if(*incy==0) info = 7;
+ else if(*lda<std::max(1,*m)) info = 9;
+ if(info)
+ return xerbla_(SCALAR_SUFFIX_UP"GERU ",&info,6);
+
+ if(alpha==Scalar(0))
+ return 1;
+
+ Scalar* x_cpy = get_compact_vector(x,*m,*incx);
+ Scalar* y_cpy = get_compact_vector(y,*n,*incy);
+
+ internal::general_rank1_update<Scalar,int,ColMajor,false,false>::run(*m, *n, a, *lda, x_cpy, y_cpy, alpha);
+
+ if(x_cpy!=x) delete[] x_cpy;
+ if(y_cpy!=y) delete[] y_cpy;
+
+ return 1;
+}
+
+/** ZGERC performs the rank 1 operation
+ *
+ * A := alpha*x*conjg( y' ) + A,
+ *
+ * where alpha is a scalar, x is an m element vector, y is an n element
+ * vector and A is an m by n matrix.
+ */
+int EIGEN_BLAS_FUNC(gerc)(int *m, int *n, RealScalar *palpha, RealScalar *px, int *incx, RealScalar *py, int *incy, RealScalar *pa, int *lda)
+{
+ Scalar* x = reinterpret_cast<Scalar*>(px);
+ Scalar* y = reinterpret_cast<Scalar*>(py);
+ Scalar* a = reinterpret_cast<Scalar*>(pa);
+ Scalar alpha = *reinterpret_cast<Scalar*>(palpha);
+
+ int info = 0;
+ if(*m<0) info = 1;
+ else if(*n<0) info = 2;
+ else if(*incx==0) info = 5;
+ else if(*incy==0) info = 7;
+ else if(*lda<std::max(1,*m)) info = 9;
+ if(info)
+ return xerbla_(SCALAR_SUFFIX_UP"GERC ",&info,6);
+
+ if(alpha==Scalar(0))
+ return 1;
+
+ Scalar* x_cpy = get_compact_vector(x,*m,*incx);
+ Scalar* y_cpy = get_compact_vector(y,*n,*incy);
+
+ internal::general_rank1_update<Scalar,int,ColMajor,false,Conj>::run(*m, *n, a, *lda, x_cpy, y_cpy, alpha);
+
+ if(x_cpy!=x) delete[] x_cpy;
+ if(y_cpy!=y) delete[] y_cpy;
+
+ return 1;
+}
diff --git a/blas/level2_impl.h b/blas/level2_impl.h
new file mode 100644
index 0000000..173f40b
--- /dev/null
+++ b/blas/level2_impl.h
@@ -0,0 +1,553 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009-2010 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "common.h"
+
+template<typename Index, typename Scalar, int StorageOrder, bool ConjugateLhs, bool ConjugateRhs>
+struct general_matrix_vector_product_wrapper
+{
+ static void run(Index rows, Index cols,const Scalar *lhs, Index lhsStride, const Scalar *rhs, Index rhsIncr, Scalar* res, Index resIncr, Scalar alpha)
+ {
+ typedef internal::const_blas_data_mapper<Scalar,Index,StorageOrder> LhsMapper;
+ typedef internal::const_blas_data_mapper<Scalar,Index,RowMajor> RhsMapper;
+
+ internal::general_matrix_vector_product
+ <Index,Scalar,LhsMapper,StorageOrder,ConjugateLhs,Scalar,RhsMapper,ConjugateRhs>::run(
+ rows, cols, LhsMapper(lhs, lhsStride), RhsMapper(rhs, rhsIncr), res, resIncr, alpha);
+ }
+};
+
+int EIGEN_BLAS_FUNC(gemv)(const char *opa, const int *m, const int *n, const RealScalar *palpha,
+ const RealScalar *pa, const int *lda, const RealScalar *pb, const int *incb, const RealScalar *pbeta, RealScalar *pc, const int *incc)
+{
+ typedef void (*functype)(int, int, const Scalar *, int, const Scalar *, int , Scalar *, int, Scalar);
+ static const functype func[4] = {
+ // array index: NOTR
+ (general_matrix_vector_product_wrapper<int,Scalar,ColMajor,false,false>::run),
+ // array index: TR
+ (general_matrix_vector_product_wrapper<int,Scalar,RowMajor,false,false>::run),
+ // array index: ADJ
+ (general_matrix_vector_product_wrapper<int,Scalar,RowMajor,Conj ,false>::run),
+ 0
+ };
+
+ const Scalar* a = reinterpret_cast<const Scalar*>(pa);
+ const Scalar* b = reinterpret_cast<const Scalar*>(pb);
+ Scalar* c = reinterpret_cast<Scalar*>(pc);
+ Scalar alpha = *reinterpret_cast<const Scalar*>(palpha);
+ Scalar beta = *reinterpret_cast<const Scalar*>(pbeta);
+
+ // check arguments
+ int info = 0;
+ if(OP(*opa)==INVALID) info = 1;
+ else if(*m<0) info = 2;
+ else if(*n<0) info = 3;
+ else if(*lda<std::max(1,*m)) info = 6;
+ else if(*incb==0) info = 8;
+ else if(*incc==0) info = 11;
+ if(info)
+ return xerbla_(SCALAR_SUFFIX_UP"GEMV ",&info,6);
+
+ if(*m==0 || *n==0 || (alpha==Scalar(0) && beta==Scalar(1)))
+ return 0;
+
+ int actual_m = *m;
+ int actual_n = *n;
+ int code = OP(*opa);
+ if(code!=NOTR)
+ std::swap(actual_m,actual_n);
+
+ const Scalar* actual_b = get_compact_vector(b,actual_n,*incb);
+ Scalar* actual_c = get_compact_vector(c,actual_m,*incc);
+
+ if(beta!=Scalar(1))
+ {
+ if(beta==Scalar(0)) make_vector(actual_c, actual_m).setZero();
+ else make_vector(actual_c, actual_m) *= beta;
+ }
+
+ if(code>=4 || func[code]==0)
+ return 0;
+
+ func[code](actual_m, actual_n, a, *lda, actual_b, 1, actual_c, 1, alpha);
+
+ if(actual_b!=b) delete[] actual_b;
+ if(actual_c!=c) delete[] copy_back(actual_c,c,actual_m,*incc);
+
+ return 1;
+}
+
+int EIGEN_BLAS_FUNC(trsv)(const char *uplo, const char *opa, const char *diag, const int *n, const RealScalar *pa, const int *lda, RealScalar *pb, const int *incb)
+{
+ typedef void (*functype)(int, const Scalar *, int, Scalar *);
+ static const functype func[16] = {
+ // array index: NOTR | (UP << 2) | (NUNIT << 3)
+ (internal::triangular_solve_vector<Scalar,Scalar,int,OnTheLeft, Upper|0, false,ColMajor>::run),
+ // array index: TR | (UP << 2) | (NUNIT << 3)
+ (internal::triangular_solve_vector<Scalar,Scalar,int,OnTheLeft, Lower|0, false,RowMajor>::run),
+ // array index: ADJ | (UP << 2) | (NUNIT << 3)
+ (internal::triangular_solve_vector<Scalar,Scalar,int,OnTheLeft, Lower|0, Conj, RowMajor>::run),
+ 0,
+ // array index: NOTR | (LO << 2) | (NUNIT << 3)
+ (internal::triangular_solve_vector<Scalar,Scalar,int,OnTheLeft, Lower|0, false,ColMajor>::run),
+ // array index: TR | (LO << 2) | (NUNIT << 3)
+ (internal::triangular_solve_vector<Scalar,Scalar,int,OnTheLeft, Upper|0, false,RowMajor>::run),
+ // array index: ADJ | (LO << 2) | (NUNIT << 3)
+ (internal::triangular_solve_vector<Scalar,Scalar,int,OnTheLeft, Upper|0, Conj, RowMajor>::run),
+ 0,
+ // array index: NOTR | (UP << 2) | (UNIT << 3)
+ (internal::triangular_solve_vector<Scalar,Scalar,int,OnTheLeft, Upper|UnitDiag,false,ColMajor>::run),
+ // array index: TR | (UP << 2) | (UNIT << 3)
+ (internal::triangular_solve_vector<Scalar,Scalar,int,OnTheLeft, Lower|UnitDiag,false,RowMajor>::run),
+ // array index: ADJ | (UP << 2) | (UNIT << 3)
+ (internal::triangular_solve_vector<Scalar,Scalar,int,OnTheLeft, Lower|UnitDiag,Conj, RowMajor>::run),
+ 0,
+ // array index: NOTR | (LO << 2) | (UNIT << 3)
+ (internal::triangular_solve_vector<Scalar,Scalar,int,OnTheLeft, Lower|UnitDiag,false,ColMajor>::run),
+ // array index: TR | (LO << 2) | (UNIT << 3)
+ (internal::triangular_solve_vector<Scalar,Scalar,int,OnTheLeft, Upper|UnitDiag,false,RowMajor>::run),
+ // array index: ADJ | (LO << 2) | (UNIT << 3)
+ (internal::triangular_solve_vector<Scalar,Scalar,int,OnTheLeft, Upper|UnitDiag,Conj, RowMajor>::run),
+ 0
+ };
+
+ const Scalar* a = reinterpret_cast<const Scalar*>(pa);
+ Scalar* b = reinterpret_cast<Scalar*>(pb);
+
+ int info = 0;
+ if(UPLO(*uplo)==INVALID) info = 1;
+ else if(OP(*opa)==INVALID) info = 2;
+ else if(DIAG(*diag)==INVALID) info = 3;
+ else if(*n<0) info = 4;
+ else if(*lda<std::max(1,*n)) info = 6;
+ else if(*incb==0) info = 8;
+ if(info)
+ return xerbla_(SCALAR_SUFFIX_UP"TRSV ",&info,6);
+
+ Scalar* actual_b = get_compact_vector(b,*n,*incb);
+
+ int code = OP(*opa) | (UPLO(*uplo) << 2) | (DIAG(*diag) << 3);
+ func[code](*n, a, *lda, actual_b);
+
+ if(actual_b!=b) delete[] copy_back(actual_b,b,*n,*incb);
+
+ return 0;
+}
+
+
+
+int EIGEN_BLAS_FUNC(trmv)(const char *uplo, const char *opa, const char *diag, const int *n, const RealScalar *pa, const int *lda, RealScalar *pb, const int *incb)
+{
+ typedef void (*functype)(int, int, const Scalar *, int, const Scalar *, int, Scalar *, int, const Scalar&);
+ static const functype func[16] = {
+ // array index: NOTR | (UP << 2) | (NUNIT << 3)
+ (internal::triangular_matrix_vector_product<int,Upper|0, Scalar,false,Scalar,false,ColMajor>::run),
+ // array index: TR | (UP << 2) | (NUNIT << 3)
+ (internal::triangular_matrix_vector_product<int,Lower|0, Scalar,false,Scalar,false,RowMajor>::run),
+ // array index: ADJ | (UP << 2) | (NUNIT << 3)
+ (internal::triangular_matrix_vector_product<int,Lower|0, Scalar,Conj, Scalar,false,RowMajor>::run),
+ 0,
+ // array index: NOTR | (LO << 2) | (NUNIT << 3)
+ (internal::triangular_matrix_vector_product<int,Lower|0, Scalar,false,Scalar,false,ColMajor>::run),
+ // array index: TR | (LO << 2) | (NUNIT << 3)
+ (internal::triangular_matrix_vector_product<int,Upper|0, Scalar,false,Scalar,false,RowMajor>::run),
+ // array index: ADJ | (LO << 2) | (NUNIT << 3)
+ (internal::triangular_matrix_vector_product<int,Upper|0, Scalar,Conj, Scalar,false,RowMajor>::run),
+ 0,
+ // array index: NOTR | (UP << 2) | (UNIT << 3)
+ (internal::triangular_matrix_vector_product<int,Upper|UnitDiag,Scalar,false,Scalar,false,ColMajor>::run),
+ // array index: TR | (UP << 2) | (UNIT << 3)
+ (internal::triangular_matrix_vector_product<int,Lower|UnitDiag,Scalar,false,Scalar,false,RowMajor>::run),
+ // array index: ADJ | (UP << 2) | (UNIT << 3)
+ (internal::triangular_matrix_vector_product<int,Lower|UnitDiag,Scalar,Conj, Scalar,false,RowMajor>::run),
+ 0,
+ // array index: NOTR | (LO << 2) | (UNIT << 3)
+ (internal::triangular_matrix_vector_product<int,Lower|UnitDiag,Scalar,false,Scalar,false,ColMajor>::run),
+ // array index: TR | (LO << 2) | (UNIT << 3)
+ (internal::triangular_matrix_vector_product<int,Upper|UnitDiag,Scalar,false,Scalar,false,RowMajor>::run),
+ // array index: ADJ | (LO << 2) | (UNIT << 3)
+ (internal::triangular_matrix_vector_product<int,Upper|UnitDiag,Scalar,Conj, Scalar,false,RowMajor>::run),
+ 0
+ };
+
+ const Scalar* a = reinterpret_cast<const Scalar*>(pa);
+ Scalar* b = reinterpret_cast<Scalar*>(pb);
+
+ int info = 0;
+ if(UPLO(*uplo)==INVALID) info = 1;
+ else if(OP(*opa)==INVALID) info = 2;
+ else if(DIAG(*diag)==INVALID) info = 3;
+ else if(*n<0) info = 4;
+ else if(*lda<std::max(1,*n)) info = 6;
+ else if(*incb==0) info = 8;
+ if(info)
+ return xerbla_(SCALAR_SUFFIX_UP"TRMV ",&info,6);
+
+ if(*n==0)
+ return 1;
+
+ Scalar* actual_b = get_compact_vector(b,*n,*incb);
+ Matrix<Scalar,Dynamic,1> res(*n);
+ res.setZero();
+
+ int code = OP(*opa) | (UPLO(*uplo) << 2) | (DIAG(*diag) << 3);
+ if(code>=16 || func[code]==0)
+ return 0;
+
+ func[code](*n, *n, a, *lda, actual_b, 1, res.data(), 1, Scalar(1));
+
+ copy_back(res.data(),b,*n,*incb);
+ if(actual_b!=b) delete[] actual_b;
+
+ return 1;
+}
+
+/** GBMV performs one of the matrix-vector operations
+ *
+ * y := alpha*A*x + beta*y, or y := alpha*A'*x + beta*y,
+ *
+ * where alpha and beta are scalars, x and y are vectors and A is an
+ * m by n band matrix, with kl sub-diagonals and ku super-diagonals.
+ */
+int EIGEN_BLAS_FUNC(gbmv)(char *trans, int *m, int *n, int *kl, int *ku, RealScalar *palpha, RealScalar *pa, int *lda,
+ RealScalar *px, int *incx, RealScalar *pbeta, RealScalar *py, int *incy)
+{
+ const Scalar* a = reinterpret_cast<const Scalar*>(pa);
+ const Scalar* x = reinterpret_cast<const Scalar*>(px);
+ Scalar* y = reinterpret_cast<Scalar*>(py);
+ Scalar alpha = *reinterpret_cast<const Scalar*>(palpha);
+ Scalar beta = *reinterpret_cast<const Scalar*>(pbeta);
+ int coeff_rows = *kl+*ku+1;
+
+ int info = 0;
+ if(OP(*trans)==INVALID) info = 1;
+ else if(*m<0) info = 2;
+ else if(*n<0) info = 3;
+ else if(*kl<0) info = 4;
+ else if(*ku<0) info = 5;
+ else if(*lda<coeff_rows) info = 8;
+ else if(*incx==0) info = 10;
+ else if(*incy==0) info = 13;
+ if(info)
+ return xerbla_(SCALAR_SUFFIX_UP"GBMV ",&info,6);
+
+ if(*m==0 || *n==0 || (alpha==Scalar(0) && beta==Scalar(1)))
+ return 0;
+
+ int actual_m = *m;
+ int actual_n = *n;
+ if(OP(*trans)!=NOTR)
+ std::swap(actual_m,actual_n);
+
+ const Scalar* actual_x = get_compact_vector(x,actual_n,*incx);
+ Scalar* actual_y = get_compact_vector(y,actual_m,*incy);
+
+ if(beta!=Scalar(1))
+ {
+ if(beta==Scalar(0)) make_vector(actual_y, actual_m).setZero();
+ else make_vector(actual_y, actual_m) *= beta;
+ }
+
+ ConstMatrixType mat_coeffs(a,coeff_rows,*n,*lda);
+
+ int nb = std::min(*n,(*m)+(*ku));
+ for(int j=0; j<nb; ++j)
+ {
+ int start = std::max(0,j - *ku);
+ int end = std::min((*m)-1,j + *kl);
+ int len = end - start + 1;
+ int offset = (*ku) - j + start;
+ if(OP(*trans)==NOTR)
+ make_vector(actual_y+start,len) += (alpha*actual_x[j]) * mat_coeffs.col(j).segment(offset,len);
+ else if(OP(*trans)==TR)
+ actual_y[j] += alpha * ( mat_coeffs.col(j).segment(offset,len).transpose() * make_vector(actual_x+start,len) ).value();
+ else
+ actual_y[j] += alpha * ( mat_coeffs.col(j).segment(offset,len).adjoint() * make_vector(actual_x+start,len) ).value();
+ }
+
+ if(actual_x!=x) delete[] actual_x;
+ if(actual_y!=y) delete[] copy_back(actual_y,y,actual_m,*incy);
+
+ return 0;
+}
+
+#if 0
+/** TBMV performs one of the matrix-vector operations
+ *
+ * x := A*x, or x := A'*x,
+ *
+ * where x is an n element vector and A is an n by n unit, or non-unit,
+ * upper or lower triangular band matrix, with ( k + 1 ) diagonals.
+ */
+int EIGEN_BLAS_FUNC(tbmv)(char *uplo, char *opa, char *diag, int *n, int *k, RealScalar *pa, int *lda, RealScalar *px, int *incx)
+{
+ Scalar* a = reinterpret_cast<Scalar*>(pa);
+ Scalar* x = reinterpret_cast<Scalar*>(px);
+ int coeff_rows = *k + 1;
+
+ int info = 0;
+ if(UPLO(*uplo)==INVALID) info = 1;
+ else if(OP(*opa)==INVALID) info = 2;
+ else if(DIAG(*diag)==INVALID) info = 3;
+ else if(*n<0) info = 4;
+ else if(*k<0) info = 5;
+ else if(*lda<coeff_rows) info = 7;
+ else if(*incx==0) info = 9;
+ if(info)
+ return xerbla_(SCALAR_SUFFIX_UP"TBMV ",&info,6);
+
+ if(*n==0)
+ return 0;
+
+ int actual_n = *n;
+
+ Scalar* actual_x = get_compact_vector(x,actual_n,*incx);
+
+ MatrixType mat_coeffs(a,coeff_rows,*n,*lda);
+
+ int ku = UPLO(*uplo)==UPPER ? *k : 0;
+ int kl = UPLO(*uplo)==LOWER ? *k : 0;
+
+ for(int j=0; j<*n; ++j)
+ {
+ int start = std::max(0,j - ku);
+ int end = std::min((*m)-1,j + kl);
+ int len = end - start + 1;
+ int offset = (ku) - j + start;
+
+ if(OP(*trans)==NOTR)
+ make_vector(actual_y+start,len) += (alpha*actual_x[j]) * mat_coeffs.col(j).segment(offset,len);
+ else if(OP(*trans)==TR)
+ actual_y[j] += alpha * ( mat_coeffs.col(j).segment(offset,len).transpose() * make_vector(actual_x+start,len) ).value();
+ else
+ actual_y[j] += alpha * ( mat_coeffs.col(j).segment(offset,len).adjoint() * make_vector(actual_x+start,len) ).value();
+ }
+
+ if(actual_x!=x) delete[] actual_x;
+ if(actual_y!=y) delete[] copy_back(actual_y,y,actual_m,*incy);
+
+ return 0;
+}
+#endif
+
+/** DTBSV solves one of the systems of equations
+ *
+ * A*x = b, or A'*x = b,
+ *
+ * where b and x are n element vectors and A is an n by n unit, or
+ * non-unit, upper or lower triangular band matrix, with ( k + 1 )
+ * diagonals.
+ *
+ * No test for singularity or near-singularity is included in this
+ * routine. Such tests must be performed before calling this routine.
+ */
+int EIGEN_BLAS_FUNC(tbsv)(char *uplo, char *op, char *diag, int *n, int *k, RealScalar *pa, int *lda, RealScalar *px, int *incx)
+{
+ typedef void (*functype)(int, int, const Scalar *, int, Scalar *);
+ static const functype func[16] = {
+ // array index: NOTR | (UP << 2) | (NUNIT << 3)
+ (internal::band_solve_triangular_selector<int,Upper|0, Scalar,false,Scalar,ColMajor>::run),
+ // array index: TR | (UP << 2) | (NUNIT << 3)
+ (internal::band_solve_triangular_selector<int,Lower|0, Scalar,false,Scalar,RowMajor>::run),
+ // array index: ADJ | (UP << 2) | (NUNIT << 3)
+ (internal::band_solve_triangular_selector<int,Lower|0, Scalar,Conj, Scalar,RowMajor>::run),
+ 0,
+ // array index: NOTR | (LO << 2) | (NUNIT << 3)
+ (internal::band_solve_triangular_selector<int,Lower|0, Scalar,false,Scalar,ColMajor>::run),
+ // array index: TR | (LO << 2) | (NUNIT << 3)
+ (internal::band_solve_triangular_selector<int,Upper|0, Scalar,false,Scalar,RowMajor>::run),
+ // array index: ADJ | (LO << 2) | (NUNIT << 3)
+ (internal::band_solve_triangular_selector<int,Upper|0, Scalar,Conj, Scalar,RowMajor>::run),
+ 0,
+ // array index: NOTR | (UP << 2) | (UNIT << 3)
+ (internal::band_solve_triangular_selector<int,Upper|UnitDiag,Scalar,false,Scalar,ColMajor>::run),
+ // array index: TR | (UP << 2) | (UNIT << 3)
+ (internal::band_solve_triangular_selector<int,Lower|UnitDiag,Scalar,false,Scalar,RowMajor>::run),
+ // array index: ADJ | (UP << 2) | (UNIT << 3)
+ (internal::band_solve_triangular_selector<int,Lower|UnitDiag,Scalar,Conj, Scalar,RowMajor>::run),
+ 0,
+ // array index: NOTR | (LO << 2) | (UNIT << 3)
+ (internal::band_solve_triangular_selector<int,Lower|UnitDiag,Scalar,false,Scalar,ColMajor>::run),
+ // array index: TR | (LO << 2) | (UNIT << 3)
+ (internal::band_solve_triangular_selector<int,Upper|UnitDiag,Scalar,false,Scalar,RowMajor>::run),
+ // array index: ADJ | (LO << 2) | (UNIT << 3)
+ (internal::band_solve_triangular_selector<int,Upper|UnitDiag,Scalar,Conj, Scalar,RowMajor>::run),
+ 0,
+ };
+
+ Scalar* a = reinterpret_cast<Scalar*>(pa);
+ Scalar* x = reinterpret_cast<Scalar*>(px);
+ int coeff_rows = *k+1;
+
+ int info = 0;
+ if(UPLO(*uplo)==INVALID) info = 1;
+ else if(OP(*op)==INVALID) info = 2;
+ else if(DIAG(*diag)==INVALID) info = 3;
+ else if(*n<0) info = 4;
+ else if(*k<0) info = 5;
+ else if(*lda<coeff_rows) info = 7;
+ else if(*incx==0) info = 9;
+ if(info)
+ return xerbla_(SCALAR_SUFFIX_UP"TBSV ",&info,6);
+
+ if(*n==0 || (*k==0 && DIAG(*diag)==UNIT))
+ return 0;
+
+ int actual_n = *n;
+
+ Scalar* actual_x = get_compact_vector(x,actual_n,*incx);
+
+ int code = OP(*op) | (UPLO(*uplo) << 2) | (DIAG(*diag) << 3);
+ if(code>=16 || func[code]==0)
+ return 0;
+
+ func[code](*n, *k, a, *lda, actual_x);
+
+ if(actual_x!=x) delete[] copy_back(actual_x,x,actual_n,*incx);
+
+ return 0;
+}
+
+/** DTPMV performs one of the matrix-vector operations
+ *
+ * x := A*x, or x := A'*x,
+ *
+ * where x is an n element vector and A is an n by n unit, or non-unit,
+ * upper or lower triangular matrix, supplied in packed form.
+ */
+int EIGEN_BLAS_FUNC(tpmv)(char *uplo, char *opa, char *diag, int *n, RealScalar *pap, RealScalar *px, int *incx)
+{
+ typedef void (*functype)(int, const Scalar*, const Scalar*, Scalar*, Scalar);
+ static const functype func[16] = {
+ // array index: NOTR | (UP << 2) | (NUNIT << 3)
+ (internal::packed_triangular_matrix_vector_product<int,Upper|0, Scalar,false,Scalar,false,ColMajor>::run),
+ // array index: TR | (UP << 2) | (NUNIT << 3)
+ (internal::packed_triangular_matrix_vector_product<int,Lower|0, Scalar,false,Scalar,false,RowMajor>::run),
+ // array index: ADJ | (UP << 2) | (NUNIT << 3)
+ (internal::packed_triangular_matrix_vector_product<int,Lower|0, Scalar,Conj, Scalar,false,RowMajor>::run),
+ 0,
+ // array index: NOTR | (LO << 2) | (NUNIT << 3)
+ (internal::packed_triangular_matrix_vector_product<int,Lower|0, Scalar,false,Scalar,false,ColMajor>::run),
+ // array index: TR | (LO << 2) | (NUNIT << 3)
+ (internal::packed_triangular_matrix_vector_product<int,Upper|0, Scalar,false,Scalar,false,RowMajor>::run),
+ // array index: ADJ | (LO << 2) | (NUNIT << 3)
+ (internal::packed_triangular_matrix_vector_product<int,Upper|0, Scalar,Conj, Scalar,false,RowMajor>::run),
+ 0,
+ // array index: NOTR | (UP << 2) | (UNIT << 3)
+ (internal::packed_triangular_matrix_vector_product<int,Upper|UnitDiag,Scalar,false,Scalar,false,ColMajor>::run),
+ // array index: TR | (UP << 2) | (UNIT << 3)
+ (internal::packed_triangular_matrix_vector_product<int,Lower|UnitDiag,Scalar,false,Scalar,false,RowMajor>::run),
+ // array index: ADJ | (UP << 2) | (UNIT << 3)
+ (internal::packed_triangular_matrix_vector_product<int,Lower|UnitDiag,Scalar,Conj, Scalar,false,RowMajor>::run),
+ 0,
+ // array index: NOTR | (LO << 2) | (UNIT << 3)
+ (internal::packed_triangular_matrix_vector_product<int,Lower|UnitDiag,Scalar,false,Scalar,false,ColMajor>::run),
+ // array index: TR | (LO << 2) | (UNIT << 3)
+ (internal::packed_triangular_matrix_vector_product<int,Upper|UnitDiag,Scalar,false,Scalar,false,RowMajor>::run),
+ // array index: ADJ | (LO << 2) | (UNIT << 3)
+ (internal::packed_triangular_matrix_vector_product<int,Upper|UnitDiag,Scalar,Conj, Scalar,false,RowMajor>::run),
+ 0
+ };
+
+ Scalar* ap = reinterpret_cast<Scalar*>(pap);
+ Scalar* x = reinterpret_cast<Scalar*>(px);
+
+ int info = 0;
+ if(UPLO(*uplo)==INVALID) info = 1;
+ else if(OP(*opa)==INVALID) info = 2;
+ else if(DIAG(*diag)==INVALID) info = 3;
+ else if(*n<0) info = 4;
+ else if(*incx==0) info = 7;
+ if(info)
+ return xerbla_(SCALAR_SUFFIX_UP"TPMV ",&info,6);
+
+ if(*n==0)
+ return 1;
+
+ Scalar* actual_x = get_compact_vector(x,*n,*incx);
+ Matrix<Scalar,Dynamic,1> res(*n);
+ res.setZero();
+
+ int code = OP(*opa) | (UPLO(*uplo) << 2) | (DIAG(*diag) << 3);
+ if(code>=16 || func[code]==0)
+ return 0;
+
+ func[code](*n, ap, actual_x, res.data(), Scalar(1));
+
+ copy_back(res.data(),x,*n,*incx);
+ if(actual_x!=x) delete[] actual_x;
+
+ return 1;
+}
+
+/** DTPSV solves one of the systems of equations
+ *
+ * A*x = b, or A'*x = b,
+ *
+ * where b and x are n element vectors and A is an n by n unit, or
+ * non-unit, upper or lower triangular matrix, supplied in packed form.
+ *
+ * No test for singularity or near-singularity is included in this
+ * routine. Such tests must be performed before calling this routine.
+ */
+int EIGEN_BLAS_FUNC(tpsv)(char *uplo, char *opa, char *diag, int *n, RealScalar *pap, RealScalar *px, int *incx)
+{
+ typedef void (*functype)(int, const Scalar*, Scalar*);
+ static const functype func[16] = {
+ // array index: NOTR | (UP << 2) | (NUNIT << 3)
+ (internal::packed_triangular_solve_vector<Scalar,Scalar,int,OnTheLeft, Upper|0, false,ColMajor>::run),
+ // array index: TR | (UP << 2) | (NUNIT << 3)
+ (internal::packed_triangular_solve_vector<Scalar,Scalar,int,OnTheLeft, Lower|0, false,RowMajor>::run),
+ // array index: ADJ | (UP << 2) | (NUNIT << 3)
+ (internal::packed_triangular_solve_vector<Scalar,Scalar,int,OnTheLeft, Lower|0, Conj, RowMajor>::run),
+ 0,
+ // array index: NOTR | (LO << 2) | (NUNIT << 3)
+ (internal::packed_triangular_solve_vector<Scalar,Scalar,int,OnTheLeft, Lower|0, false,ColMajor>::run),
+ // array index: TR | (LO << 2) | (NUNIT << 3)
+ (internal::packed_triangular_solve_vector<Scalar,Scalar,int,OnTheLeft, Upper|0, false,RowMajor>::run),
+ // array index: ADJ | (LO << 2) | (NUNIT << 3)
+ (internal::packed_triangular_solve_vector<Scalar,Scalar,int,OnTheLeft, Upper|0, Conj, RowMajor>::run),
+ 0,
+ // array index: NOTR | (UP << 2) | (UNIT << 3)
+ (internal::packed_triangular_solve_vector<Scalar,Scalar,int,OnTheLeft, Upper|UnitDiag,false,ColMajor>::run),
+ // array index: TR | (UP << 2) | (UNIT << 3)
+ (internal::packed_triangular_solve_vector<Scalar,Scalar,int,OnTheLeft, Lower|UnitDiag,false,RowMajor>::run),
+ // array index: ADJ | (UP << 2) | (UNIT << 3)
+ (internal::packed_triangular_solve_vector<Scalar,Scalar,int,OnTheLeft, Lower|UnitDiag,Conj, RowMajor>::run),
+ 0,
+ // array index: NOTR | (LO << 2) | (UNIT << 3)
+ (internal::packed_triangular_solve_vector<Scalar,Scalar,int,OnTheLeft, Lower|UnitDiag,false,ColMajor>::run),
+ // array index: TR | (LO << 2) | (UNIT << 3)
+ (internal::packed_triangular_solve_vector<Scalar,Scalar,int,OnTheLeft, Upper|UnitDiag,false,RowMajor>::run),
+ // array index: ADJ | (LO << 2) | (UNIT << 3)
+ (internal::packed_triangular_solve_vector<Scalar,Scalar,int,OnTheLeft, Upper|UnitDiag,Conj, RowMajor>::run),
+ 0
+ };
+
+ Scalar* ap = reinterpret_cast<Scalar*>(pap);
+ Scalar* x = reinterpret_cast<Scalar*>(px);
+
+ int info = 0;
+ if(UPLO(*uplo)==INVALID) info = 1;
+ else if(OP(*opa)==INVALID) info = 2;
+ else if(DIAG(*diag)==INVALID) info = 3;
+ else if(*n<0) info = 4;
+ else if(*incx==0) info = 7;
+ if(info)
+ return xerbla_(SCALAR_SUFFIX_UP"TPSV ",&info,6);
+
+ Scalar* actual_x = get_compact_vector(x,*n,*incx);
+
+ int code = OP(*opa) | (UPLO(*uplo) << 2) | (DIAG(*diag) << 3);
+ func[code](*n, ap, actual_x);
+
+ if(actual_x!=x) delete[] copy_back(actual_x,x,*n,*incx);
+
+ return 1;
+}
diff --git a/blas/level2_real_impl.h b/blas/level2_real_impl.h
new file mode 100644
index 0000000..7620f0a
--- /dev/null
+++ b/blas/level2_real_impl.h
@@ -0,0 +1,306 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009-2010 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "common.h"
+
+// y = alpha*A*x + beta*y
+int EIGEN_BLAS_FUNC(symv) (const char *uplo, const int *n, const RealScalar *palpha, const RealScalar *pa, const int *lda,
+ const RealScalar *px, const int *incx, const RealScalar *pbeta, RealScalar *py, const int *incy)
+{
+ typedef void (*functype)(int, const Scalar*, int, const Scalar*, Scalar*, Scalar);
+ static const functype func[2] = {
+ // array index: UP
+ (internal::selfadjoint_matrix_vector_product<Scalar,int,ColMajor,Upper,false,false>::run),
+ // array index: LO
+ (internal::selfadjoint_matrix_vector_product<Scalar,int,ColMajor,Lower,false,false>::run),
+ };
+
+ const Scalar* a = reinterpret_cast<const Scalar*>(pa);
+ const Scalar* x = reinterpret_cast<const Scalar*>(px);
+ Scalar* y = reinterpret_cast<Scalar*>(py);
+ Scalar alpha = *reinterpret_cast<const Scalar*>(palpha);
+ Scalar beta = *reinterpret_cast<const Scalar*>(pbeta);
+
+ // check arguments
+ int info = 0;
+ if(UPLO(*uplo)==INVALID) info = 1;
+ else if(*n<0) info = 2;
+ else if(*lda<std::max(1,*n)) info = 5;
+ else if(*incx==0) info = 7;
+ else if(*incy==0) info = 10;
+ if(info)
+ return xerbla_(SCALAR_SUFFIX_UP"SYMV ",&info,6);
+
+ if(*n==0)
+ return 0;
+
+ const Scalar* actual_x = get_compact_vector(x,*n,*incx);
+ Scalar* actual_y = get_compact_vector(y,*n,*incy);
+
+ if(beta!=Scalar(1))
+ {
+ if(beta==Scalar(0)) make_vector(actual_y, *n).setZero();
+ else make_vector(actual_y, *n) *= beta;
+ }
+
+ int code = UPLO(*uplo);
+ if(code>=2 || func[code]==0)
+ return 0;
+
+ func[code](*n, a, *lda, actual_x, actual_y, alpha);
+
+ if(actual_x!=x) delete[] actual_x;
+ if(actual_y!=y) delete[] copy_back(actual_y,y,*n,*incy);
+
+ return 1;
+}
+
+// C := alpha*x*x' + C
+int EIGEN_BLAS_FUNC(syr)(const char *uplo, const int *n, const RealScalar *palpha, const RealScalar *px, const int *incx, RealScalar *pc, const int *ldc)
+{
+
+ typedef void (*functype)(int, Scalar*, int, const Scalar*, const Scalar*, const Scalar&);
+ static const functype func[2] = {
+ // array index: UP
+ (selfadjoint_rank1_update<Scalar,int,ColMajor,Upper,false,Conj>::run),
+ // array index: LO
+ (selfadjoint_rank1_update<Scalar,int,ColMajor,Lower,false,Conj>::run),
+ };
+
+ const Scalar* x = reinterpret_cast<const Scalar*>(px);
+ Scalar* c = reinterpret_cast<Scalar*>(pc);
+ Scalar alpha = *reinterpret_cast<const Scalar*>(palpha);
+
+ int info = 0;
+ if(UPLO(*uplo)==INVALID) info = 1;
+ else if(*n<0) info = 2;
+ else if(*incx==0) info = 5;
+ else if(*ldc<std::max(1,*n)) info = 7;
+ if(info)
+ return xerbla_(SCALAR_SUFFIX_UP"SYR ",&info,6);
+
+ if(*n==0 || alpha==Scalar(0)) return 1;
+
+ // if the increment is not 1, let's copy it to a temporary vector to enable vectorization
+ const Scalar* x_cpy = get_compact_vector(x,*n,*incx);
+
+ int code = UPLO(*uplo);
+ if(code>=2 || func[code]==0)
+ return 0;
+
+ func[code](*n, c, *ldc, x_cpy, x_cpy, alpha);
+
+ if(x_cpy!=x) delete[] x_cpy;
+
+ return 1;
+}
+
+// C := alpha*x*y' + alpha*y*x' + C
+int EIGEN_BLAS_FUNC(syr2)(const char *uplo, const int *n, const RealScalar *palpha, const RealScalar *px, const int *incx, const RealScalar *py, const int *incy, RealScalar *pc, const int *ldc)
+{
+ typedef void (*functype)(int, Scalar*, int, const Scalar*, const Scalar*, Scalar);
+ static const functype func[2] = {
+ // array index: UP
+ (internal::rank2_update_selector<Scalar,int,Upper>::run),
+ // array index: LO
+ (internal::rank2_update_selector<Scalar,int,Lower>::run),
+ };
+
+ const Scalar* x = reinterpret_cast<const Scalar*>(px);
+ const Scalar* y = reinterpret_cast<const Scalar*>(py);
+ Scalar* c = reinterpret_cast<Scalar*>(pc);
+ Scalar alpha = *reinterpret_cast<const Scalar*>(palpha);
+
+ int info = 0;
+ if(UPLO(*uplo)==INVALID) info = 1;
+ else if(*n<0) info = 2;
+ else if(*incx==0) info = 5;
+ else if(*incy==0) info = 7;
+ else if(*ldc<std::max(1,*n)) info = 9;
+ if(info)
+ return xerbla_(SCALAR_SUFFIX_UP"SYR2 ",&info,6);
+
+ if(alpha==Scalar(0))
+ return 1;
+
+ const Scalar* x_cpy = get_compact_vector(x,*n,*incx);
+ const Scalar* y_cpy = get_compact_vector(y,*n,*incy);
+
+ int code = UPLO(*uplo);
+ if(code>=2 || func[code]==0)
+ return 0;
+
+ func[code](*n, c, *ldc, x_cpy, y_cpy, alpha);
+
+ if(x_cpy!=x) delete[] x_cpy;
+ if(y_cpy!=y) delete[] y_cpy;
+
+// int code = UPLO(*uplo);
+// if(code>=2 || func[code]==0)
+// return 0;
+
+// func[code](*n, a, *inca, b, *incb, c, *ldc, alpha);
+ return 1;
+}
+
+/** DSBMV performs the matrix-vector operation
+ *
+ * y := alpha*A*x + beta*y,
+ *
+ * where alpha and beta are scalars, x and y are n element vectors and
+ * A is an n by n symmetric band matrix, with k super-diagonals.
+ */
+// int EIGEN_BLAS_FUNC(sbmv)( char *uplo, int *n, int *k, RealScalar *alpha, RealScalar *a, int *lda,
+// RealScalar *x, int *incx, RealScalar *beta, RealScalar *y, int *incy)
+// {
+// return 1;
+// }
+
+
+/** DSPMV performs the matrix-vector operation
+ *
+ * y := alpha*A*x + beta*y,
+ *
+ * where alpha and beta are scalars, x and y are n element vectors and
+ * A is an n by n symmetric matrix, supplied in packed form.
+ *
+ */
+// int EIGEN_BLAS_FUNC(spmv)(char *uplo, int *n, RealScalar *alpha, RealScalar *ap, RealScalar *x, int *incx, RealScalar *beta, RealScalar *y, int *incy)
+// {
+// return 1;
+// }
+
+/** DSPR performs the symmetric rank 1 operation
+ *
+ * A := alpha*x*x' + A,
+ *
+ * where alpha is a real scalar, x is an n element vector and A is an
+ * n by n symmetric matrix, supplied in packed form.
+ */
+int EIGEN_BLAS_FUNC(spr)(char *uplo, int *n, Scalar *palpha, Scalar *px, int *incx, Scalar *pap)
+{
+ typedef void (*functype)(int, Scalar*, const Scalar*, Scalar);
+ static const functype func[2] = {
+ // array index: UP
+ (internal::selfadjoint_packed_rank1_update<Scalar,int,ColMajor,Upper,false,false>::run),
+ // array index: LO
+ (internal::selfadjoint_packed_rank1_update<Scalar,int,ColMajor,Lower,false,false>::run),
+ };
+
+ Scalar* x = reinterpret_cast<Scalar*>(px);
+ Scalar* ap = reinterpret_cast<Scalar*>(pap);
+ Scalar alpha = *reinterpret_cast<Scalar*>(palpha);
+
+ int info = 0;
+ if(UPLO(*uplo)==INVALID) info = 1;
+ else if(*n<0) info = 2;
+ else if(*incx==0) info = 5;
+ if(info)
+ return xerbla_(SCALAR_SUFFIX_UP"SPR ",&info,6);
+
+ if(alpha==Scalar(0))
+ return 1;
+
+ Scalar* x_cpy = get_compact_vector(x, *n, *incx);
+
+ int code = UPLO(*uplo);
+ if(code>=2 || func[code]==0)
+ return 0;
+
+ func[code](*n, ap, x_cpy, alpha);
+
+ if(x_cpy!=x) delete[] x_cpy;
+
+ return 1;
+}
+
+/** DSPR2 performs the symmetric rank 2 operation
+ *
+ * A := alpha*x*y' + alpha*y*x' + A,
+ *
+ * where alpha is a scalar, x and y are n element vectors and A is an
+ * n by n symmetric matrix, supplied in packed form.
+ */
+int EIGEN_BLAS_FUNC(spr2)(char *uplo, int *n, RealScalar *palpha, RealScalar *px, int *incx, RealScalar *py, int *incy, RealScalar *pap)
+{
+ typedef void (*functype)(int, Scalar*, const Scalar*, const Scalar*, Scalar);
+ static const functype func[2] = {
+ // array index: UP
+ (internal::packed_rank2_update_selector<Scalar,int,Upper>::run),
+ // array index: LO
+ (internal::packed_rank2_update_selector<Scalar,int,Lower>::run),
+ };
+
+ Scalar* x = reinterpret_cast<Scalar*>(px);
+ Scalar* y = reinterpret_cast<Scalar*>(py);
+ Scalar* ap = reinterpret_cast<Scalar*>(pap);
+ Scalar alpha = *reinterpret_cast<Scalar*>(palpha);
+
+ int info = 0;
+ if(UPLO(*uplo)==INVALID) info = 1;
+ else if(*n<0) info = 2;
+ else if(*incx==0) info = 5;
+ else if(*incy==0) info = 7;
+ if(info)
+ return xerbla_(SCALAR_SUFFIX_UP"SPR2 ",&info,6);
+
+ if(alpha==Scalar(0))
+ return 1;
+
+ Scalar* x_cpy = get_compact_vector(x, *n, *incx);
+ Scalar* y_cpy = get_compact_vector(y, *n, *incy);
+
+ int code = UPLO(*uplo);
+ if(code>=2 || func[code]==0)
+ return 0;
+
+ func[code](*n, ap, x_cpy, y_cpy, alpha);
+
+ if(x_cpy!=x) delete[] x_cpy;
+ if(y_cpy!=y) delete[] y_cpy;
+
+ return 1;
+}
+
+/** DGER performs the rank 1 operation
+ *
+ * A := alpha*x*y' + A,
+ *
+ * where alpha is a scalar, x is an m element vector, y is an n element
+ * vector and A is an m by n matrix.
+ */
+int EIGEN_BLAS_FUNC(ger)(int *m, int *n, Scalar *palpha, Scalar *px, int *incx, Scalar *py, int *incy, Scalar *pa, int *lda)
+{
+ Scalar* x = reinterpret_cast<Scalar*>(px);
+ Scalar* y = reinterpret_cast<Scalar*>(py);
+ Scalar* a = reinterpret_cast<Scalar*>(pa);
+ Scalar alpha = *reinterpret_cast<Scalar*>(palpha);
+
+ int info = 0;
+ if(*m<0) info = 1;
+ else if(*n<0) info = 2;
+ else if(*incx==0) info = 5;
+ else if(*incy==0) info = 7;
+ else if(*lda<std::max(1,*m)) info = 9;
+ if(info)
+ return xerbla_(SCALAR_SUFFIX_UP"GER ",&info,6);
+
+ if(alpha==Scalar(0))
+ return 1;
+
+ Scalar* x_cpy = get_compact_vector(x,*m,*incx);
+ Scalar* y_cpy = get_compact_vector(y,*n,*incy);
+
+ internal::general_rank1_update<Scalar,int,ColMajor,false,false>::run(*m, *n, a, *lda, x_cpy, y_cpy, alpha);
+
+ if(x_cpy!=x) delete[] x_cpy;
+ if(y_cpy!=y) delete[] y_cpy;
+
+ return 1;
+}
diff --git a/blas/level3_impl.h b/blas/level3_impl.h
new file mode 100644
index 0000000..66216c9
--- /dev/null
+++ b/blas/level3_impl.h
@@ -0,0 +1,702 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009-2010 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+#include <iostream>
+#include "common.h"
+
+int EIGEN_BLAS_FUNC(gemm)(const char *opa, const char *opb, const int *m, const int *n, const int *k, const RealScalar *palpha,
+ const RealScalar *pa, const int *lda, const RealScalar *pb, const int *ldb, const RealScalar *pbeta, RealScalar *pc, const int *ldc)
+{
+// std::cerr << "in gemm " << *opa << " " << *opb << " " << *m << " " << *n << " " << *k << " " << *lda << " " << *ldb << " " << *ldc << " " << *palpha << " " << *pbeta << "\n";
+ typedef void (*functype)(DenseIndex, DenseIndex, DenseIndex, const Scalar *, DenseIndex, const Scalar *, DenseIndex, Scalar *, DenseIndex, DenseIndex, Scalar, internal::level3_blocking<Scalar,Scalar>&, Eigen::internal::GemmParallelInfo<DenseIndex>*);
+ static const functype func[12] = {
+ // array index: NOTR | (NOTR << 2)
+ (internal::general_matrix_matrix_product<DenseIndex,Scalar,ColMajor,false,Scalar,ColMajor,false,ColMajor,1>::run),
+ // array index: TR | (NOTR << 2)
+ (internal::general_matrix_matrix_product<DenseIndex,Scalar,RowMajor,false,Scalar,ColMajor,false,ColMajor,1>::run),
+ // array index: ADJ | (NOTR << 2)
+ (internal::general_matrix_matrix_product<DenseIndex,Scalar,RowMajor,Conj, Scalar,ColMajor,false,ColMajor,1>::run),
+ 0,
+ // array index: NOTR | (TR << 2)
+ (internal::general_matrix_matrix_product<DenseIndex,Scalar,ColMajor,false,Scalar,RowMajor,false,ColMajor,1>::run),
+ // array index: TR | (TR << 2)
+ (internal::general_matrix_matrix_product<DenseIndex,Scalar,RowMajor,false,Scalar,RowMajor,false,ColMajor,1>::run),
+ // array index: ADJ | (TR << 2)
+ (internal::general_matrix_matrix_product<DenseIndex,Scalar,RowMajor,Conj, Scalar,RowMajor,false,ColMajor,1>::run),
+ 0,
+ // array index: NOTR | (ADJ << 2)
+ (internal::general_matrix_matrix_product<DenseIndex,Scalar,ColMajor,false,Scalar,RowMajor,Conj, ColMajor,1>::run),
+ // array index: TR | (ADJ << 2)
+ (internal::general_matrix_matrix_product<DenseIndex,Scalar,RowMajor,false,Scalar,RowMajor,Conj, ColMajor,1>::run),
+ // array index: ADJ | (ADJ << 2)
+ (internal::general_matrix_matrix_product<DenseIndex,Scalar,RowMajor,Conj, Scalar,RowMajor,Conj, ColMajor,1>::run),
+ 0
+ };
+
+ const Scalar* a = reinterpret_cast<const Scalar*>(pa);
+ const Scalar* b = reinterpret_cast<const Scalar*>(pb);
+ Scalar* c = reinterpret_cast<Scalar*>(pc);
+ Scalar alpha = *reinterpret_cast<const Scalar*>(palpha);
+ Scalar beta = *reinterpret_cast<const Scalar*>(pbeta);
+
+ int info = 0;
+ if(OP(*opa)==INVALID) info = 1;
+ else if(OP(*opb)==INVALID) info = 2;
+ else if(*m<0) info = 3;
+ else if(*n<0) info = 4;
+ else if(*k<0) info = 5;
+ else if(*lda<std::max(1,(OP(*opa)==NOTR)?*m:*k)) info = 8;
+ else if(*ldb<std::max(1,(OP(*opb)==NOTR)?*k:*n)) info = 10;
+ else if(*ldc<std::max(1,*m)) info = 13;
+ if(info)
+ return xerbla_(SCALAR_SUFFIX_UP"GEMM ",&info,6);
+
+ if (*m == 0 || *n == 0)
+ return 0;
+
+ if(beta!=Scalar(1))
+ {
+ if(beta==Scalar(0)) matrix(c, *m, *n, *ldc).setZero();
+ else matrix(c, *m, *n, *ldc) *= beta;
+ }
+
+ if(*k == 0)
+ return 0;
+
+ internal::gemm_blocking_space<ColMajor,Scalar,Scalar,Dynamic,Dynamic,Dynamic> blocking(*m,*n,*k,1,true);
+
+ int code = OP(*opa) | (OP(*opb) << 2);
+ func[code](*m, *n, *k, a, *lda, b, *ldb, c, 1, *ldc, alpha, blocking, 0);
+ return 0;
+}
+
+int EIGEN_BLAS_FUNC(trsm)(const char *side, const char *uplo, const char *opa, const char *diag, const int *m, const int *n,
+ const RealScalar *palpha, const RealScalar *pa, const int *lda, RealScalar *pb, const int *ldb)
+{
+// std::cerr << "in trsm " << *side << " " << *uplo << " " << *opa << " " << *diag << " " << *m << "," << *n << " " << *palpha << " " << *lda << " " << *ldb<< "\n";
+ typedef void (*functype)(DenseIndex, DenseIndex, const Scalar *, DenseIndex, Scalar *, DenseIndex, DenseIndex, internal::level3_blocking<Scalar,Scalar>&);
+ static const functype func[32] = {
+ // array index: NOTR | (LEFT << 2) | (UP << 3) | (NUNIT << 4)
+ (internal::triangular_solve_matrix<Scalar,DenseIndex,OnTheLeft, Upper|0, false,ColMajor,ColMajor,1>::run),
+ // array index: TR | (LEFT << 2) | (UP << 3) | (NUNIT << 4)
+ (internal::triangular_solve_matrix<Scalar,DenseIndex,OnTheLeft, Lower|0, false,RowMajor,ColMajor,1>::run),
+ // array index: ADJ | (LEFT << 2) | (UP << 3) | (NUNIT << 4)
+ (internal::triangular_solve_matrix<Scalar,DenseIndex,OnTheLeft, Lower|0, Conj, RowMajor,ColMajor,1>::run),\
+ 0,
+ // array index: NOTR | (RIGHT << 2) | (UP << 3) | (NUNIT << 4)
+ (internal::triangular_solve_matrix<Scalar,DenseIndex,OnTheRight,Upper|0, false,ColMajor,ColMajor,1>::run),
+ // array index: TR | (RIGHT << 2) | (UP << 3) | (NUNIT << 4)
+ (internal::triangular_solve_matrix<Scalar,DenseIndex,OnTheRight,Lower|0, false,RowMajor,ColMajor,1>::run),
+ // array index: ADJ | (RIGHT << 2) | (UP << 3) | (NUNIT << 4)
+ (internal::triangular_solve_matrix<Scalar,DenseIndex,OnTheRight,Lower|0, Conj, RowMajor,ColMajor,1>::run),
+ 0,
+ // array index: NOTR | (LEFT << 2) | (LO << 3) | (NUNIT << 4)
+ (internal::triangular_solve_matrix<Scalar,DenseIndex,OnTheLeft, Lower|0, false,ColMajor,ColMajor,1>::run),
+ // array index: TR | (LEFT << 2) | (LO << 3) | (NUNIT << 4)
+ (internal::triangular_solve_matrix<Scalar,DenseIndex,OnTheLeft, Upper|0, false,RowMajor,ColMajor,1>::run),
+ // array index: ADJ | (LEFT << 2) | (LO << 3) | (NUNIT << 4)
+ (internal::triangular_solve_matrix<Scalar,DenseIndex,OnTheLeft, Upper|0, Conj, RowMajor,ColMajor,1>::run),
+ 0,
+ // array index: NOTR | (RIGHT << 2) | (LO << 3) | (NUNIT << 4)
+ (internal::triangular_solve_matrix<Scalar,DenseIndex,OnTheRight,Lower|0, false,ColMajor,ColMajor,1>::run),
+ // array index: TR | (RIGHT << 2) | (LO << 3) | (NUNIT << 4)
+ (internal::triangular_solve_matrix<Scalar,DenseIndex,OnTheRight,Upper|0, false,RowMajor,ColMajor,1>::run),
+ // array index: ADJ | (RIGHT << 2) | (LO << 3) | (NUNIT << 4)
+ (internal::triangular_solve_matrix<Scalar,DenseIndex,OnTheRight,Upper|0, Conj, RowMajor,ColMajor,1>::run),
+ 0,
+ // array index: NOTR | (LEFT << 2) | (UP << 3) | (UNIT << 4)
+ (internal::triangular_solve_matrix<Scalar,DenseIndex,OnTheLeft, Upper|UnitDiag,false,ColMajor,ColMajor,1>::run),
+ // array index: TR | (LEFT << 2) | (UP << 3) | (UNIT << 4)
+ (internal::triangular_solve_matrix<Scalar,DenseIndex,OnTheLeft, Lower|UnitDiag,false,RowMajor,ColMajor,1>::run),
+ // array index: ADJ | (LEFT << 2) | (UP << 3) | (UNIT << 4)
+ (internal::triangular_solve_matrix<Scalar,DenseIndex,OnTheLeft, Lower|UnitDiag,Conj, RowMajor,ColMajor,1>::run),
+ 0,
+ // array index: NOTR | (RIGHT << 2) | (UP << 3) | (UNIT << 4)
+ (internal::triangular_solve_matrix<Scalar,DenseIndex,OnTheRight,Upper|UnitDiag,false,ColMajor,ColMajor,1>::run),
+ // array index: TR | (RIGHT << 2) | (UP << 3) | (UNIT << 4)
+ (internal::triangular_solve_matrix<Scalar,DenseIndex,OnTheRight,Lower|UnitDiag,false,RowMajor,ColMajor,1>::run),
+ // array index: ADJ | (RIGHT << 2) | (UP << 3) | (UNIT << 4)
+ (internal::triangular_solve_matrix<Scalar,DenseIndex,OnTheRight,Lower|UnitDiag,Conj, RowMajor,ColMajor,1>::run),
+ 0,
+ // array index: NOTR | (LEFT << 2) | (LO << 3) | (UNIT << 4)
+ (internal::triangular_solve_matrix<Scalar,DenseIndex,OnTheLeft, Lower|UnitDiag,false,ColMajor,ColMajor,1>::run),
+ // array index: TR | (LEFT << 2) | (LO << 3) | (UNIT << 4)
+ (internal::triangular_solve_matrix<Scalar,DenseIndex,OnTheLeft, Upper|UnitDiag,false,RowMajor,ColMajor,1>::run),
+ // array index: ADJ | (LEFT << 2) | (LO << 3) | (UNIT << 4)
+ (internal::triangular_solve_matrix<Scalar,DenseIndex,OnTheLeft, Upper|UnitDiag,Conj, RowMajor,ColMajor,1>::run),
+ 0,
+ // array index: NOTR | (RIGHT << 2) | (LO << 3) | (UNIT << 4)
+ (internal::triangular_solve_matrix<Scalar,DenseIndex,OnTheRight,Lower|UnitDiag,false,ColMajor,ColMajor,1>::run),
+ // array index: TR | (RIGHT << 2) | (LO << 3) | (UNIT << 4)
+ (internal::triangular_solve_matrix<Scalar,DenseIndex,OnTheRight,Upper|UnitDiag,false,RowMajor,ColMajor,1>::run),
+ // array index: ADJ | (RIGHT << 2) | (LO << 3) | (UNIT << 4)
+ (internal::triangular_solve_matrix<Scalar,DenseIndex,OnTheRight,Upper|UnitDiag,Conj, RowMajor,ColMajor,1>::run),
+ 0
+ };
+
+ const Scalar* a = reinterpret_cast<const Scalar*>(pa);
+ Scalar* b = reinterpret_cast<Scalar*>(pb);
+ Scalar alpha = *reinterpret_cast<const Scalar*>(palpha);
+
+ int info = 0;
+ if(SIDE(*side)==INVALID) info = 1;
+ else if(UPLO(*uplo)==INVALID) info = 2;
+ else if(OP(*opa)==INVALID) info = 3;
+ else if(DIAG(*diag)==INVALID) info = 4;
+ else if(*m<0) info = 5;
+ else if(*n<0) info = 6;
+ else if(*lda<std::max(1,(SIDE(*side)==LEFT)?*m:*n)) info = 9;
+ else if(*ldb<std::max(1,*m)) info = 11;
+ if(info)
+ return xerbla_(SCALAR_SUFFIX_UP"TRSM ",&info,6);
+
+ if(*m==0 || *n==0)
+ return 0;
+
+ int code = OP(*opa) | (SIDE(*side) << 2) | (UPLO(*uplo) << 3) | (DIAG(*diag) << 4);
+
+ if(SIDE(*side)==LEFT)
+ {
+ internal::gemm_blocking_space<ColMajor,Scalar,Scalar,Dynamic,Dynamic,Dynamic,4> blocking(*m,*n,*m,1,false);
+ func[code](*m, *n, a, *lda, b, 1, *ldb, blocking);
+ }
+ else
+ {
+ internal::gemm_blocking_space<ColMajor,Scalar,Scalar,Dynamic,Dynamic,Dynamic,4> blocking(*m,*n,*n,1,false);
+ func[code](*n, *m, a, *lda, b, 1, *ldb, blocking);
+ }
+
+ if(alpha!=Scalar(1))
+ matrix(b,*m,*n,*ldb) *= alpha;
+
+ return 0;
+}
+
+
+// b = alpha*op(a)*b for side = 'L'or'l'
+// b = alpha*b*op(a) for side = 'R'or'r'
+int EIGEN_BLAS_FUNC(trmm)(const char *side, const char *uplo, const char *opa, const char *diag, const int *m, const int *n,
+ const RealScalar *palpha, const RealScalar *pa, const int *lda, RealScalar *pb, const int *ldb)
+{
+// std::cerr << "in trmm " << *side << " " << *uplo << " " << *opa << " " << *diag << " " << *m << " " << *n << " " << *lda << " " << *ldb << " " << *palpha << "\n";
+ typedef void (*functype)(DenseIndex, DenseIndex, DenseIndex, const Scalar *, DenseIndex, const Scalar *, DenseIndex, Scalar *, DenseIndex, DenseIndex, const Scalar&, internal::level3_blocking<Scalar,Scalar>&);
+ static const functype func[32] = {
+ // array index: NOTR | (LEFT << 2) | (UP << 3) | (NUNIT << 4)
+ (internal::product_triangular_matrix_matrix<Scalar,DenseIndex,Upper|0, true, ColMajor,false,ColMajor,false,ColMajor,1>::run),
+ // array index: TR | (LEFT << 2) | (UP << 3) | (NUNIT << 4)
+ (internal::product_triangular_matrix_matrix<Scalar,DenseIndex,Lower|0, true, RowMajor,false,ColMajor,false,ColMajor,1>::run),
+ // array index: ADJ | (LEFT << 2) | (UP << 3) | (NUNIT << 4)
+ (internal::product_triangular_matrix_matrix<Scalar,DenseIndex,Lower|0, true, RowMajor,Conj, ColMajor,false,ColMajor,1>::run),
+ 0,
+ // array index: NOTR | (RIGHT << 2) | (UP << 3) | (NUNIT << 4)
+ (internal::product_triangular_matrix_matrix<Scalar,DenseIndex,Upper|0, false,ColMajor,false,ColMajor,false,ColMajor,1>::run),
+ // array index: TR | (RIGHT << 2) | (UP << 3) | (NUNIT << 4)
+ (internal::product_triangular_matrix_matrix<Scalar,DenseIndex,Lower|0, false,ColMajor,false,RowMajor,false,ColMajor,1>::run),
+ // array index: ADJ | (RIGHT << 2) | (UP << 3) | (NUNIT << 4)
+ (internal::product_triangular_matrix_matrix<Scalar,DenseIndex,Lower|0, false,ColMajor,false,RowMajor,Conj, ColMajor,1>::run),
+ 0,
+ // array index: NOTR | (LEFT << 2) | (LO << 3) | (NUNIT << 4)
+ (internal::product_triangular_matrix_matrix<Scalar,DenseIndex,Lower|0, true, ColMajor,false,ColMajor,false,ColMajor,1>::run),
+ // array index: TR | (LEFT << 2) | (LO << 3) | (NUNIT << 4)
+ (internal::product_triangular_matrix_matrix<Scalar,DenseIndex,Upper|0, true, RowMajor,false,ColMajor,false,ColMajor,1>::run),
+ // array index: ADJ | (LEFT << 2) | (LO << 3) | (NUNIT << 4)
+ (internal::product_triangular_matrix_matrix<Scalar,DenseIndex,Upper|0, true, RowMajor,Conj, ColMajor,false,ColMajor,1>::run),
+ 0,
+ // array index: NOTR | (RIGHT << 2) | (LO << 3) | (NUNIT << 4)
+ (internal::product_triangular_matrix_matrix<Scalar,DenseIndex,Lower|0, false,ColMajor,false,ColMajor,false,ColMajor,1>::run),
+ // array index: TR | (RIGHT << 2) | (LO << 3) | (NUNIT << 4)
+ (internal::product_triangular_matrix_matrix<Scalar,DenseIndex,Upper|0, false,ColMajor,false,RowMajor,false,ColMajor,1>::run),
+ // array index: ADJ | (RIGHT << 2) | (LO << 3) | (NUNIT << 4)
+ (internal::product_triangular_matrix_matrix<Scalar,DenseIndex,Upper|0, false,ColMajor,false,RowMajor,Conj, ColMajor,1>::run),
+ 0,
+ // array index: NOTR | (LEFT << 2) | (UP << 3) | (UNIT << 4)
+ (internal::product_triangular_matrix_matrix<Scalar,DenseIndex,Upper|UnitDiag,true, ColMajor,false,ColMajor,false,ColMajor,1>::run),
+ // array index: TR | (LEFT << 2) | (UP << 3) | (UNIT << 4)
+ (internal::product_triangular_matrix_matrix<Scalar,DenseIndex,Lower|UnitDiag,true, RowMajor,false,ColMajor,false,ColMajor,1>::run),
+ // array index: ADJ | (LEFT << 2) | (UP << 3) | (UNIT << 4)
+ (internal::product_triangular_matrix_matrix<Scalar,DenseIndex,Lower|UnitDiag,true, RowMajor,Conj, ColMajor,false,ColMajor,1>::run),
+ 0,
+ // array index: NOTR | (RIGHT << 2) | (UP << 3) | (UNIT << 4)
+ (internal::product_triangular_matrix_matrix<Scalar,DenseIndex,Upper|UnitDiag,false,ColMajor,false,ColMajor,false,ColMajor,1>::run),
+ // array index: TR | (RIGHT << 2) | (UP << 3) | (UNIT << 4)
+ (internal::product_triangular_matrix_matrix<Scalar,DenseIndex,Lower|UnitDiag,false,ColMajor,false,RowMajor,false,ColMajor,1>::run),
+ // array index: ADJ | (RIGHT << 2) | (UP << 3) | (UNIT << 4)
+ (internal::product_triangular_matrix_matrix<Scalar,DenseIndex,Lower|UnitDiag,false,ColMajor,false,RowMajor,Conj, ColMajor,1>::run),
+ 0,
+ // array index: NOTR | (LEFT << 2) | (LO << 3) | (UNIT << 4)
+ (internal::product_triangular_matrix_matrix<Scalar,DenseIndex,Lower|UnitDiag,true, ColMajor,false,ColMajor,false,ColMajor,1>::run),
+ // array index: TR | (LEFT << 2) | (LO << 3) | (UNIT << 4)
+ (internal::product_triangular_matrix_matrix<Scalar,DenseIndex,Upper|UnitDiag,true, RowMajor,false,ColMajor,false,ColMajor,1>::run),
+ // array index: ADJ | (LEFT << 2) | (LO << 3) | (UNIT << 4)
+ (internal::product_triangular_matrix_matrix<Scalar,DenseIndex,Upper|UnitDiag,true, RowMajor,Conj, ColMajor,false,ColMajor,1>::run),
+ 0,
+ // array index: NOTR | (RIGHT << 2) | (LO << 3) | (UNIT << 4)
+ (internal::product_triangular_matrix_matrix<Scalar,DenseIndex,Lower|UnitDiag,false,ColMajor,false,ColMajor,false,ColMajor,1>::run),
+ // array index: TR | (RIGHT << 2) | (LO << 3) | (UNIT << 4)
+ (internal::product_triangular_matrix_matrix<Scalar,DenseIndex,Upper|UnitDiag,false,ColMajor,false,RowMajor,false,ColMajor,1>::run),
+ // array index: ADJ | (RIGHT << 2) | (LO << 3) | (UNIT << 4)
+ (internal::product_triangular_matrix_matrix<Scalar,DenseIndex,Upper|UnitDiag,false,ColMajor,false,RowMajor,Conj, ColMajor,1>::run),
+ 0
+ };
+
+ const Scalar* a = reinterpret_cast<const Scalar*>(pa);
+ Scalar* b = reinterpret_cast<Scalar*>(pb);
+ Scalar alpha = *reinterpret_cast<const Scalar*>(palpha);
+
+ int info = 0;
+ if(SIDE(*side)==INVALID) info = 1;
+ else if(UPLO(*uplo)==INVALID) info = 2;
+ else if(OP(*opa)==INVALID) info = 3;
+ else if(DIAG(*diag)==INVALID) info = 4;
+ else if(*m<0) info = 5;
+ else if(*n<0) info = 6;
+ else if(*lda<std::max(1,(SIDE(*side)==LEFT)?*m:*n)) info = 9;
+ else if(*ldb<std::max(1,*m)) info = 11;
+ if(info)
+ return xerbla_(SCALAR_SUFFIX_UP"TRMM ",&info,6);
+
+ int code = OP(*opa) | (SIDE(*side) << 2) | (UPLO(*uplo) << 3) | (DIAG(*diag) << 4);
+
+ if(*m==0 || *n==0)
+ return 1;
+
+ // FIXME find a way to avoid this copy
+ Matrix<Scalar,Dynamic,Dynamic,ColMajor> tmp = matrix(b,*m,*n,*ldb);
+ matrix(b,*m,*n,*ldb).setZero();
+
+ if(SIDE(*side)==LEFT)
+ {
+ internal::gemm_blocking_space<ColMajor,Scalar,Scalar,Dynamic,Dynamic,Dynamic,4> blocking(*m,*n,*m,1,false);
+ func[code](*m, *n, *m, a, *lda, tmp.data(), tmp.outerStride(), b, 1, *ldb, alpha, blocking);
+ }
+ else
+ {
+ internal::gemm_blocking_space<ColMajor,Scalar,Scalar,Dynamic,Dynamic,Dynamic,4> blocking(*m,*n,*n,1,false);
+ func[code](*m, *n, *n, tmp.data(), tmp.outerStride(), a, *lda, b, 1, *ldb, alpha, blocking);
+ }
+ return 1;
+}
+
+// c = alpha*a*b + beta*c for side = 'L'or'l'
+// c = alpha*b*a + beta*c for side = 'R'or'r
+int EIGEN_BLAS_FUNC(symm)(const char *side, const char *uplo, const int *m, const int *n, const RealScalar *palpha,
+ const RealScalar *pa, const int *lda, const RealScalar *pb, const int *ldb, const RealScalar *pbeta, RealScalar *pc, const int *ldc)
+{
+// std::cerr << "in symm " << *side << " " << *uplo << " " << *m << "x" << *n << " lda:" << *lda << " ldb:" << *ldb << " ldc:" << *ldc << " alpha:" << *palpha << " beta:" << *pbeta << "\n";
+ const Scalar* a = reinterpret_cast<const Scalar*>(pa);
+ const Scalar* b = reinterpret_cast<const Scalar*>(pb);
+ Scalar* c = reinterpret_cast<Scalar*>(pc);
+ Scalar alpha = *reinterpret_cast<const Scalar*>(palpha);
+ Scalar beta = *reinterpret_cast<const Scalar*>(pbeta);
+
+ int info = 0;
+ if(SIDE(*side)==INVALID) info = 1;
+ else if(UPLO(*uplo)==INVALID) info = 2;
+ else if(*m<0) info = 3;
+ else if(*n<0) info = 4;
+ else if(*lda<std::max(1,(SIDE(*side)==LEFT)?*m:*n)) info = 7;
+ else if(*ldb<std::max(1,*m)) info = 9;
+ else if(*ldc<std::max(1,*m)) info = 12;
+ if(info)
+ return xerbla_(SCALAR_SUFFIX_UP"SYMM ",&info,6);
+
+ if(beta!=Scalar(1))
+ {
+ if(beta==Scalar(0)) matrix(c, *m, *n, *ldc).setZero();
+ else matrix(c, *m, *n, *ldc) *= beta;
+ }
+
+ if(*m==0 || *n==0)
+ {
+ return 1;
+ }
+
+ int size = (SIDE(*side)==LEFT) ? (*m) : (*n);
+ #if ISCOMPLEX
+ // FIXME add support for symmetric complex matrix
+ Matrix<Scalar,Dynamic,Dynamic,ColMajor> matA(size,size);
+ if(UPLO(*uplo)==UP)
+ {
+ matA.triangularView<Upper>() = matrix(a,size,size,*lda);
+ matA.triangularView<Lower>() = matrix(a,size,size,*lda).transpose();
+ }
+ else if(UPLO(*uplo)==LO)
+ {
+ matA.triangularView<Lower>() = matrix(a,size,size,*lda);
+ matA.triangularView<Upper>() = matrix(a,size,size,*lda).transpose();
+ }
+ if(SIDE(*side)==LEFT)
+ matrix(c, *m, *n, *ldc) += alpha * matA * matrix(b, *m, *n, *ldb);
+ else if(SIDE(*side)==RIGHT)
+ matrix(c, *m, *n, *ldc) += alpha * matrix(b, *m, *n, *ldb) * matA;
+ #else
+ internal::gemm_blocking_space<ColMajor,Scalar,Scalar,Dynamic,Dynamic,Dynamic> blocking(*m,*n,size,1,false);
+
+ if(SIDE(*side)==LEFT)
+ if(UPLO(*uplo)==UP) internal::product_selfadjoint_matrix<Scalar, DenseIndex, RowMajor,true,false, ColMajor,false,false, ColMajor,1>::run(*m, *n, a, *lda, b, *ldb, c, 1, *ldc, alpha, blocking);
+ else if(UPLO(*uplo)==LO) internal::product_selfadjoint_matrix<Scalar, DenseIndex, ColMajor,true,false, ColMajor,false,false, ColMajor,1>::run(*m, *n, a, *lda, b, *ldb, c, 1, *ldc, alpha, blocking);
+ else return 0;
+ else if(SIDE(*side)==RIGHT)
+ if(UPLO(*uplo)==UP) internal::product_selfadjoint_matrix<Scalar, DenseIndex, ColMajor,false,false, RowMajor,true,false, ColMajor,1>::run(*m, *n, b, *ldb, a, *lda, c, 1, *ldc, alpha, blocking);
+ else if(UPLO(*uplo)==LO) internal::product_selfadjoint_matrix<Scalar, DenseIndex, ColMajor,false,false, ColMajor,true,false, ColMajor,1>::run(*m, *n, b, *ldb, a, *lda, c, 1, *ldc, alpha, blocking);
+ else return 0;
+ else
+ return 0;
+ #endif
+
+ return 0;
+}
+
+// c = alpha*a*a' + beta*c for op = 'N'or'n'
+// c = alpha*a'*a + beta*c for op = 'T'or't','C'or'c'
+int EIGEN_BLAS_FUNC(syrk)(const char *uplo, const char *op, const int *n, const int *k,
+ const RealScalar *palpha, const RealScalar *pa, const int *lda, const RealScalar *pbeta, RealScalar *pc, const int *ldc)
+{
+// std::cerr << "in syrk " << *uplo << " " << *op << " " << *n << " " << *k << " " << *palpha << " " << *lda << " " << *pbeta << " " << *ldc << "\n";
+ #if !ISCOMPLEX
+ typedef void (*functype)(DenseIndex, DenseIndex, const Scalar *, DenseIndex, const Scalar *, DenseIndex, Scalar *, DenseIndex, DenseIndex, const Scalar&, internal::level3_blocking<Scalar,Scalar>&);
+ static const functype func[8] = {
+ // array index: NOTR | (UP << 2)
+ (internal::general_matrix_matrix_triangular_product<DenseIndex,Scalar,ColMajor,false,Scalar,RowMajor,Conj,ColMajor, 1, Upper>::run),
+ // array index: TR | (UP << 2)
+ (internal::general_matrix_matrix_triangular_product<DenseIndex,Scalar,RowMajor,false,Scalar,ColMajor,Conj,ColMajor, 1, Upper>::run),
+ // array index: ADJ | (UP << 2)
+ (internal::general_matrix_matrix_triangular_product<DenseIndex,Scalar,RowMajor,Conj, Scalar,ColMajor,false,ColMajor, 1, Upper>::run),
+ 0,
+ // array index: NOTR | (LO << 2)
+ (internal::general_matrix_matrix_triangular_product<DenseIndex,Scalar,ColMajor,false,Scalar,RowMajor,Conj,ColMajor, 1, Lower>::run),
+ // array index: TR | (LO << 2)
+ (internal::general_matrix_matrix_triangular_product<DenseIndex,Scalar,RowMajor,false,Scalar,ColMajor,Conj,ColMajor, 1, Lower>::run),
+ // array index: ADJ | (LO << 2)
+ (internal::general_matrix_matrix_triangular_product<DenseIndex,Scalar,RowMajor,Conj, Scalar,ColMajor,false,ColMajor, 1, Lower>::run),
+ 0
+ };
+ #endif
+
+ const Scalar* a = reinterpret_cast<const Scalar*>(pa);
+ Scalar* c = reinterpret_cast<Scalar*>(pc);
+ Scalar alpha = *reinterpret_cast<const Scalar*>(palpha);
+ Scalar beta = *reinterpret_cast<const Scalar*>(pbeta);
+
+ int info = 0;
+ if(UPLO(*uplo)==INVALID) info = 1;
+ else if(OP(*op)==INVALID || (ISCOMPLEX && OP(*op)==ADJ) ) info = 2;
+ else if(*n<0) info = 3;
+ else if(*k<0) info = 4;
+ else if(*lda<std::max(1,(OP(*op)==NOTR)?*n:*k)) info = 7;
+ else if(*ldc<std::max(1,*n)) info = 10;
+ if(info)
+ return xerbla_(SCALAR_SUFFIX_UP"SYRK ",&info,6);
+
+ if(beta!=Scalar(1))
+ {
+ if(UPLO(*uplo)==UP)
+ if(beta==Scalar(0)) matrix(c, *n, *n, *ldc).triangularView<Upper>().setZero();
+ else matrix(c, *n, *n, *ldc).triangularView<Upper>() *= beta;
+ else
+ if(beta==Scalar(0)) matrix(c, *n, *n, *ldc).triangularView<Lower>().setZero();
+ else matrix(c, *n, *n, *ldc).triangularView<Lower>() *= beta;
+ }
+
+ if(*n==0 || *k==0)
+ return 0;
+
+ #if ISCOMPLEX
+ // FIXME add support for symmetric complex matrix
+ if(UPLO(*uplo)==UP)
+ {
+ if(OP(*op)==NOTR)
+ matrix(c, *n, *n, *ldc).triangularView<Upper>() += alpha * matrix(a,*n,*k,*lda) * matrix(a,*n,*k,*lda).transpose();
+ else
+ matrix(c, *n, *n, *ldc).triangularView<Upper>() += alpha * matrix(a,*k,*n,*lda).transpose() * matrix(a,*k,*n,*lda);
+ }
+ else
+ {
+ if(OP(*op)==NOTR)
+ matrix(c, *n, *n, *ldc).triangularView<Lower>() += alpha * matrix(a,*n,*k,*lda) * matrix(a,*n,*k,*lda).transpose();
+ else
+ matrix(c, *n, *n, *ldc).triangularView<Lower>() += alpha * matrix(a,*k,*n,*lda).transpose() * matrix(a,*k,*n,*lda);
+ }
+ #else
+ internal::gemm_blocking_space<ColMajor,Scalar,Scalar,Dynamic,Dynamic,Dynamic> blocking(*n,*n,*k,1,false);
+
+ int code = OP(*op) | (UPLO(*uplo) << 2);
+ func[code](*n, *k, a, *lda, a, *lda, c, 1, *ldc, alpha, blocking);
+ #endif
+
+ return 0;
+}
+
+// c = alpha*a*b' + alpha*b*a' + beta*c for op = 'N'or'n'
+// c = alpha*a'*b + alpha*b'*a + beta*c for op = 'T'or't'
+int EIGEN_BLAS_FUNC(syr2k)(const char *uplo, const char *op, const int *n, const int *k, const RealScalar *palpha,
+ const RealScalar *pa, const int *lda, const RealScalar *pb, const int *ldb, const RealScalar *pbeta, RealScalar *pc, const int *ldc)
+{
+ const Scalar* a = reinterpret_cast<const Scalar*>(pa);
+ const Scalar* b = reinterpret_cast<const Scalar*>(pb);
+ Scalar* c = reinterpret_cast<Scalar*>(pc);
+ Scalar alpha = *reinterpret_cast<const Scalar*>(palpha);
+ Scalar beta = *reinterpret_cast<const Scalar*>(pbeta);
+
+// std::cerr << "in syr2k " << *uplo << " " << *op << " " << *n << " " << *k << " " << alpha << " " << *lda << " " << *ldb << " " << beta << " " << *ldc << "\n";
+
+ int info = 0;
+ if(UPLO(*uplo)==INVALID) info = 1;
+ else if(OP(*op)==INVALID || (ISCOMPLEX && OP(*op)==ADJ) ) info = 2;
+ else if(*n<0) info = 3;
+ else if(*k<0) info = 4;
+ else if(*lda<std::max(1,(OP(*op)==NOTR)?*n:*k)) info = 7;
+ else if(*ldb<std::max(1,(OP(*op)==NOTR)?*n:*k)) info = 9;
+ else if(*ldc<std::max(1,*n)) info = 12;
+ if(info)
+ return xerbla_(SCALAR_SUFFIX_UP"SYR2K",&info,6);
+
+ if(beta!=Scalar(1))
+ {
+ if(UPLO(*uplo)==UP)
+ if(beta==Scalar(0)) matrix(c, *n, *n, *ldc).triangularView<Upper>().setZero();
+ else matrix(c, *n, *n, *ldc).triangularView<Upper>() *= beta;
+ else
+ if(beta==Scalar(0)) matrix(c, *n, *n, *ldc).triangularView<Lower>().setZero();
+ else matrix(c, *n, *n, *ldc).triangularView<Lower>() *= beta;
+ }
+
+ if(*k==0)
+ return 1;
+
+ if(OP(*op)==NOTR)
+ {
+ if(UPLO(*uplo)==UP)
+ {
+ matrix(c, *n, *n, *ldc).triangularView<Upper>()
+ += alpha *matrix(a, *n, *k, *lda)*matrix(b, *n, *k, *ldb).transpose()
+ + alpha*matrix(b, *n, *k, *ldb)*matrix(a, *n, *k, *lda).transpose();
+ }
+ else if(UPLO(*uplo)==LO)
+ matrix(c, *n, *n, *ldc).triangularView<Lower>()
+ += alpha*matrix(a, *n, *k, *lda)*matrix(b, *n, *k, *ldb).transpose()
+ + alpha*matrix(b, *n, *k, *ldb)*matrix(a, *n, *k, *lda).transpose();
+ }
+ else if(OP(*op)==TR || OP(*op)==ADJ)
+ {
+ if(UPLO(*uplo)==UP)
+ matrix(c, *n, *n, *ldc).triangularView<Upper>()
+ += alpha*matrix(a, *k, *n, *lda).transpose()*matrix(b, *k, *n, *ldb)
+ + alpha*matrix(b, *k, *n, *ldb).transpose()*matrix(a, *k, *n, *lda);
+ else if(UPLO(*uplo)==LO)
+ matrix(c, *n, *n, *ldc).triangularView<Lower>()
+ += alpha*matrix(a, *k, *n, *lda).transpose()*matrix(b, *k, *n, *ldb)
+ + alpha*matrix(b, *k, *n, *ldb).transpose()*matrix(a, *k, *n, *lda);
+ }
+
+ return 0;
+}
+
+
+#if ISCOMPLEX
+
+// c = alpha*a*b + beta*c for side = 'L'or'l'
+// c = alpha*b*a + beta*c for side = 'R'or'r
+int EIGEN_BLAS_FUNC(hemm)(const char *side, const char *uplo, const int *m, const int *n, const RealScalar *palpha,
+ const RealScalar *pa, const int *lda, const RealScalar *pb, const int *ldb, const RealScalar *pbeta, RealScalar *pc, const int *ldc)
+{
+ const Scalar* a = reinterpret_cast<const Scalar*>(pa);
+ const Scalar* b = reinterpret_cast<const Scalar*>(pb);
+ Scalar* c = reinterpret_cast<Scalar*>(pc);
+ Scalar alpha = *reinterpret_cast<const Scalar*>(palpha);
+ Scalar beta = *reinterpret_cast<const Scalar*>(pbeta);
+
+// std::cerr << "in hemm " << *side << " " << *uplo << " " << *m << " " << *n << " " << alpha << " " << *lda << " " << beta << " " << *ldc << "\n";
+
+ int info = 0;
+ if(SIDE(*side)==INVALID) info = 1;
+ else if(UPLO(*uplo)==INVALID) info = 2;
+ else if(*m<0) info = 3;
+ else if(*n<0) info = 4;
+ else if(*lda<std::max(1,(SIDE(*side)==LEFT)?*m:*n)) info = 7;
+ else if(*ldb<std::max(1,*m)) info = 9;
+ else if(*ldc<std::max(1,*m)) info = 12;
+ if(info)
+ return xerbla_(SCALAR_SUFFIX_UP"HEMM ",&info,6);
+
+ if(beta==Scalar(0)) matrix(c, *m, *n, *ldc).setZero();
+ else if(beta!=Scalar(1)) matrix(c, *m, *n, *ldc) *= beta;
+
+ if(*m==0 || *n==0)
+ {
+ return 1;
+ }
+
+ int size = (SIDE(*side)==LEFT) ? (*m) : (*n);
+ internal::gemm_blocking_space<ColMajor,Scalar,Scalar,Dynamic,Dynamic,Dynamic> blocking(*m,*n,size,1,false);
+
+ if(SIDE(*side)==LEFT)
+ {
+ if(UPLO(*uplo)==UP) internal::product_selfadjoint_matrix<Scalar,DenseIndex,RowMajor,true,Conj, ColMajor,false,false, ColMajor, 1>
+ ::run(*m, *n, a, *lda, b, *ldb, c, 1, *ldc, alpha, blocking);
+ else if(UPLO(*uplo)==LO) internal::product_selfadjoint_matrix<Scalar,DenseIndex,ColMajor,true,false, ColMajor,false,false, ColMajor,1>
+ ::run(*m, *n, a, *lda, b, *ldb, c, 1, *ldc, alpha, blocking);
+ else return 0;
+ }
+ else if(SIDE(*side)==RIGHT)
+ {
+ if(UPLO(*uplo)==UP) matrix(c,*m,*n,*ldc) += alpha * matrix(b,*m,*n,*ldb) * matrix(a,*n,*n,*lda).selfadjointView<Upper>();/*internal::product_selfadjoint_matrix<Scalar,DenseIndex,ColMajor,false,false, RowMajor,true,Conj, ColMajor, 1>
+ ::run(*m, *n, b, *ldb, a, *lda, c, 1, *ldc, alpha, blocking);*/
+ else if(UPLO(*uplo)==LO) internal::product_selfadjoint_matrix<Scalar,DenseIndex,ColMajor,false,false, ColMajor,true,false, ColMajor,1>
+ ::run(*m, *n, b, *ldb, a, *lda, c, 1, *ldc, alpha, blocking);
+ else return 0;
+ }
+ else
+ {
+ return 0;
+ }
+
+ return 0;
+}
+
+// c = alpha*a*conj(a') + beta*c for op = 'N'or'n'
+// c = alpha*conj(a')*a + beta*c for op = 'C'or'c'
+int EIGEN_BLAS_FUNC(herk)(const char *uplo, const char *op, const int *n, const int *k,
+ const RealScalar *palpha, const RealScalar *pa, const int *lda, const RealScalar *pbeta, RealScalar *pc, const int *ldc)
+{
+// std::cerr << "in herk " << *uplo << " " << *op << " " << *n << " " << *k << " " << *palpha << " " << *lda << " " << *pbeta << " " << *ldc << "\n";
+
+ typedef void (*functype)(DenseIndex, DenseIndex, const Scalar *, DenseIndex, const Scalar *, DenseIndex, Scalar *, DenseIndex, DenseIndex, const Scalar&, internal::level3_blocking<Scalar,Scalar>&);
+ static const functype func[8] = {
+ // array index: NOTR | (UP << 2)
+ (internal::general_matrix_matrix_triangular_product<DenseIndex,Scalar,ColMajor,false,Scalar,RowMajor,Conj, ColMajor,1,Upper>::run),
+ 0,
+ // array index: ADJ | (UP << 2)
+ (internal::general_matrix_matrix_triangular_product<DenseIndex,Scalar,RowMajor,Conj, Scalar,ColMajor,false,ColMajor,1,Upper>::run),
+ 0,
+ // array index: NOTR | (LO << 2)
+ (internal::general_matrix_matrix_triangular_product<DenseIndex,Scalar,ColMajor,false,Scalar,RowMajor,Conj, ColMajor,1,Lower>::run),
+ 0,
+ // array index: ADJ | (LO << 2)
+ (internal::general_matrix_matrix_triangular_product<DenseIndex,Scalar,RowMajor,Conj, Scalar,ColMajor,false,ColMajor,1,Lower>::run),
+ 0
+ };
+
+ const Scalar* a = reinterpret_cast<const Scalar*>(pa);
+ Scalar* c = reinterpret_cast<Scalar*>(pc);
+ RealScalar alpha = *palpha;
+ RealScalar beta = *pbeta;
+
+// std::cerr << "in herk " << *uplo << " " << *op << " " << *n << " " << *k << " " << alpha << " " << *lda << " " << beta << " " << *ldc << "\n";
+
+ int info = 0;
+ if(UPLO(*uplo)==INVALID) info = 1;
+ else if((OP(*op)==INVALID) || (OP(*op)==TR)) info = 2;
+ else if(*n<0) info = 3;
+ else if(*k<0) info = 4;
+ else if(*lda<std::max(1,(OP(*op)==NOTR)?*n:*k)) info = 7;
+ else if(*ldc<std::max(1,*n)) info = 10;
+ if(info)
+ return xerbla_(SCALAR_SUFFIX_UP"HERK ",&info,6);
+
+ int code = OP(*op) | (UPLO(*uplo) << 2);
+
+ if(beta!=RealScalar(1))
+ {
+ if(UPLO(*uplo)==UP)
+ if(beta==Scalar(0)) matrix(c, *n, *n, *ldc).triangularView<Upper>().setZero();
+ else matrix(c, *n, *n, *ldc).triangularView<StrictlyUpper>() *= beta;
+ else
+ if(beta==Scalar(0)) matrix(c, *n, *n, *ldc).triangularView<Lower>().setZero();
+ else matrix(c, *n, *n, *ldc).triangularView<StrictlyLower>() *= beta;
+
+ if(beta!=Scalar(0))
+ {
+ matrix(c, *n, *n, *ldc).diagonal().real() *= beta;
+ matrix(c, *n, *n, *ldc).diagonal().imag().setZero();
+ }
+ }
+
+ if(*k>0 && alpha!=RealScalar(0))
+ {
+ internal::gemm_blocking_space<ColMajor,Scalar,Scalar,Dynamic,Dynamic,Dynamic> blocking(*n,*n,*k,1,false);
+ func[code](*n, *k, a, *lda, a, *lda, c, 1, *ldc, alpha, blocking);
+ matrix(c, *n, *n, *ldc).diagonal().imag().setZero();
+ }
+ return 0;
+}
+
+// c = alpha*a*conj(b') + conj(alpha)*b*conj(a') + beta*c, for op = 'N'or'n'
+// c = alpha*conj(a')*b + conj(alpha)*conj(b')*a + beta*c, for op = 'C'or'c'
+int EIGEN_BLAS_FUNC(her2k)(const char *uplo, const char *op, const int *n, const int *k,
+ const RealScalar *palpha, const RealScalar *pa, const int *lda, const RealScalar *pb, const int *ldb, const RealScalar *pbeta, RealScalar *pc, const int *ldc)
+{
+ const Scalar* a = reinterpret_cast<const Scalar*>(pa);
+ const Scalar* b = reinterpret_cast<const Scalar*>(pb);
+ Scalar* c = reinterpret_cast<Scalar*>(pc);
+ Scalar alpha = *reinterpret_cast<const Scalar*>(palpha);
+ RealScalar beta = *pbeta;
+
+// std::cerr << "in her2k " << *uplo << " " << *op << " " << *n << " " << *k << " " << alpha << " " << *lda << " " << *ldb << " " << beta << " " << *ldc << "\n";
+
+ int info = 0;
+ if(UPLO(*uplo)==INVALID) info = 1;
+ else if((OP(*op)==INVALID) || (OP(*op)==TR)) info = 2;
+ else if(*n<0) info = 3;
+ else if(*k<0) info = 4;
+ else if(*lda<std::max(1,(OP(*op)==NOTR)?*n:*k)) info = 7;
+ else if(*ldb<std::max(1,(OP(*op)==NOTR)?*n:*k)) info = 9;
+ else if(*ldc<std::max(1,*n)) info = 12;
+ if(info)
+ return xerbla_(SCALAR_SUFFIX_UP"HER2K",&info,6);
+
+ if(beta!=RealScalar(1))
+ {
+ if(UPLO(*uplo)==UP)
+ if(beta==Scalar(0)) matrix(c, *n, *n, *ldc).triangularView<Upper>().setZero();
+ else matrix(c, *n, *n, *ldc).triangularView<StrictlyUpper>() *= beta;
+ else
+ if(beta==Scalar(0)) matrix(c, *n, *n, *ldc).triangularView<Lower>().setZero();
+ else matrix(c, *n, *n, *ldc).triangularView<StrictlyLower>() *= beta;
+
+ if(beta!=Scalar(0))
+ {
+ matrix(c, *n, *n, *ldc).diagonal().real() *= beta;
+ matrix(c, *n, *n, *ldc).diagonal().imag().setZero();
+ }
+ }
+ else if(*k>0 && alpha!=Scalar(0))
+ matrix(c, *n, *n, *ldc).diagonal().imag().setZero();
+
+ if(*k==0)
+ return 1;
+
+ if(OP(*op)==NOTR)
+ {
+ if(UPLO(*uplo)==UP)
+ {
+ matrix(c, *n, *n, *ldc).triangularView<Upper>()
+ += alpha *matrix(a, *n, *k, *lda)*matrix(b, *n, *k, *ldb).adjoint()
+ + numext::conj(alpha)*matrix(b, *n, *k, *ldb)*matrix(a, *n, *k, *lda).adjoint();
+ }
+ else if(UPLO(*uplo)==LO)
+ matrix(c, *n, *n, *ldc).triangularView<Lower>()
+ += alpha*matrix(a, *n, *k, *lda)*matrix(b, *n, *k, *ldb).adjoint()
+ + numext::conj(alpha)*matrix(b, *n, *k, *ldb)*matrix(a, *n, *k, *lda).adjoint();
+ }
+ else if(OP(*op)==ADJ)
+ {
+ if(UPLO(*uplo)==UP)
+ matrix(c, *n, *n, *ldc).triangularView<Upper>()
+ += alpha*matrix(a, *k, *n, *lda).adjoint()*matrix(b, *k, *n, *ldb)
+ + numext::conj(alpha)*matrix(b, *k, *n, *ldb).adjoint()*matrix(a, *k, *n, *lda);
+ else if(UPLO(*uplo)==LO)
+ matrix(c, *n, *n, *ldc).triangularView<Lower>()
+ += alpha*matrix(a, *k, *n, *lda).adjoint()*matrix(b, *k, *n, *ldb)
+ + numext::conj(alpha)*matrix(b, *k, *n, *ldb).adjoint()*matrix(a, *k, *n, *lda);
+ }
+
+ return 1;
+}
+
+#endif // ISCOMPLEX
diff --git a/blas/single.cpp b/blas/single.cpp
new file mode 100644
index 0000000..e66879a
--- /dev/null
+++ b/blas/single.cpp
@@ -0,0 +1,22 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#define SCALAR float
+#define SCALAR_SUFFIX s
+#define SCALAR_SUFFIX_UP "S"
+#define ISCOMPLEX 0
+
+#include "level1_impl.h"
+#include "level1_real_impl.h"
+#include "level2_impl.h"
+#include "level2_real_impl.h"
+#include "level3_impl.h"
+
+float EIGEN_BLAS_FUNC(dsdot)(int* n, float* alpha, float* x, int* incx, float* y, int* incy)
+{ return double(*alpha) + BLASFUNC(dsdot)(n, x, incx, y, incy); }
diff --git a/blas/testing/CMakeLists.txt b/blas/testing/CMakeLists.txt
new file mode 100644
index 0000000..52c23ac
--- /dev/null
+++ b/blas/testing/CMakeLists.txt
@@ -0,0 +1,40 @@
+
+macro(ei_add_blas_test testname)
+
+ set(targetname ${testname})
+
+ set(filename ${testname}.f)
+ add_executable(${targetname} ${filename})
+
+ target_link_libraries(${targetname} eigen_blas)
+
+ if(EIGEN_STANDARD_LIBRARIES_TO_LINK_TO)
+ target_link_libraries(${targetname} ${EIGEN_STANDARD_LIBRARIES_TO_LINK_TO})
+ endif()
+
+ target_link_libraries(${targetname} ${EXTERNAL_LIBS})
+
+ add_test(${testname} "${Eigen_SOURCE_DIR}/blas/testing/runblastest.sh" "${testname}" "${Eigen_SOURCE_DIR}/blas/testing/${testname}.dat")
+ add_dependencies(buildtests ${targetname})
+
+endmacro()
+
+ei_add_blas_test(sblat1)
+ei_add_blas_test(sblat2)
+ei_add_blas_test(sblat3)
+
+ei_add_blas_test(dblat1)
+ei_add_blas_test(dblat2)
+ei_add_blas_test(dblat3)
+
+ei_add_blas_test(cblat1)
+ei_add_blas_test(cblat2)
+ei_add_blas_test(cblat3)
+
+ei_add_blas_test(zblat1)
+ei_add_blas_test(zblat2)
+ei_add_blas_test(zblat3)
+
+# add_custom_target(level1)
+# add_dependencies(level1 sblat1)
+
diff --git a/blas/testing/cblat1.f b/blas/testing/cblat1.f
new file mode 100644
index 0000000..73015f5
--- /dev/null
+++ b/blas/testing/cblat1.f
@@ -0,0 +1,724 @@
+*> \brief \b CBLAT1
+*
+* =========== DOCUMENTATION ===========
+*
+* Online html documentation available at
+* http://www.netlib.org/lapack/explore-html/
+*
+* Definition:
+* ===========
+*
+* PROGRAM CBLAT1
+*
+*
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
+*>
+*> Test program for the COMPLEX Level 1 BLAS.
+*> Based upon the original BLAS test routine together with:
+*>
+*> F06GAF Example Program Text
+*> \endverbatim
+*
+* Authors:
+* ========
+*
+*> \author Univ. of Tennessee
+*> \author Univ. of California Berkeley
+*> \author Univ. of Colorado Denver
+*> \author NAG Ltd.
+*
+*> \date April 2012
+*
+*> \ingroup complex_blas_testing
+*
+* =====================================================================
+ PROGRAM CBLAT1
+*
+* -- Reference BLAS test routine (version 3.4.1) --
+* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
+* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+* April 2012
+*
+* =====================================================================
+*
+* .. Parameters ..
+ INTEGER NOUT
+ PARAMETER (NOUT=6)
+* .. Scalars in Common ..
+ INTEGER ICASE, INCX, INCY, MODE, N
+ LOGICAL PASS
+* .. Local Scalars ..
+ REAL SFAC
+ INTEGER IC
+* .. External Subroutines ..
+ EXTERNAL CHECK1, CHECK2, HEADER
+* .. Common blocks ..
+ COMMON /COMBLA/ICASE, N, INCX, INCY, MODE, PASS
+* .. Data statements ..
+ DATA SFAC/9.765625E-4/
+* .. Executable Statements ..
+ WRITE (NOUT,99999)
+ DO 20 IC = 1, 10
+ ICASE = IC
+ CALL HEADER
+*
+* Initialize PASS, INCX, INCY, and MODE for a new case.
+* The value 9999 for INCX, INCY or MODE will appear in the
+* detailed output, if any, for cases that do not involve
+* these parameters.
+*
+ PASS = .TRUE.
+ INCX = 9999
+ INCY = 9999
+ MODE = 9999
+ IF (ICASE.LE.5) THEN
+ CALL CHECK2(SFAC)
+ ELSE IF (ICASE.GE.6) THEN
+ CALL CHECK1(SFAC)
+ END IF
+* -- Print
+ IF (PASS) WRITE (NOUT,99998)
+ 20 CONTINUE
+ STOP
+*
+99999 FORMAT (' Complex BLAS Test Program Results',/1X)
+99998 FORMAT (' ----- PASS -----')
+ END
+ SUBROUTINE HEADER
+* .. Parameters ..
+ INTEGER NOUT
+ PARAMETER (NOUT=6)
+* .. Scalars in Common ..
+ INTEGER ICASE, INCX, INCY, MODE, N
+ LOGICAL PASS
+* .. Local Arrays ..
+ CHARACTER*6 L(10)
+* .. Common blocks ..
+ COMMON /COMBLA/ICASE, N, INCX, INCY, MODE, PASS
+* .. Data statements ..
+ DATA L(1)/'CDOTC '/
+ DATA L(2)/'CDOTU '/
+ DATA L(3)/'CAXPY '/
+ DATA L(4)/'CCOPY '/
+ DATA L(5)/'CSWAP '/
+ DATA L(6)/'SCNRM2'/
+ DATA L(7)/'SCASUM'/
+ DATA L(8)/'CSCAL '/
+ DATA L(9)/'CSSCAL'/
+ DATA L(10)/'ICAMAX'/
+* .. Executable Statements ..
+ WRITE (NOUT,99999) ICASE, L(ICASE)
+ RETURN
+*
+99999 FORMAT (/' Test of subprogram number',I3,12X,A6)
+ END
+ SUBROUTINE CHECK1(SFAC)
+* .. Parameters ..
+ INTEGER NOUT
+ PARAMETER (NOUT=6)
+* .. Scalar Arguments ..
+ REAL SFAC
+* .. Scalars in Common ..
+ INTEGER ICASE, INCX, INCY, MODE, N
+ LOGICAL PASS
+* .. Local Scalars ..
+ COMPLEX CA
+ REAL SA
+ INTEGER I, J, LEN, NP1
+* .. Local Arrays ..
+ COMPLEX CTRUE5(8,5,2), CTRUE6(8,5,2), CV(8,5,2), CX(8),
+ + MWPCS(5), MWPCT(5)
+ REAL STRUE2(5), STRUE4(5)
+ INTEGER ITRUE3(5)
+* .. External Functions ..
+ REAL SCASUM, SCNRM2
+ INTEGER ICAMAX
+ EXTERNAL SCASUM, SCNRM2, ICAMAX
+* .. External Subroutines ..
+ EXTERNAL CSCAL, CSSCAL, CTEST, ITEST1, STEST1
+* .. Intrinsic Functions ..
+ INTRINSIC MAX
+* .. Common blocks ..
+ COMMON /COMBLA/ICASE, N, INCX, INCY, MODE, PASS
+* .. Data statements ..
+ DATA SA, CA/0.3E0, (0.4E0,-0.7E0)/
+ DATA ((CV(I,J,1),I=1,8),J=1,5)/(0.1E0,0.1E0),
+ + (1.0E0,2.0E0), (1.0E0,2.0E0), (1.0E0,2.0E0),
+ + (1.0E0,2.0E0), (1.0E0,2.0E0), (1.0E0,2.0E0),
+ + (1.0E0,2.0E0), (0.3E0,-0.4E0), (3.0E0,4.0E0),
+ + (3.0E0,4.0E0), (3.0E0,4.0E0), (3.0E0,4.0E0),
+ + (3.0E0,4.0E0), (3.0E0,4.0E0), (3.0E0,4.0E0),
+ + (0.1E0,-0.3E0), (0.5E0,-0.1E0), (5.0E0,6.0E0),
+ + (5.0E0,6.0E0), (5.0E0,6.0E0), (5.0E0,6.0E0),
+ + (5.0E0,6.0E0), (5.0E0,6.0E0), (0.1E0,0.1E0),
+ + (-0.6E0,0.1E0), (0.1E0,-0.3E0), (7.0E0,8.0E0),
+ + (7.0E0,8.0E0), (7.0E0,8.0E0), (7.0E0,8.0E0),
+ + (7.0E0,8.0E0), (0.3E0,0.1E0), (0.5E0,0.0E0),
+ + (0.0E0,0.5E0), (0.0E0,0.2E0), (2.0E0,3.0E0),
+ + (2.0E0,3.0E0), (2.0E0,3.0E0), (2.0E0,3.0E0)/
+ DATA ((CV(I,J,2),I=1,8),J=1,5)/(0.1E0,0.1E0),
+ + (4.0E0,5.0E0), (4.0E0,5.0E0), (4.0E0,5.0E0),
+ + (4.0E0,5.0E0), (4.0E0,5.0E0), (4.0E0,5.0E0),
+ + (4.0E0,5.0E0), (0.3E0,-0.4E0), (6.0E0,7.0E0),
+ + (6.0E0,7.0E0), (6.0E0,7.0E0), (6.0E0,7.0E0),
+ + (6.0E0,7.0E0), (6.0E0,7.0E0), (6.0E0,7.0E0),
+ + (0.1E0,-0.3E0), (8.0E0,9.0E0), (0.5E0,-0.1E0),
+ + (2.0E0,5.0E0), (2.0E0,5.0E0), (2.0E0,5.0E0),
+ + (2.0E0,5.0E0), (2.0E0,5.0E0), (0.1E0,0.1E0),
+ + (3.0E0,6.0E0), (-0.6E0,0.1E0), (4.0E0,7.0E0),
+ + (0.1E0,-0.3E0), (7.0E0,2.0E0), (7.0E0,2.0E0),
+ + (7.0E0,2.0E0), (0.3E0,0.1E0), (5.0E0,8.0E0),
+ + (0.5E0,0.0E0), (6.0E0,9.0E0), (0.0E0,0.5E0),
+ + (8.0E0,3.0E0), (0.0E0,0.2E0), (9.0E0,4.0E0)/
+ DATA STRUE2/0.0E0, 0.5E0, 0.6E0, 0.7E0, 0.8E0/
+ DATA STRUE4/0.0E0, 0.7E0, 1.0E0, 1.3E0, 1.6E0/
+ DATA ((CTRUE5(I,J,1),I=1,8),J=1,5)/(0.1E0,0.1E0),
+ + (1.0E0,2.0E0), (1.0E0,2.0E0), (1.0E0,2.0E0),
+ + (1.0E0,2.0E0), (1.0E0,2.0E0), (1.0E0,2.0E0),
+ + (1.0E0,2.0E0), (-0.16E0,-0.37E0), (3.0E0,4.0E0),
+ + (3.0E0,4.0E0), (3.0E0,4.0E0), (3.0E0,4.0E0),
+ + (3.0E0,4.0E0), (3.0E0,4.0E0), (3.0E0,4.0E0),
+ + (-0.17E0,-0.19E0), (0.13E0,-0.39E0),
+ + (5.0E0,6.0E0), (5.0E0,6.0E0), (5.0E0,6.0E0),
+ + (5.0E0,6.0E0), (5.0E0,6.0E0), (5.0E0,6.0E0),
+ + (0.11E0,-0.03E0), (-0.17E0,0.46E0),
+ + (-0.17E0,-0.19E0), (7.0E0,8.0E0), (7.0E0,8.0E0),
+ + (7.0E0,8.0E0), (7.0E0,8.0E0), (7.0E0,8.0E0),
+ + (0.19E0,-0.17E0), (0.20E0,-0.35E0),
+ + (0.35E0,0.20E0), (0.14E0,0.08E0),
+ + (2.0E0,3.0E0), (2.0E0,3.0E0), (2.0E0,3.0E0),
+ + (2.0E0,3.0E0)/
+ DATA ((CTRUE5(I,J,2),I=1,8),J=1,5)/(0.1E0,0.1E0),
+ + (4.0E0,5.0E0), (4.0E0,5.0E0), (4.0E0,5.0E0),
+ + (4.0E0,5.0E0), (4.0E0,5.0E0), (4.0E0,5.0E0),
+ + (4.0E0,5.0E0), (-0.16E0,-0.37E0), (6.0E0,7.0E0),
+ + (6.0E0,7.0E0), (6.0E0,7.0E0), (6.0E0,7.0E0),
+ + (6.0E0,7.0E0), (6.0E0,7.0E0), (6.0E0,7.0E0),
+ + (-0.17E0,-0.19E0), (8.0E0,9.0E0),
+ + (0.13E0,-0.39E0), (2.0E0,5.0E0), (2.0E0,5.0E0),
+ + (2.0E0,5.0E0), (2.0E0,5.0E0), (2.0E0,5.0E0),
+ + (0.11E0,-0.03E0), (3.0E0,6.0E0),
+ + (-0.17E0,0.46E0), (4.0E0,7.0E0),
+ + (-0.17E0,-0.19E0), (7.0E0,2.0E0), (7.0E0,2.0E0),
+ + (7.0E0,2.0E0), (0.19E0,-0.17E0), (5.0E0,8.0E0),
+ + (0.20E0,-0.35E0), (6.0E0,9.0E0),
+ + (0.35E0,0.20E0), (8.0E0,3.0E0),
+ + (0.14E0,0.08E0), (9.0E0,4.0E0)/
+ DATA ((CTRUE6(I,J,1),I=1,8),J=1,5)/(0.1E0,0.1E0),
+ + (1.0E0,2.0E0), (1.0E0,2.0E0), (1.0E0,2.0E0),
+ + (1.0E0,2.0E0), (1.0E0,2.0E0), (1.0E0,2.0E0),
+ + (1.0E0,2.0E0), (0.09E0,-0.12E0), (3.0E0,4.0E0),
+ + (3.0E0,4.0E0), (3.0E0,4.0E0), (3.0E0,4.0E0),
+ + (3.0E0,4.0E0), (3.0E0,4.0E0), (3.0E0,4.0E0),
+ + (0.03E0,-0.09E0), (0.15E0,-0.03E0),
+ + (5.0E0,6.0E0), (5.0E0,6.0E0), (5.0E0,6.0E0),
+ + (5.0E0,6.0E0), (5.0E0,6.0E0), (5.0E0,6.0E0),
+ + (0.03E0,0.03E0), (-0.18E0,0.03E0),
+ + (0.03E0,-0.09E0), (7.0E0,8.0E0), (7.0E0,8.0E0),
+ + (7.0E0,8.0E0), (7.0E0,8.0E0), (7.0E0,8.0E0),
+ + (0.09E0,0.03E0), (0.15E0,0.00E0),
+ + (0.00E0,0.15E0), (0.00E0,0.06E0), (2.0E0,3.0E0),
+ + (2.0E0,3.0E0), (2.0E0,3.0E0), (2.0E0,3.0E0)/
+ DATA ((CTRUE6(I,J,2),I=1,8),J=1,5)/(0.1E0,0.1E0),
+ + (4.0E0,5.0E0), (4.0E0,5.0E0), (4.0E0,5.0E0),
+ + (4.0E0,5.0E0), (4.0E0,5.0E0), (4.0E0,5.0E0),
+ + (4.0E0,5.0E0), (0.09E0,-0.12E0), (6.0E0,7.0E0),
+ + (6.0E0,7.0E0), (6.0E0,7.0E0), (6.0E0,7.0E0),
+ + (6.0E0,7.0E0), (6.0E0,7.0E0), (6.0E0,7.0E0),
+ + (0.03E0,-0.09E0), (8.0E0,9.0E0),
+ + (0.15E0,-0.03E0), (2.0E0,5.0E0), (2.0E0,5.0E0),
+ + (2.0E0,5.0E0), (2.0E0,5.0E0), (2.0E0,5.0E0),
+ + (0.03E0,0.03E0), (3.0E0,6.0E0),
+ + (-0.18E0,0.03E0), (4.0E0,7.0E0),
+ + (0.03E0,-0.09E0), (7.0E0,2.0E0), (7.0E0,2.0E0),
+ + (7.0E0,2.0E0), (0.09E0,0.03E0), (5.0E0,8.0E0),
+ + (0.15E0,0.00E0), (6.0E0,9.0E0), (0.00E0,0.15E0),
+ + (8.0E0,3.0E0), (0.00E0,0.06E0), (9.0E0,4.0E0)/
+ DATA ITRUE3/0, 1, 2, 2, 2/
+* .. Executable Statements ..
+ DO 60 INCX = 1, 2
+ DO 40 NP1 = 1, 5
+ N = NP1 - 1
+ LEN = 2*MAX(N,1)
+* .. Set vector arguments ..
+ DO 20 I = 1, LEN
+ CX(I) = CV(I,NP1,INCX)
+ 20 CONTINUE
+ IF (ICASE.EQ.6) THEN
+* .. SCNRM2 ..
+ CALL STEST1(SCNRM2(N,CX,INCX),STRUE2(NP1),STRUE2(NP1),
+ + SFAC)
+ ELSE IF (ICASE.EQ.7) THEN
+* .. SCASUM ..
+ CALL STEST1(SCASUM(N,CX,INCX),STRUE4(NP1),STRUE4(NP1),
+ + SFAC)
+ ELSE IF (ICASE.EQ.8) THEN
+* .. CSCAL ..
+ CALL CSCAL(N,CA,CX,INCX)
+ CALL CTEST(LEN,CX,CTRUE5(1,NP1,INCX),CTRUE5(1,NP1,INCX),
+ + SFAC)
+ ELSE IF (ICASE.EQ.9) THEN
+* .. CSSCAL ..
+ CALL CSSCAL(N,SA,CX,INCX)
+ CALL CTEST(LEN,CX,CTRUE6(1,NP1,INCX),CTRUE6(1,NP1,INCX),
+ + SFAC)
+ ELSE IF (ICASE.EQ.10) THEN
+* .. ICAMAX ..
+ CALL ITEST1(ICAMAX(N,CX,INCX),ITRUE3(NP1))
+ ELSE
+ WRITE (NOUT,*) ' Shouldn''t be here in CHECK1'
+ STOP
+ END IF
+*
+ 40 CONTINUE
+ 60 CONTINUE
+*
+ INCX = 1
+ IF (ICASE.EQ.8) THEN
+* CSCAL
+* Add a test for alpha equal to zero.
+ CA = (0.0E0,0.0E0)
+ DO 80 I = 1, 5
+ MWPCT(I) = (0.0E0,0.0E0)
+ MWPCS(I) = (1.0E0,1.0E0)
+ 80 CONTINUE
+ CALL CSCAL(5,CA,CX,INCX)
+ CALL CTEST(5,CX,MWPCT,MWPCS,SFAC)
+ ELSE IF (ICASE.EQ.9) THEN
+* CSSCAL
+* Add a test for alpha equal to zero.
+ SA = 0.0E0
+ DO 100 I = 1, 5
+ MWPCT(I) = (0.0E0,0.0E0)
+ MWPCS(I) = (1.0E0,1.0E0)
+ 100 CONTINUE
+ CALL CSSCAL(5,SA,CX,INCX)
+ CALL CTEST(5,CX,MWPCT,MWPCS,SFAC)
+* Add a test for alpha equal to one.
+ SA = 1.0E0
+ DO 120 I = 1, 5
+ MWPCT(I) = CX(I)
+ MWPCS(I) = CX(I)
+ 120 CONTINUE
+ CALL CSSCAL(5,SA,CX,INCX)
+ CALL CTEST(5,CX,MWPCT,MWPCS,SFAC)
+* Add a test for alpha equal to minus one.
+ SA = -1.0E0
+ DO 140 I = 1, 5
+ MWPCT(I) = -CX(I)
+ MWPCS(I) = -CX(I)
+ 140 CONTINUE
+ CALL CSSCAL(5,SA,CX,INCX)
+ CALL CTEST(5,CX,MWPCT,MWPCS,SFAC)
+ END IF
+ RETURN
+ END
+ SUBROUTINE CHECK2(SFAC)
+* .. Parameters ..
+ INTEGER NOUT
+ PARAMETER (NOUT=6)
+* .. Scalar Arguments ..
+ REAL SFAC
+* .. Scalars in Common ..
+ INTEGER ICASE, INCX, INCY, MODE, N
+ LOGICAL PASS
+* .. Local Scalars ..
+ COMPLEX CA
+ INTEGER I, J, KI, KN, KSIZE, LENX, LENY, MX, MY
+* .. Local Arrays ..
+ COMPLEX CDOT(1), CSIZE1(4), CSIZE2(7,2), CSIZE3(14),
+ + CT10X(7,4,4), CT10Y(7,4,4), CT6(4,4), CT7(4,4),
+ + CT8(7,4,4), CX(7), CX1(7), CY(7), CY1(7)
+ INTEGER INCXS(4), INCYS(4), LENS(4,2), NS(4)
+* .. External Functions ..
+ COMPLEX CDOTC, CDOTU
+ EXTERNAL CDOTC, CDOTU
+* .. External Subroutines ..
+ EXTERNAL CAXPY, CCOPY, CSWAP, CTEST
+* .. Intrinsic Functions ..
+ INTRINSIC ABS, MIN
+* .. Common blocks ..
+ COMMON /COMBLA/ICASE, N, INCX, INCY, MODE, PASS
+* .. Data statements ..
+ DATA CA/(0.4E0,-0.7E0)/
+ DATA INCXS/1, 2, -2, -1/
+ DATA INCYS/1, -2, 1, -2/
+ DATA LENS/1, 1, 2, 4, 1, 1, 3, 7/
+ DATA NS/0, 1, 2, 4/
+ DATA CX1/(0.7E0,-0.8E0), (-0.4E0,-0.7E0),
+ + (-0.1E0,-0.9E0), (0.2E0,-0.8E0),
+ + (-0.9E0,-0.4E0), (0.1E0,0.4E0), (-0.6E0,0.6E0)/
+ DATA CY1/(0.6E0,-0.6E0), (-0.9E0,0.5E0),
+ + (0.7E0,-0.6E0), (0.1E0,-0.5E0), (-0.1E0,-0.2E0),
+ + (-0.5E0,-0.3E0), (0.8E0,-0.7E0)/
+ DATA ((CT8(I,J,1),I=1,7),J=1,4)/(0.6E0,-0.6E0),
+ + (0.0E0,0.0E0), (0.0E0,0.0E0), (0.0E0,0.0E0),
+ + (0.0E0,0.0E0), (0.0E0,0.0E0), (0.0E0,0.0E0),
+ + (0.32E0,-1.41E0), (0.0E0,0.0E0), (0.0E0,0.0E0),
+ + (0.0E0,0.0E0), (0.0E0,0.0E0), (0.0E0,0.0E0),
+ + (0.0E0,0.0E0), (0.32E0,-1.41E0),
+ + (-1.55E0,0.5E0), (0.0E0,0.0E0), (0.0E0,0.0E0),
+ + (0.0E0,0.0E0), (0.0E0,0.0E0), (0.0E0,0.0E0),
+ + (0.32E0,-1.41E0), (-1.55E0,0.5E0),
+ + (0.03E0,-0.89E0), (-0.38E0,-0.96E0),
+ + (0.0E0,0.0E0), (0.0E0,0.0E0), (0.0E0,0.0E0)/
+ DATA ((CT8(I,J,2),I=1,7),J=1,4)/(0.6E0,-0.6E0),
+ + (0.0E0,0.0E0), (0.0E0,0.0E0), (0.0E0,0.0E0),
+ + (0.0E0,0.0E0), (0.0E0,0.0E0), (0.0E0,0.0E0),
+ + (0.32E0,-1.41E0), (0.0E0,0.0E0), (0.0E0,0.0E0),
+ + (0.0E0,0.0E0), (0.0E0,0.0E0), (0.0E0,0.0E0),
+ + (0.0E0,0.0E0), (-0.07E0,-0.89E0),
+ + (-0.9E0,0.5E0), (0.42E0,-1.41E0), (0.0E0,0.0E0),
+ + (0.0E0,0.0E0), (0.0E0,0.0E0), (0.0E0,0.0E0),
+ + (0.78E0,0.06E0), (-0.9E0,0.5E0),
+ + (0.06E0,-0.13E0), (0.1E0,-0.5E0),
+ + (-0.77E0,-0.49E0), (-0.5E0,-0.3E0),
+ + (0.52E0,-1.51E0)/
+ DATA ((CT8(I,J,3),I=1,7),J=1,4)/(0.6E0,-0.6E0),
+ + (0.0E0,0.0E0), (0.0E0,0.0E0), (0.0E0,0.0E0),
+ + (0.0E0,0.0E0), (0.0E0,0.0E0), (0.0E0,0.0E0),
+ + (0.32E0,-1.41E0), (0.0E0,0.0E0), (0.0E0,0.0E0),
+ + (0.0E0,0.0E0), (0.0E0,0.0E0), (0.0E0,0.0E0),
+ + (0.0E0,0.0E0), (-0.07E0,-0.89E0),
+ + (-1.18E0,-0.31E0), (0.0E0,0.0E0), (0.0E0,0.0E0),
+ + (0.0E0,0.0E0), (0.0E0,0.0E0), (0.0E0,0.0E0),
+ + (0.78E0,0.06E0), (-1.54E0,0.97E0),
+ + (0.03E0,-0.89E0), (-0.18E0,-1.31E0),
+ + (0.0E0,0.0E0), (0.0E0,0.0E0), (0.0E0,0.0E0)/
+ DATA ((CT8(I,J,4),I=1,7),J=1,4)/(0.6E0,-0.6E0),
+ + (0.0E0,0.0E0), (0.0E0,0.0E0), (0.0E0,0.0E0),
+ + (0.0E0,0.0E0), (0.0E0,0.0E0), (0.0E0,0.0E0),
+ + (0.32E0,-1.41E0), (0.0E0,0.0E0), (0.0E0,0.0E0),
+ + (0.0E0,0.0E0), (0.0E0,0.0E0), (0.0E0,0.0E0),
+ + (0.0E0,0.0E0), (0.32E0,-1.41E0), (-0.9E0,0.5E0),
+ + (0.05E0,-0.6E0), (0.0E0,0.0E0), (0.0E0,0.0E0),
+ + (0.0E0,0.0E0), (0.0E0,0.0E0), (0.32E0,-1.41E0),
+ + (-0.9E0,0.5E0), (0.05E0,-0.6E0), (0.1E0,-0.5E0),
+ + (-0.77E0,-0.49E0), (-0.5E0,-0.3E0),
+ + (0.32E0,-1.16E0)/
+ DATA CT7/(0.0E0,0.0E0), (-0.06E0,-0.90E0),
+ + (0.65E0,-0.47E0), (-0.34E0,-1.22E0),
+ + (0.0E0,0.0E0), (-0.06E0,-0.90E0),
+ + (-0.59E0,-1.46E0), (-1.04E0,-0.04E0),
+ + (0.0E0,0.0E0), (-0.06E0,-0.90E0),
+ + (-0.83E0,0.59E0), (0.07E0,-0.37E0),
+ + (0.0E0,0.0E0), (-0.06E0,-0.90E0),
+ + (-0.76E0,-1.15E0), (-1.33E0,-1.82E0)/
+ DATA CT6/(0.0E0,0.0E0), (0.90E0,0.06E0),
+ + (0.91E0,-0.77E0), (1.80E0,-0.10E0),
+ + (0.0E0,0.0E0), (0.90E0,0.06E0), (1.45E0,0.74E0),
+ + (0.20E0,0.90E0), (0.0E0,0.0E0), (0.90E0,0.06E0),
+ + (-0.55E0,0.23E0), (0.83E0,-0.39E0),
+ + (0.0E0,0.0E0), (0.90E0,0.06E0), (1.04E0,0.79E0),
+ + (1.95E0,1.22E0)/
+ DATA ((CT10X(I,J,1),I=1,7),J=1,4)/(0.7E0,-0.8E0),
+ + (0.0E0,0.0E0), (0.0E0,0.0E0), (0.0E0,0.0E0),
+ + (0.0E0,0.0E0), (0.0E0,0.0E0), (0.0E0,0.0E0),
+ + (0.6E0,-0.6E0), (0.0E0,0.0E0), (0.0E0,0.0E0),
+ + (0.0E0,0.0E0), (0.0E0,0.0E0), (0.0E0,0.0E0),
+ + (0.0E0,0.0E0), (0.6E0,-0.6E0), (-0.9E0,0.5E0),
+ + (0.0E0,0.0E0), (0.0E0,0.0E0), (0.0E0,0.0E0),
+ + (0.0E0,0.0E0), (0.0E0,0.0E0), (0.6E0,-0.6E0),
+ + (-0.9E0,0.5E0), (0.7E0,-0.6E0), (0.1E0,-0.5E0),
+ + (0.0E0,0.0E0), (0.0E0,0.0E0), (0.0E0,0.0E0)/
+ DATA ((CT10X(I,J,2),I=1,7),J=1,4)/(0.7E0,-0.8E0),
+ + (0.0E0,0.0E0), (0.0E0,0.0E0), (0.0E0,0.0E0),
+ + (0.0E0,0.0E0), (0.0E0,0.0E0), (0.0E0,0.0E0),
+ + (0.6E0,-0.6E0), (0.0E0,0.0E0), (0.0E0,0.0E0),
+ + (0.0E0,0.0E0), (0.0E0,0.0E0), (0.0E0,0.0E0),
+ + (0.0E0,0.0E0), (0.7E0,-0.6E0), (-0.4E0,-0.7E0),
+ + (0.6E0,-0.6E0), (0.0E0,0.0E0), (0.0E0,0.0E0),
+ + (0.0E0,0.0E0), (0.0E0,0.0E0), (0.8E0,-0.7E0),
+ + (-0.4E0,-0.7E0), (-0.1E0,-0.2E0),
+ + (0.2E0,-0.8E0), (0.7E0,-0.6E0), (0.1E0,0.4E0),
+ + (0.6E0,-0.6E0)/
+ DATA ((CT10X(I,J,3),I=1,7),J=1,4)/(0.7E0,-0.8E0),
+ + (0.0E0,0.0E0), (0.0E0,0.0E0), (0.0E0,0.0E0),
+ + (0.0E0,0.0E0), (0.0E0,0.0E0), (0.0E0,0.0E0),
+ + (0.6E0,-0.6E0), (0.0E0,0.0E0), (0.0E0,0.0E0),
+ + (0.0E0,0.0E0), (0.0E0,0.0E0), (0.0E0,0.0E0),
+ + (0.0E0,0.0E0), (-0.9E0,0.5E0), (-0.4E0,-0.7E0),
+ + (0.6E0,-0.6E0), (0.0E0,0.0E0), (0.0E0,0.0E0),
+ + (0.0E0,0.0E0), (0.0E0,0.0E0), (0.1E0,-0.5E0),
+ + (-0.4E0,-0.7E0), (0.7E0,-0.6E0), (0.2E0,-0.8E0),
+ + (-0.9E0,0.5E0), (0.1E0,0.4E0), (0.6E0,-0.6E0)/
+ DATA ((CT10X(I,J,4),I=1,7),J=1,4)/(0.7E0,-0.8E0),
+ + (0.0E0,0.0E0), (0.0E0,0.0E0), (0.0E0,0.0E0),
+ + (0.0E0,0.0E0), (0.0E0,0.0E0), (0.0E0,0.0E0),
+ + (0.6E0,-0.6E0), (0.0E0,0.0E0), (0.0E0,0.0E0),
+ + (0.0E0,0.0E0), (0.0E0,0.0E0), (0.0E0,0.0E0),
+ + (0.0E0,0.0E0), (0.6E0,-0.6E0), (0.7E0,-0.6E0),
+ + (0.0E0,0.0E0), (0.0E0,0.0E0), (0.0E0,0.0E0),
+ + (0.0E0,0.0E0), (0.0E0,0.0E0), (0.6E0,-0.6E0),
+ + (0.7E0,-0.6E0), (-0.1E0,-0.2E0), (0.8E0,-0.7E0),
+ + (0.0E0,0.0E0), (0.0E0,0.0E0), (0.0E0,0.0E0)/
+ DATA ((CT10Y(I,J,1),I=1,7),J=1,4)/(0.6E0,-0.6E0),
+ + (0.0E0,0.0E0), (0.0E0,0.0E0), (0.0E0,0.0E0),
+ + (0.0E0,0.0E0), (0.0E0,0.0E0), (0.0E0,0.0E0),
+ + (0.7E0,-0.8E0), (0.0E0,0.0E0), (0.0E0,0.0E0),
+ + (0.0E0,0.0E0), (0.0E0,0.0E0), (0.0E0,0.0E0),
+ + (0.0E0,0.0E0), (0.7E0,-0.8E0), (-0.4E0,-0.7E0),
+ + (0.0E0,0.0E0), (0.0E0,0.0E0), (0.0E0,0.0E0),
+ + (0.0E0,0.0E0), (0.0E0,0.0E0), (0.7E0,-0.8E0),
+ + (-0.4E0,-0.7E0), (-0.1E0,-0.9E0),
+ + (0.2E0,-0.8E0), (0.0E0,0.0E0), (0.0E0,0.0E0),
+ + (0.0E0,0.0E0)/
+ DATA ((CT10Y(I,J,2),I=1,7),J=1,4)/(0.6E0,-0.6E0),
+ + (0.0E0,0.0E0), (0.0E0,0.0E0), (0.0E0,0.0E0),
+ + (0.0E0,0.0E0), (0.0E0,0.0E0), (0.0E0,0.0E0),
+ + (0.7E0,-0.8E0), (0.0E0,0.0E0), (0.0E0,0.0E0),
+ + (0.0E0,0.0E0), (0.0E0,0.0E0), (0.0E0,0.0E0),
+ + (0.0E0,0.0E0), (-0.1E0,-0.9E0), (-0.9E0,0.5E0),
+ + (0.7E0,-0.8E0), (0.0E0,0.0E0), (0.0E0,0.0E0),
+ + (0.0E0,0.0E0), (0.0E0,0.0E0), (-0.6E0,0.6E0),
+ + (-0.9E0,0.5E0), (-0.9E0,-0.4E0), (0.1E0,-0.5E0),
+ + (-0.1E0,-0.9E0), (-0.5E0,-0.3E0),
+ + (0.7E0,-0.8E0)/
+ DATA ((CT10Y(I,J,3),I=1,7),J=1,4)/(0.6E0,-0.6E0),
+ + (0.0E0,0.0E0), (0.0E0,0.0E0), (0.0E0,0.0E0),
+ + (0.0E0,0.0E0), (0.0E0,0.0E0), (0.0E0,0.0E0),
+ + (0.7E0,-0.8E0), (0.0E0,0.0E0), (0.0E0,0.0E0),
+ + (0.0E0,0.0E0), (0.0E0,0.0E0), (0.0E0,0.0E0),
+ + (0.0E0,0.0E0), (-0.1E0,-0.9E0), (0.7E0,-0.8E0),
+ + (0.0E0,0.0E0), (0.0E0,0.0E0), (0.0E0,0.0E0),
+ + (0.0E0,0.0E0), (0.0E0,0.0E0), (-0.6E0,0.6E0),
+ + (-0.9E0,-0.4E0), (-0.1E0,-0.9E0),
+ + (0.7E0,-0.8E0), (0.0E0,0.0E0), (0.0E0,0.0E0),
+ + (0.0E0,0.0E0)/
+ DATA ((CT10Y(I,J,4),I=1,7),J=1,4)/(0.6E0,-0.6E0),
+ + (0.0E0,0.0E0), (0.0E0,0.0E0), (0.0E0,0.0E0),
+ + (0.0E0,0.0E0), (0.0E0,0.0E0), (0.0E0,0.0E0),
+ + (0.7E0,-0.8E0), (0.0E0,0.0E0), (0.0E0,0.0E0),
+ + (0.0E0,0.0E0), (0.0E0,0.0E0), (0.0E0,0.0E0),
+ + (0.0E0,0.0E0), (0.7E0,-0.8E0), (-0.9E0,0.5E0),
+ + (-0.4E0,-0.7E0), (0.0E0,0.0E0), (0.0E0,0.0E0),
+ + (0.0E0,0.0E0), (0.0E0,0.0E0), (0.7E0,-0.8E0),
+ + (-0.9E0,0.5E0), (-0.4E0,-0.7E0), (0.1E0,-0.5E0),
+ + (-0.1E0,-0.9E0), (-0.5E0,-0.3E0),
+ + (0.2E0,-0.8E0)/
+ DATA CSIZE1/(0.0E0,0.0E0), (0.9E0,0.9E0),
+ + (1.63E0,1.73E0), (2.90E0,2.78E0)/
+ DATA CSIZE3/(0.0E0,0.0E0), (0.0E0,0.0E0),
+ + (0.0E0,0.0E0), (0.0E0,0.0E0), (0.0E0,0.0E0),
+ + (0.0E0,0.0E0), (0.0E0,0.0E0), (1.17E0,1.17E0),
+ + (1.17E0,1.17E0), (1.17E0,1.17E0),
+ + (1.17E0,1.17E0), (1.17E0,1.17E0),
+ + (1.17E0,1.17E0), (1.17E0,1.17E0)/
+ DATA CSIZE2/(0.0E0,0.0E0), (0.0E0,0.0E0),
+ + (0.0E0,0.0E0), (0.0E0,0.0E0), (0.0E0,0.0E0),
+ + (0.0E0,0.0E0), (0.0E0,0.0E0), (1.54E0,1.54E0),
+ + (1.54E0,1.54E0), (1.54E0,1.54E0),
+ + (1.54E0,1.54E0), (1.54E0,1.54E0),
+ + (1.54E0,1.54E0), (1.54E0,1.54E0)/
+* .. Executable Statements ..
+ DO 60 KI = 1, 4
+ INCX = INCXS(KI)
+ INCY = INCYS(KI)
+ MX = ABS(INCX)
+ MY = ABS(INCY)
+*
+ DO 40 KN = 1, 4
+ N = NS(KN)
+ KSIZE = MIN(2,KN)
+ LENX = LENS(KN,MX)
+ LENY = LENS(KN,MY)
+* .. initialize all argument arrays ..
+ DO 20 I = 1, 7
+ CX(I) = CX1(I)
+ CY(I) = CY1(I)
+ 20 CONTINUE
+ IF (ICASE.EQ.1) THEN
+* .. CDOTC ..
+ CDOT(1) = CDOTC(N,CX,INCX,CY,INCY)
+ CALL CTEST(1,CDOT,CT6(KN,KI),CSIZE1(KN),SFAC)
+ ELSE IF (ICASE.EQ.2) THEN
+* .. CDOTU ..
+ CDOT(1) = CDOTU(N,CX,INCX,CY,INCY)
+ CALL CTEST(1,CDOT,CT7(KN,KI),CSIZE1(KN),SFAC)
+ ELSE IF (ICASE.EQ.3) THEN
+* .. CAXPY ..
+ CALL CAXPY(N,CA,CX,INCX,CY,INCY)
+ CALL CTEST(LENY,CY,CT8(1,KN,KI),CSIZE2(1,KSIZE),SFAC)
+ ELSE IF (ICASE.EQ.4) THEN
+* .. CCOPY ..
+ CALL CCOPY(N,CX,INCX,CY,INCY)
+ CALL CTEST(LENY,CY,CT10Y(1,KN,KI),CSIZE3,1.0E0)
+ ELSE IF (ICASE.EQ.5) THEN
+* .. CSWAP ..
+ CALL CSWAP(N,CX,INCX,CY,INCY)
+ CALL CTEST(LENX,CX,CT10X(1,KN,KI),CSIZE3,1.0E0)
+ CALL CTEST(LENY,CY,CT10Y(1,KN,KI),CSIZE3,1.0E0)
+ ELSE
+ WRITE (NOUT,*) ' Shouldn''t be here in CHECK2'
+ STOP
+ END IF
+*
+ 40 CONTINUE
+ 60 CONTINUE
+ RETURN
+ END
+ SUBROUTINE STEST(LEN,SCOMP,STRUE,SSIZE,SFAC)
+* ********************************* STEST **************************
+*
+* THIS SUBR COMPARES ARRAYS SCOMP() AND STRUE() OF LENGTH LEN TO
+* SEE IF THE TERM BY TERM DIFFERENCES, MULTIPLIED BY SFAC, ARE
+* NEGLIGIBLE.
+*
+* C. L. LAWSON, JPL, 1974 DEC 10
+*
+* .. Parameters ..
+ INTEGER NOUT
+ REAL ZERO
+ PARAMETER (NOUT=6, ZERO=0.0E0)
+* .. Scalar Arguments ..
+ REAL SFAC
+ INTEGER LEN
+* .. Array Arguments ..
+ REAL SCOMP(LEN), SSIZE(LEN), STRUE(LEN)
+* .. Scalars in Common ..
+ INTEGER ICASE, INCX, INCY, MODE, N
+ LOGICAL PASS
+* .. Local Scalars ..
+ REAL SD
+ INTEGER I
+* .. External Functions ..
+ REAL SDIFF
+ EXTERNAL SDIFF
+* .. Intrinsic Functions ..
+ INTRINSIC ABS
+* .. Common blocks ..
+ COMMON /COMBLA/ICASE, N, INCX, INCY, MODE, PASS
+* .. Executable Statements ..
+*
+ DO 40 I = 1, LEN
+ SD = SCOMP(I) - STRUE(I)
+ IF (ABS(SFAC*SD) .LE. ABS(SSIZE(I))*EPSILON(ZERO))
+ + GO TO 40
+*
+* HERE SCOMP(I) IS NOT CLOSE TO STRUE(I).
+*
+ IF ( .NOT. PASS) GO TO 20
+* PRINT FAIL MESSAGE AND HEADER.
+ PASS = .FALSE.
+ WRITE (NOUT,99999)
+ WRITE (NOUT,99998)
+ 20 WRITE (NOUT,99997) ICASE, N, INCX, INCY, MODE, I, SCOMP(I),
+ + STRUE(I), SD, SSIZE(I)
+ 40 CONTINUE
+ RETURN
+*
+99999 FORMAT (' FAIL')
+99998 FORMAT (/' CASE N INCX INCY MODE I ',
+ + ' COMP(I) TRUE(I) DIFFERENCE',
+ + ' SIZE(I)',/1X)
+99997 FORMAT (1X,I4,I3,3I5,I3,2E36.8,2E12.4)
+ END
+ SUBROUTINE STEST1(SCOMP1,STRUE1,SSIZE,SFAC)
+* ************************* STEST1 *****************************
+*
+* THIS IS AN INTERFACE SUBROUTINE TO ACCOMMODATE THE FORTRAN
+* REQUIREMENT THAT WHEN A DUMMY ARGUMENT IS AN ARRAY, THE
+* ACTUAL ARGUMENT MUST ALSO BE AN ARRAY OR AN ARRAY ELEMENT.
+*
+* C.L. LAWSON, JPL, 1978 DEC 6
+*
+* .. Scalar Arguments ..
+ REAL SCOMP1, SFAC, STRUE1
+* .. Array Arguments ..
+ REAL SSIZE(*)
+* .. Local Arrays ..
+ REAL SCOMP(1), STRUE(1)
+* .. External Subroutines ..
+ EXTERNAL STEST
+* .. Executable Statements ..
+*
+ SCOMP(1) = SCOMP1
+ STRUE(1) = STRUE1
+ CALL STEST(1,SCOMP,STRUE,SSIZE,SFAC)
+*
+ RETURN
+ END
+ REAL FUNCTION SDIFF(SA,SB)
+* ********************************* SDIFF **************************
+* COMPUTES DIFFERENCE OF TWO NUMBERS. C. L. LAWSON, JPL 1974 FEB 15
+*
+* .. Scalar Arguments ..
+ REAL SA, SB
+* .. Executable Statements ..
+ SDIFF = SA - SB
+ RETURN
+ END
+ SUBROUTINE CTEST(LEN,CCOMP,CTRUE,CSIZE,SFAC)
+* **************************** CTEST *****************************
+*
+* C.L. LAWSON, JPL, 1978 DEC 6
+*
+* .. Scalar Arguments ..
+ REAL SFAC
+ INTEGER LEN
+* .. Array Arguments ..
+ COMPLEX CCOMP(LEN), CSIZE(LEN), CTRUE(LEN)
+* .. Local Scalars ..
+ INTEGER I
+* .. Local Arrays ..
+ REAL SCOMP(20), SSIZE(20), STRUE(20)
+* .. External Subroutines ..
+ EXTERNAL STEST
+* .. Intrinsic Functions ..
+ INTRINSIC AIMAG, REAL
+* .. Executable Statements ..
+ DO 20 I = 1, LEN
+ SCOMP(2*I-1) = REAL(CCOMP(I))
+ SCOMP(2*I) = AIMAG(CCOMP(I))
+ STRUE(2*I-1) = REAL(CTRUE(I))
+ STRUE(2*I) = AIMAG(CTRUE(I))
+ SSIZE(2*I-1) = REAL(CSIZE(I))
+ SSIZE(2*I) = AIMAG(CSIZE(I))
+ 20 CONTINUE
+*
+ CALL STEST(2*LEN,SCOMP,STRUE,SSIZE,SFAC)
+ RETURN
+ END
+ SUBROUTINE ITEST1(ICOMP,ITRUE)
+* ********************************* ITEST1 *************************
+*
+* THIS SUBROUTINE COMPARES THE VARIABLES ICOMP AND ITRUE FOR
+* EQUALITY.
+* C. L. LAWSON, JPL, 1974 DEC 10
+*
+* .. Parameters ..
+ INTEGER NOUT
+ PARAMETER (NOUT=6)
+* .. Scalar Arguments ..
+ INTEGER ICOMP, ITRUE
+* .. Scalars in Common ..
+ INTEGER ICASE, INCX, INCY, MODE, N
+ LOGICAL PASS
+* .. Local Scalars ..
+ INTEGER ID
+* .. Common blocks ..
+ COMMON /COMBLA/ICASE, N, INCX, INCY, MODE, PASS
+* .. Executable Statements ..
+ IF (ICOMP.EQ.ITRUE) GO TO 40
+*
+* HERE ICOMP IS NOT EQUAL TO ITRUE.
+*
+ IF ( .NOT. PASS) GO TO 20
+* PRINT FAIL MESSAGE AND HEADER.
+ PASS = .FALSE.
+ WRITE (NOUT,99999)
+ WRITE (NOUT,99998)
+ 20 ID = ICOMP - ITRUE
+ WRITE (NOUT,99997) ICASE, N, INCX, INCY, MODE, ICOMP, ITRUE, ID
+ 40 CONTINUE
+ RETURN
+*
+99999 FORMAT (' FAIL')
+99998 FORMAT (/' CASE N INCX INCY MODE ',
+ + ' COMP TRUE DIFFERENCE',
+ + /1X)
+99997 FORMAT (1X,I4,I3,3I5,2I36,I12)
+ END
diff --git a/blas/testing/cblat2.dat b/blas/testing/cblat2.dat
new file mode 100644
index 0000000..ae98730
--- /dev/null
+++ b/blas/testing/cblat2.dat
@@ -0,0 +1,35 @@
+'cblat2.summ' NAME OF SUMMARY OUTPUT FILE
+6 UNIT NUMBER OF SUMMARY FILE
+'cblat2.snap' NAME OF SNAPSHOT OUTPUT FILE
+-1 UNIT NUMBER OF SNAPSHOT FILE (NOT USED IF .LT. 0)
+F LOGICAL FLAG, T TO REWIND SNAPSHOT FILE AFTER EACH RECORD.
+F LOGICAL FLAG, T TO STOP ON FAILURES.
+T LOGICAL FLAG, T TO TEST ERROR EXITS.
+16.0 THRESHOLD VALUE OF TEST RATIO
+6 NUMBER OF VALUES OF N
+0 1 2 3 5 9 VALUES OF N
+4 NUMBER OF VALUES OF K
+0 1 2 4 VALUES OF K
+4 NUMBER OF VALUES OF INCX AND INCY
+1 2 -1 -2 VALUES OF INCX AND INCY
+3 NUMBER OF VALUES OF ALPHA
+(0.0,0.0) (1.0,0.0) (0.7,-0.9) VALUES OF ALPHA
+3 NUMBER OF VALUES OF BETA
+(0.0,0.0) (1.0,0.0) (1.3,-1.1) VALUES OF BETA
+CGEMV T PUT F FOR NO TEST. SAME COLUMNS.
+CGBMV T PUT F FOR NO TEST. SAME COLUMNS.
+CHEMV T PUT F FOR NO TEST. SAME COLUMNS.
+CHBMV T PUT F FOR NO TEST. SAME COLUMNS.
+CHPMV T PUT F FOR NO TEST. SAME COLUMNS.
+CTRMV T PUT F FOR NO TEST. SAME COLUMNS.
+CTBMV T PUT F FOR NO TEST. SAME COLUMNS.
+CTPMV T PUT F FOR NO TEST. SAME COLUMNS.
+CTRSV T PUT F FOR NO TEST. SAME COLUMNS.
+CTBSV T PUT F FOR NO TEST. SAME COLUMNS.
+CTPSV T PUT F FOR NO TEST. SAME COLUMNS.
+CGERC T PUT F FOR NO TEST. SAME COLUMNS.
+CGERU T PUT F FOR NO TEST. SAME COLUMNS.
+CHER T PUT F FOR NO TEST. SAME COLUMNS.
+CHPR T PUT F FOR NO TEST. SAME COLUMNS.
+CHER2 T PUT F FOR NO TEST. SAME COLUMNS.
+CHPR2 T PUT F FOR NO TEST. SAME COLUMNS.
diff --git a/blas/testing/cblat2.f b/blas/testing/cblat2.f
new file mode 100644
index 0000000..5833ea8
--- /dev/null
+++ b/blas/testing/cblat2.f
@@ -0,0 +1,3279 @@
+*> \brief \b CBLAT2
+*
+* =========== DOCUMENTATION ===========
+*
+* Online html documentation available at
+* http://www.netlib.org/lapack/explore-html/
+*
+* Definition:
+* ===========
+*
+* PROGRAM CBLAT2
+*
+*
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
+*>
+*> Test program for the COMPLEX Level 2 Blas.
+*>
+*> The program must be driven by a short data file. The first 18 records
+*> of the file are read using list-directed input, the last 17 records
+*> are read using the format ( A6, L2 ). An annotated example of a data
+*> file can be obtained by deleting the first 3 characters from the
+*> following 35 lines:
+*> 'cblat2.out' NAME OF SUMMARY OUTPUT FILE
+*> 6 UNIT NUMBER OF SUMMARY FILE
+*> 'CBLA2T.SNAP' NAME OF SNAPSHOT OUTPUT FILE
+*> -1 UNIT NUMBER OF SNAPSHOT FILE (NOT USED IF .LT. 0)
+*> F LOGICAL FLAG, T TO REWIND SNAPSHOT FILE AFTER EACH RECORD.
+*> F LOGICAL FLAG, T TO STOP ON FAILURES.
+*> T LOGICAL FLAG, T TO TEST ERROR EXITS.
+*> 16.0 THRESHOLD VALUE OF TEST RATIO
+*> 6 NUMBER OF VALUES OF N
+*> 0 1 2 3 5 9 VALUES OF N
+*> 4 NUMBER OF VALUES OF K
+*> 0 1 2 4 VALUES OF K
+*> 4 NUMBER OF VALUES OF INCX AND INCY
+*> 1 2 -1 -2 VALUES OF INCX AND INCY
+*> 3 NUMBER OF VALUES OF ALPHA
+*> (0.0,0.0) (1.0,0.0) (0.7,-0.9) VALUES OF ALPHA
+*> 3 NUMBER OF VALUES OF BETA
+*> (0.0,0.0) (1.0,0.0) (1.3,-1.1) VALUES OF BETA
+*> CGEMV T PUT F FOR NO TEST. SAME COLUMNS.
+*> CGBMV T PUT F FOR NO TEST. SAME COLUMNS.
+*> CHEMV T PUT F FOR NO TEST. SAME COLUMNS.
+*> CHBMV T PUT F FOR NO TEST. SAME COLUMNS.
+*> CHPMV T PUT F FOR NO TEST. SAME COLUMNS.
+*> CTRMV T PUT F FOR NO TEST. SAME COLUMNS.
+*> CTBMV T PUT F FOR NO TEST. SAME COLUMNS.
+*> CTPMV T PUT F FOR NO TEST. SAME COLUMNS.
+*> CTRSV T PUT F FOR NO TEST. SAME COLUMNS.
+*> CTBSV T PUT F FOR NO TEST. SAME COLUMNS.
+*> CTPSV T PUT F FOR NO TEST. SAME COLUMNS.
+*> CGERC T PUT F FOR NO TEST. SAME COLUMNS.
+*> CGERU T PUT F FOR NO TEST. SAME COLUMNS.
+*> CHER T PUT F FOR NO TEST. SAME COLUMNS.
+*> CHPR T PUT F FOR NO TEST. SAME COLUMNS.
+*> CHER2 T PUT F FOR NO TEST. SAME COLUMNS.
+*> CHPR2 T PUT F FOR NO TEST. SAME COLUMNS.
+*>
+*> Further Details
+*> ===============
+*>
+*> See:
+*>
+*> Dongarra J. J., Du Croz J. J., Hammarling S. and Hanson R. J..
+*> An extended set of Fortran Basic Linear Algebra Subprograms.
+*>
+*> Technical Memoranda Nos. 41 (revision 3) and 81, Mathematics
+*> and Computer Science Division, Argonne National Laboratory,
+*> 9700 South Cass Avenue, Argonne, Illinois 60439, US.
+*>
+*> Or
+*>
+*> NAG Technical Reports TR3/87 and TR4/87, Numerical Algorithms
+*> Group Ltd., NAG Central Office, 256 Banbury Road, Oxford
+*> OX2 7DE, UK, and Numerical Algorithms Group Inc., 1101 31st
+*> Street, Suite 100, Downers Grove, Illinois 60515-1263, USA.
+*>
+*>
+*> -- Written on 10-August-1987.
+*> Richard Hanson, Sandia National Labs.
+*> Jeremy Du Croz, NAG Central Office.
+*>
+*> 10-9-00: Change STATUS='NEW' to 'UNKNOWN' so that the testers
+*> can be run multiple times without deleting generated
+*> output files (susan)
+*> \endverbatim
+*
+* Authors:
+* ========
+*
+*> \author Univ. of Tennessee
+*> \author Univ. of California Berkeley
+*> \author Univ. of Colorado Denver
+*> \author NAG Ltd.
+*
+*> \date April 2012
+*
+*> \ingroup complex_blas_testing
+*
+* =====================================================================
+ PROGRAM CBLAT2
+*
+* -- Reference BLAS test routine (version 3.4.1) --
+* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
+* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+* April 2012
+*
+* =====================================================================
+*
+* .. Parameters ..
+ INTEGER NIN
+ PARAMETER ( NIN = 5 )
+ INTEGER NSUBS
+ PARAMETER ( NSUBS = 17 )
+ COMPLEX ZERO, ONE
+ PARAMETER ( ZERO = ( 0.0, 0.0 ), ONE = ( 1.0, 0.0 ) )
+ REAL RZERO
+ PARAMETER ( RZERO = 0.0 )
+ INTEGER NMAX, INCMAX
+ PARAMETER ( NMAX = 65, INCMAX = 2 )
+ INTEGER NINMAX, NIDMAX, NKBMAX, NALMAX, NBEMAX
+ PARAMETER ( NINMAX = 7, NIDMAX = 9, NKBMAX = 7,
+ $ NALMAX = 7, NBEMAX = 7 )
+* .. Local Scalars ..
+ REAL EPS, ERR, THRESH
+ INTEGER I, ISNUM, J, N, NALF, NBET, NIDIM, NINC, NKB,
+ $ NOUT, NTRA
+ LOGICAL FATAL, LTESTT, REWI, SAME, SFATAL, TRACE,
+ $ TSTERR
+ CHARACTER*1 TRANS
+ CHARACTER*6 SNAMET
+ CHARACTER*32 SNAPS, SUMMRY
+* .. Local Arrays ..
+ COMPLEX A( NMAX, NMAX ), AA( NMAX*NMAX ),
+ $ ALF( NALMAX ), AS( NMAX*NMAX ), BET( NBEMAX ),
+ $ X( NMAX ), XS( NMAX*INCMAX ),
+ $ XX( NMAX*INCMAX ), Y( NMAX ),
+ $ YS( NMAX*INCMAX ), YT( NMAX ),
+ $ YY( NMAX*INCMAX ), Z( 2*NMAX )
+ REAL G( NMAX )
+ INTEGER IDIM( NIDMAX ), INC( NINMAX ), KB( NKBMAX )
+ LOGICAL LTEST( NSUBS )
+ CHARACTER*6 SNAMES( NSUBS )
+* .. External Functions ..
+ REAL SDIFF
+ LOGICAL LCE
+ EXTERNAL SDIFF, LCE
+* .. External Subroutines ..
+ EXTERNAL CCHK1, CCHK2, CCHK3, CCHK4, CCHK5, CCHK6,
+ $ CCHKE, CMVCH
+* .. Intrinsic Functions ..
+ INTRINSIC ABS, MAX, MIN
+* .. Scalars in Common ..
+ INTEGER INFOT, NOUTC
+ LOGICAL LERR, OK
+ CHARACTER*6 SRNAMT
+* .. Common blocks ..
+ COMMON /INFOC/INFOT, NOUTC, OK, LERR
+ COMMON /SRNAMC/SRNAMT
+* .. Data statements ..
+ DATA SNAMES/'CGEMV ', 'CGBMV ', 'CHEMV ', 'CHBMV ',
+ $ 'CHPMV ', 'CTRMV ', 'CTBMV ', 'CTPMV ',
+ $ 'CTRSV ', 'CTBSV ', 'CTPSV ', 'CGERC ',
+ $ 'CGERU ', 'CHER ', 'CHPR ', 'CHER2 ',
+ $ 'CHPR2 '/
+* .. Executable Statements ..
+*
+* Read name and unit number for summary output file and open file.
+*
+ READ( NIN, FMT = * )SUMMRY
+ READ( NIN, FMT = * )NOUT
+ OPEN( NOUT, FILE = SUMMRY, STATUS = 'UNKNOWN' )
+ NOUTC = NOUT
+*
+* Read name and unit number for snapshot output file and open file.
+*
+ READ( NIN, FMT = * )SNAPS
+ READ( NIN, FMT = * )NTRA
+ TRACE = NTRA.GE.0
+ IF( TRACE )THEN
+ OPEN( NTRA, FILE = SNAPS, STATUS = 'UNKNOWN' )
+ END IF
+* Read the flag that directs rewinding of the snapshot file.
+ READ( NIN, FMT = * )REWI
+ REWI = REWI.AND.TRACE
+* Read the flag that directs stopping on any failure.
+ READ( NIN, FMT = * )SFATAL
+* Read the flag that indicates whether error exits are to be tested.
+ READ( NIN, FMT = * )TSTERR
+* Read the threshold value of the test ratio
+ READ( NIN, FMT = * )THRESH
+*
+* Read and check the parameter values for the tests.
+*
+* Values of N
+ READ( NIN, FMT = * )NIDIM
+ IF( NIDIM.LT.1.OR.NIDIM.GT.NIDMAX )THEN
+ WRITE( NOUT, FMT = 9997 )'N', NIDMAX
+ GO TO 230
+ END IF
+ READ( NIN, FMT = * )( IDIM( I ), I = 1, NIDIM )
+ DO 10 I = 1, NIDIM
+ IF( IDIM( I ).LT.0.OR.IDIM( I ).GT.NMAX )THEN
+ WRITE( NOUT, FMT = 9996 )NMAX
+ GO TO 230
+ END IF
+ 10 CONTINUE
+* Values of K
+ READ( NIN, FMT = * )NKB
+ IF( NKB.LT.1.OR.NKB.GT.NKBMAX )THEN
+ WRITE( NOUT, FMT = 9997 )'K', NKBMAX
+ GO TO 230
+ END IF
+ READ( NIN, FMT = * )( KB( I ), I = 1, NKB )
+ DO 20 I = 1, NKB
+ IF( KB( I ).LT.0 )THEN
+ WRITE( NOUT, FMT = 9995 )
+ GO TO 230
+ END IF
+ 20 CONTINUE
+* Values of INCX and INCY
+ READ( NIN, FMT = * )NINC
+ IF( NINC.LT.1.OR.NINC.GT.NINMAX )THEN
+ WRITE( NOUT, FMT = 9997 )'INCX AND INCY', NINMAX
+ GO TO 230
+ END IF
+ READ( NIN, FMT = * )( INC( I ), I = 1, NINC )
+ DO 30 I = 1, NINC
+ IF( INC( I ).EQ.0.OR.ABS( INC( I ) ).GT.INCMAX )THEN
+ WRITE( NOUT, FMT = 9994 )INCMAX
+ GO TO 230
+ END IF
+ 30 CONTINUE
+* Values of ALPHA
+ READ( NIN, FMT = * )NALF
+ IF( NALF.LT.1.OR.NALF.GT.NALMAX )THEN
+ WRITE( NOUT, FMT = 9997 )'ALPHA', NALMAX
+ GO TO 230
+ END IF
+ READ( NIN, FMT = * )( ALF( I ), I = 1, NALF )
+* Values of BETA
+ READ( NIN, FMT = * )NBET
+ IF( NBET.LT.1.OR.NBET.GT.NBEMAX )THEN
+ WRITE( NOUT, FMT = 9997 )'BETA', NBEMAX
+ GO TO 230
+ END IF
+ READ( NIN, FMT = * )( BET( I ), I = 1, NBET )
+*
+* Report values of parameters.
+*
+ WRITE( NOUT, FMT = 9993 )
+ WRITE( NOUT, FMT = 9992 )( IDIM( I ), I = 1, NIDIM )
+ WRITE( NOUT, FMT = 9991 )( KB( I ), I = 1, NKB )
+ WRITE( NOUT, FMT = 9990 )( INC( I ), I = 1, NINC )
+ WRITE( NOUT, FMT = 9989 )( ALF( I ), I = 1, NALF )
+ WRITE( NOUT, FMT = 9988 )( BET( I ), I = 1, NBET )
+ IF( .NOT.TSTERR )THEN
+ WRITE( NOUT, FMT = * )
+ WRITE( NOUT, FMT = 9980 )
+ END IF
+ WRITE( NOUT, FMT = * )
+ WRITE( NOUT, FMT = 9999 )THRESH
+ WRITE( NOUT, FMT = * )
+*
+* Read names of subroutines and flags which indicate
+* whether they are to be tested.
+*
+ DO 40 I = 1, NSUBS
+ LTEST( I ) = .FALSE.
+ 40 CONTINUE
+ 50 READ( NIN, FMT = 9984, END = 80 )SNAMET, LTESTT
+ DO 60 I = 1, NSUBS
+ IF( SNAMET.EQ.SNAMES( I ) )
+ $ GO TO 70
+ 60 CONTINUE
+ WRITE( NOUT, FMT = 9986 )SNAMET
+ STOP
+ 70 LTEST( I ) = LTESTT
+ GO TO 50
+*
+ 80 CONTINUE
+ CLOSE ( NIN )
+*
+* Compute EPS (the machine precision).
+*
+ EPS = EPSILON(RZERO)
+ WRITE( NOUT, FMT = 9998 )EPS
+*
+* Check the reliability of CMVCH using exact data.
+*
+ N = MIN( 32, NMAX )
+ DO 120 J = 1, N
+ DO 110 I = 1, N
+ A( I, J ) = MAX( I - J + 1, 0 )
+ 110 CONTINUE
+ X( J ) = J
+ Y( J ) = ZERO
+ 120 CONTINUE
+ DO 130 J = 1, N
+ YY( J ) = J*( ( J + 1 )*J )/2 - ( ( J + 1 )*J*( J - 1 ) )/3
+ 130 CONTINUE
+* YY holds the exact result. On exit from CMVCH YT holds
+* the result computed by CMVCH.
+ TRANS = 'N'
+ CALL CMVCH( TRANS, N, N, ONE, A, NMAX, X, 1, ZERO, Y, 1, YT, G,
+ $ YY, EPS, ERR, FATAL, NOUT, .TRUE. )
+ SAME = LCE( YY, YT, N )
+ IF( .NOT.SAME.OR.ERR.NE.RZERO )THEN
+ WRITE( NOUT, FMT = 9985 )TRANS, SAME, ERR
+ STOP
+ END IF
+ TRANS = 'T'
+ CALL CMVCH( TRANS, N, N, ONE, A, NMAX, X, -1, ZERO, Y, -1, YT, G,
+ $ YY, EPS, ERR, FATAL, NOUT, .TRUE. )
+ SAME = LCE( YY, YT, N )
+ IF( .NOT.SAME.OR.ERR.NE.RZERO )THEN
+ WRITE( NOUT, FMT = 9985 )TRANS, SAME, ERR
+ STOP
+ END IF
+*
+* Test each subroutine in turn.
+*
+ DO 210 ISNUM = 1, NSUBS
+ WRITE( NOUT, FMT = * )
+ IF( .NOT.LTEST( ISNUM ) )THEN
+* Subprogram is not to be tested.
+ WRITE( NOUT, FMT = 9983 )SNAMES( ISNUM )
+ ELSE
+ SRNAMT = SNAMES( ISNUM )
+* Test error exits.
+ IF( TSTERR )THEN
+ CALL CCHKE( ISNUM, SNAMES( ISNUM ), NOUT )
+ WRITE( NOUT, FMT = * )
+ END IF
+* Test computations.
+ INFOT = 0
+ OK = .TRUE.
+ FATAL = .FALSE.
+ GO TO ( 140, 140, 150, 150, 150, 160, 160,
+ $ 160, 160, 160, 160, 170, 170, 180,
+ $ 180, 190, 190 )ISNUM
+* Test CGEMV, 01, and CGBMV, 02.
+ 140 CALL CCHK1( SNAMES( ISNUM ), EPS, THRESH, NOUT, NTRA, TRACE,
+ $ REWI, FATAL, NIDIM, IDIM, NKB, KB, NALF, ALF,
+ $ NBET, BET, NINC, INC, NMAX, INCMAX, A, AA, AS,
+ $ X, XX, XS, Y, YY, YS, YT, G )
+ GO TO 200
+* Test CHEMV, 03, CHBMV, 04, and CHPMV, 05.
+ 150 CALL CCHK2( SNAMES( ISNUM ), EPS, THRESH, NOUT, NTRA, TRACE,
+ $ REWI, FATAL, NIDIM, IDIM, NKB, KB, NALF, ALF,
+ $ NBET, BET, NINC, INC, NMAX, INCMAX, A, AA, AS,
+ $ X, XX, XS, Y, YY, YS, YT, G )
+ GO TO 200
+* Test CTRMV, 06, CTBMV, 07, CTPMV, 08,
+* CTRSV, 09, CTBSV, 10, and CTPSV, 11.
+ 160 CALL CCHK3( SNAMES( ISNUM ), EPS, THRESH, NOUT, NTRA, TRACE,
+ $ REWI, FATAL, NIDIM, IDIM, NKB, KB, NINC, INC,
+ $ NMAX, INCMAX, A, AA, AS, Y, YY, YS, YT, G, Z )
+ GO TO 200
+* Test CGERC, 12, CGERU, 13.
+ 170 CALL CCHK4( SNAMES( ISNUM ), EPS, THRESH, NOUT, NTRA, TRACE,
+ $ REWI, FATAL, NIDIM, IDIM, NALF, ALF, NINC, INC,
+ $ NMAX, INCMAX, A, AA, AS, X, XX, XS, Y, YY, YS,
+ $ YT, G, Z )
+ GO TO 200
+* Test CHER, 14, and CHPR, 15.
+ 180 CALL CCHK5( SNAMES( ISNUM ), EPS, THRESH, NOUT, NTRA, TRACE,
+ $ REWI, FATAL, NIDIM, IDIM, NALF, ALF, NINC, INC,
+ $ NMAX, INCMAX, A, AA, AS, X, XX, XS, Y, YY, YS,
+ $ YT, G, Z )
+ GO TO 200
+* Test CHER2, 16, and CHPR2, 17.
+ 190 CALL CCHK6( SNAMES( ISNUM ), EPS, THRESH, NOUT, NTRA, TRACE,
+ $ REWI, FATAL, NIDIM, IDIM, NALF, ALF, NINC, INC,
+ $ NMAX, INCMAX, A, AA, AS, X, XX, XS, Y, YY, YS,
+ $ YT, G, Z )
+*
+ 200 IF( FATAL.AND.SFATAL )
+ $ GO TO 220
+ END IF
+ 210 CONTINUE
+ WRITE( NOUT, FMT = 9982 )
+ GO TO 240
+*
+ 220 CONTINUE
+ WRITE( NOUT, FMT = 9981 )
+ GO TO 240
+*
+ 230 CONTINUE
+ WRITE( NOUT, FMT = 9987 )
+*
+ 240 CONTINUE
+ IF( TRACE )
+ $ CLOSE ( NTRA )
+ CLOSE ( NOUT )
+ STOP
+*
+ 9999 FORMAT( ' ROUTINES PASS COMPUTATIONAL TESTS IF TEST RATIO IS LES',
+ $ 'S THAN', F8.2 )
+ 9998 FORMAT( ' RELATIVE MACHINE PRECISION IS TAKEN TO BE', 1P, E9.1 )
+ 9997 FORMAT( ' NUMBER OF VALUES OF ', A, ' IS LESS THAN 1 OR GREATER ',
+ $ 'THAN ', I2 )
+ 9996 FORMAT( ' VALUE OF N IS LESS THAN 0 OR GREATER THAN ', I2 )
+ 9995 FORMAT( ' VALUE OF K IS LESS THAN 0' )
+ 9994 FORMAT( ' ABSOLUTE VALUE OF INCX OR INCY IS 0 OR GREATER THAN ',
+ $ I2 )
+ 9993 FORMAT( ' TESTS OF THE COMPLEX LEVEL 2 BLAS', //' THE F',
+ $ 'OLLOWING PARAMETER VALUES WILL BE USED:' )
+ 9992 FORMAT( ' FOR N ', 9I6 )
+ 9991 FORMAT( ' FOR K ', 7I6 )
+ 9990 FORMAT( ' FOR INCX AND INCY ', 7I6 )
+ 9989 FORMAT( ' FOR ALPHA ',
+ $ 7( '(', F4.1, ',', F4.1, ') ', : ) )
+ 9988 FORMAT( ' FOR BETA ',
+ $ 7( '(', F4.1, ',', F4.1, ') ', : ) )
+ 9987 FORMAT( ' AMEND DATA FILE OR INCREASE ARRAY SIZES IN PROGRAM',
+ $ /' ******* TESTS ABANDONED *******' )
+ 9986 FORMAT( ' SUBPROGRAM NAME ', A6, ' NOT RECOGNIZED', /' ******* T',
+ $ 'ESTS ABANDONED *******' )
+ 9985 FORMAT( ' ERROR IN CMVCH - IN-LINE DOT PRODUCTS ARE BEING EVALU',
+ $ 'ATED WRONGLY.', /' CMVCH WAS CALLED WITH TRANS = ', A1,
+ $ ' AND RETURNED SAME = ', L1, ' AND ERR = ', F12.3, '.', /
+ $ ' THIS MAY BE DUE TO FAULTS IN THE ARITHMETIC OR THE COMPILER.'
+ $ , /' ******* TESTS ABANDONED *******' )
+ 9984 FORMAT( A6, L2 )
+ 9983 FORMAT( 1X, A6, ' WAS NOT TESTED' )
+ 9982 FORMAT( /' END OF TESTS' )
+ 9981 FORMAT( /' ******* FATAL ERROR - TESTS ABANDONED *******' )
+ 9980 FORMAT( ' ERROR-EXITS WILL NOT BE TESTED' )
+*
+* End of CBLAT2.
+*
+ END
+ SUBROUTINE CCHK1( SNAME, EPS, THRESH, NOUT, NTRA, TRACE, REWI,
+ $ FATAL, NIDIM, IDIM, NKB, KB, NALF, ALF, NBET,
+ $ BET, NINC, INC, NMAX, INCMAX, A, AA, AS, X, XX,
+ $ XS, Y, YY, YS, YT, G )
+*
+* Tests CGEMV and CGBMV.
+*
+* Auxiliary routine for test program for Level 2 Blas.
+*
+* -- Written on 10-August-1987.
+* Richard Hanson, Sandia National Labs.
+* Jeremy Du Croz, NAG Central Office.
+*
+* .. Parameters ..
+ COMPLEX ZERO, HALF
+ PARAMETER ( ZERO = ( 0.0, 0.0 ), HALF = ( 0.5, 0.0 ) )
+ REAL RZERO
+ PARAMETER ( RZERO = 0.0 )
+* .. Scalar Arguments ..
+ REAL EPS, THRESH
+ INTEGER INCMAX, NALF, NBET, NIDIM, NINC, NKB, NMAX,
+ $ NOUT, NTRA
+ LOGICAL FATAL, REWI, TRACE
+ CHARACTER*6 SNAME
+* .. Array Arguments ..
+ COMPLEX A( NMAX, NMAX ), AA( NMAX*NMAX ), ALF( NALF ),
+ $ AS( NMAX*NMAX ), BET( NBET ), X( NMAX ),
+ $ XS( NMAX*INCMAX ), XX( NMAX*INCMAX ),
+ $ Y( NMAX ), YS( NMAX*INCMAX ), YT( NMAX ),
+ $ YY( NMAX*INCMAX )
+ REAL G( NMAX )
+ INTEGER IDIM( NIDIM ), INC( NINC ), KB( NKB )
+* .. Local Scalars ..
+ COMPLEX ALPHA, ALS, BETA, BLS, TRANSL
+ REAL ERR, ERRMAX
+ INTEGER I, IA, IB, IC, IKU, IM, IN, INCX, INCXS, INCY,
+ $ INCYS, IX, IY, KL, KLS, KU, KUS, LAA, LDA,
+ $ LDAS, LX, LY, M, ML, MS, N, NARGS, NC, ND, NK,
+ $ NL, NS
+ LOGICAL BANDED, FULL, NULL, RESET, SAME, TRAN
+ CHARACTER*1 TRANS, TRANSS
+ CHARACTER*3 ICH
+* .. Local Arrays ..
+ LOGICAL ISAME( 13 )
+* .. External Functions ..
+ LOGICAL LCE, LCERES
+ EXTERNAL LCE, LCERES
+* .. External Subroutines ..
+ EXTERNAL CGBMV, CGEMV, CMAKE, CMVCH
+* .. Intrinsic Functions ..
+ INTRINSIC ABS, MAX, MIN
+* .. Scalars in Common ..
+ INTEGER INFOT, NOUTC
+ LOGICAL LERR, OK
+* .. Common blocks ..
+ COMMON /INFOC/INFOT, NOUTC, OK, LERR
+* .. Data statements ..
+ DATA ICH/'NTC'/
+* .. Executable Statements ..
+ FULL = SNAME( 3: 3 ).EQ.'E'
+ BANDED = SNAME( 3: 3 ).EQ.'B'
+* Define the number of arguments.
+ IF( FULL )THEN
+ NARGS = 11
+ ELSE IF( BANDED )THEN
+ NARGS = 13
+ END IF
+*
+ NC = 0
+ RESET = .TRUE.
+ ERRMAX = RZERO
+*
+ DO 120 IN = 1, NIDIM
+ N = IDIM( IN )
+ ND = N/2 + 1
+*
+ DO 110 IM = 1, 2
+ IF( IM.EQ.1 )
+ $ M = MAX( N - ND, 0 )
+ IF( IM.EQ.2 )
+ $ M = MIN( N + ND, NMAX )
+*
+ IF( BANDED )THEN
+ NK = NKB
+ ELSE
+ NK = 1
+ END IF
+ DO 100 IKU = 1, NK
+ IF( BANDED )THEN
+ KU = KB( IKU )
+ KL = MAX( KU - 1, 0 )
+ ELSE
+ KU = N - 1
+ KL = M - 1
+ END IF
+* Set LDA to 1 more than minimum value if room.
+ IF( BANDED )THEN
+ LDA = KL + KU + 1
+ ELSE
+ LDA = M
+ END IF
+ IF( LDA.LT.NMAX )
+ $ LDA = LDA + 1
+* Skip tests if not enough room.
+ IF( LDA.GT.NMAX )
+ $ GO TO 100
+ LAA = LDA*N
+ NULL = N.LE.0.OR.M.LE.0
+*
+* Generate the matrix A.
+*
+ TRANSL = ZERO
+ CALL CMAKE( SNAME( 2: 3 ), ' ', ' ', M, N, A, NMAX, AA,
+ $ LDA, KL, KU, RESET, TRANSL )
+*
+ DO 90 IC = 1, 3
+ TRANS = ICH( IC: IC )
+ TRAN = TRANS.EQ.'T'.OR.TRANS.EQ.'C'
+*
+ IF( TRAN )THEN
+ ML = N
+ NL = M
+ ELSE
+ ML = M
+ NL = N
+ END IF
+*
+ DO 80 IX = 1, NINC
+ INCX = INC( IX )
+ LX = ABS( INCX )*NL
+*
+* Generate the vector X.
+*
+ TRANSL = HALF
+ CALL CMAKE( 'GE', ' ', ' ', 1, NL, X, 1, XX,
+ $ ABS( INCX ), 0, NL - 1, RESET, TRANSL )
+ IF( NL.GT.1 )THEN
+ X( NL/2 ) = ZERO
+ XX( 1 + ABS( INCX )*( NL/2 - 1 ) ) = ZERO
+ END IF
+*
+ DO 70 IY = 1, NINC
+ INCY = INC( IY )
+ LY = ABS( INCY )*ML
+*
+ DO 60 IA = 1, NALF
+ ALPHA = ALF( IA )
+*
+ DO 50 IB = 1, NBET
+ BETA = BET( IB )
+*
+* Generate the vector Y.
+*
+ TRANSL = ZERO
+ CALL CMAKE( 'GE', ' ', ' ', 1, ML, Y, 1,
+ $ YY, ABS( INCY ), 0, ML - 1,
+ $ RESET, TRANSL )
+*
+ NC = NC + 1
+*
+* Save every datum before calling the
+* subroutine.
+*
+ TRANSS = TRANS
+ MS = M
+ NS = N
+ KLS = KL
+ KUS = KU
+ ALS = ALPHA
+ DO 10 I = 1, LAA
+ AS( I ) = AA( I )
+ 10 CONTINUE
+ LDAS = LDA
+ DO 20 I = 1, LX
+ XS( I ) = XX( I )
+ 20 CONTINUE
+ INCXS = INCX
+ BLS = BETA
+ DO 30 I = 1, LY
+ YS( I ) = YY( I )
+ 30 CONTINUE
+ INCYS = INCY
+*
+* Call the subroutine.
+*
+ IF( FULL )THEN
+ IF( TRACE )
+ $ WRITE( NTRA, FMT = 9994 )NC, SNAME,
+ $ TRANS, M, N, ALPHA, LDA, INCX, BETA,
+ $ INCY
+ IF( REWI )
+ $ REWIND NTRA
+ CALL CGEMV( TRANS, M, N, ALPHA, AA,
+ $ LDA, XX, INCX, BETA, YY,
+ $ INCY )
+ ELSE IF( BANDED )THEN
+ IF( TRACE )
+ $ WRITE( NTRA, FMT = 9995 )NC, SNAME,
+ $ TRANS, M, N, KL, KU, ALPHA, LDA,
+ $ INCX, BETA, INCY
+ IF( REWI )
+ $ REWIND NTRA
+ CALL CGBMV( TRANS, M, N, KL, KU, ALPHA,
+ $ AA, LDA, XX, INCX, BETA,
+ $ YY, INCY )
+ END IF
+*
+* Check if error-exit was taken incorrectly.
+*
+ IF( .NOT.OK )THEN
+ WRITE( NOUT, FMT = 9993 )
+ FATAL = .TRUE.
+ GO TO 130
+ END IF
+*
+* See what data changed inside subroutines.
+*
+ ISAME( 1 ) = TRANS.EQ.TRANSS
+ ISAME( 2 ) = MS.EQ.M
+ ISAME( 3 ) = NS.EQ.N
+ IF( FULL )THEN
+ ISAME( 4 ) = ALS.EQ.ALPHA
+ ISAME( 5 ) = LCE( AS, AA, LAA )
+ ISAME( 6 ) = LDAS.EQ.LDA
+ ISAME( 7 ) = LCE( XS, XX, LX )
+ ISAME( 8 ) = INCXS.EQ.INCX
+ ISAME( 9 ) = BLS.EQ.BETA
+ IF( NULL )THEN
+ ISAME( 10 ) = LCE( YS, YY, LY )
+ ELSE
+ ISAME( 10 ) = LCERES( 'GE', ' ', 1,
+ $ ML, YS, YY,
+ $ ABS( INCY ) )
+ END IF
+ ISAME( 11 ) = INCYS.EQ.INCY
+ ELSE IF( BANDED )THEN
+ ISAME( 4 ) = KLS.EQ.KL
+ ISAME( 5 ) = KUS.EQ.KU
+ ISAME( 6 ) = ALS.EQ.ALPHA
+ ISAME( 7 ) = LCE( AS, AA, LAA )
+ ISAME( 8 ) = LDAS.EQ.LDA
+ ISAME( 9 ) = LCE( XS, XX, LX )
+ ISAME( 10 ) = INCXS.EQ.INCX
+ ISAME( 11 ) = BLS.EQ.BETA
+ IF( NULL )THEN
+ ISAME( 12 ) = LCE( YS, YY, LY )
+ ELSE
+ ISAME( 12 ) = LCERES( 'GE', ' ', 1,
+ $ ML, YS, YY,
+ $ ABS( INCY ) )
+ END IF
+ ISAME( 13 ) = INCYS.EQ.INCY
+ END IF
+*
+* If data was incorrectly changed, report
+* and return.
+*
+ SAME = .TRUE.
+ DO 40 I = 1, NARGS
+ SAME = SAME.AND.ISAME( I )
+ IF( .NOT.ISAME( I ) )
+ $ WRITE( NOUT, FMT = 9998 )I
+ 40 CONTINUE
+ IF( .NOT.SAME )THEN
+ FATAL = .TRUE.
+ GO TO 130
+ END IF
+*
+ IF( .NOT.NULL )THEN
+*
+* Check the result.
+*
+ CALL CMVCH( TRANS, M, N, ALPHA, A,
+ $ NMAX, X, INCX, BETA, Y,
+ $ INCY, YT, G, YY, EPS, ERR,
+ $ FATAL, NOUT, .TRUE. )
+ ERRMAX = MAX( ERRMAX, ERR )
+* If got really bad answer, report and
+* return.
+ IF( FATAL )
+ $ GO TO 130
+ ELSE
+* Avoid repeating tests with M.le.0 or
+* N.le.0.
+ GO TO 110
+ END IF
+*
+ 50 CONTINUE
+*
+ 60 CONTINUE
+*
+ 70 CONTINUE
+*
+ 80 CONTINUE
+*
+ 90 CONTINUE
+*
+ 100 CONTINUE
+*
+ 110 CONTINUE
+*
+ 120 CONTINUE
+*
+* Report result.
+*
+ IF( ERRMAX.LT.THRESH )THEN
+ WRITE( NOUT, FMT = 9999 )SNAME, NC
+ ELSE
+ WRITE( NOUT, FMT = 9997 )SNAME, NC, ERRMAX
+ END IF
+ GO TO 140
+*
+ 130 CONTINUE
+ WRITE( NOUT, FMT = 9996 )SNAME
+ IF( FULL )THEN
+ WRITE( NOUT, FMT = 9994 )NC, SNAME, TRANS, M, N, ALPHA, LDA,
+ $ INCX, BETA, INCY
+ ELSE IF( BANDED )THEN
+ WRITE( NOUT, FMT = 9995 )NC, SNAME, TRANS, M, N, KL, KU,
+ $ ALPHA, LDA, INCX, BETA, INCY
+ END IF
+*
+ 140 CONTINUE
+ RETURN
+*
+ 9999 FORMAT( ' ', A6, ' PASSED THE COMPUTATIONAL TESTS (', I6, ' CALL',
+ $ 'S)' )
+ 9998 FORMAT( ' ******* FATAL ERROR - PARAMETER NUMBER ', I2, ' WAS CH',
+ $ 'ANGED INCORRECTLY *******' )
+ 9997 FORMAT( ' ', A6, ' COMPLETED THE COMPUTATIONAL TESTS (', I6, ' C',
+ $ 'ALLS)', /' ******* BUT WITH MAXIMUM TEST RATIO', F8.2,
+ $ ' - SUSPECT *******' )
+ 9996 FORMAT( ' ******* ', A6, ' FAILED ON CALL NUMBER:' )
+ 9995 FORMAT( 1X, I6, ': ', A6, '(''', A1, ''',', 4( I3, ',' ), '(',
+ $ F4.1, ',', F4.1, '), A,', I3, ', X,', I2, ',(', F4.1, ',',
+ $ F4.1, '), Y,', I2, ') .' )
+ 9994 FORMAT( 1X, I6, ': ', A6, '(''', A1, ''',', 2( I3, ',' ), '(',
+ $ F4.1, ',', F4.1, '), A,', I3, ', X,', I2, ',(', F4.1, ',',
+ $ F4.1, '), Y,', I2, ') .' )
+ 9993 FORMAT( ' ******* FATAL ERROR - ERROR-EXIT TAKEN ON VALID CALL *',
+ $ '******' )
+*
+* End of CCHK1.
+*
+ END
+ SUBROUTINE CCHK2( SNAME, EPS, THRESH, NOUT, NTRA, TRACE, REWI,
+ $ FATAL, NIDIM, IDIM, NKB, KB, NALF, ALF, NBET,
+ $ BET, NINC, INC, NMAX, INCMAX, A, AA, AS, X, XX,
+ $ XS, Y, YY, YS, YT, G )
+*
+* Tests CHEMV, CHBMV and CHPMV.
+*
+* Auxiliary routine for test program for Level 2 Blas.
+*
+* -- Written on 10-August-1987.
+* Richard Hanson, Sandia National Labs.
+* Jeremy Du Croz, NAG Central Office.
+*
+* .. Parameters ..
+ COMPLEX ZERO, HALF
+ PARAMETER ( ZERO = ( 0.0, 0.0 ), HALF = ( 0.5, 0.0 ) )
+ REAL RZERO
+ PARAMETER ( RZERO = 0.0 )
+* .. Scalar Arguments ..
+ REAL EPS, THRESH
+ INTEGER INCMAX, NALF, NBET, NIDIM, NINC, NKB, NMAX,
+ $ NOUT, NTRA
+ LOGICAL FATAL, REWI, TRACE
+ CHARACTER*6 SNAME
+* .. Array Arguments ..
+ COMPLEX A( NMAX, NMAX ), AA( NMAX*NMAX ), ALF( NALF ),
+ $ AS( NMAX*NMAX ), BET( NBET ), X( NMAX ),
+ $ XS( NMAX*INCMAX ), XX( NMAX*INCMAX ),
+ $ Y( NMAX ), YS( NMAX*INCMAX ), YT( NMAX ),
+ $ YY( NMAX*INCMAX )
+ REAL G( NMAX )
+ INTEGER IDIM( NIDIM ), INC( NINC ), KB( NKB )
+* .. Local Scalars ..
+ COMPLEX ALPHA, ALS, BETA, BLS, TRANSL
+ REAL ERR, ERRMAX
+ INTEGER I, IA, IB, IC, IK, IN, INCX, INCXS, INCY,
+ $ INCYS, IX, IY, K, KS, LAA, LDA, LDAS, LX, LY,
+ $ N, NARGS, NC, NK, NS
+ LOGICAL BANDED, FULL, NULL, PACKED, RESET, SAME
+ CHARACTER*1 UPLO, UPLOS
+ CHARACTER*2 ICH
+* .. Local Arrays ..
+ LOGICAL ISAME( 13 )
+* .. External Functions ..
+ LOGICAL LCE, LCERES
+ EXTERNAL LCE, LCERES
+* .. External Subroutines ..
+ EXTERNAL CHBMV, CHEMV, CHPMV, CMAKE, CMVCH
+* .. Intrinsic Functions ..
+ INTRINSIC ABS, MAX
+* .. Scalars in Common ..
+ INTEGER INFOT, NOUTC
+ LOGICAL LERR, OK
+* .. Common blocks ..
+ COMMON /INFOC/INFOT, NOUTC, OK, LERR
+* .. Data statements ..
+ DATA ICH/'UL'/
+* .. Executable Statements ..
+ FULL = SNAME( 3: 3 ).EQ.'E'
+ BANDED = SNAME( 3: 3 ).EQ.'B'
+ PACKED = SNAME( 3: 3 ).EQ.'P'
+* Define the number of arguments.
+ IF( FULL )THEN
+ NARGS = 10
+ ELSE IF( BANDED )THEN
+ NARGS = 11
+ ELSE IF( PACKED )THEN
+ NARGS = 9
+ END IF
+*
+ NC = 0
+ RESET = .TRUE.
+ ERRMAX = RZERO
+*
+ DO 110 IN = 1, NIDIM
+ N = IDIM( IN )
+*
+ IF( BANDED )THEN
+ NK = NKB
+ ELSE
+ NK = 1
+ END IF
+ DO 100 IK = 1, NK
+ IF( BANDED )THEN
+ K = KB( IK )
+ ELSE
+ K = N - 1
+ END IF
+* Set LDA to 1 more than minimum value if room.
+ IF( BANDED )THEN
+ LDA = K + 1
+ ELSE
+ LDA = N
+ END IF
+ IF( LDA.LT.NMAX )
+ $ LDA = LDA + 1
+* Skip tests if not enough room.
+ IF( LDA.GT.NMAX )
+ $ GO TO 100
+ IF( PACKED )THEN
+ LAA = ( N*( N + 1 ) )/2
+ ELSE
+ LAA = LDA*N
+ END IF
+ NULL = N.LE.0
+*
+ DO 90 IC = 1, 2
+ UPLO = ICH( IC: IC )
+*
+* Generate the matrix A.
+*
+ TRANSL = ZERO
+ CALL CMAKE( SNAME( 2: 3 ), UPLO, ' ', N, N, A, NMAX, AA,
+ $ LDA, K, K, RESET, TRANSL )
+*
+ DO 80 IX = 1, NINC
+ INCX = INC( IX )
+ LX = ABS( INCX )*N
+*
+* Generate the vector X.
+*
+ TRANSL = HALF
+ CALL CMAKE( 'GE', ' ', ' ', 1, N, X, 1, XX,
+ $ ABS( INCX ), 0, N - 1, RESET, TRANSL )
+ IF( N.GT.1 )THEN
+ X( N/2 ) = ZERO
+ XX( 1 + ABS( INCX )*( N/2 - 1 ) ) = ZERO
+ END IF
+*
+ DO 70 IY = 1, NINC
+ INCY = INC( IY )
+ LY = ABS( INCY )*N
+*
+ DO 60 IA = 1, NALF
+ ALPHA = ALF( IA )
+*
+ DO 50 IB = 1, NBET
+ BETA = BET( IB )
+*
+* Generate the vector Y.
+*
+ TRANSL = ZERO
+ CALL CMAKE( 'GE', ' ', ' ', 1, N, Y, 1, YY,
+ $ ABS( INCY ), 0, N - 1, RESET,
+ $ TRANSL )
+*
+ NC = NC + 1
+*
+* Save every datum before calling the
+* subroutine.
+*
+ UPLOS = UPLO
+ NS = N
+ KS = K
+ ALS = ALPHA
+ DO 10 I = 1, LAA
+ AS( I ) = AA( I )
+ 10 CONTINUE
+ LDAS = LDA
+ DO 20 I = 1, LX
+ XS( I ) = XX( I )
+ 20 CONTINUE
+ INCXS = INCX
+ BLS = BETA
+ DO 30 I = 1, LY
+ YS( I ) = YY( I )
+ 30 CONTINUE
+ INCYS = INCY
+*
+* Call the subroutine.
+*
+ IF( FULL )THEN
+ IF( TRACE )
+ $ WRITE( NTRA, FMT = 9993 )NC, SNAME,
+ $ UPLO, N, ALPHA, LDA, INCX, BETA, INCY
+ IF( REWI )
+ $ REWIND NTRA
+ CALL CHEMV( UPLO, N, ALPHA, AA, LDA, XX,
+ $ INCX, BETA, YY, INCY )
+ ELSE IF( BANDED )THEN
+ IF( TRACE )
+ $ WRITE( NTRA, FMT = 9994 )NC, SNAME,
+ $ UPLO, N, K, ALPHA, LDA, INCX, BETA,
+ $ INCY
+ IF( REWI )
+ $ REWIND NTRA
+ CALL CHBMV( UPLO, N, K, ALPHA, AA, LDA,
+ $ XX, INCX, BETA, YY, INCY )
+ ELSE IF( PACKED )THEN
+ IF( TRACE )
+ $ WRITE( NTRA, FMT = 9995 )NC, SNAME,
+ $ UPLO, N, ALPHA, INCX, BETA, INCY
+ IF( REWI )
+ $ REWIND NTRA
+ CALL CHPMV( UPLO, N, ALPHA, AA, XX, INCX,
+ $ BETA, YY, INCY )
+ END IF
+*
+* Check if error-exit was taken incorrectly.
+*
+ IF( .NOT.OK )THEN
+ WRITE( NOUT, FMT = 9992 )
+ FATAL = .TRUE.
+ GO TO 120
+ END IF
+*
+* See what data changed inside subroutines.
+*
+ ISAME( 1 ) = UPLO.EQ.UPLOS
+ ISAME( 2 ) = NS.EQ.N
+ IF( FULL )THEN
+ ISAME( 3 ) = ALS.EQ.ALPHA
+ ISAME( 4 ) = LCE( AS, AA, LAA )
+ ISAME( 5 ) = LDAS.EQ.LDA
+ ISAME( 6 ) = LCE( XS, XX, LX )
+ ISAME( 7 ) = INCXS.EQ.INCX
+ ISAME( 8 ) = BLS.EQ.BETA
+ IF( NULL )THEN
+ ISAME( 9 ) = LCE( YS, YY, LY )
+ ELSE
+ ISAME( 9 ) = LCERES( 'GE', ' ', 1, N,
+ $ YS, YY, ABS( INCY ) )
+ END IF
+ ISAME( 10 ) = INCYS.EQ.INCY
+ ELSE IF( BANDED )THEN
+ ISAME( 3 ) = KS.EQ.K
+ ISAME( 4 ) = ALS.EQ.ALPHA
+ ISAME( 5 ) = LCE( AS, AA, LAA )
+ ISAME( 6 ) = LDAS.EQ.LDA
+ ISAME( 7 ) = LCE( XS, XX, LX )
+ ISAME( 8 ) = INCXS.EQ.INCX
+ ISAME( 9 ) = BLS.EQ.BETA
+ IF( NULL )THEN
+ ISAME( 10 ) = LCE( YS, YY, LY )
+ ELSE
+ ISAME( 10 ) = LCERES( 'GE', ' ', 1, N,
+ $ YS, YY, ABS( INCY ) )
+ END IF
+ ISAME( 11 ) = INCYS.EQ.INCY
+ ELSE IF( PACKED )THEN
+ ISAME( 3 ) = ALS.EQ.ALPHA
+ ISAME( 4 ) = LCE( AS, AA, LAA )
+ ISAME( 5 ) = LCE( XS, XX, LX )
+ ISAME( 6 ) = INCXS.EQ.INCX
+ ISAME( 7 ) = BLS.EQ.BETA
+ IF( NULL )THEN
+ ISAME( 8 ) = LCE( YS, YY, LY )
+ ELSE
+ ISAME( 8 ) = LCERES( 'GE', ' ', 1, N,
+ $ YS, YY, ABS( INCY ) )
+ END IF
+ ISAME( 9 ) = INCYS.EQ.INCY
+ END IF
+*
+* If data was incorrectly changed, report and
+* return.
+*
+ SAME = .TRUE.
+ DO 40 I = 1, NARGS
+ SAME = SAME.AND.ISAME( I )
+ IF( .NOT.ISAME( I ) )
+ $ WRITE( NOUT, FMT = 9998 )I
+ 40 CONTINUE
+ IF( .NOT.SAME )THEN
+ FATAL = .TRUE.
+ GO TO 120
+ END IF
+*
+ IF( .NOT.NULL )THEN
+*
+* Check the result.
+*
+ CALL CMVCH( 'N', N, N, ALPHA, A, NMAX, X,
+ $ INCX, BETA, Y, INCY, YT, G,
+ $ YY, EPS, ERR, FATAL, NOUT,
+ $ .TRUE. )
+ ERRMAX = MAX( ERRMAX, ERR )
+* If got really bad answer, report and
+* return.
+ IF( FATAL )
+ $ GO TO 120
+ ELSE
+* Avoid repeating tests with N.le.0
+ GO TO 110
+ END IF
+*
+ 50 CONTINUE
+*
+ 60 CONTINUE
+*
+ 70 CONTINUE
+*
+ 80 CONTINUE
+*
+ 90 CONTINUE
+*
+ 100 CONTINUE
+*
+ 110 CONTINUE
+*
+* Report result.
+*
+ IF( ERRMAX.LT.THRESH )THEN
+ WRITE( NOUT, FMT = 9999 )SNAME, NC
+ ELSE
+ WRITE( NOUT, FMT = 9997 )SNAME, NC, ERRMAX
+ END IF
+ GO TO 130
+*
+ 120 CONTINUE
+ WRITE( NOUT, FMT = 9996 )SNAME
+ IF( FULL )THEN
+ WRITE( NOUT, FMT = 9993 )NC, SNAME, UPLO, N, ALPHA, LDA, INCX,
+ $ BETA, INCY
+ ELSE IF( BANDED )THEN
+ WRITE( NOUT, FMT = 9994 )NC, SNAME, UPLO, N, K, ALPHA, LDA,
+ $ INCX, BETA, INCY
+ ELSE IF( PACKED )THEN
+ WRITE( NOUT, FMT = 9995 )NC, SNAME, UPLO, N, ALPHA, INCX,
+ $ BETA, INCY
+ END IF
+*
+ 130 CONTINUE
+ RETURN
+*
+ 9999 FORMAT( ' ', A6, ' PASSED THE COMPUTATIONAL TESTS (', I6, ' CALL',
+ $ 'S)' )
+ 9998 FORMAT( ' ******* FATAL ERROR - PARAMETER NUMBER ', I2, ' WAS CH',
+ $ 'ANGED INCORRECTLY *******' )
+ 9997 FORMAT( ' ', A6, ' COMPLETED THE COMPUTATIONAL TESTS (', I6, ' C',
+ $ 'ALLS)', /' ******* BUT WITH MAXIMUM TEST RATIO', F8.2,
+ $ ' - SUSPECT *******' )
+ 9996 FORMAT( ' ******* ', A6, ' FAILED ON CALL NUMBER:' )
+ 9995 FORMAT( 1X, I6, ': ', A6, '(''', A1, ''',', I3, ',(', F4.1, ',',
+ $ F4.1, '), AP, X,', I2, ',(', F4.1, ',', F4.1, '), Y,', I2,
+ $ ') .' )
+ 9994 FORMAT( 1X, I6, ': ', A6, '(''', A1, ''',', 2( I3, ',' ), '(',
+ $ F4.1, ',', F4.1, '), A,', I3, ', X,', I2, ',(', F4.1, ',',
+ $ F4.1, '), Y,', I2, ') .' )
+ 9993 FORMAT( 1X, I6, ': ', A6, '(''', A1, ''',', I3, ',(', F4.1, ',',
+ $ F4.1, '), A,', I3, ', X,', I2, ',(', F4.1, ',', F4.1, '), ',
+ $ 'Y,', I2, ') .' )
+ 9992 FORMAT( ' ******* FATAL ERROR - ERROR-EXIT TAKEN ON VALID CALL *',
+ $ '******' )
+*
+* End of CCHK2.
+*
+ END
+ SUBROUTINE CCHK3( SNAME, EPS, THRESH, NOUT, NTRA, TRACE, REWI,
+ $ FATAL, NIDIM, IDIM, NKB, KB, NINC, INC, NMAX,
+ $ INCMAX, A, AA, AS, X, XX, XS, XT, G, Z )
+*
+* Tests CTRMV, CTBMV, CTPMV, CTRSV, CTBSV and CTPSV.
+*
+* Auxiliary routine for test program for Level 2 Blas.
+*
+* -- Written on 10-August-1987.
+* Richard Hanson, Sandia National Labs.
+* Jeremy Du Croz, NAG Central Office.
+*
+* .. Parameters ..
+ COMPLEX ZERO, HALF, ONE
+ PARAMETER ( ZERO = ( 0.0, 0.0 ), HALF = ( 0.5, 0.0 ),
+ $ ONE = ( 1.0, 0.0 ) )
+ REAL RZERO
+ PARAMETER ( RZERO = 0.0 )
+* .. Scalar Arguments ..
+ REAL EPS, THRESH
+ INTEGER INCMAX, NIDIM, NINC, NKB, NMAX, NOUT, NTRA
+ LOGICAL FATAL, REWI, TRACE
+ CHARACTER*6 SNAME
+* .. Array Arguments ..
+ COMPLEX A( NMAX, NMAX ), AA( NMAX*NMAX ),
+ $ AS( NMAX*NMAX ), X( NMAX ), XS( NMAX*INCMAX ),
+ $ XT( NMAX ), XX( NMAX*INCMAX ), Z( NMAX )
+ REAL G( NMAX )
+ INTEGER IDIM( NIDIM ), INC( NINC ), KB( NKB )
+* .. Local Scalars ..
+ COMPLEX TRANSL
+ REAL ERR, ERRMAX
+ INTEGER I, ICD, ICT, ICU, IK, IN, INCX, INCXS, IX, K,
+ $ KS, LAA, LDA, LDAS, LX, N, NARGS, NC, NK, NS
+ LOGICAL BANDED, FULL, NULL, PACKED, RESET, SAME
+ CHARACTER*1 DIAG, DIAGS, TRANS, TRANSS, UPLO, UPLOS
+ CHARACTER*2 ICHD, ICHU
+ CHARACTER*3 ICHT
+* .. Local Arrays ..
+ LOGICAL ISAME( 13 )
+* .. External Functions ..
+ LOGICAL LCE, LCERES
+ EXTERNAL LCE, LCERES
+* .. External Subroutines ..
+ EXTERNAL CMAKE, CMVCH, CTBMV, CTBSV, CTPMV, CTPSV,
+ $ CTRMV, CTRSV
+* .. Intrinsic Functions ..
+ INTRINSIC ABS, MAX
+* .. Scalars in Common ..
+ INTEGER INFOT, NOUTC
+ LOGICAL LERR, OK
+* .. Common blocks ..
+ COMMON /INFOC/INFOT, NOUTC, OK, LERR
+* .. Data statements ..
+ DATA ICHU/'UL'/, ICHT/'NTC'/, ICHD/'UN'/
+* .. Executable Statements ..
+ FULL = SNAME( 3: 3 ).EQ.'R'
+ BANDED = SNAME( 3: 3 ).EQ.'B'
+ PACKED = SNAME( 3: 3 ).EQ.'P'
+* Define the number of arguments.
+ IF( FULL )THEN
+ NARGS = 8
+ ELSE IF( BANDED )THEN
+ NARGS = 9
+ ELSE IF( PACKED )THEN
+ NARGS = 7
+ END IF
+*
+ NC = 0
+ RESET = .TRUE.
+ ERRMAX = RZERO
+* Set up zero vector for CMVCH.
+ DO 10 I = 1, NMAX
+ Z( I ) = ZERO
+ 10 CONTINUE
+*
+ DO 110 IN = 1, NIDIM
+ N = IDIM( IN )
+*
+ IF( BANDED )THEN
+ NK = NKB
+ ELSE
+ NK = 1
+ END IF
+ DO 100 IK = 1, NK
+ IF( BANDED )THEN
+ K = KB( IK )
+ ELSE
+ K = N - 1
+ END IF
+* Set LDA to 1 more than minimum value if room.
+ IF( BANDED )THEN
+ LDA = K + 1
+ ELSE
+ LDA = N
+ END IF
+ IF( LDA.LT.NMAX )
+ $ LDA = LDA + 1
+* Skip tests if not enough room.
+ IF( LDA.GT.NMAX )
+ $ GO TO 100
+ IF( PACKED )THEN
+ LAA = ( N*( N + 1 ) )/2
+ ELSE
+ LAA = LDA*N
+ END IF
+ NULL = N.LE.0
+*
+ DO 90 ICU = 1, 2
+ UPLO = ICHU( ICU: ICU )
+*
+ DO 80 ICT = 1, 3
+ TRANS = ICHT( ICT: ICT )
+*
+ DO 70 ICD = 1, 2
+ DIAG = ICHD( ICD: ICD )
+*
+* Generate the matrix A.
+*
+ TRANSL = ZERO
+ CALL CMAKE( SNAME( 2: 3 ), UPLO, DIAG, N, N, A,
+ $ NMAX, AA, LDA, K, K, RESET, TRANSL )
+*
+ DO 60 IX = 1, NINC
+ INCX = INC( IX )
+ LX = ABS( INCX )*N
+*
+* Generate the vector X.
+*
+ TRANSL = HALF
+ CALL CMAKE( 'GE', ' ', ' ', 1, N, X, 1, XX,
+ $ ABS( INCX ), 0, N - 1, RESET,
+ $ TRANSL )
+ IF( N.GT.1 )THEN
+ X( N/2 ) = ZERO
+ XX( 1 + ABS( INCX )*( N/2 - 1 ) ) = ZERO
+ END IF
+*
+ NC = NC + 1
+*
+* Save every datum before calling the subroutine.
+*
+ UPLOS = UPLO
+ TRANSS = TRANS
+ DIAGS = DIAG
+ NS = N
+ KS = K
+ DO 20 I = 1, LAA
+ AS( I ) = AA( I )
+ 20 CONTINUE
+ LDAS = LDA
+ DO 30 I = 1, LX
+ XS( I ) = XX( I )
+ 30 CONTINUE
+ INCXS = INCX
+*
+* Call the subroutine.
+*
+ IF( SNAME( 4: 5 ).EQ.'MV' )THEN
+ IF( FULL )THEN
+ IF( TRACE )
+ $ WRITE( NTRA, FMT = 9993 )NC, SNAME,
+ $ UPLO, TRANS, DIAG, N, LDA, INCX
+ IF( REWI )
+ $ REWIND NTRA
+ CALL CTRMV( UPLO, TRANS, DIAG, N, AA, LDA,
+ $ XX, INCX )
+ ELSE IF( BANDED )THEN
+ IF( TRACE )
+ $ WRITE( NTRA, FMT = 9994 )NC, SNAME,
+ $ UPLO, TRANS, DIAG, N, K, LDA, INCX
+ IF( REWI )
+ $ REWIND NTRA
+ CALL CTBMV( UPLO, TRANS, DIAG, N, K, AA,
+ $ LDA, XX, INCX )
+ ELSE IF( PACKED )THEN
+ IF( TRACE )
+ $ WRITE( NTRA, FMT = 9995 )NC, SNAME,
+ $ UPLO, TRANS, DIAG, N, INCX
+ IF( REWI )
+ $ REWIND NTRA
+ CALL CTPMV( UPLO, TRANS, DIAG, N, AA, XX,
+ $ INCX )
+ END IF
+ ELSE IF( SNAME( 4: 5 ).EQ.'SV' )THEN
+ IF( FULL )THEN
+ IF( TRACE )
+ $ WRITE( NTRA, FMT = 9993 )NC, SNAME,
+ $ UPLO, TRANS, DIAG, N, LDA, INCX
+ IF( REWI )
+ $ REWIND NTRA
+ CALL CTRSV( UPLO, TRANS, DIAG, N, AA, LDA,
+ $ XX, INCX )
+ ELSE IF( BANDED )THEN
+ IF( TRACE )
+ $ WRITE( NTRA, FMT = 9994 )NC, SNAME,
+ $ UPLO, TRANS, DIAG, N, K, LDA, INCX
+ IF( REWI )
+ $ REWIND NTRA
+ CALL CTBSV( UPLO, TRANS, DIAG, N, K, AA,
+ $ LDA, XX, INCX )
+ ELSE IF( PACKED )THEN
+ IF( TRACE )
+ $ WRITE( NTRA, FMT = 9995 )NC, SNAME,
+ $ UPLO, TRANS, DIAG, N, INCX
+ IF( REWI )
+ $ REWIND NTRA
+ CALL CTPSV( UPLO, TRANS, DIAG, N, AA, XX,
+ $ INCX )
+ END IF
+ END IF
+*
+* Check if error-exit was taken incorrectly.
+*
+ IF( .NOT.OK )THEN
+ WRITE( NOUT, FMT = 9992 )
+ FATAL = .TRUE.
+ GO TO 120
+ END IF
+*
+* See what data changed inside subroutines.
+*
+ ISAME( 1 ) = UPLO.EQ.UPLOS
+ ISAME( 2 ) = TRANS.EQ.TRANSS
+ ISAME( 3 ) = DIAG.EQ.DIAGS
+ ISAME( 4 ) = NS.EQ.N
+ IF( FULL )THEN
+ ISAME( 5 ) = LCE( AS, AA, LAA )
+ ISAME( 6 ) = LDAS.EQ.LDA
+ IF( NULL )THEN
+ ISAME( 7 ) = LCE( XS, XX, LX )
+ ELSE
+ ISAME( 7 ) = LCERES( 'GE', ' ', 1, N, XS,
+ $ XX, ABS( INCX ) )
+ END IF
+ ISAME( 8 ) = INCXS.EQ.INCX
+ ELSE IF( BANDED )THEN
+ ISAME( 5 ) = KS.EQ.K
+ ISAME( 6 ) = LCE( AS, AA, LAA )
+ ISAME( 7 ) = LDAS.EQ.LDA
+ IF( NULL )THEN
+ ISAME( 8 ) = LCE( XS, XX, LX )
+ ELSE
+ ISAME( 8 ) = LCERES( 'GE', ' ', 1, N, XS,
+ $ XX, ABS( INCX ) )
+ END IF
+ ISAME( 9 ) = INCXS.EQ.INCX
+ ELSE IF( PACKED )THEN
+ ISAME( 5 ) = LCE( AS, AA, LAA )
+ IF( NULL )THEN
+ ISAME( 6 ) = LCE( XS, XX, LX )
+ ELSE
+ ISAME( 6 ) = LCERES( 'GE', ' ', 1, N, XS,
+ $ XX, ABS( INCX ) )
+ END IF
+ ISAME( 7 ) = INCXS.EQ.INCX
+ END IF
+*
+* If data was incorrectly changed, report and
+* return.
+*
+ SAME = .TRUE.
+ DO 40 I = 1, NARGS
+ SAME = SAME.AND.ISAME( I )
+ IF( .NOT.ISAME( I ) )
+ $ WRITE( NOUT, FMT = 9998 )I
+ 40 CONTINUE
+ IF( .NOT.SAME )THEN
+ FATAL = .TRUE.
+ GO TO 120
+ END IF
+*
+ IF( .NOT.NULL )THEN
+ IF( SNAME( 4: 5 ).EQ.'MV' )THEN
+*
+* Check the result.
+*
+ CALL CMVCH( TRANS, N, N, ONE, A, NMAX, X,
+ $ INCX, ZERO, Z, INCX, XT, G,
+ $ XX, EPS, ERR, FATAL, NOUT,
+ $ .TRUE. )
+ ELSE IF( SNAME( 4: 5 ).EQ.'SV' )THEN
+*
+* Compute approximation to original vector.
+*
+ DO 50 I = 1, N
+ Z( I ) = XX( 1 + ( I - 1 )*
+ $ ABS( INCX ) )
+ XX( 1 + ( I - 1 )*ABS( INCX ) )
+ $ = X( I )
+ 50 CONTINUE
+ CALL CMVCH( TRANS, N, N, ONE, A, NMAX, Z,
+ $ INCX, ZERO, X, INCX, XT, G,
+ $ XX, EPS, ERR, FATAL, NOUT,
+ $ .FALSE. )
+ END IF
+ ERRMAX = MAX( ERRMAX, ERR )
+* If got really bad answer, report and return.
+ IF( FATAL )
+ $ GO TO 120
+ ELSE
+* Avoid repeating tests with N.le.0.
+ GO TO 110
+ END IF
+*
+ 60 CONTINUE
+*
+ 70 CONTINUE
+*
+ 80 CONTINUE
+*
+ 90 CONTINUE
+*
+ 100 CONTINUE
+*
+ 110 CONTINUE
+*
+* Report result.
+*
+ IF( ERRMAX.LT.THRESH )THEN
+ WRITE( NOUT, FMT = 9999 )SNAME, NC
+ ELSE
+ WRITE( NOUT, FMT = 9997 )SNAME, NC, ERRMAX
+ END IF
+ GO TO 130
+*
+ 120 CONTINUE
+ WRITE( NOUT, FMT = 9996 )SNAME
+ IF( FULL )THEN
+ WRITE( NOUT, FMT = 9993 )NC, SNAME, UPLO, TRANS, DIAG, N, LDA,
+ $ INCX
+ ELSE IF( BANDED )THEN
+ WRITE( NOUT, FMT = 9994 )NC, SNAME, UPLO, TRANS, DIAG, N, K,
+ $ LDA, INCX
+ ELSE IF( PACKED )THEN
+ WRITE( NOUT, FMT = 9995 )NC, SNAME, UPLO, TRANS, DIAG, N, INCX
+ END IF
+*
+ 130 CONTINUE
+ RETURN
+*
+ 9999 FORMAT( ' ', A6, ' PASSED THE COMPUTATIONAL TESTS (', I6, ' CALL',
+ $ 'S)' )
+ 9998 FORMAT( ' ******* FATAL ERROR - PARAMETER NUMBER ', I2, ' WAS CH',
+ $ 'ANGED INCORRECTLY *******' )
+ 9997 FORMAT( ' ', A6, ' COMPLETED THE COMPUTATIONAL TESTS (', I6, ' C',
+ $ 'ALLS)', /' ******* BUT WITH MAXIMUM TEST RATIO', F8.2,
+ $ ' - SUSPECT *******' )
+ 9996 FORMAT( ' ******* ', A6, ' FAILED ON CALL NUMBER:' )
+ 9995 FORMAT( 1X, I6, ': ', A6, '(', 3( '''', A1, ''',' ), I3, ', AP, ',
+ $ 'X,', I2, ') .' )
+ 9994 FORMAT( 1X, I6, ': ', A6, '(', 3( '''', A1, ''',' ), 2( I3, ',' ),
+ $ ' A,', I3, ', X,', I2, ') .' )
+ 9993 FORMAT( 1X, I6, ': ', A6, '(', 3( '''', A1, ''',' ), I3, ', A,',
+ $ I3, ', X,', I2, ') .' )
+ 9992 FORMAT( ' ******* FATAL ERROR - ERROR-EXIT TAKEN ON VALID CALL *',
+ $ '******' )
+*
+* End of CCHK3.
+*
+ END
+ SUBROUTINE CCHK4( SNAME, EPS, THRESH, NOUT, NTRA, TRACE, REWI,
+ $ FATAL, NIDIM, IDIM, NALF, ALF, NINC, INC, NMAX,
+ $ INCMAX, A, AA, AS, X, XX, XS, Y, YY, YS, YT, G,
+ $ Z )
+*
+* Tests CGERC and CGERU.
+*
+* Auxiliary routine for test program for Level 2 Blas.
+*
+* -- Written on 10-August-1987.
+* Richard Hanson, Sandia National Labs.
+* Jeremy Du Croz, NAG Central Office.
+*
+* .. Parameters ..
+ COMPLEX ZERO, HALF, ONE
+ PARAMETER ( ZERO = ( 0.0, 0.0 ), HALF = ( 0.5, 0.0 ),
+ $ ONE = ( 1.0, 0.0 ) )
+ REAL RZERO
+ PARAMETER ( RZERO = 0.0 )
+* .. Scalar Arguments ..
+ REAL EPS, THRESH
+ INTEGER INCMAX, NALF, NIDIM, NINC, NMAX, NOUT, NTRA
+ LOGICAL FATAL, REWI, TRACE
+ CHARACTER*6 SNAME
+* .. Array Arguments ..
+ COMPLEX A( NMAX, NMAX ), AA( NMAX*NMAX ), ALF( NALF ),
+ $ AS( NMAX*NMAX ), X( NMAX ), XS( NMAX*INCMAX ),
+ $ XX( NMAX*INCMAX ), Y( NMAX ),
+ $ YS( NMAX*INCMAX ), YT( NMAX ),
+ $ YY( NMAX*INCMAX ), Z( NMAX )
+ REAL G( NMAX )
+ INTEGER IDIM( NIDIM ), INC( NINC )
+* .. Local Scalars ..
+ COMPLEX ALPHA, ALS, TRANSL
+ REAL ERR, ERRMAX
+ INTEGER I, IA, IM, IN, INCX, INCXS, INCY, INCYS, IX,
+ $ IY, J, LAA, LDA, LDAS, LX, LY, M, MS, N, NARGS,
+ $ NC, ND, NS
+ LOGICAL CONJ, NULL, RESET, SAME
+* .. Local Arrays ..
+ COMPLEX W( 1 )
+ LOGICAL ISAME( 13 )
+* .. External Functions ..
+ LOGICAL LCE, LCERES
+ EXTERNAL LCE, LCERES
+* .. External Subroutines ..
+ EXTERNAL CGERC, CGERU, CMAKE, CMVCH
+* .. Intrinsic Functions ..
+ INTRINSIC ABS, CONJG, MAX, MIN
+* .. Scalars in Common ..
+ INTEGER INFOT, NOUTC
+ LOGICAL LERR, OK
+* .. Common blocks ..
+ COMMON /INFOC/INFOT, NOUTC, OK, LERR
+* .. Executable Statements ..
+ CONJ = SNAME( 5: 5 ).EQ.'C'
+* Define the number of arguments.
+ NARGS = 9
+*
+ NC = 0
+ RESET = .TRUE.
+ ERRMAX = RZERO
+*
+ DO 120 IN = 1, NIDIM
+ N = IDIM( IN )
+ ND = N/2 + 1
+*
+ DO 110 IM = 1, 2
+ IF( IM.EQ.1 )
+ $ M = MAX( N - ND, 0 )
+ IF( IM.EQ.2 )
+ $ M = MIN( N + ND, NMAX )
+*
+* Set LDA to 1 more than minimum value if room.
+ LDA = M
+ IF( LDA.LT.NMAX )
+ $ LDA = LDA + 1
+* Skip tests if not enough room.
+ IF( LDA.GT.NMAX )
+ $ GO TO 110
+ LAA = LDA*N
+ NULL = N.LE.0.OR.M.LE.0
+*
+ DO 100 IX = 1, NINC
+ INCX = INC( IX )
+ LX = ABS( INCX )*M
+*
+* Generate the vector X.
+*
+ TRANSL = HALF
+ CALL CMAKE( 'GE', ' ', ' ', 1, M, X, 1, XX, ABS( INCX ),
+ $ 0, M - 1, RESET, TRANSL )
+ IF( M.GT.1 )THEN
+ X( M/2 ) = ZERO
+ XX( 1 + ABS( INCX )*( M/2 - 1 ) ) = ZERO
+ END IF
+*
+ DO 90 IY = 1, NINC
+ INCY = INC( IY )
+ LY = ABS( INCY )*N
+*
+* Generate the vector Y.
+*
+ TRANSL = ZERO
+ CALL CMAKE( 'GE', ' ', ' ', 1, N, Y, 1, YY,
+ $ ABS( INCY ), 0, N - 1, RESET, TRANSL )
+ IF( N.GT.1 )THEN
+ Y( N/2 ) = ZERO
+ YY( 1 + ABS( INCY )*( N/2 - 1 ) ) = ZERO
+ END IF
+*
+ DO 80 IA = 1, NALF
+ ALPHA = ALF( IA )
+*
+* Generate the matrix A.
+*
+ TRANSL = ZERO
+ CALL CMAKE( SNAME( 2: 3 ), ' ', ' ', M, N, A, NMAX,
+ $ AA, LDA, M - 1, N - 1, RESET, TRANSL )
+*
+ NC = NC + 1
+*
+* Save every datum before calling the subroutine.
+*
+ MS = M
+ NS = N
+ ALS = ALPHA
+ DO 10 I = 1, LAA
+ AS( I ) = AA( I )
+ 10 CONTINUE
+ LDAS = LDA
+ DO 20 I = 1, LX
+ XS( I ) = XX( I )
+ 20 CONTINUE
+ INCXS = INCX
+ DO 30 I = 1, LY
+ YS( I ) = YY( I )
+ 30 CONTINUE
+ INCYS = INCY
+*
+* Call the subroutine.
+*
+ IF( TRACE )
+ $ WRITE( NTRA, FMT = 9994 )NC, SNAME, M, N,
+ $ ALPHA, INCX, INCY, LDA
+ IF( CONJ )THEN
+ IF( REWI )
+ $ REWIND NTRA
+ CALL CGERC( M, N, ALPHA, XX, INCX, YY, INCY, AA,
+ $ LDA )
+ ELSE
+ IF( REWI )
+ $ REWIND NTRA
+ CALL CGERU( M, N, ALPHA, XX, INCX, YY, INCY, AA,
+ $ LDA )
+ END IF
+*
+* Check if error-exit was taken incorrectly.
+*
+ IF( .NOT.OK )THEN
+ WRITE( NOUT, FMT = 9993 )
+ FATAL = .TRUE.
+ GO TO 140
+ END IF
+*
+* See what data changed inside subroutine.
+*
+ ISAME( 1 ) = MS.EQ.M
+ ISAME( 2 ) = NS.EQ.N
+ ISAME( 3 ) = ALS.EQ.ALPHA
+ ISAME( 4 ) = LCE( XS, XX, LX )
+ ISAME( 5 ) = INCXS.EQ.INCX
+ ISAME( 6 ) = LCE( YS, YY, LY )
+ ISAME( 7 ) = INCYS.EQ.INCY
+ IF( NULL )THEN
+ ISAME( 8 ) = LCE( AS, AA, LAA )
+ ELSE
+ ISAME( 8 ) = LCERES( 'GE', ' ', M, N, AS, AA,
+ $ LDA )
+ END IF
+ ISAME( 9 ) = LDAS.EQ.LDA
+*
+* If data was incorrectly changed, report and return.
+*
+ SAME = .TRUE.
+ DO 40 I = 1, NARGS
+ SAME = SAME.AND.ISAME( I )
+ IF( .NOT.ISAME( I ) )
+ $ WRITE( NOUT, FMT = 9998 )I
+ 40 CONTINUE
+ IF( .NOT.SAME )THEN
+ FATAL = .TRUE.
+ GO TO 140
+ END IF
+*
+ IF( .NOT.NULL )THEN
+*
+* Check the result column by column.
+*
+ IF( INCX.GT.0 )THEN
+ DO 50 I = 1, M
+ Z( I ) = X( I )
+ 50 CONTINUE
+ ELSE
+ DO 60 I = 1, M
+ Z( I ) = X( M - I + 1 )
+ 60 CONTINUE
+ END IF
+ DO 70 J = 1, N
+ IF( INCY.GT.0 )THEN
+ W( 1 ) = Y( J )
+ ELSE
+ W( 1 ) = Y( N - J + 1 )
+ END IF
+ IF( CONJ )
+ $ W( 1 ) = CONJG( W( 1 ) )
+ CALL CMVCH( 'N', M, 1, ALPHA, Z, NMAX, W, 1,
+ $ ONE, A( 1, J ), 1, YT, G,
+ $ AA( 1 + ( J - 1 )*LDA ), EPS,
+ $ ERR, FATAL, NOUT, .TRUE. )
+ ERRMAX = MAX( ERRMAX, ERR )
+* If got really bad answer, report and return.
+ IF( FATAL )
+ $ GO TO 130
+ 70 CONTINUE
+ ELSE
+* Avoid repeating tests with M.le.0 or N.le.0.
+ GO TO 110
+ END IF
+*
+ 80 CONTINUE
+*
+ 90 CONTINUE
+*
+ 100 CONTINUE
+*
+ 110 CONTINUE
+*
+ 120 CONTINUE
+*
+* Report result.
+*
+ IF( ERRMAX.LT.THRESH )THEN
+ WRITE( NOUT, FMT = 9999 )SNAME, NC
+ ELSE
+ WRITE( NOUT, FMT = 9997 )SNAME, NC, ERRMAX
+ END IF
+ GO TO 150
+*
+ 130 CONTINUE
+ WRITE( NOUT, FMT = 9995 )J
+*
+ 140 CONTINUE
+ WRITE( NOUT, FMT = 9996 )SNAME
+ WRITE( NOUT, FMT = 9994 )NC, SNAME, M, N, ALPHA, INCX, INCY, LDA
+*
+ 150 CONTINUE
+ RETURN
+*
+ 9999 FORMAT( ' ', A6, ' PASSED THE COMPUTATIONAL TESTS (', I6, ' CALL',
+ $ 'S)' )
+ 9998 FORMAT( ' ******* FATAL ERROR - PARAMETER NUMBER ', I2, ' WAS CH',
+ $ 'ANGED INCORRECTLY *******' )
+ 9997 FORMAT( ' ', A6, ' COMPLETED THE COMPUTATIONAL TESTS (', I6, ' C',
+ $ 'ALLS)', /' ******* BUT WITH MAXIMUM TEST RATIO', F8.2,
+ $ ' - SUSPECT *******' )
+ 9996 FORMAT( ' ******* ', A6, ' FAILED ON CALL NUMBER:' )
+ 9995 FORMAT( ' THESE ARE THE RESULTS FOR COLUMN ', I3 )
+ 9994 FORMAT( 1X, I6, ': ', A6, '(', 2( I3, ',' ), '(', F4.1, ',', F4.1,
+ $ '), X,', I2, ', Y,', I2, ', A,', I3, ') ',
+ $ ' .' )
+ 9993 FORMAT( ' ******* FATAL ERROR - ERROR-EXIT TAKEN ON VALID CALL *',
+ $ '******' )
+*
+* End of CCHK4.
+*
+ END
+ SUBROUTINE CCHK5( SNAME, EPS, THRESH, NOUT, NTRA, TRACE, REWI,
+ $ FATAL, NIDIM, IDIM, NALF, ALF, NINC, INC, NMAX,
+ $ INCMAX, A, AA, AS, X, XX, XS, Y, YY, YS, YT, G,
+ $ Z )
+*
+* Tests CHER and CHPR.
+*
+* Auxiliary routine for test program for Level 2 Blas.
+*
+* -- Written on 10-August-1987.
+* Richard Hanson, Sandia National Labs.
+* Jeremy Du Croz, NAG Central Office.
+*
+* .. Parameters ..
+ COMPLEX ZERO, HALF, ONE
+ PARAMETER ( ZERO = ( 0.0, 0.0 ), HALF = ( 0.5, 0.0 ),
+ $ ONE = ( 1.0, 0.0 ) )
+ REAL RZERO
+ PARAMETER ( RZERO = 0.0 )
+* .. Scalar Arguments ..
+ REAL EPS, THRESH
+ INTEGER INCMAX, NALF, NIDIM, NINC, NMAX, NOUT, NTRA
+ LOGICAL FATAL, REWI, TRACE
+ CHARACTER*6 SNAME
+* .. Array Arguments ..
+ COMPLEX A( NMAX, NMAX ), AA( NMAX*NMAX ), ALF( NALF ),
+ $ AS( NMAX*NMAX ), X( NMAX ), XS( NMAX*INCMAX ),
+ $ XX( NMAX*INCMAX ), Y( NMAX ),
+ $ YS( NMAX*INCMAX ), YT( NMAX ),
+ $ YY( NMAX*INCMAX ), Z( NMAX )
+ REAL G( NMAX )
+ INTEGER IDIM( NIDIM ), INC( NINC )
+* .. Local Scalars ..
+ COMPLEX ALPHA, TRANSL
+ REAL ERR, ERRMAX, RALPHA, RALS
+ INTEGER I, IA, IC, IN, INCX, INCXS, IX, J, JA, JJ, LAA,
+ $ LDA, LDAS, LJ, LX, N, NARGS, NC, NS
+ LOGICAL FULL, NULL, PACKED, RESET, SAME, UPPER
+ CHARACTER*1 UPLO, UPLOS
+ CHARACTER*2 ICH
+* .. Local Arrays ..
+ COMPLEX W( 1 )
+ LOGICAL ISAME( 13 )
+* .. External Functions ..
+ LOGICAL LCE, LCERES
+ EXTERNAL LCE, LCERES
+* .. External Subroutines ..
+ EXTERNAL CHER, CHPR, CMAKE, CMVCH
+* .. Intrinsic Functions ..
+ INTRINSIC ABS, CMPLX, CONJG, MAX, REAL
+* .. Scalars in Common ..
+ INTEGER INFOT, NOUTC
+ LOGICAL LERR, OK
+* .. Common blocks ..
+ COMMON /INFOC/INFOT, NOUTC, OK, LERR
+* .. Data statements ..
+ DATA ICH/'UL'/
+* .. Executable Statements ..
+ FULL = SNAME( 3: 3 ).EQ.'E'
+ PACKED = SNAME( 3: 3 ).EQ.'P'
+* Define the number of arguments.
+ IF( FULL )THEN
+ NARGS = 7
+ ELSE IF( PACKED )THEN
+ NARGS = 6
+ END IF
+*
+ NC = 0
+ RESET = .TRUE.
+ ERRMAX = RZERO
+*
+ DO 100 IN = 1, NIDIM
+ N = IDIM( IN )
+* Set LDA to 1 more than minimum value if room.
+ LDA = N
+ IF( LDA.LT.NMAX )
+ $ LDA = LDA + 1
+* Skip tests if not enough room.
+ IF( LDA.GT.NMAX )
+ $ GO TO 100
+ IF( PACKED )THEN
+ LAA = ( N*( N + 1 ) )/2
+ ELSE
+ LAA = LDA*N
+ END IF
+*
+ DO 90 IC = 1, 2
+ UPLO = ICH( IC: IC )
+ UPPER = UPLO.EQ.'U'
+*
+ DO 80 IX = 1, NINC
+ INCX = INC( IX )
+ LX = ABS( INCX )*N
+*
+* Generate the vector X.
+*
+ TRANSL = HALF
+ CALL CMAKE( 'GE', ' ', ' ', 1, N, X, 1, XX, ABS( INCX ),
+ $ 0, N - 1, RESET, TRANSL )
+ IF( N.GT.1 )THEN
+ X( N/2 ) = ZERO
+ XX( 1 + ABS( INCX )*( N/2 - 1 ) ) = ZERO
+ END IF
+*
+ DO 70 IA = 1, NALF
+ RALPHA = REAL( ALF( IA ) )
+ ALPHA = CMPLX( RALPHA, RZERO )
+ NULL = N.LE.0.OR.RALPHA.EQ.RZERO
+*
+* Generate the matrix A.
+*
+ TRANSL = ZERO
+ CALL CMAKE( SNAME( 2: 3 ), UPLO, ' ', N, N, A, NMAX,
+ $ AA, LDA, N - 1, N - 1, RESET, TRANSL )
+*
+ NC = NC + 1
+*
+* Save every datum before calling the subroutine.
+*
+ UPLOS = UPLO
+ NS = N
+ RALS = RALPHA
+ DO 10 I = 1, LAA
+ AS( I ) = AA( I )
+ 10 CONTINUE
+ LDAS = LDA
+ DO 20 I = 1, LX
+ XS( I ) = XX( I )
+ 20 CONTINUE
+ INCXS = INCX
+*
+* Call the subroutine.
+*
+ IF( FULL )THEN
+ IF( TRACE )
+ $ WRITE( NTRA, FMT = 9993 )NC, SNAME, UPLO, N,
+ $ RALPHA, INCX, LDA
+ IF( REWI )
+ $ REWIND NTRA
+ CALL CHER( UPLO, N, RALPHA, XX, INCX, AA, LDA )
+ ELSE IF( PACKED )THEN
+ IF( TRACE )
+ $ WRITE( NTRA, FMT = 9994 )NC, SNAME, UPLO, N,
+ $ RALPHA, INCX
+ IF( REWI )
+ $ REWIND NTRA
+ CALL CHPR( UPLO, N, RALPHA, XX, INCX, AA )
+ END IF
+*
+* Check if error-exit was taken incorrectly.
+*
+ IF( .NOT.OK )THEN
+ WRITE( NOUT, FMT = 9992 )
+ FATAL = .TRUE.
+ GO TO 120
+ END IF
+*
+* See what data changed inside subroutines.
+*
+ ISAME( 1 ) = UPLO.EQ.UPLOS
+ ISAME( 2 ) = NS.EQ.N
+ ISAME( 3 ) = RALS.EQ.RALPHA
+ ISAME( 4 ) = LCE( XS, XX, LX )
+ ISAME( 5 ) = INCXS.EQ.INCX
+ IF( NULL )THEN
+ ISAME( 6 ) = LCE( AS, AA, LAA )
+ ELSE
+ ISAME( 6 ) = LCERES( SNAME( 2: 3 ), UPLO, N, N, AS,
+ $ AA, LDA )
+ END IF
+ IF( .NOT.PACKED )THEN
+ ISAME( 7 ) = LDAS.EQ.LDA
+ END IF
+*
+* If data was incorrectly changed, report and return.
+*
+ SAME = .TRUE.
+ DO 30 I = 1, NARGS
+ SAME = SAME.AND.ISAME( I )
+ IF( .NOT.ISAME( I ) )
+ $ WRITE( NOUT, FMT = 9998 )I
+ 30 CONTINUE
+ IF( .NOT.SAME )THEN
+ FATAL = .TRUE.
+ GO TO 120
+ END IF
+*
+ IF( .NOT.NULL )THEN
+*
+* Check the result column by column.
+*
+ IF( INCX.GT.0 )THEN
+ DO 40 I = 1, N
+ Z( I ) = X( I )
+ 40 CONTINUE
+ ELSE
+ DO 50 I = 1, N
+ Z( I ) = X( N - I + 1 )
+ 50 CONTINUE
+ END IF
+ JA = 1
+ DO 60 J = 1, N
+ W( 1 ) = CONJG( Z( J ) )
+ IF( UPPER )THEN
+ JJ = 1
+ LJ = J
+ ELSE
+ JJ = J
+ LJ = N - J + 1
+ END IF
+ CALL CMVCH( 'N', LJ, 1, ALPHA, Z( JJ ), LJ, W,
+ $ 1, ONE, A( JJ, J ), 1, YT, G,
+ $ AA( JA ), EPS, ERR, FATAL, NOUT,
+ $ .TRUE. )
+ IF( FULL )THEN
+ IF( UPPER )THEN
+ JA = JA + LDA
+ ELSE
+ JA = JA + LDA + 1
+ END IF
+ ELSE
+ JA = JA + LJ
+ END IF
+ ERRMAX = MAX( ERRMAX, ERR )
+* If got really bad answer, report and return.
+ IF( FATAL )
+ $ GO TO 110
+ 60 CONTINUE
+ ELSE
+* Avoid repeating tests if N.le.0.
+ IF( N.LE.0 )
+ $ GO TO 100
+ END IF
+*
+ 70 CONTINUE
+*
+ 80 CONTINUE
+*
+ 90 CONTINUE
+*
+ 100 CONTINUE
+*
+* Report result.
+*
+ IF( ERRMAX.LT.THRESH )THEN
+ WRITE( NOUT, FMT = 9999 )SNAME, NC
+ ELSE
+ WRITE( NOUT, FMT = 9997 )SNAME, NC, ERRMAX
+ END IF
+ GO TO 130
+*
+ 110 CONTINUE
+ WRITE( NOUT, FMT = 9995 )J
+*
+ 120 CONTINUE
+ WRITE( NOUT, FMT = 9996 )SNAME
+ IF( FULL )THEN
+ WRITE( NOUT, FMT = 9993 )NC, SNAME, UPLO, N, RALPHA, INCX, LDA
+ ELSE IF( PACKED )THEN
+ WRITE( NOUT, FMT = 9994 )NC, SNAME, UPLO, N, RALPHA, INCX
+ END IF
+*
+ 130 CONTINUE
+ RETURN
+*
+ 9999 FORMAT( ' ', A6, ' PASSED THE COMPUTATIONAL TESTS (', I6, ' CALL',
+ $ 'S)' )
+ 9998 FORMAT( ' ******* FATAL ERROR - PARAMETER NUMBER ', I2, ' WAS CH',
+ $ 'ANGED INCORRECTLY *******' )
+ 9997 FORMAT( ' ', A6, ' COMPLETED THE COMPUTATIONAL TESTS (', I6, ' C',
+ $ 'ALLS)', /' ******* BUT WITH MAXIMUM TEST RATIO', F8.2,
+ $ ' - SUSPECT *******' )
+ 9996 FORMAT( ' ******* ', A6, ' FAILED ON CALL NUMBER:' )
+ 9995 FORMAT( ' THESE ARE THE RESULTS FOR COLUMN ', I3 )
+ 9994 FORMAT( 1X, I6, ': ', A6, '(''', A1, ''',', I3, ',', F4.1, ', X,',
+ $ I2, ', AP) .' )
+ 9993 FORMAT( 1X, I6, ': ', A6, '(''', A1, ''',', I3, ',', F4.1, ', X,',
+ $ I2, ', A,', I3, ') .' )
+ 9992 FORMAT( ' ******* FATAL ERROR - ERROR-EXIT TAKEN ON VALID CALL *',
+ $ '******' )
+*
+* End of CCHK5.
+*
+ END
+ SUBROUTINE CCHK6( SNAME, EPS, THRESH, NOUT, NTRA, TRACE, REWI,
+ $ FATAL, NIDIM, IDIM, NALF, ALF, NINC, INC, NMAX,
+ $ INCMAX, A, AA, AS, X, XX, XS, Y, YY, YS, YT, G,
+ $ Z )
+*
+* Tests CHER2 and CHPR2.
+*
+* Auxiliary routine for test program for Level 2 Blas.
+*
+* -- Written on 10-August-1987.
+* Richard Hanson, Sandia National Labs.
+* Jeremy Du Croz, NAG Central Office.
+*
+* .. Parameters ..
+ COMPLEX ZERO, HALF, ONE
+ PARAMETER ( ZERO = ( 0.0, 0.0 ), HALF = ( 0.5, 0.0 ),
+ $ ONE = ( 1.0, 0.0 ) )
+ REAL RZERO
+ PARAMETER ( RZERO = 0.0 )
+* .. Scalar Arguments ..
+ REAL EPS, THRESH
+ INTEGER INCMAX, NALF, NIDIM, NINC, NMAX, NOUT, NTRA
+ LOGICAL FATAL, REWI, TRACE
+ CHARACTER*6 SNAME
+* .. Array Arguments ..
+ COMPLEX A( NMAX, NMAX ), AA( NMAX*NMAX ), ALF( NALF ),
+ $ AS( NMAX*NMAX ), X( NMAX ), XS( NMAX*INCMAX ),
+ $ XX( NMAX*INCMAX ), Y( NMAX ),
+ $ YS( NMAX*INCMAX ), YT( NMAX ),
+ $ YY( NMAX*INCMAX ), Z( NMAX, 2 )
+ REAL G( NMAX )
+ INTEGER IDIM( NIDIM ), INC( NINC )
+* .. Local Scalars ..
+ COMPLEX ALPHA, ALS, TRANSL
+ REAL ERR, ERRMAX
+ INTEGER I, IA, IC, IN, INCX, INCXS, INCY, INCYS, IX,
+ $ IY, J, JA, JJ, LAA, LDA, LDAS, LJ, LX, LY, N,
+ $ NARGS, NC, NS
+ LOGICAL FULL, NULL, PACKED, RESET, SAME, UPPER
+ CHARACTER*1 UPLO, UPLOS
+ CHARACTER*2 ICH
+* .. Local Arrays ..
+ COMPLEX W( 2 )
+ LOGICAL ISAME( 13 )
+* .. External Functions ..
+ LOGICAL LCE, LCERES
+ EXTERNAL LCE, LCERES
+* .. External Subroutines ..
+ EXTERNAL CHER2, CHPR2, CMAKE, CMVCH
+* .. Intrinsic Functions ..
+ INTRINSIC ABS, CONJG, MAX
+* .. Scalars in Common ..
+ INTEGER INFOT, NOUTC
+ LOGICAL LERR, OK
+* .. Common blocks ..
+ COMMON /INFOC/INFOT, NOUTC, OK, LERR
+* .. Data statements ..
+ DATA ICH/'UL'/
+* .. Executable Statements ..
+ FULL = SNAME( 3: 3 ).EQ.'E'
+ PACKED = SNAME( 3: 3 ).EQ.'P'
+* Define the number of arguments.
+ IF( FULL )THEN
+ NARGS = 9
+ ELSE IF( PACKED )THEN
+ NARGS = 8
+ END IF
+*
+ NC = 0
+ RESET = .TRUE.
+ ERRMAX = RZERO
+*
+ DO 140 IN = 1, NIDIM
+ N = IDIM( IN )
+* Set LDA to 1 more than minimum value if room.
+ LDA = N
+ IF( LDA.LT.NMAX )
+ $ LDA = LDA + 1
+* Skip tests if not enough room.
+ IF( LDA.GT.NMAX )
+ $ GO TO 140
+ IF( PACKED )THEN
+ LAA = ( N*( N + 1 ) )/2
+ ELSE
+ LAA = LDA*N
+ END IF
+*
+ DO 130 IC = 1, 2
+ UPLO = ICH( IC: IC )
+ UPPER = UPLO.EQ.'U'
+*
+ DO 120 IX = 1, NINC
+ INCX = INC( IX )
+ LX = ABS( INCX )*N
+*
+* Generate the vector X.
+*
+ TRANSL = HALF
+ CALL CMAKE( 'GE', ' ', ' ', 1, N, X, 1, XX, ABS( INCX ),
+ $ 0, N - 1, RESET, TRANSL )
+ IF( N.GT.1 )THEN
+ X( N/2 ) = ZERO
+ XX( 1 + ABS( INCX )*( N/2 - 1 ) ) = ZERO
+ END IF
+*
+ DO 110 IY = 1, NINC
+ INCY = INC( IY )
+ LY = ABS( INCY )*N
+*
+* Generate the vector Y.
+*
+ TRANSL = ZERO
+ CALL CMAKE( 'GE', ' ', ' ', 1, N, Y, 1, YY,
+ $ ABS( INCY ), 0, N - 1, RESET, TRANSL )
+ IF( N.GT.1 )THEN
+ Y( N/2 ) = ZERO
+ YY( 1 + ABS( INCY )*( N/2 - 1 ) ) = ZERO
+ END IF
+*
+ DO 100 IA = 1, NALF
+ ALPHA = ALF( IA )
+ NULL = N.LE.0.OR.ALPHA.EQ.ZERO
+*
+* Generate the matrix A.
+*
+ TRANSL = ZERO
+ CALL CMAKE( SNAME( 2: 3 ), UPLO, ' ', N, N, A,
+ $ NMAX, AA, LDA, N - 1, N - 1, RESET,
+ $ TRANSL )
+*
+ NC = NC + 1
+*
+* Save every datum before calling the subroutine.
+*
+ UPLOS = UPLO
+ NS = N
+ ALS = ALPHA
+ DO 10 I = 1, LAA
+ AS( I ) = AA( I )
+ 10 CONTINUE
+ LDAS = LDA
+ DO 20 I = 1, LX
+ XS( I ) = XX( I )
+ 20 CONTINUE
+ INCXS = INCX
+ DO 30 I = 1, LY
+ YS( I ) = YY( I )
+ 30 CONTINUE
+ INCYS = INCY
+*
+* Call the subroutine.
+*
+ IF( FULL )THEN
+ IF( TRACE )
+ $ WRITE( NTRA, FMT = 9993 )NC, SNAME, UPLO, N,
+ $ ALPHA, INCX, INCY, LDA
+ IF( REWI )
+ $ REWIND NTRA
+ CALL CHER2( UPLO, N, ALPHA, XX, INCX, YY, INCY,
+ $ AA, LDA )
+ ELSE IF( PACKED )THEN
+ IF( TRACE )
+ $ WRITE( NTRA, FMT = 9994 )NC, SNAME, UPLO, N,
+ $ ALPHA, INCX, INCY
+ IF( REWI )
+ $ REWIND NTRA
+ CALL CHPR2( UPLO, N, ALPHA, XX, INCX, YY, INCY,
+ $ AA )
+ END IF
+*
+* Check if error-exit was taken incorrectly.
+*
+ IF( .NOT.OK )THEN
+ WRITE( NOUT, FMT = 9992 )
+ FATAL = .TRUE.
+ GO TO 160
+ END IF
+*
+* See what data changed inside subroutines.
+*
+ ISAME( 1 ) = UPLO.EQ.UPLOS
+ ISAME( 2 ) = NS.EQ.N
+ ISAME( 3 ) = ALS.EQ.ALPHA
+ ISAME( 4 ) = LCE( XS, XX, LX )
+ ISAME( 5 ) = INCXS.EQ.INCX
+ ISAME( 6 ) = LCE( YS, YY, LY )
+ ISAME( 7 ) = INCYS.EQ.INCY
+ IF( NULL )THEN
+ ISAME( 8 ) = LCE( AS, AA, LAA )
+ ELSE
+ ISAME( 8 ) = LCERES( SNAME( 2: 3 ), UPLO, N, N,
+ $ AS, AA, LDA )
+ END IF
+ IF( .NOT.PACKED )THEN
+ ISAME( 9 ) = LDAS.EQ.LDA
+ END IF
+*
+* If data was incorrectly changed, report and return.
+*
+ SAME = .TRUE.
+ DO 40 I = 1, NARGS
+ SAME = SAME.AND.ISAME( I )
+ IF( .NOT.ISAME( I ) )
+ $ WRITE( NOUT, FMT = 9998 )I
+ 40 CONTINUE
+ IF( .NOT.SAME )THEN
+ FATAL = .TRUE.
+ GO TO 160
+ END IF
+*
+ IF( .NOT.NULL )THEN
+*
+* Check the result column by column.
+*
+ IF( INCX.GT.0 )THEN
+ DO 50 I = 1, N
+ Z( I, 1 ) = X( I )
+ 50 CONTINUE
+ ELSE
+ DO 60 I = 1, N
+ Z( I, 1 ) = X( N - I + 1 )
+ 60 CONTINUE
+ END IF
+ IF( INCY.GT.0 )THEN
+ DO 70 I = 1, N
+ Z( I, 2 ) = Y( I )
+ 70 CONTINUE
+ ELSE
+ DO 80 I = 1, N
+ Z( I, 2 ) = Y( N - I + 1 )
+ 80 CONTINUE
+ END IF
+ JA = 1
+ DO 90 J = 1, N
+ W( 1 ) = ALPHA*CONJG( Z( J, 2 ) )
+ W( 2 ) = CONJG( ALPHA )*CONJG( Z( J, 1 ) )
+ IF( UPPER )THEN
+ JJ = 1
+ LJ = J
+ ELSE
+ JJ = J
+ LJ = N - J + 1
+ END IF
+ CALL CMVCH( 'N', LJ, 2, ONE, Z( JJ, 1 ),
+ $ NMAX, W, 1, ONE, A( JJ, J ), 1,
+ $ YT, G, AA( JA ), EPS, ERR, FATAL,
+ $ NOUT, .TRUE. )
+ IF( FULL )THEN
+ IF( UPPER )THEN
+ JA = JA + LDA
+ ELSE
+ JA = JA + LDA + 1
+ END IF
+ ELSE
+ JA = JA + LJ
+ END IF
+ ERRMAX = MAX( ERRMAX, ERR )
+* If got really bad answer, report and return.
+ IF( FATAL )
+ $ GO TO 150
+ 90 CONTINUE
+ ELSE
+* Avoid repeating tests with N.le.0.
+ IF( N.LE.0 )
+ $ GO TO 140
+ END IF
+*
+ 100 CONTINUE
+*
+ 110 CONTINUE
+*
+ 120 CONTINUE
+*
+ 130 CONTINUE
+*
+ 140 CONTINUE
+*
+* Report result.
+*
+ IF( ERRMAX.LT.THRESH )THEN
+ WRITE( NOUT, FMT = 9999 )SNAME, NC
+ ELSE
+ WRITE( NOUT, FMT = 9997 )SNAME, NC, ERRMAX
+ END IF
+ GO TO 170
+*
+ 150 CONTINUE
+ WRITE( NOUT, FMT = 9995 )J
+*
+ 160 CONTINUE
+ WRITE( NOUT, FMT = 9996 )SNAME
+ IF( FULL )THEN
+ WRITE( NOUT, FMT = 9993 )NC, SNAME, UPLO, N, ALPHA, INCX,
+ $ INCY, LDA
+ ELSE IF( PACKED )THEN
+ WRITE( NOUT, FMT = 9994 )NC, SNAME, UPLO, N, ALPHA, INCX, INCY
+ END IF
+*
+ 170 CONTINUE
+ RETURN
+*
+ 9999 FORMAT( ' ', A6, ' PASSED THE COMPUTATIONAL TESTS (', I6, ' CALL',
+ $ 'S)' )
+ 9998 FORMAT( ' ******* FATAL ERROR - PARAMETER NUMBER ', I2, ' WAS CH',
+ $ 'ANGED INCORRECTLY *******' )
+ 9997 FORMAT( ' ', A6, ' COMPLETED THE COMPUTATIONAL TESTS (', I6, ' C',
+ $ 'ALLS)', /' ******* BUT WITH MAXIMUM TEST RATIO', F8.2,
+ $ ' - SUSPECT *******' )
+ 9996 FORMAT( ' ******* ', A6, ' FAILED ON CALL NUMBER:' )
+ 9995 FORMAT( ' THESE ARE THE RESULTS FOR COLUMN ', I3 )
+ 9994 FORMAT( 1X, I6, ': ', A6, '(''', A1, ''',', I3, ',(', F4.1, ',',
+ $ F4.1, '), X,', I2, ', Y,', I2, ', AP) ',
+ $ ' .' )
+ 9993 FORMAT( 1X, I6, ': ', A6, '(''', A1, ''',', I3, ',(', F4.1, ',',
+ $ F4.1, '), X,', I2, ', Y,', I2, ', A,', I3, ') ',
+ $ ' .' )
+ 9992 FORMAT( ' ******* FATAL ERROR - ERROR-EXIT TAKEN ON VALID CALL *',
+ $ '******' )
+*
+* End of CCHK6.
+*
+ END
+ SUBROUTINE CCHKE( ISNUM, SRNAMT, NOUT )
+*
+* Tests the error exits from the Level 2 Blas.
+* Requires a special version of the error-handling routine XERBLA.
+* ALPHA, RALPHA, BETA, A, X and Y should not need to be defined.
+*
+* Auxiliary routine for test program for Level 2 Blas.
+*
+* -- Written on 10-August-1987.
+* Richard Hanson, Sandia National Labs.
+* Jeremy Du Croz, NAG Central Office.
+*
+* .. Scalar Arguments ..
+ INTEGER ISNUM, NOUT
+ CHARACTER*6 SRNAMT
+* .. Scalars in Common ..
+ INTEGER INFOT, NOUTC
+ LOGICAL LERR, OK
+* .. Local Scalars ..
+ COMPLEX ALPHA, BETA
+ REAL RALPHA
+* .. Local Arrays ..
+ COMPLEX A( 1, 1 ), X( 1 ), Y( 1 )
+* .. External Subroutines ..
+ EXTERNAL CGBMV, CGEMV, CGERC, CGERU, CHBMV, CHEMV, CHER,
+ $ CHER2, CHKXER, CHPMV, CHPR, CHPR2, CTBMV,
+ $ CTBSV, CTPMV, CTPSV, CTRMV, CTRSV
+* .. Common blocks ..
+ COMMON /INFOC/INFOT, NOUTC, OK, LERR
+* .. Executable Statements ..
+* OK is set to .FALSE. by the special version of XERBLA or by CHKXER
+* if anything is wrong.
+ OK = .TRUE.
+* LERR is set to .TRUE. by the special version of XERBLA each time
+* it is called, and is then tested and re-set by CHKXER.
+ LERR = .FALSE.
+ GO TO ( 10, 20, 30, 40, 50, 60, 70, 80,
+ $ 90, 100, 110, 120, 130, 140, 150, 160,
+ $ 170 )ISNUM
+ 10 INFOT = 1
+ CALL CGEMV( '/', 0, 0, ALPHA, A, 1, X, 1, BETA, Y, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 2
+ CALL CGEMV( 'N', -1, 0, ALPHA, A, 1, X, 1, BETA, Y, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 3
+ CALL CGEMV( 'N', 0, -1, ALPHA, A, 1, X, 1, BETA, Y, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 6
+ CALL CGEMV( 'N', 2, 0, ALPHA, A, 1, X, 1, BETA, Y, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 8
+ CALL CGEMV( 'N', 0, 0, ALPHA, A, 1, X, 0, BETA, Y, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 11
+ CALL CGEMV( 'N', 0, 0, ALPHA, A, 1, X, 1, BETA, Y, 0 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ GO TO 180
+ 20 INFOT = 1
+ CALL CGBMV( '/', 0, 0, 0, 0, ALPHA, A, 1, X, 1, BETA, Y, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 2
+ CALL CGBMV( 'N', -1, 0, 0, 0, ALPHA, A, 1, X, 1, BETA, Y, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 3
+ CALL CGBMV( 'N', 0, -1, 0, 0, ALPHA, A, 1, X, 1, BETA, Y, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 4
+ CALL CGBMV( 'N', 0, 0, -1, 0, ALPHA, A, 1, X, 1, BETA, Y, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 5
+ CALL CGBMV( 'N', 2, 0, 0, -1, ALPHA, A, 1, X, 1, BETA, Y, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 8
+ CALL CGBMV( 'N', 0, 0, 1, 0, ALPHA, A, 1, X, 1, BETA, Y, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 10
+ CALL CGBMV( 'N', 0, 0, 0, 0, ALPHA, A, 1, X, 0, BETA, Y, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 13
+ CALL CGBMV( 'N', 0, 0, 0, 0, ALPHA, A, 1, X, 1, BETA, Y, 0 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ GO TO 180
+ 30 INFOT = 1
+ CALL CHEMV( '/', 0, ALPHA, A, 1, X, 1, BETA, Y, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 2
+ CALL CHEMV( 'U', -1, ALPHA, A, 1, X, 1, BETA, Y, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 5
+ CALL CHEMV( 'U', 2, ALPHA, A, 1, X, 1, BETA, Y, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 7
+ CALL CHEMV( 'U', 0, ALPHA, A, 1, X, 0, BETA, Y, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 10
+ CALL CHEMV( 'U', 0, ALPHA, A, 1, X, 1, BETA, Y, 0 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ GO TO 180
+ 40 INFOT = 1
+ CALL CHBMV( '/', 0, 0, ALPHA, A, 1, X, 1, BETA, Y, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 2
+ CALL CHBMV( 'U', -1, 0, ALPHA, A, 1, X, 1, BETA, Y, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 3
+ CALL CHBMV( 'U', 0, -1, ALPHA, A, 1, X, 1, BETA, Y, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 6
+ CALL CHBMV( 'U', 0, 1, ALPHA, A, 1, X, 1, BETA, Y, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 8
+ CALL CHBMV( 'U', 0, 0, ALPHA, A, 1, X, 0, BETA, Y, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 11
+ CALL CHBMV( 'U', 0, 0, ALPHA, A, 1, X, 1, BETA, Y, 0 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ GO TO 180
+ 50 INFOT = 1
+ CALL CHPMV( '/', 0, ALPHA, A, X, 1, BETA, Y, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 2
+ CALL CHPMV( 'U', -1, ALPHA, A, X, 1, BETA, Y, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 6
+ CALL CHPMV( 'U', 0, ALPHA, A, X, 0, BETA, Y, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 9
+ CALL CHPMV( 'U', 0, ALPHA, A, X, 1, BETA, Y, 0 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ GO TO 180
+ 60 INFOT = 1
+ CALL CTRMV( '/', 'N', 'N', 0, A, 1, X, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 2
+ CALL CTRMV( 'U', '/', 'N', 0, A, 1, X, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 3
+ CALL CTRMV( 'U', 'N', '/', 0, A, 1, X, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 4
+ CALL CTRMV( 'U', 'N', 'N', -1, A, 1, X, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 6
+ CALL CTRMV( 'U', 'N', 'N', 2, A, 1, X, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 8
+ CALL CTRMV( 'U', 'N', 'N', 0, A, 1, X, 0 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ GO TO 180
+ 70 INFOT = 1
+ CALL CTBMV( '/', 'N', 'N', 0, 0, A, 1, X, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 2
+ CALL CTBMV( 'U', '/', 'N', 0, 0, A, 1, X, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 3
+ CALL CTBMV( 'U', 'N', '/', 0, 0, A, 1, X, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 4
+ CALL CTBMV( 'U', 'N', 'N', -1, 0, A, 1, X, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 5
+ CALL CTBMV( 'U', 'N', 'N', 0, -1, A, 1, X, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 7
+ CALL CTBMV( 'U', 'N', 'N', 0, 1, A, 1, X, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 9
+ CALL CTBMV( 'U', 'N', 'N', 0, 0, A, 1, X, 0 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ GO TO 180
+ 80 INFOT = 1
+ CALL CTPMV( '/', 'N', 'N', 0, A, X, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 2
+ CALL CTPMV( 'U', '/', 'N', 0, A, X, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 3
+ CALL CTPMV( 'U', 'N', '/', 0, A, X, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 4
+ CALL CTPMV( 'U', 'N', 'N', -1, A, X, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 7
+ CALL CTPMV( 'U', 'N', 'N', 0, A, X, 0 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ GO TO 180
+ 90 INFOT = 1
+ CALL CTRSV( '/', 'N', 'N', 0, A, 1, X, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 2
+ CALL CTRSV( 'U', '/', 'N', 0, A, 1, X, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 3
+ CALL CTRSV( 'U', 'N', '/', 0, A, 1, X, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 4
+ CALL CTRSV( 'U', 'N', 'N', -1, A, 1, X, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 6
+ CALL CTRSV( 'U', 'N', 'N', 2, A, 1, X, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 8
+ CALL CTRSV( 'U', 'N', 'N', 0, A, 1, X, 0 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ GO TO 180
+ 100 INFOT = 1
+ CALL CTBSV( '/', 'N', 'N', 0, 0, A, 1, X, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 2
+ CALL CTBSV( 'U', '/', 'N', 0, 0, A, 1, X, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 3
+ CALL CTBSV( 'U', 'N', '/', 0, 0, A, 1, X, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 4
+ CALL CTBSV( 'U', 'N', 'N', -1, 0, A, 1, X, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 5
+ CALL CTBSV( 'U', 'N', 'N', 0, -1, A, 1, X, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 7
+ CALL CTBSV( 'U', 'N', 'N', 0, 1, A, 1, X, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 9
+ CALL CTBSV( 'U', 'N', 'N', 0, 0, A, 1, X, 0 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ GO TO 180
+ 110 INFOT = 1
+ CALL CTPSV( '/', 'N', 'N', 0, A, X, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 2
+ CALL CTPSV( 'U', '/', 'N', 0, A, X, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 3
+ CALL CTPSV( 'U', 'N', '/', 0, A, X, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 4
+ CALL CTPSV( 'U', 'N', 'N', -1, A, X, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 7
+ CALL CTPSV( 'U', 'N', 'N', 0, A, X, 0 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ GO TO 180
+ 120 INFOT = 1
+ CALL CGERC( -1, 0, ALPHA, X, 1, Y, 1, A, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 2
+ CALL CGERC( 0, -1, ALPHA, X, 1, Y, 1, A, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 5
+ CALL CGERC( 0, 0, ALPHA, X, 0, Y, 1, A, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 7
+ CALL CGERC( 0, 0, ALPHA, X, 1, Y, 0, A, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 9
+ CALL CGERC( 2, 0, ALPHA, X, 1, Y, 1, A, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ GO TO 180
+ 130 INFOT = 1
+ CALL CGERU( -1, 0, ALPHA, X, 1, Y, 1, A, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 2
+ CALL CGERU( 0, -1, ALPHA, X, 1, Y, 1, A, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 5
+ CALL CGERU( 0, 0, ALPHA, X, 0, Y, 1, A, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 7
+ CALL CGERU( 0, 0, ALPHA, X, 1, Y, 0, A, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 9
+ CALL CGERU( 2, 0, ALPHA, X, 1, Y, 1, A, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ GO TO 180
+ 140 INFOT = 1
+ CALL CHER( '/', 0, RALPHA, X, 1, A, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 2
+ CALL CHER( 'U', -1, RALPHA, X, 1, A, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 5
+ CALL CHER( 'U', 0, RALPHA, X, 0, A, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 7
+ CALL CHER( 'U', 2, RALPHA, X, 1, A, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ GO TO 180
+ 150 INFOT = 1
+ CALL CHPR( '/', 0, RALPHA, X, 1, A )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 2
+ CALL CHPR( 'U', -1, RALPHA, X, 1, A )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 5
+ CALL CHPR( 'U', 0, RALPHA, X, 0, A )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ GO TO 180
+ 160 INFOT = 1
+ CALL CHER2( '/', 0, ALPHA, X, 1, Y, 1, A, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 2
+ CALL CHER2( 'U', -1, ALPHA, X, 1, Y, 1, A, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 5
+ CALL CHER2( 'U', 0, ALPHA, X, 0, Y, 1, A, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 7
+ CALL CHER2( 'U', 0, ALPHA, X, 1, Y, 0, A, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 9
+ CALL CHER2( 'U', 2, ALPHA, X, 1, Y, 1, A, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ GO TO 180
+ 170 INFOT = 1
+ CALL CHPR2( '/', 0, ALPHA, X, 1, Y, 1, A )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 2
+ CALL CHPR2( 'U', -1, ALPHA, X, 1, Y, 1, A )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 5
+ CALL CHPR2( 'U', 0, ALPHA, X, 0, Y, 1, A )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 7
+ CALL CHPR2( 'U', 0, ALPHA, X, 1, Y, 0, A )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+*
+ 180 IF( OK )THEN
+ WRITE( NOUT, FMT = 9999 )SRNAMT
+ ELSE
+ WRITE( NOUT, FMT = 9998 )SRNAMT
+ END IF
+ RETURN
+*
+ 9999 FORMAT( ' ', A6, ' PASSED THE TESTS OF ERROR-EXITS' )
+ 9998 FORMAT( ' ******* ', A6, ' FAILED THE TESTS OF ERROR-EXITS *****',
+ $ '**' )
+*
+* End of CCHKE.
+*
+ END
+ SUBROUTINE CMAKE( TYPE, UPLO, DIAG, M, N, A, NMAX, AA, LDA, KL,
+ $ KU, RESET, TRANSL )
+*
+* Generates values for an M by N matrix A within the bandwidth
+* defined by KL and KU.
+* Stores the values in the array AA in the data structure required
+* by the routine, with unwanted elements set to rogue value.
+*
+* TYPE is 'GE', 'GB', 'HE', 'HB', 'HP', 'TR', 'TB' OR 'TP'.
+*
+* Auxiliary routine for test program for Level 2 Blas.
+*
+* -- Written on 10-August-1987.
+* Richard Hanson, Sandia National Labs.
+* Jeremy Du Croz, NAG Central Office.
+*
+* .. Parameters ..
+ COMPLEX ZERO, ONE
+ PARAMETER ( ZERO = ( 0.0, 0.0 ), ONE = ( 1.0, 0.0 ) )
+ COMPLEX ROGUE
+ PARAMETER ( ROGUE = ( -1.0E10, 1.0E10 ) )
+ REAL RZERO
+ PARAMETER ( RZERO = 0.0 )
+ REAL RROGUE
+ PARAMETER ( RROGUE = -1.0E10 )
+* .. Scalar Arguments ..
+ COMPLEX TRANSL
+ INTEGER KL, KU, LDA, M, N, NMAX
+ LOGICAL RESET
+ CHARACTER*1 DIAG, UPLO
+ CHARACTER*2 TYPE
+* .. Array Arguments ..
+ COMPLEX A( NMAX, * ), AA( * )
+* .. Local Scalars ..
+ INTEGER I, I1, I2, I3, IBEG, IEND, IOFF, J, JJ, KK
+ LOGICAL GEN, LOWER, SYM, TRI, UNIT, UPPER
+* .. External Functions ..
+ COMPLEX CBEG
+ EXTERNAL CBEG
+* .. Intrinsic Functions ..
+ INTRINSIC CMPLX, CONJG, MAX, MIN, REAL
+* .. Executable Statements ..
+ GEN = TYPE( 1: 1 ).EQ.'G'
+ SYM = TYPE( 1: 1 ).EQ.'H'
+ TRI = TYPE( 1: 1 ).EQ.'T'
+ UPPER = ( SYM.OR.TRI ).AND.UPLO.EQ.'U'
+ LOWER = ( SYM.OR.TRI ).AND.UPLO.EQ.'L'
+ UNIT = TRI.AND.DIAG.EQ.'U'
+*
+* Generate data in array A.
+*
+ DO 20 J = 1, N
+ DO 10 I = 1, M
+ IF( GEN.OR.( UPPER.AND.I.LE.J ).OR.( LOWER.AND.I.GE.J ) )
+ $ THEN
+ IF( ( I.LE.J.AND.J - I.LE.KU ).OR.
+ $ ( I.GE.J.AND.I - J.LE.KL ) )THEN
+ A( I, J ) = CBEG( RESET ) + TRANSL
+ ELSE
+ A( I, J ) = ZERO
+ END IF
+ IF( I.NE.J )THEN
+ IF( SYM )THEN
+ A( J, I ) = CONJG( A( I, J ) )
+ ELSE IF( TRI )THEN
+ A( J, I ) = ZERO
+ END IF
+ END IF
+ END IF
+ 10 CONTINUE
+ IF( SYM )
+ $ A( J, J ) = CMPLX( REAL( A( J, J ) ), RZERO )
+ IF( TRI )
+ $ A( J, J ) = A( J, J ) + ONE
+ IF( UNIT )
+ $ A( J, J ) = ONE
+ 20 CONTINUE
+*
+* Store elements in array AS in data structure required by routine.
+*
+ IF( TYPE.EQ.'GE' )THEN
+ DO 50 J = 1, N
+ DO 30 I = 1, M
+ AA( I + ( J - 1 )*LDA ) = A( I, J )
+ 30 CONTINUE
+ DO 40 I = M + 1, LDA
+ AA( I + ( J - 1 )*LDA ) = ROGUE
+ 40 CONTINUE
+ 50 CONTINUE
+ ELSE IF( TYPE.EQ.'GB' )THEN
+ DO 90 J = 1, N
+ DO 60 I1 = 1, KU + 1 - J
+ AA( I1 + ( J - 1 )*LDA ) = ROGUE
+ 60 CONTINUE
+ DO 70 I2 = I1, MIN( KL + KU + 1, KU + 1 + M - J )
+ AA( I2 + ( J - 1 )*LDA ) = A( I2 + J - KU - 1, J )
+ 70 CONTINUE
+ DO 80 I3 = I2, LDA
+ AA( I3 + ( J - 1 )*LDA ) = ROGUE
+ 80 CONTINUE
+ 90 CONTINUE
+ ELSE IF( TYPE.EQ.'HE'.OR.TYPE.EQ.'TR' )THEN
+ DO 130 J = 1, N
+ IF( UPPER )THEN
+ IBEG = 1
+ IF( UNIT )THEN
+ IEND = J - 1
+ ELSE
+ IEND = J
+ END IF
+ ELSE
+ IF( UNIT )THEN
+ IBEG = J + 1
+ ELSE
+ IBEG = J
+ END IF
+ IEND = N
+ END IF
+ DO 100 I = 1, IBEG - 1
+ AA( I + ( J - 1 )*LDA ) = ROGUE
+ 100 CONTINUE
+ DO 110 I = IBEG, IEND
+ AA( I + ( J - 1 )*LDA ) = A( I, J )
+ 110 CONTINUE
+ DO 120 I = IEND + 1, LDA
+ AA( I + ( J - 1 )*LDA ) = ROGUE
+ 120 CONTINUE
+ IF( SYM )THEN
+ JJ = J + ( J - 1 )*LDA
+ AA( JJ ) = CMPLX( REAL( AA( JJ ) ), RROGUE )
+ END IF
+ 130 CONTINUE
+ ELSE IF( TYPE.EQ.'HB'.OR.TYPE.EQ.'TB' )THEN
+ DO 170 J = 1, N
+ IF( UPPER )THEN
+ KK = KL + 1
+ IBEG = MAX( 1, KL + 2 - J )
+ IF( UNIT )THEN
+ IEND = KL
+ ELSE
+ IEND = KL + 1
+ END IF
+ ELSE
+ KK = 1
+ IF( UNIT )THEN
+ IBEG = 2
+ ELSE
+ IBEG = 1
+ END IF
+ IEND = MIN( KL + 1, 1 + M - J )
+ END IF
+ DO 140 I = 1, IBEG - 1
+ AA( I + ( J - 1 )*LDA ) = ROGUE
+ 140 CONTINUE
+ DO 150 I = IBEG, IEND
+ AA( I + ( J - 1 )*LDA ) = A( I + J - KK, J )
+ 150 CONTINUE
+ DO 160 I = IEND + 1, LDA
+ AA( I + ( J - 1 )*LDA ) = ROGUE
+ 160 CONTINUE
+ IF( SYM )THEN
+ JJ = KK + ( J - 1 )*LDA
+ AA( JJ ) = CMPLX( REAL( AA( JJ ) ), RROGUE )
+ END IF
+ 170 CONTINUE
+ ELSE IF( TYPE.EQ.'HP'.OR.TYPE.EQ.'TP' )THEN
+ IOFF = 0
+ DO 190 J = 1, N
+ IF( UPPER )THEN
+ IBEG = 1
+ IEND = J
+ ELSE
+ IBEG = J
+ IEND = N
+ END IF
+ DO 180 I = IBEG, IEND
+ IOFF = IOFF + 1
+ AA( IOFF ) = A( I, J )
+ IF( I.EQ.J )THEN
+ IF( UNIT )
+ $ AA( IOFF ) = ROGUE
+ IF( SYM )
+ $ AA( IOFF ) = CMPLX( REAL( AA( IOFF ) ), RROGUE )
+ END IF
+ 180 CONTINUE
+ 190 CONTINUE
+ END IF
+ RETURN
+*
+* End of CMAKE.
+*
+ END
+ SUBROUTINE CMVCH( TRANS, M, N, ALPHA, A, NMAX, X, INCX, BETA, Y,
+ $ INCY, YT, G, YY, EPS, ERR, FATAL, NOUT, MV )
+*
+* Checks the results of the computational tests.
+*
+* Auxiliary routine for test program for Level 2 Blas.
+*
+* -- Written on 10-August-1987.
+* Richard Hanson, Sandia National Labs.
+* Jeremy Du Croz, NAG Central Office.
+*
+* .. Parameters ..
+ COMPLEX ZERO
+ PARAMETER ( ZERO = ( 0.0, 0.0 ) )
+ REAL RZERO, RONE
+ PARAMETER ( RZERO = 0.0, RONE = 1.0 )
+* .. Scalar Arguments ..
+ COMPLEX ALPHA, BETA
+ REAL EPS, ERR
+ INTEGER INCX, INCY, M, N, NMAX, NOUT
+ LOGICAL FATAL, MV
+ CHARACTER*1 TRANS
+* .. Array Arguments ..
+ COMPLEX A( NMAX, * ), X( * ), Y( * ), YT( * ), YY( * )
+ REAL G( * )
+* .. Local Scalars ..
+ COMPLEX C
+ REAL ERRI
+ INTEGER I, INCXL, INCYL, IY, J, JX, KX, KY, ML, NL
+ LOGICAL CTRAN, TRAN
+* .. Intrinsic Functions ..
+ INTRINSIC ABS, AIMAG, CONJG, MAX, REAL, SQRT
+* .. Statement Functions ..
+ REAL ABS1
+* .. Statement Function definitions ..
+ ABS1( C ) = ABS( REAL( C ) ) + ABS( AIMAG( C ) )
+* .. Executable Statements ..
+ TRAN = TRANS.EQ.'T'
+ CTRAN = TRANS.EQ.'C'
+ IF( TRAN.OR.CTRAN )THEN
+ ML = N
+ NL = M
+ ELSE
+ ML = M
+ NL = N
+ END IF
+ IF( INCX.LT.0 )THEN
+ KX = NL
+ INCXL = -1
+ ELSE
+ KX = 1
+ INCXL = 1
+ END IF
+ IF( INCY.LT.0 )THEN
+ KY = ML
+ INCYL = -1
+ ELSE
+ KY = 1
+ INCYL = 1
+ END IF
+*
+* Compute expected result in YT using data in A, X and Y.
+* Compute gauges in G.
+*
+ IY = KY
+ DO 40 I = 1, ML
+ YT( IY ) = ZERO
+ G( IY ) = RZERO
+ JX = KX
+ IF( TRAN )THEN
+ DO 10 J = 1, NL
+ YT( IY ) = YT( IY ) + A( J, I )*X( JX )
+ G( IY ) = G( IY ) + ABS1( A( J, I ) )*ABS1( X( JX ) )
+ JX = JX + INCXL
+ 10 CONTINUE
+ ELSE IF( CTRAN )THEN
+ DO 20 J = 1, NL
+ YT( IY ) = YT( IY ) + CONJG( A( J, I ) )*X( JX )
+ G( IY ) = G( IY ) + ABS1( A( J, I ) )*ABS1( X( JX ) )
+ JX = JX + INCXL
+ 20 CONTINUE
+ ELSE
+ DO 30 J = 1, NL
+ YT( IY ) = YT( IY ) + A( I, J )*X( JX )
+ G( IY ) = G( IY ) + ABS1( A( I, J ) )*ABS1( X( JX ) )
+ JX = JX + INCXL
+ 30 CONTINUE
+ END IF
+ YT( IY ) = ALPHA*YT( IY ) + BETA*Y( IY )
+ G( IY ) = ABS1( ALPHA )*G( IY ) + ABS1( BETA )*ABS1( Y( IY ) )
+ IY = IY + INCYL
+ 40 CONTINUE
+*
+* Compute the error ratio for this result.
+*
+ ERR = ZERO
+ DO 50 I = 1, ML
+ ERRI = ABS( YT( I ) - YY( 1 + ( I - 1 )*ABS( INCY ) ) )/EPS
+ IF( G( I ).NE.RZERO )
+ $ ERRI = ERRI/G( I )
+ ERR = MAX( ERR, ERRI )
+ IF( ERR*SQRT( EPS ).GE.RONE )
+ $ GO TO 60
+ 50 CONTINUE
+* If the loop completes, all results are at least half accurate.
+ GO TO 80
+*
+* Report fatal error.
+*
+ 60 FATAL = .TRUE.
+ WRITE( NOUT, FMT = 9999 )
+ DO 70 I = 1, ML
+ IF( MV )THEN
+ WRITE( NOUT, FMT = 9998 )I, YT( I ),
+ $ YY( 1 + ( I - 1 )*ABS( INCY ) )
+ ELSE
+ WRITE( NOUT, FMT = 9998 )I,
+ $ YY( 1 + ( I - 1 )*ABS( INCY ) ), YT( I )
+ END IF
+ 70 CONTINUE
+*
+ 80 CONTINUE
+ RETURN
+*
+ 9999 FORMAT( ' ******* FATAL ERROR - COMPUTED RESULT IS LESS THAN HAL',
+ $ 'F ACCURATE *******', /' EXPECTED RE',
+ $ 'SULT COMPUTED RESULT' )
+ 9998 FORMAT( 1X, I7, 2( ' (', G15.6, ',', G15.6, ')' ) )
+*
+* End of CMVCH.
+*
+ END
+ LOGICAL FUNCTION LCE( RI, RJ, LR )
+*
+* Tests if two arrays are identical.
+*
+* Auxiliary routine for test program for Level 2 Blas.
+*
+* -- Written on 10-August-1987.
+* Richard Hanson, Sandia National Labs.
+* Jeremy Du Croz, NAG Central Office.
+*
+* .. Scalar Arguments ..
+ INTEGER LR
+* .. Array Arguments ..
+ COMPLEX RI( * ), RJ( * )
+* .. Local Scalars ..
+ INTEGER I
+* .. Executable Statements ..
+ DO 10 I = 1, LR
+ IF( RI( I ).NE.RJ( I ) )
+ $ GO TO 20
+ 10 CONTINUE
+ LCE = .TRUE.
+ GO TO 30
+ 20 CONTINUE
+ LCE = .FALSE.
+ 30 RETURN
+*
+* End of LCE.
+*
+ END
+ LOGICAL FUNCTION LCERES( TYPE, UPLO, M, N, AA, AS, LDA )
+*
+* Tests if selected elements in two arrays are equal.
+*
+* TYPE is 'GE', 'HE' or 'HP'.
+*
+* Auxiliary routine for test program for Level 2 Blas.
+*
+* -- Written on 10-August-1987.
+* Richard Hanson, Sandia National Labs.
+* Jeremy Du Croz, NAG Central Office.
+*
+* .. Scalar Arguments ..
+ INTEGER LDA, M, N
+ CHARACTER*1 UPLO
+ CHARACTER*2 TYPE
+* .. Array Arguments ..
+ COMPLEX AA( LDA, * ), AS( LDA, * )
+* .. Local Scalars ..
+ INTEGER I, IBEG, IEND, J
+ LOGICAL UPPER
+* .. Executable Statements ..
+ UPPER = UPLO.EQ.'U'
+ IF( TYPE.EQ.'GE' )THEN
+ DO 20 J = 1, N
+ DO 10 I = M + 1, LDA
+ IF( AA( I, J ).NE.AS( I, J ) )
+ $ GO TO 70
+ 10 CONTINUE
+ 20 CONTINUE
+ ELSE IF( TYPE.EQ.'HE' )THEN
+ DO 50 J = 1, N
+ IF( UPPER )THEN
+ IBEG = 1
+ IEND = J
+ ELSE
+ IBEG = J
+ IEND = N
+ END IF
+ DO 30 I = 1, IBEG - 1
+ IF( AA( I, J ).NE.AS( I, J ) )
+ $ GO TO 70
+ 30 CONTINUE
+ DO 40 I = IEND + 1, LDA
+ IF( AA( I, J ).NE.AS( I, J ) )
+ $ GO TO 70
+ 40 CONTINUE
+ 50 CONTINUE
+ END IF
+*
+ LCERES = .TRUE.
+ GO TO 80
+ 70 CONTINUE
+ LCERES = .FALSE.
+ 80 RETURN
+*
+* End of LCERES.
+*
+ END
+ COMPLEX FUNCTION CBEG( RESET )
+*
+* Generates complex numbers as pairs of random numbers uniformly
+* distributed between -0.5 and 0.5.
+*
+* Auxiliary routine for test program for Level 2 Blas.
+*
+* -- Written on 10-August-1987.
+* Richard Hanson, Sandia National Labs.
+* Jeremy Du Croz, NAG Central Office.
+*
+* .. Scalar Arguments ..
+ LOGICAL RESET
+* .. Local Scalars ..
+ INTEGER I, IC, J, MI, MJ
+* .. Save statement ..
+ SAVE I, IC, J, MI, MJ
+* .. Intrinsic Functions ..
+ INTRINSIC CMPLX
+* .. Executable Statements ..
+ IF( RESET )THEN
+* Initialize local variables.
+ MI = 891
+ MJ = 457
+ I = 7
+ J = 7
+ IC = 0
+ RESET = .FALSE.
+ END IF
+*
+* The sequence of values of I or J is bounded between 1 and 999.
+* If initial I or J = 1,2,3,6,7 or 9, the period will be 50.
+* If initial I or J = 4 or 8, the period will be 25.
+* If initial I or J = 5, the period will be 10.
+* IC is used to break up the period by skipping 1 value of I or J
+* in 6.
+*
+ IC = IC + 1
+ 10 I = I*MI
+ J = J*MJ
+ I = I - 1000*( I/1000 )
+ J = J - 1000*( J/1000 )
+ IF( IC.GE.5 )THEN
+ IC = 0
+ GO TO 10
+ END IF
+ CBEG = CMPLX( ( I - 500 )/1001.0, ( J - 500 )/1001.0 )
+ RETURN
+*
+* End of CBEG.
+*
+ END
+ REAL FUNCTION SDIFF( X, Y )
+*
+* Auxiliary routine for test program for Level 2 Blas.
+*
+* -- Written on 10-August-1987.
+* Richard Hanson, Sandia National Labs.
+*
+* .. Scalar Arguments ..
+ REAL X, Y
+* .. Executable Statements ..
+ SDIFF = X - Y
+ RETURN
+*
+* End of SDIFF.
+*
+ END
+ SUBROUTINE CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+*
+* Tests whether XERBLA has detected an error when it should.
+*
+* Auxiliary routine for test program for Level 2 Blas.
+*
+* -- Written on 10-August-1987.
+* Richard Hanson, Sandia National Labs.
+* Jeremy Du Croz, NAG Central Office.
+*
+* .. Scalar Arguments ..
+ INTEGER INFOT, NOUT
+ LOGICAL LERR, OK
+ CHARACTER*6 SRNAMT
+* .. Executable Statements ..
+ IF( .NOT.LERR )THEN
+ WRITE( NOUT, FMT = 9999 )INFOT, SRNAMT
+ OK = .FALSE.
+ END IF
+ LERR = .FALSE.
+ RETURN
+*
+ 9999 FORMAT( ' ***** ILLEGAL VALUE OF PARAMETER NUMBER ', I2, ' NOT D',
+ $ 'ETECTED BY ', A6, ' *****' )
+*
+* End of CHKXER.
+*
+ END
+ SUBROUTINE XERBLA( SRNAME, INFO )
+*
+* This is a special version of XERBLA to be used only as part of
+* the test program for testing error exits from the Level 2 BLAS
+* routines.
+*
+* XERBLA is an error handler for the Level 2 BLAS routines.
+*
+* It is called by the Level 2 BLAS routines if an input parameter is
+* invalid.
+*
+* Auxiliary routine for test program for Level 2 Blas.
+*
+* -- Written on 10-August-1987.
+* Richard Hanson, Sandia National Labs.
+* Jeremy Du Croz, NAG Central Office.
+*
+* .. Scalar Arguments ..
+ INTEGER INFO
+ CHARACTER*6 SRNAME
+* .. Scalars in Common ..
+ INTEGER INFOT, NOUT
+ LOGICAL LERR, OK
+ CHARACTER*6 SRNAMT
+* .. Common blocks ..
+ COMMON /INFOC/INFOT, NOUT, OK, LERR
+ COMMON /SRNAMC/SRNAMT
+* .. Executable Statements ..
+ LERR = .TRUE.
+ IF( INFO.NE.INFOT )THEN
+ IF( INFOT.NE.0 )THEN
+ WRITE( NOUT, FMT = 9999 )INFO, INFOT
+ ELSE
+ WRITE( NOUT, FMT = 9997 )INFO
+ END IF
+ OK = .FALSE.
+ END IF
+ IF( SRNAME.NE.SRNAMT )THEN
+ WRITE( NOUT, FMT = 9998 )SRNAME, SRNAMT
+ OK = .FALSE.
+ END IF
+ RETURN
+*
+ 9999 FORMAT( ' ******* XERBLA WAS CALLED WITH INFO = ', I6, ' INSTEAD',
+ $ ' OF ', I2, ' *******' )
+ 9998 FORMAT( ' ******* XERBLA WAS CALLED WITH SRNAME = ', A6, ' INSTE',
+ $ 'AD OF ', A6, ' *******' )
+ 9997 FORMAT( ' ******* XERBLA WAS CALLED WITH INFO = ', I6,
+ $ ' *******' )
+*
+* End of XERBLA
+*
+ END
+
diff --git a/blas/testing/cblat3.dat b/blas/testing/cblat3.dat
new file mode 100644
index 0000000..59881ea
--- /dev/null
+++ b/blas/testing/cblat3.dat
@@ -0,0 +1,23 @@
+'cblat3.summ' NAME OF SUMMARY OUTPUT FILE
+6 UNIT NUMBER OF SUMMARY FILE
+'cblat3.snap' NAME OF SNAPSHOT OUTPUT FILE
+-1 UNIT NUMBER OF SNAPSHOT FILE (NOT USED IF .LT. 0)
+F LOGICAL FLAG, T TO REWIND SNAPSHOT FILE AFTER EACH RECORD.
+F LOGICAL FLAG, T TO STOP ON FAILURES.
+F LOGICAL FLAG, T TO TEST ERROR EXITS.
+16.0 THRESHOLD VALUE OF TEST RATIO
+6 NUMBER OF VALUES OF N
+0 1 2 3 5 9 VALUES OF N
+3 NUMBER OF VALUES OF ALPHA
+(0.0,0.0) (1.0,0.0) (0.7,-0.9) VALUES OF ALPHA
+3 NUMBER OF VALUES OF BETA
+(0.0,0.0) (1.0,0.0) (1.3,-1.1) VALUES OF BETA
+CGEMM T PUT F FOR NO TEST. SAME COLUMNS.
+CHEMM T PUT F FOR NO TEST. SAME COLUMNS.
+CSYMM T PUT F FOR NO TEST. SAME COLUMNS.
+CTRMM T PUT F FOR NO TEST. SAME COLUMNS.
+CTRSM T PUT F FOR NO TEST. SAME COLUMNS.
+CHERK T PUT F FOR NO TEST. SAME COLUMNS.
+CSYRK T PUT F FOR NO TEST. SAME COLUMNS.
+CHER2K T PUT F FOR NO TEST. SAME COLUMNS.
+CSYR2K T PUT F FOR NO TEST. SAME COLUMNS.
diff --git a/blas/testing/cblat3.f b/blas/testing/cblat3.f
new file mode 100644
index 0000000..09f2cb9
--- /dev/null
+++ b/blas/testing/cblat3.f
@@ -0,0 +1,3492 @@
+*> \brief \b CBLAT3
+*
+* =========== DOCUMENTATION ===========
+*
+* Online html documentation available at
+* http://www.netlib.org/lapack/explore-html/
+*
+* Definition:
+* ===========
+*
+* PROGRAM CBLAT3
+*
+*
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
+*>
+*> Test program for the COMPLEX Level 3 Blas.
+*>
+*> The program must be driven by a short data file. The first 14 records
+*> of the file are read using list-directed input, the last 9 records
+*> are read using the format ( A6, L2 ). An annotated example of a data
+*> file can be obtained by deleting the first 3 characters from the
+*> following 23 lines:
+*> 'cblat3.out' NAME OF SUMMARY OUTPUT FILE
+*> 6 UNIT NUMBER OF SUMMARY FILE
+*> 'CBLAT3.SNAP' NAME OF SNAPSHOT OUTPUT FILE
+*> -1 UNIT NUMBER OF SNAPSHOT FILE (NOT USED IF .LT. 0)
+*> F LOGICAL FLAG, T TO REWIND SNAPSHOT FILE AFTER EACH RECORD.
+*> F LOGICAL FLAG, T TO STOP ON FAILURES.
+*> T LOGICAL FLAG, T TO TEST ERROR EXITS.
+*> 16.0 THRESHOLD VALUE OF TEST RATIO
+*> 6 NUMBER OF VALUES OF N
+*> 0 1 2 3 5 9 VALUES OF N
+*> 3 NUMBER OF VALUES OF ALPHA
+*> (0.0,0.0) (1.0,0.0) (0.7,-0.9) VALUES OF ALPHA
+*> 3 NUMBER OF VALUES OF BETA
+*> (0.0,0.0) (1.0,0.0) (1.3,-1.1) VALUES OF BETA
+*> CGEMM T PUT F FOR NO TEST. SAME COLUMNS.
+*> CHEMM T PUT F FOR NO TEST. SAME COLUMNS.
+*> CSYMM T PUT F FOR NO TEST. SAME COLUMNS.
+*> CTRMM T PUT F FOR NO TEST. SAME COLUMNS.
+*> CTRSM T PUT F FOR NO TEST. SAME COLUMNS.
+*> CHERK T PUT F FOR NO TEST. SAME COLUMNS.
+*> CSYRK T PUT F FOR NO TEST. SAME COLUMNS.
+*> CHER2K T PUT F FOR NO TEST. SAME COLUMNS.
+*> CSYR2K T PUT F FOR NO TEST. SAME COLUMNS.
+*>
+*> Further Details
+*> ===============
+*>
+*> See:
+*>
+*> Dongarra J. J., Du Croz J. J., Duff I. S. and Hammarling S.
+*> A Set of Level 3 Basic Linear Algebra Subprograms.
+*>
+*> Technical Memorandum No.88 (Revision 1), Mathematics and
+*> Computer Science Division, Argonne National Laboratory, 9700
+*> South Cass Avenue, Argonne, Illinois 60439, US.
+*>
+*> -- Written on 8-February-1989.
+*> Jack Dongarra, Argonne National Laboratory.
+*> Iain Duff, AERE Harwell.
+*> Jeremy Du Croz, Numerical Algorithms Group Ltd.
+*> Sven Hammarling, Numerical Algorithms Group Ltd.
+*>
+*> 10-9-00: Change STATUS='NEW' to 'UNKNOWN' so that the testers
+*> can be run multiple times without deleting generated
+*> output files (susan)
+*> \endverbatim
+*
+* Authors:
+* ========
+*
+*> \author Univ. of Tennessee
+*> \author Univ. of California Berkeley
+*> \author Univ. of Colorado Denver
+*> \author NAG Ltd.
+*
+*> \date April 2012
+*
+*> \ingroup complex_blas_testing
+*
+* =====================================================================
+ PROGRAM CBLAT3
+*
+* -- Reference BLAS test routine (version 3.4.1) --
+* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
+* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+* April 2012
+*
+* =====================================================================
+*
+* .. Parameters ..
+ INTEGER NIN
+ PARAMETER ( NIN = 5 )
+ INTEGER NSUBS
+ PARAMETER ( NSUBS = 9 )
+ COMPLEX ZERO, ONE
+ PARAMETER ( ZERO = ( 0.0, 0.0 ), ONE = ( 1.0, 0.0 ) )
+ REAL RZERO
+ PARAMETER ( RZERO = 0.0 )
+ INTEGER NMAX
+ PARAMETER ( NMAX = 65 )
+ INTEGER NIDMAX, NALMAX, NBEMAX
+ PARAMETER ( NIDMAX = 9, NALMAX = 7, NBEMAX = 7 )
+* .. Local Scalars ..
+ REAL EPS, ERR, THRESH
+ INTEGER I, ISNUM, J, N, NALF, NBET, NIDIM, NOUT, NTRA
+ LOGICAL FATAL, LTESTT, REWI, SAME, SFATAL, TRACE,
+ $ TSTERR
+ CHARACTER*1 TRANSA, TRANSB
+ CHARACTER*6 SNAMET
+ CHARACTER*32 SNAPS, SUMMRY
+* .. Local Arrays ..
+ COMPLEX AA( NMAX*NMAX ), AB( NMAX, 2*NMAX ),
+ $ ALF( NALMAX ), AS( NMAX*NMAX ),
+ $ BB( NMAX*NMAX ), BET( NBEMAX ),
+ $ BS( NMAX*NMAX ), C( NMAX, NMAX ),
+ $ CC( NMAX*NMAX ), CS( NMAX*NMAX ), CT( NMAX ),
+ $ W( 2*NMAX )
+ REAL G( NMAX )
+ INTEGER IDIM( NIDMAX )
+ LOGICAL LTEST( NSUBS )
+ CHARACTER*6 SNAMES( NSUBS )
+* .. External Functions ..
+ REAL SDIFF
+ LOGICAL LCE
+ EXTERNAL SDIFF, LCE
+* .. External Subroutines ..
+ EXTERNAL CCHK1, CCHK2, CCHK3, CCHK4, CCHK5, CCHKE, CMMCH
+* .. Intrinsic Functions ..
+ INTRINSIC MAX, MIN
+* .. Scalars in Common ..
+ INTEGER INFOT, NOUTC
+ LOGICAL LERR, OK
+ CHARACTER*6 SRNAMT
+* .. Common blocks ..
+ COMMON /INFOC/INFOT, NOUTC, OK, LERR
+ COMMON /SRNAMC/SRNAMT
+* .. Data statements ..
+ DATA SNAMES/'CGEMM ', 'CHEMM ', 'CSYMM ', 'CTRMM ',
+ $ 'CTRSM ', 'CHERK ', 'CSYRK ', 'CHER2K',
+ $ 'CSYR2K'/
+* .. Executable Statements ..
+*
+* Read name and unit number for summary output file and open file.
+*
+ READ( NIN, FMT = * )SUMMRY
+ READ( NIN, FMT = * )NOUT
+ OPEN( NOUT, FILE = SUMMRY )
+ NOUTC = NOUT
+*
+* Read name and unit number for snapshot output file and open file.
+*
+ READ( NIN, FMT = * )SNAPS
+ READ( NIN, FMT = * )NTRA
+ TRACE = NTRA.GE.0
+ IF( TRACE )THEN
+ OPEN( NTRA, FILE = SNAPS )
+ END IF
+* Read the flag that directs rewinding of the snapshot file.
+ READ( NIN, FMT = * )REWI
+ REWI = REWI.AND.TRACE
+* Read the flag that directs stopping on any failure.
+ READ( NIN, FMT = * )SFATAL
+* Read the flag that indicates whether error exits are to be tested.
+ READ( NIN, FMT = * )TSTERR
+* Read the threshold value of the test ratio
+ READ( NIN, FMT = * )THRESH
+*
+* Read and check the parameter values for the tests.
+*
+* Values of N
+ READ( NIN, FMT = * )NIDIM
+ IF( NIDIM.LT.1.OR.NIDIM.GT.NIDMAX )THEN
+ WRITE( NOUT, FMT = 9997 )'N', NIDMAX
+ GO TO 220
+ END IF
+ READ( NIN, FMT = * )( IDIM( I ), I = 1, NIDIM )
+ DO 10 I = 1, NIDIM
+ IF( IDIM( I ).LT.0.OR.IDIM( I ).GT.NMAX )THEN
+ WRITE( NOUT, FMT = 9996 )NMAX
+ GO TO 220
+ END IF
+ 10 CONTINUE
+* Values of ALPHA
+ READ( NIN, FMT = * )NALF
+ IF( NALF.LT.1.OR.NALF.GT.NALMAX )THEN
+ WRITE( NOUT, FMT = 9997 )'ALPHA', NALMAX
+ GO TO 220
+ END IF
+ READ( NIN, FMT = * )( ALF( I ), I = 1, NALF )
+* Values of BETA
+ READ( NIN, FMT = * )NBET
+ IF( NBET.LT.1.OR.NBET.GT.NBEMAX )THEN
+ WRITE( NOUT, FMT = 9997 )'BETA', NBEMAX
+ GO TO 220
+ END IF
+ READ( NIN, FMT = * )( BET( I ), I = 1, NBET )
+*
+* Report values of parameters.
+*
+ WRITE( NOUT, FMT = 9995 )
+ WRITE( NOUT, FMT = 9994 )( IDIM( I ), I = 1, NIDIM )
+ WRITE( NOUT, FMT = 9993 )( ALF( I ), I = 1, NALF )
+ WRITE( NOUT, FMT = 9992 )( BET( I ), I = 1, NBET )
+ IF( .NOT.TSTERR )THEN
+ WRITE( NOUT, FMT = * )
+ WRITE( NOUT, FMT = 9984 )
+ END IF
+ WRITE( NOUT, FMT = * )
+ WRITE( NOUT, FMT = 9999 )THRESH
+ WRITE( NOUT, FMT = * )
+*
+* Read names of subroutines and flags which indicate
+* whether they are to be tested.
+*
+ DO 20 I = 1, NSUBS
+ LTEST( I ) = .FALSE.
+ 20 CONTINUE
+ 30 READ( NIN, FMT = 9988, END = 60 )SNAMET, LTESTT
+ DO 40 I = 1, NSUBS
+ IF( SNAMET.EQ.SNAMES( I ) )
+ $ GO TO 50
+ 40 CONTINUE
+ WRITE( NOUT, FMT = 9990 )SNAMET
+ STOP
+ 50 LTEST( I ) = LTESTT
+ GO TO 30
+*
+ 60 CONTINUE
+ CLOSE ( NIN )
+*
+* Compute EPS (the machine precision).
+*
+ EPS = EPSILON(RZERO)
+ WRITE( NOUT, FMT = 9998 )EPS
+*
+* Check the reliability of CMMCH using exact data.
+*
+ N = MIN( 32, NMAX )
+ DO 100 J = 1, N
+ DO 90 I = 1, N
+ AB( I, J ) = MAX( I - J + 1, 0 )
+ 90 CONTINUE
+ AB( J, NMAX + 1 ) = J
+ AB( 1, NMAX + J ) = J
+ C( J, 1 ) = ZERO
+ 100 CONTINUE
+ DO 110 J = 1, N
+ CC( J ) = J*( ( J + 1 )*J )/2 - ( ( J + 1 )*J*( J - 1 ) )/3
+ 110 CONTINUE
+* CC holds the exact result. On exit from CMMCH CT holds
+* the result computed by CMMCH.
+ TRANSA = 'N'
+ TRANSB = 'N'
+ CALL CMMCH( TRANSA, TRANSB, N, 1, N, ONE, AB, NMAX,
+ $ AB( 1, NMAX + 1 ), NMAX, ZERO, C, NMAX, CT, G, CC,
+ $ NMAX, EPS, ERR, FATAL, NOUT, .TRUE. )
+ SAME = LCE( CC, CT, N )
+ IF( .NOT.SAME.OR.ERR.NE.RZERO )THEN
+ WRITE( NOUT, FMT = 9989 )TRANSA, TRANSB, SAME, ERR
+ STOP
+ END IF
+ TRANSB = 'C'
+ CALL CMMCH( TRANSA, TRANSB, N, 1, N, ONE, AB, NMAX,
+ $ AB( 1, NMAX + 1 ), NMAX, ZERO, C, NMAX, CT, G, CC,
+ $ NMAX, EPS, ERR, FATAL, NOUT, .TRUE. )
+ SAME = LCE( CC, CT, N )
+ IF( .NOT.SAME.OR.ERR.NE.RZERO )THEN
+ WRITE( NOUT, FMT = 9989 )TRANSA, TRANSB, SAME, ERR
+ STOP
+ END IF
+ DO 120 J = 1, N
+ AB( J, NMAX + 1 ) = N - J + 1
+ AB( 1, NMAX + J ) = N - J + 1
+ 120 CONTINUE
+ DO 130 J = 1, N
+ CC( N - J + 1 ) = J*( ( J + 1 )*J )/2 -
+ $ ( ( J + 1 )*J*( J - 1 ) )/3
+ 130 CONTINUE
+ TRANSA = 'C'
+ TRANSB = 'N'
+ CALL CMMCH( TRANSA, TRANSB, N, 1, N, ONE, AB, NMAX,
+ $ AB( 1, NMAX + 1 ), NMAX, ZERO, C, NMAX, CT, G, CC,
+ $ NMAX, EPS, ERR, FATAL, NOUT, .TRUE. )
+ SAME = LCE( CC, CT, N )
+ IF( .NOT.SAME.OR.ERR.NE.RZERO )THEN
+ WRITE( NOUT, FMT = 9989 )TRANSA, TRANSB, SAME, ERR
+ STOP
+ END IF
+ TRANSB = 'C'
+ CALL CMMCH( TRANSA, TRANSB, N, 1, N, ONE, AB, NMAX,
+ $ AB( 1, NMAX + 1 ), NMAX, ZERO, C, NMAX, CT, G, CC,
+ $ NMAX, EPS, ERR, FATAL, NOUT, .TRUE. )
+ SAME = LCE( CC, CT, N )
+ IF( .NOT.SAME.OR.ERR.NE.RZERO )THEN
+ WRITE( NOUT, FMT = 9989 )TRANSA, TRANSB, SAME, ERR
+ STOP
+ END IF
+*
+* Test each subroutine in turn.
+*
+ DO 200 ISNUM = 1, NSUBS
+ WRITE( NOUT, FMT = * )
+ IF( .NOT.LTEST( ISNUM ) )THEN
+* Subprogram is not to be tested.
+ WRITE( NOUT, FMT = 9987 )SNAMES( ISNUM )
+ ELSE
+ SRNAMT = SNAMES( ISNUM )
+* Test error exits.
+ IF( TSTERR )THEN
+ CALL CCHKE( ISNUM, SNAMES( ISNUM ), NOUT )
+ WRITE( NOUT, FMT = * )
+ END IF
+* Test computations.
+ INFOT = 0
+ OK = .TRUE.
+ FATAL = .FALSE.
+ GO TO ( 140, 150, 150, 160, 160, 170, 170,
+ $ 180, 180 )ISNUM
+* Test CGEMM, 01.
+ 140 CALL CCHK1( SNAMES( ISNUM ), EPS, THRESH, NOUT, NTRA, TRACE,
+ $ REWI, FATAL, NIDIM, IDIM, NALF, ALF, NBET, BET,
+ $ NMAX, AB, AA, AS, AB( 1, NMAX + 1 ), BB, BS, C,
+ $ CC, CS, CT, G )
+ GO TO 190
+* Test CHEMM, 02, CSYMM, 03.
+ 150 CALL CCHK2( SNAMES( ISNUM ), EPS, THRESH, NOUT, NTRA, TRACE,
+ $ REWI, FATAL, NIDIM, IDIM, NALF, ALF, NBET, BET,
+ $ NMAX, AB, AA, AS, AB( 1, NMAX + 1 ), BB, BS, C,
+ $ CC, CS, CT, G )
+ GO TO 190
+* Test CTRMM, 04, CTRSM, 05.
+ 160 CALL CCHK3( SNAMES( ISNUM ), EPS, THRESH, NOUT, NTRA, TRACE,
+ $ REWI, FATAL, NIDIM, IDIM, NALF, ALF, NMAX, AB,
+ $ AA, AS, AB( 1, NMAX + 1 ), BB, BS, CT, G, C )
+ GO TO 190
+* Test CHERK, 06, CSYRK, 07.
+ 170 CALL CCHK4( SNAMES( ISNUM ), EPS, THRESH, NOUT, NTRA, TRACE,
+ $ REWI, FATAL, NIDIM, IDIM, NALF, ALF, NBET, BET,
+ $ NMAX, AB, AA, AS, AB( 1, NMAX + 1 ), BB, BS, C,
+ $ CC, CS, CT, G )
+ GO TO 190
+* Test CHER2K, 08, CSYR2K, 09.
+ 180 CALL CCHK5( SNAMES( ISNUM ), EPS, THRESH, NOUT, NTRA, TRACE,
+ $ REWI, FATAL, NIDIM, IDIM, NALF, ALF, NBET, BET,
+ $ NMAX, AB, AA, AS, BB, BS, C, CC, CS, CT, G, W )
+ GO TO 190
+*
+ 190 IF( FATAL.AND.SFATAL )
+ $ GO TO 210
+ END IF
+ 200 CONTINUE
+ WRITE( NOUT, FMT = 9986 )
+ GO TO 230
+*
+ 210 CONTINUE
+ WRITE( NOUT, FMT = 9985 )
+ GO TO 230
+*
+ 220 CONTINUE
+ WRITE( NOUT, FMT = 9991 )
+*
+ 230 CONTINUE
+ IF( TRACE )
+ $ CLOSE ( NTRA )
+ CLOSE ( NOUT )
+ STOP
+*
+ 9999 FORMAT( ' ROUTINES PASS COMPUTATIONAL TESTS IF TEST RATIO IS LES',
+ $ 'S THAN', F8.2 )
+ 9998 FORMAT( ' RELATIVE MACHINE PRECISION IS TAKEN TO BE', 1P, E9.1 )
+ 9997 FORMAT( ' NUMBER OF VALUES OF ', A, ' IS LESS THAN 1 OR GREATER ',
+ $ 'THAN ', I2 )
+ 9996 FORMAT( ' VALUE OF N IS LESS THAN 0 OR GREATER THAN ', I2 )
+ 9995 FORMAT( ' TESTS OF THE COMPLEX LEVEL 3 BLAS', //' THE F',
+ $ 'OLLOWING PARAMETER VALUES WILL BE USED:' )
+ 9994 FORMAT( ' FOR N ', 9I6 )
+ 9993 FORMAT( ' FOR ALPHA ',
+ $ 7( '(', F4.1, ',', F4.1, ') ', : ) )
+ 9992 FORMAT( ' FOR BETA ',
+ $ 7( '(', F4.1, ',', F4.1, ') ', : ) )
+ 9991 FORMAT( ' AMEND DATA FILE OR INCREASE ARRAY SIZES IN PROGRAM',
+ $ /' ******* TESTS ABANDONED *******' )
+ 9990 FORMAT( ' SUBPROGRAM NAME ', A6, ' NOT RECOGNIZED', /' ******* T',
+ $ 'ESTS ABANDONED *******' )
+ 9989 FORMAT( ' ERROR IN CMMCH - IN-LINE DOT PRODUCTS ARE BEING EVALU',
+ $ 'ATED WRONGLY.', /' CMMCH WAS CALLED WITH TRANSA = ', A1,
+ $ ' AND TRANSB = ', A1, /' AND RETURNED SAME = ', L1, ' AND ',
+ $ 'ERR = ', F12.3, '.', /' THIS MAY BE DUE TO FAULTS IN THE ',
+ $ 'ARITHMETIC OR THE COMPILER.', /' ******* TESTS ABANDONED ',
+ $ '*******' )
+ 9988 FORMAT( A6, L2 )
+ 9987 FORMAT( 1X, A6, ' WAS NOT TESTED' )
+ 9986 FORMAT( /' END OF TESTS' )
+ 9985 FORMAT( /' ******* FATAL ERROR - TESTS ABANDONED *******' )
+ 9984 FORMAT( ' ERROR-EXITS WILL NOT BE TESTED' )
+*
+* End of CBLAT3.
+*
+ END
+ SUBROUTINE CCHK1( SNAME, EPS, THRESH, NOUT, NTRA, TRACE, REWI,
+ $ FATAL, NIDIM, IDIM, NALF, ALF, NBET, BET, NMAX,
+ $ A, AA, AS, B, BB, BS, C, CC, CS, CT, G )
+*
+* Tests CGEMM.
+*
+* Auxiliary routine for test program for Level 3 Blas.
+*
+* -- Written on 8-February-1989.
+* Jack Dongarra, Argonne National Laboratory.
+* Iain Duff, AERE Harwell.
+* Jeremy Du Croz, Numerical Algorithms Group Ltd.
+* Sven Hammarling, Numerical Algorithms Group Ltd.
+*
+* .. Parameters ..
+ COMPLEX ZERO
+ PARAMETER ( ZERO = ( 0.0, 0.0 ) )
+ REAL RZERO
+ PARAMETER ( RZERO = 0.0 )
+* .. Scalar Arguments ..
+ REAL EPS, THRESH
+ INTEGER NALF, NBET, NIDIM, NMAX, NOUT, NTRA
+ LOGICAL FATAL, REWI, TRACE
+ CHARACTER*6 SNAME
+* .. Array Arguments ..
+ COMPLEX A( NMAX, NMAX ), AA( NMAX*NMAX ), ALF( NALF ),
+ $ AS( NMAX*NMAX ), B( NMAX, NMAX ),
+ $ BB( NMAX*NMAX ), BET( NBET ), BS( NMAX*NMAX ),
+ $ C( NMAX, NMAX ), CC( NMAX*NMAX ),
+ $ CS( NMAX*NMAX ), CT( NMAX )
+ REAL G( NMAX )
+ INTEGER IDIM( NIDIM )
+* .. Local Scalars ..
+ COMPLEX ALPHA, ALS, BETA, BLS
+ REAL ERR, ERRMAX
+ INTEGER I, IA, IB, ICA, ICB, IK, IM, IN, K, KS, LAA,
+ $ LBB, LCC, LDA, LDAS, LDB, LDBS, LDC, LDCS, M,
+ $ MA, MB, MS, N, NA, NARGS, NB, NC, NS
+ LOGICAL NULL, RESET, SAME, TRANA, TRANB
+ CHARACTER*1 TRANAS, TRANBS, TRANSA, TRANSB
+ CHARACTER*3 ICH
+* .. Local Arrays ..
+ LOGICAL ISAME( 13 )
+* .. External Functions ..
+ LOGICAL LCE, LCERES
+ EXTERNAL LCE, LCERES
+* .. External Subroutines ..
+ EXTERNAL CGEMM, CMAKE, CMMCH
+* .. Intrinsic Functions ..
+ INTRINSIC MAX
+* .. Scalars in Common ..
+ INTEGER INFOT, NOUTC
+ LOGICAL LERR, OK
+* .. Common blocks ..
+ COMMON /INFOC/INFOT, NOUTC, OK, LERR
+* .. Data statements ..
+ DATA ICH/'NTC'/
+* .. Executable Statements ..
+*
+ NARGS = 13
+ NC = 0
+ RESET = .TRUE.
+ ERRMAX = RZERO
+*
+ DO 110 IM = 1, NIDIM
+ M = IDIM( IM )
+*
+ DO 100 IN = 1, NIDIM
+ N = IDIM( IN )
+* Set LDC to 1 more than minimum value if room.
+ LDC = M
+ IF( LDC.LT.NMAX )
+ $ LDC = LDC + 1
+* Skip tests if not enough room.
+ IF( LDC.GT.NMAX )
+ $ GO TO 100
+ LCC = LDC*N
+ NULL = N.LE.0.OR.M.LE.0
+*
+ DO 90 IK = 1, NIDIM
+ K = IDIM( IK )
+*
+ DO 80 ICA = 1, 3
+ TRANSA = ICH( ICA: ICA )
+ TRANA = TRANSA.EQ.'T'.OR.TRANSA.EQ.'C'
+*
+ IF( TRANA )THEN
+ MA = K
+ NA = M
+ ELSE
+ MA = M
+ NA = K
+ END IF
+* Set LDA to 1 more than minimum value if room.
+ LDA = MA
+ IF( LDA.LT.NMAX )
+ $ LDA = LDA + 1
+* Skip tests if not enough room.
+ IF( LDA.GT.NMAX )
+ $ GO TO 80
+ LAA = LDA*NA
+*
+* Generate the matrix A.
+*
+ CALL CMAKE( 'GE', ' ', ' ', MA, NA, A, NMAX, AA, LDA,
+ $ RESET, ZERO )
+*
+ DO 70 ICB = 1, 3
+ TRANSB = ICH( ICB: ICB )
+ TRANB = TRANSB.EQ.'T'.OR.TRANSB.EQ.'C'
+*
+ IF( TRANB )THEN
+ MB = N
+ NB = K
+ ELSE
+ MB = K
+ NB = N
+ END IF
+* Set LDB to 1 more than minimum value if room.
+ LDB = MB
+ IF( LDB.LT.NMAX )
+ $ LDB = LDB + 1
+* Skip tests if not enough room.
+ IF( LDB.GT.NMAX )
+ $ GO TO 70
+ LBB = LDB*NB
+*
+* Generate the matrix B.
+*
+ CALL CMAKE( 'GE', ' ', ' ', MB, NB, B, NMAX, BB,
+ $ LDB, RESET, ZERO )
+*
+ DO 60 IA = 1, NALF
+ ALPHA = ALF( IA )
+*
+ DO 50 IB = 1, NBET
+ BETA = BET( IB )
+*
+* Generate the matrix C.
+*
+ CALL CMAKE( 'GE', ' ', ' ', M, N, C, NMAX,
+ $ CC, LDC, RESET, ZERO )
+*
+ NC = NC + 1
+*
+* Save every datum before calling the
+* subroutine.
+*
+ TRANAS = TRANSA
+ TRANBS = TRANSB
+ MS = M
+ NS = N
+ KS = K
+ ALS = ALPHA
+ DO 10 I = 1, LAA
+ AS( I ) = AA( I )
+ 10 CONTINUE
+ LDAS = LDA
+ DO 20 I = 1, LBB
+ BS( I ) = BB( I )
+ 20 CONTINUE
+ LDBS = LDB
+ BLS = BETA
+ DO 30 I = 1, LCC
+ CS( I ) = CC( I )
+ 30 CONTINUE
+ LDCS = LDC
+*
+* Call the subroutine.
+*
+ IF( TRACE )
+ $ WRITE( NTRA, FMT = 9995 )NC, SNAME,
+ $ TRANSA, TRANSB, M, N, K, ALPHA, LDA, LDB,
+ $ BETA, LDC
+ IF( REWI )
+ $ REWIND NTRA
+ CALL CGEMM( TRANSA, TRANSB, M, N, K, ALPHA,
+ $ AA, LDA, BB, LDB, BETA, CC, LDC )
+*
+* Check if error-exit was taken incorrectly.
+*
+ IF( .NOT.OK )THEN
+ WRITE( NOUT, FMT = 9994 )
+ FATAL = .TRUE.
+ GO TO 120
+ END IF
+*
+* See what data changed inside subroutines.
+*
+ ISAME( 1 ) = TRANSA.EQ.TRANAS
+ ISAME( 2 ) = TRANSB.EQ.TRANBS
+ ISAME( 3 ) = MS.EQ.M
+ ISAME( 4 ) = NS.EQ.N
+ ISAME( 5 ) = KS.EQ.K
+ ISAME( 6 ) = ALS.EQ.ALPHA
+ ISAME( 7 ) = LCE( AS, AA, LAA )
+ ISAME( 8 ) = LDAS.EQ.LDA
+ ISAME( 9 ) = LCE( BS, BB, LBB )
+ ISAME( 10 ) = LDBS.EQ.LDB
+ ISAME( 11 ) = BLS.EQ.BETA
+ IF( NULL )THEN
+ ISAME( 12 ) = LCE( CS, CC, LCC )
+ ELSE
+ ISAME( 12 ) = LCERES( 'GE', ' ', M, N, CS,
+ $ CC, LDC )
+ END IF
+ ISAME( 13 ) = LDCS.EQ.LDC
+*
+* If data was incorrectly changed, report
+* and return.
+*
+ SAME = .TRUE.
+ DO 40 I = 1, NARGS
+ SAME = SAME.AND.ISAME( I )
+ IF( .NOT.ISAME( I ) )
+ $ WRITE( NOUT, FMT = 9998 )I
+ 40 CONTINUE
+ IF( .NOT.SAME )THEN
+ FATAL = .TRUE.
+ GO TO 120
+ END IF
+*
+ IF( .NOT.NULL )THEN
+*
+* Check the result.
+*
+ CALL CMMCH( TRANSA, TRANSB, M, N, K,
+ $ ALPHA, A, NMAX, B, NMAX, BETA,
+ $ C, NMAX, CT, G, CC, LDC, EPS,
+ $ ERR, FATAL, NOUT, .TRUE. )
+ ERRMAX = MAX( ERRMAX, ERR )
+* If got really bad answer, report and
+* return.
+ IF( FATAL )
+ $ GO TO 120
+ END IF
+*
+ 50 CONTINUE
+*
+ 60 CONTINUE
+*
+ 70 CONTINUE
+*
+ 80 CONTINUE
+*
+ 90 CONTINUE
+*
+ 100 CONTINUE
+*
+ 110 CONTINUE
+*
+* Report result.
+*
+ IF( ERRMAX.LT.THRESH )THEN
+ WRITE( NOUT, FMT = 9999 )SNAME, NC
+ ELSE
+ WRITE( NOUT, FMT = 9997 )SNAME, NC, ERRMAX
+ END IF
+ GO TO 130
+*
+ 120 CONTINUE
+ WRITE( NOUT, FMT = 9996 )SNAME
+ WRITE( NOUT, FMT = 9995 )NC, SNAME, TRANSA, TRANSB, M, N, K,
+ $ ALPHA, LDA, LDB, BETA, LDC
+*
+ 130 CONTINUE
+ RETURN
+*
+ 9999 FORMAT( ' ', A6, ' PASSED THE COMPUTATIONAL TESTS (', I6, ' CALL',
+ $ 'S)' )
+ 9998 FORMAT( ' ******* FATAL ERROR - PARAMETER NUMBER ', I2, ' WAS CH',
+ $ 'ANGED INCORRECTLY *******' )
+ 9997 FORMAT( ' ', A6, ' COMPLETED THE COMPUTATIONAL TESTS (', I6, ' C',
+ $ 'ALLS)', /' ******* BUT WITH MAXIMUM TEST RATIO', F8.2,
+ $ ' - SUSPECT *******' )
+ 9996 FORMAT( ' ******* ', A6, ' FAILED ON CALL NUMBER:' )
+ 9995 FORMAT( 1X, I6, ': ', A6, '(''', A1, ''',''', A1, ''',',
+ $ 3( I3, ',' ), '(', F4.1, ',', F4.1, '), A,', I3, ', B,', I3,
+ $ ',(', F4.1, ',', F4.1, '), C,', I3, ').' )
+ 9994 FORMAT( ' ******* FATAL ERROR - ERROR-EXIT TAKEN ON VALID CALL *',
+ $ '******' )
+*
+* End of CCHK1.
+*
+ END
+ SUBROUTINE CCHK2( SNAME, EPS, THRESH, NOUT, NTRA, TRACE, REWI,
+ $ FATAL, NIDIM, IDIM, NALF, ALF, NBET, BET, NMAX,
+ $ A, AA, AS, B, BB, BS, C, CC, CS, CT, G )
+*
+* Tests CHEMM and CSYMM.
+*
+* Auxiliary routine for test program for Level 3 Blas.
+*
+* -- Written on 8-February-1989.
+* Jack Dongarra, Argonne National Laboratory.
+* Iain Duff, AERE Harwell.
+* Jeremy Du Croz, Numerical Algorithms Group Ltd.
+* Sven Hammarling, Numerical Algorithms Group Ltd.
+*
+* .. Parameters ..
+ COMPLEX ZERO
+ PARAMETER ( ZERO = ( 0.0, 0.0 ) )
+ REAL RZERO
+ PARAMETER ( RZERO = 0.0 )
+* .. Scalar Arguments ..
+ REAL EPS, THRESH
+ INTEGER NALF, NBET, NIDIM, NMAX, NOUT, NTRA
+ LOGICAL FATAL, REWI, TRACE
+ CHARACTER*6 SNAME
+* .. Array Arguments ..
+ COMPLEX A( NMAX, NMAX ), AA( NMAX*NMAX ), ALF( NALF ),
+ $ AS( NMAX*NMAX ), B( NMAX, NMAX ),
+ $ BB( NMAX*NMAX ), BET( NBET ), BS( NMAX*NMAX ),
+ $ C( NMAX, NMAX ), CC( NMAX*NMAX ),
+ $ CS( NMAX*NMAX ), CT( NMAX )
+ REAL G( NMAX )
+ INTEGER IDIM( NIDIM )
+* .. Local Scalars ..
+ COMPLEX ALPHA, ALS, BETA, BLS
+ REAL ERR, ERRMAX
+ INTEGER I, IA, IB, ICS, ICU, IM, IN, LAA, LBB, LCC,
+ $ LDA, LDAS, LDB, LDBS, LDC, LDCS, M, MS, N, NA,
+ $ NARGS, NC, NS
+ LOGICAL CONJ, LEFT, NULL, RESET, SAME
+ CHARACTER*1 SIDE, SIDES, UPLO, UPLOS
+ CHARACTER*2 ICHS, ICHU
+* .. Local Arrays ..
+ LOGICAL ISAME( 13 )
+* .. External Functions ..
+ LOGICAL LCE, LCERES
+ EXTERNAL LCE, LCERES
+* .. External Subroutines ..
+ EXTERNAL CHEMM, CMAKE, CMMCH, CSYMM
+* .. Intrinsic Functions ..
+ INTRINSIC MAX
+* .. Scalars in Common ..
+ INTEGER INFOT, NOUTC
+ LOGICAL LERR, OK
+* .. Common blocks ..
+ COMMON /INFOC/INFOT, NOUTC, OK, LERR
+* .. Data statements ..
+ DATA ICHS/'LR'/, ICHU/'UL'/
+* .. Executable Statements ..
+ CONJ = SNAME( 2: 3 ).EQ.'HE'
+*
+ NARGS = 12
+ NC = 0
+ RESET = .TRUE.
+ ERRMAX = RZERO
+*
+ DO 100 IM = 1, NIDIM
+ M = IDIM( IM )
+*
+ DO 90 IN = 1, NIDIM
+ N = IDIM( IN )
+* Set LDC to 1 more than minimum value if room.
+ LDC = M
+ IF( LDC.LT.NMAX )
+ $ LDC = LDC + 1
+* Skip tests if not enough room.
+ IF( LDC.GT.NMAX )
+ $ GO TO 90
+ LCC = LDC*N
+ NULL = N.LE.0.OR.M.LE.0
+* Set LDB to 1 more than minimum value if room.
+ LDB = M
+ IF( LDB.LT.NMAX )
+ $ LDB = LDB + 1
+* Skip tests if not enough room.
+ IF( LDB.GT.NMAX )
+ $ GO TO 90
+ LBB = LDB*N
+*
+* Generate the matrix B.
+*
+ CALL CMAKE( 'GE', ' ', ' ', M, N, B, NMAX, BB, LDB, RESET,
+ $ ZERO )
+*
+ DO 80 ICS = 1, 2
+ SIDE = ICHS( ICS: ICS )
+ LEFT = SIDE.EQ.'L'
+*
+ IF( LEFT )THEN
+ NA = M
+ ELSE
+ NA = N
+ END IF
+* Set LDA to 1 more than minimum value if room.
+ LDA = NA
+ IF( LDA.LT.NMAX )
+ $ LDA = LDA + 1
+* Skip tests if not enough room.
+ IF( LDA.GT.NMAX )
+ $ GO TO 80
+ LAA = LDA*NA
+*
+ DO 70 ICU = 1, 2
+ UPLO = ICHU( ICU: ICU )
+*
+* Generate the hermitian or symmetric matrix A.
+*
+ CALL CMAKE( SNAME( 2: 3 ), UPLO, ' ', NA, NA, A, NMAX,
+ $ AA, LDA, RESET, ZERO )
+*
+ DO 60 IA = 1, NALF
+ ALPHA = ALF( IA )
+*
+ DO 50 IB = 1, NBET
+ BETA = BET( IB )
+*
+* Generate the matrix C.
+*
+ CALL CMAKE( 'GE', ' ', ' ', M, N, C, NMAX, CC,
+ $ LDC, RESET, ZERO )
+*
+ NC = NC + 1
+*
+* Save every datum before calling the
+* subroutine.
+*
+ SIDES = SIDE
+ UPLOS = UPLO
+ MS = M
+ NS = N
+ ALS = ALPHA
+ DO 10 I = 1, LAA
+ AS( I ) = AA( I )
+ 10 CONTINUE
+ LDAS = LDA
+ DO 20 I = 1, LBB
+ BS( I ) = BB( I )
+ 20 CONTINUE
+ LDBS = LDB
+ BLS = BETA
+ DO 30 I = 1, LCC
+ CS( I ) = CC( I )
+ 30 CONTINUE
+ LDCS = LDC
+*
+* Call the subroutine.
+*
+ IF( TRACE )
+ $ WRITE( NTRA, FMT = 9995 )NC, SNAME, SIDE,
+ $ UPLO, M, N, ALPHA, LDA, LDB, BETA, LDC
+ IF( REWI )
+ $ REWIND NTRA
+ IF( CONJ )THEN
+ CALL CHEMM( SIDE, UPLO, M, N, ALPHA, AA, LDA,
+ $ BB, LDB, BETA, CC, LDC )
+ ELSE
+ CALL CSYMM( SIDE, UPLO, M, N, ALPHA, AA, LDA,
+ $ BB, LDB, BETA, CC, LDC )
+ END IF
+*
+* Check if error-exit was taken incorrectly.
+*
+ IF( .NOT.OK )THEN
+ WRITE( NOUT, FMT = 9994 )
+ FATAL = .TRUE.
+ GO TO 110
+ END IF
+*
+* See what data changed inside subroutines.
+*
+ ISAME( 1 ) = SIDES.EQ.SIDE
+ ISAME( 2 ) = UPLOS.EQ.UPLO
+ ISAME( 3 ) = MS.EQ.M
+ ISAME( 4 ) = NS.EQ.N
+ ISAME( 5 ) = ALS.EQ.ALPHA
+ ISAME( 6 ) = LCE( AS, AA, LAA )
+ ISAME( 7 ) = LDAS.EQ.LDA
+ ISAME( 8 ) = LCE( BS, BB, LBB )
+ ISAME( 9 ) = LDBS.EQ.LDB
+ ISAME( 10 ) = BLS.EQ.BETA
+ IF( NULL )THEN
+ ISAME( 11 ) = LCE( CS, CC, LCC )
+ ELSE
+ ISAME( 11 ) = LCERES( 'GE', ' ', M, N, CS,
+ $ CC, LDC )
+ END IF
+ ISAME( 12 ) = LDCS.EQ.LDC
+*
+* If data was incorrectly changed, report and
+* return.
+*
+ SAME = .TRUE.
+ DO 40 I = 1, NARGS
+ SAME = SAME.AND.ISAME( I )
+ IF( .NOT.ISAME( I ) )
+ $ WRITE( NOUT, FMT = 9998 )I
+ 40 CONTINUE
+ IF( .NOT.SAME )THEN
+ FATAL = .TRUE.
+ GO TO 110
+ END IF
+*
+ IF( .NOT.NULL )THEN
+*
+* Check the result.
+*
+ IF( LEFT )THEN
+ CALL CMMCH( 'N', 'N', M, N, M, ALPHA, A,
+ $ NMAX, B, NMAX, BETA, C, NMAX,
+ $ CT, G, CC, LDC, EPS, ERR,
+ $ FATAL, NOUT, .TRUE. )
+ ELSE
+ CALL CMMCH( 'N', 'N', M, N, N, ALPHA, B,
+ $ NMAX, A, NMAX, BETA, C, NMAX,
+ $ CT, G, CC, LDC, EPS, ERR,
+ $ FATAL, NOUT, .TRUE. )
+ END IF
+ ERRMAX = MAX( ERRMAX, ERR )
+* If got really bad answer, report and
+* return.
+ IF( FATAL )
+ $ GO TO 110
+ END IF
+*
+ 50 CONTINUE
+*
+ 60 CONTINUE
+*
+ 70 CONTINUE
+*
+ 80 CONTINUE
+*
+ 90 CONTINUE
+*
+ 100 CONTINUE
+*
+* Report result.
+*
+ IF( ERRMAX.LT.THRESH )THEN
+ WRITE( NOUT, FMT = 9999 )SNAME, NC
+ ELSE
+ WRITE( NOUT, FMT = 9997 )SNAME, NC, ERRMAX
+ END IF
+ GO TO 120
+*
+ 110 CONTINUE
+ WRITE( NOUT, FMT = 9996 )SNAME
+ WRITE( NOUT, FMT = 9995 )NC, SNAME, SIDE, UPLO, M, N, ALPHA, LDA,
+ $ LDB, BETA, LDC
+*
+ 120 CONTINUE
+ RETURN
+*
+ 9999 FORMAT( ' ', A6, ' PASSED THE COMPUTATIONAL TESTS (', I6, ' CALL',
+ $ 'S)' )
+ 9998 FORMAT( ' ******* FATAL ERROR - PARAMETER NUMBER ', I2, ' WAS CH',
+ $ 'ANGED INCORRECTLY *******' )
+ 9997 FORMAT( ' ', A6, ' COMPLETED THE COMPUTATIONAL TESTS (', I6, ' C',
+ $ 'ALLS)', /' ******* BUT WITH MAXIMUM TEST RATIO', F8.2,
+ $ ' - SUSPECT *******' )
+ 9996 FORMAT( ' ******* ', A6, ' FAILED ON CALL NUMBER:' )
+ 9995 FORMAT( 1X, I6, ': ', A6, '(', 2( '''', A1, ''',' ), 2( I3, ',' ),
+ $ '(', F4.1, ',', F4.1, '), A,', I3, ', B,', I3, ',(', F4.1,
+ $ ',', F4.1, '), C,', I3, ') .' )
+ 9994 FORMAT( ' ******* FATAL ERROR - ERROR-EXIT TAKEN ON VALID CALL *',
+ $ '******' )
+*
+* End of CCHK2.
+*
+ END
+ SUBROUTINE CCHK3( SNAME, EPS, THRESH, NOUT, NTRA, TRACE, REWI,
+ $ FATAL, NIDIM, IDIM, NALF, ALF, NMAX, A, AA, AS,
+ $ B, BB, BS, CT, G, C )
+*
+* Tests CTRMM and CTRSM.
+*
+* Auxiliary routine for test program for Level 3 Blas.
+*
+* -- Written on 8-February-1989.
+* Jack Dongarra, Argonne National Laboratory.
+* Iain Duff, AERE Harwell.
+* Jeremy Du Croz, Numerical Algorithms Group Ltd.
+* Sven Hammarling, Numerical Algorithms Group Ltd.
+*
+* .. Parameters ..
+ COMPLEX ZERO, ONE
+ PARAMETER ( ZERO = ( 0.0, 0.0 ), ONE = ( 1.0, 0.0 ) )
+ REAL RZERO
+ PARAMETER ( RZERO = 0.0 )
+* .. Scalar Arguments ..
+ REAL EPS, THRESH
+ INTEGER NALF, NIDIM, NMAX, NOUT, NTRA
+ LOGICAL FATAL, REWI, TRACE
+ CHARACTER*6 SNAME
+* .. Array Arguments ..
+ COMPLEX A( NMAX, NMAX ), AA( NMAX*NMAX ), ALF( NALF ),
+ $ AS( NMAX*NMAX ), B( NMAX, NMAX ),
+ $ BB( NMAX*NMAX ), BS( NMAX*NMAX ),
+ $ C( NMAX, NMAX ), CT( NMAX )
+ REAL G( NMAX )
+ INTEGER IDIM( NIDIM )
+* .. Local Scalars ..
+ COMPLEX ALPHA, ALS
+ REAL ERR, ERRMAX
+ INTEGER I, IA, ICD, ICS, ICT, ICU, IM, IN, J, LAA, LBB,
+ $ LDA, LDAS, LDB, LDBS, M, MS, N, NA, NARGS, NC,
+ $ NS
+ LOGICAL LEFT, NULL, RESET, SAME
+ CHARACTER*1 DIAG, DIAGS, SIDE, SIDES, TRANAS, TRANSA, UPLO,
+ $ UPLOS
+ CHARACTER*2 ICHD, ICHS, ICHU
+ CHARACTER*3 ICHT
+* .. Local Arrays ..
+ LOGICAL ISAME( 13 )
+* .. External Functions ..
+ LOGICAL LCE, LCERES
+ EXTERNAL LCE, LCERES
+* .. External Subroutines ..
+ EXTERNAL CMAKE, CMMCH, CTRMM, CTRSM
+* .. Intrinsic Functions ..
+ INTRINSIC MAX
+* .. Scalars in Common ..
+ INTEGER INFOT, NOUTC
+ LOGICAL LERR, OK
+* .. Common blocks ..
+ COMMON /INFOC/INFOT, NOUTC, OK, LERR
+* .. Data statements ..
+ DATA ICHU/'UL'/, ICHT/'NTC'/, ICHD/'UN'/, ICHS/'LR'/
+* .. Executable Statements ..
+*
+ NARGS = 11
+ NC = 0
+ RESET = .TRUE.
+ ERRMAX = RZERO
+* Set up zero matrix for CMMCH.
+ DO 20 J = 1, NMAX
+ DO 10 I = 1, NMAX
+ C( I, J ) = ZERO
+ 10 CONTINUE
+ 20 CONTINUE
+*
+ DO 140 IM = 1, NIDIM
+ M = IDIM( IM )
+*
+ DO 130 IN = 1, NIDIM
+ N = IDIM( IN )
+* Set LDB to 1 more than minimum value if room.
+ LDB = M
+ IF( LDB.LT.NMAX )
+ $ LDB = LDB + 1
+* Skip tests if not enough room.
+ IF( LDB.GT.NMAX )
+ $ GO TO 130
+ LBB = LDB*N
+ NULL = M.LE.0.OR.N.LE.0
+*
+ DO 120 ICS = 1, 2
+ SIDE = ICHS( ICS: ICS )
+ LEFT = SIDE.EQ.'L'
+ IF( LEFT )THEN
+ NA = M
+ ELSE
+ NA = N
+ END IF
+* Set LDA to 1 more than minimum value if room.
+ LDA = NA
+ IF( LDA.LT.NMAX )
+ $ LDA = LDA + 1
+* Skip tests if not enough room.
+ IF( LDA.GT.NMAX )
+ $ GO TO 130
+ LAA = LDA*NA
+*
+ DO 110 ICU = 1, 2
+ UPLO = ICHU( ICU: ICU )
+*
+ DO 100 ICT = 1, 3
+ TRANSA = ICHT( ICT: ICT )
+*
+ DO 90 ICD = 1, 2
+ DIAG = ICHD( ICD: ICD )
+*
+ DO 80 IA = 1, NALF
+ ALPHA = ALF( IA )
+*
+* Generate the matrix A.
+*
+ CALL CMAKE( 'TR', UPLO, DIAG, NA, NA, A,
+ $ NMAX, AA, LDA, RESET, ZERO )
+*
+* Generate the matrix B.
+*
+ CALL CMAKE( 'GE', ' ', ' ', M, N, B, NMAX,
+ $ BB, LDB, RESET, ZERO )
+*
+ NC = NC + 1
+*
+* Save every datum before calling the
+* subroutine.
+*
+ SIDES = SIDE
+ UPLOS = UPLO
+ TRANAS = TRANSA
+ DIAGS = DIAG
+ MS = M
+ NS = N
+ ALS = ALPHA
+ DO 30 I = 1, LAA
+ AS( I ) = AA( I )
+ 30 CONTINUE
+ LDAS = LDA
+ DO 40 I = 1, LBB
+ BS( I ) = BB( I )
+ 40 CONTINUE
+ LDBS = LDB
+*
+* Call the subroutine.
+*
+ IF( SNAME( 4: 5 ).EQ.'MM' )THEN
+ IF( TRACE )
+ $ WRITE( NTRA, FMT = 9995 )NC, SNAME,
+ $ SIDE, UPLO, TRANSA, DIAG, M, N, ALPHA,
+ $ LDA, LDB
+ IF( REWI )
+ $ REWIND NTRA
+ CALL CTRMM( SIDE, UPLO, TRANSA, DIAG, M,
+ $ N, ALPHA, AA, LDA, BB, LDB )
+ ELSE IF( SNAME( 4: 5 ).EQ.'SM' )THEN
+ IF( TRACE )
+ $ WRITE( NTRA, FMT = 9995 )NC, SNAME,
+ $ SIDE, UPLO, TRANSA, DIAG, M, N, ALPHA,
+ $ LDA, LDB
+ IF( REWI )
+ $ REWIND NTRA
+ CALL CTRSM( SIDE, UPLO, TRANSA, DIAG, M,
+ $ N, ALPHA, AA, LDA, BB, LDB )
+ END IF
+*
+* Check if error-exit was taken incorrectly.
+*
+ IF( .NOT.OK )THEN
+ WRITE( NOUT, FMT = 9994 )
+ FATAL = .TRUE.
+ GO TO 150
+ END IF
+*
+* See what data changed inside subroutines.
+*
+ ISAME( 1 ) = SIDES.EQ.SIDE
+ ISAME( 2 ) = UPLOS.EQ.UPLO
+ ISAME( 3 ) = TRANAS.EQ.TRANSA
+ ISAME( 4 ) = DIAGS.EQ.DIAG
+ ISAME( 5 ) = MS.EQ.M
+ ISAME( 6 ) = NS.EQ.N
+ ISAME( 7 ) = ALS.EQ.ALPHA
+ ISAME( 8 ) = LCE( AS, AA, LAA )
+ ISAME( 9 ) = LDAS.EQ.LDA
+ IF( NULL )THEN
+ ISAME( 10 ) = LCE( BS, BB, LBB )
+ ELSE
+ ISAME( 10 ) = LCERES( 'GE', ' ', M, N, BS,
+ $ BB, LDB )
+ END IF
+ ISAME( 11 ) = LDBS.EQ.LDB
+*
+* If data was incorrectly changed, report and
+* return.
+*
+ SAME = .TRUE.
+ DO 50 I = 1, NARGS
+ SAME = SAME.AND.ISAME( I )
+ IF( .NOT.ISAME( I ) )
+ $ WRITE( NOUT, FMT = 9998 )I
+ 50 CONTINUE
+ IF( .NOT.SAME )THEN
+ FATAL = .TRUE.
+ GO TO 150
+ END IF
+*
+ IF( .NOT.NULL )THEN
+ IF( SNAME( 4: 5 ).EQ.'MM' )THEN
+*
+* Check the result.
+*
+ IF( LEFT )THEN
+ CALL CMMCH( TRANSA, 'N', M, N, M,
+ $ ALPHA, A, NMAX, B, NMAX,
+ $ ZERO, C, NMAX, CT, G,
+ $ BB, LDB, EPS, ERR,
+ $ FATAL, NOUT, .TRUE. )
+ ELSE
+ CALL CMMCH( 'N', TRANSA, M, N, N,
+ $ ALPHA, B, NMAX, A, NMAX,
+ $ ZERO, C, NMAX, CT, G,
+ $ BB, LDB, EPS, ERR,
+ $ FATAL, NOUT, .TRUE. )
+ END IF
+ ELSE IF( SNAME( 4: 5 ).EQ.'SM' )THEN
+*
+* Compute approximation to original
+* matrix.
+*
+ DO 70 J = 1, N
+ DO 60 I = 1, M
+ C( I, J ) = BB( I + ( J - 1 )*
+ $ LDB )
+ BB( I + ( J - 1 )*LDB ) = ALPHA*
+ $ B( I, J )
+ 60 CONTINUE
+ 70 CONTINUE
+*
+ IF( LEFT )THEN
+ CALL CMMCH( TRANSA, 'N', M, N, M,
+ $ ONE, A, NMAX, C, NMAX,
+ $ ZERO, B, NMAX, CT, G,
+ $ BB, LDB, EPS, ERR,
+ $ FATAL, NOUT, .FALSE. )
+ ELSE
+ CALL CMMCH( 'N', TRANSA, M, N, N,
+ $ ONE, C, NMAX, A, NMAX,
+ $ ZERO, B, NMAX, CT, G,
+ $ BB, LDB, EPS, ERR,
+ $ FATAL, NOUT, .FALSE. )
+ END IF
+ END IF
+ ERRMAX = MAX( ERRMAX, ERR )
+* If got really bad answer, report and
+* return.
+ IF( FATAL )
+ $ GO TO 150
+ END IF
+*
+ 80 CONTINUE
+*
+ 90 CONTINUE
+*
+ 100 CONTINUE
+*
+ 110 CONTINUE
+*
+ 120 CONTINUE
+*
+ 130 CONTINUE
+*
+ 140 CONTINUE
+*
+* Report result.
+*
+ IF( ERRMAX.LT.THRESH )THEN
+ WRITE( NOUT, FMT = 9999 )SNAME, NC
+ ELSE
+ WRITE( NOUT, FMT = 9997 )SNAME, NC, ERRMAX
+ END IF
+ GO TO 160
+*
+ 150 CONTINUE
+ WRITE( NOUT, FMT = 9996 )SNAME
+ WRITE( NOUT, FMT = 9995 )NC, SNAME, SIDE, UPLO, TRANSA, DIAG, M,
+ $ N, ALPHA, LDA, LDB
+*
+ 160 CONTINUE
+ RETURN
+*
+ 9999 FORMAT( ' ', A6, ' PASSED THE COMPUTATIONAL TESTS (', I6, ' CALL',
+ $ 'S)' )
+ 9998 FORMAT( ' ******* FATAL ERROR - PARAMETER NUMBER ', I2, ' WAS CH',
+ $ 'ANGED INCORRECTLY *******' )
+ 9997 FORMAT( ' ', A6, ' COMPLETED THE COMPUTATIONAL TESTS (', I6, ' C',
+ $ 'ALLS)', /' ******* BUT WITH MAXIMUM TEST RATIO', F8.2,
+ $ ' - SUSPECT *******' )
+ 9996 FORMAT( ' ******* ', A6, ' FAILED ON CALL NUMBER:' )
+ 9995 FORMAT( 1X, I6, ': ', A6, '(', 4( '''', A1, ''',' ), 2( I3, ',' ),
+ $ '(', F4.1, ',', F4.1, '), A,', I3, ', B,', I3, ') ',
+ $ ' .' )
+ 9994 FORMAT( ' ******* FATAL ERROR - ERROR-EXIT TAKEN ON VALID CALL *',
+ $ '******' )
+*
+* End of CCHK3.
+*
+ END
+ SUBROUTINE CCHK4( SNAME, EPS, THRESH, NOUT, NTRA, TRACE, REWI,
+ $ FATAL, NIDIM, IDIM, NALF, ALF, NBET, BET, NMAX,
+ $ A, AA, AS, B, BB, BS, C, CC, CS, CT, G )
+*
+* Tests CHERK and CSYRK.
+*
+* Auxiliary routine for test program for Level 3 Blas.
+*
+* -- Written on 8-February-1989.
+* Jack Dongarra, Argonne National Laboratory.
+* Iain Duff, AERE Harwell.
+* Jeremy Du Croz, Numerical Algorithms Group Ltd.
+* Sven Hammarling, Numerical Algorithms Group Ltd.
+*
+* .. Parameters ..
+ COMPLEX ZERO
+ PARAMETER ( ZERO = ( 0.0, 0.0 ) )
+ REAL RONE, RZERO
+ PARAMETER ( RONE = 1.0, RZERO = 0.0 )
+* .. Scalar Arguments ..
+ REAL EPS, THRESH
+ INTEGER NALF, NBET, NIDIM, NMAX, NOUT, NTRA
+ LOGICAL FATAL, REWI, TRACE
+ CHARACTER*6 SNAME
+* .. Array Arguments ..
+ COMPLEX A( NMAX, NMAX ), AA( NMAX*NMAX ), ALF( NALF ),
+ $ AS( NMAX*NMAX ), B( NMAX, NMAX ),
+ $ BB( NMAX*NMAX ), BET( NBET ), BS( NMAX*NMAX ),
+ $ C( NMAX, NMAX ), CC( NMAX*NMAX ),
+ $ CS( NMAX*NMAX ), CT( NMAX )
+ REAL G( NMAX )
+ INTEGER IDIM( NIDIM )
+* .. Local Scalars ..
+ COMPLEX ALPHA, ALS, BETA, BETS
+ REAL ERR, ERRMAX, RALPHA, RALS, RBETA, RBETS
+ INTEGER I, IA, IB, ICT, ICU, IK, IN, J, JC, JJ, K, KS,
+ $ LAA, LCC, LDA, LDAS, LDC, LDCS, LJ, MA, N, NA,
+ $ NARGS, NC, NS
+ LOGICAL CONJ, NULL, RESET, SAME, TRAN, UPPER
+ CHARACTER*1 TRANS, TRANSS, TRANST, UPLO, UPLOS
+ CHARACTER*2 ICHT, ICHU
+* .. Local Arrays ..
+ LOGICAL ISAME( 13 )
+* .. External Functions ..
+ LOGICAL LCE, LCERES
+ EXTERNAL LCE, LCERES
+* .. External Subroutines ..
+ EXTERNAL CHERK, CMAKE, CMMCH, CSYRK
+* .. Intrinsic Functions ..
+ INTRINSIC CMPLX, MAX, REAL
+* .. Scalars in Common ..
+ INTEGER INFOT, NOUTC
+ LOGICAL LERR, OK
+* .. Common blocks ..
+ COMMON /INFOC/INFOT, NOUTC, OK, LERR
+* .. Data statements ..
+ DATA ICHT/'NC'/, ICHU/'UL'/
+* .. Executable Statements ..
+ CONJ = SNAME( 2: 3 ).EQ.'HE'
+*
+ NARGS = 10
+ NC = 0
+ RESET = .TRUE.
+ ERRMAX = RZERO
+*
+ DO 100 IN = 1, NIDIM
+ N = IDIM( IN )
+* Set LDC to 1 more than minimum value if room.
+ LDC = N
+ IF( LDC.LT.NMAX )
+ $ LDC = LDC + 1
+* Skip tests if not enough room.
+ IF( LDC.GT.NMAX )
+ $ GO TO 100
+ LCC = LDC*N
+*
+ DO 90 IK = 1, NIDIM
+ K = IDIM( IK )
+*
+ DO 80 ICT = 1, 2
+ TRANS = ICHT( ICT: ICT )
+ TRAN = TRANS.EQ.'C'
+ IF( TRAN.AND..NOT.CONJ )
+ $ TRANS = 'T'
+ IF( TRAN )THEN
+ MA = K
+ NA = N
+ ELSE
+ MA = N
+ NA = K
+ END IF
+* Set LDA to 1 more than minimum value if room.
+ LDA = MA
+ IF( LDA.LT.NMAX )
+ $ LDA = LDA + 1
+* Skip tests if not enough room.
+ IF( LDA.GT.NMAX )
+ $ GO TO 80
+ LAA = LDA*NA
+*
+* Generate the matrix A.
+*
+ CALL CMAKE( 'GE', ' ', ' ', MA, NA, A, NMAX, AA, LDA,
+ $ RESET, ZERO )
+*
+ DO 70 ICU = 1, 2
+ UPLO = ICHU( ICU: ICU )
+ UPPER = UPLO.EQ.'U'
+*
+ DO 60 IA = 1, NALF
+ ALPHA = ALF( IA )
+ IF( CONJ )THEN
+ RALPHA = REAL( ALPHA )
+ ALPHA = CMPLX( RALPHA, RZERO )
+ END IF
+*
+ DO 50 IB = 1, NBET
+ BETA = BET( IB )
+ IF( CONJ )THEN
+ RBETA = REAL( BETA )
+ BETA = CMPLX( RBETA, RZERO )
+ END IF
+ NULL = N.LE.0
+ IF( CONJ )
+ $ NULL = NULL.OR.( ( K.LE.0.OR.RALPHA.EQ.
+ $ RZERO ).AND.RBETA.EQ.RONE )
+*
+* Generate the matrix C.
+*
+ CALL CMAKE( SNAME( 2: 3 ), UPLO, ' ', N, N, C,
+ $ NMAX, CC, LDC, RESET, ZERO )
+*
+ NC = NC + 1
+*
+* Save every datum before calling the subroutine.
+*
+ UPLOS = UPLO
+ TRANSS = TRANS
+ NS = N
+ KS = K
+ IF( CONJ )THEN
+ RALS = RALPHA
+ ELSE
+ ALS = ALPHA
+ END IF
+ DO 10 I = 1, LAA
+ AS( I ) = AA( I )
+ 10 CONTINUE
+ LDAS = LDA
+ IF( CONJ )THEN
+ RBETS = RBETA
+ ELSE
+ BETS = BETA
+ END IF
+ DO 20 I = 1, LCC
+ CS( I ) = CC( I )
+ 20 CONTINUE
+ LDCS = LDC
+*
+* Call the subroutine.
+*
+ IF( CONJ )THEN
+ IF( TRACE )
+ $ WRITE( NTRA, FMT = 9994 )NC, SNAME, UPLO,
+ $ TRANS, N, K, RALPHA, LDA, RBETA, LDC
+ IF( REWI )
+ $ REWIND NTRA
+ CALL CHERK( UPLO, TRANS, N, K, RALPHA, AA,
+ $ LDA, RBETA, CC, LDC )
+ ELSE
+ IF( TRACE )
+ $ WRITE( NTRA, FMT = 9993 )NC, SNAME, UPLO,
+ $ TRANS, N, K, ALPHA, LDA, BETA, LDC
+ IF( REWI )
+ $ REWIND NTRA
+ CALL CSYRK( UPLO, TRANS, N, K, ALPHA, AA,
+ $ LDA, BETA, CC, LDC )
+ END IF
+*
+* Check if error-exit was taken incorrectly.
+*
+ IF( .NOT.OK )THEN
+ WRITE( NOUT, FMT = 9992 )
+ FATAL = .TRUE.
+ GO TO 120
+ END IF
+*
+* See what data changed inside subroutines.
+*
+ ISAME( 1 ) = UPLOS.EQ.UPLO
+ ISAME( 2 ) = TRANSS.EQ.TRANS
+ ISAME( 3 ) = NS.EQ.N
+ ISAME( 4 ) = KS.EQ.K
+ IF( CONJ )THEN
+ ISAME( 5 ) = RALS.EQ.RALPHA
+ ELSE
+ ISAME( 5 ) = ALS.EQ.ALPHA
+ END IF
+ ISAME( 6 ) = LCE( AS, AA, LAA )
+ ISAME( 7 ) = LDAS.EQ.LDA
+ IF( CONJ )THEN
+ ISAME( 8 ) = RBETS.EQ.RBETA
+ ELSE
+ ISAME( 8 ) = BETS.EQ.BETA
+ END IF
+ IF( NULL )THEN
+ ISAME( 9 ) = LCE( CS, CC, LCC )
+ ELSE
+ ISAME( 9 ) = LCERES( SNAME( 2: 3 ), UPLO, N,
+ $ N, CS, CC, LDC )
+ END IF
+ ISAME( 10 ) = LDCS.EQ.LDC
+*
+* If data was incorrectly changed, report and
+* return.
+*
+ SAME = .TRUE.
+ DO 30 I = 1, NARGS
+ SAME = SAME.AND.ISAME( I )
+ IF( .NOT.ISAME( I ) )
+ $ WRITE( NOUT, FMT = 9998 )I
+ 30 CONTINUE
+ IF( .NOT.SAME )THEN
+ FATAL = .TRUE.
+ GO TO 120
+ END IF
+*
+ IF( .NOT.NULL )THEN
+*
+* Check the result column by column.
+*
+ IF( CONJ )THEN
+ TRANST = 'C'
+ ELSE
+ TRANST = 'T'
+ END IF
+ JC = 1
+ DO 40 J = 1, N
+ IF( UPPER )THEN
+ JJ = 1
+ LJ = J
+ ELSE
+ JJ = J
+ LJ = N - J + 1
+ END IF
+ IF( TRAN )THEN
+ CALL CMMCH( TRANST, 'N', LJ, 1, K,
+ $ ALPHA, A( 1, JJ ), NMAX,
+ $ A( 1, J ), NMAX, BETA,
+ $ C( JJ, J ), NMAX, CT, G,
+ $ CC( JC ), LDC, EPS, ERR,
+ $ FATAL, NOUT, .TRUE. )
+ ELSE
+ CALL CMMCH( 'N', TRANST, LJ, 1, K,
+ $ ALPHA, A( JJ, 1 ), NMAX,
+ $ A( J, 1 ), NMAX, BETA,
+ $ C( JJ, J ), NMAX, CT, G,
+ $ CC( JC ), LDC, EPS, ERR,
+ $ FATAL, NOUT, .TRUE. )
+ END IF
+ IF( UPPER )THEN
+ JC = JC + LDC
+ ELSE
+ JC = JC + LDC + 1
+ END IF
+ ERRMAX = MAX( ERRMAX, ERR )
+* If got really bad answer, report and
+* return.
+ IF( FATAL )
+ $ GO TO 110
+ 40 CONTINUE
+ END IF
+*
+ 50 CONTINUE
+*
+ 60 CONTINUE
+*
+ 70 CONTINUE
+*
+ 80 CONTINUE
+*
+ 90 CONTINUE
+*
+ 100 CONTINUE
+*
+* Report result.
+*
+ IF( ERRMAX.LT.THRESH )THEN
+ WRITE( NOUT, FMT = 9999 )SNAME, NC
+ ELSE
+ WRITE( NOUT, FMT = 9997 )SNAME, NC, ERRMAX
+ END IF
+ GO TO 130
+*
+ 110 CONTINUE
+ IF( N.GT.1 )
+ $ WRITE( NOUT, FMT = 9995 )J
+*
+ 120 CONTINUE
+ WRITE( NOUT, FMT = 9996 )SNAME
+ IF( CONJ )THEN
+ WRITE( NOUT, FMT = 9994 )NC, SNAME, UPLO, TRANS, N, K, RALPHA,
+ $ LDA, RBETA, LDC
+ ELSE
+ WRITE( NOUT, FMT = 9993 )NC, SNAME, UPLO, TRANS, N, K, ALPHA,
+ $ LDA, BETA, LDC
+ END IF
+*
+ 130 CONTINUE
+ RETURN
+*
+ 9999 FORMAT( ' ', A6, ' PASSED THE COMPUTATIONAL TESTS (', I6, ' CALL',
+ $ 'S)' )
+ 9998 FORMAT( ' ******* FATAL ERROR - PARAMETER NUMBER ', I2, ' WAS CH',
+ $ 'ANGED INCORRECTLY *******' )
+ 9997 FORMAT( ' ', A6, ' COMPLETED THE COMPUTATIONAL TESTS (', I6, ' C',
+ $ 'ALLS)', /' ******* BUT WITH MAXIMUM TEST RATIO', F8.2,
+ $ ' - SUSPECT *******' )
+ 9996 FORMAT( ' ******* ', A6, ' FAILED ON CALL NUMBER:' )
+ 9995 FORMAT( ' THESE ARE THE RESULTS FOR COLUMN ', I3 )
+ 9994 FORMAT( 1X, I6, ': ', A6, '(', 2( '''', A1, ''',' ), 2( I3, ',' ),
+ $ F4.1, ', A,', I3, ',', F4.1, ', C,', I3, ') ',
+ $ ' .' )
+ 9993 FORMAT( 1X, I6, ': ', A6, '(', 2( '''', A1, ''',' ), 2( I3, ',' ),
+ $ '(', F4.1, ',', F4.1, ') , A,', I3, ',(', F4.1, ',', F4.1,
+ $ '), C,', I3, ') .' )
+ 9992 FORMAT( ' ******* FATAL ERROR - ERROR-EXIT TAKEN ON VALID CALL *',
+ $ '******' )
+*
+* End of CCHK4.
+*
+ END
+ SUBROUTINE CCHK5( SNAME, EPS, THRESH, NOUT, NTRA, TRACE, REWI,
+ $ FATAL, NIDIM, IDIM, NALF, ALF, NBET, BET, NMAX,
+ $ AB, AA, AS, BB, BS, C, CC, CS, CT, G, W )
+*
+* Tests CHER2K and CSYR2K.
+*
+* Auxiliary routine for test program for Level 3 Blas.
+*
+* -- Written on 8-February-1989.
+* Jack Dongarra, Argonne National Laboratory.
+* Iain Duff, AERE Harwell.
+* Jeremy Du Croz, Numerical Algorithms Group Ltd.
+* Sven Hammarling, Numerical Algorithms Group Ltd.
+*
+* .. Parameters ..
+ COMPLEX ZERO, ONE
+ PARAMETER ( ZERO = ( 0.0, 0.0 ), ONE = ( 1.0, 0.0 ) )
+ REAL RONE, RZERO
+ PARAMETER ( RONE = 1.0, RZERO = 0.0 )
+* .. Scalar Arguments ..
+ REAL EPS, THRESH
+ INTEGER NALF, NBET, NIDIM, NMAX, NOUT, NTRA
+ LOGICAL FATAL, REWI, TRACE
+ CHARACTER*6 SNAME
+* .. Array Arguments ..
+ COMPLEX AA( NMAX*NMAX ), AB( 2*NMAX*NMAX ),
+ $ ALF( NALF ), AS( NMAX*NMAX ), BB( NMAX*NMAX ),
+ $ BET( NBET ), BS( NMAX*NMAX ), C( NMAX, NMAX ),
+ $ CC( NMAX*NMAX ), CS( NMAX*NMAX ), CT( NMAX ),
+ $ W( 2*NMAX )
+ REAL G( NMAX )
+ INTEGER IDIM( NIDIM )
+* .. Local Scalars ..
+ COMPLEX ALPHA, ALS, BETA, BETS
+ REAL ERR, ERRMAX, RBETA, RBETS
+ INTEGER I, IA, IB, ICT, ICU, IK, IN, J, JC, JJ, JJAB,
+ $ K, KS, LAA, LBB, LCC, LDA, LDAS, LDB, LDBS,
+ $ LDC, LDCS, LJ, MA, N, NA, NARGS, NC, NS
+ LOGICAL CONJ, NULL, RESET, SAME, TRAN, UPPER
+ CHARACTER*1 TRANS, TRANSS, TRANST, UPLO, UPLOS
+ CHARACTER*2 ICHT, ICHU
+* .. Local Arrays ..
+ LOGICAL ISAME( 13 )
+* .. External Functions ..
+ LOGICAL LCE, LCERES
+ EXTERNAL LCE, LCERES
+* .. External Subroutines ..
+ EXTERNAL CHER2K, CMAKE, CMMCH, CSYR2K
+* .. Intrinsic Functions ..
+ INTRINSIC CMPLX, CONJG, MAX, REAL
+* .. Scalars in Common ..
+ INTEGER INFOT, NOUTC
+ LOGICAL LERR, OK
+* .. Common blocks ..
+ COMMON /INFOC/INFOT, NOUTC, OK, LERR
+* .. Data statements ..
+ DATA ICHT/'NC'/, ICHU/'UL'/
+* .. Executable Statements ..
+ CONJ = SNAME( 2: 3 ).EQ.'HE'
+*
+ NARGS = 12
+ NC = 0
+ RESET = .TRUE.
+ ERRMAX = RZERO
+*
+ DO 130 IN = 1, NIDIM
+ N = IDIM( IN )
+* Set LDC to 1 more than minimum value if room.
+ LDC = N
+ IF( LDC.LT.NMAX )
+ $ LDC = LDC + 1
+* Skip tests if not enough room.
+ IF( LDC.GT.NMAX )
+ $ GO TO 130
+ LCC = LDC*N
+*
+ DO 120 IK = 1, NIDIM
+ K = IDIM( IK )
+*
+ DO 110 ICT = 1, 2
+ TRANS = ICHT( ICT: ICT )
+ TRAN = TRANS.EQ.'C'
+ IF( TRAN.AND..NOT.CONJ )
+ $ TRANS = 'T'
+ IF( TRAN )THEN
+ MA = K
+ NA = N
+ ELSE
+ MA = N
+ NA = K
+ END IF
+* Set LDA to 1 more than minimum value if room.
+ LDA = MA
+ IF( LDA.LT.NMAX )
+ $ LDA = LDA + 1
+* Skip tests if not enough room.
+ IF( LDA.GT.NMAX )
+ $ GO TO 110
+ LAA = LDA*NA
+*
+* Generate the matrix A.
+*
+ IF( TRAN )THEN
+ CALL CMAKE( 'GE', ' ', ' ', MA, NA, AB, 2*NMAX, AA,
+ $ LDA, RESET, ZERO )
+ ELSE
+ CALL CMAKE( 'GE', ' ', ' ', MA, NA, AB, NMAX, AA, LDA,
+ $ RESET, ZERO )
+ END IF
+*
+* Generate the matrix B.
+*
+ LDB = LDA
+ LBB = LAA
+ IF( TRAN )THEN
+ CALL CMAKE( 'GE', ' ', ' ', MA, NA, AB( K + 1 ),
+ $ 2*NMAX, BB, LDB, RESET, ZERO )
+ ELSE
+ CALL CMAKE( 'GE', ' ', ' ', MA, NA, AB( K*NMAX + 1 ),
+ $ NMAX, BB, LDB, RESET, ZERO )
+ END IF
+*
+ DO 100 ICU = 1, 2
+ UPLO = ICHU( ICU: ICU )
+ UPPER = UPLO.EQ.'U'
+*
+ DO 90 IA = 1, NALF
+ ALPHA = ALF( IA )
+*
+ DO 80 IB = 1, NBET
+ BETA = BET( IB )
+ IF( CONJ )THEN
+ RBETA = REAL( BETA )
+ BETA = CMPLX( RBETA, RZERO )
+ END IF
+ NULL = N.LE.0
+ IF( CONJ )
+ $ NULL = NULL.OR.( ( K.LE.0.OR.ALPHA.EQ.
+ $ ZERO ).AND.RBETA.EQ.RONE )
+*
+* Generate the matrix C.
+*
+ CALL CMAKE( SNAME( 2: 3 ), UPLO, ' ', N, N, C,
+ $ NMAX, CC, LDC, RESET, ZERO )
+*
+ NC = NC + 1
+*
+* Save every datum before calling the subroutine.
+*
+ UPLOS = UPLO
+ TRANSS = TRANS
+ NS = N
+ KS = K
+ ALS = ALPHA
+ DO 10 I = 1, LAA
+ AS( I ) = AA( I )
+ 10 CONTINUE
+ LDAS = LDA
+ DO 20 I = 1, LBB
+ BS( I ) = BB( I )
+ 20 CONTINUE
+ LDBS = LDB
+ IF( CONJ )THEN
+ RBETS = RBETA
+ ELSE
+ BETS = BETA
+ END IF
+ DO 30 I = 1, LCC
+ CS( I ) = CC( I )
+ 30 CONTINUE
+ LDCS = LDC
+*
+* Call the subroutine.
+*
+ IF( CONJ )THEN
+ IF( TRACE )
+ $ WRITE( NTRA, FMT = 9994 )NC, SNAME, UPLO,
+ $ TRANS, N, K, ALPHA, LDA, LDB, RBETA, LDC
+ IF( REWI )
+ $ REWIND NTRA
+ CALL CHER2K( UPLO, TRANS, N, K, ALPHA, AA,
+ $ LDA, BB, LDB, RBETA, CC, LDC )
+ ELSE
+ IF( TRACE )
+ $ WRITE( NTRA, FMT = 9993 )NC, SNAME, UPLO,
+ $ TRANS, N, K, ALPHA, LDA, LDB, BETA, LDC
+ IF( REWI )
+ $ REWIND NTRA
+ CALL CSYR2K( UPLO, TRANS, N, K, ALPHA, AA,
+ $ LDA, BB, LDB, BETA, CC, LDC )
+ END IF
+*
+* Check if error-exit was taken incorrectly.
+*
+ IF( .NOT.OK )THEN
+ WRITE( NOUT, FMT = 9992 )
+ FATAL = .TRUE.
+ GO TO 150
+ END IF
+*
+* See what data changed inside subroutines.
+*
+ ISAME( 1 ) = UPLOS.EQ.UPLO
+ ISAME( 2 ) = TRANSS.EQ.TRANS
+ ISAME( 3 ) = NS.EQ.N
+ ISAME( 4 ) = KS.EQ.K
+ ISAME( 5 ) = ALS.EQ.ALPHA
+ ISAME( 6 ) = LCE( AS, AA, LAA )
+ ISAME( 7 ) = LDAS.EQ.LDA
+ ISAME( 8 ) = LCE( BS, BB, LBB )
+ ISAME( 9 ) = LDBS.EQ.LDB
+ IF( CONJ )THEN
+ ISAME( 10 ) = RBETS.EQ.RBETA
+ ELSE
+ ISAME( 10 ) = BETS.EQ.BETA
+ END IF
+ IF( NULL )THEN
+ ISAME( 11 ) = LCE( CS, CC, LCC )
+ ELSE
+ ISAME( 11 ) = LCERES( 'HE', UPLO, N, N, CS,
+ $ CC, LDC )
+ END IF
+ ISAME( 12 ) = LDCS.EQ.LDC
+*
+* If data was incorrectly changed, report and
+* return.
+*
+ SAME = .TRUE.
+ DO 40 I = 1, NARGS
+ SAME = SAME.AND.ISAME( I )
+ IF( .NOT.ISAME( I ) )
+ $ WRITE( NOUT, FMT = 9998 )I
+ 40 CONTINUE
+ IF( .NOT.SAME )THEN
+ FATAL = .TRUE.
+ GO TO 150
+ END IF
+*
+ IF( .NOT.NULL )THEN
+*
+* Check the result column by column.
+*
+ IF( CONJ )THEN
+ TRANST = 'C'
+ ELSE
+ TRANST = 'T'
+ END IF
+ JJAB = 1
+ JC = 1
+ DO 70 J = 1, N
+ IF( UPPER )THEN
+ JJ = 1
+ LJ = J
+ ELSE
+ JJ = J
+ LJ = N - J + 1
+ END IF
+ IF( TRAN )THEN
+ DO 50 I = 1, K
+ W( I ) = ALPHA*AB( ( J - 1 )*2*
+ $ NMAX + K + I )
+ IF( CONJ )THEN
+ W( K + I ) = CONJG( ALPHA )*
+ $ AB( ( J - 1 )*2*
+ $ NMAX + I )
+ ELSE
+ W( K + I ) = ALPHA*
+ $ AB( ( J - 1 )*2*
+ $ NMAX + I )
+ END IF
+ 50 CONTINUE
+ CALL CMMCH( TRANST, 'N', LJ, 1, 2*K,
+ $ ONE, AB( JJAB ), 2*NMAX, W,
+ $ 2*NMAX, BETA, C( JJ, J ),
+ $ NMAX, CT, G, CC( JC ), LDC,
+ $ EPS, ERR, FATAL, NOUT,
+ $ .TRUE. )
+ ELSE
+ DO 60 I = 1, K
+ IF( CONJ )THEN
+ W( I ) = ALPHA*CONJG( AB( ( K +
+ $ I - 1 )*NMAX + J ) )
+ W( K + I ) = CONJG( ALPHA*
+ $ AB( ( I - 1 )*NMAX +
+ $ J ) )
+ ELSE
+ W( I ) = ALPHA*AB( ( K + I - 1 )*
+ $ NMAX + J )
+ W( K + I ) = ALPHA*
+ $ AB( ( I - 1 )*NMAX +
+ $ J )
+ END IF
+ 60 CONTINUE
+ CALL CMMCH( 'N', 'N', LJ, 1, 2*K, ONE,
+ $ AB( JJ ), NMAX, W, 2*NMAX,
+ $ BETA, C( JJ, J ), NMAX, CT,
+ $ G, CC( JC ), LDC, EPS, ERR,
+ $ FATAL, NOUT, .TRUE. )
+ END IF
+ IF( UPPER )THEN
+ JC = JC + LDC
+ ELSE
+ JC = JC + LDC + 1
+ IF( TRAN )
+ $ JJAB = JJAB + 2*NMAX
+ END IF
+ ERRMAX = MAX( ERRMAX, ERR )
+* If got really bad answer, report and
+* return.
+ IF( FATAL )
+ $ GO TO 140
+ 70 CONTINUE
+ END IF
+*
+ 80 CONTINUE
+*
+ 90 CONTINUE
+*
+ 100 CONTINUE
+*
+ 110 CONTINUE
+*
+ 120 CONTINUE
+*
+ 130 CONTINUE
+*
+* Report result.
+*
+ IF( ERRMAX.LT.THRESH )THEN
+ WRITE( NOUT, FMT = 9999 )SNAME, NC
+ ELSE
+ WRITE( NOUT, FMT = 9997 )SNAME, NC, ERRMAX
+ END IF
+ GO TO 160
+*
+ 140 CONTINUE
+ IF( N.GT.1 )
+ $ WRITE( NOUT, FMT = 9995 )J
+*
+ 150 CONTINUE
+ WRITE( NOUT, FMT = 9996 )SNAME
+ IF( CONJ )THEN
+ WRITE( NOUT, FMT = 9994 )NC, SNAME, UPLO, TRANS, N, K, ALPHA,
+ $ LDA, LDB, RBETA, LDC
+ ELSE
+ WRITE( NOUT, FMT = 9993 )NC, SNAME, UPLO, TRANS, N, K, ALPHA,
+ $ LDA, LDB, BETA, LDC
+ END IF
+*
+ 160 CONTINUE
+ RETURN
+*
+ 9999 FORMAT( ' ', A6, ' PASSED THE COMPUTATIONAL TESTS (', I6, ' CALL',
+ $ 'S)' )
+ 9998 FORMAT( ' ******* FATAL ERROR - PARAMETER NUMBER ', I2, ' WAS CH',
+ $ 'ANGED INCORRECTLY *******' )
+ 9997 FORMAT( ' ', A6, ' COMPLETED THE COMPUTATIONAL TESTS (', I6, ' C',
+ $ 'ALLS)', /' ******* BUT WITH MAXIMUM TEST RATIO', F8.2,
+ $ ' - SUSPECT *******' )
+ 9996 FORMAT( ' ******* ', A6, ' FAILED ON CALL NUMBER:' )
+ 9995 FORMAT( ' THESE ARE THE RESULTS FOR COLUMN ', I3 )
+ 9994 FORMAT( 1X, I6, ': ', A6, '(', 2( '''', A1, ''',' ), 2( I3, ',' ),
+ $ '(', F4.1, ',', F4.1, '), A,', I3, ', B,', I3, ',', F4.1,
+ $ ', C,', I3, ') .' )
+ 9993 FORMAT( 1X, I6, ': ', A6, '(', 2( '''', A1, ''',' ), 2( I3, ',' ),
+ $ '(', F4.1, ',', F4.1, '), A,', I3, ', B,', I3, ',(', F4.1,
+ $ ',', F4.1, '), C,', I3, ') .' )
+ 9992 FORMAT( ' ******* FATAL ERROR - ERROR-EXIT TAKEN ON VALID CALL *',
+ $ '******' )
+*
+* End of CCHK5.
+*
+ END
+ SUBROUTINE CCHKE( ISNUM, SRNAMT, NOUT )
+*
+* Tests the error exits from the Level 3 Blas.
+* Requires a special version of the error-handling routine XERBLA.
+* A, B and C should not need to be defined.
+*
+* Auxiliary routine for test program for Level 3 Blas.
+*
+* -- Written on 8-February-1989.
+* Jack Dongarra, Argonne National Laboratory.
+* Iain Duff, AERE Harwell.
+* Jeremy Du Croz, Numerical Algorithms Group Ltd.
+* Sven Hammarling, Numerical Algorithms Group Ltd.
+*
+* 3-19-92: Initialize ALPHA, BETA, RALPHA, and RBETA (eca)
+* 3-19-92: Fix argument 12 in calls to CSYMM and CHEMM
+* with INFOT = 9 (eca)
+*
+* .. Scalar Arguments ..
+ INTEGER ISNUM, NOUT
+ CHARACTER*6 SRNAMT
+* .. Scalars in Common ..
+ INTEGER INFOT, NOUTC
+ LOGICAL LERR, OK
+* .. Parameters ..
+ REAL ONE, TWO
+ PARAMETER ( ONE = 1.0E0, TWO = 2.0E0 )
+* .. Local Scalars ..
+ COMPLEX ALPHA, BETA
+ REAL RALPHA, RBETA
+* .. Local Arrays ..
+ COMPLEX A( 2, 1 ), B( 2, 1 ), C( 2, 1 )
+* .. External Subroutines ..
+ EXTERNAL CGEMM, CHEMM, CHER2K, CHERK, CHKXER, CSYMM,
+ $ CSYR2K, CSYRK, CTRMM, CTRSM
+* .. Common blocks ..
+ COMMON /INFOC/INFOT, NOUTC, OK, LERR
+* .. Executable Statements ..
+* OK is set to .FALSE. by the special version of XERBLA or by CHKXER
+* if anything is wrong.
+ OK = .TRUE.
+* LERR is set to .TRUE. by the special version of XERBLA each time
+* it is called, and is then tested and re-set by CHKXER.
+ LERR = .FALSE.
+*
+* Initialize ALPHA, BETA, RALPHA, and RBETA.
+*
+ ALPHA = CMPLX( ONE, -ONE )
+ BETA = CMPLX( TWO, -TWO )
+ RALPHA = ONE
+ RBETA = TWO
+*
+ GO TO ( 10, 20, 30, 40, 50, 60, 70, 80,
+ $ 90 )ISNUM
+ 10 INFOT = 1
+ CALL CGEMM( '/', 'N', 0, 0, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 1
+ CALL CGEMM( '/', 'C', 0, 0, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 1
+ CALL CGEMM( '/', 'T', 0, 0, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 2
+ CALL CGEMM( 'N', '/', 0, 0, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 2
+ CALL CGEMM( 'C', '/', 0, 0, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 2
+ CALL CGEMM( 'T', '/', 0, 0, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 3
+ CALL CGEMM( 'N', 'N', -1, 0, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 3
+ CALL CGEMM( 'N', 'C', -1, 0, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 3
+ CALL CGEMM( 'N', 'T', -1, 0, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 3
+ CALL CGEMM( 'C', 'N', -1, 0, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 3
+ CALL CGEMM( 'C', 'C', -1, 0, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 3
+ CALL CGEMM( 'C', 'T', -1, 0, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 3
+ CALL CGEMM( 'T', 'N', -1, 0, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 3
+ CALL CGEMM( 'T', 'C', -1, 0, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 3
+ CALL CGEMM( 'T', 'T', -1, 0, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 4
+ CALL CGEMM( 'N', 'N', 0, -1, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 4
+ CALL CGEMM( 'N', 'C', 0, -1, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 4
+ CALL CGEMM( 'N', 'T', 0, -1, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 4
+ CALL CGEMM( 'C', 'N', 0, -1, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 4
+ CALL CGEMM( 'C', 'C', 0, -1, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 4
+ CALL CGEMM( 'C', 'T', 0, -1, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 4
+ CALL CGEMM( 'T', 'N', 0, -1, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 4
+ CALL CGEMM( 'T', 'C', 0, -1, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 4
+ CALL CGEMM( 'T', 'T', 0, -1, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 5
+ CALL CGEMM( 'N', 'N', 0, 0, -1, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 5
+ CALL CGEMM( 'N', 'C', 0, 0, -1, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 5
+ CALL CGEMM( 'N', 'T', 0, 0, -1, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 5
+ CALL CGEMM( 'C', 'N', 0, 0, -1, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 5
+ CALL CGEMM( 'C', 'C', 0, 0, -1, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 5
+ CALL CGEMM( 'C', 'T', 0, 0, -1, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 5
+ CALL CGEMM( 'T', 'N', 0, 0, -1, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 5
+ CALL CGEMM( 'T', 'C', 0, 0, -1, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 5
+ CALL CGEMM( 'T', 'T', 0, 0, -1, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 8
+ CALL CGEMM( 'N', 'N', 2, 0, 0, ALPHA, A, 1, B, 1, BETA, C, 2 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 8
+ CALL CGEMM( 'N', 'C', 2, 0, 0, ALPHA, A, 1, B, 1, BETA, C, 2 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 8
+ CALL CGEMM( 'N', 'T', 2, 0, 0, ALPHA, A, 1, B, 1, BETA, C, 2 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 8
+ CALL CGEMM( 'C', 'N', 0, 0, 2, ALPHA, A, 1, B, 2, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 8
+ CALL CGEMM( 'C', 'C', 0, 0, 2, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 8
+ CALL CGEMM( 'C', 'T', 0, 0, 2, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 8
+ CALL CGEMM( 'T', 'N', 0, 0, 2, ALPHA, A, 1, B, 2, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 8
+ CALL CGEMM( 'T', 'C', 0, 0, 2, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 8
+ CALL CGEMM( 'T', 'T', 0, 0, 2, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 10
+ CALL CGEMM( 'N', 'N', 0, 0, 2, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 10
+ CALL CGEMM( 'C', 'N', 0, 0, 2, ALPHA, A, 2, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 10
+ CALL CGEMM( 'T', 'N', 0, 0, 2, ALPHA, A, 2, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 10
+ CALL CGEMM( 'N', 'C', 0, 2, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 10
+ CALL CGEMM( 'C', 'C', 0, 2, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 10
+ CALL CGEMM( 'T', 'C', 0, 2, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 10
+ CALL CGEMM( 'N', 'T', 0, 2, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 10
+ CALL CGEMM( 'C', 'T', 0, 2, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 10
+ CALL CGEMM( 'T', 'T', 0, 2, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 13
+ CALL CGEMM( 'N', 'N', 2, 0, 0, ALPHA, A, 2, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 13
+ CALL CGEMM( 'N', 'C', 2, 0, 0, ALPHA, A, 2, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 13
+ CALL CGEMM( 'N', 'T', 2, 0, 0, ALPHA, A, 2, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 13
+ CALL CGEMM( 'C', 'N', 2, 0, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 13
+ CALL CGEMM( 'C', 'C', 2, 0, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 13
+ CALL CGEMM( 'C', 'T', 2, 0, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 13
+ CALL CGEMM( 'T', 'N', 2, 0, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 13
+ CALL CGEMM( 'T', 'C', 2, 0, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 13
+ CALL CGEMM( 'T', 'T', 2, 0, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ GO TO 100
+ 20 INFOT = 1
+ CALL CHEMM( '/', 'U', 0, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 2
+ CALL CHEMM( 'L', '/', 0, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 3
+ CALL CHEMM( 'L', 'U', -1, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 3
+ CALL CHEMM( 'R', 'U', -1, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 3
+ CALL CHEMM( 'L', 'L', -1, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 3
+ CALL CHEMM( 'R', 'L', -1, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 4
+ CALL CHEMM( 'L', 'U', 0, -1, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 4
+ CALL CHEMM( 'R', 'U', 0, -1, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 4
+ CALL CHEMM( 'L', 'L', 0, -1, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 4
+ CALL CHEMM( 'R', 'L', 0, -1, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 7
+ CALL CHEMM( 'L', 'U', 2, 0, ALPHA, A, 1, B, 2, BETA, C, 2 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 7
+ CALL CHEMM( 'R', 'U', 0, 2, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 7
+ CALL CHEMM( 'L', 'L', 2, 0, ALPHA, A, 1, B, 2, BETA, C, 2 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 7
+ CALL CHEMM( 'R', 'L', 0, 2, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 9
+ CALL CHEMM( 'L', 'U', 2, 0, ALPHA, A, 2, B, 1, BETA, C, 2 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 9
+ CALL CHEMM( 'R', 'U', 2, 0, ALPHA, A, 1, B, 1, BETA, C, 2 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 9
+ CALL CHEMM( 'L', 'L', 2, 0, ALPHA, A, 2, B, 1, BETA, C, 2 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 9
+ CALL CHEMM( 'R', 'L', 2, 0, ALPHA, A, 1, B, 1, BETA, C, 2 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 12
+ CALL CHEMM( 'L', 'U', 2, 0, ALPHA, A, 2, B, 2, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 12
+ CALL CHEMM( 'R', 'U', 2, 0, ALPHA, A, 1, B, 2, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 12
+ CALL CHEMM( 'L', 'L', 2, 0, ALPHA, A, 2, B, 2, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 12
+ CALL CHEMM( 'R', 'L', 2, 0, ALPHA, A, 1, B, 2, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ GO TO 100
+ 30 INFOT = 1
+ CALL CSYMM( '/', 'U', 0, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 2
+ CALL CSYMM( 'L', '/', 0, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 3
+ CALL CSYMM( 'L', 'U', -1, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 3
+ CALL CSYMM( 'R', 'U', -1, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 3
+ CALL CSYMM( 'L', 'L', -1, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 3
+ CALL CSYMM( 'R', 'L', -1, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 4
+ CALL CSYMM( 'L', 'U', 0, -1, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 4
+ CALL CSYMM( 'R', 'U', 0, -1, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 4
+ CALL CSYMM( 'L', 'L', 0, -1, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 4
+ CALL CSYMM( 'R', 'L', 0, -1, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 7
+ CALL CSYMM( 'L', 'U', 2, 0, ALPHA, A, 1, B, 2, BETA, C, 2 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 7
+ CALL CSYMM( 'R', 'U', 0, 2, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 7
+ CALL CSYMM( 'L', 'L', 2, 0, ALPHA, A, 1, B, 2, BETA, C, 2 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 7
+ CALL CSYMM( 'R', 'L', 0, 2, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 9
+ CALL CSYMM( 'L', 'U', 2, 0, ALPHA, A, 2, B, 1, BETA, C, 2 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 9
+ CALL CSYMM( 'R', 'U', 2, 0, ALPHA, A, 1, B, 1, BETA, C, 2 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 9
+ CALL CSYMM( 'L', 'L', 2, 0, ALPHA, A, 2, B, 1, BETA, C, 2 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 9
+ CALL CSYMM( 'R', 'L', 2, 0, ALPHA, A, 1, B, 1, BETA, C, 2 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 12
+ CALL CSYMM( 'L', 'U', 2, 0, ALPHA, A, 2, B, 2, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 12
+ CALL CSYMM( 'R', 'U', 2, 0, ALPHA, A, 1, B, 2, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 12
+ CALL CSYMM( 'L', 'L', 2, 0, ALPHA, A, 2, B, 2, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 12
+ CALL CSYMM( 'R', 'L', 2, 0, ALPHA, A, 1, B, 2, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ GO TO 100
+ 40 INFOT = 1
+ CALL CTRMM( '/', 'U', 'N', 'N', 0, 0, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 2
+ CALL CTRMM( 'L', '/', 'N', 'N', 0, 0, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 3
+ CALL CTRMM( 'L', 'U', '/', 'N', 0, 0, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 4
+ CALL CTRMM( 'L', 'U', 'N', '/', 0, 0, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 5
+ CALL CTRMM( 'L', 'U', 'N', 'N', -1, 0, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 5
+ CALL CTRMM( 'L', 'U', 'C', 'N', -1, 0, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 5
+ CALL CTRMM( 'L', 'U', 'T', 'N', -1, 0, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 5
+ CALL CTRMM( 'R', 'U', 'N', 'N', -1, 0, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 5
+ CALL CTRMM( 'R', 'U', 'C', 'N', -1, 0, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 5
+ CALL CTRMM( 'R', 'U', 'T', 'N', -1, 0, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 5
+ CALL CTRMM( 'L', 'L', 'N', 'N', -1, 0, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 5
+ CALL CTRMM( 'L', 'L', 'C', 'N', -1, 0, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 5
+ CALL CTRMM( 'L', 'L', 'T', 'N', -1, 0, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 5
+ CALL CTRMM( 'R', 'L', 'N', 'N', -1, 0, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 5
+ CALL CTRMM( 'R', 'L', 'C', 'N', -1, 0, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 5
+ CALL CTRMM( 'R', 'L', 'T', 'N', -1, 0, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 6
+ CALL CTRMM( 'L', 'U', 'N', 'N', 0, -1, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 6
+ CALL CTRMM( 'L', 'U', 'C', 'N', 0, -1, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 6
+ CALL CTRMM( 'L', 'U', 'T', 'N', 0, -1, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 6
+ CALL CTRMM( 'R', 'U', 'N', 'N', 0, -1, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 6
+ CALL CTRMM( 'R', 'U', 'C', 'N', 0, -1, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 6
+ CALL CTRMM( 'R', 'U', 'T', 'N', 0, -1, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 6
+ CALL CTRMM( 'L', 'L', 'N', 'N', 0, -1, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 6
+ CALL CTRMM( 'L', 'L', 'C', 'N', 0, -1, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 6
+ CALL CTRMM( 'L', 'L', 'T', 'N', 0, -1, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 6
+ CALL CTRMM( 'R', 'L', 'N', 'N', 0, -1, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 6
+ CALL CTRMM( 'R', 'L', 'C', 'N', 0, -1, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 6
+ CALL CTRMM( 'R', 'L', 'T', 'N', 0, -1, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 9
+ CALL CTRMM( 'L', 'U', 'N', 'N', 2, 0, ALPHA, A, 1, B, 2 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 9
+ CALL CTRMM( 'L', 'U', 'C', 'N', 2, 0, ALPHA, A, 1, B, 2 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 9
+ CALL CTRMM( 'L', 'U', 'T', 'N', 2, 0, ALPHA, A, 1, B, 2 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 9
+ CALL CTRMM( 'R', 'U', 'N', 'N', 0, 2, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 9
+ CALL CTRMM( 'R', 'U', 'C', 'N', 0, 2, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 9
+ CALL CTRMM( 'R', 'U', 'T', 'N', 0, 2, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 9
+ CALL CTRMM( 'L', 'L', 'N', 'N', 2, 0, ALPHA, A, 1, B, 2 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 9
+ CALL CTRMM( 'L', 'L', 'C', 'N', 2, 0, ALPHA, A, 1, B, 2 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 9
+ CALL CTRMM( 'L', 'L', 'T', 'N', 2, 0, ALPHA, A, 1, B, 2 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 9
+ CALL CTRMM( 'R', 'L', 'N', 'N', 0, 2, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 9
+ CALL CTRMM( 'R', 'L', 'C', 'N', 0, 2, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 9
+ CALL CTRMM( 'R', 'L', 'T', 'N', 0, 2, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 11
+ CALL CTRMM( 'L', 'U', 'N', 'N', 2, 0, ALPHA, A, 2, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 11
+ CALL CTRMM( 'L', 'U', 'C', 'N', 2, 0, ALPHA, A, 2, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 11
+ CALL CTRMM( 'L', 'U', 'T', 'N', 2, 0, ALPHA, A, 2, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 11
+ CALL CTRMM( 'R', 'U', 'N', 'N', 2, 0, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 11
+ CALL CTRMM( 'R', 'U', 'C', 'N', 2, 0, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 11
+ CALL CTRMM( 'R', 'U', 'T', 'N', 2, 0, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 11
+ CALL CTRMM( 'L', 'L', 'N', 'N', 2, 0, ALPHA, A, 2, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 11
+ CALL CTRMM( 'L', 'L', 'C', 'N', 2, 0, ALPHA, A, 2, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 11
+ CALL CTRMM( 'L', 'L', 'T', 'N', 2, 0, ALPHA, A, 2, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 11
+ CALL CTRMM( 'R', 'L', 'N', 'N', 2, 0, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 11
+ CALL CTRMM( 'R', 'L', 'C', 'N', 2, 0, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 11
+ CALL CTRMM( 'R', 'L', 'T', 'N', 2, 0, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ GO TO 100
+ 50 INFOT = 1
+ CALL CTRSM( '/', 'U', 'N', 'N', 0, 0, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 2
+ CALL CTRSM( 'L', '/', 'N', 'N', 0, 0, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 3
+ CALL CTRSM( 'L', 'U', '/', 'N', 0, 0, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 4
+ CALL CTRSM( 'L', 'U', 'N', '/', 0, 0, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 5
+ CALL CTRSM( 'L', 'U', 'N', 'N', -1, 0, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 5
+ CALL CTRSM( 'L', 'U', 'C', 'N', -1, 0, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 5
+ CALL CTRSM( 'L', 'U', 'T', 'N', -1, 0, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 5
+ CALL CTRSM( 'R', 'U', 'N', 'N', -1, 0, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 5
+ CALL CTRSM( 'R', 'U', 'C', 'N', -1, 0, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 5
+ CALL CTRSM( 'R', 'U', 'T', 'N', -1, 0, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 5
+ CALL CTRSM( 'L', 'L', 'N', 'N', -1, 0, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 5
+ CALL CTRSM( 'L', 'L', 'C', 'N', -1, 0, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 5
+ CALL CTRSM( 'L', 'L', 'T', 'N', -1, 0, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 5
+ CALL CTRSM( 'R', 'L', 'N', 'N', -1, 0, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 5
+ CALL CTRSM( 'R', 'L', 'C', 'N', -1, 0, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 5
+ CALL CTRSM( 'R', 'L', 'T', 'N', -1, 0, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 6
+ CALL CTRSM( 'L', 'U', 'N', 'N', 0, -1, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 6
+ CALL CTRSM( 'L', 'U', 'C', 'N', 0, -1, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 6
+ CALL CTRSM( 'L', 'U', 'T', 'N', 0, -1, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 6
+ CALL CTRSM( 'R', 'U', 'N', 'N', 0, -1, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 6
+ CALL CTRSM( 'R', 'U', 'C', 'N', 0, -1, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 6
+ CALL CTRSM( 'R', 'U', 'T', 'N', 0, -1, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 6
+ CALL CTRSM( 'L', 'L', 'N', 'N', 0, -1, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 6
+ CALL CTRSM( 'L', 'L', 'C', 'N', 0, -1, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 6
+ CALL CTRSM( 'L', 'L', 'T', 'N', 0, -1, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 6
+ CALL CTRSM( 'R', 'L', 'N', 'N', 0, -1, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 6
+ CALL CTRSM( 'R', 'L', 'C', 'N', 0, -1, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 6
+ CALL CTRSM( 'R', 'L', 'T', 'N', 0, -1, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 9
+ CALL CTRSM( 'L', 'U', 'N', 'N', 2, 0, ALPHA, A, 1, B, 2 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 9
+ CALL CTRSM( 'L', 'U', 'C', 'N', 2, 0, ALPHA, A, 1, B, 2 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 9
+ CALL CTRSM( 'L', 'U', 'T', 'N', 2, 0, ALPHA, A, 1, B, 2 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 9
+ CALL CTRSM( 'R', 'U', 'N', 'N', 0, 2, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 9
+ CALL CTRSM( 'R', 'U', 'C', 'N', 0, 2, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 9
+ CALL CTRSM( 'R', 'U', 'T', 'N', 0, 2, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 9
+ CALL CTRSM( 'L', 'L', 'N', 'N', 2, 0, ALPHA, A, 1, B, 2 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 9
+ CALL CTRSM( 'L', 'L', 'C', 'N', 2, 0, ALPHA, A, 1, B, 2 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 9
+ CALL CTRSM( 'L', 'L', 'T', 'N', 2, 0, ALPHA, A, 1, B, 2 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 9
+ CALL CTRSM( 'R', 'L', 'N', 'N', 0, 2, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 9
+ CALL CTRSM( 'R', 'L', 'C', 'N', 0, 2, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 9
+ CALL CTRSM( 'R', 'L', 'T', 'N', 0, 2, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 11
+ CALL CTRSM( 'L', 'U', 'N', 'N', 2, 0, ALPHA, A, 2, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 11
+ CALL CTRSM( 'L', 'U', 'C', 'N', 2, 0, ALPHA, A, 2, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 11
+ CALL CTRSM( 'L', 'U', 'T', 'N', 2, 0, ALPHA, A, 2, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 11
+ CALL CTRSM( 'R', 'U', 'N', 'N', 2, 0, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 11
+ CALL CTRSM( 'R', 'U', 'C', 'N', 2, 0, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 11
+ CALL CTRSM( 'R', 'U', 'T', 'N', 2, 0, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 11
+ CALL CTRSM( 'L', 'L', 'N', 'N', 2, 0, ALPHA, A, 2, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 11
+ CALL CTRSM( 'L', 'L', 'C', 'N', 2, 0, ALPHA, A, 2, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 11
+ CALL CTRSM( 'L', 'L', 'T', 'N', 2, 0, ALPHA, A, 2, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 11
+ CALL CTRSM( 'R', 'L', 'N', 'N', 2, 0, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 11
+ CALL CTRSM( 'R', 'L', 'C', 'N', 2, 0, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 11
+ CALL CTRSM( 'R', 'L', 'T', 'N', 2, 0, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ GO TO 100
+ 60 INFOT = 1
+ CALL CHERK( '/', 'N', 0, 0, RALPHA, A, 1, RBETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 2
+ CALL CHERK( 'U', 'T', 0, 0, RALPHA, A, 1, RBETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 3
+ CALL CHERK( 'U', 'N', -1, 0, RALPHA, A, 1, RBETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 3
+ CALL CHERK( 'U', 'C', -1, 0, RALPHA, A, 1, RBETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 3
+ CALL CHERK( 'L', 'N', -1, 0, RALPHA, A, 1, RBETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 3
+ CALL CHERK( 'L', 'C', -1, 0, RALPHA, A, 1, RBETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 4
+ CALL CHERK( 'U', 'N', 0, -1, RALPHA, A, 1, RBETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 4
+ CALL CHERK( 'U', 'C', 0, -1, RALPHA, A, 1, RBETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 4
+ CALL CHERK( 'L', 'N', 0, -1, RALPHA, A, 1, RBETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 4
+ CALL CHERK( 'L', 'C', 0, -1, RALPHA, A, 1, RBETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 7
+ CALL CHERK( 'U', 'N', 2, 0, RALPHA, A, 1, RBETA, C, 2 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 7
+ CALL CHERK( 'U', 'C', 0, 2, RALPHA, A, 1, RBETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 7
+ CALL CHERK( 'L', 'N', 2, 0, RALPHA, A, 1, RBETA, C, 2 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 7
+ CALL CHERK( 'L', 'C', 0, 2, RALPHA, A, 1, RBETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 10
+ CALL CHERK( 'U', 'N', 2, 0, RALPHA, A, 2, RBETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 10
+ CALL CHERK( 'U', 'C', 2, 0, RALPHA, A, 1, RBETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 10
+ CALL CHERK( 'L', 'N', 2, 0, RALPHA, A, 2, RBETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 10
+ CALL CHERK( 'L', 'C', 2, 0, RALPHA, A, 1, RBETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ GO TO 100
+ 70 INFOT = 1
+ CALL CSYRK( '/', 'N', 0, 0, ALPHA, A, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 2
+ CALL CSYRK( 'U', 'C', 0, 0, ALPHA, A, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 3
+ CALL CSYRK( 'U', 'N', -1, 0, ALPHA, A, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 3
+ CALL CSYRK( 'U', 'T', -1, 0, ALPHA, A, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 3
+ CALL CSYRK( 'L', 'N', -1, 0, ALPHA, A, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 3
+ CALL CSYRK( 'L', 'T', -1, 0, ALPHA, A, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 4
+ CALL CSYRK( 'U', 'N', 0, -1, ALPHA, A, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 4
+ CALL CSYRK( 'U', 'T', 0, -1, ALPHA, A, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 4
+ CALL CSYRK( 'L', 'N', 0, -1, ALPHA, A, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 4
+ CALL CSYRK( 'L', 'T', 0, -1, ALPHA, A, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 7
+ CALL CSYRK( 'U', 'N', 2, 0, ALPHA, A, 1, BETA, C, 2 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 7
+ CALL CSYRK( 'U', 'T', 0, 2, ALPHA, A, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 7
+ CALL CSYRK( 'L', 'N', 2, 0, ALPHA, A, 1, BETA, C, 2 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 7
+ CALL CSYRK( 'L', 'T', 0, 2, ALPHA, A, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 10
+ CALL CSYRK( 'U', 'N', 2, 0, ALPHA, A, 2, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 10
+ CALL CSYRK( 'U', 'T', 2, 0, ALPHA, A, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 10
+ CALL CSYRK( 'L', 'N', 2, 0, ALPHA, A, 2, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 10
+ CALL CSYRK( 'L', 'T', 2, 0, ALPHA, A, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ GO TO 100
+ 80 INFOT = 1
+ CALL CHER2K( '/', 'N', 0, 0, ALPHA, A, 1, B, 1, RBETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 2
+ CALL CHER2K( 'U', 'T', 0, 0, ALPHA, A, 1, B, 1, RBETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 3
+ CALL CHER2K( 'U', 'N', -1, 0, ALPHA, A, 1, B, 1, RBETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 3
+ CALL CHER2K( 'U', 'C', -1, 0, ALPHA, A, 1, B, 1, RBETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 3
+ CALL CHER2K( 'L', 'N', -1, 0, ALPHA, A, 1, B, 1, RBETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 3
+ CALL CHER2K( 'L', 'C', -1, 0, ALPHA, A, 1, B, 1, RBETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 4
+ CALL CHER2K( 'U', 'N', 0, -1, ALPHA, A, 1, B, 1, RBETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 4
+ CALL CHER2K( 'U', 'C', 0, -1, ALPHA, A, 1, B, 1, RBETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 4
+ CALL CHER2K( 'L', 'N', 0, -1, ALPHA, A, 1, B, 1, RBETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 4
+ CALL CHER2K( 'L', 'C', 0, -1, ALPHA, A, 1, B, 1, RBETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 7
+ CALL CHER2K( 'U', 'N', 2, 0, ALPHA, A, 1, B, 1, RBETA, C, 2 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 7
+ CALL CHER2K( 'U', 'C', 0, 2, ALPHA, A, 1, B, 1, RBETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 7
+ CALL CHER2K( 'L', 'N', 2, 0, ALPHA, A, 1, B, 1, RBETA, C, 2 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 7
+ CALL CHER2K( 'L', 'C', 0, 2, ALPHA, A, 1, B, 1, RBETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 9
+ CALL CHER2K( 'U', 'N', 2, 0, ALPHA, A, 2, B, 1, RBETA, C, 2 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 9
+ CALL CHER2K( 'U', 'C', 0, 2, ALPHA, A, 2, B, 1, RBETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 9
+ CALL CHER2K( 'L', 'N', 2, 0, ALPHA, A, 2, B, 1, RBETA, C, 2 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 9
+ CALL CHER2K( 'L', 'C', 0, 2, ALPHA, A, 2, B, 1, RBETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 12
+ CALL CHER2K( 'U', 'N', 2, 0, ALPHA, A, 2, B, 2, RBETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 12
+ CALL CHER2K( 'U', 'C', 2, 0, ALPHA, A, 1, B, 1, RBETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 12
+ CALL CHER2K( 'L', 'N', 2, 0, ALPHA, A, 2, B, 2, RBETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 12
+ CALL CHER2K( 'L', 'C', 2, 0, ALPHA, A, 1, B, 1, RBETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ GO TO 100
+ 90 INFOT = 1
+ CALL CSYR2K( '/', 'N', 0, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 2
+ CALL CSYR2K( 'U', 'C', 0, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 3
+ CALL CSYR2K( 'U', 'N', -1, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 3
+ CALL CSYR2K( 'U', 'T', -1, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 3
+ CALL CSYR2K( 'L', 'N', -1, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 3
+ CALL CSYR2K( 'L', 'T', -1, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 4
+ CALL CSYR2K( 'U', 'N', 0, -1, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 4
+ CALL CSYR2K( 'U', 'T', 0, -1, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 4
+ CALL CSYR2K( 'L', 'N', 0, -1, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 4
+ CALL CSYR2K( 'L', 'T', 0, -1, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 7
+ CALL CSYR2K( 'U', 'N', 2, 0, ALPHA, A, 1, B, 1, BETA, C, 2 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 7
+ CALL CSYR2K( 'U', 'T', 0, 2, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 7
+ CALL CSYR2K( 'L', 'N', 2, 0, ALPHA, A, 1, B, 1, BETA, C, 2 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 7
+ CALL CSYR2K( 'L', 'T', 0, 2, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 9
+ CALL CSYR2K( 'U', 'N', 2, 0, ALPHA, A, 2, B, 1, BETA, C, 2 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 9
+ CALL CSYR2K( 'U', 'T', 0, 2, ALPHA, A, 2, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 9
+ CALL CSYR2K( 'L', 'N', 2, 0, ALPHA, A, 2, B, 1, BETA, C, 2 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 9
+ CALL CSYR2K( 'L', 'T', 0, 2, ALPHA, A, 2, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 12
+ CALL CSYR2K( 'U', 'N', 2, 0, ALPHA, A, 2, B, 2, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 12
+ CALL CSYR2K( 'U', 'T', 2, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 12
+ CALL CSYR2K( 'L', 'N', 2, 0, ALPHA, A, 2, B, 2, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 12
+ CALL CSYR2K( 'L', 'T', 2, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+*
+ 100 IF( OK )THEN
+ WRITE( NOUT, FMT = 9999 )SRNAMT
+ ELSE
+ WRITE( NOUT, FMT = 9998 )SRNAMT
+ END IF
+ RETURN
+*
+ 9999 FORMAT( ' ', A6, ' PASSED THE TESTS OF ERROR-EXITS' )
+ 9998 FORMAT( ' ******* ', A6, ' FAILED THE TESTS OF ERROR-EXITS *****',
+ $ '**' )
+*
+* End of CCHKE.
+*
+ END
+ SUBROUTINE CMAKE( TYPE, UPLO, DIAG, M, N, A, NMAX, AA, LDA, RESET,
+ $ TRANSL )
+*
+* Generates values for an M by N matrix A.
+* Stores the values in the array AA in the data structure required
+* by the routine, with unwanted elements set to rogue value.
+*
+* TYPE is 'GE', 'HE', 'SY' or 'TR'.
+*
+* Auxiliary routine for test program for Level 3 Blas.
+*
+* -- Written on 8-February-1989.
+* Jack Dongarra, Argonne National Laboratory.
+* Iain Duff, AERE Harwell.
+* Jeremy Du Croz, Numerical Algorithms Group Ltd.
+* Sven Hammarling, Numerical Algorithms Group Ltd.
+*
+* .. Parameters ..
+ COMPLEX ZERO, ONE
+ PARAMETER ( ZERO = ( 0.0, 0.0 ), ONE = ( 1.0, 0.0 ) )
+ COMPLEX ROGUE
+ PARAMETER ( ROGUE = ( -1.0E10, 1.0E10 ) )
+ REAL RZERO
+ PARAMETER ( RZERO = 0.0 )
+ REAL RROGUE
+ PARAMETER ( RROGUE = -1.0E10 )
+* .. Scalar Arguments ..
+ COMPLEX TRANSL
+ INTEGER LDA, M, N, NMAX
+ LOGICAL RESET
+ CHARACTER*1 DIAG, UPLO
+ CHARACTER*2 TYPE
+* .. Array Arguments ..
+ COMPLEX A( NMAX, * ), AA( * )
+* .. Local Scalars ..
+ INTEGER I, IBEG, IEND, J, JJ
+ LOGICAL GEN, HER, LOWER, SYM, TRI, UNIT, UPPER
+* .. External Functions ..
+ COMPLEX CBEG
+ EXTERNAL CBEG
+* .. Intrinsic Functions ..
+ INTRINSIC CMPLX, CONJG, REAL
+* .. Executable Statements ..
+ GEN = TYPE.EQ.'GE'
+ HER = TYPE.EQ.'HE'
+ SYM = TYPE.EQ.'SY'
+ TRI = TYPE.EQ.'TR'
+ UPPER = ( HER.OR.SYM.OR.TRI ).AND.UPLO.EQ.'U'
+ LOWER = ( HER.OR.SYM.OR.TRI ).AND.UPLO.EQ.'L'
+ UNIT = TRI.AND.DIAG.EQ.'U'
+*
+* Generate data in array A.
+*
+ DO 20 J = 1, N
+ DO 10 I = 1, M
+ IF( GEN.OR.( UPPER.AND.I.LE.J ).OR.( LOWER.AND.I.GE.J ) )
+ $ THEN
+ A( I, J ) = CBEG( RESET ) + TRANSL
+ IF( I.NE.J )THEN
+* Set some elements to zero
+ IF( N.GT.3.AND.J.EQ.N/2 )
+ $ A( I, J ) = ZERO
+ IF( HER )THEN
+ A( J, I ) = CONJG( A( I, J ) )
+ ELSE IF( SYM )THEN
+ A( J, I ) = A( I, J )
+ ELSE IF( TRI )THEN
+ A( J, I ) = ZERO
+ END IF
+ END IF
+ END IF
+ 10 CONTINUE
+ IF( HER )
+ $ A( J, J ) = CMPLX( REAL( A( J, J ) ), RZERO )
+ IF( TRI )
+ $ A( J, J ) = A( J, J ) + ONE
+ IF( UNIT )
+ $ A( J, J ) = ONE
+ 20 CONTINUE
+*
+* Store elements in array AS in data structure required by routine.
+*
+ IF( TYPE.EQ.'GE' )THEN
+ DO 50 J = 1, N
+ DO 30 I = 1, M
+ AA( I + ( J - 1 )*LDA ) = A( I, J )
+ 30 CONTINUE
+ DO 40 I = M + 1, LDA
+ AA( I + ( J - 1 )*LDA ) = ROGUE
+ 40 CONTINUE
+ 50 CONTINUE
+ ELSE IF( TYPE.EQ.'HE'.OR.TYPE.EQ.'SY'.OR.TYPE.EQ.'TR' )THEN
+ DO 90 J = 1, N
+ IF( UPPER )THEN
+ IBEG = 1
+ IF( UNIT )THEN
+ IEND = J - 1
+ ELSE
+ IEND = J
+ END IF
+ ELSE
+ IF( UNIT )THEN
+ IBEG = J + 1
+ ELSE
+ IBEG = J
+ END IF
+ IEND = N
+ END IF
+ DO 60 I = 1, IBEG - 1
+ AA( I + ( J - 1 )*LDA ) = ROGUE
+ 60 CONTINUE
+ DO 70 I = IBEG, IEND
+ AA( I + ( J - 1 )*LDA ) = A( I, J )
+ 70 CONTINUE
+ DO 80 I = IEND + 1, LDA
+ AA( I + ( J - 1 )*LDA ) = ROGUE
+ 80 CONTINUE
+ IF( HER )THEN
+ JJ = J + ( J - 1 )*LDA
+ AA( JJ ) = CMPLX( REAL( AA( JJ ) ), RROGUE )
+ END IF
+ 90 CONTINUE
+ END IF
+ RETURN
+*
+* End of CMAKE.
+*
+ END
+ SUBROUTINE CMMCH( TRANSA, TRANSB, M, N, KK, ALPHA, A, LDA, B, LDB,
+ $ BETA, C, LDC, CT, G, CC, LDCC, EPS, ERR, FATAL,
+ $ NOUT, MV )
+*
+* Checks the results of the computational tests.
+*
+* Auxiliary routine for test program for Level 3 Blas.
+*
+* -- Written on 8-February-1989.
+* Jack Dongarra, Argonne National Laboratory.
+* Iain Duff, AERE Harwell.
+* Jeremy Du Croz, Numerical Algorithms Group Ltd.
+* Sven Hammarling, Numerical Algorithms Group Ltd.
+*
+* .. Parameters ..
+ COMPLEX ZERO
+ PARAMETER ( ZERO = ( 0.0, 0.0 ) )
+ REAL RZERO, RONE
+ PARAMETER ( RZERO = 0.0, RONE = 1.0 )
+* .. Scalar Arguments ..
+ COMPLEX ALPHA, BETA
+ REAL EPS, ERR
+ INTEGER KK, LDA, LDB, LDC, LDCC, M, N, NOUT
+ LOGICAL FATAL, MV
+ CHARACTER*1 TRANSA, TRANSB
+* .. Array Arguments ..
+ COMPLEX A( LDA, * ), B( LDB, * ), C( LDC, * ),
+ $ CC( LDCC, * ), CT( * )
+ REAL G( * )
+* .. Local Scalars ..
+ COMPLEX CL
+ REAL ERRI
+ INTEGER I, J, K
+ LOGICAL CTRANA, CTRANB, TRANA, TRANB
+* .. Intrinsic Functions ..
+ INTRINSIC ABS, AIMAG, CONJG, MAX, REAL, SQRT
+* .. Statement Functions ..
+ REAL ABS1
+* .. Statement Function definitions ..
+ ABS1( CL ) = ABS( REAL( CL ) ) + ABS( AIMAG( CL ) )
+* .. Executable Statements ..
+ TRANA = TRANSA.EQ.'T'.OR.TRANSA.EQ.'C'
+ TRANB = TRANSB.EQ.'T'.OR.TRANSB.EQ.'C'
+ CTRANA = TRANSA.EQ.'C'
+ CTRANB = TRANSB.EQ.'C'
+*
+* Compute expected result, one column at a time, in CT using data
+* in A, B and C.
+* Compute gauges in G.
+*
+ DO 220 J = 1, N
+*
+ DO 10 I = 1, M
+ CT( I ) = ZERO
+ G( I ) = RZERO
+ 10 CONTINUE
+ IF( .NOT.TRANA.AND..NOT.TRANB )THEN
+ DO 30 K = 1, KK
+ DO 20 I = 1, M
+ CT( I ) = CT( I ) + A( I, K )*B( K, J )
+ G( I ) = G( I ) + ABS1( A( I, K ) )*ABS1( B( K, J ) )
+ 20 CONTINUE
+ 30 CONTINUE
+ ELSE IF( TRANA.AND..NOT.TRANB )THEN
+ IF( CTRANA )THEN
+ DO 50 K = 1, KK
+ DO 40 I = 1, M
+ CT( I ) = CT( I ) + CONJG( A( K, I ) )*B( K, J )
+ G( I ) = G( I ) + ABS1( A( K, I ) )*
+ $ ABS1( B( K, J ) )
+ 40 CONTINUE
+ 50 CONTINUE
+ ELSE
+ DO 70 K = 1, KK
+ DO 60 I = 1, M
+ CT( I ) = CT( I ) + A( K, I )*B( K, J )
+ G( I ) = G( I ) + ABS1( A( K, I ) )*
+ $ ABS1( B( K, J ) )
+ 60 CONTINUE
+ 70 CONTINUE
+ END IF
+ ELSE IF( .NOT.TRANA.AND.TRANB )THEN
+ IF( CTRANB )THEN
+ DO 90 K = 1, KK
+ DO 80 I = 1, M
+ CT( I ) = CT( I ) + A( I, K )*CONJG( B( J, K ) )
+ G( I ) = G( I ) + ABS1( A( I, K ) )*
+ $ ABS1( B( J, K ) )
+ 80 CONTINUE
+ 90 CONTINUE
+ ELSE
+ DO 110 K = 1, KK
+ DO 100 I = 1, M
+ CT( I ) = CT( I ) + A( I, K )*B( J, K )
+ G( I ) = G( I ) + ABS1( A( I, K ) )*
+ $ ABS1( B( J, K ) )
+ 100 CONTINUE
+ 110 CONTINUE
+ END IF
+ ELSE IF( TRANA.AND.TRANB )THEN
+ IF( CTRANA )THEN
+ IF( CTRANB )THEN
+ DO 130 K = 1, KK
+ DO 120 I = 1, M
+ CT( I ) = CT( I ) + CONJG( A( K, I ) )*
+ $ CONJG( B( J, K ) )
+ G( I ) = G( I ) + ABS1( A( K, I ) )*
+ $ ABS1( B( J, K ) )
+ 120 CONTINUE
+ 130 CONTINUE
+ ELSE
+ DO 150 K = 1, KK
+ DO 140 I = 1, M
+ CT( I ) = CT( I ) + CONJG( A( K, I ) )*B( J, K )
+ G( I ) = G( I ) + ABS1( A( K, I ) )*
+ $ ABS1( B( J, K ) )
+ 140 CONTINUE
+ 150 CONTINUE
+ END IF
+ ELSE
+ IF( CTRANB )THEN
+ DO 170 K = 1, KK
+ DO 160 I = 1, M
+ CT( I ) = CT( I ) + A( K, I )*CONJG( B( J, K ) )
+ G( I ) = G( I ) + ABS1( A( K, I ) )*
+ $ ABS1( B( J, K ) )
+ 160 CONTINUE
+ 170 CONTINUE
+ ELSE
+ DO 190 K = 1, KK
+ DO 180 I = 1, M
+ CT( I ) = CT( I ) + A( K, I )*B( J, K )
+ G( I ) = G( I ) + ABS1( A( K, I ) )*
+ $ ABS1( B( J, K ) )
+ 180 CONTINUE
+ 190 CONTINUE
+ END IF
+ END IF
+ END IF
+ DO 200 I = 1, M
+ CT( I ) = ALPHA*CT( I ) + BETA*C( I, J )
+ G( I ) = ABS1( ALPHA )*G( I ) +
+ $ ABS1( BETA )*ABS1( C( I, J ) )
+ 200 CONTINUE
+*
+* Compute the error ratio for this result.
+*
+ ERR = ZERO
+ DO 210 I = 1, M
+ ERRI = ABS1( CT( I ) - CC( I, J ) )/EPS
+ IF( G( I ).NE.RZERO )
+ $ ERRI = ERRI/G( I )
+ ERR = MAX( ERR, ERRI )
+ IF( ERR*SQRT( EPS ).GE.RONE )
+ $ GO TO 230
+ 210 CONTINUE
+*
+ 220 CONTINUE
+*
+* If the loop completes, all results are at least half accurate.
+ GO TO 250
+*
+* Report fatal error.
+*
+ 230 FATAL = .TRUE.
+ WRITE( NOUT, FMT = 9999 )
+ DO 240 I = 1, M
+ IF( MV )THEN
+ WRITE( NOUT, FMT = 9998 )I, CT( I ), CC( I, J )
+ ELSE
+ WRITE( NOUT, FMT = 9998 )I, CC( I, J ), CT( I )
+ END IF
+ 240 CONTINUE
+ IF( N.GT.1 )
+ $ WRITE( NOUT, FMT = 9997 )J
+*
+ 250 CONTINUE
+ RETURN
+*
+ 9999 FORMAT( ' ******* FATAL ERROR - COMPUTED RESULT IS LESS THAN HAL',
+ $ 'F ACCURATE *******', /' EXPECTED RE',
+ $ 'SULT COMPUTED RESULT' )
+ 9998 FORMAT( 1X, I7, 2( ' (', G15.6, ',', G15.6, ')' ) )
+ 9997 FORMAT( ' THESE ARE THE RESULTS FOR COLUMN ', I3 )
+*
+* End of CMMCH.
+*
+ END
+ LOGICAL FUNCTION LCE( RI, RJ, LR )
+*
+* Tests if two arrays are identical.
+*
+* Auxiliary routine for test program for Level 3 Blas.
+*
+* -- Written on 8-February-1989.
+* Jack Dongarra, Argonne National Laboratory.
+* Iain Duff, AERE Harwell.
+* Jeremy Du Croz, Numerical Algorithms Group Ltd.
+* Sven Hammarling, Numerical Algorithms Group Ltd.
+*
+* .. Scalar Arguments ..
+ INTEGER LR
+* .. Array Arguments ..
+ COMPLEX RI( * ), RJ( * )
+* .. Local Scalars ..
+ INTEGER I
+* .. Executable Statements ..
+ DO 10 I = 1, LR
+ IF( RI( I ).NE.RJ( I ) )
+ $ GO TO 20
+ 10 CONTINUE
+ LCE = .TRUE.
+ GO TO 30
+ 20 CONTINUE
+ LCE = .FALSE.
+ 30 RETURN
+*
+* End of LCE.
+*
+ END
+ LOGICAL FUNCTION LCERES( TYPE, UPLO, M, N, AA, AS, LDA )
+*
+* Tests if selected elements in two arrays are equal.
+*
+* TYPE is 'GE' or 'HE' or 'SY'.
+*
+* Auxiliary routine for test program for Level 3 Blas.
+*
+* -- Written on 8-February-1989.
+* Jack Dongarra, Argonne National Laboratory.
+* Iain Duff, AERE Harwell.
+* Jeremy Du Croz, Numerical Algorithms Group Ltd.
+* Sven Hammarling, Numerical Algorithms Group Ltd.
+*
+* .. Scalar Arguments ..
+ INTEGER LDA, M, N
+ CHARACTER*1 UPLO
+ CHARACTER*2 TYPE
+* .. Array Arguments ..
+ COMPLEX AA( LDA, * ), AS( LDA, * )
+* .. Local Scalars ..
+ INTEGER I, IBEG, IEND, J
+ LOGICAL UPPER
+* .. Executable Statements ..
+ UPPER = UPLO.EQ.'U'
+ IF( TYPE.EQ.'GE' )THEN
+ DO 20 J = 1, N
+ DO 10 I = M + 1, LDA
+ IF( AA( I, J ).NE.AS( I, J ) )
+ $ GO TO 70
+ 10 CONTINUE
+ 20 CONTINUE
+ ELSE IF( TYPE.EQ.'HE'.OR.TYPE.EQ.'SY' )THEN
+ DO 50 J = 1, N
+ IF( UPPER )THEN
+ IBEG = 1
+ IEND = J
+ ELSE
+ IBEG = J
+ IEND = N
+ END IF
+ DO 30 I = 1, IBEG - 1
+ IF( AA( I, J ).NE.AS( I, J ) )
+ $ GO TO 70
+ 30 CONTINUE
+ DO 40 I = IEND + 1, LDA
+ IF( AA( I, J ).NE.AS( I, J ) )
+ $ GO TO 70
+ 40 CONTINUE
+ 50 CONTINUE
+ END IF
+*
+ LCERES = .TRUE.
+ GO TO 80
+ 70 CONTINUE
+ LCERES = .FALSE.
+ 80 RETURN
+*
+* End of LCERES.
+*
+ END
+ COMPLEX FUNCTION CBEG( RESET )
+*
+* Generates complex numbers as pairs of random numbers uniformly
+* distributed between -0.5 and 0.5.
+*
+* Auxiliary routine for test program for Level 3 Blas.
+*
+* -- Written on 8-February-1989.
+* Jack Dongarra, Argonne National Laboratory.
+* Iain Duff, AERE Harwell.
+* Jeremy Du Croz, Numerical Algorithms Group Ltd.
+* Sven Hammarling, Numerical Algorithms Group Ltd.
+*
+* .. Scalar Arguments ..
+ LOGICAL RESET
+* .. Local Scalars ..
+ INTEGER I, IC, J, MI, MJ
+* .. Save statement ..
+ SAVE I, IC, J, MI, MJ
+* .. Intrinsic Functions ..
+ INTRINSIC CMPLX
+* .. Executable Statements ..
+ IF( RESET )THEN
+* Initialize local variables.
+ MI = 891
+ MJ = 457
+ I = 7
+ J = 7
+ IC = 0
+ RESET = .FALSE.
+ END IF
+*
+* The sequence of values of I or J is bounded between 1 and 999.
+* If initial I or J = 1,2,3,6,7 or 9, the period will be 50.
+* If initial I or J = 4 or 8, the period will be 25.
+* If initial I or J = 5, the period will be 10.
+* IC is used to break up the period by skipping 1 value of I or J
+* in 6.
+*
+ IC = IC + 1
+ 10 I = I*MI
+ J = J*MJ
+ I = I - 1000*( I/1000 )
+ J = J - 1000*( J/1000 )
+ IF( IC.GE.5 )THEN
+ IC = 0
+ GO TO 10
+ END IF
+ CBEG = CMPLX( ( I - 500 )/1001.0, ( J - 500 )/1001.0 )
+ RETURN
+*
+* End of CBEG.
+*
+ END
+ REAL FUNCTION SDIFF( X, Y )
+*
+* Auxiliary routine for test program for Level 3 Blas.
+*
+* -- Written on 8-February-1989.
+* Jack Dongarra, Argonne National Laboratory.
+* Iain Duff, AERE Harwell.
+* Jeremy Du Croz, Numerical Algorithms Group Ltd.
+* Sven Hammarling, Numerical Algorithms Group Ltd.
+*
+* .. Scalar Arguments ..
+ REAL X, Y
+* .. Executable Statements ..
+ SDIFF = X - Y
+ RETURN
+*
+* End of SDIFF.
+*
+ END
+ SUBROUTINE CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+*
+* Tests whether XERBLA has detected an error when it should.
+*
+* Auxiliary routine for test program for Level 3 Blas.
+*
+* -- Written on 8-February-1989.
+* Jack Dongarra, Argonne National Laboratory.
+* Iain Duff, AERE Harwell.
+* Jeremy Du Croz, Numerical Algorithms Group Ltd.
+* Sven Hammarling, Numerical Algorithms Group Ltd.
+*
+* .. Scalar Arguments ..
+ INTEGER INFOT, NOUT
+ LOGICAL LERR, OK
+ CHARACTER*6 SRNAMT
+* .. Executable Statements ..
+ IF( .NOT.LERR )THEN
+ WRITE( NOUT, FMT = 9999 )INFOT, SRNAMT
+ OK = .FALSE.
+ END IF
+ LERR = .FALSE.
+ RETURN
+*
+ 9999 FORMAT( ' ***** ILLEGAL VALUE OF PARAMETER NUMBER ', I2, ' NOT D',
+ $ 'ETECTED BY ', A6, ' *****' )
+*
+* End of CHKXER.
+*
+ END
+ SUBROUTINE XERBLA( SRNAME, INFO )
+*
+* This is a special version of XERBLA to be used only as part of
+* the test program for testing error exits from the Level 3 BLAS
+* routines.
+*
+* XERBLA is an error handler for the Level 3 BLAS routines.
+*
+* It is called by the Level 3 BLAS routines if an input parameter is
+* invalid.
+*
+* Auxiliary routine for test program for Level 3 Blas.
+*
+* -- Written on 8-February-1989.
+* Jack Dongarra, Argonne National Laboratory.
+* Iain Duff, AERE Harwell.
+* Jeremy Du Croz, Numerical Algorithms Group Ltd.
+* Sven Hammarling, Numerical Algorithms Group Ltd.
+*
+* .. Scalar Arguments ..
+ INTEGER INFO
+ CHARACTER*6 SRNAME
+* .. Scalars in Common ..
+ INTEGER INFOT, NOUT
+ LOGICAL LERR, OK
+ CHARACTER*6 SRNAMT
+* .. Common blocks ..
+ COMMON /INFOC/INFOT, NOUT, OK, LERR
+ COMMON /SRNAMC/SRNAMT
+* .. Executable Statements ..
+ LERR = .TRUE.
+ IF( INFO.NE.INFOT )THEN
+ IF( INFOT.NE.0 )THEN
+ WRITE( NOUT, FMT = 9999 )INFO, INFOT
+ ELSE
+ WRITE( NOUT, FMT = 9997 )INFO
+ END IF
+ OK = .FALSE.
+ END IF
+ IF( SRNAME.NE.SRNAMT )THEN
+ WRITE( NOUT, FMT = 9998 )SRNAME, SRNAMT
+ OK = .FALSE.
+ END IF
+ RETURN
+*
+ 9999 FORMAT( ' ******* XERBLA WAS CALLED WITH INFO = ', I6, ' INSTEAD',
+ $ ' OF ', I2, ' *******' )
+ 9998 FORMAT( ' ******* XERBLA WAS CALLED WITH SRNAME = ', A6, ' INSTE',
+ $ 'AD OF ', A6, ' *******' )
+ 9997 FORMAT( ' ******* XERBLA WAS CALLED WITH INFO = ', I6,
+ $ ' *******' )
+*
+* End of XERBLA
+*
+ END
+
diff --git a/blas/testing/dblat1.f b/blas/testing/dblat1.f
new file mode 100644
index 0000000..03d9f13
--- /dev/null
+++ b/blas/testing/dblat1.f
@@ -0,0 +1,1065 @@
+*> \brief \b DBLAT1
+*
+* =========== DOCUMENTATION ===========
+*
+* Online html documentation available at
+* http://www.netlib.org/lapack/explore-html/
+*
+* Definition:
+* ===========
+*
+* PROGRAM DBLAT1
+*
+*
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
+*>
+*> Test program for the DOUBLE PRECISION Level 1 BLAS.
+*>
+*> Based upon the original BLAS test routine together with:
+*> F06EAF Example Program Text
+*> \endverbatim
+*
+* Authors:
+* ========
+*
+*> \author Univ. of Tennessee
+*> \author Univ. of California Berkeley
+*> \author Univ. of Colorado Denver
+*> \author NAG Ltd.
+*
+*> \date April 2012
+*
+*> \ingroup double_blas_testing
+*
+* =====================================================================
+ PROGRAM DBLAT1
+*
+* -- Reference BLAS test routine (version 3.4.1) --
+* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
+* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+* April 2012
+*
+* =====================================================================
+*
+* .. Parameters ..
+ INTEGER NOUT
+ PARAMETER (NOUT=6)
+* .. Scalars in Common ..
+ INTEGER ICASE, INCX, INCY, N
+ LOGICAL PASS
+* .. Local Scalars ..
+ DOUBLE PRECISION SFAC
+ INTEGER IC
+* .. External Subroutines ..
+ EXTERNAL CHECK0, CHECK1, CHECK2, CHECK3, HEADER
+* .. Common blocks ..
+ COMMON /COMBLA/ICASE, N, INCX, INCY, PASS
+* .. Data statements ..
+ DATA SFAC/9.765625D-4/
+* .. Executable Statements ..
+ WRITE (NOUT,99999)
+ DO 20 IC = 1, 13
+ ICASE = IC
+ CALL HEADER
+*
+* .. Initialize PASS, INCX, and INCY for a new case. ..
+* .. the value 9999 for INCX or INCY will appear in the ..
+* .. detailed output, if any, for cases that do not involve ..
+* .. these parameters ..
+*
+ PASS = .TRUE.
+ INCX = 9999
+ INCY = 9999
+ IF (ICASE.EQ.3 .OR. ICASE.EQ.11) THEN
+ CALL CHECK0(SFAC)
+ ELSE IF (ICASE.EQ.7 .OR. ICASE.EQ.8 .OR. ICASE.EQ.9 .OR.
+ + ICASE.EQ.10) THEN
+ CALL CHECK1(SFAC)
+ ELSE IF (ICASE.EQ.1 .OR. ICASE.EQ.2 .OR. ICASE.EQ.5 .OR.
+ + ICASE.EQ.6 .OR. ICASE.EQ.12 .OR. ICASE.EQ.13) THEN
+ CALL CHECK2(SFAC)
+ ELSE IF (ICASE.EQ.4) THEN
+ CALL CHECK3(SFAC)
+ END IF
+* -- Print
+ IF (PASS) WRITE (NOUT,99998)
+ 20 CONTINUE
+ STOP
+*
+99999 FORMAT (' Real BLAS Test Program Results',/1X)
+99998 FORMAT (' ----- PASS -----')
+ END
+ SUBROUTINE HEADER
+* .. Parameters ..
+ INTEGER NOUT
+ PARAMETER (NOUT=6)
+* .. Scalars in Common ..
+ INTEGER ICASE, INCX, INCY, N
+ LOGICAL PASS
+* .. Local Arrays ..
+ CHARACTER*6 L(13)
+* .. Common blocks ..
+ COMMON /COMBLA/ICASE, N, INCX, INCY, PASS
+* .. Data statements ..
+ DATA L(1)/' DDOT '/
+ DATA L(2)/'DAXPY '/
+ DATA L(3)/'DROTG '/
+ DATA L(4)/' DROT '/
+ DATA L(5)/'DCOPY '/
+ DATA L(6)/'DSWAP '/
+ DATA L(7)/'DNRM2 '/
+ DATA L(8)/'DASUM '/
+ DATA L(9)/'DSCAL '/
+ DATA L(10)/'IDAMAX'/
+ DATA L(11)/'DROTMG'/
+ DATA L(12)/'DROTM '/
+ DATA L(13)/'DSDOT '/
+* .. Executable Statements ..
+ WRITE (NOUT,99999) ICASE, L(ICASE)
+ RETURN
+*
+99999 FORMAT (/' Test of subprogram number',I3,12X,A6)
+ END
+ SUBROUTINE CHECK0(SFAC)
+* .. Parameters ..
+ INTEGER NOUT
+ PARAMETER (NOUT=6)
+* .. Scalar Arguments ..
+ DOUBLE PRECISION SFAC
+* .. Scalars in Common ..
+ INTEGER ICASE, INCX, INCY, N
+ LOGICAL PASS
+* .. Local Scalars ..
+ DOUBLE PRECISION SA, SB, SC, SS, D12
+ INTEGER I, K
+* .. Local Arrays ..
+ DOUBLE PRECISION DA1(8), DATRUE(8), DB1(8), DBTRUE(8), DC1(8),
+ $ DS1(8), DAB(4,9), DTEMP(9), DTRUE(9,9)
+* .. External Subroutines ..
+ EXTERNAL DROTG, DROTMG, STEST1
+* .. Common blocks ..
+ COMMON /COMBLA/ICASE, N, INCX, INCY, PASS
+* .. Data statements ..
+ DATA DA1/0.3D0, 0.4D0, -0.3D0, -0.4D0, -0.3D0, 0.0D0,
+ + 0.0D0, 1.0D0/
+ DATA DB1/0.4D0, 0.3D0, 0.4D0, 0.3D0, -0.4D0, 0.0D0,
+ + 1.0D0, 0.0D0/
+ DATA DC1/0.6D0, 0.8D0, -0.6D0, 0.8D0, 0.6D0, 1.0D0,
+ + 0.0D0, 1.0D0/
+ DATA DS1/0.8D0, 0.6D0, 0.8D0, -0.6D0, 0.8D0, 0.0D0,
+ + 1.0D0, 0.0D0/
+ DATA DATRUE/0.5D0, 0.5D0, 0.5D0, -0.5D0, -0.5D0,
+ + 0.0D0, 1.0D0, 1.0D0/
+ DATA DBTRUE/0.0D0, 0.6D0, 0.0D0, -0.6D0, 0.0D0,
+ + 0.0D0, 1.0D0, 0.0D0/
+* INPUT FOR MODIFIED GIVENS
+ DATA DAB/ .1D0,.3D0,1.2D0,.2D0,
+ A .7D0, .2D0, .6D0, 4.2D0,
+ B 0.D0,0.D0,0.D0,0.D0,
+ C 4.D0, -1.D0, 2.D0, 4.D0,
+ D 6.D-10, 2.D-2, 1.D5, 10.D0,
+ E 4.D10, 2.D-2, 1.D-5, 10.D0,
+ F 2.D-10, 4.D-2, 1.D5, 10.D0,
+ G 2.D10, 4.D-2, 1.D-5, 10.D0,
+ H 4.D0, -2.D0, 8.D0, 4.D0 /
+* TRUE RESULTS FOR MODIFIED GIVENS
+ DATA DTRUE/0.D0,0.D0, 1.3D0, .2D0, 0.D0,0.D0,0.D0, .5D0, 0.D0,
+ A 0.D0,0.D0, 4.5D0, 4.2D0, 1.D0, .5D0, 0.D0,0.D0,0.D0,
+ B 0.D0,0.D0,0.D0,0.D0, -2.D0, 0.D0,0.D0,0.D0,0.D0,
+ C 0.D0,0.D0,0.D0, 4.D0, -1.D0, 0.D0,0.D0,0.D0,0.D0,
+ D 0.D0, 15.D-3, 0.D0, 10.D0, -1.D0, 0.D0, -1.D-4,
+ E 0.D0, 1.D0,
+ F 0.D0,0.D0, 6144.D-5, 10.D0, -1.D0, 4096.D0, -1.D6,
+ G 0.D0, 1.D0,
+ H 0.D0,0.D0,15.D0,10.D0,-1.D0, 5.D-5, 0.D0,1.D0,0.D0,
+ I 0.D0,0.D0, 15.D0, 10.D0, -1. D0, 5.D5, -4096.D0,
+ J 1.D0, 4096.D-6,
+ K 0.D0,0.D0, 7.D0, 4.D0, 0.D0,0.D0, -.5D0, -.25D0, 0.D0/
+* 4096 = 2 ** 12
+ DATA D12 /4096.D0/
+ DTRUE(1,1) = 12.D0 / 130.D0
+ DTRUE(2,1) = 36.D0 / 130.D0
+ DTRUE(7,1) = -1.D0 / 6.D0
+ DTRUE(1,2) = 14.D0 / 75.D0
+ DTRUE(2,2) = 49.D0 / 75.D0
+ DTRUE(9,2) = 1.D0 / 7.D0
+ DTRUE(1,5) = 45.D-11 * (D12 * D12)
+ DTRUE(3,5) = 4.D5 / (3.D0 * D12)
+ DTRUE(6,5) = 1.D0 / D12
+ DTRUE(8,5) = 1.D4 / (3.D0 * D12)
+ DTRUE(1,6) = 4.D10 / (1.5D0 * D12 * D12)
+ DTRUE(2,6) = 2.D-2 / 1.5D0
+ DTRUE(8,6) = 5.D-7 * D12
+ DTRUE(1,7) = 4.D0 / 150.D0
+ DTRUE(2,7) = (2.D-10 / 1.5D0) * (D12 * D12)
+ DTRUE(7,7) = -DTRUE(6,5)
+ DTRUE(9,7) = 1.D4 / D12
+ DTRUE(1,8) = DTRUE(1,7)
+ DTRUE(2,8) = 2.D10 / (1.5D0 * D12 * D12)
+ DTRUE(1,9) = 32.D0 / 7.D0
+ DTRUE(2,9) = -16.D0 / 7.D0
+* .. Executable Statements ..
+*
+* Compute true values which cannot be prestored
+* in decimal notation
+*
+ DBTRUE(1) = 1.0D0/0.6D0
+ DBTRUE(3) = -1.0D0/0.6D0
+ DBTRUE(5) = 1.0D0/0.6D0
+*
+ DO 20 K = 1, 8
+* .. Set N=K for identification in output if any ..
+ N = K
+ IF (ICASE.EQ.3) THEN
+* .. DROTG ..
+ IF (K.GT.8) GO TO 40
+ SA = DA1(K)
+ SB = DB1(K)
+ CALL DROTG(SA,SB,SC,SS)
+ CALL STEST1(SA,DATRUE(K),DATRUE(K),SFAC)
+ CALL STEST1(SB,DBTRUE(K),DBTRUE(K),SFAC)
+ CALL STEST1(SC,DC1(K),DC1(K),SFAC)
+ CALL STEST1(SS,DS1(K),DS1(K),SFAC)
+ ELSEIF (ICASE.EQ.11) THEN
+* .. DROTMG ..
+ DO I=1,4
+ DTEMP(I)= DAB(I,K)
+ DTEMP(I+4) = 0.0
+ END DO
+ DTEMP(9) = 0.0
+ CALL DROTMG(DTEMP(1),DTEMP(2),DTEMP(3),DTEMP(4),DTEMP(5))
+ CALL STEST(9,DTEMP,DTRUE(1,K),DTRUE(1,K),SFAC)
+ ELSE
+ WRITE (NOUT,*) ' Shouldn''t be here in CHECK0'
+ STOP
+ END IF
+ 20 CONTINUE
+ 40 RETURN
+ END
+ SUBROUTINE CHECK1(SFAC)
+* .. Parameters ..
+ INTEGER NOUT
+ PARAMETER (NOUT=6)
+* .. Scalar Arguments ..
+ DOUBLE PRECISION SFAC
+* .. Scalars in Common ..
+ INTEGER ICASE, INCX, INCY, N
+ LOGICAL PASS
+* .. Local Scalars ..
+ INTEGER I, LEN, NP1
+* .. Local Arrays ..
+ DOUBLE PRECISION DTRUE1(5), DTRUE3(5), DTRUE5(8,5,2), DV(8,5,2),
+ + SA(10), STEMP(1), STRUE(8), SX(8)
+ INTEGER ITRUE2(5)
+* .. External Functions ..
+ DOUBLE PRECISION DASUM, DNRM2
+ INTEGER IDAMAX
+ EXTERNAL DASUM, DNRM2, IDAMAX
+* .. External Subroutines ..
+ EXTERNAL ITEST1, DSCAL, STEST, STEST1
+* .. Intrinsic Functions ..
+ INTRINSIC MAX
+* .. Common blocks ..
+ COMMON /COMBLA/ICASE, N, INCX, INCY, PASS
+* .. Data statements ..
+ DATA SA/0.3D0, -1.0D0, 0.0D0, 1.0D0, 0.3D0, 0.3D0,
+ + 0.3D0, 0.3D0, 0.3D0, 0.3D0/
+ DATA DV/0.1D0, 2.0D0, 2.0D0, 2.0D0, 2.0D0, 2.0D0,
+ + 2.0D0, 2.0D0, 0.3D0, 3.0D0, 3.0D0, 3.0D0, 3.0D0,
+ + 3.0D0, 3.0D0, 3.0D0, 0.3D0, -0.4D0, 4.0D0,
+ + 4.0D0, 4.0D0, 4.0D0, 4.0D0, 4.0D0, 0.2D0,
+ + -0.6D0, 0.3D0, 5.0D0, 5.0D0, 5.0D0, 5.0D0,
+ + 5.0D0, 0.1D0, -0.3D0, 0.5D0, -0.1D0, 6.0D0,
+ + 6.0D0, 6.0D0, 6.0D0, 0.1D0, 8.0D0, 8.0D0, 8.0D0,
+ + 8.0D0, 8.0D0, 8.0D0, 8.0D0, 0.3D0, 9.0D0, 9.0D0,
+ + 9.0D0, 9.0D0, 9.0D0, 9.0D0, 9.0D0, 0.3D0, 2.0D0,
+ + -0.4D0, 2.0D0, 2.0D0, 2.0D0, 2.0D0, 2.0D0,
+ + 0.2D0, 3.0D0, -0.6D0, 5.0D0, 0.3D0, 2.0D0,
+ + 2.0D0, 2.0D0, 0.1D0, 4.0D0, -0.3D0, 6.0D0,
+ + -0.5D0, 7.0D0, -0.1D0, 3.0D0/
+ DATA DTRUE1/0.0D0, 0.3D0, 0.5D0, 0.7D0, 0.6D0/
+ DATA DTRUE3/0.0D0, 0.3D0, 0.7D0, 1.1D0, 1.0D0/
+ DATA DTRUE5/0.10D0, 2.0D0, 2.0D0, 2.0D0, 2.0D0,
+ + 2.0D0, 2.0D0, 2.0D0, -0.3D0, 3.0D0, 3.0D0,
+ + 3.0D0, 3.0D0, 3.0D0, 3.0D0, 3.0D0, 0.0D0, 0.0D0,
+ + 4.0D0, 4.0D0, 4.0D0, 4.0D0, 4.0D0, 4.0D0,
+ + 0.20D0, -0.60D0, 0.30D0, 5.0D0, 5.0D0, 5.0D0,
+ + 5.0D0, 5.0D0, 0.03D0, -0.09D0, 0.15D0, -0.03D0,
+ + 6.0D0, 6.0D0, 6.0D0, 6.0D0, 0.10D0, 8.0D0,
+ + 8.0D0, 8.0D0, 8.0D0, 8.0D0, 8.0D0, 8.0D0,
+ + 0.09D0, 9.0D0, 9.0D0, 9.0D0, 9.0D0, 9.0D0,
+ + 9.0D0, 9.0D0, 0.09D0, 2.0D0, -0.12D0, 2.0D0,
+ + 2.0D0, 2.0D0, 2.0D0, 2.0D0, 0.06D0, 3.0D0,
+ + -0.18D0, 5.0D0, 0.09D0, 2.0D0, 2.0D0, 2.0D0,
+ + 0.03D0, 4.0D0, -0.09D0, 6.0D0, -0.15D0, 7.0D0,
+ + -0.03D0, 3.0D0/
+ DATA ITRUE2/0, 1, 2, 2, 3/
+* .. Executable Statements ..
+ DO 80 INCX = 1, 2
+ DO 60 NP1 = 1, 5
+ N = NP1 - 1
+ LEN = 2*MAX(N,1)
+* .. Set vector arguments ..
+ DO 20 I = 1, LEN
+ SX(I) = DV(I,NP1,INCX)
+ 20 CONTINUE
+*
+ IF (ICASE.EQ.7) THEN
+* .. DNRM2 ..
+ STEMP(1) = DTRUE1(NP1)
+ CALL STEST1(DNRM2(N,SX,INCX),STEMP(1),STEMP,SFAC)
+ ELSE IF (ICASE.EQ.8) THEN
+* .. DASUM ..
+ STEMP(1) = DTRUE3(NP1)
+ CALL STEST1(DASUM(N,SX,INCX),STEMP(1),STEMP,SFAC)
+ ELSE IF (ICASE.EQ.9) THEN
+* .. DSCAL ..
+ CALL DSCAL(N,SA((INCX-1)*5+NP1),SX,INCX)
+ DO 40 I = 1, LEN
+ STRUE(I) = DTRUE5(I,NP1,INCX)
+ 40 CONTINUE
+ CALL STEST(LEN,SX,STRUE,STRUE,SFAC)
+ ELSE IF (ICASE.EQ.10) THEN
+* .. IDAMAX ..
+ CALL ITEST1(IDAMAX(N,SX,INCX),ITRUE2(NP1))
+ ELSE
+ WRITE (NOUT,*) ' Shouldn''t be here in CHECK1'
+ STOP
+ END IF
+ 60 CONTINUE
+ 80 CONTINUE
+ RETURN
+ END
+ SUBROUTINE CHECK2(SFAC)
+* .. Parameters ..
+ INTEGER NOUT
+ PARAMETER (NOUT=6)
+* .. Scalar Arguments ..
+ DOUBLE PRECISION SFAC
+* .. Scalars in Common ..
+ INTEGER ICASE, INCX, INCY, N
+ LOGICAL PASS
+* .. Local Scalars ..
+ DOUBLE PRECISION SA
+ INTEGER I, J, KI, KN, KNI, KPAR, KSIZE, LENX, LENY,
+ $ MX, MY
+* .. Local Arrays ..
+ DOUBLE PRECISION DT10X(7,4,4), DT10Y(7,4,4), DT7(4,4),
+ $ DT8(7,4,4), DX1(7),
+ $ DY1(7), SSIZE1(4), SSIZE2(14,2), SSIZE(7),
+ $ STX(7), STY(7), SX(7), SY(7),
+ $ DPAR(5,4), DT19X(7,4,16),DT19XA(7,4,4),
+ $ DT19XB(7,4,4), DT19XC(7,4,4),DT19XD(7,4,4),
+ $ DT19Y(7,4,16), DT19YA(7,4,4),DT19YB(7,4,4),
+ $ DT19YC(7,4,4), DT19YD(7,4,4), DTEMP(5)
+ INTEGER INCXS(4), INCYS(4), LENS(4,2), NS(4)
+* .. External Functions ..
+ DOUBLE PRECISION DDOT, DSDOT
+ EXTERNAL DDOT, DSDOT
+* .. External Subroutines ..
+ EXTERNAL DAXPY, DCOPY, DROTM, DSWAP, STEST, STEST1
+* .. Intrinsic Functions ..
+ INTRINSIC ABS, MIN
+* .. Common blocks ..
+ COMMON /COMBLA/ICASE, N, INCX, INCY, PASS
+* .. Data statements ..
+ EQUIVALENCE (DT19X(1,1,1),DT19XA(1,1,1)),(DT19X(1,1,5),
+ A DT19XB(1,1,1)),(DT19X(1,1,9),DT19XC(1,1,1)),
+ B (DT19X(1,1,13),DT19XD(1,1,1))
+ EQUIVALENCE (DT19Y(1,1,1),DT19YA(1,1,1)),(DT19Y(1,1,5),
+ A DT19YB(1,1,1)),(DT19Y(1,1,9),DT19YC(1,1,1)),
+ B (DT19Y(1,1,13),DT19YD(1,1,1))
+
+ DATA SA/0.3D0/
+ DATA INCXS/1, 2, -2, -1/
+ DATA INCYS/1, -2, 1, -2/
+ DATA LENS/1, 1, 2, 4, 1, 1, 3, 7/
+ DATA NS/0, 1, 2, 4/
+ DATA DX1/0.6D0, 0.1D0, -0.5D0, 0.8D0, 0.9D0, -0.3D0,
+ + -0.4D0/
+ DATA DY1/0.5D0, -0.9D0, 0.3D0, 0.7D0, -0.6D0, 0.2D0,
+ + 0.8D0/
+ DATA DT7/0.0D0, 0.30D0, 0.21D0, 0.62D0, 0.0D0,
+ + 0.30D0, -0.07D0, 0.85D0, 0.0D0, 0.30D0, -0.79D0,
+ + -0.74D0, 0.0D0, 0.30D0, 0.33D0, 1.27D0/
+ DATA DT8/0.5D0, 0.0D0, 0.0D0, 0.0D0, 0.0D0, 0.0D0,
+ + 0.0D0, 0.68D0, 0.0D0, 0.0D0, 0.0D0, 0.0D0,
+ + 0.0D0, 0.0D0, 0.68D0, -0.87D0, 0.0D0, 0.0D0,
+ + 0.0D0, 0.0D0, 0.0D0, 0.68D0, -0.87D0, 0.15D0,
+ + 0.94D0, 0.0D0, 0.0D0, 0.0D0, 0.5D0, 0.0D0,
+ + 0.0D0, 0.0D0, 0.0D0, 0.0D0, 0.0D0, 0.68D0,
+ + 0.0D0, 0.0D0, 0.0D0, 0.0D0, 0.0D0, 0.0D0,
+ + 0.35D0, -0.9D0, 0.48D0, 0.0D0, 0.0D0, 0.0D0,
+ + 0.0D0, 0.38D0, -0.9D0, 0.57D0, 0.7D0, -0.75D0,
+ + 0.2D0, 0.98D0, 0.5D0, 0.0D0, 0.0D0, 0.0D0,
+ + 0.0D0, 0.0D0, 0.0D0, 0.68D0, 0.0D0, 0.0D0,
+ + 0.0D0, 0.0D0, 0.0D0, 0.0D0, 0.35D0, -0.72D0,
+ + 0.0D0, 0.0D0, 0.0D0, 0.0D0, 0.0D0, 0.38D0,
+ + -0.63D0, 0.15D0, 0.88D0, 0.0D0, 0.0D0, 0.0D0,
+ + 0.5D0, 0.0D0, 0.0D0, 0.0D0, 0.0D0, 0.0D0, 0.0D0,
+ + 0.68D0, 0.0D0, 0.0D0, 0.0D0, 0.0D0, 0.0D0,
+ + 0.0D0, 0.68D0, -0.9D0, 0.33D0, 0.0D0, 0.0D0,
+ + 0.0D0, 0.0D0, 0.68D0, -0.9D0, 0.33D0, 0.7D0,
+ + -0.75D0, 0.2D0, 1.04D0/
+ DATA DT10X/0.6D0, 0.0D0, 0.0D0, 0.0D0, 0.0D0, 0.0D0,
+ + 0.0D0, 0.5D0, 0.0D0, 0.0D0, 0.0D0, 0.0D0, 0.0D0,
+ + 0.0D0, 0.5D0, -0.9D0, 0.0D0, 0.0D0, 0.0D0,
+ + 0.0D0, 0.0D0, 0.5D0, -0.9D0, 0.3D0, 0.7D0,
+ + 0.0D0, 0.0D0, 0.0D0, 0.6D0, 0.0D0, 0.0D0, 0.0D0,
+ + 0.0D0, 0.0D0, 0.0D0, 0.5D0, 0.0D0, 0.0D0, 0.0D0,
+ + 0.0D0, 0.0D0, 0.0D0, 0.3D0, 0.1D0, 0.5D0, 0.0D0,
+ + 0.0D0, 0.0D0, 0.0D0, 0.8D0, 0.1D0, -0.6D0,
+ + 0.8D0, 0.3D0, -0.3D0, 0.5D0, 0.6D0, 0.0D0,
+ + 0.0D0, 0.0D0, 0.0D0, 0.0D0, 0.0D0, 0.5D0, 0.0D0,
+ + 0.0D0, 0.0D0, 0.0D0, 0.0D0, 0.0D0, -0.9D0,
+ + 0.1D0, 0.5D0, 0.0D0, 0.0D0, 0.0D0, 0.0D0, 0.7D0,
+ + 0.1D0, 0.3D0, 0.8D0, -0.9D0, -0.3D0, 0.5D0,
+ + 0.6D0, 0.0D0, 0.0D0, 0.0D0, 0.0D0, 0.0D0, 0.0D0,
+ + 0.5D0, 0.0D0, 0.0D0, 0.0D0, 0.0D0, 0.0D0, 0.0D0,
+ + 0.5D0, 0.3D0, 0.0D0, 0.0D0, 0.0D0, 0.0D0, 0.0D0,
+ + 0.5D0, 0.3D0, -0.6D0, 0.8D0, 0.0D0, 0.0D0,
+ + 0.0D0/
+ DATA DT10Y/0.5D0, 0.0D0, 0.0D0, 0.0D0, 0.0D0, 0.0D0,
+ + 0.0D0, 0.6D0, 0.0D0, 0.0D0, 0.0D0, 0.0D0, 0.0D0,
+ + 0.0D0, 0.6D0, 0.1D0, 0.0D0, 0.0D0, 0.0D0, 0.0D0,
+ + 0.0D0, 0.6D0, 0.1D0, -0.5D0, 0.8D0, 0.0D0,
+ + 0.0D0, 0.0D0, 0.5D0, 0.0D0, 0.0D0, 0.0D0, 0.0D0,
+ + 0.0D0, 0.0D0, 0.6D0, 0.0D0, 0.0D0, 0.0D0, 0.0D0,
+ + 0.0D0, 0.0D0, -0.5D0, -0.9D0, 0.6D0, 0.0D0,
+ + 0.0D0, 0.0D0, 0.0D0, -0.4D0, -0.9D0, 0.9D0,
+ + 0.7D0, -0.5D0, 0.2D0, 0.6D0, 0.5D0, 0.0D0,
+ + 0.0D0, 0.0D0, 0.0D0, 0.0D0, 0.0D0, 0.6D0, 0.0D0,
+ + 0.0D0, 0.0D0, 0.0D0, 0.0D0, 0.0D0, -0.5D0,
+ + 0.6D0, 0.0D0, 0.0D0, 0.0D0, 0.0D0, 0.0D0,
+ + -0.4D0, 0.9D0, -0.5D0, 0.6D0, 0.0D0, 0.0D0,
+ + 0.0D0, 0.5D0, 0.0D0, 0.0D0, 0.0D0, 0.0D0, 0.0D0,
+ + 0.0D0, 0.6D0, 0.0D0, 0.0D0, 0.0D0, 0.0D0, 0.0D0,
+ + 0.0D0, 0.6D0, -0.9D0, 0.1D0, 0.0D0, 0.0D0,
+ + 0.0D0, 0.0D0, 0.6D0, -0.9D0, 0.1D0, 0.7D0,
+ + -0.5D0, 0.2D0, 0.8D0/
+ DATA SSIZE1/0.0D0, 0.3D0, 1.6D0, 3.2D0/
+ DATA SSIZE2/0.0D0, 0.0D0, 0.0D0, 0.0D0, 0.0D0, 0.0D0,
+ + 0.0D0, 0.0D0, 0.0D0, 0.0D0, 0.0D0, 0.0D0, 0.0D0,
+ + 0.0D0, 1.17D0, 1.17D0, 1.17D0, 1.17D0, 1.17D0,
+ + 1.17D0, 1.17D0, 1.17D0, 1.17D0, 1.17D0, 1.17D0,
+ + 1.17D0, 1.17D0, 1.17D0/
+*
+* FOR DROTM
+*
+ DATA DPAR/-2.D0, 0.D0,0.D0,0.D0,0.D0,
+ A -1.D0, 2.D0, -3.D0, -4.D0, 5.D0,
+ B 0.D0, 0.D0, 2.D0, -3.D0, 0.D0,
+ C 1.D0, 5.D0, 2.D0, 0.D0, -4.D0/
+* TRUE X RESULTS F0R ROTATIONS DROTM
+ DATA DT19XA/.6D0, 0.D0,0.D0,0.D0,0.D0,0.D0,0.D0,
+ A .6D0, 0.D0,0.D0,0.D0,0.D0,0.D0,0.D0,
+ B .6D0, 0.D0,0.D0,0.D0,0.D0,0.D0,0.D0,
+ C .6D0, 0.D0,0.D0,0.D0,0.D0,0.D0,0.D0,
+ D .6D0, 0.D0,0.D0,0.D0,0.D0,0.D0,0.D0,
+ E -.8D0, 0.D0,0.D0,0.D0,0.D0,0.D0,0.D0,
+ F -.9D0, 0.D0,0.D0,0.D0,0.D0,0.D0,0.D0,
+ G 3.5D0, 0.D0,0.D0,0.D0,0.D0,0.D0,0.D0,
+ H .6D0, .1D0, 0.D0,0.D0,0.D0,0.D0,0.D0,
+ I -.8D0, 3.8D0, 0.D0,0.D0,0.D0,0.D0,0.D0,
+ J -.9D0, 2.8D0, 0.D0,0.D0,0.D0,0.D0,0.D0,
+ K 3.5D0, -.4D0, 0.D0,0.D0,0.D0,0.D0,0.D0,
+ L .6D0, .1D0, -.5D0, .8D0, 0.D0,0.D0,0.D0,
+ M -.8D0, 3.8D0, -2.2D0, -1.2D0, 0.D0,0.D0,0.D0,
+ N -.9D0, 2.8D0, -1.4D0, -1.3D0, 0.D0,0.D0,0.D0,
+ O 3.5D0, -.4D0, -2.2D0, 4.7D0, 0.D0,0.D0,0.D0/
+*
+ DATA DT19XB/.6D0, 0.D0,0.D0,0.D0,0.D0,0.D0,0.D0,
+ A .6D0, 0.D0,0.D0,0.D0,0.D0,0.D0,0.D0,
+ B .6D0, 0.D0,0.D0,0.D0,0.D0,0.D0,0.D0,
+ C .6D0, 0.D0,0.D0,0.D0,0.D0,0.D0,0.D0,
+ D .6D0, 0.D0,0.D0,0.D0,0.D0,0.D0,0.D0,
+ E -.8D0, 0.D0,0.D0,0.D0,0.D0,0.D0,0.D0,
+ F -.9D0, 0.D0,0.D0,0.D0,0.D0,0.D0,0.D0,
+ G 3.5D0, 0.D0,0.D0,0.D0,0.D0,0.D0,0.D0,
+ H .6D0, .1D0, -.5D0, 0.D0,0.D0,0.D0,0.D0,
+ I 0.D0, .1D0, -3.0D0, 0.D0,0.D0,0.D0,0.D0,
+ J -.3D0, .1D0, -2.0D0, 0.D0,0.D0,0.D0,0.D0,
+ K 3.3D0, .1D0, -2.0D0, 0.D0,0.D0,0.D0,0.D0,
+ L .6D0, .1D0, -.5D0, .8D0, .9D0, -.3D0, -.4D0,
+ M -2.0D0, .1D0, 1.4D0, .8D0, .6D0, -.3D0, -2.8D0,
+ N -1.8D0, .1D0, 1.3D0, .8D0, 0.D0, -.3D0, -1.9D0,
+ O 3.8D0, .1D0, -3.1D0, .8D0, 4.8D0, -.3D0, -1.5D0 /
+*
+ DATA DT19XC/.6D0, 0.D0,0.D0,0.D0,0.D0,0.D0,0.D0,
+ A .6D0, 0.D0,0.D0,0.D0,0.D0,0.D0,0.D0,
+ B .6D0, 0.D0,0.D0,0.D0,0.D0,0.D0,0.D0,
+ C .6D0, 0.D0,0.D0,0.D0,0.D0,0.D0,0.D0,
+ D .6D0, 0.D0,0.D0,0.D0,0.D0,0.D0,0.D0,
+ E -.8D0, 0.D0,0.D0,0.D0,0.D0,0.D0,0.D0,
+ F -.9D0, 0.D0,0.D0,0.D0,0.D0,0.D0,0.D0,
+ G 3.5D0, 0.D0,0.D0,0.D0,0.D0,0.D0,0.D0,
+ H .6D0, .1D0, -.5D0, 0.D0,0.D0,0.D0,0.D0,
+ I 4.8D0, .1D0, -3.0D0, 0.D0,0.D0,0.D0,0.D0,
+ J 3.3D0, .1D0, -2.0D0, 0.D0,0.D0,0.D0,0.D0,
+ K 2.1D0, .1D0, -2.0D0, 0.D0,0.D0,0.D0,0.D0,
+ L .6D0, .1D0, -.5D0, .8D0, .9D0, -.3D0, -.4D0,
+ M -1.6D0, .1D0, -2.2D0, .8D0, 5.4D0, -.3D0, -2.8D0,
+ N -1.5D0, .1D0, -1.4D0, .8D0, 3.6D0, -.3D0, -1.9D0,
+ O 3.7D0, .1D0, -2.2D0, .8D0, 3.6D0, -.3D0, -1.5D0 /
+*
+ DATA DT19XD/.6D0, 0.D0,0.D0,0.D0,0.D0,0.D0,0.D0,
+ A .6D0, 0.D0,0.D0,0.D0,0.D0,0.D0,0.D0,
+ B .6D0, 0.D0,0.D0,0.D0,0.D0,0.D0,0.D0,
+ C .6D0, 0.D0,0.D0,0.D0,0.D0,0.D0,0.D0,
+ D .6D0, 0.D0,0.D0,0.D0,0.D0,0.D0,0.D0,
+ E -.8D0, 0.D0,0.D0,0.D0,0.D0,0.D0,0.D0,
+ F -.9D0, 0.D0,0.D0,0.D0,0.D0,0.D0,0.D0,
+ G 3.5D0, 0.D0,0.D0,0.D0,0.D0,0.D0,0.D0,
+ H .6D0, .1D0, 0.D0,0.D0,0.D0,0.D0,0.D0,
+ I -.8D0, -1.0D0, 0.D0,0.D0,0.D0,0.D0,0.D0,
+ J -.9D0, -.8D0, 0.D0,0.D0,0.D0,0.D0,0.D0,
+ K 3.5D0, .8D0, 0.D0,0.D0,0.D0,0.D0,0.D0,
+ L .6D0, .1D0, -.5D0, .8D0, 0.D0,0.D0,0.D0,
+ M -.8D0, -1.0D0, 1.4D0, -1.6D0, 0.D0,0.D0,0.D0,
+ N -.9D0, -.8D0, 1.3D0, -1.6D0, 0.D0,0.D0,0.D0,
+ O 3.5D0, .8D0, -3.1D0, 4.8D0, 0.D0,0.D0,0.D0/
+* TRUE Y RESULTS FOR ROTATIONS DROTM
+ DATA DT19YA/.5D0, 0.D0,0.D0,0.D0,0.D0,0.D0,0.D0,
+ A .5D0, 0.D0,0.D0,0.D0,0.D0,0.D0,0.D0,
+ B .5D0, 0.D0,0.D0,0.D0,0.D0,0.D0,0.D0,
+ C .5D0, 0.D0,0.D0,0.D0,0.D0,0.D0,0.D0,
+ D .5D0, 0.D0,0.D0,0.D0,0.D0,0.D0,0.D0,
+ E .7D0, 0.D0,0.D0,0.D0,0.D0,0.D0,0.D0,
+ F 1.7D0, 0.D0,0.D0,0.D0,0.D0,0.D0,0.D0,
+ G -2.6D0, 0.D0,0.D0,0.D0,0.D0,0.D0,0.D0,
+ H .5D0, -.9D0, 0.D0,0.D0,0.D0,0.D0,0.D0,
+ I .7D0, -4.8D0, 0.D0,0.D0,0.D0,0.D0,0.D0,
+ J 1.7D0, -.7D0, 0.D0,0.D0,0.D0,0.D0,0.D0,
+ K -2.6D0, 3.5D0, 0.D0,0.D0,0.D0,0.D0,0.D0,
+ L .5D0, -.9D0, .3D0, .7D0, 0.D0,0.D0,0.D0,
+ M .7D0, -4.8D0, 3.0D0, 1.1D0, 0.D0,0.D0,0.D0,
+ N 1.7D0, -.7D0, -.7D0, 2.3D0, 0.D0,0.D0,0.D0,
+ O -2.6D0, 3.5D0, -.7D0, -3.6D0, 0.D0,0.D0,0.D0/
+*
+ DATA DT19YB/.5D0, 0.D0,0.D0,0.D0,0.D0,0.D0,0.D0,
+ A .5D0, 0.D0,0.D0,0.D0,0.D0,0.D0,0.D0,
+ B .5D0, 0.D0,0.D0,0.D0,0.D0,0.D0,0.D0,
+ C .5D0, 0.D0,0.D0,0.D0,0.D0,0.D0,0.D0,
+ D .5D0, 0.D0,0.D0,0.D0,0.D0,0.D0,0.D0,
+ E .7D0, 0.D0,0.D0,0.D0,0.D0,0.D0,0.D0,
+ F 1.7D0, 0.D0,0.D0,0.D0,0.D0,0.D0,0.D0,
+ G -2.6D0, 0.D0,0.D0,0.D0,0.D0,0.D0,0.D0,
+ H .5D0, -.9D0, .3D0, 0.D0,0.D0,0.D0,0.D0,
+ I 4.0D0, -.9D0, -.3D0, 0.D0,0.D0,0.D0,0.D0,
+ J -.5D0, -.9D0, 1.5D0, 0.D0,0.D0,0.D0,0.D0,
+ K -1.5D0, -.9D0, -1.8D0, 0.D0,0.D0,0.D0,0.D0,
+ L .5D0, -.9D0, .3D0, .7D0, -.6D0, .2D0, .8D0,
+ M 3.7D0, -.9D0, -1.2D0, .7D0, -1.5D0, .2D0, 2.2D0,
+ N -.3D0, -.9D0, 2.1D0, .7D0, -1.6D0, .2D0, 2.0D0,
+ O -1.6D0, -.9D0, -2.1D0, .7D0, 2.9D0, .2D0, -3.8D0 /
+*
+ DATA DT19YC/.5D0, 0.D0,0.D0,0.D0,0.D0,0.D0,0.D0,
+ A .5D0, 0.D0,0.D0,0.D0,0.D0,0.D0,0.D0,
+ B .5D0, 0.D0,0.D0,0.D0,0.D0,0.D0,0.D0,
+ C .5D0, 0.D0,0.D0,0.D0,0.D0,0.D0,0.D0,
+ D .5D0, 0.D0,0.D0,0.D0,0.D0,0.D0,0.D0,
+ E .7D0, 0.D0,0.D0,0.D0,0.D0,0.D0,0.D0,
+ F 1.7D0, 0.D0,0.D0,0.D0,0.D0,0.D0,0.D0,
+ G -2.6D0, 0.D0,0.D0,0.D0,0.D0,0.D0,0.D0,
+ H .5D0, -.9D0, 0.D0,0.D0,0.D0,0.D0,0.D0,
+ I 4.0D0, -6.3D0, 0.D0,0.D0,0.D0,0.D0,0.D0,
+ J -.5D0, .3D0, 0.D0,0.D0,0.D0,0.D0,0.D0,
+ K -1.5D0, 3.0D0, 0.D0,0.D0,0.D0,0.D0,0.D0,
+ L .5D0, -.9D0, .3D0, .7D0, 0.D0,0.D0,0.D0,
+ M 3.7D0, -7.2D0, 3.0D0, 1.7D0, 0.D0,0.D0,0.D0,
+ N -.3D0, .9D0, -.7D0, 1.9D0, 0.D0,0.D0,0.D0,
+ O -1.6D0, 2.7D0, -.7D0, -3.4D0, 0.D0,0.D0,0.D0/
+*
+ DATA DT19YD/.5D0, 0.D0,0.D0,0.D0,0.D0,0.D0,0.D0,
+ A .5D0, 0.D0,0.D0,0.D0,0.D0,0.D0,0.D0,
+ B .5D0, 0.D0,0.D0,0.D0,0.D0,0.D0,0.D0,
+ C .5D0, 0.D0,0.D0,0.D0,0.D0,0.D0,0.D0,
+ D .5D0, 0.D0,0.D0,0.D0,0.D0,0.D0,0.D0,
+ E .7D0, 0.D0,0.D0,0.D0,0.D0,0.D0,0.D0,
+ F 1.7D0, 0.D0,0.D0,0.D0,0.D0,0.D0,0.D0,
+ G -2.6D0, 0.D0,0.D0,0.D0,0.D0,0.D0,0.D0,
+ H .5D0, -.9D0, .3D0, 0.D0,0.D0,0.D0,0.D0,
+ I .7D0, -.9D0, 1.2D0, 0.D0,0.D0,0.D0,0.D0,
+ J 1.7D0, -.9D0, .5D0, 0.D0,0.D0,0.D0,0.D0,
+ K -2.6D0, -.9D0, -1.3D0, 0.D0,0.D0,0.D0,0.D0,
+ L .5D0, -.9D0, .3D0, .7D0, -.6D0, .2D0, .8D0,
+ M .7D0, -.9D0, 1.2D0, .7D0, -1.5D0, .2D0, 1.6D0,
+ N 1.7D0, -.9D0, .5D0, .7D0, -1.6D0, .2D0, 2.4D0,
+ O -2.6D0, -.9D0, -1.3D0, .7D0, 2.9D0, .2D0, -4.0D0 /
+*
+* .. Executable Statements ..
+*
+ DO 120 KI = 1, 4
+ INCX = INCXS(KI)
+ INCY = INCYS(KI)
+ MX = ABS(INCX)
+ MY = ABS(INCY)
+*
+ DO 100 KN = 1, 4
+ N = NS(KN)
+ KSIZE = MIN(2,KN)
+ LENX = LENS(KN,MX)
+ LENY = LENS(KN,MY)
+* .. Initialize all argument arrays ..
+ DO 20 I = 1, 7
+ SX(I) = DX1(I)
+ SY(I) = DY1(I)
+ 20 CONTINUE
+*
+ IF (ICASE.EQ.1) THEN
+* .. DDOT ..
+ CALL STEST1(DDOT(N,SX,INCX,SY,INCY),DT7(KN,KI),SSIZE1(KN)
+ + ,SFAC)
+ ELSE IF (ICASE.EQ.2) THEN
+* .. DAXPY ..
+ CALL DAXPY(N,SA,SX,INCX,SY,INCY)
+ DO 40 J = 1, LENY
+ STY(J) = DT8(J,KN,KI)
+ 40 CONTINUE
+ CALL STEST(LENY,SY,STY,SSIZE2(1,KSIZE),SFAC)
+ ELSE IF (ICASE.EQ.5) THEN
+* .. DCOPY ..
+ DO 60 I = 1, 7
+ STY(I) = DT10Y(I,KN,KI)
+ 60 CONTINUE
+ CALL DCOPY(N,SX,INCX,SY,INCY)
+ CALL STEST(LENY,SY,STY,SSIZE2(1,1),1.0D0)
+ ELSE IF (ICASE.EQ.6) THEN
+* .. DSWAP ..
+ CALL DSWAP(N,SX,INCX,SY,INCY)
+ DO 80 I = 1, 7
+ STX(I) = DT10X(I,KN,KI)
+ STY(I) = DT10Y(I,KN,KI)
+ 80 CONTINUE
+ CALL STEST(LENX,SX,STX,SSIZE2(1,1),1.0D0)
+ CALL STEST(LENY,SY,STY,SSIZE2(1,1),1.0D0)
+ ELSE IF (ICASE.EQ.12) THEN
+* .. DROTM ..
+ KNI=KN+4*(KI-1)
+ DO KPAR=1,4
+ DO I=1,7
+ SX(I) = DX1(I)
+ SY(I) = DY1(I)
+ STX(I)= DT19X(I,KPAR,KNI)
+ STY(I)= DT19Y(I,KPAR,KNI)
+ END DO
+*
+ DO I=1,5
+ DTEMP(I) = DPAR(I,KPAR)
+ END DO
+*
+ DO I=1,LENX
+ SSIZE(I)=STX(I)
+ END DO
+* SEE REMARK ABOVE ABOUT DT11X(1,2,7)
+* AND DT11X(5,3,8).
+ IF ((KPAR .EQ. 2) .AND. (KNI .EQ. 7))
+ $ SSIZE(1) = 2.4D0
+ IF ((KPAR .EQ. 3) .AND. (KNI .EQ. 8))
+ $ SSIZE(5) = 1.8D0
+*
+ CALL DROTM(N,SX,INCX,SY,INCY,DTEMP)
+ CALL STEST(LENX,SX,STX,SSIZE,SFAC)
+ CALL STEST(LENY,SY,STY,STY,SFAC)
+ END DO
+ ELSE IF (ICASE.EQ.13) THEN
+* .. DSDOT ..
+ CALL TESTDSDOT(REAL(DSDOT(N,REAL(SX),INCX,REAL(SY),INCY)),
+ $ REAL(DT7(KN,KI)),REAL(SSIZE1(KN)), .3125E-1)
+ ELSE
+ WRITE (NOUT,*) ' Shouldn''t be here in CHECK2'
+ STOP
+ END IF
+ 100 CONTINUE
+ 120 CONTINUE
+ RETURN
+ END
+ SUBROUTINE CHECK3(SFAC)
+* .. Parameters ..
+ INTEGER NOUT
+ PARAMETER (NOUT=6)
+* .. Scalar Arguments ..
+ DOUBLE PRECISION SFAC
+* .. Scalars in Common ..
+ INTEGER ICASE, INCX, INCY, N
+ LOGICAL PASS
+* .. Local Scalars ..
+ DOUBLE PRECISION SC, SS
+ INTEGER I, K, KI, KN, KSIZE, LENX, LENY, MX, MY
+* .. Local Arrays ..
+ DOUBLE PRECISION COPYX(5), COPYY(5), DT9X(7,4,4), DT9Y(7,4,4),
+ + DX1(7), DY1(7), MWPC(11), MWPS(11), MWPSTX(5),
+ + MWPSTY(5), MWPTX(11,5), MWPTY(11,5), MWPX(5),
+ + MWPY(5), SSIZE2(14,2), STX(7), STY(7), SX(7),
+ + SY(7)
+ INTEGER INCXS(4), INCYS(4), LENS(4,2), MWPINX(11),
+ + MWPINY(11), MWPN(11), NS(4)
+* .. External Subroutines ..
+ EXTERNAL DROT, STEST
+* .. Intrinsic Functions ..
+ INTRINSIC ABS, MIN
+* .. Common blocks ..
+ COMMON /COMBLA/ICASE, N, INCX, INCY, PASS
+* .. Data statements ..
+ DATA INCXS/1, 2, -2, -1/
+ DATA INCYS/1, -2, 1, -2/
+ DATA LENS/1, 1, 2, 4, 1, 1, 3, 7/
+ DATA NS/0, 1, 2, 4/
+ DATA DX1/0.6D0, 0.1D0, -0.5D0, 0.8D0, 0.9D0, -0.3D0,
+ + -0.4D0/
+ DATA DY1/0.5D0, -0.9D0, 0.3D0, 0.7D0, -0.6D0, 0.2D0,
+ + 0.8D0/
+ DATA SC, SS/0.8D0, 0.6D0/
+ DATA DT9X/0.6D0, 0.0D0, 0.0D0, 0.0D0, 0.0D0, 0.0D0,
+ + 0.0D0, 0.78D0, 0.0D0, 0.0D0, 0.0D0, 0.0D0,
+ + 0.0D0, 0.0D0, 0.78D0, -0.46D0, 0.0D0, 0.0D0,
+ + 0.0D0, 0.0D0, 0.0D0, 0.78D0, -0.46D0, -0.22D0,
+ + 1.06D0, 0.0D0, 0.0D0, 0.0D0, 0.6D0, 0.0D0,
+ + 0.0D0, 0.0D0, 0.0D0, 0.0D0, 0.0D0, 0.78D0,
+ + 0.0D0, 0.0D0, 0.0D0, 0.0D0, 0.0D0, 0.0D0,
+ + 0.66D0, 0.1D0, -0.1D0, 0.0D0, 0.0D0, 0.0D0,
+ + 0.0D0, 0.96D0, 0.1D0, -0.76D0, 0.8D0, 0.90D0,
+ + -0.3D0, -0.02D0, 0.6D0, 0.0D0, 0.0D0, 0.0D0,
+ + 0.0D0, 0.0D0, 0.0D0, 0.78D0, 0.0D0, 0.0D0,
+ + 0.0D0, 0.0D0, 0.0D0, 0.0D0, -0.06D0, 0.1D0,
+ + -0.1D0, 0.0D0, 0.0D0, 0.0D0, 0.0D0, 0.90D0,
+ + 0.1D0, -0.22D0, 0.8D0, 0.18D0, -0.3D0, -0.02D0,
+ + 0.6D0, 0.0D0, 0.0D0, 0.0D0, 0.0D0, 0.0D0, 0.0D0,
+ + 0.78D0, 0.0D0, 0.0D0, 0.0D0, 0.0D0, 0.0D0,
+ + 0.0D0, 0.78D0, 0.26D0, 0.0D0, 0.0D0, 0.0D0,
+ + 0.0D0, 0.0D0, 0.78D0, 0.26D0, -0.76D0, 1.12D0,
+ + 0.0D0, 0.0D0, 0.0D0/
+ DATA DT9Y/0.5D0, 0.0D0, 0.0D0, 0.0D0, 0.0D0, 0.0D0,
+ + 0.0D0, 0.04D0, 0.0D0, 0.0D0, 0.0D0, 0.0D0,
+ + 0.0D0, 0.0D0, 0.04D0, -0.78D0, 0.0D0, 0.0D0,
+ + 0.0D0, 0.0D0, 0.0D0, 0.04D0, -0.78D0, 0.54D0,
+ + 0.08D0, 0.0D0, 0.0D0, 0.0D0, 0.5D0, 0.0D0,
+ + 0.0D0, 0.0D0, 0.0D0, 0.0D0, 0.0D0, 0.04D0,
+ + 0.0D0, 0.0D0, 0.0D0, 0.0D0, 0.0D0, 0.0D0, 0.7D0,
+ + -0.9D0, -0.12D0, 0.0D0, 0.0D0, 0.0D0, 0.0D0,
+ + 0.64D0, -0.9D0, -0.30D0, 0.7D0, -0.18D0, 0.2D0,
+ + 0.28D0, 0.5D0, 0.0D0, 0.0D0, 0.0D0, 0.0D0,
+ + 0.0D0, 0.0D0, 0.04D0, 0.0D0, 0.0D0, 0.0D0,
+ + 0.0D0, 0.0D0, 0.0D0, 0.7D0, -1.08D0, 0.0D0,
+ + 0.0D0, 0.0D0, 0.0D0, 0.0D0, 0.64D0, -1.26D0,
+ + 0.54D0, 0.20D0, 0.0D0, 0.0D0, 0.0D0, 0.5D0,
+ + 0.0D0, 0.0D0, 0.0D0, 0.0D0, 0.0D0, 0.0D0,
+ + 0.04D0, 0.0D0, 0.0D0, 0.0D0, 0.0D0, 0.0D0,
+ + 0.0D0, 0.04D0, -0.9D0, 0.18D0, 0.0D0, 0.0D0,
+ + 0.0D0, 0.0D0, 0.04D0, -0.9D0, 0.18D0, 0.7D0,
+ + -0.18D0, 0.2D0, 0.16D0/
+ DATA SSIZE2/0.0D0, 0.0D0, 0.0D0, 0.0D0, 0.0D0, 0.0D0,
+ + 0.0D0, 0.0D0, 0.0D0, 0.0D0, 0.0D0, 0.0D0, 0.0D0,
+ + 0.0D0, 1.17D0, 1.17D0, 1.17D0, 1.17D0, 1.17D0,
+ + 1.17D0, 1.17D0, 1.17D0, 1.17D0, 1.17D0, 1.17D0,
+ + 1.17D0, 1.17D0, 1.17D0/
+* .. Executable Statements ..
+*
+ DO 60 KI = 1, 4
+ INCX = INCXS(KI)
+ INCY = INCYS(KI)
+ MX = ABS(INCX)
+ MY = ABS(INCY)
+*
+ DO 40 KN = 1, 4
+ N = NS(KN)
+ KSIZE = MIN(2,KN)
+ LENX = LENS(KN,MX)
+ LENY = LENS(KN,MY)
+*
+ IF (ICASE.EQ.4) THEN
+* .. DROT ..
+ DO 20 I = 1, 7
+ SX(I) = DX1(I)
+ SY(I) = DY1(I)
+ STX(I) = DT9X(I,KN,KI)
+ STY(I) = DT9Y(I,KN,KI)
+ 20 CONTINUE
+ CALL DROT(N,SX,INCX,SY,INCY,SC,SS)
+ CALL STEST(LENX,SX,STX,SSIZE2(1,KSIZE),SFAC)
+ CALL STEST(LENY,SY,STY,SSIZE2(1,KSIZE),SFAC)
+ ELSE
+ WRITE (NOUT,*) ' Shouldn''t be here in CHECK3'
+ STOP
+ END IF
+ 40 CONTINUE
+ 60 CONTINUE
+*
+ MWPC(1) = 1
+ DO 80 I = 2, 11
+ MWPC(I) = 0
+ 80 CONTINUE
+ MWPS(1) = 0
+ DO 100 I = 2, 6
+ MWPS(I) = 1
+ 100 CONTINUE
+ DO 120 I = 7, 11
+ MWPS(I) = -1
+ 120 CONTINUE
+ MWPINX(1) = 1
+ MWPINX(2) = 1
+ MWPINX(3) = 1
+ MWPINX(4) = -1
+ MWPINX(5) = 1
+ MWPINX(6) = -1
+ MWPINX(7) = 1
+ MWPINX(8) = 1
+ MWPINX(9) = -1
+ MWPINX(10) = 1
+ MWPINX(11) = -1
+ MWPINY(1) = 1
+ MWPINY(2) = 1
+ MWPINY(3) = -1
+ MWPINY(4) = -1
+ MWPINY(5) = 2
+ MWPINY(6) = 1
+ MWPINY(7) = 1
+ MWPINY(8) = -1
+ MWPINY(9) = -1
+ MWPINY(10) = 2
+ MWPINY(11) = 1
+ DO 140 I = 1, 11
+ MWPN(I) = 5
+ 140 CONTINUE
+ MWPN(5) = 3
+ MWPN(10) = 3
+ DO 160 I = 1, 5
+ MWPX(I) = I
+ MWPY(I) = I
+ MWPTX(1,I) = I
+ MWPTY(1,I) = I
+ MWPTX(2,I) = I
+ MWPTY(2,I) = -I
+ MWPTX(3,I) = 6 - I
+ MWPTY(3,I) = I - 6
+ MWPTX(4,I) = I
+ MWPTY(4,I) = -I
+ MWPTX(6,I) = 6 - I
+ MWPTY(6,I) = I - 6
+ MWPTX(7,I) = -I
+ MWPTY(7,I) = I
+ MWPTX(8,I) = I - 6
+ MWPTY(8,I) = 6 - I
+ MWPTX(9,I) = -I
+ MWPTY(9,I) = I
+ MWPTX(11,I) = I - 6
+ MWPTY(11,I) = 6 - I
+ 160 CONTINUE
+ MWPTX(5,1) = 1
+ MWPTX(5,2) = 3
+ MWPTX(5,3) = 5
+ MWPTX(5,4) = 4
+ MWPTX(5,5) = 5
+ MWPTY(5,1) = -1
+ MWPTY(5,2) = 2
+ MWPTY(5,3) = -2
+ MWPTY(5,4) = 4
+ MWPTY(5,5) = -3
+ MWPTX(10,1) = -1
+ MWPTX(10,2) = -3
+ MWPTX(10,3) = -5
+ MWPTX(10,4) = 4
+ MWPTX(10,5) = 5
+ MWPTY(10,1) = 1
+ MWPTY(10,2) = 2
+ MWPTY(10,3) = 2
+ MWPTY(10,4) = 4
+ MWPTY(10,5) = 3
+ DO 200 I = 1, 11
+ INCX = MWPINX(I)
+ INCY = MWPINY(I)
+ DO 180 K = 1, 5
+ COPYX(K) = MWPX(K)
+ COPYY(K) = MWPY(K)
+ MWPSTX(K) = MWPTX(I,K)
+ MWPSTY(K) = MWPTY(I,K)
+ 180 CONTINUE
+ CALL DROT(MWPN(I),COPYX,INCX,COPYY,INCY,MWPC(I),MWPS(I))
+ CALL STEST(5,COPYX,MWPSTX,MWPSTX,SFAC)
+ CALL STEST(5,COPYY,MWPSTY,MWPSTY,SFAC)
+ 200 CONTINUE
+ RETURN
+ END
+ SUBROUTINE STEST(LEN,SCOMP,STRUE,SSIZE,SFAC)
+* ********************************* STEST **************************
+*
+* THIS SUBR COMPARES ARRAYS SCOMP() AND STRUE() OF LENGTH LEN TO
+* SEE IF THE TERM BY TERM DIFFERENCES, MULTIPLIED BY SFAC, ARE
+* NEGLIGIBLE.
+*
+* C. L. LAWSON, JPL, 1974 DEC 10
+*
+* .. Parameters ..
+ INTEGER NOUT
+ DOUBLE PRECISION ZERO
+ PARAMETER (NOUT=6, ZERO=0.0D0)
+* .. Scalar Arguments ..
+ DOUBLE PRECISION SFAC
+ INTEGER LEN
+* .. Array Arguments ..
+ DOUBLE PRECISION SCOMP(LEN), SSIZE(LEN), STRUE(LEN)
+* .. Scalars in Common ..
+ INTEGER ICASE, INCX, INCY, N
+ LOGICAL PASS
+* .. Local Scalars ..
+ DOUBLE PRECISION SD
+ INTEGER I
+* .. External Functions ..
+ DOUBLE PRECISION SDIFF
+ EXTERNAL SDIFF
+* .. Intrinsic Functions ..
+ INTRINSIC ABS
+* .. Common blocks ..
+ COMMON /COMBLA/ICASE, N, INCX, INCY, PASS
+* .. Executable Statements ..
+*
+ DO 40 I = 1, LEN
+ SD = SCOMP(I) - STRUE(I)
+ IF (ABS(SFAC*SD) .LE. ABS(SSIZE(I))*EPSILON(ZERO))
+ + GO TO 40
+*
+* HERE SCOMP(I) IS NOT CLOSE TO STRUE(I).
+*
+ IF ( .NOT. PASS) GO TO 20
+* PRINT FAIL MESSAGE AND HEADER.
+ PASS = .FALSE.
+ WRITE (NOUT,99999)
+ WRITE (NOUT,99998)
+ 20 WRITE (NOUT,99997) ICASE, N, INCX, INCY, I, SCOMP(I),
+ + STRUE(I), SD, SSIZE(I)
+ 40 CONTINUE
+ RETURN
+*
+99999 FORMAT (' FAIL')
+99998 FORMAT (/' CASE N INCX INCY I ',
+ + ' COMP(I) TRUE(I) DIFFERENCE',
+ + ' SIZE(I)',/1X)
+99997 FORMAT (1X,I4,I3,2I5,I3,2D36.8,2D12.4)
+ END
+ SUBROUTINE TESTDSDOT(SCOMP,STRUE,SSIZE,SFAC)
+* ********************************* STEST **************************
+*
+* THIS SUBR COMPARES ARRAYS SCOMP() AND STRUE() OF LENGTH LEN TO
+* SEE IF THE TERM BY TERM DIFFERENCES, MULTIPLIED BY SFAC, ARE
+* NEGLIGIBLE.
+*
+* C. L. LAWSON, JPL, 1974 DEC 10
+*
+* .. Parameters ..
+ INTEGER NOUT
+ REAL ZERO
+ PARAMETER (NOUT=6, ZERO=0.0E0)
+* .. Scalar Arguments ..
+ REAL SFAC, SCOMP, SSIZE, STRUE
+* .. Scalars in Common ..
+ INTEGER ICASE, INCX, INCY, N
+ LOGICAL PASS
+* .. Local Scalars ..
+ REAL SD
+* .. Intrinsic Functions ..
+ INTRINSIC ABS
+* .. Common blocks ..
+ COMMON /COMBLA/ICASE, N, INCX, INCY, PASS
+* .. Executable Statements ..
+*
+ SD = SCOMP - STRUE
+ IF (ABS(SFAC*SD) .LE. ABS(SSIZE) * EPSILON(ZERO))
+ + GO TO 40
+*
+* HERE SCOMP(I) IS NOT CLOSE TO STRUE(I).
+*
+ IF ( .NOT. PASS) GO TO 20
+* PRINT FAIL MESSAGE AND HEADER.
+ PASS = .FALSE.
+ WRITE (NOUT,99999)
+ WRITE (NOUT,99998)
+ 20 WRITE (NOUT,99997) ICASE, N, INCX, INCY, SCOMP,
+ + STRUE, SD, SSIZE
+ 40 CONTINUE
+ RETURN
+*
+99999 FORMAT (' FAIL')
+99998 FORMAT (/' CASE N INCX INCY ',
+ + ' COMP(I) TRUE(I) DIFFERENCE',
+ + ' SIZE(I)',/1X)
+99997 FORMAT (1X,I4,I3,1I5,I3,2E36.8,2E12.4)
+ END
+ SUBROUTINE STEST1(SCOMP1,STRUE1,SSIZE,SFAC)
+* ************************* STEST1 *****************************
+*
+* THIS IS AN INTERFACE SUBROUTINE TO ACCOMMODATE THE FORTRAN
+* REQUIREMENT THAT WHEN A DUMMY ARGUMENT IS AN ARRAY, THE
+* ACTUAL ARGUMENT MUST ALSO BE AN ARRAY OR AN ARRAY ELEMENT.
+*
+* C.L. LAWSON, JPL, 1978 DEC 6
+*
+* .. Scalar Arguments ..
+ DOUBLE PRECISION SCOMP1, SFAC, STRUE1
+* .. Array Arguments ..
+ DOUBLE PRECISION SSIZE(*)
+* .. Local Arrays ..
+ DOUBLE PRECISION SCOMP(1), STRUE(1)
+* .. External Subroutines ..
+ EXTERNAL STEST
+* .. Executable Statements ..
+*
+ SCOMP(1) = SCOMP1
+ STRUE(1) = STRUE1
+ CALL STEST(1,SCOMP,STRUE,SSIZE,SFAC)
+*
+ RETURN
+ END
+ DOUBLE PRECISION FUNCTION SDIFF(SA,SB)
+* ********************************* SDIFF **************************
+* COMPUTES DIFFERENCE OF TWO NUMBERS. C. L. LAWSON, JPL 1974 FEB 15
+*
+* .. Scalar Arguments ..
+ DOUBLE PRECISION SA, SB
+* .. Executable Statements ..
+ SDIFF = SA - SB
+ RETURN
+ END
+ SUBROUTINE ITEST1(ICOMP,ITRUE)
+* ********************************* ITEST1 *************************
+*
+* THIS SUBROUTINE COMPARES THE VARIABLES ICOMP AND ITRUE FOR
+* EQUALITY.
+* C. L. LAWSON, JPL, 1974 DEC 10
+*
+* .. Parameters ..
+ INTEGER NOUT
+ PARAMETER (NOUT=6)
+* .. Scalar Arguments ..
+ INTEGER ICOMP, ITRUE
+* .. Scalars in Common ..
+ INTEGER ICASE, INCX, INCY, N
+ LOGICAL PASS
+* .. Local Scalars ..
+ INTEGER ID
+* .. Common blocks ..
+ COMMON /COMBLA/ICASE, N, INCX, INCY, PASS
+* .. Executable Statements ..
+*
+ IF (ICOMP.EQ.ITRUE) GO TO 40
+*
+* HERE ICOMP IS NOT EQUAL TO ITRUE.
+*
+ IF ( .NOT. PASS) GO TO 20
+* PRINT FAIL MESSAGE AND HEADER.
+ PASS = .FALSE.
+ WRITE (NOUT,99999)
+ WRITE (NOUT,99998)
+ 20 ID = ICOMP - ITRUE
+ WRITE (NOUT,99997) ICASE, N, INCX, INCY, ICOMP, ITRUE, ID
+ 40 CONTINUE
+ RETURN
+*
+99999 FORMAT (' FAIL')
+99998 FORMAT (/' CASE N INCX INCY ',
+ + ' COMP TRUE DIFFERENCE',
+ + /1X)
+99997 FORMAT (1X,I4,I3,2I5,2I36,I12)
+ END
diff --git a/blas/testing/dblat2.dat b/blas/testing/dblat2.dat
new file mode 100644
index 0000000..3755b83
--- /dev/null
+++ b/blas/testing/dblat2.dat
@@ -0,0 +1,34 @@
+'dblat2.summ' NAME OF SUMMARY OUTPUT FILE
+6 UNIT NUMBER OF SUMMARY FILE
+'dblat2.snap' NAME OF SNAPSHOT OUTPUT FILE
+-1 UNIT NUMBER OF SNAPSHOT FILE (NOT USED IF .LT. 0)
+F LOGICAL FLAG, T TO REWIND SNAPSHOT FILE AFTER EACH RECORD.
+F LOGICAL FLAG, T TO STOP ON FAILURES.
+T LOGICAL FLAG, T TO TEST ERROR EXITS.
+16.0 THRESHOLD VALUE OF TEST RATIO
+6 NUMBER OF VALUES OF N
+0 1 2 3 5 9 VALUES OF N
+4 NUMBER OF VALUES OF K
+0 1 2 4 VALUES OF K
+4 NUMBER OF VALUES OF INCX AND INCY
+1 2 -1 -2 VALUES OF INCX AND INCY
+3 NUMBER OF VALUES OF ALPHA
+0.0 1.0 0.7 VALUES OF ALPHA
+3 NUMBER OF VALUES OF BETA
+0.0 1.0 0.9 VALUES OF BETA
+DGEMV T PUT F FOR NO TEST. SAME COLUMNS.
+DGBMV T PUT F FOR NO TEST. SAME COLUMNS.
+DSYMV T PUT F FOR NO TEST. SAME COLUMNS.
+DSBMV T PUT F FOR NO TEST. SAME COLUMNS.
+DSPMV T PUT F FOR NO TEST. SAME COLUMNS.
+DTRMV T PUT F FOR NO TEST. SAME COLUMNS.
+DTBMV T PUT F FOR NO TEST. SAME COLUMNS.
+DTPMV T PUT F FOR NO TEST. SAME COLUMNS.
+DTRSV T PUT F FOR NO TEST. SAME COLUMNS.
+DTBSV T PUT F FOR NO TEST. SAME COLUMNS.
+DTPSV T PUT F FOR NO TEST. SAME COLUMNS.
+DGER T PUT F FOR NO TEST. SAME COLUMNS.
+DSYR T PUT F FOR NO TEST. SAME COLUMNS.
+DSPR T PUT F FOR NO TEST. SAME COLUMNS.
+DSYR2 T PUT F FOR NO TEST. SAME COLUMNS.
+DSPR2 T PUT F FOR NO TEST. SAME COLUMNS.
diff --git a/blas/testing/dblat2.f b/blas/testing/dblat2.f
new file mode 100644
index 0000000..0fa80af
--- /dev/null
+++ b/blas/testing/dblat2.f
@@ -0,0 +1,3176 @@
+*> \brief \b DBLAT2
+*
+* =========== DOCUMENTATION ===========
+*
+* Online html documentation available at
+* http://www.netlib.org/lapack/explore-html/
+*
+* Definition:
+* ===========
+*
+* PROGRAM DBLAT2
+*
+*
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
+*>
+*> Test program for the DOUBLE PRECISION Level 2 Blas.
+*>
+*> The program must be driven by a short data file. The first 18 records
+*> of the file are read using list-directed input, the last 16 records
+*> are read using the format ( A6, L2 ). An annotated example of a data
+*> file can be obtained by deleting the first 3 characters from the
+*> following 34 lines:
+*> 'dblat2.out' NAME OF SUMMARY OUTPUT FILE
+*> 6 UNIT NUMBER OF SUMMARY FILE
+*> 'DBLAT2.SNAP' NAME OF SNAPSHOT OUTPUT FILE
+*> -1 UNIT NUMBER OF SNAPSHOT FILE (NOT USED IF .LT. 0)
+*> F LOGICAL FLAG, T TO REWIND SNAPSHOT FILE AFTER EACH RECORD.
+*> F LOGICAL FLAG, T TO STOP ON FAILURES.
+*> T LOGICAL FLAG, T TO TEST ERROR EXITS.
+*> 16.0 THRESHOLD VALUE OF TEST RATIO
+*> 6 NUMBER OF VALUES OF N
+*> 0 1 2 3 5 9 VALUES OF N
+*> 4 NUMBER OF VALUES OF K
+*> 0 1 2 4 VALUES OF K
+*> 4 NUMBER OF VALUES OF INCX AND INCY
+*> 1 2 -1 -2 VALUES OF INCX AND INCY
+*> 3 NUMBER OF VALUES OF ALPHA
+*> 0.0 1.0 0.7 VALUES OF ALPHA
+*> 3 NUMBER OF VALUES OF BETA
+*> 0.0 1.0 0.9 VALUES OF BETAC
+*> DGEMV T PUT F FOR NO TEST. SAME COLUMNS.
+*> DGBMV T PUT F FOR NO TEST. SAME COLUMNS.
+*> DSYMV T PUT F FOR NO TEST. SAME COLUMNS.
+*> DSBMV T PUT F FOR NO TEST. SAME COLUMNS.
+*> DSPMV T PUT F FOR NO TEST. SAME COLUMNS.
+*> DTRMV T PUT F FOR NO TEST. SAME COLUMNS.
+*> DTBMV T PUT F FOR NO TEST. SAME COLUMNS.
+*> DTPMV T PUT F FOR NO TEST. SAME COLUMNS.
+*> DTRSV T PUT F FOR NO TEST. SAME COLUMNS.
+*> DTBSV T PUT F FOR NO TEST. SAME COLUMNS.
+*> DTPSV T PUT F FOR NO TEST. SAME COLUMNS.
+*> DGER T PUT F FOR NO TEST. SAME COLUMNS.
+*> DSYR T PUT F FOR NO TEST. SAME COLUMNS.
+*> DSPR T PUT F FOR NO TEST. SAME COLUMNS.
+*> DSYR2 T PUT F FOR NO TEST. SAME COLUMNS.
+*> DSPR2 T PUT F FOR NO TEST. SAME COLUMNS.
+*>
+*> Further Details
+*> ===============
+*>
+*> See:
+*>
+*> Dongarra J. J., Du Croz J. J., Hammarling S. and Hanson R. J..
+*> An extended set of Fortran Basic Linear Algebra Subprograms.
+*>
+*> Technical Memoranda Nos. 41 (revision 3) and 81, Mathematics
+*> and Computer Science Division, Argonne National Laboratory,
+*> 9700 South Cass Avenue, Argonne, Illinois 60439, US.
+*>
+*> Or
+*>
+*> NAG Technical Reports TR3/87 and TR4/87, Numerical Algorithms
+*> Group Ltd., NAG Central Office, 256 Banbury Road, Oxford
+*> OX2 7DE, UK, and Numerical Algorithms Group Inc., 1101 31st
+*> Street, Suite 100, Downers Grove, Illinois 60515-1263, USA.
+*>
+*>
+*> -- Written on 10-August-1987.
+*> Richard Hanson, Sandia National Labs.
+*> Jeremy Du Croz, NAG Central Office.
+*>
+*> 10-9-00: Change STATUS='NEW' to 'UNKNOWN' so that the testers
+*> can be run multiple times without deleting generated
+*> output files (susan)
+*> \endverbatim
+*
+* Authors:
+* ========
+*
+*> \author Univ. of Tennessee
+*> \author Univ. of California Berkeley
+*> \author Univ. of Colorado Denver
+*> \author NAG Ltd.
+*
+*> \date April 2012
+*
+*> \ingroup double_blas_testing
+*
+* =====================================================================
+ PROGRAM DBLAT2
+*
+* -- Reference BLAS test routine (version 3.4.1) --
+* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
+* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+* April 2012
+*
+* =====================================================================
+*
+* .. Parameters ..
+ INTEGER NIN
+ PARAMETER ( NIN = 5 )
+ INTEGER NSUBS
+ PARAMETER ( NSUBS = 16 )
+ DOUBLE PRECISION ZERO, ONE
+ PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0 )
+ INTEGER NMAX, INCMAX
+ PARAMETER ( NMAX = 65, INCMAX = 2 )
+ INTEGER NINMAX, NIDMAX, NKBMAX, NALMAX, NBEMAX
+ PARAMETER ( NINMAX = 7, NIDMAX = 9, NKBMAX = 7,
+ $ NALMAX = 7, NBEMAX = 7 )
+* .. Local Scalars ..
+ DOUBLE PRECISION EPS, ERR, THRESH
+ INTEGER I, ISNUM, J, N, NALF, NBET, NIDIM, NINC, NKB,
+ $ NOUT, NTRA
+ LOGICAL FATAL, LTESTT, REWI, SAME, SFATAL, TRACE,
+ $ TSTERR
+ CHARACTER*1 TRANS
+ CHARACTER*6 SNAMET
+ CHARACTER*32 SNAPS, SUMMRY
+* .. Local Arrays ..
+ DOUBLE PRECISION A( NMAX, NMAX ), AA( NMAX*NMAX ),
+ $ ALF( NALMAX ), AS( NMAX*NMAX ), BET( NBEMAX ),
+ $ G( NMAX ), X( NMAX ), XS( NMAX*INCMAX ),
+ $ XX( NMAX*INCMAX ), Y( NMAX ),
+ $ YS( NMAX*INCMAX ), YT( NMAX ),
+ $ YY( NMAX*INCMAX ), Z( 2*NMAX )
+ INTEGER IDIM( NIDMAX ), INC( NINMAX ), KB( NKBMAX )
+ LOGICAL LTEST( NSUBS )
+ CHARACTER*6 SNAMES( NSUBS )
+* .. External Functions ..
+ DOUBLE PRECISION DDIFF
+ LOGICAL LDE
+ EXTERNAL DDIFF, LDE
+* .. External Subroutines ..
+ EXTERNAL DCHK1, DCHK2, DCHK3, DCHK4, DCHK5, DCHK6,
+ $ DCHKE, DMVCH
+* .. Intrinsic Functions ..
+ INTRINSIC ABS, MAX, MIN
+* .. Scalars in Common ..
+ INTEGER INFOT, NOUTC
+ LOGICAL LERR, OK
+ CHARACTER*6 SRNAMT
+* .. Common blocks ..
+ COMMON /INFOC/INFOT, NOUTC, OK, LERR
+ COMMON /SRNAMC/SRNAMT
+* .. Data statements ..
+ DATA SNAMES/'DGEMV ', 'DGBMV ', 'DSYMV ', 'DSBMV ',
+ $ 'DSPMV ', 'DTRMV ', 'DTBMV ', 'DTPMV ',
+ $ 'DTRSV ', 'DTBSV ', 'DTPSV ', 'DGER ',
+ $ 'DSYR ', 'DSPR ', 'DSYR2 ', 'DSPR2 '/
+* .. Executable Statements ..
+*
+* Read name and unit number for summary output file and open file.
+*
+ READ( NIN, FMT = * )SUMMRY
+ READ( NIN, FMT = * )NOUT
+ OPEN( NOUT, FILE = SUMMRY, STATUS = 'UNKNOWN' )
+ NOUTC = NOUT
+*
+* Read name and unit number for snapshot output file and open file.
+*
+ READ( NIN, FMT = * )SNAPS
+ READ( NIN, FMT = * )NTRA
+ TRACE = NTRA.GE.0
+ IF( TRACE )THEN
+ OPEN( NTRA, FILE = SNAPS, STATUS = 'UNKNOWN' )
+ END IF
+* Read the flag that directs rewinding of the snapshot file.
+ READ( NIN, FMT = * )REWI
+ REWI = REWI.AND.TRACE
+* Read the flag that directs stopping on any failure.
+ READ( NIN, FMT = * )SFATAL
+* Read the flag that indicates whether error exits are to be tested.
+ READ( NIN, FMT = * )TSTERR
+* Read the threshold value of the test ratio
+ READ( NIN, FMT = * )THRESH
+*
+* Read and check the parameter values for the tests.
+*
+* Values of N
+ READ( NIN, FMT = * )NIDIM
+ IF( NIDIM.LT.1.OR.NIDIM.GT.NIDMAX )THEN
+ WRITE( NOUT, FMT = 9997 )'N', NIDMAX
+ GO TO 230
+ END IF
+ READ( NIN, FMT = * )( IDIM( I ), I = 1, NIDIM )
+ DO 10 I = 1, NIDIM
+ IF( IDIM( I ).LT.0.OR.IDIM( I ).GT.NMAX )THEN
+ WRITE( NOUT, FMT = 9996 )NMAX
+ GO TO 230
+ END IF
+ 10 CONTINUE
+* Values of K
+ READ( NIN, FMT = * )NKB
+ IF( NKB.LT.1.OR.NKB.GT.NKBMAX )THEN
+ WRITE( NOUT, FMT = 9997 )'K', NKBMAX
+ GO TO 230
+ END IF
+ READ( NIN, FMT = * )( KB( I ), I = 1, NKB )
+ DO 20 I = 1, NKB
+ IF( KB( I ).LT.0 )THEN
+ WRITE( NOUT, FMT = 9995 )
+ GO TO 230
+ END IF
+ 20 CONTINUE
+* Values of INCX and INCY
+ READ( NIN, FMT = * )NINC
+ IF( NINC.LT.1.OR.NINC.GT.NINMAX )THEN
+ WRITE( NOUT, FMT = 9997 )'INCX AND INCY', NINMAX
+ GO TO 230
+ END IF
+ READ( NIN, FMT = * )( INC( I ), I = 1, NINC )
+ DO 30 I = 1, NINC
+ IF( INC( I ).EQ.0.OR.ABS( INC( I ) ).GT.INCMAX )THEN
+ WRITE( NOUT, FMT = 9994 )INCMAX
+ GO TO 230
+ END IF
+ 30 CONTINUE
+* Values of ALPHA
+ READ( NIN, FMT = * )NALF
+ IF( NALF.LT.1.OR.NALF.GT.NALMAX )THEN
+ WRITE( NOUT, FMT = 9997 )'ALPHA', NALMAX
+ GO TO 230
+ END IF
+ READ( NIN, FMT = * )( ALF( I ), I = 1, NALF )
+* Values of BETA
+ READ( NIN, FMT = * )NBET
+ IF( NBET.LT.1.OR.NBET.GT.NBEMAX )THEN
+ WRITE( NOUT, FMT = 9997 )'BETA', NBEMAX
+ GO TO 230
+ END IF
+ READ( NIN, FMT = * )( BET( I ), I = 1, NBET )
+*
+* Report values of parameters.
+*
+ WRITE( NOUT, FMT = 9993 )
+ WRITE( NOUT, FMT = 9992 )( IDIM( I ), I = 1, NIDIM )
+ WRITE( NOUT, FMT = 9991 )( KB( I ), I = 1, NKB )
+ WRITE( NOUT, FMT = 9990 )( INC( I ), I = 1, NINC )
+ WRITE( NOUT, FMT = 9989 )( ALF( I ), I = 1, NALF )
+ WRITE( NOUT, FMT = 9988 )( BET( I ), I = 1, NBET )
+ IF( .NOT.TSTERR )THEN
+ WRITE( NOUT, FMT = * )
+ WRITE( NOUT, FMT = 9980 )
+ END IF
+ WRITE( NOUT, FMT = * )
+ WRITE( NOUT, FMT = 9999 )THRESH
+ WRITE( NOUT, FMT = * )
+*
+* Read names of subroutines and flags which indicate
+* whether they are to be tested.
+*
+ DO 40 I = 1, NSUBS
+ LTEST( I ) = .FALSE.
+ 40 CONTINUE
+ 50 READ( NIN, FMT = 9984, END = 80 )SNAMET, LTESTT
+ DO 60 I = 1, NSUBS
+ IF( SNAMET.EQ.SNAMES( I ) )
+ $ GO TO 70
+ 60 CONTINUE
+ WRITE( NOUT, FMT = 9986 )SNAMET
+ STOP
+ 70 LTEST( I ) = LTESTT
+ GO TO 50
+*
+ 80 CONTINUE
+ CLOSE ( NIN )
+*
+* Compute EPS (the machine precision).
+*
+ EPS = EPSILON(ZERO)
+ WRITE( NOUT, FMT = 9998 )EPS
+*
+* Check the reliability of DMVCH using exact data.
+*
+ N = MIN( 32, NMAX )
+ DO 120 J = 1, N
+ DO 110 I = 1, N
+ A( I, J ) = MAX( I - J + 1, 0 )
+ 110 CONTINUE
+ X( J ) = J
+ Y( J ) = ZERO
+ 120 CONTINUE
+ DO 130 J = 1, N
+ YY( J ) = J*( ( J + 1 )*J )/2 - ( ( J + 1 )*J*( J - 1 ) )/3
+ 130 CONTINUE
+* YY holds the exact result. On exit from DMVCH YT holds
+* the result computed by DMVCH.
+ TRANS = 'N'
+ CALL DMVCH( TRANS, N, N, ONE, A, NMAX, X, 1, ZERO, Y, 1, YT, G,
+ $ YY, EPS, ERR, FATAL, NOUT, .TRUE. )
+ SAME = LDE( YY, YT, N )
+ IF( .NOT.SAME.OR.ERR.NE.ZERO )THEN
+ WRITE( NOUT, FMT = 9985 )TRANS, SAME, ERR
+ STOP
+ END IF
+ TRANS = 'T'
+ CALL DMVCH( TRANS, N, N, ONE, A, NMAX, X, -1, ZERO, Y, -1, YT, G,
+ $ YY, EPS, ERR, FATAL, NOUT, .TRUE. )
+ SAME = LDE( YY, YT, N )
+ IF( .NOT.SAME.OR.ERR.NE.ZERO )THEN
+ WRITE( NOUT, FMT = 9985 )TRANS, SAME, ERR
+ STOP
+ END IF
+*
+* Test each subroutine in turn.
+*
+ DO 210 ISNUM = 1, NSUBS
+ WRITE( NOUT, FMT = * )
+ IF( .NOT.LTEST( ISNUM ) )THEN
+* Subprogram is not to be tested.
+ WRITE( NOUT, FMT = 9983 )SNAMES( ISNUM )
+ ELSE
+ SRNAMT = SNAMES( ISNUM )
+* Test error exits.
+ IF( TSTERR )THEN
+ CALL DCHKE( ISNUM, SNAMES( ISNUM ), NOUT )
+ WRITE( NOUT, FMT = * )
+ END IF
+* Test computations.
+ INFOT = 0
+ OK = .TRUE.
+ FATAL = .FALSE.
+ GO TO ( 140, 140, 150, 150, 150, 160, 160,
+ $ 160, 160, 160, 160, 170, 180, 180,
+ $ 190, 190 )ISNUM
+* Test DGEMV, 01, and DGBMV, 02.
+ 140 CALL DCHK1( SNAMES( ISNUM ), EPS, THRESH, NOUT, NTRA, TRACE,
+ $ REWI, FATAL, NIDIM, IDIM, NKB, KB, NALF, ALF,
+ $ NBET, BET, NINC, INC, NMAX, INCMAX, A, AA, AS,
+ $ X, XX, XS, Y, YY, YS, YT, G )
+ GO TO 200
+* Test DSYMV, 03, DSBMV, 04, and DSPMV, 05.
+ 150 CALL DCHK2( SNAMES( ISNUM ), EPS, THRESH, NOUT, NTRA, TRACE,
+ $ REWI, FATAL, NIDIM, IDIM, NKB, KB, NALF, ALF,
+ $ NBET, BET, NINC, INC, NMAX, INCMAX, A, AA, AS,
+ $ X, XX, XS, Y, YY, YS, YT, G )
+ GO TO 200
+* Test DTRMV, 06, DTBMV, 07, DTPMV, 08,
+* DTRSV, 09, DTBSV, 10, and DTPSV, 11.
+ 160 CALL DCHK3( SNAMES( ISNUM ), EPS, THRESH, NOUT, NTRA, TRACE,
+ $ REWI, FATAL, NIDIM, IDIM, NKB, KB, NINC, INC,
+ $ NMAX, INCMAX, A, AA, AS, Y, YY, YS, YT, G, Z )
+ GO TO 200
+* Test DGER, 12.
+ 170 CALL DCHK4( SNAMES( ISNUM ), EPS, THRESH, NOUT, NTRA, TRACE,
+ $ REWI, FATAL, NIDIM, IDIM, NALF, ALF, NINC, INC,
+ $ NMAX, INCMAX, A, AA, AS, X, XX, XS, Y, YY, YS,
+ $ YT, G, Z )
+ GO TO 200
+* Test DSYR, 13, and DSPR, 14.
+ 180 CALL DCHK5( SNAMES( ISNUM ), EPS, THRESH, NOUT, NTRA, TRACE,
+ $ REWI, FATAL, NIDIM, IDIM, NALF, ALF, NINC, INC,
+ $ NMAX, INCMAX, A, AA, AS, X, XX, XS, Y, YY, YS,
+ $ YT, G, Z )
+ GO TO 200
+* Test DSYR2, 15, and DSPR2, 16.
+ 190 CALL DCHK6( SNAMES( ISNUM ), EPS, THRESH, NOUT, NTRA, TRACE,
+ $ REWI, FATAL, NIDIM, IDIM, NALF, ALF, NINC, INC,
+ $ NMAX, INCMAX, A, AA, AS, X, XX, XS, Y, YY, YS,
+ $ YT, G, Z )
+*
+ 200 IF( FATAL.AND.SFATAL )
+ $ GO TO 220
+ END IF
+ 210 CONTINUE
+ WRITE( NOUT, FMT = 9982 )
+ GO TO 240
+*
+ 220 CONTINUE
+ WRITE( NOUT, FMT = 9981 )
+ GO TO 240
+*
+ 230 CONTINUE
+ WRITE( NOUT, FMT = 9987 )
+*
+ 240 CONTINUE
+ IF( TRACE )
+ $ CLOSE ( NTRA )
+ CLOSE ( NOUT )
+ STOP
+*
+ 9999 FORMAT( ' ROUTINES PASS COMPUTATIONAL TESTS IF TEST RATIO IS LES',
+ $ 'S THAN', F8.2 )
+ 9998 FORMAT( ' RELATIVE MACHINE PRECISION IS TAKEN TO BE', 1P, D9.1 )
+ 9997 FORMAT( ' NUMBER OF VALUES OF ', A, ' IS LESS THAN 1 OR GREATER ',
+ $ 'THAN ', I2 )
+ 9996 FORMAT( ' VALUE OF N IS LESS THAN 0 OR GREATER THAN ', I2 )
+ 9995 FORMAT( ' VALUE OF K IS LESS THAN 0' )
+ 9994 FORMAT( ' ABSOLUTE VALUE OF INCX OR INCY IS 0 OR GREATER THAN ',
+ $ I2 )
+ 9993 FORMAT( ' TESTS OF THE DOUBLE PRECISION LEVEL 2 BLAS', //' THE F',
+ $ 'OLLOWING PARAMETER VALUES WILL BE USED:' )
+ 9992 FORMAT( ' FOR N ', 9I6 )
+ 9991 FORMAT( ' FOR K ', 7I6 )
+ 9990 FORMAT( ' FOR INCX AND INCY ', 7I6 )
+ 9989 FORMAT( ' FOR ALPHA ', 7F6.1 )
+ 9988 FORMAT( ' FOR BETA ', 7F6.1 )
+ 9987 FORMAT( ' AMEND DATA FILE OR INCREASE ARRAY SIZES IN PROGRAM',
+ $ /' ******* TESTS ABANDONED *******' )
+ 9986 FORMAT( ' SUBPROGRAM NAME ', A6, ' NOT RECOGNIZED', /' ******* T',
+ $ 'ESTS ABANDONED *******' )
+ 9985 FORMAT( ' ERROR IN DMVCH - IN-LINE DOT PRODUCTS ARE BEING EVALU',
+ $ 'ATED WRONGLY.', /' DMVCH WAS CALLED WITH TRANS = ', A1,
+ $ ' AND RETURNED SAME = ', L1, ' AND ERR = ', F12.3, '.', /
+ $ ' THIS MAY BE DUE TO FAULTS IN THE ARITHMETIC OR THE COMPILER.'
+ $ , /' ******* TESTS ABANDONED *******' )
+ 9984 FORMAT( A6, L2 )
+ 9983 FORMAT( 1X, A6, ' WAS NOT TESTED' )
+ 9982 FORMAT( /' END OF TESTS' )
+ 9981 FORMAT( /' ******* FATAL ERROR - TESTS ABANDONED *******' )
+ 9980 FORMAT( ' ERROR-EXITS WILL NOT BE TESTED' )
+*
+* End of DBLAT2.
+*
+ END
+ SUBROUTINE DCHK1( SNAME, EPS, THRESH, NOUT, NTRA, TRACE, REWI,
+ $ FATAL, NIDIM, IDIM, NKB, KB, NALF, ALF, NBET,
+ $ BET, NINC, INC, NMAX, INCMAX, A, AA, AS, X, XX,
+ $ XS, Y, YY, YS, YT, G )
+*
+* Tests DGEMV and DGBMV.
+*
+* Auxiliary routine for test program for Level 2 Blas.
+*
+* -- Written on 10-August-1987.
+* Richard Hanson, Sandia National Labs.
+* Jeremy Du Croz, NAG Central Office.
+*
+* .. Parameters ..
+ DOUBLE PRECISION ZERO, HALF
+ PARAMETER ( ZERO = 0.0D0, HALF = 0.5D0 )
+* .. Scalar Arguments ..
+ DOUBLE PRECISION EPS, THRESH
+ INTEGER INCMAX, NALF, NBET, NIDIM, NINC, NKB, NMAX,
+ $ NOUT, NTRA
+ LOGICAL FATAL, REWI, TRACE
+ CHARACTER*6 SNAME
+* .. Array Arguments ..
+ DOUBLE PRECISION A( NMAX, NMAX ), AA( NMAX*NMAX ), ALF( NALF ),
+ $ AS( NMAX*NMAX ), BET( NBET ), G( NMAX ),
+ $ X( NMAX ), XS( NMAX*INCMAX ),
+ $ XX( NMAX*INCMAX ), Y( NMAX ),
+ $ YS( NMAX*INCMAX ), YT( NMAX ),
+ $ YY( NMAX*INCMAX )
+ INTEGER IDIM( NIDIM ), INC( NINC ), KB( NKB )
+* .. Local Scalars ..
+ DOUBLE PRECISION ALPHA, ALS, BETA, BLS, ERR, ERRMAX, TRANSL
+ INTEGER I, IA, IB, IC, IKU, IM, IN, INCX, INCXS, INCY,
+ $ INCYS, IX, IY, KL, KLS, KU, KUS, LAA, LDA,
+ $ LDAS, LX, LY, M, ML, MS, N, NARGS, NC, ND, NK,
+ $ NL, NS
+ LOGICAL BANDED, FULL, NULL, RESET, SAME, TRAN
+ CHARACTER*1 TRANS, TRANSS
+ CHARACTER*3 ICH
+* .. Local Arrays ..
+ LOGICAL ISAME( 13 )
+* .. External Functions ..
+ LOGICAL LDE, LDERES
+ EXTERNAL LDE, LDERES
+* .. External Subroutines ..
+ EXTERNAL DGBMV, DGEMV, DMAKE, DMVCH
+* .. Intrinsic Functions ..
+ INTRINSIC ABS, MAX, MIN
+* .. Scalars in Common ..
+ INTEGER INFOT, NOUTC
+ LOGICAL LERR, OK
+* .. Common blocks ..
+ COMMON /INFOC/INFOT, NOUTC, OK, LERR
+* .. Data statements ..
+ DATA ICH/'NTC'/
+* .. Executable Statements ..
+ FULL = SNAME( 3: 3 ).EQ.'E'
+ BANDED = SNAME( 3: 3 ).EQ.'B'
+* Define the number of arguments.
+ IF( FULL )THEN
+ NARGS = 11
+ ELSE IF( BANDED )THEN
+ NARGS = 13
+ END IF
+*
+ NC = 0
+ RESET = .TRUE.
+ ERRMAX = ZERO
+*
+ DO 120 IN = 1, NIDIM
+ N = IDIM( IN )
+ ND = N/2 + 1
+*
+ DO 110 IM = 1, 2
+ IF( IM.EQ.1 )
+ $ M = MAX( N - ND, 0 )
+ IF( IM.EQ.2 )
+ $ M = MIN( N + ND, NMAX )
+*
+ IF( BANDED )THEN
+ NK = NKB
+ ELSE
+ NK = 1
+ END IF
+ DO 100 IKU = 1, NK
+ IF( BANDED )THEN
+ KU = KB( IKU )
+ KL = MAX( KU - 1, 0 )
+ ELSE
+ KU = N - 1
+ KL = M - 1
+ END IF
+* Set LDA to 1 more than minimum value if room.
+ IF( BANDED )THEN
+ LDA = KL + KU + 1
+ ELSE
+ LDA = M
+ END IF
+ IF( LDA.LT.NMAX )
+ $ LDA = LDA + 1
+* Skip tests if not enough room.
+ IF( LDA.GT.NMAX )
+ $ GO TO 100
+ LAA = LDA*N
+ NULL = N.LE.0.OR.M.LE.0
+*
+* Generate the matrix A.
+*
+ TRANSL = ZERO
+ CALL DMAKE( SNAME( 2: 3 ), ' ', ' ', M, N, A, NMAX, AA,
+ $ LDA, KL, KU, RESET, TRANSL )
+*
+ DO 90 IC = 1, 3
+ TRANS = ICH( IC: IC )
+ TRAN = TRANS.EQ.'T'.OR.TRANS.EQ.'C'
+*
+ IF( TRAN )THEN
+ ML = N
+ NL = M
+ ELSE
+ ML = M
+ NL = N
+ END IF
+*
+ DO 80 IX = 1, NINC
+ INCX = INC( IX )
+ LX = ABS( INCX )*NL
+*
+* Generate the vector X.
+*
+ TRANSL = HALF
+ CALL DMAKE( 'GE', ' ', ' ', 1, NL, X, 1, XX,
+ $ ABS( INCX ), 0, NL - 1, RESET, TRANSL )
+ IF( NL.GT.1 )THEN
+ X( NL/2 ) = ZERO
+ XX( 1 + ABS( INCX )*( NL/2 - 1 ) ) = ZERO
+ END IF
+*
+ DO 70 IY = 1, NINC
+ INCY = INC( IY )
+ LY = ABS( INCY )*ML
+*
+ DO 60 IA = 1, NALF
+ ALPHA = ALF( IA )
+*
+ DO 50 IB = 1, NBET
+ BETA = BET( IB )
+*
+* Generate the vector Y.
+*
+ TRANSL = ZERO
+ CALL DMAKE( 'GE', ' ', ' ', 1, ML, Y, 1,
+ $ YY, ABS( INCY ), 0, ML - 1,
+ $ RESET, TRANSL )
+*
+ NC = NC + 1
+*
+* Save every datum before calling the
+* subroutine.
+*
+ TRANSS = TRANS
+ MS = M
+ NS = N
+ KLS = KL
+ KUS = KU
+ ALS = ALPHA
+ DO 10 I = 1, LAA
+ AS( I ) = AA( I )
+ 10 CONTINUE
+ LDAS = LDA
+ DO 20 I = 1, LX
+ XS( I ) = XX( I )
+ 20 CONTINUE
+ INCXS = INCX
+ BLS = BETA
+ DO 30 I = 1, LY
+ YS( I ) = YY( I )
+ 30 CONTINUE
+ INCYS = INCY
+*
+* Call the subroutine.
+*
+ IF( FULL )THEN
+ IF( TRACE )
+ $ WRITE( NTRA, FMT = 9994 )NC, SNAME,
+ $ TRANS, M, N, ALPHA, LDA, INCX, BETA,
+ $ INCY
+ IF( REWI )
+ $ REWIND NTRA
+ CALL DGEMV( TRANS, M, N, ALPHA, AA,
+ $ LDA, XX, INCX, BETA, YY,
+ $ INCY )
+ ELSE IF( BANDED )THEN
+ IF( TRACE )
+ $ WRITE( NTRA, FMT = 9995 )NC, SNAME,
+ $ TRANS, M, N, KL, KU, ALPHA, LDA,
+ $ INCX, BETA, INCY
+ IF( REWI )
+ $ REWIND NTRA
+ CALL DGBMV( TRANS, M, N, KL, KU, ALPHA,
+ $ AA, LDA, XX, INCX, BETA,
+ $ YY, INCY )
+ END IF
+*
+* Check if error-exit was taken incorrectly.
+*
+ IF( .NOT.OK )THEN
+ WRITE( NOUT, FMT = 9993 )
+ FATAL = .TRUE.
+ GO TO 130
+ END IF
+*
+* See what data changed inside subroutines.
+*
+ ISAME( 1 ) = TRANS.EQ.TRANSS
+ ISAME( 2 ) = MS.EQ.M
+ ISAME( 3 ) = NS.EQ.N
+ IF( FULL )THEN
+ ISAME( 4 ) = ALS.EQ.ALPHA
+ ISAME( 5 ) = LDE( AS, AA, LAA )
+ ISAME( 6 ) = LDAS.EQ.LDA
+ ISAME( 7 ) = LDE( XS, XX, LX )
+ ISAME( 8 ) = INCXS.EQ.INCX
+ ISAME( 9 ) = BLS.EQ.BETA
+ IF( NULL )THEN
+ ISAME( 10 ) = LDE( YS, YY, LY )
+ ELSE
+ ISAME( 10 ) = LDERES( 'GE', ' ', 1,
+ $ ML, YS, YY,
+ $ ABS( INCY ) )
+ END IF
+ ISAME( 11 ) = INCYS.EQ.INCY
+ ELSE IF( BANDED )THEN
+ ISAME( 4 ) = KLS.EQ.KL
+ ISAME( 5 ) = KUS.EQ.KU
+ ISAME( 6 ) = ALS.EQ.ALPHA
+ ISAME( 7 ) = LDE( AS, AA, LAA )
+ ISAME( 8 ) = LDAS.EQ.LDA
+ ISAME( 9 ) = LDE( XS, XX, LX )
+ ISAME( 10 ) = INCXS.EQ.INCX
+ ISAME( 11 ) = BLS.EQ.BETA
+ IF( NULL )THEN
+ ISAME( 12 ) = LDE( YS, YY, LY )
+ ELSE
+ ISAME( 12 ) = LDERES( 'GE', ' ', 1,
+ $ ML, YS, YY,
+ $ ABS( INCY ) )
+ END IF
+ ISAME( 13 ) = INCYS.EQ.INCY
+ END IF
+*
+* If data was incorrectly changed, report
+* and return.
+*
+ SAME = .TRUE.
+ DO 40 I = 1, NARGS
+ SAME = SAME.AND.ISAME( I )
+ IF( .NOT.ISAME( I ) )
+ $ WRITE( NOUT, FMT = 9998 )I
+ 40 CONTINUE
+ IF( .NOT.SAME )THEN
+ FATAL = .TRUE.
+ GO TO 130
+ END IF
+*
+ IF( .NOT.NULL )THEN
+*
+* Check the result.
+*
+ CALL DMVCH( TRANS, M, N, ALPHA, A,
+ $ NMAX, X, INCX, BETA, Y,
+ $ INCY, YT, G, YY, EPS, ERR,
+ $ FATAL, NOUT, .TRUE. )
+ ERRMAX = MAX( ERRMAX, ERR )
+* If got really bad answer, report and
+* return.
+ IF( FATAL )
+ $ GO TO 130
+ ELSE
+* Avoid repeating tests with M.le.0 or
+* N.le.0.
+ GO TO 110
+ END IF
+*
+ 50 CONTINUE
+*
+ 60 CONTINUE
+*
+ 70 CONTINUE
+*
+ 80 CONTINUE
+*
+ 90 CONTINUE
+*
+ 100 CONTINUE
+*
+ 110 CONTINUE
+*
+ 120 CONTINUE
+*
+* Report result.
+*
+ IF( ERRMAX.LT.THRESH )THEN
+ WRITE( NOUT, FMT = 9999 )SNAME, NC
+ ELSE
+ WRITE( NOUT, FMT = 9997 )SNAME, NC, ERRMAX
+ END IF
+ GO TO 140
+*
+ 130 CONTINUE
+ WRITE( NOUT, FMT = 9996 )SNAME
+ IF( FULL )THEN
+ WRITE( NOUT, FMT = 9994 )NC, SNAME, TRANS, M, N, ALPHA, LDA,
+ $ INCX, BETA, INCY
+ ELSE IF( BANDED )THEN
+ WRITE( NOUT, FMT = 9995 )NC, SNAME, TRANS, M, N, KL, KU,
+ $ ALPHA, LDA, INCX, BETA, INCY
+ END IF
+*
+ 140 CONTINUE
+ RETURN
+*
+ 9999 FORMAT( ' ', A6, ' PASSED THE COMPUTATIONAL TESTS (', I6, ' CALL',
+ $ 'S)' )
+ 9998 FORMAT( ' ******* FATAL ERROR - PARAMETER NUMBER ', I2, ' WAS CH',
+ $ 'ANGED INCORRECTLY *******' )
+ 9997 FORMAT( ' ', A6, ' COMPLETED THE COMPUTATIONAL TESTS (', I6, ' C',
+ $ 'ALLS)', /' ******* BUT WITH MAXIMUM TEST RATIO', F8.2,
+ $ ' - SUSPECT *******' )
+ 9996 FORMAT( ' ******* ', A6, ' FAILED ON CALL NUMBER:' )
+ 9995 FORMAT( 1X, I6, ': ', A6, '(''', A1, ''',', 4( I3, ',' ), F4.1,
+ $ ', A,', I3, ', X,', I2, ',', F4.1, ', Y,', I2, ') .' )
+ 9994 FORMAT( 1X, I6, ': ', A6, '(''', A1, ''',', 2( I3, ',' ), F4.1,
+ $ ', A,', I3, ', X,', I2, ',', F4.1, ', Y,', I2,
+ $ ') .' )
+ 9993 FORMAT( ' ******* FATAL ERROR - ERROR-EXIT TAKEN ON VALID CALL *',
+ $ '******' )
+*
+* End of DCHK1.
+*
+ END
+ SUBROUTINE DCHK2( SNAME, EPS, THRESH, NOUT, NTRA, TRACE, REWI,
+ $ FATAL, NIDIM, IDIM, NKB, KB, NALF, ALF, NBET,
+ $ BET, NINC, INC, NMAX, INCMAX, A, AA, AS, X, XX,
+ $ XS, Y, YY, YS, YT, G )
+*
+* Tests DSYMV, DSBMV and DSPMV.
+*
+* Auxiliary routine for test program for Level 2 Blas.
+*
+* -- Written on 10-August-1987.
+* Richard Hanson, Sandia National Labs.
+* Jeremy Du Croz, NAG Central Office.
+*
+* .. Parameters ..
+ DOUBLE PRECISION ZERO, HALF
+ PARAMETER ( ZERO = 0.0D0, HALF = 0.5D0 )
+* .. Scalar Arguments ..
+ DOUBLE PRECISION EPS, THRESH
+ INTEGER INCMAX, NALF, NBET, NIDIM, NINC, NKB, NMAX,
+ $ NOUT, NTRA
+ LOGICAL FATAL, REWI, TRACE
+ CHARACTER*6 SNAME
+* .. Array Arguments ..
+ DOUBLE PRECISION A( NMAX, NMAX ), AA( NMAX*NMAX ), ALF( NALF ),
+ $ AS( NMAX*NMAX ), BET( NBET ), G( NMAX ),
+ $ X( NMAX ), XS( NMAX*INCMAX ),
+ $ XX( NMAX*INCMAX ), Y( NMAX ),
+ $ YS( NMAX*INCMAX ), YT( NMAX ),
+ $ YY( NMAX*INCMAX )
+ INTEGER IDIM( NIDIM ), INC( NINC ), KB( NKB )
+* .. Local Scalars ..
+ DOUBLE PRECISION ALPHA, ALS, BETA, BLS, ERR, ERRMAX, TRANSL
+ INTEGER I, IA, IB, IC, IK, IN, INCX, INCXS, INCY,
+ $ INCYS, IX, IY, K, KS, LAA, LDA, LDAS, LX, LY,
+ $ N, NARGS, NC, NK, NS
+ LOGICAL BANDED, FULL, NULL, PACKED, RESET, SAME
+ CHARACTER*1 UPLO, UPLOS
+ CHARACTER*2 ICH
+* .. Local Arrays ..
+ LOGICAL ISAME( 13 )
+* .. External Functions ..
+ LOGICAL LDE, LDERES
+ EXTERNAL LDE, LDERES
+* .. External Subroutines ..
+ EXTERNAL DMAKE, DMVCH, DSBMV, DSPMV, DSYMV
+* .. Intrinsic Functions ..
+ INTRINSIC ABS, MAX
+* .. Scalars in Common ..
+ INTEGER INFOT, NOUTC
+ LOGICAL LERR, OK
+* .. Common blocks ..
+ COMMON /INFOC/INFOT, NOUTC, OK, LERR
+* .. Data statements ..
+ DATA ICH/'UL'/
+* .. Executable Statements ..
+ FULL = SNAME( 3: 3 ).EQ.'Y'
+ BANDED = SNAME( 3: 3 ).EQ.'B'
+ PACKED = SNAME( 3: 3 ).EQ.'P'
+* Define the number of arguments.
+ IF( FULL )THEN
+ NARGS = 10
+ ELSE IF( BANDED )THEN
+ NARGS = 11
+ ELSE IF( PACKED )THEN
+ NARGS = 9
+ END IF
+*
+ NC = 0
+ RESET = .TRUE.
+ ERRMAX = ZERO
+*
+ DO 110 IN = 1, NIDIM
+ N = IDIM( IN )
+*
+ IF( BANDED )THEN
+ NK = NKB
+ ELSE
+ NK = 1
+ END IF
+ DO 100 IK = 1, NK
+ IF( BANDED )THEN
+ K = KB( IK )
+ ELSE
+ K = N - 1
+ END IF
+* Set LDA to 1 more than minimum value if room.
+ IF( BANDED )THEN
+ LDA = K + 1
+ ELSE
+ LDA = N
+ END IF
+ IF( LDA.LT.NMAX )
+ $ LDA = LDA + 1
+* Skip tests if not enough room.
+ IF( LDA.GT.NMAX )
+ $ GO TO 100
+ IF( PACKED )THEN
+ LAA = ( N*( N + 1 ) )/2
+ ELSE
+ LAA = LDA*N
+ END IF
+ NULL = N.LE.0
+*
+ DO 90 IC = 1, 2
+ UPLO = ICH( IC: IC )
+*
+* Generate the matrix A.
+*
+ TRANSL = ZERO
+ CALL DMAKE( SNAME( 2: 3 ), UPLO, ' ', N, N, A, NMAX, AA,
+ $ LDA, K, K, RESET, TRANSL )
+*
+ DO 80 IX = 1, NINC
+ INCX = INC( IX )
+ LX = ABS( INCX )*N
+*
+* Generate the vector X.
+*
+ TRANSL = HALF
+ CALL DMAKE( 'GE', ' ', ' ', 1, N, X, 1, XX,
+ $ ABS( INCX ), 0, N - 1, RESET, TRANSL )
+ IF( N.GT.1 )THEN
+ X( N/2 ) = ZERO
+ XX( 1 + ABS( INCX )*( N/2 - 1 ) ) = ZERO
+ END IF
+*
+ DO 70 IY = 1, NINC
+ INCY = INC( IY )
+ LY = ABS( INCY )*N
+*
+ DO 60 IA = 1, NALF
+ ALPHA = ALF( IA )
+*
+ DO 50 IB = 1, NBET
+ BETA = BET( IB )
+*
+* Generate the vector Y.
+*
+ TRANSL = ZERO
+ CALL DMAKE( 'GE', ' ', ' ', 1, N, Y, 1, YY,
+ $ ABS( INCY ), 0, N - 1, RESET,
+ $ TRANSL )
+*
+ NC = NC + 1
+*
+* Save every datum before calling the
+* subroutine.
+*
+ UPLOS = UPLO
+ NS = N
+ KS = K
+ ALS = ALPHA
+ DO 10 I = 1, LAA
+ AS( I ) = AA( I )
+ 10 CONTINUE
+ LDAS = LDA
+ DO 20 I = 1, LX
+ XS( I ) = XX( I )
+ 20 CONTINUE
+ INCXS = INCX
+ BLS = BETA
+ DO 30 I = 1, LY
+ YS( I ) = YY( I )
+ 30 CONTINUE
+ INCYS = INCY
+*
+* Call the subroutine.
+*
+ IF( FULL )THEN
+ IF( TRACE )
+ $ WRITE( NTRA, FMT = 9993 )NC, SNAME,
+ $ UPLO, N, ALPHA, LDA, INCX, BETA, INCY
+ IF( REWI )
+ $ REWIND NTRA
+ CALL DSYMV( UPLO, N, ALPHA, AA, LDA, XX,
+ $ INCX, BETA, YY, INCY )
+ ELSE IF( BANDED )THEN
+ IF( TRACE )
+ $ WRITE( NTRA, FMT = 9994 )NC, SNAME,
+ $ UPLO, N, K, ALPHA, LDA, INCX, BETA,
+ $ INCY
+ IF( REWI )
+ $ REWIND NTRA
+ CALL DSBMV( UPLO, N, K, ALPHA, AA, LDA,
+ $ XX, INCX, BETA, YY, INCY )
+ ELSE IF( PACKED )THEN
+ IF( TRACE )
+ $ WRITE( NTRA, FMT = 9995 )NC, SNAME,
+ $ UPLO, N, ALPHA, INCX, BETA, INCY
+ IF( REWI )
+ $ REWIND NTRA
+ CALL DSPMV( UPLO, N, ALPHA, AA, XX, INCX,
+ $ BETA, YY, INCY )
+ END IF
+*
+* Check if error-exit was taken incorrectly.
+*
+ IF( .NOT.OK )THEN
+ WRITE( NOUT, FMT = 9992 )
+ FATAL = .TRUE.
+ GO TO 120
+ END IF
+*
+* See what data changed inside subroutines.
+*
+ ISAME( 1 ) = UPLO.EQ.UPLOS
+ ISAME( 2 ) = NS.EQ.N
+ IF( FULL )THEN
+ ISAME( 3 ) = ALS.EQ.ALPHA
+ ISAME( 4 ) = LDE( AS, AA, LAA )
+ ISAME( 5 ) = LDAS.EQ.LDA
+ ISAME( 6 ) = LDE( XS, XX, LX )
+ ISAME( 7 ) = INCXS.EQ.INCX
+ ISAME( 8 ) = BLS.EQ.BETA
+ IF( NULL )THEN
+ ISAME( 9 ) = LDE( YS, YY, LY )
+ ELSE
+ ISAME( 9 ) = LDERES( 'GE', ' ', 1, N,
+ $ YS, YY, ABS( INCY ) )
+ END IF
+ ISAME( 10 ) = INCYS.EQ.INCY
+ ELSE IF( BANDED )THEN
+ ISAME( 3 ) = KS.EQ.K
+ ISAME( 4 ) = ALS.EQ.ALPHA
+ ISAME( 5 ) = LDE( AS, AA, LAA )
+ ISAME( 6 ) = LDAS.EQ.LDA
+ ISAME( 7 ) = LDE( XS, XX, LX )
+ ISAME( 8 ) = INCXS.EQ.INCX
+ ISAME( 9 ) = BLS.EQ.BETA
+ IF( NULL )THEN
+ ISAME( 10 ) = LDE( YS, YY, LY )
+ ELSE
+ ISAME( 10 ) = LDERES( 'GE', ' ', 1, N,
+ $ YS, YY, ABS( INCY ) )
+ END IF
+ ISAME( 11 ) = INCYS.EQ.INCY
+ ELSE IF( PACKED )THEN
+ ISAME( 3 ) = ALS.EQ.ALPHA
+ ISAME( 4 ) = LDE( AS, AA, LAA )
+ ISAME( 5 ) = LDE( XS, XX, LX )
+ ISAME( 6 ) = INCXS.EQ.INCX
+ ISAME( 7 ) = BLS.EQ.BETA
+ IF( NULL )THEN
+ ISAME( 8 ) = LDE( YS, YY, LY )
+ ELSE
+ ISAME( 8 ) = LDERES( 'GE', ' ', 1, N,
+ $ YS, YY, ABS( INCY ) )
+ END IF
+ ISAME( 9 ) = INCYS.EQ.INCY
+ END IF
+*
+* If data was incorrectly changed, report and
+* return.
+*
+ SAME = .TRUE.
+ DO 40 I = 1, NARGS
+ SAME = SAME.AND.ISAME( I )
+ IF( .NOT.ISAME( I ) )
+ $ WRITE( NOUT, FMT = 9998 )I
+ 40 CONTINUE
+ IF( .NOT.SAME )THEN
+ FATAL = .TRUE.
+ GO TO 120
+ END IF
+*
+ IF( .NOT.NULL )THEN
+*
+* Check the result.
+*
+ CALL DMVCH( 'N', N, N, ALPHA, A, NMAX, X,
+ $ INCX, BETA, Y, INCY, YT, G,
+ $ YY, EPS, ERR, FATAL, NOUT,
+ $ .TRUE. )
+ ERRMAX = MAX( ERRMAX, ERR )
+* If got really bad answer, report and
+* return.
+ IF( FATAL )
+ $ GO TO 120
+ ELSE
+* Avoid repeating tests with N.le.0
+ GO TO 110
+ END IF
+*
+ 50 CONTINUE
+*
+ 60 CONTINUE
+*
+ 70 CONTINUE
+*
+ 80 CONTINUE
+*
+ 90 CONTINUE
+*
+ 100 CONTINUE
+*
+ 110 CONTINUE
+*
+* Report result.
+*
+ IF( ERRMAX.LT.THRESH )THEN
+ WRITE( NOUT, FMT = 9999 )SNAME, NC
+ ELSE
+ WRITE( NOUT, FMT = 9997 )SNAME, NC, ERRMAX
+ END IF
+ GO TO 130
+*
+ 120 CONTINUE
+ WRITE( NOUT, FMT = 9996 )SNAME
+ IF( FULL )THEN
+ WRITE( NOUT, FMT = 9993 )NC, SNAME, UPLO, N, ALPHA, LDA, INCX,
+ $ BETA, INCY
+ ELSE IF( BANDED )THEN
+ WRITE( NOUT, FMT = 9994 )NC, SNAME, UPLO, N, K, ALPHA, LDA,
+ $ INCX, BETA, INCY
+ ELSE IF( PACKED )THEN
+ WRITE( NOUT, FMT = 9995 )NC, SNAME, UPLO, N, ALPHA, INCX,
+ $ BETA, INCY
+ END IF
+*
+ 130 CONTINUE
+ RETURN
+*
+ 9999 FORMAT( ' ', A6, ' PASSED THE COMPUTATIONAL TESTS (', I6, ' CALL',
+ $ 'S)' )
+ 9998 FORMAT( ' ******* FATAL ERROR - PARAMETER NUMBER ', I2, ' WAS CH',
+ $ 'ANGED INCORRECTLY *******' )
+ 9997 FORMAT( ' ', A6, ' COMPLETED THE COMPUTATIONAL TESTS (', I6, ' C',
+ $ 'ALLS)', /' ******* BUT WITH MAXIMUM TEST RATIO', F8.2,
+ $ ' - SUSPECT *******' )
+ 9996 FORMAT( ' ******* ', A6, ' FAILED ON CALL NUMBER:' )
+ 9995 FORMAT( 1X, I6, ': ', A6, '(''', A1, ''',', I3, ',', F4.1, ', AP',
+ $ ', X,', I2, ',', F4.1, ', Y,', I2, ') .' )
+ 9994 FORMAT( 1X, I6, ': ', A6, '(''', A1, ''',', 2( I3, ',' ), F4.1,
+ $ ', A,', I3, ', X,', I2, ',', F4.1, ', Y,', I2,
+ $ ') .' )
+ 9993 FORMAT( 1X, I6, ': ', A6, '(''', A1, ''',', I3, ',', F4.1, ', A,',
+ $ I3, ', X,', I2, ',', F4.1, ', Y,', I2, ') .' )
+ 9992 FORMAT( ' ******* FATAL ERROR - ERROR-EXIT TAKEN ON VALID CALL *',
+ $ '******' )
+*
+* End of DCHK2.
+*
+ END
+ SUBROUTINE DCHK3( SNAME, EPS, THRESH, NOUT, NTRA, TRACE, REWI,
+ $ FATAL, NIDIM, IDIM, NKB, KB, NINC, INC, NMAX,
+ $ INCMAX, A, AA, AS, X, XX, XS, XT, G, Z )
+*
+* Tests DTRMV, DTBMV, DTPMV, DTRSV, DTBSV and DTPSV.
+*
+* Auxiliary routine for test program for Level 2 Blas.
+*
+* -- Written on 10-August-1987.
+* Richard Hanson, Sandia National Labs.
+* Jeremy Du Croz, NAG Central Office.
+*
+* .. Parameters ..
+ DOUBLE PRECISION ZERO, HALF, ONE
+ PARAMETER ( ZERO = 0.0D0, HALF = 0.5D0, ONE = 1.0D0 )
+* .. Scalar Arguments ..
+ DOUBLE PRECISION EPS, THRESH
+ INTEGER INCMAX, NIDIM, NINC, NKB, NMAX, NOUT, NTRA
+ LOGICAL FATAL, REWI, TRACE
+ CHARACTER*6 SNAME
+* .. Array Arguments ..
+ DOUBLE PRECISION A( NMAX, NMAX ), AA( NMAX*NMAX ),
+ $ AS( NMAX*NMAX ), G( NMAX ), X( NMAX ),
+ $ XS( NMAX*INCMAX ), XT( NMAX ),
+ $ XX( NMAX*INCMAX ), Z( NMAX )
+ INTEGER IDIM( NIDIM ), INC( NINC ), KB( NKB )
+* .. Local Scalars ..
+ DOUBLE PRECISION ERR, ERRMAX, TRANSL
+ INTEGER I, ICD, ICT, ICU, IK, IN, INCX, INCXS, IX, K,
+ $ KS, LAA, LDA, LDAS, LX, N, NARGS, NC, NK, NS
+ LOGICAL BANDED, FULL, NULL, PACKED, RESET, SAME
+ CHARACTER*1 DIAG, DIAGS, TRANS, TRANSS, UPLO, UPLOS
+ CHARACTER*2 ICHD, ICHU
+ CHARACTER*3 ICHT
+* .. Local Arrays ..
+ LOGICAL ISAME( 13 )
+* .. External Functions ..
+ LOGICAL LDE, LDERES
+ EXTERNAL LDE, LDERES
+* .. External Subroutines ..
+ EXTERNAL DMAKE, DMVCH, DTBMV, DTBSV, DTPMV, DTPSV,
+ $ DTRMV, DTRSV
+* .. Intrinsic Functions ..
+ INTRINSIC ABS, MAX
+* .. Scalars in Common ..
+ INTEGER INFOT, NOUTC
+ LOGICAL LERR, OK
+* .. Common blocks ..
+ COMMON /INFOC/INFOT, NOUTC, OK, LERR
+* .. Data statements ..
+ DATA ICHU/'UL'/, ICHT/'NTC'/, ICHD/'UN'/
+* .. Executable Statements ..
+ FULL = SNAME( 3: 3 ).EQ.'R'
+ BANDED = SNAME( 3: 3 ).EQ.'B'
+ PACKED = SNAME( 3: 3 ).EQ.'P'
+* Define the number of arguments.
+ IF( FULL )THEN
+ NARGS = 8
+ ELSE IF( BANDED )THEN
+ NARGS = 9
+ ELSE IF( PACKED )THEN
+ NARGS = 7
+ END IF
+*
+ NC = 0
+ RESET = .TRUE.
+ ERRMAX = ZERO
+* Set up zero vector for DMVCH.
+ DO 10 I = 1, NMAX
+ Z( I ) = ZERO
+ 10 CONTINUE
+*
+ DO 110 IN = 1, NIDIM
+ N = IDIM( IN )
+*
+ IF( BANDED )THEN
+ NK = NKB
+ ELSE
+ NK = 1
+ END IF
+ DO 100 IK = 1, NK
+ IF( BANDED )THEN
+ K = KB( IK )
+ ELSE
+ K = N - 1
+ END IF
+* Set LDA to 1 more than minimum value if room.
+ IF( BANDED )THEN
+ LDA = K + 1
+ ELSE
+ LDA = N
+ END IF
+ IF( LDA.LT.NMAX )
+ $ LDA = LDA + 1
+* Skip tests if not enough room.
+ IF( LDA.GT.NMAX )
+ $ GO TO 100
+ IF( PACKED )THEN
+ LAA = ( N*( N + 1 ) )/2
+ ELSE
+ LAA = LDA*N
+ END IF
+ NULL = N.LE.0
+*
+ DO 90 ICU = 1, 2
+ UPLO = ICHU( ICU: ICU )
+*
+ DO 80 ICT = 1, 3
+ TRANS = ICHT( ICT: ICT )
+*
+ DO 70 ICD = 1, 2
+ DIAG = ICHD( ICD: ICD )
+*
+* Generate the matrix A.
+*
+ TRANSL = ZERO
+ CALL DMAKE( SNAME( 2: 3 ), UPLO, DIAG, N, N, A,
+ $ NMAX, AA, LDA, K, K, RESET, TRANSL )
+*
+ DO 60 IX = 1, NINC
+ INCX = INC( IX )
+ LX = ABS( INCX )*N
+*
+* Generate the vector X.
+*
+ TRANSL = HALF
+ CALL DMAKE( 'GE', ' ', ' ', 1, N, X, 1, XX,
+ $ ABS( INCX ), 0, N - 1, RESET,
+ $ TRANSL )
+ IF( N.GT.1 )THEN
+ X( N/2 ) = ZERO
+ XX( 1 + ABS( INCX )*( N/2 - 1 ) ) = ZERO
+ END IF
+*
+ NC = NC + 1
+*
+* Save every datum before calling the subroutine.
+*
+ UPLOS = UPLO
+ TRANSS = TRANS
+ DIAGS = DIAG
+ NS = N
+ KS = K
+ DO 20 I = 1, LAA
+ AS( I ) = AA( I )
+ 20 CONTINUE
+ LDAS = LDA
+ DO 30 I = 1, LX
+ XS( I ) = XX( I )
+ 30 CONTINUE
+ INCXS = INCX
+*
+* Call the subroutine.
+*
+ IF( SNAME( 4: 5 ).EQ.'MV' )THEN
+ IF( FULL )THEN
+ IF( TRACE )
+ $ WRITE( NTRA, FMT = 9993 )NC, SNAME,
+ $ UPLO, TRANS, DIAG, N, LDA, INCX
+ IF( REWI )
+ $ REWIND NTRA
+ CALL DTRMV( UPLO, TRANS, DIAG, N, AA, LDA,
+ $ XX, INCX )
+ ELSE IF( BANDED )THEN
+ IF( TRACE )
+ $ WRITE( NTRA, FMT = 9994 )NC, SNAME,
+ $ UPLO, TRANS, DIAG, N, K, LDA, INCX
+ IF( REWI )
+ $ REWIND NTRA
+ CALL DTBMV( UPLO, TRANS, DIAG, N, K, AA,
+ $ LDA, XX, INCX )
+ ELSE IF( PACKED )THEN
+ IF( TRACE )
+ $ WRITE( NTRA, FMT = 9995 )NC, SNAME,
+ $ UPLO, TRANS, DIAG, N, INCX
+ IF( REWI )
+ $ REWIND NTRA
+ CALL DTPMV( UPLO, TRANS, DIAG, N, AA, XX,
+ $ INCX )
+ END IF
+ ELSE IF( SNAME( 4: 5 ).EQ.'SV' )THEN
+ IF( FULL )THEN
+ IF( TRACE )
+ $ WRITE( NTRA, FMT = 9993 )NC, SNAME,
+ $ UPLO, TRANS, DIAG, N, LDA, INCX
+ IF( REWI )
+ $ REWIND NTRA
+ CALL DTRSV( UPLO, TRANS, DIAG, N, AA, LDA,
+ $ XX, INCX )
+ ELSE IF( BANDED )THEN
+ IF( TRACE )
+ $ WRITE( NTRA, FMT = 9994 )NC, SNAME,
+ $ UPLO, TRANS, DIAG, N, K, LDA, INCX
+ IF( REWI )
+ $ REWIND NTRA
+ CALL DTBSV( UPLO, TRANS, DIAG, N, K, AA,
+ $ LDA, XX, INCX )
+ ELSE IF( PACKED )THEN
+ IF( TRACE )
+ $ WRITE( NTRA, FMT = 9995 )NC, SNAME,
+ $ UPLO, TRANS, DIAG, N, INCX
+ IF( REWI )
+ $ REWIND NTRA
+ CALL DTPSV( UPLO, TRANS, DIAG, N, AA, XX,
+ $ INCX )
+ END IF
+ END IF
+*
+* Check if error-exit was taken incorrectly.
+*
+ IF( .NOT.OK )THEN
+ WRITE( NOUT, FMT = 9992 )
+ FATAL = .TRUE.
+ GO TO 120
+ END IF
+*
+* See what data changed inside subroutines.
+*
+ ISAME( 1 ) = UPLO.EQ.UPLOS
+ ISAME( 2 ) = TRANS.EQ.TRANSS
+ ISAME( 3 ) = DIAG.EQ.DIAGS
+ ISAME( 4 ) = NS.EQ.N
+ IF( FULL )THEN
+ ISAME( 5 ) = LDE( AS, AA, LAA )
+ ISAME( 6 ) = LDAS.EQ.LDA
+ IF( NULL )THEN
+ ISAME( 7 ) = LDE( XS, XX, LX )
+ ELSE
+ ISAME( 7 ) = LDERES( 'GE', ' ', 1, N, XS,
+ $ XX, ABS( INCX ) )
+ END IF
+ ISAME( 8 ) = INCXS.EQ.INCX
+ ELSE IF( BANDED )THEN
+ ISAME( 5 ) = KS.EQ.K
+ ISAME( 6 ) = LDE( AS, AA, LAA )
+ ISAME( 7 ) = LDAS.EQ.LDA
+ IF( NULL )THEN
+ ISAME( 8 ) = LDE( XS, XX, LX )
+ ELSE
+ ISAME( 8 ) = LDERES( 'GE', ' ', 1, N, XS,
+ $ XX, ABS( INCX ) )
+ END IF
+ ISAME( 9 ) = INCXS.EQ.INCX
+ ELSE IF( PACKED )THEN
+ ISAME( 5 ) = LDE( AS, AA, LAA )
+ IF( NULL )THEN
+ ISAME( 6 ) = LDE( XS, XX, LX )
+ ELSE
+ ISAME( 6 ) = LDERES( 'GE', ' ', 1, N, XS,
+ $ XX, ABS( INCX ) )
+ END IF
+ ISAME( 7 ) = INCXS.EQ.INCX
+ END IF
+*
+* If data was incorrectly changed, report and
+* return.
+*
+ SAME = .TRUE.
+ DO 40 I = 1, NARGS
+ SAME = SAME.AND.ISAME( I )
+ IF( .NOT.ISAME( I ) )
+ $ WRITE( NOUT, FMT = 9998 )I
+ 40 CONTINUE
+ IF( .NOT.SAME )THEN
+ FATAL = .TRUE.
+ GO TO 120
+ END IF
+*
+ IF( .NOT.NULL )THEN
+ IF( SNAME( 4: 5 ).EQ.'MV' )THEN
+*
+* Check the result.
+*
+ CALL DMVCH( TRANS, N, N, ONE, A, NMAX, X,
+ $ INCX, ZERO, Z, INCX, XT, G,
+ $ XX, EPS, ERR, FATAL, NOUT,
+ $ .TRUE. )
+ ELSE IF( SNAME( 4: 5 ).EQ.'SV' )THEN
+*
+* Compute approximation to original vector.
+*
+ DO 50 I = 1, N
+ Z( I ) = XX( 1 + ( I - 1 )*
+ $ ABS( INCX ) )
+ XX( 1 + ( I - 1 )*ABS( INCX ) )
+ $ = X( I )
+ 50 CONTINUE
+ CALL DMVCH( TRANS, N, N, ONE, A, NMAX, Z,
+ $ INCX, ZERO, X, INCX, XT, G,
+ $ XX, EPS, ERR, FATAL, NOUT,
+ $ .FALSE. )
+ END IF
+ ERRMAX = MAX( ERRMAX, ERR )
+* If got really bad answer, report and return.
+ IF( FATAL )
+ $ GO TO 120
+ ELSE
+* Avoid repeating tests with N.le.0.
+ GO TO 110
+ END IF
+*
+ 60 CONTINUE
+*
+ 70 CONTINUE
+*
+ 80 CONTINUE
+*
+ 90 CONTINUE
+*
+ 100 CONTINUE
+*
+ 110 CONTINUE
+*
+* Report result.
+*
+ IF( ERRMAX.LT.THRESH )THEN
+ WRITE( NOUT, FMT = 9999 )SNAME, NC
+ ELSE
+ WRITE( NOUT, FMT = 9997 )SNAME, NC, ERRMAX
+ END IF
+ GO TO 130
+*
+ 120 CONTINUE
+ WRITE( NOUT, FMT = 9996 )SNAME
+ IF( FULL )THEN
+ WRITE( NOUT, FMT = 9993 )NC, SNAME, UPLO, TRANS, DIAG, N, LDA,
+ $ INCX
+ ELSE IF( BANDED )THEN
+ WRITE( NOUT, FMT = 9994 )NC, SNAME, UPLO, TRANS, DIAG, N, K,
+ $ LDA, INCX
+ ELSE IF( PACKED )THEN
+ WRITE( NOUT, FMT = 9995 )NC, SNAME, UPLO, TRANS, DIAG, N, INCX
+ END IF
+*
+ 130 CONTINUE
+ RETURN
+*
+ 9999 FORMAT( ' ', A6, ' PASSED THE COMPUTATIONAL TESTS (', I6, ' CALL',
+ $ 'S)' )
+ 9998 FORMAT( ' ******* FATAL ERROR - PARAMETER NUMBER ', I2, ' WAS CH',
+ $ 'ANGED INCORRECTLY *******' )
+ 9997 FORMAT( ' ', A6, ' COMPLETED THE COMPUTATIONAL TESTS (', I6, ' C',
+ $ 'ALLS)', /' ******* BUT WITH MAXIMUM TEST RATIO', F8.2,
+ $ ' - SUSPECT *******' )
+ 9996 FORMAT( ' ******* ', A6, ' FAILED ON CALL NUMBER:' )
+ 9995 FORMAT( 1X, I6, ': ', A6, '(', 3( '''', A1, ''',' ), I3, ', AP, ',
+ $ 'X,', I2, ') .' )
+ 9994 FORMAT( 1X, I6, ': ', A6, '(', 3( '''', A1, ''',' ), 2( I3, ',' ),
+ $ ' A,', I3, ', X,', I2, ') .' )
+ 9993 FORMAT( 1X, I6, ': ', A6, '(', 3( '''', A1, ''',' ), I3, ', A,',
+ $ I3, ', X,', I2, ') .' )
+ 9992 FORMAT( ' ******* FATAL ERROR - ERROR-EXIT TAKEN ON VALID CALL *',
+ $ '******' )
+*
+* End of DCHK3.
+*
+ END
+ SUBROUTINE DCHK4( SNAME, EPS, THRESH, NOUT, NTRA, TRACE, REWI,
+ $ FATAL, NIDIM, IDIM, NALF, ALF, NINC, INC, NMAX,
+ $ INCMAX, A, AA, AS, X, XX, XS, Y, YY, YS, YT, G,
+ $ Z )
+*
+* Tests DGER.
+*
+* Auxiliary routine for test program for Level 2 Blas.
+*
+* -- Written on 10-August-1987.
+* Richard Hanson, Sandia National Labs.
+* Jeremy Du Croz, NAG Central Office.
+*
+* .. Parameters ..
+ DOUBLE PRECISION ZERO, HALF, ONE
+ PARAMETER ( ZERO = 0.0D0, HALF = 0.5D0, ONE = 1.0D0 )
+* .. Scalar Arguments ..
+ DOUBLE PRECISION EPS, THRESH
+ INTEGER INCMAX, NALF, NIDIM, NINC, NMAX, NOUT, NTRA
+ LOGICAL FATAL, REWI, TRACE
+ CHARACTER*6 SNAME
+* .. Array Arguments ..
+ DOUBLE PRECISION A( NMAX, NMAX ), AA( NMAX*NMAX ), ALF( NALF ),
+ $ AS( NMAX*NMAX ), G( NMAX ), X( NMAX ),
+ $ XS( NMAX*INCMAX ), XX( NMAX*INCMAX ),
+ $ Y( NMAX ), YS( NMAX*INCMAX ), YT( NMAX ),
+ $ YY( NMAX*INCMAX ), Z( NMAX )
+ INTEGER IDIM( NIDIM ), INC( NINC )
+* .. Local Scalars ..
+ DOUBLE PRECISION ALPHA, ALS, ERR, ERRMAX, TRANSL
+ INTEGER I, IA, IM, IN, INCX, INCXS, INCY, INCYS, IX,
+ $ IY, J, LAA, LDA, LDAS, LX, LY, M, MS, N, NARGS,
+ $ NC, ND, NS
+ LOGICAL NULL, RESET, SAME
+* .. Local Arrays ..
+ DOUBLE PRECISION W( 1 )
+ LOGICAL ISAME( 13 )
+* .. External Functions ..
+ LOGICAL LDE, LDERES
+ EXTERNAL LDE, LDERES
+* .. External Subroutines ..
+ EXTERNAL DGER, DMAKE, DMVCH
+* .. Intrinsic Functions ..
+ INTRINSIC ABS, MAX, MIN
+* .. Scalars in Common ..
+ INTEGER INFOT, NOUTC
+ LOGICAL LERR, OK
+* .. Common blocks ..
+ COMMON /INFOC/INFOT, NOUTC, OK, LERR
+* .. Executable Statements ..
+* Define the number of arguments.
+ NARGS = 9
+*
+ NC = 0
+ RESET = .TRUE.
+ ERRMAX = ZERO
+*
+ DO 120 IN = 1, NIDIM
+ N = IDIM( IN )
+ ND = N/2 + 1
+*
+ DO 110 IM = 1, 2
+ IF( IM.EQ.1 )
+ $ M = MAX( N - ND, 0 )
+ IF( IM.EQ.2 )
+ $ M = MIN( N + ND, NMAX )
+*
+* Set LDA to 1 more than minimum value if room.
+ LDA = M
+ IF( LDA.LT.NMAX )
+ $ LDA = LDA + 1
+* Skip tests if not enough room.
+ IF( LDA.GT.NMAX )
+ $ GO TO 110
+ LAA = LDA*N
+ NULL = N.LE.0.OR.M.LE.0
+*
+ DO 100 IX = 1, NINC
+ INCX = INC( IX )
+ LX = ABS( INCX )*M
+*
+* Generate the vector X.
+*
+ TRANSL = HALF
+ CALL DMAKE( 'GE', ' ', ' ', 1, M, X, 1, XX, ABS( INCX ),
+ $ 0, M - 1, RESET, TRANSL )
+ IF( M.GT.1 )THEN
+ X( M/2 ) = ZERO
+ XX( 1 + ABS( INCX )*( M/2 - 1 ) ) = ZERO
+ END IF
+*
+ DO 90 IY = 1, NINC
+ INCY = INC( IY )
+ LY = ABS( INCY )*N
+*
+* Generate the vector Y.
+*
+ TRANSL = ZERO
+ CALL DMAKE( 'GE', ' ', ' ', 1, N, Y, 1, YY,
+ $ ABS( INCY ), 0, N - 1, RESET, TRANSL )
+ IF( N.GT.1 )THEN
+ Y( N/2 ) = ZERO
+ YY( 1 + ABS( INCY )*( N/2 - 1 ) ) = ZERO
+ END IF
+*
+ DO 80 IA = 1, NALF
+ ALPHA = ALF( IA )
+*
+* Generate the matrix A.
+*
+ TRANSL = ZERO
+ CALL DMAKE( SNAME( 2: 3 ), ' ', ' ', M, N, A, NMAX,
+ $ AA, LDA, M - 1, N - 1, RESET, TRANSL )
+*
+ NC = NC + 1
+*
+* Save every datum before calling the subroutine.
+*
+ MS = M
+ NS = N
+ ALS = ALPHA
+ DO 10 I = 1, LAA
+ AS( I ) = AA( I )
+ 10 CONTINUE
+ LDAS = LDA
+ DO 20 I = 1, LX
+ XS( I ) = XX( I )
+ 20 CONTINUE
+ INCXS = INCX
+ DO 30 I = 1, LY
+ YS( I ) = YY( I )
+ 30 CONTINUE
+ INCYS = INCY
+*
+* Call the subroutine.
+*
+ IF( TRACE )
+ $ WRITE( NTRA, FMT = 9994 )NC, SNAME, M, N,
+ $ ALPHA, INCX, INCY, LDA
+ IF( REWI )
+ $ REWIND NTRA
+ CALL DGER( M, N, ALPHA, XX, INCX, YY, INCY, AA,
+ $ LDA )
+*
+* Check if error-exit was taken incorrectly.
+*
+ IF( .NOT.OK )THEN
+ WRITE( NOUT, FMT = 9993 )
+ FATAL = .TRUE.
+ GO TO 140
+ END IF
+*
+* See what data changed inside subroutine.
+*
+ ISAME( 1 ) = MS.EQ.M
+ ISAME( 2 ) = NS.EQ.N
+ ISAME( 3 ) = ALS.EQ.ALPHA
+ ISAME( 4 ) = LDE( XS, XX, LX )
+ ISAME( 5 ) = INCXS.EQ.INCX
+ ISAME( 6 ) = LDE( YS, YY, LY )
+ ISAME( 7 ) = INCYS.EQ.INCY
+ IF( NULL )THEN
+ ISAME( 8 ) = LDE( AS, AA, LAA )
+ ELSE
+ ISAME( 8 ) = LDERES( 'GE', ' ', M, N, AS, AA,
+ $ LDA )
+ END IF
+ ISAME( 9 ) = LDAS.EQ.LDA
+*
+* If data was incorrectly changed, report and return.
+*
+ SAME = .TRUE.
+ DO 40 I = 1, NARGS
+ SAME = SAME.AND.ISAME( I )
+ IF( .NOT.ISAME( I ) )
+ $ WRITE( NOUT, FMT = 9998 )I
+ 40 CONTINUE
+ IF( .NOT.SAME )THEN
+ FATAL = .TRUE.
+ GO TO 140
+ END IF
+*
+ IF( .NOT.NULL )THEN
+*
+* Check the result column by column.
+*
+ IF( INCX.GT.0 )THEN
+ DO 50 I = 1, M
+ Z( I ) = X( I )
+ 50 CONTINUE
+ ELSE
+ DO 60 I = 1, M
+ Z( I ) = X( M - I + 1 )
+ 60 CONTINUE
+ END IF
+ DO 70 J = 1, N
+ IF( INCY.GT.0 )THEN
+ W( 1 ) = Y( J )
+ ELSE
+ W( 1 ) = Y( N - J + 1 )
+ END IF
+ CALL DMVCH( 'N', M, 1, ALPHA, Z, NMAX, W, 1,
+ $ ONE, A( 1, J ), 1, YT, G,
+ $ AA( 1 + ( J - 1 )*LDA ), EPS,
+ $ ERR, FATAL, NOUT, .TRUE. )
+ ERRMAX = MAX( ERRMAX, ERR )
+* If got really bad answer, report and return.
+ IF( FATAL )
+ $ GO TO 130
+ 70 CONTINUE
+ ELSE
+* Avoid repeating tests with M.le.0 or N.le.0.
+ GO TO 110
+ END IF
+*
+ 80 CONTINUE
+*
+ 90 CONTINUE
+*
+ 100 CONTINUE
+*
+ 110 CONTINUE
+*
+ 120 CONTINUE
+*
+* Report result.
+*
+ IF( ERRMAX.LT.THRESH )THEN
+ WRITE( NOUT, FMT = 9999 )SNAME, NC
+ ELSE
+ WRITE( NOUT, FMT = 9997 )SNAME, NC, ERRMAX
+ END IF
+ GO TO 150
+*
+ 130 CONTINUE
+ WRITE( NOUT, FMT = 9995 )J
+*
+ 140 CONTINUE
+ WRITE( NOUT, FMT = 9996 )SNAME
+ WRITE( NOUT, FMT = 9994 )NC, SNAME, M, N, ALPHA, INCX, INCY, LDA
+*
+ 150 CONTINUE
+ RETURN
+*
+ 9999 FORMAT( ' ', A6, ' PASSED THE COMPUTATIONAL TESTS (', I6, ' CALL',
+ $ 'S)' )
+ 9998 FORMAT( ' ******* FATAL ERROR - PARAMETER NUMBER ', I2, ' WAS CH',
+ $ 'ANGED INCORRECTLY *******' )
+ 9997 FORMAT( ' ', A6, ' COMPLETED THE COMPUTATIONAL TESTS (', I6, ' C',
+ $ 'ALLS)', /' ******* BUT WITH MAXIMUM TEST RATIO', F8.2,
+ $ ' - SUSPECT *******' )
+ 9996 FORMAT( ' ******* ', A6, ' FAILED ON CALL NUMBER:' )
+ 9995 FORMAT( ' THESE ARE THE RESULTS FOR COLUMN ', I3 )
+ 9994 FORMAT( 1X, I6, ': ', A6, '(', 2( I3, ',' ), F4.1, ', X,', I2,
+ $ ', Y,', I2, ', A,', I3, ') .' )
+ 9993 FORMAT( ' ******* FATAL ERROR - ERROR-EXIT TAKEN ON VALID CALL *',
+ $ '******' )
+*
+* End of DCHK4.
+*
+ END
+ SUBROUTINE DCHK5( SNAME, EPS, THRESH, NOUT, NTRA, TRACE, REWI,
+ $ FATAL, NIDIM, IDIM, NALF, ALF, NINC, INC, NMAX,
+ $ INCMAX, A, AA, AS, X, XX, XS, Y, YY, YS, YT, G,
+ $ Z )
+*
+* Tests DSYR and DSPR.
+*
+* Auxiliary routine for test program for Level 2 Blas.
+*
+* -- Written on 10-August-1987.
+* Richard Hanson, Sandia National Labs.
+* Jeremy Du Croz, NAG Central Office.
+*
+* .. Parameters ..
+ DOUBLE PRECISION ZERO, HALF, ONE
+ PARAMETER ( ZERO = 0.0D0, HALF = 0.5D0, ONE = 1.0D0 )
+* .. Scalar Arguments ..
+ DOUBLE PRECISION EPS, THRESH
+ INTEGER INCMAX, NALF, NIDIM, NINC, NMAX, NOUT, NTRA
+ LOGICAL FATAL, REWI, TRACE
+ CHARACTER*6 SNAME
+* .. Array Arguments ..
+ DOUBLE PRECISION A( NMAX, NMAX ), AA( NMAX*NMAX ), ALF( NALF ),
+ $ AS( NMAX*NMAX ), G( NMAX ), X( NMAX ),
+ $ XS( NMAX*INCMAX ), XX( NMAX*INCMAX ),
+ $ Y( NMAX ), YS( NMAX*INCMAX ), YT( NMAX ),
+ $ YY( NMAX*INCMAX ), Z( NMAX )
+ INTEGER IDIM( NIDIM ), INC( NINC )
+* .. Local Scalars ..
+ DOUBLE PRECISION ALPHA, ALS, ERR, ERRMAX, TRANSL
+ INTEGER I, IA, IC, IN, INCX, INCXS, IX, J, JA, JJ, LAA,
+ $ LDA, LDAS, LJ, LX, N, NARGS, NC, NS
+ LOGICAL FULL, NULL, PACKED, RESET, SAME, UPPER
+ CHARACTER*1 UPLO, UPLOS
+ CHARACTER*2 ICH
+* .. Local Arrays ..
+ DOUBLE PRECISION W( 1 )
+ LOGICAL ISAME( 13 )
+* .. External Functions ..
+ LOGICAL LDE, LDERES
+ EXTERNAL LDE, LDERES
+* .. External Subroutines ..
+ EXTERNAL DMAKE, DMVCH, DSPR, DSYR
+* .. Intrinsic Functions ..
+ INTRINSIC ABS, MAX
+* .. Scalars in Common ..
+ INTEGER INFOT, NOUTC
+ LOGICAL LERR, OK
+* .. Common blocks ..
+ COMMON /INFOC/INFOT, NOUTC, OK, LERR
+* .. Data statements ..
+ DATA ICH/'UL'/
+* .. Executable Statements ..
+ FULL = SNAME( 3: 3 ).EQ.'Y'
+ PACKED = SNAME( 3: 3 ).EQ.'P'
+* Define the number of arguments.
+ IF( FULL )THEN
+ NARGS = 7
+ ELSE IF( PACKED )THEN
+ NARGS = 6
+ END IF
+*
+ NC = 0
+ RESET = .TRUE.
+ ERRMAX = ZERO
+*
+ DO 100 IN = 1, NIDIM
+ N = IDIM( IN )
+* Set LDA to 1 more than minimum value if room.
+ LDA = N
+ IF( LDA.LT.NMAX )
+ $ LDA = LDA + 1
+* Skip tests if not enough room.
+ IF( LDA.GT.NMAX )
+ $ GO TO 100
+ IF( PACKED )THEN
+ LAA = ( N*( N + 1 ) )/2
+ ELSE
+ LAA = LDA*N
+ END IF
+*
+ DO 90 IC = 1, 2
+ UPLO = ICH( IC: IC )
+ UPPER = UPLO.EQ.'U'
+*
+ DO 80 IX = 1, NINC
+ INCX = INC( IX )
+ LX = ABS( INCX )*N
+*
+* Generate the vector X.
+*
+ TRANSL = HALF
+ CALL DMAKE( 'GE', ' ', ' ', 1, N, X, 1, XX, ABS( INCX ),
+ $ 0, N - 1, RESET, TRANSL )
+ IF( N.GT.1 )THEN
+ X( N/2 ) = ZERO
+ XX( 1 + ABS( INCX )*( N/2 - 1 ) ) = ZERO
+ END IF
+*
+ DO 70 IA = 1, NALF
+ ALPHA = ALF( IA )
+ NULL = N.LE.0.OR.ALPHA.EQ.ZERO
+*
+* Generate the matrix A.
+*
+ TRANSL = ZERO
+ CALL DMAKE( SNAME( 2: 3 ), UPLO, ' ', N, N, A, NMAX,
+ $ AA, LDA, N - 1, N - 1, RESET, TRANSL )
+*
+ NC = NC + 1
+*
+* Save every datum before calling the subroutine.
+*
+ UPLOS = UPLO
+ NS = N
+ ALS = ALPHA
+ DO 10 I = 1, LAA
+ AS( I ) = AA( I )
+ 10 CONTINUE
+ LDAS = LDA
+ DO 20 I = 1, LX
+ XS( I ) = XX( I )
+ 20 CONTINUE
+ INCXS = INCX
+*
+* Call the subroutine.
+*
+ IF( FULL )THEN
+ IF( TRACE )
+ $ WRITE( NTRA, FMT = 9993 )NC, SNAME, UPLO, N,
+ $ ALPHA, INCX, LDA
+ IF( REWI )
+ $ REWIND NTRA
+ CALL DSYR( UPLO, N, ALPHA, XX, INCX, AA, LDA )
+ ELSE IF( PACKED )THEN
+ IF( TRACE )
+ $ WRITE( NTRA, FMT = 9994 )NC, SNAME, UPLO, N,
+ $ ALPHA, INCX
+ IF( REWI )
+ $ REWIND NTRA
+ CALL DSPR( UPLO, N, ALPHA, XX, INCX, AA )
+ END IF
+*
+* Check if error-exit was taken incorrectly.
+*
+ IF( .NOT.OK )THEN
+ WRITE( NOUT, FMT = 9992 )
+ FATAL = .TRUE.
+ GO TO 120
+ END IF
+*
+* See what data changed inside subroutines.
+*
+ ISAME( 1 ) = UPLO.EQ.UPLOS
+ ISAME( 2 ) = NS.EQ.N
+ ISAME( 3 ) = ALS.EQ.ALPHA
+ ISAME( 4 ) = LDE( XS, XX, LX )
+ ISAME( 5 ) = INCXS.EQ.INCX
+ IF( NULL )THEN
+ ISAME( 6 ) = LDE( AS, AA, LAA )
+ ELSE
+ ISAME( 6 ) = LDERES( SNAME( 2: 3 ), UPLO, N, N, AS,
+ $ AA, LDA )
+ END IF
+ IF( .NOT.PACKED )THEN
+ ISAME( 7 ) = LDAS.EQ.LDA
+ END IF
+*
+* If data was incorrectly changed, report and return.
+*
+ SAME = .TRUE.
+ DO 30 I = 1, NARGS
+ SAME = SAME.AND.ISAME( I )
+ IF( .NOT.ISAME( I ) )
+ $ WRITE( NOUT, FMT = 9998 )I
+ 30 CONTINUE
+ IF( .NOT.SAME )THEN
+ FATAL = .TRUE.
+ GO TO 120
+ END IF
+*
+ IF( .NOT.NULL )THEN
+*
+* Check the result column by column.
+*
+ IF( INCX.GT.0 )THEN
+ DO 40 I = 1, N
+ Z( I ) = X( I )
+ 40 CONTINUE
+ ELSE
+ DO 50 I = 1, N
+ Z( I ) = X( N - I + 1 )
+ 50 CONTINUE
+ END IF
+ JA = 1
+ DO 60 J = 1, N
+ W( 1 ) = Z( J )
+ IF( UPPER )THEN
+ JJ = 1
+ LJ = J
+ ELSE
+ JJ = J
+ LJ = N - J + 1
+ END IF
+ CALL DMVCH( 'N', LJ, 1, ALPHA, Z( JJ ), LJ, W,
+ $ 1, ONE, A( JJ, J ), 1, YT, G,
+ $ AA( JA ), EPS, ERR, FATAL, NOUT,
+ $ .TRUE. )
+ IF( FULL )THEN
+ IF( UPPER )THEN
+ JA = JA + LDA
+ ELSE
+ JA = JA + LDA + 1
+ END IF
+ ELSE
+ JA = JA + LJ
+ END IF
+ ERRMAX = MAX( ERRMAX, ERR )
+* If got really bad answer, report and return.
+ IF( FATAL )
+ $ GO TO 110
+ 60 CONTINUE
+ ELSE
+* Avoid repeating tests if N.le.0.
+ IF( N.LE.0 )
+ $ GO TO 100
+ END IF
+*
+ 70 CONTINUE
+*
+ 80 CONTINUE
+*
+ 90 CONTINUE
+*
+ 100 CONTINUE
+*
+* Report result.
+*
+ IF( ERRMAX.LT.THRESH )THEN
+ WRITE( NOUT, FMT = 9999 )SNAME, NC
+ ELSE
+ WRITE( NOUT, FMT = 9997 )SNAME, NC, ERRMAX
+ END IF
+ GO TO 130
+*
+ 110 CONTINUE
+ WRITE( NOUT, FMT = 9995 )J
+*
+ 120 CONTINUE
+ WRITE( NOUT, FMT = 9996 )SNAME
+ IF( FULL )THEN
+ WRITE( NOUT, FMT = 9993 )NC, SNAME, UPLO, N, ALPHA, INCX, LDA
+ ELSE IF( PACKED )THEN
+ WRITE( NOUT, FMT = 9994 )NC, SNAME, UPLO, N, ALPHA, INCX
+ END IF
+*
+ 130 CONTINUE
+ RETURN
+*
+ 9999 FORMAT( ' ', A6, ' PASSED THE COMPUTATIONAL TESTS (', I6, ' CALL',
+ $ 'S)' )
+ 9998 FORMAT( ' ******* FATAL ERROR - PARAMETER NUMBER ', I2, ' WAS CH',
+ $ 'ANGED INCORRECTLY *******' )
+ 9997 FORMAT( ' ', A6, ' COMPLETED THE COMPUTATIONAL TESTS (', I6, ' C',
+ $ 'ALLS)', /' ******* BUT WITH MAXIMUM TEST RATIO', F8.2,
+ $ ' - SUSPECT *******' )
+ 9996 FORMAT( ' ******* ', A6, ' FAILED ON CALL NUMBER:' )
+ 9995 FORMAT( ' THESE ARE THE RESULTS FOR COLUMN ', I3 )
+ 9994 FORMAT( 1X, I6, ': ', A6, '(''', A1, ''',', I3, ',', F4.1, ', X,',
+ $ I2, ', AP) .' )
+ 9993 FORMAT( 1X, I6, ': ', A6, '(''', A1, ''',', I3, ',', F4.1, ', X,',
+ $ I2, ', A,', I3, ') .' )
+ 9992 FORMAT( ' ******* FATAL ERROR - ERROR-EXIT TAKEN ON VALID CALL *',
+ $ '******' )
+*
+* End of DCHK5.
+*
+ END
+ SUBROUTINE DCHK6( SNAME, EPS, THRESH, NOUT, NTRA, TRACE, REWI,
+ $ FATAL, NIDIM, IDIM, NALF, ALF, NINC, INC, NMAX,
+ $ INCMAX, A, AA, AS, X, XX, XS, Y, YY, YS, YT, G,
+ $ Z )
+*
+* Tests DSYR2 and DSPR2.
+*
+* Auxiliary routine for test program for Level 2 Blas.
+*
+* -- Written on 10-August-1987.
+* Richard Hanson, Sandia National Labs.
+* Jeremy Du Croz, NAG Central Office.
+*
+* .. Parameters ..
+ DOUBLE PRECISION ZERO, HALF, ONE
+ PARAMETER ( ZERO = 0.0D0, HALF = 0.5D0, ONE = 1.0D0 )
+* .. Scalar Arguments ..
+ DOUBLE PRECISION EPS, THRESH
+ INTEGER INCMAX, NALF, NIDIM, NINC, NMAX, NOUT, NTRA
+ LOGICAL FATAL, REWI, TRACE
+ CHARACTER*6 SNAME
+* .. Array Arguments ..
+ DOUBLE PRECISION A( NMAX, NMAX ), AA( NMAX*NMAX ), ALF( NALF ),
+ $ AS( NMAX*NMAX ), G( NMAX ), X( NMAX ),
+ $ XS( NMAX*INCMAX ), XX( NMAX*INCMAX ),
+ $ Y( NMAX ), YS( NMAX*INCMAX ), YT( NMAX ),
+ $ YY( NMAX*INCMAX ), Z( NMAX, 2 )
+ INTEGER IDIM( NIDIM ), INC( NINC )
+* .. Local Scalars ..
+ DOUBLE PRECISION ALPHA, ALS, ERR, ERRMAX, TRANSL
+ INTEGER I, IA, IC, IN, INCX, INCXS, INCY, INCYS, IX,
+ $ IY, J, JA, JJ, LAA, LDA, LDAS, LJ, LX, LY, N,
+ $ NARGS, NC, NS
+ LOGICAL FULL, NULL, PACKED, RESET, SAME, UPPER
+ CHARACTER*1 UPLO, UPLOS
+ CHARACTER*2 ICH
+* .. Local Arrays ..
+ DOUBLE PRECISION W( 2 )
+ LOGICAL ISAME( 13 )
+* .. External Functions ..
+ LOGICAL LDE, LDERES
+ EXTERNAL LDE, LDERES
+* .. External Subroutines ..
+ EXTERNAL DMAKE, DMVCH, DSPR2, DSYR2
+* .. Intrinsic Functions ..
+ INTRINSIC ABS, MAX
+* .. Scalars in Common ..
+ INTEGER INFOT, NOUTC
+ LOGICAL LERR, OK
+* .. Common blocks ..
+ COMMON /INFOC/INFOT, NOUTC, OK, LERR
+* .. Data statements ..
+ DATA ICH/'UL'/
+* .. Executable Statements ..
+ FULL = SNAME( 3: 3 ).EQ.'Y'
+ PACKED = SNAME( 3: 3 ).EQ.'P'
+* Define the number of arguments.
+ IF( FULL )THEN
+ NARGS = 9
+ ELSE IF( PACKED )THEN
+ NARGS = 8
+ END IF
+*
+ NC = 0
+ RESET = .TRUE.
+ ERRMAX = ZERO
+*
+ DO 140 IN = 1, NIDIM
+ N = IDIM( IN )
+* Set LDA to 1 more than minimum value if room.
+ LDA = N
+ IF( LDA.LT.NMAX )
+ $ LDA = LDA + 1
+* Skip tests if not enough room.
+ IF( LDA.GT.NMAX )
+ $ GO TO 140
+ IF( PACKED )THEN
+ LAA = ( N*( N + 1 ) )/2
+ ELSE
+ LAA = LDA*N
+ END IF
+*
+ DO 130 IC = 1, 2
+ UPLO = ICH( IC: IC )
+ UPPER = UPLO.EQ.'U'
+*
+ DO 120 IX = 1, NINC
+ INCX = INC( IX )
+ LX = ABS( INCX )*N
+*
+* Generate the vector X.
+*
+ TRANSL = HALF
+ CALL DMAKE( 'GE', ' ', ' ', 1, N, X, 1, XX, ABS( INCX ),
+ $ 0, N - 1, RESET, TRANSL )
+ IF( N.GT.1 )THEN
+ X( N/2 ) = ZERO
+ XX( 1 + ABS( INCX )*( N/2 - 1 ) ) = ZERO
+ END IF
+*
+ DO 110 IY = 1, NINC
+ INCY = INC( IY )
+ LY = ABS( INCY )*N
+*
+* Generate the vector Y.
+*
+ TRANSL = ZERO
+ CALL DMAKE( 'GE', ' ', ' ', 1, N, Y, 1, YY,
+ $ ABS( INCY ), 0, N - 1, RESET, TRANSL )
+ IF( N.GT.1 )THEN
+ Y( N/2 ) = ZERO
+ YY( 1 + ABS( INCY )*( N/2 - 1 ) ) = ZERO
+ END IF
+*
+ DO 100 IA = 1, NALF
+ ALPHA = ALF( IA )
+ NULL = N.LE.0.OR.ALPHA.EQ.ZERO
+*
+* Generate the matrix A.
+*
+ TRANSL = ZERO
+ CALL DMAKE( SNAME( 2: 3 ), UPLO, ' ', N, N, A,
+ $ NMAX, AA, LDA, N - 1, N - 1, RESET,
+ $ TRANSL )
+*
+ NC = NC + 1
+*
+* Save every datum before calling the subroutine.
+*
+ UPLOS = UPLO
+ NS = N
+ ALS = ALPHA
+ DO 10 I = 1, LAA
+ AS( I ) = AA( I )
+ 10 CONTINUE
+ LDAS = LDA
+ DO 20 I = 1, LX
+ XS( I ) = XX( I )
+ 20 CONTINUE
+ INCXS = INCX
+ DO 30 I = 1, LY
+ YS( I ) = YY( I )
+ 30 CONTINUE
+ INCYS = INCY
+*
+* Call the subroutine.
+*
+ IF( FULL )THEN
+ IF( TRACE )
+ $ WRITE( NTRA, FMT = 9993 )NC, SNAME, UPLO, N,
+ $ ALPHA, INCX, INCY, LDA
+ IF( REWI )
+ $ REWIND NTRA
+ CALL DSYR2( UPLO, N, ALPHA, XX, INCX, YY, INCY,
+ $ AA, LDA )
+ ELSE IF( PACKED )THEN
+ IF( TRACE )
+ $ WRITE( NTRA, FMT = 9994 )NC, SNAME, UPLO, N,
+ $ ALPHA, INCX, INCY
+ IF( REWI )
+ $ REWIND NTRA
+ CALL DSPR2( UPLO, N, ALPHA, XX, INCX, YY, INCY,
+ $ AA )
+ END IF
+*
+* Check if error-exit was taken incorrectly.
+*
+ IF( .NOT.OK )THEN
+ WRITE( NOUT, FMT = 9992 )
+ FATAL = .TRUE.
+ GO TO 160
+ END IF
+*
+* See what data changed inside subroutines.
+*
+ ISAME( 1 ) = UPLO.EQ.UPLOS
+ ISAME( 2 ) = NS.EQ.N
+ ISAME( 3 ) = ALS.EQ.ALPHA
+ ISAME( 4 ) = LDE( XS, XX, LX )
+ ISAME( 5 ) = INCXS.EQ.INCX
+ ISAME( 6 ) = LDE( YS, YY, LY )
+ ISAME( 7 ) = INCYS.EQ.INCY
+ IF( NULL )THEN
+ ISAME( 8 ) = LDE( AS, AA, LAA )
+ ELSE
+ ISAME( 8 ) = LDERES( SNAME( 2: 3 ), UPLO, N, N,
+ $ AS, AA, LDA )
+ END IF
+ IF( .NOT.PACKED )THEN
+ ISAME( 9 ) = LDAS.EQ.LDA
+ END IF
+*
+* If data was incorrectly changed, report and return.
+*
+ SAME = .TRUE.
+ DO 40 I = 1, NARGS
+ SAME = SAME.AND.ISAME( I )
+ IF( .NOT.ISAME( I ) )
+ $ WRITE( NOUT, FMT = 9998 )I
+ 40 CONTINUE
+ IF( .NOT.SAME )THEN
+ FATAL = .TRUE.
+ GO TO 160
+ END IF
+*
+ IF( .NOT.NULL )THEN
+*
+* Check the result column by column.
+*
+ IF( INCX.GT.0 )THEN
+ DO 50 I = 1, N
+ Z( I, 1 ) = X( I )
+ 50 CONTINUE
+ ELSE
+ DO 60 I = 1, N
+ Z( I, 1 ) = X( N - I + 1 )
+ 60 CONTINUE
+ END IF
+ IF( INCY.GT.0 )THEN
+ DO 70 I = 1, N
+ Z( I, 2 ) = Y( I )
+ 70 CONTINUE
+ ELSE
+ DO 80 I = 1, N
+ Z( I, 2 ) = Y( N - I + 1 )
+ 80 CONTINUE
+ END IF
+ JA = 1
+ DO 90 J = 1, N
+ W( 1 ) = Z( J, 2 )
+ W( 2 ) = Z( J, 1 )
+ IF( UPPER )THEN
+ JJ = 1
+ LJ = J
+ ELSE
+ JJ = J
+ LJ = N - J + 1
+ END IF
+ CALL DMVCH( 'N', LJ, 2, ALPHA, Z( JJ, 1 ),
+ $ NMAX, W, 1, ONE, A( JJ, J ), 1,
+ $ YT, G, AA( JA ), EPS, ERR, FATAL,
+ $ NOUT, .TRUE. )
+ IF( FULL )THEN
+ IF( UPPER )THEN
+ JA = JA + LDA
+ ELSE
+ JA = JA + LDA + 1
+ END IF
+ ELSE
+ JA = JA + LJ
+ END IF
+ ERRMAX = MAX( ERRMAX, ERR )
+* If got really bad answer, report and return.
+ IF( FATAL )
+ $ GO TO 150
+ 90 CONTINUE
+ ELSE
+* Avoid repeating tests with N.le.0.
+ IF( N.LE.0 )
+ $ GO TO 140
+ END IF
+*
+ 100 CONTINUE
+*
+ 110 CONTINUE
+*
+ 120 CONTINUE
+*
+ 130 CONTINUE
+*
+ 140 CONTINUE
+*
+* Report result.
+*
+ IF( ERRMAX.LT.THRESH )THEN
+ WRITE( NOUT, FMT = 9999 )SNAME, NC
+ ELSE
+ WRITE( NOUT, FMT = 9997 )SNAME, NC, ERRMAX
+ END IF
+ GO TO 170
+*
+ 150 CONTINUE
+ WRITE( NOUT, FMT = 9995 )J
+*
+ 160 CONTINUE
+ WRITE( NOUT, FMT = 9996 )SNAME
+ IF( FULL )THEN
+ WRITE( NOUT, FMT = 9993 )NC, SNAME, UPLO, N, ALPHA, INCX,
+ $ INCY, LDA
+ ELSE IF( PACKED )THEN
+ WRITE( NOUT, FMT = 9994 )NC, SNAME, UPLO, N, ALPHA, INCX, INCY
+ END IF
+*
+ 170 CONTINUE
+ RETURN
+*
+ 9999 FORMAT( ' ', A6, ' PASSED THE COMPUTATIONAL TESTS (', I6, ' CALL',
+ $ 'S)' )
+ 9998 FORMAT( ' ******* FATAL ERROR - PARAMETER NUMBER ', I2, ' WAS CH',
+ $ 'ANGED INCORRECTLY *******' )
+ 9997 FORMAT( ' ', A6, ' COMPLETED THE COMPUTATIONAL TESTS (', I6, ' C',
+ $ 'ALLS)', /' ******* BUT WITH MAXIMUM TEST RATIO', F8.2,
+ $ ' - SUSPECT *******' )
+ 9996 FORMAT( ' ******* ', A6, ' FAILED ON CALL NUMBER:' )
+ 9995 FORMAT( ' THESE ARE THE RESULTS FOR COLUMN ', I3 )
+ 9994 FORMAT( 1X, I6, ': ', A6, '(''', A1, ''',', I3, ',', F4.1, ', X,',
+ $ I2, ', Y,', I2, ', AP) .' )
+ 9993 FORMAT( 1X, I6, ': ', A6, '(''', A1, ''',', I3, ',', F4.1, ', X,',
+ $ I2, ', Y,', I2, ', A,', I3, ') .' )
+ 9992 FORMAT( ' ******* FATAL ERROR - ERROR-EXIT TAKEN ON VALID CALL *',
+ $ '******' )
+*
+* End of DCHK6.
+*
+ END
+ SUBROUTINE DCHKE( ISNUM, SRNAMT, NOUT )
+*
+* Tests the error exits from the Level 2 Blas.
+* Requires a special version of the error-handling routine XERBLA.
+* ALPHA, BETA, A, X and Y should not need to be defined.
+*
+* Auxiliary routine for test program for Level 2 Blas.
+*
+* -- Written on 10-August-1987.
+* Richard Hanson, Sandia National Labs.
+* Jeremy Du Croz, NAG Central Office.
+*
+* .. Scalar Arguments ..
+ INTEGER ISNUM, NOUT
+ CHARACTER*6 SRNAMT
+* .. Scalars in Common ..
+ INTEGER INFOT, NOUTC
+ LOGICAL LERR, OK
+* .. Local Scalars ..
+ DOUBLE PRECISION ALPHA, BETA
+* .. Local Arrays ..
+ DOUBLE PRECISION A( 1, 1 ), X( 1 ), Y( 1 )
+* .. External Subroutines ..
+ EXTERNAL CHKXER, DGBMV, DGEMV, DGER, DSBMV, DSPMV, DSPR,
+ $ DSPR2, DSYMV, DSYR, DSYR2, DTBMV, DTBSV, DTPMV,
+ $ DTPSV, DTRMV, DTRSV
+* .. Common blocks ..
+ COMMON /INFOC/INFOT, NOUTC, OK, LERR
+* .. Executable Statements ..
+* OK is set to .FALSE. by the special version of XERBLA or by CHKXER
+* if anything is wrong.
+ OK = .TRUE.
+* LERR is set to .TRUE. by the special version of XERBLA each time
+* it is called, and is then tested and re-set by CHKXER.
+ LERR = .FALSE.
+ GO TO ( 10, 20, 30, 40, 50, 60, 70, 80,
+ $ 90, 100, 110, 120, 130, 140, 150,
+ $ 160 )ISNUM
+ 10 INFOT = 1
+ CALL DGEMV( '/', 0, 0, ALPHA, A, 1, X, 1, BETA, Y, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 2
+ CALL DGEMV( 'N', -1, 0, ALPHA, A, 1, X, 1, BETA, Y, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 3
+ CALL DGEMV( 'N', 0, -1, ALPHA, A, 1, X, 1, BETA, Y, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 6
+ CALL DGEMV( 'N', 2, 0, ALPHA, A, 1, X, 1, BETA, Y, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 8
+ CALL DGEMV( 'N', 0, 0, ALPHA, A, 1, X, 0, BETA, Y, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 11
+ CALL DGEMV( 'N', 0, 0, ALPHA, A, 1, X, 1, BETA, Y, 0 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ GO TO 170
+ 20 INFOT = 1
+ CALL DGBMV( '/', 0, 0, 0, 0, ALPHA, A, 1, X, 1, BETA, Y, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 2
+ CALL DGBMV( 'N', -1, 0, 0, 0, ALPHA, A, 1, X, 1, BETA, Y, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 3
+ CALL DGBMV( 'N', 0, -1, 0, 0, ALPHA, A, 1, X, 1, BETA, Y, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 4
+ CALL DGBMV( 'N', 0, 0, -1, 0, ALPHA, A, 1, X, 1, BETA, Y, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 5
+ CALL DGBMV( 'N', 2, 0, 0, -1, ALPHA, A, 1, X, 1, BETA, Y, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 8
+ CALL DGBMV( 'N', 0, 0, 1, 0, ALPHA, A, 1, X, 1, BETA, Y, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 10
+ CALL DGBMV( 'N', 0, 0, 0, 0, ALPHA, A, 1, X, 0, BETA, Y, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 13
+ CALL DGBMV( 'N', 0, 0, 0, 0, ALPHA, A, 1, X, 1, BETA, Y, 0 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ GO TO 170
+ 30 INFOT = 1
+ CALL DSYMV( '/', 0, ALPHA, A, 1, X, 1, BETA, Y, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 2
+ CALL DSYMV( 'U', -1, ALPHA, A, 1, X, 1, BETA, Y, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 5
+ CALL DSYMV( 'U', 2, ALPHA, A, 1, X, 1, BETA, Y, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 7
+ CALL DSYMV( 'U', 0, ALPHA, A, 1, X, 0, BETA, Y, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 10
+ CALL DSYMV( 'U', 0, ALPHA, A, 1, X, 1, BETA, Y, 0 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ GO TO 170
+ 40 INFOT = 1
+ CALL DSBMV( '/', 0, 0, ALPHA, A, 1, X, 1, BETA, Y, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 2
+ CALL DSBMV( 'U', -1, 0, ALPHA, A, 1, X, 1, BETA, Y, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 3
+ CALL DSBMV( 'U', 0, -1, ALPHA, A, 1, X, 1, BETA, Y, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 6
+ CALL DSBMV( 'U', 0, 1, ALPHA, A, 1, X, 1, BETA, Y, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 8
+ CALL DSBMV( 'U', 0, 0, ALPHA, A, 1, X, 0, BETA, Y, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 11
+ CALL DSBMV( 'U', 0, 0, ALPHA, A, 1, X, 1, BETA, Y, 0 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ GO TO 170
+ 50 INFOT = 1
+ CALL DSPMV( '/', 0, ALPHA, A, X, 1, BETA, Y, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 2
+ CALL DSPMV( 'U', -1, ALPHA, A, X, 1, BETA, Y, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 6
+ CALL DSPMV( 'U', 0, ALPHA, A, X, 0, BETA, Y, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 9
+ CALL DSPMV( 'U', 0, ALPHA, A, X, 1, BETA, Y, 0 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ GO TO 170
+ 60 INFOT = 1
+ CALL DTRMV( '/', 'N', 'N', 0, A, 1, X, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 2
+ CALL DTRMV( 'U', '/', 'N', 0, A, 1, X, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 3
+ CALL DTRMV( 'U', 'N', '/', 0, A, 1, X, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 4
+ CALL DTRMV( 'U', 'N', 'N', -1, A, 1, X, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 6
+ CALL DTRMV( 'U', 'N', 'N', 2, A, 1, X, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 8
+ CALL DTRMV( 'U', 'N', 'N', 0, A, 1, X, 0 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ GO TO 170
+ 70 INFOT = 1
+ CALL DTBMV( '/', 'N', 'N', 0, 0, A, 1, X, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 2
+ CALL DTBMV( 'U', '/', 'N', 0, 0, A, 1, X, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 3
+ CALL DTBMV( 'U', 'N', '/', 0, 0, A, 1, X, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 4
+ CALL DTBMV( 'U', 'N', 'N', -1, 0, A, 1, X, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 5
+ CALL DTBMV( 'U', 'N', 'N', 0, -1, A, 1, X, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 7
+ CALL DTBMV( 'U', 'N', 'N', 0, 1, A, 1, X, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 9
+ CALL DTBMV( 'U', 'N', 'N', 0, 0, A, 1, X, 0 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ GO TO 170
+ 80 INFOT = 1
+ CALL DTPMV( '/', 'N', 'N', 0, A, X, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 2
+ CALL DTPMV( 'U', '/', 'N', 0, A, X, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 3
+ CALL DTPMV( 'U', 'N', '/', 0, A, X, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 4
+ CALL DTPMV( 'U', 'N', 'N', -1, A, X, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 7
+ CALL DTPMV( 'U', 'N', 'N', 0, A, X, 0 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ GO TO 170
+ 90 INFOT = 1
+ CALL DTRSV( '/', 'N', 'N', 0, A, 1, X, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 2
+ CALL DTRSV( 'U', '/', 'N', 0, A, 1, X, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 3
+ CALL DTRSV( 'U', 'N', '/', 0, A, 1, X, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 4
+ CALL DTRSV( 'U', 'N', 'N', -1, A, 1, X, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 6
+ CALL DTRSV( 'U', 'N', 'N', 2, A, 1, X, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 8
+ CALL DTRSV( 'U', 'N', 'N', 0, A, 1, X, 0 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ GO TO 170
+ 100 INFOT = 1
+ CALL DTBSV( '/', 'N', 'N', 0, 0, A, 1, X, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 2
+ CALL DTBSV( 'U', '/', 'N', 0, 0, A, 1, X, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 3
+ CALL DTBSV( 'U', 'N', '/', 0, 0, A, 1, X, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 4
+ CALL DTBSV( 'U', 'N', 'N', -1, 0, A, 1, X, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 5
+ CALL DTBSV( 'U', 'N', 'N', 0, -1, A, 1, X, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 7
+ CALL DTBSV( 'U', 'N', 'N', 0, 1, A, 1, X, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 9
+ CALL DTBSV( 'U', 'N', 'N', 0, 0, A, 1, X, 0 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ GO TO 170
+ 110 INFOT = 1
+ CALL DTPSV( '/', 'N', 'N', 0, A, X, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 2
+ CALL DTPSV( 'U', '/', 'N', 0, A, X, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 3
+ CALL DTPSV( 'U', 'N', '/', 0, A, X, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 4
+ CALL DTPSV( 'U', 'N', 'N', -1, A, X, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 7
+ CALL DTPSV( 'U', 'N', 'N', 0, A, X, 0 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ GO TO 170
+ 120 INFOT = 1
+ CALL DGER( -1, 0, ALPHA, X, 1, Y, 1, A, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 2
+ CALL DGER( 0, -1, ALPHA, X, 1, Y, 1, A, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 5
+ CALL DGER( 0, 0, ALPHA, X, 0, Y, 1, A, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 7
+ CALL DGER( 0, 0, ALPHA, X, 1, Y, 0, A, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 9
+ CALL DGER( 2, 0, ALPHA, X, 1, Y, 1, A, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ GO TO 170
+ 130 INFOT = 1
+ CALL DSYR( '/', 0, ALPHA, X, 1, A, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 2
+ CALL DSYR( 'U', -1, ALPHA, X, 1, A, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 5
+ CALL DSYR( 'U', 0, ALPHA, X, 0, A, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 7
+ CALL DSYR( 'U', 2, ALPHA, X, 1, A, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ GO TO 170
+ 140 INFOT = 1
+ CALL DSPR( '/', 0, ALPHA, X, 1, A )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 2
+ CALL DSPR( 'U', -1, ALPHA, X, 1, A )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 5
+ CALL DSPR( 'U', 0, ALPHA, X, 0, A )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ GO TO 170
+ 150 INFOT = 1
+ CALL DSYR2( '/', 0, ALPHA, X, 1, Y, 1, A, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 2
+ CALL DSYR2( 'U', -1, ALPHA, X, 1, Y, 1, A, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 5
+ CALL DSYR2( 'U', 0, ALPHA, X, 0, Y, 1, A, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 7
+ CALL DSYR2( 'U', 0, ALPHA, X, 1, Y, 0, A, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 9
+ CALL DSYR2( 'U', 2, ALPHA, X, 1, Y, 1, A, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ GO TO 170
+ 160 INFOT = 1
+ CALL DSPR2( '/', 0, ALPHA, X, 1, Y, 1, A )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 2
+ CALL DSPR2( 'U', -1, ALPHA, X, 1, Y, 1, A )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 5
+ CALL DSPR2( 'U', 0, ALPHA, X, 0, Y, 1, A )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 7
+ CALL DSPR2( 'U', 0, ALPHA, X, 1, Y, 0, A )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+*
+ 170 IF( OK )THEN
+ WRITE( NOUT, FMT = 9999 )SRNAMT
+ ELSE
+ WRITE( NOUT, FMT = 9998 )SRNAMT
+ END IF
+ RETURN
+*
+ 9999 FORMAT( ' ', A6, ' PASSED THE TESTS OF ERROR-EXITS' )
+ 9998 FORMAT( ' ******* ', A6, ' FAILED THE TESTS OF ERROR-EXITS *****',
+ $ '**' )
+*
+* End of DCHKE.
+*
+ END
+ SUBROUTINE DMAKE( TYPE, UPLO, DIAG, M, N, A, NMAX, AA, LDA, KL,
+ $ KU, RESET, TRANSL )
+*
+* Generates values for an M by N matrix A within the bandwidth
+* defined by KL and KU.
+* Stores the values in the array AA in the data structure required
+* by the routine, with unwanted elements set to rogue value.
+*
+* TYPE is 'GE', 'GB', 'SY', 'SB', 'SP', 'TR', 'TB' OR 'TP'.
+*
+* Auxiliary routine for test program for Level 2 Blas.
+*
+* -- Written on 10-August-1987.
+* Richard Hanson, Sandia National Labs.
+* Jeremy Du Croz, NAG Central Office.
+*
+* .. Parameters ..
+ DOUBLE PRECISION ZERO, ONE
+ PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0 )
+ DOUBLE PRECISION ROGUE
+ PARAMETER ( ROGUE = -1.0D10 )
+* .. Scalar Arguments ..
+ DOUBLE PRECISION TRANSL
+ INTEGER KL, KU, LDA, M, N, NMAX
+ LOGICAL RESET
+ CHARACTER*1 DIAG, UPLO
+ CHARACTER*2 TYPE
+* .. Array Arguments ..
+ DOUBLE PRECISION A( NMAX, * ), AA( * )
+* .. Local Scalars ..
+ INTEGER I, I1, I2, I3, IBEG, IEND, IOFF, J, KK
+ LOGICAL GEN, LOWER, SYM, TRI, UNIT, UPPER
+* .. External Functions ..
+ DOUBLE PRECISION DBEG
+ EXTERNAL DBEG
+* .. Intrinsic Functions ..
+ INTRINSIC MAX, MIN
+* .. Executable Statements ..
+ GEN = TYPE( 1: 1 ).EQ.'G'
+ SYM = TYPE( 1: 1 ).EQ.'S'
+ TRI = TYPE( 1: 1 ).EQ.'T'
+ UPPER = ( SYM.OR.TRI ).AND.UPLO.EQ.'U'
+ LOWER = ( SYM.OR.TRI ).AND.UPLO.EQ.'L'
+ UNIT = TRI.AND.DIAG.EQ.'U'
+*
+* Generate data in array A.
+*
+ DO 20 J = 1, N
+ DO 10 I = 1, M
+ IF( GEN.OR.( UPPER.AND.I.LE.J ).OR.( LOWER.AND.I.GE.J ) )
+ $ THEN
+ IF( ( I.LE.J.AND.J - I.LE.KU ).OR.
+ $ ( I.GE.J.AND.I - J.LE.KL ) )THEN
+ A( I, J ) = DBEG( RESET ) + TRANSL
+ ELSE
+ A( I, J ) = ZERO
+ END IF
+ IF( I.NE.J )THEN
+ IF( SYM )THEN
+ A( J, I ) = A( I, J )
+ ELSE IF( TRI )THEN
+ A( J, I ) = ZERO
+ END IF
+ END IF
+ END IF
+ 10 CONTINUE
+ IF( TRI )
+ $ A( J, J ) = A( J, J ) + ONE
+ IF( UNIT )
+ $ A( J, J ) = ONE
+ 20 CONTINUE
+*
+* Store elements in array AS in data structure required by routine.
+*
+ IF( TYPE.EQ.'GE' )THEN
+ DO 50 J = 1, N
+ DO 30 I = 1, M
+ AA( I + ( J - 1 )*LDA ) = A( I, J )
+ 30 CONTINUE
+ DO 40 I = M + 1, LDA
+ AA( I + ( J - 1 )*LDA ) = ROGUE
+ 40 CONTINUE
+ 50 CONTINUE
+ ELSE IF( TYPE.EQ.'GB' )THEN
+ DO 90 J = 1, N
+ DO 60 I1 = 1, KU + 1 - J
+ AA( I1 + ( J - 1 )*LDA ) = ROGUE
+ 60 CONTINUE
+ DO 70 I2 = I1, MIN( KL + KU + 1, KU + 1 + M - J )
+ AA( I2 + ( J - 1 )*LDA ) = A( I2 + J - KU - 1, J )
+ 70 CONTINUE
+ DO 80 I3 = I2, LDA
+ AA( I3 + ( J - 1 )*LDA ) = ROGUE
+ 80 CONTINUE
+ 90 CONTINUE
+ ELSE IF( TYPE.EQ.'SY'.OR.TYPE.EQ.'TR' )THEN
+ DO 130 J = 1, N
+ IF( UPPER )THEN
+ IBEG = 1
+ IF( UNIT )THEN
+ IEND = J - 1
+ ELSE
+ IEND = J
+ END IF
+ ELSE
+ IF( UNIT )THEN
+ IBEG = J + 1
+ ELSE
+ IBEG = J
+ END IF
+ IEND = N
+ END IF
+ DO 100 I = 1, IBEG - 1
+ AA( I + ( J - 1 )*LDA ) = ROGUE
+ 100 CONTINUE
+ DO 110 I = IBEG, IEND
+ AA( I + ( J - 1 )*LDA ) = A( I, J )
+ 110 CONTINUE
+ DO 120 I = IEND + 1, LDA
+ AA( I + ( J - 1 )*LDA ) = ROGUE
+ 120 CONTINUE
+ 130 CONTINUE
+ ELSE IF( TYPE.EQ.'SB'.OR.TYPE.EQ.'TB' )THEN
+ DO 170 J = 1, N
+ IF( UPPER )THEN
+ KK = KL + 1
+ IBEG = MAX( 1, KL + 2 - J )
+ IF( UNIT )THEN
+ IEND = KL
+ ELSE
+ IEND = KL + 1
+ END IF
+ ELSE
+ KK = 1
+ IF( UNIT )THEN
+ IBEG = 2
+ ELSE
+ IBEG = 1
+ END IF
+ IEND = MIN( KL + 1, 1 + M - J )
+ END IF
+ DO 140 I = 1, IBEG - 1
+ AA( I + ( J - 1 )*LDA ) = ROGUE
+ 140 CONTINUE
+ DO 150 I = IBEG, IEND
+ AA( I + ( J - 1 )*LDA ) = A( I + J - KK, J )
+ 150 CONTINUE
+ DO 160 I = IEND + 1, LDA
+ AA( I + ( J - 1 )*LDA ) = ROGUE
+ 160 CONTINUE
+ 170 CONTINUE
+ ELSE IF( TYPE.EQ.'SP'.OR.TYPE.EQ.'TP' )THEN
+ IOFF = 0
+ DO 190 J = 1, N
+ IF( UPPER )THEN
+ IBEG = 1
+ IEND = J
+ ELSE
+ IBEG = J
+ IEND = N
+ END IF
+ DO 180 I = IBEG, IEND
+ IOFF = IOFF + 1
+ AA( IOFF ) = A( I, J )
+ IF( I.EQ.J )THEN
+ IF( UNIT )
+ $ AA( IOFF ) = ROGUE
+ END IF
+ 180 CONTINUE
+ 190 CONTINUE
+ END IF
+ RETURN
+*
+* End of DMAKE.
+*
+ END
+ SUBROUTINE DMVCH( TRANS, M, N, ALPHA, A, NMAX, X, INCX, BETA, Y,
+ $ INCY, YT, G, YY, EPS, ERR, FATAL, NOUT, MV )
+*
+* Checks the results of the computational tests.
+*
+* Auxiliary routine for test program for Level 2 Blas.
+*
+* -- Written on 10-August-1987.
+* Richard Hanson, Sandia National Labs.
+* Jeremy Du Croz, NAG Central Office.
+*
+* .. Parameters ..
+ DOUBLE PRECISION ZERO, ONE
+ PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0 )
+* .. Scalar Arguments ..
+ DOUBLE PRECISION ALPHA, BETA, EPS, ERR
+ INTEGER INCX, INCY, M, N, NMAX, NOUT
+ LOGICAL FATAL, MV
+ CHARACTER*1 TRANS
+* .. Array Arguments ..
+ DOUBLE PRECISION A( NMAX, * ), G( * ), X( * ), Y( * ), YT( * ),
+ $ YY( * )
+* .. Local Scalars ..
+ DOUBLE PRECISION ERRI
+ INTEGER I, INCXL, INCYL, IY, J, JX, KX, KY, ML, NL
+ LOGICAL TRAN
+* .. Intrinsic Functions ..
+ INTRINSIC ABS, MAX, SQRT
+* .. Executable Statements ..
+ TRAN = TRANS.EQ.'T'.OR.TRANS.EQ.'C'
+ IF( TRAN )THEN
+ ML = N
+ NL = M
+ ELSE
+ ML = M
+ NL = N
+ END IF
+ IF( INCX.LT.0 )THEN
+ KX = NL
+ INCXL = -1
+ ELSE
+ KX = 1
+ INCXL = 1
+ END IF
+ IF( INCY.LT.0 )THEN
+ KY = ML
+ INCYL = -1
+ ELSE
+ KY = 1
+ INCYL = 1
+ END IF
+*
+* Compute expected result in YT using data in A, X and Y.
+* Compute gauges in G.
+*
+ IY = KY
+ DO 30 I = 1, ML
+ YT( IY ) = ZERO
+ G( IY ) = ZERO
+ JX = KX
+ IF( TRAN )THEN
+ DO 10 J = 1, NL
+ YT( IY ) = YT( IY ) + A( J, I )*X( JX )
+ G( IY ) = G( IY ) + ABS( A( J, I )*X( JX ) )
+ JX = JX + INCXL
+ 10 CONTINUE
+ ELSE
+ DO 20 J = 1, NL
+ YT( IY ) = YT( IY ) + A( I, J )*X( JX )
+ G( IY ) = G( IY ) + ABS( A( I, J )*X( JX ) )
+ JX = JX + INCXL
+ 20 CONTINUE
+ END IF
+ YT( IY ) = ALPHA*YT( IY ) + BETA*Y( IY )
+ G( IY ) = ABS( ALPHA )*G( IY ) + ABS( BETA*Y( IY ) )
+ IY = IY + INCYL
+ 30 CONTINUE
+*
+* Compute the error ratio for this result.
+*
+ ERR = ZERO
+ DO 40 I = 1, ML
+ ERRI = ABS( YT( I ) - YY( 1 + ( I - 1 )*ABS( INCY ) ) )/EPS
+ IF( G( I ).NE.ZERO )
+ $ ERRI = ERRI/G( I )
+ ERR = MAX( ERR, ERRI )
+ IF( ERR*SQRT( EPS ).GE.ONE )
+ $ GO TO 50
+ 40 CONTINUE
+* If the loop completes, all results are at least half accurate.
+ GO TO 70
+*
+* Report fatal error.
+*
+ 50 FATAL = .TRUE.
+ WRITE( NOUT, FMT = 9999 )
+ DO 60 I = 1, ML
+ IF( MV )THEN
+ WRITE( NOUT, FMT = 9998 )I, YT( I ),
+ $ YY( 1 + ( I - 1 )*ABS( INCY ) )
+ ELSE
+ WRITE( NOUT, FMT = 9998 )I,
+ $ YY( 1 + ( I - 1 )*ABS( INCY ) ), YT( I )
+ END IF
+ 60 CONTINUE
+*
+ 70 CONTINUE
+ RETURN
+*
+ 9999 FORMAT( ' ******* FATAL ERROR - COMPUTED RESULT IS LESS THAN HAL',
+ $ 'F ACCURATE *******', /' EXPECTED RESULT COMPU',
+ $ 'TED RESULT' )
+ 9998 FORMAT( 1X, I7, 2G18.6 )
+*
+* End of DMVCH.
+*
+ END
+ LOGICAL FUNCTION LDE( RI, RJ, LR )
+*
+* Tests if two arrays are identical.
+*
+* Auxiliary routine for test program for Level 2 Blas.
+*
+* -- Written on 10-August-1987.
+* Richard Hanson, Sandia National Labs.
+* Jeremy Du Croz, NAG Central Office.
+*
+* .. Scalar Arguments ..
+ INTEGER LR
+* .. Array Arguments ..
+ DOUBLE PRECISION RI( * ), RJ( * )
+* .. Local Scalars ..
+ INTEGER I
+* .. Executable Statements ..
+ DO 10 I = 1, LR
+ IF( RI( I ).NE.RJ( I ) )
+ $ GO TO 20
+ 10 CONTINUE
+ LDE = .TRUE.
+ GO TO 30
+ 20 CONTINUE
+ LDE = .FALSE.
+ 30 RETURN
+*
+* End of LDE.
+*
+ END
+ LOGICAL FUNCTION LDERES( TYPE, UPLO, M, N, AA, AS, LDA )
+*
+* Tests if selected elements in two arrays are equal.
+*
+* TYPE is 'GE', 'SY' or 'SP'.
+*
+* Auxiliary routine for test program for Level 2 Blas.
+*
+* -- Written on 10-August-1987.
+* Richard Hanson, Sandia National Labs.
+* Jeremy Du Croz, NAG Central Office.
+*
+* .. Scalar Arguments ..
+ INTEGER LDA, M, N
+ CHARACTER*1 UPLO
+ CHARACTER*2 TYPE
+* .. Array Arguments ..
+ DOUBLE PRECISION AA( LDA, * ), AS( LDA, * )
+* .. Local Scalars ..
+ INTEGER I, IBEG, IEND, J
+ LOGICAL UPPER
+* .. Executable Statements ..
+ UPPER = UPLO.EQ.'U'
+ IF( TYPE.EQ.'GE' )THEN
+ DO 20 J = 1, N
+ DO 10 I = M + 1, LDA
+ IF( AA( I, J ).NE.AS( I, J ) )
+ $ GO TO 70
+ 10 CONTINUE
+ 20 CONTINUE
+ ELSE IF( TYPE.EQ.'SY' )THEN
+ DO 50 J = 1, N
+ IF( UPPER )THEN
+ IBEG = 1
+ IEND = J
+ ELSE
+ IBEG = J
+ IEND = N
+ END IF
+ DO 30 I = 1, IBEG - 1
+ IF( AA( I, J ).NE.AS( I, J ) )
+ $ GO TO 70
+ 30 CONTINUE
+ DO 40 I = IEND + 1, LDA
+ IF( AA( I, J ).NE.AS( I, J ) )
+ $ GO TO 70
+ 40 CONTINUE
+ 50 CONTINUE
+ END IF
+*
+ LDERES = .TRUE.
+ GO TO 80
+ 70 CONTINUE
+ LDERES = .FALSE.
+ 80 RETURN
+*
+* End of LDERES.
+*
+ END
+ DOUBLE PRECISION FUNCTION DBEG( RESET )
+*
+* Generates random numbers uniformly distributed between -0.5 and 0.5.
+*
+* Auxiliary routine for test program for Level 2 Blas.
+*
+* -- Written on 10-August-1987.
+* Richard Hanson, Sandia National Labs.
+* Jeremy Du Croz, NAG Central Office.
+*
+* .. Scalar Arguments ..
+ LOGICAL RESET
+* .. Local Scalars ..
+ INTEGER I, IC, MI
+* .. Save statement ..
+ SAVE I, IC, MI
+* .. Intrinsic Functions ..
+ INTRINSIC DBLE
+* .. Executable Statements ..
+ IF( RESET )THEN
+* Initialize local variables.
+ MI = 891
+ I = 7
+ IC = 0
+ RESET = .FALSE.
+ END IF
+*
+* The sequence of values of I is bounded between 1 and 999.
+* If initial I = 1,2,3,6,7 or 9, the period will be 50.
+* If initial I = 4 or 8, the period will be 25.
+* If initial I = 5, the period will be 10.
+* IC is used to break up the period by skipping 1 value of I in 6.
+*
+ IC = IC + 1
+ 10 I = I*MI
+ I = I - 1000*( I/1000 )
+ IF( IC.GE.5 )THEN
+ IC = 0
+ GO TO 10
+ END IF
+ DBEG = DBLE( I - 500 )/1001.0D0
+ RETURN
+*
+* End of DBEG.
+*
+ END
+ DOUBLE PRECISION FUNCTION DDIFF( X, Y )
+*
+* Auxiliary routine for test program for Level 2 Blas.
+*
+* -- Written on 10-August-1987.
+* Richard Hanson, Sandia National Labs.
+*
+* .. Scalar Arguments ..
+ DOUBLE PRECISION X, Y
+* .. Executable Statements ..
+ DDIFF = X - Y
+ RETURN
+*
+* End of DDIFF.
+*
+ END
+ SUBROUTINE CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+*
+* Tests whether XERBLA has detected an error when it should.
+*
+* Auxiliary routine for test program for Level 2 Blas.
+*
+* -- Written on 10-August-1987.
+* Richard Hanson, Sandia National Labs.
+* Jeremy Du Croz, NAG Central Office.
+*
+* .. Scalar Arguments ..
+ INTEGER INFOT, NOUT
+ LOGICAL LERR, OK
+ CHARACTER*6 SRNAMT
+* .. Executable Statements ..
+ IF( .NOT.LERR )THEN
+ WRITE( NOUT, FMT = 9999 )INFOT, SRNAMT
+ OK = .FALSE.
+ END IF
+ LERR = .FALSE.
+ RETURN
+*
+ 9999 FORMAT( ' ***** ILLEGAL VALUE OF PARAMETER NUMBER ', I2, ' NOT D',
+ $ 'ETECTED BY ', A6, ' *****' )
+*
+* End of CHKXER.
+*
+ END
+ SUBROUTINE XERBLA( SRNAME, INFO )
+*
+* This is a special version of XERBLA to be used only as part of
+* the test program for testing error exits from the Level 2 BLAS
+* routines.
+*
+* XERBLA is an error handler for the Level 2 BLAS routines.
+*
+* It is called by the Level 2 BLAS routines if an input parameter is
+* invalid.
+*
+* Auxiliary routine for test program for Level 2 Blas.
+*
+* -- Written on 10-August-1987.
+* Richard Hanson, Sandia National Labs.
+* Jeremy Du Croz, NAG Central Office.
+*
+* .. Scalar Arguments ..
+ INTEGER INFO
+ CHARACTER*6 SRNAME
+* .. Scalars in Common ..
+ INTEGER INFOT, NOUT
+ LOGICAL LERR, OK
+ CHARACTER*6 SRNAMT
+* .. Common blocks ..
+ COMMON /INFOC/INFOT, NOUT, OK, LERR
+ COMMON /SRNAMC/SRNAMT
+* .. Executable Statements ..
+ LERR = .TRUE.
+ IF( INFO.NE.INFOT )THEN
+ IF( INFOT.NE.0 )THEN
+ WRITE( NOUT, FMT = 9999 )INFO, INFOT
+ ELSE
+ WRITE( NOUT, FMT = 9997 )INFO
+ END IF
+ OK = .FALSE.
+ END IF
+ IF( SRNAME.NE.SRNAMT )THEN
+ WRITE( NOUT, FMT = 9998 )SRNAME, SRNAMT
+ OK = .FALSE.
+ END IF
+ RETURN
+*
+ 9999 FORMAT( ' ******* XERBLA WAS CALLED WITH INFO = ', I6, ' INSTEAD',
+ $ ' OF ', I2, ' *******' )
+ 9998 FORMAT( ' ******* XERBLA WAS CALLED WITH SRNAME = ', A6, ' INSTE',
+ $ 'AD OF ', A6, ' *******' )
+ 9997 FORMAT( ' ******* XERBLA WAS CALLED WITH INFO = ', I6,
+ $ ' *******' )
+*
+* End of XERBLA
+*
+ END
+
diff --git a/blas/testing/dblat3.dat b/blas/testing/dblat3.dat
new file mode 100644
index 0000000..5cbc2e6
--- /dev/null
+++ b/blas/testing/dblat3.dat
@@ -0,0 +1,20 @@
+'dblat3.summ' NAME OF SUMMARY OUTPUT FILE
+6 UNIT NUMBER OF SUMMARY FILE
+'dblat3.snap' NAME OF SNAPSHOT OUTPUT FILE
+-1 UNIT NUMBER OF SNAPSHOT FILE (NOT USED IF .LT. 0)
+F LOGICAL FLAG, T TO REWIND SNAPSHOT FILE AFTER EACH RECORD.
+F LOGICAL FLAG, T TO STOP ON FAILURES.
+T LOGICAL FLAG, T TO TEST ERROR EXITS.
+16.0 THRESHOLD VALUE OF TEST RATIO
+6 NUMBER OF VALUES OF N
+0 1 2 3 5 9 VALUES OF N
+3 NUMBER OF VALUES OF ALPHA
+0.0 1.0 0.7 VALUES OF ALPHA
+3 NUMBER OF VALUES OF BETA
+0.0 1.0 1.3 VALUES OF BETA
+DGEMM T PUT F FOR NO TEST. SAME COLUMNS.
+DSYMM T PUT F FOR NO TEST. SAME COLUMNS.
+DTRMM T PUT F FOR NO TEST. SAME COLUMNS.
+DTRSM T PUT F FOR NO TEST. SAME COLUMNS.
+DSYRK T PUT F FOR NO TEST. SAME COLUMNS.
+DSYR2K T PUT F FOR NO TEST. SAME COLUMNS.
diff --git a/blas/testing/dblat3.f b/blas/testing/dblat3.f
new file mode 100644
index 0000000..8d37c74
--- /dev/null
+++ b/blas/testing/dblat3.f
@@ -0,0 +1,2873 @@
+*> \brief \b DBLAT3
+*
+* =========== DOCUMENTATION ===========
+*
+* Online html documentation available at
+* http://www.netlib.org/lapack/explore-html/
+*
+* Definition:
+* ===========
+*
+* PROGRAM DBLAT3
+*
+*
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
+*>
+*> Test program for the DOUBLE PRECISION Level 3 Blas.
+*>
+*> The program must be driven by a short data file. The first 14 records
+*> of the file are read using list-directed input, the last 6 records
+*> are read using the format ( A6, L2 ). An annotated example of a data
+*> file can be obtained by deleting the first 3 characters from the
+*> following 20 lines:
+*> 'dblat3.out' NAME OF SUMMARY OUTPUT FILE
+*> 6 UNIT NUMBER OF SUMMARY FILE
+*> 'DBLAT3.SNAP' NAME OF SNAPSHOT OUTPUT FILE
+*> -1 UNIT NUMBER OF SNAPSHOT FILE (NOT USED IF .LT. 0)
+*> F LOGICAL FLAG, T TO REWIND SNAPSHOT FILE AFTER EACH RECORD.
+*> F LOGICAL FLAG, T TO STOP ON FAILURES.
+*> T LOGICAL FLAG, T TO TEST ERROR EXITS.
+*> 16.0 THRESHOLD VALUE OF TEST RATIO
+*> 6 NUMBER OF VALUES OF N
+*> 0 1 2 3 5 9 VALUES OF N
+*> 3 NUMBER OF VALUES OF ALPHA
+*> 0.0 1.0 0.7 VALUES OF ALPHA
+*> 3 NUMBER OF VALUES OF BETA
+*> 0.0 1.0 1.3 VALUES OF BETA
+*> DGEMM T PUT F FOR NO TEST. SAME COLUMNS.
+*> DSYMM T PUT F FOR NO TEST. SAME COLUMNS.
+*> DTRMM T PUT F FOR NO TEST. SAME COLUMNS.
+*> DTRSM T PUT F FOR NO TEST. SAME COLUMNS.
+*> DSYRK T PUT F FOR NO TEST. SAME COLUMNS.
+*> DSYR2K T PUT F FOR NO TEST. SAME COLUMNS.
+*>
+*> Further Details
+*> ===============
+*>
+*> See:
+*>
+*> Dongarra J. J., Du Croz J. J., Duff I. S. and Hammarling S.
+*> A Set of Level 3 Basic Linear Algebra Subprograms.
+*>
+*> Technical Memorandum No.88 (Revision 1), Mathematics and
+*> Computer Science Division, Argonne National Laboratory, 9700
+*> South Cass Avenue, Argonne, Illinois 60439, US.
+*>
+*> -- Written on 8-February-1989.
+*> Jack Dongarra, Argonne National Laboratory.
+*> Iain Duff, AERE Harwell.
+*> Jeremy Du Croz, Numerical Algorithms Group Ltd.
+*> Sven Hammarling, Numerical Algorithms Group Ltd.
+*>
+*> 10-9-00: Change STATUS='NEW' to 'UNKNOWN' so that the testers
+*> can be run multiple times without deleting generated
+*> output files (susan)
+*> \endverbatim
+*
+* Authors:
+* ========
+*
+*> \author Univ. of Tennessee
+*> \author Univ. of California Berkeley
+*> \author Univ. of Colorado Denver
+*> \author NAG Ltd.
+*
+*> \date April 2012
+*
+*> \ingroup double_blas_testing
+*
+* =====================================================================
+ PROGRAM DBLAT3
+*
+* -- Reference BLAS test routine (version 3.4.1) --
+* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
+* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+* April 2012
+*
+* =====================================================================
+*
+* .. Parameters ..
+ INTEGER NIN
+ PARAMETER ( NIN = 5 )
+ INTEGER NSUBS
+ PARAMETER ( NSUBS = 6 )
+ DOUBLE PRECISION ZERO, ONE
+ PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0 )
+ INTEGER NMAX
+ PARAMETER ( NMAX = 65 )
+ INTEGER NIDMAX, NALMAX, NBEMAX
+ PARAMETER ( NIDMAX = 9, NALMAX = 7, NBEMAX = 7 )
+* .. Local Scalars ..
+ DOUBLE PRECISION EPS, ERR, THRESH
+ INTEGER I, ISNUM, J, N, NALF, NBET, NIDIM, NOUT, NTRA
+ LOGICAL FATAL, LTESTT, REWI, SAME, SFATAL, TRACE,
+ $ TSTERR
+ CHARACTER*1 TRANSA, TRANSB
+ CHARACTER*6 SNAMET
+ CHARACTER*32 SNAPS, SUMMRY
+* .. Local Arrays ..
+ DOUBLE PRECISION AA( NMAX*NMAX ), AB( NMAX, 2*NMAX ),
+ $ ALF( NALMAX ), AS( NMAX*NMAX ),
+ $ BB( NMAX*NMAX ), BET( NBEMAX ),
+ $ BS( NMAX*NMAX ), C( NMAX, NMAX ),
+ $ CC( NMAX*NMAX ), CS( NMAX*NMAX ), CT( NMAX ),
+ $ G( NMAX ), W( 2*NMAX )
+ INTEGER IDIM( NIDMAX )
+ LOGICAL LTEST( NSUBS )
+ CHARACTER*6 SNAMES( NSUBS )
+* .. External Functions ..
+ DOUBLE PRECISION DDIFF
+ LOGICAL LDE
+ EXTERNAL DDIFF, LDE
+* .. External Subroutines ..
+ EXTERNAL DCHK1, DCHK2, DCHK3, DCHK4, DCHK5, DCHKE, DMMCH
+* .. Intrinsic Functions ..
+ INTRINSIC MAX, MIN
+* .. Scalars in Common ..
+ INTEGER INFOT, NOUTC
+ LOGICAL LERR, OK
+ CHARACTER*6 SRNAMT
+* .. Common blocks ..
+ COMMON /INFOC/INFOT, NOUTC, OK, LERR
+ COMMON /SRNAMC/SRNAMT
+* .. Data statements ..
+ DATA SNAMES/'DGEMM ', 'DSYMM ', 'DTRMM ', 'DTRSM ',
+ $ 'DSYRK ', 'DSYR2K'/
+* .. Executable Statements ..
+*
+* Read name and unit number for summary output file and open file.
+*
+ READ( NIN, FMT = * )SUMMRY
+ READ( NIN, FMT = * )NOUT
+ OPEN( NOUT, FILE = SUMMRY, STATUS = 'UNKNOWN' )
+ NOUTC = NOUT
+*
+* Read name and unit number for snapshot output file and open file.
+*
+ READ( NIN, FMT = * )SNAPS
+ READ( NIN, FMT = * )NTRA
+ TRACE = NTRA.GE.0
+ IF( TRACE )THEN
+ OPEN( NTRA, FILE = SNAPS, STATUS = 'UNKNOWN' )
+ END IF
+* Read the flag that directs rewinding of the snapshot file.
+ READ( NIN, FMT = * )REWI
+ REWI = REWI.AND.TRACE
+* Read the flag that directs stopping on any failure.
+ READ( NIN, FMT = * )SFATAL
+* Read the flag that indicates whether error exits are to be tested.
+ READ( NIN, FMT = * )TSTERR
+* Read the threshold value of the test ratio
+ READ( NIN, FMT = * )THRESH
+*
+* Read and check the parameter values for the tests.
+*
+* Values of N
+ READ( NIN, FMT = * )NIDIM
+ IF( NIDIM.LT.1.OR.NIDIM.GT.NIDMAX )THEN
+ WRITE( NOUT, FMT = 9997 )'N', NIDMAX
+ GO TO 220
+ END IF
+ READ( NIN, FMT = * )( IDIM( I ), I = 1, NIDIM )
+ DO 10 I = 1, NIDIM
+ IF( IDIM( I ).LT.0.OR.IDIM( I ).GT.NMAX )THEN
+ WRITE( NOUT, FMT = 9996 )NMAX
+ GO TO 220
+ END IF
+ 10 CONTINUE
+* Values of ALPHA
+ READ( NIN, FMT = * )NALF
+ IF( NALF.LT.1.OR.NALF.GT.NALMAX )THEN
+ WRITE( NOUT, FMT = 9997 )'ALPHA', NALMAX
+ GO TO 220
+ END IF
+ READ( NIN, FMT = * )( ALF( I ), I = 1, NALF )
+* Values of BETA
+ READ( NIN, FMT = * )NBET
+ IF( NBET.LT.1.OR.NBET.GT.NBEMAX )THEN
+ WRITE( NOUT, FMT = 9997 )'BETA', NBEMAX
+ GO TO 220
+ END IF
+ READ( NIN, FMT = * )( BET( I ), I = 1, NBET )
+*
+* Report values of parameters.
+*
+ WRITE( NOUT, FMT = 9995 )
+ WRITE( NOUT, FMT = 9994 )( IDIM( I ), I = 1, NIDIM )
+ WRITE( NOUT, FMT = 9993 )( ALF( I ), I = 1, NALF )
+ WRITE( NOUT, FMT = 9992 )( BET( I ), I = 1, NBET )
+ IF( .NOT.TSTERR )THEN
+ WRITE( NOUT, FMT = * )
+ WRITE( NOUT, FMT = 9984 )
+ END IF
+ WRITE( NOUT, FMT = * )
+ WRITE( NOUT, FMT = 9999 )THRESH
+ WRITE( NOUT, FMT = * )
+*
+* Read names of subroutines and flags which indicate
+* whether they are to be tested.
+*
+ DO 20 I = 1, NSUBS
+ LTEST( I ) = .FALSE.
+ 20 CONTINUE
+ 30 READ( NIN, FMT = 9988, END = 60 )SNAMET, LTESTT
+ DO 40 I = 1, NSUBS
+ IF( SNAMET.EQ.SNAMES( I ) )
+ $ GO TO 50
+ 40 CONTINUE
+ WRITE( NOUT, FMT = 9990 )SNAMET
+ STOP
+ 50 LTEST( I ) = LTESTT
+ GO TO 30
+*
+ 60 CONTINUE
+ CLOSE ( NIN )
+*
+* Compute EPS (the machine precision).
+*
+ EPS = EPSILON(ZERO)
+ WRITE( NOUT, FMT = 9998 )EPS
+*
+* Check the reliability of DMMCH using exact data.
+*
+ N = MIN( 32, NMAX )
+ DO 100 J = 1, N
+ DO 90 I = 1, N
+ AB( I, J ) = MAX( I - J + 1, 0 )
+ 90 CONTINUE
+ AB( J, NMAX + 1 ) = J
+ AB( 1, NMAX + J ) = J
+ C( J, 1 ) = ZERO
+ 100 CONTINUE
+ DO 110 J = 1, N
+ CC( J ) = J*( ( J + 1 )*J )/2 - ( ( J + 1 )*J*( J - 1 ) )/3
+ 110 CONTINUE
+* CC holds the exact result. On exit from DMMCH CT holds
+* the result computed by DMMCH.
+ TRANSA = 'N'
+ TRANSB = 'N'
+ CALL DMMCH( TRANSA, TRANSB, N, 1, N, ONE, AB, NMAX,
+ $ AB( 1, NMAX + 1 ), NMAX, ZERO, C, NMAX, CT, G, CC,
+ $ NMAX, EPS, ERR, FATAL, NOUT, .TRUE. )
+ SAME = LDE( CC, CT, N )
+ IF( .NOT.SAME.OR.ERR.NE.ZERO )THEN
+ WRITE( NOUT, FMT = 9989 )TRANSA, TRANSB, SAME, ERR
+ STOP
+ END IF
+ TRANSB = 'T'
+ CALL DMMCH( TRANSA, TRANSB, N, 1, N, ONE, AB, NMAX,
+ $ AB( 1, NMAX + 1 ), NMAX, ZERO, C, NMAX, CT, G, CC,
+ $ NMAX, EPS, ERR, FATAL, NOUT, .TRUE. )
+ SAME = LDE( CC, CT, N )
+ IF( .NOT.SAME.OR.ERR.NE.ZERO )THEN
+ WRITE( NOUT, FMT = 9989 )TRANSA, TRANSB, SAME, ERR
+ STOP
+ END IF
+ DO 120 J = 1, N
+ AB( J, NMAX + 1 ) = N - J + 1
+ AB( 1, NMAX + J ) = N - J + 1
+ 120 CONTINUE
+ DO 130 J = 1, N
+ CC( N - J + 1 ) = J*( ( J + 1 )*J )/2 -
+ $ ( ( J + 1 )*J*( J - 1 ) )/3
+ 130 CONTINUE
+ TRANSA = 'T'
+ TRANSB = 'N'
+ CALL DMMCH( TRANSA, TRANSB, N, 1, N, ONE, AB, NMAX,
+ $ AB( 1, NMAX + 1 ), NMAX, ZERO, C, NMAX, CT, G, CC,
+ $ NMAX, EPS, ERR, FATAL, NOUT, .TRUE. )
+ SAME = LDE( CC, CT, N )
+ IF( .NOT.SAME.OR.ERR.NE.ZERO )THEN
+ WRITE( NOUT, FMT = 9989 )TRANSA, TRANSB, SAME, ERR
+ STOP
+ END IF
+ TRANSB = 'T'
+ CALL DMMCH( TRANSA, TRANSB, N, 1, N, ONE, AB, NMAX,
+ $ AB( 1, NMAX + 1 ), NMAX, ZERO, C, NMAX, CT, G, CC,
+ $ NMAX, EPS, ERR, FATAL, NOUT, .TRUE. )
+ SAME = LDE( CC, CT, N )
+ IF( .NOT.SAME.OR.ERR.NE.ZERO )THEN
+ WRITE( NOUT, FMT = 9989 )TRANSA, TRANSB, SAME, ERR
+ STOP
+ END IF
+*
+* Test each subroutine in turn.
+*
+ DO 200 ISNUM = 1, NSUBS
+ WRITE( NOUT, FMT = * )
+ IF( .NOT.LTEST( ISNUM ) )THEN
+* Subprogram is not to be tested.
+ WRITE( NOUT, FMT = 9987 )SNAMES( ISNUM )
+ ELSE
+ SRNAMT = SNAMES( ISNUM )
+* Test error exits.
+ IF( TSTERR )THEN
+ CALL DCHKE( ISNUM, SNAMES( ISNUM ), NOUT )
+ WRITE( NOUT, FMT = * )
+ END IF
+* Test computations.
+ INFOT = 0
+ OK = .TRUE.
+ FATAL = .FALSE.
+ GO TO ( 140, 150, 160, 160, 170, 180 )ISNUM
+* Test DGEMM, 01.
+ 140 CALL DCHK1( SNAMES( ISNUM ), EPS, THRESH, NOUT, NTRA, TRACE,
+ $ REWI, FATAL, NIDIM, IDIM, NALF, ALF, NBET, BET,
+ $ NMAX, AB, AA, AS, AB( 1, NMAX + 1 ), BB, BS, C,
+ $ CC, CS, CT, G )
+ GO TO 190
+* Test DSYMM, 02.
+ 150 CALL DCHK2( SNAMES( ISNUM ), EPS, THRESH, NOUT, NTRA, TRACE,
+ $ REWI, FATAL, NIDIM, IDIM, NALF, ALF, NBET, BET,
+ $ NMAX, AB, AA, AS, AB( 1, NMAX + 1 ), BB, BS, C,
+ $ CC, CS, CT, G )
+ GO TO 190
+* Test DTRMM, 03, DTRSM, 04.
+ 160 CALL DCHK3( SNAMES( ISNUM ), EPS, THRESH, NOUT, NTRA, TRACE,
+ $ REWI, FATAL, NIDIM, IDIM, NALF, ALF, NMAX, AB,
+ $ AA, AS, AB( 1, NMAX + 1 ), BB, BS, CT, G, C )
+ GO TO 190
+* Test DSYRK, 05.
+ 170 CALL DCHK4( SNAMES( ISNUM ), EPS, THRESH, NOUT, NTRA, TRACE,
+ $ REWI, FATAL, NIDIM, IDIM, NALF, ALF, NBET, BET,
+ $ NMAX, AB, AA, AS, AB( 1, NMAX + 1 ), BB, BS, C,
+ $ CC, CS, CT, G )
+ GO TO 190
+* Test DSYR2K, 06.
+ 180 CALL DCHK5( SNAMES( ISNUM ), EPS, THRESH, NOUT, NTRA, TRACE,
+ $ REWI, FATAL, NIDIM, IDIM, NALF, ALF, NBET, BET,
+ $ NMAX, AB, AA, AS, BB, BS, C, CC, CS, CT, G, W )
+ GO TO 190
+*
+ 190 IF( FATAL.AND.SFATAL )
+ $ GO TO 210
+ END IF
+ 200 CONTINUE
+ WRITE( NOUT, FMT = 9986 )
+ GO TO 230
+*
+ 210 CONTINUE
+ WRITE( NOUT, FMT = 9985 )
+ GO TO 230
+*
+ 220 CONTINUE
+ WRITE( NOUT, FMT = 9991 )
+*
+ 230 CONTINUE
+ IF( TRACE )
+ $ CLOSE ( NTRA )
+ CLOSE ( NOUT )
+ STOP
+*
+ 9999 FORMAT( ' ROUTINES PASS COMPUTATIONAL TESTS IF TEST RATIO IS LES',
+ $ 'S THAN', F8.2 )
+ 9998 FORMAT( ' RELATIVE MACHINE PRECISION IS TAKEN TO BE', 1P, D9.1 )
+ 9997 FORMAT( ' NUMBER OF VALUES OF ', A, ' IS LESS THAN 1 OR GREATER ',
+ $ 'THAN ', I2 )
+ 9996 FORMAT( ' VALUE OF N IS LESS THAN 0 OR GREATER THAN ', I2 )
+ 9995 FORMAT( ' TESTS OF THE DOUBLE PRECISION LEVEL 3 BLAS', //' THE F',
+ $ 'OLLOWING PARAMETER VALUES WILL BE USED:' )
+ 9994 FORMAT( ' FOR N ', 9I6 )
+ 9993 FORMAT( ' FOR ALPHA ', 7F6.1 )
+ 9992 FORMAT( ' FOR BETA ', 7F6.1 )
+ 9991 FORMAT( ' AMEND DATA FILE OR INCREASE ARRAY SIZES IN PROGRAM',
+ $ /' ******* TESTS ABANDONED *******' )
+ 9990 FORMAT( ' SUBPROGRAM NAME ', A6, ' NOT RECOGNIZED', /' ******* T',
+ $ 'ESTS ABANDONED *******' )
+ 9989 FORMAT( ' ERROR IN DMMCH - IN-LINE DOT PRODUCTS ARE BEING EVALU',
+ $ 'ATED WRONGLY.', /' DMMCH WAS CALLED WITH TRANSA = ', A1,
+ $ ' AND TRANSB = ', A1, /' AND RETURNED SAME = ', L1, ' AND ',
+ $ 'ERR = ', F12.3, '.', /' THIS MAY BE DUE TO FAULTS IN THE ',
+ $ 'ARITHMETIC OR THE COMPILER.', /' ******* TESTS ABANDONED ',
+ $ '*******' )
+ 9988 FORMAT( A6, L2 )
+ 9987 FORMAT( 1X, A6, ' WAS NOT TESTED' )
+ 9986 FORMAT( /' END OF TESTS' )
+ 9985 FORMAT( /' ******* FATAL ERROR - TESTS ABANDONED *******' )
+ 9984 FORMAT( ' ERROR-EXITS WILL NOT BE TESTED' )
+*
+* End of DBLAT3.
+*
+ END
+ SUBROUTINE DCHK1( SNAME, EPS, THRESH, NOUT, NTRA, TRACE, REWI,
+ $ FATAL, NIDIM, IDIM, NALF, ALF, NBET, BET, NMAX,
+ $ A, AA, AS, B, BB, BS, C, CC, CS, CT, G )
+*
+* Tests DGEMM.
+*
+* Auxiliary routine for test program for Level 3 Blas.
+*
+* -- Written on 8-February-1989.
+* Jack Dongarra, Argonne National Laboratory.
+* Iain Duff, AERE Harwell.
+* Jeremy Du Croz, Numerical Algorithms Group Ltd.
+* Sven Hammarling, Numerical Algorithms Group Ltd.
+*
+* .. Parameters ..
+ DOUBLE PRECISION ZERO
+ PARAMETER ( ZERO = 0.0D0 )
+* .. Scalar Arguments ..
+ DOUBLE PRECISION EPS, THRESH
+ INTEGER NALF, NBET, NIDIM, NMAX, NOUT, NTRA
+ LOGICAL FATAL, REWI, TRACE
+ CHARACTER*6 SNAME
+* .. Array Arguments ..
+ DOUBLE PRECISION A( NMAX, NMAX ), AA( NMAX*NMAX ), ALF( NALF ),
+ $ AS( NMAX*NMAX ), B( NMAX, NMAX ),
+ $ BB( NMAX*NMAX ), BET( NBET ), BS( NMAX*NMAX ),
+ $ C( NMAX, NMAX ), CC( NMAX*NMAX ),
+ $ CS( NMAX*NMAX ), CT( NMAX ), G( NMAX )
+ INTEGER IDIM( NIDIM )
+* .. Local Scalars ..
+ DOUBLE PRECISION ALPHA, ALS, BETA, BLS, ERR, ERRMAX
+ INTEGER I, IA, IB, ICA, ICB, IK, IM, IN, K, KS, LAA,
+ $ LBB, LCC, LDA, LDAS, LDB, LDBS, LDC, LDCS, M,
+ $ MA, MB, MS, N, NA, NARGS, NB, NC, NS
+ LOGICAL NULL, RESET, SAME, TRANA, TRANB
+ CHARACTER*1 TRANAS, TRANBS, TRANSA, TRANSB
+ CHARACTER*3 ICH
+* .. Local Arrays ..
+ LOGICAL ISAME( 13 )
+* .. External Functions ..
+ LOGICAL LDE, LDERES
+ EXTERNAL LDE, LDERES
+* .. External Subroutines ..
+ EXTERNAL DGEMM, DMAKE, DMMCH
+* .. Intrinsic Functions ..
+ INTRINSIC MAX
+* .. Scalars in Common ..
+ INTEGER INFOT, NOUTC
+ LOGICAL LERR, OK
+* .. Common blocks ..
+ COMMON /INFOC/INFOT, NOUTC, OK, LERR
+* .. Data statements ..
+ DATA ICH/'NTC'/
+* .. Executable Statements ..
+*
+ NARGS = 13
+ NC = 0
+ RESET = .TRUE.
+ ERRMAX = ZERO
+*
+ DO 110 IM = 1, NIDIM
+ M = IDIM( IM )
+*
+ DO 100 IN = 1, NIDIM
+ N = IDIM( IN )
+* Set LDC to 1 more than minimum value if room.
+ LDC = M
+ IF( LDC.LT.NMAX )
+ $ LDC = LDC + 1
+* Skip tests if not enough room.
+ IF( LDC.GT.NMAX )
+ $ GO TO 100
+ LCC = LDC*N
+ NULL = N.LE.0.OR.M.LE.0
+*
+ DO 90 IK = 1, NIDIM
+ K = IDIM( IK )
+*
+ DO 80 ICA = 1, 3
+ TRANSA = ICH( ICA: ICA )
+ TRANA = TRANSA.EQ.'T'.OR.TRANSA.EQ.'C'
+*
+ IF( TRANA )THEN
+ MA = K
+ NA = M
+ ELSE
+ MA = M
+ NA = K
+ END IF
+* Set LDA to 1 more than minimum value if room.
+ LDA = MA
+ IF( LDA.LT.NMAX )
+ $ LDA = LDA + 1
+* Skip tests if not enough room.
+ IF( LDA.GT.NMAX )
+ $ GO TO 80
+ LAA = LDA*NA
+*
+* Generate the matrix A.
+*
+ CALL DMAKE( 'GE', ' ', ' ', MA, NA, A, NMAX, AA, LDA,
+ $ RESET, ZERO )
+*
+ DO 70 ICB = 1, 3
+ TRANSB = ICH( ICB: ICB )
+ TRANB = TRANSB.EQ.'T'.OR.TRANSB.EQ.'C'
+*
+ IF( TRANB )THEN
+ MB = N
+ NB = K
+ ELSE
+ MB = K
+ NB = N
+ END IF
+* Set LDB to 1 more than minimum value if room.
+ LDB = MB
+ IF( LDB.LT.NMAX )
+ $ LDB = LDB + 1
+* Skip tests if not enough room.
+ IF( LDB.GT.NMAX )
+ $ GO TO 70
+ LBB = LDB*NB
+*
+* Generate the matrix B.
+*
+ CALL DMAKE( 'GE', ' ', ' ', MB, NB, B, NMAX, BB,
+ $ LDB, RESET, ZERO )
+*
+ DO 60 IA = 1, NALF
+ ALPHA = ALF( IA )
+*
+ DO 50 IB = 1, NBET
+ BETA = BET( IB )
+*
+* Generate the matrix C.
+*
+ CALL DMAKE( 'GE', ' ', ' ', M, N, C, NMAX,
+ $ CC, LDC, RESET, ZERO )
+*
+ NC = NC + 1
+*
+* Save every datum before calling the
+* subroutine.
+*
+ TRANAS = TRANSA
+ TRANBS = TRANSB
+ MS = M
+ NS = N
+ KS = K
+ ALS = ALPHA
+ DO 10 I = 1, LAA
+ AS( I ) = AA( I )
+ 10 CONTINUE
+ LDAS = LDA
+ DO 20 I = 1, LBB
+ BS( I ) = BB( I )
+ 20 CONTINUE
+ LDBS = LDB
+ BLS = BETA
+ DO 30 I = 1, LCC
+ CS( I ) = CC( I )
+ 30 CONTINUE
+ LDCS = LDC
+*
+* Call the subroutine.
+*
+ IF( TRACE )
+ $ WRITE( NTRA, FMT = 9995 )NC, SNAME,
+ $ TRANSA, TRANSB, M, N, K, ALPHA, LDA, LDB,
+ $ BETA, LDC
+ IF( REWI )
+ $ REWIND NTRA
+ CALL DGEMM( TRANSA, TRANSB, M, N, K, ALPHA,
+ $ AA, LDA, BB, LDB, BETA, CC, LDC )
+*
+* Check if error-exit was taken incorrectly.
+*
+ IF( .NOT.OK )THEN
+ WRITE( NOUT, FMT = 9994 )
+ FATAL = .TRUE.
+ GO TO 120
+ END IF
+*
+* See what data changed inside subroutines.
+*
+ ISAME( 1 ) = TRANSA.EQ.TRANAS
+ ISAME( 2 ) = TRANSB.EQ.TRANBS
+ ISAME( 3 ) = MS.EQ.M
+ ISAME( 4 ) = NS.EQ.N
+ ISAME( 5 ) = KS.EQ.K
+ ISAME( 6 ) = ALS.EQ.ALPHA
+ ISAME( 7 ) = LDE( AS, AA, LAA )
+ ISAME( 8 ) = LDAS.EQ.LDA
+ ISAME( 9 ) = LDE( BS, BB, LBB )
+ ISAME( 10 ) = LDBS.EQ.LDB
+ ISAME( 11 ) = BLS.EQ.BETA
+ IF( NULL )THEN
+ ISAME( 12 ) = LDE( CS, CC, LCC )
+ ELSE
+ ISAME( 12 ) = LDERES( 'GE', ' ', M, N, CS,
+ $ CC, LDC )
+ END IF
+ ISAME( 13 ) = LDCS.EQ.LDC
+*
+* If data was incorrectly changed, report
+* and return.
+*
+ SAME = .TRUE.
+ DO 40 I = 1, NARGS
+ SAME = SAME.AND.ISAME( I )
+ IF( .NOT.ISAME( I ) )
+ $ WRITE( NOUT, FMT = 9998 )I
+ 40 CONTINUE
+ IF( .NOT.SAME )THEN
+ FATAL = .TRUE.
+ GO TO 120
+ END IF
+*
+ IF( .NOT.NULL )THEN
+*
+* Check the result.
+*
+ CALL DMMCH( TRANSA, TRANSB, M, N, K,
+ $ ALPHA, A, NMAX, B, NMAX, BETA,
+ $ C, NMAX, CT, G, CC, LDC, EPS,
+ $ ERR, FATAL, NOUT, .TRUE. )
+ ERRMAX = MAX( ERRMAX, ERR )
+* If got really bad answer, report and
+* return.
+ IF( FATAL )
+ $ GO TO 120
+ END IF
+*
+ 50 CONTINUE
+*
+ 60 CONTINUE
+*
+ 70 CONTINUE
+*
+ 80 CONTINUE
+*
+ 90 CONTINUE
+*
+ 100 CONTINUE
+*
+ 110 CONTINUE
+*
+* Report result.
+*
+ IF( ERRMAX.LT.THRESH )THEN
+ WRITE( NOUT, FMT = 9999 )SNAME, NC
+ ELSE
+ WRITE( NOUT, FMT = 9997 )SNAME, NC, ERRMAX
+ END IF
+ GO TO 130
+*
+ 120 CONTINUE
+ WRITE( NOUT, FMT = 9996 )SNAME
+ WRITE( NOUT, FMT = 9995 )NC, SNAME, TRANSA, TRANSB, M, N, K,
+ $ ALPHA, LDA, LDB, BETA, LDC
+*
+ 130 CONTINUE
+ RETURN
+*
+ 9999 FORMAT( ' ', A6, ' PASSED THE COMPUTATIONAL TESTS (', I6, ' CALL',
+ $ 'S)' )
+ 9998 FORMAT( ' ******* FATAL ERROR - PARAMETER NUMBER ', I2, ' WAS CH',
+ $ 'ANGED INCORRECTLY *******' )
+ 9997 FORMAT( ' ', A6, ' COMPLETED THE COMPUTATIONAL TESTS (', I6, ' C',
+ $ 'ALLS)', /' ******* BUT WITH MAXIMUM TEST RATIO', F8.2,
+ $ ' - SUSPECT *******' )
+ 9996 FORMAT( ' ******* ', A6, ' FAILED ON CALL NUMBER:' )
+ 9995 FORMAT( 1X, I6, ': ', A6, '(''', A1, ''',''', A1, ''',',
+ $ 3( I3, ',' ), F4.1, ', A,', I3, ', B,', I3, ',', F4.1, ', ',
+ $ 'C,', I3, ').' )
+ 9994 FORMAT( ' ******* FATAL ERROR - ERROR-EXIT TAKEN ON VALID CALL *',
+ $ '******' )
+*
+* End of DCHK1.
+*
+ END
+ SUBROUTINE DCHK2( SNAME, EPS, THRESH, NOUT, NTRA, TRACE, REWI,
+ $ FATAL, NIDIM, IDIM, NALF, ALF, NBET, BET, NMAX,
+ $ A, AA, AS, B, BB, BS, C, CC, CS, CT, G )
+*
+* Tests DSYMM.
+*
+* Auxiliary routine for test program for Level 3 Blas.
+*
+* -- Written on 8-February-1989.
+* Jack Dongarra, Argonne National Laboratory.
+* Iain Duff, AERE Harwell.
+* Jeremy Du Croz, Numerical Algorithms Group Ltd.
+* Sven Hammarling, Numerical Algorithms Group Ltd.
+*
+* .. Parameters ..
+ DOUBLE PRECISION ZERO
+ PARAMETER ( ZERO = 0.0D0 )
+* .. Scalar Arguments ..
+ DOUBLE PRECISION EPS, THRESH
+ INTEGER NALF, NBET, NIDIM, NMAX, NOUT, NTRA
+ LOGICAL FATAL, REWI, TRACE
+ CHARACTER*6 SNAME
+* .. Array Arguments ..
+ DOUBLE PRECISION A( NMAX, NMAX ), AA( NMAX*NMAX ), ALF( NALF ),
+ $ AS( NMAX*NMAX ), B( NMAX, NMAX ),
+ $ BB( NMAX*NMAX ), BET( NBET ), BS( NMAX*NMAX ),
+ $ C( NMAX, NMAX ), CC( NMAX*NMAX ),
+ $ CS( NMAX*NMAX ), CT( NMAX ), G( NMAX )
+ INTEGER IDIM( NIDIM )
+* .. Local Scalars ..
+ DOUBLE PRECISION ALPHA, ALS, BETA, BLS, ERR, ERRMAX
+ INTEGER I, IA, IB, ICS, ICU, IM, IN, LAA, LBB, LCC,
+ $ LDA, LDAS, LDB, LDBS, LDC, LDCS, M, MS, N, NA,
+ $ NARGS, NC, NS
+ LOGICAL LEFT, NULL, RESET, SAME
+ CHARACTER*1 SIDE, SIDES, UPLO, UPLOS
+ CHARACTER*2 ICHS, ICHU
+* .. Local Arrays ..
+ LOGICAL ISAME( 13 )
+* .. External Functions ..
+ LOGICAL LDE, LDERES
+ EXTERNAL LDE, LDERES
+* .. External Subroutines ..
+ EXTERNAL DMAKE, DMMCH, DSYMM
+* .. Intrinsic Functions ..
+ INTRINSIC MAX
+* .. Scalars in Common ..
+ INTEGER INFOT, NOUTC
+ LOGICAL LERR, OK
+* .. Common blocks ..
+ COMMON /INFOC/INFOT, NOUTC, OK, LERR
+* .. Data statements ..
+ DATA ICHS/'LR'/, ICHU/'UL'/
+* .. Executable Statements ..
+*
+ NARGS = 12
+ NC = 0
+ RESET = .TRUE.
+ ERRMAX = ZERO
+*
+ DO 100 IM = 1, NIDIM
+ M = IDIM( IM )
+*
+ DO 90 IN = 1, NIDIM
+ N = IDIM( IN )
+* Set LDC to 1 more than minimum value if room.
+ LDC = M
+ IF( LDC.LT.NMAX )
+ $ LDC = LDC + 1
+* Skip tests if not enough room.
+ IF( LDC.GT.NMAX )
+ $ GO TO 90
+ LCC = LDC*N
+ NULL = N.LE.0.OR.M.LE.0
+*
+* Set LDB to 1 more than minimum value if room.
+ LDB = M
+ IF( LDB.LT.NMAX )
+ $ LDB = LDB + 1
+* Skip tests if not enough room.
+ IF( LDB.GT.NMAX )
+ $ GO TO 90
+ LBB = LDB*N
+*
+* Generate the matrix B.
+*
+ CALL DMAKE( 'GE', ' ', ' ', M, N, B, NMAX, BB, LDB, RESET,
+ $ ZERO )
+*
+ DO 80 ICS = 1, 2
+ SIDE = ICHS( ICS: ICS )
+ LEFT = SIDE.EQ.'L'
+*
+ IF( LEFT )THEN
+ NA = M
+ ELSE
+ NA = N
+ END IF
+* Set LDA to 1 more than minimum value if room.
+ LDA = NA
+ IF( LDA.LT.NMAX )
+ $ LDA = LDA + 1
+* Skip tests if not enough room.
+ IF( LDA.GT.NMAX )
+ $ GO TO 80
+ LAA = LDA*NA
+*
+ DO 70 ICU = 1, 2
+ UPLO = ICHU( ICU: ICU )
+*
+* Generate the symmetric matrix A.
+*
+ CALL DMAKE( 'SY', UPLO, ' ', NA, NA, A, NMAX, AA, LDA,
+ $ RESET, ZERO )
+*
+ DO 60 IA = 1, NALF
+ ALPHA = ALF( IA )
+*
+ DO 50 IB = 1, NBET
+ BETA = BET( IB )
+*
+* Generate the matrix C.
+*
+ CALL DMAKE( 'GE', ' ', ' ', M, N, C, NMAX, CC,
+ $ LDC, RESET, ZERO )
+*
+ NC = NC + 1
+*
+* Save every datum before calling the
+* subroutine.
+*
+ SIDES = SIDE
+ UPLOS = UPLO
+ MS = M
+ NS = N
+ ALS = ALPHA
+ DO 10 I = 1, LAA
+ AS( I ) = AA( I )
+ 10 CONTINUE
+ LDAS = LDA
+ DO 20 I = 1, LBB
+ BS( I ) = BB( I )
+ 20 CONTINUE
+ LDBS = LDB
+ BLS = BETA
+ DO 30 I = 1, LCC
+ CS( I ) = CC( I )
+ 30 CONTINUE
+ LDCS = LDC
+*
+* Call the subroutine.
+*
+ IF( TRACE )
+ $ WRITE( NTRA, FMT = 9995 )NC, SNAME, SIDE,
+ $ UPLO, M, N, ALPHA, LDA, LDB, BETA, LDC
+ IF( REWI )
+ $ REWIND NTRA
+ CALL DSYMM( SIDE, UPLO, M, N, ALPHA, AA, LDA,
+ $ BB, LDB, BETA, CC, LDC )
+*
+* Check if error-exit was taken incorrectly.
+*
+ IF( .NOT.OK )THEN
+ WRITE( NOUT, FMT = 9994 )
+ FATAL = .TRUE.
+ GO TO 110
+ END IF
+*
+* See what data changed inside subroutines.
+*
+ ISAME( 1 ) = SIDES.EQ.SIDE
+ ISAME( 2 ) = UPLOS.EQ.UPLO
+ ISAME( 3 ) = MS.EQ.M
+ ISAME( 4 ) = NS.EQ.N
+ ISAME( 5 ) = ALS.EQ.ALPHA
+ ISAME( 6 ) = LDE( AS, AA, LAA )
+ ISAME( 7 ) = LDAS.EQ.LDA
+ ISAME( 8 ) = LDE( BS, BB, LBB )
+ ISAME( 9 ) = LDBS.EQ.LDB
+ ISAME( 10 ) = BLS.EQ.BETA
+ IF( NULL )THEN
+ ISAME( 11 ) = LDE( CS, CC, LCC )
+ ELSE
+ ISAME( 11 ) = LDERES( 'GE', ' ', M, N, CS,
+ $ CC, LDC )
+ END IF
+ ISAME( 12 ) = LDCS.EQ.LDC
+*
+* If data was incorrectly changed, report and
+* return.
+*
+ SAME = .TRUE.
+ DO 40 I = 1, NARGS
+ SAME = SAME.AND.ISAME( I )
+ IF( .NOT.ISAME( I ) )
+ $ WRITE( NOUT, FMT = 9998 )I
+ 40 CONTINUE
+ IF( .NOT.SAME )THEN
+ FATAL = .TRUE.
+ GO TO 110
+ END IF
+*
+ IF( .NOT.NULL )THEN
+*
+* Check the result.
+*
+ IF( LEFT )THEN
+ CALL DMMCH( 'N', 'N', M, N, M, ALPHA, A,
+ $ NMAX, B, NMAX, BETA, C, NMAX,
+ $ CT, G, CC, LDC, EPS, ERR,
+ $ FATAL, NOUT, .TRUE. )
+ ELSE
+ CALL DMMCH( 'N', 'N', M, N, N, ALPHA, B,
+ $ NMAX, A, NMAX, BETA, C, NMAX,
+ $ CT, G, CC, LDC, EPS, ERR,
+ $ FATAL, NOUT, .TRUE. )
+ END IF
+ ERRMAX = MAX( ERRMAX, ERR )
+* If got really bad answer, report and
+* return.
+ IF( FATAL )
+ $ GO TO 110
+ END IF
+*
+ 50 CONTINUE
+*
+ 60 CONTINUE
+*
+ 70 CONTINUE
+*
+ 80 CONTINUE
+*
+ 90 CONTINUE
+*
+ 100 CONTINUE
+*
+* Report result.
+*
+ IF( ERRMAX.LT.THRESH )THEN
+ WRITE( NOUT, FMT = 9999 )SNAME, NC
+ ELSE
+ WRITE( NOUT, FMT = 9997 )SNAME, NC, ERRMAX
+ END IF
+ GO TO 120
+*
+ 110 CONTINUE
+ WRITE( NOUT, FMT = 9996 )SNAME
+ WRITE( NOUT, FMT = 9995 )NC, SNAME, SIDE, UPLO, M, N, ALPHA, LDA,
+ $ LDB, BETA, LDC
+*
+ 120 CONTINUE
+ RETURN
+*
+ 9999 FORMAT( ' ', A6, ' PASSED THE COMPUTATIONAL TESTS (', I6, ' CALL',
+ $ 'S)' )
+ 9998 FORMAT( ' ******* FATAL ERROR - PARAMETER NUMBER ', I2, ' WAS CH',
+ $ 'ANGED INCORRECTLY *******' )
+ 9997 FORMAT( ' ', A6, ' COMPLETED THE COMPUTATIONAL TESTS (', I6, ' C',
+ $ 'ALLS)', /' ******* BUT WITH MAXIMUM TEST RATIO', F8.2,
+ $ ' - SUSPECT *******' )
+ 9996 FORMAT( ' ******* ', A6, ' FAILED ON CALL NUMBER:' )
+ 9995 FORMAT( 1X, I6, ': ', A6, '(', 2( '''', A1, ''',' ), 2( I3, ',' ),
+ $ F4.1, ', A,', I3, ', B,', I3, ',', F4.1, ', C,', I3, ') ',
+ $ ' .' )
+ 9994 FORMAT( ' ******* FATAL ERROR - ERROR-EXIT TAKEN ON VALID CALL *',
+ $ '******' )
+*
+* End of DCHK2.
+*
+ END
+ SUBROUTINE DCHK3( SNAME, EPS, THRESH, NOUT, NTRA, TRACE, REWI,
+ $ FATAL, NIDIM, IDIM, NALF, ALF, NMAX, A, AA, AS,
+ $ B, BB, BS, CT, G, C )
+*
+* Tests DTRMM and DTRSM.
+*
+* Auxiliary routine for test program for Level 3 Blas.
+*
+* -- Written on 8-February-1989.
+* Jack Dongarra, Argonne National Laboratory.
+* Iain Duff, AERE Harwell.
+* Jeremy Du Croz, Numerical Algorithms Group Ltd.
+* Sven Hammarling, Numerical Algorithms Group Ltd.
+*
+* .. Parameters ..
+ DOUBLE PRECISION ZERO, ONE
+ PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0 )
+* .. Scalar Arguments ..
+ DOUBLE PRECISION EPS, THRESH
+ INTEGER NALF, NIDIM, NMAX, NOUT, NTRA
+ LOGICAL FATAL, REWI, TRACE
+ CHARACTER*6 SNAME
+* .. Array Arguments ..
+ DOUBLE PRECISION A( NMAX, NMAX ), AA( NMAX*NMAX ), ALF( NALF ),
+ $ AS( NMAX*NMAX ), B( NMAX, NMAX ),
+ $ BB( NMAX*NMAX ), BS( NMAX*NMAX ),
+ $ C( NMAX, NMAX ), CT( NMAX ), G( NMAX )
+ INTEGER IDIM( NIDIM )
+* .. Local Scalars ..
+ DOUBLE PRECISION ALPHA, ALS, ERR, ERRMAX
+ INTEGER I, IA, ICD, ICS, ICT, ICU, IM, IN, J, LAA, LBB,
+ $ LDA, LDAS, LDB, LDBS, M, MS, N, NA, NARGS, NC,
+ $ NS
+ LOGICAL LEFT, NULL, RESET, SAME
+ CHARACTER*1 DIAG, DIAGS, SIDE, SIDES, TRANAS, TRANSA, UPLO,
+ $ UPLOS
+ CHARACTER*2 ICHD, ICHS, ICHU
+ CHARACTER*3 ICHT
+* .. Local Arrays ..
+ LOGICAL ISAME( 13 )
+* .. External Functions ..
+ LOGICAL LDE, LDERES
+ EXTERNAL LDE, LDERES
+* .. External Subroutines ..
+ EXTERNAL DMAKE, DMMCH, DTRMM, DTRSM
+* .. Intrinsic Functions ..
+ INTRINSIC MAX
+* .. Scalars in Common ..
+ INTEGER INFOT, NOUTC
+ LOGICAL LERR, OK
+* .. Common blocks ..
+ COMMON /INFOC/INFOT, NOUTC, OK, LERR
+* .. Data statements ..
+ DATA ICHU/'UL'/, ICHT/'NTC'/, ICHD/'UN'/, ICHS/'LR'/
+* .. Executable Statements ..
+*
+ NARGS = 11
+ NC = 0
+ RESET = .TRUE.
+ ERRMAX = ZERO
+* Set up zero matrix for DMMCH.
+ DO 20 J = 1, NMAX
+ DO 10 I = 1, NMAX
+ C( I, J ) = ZERO
+ 10 CONTINUE
+ 20 CONTINUE
+*
+ DO 140 IM = 1, NIDIM
+ M = IDIM( IM )
+*
+ DO 130 IN = 1, NIDIM
+ N = IDIM( IN )
+* Set LDB to 1 more than minimum value if room.
+ LDB = M
+ IF( LDB.LT.NMAX )
+ $ LDB = LDB + 1
+* Skip tests if not enough room.
+ IF( LDB.GT.NMAX )
+ $ GO TO 130
+ LBB = LDB*N
+ NULL = M.LE.0.OR.N.LE.0
+*
+ DO 120 ICS = 1, 2
+ SIDE = ICHS( ICS: ICS )
+ LEFT = SIDE.EQ.'L'
+ IF( LEFT )THEN
+ NA = M
+ ELSE
+ NA = N
+ END IF
+* Set LDA to 1 more than minimum value if room.
+ LDA = NA
+ IF( LDA.LT.NMAX )
+ $ LDA = LDA + 1
+* Skip tests if not enough room.
+ IF( LDA.GT.NMAX )
+ $ GO TO 130
+ LAA = LDA*NA
+*
+ DO 110 ICU = 1, 2
+ UPLO = ICHU( ICU: ICU )
+*
+ DO 100 ICT = 1, 3
+ TRANSA = ICHT( ICT: ICT )
+*
+ DO 90 ICD = 1, 2
+ DIAG = ICHD( ICD: ICD )
+*
+ DO 80 IA = 1, NALF
+ ALPHA = ALF( IA )
+*
+* Generate the matrix A.
+*
+ CALL DMAKE( 'TR', UPLO, DIAG, NA, NA, A,
+ $ NMAX, AA, LDA, RESET, ZERO )
+*
+* Generate the matrix B.
+*
+ CALL DMAKE( 'GE', ' ', ' ', M, N, B, NMAX,
+ $ BB, LDB, RESET, ZERO )
+*
+ NC = NC + 1
+*
+* Save every datum before calling the
+* subroutine.
+*
+ SIDES = SIDE
+ UPLOS = UPLO
+ TRANAS = TRANSA
+ DIAGS = DIAG
+ MS = M
+ NS = N
+ ALS = ALPHA
+ DO 30 I = 1, LAA
+ AS( I ) = AA( I )
+ 30 CONTINUE
+ LDAS = LDA
+ DO 40 I = 1, LBB
+ BS( I ) = BB( I )
+ 40 CONTINUE
+ LDBS = LDB
+*
+* Call the subroutine.
+*
+ IF( SNAME( 4: 5 ).EQ.'MM' )THEN
+ IF( TRACE )
+ $ WRITE( NTRA, FMT = 9995 )NC, SNAME,
+ $ SIDE, UPLO, TRANSA, DIAG, M, N, ALPHA,
+ $ LDA, LDB
+ IF( REWI )
+ $ REWIND NTRA
+ CALL DTRMM( SIDE, UPLO, TRANSA, DIAG, M,
+ $ N, ALPHA, AA, LDA, BB, LDB )
+ ELSE IF( SNAME( 4: 5 ).EQ.'SM' )THEN
+ IF( TRACE )
+ $ WRITE( NTRA, FMT = 9995 )NC, SNAME,
+ $ SIDE, UPLO, TRANSA, DIAG, M, N, ALPHA,
+ $ LDA, LDB
+ IF( REWI )
+ $ REWIND NTRA
+ CALL DTRSM( SIDE, UPLO, TRANSA, DIAG, M,
+ $ N, ALPHA, AA, LDA, BB, LDB )
+ END IF
+*
+* Check if error-exit was taken incorrectly.
+*
+ IF( .NOT.OK )THEN
+ WRITE( NOUT, FMT = 9994 )
+ FATAL = .TRUE.
+ GO TO 150
+ END IF
+*
+* See what data changed inside subroutines.
+*
+ ISAME( 1 ) = SIDES.EQ.SIDE
+ ISAME( 2 ) = UPLOS.EQ.UPLO
+ ISAME( 3 ) = TRANAS.EQ.TRANSA
+ ISAME( 4 ) = DIAGS.EQ.DIAG
+ ISAME( 5 ) = MS.EQ.M
+ ISAME( 6 ) = NS.EQ.N
+ ISAME( 7 ) = ALS.EQ.ALPHA
+ ISAME( 8 ) = LDE( AS, AA, LAA )
+ ISAME( 9 ) = LDAS.EQ.LDA
+ IF( NULL )THEN
+ ISAME( 10 ) = LDE( BS, BB, LBB )
+ ELSE
+ ISAME( 10 ) = LDERES( 'GE', ' ', M, N, BS,
+ $ BB, LDB )
+ END IF
+ ISAME( 11 ) = LDBS.EQ.LDB
+*
+* If data was incorrectly changed, report and
+* return.
+*
+ SAME = .TRUE.
+ DO 50 I = 1, NARGS
+ SAME = SAME.AND.ISAME( I )
+ IF( .NOT.ISAME( I ) )
+ $ WRITE( NOUT, FMT = 9998 )I
+ 50 CONTINUE
+ IF( .NOT.SAME )THEN
+ FATAL = .TRUE.
+ GO TO 150
+ END IF
+*
+ IF( .NOT.NULL )THEN
+ IF( SNAME( 4: 5 ).EQ.'MM' )THEN
+*
+* Check the result.
+*
+ IF( LEFT )THEN
+ CALL DMMCH( TRANSA, 'N', M, N, M,
+ $ ALPHA, A, NMAX, B, NMAX,
+ $ ZERO, C, NMAX, CT, G,
+ $ BB, LDB, EPS, ERR,
+ $ FATAL, NOUT, .TRUE. )
+ ELSE
+ CALL DMMCH( 'N', TRANSA, M, N, N,
+ $ ALPHA, B, NMAX, A, NMAX,
+ $ ZERO, C, NMAX, CT, G,
+ $ BB, LDB, EPS, ERR,
+ $ FATAL, NOUT, .TRUE. )
+ END IF
+ ELSE IF( SNAME( 4: 5 ).EQ.'SM' )THEN
+*
+* Compute approximation to original
+* matrix.
+*
+ DO 70 J = 1, N
+ DO 60 I = 1, M
+ C( I, J ) = BB( I + ( J - 1 )*
+ $ LDB )
+ BB( I + ( J - 1 )*LDB ) = ALPHA*
+ $ B( I, J )
+ 60 CONTINUE
+ 70 CONTINUE
+*
+ IF( LEFT )THEN
+ CALL DMMCH( TRANSA, 'N', M, N, M,
+ $ ONE, A, NMAX, C, NMAX,
+ $ ZERO, B, NMAX, CT, G,
+ $ BB, LDB, EPS, ERR,
+ $ FATAL, NOUT, .FALSE. )
+ ELSE
+ CALL DMMCH( 'N', TRANSA, M, N, N,
+ $ ONE, C, NMAX, A, NMAX,
+ $ ZERO, B, NMAX, CT, G,
+ $ BB, LDB, EPS, ERR,
+ $ FATAL, NOUT, .FALSE. )
+ END IF
+ END IF
+ ERRMAX = MAX( ERRMAX, ERR )
+* If got really bad answer, report and
+* return.
+ IF( FATAL )
+ $ GO TO 150
+ END IF
+*
+ 80 CONTINUE
+*
+ 90 CONTINUE
+*
+ 100 CONTINUE
+*
+ 110 CONTINUE
+*
+ 120 CONTINUE
+*
+ 130 CONTINUE
+*
+ 140 CONTINUE
+*
+* Report result.
+*
+ IF( ERRMAX.LT.THRESH )THEN
+ WRITE( NOUT, FMT = 9999 )SNAME, NC
+ ELSE
+ WRITE( NOUT, FMT = 9997 )SNAME, NC, ERRMAX
+ END IF
+ GO TO 160
+*
+ 150 CONTINUE
+ WRITE( NOUT, FMT = 9996 )SNAME
+ WRITE( NOUT, FMT = 9995 )NC, SNAME, SIDE, UPLO, TRANSA, DIAG, M,
+ $ N, ALPHA, LDA, LDB
+*
+ 160 CONTINUE
+ RETURN
+*
+ 9999 FORMAT( ' ', A6, ' PASSED THE COMPUTATIONAL TESTS (', I6, ' CALL',
+ $ 'S)' )
+ 9998 FORMAT( ' ******* FATAL ERROR - PARAMETER NUMBER ', I2, ' WAS CH',
+ $ 'ANGED INCORRECTLY *******' )
+ 9997 FORMAT( ' ', A6, ' COMPLETED THE COMPUTATIONAL TESTS (', I6, ' C',
+ $ 'ALLS)', /' ******* BUT WITH MAXIMUM TEST RATIO', F8.2,
+ $ ' - SUSPECT *******' )
+ 9996 FORMAT( ' ******* ', A6, ' FAILED ON CALL NUMBER:' )
+ 9995 FORMAT( 1X, I6, ': ', A6, '(', 4( '''', A1, ''',' ), 2( I3, ',' ),
+ $ F4.1, ', A,', I3, ', B,', I3, ') .' )
+ 9994 FORMAT( ' ******* FATAL ERROR - ERROR-EXIT TAKEN ON VALID CALL *',
+ $ '******' )
+*
+* End of DCHK3.
+*
+ END
+ SUBROUTINE DCHK4( SNAME, EPS, THRESH, NOUT, NTRA, TRACE, REWI,
+ $ FATAL, NIDIM, IDIM, NALF, ALF, NBET, BET, NMAX,
+ $ A, AA, AS, B, BB, BS, C, CC, CS, CT, G )
+*
+* Tests DSYRK.
+*
+* Auxiliary routine for test program for Level 3 Blas.
+*
+* -- Written on 8-February-1989.
+* Jack Dongarra, Argonne National Laboratory.
+* Iain Duff, AERE Harwell.
+* Jeremy Du Croz, Numerical Algorithms Group Ltd.
+* Sven Hammarling, Numerical Algorithms Group Ltd.
+*
+* .. Parameters ..
+ DOUBLE PRECISION ZERO
+ PARAMETER ( ZERO = 0.0D0 )
+* .. Scalar Arguments ..
+ DOUBLE PRECISION EPS, THRESH
+ INTEGER NALF, NBET, NIDIM, NMAX, NOUT, NTRA
+ LOGICAL FATAL, REWI, TRACE
+ CHARACTER*6 SNAME
+* .. Array Arguments ..
+ DOUBLE PRECISION A( NMAX, NMAX ), AA( NMAX*NMAX ), ALF( NALF ),
+ $ AS( NMAX*NMAX ), B( NMAX, NMAX ),
+ $ BB( NMAX*NMAX ), BET( NBET ), BS( NMAX*NMAX ),
+ $ C( NMAX, NMAX ), CC( NMAX*NMAX ),
+ $ CS( NMAX*NMAX ), CT( NMAX ), G( NMAX )
+ INTEGER IDIM( NIDIM )
+* .. Local Scalars ..
+ DOUBLE PRECISION ALPHA, ALS, BETA, BETS, ERR, ERRMAX
+ INTEGER I, IA, IB, ICT, ICU, IK, IN, J, JC, JJ, K, KS,
+ $ LAA, LCC, LDA, LDAS, LDC, LDCS, LJ, MA, N, NA,
+ $ NARGS, NC, NS
+ LOGICAL NULL, RESET, SAME, TRAN, UPPER
+ CHARACTER*1 TRANS, TRANSS, UPLO, UPLOS
+ CHARACTER*2 ICHU
+ CHARACTER*3 ICHT
+* .. Local Arrays ..
+ LOGICAL ISAME( 13 )
+* .. External Functions ..
+ LOGICAL LDE, LDERES
+ EXTERNAL LDE, LDERES
+* .. External Subroutines ..
+ EXTERNAL DMAKE, DMMCH, DSYRK
+* .. Intrinsic Functions ..
+ INTRINSIC MAX
+* .. Scalars in Common ..
+ INTEGER INFOT, NOUTC
+ LOGICAL LERR, OK
+* .. Common blocks ..
+ COMMON /INFOC/INFOT, NOUTC, OK, LERR
+* .. Data statements ..
+ DATA ICHT/'NTC'/, ICHU/'UL'/
+* .. Executable Statements ..
+*
+ NARGS = 10
+ NC = 0
+ RESET = .TRUE.
+ ERRMAX = ZERO
+*
+ DO 100 IN = 1, NIDIM
+ N = IDIM( IN )
+* Set LDC to 1 more than minimum value if room.
+ LDC = N
+ IF( LDC.LT.NMAX )
+ $ LDC = LDC + 1
+* Skip tests if not enough room.
+ IF( LDC.GT.NMAX )
+ $ GO TO 100
+ LCC = LDC*N
+ NULL = N.LE.0
+*
+ DO 90 IK = 1, NIDIM
+ K = IDIM( IK )
+*
+ DO 80 ICT = 1, 3
+ TRANS = ICHT( ICT: ICT )
+ TRAN = TRANS.EQ.'T'.OR.TRANS.EQ.'C'
+ IF( TRAN )THEN
+ MA = K
+ NA = N
+ ELSE
+ MA = N
+ NA = K
+ END IF
+* Set LDA to 1 more than minimum value if room.
+ LDA = MA
+ IF( LDA.LT.NMAX )
+ $ LDA = LDA + 1
+* Skip tests if not enough room.
+ IF( LDA.GT.NMAX )
+ $ GO TO 80
+ LAA = LDA*NA
+*
+* Generate the matrix A.
+*
+ CALL DMAKE( 'GE', ' ', ' ', MA, NA, A, NMAX, AA, LDA,
+ $ RESET, ZERO )
+*
+ DO 70 ICU = 1, 2
+ UPLO = ICHU( ICU: ICU )
+ UPPER = UPLO.EQ.'U'
+*
+ DO 60 IA = 1, NALF
+ ALPHA = ALF( IA )
+*
+ DO 50 IB = 1, NBET
+ BETA = BET( IB )
+*
+* Generate the matrix C.
+*
+ CALL DMAKE( 'SY', UPLO, ' ', N, N, C, NMAX, CC,
+ $ LDC, RESET, ZERO )
+*
+ NC = NC + 1
+*
+* Save every datum before calling the subroutine.
+*
+ UPLOS = UPLO
+ TRANSS = TRANS
+ NS = N
+ KS = K
+ ALS = ALPHA
+ DO 10 I = 1, LAA
+ AS( I ) = AA( I )
+ 10 CONTINUE
+ LDAS = LDA
+ BETS = BETA
+ DO 20 I = 1, LCC
+ CS( I ) = CC( I )
+ 20 CONTINUE
+ LDCS = LDC
+*
+* Call the subroutine.
+*
+ IF( TRACE )
+ $ WRITE( NTRA, FMT = 9994 )NC, SNAME, UPLO,
+ $ TRANS, N, K, ALPHA, LDA, BETA, LDC
+ IF( REWI )
+ $ REWIND NTRA
+ CALL DSYRK( UPLO, TRANS, N, K, ALPHA, AA, LDA,
+ $ BETA, CC, LDC )
+*
+* Check if error-exit was taken incorrectly.
+*
+ IF( .NOT.OK )THEN
+ WRITE( NOUT, FMT = 9993 )
+ FATAL = .TRUE.
+ GO TO 120
+ END IF
+*
+* See what data changed inside subroutines.
+*
+ ISAME( 1 ) = UPLOS.EQ.UPLO
+ ISAME( 2 ) = TRANSS.EQ.TRANS
+ ISAME( 3 ) = NS.EQ.N
+ ISAME( 4 ) = KS.EQ.K
+ ISAME( 5 ) = ALS.EQ.ALPHA
+ ISAME( 6 ) = LDE( AS, AA, LAA )
+ ISAME( 7 ) = LDAS.EQ.LDA
+ ISAME( 8 ) = BETS.EQ.BETA
+ IF( NULL )THEN
+ ISAME( 9 ) = LDE( CS, CC, LCC )
+ ELSE
+ ISAME( 9 ) = LDERES( 'SY', UPLO, N, N, CS,
+ $ CC, LDC )
+ END IF
+ ISAME( 10 ) = LDCS.EQ.LDC
+*
+* If data was incorrectly changed, report and
+* return.
+*
+ SAME = .TRUE.
+ DO 30 I = 1, NARGS
+ SAME = SAME.AND.ISAME( I )
+ IF( .NOT.ISAME( I ) )
+ $ WRITE( NOUT, FMT = 9998 )I
+ 30 CONTINUE
+ IF( .NOT.SAME )THEN
+ FATAL = .TRUE.
+ GO TO 120
+ END IF
+*
+ IF( .NOT.NULL )THEN
+*
+* Check the result column by column.
+*
+ JC = 1
+ DO 40 J = 1, N
+ IF( UPPER )THEN
+ JJ = 1
+ LJ = J
+ ELSE
+ JJ = J
+ LJ = N - J + 1
+ END IF
+ IF( TRAN )THEN
+ CALL DMMCH( 'T', 'N', LJ, 1, K, ALPHA,
+ $ A( 1, JJ ), NMAX,
+ $ A( 1, J ), NMAX, BETA,
+ $ C( JJ, J ), NMAX, CT, G,
+ $ CC( JC ), LDC, EPS, ERR,
+ $ FATAL, NOUT, .TRUE. )
+ ELSE
+ CALL DMMCH( 'N', 'T', LJ, 1, K, ALPHA,
+ $ A( JJ, 1 ), NMAX,
+ $ A( J, 1 ), NMAX, BETA,
+ $ C( JJ, J ), NMAX, CT, G,
+ $ CC( JC ), LDC, EPS, ERR,
+ $ FATAL, NOUT, .TRUE. )
+ END IF
+ IF( UPPER )THEN
+ JC = JC + LDC
+ ELSE
+ JC = JC + LDC + 1
+ END IF
+ ERRMAX = MAX( ERRMAX, ERR )
+* If got really bad answer, report and
+* return.
+ IF( FATAL )
+ $ GO TO 110
+ 40 CONTINUE
+ END IF
+*
+ 50 CONTINUE
+*
+ 60 CONTINUE
+*
+ 70 CONTINUE
+*
+ 80 CONTINUE
+*
+ 90 CONTINUE
+*
+ 100 CONTINUE
+*
+* Report result.
+*
+ IF( ERRMAX.LT.THRESH )THEN
+ WRITE( NOUT, FMT = 9999 )SNAME, NC
+ ELSE
+ WRITE( NOUT, FMT = 9997 )SNAME, NC, ERRMAX
+ END IF
+ GO TO 130
+*
+ 110 CONTINUE
+ IF( N.GT.1 )
+ $ WRITE( NOUT, FMT = 9995 )J
+*
+ 120 CONTINUE
+ WRITE( NOUT, FMT = 9996 )SNAME
+ WRITE( NOUT, FMT = 9994 )NC, SNAME, UPLO, TRANS, N, K, ALPHA,
+ $ LDA, BETA, LDC
+*
+ 130 CONTINUE
+ RETURN
+*
+ 9999 FORMAT( ' ', A6, ' PASSED THE COMPUTATIONAL TESTS (', I6, ' CALL',
+ $ 'S)' )
+ 9998 FORMAT( ' ******* FATAL ERROR - PARAMETER NUMBER ', I2, ' WAS CH',
+ $ 'ANGED INCORRECTLY *******' )
+ 9997 FORMAT( ' ', A6, ' COMPLETED THE COMPUTATIONAL TESTS (', I6, ' C',
+ $ 'ALLS)', /' ******* BUT WITH MAXIMUM TEST RATIO', F8.2,
+ $ ' - SUSPECT *******' )
+ 9996 FORMAT( ' ******* ', A6, ' FAILED ON CALL NUMBER:' )
+ 9995 FORMAT( ' THESE ARE THE RESULTS FOR COLUMN ', I3 )
+ 9994 FORMAT( 1X, I6, ': ', A6, '(', 2( '''', A1, ''',' ), 2( I3, ',' ),
+ $ F4.1, ', A,', I3, ',', F4.1, ', C,', I3, ') .' )
+ 9993 FORMAT( ' ******* FATAL ERROR - ERROR-EXIT TAKEN ON VALID CALL *',
+ $ '******' )
+*
+* End of DCHK4.
+*
+ END
+ SUBROUTINE DCHK5( SNAME, EPS, THRESH, NOUT, NTRA, TRACE, REWI,
+ $ FATAL, NIDIM, IDIM, NALF, ALF, NBET, BET, NMAX,
+ $ AB, AA, AS, BB, BS, C, CC, CS, CT, G, W )
+*
+* Tests DSYR2K.
+*
+* Auxiliary routine for test program for Level 3 Blas.
+*
+* -- Written on 8-February-1989.
+* Jack Dongarra, Argonne National Laboratory.
+* Iain Duff, AERE Harwell.
+* Jeremy Du Croz, Numerical Algorithms Group Ltd.
+* Sven Hammarling, Numerical Algorithms Group Ltd.
+*
+* .. Parameters ..
+ DOUBLE PRECISION ZERO
+ PARAMETER ( ZERO = 0.0D0 )
+* .. Scalar Arguments ..
+ DOUBLE PRECISION EPS, THRESH
+ INTEGER NALF, NBET, NIDIM, NMAX, NOUT, NTRA
+ LOGICAL FATAL, REWI, TRACE
+ CHARACTER*6 SNAME
+* .. Array Arguments ..
+ DOUBLE PRECISION AA( NMAX*NMAX ), AB( 2*NMAX*NMAX ),
+ $ ALF( NALF ), AS( NMAX*NMAX ), BB( NMAX*NMAX ),
+ $ BET( NBET ), BS( NMAX*NMAX ), C( NMAX, NMAX ),
+ $ CC( NMAX*NMAX ), CS( NMAX*NMAX ), CT( NMAX ),
+ $ G( NMAX ), W( 2*NMAX )
+ INTEGER IDIM( NIDIM )
+* .. Local Scalars ..
+ DOUBLE PRECISION ALPHA, ALS, BETA, BETS, ERR, ERRMAX
+ INTEGER I, IA, IB, ICT, ICU, IK, IN, J, JC, JJ, JJAB,
+ $ K, KS, LAA, LBB, LCC, LDA, LDAS, LDB, LDBS,
+ $ LDC, LDCS, LJ, MA, N, NA, NARGS, NC, NS
+ LOGICAL NULL, RESET, SAME, TRAN, UPPER
+ CHARACTER*1 TRANS, TRANSS, UPLO, UPLOS
+ CHARACTER*2 ICHU
+ CHARACTER*3 ICHT
+* .. Local Arrays ..
+ LOGICAL ISAME( 13 )
+* .. External Functions ..
+ LOGICAL LDE, LDERES
+ EXTERNAL LDE, LDERES
+* .. External Subroutines ..
+ EXTERNAL DMAKE, DMMCH, DSYR2K
+* .. Intrinsic Functions ..
+ INTRINSIC MAX
+* .. Scalars in Common ..
+ INTEGER INFOT, NOUTC
+ LOGICAL LERR, OK
+* .. Common blocks ..
+ COMMON /INFOC/INFOT, NOUTC, OK, LERR
+* .. Data statements ..
+ DATA ICHT/'NTC'/, ICHU/'UL'/
+* .. Executable Statements ..
+*
+ NARGS = 12
+ NC = 0
+ RESET = .TRUE.
+ ERRMAX = ZERO
+*
+ DO 130 IN = 1, NIDIM
+ N = IDIM( IN )
+* Set LDC to 1 more than minimum value if room.
+ LDC = N
+ IF( LDC.LT.NMAX )
+ $ LDC = LDC + 1
+* Skip tests if not enough room.
+ IF( LDC.GT.NMAX )
+ $ GO TO 130
+ LCC = LDC*N
+ NULL = N.LE.0
+*
+ DO 120 IK = 1, NIDIM
+ K = IDIM( IK )
+*
+ DO 110 ICT = 1, 3
+ TRANS = ICHT( ICT: ICT )
+ TRAN = TRANS.EQ.'T'.OR.TRANS.EQ.'C'
+ IF( TRAN )THEN
+ MA = K
+ NA = N
+ ELSE
+ MA = N
+ NA = K
+ END IF
+* Set LDA to 1 more than minimum value if room.
+ LDA = MA
+ IF( LDA.LT.NMAX )
+ $ LDA = LDA + 1
+* Skip tests if not enough room.
+ IF( LDA.GT.NMAX )
+ $ GO TO 110
+ LAA = LDA*NA
+*
+* Generate the matrix A.
+*
+ IF( TRAN )THEN
+ CALL DMAKE( 'GE', ' ', ' ', MA, NA, AB, 2*NMAX, AA,
+ $ LDA, RESET, ZERO )
+ ELSE
+ CALL DMAKE( 'GE', ' ', ' ', MA, NA, AB, NMAX, AA, LDA,
+ $ RESET, ZERO )
+ END IF
+*
+* Generate the matrix B.
+*
+ LDB = LDA
+ LBB = LAA
+ IF( TRAN )THEN
+ CALL DMAKE( 'GE', ' ', ' ', MA, NA, AB( K + 1 ),
+ $ 2*NMAX, BB, LDB, RESET, ZERO )
+ ELSE
+ CALL DMAKE( 'GE', ' ', ' ', MA, NA, AB( K*NMAX + 1 ),
+ $ NMAX, BB, LDB, RESET, ZERO )
+ END IF
+*
+ DO 100 ICU = 1, 2
+ UPLO = ICHU( ICU: ICU )
+ UPPER = UPLO.EQ.'U'
+*
+ DO 90 IA = 1, NALF
+ ALPHA = ALF( IA )
+*
+ DO 80 IB = 1, NBET
+ BETA = BET( IB )
+*
+* Generate the matrix C.
+*
+ CALL DMAKE( 'SY', UPLO, ' ', N, N, C, NMAX, CC,
+ $ LDC, RESET, ZERO )
+*
+ NC = NC + 1
+*
+* Save every datum before calling the subroutine.
+*
+ UPLOS = UPLO
+ TRANSS = TRANS
+ NS = N
+ KS = K
+ ALS = ALPHA
+ DO 10 I = 1, LAA
+ AS( I ) = AA( I )
+ 10 CONTINUE
+ LDAS = LDA
+ DO 20 I = 1, LBB
+ BS( I ) = BB( I )
+ 20 CONTINUE
+ LDBS = LDB
+ BETS = BETA
+ DO 30 I = 1, LCC
+ CS( I ) = CC( I )
+ 30 CONTINUE
+ LDCS = LDC
+*
+* Call the subroutine.
+*
+ IF( TRACE )
+ $ WRITE( NTRA, FMT = 9994 )NC, SNAME, UPLO,
+ $ TRANS, N, K, ALPHA, LDA, LDB, BETA, LDC
+ IF( REWI )
+ $ REWIND NTRA
+ CALL DSYR2K( UPLO, TRANS, N, K, ALPHA, AA, LDA,
+ $ BB, LDB, BETA, CC, LDC )
+*
+* Check if error-exit was taken incorrectly.
+*
+ IF( .NOT.OK )THEN
+ WRITE( NOUT, FMT = 9993 )
+ FATAL = .TRUE.
+ GO TO 150
+ END IF
+*
+* See what data changed inside subroutines.
+*
+ ISAME( 1 ) = UPLOS.EQ.UPLO
+ ISAME( 2 ) = TRANSS.EQ.TRANS
+ ISAME( 3 ) = NS.EQ.N
+ ISAME( 4 ) = KS.EQ.K
+ ISAME( 5 ) = ALS.EQ.ALPHA
+ ISAME( 6 ) = LDE( AS, AA, LAA )
+ ISAME( 7 ) = LDAS.EQ.LDA
+ ISAME( 8 ) = LDE( BS, BB, LBB )
+ ISAME( 9 ) = LDBS.EQ.LDB
+ ISAME( 10 ) = BETS.EQ.BETA
+ IF( NULL )THEN
+ ISAME( 11 ) = LDE( CS, CC, LCC )
+ ELSE
+ ISAME( 11 ) = LDERES( 'SY', UPLO, N, N, CS,
+ $ CC, LDC )
+ END IF
+ ISAME( 12 ) = LDCS.EQ.LDC
+*
+* If data was incorrectly changed, report and
+* return.
+*
+ SAME = .TRUE.
+ DO 40 I = 1, NARGS
+ SAME = SAME.AND.ISAME( I )
+ IF( .NOT.ISAME( I ) )
+ $ WRITE( NOUT, FMT = 9998 )I
+ 40 CONTINUE
+ IF( .NOT.SAME )THEN
+ FATAL = .TRUE.
+ GO TO 150
+ END IF
+*
+ IF( .NOT.NULL )THEN
+*
+* Check the result column by column.
+*
+ JJAB = 1
+ JC = 1
+ DO 70 J = 1, N
+ IF( UPPER )THEN
+ JJ = 1
+ LJ = J
+ ELSE
+ JJ = J
+ LJ = N - J + 1
+ END IF
+ IF( TRAN )THEN
+ DO 50 I = 1, K
+ W( I ) = AB( ( J - 1 )*2*NMAX + K +
+ $ I )
+ W( K + I ) = AB( ( J - 1 )*2*NMAX +
+ $ I )
+ 50 CONTINUE
+ CALL DMMCH( 'T', 'N', LJ, 1, 2*K,
+ $ ALPHA, AB( JJAB ), 2*NMAX,
+ $ W, 2*NMAX, BETA,
+ $ C( JJ, J ), NMAX, CT, G,
+ $ CC( JC ), LDC, EPS, ERR,
+ $ FATAL, NOUT, .TRUE. )
+ ELSE
+ DO 60 I = 1, K
+ W( I ) = AB( ( K + I - 1 )*NMAX +
+ $ J )
+ W( K + I ) = AB( ( I - 1 )*NMAX +
+ $ J )
+ 60 CONTINUE
+ CALL DMMCH( 'N', 'N', LJ, 1, 2*K,
+ $ ALPHA, AB( JJ ), NMAX, W,
+ $ 2*NMAX, BETA, C( JJ, J ),
+ $ NMAX, CT, G, CC( JC ), LDC,
+ $ EPS, ERR, FATAL, NOUT,
+ $ .TRUE. )
+ END IF
+ IF( UPPER )THEN
+ JC = JC + LDC
+ ELSE
+ JC = JC + LDC + 1
+ IF( TRAN )
+ $ JJAB = JJAB + 2*NMAX
+ END IF
+ ERRMAX = MAX( ERRMAX, ERR )
+* If got really bad answer, report and
+* return.
+ IF( FATAL )
+ $ GO TO 140
+ 70 CONTINUE
+ END IF
+*
+ 80 CONTINUE
+*
+ 90 CONTINUE
+*
+ 100 CONTINUE
+*
+ 110 CONTINUE
+*
+ 120 CONTINUE
+*
+ 130 CONTINUE
+*
+* Report result.
+*
+ IF( ERRMAX.LT.THRESH )THEN
+ WRITE( NOUT, FMT = 9999 )SNAME, NC
+ ELSE
+ WRITE( NOUT, FMT = 9997 )SNAME, NC, ERRMAX
+ END IF
+ GO TO 160
+*
+ 140 CONTINUE
+ IF( N.GT.1 )
+ $ WRITE( NOUT, FMT = 9995 )J
+*
+ 150 CONTINUE
+ WRITE( NOUT, FMT = 9996 )SNAME
+ WRITE( NOUT, FMT = 9994 )NC, SNAME, UPLO, TRANS, N, K, ALPHA,
+ $ LDA, LDB, BETA, LDC
+*
+ 160 CONTINUE
+ RETURN
+*
+ 9999 FORMAT( ' ', A6, ' PASSED THE COMPUTATIONAL TESTS (', I6, ' CALL',
+ $ 'S)' )
+ 9998 FORMAT( ' ******* FATAL ERROR - PARAMETER NUMBER ', I2, ' WAS CH',
+ $ 'ANGED INCORRECTLY *******' )
+ 9997 FORMAT( ' ', A6, ' COMPLETED THE COMPUTATIONAL TESTS (', I6, ' C',
+ $ 'ALLS)', /' ******* BUT WITH MAXIMUM TEST RATIO', F8.2,
+ $ ' - SUSPECT *******' )
+ 9996 FORMAT( ' ******* ', A6, ' FAILED ON CALL NUMBER:' )
+ 9995 FORMAT( ' THESE ARE THE RESULTS FOR COLUMN ', I3 )
+ 9994 FORMAT( 1X, I6, ': ', A6, '(', 2( '''', A1, ''',' ), 2( I3, ',' ),
+ $ F4.1, ', A,', I3, ', B,', I3, ',', F4.1, ', C,', I3, ') ',
+ $ ' .' )
+ 9993 FORMAT( ' ******* FATAL ERROR - ERROR-EXIT TAKEN ON VALID CALL *',
+ $ '******' )
+*
+* End of DCHK5.
+*
+ END
+ SUBROUTINE DCHKE( ISNUM, SRNAMT, NOUT )
+*
+* Tests the error exits from the Level 3 Blas.
+* Requires a special version of the error-handling routine XERBLA.
+* A, B and C should not need to be defined.
+*
+* Auxiliary routine for test program for Level 3 Blas.
+*
+* -- Written on 8-February-1989.
+* Jack Dongarra, Argonne National Laboratory.
+* Iain Duff, AERE Harwell.
+* Jeremy Du Croz, Numerical Algorithms Group Ltd.
+* Sven Hammarling, Numerical Algorithms Group Ltd.
+*
+* 3-19-92: Initialize ALPHA and BETA (eca)
+* 3-19-92: Fix argument 12 in calls to SSYMM with INFOT = 9 (eca)
+*
+* .. Scalar Arguments ..
+ INTEGER ISNUM, NOUT
+ CHARACTER*6 SRNAMT
+* .. Scalars in Common ..
+ INTEGER INFOT, NOUTC
+ LOGICAL LERR, OK
+* .. Parameters ..
+ DOUBLE PRECISION ONE, TWO
+ PARAMETER ( ONE = 1.0D0, TWO = 2.0D0 )
+* .. Local Scalars ..
+ DOUBLE PRECISION ALPHA, BETA
+* .. Local Arrays ..
+ DOUBLE PRECISION A( 2, 1 ), B( 2, 1 ), C( 2, 1 )
+* .. External Subroutines ..
+ EXTERNAL CHKXER, DGEMM, DSYMM, DSYR2K, DSYRK, DTRMM,
+ $ DTRSM
+* .. Common blocks ..
+ COMMON /INFOC/INFOT, NOUTC, OK, LERR
+* .. Executable Statements ..
+* OK is set to .FALSE. by the special version of XERBLA or by CHKXER
+* if anything is wrong.
+ OK = .TRUE.
+* LERR is set to .TRUE. by the special version of XERBLA each time
+* it is called, and is then tested and re-set by CHKXER.
+ LERR = .FALSE.
+*
+* Initialize ALPHA and BETA.
+*
+ ALPHA = ONE
+ BETA = TWO
+*
+ GO TO ( 10, 20, 30, 40, 50, 60 )ISNUM
+ 10 INFOT = 1
+ CALL DGEMM( '/', 'N', 0, 0, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 1
+ CALL DGEMM( '/', 'T', 0, 0, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 2
+ CALL DGEMM( 'N', '/', 0, 0, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 2
+ CALL DGEMM( 'T', '/', 0, 0, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 3
+ CALL DGEMM( 'N', 'N', -1, 0, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 3
+ CALL DGEMM( 'N', 'T', -1, 0, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 3
+ CALL DGEMM( 'T', 'N', -1, 0, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 3
+ CALL DGEMM( 'T', 'T', -1, 0, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 4
+ CALL DGEMM( 'N', 'N', 0, -1, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 4
+ CALL DGEMM( 'N', 'T', 0, -1, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 4
+ CALL DGEMM( 'T', 'N', 0, -1, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 4
+ CALL DGEMM( 'T', 'T', 0, -1, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 5
+ CALL DGEMM( 'N', 'N', 0, 0, -1, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 5
+ CALL DGEMM( 'N', 'T', 0, 0, -1, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 5
+ CALL DGEMM( 'T', 'N', 0, 0, -1, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 5
+ CALL DGEMM( 'T', 'T', 0, 0, -1, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 8
+ CALL DGEMM( 'N', 'N', 2, 0, 0, ALPHA, A, 1, B, 1, BETA, C, 2 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 8
+ CALL DGEMM( 'N', 'T', 2, 0, 0, ALPHA, A, 1, B, 1, BETA, C, 2 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 8
+ CALL DGEMM( 'T', 'N', 0, 0, 2, ALPHA, A, 1, B, 2, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 8
+ CALL DGEMM( 'T', 'T', 0, 0, 2, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 10
+ CALL DGEMM( 'N', 'N', 0, 0, 2, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 10
+ CALL DGEMM( 'T', 'N', 0, 0, 2, ALPHA, A, 2, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 10
+ CALL DGEMM( 'N', 'T', 0, 2, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 10
+ CALL DGEMM( 'T', 'T', 0, 2, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 13
+ CALL DGEMM( 'N', 'N', 2, 0, 0, ALPHA, A, 2, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 13
+ CALL DGEMM( 'N', 'T', 2, 0, 0, ALPHA, A, 2, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 13
+ CALL DGEMM( 'T', 'N', 2, 0, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 13
+ CALL DGEMM( 'T', 'T', 2, 0, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ GO TO 70
+ 20 INFOT = 1
+ CALL DSYMM( '/', 'U', 0, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 2
+ CALL DSYMM( 'L', '/', 0, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 3
+ CALL DSYMM( 'L', 'U', -1, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 3
+ CALL DSYMM( 'R', 'U', -1, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 3
+ CALL DSYMM( 'L', 'L', -1, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 3
+ CALL DSYMM( 'R', 'L', -1, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 4
+ CALL DSYMM( 'L', 'U', 0, -1, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 4
+ CALL DSYMM( 'R', 'U', 0, -1, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 4
+ CALL DSYMM( 'L', 'L', 0, -1, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 4
+ CALL DSYMM( 'R', 'L', 0, -1, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 7
+ CALL DSYMM( 'L', 'U', 2, 0, ALPHA, A, 1, B, 2, BETA, C, 2 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 7
+ CALL DSYMM( 'R', 'U', 0, 2, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 7
+ CALL DSYMM( 'L', 'L', 2, 0, ALPHA, A, 1, B, 2, BETA, C, 2 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 7
+ CALL DSYMM( 'R', 'L', 0, 2, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 9
+ CALL DSYMM( 'L', 'U', 2, 0, ALPHA, A, 2, B, 1, BETA, C, 2 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 9
+ CALL DSYMM( 'R', 'U', 2, 0, ALPHA, A, 1, B, 1, BETA, C, 2 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 9
+ CALL DSYMM( 'L', 'L', 2, 0, ALPHA, A, 2, B, 1, BETA, C, 2 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 9
+ CALL DSYMM( 'R', 'L', 2, 0, ALPHA, A, 1, B, 1, BETA, C, 2 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 12
+ CALL DSYMM( 'L', 'U', 2, 0, ALPHA, A, 2, B, 2, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 12
+ CALL DSYMM( 'R', 'U', 2, 0, ALPHA, A, 1, B, 2, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 12
+ CALL DSYMM( 'L', 'L', 2, 0, ALPHA, A, 2, B, 2, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 12
+ CALL DSYMM( 'R', 'L', 2, 0, ALPHA, A, 1, B, 2, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ GO TO 70
+ 30 INFOT = 1
+ CALL DTRMM( '/', 'U', 'N', 'N', 0, 0, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 2
+ CALL DTRMM( 'L', '/', 'N', 'N', 0, 0, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 3
+ CALL DTRMM( 'L', 'U', '/', 'N', 0, 0, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 4
+ CALL DTRMM( 'L', 'U', 'N', '/', 0, 0, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 5
+ CALL DTRMM( 'L', 'U', 'N', 'N', -1, 0, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 5
+ CALL DTRMM( 'L', 'U', 'T', 'N', -1, 0, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 5
+ CALL DTRMM( 'R', 'U', 'N', 'N', -1, 0, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 5
+ CALL DTRMM( 'R', 'U', 'T', 'N', -1, 0, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 5
+ CALL DTRMM( 'L', 'L', 'N', 'N', -1, 0, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 5
+ CALL DTRMM( 'L', 'L', 'T', 'N', -1, 0, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 5
+ CALL DTRMM( 'R', 'L', 'N', 'N', -1, 0, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 5
+ CALL DTRMM( 'R', 'L', 'T', 'N', -1, 0, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 6
+ CALL DTRMM( 'L', 'U', 'N', 'N', 0, -1, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 6
+ CALL DTRMM( 'L', 'U', 'T', 'N', 0, -1, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 6
+ CALL DTRMM( 'R', 'U', 'N', 'N', 0, -1, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 6
+ CALL DTRMM( 'R', 'U', 'T', 'N', 0, -1, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 6
+ CALL DTRMM( 'L', 'L', 'N', 'N', 0, -1, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 6
+ CALL DTRMM( 'L', 'L', 'T', 'N', 0, -1, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 6
+ CALL DTRMM( 'R', 'L', 'N', 'N', 0, -1, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 6
+ CALL DTRMM( 'R', 'L', 'T', 'N', 0, -1, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 9
+ CALL DTRMM( 'L', 'U', 'N', 'N', 2, 0, ALPHA, A, 1, B, 2 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 9
+ CALL DTRMM( 'L', 'U', 'T', 'N', 2, 0, ALPHA, A, 1, B, 2 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 9
+ CALL DTRMM( 'R', 'U', 'N', 'N', 0, 2, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 9
+ CALL DTRMM( 'R', 'U', 'T', 'N', 0, 2, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 9
+ CALL DTRMM( 'L', 'L', 'N', 'N', 2, 0, ALPHA, A, 1, B, 2 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 9
+ CALL DTRMM( 'L', 'L', 'T', 'N', 2, 0, ALPHA, A, 1, B, 2 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 9
+ CALL DTRMM( 'R', 'L', 'N', 'N', 0, 2, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 9
+ CALL DTRMM( 'R', 'L', 'T', 'N', 0, 2, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 11
+ CALL DTRMM( 'L', 'U', 'N', 'N', 2, 0, ALPHA, A, 2, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 11
+ CALL DTRMM( 'L', 'U', 'T', 'N', 2, 0, ALPHA, A, 2, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 11
+ CALL DTRMM( 'R', 'U', 'N', 'N', 2, 0, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 11
+ CALL DTRMM( 'R', 'U', 'T', 'N', 2, 0, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 11
+ CALL DTRMM( 'L', 'L', 'N', 'N', 2, 0, ALPHA, A, 2, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 11
+ CALL DTRMM( 'L', 'L', 'T', 'N', 2, 0, ALPHA, A, 2, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 11
+ CALL DTRMM( 'R', 'L', 'N', 'N', 2, 0, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 11
+ CALL DTRMM( 'R', 'L', 'T', 'N', 2, 0, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ GO TO 70
+ 40 INFOT = 1
+ CALL DTRSM( '/', 'U', 'N', 'N', 0, 0, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 2
+ CALL DTRSM( 'L', '/', 'N', 'N', 0, 0, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 3
+ CALL DTRSM( 'L', 'U', '/', 'N', 0, 0, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 4
+ CALL DTRSM( 'L', 'U', 'N', '/', 0, 0, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 5
+ CALL DTRSM( 'L', 'U', 'N', 'N', -1, 0, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 5
+ CALL DTRSM( 'L', 'U', 'T', 'N', -1, 0, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 5
+ CALL DTRSM( 'R', 'U', 'N', 'N', -1, 0, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 5
+ CALL DTRSM( 'R', 'U', 'T', 'N', -1, 0, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 5
+ CALL DTRSM( 'L', 'L', 'N', 'N', -1, 0, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 5
+ CALL DTRSM( 'L', 'L', 'T', 'N', -1, 0, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 5
+ CALL DTRSM( 'R', 'L', 'N', 'N', -1, 0, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 5
+ CALL DTRSM( 'R', 'L', 'T', 'N', -1, 0, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 6
+ CALL DTRSM( 'L', 'U', 'N', 'N', 0, -1, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 6
+ CALL DTRSM( 'L', 'U', 'T', 'N', 0, -1, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 6
+ CALL DTRSM( 'R', 'U', 'N', 'N', 0, -1, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 6
+ CALL DTRSM( 'R', 'U', 'T', 'N', 0, -1, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 6
+ CALL DTRSM( 'L', 'L', 'N', 'N', 0, -1, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 6
+ CALL DTRSM( 'L', 'L', 'T', 'N', 0, -1, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 6
+ CALL DTRSM( 'R', 'L', 'N', 'N', 0, -1, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 6
+ CALL DTRSM( 'R', 'L', 'T', 'N', 0, -1, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 9
+ CALL DTRSM( 'L', 'U', 'N', 'N', 2, 0, ALPHA, A, 1, B, 2 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 9
+ CALL DTRSM( 'L', 'U', 'T', 'N', 2, 0, ALPHA, A, 1, B, 2 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 9
+ CALL DTRSM( 'R', 'U', 'N', 'N', 0, 2, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 9
+ CALL DTRSM( 'R', 'U', 'T', 'N', 0, 2, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 9
+ CALL DTRSM( 'L', 'L', 'N', 'N', 2, 0, ALPHA, A, 1, B, 2 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 9
+ CALL DTRSM( 'L', 'L', 'T', 'N', 2, 0, ALPHA, A, 1, B, 2 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 9
+ CALL DTRSM( 'R', 'L', 'N', 'N', 0, 2, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 9
+ CALL DTRSM( 'R', 'L', 'T', 'N', 0, 2, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 11
+ CALL DTRSM( 'L', 'U', 'N', 'N', 2, 0, ALPHA, A, 2, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 11
+ CALL DTRSM( 'L', 'U', 'T', 'N', 2, 0, ALPHA, A, 2, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 11
+ CALL DTRSM( 'R', 'U', 'N', 'N', 2, 0, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 11
+ CALL DTRSM( 'R', 'U', 'T', 'N', 2, 0, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 11
+ CALL DTRSM( 'L', 'L', 'N', 'N', 2, 0, ALPHA, A, 2, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 11
+ CALL DTRSM( 'L', 'L', 'T', 'N', 2, 0, ALPHA, A, 2, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 11
+ CALL DTRSM( 'R', 'L', 'N', 'N', 2, 0, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 11
+ CALL DTRSM( 'R', 'L', 'T', 'N', 2, 0, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ GO TO 70
+ 50 INFOT = 1
+ CALL DSYRK( '/', 'N', 0, 0, ALPHA, A, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 2
+ CALL DSYRK( 'U', '/', 0, 0, ALPHA, A, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 3
+ CALL DSYRK( 'U', 'N', -1, 0, ALPHA, A, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 3
+ CALL DSYRK( 'U', 'T', -1, 0, ALPHA, A, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 3
+ CALL DSYRK( 'L', 'N', -1, 0, ALPHA, A, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 3
+ CALL DSYRK( 'L', 'T', -1, 0, ALPHA, A, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 4
+ CALL DSYRK( 'U', 'N', 0, -1, ALPHA, A, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 4
+ CALL DSYRK( 'U', 'T', 0, -1, ALPHA, A, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 4
+ CALL DSYRK( 'L', 'N', 0, -1, ALPHA, A, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 4
+ CALL DSYRK( 'L', 'T', 0, -1, ALPHA, A, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 7
+ CALL DSYRK( 'U', 'N', 2, 0, ALPHA, A, 1, BETA, C, 2 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 7
+ CALL DSYRK( 'U', 'T', 0, 2, ALPHA, A, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 7
+ CALL DSYRK( 'L', 'N', 2, 0, ALPHA, A, 1, BETA, C, 2 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 7
+ CALL DSYRK( 'L', 'T', 0, 2, ALPHA, A, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 10
+ CALL DSYRK( 'U', 'N', 2, 0, ALPHA, A, 2, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 10
+ CALL DSYRK( 'U', 'T', 2, 0, ALPHA, A, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 10
+ CALL DSYRK( 'L', 'N', 2, 0, ALPHA, A, 2, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 10
+ CALL DSYRK( 'L', 'T', 2, 0, ALPHA, A, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ GO TO 70
+ 60 INFOT = 1
+ CALL DSYR2K( '/', 'N', 0, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 2
+ CALL DSYR2K( 'U', '/', 0, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 3
+ CALL DSYR2K( 'U', 'N', -1, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 3
+ CALL DSYR2K( 'U', 'T', -1, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 3
+ CALL DSYR2K( 'L', 'N', -1, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 3
+ CALL DSYR2K( 'L', 'T', -1, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 4
+ CALL DSYR2K( 'U', 'N', 0, -1, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 4
+ CALL DSYR2K( 'U', 'T', 0, -1, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 4
+ CALL DSYR2K( 'L', 'N', 0, -1, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 4
+ CALL DSYR2K( 'L', 'T', 0, -1, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 7
+ CALL DSYR2K( 'U', 'N', 2, 0, ALPHA, A, 1, B, 1, BETA, C, 2 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 7
+ CALL DSYR2K( 'U', 'T', 0, 2, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 7
+ CALL DSYR2K( 'L', 'N', 2, 0, ALPHA, A, 1, B, 1, BETA, C, 2 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 7
+ CALL DSYR2K( 'L', 'T', 0, 2, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 9
+ CALL DSYR2K( 'U', 'N', 2, 0, ALPHA, A, 2, B, 1, BETA, C, 2 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 9
+ CALL DSYR2K( 'U', 'T', 0, 2, ALPHA, A, 2, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 9
+ CALL DSYR2K( 'L', 'N', 2, 0, ALPHA, A, 2, B, 1, BETA, C, 2 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 9
+ CALL DSYR2K( 'L', 'T', 0, 2, ALPHA, A, 2, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 12
+ CALL DSYR2K( 'U', 'N', 2, 0, ALPHA, A, 2, B, 2, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 12
+ CALL DSYR2K( 'U', 'T', 2, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 12
+ CALL DSYR2K( 'L', 'N', 2, 0, ALPHA, A, 2, B, 2, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 12
+ CALL DSYR2K( 'L', 'T', 2, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+*
+ 70 IF( OK )THEN
+ WRITE( NOUT, FMT = 9999 )SRNAMT
+ ELSE
+ WRITE( NOUT, FMT = 9998 )SRNAMT
+ END IF
+ RETURN
+*
+ 9999 FORMAT( ' ', A6, ' PASSED THE TESTS OF ERROR-EXITS' )
+ 9998 FORMAT( ' ******* ', A6, ' FAILED THE TESTS OF ERROR-EXITS *****',
+ $ '**' )
+*
+* End of DCHKE.
+*
+ END
+ SUBROUTINE DMAKE( TYPE, UPLO, DIAG, M, N, A, NMAX, AA, LDA, RESET,
+ $ TRANSL )
+*
+* Generates values for an M by N matrix A.
+* Stores the values in the array AA in the data structure required
+* by the routine, with unwanted elements set to rogue value.
+*
+* TYPE is 'GE', 'SY' or 'TR'.
+*
+* Auxiliary routine for test program for Level 3 Blas.
+*
+* -- Written on 8-February-1989.
+* Jack Dongarra, Argonne National Laboratory.
+* Iain Duff, AERE Harwell.
+* Jeremy Du Croz, Numerical Algorithms Group Ltd.
+* Sven Hammarling, Numerical Algorithms Group Ltd.
+*
+* .. Parameters ..
+ DOUBLE PRECISION ZERO, ONE
+ PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0 )
+ DOUBLE PRECISION ROGUE
+ PARAMETER ( ROGUE = -1.0D10 )
+* .. Scalar Arguments ..
+ DOUBLE PRECISION TRANSL
+ INTEGER LDA, M, N, NMAX
+ LOGICAL RESET
+ CHARACTER*1 DIAG, UPLO
+ CHARACTER*2 TYPE
+* .. Array Arguments ..
+ DOUBLE PRECISION A( NMAX, * ), AA( * )
+* .. Local Scalars ..
+ INTEGER I, IBEG, IEND, J
+ LOGICAL GEN, LOWER, SYM, TRI, UNIT, UPPER
+* .. External Functions ..
+ DOUBLE PRECISION DBEG
+ EXTERNAL DBEG
+* .. Executable Statements ..
+ GEN = TYPE.EQ.'GE'
+ SYM = TYPE.EQ.'SY'
+ TRI = TYPE.EQ.'TR'
+ UPPER = ( SYM.OR.TRI ).AND.UPLO.EQ.'U'
+ LOWER = ( SYM.OR.TRI ).AND.UPLO.EQ.'L'
+ UNIT = TRI.AND.DIAG.EQ.'U'
+*
+* Generate data in array A.
+*
+ DO 20 J = 1, N
+ DO 10 I = 1, M
+ IF( GEN.OR.( UPPER.AND.I.LE.J ).OR.( LOWER.AND.I.GE.J ) )
+ $ THEN
+ A( I, J ) = DBEG( RESET ) + TRANSL
+ IF( I.NE.J )THEN
+* Set some elements to zero
+ IF( N.GT.3.AND.J.EQ.N/2 )
+ $ A( I, J ) = ZERO
+ IF( SYM )THEN
+ A( J, I ) = A( I, J )
+ ELSE IF( TRI )THEN
+ A( J, I ) = ZERO
+ END IF
+ END IF
+ END IF
+ 10 CONTINUE
+ IF( TRI )
+ $ A( J, J ) = A( J, J ) + ONE
+ IF( UNIT )
+ $ A( J, J ) = ONE
+ 20 CONTINUE
+*
+* Store elements in array AS in data structure required by routine.
+*
+ IF( TYPE.EQ.'GE' )THEN
+ DO 50 J = 1, N
+ DO 30 I = 1, M
+ AA( I + ( J - 1 )*LDA ) = A( I, J )
+ 30 CONTINUE
+ DO 40 I = M + 1, LDA
+ AA( I + ( J - 1 )*LDA ) = ROGUE
+ 40 CONTINUE
+ 50 CONTINUE
+ ELSE IF( TYPE.EQ.'SY'.OR.TYPE.EQ.'TR' )THEN
+ DO 90 J = 1, N
+ IF( UPPER )THEN
+ IBEG = 1
+ IF( UNIT )THEN
+ IEND = J - 1
+ ELSE
+ IEND = J
+ END IF
+ ELSE
+ IF( UNIT )THEN
+ IBEG = J + 1
+ ELSE
+ IBEG = J
+ END IF
+ IEND = N
+ END IF
+ DO 60 I = 1, IBEG - 1
+ AA( I + ( J - 1 )*LDA ) = ROGUE
+ 60 CONTINUE
+ DO 70 I = IBEG, IEND
+ AA( I + ( J - 1 )*LDA ) = A( I, J )
+ 70 CONTINUE
+ DO 80 I = IEND + 1, LDA
+ AA( I + ( J - 1 )*LDA ) = ROGUE
+ 80 CONTINUE
+ 90 CONTINUE
+ END IF
+ RETURN
+*
+* End of DMAKE.
+*
+ END
+ SUBROUTINE DMMCH( TRANSA, TRANSB, M, N, KK, ALPHA, A, LDA, B, LDB,
+ $ BETA, C, LDC, CT, G, CC, LDCC, EPS, ERR, FATAL,
+ $ NOUT, MV )
+*
+* Checks the results of the computational tests.
+*
+* Auxiliary routine for test program for Level 3 Blas.
+*
+* -- Written on 8-February-1989.
+* Jack Dongarra, Argonne National Laboratory.
+* Iain Duff, AERE Harwell.
+* Jeremy Du Croz, Numerical Algorithms Group Ltd.
+* Sven Hammarling, Numerical Algorithms Group Ltd.
+*
+* .. Parameters ..
+ DOUBLE PRECISION ZERO, ONE
+ PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0 )
+* .. Scalar Arguments ..
+ DOUBLE PRECISION ALPHA, BETA, EPS, ERR
+ INTEGER KK, LDA, LDB, LDC, LDCC, M, N, NOUT
+ LOGICAL FATAL, MV
+ CHARACTER*1 TRANSA, TRANSB
+* .. Array Arguments ..
+ DOUBLE PRECISION A( LDA, * ), B( LDB, * ), C( LDC, * ),
+ $ CC( LDCC, * ), CT( * ), G( * )
+* .. Local Scalars ..
+ DOUBLE PRECISION ERRI
+ INTEGER I, J, K
+ LOGICAL TRANA, TRANB
+* .. Intrinsic Functions ..
+ INTRINSIC ABS, MAX, SQRT
+* .. Executable Statements ..
+ TRANA = TRANSA.EQ.'T'.OR.TRANSA.EQ.'C'
+ TRANB = TRANSB.EQ.'T'.OR.TRANSB.EQ.'C'
+*
+* Compute expected result, one column at a time, in CT using data
+* in A, B and C.
+* Compute gauges in G.
+*
+ DO 120 J = 1, N
+*
+ DO 10 I = 1, M
+ CT( I ) = ZERO
+ G( I ) = ZERO
+ 10 CONTINUE
+ IF( .NOT.TRANA.AND..NOT.TRANB )THEN
+ DO 30 K = 1, KK
+ DO 20 I = 1, M
+ CT( I ) = CT( I ) + A( I, K )*B( K, J )
+ G( I ) = G( I ) + ABS( A( I, K ) )*ABS( B( K, J ) )
+ 20 CONTINUE
+ 30 CONTINUE
+ ELSE IF( TRANA.AND..NOT.TRANB )THEN
+ DO 50 K = 1, KK
+ DO 40 I = 1, M
+ CT( I ) = CT( I ) + A( K, I )*B( K, J )
+ G( I ) = G( I ) + ABS( A( K, I ) )*ABS( B( K, J ) )
+ 40 CONTINUE
+ 50 CONTINUE
+ ELSE IF( .NOT.TRANA.AND.TRANB )THEN
+ DO 70 K = 1, KK
+ DO 60 I = 1, M
+ CT( I ) = CT( I ) + A( I, K )*B( J, K )
+ G( I ) = G( I ) + ABS( A( I, K ) )*ABS( B( J, K ) )
+ 60 CONTINUE
+ 70 CONTINUE
+ ELSE IF( TRANA.AND.TRANB )THEN
+ DO 90 K = 1, KK
+ DO 80 I = 1, M
+ CT( I ) = CT( I ) + A( K, I )*B( J, K )
+ G( I ) = G( I ) + ABS( A( K, I ) )*ABS( B( J, K ) )
+ 80 CONTINUE
+ 90 CONTINUE
+ END IF
+ DO 100 I = 1, M
+ CT( I ) = ALPHA*CT( I ) + BETA*C( I, J )
+ G( I ) = ABS( ALPHA )*G( I ) + ABS( BETA )*ABS( C( I, J ) )
+ 100 CONTINUE
+*
+* Compute the error ratio for this result.
+*
+ ERR = ZERO
+ DO 110 I = 1, M
+ ERRI = ABS( CT( I ) - CC( I, J ) )/EPS
+ IF( G( I ).NE.ZERO )
+ $ ERRI = ERRI/G( I )
+ ERR = MAX( ERR, ERRI )
+ IF( ERR*SQRT( EPS ).GE.ONE )
+ $ GO TO 130
+ 110 CONTINUE
+*
+ 120 CONTINUE
+*
+* If the loop completes, all results are at least half accurate.
+ GO TO 150
+*
+* Report fatal error.
+*
+ 130 FATAL = .TRUE.
+ WRITE( NOUT, FMT = 9999 )
+ DO 140 I = 1, M
+ IF( MV )THEN
+ WRITE( NOUT, FMT = 9998 )I, CT( I ), CC( I, J )
+ ELSE
+ WRITE( NOUT, FMT = 9998 )I, CC( I, J ), CT( I )
+ END IF
+ 140 CONTINUE
+ IF( N.GT.1 )
+ $ WRITE( NOUT, FMT = 9997 )J
+*
+ 150 CONTINUE
+ RETURN
+*
+ 9999 FORMAT( ' ******* FATAL ERROR - COMPUTED RESULT IS LESS THAN HAL',
+ $ 'F ACCURATE *******', /' EXPECTED RESULT COMPU',
+ $ 'TED RESULT' )
+ 9998 FORMAT( 1X, I7, 2G18.6 )
+ 9997 FORMAT( ' THESE ARE THE RESULTS FOR COLUMN ', I3 )
+*
+* End of DMMCH.
+*
+ END
+ LOGICAL FUNCTION LDE( RI, RJ, LR )
+*
+* Tests if two arrays are identical.
+*
+* Auxiliary routine for test program for Level 3 Blas.
+*
+* -- Written on 8-February-1989.
+* Jack Dongarra, Argonne National Laboratory.
+* Iain Duff, AERE Harwell.
+* Jeremy Du Croz, Numerical Algorithms Group Ltd.
+* Sven Hammarling, Numerical Algorithms Group Ltd.
+*
+* .. Scalar Arguments ..
+ INTEGER LR
+* .. Array Arguments ..
+ DOUBLE PRECISION RI( * ), RJ( * )
+* .. Local Scalars ..
+ INTEGER I
+* .. Executable Statements ..
+ DO 10 I = 1, LR
+ IF( RI( I ).NE.RJ( I ) )
+ $ GO TO 20
+ 10 CONTINUE
+ LDE = .TRUE.
+ GO TO 30
+ 20 CONTINUE
+ LDE = .FALSE.
+ 30 RETURN
+*
+* End of LDE.
+*
+ END
+ LOGICAL FUNCTION LDERES( TYPE, UPLO, M, N, AA, AS, LDA )
+*
+* Tests if selected elements in two arrays are equal.
+*
+* TYPE is 'GE' or 'SY'.
+*
+* Auxiliary routine for test program for Level 3 Blas.
+*
+* -- Written on 8-February-1989.
+* Jack Dongarra, Argonne National Laboratory.
+* Iain Duff, AERE Harwell.
+* Jeremy Du Croz, Numerical Algorithms Group Ltd.
+* Sven Hammarling, Numerical Algorithms Group Ltd.
+*
+* .. Scalar Arguments ..
+ INTEGER LDA, M, N
+ CHARACTER*1 UPLO
+ CHARACTER*2 TYPE
+* .. Array Arguments ..
+ DOUBLE PRECISION AA( LDA, * ), AS( LDA, * )
+* .. Local Scalars ..
+ INTEGER I, IBEG, IEND, J
+ LOGICAL UPPER
+* .. Executable Statements ..
+ UPPER = UPLO.EQ.'U'
+ IF( TYPE.EQ.'GE' )THEN
+ DO 20 J = 1, N
+ DO 10 I = M + 1, LDA
+ IF( AA( I, J ).NE.AS( I, J ) )
+ $ GO TO 70
+ 10 CONTINUE
+ 20 CONTINUE
+ ELSE IF( TYPE.EQ.'SY' )THEN
+ DO 50 J = 1, N
+ IF( UPPER )THEN
+ IBEG = 1
+ IEND = J
+ ELSE
+ IBEG = J
+ IEND = N
+ END IF
+ DO 30 I = 1, IBEG - 1
+ IF( AA( I, J ).NE.AS( I, J ) )
+ $ GO TO 70
+ 30 CONTINUE
+ DO 40 I = IEND + 1, LDA
+ IF( AA( I, J ).NE.AS( I, J ) )
+ $ GO TO 70
+ 40 CONTINUE
+ 50 CONTINUE
+ END IF
+*
+ LDERES = .TRUE.
+ GO TO 80
+ 70 CONTINUE
+ LDERES = .FALSE.
+ 80 RETURN
+*
+* End of LDERES.
+*
+ END
+ DOUBLE PRECISION FUNCTION DBEG( RESET )
+*
+* Generates random numbers uniformly distributed between -0.5 and 0.5.
+*
+* Auxiliary routine for test program for Level 3 Blas.
+*
+* -- Written on 8-February-1989.
+* Jack Dongarra, Argonne National Laboratory.
+* Iain Duff, AERE Harwell.
+* Jeremy Du Croz, Numerical Algorithms Group Ltd.
+* Sven Hammarling, Numerical Algorithms Group Ltd.
+*
+* .. Scalar Arguments ..
+ LOGICAL RESET
+* .. Local Scalars ..
+ INTEGER I, IC, MI
+* .. Save statement ..
+ SAVE I, IC, MI
+* .. Executable Statements ..
+ IF( RESET )THEN
+* Initialize local variables.
+ MI = 891
+ I = 7
+ IC = 0
+ RESET = .FALSE.
+ END IF
+*
+* The sequence of values of I is bounded between 1 and 999.
+* If initial I = 1,2,3,6,7 or 9, the period will be 50.
+* If initial I = 4 or 8, the period will be 25.
+* If initial I = 5, the period will be 10.
+* IC is used to break up the period by skipping 1 value of I in 6.
+*
+ IC = IC + 1
+ 10 I = I*MI
+ I = I - 1000*( I/1000 )
+ IF( IC.GE.5 )THEN
+ IC = 0
+ GO TO 10
+ END IF
+ DBEG = ( I - 500 )/1001.0D0
+ RETURN
+*
+* End of DBEG.
+*
+ END
+ DOUBLE PRECISION FUNCTION DDIFF( X, Y )
+*
+* Auxiliary routine for test program for Level 3 Blas.
+*
+* -- Written on 8-February-1989.
+* Jack Dongarra, Argonne National Laboratory.
+* Iain Duff, AERE Harwell.
+* Jeremy Du Croz, Numerical Algorithms Group Ltd.
+* Sven Hammarling, Numerical Algorithms Group Ltd.
+*
+* .. Scalar Arguments ..
+ DOUBLE PRECISION X, Y
+* .. Executable Statements ..
+ DDIFF = X - Y
+ RETURN
+*
+* End of DDIFF.
+*
+ END
+ SUBROUTINE CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+*
+* Tests whether XERBLA has detected an error when it should.
+*
+* Auxiliary routine for test program for Level 3 Blas.
+*
+* -- Written on 8-February-1989.
+* Jack Dongarra, Argonne National Laboratory.
+* Iain Duff, AERE Harwell.
+* Jeremy Du Croz, Numerical Algorithms Group Ltd.
+* Sven Hammarling, Numerical Algorithms Group Ltd.
+*
+* .. Scalar Arguments ..
+ INTEGER INFOT, NOUT
+ LOGICAL LERR, OK
+ CHARACTER*6 SRNAMT
+* .. Executable Statements ..
+ IF( .NOT.LERR )THEN
+ WRITE( NOUT, FMT = 9999 )INFOT, SRNAMT
+ OK = .FALSE.
+ END IF
+ LERR = .FALSE.
+ RETURN
+*
+ 9999 FORMAT( ' ***** ILLEGAL VALUE OF PARAMETER NUMBER ', I2, ' NOT D',
+ $ 'ETECTED BY ', A6, ' *****' )
+*
+* End of CHKXER.
+*
+ END
+ SUBROUTINE XERBLA( SRNAME, INFO )
+*
+* This is a special version of XERBLA to be used only as part of
+* the test program for testing error exits from the Level 3 BLAS
+* routines.
+*
+* XERBLA is an error handler for the Level 3 BLAS routines.
+*
+* It is called by the Level 3 BLAS routines if an input parameter is
+* invalid.
+*
+* Auxiliary routine for test program for Level 3 Blas.
+*
+* -- Written on 8-February-1989.
+* Jack Dongarra, Argonne National Laboratory.
+* Iain Duff, AERE Harwell.
+* Jeremy Du Croz, Numerical Algorithms Group Ltd.
+* Sven Hammarling, Numerical Algorithms Group Ltd.
+*
+* .. Scalar Arguments ..
+ INTEGER INFO
+ CHARACTER*6 SRNAME
+* .. Scalars in Common ..
+ INTEGER INFOT, NOUT
+ LOGICAL LERR, OK
+ CHARACTER*6 SRNAMT
+* .. Common blocks ..
+ COMMON /INFOC/INFOT, NOUT, OK, LERR
+ COMMON /SRNAMC/SRNAMT
+* .. Executable Statements ..
+ LERR = .TRUE.
+ IF( INFO.NE.INFOT )THEN
+ IF( INFOT.NE.0 )THEN
+ WRITE( NOUT, FMT = 9999 )INFO, INFOT
+ ELSE
+ WRITE( NOUT, FMT = 9997 )INFO
+ END IF
+ OK = .FALSE.
+ END IF
+ IF( SRNAME.NE.SRNAMT )THEN
+ WRITE( NOUT, FMT = 9998 )SRNAME, SRNAMT
+ OK = .FALSE.
+ END IF
+ RETURN
+*
+ 9999 FORMAT( ' ******* XERBLA WAS CALLED WITH INFO = ', I6, ' INSTEAD',
+ $ ' OF ', I2, ' *******' )
+ 9998 FORMAT( ' ******* XERBLA WAS CALLED WITH SRNAME = ', A6, ' INSTE',
+ $ 'AD OF ', A6, ' *******' )
+ 9997 FORMAT( ' ******* XERBLA WAS CALLED WITH INFO = ', I6,
+ $ ' *******' )
+*
+* End of XERBLA
+*
+ END
+
diff --git a/blas/testing/sblat1.f b/blas/testing/sblat1.f
new file mode 100644
index 0000000..4d43d9b
--- /dev/null
+++ b/blas/testing/sblat1.f
@@ -0,0 +1,1021 @@
+*> \brief \b SBLAT1
+*
+* =========== DOCUMENTATION ===========
+*
+* Online html documentation available at
+* http://www.netlib.org/lapack/explore-html/
+*
+* Definition:
+* ===========
+*
+* PROGRAM SBLAT1
+*
+*
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
+*>
+*> Test program for the REAL Level 1 BLAS.
+*>
+*> Based upon the original BLAS test routine together with:
+*> F06EAF Example Program Text
+*> \endverbatim
+*
+* Authors:
+* ========
+*
+*> \author Univ. of Tennessee
+*> \author Univ. of California Berkeley
+*> \author Univ. of Colorado Denver
+*> \author NAG Ltd.
+*
+*> \date April 2012
+*
+*> \ingroup single_blas_testing
+*
+* =====================================================================
+ PROGRAM SBLAT1
+*
+* -- Reference BLAS test routine (version 3.4.1) --
+* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
+* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+* April 2012
+*
+* =====================================================================
+*
+* .. Parameters ..
+ INTEGER NOUT
+ PARAMETER (NOUT=6)
+* .. Scalars in Common ..
+ INTEGER ICASE, INCX, INCY, N
+ LOGICAL PASS
+* .. Local Scalars ..
+ REAL SFAC
+ INTEGER IC
+* .. External Subroutines ..
+ EXTERNAL CHECK0, CHECK1, CHECK2, CHECK3, HEADER
+* .. Common blocks ..
+ COMMON /COMBLA/ICASE, N, INCX, INCY, PASS
+* .. Data statements ..
+ DATA SFAC/9.765625E-4/
+* .. Executable Statements ..
+ WRITE (NOUT,99999)
+ DO 20 IC = 1, 13
+ ICASE = IC
+ CALL HEADER
+*
+* .. Initialize PASS, INCX, and INCY for a new case. ..
+* .. the value 9999 for INCX or INCY will appear in the ..
+* .. detailed output, if any, for cases that do not involve ..
+* .. these parameters ..
+*
+ PASS = .TRUE.
+ INCX = 9999
+ INCY = 9999
+ IF (ICASE.EQ.3 .OR. ICASE.EQ.11) THEN
+ CALL CHECK0(SFAC)
+ ELSE IF (ICASE.EQ.7 .OR. ICASE.EQ.8 .OR. ICASE.EQ.9 .OR.
+ + ICASE.EQ.10) THEN
+ CALL CHECK1(SFAC)
+ ELSE IF (ICASE.EQ.1 .OR. ICASE.EQ.2 .OR. ICASE.EQ.5 .OR.
+ + ICASE.EQ.6 .OR. ICASE.EQ.12 .OR. ICASE.EQ.13) THEN
+ CALL CHECK2(SFAC)
+ ELSE IF (ICASE.EQ.4) THEN
+ CALL CHECK3(SFAC)
+ END IF
+* -- Print
+ IF (PASS) WRITE (NOUT,99998)
+ 20 CONTINUE
+ STOP
+*
+99999 FORMAT (' Real BLAS Test Program Results',/1X)
+99998 FORMAT (' ----- PASS -----')
+ END
+ SUBROUTINE HEADER
+* .. Parameters ..
+ INTEGER NOUT
+ PARAMETER (NOUT=6)
+* .. Scalars in Common ..
+ INTEGER ICASE, INCX, INCY, N
+ LOGICAL PASS
+* .. Local Arrays ..
+ CHARACTER*6 L(13)
+* .. Common blocks ..
+ COMMON /COMBLA/ICASE, N, INCX, INCY, PASS
+* .. Data statements ..
+ DATA L(1)/' SDOT '/
+ DATA L(2)/'SAXPY '/
+ DATA L(3)/'SROTG '/
+ DATA L(4)/' SROT '/
+ DATA L(5)/'SCOPY '/
+ DATA L(6)/'SSWAP '/
+ DATA L(7)/'SNRM2 '/
+ DATA L(8)/'SASUM '/
+ DATA L(9)/'SSCAL '/
+ DATA L(10)/'ISAMAX'/
+ DATA L(11)/'SROTMG'/
+ DATA L(12)/'SROTM '/
+ DATA L(13)/'SDSDOT'/
+* .. Executable Statements ..
+ WRITE (NOUT,99999) ICASE, L(ICASE)
+ RETURN
+*
+99999 FORMAT (/' Test of subprogram number',I3,12X,A6)
+ END
+ SUBROUTINE CHECK0(SFAC)
+* .. Parameters ..
+ INTEGER NOUT
+ PARAMETER (NOUT=6)
+* .. Scalar Arguments ..
+ REAL SFAC
+* .. Scalars in Common ..
+ INTEGER ICASE, INCX, INCY, N
+ LOGICAL PASS
+* .. Local Scalars ..
+ REAL D12, SA, SB, SC, SS
+ INTEGER I, K
+* .. Local Arrays ..
+ REAL DA1(8), DATRUE(8), DB1(8), DBTRUE(8), DC1(8),
+ + DS1(8), DAB(4,9), DTEMP(9), DTRUE(9,9)
+* .. External Subroutines ..
+ EXTERNAL SROTG, SROTMG, STEST1
+* .. Common blocks ..
+ COMMON /COMBLA/ICASE, N, INCX, INCY, PASS
+* .. Data statements ..
+ DATA DA1/0.3E0, 0.4E0, -0.3E0, -0.4E0, -0.3E0, 0.0E0,
+ + 0.0E0, 1.0E0/
+ DATA DB1/0.4E0, 0.3E0, 0.4E0, 0.3E0, -0.4E0, 0.0E0,
+ + 1.0E0, 0.0E0/
+ DATA DC1/0.6E0, 0.8E0, -0.6E0, 0.8E0, 0.6E0, 1.0E0,
+ + 0.0E0, 1.0E0/
+ DATA DS1/0.8E0, 0.6E0, 0.8E0, -0.6E0, 0.8E0, 0.0E0,
+ + 1.0E0, 0.0E0/
+ DATA DATRUE/0.5E0, 0.5E0, 0.5E0, -0.5E0, -0.5E0,
+ + 0.0E0, 1.0E0, 1.0E0/
+ DATA DBTRUE/0.0E0, 0.6E0, 0.0E0, -0.6E0, 0.0E0,
+ + 0.0E0, 1.0E0, 0.0E0/
+* INPUT FOR MODIFIED GIVENS
+ DATA DAB/ .1E0,.3E0,1.2E0,.2E0,
+ A .7E0, .2E0, .6E0, 4.2E0,
+ B 0.E0,0.E0,0.E0,0.E0,
+ C 4.E0, -1.E0, 2.E0, 4.E0,
+ D 6.E-10, 2.E-2, 1.E5, 10.E0,
+ E 4.E10, 2.E-2, 1.E-5, 10.E0,
+ F 2.E-10, 4.E-2, 1.E5, 10.E0,
+ G 2.E10, 4.E-2, 1.E-5, 10.E0,
+ H 4.E0, -2.E0, 8.E0, 4.E0 /
+* TRUE RESULTS FOR MODIFIED GIVENS
+ DATA DTRUE/0.E0,0.E0, 1.3E0, .2E0, 0.E0,0.E0,0.E0, .5E0, 0.E0,
+ A 0.E0,0.E0, 4.5E0, 4.2E0, 1.E0, .5E0, 0.E0,0.E0,0.E0,
+ B 0.E0,0.E0,0.E0,0.E0, -2.E0, 0.E0,0.E0,0.E0,0.E0,
+ C 0.E0,0.E0,0.E0, 4.E0, -1.E0, 0.E0,0.E0,0.E0,0.E0,
+ D 0.E0, 15.E-3, 0.E0, 10.E0, -1.E0, 0.E0, -1.E-4,
+ E 0.E0, 1.E0,
+ F 0.E0,0.E0, 6144.E-5, 10.E0, -1.E0, 4096.E0, -1.E6,
+ G 0.E0, 1.E0,
+ H 0.E0,0.E0,15.E0,10.E0,-1.E0, 5.E-5, 0.E0,1.E0,0.E0,
+ I 0.E0,0.E0, 15.E0, 10.E0, -1. E0, 5.E5, -4096.E0,
+ J 1.E0, 4096.E-6,
+ K 0.E0,0.E0, 7.E0, 4.E0, 0.E0,0.E0, -.5E0, -.25E0, 0.E0/
+* 4096 = 2 ** 12
+ DATA D12 /4096.E0/
+ DTRUE(1,1) = 12.E0 / 130.E0
+ DTRUE(2,1) = 36.E0 / 130.E0
+ DTRUE(7,1) = -1.E0 / 6.E0
+ DTRUE(1,2) = 14.E0 / 75.E0
+ DTRUE(2,2) = 49.E0 / 75.E0
+ DTRUE(9,2) = 1.E0 / 7.E0
+ DTRUE(1,5) = 45.E-11 * (D12 * D12)
+ DTRUE(3,5) = 4.E5 / (3.E0 * D12)
+ DTRUE(6,5) = 1.E0 / D12
+ DTRUE(8,5) = 1.E4 / (3.E0 * D12)
+ DTRUE(1,6) = 4.E10 / (1.5E0 * D12 * D12)
+ DTRUE(2,6) = 2.E-2 / 1.5E0
+ DTRUE(8,6) = 5.E-7 * D12
+ DTRUE(1,7) = 4.E0 / 150.E0
+ DTRUE(2,7) = (2.E-10 / 1.5E0) * (D12 * D12)
+ DTRUE(7,7) = -DTRUE(6,5)
+ DTRUE(9,7) = 1.E4 / D12
+ DTRUE(1,8) = DTRUE(1,7)
+ DTRUE(2,8) = 2.E10 / (1.5E0 * D12 * D12)
+ DTRUE(1,9) = 32.E0 / 7.E0
+ DTRUE(2,9) = -16.E0 / 7.E0
+* .. Executable Statements ..
+*
+* Compute true values which cannot be prestored
+* in decimal notation
+*
+ DBTRUE(1) = 1.0E0/0.6E0
+ DBTRUE(3) = -1.0E0/0.6E0
+ DBTRUE(5) = 1.0E0/0.6E0
+*
+ DO 20 K = 1, 8
+* .. Set N=K for identification in output if any ..
+ N = K
+ IF (ICASE.EQ.3) THEN
+* .. SROTG ..
+ IF (K.GT.8) GO TO 40
+ SA = DA1(K)
+ SB = DB1(K)
+ CALL SROTG(SA,SB,SC,SS)
+ CALL STEST1(SA,DATRUE(K),DATRUE(K),SFAC)
+ CALL STEST1(SB,DBTRUE(K),DBTRUE(K),SFAC)
+ CALL STEST1(SC,DC1(K),DC1(K),SFAC)
+ CALL STEST1(SS,DS1(K),DS1(K),SFAC)
+ ELSEIF (ICASE.EQ.11) THEN
+* .. SROTMG ..
+ DO I=1,4
+ DTEMP(I)= DAB(I,K)
+ DTEMP(I+4) = 0.0
+ END DO
+ DTEMP(9) = 0.0
+ CALL SROTMG(DTEMP(1),DTEMP(2),DTEMP(3),DTEMP(4),DTEMP(5))
+ CALL STEST(9,DTEMP,DTRUE(1,K),DTRUE(1,K),SFAC)
+ ELSE
+ WRITE (NOUT,*) ' Shouldn''t be here in CHECK0'
+ STOP
+ END IF
+ 20 CONTINUE
+ 40 RETURN
+ END
+ SUBROUTINE CHECK1(SFAC)
+* .. Parameters ..
+ INTEGER NOUT
+ PARAMETER (NOUT=6)
+* .. Scalar Arguments ..
+ REAL SFAC
+* .. Scalars in Common ..
+ INTEGER ICASE, INCX, INCY, N
+ LOGICAL PASS
+* .. Local Scalars ..
+ INTEGER I, LEN, NP1
+* .. Local Arrays ..
+ REAL DTRUE1(5), DTRUE3(5), DTRUE5(8,5,2), DV(8,5,2),
+ + SA(10), STEMP(1), STRUE(8), SX(8)
+ INTEGER ITRUE2(5)
+* .. External Functions ..
+ REAL SASUM, SNRM2
+ INTEGER ISAMAX
+ EXTERNAL SASUM, SNRM2, ISAMAX
+* .. External Subroutines ..
+ EXTERNAL ITEST1, SSCAL, STEST, STEST1
+* .. Intrinsic Functions ..
+ INTRINSIC MAX
+* .. Common blocks ..
+ COMMON /COMBLA/ICASE, N, INCX, INCY, PASS
+* .. Data statements ..
+ DATA SA/0.3E0, -1.0E0, 0.0E0, 1.0E0, 0.3E0, 0.3E0,
+ + 0.3E0, 0.3E0, 0.3E0, 0.3E0/
+ DATA DV/0.1E0, 2.0E0, 2.0E0, 2.0E0, 2.0E0, 2.0E0,
+ + 2.0E0, 2.0E0, 0.3E0, 3.0E0, 3.0E0, 3.0E0, 3.0E0,
+ + 3.0E0, 3.0E0, 3.0E0, 0.3E0, -0.4E0, 4.0E0,
+ + 4.0E0, 4.0E0, 4.0E0, 4.0E0, 4.0E0, 0.2E0,
+ + -0.6E0, 0.3E0, 5.0E0, 5.0E0, 5.0E0, 5.0E0,
+ + 5.0E0, 0.1E0, -0.3E0, 0.5E0, -0.1E0, 6.0E0,
+ + 6.0E0, 6.0E0, 6.0E0, 0.1E0, 8.0E0, 8.0E0, 8.0E0,
+ + 8.0E0, 8.0E0, 8.0E0, 8.0E0, 0.3E0, 9.0E0, 9.0E0,
+ + 9.0E0, 9.0E0, 9.0E0, 9.0E0, 9.0E0, 0.3E0, 2.0E0,
+ + -0.4E0, 2.0E0, 2.0E0, 2.0E0, 2.0E0, 2.0E0,
+ + 0.2E0, 3.0E0, -0.6E0, 5.0E0, 0.3E0, 2.0E0,
+ + 2.0E0, 2.0E0, 0.1E0, 4.0E0, -0.3E0, 6.0E0,
+ + -0.5E0, 7.0E0, -0.1E0, 3.0E0/
+ DATA DTRUE1/0.0E0, 0.3E0, 0.5E0, 0.7E0, 0.6E0/
+ DATA DTRUE3/0.0E0, 0.3E0, 0.7E0, 1.1E0, 1.0E0/
+ DATA DTRUE5/0.10E0, 2.0E0, 2.0E0, 2.0E0, 2.0E0,
+ + 2.0E0, 2.0E0, 2.0E0, -0.3E0, 3.0E0, 3.0E0,
+ + 3.0E0, 3.0E0, 3.0E0, 3.0E0, 3.0E0, 0.0E0, 0.0E0,
+ + 4.0E0, 4.0E0, 4.0E0, 4.0E0, 4.0E0, 4.0E0,
+ + 0.20E0, -0.60E0, 0.30E0, 5.0E0, 5.0E0, 5.0E0,
+ + 5.0E0, 5.0E0, 0.03E0, -0.09E0, 0.15E0, -0.03E0,
+ + 6.0E0, 6.0E0, 6.0E0, 6.0E0, 0.10E0, 8.0E0,
+ + 8.0E0, 8.0E0, 8.0E0, 8.0E0, 8.0E0, 8.0E0,
+ + 0.09E0, 9.0E0, 9.0E0, 9.0E0, 9.0E0, 9.0E0,
+ + 9.0E0, 9.0E0, 0.09E0, 2.0E0, -0.12E0, 2.0E0,
+ + 2.0E0, 2.0E0, 2.0E0, 2.0E0, 0.06E0, 3.0E0,
+ + -0.18E0, 5.0E0, 0.09E0, 2.0E0, 2.0E0, 2.0E0,
+ + 0.03E0, 4.0E0, -0.09E0, 6.0E0, -0.15E0, 7.0E0,
+ + -0.03E0, 3.0E0/
+ DATA ITRUE2/0, 1, 2, 2, 3/
+* .. Executable Statements ..
+ DO 80 INCX = 1, 2
+ DO 60 NP1 = 1, 5
+ N = NP1 - 1
+ LEN = 2*MAX(N,1)
+* .. Set vector arguments ..
+ DO 20 I = 1, LEN
+ SX(I) = DV(I,NP1,INCX)
+ 20 CONTINUE
+*
+ IF (ICASE.EQ.7) THEN
+* .. SNRM2 ..
+ STEMP(1) = DTRUE1(NP1)
+ CALL STEST1(SNRM2(N,SX,INCX),STEMP(1),STEMP,SFAC)
+ ELSE IF (ICASE.EQ.8) THEN
+* .. SASUM ..
+ STEMP(1) = DTRUE3(NP1)
+ CALL STEST1(SASUM(N,SX,INCX),STEMP(1),STEMP,SFAC)
+ ELSE IF (ICASE.EQ.9) THEN
+* .. SSCAL ..
+ CALL SSCAL(N,SA((INCX-1)*5+NP1),SX,INCX)
+ DO 40 I = 1, LEN
+ STRUE(I) = DTRUE5(I,NP1,INCX)
+ 40 CONTINUE
+ CALL STEST(LEN,SX,STRUE,STRUE,SFAC)
+ ELSE IF (ICASE.EQ.10) THEN
+* .. ISAMAX ..
+ CALL ITEST1(ISAMAX(N,SX,INCX),ITRUE2(NP1))
+ ELSE
+ WRITE (NOUT,*) ' Shouldn''t be here in CHECK1'
+ STOP
+ END IF
+ 60 CONTINUE
+ 80 CONTINUE
+ RETURN
+ END
+ SUBROUTINE CHECK2(SFAC)
+* .. Parameters ..
+ INTEGER NOUT
+ PARAMETER (NOUT=6)
+* .. Scalar Arguments ..
+ REAL SFAC
+* .. Scalars in Common ..
+ INTEGER ICASE, INCX, INCY, N
+ LOGICAL PASS
+* .. Local Scalars ..
+ REAL SA
+ INTEGER I, J, KI, KN, KNI, KPAR, KSIZE, LENX, LENY,
+ $ MX, MY
+* .. Local Arrays ..
+ REAL DT10X(7,4,4), DT10Y(7,4,4), DT7(4,4),
+ $ DT8(7,4,4), DX1(7),
+ $ DY1(7), SSIZE1(4), SSIZE2(14,2), SSIZE3(4),
+ $ SSIZE(7), STX(7), STY(7), SX(7), SY(7),
+ $ DPAR(5,4), DT19X(7,4,16),DT19XA(7,4,4),
+ $ DT19XB(7,4,4), DT19XC(7,4,4),DT19XD(7,4,4),
+ $ DT19Y(7,4,16), DT19YA(7,4,4),DT19YB(7,4,4),
+ $ DT19YC(7,4,4), DT19YD(7,4,4), DTEMP(5),
+ $ ST7B(4,4)
+ INTEGER INCXS(4), INCYS(4), LENS(4,2), NS(4)
+* .. External Functions ..
+ REAL SDOT, SDSDOT
+ EXTERNAL SDOT, SDSDOT
+* .. External Subroutines ..
+ EXTERNAL SAXPY, SCOPY, SROTM, SSWAP, STEST, STEST1
+* .. Intrinsic Functions ..
+ INTRINSIC ABS, MIN
+* .. Common blocks ..
+ COMMON /COMBLA/ICASE, N, INCX, INCY, PASS
+* .. Data statements ..
+ EQUIVALENCE (DT19X(1,1,1),DT19XA(1,1,1)),(DT19X(1,1,5),
+ A DT19XB(1,1,1)),(DT19X(1,1,9),DT19XC(1,1,1)),
+ B (DT19X(1,1,13),DT19XD(1,1,1))
+ EQUIVALENCE (DT19Y(1,1,1),DT19YA(1,1,1)),(DT19Y(1,1,5),
+ A DT19YB(1,1,1)),(DT19Y(1,1,9),DT19YC(1,1,1)),
+ B (DT19Y(1,1,13),DT19YD(1,1,1))
+
+ DATA SA/0.3E0/
+ DATA INCXS/1, 2, -2, -1/
+ DATA INCYS/1, -2, 1, -2/
+ DATA LENS/1, 1, 2, 4, 1, 1, 3, 7/
+ DATA NS/0, 1, 2, 4/
+ DATA DX1/0.6E0, 0.1E0, -0.5E0, 0.8E0, 0.9E0, -0.3E0,
+ + -0.4E0/
+ DATA DY1/0.5E0, -0.9E0, 0.3E0, 0.7E0, -0.6E0, 0.2E0,
+ + 0.8E0/
+ DATA DT7/0.0E0, 0.30E0, 0.21E0, 0.62E0, 0.0E0,
+ + 0.30E0, -0.07E0, 0.85E0, 0.0E0, 0.30E0, -0.79E0,
+ + -0.74E0, 0.0E0, 0.30E0, 0.33E0, 1.27E0/
+ DATA ST7B/ .1, .4, .31, .72, .1, .4, .03, .95,
+ + .1, .4, -.69, -.64, .1, .4, .43, 1.37/
+ DATA DT8/0.5E0, 0.0E0, 0.0E0, 0.0E0, 0.0E0, 0.0E0,
+ + 0.0E0, 0.68E0, 0.0E0, 0.0E0, 0.0E0, 0.0E0,
+ + 0.0E0, 0.0E0, 0.68E0, -0.87E0, 0.0E0, 0.0E0,
+ + 0.0E0, 0.0E0, 0.0E0, 0.68E0, -0.87E0, 0.15E0,
+ + 0.94E0, 0.0E0, 0.0E0, 0.0E0, 0.5E0, 0.0E0,
+ + 0.0E0, 0.0E0, 0.0E0, 0.0E0, 0.0E0, 0.68E0,
+ + 0.0E0, 0.0E0, 0.0E0, 0.0E0, 0.0E0, 0.0E0,
+ + 0.35E0, -0.9E0, 0.48E0, 0.0E0, 0.0E0, 0.0E0,
+ + 0.0E0, 0.38E0, -0.9E0, 0.57E0, 0.7E0, -0.75E0,
+ + 0.2E0, 0.98E0, 0.5E0, 0.0E0, 0.0E0, 0.0E0,
+ + 0.0E0, 0.0E0, 0.0E0, 0.68E0, 0.0E0, 0.0E0,
+ + 0.0E0, 0.0E0, 0.0E0, 0.0E0, 0.35E0, -0.72E0,
+ + 0.0E0, 0.0E0, 0.0E0, 0.0E0, 0.0E0, 0.38E0,
+ + -0.63E0, 0.15E0, 0.88E0, 0.0E0, 0.0E0, 0.0E0,
+ + 0.5E0, 0.0E0, 0.0E0, 0.0E0, 0.0E0, 0.0E0, 0.0E0,
+ + 0.68E0, 0.0E0, 0.0E0, 0.0E0, 0.0E0, 0.0E0,
+ + 0.0E0, 0.68E0, -0.9E0, 0.33E0, 0.0E0, 0.0E0,
+ + 0.0E0, 0.0E0, 0.68E0, -0.9E0, 0.33E0, 0.7E0,
+ + -0.75E0, 0.2E0, 1.04E0/
+ DATA DT10X/0.6E0, 0.0E0, 0.0E0, 0.0E0, 0.0E0, 0.0E0,
+ + 0.0E0, 0.5E0, 0.0E0, 0.0E0, 0.0E0, 0.0E0, 0.0E0,
+ + 0.0E0, 0.5E0, -0.9E0, 0.0E0, 0.0E0, 0.0E0,
+ + 0.0E0, 0.0E0, 0.5E0, -0.9E0, 0.3E0, 0.7E0,
+ + 0.0E0, 0.0E0, 0.0E0, 0.6E0, 0.0E0, 0.0E0, 0.0E0,
+ + 0.0E0, 0.0E0, 0.0E0, 0.5E0, 0.0E0, 0.0E0, 0.0E0,
+ + 0.0E0, 0.0E0, 0.0E0, 0.3E0, 0.1E0, 0.5E0, 0.0E0,
+ + 0.0E0, 0.0E0, 0.0E0, 0.8E0, 0.1E0, -0.6E0,
+ + 0.8E0, 0.3E0, -0.3E0, 0.5E0, 0.6E0, 0.0E0,
+ + 0.0E0, 0.0E0, 0.0E0, 0.0E0, 0.0E0, 0.5E0, 0.0E0,
+ + 0.0E0, 0.0E0, 0.0E0, 0.0E0, 0.0E0, -0.9E0,
+ + 0.1E0, 0.5E0, 0.0E0, 0.0E0, 0.0E0, 0.0E0, 0.7E0,
+ + 0.1E0, 0.3E0, 0.8E0, -0.9E0, -0.3E0, 0.5E0,
+ + 0.6E0, 0.0E0, 0.0E0, 0.0E0, 0.0E0, 0.0E0, 0.0E0,
+ + 0.5E0, 0.0E0, 0.0E0, 0.0E0, 0.0E0, 0.0E0, 0.0E0,
+ + 0.5E0, 0.3E0, 0.0E0, 0.0E0, 0.0E0, 0.0E0, 0.0E0,
+ + 0.5E0, 0.3E0, -0.6E0, 0.8E0, 0.0E0, 0.0E0,
+ + 0.0E0/
+ DATA DT10Y/0.5E0, 0.0E0, 0.0E0, 0.0E0, 0.0E0, 0.0E0,
+ + 0.0E0, 0.6E0, 0.0E0, 0.0E0, 0.0E0, 0.0E0, 0.0E0,
+ + 0.0E0, 0.6E0, 0.1E0, 0.0E0, 0.0E0, 0.0E0, 0.0E0,
+ + 0.0E0, 0.6E0, 0.1E0, -0.5E0, 0.8E0, 0.0E0,
+ + 0.0E0, 0.0E0, 0.5E0, 0.0E0, 0.0E0, 0.0E0, 0.0E0,
+ + 0.0E0, 0.0E0, 0.6E0, 0.0E0, 0.0E0, 0.0E0, 0.0E0,
+ + 0.0E0, 0.0E0, -0.5E0, -0.9E0, 0.6E0, 0.0E0,
+ + 0.0E0, 0.0E0, 0.0E0, -0.4E0, -0.9E0, 0.9E0,
+ + 0.7E0, -0.5E0, 0.2E0, 0.6E0, 0.5E0, 0.0E0,
+ + 0.0E0, 0.0E0, 0.0E0, 0.0E0, 0.0E0, 0.6E0, 0.0E0,
+ + 0.0E0, 0.0E0, 0.0E0, 0.0E0, 0.0E0, -0.5E0,
+ + 0.6E0, 0.0E0, 0.0E0, 0.0E0, 0.0E0, 0.0E0,
+ + -0.4E0, 0.9E0, -0.5E0, 0.6E0, 0.0E0, 0.0E0,
+ + 0.0E0, 0.5E0, 0.0E0, 0.0E0, 0.0E0, 0.0E0, 0.0E0,
+ + 0.0E0, 0.6E0, 0.0E0, 0.0E0, 0.0E0, 0.0E0, 0.0E0,
+ + 0.0E0, 0.6E0, -0.9E0, 0.1E0, 0.0E0, 0.0E0,
+ + 0.0E0, 0.0E0, 0.6E0, -0.9E0, 0.1E0, 0.7E0,
+ + -0.5E0, 0.2E0, 0.8E0/
+ DATA SSIZE1/0.0E0, 0.3E0, 1.6E0, 3.2E0/
+ DATA SSIZE2/0.0E0, 0.0E0, 0.0E0, 0.0E0, 0.0E0, 0.0E0,
+ + 0.0E0, 0.0E0, 0.0E0, 0.0E0, 0.0E0, 0.0E0, 0.0E0,
+ + 0.0E0, 1.17E0, 1.17E0, 1.17E0, 1.17E0, 1.17E0,
+ + 1.17E0, 1.17E0, 1.17E0, 1.17E0, 1.17E0, 1.17E0,
+ + 1.17E0, 1.17E0, 1.17E0/
+ DATA SSIZE3/ .1, .4, 1.7, 3.3 /
+*
+* FOR DROTM
+*
+ DATA DPAR/-2.E0, 0.E0,0.E0,0.E0,0.E0,
+ A -1.E0, 2.E0, -3.E0, -4.E0, 5.E0,
+ B 0.E0, 0.E0, 2.E0, -3.E0, 0.E0,
+ C 1.E0, 5.E0, 2.E0, 0.E0, -4.E0/
+* TRUE X RESULTS F0R ROTATIONS DROTM
+ DATA DT19XA/.6E0, 0.E0,0.E0,0.E0,0.E0,0.E0,0.E0,
+ A .6E0, 0.E0,0.E0,0.E0,0.E0,0.E0,0.E0,
+ B .6E0, 0.E0,0.E0,0.E0,0.E0,0.E0,0.E0,
+ C .6E0, 0.E0,0.E0,0.E0,0.E0,0.E0,0.E0,
+ D .6E0, 0.E0,0.E0,0.E0,0.E0,0.E0,0.E0,
+ E -.8E0, 0.E0,0.E0,0.E0,0.E0,0.E0,0.E0,
+ F -.9E0, 0.E0,0.E0,0.E0,0.E0,0.E0,0.E0,
+ G 3.5E0, 0.E0,0.E0,0.E0,0.E0,0.E0,0.E0,
+ H .6E0, .1E0, 0.E0,0.E0,0.E0,0.E0,0.E0,
+ I -.8E0, 3.8E0, 0.E0,0.E0,0.E0,0.E0,0.E0,
+ J -.9E0, 2.8E0, 0.E0,0.E0,0.E0,0.E0,0.E0,
+ K 3.5E0, -.4E0, 0.E0,0.E0,0.E0,0.E0,0.E0,
+ L .6E0, .1E0, -.5E0, .8E0, 0.E0,0.E0,0.E0,
+ M -.8E0, 3.8E0, -2.2E0, -1.2E0, 0.E0,0.E0,0.E0,
+ N -.9E0, 2.8E0, -1.4E0, -1.3E0, 0.E0,0.E0,0.E0,
+ O 3.5E0, -.4E0, -2.2E0, 4.7E0, 0.E0,0.E0,0.E0/
+*
+ DATA DT19XB/.6E0, 0.E0,0.E0,0.E0,0.E0,0.E0,0.E0,
+ A .6E0, 0.E0,0.E0,0.E0,0.E0,0.E0,0.E0,
+ B .6E0, 0.E0,0.E0,0.E0,0.E0,0.E0,0.E0,
+ C .6E0, 0.E0,0.E0,0.E0,0.E0,0.E0,0.E0,
+ D .6E0, 0.E0,0.E0,0.E0,0.E0,0.E0,0.E0,
+ E -.8E0, 0.E0,0.E0,0.E0,0.E0,0.E0,0.E0,
+ F -.9E0, 0.E0,0.E0,0.E0,0.E0,0.E0,0.E0,
+ G 3.5E0, 0.E0,0.E0,0.E0,0.E0,0.E0,0.E0,
+ H .6E0, .1E0, -.5E0, 0.E0,0.E0,0.E0,0.E0,
+ I 0.E0, .1E0, -3.0E0, 0.E0,0.E0,0.E0,0.E0,
+ J -.3E0, .1E0, -2.0E0, 0.E0,0.E0,0.E0,0.E0,
+ K 3.3E0, .1E0, -2.0E0, 0.E0,0.E0,0.E0,0.E0,
+ L .6E0, .1E0, -.5E0, .8E0, .9E0, -.3E0, -.4E0,
+ M -2.0E0, .1E0, 1.4E0, .8E0, .6E0, -.3E0, -2.8E0,
+ N -1.8E0, .1E0, 1.3E0, .8E0, 0.E0, -.3E0, -1.9E0,
+ O 3.8E0, .1E0, -3.1E0, .8E0, 4.8E0, -.3E0, -1.5E0 /
+*
+ DATA DT19XC/.6E0, 0.E0,0.E0,0.E0,0.E0,0.E0,0.E0,
+ A .6E0, 0.E0,0.E0,0.E0,0.E0,0.E0,0.E0,
+ B .6E0, 0.E0,0.E0,0.E0,0.E0,0.E0,0.E0,
+ C .6E0, 0.E0,0.E0,0.E0,0.E0,0.E0,0.E0,
+ D .6E0, 0.E0,0.E0,0.E0,0.E0,0.E0,0.E0,
+ E -.8E0, 0.E0,0.E0,0.E0,0.E0,0.E0,0.E0,
+ F -.9E0, 0.E0,0.E0,0.E0,0.E0,0.E0,0.E0,
+ G 3.5E0, 0.E0,0.E0,0.E0,0.E0,0.E0,0.E0,
+ H .6E0, .1E0, -.5E0, 0.E0,0.E0,0.E0,0.E0,
+ I 4.8E0, .1E0, -3.0E0, 0.E0,0.E0,0.E0,0.E0,
+ J 3.3E0, .1E0, -2.0E0, 0.E0,0.E0,0.E0,0.E0,
+ K 2.1E0, .1E0, -2.0E0, 0.E0,0.E0,0.E0,0.E0,
+ L .6E0, .1E0, -.5E0, .8E0, .9E0, -.3E0, -.4E0,
+ M -1.6E0, .1E0, -2.2E0, .8E0, 5.4E0, -.3E0, -2.8E0,
+ N -1.5E0, .1E0, -1.4E0, .8E0, 3.6E0, -.3E0, -1.9E0,
+ O 3.7E0, .1E0, -2.2E0, .8E0, 3.6E0, -.3E0, -1.5E0 /
+*
+ DATA DT19XD/.6E0, 0.E0,0.E0,0.E0,0.E0,0.E0,0.E0,
+ A .6E0, 0.E0,0.E0,0.E0,0.E0,0.E0,0.E0,
+ B .6E0, 0.E0,0.E0,0.E0,0.E0,0.E0,0.E0,
+ C .6E0, 0.E0,0.E0,0.E0,0.E0,0.E0,0.E0,
+ D .6E0, 0.E0,0.E0,0.E0,0.E0,0.E0,0.E0,
+ E -.8E0, 0.E0,0.E0,0.E0,0.E0,0.E0,0.E0,
+ F -.9E0, 0.E0,0.E0,0.E0,0.E0,0.E0,0.E0,
+ G 3.5E0, 0.E0,0.E0,0.E0,0.E0,0.E0,0.E0,
+ H .6E0, .1E0, 0.E0,0.E0,0.E0,0.E0,0.E0,
+ I -.8E0, -1.0E0, 0.E0,0.E0,0.E0,0.E0,0.E0,
+ J -.9E0, -.8E0, 0.E0,0.E0,0.E0,0.E0,0.E0,
+ K 3.5E0, .8E0, 0.E0,0.E0,0.E0,0.E0,0.E0,
+ L .6E0, .1E0, -.5E0, .8E0, 0.E0,0.E0,0.E0,
+ M -.8E0, -1.0E0, 1.4E0, -1.6E0, 0.E0,0.E0,0.E0,
+ N -.9E0, -.8E0, 1.3E0, -1.6E0, 0.E0,0.E0,0.E0,
+ O 3.5E0, .8E0, -3.1E0, 4.8E0, 0.E0,0.E0,0.E0/
+* TRUE Y RESULTS FOR ROTATIONS DROTM
+ DATA DT19YA/.5E0, 0.E0,0.E0,0.E0,0.E0,0.E0,0.E0,
+ A .5E0, 0.E0,0.E0,0.E0,0.E0,0.E0,0.E0,
+ B .5E0, 0.E0,0.E0,0.E0,0.E0,0.E0,0.E0,
+ C .5E0, 0.E0,0.E0,0.E0,0.E0,0.E0,0.E0,
+ D .5E0, 0.E0,0.E0,0.E0,0.E0,0.E0,0.E0,
+ E .7E0, 0.E0,0.E0,0.E0,0.E0,0.E0,0.E0,
+ F 1.7E0, 0.E0,0.E0,0.E0,0.E0,0.E0,0.E0,
+ G -2.6E0, 0.E0,0.E0,0.E0,0.E0,0.E0,0.E0,
+ H .5E0, -.9E0, 0.E0,0.E0,0.E0,0.E0,0.E0,
+ I .7E0, -4.8E0, 0.E0,0.E0,0.E0,0.E0,0.E0,
+ J 1.7E0, -.7E0, 0.E0,0.E0,0.E0,0.E0,0.E0,
+ K -2.6E0, 3.5E0, 0.E0,0.E0,0.E0,0.E0,0.E0,
+ L .5E0, -.9E0, .3E0, .7E0, 0.E0,0.E0,0.E0,
+ M .7E0, -4.8E0, 3.0E0, 1.1E0, 0.E0,0.E0,0.E0,
+ N 1.7E0, -.7E0, -.7E0, 2.3E0, 0.E0,0.E0,0.E0,
+ O -2.6E0, 3.5E0, -.7E0, -3.6E0, 0.E0,0.E0,0.E0/
+*
+ DATA DT19YB/.5E0, 0.E0,0.E0,0.E0,0.E0,0.E0,0.E0,
+ A .5E0, 0.E0,0.E0,0.E0,0.E0,0.E0,0.E0,
+ B .5E0, 0.E0,0.E0,0.E0,0.E0,0.E0,0.E0,
+ C .5E0, 0.E0,0.E0,0.E0,0.E0,0.E0,0.E0,
+ D .5E0, 0.E0,0.E0,0.E0,0.E0,0.E0,0.E0,
+ E .7E0, 0.E0,0.E0,0.E0,0.E0,0.E0,0.E0,
+ F 1.7E0, 0.E0,0.E0,0.E0,0.E0,0.E0,0.E0,
+ G -2.6E0, 0.E0,0.E0,0.E0,0.E0,0.E0,0.E0,
+ H .5E0, -.9E0, .3E0, 0.E0,0.E0,0.E0,0.E0,
+ I 4.0E0, -.9E0, -.3E0, 0.E0,0.E0,0.E0,0.E0,
+ J -.5E0, -.9E0, 1.5E0, 0.E0,0.E0,0.E0,0.E0,
+ K -1.5E0, -.9E0, -1.8E0, 0.E0,0.E0,0.E0,0.E0,
+ L .5E0, -.9E0, .3E0, .7E0, -.6E0, .2E0, .8E0,
+ M 3.7E0, -.9E0, -1.2E0, .7E0, -1.5E0, .2E0, 2.2E0,
+ N -.3E0, -.9E0, 2.1E0, .7E0, -1.6E0, .2E0, 2.0E0,
+ O -1.6E0, -.9E0, -2.1E0, .7E0, 2.9E0, .2E0, -3.8E0 /
+*
+ DATA DT19YC/.5E0, 0.E0,0.E0,0.E0,0.E0,0.E0,0.E0,
+ A .5E0, 0.E0,0.E0,0.E0,0.E0,0.E0,0.E0,
+ B .5E0, 0.E0,0.E0,0.E0,0.E0,0.E0,0.E0,
+ C .5E0, 0.E0,0.E0,0.E0,0.E0,0.E0,0.E0,
+ D .5E0, 0.E0,0.E0,0.E0,0.E0,0.E0,0.E0,
+ E .7E0, 0.E0,0.E0,0.E0,0.E0,0.E0,0.E0,
+ F 1.7E0, 0.E0,0.E0,0.E0,0.E0,0.E0,0.E0,
+ G -2.6E0, 0.E0,0.E0,0.E0,0.E0,0.E0,0.E0,
+ H .5E0, -.9E0, 0.E0,0.E0,0.E0,0.E0,0.E0,
+ I 4.0E0, -6.3E0, 0.E0,0.E0,0.E0,0.E0,0.E0,
+ J -.5E0, .3E0, 0.E0,0.E0,0.E0,0.E0,0.E0,
+ K -1.5E0, 3.0E0, 0.E0,0.E0,0.E0,0.E0,0.E0,
+ L .5E0, -.9E0, .3E0, .7E0, 0.E0,0.E0,0.E0,
+ M 3.7E0, -7.2E0, 3.0E0, 1.7E0, 0.E0,0.E0,0.E0,
+ N -.3E0, .9E0, -.7E0, 1.9E0, 0.E0,0.E0,0.E0,
+ O -1.6E0, 2.7E0, -.7E0, -3.4E0, 0.E0,0.E0,0.E0/
+*
+ DATA DT19YD/.5E0, 0.E0,0.E0,0.E0,0.E0,0.E0,0.E0,
+ A .5E0, 0.E0,0.E0,0.E0,0.E0,0.E0,0.E0,
+ B .5E0, 0.E0,0.E0,0.E0,0.E0,0.E0,0.E0,
+ C .5E0, 0.E0,0.E0,0.E0,0.E0,0.E0,0.E0,
+ D .5E0, 0.E0,0.E0,0.E0,0.E0,0.E0,0.E0,
+ E .7E0, 0.E0,0.E0,0.E0,0.E0,0.E0,0.E0,
+ F 1.7E0, 0.E0,0.E0,0.E0,0.E0,0.E0,0.E0,
+ G -2.6E0, 0.E0,0.E0,0.E0,0.E0,0.E0,0.E0,
+ H .5E0, -.9E0, .3E0, 0.E0,0.E0,0.E0,0.E0,
+ I .7E0, -.9E0, 1.2E0, 0.E0,0.E0,0.E0,0.E0,
+ J 1.7E0, -.9E0, .5E0, 0.E0,0.E0,0.E0,0.E0,
+ K -2.6E0, -.9E0, -1.3E0, 0.E0,0.E0,0.E0,0.E0,
+ L .5E0, -.9E0, .3E0, .7E0, -.6E0, .2E0, .8E0,
+ M .7E0, -.9E0, 1.2E0, .7E0, -1.5E0, .2E0, 1.6E0,
+ N 1.7E0, -.9E0, .5E0, .7E0, -1.6E0, .2E0, 2.4E0,
+ O -2.6E0, -.9E0, -1.3E0, .7E0, 2.9E0, .2E0, -4.0E0 /
+*
+* .. Executable Statements ..
+*
+ DO 120 KI = 1, 4
+ INCX = INCXS(KI)
+ INCY = INCYS(KI)
+ MX = ABS(INCX)
+ MY = ABS(INCY)
+*
+ DO 100 KN = 1, 4
+ N = NS(KN)
+ KSIZE = MIN(2,KN)
+ LENX = LENS(KN,MX)
+ LENY = LENS(KN,MY)
+* .. Initialize all argument arrays ..
+ DO 20 I = 1, 7
+ SX(I) = DX1(I)
+ SY(I) = DY1(I)
+ 20 CONTINUE
+*
+ IF (ICASE.EQ.1) THEN
+* .. SDOT ..
+ CALL STEST1(SDOT(N,SX,INCX,SY,INCY),DT7(KN,KI),SSIZE1(KN)
+ + ,SFAC)
+ ELSE IF (ICASE.EQ.2) THEN
+* .. SAXPY ..
+ CALL SAXPY(N,SA,SX,INCX,SY,INCY)
+ DO 40 J = 1, LENY
+ STY(J) = DT8(J,KN,KI)
+ 40 CONTINUE
+ CALL STEST(LENY,SY,STY,SSIZE2(1,KSIZE),SFAC)
+ ELSE IF (ICASE.EQ.5) THEN
+* .. SCOPY ..
+ DO 60 I = 1, 7
+ STY(I) = DT10Y(I,KN,KI)
+ 60 CONTINUE
+ CALL SCOPY(N,SX,INCX,SY,INCY)
+ CALL STEST(LENY,SY,STY,SSIZE2(1,1),1.0E0)
+ ELSE IF (ICASE.EQ.6) THEN
+* .. SSWAP ..
+ CALL SSWAP(N,SX,INCX,SY,INCY)
+ DO 80 I = 1, 7
+ STX(I) = DT10X(I,KN,KI)
+ STY(I) = DT10Y(I,KN,KI)
+ 80 CONTINUE
+ CALL STEST(LENX,SX,STX,SSIZE2(1,1),1.0E0)
+ CALL STEST(LENY,SY,STY,SSIZE2(1,1),1.0E0)
+ ELSEIF (ICASE.EQ.12) THEN
+* .. SROTM ..
+ KNI=KN+4*(KI-1)
+ DO KPAR=1,4
+ DO I=1,7
+ SX(I) = DX1(I)
+ SY(I) = DY1(I)
+ STX(I)= DT19X(I,KPAR,KNI)
+ STY(I)= DT19Y(I,KPAR,KNI)
+ END DO
+*
+ DO I=1,5
+ DTEMP(I) = DPAR(I,KPAR)
+ END DO
+*
+ DO I=1,LENX
+ SSIZE(I)=STX(I)
+ END DO
+* SEE REMARK ABOVE ABOUT DT11X(1,2,7)
+* AND DT11X(5,3,8).
+ IF ((KPAR .EQ. 2) .AND. (KNI .EQ. 7))
+ $ SSIZE(1) = 2.4E0
+ IF ((KPAR .EQ. 3) .AND. (KNI .EQ. 8))
+ $ SSIZE(5) = 1.8E0
+*
+ CALL SROTM(N,SX,INCX,SY,INCY,DTEMP)
+ CALL STEST(LENX,SX,STX,SSIZE,SFAC)
+ CALL STEST(LENY,SY,STY,STY,SFAC)
+ END DO
+ ELSEIF (ICASE.EQ.13) THEN
+* .. SDSROT ..
+ CALL STEST1 (SDSDOT(N,.1,SX,INCX,SY,INCY),
+ $ ST7B(KN,KI),SSIZE3(KN),SFAC)
+ ELSE
+ WRITE (NOUT,*) ' Shouldn''t be here in CHECK2'
+ STOP
+ END IF
+ 100 CONTINUE
+ 120 CONTINUE
+ RETURN
+ END
+ SUBROUTINE CHECK3(SFAC)
+* .. Parameters ..
+ INTEGER NOUT
+ PARAMETER (NOUT=6)
+* .. Scalar Arguments ..
+ REAL SFAC
+* .. Scalars in Common ..
+ INTEGER ICASE, INCX, INCY, N
+ LOGICAL PASS
+* .. Local Scalars ..
+ REAL SC, SS
+ INTEGER I, K, KI, KN, KSIZE, LENX, LENY, MX, MY
+* .. Local Arrays ..
+ REAL COPYX(5), COPYY(5), DT9X(7,4,4), DT9Y(7,4,4),
+ + DX1(7), DY1(7), MWPC(11), MWPS(11), MWPSTX(5),
+ + MWPSTY(5), MWPTX(11,5), MWPTY(11,5), MWPX(5),
+ + MWPY(5), SSIZE2(14,2), STX(7), STY(7), SX(7),
+ + SY(7)
+ INTEGER INCXS(4), INCYS(4), LENS(4,2), MWPINX(11),
+ + MWPINY(11), MWPN(11), NS(4)
+* .. External Subroutines ..
+ EXTERNAL SROT, STEST
+* .. Intrinsic Functions ..
+ INTRINSIC ABS, MIN
+* .. Common blocks ..
+ COMMON /COMBLA/ICASE, N, INCX, INCY, PASS
+* .. Data statements ..
+ DATA INCXS/1, 2, -2, -1/
+ DATA INCYS/1, -2, 1, -2/
+ DATA LENS/1, 1, 2, 4, 1, 1, 3, 7/
+ DATA NS/0, 1, 2, 4/
+ DATA DX1/0.6E0, 0.1E0, -0.5E0, 0.8E0, 0.9E0, -0.3E0,
+ + -0.4E0/
+ DATA DY1/0.5E0, -0.9E0, 0.3E0, 0.7E0, -0.6E0, 0.2E0,
+ + 0.8E0/
+ DATA SC, SS/0.8E0, 0.6E0/
+ DATA DT9X/0.6E0, 0.0E0, 0.0E0, 0.0E0, 0.0E0, 0.0E0,
+ + 0.0E0, 0.78E0, 0.0E0, 0.0E0, 0.0E0, 0.0E0,
+ + 0.0E0, 0.0E0, 0.78E0, -0.46E0, 0.0E0, 0.0E0,
+ + 0.0E0, 0.0E0, 0.0E0, 0.78E0, -0.46E0, -0.22E0,
+ + 1.06E0, 0.0E0, 0.0E0, 0.0E0, 0.6E0, 0.0E0,
+ + 0.0E0, 0.0E0, 0.0E0, 0.0E0, 0.0E0, 0.78E0,
+ + 0.0E0, 0.0E0, 0.0E0, 0.0E0, 0.0E0, 0.0E0,
+ + 0.66E0, 0.1E0, -0.1E0, 0.0E0, 0.0E0, 0.0E0,
+ + 0.0E0, 0.96E0, 0.1E0, -0.76E0, 0.8E0, 0.90E0,
+ + -0.3E0, -0.02E0, 0.6E0, 0.0E0, 0.0E0, 0.0E0,
+ + 0.0E0, 0.0E0, 0.0E0, 0.78E0, 0.0E0, 0.0E0,
+ + 0.0E0, 0.0E0, 0.0E0, 0.0E0, -0.06E0, 0.1E0,
+ + -0.1E0, 0.0E0, 0.0E0, 0.0E0, 0.0E0, 0.90E0,
+ + 0.1E0, -0.22E0, 0.8E0, 0.18E0, -0.3E0, -0.02E0,
+ + 0.6E0, 0.0E0, 0.0E0, 0.0E0, 0.0E0, 0.0E0, 0.0E0,
+ + 0.78E0, 0.0E0, 0.0E0, 0.0E0, 0.0E0, 0.0E0,
+ + 0.0E0, 0.78E0, 0.26E0, 0.0E0, 0.0E0, 0.0E0,
+ + 0.0E0, 0.0E0, 0.78E0, 0.26E0, -0.76E0, 1.12E0,
+ + 0.0E0, 0.0E0, 0.0E0/
+ DATA DT9Y/0.5E0, 0.0E0, 0.0E0, 0.0E0, 0.0E0, 0.0E0,
+ + 0.0E0, 0.04E0, 0.0E0, 0.0E0, 0.0E0, 0.0E0,
+ + 0.0E0, 0.0E0, 0.04E0, -0.78E0, 0.0E0, 0.0E0,
+ + 0.0E0, 0.0E0, 0.0E0, 0.04E0, -0.78E0, 0.54E0,
+ + 0.08E0, 0.0E0, 0.0E0, 0.0E0, 0.5E0, 0.0E0,
+ + 0.0E0, 0.0E0, 0.0E0, 0.0E0, 0.0E0, 0.04E0,
+ + 0.0E0, 0.0E0, 0.0E0, 0.0E0, 0.0E0, 0.0E0, 0.7E0,
+ + -0.9E0, -0.12E0, 0.0E0, 0.0E0, 0.0E0, 0.0E0,
+ + 0.64E0, -0.9E0, -0.30E0, 0.7E0, -0.18E0, 0.2E0,
+ + 0.28E0, 0.5E0, 0.0E0, 0.0E0, 0.0E0, 0.0E0,
+ + 0.0E0, 0.0E0, 0.04E0, 0.0E0, 0.0E0, 0.0E0,
+ + 0.0E0, 0.0E0, 0.0E0, 0.7E0, -1.08E0, 0.0E0,
+ + 0.0E0, 0.0E0, 0.0E0, 0.0E0, 0.64E0, -1.26E0,
+ + 0.54E0, 0.20E0, 0.0E0, 0.0E0, 0.0E0, 0.5E0,
+ + 0.0E0, 0.0E0, 0.0E0, 0.0E0, 0.0E0, 0.0E0,
+ + 0.04E0, 0.0E0, 0.0E0, 0.0E0, 0.0E0, 0.0E0,
+ + 0.0E0, 0.04E0, -0.9E0, 0.18E0, 0.0E0, 0.0E0,
+ + 0.0E0, 0.0E0, 0.04E0, -0.9E0, 0.18E0, 0.7E0,
+ + -0.18E0, 0.2E0, 0.16E0/
+ DATA SSIZE2/0.0E0, 0.0E0, 0.0E0, 0.0E0, 0.0E0, 0.0E0,
+ + 0.0E0, 0.0E0, 0.0E0, 0.0E0, 0.0E0, 0.0E0, 0.0E0,
+ + 0.0E0, 1.17E0, 1.17E0, 1.17E0, 1.17E0, 1.17E0,
+ + 1.17E0, 1.17E0, 1.17E0, 1.17E0, 1.17E0, 1.17E0,
+ + 1.17E0, 1.17E0, 1.17E0/
+* .. Executable Statements ..
+*
+ DO 60 KI = 1, 4
+ INCX = INCXS(KI)
+ INCY = INCYS(KI)
+ MX = ABS(INCX)
+ MY = ABS(INCY)
+*
+ DO 40 KN = 1, 4
+ N = NS(KN)
+ KSIZE = MIN(2,KN)
+ LENX = LENS(KN,MX)
+ LENY = LENS(KN,MY)
+*
+ IF (ICASE.EQ.4) THEN
+* .. SROT ..
+ DO 20 I = 1, 7
+ SX(I) = DX1(I)
+ SY(I) = DY1(I)
+ STX(I) = DT9X(I,KN,KI)
+ STY(I) = DT9Y(I,KN,KI)
+ 20 CONTINUE
+ CALL SROT(N,SX,INCX,SY,INCY,SC,SS)
+ CALL STEST(LENX,SX,STX,SSIZE2(1,KSIZE),SFAC)
+ CALL STEST(LENY,SY,STY,SSIZE2(1,KSIZE),SFAC)
+ ELSE
+ WRITE (NOUT,*) ' Shouldn''t be here in CHECK3'
+ STOP
+ END IF
+ 40 CONTINUE
+ 60 CONTINUE
+*
+ MWPC(1) = 1
+ DO 80 I = 2, 11
+ MWPC(I) = 0
+ 80 CONTINUE
+ MWPS(1) = 0
+ DO 100 I = 2, 6
+ MWPS(I) = 1
+ 100 CONTINUE
+ DO 120 I = 7, 11
+ MWPS(I) = -1
+ 120 CONTINUE
+ MWPINX(1) = 1
+ MWPINX(2) = 1
+ MWPINX(3) = 1
+ MWPINX(4) = -1
+ MWPINX(5) = 1
+ MWPINX(6) = -1
+ MWPINX(7) = 1
+ MWPINX(8) = 1
+ MWPINX(9) = -1
+ MWPINX(10) = 1
+ MWPINX(11) = -1
+ MWPINY(1) = 1
+ MWPINY(2) = 1
+ MWPINY(3) = -1
+ MWPINY(4) = -1
+ MWPINY(5) = 2
+ MWPINY(6) = 1
+ MWPINY(7) = 1
+ MWPINY(8) = -1
+ MWPINY(9) = -1
+ MWPINY(10) = 2
+ MWPINY(11) = 1
+ DO 140 I = 1, 11
+ MWPN(I) = 5
+ 140 CONTINUE
+ MWPN(5) = 3
+ MWPN(10) = 3
+ DO 160 I = 1, 5
+ MWPX(I) = I
+ MWPY(I) = I
+ MWPTX(1,I) = I
+ MWPTY(1,I) = I
+ MWPTX(2,I) = I
+ MWPTY(2,I) = -I
+ MWPTX(3,I) = 6 - I
+ MWPTY(3,I) = I - 6
+ MWPTX(4,I) = I
+ MWPTY(4,I) = -I
+ MWPTX(6,I) = 6 - I
+ MWPTY(6,I) = I - 6
+ MWPTX(7,I) = -I
+ MWPTY(7,I) = I
+ MWPTX(8,I) = I - 6
+ MWPTY(8,I) = 6 - I
+ MWPTX(9,I) = -I
+ MWPTY(9,I) = I
+ MWPTX(11,I) = I - 6
+ MWPTY(11,I) = 6 - I
+ 160 CONTINUE
+ MWPTX(5,1) = 1
+ MWPTX(5,2) = 3
+ MWPTX(5,3) = 5
+ MWPTX(5,4) = 4
+ MWPTX(5,5) = 5
+ MWPTY(5,1) = -1
+ MWPTY(5,2) = 2
+ MWPTY(5,3) = -2
+ MWPTY(5,4) = 4
+ MWPTY(5,5) = -3
+ MWPTX(10,1) = -1
+ MWPTX(10,2) = -3
+ MWPTX(10,3) = -5
+ MWPTX(10,4) = 4
+ MWPTX(10,5) = 5
+ MWPTY(10,1) = 1
+ MWPTY(10,2) = 2
+ MWPTY(10,3) = 2
+ MWPTY(10,4) = 4
+ MWPTY(10,5) = 3
+ DO 200 I = 1, 11
+ INCX = MWPINX(I)
+ INCY = MWPINY(I)
+ DO 180 K = 1, 5
+ COPYX(K) = MWPX(K)
+ COPYY(K) = MWPY(K)
+ MWPSTX(K) = MWPTX(I,K)
+ MWPSTY(K) = MWPTY(I,K)
+ 180 CONTINUE
+ CALL SROT(MWPN(I),COPYX,INCX,COPYY,INCY,MWPC(I),MWPS(I))
+ CALL STEST(5,COPYX,MWPSTX,MWPSTX,SFAC)
+ CALL STEST(5,COPYY,MWPSTY,MWPSTY,SFAC)
+ 200 CONTINUE
+ RETURN
+ END
+ SUBROUTINE STEST(LEN,SCOMP,STRUE,SSIZE,SFAC)
+* ********************************* STEST **************************
+*
+* THIS SUBR COMPARES ARRAYS SCOMP() AND STRUE() OF LENGTH LEN TO
+* SEE IF THE TERM BY TERM DIFFERENCES, MULTIPLIED BY SFAC, ARE
+* NEGLIGIBLE.
+*
+* C. L. LAWSON, JPL, 1974 DEC 10
+*
+* .. Parameters ..
+ INTEGER NOUT
+ REAL ZERO
+ PARAMETER (NOUT=6, ZERO=0.0E0)
+* .. Scalar Arguments ..
+ REAL SFAC
+ INTEGER LEN
+* .. Array Arguments ..
+ REAL SCOMP(LEN), SSIZE(LEN), STRUE(LEN)
+* .. Scalars in Common ..
+ INTEGER ICASE, INCX, INCY, N
+ LOGICAL PASS
+* .. Local Scalars ..
+ REAL SD
+ INTEGER I
+* .. External Functions ..
+ REAL SDIFF
+ EXTERNAL SDIFF
+* .. Intrinsic Functions ..
+ INTRINSIC ABS
+* .. Common blocks ..
+ COMMON /COMBLA/ICASE, N, INCX, INCY, PASS
+* .. Executable Statements ..
+*
+ DO 40 I = 1, LEN
+ SD = SCOMP(I) - STRUE(I)
+ IF (ABS(SFAC*SD) .LE. ABS(SSIZE(I))*EPSILON(ZERO))
+ + GO TO 40
+*
+* HERE SCOMP(I) IS NOT CLOSE TO STRUE(I).
+*
+ IF ( .NOT. PASS) GO TO 20
+* PRINT FAIL MESSAGE AND HEADER.
+ PASS = .FALSE.
+ WRITE (NOUT,99999)
+ WRITE (NOUT,99998)
+ 20 WRITE (NOUT,99997) ICASE, N, INCX, INCY, I, SCOMP(I),
+ + STRUE(I), SD, SSIZE(I)
+ 40 CONTINUE
+ RETURN
+*
+99999 FORMAT (' FAIL')
+99998 FORMAT (/' CASE N INCX INCY I ',
+ + ' COMP(I) TRUE(I) DIFFERENCE',
+ + ' SIZE(I)',/1X)
+99997 FORMAT (1X,I4,I3,2I5,I3,2E36.8,2E12.4)
+ END
+ SUBROUTINE STEST1(SCOMP1,STRUE1,SSIZE,SFAC)
+* ************************* STEST1 *****************************
+*
+* THIS IS AN INTERFACE SUBROUTINE TO ACCOMMODATE THE FORTRAN
+* REQUIREMENT THAT WHEN A DUMMY ARGUMENT IS AN ARRAY, THE
+* ACTUAL ARGUMENT MUST ALSO BE AN ARRAY OR AN ARRAY ELEMENT.
+*
+* C.L. LAWSON, JPL, 1978 DEC 6
+*
+* .. Scalar Arguments ..
+ REAL SCOMP1, SFAC, STRUE1
+* .. Array Arguments ..
+ REAL SSIZE(*)
+* .. Local Arrays ..
+ REAL SCOMP(1), STRUE(1)
+* .. External Subroutines ..
+ EXTERNAL STEST
+* .. Executable Statements ..
+*
+ SCOMP(1) = SCOMP1
+ STRUE(1) = STRUE1
+ CALL STEST(1,SCOMP,STRUE,SSIZE,SFAC)
+*
+ RETURN
+ END
+ REAL FUNCTION SDIFF(SA,SB)
+* ********************************* SDIFF **************************
+* COMPUTES DIFFERENCE OF TWO NUMBERS. C. L. LAWSON, JPL 1974 FEB 15
+*
+* .. Scalar Arguments ..
+ REAL SA, SB
+* .. Executable Statements ..
+ SDIFF = SA - SB
+ RETURN
+ END
+ SUBROUTINE ITEST1(ICOMP,ITRUE)
+* ********************************* ITEST1 *************************
+*
+* THIS SUBROUTINE COMPARES THE VARIABLES ICOMP AND ITRUE FOR
+* EQUALITY.
+* C. L. LAWSON, JPL, 1974 DEC 10
+*
+* .. Parameters ..
+ INTEGER NOUT
+ PARAMETER (NOUT=6)
+* .. Scalar Arguments ..
+ INTEGER ICOMP, ITRUE
+* .. Scalars in Common ..
+ INTEGER ICASE, INCX, INCY, N
+ LOGICAL PASS
+* .. Local Scalars ..
+ INTEGER ID
+* .. Common blocks ..
+ COMMON /COMBLA/ICASE, N, INCX, INCY, PASS
+* .. Executable Statements ..
+*
+ IF (ICOMP.EQ.ITRUE) GO TO 40
+*
+* HERE ICOMP IS NOT EQUAL TO ITRUE.
+*
+ IF ( .NOT. PASS) GO TO 20
+* PRINT FAIL MESSAGE AND HEADER.
+ PASS = .FALSE.
+ WRITE (NOUT,99999)
+ WRITE (NOUT,99998)
+ 20 ID = ICOMP - ITRUE
+ WRITE (NOUT,99997) ICASE, N, INCX, INCY, ICOMP, ITRUE, ID
+ 40 CONTINUE
+ RETURN
+*
+99999 FORMAT (' FAIL')
+99998 FORMAT (/' CASE N INCX INCY ',
+ + ' COMP TRUE DIFFERENCE',
+ + /1X)
+99997 FORMAT (1X,I4,I3,2I5,2I36,I12)
+ END
diff --git a/blas/testing/sblat2.dat b/blas/testing/sblat2.dat
new file mode 100644
index 0000000..f537d30
--- /dev/null
+++ b/blas/testing/sblat2.dat
@@ -0,0 +1,34 @@
+'sblat2.summ' NAME OF SUMMARY OUTPUT FILE
+6 UNIT NUMBER OF SUMMARY FILE
+'sblat2.snap' NAME OF SNAPSHOT OUTPUT FILE
+-1 UNIT NUMBER OF SNAPSHOT FILE (NOT USED IF .LT. 0)
+F LOGICAL FLAG, T TO REWIND SNAPSHOT FILE AFTER EACH RECORD.
+F LOGICAL FLAG, T TO STOP ON FAILURES.
+T LOGICAL FLAG, T TO TEST ERROR EXITS.
+16.0 THRESHOLD VALUE OF TEST RATIO
+6 NUMBER OF VALUES OF N
+0 1 2 3 5 9 VALUES OF N
+4 NUMBER OF VALUES OF K
+0 1 2 4 VALUES OF K
+4 NUMBER OF VALUES OF INCX AND INCY
+1 2 -1 -2 VALUES OF INCX AND INCY
+3 NUMBER OF VALUES OF ALPHA
+0.0 1.0 0.7 VALUES OF ALPHA
+3 NUMBER OF VALUES OF BETA
+0.0 1.0 0.9 VALUES OF BETA
+SGEMV T PUT F FOR NO TEST. SAME COLUMNS.
+SGBMV T PUT F FOR NO TEST. SAME COLUMNS.
+SSYMV T PUT F FOR NO TEST. SAME COLUMNS.
+SSBMV T PUT F FOR NO TEST. SAME COLUMNS.
+SSPMV T PUT F FOR NO TEST. SAME COLUMNS.
+STRMV T PUT F FOR NO TEST. SAME COLUMNS.
+STBMV T PUT F FOR NO TEST. SAME COLUMNS.
+STPMV T PUT F FOR NO TEST. SAME COLUMNS.
+STRSV T PUT F FOR NO TEST. SAME COLUMNS.
+STBSV T PUT F FOR NO TEST. SAME COLUMNS.
+STPSV T PUT F FOR NO TEST. SAME COLUMNS.
+SGER T PUT F FOR NO TEST. SAME COLUMNS.
+SSYR T PUT F FOR NO TEST. SAME COLUMNS.
+SSPR T PUT F FOR NO TEST. SAME COLUMNS.
+SSYR2 T PUT F FOR NO TEST. SAME COLUMNS.
+SSPR2 T PUT F FOR NO TEST. SAME COLUMNS.
diff --git a/blas/testing/sblat2.f b/blas/testing/sblat2.f
new file mode 100644
index 0000000..71605ed
--- /dev/null
+++ b/blas/testing/sblat2.f
@@ -0,0 +1,3176 @@
+*> \brief \b SBLAT2
+*
+* =========== DOCUMENTATION ===========
+*
+* Online html documentation available at
+* http://www.netlib.org/lapack/explore-html/
+*
+* Definition:
+* ===========
+*
+* PROGRAM SBLAT2
+*
+*
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
+*>
+*> Test program for the REAL Level 2 Blas.
+*>
+*> The program must be driven by a short data file. The first 18 records
+*> of the file are read using list-directed input, the last 16 records
+*> are read using the format ( A6, L2 ). An annotated example of a data
+*> file can be obtained by deleting the first 3 characters from the
+*> following 34 lines:
+*> 'sblat2.out' NAME OF SUMMARY OUTPUT FILE
+*> 6 UNIT NUMBER OF SUMMARY FILE
+*> 'SBLAT2.SNAP' NAME OF SNAPSHOT OUTPUT FILE
+*> -1 UNIT NUMBER OF SNAPSHOT FILE (NOT USED IF .LT. 0)
+*> F LOGICAL FLAG, T TO REWIND SNAPSHOT FILE AFTER EACH RECORD.
+*> F LOGICAL FLAG, T TO STOP ON FAILURES.
+*> T LOGICAL FLAG, T TO TEST ERROR EXITS.
+*> 16.0 THRESHOLD VALUE OF TEST RATIO
+*> 6 NUMBER OF VALUES OF N
+*> 0 1 2 3 5 9 VALUES OF N
+*> 4 NUMBER OF VALUES OF K
+*> 0 1 2 4 VALUES OF K
+*> 4 NUMBER OF VALUES OF INCX AND INCY
+*> 1 2 -1 -2 VALUES OF INCX AND INCY
+*> 3 NUMBER OF VALUES OF ALPHA
+*> 0.0 1.0 0.7 VALUES OF ALPHA
+*> 3 NUMBER OF VALUES OF BETA
+*> 0.0 1.0 0.9 VALUES OF BETA
+*> SGEMV T PUT F FOR NO TEST. SAME COLUMNS.
+*> SGBMV T PUT F FOR NO TEST. SAME COLUMNS.
+*> SSYMV T PUT F FOR NO TEST. SAME COLUMNS.
+*> SSBMV T PUT F FOR NO TEST. SAME COLUMNS.
+*> SSPMV T PUT F FOR NO TEST. SAME COLUMNS.
+*> STRMV T PUT F FOR NO TEST. SAME COLUMNS.
+*> STBMV T PUT F FOR NO TEST. SAME COLUMNS.
+*> STPMV T PUT F FOR NO TEST. SAME COLUMNS.
+*> STRSV T PUT F FOR NO TEST. SAME COLUMNS.
+*> STBSV T PUT F FOR NO TEST. SAME COLUMNS.
+*> STPSV T PUT F FOR NO TEST. SAME COLUMNS.
+*> SGER T PUT F FOR NO TEST. SAME COLUMNS.
+*> SSYR T PUT F FOR NO TEST. SAME COLUMNS.
+*> SSPR T PUT F FOR NO TEST. SAME COLUMNS.
+*> SSYR2 T PUT F FOR NO TEST. SAME COLUMNS.
+*> SSPR2 T PUT F FOR NO TEST. SAME COLUMNS.
+*>
+*> Further Details
+*> ===============
+*>
+*> See:
+*>
+*> Dongarra J. J., Du Croz J. J., Hammarling S. and Hanson R. J..
+*> An extended set of Fortran Basic Linear Algebra Subprograms.
+*>
+*> Technical Memoranda Nos. 41 (revision 3) and 81, Mathematics
+*> and Computer Science Division, Argonne National Laboratory,
+*> 9700 South Cass Avenue, Argonne, Illinois 60439, US.
+*>
+*> Or
+*>
+*> NAG Technical Reports TR3/87 and TR4/87, Numerical Algorithms
+*> Group Ltd., NAG Central Office, 256 Banbury Road, Oxford
+*> OX2 7DE, UK, and Numerical Algorithms Group Inc., 1101 31st
+*> Street, Suite 100, Downers Grove, Illinois 60515-1263, USA.
+*>
+*>
+*> -- Written on 10-August-1987.
+*> Richard Hanson, Sandia National Labs.
+*> Jeremy Du Croz, NAG Central Office.
+*>
+*> 10-9-00: Change STATUS='NEW' to 'UNKNOWN' so that the testers
+*> can be run multiple times without deleting generated
+*> output files (susan)
+*> \endverbatim
+*
+* Authors:
+* ========
+*
+*> \author Univ. of Tennessee
+*> \author Univ. of California Berkeley
+*> \author Univ. of Colorado Denver
+*> \author NAG Ltd.
+*
+*> \date April 2012
+*
+*> \ingroup single_blas_testing
+*
+* =====================================================================
+ PROGRAM SBLAT2
+*
+* -- Reference BLAS test routine (version 3.4.1) --
+* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
+* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+* April 2012
+*
+* =====================================================================
+*
+* .. Parameters ..
+ INTEGER NIN
+ PARAMETER ( NIN = 5 )
+ INTEGER NSUBS
+ PARAMETER ( NSUBS = 16 )
+ REAL ZERO, ONE
+ PARAMETER ( ZERO = 0.0, ONE = 1.0 )
+ INTEGER NMAX, INCMAX
+ PARAMETER ( NMAX = 65, INCMAX = 2 )
+ INTEGER NINMAX, NIDMAX, NKBMAX, NALMAX, NBEMAX
+ PARAMETER ( NINMAX = 7, NIDMAX = 9, NKBMAX = 7,
+ $ NALMAX = 7, NBEMAX = 7 )
+* .. Local Scalars ..
+ REAL EPS, ERR, THRESH
+ INTEGER I, ISNUM, J, N, NALF, NBET, NIDIM, NINC, NKB,
+ $ NOUT, NTRA
+ LOGICAL FATAL, LTESTT, REWI, SAME, SFATAL, TRACE,
+ $ TSTERR
+ CHARACTER*1 TRANS
+ CHARACTER*6 SNAMET
+ CHARACTER*32 SNAPS, SUMMRY
+* .. Local Arrays ..
+ REAL A( NMAX, NMAX ), AA( NMAX*NMAX ),
+ $ ALF( NALMAX ), AS( NMAX*NMAX ), BET( NBEMAX ),
+ $ G( NMAX ), X( NMAX ), XS( NMAX*INCMAX ),
+ $ XX( NMAX*INCMAX ), Y( NMAX ),
+ $ YS( NMAX*INCMAX ), YT( NMAX ),
+ $ YY( NMAX*INCMAX ), Z( 2*NMAX )
+ INTEGER IDIM( NIDMAX ), INC( NINMAX ), KB( NKBMAX )
+ LOGICAL LTEST( NSUBS )
+ CHARACTER*6 SNAMES( NSUBS )
+* .. External Functions ..
+ REAL SDIFF
+ LOGICAL LSE
+ EXTERNAL SDIFF, LSE
+* .. External Subroutines ..
+ EXTERNAL SCHK1, SCHK2, SCHK3, SCHK4, SCHK5, SCHK6,
+ $ SCHKE, SMVCH
+* .. Intrinsic Functions ..
+ INTRINSIC ABS, MAX, MIN
+* .. Scalars in Common ..
+ INTEGER INFOT, NOUTC
+ LOGICAL LERR, OK
+ CHARACTER*6 SRNAMT
+* .. Common blocks ..
+ COMMON /INFOC/INFOT, NOUTC, OK, LERR
+ COMMON /SRNAMC/SRNAMT
+* .. Data statements ..
+ DATA SNAMES/'SGEMV ', 'SGBMV ', 'SSYMV ', 'SSBMV ',
+ $ 'SSPMV ', 'STRMV ', 'STBMV ', 'STPMV ',
+ $ 'STRSV ', 'STBSV ', 'STPSV ', 'SGER ',
+ $ 'SSYR ', 'SSPR ', 'SSYR2 ', 'SSPR2 '/
+* .. Executable Statements ..
+*
+* Read name and unit number for summary output file and open file.
+*
+ READ( NIN, FMT = * )SUMMRY
+ READ( NIN, FMT = * )NOUT
+ OPEN( NOUT, FILE = SUMMRY, STATUS = 'UNKNOWN' )
+ NOUTC = NOUT
+*
+* Read name and unit number for snapshot output file and open file.
+*
+ READ( NIN, FMT = * )SNAPS
+ READ( NIN, FMT = * )NTRA
+ TRACE = NTRA.GE.0
+ IF( TRACE )THEN
+ OPEN( NTRA, FILE = SNAPS, STATUS = 'UNKNOWN' )
+ END IF
+* Read the flag that directs rewinding of the snapshot file.
+ READ( NIN, FMT = * )REWI
+ REWI = REWI.AND.TRACE
+* Read the flag that directs stopping on any failure.
+ READ( NIN, FMT = * )SFATAL
+* Read the flag that indicates whether error exits are to be tested.
+ READ( NIN, FMT = * )TSTERR
+* Read the threshold value of the test ratio
+ READ( NIN, FMT = * )THRESH
+*
+* Read and check the parameter values for the tests.
+*
+* Values of N
+ READ( NIN, FMT = * )NIDIM
+ IF( NIDIM.LT.1.OR.NIDIM.GT.NIDMAX )THEN
+ WRITE( NOUT, FMT = 9997 )'N', NIDMAX
+ GO TO 230
+ END IF
+ READ( NIN, FMT = * )( IDIM( I ), I = 1, NIDIM )
+ DO 10 I = 1, NIDIM
+ IF( IDIM( I ).LT.0.OR.IDIM( I ).GT.NMAX )THEN
+ WRITE( NOUT, FMT = 9996 )NMAX
+ GO TO 230
+ END IF
+ 10 CONTINUE
+* Values of K
+ READ( NIN, FMT = * )NKB
+ IF( NKB.LT.1.OR.NKB.GT.NKBMAX )THEN
+ WRITE( NOUT, FMT = 9997 )'K', NKBMAX
+ GO TO 230
+ END IF
+ READ( NIN, FMT = * )( KB( I ), I = 1, NKB )
+ DO 20 I = 1, NKB
+ IF( KB( I ).LT.0 )THEN
+ WRITE( NOUT, FMT = 9995 )
+ GO TO 230
+ END IF
+ 20 CONTINUE
+* Values of INCX and INCY
+ READ( NIN, FMT = * )NINC
+ IF( NINC.LT.1.OR.NINC.GT.NINMAX )THEN
+ WRITE( NOUT, FMT = 9997 )'INCX AND INCY', NINMAX
+ GO TO 230
+ END IF
+ READ( NIN, FMT = * )( INC( I ), I = 1, NINC )
+ DO 30 I = 1, NINC
+ IF( INC( I ).EQ.0.OR.ABS( INC( I ) ).GT.INCMAX )THEN
+ WRITE( NOUT, FMT = 9994 )INCMAX
+ GO TO 230
+ END IF
+ 30 CONTINUE
+* Values of ALPHA
+ READ( NIN, FMT = * )NALF
+ IF( NALF.LT.1.OR.NALF.GT.NALMAX )THEN
+ WRITE( NOUT, FMT = 9997 )'ALPHA', NALMAX
+ GO TO 230
+ END IF
+ READ( NIN, FMT = * )( ALF( I ), I = 1, NALF )
+* Values of BETA
+ READ( NIN, FMT = * )NBET
+ IF( NBET.LT.1.OR.NBET.GT.NBEMAX )THEN
+ WRITE( NOUT, FMT = 9997 )'BETA', NBEMAX
+ GO TO 230
+ END IF
+ READ( NIN, FMT = * )( BET( I ), I = 1, NBET )
+*
+* Report values of parameters.
+*
+ WRITE( NOUT, FMT = 9993 )
+ WRITE( NOUT, FMT = 9992 )( IDIM( I ), I = 1, NIDIM )
+ WRITE( NOUT, FMT = 9991 )( KB( I ), I = 1, NKB )
+ WRITE( NOUT, FMT = 9990 )( INC( I ), I = 1, NINC )
+ WRITE( NOUT, FMT = 9989 )( ALF( I ), I = 1, NALF )
+ WRITE( NOUT, FMT = 9988 )( BET( I ), I = 1, NBET )
+ IF( .NOT.TSTERR )THEN
+ WRITE( NOUT, FMT = * )
+ WRITE( NOUT, FMT = 9980 )
+ END IF
+ WRITE( NOUT, FMT = * )
+ WRITE( NOUT, FMT = 9999 )THRESH
+ WRITE( NOUT, FMT = * )
+*
+* Read names of subroutines and flags which indicate
+* whether they are to be tested.
+*
+ DO 40 I = 1, NSUBS
+ LTEST( I ) = .FALSE.
+ 40 CONTINUE
+ 50 READ( NIN, FMT = 9984, END = 80 )SNAMET, LTESTT
+ DO 60 I = 1, NSUBS
+ IF( SNAMET.EQ.SNAMES( I ) )
+ $ GO TO 70
+ 60 CONTINUE
+ WRITE( NOUT, FMT = 9986 )SNAMET
+ STOP
+ 70 LTEST( I ) = LTESTT
+ GO TO 50
+*
+ 80 CONTINUE
+ CLOSE ( NIN )
+*
+* Compute EPS (the machine precision).
+*
+ EPS = EPSILON(ZERO)
+ WRITE( NOUT, FMT = 9998 )EPS
+*
+* Check the reliability of SMVCH using exact data.
+*
+ N = MIN( 32, NMAX )
+ DO 120 J = 1, N
+ DO 110 I = 1, N
+ A( I, J ) = MAX( I - J + 1, 0 )
+ 110 CONTINUE
+ X( J ) = J
+ Y( J ) = ZERO
+ 120 CONTINUE
+ DO 130 J = 1, N
+ YY( J ) = J*( ( J + 1 )*J )/2 - ( ( J + 1 )*J*( J - 1 ) )/3
+ 130 CONTINUE
+* YY holds the exact result. On exit from SMVCH YT holds
+* the result computed by SMVCH.
+ TRANS = 'N'
+ CALL SMVCH( TRANS, N, N, ONE, A, NMAX, X, 1, ZERO, Y, 1, YT, G,
+ $ YY, EPS, ERR, FATAL, NOUT, .TRUE. )
+ SAME = LSE( YY, YT, N )
+ IF( .NOT.SAME.OR.ERR.NE.ZERO )THEN
+ WRITE( NOUT, FMT = 9985 )TRANS, SAME, ERR
+ STOP
+ END IF
+ TRANS = 'T'
+ CALL SMVCH( TRANS, N, N, ONE, A, NMAX, X, -1, ZERO, Y, -1, YT, G,
+ $ YY, EPS, ERR, FATAL, NOUT, .TRUE. )
+ SAME = LSE( YY, YT, N )
+ IF( .NOT.SAME.OR.ERR.NE.ZERO )THEN
+ WRITE( NOUT, FMT = 9985 )TRANS, SAME, ERR
+ STOP
+ END IF
+*
+* Test each subroutine in turn.
+*
+ DO 210 ISNUM = 1, NSUBS
+ WRITE( NOUT, FMT = * )
+ IF( .NOT.LTEST( ISNUM ) )THEN
+* Subprogram is not to be tested.
+ WRITE( NOUT, FMT = 9983 )SNAMES( ISNUM )
+ ELSE
+ SRNAMT = SNAMES( ISNUM )
+* Test error exits.
+ IF( TSTERR )THEN
+ CALL SCHKE( ISNUM, SNAMES( ISNUM ), NOUT )
+ WRITE( NOUT, FMT = * )
+ END IF
+* Test computations.
+ INFOT = 0
+ OK = .TRUE.
+ FATAL = .FALSE.
+ GO TO ( 140, 140, 150, 150, 150, 160, 160,
+ $ 160, 160, 160, 160, 170, 180, 180,
+ $ 190, 190 )ISNUM
+* Test SGEMV, 01, and SGBMV, 02.
+ 140 CALL SCHK1( SNAMES( ISNUM ), EPS, THRESH, NOUT, NTRA, TRACE,
+ $ REWI, FATAL, NIDIM, IDIM, NKB, KB, NALF, ALF,
+ $ NBET, BET, NINC, INC, NMAX, INCMAX, A, AA, AS,
+ $ X, XX, XS, Y, YY, YS, YT, G )
+ GO TO 200
+* Test SSYMV, 03, SSBMV, 04, and SSPMV, 05.
+ 150 CALL SCHK2( SNAMES( ISNUM ), EPS, THRESH, NOUT, NTRA, TRACE,
+ $ REWI, FATAL, NIDIM, IDIM, NKB, KB, NALF, ALF,
+ $ NBET, BET, NINC, INC, NMAX, INCMAX, A, AA, AS,
+ $ X, XX, XS, Y, YY, YS, YT, G )
+ GO TO 200
+* Test STRMV, 06, STBMV, 07, STPMV, 08,
+* STRSV, 09, STBSV, 10, and STPSV, 11.
+ 160 CALL SCHK3( SNAMES( ISNUM ), EPS, THRESH, NOUT, NTRA, TRACE,
+ $ REWI, FATAL, NIDIM, IDIM, NKB, KB, NINC, INC,
+ $ NMAX, INCMAX, A, AA, AS, Y, YY, YS, YT, G, Z )
+ GO TO 200
+* Test SGER, 12.
+ 170 CALL SCHK4( SNAMES( ISNUM ), EPS, THRESH, NOUT, NTRA, TRACE,
+ $ REWI, FATAL, NIDIM, IDIM, NALF, ALF, NINC, INC,
+ $ NMAX, INCMAX, A, AA, AS, X, XX, XS, Y, YY, YS,
+ $ YT, G, Z )
+ GO TO 200
+* Test SSYR, 13, and SSPR, 14.
+ 180 CALL SCHK5( SNAMES( ISNUM ), EPS, THRESH, NOUT, NTRA, TRACE,
+ $ REWI, FATAL, NIDIM, IDIM, NALF, ALF, NINC, INC,
+ $ NMAX, INCMAX, A, AA, AS, X, XX, XS, Y, YY, YS,
+ $ YT, G, Z )
+ GO TO 200
+* Test SSYR2, 15, and SSPR2, 16.
+ 190 CALL SCHK6( SNAMES( ISNUM ), EPS, THRESH, NOUT, NTRA, TRACE,
+ $ REWI, FATAL, NIDIM, IDIM, NALF, ALF, NINC, INC,
+ $ NMAX, INCMAX, A, AA, AS, X, XX, XS, Y, YY, YS,
+ $ YT, G, Z )
+*
+ 200 IF( FATAL.AND.SFATAL )
+ $ GO TO 220
+ END IF
+ 210 CONTINUE
+ WRITE( NOUT, FMT = 9982 )
+ GO TO 240
+*
+ 220 CONTINUE
+ WRITE( NOUT, FMT = 9981 )
+ GO TO 240
+*
+ 230 CONTINUE
+ WRITE( NOUT, FMT = 9987 )
+*
+ 240 CONTINUE
+ IF( TRACE )
+ $ CLOSE ( NTRA )
+ CLOSE ( NOUT )
+ STOP
+*
+ 9999 FORMAT( ' ROUTINES PASS COMPUTATIONAL TESTS IF TEST RATIO IS LES',
+ $ 'S THAN', F8.2 )
+ 9998 FORMAT( ' RELATIVE MACHINE PRECISION IS TAKEN TO BE', 1P, E9.1 )
+ 9997 FORMAT( ' NUMBER OF VALUES OF ', A, ' IS LESS THAN 1 OR GREATER ',
+ $ 'THAN ', I2 )
+ 9996 FORMAT( ' VALUE OF N IS LESS THAN 0 OR GREATER THAN ', I2 )
+ 9995 FORMAT( ' VALUE OF K IS LESS THAN 0' )
+ 9994 FORMAT( ' ABSOLUTE VALUE OF INCX OR INCY IS 0 OR GREATER THAN ',
+ $ I2 )
+ 9993 FORMAT( ' TESTS OF THE REAL LEVEL 2 BLAS', //' THE F',
+ $ 'OLLOWING PARAMETER VALUES WILL BE USED:' )
+ 9992 FORMAT( ' FOR N ', 9I6 )
+ 9991 FORMAT( ' FOR K ', 7I6 )
+ 9990 FORMAT( ' FOR INCX AND INCY ', 7I6 )
+ 9989 FORMAT( ' FOR ALPHA ', 7F6.1 )
+ 9988 FORMAT( ' FOR BETA ', 7F6.1 )
+ 9987 FORMAT( ' AMEND DATA FILE OR INCREASE ARRAY SIZES IN PROGRAM',
+ $ /' ******* TESTS ABANDONED *******' )
+ 9986 FORMAT( ' SUBPROGRAM NAME ', A6, ' NOT RECOGNIZED', /' ******* T',
+ $ 'ESTS ABANDONED *******' )
+ 9985 FORMAT( ' ERROR IN SMVCH - IN-LINE DOT PRODUCTS ARE BEING EVALU',
+ $ 'ATED WRONGLY.', /' SMVCH WAS CALLED WITH TRANS = ', A1,
+ $ ' AND RETURNED SAME = ', L1, ' AND ERR = ', F12.3, '.', /
+ $ ' THIS MAY BE DUE TO FAULTS IN THE ARITHMETIC OR THE COMPILER.'
+ $ , /' ******* TESTS ABANDONED *******' )
+ 9984 FORMAT( A6, L2 )
+ 9983 FORMAT( 1X, A6, ' WAS NOT TESTED' )
+ 9982 FORMAT( /' END OF TESTS' )
+ 9981 FORMAT( /' ******* FATAL ERROR - TESTS ABANDONED *******' )
+ 9980 FORMAT( ' ERROR-EXITS WILL NOT BE TESTED' )
+*
+* End of SBLAT2.
+*
+ END
+ SUBROUTINE SCHK1( SNAME, EPS, THRESH, NOUT, NTRA, TRACE, REWI,
+ $ FATAL, NIDIM, IDIM, NKB, KB, NALF, ALF, NBET,
+ $ BET, NINC, INC, NMAX, INCMAX, A, AA, AS, X, XX,
+ $ XS, Y, YY, YS, YT, G )
+*
+* Tests SGEMV and SGBMV.
+*
+* Auxiliary routine for test program for Level 2 Blas.
+*
+* -- Written on 10-August-1987.
+* Richard Hanson, Sandia National Labs.
+* Jeremy Du Croz, NAG Central Office.
+*
+* .. Parameters ..
+ REAL ZERO, HALF
+ PARAMETER ( ZERO = 0.0, HALF = 0.5 )
+* .. Scalar Arguments ..
+ REAL EPS, THRESH
+ INTEGER INCMAX, NALF, NBET, NIDIM, NINC, NKB, NMAX,
+ $ NOUT, NTRA
+ LOGICAL FATAL, REWI, TRACE
+ CHARACTER*6 SNAME
+* .. Array Arguments ..
+ REAL A( NMAX, NMAX ), AA( NMAX*NMAX ), ALF( NALF ),
+ $ AS( NMAX*NMAX ), BET( NBET ), G( NMAX ),
+ $ X( NMAX ), XS( NMAX*INCMAX ),
+ $ XX( NMAX*INCMAX ), Y( NMAX ),
+ $ YS( NMAX*INCMAX ), YT( NMAX ),
+ $ YY( NMAX*INCMAX )
+ INTEGER IDIM( NIDIM ), INC( NINC ), KB( NKB )
+* .. Local Scalars ..
+ REAL ALPHA, ALS, BETA, BLS, ERR, ERRMAX, TRANSL
+ INTEGER I, IA, IB, IC, IKU, IM, IN, INCX, INCXS, INCY,
+ $ INCYS, IX, IY, KL, KLS, KU, KUS, LAA, LDA,
+ $ LDAS, LX, LY, M, ML, MS, N, NARGS, NC, ND, NK,
+ $ NL, NS
+ LOGICAL BANDED, FULL, NULL, RESET, SAME, TRAN
+ CHARACTER*1 TRANS, TRANSS
+ CHARACTER*3 ICH
+* .. Local Arrays ..
+ LOGICAL ISAME( 13 )
+* .. External Functions ..
+ LOGICAL LSE, LSERES
+ EXTERNAL LSE, LSERES
+* .. External Subroutines ..
+ EXTERNAL SGBMV, SGEMV, SMAKE, SMVCH
+* .. Intrinsic Functions ..
+ INTRINSIC ABS, MAX, MIN
+* .. Scalars in Common ..
+ INTEGER INFOT, NOUTC
+ LOGICAL LERR, OK
+* .. Common blocks ..
+ COMMON /INFOC/INFOT, NOUTC, OK, LERR
+* .. Data statements ..
+ DATA ICH/'NTC'/
+* .. Executable Statements ..
+ FULL = SNAME( 3: 3 ).EQ.'E'
+ BANDED = SNAME( 3: 3 ).EQ.'B'
+* Define the number of arguments.
+ IF( FULL )THEN
+ NARGS = 11
+ ELSE IF( BANDED )THEN
+ NARGS = 13
+ END IF
+*
+ NC = 0
+ RESET = .TRUE.
+ ERRMAX = ZERO
+*
+ DO 120 IN = 1, NIDIM
+ N = IDIM( IN )
+ ND = N/2 + 1
+*
+ DO 110 IM = 1, 2
+ IF( IM.EQ.1 )
+ $ M = MAX( N - ND, 0 )
+ IF( IM.EQ.2 )
+ $ M = MIN( N + ND, NMAX )
+*
+ IF( BANDED )THEN
+ NK = NKB
+ ELSE
+ NK = 1
+ END IF
+ DO 100 IKU = 1, NK
+ IF( BANDED )THEN
+ KU = KB( IKU )
+ KL = MAX( KU - 1, 0 )
+ ELSE
+ KU = N - 1
+ KL = M - 1
+ END IF
+* Set LDA to 1 more than minimum value if room.
+ IF( BANDED )THEN
+ LDA = KL + KU + 1
+ ELSE
+ LDA = M
+ END IF
+ IF( LDA.LT.NMAX )
+ $ LDA = LDA + 1
+* Skip tests if not enough room.
+ IF( LDA.GT.NMAX )
+ $ GO TO 100
+ LAA = LDA*N
+ NULL = N.LE.0.OR.M.LE.0
+*
+* Generate the matrix A.
+*
+ TRANSL = ZERO
+ CALL SMAKE( SNAME( 2: 3 ), ' ', ' ', M, N, A, NMAX, AA,
+ $ LDA, KL, KU, RESET, TRANSL )
+*
+ DO 90 IC = 1, 3
+ TRANS = ICH( IC: IC )
+ TRAN = TRANS.EQ.'T'.OR.TRANS.EQ.'C'
+*
+ IF( TRAN )THEN
+ ML = N
+ NL = M
+ ELSE
+ ML = M
+ NL = N
+ END IF
+*
+ DO 80 IX = 1, NINC
+ INCX = INC( IX )
+ LX = ABS( INCX )*NL
+*
+* Generate the vector X.
+*
+ TRANSL = HALF
+ CALL SMAKE( 'GE', ' ', ' ', 1, NL, X, 1, XX,
+ $ ABS( INCX ), 0, NL - 1, RESET, TRANSL )
+ IF( NL.GT.1 )THEN
+ X( NL/2 ) = ZERO
+ XX( 1 + ABS( INCX )*( NL/2 - 1 ) ) = ZERO
+ END IF
+*
+ DO 70 IY = 1, NINC
+ INCY = INC( IY )
+ LY = ABS( INCY )*ML
+*
+ DO 60 IA = 1, NALF
+ ALPHA = ALF( IA )
+*
+ DO 50 IB = 1, NBET
+ BETA = BET( IB )
+*
+* Generate the vector Y.
+*
+ TRANSL = ZERO
+ CALL SMAKE( 'GE', ' ', ' ', 1, ML, Y, 1,
+ $ YY, ABS( INCY ), 0, ML - 1,
+ $ RESET, TRANSL )
+*
+ NC = NC + 1
+*
+* Save every datum before calling the
+* subroutine.
+*
+ TRANSS = TRANS
+ MS = M
+ NS = N
+ KLS = KL
+ KUS = KU
+ ALS = ALPHA
+ DO 10 I = 1, LAA
+ AS( I ) = AA( I )
+ 10 CONTINUE
+ LDAS = LDA
+ DO 20 I = 1, LX
+ XS( I ) = XX( I )
+ 20 CONTINUE
+ INCXS = INCX
+ BLS = BETA
+ DO 30 I = 1, LY
+ YS( I ) = YY( I )
+ 30 CONTINUE
+ INCYS = INCY
+*
+* Call the subroutine.
+*
+ IF( FULL )THEN
+ IF( TRACE )
+ $ WRITE( NTRA, FMT = 9994 )NC, SNAME,
+ $ TRANS, M, N, ALPHA, LDA, INCX, BETA,
+ $ INCY
+ IF( REWI )
+ $ REWIND NTRA
+ CALL SGEMV( TRANS, M, N, ALPHA, AA,
+ $ LDA, XX, INCX, BETA, YY,
+ $ INCY )
+ ELSE IF( BANDED )THEN
+ IF( TRACE )
+ $ WRITE( NTRA, FMT = 9995 )NC, SNAME,
+ $ TRANS, M, N, KL, KU, ALPHA, LDA,
+ $ INCX, BETA, INCY
+ IF( REWI )
+ $ REWIND NTRA
+ CALL SGBMV( TRANS, M, N, KL, KU, ALPHA,
+ $ AA, LDA, XX, INCX, BETA,
+ $ YY, INCY )
+ END IF
+*
+* Check if error-exit was taken incorrectly.
+*
+ IF( .NOT.OK )THEN
+ WRITE( NOUT, FMT = 9993 )
+ FATAL = .TRUE.
+ GO TO 130
+ END IF
+*
+* See what data changed inside subroutines.
+*
+ ISAME( 1 ) = TRANS.EQ.TRANSS
+ ISAME( 2 ) = MS.EQ.M
+ ISAME( 3 ) = NS.EQ.N
+ IF( FULL )THEN
+ ISAME( 4 ) = ALS.EQ.ALPHA
+ ISAME( 5 ) = LSE( AS, AA, LAA )
+ ISAME( 6 ) = LDAS.EQ.LDA
+ ISAME( 7 ) = LSE( XS, XX, LX )
+ ISAME( 8 ) = INCXS.EQ.INCX
+ ISAME( 9 ) = BLS.EQ.BETA
+ IF( NULL )THEN
+ ISAME( 10 ) = LSE( YS, YY, LY )
+ ELSE
+ ISAME( 10 ) = LSERES( 'GE', ' ', 1,
+ $ ML, YS, YY,
+ $ ABS( INCY ) )
+ END IF
+ ISAME( 11 ) = INCYS.EQ.INCY
+ ELSE IF( BANDED )THEN
+ ISAME( 4 ) = KLS.EQ.KL
+ ISAME( 5 ) = KUS.EQ.KU
+ ISAME( 6 ) = ALS.EQ.ALPHA
+ ISAME( 7 ) = LSE( AS, AA, LAA )
+ ISAME( 8 ) = LDAS.EQ.LDA
+ ISAME( 9 ) = LSE( XS, XX, LX )
+ ISAME( 10 ) = INCXS.EQ.INCX
+ ISAME( 11 ) = BLS.EQ.BETA
+ IF( NULL )THEN
+ ISAME( 12 ) = LSE( YS, YY, LY )
+ ELSE
+ ISAME( 12 ) = LSERES( 'GE', ' ', 1,
+ $ ML, YS, YY,
+ $ ABS( INCY ) )
+ END IF
+ ISAME( 13 ) = INCYS.EQ.INCY
+ END IF
+*
+* If data was incorrectly changed, report
+* and return.
+*
+ SAME = .TRUE.
+ DO 40 I = 1, NARGS
+ SAME = SAME.AND.ISAME( I )
+ IF( .NOT.ISAME( I ) )
+ $ WRITE( NOUT, FMT = 9998 )I
+ 40 CONTINUE
+ IF( .NOT.SAME )THEN
+ FATAL = .TRUE.
+ GO TO 130
+ END IF
+*
+ IF( .NOT.NULL )THEN
+*
+* Check the result.
+*
+ CALL SMVCH( TRANS, M, N, ALPHA, A,
+ $ NMAX, X, INCX, BETA, Y,
+ $ INCY, YT, G, YY, EPS, ERR,
+ $ FATAL, NOUT, .TRUE. )
+ ERRMAX = MAX( ERRMAX, ERR )
+* If got really bad answer, report and
+* return.
+ IF( FATAL )
+ $ GO TO 130
+ ELSE
+* Avoid repeating tests with M.le.0 or
+* N.le.0.
+ GO TO 110
+ END IF
+*
+ 50 CONTINUE
+*
+ 60 CONTINUE
+*
+ 70 CONTINUE
+*
+ 80 CONTINUE
+*
+ 90 CONTINUE
+*
+ 100 CONTINUE
+*
+ 110 CONTINUE
+*
+ 120 CONTINUE
+*
+* Report result.
+*
+ IF( ERRMAX.LT.THRESH )THEN
+ WRITE( NOUT, FMT = 9999 )SNAME, NC
+ ELSE
+ WRITE( NOUT, FMT = 9997 )SNAME, NC, ERRMAX
+ END IF
+ GO TO 140
+*
+ 130 CONTINUE
+ WRITE( NOUT, FMT = 9996 )SNAME
+ IF( FULL )THEN
+ WRITE( NOUT, FMT = 9994 )NC, SNAME, TRANS, M, N, ALPHA, LDA,
+ $ INCX, BETA, INCY
+ ELSE IF( BANDED )THEN
+ WRITE( NOUT, FMT = 9995 )NC, SNAME, TRANS, M, N, KL, KU,
+ $ ALPHA, LDA, INCX, BETA, INCY
+ END IF
+*
+ 140 CONTINUE
+ RETURN
+*
+ 9999 FORMAT( ' ', A6, ' PASSED THE COMPUTATIONAL TESTS (', I6, ' CALL',
+ $ 'S)' )
+ 9998 FORMAT( ' ******* FATAL ERROR - PARAMETER NUMBER ', I2, ' WAS CH',
+ $ 'ANGED INCORRECTLY *******' )
+ 9997 FORMAT( ' ', A6, ' COMPLETED THE COMPUTATIONAL TESTS (', I6, ' C',
+ $ 'ALLS)', /' ******* BUT WITH MAXIMUM TEST RATIO', F8.2,
+ $ ' - SUSPECT *******' )
+ 9996 FORMAT( ' ******* ', A6, ' FAILED ON CALL NUMBER:' )
+ 9995 FORMAT( 1X, I6, ': ', A6, '(''', A1, ''',', 4( I3, ',' ), F4.1,
+ $ ', A,', I3, ', X,', I2, ',', F4.1, ', Y,', I2, ') .' )
+ 9994 FORMAT( 1X, I6, ': ', A6, '(''', A1, ''',', 2( I3, ',' ), F4.1,
+ $ ', A,', I3, ', X,', I2, ',', F4.1, ', Y,', I2,
+ $ ') .' )
+ 9993 FORMAT( ' ******* FATAL ERROR - ERROR-EXIT TAKEN ON VALID CALL *',
+ $ '******' )
+*
+* End of SCHK1.
+*
+ END
+ SUBROUTINE SCHK2( SNAME, EPS, THRESH, NOUT, NTRA, TRACE, REWI,
+ $ FATAL, NIDIM, IDIM, NKB, KB, NALF, ALF, NBET,
+ $ BET, NINC, INC, NMAX, INCMAX, A, AA, AS, X, XX,
+ $ XS, Y, YY, YS, YT, G )
+*
+* Tests SSYMV, SSBMV and SSPMV.
+*
+* Auxiliary routine for test program for Level 2 Blas.
+*
+* -- Written on 10-August-1987.
+* Richard Hanson, Sandia National Labs.
+* Jeremy Du Croz, NAG Central Office.
+*
+* .. Parameters ..
+ REAL ZERO, HALF
+ PARAMETER ( ZERO = 0.0, HALF = 0.5 )
+* .. Scalar Arguments ..
+ REAL EPS, THRESH
+ INTEGER INCMAX, NALF, NBET, NIDIM, NINC, NKB, NMAX,
+ $ NOUT, NTRA
+ LOGICAL FATAL, REWI, TRACE
+ CHARACTER*6 SNAME
+* .. Array Arguments ..
+ REAL A( NMAX, NMAX ), AA( NMAX*NMAX ), ALF( NALF ),
+ $ AS( NMAX*NMAX ), BET( NBET ), G( NMAX ),
+ $ X( NMAX ), XS( NMAX*INCMAX ),
+ $ XX( NMAX*INCMAX ), Y( NMAX ),
+ $ YS( NMAX*INCMAX ), YT( NMAX ),
+ $ YY( NMAX*INCMAX )
+ INTEGER IDIM( NIDIM ), INC( NINC ), KB( NKB )
+* .. Local Scalars ..
+ REAL ALPHA, ALS, BETA, BLS, ERR, ERRMAX, TRANSL
+ INTEGER I, IA, IB, IC, IK, IN, INCX, INCXS, INCY,
+ $ INCYS, IX, IY, K, KS, LAA, LDA, LDAS, LX, LY,
+ $ N, NARGS, NC, NK, NS
+ LOGICAL BANDED, FULL, NULL, PACKED, RESET, SAME
+ CHARACTER*1 UPLO, UPLOS
+ CHARACTER*2 ICH
+* .. Local Arrays ..
+ LOGICAL ISAME( 13 )
+* .. External Functions ..
+ LOGICAL LSE, LSERES
+ EXTERNAL LSE, LSERES
+* .. External Subroutines ..
+ EXTERNAL SMAKE, SMVCH, SSBMV, SSPMV, SSYMV
+* .. Intrinsic Functions ..
+ INTRINSIC ABS, MAX
+* .. Scalars in Common ..
+ INTEGER INFOT, NOUTC
+ LOGICAL LERR, OK
+* .. Common blocks ..
+ COMMON /INFOC/INFOT, NOUTC, OK, LERR
+* .. Data statements ..
+ DATA ICH/'UL'/
+* .. Executable Statements ..
+ FULL = SNAME( 3: 3 ).EQ.'Y'
+ BANDED = SNAME( 3: 3 ).EQ.'B'
+ PACKED = SNAME( 3: 3 ).EQ.'P'
+* Define the number of arguments.
+ IF( FULL )THEN
+ NARGS = 10
+ ELSE IF( BANDED )THEN
+ NARGS = 11
+ ELSE IF( PACKED )THEN
+ NARGS = 9
+ END IF
+*
+ NC = 0
+ RESET = .TRUE.
+ ERRMAX = ZERO
+*
+ DO 110 IN = 1, NIDIM
+ N = IDIM( IN )
+*
+ IF( BANDED )THEN
+ NK = NKB
+ ELSE
+ NK = 1
+ END IF
+ DO 100 IK = 1, NK
+ IF( BANDED )THEN
+ K = KB( IK )
+ ELSE
+ K = N - 1
+ END IF
+* Set LDA to 1 more than minimum value if room.
+ IF( BANDED )THEN
+ LDA = K + 1
+ ELSE
+ LDA = N
+ END IF
+ IF( LDA.LT.NMAX )
+ $ LDA = LDA + 1
+* Skip tests if not enough room.
+ IF( LDA.GT.NMAX )
+ $ GO TO 100
+ IF( PACKED )THEN
+ LAA = ( N*( N + 1 ) )/2
+ ELSE
+ LAA = LDA*N
+ END IF
+ NULL = N.LE.0
+*
+ DO 90 IC = 1, 2
+ UPLO = ICH( IC: IC )
+*
+* Generate the matrix A.
+*
+ TRANSL = ZERO
+ CALL SMAKE( SNAME( 2: 3 ), UPLO, ' ', N, N, A, NMAX, AA,
+ $ LDA, K, K, RESET, TRANSL )
+*
+ DO 80 IX = 1, NINC
+ INCX = INC( IX )
+ LX = ABS( INCX )*N
+*
+* Generate the vector X.
+*
+ TRANSL = HALF
+ CALL SMAKE( 'GE', ' ', ' ', 1, N, X, 1, XX,
+ $ ABS( INCX ), 0, N - 1, RESET, TRANSL )
+ IF( N.GT.1 )THEN
+ X( N/2 ) = ZERO
+ XX( 1 + ABS( INCX )*( N/2 - 1 ) ) = ZERO
+ END IF
+*
+ DO 70 IY = 1, NINC
+ INCY = INC( IY )
+ LY = ABS( INCY )*N
+*
+ DO 60 IA = 1, NALF
+ ALPHA = ALF( IA )
+*
+ DO 50 IB = 1, NBET
+ BETA = BET( IB )
+*
+* Generate the vector Y.
+*
+ TRANSL = ZERO
+ CALL SMAKE( 'GE', ' ', ' ', 1, N, Y, 1, YY,
+ $ ABS( INCY ), 0, N - 1, RESET,
+ $ TRANSL )
+*
+ NC = NC + 1
+*
+* Save every datum before calling the
+* subroutine.
+*
+ UPLOS = UPLO
+ NS = N
+ KS = K
+ ALS = ALPHA
+ DO 10 I = 1, LAA
+ AS( I ) = AA( I )
+ 10 CONTINUE
+ LDAS = LDA
+ DO 20 I = 1, LX
+ XS( I ) = XX( I )
+ 20 CONTINUE
+ INCXS = INCX
+ BLS = BETA
+ DO 30 I = 1, LY
+ YS( I ) = YY( I )
+ 30 CONTINUE
+ INCYS = INCY
+*
+* Call the subroutine.
+*
+ IF( FULL )THEN
+ IF( TRACE )
+ $ WRITE( NTRA, FMT = 9993 )NC, SNAME,
+ $ UPLO, N, ALPHA, LDA, INCX, BETA, INCY
+ IF( REWI )
+ $ REWIND NTRA
+ CALL SSYMV( UPLO, N, ALPHA, AA, LDA, XX,
+ $ INCX, BETA, YY, INCY )
+ ELSE IF( BANDED )THEN
+ IF( TRACE )
+ $ WRITE( NTRA, FMT = 9994 )NC, SNAME,
+ $ UPLO, N, K, ALPHA, LDA, INCX, BETA,
+ $ INCY
+ IF( REWI )
+ $ REWIND NTRA
+ CALL SSBMV( UPLO, N, K, ALPHA, AA, LDA,
+ $ XX, INCX, BETA, YY, INCY )
+ ELSE IF( PACKED )THEN
+ IF( TRACE )
+ $ WRITE( NTRA, FMT = 9995 )NC, SNAME,
+ $ UPLO, N, ALPHA, INCX, BETA, INCY
+ IF( REWI )
+ $ REWIND NTRA
+ CALL SSPMV( UPLO, N, ALPHA, AA, XX, INCX,
+ $ BETA, YY, INCY )
+ END IF
+*
+* Check if error-exit was taken incorrectly.
+*
+ IF( .NOT.OK )THEN
+ WRITE( NOUT, FMT = 9992 )
+ FATAL = .TRUE.
+ GO TO 120
+ END IF
+*
+* See what data changed inside subroutines.
+*
+ ISAME( 1 ) = UPLO.EQ.UPLOS
+ ISAME( 2 ) = NS.EQ.N
+ IF( FULL )THEN
+ ISAME( 3 ) = ALS.EQ.ALPHA
+ ISAME( 4 ) = LSE( AS, AA, LAA )
+ ISAME( 5 ) = LDAS.EQ.LDA
+ ISAME( 6 ) = LSE( XS, XX, LX )
+ ISAME( 7 ) = INCXS.EQ.INCX
+ ISAME( 8 ) = BLS.EQ.BETA
+ IF( NULL )THEN
+ ISAME( 9 ) = LSE( YS, YY, LY )
+ ELSE
+ ISAME( 9 ) = LSERES( 'GE', ' ', 1, N,
+ $ YS, YY, ABS( INCY ) )
+ END IF
+ ISAME( 10 ) = INCYS.EQ.INCY
+ ELSE IF( BANDED )THEN
+ ISAME( 3 ) = KS.EQ.K
+ ISAME( 4 ) = ALS.EQ.ALPHA
+ ISAME( 5 ) = LSE( AS, AA, LAA )
+ ISAME( 6 ) = LDAS.EQ.LDA
+ ISAME( 7 ) = LSE( XS, XX, LX )
+ ISAME( 8 ) = INCXS.EQ.INCX
+ ISAME( 9 ) = BLS.EQ.BETA
+ IF( NULL )THEN
+ ISAME( 10 ) = LSE( YS, YY, LY )
+ ELSE
+ ISAME( 10 ) = LSERES( 'GE', ' ', 1, N,
+ $ YS, YY, ABS( INCY ) )
+ END IF
+ ISAME( 11 ) = INCYS.EQ.INCY
+ ELSE IF( PACKED )THEN
+ ISAME( 3 ) = ALS.EQ.ALPHA
+ ISAME( 4 ) = LSE( AS, AA, LAA )
+ ISAME( 5 ) = LSE( XS, XX, LX )
+ ISAME( 6 ) = INCXS.EQ.INCX
+ ISAME( 7 ) = BLS.EQ.BETA
+ IF( NULL )THEN
+ ISAME( 8 ) = LSE( YS, YY, LY )
+ ELSE
+ ISAME( 8 ) = LSERES( 'GE', ' ', 1, N,
+ $ YS, YY, ABS( INCY ) )
+ END IF
+ ISAME( 9 ) = INCYS.EQ.INCY
+ END IF
+*
+* If data was incorrectly changed, report and
+* return.
+*
+ SAME = .TRUE.
+ DO 40 I = 1, NARGS
+ SAME = SAME.AND.ISAME( I )
+ IF( .NOT.ISAME( I ) )
+ $ WRITE( NOUT, FMT = 9998 )I
+ 40 CONTINUE
+ IF( .NOT.SAME )THEN
+ FATAL = .TRUE.
+ GO TO 120
+ END IF
+*
+ IF( .NOT.NULL )THEN
+*
+* Check the result.
+*
+ CALL SMVCH( 'N', N, N, ALPHA, A, NMAX, X,
+ $ INCX, BETA, Y, INCY, YT, G,
+ $ YY, EPS, ERR, FATAL, NOUT,
+ $ .TRUE. )
+ ERRMAX = MAX( ERRMAX, ERR )
+* If got really bad answer, report and
+* return.
+ IF( FATAL )
+ $ GO TO 120
+ ELSE
+* Avoid repeating tests with N.le.0
+ GO TO 110
+ END IF
+*
+ 50 CONTINUE
+*
+ 60 CONTINUE
+*
+ 70 CONTINUE
+*
+ 80 CONTINUE
+*
+ 90 CONTINUE
+*
+ 100 CONTINUE
+*
+ 110 CONTINUE
+*
+* Report result.
+*
+ IF( ERRMAX.LT.THRESH )THEN
+ WRITE( NOUT, FMT = 9999 )SNAME, NC
+ ELSE
+ WRITE( NOUT, FMT = 9997 )SNAME, NC, ERRMAX
+ END IF
+ GO TO 130
+*
+ 120 CONTINUE
+ WRITE( NOUT, FMT = 9996 )SNAME
+ IF( FULL )THEN
+ WRITE( NOUT, FMT = 9993 )NC, SNAME, UPLO, N, ALPHA, LDA, INCX,
+ $ BETA, INCY
+ ELSE IF( BANDED )THEN
+ WRITE( NOUT, FMT = 9994 )NC, SNAME, UPLO, N, K, ALPHA, LDA,
+ $ INCX, BETA, INCY
+ ELSE IF( PACKED )THEN
+ WRITE( NOUT, FMT = 9995 )NC, SNAME, UPLO, N, ALPHA, INCX,
+ $ BETA, INCY
+ END IF
+*
+ 130 CONTINUE
+ RETURN
+*
+ 9999 FORMAT( ' ', A6, ' PASSED THE COMPUTATIONAL TESTS (', I6, ' CALL',
+ $ 'S)' )
+ 9998 FORMAT( ' ******* FATAL ERROR - PARAMETER NUMBER ', I2, ' WAS CH',
+ $ 'ANGED INCORRECTLY *******' )
+ 9997 FORMAT( ' ', A6, ' COMPLETED THE COMPUTATIONAL TESTS (', I6, ' C',
+ $ 'ALLS)', /' ******* BUT WITH MAXIMUM TEST RATIO', F8.2,
+ $ ' - SUSPECT *******' )
+ 9996 FORMAT( ' ******* ', A6, ' FAILED ON CALL NUMBER:' )
+ 9995 FORMAT( 1X, I6, ': ', A6, '(''', A1, ''',', I3, ',', F4.1, ', AP',
+ $ ', X,', I2, ',', F4.1, ', Y,', I2, ') .' )
+ 9994 FORMAT( 1X, I6, ': ', A6, '(''', A1, ''',', 2( I3, ',' ), F4.1,
+ $ ', A,', I3, ', X,', I2, ',', F4.1, ', Y,', I2,
+ $ ') .' )
+ 9993 FORMAT( 1X, I6, ': ', A6, '(''', A1, ''',', I3, ',', F4.1, ', A,',
+ $ I3, ', X,', I2, ',', F4.1, ', Y,', I2, ') .' )
+ 9992 FORMAT( ' ******* FATAL ERROR - ERROR-EXIT TAKEN ON VALID CALL *',
+ $ '******' )
+*
+* End of SCHK2.
+*
+ END
+ SUBROUTINE SCHK3( SNAME, EPS, THRESH, NOUT, NTRA, TRACE, REWI,
+ $ FATAL, NIDIM, IDIM, NKB, KB, NINC, INC, NMAX,
+ $ INCMAX, A, AA, AS, X, XX, XS, XT, G, Z )
+*
+* Tests STRMV, STBMV, STPMV, STRSV, STBSV and STPSV.
+*
+* Auxiliary routine for test program for Level 2 Blas.
+*
+* -- Written on 10-August-1987.
+* Richard Hanson, Sandia National Labs.
+* Jeremy Du Croz, NAG Central Office.
+*
+* .. Parameters ..
+ REAL ZERO, HALF, ONE
+ PARAMETER ( ZERO = 0.0, HALF = 0.5, ONE = 1.0 )
+* .. Scalar Arguments ..
+ REAL EPS, THRESH
+ INTEGER INCMAX, NIDIM, NINC, NKB, NMAX, NOUT, NTRA
+ LOGICAL FATAL, REWI, TRACE
+ CHARACTER*6 SNAME
+* .. Array Arguments ..
+ REAL A( NMAX, NMAX ), AA( NMAX*NMAX ),
+ $ AS( NMAX*NMAX ), G( NMAX ), X( NMAX ),
+ $ XS( NMAX*INCMAX ), XT( NMAX ),
+ $ XX( NMAX*INCMAX ), Z( NMAX )
+ INTEGER IDIM( NIDIM ), INC( NINC ), KB( NKB )
+* .. Local Scalars ..
+ REAL ERR, ERRMAX, TRANSL
+ INTEGER I, ICD, ICT, ICU, IK, IN, INCX, INCXS, IX, K,
+ $ KS, LAA, LDA, LDAS, LX, N, NARGS, NC, NK, NS
+ LOGICAL BANDED, FULL, NULL, PACKED, RESET, SAME
+ CHARACTER*1 DIAG, DIAGS, TRANS, TRANSS, UPLO, UPLOS
+ CHARACTER*2 ICHD, ICHU
+ CHARACTER*3 ICHT
+* .. Local Arrays ..
+ LOGICAL ISAME( 13 )
+* .. External Functions ..
+ LOGICAL LSE, LSERES
+ EXTERNAL LSE, LSERES
+* .. External Subroutines ..
+ EXTERNAL SMAKE, SMVCH, STBMV, STBSV, STPMV, STPSV,
+ $ STRMV, STRSV
+* .. Intrinsic Functions ..
+ INTRINSIC ABS, MAX
+* .. Scalars in Common ..
+ INTEGER INFOT, NOUTC
+ LOGICAL LERR, OK
+* .. Common blocks ..
+ COMMON /INFOC/INFOT, NOUTC, OK, LERR
+* .. Data statements ..
+ DATA ICHU/'UL'/, ICHT/'NTC'/, ICHD/'UN'/
+* .. Executable Statements ..
+ FULL = SNAME( 3: 3 ).EQ.'R'
+ BANDED = SNAME( 3: 3 ).EQ.'B'
+ PACKED = SNAME( 3: 3 ).EQ.'P'
+* Define the number of arguments.
+ IF( FULL )THEN
+ NARGS = 8
+ ELSE IF( BANDED )THEN
+ NARGS = 9
+ ELSE IF( PACKED )THEN
+ NARGS = 7
+ END IF
+*
+ NC = 0
+ RESET = .TRUE.
+ ERRMAX = ZERO
+* Set up zero vector for SMVCH.
+ DO 10 I = 1, NMAX
+ Z( I ) = ZERO
+ 10 CONTINUE
+*
+ DO 110 IN = 1, NIDIM
+ N = IDIM( IN )
+*
+ IF( BANDED )THEN
+ NK = NKB
+ ELSE
+ NK = 1
+ END IF
+ DO 100 IK = 1, NK
+ IF( BANDED )THEN
+ K = KB( IK )
+ ELSE
+ K = N - 1
+ END IF
+* Set LDA to 1 more than minimum value if room.
+ IF( BANDED )THEN
+ LDA = K + 1
+ ELSE
+ LDA = N
+ END IF
+ IF( LDA.LT.NMAX )
+ $ LDA = LDA + 1
+* Skip tests if not enough room.
+ IF( LDA.GT.NMAX )
+ $ GO TO 100
+ IF( PACKED )THEN
+ LAA = ( N*( N + 1 ) )/2
+ ELSE
+ LAA = LDA*N
+ END IF
+ NULL = N.LE.0
+*
+ DO 90 ICU = 1, 2
+ UPLO = ICHU( ICU: ICU )
+*
+ DO 80 ICT = 1, 3
+ TRANS = ICHT( ICT: ICT )
+*
+ DO 70 ICD = 1, 2
+ DIAG = ICHD( ICD: ICD )
+*
+* Generate the matrix A.
+*
+ TRANSL = ZERO
+ CALL SMAKE( SNAME( 2: 3 ), UPLO, DIAG, N, N, A,
+ $ NMAX, AA, LDA, K, K, RESET, TRANSL )
+*
+ DO 60 IX = 1, NINC
+ INCX = INC( IX )
+ LX = ABS( INCX )*N
+*
+* Generate the vector X.
+*
+ TRANSL = HALF
+ CALL SMAKE( 'GE', ' ', ' ', 1, N, X, 1, XX,
+ $ ABS( INCX ), 0, N - 1, RESET,
+ $ TRANSL )
+ IF( N.GT.1 )THEN
+ X( N/2 ) = ZERO
+ XX( 1 + ABS( INCX )*( N/2 - 1 ) ) = ZERO
+ END IF
+*
+ NC = NC + 1
+*
+* Save every datum before calling the subroutine.
+*
+ UPLOS = UPLO
+ TRANSS = TRANS
+ DIAGS = DIAG
+ NS = N
+ KS = K
+ DO 20 I = 1, LAA
+ AS( I ) = AA( I )
+ 20 CONTINUE
+ LDAS = LDA
+ DO 30 I = 1, LX
+ XS( I ) = XX( I )
+ 30 CONTINUE
+ INCXS = INCX
+*
+* Call the subroutine.
+*
+ IF( SNAME( 4: 5 ).EQ.'MV' )THEN
+ IF( FULL )THEN
+ IF( TRACE )
+ $ WRITE( NTRA, FMT = 9993 )NC, SNAME,
+ $ UPLO, TRANS, DIAG, N, LDA, INCX
+ IF( REWI )
+ $ REWIND NTRA
+ CALL STRMV( UPLO, TRANS, DIAG, N, AA, LDA,
+ $ XX, INCX )
+ ELSE IF( BANDED )THEN
+ IF( TRACE )
+ $ WRITE( NTRA, FMT = 9994 )NC, SNAME,
+ $ UPLO, TRANS, DIAG, N, K, LDA, INCX
+ IF( REWI )
+ $ REWIND NTRA
+ CALL STBMV( UPLO, TRANS, DIAG, N, K, AA,
+ $ LDA, XX, INCX )
+ ELSE IF( PACKED )THEN
+ IF( TRACE )
+ $ WRITE( NTRA, FMT = 9995 )NC, SNAME,
+ $ UPLO, TRANS, DIAG, N, INCX
+ IF( REWI )
+ $ REWIND NTRA
+ CALL STPMV( UPLO, TRANS, DIAG, N, AA, XX,
+ $ INCX )
+ END IF
+ ELSE IF( SNAME( 4: 5 ).EQ.'SV' )THEN
+ IF( FULL )THEN
+ IF( TRACE )
+ $ WRITE( NTRA, FMT = 9993 )NC, SNAME,
+ $ UPLO, TRANS, DIAG, N, LDA, INCX
+ IF( REWI )
+ $ REWIND NTRA
+ CALL STRSV( UPLO, TRANS, DIAG, N, AA, LDA,
+ $ XX, INCX )
+ ELSE IF( BANDED )THEN
+ IF( TRACE )
+ $ WRITE( NTRA, FMT = 9994 )NC, SNAME,
+ $ UPLO, TRANS, DIAG, N, K, LDA, INCX
+ IF( REWI )
+ $ REWIND NTRA
+ CALL STBSV( UPLO, TRANS, DIAG, N, K, AA,
+ $ LDA, XX, INCX )
+ ELSE IF( PACKED )THEN
+ IF( TRACE )
+ $ WRITE( NTRA, FMT = 9995 )NC, SNAME,
+ $ UPLO, TRANS, DIAG, N, INCX
+ IF( REWI )
+ $ REWIND NTRA
+ CALL STPSV( UPLO, TRANS, DIAG, N, AA, XX,
+ $ INCX )
+ END IF
+ END IF
+*
+* Check if error-exit was taken incorrectly.
+*
+ IF( .NOT.OK )THEN
+ WRITE( NOUT, FMT = 9992 )
+ FATAL = .TRUE.
+ GO TO 120
+ END IF
+*
+* See what data changed inside subroutines.
+*
+ ISAME( 1 ) = UPLO.EQ.UPLOS
+ ISAME( 2 ) = TRANS.EQ.TRANSS
+ ISAME( 3 ) = DIAG.EQ.DIAGS
+ ISAME( 4 ) = NS.EQ.N
+ IF( FULL )THEN
+ ISAME( 5 ) = LSE( AS, AA, LAA )
+ ISAME( 6 ) = LDAS.EQ.LDA
+ IF( NULL )THEN
+ ISAME( 7 ) = LSE( XS, XX, LX )
+ ELSE
+ ISAME( 7 ) = LSERES( 'GE', ' ', 1, N, XS,
+ $ XX, ABS( INCX ) )
+ END IF
+ ISAME( 8 ) = INCXS.EQ.INCX
+ ELSE IF( BANDED )THEN
+ ISAME( 5 ) = KS.EQ.K
+ ISAME( 6 ) = LSE( AS, AA, LAA )
+ ISAME( 7 ) = LDAS.EQ.LDA
+ IF( NULL )THEN
+ ISAME( 8 ) = LSE( XS, XX, LX )
+ ELSE
+ ISAME( 8 ) = LSERES( 'GE', ' ', 1, N, XS,
+ $ XX, ABS( INCX ) )
+ END IF
+ ISAME( 9 ) = INCXS.EQ.INCX
+ ELSE IF( PACKED )THEN
+ ISAME( 5 ) = LSE( AS, AA, LAA )
+ IF( NULL )THEN
+ ISAME( 6 ) = LSE( XS, XX, LX )
+ ELSE
+ ISAME( 6 ) = LSERES( 'GE', ' ', 1, N, XS,
+ $ XX, ABS( INCX ) )
+ END IF
+ ISAME( 7 ) = INCXS.EQ.INCX
+ END IF
+*
+* If data was incorrectly changed, report and
+* return.
+*
+ SAME = .TRUE.
+ DO 40 I = 1, NARGS
+ SAME = SAME.AND.ISAME( I )
+ IF( .NOT.ISAME( I ) )
+ $ WRITE( NOUT, FMT = 9998 )I
+ 40 CONTINUE
+ IF( .NOT.SAME )THEN
+ FATAL = .TRUE.
+ GO TO 120
+ END IF
+*
+ IF( .NOT.NULL )THEN
+ IF( SNAME( 4: 5 ).EQ.'MV' )THEN
+*
+* Check the result.
+*
+ CALL SMVCH( TRANS, N, N, ONE, A, NMAX, X,
+ $ INCX, ZERO, Z, INCX, XT, G,
+ $ XX, EPS, ERR, FATAL, NOUT,
+ $ .TRUE. )
+ ELSE IF( SNAME( 4: 5 ).EQ.'SV' )THEN
+*
+* Compute approximation to original vector.
+*
+ DO 50 I = 1, N
+ Z( I ) = XX( 1 + ( I - 1 )*
+ $ ABS( INCX ) )
+ XX( 1 + ( I - 1 )*ABS( INCX ) )
+ $ = X( I )
+ 50 CONTINUE
+ CALL SMVCH( TRANS, N, N, ONE, A, NMAX, Z,
+ $ INCX, ZERO, X, INCX, XT, G,
+ $ XX, EPS, ERR, FATAL, NOUT,
+ $ .FALSE. )
+ END IF
+ ERRMAX = MAX( ERRMAX, ERR )
+* If got really bad answer, report and return.
+ IF( FATAL )
+ $ GO TO 120
+ ELSE
+* Avoid repeating tests with N.le.0.
+ GO TO 110
+ END IF
+*
+ 60 CONTINUE
+*
+ 70 CONTINUE
+*
+ 80 CONTINUE
+*
+ 90 CONTINUE
+*
+ 100 CONTINUE
+*
+ 110 CONTINUE
+*
+* Report result.
+*
+ IF( ERRMAX.LT.THRESH )THEN
+ WRITE( NOUT, FMT = 9999 )SNAME, NC
+ ELSE
+ WRITE( NOUT, FMT = 9997 )SNAME, NC, ERRMAX
+ END IF
+ GO TO 130
+*
+ 120 CONTINUE
+ WRITE( NOUT, FMT = 9996 )SNAME
+ IF( FULL )THEN
+ WRITE( NOUT, FMT = 9993 )NC, SNAME, UPLO, TRANS, DIAG, N, LDA,
+ $ INCX
+ ELSE IF( BANDED )THEN
+ WRITE( NOUT, FMT = 9994 )NC, SNAME, UPLO, TRANS, DIAG, N, K,
+ $ LDA, INCX
+ ELSE IF( PACKED )THEN
+ WRITE( NOUT, FMT = 9995 )NC, SNAME, UPLO, TRANS, DIAG, N, INCX
+ END IF
+*
+ 130 CONTINUE
+ RETURN
+*
+ 9999 FORMAT( ' ', A6, ' PASSED THE COMPUTATIONAL TESTS (', I6, ' CALL',
+ $ 'S)' )
+ 9998 FORMAT( ' ******* FATAL ERROR - PARAMETER NUMBER ', I2, ' WAS CH',
+ $ 'ANGED INCORRECTLY *******' )
+ 9997 FORMAT( ' ', A6, ' COMPLETED THE COMPUTATIONAL TESTS (', I6, ' C',
+ $ 'ALLS)', /' ******* BUT WITH MAXIMUM TEST RATIO', F8.2,
+ $ ' - SUSPECT *******' )
+ 9996 FORMAT( ' ******* ', A6, ' FAILED ON CALL NUMBER:' )
+ 9995 FORMAT( 1X, I6, ': ', A6, '(', 3( '''', A1, ''',' ), I3, ', AP, ',
+ $ 'X,', I2, ') .' )
+ 9994 FORMAT( 1X, I6, ': ', A6, '(', 3( '''', A1, ''',' ), 2( I3, ',' ),
+ $ ' A,', I3, ', X,', I2, ') .' )
+ 9993 FORMAT( 1X, I6, ': ', A6, '(', 3( '''', A1, ''',' ), I3, ', A,',
+ $ I3, ', X,', I2, ') .' )
+ 9992 FORMAT( ' ******* FATAL ERROR - ERROR-EXIT TAKEN ON VALID CALL *',
+ $ '******' )
+*
+* End of SCHK3.
+*
+ END
+ SUBROUTINE SCHK4( SNAME, EPS, THRESH, NOUT, NTRA, TRACE, REWI,
+ $ FATAL, NIDIM, IDIM, NALF, ALF, NINC, INC, NMAX,
+ $ INCMAX, A, AA, AS, X, XX, XS, Y, YY, YS, YT, G,
+ $ Z )
+*
+* Tests SGER.
+*
+* Auxiliary routine for test program for Level 2 Blas.
+*
+* -- Written on 10-August-1987.
+* Richard Hanson, Sandia National Labs.
+* Jeremy Du Croz, NAG Central Office.
+*
+* .. Parameters ..
+ REAL ZERO, HALF, ONE
+ PARAMETER ( ZERO = 0.0, HALF = 0.5, ONE = 1.0 )
+* .. Scalar Arguments ..
+ REAL EPS, THRESH
+ INTEGER INCMAX, NALF, NIDIM, NINC, NMAX, NOUT, NTRA
+ LOGICAL FATAL, REWI, TRACE
+ CHARACTER*6 SNAME
+* .. Array Arguments ..
+ REAL A( NMAX, NMAX ), AA( NMAX*NMAX ), ALF( NALF ),
+ $ AS( NMAX*NMAX ), G( NMAX ), X( NMAX ),
+ $ XS( NMAX*INCMAX ), XX( NMAX*INCMAX ),
+ $ Y( NMAX ), YS( NMAX*INCMAX ), YT( NMAX ),
+ $ YY( NMAX*INCMAX ), Z( NMAX )
+ INTEGER IDIM( NIDIM ), INC( NINC )
+* .. Local Scalars ..
+ REAL ALPHA, ALS, ERR, ERRMAX, TRANSL
+ INTEGER I, IA, IM, IN, INCX, INCXS, INCY, INCYS, IX,
+ $ IY, J, LAA, LDA, LDAS, LX, LY, M, MS, N, NARGS,
+ $ NC, ND, NS
+ LOGICAL NULL, RESET, SAME
+* .. Local Arrays ..
+ REAL W( 1 )
+ LOGICAL ISAME( 13 )
+* .. External Functions ..
+ LOGICAL LSE, LSERES
+ EXTERNAL LSE, LSERES
+* .. External Subroutines ..
+ EXTERNAL SGER, SMAKE, SMVCH
+* .. Intrinsic Functions ..
+ INTRINSIC ABS, MAX, MIN
+* .. Scalars in Common ..
+ INTEGER INFOT, NOUTC
+ LOGICAL LERR, OK
+* .. Common blocks ..
+ COMMON /INFOC/INFOT, NOUTC, OK, LERR
+* .. Executable Statements ..
+* Define the number of arguments.
+ NARGS = 9
+*
+ NC = 0
+ RESET = .TRUE.
+ ERRMAX = ZERO
+*
+ DO 120 IN = 1, NIDIM
+ N = IDIM( IN )
+ ND = N/2 + 1
+*
+ DO 110 IM = 1, 2
+ IF( IM.EQ.1 )
+ $ M = MAX( N - ND, 0 )
+ IF( IM.EQ.2 )
+ $ M = MIN( N + ND, NMAX )
+*
+* Set LDA to 1 more than minimum value if room.
+ LDA = M
+ IF( LDA.LT.NMAX )
+ $ LDA = LDA + 1
+* Skip tests if not enough room.
+ IF( LDA.GT.NMAX )
+ $ GO TO 110
+ LAA = LDA*N
+ NULL = N.LE.0.OR.M.LE.0
+*
+ DO 100 IX = 1, NINC
+ INCX = INC( IX )
+ LX = ABS( INCX )*M
+*
+* Generate the vector X.
+*
+ TRANSL = HALF
+ CALL SMAKE( 'GE', ' ', ' ', 1, M, X, 1, XX, ABS( INCX ),
+ $ 0, M - 1, RESET, TRANSL )
+ IF( M.GT.1 )THEN
+ X( M/2 ) = ZERO
+ XX( 1 + ABS( INCX )*( M/2 - 1 ) ) = ZERO
+ END IF
+*
+ DO 90 IY = 1, NINC
+ INCY = INC( IY )
+ LY = ABS( INCY )*N
+*
+* Generate the vector Y.
+*
+ TRANSL = ZERO
+ CALL SMAKE( 'GE', ' ', ' ', 1, N, Y, 1, YY,
+ $ ABS( INCY ), 0, N - 1, RESET, TRANSL )
+ IF( N.GT.1 )THEN
+ Y( N/2 ) = ZERO
+ YY( 1 + ABS( INCY )*( N/2 - 1 ) ) = ZERO
+ END IF
+*
+ DO 80 IA = 1, NALF
+ ALPHA = ALF( IA )
+*
+* Generate the matrix A.
+*
+ TRANSL = ZERO
+ CALL SMAKE( SNAME( 2: 3 ), ' ', ' ', M, N, A, NMAX,
+ $ AA, LDA, M - 1, N - 1, RESET, TRANSL )
+*
+ NC = NC + 1
+*
+* Save every datum before calling the subroutine.
+*
+ MS = M
+ NS = N
+ ALS = ALPHA
+ DO 10 I = 1, LAA
+ AS( I ) = AA( I )
+ 10 CONTINUE
+ LDAS = LDA
+ DO 20 I = 1, LX
+ XS( I ) = XX( I )
+ 20 CONTINUE
+ INCXS = INCX
+ DO 30 I = 1, LY
+ YS( I ) = YY( I )
+ 30 CONTINUE
+ INCYS = INCY
+*
+* Call the subroutine.
+*
+ IF( TRACE )
+ $ WRITE( NTRA, FMT = 9994 )NC, SNAME, M, N,
+ $ ALPHA, INCX, INCY, LDA
+ IF( REWI )
+ $ REWIND NTRA
+ CALL SGER( M, N, ALPHA, XX, INCX, YY, INCY, AA,
+ $ LDA )
+*
+* Check if error-exit was taken incorrectly.
+*
+ IF( .NOT.OK )THEN
+ WRITE( NOUT, FMT = 9993 )
+ FATAL = .TRUE.
+ GO TO 140
+ END IF
+*
+* See what data changed inside subroutine.
+*
+ ISAME( 1 ) = MS.EQ.M
+ ISAME( 2 ) = NS.EQ.N
+ ISAME( 3 ) = ALS.EQ.ALPHA
+ ISAME( 4 ) = LSE( XS, XX, LX )
+ ISAME( 5 ) = INCXS.EQ.INCX
+ ISAME( 6 ) = LSE( YS, YY, LY )
+ ISAME( 7 ) = INCYS.EQ.INCY
+ IF( NULL )THEN
+ ISAME( 8 ) = LSE( AS, AA, LAA )
+ ELSE
+ ISAME( 8 ) = LSERES( 'GE', ' ', M, N, AS, AA,
+ $ LDA )
+ END IF
+ ISAME( 9 ) = LDAS.EQ.LDA
+*
+* If data was incorrectly changed, report and return.
+*
+ SAME = .TRUE.
+ DO 40 I = 1, NARGS
+ SAME = SAME.AND.ISAME( I )
+ IF( .NOT.ISAME( I ) )
+ $ WRITE( NOUT, FMT = 9998 )I
+ 40 CONTINUE
+ IF( .NOT.SAME )THEN
+ FATAL = .TRUE.
+ GO TO 140
+ END IF
+*
+ IF( .NOT.NULL )THEN
+*
+* Check the result column by column.
+*
+ IF( INCX.GT.0 )THEN
+ DO 50 I = 1, M
+ Z( I ) = X( I )
+ 50 CONTINUE
+ ELSE
+ DO 60 I = 1, M
+ Z( I ) = X( M - I + 1 )
+ 60 CONTINUE
+ END IF
+ DO 70 J = 1, N
+ IF( INCY.GT.0 )THEN
+ W( 1 ) = Y( J )
+ ELSE
+ W( 1 ) = Y( N - J + 1 )
+ END IF
+ CALL SMVCH( 'N', M, 1, ALPHA, Z, NMAX, W, 1,
+ $ ONE, A( 1, J ), 1, YT, G,
+ $ AA( 1 + ( J - 1 )*LDA ), EPS,
+ $ ERR, FATAL, NOUT, .TRUE. )
+ ERRMAX = MAX( ERRMAX, ERR )
+* If got really bad answer, report and return.
+ IF( FATAL )
+ $ GO TO 130
+ 70 CONTINUE
+ ELSE
+* Avoid repeating tests with M.le.0 or N.le.0.
+ GO TO 110
+ END IF
+*
+ 80 CONTINUE
+*
+ 90 CONTINUE
+*
+ 100 CONTINUE
+*
+ 110 CONTINUE
+*
+ 120 CONTINUE
+*
+* Report result.
+*
+ IF( ERRMAX.LT.THRESH )THEN
+ WRITE( NOUT, FMT = 9999 )SNAME, NC
+ ELSE
+ WRITE( NOUT, FMT = 9997 )SNAME, NC, ERRMAX
+ END IF
+ GO TO 150
+*
+ 130 CONTINUE
+ WRITE( NOUT, FMT = 9995 )J
+*
+ 140 CONTINUE
+ WRITE( NOUT, FMT = 9996 )SNAME
+ WRITE( NOUT, FMT = 9994 )NC, SNAME, M, N, ALPHA, INCX, INCY, LDA
+*
+ 150 CONTINUE
+ RETURN
+*
+ 9999 FORMAT( ' ', A6, ' PASSED THE COMPUTATIONAL TESTS (', I6, ' CALL',
+ $ 'S)' )
+ 9998 FORMAT( ' ******* FATAL ERROR - PARAMETER NUMBER ', I2, ' WAS CH',
+ $ 'ANGED INCORRECTLY *******' )
+ 9997 FORMAT( ' ', A6, ' COMPLETED THE COMPUTATIONAL TESTS (', I6, ' C',
+ $ 'ALLS)', /' ******* BUT WITH MAXIMUM TEST RATIO', F8.2,
+ $ ' - SUSPECT *******' )
+ 9996 FORMAT( ' ******* ', A6, ' FAILED ON CALL NUMBER:' )
+ 9995 FORMAT( ' THESE ARE THE RESULTS FOR COLUMN ', I3 )
+ 9994 FORMAT( 1X, I6, ': ', A6, '(', 2( I3, ',' ), F4.1, ', X,', I2,
+ $ ', Y,', I2, ', A,', I3, ') .' )
+ 9993 FORMAT( ' ******* FATAL ERROR - ERROR-EXIT TAKEN ON VALID CALL *',
+ $ '******' )
+*
+* End of SCHK4.
+*
+ END
+ SUBROUTINE SCHK5( SNAME, EPS, THRESH, NOUT, NTRA, TRACE, REWI,
+ $ FATAL, NIDIM, IDIM, NALF, ALF, NINC, INC, NMAX,
+ $ INCMAX, A, AA, AS, X, XX, XS, Y, YY, YS, YT, G,
+ $ Z )
+*
+* Tests SSYR and SSPR.
+*
+* Auxiliary routine for test program for Level 2 Blas.
+*
+* -- Written on 10-August-1987.
+* Richard Hanson, Sandia National Labs.
+* Jeremy Du Croz, NAG Central Office.
+*
+* .. Parameters ..
+ REAL ZERO, HALF, ONE
+ PARAMETER ( ZERO = 0.0, HALF = 0.5, ONE = 1.0 )
+* .. Scalar Arguments ..
+ REAL EPS, THRESH
+ INTEGER INCMAX, NALF, NIDIM, NINC, NMAX, NOUT, NTRA
+ LOGICAL FATAL, REWI, TRACE
+ CHARACTER*6 SNAME
+* .. Array Arguments ..
+ REAL A( NMAX, NMAX ), AA( NMAX*NMAX ), ALF( NALF ),
+ $ AS( NMAX*NMAX ), G( NMAX ), X( NMAX ),
+ $ XS( NMAX*INCMAX ), XX( NMAX*INCMAX ),
+ $ Y( NMAX ), YS( NMAX*INCMAX ), YT( NMAX ),
+ $ YY( NMAX*INCMAX ), Z( NMAX )
+ INTEGER IDIM( NIDIM ), INC( NINC )
+* .. Local Scalars ..
+ REAL ALPHA, ALS, ERR, ERRMAX, TRANSL
+ INTEGER I, IA, IC, IN, INCX, INCXS, IX, J, JA, JJ, LAA,
+ $ LDA, LDAS, LJ, LX, N, NARGS, NC, NS
+ LOGICAL FULL, NULL, PACKED, RESET, SAME, UPPER
+ CHARACTER*1 UPLO, UPLOS
+ CHARACTER*2 ICH
+* .. Local Arrays ..
+ REAL W( 1 )
+ LOGICAL ISAME( 13 )
+* .. External Functions ..
+ LOGICAL LSE, LSERES
+ EXTERNAL LSE, LSERES
+* .. External Subroutines ..
+ EXTERNAL SMAKE, SMVCH, SSPR, SSYR
+* .. Intrinsic Functions ..
+ INTRINSIC ABS, MAX
+* .. Scalars in Common ..
+ INTEGER INFOT, NOUTC
+ LOGICAL LERR, OK
+* .. Common blocks ..
+ COMMON /INFOC/INFOT, NOUTC, OK, LERR
+* .. Data statements ..
+ DATA ICH/'UL'/
+* .. Executable Statements ..
+ FULL = SNAME( 3: 3 ).EQ.'Y'
+ PACKED = SNAME( 3: 3 ).EQ.'P'
+* Define the number of arguments.
+ IF( FULL )THEN
+ NARGS = 7
+ ELSE IF( PACKED )THEN
+ NARGS = 6
+ END IF
+*
+ NC = 0
+ RESET = .TRUE.
+ ERRMAX = ZERO
+*
+ DO 100 IN = 1, NIDIM
+ N = IDIM( IN )
+* Set LDA to 1 more than minimum value if room.
+ LDA = N
+ IF( LDA.LT.NMAX )
+ $ LDA = LDA + 1
+* Skip tests if not enough room.
+ IF( LDA.GT.NMAX )
+ $ GO TO 100
+ IF( PACKED )THEN
+ LAA = ( N*( N + 1 ) )/2
+ ELSE
+ LAA = LDA*N
+ END IF
+*
+ DO 90 IC = 1, 2
+ UPLO = ICH( IC: IC )
+ UPPER = UPLO.EQ.'U'
+*
+ DO 80 IX = 1, NINC
+ INCX = INC( IX )
+ LX = ABS( INCX )*N
+*
+* Generate the vector X.
+*
+ TRANSL = HALF
+ CALL SMAKE( 'GE', ' ', ' ', 1, N, X, 1, XX, ABS( INCX ),
+ $ 0, N - 1, RESET, TRANSL )
+ IF( N.GT.1 )THEN
+ X( N/2 ) = ZERO
+ XX( 1 + ABS( INCX )*( N/2 - 1 ) ) = ZERO
+ END IF
+*
+ DO 70 IA = 1, NALF
+ ALPHA = ALF( IA )
+ NULL = N.LE.0.OR.ALPHA.EQ.ZERO
+*
+* Generate the matrix A.
+*
+ TRANSL = ZERO
+ CALL SMAKE( SNAME( 2: 3 ), UPLO, ' ', N, N, A, NMAX,
+ $ AA, LDA, N - 1, N - 1, RESET, TRANSL )
+*
+ NC = NC + 1
+*
+* Save every datum before calling the subroutine.
+*
+ UPLOS = UPLO
+ NS = N
+ ALS = ALPHA
+ DO 10 I = 1, LAA
+ AS( I ) = AA( I )
+ 10 CONTINUE
+ LDAS = LDA
+ DO 20 I = 1, LX
+ XS( I ) = XX( I )
+ 20 CONTINUE
+ INCXS = INCX
+*
+* Call the subroutine.
+*
+ IF( FULL )THEN
+ IF( TRACE )
+ $ WRITE( NTRA, FMT = 9993 )NC, SNAME, UPLO, N,
+ $ ALPHA, INCX, LDA
+ IF( REWI )
+ $ REWIND NTRA
+ CALL SSYR( UPLO, N, ALPHA, XX, INCX, AA, LDA )
+ ELSE IF( PACKED )THEN
+ IF( TRACE )
+ $ WRITE( NTRA, FMT = 9994 )NC, SNAME, UPLO, N,
+ $ ALPHA, INCX
+ IF( REWI )
+ $ REWIND NTRA
+ CALL SSPR( UPLO, N, ALPHA, XX, INCX, AA )
+ END IF
+*
+* Check if error-exit was taken incorrectly.
+*
+ IF( .NOT.OK )THEN
+ WRITE( NOUT, FMT = 9992 )
+ FATAL = .TRUE.
+ GO TO 120
+ END IF
+*
+* See what data changed inside subroutines.
+*
+ ISAME( 1 ) = UPLO.EQ.UPLOS
+ ISAME( 2 ) = NS.EQ.N
+ ISAME( 3 ) = ALS.EQ.ALPHA
+ ISAME( 4 ) = LSE( XS, XX, LX )
+ ISAME( 5 ) = INCXS.EQ.INCX
+ IF( NULL )THEN
+ ISAME( 6 ) = LSE( AS, AA, LAA )
+ ELSE
+ ISAME( 6 ) = LSERES( SNAME( 2: 3 ), UPLO, N, N, AS,
+ $ AA, LDA )
+ END IF
+ IF( .NOT.PACKED )THEN
+ ISAME( 7 ) = LDAS.EQ.LDA
+ END IF
+*
+* If data was incorrectly changed, report and return.
+*
+ SAME = .TRUE.
+ DO 30 I = 1, NARGS
+ SAME = SAME.AND.ISAME( I )
+ IF( .NOT.ISAME( I ) )
+ $ WRITE( NOUT, FMT = 9998 )I
+ 30 CONTINUE
+ IF( .NOT.SAME )THEN
+ FATAL = .TRUE.
+ GO TO 120
+ END IF
+*
+ IF( .NOT.NULL )THEN
+*
+* Check the result column by column.
+*
+ IF( INCX.GT.0 )THEN
+ DO 40 I = 1, N
+ Z( I ) = X( I )
+ 40 CONTINUE
+ ELSE
+ DO 50 I = 1, N
+ Z( I ) = X( N - I + 1 )
+ 50 CONTINUE
+ END IF
+ JA = 1
+ DO 60 J = 1, N
+ W( 1 ) = Z( J )
+ IF( UPPER )THEN
+ JJ = 1
+ LJ = J
+ ELSE
+ JJ = J
+ LJ = N - J + 1
+ END IF
+ CALL SMVCH( 'N', LJ, 1, ALPHA, Z( JJ ), LJ, W,
+ $ 1, ONE, A( JJ, J ), 1, YT, G,
+ $ AA( JA ), EPS, ERR, FATAL, NOUT,
+ $ .TRUE. )
+ IF( FULL )THEN
+ IF( UPPER )THEN
+ JA = JA + LDA
+ ELSE
+ JA = JA + LDA + 1
+ END IF
+ ELSE
+ JA = JA + LJ
+ END IF
+ ERRMAX = MAX( ERRMAX, ERR )
+* If got really bad answer, report and return.
+ IF( FATAL )
+ $ GO TO 110
+ 60 CONTINUE
+ ELSE
+* Avoid repeating tests if N.le.0.
+ IF( N.LE.0 )
+ $ GO TO 100
+ END IF
+*
+ 70 CONTINUE
+*
+ 80 CONTINUE
+*
+ 90 CONTINUE
+*
+ 100 CONTINUE
+*
+* Report result.
+*
+ IF( ERRMAX.LT.THRESH )THEN
+ WRITE( NOUT, FMT = 9999 )SNAME, NC
+ ELSE
+ WRITE( NOUT, FMT = 9997 )SNAME, NC, ERRMAX
+ END IF
+ GO TO 130
+*
+ 110 CONTINUE
+ WRITE( NOUT, FMT = 9995 )J
+*
+ 120 CONTINUE
+ WRITE( NOUT, FMT = 9996 )SNAME
+ IF( FULL )THEN
+ WRITE( NOUT, FMT = 9993 )NC, SNAME, UPLO, N, ALPHA, INCX, LDA
+ ELSE IF( PACKED )THEN
+ WRITE( NOUT, FMT = 9994 )NC, SNAME, UPLO, N, ALPHA, INCX
+ END IF
+*
+ 130 CONTINUE
+ RETURN
+*
+ 9999 FORMAT( ' ', A6, ' PASSED THE COMPUTATIONAL TESTS (', I6, ' CALL',
+ $ 'S)' )
+ 9998 FORMAT( ' ******* FATAL ERROR - PARAMETER NUMBER ', I2, ' WAS CH',
+ $ 'ANGED INCORRECTLY *******' )
+ 9997 FORMAT( ' ', A6, ' COMPLETED THE COMPUTATIONAL TESTS (', I6, ' C',
+ $ 'ALLS)', /' ******* BUT WITH MAXIMUM TEST RATIO', F8.2,
+ $ ' - SUSPECT *******' )
+ 9996 FORMAT( ' ******* ', A6, ' FAILED ON CALL NUMBER:' )
+ 9995 FORMAT( ' THESE ARE THE RESULTS FOR COLUMN ', I3 )
+ 9994 FORMAT( 1X, I6, ': ', A6, '(''', A1, ''',', I3, ',', F4.1, ', X,',
+ $ I2, ', AP) .' )
+ 9993 FORMAT( 1X, I6, ': ', A6, '(''', A1, ''',', I3, ',', F4.1, ', X,',
+ $ I2, ', A,', I3, ') .' )
+ 9992 FORMAT( ' ******* FATAL ERROR - ERROR-EXIT TAKEN ON VALID CALL *',
+ $ '******' )
+*
+* End of SCHK5.
+*
+ END
+ SUBROUTINE SCHK6( SNAME, EPS, THRESH, NOUT, NTRA, TRACE, REWI,
+ $ FATAL, NIDIM, IDIM, NALF, ALF, NINC, INC, NMAX,
+ $ INCMAX, A, AA, AS, X, XX, XS, Y, YY, YS, YT, G,
+ $ Z )
+*
+* Tests SSYR2 and SSPR2.
+*
+* Auxiliary routine for test program for Level 2 Blas.
+*
+* -- Written on 10-August-1987.
+* Richard Hanson, Sandia National Labs.
+* Jeremy Du Croz, NAG Central Office.
+*
+* .. Parameters ..
+ REAL ZERO, HALF, ONE
+ PARAMETER ( ZERO = 0.0, HALF = 0.5, ONE = 1.0 )
+* .. Scalar Arguments ..
+ REAL EPS, THRESH
+ INTEGER INCMAX, NALF, NIDIM, NINC, NMAX, NOUT, NTRA
+ LOGICAL FATAL, REWI, TRACE
+ CHARACTER*6 SNAME
+* .. Array Arguments ..
+ REAL A( NMAX, NMAX ), AA( NMAX*NMAX ), ALF( NALF ),
+ $ AS( NMAX*NMAX ), G( NMAX ), X( NMAX ),
+ $ XS( NMAX*INCMAX ), XX( NMAX*INCMAX ),
+ $ Y( NMAX ), YS( NMAX*INCMAX ), YT( NMAX ),
+ $ YY( NMAX*INCMAX ), Z( NMAX, 2 )
+ INTEGER IDIM( NIDIM ), INC( NINC )
+* .. Local Scalars ..
+ REAL ALPHA, ALS, ERR, ERRMAX, TRANSL
+ INTEGER I, IA, IC, IN, INCX, INCXS, INCY, INCYS, IX,
+ $ IY, J, JA, JJ, LAA, LDA, LDAS, LJ, LX, LY, N,
+ $ NARGS, NC, NS
+ LOGICAL FULL, NULL, PACKED, RESET, SAME, UPPER
+ CHARACTER*1 UPLO, UPLOS
+ CHARACTER*2 ICH
+* .. Local Arrays ..
+ REAL W( 2 )
+ LOGICAL ISAME( 13 )
+* .. External Functions ..
+ LOGICAL LSE, LSERES
+ EXTERNAL LSE, LSERES
+* .. External Subroutines ..
+ EXTERNAL SMAKE, SMVCH, SSPR2, SSYR2
+* .. Intrinsic Functions ..
+ INTRINSIC ABS, MAX
+* .. Scalars in Common ..
+ INTEGER INFOT, NOUTC
+ LOGICAL LERR, OK
+* .. Common blocks ..
+ COMMON /INFOC/INFOT, NOUTC, OK, LERR
+* .. Data statements ..
+ DATA ICH/'UL'/
+* .. Executable Statements ..
+ FULL = SNAME( 3: 3 ).EQ.'Y'
+ PACKED = SNAME( 3: 3 ).EQ.'P'
+* Define the number of arguments.
+ IF( FULL )THEN
+ NARGS = 9
+ ELSE IF( PACKED )THEN
+ NARGS = 8
+ END IF
+*
+ NC = 0
+ RESET = .TRUE.
+ ERRMAX = ZERO
+*
+ DO 140 IN = 1, NIDIM
+ N = IDIM( IN )
+* Set LDA to 1 more than minimum value if room.
+ LDA = N
+ IF( LDA.LT.NMAX )
+ $ LDA = LDA + 1
+* Skip tests if not enough room.
+ IF( LDA.GT.NMAX )
+ $ GO TO 140
+ IF( PACKED )THEN
+ LAA = ( N*( N + 1 ) )/2
+ ELSE
+ LAA = LDA*N
+ END IF
+*
+ DO 130 IC = 1, 2
+ UPLO = ICH( IC: IC )
+ UPPER = UPLO.EQ.'U'
+*
+ DO 120 IX = 1, NINC
+ INCX = INC( IX )
+ LX = ABS( INCX )*N
+*
+* Generate the vector X.
+*
+ TRANSL = HALF
+ CALL SMAKE( 'GE', ' ', ' ', 1, N, X, 1, XX, ABS( INCX ),
+ $ 0, N - 1, RESET, TRANSL )
+ IF( N.GT.1 )THEN
+ X( N/2 ) = ZERO
+ XX( 1 + ABS( INCX )*( N/2 - 1 ) ) = ZERO
+ END IF
+*
+ DO 110 IY = 1, NINC
+ INCY = INC( IY )
+ LY = ABS( INCY )*N
+*
+* Generate the vector Y.
+*
+ TRANSL = ZERO
+ CALL SMAKE( 'GE', ' ', ' ', 1, N, Y, 1, YY,
+ $ ABS( INCY ), 0, N - 1, RESET, TRANSL )
+ IF( N.GT.1 )THEN
+ Y( N/2 ) = ZERO
+ YY( 1 + ABS( INCY )*( N/2 - 1 ) ) = ZERO
+ END IF
+*
+ DO 100 IA = 1, NALF
+ ALPHA = ALF( IA )
+ NULL = N.LE.0.OR.ALPHA.EQ.ZERO
+*
+* Generate the matrix A.
+*
+ TRANSL = ZERO
+ CALL SMAKE( SNAME( 2: 3 ), UPLO, ' ', N, N, A,
+ $ NMAX, AA, LDA, N - 1, N - 1, RESET,
+ $ TRANSL )
+*
+ NC = NC + 1
+*
+* Save every datum before calling the subroutine.
+*
+ UPLOS = UPLO
+ NS = N
+ ALS = ALPHA
+ DO 10 I = 1, LAA
+ AS( I ) = AA( I )
+ 10 CONTINUE
+ LDAS = LDA
+ DO 20 I = 1, LX
+ XS( I ) = XX( I )
+ 20 CONTINUE
+ INCXS = INCX
+ DO 30 I = 1, LY
+ YS( I ) = YY( I )
+ 30 CONTINUE
+ INCYS = INCY
+*
+* Call the subroutine.
+*
+ IF( FULL )THEN
+ IF( TRACE )
+ $ WRITE( NTRA, FMT = 9993 )NC, SNAME, UPLO, N,
+ $ ALPHA, INCX, INCY, LDA
+ IF( REWI )
+ $ REWIND NTRA
+ CALL SSYR2( UPLO, N, ALPHA, XX, INCX, YY, INCY,
+ $ AA, LDA )
+ ELSE IF( PACKED )THEN
+ IF( TRACE )
+ $ WRITE( NTRA, FMT = 9994 )NC, SNAME, UPLO, N,
+ $ ALPHA, INCX, INCY
+ IF( REWI )
+ $ REWIND NTRA
+ CALL SSPR2( UPLO, N, ALPHA, XX, INCX, YY, INCY,
+ $ AA )
+ END IF
+*
+* Check if error-exit was taken incorrectly.
+*
+ IF( .NOT.OK )THEN
+ WRITE( NOUT, FMT = 9992 )
+ FATAL = .TRUE.
+ GO TO 160
+ END IF
+*
+* See what data changed inside subroutines.
+*
+ ISAME( 1 ) = UPLO.EQ.UPLOS
+ ISAME( 2 ) = NS.EQ.N
+ ISAME( 3 ) = ALS.EQ.ALPHA
+ ISAME( 4 ) = LSE( XS, XX, LX )
+ ISAME( 5 ) = INCXS.EQ.INCX
+ ISAME( 6 ) = LSE( YS, YY, LY )
+ ISAME( 7 ) = INCYS.EQ.INCY
+ IF( NULL )THEN
+ ISAME( 8 ) = LSE( AS, AA, LAA )
+ ELSE
+ ISAME( 8 ) = LSERES( SNAME( 2: 3 ), UPLO, N, N,
+ $ AS, AA, LDA )
+ END IF
+ IF( .NOT.PACKED )THEN
+ ISAME( 9 ) = LDAS.EQ.LDA
+ END IF
+*
+* If data was incorrectly changed, report and return.
+*
+ SAME = .TRUE.
+ DO 40 I = 1, NARGS
+ SAME = SAME.AND.ISAME( I )
+ IF( .NOT.ISAME( I ) )
+ $ WRITE( NOUT, FMT = 9998 )I
+ 40 CONTINUE
+ IF( .NOT.SAME )THEN
+ FATAL = .TRUE.
+ GO TO 160
+ END IF
+*
+ IF( .NOT.NULL )THEN
+*
+* Check the result column by column.
+*
+ IF( INCX.GT.0 )THEN
+ DO 50 I = 1, N
+ Z( I, 1 ) = X( I )
+ 50 CONTINUE
+ ELSE
+ DO 60 I = 1, N
+ Z( I, 1 ) = X( N - I + 1 )
+ 60 CONTINUE
+ END IF
+ IF( INCY.GT.0 )THEN
+ DO 70 I = 1, N
+ Z( I, 2 ) = Y( I )
+ 70 CONTINUE
+ ELSE
+ DO 80 I = 1, N
+ Z( I, 2 ) = Y( N - I + 1 )
+ 80 CONTINUE
+ END IF
+ JA = 1
+ DO 90 J = 1, N
+ W( 1 ) = Z( J, 2 )
+ W( 2 ) = Z( J, 1 )
+ IF( UPPER )THEN
+ JJ = 1
+ LJ = J
+ ELSE
+ JJ = J
+ LJ = N - J + 1
+ END IF
+ CALL SMVCH( 'N', LJ, 2, ALPHA, Z( JJ, 1 ),
+ $ NMAX, W, 1, ONE, A( JJ, J ), 1,
+ $ YT, G, AA( JA ), EPS, ERR, FATAL,
+ $ NOUT, .TRUE. )
+ IF( FULL )THEN
+ IF( UPPER )THEN
+ JA = JA + LDA
+ ELSE
+ JA = JA + LDA + 1
+ END IF
+ ELSE
+ JA = JA + LJ
+ END IF
+ ERRMAX = MAX( ERRMAX, ERR )
+* If got really bad answer, report and return.
+ IF( FATAL )
+ $ GO TO 150
+ 90 CONTINUE
+ ELSE
+* Avoid repeating tests with N.le.0.
+ IF( N.LE.0 )
+ $ GO TO 140
+ END IF
+*
+ 100 CONTINUE
+*
+ 110 CONTINUE
+*
+ 120 CONTINUE
+*
+ 130 CONTINUE
+*
+ 140 CONTINUE
+*
+* Report result.
+*
+ IF( ERRMAX.LT.THRESH )THEN
+ WRITE( NOUT, FMT = 9999 )SNAME, NC
+ ELSE
+ WRITE( NOUT, FMT = 9997 )SNAME, NC, ERRMAX
+ END IF
+ GO TO 170
+*
+ 150 CONTINUE
+ WRITE( NOUT, FMT = 9995 )J
+*
+ 160 CONTINUE
+ WRITE( NOUT, FMT = 9996 )SNAME
+ IF( FULL )THEN
+ WRITE( NOUT, FMT = 9993 )NC, SNAME, UPLO, N, ALPHA, INCX,
+ $ INCY, LDA
+ ELSE IF( PACKED )THEN
+ WRITE( NOUT, FMT = 9994 )NC, SNAME, UPLO, N, ALPHA, INCX, INCY
+ END IF
+*
+ 170 CONTINUE
+ RETURN
+*
+ 9999 FORMAT( ' ', A6, ' PASSED THE COMPUTATIONAL TESTS (', I6, ' CALL',
+ $ 'S)' )
+ 9998 FORMAT( ' ******* FATAL ERROR - PARAMETER NUMBER ', I2, ' WAS CH',
+ $ 'ANGED INCORRECTLY *******' )
+ 9997 FORMAT( ' ', A6, ' COMPLETED THE COMPUTATIONAL TESTS (', I6, ' C',
+ $ 'ALLS)', /' ******* BUT WITH MAXIMUM TEST RATIO', F8.2,
+ $ ' - SUSPECT *******' )
+ 9996 FORMAT( ' ******* ', A6, ' FAILED ON CALL NUMBER:' )
+ 9995 FORMAT( ' THESE ARE THE RESULTS FOR COLUMN ', I3 )
+ 9994 FORMAT( 1X, I6, ': ', A6, '(''', A1, ''',', I3, ',', F4.1, ', X,',
+ $ I2, ', Y,', I2, ', AP) .' )
+ 9993 FORMAT( 1X, I6, ': ', A6, '(''', A1, ''',', I3, ',', F4.1, ', X,',
+ $ I2, ', Y,', I2, ', A,', I3, ') .' )
+ 9992 FORMAT( ' ******* FATAL ERROR - ERROR-EXIT TAKEN ON VALID CALL *',
+ $ '******' )
+*
+* End of SCHK6.
+*
+ END
+ SUBROUTINE SCHKE( ISNUM, SRNAMT, NOUT )
+*
+* Tests the error exits from the Level 2 Blas.
+* Requires a special version of the error-handling routine XERBLA.
+* ALPHA, BETA, A, X and Y should not need to be defined.
+*
+* Auxiliary routine for test program for Level 2 Blas.
+*
+* -- Written on 10-August-1987.
+* Richard Hanson, Sandia National Labs.
+* Jeremy Du Croz, NAG Central Office.
+*
+* .. Scalar Arguments ..
+ INTEGER ISNUM, NOUT
+ CHARACTER*6 SRNAMT
+* .. Scalars in Common ..
+ INTEGER INFOT, NOUTC
+ LOGICAL LERR, OK
+* .. Local Scalars ..
+ REAL ALPHA, BETA
+* .. Local Arrays ..
+ REAL A( 1, 1 ), X( 1 ), Y( 1 )
+* .. External Subroutines ..
+ EXTERNAL CHKXER, SGBMV, SGEMV, SGER, SSBMV, SSPMV, SSPR,
+ $ SSPR2, SSYMV, SSYR, SSYR2, STBMV, STBSV, STPMV,
+ $ STPSV, STRMV, STRSV
+* .. Common blocks ..
+ COMMON /INFOC/INFOT, NOUTC, OK, LERR
+* .. Executable Statements ..
+* OK is set to .FALSE. by the special version of XERBLA or by CHKXER
+* if anything is wrong.
+ OK = .TRUE.
+* LERR is set to .TRUE. by the special version of XERBLA each time
+* it is called, and is then tested and re-set by CHKXER.
+ LERR = .FALSE.
+ GO TO ( 10, 20, 30, 40, 50, 60, 70, 80,
+ $ 90, 100, 110, 120, 130, 140, 150,
+ $ 160 )ISNUM
+ 10 INFOT = 1
+ CALL SGEMV( '/', 0, 0, ALPHA, A, 1, X, 1, BETA, Y, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 2
+ CALL SGEMV( 'N', -1, 0, ALPHA, A, 1, X, 1, BETA, Y, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 3
+ CALL SGEMV( 'N', 0, -1, ALPHA, A, 1, X, 1, BETA, Y, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 6
+ CALL SGEMV( 'N', 2, 0, ALPHA, A, 1, X, 1, BETA, Y, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 8
+ CALL SGEMV( 'N', 0, 0, ALPHA, A, 1, X, 0, BETA, Y, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 11
+ CALL SGEMV( 'N', 0, 0, ALPHA, A, 1, X, 1, BETA, Y, 0 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ GO TO 170
+ 20 INFOT = 1
+ CALL SGBMV( '/', 0, 0, 0, 0, ALPHA, A, 1, X, 1, BETA, Y, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 2
+ CALL SGBMV( 'N', -1, 0, 0, 0, ALPHA, A, 1, X, 1, BETA, Y, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 3
+ CALL SGBMV( 'N', 0, -1, 0, 0, ALPHA, A, 1, X, 1, BETA, Y, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 4
+ CALL SGBMV( 'N', 0, 0, -1, 0, ALPHA, A, 1, X, 1, BETA, Y, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 5
+ CALL SGBMV( 'N', 2, 0, 0, -1, ALPHA, A, 1, X, 1, BETA, Y, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 8
+ CALL SGBMV( 'N', 0, 0, 1, 0, ALPHA, A, 1, X, 1, BETA, Y, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 10
+ CALL SGBMV( 'N', 0, 0, 0, 0, ALPHA, A, 1, X, 0, BETA, Y, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 13
+ CALL SGBMV( 'N', 0, 0, 0, 0, ALPHA, A, 1, X, 1, BETA, Y, 0 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ GO TO 170
+ 30 INFOT = 1
+ CALL SSYMV( '/', 0, ALPHA, A, 1, X, 1, BETA, Y, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 2
+ CALL SSYMV( 'U', -1, ALPHA, A, 1, X, 1, BETA, Y, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 5
+ CALL SSYMV( 'U', 2, ALPHA, A, 1, X, 1, BETA, Y, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 7
+ CALL SSYMV( 'U', 0, ALPHA, A, 1, X, 0, BETA, Y, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 10
+ CALL SSYMV( 'U', 0, ALPHA, A, 1, X, 1, BETA, Y, 0 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ GO TO 170
+ 40 INFOT = 1
+ CALL SSBMV( '/', 0, 0, ALPHA, A, 1, X, 1, BETA, Y, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 2
+ CALL SSBMV( 'U', -1, 0, ALPHA, A, 1, X, 1, BETA, Y, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 3
+ CALL SSBMV( 'U', 0, -1, ALPHA, A, 1, X, 1, BETA, Y, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 6
+ CALL SSBMV( 'U', 0, 1, ALPHA, A, 1, X, 1, BETA, Y, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 8
+ CALL SSBMV( 'U', 0, 0, ALPHA, A, 1, X, 0, BETA, Y, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 11
+ CALL SSBMV( 'U', 0, 0, ALPHA, A, 1, X, 1, BETA, Y, 0 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ GO TO 170
+ 50 INFOT = 1
+ CALL SSPMV( '/', 0, ALPHA, A, X, 1, BETA, Y, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 2
+ CALL SSPMV( 'U', -1, ALPHA, A, X, 1, BETA, Y, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 6
+ CALL SSPMV( 'U', 0, ALPHA, A, X, 0, BETA, Y, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 9
+ CALL SSPMV( 'U', 0, ALPHA, A, X, 1, BETA, Y, 0 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ GO TO 170
+ 60 INFOT = 1
+ CALL STRMV( '/', 'N', 'N', 0, A, 1, X, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 2
+ CALL STRMV( 'U', '/', 'N', 0, A, 1, X, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 3
+ CALL STRMV( 'U', 'N', '/', 0, A, 1, X, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 4
+ CALL STRMV( 'U', 'N', 'N', -1, A, 1, X, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 6
+ CALL STRMV( 'U', 'N', 'N', 2, A, 1, X, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 8
+ CALL STRMV( 'U', 'N', 'N', 0, A, 1, X, 0 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ GO TO 170
+ 70 INFOT = 1
+ CALL STBMV( '/', 'N', 'N', 0, 0, A, 1, X, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 2
+ CALL STBMV( 'U', '/', 'N', 0, 0, A, 1, X, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 3
+ CALL STBMV( 'U', 'N', '/', 0, 0, A, 1, X, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 4
+ CALL STBMV( 'U', 'N', 'N', -1, 0, A, 1, X, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 5
+ CALL STBMV( 'U', 'N', 'N', 0, -1, A, 1, X, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 7
+ CALL STBMV( 'U', 'N', 'N', 0, 1, A, 1, X, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 9
+ CALL STBMV( 'U', 'N', 'N', 0, 0, A, 1, X, 0 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ GO TO 170
+ 80 INFOT = 1
+ CALL STPMV( '/', 'N', 'N', 0, A, X, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 2
+ CALL STPMV( 'U', '/', 'N', 0, A, X, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 3
+ CALL STPMV( 'U', 'N', '/', 0, A, X, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 4
+ CALL STPMV( 'U', 'N', 'N', -1, A, X, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 7
+ CALL STPMV( 'U', 'N', 'N', 0, A, X, 0 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ GO TO 170
+ 90 INFOT = 1
+ CALL STRSV( '/', 'N', 'N', 0, A, 1, X, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 2
+ CALL STRSV( 'U', '/', 'N', 0, A, 1, X, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 3
+ CALL STRSV( 'U', 'N', '/', 0, A, 1, X, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 4
+ CALL STRSV( 'U', 'N', 'N', -1, A, 1, X, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 6
+ CALL STRSV( 'U', 'N', 'N', 2, A, 1, X, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 8
+ CALL STRSV( 'U', 'N', 'N', 0, A, 1, X, 0 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ GO TO 170
+ 100 INFOT = 1
+ CALL STBSV( '/', 'N', 'N', 0, 0, A, 1, X, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 2
+ CALL STBSV( 'U', '/', 'N', 0, 0, A, 1, X, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 3
+ CALL STBSV( 'U', 'N', '/', 0, 0, A, 1, X, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 4
+ CALL STBSV( 'U', 'N', 'N', -1, 0, A, 1, X, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 5
+ CALL STBSV( 'U', 'N', 'N', 0, -1, A, 1, X, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 7
+ CALL STBSV( 'U', 'N', 'N', 0, 1, A, 1, X, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 9
+ CALL STBSV( 'U', 'N', 'N', 0, 0, A, 1, X, 0 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ GO TO 170
+ 110 INFOT = 1
+ CALL STPSV( '/', 'N', 'N', 0, A, X, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 2
+ CALL STPSV( 'U', '/', 'N', 0, A, X, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 3
+ CALL STPSV( 'U', 'N', '/', 0, A, X, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 4
+ CALL STPSV( 'U', 'N', 'N', -1, A, X, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 7
+ CALL STPSV( 'U', 'N', 'N', 0, A, X, 0 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ GO TO 170
+ 120 INFOT = 1
+ CALL SGER( -1, 0, ALPHA, X, 1, Y, 1, A, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 2
+ CALL SGER( 0, -1, ALPHA, X, 1, Y, 1, A, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 5
+ CALL SGER( 0, 0, ALPHA, X, 0, Y, 1, A, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 7
+ CALL SGER( 0, 0, ALPHA, X, 1, Y, 0, A, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 9
+ CALL SGER( 2, 0, ALPHA, X, 1, Y, 1, A, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ GO TO 170
+ 130 INFOT = 1
+ CALL SSYR( '/', 0, ALPHA, X, 1, A, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 2
+ CALL SSYR( 'U', -1, ALPHA, X, 1, A, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 5
+ CALL SSYR( 'U', 0, ALPHA, X, 0, A, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 7
+ CALL SSYR( 'U', 2, ALPHA, X, 1, A, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ GO TO 170
+ 140 INFOT = 1
+ CALL SSPR( '/', 0, ALPHA, X, 1, A )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 2
+ CALL SSPR( 'U', -1, ALPHA, X, 1, A )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 5
+ CALL SSPR( 'U', 0, ALPHA, X, 0, A )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ GO TO 170
+ 150 INFOT = 1
+ CALL SSYR2( '/', 0, ALPHA, X, 1, Y, 1, A, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 2
+ CALL SSYR2( 'U', -1, ALPHA, X, 1, Y, 1, A, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 5
+ CALL SSYR2( 'U', 0, ALPHA, X, 0, Y, 1, A, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 7
+ CALL SSYR2( 'U', 0, ALPHA, X, 1, Y, 0, A, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 9
+ CALL SSYR2( 'U', 2, ALPHA, X, 1, Y, 1, A, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ GO TO 170
+ 160 INFOT = 1
+ CALL SSPR2( '/', 0, ALPHA, X, 1, Y, 1, A )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 2
+ CALL SSPR2( 'U', -1, ALPHA, X, 1, Y, 1, A )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 5
+ CALL SSPR2( 'U', 0, ALPHA, X, 0, Y, 1, A )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 7
+ CALL SSPR2( 'U', 0, ALPHA, X, 1, Y, 0, A )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+*
+ 170 IF( OK )THEN
+ WRITE( NOUT, FMT = 9999 )SRNAMT
+ ELSE
+ WRITE( NOUT, FMT = 9998 )SRNAMT
+ END IF
+ RETURN
+*
+ 9999 FORMAT( ' ', A6, ' PASSED THE TESTS OF ERROR-EXITS' )
+ 9998 FORMAT( ' ******* ', A6, ' FAILED THE TESTS OF ERROR-EXITS *****',
+ $ '**' )
+*
+* End of SCHKE.
+*
+ END
+ SUBROUTINE SMAKE( TYPE, UPLO, DIAG, M, N, A, NMAX, AA, LDA, KL,
+ $ KU, RESET, TRANSL )
+*
+* Generates values for an M by N matrix A within the bandwidth
+* defined by KL and KU.
+* Stores the values in the array AA in the data structure required
+* by the routine, with unwanted elements set to rogue value.
+*
+* TYPE is 'GE', 'GB', 'SY', 'SB', 'SP', 'TR', 'TB' OR 'TP'.
+*
+* Auxiliary routine for test program for Level 2 Blas.
+*
+* -- Written on 10-August-1987.
+* Richard Hanson, Sandia National Labs.
+* Jeremy Du Croz, NAG Central Office.
+*
+* .. Parameters ..
+ REAL ZERO, ONE
+ PARAMETER ( ZERO = 0.0, ONE = 1.0 )
+ REAL ROGUE
+ PARAMETER ( ROGUE = -1.0E10 )
+* .. Scalar Arguments ..
+ REAL TRANSL
+ INTEGER KL, KU, LDA, M, N, NMAX
+ LOGICAL RESET
+ CHARACTER*1 DIAG, UPLO
+ CHARACTER*2 TYPE
+* .. Array Arguments ..
+ REAL A( NMAX, * ), AA( * )
+* .. Local Scalars ..
+ INTEGER I, I1, I2, I3, IBEG, IEND, IOFF, J, KK
+ LOGICAL GEN, LOWER, SYM, TRI, UNIT, UPPER
+* .. External Functions ..
+ REAL SBEG
+ EXTERNAL SBEG
+* .. Intrinsic Functions ..
+ INTRINSIC MAX, MIN
+* .. Executable Statements ..
+ GEN = TYPE( 1: 1 ).EQ.'G'
+ SYM = TYPE( 1: 1 ).EQ.'S'
+ TRI = TYPE( 1: 1 ).EQ.'T'
+ UPPER = ( SYM.OR.TRI ).AND.UPLO.EQ.'U'
+ LOWER = ( SYM.OR.TRI ).AND.UPLO.EQ.'L'
+ UNIT = TRI.AND.DIAG.EQ.'U'
+*
+* Generate data in array A.
+*
+ DO 20 J = 1, N
+ DO 10 I = 1, M
+ IF( GEN.OR.( UPPER.AND.I.LE.J ).OR.( LOWER.AND.I.GE.J ) )
+ $ THEN
+ IF( ( I.LE.J.AND.J - I.LE.KU ).OR.
+ $ ( I.GE.J.AND.I - J.LE.KL ) )THEN
+ A( I, J ) = SBEG( RESET ) + TRANSL
+ ELSE
+ A( I, J ) = ZERO
+ END IF
+ IF( I.NE.J )THEN
+ IF( SYM )THEN
+ A( J, I ) = A( I, J )
+ ELSE IF( TRI )THEN
+ A( J, I ) = ZERO
+ END IF
+ END IF
+ END IF
+ 10 CONTINUE
+ IF( TRI )
+ $ A( J, J ) = A( J, J ) + ONE
+ IF( UNIT )
+ $ A( J, J ) = ONE
+ 20 CONTINUE
+*
+* Store elements in array AS in data structure required by routine.
+*
+ IF( TYPE.EQ.'GE' )THEN
+ DO 50 J = 1, N
+ DO 30 I = 1, M
+ AA( I + ( J - 1 )*LDA ) = A( I, J )
+ 30 CONTINUE
+ DO 40 I = M + 1, LDA
+ AA( I + ( J - 1 )*LDA ) = ROGUE
+ 40 CONTINUE
+ 50 CONTINUE
+ ELSE IF( TYPE.EQ.'GB' )THEN
+ DO 90 J = 1, N
+ DO 60 I1 = 1, KU + 1 - J
+ AA( I1 + ( J - 1 )*LDA ) = ROGUE
+ 60 CONTINUE
+ DO 70 I2 = I1, MIN( KL + KU + 1, KU + 1 + M - J )
+ AA( I2 + ( J - 1 )*LDA ) = A( I2 + J - KU - 1, J )
+ 70 CONTINUE
+ DO 80 I3 = I2, LDA
+ AA( I3 + ( J - 1 )*LDA ) = ROGUE
+ 80 CONTINUE
+ 90 CONTINUE
+ ELSE IF( TYPE.EQ.'SY'.OR.TYPE.EQ.'TR' )THEN
+ DO 130 J = 1, N
+ IF( UPPER )THEN
+ IBEG = 1
+ IF( UNIT )THEN
+ IEND = J - 1
+ ELSE
+ IEND = J
+ END IF
+ ELSE
+ IF( UNIT )THEN
+ IBEG = J + 1
+ ELSE
+ IBEG = J
+ END IF
+ IEND = N
+ END IF
+ DO 100 I = 1, IBEG - 1
+ AA( I + ( J - 1 )*LDA ) = ROGUE
+ 100 CONTINUE
+ DO 110 I = IBEG, IEND
+ AA( I + ( J - 1 )*LDA ) = A( I, J )
+ 110 CONTINUE
+ DO 120 I = IEND + 1, LDA
+ AA( I + ( J - 1 )*LDA ) = ROGUE
+ 120 CONTINUE
+ 130 CONTINUE
+ ELSE IF( TYPE.EQ.'SB'.OR.TYPE.EQ.'TB' )THEN
+ DO 170 J = 1, N
+ IF( UPPER )THEN
+ KK = KL + 1
+ IBEG = MAX( 1, KL + 2 - J )
+ IF( UNIT )THEN
+ IEND = KL
+ ELSE
+ IEND = KL + 1
+ END IF
+ ELSE
+ KK = 1
+ IF( UNIT )THEN
+ IBEG = 2
+ ELSE
+ IBEG = 1
+ END IF
+ IEND = MIN( KL + 1, 1 + M - J )
+ END IF
+ DO 140 I = 1, IBEG - 1
+ AA( I + ( J - 1 )*LDA ) = ROGUE
+ 140 CONTINUE
+ DO 150 I = IBEG, IEND
+ AA( I + ( J - 1 )*LDA ) = A( I + J - KK, J )
+ 150 CONTINUE
+ DO 160 I = IEND + 1, LDA
+ AA( I + ( J - 1 )*LDA ) = ROGUE
+ 160 CONTINUE
+ 170 CONTINUE
+ ELSE IF( TYPE.EQ.'SP'.OR.TYPE.EQ.'TP' )THEN
+ IOFF = 0
+ DO 190 J = 1, N
+ IF( UPPER )THEN
+ IBEG = 1
+ IEND = J
+ ELSE
+ IBEG = J
+ IEND = N
+ END IF
+ DO 180 I = IBEG, IEND
+ IOFF = IOFF + 1
+ AA( IOFF ) = A( I, J )
+ IF( I.EQ.J )THEN
+ IF( UNIT )
+ $ AA( IOFF ) = ROGUE
+ END IF
+ 180 CONTINUE
+ 190 CONTINUE
+ END IF
+ RETURN
+*
+* End of SMAKE.
+*
+ END
+ SUBROUTINE SMVCH( TRANS, M, N, ALPHA, A, NMAX, X, INCX, BETA, Y,
+ $ INCY, YT, G, YY, EPS, ERR, FATAL, NOUT, MV )
+*
+* Checks the results of the computational tests.
+*
+* Auxiliary routine for test program for Level 2 Blas.
+*
+* -- Written on 10-August-1987.
+* Richard Hanson, Sandia National Labs.
+* Jeremy Du Croz, NAG Central Office.
+*
+* .. Parameters ..
+ REAL ZERO, ONE
+ PARAMETER ( ZERO = 0.0, ONE = 1.0 )
+* .. Scalar Arguments ..
+ REAL ALPHA, BETA, EPS, ERR
+ INTEGER INCX, INCY, M, N, NMAX, NOUT
+ LOGICAL FATAL, MV
+ CHARACTER*1 TRANS
+* .. Array Arguments ..
+ REAL A( NMAX, * ), G( * ), X( * ), Y( * ), YT( * ),
+ $ YY( * )
+* .. Local Scalars ..
+ REAL ERRI
+ INTEGER I, INCXL, INCYL, IY, J, JX, KX, KY, ML, NL
+ LOGICAL TRAN
+* .. Intrinsic Functions ..
+ INTRINSIC ABS, MAX, SQRT
+* .. Executable Statements ..
+ TRAN = TRANS.EQ.'T'.OR.TRANS.EQ.'C'
+ IF( TRAN )THEN
+ ML = N
+ NL = M
+ ELSE
+ ML = M
+ NL = N
+ END IF
+ IF( INCX.LT.0 )THEN
+ KX = NL
+ INCXL = -1
+ ELSE
+ KX = 1
+ INCXL = 1
+ END IF
+ IF( INCY.LT.0 )THEN
+ KY = ML
+ INCYL = -1
+ ELSE
+ KY = 1
+ INCYL = 1
+ END IF
+*
+* Compute expected result in YT using data in A, X and Y.
+* Compute gauges in G.
+*
+ IY = KY
+ DO 30 I = 1, ML
+ YT( IY ) = ZERO
+ G( IY ) = ZERO
+ JX = KX
+ IF( TRAN )THEN
+ DO 10 J = 1, NL
+ YT( IY ) = YT( IY ) + A( J, I )*X( JX )
+ G( IY ) = G( IY ) + ABS( A( J, I )*X( JX ) )
+ JX = JX + INCXL
+ 10 CONTINUE
+ ELSE
+ DO 20 J = 1, NL
+ YT( IY ) = YT( IY ) + A( I, J )*X( JX )
+ G( IY ) = G( IY ) + ABS( A( I, J )*X( JX ) )
+ JX = JX + INCXL
+ 20 CONTINUE
+ END IF
+ YT( IY ) = ALPHA*YT( IY ) + BETA*Y( IY )
+ G( IY ) = ABS( ALPHA )*G( IY ) + ABS( BETA*Y( IY ) )
+ IY = IY + INCYL
+ 30 CONTINUE
+*
+* Compute the error ratio for this result.
+*
+ ERR = ZERO
+ DO 40 I = 1, ML
+ ERRI = ABS( YT( I ) - YY( 1 + ( I - 1 )*ABS( INCY ) ) )/EPS
+ IF( G( I ).NE.ZERO )
+ $ ERRI = ERRI/G( I )
+ ERR = MAX( ERR, ERRI )
+ IF( ERR*SQRT( EPS ).GE.ONE )
+ $ GO TO 50
+ 40 CONTINUE
+* If the loop completes, all results are at least half accurate.
+ GO TO 70
+*
+* Report fatal error.
+*
+ 50 FATAL = .TRUE.
+ WRITE( NOUT, FMT = 9999 )
+ DO 60 I = 1, ML
+ IF( MV )THEN
+ WRITE( NOUT, FMT = 9998 )I, YT( I ),
+ $ YY( 1 + ( I - 1 )*ABS( INCY ) )
+ ELSE
+ WRITE( NOUT, FMT = 9998 )I,
+ $ YY( 1 + ( I - 1 )*ABS( INCY ) ), YT(I)
+ END IF
+ 60 CONTINUE
+*
+ 70 CONTINUE
+ RETURN
+*
+ 9999 FORMAT( ' ******* FATAL ERROR - COMPUTED RESULT IS LESS THAN HAL',
+ $ 'F ACCURATE *******', /' EXPECTED RESULT COMPU',
+ $ 'TED RESULT' )
+ 9998 FORMAT( 1X, I7, 2G18.6 )
+*
+* End of SMVCH.
+*
+ END
+ LOGICAL FUNCTION LSE( RI, RJ, LR )
+*
+* Tests if two arrays are identical.
+*
+* Auxiliary routine for test program for Level 2 Blas.
+*
+* -- Written on 10-August-1987.
+* Richard Hanson, Sandia National Labs.
+* Jeremy Du Croz, NAG Central Office.
+*
+* .. Scalar Arguments ..
+ INTEGER LR
+* .. Array Arguments ..
+ REAL RI( * ), RJ( * )
+* .. Local Scalars ..
+ INTEGER I
+* .. Executable Statements ..
+ DO 10 I = 1, LR
+ IF( RI( I ).NE.RJ( I ) )
+ $ GO TO 20
+ 10 CONTINUE
+ LSE = .TRUE.
+ GO TO 30
+ 20 CONTINUE
+ LSE = .FALSE.
+ 30 RETURN
+*
+* End of LSE.
+*
+ END
+ LOGICAL FUNCTION LSERES( TYPE, UPLO, M, N, AA, AS, LDA )
+*
+* Tests if selected elements in two arrays are equal.
+*
+* TYPE is 'GE', 'SY' or 'SP'.
+*
+* Auxiliary routine for test program for Level 2 Blas.
+*
+* -- Written on 10-August-1987.
+* Richard Hanson, Sandia National Labs.
+* Jeremy Du Croz, NAG Central Office.
+*
+* .. Scalar Arguments ..
+ INTEGER LDA, M, N
+ CHARACTER*1 UPLO
+ CHARACTER*2 TYPE
+* .. Array Arguments ..
+ REAL AA( LDA, * ), AS( LDA, * )
+* .. Local Scalars ..
+ INTEGER I, IBEG, IEND, J
+ LOGICAL UPPER
+* .. Executable Statements ..
+ UPPER = UPLO.EQ.'U'
+ IF( TYPE.EQ.'GE' )THEN
+ DO 20 J = 1, N
+ DO 10 I = M + 1, LDA
+ IF( AA( I, J ).NE.AS( I, J ) )
+ $ GO TO 70
+ 10 CONTINUE
+ 20 CONTINUE
+ ELSE IF( TYPE.EQ.'SY' )THEN
+ DO 50 J = 1, N
+ IF( UPPER )THEN
+ IBEG = 1
+ IEND = J
+ ELSE
+ IBEG = J
+ IEND = N
+ END IF
+ DO 30 I = 1, IBEG - 1
+ IF( AA( I, J ).NE.AS( I, J ) )
+ $ GO TO 70
+ 30 CONTINUE
+ DO 40 I = IEND + 1, LDA
+ IF( AA( I, J ).NE.AS( I, J ) )
+ $ GO TO 70
+ 40 CONTINUE
+ 50 CONTINUE
+ END IF
+*
+ LSERES = .TRUE.
+ GO TO 80
+ 70 CONTINUE
+ LSERES = .FALSE.
+ 80 RETURN
+*
+* End of LSERES.
+*
+ END
+ REAL FUNCTION SBEG( RESET )
+*
+* Generates random numbers uniformly distributed between -0.5 and 0.5.
+*
+* Auxiliary routine for test program for Level 2 Blas.
+*
+* -- Written on 10-August-1987.
+* Richard Hanson, Sandia National Labs.
+* Jeremy Du Croz, NAG Central Office.
+*
+* .. Scalar Arguments ..
+ LOGICAL RESET
+* .. Local Scalars ..
+ INTEGER I, IC, MI
+* .. Save statement ..
+ SAVE I, IC, MI
+* .. Intrinsic Functions ..
+ INTRINSIC REAL
+* .. Executable Statements ..
+ IF( RESET )THEN
+* Initialize local variables.
+ MI = 891
+ I = 7
+ IC = 0
+ RESET = .FALSE.
+ END IF
+*
+* The sequence of values of I is bounded between 1 and 999.
+* If initial I = 1,2,3,6,7 or 9, the period will be 50.
+* If initial I = 4 or 8, the period will be 25.
+* If initial I = 5, the period will be 10.
+* IC is used to break up the period by skipping 1 value of I in 6.
+*
+ IC = IC + 1
+ 10 I = I*MI
+ I = I - 1000*( I/1000 )
+ IF( IC.GE.5 )THEN
+ IC = 0
+ GO TO 10
+ END IF
+ SBEG = REAL( I - 500 )/1001.0
+ RETURN
+*
+* End of SBEG.
+*
+ END
+ REAL FUNCTION SDIFF( X, Y )
+*
+* Auxiliary routine for test program for Level 2 Blas.
+*
+* -- Written on 10-August-1987.
+* Richard Hanson, Sandia National Labs.
+*
+* .. Scalar Arguments ..
+ REAL X, Y
+* .. Executable Statements ..
+ SDIFF = X - Y
+ RETURN
+*
+* End of SDIFF.
+*
+ END
+ SUBROUTINE CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+*
+* Tests whether XERBLA has detected an error when it should.
+*
+* Auxiliary routine for test program for Level 2 Blas.
+*
+* -- Written on 10-August-1987.
+* Richard Hanson, Sandia National Labs.
+* Jeremy Du Croz, NAG Central Office.
+*
+* .. Scalar Arguments ..
+ INTEGER INFOT, NOUT
+ LOGICAL LERR, OK
+ CHARACTER*6 SRNAMT
+* .. Executable Statements ..
+ IF( .NOT.LERR )THEN
+ WRITE( NOUT, FMT = 9999 )INFOT, SRNAMT
+ OK = .FALSE.
+ END IF
+ LERR = .FALSE.
+ RETURN
+*
+ 9999 FORMAT( ' ***** ILLEGAL VALUE OF PARAMETER NUMBER ', I2, ' NOT D',
+ $ 'ETECTED BY ', A6, ' *****' )
+*
+* End of CHKXER.
+*
+ END
+ SUBROUTINE XERBLA( SRNAME, INFO )
+*
+* This is a special version of XERBLA to be used only as part of
+* the test program for testing error exits from the Level 2 BLAS
+* routines.
+*
+* XERBLA is an error handler for the Level 2 BLAS routines.
+*
+* It is called by the Level 2 BLAS routines if an input parameter is
+* invalid.
+*
+* Auxiliary routine for test program for Level 2 Blas.
+*
+* -- Written on 10-August-1987.
+* Richard Hanson, Sandia National Labs.
+* Jeremy Du Croz, NAG Central Office.
+*
+* .. Scalar Arguments ..
+ INTEGER INFO
+ CHARACTER*6 SRNAME
+* .. Scalars in Common ..
+ INTEGER INFOT, NOUT
+ LOGICAL LERR, OK
+ CHARACTER*6 SRNAMT
+* .. Common blocks ..
+ COMMON /INFOC/INFOT, NOUT, OK, LERR
+ COMMON /SRNAMC/SRNAMT
+* .. Executable Statements ..
+ LERR = .TRUE.
+ IF( INFO.NE.INFOT )THEN
+ IF( INFOT.NE.0 )THEN
+ WRITE( NOUT, FMT = 9999 )INFO, INFOT
+ ELSE
+ WRITE( NOUT, FMT = 9997 )INFO
+ END IF
+ OK = .FALSE.
+ END IF
+ IF( SRNAME.NE.SRNAMT )THEN
+ WRITE( NOUT, FMT = 9998 )SRNAME, SRNAMT
+ OK = .FALSE.
+ END IF
+ RETURN
+*
+ 9999 FORMAT( ' ******* XERBLA WAS CALLED WITH INFO = ', I6, ' INSTEAD',
+ $ ' OF ', I2, ' *******' )
+ 9998 FORMAT( ' ******* XERBLA WAS CALLED WITH SRNAME = ', A6, ' INSTE',
+ $ 'AD OF ', A6, ' *******' )
+ 9997 FORMAT( ' ******* XERBLA WAS CALLED WITH INFO = ', I6,
+ $ ' *******' )
+*
+* End of XERBLA
+*
+ END
+
diff --git a/blas/testing/sblat3.dat b/blas/testing/sblat3.dat
new file mode 100644
index 0000000..680e736
--- /dev/null
+++ b/blas/testing/sblat3.dat
@@ -0,0 +1,20 @@
+'sblat3.summ' NAME OF SUMMARY OUTPUT FILE
+6 UNIT NUMBER OF SUMMARY FILE
+'sblat3.snap' NAME OF SNAPSHOT OUTPUT FILE
+-1 UNIT NUMBER OF SNAPSHOT FILE (NOT USED IF .LT. 0)
+F LOGICAL FLAG, T TO REWIND SNAPSHOT FILE AFTER EACH RECORD.
+F LOGICAL FLAG, T TO STOP ON FAILURES.
+T LOGICAL FLAG, T TO TEST ERROR EXITS.
+16.0 THRESHOLD VALUE OF TEST RATIO
+6 NUMBER OF VALUES OF N
+0 1 2 3 5 9 VALUES OF N
+3 NUMBER OF VALUES OF ALPHA
+0.0 1.0 0.7 VALUES OF ALPHA
+3 NUMBER OF VALUES OF BETA
+0.0 1.0 1.3 VALUES OF BETA
+SGEMM T PUT F FOR NO TEST. SAME COLUMNS.
+SSYMM T PUT F FOR NO TEST. SAME COLUMNS.
+STRMM T PUT F FOR NO TEST. SAME COLUMNS.
+STRSM T PUT F FOR NO TEST. SAME COLUMNS.
+SSYRK T PUT F FOR NO TEST. SAME COLUMNS.
+SSYR2K T PUT F FOR NO TEST. SAME COLUMNS.
diff --git a/blas/testing/sblat3.f b/blas/testing/sblat3.f
new file mode 100644
index 0000000..8792696
--- /dev/null
+++ b/blas/testing/sblat3.f
@@ -0,0 +1,2873 @@
+*> \brief \b SBLAT3
+*
+* =========== DOCUMENTATION ===========
+*
+* Online html documentation available at
+* http://www.netlib.org/lapack/explore-html/
+*
+* Definition:
+* ===========
+*
+* PROGRAM SBLAT3
+*
+*
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
+*>
+*> Test program for the REAL Level 3 Blas.
+*>
+*> The program must be driven by a short data file. The first 14 records
+*> of the file are read using list-directed input, the last 6 records
+*> are read using the format ( A6, L2 ). An annotated example of a data
+*> file can be obtained by deleting the first 3 characters from the
+*> following 20 lines:
+*> 'sblat3.out' NAME OF SUMMARY OUTPUT FILE
+*> 6 UNIT NUMBER OF SUMMARY FILE
+*> 'SBLAT3.SNAP' NAME OF SNAPSHOT OUTPUT FILE
+*> -1 UNIT NUMBER OF SNAPSHOT FILE (NOT USED IF .LT. 0)
+*> F LOGICAL FLAG, T TO REWIND SNAPSHOT FILE AFTER EACH RECORD.
+*> F LOGICAL FLAG, T TO STOP ON FAILURES.
+*> T LOGICAL FLAG, T TO TEST ERROR EXITS.
+*> 16.0 THRESHOLD VALUE OF TEST RATIO
+*> 6 NUMBER OF VALUES OF N
+*> 0 1 2 3 5 9 VALUES OF N
+*> 3 NUMBER OF VALUES OF ALPHA
+*> 0.0 1.0 0.7 VALUES OF ALPHA
+*> 3 NUMBER OF VALUES OF BETA
+*> 0.0 1.0 1.3 VALUES OF BETA
+*> SGEMM T PUT F FOR NO TEST. SAME COLUMNS.
+*> SSYMM T PUT F FOR NO TEST. SAME COLUMNS.
+*> STRMM T PUT F FOR NO TEST. SAME COLUMNS.
+*> STRSM T PUT F FOR NO TEST. SAME COLUMNS.
+*> SSYRK T PUT F FOR NO TEST. SAME COLUMNS.
+*> SSYR2K T PUT F FOR NO TEST. SAME COLUMNS.
+*>
+*> Further Details
+*> ===============
+*>
+*> See:
+*>
+*> Dongarra J. J., Du Croz J. J., Duff I. S. and Hammarling S.
+*> A Set of Level 3 Basic Linear Algebra Subprograms.
+*>
+*> Technical Memorandum No.88 (Revision 1), Mathematics and
+*> Computer Science Division, Argonne National Laboratory, 9700
+*> South Cass Avenue, Argonne, Illinois 60439, US.
+*>
+*> -- Written on 8-February-1989.
+*> Jack Dongarra, Argonne National Laboratory.
+*> Iain Duff, AERE Harwell.
+*> Jeremy Du Croz, Numerical Algorithms Group Ltd.
+*> Sven Hammarling, Numerical Algorithms Group Ltd.
+*>
+*> 10-9-00: Change STATUS='NEW' to 'UNKNOWN' so that the testers
+*> can be run multiple times without deleting generated
+*> output files (susan)
+*> \endverbatim
+*
+* Authors:
+* ========
+*
+*> \author Univ. of Tennessee
+*> \author Univ. of California Berkeley
+*> \author Univ. of Colorado Denver
+*> \author NAG Ltd.
+*
+*> \date April 2012
+*
+*> \ingroup single_blas_testing
+*
+* =====================================================================
+ PROGRAM SBLAT3
+*
+* -- Reference BLAS test routine (version 3.4.1) --
+* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
+* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+* April 2012
+*
+* =====================================================================
+*
+* .. Parameters ..
+ INTEGER NIN
+ PARAMETER ( NIN = 5 )
+ INTEGER NSUBS
+ PARAMETER ( NSUBS = 6 )
+ REAL ZERO, ONE
+ PARAMETER ( ZERO = 0.0, ONE = 1.0 )
+ INTEGER NMAX
+ PARAMETER ( NMAX = 65 )
+ INTEGER NIDMAX, NALMAX, NBEMAX
+ PARAMETER ( NIDMAX = 9, NALMAX = 7, NBEMAX = 7 )
+* .. Local Scalars ..
+ REAL EPS, ERR, THRESH
+ INTEGER I, ISNUM, J, N, NALF, NBET, NIDIM, NOUT, NTRA
+ LOGICAL FATAL, LTESTT, REWI, SAME, SFATAL, TRACE,
+ $ TSTERR
+ CHARACTER*1 TRANSA, TRANSB
+ CHARACTER*6 SNAMET
+ CHARACTER*32 SNAPS, SUMMRY
+* .. Local Arrays ..
+ REAL AA( NMAX*NMAX ), AB( NMAX, 2*NMAX ),
+ $ ALF( NALMAX ), AS( NMAX*NMAX ),
+ $ BB( NMAX*NMAX ), BET( NBEMAX ),
+ $ BS( NMAX*NMAX ), C( NMAX, NMAX ),
+ $ CC( NMAX*NMAX ), CS( NMAX*NMAX ), CT( NMAX ),
+ $ G( NMAX ), W( 2*NMAX )
+ INTEGER IDIM( NIDMAX )
+ LOGICAL LTEST( NSUBS )
+ CHARACTER*6 SNAMES( NSUBS )
+* .. External Functions ..
+ REAL SDIFF
+ LOGICAL LSE
+ EXTERNAL SDIFF, LSE
+* .. External Subroutines ..
+ EXTERNAL SCHK1, SCHK2, SCHK3, SCHK4, SCHK5, SCHKE, SMMCH
+* .. Intrinsic Functions ..
+ INTRINSIC MAX, MIN
+* .. Scalars in Common ..
+ INTEGER INFOT, NOUTC
+ LOGICAL LERR, OK
+ CHARACTER*6 SRNAMT
+* .. Common blocks ..
+ COMMON /INFOC/INFOT, NOUTC, OK, LERR
+ COMMON /SRNAMC/SRNAMT
+* .. Data statements ..
+ DATA SNAMES/'SGEMM ', 'SSYMM ', 'STRMM ', 'STRSM ',
+ $ 'SSYRK ', 'SSYR2K'/
+* .. Executable Statements ..
+*
+* Read name and unit number for summary output file and open file.
+*
+ READ( NIN, FMT = * )SUMMRY
+ READ( NIN, FMT = * )NOUT
+ OPEN( NOUT, FILE = SUMMRY )
+ NOUTC = NOUT
+*
+* Read name and unit number for snapshot output file and open file.
+*
+ READ( NIN, FMT = * )SNAPS
+ READ( NIN, FMT = * )NTRA
+ TRACE = NTRA.GE.0
+ IF( TRACE )THEN
+ OPEN( NTRA, FILE = SNAPS )
+ END IF
+* Read the flag that directs rewinding of the snapshot file.
+ READ( NIN, FMT = * )REWI
+ REWI = REWI.AND.TRACE
+* Read the flag that directs stopping on any failure.
+ READ( NIN, FMT = * )SFATAL
+* Read the flag that indicates whether error exits are to be tested.
+ READ( NIN, FMT = * )TSTERR
+* Read the threshold value of the test ratio
+ READ( NIN, FMT = * )THRESH
+*
+* Read and check the parameter values for the tests.
+*
+* Values of N
+ READ( NIN, FMT = * )NIDIM
+ IF( NIDIM.LT.1.OR.NIDIM.GT.NIDMAX )THEN
+ WRITE( NOUT, FMT = 9997 )'N', NIDMAX
+ GO TO 220
+ END IF
+ READ( NIN, FMT = * )( IDIM( I ), I = 1, NIDIM )
+ DO 10 I = 1, NIDIM
+ IF( IDIM( I ).LT.0.OR.IDIM( I ).GT.NMAX )THEN
+ WRITE( NOUT, FMT = 9996 )NMAX
+ GO TO 220
+ END IF
+ 10 CONTINUE
+* Values of ALPHA
+ READ( NIN, FMT = * )NALF
+ IF( NALF.LT.1.OR.NALF.GT.NALMAX )THEN
+ WRITE( NOUT, FMT = 9997 )'ALPHA', NALMAX
+ GO TO 220
+ END IF
+ READ( NIN, FMT = * )( ALF( I ), I = 1, NALF )
+* Values of BETA
+ READ( NIN, FMT = * )NBET
+ IF( NBET.LT.1.OR.NBET.GT.NBEMAX )THEN
+ WRITE( NOUT, FMT = 9997 )'BETA', NBEMAX
+ GO TO 220
+ END IF
+ READ( NIN, FMT = * )( BET( I ), I = 1, NBET )
+*
+* Report values of parameters.
+*
+ WRITE( NOUT, FMT = 9995 )
+ WRITE( NOUT, FMT = 9994 )( IDIM( I ), I = 1, NIDIM )
+ WRITE( NOUT, FMT = 9993 )( ALF( I ), I = 1, NALF )
+ WRITE( NOUT, FMT = 9992 )( BET( I ), I = 1, NBET )
+ IF( .NOT.TSTERR )THEN
+ WRITE( NOUT, FMT = * )
+ WRITE( NOUT, FMT = 9984 )
+ END IF
+ WRITE( NOUT, FMT = * )
+ WRITE( NOUT, FMT = 9999 )THRESH
+ WRITE( NOUT, FMT = * )
+*
+* Read names of subroutines and flags which indicate
+* whether they are to be tested.
+*
+ DO 20 I = 1, NSUBS
+ LTEST( I ) = .FALSE.
+ 20 CONTINUE
+ 30 READ( NIN, FMT = 9988, END = 60 )SNAMET, LTESTT
+ DO 40 I = 1, NSUBS
+ IF( SNAMET.EQ.SNAMES( I ) )
+ $ GO TO 50
+ 40 CONTINUE
+ WRITE( NOUT, FMT = 9990 )SNAMET
+ STOP
+ 50 LTEST( I ) = LTESTT
+ GO TO 30
+*
+ 60 CONTINUE
+ CLOSE ( NIN )
+*
+* Compute EPS (the machine precision).
+*
+ EPS = EPSILON(ZERO)
+ WRITE( NOUT, FMT = 9998 )EPS
+*
+* Check the reliability of SMMCH using exact data.
+*
+ N = MIN( 32, NMAX )
+ DO 100 J = 1, N
+ DO 90 I = 1, N
+ AB( I, J ) = MAX( I - J + 1, 0 )
+ 90 CONTINUE
+ AB( J, NMAX + 1 ) = J
+ AB( 1, NMAX + J ) = J
+ C( J, 1 ) = ZERO
+ 100 CONTINUE
+ DO 110 J = 1, N
+ CC( J ) = J*( ( J + 1 )*J )/2 - ( ( J + 1 )*J*( J - 1 ) )/3
+ 110 CONTINUE
+* CC holds the exact result. On exit from SMMCH CT holds
+* the result computed by SMMCH.
+ TRANSA = 'N'
+ TRANSB = 'N'
+ CALL SMMCH( TRANSA, TRANSB, N, 1, N, ONE, AB, NMAX,
+ $ AB( 1, NMAX + 1 ), NMAX, ZERO, C, NMAX, CT, G, CC,
+ $ NMAX, EPS, ERR, FATAL, NOUT, .TRUE. )
+ SAME = LSE( CC, CT, N )
+ IF( .NOT.SAME.OR.ERR.NE.ZERO )THEN
+ WRITE( NOUT, FMT = 9989 )TRANSA, TRANSB, SAME, ERR
+ STOP
+ END IF
+ TRANSB = 'T'
+ CALL SMMCH( TRANSA, TRANSB, N, 1, N, ONE, AB, NMAX,
+ $ AB( 1, NMAX + 1 ), NMAX, ZERO, C, NMAX, CT, G, CC,
+ $ NMAX, EPS, ERR, FATAL, NOUT, .TRUE. )
+ SAME = LSE( CC, CT, N )
+ IF( .NOT.SAME.OR.ERR.NE.ZERO )THEN
+ WRITE( NOUT, FMT = 9989 )TRANSA, TRANSB, SAME, ERR
+ STOP
+ END IF
+ DO 120 J = 1, N
+ AB( J, NMAX + 1 ) = N - J + 1
+ AB( 1, NMAX + J ) = N - J + 1
+ 120 CONTINUE
+ DO 130 J = 1, N
+ CC( N - J + 1 ) = J*( ( J + 1 )*J )/2 -
+ $ ( ( J + 1 )*J*( J - 1 ) )/3
+ 130 CONTINUE
+ TRANSA = 'T'
+ TRANSB = 'N'
+ CALL SMMCH( TRANSA, TRANSB, N, 1, N, ONE, AB, NMAX,
+ $ AB( 1, NMAX + 1 ), NMAX, ZERO, C, NMAX, CT, G, CC,
+ $ NMAX, EPS, ERR, FATAL, NOUT, .TRUE. )
+ SAME = LSE( CC, CT, N )
+ IF( .NOT.SAME.OR.ERR.NE.ZERO )THEN
+ WRITE( NOUT, FMT = 9989 )TRANSA, TRANSB, SAME, ERR
+ STOP
+ END IF
+ TRANSB = 'T'
+ CALL SMMCH( TRANSA, TRANSB, N, 1, N, ONE, AB, NMAX,
+ $ AB( 1, NMAX + 1 ), NMAX, ZERO, C, NMAX, CT, G, CC,
+ $ NMAX, EPS, ERR, FATAL, NOUT, .TRUE. )
+ SAME = LSE( CC, CT, N )
+ IF( .NOT.SAME.OR.ERR.NE.ZERO )THEN
+ WRITE( NOUT, FMT = 9989 )TRANSA, TRANSB, SAME, ERR
+ STOP
+ END IF
+*
+* Test each subroutine in turn.
+*
+ DO 200 ISNUM = 1, NSUBS
+ WRITE( NOUT, FMT = * )
+ IF( .NOT.LTEST( ISNUM ) )THEN
+* Subprogram is not to be tested.
+ WRITE( NOUT, FMT = 9987 )SNAMES( ISNUM )
+ ELSE
+ SRNAMT = SNAMES( ISNUM )
+* Test error exits.
+ IF( TSTERR )THEN
+ CALL SCHKE( ISNUM, SNAMES( ISNUM ), NOUT )
+ WRITE( NOUT, FMT = * )
+ END IF
+* Test computations.
+ INFOT = 0
+ OK = .TRUE.
+ FATAL = .FALSE.
+ GO TO ( 140, 150, 160, 160, 170, 180 )ISNUM
+* Test SGEMM, 01.
+ 140 CALL SCHK1( SNAMES( ISNUM ), EPS, THRESH, NOUT, NTRA, TRACE,
+ $ REWI, FATAL, NIDIM, IDIM, NALF, ALF, NBET, BET,
+ $ NMAX, AB, AA, AS, AB( 1, NMAX + 1 ), BB, BS, C,
+ $ CC, CS, CT, G )
+ GO TO 190
+* Test SSYMM, 02.
+ 150 CALL SCHK2( SNAMES( ISNUM ), EPS, THRESH, NOUT, NTRA, TRACE,
+ $ REWI, FATAL, NIDIM, IDIM, NALF, ALF, NBET, BET,
+ $ NMAX, AB, AA, AS, AB( 1, NMAX + 1 ), BB, BS, C,
+ $ CC, CS, CT, G )
+ GO TO 190
+* Test STRMM, 03, STRSM, 04.
+ 160 CALL SCHK3( SNAMES( ISNUM ), EPS, THRESH, NOUT, NTRA, TRACE,
+ $ REWI, FATAL, NIDIM, IDIM, NALF, ALF, NMAX, AB,
+ $ AA, AS, AB( 1, NMAX + 1 ), BB, BS, CT, G, C )
+ GO TO 190
+* Test SSYRK, 05.
+ 170 CALL SCHK4( SNAMES( ISNUM ), EPS, THRESH, NOUT, NTRA, TRACE,
+ $ REWI, FATAL, NIDIM, IDIM, NALF, ALF, NBET, BET,
+ $ NMAX, AB, AA, AS, AB( 1, NMAX + 1 ), BB, BS, C,
+ $ CC, CS, CT, G )
+ GO TO 190
+* Test SSYR2K, 06.
+ 180 CALL SCHK5( SNAMES( ISNUM ), EPS, THRESH, NOUT, NTRA, TRACE,
+ $ REWI, FATAL, NIDIM, IDIM, NALF, ALF, NBET, BET,
+ $ NMAX, AB, AA, AS, BB, BS, C, CC, CS, CT, G, W )
+ GO TO 190
+*
+ 190 IF( FATAL.AND.SFATAL )
+ $ GO TO 210
+ END IF
+ 200 CONTINUE
+ WRITE( NOUT, FMT = 9986 )
+ GO TO 230
+*
+ 210 CONTINUE
+ WRITE( NOUT, FMT = 9985 )
+ GO TO 230
+*
+ 220 CONTINUE
+ WRITE( NOUT, FMT = 9991 )
+*
+ 230 CONTINUE
+ IF( TRACE )
+ $ CLOSE ( NTRA )
+ CLOSE ( NOUT )
+ STOP
+*
+ 9999 FORMAT( ' ROUTINES PASS COMPUTATIONAL TESTS IF TEST RATIO IS LES',
+ $ 'S THAN', F8.2 )
+ 9998 FORMAT( ' RELATIVE MACHINE PRECISION IS TAKEN TO BE', 1P, E9.1 )
+ 9997 FORMAT( ' NUMBER OF VALUES OF ', A, ' IS LESS THAN 1 OR GREATER ',
+ $ 'THAN ', I2 )
+ 9996 FORMAT( ' VALUE OF N IS LESS THAN 0 OR GREATER THAN ', I2 )
+ 9995 FORMAT( ' TESTS OF THE REAL LEVEL 3 BLAS', //' THE F',
+ $ 'OLLOWING PARAMETER VALUES WILL BE USED:' )
+ 9994 FORMAT( ' FOR N ', 9I6 )
+ 9993 FORMAT( ' FOR ALPHA ', 7F6.1 )
+ 9992 FORMAT( ' FOR BETA ', 7F6.1 )
+ 9991 FORMAT( ' AMEND DATA FILE OR INCREASE ARRAY SIZES IN PROGRAM',
+ $ /' ******* TESTS ABANDONED *******' )
+ 9990 FORMAT( ' SUBPROGRAM NAME ', A6, ' NOT RECOGNIZED', /' ******* T',
+ $ 'ESTS ABANDONED *******' )
+ 9989 FORMAT( ' ERROR IN SMMCH - IN-LINE DOT PRODUCTS ARE BEING EVALU',
+ $ 'ATED WRONGLY.', /' SMMCH WAS CALLED WITH TRANSA = ', A1,
+ $ ' AND TRANSB = ', A1, /' AND RETURNED SAME = ', L1, ' AND ',
+ $ 'ERR = ', F12.3, '.', /' THIS MAY BE DUE TO FAULTS IN THE ',
+ $ 'ARITHMETIC OR THE COMPILER.', /' ******* TESTS ABANDONED ',
+ $ '*******' )
+ 9988 FORMAT( A6, L2 )
+ 9987 FORMAT( 1X, A6, ' WAS NOT TESTED' )
+ 9986 FORMAT( /' END OF TESTS' )
+ 9985 FORMAT( /' ******* FATAL ERROR - TESTS ABANDONED *******' )
+ 9984 FORMAT( ' ERROR-EXITS WILL NOT BE TESTED' )
+*
+* End of SBLAT3.
+*
+ END
+ SUBROUTINE SCHK1( SNAME, EPS, THRESH, NOUT, NTRA, TRACE, REWI,
+ $ FATAL, NIDIM, IDIM, NALF, ALF, NBET, BET, NMAX,
+ $ A, AA, AS, B, BB, BS, C, CC, CS, CT, G )
+*
+* Tests SGEMM.
+*
+* Auxiliary routine for test program for Level 3 Blas.
+*
+* -- Written on 8-February-1989.
+* Jack Dongarra, Argonne National Laboratory.
+* Iain Duff, AERE Harwell.
+* Jeremy Du Croz, Numerical Algorithms Group Ltd.
+* Sven Hammarling, Numerical Algorithms Group Ltd.
+*
+* .. Parameters ..
+ REAL ZERO
+ PARAMETER ( ZERO = 0.0 )
+* .. Scalar Arguments ..
+ REAL EPS, THRESH
+ INTEGER NALF, NBET, NIDIM, NMAX, NOUT, NTRA
+ LOGICAL FATAL, REWI, TRACE
+ CHARACTER*6 SNAME
+* .. Array Arguments ..
+ REAL A( NMAX, NMAX ), AA( NMAX*NMAX ), ALF( NALF ),
+ $ AS( NMAX*NMAX ), B( NMAX, NMAX ),
+ $ BB( NMAX*NMAX ), BET( NBET ), BS( NMAX*NMAX ),
+ $ C( NMAX, NMAX ), CC( NMAX*NMAX ),
+ $ CS( NMAX*NMAX ), CT( NMAX ), G( NMAX )
+ INTEGER IDIM( NIDIM )
+* .. Local Scalars ..
+ REAL ALPHA, ALS, BETA, BLS, ERR, ERRMAX
+ INTEGER I, IA, IB, ICA, ICB, IK, IM, IN, K, KS, LAA,
+ $ LBB, LCC, LDA, LDAS, LDB, LDBS, LDC, LDCS, M,
+ $ MA, MB, MS, N, NA, NARGS, NB, NC, NS
+ LOGICAL NULL, RESET, SAME, TRANA, TRANB
+ CHARACTER*1 TRANAS, TRANBS, TRANSA, TRANSB
+ CHARACTER*3 ICH
+* .. Local Arrays ..
+ LOGICAL ISAME( 13 )
+* .. External Functions ..
+ LOGICAL LSE, LSERES
+ EXTERNAL LSE, LSERES
+* .. External Subroutines ..
+ EXTERNAL SGEMM, SMAKE, SMMCH
+* .. Intrinsic Functions ..
+ INTRINSIC MAX
+* .. Scalars in Common ..
+ INTEGER INFOT, NOUTC
+ LOGICAL LERR, OK
+* .. Common blocks ..
+ COMMON /INFOC/INFOT, NOUTC, OK, LERR
+* .. Data statements ..
+ DATA ICH/'NTC'/
+* .. Executable Statements ..
+*
+ NARGS = 13
+ NC = 0
+ RESET = .TRUE.
+ ERRMAX = ZERO
+*
+ DO 110 IM = 1, NIDIM
+ M = IDIM( IM )
+*
+ DO 100 IN = 1, NIDIM
+ N = IDIM( IN )
+* Set LDC to 1 more than minimum value if room.
+ LDC = M
+ IF( LDC.LT.NMAX )
+ $ LDC = LDC + 1
+* Skip tests if not enough room.
+ IF( LDC.GT.NMAX )
+ $ GO TO 100
+ LCC = LDC*N
+ NULL = N.LE.0.OR.M.LE.0
+*
+ DO 90 IK = 1, NIDIM
+ K = IDIM( IK )
+*
+ DO 80 ICA = 1, 3
+ TRANSA = ICH( ICA: ICA )
+ TRANA = TRANSA.EQ.'T'.OR.TRANSA.EQ.'C'
+*
+ IF( TRANA )THEN
+ MA = K
+ NA = M
+ ELSE
+ MA = M
+ NA = K
+ END IF
+* Set LDA to 1 more than minimum value if room.
+ LDA = MA
+ IF( LDA.LT.NMAX )
+ $ LDA = LDA + 1
+* Skip tests if not enough room.
+ IF( LDA.GT.NMAX )
+ $ GO TO 80
+ LAA = LDA*NA
+*
+* Generate the matrix A.
+*
+ CALL SMAKE( 'GE', ' ', ' ', MA, NA, A, NMAX, AA, LDA,
+ $ RESET, ZERO )
+*
+ DO 70 ICB = 1, 3
+ TRANSB = ICH( ICB: ICB )
+ TRANB = TRANSB.EQ.'T'.OR.TRANSB.EQ.'C'
+*
+ IF( TRANB )THEN
+ MB = N
+ NB = K
+ ELSE
+ MB = K
+ NB = N
+ END IF
+* Set LDB to 1 more than minimum value if room.
+ LDB = MB
+ IF( LDB.LT.NMAX )
+ $ LDB = LDB + 1
+* Skip tests if not enough room.
+ IF( LDB.GT.NMAX )
+ $ GO TO 70
+ LBB = LDB*NB
+*
+* Generate the matrix B.
+*
+ CALL SMAKE( 'GE', ' ', ' ', MB, NB, B, NMAX, BB,
+ $ LDB, RESET, ZERO )
+*
+ DO 60 IA = 1, NALF
+ ALPHA = ALF( IA )
+*
+ DO 50 IB = 1, NBET
+ BETA = BET( IB )
+*
+* Generate the matrix C.
+*
+ CALL SMAKE( 'GE', ' ', ' ', M, N, C, NMAX,
+ $ CC, LDC, RESET, ZERO )
+*
+ NC = NC + 1
+*
+* Save every datum before calling the
+* subroutine.
+*
+ TRANAS = TRANSA
+ TRANBS = TRANSB
+ MS = M
+ NS = N
+ KS = K
+ ALS = ALPHA
+ DO 10 I = 1, LAA
+ AS( I ) = AA( I )
+ 10 CONTINUE
+ LDAS = LDA
+ DO 20 I = 1, LBB
+ BS( I ) = BB( I )
+ 20 CONTINUE
+ LDBS = LDB
+ BLS = BETA
+ DO 30 I = 1, LCC
+ CS( I ) = CC( I )
+ 30 CONTINUE
+ LDCS = LDC
+*
+* Call the subroutine.
+*
+ IF( TRACE )
+ $ WRITE( NTRA, FMT = 9995 )NC, SNAME,
+ $ TRANSA, TRANSB, M, N, K, ALPHA, LDA, LDB,
+ $ BETA, LDC
+ IF( REWI )
+ $ REWIND NTRA
+ CALL SGEMM( TRANSA, TRANSB, M, N, K, ALPHA,
+ $ AA, LDA, BB, LDB, BETA, CC, LDC )
+*
+* Check if error-exit was taken incorrectly.
+*
+ IF( .NOT.OK )THEN
+ WRITE( NOUT, FMT = 9994 )
+ FATAL = .TRUE.
+ GO TO 120
+ END IF
+*
+* See what data changed inside subroutines.
+*
+ ISAME( 1 ) = TRANSA.EQ.TRANAS
+ ISAME( 2 ) = TRANSB.EQ.TRANBS
+ ISAME( 3 ) = MS.EQ.M
+ ISAME( 4 ) = NS.EQ.N
+ ISAME( 5 ) = KS.EQ.K
+ ISAME( 6 ) = ALS.EQ.ALPHA
+ ISAME( 7 ) = LSE( AS, AA, LAA )
+ ISAME( 8 ) = LDAS.EQ.LDA
+ ISAME( 9 ) = LSE( BS, BB, LBB )
+ ISAME( 10 ) = LDBS.EQ.LDB
+ ISAME( 11 ) = BLS.EQ.BETA
+ IF( NULL )THEN
+ ISAME( 12 ) = LSE( CS, CC, LCC )
+ ELSE
+ ISAME( 12 ) = LSERES( 'GE', ' ', M, N, CS,
+ $ CC, LDC )
+ END IF
+ ISAME( 13 ) = LDCS.EQ.LDC
+*
+* If data was incorrectly changed, report
+* and return.
+*
+ SAME = .TRUE.
+ DO 40 I = 1, NARGS
+ SAME = SAME.AND.ISAME( I )
+ IF( .NOT.ISAME( I ) )
+ $ WRITE( NOUT, FMT = 9998 )I
+ 40 CONTINUE
+ IF( .NOT.SAME )THEN
+ FATAL = .TRUE.
+ GO TO 120
+ END IF
+*
+ IF( .NOT.NULL )THEN
+*
+* Check the result.
+*
+ CALL SMMCH( TRANSA, TRANSB, M, N, K,
+ $ ALPHA, A, NMAX, B, NMAX, BETA,
+ $ C, NMAX, CT, G, CC, LDC, EPS,
+ $ ERR, FATAL, NOUT, .TRUE. )
+ ERRMAX = MAX( ERRMAX, ERR )
+* If got really bad answer, report and
+* return.
+ IF( FATAL )
+ $ GO TO 120
+ END IF
+*
+ 50 CONTINUE
+*
+ 60 CONTINUE
+*
+ 70 CONTINUE
+*
+ 80 CONTINUE
+*
+ 90 CONTINUE
+*
+ 100 CONTINUE
+*
+ 110 CONTINUE
+*
+* Report result.
+*
+ IF( ERRMAX.LT.THRESH )THEN
+ WRITE( NOUT, FMT = 9999 )SNAME, NC
+ ELSE
+ WRITE( NOUT, FMT = 9997 )SNAME, NC, ERRMAX
+ END IF
+ GO TO 130
+*
+ 120 CONTINUE
+ WRITE( NOUT, FMT = 9996 )SNAME
+ WRITE( NOUT, FMT = 9995 )NC, SNAME, TRANSA, TRANSB, M, N, K,
+ $ ALPHA, LDA, LDB, BETA, LDC
+*
+ 130 CONTINUE
+ RETURN
+*
+ 9999 FORMAT( ' ', A6, ' PASSED THE COMPUTATIONAL TESTS (', I6, ' CALL',
+ $ 'S)' )
+ 9998 FORMAT( ' ******* FATAL ERROR - PARAMETER NUMBER ', I2, ' WAS CH',
+ $ 'ANGED INCORRECTLY *******' )
+ 9997 FORMAT( ' ', A6, ' COMPLETED THE COMPUTATIONAL TESTS (', I6, ' C',
+ $ 'ALLS)', /' ******* BUT WITH MAXIMUM TEST RATIO', F8.2,
+ $ ' - SUSPECT *******' )
+ 9996 FORMAT( ' ******* ', A6, ' FAILED ON CALL NUMBER:' )
+ 9995 FORMAT( 1X, I6, ': ', A6, '(''', A1, ''',''', A1, ''',',
+ $ 3( I3, ',' ), F4.1, ', A,', I3, ', B,', I3, ',', F4.1, ', ',
+ $ 'C,', I3, ').' )
+ 9994 FORMAT( ' ******* FATAL ERROR - ERROR-EXIT TAKEN ON VALID CALL *',
+ $ '******' )
+*
+* End of SCHK1.
+*
+ END
+ SUBROUTINE SCHK2( SNAME, EPS, THRESH, NOUT, NTRA, TRACE, REWI,
+ $ FATAL, NIDIM, IDIM, NALF, ALF, NBET, BET, NMAX,
+ $ A, AA, AS, B, BB, BS, C, CC, CS, CT, G )
+*
+* Tests SSYMM.
+*
+* Auxiliary routine for test program for Level 3 Blas.
+*
+* -- Written on 8-February-1989.
+* Jack Dongarra, Argonne National Laboratory.
+* Iain Duff, AERE Harwell.
+* Jeremy Du Croz, Numerical Algorithms Group Ltd.
+* Sven Hammarling, Numerical Algorithms Group Ltd.
+*
+* .. Parameters ..
+ REAL ZERO
+ PARAMETER ( ZERO = 0.0 )
+* .. Scalar Arguments ..
+ REAL EPS, THRESH
+ INTEGER NALF, NBET, NIDIM, NMAX, NOUT, NTRA
+ LOGICAL FATAL, REWI, TRACE
+ CHARACTER*6 SNAME
+* .. Array Arguments ..
+ REAL A( NMAX, NMAX ), AA( NMAX*NMAX ), ALF( NALF ),
+ $ AS( NMAX*NMAX ), B( NMAX, NMAX ),
+ $ BB( NMAX*NMAX ), BET( NBET ), BS( NMAX*NMAX ),
+ $ C( NMAX, NMAX ), CC( NMAX*NMAX ),
+ $ CS( NMAX*NMAX ), CT( NMAX ), G( NMAX )
+ INTEGER IDIM( NIDIM )
+* .. Local Scalars ..
+ REAL ALPHA, ALS, BETA, BLS, ERR, ERRMAX
+ INTEGER I, IA, IB, ICS, ICU, IM, IN, LAA, LBB, LCC,
+ $ LDA, LDAS, LDB, LDBS, LDC, LDCS, M, MS, N, NA,
+ $ NARGS, NC, NS
+ LOGICAL LEFT, NULL, RESET, SAME
+ CHARACTER*1 SIDE, SIDES, UPLO, UPLOS
+ CHARACTER*2 ICHS, ICHU
+* .. Local Arrays ..
+ LOGICAL ISAME( 13 )
+* .. External Functions ..
+ LOGICAL LSE, LSERES
+ EXTERNAL LSE, LSERES
+* .. External Subroutines ..
+ EXTERNAL SMAKE, SMMCH, SSYMM
+* .. Intrinsic Functions ..
+ INTRINSIC MAX
+* .. Scalars in Common ..
+ INTEGER INFOT, NOUTC
+ LOGICAL LERR, OK
+* .. Common blocks ..
+ COMMON /INFOC/INFOT, NOUTC, OK, LERR
+* .. Data statements ..
+ DATA ICHS/'LR'/, ICHU/'UL'/
+* .. Executable Statements ..
+*
+ NARGS = 12
+ NC = 0
+ RESET = .TRUE.
+ ERRMAX = ZERO
+*
+ DO 100 IM = 1, NIDIM
+ M = IDIM( IM )
+*
+ DO 90 IN = 1, NIDIM
+ N = IDIM( IN )
+* Set LDC to 1 more than minimum value if room.
+ LDC = M
+ IF( LDC.LT.NMAX )
+ $ LDC = LDC + 1
+* Skip tests if not enough room.
+ IF( LDC.GT.NMAX )
+ $ GO TO 90
+ LCC = LDC*N
+ NULL = N.LE.0.OR.M.LE.0
+*
+* Set LDB to 1 more than minimum value if room.
+ LDB = M
+ IF( LDB.LT.NMAX )
+ $ LDB = LDB + 1
+* Skip tests if not enough room.
+ IF( LDB.GT.NMAX )
+ $ GO TO 90
+ LBB = LDB*N
+*
+* Generate the matrix B.
+*
+ CALL SMAKE( 'GE', ' ', ' ', M, N, B, NMAX, BB, LDB, RESET,
+ $ ZERO )
+*
+ DO 80 ICS = 1, 2
+ SIDE = ICHS( ICS: ICS )
+ LEFT = SIDE.EQ.'L'
+*
+ IF( LEFT )THEN
+ NA = M
+ ELSE
+ NA = N
+ END IF
+* Set LDA to 1 more than minimum value if room.
+ LDA = NA
+ IF( LDA.LT.NMAX )
+ $ LDA = LDA + 1
+* Skip tests if not enough room.
+ IF( LDA.GT.NMAX )
+ $ GO TO 80
+ LAA = LDA*NA
+*
+ DO 70 ICU = 1, 2
+ UPLO = ICHU( ICU: ICU )
+*
+* Generate the symmetric matrix A.
+*
+ CALL SMAKE( 'SY', UPLO, ' ', NA, NA, A, NMAX, AA, LDA,
+ $ RESET, ZERO )
+*
+ DO 60 IA = 1, NALF
+ ALPHA = ALF( IA )
+*
+ DO 50 IB = 1, NBET
+ BETA = BET( IB )
+*
+* Generate the matrix C.
+*
+ CALL SMAKE( 'GE', ' ', ' ', M, N, C, NMAX, CC,
+ $ LDC, RESET, ZERO )
+*
+ NC = NC + 1
+*
+* Save every datum before calling the
+* subroutine.
+*
+ SIDES = SIDE
+ UPLOS = UPLO
+ MS = M
+ NS = N
+ ALS = ALPHA
+ DO 10 I = 1, LAA
+ AS( I ) = AA( I )
+ 10 CONTINUE
+ LDAS = LDA
+ DO 20 I = 1, LBB
+ BS( I ) = BB( I )
+ 20 CONTINUE
+ LDBS = LDB
+ BLS = BETA
+ DO 30 I = 1, LCC
+ CS( I ) = CC( I )
+ 30 CONTINUE
+ LDCS = LDC
+*
+* Call the subroutine.
+*
+ IF( TRACE )
+ $ WRITE( NTRA, FMT = 9995 )NC, SNAME, SIDE,
+ $ UPLO, M, N, ALPHA, LDA, LDB, BETA, LDC
+ IF( REWI )
+ $ REWIND NTRA
+ CALL SSYMM( SIDE, UPLO, M, N, ALPHA, AA, LDA,
+ $ BB, LDB, BETA, CC, LDC )
+*
+* Check if error-exit was taken incorrectly.
+*
+ IF( .NOT.OK )THEN
+ WRITE( NOUT, FMT = 9994 )
+ FATAL = .TRUE.
+ GO TO 110
+ END IF
+*
+* See what data changed inside subroutines.
+*
+ ISAME( 1 ) = SIDES.EQ.SIDE
+ ISAME( 2 ) = UPLOS.EQ.UPLO
+ ISAME( 3 ) = MS.EQ.M
+ ISAME( 4 ) = NS.EQ.N
+ ISAME( 5 ) = ALS.EQ.ALPHA
+ ISAME( 6 ) = LSE( AS, AA, LAA )
+ ISAME( 7 ) = LDAS.EQ.LDA
+ ISAME( 8 ) = LSE( BS, BB, LBB )
+ ISAME( 9 ) = LDBS.EQ.LDB
+ ISAME( 10 ) = BLS.EQ.BETA
+ IF( NULL )THEN
+ ISAME( 11 ) = LSE( CS, CC, LCC )
+ ELSE
+ ISAME( 11 ) = LSERES( 'GE', ' ', M, N, CS,
+ $ CC, LDC )
+ END IF
+ ISAME( 12 ) = LDCS.EQ.LDC
+*
+* If data was incorrectly changed, report and
+* return.
+*
+ SAME = .TRUE.
+ DO 40 I = 1, NARGS
+ SAME = SAME.AND.ISAME( I )
+ IF( .NOT.ISAME( I ) )
+ $ WRITE( NOUT, FMT = 9998 )I
+ 40 CONTINUE
+ IF( .NOT.SAME )THEN
+ FATAL = .TRUE.
+ GO TO 110
+ END IF
+*
+ IF( .NOT.NULL )THEN
+*
+* Check the result.
+*
+ IF( LEFT )THEN
+ CALL SMMCH( 'N', 'N', M, N, M, ALPHA, A,
+ $ NMAX, B, NMAX, BETA, C, NMAX,
+ $ CT, G, CC, LDC, EPS, ERR,
+ $ FATAL, NOUT, .TRUE. )
+ ELSE
+ CALL SMMCH( 'N', 'N', M, N, N, ALPHA, B,
+ $ NMAX, A, NMAX, BETA, C, NMAX,
+ $ CT, G, CC, LDC, EPS, ERR,
+ $ FATAL, NOUT, .TRUE. )
+ END IF
+ ERRMAX = MAX( ERRMAX, ERR )
+* If got really bad answer, report and
+* return.
+ IF( FATAL )
+ $ GO TO 110
+ END IF
+*
+ 50 CONTINUE
+*
+ 60 CONTINUE
+*
+ 70 CONTINUE
+*
+ 80 CONTINUE
+*
+ 90 CONTINUE
+*
+ 100 CONTINUE
+*
+* Report result.
+*
+ IF( ERRMAX.LT.THRESH )THEN
+ WRITE( NOUT, FMT = 9999 )SNAME, NC
+ ELSE
+ WRITE( NOUT, FMT = 9997 )SNAME, NC, ERRMAX
+ END IF
+ GO TO 120
+*
+ 110 CONTINUE
+ WRITE( NOUT, FMT = 9996 )SNAME
+ WRITE( NOUT, FMT = 9995 )NC, SNAME, SIDE, UPLO, M, N, ALPHA, LDA,
+ $ LDB, BETA, LDC
+*
+ 120 CONTINUE
+ RETURN
+*
+ 9999 FORMAT( ' ', A6, ' PASSED THE COMPUTATIONAL TESTS (', I6, ' CALL',
+ $ 'S)' )
+ 9998 FORMAT( ' ******* FATAL ERROR - PARAMETER NUMBER ', I2, ' WAS CH',
+ $ 'ANGED INCORRECTLY *******' )
+ 9997 FORMAT( ' ', A6, ' COMPLETED THE COMPUTATIONAL TESTS (', I6, ' C',
+ $ 'ALLS)', /' ******* BUT WITH MAXIMUM TEST RATIO', F8.2,
+ $ ' - SUSPECT *******' )
+ 9996 FORMAT( ' ******* ', A6, ' FAILED ON CALL NUMBER:' )
+ 9995 FORMAT( 1X, I6, ': ', A6, '(', 2( '''', A1, ''',' ), 2( I3, ',' ),
+ $ F4.1, ', A,', I3, ', B,', I3, ',', F4.1, ', C,', I3, ') ',
+ $ ' .' )
+ 9994 FORMAT( ' ******* FATAL ERROR - ERROR-EXIT TAKEN ON VALID CALL *',
+ $ '******' )
+*
+* End of SCHK2.
+*
+ END
+ SUBROUTINE SCHK3( SNAME, EPS, THRESH, NOUT, NTRA, TRACE, REWI,
+ $ FATAL, NIDIM, IDIM, NALF, ALF, NMAX, A, AA, AS,
+ $ B, BB, BS, CT, G, C )
+*
+* Tests STRMM and STRSM.
+*
+* Auxiliary routine for test program for Level 3 Blas.
+*
+* -- Written on 8-February-1989.
+* Jack Dongarra, Argonne National Laboratory.
+* Iain Duff, AERE Harwell.
+* Jeremy Du Croz, Numerical Algorithms Group Ltd.
+* Sven Hammarling, Numerical Algorithms Group Ltd.
+*
+* .. Parameters ..
+ REAL ZERO, ONE
+ PARAMETER ( ZERO = 0.0, ONE = 1.0 )
+* .. Scalar Arguments ..
+ REAL EPS, THRESH
+ INTEGER NALF, NIDIM, NMAX, NOUT, NTRA
+ LOGICAL FATAL, REWI, TRACE
+ CHARACTER*6 SNAME
+* .. Array Arguments ..
+ REAL A( NMAX, NMAX ), AA( NMAX*NMAX ), ALF( NALF ),
+ $ AS( NMAX*NMAX ), B( NMAX, NMAX ),
+ $ BB( NMAX*NMAX ), BS( NMAX*NMAX ),
+ $ C( NMAX, NMAX ), CT( NMAX ), G( NMAX )
+ INTEGER IDIM( NIDIM )
+* .. Local Scalars ..
+ REAL ALPHA, ALS, ERR, ERRMAX
+ INTEGER I, IA, ICD, ICS, ICT, ICU, IM, IN, J, LAA, LBB,
+ $ LDA, LDAS, LDB, LDBS, M, MS, N, NA, NARGS, NC,
+ $ NS
+ LOGICAL LEFT, NULL, RESET, SAME
+ CHARACTER*1 DIAG, DIAGS, SIDE, SIDES, TRANAS, TRANSA, UPLO,
+ $ UPLOS
+ CHARACTER*2 ICHD, ICHS, ICHU
+ CHARACTER*3 ICHT
+* .. Local Arrays ..
+ LOGICAL ISAME( 13 )
+* .. External Functions ..
+ LOGICAL LSE, LSERES
+ EXTERNAL LSE, LSERES
+* .. External Subroutines ..
+ EXTERNAL SMAKE, SMMCH, STRMM, STRSM
+* .. Intrinsic Functions ..
+ INTRINSIC MAX
+* .. Scalars in Common ..
+ INTEGER INFOT, NOUTC
+ LOGICAL LERR, OK
+* .. Common blocks ..
+ COMMON /INFOC/INFOT, NOUTC, OK, LERR
+* .. Data statements ..
+ DATA ICHU/'UL'/, ICHT/'NTC'/, ICHD/'UN'/, ICHS/'LR'/
+* .. Executable Statements ..
+*
+ NARGS = 11
+ NC = 0
+ RESET = .TRUE.
+ ERRMAX = ZERO
+* Set up zero matrix for SMMCH.
+ DO 20 J = 1, NMAX
+ DO 10 I = 1, NMAX
+ C( I, J ) = ZERO
+ 10 CONTINUE
+ 20 CONTINUE
+*
+ DO 140 IM = 1, NIDIM
+ M = IDIM( IM )
+*
+ DO 130 IN = 1, NIDIM
+ N = IDIM( IN )
+* Set LDB to 1 more than minimum value if room.
+ LDB = M
+ IF( LDB.LT.NMAX )
+ $ LDB = LDB + 1
+* Skip tests if not enough room.
+ IF( LDB.GT.NMAX )
+ $ GO TO 130
+ LBB = LDB*N
+ NULL = M.LE.0.OR.N.LE.0
+*
+ DO 120 ICS = 1, 2
+ SIDE = ICHS( ICS: ICS )
+ LEFT = SIDE.EQ.'L'
+ IF( LEFT )THEN
+ NA = M
+ ELSE
+ NA = N
+ END IF
+* Set LDA to 1 more than minimum value if room.
+ LDA = NA
+ IF( LDA.LT.NMAX )
+ $ LDA = LDA + 1
+* Skip tests if not enough room.
+ IF( LDA.GT.NMAX )
+ $ GO TO 130
+ LAA = LDA*NA
+*
+ DO 110 ICU = 1, 2
+ UPLO = ICHU( ICU: ICU )
+*
+ DO 100 ICT = 1, 3
+ TRANSA = ICHT( ICT: ICT )
+*
+ DO 90 ICD = 1, 2
+ DIAG = ICHD( ICD: ICD )
+*
+ DO 80 IA = 1, NALF
+ ALPHA = ALF( IA )
+*
+* Generate the matrix A.
+*
+ CALL SMAKE( 'TR', UPLO, DIAG, NA, NA, A,
+ $ NMAX, AA, LDA, RESET, ZERO )
+*
+* Generate the matrix B.
+*
+ CALL SMAKE( 'GE', ' ', ' ', M, N, B, NMAX,
+ $ BB, LDB, RESET, ZERO )
+*
+ NC = NC + 1
+*
+* Save every datum before calling the
+* subroutine.
+*
+ SIDES = SIDE
+ UPLOS = UPLO
+ TRANAS = TRANSA
+ DIAGS = DIAG
+ MS = M
+ NS = N
+ ALS = ALPHA
+ DO 30 I = 1, LAA
+ AS( I ) = AA( I )
+ 30 CONTINUE
+ LDAS = LDA
+ DO 40 I = 1, LBB
+ BS( I ) = BB( I )
+ 40 CONTINUE
+ LDBS = LDB
+*
+* Call the subroutine.
+*
+ IF( SNAME( 4: 5 ).EQ.'MM' )THEN
+ IF( TRACE )
+ $ WRITE( NTRA, FMT = 9995 )NC, SNAME,
+ $ SIDE, UPLO, TRANSA, DIAG, M, N, ALPHA,
+ $ LDA, LDB
+ IF( REWI )
+ $ REWIND NTRA
+ CALL STRMM( SIDE, UPLO, TRANSA, DIAG, M,
+ $ N, ALPHA, AA, LDA, BB, LDB )
+ ELSE IF( SNAME( 4: 5 ).EQ.'SM' )THEN
+ IF( TRACE )
+ $ WRITE( NTRA, FMT = 9995 )NC, SNAME,
+ $ SIDE, UPLO, TRANSA, DIAG, M, N, ALPHA,
+ $ LDA, LDB
+ IF( REWI )
+ $ REWIND NTRA
+ CALL STRSM( SIDE, UPLO, TRANSA, DIAG, M,
+ $ N, ALPHA, AA, LDA, BB, LDB )
+ END IF
+*
+* Check if error-exit was taken incorrectly.
+*
+ IF( .NOT.OK )THEN
+ WRITE( NOUT, FMT = 9994 )
+ FATAL = .TRUE.
+ GO TO 150
+ END IF
+*
+* See what data changed inside subroutines.
+*
+ ISAME( 1 ) = SIDES.EQ.SIDE
+ ISAME( 2 ) = UPLOS.EQ.UPLO
+ ISAME( 3 ) = TRANAS.EQ.TRANSA
+ ISAME( 4 ) = DIAGS.EQ.DIAG
+ ISAME( 5 ) = MS.EQ.M
+ ISAME( 6 ) = NS.EQ.N
+ ISAME( 7 ) = ALS.EQ.ALPHA
+ ISAME( 8 ) = LSE( AS, AA, LAA )
+ ISAME( 9 ) = LDAS.EQ.LDA
+ IF( NULL )THEN
+ ISAME( 10 ) = LSE( BS, BB, LBB )
+ ELSE
+ ISAME( 10 ) = LSERES( 'GE', ' ', M, N, BS,
+ $ BB, LDB )
+ END IF
+ ISAME( 11 ) = LDBS.EQ.LDB
+*
+* If data was incorrectly changed, report and
+* return.
+*
+ SAME = .TRUE.
+ DO 50 I = 1, NARGS
+ SAME = SAME.AND.ISAME( I )
+ IF( .NOT.ISAME( I ) )
+ $ WRITE( NOUT, FMT = 9998 )I
+ 50 CONTINUE
+ IF( .NOT.SAME )THEN
+ FATAL = .TRUE.
+ GO TO 150
+ END IF
+*
+ IF( .NOT.NULL )THEN
+ IF( SNAME( 4: 5 ).EQ.'MM' )THEN
+*
+* Check the result.
+*
+ IF( LEFT )THEN
+ CALL SMMCH( TRANSA, 'N', M, N, M,
+ $ ALPHA, A, NMAX, B, NMAX,
+ $ ZERO, C, NMAX, CT, G,
+ $ BB, LDB, EPS, ERR,
+ $ FATAL, NOUT, .TRUE. )
+ ELSE
+ CALL SMMCH( 'N', TRANSA, M, N, N,
+ $ ALPHA, B, NMAX, A, NMAX,
+ $ ZERO, C, NMAX, CT, G,
+ $ BB, LDB, EPS, ERR,
+ $ FATAL, NOUT, .TRUE. )
+ END IF
+ ELSE IF( SNAME( 4: 5 ).EQ.'SM' )THEN
+*
+* Compute approximation to original
+* matrix.
+*
+ DO 70 J = 1, N
+ DO 60 I = 1, M
+ C( I, J ) = BB( I + ( J - 1 )*
+ $ LDB )
+ BB( I + ( J - 1 )*LDB ) = ALPHA*
+ $ B( I, J )
+ 60 CONTINUE
+ 70 CONTINUE
+*
+ IF( LEFT )THEN
+ CALL SMMCH( TRANSA, 'N', M, N, M,
+ $ ONE, A, NMAX, C, NMAX,
+ $ ZERO, B, NMAX, CT, G,
+ $ BB, LDB, EPS, ERR,
+ $ FATAL, NOUT, .FALSE. )
+ ELSE
+ CALL SMMCH( 'N', TRANSA, M, N, N,
+ $ ONE, C, NMAX, A, NMAX,
+ $ ZERO, B, NMAX, CT, G,
+ $ BB, LDB, EPS, ERR,
+ $ FATAL, NOUT, .FALSE. )
+ END IF
+ END IF
+ ERRMAX = MAX( ERRMAX, ERR )
+* If got really bad answer, report and
+* return.
+ IF( FATAL )
+ $ GO TO 150
+ END IF
+*
+ 80 CONTINUE
+*
+ 90 CONTINUE
+*
+ 100 CONTINUE
+*
+ 110 CONTINUE
+*
+ 120 CONTINUE
+*
+ 130 CONTINUE
+*
+ 140 CONTINUE
+*
+* Report result.
+*
+ IF( ERRMAX.LT.THRESH )THEN
+ WRITE( NOUT, FMT = 9999 )SNAME, NC
+ ELSE
+ WRITE( NOUT, FMT = 9997 )SNAME, NC, ERRMAX
+ END IF
+ GO TO 160
+*
+ 150 CONTINUE
+ WRITE( NOUT, FMT = 9996 )SNAME
+ WRITE( NOUT, FMT = 9995 )NC, SNAME, SIDE, UPLO, TRANSA, DIAG, M,
+ $ N, ALPHA, LDA, LDB
+*
+ 160 CONTINUE
+ RETURN
+*
+ 9999 FORMAT( ' ', A6, ' PASSED THE COMPUTATIONAL TESTS (', I6, ' CALL',
+ $ 'S)' )
+ 9998 FORMAT( ' ******* FATAL ERROR - PARAMETER NUMBER ', I2, ' WAS CH',
+ $ 'ANGED INCORRECTLY *******' )
+ 9997 FORMAT( ' ', A6, ' COMPLETED THE COMPUTATIONAL TESTS (', I6, ' C',
+ $ 'ALLS)', /' ******* BUT WITH MAXIMUM TEST RATIO', F8.2,
+ $ ' - SUSPECT *******' )
+ 9996 FORMAT( ' ******* ', A6, ' FAILED ON CALL NUMBER:' )
+ 9995 FORMAT( 1X, I6, ': ', A6, '(', 4( '''', A1, ''',' ), 2( I3, ',' ),
+ $ F4.1, ', A,', I3, ', B,', I3, ') .' )
+ 9994 FORMAT( ' ******* FATAL ERROR - ERROR-EXIT TAKEN ON VALID CALL *',
+ $ '******' )
+*
+* End of SCHK3.
+*
+ END
+ SUBROUTINE SCHK4( SNAME, EPS, THRESH, NOUT, NTRA, TRACE, REWI,
+ $ FATAL, NIDIM, IDIM, NALF, ALF, NBET, BET, NMAX,
+ $ A, AA, AS, B, BB, BS, C, CC, CS, CT, G )
+*
+* Tests SSYRK.
+*
+* Auxiliary routine for test program for Level 3 Blas.
+*
+* -- Written on 8-February-1989.
+* Jack Dongarra, Argonne National Laboratory.
+* Iain Duff, AERE Harwell.
+* Jeremy Du Croz, Numerical Algorithms Group Ltd.
+* Sven Hammarling, Numerical Algorithms Group Ltd.
+*
+* .. Parameters ..
+ REAL ZERO
+ PARAMETER ( ZERO = 0.0 )
+* .. Scalar Arguments ..
+ REAL EPS, THRESH
+ INTEGER NALF, NBET, NIDIM, NMAX, NOUT, NTRA
+ LOGICAL FATAL, REWI, TRACE
+ CHARACTER*6 SNAME
+* .. Array Arguments ..
+ REAL A( NMAX, NMAX ), AA( NMAX*NMAX ), ALF( NALF ),
+ $ AS( NMAX*NMAX ), B( NMAX, NMAX ),
+ $ BB( NMAX*NMAX ), BET( NBET ), BS( NMAX*NMAX ),
+ $ C( NMAX, NMAX ), CC( NMAX*NMAX ),
+ $ CS( NMAX*NMAX ), CT( NMAX ), G( NMAX )
+ INTEGER IDIM( NIDIM )
+* .. Local Scalars ..
+ REAL ALPHA, ALS, BETA, BETS, ERR, ERRMAX
+ INTEGER I, IA, IB, ICT, ICU, IK, IN, J, JC, JJ, K, KS,
+ $ LAA, LCC, LDA, LDAS, LDC, LDCS, LJ, MA, N, NA,
+ $ NARGS, NC, NS
+ LOGICAL NULL, RESET, SAME, TRAN, UPPER
+ CHARACTER*1 TRANS, TRANSS, UPLO, UPLOS
+ CHARACTER*2 ICHU
+ CHARACTER*3 ICHT
+* .. Local Arrays ..
+ LOGICAL ISAME( 13 )
+* .. External Functions ..
+ LOGICAL LSE, LSERES
+ EXTERNAL LSE, LSERES
+* .. External Subroutines ..
+ EXTERNAL SMAKE, SMMCH, SSYRK
+* .. Intrinsic Functions ..
+ INTRINSIC MAX
+* .. Scalars in Common ..
+ INTEGER INFOT, NOUTC
+ LOGICAL LERR, OK
+* .. Common blocks ..
+ COMMON /INFOC/INFOT, NOUTC, OK, LERR
+* .. Data statements ..
+ DATA ICHT/'NTC'/, ICHU/'UL'/
+* .. Executable Statements ..
+*
+ NARGS = 10
+ NC = 0
+ RESET = .TRUE.
+ ERRMAX = ZERO
+*
+ DO 100 IN = 1, NIDIM
+ N = IDIM( IN )
+* Set LDC to 1 more than minimum value if room.
+ LDC = N
+ IF( LDC.LT.NMAX )
+ $ LDC = LDC + 1
+* Skip tests if not enough room.
+ IF( LDC.GT.NMAX )
+ $ GO TO 100
+ LCC = LDC*N
+ NULL = N.LE.0
+*
+ DO 90 IK = 1, NIDIM
+ K = IDIM( IK )
+*
+ DO 80 ICT = 1, 3
+ TRANS = ICHT( ICT: ICT )
+ TRAN = TRANS.EQ.'T'.OR.TRANS.EQ.'C'
+ IF( TRAN )THEN
+ MA = K
+ NA = N
+ ELSE
+ MA = N
+ NA = K
+ END IF
+* Set LDA to 1 more than minimum value if room.
+ LDA = MA
+ IF( LDA.LT.NMAX )
+ $ LDA = LDA + 1
+* Skip tests if not enough room.
+ IF( LDA.GT.NMAX )
+ $ GO TO 80
+ LAA = LDA*NA
+*
+* Generate the matrix A.
+*
+ CALL SMAKE( 'GE', ' ', ' ', MA, NA, A, NMAX, AA, LDA,
+ $ RESET, ZERO )
+*
+ DO 70 ICU = 1, 2
+ UPLO = ICHU( ICU: ICU )
+ UPPER = UPLO.EQ.'U'
+*
+ DO 60 IA = 1, NALF
+ ALPHA = ALF( IA )
+*
+ DO 50 IB = 1, NBET
+ BETA = BET( IB )
+*
+* Generate the matrix C.
+*
+ CALL SMAKE( 'SY', UPLO, ' ', N, N, C, NMAX, CC,
+ $ LDC, RESET, ZERO )
+*
+ NC = NC + 1
+*
+* Save every datum before calling the subroutine.
+*
+ UPLOS = UPLO
+ TRANSS = TRANS
+ NS = N
+ KS = K
+ ALS = ALPHA
+ DO 10 I = 1, LAA
+ AS( I ) = AA( I )
+ 10 CONTINUE
+ LDAS = LDA
+ BETS = BETA
+ DO 20 I = 1, LCC
+ CS( I ) = CC( I )
+ 20 CONTINUE
+ LDCS = LDC
+*
+* Call the subroutine.
+*
+ IF( TRACE )
+ $ WRITE( NTRA, FMT = 9994 )NC, SNAME, UPLO,
+ $ TRANS, N, K, ALPHA, LDA, BETA, LDC
+ IF( REWI )
+ $ REWIND NTRA
+ CALL SSYRK( UPLO, TRANS, N, K, ALPHA, AA, LDA,
+ $ BETA, CC, LDC )
+*
+* Check if error-exit was taken incorrectly.
+*
+ IF( .NOT.OK )THEN
+ WRITE( NOUT, FMT = 9993 )
+ FATAL = .TRUE.
+ GO TO 120
+ END IF
+*
+* See what data changed inside subroutines.
+*
+ ISAME( 1 ) = UPLOS.EQ.UPLO
+ ISAME( 2 ) = TRANSS.EQ.TRANS
+ ISAME( 3 ) = NS.EQ.N
+ ISAME( 4 ) = KS.EQ.K
+ ISAME( 5 ) = ALS.EQ.ALPHA
+ ISAME( 6 ) = LSE( AS, AA, LAA )
+ ISAME( 7 ) = LDAS.EQ.LDA
+ ISAME( 8 ) = BETS.EQ.BETA
+ IF( NULL )THEN
+ ISAME( 9 ) = LSE( CS, CC, LCC )
+ ELSE
+ ISAME( 9 ) = LSERES( 'SY', UPLO, N, N, CS,
+ $ CC, LDC )
+ END IF
+ ISAME( 10 ) = LDCS.EQ.LDC
+*
+* If data was incorrectly changed, report and
+* return.
+*
+ SAME = .TRUE.
+ DO 30 I = 1, NARGS
+ SAME = SAME.AND.ISAME( I )
+ IF( .NOT.ISAME( I ) )
+ $ WRITE( NOUT, FMT = 9998 )I
+ 30 CONTINUE
+ IF( .NOT.SAME )THEN
+ FATAL = .TRUE.
+ GO TO 120
+ END IF
+*
+ IF( .NOT.NULL )THEN
+*
+* Check the result column by column.
+*
+ JC = 1
+ DO 40 J = 1, N
+ IF( UPPER )THEN
+ JJ = 1
+ LJ = J
+ ELSE
+ JJ = J
+ LJ = N - J + 1
+ END IF
+ IF( TRAN )THEN
+ CALL SMMCH( 'T', 'N', LJ, 1, K, ALPHA,
+ $ A( 1, JJ ), NMAX,
+ $ A( 1, J ), NMAX, BETA,
+ $ C( JJ, J ), NMAX, CT, G,
+ $ CC( JC ), LDC, EPS, ERR,
+ $ FATAL, NOUT, .TRUE. )
+ ELSE
+ CALL SMMCH( 'N', 'T', LJ, 1, K, ALPHA,
+ $ A( JJ, 1 ), NMAX,
+ $ A( J, 1 ), NMAX, BETA,
+ $ C( JJ, J ), NMAX, CT, G,
+ $ CC( JC ), LDC, EPS, ERR,
+ $ FATAL, NOUT, .TRUE. )
+ END IF
+ IF( UPPER )THEN
+ JC = JC + LDC
+ ELSE
+ JC = JC + LDC + 1
+ END IF
+ ERRMAX = MAX( ERRMAX, ERR )
+* If got really bad answer, report and
+* return.
+ IF( FATAL )
+ $ GO TO 110
+ 40 CONTINUE
+ END IF
+*
+ 50 CONTINUE
+*
+ 60 CONTINUE
+*
+ 70 CONTINUE
+*
+ 80 CONTINUE
+*
+ 90 CONTINUE
+*
+ 100 CONTINUE
+*
+* Report result.
+*
+ IF( ERRMAX.LT.THRESH )THEN
+ WRITE( NOUT, FMT = 9999 )SNAME, NC
+ ELSE
+ WRITE( NOUT, FMT = 9997 )SNAME, NC, ERRMAX
+ END IF
+ GO TO 130
+*
+ 110 CONTINUE
+ IF( N.GT.1 )
+ $ WRITE( NOUT, FMT = 9995 )J
+*
+ 120 CONTINUE
+ WRITE( NOUT, FMT = 9996 )SNAME
+ WRITE( NOUT, FMT = 9994 )NC, SNAME, UPLO, TRANS, N, K, ALPHA,
+ $ LDA, BETA, LDC
+*
+ 130 CONTINUE
+ RETURN
+*
+ 9999 FORMAT( ' ', A6, ' PASSED THE COMPUTATIONAL TESTS (', I6, ' CALL',
+ $ 'S)' )
+ 9998 FORMAT( ' ******* FATAL ERROR - PARAMETER NUMBER ', I2, ' WAS CH',
+ $ 'ANGED INCORRECTLY *******' )
+ 9997 FORMAT( ' ', A6, ' COMPLETED THE COMPUTATIONAL TESTS (', I6, ' C',
+ $ 'ALLS)', /' ******* BUT WITH MAXIMUM TEST RATIO', F8.2,
+ $ ' - SUSPECT *******' )
+ 9996 FORMAT( ' ******* ', A6, ' FAILED ON CALL NUMBER:' )
+ 9995 FORMAT( ' THESE ARE THE RESULTS FOR COLUMN ', I3 )
+ 9994 FORMAT( 1X, I6, ': ', A6, '(', 2( '''', A1, ''',' ), 2( I3, ',' ),
+ $ F4.1, ', A,', I3, ',', F4.1, ', C,', I3, ') .' )
+ 9993 FORMAT( ' ******* FATAL ERROR - ERROR-EXIT TAKEN ON VALID CALL *',
+ $ '******' )
+*
+* End of SCHK4.
+*
+ END
+ SUBROUTINE SCHK5( SNAME, EPS, THRESH, NOUT, NTRA, TRACE, REWI,
+ $ FATAL, NIDIM, IDIM, NALF, ALF, NBET, BET, NMAX,
+ $ AB, AA, AS, BB, BS, C, CC, CS, CT, G, W )
+*
+* Tests SSYR2K.
+*
+* Auxiliary routine for test program for Level 3 Blas.
+*
+* -- Written on 8-February-1989.
+* Jack Dongarra, Argonne National Laboratory.
+* Iain Duff, AERE Harwell.
+* Jeremy Du Croz, Numerical Algorithms Group Ltd.
+* Sven Hammarling, Numerical Algorithms Group Ltd.
+*
+* .. Parameters ..
+ REAL ZERO
+ PARAMETER ( ZERO = 0.0 )
+* .. Scalar Arguments ..
+ REAL EPS, THRESH
+ INTEGER NALF, NBET, NIDIM, NMAX, NOUT, NTRA
+ LOGICAL FATAL, REWI, TRACE
+ CHARACTER*6 SNAME
+* .. Array Arguments ..
+ REAL AA( NMAX*NMAX ), AB( 2*NMAX*NMAX ),
+ $ ALF( NALF ), AS( NMAX*NMAX ), BB( NMAX*NMAX ),
+ $ BET( NBET ), BS( NMAX*NMAX ), C( NMAX, NMAX ),
+ $ CC( NMAX*NMAX ), CS( NMAX*NMAX ), CT( NMAX ),
+ $ G( NMAX ), W( 2*NMAX )
+ INTEGER IDIM( NIDIM )
+* .. Local Scalars ..
+ REAL ALPHA, ALS, BETA, BETS, ERR, ERRMAX
+ INTEGER I, IA, IB, ICT, ICU, IK, IN, J, JC, JJ, JJAB,
+ $ K, KS, LAA, LBB, LCC, LDA, LDAS, LDB, LDBS,
+ $ LDC, LDCS, LJ, MA, N, NA, NARGS, NC, NS
+ LOGICAL NULL, RESET, SAME, TRAN, UPPER
+ CHARACTER*1 TRANS, TRANSS, UPLO, UPLOS
+ CHARACTER*2 ICHU
+ CHARACTER*3 ICHT
+* .. Local Arrays ..
+ LOGICAL ISAME( 13 )
+* .. External Functions ..
+ LOGICAL LSE, LSERES
+ EXTERNAL LSE, LSERES
+* .. External Subroutines ..
+ EXTERNAL SMAKE, SMMCH, SSYR2K
+* .. Intrinsic Functions ..
+ INTRINSIC MAX
+* .. Scalars in Common ..
+ INTEGER INFOT, NOUTC
+ LOGICAL LERR, OK
+* .. Common blocks ..
+ COMMON /INFOC/INFOT, NOUTC, OK, LERR
+* .. Data statements ..
+ DATA ICHT/'NTC'/, ICHU/'UL'/
+* .. Executable Statements ..
+*
+ NARGS = 12
+ NC = 0
+ RESET = .TRUE.
+ ERRMAX = ZERO
+*
+ DO 130 IN = 1, NIDIM
+ N = IDIM( IN )
+* Set LDC to 1 more than minimum value if room.
+ LDC = N
+ IF( LDC.LT.NMAX )
+ $ LDC = LDC + 1
+* Skip tests if not enough room.
+ IF( LDC.GT.NMAX )
+ $ GO TO 130
+ LCC = LDC*N
+ NULL = N.LE.0
+*
+ DO 120 IK = 1, NIDIM
+ K = IDIM( IK )
+*
+ DO 110 ICT = 1, 3
+ TRANS = ICHT( ICT: ICT )
+ TRAN = TRANS.EQ.'T'.OR.TRANS.EQ.'C'
+ IF( TRAN )THEN
+ MA = K
+ NA = N
+ ELSE
+ MA = N
+ NA = K
+ END IF
+* Set LDA to 1 more than minimum value if room.
+ LDA = MA
+ IF( LDA.LT.NMAX )
+ $ LDA = LDA + 1
+* Skip tests if not enough room.
+ IF( LDA.GT.NMAX )
+ $ GO TO 110
+ LAA = LDA*NA
+*
+* Generate the matrix A.
+*
+ IF( TRAN )THEN
+ CALL SMAKE( 'GE', ' ', ' ', MA, NA, AB, 2*NMAX, AA,
+ $ LDA, RESET, ZERO )
+ ELSE
+ CALL SMAKE( 'GE', ' ', ' ', MA, NA, AB, NMAX, AA, LDA,
+ $ RESET, ZERO )
+ END IF
+*
+* Generate the matrix B.
+*
+ LDB = LDA
+ LBB = LAA
+ IF( TRAN )THEN
+ CALL SMAKE( 'GE', ' ', ' ', MA, NA, AB( K + 1 ),
+ $ 2*NMAX, BB, LDB, RESET, ZERO )
+ ELSE
+ CALL SMAKE( 'GE', ' ', ' ', MA, NA, AB( K*NMAX + 1 ),
+ $ NMAX, BB, LDB, RESET, ZERO )
+ END IF
+*
+ DO 100 ICU = 1, 2
+ UPLO = ICHU( ICU: ICU )
+ UPPER = UPLO.EQ.'U'
+*
+ DO 90 IA = 1, NALF
+ ALPHA = ALF( IA )
+*
+ DO 80 IB = 1, NBET
+ BETA = BET( IB )
+*
+* Generate the matrix C.
+*
+ CALL SMAKE( 'SY', UPLO, ' ', N, N, C, NMAX, CC,
+ $ LDC, RESET, ZERO )
+*
+ NC = NC + 1
+*
+* Save every datum before calling the subroutine.
+*
+ UPLOS = UPLO
+ TRANSS = TRANS
+ NS = N
+ KS = K
+ ALS = ALPHA
+ DO 10 I = 1, LAA
+ AS( I ) = AA( I )
+ 10 CONTINUE
+ LDAS = LDA
+ DO 20 I = 1, LBB
+ BS( I ) = BB( I )
+ 20 CONTINUE
+ LDBS = LDB
+ BETS = BETA
+ DO 30 I = 1, LCC
+ CS( I ) = CC( I )
+ 30 CONTINUE
+ LDCS = LDC
+*
+* Call the subroutine.
+*
+ IF( TRACE )
+ $ WRITE( NTRA, FMT = 9994 )NC, SNAME, UPLO,
+ $ TRANS, N, K, ALPHA, LDA, LDB, BETA, LDC
+ IF( REWI )
+ $ REWIND NTRA
+ CALL SSYR2K( UPLO, TRANS, N, K, ALPHA, AA, LDA,
+ $ BB, LDB, BETA, CC, LDC )
+*
+* Check if error-exit was taken incorrectly.
+*
+ IF( .NOT.OK )THEN
+ WRITE( NOUT, FMT = 9993 )
+ FATAL = .TRUE.
+ GO TO 150
+ END IF
+*
+* See what data changed inside subroutines.
+*
+ ISAME( 1 ) = UPLOS.EQ.UPLO
+ ISAME( 2 ) = TRANSS.EQ.TRANS
+ ISAME( 3 ) = NS.EQ.N
+ ISAME( 4 ) = KS.EQ.K
+ ISAME( 5 ) = ALS.EQ.ALPHA
+ ISAME( 6 ) = LSE( AS, AA, LAA )
+ ISAME( 7 ) = LDAS.EQ.LDA
+ ISAME( 8 ) = LSE( BS, BB, LBB )
+ ISAME( 9 ) = LDBS.EQ.LDB
+ ISAME( 10 ) = BETS.EQ.BETA
+ IF( NULL )THEN
+ ISAME( 11 ) = LSE( CS, CC, LCC )
+ ELSE
+ ISAME( 11 ) = LSERES( 'SY', UPLO, N, N, CS,
+ $ CC, LDC )
+ END IF
+ ISAME( 12 ) = LDCS.EQ.LDC
+*
+* If data was incorrectly changed, report and
+* return.
+*
+ SAME = .TRUE.
+ DO 40 I = 1, NARGS
+ SAME = SAME.AND.ISAME( I )
+ IF( .NOT.ISAME( I ) )
+ $ WRITE( NOUT, FMT = 9998 )I
+ 40 CONTINUE
+ IF( .NOT.SAME )THEN
+ FATAL = .TRUE.
+ GO TO 150
+ END IF
+*
+ IF( .NOT.NULL )THEN
+*
+* Check the result column by column.
+*
+ JJAB = 1
+ JC = 1
+ DO 70 J = 1, N
+ IF( UPPER )THEN
+ JJ = 1
+ LJ = J
+ ELSE
+ JJ = J
+ LJ = N - J + 1
+ END IF
+ IF( TRAN )THEN
+ DO 50 I = 1, K
+ W( I ) = AB( ( J - 1 )*2*NMAX + K +
+ $ I )
+ W( K + I ) = AB( ( J - 1 )*2*NMAX +
+ $ I )
+ 50 CONTINUE
+ CALL SMMCH( 'T', 'N', LJ, 1, 2*K,
+ $ ALPHA, AB( JJAB ), 2*NMAX,
+ $ W, 2*NMAX, BETA,
+ $ C( JJ, J ), NMAX, CT, G,
+ $ CC( JC ), LDC, EPS, ERR,
+ $ FATAL, NOUT, .TRUE. )
+ ELSE
+ DO 60 I = 1, K
+ W( I ) = AB( ( K + I - 1 )*NMAX +
+ $ J )
+ W( K + I ) = AB( ( I - 1 )*NMAX +
+ $ J )
+ 60 CONTINUE
+ CALL SMMCH( 'N', 'N', LJ, 1, 2*K,
+ $ ALPHA, AB( JJ ), NMAX, W,
+ $ 2*NMAX, BETA, C( JJ, J ),
+ $ NMAX, CT, G, CC( JC ), LDC,
+ $ EPS, ERR, FATAL, NOUT,
+ $ .TRUE. )
+ END IF
+ IF( UPPER )THEN
+ JC = JC + LDC
+ ELSE
+ JC = JC + LDC + 1
+ IF( TRAN )
+ $ JJAB = JJAB + 2*NMAX
+ END IF
+ ERRMAX = MAX( ERRMAX, ERR )
+* If got really bad answer, report and
+* return.
+ IF( FATAL )
+ $ GO TO 140
+ 70 CONTINUE
+ END IF
+*
+ 80 CONTINUE
+*
+ 90 CONTINUE
+*
+ 100 CONTINUE
+*
+ 110 CONTINUE
+*
+ 120 CONTINUE
+*
+ 130 CONTINUE
+*
+* Report result.
+*
+ IF( ERRMAX.LT.THRESH )THEN
+ WRITE( NOUT, FMT = 9999 )SNAME, NC
+ ELSE
+ WRITE( NOUT, FMT = 9997 )SNAME, NC, ERRMAX
+ END IF
+ GO TO 160
+*
+ 140 CONTINUE
+ IF( N.GT.1 )
+ $ WRITE( NOUT, FMT = 9995 )J
+*
+ 150 CONTINUE
+ WRITE( NOUT, FMT = 9996 )SNAME
+ WRITE( NOUT, FMT = 9994 )NC, SNAME, UPLO, TRANS, N, K, ALPHA,
+ $ LDA, LDB, BETA, LDC
+*
+ 160 CONTINUE
+ RETURN
+*
+ 9999 FORMAT( ' ', A6, ' PASSED THE COMPUTATIONAL TESTS (', I6, ' CALL',
+ $ 'S)' )
+ 9998 FORMAT( ' ******* FATAL ERROR - PARAMETER NUMBER ', I2, ' WAS CH',
+ $ 'ANGED INCORRECTLY *******' )
+ 9997 FORMAT( ' ', A6, ' COMPLETED THE COMPUTATIONAL TESTS (', I6, ' C',
+ $ 'ALLS)', /' ******* BUT WITH MAXIMUM TEST RATIO', F8.2,
+ $ ' - SUSPECT *******' )
+ 9996 FORMAT( ' ******* ', A6, ' FAILED ON CALL NUMBER:' )
+ 9995 FORMAT( ' THESE ARE THE RESULTS FOR COLUMN ', I3 )
+ 9994 FORMAT( 1X, I6, ': ', A6, '(', 2( '''', A1, ''',' ), 2( I3, ',' ),
+ $ F4.1, ', A,', I3, ', B,', I3, ',', F4.1, ', C,', I3, ') ',
+ $ ' .' )
+ 9993 FORMAT( ' ******* FATAL ERROR - ERROR-EXIT TAKEN ON VALID CALL *',
+ $ '******' )
+*
+* End of SCHK5.
+*
+ END
+ SUBROUTINE SCHKE( ISNUM, SRNAMT, NOUT )
+*
+* Tests the error exits from the Level 3 Blas.
+* Requires a special version of the error-handling routine XERBLA.
+* A, B and C should not need to be defined.
+*
+* Auxiliary routine for test program for Level 3 Blas.
+*
+* -- Written on 8-February-1989.
+* Jack Dongarra, Argonne National Laboratory.
+* Iain Duff, AERE Harwell.
+* Jeremy Du Croz, Numerical Algorithms Group Ltd.
+* Sven Hammarling, Numerical Algorithms Group Ltd.
+*
+* 3-19-92: Initialize ALPHA and BETA (eca)
+* 3-19-92: Fix argument 12 in calls to SSYMM with INFOT = 9 (eca)
+*
+* .. Scalar Arguments ..
+ INTEGER ISNUM, NOUT
+ CHARACTER*6 SRNAMT
+* .. Scalars in Common ..
+ INTEGER INFOT, NOUTC
+ LOGICAL LERR, OK
+* .. Parameters ..
+ REAL ONE, TWO
+ PARAMETER ( ONE = 1.0E0, TWO = 2.0E0 )
+* .. Local Scalars ..
+ REAL ALPHA, BETA
+* .. Local Arrays ..
+ REAL A( 2, 1 ), B( 2, 1 ), C( 2, 1 )
+* .. External Subroutines ..
+ EXTERNAL CHKXER, SGEMM, SSYMM, SSYR2K, SSYRK, STRMM,
+ $ STRSM
+* .. Common blocks ..
+ COMMON /INFOC/INFOT, NOUTC, OK, LERR
+* .. Executable Statements ..
+* OK is set to .FALSE. by the special version of XERBLA or by CHKXER
+* if anything is wrong.
+ OK = .TRUE.
+* LERR is set to .TRUE. by the special version of XERBLA each time
+* it is called, and is then tested and re-set by CHKXER.
+ LERR = .FALSE.
+*
+* Initialize ALPHA and BETA.
+*
+ ALPHA = ONE
+ BETA = TWO
+*
+ GO TO ( 10, 20, 30, 40, 50, 60 )ISNUM
+ 10 INFOT = 1
+ CALL SGEMM( '/', 'N', 0, 0, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 1
+ CALL SGEMM( '/', 'T', 0, 0, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 2
+ CALL SGEMM( 'N', '/', 0, 0, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 2
+ CALL SGEMM( 'T', '/', 0, 0, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 3
+ CALL SGEMM( 'N', 'N', -1, 0, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 3
+ CALL SGEMM( 'N', 'T', -1, 0, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 3
+ CALL SGEMM( 'T', 'N', -1, 0, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 3
+ CALL SGEMM( 'T', 'T', -1, 0, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 4
+ CALL SGEMM( 'N', 'N', 0, -1, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 4
+ CALL SGEMM( 'N', 'T', 0, -1, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 4
+ CALL SGEMM( 'T', 'N', 0, -1, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 4
+ CALL SGEMM( 'T', 'T', 0, -1, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 5
+ CALL SGEMM( 'N', 'N', 0, 0, -1, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 5
+ CALL SGEMM( 'N', 'T', 0, 0, -1, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 5
+ CALL SGEMM( 'T', 'N', 0, 0, -1, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 5
+ CALL SGEMM( 'T', 'T', 0, 0, -1, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 8
+ CALL SGEMM( 'N', 'N', 2, 0, 0, ALPHA, A, 1, B, 1, BETA, C, 2 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 8
+ CALL SGEMM( 'N', 'T', 2, 0, 0, ALPHA, A, 1, B, 1, BETA, C, 2 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 8
+ CALL SGEMM( 'T', 'N', 0, 0, 2, ALPHA, A, 1, B, 2, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 8
+ CALL SGEMM( 'T', 'T', 0, 0, 2, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 10
+ CALL SGEMM( 'N', 'N', 0, 0, 2, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 10
+ CALL SGEMM( 'T', 'N', 0, 0, 2, ALPHA, A, 2, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 10
+ CALL SGEMM( 'N', 'T', 0, 2, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 10
+ CALL SGEMM( 'T', 'T', 0, 2, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 13
+ CALL SGEMM( 'N', 'N', 2, 0, 0, ALPHA, A, 2, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 13
+ CALL SGEMM( 'N', 'T', 2, 0, 0, ALPHA, A, 2, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 13
+ CALL SGEMM( 'T', 'N', 2, 0, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 13
+ CALL SGEMM( 'T', 'T', 2, 0, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ GO TO 70
+ 20 INFOT = 1
+ CALL SSYMM( '/', 'U', 0, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 2
+ CALL SSYMM( 'L', '/', 0, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 3
+ CALL SSYMM( 'L', 'U', -1, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 3
+ CALL SSYMM( 'R', 'U', -1, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 3
+ CALL SSYMM( 'L', 'L', -1, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 3
+ CALL SSYMM( 'R', 'L', -1, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 4
+ CALL SSYMM( 'L', 'U', 0, -1, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 4
+ CALL SSYMM( 'R', 'U', 0, -1, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 4
+ CALL SSYMM( 'L', 'L', 0, -1, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 4
+ CALL SSYMM( 'R', 'L', 0, -1, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 7
+ CALL SSYMM( 'L', 'U', 2, 0, ALPHA, A, 1, B, 2, BETA, C, 2 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 7
+ CALL SSYMM( 'R', 'U', 0, 2, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 7
+ CALL SSYMM( 'L', 'L', 2, 0, ALPHA, A, 1, B, 2, BETA, C, 2 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 7
+ CALL SSYMM( 'R', 'L', 0, 2, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 9
+ CALL SSYMM( 'L', 'U', 2, 0, ALPHA, A, 2, B, 1, BETA, C, 2 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 9
+ CALL SSYMM( 'R', 'U', 2, 0, ALPHA, A, 1, B, 1, BETA, C, 2 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 9
+ CALL SSYMM( 'L', 'L', 2, 0, ALPHA, A, 2, B, 1, BETA, C, 2 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 9
+ CALL SSYMM( 'R', 'L', 2, 0, ALPHA, A, 1, B, 1, BETA, C, 2 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 12
+ CALL SSYMM( 'L', 'U', 2, 0, ALPHA, A, 2, B, 2, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 12
+ CALL SSYMM( 'R', 'U', 2, 0, ALPHA, A, 1, B, 2, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 12
+ CALL SSYMM( 'L', 'L', 2, 0, ALPHA, A, 2, B, 2, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 12
+ CALL SSYMM( 'R', 'L', 2, 0, ALPHA, A, 1, B, 2, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ GO TO 70
+ 30 INFOT = 1
+ CALL STRMM( '/', 'U', 'N', 'N', 0, 0, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 2
+ CALL STRMM( 'L', '/', 'N', 'N', 0, 0, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 3
+ CALL STRMM( 'L', 'U', '/', 'N', 0, 0, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 4
+ CALL STRMM( 'L', 'U', 'N', '/', 0, 0, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 5
+ CALL STRMM( 'L', 'U', 'N', 'N', -1, 0, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 5
+ CALL STRMM( 'L', 'U', 'T', 'N', -1, 0, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 5
+ CALL STRMM( 'R', 'U', 'N', 'N', -1, 0, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 5
+ CALL STRMM( 'R', 'U', 'T', 'N', -1, 0, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 5
+ CALL STRMM( 'L', 'L', 'N', 'N', -1, 0, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 5
+ CALL STRMM( 'L', 'L', 'T', 'N', -1, 0, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 5
+ CALL STRMM( 'R', 'L', 'N', 'N', -1, 0, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 5
+ CALL STRMM( 'R', 'L', 'T', 'N', -1, 0, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 6
+ CALL STRMM( 'L', 'U', 'N', 'N', 0, -1, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 6
+ CALL STRMM( 'L', 'U', 'T', 'N', 0, -1, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 6
+ CALL STRMM( 'R', 'U', 'N', 'N', 0, -1, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 6
+ CALL STRMM( 'R', 'U', 'T', 'N', 0, -1, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 6
+ CALL STRMM( 'L', 'L', 'N', 'N', 0, -1, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 6
+ CALL STRMM( 'L', 'L', 'T', 'N', 0, -1, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 6
+ CALL STRMM( 'R', 'L', 'N', 'N', 0, -1, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 6
+ CALL STRMM( 'R', 'L', 'T', 'N', 0, -1, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 9
+ CALL STRMM( 'L', 'U', 'N', 'N', 2, 0, ALPHA, A, 1, B, 2 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 9
+ CALL STRMM( 'L', 'U', 'T', 'N', 2, 0, ALPHA, A, 1, B, 2 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 9
+ CALL STRMM( 'R', 'U', 'N', 'N', 0, 2, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 9
+ CALL STRMM( 'R', 'U', 'T', 'N', 0, 2, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 9
+ CALL STRMM( 'L', 'L', 'N', 'N', 2, 0, ALPHA, A, 1, B, 2 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 9
+ CALL STRMM( 'L', 'L', 'T', 'N', 2, 0, ALPHA, A, 1, B, 2 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 9
+ CALL STRMM( 'R', 'L', 'N', 'N', 0, 2, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 9
+ CALL STRMM( 'R', 'L', 'T', 'N', 0, 2, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 11
+ CALL STRMM( 'L', 'U', 'N', 'N', 2, 0, ALPHA, A, 2, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 11
+ CALL STRMM( 'L', 'U', 'T', 'N', 2, 0, ALPHA, A, 2, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 11
+ CALL STRMM( 'R', 'U', 'N', 'N', 2, 0, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 11
+ CALL STRMM( 'R', 'U', 'T', 'N', 2, 0, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 11
+ CALL STRMM( 'L', 'L', 'N', 'N', 2, 0, ALPHA, A, 2, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 11
+ CALL STRMM( 'L', 'L', 'T', 'N', 2, 0, ALPHA, A, 2, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 11
+ CALL STRMM( 'R', 'L', 'N', 'N', 2, 0, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 11
+ CALL STRMM( 'R', 'L', 'T', 'N', 2, 0, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ GO TO 70
+ 40 INFOT = 1
+ CALL STRSM( '/', 'U', 'N', 'N', 0, 0, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 2
+ CALL STRSM( 'L', '/', 'N', 'N', 0, 0, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 3
+ CALL STRSM( 'L', 'U', '/', 'N', 0, 0, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 4
+ CALL STRSM( 'L', 'U', 'N', '/', 0, 0, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 5
+ CALL STRSM( 'L', 'U', 'N', 'N', -1, 0, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 5
+ CALL STRSM( 'L', 'U', 'T', 'N', -1, 0, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 5
+ CALL STRSM( 'R', 'U', 'N', 'N', -1, 0, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 5
+ CALL STRSM( 'R', 'U', 'T', 'N', -1, 0, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 5
+ CALL STRSM( 'L', 'L', 'N', 'N', -1, 0, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 5
+ CALL STRSM( 'L', 'L', 'T', 'N', -1, 0, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 5
+ CALL STRSM( 'R', 'L', 'N', 'N', -1, 0, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 5
+ CALL STRSM( 'R', 'L', 'T', 'N', -1, 0, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 6
+ CALL STRSM( 'L', 'U', 'N', 'N', 0, -1, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 6
+ CALL STRSM( 'L', 'U', 'T', 'N', 0, -1, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 6
+ CALL STRSM( 'R', 'U', 'N', 'N', 0, -1, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 6
+ CALL STRSM( 'R', 'U', 'T', 'N', 0, -1, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 6
+ CALL STRSM( 'L', 'L', 'N', 'N', 0, -1, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 6
+ CALL STRSM( 'L', 'L', 'T', 'N', 0, -1, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 6
+ CALL STRSM( 'R', 'L', 'N', 'N', 0, -1, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 6
+ CALL STRSM( 'R', 'L', 'T', 'N', 0, -1, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 9
+ CALL STRSM( 'L', 'U', 'N', 'N', 2, 0, ALPHA, A, 1, B, 2 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 9
+ CALL STRSM( 'L', 'U', 'T', 'N', 2, 0, ALPHA, A, 1, B, 2 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 9
+ CALL STRSM( 'R', 'U', 'N', 'N', 0, 2, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 9
+ CALL STRSM( 'R', 'U', 'T', 'N', 0, 2, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 9
+ CALL STRSM( 'L', 'L', 'N', 'N', 2, 0, ALPHA, A, 1, B, 2 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 9
+ CALL STRSM( 'L', 'L', 'T', 'N', 2, 0, ALPHA, A, 1, B, 2 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 9
+ CALL STRSM( 'R', 'L', 'N', 'N', 0, 2, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 9
+ CALL STRSM( 'R', 'L', 'T', 'N', 0, 2, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 11
+ CALL STRSM( 'L', 'U', 'N', 'N', 2, 0, ALPHA, A, 2, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 11
+ CALL STRSM( 'L', 'U', 'T', 'N', 2, 0, ALPHA, A, 2, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 11
+ CALL STRSM( 'R', 'U', 'N', 'N', 2, 0, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 11
+ CALL STRSM( 'R', 'U', 'T', 'N', 2, 0, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 11
+ CALL STRSM( 'L', 'L', 'N', 'N', 2, 0, ALPHA, A, 2, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 11
+ CALL STRSM( 'L', 'L', 'T', 'N', 2, 0, ALPHA, A, 2, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 11
+ CALL STRSM( 'R', 'L', 'N', 'N', 2, 0, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 11
+ CALL STRSM( 'R', 'L', 'T', 'N', 2, 0, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ GO TO 70
+ 50 INFOT = 1
+ CALL SSYRK( '/', 'N', 0, 0, ALPHA, A, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 2
+ CALL SSYRK( 'U', '/', 0, 0, ALPHA, A, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 3
+ CALL SSYRK( 'U', 'N', -1, 0, ALPHA, A, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 3
+ CALL SSYRK( 'U', 'T', -1, 0, ALPHA, A, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 3
+ CALL SSYRK( 'L', 'N', -1, 0, ALPHA, A, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 3
+ CALL SSYRK( 'L', 'T', -1, 0, ALPHA, A, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 4
+ CALL SSYRK( 'U', 'N', 0, -1, ALPHA, A, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 4
+ CALL SSYRK( 'U', 'T', 0, -1, ALPHA, A, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 4
+ CALL SSYRK( 'L', 'N', 0, -1, ALPHA, A, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 4
+ CALL SSYRK( 'L', 'T', 0, -1, ALPHA, A, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 7
+ CALL SSYRK( 'U', 'N', 2, 0, ALPHA, A, 1, BETA, C, 2 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 7
+ CALL SSYRK( 'U', 'T', 0, 2, ALPHA, A, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 7
+ CALL SSYRK( 'L', 'N', 2, 0, ALPHA, A, 1, BETA, C, 2 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 7
+ CALL SSYRK( 'L', 'T', 0, 2, ALPHA, A, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 10
+ CALL SSYRK( 'U', 'N', 2, 0, ALPHA, A, 2, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 10
+ CALL SSYRK( 'U', 'T', 2, 0, ALPHA, A, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 10
+ CALL SSYRK( 'L', 'N', 2, 0, ALPHA, A, 2, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 10
+ CALL SSYRK( 'L', 'T', 2, 0, ALPHA, A, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ GO TO 70
+ 60 INFOT = 1
+ CALL SSYR2K( '/', 'N', 0, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 2
+ CALL SSYR2K( 'U', '/', 0, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 3
+ CALL SSYR2K( 'U', 'N', -1, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 3
+ CALL SSYR2K( 'U', 'T', -1, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 3
+ CALL SSYR2K( 'L', 'N', -1, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 3
+ CALL SSYR2K( 'L', 'T', -1, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 4
+ CALL SSYR2K( 'U', 'N', 0, -1, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 4
+ CALL SSYR2K( 'U', 'T', 0, -1, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 4
+ CALL SSYR2K( 'L', 'N', 0, -1, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 4
+ CALL SSYR2K( 'L', 'T', 0, -1, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 7
+ CALL SSYR2K( 'U', 'N', 2, 0, ALPHA, A, 1, B, 1, BETA, C, 2 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 7
+ CALL SSYR2K( 'U', 'T', 0, 2, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 7
+ CALL SSYR2K( 'L', 'N', 2, 0, ALPHA, A, 1, B, 1, BETA, C, 2 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 7
+ CALL SSYR2K( 'L', 'T', 0, 2, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 9
+ CALL SSYR2K( 'U', 'N', 2, 0, ALPHA, A, 2, B, 1, BETA, C, 2 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 9
+ CALL SSYR2K( 'U', 'T', 0, 2, ALPHA, A, 2, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 9
+ CALL SSYR2K( 'L', 'N', 2, 0, ALPHA, A, 2, B, 1, BETA, C, 2 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 9
+ CALL SSYR2K( 'L', 'T', 0, 2, ALPHA, A, 2, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 12
+ CALL SSYR2K( 'U', 'N', 2, 0, ALPHA, A, 2, B, 2, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 12
+ CALL SSYR2K( 'U', 'T', 2, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 12
+ CALL SSYR2K( 'L', 'N', 2, 0, ALPHA, A, 2, B, 2, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 12
+ CALL SSYR2K( 'L', 'T', 2, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+*
+ 70 IF( OK )THEN
+ WRITE( NOUT, FMT = 9999 )SRNAMT
+ ELSE
+ WRITE( NOUT, FMT = 9998 )SRNAMT
+ END IF
+ RETURN
+*
+ 9999 FORMAT( ' ', A6, ' PASSED THE TESTS OF ERROR-EXITS' )
+ 9998 FORMAT( ' ******* ', A6, ' FAILED THE TESTS OF ERROR-EXITS *****',
+ $ '**' )
+*
+* End of SCHKE.
+*
+ END
+ SUBROUTINE SMAKE( TYPE, UPLO, DIAG, M, N, A, NMAX, AA, LDA, RESET,
+ $ TRANSL )
+*
+* Generates values for an M by N matrix A.
+* Stores the values in the array AA in the data structure required
+* by the routine, with unwanted elements set to rogue value.
+*
+* TYPE is 'GE', 'SY' or 'TR'.
+*
+* Auxiliary routine for test program for Level 3 Blas.
+*
+* -- Written on 8-February-1989.
+* Jack Dongarra, Argonne National Laboratory.
+* Iain Duff, AERE Harwell.
+* Jeremy Du Croz, Numerical Algorithms Group Ltd.
+* Sven Hammarling, Numerical Algorithms Group Ltd.
+*
+* .. Parameters ..
+ REAL ZERO, ONE
+ PARAMETER ( ZERO = 0.0, ONE = 1.0 )
+ REAL ROGUE
+ PARAMETER ( ROGUE = -1.0E10 )
+* .. Scalar Arguments ..
+ REAL TRANSL
+ INTEGER LDA, M, N, NMAX
+ LOGICAL RESET
+ CHARACTER*1 DIAG, UPLO
+ CHARACTER*2 TYPE
+* .. Array Arguments ..
+ REAL A( NMAX, * ), AA( * )
+* .. Local Scalars ..
+ INTEGER I, IBEG, IEND, J
+ LOGICAL GEN, LOWER, SYM, TRI, UNIT, UPPER
+* .. External Functions ..
+ REAL SBEG
+ EXTERNAL SBEG
+* .. Executable Statements ..
+ GEN = TYPE.EQ.'GE'
+ SYM = TYPE.EQ.'SY'
+ TRI = TYPE.EQ.'TR'
+ UPPER = ( SYM.OR.TRI ).AND.UPLO.EQ.'U'
+ LOWER = ( SYM.OR.TRI ).AND.UPLO.EQ.'L'
+ UNIT = TRI.AND.DIAG.EQ.'U'
+*
+* Generate data in array A.
+*
+ DO 20 J = 1, N
+ DO 10 I = 1, M
+ IF( GEN.OR.( UPPER.AND.I.LE.J ).OR.( LOWER.AND.I.GE.J ) )
+ $ THEN
+ A( I, J ) = SBEG( RESET ) + TRANSL
+ IF( I.NE.J )THEN
+* Set some elements to zero
+ IF( N.GT.3.AND.J.EQ.N/2 )
+ $ A( I, J ) = ZERO
+ IF( SYM )THEN
+ A( J, I ) = A( I, J )
+ ELSE IF( TRI )THEN
+ A( J, I ) = ZERO
+ END IF
+ END IF
+ END IF
+ 10 CONTINUE
+ IF( TRI )
+ $ A( J, J ) = A( J, J ) + ONE
+ IF( UNIT )
+ $ A( J, J ) = ONE
+ 20 CONTINUE
+*
+* Store elements in array AS in data structure required by routine.
+*
+ IF( TYPE.EQ.'GE' )THEN
+ DO 50 J = 1, N
+ DO 30 I = 1, M
+ AA( I + ( J - 1 )*LDA ) = A( I, J )
+ 30 CONTINUE
+ DO 40 I = M + 1, LDA
+ AA( I + ( J - 1 )*LDA ) = ROGUE
+ 40 CONTINUE
+ 50 CONTINUE
+ ELSE IF( TYPE.EQ.'SY'.OR.TYPE.EQ.'TR' )THEN
+ DO 90 J = 1, N
+ IF( UPPER )THEN
+ IBEG = 1
+ IF( UNIT )THEN
+ IEND = J - 1
+ ELSE
+ IEND = J
+ END IF
+ ELSE
+ IF( UNIT )THEN
+ IBEG = J + 1
+ ELSE
+ IBEG = J
+ END IF
+ IEND = N
+ END IF
+ DO 60 I = 1, IBEG - 1
+ AA( I + ( J - 1 )*LDA ) = ROGUE
+ 60 CONTINUE
+ DO 70 I = IBEG, IEND
+ AA( I + ( J - 1 )*LDA ) = A( I, J )
+ 70 CONTINUE
+ DO 80 I = IEND + 1, LDA
+ AA( I + ( J - 1 )*LDA ) = ROGUE
+ 80 CONTINUE
+ 90 CONTINUE
+ END IF
+ RETURN
+*
+* End of SMAKE.
+*
+ END
+ SUBROUTINE SMMCH( TRANSA, TRANSB, M, N, KK, ALPHA, A, LDA, B, LDB,
+ $ BETA, C, LDC, CT, G, CC, LDCC, EPS, ERR, FATAL,
+ $ NOUT, MV )
+*
+* Checks the results of the computational tests.
+*
+* Auxiliary routine for test program for Level 3 Blas.
+*
+* -- Written on 8-February-1989.
+* Jack Dongarra, Argonne National Laboratory.
+* Iain Duff, AERE Harwell.
+* Jeremy Du Croz, Numerical Algorithms Group Ltd.
+* Sven Hammarling, Numerical Algorithms Group Ltd.
+*
+* .. Parameters ..
+ REAL ZERO, ONE
+ PARAMETER ( ZERO = 0.0, ONE = 1.0 )
+* .. Scalar Arguments ..
+ REAL ALPHA, BETA, EPS, ERR
+ INTEGER KK, LDA, LDB, LDC, LDCC, M, N, NOUT
+ LOGICAL FATAL, MV
+ CHARACTER*1 TRANSA, TRANSB
+* .. Array Arguments ..
+ REAL A( LDA, * ), B( LDB, * ), C( LDC, * ),
+ $ CC( LDCC, * ), CT( * ), G( * )
+* .. Local Scalars ..
+ REAL ERRI
+ INTEGER I, J, K
+ LOGICAL TRANA, TRANB
+* .. Intrinsic Functions ..
+ INTRINSIC ABS, MAX, SQRT
+* .. Executable Statements ..
+ TRANA = TRANSA.EQ.'T'.OR.TRANSA.EQ.'C'
+ TRANB = TRANSB.EQ.'T'.OR.TRANSB.EQ.'C'
+*
+* Compute expected result, one column at a time, in CT using data
+* in A, B and C.
+* Compute gauges in G.
+*
+ DO 120 J = 1, N
+*
+ DO 10 I = 1, M
+ CT( I ) = ZERO
+ G( I ) = ZERO
+ 10 CONTINUE
+ IF( .NOT.TRANA.AND..NOT.TRANB )THEN
+ DO 30 K = 1, KK
+ DO 20 I = 1, M
+ CT( I ) = CT( I ) + A( I, K )*B( K, J )
+ G( I ) = G( I ) + ABS( A( I, K ) )*ABS( B( K, J ) )
+ 20 CONTINUE
+ 30 CONTINUE
+ ELSE IF( TRANA.AND..NOT.TRANB )THEN
+ DO 50 K = 1, KK
+ DO 40 I = 1, M
+ CT( I ) = CT( I ) + A( K, I )*B( K, J )
+ G( I ) = G( I ) + ABS( A( K, I ) )*ABS( B( K, J ) )
+ 40 CONTINUE
+ 50 CONTINUE
+ ELSE IF( .NOT.TRANA.AND.TRANB )THEN
+ DO 70 K = 1, KK
+ DO 60 I = 1, M
+ CT( I ) = CT( I ) + A( I, K )*B( J, K )
+ G( I ) = G( I ) + ABS( A( I, K ) )*ABS( B( J, K ) )
+ 60 CONTINUE
+ 70 CONTINUE
+ ELSE IF( TRANA.AND.TRANB )THEN
+ DO 90 K = 1, KK
+ DO 80 I = 1, M
+ CT( I ) = CT( I ) + A( K, I )*B( J, K )
+ G( I ) = G( I ) + ABS( A( K, I ) )*ABS( B( J, K ) )
+ 80 CONTINUE
+ 90 CONTINUE
+ END IF
+ DO 100 I = 1, M
+ CT( I ) = ALPHA*CT( I ) + BETA*C( I, J )
+ G( I ) = ABS( ALPHA )*G( I ) + ABS( BETA )*ABS( C( I, J ) )
+ 100 CONTINUE
+*
+* Compute the error ratio for this result.
+*
+ ERR = ZERO
+ DO 110 I = 1, M
+ ERRI = ABS( CT( I ) - CC( I, J ) )/EPS
+ IF( G( I ).NE.ZERO )
+ $ ERRI = ERRI/G( I )
+ ERR = MAX( ERR, ERRI )
+ IF( ERR*SQRT( EPS ).GE.ONE )
+ $ GO TO 130
+ 110 CONTINUE
+*
+ 120 CONTINUE
+*
+* If the loop completes, all results are at least half accurate.
+ GO TO 150
+*
+* Report fatal error.
+*
+ 130 FATAL = .TRUE.
+ WRITE( NOUT, FMT = 9999 )
+ DO 140 I = 1, M
+ IF( MV )THEN
+ WRITE( NOUT, FMT = 9998 )I, CT( I ), CC( I, J )
+ ELSE
+ WRITE( NOUT, FMT = 9998 )I, CC( I, J ), CT( I )
+ END IF
+ 140 CONTINUE
+ IF( N.GT.1 )
+ $ WRITE( NOUT, FMT = 9997 )J
+*
+ 150 CONTINUE
+ RETURN
+*
+ 9999 FORMAT( ' ******* FATAL ERROR - COMPUTED RESULT IS LESS THAN HAL',
+ $ 'F ACCURATE *******', /' EXPECTED RESULT COMPU',
+ $ 'TED RESULT' )
+ 9998 FORMAT( 1X, I7, 2G18.6 )
+ 9997 FORMAT( ' THESE ARE THE RESULTS FOR COLUMN ', I3 )
+*
+* End of SMMCH.
+*
+ END
+ LOGICAL FUNCTION LSE( RI, RJ, LR )
+*
+* Tests if two arrays are identical.
+*
+* Auxiliary routine for test program for Level 3 Blas.
+*
+* -- Written on 8-February-1989.
+* Jack Dongarra, Argonne National Laboratory.
+* Iain Duff, AERE Harwell.
+* Jeremy Du Croz, Numerical Algorithms Group Ltd.
+* Sven Hammarling, Numerical Algorithms Group Ltd.
+*
+* .. Scalar Arguments ..
+ INTEGER LR
+* .. Array Arguments ..
+ REAL RI( * ), RJ( * )
+* .. Local Scalars ..
+ INTEGER I
+* .. Executable Statements ..
+ DO 10 I = 1, LR
+ IF( RI( I ).NE.RJ( I ) )
+ $ GO TO 20
+ 10 CONTINUE
+ LSE = .TRUE.
+ GO TO 30
+ 20 CONTINUE
+ LSE = .FALSE.
+ 30 RETURN
+*
+* End of LSE.
+*
+ END
+ LOGICAL FUNCTION LSERES( TYPE, UPLO, M, N, AA, AS, LDA )
+*
+* Tests if selected elements in two arrays are equal.
+*
+* TYPE is 'GE' or 'SY'.
+*
+* Auxiliary routine for test program for Level 3 Blas.
+*
+* -- Written on 8-February-1989.
+* Jack Dongarra, Argonne National Laboratory.
+* Iain Duff, AERE Harwell.
+* Jeremy Du Croz, Numerical Algorithms Group Ltd.
+* Sven Hammarling, Numerical Algorithms Group Ltd.
+*
+* .. Scalar Arguments ..
+ INTEGER LDA, M, N
+ CHARACTER*1 UPLO
+ CHARACTER*2 TYPE
+* .. Array Arguments ..
+ REAL AA( LDA, * ), AS( LDA, * )
+* .. Local Scalars ..
+ INTEGER I, IBEG, IEND, J
+ LOGICAL UPPER
+* .. Executable Statements ..
+ UPPER = UPLO.EQ.'U'
+ IF( TYPE.EQ.'GE' )THEN
+ DO 20 J = 1, N
+ DO 10 I = M + 1, LDA
+ IF( AA( I, J ).NE.AS( I, J ) )
+ $ GO TO 70
+ 10 CONTINUE
+ 20 CONTINUE
+ ELSE IF( TYPE.EQ.'SY' )THEN
+ DO 50 J = 1, N
+ IF( UPPER )THEN
+ IBEG = 1
+ IEND = J
+ ELSE
+ IBEG = J
+ IEND = N
+ END IF
+ DO 30 I = 1, IBEG - 1
+ IF( AA( I, J ).NE.AS( I, J ) )
+ $ GO TO 70
+ 30 CONTINUE
+ DO 40 I = IEND + 1, LDA
+ IF( AA( I, J ).NE.AS( I, J ) )
+ $ GO TO 70
+ 40 CONTINUE
+ 50 CONTINUE
+ END IF
+*
+ LSERES = .TRUE.
+ GO TO 80
+ 70 CONTINUE
+ LSERES = .FALSE.
+ 80 RETURN
+*
+* End of LSERES.
+*
+ END
+ REAL FUNCTION SBEG( RESET )
+*
+* Generates random numbers uniformly distributed between -0.5 and 0.5.
+*
+* Auxiliary routine for test program for Level 3 Blas.
+*
+* -- Written on 8-February-1989.
+* Jack Dongarra, Argonne National Laboratory.
+* Iain Duff, AERE Harwell.
+* Jeremy Du Croz, Numerical Algorithms Group Ltd.
+* Sven Hammarling, Numerical Algorithms Group Ltd.
+*
+* .. Scalar Arguments ..
+ LOGICAL RESET
+* .. Local Scalars ..
+ INTEGER I, IC, MI
+* .. Save statement ..
+ SAVE I, IC, MI
+* .. Executable Statements ..
+ IF( RESET )THEN
+* Initialize local variables.
+ MI = 891
+ I = 7
+ IC = 0
+ RESET = .FALSE.
+ END IF
+*
+* The sequence of values of I is bounded between 1 and 999.
+* If initial I = 1,2,3,6,7 or 9, the period will be 50.
+* If initial I = 4 or 8, the period will be 25.
+* If initial I = 5, the period will be 10.
+* IC is used to break up the period by skipping 1 value of I in 6.
+*
+ IC = IC + 1
+ 10 I = I*MI
+ I = I - 1000*( I/1000 )
+ IF( IC.GE.5 )THEN
+ IC = 0
+ GO TO 10
+ END IF
+ SBEG = ( I - 500 )/1001.0
+ RETURN
+*
+* End of SBEG.
+*
+ END
+ REAL FUNCTION SDIFF( X, Y )
+*
+* Auxiliary routine for test program for Level 3 Blas.
+*
+* -- Written on 8-February-1989.
+* Jack Dongarra, Argonne National Laboratory.
+* Iain Duff, AERE Harwell.
+* Jeremy Du Croz, Numerical Algorithms Group Ltd.
+* Sven Hammarling, Numerical Algorithms Group Ltd.
+*
+* .. Scalar Arguments ..
+ REAL X, Y
+* .. Executable Statements ..
+ SDIFF = X - Y
+ RETURN
+*
+* End of SDIFF.
+*
+ END
+ SUBROUTINE CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+*
+* Tests whether XERBLA has detected an error when it should.
+*
+* Auxiliary routine for test program for Level 3 Blas.
+*
+* -- Written on 8-February-1989.
+* Jack Dongarra, Argonne National Laboratory.
+* Iain Duff, AERE Harwell.
+* Jeremy Du Croz, Numerical Algorithms Group Ltd.
+* Sven Hammarling, Numerical Algorithms Group Ltd.
+*
+* .. Scalar Arguments ..
+ INTEGER INFOT, NOUT
+ LOGICAL LERR, OK
+ CHARACTER*6 SRNAMT
+* .. Executable Statements ..
+ IF( .NOT.LERR )THEN
+ WRITE( NOUT, FMT = 9999 )INFOT, SRNAMT
+ OK = .FALSE.
+ END IF
+ LERR = .FALSE.
+ RETURN
+*
+ 9999 FORMAT( ' ***** ILLEGAL VALUE OF PARAMETER NUMBER ', I2, ' NOT D',
+ $ 'ETECTED BY ', A6, ' *****' )
+*
+* End of CHKXER.
+*
+ END
+ SUBROUTINE XERBLA( SRNAME, INFO )
+*
+* This is a special version of XERBLA to be used only as part of
+* the test program for testing error exits from the Level 3 BLAS
+* routines.
+*
+* XERBLA is an error handler for the Level 3 BLAS routines.
+*
+* It is called by the Level 3 BLAS routines if an input parameter is
+* invalid.
+*
+* Auxiliary routine for test program for Level 3 Blas.
+*
+* -- Written on 8-February-1989.
+* Jack Dongarra, Argonne National Laboratory.
+* Iain Duff, AERE Harwell.
+* Jeremy Du Croz, Numerical Algorithms Group Ltd.
+* Sven Hammarling, Numerical Algorithms Group Ltd.
+*
+* .. Scalar Arguments ..
+ INTEGER INFO
+ CHARACTER*6 SRNAME
+* .. Scalars in Common ..
+ INTEGER INFOT, NOUT
+ LOGICAL LERR, OK
+ CHARACTER*6 SRNAMT
+* .. Common blocks ..
+ COMMON /INFOC/INFOT, NOUT, OK, LERR
+ COMMON /SRNAMC/SRNAMT
+* .. Executable Statements ..
+ LERR = .TRUE.
+ IF( INFO.NE.INFOT )THEN
+ IF( INFOT.NE.0 )THEN
+ WRITE( NOUT, FMT = 9999 )INFO, INFOT
+ ELSE
+ WRITE( NOUT, FMT = 9997 )INFO
+ END IF
+ OK = .FALSE.
+ END IF
+ IF( SRNAME.NE.SRNAMT )THEN
+ WRITE( NOUT, FMT = 9998 )SRNAME, SRNAMT
+ OK = .FALSE.
+ END IF
+ RETURN
+*
+ 9999 FORMAT( ' ******* XERBLA WAS CALLED WITH INFO = ', I6, ' INSTEAD',
+ $ ' OF ', I2, ' *******' )
+ 9998 FORMAT( ' ******* XERBLA WAS CALLED WITH SRNAME = ', A6, ' INSTE',
+ $ 'AD OF ', A6, ' *******' )
+ 9997 FORMAT( ' ******* XERBLA WAS CALLED WITH INFO = ', I6,
+ $ ' *******' )
+*
+* End of XERBLA
+*
+ END
+
diff --git a/blas/testing/zblat1.f b/blas/testing/zblat1.f
new file mode 100644
index 0000000..c00b67d
--- /dev/null
+++ b/blas/testing/zblat1.f
@@ -0,0 +1,724 @@
+*> \brief \b ZBLAT1
+*
+* =========== DOCUMENTATION ===========
+*
+* Online html documentation available at
+* http://www.netlib.org/lapack/explore-html/
+*
+* Definition:
+* ===========
+*
+* PROGRAM ZBLAT1
+*
+*
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
+*>
+*> Test program for the COMPLEX*16 Level 1 BLAS.
+*>
+*> Based upon the original BLAS test routine together with:
+*> F06GAF Example Program Text
+*> \endverbatim
+*
+* Authors:
+* ========
+*
+*> \author Univ. of Tennessee
+*> \author Univ. of California Berkeley
+*> \author Univ. of Colorado Denver
+*> \author NAG Ltd.
+*
+*> \date April 2012
+*
+*> \ingroup complex16_blas_testing
+*
+* =====================================================================
+ PROGRAM ZBLAT1
+*
+* -- Reference BLAS test routine (version 3.4.1) --
+* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
+* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+* April 2012
+*
+* =====================================================================
+*
+* .. Parameters ..
+ INTEGER NOUT
+ PARAMETER (NOUT=6)
+* .. Scalars in Common ..
+ INTEGER ICASE, INCX, INCY, MODE, N
+ LOGICAL PASS
+* .. Local Scalars ..
+ DOUBLE PRECISION SFAC
+ INTEGER IC
+* .. External Subroutines ..
+ EXTERNAL CHECK1, CHECK2, HEADER
+* .. Common blocks ..
+ COMMON /COMBLA/ICASE, N, INCX, INCY, MODE, PASS
+* .. Data statements ..
+ DATA SFAC/9.765625D-4/
+* .. Executable Statements ..
+ WRITE (NOUT,99999)
+ DO 20 IC = 1, 10
+ ICASE = IC
+ CALL HEADER
+*
+* Initialize PASS, INCX, INCY, and MODE for a new case.
+* The value 9999 for INCX, INCY or MODE will appear in the
+* detailed output, if any, for cases that do not involve
+* these parameters.
+*
+ PASS = .TRUE.
+ INCX = 9999
+ INCY = 9999
+ MODE = 9999
+ IF (ICASE.LE.5) THEN
+ CALL CHECK2(SFAC)
+ ELSE IF (ICASE.GE.6) THEN
+ CALL CHECK1(SFAC)
+ END IF
+* -- Print
+ IF (PASS) WRITE (NOUT,99998)
+ 20 CONTINUE
+ STOP
+*
+99999 FORMAT (' Complex BLAS Test Program Results',/1X)
+99998 FORMAT (' ----- PASS -----')
+ END
+ SUBROUTINE HEADER
+* .. Parameters ..
+ INTEGER NOUT
+ PARAMETER (NOUT=6)
+* .. Scalars in Common ..
+ INTEGER ICASE, INCX, INCY, MODE, N
+ LOGICAL PASS
+* .. Local Arrays ..
+ CHARACTER*6 L(10)
+* .. Common blocks ..
+ COMMON /COMBLA/ICASE, N, INCX, INCY, MODE, PASS
+* .. Data statements ..
+ DATA L(1)/'ZDOTC '/
+ DATA L(2)/'ZDOTU '/
+ DATA L(3)/'ZAXPY '/
+ DATA L(4)/'ZCOPY '/
+ DATA L(5)/'ZSWAP '/
+ DATA L(6)/'DZNRM2'/
+ DATA L(7)/'DZASUM'/
+ DATA L(8)/'ZSCAL '/
+ DATA L(9)/'ZDSCAL'/
+ DATA L(10)/'IZAMAX'/
+* .. Executable Statements ..
+ WRITE (NOUT,99999) ICASE, L(ICASE)
+ RETURN
+*
+99999 FORMAT (/' Test of subprogram number',I3,12X,A6)
+ END
+ SUBROUTINE CHECK1(SFAC)
+* .. Parameters ..
+ INTEGER NOUT
+ PARAMETER (NOUT=6)
+* .. Scalar Arguments ..
+ DOUBLE PRECISION SFAC
+* .. Scalars in Common ..
+ INTEGER ICASE, INCX, INCY, MODE, N
+ LOGICAL PASS
+* .. Local Scalars ..
+ COMPLEX*16 CA
+ DOUBLE PRECISION SA
+ INTEGER I, J, LEN, NP1
+* .. Local Arrays ..
+ COMPLEX*16 CTRUE5(8,5,2), CTRUE6(8,5,2), CV(8,5,2), CX(8),
+ + MWPCS(5), MWPCT(5)
+ DOUBLE PRECISION STRUE2(5), STRUE4(5)
+ INTEGER ITRUE3(5)
+* .. External Functions ..
+ DOUBLE PRECISION DZASUM, DZNRM2
+ INTEGER IZAMAX
+ EXTERNAL DZASUM, DZNRM2, IZAMAX
+* .. External Subroutines ..
+ EXTERNAL ZSCAL, ZDSCAL, CTEST, ITEST1, STEST1
+* .. Intrinsic Functions ..
+ INTRINSIC MAX
+* .. Common blocks ..
+ COMMON /COMBLA/ICASE, N, INCX, INCY, MODE, PASS
+* .. Data statements ..
+ DATA SA, CA/0.3D0, (0.4D0,-0.7D0)/
+ DATA ((CV(I,J,1),I=1,8),J=1,5)/(0.1D0,0.1D0),
+ + (1.0D0,2.0D0), (1.0D0,2.0D0), (1.0D0,2.0D0),
+ + (1.0D0,2.0D0), (1.0D0,2.0D0), (1.0D0,2.0D0),
+ + (1.0D0,2.0D0), (0.3D0,-0.4D0), (3.0D0,4.0D0),
+ + (3.0D0,4.0D0), (3.0D0,4.0D0), (3.0D0,4.0D0),
+ + (3.0D0,4.0D0), (3.0D0,4.0D0), (3.0D0,4.0D0),
+ + (0.1D0,-0.3D0), (0.5D0,-0.1D0), (5.0D0,6.0D0),
+ + (5.0D0,6.0D0), (5.0D0,6.0D0), (5.0D0,6.0D0),
+ + (5.0D0,6.0D0), (5.0D0,6.0D0), (0.1D0,0.1D0),
+ + (-0.6D0,0.1D0), (0.1D0,-0.3D0), (7.0D0,8.0D0),
+ + (7.0D0,8.0D0), (7.0D0,8.0D0), (7.0D0,8.0D0),
+ + (7.0D0,8.0D0), (0.3D0,0.1D0), (0.5D0,0.0D0),
+ + (0.0D0,0.5D0), (0.0D0,0.2D0), (2.0D0,3.0D0),
+ + (2.0D0,3.0D0), (2.0D0,3.0D0), (2.0D0,3.0D0)/
+ DATA ((CV(I,J,2),I=1,8),J=1,5)/(0.1D0,0.1D0),
+ + (4.0D0,5.0D0), (4.0D0,5.0D0), (4.0D0,5.0D0),
+ + (4.0D0,5.0D0), (4.0D0,5.0D0), (4.0D0,5.0D0),
+ + (4.0D0,5.0D0), (0.3D0,-0.4D0), (6.0D0,7.0D0),
+ + (6.0D0,7.0D0), (6.0D0,7.0D0), (6.0D0,7.0D0),
+ + (6.0D0,7.0D0), (6.0D0,7.0D0), (6.0D0,7.0D0),
+ + (0.1D0,-0.3D0), (8.0D0,9.0D0), (0.5D0,-0.1D0),
+ + (2.0D0,5.0D0), (2.0D0,5.0D0), (2.0D0,5.0D0),
+ + (2.0D0,5.0D0), (2.0D0,5.0D0), (0.1D0,0.1D0),
+ + (3.0D0,6.0D0), (-0.6D0,0.1D0), (4.0D0,7.0D0),
+ + (0.1D0,-0.3D0), (7.0D0,2.0D0), (7.0D0,2.0D0),
+ + (7.0D0,2.0D0), (0.3D0,0.1D0), (5.0D0,8.0D0),
+ + (0.5D0,0.0D0), (6.0D0,9.0D0), (0.0D0,0.5D0),
+ + (8.0D0,3.0D0), (0.0D0,0.2D0), (9.0D0,4.0D0)/
+ DATA STRUE2/0.0D0, 0.5D0, 0.6D0, 0.7D0, 0.8D0/
+ DATA STRUE4/0.0D0, 0.7D0, 1.0D0, 1.3D0, 1.6D0/
+ DATA ((CTRUE5(I,J,1),I=1,8),J=1,5)/(0.1D0,0.1D0),
+ + (1.0D0,2.0D0), (1.0D0,2.0D0), (1.0D0,2.0D0),
+ + (1.0D0,2.0D0), (1.0D0,2.0D0), (1.0D0,2.0D0),
+ + (1.0D0,2.0D0), (-0.16D0,-0.37D0), (3.0D0,4.0D0),
+ + (3.0D0,4.0D0), (3.0D0,4.0D0), (3.0D0,4.0D0),
+ + (3.0D0,4.0D0), (3.0D0,4.0D0), (3.0D0,4.0D0),
+ + (-0.17D0,-0.19D0), (0.13D0,-0.39D0),
+ + (5.0D0,6.0D0), (5.0D0,6.0D0), (5.0D0,6.0D0),
+ + (5.0D0,6.0D0), (5.0D0,6.0D0), (5.0D0,6.0D0),
+ + (0.11D0,-0.03D0), (-0.17D0,0.46D0),
+ + (-0.17D0,-0.19D0), (7.0D0,8.0D0), (7.0D0,8.0D0),
+ + (7.0D0,8.0D0), (7.0D0,8.0D0), (7.0D0,8.0D0),
+ + (0.19D0,-0.17D0), (0.20D0,-0.35D0),
+ + (0.35D0,0.20D0), (0.14D0,0.08D0),
+ + (2.0D0,3.0D0), (2.0D0,3.0D0), (2.0D0,3.0D0),
+ + (2.0D0,3.0D0)/
+ DATA ((CTRUE5(I,J,2),I=1,8),J=1,5)/(0.1D0,0.1D0),
+ + (4.0D0,5.0D0), (4.0D0,5.0D0), (4.0D0,5.0D0),
+ + (4.0D0,5.0D0), (4.0D0,5.0D0), (4.0D0,5.0D0),
+ + (4.0D0,5.0D0), (-0.16D0,-0.37D0), (6.0D0,7.0D0),
+ + (6.0D0,7.0D0), (6.0D0,7.0D0), (6.0D0,7.0D0),
+ + (6.0D0,7.0D0), (6.0D0,7.0D0), (6.0D0,7.0D0),
+ + (-0.17D0,-0.19D0), (8.0D0,9.0D0),
+ + (0.13D0,-0.39D0), (2.0D0,5.0D0), (2.0D0,5.0D0),
+ + (2.0D0,5.0D0), (2.0D0,5.0D0), (2.0D0,5.0D0),
+ + (0.11D0,-0.03D0), (3.0D0,6.0D0),
+ + (-0.17D0,0.46D0), (4.0D0,7.0D0),
+ + (-0.17D0,-0.19D0), (7.0D0,2.0D0), (7.0D0,2.0D0),
+ + (7.0D0,2.0D0), (0.19D0,-0.17D0), (5.0D0,8.0D0),
+ + (0.20D0,-0.35D0), (6.0D0,9.0D0),
+ + (0.35D0,0.20D0), (8.0D0,3.0D0),
+ + (0.14D0,0.08D0), (9.0D0,4.0D0)/
+ DATA ((CTRUE6(I,J,1),I=1,8),J=1,5)/(0.1D0,0.1D0),
+ + (1.0D0,2.0D0), (1.0D0,2.0D0), (1.0D0,2.0D0),
+ + (1.0D0,2.0D0), (1.0D0,2.0D0), (1.0D0,2.0D0),
+ + (1.0D0,2.0D0), (0.09D0,-0.12D0), (3.0D0,4.0D0),
+ + (3.0D0,4.0D0), (3.0D0,4.0D0), (3.0D0,4.0D0),
+ + (3.0D0,4.0D0), (3.0D0,4.0D0), (3.0D0,4.0D0),
+ + (0.03D0,-0.09D0), (0.15D0,-0.03D0),
+ + (5.0D0,6.0D0), (5.0D0,6.0D0), (5.0D0,6.0D0),
+ + (5.0D0,6.0D0), (5.0D0,6.0D0), (5.0D0,6.0D0),
+ + (0.03D0,0.03D0), (-0.18D0,0.03D0),
+ + (0.03D0,-0.09D0), (7.0D0,8.0D0), (7.0D0,8.0D0),
+ + (7.0D0,8.0D0), (7.0D0,8.0D0), (7.0D0,8.0D0),
+ + (0.09D0,0.03D0), (0.15D0,0.00D0),
+ + (0.00D0,0.15D0), (0.00D0,0.06D0), (2.0D0,3.0D0),
+ + (2.0D0,3.0D0), (2.0D0,3.0D0), (2.0D0,3.0D0)/
+ DATA ((CTRUE6(I,J,2),I=1,8),J=1,5)/(0.1D0,0.1D0),
+ + (4.0D0,5.0D0), (4.0D0,5.0D0), (4.0D0,5.0D0),
+ + (4.0D0,5.0D0), (4.0D0,5.0D0), (4.0D0,5.0D0),
+ + (4.0D0,5.0D0), (0.09D0,-0.12D0), (6.0D0,7.0D0),
+ + (6.0D0,7.0D0), (6.0D0,7.0D0), (6.0D0,7.0D0),
+ + (6.0D0,7.0D0), (6.0D0,7.0D0), (6.0D0,7.0D0),
+ + (0.03D0,-0.09D0), (8.0D0,9.0D0),
+ + (0.15D0,-0.03D0), (2.0D0,5.0D0), (2.0D0,5.0D0),
+ + (2.0D0,5.0D0), (2.0D0,5.0D0), (2.0D0,5.0D0),
+ + (0.03D0,0.03D0), (3.0D0,6.0D0),
+ + (-0.18D0,0.03D0), (4.0D0,7.0D0),
+ + (0.03D0,-0.09D0), (7.0D0,2.0D0), (7.0D0,2.0D0),
+ + (7.0D0,2.0D0), (0.09D0,0.03D0), (5.0D0,8.0D0),
+ + (0.15D0,0.00D0), (6.0D0,9.0D0), (0.00D0,0.15D0),
+ + (8.0D0,3.0D0), (0.00D0,0.06D0), (9.0D0,4.0D0)/
+ DATA ITRUE3/0, 1, 2, 2, 2/
+* .. Executable Statements ..
+ DO 60 INCX = 1, 2
+ DO 40 NP1 = 1, 5
+ N = NP1 - 1
+ LEN = 2*MAX(N,1)
+* .. Set vector arguments ..
+ DO 20 I = 1, LEN
+ CX(I) = CV(I,NP1,INCX)
+ 20 CONTINUE
+ IF (ICASE.EQ.6) THEN
+* .. DZNRM2 ..
+ CALL STEST1(DZNRM2(N,CX,INCX),STRUE2(NP1),STRUE2(NP1),
+ + SFAC)
+ ELSE IF (ICASE.EQ.7) THEN
+* .. DZASUM ..
+ CALL STEST1(DZASUM(N,CX,INCX),STRUE4(NP1),STRUE4(NP1),
+ + SFAC)
+ ELSE IF (ICASE.EQ.8) THEN
+* .. ZSCAL ..
+ CALL ZSCAL(N,CA,CX,INCX)
+ CALL CTEST(LEN,CX,CTRUE5(1,NP1,INCX),CTRUE5(1,NP1,INCX),
+ + SFAC)
+ ELSE IF (ICASE.EQ.9) THEN
+* .. ZDSCAL ..
+ CALL ZDSCAL(N,SA,CX,INCX)
+ CALL CTEST(LEN,CX,CTRUE6(1,NP1,INCX),CTRUE6(1,NP1,INCX),
+ + SFAC)
+ ELSE IF (ICASE.EQ.10) THEN
+* .. IZAMAX ..
+ CALL ITEST1(IZAMAX(N,CX,INCX),ITRUE3(NP1))
+ ELSE
+ WRITE (NOUT,*) ' Shouldn''t be here in CHECK1'
+ STOP
+ END IF
+*
+ 40 CONTINUE
+ 60 CONTINUE
+*
+ INCX = 1
+ IF (ICASE.EQ.8) THEN
+* ZSCAL
+* Add a test for alpha equal to zero.
+ CA = (0.0D0,0.0D0)
+ DO 80 I = 1, 5
+ MWPCT(I) = (0.0D0,0.0D0)
+ MWPCS(I) = (1.0D0,1.0D0)
+ 80 CONTINUE
+ CALL ZSCAL(5,CA,CX,INCX)
+ CALL CTEST(5,CX,MWPCT,MWPCS,SFAC)
+ ELSE IF (ICASE.EQ.9) THEN
+* ZDSCAL
+* Add a test for alpha equal to zero.
+ SA = 0.0D0
+ DO 100 I = 1, 5
+ MWPCT(I) = (0.0D0,0.0D0)
+ MWPCS(I) = (1.0D0,1.0D0)
+ 100 CONTINUE
+ CALL ZDSCAL(5,SA,CX,INCX)
+ CALL CTEST(5,CX,MWPCT,MWPCS,SFAC)
+* Add a test for alpha equal to one.
+ SA = 1.0D0
+ DO 120 I = 1, 5
+ MWPCT(I) = CX(I)
+ MWPCS(I) = CX(I)
+ 120 CONTINUE
+ CALL ZDSCAL(5,SA,CX,INCX)
+ CALL CTEST(5,CX,MWPCT,MWPCS,SFAC)
+* Add a test for alpha equal to minus one.
+ SA = -1.0D0
+ DO 140 I = 1, 5
+ MWPCT(I) = -CX(I)
+ MWPCS(I) = -CX(I)
+ 140 CONTINUE
+ CALL ZDSCAL(5,SA,CX,INCX)
+ CALL CTEST(5,CX,MWPCT,MWPCS,SFAC)
+ END IF
+ RETURN
+ END
+ SUBROUTINE CHECK2(SFAC)
+* .. Parameters ..
+ INTEGER NOUT
+ PARAMETER (NOUT=6)
+* .. Scalar Arguments ..
+ DOUBLE PRECISION SFAC
+* .. Scalars in Common ..
+ INTEGER ICASE, INCX, INCY, MODE, N
+ LOGICAL PASS
+* .. Local Scalars ..
+ COMPLEX*16 CA
+ INTEGER I, J, KI, KN, KSIZE, LENX, LENY, MX, MY
+* .. Local Arrays ..
+ COMPLEX*16 CDOT(1), CSIZE1(4), CSIZE2(7,2), CSIZE3(14),
+ + CT10X(7,4,4), CT10Y(7,4,4), CT6(4,4), CT7(4,4),
+ + CT8(7,4,4), CX(7), CX1(7), CY(7), CY1(7)
+ INTEGER INCXS(4), INCYS(4), LENS(4,2), NS(4)
+* .. External Functions ..
+ COMPLEX*16 ZDOTC, ZDOTU
+ EXTERNAL ZDOTC, ZDOTU
+* .. External Subroutines ..
+ EXTERNAL ZAXPY, ZCOPY, ZSWAP, CTEST
+* .. Intrinsic Functions ..
+ INTRINSIC ABS, MIN
+* .. Common blocks ..
+ COMMON /COMBLA/ICASE, N, INCX, INCY, MODE, PASS
+* .. Data statements ..
+ DATA CA/(0.4D0,-0.7D0)/
+ DATA INCXS/1, 2, -2, -1/
+ DATA INCYS/1, -2, 1, -2/
+ DATA LENS/1, 1, 2, 4, 1, 1, 3, 7/
+ DATA NS/0, 1, 2, 4/
+ DATA CX1/(0.7D0,-0.8D0), (-0.4D0,-0.7D0),
+ + (-0.1D0,-0.9D0), (0.2D0,-0.8D0),
+ + (-0.9D0,-0.4D0), (0.1D0,0.4D0), (-0.6D0,0.6D0)/
+ DATA CY1/(0.6D0,-0.6D0), (-0.9D0,0.5D0),
+ + (0.7D0,-0.6D0), (0.1D0,-0.5D0), (-0.1D0,-0.2D0),
+ + (-0.5D0,-0.3D0), (0.8D0,-0.7D0)/
+ DATA ((CT8(I,J,1),I=1,7),J=1,4)/(0.6D0,-0.6D0),
+ + (0.0D0,0.0D0), (0.0D0,0.0D0), (0.0D0,0.0D0),
+ + (0.0D0,0.0D0), (0.0D0,0.0D0), (0.0D0,0.0D0),
+ + (0.32D0,-1.41D0), (0.0D0,0.0D0), (0.0D0,0.0D0),
+ + (0.0D0,0.0D0), (0.0D0,0.0D0), (0.0D0,0.0D0),
+ + (0.0D0,0.0D0), (0.32D0,-1.41D0),
+ + (-1.55D0,0.5D0), (0.0D0,0.0D0), (0.0D0,0.0D0),
+ + (0.0D0,0.0D0), (0.0D0,0.0D0), (0.0D0,0.0D0),
+ + (0.32D0,-1.41D0), (-1.55D0,0.5D0),
+ + (0.03D0,-0.89D0), (-0.38D0,-0.96D0),
+ + (0.0D0,0.0D0), (0.0D0,0.0D0), (0.0D0,0.0D0)/
+ DATA ((CT8(I,J,2),I=1,7),J=1,4)/(0.6D0,-0.6D0),
+ + (0.0D0,0.0D0), (0.0D0,0.0D0), (0.0D0,0.0D0),
+ + (0.0D0,0.0D0), (0.0D0,0.0D0), (0.0D0,0.0D0),
+ + (0.32D0,-1.41D0), (0.0D0,0.0D0), (0.0D0,0.0D0),
+ + (0.0D0,0.0D0), (0.0D0,0.0D0), (0.0D0,0.0D0),
+ + (0.0D0,0.0D0), (-0.07D0,-0.89D0),
+ + (-0.9D0,0.5D0), (0.42D0,-1.41D0), (0.0D0,0.0D0),
+ + (0.0D0,0.0D0), (0.0D0,0.0D0), (0.0D0,0.0D0),
+ + (0.78D0,0.06D0), (-0.9D0,0.5D0),
+ + (0.06D0,-0.13D0), (0.1D0,-0.5D0),
+ + (-0.77D0,-0.49D0), (-0.5D0,-0.3D0),
+ + (0.52D0,-1.51D0)/
+ DATA ((CT8(I,J,3),I=1,7),J=1,4)/(0.6D0,-0.6D0),
+ + (0.0D0,0.0D0), (0.0D0,0.0D0), (0.0D0,0.0D0),
+ + (0.0D0,0.0D0), (0.0D0,0.0D0), (0.0D0,0.0D0),
+ + (0.32D0,-1.41D0), (0.0D0,0.0D0), (0.0D0,0.0D0),
+ + (0.0D0,0.0D0), (0.0D0,0.0D0), (0.0D0,0.0D0),
+ + (0.0D0,0.0D0), (-0.07D0,-0.89D0),
+ + (-1.18D0,-0.31D0), (0.0D0,0.0D0), (0.0D0,0.0D0),
+ + (0.0D0,0.0D0), (0.0D0,0.0D0), (0.0D0,0.0D0),
+ + (0.78D0,0.06D0), (-1.54D0,0.97D0),
+ + (0.03D0,-0.89D0), (-0.18D0,-1.31D0),
+ + (0.0D0,0.0D0), (0.0D0,0.0D0), (0.0D0,0.0D0)/
+ DATA ((CT8(I,J,4),I=1,7),J=1,4)/(0.6D0,-0.6D0),
+ + (0.0D0,0.0D0), (0.0D0,0.0D0), (0.0D0,0.0D0),
+ + (0.0D0,0.0D0), (0.0D0,0.0D0), (0.0D0,0.0D0),
+ + (0.32D0,-1.41D0), (0.0D0,0.0D0), (0.0D0,0.0D0),
+ + (0.0D0,0.0D0), (0.0D0,0.0D0), (0.0D0,0.0D0),
+ + (0.0D0,0.0D0), (0.32D0,-1.41D0), (-0.9D0,0.5D0),
+ + (0.05D0,-0.6D0), (0.0D0,0.0D0), (0.0D0,0.0D0),
+ + (0.0D0,0.0D0), (0.0D0,0.0D0), (0.32D0,-1.41D0),
+ + (-0.9D0,0.5D0), (0.05D0,-0.6D0), (0.1D0,-0.5D0),
+ + (-0.77D0,-0.49D0), (-0.5D0,-0.3D0),
+ + (0.32D0,-1.16D0)/
+ DATA CT7/(0.0D0,0.0D0), (-0.06D0,-0.90D0),
+ + (0.65D0,-0.47D0), (-0.34D0,-1.22D0),
+ + (0.0D0,0.0D0), (-0.06D0,-0.90D0),
+ + (-0.59D0,-1.46D0), (-1.04D0,-0.04D0),
+ + (0.0D0,0.0D0), (-0.06D0,-0.90D0),
+ + (-0.83D0,0.59D0), (0.07D0,-0.37D0),
+ + (0.0D0,0.0D0), (-0.06D0,-0.90D0),
+ + (-0.76D0,-1.15D0), (-1.33D0,-1.82D0)/
+ DATA CT6/(0.0D0,0.0D0), (0.90D0,0.06D0),
+ + (0.91D0,-0.77D0), (1.80D0,-0.10D0),
+ + (0.0D0,0.0D0), (0.90D0,0.06D0), (1.45D0,0.74D0),
+ + (0.20D0,0.90D0), (0.0D0,0.0D0), (0.90D0,0.06D0),
+ + (-0.55D0,0.23D0), (0.83D0,-0.39D0),
+ + (0.0D0,0.0D0), (0.90D0,0.06D0), (1.04D0,0.79D0),
+ + (1.95D0,1.22D0)/
+ DATA ((CT10X(I,J,1),I=1,7),J=1,4)/(0.7D0,-0.8D0),
+ + (0.0D0,0.0D0), (0.0D0,0.0D0), (0.0D0,0.0D0),
+ + (0.0D0,0.0D0), (0.0D0,0.0D0), (0.0D0,0.0D0),
+ + (0.6D0,-0.6D0), (0.0D0,0.0D0), (0.0D0,0.0D0),
+ + (0.0D0,0.0D0), (0.0D0,0.0D0), (0.0D0,0.0D0),
+ + (0.0D0,0.0D0), (0.6D0,-0.6D0), (-0.9D0,0.5D0),
+ + (0.0D0,0.0D0), (0.0D0,0.0D0), (0.0D0,0.0D0),
+ + (0.0D0,0.0D0), (0.0D0,0.0D0), (0.6D0,-0.6D0),
+ + (-0.9D0,0.5D0), (0.7D0,-0.6D0), (0.1D0,-0.5D0),
+ + (0.0D0,0.0D0), (0.0D0,0.0D0), (0.0D0,0.0D0)/
+ DATA ((CT10X(I,J,2),I=1,7),J=1,4)/(0.7D0,-0.8D0),
+ + (0.0D0,0.0D0), (0.0D0,0.0D0), (0.0D0,0.0D0),
+ + (0.0D0,0.0D0), (0.0D0,0.0D0), (0.0D0,0.0D0),
+ + (0.6D0,-0.6D0), (0.0D0,0.0D0), (0.0D0,0.0D0),
+ + (0.0D0,0.0D0), (0.0D0,0.0D0), (0.0D0,0.0D0),
+ + (0.0D0,0.0D0), (0.7D0,-0.6D0), (-0.4D0,-0.7D0),
+ + (0.6D0,-0.6D0), (0.0D0,0.0D0), (0.0D0,0.0D0),
+ + (0.0D0,0.0D0), (0.0D0,0.0D0), (0.8D0,-0.7D0),
+ + (-0.4D0,-0.7D0), (-0.1D0,-0.2D0),
+ + (0.2D0,-0.8D0), (0.7D0,-0.6D0), (0.1D0,0.4D0),
+ + (0.6D0,-0.6D0)/
+ DATA ((CT10X(I,J,3),I=1,7),J=1,4)/(0.7D0,-0.8D0),
+ + (0.0D0,0.0D0), (0.0D0,0.0D0), (0.0D0,0.0D0),
+ + (0.0D0,0.0D0), (0.0D0,0.0D0), (0.0D0,0.0D0),
+ + (0.6D0,-0.6D0), (0.0D0,0.0D0), (0.0D0,0.0D0),
+ + (0.0D0,0.0D0), (0.0D0,0.0D0), (0.0D0,0.0D0),
+ + (0.0D0,0.0D0), (-0.9D0,0.5D0), (-0.4D0,-0.7D0),
+ + (0.6D0,-0.6D0), (0.0D0,0.0D0), (0.0D0,0.0D0),
+ + (0.0D0,0.0D0), (0.0D0,0.0D0), (0.1D0,-0.5D0),
+ + (-0.4D0,-0.7D0), (0.7D0,-0.6D0), (0.2D0,-0.8D0),
+ + (-0.9D0,0.5D0), (0.1D0,0.4D0), (0.6D0,-0.6D0)/
+ DATA ((CT10X(I,J,4),I=1,7),J=1,4)/(0.7D0,-0.8D0),
+ + (0.0D0,0.0D0), (0.0D0,0.0D0), (0.0D0,0.0D0),
+ + (0.0D0,0.0D0), (0.0D0,0.0D0), (0.0D0,0.0D0),
+ + (0.6D0,-0.6D0), (0.0D0,0.0D0), (0.0D0,0.0D0),
+ + (0.0D0,0.0D0), (0.0D0,0.0D0), (0.0D0,0.0D0),
+ + (0.0D0,0.0D0), (0.6D0,-0.6D0), (0.7D0,-0.6D0),
+ + (0.0D0,0.0D0), (0.0D0,0.0D0), (0.0D0,0.0D0),
+ + (0.0D0,0.0D0), (0.0D0,0.0D0), (0.6D0,-0.6D0),
+ + (0.7D0,-0.6D0), (-0.1D0,-0.2D0), (0.8D0,-0.7D0),
+ + (0.0D0,0.0D0), (0.0D0,0.0D0), (0.0D0,0.0D0)/
+ DATA ((CT10Y(I,J,1),I=1,7),J=1,4)/(0.6D0,-0.6D0),
+ + (0.0D0,0.0D0), (0.0D0,0.0D0), (0.0D0,0.0D0),
+ + (0.0D0,0.0D0), (0.0D0,0.0D0), (0.0D0,0.0D0),
+ + (0.7D0,-0.8D0), (0.0D0,0.0D0), (0.0D0,0.0D0),
+ + (0.0D0,0.0D0), (0.0D0,0.0D0), (0.0D0,0.0D0),
+ + (0.0D0,0.0D0), (0.7D0,-0.8D0), (-0.4D0,-0.7D0),
+ + (0.0D0,0.0D0), (0.0D0,0.0D0), (0.0D0,0.0D0),
+ + (0.0D0,0.0D0), (0.0D0,0.0D0), (0.7D0,-0.8D0),
+ + (-0.4D0,-0.7D0), (-0.1D0,-0.9D0),
+ + (0.2D0,-0.8D0), (0.0D0,0.0D0), (0.0D0,0.0D0),
+ + (0.0D0,0.0D0)/
+ DATA ((CT10Y(I,J,2),I=1,7),J=1,4)/(0.6D0,-0.6D0),
+ + (0.0D0,0.0D0), (0.0D0,0.0D0), (0.0D0,0.0D0),
+ + (0.0D0,0.0D0), (0.0D0,0.0D0), (0.0D0,0.0D0),
+ + (0.7D0,-0.8D0), (0.0D0,0.0D0), (0.0D0,0.0D0),
+ + (0.0D0,0.0D0), (0.0D0,0.0D0), (0.0D0,0.0D0),
+ + (0.0D0,0.0D0), (-0.1D0,-0.9D0), (-0.9D0,0.5D0),
+ + (0.7D0,-0.8D0), (0.0D0,0.0D0), (0.0D0,0.0D0),
+ + (0.0D0,0.0D0), (0.0D0,0.0D0), (-0.6D0,0.6D0),
+ + (-0.9D0,0.5D0), (-0.9D0,-0.4D0), (0.1D0,-0.5D0),
+ + (-0.1D0,-0.9D0), (-0.5D0,-0.3D0),
+ + (0.7D0,-0.8D0)/
+ DATA ((CT10Y(I,J,3),I=1,7),J=1,4)/(0.6D0,-0.6D0),
+ + (0.0D0,0.0D0), (0.0D0,0.0D0), (0.0D0,0.0D0),
+ + (0.0D0,0.0D0), (0.0D0,0.0D0), (0.0D0,0.0D0),
+ + (0.7D0,-0.8D0), (0.0D0,0.0D0), (0.0D0,0.0D0),
+ + (0.0D0,0.0D0), (0.0D0,0.0D0), (0.0D0,0.0D0),
+ + (0.0D0,0.0D0), (-0.1D0,-0.9D0), (0.7D0,-0.8D0),
+ + (0.0D0,0.0D0), (0.0D0,0.0D0), (0.0D0,0.0D0),
+ + (0.0D0,0.0D0), (0.0D0,0.0D0), (-0.6D0,0.6D0),
+ + (-0.9D0,-0.4D0), (-0.1D0,-0.9D0),
+ + (0.7D0,-0.8D0), (0.0D0,0.0D0), (0.0D0,0.0D0),
+ + (0.0D0,0.0D0)/
+ DATA ((CT10Y(I,J,4),I=1,7),J=1,4)/(0.6D0,-0.6D0),
+ + (0.0D0,0.0D0), (0.0D0,0.0D0), (0.0D0,0.0D0),
+ + (0.0D0,0.0D0), (0.0D0,0.0D0), (0.0D0,0.0D0),
+ + (0.7D0,-0.8D0), (0.0D0,0.0D0), (0.0D0,0.0D0),
+ + (0.0D0,0.0D0), (0.0D0,0.0D0), (0.0D0,0.0D0),
+ + (0.0D0,0.0D0), (0.7D0,-0.8D0), (-0.9D0,0.5D0),
+ + (-0.4D0,-0.7D0), (0.0D0,0.0D0), (0.0D0,0.0D0),
+ + (0.0D0,0.0D0), (0.0D0,0.0D0), (0.7D0,-0.8D0),
+ + (-0.9D0,0.5D0), (-0.4D0,-0.7D0), (0.1D0,-0.5D0),
+ + (-0.1D0,-0.9D0), (-0.5D0,-0.3D0),
+ + (0.2D0,-0.8D0)/
+ DATA CSIZE1/(0.0D0,0.0D0), (0.9D0,0.9D0),
+ + (1.63D0,1.73D0), (2.90D0,2.78D0)/
+ DATA CSIZE3/(0.0D0,0.0D0), (0.0D0,0.0D0),
+ + (0.0D0,0.0D0), (0.0D0,0.0D0), (0.0D0,0.0D0),
+ + (0.0D0,0.0D0), (0.0D0,0.0D0), (1.17D0,1.17D0),
+ + (1.17D0,1.17D0), (1.17D0,1.17D0),
+ + (1.17D0,1.17D0), (1.17D0,1.17D0),
+ + (1.17D0,1.17D0), (1.17D0,1.17D0)/
+ DATA CSIZE2/(0.0D0,0.0D0), (0.0D0,0.0D0),
+ + (0.0D0,0.0D0), (0.0D0,0.0D0), (0.0D0,0.0D0),
+ + (0.0D0,0.0D0), (0.0D0,0.0D0), (1.54D0,1.54D0),
+ + (1.54D0,1.54D0), (1.54D0,1.54D0),
+ + (1.54D0,1.54D0), (1.54D0,1.54D0),
+ + (1.54D0,1.54D0), (1.54D0,1.54D0)/
+* .. Executable Statements ..
+ DO 60 KI = 1, 4
+ INCX = INCXS(KI)
+ INCY = INCYS(KI)
+ MX = ABS(INCX)
+ MY = ABS(INCY)
+*
+ DO 40 KN = 1, 4
+ N = NS(KN)
+ KSIZE = MIN(2,KN)
+ LENX = LENS(KN,MX)
+ LENY = LENS(KN,MY)
+* .. initialize all argument arrays ..
+ DO 20 I = 1, 7
+ CX(I) = CX1(I)
+ CY(I) = CY1(I)
+ 20 CONTINUE
+ IF (ICASE.EQ.1) THEN
+* .. ZDOTC ..
+ CDOT(1) = ZDOTC(N,CX,INCX,CY,INCY)
+ CALL CTEST(1,CDOT,CT6(KN,KI),CSIZE1(KN),SFAC)
+ ELSE IF (ICASE.EQ.2) THEN
+* .. ZDOTU ..
+ CDOT(1) = ZDOTU(N,CX,INCX,CY,INCY)
+ CALL CTEST(1,CDOT,CT7(KN,KI),CSIZE1(KN),SFAC)
+ ELSE IF (ICASE.EQ.3) THEN
+* .. ZAXPY ..
+ CALL ZAXPY(N,CA,CX,INCX,CY,INCY)
+ CALL CTEST(LENY,CY,CT8(1,KN,KI),CSIZE2(1,KSIZE),SFAC)
+ ELSE IF (ICASE.EQ.4) THEN
+* .. ZCOPY ..
+ CALL ZCOPY(N,CX,INCX,CY,INCY)
+ CALL CTEST(LENY,CY,CT10Y(1,KN,KI),CSIZE3,1.0D0)
+ ELSE IF (ICASE.EQ.5) THEN
+* .. ZSWAP ..
+ CALL ZSWAP(N,CX,INCX,CY,INCY)
+ CALL CTEST(LENX,CX,CT10X(1,KN,KI),CSIZE3,1.0D0)
+ CALL CTEST(LENY,CY,CT10Y(1,KN,KI),CSIZE3,1.0D0)
+ ELSE
+ WRITE (NOUT,*) ' Shouldn''t be here in CHECK2'
+ STOP
+ END IF
+*
+ 40 CONTINUE
+ 60 CONTINUE
+ RETURN
+ END
+ SUBROUTINE STEST(LEN,SCOMP,STRUE,SSIZE,SFAC)
+* ********************************* STEST **************************
+*
+* THIS SUBR COMPARES ARRAYS SCOMP() AND STRUE() OF LENGTH LEN TO
+* SEE IF THE TERM BY TERM DIFFERENCES, MULTIPLIED BY SFAC, ARE
+* NEGLIGIBLE.
+*
+* C. L. LAWSON, JPL, 1974 DEC 10
+*
+* .. Parameters ..
+ INTEGER NOUT
+ DOUBLE PRECISION ZERO
+ PARAMETER (NOUT=6, ZERO=0.0D0)
+* .. Scalar Arguments ..
+ DOUBLE PRECISION SFAC
+ INTEGER LEN
+* .. Array Arguments ..
+ DOUBLE PRECISION SCOMP(LEN), SSIZE(LEN), STRUE(LEN)
+* .. Scalars in Common ..
+ INTEGER ICASE, INCX, INCY, MODE, N
+ LOGICAL PASS
+* .. Local Scalars ..
+ DOUBLE PRECISION SD
+ INTEGER I
+* .. External Functions ..
+ DOUBLE PRECISION SDIFF
+ EXTERNAL SDIFF
+* .. Intrinsic Functions ..
+ INTRINSIC ABS
+* .. Common blocks ..
+ COMMON /COMBLA/ICASE, N, INCX, INCY, MODE, PASS
+* .. Executable Statements ..
+*
+ DO 40 I = 1, LEN
+ SD = SCOMP(I) - STRUE(I)
+ IF (ABS(SFAC*SD) .LE. ABS(SSIZE(I))*EPSILON(ZERO))
+ + GO TO 40
+*
+* HERE SCOMP(I) IS NOT CLOSE TO STRUE(I).
+*
+ IF ( .NOT. PASS) GO TO 20
+* PRINT FAIL MESSAGE AND HEADER.
+ PASS = .FALSE.
+ WRITE (NOUT,99999)
+ WRITE (NOUT,99998)
+ 20 WRITE (NOUT,99997) ICASE, N, INCX, INCY, MODE, I, SCOMP(I),
+ + STRUE(I), SD, SSIZE(I)
+ 40 CONTINUE
+ RETURN
+*
+99999 FORMAT (' FAIL')
+99998 FORMAT (/' CASE N INCX INCY MODE I ',
+ + ' COMP(I) TRUE(I) DIFFERENCE',
+ + ' SIZE(I)',/1X)
+99997 FORMAT (1X,I4,I3,3I5,I3,2D36.8,2D12.4)
+ END
+ SUBROUTINE STEST1(SCOMP1,STRUE1,SSIZE,SFAC)
+* ************************* STEST1 *****************************
+*
+* THIS IS AN INTERFACE SUBROUTINE TO ACCOMMODATE THE FORTRAN
+* REQUIREMENT THAT WHEN A DUMMY ARGUMENT IS AN ARRAY, THE
+* ACTUAL ARGUMENT MUST ALSO BE AN ARRAY OR AN ARRAY ELEMENT.
+*
+* C.L. LAWSON, JPL, 1978 DEC 6
+*
+* .. Scalar Arguments ..
+ DOUBLE PRECISION SCOMP1, SFAC, STRUE1
+* .. Array Arguments ..
+ DOUBLE PRECISION SSIZE(*)
+* .. Local Arrays ..
+ DOUBLE PRECISION SCOMP(1), STRUE(1)
+* .. External Subroutines ..
+ EXTERNAL STEST
+* .. Executable Statements ..
+*
+ SCOMP(1) = SCOMP1
+ STRUE(1) = STRUE1
+ CALL STEST(1,SCOMP,STRUE,SSIZE,SFAC)
+*
+ RETURN
+ END
+ DOUBLE PRECISION FUNCTION SDIFF(SA,SB)
+* ********************************* SDIFF **************************
+* COMPUTES DIFFERENCE OF TWO NUMBERS. C. L. LAWSON, JPL 1974 FEB 15
+*
+* .. Scalar Arguments ..
+ DOUBLE PRECISION SA, SB
+* .. Executable Statements ..
+ SDIFF = SA - SB
+ RETURN
+ END
+ SUBROUTINE CTEST(LEN,CCOMP,CTRUE,CSIZE,SFAC)
+* **************************** CTEST *****************************
+*
+* C.L. LAWSON, JPL, 1978 DEC 6
+*
+* .. Scalar Arguments ..
+ DOUBLE PRECISION SFAC
+ INTEGER LEN
+* .. Array Arguments ..
+ COMPLEX*16 CCOMP(LEN), CSIZE(LEN), CTRUE(LEN)
+* .. Local Scalars ..
+ INTEGER I
+* .. Local Arrays ..
+ DOUBLE PRECISION SCOMP(20), SSIZE(20), STRUE(20)
+* .. External Subroutines ..
+ EXTERNAL STEST
+* .. Intrinsic Functions ..
+ INTRINSIC DIMAG, DBLE
+* .. Executable Statements ..
+ DO 20 I = 1, LEN
+ SCOMP(2*I-1) = DBLE(CCOMP(I))
+ SCOMP(2*I) = DIMAG(CCOMP(I))
+ STRUE(2*I-1) = DBLE(CTRUE(I))
+ STRUE(2*I) = DIMAG(CTRUE(I))
+ SSIZE(2*I-1) = DBLE(CSIZE(I))
+ SSIZE(2*I) = DIMAG(CSIZE(I))
+ 20 CONTINUE
+*
+ CALL STEST(2*LEN,SCOMP,STRUE,SSIZE,SFAC)
+ RETURN
+ END
+ SUBROUTINE ITEST1(ICOMP,ITRUE)
+* ********************************* ITEST1 *************************
+*
+* THIS SUBROUTINE COMPARES THE VARIABLES ICOMP AND ITRUE FOR
+* EQUALITY.
+* C. L. LAWSON, JPL, 1974 DEC 10
+*
+* .. Parameters ..
+ INTEGER NOUT
+ PARAMETER (NOUT=6)
+* .. Scalar Arguments ..
+ INTEGER ICOMP, ITRUE
+* .. Scalars in Common ..
+ INTEGER ICASE, INCX, INCY, MODE, N
+ LOGICAL PASS
+* .. Local Scalars ..
+ INTEGER ID
+* .. Common blocks ..
+ COMMON /COMBLA/ICASE, N, INCX, INCY, MODE, PASS
+* .. Executable Statements ..
+ IF (ICOMP.EQ.ITRUE) GO TO 40
+*
+* HERE ICOMP IS NOT EQUAL TO ITRUE.
+*
+ IF ( .NOT. PASS) GO TO 20
+* PRINT FAIL MESSAGE AND HEADER.
+ PASS = .FALSE.
+ WRITE (NOUT,99999)
+ WRITE (NOUT,99998)
+ 20 ID = ICOMP - ITRUE
+ WRITE (NOUT,99997) ICASE, N, INCX, INCY, MODE, ICOMP, ITRUE, ID
+ 40 CONTINUE
+ RETURN
+*
+99999 FORMAT (' FAIL')
+99998 FORMAT (/' CASE N INCX INCY MODE ',
+ + ' COMP TRUE DIFFERENCE',
+ + /1X)
+99997 FORMAT (1X,I4,I3,3I5,2I36,I12)
+ END
diff --git a/blas/testing/zblat2.dat b/blas/testing/zblat2.dat
new file mode 100644
index 0000000..c922440
--- /dev/null
+++ b/blas/testing/zblat2.dat
@@ -0,0 +1,35 @@
+'zblat2.summ' NAME OF SUMMARY OUTPUT FILE
+6 UNIT NUMBER OF SUMMARY FILE
+'cbla2t.snap' NAME OF SNAPSHOT OUTPUT FILE
+-1 UNIT NUMBER OF SNAPSHOT FILE (NOT USED IF .LT. 0)
+F LOGICAL FLAG, T TO REWIND SNAPSHOT FILE AFTER EACH RECORD.
+F LOGICAL FLAG, T TO STOP ON FAILURES.
+T LOGICAL FLAG, T TO TEST ERROR EXITS.
+16.0 THRESHOLD VALUE OF TEST RATIO
+6 NUMBER OF VALUES OF N
+0 1 2 3 5 9 VALUES OF N
+4 NUMBER OF VALUES OF K
+0 1 2 4 VALUES OF K
+4 NUMBER OF VALUES OF INCX AND INCY
+1 2 -1 -2 VALUES OF INCX AND INCY
+3 NUMBER OF VALUES OF ALPHA
+(0.0,0.0) (1.0,0.0) (0.7,-0.9) VALUES OF ALPHA
+3 NUMBER OF VALUES OF BETA
+(0.0,0.0) (1.0,0.0) (1.3,-1.1) VALUES OF BETA
+ZGEMV T PUT F FOR NO TEST. SAME COLUMNS.
+ZGBMV T PUT F FOR NO TEST. SAME COLUMNS.
+ZHEMV T PUT F FOR NO TEST. SAME COLUMNS.
+ZHBMV T PUT F FOR NO TEST. SAME COLUMNS.
+ZHPMV T PUT F FOR NO TEST. SAME COLUMNS.
+ZTRMV T PUT F FOR NO TEST. SAME COLUMNS.
+ZTBMV T PUT F FOR NO TEST. SAME COLUMNS.
+ZTPMV T PUT F FOR NO TEST. SAME COLUMNS.
+ZTRSV T PUT F FOR NO TEST. SAME COLUMNS.
+ZTBSV T PUT F FOR NO TEST. SAME COLUMNS.
+ZTPSV T PUT F FOR NO TEST. SAME COLUMNS.
+ZGERC T PUT F FOR NO TEST. SAME COLUMNS.
+ZGERU T PUT F FOR NO TEST. SAME COLUMNS.
+ZHER T PUT F FOR NO TEST. SAME COLUMNS.
+ZHPR T PUT F FOR NO TEST. SAME COLUMNS.
+ZHER2 T PUT F FOR NO TEST. SAME COLUMNS.
+ZHPR2 T PUT F FOR NO TEST. SAME COLUMNS.
diff --git a/blas/testing/zblat2.f b/blas/testing/zblat2.f
new file mode 100644
index 0000000..53129a1
--- /dev/null
+++ b/blas/testing/zblat2.f
@@ -0,0 +1,3287 @@
+*> \brief \b ZBLAT2
+*
+* =========== DOCUMENTATION ===========
+*
+* Online html documentation available at
+* http://www.netlib.org/lapack/explore-html/
+*
+* Definition:
+* ===========
+*
+* PROGRAM ZBLAT2
+*
+*
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
+*>
+*> Test program for the COMPLEX*16 Level 2 Blas.
+*>
+*> The program must be driven by a short data file. The first 18 records
+*> of the file are read using list-directed input, the last 17 records
+*> are read using the format ( A6, L2 ). An annotated example of a data
+*> file can be obtained by deleting the first 3 characters from the
+*> following 35 lines:
+*> 'zblat2.out' NAME OF SUMMARY OUTPUT FILE
+*> 6 UNIT NUMBER OF SUMMARY FILE
+*> 'CBLA2T.SNAP' NAME OF SNAPSHOT OUTPUT FILE
+*> -1 UNIT NUMBER OF SNAPSHOT FILE (NOT USED IF .LT. 0)
+*> F LOGICAL FLAG, T TO REWIND SNAPSHOT FILE AFTER EACH RECORD.
+*> F LOGICAL FLAG, T TO STOP ON FAILURES.
+*> T LOGICAL FLAG, T TO TEST ERROR EXITS.
+*> 16.0 THRESHOLD VALUE OF TEST RATIO
+*> 6 NUMBER OF VALUES OF N
+*> 0 1 2 3 5 9 VALUES OF N
+*> 4 NUMBER OF VALUES OF K
+*> 0 1 2 4 VALUES OF K
+*> 4 NUMBER OF VALUES OF INCX AND INCY
+*> 1 2 -1 -2 VALUES OF INCX AND INCY
+*> 3 NUMBER OF VALUES OF ALPHA
+*> (0.0,0.0) (1.0,0.0) (0.7,-0.9) VALUES OF ALPHA
+*> 3 NUMBER OF VALUES OF BETA
+*> (0.0,0.0) (1.0,0.0) (1.3,-1.1) VALUES OF BETA
+*> ZGEMV T PUT F FOR NO TEST. SAME COLUMNS.
+*> ZGBMV T PUT F FOR NO TEST. SAME COLUMNS.
+*> ZHEMV T PUT F FOR NO TEST. SAME COLUMNS.
+*> ZHBMV T PUT F FOR NO TEST. SAME COLUMNS.
+*> ZHPMV T PUT F FOR NO TEST. SAME COLUMNS.
+*> ZTRMV T PUT F FOR NO TEST. SAME COLUMNS.
+*> ZTBMV T PUT F FOR NO TEST. SAME COLUMNS.
+*> ZTPMV T PUT F FOR NO TEST. SAME COLUMNS.
+*> ZTRSV T PUT F FOR NO TEST. SAME COLUMNS.
+*> ZTBSV T PUT F FOR NO TEST. SAME COLUMNS.
+*> ZTPSV T PUT F FOR NO TEST. SAME COLUMNS.
+*> ZGERC T PUT F FOR NO TEST. SAME COLUMNS.
+*> ZGERU T PUT F FOR NO TEST. SAME COLUMNS.
+*> ZHER T PUT F FOR NO TEST. SAME COLUMNS.
+*> ZHPR T PUT F FOR NO TEST. SAME COLUMNS.
+*> ZHER2 T PUT F FOR NO TEST. SAME COLUMNS.
+*> ZHPR2 T PUT F FOR NO TEST. SAME COLUMNS.
+*>
+*> Further Details
+*> ===============
+*>
+*> See:
+*>
+*> Dongarra J. J., Du Croz J. J., Hammarling S. and Hanson R. J..
+*> An extended set of Fortran Basic Linear Algebra Subprograms.
+*>
+*> Technical Memoranda Nos. 41 (revision 3) and 81, Mathematics
+*> and Computer Science Division, Argonne National Laboratory,
+*> 9700 South Cass Avenue, Argonne, Illinois 60439, US.
+*>
+*> Or
+*>
+*> NAG Technical Reports TR3/87 and TR4/87, Numerical Algorithms
+*> Group Ltd., NAG Central Office, 256 Banbury Road, Oxford
+*> OX2 7DE, UK, and Numerical Algorithms Group Inc., 1101 31st
+*> Street, Suite 100, Downers Grove, Illinois 60515-1263, USA.
+*>
+*>
+*> -- Written on 10-August-1987.
+*> Richard Hanson, Sandia National Labs.
+*> Jeremy Du Croz, NAG Central Office.
+*>
+*> 10-9-00: Change STATUS='NEW' to 'UNKNOWN' so that the testers
+*> can be run multiple times without deleting generated
+*> output files (susan)
+*> \endverbatim
+*
+* Authors:
+* ========
+*
+*> \author Univ. of Tennessee
+*> \author Univ. of California Berkeley
+*> \author Univ. of Colorado Denver
+*> \author NAG Ltd.
+*
+*> \date April 2012
+*
+*> \ingroup complex16_blas_testing
+*
+* =====================================================================
+ PROGRAM ZBLAT2
+*
+* -- Reference BLAS test routine (version 3.4.1) --
+* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
+* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+* April 2012
+*
+* =====================================================================
+*
+* .. Parameters ..
+ INTEGER NIN
+ PARAMETER ( NIN = 5 )
+ INTEGER NSUBS
+ PARAMETER ( NSUBS = 17 )
+ COMPLEX*16 ZERO, ONE
+ PARAMETER ( ZERO = ( 0.0D0, 0.0D0 ),
+ $ ONE = ( 1.0D0, 0.0D0 ) )
+ DOUBLE PRECISION RZERO
+ PARAMETER ( RZERO = 0.0D0 )
+ INTEGER NMAX, INCMAX
+ PARAMETER ( NMAX = 65, INCMAX = 2 )
+ INTEGER NINMAX, NIDMAX, NKBMAX, NALMAX, NBEMAX
+ PARAMETER ( NINMAX = 7, NIDMAX = 9, NKBMAX = 7,
+ $ NALMAX = 7, NBEMAX = 7 )
+* .. Local Scalars ..
+ DOUBLE PRECISION EPS, ERR, THRESH
+ INTEGER I, ISNUM, J, N, NALF, NBET, NIDIM, NINC, NKB,
+ $ NOUT, NTRA
+ LOGICAL FATAL, LTESTT, REWI, SAME, SFATAL, TRACE,
+ $ TSTERR
+ CHARACTER*1 TRANS
+ CHARACTER*6 SNAMET
+ CHARACTER*32 SNAPS, SUMMRY
+* .. Local Arrays ..
+ COMPLEX*16 A( NMAX, NMAX ), AA( NMAX*NMAX ),
+ $ ALF( NALMAX ), AS( NMAX*NMAX ), BET( NBEMAX ),
+ $ X( NMAX ), XS( NMAX*INCMAX ),
+ $ XX( NMAX*INCMAX ), Y( NMAX ),
+ $ YS( NMAX*INCMAX ), YT( NMAX ),
+ $ YY( NMAX*INCMAX ), Z( 2*NMAX )
+ DOUBLE PRECISION G( NMAX )
+ INTEGER IDIM( NIDMAX ), INC( NINMAX ), KB( NKBMAX )
+ LOGICAL LTEST( NSUBS )
+ CHARACTER*6 SNAMES( NSUBS )
+* .. External Functions ..
+ DOUBLE PRECISION DDIFF
+ LOGICAL LZE
+ EXTERNAL DDIFF, LZE
+* .. External Subroutines ..
+ EXTERNAL ZCHK1, ZCHK2, ZCHK3, ZCHK4, ZCHK5, ZCHK6,
+ $ ZCHKE, ZMVCH
+* .. Intrinsic Functions ..
+ INTRINSIC ABS, MAX, MIN
+* .. Scalars in Common ..
+ INTEGER INFOT, NOUTC
+ LOGICAL LERR, OK
+ CHARACTER*6 SRNAMT
+* .. Common blocks ..
+ COMMON /INFOC/INFOT, NOUTC, OK, LERR
+ COMMON /SRNAMC/SRNAMT
+* .. Data statements ..
+ DATA SNAMES/'ZGEMV ', 'ZGBMV ', 'ZHEMV ', 'ZHBMV ',
+ $ 'ZHPMV ', 'ZTRMV ', 'ZTBMV ', 'ZTPMV ',
+ $ 'ZTRSV ', 'ZTBSV ', 'ZTPSV ', 'ZGERC ',
+ $ 'ZGERU ', 'ZHER ', 'ZHPR ', 'ZHER2 ',
+ $ 'ZHPR2 '/
+* .. Executable Statements ..
+*
+* Read name and unit number for summary output file and open file.
+*
+ READ( NIN, FMT = * )SUMMRY
+ READ( NIN, FMT = * )NOUT
+ OPEN( NOUT, FILE = SUMMRY, STATUS = 'UNKNOWN' )
+ NOUTC = NOUT
+*
+* Read name and unit number for snapshot output file and open file.
+*
+ READ( NIN, FMT = * )SNAPS
+ READ( NIN, FMT = * )NTRA
+ TRACE = NTRA.GE.0
+ IF( TRACE )THEN
+ OPEN( NTRA, FILE = SNAPS, STATUS = 'UNKNOWN' )
+ END IF
+* Read the flag that directs rewinding of the snapshot file.
+ READ( NIN, FMT = * )REWI
+ REWI = REWI.AND.TRACE
+* Read the flag that directs stopping on any failure.
+ READ( NIN, FMT = * )SFATAL
+* Read the flag that indicates whether error exits are to be tested.
+ READ( NIN, FMT = * )TSTERR
+* Read the threshold value of the test ratio
+ READ( NIN, FMT = * )THRESH
+*
+* Read and check the parameter values for the tests.
+*
+* Values of N
+ READ( NIN, FMT = * )NIDIM
+ IF( NIDIM.LT.1.OR.NIDIM.GT.NIDMAX )THEN
+ WRITE( NOUT, FMT = 9997 )'N', NIDMAX
+ GO TO 230
+ END IF
+ READ( NIN, FMT = * )( IDIM( I ), I = 1, NIDIM )
+ DO 10 I = 1, NIDIM
+ IF( IDIM( I ).LT.0.OR.IDIM( I ).GT.NMAX )THEN
+ WRITE( NOUT, FMT = 9996 )NMAX
+ GO TO 230
+ END IF
+ 10 CONTINUE
+* Values of K
+ READ( NIN, FMT = * )NKB
+ IF( NKB.LT.1.OR.NKB.GT.NKBMAX )THEN
+ WRITE( NOUT, FMT = 9997 )'K', NKBMAX
+ GO TO 230
+ END IF
+ READ( NIN, FMT = * )( KB( I ), I = 1, NKB )
+ DO 20 I = 1, NKB
+ IF( KB( I ).LT.0 )THEN
+ WRITE( NOUT, FMT = 9995 )
+ GO TO 230
+ END IF
+ 20 CONTINUE
+* Values of INCX and INCY
+ READ( NIN, FMT = * )NINC
+ IF( NINC.LT.1.OR.NINC.GT.NINMAX )THEN
+ WRITE( NOUT, FMT = 9997 )'INCX AND INCY', NINMAX
+ GO TO 230
+ END IF
+ READ( NIN, FMT = * )( INC( I ), I = 1, NINC )
+ DO 30 I = 1, NINC
+ IF( INC( I ).EQ.0.OR.ABS( INC( I ) ).GT.INCMAX )THEN
+ WRITE( NOUT, FMT = 9994 )INCMAX
+ GO TO 230
+ END IF
+ 30 CONTINUE
+* Values of ALPHA
+ READ( NIN, FMT = * )NALF
+ IF( NALF.LT.1.OR.NALF.GT.NALMAX )THEN
+ WRITE( NOUT, FMT = 9997 )'ALPHA', NALMAX
+ GO TO 230
+ END IF
+ READ( NIN, FMT = * )( ALF( I ), I = 1, NALF )
+* Values of BETA
+ READ( NIN, FMT = * )NBET
+ IF( NBET.LT.1.OR.NBET.GT.NBEMAX )THEN
+ WRITE( NOUT, FMT = 9997 )'BETA', NBEMAX
+ GO TO 230
+ END IF
+ READ( NIN, FMT = * )( BET( I ), I = 1, NBET )
+*
+* Report values of parameters.
+*
+ WRITE( NOUT, FMT = 9993 )
+ WRITE( NOUT, FMT = 9992 )( IDIM( I ), I = 1, NIDIM )
+ WRITE( NOUT, FMT = 9991 )( KB( I ), I = 1, NKB )
+ WRITE( NOUT, FMT = 9990 )( INC( I ), I = 1, NINC )
+ WRITE( NOUT, FMT = 9989 )( ALF( I ), I = 1, NALF )
+ WRITE( NOUT, FMT = 9988 )( BET( I ), I = 1, NBET )
+ IF( .NOT.TSTERR )THEN
+ WRITE( NOUT, FMT = * )
+ WRITE( NOUT, FMT = 9980 )
+ END IF
+ WRITE( NOUT, FMT = * )
+ WRITE( NOUT, FMT = 9999 )THRESH
+ WRITE( NOUT, FMT = * )
+*
+* Read names of subroutines and flags which indicate
+* whether they are to be tested.
+*
+ DO 40 I = 1, NSUBS
+ LTEST( I ) = .FALSE.
+ 40 CONTINUE
+ 50 READ( NIN, FMT = 9984, END = 80 )SNAMET, LTESTT
+ DO 60 I = 1, NSUBS
+ IF( SNAMET.EQ.SNAMES( I ) )
+ $ GO TO 70
+ 60 CONTINUE
+ WRITE( NOUT, FMT = 9986 )SNAMET
+ STOP
+ 70 LTEST( I ) = LTESTT
+ GO TO 50
+*
+ 80 CONTINUE
+ CLOSE ( NIN )
+*
+* Compute EPS (the machine precision).
+*
+ EPS = EPSILON(RZERO)
+ WRITE( NOUT, FMT = 9998 )EPS
+*
+* Check the reliability of ZMVCH using exact data.
+*
+ N = MIN( 32, NMAX )
+ DO 120 J = 1, N
+ DO 110 I = 1, N
+ A( I, J ) = MAX( I - J + 1, 0 )
+ 110 CONTINUE
+ X( J ) = J
+ Y( J ) = ZERO
+ 120 CONTINUE
+ DO 130 J = 1, N
+ YY( J ) = J*( ( J + 1 )*J )/2 - ( ( J + 1 )*J*( J - 1 ) )/3
+ 130 CONTINUE
+* YY holds the exact result. On exit from ZMVCH YT holds
+* the result computed by ZMVCH.
+ TRANS = 'N'
+ CALL ZMVCH( TRANS, N, N, ONE, A, NMAX, X, 1, ZERO, Y, 1, YT, G,
+ $ YY, EPS, ERR, FATAL, NOUT, .TRUE. )
+ SAME = LZE( YY, YT, N )
+ IF( .NOT.SAME.OR.ERR.NE.RZERO )THEN
+ WRITE( NOUT, FMT = 9985 )TRANS, SAME, ERR
+ STOP
+ END IF
+ TRANS = 'T'
+ CALL ZMVCH( TRANS, N, N, ONE, A, NMAX, X, -1, ZERO, Y, -1, YT, G,
+ $ YY, EPS, ERR, FATAL, NOUT, .TRUE. )
+ SAME = LZE( YY, YT, N )
+ IF( .NOT.SAME.OR.ERR.NE.RZERO )THEN
+ WRITE( NOUT, FMT = 9985 )TRANS, SAME, ERR
+ STOP
+ END IF
+*
+* Test each subroutine in turn.
+*
+ DO 210 ISNUM = 1, NSUBS
+ WRITE( NOUT, FMT = * )
+ IF( .NOT.LTEST( ISNUM ) )THEN
+* Subprogram is not to be tested.
+ WRITE( NOUT, FMT = 9983 )SNAMES( ISNUM )
+ ELSE
+ SRNAMT = SNAMES( ISNUM )
+* Test error exits.
+ IF( TSTERR )THEN
+ CALL ZCHKE( ISNUM, SNAMES( ISNUM ), NOUT )
+ WRITE( NOUT, FMT = * )
+ END IF
+* Test computations.
+ INFOT = 0
+ OK = .TRUE.
+ FATAL = .FALSE.
+ GO TO ( 140, 140, 150, 150, 150, 160, 160,
+ $ 160, 160, 160, 160, 170, 170, 180,
+ $ 180, 190, 190 )ISNUM
+* Test ZGEMV, 01, and ZGBMV, 02.
+ 140 CALL ZCHK1( SNAMES( ISNUM ), EPS, THRESH, NOUT, NTRA, TRACE,
+ $ REWI, FATAL, NIDIM, IDIM, NKB, KB, NALF, ALF,
+ $ NBET, BET, NINC, INC, NMAX, INCMAX, A, AA, AS,
+ $ X, XX, XS, Y, YY, YS, YT, G )
+ GO TO 200
+* Test ZHEMV, 03, ZHBMV, 04, and ZHPMV, 05.
+ 150 CALL ZCHK2( SNAMES( ISNUM ), EPS, THRESH, NOUT, NTRA, TRACE,
+ $ REWI, FATAL, NIDIM, IDIM, NKB, KB, NALF, ALF,
+ $ NBET, BET, NINC, INC, NMAX, INCMAX, A, AA, AS,
+ $ X, XX, XS, Y, YY, YS, YT, G )
+ GO TO 200
+* Test ZTRMV, 06, ZTBMV, 07, ZTPMV, 08,
+* ZTRSV, 09, ZTBSV, 10, and ZTPSV, 11.
+ 160 CALL ZCHK3( SNAMES( ISNUM ), EPS, THRESH, NOUT, NTRA, TRACE,
+ $ REWI, FATAL, NIDIM, IDIM, NKB, KB, NINC, INC,
+ $ NMAX, INCMAX, A, AA, AS, Y, YY, YS, YT, G, Z )
+ GO TO 200
+* Test ZGERC, 12, ZGERU, 13.
+ 170 CALL ZCHK4( SNAMES( ISNUM ), EPS, THRESH, NOUT, NTRA, TRACE,
+ $ REWI, FATAL, NIDIM, IDIM, NALF, ALF, NINC, INC,
+ $ NMAX, INCMAX, A, AA, AS, X, XX, XS, Y, YY, YS,
+ $ YT, G, Z )
+ GO TO 200
+* Test ZHER, 14, and ZHPR, 15.
+ 180 CALL ZCHK5( SNAMES( ISNUM ), EPS, THRESH, NOUT, NTRA, TRACE,
+ $ REWI, FATAL, NIDIM, IDIM, NALF, ALF, NINC, INC,
+ $ NMAX, INCMAX, A, AA, AS, X, XX, XS, Y, YY, YS,
+ $ YT, G, Z )
+ GO TO 200
+* Test ZHER2, 16, and ZHPR2, 17.
+ 190 CALL ZCHK6( SNAMES( ISNUM ), EPS, THRESH, NOUT, NTRA, TRACE,
+ $ REWI, FATAL, NIDIM, IDIM, NALF, ALF, NINC, INC,
+ $ NMAX, INCMAX, A, AA, AS, X, XX, XS, Y, YY, YS,
+ $ YT, G, Z )
+*
+ 200 IF( FATAL.AND.SFATAL )
+ $ GO TO 220
+ END IF
+ 210 CONTINUE
+ WRITE( NOUT, FMT = 9982 )
+ GO TO 240
+*
+ 220 CONTINUE
+ WRITE( NOUT, FMT = 9981 )
+ GO TO 240
+*
+ 230 CONTINUE
+ WRITE( NOUT, FMT = 9987 )
+*
+ 240 CONTINUE
+ IF( TRACE )
+ $ CLOSE ( NTRA )
+ CLOSE ( NOUT )
+ STOP
+*
+ 9999 FORMAT( ' ROUTINES PASS COMPUTATIONAL TESTS IF TEST RATIO IS LES',
+ $ 'S THAN', F8.2 )
+ 9998 FORMAT( ' RELATIVE MACHINE PRECISION IS TAKEN TO BE', 1P, D9.1 )
+ 9997 FORMAT( ' NUMBER OF VALUES OF ', A, ' IS LESS THAN 1 OR GREATER ',
+ $ 'THAN ', I2 )
+ 9996 FORMAT( ' VALUE OF N IS LESS THAN 0 OR GREATER THAN ', I2 )
+ 9995 FORMAT( ' VALUE OF K IS LESS THAN 0' )
+ 9994 FORMAT( ' ABSOLUTE VALUE OF INCX OR INCY IS 0 OR GREATER THAN ',
+ $ I2 )
+ 9993 FORMAT( ' TESTS OF THE COMPLEX*16 LEVEL 2 BLAS', //' THE F',
+ $ 'OLLOWING PARAMETER VALUES WILL BE USED:' )
+ 9992 FORMAT( ' FOR N ', 9I6 )
+ 9991 FORMAT( ' FOR K ', 7I6 )
+ 9990 FORMAT( ' FOR INCX AND INCY ', 7I6 )
+ 9989 FORMAT( ' FOR ALPHA ',
+ $ 7( '(', F4.1, ',', F4.1, ') ', : ) )
+ 9988 FORMAT( ' FOR BETA ',
+ $ 7( '(', F4.1, ',', F4.1, ') ', : ) )
+ 9987 FORMAT( ' AMEND DATA FILE OR INCREASE ARRAY SIZES IN PROGRAM',
+ $ /' ******* TESTS ABANDONED *******' )
+ 9986 FORMAT( ' SUBPROGRAM NAME ', A6, ' NOT RECOGNIZED', /' ******* T',
+ $ 'ESTS ABANDONED *******' )
+ 9985 FORMAT( ' ERROR IN ZMVCH - IN-LINE DOT PRODUCTS ARE BEING EVALU',
+ $ 'ATED WRONGLY.', /' ZMVCH WAS CALLED WITH TRANS = ', A1,
+ $ ' AND RETURNED SAME = ', L1, ' AND ERR = ', F12.3, '.', /
+ $ ' THIS MAY BE DUE TO FAULTS IN THE ARITHMETIC OR THE COMPILER.'
+ $ , /' ******* TESTS ABANDONED *******' )
+ 9984 FORMAT( A6, L2 )
+ 9983 FORMAT( 1X, A6, ' WAS NOT TESTED' )
+ 9982 FORMAT( /' END OF TESTS' )
+ 9981 FORMAT( /' ******* FATAL ERROR - TESTS ABANDONED *******' )
+ 9980 FORMAT( ' ERROR-EXITS WILL NOT BE TESTED' )
+*
+* End of ZBLAT2.
+*
+ END
+ SUBROUTINE ZCHK1( SNAME, EPS, THRESH, NOUT, NTRA, TRACE, REWI,
+ $ FATAL, NIDIM, IDIM, NKB, KB, NALF, ALF, NBET,
+ $ BET, NINC, INC, NMAX, INCMAX, A, AA, AS, X, XX,
+ $ XS, Y, YY, YS, YT, G )
+*
+* Tests ZGEMV and ZGBMV.
+*
+* Auxiliary routine for test program for Level 2 Blas.
+*
+* -- Written on 10-August-1987.
+* Richard Hanson, Sandia National Labs.
+* Jeremy Du Croz, NAG Central Office.
+*
+* .. Parameters ..
+ COMPLEX*16 ZERO, HALF
+ PARAMETER ( ZERO = ( 0.0D0, 0.0D0 ),
+ $ HALF = ( 0.5D0, 0.0D0 ) )
+ DOUBLE PRECISION RZERO
+ PARAMETER ( RZERO = 0.0D0 )
+* .. Scalar Arguments ..
+ DOUBLE PRECISION EPS, THRESH
+ INTEGER INCMAX, NALF, NBET, NIDIM, NINC, NKB, NMAX,
+ $ NOUT, NTRA
+ LOGICAL FATAL, REWI, TRACE
+ CHARACTER*6 SNAME
+* .. Array Arguments ..
+ COMPLEX*16 A( NMAX, NMAX ), AA( NMAX*NMAX ), ALF( NALF ),
+ $ AS( NMAX*NMAX ), BET( NBET ), X( NMAX ),
+ $ XS( NMAX*INCMAX ), XX( NMAX*INCMAX ),
+ $ Y( NMAX ), YS( NMAX*INCMAX ), YT( NMAX ),
+ $ YY( NMAX*INCMAX )
+ DOUBLE PRECISION G( NMAX )
+ INTEGER IDIM( NIDIM ), INC( NINC ), KB( NKB )
+* .. Local Scalars ..
+ COMPLEX*16 ALPHA, ALS, BETA, BLS, TRANSL
+ DOUBLE PRECISION ERR, ERRMAX
+ INTEGER I, IA, IB, IC, IKU, IM, IN, INCX, INCXS, INCY,
+ $ INCYS, IX, IY, KL, KLS, KU, KUS, LAA, LDA,
+ $ LDAS, LX, LY, M, ML, MS, N, NARGS, NC, ND, NK,
+ $ NL, NS
+ LOGICAL BANDED, FULL, NULL, RESET, SAME, TRAN
+ CHARACTER*1 TRANS, TRANSS
+ CHARACTER*3 ICH
+* .. Local Arrays ..
+ LOGICAL ISAME( 13 )
+* .. External Functions ..
+ LOGICAL LZE, LZERES
+ EXTERNAL LZE, LZERES
+* .. External Subroutines ..
+ EXTERNAL ZGBMV, ZGEMV, ZMAKE, ZMVCH
+* .. Intrinsic Functions ..
+ INTRINSIC ABS, MAX, MIN
+* .. Scalars in Common ..
+ INTEGER INFOT, NOUTC
+ LOGICAL LERR, OK
+* .. Common blocks ..
+ COMMON /INFOC/INFOT, NOUTC, OK, LERR
+* .. Data statements ..
+ DATA ICH/'NTC'/
+* .. Executable Statements ..
+ FULL = SNAME( 3: 3 ).EQ.'E'
+ BANDED = SNAME( 3: 3 ).EQ.'B'
+* Define the number of arguments.
+ IF( FULL )THEN
+ NARGS = 11
+ ELSE IF( BANDED )THEN
+ NARGS = 13
+ END IF
+*
+ NC = 0
+ RESET = .TRUE.
+ ERRMAX = RZERO
+*
+ DO 120 IN = 1, NIDIM
+ N = IDIM( IN )
+ ND = N/2 + 1
+*
+ DO 110 IM = 1, 2
+ IF( IM.EQ.1 )
+ $ M = MAX( N - ND, 0 )
+ IF( IM.EQ.2 )
+ $ M = MIN( N + ND, NMAX )
+*
+ IF( BANDED )THEN
+ NK = NKB
+ ELSE
+ NK = 1
+ END IF
+ DO 100 IKU = 1, NK
+ IF( BANDED )THEN
+ KU = KB( IKU )
+ KL = MAX( KU - 1, 0 )
+ ELSE
+ KU = N - 1
+ KL = M - 1
+ END IF
+* Set LDA to 1 more than minimum value if room.
+ IF( BANDED )THEN
+ LDA = KL + KU + 1
+ ELSE
+ LDA = M
+ END IF
+ IF( LDA.LT.NMAX )
+ $ LDA = LDA + 1
+* Skip tests if not enough room.
+ IF( LDA.GT.NMAX )
+ $ GO TO 100
+ LAA = LDA*N
+ NULL = N.LE.0.OR.M.LE.0
+*
+* Generate the matrix A.
+*
+ TRANSL = ZERO
+ CALL ZMAKE( SNAME( 2: 3 ), ' ', ' ', M, N, A, NMAX, AA,
+ $ LDA, KL, KU, RESET, TRANSL )
+*
+ DO 90 IC = 1, 3
+ TRANS = ICH( IC: IC )
+ TRAN = TRANS.EQ.'T'.OR.TRANS.EQ.'C'
+*
+ IF( TRAN )THEN
+ ML = N
+ NL = M
+ ELSE
+ ML = M
+ NL = N
+ END IF
+*
+ DO 80 IX = 1, NINC
+ INCX = INC( IX )
+ LX = ABS( INCX )*NL
+*
+* Generate the vector X.
+*
+ TRANSL = HALF
+ CALL ZMAKE( 'GE', ' ', ' ', 1, NL, X, 1, XX,
+ $ ABS( INCX ), 0, NL - 1, RESET, TRANSL )
+ IF( NL.GT.1 )THEN
+ X( NL/2 ) = ZERO
+ XX( 1 + ABS( INCX )*( NL/2 - 1 ) ) = ZERO
+ END IF
+*
+ DO 70 IY = 1, NINC
+ INCY = INC( IY )
+ LY = ABS( INCY )*ML
+*
+ DO 60 IA = 1, NALF
+ ALPHA = ALF( IA )
+*
+ DO 50 IB = 1, NBET
+ BETA = BET( IB )
+*
+* Generate the vector Y.
+*
+ TRANSL = ZERO
+ CALL ZMAKE( 'GE', ' ', ' ', 1, ML, Y, 1,
+ $ YY, ABS( INCY ), 0, ML - 1,
+ $ RESET, TRANSL )
+*
+ NC = NC + 1
+*
+* Save every datum before calling the
+* subroutine.
+*
+ TRANSS = TRANS
+ MS = M
+ NS = N
+ KLS = KL
+ KUS = KU
+ ALS = ALPHA
+ DO 10 I = 1, LAA
+ AS( I ) = AA( I )
+ 10 CONTINUE
+ LDAS = LDA
+ DO 20 I = 1, LX
+ XS( I ) = XX( I )
+ 20 CONTINUE
+ INCXS = INCX
+ BLS = BETA
+ DO 30 I = 1, LY
+ YS( I ) = YY( I )
+ 30 CONTINUE
+ INCYS = INCY
+*
+* Call the subroutine.
+*
+ IF( FULL )THEN
+ IF( TRACE )
+ $ WRITE( NTRA, FMT = 9994 )NC, SNAME,
+ $ TRANS, M, N, ALPHA, LDA, INCX, BETA,
+ $ INCY
+ IF( REWI )
+ $ REWIND NTRA
+ CALL ZGEMV( TRANS, M, N, ALPHA, AA,
+ $ LDA, XX, INCX, BETA, YY,
+ $ INCY )
+ ELSE IF( BANDED )THEN
+ IF( TRACE )
+ $ WRITE( NTRA, FMT = 9995 )NC, SNAME,
+ $ TRANS, M, N, KL, KU, ALPHA, LDA,
+ $ INCX, BETA, INCY
+ IF( REWI )
+ $ REWIND NTRA
+ CALL ZGBMV( TRANS, M, N, KL, KU, ALPHA,
+ $ AA, LDA, XX, INCX, BETA,
+ $ YY, INCY )
+ END IF
+*
+* Check if error-exit was taken incorrectly.
+*
+ IF( .NOT.OK )THEN
+ WRITE( NOUT, FMT = 9993 )
+ FATAL = .TRUE.
+ GO TO 130
+ END IF
+*
+* See what data changed inside subroutines.
+*
+ ISAME( 1 ) = TRANS.EQ.TRANSS
+ ISAME( 2 ) = MS.EQ.M
+ ISAME( 3 ) = NS.EQ.N
+ IF( FULL )THEN
+ ISAME( 4 ) = ALS.EQ.ALPHA
+ ISAME( 5 ) = LZE( AS, AA, LAA )
+ ISAME( 6 ) = LDAS.EQ.LDA
+ ISAME( 7 ) = LZE( XS, XX, LX )
+ ISAME( 8 ) = INCXS.EQ.INCX
+ ISAME( 9 ) = BLS.EQ.BETA
+ IF( NULL )THEN
+ ISAME( 10 ) = LZE( YS, YY, LY )
+ ELSE
+ ISAME( 10 ) = LZERES( 'GE', ' ', 1,
+ $ ML, YS, YY,
+ $ ABS( INCY ) )
+ END IF
+ ISAME( 11 ) = INCYS.EQ.INCY
+ ELSE IF( BANDED )THEN
+ ISAME( 4 ) = KLS.EQ.KL
+ ISAME( 5 ) = KUS.EQ.KU
+ ISAME( 6 ) = ALS.EQ.ALPHA
+ ISAME( 7 ) = LZE( AS, AA, LAA )
+ ISAME( 8 ) = LDAS.EQ.LDA
+ ISAME( 9 ) = LZE( XS, XX, LX )
+ ISAME( 10 ) = INCXS.EQ.INCX
+ ISAME( 11 ) = BLS.EQ.BETA
+ IF( NULL )THEN
+ ISAME( 12 ) = LZE( YS, YY, LY )
+ ELSE
+ ISAME( 12 ) = LZERES( 'GE', ' ', 1,
+ $ ML, YS, YY,
+ $ ABS( INCY ) )
+ END IF
+ ISAME( 13 ) = INCYS.EQ.INCY
+ END IF
+*
+* If data was incorrectly changed, report
+* and return.
+*
+ SAME = .TRUE.
+ DO 40 I = 1, NARGS
+ SAME = SAME.AND.ISAME( I )
+ IF( .NOT.ISAME( I ) )
+ $ WRITE( NOUT, FMT = 9998 )I
+ 40 CONTINUE
+ IF( .NOT.SAME )THEN
+ FATAL = .TRUE.
+ GO TO 130
+ END IF
+*
+ IF( .NOT.NULL )THEN
+*
+* Check the result.
+*
+ CALL ZMVCH( TRANS, M, N, ALPHA, A,
+ $ NMAX, X, INCX, BETA, Y,
+ $ INCY, YT, G, YY, EPS, ERR,
+ $ FATAL, NOUT, .TRUE. )
+ ERRMAX = MAX( ERRMAX, ERR )
+* If got really bad answer, report and
+* return.
+ IF( FATAL )
+ $ GO TO 130
+ ELSE
+* Avoid repeating tests with M.le.0 or
+* N.le.0.
+ GO TO 110
+ END IF
+*
+ 50 CONTINUE
+*
+ 60 CONTINUE
+*
+ 70 CONTINUE
+*
+ 80 CONTINUE
+*
+ 90 CONTINUE
+*
+ 100 CONTINUE
+*
+ 110 CONTINUE
+*
+ 120 CONTINUE
+*
+* Report result.
+*
+ IF( ERRMAX.LT.THRESH )THEN
+ WRITE( NOUT, FMT = 9999 )SNAME, NC
+ ELSE
+ WRITE( NOUT, FMT = 9997 )SNAME, NC, ERRMAX
+ END IF
+ GO TO 140
+*
+ 130 CONTINUE
+ WRITE( NOUT, FMT = 9996 )SNAME
+ IF( FULL )THEN
+ WRITE( NOUT, FMT = 9994 )NC, SNAME, TRANS, M, N, ALPHA, LDA,
+ $ INCX, BETA, INCY
+ ELSE IF( BANDED )THEN
+ WRITE( NOUT, FMT = 9995 )NC, SNAME, TRANS, M, N, KL, KU,
+ $ ALPHA, LDA, INCX, BETA, INCY
+ END IF
+*
+ 140 CONTINUE
+ RETURN
+*
+ 9999 FORMAT( ' ', A6, ' PASSED THE COMPUTATIONAL TESTS (', I6, ' CALL',
+ $ 'S)' )
+ 9998 FORMAT( ' ******* FATAL ERROR - PARAMETER NUMBER ', I2, ' WAS CH',
+ $ 'ANGED INCORRECTLY *******' )
+ 9997 FORMAT( ' ', A6, ' COMPLETED THE COMPUTATIONAL TESTS (', I6, ' C',
+ $ 'ALLS)', /' ******* BUT WITH MAXIMUM TEST RATIO', F8.2,
+ $ ' - SUSPECT *******' )
+ 9996 FORMAT( ' ******* ', A6, ' FAILED ON CALL NUMBER:' )
+ 9995 FORMAT( 1X, I6, ': ', A6, '(''', A1, ''',', 4( I3, ',' ), '(',
+ $ F4.1, ',', F4.1, '), A,', I3, ', X,', I2, ',(', F4.1, ',',
+ $ F4.1, '), Y,', I2, ') .' )
+ 9994 FORMAT( 1X, I6, ': ', A6, '(''', A1, ''',', 2( I3, ',' ), '(',
+ $ F4.1, ',', F4.1, '), A,', I3, ', X,', I2, ',(', F4.1, ',',
+ $ F4.1, '), Y,', I2, ') .' )
+ 9993 FORMAT( ' ******* FATAL ERROR - ERROR-EXIT TAKEN ON VALID CALL *',
+ $ '******' )
+*
+* End of ZCHK1.
+*
+ END
+ SUBROUTINE ZCHK2( SNAME, EPS, THRESH, NOUT, NTRA, TRACE, REWI,
+ $ FATAL, NIDIM, IDIM, NKB, KB, NALF, ALF, NBET,
+ $ BET, NINC, INC, NMAX, INCMAX, A, AA, AS, X, XX,
+ $ XS, Y, YY, YS, YT, G )
+*
+* Tests ZHEMV, ZHBMV and ZHPMV.
+*
+* Auxiliary routine for test program for Level 2 Blas.
+*
+* -- Written on 10-August-1987.
+* Richard Hanson, Sandia National Labs.
+* Jeremy Du Croz, NAG Central Office.
+*
+* .. Parameters ..
+ COMPLEX*16 ZERO, HALF
+ PARAMETER ( ZERO = ( 0.0D0, 0.0D0 ),
+ $ HALF = ( 0.5D0, 0.0D0 ) )
+ DOUBLE PRECISION RZERO
+ PARAMETER ( RZERO = 0.0D0 )
+* .. Scalar Arguments ..
+ DOUBLE PRECISION EPS, THRESH
+ INTEGER INCMAX, NALF, NBET, NIDIM, NINC, NKB, NMAX,
+ $ NOUT, NTRA
+ LOGICAL FATAL, REWI, TRACE
+ CHARACTER*6 SNAME
+* .. Array Arguments ..
+ COMPLEX*16 A( NMAX, NMAX ), AA( NMAX*NMAX ), ALF( NALF ),
+ $ AS( NMAX*NMAX ), BET( NBET ), X( NMAX ),
+ $ XS( NMAX*INCMAX ), XX( NMAX*INCMAX ),
+ $ Y( NMAX ), YS( NMAX*INCMAX ), YT( NMAX ),
+ $ YY( NMAX*INCMAX )
+ DOUBLE PRECISION G( NMAX )
+ INTEGER IDIM( NIDIM ), INC( NINC ), KB( NKB )
+* .. Local Scalars ..
+ COMPLEX*16 ALPHA, ALS, BETA, BLS, TRANSL
+ DOUBLE PRECISION ERR, ERRMAX
+ INTEGER I, IA, IB, IC, IK, IN, INCX, INCXS, INCY,
+ $ INCYS, IX, IY, K, KS, LAA, LDA, LDAS, LX, LY,
+ $ N, NARGS, NC, NK, NS
+ LOGICAL BANDED, FULL, NULL, PACKED, RESET, SAME
+ CHARACTER*1 UPLO, UPLOS
+ CHARACTER*2 ICH
+* .. Local Arrays ..
+ LOGICAL ISAME( 13 )
+* .. External Functions ..
+ LOGICAL LZE, LZERES
+ EXTERNAL LZE, LZERES
+* .. External Subroutines ..
+ EXTERNAL ZHBMV, ZHEMV, ZHPMV, ZMAKE, ZMVCH
+* .. Intrinsic Functions ..
+ INTRINSIC ABS, MAX
+* .. Scalars in Common ..
+ INTEGER INFOT, NOUTC
+ LOGICAL LERR, OK
+* .. Common blocks ..
+ COMMON /INFOC/INFOT, NOUTC, OK, LERR
+* .. Data statements ..
+ DATA ICH/'UL'/
+* .. Executable Statements ..
+ FULL = SNAME( 3: 3 ).EQ.'E'
+ BANDED = SNAME( 3: 3 ).EQ.'B'
+ PACKED = SNAME( 3: 3 ).EQ.'P'
+* Define the number of arguments.
+ IF( FULL )THEN
+ NARGS = 10
+ ELSE IF( BANDED )THEN
+ NARGS = 11
+ ELSE IF( PACKED )THEN
+ NARGS = 9
+ END IF
+*
+ NC = 0
+ RESET = .TRUE.
+ ERRMAX = RZERO
+*
+ DO 110 IN = 1, NIDIM
+ N = IDIM( IN )
+*
+ IF( BANDED )THEN
+ NK = NKB
+ ELSE
+ NK = 1
+ END IF
+ DO 100 IK = 1, NK
+ IF( BANDED )THEN
+ K = KB( IK )
+ ELSE
+ K = N - 1
+ END IF
+* Set LDA to 1 more than minimum value if room.
+ IF( BANDED )THEN
+ LDA = K + 1
+ ELSE
+ LDA = N
+ END IF
+ IF( LDA.LT.NMAX )
+ $ LDA = LDA + 1
+* Skip tests if not enough room.
+ IF( LDA.GT.NMAX )
+ $ GO TO 100
+ IF( PACKED )THEN
+ LAA = ( N*( N + 1 ) )/2
+ ELSE
+ LAA = LDA*N
+ END IF
+ NULL = N.LE.0
+*
+ DO 90 IC = 1, 2
+ UPLO = ICH( IC: IC )
+*
+* Generate the matrix A.
+*
+ TRANSL = ZERO
+ CALL ZMAKE( SNAME( 2: 3 ), UPLO, ' ', N, N, A, NMAX, AA,
+ $ LDA, K, K, RESET, TRANSL )
+*
+ DO 80 IX = 1, NINC
+ INCX = INC( IX )
+ LX = ABS( INCX )*N
+*
+* Generate the vector X.
+*
+ TRANSL = HALF
+ CALL ZMAKE( 'GE', ' ', ' ', 1, N, X, 1, XX,
+ $ ABS( INCX ), 0, N - 1, RESET, TRANSL )
+ IF( N.GT.1 )THEN
+ X( N/2 ) = ZERO
+ XX( 1 + ABS( INCX )*( N/2 - 1 ) ) = ZERO
+ END IF
+*
+ DO 70 IY = 1, NINC
+ INCY = INC( IY )
+ LY = ABS( INCY )*N
+*
+ DO 60 IA = 1, NALF
+ ALPHA = ALF( IA )
+*
+ DO 50 IB = 1, NBET
+ BETA = BET( IB )
+*
+* Generate the vector Y.
+*
+ TRANSL = ZERO
+ CALL ZMAKE( 'GE', ' ', ' ', 1, N, Y, 1, YY,
+ $ ABS( INCY ), 0, N - 1, RESET,
+ $ TRANSL )
+*
+ NC = NC + 1
+*
+* Save every datum before calling the
+* subroutine.
+*
+ UPLOS = UPLO
+ NS = N
+ KS = K
+ ALS = ALPHA
+ DO 10 I = 1, LAA
+ AS( I ) = AA( I )
+ 10 CONTINUE
+ LDAS = LDA
+ DO 20 I = 1, LX
+ XS( I ) = XX( I )
+ 20 CONTINUE
+ INCXS = INCX
+ BLS = BETA
+ DO 30 I = 1, LY
+ YS( I ) = YY( I )
+ 30 CONTINUE
+ INCYS = INCY
+*
+* Call the subroutine.
+*
+ IF( FULL )THEN
+ IF( TRACE )
+ $ WRITE( NTRA, FMT = 9993 )NC, SNAME,
+ $ UPLO, N, ALPHA, LDA, INCX, BETA, INCY
+ IF( REWI )
+ $ REWIND NTRA
+ CALL ZHEMV( UPLO, N, ALPHA, AA, LDA, XX,
+ $ INCX, BETA, YY, INCY )
+ ELSE IF( BANDED )THEN
+ IF( TRACE )
+ $ WRITE( NTRA, FMT = 9994 )NC, SNAME,
+ $ UPLO, N, K, ALPHA, LDA, INCX, BETA,
+ $ INCY
+ IF( REWI )
+ $ REWIND NTRA
+ CALL ZHBMV( UPLO, N, K, ALPHA, AA, LDA,
+ $ XX, INCX, BETA, YY, INCY )
+ ELSE IF( PACKED )THEN
+ IF( TRACE )
+ $ WRITE( NTRA, FMT = 9995 )NC, SNAME,
+ $ UPLO, N, ALPHA, INCX, BETA, INCY
+ IF( REWI )
+ $ REWIND NTRA
+ CALL ZHPMV( UPLO, N, ALPHA, AA, XX, INCX,
+ $ BETA, YY, INCY )
+ END IF
+*
+* Check if error-exit was taken incorrectly.
+*
+ IF( .NOT.OK )THEN
+ WRITE( NOUT, FMT = 9992 )
+ FATAL = .TRUE.
+ GO TO 120
+ END IF
+*
+* See what data changed inside subroutines.
+*
+ ISAME( 1 ) = UPLO.EQ.UPLOS
+ ISAME( 2 ) = NS.EQ.N
+ IF( FULL )THEN
+ ISAME( 3 ) = ALS.EQ.ALPHA
+ ISAME( 4 ) = LZE( AS, AA, LAA )
+ ISAME( 5 ) = LDAS.EQ.LDA
+ ISAME( 6 ) = LZE( XS, XX, LX )
+ ISAME( 7 ) = INCXS.EQ.INCX
+ ISAME( 8 ) = BLS.EQ.BETA
+ IF( NULL )THEN
+ ISAME( 9 ) = LZE( YS, YY, LY )
+ ELSE
+ ISAME( 9 ) = LZERES( 'GE', ' ', 1, N,
+ $ YS, YY, ABS( INCY ) )
+ END IF
+ ISAME( 10 ) = INCYS.EQ.INCY
+ ELSE IF( BANDED )THEN
+ ISAME( 3 ) = KS.EQ.K
+ ISAME( 4 ) = ALS.EQ.ALPHA
+ ISAME( 5 ) = LZE( AS, AA, LAA )
+ ISAME( 6 ) = LDAS.EQ.LDA
+ ISAME( 7 ) = LZE( XS, XX, LX )
+ ISAME( 8 ) = INCXS.EQ.INCX
+ ISAME( 9 ) = BLS.EQ.BETA
+ IF( NULL )THEN
+ ISAME( 10 ) = LZE( YS, YY, LY )
+ ELSE
+ ISAME( 10 ) = LZERES( 'GE', ' ', 1, N,
+ $ YS, YY, ABS( INCY ) )
+ END IF
+ ISAME( 11 ) = INCYS.EQ.INCY
+ ELSE IF( PACKED )THEN
+ ISAME( 3 ) = ALS.EQ.ALPHA
+ ISAME( 4 ) = LZE( AS, AA, LAA )
+ ISAME( 5 ) = LZE( XS, XX, LX )
+ ISAME( 6 ) = INCXS.EQ.INCX
+ ISAME( 7 ) = BLS.EQ.BETA
+ IF( NULL )THEN
+ ISAME( 8 ) = LZE( YS, YY, LY )
+ ELSE
+ ISAME( 8 ) = LZERES( 'GE', ' ', 1, N,
+ $ YS, YY, ABS( INCY ) )
+ END IF
+ ISAME( 9 ) = INCYS.EQ.INCY
+ END IF
+*
+* If data was incorrectly changed, report and
+* return.
+*
+ SAME = .TRUE.
+ DO 40 I = 1, NARGS
+ SAME = SAME.AND.ISAME( I )
+ IF( .NOT.ISAME( I ) )
+ $ WRITE( NOUT, FMT = 9998 )I
+ 40 CONTINUE
+ IF( .NOT.SAME )THEN
+ FATAL = .TRUE.
+ GO TO 120
+ END IF
+*
+ IF( .NOT.NULL )THEN
+*
+* Check the result.
+*
+ CALL ZMVCH( 'N', N, N, ALPHA, A, NMAX, X,
+ $ INCX, BETA, Y, INCY, YT, G,
+ $ YY, EPS, ERR, FATAL, NOUT,
+ $ .TRUE. )
+ ERRMAX = MAX( ERRMAX, ERR )
+* If got really bad answer, report and
+* return.
+ IF( FATAL )
+ $ GO TO 120
+ ELSE
+* Avoid repeating tests with N.le.0
+ GO TO 110
+ END IF
+*
+ 50 CONTINUE
+*
+ 60 CONTINUE
+*
+ 70 CONTINUE
+*
+ 80 CONTINUE
+*
+ 90 CONTINUE
+*
+ 100 CONTINUE
+*
+ 110 CONTINUE
+*
+* Report result.
+*
+ IF( ERRMAX.LT.THRESH )THEN
+ WRITE( NOUT, FMT = 9999 )SNAME, NC
+ ELSE
+ WRITE( NOUT, FMT = 9997 )SNAME, NC, ERRMAX
+ END IF
+ GO TO 130
+*
+ 120 CONTINUE
+ WRITE( NOUT, FMT = 9996 )SNAME
+ IF( FULL )THEN
+ WRITE( NOUT, FMT = 9993 )NC, SNAME, UPLO, N, ALPHA, LDA, INCX,
+ $ BETA, INCY
+ ELSE IF( BANDED )THEN
+ WRITE( NOUT, FMT = 9994 )NC, SNAME, UPLO, N, K, ALPHA, LDA,
+ $ INCX, BETA, INCY
+ ELSE IF( PACKED )THEN
+ WRITE( NOUT, FMT = 9995 )NC, SNAME, UPLO, N, ALPHA, INCX,
+ $ BETA, INCY
+ END IF
+*
+ 130 CONTINUE
+ RETURN
+*
+ 9999 FORMAT( ' ', A6, ' PASSED THE COMPUTATIONAL TESTS (', I6, ' CALL',
+ $ 'S)' )
+ 9998 FORMAT( ' ******* FATAL ERROR - PARAMETER NUMBER ', I2, ' WAS CH',
+ $ 'ANGED INCORRECTLY *******' )
+ 9997 FORMAT( ' ', A6, ' COMPLETED THE COMPUTATIONAL TESTS (', I6, ' C',
+ $ 'ALLS)', /' ******* BUT WITH MAXIMUM TEST RATIO', F8.2,
+ $ ' - SUSPECT *******' )
+ 9996 FORMAT( ' ******* ', A6, ' FAILED ON CALL NUMBER:' )
+ 9995 FORMAT( 1X, I6, ': ', A6, '(''', A1, ''',', I3, ',(', F4.1, ',',
+ $ F4.1, '), AP, X,', I2, ',(', F4.1, ',', F4.1, '), Y,', I2,
+ $ ') .' )
+ 9994 FORMAT( 1X, I6, ': ', A6, '(''', A1, ''',', 2( I3, ',' ), '(',
+ $ F4.1, ',', F4.1, '), A,', I3, ', X,', I2, ',(', F4.1, ',',
+ $ F4.1, '), Y,', I2, ') .' )
+ 9993 FORMAT( 1X, I6, ': ', A6, '(''', A1, ''',', I3, ',(', F4.1, ',',
+ $ F4.1, '), A,', I3, ', X,', I2, ',(', F4.1, ',', F4.1, '), ',
+ $ 'Y,', I2, ') .' )
+ 9992 FORMAT( ' ******* FATAL ERROR - ERROR-EXIT TAKEN ON VALID CALL *',
+ $ '******' )
+*
+* End of ZCHK2.
+*
+ END
+ SUBROUTINE ZCHK3( SNAME, EPS, THRESH, NOUT, NTRA, TRACE, REWI,
+ $ FATAL, NIDIM, IDIM, NKB, KB, NINC, INC, NMAX,
+ $ INCMAX, A, AA, AS, X, XX, XS, XT, G, Z )
+*
+* Tests ZTRMV, ZTBMV, ZTPMV, ZTRSV, ZTBSV and ZTPSV.
+*
+* Auxiliary routine for test program for Level 2 Blas.
+*
+* -- Written on 10-August-1987.
+* Richard Hanson, Sandia National Labs.
+* Jeremy Du Croz, NAG Central Office.
+*
+* .. Parameters ..
+ COMPLEX*16 ZERO, HALF, ONE
+ PARAMETER ( ZERO = ( 0.0D0, 0.0D0 ),
+ $ HALF = ( 0.5D0, 0.0D0 ),
+ $ ONE = ( 1.0D0, 0.0D0 ) )
+ DOUBLE PRECISION RZERO
+ PARAMETER ( RZERO = 0.0D0 )
+* .. Scalar Arguments ..
+ DOUBLE PRECISION EPS, THRESH
+ INTEGER INCMAX, NIDIM, NINC, NKB, NMAX, NOUT, NTRA
+ LOGICAL FATAL, REWI, TRACE
+ CHARACTER*6 SNAME
+* .. Array Arguments ..
+ COMPLEX*16 A( NMAX, NMAX ), AA( NMAX*NMAX ),
+ $ AS( NMAX*NMAX ), X( NMAX ), XS( NMAX*INCMAX ),
+ $ XT( NMAX ), XX( NMAX*INCMAX ), Z( NMAX )
+ DOUBLE PRECISION G( NMAX )
+ INTEGER IDIM( NIDIM ), INC( NINC ), KB( NKB )
+* .. Local Scalars ..
+ COMPLEX*16 TRANSL
+ DOUBLE PRECISION ERR, ERRMAX
+ INTEGER I, ICD, ICT, ICU, IK, IN, INCX, INCXS, IX, K,
+ $ KS, LAA, LDA, LDAS, LX, N, NARGS, NC, NK, NS
+ LOGICAL BANDED, FULL, NULL, PACKED, RESET, SAME
+ CHARACTER*1 DIAG, DIAGS, TRANS, TRANSS, UPLO, UPLOS
+ CHARACTER*2 ICHD, ICHU
+ CHARACTER*3 ICHT
+* .. Local Arrays ..
+ LOGICAL ISAME( 13 )
+* .. External Functions ..
+ LOGICAL LZE, LZERES
+ EXTERNAL LZE, LZERES
+* .. External Subroutines ..
+ EXTERNAL ZMAKE, ZMVCH, ZTBMV, ZTBSV, ZTPMV, ZTPSV,
+ $ ZTRMV, ZTRSV
+* .. Intrinsic Functions ..
+ INTRINSIC ABS, MAX
+* .. Scalars in Common ..
+ INTEGER INFOT, NOUTC
+ LOGICAL LERR, OK
+* .. Common blocks ..
+ COMMON /INFOC/INFOT, NOUTC, OK, LERR
+* .. Data statements ..
+ DATA ICHU/'UL'/, ICHT/'NTC'/, ICHD/'UN'/
+* .. Executable Statements ..
+ FULL = SNAME( 3: 3 ).EQ.'R'
+ BANDED = SNAME( 3: 3 ).EQ.'B'
+ PACKED = SNAME( 3: 3 ).EQ.'P'
+* Define the number of arguments.
+ IF( FULL )THEN
+ NARGS = 8
+ ELSE IF( BANDED )THEN
+ NARGS = 9
+ ELSE IF( PACKED )THEN
+ NARGS = 7
+ END IF
+*
+ NC = 0
+ RESET = .TRUE.
+ ERRMAX = RZERO
+* Set up zero vector for ZMVCH.
+ DO 10 I = 1, NMAX
+ Z( I ) = ZERO
+ 10 CONTINUE
+*
+ DO 110 IN = 1, NIDIM
+ N = IDIM( IN )
+*
+ IF( BANDED )THEN
+ NK = NKB
+ ELSE
+ NK = 1
+ END IF
+ DO 100 IK = 1, NK
+ IF( BANDED )THEN
+ K = KB( IK )
+ ELSE
+ K = N - 1
+ END IF
+* Set LDA to 1 more than minimum value if room.
+ IF( BANDED )THEN
+ LDA = K + 1
+ ELSE
+ LDA = N
+ END IF
+ IF( LDA.LT.NMAX )
+ $ LDA = LDA + 1
+* Skip tests if not enough room.
+ IF( LDA.GT.NMAX )
+ $ GO TO 100
+ IF( PACKED )THEN
+ LAA = ( N*( N + 1 ) )/2
+ ELSE
+ LAA = LDA*N
+ END IF
+ NULL = N.LE.0
+*
+ DO 90 ICU = 1, 2
+ UPLO = ICHU( ICU: ICU )
+*
+ DO 80 ICT = 1, 3
+ TRANS = ICHT( ICT: ICT )
+*
+ DO 70 ICD = 1, 2
+ DIAG = ICHD( ICD: ICD )
+*
+* Generate the matrix A.
+*
+ TRANSL = ZERO
+ CALL ZMAKE( SNAME( 2: 3 ), UPLO, DIAG, N, N, A,
+ $ NMAX, AA, LDA, K, K, RESET, TRANSL )
+*
+ DO 60 IX = 1, NINC
+ INCX = INC( IX )
+ LX = ABS( INCX )*N
+*
+* Generate the vector X.
+*
+ TRANSL = HALF
+ CALL ZMAKE( 'GE', ' ', ' ', 1, N, X, 1, XX,
+ $ ABS( INCX ), 0, N - 1, RESET,
+ $ TRANSL )
+ IF( N.GT.1 )THEN
+ X( N/2 ) = ZERO
+ XX( 1 + ABS( INCX )*( N/2 - 1 ) ) = ZERO
+ END IF
+*
+ NC = NC + 1
+*
+* Save every datum before calling the subroutine.
+*
+ UPLOS = UPLO
+ TRANSS = TRANS
+ DIAGS = DIAG
+ NS = N
+ KS = K
+ DO 20 I = 1, LAA
+ AS( I ) = AA( I )
+ 20 CONTINUE
+ LDAS = LDA
+ DO 30 I = 1, LX
+ XS( I ) = XX( I )
+ 30 CONTINUE
+ INCXS = INCX
+*
+* Call the subroutine.
+*
+ IF( SNAME( 4: 5 ).EQ.'MV' )THEN
+ IF( FULL )THEN
+ IF( TRACE )
+ $ WRITE( NTRA, FMT = 9993 )NC, SNAME,
+ $ UPLO, TRANS, DIAG, N, LDA, INCX
+ IF( REWI )
+ $ REWIND NTRA
+ CALL ZTRMV( UPLO, TRANS, DIAG, N, AA, LDA,
+ $ XX, INCX )
+ ELSE IF( BANDED )THEN
+ IF( TRACE )
+ $ WRITE( NTRA, FMT = 9994 )NC, SNAME,
+ $ UPLO, TRANS, DIAG, N, K, LDA, INCX
+ IF( REWI )
+ $ REWIND NTRA
+ CALL ZTBMV( UPLO, TRANS, DIAG, N, K, AA,
+ $ LDA, XX, INCX )
+ ELSE IF( PACKED )THEN
+ IF( TRACE )
+ $ WRITE( NTRA, FMT = 9995 )NC, SNAME,
+ $ UPLO, TRANS, DIAG, N, INCX
+ IF( REWI )
+ $ REWIND NTRA
+ CALL ZTPMV( UPLO, TRANS, DIAG, N, AA, XX,
+ $ INCX )
+ END IF
+ ELSE IF( SNAME( 4: 5 ).EQ.'SV' )THEN
+ IF( FULL )THEN
+ IF( TRACE )
+ $ WRITE( NTRA, FMT = 9993 )NC, SNAME,
+ $ UPLO, TRANS, DIAG, N, LDA, INCX
+ IF( REWI )
+ $ REWIND NTRA
+ CALL ZTRSV( UPLO, TRANS, DIAG, N, AA, LDA,
+ $ XX, INCX )
+ ELSE IF( BANDED )THEN
+ IF( TRACE )
+ $ WRITE( NTRA, FMT = 9994 )NC, SNAME,
+ $ UPLO, TRANS, DIAG, N, K, LDA, INCX
+ IF( REWI )
+ $ REWIND NTRA
+ CALL ZTBSV( UPLO, TRANS, DIAG, N, K, AA,
+ $ LDA, XX, INCX )
+ ELSE IF( PACKED )THEN
+ IF( TRACE )
+ $ WRITE( NTRA, FMT = 9995 )NC, SNAME,
+ $ UPLO, TRANS, DIAG, N, INCX
+ IF( REWI )
+ $ REWIND NTRA
+ CALL ZTPSV( UPLO, TRANS, DIAG, N, AA, XX,
+ $ INCX )
+ END IF
+ END IF
+*
+* Check if error-exit was taken incorrectly.
+*
+ IF( .NOT.OK )THEN
+ WRITE( NOUT, FMT = 9992 )
+ FATAL = .TRUE.
+ GO TO 120
+ END IF
+*
+* See what data changed inside subroutines.
+*
+ ISAME( 1 ) = UPLO.EQ.UPLOS
+ ISAME( 2 ) = TRANS.EQ.TRANSS
+ ISAME( 3 ) = DIAG.EQ.DIAGS
+ ISAME( 4 ) = NS.EQ.N
+ IF( FULL )THEN
+ ISAME( 5 ) = LZE( AS, AA, LAA )
+ ISAME( 6 ) = LDAS.EQ.LDA
+ IF( NULL )THEN
+ ISAME( 7 ) = LZE( XS, XX, LX )
+ ELSE
+ ISAME( 7 ) = LZERES( 'GE', ' ', 1, N, XS,
+ $ XX, ABS( INCX ) )
+ END IF
+ ISAME( 8 ) = INCXS.EQ.INCX
+ ELSE IF( BANDED )THEN
+ ISAME( 5 ) = KS.EQ.K
+ ISAME( 6 ) = LZE( AS, AA, LAA )
+ ISAME( 7 ) = LDAS.EQ.LDA
+ IF( NULL )THEN
+ ISAME( 8 ) = LZE( XS, XX, LX )
+ ELSE
+ ISAME( 8 ) = LZERES( 'GE', ' ', 1, N, XS,
+ $ XX, ABS( INCX ) )
+ END IF
+ ISAME( 9 ) = INCXS.EQ.INCX
+ ELSE IF( PACKED )THEN
+ ISAME( 5 ) = LZE( AS, AA, LAA )
+ IF( NULL )THEN
+ ISAME( 6 ) = LZE( XS, XX, LX )
+ ELSE
+ ISAME( 6 ) = LZERES( 'GE', ' ', 1, N, XS,
+ $ XX, ABS( INCX ) )
+ END IF
+ ISAME( 7 ) = INCXS.EQ.INCX
+ END IF
+*
+* If data was incorrectly changed, report and
+* return.
+*
+ SAME = .TRUE.
+ DO 40 I = 1, NARGS
+ SAME = SAME.AND.ISAME( I )
+ IF( .NOT.ISAME( I ) )
+ $ WRITE( NOUT, FMT = 9998 )I
+ 40 CONTINUE
+ IF( .NOT.SAME )THEN
+ FATAL = .TRUE.
+ GO TO 120
+ END IF
+*
+ IF( .NOT.NULL )THEN
+ IF( SNAME( 4: 5 ).EQ.'MV' )THEN
+*
+* Check the result.
+*
+ CALL ZMVCH( TRANS, N, N, ONE, A, NMAX, X,
+ $ INCX, ZERO, Z, INCX, XT, G,
+ $ XX, EPS, ERR, FATAL, NOUT,
+ $ .TRUE. )
+ ELSE IF( SNAME( 4: 5 ).EQ.'SV' )THEN
+*
+* Compute approximation to original vector.
+*
+ DO 50 I = 1, N
+ Z( I ) = XX( 1 + ( I - 1 )*
+ $ ABS( INCX ) )
+ XX( 1 + ( I - 1 )*ABS( INCX ) )
+ $ = X( I )
+ 50 CONTINUE
+ CALL ZMVCH( TRANS, N, N, ONE, A, NMAX, Z,
+ $ INCX, ZERO, X, INCX, XT, G,
+ $ XX, EPS, ERR, FATAL, NOUT,
+ $ .FALSE. )
+ END IF
+ ERRMAX = MAX( ERRMAX, ERR )
+* If got really bad answer, report and return.
+ IF( FATAL )
+ $ GO TO 120
+ ELSE
+* Avoid repeating tests with N.le.0.
+ GO TO 110
+ END IF
+*
+ 60 CONTINUE
+*
+ 70 CONTINUE
+*
+ 80 CONTINUE
+*
+ 90 CONTINUE
+*
+ 100 CONTINUE
+*
+ 110 CONTINUE
+*
+* Report result.
+*
+ IF( ERRMAX.LT.THRESH )THEN
+ WRITE( NOUT, FMT = 9999 )SNAME, NC
+ ELSE
+ WRITE( NOUT, FMT = 9997 )SNAME, NC, ERRMAX
+ END IF
+ GO TO 130
+*
+ 120 CONTINUE
+ WRITE( NOUT, FMT = 9996 )SNAME
+ IF( FULL )THEN
+ WRITE( NOUT, FMT = 9993 )NC, SNAME, UPLO, TRANS, DIAG, N, LDA,
+ $ INCX
+ ELSE IF( BANDED )THEN
+ WRITE( NOUT, FMT = 9994 )NC, SNAME, UPLO, TRANS, DIAG, N, K,
+ $ LDA, INCX
+ ELSE IF( PACKED )THEN
+ WRITE( NOUT, FMT = 9995 )NC, SNAME, UPLO, TRANS, DIAG, N, INCX
+ END IF
+*
+ 130 CONTINUE
+ RETURN
+*
+ 9999 FORMAT( ' ', A6, ' PASSED THE COMPUTATIONAL TESTS (', I6, ' CALL',
+ $ 'S)' )
+ 9998 FORMAT( ' ******* FATAL ERROR - PARAMETER NUMBER ', I2, ' WAS CH',
+ $ 'ANGED INCORRECTLY *******' )
+ 9997 FORMAT( ' ', A6, ' COMPLETED THE COMPUTATIONAL TESTS (', I6, ' C',
+ $ 'ALLS)', /' ******* BUT WITH MAXIMUM TEST RATIO', F8.2,
+ $ ' - SUSPECT *******' )
+ 9996 FORMAT( ' ******* ', A6, ' FAILED ON CALL NUMBER:' )
+ 9995 FORMAT( 1X, I6, ': ', A6, '(', 3( '''', A1, ''',' ), I3, ', AP, ',
+ $ 'X,', I2, ') .' )
+ 9994 FORMAT( 1X, I6, ': ', A6, '(', 3( '''', A1, ''',' ), 2( I3, ',' ),
+ $ ' A,', I3, ', X,', I2, ') .' )
+ 9993 FORMAT( 1X, I6, ': ', A6, '(', 3( '''', A1, ''',' ), I3, ', A,',
+ $ I3, ', X,', I2, ') .' )
+ 9992 FORMAT( ' ******* FATAL ERROR - ERROR-EXIT TAKEN ON VALID CALL *',
+ $ '******' )
+*
+* End of ZCHK3.
+*
+ END
+ SUBROUTINE ZCHK4( SNAME, EPS, THRESH, NOUT, NTRA, TRACE, REWI,
+ $ FATAL, NIDIM, IDIM, NALF, ALF, NINC, INC, NMAX,
+ $ INCMAX, A, AA, AS, X, XX, XS, Y, YY, YS, YT, G,
+ $ Z )
+*
+* Tests ZGERC and ZGERU.
+*
+* Auxiliary routine for test program for Level 2 Blas.
+*
+* -- Written on 10-August-1987.
+* Richard Hanson, Sandia National Labs.
+* Jeremy Du Croz, NAG Central Office.
+*
+* .. Parameters ..
+ COMPLEX*16 ZERO, HALF, ONE
+ PARAMETER ( ZERO = ( 0.0D0, 0.0D0 ),
+ $ HALF = ( 0.5D0, 0.0D0 ),
+ $ ONE = ( 1.0D0, 0.0D0 ) )
+ DOUBLE PRECISION RZERO
+ PARAMETER ( RZERO = 0.0D0 )
+* .. Scalar Arguments ..
+ DOUBLE PRECISION EPS, THRESH
+ INTEGER INCMAX, NALF, NIDIM, NINC, NMAX, NOUT, NTRA
+ LOGICAL FATAL, REWI, TRACE
+ CHARACTER*6 SNAME
+* .. Array Arguments ..
+ COMPLEX*16 A( NMAX, NMAX ), AA( NMAX*NMAX ), ALF( NALF ),
+ $ AS( NMAX*NMAX ), X( NMAX ), XS( NMAX*INCMAX ),
+ $ XX( NMAX*INCMAX ), Y( NMAX ),
+ $ YS( NMAX*INCMAX ), YT( NMAX ),
+ $ YY( NMAX*INCMAX ), Z( NMAX )
+ DOUBLE PRECISION G( NMAX )
+ INTEGER IDIM( NIDIM ), INC( NINC )
+* .. Local Scalars ..
+ COMPLEX*16 ALPHA, ALS, TRANSL
+ DOUBLE PRECISION ERR, ERRMAX
+ INTEGER I, IA, IM, IN, INCX, INCXS, INCY, INCYS, IX,
+ $ IY, J, LAA, LDA, LDAS, LX, LY, M, MS, N, NARGS,
+ $ NC, ND, NS
+ LOGICAL CONJ, NULL, RESET, SAME
+* .. Local Arrays ..
+ COMPLEX*16 W( 1 )
+ LOGICAL ISAME( 13 )
+* .. External Functions ..
+ LOGICAL LZE, LZERES
+ EXTERNAL LZE, LZERES
+* .. External Subroutines ..
+ EXTERNAL ZGERC, ZGERU, ZMAKE, ZMVCH
+* .. Intrinsic Functions ..
+ INTRINSIC ABS, DCONJG, MAX, MIN
+* .. Scalars in Common ..
+ INTEGER INFOT, NOUTC
+ LOGICAL LERR, OK
+* .. Common blocks ..
+ COMMON /INFOC/INFOT, NOUTC, OK, LERR
+* .. Executable Statements ..
+ CONJ = SNAME( 5: 5 ).EQ.'C'
+* Define the number of arguments.
+ NARGS = 9
+*
+ NC = 0
+ RESET = .TRUE.
+ ERRMAX = RZERO
+*
+ DO 120 IN = 1, NIDIM
+ N = IDIM( IN )
+ ND = N/2 + 1
+*
+ DO 110 IM = 1, 2
+ IF( IM.EQ.1 )
+ $ M = MAX( N - ND, 0 )
+ IF( IM.EQ.2 )
+ $ M = MIN( N + ND, NMAX )
+*
+* Set LDA to 1 more than minimum value if room.
+ LDA = M
+ IF( LDA.LT.NMAX )
+ $ LDA = LDA + 1
+* Skip tests if not enough room.
+ IF( LDA.GT.NMAX )
+ $ GO TO 110
+ LAA = LDA*N
+ NULL = N.LE.0.OR.M.LE.0
+*
+ DO 100 IX = 1, NINC
+ INCX = INC( IX )
+ LX = ABS( INCX )*M
+*
+* Generate the vector X.
+*
+ TRANSL = HALF
+ CALL ZMAKE( 'GE', ' ', ' ', 1, M, X, 1, XX, ABS( INCX ),
+ $ 0, M - 1, RESET, TRANSL )
+ IF( M.GT.1 )THEN
+ X( M/2 ) = ZERO
+ XX( 1 + ABS( INCX )*( M/2 - 1 ) ) = ZERO
+ END IF
+*
+ DO 90 IY = 1, NINC
+ INCY = INC( IY )
+ LY = ABS( INCY )*N
+*
+* Generate the vector Y.
+*
+ TRANSL = ZERO
+ CALL ZMAKE( 'GE', ' ', ' ', 1, N, Y, 1, YY,
+ $ ABS( INCY ), 0, N - 1, RESET, TRANSL )
+ IF( N.GT.1 )THEN
+ Y( N/2 ) = ZERO
+ YY( 1 + ABS( INCY )*( N/2 - 1 ) ) = ZERO
+ END IF
+*
+ DO 80 IA = 1, NALF
+ ALPHA = ALF( IA )
+*
+* Generate the matrix A.
+*
+ TRANSL = ZERO
+ CALL ZMAKE( SNAME( 2: 3 ), ' ', ' ', M, N, A, NMAX,
+ $ AA, LDA, M - 1, N - 1, RESET, TRANSL )
+*
+ NC = NC + 1
+*
+* Save every datum before calling the subroutine.
+*
+ MS = M
+ NS = N
+ ALS = ALPHA
+ DO 10 I = 1, LAA
+ AS( I ) = AA( I )
+ 10 CONTINUE
+ LDAS = LDA
+ DO 20 I = 1, LX
+ XS( I ) = XX( I )
+ 20 CONTINUE
+ INCXS = INCX
+ DO 30 I = 1, LY
+ YS( I ) = YY( I )
+ 30 CONTINUE
+ INCYS = INCY
+*
+* Call the subroutine.
+*
+ IF( TRACE )
+ $ WRITE( NTRA, FMT = 9994 )NC, SNAME, M, N,
+ $ ALPHA, INCX, INCY, LDA
+ IF( CONJ )THEN
+ IF( REWI )
+ $ REWIND NTRA
+ CALL ZGERC( M, N, ALPHA, XX, INCX, YY, INCY, AA,
+ $ LDA )
+ ELSE
+ IF( REWI )
+ $ REWIND NTRA
+ CALL ZGERU( M, N, ALPHA, XX, INCX, YY, INCY, AA,
+ $ LDA )
+ END IF
+*
+* Check if error-exit was taken incorrectly.
+*
+ IF( .NOT.OK )THEN
+ WRITE( NOUT, FMT = 9993 )
+ FATAL = .TRUE.
+ GO TO 140
+ END IF
+*
+* See what data changed inside subroutine.
+*
+ ISAME( 1 ) = MS.EQ.M
+ ISAME( 2 ) = NS.EQ.N
+ ISAME( 3 ) = ALS.EQ.ALPHA
+ ISAME( 4 ) = LZE( XS, XX, LX )
+ ISAME( 5 ) = INCXS.EQ.INCX
+ ISAME( 6 ) = LZE( YS, YY, LY )
+ ISAME( 7 ) = INCYS.EQ.INCY
+ IF( NULL )THEN
+ ISAME( 8 ) = LZE( AS, AA, LAA )
+ ELSE
+ ISAME( 8 ) = LZERES( 'GE', ' ', M, N, AS, AA,
+ $ LDA )
+ END IF
+ ISAME( 9 ) = LDAS.EQ.LDA
+*
+* If data was incorrectly changed, report and return.
+*
+ SAME = .TRUE.
+ DO 40 I = 1, NARGS
+ SAME = SAME.AND.ISAME( I )
+ IF( .NOT.ISAME( I ) )
+ $ WRITE( NOUT, FMT = 9998 )I
+ 40 CONTINUE
+ IF( .NOT.SAME )THEN
+ FATAL = .TRUE.
+ GO TO 140
+ END IF
+*
+ IF( .NOT.NULL )THEN
+*
+* Check the result column by column.
+*
+ IF( INCX.GT.0 )THEN
+ DO 50 I = 1, M
+ Z( I ) = X( I )
+ 50 CONTINUE
+ ELSE
+ DO 60 I = 1, M
+ Z( I ) = X( M - I + 1 )
+ 60 CONTINUE
+ END IF
+ DO 70 J = 1, N
+ IF( INCY.GT.0 )THEN
+ W( 1 ) = Y( J )
+ ELSE
+ W( 1 ) = Y( N - J + 1 )
+ END IF
+ IF( CONJ )
+ $ W( 1 ) = DCONJG( W( 1 ) )
+ CALL ZMVCH( 'N', M, 1, ALPHA, Z, NMAX, W, 1,
+ $ ONE, A( 1, J ), 1, YT, G,
+ $ AA( 1 + ( J - 1 )*LDA ), EPS,
+ $ ERR, FATAL, NOUT, .TRUE. )
+ ERRMAX = MAX( ERRMAX, ERR )
+* If got really bad answer, report and return.
+ IF( FATAL )
+ $ GO TO 130
+ 70 CONTINUE
+ ELSE
+* Avoid repeating tests with M.le.0 or N.le.0.
+ GO TO 110
+ END IF
+*
+ 80 CONTINUE
+*
+ 90 CONTINUE
+*
+ 100 CONTINUE
+*
+ 110 CONTINUE
+*
+ 120 CONTINUE
+*
+* Report result.
+*
+ IF( ERRMAX.LT.THRESH )THEN
+ WRITE( NOUT, FMT = 9999 )SNAME, NC
+ ELSE
+ WRITE( NOUT, FMT = 9997 )SNAME, NC, ERRMAX
+ END IF
+ GO TO 150
+*
+ 130 CONTINUE
+ WRITE( NOUT, FMT = 9995 )J
+*
+ 140 CONTINUE
+ WRITE( NOUT, FMT = 9996 )SNAME
+ WRITE( NOUT, FMT = 9994 )NC, SNAME, M, N, ALPHA, INCX, INCY, LDA
+*
+ 150 CONTINUE
+ RETURN
+*
+ 9999 FORMAT( ' ', A6, ' PASSED THE COMPUTATIONAL TESTS (', I6, ' CALL',
+ $ 'S)' )
+ 9998 FORMAT( ' ******* FATAL ERROR - PARAMETER NUMBER ', I2, ' WAS CH',
+ $ 'ANGED INCORRECTLY *******' )
+ 9997 FORMAT( ' ', A6, ' COMPLETED THE COMPUTATIONAL TESTS (', I6, ' C',
+ $ 'ALLS)', /' ******* BUT WITH MAXIMUM TEST RATIO', F8.2,
+ $ ' - SUSPECT *******' )
+ 9996 FORMAT( ' ******* ', A6, ' FAILED ON CALL NUMBER:' )
+ 9995 FORMAT( ' THESE ARE THE RESULTS FOR COLUMN ', I3 )
+ 9994 FORMAT( 1X, I6, ': ', A6, '(', 2( I3, ',' ), '(', F4.1, ',', F4.1,
+ $ '), X,', I2, ', Y,', I2, ', A,', I3, ') ',
+ $ ' .' )
+ 9993 FORMAT( ' ******* FATAL ERROR - ERROR-EXIT TAKEN ON VALID CALL *',
+ $ '******' )
+*
+* End of ZCHK4.
+*
+ END
+ SUBROUTINE ZCHK5( SNAME, EPS, THRESH, NOUT, NTRA, TRACE, REWI,
+ $ FATAL, NIDIM, IDIM, NALF, ALF, NINC, INC, NMAX,
+ $ INCMAX, A, AA, AS, X, XX, XS, Y, YY, YS, YT, G,
+ $ Z )
+*
+* Tests ZHER and ZHPR.
+*
+* Auxiliary routine for test program for Level 2 Blas.
+*
+* -- Written on 10-August-1987.
+* Richard Hanson, Sandia National Labs.
+* Jeremy Du Croz, NAG Central Office.
+*
+* .. Parameters ..
+ COMPLEX*16 ZERO, HALF, ONE
+ PARAMETER ( ZERO = ( 0.0D0, 0.0D0 ),
+ $ HALF = ( 0.5D0, 0.0D0 ),
+ $ ONE = ( 1.0D0, 0.0D0 ) )
+ DOUBLE PRECISION RZERO
+ PARAMETER ( RZERO = 0.0D0 )
+* .. Scalar Arguments ..
+ DOUBLE PRECISION EPS, THRESH
+ INTEGER INCMAX, NALF, NIDIM, NINC, NMAX, NOUT, NTRA
+ LOGICAL FATAL, REWI, TRACE
+ CHARACTER*6 SNAME
+* .. Array Arguments ..
+ COMPLEX*16 A( NMAX, NMAX ), AA( NMAX*NMAX ), ALF( NALF ),
+ $ AS( NMAX*NMAX ), X( NMAX ), XS( NMAX*INCMAX ),
+ $ XX( NMAX*INCMAX ), Y( NMAX ),
+ $ YS( NMAX*INCMAX ), YT( NMAX ),
+ $ YY( NMAX*INCMAX ), Z( NMAX )
+ DOUBLE PRECISION G( NMAX )
+ INTEGER IDIM( NIDIM ), INC( NINC )
+* .. Local Scalars ..
+ COMPLEX*16 ALPHA, TRANSL
+ DOUBLE PRECISION ERR, ERRMAX, RALPHA, RALS
+ INTEGER I, IA, IC, IN, INCX, INCXS, IX, J, JA, JJ, LAA,
+ $ LDA, LDAS, LJ, LX, N, NARGS, NC, NS
+ LOGICAL FULL, NULL, PACKED, RESET, SAME, UPPER
+ CHARACTER*1 UPLO, UPLOS
+ CHARACTER*2 ICH
+* .. Local Arrays ..
+ COMPLEX*16 W( 1 )
+ LOGICAL ISAME( 13 )
+* .. External Functions ..
+ LOGICAL LZE, LZERES
+ EXTERNAL LZE, LZERES
+* .. External Subroutines ..
+ EXTERNAL ZHER, ZHPR, ZMAKE, ZMVCH
+* .. Intrinsic Functions ..
+ INTRINSIC ABS, DBLE, DCMPLX, DCONJG, MAX
+* .. Scalars in Common ..
+ INTEGER INFOT, NOUTC
+ LOGICAL LERR, OK
+* .. Common blocks ..
+ COMMON /INFOC/INFOT, NOUTC, OK, LERR
+* .. Data statements ..
+ DATA ICH/'UL'/
+* .. Executable Statements ..
+ FULL = SNAME( 3: 3 ).EQ.'E'
+ PACKED = SNAME( 3: 3 ).EQ.'P'
+* Define the number of arguments.
+ IF( FULL )THEN
+ NARGS = 7
+ ELSE IF( PACKED )THEN
+ NARGS = 6
+ END IF
+*
+ NC = 0
+ RESET = .TRUE.
+ ERRMAX = RZERO
+*
+ DO 100 IN = 1, NIDIM
+ N = IDIM( IN )
+* Set LDA to 1 more than minimum value if room.
+ LDA = N
+ IF( LDA.LT.NMAX )
+ $ LDA = LDA + 1
+* Skip tests if not enough room.
+ IF( LDA.GT.NMAX )
+ $ GO TO 100
+ IF( PACKED )THEN
+ LAA = ( N*( N + 1 ) )/2
+ ELSE
+ LAA = LDA*N
+ END IF
+*
+ DO 90 IC = 1, 2
+ UPLO = ICH( IC: IC )
+ UPPER = UPLO.EQ.'U'
+*
+ DO 80 IX = 1, NINC
+ INCX = INC( IX )
+ LX = ABS( INCX )*N
+*
+* Generate the vector X.
+*
+ TRANSL = HALF
+ CALL ZMAKE( 'GE', ' ', ' ', 1, N, X, 1, XX, ABS( INCX ),
+ $ 0, N - 1, RESET, TRANSL )
+ IF( N.GT.1 )THEN
+ X( N/2 ) = ZERO
+ XX( 1 + ABS( INCX )*( N/2 - 1 ) ) = ZERO
+ END IF
+*
+ DO 70 IA = 1, NALF
+ RALPHA = DBLE( ALF( IA ) )
+ ALPHA = DCMPLX( RALPHA, RZERO )
+ NULL = N.LE.0.OR.RALPHA.EQ.RZERO
+*
+* Generate the matrix A.
+*
+ TRANSL = ZERO
+ CALL ZMAKE( SNAME( 2: 3 ), UPLO, ' ', N, N, A, NMAX,
+ $ AA, LDA, N - 1, N - 1, RESET, TRANSL )
+*
+ NC = NC + 1
+*
+* Save every datum before calling the subroutine.
+*
+ UPLOS = UPLO
+ NS = N
+ RALS = RALPHA
+ DO 10 I = 1, LAA
+ AS( I ) = AA( I )
+ 10 CONTINUE
+ LDAS = LDA
+ DO 20 I = 1, LX
+ XS( I ) = XX( I )
+ 20 CONTINUE
+ INCXS = INCX
+*
+* Call the subroutine.
+*
+ IF( FULL )THEN
+ IF( TRACE )
+ $ WRITE( NTRA, FMT = 9993 )NC, SNAME, UPLO, N,
+ $ RALPHA, INCX, LDA
+ IF( REWI )
+ $ REWIND NTRA
+ CALL ZHER( UPLO, N, RALPHA, XX, INCX, AA, LDA )
+ ELSE IF( PACKED )THEN
+ IF( TRACE )
+ $ WRITE( NTRA, FMT = 9994 )NC, SNAME, UPLO, N,
+ $ RALPHA, INCX
+ IF( REWI )
+ $ REWIND NTRA
+ CALL ZHPR( UPLO, N, RALPHA, XX, INCX, AA )
+ END IF
+*
+* Check if error-exit was taken incorrectly.
+*
+ IF( .NOT.OK )THEN
+ WRITE( NOUT, FMT = 9992 )
+ FATAL = .TRUE.
+ GO TO 120
+ END IF
+*
+* See what data changed inside subroutines.
+*
+ ISAME( 1 ) = UPLO.EQ.UPLOS
+ ISAME( 2 ) = NS.EQ.N
+ ISAME( 3 ) = RALS.EQ.RALPHA
+ ISAME( 4 ) = LZE( XS, XX, LX )
+ ISAME( 5 ) = INCXS.EQ.INCX
+ IF( NULL )THEN
+ ISAME( 6 ) = LZE( AS, AA, LAA )
+ ELSE
+ ISAME( 6 ) = LZERES( SNAME( 2: 3 ), UPLO, N, N, AS,
+ $ AA, LDA )
+ END IF
+ IF( .NOT.PACKED )THEN
+ ISAME( 7 ) = LDAS.EQ.LDA
+ END IF
+*
+* If data was incorrectly changed, report and return.
+*
+ SAME = .TRUE.
+ DO 30 I = 1, NARGS
+ SAME = SAME.AND.ISAME( I )
+ IF( .NOT.ISAME( I ) )
+ $ WRITE( NOUT, FMT = 9998 )I
+ 30 CONTINUE
+ IF( .NOT.SAME )THEN
+ FATAL = .TRUE.
+ GO TO 120
+ END IF
+*
+ IF( .NOT.NULL )THEN
+*
+* Check the result column by column.
+*
+ IF( INCX.GT.0 )THEN
+ DO 40 I = 1, N
+ Z( I ) = X( I )
+ 40 CONTINUE
+ ELSE
+ DO 50 I = 1, N
+ Z( I ) = X( N - I + 1 )
+ 50 CONTINUE
+ END IF
+ JA = 1
+ DO 60 J = 1, N
+ W( 1 ) = DCONJG( Z( J ) )
+ IF( UPPER )THEN
+ JJ = 1
+ LJ = J
+ ELSE
+ JJ = J
+ LJ = N - J + 1
+ END IF
+ CALL ZMVCH( 'N', LJ, 1, ALPHA, Z( JJ ), LJ, W,
+ $ 1, ONE, A( JJ, J ), 1, YT, G,
+ $ AA( JA ), EPS, ERR, FATAL, NOUT,
+ $ .TRUE. )
+ IF( FULL )THEN
+ IF( UPPER )THEN
+ JA = JA + LDA
+ ELSE
+ JA = JA + LDA + 1
+ END IF
+ ELSE
+ JA = JA + LJ
+ END IF
+ ERRMAX = MAX( ERRMAX, ERR )
+* If got really bad answer, report and return.
+ IF( FATAL )
+ $ GO TO 110
+ 60 CONTINUE
+ ELSE
+* Avoid repeating tests if N.le.0.
+ IF( N.LE.0 )
+ $ GO TO 100
+ END IF
+*
+ 70 CONTINUE
+*
+ 80 CONTINUE
+*
+ 90 CONTINUE
+*
+ 100 CONTINUE
+*
+* Report result.
+*
+ IF( ERRMAX.LT.THRESH )THEN
+ WRITE( NOUT, FMT = 9999 )SNAME, NC
+ ELSE
+ WRITE( NOUT, FMT = 9997 )SNAME, NC, ERRMAX
+ END IF
+ GO TO 130
+*
+ 110 CONTINUE
+ WRITE( NOUT, FMT = 9995 )J
+*
+ 120 CONTINUE
+ WRITE( NOUT, FMT = 9996 )SNAME
+ IF( FULL )THEN
+ WRITE( NOUT, FMT = 9993 )NC, SNAME, UPLO, N, RALPHA, INCX, LDA
+ ELSE IF( PACKED )THEN
+ WRITE( NOUT, FMT = 9994 )NC, SNAME, UPLO, N, RALPHA, INCX
+ END IF
+*
+ 130 CONTINUE
+ RETURN
+*
+ 9999 FORMAT( ' ', A6, ' PASSED THE COMPUTATIONAL TESTS (', I6, ' CALL',
+ $ 'S)' )
+ 9998 FORMAT( ' ******* FATAL ERROR - PARAMETER NUMBER ', I2, ' WAS CH',
+ $ 'ANGED INCORRECTLY *******' )
+ 9997 FORMAT( ' ', A6, ' COMPLETED THE COMPUTATIONAL TESTS (', I6, ' C',
+ $ 'ALLS)', /' ******* BUT WITH MAXIMUM TEST RATIO', F8.2,
+ $ ' - SUSPECT *******' )
+ 9996 FORMAT( ' ******* ', A6, ' FAILED ON CALL NUMBER:' )
+ 9995 FORMAT( ' THESE ARE THE RESULTS FOR COLUMN ', I3 )
+ 9994 FORMAT( 1X, I6, ': ', A6, '(''', A1, ''',', I3, ',', F4.1, ', X,',
+ $ I2, ', AP) .' )
+ 9993 FORMAT( 1X, I6, ': ', A6, '(''', A1, ''',', I3, ',', F4.1, ', X,',
+ $ I2, ', A,', I3, ') .' )
+ 9992 FORMAT( ' ******* FATAL ERROR - ERROR-EXIT TAKEN ON VALID CALL *',
+ $ '******' )
+*
+* End of ZCHK5.
+*
+ END
+ SUBROUTINE ZCHK6( SNAME, EPS, THRESH, NOUT, NTRA, TRACE, REWI,
+ $ FATAL, NIDIM, IDIM, NALF, ALF, NINC, INC, NMAX,
+ $ INCMAX, A, AA, AS, X, XX, XS, Y, YY, YS, YT, G,
+ $ Z )
+*
+* Tests ZHER2 and ZHPR2.
+*
+* Auxiliary routine for test program for Level 2 Blas.
+*
+* -- Written on 10-August-1987.
+* Richard Hanson, Sandia National Labs.
+* Jeremy Du Croz, NAG Central Office.
+*
+* .. Parameters ..
+ COMPLEX*16 ZERO, HALF, ONE
+ PARAMETER ( ZERO = ( 0.0D0, 0.0D0 ),
+ $ HALF = ( 0.5D0, 0.0D0 ),
+ $ ONE = ( 1.0D0, 0.0D0 ) )
+ DOUBLE PRECISION RZERO
+ PARAMETER ( RZERO = 0.0D0 )
+* .. Scalar Arguments ..
+ DOUBLE PRECISION EPS, THRESH
+ INTEGER INCMAX, NALF, NIDIM, NINC, NMAX, NOUT, NTRA
+ LOGICAL FATAL, REWI, TRACE
+ CHARACTER*6 SNAME
+* .. Array Arguments ..
+ COMPLEX*16 A( NMAX, NMAX ), AA( NMAX*NMAX ), ALF( NALF ),
+ $ AS( NMAX*NMAX ), X( NMAX ), XS( NMAX*INCMAX ),
+ $ XX( NMAX*INCMAX ), Y( NMAX ),
+ $ YS( NMAX*INCMAX ), YT( NMAX ),
+ $ YY( NMAX*INCMAX ), Z( NMAX, 2 )
+ DOUBLE PRECISION G( NMAX )
+ INTEGER IDIM( NIDIM ), INC( NINC )
+* .. Local Scalars ..
+ COMPLEX*16 ALPHA, ALS, TRANSL
+ DOUBLE PRECISION ERR, ERRMAX
+ INTEGER I, IA, IC, IN, INCX, INCXS, INCY, INCYS, IX,
+ $ IY, J, JA, JJ, LAA, LDA, LDAS, LJ, LX, LY, N,
+ $ NARGS, NC, NS
+ LOGICAL FULL, NULL, PACKED, RESET, SAME, UPPER
+ CHARACTER*1 UPLO, UPLOS
+ CHARACTER*2 ICH
+* .. Local Arrays ..
+ COMPLEX*16 W( 2 )
+ LOGICAL ISAME( 13 )
+* .. External Functions ..
+ LOGICAL LZE, LZERES
+ EXTERNAL LZE, LZERES
+* .. External Subroutines ..
+ EXTERNAL ZHER2, ZHPR2, ZMAKE, ZMVCH
+* .. Intrinsic Functions ..
+ INTRINSIC ABS, DCONJG, MAX
+* .. Scalars in Common ..
+ INTEGER INFOT, NOUTC
+ LOGICAL LERR, OK
+* .. Common blocks ..
+ COMMON /INFOC/INFOT, NOUTC, OK, LERR
+* .. Data statements ..
+ DATA ICH/'UL'/
+* .. Executable Statements ..
+ FULL = SNAME( 3: 3 ).EQ.'E'
+ PACKED = SNAME( 3: 3 ).EQ.'P'
+* Define the number of arguments.
+ IF( FULL )THEN
+ NARGS = 9
+ ELSE IF( PACKED )THEN
+ NARGS = 8
+ END IF
+*
+ NC = 0
+ RESET = .TRUE.
+ ERRMAX = RZERO
+*
+ DO 140 IN = 1, NIDIM
+ N = IDIM( IN )
+* Set LDA to 1 more than minimum value if room.
+ LDA = N
+ IF( LDA.LT.NMAX )
+ $ LDA = LDA + 1
+* Skip tests if not enough room.
+ IF( LDA.GT.NMAX )
+ $ GO TO 140
+ IF( PACKED )THEN
+ LAA = ( N*( N + 1 ) )/2
+ ELSE
+ LAA = LDA*N
+ END IF
+*
+ DO 130 IC = 1, 2
+ UPLO = ICH( IC: IC )
+ UPPER = UPLO.EQ.'U'
+*
+ DO 120 IX = 1, NINC
+ INCX = INC( IX )
+ LX = ABS( INCX )*N
+*
+* Generate the vector X.
+*
+ TRANSL = HALF
+ CALL ZMAKE( 'GE', ' ', ' ', 1, N, X, 1, XX, ABS( INCX ),
+ $ 0, N - 1, RESET, TRANSL )
+ IF( N.GT.1 )THEN
+ X( N/2 ) = ZERO
+ XX( 1 + ABS( INCX )*( N/2 - 1 ) ) = ZERO
+ END IF
+*
+ DO 110 IY = 1, NINC
+ INCY = INC( IY )
+ LY = ABS( INCY )*N
+*
+* Generate the vector Y.
+*
+ TRANSL = ZERO
+ CALL ZMAKE( 'GE', ' ', ' ', 1, N, Y, 1, YY,
+ $ ABS( INCY ), 0, N - 1, RESET, TRANSL )
+ IF( N.GT.1 )THEN
+ Y( N/2 ) = ZERO
+ YY( 1 + ABS( INCY )*( N/2 - 1 ) ) = ZERO
+ END IF
+*
+ DO 100 IA = 1, NALF
+ ALPHA = ALF( IA )
+ NULL = N.LE.0.OR.ALPHA.EQ.ZERO
+*
+* Generate the matrix A.
+*
+ TRANSL = ZERO
+ CALL ZMAKE( SNAME( 2: 3 ), UPLO, ' ', N, N, A,
+ $ NMAX, AA, LDA, N - 1, N - 1, RESET,
+ $ TRANSL )
+*
+ NC = NC + 1
+*
+* Save every datum before calling the subroutine.
+*
+ UPLOS = UPLO
+ NS = N
+ ALS = ALPHA
+ DO 10 I = 1, LAA
+ AS( I ) = AA( I )
+ 10 CONTINUE
+ LDAS = LDA
+ DO 20 I = 1, LX
+ XS( I ) = XX( I )
+ 20 CONTINUE
+ INCXS = INCX
+ DO 30 I = 1, LY
+ YS( I ) = YY( I )
+ 30 CONTINUE
+ INCYS = INCY
+*
+* Call the subroutine.
+*
+ IF( FULL )THEN
+ IF( TRACE )
+ $ WRITE( NTRA, FMT = 9993 )NC, SNAME, UPLO, N,
+ $ ALPHA, INCX, INCY, LDA
+ IF( REWI )
+ $ REWIND NTRA
+ CALL ZHER2( UPLO, N, ALPHA, XX, INCX, YY, INCY,
+ $ AA, LDA )
+ ELSE IF( PACKED )THEN
+ IF( TRACE )
+ $ WRITE( NTRA, FMT = 9994 )NC, SNAME, UPLO, N,
+ $ ALPHA, INCX, INCY
+ IF( REWI )
+ $ REWIND NTRA
+ CALL ZHPR2( UPLO, N, ALPHA, XX, INCX, YY, INCY,
+ $ AA )
+ END IF
+*
+* Check if error-exit was taken incorrectly.
+*
+ IF( .NOT.OK )THEN
+ WRITE( NOUT, FMT = 9992 )
+ FATAL = .TRUE.
+ GO TO 160
+ END IF
+*
+* See what data changed inside subroutines.
+*
+ ISAME( 1 ) = UPLO.EQ.UPLOS
+ ISAME( 2 ) = NS.EQ.N
+ ISAME( 3 ) = ALS.EQ.ALPHA
+ ISAME( 4 ) = LZE( XS, XX, LX )
+ ISAME( 5 ) = INCXS.EQ.INCX
+ ISAME( 6 ) = LZE( YS, YY, LY )
+ ISAME( 7 ) = INCYS.EQ.INCY
+ IF( NULL )THEN
+ ISAME( 8 ) = LZE( AS, AA, LAA )
+ ELSE
+ ISAME( 8 ) = LZERES( SNAME( 2: 3 ), UPLO, N, N,
+ $ AS, AA, LDA )
+ END IF
+ IF( .NOT.PACKED )THEN
+ ISAME( 9 ) = LDAS.EQ.LDA
+ END IF
+*
+* If data was incorrectly changed, report and return.
+*
+ SAME = .TRUE.
+ DO 40 I = 1, NARGS
+ SAME = SAME.AND.ISAME( I )
+ IF( .NOT.ISAME( I ) )
+ $ WRITE( NOUT, FMT = 9998 )I
+ 40 CONTINUE
+ IF( .NOT.SAME )THEN
+ FATAL = .TRUE.
+ GO TO 160
+ END IF
+*
+ IF( .NOT.NULL )THEN
+*
+* Check the result column by column.
+*
+ IF( INCX.GT.0 )THEN
+ DO 50 I = 1, N
+ Z( I, 1 ) = X( I )
+ 50 CONTINUE
+ ELSE
+ DO 60 I = 1, N
+ Z( I, 1 ) = X( N - I + 1 )
+ 60 CONTINUE
+ END IF
+ IF( INCY.GT.0 )THEN
+ DO 70 I = 1, N
+ Z( I, 2 ) = Y( I )
+ 70 CONTINUE
+ ELSE
+ DO 80 I = 1, N
+ Z( I, 2 ) = Y( N - I + 1 )
+ 80 CONTINUE
+ END IF
+ JA = 1
+ DO 90 J = 1, N
+ W( 1 ) = ALPHA*DCONJG( Z( J, 2 ) )
+ W( 2 ) = DCONJG( ALPHA )*DCONJG( Z( J, 1 ) )
+ IF( UPPER )THEN
+ JJ = 1
+ LJ = J
+ ELSE
+ JJ = J
+ LJ = N - J + 1
+ END IF
+ CALL ZMVCH( 'N', LJ, 2, ONE, Z( JJ, 1 ),
+ $ NMAX, W, 1, ONE, A( JJ, J ), 1,
+ $ YT, G, AA( JA ), EPS, ERR, FATAL,
+ $ NOUT, .TRUE. )
+ IF( FULL )THEN
+ IF( UPPER )THEN
+ JA = JA + LDA
+ ELSE
+ JA = JA + LDA + 1
+ END IF
+ ELSE
+ JA = JA + LJ
+ END IF
+ ERRMAX = MAX( ERRMAX, ERR )
+* If got really bad answer, report and return.
+ IF( FATAL )
+ $ GO TO 150
+ 90 CONTINUE
+ ELSE
+* Avoid repeating tests with N.le.0.
+ IF( N.LE.0 )
+ $ GO TO 140
+ END IF
+*
+ 100 CONTINUE
+*
+ 110 CONTINUE
+*
+ 120 CONTINUE
+*
+ 130 CONTINUE
+*
+ 140 CONTINUE
+*
+* Report result.
+*
+ IF( ERRMAX.LT.THRESH )THEN
+ WRITE( NOUT, FMT = 9999 )SNAME, NC
+ ELSE
+ WRITE( NOUT, FMT = 9997 )SNAME, NC, ERRMAX
+ END IF
+ GO TO 170
+*
+ 150 CONTINUE
+ WRITE( NOUT, FMT = 9995 )J
+*
+ 160 CONTINUE
+ WRITE( NOUT, FMT = 9996 )SNAME
+ IF( FULL )THEN
+ WRITE( NOUT, FMT = 9993 )NC, SNAME, UPLO, N, ALPHA, INCX,
+ $ INCY, LDA
+ ELSE IF( PACKED )THEN
+ WRITE( NOUT, FMT = 9994 )NC, SNAME, UPLO, N, ALPHA, INCX, INCY
+ END IF
+*
+ 170 CONTINUE
+ RETURN
+*
+ 9999 FORMAT( ' ', A6, ' PASSED THE COMPUTATIONAL TESTS (', I6, ' CALL',
+ $ 'S)' )
+ 9998 FORMAT( ' ******* FATAL ERROR - PARAMETER NUMBER ', I2, ' WAS CH',
+ $ 'ANGED INCORRECTLY *******' )
+ 9997 FORMAT( ' ', A6, ' COMPLETED THE COMPUTATIONAL TESTS (', I6, ' C',
+ $ 'ALLS)', /' ******* BUT WITH MAXIMUM TEST RATIO', F8.2,
+ $ ' - SUSPECT *******' )
+ 9996 FORMAT( ' ******* ', A6, ' FAILED ON CALL NUMBER:' )
+ 9995 FORMAT( ' THESE ARE THE RESULTS FOR COLUMN ', I3 )
+ 9994 FORMAT( 1X, I6, ': ', A6, '(''', A1, ''',', I3, ',(', F4.1, ',',
+ $ F4.1, '), X,', I2, ', Y,', I2, ', AP) ',
+ $ ' .' )
+ 9993 FORMAT( 1X, I6, ': ', A6, '(''', A1, ''',', I3, ',(', F4.1, ',',
+ $ F4.1, '), X,', I2, ', Y,', I2, ', A,', I3, ') ',
+ $ ' .' )
+ 9992 FORMAT( ' ******* FATAL ERROR - ERROR-EXIT TAKEN ON VALID CALL *',
+ $ '******' )
+*
+* End of ZCHK6.
+*
+ END
+ SUBROUTINE ZCHKE( ISNUM, SRNAMT, NOUT )
+*
+* Tests the error exits from the Level 2 Blas.
+* Requires a special version of the error-handling routine XERBLA.
+* ALPHA, RALPHA, BETA, A, X and Y should not need to be defined.
+*
+* Auxiliary routine for test program for Level 2 Blas.
+*
+* -- Written on 10-August-1987.
+* Richard Hanson, Sandia National Labs.
+* Jeremy Du Croz, NAG Central Office.
+*
+* .. Scalar Arguments ..
+ INTEGER ISNUM, NOUT
+ CHARACTER*6 SRNAMT
+* .. Scalars in Common ..
+ INTEGER INFOT, NOUTC
+ LOGICAL LERR, OK
+* .. Local Scalars ..
+ COMPLEX*16 ALPHA, BETA
+ DOUBLE PRECISION RALPHA
+* .. Local Arrays ..
+ COMPLEX*16 A( 1, 1 ), X( 1 ), Y( 1 )
+* .. External Subroutines ..
+ EXTERNAL CHKXER, ZGBMV, ZGEMV, ZGERC, ZGERU, ZHBMV,
+ $ ZHEMV, ZHER, ZHER2, ZHPMV, ZHPR, ZHPR2, ZTBMV,
+ $ ZTBSV, ZTPMV, ZTPSV, ZTRMV, ZTRSV
+* .. Common blocks ..
+ COMMON /INFOC/INFOT, NOUTC, OK, LERR
+* .. Executable Statements ..
+* OK is set to .FALSE. by the special version of XERBLA or by CHKXER
+* if anything is wrong.
+ OK = .TRUE.
+* LERR is set to .TRUE. by the special version of XERBLA each time
+* it is called, and is then tested and re-set by CHKXER.
+ LERR = .FALSE.
+ GO TO ( 10, 20, 30, 40, 50, 60, 70, 80,
+ $ 90, 100, 110, 120, 130, 140, 150, 160,
+ $ 170 )ISNUM
+ 10 INFOT = 1
+ CALL ZGEMV( '/', 0, 0, ALPHA, A, 1, X, 1, BETA, Y, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 2
+ CALL ZGEMV( 'N', -1, 0, ALPHA, A, 1, X, 1, BETA, Y, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 3
+ CALL ZGEMV( 'N', 0, -1, ALPHA, A, 1, X, 1, BETA, Y, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 6
+ CALL ZGEMV( 'N', 2, 0, ALPHA, A, 1, X, 1, BETA, Y, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 8
+ CALL ZGEMV( 'N', 0, 0, ALPHA, A, 1, X, 0, BETA, Y, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 11
+ CALL ZGEMV( 'N', 0, 0, ALPHA, A, 1, X, 1, BETA, Y, 0 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ GO TO 180
+ 20 INFOT = 1
+ CALL ZGBMV( '/', 0, 0, 0, 0, ALPHA, A, 1, X, 1, BETA, Y, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 2
+ CALL ZGBMV( 'N', -1, 0, 0, 0, ALPHA, A, 1, X, 1, BETA, Y, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 3
+ CALL ZGBMV( 'N', 0, -1, 0, 0, ALPHA, A, 1, X, 1, BETA, Y, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 4
+ CALL ZGBMV( 'N', 0, 0, -1, 0, ALPHA, A, 1, X, 1, BETA, Y, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 5
+ CALL ZGBMV( 'N', 2, 0, 0, -1, ALPHA, A, 1, X, 1, BETA, Y, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 8
+ CALL ZGBMV( 'N', 0, 0, 1, 0, ALPHA, A, 1, X, 1, BETA, Y, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 10
+ CALL ZGBMV( 'N', 0, 0, 0, 0, ALPHA, A, 1, X, 0, BETA, Y, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 13
+ CALL ZGBMV( 'N', 0, 0, 0, 0, ALPHA, A, 1, X, 1, BETA, Y, 0 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ GO TO 180
+ 30 INFOT = 1
+ CALL ZHEMV( '/', 0, ALPHA, A, 1, X, 1, BETA, Y, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 2
+ CALL ZHEMV( 'U', -1, ALPHA, A, 1, X, 1, BETA, Y, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 5
+ CALL ZHEMV( 'U', 2, ALPHA, A, 1, X, 1, BETA, Y, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 7
+ CALL ZHEMV( 'U', 0, ALPHA, A, 1, X, 0, BETA, Y, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 10
+ CALL ZHEMV( 'U', 0, ALPHA, A, 1, X, 1, BETA, Y, 0 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ GO TO 180
+ 40 INFOT = 1
+ CALL ZHBMV( '/', 0, 0, ALPHA, A, 1, X, 1, BETA, Y, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 2
+ CALL ZHBMV( 'U', -1, 0, ALPHA, A, 1, X, 1, BETA, Y, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 3
+ CALL ZHBMV( 'U', 0, -1, ALPHA, A, 1, X, 1, BETA, Y, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 6
+ CALL ZHBMV( 'U', 0, 1, ALPHA, A, 1, X, 1, BETA, Y, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 8
+ CALL ZHBMV( 'U', 0, 0, ALPHA, A, 1, X, 0, BETA, Y, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 11
+ CALL ZHBMV( 'U', 0, 0, ALPHA, A, 1, X, 1, BETA, Y, 0 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ GO TO 180
+ 50 INFOT = 1
+ CALL ZHPMV( '/', 0, ALPHA, A, X, 1, BETA, Y, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 2
+ CALL ZHPMV( 'U', -1, ALPHA, A, X, 1, BETA, Y, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 6
+ CALL ZHPMV( 'U', 0, ALPHA, A, X, 0, BETA, Y, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 9
+ CALL ZHPMV( 'U', 0, ALPHA, A, X, 1, BETA, Y, 0 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ GO TO 180
+ 60 INFOT = 1
+ CALL ZTRMV( '/', 'N', 'N', 0, A, 1, X, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 2
+ CALL ZTRMV( 'U', '/', 'N', 0, A, 1, X, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 3
+ CALL ZTRMV( 'U', 'N', '/', 0, A, 1, X, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 4
+ CALL ZTRMV( 'U', 'N', 'N', -1, A, 1, X, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 6
+ CALL ZTRMV( 'U', 'N', 'N', 2, A, 1, X, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 8
+ CALL ZTRMV( 'U', 'N', 'N', 0, A, 1, X, 0 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ GO TO 180
+ 70 INFOT = 1
+ CALL ZTBMV( '/', 'N', 'N', 0, 0, A, 1, X, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 2
+ CALL ZTBMV( 'U', '/', 'N', 0, 0, A, 1, X, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 3
+ CALL ZTBMV( 'U', 'N', '/', 0, 0, A, 1, X, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 4
+ CALL ZTBMV( 'U', 'N', 'N', -1, 0, A, 1, X, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 5
+ CALL ZTBMV( 'U', 'N', 'N', 0, -1, A, 1, X, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 7
+ CALL ZTBMV( 'U', 'N', 'N', 0, 1, A, 1, X, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 9
+ CALL ZTBMV( 'U', 'N', 'N', 0, 0, A, 1, X, 0 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ GO TO 180
+ 80 INFOT = 1
+ CALL ZTPMV( '/', 'N', 'N', 0, A, X, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 2
+ CALL ZTPMV( 'U', '/', 'N', 0, A, X, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 3
+ CALL ZTPMV( 'U', 'N', '/', 0, A, X, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 4
+ CALL ZTPMV( 'U', 'N', 'N', -1, A, X, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 7
+ CALL ZTPMV( 'U', 'N', 'N', 0, A, X, 0 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ GO TO 180
+ 90 INFOT = 1
+ CALL ZTRSV( '/', 'N', 'N', 0, A, 1, X, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 2
+ CALL ZTRSV( 'U', '/', 'N', 0, A, 1, X, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 3
+ CALL ZTRSV( 'U', 'N', '/', 0, A, 1, X, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 4
+ CALL ZTRSV( 'U', 'N', 'N', -1, A, 1, X, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 6
+ CALL ZTRSV( 'U', 'N', 'N', 2, A, 1, X, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 8
+ CALL ZTRSV( 'U', 'N', 'N', 0, A, 1, X, 0 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ GO TO 180
+ 100 INFOT = 1
+ CALL ZTBSV( '/', 'N', 'N', 0, 0, A, 1, X, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 2
+ CALL ZTBSV( 'U', '/', 'N', 0, 0, A, 1, X, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 3
+ CALL ZTBSV( 'U', 'N', '/', 0, 0, A, 1, X, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 4
+ CALL ZTBSV( 'U', 'N', 'N', -1, 0, A, 1, X, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 5
+ CALL ZTBSV( 'U', 'N', 'N', 0, -1, A, 1, X, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 7
+ CALL ZTBSV( 'U', 'N', 'N', 0, 1, A, 1, X, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 9
+ CALL ZTBSV( 'U', 'N', 'N', 0, 0, A, 1, X, 0 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ GO TO 180
+ 110 INFOT = 1
+ CALL ZTPSV( '/', 'N', 'N', 0, A, X, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 2
+ CALL ZTPSV( 'U', '/', 'N', 0, A, X, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 3
+ CALL ZTPSV( 'U', 'N', '/', 0, A, X, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 4
+ CALL ZTPSV( 'U', 'N', 'N', -1, A, X, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 7
+ CALL ZTPSV( 'U', 'N', 'N', 0, A, X, 0 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ GO TO 180
+ 120 INFOT = 1
+ CALL ZGERC( -1, 0, ALPHA, X, 1, Y, 1, A, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 2
+ CALL ZGERC( 0, -1, ALPHA, X, 1, Y, 1, A, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 5
+ CALL ZGERC( 0, 0, ALPHA, X, 0, Y, 1, A, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 7
+ CALL ZGERC( 0, 0, ALPHA, X, 1, Y, 0, A, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 9
+ CALL ZGERC( 2, 0, ALPHA, X, 1, Y, 1, A, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ GO TO 180
+ 130 INFOT = 1
+ CALL ZGERU( -1, 0, ALPHA, X, 1, Y, 1, A, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 2
+ CALL ZGERU( 0, -1, ALPHA, X, 1, Y, 1, A, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 5
+ CALL ZGERU( 0, 0, ALPHA, X, 0, Y, 1, A, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 7
+ CALL ZGERU( 0, 0, ALPHA, X, 1, Y, 0, A, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 9
+ CALL ZGERU( 2, 0, ALPHA, X, 1, Y, 1, A, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ GO TO 180
+ 140 INFOT = 1
+ CALL ZHER( '/', 0, RALPHA, X, 1, A, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 2
+ CALL ZHER( 'U', -1, RALPHA, X, 1, A, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 5
+ CALL ZHER( 'U', 0, RALPHA, X, 0, A, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 7
+ CALL ZHER( 'U', 2, RALPHA, X, 1, A, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ GO TO 180
+ 150 INFOT = 1
+ CALL ZHPR( '/', 0, RALPHA, X, 1, A )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 2
+ CALL ZHPR( 'U', -1, RALPHA, X, 1, A )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 5
+ CALL ZHPR( 'U', 0, RALPHA, X, 0, A )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ GO TO 180
+ 160 INFOT = 1
+ CALL ZHER2( '/', 0, ALPHA, X, 1, Y, 1, A, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 2
+ CALL ZHER2( 'U', -1, ALPHA, X, 1, Y, 1, A, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 5
+ CALL ZHER2( 'U', 0, ALPHA, X, 0, Y, 1, A, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 7
+ CALL ZHER2( 'U', 0, ALPHA, X, 1, Y, 0, A, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 9
+ CALL ZHER2( 'U', 2, ALPHA, X, 1, Y, 1, A, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ GO TO 180
+ 170 INFOT = 1
+ CALL ZHPR2( '/', 0, ALPHA, X, 1, Y, 1, A )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 2
+ CALL ZHPR2( 'U', -1, ALPHA, X, 1, Y, 1, A )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 5
+ CALL ZHPR2( 'U', 0, ALPHA, X, 0, Y, 1, A )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 7
+ CALL ZHPR2( 'U', 0, ALPHA, X, 1, Y, 0, A )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+*
+ 180 IF( OK )THEN
+ WRITE( NOUT, FMT = 9999 )SRNAMT
+ ELSE
+ WRITE( NOUT, FMT = 9998 )SRNAMT
+ END IF
+ RETURN
+*
+ 9999 FORMAT( ' ', A6, ' PASSED THE TESTS OF ERROR-EXITS' )
+ 9998 FORMAT( ' ******* ', A6, ' FAILED THE TESTS OF ERROR-EXITS *****',
+ $ '**' )
+*
+* End of ZCHKE.
+*
+ END
+ SUBROUTINE ZMAKE( TYPE, UPLO, DIAG, M, N, A, NMAX, AA, LDA, KL,
+ $ KU, RESET, TRANSL )
+*
+* Generates values for an M by N matrix A within the bandwidth
+* defined by KL and KU.
+* Stores the values in the array AA in the data structure required
+* by the routine, with unwanted elements set to rogue value.
+*
+* TYPE is 'GE', 'GB', 'HE', 'HB', 'HP', 'TR', 'TB' OR 'TP'.
+*
+* Auxiliary routine for test program for Level 2 Blas.
+*
+* -- Written on 10-August-1987.
+* Richard Hanson, Sandia National Labs.
+* Jeremy Du Croz, NAG Central Office.
+*
+* .. Parameters ..
+ COMPLEX*16 ZERO, ONE
+ PARAMETER ( ZERO = ( 0.0D0, 0.0D0 ),
+ $ ONE = ( 1.0D0, 0.0D0 ) )
+ COMPLEX*16 ROGUE
+ PARAMETER ( ROGUE = ( -1.0D10, 1.0D10 ) )
+ DOUBLE PRECISION RZERO
+ PARAMETER ( RZERO = 0.0D0 )
+ DOUBLE PRECISION RROGUE
+ PARAMETER ( RROGUE = -1.0D10 )
+* .. Scalar Arguments ..
+ COMPLEX*16 TRANSL
+ INTEGER KL, KU, LDA, M, N, NMAX
+ LOGICAL RESET
+ CHARACTER*1 DIAG, UPLO
+ CHARACTER*2 TYPE
+* .. Array Arguments ..
+ COMPLEX*16 A( NMAX, * ), AA( * )
+* .. Local Scalars ..
+ INTEGER I, I1, I2, I3, IBEG, IEND, IOFF, J, JJ, KK
+ LOGICAL GEN, LOWER, SYM, TRI, UNIT, UPPER
+* .. External Functions ..
+ COMPLEX*16 ZBEG
+ EXTERNAL ZBEG
+* .. Intrinsic Functions ..
+ INTRINSIC DBLE, DCMPLX, DCONJG, MAX, MIN
+* .. Executable Statements ..
+ GEN = TYPE( 1: 1 ).EQ.'G'
+ SYM = TYPE( 1: 1 ).EQ.'H'
+ TRI = TYPE( 1: 1 ).EQ.'T'
+ UPPER = ( SYM.OR.TRI ).AND.UPLO.EQ.'U'
+ LOWER = ( SYM.OR.TRI ).AND.UPLO.EQ.'L'
+ UNIT = TRI.AND.DIAG.EQ.'U'
+*
+* Generate data in array A.
+*
+ DO 20 J = 1, N
+ DO 10 I = 1, M
+ IF( GEN.OR.( UPPER.AND.I.LE.J ).OR.( LOWER.AND.I.GE.J ) )
+ $ THEN
+ IF( ( I.LE.J.AND.J - I.LE.KU ).OR.
+ $ ( I.GE.J.AND.I - J.LE.KL ) )THEN
+ A( I, J ) = ZBEG( RESET ) + TRANSL
+ ELSE
+ A( I, J ) = ZERO
+ END IF
+ IF( I.NE.J )THEN
+ IF( SYM )THEN
+ A( J, I ) = DCONJG( A( I, J ) )
+ ELSE IF( TRI )THEN
+ A( J, I ) = ZERO
+ END IF
+ END IF
+ END IF
+ 10 CONTINUE
+ IF( SYM )
+ $ A( J, J ) = DCMPLX( DBLE( A( J, J ) ), RZERO )
+ IF( TRI )
+ $ A( J, J ) = A( J, J ) + ONE
+ IF( UNIT )
+ $ A( J, J ) = ONE
+ 20 CONTINUE
+*
+* Store elements in array AS in data structure required by routine.
+*
+ IF( TYPE.EQ.'GE' )THEN
+ DO 50 J = 1, N
+ DO 30 I = 1, M
+ AA( I + ( J - 1 )*LDA ) = A( I, J )
+ 30 CONTINUE
+ DO 40 I = M + 1, LDA
+ AA( I + ( J - 1 )*LDA ) = ROGUE
+ 40 CONTINUE
+ 50 CONTINUE
+ ELSE IF( TYPE.EQ.'GB' )THEN
+ DO 90 J = 1, N
+ DO 60 I1 = 1, KU + 1 - J
+ AA( I1 + ( J - 1 )*LDA ) = ROGUE
+ 60 CONTINUE
+ DO 70 I2 = I1, MIN( KL + KU + 1, KU + 1 + M - J )
+ AA( I2 + ( J - 1 )*LDA ) = A( I2 + J - KU - 1, J )
+ 70 CONTINUE
+ DO 80 I3 = I2, LDA
+ AA( I3 + ( J - 1 )*LDA ) = ROGUE
+ 80 CONTINUE
+ 90 CONTINUE
+ ELSE IF( TYPE.EQ.'HE'.OR.TYPE.EQ.'TR' )THEN
+ DO 130 J = 1, N
+ IF( UPPER )THEN
+ IBEG = 1
+ IF( UNIT )THEN
+ IEND = J - 1
+ ELSE
+ IEND = J
+ END IF
+ ELSE
+ IF( UNIT )THEN
+ IBEG = J + 1
+ ELSE
+ IBEG = J
+ END IF
+ IEND = N
+ END IF
+ DO 100 I = 1, IBEG - 1
+ AA( I + ( J - 1 )*LDA ) = ROGUE
+ 100 CONTINUE
+ DO 110 I = IBEG, IEND
+ AA( I + ( J - 1 )*LDA ) = A( I, J )
+ 110 CONTINUE
+ DO 120 I = IEND + 1, LDA
+ AA( I + ( J - 1 )*LDA ) = ROGUE
+ 120 CONTINUE
+ IF( SYM )THEN
+ JJ = J + ( J - 1 )*LDA
+ AA( JJ ) = DCMPLX( DBLE( AA( JJ ) ), RROGUE )
+ END IF
+ 130 CONTINUE
+ ELSE IF( TYPE.EQ.'HB'.OR.TYPE.EQ.'TB' )THEN
+ DO 170 J = 1, N
+ IF( UPPER )THEN
+ KK = KL + 1
+ IBEG = MAX( 1, KL + 2 - J )
+ IF( UNIT )THEN
+ IEND = KL
+ ELSE
+ IEND = KL + 1
+ END IF
+ ELSE
+ KK = 1
+ IF( UNIT )THEN
+ IBEG = 2
+ ELSE
+ IBEG = 1
+ END IF
+ IEND = MIN( KL + 1, 1 + M - J )
+ END IF
+ DO 140 I = 1, IBEG - 1
+ AA( I + ( J - 1 )*LDA ) = ROGUE
+ 140 CONTINUE
+ DO 150 I = IBEG, IEND
+ AA( I + ( J - 1 )*LDA ) = A( I + J - KK, J )
+ 150 CONTINUE
+ DO 160 I = IEND + 1, LDA
+ AA( I + ( J - 1 )*LDA ) = ROGUE
+ 160 CONTINUE
+ IF( SYM )THEN
+ JJ = KK + ( J - 1 )*LDA
+ AA( JJ ) = DCMPLX( DBLE( AA( JJ ) ), RROGUE )
+ END IF
+ 170 CONTINUE
+ ELSE IF( TYPE.EQ.'HP'.OR.TYPE.EQ.'TP' )THEN
+ IOFF = 0
+ DO 190 J = 1, N
+ IF( UPPER )THEN
+ IBEG = 1
+ IEND = J
+ ELSE
+ IBEG = J
+ IEND = N
+ END IF
+ DO 180 I = IBEG, IEND
+ IOFF = IOFF + 1
+ AA( IOFF ) = A( I, J )
+ IF( I.EQ.J )THEN
+ IF( UNIT )
+ $ AA( IOFF ) = ROGUE
+ IF( SYM )
+ $ AA( IOFF ) = DCMPLX( DBLE( AA( IOFF ) ), RROGUE )
+ END IF
+ 180 CONTINUE
+ 190 CONTINUE
+ END IF
+ RETURN
+*
+* End of ZMAKE.
+*
+ END
+ SUBROUTINE ZMVCH( TRANS, M, N, ALPHA, A, NMAX, X, INCX, BETA, Y,
+ $ INCY, YT, G, YY, EPS, ERR, FATAL, NOUT, MV )
+*
+* Checks the results of the computational tests.
+*
+* Auxiliary routine for test program for Level 2 Blas.
+*
+* -- Written on 10-August-1987.
+* Richard Hanson, Sandia National Labs.
+* Jeremy Du Croz, NAG Central Office.
+*
+* .. Parameters ..
+ COMPLEX*16 ZERO
+ PARAMETER ( ZERO = ( 0.0D0, 0.0D0 ) )
+ DOUBLE PRECISION RZERO, RONE
+ PARAMETER ( RZERO = 0.0D0, RONE = 1.0D0 )
+* .. Scalar Arguments ..
+ COMPLEX*16 ALPHA, BETA
+ DOUBLE PRECISION EPS, ERR
+ INTEGER INCX, INCY, M, N, NMAX, NOUT
+ LOGICAL FATAL, MV
+ CHARACTER*1 TRANS
+* .. Array Arguments ..
+ COMPLEX*16 A( NMAX, * ), X( * ), Y( * ), YT( * ), YY( * )
+ DOUBLE PRECISION G( * )
+* .. Local Scalars ..
+ COMPLEX*16 C
+ DOUBLE PRECISION ERRI
+ INTEGER I, INCXL, INCYL, IY, J, JX, KX, KY, ML, NL
+ LOGICAL CTRAN, TRAN
+* .. Intrinsic Functions ..
+ INTRINSIC ABS, DBLE, DCONJG, DIMAG, MAX, SQRT
+* .. Statement Functions ..
+ DOUBLE PRECISION ABS1
+* .. Statement Function definitions ..
+ ABS1( C ) = ABS( DBLE( C ) ) + ABS( DIMAG( C ) )
+* .. Executable Statements ..
+ TRAN = TRANS.EQ.'T'
+ CTRAN = TRANS.EQ.'C'
+ IF( TRAN.OR.CTRAN )THEN
+ ML = N
+ NL = M
+ ELSE
+ ML = M
+ NL = N
+ END IF
+ IF( INCX.LT.0 )THEN
+ KX = NL
+ INCXL = -1
+ ELSE
+ KX = 1
+ INCXL = 1
+ END IF
+ IF( INCY.LT.0 )THEN
+ KY = ML
+ INCYL = -1
+ ELSE
+ KY = 1
+ INCYL = 1
+ END IF
+*
+* Compute expected result in YT using data in A, X and Y.
+* Compute gauges in G.
+*
+ IY = KY
+ DO 40 I = 1, ML
+ YT( IY ) = ZERO
+ G( IY ) = RZERO
+ JX = KX
+ IF( TRAN )THEN
+ DO 10 J = 1, NL
+ YT( IY ) = YT( IY ) + A( J, I )*X( JX )
+ G( IY ) = G( IY ) + ABS1( A( J, I ) )*ABS1( X( JX ) )
+ JX = JX + INCXL
+ 10 CONTINUE
+ ELSE IF( CTRAN )THEN
+ DO 20 J = 1, NL
+ YT( IY ) = YT( IY ) + DCONJG( A( J, I ) )*X( JX )
+ G( IY ) = G( IY ) + ABS1( A( J, I ) )*ABS1( X( JX ) )
+ JX = JX + INCXL
+ 20 CONTINUE
+ ELSE
+ DO 30 J = 1, NL
+ YT( IY ) = YT( IY ) + A( I, J )*X( JX )
+ G( IY ) = G( IY ) + ABS1( A( I, J ) )*ABS1( X( JX ) )
+ JX = JX + INCXL
+ 30 CONTINUE
+ END IF
+ YT( IY ) = ALPHA*YT( IY ) + BETA*Y( IY )
+ G( IY ) = ABS1( ALPHA )*G( IY ) + ABS1( BETA )*ABS1( Y( IY ) )
+ IY = IY + INCYL
+ 40 CONTINUE
+*
+* Compute the error ratio for this result.
+*
+ ERR = ZERO
+ DO 50 I = 1, ML
+ ERRI = ABS( YT( I ) - YY( 1 + ( I - 1 )*ABS( INCY ) ) )/EPS
+ IF( G( I ).NE.RZERO )
+ $ ERRI = ERRI/G( I )
+ ERR = MAX( ERR, ERRI )
+ IF( ERR*SQRT( EPS ).GE.RONE )
+ $ GO TO 60
+ 50 CONTINUE
+* If the loop completes, all results are at least half accurate.
+ GO TO 80
+*
+* Report fatal error.
+*
+ 60 FATAL = .TRUE.
+ WRITE( NOUT, FMT = 9999 )
+ DO 70 I = 1, ML
+ IF( MV )THEN
+ WRITE( NOUT, FMT = 9998 )I, YT( I ),
+ $ YY( 1 + ( I - 1 )*ABS( INCY ) )
+ ELSE
+ WRITE( NOUT, FMT = 9998 )I,
+ $ YY( 1 + ( I - 1 )*ABS( INCY ) ), YT( I )
+ END IF
+ 70 CONTINUE
+*
+ 80 CONTINUE
+ RETURN
+*
+ 9999 FORMAT( ' ******* FATAL ERROR - COMPUTED RESULT IS LESS THAN HAL',
+ $ 'F ACCURATE *******', /' EXPECTED RE',
+ $ 'SULT COMPUTED RESULT' )
+ 9998 FORMAT( 1X, I7, 2( ' (', G15.6, ',', G15.6, ')' ) )
+*
+* End of ZMVCH.
+*
+ END
+ LOGICAL FUNCTION LZE( RI, RJ, LR )
+*
+* Tests if two arrays are identical.
+*
+* Auxiliary routine for test program for Level 2 Blas.
+*
+* -- Written on 10-August-1987.
+* Richard Hanson, Sandia National Labs.
+* Jeremy Du Croz, NAG Central Office.
+*
+* .. Scalar Arguments ..
+ INTEGER LR
+* .. Array Arguments ..
+ COMPLEX*16 RI( * ), RJ( * )
+* .. Local Scalars ..
+ INTEGER I
+* .. Executable Statements ..
+ DO 10 I = 1, LR
+ IF( RI( I ).NE.RJ( I ) )
+ $ GO TO 20
+ 10 CONTINUE
+ LZE = .TRUE.
+ GO TO 30
+ 20 CONTINUE
+ LZE = .FALSE.
+ 30 RETURN
+*
+* End of LZE.
+*
+ END
+ LOGICAL FUNCTION LZERES( TYPE, UPLO, M, N, AA, AS, LDA )
+*
+* Tests if selected elements in two arrays are equal.
+*
+* TYPE is 'GE', 'HE' or 'HP'.
+*
+* Auxiliary routine for test program for Level 2 Blas.
+*
+* -- Written on 10-August-1987.
+* Richard Hanson, Sandia National Labs.
+* Jeremy Du Croz, NAG Central Office.
+*
+* .. Scalar Arguments ..
+ INTEGER LDA, M, N
+ CHARACTER*1 UPLO
+ CHARACTER*2 TYPE
+* .. Array Arguments ..
+ COMPLEX*16 AA( LDA, * ), AS( LDA, * )
+* .. Local Scalars ..
+ INTEGER I, IBEG, IEND, J
+ LOGICAL UPPER
+* .. Executable Statements ..
+ UPPER = UPLO.EQ.'U'
+ IF( TYPE.EQ.'GE' )THEN
+ DO 20 J = 1, N
+ DO 10 I = M + 1, LDA
+ IF( AA( I, J ).NE.AS( I, J ) )
+ $ GO TO 70
+ 10 CONTINUE
+ 20 CONTINUE
+ ELSE IF( TYPE.EQ.'HE' )THEN
+ DO 50 J = 1, N
+ IF( UPPER )THEN
+ IBEG = 1
+ IEND = J
+ ELSE
+ IBEG = J
+ IEND = N
+ END IF
+ DO 30 I = 1, IBEG - 1
+ IF( AA( I, J ).NE.AS( I, J ) )
+ $ GO TO 70
+ 30 CONTINUE
+ DO 40 I = IEND + 1, LDA
+ IF( AA( I, J ).NE.AS( I, J ) )
+ $ GO TO 70
+ 40 CONTINUE
+ 50 CONTINUE
+ END IF
+*
+ LZERES = .TRUE.
+ GO TO 80
+ 70 CONTINUE
+ LZERES = .FALSE.
+ 80 RETURN
+*
+* End of LZERES.
+*
+ END
+ COMPLEX*16 FUNCTION ZBEG( RESET )
+*
+* Generates complex numbers as pairs of random numbers uniformly
+* distributed between -0.5 and 0.5.
+*
+* Auxiliary routine for test program for Level 2 Blas.
+*
+* -- Written on 10-August-1987.
+* Richard Hanson, Sandia National Labs.
+* Jeremy Du Croz, NAG Central Office.
+*
+* .. Scalar Arguments ..
+ LOGICAL RESET
+* .. Local Scalars ..
+ INTEGER I, IC, J, MI, MJ
+* .. Save statement ..
+ SAVE I, IC, J, MI, MJ
+* .. Intrinsic Functions ..
+ INTRINSIC DCMPLX
+* .. Executable Statements ..
+ IF( RESET )THEN
+* Initialize local variables.
+ MI = 891
+ MJ = 457
+ I = 7
+ J = 7
+ IC = 0
+ RESET = .FALSE.
+ END IF
+*
+* The sequence of values of I or J is bounded between 1 and 999.
+* If initial I or J = 1,2,3,6,7 or 9, the period will be 50.
+* If initial I or J = 4 or 8, the period will be 25.
+* If initial I or J = 5, the period will be 10.
+* IC is used to break up the period by skipping 1 value of I or J
+* in 6.
+*
+ IC = IC + 1
+ 10 I = I*MI
+ J = J*MJ
+ I = I - 1000*( I/1000 )
+ J = J - 1000*( J/1000 )
+ IF( IC.GE.5 )THEN
+ IC = 0
+ GO TO 10
+ END IF
+ ZBEG = DCMPLX( ( I - 500 )/1001.0D0, ( J - 500 )/1001.0D0 )
+ RETURN
+*
+* End of ZBEG.
+*
+ END
+ DOUBLE PRECISION FUNCTION DDIFF( X, Y )
+*
+* Auxiliary routine for test program for Level 2 Blas.
+*
+* -- Written on 10-August-1987.
+* Richard Hanson, Sandia National Labs.
+*
+* .. Scalar Arguments ..
+ DOUBLE PRECISION X, Y
+* .. Executable Statements ..
+ DDIFF = X - Y
+ RETURN
+*
+* End of DDIFF.
+*
+ END
+ SUBROUTINE CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+*
+* Tests whether XERBLA has detected an error when it should.
+*
+* Auxiliary routine for test program for Level 2 Blas.
+*
+* -- Written on 10-August-1987.
+* Richard Hanson, Sandia National Labs.
+* Jeremy Du Croz, NAG Central Office.
+*
+* .. Scalar Arguments ..
+ INTEGER INFOT, NOUT
+ LOGICAL LERR, OK
+ CHARACTER*6 SRNAMT
+* .. Executable Statements ..
+ IF( .NOT.LERR )THEN
+ WRITE( NOUT, FMT = 9999 )INFOT, SRNAMT
+ OK = .FALSE.
+ END IF
+ LERR = .FALSE.
+ RETURN
+*
+ 9999 FORMAT( ' ***** ILLEGAL VALUE OF PARAMETER NUMBER ', I2, ' NOT D',
+ $ 'ETECTED BY ', A6, ' *****' )
+*
+* End of CHKXER.
+*
+ END
+ SUBROUTINE XERBLA( SRNAME, INFO )
+*
+* This is a special version of XERBLA to be used only as part of
+* the test program for testing error exits from the Level 2 BLAS
+* routines.
+*
+* XERBLA is an error handler for the Level 2 BLAS routines.
+*
+* It is called by the Level 2 BLAS routines if an input parameter is
+* invalid.
+*
+* Auxiliary routine for test program for Level 2 Blas.
+*
+* -- Written on 10-August-1987.
+* Richard Hanson, Sandia National Labs.
+* Jeremy Du Croz, NAG Central Office.
+*
+* .. Scalar Arguments ..
+ INTEGER INFO
+ CHARACTER*6 SRNAME
+* .. Scalars in Common ..
+ INTEGER INFOT, NOUT
+ LOGICAL LERR, OK
+ CHARACTER*6 SRNAMT
+* .. Common blocks ..
+ COMMON /INFOC/INFOT, NOUT, OK, LERR
+ COMMON /SRNAMC/SRNAMT
+* .. Executable Statements ..
+ LERR = .TRUE.
+ IF( INFO.NE.INFOT )THEN
+ IF( INFOT.NE.0 )THEN
+ WRITE( NOUT, FMT = 9999 )INFO, INFOT
+ ELSE
+ WRITE( NOUT, FMT = 9997 )INFO
+ END IF
+ OK = .FALSE.
+ END IF
+ IF( SRNAME.NE.SRNAMT )THEN
+ WRITE( NOUT, FMT = 9998 )SRNAME, SRNAMT
+ OK = .FALSE.
+ END IF
+ RETURN
+*
+ 9999 FORMAT( ' ******* XERBLA WAS CALLED WITH INFO = ', I6, ' INSTEAD',
+ $ ' OF ', I2, ' *******' )
+ 9998 FORMAT( ' ******* XERBLA WAS CALLED WITH SRNAME = ', A6, ' INSTE',
+ $ 'AD OF ', A6, ' *******' )
+ 9997 FORMAT( ' ******* XERBLA WAS CALLED WITH INFO = ', I6,
+ $ ' *******' )
+*
+* End of XERBLA
+*
+ END
+
diff --git a/blas/testing/zblat3.dat b/blas/testing/zblat3.dat
new file mode 100644
index 0000000..ede516f
--- /dev/null
+++ b/blas/testing/zblat3.dat
@@ -0,0 +1,23 @@
+'zblat3.summ' NAME OF SUMMARY OUTPUT FILE
+6 UNIT NUMBER OF SUMMARY FILE
+'zblat3.snap' NAME OF SNAPSHOT OUTPUT FILE
+-1 UNIT NUMBER OF SNAPSHOT FILE (NOT USED IF .LT. 0)
+F LOGICAL FLAG, T TO REWIND SNAPSHOT FILE AFTER EACH RECORD.
+F LOGICAL FLAG, T TO STOP ON FAILURES.
+F LOGICAL FLAG, T TO TEST ERROR EXITS.
+16.0 THRESHOLD VALUE OF TEST RATIO
+6 NUMBER OF VALUES OF N
+0 1 2 3 5 9 VALUES OF N
+3 NUMBER OF VALUES OF ALPHA
+(0.0,0.0) (1.0,0.0) (0.7,-0.9) VALUES OF ALPHA
+3 NUMBER OF VALUES OF BETA
+(0.0,0.0) (1.0,0.0) (1.3,-1.1) VALUES OF BETA
+ZGEMM T PUT F FOR NO TEST. SAME COLUMNS.
+ZHEMM T PUT F FOR NO TEST. SAME COLUMNS.
+ZSYMM T PUT F FOR NO TEST. SAME COLUMNS.
+ZTRMM T PUT F FOR NO TEST. SAME COLUMNS.
+ZTRSM T PUT F FOR NO TEST. SAME COLUMNS.
+ZHERK T PUT F FOR NO TEST. SAME COLUMNS.
+ZSYRK T PUT F FOR NO TEST. SAME COLUMNS.
+ZHER2K T PUT F FOR NO TEST. SAME COLUMNS.
+ZSYR2K T PUT F FOR NO TEST. SAME COLUMNS.
diff --git a/blas/testing/zblat3.f b/blas/testing/zblat3.f
new file mode 100644
index 0000000..59ca241
--- /dev/null
+++ b/blas/testing/zblat3.f
@@ -0,0 +1,3502 @@
+*> \brief \b ZBLAT3
+*
+* =========== DOCUMENTATION ===========
+*
+* Online html documentation available at
+* http://www.netlib.org/lapack/explore-html/
+*
+* Definition:
+* ===========
+*
+* PROGRAM ZBLAT3
+*
+*
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
+*>
+*> Test program for the COMPLEX*16 Level 3 Blas.
+*>
+*> The program must be driven by a short data file. The first 14 records
+*> of the file are read using list-directed input, the last 9 records
+*> are read using the format ( A6, L2 ). An annotated example of a data
+*> file can be obtained by deleting the first 3 characters from the
+*> following 23 lines:
+*> 'zblat3.out' NAME OF SUMMARY OUTPUT FILE
+*> 6 UNIT NUMBER OF SUMMARY FILE
+*> 'ZBLAT3.SNAP' NAME OF SNAPSHOT OUTPUT FILE
+*> -1 UNIT NUMBER OF SNAPSHOT FILE (NOT USED IF .LT. 0)
+*> F LOGICAL FLAG, T TO REWIND SNAPSHOT FILE AFTER EACH RECORD.
+*> F LOGICAL FLAG, T TO STOP ON FAILURES.
+*> T LOGICAL FLAG, T TO TEST ERROR EXITS.
+*> 16.0 THRESHOLD VALUE OF TEST RATIO
+*> 6 NUMBER OF VALUES OF N
+*> 0 1 2 3 5 9 VALUES OF N
+*> 3 NUMBER OF VALUES OF ALPHA
+*> (0.0,0.0) (1.0,0.0) (0.7,-0.9) VALUES OF ALPHA
+*> 3 NUMBER OF VALUES OF BETA
+*> (0.0,0.0) (1.0,0.0) (1.3,-1.1) VALUES OF BETA
+*> ZGEMM T PUT F FOR NO TEST. SAME COLUMNS.
+*> ZHEMM T PUT F FOR NO TEST. SAME COLUMNS.
+*> ZSYMM T PUT F FOR NO TEST. SAME COLUMNS.
+*> ZTRMM T PUT F FOR NO TEST. SAME COLUMNS.
+*> ZTRSM T PUT F FOR NO TEST. SAME COLUMNS.
+*> ZHERK T PUT F FOR NO TEST. SAME COLUMNS.
+*> ZSYRK T PUT F FOR NO TEST. SAME COLUMNS.
+*> ZHER2K T PUT F FOR NO TEST. SAME COLUMNS.
+*> ZSYR2K T PUT F FOR NO TEST. SAME COLUMNS.
+*>
+*>
+*> Further Details
+*> ===============
+*>
+*> See:
+*>
+*> Dongarra J. J., Du Croz J. J., Duff I. S. and Hammarling S.
+*> A Set of Level 3 Basic Linear Algebra Subprograms.
+*>
+*> Technical Memorandum No.88 (Revision 1), Mathematics and
+*> Computer Science Division, Argonne National Laboratory, 9700
+*> South Cass Avenue, Argonne, Illinois 60439, US.
+*>
+*> -- Written on 8-February-1989.
+*> Jack Dongarra, Argonne National Laboratory.
+*> Iain Duff, AERE Harwell.
+*> Jeremy Du Croz, Numerical Algorithms Group Ltd.
+*> Sven Hammarling, Numerical Algorithms Group Ltd.
+*>
+*> 10-9-00: Change STATUS='NEW' to 'UNKNOWN' so that the testers
+*> can be run multiple times without deleting generated
+*> output files (susan)
+*> \endverbatim
+*
+* Authors:
+* ========
+*
+*> \author Univ. of Tennessee
+*> \author Univ. of California Berkeley
+*> \author Univ. of Colorado Denver
+*> \author NAG Ltd.
+*
+*> \date April 2012
+*
+*> \ingroup complex16_blas_testing
+*
+* =====================================================================
+ PROGRAM ZBLAT3
+*
+* -- Reference BLAS test routine (version 3.4.1) --
+* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
+* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+* April 2012
+*
+* =====================================================================
+*
+* .. Parameters ..
+ INTEGER NIN
+ PARAMETER ( NIN = 5 )
+ INTEGER NSUBS
+ PARAMETER ( NSUBS = 9 )
+ COMPLEX*16 ZERO, ONE
+ PARAMETER ( ZERO = ( 0.0D0, 0.0D0 ),
+ $ ONE = ( 1.0D0, 0.0D0 ) )
+ DOUBLE PRECISION RZERO
+ PARAMETER ( RZERO = 0.0D0 )
+ INTEGER NMAX
+ PARAMETER ( NMAX = 65 )
+ INTEGER NIDMAX, NALMAX, NBEMAX
+ PARAMETER ( NIDMAX = 9, NALMAX = 7, NBEMAX = 7 )
+* .. Local Scalars ..
+ DOUBLE PRECISION EPS, ERR, THRESH
+ INTEGER I, ISNUM, J, N, NALF, NBET, NIDIM, NOUT, NTRA
+ LOGICAL FATAL, LTESTT, REWI, SAME, SFATAL, TRACE,
+ $ TSTERR
+ CHARACTER*1 TRANSA, TRANSB
+ CHARACTER*6 SNAMET
+ CHARACTER*32 SNAPS, SUMMRY
+* .. Local Arrays ..
+ COMPLEX*16 AA( NMAX*NMAX ), AB( NMAX, 2*NMAX ),
+ $ ALF( NALMAX ), AS( NMAX*NMAX ),
+ $ BB( NMAX*NMAX ), BET( NBEMAX ),
+ $ BS( NMAX*NMAX ), C( NMAX, NMAX ),
+ $ CC( NMAX*NMAX ), CS( NMAX*NMAX ), CT( NMAX ),
+ $ W( 2*NMAX )
+ DOUBLE PRECISION G( NMAX )
+ INTEGER IDIM( NIDMAX )
+ LOGICAL LTEST( NSUBS )
+ CHARACTER*6 SNAMES( NSUBS )
+* .. External Functions ..
+ DOUBLE PRECISION DDIFF
+ LOGICAL LZE
+ EXTERNAL DDIFF, LZE
+* .. External Subroutines ..
+ EXTERNAL ZCHK1, ZCHK2, ZCHK3, ZCHK4, ZCHK5, ZCHKE, ZMMCH
+* .. Intrinsic Functions ..
+ INTRINSIC MAX, MIN
+* .. Scalars in Common ..
+ INTEGER INFOT, NOUTC
+ LOGICAL LERR, OK
+ CHARACTER*6 SRNAMT
+* .. Common blocks ..
+ COMMON /INFOC/INFOT, NOUTC, OK, LERR
+ COMMON /SRNAMC/SRNAMT
+* .. Data statements ..
+ DATA SNAMES/'ZGEMM ', 'ZHEMM ', 'ZSYMM ', 'ZTRMM ',
+ $ 'ZTRSM ', 'ZHERK ', 'ZSYRK ', 'ZHER2K',
+ $ 'ZSYR2K'/
+* .. Executable Statements ..
+*
+* Read name and unit number for summary output file and open file.
+*
+ READ( NIN, FMT = * )SUMMRY
+ READ( NIN, FMT = * )NOUT
+ OPEN( NOUT, FILE = SUMMRY, STATUS = 'UNKNOWN' )
+ NOUTC = NOUT
+*
+* Read name and unit number for snapshot output file and open file.
+*
+ READ( NIN, FMT = * )SNAPS
+ READ( NIN, FMT = * )NTRA
+ TRACE = NTRA.GE.0
+ IF( TRACE )THEN
+ OPEN( NTRA, FILE = SNAPS, STATUS = 'UNKNOWN' )
+ END IF
+* Read the flag that directs rewinding of the snapshot file.
+ READ( NIN, FMT = * )REWI
+ REWI = REWI.AND.TRACE
+* Read the flag that directs stopping on any failure.
+ READ( NIN, FMT = * )SFATAL
+* Read the flag that indicates whether error exits are to be tested.
+ READ( NIN, FMT = * )TSTERR
+* Read the threshold value of the test ratio
+ READ( NIN, FMT = * )THRESH
+*
+* Read and check the parameter values for the tests.
+*
+* Values of N
+ READ( NIN, FMT = * )NIDIM
+ IF( NIDIM.LT.1.OR.NIDIM.GT.NIDMAX )THEN
+ WRITE( NOUT, FMT = 9997 )'N', NIDMAX
+ GO TO 220
+ END IF
+ READ( NIN, FMT = * )( IDIM( I ), I = 1, NIDIM )
+ DO 10 I = 1, NIDIM
+ IF( IDIM( I ).LT.0.OR.IDIM( I ).GT.NMAX )THEN
+ WRITE( NOUT, FMT = 9996 )NMAX
+ GO TO 220
+ END IF
+ 10 CONTINUE
+* Values of ALPHA
+ READ( NIN, FMT = * )NALF
+ IF( NALF.LT.1.OR.NALF.GT.NALMAX )THEN
+ WRITE( NOUT, FMT = 9997 )'ALPHA', NALMAX
+ GO TO 220
+ END IF
+ READ( NIN, FMT = * )( ALF( I ), I = 1, NALF )
+* Values of BETA
+ READ( NIN, FMT = * )NBET
+ IF( NBET.LT.1.OR.NBET.GT.NBEMAX )THEN
+ WRITE( NOUT, FMT = 9997 )'BETA', NBEMAX
+ GO TO 220
+ END IF
+ READ( NIN, FMT = * )( BET( I ), I = 1, NBET )
+*
+* Report values of parameters.
+*
+ WRITE( NOUT, FMT = 9995 )
+ WRITE( NOUT, FMT = 9994 )( IDIM( I ), I = 1, NIDIM )
+ WRITE( NOUT, FMT = 9993 )( ALF( I ), I = 1, NALF )
+ WRITE( NOUT, FMT = 9992 )( BET( I ), I = 1, NBET )
+ IF( .NOT.TSTERR )THEN
+ WRITE( NOUT, FMT = * )
+ WRITE( NOUT, FMT = 9984 )
+ END IF
+ WRITE( NOUT, FMT = * )
+ WRITE( NOUT, FMT = 9999 )THRESH
+ WRITE( NOUT, FMT = * )
+*
+* Read names of subroutines and flags which indicate
+* whether they are to be tested.
+*
+ DO 20 I = 1, NSUBS
+ LTEST( I ) = .FALSE.
+ 20 CONTINUE
+ 30 READ( NIN, FMT = 9988, END = 60 )SNAMET, LTESTT
+ DO 40 I = 1, NSUBS
+ IF( SNAMET.EQ.SNAMES( I ) )
+ $ GO TO 50
+ 40 CONTINUE
+ WRITE( NOUT, FMT = 9990 )SNAMET
+ STOP
+ 50 LTEST( I ) = LTESTT
+ GO TO 30
+*
+ 60 CONTINUE
+ CLOSE ( NIN )
+*
+* Compute EPS (the machine precision).
+*
+ EPS = EPSILON(RZERO)
+ WRITE( NOUT, FMT = 9998 )EPS
+*
+* Check the reliability of ZMMCH using exact data.
+*
+ N = MIN( 32, NMAX )
+ DO 100 J = 1, N
+ DO 90 I = 1, N
+ AB( I, J ) = MAX( I - J + 1, 0 )
+ 90 CONTINUE
+ AB( J, NMAX + 1 ) = J
+ AB( 1, NMAX + J ) = J
+ C( J, 1 ) = ZERO
+ 100 CONTINUE
+ DO 110 J = 1, N
+ CC( J ) = J*( ( J + 1 )*J )/2 - ( ( J + 1 )*J*( J - 1 ) )/3
+ 110 CONTINUE
+* CC holds the exact result. On exit from ZMMCH CT holds
+* the result computed by ZMMCH.
+ TRANSA = 'N'
+ TRANSB = 'N'
+ CALL ZMMCH( TRANSA, TRANSB, N, 1, N, ONE, AB, NMAX,
+ $ AB( 1, NMAX + 1 ), NMAX, ZERO, C, NMAX, CT, G, CC,
+ $ NMAX, EPS, ERR, FATAL, NOUT, .TRUE. )
+ SAME = LZE( CC, CT, N )
+ IF( .NOT.SAME.OR.ERR.NE.RZERO )THEN
+ WRITE( NOUT, FMT = 9989 )TRANSA, TRANSB, SAME, ERR
+ STOP
+ END IF
+ TRANSB = 'C'
+ CALL ZMMCH( TRANSA, TRANSB, N, 1, N, ONE, AB, NMAX,
+ $ AB( 1, NMAX + 1 ), NMAX, ZERO, C, NMAX, CT, G, CC,
+ $ NMAX, EPS, ERR, FATAL, NOUT, .TRUE. )
+ SAME = LZE( CC, CT, N )
+ IF( .NOT.SAME.OR.ERR.NE.RZERO )THEN
+ WRITE( NOUT, FMT = 9989 )TRANSA, TRANSB, SAME, ERR
+ STOP
+ END IF
+ DO 120 J = 1, N
+ AB( J, NMAX + 1 ) = N - J + 1
+ AB( 1, NMAX + J ) = N - J + 1
+ 120 CONTINUE
+ DO 130 J = 1, N
+ CC( N - J + 1 ) = J*( ( J + 1 )*J )/2 -
+ $ ( ( J + 1 )*J*( J - 1 ) )/3
+ 130 CONTINUE
+ TRANSA = 'C'
+ TRANSB = 'N'
+ CALL ZMMCH( TRANSA, TRANSB, N, 1, N, ONE, AB, NMAX,
+ $ AB( 1, NMAX + 1 ), NMAX, ZERO, C, NMAX, CT, G, CC,
+ $ NMAX, EPS, ERR, FATAL, NOUT, .TRUE. )
+ SAME = LZE( CC, CT, N )
+ IF( .NOT.SAME.OR.ERR.NE.RZERO )THEN
+ WRITE( NOUT, FMT = 9989 )TRANSA, TRANSB, SAME, ERR
+ STOP
+ END IF
+ TRANSB = 'C'
+ CALL ZMMCH( TRANSA, TRANSB, N, 1, N, ONE, AB, NMAX,
+ $ AB( 1, NMAX + 1 ), NMAX, ZERO, C, NMAX, CT, G, CC,
+ $ NMAX, EPS, ERR, FATAL, NOUT, .TRUE. )
+ SAME = LZE( CC, CT, N )
+ IF( .NOT.SAME.OR.ERR.NE.RZERO )THEN
+ WRITE( NOUT, FMT = 9989 )TRANSA, TRANSB, SAME, ERR
+ STOP
+ END IF
+*
+* Test each subroutine in turn.
+*
+ DO 200 ISNUM = 1, NSUBS
+ WRITE( NOUT, FMT = * )
+ IF( .NOT.LTEST( ISNUM ) )THEN
+* Subprogram is not to be tested.
+ WRITE( NOUT, FMT = 9987 )SNAMES( ISNUM )
+ ELSE
+ SRNAMT = SNAMES( ISNUM )
+* Test error exits.
+ IF( TSTERR )THEN
+ CALL ZCHKE( ISNUM, SNAMES( ISNUM ), NOUT )
+ WRITE( NOUT, FMT = * )
+ END IF
+* Test computations.
+ INFOT = 0
+ OK = .TRUE.
+ FATAL = .FALSE.
+ GO TO ( 140, 150, 150, 160, 160, 170, 170,
+ $ 180, 180 )ISNUM
+* Test ZGEMM, 01.
+ 140 CALL ZCHK1( SNAMES( ISNUM ), EPS, THRESH, NOUT, NTRA, TRACE,
+ $ REWI, FATAL, NIDIM, IDIM, NALF, ALF, NBET, BET,
+ $ NMAX, AB, AA, AS, AB( 1, NMAX + 1 ), BB, BS, C,
+ $ CC, CS, CT, G )
+ GO TO 190
+* Test ZHEMM, 02, ZSYMM, 03.
+ 150 CALL ZCHK2( SNAMES( ISNUM ), EPS, THRESH, NOUT, NTRA, TRACE,
+ $ REWI, FATAL, NIDIM, IDIM, NALF, ALF, NBET, BET,
+ $ NMAX, AB, AA, AS, AB( 1, NMAX + 1 ), BB, BS, C,
+ $ CC, CS, CT, G )
+ GO TO 190
+* Test ZTRMM, 04, ZTRSM, 05.
+ 160 CALL ZCHK3( SNAMES( ISNUM ), EPS, THRESH, NOUT, NTRA, TRACE,
+ $ REWI, FATAL, NIDIM, IDIM, NALF, ALF, NMAX, AB,
+ $ AA, AS, AB( 1, NMAX + 1 ), BB, BS, CT, G, C )
+ GO TO 190
+* Test ZHERK, 06, ZSYRK, 07.
+ 170 CALL ZCHK4( SNAMES( ISNUM ), EPS, THRESH, NOUT, NTRA, TRACE,
+ $ REWI, FATAL, NIDIM, IDIM, NALF, ALF, NBET, BET,
+ $ NMAX, AB, AA, AS, AB( 1, NMAX + 1 ), BB, BS, C,
+ $ CC, CS, CT, G )
+ GO TO 190
+* Test ZHER2K, 08, ZSYR2K, 09.
+ 180 CALL ZCHK5( SNAMES( ISNUM ), EPS, THRESH, NOUT, NTRA, TRACE,
+ $ REWI, FATAL, NIDIM, IDIM, NALF, ALF, NBET, BET,
+ $ NMAX, AB, AA, AS, BB, BS, C, CC, CS, CT, G, W )
+ GO TO 190
+*
+ 190 IF( FATAL.AND.SFATAL )
+ $ GO TO 210
+ END IF
+ 200 CONTINUE
+ WRITE( NOUT, FMT = 9986 )
+ GO TO 230
+*
+ 210 CONTINUE
+ WRITE( NOUT, FMT = 9985 )
+ GO TO 230
+*
+ 220 CONTINUE
+ WRITE( NOUT, FMT = 9991 )
+*
+ 230 CONTINUE
+ IF( TRACE )
+ $ CLOSE ( NTRA )
+ CLOSE ( NOUT )
+ STOP
+*
+ 9999 FORMAT( ' ROUTINES PASS COMPUTATIONAL TESTS IF TEST RATIO IS LES',
+ $ 'S THAN', F8.2 )
+ 9998 FORMAT( ' RELATIVE MACHINE PRECISION IS TAKEN TO BE', 1P, D9.1 )
+ 9997 FORMAT( ' NUMBER OF VALUES OF ', A, ' IS LESS THAN 1 OR GREATER ',
+ $ 'THAN ', I2 )
+ 9996 FORMAT( ' VALUE OF N IS LESS THAN 0 OR GREATER THAN ', I2 )
+ 9995 FORMAT( ' TESTS OF THE COMPLEX*16 LEVEL 3 BLAS', //' THE F',
+ $ 'OLLOWING PARAMETER VALUES WILL BE USED:' )
+ 9994 FORMAT( ' FOR N ', 9I6 )
+ 9993 FORMAT( ' FOR ALPHA ',
+ $ 7( '(', F4.1, ',', F4.1, ') ', : ) )
+ 9992 FORMAT( ' FOR BETA ',
+ $ 7( '(', F4.1, ',', F4.1, ') ', : ) )
+ 9991 FORMAT( ' AMEND DATA FILE OR INCREASE ARRAY SIZES IN PROGRAM',
+ $ /' ******* TESTS ABANDONED *******' )
+ 9990 FORMAT( ' SUBPROGRAM NAME ', A6, ' NOT RECOGNIZED', /' ******* T',
+ $ 'ESTS ABANDONED *******' )
+ 9989 FORMAT( ' ERROR IN ZMMCH - IN-LINE DOT PRODUCTS ARE BEING EVALU',
+ $ 'ATED WRONGLY.', /' ZMMCH WAS CALLED WITH TRANSA = ', A1,
+ $ ' AND TRANSB = ', A1, /' AND RETURNED SAME = ', L1, ' AND ',
+ $ 'ERR = ', F12.3, '.', /' THIS MAY BE DUE TO FAULTS IN THE ',
+ $ 'ARITHMETIC OR THE COMPILER.', /' ******* TESTS ABANDONED ',
+ $ '*******' )
+ 9988 FORMAT( A6, L2 )
+ 9987 FORMAT( 1X, A6, ' WAS NOT TESTED' )
+ 9986 FORMAT( /' END OF TESTS' )
+ 9985 FORMAT( /' ******* FATAL ERROR - TESTS ABANDONED *******' )
+ 9984 FORMAT( ' ERROR-EXITS WILL NOT BE TESTED' )
+*
+* End of ZBLAT3.
+*
+ END
+ SUBROUTINE ZCHK1( SNAME, EPS, THRESH, NOUT, NTRA, TRACE, REWI,
+ $ FATAL, NIDIM, IDIM, NALF, ALF, NBET, BET, NMAX,
+ $ A, AA, AS, B, BB, BS, C, CC, CS, CT, G )
+*
+* Tests ZGEMM.
+*
+* Auxiliary routine for test program for Level 3 Blas.
+*
+* -- Written on 8-February-1989.
+* Jack Dongarra, Argonne National Laboratory.
+* Iain Duff, AERE Harwell.
+* Jeremy Du Croz, Numerical Algorithms Group Ltd.
+* Sven Hammarling, Numerical Algorithms Group Ltd.
+*
+* .. Parameters ..
+ COMPLEX*16 ZERO
+ PARAMETER ( ZERO = ( 0.0D0, 0.0D0 ) )
+ DOUBLE PRECISION RZERO
+ PARAMETER ( RZERO = 0.0D0 )
+* .. Scalar Arguments ..
+ DOUBLE PRECISION EPS, THRESH
+ INTEGER NALF, NBET, NIDIM, NMAX, NOUT, NTRA
+ LOGICAL FATAL, REWI, TRACE
+ CHARACTER*6 SNAME
+* .. Array Arguments ..
+ COMPLEX*16 A( NMAX, NMAX ), AA( NMAX*NMAX ), ALF( NALF ),
+ $ AS( NMAX*NMAX ), B( NMAX, NMAX ),
+ $ BB( NMAX*NMAX ), BET( NBET ), BS( NMAX*NMAX ),
+ $ C( NMAX, NMAX ), CC( NMAX*NMAX ),
+ $ CS( NMAX*NMAX ), CT( NMAX )
+ DOUBLE PRECISION G( NMAX )
+ INTEGER IDIM( NIDIM )
+* .. Local Scalars ..
+ COMPLEX*16 ALPHA, ALS, BETA, BLS
+ DOUBLE PRECISION ERR, ERRMAX
+ INTEGER I, IA, IB, ICA, ICB, IK, IM, IN, K, KS, LAA,
+ $ LBB, LCC, LDA, LDAS, LDB, LDBS, LDC, LDCS, M,
+ $ MA, MB, MS, N, NA, NARGS, NB, NC, NS
+ LOGICAL NULL, RESET, SAME, TRANA, TRANB
+ CHARACTER*1 TRANAS, TRANBS, TRANSA, TRANSB
+ CHARACTER*3 ICH
+* .. Local Arrays ..
+ LOGICAL ISAME( 13 )
+* .. External Functions ..
+ LOGICAL LZE, LZERES
+ EXTERNAL LZE, LZERES
+* .. External Subroutines ..
+ EXTERNAL ZGEMM, ZMAKE, ZMMCH
+* .. Intrinsic Functions ..
+ INTRINSIC MAX
+* .. Scalars in Common ..
+ INTEGER INFOT, NOUTC
+ LOGICAL LERR, OK
+* .. Common blocks ..
+ COMMON /INFOC/INFOT, NOUTC, OK, LERR
+* .. Data statements ..
+ DATA ICH/'NTC'/
+* .. Executable Statements ..
+*
+ NARGS = 13
+ NC = 0
+ RESET = .TRUE.
+ ERRMAX = RZERO
+*
+ DO 110 IM = 1, NIDIM
+ M = IDIM( IM )
+*
+ DO 100 IN = 1, NIDIM
+ N = IDIM( IN )
+* Set LDC to 1 more than minimum value if room.
+ LDC = M
+ IF( LDC.LT.NMAX )
+ $ LDC = LDC + 1
+* Skip tests if not enough room.
+ IF( LDC.GT.NMAX )
+ $ GO TO 100
+ LCC = LDC*N
+ NULL = N.LE.0.OR.M.LE.0
+*
+ DO 90 IK = 1, NIDIM
+ K = IDIM( IK )
+*
+ DO 80 ICA = 1, 3
+ TRANSA = ICH( ICA: ICA )
+ TRANA = TRANSA.EQ.'T'.OR.TRANSA.EQ.'C'
+*
+ IF( TRANA )THEN
+ MA = K
+ NA = M
+ ELSE
+ MA = M
+ NA = K
+ END IF
+* Set LDA to 1 more than minimum value if room.
+ LDA = MA
+ IF( LDA.LT.NMAX )
+ $ LDA = LDA + 1
+* Skip tests if not enough room.
+ IF( LDA.GT.NMAX )
+ $ GO TO 80
+ LAA = LDA*NA
+*
+* Generate the matrix A.
+*
+ CALL ZMAKE( 'GE', ' ', ' ', MA, NA, A, NMAX, AA, LDA,
+ $ RESET, ZERO )
+*
+ DO 70 ICB = 1, 3
+ TRANSB = ICH( ICB: ICB )
+ TRANB = TRANSB.EQ.'T'.OR.TRANSB.EQ.'C'
+*
+ IF( TRANB )THEN
+ MB = N
+ NB = K
+ ELSE
+ MB = K
+ NB = N
+ END IF
+* Set LDB to 1 more than minimum value if room.
+ LDB = MB
+ IF( LDB.LT.NMAX )
+ $ LDB = LDB + 1
+* Skip tests if not enough room.
+ IF( LDB.GT.NMAX )
+ $ GO TO 70
+ LBB = LDB*NB
+*
+* Generate the matrix B.
+*
+ CALL ZMAKE( 'GE', ' ', ' ', MB, NB, B, NMAX, BB,
+ $ LDB, RESET, ZERO )
+*
+ DO 60 IA = 1, NALF
+ ALPHA = ALF( IA )
+*
+ DO 50 IB = 1, NBET
+ BETA = BET( IB )
+*
+* Generate the matrix C.
+*
+ CALL ZMAKE( 'GE', ' ', ' ', M, N, C, NMAX,
+ $ CC, LDC, RESET, ZERO )
+*
+ NC = NC + 1
+*
+* Save every datum before calling the
+* subroutine.
+*
+ TRANAS = TRANSA
+ TRANBS = TRANSB
+ MS = M
+ NS = N
+ KS = K
+ ALS = ALPHA
+ DO 10 I = 1, LAA
+ AS( I ) = AA( I )
+ 10 CONTINUE
+ LDAS = LDA
+ DO 20 I = 1, LBB
+ BS( I ) = BB( I )
+ 20 CONTINUE
+ LDBS = LDB
+ BLS = BETA
+ DO 30 I = 1, LCC
+ CS( I ) = CC( I )
+ 30 CONTINUE
+ LDCS = LDC
+*
+* Call the subroutine.
+*
+ IF( TRACE )
+ $ WRITE( NTRA, FMT = 9995 )NC, SNAME,
+ $ TRANSA, TRANSB, M, N, K, ALPHA, LDA, LDB,
+ $ BETA, LDC
+ IF( REWI )
+ $ REWIND NTRA
+ CALL ZGEMM( TRANSA, TRANSB, M, N, K, ALPHA,
+ $ AA, LDA, BB, LDB, BETA, CC, LDC )
+*
+* Check if error-exit was taken incorrectly.
+*
+ IF( .NOT.OK )THEN
+ WRITE( NOUT, FMT = 9994 )
+ FATAL = .TRUE.
+ GO TO 120
+ END IF
+*
+* See what data changed inside subroutines.
+*
+ ISAME( 1 ) = TRANSA.EQ.TRANAS
+ ISAME( 2 ) = TRANSB.EQ.TRANBS
+ ISAME( 3 ) = MS.EQ.M
+ ISAME( 4 ) = NS.EQ.N
+ ISAME( 5 ) = KS.EQ.K
+ ISAME( 6 ) = ALS.EQ.ALPHA
+ ISAME( 7 ) = LZE( AS, AA, LAA )
+ ISAME( 8 ) = LDAS.EQ.LDA
+ ISAME( 9 ) = LZE( BS, BB, LBB )
+ ISAME( 10 ) = LDBS.EQ.LDB
+ ISAME( 11 ) = BLS.EQ.BETA
+ IF( NULL )THEN
+ ISAME( 12 ) = LZE( CS, CC, LCC )
+ ELSE
+ ISAME( 12 ) = LZERES( 'GE', ' ', M, N, CS,
+ $ CC, LDC )
+ END IF
+ ISAME( 13 ) = LDCS.EQ.LDC
+*
+* If data was incorrectly changed, report
+* and return.
+*
+ SAME = .TRUE.
+ DO 40 I = 1, NARGS
+ SAME = SAME.AND.ISAME( I )
+ IF( .NOT.ISAME( I ) )
+ $ WRITE( NOUT, FMT = 9998 )I
+ 40 CONTINUE
+ IF( .NOT.SAME )THEN
+ FATAL = .TRUE.
+ GO TO 120
+ END IF
+*
+ IF( .NOT.NULL )THEN
+*
+* Check the result.
+*
+ CALL ZMMCH( TRANSA, TRANSB, M, N, K,
+ $ ALPHA, A, NMAX, B, NMAX, BETA,
+ $ C, NMAX, CT, G, CC, LDC, EPS,
+ $ ERR, FATAL, NOUT, .TRUE. )
+ ERRMAX = MAX( ERRMAX, ERR )
+* If got really bad answer, report and
+* return.
+ IF( FATAL )
+ $ GO TO 120
+ END IF
+*
+ 50 CONTINUE
+*
+ 60 CONTINUE
+*
+ 70 CONTINUE
+*
+ 80 CONTINUE
+*
+ 90 CONTINUE
+*
+ 100 CONTINUE
+*
+ 110 CONTINUE
+*
+* Report result.
+*
+ IF( ERRMAX.LT.THRESH )THEN
+ WRITE( NOUT, FMT = 9999 )SNAME, NC
+ ELSE
+ WRITE( NOUT, FMT = 9997 )SNAME, NC, ERRMAX
+ END IF
+ GO TO 130
+*
+ 120 CONTINUE
+ WRITE( NOUT, FMT = 9996 )SNAME
+ WRITE( NOUT, FMT = 9995 )NC, SNAME, TRANSA, TRANSB, M, N, K,
+ $ ALPHA, LDA, LDB, BETA, LDC
+*
+ 130 CONTINUE
+ RETURN
+*
+ 9999 FORMAT( ' ', A6, ' PASSED THE COMPUTATIONAL TESTS (', I6, ' CALL',
+ $ 'S)' )
+ 9998 FORMAT( ' ******* FATAL ERROR - PARAMETER NUMBER ', I2, ' WAS CH',
+ $ 'ANGED INCORRECTLY *******' )
+ 9997 FORMAT( ' ', A6, ' COMPLETED THE COMPUTATIONAL TESTS (', I6, ' C',
+ $ 'ALLS)', /' ******* BUT WITH MAXIMUM TEST RATIO', F8.2,
+ $ ' - SUSPECT *******' )
+ 9996 FORMAT( ' ******* ', A6, ' FAILED ON CALL NUMBER:' )
+ 9995 FORMAT( 1X, I6, ': ', A6, '(''', A1, ''',''', A1, ''',',
+ $ 3( I3, ',' ), '(', F4.1, ',', F4.1, '), A,', I3, ', B,', I3,
+ $ ',(', F4.1, ',', F4.1, '), C,', I3, ').' )
+ 9994 FORMAT( ' ******* FATAL ERROR - ERROR-EXIT TAKEN ON VALID CALL *',
+ $ '******' )
+*
+* End of ZCHK1.
+*
+ END
+ SUBROUTINE ZCHK2( SNAME, EPS, THRESH, NOUT, NTRA, TRACE, REWI,
+ $ FATAL, NIDIM, IDIM, NALF, ALF, NBET, BET, NMAX,
+ $ A, AA, AS, B, BB, BS, C, CC, CS, CT, G )
+*
+* Tests ZHEMM and ZSYMM.
+*
+* Auxiliary routine for test program for Level 3 Blas.
+*
+* -- Written on 8-February-1989.
+* Jack Dongarra, Argonne National Laboratory.
+* Iain Duff, AERE Harwell.
+* Jeremy Du Croz, Numerical Algorithms Group Ltd.
+* Sven Hammarling, Numerical Algorithms Group Ltd.
+*
+* .. Parameters ..
+ COMPLEX*16 ZERO
+ PARAMETER ( ZERO = ( 0.0D0, 0.0D0 ) )
+ DOUBLE PRECISION RZERO
+ PARAMETER ( RZERO = 0.0D0 )
+* .. Scalar Arguments ..
+ DOUBLE PRECISION EPS, THRESH
+ INTEGER NALF, NBET, NIDIM, NMAX, NOUT, NTRA
+ LOGICAL FATAL, REWI, TRACE
+ CHARACTER*6 SNAME
+* .. Array Arguments ..
+ COMPLEX*16 A( NMAX, NMAX ), AA( NMAX*NMAX ), ALF( NALF ),
+ $ AS( NMAX*NMAX ), B( NMAX, NMAX ),
+ $ BB( NMAX*NMAX ), BET( NBET ), BS( NMAX*NMAX ),
+ $ C( NMAX, NMAX ), CC( NMAX*NMAX ),
+ $ CS( NMAX*NMAX ), CT( NMAX )
+ DOUBLE PRECISION G( NMAX )
+ INTEGER IDIM( NIDIM )
+* .. Local Scalars ..
+ COMPLEX*16 ALPHA, ALS, BETA, BLS
+ DOUBLE PRECISION ERR, ERRMAX
+ INTEGER I, IA, IB, ICS, ICU, IM, IN, LAA, LBB, LCC,
+ $ LDA, LDAS, LDB, LDBS, LDC, LDCS, M, MS, N, NA,
+ $ NARGS, NC, NS
+ LOGICAL CONJ, LEFT, NULL, RESET, SAME
+ CHARACTER*1 SIDE, SIDES, UPLO, UPLOS
+ CHARACTER*2 ICHS, ICHU
+* .. Local Arrays ..
+ LOGICAL ISAME( 13 )
+* .. External Functions ..
+ LOGICAL LZE, LZERES
+ EXTERNAL LZE, LZERES
+* .. External Subroutines ..
+ EXTERNAL ZHEMM, ZMAKE, ZMMCH, ZSYMM
+* .. Intrinsic Functions ..
+ INTRINSIC MAX
+* .. Scalars in Common ..
+ INTEGER INFOT, NOUTC
+ LOGICAL LERR, OK
+* .. Common blocks ..
+ COMMON /INFOC/INFOT, NOUTC, OK, LERR
+* .. Data statements ..
+ DATA ICHS/'LR'/, ICHU/'UL'/
+* .. Executable Statements ..
+ CONJ = SNAME( 2: 3 ).EQ.'HE'
+*
+ NARGS = 12
+ NC = 0
+ RESET = .TRUE.
+ ERRMAX = RZERO
+*
+ DO 100 IM = 1, NIDIM
+ M = IDIM( IM )
+*
+ DO 90 IN = 1, NIDIM
+ N = IDIM( IN )
+* Set LDC to 1 more than minimum value if room.
+ LDC = M
+ IF( LDC.LT.NMAX )
+ $ LDC = LDC + 1
+* Skip tests if not enough room.
+ IF( LDC.GT.NMAX )
+ $ GO TO 90
+ LCC = LDC*N
+ NULL = N.LE.0.OR.M.LE.0
+* Set LDB to 1 more than minimum value if room.
+ LDB = M
+ IF( LDB.LT.NMAX )
+ $ LDB = LDB + 1
+* Skip tests if not enough room.
+ IF( LDB.GT.NMAX )
+ $ GO TO 90
+ LBB = LDB*N
+*
+* Generate the matrix B.
+*
+ CALL ZMAKE( 'GE', ' ', ' ', M, N, B, NMAX, BB, LDB, RESET,
+ $ ZERO )
+*
+ DO 80 ICS = 1, 2
+ SIDE = ICHS( ICS: ICS )
+ LEFT = SIDE.EQ.'L'
+*
+ IF( LEFT )THEN
+ NA = M
+ ELSE
+ NA = N
+ END IF
+* Set LDA to 1 more than minimum value if room.
+ LDA = NA
+ IF( LDA.LT.NMAX )
+ $ LDA = LDA + 1
+* Skip tests if not enough room.
+ IF( LDA.GT.NMAX )
+ $ GO TO 80
+ LAA = LDA*NA
+*
+ DO 70 ICU = 1, 2
+ UPLO = ICHU( ICU: ICU )
+*
+* Generate the hermitian or symmetric matrix A.
+*
+ CALL ZMAKE( SNAME( 2: 3 ), UPLO, ' ', NA, NA, A, NMAX,
+ $ AA, LDA, RESET, ZERO )
+*
+ DO 60 IA = 1, NALF
+ ALPHA = ALF( IA )
+*
+ DO 50 IB = 1, NBET
+ BETA = BET( IB )
+*
+* Generate the matrix C.
+*
+ CALL ZMAKE( 'GE', ' ', ' ', M, N, C, NMAX, CC,
+ $ LDC, RESET, ZERO )
+*
+ NC = NC + 1
+*
+* Save every datum before calling the
+* subroutine.
+*
+ SIDES = SIDE
+ UPLOS = UPLO
+ MS = M
+ NS = N
+ ALS = ALPHA
+ DO 10 I = 1, LAA
+ AS( I ) = AA( I )
+ 10 CONTINUE
+ LDAS = LDA
+ DO 20 I = 1, LBB
+ BS( I ) = BB( I )
+ 20 CONTINUE
+ LDBS = LDB
+ BLS = BETA
+ DO 30 I = 1, LCC
+ CS( I ) = CC( I )
+ 30 CONTINUE
+ LDCS = LDC
+*
+* Call the subroutine.
+*
+ IF( TRACE )
+ $ WRITE( NTRA, FMT = 9995 )NC, SNAME, SIDE,
+ $ UPLO, M, N, ALPHA, LDA, LDB, BETA, LDC
+ IF( REWI )
+ $ REWIND NTRA
+ IF( CONJ )THEN
+ CALL ZHEMM( SIDE, UPLO, M, N, ALPHA, AA, LDA,
+ $ BB, LDB, BETA, CC, LDC )
+ ELSE
+ CALL ZSYMM( SIDE, UPLO, M, N, ALPHA, AA, LDA,
+ $ BB, LDB, BETA, CC, LDC )
+ END IF
+*
+* Check if error-exit was taken incorrectly.
+*
+ IF( .NOT.OK )THEN
+ WRITE( NOUT, FMT = 9994 )
+ FATAL = .TRUE.
+ GO TO 110
+ END IF
+*
+* See what data changed inside subroutines.
+*
+ ISAME( 1 ) = SIDES.EQ.SIDE
+ ISAME( 2 ) = UPLOS.EQ.UPLO
+ ISAME( 3 ) = MS.EQ.M
+ ISAME( 4 ) = NS.EQ.N
+ ISAME( 5 ) = ALS.EQ.ALPHA
+ ISAME( 6 ) = LZE( AS, AA, LAA )
+ ISAME( 7 ) = LDAS.EQ.LDA
+ ISAME( 8 ) = LZE( BS, BB, LBB )
+ ISAME( 9 ) = LDBS.EQ.LDB
+ ISAME( 10 ) = BLS.EQ.BETA
+ IF( NULL )THEN
+ ISAME( 11 ) = LZE( CS, CC, LCC )
+ ELSE
+ ISAME( 11 ) = LZERES( 'GE', ' ', M, N, CS,
+ $ CC, LDC )
+ END IF
+ ISAME( 12 ) = LDCS.EQ.LDC
+*
+* If data was incorrectly changed, report and
+* return.
+*
+ SAME = .TRUE.
+ DO 40 I = 1, NARGS
+ SAME = SAME.AND.ISAME( I )
+ IF( .NOT.ISAME( I ) )
+ $ WRITE( NOUT, FMT = 9998 )I
+ 40 CONTINUE
+ IF( .NOT.SAME )THEN
+ FATAL = .TRUE.
+ GO TO 110
+ END IF
+*
+ IF( .NOT.NULL )THEN
+*
+* Check the result.
+*
+ IF( LEFT )THEN
+ CALL ZMMCH( 'N', 'N', M, N, M, ALPHA, A,
+ $ NMAX, B, NMAX, BETA, C, NMAX,
+ $ CT, G, CC, LDC, EPS, ERR,
+ $ FATAL, NOUT, .TRUE. )
+ ELSE
+ CALL ZMMCH( 'N', 'N', M, N, N, ALPHA, B,
+ $ NMAX, A, NMAX, BETA, C, NMAX,
+ $ CT, G, CC, LDC, EPS, ERR,
+ $ FATAL, NOUT, .TRUE. )
+ END IF
+ ERRMAX = MAX( ERRMAX, ERR )
+* If got really bad answer, report and
+* return.
+ IF( FATAL )
+ $ GO TO 110
+ END IF
+*
+ 50 CONTINUE
+*
+ 60 CONTINUE
+*
+ 70 CONTINUE
+*
+ 80 CONTINUE
+*
+ 90 CONTINUE
+*
+ 100 CONTINUE
+*
+* Report result.
+*
+ IF( ERRMAX.LT.THRESH )THEN
+ WRITE( NOUT, FMT = 9999 )SNAME, NC
+ ELSE
+ WRITE( NOUT, FMT = 9997 )SNAME, NC, ERRMAX
+ END IF
+ GO TO 120
+*
+ 110 CONTINUE
+ WRITE( NOUT, FMT = 9996 )SNAME
+ WRITE( NOUT, FMT = 9995 )NC, SNAME, SIDE, UPLO, M, N, ALPHA, LDA,
+ $ LDB, BETA, LDC
+*
+ 120 CONTINUE
+ RETURN
+*
+ 9999 FORMAT( ' ', A6, ' PASSED THE COMPUTATIONAL TESTS (', I6, ' CALL',
+ $ 'S)' )
+ 9998 FORMAT( ' ******* FATAL ERROR - PARAMETER NUMBER ', I2, ' WAS CH',
+ $ 'ANGED INCORRECTLY *******' )
+ 9997 FORMAT( ' ', A6, ' COMPLETED THE COMPUTATIONAL TESTS (', I6, ' C',
+ $ 'ALLS)', /' ******* BUT WITH MAXIMUM TEST RATIO', F8.2,
+ $ ' - SUSPECT *******' )
+ 9996 FORMAT( ' ******* ', A6, ' FAILED ON CALL NUMBER:' )
+ 9995 FORMAT( 1X, I6, ': ', A6, '(', 2( '''', A1, ''',' ), 2( I3, ',' ),
+ $ '(', F4.1, ',', F4.1, '), A,', I3, ', B,', I3, ',(', F4.1,
+ $ ',', F4.1, '), C,', I3, ') .' )
+ 9994 FORMAT( ' ******* FATAL ERROR - ERROR-EXIT TAKEN ON VALID CALL *',
+ $ '******' )
+*
+* End of ZCHK2.
+*
+ END
+ SUBROUTINE ZCHK3( SNAME, EPS, THRESH, NOUT, NTRA, TRACE, REWI,
+ $ FATAL, NIDIM, IDIM, NALF, ALF, NMAX, A, AA, AS,
+ $ B, BB, BS, CT, G, C )
+*
+* Tests ZTRMM and ZTRSM.
+*
+* Auxiliary routine for test program for Level 3 Blas.
+*
+* -- Written on 8-February-1989.
+* Jack Dongarra, Argonne National Laboratory.
+* Iain Duff, AERE Harwell.
+* Jeremy Du Croz, Numerical Algorithms Group Ltd.
+* Sven Hammarling, Numerical Algorithms Group Ltd.
+*
+* .. Parameters ..
+ COMPLEX*16 ZERO, ONE
+ PARAMETER ( ZERO = ( 0.0D0, 0.0D0 ),
+ $ ONE = ( 1.0D0, 0.0D0 ) )
+ DOUBLE PRECISION RZERO
+ PARAMETER ( RZERO = 0.0D0 )
+* .. Scalar Arguments ..
+ DOUBLE PRECISION EPS, THRESH
+ INTEGER NALF, NIDIM, NMAX, NOUT, NTRA
+ LOGICAL FATAL, REWI, TRACE
+ CHARACTER*6 SNAME
+* .. Array Arguments ..
+ COMPLEX*16 A( NMAX, NMAX ), AA( NMAX*NMAX ), ALF( NALF ),
+ $ AS( NMAX*NMAX ), B( NMAX, NMAX ),
+ $ BB( NMAX*NMAX ), BS( NMAX*NMAX ),
+ $ C( NMAX, NMAX ), CT( NMAX )
+ DOUBLE PRECISION G( NMAX )
+ INTEGER IDIM( NIDIM )
+* .. Local Scalars ..
+ COMPLEX*16 ALPHA, ALS
+ DOUBLE PRECISION ERR, ERRMAX
+ INTEGER I, IA, ICD, ICS, ICT, ICU, IM, IN, J, LAA, LBB,
+ $ LDA, LDAS, LDB, LDBS, M, MS, N, NA, NARGS, NC,
+ $ NS
+ LOGICAL LEFT, NULL, RESET, SAME
+ CHARACTER*1 DIAG, DIAGS, SIDE, SIDES, TRANAS, TRANSA, UPLO,
+ $ UPLOS
+ CHARACTER*2 ICHD, ICHS, ICHU
+ CHARACTER*3 ICHT
+* .. Local Arrays ..
+ LOGICAL ISAME( 13 )
+* .. External Functions ..
+ LOGICAL LZE, LZERES
+ EXTERNAL LZE, LZERES
+* .. External Subroutines ..
+ EXTERNAL ZMAKE, ZMMCH, ZTRMM, ZTRSM
+* .. Intrinsic Functions ..
+ INTRINSIC MAX
+* .. Scalars in Common ..
+ INTEGER INFOT, NOUTC
+ LOGICAL LERR, OK
+* .. Common blocks ..
+ COMMON /INFOC/INFOT, NOUTC, OK, LERR
+* .. Data statements ..
+ DATA ICHU/'UL'/, ICHT/'NTC'/, ICHD/'UN'/, ICHS/'LR'/
+* .. Executable Statements ..
+*
+ NARGS = 11
+ NC = 0
+ RESET = .TRUE.
+ ERRMAX = RZERO
+* Set up zero matrix for ZMMCH.
+ DO 20 J = 1, NMAX
+ DO 10 I = 1, NMAX
+ C( I, J ) = ZERO
+ 10 CONTINUE
+ 20 CONTINUE
+*
+ DO 140 IM = 1, NIDIM
+ M = IDIM( IM )
+*
+ DO 130 IN = 1, NIDIM
+ N = IDIM( IN )
+* Set LDB to 1 more than minimum value if room.
+ LDB = M
+ IF( LDB.LT.NMAX )
+ $ LDB = LDB + 1
+* Skip tests if not enough room.
+ IF( LDB.GT.NMAX )
+ $ GO TO 130
+ LBB = LDB*N
+ NULL = M.LE.0.OR.N.LE.0
+*
+ DO 120 ICS = 1, 2
+ SIDE = ICHS( ICS: ICS )
+ LEFT = SIDE.EQ.'L'
+ IF( LEFT )THEN
+ NA = M
+ ELSE
+ NA = N
+ END IF
+* Set LDA to 1 more than minimum value if room.
+ LDA = NA
+ IF( LDA.LT.NMAX )
+ $ LDA = LDA + 1
+* Skip tests if not enough room.
+ IF( LDA.GT.NMAX )
+ $ GO TO 130
+ LAA = LDA*NA
+*
+ DO 110 ICU = 1, 2
+ UPLO = ICHU( ICU: ICU )
+*
+ DO 100 ICT = 1, 3
+ TRANSA = ICHT( ICT: ICT )
+*
+ DO 90 ICD = 1, 2
+ DIAG = ICHD( ICD: ICD )
+*
+ DO 80 IA = 1, NALF
+ ALPHA = ALF( IA )
+*
+* Generate the matrix A.
+*
+ CALL ZMAKE( 'TR', UPLO, DIAG, NA, NA, A,
+ $ NMAX, AA, LDA, RESET, ZERO )
+*
+* Generate the matrix B.
+*
+ CALL ZMAKE( 'GE', ' ', ' ', M, N, B, NMAX,
+ $ BB, LDB, RESET, ZERO )
+*
+ NC = NC + 1
+*
+* Save every datum before calling the
+* subroutine.
+*
+ SIDES = SIDE
+ UPLOS = UPLO
+ TRANAS = TRANSA
+ DIAGS = DIAG
+ MS = M
+ NS = N
+ ALS = ALPHA
+ DO 30 I = 1, LAA
+ AS( I ) = AA( I )
+ 30 CONTINUE
+ LDAS = LDA
+ DO 40 I = 1, LBB
+ BS( I ) = BB( I )
+ 40 CONTINUE
+ LDBS = LDB
+*
+* Call the subroutine.
+*
+ IF( SNAME( 4: 5 ).EQ.'MM' )THEN
+ IF( TRACE )
+ $ WRITE( NTRA, FMT = 9995 )NC, SNAME,
+ $ SIDE, UPLO, TRANSA, DIAG, M, N, ALPHA,
+ $ LDA, LDB
+ IF( REWI )
+ $ REWIND NTRA
+ CALL ZTRMM( SIDE, UPLO, TRANSA, DIAG, M,
+ $ N, ALPHA, AA, LDA, BB, LDB )
+ ELSE IF( SNAME( 4: 5 ).EQ.'SM' )THEN
+ IF( TRACE )
+ $ WRITE( NTRA, FMT = 9995 )NC, SNAME,
+ $ SIDE, UPLO, TRANSA, DIAG, M, N, ALPHA,
+ $ LDA, LDB
+ IF( REWI )
+ $ REWIND NTRA
+ CALL ZTRSM( SIDE, UPLO, TRANSA, DIAG, M,
+ $ N, ALPHA, AA, LDA, BB, LDB )
+ END IF
+*
+* Check if error-exit was taken incorrectly.
+*
+ IF( .NOT.OK )THEN
+ WRITE( NOUT, FMT = 9994 )
+ FATAL = .TRUE.
+ GO TO 150
+ END IF
+*
+* See what data changed inside subroutines.
+*
+ ISAME( 1 ) = SIDES.EQ.SIDE
+ ISAME( 2 ) = UPLOS.EQ.UPLO
+ ISAME( 3 ) = TRANAS.EQ.TRANSA
+ ISAME( 4 ) = DIAGS.EQ.DIAG
+ ISAME( 5 ) = MS.EQ.M
+ ISAME( 6 ) = NS.EQ.N
+ ISAME( 7 ) = ALS.EQ.ALPHA
+ ISAME( 8 ) = LZE( AS, AA, LAA )
+ ISAME( 9 ) = LDAS.EQ.LDA
+ IF( NULL )THEN
+ ISAME( 10 ) = LZE( BS, BB, LBB )
+ ELSE
+ ISAME( 10 ) = LZERES( 'GE', ' ', M, N, BS,
+ $ BB, LDB )
+ END IF
+ ISAME( 11 ) = LDBS.EQ.LDB
+*
+* If data was incorrectly changed, report and
+* return.
+*
+ SAME = .TRUE.
+ DO 50 I = 1, NARGS
+ SAME = SAME.AND.ISAME( I )
+ IF( .NOT.ISAME( I ) )
+ $ WRITE( NOUT, FMT = 9998 )I
+ 50 CONTINUE
+ IF( .NOT.SAME )THEN
+ FATAL = .TRUE.
+ GO TO 150
+ END IF
+*
+ IF( .NOT.NULL )THEN
+ IF( SNAME( 4: 5 ).EQ.'MM' )THEN
+*
+* Check the result.
+*
+ IF( LEFT )THEN
+ CALL ZMMCH( TRANSA, 'N', M, N, M,
+ $ ALPHA, A, NMAX, B, NMAX,
+ $ ZERO, C, NMAX, CT, G,
+ $ BB, LDB, EPS, ERR,
+ $ FATAL, NOUT, .TRUE. )
+ ELSE
+ CALL ZMMCH( 'N', TRANSA, M, N, N,
+ $ ALPHA, B, NMAX, A, NMAX,
+ $ ZERO, C, NMAX, CT, G,
+ $ BB, LDB, EPS, ERR,
+ $ FATAL, NOUT, .TRUE. )
+ END IF
+ ELSE IF( SNAME( 4: 5 ).EQ.'SM' )THEN
+*
+* Compute approximation to original
+* matrix.
+*
+ DO 70 J = 1, N
+ DO 60 I = 1, M
+ C( I, J ) = BB( I + ( J - 1 )*
+ $ LDB )
+ BB( I + ( J - 1 )*LDB ) = ALPHA*
+ $ B( I, J )
+ 60 CONTINUE
+ 70 CONTINUE
+*
+ IF( LEFT )THEN
+ CALL ZMMCH( TRANSA, 'N', M, N, M,
+ $ ONE, A, NMAX, C, NMAX,
+ $ ZERO, B, NMAX, CT, G,
+ $ BB, LDB, EPS, ERR,
+ $ FATAL, NOUT, .FALSE. )
+ ELSE
+ CALL ZMMCH( 'N', TRANSA, M, N, N,
+ $ ONE, C, NMAX, A, NMAX,
+ $ ZERO, B, NMAX, CT, G,
+ $ BB, LDB, EPS, ERR,
+ $ FATAL, NOUT, .FALSE. )
+ END IF
+ END IF
+ ERRMAX = MAX( ERRMAX, ERR )
+* If got really bad answer, report and
+* return.
+ IF( FATAL )
+ $ GO TO 150
+ END IF
+*
+ 80 CONTINUE
+*
+ 90 CONTINUE
+*
+ 100 CONTINUE
+*
+ 110 CONTINUE
+*
+ 120 CONTINUE
+*
+ 130 CONTINUE
+*
+ 140 CONTINUE
+*
+* Report result.
+*
+ IF( ERRMAX.LT.THRESH )THEN
+ WRITE( NOUT, FMT = 9999 )SNAME, NC
+ ELSE
+ WRITE( NOUT, FMT = 9997 )SNAME, NC, ERRMAX
+ END IF
+ GO TO 160
+*
+ 150 CONTINUE
+ WRITE( NOUT, FMT = 9996 )SNAME
+ WRITE( NOUT, FMT = 9995 )NC, SNAME, SIDE, UPLO, TRANSA, DIAG, M,
+ $ N, ALPHA, LDA, LDB
+*
+ 160 CONTINUE
+ RETURN
+*
+ 9999 FORMAT( ' ', A6, ' PASSED THE COMPUTATIONAL TESTS (', I6, ' CALL',
+ $ 'S)' )
+ 9998 FORMAT( ' ******* FATAL ERROR - PARAMETER NUMBER ', I2, ' WAS CH',
+ $ 'ANGED INCORRECTLY *******' )
+ 9997 FORMAT( ' ', A6, ' COMPLETED THE COMPUTATIONAL TESTS (', I6, ' C',
+ $ 'ALLS)', /' ******* BUT WITH MAXIMUM TEST RATIO', F8.2,
+ $ ' - SUSPECT *******' )
+ 9996 FORMAT( ' ******* ', A6, ' FAILED ON CALL NUMBER:' )
+ 9995 FORMAT( 1X, I6, ': ', A6, '(', 4( '''', A1, ''',' ), 2( I3, ',' ),
+ $ '(', F4.1, ',', F4.1, '), A,', I3, ', B,', I3, ') ',
+ $ ' .' )
+ 9994 FORMAT( ' ******* FATAL ERROR - ERROR-EXIT TAKEN ON VALID CALL *',
+ $ '******' )
+*
+* End of ZCHK3.
+*
+ END
+ SUBROUTINE ZCHK4( SNAME, EPS, THRESH, NOUT, NTRA, TRACE, REWI,
+ $ FATAL, NIDIM, IDIM, NALF, ALF, NBET, BET, NMAX,
+ $ A, AA, AS, B, BB, BS, C, CC, CS, CT, G )
+*
+* Tests ZHERK and ZSYRK.
+*
+* Auxiliary routine for test program for Level 3 Blas.
+*
+* -- Written on 8-February-1989.
+* Jack Dongarra, Argonne National Laboratory.
+* Iain Duff, AERE Harwell.
+* Jeremy Du Croz, Numerical Algorithms Group Ltd.
+* Sven Hammarling, Numerical Algorithms Group Ltd.
+*
+* .. Parameters ..
+ COMPLEX*16 ZERO
+ PARAMETER ( ZERO = ( 0.0D0, 0.0D0 ) )
+ DOUBLE PRECISION RONE, RZERO
+ PARAMETER ( RONE = 1.0D0, RZERO = 0.0D0 )
+* .. Scalar Arguments ..
+ DOUBLE PRECISION EPS, THRESH
+ INTEGER NALF, NBET, NIDIM, NMAX, NOUT, NTRA
+ LOGICAL FATAL, REWI, TRACE
+ CHARACTER*6 SNAME
+* .. Array Arguments ..
+ COMPLEX*16 A( NMAX, NMAX ), AA( NMAX*NMAX ), ALF( NALF ),
+ $ AS( NMAX*NMAX ), B( NMAX, NMAX ),
+ $ BB( NMAX*NMAX ), BET( NBET ), BS( NMAX*NMAX ),
+ $ C( NMAX, NMAX ), CC( NMAX*NMAX ),
+ $ CS( NMAX*NMAX ), CT( NMAX )
+ DOUBLE PRECISION G( NMAX )
+ INTEGER IDIM( NIDIM )
+* .. Local Scalars ..
+ COMPLEX*16 ALPHA, ALS, BETA, BETS
+ DOUBLE PRECISION ERR, ERRMAX, RALPHA, RALS, RBETA, RBETS
+ INTEGER I, IA, IB, ICT, ICU, IK, IN, J, JC, JJ, K, KS,
+ $ LAA, LCC, LDA, LDAS, LDC, LDCS, LJ, MA, N, NA,
+ $ NARGS, NC, NS
+ LOGICAL CONJ, NULL, RESET, SAME, TRAN, UPPER
+ CHARACTER*1 TRANS, TRANSS, TRANST, UPLO, UPLOS
+ CHARACTER*2 ICHT, ICHU
+* .. Local Arrays ..
+ LOGICAL ISAME( 13 )
+* .. External Functions ..
+ LOGICAL LZE, LZERES
+ EXTERNAL LZE, LZERES
+* .. External Subroutines ..
+ EXTERNAL ZHERK, ZMAKE, ZMMCH, ZSYRK
+* .. Intrinsic Functions ..
+ INTRINSIC DCMPLX, MAX, DBLE
+* .. Scalars in Common ..
+ INTEGER INFOT, NOUTC
+ LOGICAL LERR, OK
+* .. Common blocks ..
+ COMMON /INFOC/INFOT, NOUTC, OK, LERR
+* .. Data statements ..
+ DATA ICHT/'NC'/, ICHU/'UL'/
+* .. Executable Statements ..
+ CONJ = SNAME( 2: 3 ).EQ.'HE'
+*
+ NARGS = 10
+ NC = 0
+ RESET = .TRUE.
+ ERRMAX = RZERO
+*
+ DO 100 IN = 1, NIDIM
+ N = IDIM( IN )
+* Set LDC to 1 more than minimum value if room.
+ LDC = N
+ IF( LDC.LT.NMAX )
+ $ LDC = LDC + 1
+* Skip tests if not enough room.
+ IF( LDC.GT.NMAX )
+ $ GO TO 100
+ LCC = LDC*N
+*
+ DO 90 IK = 1, NIDIM
+ K = IDIM( IK )
+*
+ DO 80 ICT = 1, 2
+ TRANS = ICHT( ICT: ICT )
+ TRAN = TRANS.EQ.'C'
+ IF( TRAN.AND..NOT.CONJ )
+ $ TRANS = 'T'
+ IF( TRAN )THEN
+ MA = K
+ NA = N
+ ELSE
+ MA = N
+ NA = K
+ END IF
+* Set LDA to 1 more than minimum value if room.
+ LDA = MA
+ IF( LDA.LT.NMAX )
+ $ LDA = LDA + 1
+* Skip tests if not enough room.
+ IF( LDA.GT.NMAX )
+ $ GO TO 80
+ LAA = LDA*NA
+*
+* Generate the matrix A.
+*
+ CALL ZMAKE( 'GE', ' ', ' ', MA, NA, A, NMAX, AA, LDA,
+ $ RESET, ZERO )
+*
+ DO 70 ICU = 1, 2
+ UPLO = ICHU( ICU: ICU )
+ UPPER = UPLO.EQ.'U'
+*
+ DO 60 IA = 1, NALF
+ ALPHA = ALF( IA )
+ IF( CONJ )THEN
+ RALPHA = DBLE( ALPHA )
+ ALPHA = DCMPLX( RALPHA, RZERO )
+ END IF
+*
+ DO 50 IB = 1, NBET
+ BETA = BET( IB )
+ IF( CONJ )THEN
+ RBETA = DBLE( BETA )
+ BETA = DCMPLX( RBETA, RZERO )
+ END IF
+ NULL = N.LE.0
+ IF( CONJ )
+ $ NULL = NULL.OR.( ( K.LE.0.OR.RALPHA.EQ.
+ $ RZERO ).AND.RBETA.EQ.RONE )
+*
+* Generate the matrix C.
+*
+ CALL ZMAKE( SNAME( 2: 3 ), UPLO, ' ', N, N, C,
+ $ NMAX, CC, LDC, RESET, ZERO )
+*
+ NC = NC + 1
+*
+* Save every datum before calling the subroutine.
+*
+ UPLOS = UPLO
+ TRANSS = TRANS
+ NS = N
+ KS = K
+ IF( CONJ )THEN
+ RALS = RALPHA
+ ELSE
+ ALS = ALPHA
+ END IF
+ DO 10 I = 1, LAA
+ AS( I ) = AA( I )
+ 10 CONTINUE
+ LDAS = LDA
+ IF( CONJ )THEN
+ RBETS = RBETA
+ ELSE
+ BETS = BETA
+ END IF
+ DO 20 I = 1, LCC
+ CS( I ) = CC( I )
+ 20 CONTINUE
+ LDCS = LDC
+*
+* Call the subroutine.
+*
+ IF( CONJ )THEN
+ IF( TRACE )
+ $ WRITE( NTRA, FMT = 9994 )NC, SNAME, UPLO,
+ $ TRANS, N, K, RALPHA, LDA, RBETA, LDC
+ IF( REWI )
+ $ REWIND NTRA
+ CALL ZHERK( UPLO, TRANS, N, K, RALPHA, AA,
+ $ LDA, RBETA, CC, LDC )
+ ELSE
+ IF( TRACE )
+ $ WRITE( NTRA, FMT = 9993 )NC, SNAME, UPLO,
+ $ TRANS, N, K, ALPHA, LDA, BETA, LDC
+ IF( REWI )
+ $ REWIND NTRA
+ CALL ZSYRK( UPLO, TRANS, N, K, ALPHA, AA,
+ $ LDA, BETA, CC, LDC )
+ END IF
+*
+* Check if error-exit was taken incorrectly.
+*
+ IF( .NOT.OK )THEN
+ WRITE( NOUT, FMT = 9992 )
+ FATAL = .TRUE.
+ GO TO 120
+ END IF
+*
+* See what data changed inside subroutines.
+*
+ ISAME( 1 ) = UPLOS.EQ.UPLO
+ ISAME( 2 ) = TRANSS.EQ.TRANS
+ ISAME( 3 ) = NS.EQ.N
+ ISAME( 4 ) = KS.EQ.K
+ IF( CONJ )THEN
+ ISAME( 5 ) = RALS.EQ.RALPHA
+ ELSE
+ ISAME( 5 ) = ALS.EQ.ALPHA
+ END IF
+ ISAME( 6 ) = LZE( AS, AA, LAA )
+ ISAME( 7 ) = LDAS.EQ.LDA
+ IF( CONJ )THEN
+ ISAME( 8 ) = RBETS.EQ.RBETA
+ ELSE
+ ISAME( 8 ) = BETS.EQ.BETA
+ END IF
+ IF( NULL )THEN
+ ISAME( 9 ) = LZE( CS, CC, LCC )
+ ELSE
+ ISAME( 9 ) = LZERES( SNAME( 2: 3 ), UPLO, N,
+ $ N, CS, CC, LDC )
+ END IF
+ ISAME( 10 ) = LDCS.EQ.LDC
+*
+* If data was incorrectly changed, report and
+* return.
+*
+ SAME = .TRUE.
+ DO 30 I = 1, NARGS
+ SAME = SAME.AND.ISAME( I )
+ IF( .NOT.ISAME( I ) )
+ $ WRITE( NOUT, FMT = 9998 )I
+ 30 CONTINUE
+ IF( .NOT.SAME )THEN
+ FATAL = .TRUE.
+ GO TO 120
+ END IF
+*
+ IF( .NOT.NULL )THEN
+*
+* Check the result column by column.
+*
+ IF( CONJ )THEN
+ TRANST = 'C'
+ ELSE
+ TRANST = 'T'
+ END IF
+ JC = 1
+ DO 40 J = 1, N
+ IF( UPPER )THEN
+ JJ = 1
+ LJ = J
+ ELSE
+ JJ = J
+ LJ = N - J + 1
+ END IF
+ IF( TRAN )THEN
+ CALL ZMMCH( TRANST, 'N', LJ, 1, K,
+ $ ALPHA, A( 1, JJ ), NMAX,
+ $ A( 1, J ), NMAX, BETA,
+ $ C( JJ, J ), NMAX, CT, G,
+ $ CC( JC ), LDC, EPS, ERR,
+ $ FATAL, NOUT, .TRUE. )
+ ELSE
+ CALL ZMMCH( 'N', TRANST, LJ, 1, K,
+ $ ALPHA, A( JJ, 1 ), NMAX,
+ $ A( J, 1 ), NMAX, BETA,
+ $ C( JJ, J ), NMAX, CT, G,
+ $ CC( JC ), LDC, EPS, ERR,
+ $ FATAL, NOUT, .TRUE. )
+ END IF
+ IF( UPPER )THEN
+ JC = JC + LDC
+ ELSE
+ JC = JC + LDC + 1
+ END IF
+ ERRMAX = MAX( ERRMAX, ERR )
+* If got really bad answer, report and
+* return.
+ IF( FATAL )
+ $ GO TO 110
+ 40 CONTINUE
+ END IF
+*
+ 50 CONTINUE
+*
+ 60 CONTINUE
+*
+ 70 CONTINUE
+*
+ 80 CONTINUE
+*
+ 90 CONTINUE
+*
+ 100 CONTINUE
+*
+* Report result.
+*
+ IF( ERRMAX.LT.THRESH )THEN
+ WRITE( NOUT, FMT = 9999 )SNAME, NC
+ ELSE
+ WRITE( NOUT, FMT = 9997 )SNAME, NC, ERRMAX
+ END IF
+ GO TO 130
+*
+ 110 CONTINUE
+ IF( N.GT.1 )
+ $ WRITE( NOUT, FMT = 9995 )J
+*
+ 120 CONTINUE
+ WRITE( NOUT, FMT = 9996 )SNAME
+ IF( CONJ )THEN
+ WRITE( NOUT, FMT = 9994 )NC, SNAME, UPLO, TRANS, N, K, RALPHA,
+ $ LDA, RBETA, LDC
+ ELSE
+ WRITE( NOUT, FMT = 9993 )NC, SNAME, UPLO, TRANS, N, K, ALPHA,
+ $ LDA, BETA, LDC
+ END IF
+*
+ 130 CONTINUE
+ RETURN
+*
+ 9999 FORMAT( ' ', A6, ' PASSED THE COMPUTATIONAL TESTS (', I6, ' CALL',
+ $ 'S)' )
+ 9998 FORMAT( ' ******* FATAL ERROR - PARAMETER NUMBER ', I2, ' WAS CH',
+ $ 'ANGED INCORRECTLY *******' )
+ 9997 FORMAT( ' ', A6, ' COMPLETED THE COMPUTATIONAL TESTS (', I6, ' C',
+ $ 'ALLS)', /' ******* BUT WITH MAXIMUM TEST RATIO', F8.2,
+ $ ' - SUSPECT *******' )
+ 9996 FORMAT( ' ******* ', A6, ' FAILED ON CALL NUMBER:' )
+ 9995 FORMAT( ' THESE ARE THE RESULTS FOR COLUMN ', I3 )
+ 9994 FORMAT( 1X, I6, ': ', A6, '(', 2( '''', A1, ''',' ), 2( I3, ',' ),
+ $ F4.1, ', A,', I3, ',', F4.1, ', C,', I3, ') ',
+ $ ' .' )
+ 9993 FORMAT( 1X, I6, ': ', A6, '(', 2( '''', A1, ''',' ), 2( I3, ',' ),
+ $ '(', F4.1, ',', F4.1, ') , A,', I3, ',(', F4.1, ',', F4.1,
+ $ '), C,', I3, ') .' )
+ 9992 FORMAT( ' ******* FATAL ERROR - ERROR-EXIT TAKEN ON VALID CALL *',
+ $ '******' )
+*
+* End of ZCHK4.
+*
+ END
+ SUBROUTINE ZCHK5( SNAME, EPS, THRESH, NOUT, NTRA, TRACE, REWI,
+ $ FATAL, NIDIM, IDIM, NALF, ALF, NBET, BET, NMAX,
+ $ AB, AA, AS, BB, BS, C, CC, CS, CT, G, W )
+*
+* Tests ZHER2K and ZSYR2K.
+*
+* Auxiliary routine for test program for Level 3 Blas.
+*
+* -- Written on 8-February-1989.
+* Jack Dongarra, Argonne National Laboratory.
+* Iain Duff, AERE Harwell.
+* Jeremy Du Croz, Numerical Algorithms Group Ltd.
+* Sven Hammarling, Numerical Algorithms Group Ltd.
+*
+* .. Parameters ..
+ COMPLEX*16 ZERO, ONE
+ PARAMETER ( ZERO = ( 0.0D0, 0.0D0 ),
+ $ ONE = ( 1.0D0, 0.0D0 ) )
+ DOUBLE PRECISION RONE, RZERO
+ PARAMETER ( RONE = 1.0D0, RZERO = 0.0D0 )
+* .. Scalar Arguments ..
+ DOUBLE PRECISION EPS, THRESH
+ INTEGER NALF, NBET, NIDIM, NMAX, NOUT, NTRA
+ LOGICAL FATAL, REWI, TRACE
+ CHARACTER*6 SNAME
+* .. Array Arguments ..
+ COMPLEX*16 AA( NMAX*NMAX ), AB( 2*NMAX*NMAX ),
+ $ ALF( NALF ), AS( NMAX*NMAX ), BB( NMAX*NMAX ),
+ $ BET( NBET ), BS( NMAX*NMAX ), C( NMAX, NMAX ),
+ $ CC( NMAX*NMAX ), CS( NMAX*NMAX ), CT( NMAX ),
+ $ W( 2*NMAX )
+ DOUBLE PRECISION G( NMAX )
+ INTEGER IDIM( NIDIM )
+* .. Local Scalars ..
+ COMPLEX*16 ALPHA, ALS, BETA, BETS
+ DOUBLE PRECISION ERR, ERRMAX, RBETA, RBETS
+ INTEGER I, IA, IB, ICT, ICU, IK, IN, J, JC, JJ, JJAB,
+ $ K, KS, LAA, LBB, LCC, LDA, LDAS, LDB, LDBS,
+ $ LDC, LDCS, LJ, MA, N, NA, NARGS, NC, NS
+ LOGICAL CONJ, NULL, RESET, SAME, TRAN, UPPER
+ CHARACTER*1 TRANS, TRANSS, TRANST, UPLO, UPLOS
+ CHARACTER*2 ICHT, ICHU
+* .. Local Arrays ..
+ LOGICAL ISAME( 13 )
+* .. External Functions ..
+ LOGICAL LZE, LZERES
+ EXTERNAL LZE, LZERES
+* .. External Subroutines ..
+ EXTERNAL ZHER2K, ZMAKE, ZMMCH, ZSYR2K
+* .. Intrinsic Functions ..
+ INTRINSIC DCMPLX, DCONJG, MAX, DBLE
+* .. Scalars in Common ..
+ INTEGER INFOT, NOUTC
+ LOGICAL LERR, OK
+* .. Common blocks ..
+ COMMON /INFOC/INFOT, NOUTC, OK, LERR
+* .. Data statements ..
+ DATA ICHT/'NC'/, ICHU/'UL'/
+* .. Executable Statements ..
+ CONJ = SNAME( 2: 3 ).EQ.'HE'
+*
+ NARGS = 12
+ NC = 0
+ RESET = .TRUE.
+ ERRMAX = RZERO
+*
+ DO 130 IN = 1, NIDIM
+ N = IDIM( IN )
+* Set LDC to 1 more than minimum value if room.
+ LDC = N
+ IF( LDC.LT.NMAX )
+ $ LDC = LDC + 1
+* Skip tests if not enough room.
+ IF( LDC.GT.NMAX )
+ $ GO TO 130
+ LCC = LDC*N
+*
+ DO 120 IK = 1, NIDIM
+ K = IDIM( IK )
+*
+ DO 110 ICT = 1, 2
+ TRANS = ICHT( ICT: ICT )
+ TRAN = TRANS.EQ.'C'
+ IF( TRAN.AND..NOT.CONJ )
+ $ TRANS = 'T'
+ IF( TRAN )THEN
+ MA = K
+ NA = N
+ ELSE
+ MA = N
+ NA = K
+ END IF
+* Set LDA to 1 more than minimum value if room.
+ LDA = MA
+ IF( LDA.LT.NMAX )
+ $ LDA = LDA + 1
+* Skip tests if not enough room.
+ IF( LDA.GT.NMAX )
+ $ GO TO 110
+ LAA = LDA*NA
+*
+* Generate the matrix A.
+*
+ IF( TRAN )THEN
+ CALL ZMAKE( 'GE', ' ', ' ', MA, NA, AB, 2*NMAX, AA,
+ $ LDA, RESET, ZERO )
+ ELSE
+ CALL ZMAKE( 'GE', ' ', ' ', MA, NA, AB, NMAX, AA, LDA,
+ $ RESET, ZERO )
+ END IF
+*
+* Generate the matrix B.
+*
+ LDB = LDA
+ LBB = LAA
+ IF( TRAN )THEN
+ CALL ZMAKE( 'GE', ' ', ' ', MA, NA, AB( K + 1 ),
+ $ 2*NMAX, BB, LDB, RESET, ZERO )
+ ELSE
+ CALL ZMAKE( 'GE', ' ', ' ', MA, NA, AB( K*NMAX + 1 ),
+ $ NMAX, BB, LDB, RESET, ZERO )
+ END IF
+*
+ DO 100 ICU = 1, 2
+ UPLO = ICHU( ICU: ICU )
+ UPPER = UPLO.EQ.'U'
+*
+ DO 90 IA = 1, NALF
+ ALPHA = ALF( IA )
+*
+ DO 80 IB = 1, NBET
+ BETA = BET( IB )
+ IF( CONJ )THEN
+ RBETA = DBLE( BETA )
+ BETA = DCMPLX( RBETA, RZERO )
+ END IF
+ NULL = N.LE.0
+ IF( CONJ )
+ $ NULL = NULL.OR.( ( K.LE.0.OR.ALPHA.EQ.
+ $ ZERO ).AND.RBETA.EQ.RONE )
+*
+* Generate the matrix C.
+*
+ CALL ZMAKE( SNAME( 2: 3 ), UPLO, ' ', N, N, C,
+ $ NMAX, CC, LDC, RESET, ZERO )
+*
+ NC = NC + 1
+*
+* Save every datum before calling the subroutine.
+*
+ UPLOS = UPLO
+ TRANSS = TRANS
+ NS = N
+ KS = K
+ ALS = ALPHA
+ DO 10 I = 1, LAA
+ AS( I ) = AA( I )
+ 10 CONTINUE
+ LDAS = LDA
+ DO 20 I = 1, LBB
+ BS( I ) = BB( I )
+ 20 CONTINUE
+ LDBS = LDB
+ IF( CONJ )THEN
+ RBETS = RBETA
+ ELSE
+ BETS = BETA
+ END IF
+ DO 30 I = 1, LCC
+ CS( I ) = CC( I )
+ 30 CONTINUE
+ LDCS = LDC
+*
+* Call the subroutine.
+*
+ IF( CONJ )THEN
+ IF( TRACE )
+ $ WRITE( NTRA, FMT = 9994 )NC, SNAME, UPLO,
+ $ TRANS, N, K, ALPHA, LDA, LDB, RBETA, LDC
+ IF( REWI )
+ $ REWIND NTRA
+ CALL ZHER2K( UPLO, TRANS, N, K, ALPHA, AA,
+ $ LDA, BB, LDB, RBETA, CC, LDC )
+ ELSE
+ IF( TRACE )
+ $ WRITE( NTRA, FMT = 9993 )NC, SNAME, UPLO,
+ $ TRANS, N, K, ALPHA, LDA, LDB, BETA, LDC
+ IF( REWI )
+ $ REWIND NTRA
+ CALL ZSYR2K( UPLO, TRANS, N, K, ALPHA, AA,
+ $ LDA, BB, LDB, BETA, CC, LDC )
+ END IF
+*
+* Check if error-exit was taken incorrectly.
+*
+ IF( .NOT.OK )THEN
+ WRITE( NOUT, FMT = 9992 )
+ FATAL = .TRUE.
+ GO TO 150
+ END IF
+*
+* See what data changed inside subroutines.
+*
+ ISAME( 1 ) = UPLOS.EQ.UPLO
+ ISAME( 2 ) = TRANSS.EQ.TRANS
+ ISAME( 3 ) = NS.EQ.N
+ ISAME( 4 ) = KS.EQ.K
+ ISAME( 5 ) = ALS.EQ.ALPHA
+ ISAME( 6 ) = LZE( AS, AA, LAA )
+ ISAME( 7 ) = LDAS.EQ.LDA
+ ISAME( 8 ) = LZE( BS, BB, LBB )
+ ISAME( 9 ) = LDBS.EQ.LDB
+ IF( CONJ )THEN
+ ISAME( 10 ) = RBETS.EQ.RBETA
+ ELSE
+ ISAME( 10 ) = BETS.EQ.BETA
+ END IF
+ IF( NULL )THEN
+ ISAME( 11 ) = LZE( CS, CC, LCC )
+ ELSE
+ ISAME( 11 ) = LZERES( 'HE', UPLO, N, N, CS,
+ $ CC, LDC )
+ END IF
+ ISAME( 12 ) = LDCS.EQ.LDC
+*
+* If data was incorrectly changed, report and
+* return.
+*
+ SAME = .TRUE.
+ DO 40 I = 1, NARGS
+ SAME = SAME.AND.ISAME( I )
+ IF( .NOT.ISAME( I ) )
+ $ WRITE( NOUT, FMT = 9998 )I
+ 40 CONTINUE
+ IF( .NOT.SAME )THEN
+ FATAL = .TRUE.
+ GO TO 150
+ END IF
+*
+ IF( .NOT.NULL )THEN
+*
+* Check the result column by column.
+*
+ IF( CONJ )THEN
+ TRANST = 'C'
+ ELSE
+ TRANST = 'T'
+ END IF
+ JJAB = 1
+ JC = 1
+ DO 70 J = 1, N
+ IF( UPPER )THEN
+ JJ = 1
+ LJ = J
+ ELSE
+ JJ = J
+ LJ = N - J + 1
+ END IF
+ IF( TRAN )THEN
+ DO 50 I = 1, K
+ W( I ) = ALPHA*AB( ( J - 1 )*2*
+ $ NMAX + K + I )
+ IF( CONJ )THEN
+ W( K + I ) = DCONJG( ALPHA )*
+ $ AB( ( J - 1 )*2*
+ $ NMAX + I )
+ ELSE
+ W( K + I ) = ALPHA*
+ $ AB( ( J - 1 )*2*
+ $ NMAX + I )
+ END IF
+ 50 CONTINUE
+ CALL ZMMCH( TRANST, 'N', LJ, 1, 2*K,
+ $ ONE, AB( JJAB ), 2*NMAX, W,
+ $ 2*NMAX, BETA, C( JJ, J ),
+ $ NMAX, CT, G, CC( JC ), LDC,
+ $ EPS, ERR, FATAL, NOUT,
+ $ .TRUE. )
+ ELSE
+ DO 60 I = 1, K
+ IF( CONJ )THEN
+ W( I ) = ALPHA*DCONJG( AB( ( K +
+ $ I - 1 )*NMAX + J ) )
+ W( K + I ) = DCONJG( ALPHA*
+ $ AB( ( I - 1 )*NMAX +
+ $ J ) )
+ ELSE
+ W( I ) = ALPHA*AB( ( K + I - 1 )*
+ $ NMAX + J )
+ W( K + I ) = ALPHA*
+ $ AB( ( I - 1 )*NMAX +
+ $ J )
+ END IF
+ 60 CONTINUE
+ CALL ZMMCH( 'N', 'N', LJ, 1, 2*K, ONE,
+ $ AB( JJ ), NMAX, W, 2*NMAX,
+ $ BETA, C( JJ, J ), NMAX, CT,
+ $ G, CC( JC ), LDC, EPS, ERR,
+ $ FATAL, NOUT, .TRUE. )
+ END IF
+ IF( UPPER )THEN
+ JC = JC + LDC
+ ELSE
+ JC = JC + LDC + 1
+ IF( TRAN )
+ $ JJAB = JJAB + 2*NMAX
+ END IF
+ ERRMAX = MAX( ERRMAX, ERR )
+* If got really bad answer, report and
+* return.
+ IF( FATAL )
+ $ GO TO 140
+ 70 CONTINUE
+ END IF
+*
+ 80 CONTINUE
+*
+ 90 CONTINUE
+*
+ 100 CONTINUE
+*
+ 110 CONTINUE
+*
+ 120 CONTINUE
+*
+ 130 CONTINUE
+*
+* Report result.
+*
+ IF( ERRMAX.LT.THRESH )THEN
+ WRITE( NOUT, FMT = 9999 )SNAME, NC
+ ELSE
+ WRITE( NOUT, FMT = 9997 )SNAME, NC, ERRMAX
+ END IF
+ GO TO 160
+*
+ 140 CONTINUE
+ IF( N.GT.1 )
+ $ WRITE( NOUT, FMT = 9995 )J
+*
+ 150 CONTINUE
+ WRITE( NOUT, FMT = 9996 )SNAME
+ IF( CONJ )THEN
+ WRITE( NOUT, FMT = 9994 )NC, SNAME, UPLO, TRANS, N, K, ALPHA,
+ $ LDA, LDB, RBETA, LDC
+ ELSE
+ WRITE( NOUT, FMT = 9993 )NC, SNAME, UPLO, TRANS, N, K, ALPHA,
+ $ LDA, LDB, BETA, LDC
+ END IF
+*
+ 160 CONTINUE
+ RETURN
+*
+ 9999 FORMAT( ' ', A6, ' PASSED THE COMPUTATIONAL TESTS (', I6, ' CALL',
+ $ 'S)' )
+ 9998 FORMAT( ' ******* FATAL ERROR - PARAMETER NUMBER ', I2, ' WAS CH',
+ $ 'ANGED INCORRECTLY *******' )
+ 9997 FORMAT( ' ', A6, ' COMPLETED THE COMPUTATIONAL TESTS (', I6, ' C',
+ $ 'ALLS)', /' ******* BUT WITH MAXIMUM TEST RATIO', F8.2,
+ $ ' - SUSPECT *******' )
+ 9996 FORMAT( ' ******* ', A6, ' FAILED ON CALL NUMBER:' )
+ 9995 FORMAT( ' THESE ARE THE RESULTS FOR COLUMN ', I3 )
+ 9994 FORMAT( 1X, I6, ': ', A6, '(', 2( '''', A1, ''',' ), 2( I3, ',' ),
+ $ '(', F4.1, ',', F4.1, '), A,', I3, ', B,', I3, ',', F4.1,
+ $ ', C,', I3, ') .' )
+ 9993 FORMAT( 1X, I6, ': ', A6, '(', 2( '''', A1, ''',' ), 2( I3, ',' ),
+ $ '(', F4.1, ',', F4.1, '), A,', I3, ', B,', I3, ',(', F4.1,
+ $ ',', F4.1, '), C,', I3, ') .' )
+ 9992 FORMAT( ' ******* FATAL ERROR - ERROR-EXIT TAKEN ON VALID CALL *',
+ $ '******' )
+*
+* End of ZCHK5.
+*
+ END
+ SUBROUTINE ZCHKE( ISNUM, SRNAMT, NOUT )
+*
+* Tests the error exits from the Level 3 Blas.
+* Requires a special version of the error-handling routine XERBLA.
+* A, B and C should not need to be defined.
+*
+* Auxiliary routine for test program for Level 3 Blas.
+*
+* -- Written on 8-February-1989.
+* Jack Dongarra, Argonne National Laboratory.
+* Iain Duff, AERE Harwell.
+* Jeremy Du Croz, Numerical Algorithms Group Ltd.
+* Sven Hammarling, Numerical Algorithms Group Ltd.
+*
+* 3-19-92: Initialize ALPHA, BETA, RALPHA, and RBETA (eca)
+* 3-19-92: Fix argument 12 in calls to ZSYMM and ZHEMM
+* with INFOT = 9 (eca)
+* 10-9-00: Declared INTRINSIC DCMPLX (susan)
+*
+* .. Scalar Arguments ..
+ INTEGER ISNUM, NOUT
+ CHARACTER*6 SRNAMT
+* .. Scalars in Common ..
+ INTEGER INFOT, NOUTC
+ LOGICAL LERR, OK
+* .. Parameters ..
+ REAL ONE, TWO
+ PARAMETER ( ONE = 1.0D0, TWO = 2.0D0 )
+* .. Local Scalars ..
+ COMPLEX*16 ALPHA, BETA
+ DOUBLE PRECISION RALPHA, RBETA
+* .. Local Arrays ..
+ COMPLEX*16 A( 2, 1 ), B( 2, 1 ), C( 2, 1 )
+* .. External Subroutines ..
+ EXTERNAL ZGEMM, ZHEMM, ZHER2K, ZHERK, CHKXER, ZSYMM,
+ $ ZSYR2K, ZSYRK, ZTRMM, ZTRSM
+* .. Intrinsic Functions ..
+ INTRINSIC DCMPLX
+* .. Common blocks ..
+ COMMON /INFOC/INFOT, NOUTC, OK, LERR
+* .. Executable Statements ..
+* OK is set to .FALSE. by the special version of XERBLA or by CHKXER
+* if anything is wrong.
+ OK = .TRUE.
+* LERR is set to .TRUE. by the special version of XERBLA each time
+* it is called, and is then tested and re-set by CHKXER.
+ LERR = .FALSE.
+*
+* Initialize ALPHA, BETA, RALPHA, and RBETA.
+*
+ ALPHA = DCMPLX( ONE, -ONE )
+ BETA = DCMPLX( TWO, -TWO )
+ RALPHA = ONE
+ RBETA = TWO
+*
+ GO TO ( 10, 20, 30, 40, 50, 60, 70, 80,
+ $ 90 )ISNUM
+ 10 INFOT = 1
+ CALL ZGEMM( '/', 'N', 0, 0, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 1
+ CALL ZGEMM( '/', 'C', 0, 0, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 1
+ CALL ZGEMM( '/', 'T', 0, 0, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 2
+ CALL ZGEMM( 'N', '/', 0, 0, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 2
+ CALL ZGEMM( 'C', '/', 0, 0, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 2
+ CALL ZGEMM( 'T', '/', 0, 0, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 3
+ CALL ZGEMM( 'N', 'N', -1, 0, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 3
+ CALL ZGEMM( 'N', 'C', -1, 0, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 3
+ CALL ZGEMM( 'N', 'T', -1, 0, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 3
+ CALL ZGEMM( 'C', 'N', -1, 0, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 3
+ CALL ZGEMM( 'C', 'C', -1, 0, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 3
+ CALL ZGEMM( 'C', 'T', -1, 0, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 3
+ CALL ZGEMM( 'T', 'N', -1, 0, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 3
+ CALL ZGEMM( 'T', 'C', -1, 0, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 3
+ CALL ZGEMM( 'T', 'T', -1, 0, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 4
+ CALL ZGEMM( 'N', 'N', 0, -1, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 4
+ CALL ZGEMM( 'N', 'C', 0, -1, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 4
+ CALL ZGEMM( 'N', 'T', 0, -1, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 4
+ CALL ZGEMM( 'C', 'N', 0, -1, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 4
+ CALL ZGEMM( 'C', 'C', 0, -1, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 4
+ CALL ZGEMM( 'C', 'T', 0, -1, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 4
+ CALL ZGEMM( 'T', 'N', 0, -1, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 4
+ CALL ZGEMM( 'T', 'C', 0, -1, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 4
+ CALL ZGEMM( 'T', 'T', 0, -1, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 5
+ CALL ZGEMM( 'N', 'N', 0, 0, -1, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 5
+ CALL ZGEMM( 'N', 'C', 0, 0, -1, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 5
+ CALL ZGEMM( 'N', 'T', 0, 0, -1, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 5
+ CALL ZGEMM( 'C', 'N', 0, 0, -1, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 5
+ CALL ZGEMM( 'C', 'C', 0, 0, -1, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 5
+ CALL ZGEMM( 'C', 'T', 0, 0, -1, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 5
+ CALL ZGEMM( 'T', 'N', 0, 0, -1, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 5
+ CALL ZGEMM( 'T', 'C', 0, 0, -1, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 5
+ CALL ZGEMM( 'T', 'T', 0, 0, -1, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 8
+ CALL ZGEMM( 'N', 'N', 2, 0, 0, ALPHA, A, 1, B, 1, BETA, C, 2 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 8
+ CALL ZGEMM( 'N', 'C', 2, 0, 0, ALPHA, A, 1, B, 1, BETA, C, 2 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 8
+ CALL ZGEMM( 'N', 'T', 2, 0, 0, ALPHA, A, 1, B, 1, BETA, C, 2 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 8
+ CALL ZGEMM( 'C', 'N', 0, 0, 2, ALPHA, A, 1, B, 2, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 8
+ CALL ZGEMM( 'C', 'C', 0, 0, 2, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 8
+ CALL ZGEMM( 'C', 'T', 0, 0, 2, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 8
+ CALL ZGEMM( 'T', 'N', 0, 0, 2, ALPHA, A, 1, B, 2, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 8
+ CALL ZGEMM( 'T', 'C', 0, 0, 2, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 8
+ CALL ZGEMM( 'T', 'T', 0, 0, 2, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 10
+ CALL ZGEMM( 'N', 'N', 0, 0, 2, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 10
+ CALL ZGEMM( 'C', 'N', 0, 0, 2, ALPHA, A, 2, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 10
+ CALL ZGEMM( 'T', 'N', 0, 0, 2, ALPHA, A, 2, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 10
+ CALL ZGEMM( 'N', 'C', 0, 2, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 10
+ CALL ZGEMM( 'C', 'C', 0, 2, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 10
+ CALL ZGEMM( 'T', 'C', 0, 2, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 10
+ CALL ZGEMM( 'N', 'T', 0, 2, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 10
+ CALL ZGEMM( 'C', 'T', 0, 2, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 10
+ CALL ZGEMM( 'T', 'T', 0, 2, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 13
+ CALL ZGEMM( 'N', 'N', 2, 0, 0, ALPHA, A, 2, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 13
+ CALL ZGEMM( 'N', 'C', 2, 0, 0, ALPHA, A, 2, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 13
+ CALL ZGEMM( 'N', 'T', 2, 0, 0, ALPHA, A, 2, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 13
+ CALL ZGEMM( 'C', 'N', 2, 0, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 13
+ CALL ZGEMM( 'C', 'C', 2, 0, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 13
+ CALL ZGEMM( 'C', 'T', 2, 0, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 13
+ CALL ZGEMM( 'T', 'N', 2, 0, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 13
+ CALL ZGEMM( 'T', 'C', 2, 0, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 13
+ CALL ZGEMM( 'T', 'T', 2, 0, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ GO TO 100
+ 20 INFOT = 1
+ CALL ZHEMM( '/', 'U', 0, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 2
+ CALL ZHEMM( 'L', '/', 0, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 3
+ CALL ZHEMM( 'L', 'U', -1, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 3
+ CALL ZHEMM( 'R', 'U', -1, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 3
+ CALL ZHEMM( 'L', 'L', -1, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 3
+ CALL ZHEMM( 'R', 'L', -1, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 4
+ CALL ZHEMM( 'L', 'U', 0, -1, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 4
+ CALL ZHEMM( 'R', 'U', 0, -1, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 4
+ CALL ZHEMM( 'L', 'L', 0, -1, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 4
+ CALL ZHEMM( 'R', 'L', 0, -1, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 7
+ CALL ZHEMM( 'L', 'U', 2, 0, ALPHA, A, 1, B, 2, BETA, C, 2 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 7
+ CALL ZHEMM( 'R', 'U', 0, 2, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 7
+ CALL ZHEMM( 'L', 'L', 2, 0, ALPHA, A, 1, B, 2, BETA, C, 2 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 7
+ CALL ZHEMM( 'R', 'L', 0, 2, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 9
+ CALL ZHEMM( 'L', 'U', 2, 0, ALPHA, A, 2, B, 1, BETA, C, 2 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 9
+ CALL ZHEMM( 'R', 'U', 2, 0, ALPHA, A, 1, B, 1, BETA, C, 2 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 9
+ CALL ZHEMM( 'L', 'L', 2, 0, ALPHA, A, 2, B, 1, BETA, C, 2 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 9
+ CALL ZHEMM( 'R', 'L', 2, 0, ALPHA, A, 1, B, 1, BETA, C, 2 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 12
+ CALL ZHEMM( 'L', 'U', 2, 0, ALPHA, A, 2, B, 2, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 12
+ CALL ZHEMM( 'R', 'U', 2, 0, ALPHA, A, 1, B, 2, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 12
+ CALL ZHEMM( 'L', 'L', 2, 0, ALPHA, A, 2, B, 2, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 12
+ CALL ZHEMM( 'R', 'L', 2, 0, ALPHA, A, 1, B, 2, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ GO TO 100
+ 30 INFOT = 1
+ CALL ZSYMM( '/', 'U', 0, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 2
+ CALL ZSYMM( 'L', '/', 0, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 3
+ CALL ZSYMM( 'L', 'U', -1, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 3
+ CALL ZSYMM( 'R', 'U', -1, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 3
+ CALL ZSYMM( 'L', 'L', -1, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 3
+ CALL ZSYMM( 'R', 'L', -1, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 4
+ CALL ZSYMM( 'L', 'U', 0, -1, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 4
+ CALL ZSYMM( 'R', 'U', 0, -1, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 4
+ CALL ZSYMM( 'L', 'L', 0, -1, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 4
+ CALL ZSYMM( 'R', 'L', 0, -1, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 7
+ CALL ZSYMM( 'L', 'U', 2, 0, ALPHA, A, 1, B, 2, BETA, C, 2 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 7
+ CALL ZSYMM( 'R', 'U', 0, 2, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 7
+ CALL ZSYMM( 'L', 'L', 2, 0, ALPHA, A, 1, B, 2, BETA, C, 2 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 7
+ CALL ZSYMM( 'R', 'L', 0, 2, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 9
+ CALL ZSYMM( 'L', 'U', 2, 0, ALPHA, A, 2, B, 1, BETA, C, 2 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 9
+ CALL ZSYMM( 'R', 'U', 2, 0, ALPHA, A, 1, B, 1, BETA, C, 2 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 9
+ CALL ZSYMM( 'L', 'L', 2, 0, ALPHA, A, 2, B, 1, BETA, C, 2 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 9
+ CALL ZSYMM( 'R', 'L', 2, 0, ALPHA, A, 1, B, 1, BETA, C, 2 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 12
+ CALL ZSYMM( 'L', 'U', 2, 0, ALPHA, A, 2, B, 2, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 12
+ CALL ZSYMM( 'R', 'U', 2, 0, ALPHA, A, 1, B, 2, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 12
+ CALL ZSYMM( 'L', 'L', 2, 0, ALPHA, A, 2, B, 2, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 12
+ CALL ZSYMM( 'R', 'L', 2, 0, ALPHA, A, 1, B, 2, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ GO TO 100
+ 40 INFOT = 1
+ CALL ZTRMM( '/', 'U', 'N', 'N', 0, 0, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 2
+ CALL ZTRMM( 'L', '/', 'N', 'N', 0, 0, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 3
+ CALL ZTRMM( 'L', 'U', '/', 'N', 0, 0, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 4
+ CALL ZTRMM( 'L', 'U', 'N', '/', 0, 0, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 5
+ CALL ZTRMM( 'L', 'U', 'N', 'N', -1, 0, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 5
+ CALL ZTRMM( 'L', 'U', 'C', 'N', -1, 0, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 5
+ CALL ZTRMM( 'L', 'U', 'T', 'N', -1, 0, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 5
+ CALL ZTRMM( 'R', 'U', 'N', 'N', -1, 0, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 5
+ CALL ZTRMM( 'R', 'U', 'C', 'N', -1, 0, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 5
+ CALL ZTRMM( 'R', 'U', 'T', 'N', -1, 0, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 5
+ CALL ZTRMM( 'L', 'L', 'N', 'N', -1, 0, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 5
+ CALL ZTRMM( 'L', 'L', 'C', 'N', -1, 0, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 5
+ CALL ZTRMM( 'L', 'L', 'T', 'N', -1, 0, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 5
+ CALL ZTRMM( 'R', 'L', 'N', 'N', -1, 0, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 5
+ CALL ZTRMM( 'R', 'L', 'C', 'N', -1, 0, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 5
+ CALL ZTRMM( 'R', 'L', 'T', 'N', -1, 0, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 6
+ CALL ZTRMM( 'L', 'U', 'N', 'N', 0, -1, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 6
+ CALL ZTRMM( 'L', 'U', 'C', 'N', 0, -1, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 6
+ CALL ZTRMM( 'L', 'U', 'T', 'N', 0, -1, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 6
+ CALL ZTRMM( 'R', 'U', 'N', 'N', 0, -1, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 6
+ CALL ZTRMM( 'R', 'U', 'C', 'N', 0, -1, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 6
+ CALL ZTRMM( 'R', 'U', 'T', 'N', 0, -1, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 6
+ CALL ZTRMM( 'L', 'L', 'N', 'N', 0, -1, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 6
+ CALL ZTRMM( 'L', 'L', 'C', 'N', 0, -1, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 6
+ CALL ZTRMM( 'L', 'L', 'T', 'N', 0, -1, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 6
+ CALL ZTRMM( 'R', 'L', 'N', 'N', 0, -1, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 6
+ CALL ZTRMM( 'R', 'L', 'C', 'N', 0, -1, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 6
+ CALL ZTRMM( 'R', 'L', 'T', 'N', 0, -1, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 9
+ CALL ZTRMM( 'L', 'U', 'N', 'N', 2, 0, ALPHA, A, 1, B, 2 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 9
+ CALL ZTRMM( 'L', 'U', 'C', 'N', 2, 0, ALPHA, A, 1, B, 2 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 9
+ CALL ZTRMM( 'L', 'U', 'T', 'N', 2, 0, ALPHA, A, 1, B, 2 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 9
+ CALL ZTRMM( 'R', 'U', 'N', 'N', 0, 2, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 9
+ CALL ZTRMM( 'R', 'U', 'C', 'N', 0, 2, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 9
+ CALL ZTRMM( 'R', 'U', 'T', 'N', 0, 2, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 9
+ CALL ZTRMM( 'L', 'L', 'N', 'N', 2, 0, ALPHA, A, 1, B, 2 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 9
+ CALL ZTRMM( 'L', 'L', 'C', 'N', 2, 0, ALPHA, A, 1, B, 2 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 9
+ CALL ZTRMM( 'L', 'L', 'T', 'N', 2, 0, ALPHA, A, 1, B, 2 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 9
+ CALL ZTRMM( 'R', 'L', 'N', 'N', 0, 2, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 9
+ CALL ZTRMM( 'R', 'L', 'C', 'N', 0, 2, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 9
+ CALL ZTRMM( 'R', 'L', 'T', 'N', 0, 2, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 11
+ CALL ZTRMM( 'L', 'U', 'N', 'N', 2, 0, ALPHA, A, 2, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 11
+ CALL ZTRMM( 'L', 'U', 'C', 'N', 2, 0, ALPHA, A, 2, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 11
+ CALL ZTRMM( 'L', 'U', 'T', 'N', 2, 0, ALPHA, A, 2, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 11
+ CALL ZTRMM( 'R', 'U', 'N', 'N', 2, 0, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 11
+ CALL ZTRMM( 'R', 'U', 'C', 'N', 2, 0, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 11
+ CALL ZTRMM( 'R', 'U', 'T', 'N', 2, 0, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 11
+ CALL ZTRMM( 'L', 'L', 'N', 'N', 2, 0, ALPHA, A, 2, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 11
+ CALL ZTRMM( 'L', 'L', 'C', 'N', 2, 0, ALPHA, A, 2, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 11
+ CALL ZTRMM( 'L', 'L', 'T', 'N', 2, 0, ALPHA, A, 2, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 11
+ CALL ZTRMM( 'R', 'L', 'N', 'N', 2, 0, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 11
+ CALL ZTRMM( 'R', 'L', 'C', 'N', 2, 0, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 11
+ CALL ZTRMM( 'R', 'L', 'T', 'N', 2, 0, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ GO TO 100
+ 50 INFOT = 1
+ CALL ZTRSM( '/', 'U', 'N', 'N', 0, 0, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 2
+ CALL ZTRSM( 'L', '/', 'N', 'N', 0, 0, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 3
+ CALL ZTRSM( 'L', 'U', '/', 'N', 0, 0, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 4
+ CALL ZTRSM( 'L', 'U', 'N', '/', 0, 0, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 5
+ CALL ZTRSM( 'L', 'U', 'N', 'N', -1, 0, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 5
+ CALL ZTRSM( 'L', 'U', 'C', 'N', -1, 0, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 5
+ CALL ZTRSM( 'L', 'U', 'T', 'N', -1, 0, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 5
+ CALL ZTRSM( 'R', 'U', 'N', 'N', -1, 0, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 5
+ CALL ZTRSM( 'R', 'U', 'C', 'N', -1, 0, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 5
+ CALL ZTRSM( 'R', 'U', 'T', 'N', -1, 0, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 5
+ CALL ZTRSM( 'L', 'L', 'N', 'N', -1, 0, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 5
+ CALL ZTRSM( 'L', 'L', 'C', 'N', -1, 0, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 5
+ CALL ZTRSM( 'L', 'L', 'T', 'N', -1, 0, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 5
+ CALL ZTRSM( 'R', 'L', 'N', 'N', -1, 0, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 5
+ CALL ZTRSM( 'R', 'L', 'C', 'N', -1, 0, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 5
+ CALL ZTRSM( 'R', 'L', 'T', 'N', -1, 0, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 6
+ CALL ZTRSM( 'L', 'U', 'N', 'N', 0, -1, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 6
+ CALL ZTRSM( 'L', 'U', 'C', 'N', 0, -1, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 6
+ CALL ZTRSM( 'L', 'U', 'T', 'N', 0, -1, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 6
+ CALL ZTRSM( 'R', 'U', 'N', 'N', 0, -1, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 6
+ CALL ZTRSM( 'R', 'U', 'C', 'N', 0, -1, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 6
+ CALL ZTRSM( 'R', 'U', 'T', 'N', 0, -1, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 6
+ CALL ZTRSM( 'L', 'L', 'N', 'N', 0, -1, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 6
+ CALL ZTRSM( 'L', 'L', 'C', 'N', 0, -1, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 6
+ CALL ZTRSM( 'L', 'L', 'T', 'N', 0, -1, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 6
+ CALL ZTRSM( 'R', 'L', 'N', 'N', 0, -1, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 6
+ CALL ZTRSM( 'R', 'L', 'C', 'N', 0, -1, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 6
+ CALL ZTRSM( 'R', 'L', 'T', 'N', 0, -1, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 9
+ CALL ZTRSM( 'L', 'U', 'N', 'N', 2, 0, ALPHA, A, 1, B, 2 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 9
+ CALL ZTRSM( 'L', 'U', 'C', 'N', 2, 0, ALPHA, A, 1, B, 2 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 9
+ CALL ZTRSM( 'L', 'U', 'T', 'N', 2, 0, ALPHA, A, 1, B, 2 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 9
+ CALL ZTRSM( 'R', 'U', 'N', 'N', 0, 2, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 9
+ CALL ZTRSM( 'R', 'U', 'C', 'N', 0, 2, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 9
+ CALL ZTRSM( 'R', 'U', 'T', 'N', 0, 2, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 9
+ CALL ZTRSM( 'L', 'L', 'N', 'N', 2, 0, ALPHA, A, 1, B, 2 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 9
+ CALL ZTRSM( 'L', 'L', 'C', 'N', 2, 0, ALPHA, A, 1, B, 2 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 9
+ CALL ZTRSM( 'L', 'L', 'T', 'N', 2, 0, ALPHA, A, 1, B, 2 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 9
+ CALL ZTRSM( 'R', 'L', 'N', 'N', 0, 2, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 9
+ CALL ZTRSM( 'R', 'L', 'C', 'N', 0, 2, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 9
+ CALL ZTRSM( 'R', 'L', 'T', 'N', 0, 2, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 11
+ CALL ZTRSM( 'L', 'U', 'N', 'N', 2, 0, ALPHA, A, 2, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 11
+ CALL ZTRSM( 'L', 'U', 'C', 'N', 2, 0, ALPHA, A, 2, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 11
+ CALL ZTRSM( 'L', 'U', 'T', 'N', 2, 0, ALPHA, A, 2, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 11
+ CALL ZTRSM( 'R', 'U', 'N', 'N', 2, 0, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 11
+ CALL ZTRSM( 'R', 'U', 'C', 'N', 2, 0, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 11
+ CALL ZTRSM( 'R', 'U', 'T', 'N', 2, 0, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 11
+ CALL ZTRSM( 'L', 'L', 'N', 'N', 2, 0, ALPHA, A, 2, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 11
+ CALL ZTRSM( 'L', 'L', 'C', 'N', 2, 0, ALPHA, A, 2, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 11
+ CALL ZTRSM( 'L', 'L', 'T', 'N', 2, 0, ALPHA, A, 2, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 11
+ CALL ZTRSM( 'R', 'L', 'N', 'N', 2, 0, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 11
+ CALL ZTRSM( 'R', 'L', 'C', 'N', 2, 0, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 11
+ CALL ZTRSM( 'R', 'L', 'T', 'N', 2, 0, ALPHA, A, 1, B, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ GO TO 100
+ 60 INFOT = 1
+ CALL ZHERK( '/', 'N', 0, 0, RALPHA, A, 1, RBETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 2
+ CALL ZHERK( 'U', 'T', 0, 0, RALPHA, A, 1, RBETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 3
+ CALL ZHERK( 'U', 'N', -1, 0, RALPHA, A, 1, RBETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 3
+ CALL ZHERK( 'U', 'C', -1, 0, RALPHA, A, 1, RBETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 3
+ CALL ZHERK( 'L', 'N', -1, 0, RALPHA, A, 1, RBETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 3
+ CALL ZHERK( 'L', 'C', -1, 0, RALPHA, A, 1, RBETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 4
+ CALL ZHERK( 'U', 'N', 0, -1, RALPHA, A, 1, RBETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 4
+ CALL ZHERK( 'U', 'C', 0, -1, RALPHA, A, 1, RBETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 4
+ CALL ZHERK( 'L', 'N', 0, -1, RALPHA, A, 1, RBETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 4
+ CALL ZHERK( 'L', 'C', 0, -1, RALPHA, A, 1, RBETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 7
+ CALL ZHERK( 'U', 'N', 2, 0, RALPHA, A, 1, RBETA, C, 2 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 7
+ CALL ZHERK( 'U', 'C', 0, 2, RALPHA, A, 1, RBETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 7
+ CALL ZHERK( 'L', 'N', 2, 0, RALPHA, A, 1, RBETA, C, 2 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 7
+ CALL ZHERK( 'L', 'C', 0, 2, RALPHA, A, 1, RBETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 10
+ CALL ZHERK( 'U', 'N', 2, 0, RALPHA, A, 2, RBETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 10
+ CALL ZHERK( 'U', 'C', 2, 0, RALPHA, A, 1, RBETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 10
+ CALL ZHERK( 'L', 'N', 2, 0, RALPHA, A, 2, RBETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 10
+ CALL ZHERK( 'L', 'C', 2, 0, RALPHA, A, 1, RBETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ GO TO 100
+ 70 INFOT = 1
+ CALL ZSYRK( '/', 'N', 0, 0, ALPHA, A, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 2
+ CALL ZSYRK( 'U', 'C', 0, 0, ALPHA, A, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 3
+ CALL ZSYRK( 'U', 'N', -1, 0, ALPHA, A, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 3
+ CALL ZSYRK( 'U', 'T', -1, 0, ALPHA, A, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 3
+ CALL ZSYRK( 'L', 'N', -1, 0, ALPHA, A, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 3
+ CALL ZSYRK( 'L', 'T', -1, 0, ALPHA, A, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 4
+ CALL ZSYRK( 'U', 'N', 0, -1, ALPHA, A, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 4
+ CALL ZSYRK( 'U', 'T', 0, -1, ALPHA, A, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 4
+ CALL ZSYRK( 'L', 'N', 0, -1, ALPHA, A, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 4
+ CALL ZSYRK( 'L', 'T', 0, -1, ALPHA, A, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 7
+ CALL ZSYRK( 'U', 'N', 2, 0, ALPHA, A, 1, BETA, C, 2 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 7
+ CALL ZSYRK( 'U', 'T', 0, 2, ALPHA, A, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 7
+ CALL ZSYRK( 'L', 'N', 2, 0, ALPHA, A, 1, BETA, C, 2 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 7
+ CALL ZSYRK( 'L', 'T', 0, 2, ALPHA, A, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 10
+ CALL ZSYRK( 'U', 'N', 2, 0, ALPHA, A, 2, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 10
+ CALL ZSYRK( 'U', 'T', 2, 0, ALPHA, A, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 10
+ CALL ZSYRK( 'L', 'N', 2, 0, ALPHA, A, 2, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 10
+ CALL ZSYRK( 'L', 'T', 2, 0, ALPHA, A, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ GO TO 100
+ 80 INFOT = 1
+ CALL ZHER2K( '/', 'N', 0, 0, ALPHA, A, 1, B, 1, RBETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 2
+ CALL ZHER2K( 'U', 'T', 0, 0, ALPHA, A, 1, B, 1, RBETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 3
+ CALL ZHER2K( 'U', 'N', -1, 0, ALPHA, A, 1, B, 1, RBETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 3
+ CALL ZHER2K( 'U', 'C', -1, 0, ALPHA, A, 1, B, 1, RBETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 3
+ CALL ZHER2K( 'L', 'N', -1, 0, ALPHA, A, 1, B, 1, RBETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 3
+ CALL ZHER2K( 'L', 'C', -1, 0, ALPHA, A, 1, B, 1, RBETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 4
+ CALL ZHER2K( 'U', 'N', 0, -1, ALPHA, A, 1, B, 1, RBETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 4
+ CALL ZHER2K( 'U', 'C', 0, -1, ALPHA, A, 1, B, 1, RBETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 4
+ CALL ZHER2K( 'L', 'N', 0, -1, ALPHA, A, 1, B, 1, RBETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 4
+ CALL ZHER2K( 'L', 'C', 0, -1, ALPHA, A, 1, B, 1, RBETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 7
+ CALL ZHER2K( 'U', 'N', 2, 0, ALPHA, A, 1, B, 1, RBETA, C, 2 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 7
+ CALL ZHER2K( 'U', 'C', 0, 2, ALPHA, A, 1, B, 1, RBETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 7
+ CALL ZHER2K( 'L', 'N', 2, 0, ALPHA, A, 1, B, 1, RBETA, C, 2 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 7
+ CALL ZHER2K( 'L', 'C', 0, 2, ALPHA, A, 1, B, 1, RBETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 9
+ CALL ZHER2K( 'U', 'N', 2, 0, ALPHA, A, 2, B, 1, RBETA, C, 2 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 9
+ CALL ZHER2K( 'U', 'C', 0, 2, ALPHA, A, 2, B, 1, RBETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 9
+ CALL ZHER2K( 'L', 'N', 2, 0, ALPHA, A, 2, B, 1, RBETA, C, 2 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 9
+ CALL ZHER2K( 'L', 'C', 0, 2, ALPHA, A, 2, B, 1, RBETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 12
+ CALL ZHER2K( 'U', 'N', 2, 0, ALPHA, A, 2, B, 2, RBETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 12
+ CALL ZHER2K( 'U', 'C', 2, 0, ALPHA, A, 1, B, 1, RBETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 12
+ CALL ZHER2K( 'L', 'N', 2, 0, ALPHA, A, 2, B, 2, RBETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 12
+ CALL ZHER2K( 'L', 'C', 2, 0, ALPHA, A, 1, B, 1, RBETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ GO TO 100
+ 90 INFOT = 1
+ CALL ZSYR2K( '/', 'N', 0, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 2
+ CALL ZSYR2K( 'U', 'C', 0, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 3
+ CALL ZSYR2K( 'U', 'N', -1, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 3
+ CALL ZSYR2K( 'U', 'T', -1, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 3
+ CALL ZSYR2K( 'L', 'N', -1, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 3
+ CALL ZSYR2K( 'L', 'T', -1, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 4
+ CALL ZSYR2K( 'U', 'N', 0, -1, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 4
+ CALL ZSYR2K( 'U', 'T', 0, -1, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 4
+ CALL ZSYR2K( 'L', 'N', 0, -1, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 4
+ CALL ZSYR2K( 'L', 'T', 0, -1, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 7
+ CALL ZSYR2K( 'U', 'N', 2, 0, ALPHA, A, 1, B, 1, BETA, C, 2 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 7
+ CALL ZSYR2K( 'U', 'T', 0, 2, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 7
+ CALL ZSYR2K( 'L', 'N', 2, 0, ALPHA, A, 1, B, 1, BETA, C, 2 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 7
+ CALL ZSYR2K( 'L', 'T', 0, 2, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 9
+ CALL ZSYR2K( 'U', 'N', 2, 0, ALPHA, A, 2, B, 1, BETA, C, 2 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 9
+ CALL ZSYR2K( 'U', 'T', 0, 2, ALPHA, A, 2, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 9
+ CALL ZSYR2K( 'L', 'N', 2, 0, ALPHA, A, 2, B, 1, BETA, C, 2 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 9
+ CALL ZSYR2K( 'L', 'T', 0, 2, ALPHA, A, 2, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 12
+ CALL ZSYR2K( 'U', 'N', 2, 0, ALPHA, A, 2, B, 2, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 12
+ CALL ZSYR2K( 'U', 'T', 2, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 12
+ CALL ZSYR2K( 'L', 'N', 2, 0, ALPHA, A, 2, B, 2, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+ INFOT = 12
+ CALL ZSYR2K( 'L', 'T', 2, 0, ALPHA, A, 1, B, 1, BETA, C, 1 )
+ CALL CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+*
+ 100 IF( OK )THEN
+ WRITE( NOUT, FMT = 9999 )SRNAMT
+ ELSE
+ WRITE( NOUT, FMT = 9998 )SRNAMT
+ END IF
+ RETURN
+*
+ 9999 FORMAT( ' ', A6, ' PASSED THE TESTS OF ERROR-EXITS' )
+ 9998 FORMAT( ' ******* ', A6, ' FAILED THE TESTS OF ERROR-EXITS *****',
+ $ '**' )
+*
+* End of ZCHKE.
+*
+ END
+ SUBROUTINE ZMAKE( TYPE, UPLO, DIAG, M, N, A, NMAX, AA, LDA, RESET,
+ $ TRANSL )
+*
+* Generates values for an M by N matrix A.
+* Stores the values in the array AA in the data structure required
+* by the routine, with unwanted elements set to rogue value.
+*
+* TYPE is 'GE', 'HE', 'SY' or 'TR'.
+*
+* Auxiliary routine for test program for Level 3 Blas.
+*
+* -- Written on 8-February-1989.
+* Jack Dongarra, Argonne National Laboratory.
+* Iain Duff, AERE Harwell.
+* Jeremy Du Croz, Numerical Algorithms Group Ltd.
+* Sven Hammarling, Numerical Algorithms Group Ltd.
+*
+* .. Parameters ..
+ COMPLEX*16 ZERO, ONE
+ PARAMETER ( ZERO = ( 0.0D0, 0.0D0 ),
+ $ ONE = ( 1.0D0, 0.0D0 ) )
+ COMPLEX*16 ROGUE
+ PARAMETER ( ROGUE = ( -1.0D10, 1.0D10 ) )
+ DOUBLE PRECISION RZERO
+ PARAMETER ( RZERO = 0.0D0 )
+ DOUBLE PRECISION RROGUE
+ PARAMETER ( RROGUE = -1.0D10 )
+* .. Scalar Arguments ..
+ COMPLEX*16 TRANSL
+ INTEGER LDA, M, N, NMAX
+ LOGICAL RESET
+ CHARACTER*1 DIAG, UPLO
+ CHARACTER*2 TYPE
+* .. Array Arguments ..
+ COMPLEX*16 A( NMAX, * ), AA( * )
+* .. Local Scalars ..
+ INTEGER I, IBEG, IEND, J, JJ
+ LOGICAL GEN, HER, LOWER, SYM, TRI, UNIT, UPPER
+* .. External Functions ..
+ COMPLEX*16 ZBEG
+ EXTERNAL ZBEG
+* .. Intrinsic Functions ..
+ INTRINSIC DCMPLX, DCONJG, DBLE
+* .. Executable Statements ..
+ GEN = TYPE.EQ.'GE'
+ HER = TYPE.EQ.'HE'
+ SYM = TYPE.EQ.'SY'
+ TRI = TYPE.EQ.'TR'
+ UPPER = ( HER.OR.SYM.OR.TRI ).AND.UPLO.EQ.'U'
+ LOWER = ( HER.OR.SYM.OR.TRI ).AND.UPLO.EQ.'L'
+ UNIT = TRI.AND.DIAG.EQ.'U'
+*
+* Generate data in array A.
+*
+ DO 20 J = 1, N
+ DO 10 I = 1, M
+ IF( GEN.OR.( UPPER.AND.I.LE.J ).OR.( LOWER.AND.I.GE.J ) )
+ $ THEN
+ A( I, J ) = ZBEG( RESET ) + TRANSL
+ IF( I.NE.J )THEN
+* Set some elements to zero
+ IF( N.GT.3.AND.J.EQ.N/2 )
+ $ A( I, J ) = ZERO
+ IF( HER )THEN
+ A( J, I ) = DCONJG( A( I, J ) )
+ ELSE IF( SYM )THEN
+ A( J, I ) = A( I, J )
+ ELSE IF( TRI )THEN
+ A( J, I ) = ZERO
+ END IF
+ END IF
+ END IF
+ 10 CONTINUE
+ IF( HER )
+ $ A( J, J ) = DCMPLX( DBLE( A( J, J ) ), RZERO )
+ IF( TRI )
+ $ A( J, J ) = A( J, J ) + ONE
+ IF( UNIT )
+ $ A( J, J ) = ONE
+ 20 CONTINUE
+*
+* Store elements in array AS in data structure required by routine.
+*
+ IF( TYPE.EQ.'GE' )THEN
+ DO 50 J = 1, N
+ DO 30 I = 1, M
+ AA( I + ( J - 1 )*LDA ) = A( I, J )
+ 30 CONTINUE
+ DO 40 I = M + 1, LDA
+ AA( I + ( J - 1 )*LDA ) = ROGUE
+ 40 CONTINUE
+ 50 CONTINUE
+ ELSE IF( TYPE.EQ.'HE'.OR.TYPE.EQ.'SY'.OR.TYPE.EQ.'TR' )THEN
+ DO 90 J = 1, N
+ IF( UPPER )THEN
+ IBEG = 1
+ IF( UNIT )THEN
+ IEND = J - 1
+ ELSE
+ IEND = J
+ END IF
+ ELSE
+ IF( UNIT )THEN
+ IBEG = J + 1
+ ELSE
+ IBEG = J
+ END IF
+ IEND = N
+ END IF
+ DO 60 I = 1, IBEG - 1
+ AA( I + ( J - 1 )*LDA ) = ROGUE
+ 60 CONTINUE
+ DO 70 I = IBEG, IEND
+ AA( I + ( J - 1 )*LDA ) = A( I, J )
+ 70 CONTINUE
+ DO 80 I = IEND + 1, LDA
+ AA( I + ( J - 1 )*LDA ) = ROGUE
+ 80 CONTINUE
+ IF( HER )THEN
+ JJ = J + ( J - 1 )*LDA
+ AA( JJ ) = DCMPLX( DBLE( AA( JJ ) ), RROGUE )
+ END IF
+ 90 CONTINUE
+ END IF
+ RETURN
+*
+* End of ZMAKE.
+*
+ END
+ SUBROUTINE ZMMCH( TRANSA, TRANSB, M, N, KK, ALPHA, A, LDA, B, LDB,
+ $ BETA, C, LDC, CT, G, CC, LDCC, EPS, ERR, FATAL,
+ $ NOUT, MV )
+*
+* Checks the results of the computational tests.
+*
+* Auxiliary routine for test program for Level 3 Blas.
+*
+* -- Written on 8-February-1989.
+* Jack Dongarra, Argonne National Laboratory.
+* Iain Duff, AERE Harwell.
+* Jeremy Du Croz, Numerical Algorithms Group Ltd.
+* Sven Hammarling, Numerical Algorithms Group Ltd.
+*
+* .. Parameters ..
+ COMPLEX*16 ZERO
+ PARAMETER ( ZERO = ( 0.0D0, 0.0D0 ) )
+ DOUBLE PRECISION RZERO, RONE
+ PARAMETER ( RZERO = 0.0D0, RONE = 1.0D0 )
+* .. Scalar Arguments ..
+ COMPLEX*16 ALPHA, BETA
+ DOUBLE PRECISION EPS, ERR
+ INTEGER KK, LDA, LDB, LDC, LDCC, M, N, NOUT
+ LOGICAL FATAL, MV
+ CHARACTER*1 TRANSA, TRANSB
+* .. Array Arguments ..
+ COMPLEX*16 A( LDA, * ), B( LDB, * ), C( LDC, * ),
+ $ CC( LDCC, * ), CT( * )
+ DOUBLE PRECISION G( * )
+* .. Local Scalars ..
+ COMPLEX*16 CL
+ DOUBLE PRECISION ERRI
+ INTEGER I, J, K
+ LOGICAL CTRANA, CTRANB, TRANA, TRANB
+* .. Intrinsic Functions ..
+ INTRINSIC ABS, DIMAG, DCONJG, MAX, DBLE, SQRT
+* .. Statement Functions ..
+ DOUBLE PRECISION ABS1
+* .. Statement Function definitions ..
+ ABS1( CL ) = ABS( DBLE( CL ) ) + ABS( DIMAG( CL ) )
+* .. Executable Statements ..
+ TRANA = TRANSA.EQ.'T'.OR.TRANSA.EQ.'C'
+ TRANB = TRANSB.EQ.'T'.OR.TRANSB.EQ.'C'
+ CTRANA = TRANSA.EQ.'C'
+ CTRANB = TRANSB.EQ.'C'
+*
+* Compute expected result, one column at a time, in CT using data
+* in A, B and C.
+* Compute gauges in G.
+*
+ DO 220 J = 1, N
+*
+ DO 10 I = 1, M
+ CT( I ) = ZERO
+ G( I ) = RZERO
+ 10 CONTINUE
+ IF( .NOT.TRANA.AND..NOT.TRANB )THEN
+ DO 30 K = 1, KK
+ DO 20 I = 1, M
+ CT( I ) = CT( I ) + A( I, K )*B( K, J )
+ G( I ) = G( I ) + ABS1( A( I, K ) )*ABS1( B( K, J ) )
+ 20 CONTINUE
+ 30 CONTINUE
+ ELSE IF( TRANA.AND..NOT.TRANB )THEN
+ IF( CTRANA )THEN
+ DO 50 K = 1, KK
+ DO 40 I = 1, M
+ CT( I ) = CT( I ) + DCONJG( A( K, I ) )*B( K, J )
+ G( I ) = G( I ) + ABS1( A( K, I ) )*
+ $ ABS1( B( K, J ) )
+ 40 CONTINUE
+ 50 CONTINUE
+ ELSE
+ DO 70 K = 1, KK
+ DO 60 I = 1, M
+ CT( I ) = CT( I ) + A( K, I )*B( K, J )
+ G( I ) = G( I ) + ABS1( A( K, I ) )*
+ $ ABS1( B( K, J ) )
+ 60 CONTINUE
+ 70 CONTINUE
+ END IF
+ ELSE IF( .NOT.TRANA.AND.TRANB )THEN
+ IF( CTRANB )THEN
+ DO 90 K = 1, KK
+ DO 80 I = 1, M
+ CT( I ) = CT( I ) + A( I, K )*DCONJG( B( J, K ) )
+ G( I ) = G( I ) + ABS1( A( I, K ) )*
+ $ ABS1( B( J, K ) )
+ 80 CONTINUE
+ 90 CONTINUE
+ ELSE
+ DO 110 K = 1, KK
+ DO 100 I = 1, M
+ CT( I ) = CT( I ) + A( I, K )*B( J, K )
+ G( I ) = G( I ) + ABS1( A( I, K ) )*
+ $ ABS1( B( J, K ) )
+ 100 CONTINUE
+ 110 CONTINUE
+ END IF
+ ELSE IF( TRANA.AND.TRANB )THEN
+ IF( CTRANA )THEN
+ IF( CTRANB )THEN
+ DO 130 K = 1, KK
+ DO 120 I = 1, M
+ CT( I ) = CT( I ) + DCONJG( A( K, I ) )*
+ $ DCONJG( B( J, K ) )
+ G( I ) = G( I ) + ABS1( A( K, I ) )*
+ $ ABS1( B( J, K ) )
+ 120 CONTINUE
+ 130 CONTINUE
+ ELSE
+ DO 150 K = 1, KK
+ DO 140 I = 1, M
+ CT( I ) = CT( I ) + DCONJG( A( K, I ) )*
+ $ B( J, K )
+ G( I ) = G( I ) + ABS1( A( K, I ) )*
+ $ ABS1( B( J, K ) )
+ 140 CONTINUE
+ 150 CONTINUE
+ END IF
+ ELSE
+ IF( CTRANB )THEN
+ DO 170 K = 1, KK
+ DO 160 I = 1, M
+ CT( I ) = CT( I ) + A( K, I )*
+ $ DCONJG( B( J, K ) )
+ G( I ) = G( I ) + ABS1( A( K, I ) )*
+ $ ABS1( B( J, K ) )
+ 160 CONTINUE
+ 170 CONTINUE
+ ELSE
+ DO 190 K = 1, KK
+ DO 180 I = 1, M
+ CT( I ) = CT( I ) + A( K, I )*B( J, K )
+ G( I ) = G( I ) + ABS1( A( K, I ) )*
+ $ ABS1( B( J, K ) )
+ 180 CONTINUE
+ 190 CONTINUE
+ END IF
+ END IF
+ END IF
+ DO 200 I = 1, M
+ CT( I ) = ALPHA*CT( I ) + BETA*C( I, J )
+ G( I ) = ABS1( ALPHA )*G( I ) +
+ $ ABS1( BETA )*ABS1( C( I, J ) )
+ 200 CONTINUE
+*
+* Compute the error ratio for this result.
+*
+ ERR = ZERO
+ DO 210 I = 1, M
+ ERRI = ABS1( CT( I ) - CC( I, J ) )/EPS
+ IF( G( I ).NE.RZERO )
+ $ ERRI = ERRI/G( I )
+ ERR = MAX( ERR, ERRI )
+ IF( ERR*SQRT( EPS ).GE.RONE )
+ $ GO TO 230
+ 210 CONTINUE
+*
+ 220 CONTINUE
+*
+* If the loop completes, all results are at least half accurate.
+ GO TO 250
+*
+* Report fatal error.
+*
+ 230 FATAL = .TRUE.
+ WRITE( NOUT, FMT = 9999 )
+ DO 240 I = 1, M
+ IF( MV )THEN
+ WRITE( NOUT, FMT = 9998 )I, CT( I ), CC( I, J )
+ ELSE
+ WRITE( NOUT, FMT = 9998 )I, CC( I, J ), CT( I )
+ END IF
+ 240 CONTINUE
+ IF( N.GT.1 )
+ $ WRITE( NOUT, FMT = 9997 )J
+*
+ 250 CONTINUE
+ RETURN
+*
+ 9999 FORMAT( ' ******* FATAL ERROR - COMPUTED RESULT IS LESS THAN HAL',
+ $ 'F ACCURATE *******', /' EXPECTED RE',
+ $ 'SULT COMPUTED RESULT' )
+ 9998 FORMAT( 1X, I7, 2( ' (', G15.6, ',', G15.6, ')' ) )
+ 9997 FORMAT( ' THESE ARE THE RESULTS FOR COLUMN ', I3 )
+*
+* End of ZMMCH.
+*
+ END
+ LOGICAL FUNCTION LZE( RI, RJ, LR )
+*
+* Tests if two arrays are identical.
+*
+* Auxiliary routine for test program for Level 3 Blas.
+*
+* -- Written on 8-February-1989.
+* Jack Dongarra, Argonne National Laboratory.
+* Iain Duff, AERE Harwell.
+* Jeremy Du Croz, Numerical Algorithms Group Ltd.
+* Sven Hammarling, Numerical Algorithms Group Ltd.
+*
+* .. Scalar Arguments ..
+ INTEGER LR
+* .. Array Arguments ..
+ COMPLEX*16 RI( * ), RJ( * )
+* .. Local Scalars ..
+ INTEGER I
+* .. Executable Statements ..
+ DO 10 I = 1, LR
+ IF( RI( I ).NE.RJ( I ) )
+ $ GO TO 20
+ 10 CONTINUE
+ LZE = .TRUE.
+ GO TO 30
+ 20 CONTINUE
+ LZE = .FALSE.
+ 30 RETURN
+*
+* End of LZE.
+*
+ END
+ LOGICAL FUNCTION LZERES( TYPE, UPLO, M, N, AA, AS, LDA )
+*
+* Tests if selected elements in two arrays are equal.
+*
+* TYPE is 'GE' or 'HE' or 'SY'.
+*
+* Auxiliary routine for test program for Level 3 Blas.
+*
+* -- Written on 8-February-1989.
+* Jack Dongarra, Argonne National Laboratory.
+* Iain Duff, AERE Harwell.
+* Jeremy Du Croz, Numerical Algorithms Group Ltd.
+* Sven Hammarling, Numerical Algorithms Group Ltd.
+*
+* .. Scalar Arguments ..
+ INTEGER LDA, M, N
+ CHARACTER*1 UPLO
+ CHARACTER*2 TYPE
+* .. Array Arguments ..
+ COMPLEX*16 AA( LDA, * ), AS( LDA, * )
+* .. Local Scalars ..
+ INTEGER I, IBEG, IEND, J
+ LOGICAL UPPER
+* .. Executable Statements ..
+ UPPER = UPLO.EQ.'U'
+ IF( TYPE.EQ.'GE' )THEN
+ DO 20 J = 1, N
+ DO 10 I = M + 1, LDA
+ IF( AA( I, J ).NE.AS( I, J ) )
+ $ GO TO 70
+ 10 CONTINUE
+ 20 CONTINUE
+ ELSE IF( TYPE.EQ.'HE'.OR.TYPE.EQ.'SY' )THEN
+ DO 50 J = 1, N
+ IF( UPPER )THEN
+ IBEG = 1
+ IEND = J
+ ELSE
+ IBEG = J
+ IEND = N
+ END IF
+ DO 30 I = 1, IBEG - 1
+ IF( AA( I, J ).NE.AS( I, J ) )
+ $ GO TO 70
+ 30 CONTINUE
+ DO 40 I = IEND + 1, LDA
+ IF( AA( I, J ).NE.AS( I, J ) )
+ $ GO TO 70
+ 40 CONTINUE
+ 50 CONTINUE
+ END IF
+*
+ LZERES = .TRUE.
+ GO TO 80
+ 70 CONTINUE
+ LZERES = .FALSE.
+ 80 RETURN
+*
+* End of LZERES.
+*
+ END
+ COMPLEX*16 FUNCTION ZBEG( RESET )
+*
+* Generates complex numbers as pairs of random numbers uniformly
+* distributed between -0.5 and 0.5.
+*
+* Auxiliary routine for test program for Level 3 Blas.
+*
+* -- Written on 8-February-1989.
+* Jack Dongarra, Argonne National Laboratory.
+* Iain Duff, AERE Harwell.
+* Jeremy Du Croz, Numerical Algorithms Group Ltd.
+* Sven Hammarling, Numerical Algorithms Group Ltd.
+*
+* .. Scalar Arguments ..
+ LOGICAL RESET
+* .. Local Scalars ..
+ INTEGER I, IC, J, MI, MJ
+* .. Save statement ..
+ SAVE I, IC, J, MI, MJ
+* .. Intrinsic Functions ..
+ INTRINSIC DCMPLX
+* .. Executable Statements ..
+ IF( RESET )THEN
+* Initialize local variables.
+ MI = 891
+ MJ = 457
+ I = 7
+ J = 7
+ IC = 0
+ RESET = .FALSE.
+ END IF
+*
+* The sequence of values of I or J is bounded between 1 and 999.
+* If initial I or J = 1,2,3,6,7 or 9, the period will be 50.
+* If initial I or J = 4 or 8, the period will be 25.
+* If initial I or J = 5, the period will be 10.
+* IC is used to break up the period by skipping 1 value of I or J
+* in 6.
+*
+ IC = IC + 1
+ 10 I = I*MI
+ J = J*MJ
+ I = I - 1000*( I/1000 )
+ J = J - 1000*( J/1000 )
+ IF( IC.GE.5 )THEN
+ IC = 0
+ GO TO 10
+ END IF
+ ZBEG = DCMPLX( ( I - 500 )/1001.0D0, ( J - 500 )/1001.0D0 )
+ RETURN
+*
+* End of ZBEG.
+*
+ END
+ DOUBLE PRECISION FUNCTION DDIFF( X, Y )
+*
+* Auxiliary routine for test program for Level 3 Blas.
+*
+* -- Written on 8-February-1989.
+* Jack Dongarra, Argonne National Laboratory.
+* Iain Duff, AERE Harwell.
+* Jeremy Du Croz, Numerical Algorithms Group Ltd.
+* Sven Hammarling, Numerical Algorithms Group Ltd.
+*
+* .. Scalar Arguments ..
+ DOUBLE PRECISION X, Y
+* .. Executable Statements ..
+ DDIFF = X - Y
+ RETURN
+*
+* End of DDIFF.
+*
+ END
+ SUBROUTINE CHKXER( SRNAMT, INFOT, NOUT, LERR, OK )
+*
+* Tests whether XERBLA has detected an error when it should.
+*
+* Auxiliary routine for test program for Level 3 Blas.
+*
+* -- Written on 8-February-1989.
+* Jack Dongarra, Argonne National Laboratory.
+* Iain Duff, AERE Harwell.
+* Jeremy Du Croz, Numerical Algorithms Group Ltd.
+* Sven Hammarling, Numerical Algorithms Group Ltd.
+*
+* .. Scalar Arguments ..
+ INTEGER INFOT, NOUT
+ LOGICAL LERR, OK
+ CHARACTER*6 SRNAMT
+* .. Executable Statements ..
+ IF( .NOT.LERR )THEN
+ WRITE( NOUT, FMT = 9999 )INFOT, SRNAMT
+ OK = .FALSE.
+ END IF
+ LERR = .FALSE.
+ RETURN
+*
+ 9999 FORMAT( ' ***** ILLEGAL VALUE OF PARAMETER NUMBER ', I2, ' NOT D',
+ $ 'ETECTED BY ', A6, ' *****' )
+*
+* End of CHKXER.
+*
+ END
+ SUBROUTINE XERBLA( SRNAME, INFO )
+*
+* This is a special version of XERBLA to be used only as part of
+* the test program for testing error exits from the Level 3 BLAS
+* routines.
+*
+* XERBLA is an error handler for the Level 3 BLAS routines.
+*
+* It is called by the Level 3 BLAS routines if an input parameter is
+* invalid.
+*
+* Auxiliary routine for test program for Level 3 Blas.
+*
+* -- Written on 8-February-1989.
+* Jack Dongarra, Argonne National Laboratory.
+* Iain Duff, AERE Harwell.
+* Jeremy Du Croz, Numerical Algorithms Group Ltd.
+* Sven Hammarling, Numerical Algorithms Group Ltd.
+*
+* .. Scalar Arguments ..
+ INTEGER INFO
+ CHARACTER*6 SRNAME
+* .. Scalars in Common ..
+ INTEGER INFOT, NOUT
+ LOGICAL LERR, OK
+ CHARACTER*6 SRNAMT
+* .. Common blocks ..
+ COMMON /INFOC/INFOT, NOUT, OK, LERR
+ COMMON /SRNAMC/SRNAMT
+* .. Executable Statements ..
+ LERR = .TRUE.
+ IF( INFO.NE.INFOT )THEN
+ IF( INFOT.NE.0 )THEN
+ WRITE( NOUT, FMT = 9999 )INFO, INFOT
+ ELSE
+ WRITE( NOUT, FMT = 9997 )INFO
+ END IF
+ OK = .FALSE.
+ END IF
+ IF( SRNAME.NE.SRNAMT )THEN
+ WRITE( NOUT, FMT = 9998 )SRNAME, SRNAMT
+ OK = .FALSE.
+ END IF
+ RETURN
+*
+ 9999 FORMAT( ' ******* XERBLA WAS CALLED WITH INFO = ', I6, ' INSTEAD',
+ $ ' OF ', I2, ' *******' )
+ 9998 FORMAT( ' ******* XERBLA WAS CALLED WITH SRNAME = ', A6, ' INSTE',
+ $ 'AD OF ', A6, ' *******' )
+ 9997 FORMAT( ' ******* XERBLA WAS CALLED WITH INFO = ', I6,
+ $ ' *******' )
+*
+* End of XERBLA
+*
+ END
+
diff --git a/blas/xerbla.cpp b/blas/xerbla.cpp
new file mode 100644
index 0000000..c373e86
--- /dev/null
+++ b/blas/xerbla.cpp
@@ -0,0 +1,23 @@
+
+#include <stdio.h>
+
+#if (defined __GNUC__) && (!defined __MINGW32__) && (!defined __CYGWIN__)
+#define EIGEN_WEAK_LINKING __attribute__ ((weak))
+#else
+#define EIGEN_WEAK_LINKING
+#endif
+
+#ifdef __cplusplus
+extern "C"
+{
+#endif
+
+EIGEN_WEAK_LINKING int xerbla_(const char * msg, int *info, int)
+{
+ printf("Eigen BLAS ERROR #%i: %s\n", *info, msg );
+ return 0;
+}
+
+#ifdef __cplusplus
+}
+#endif
diff --git a/cmake/ComputeCppCompilerChecks.cmake b/cmake/ComputeCppCompilerChecks.cmake
new file mode 100644
index 0000000..1807485
--- /dev/null
+++ b/cmake/ComputeCppCompilerChecks.cmake
@@ -0,0 +1,50 @@
+cmake_minimum_required(VERSION 3.4.3)
+
+if(CMAKE_COMPILER_IS_GNUCXX)
+ if (CMAKE_CXX_COMPILER_VERSION VERSION_LESS 4.8)
+ message(FATAL_ERROR "host compiler - gcc version must be > 4.8")
+ endif()
+elseif ("${CMAKE_CXX_COMPILER_ID}" STREQUAL "Clang")
+ if (${CMAKE_CXX_COMPILER_VERSION} VERSION_LESS 3.6)
+ message(FATAL_ERROR "host compiler - clang version must be > 3.6")
+ endif()
+endif()
+
+if(MSVC)
+ set(ComputeCpp_STL_CHECK_SRC __STL_check)
+ file(WRITE ${CMAKE_CURRENT_BINARY_DIR}/${ComputeCpp_STL_CHECK_SRC}.cpp
+ "#include <ios>\n"
+ "int main() { return 0; }\n")
+ execute_process(
+ COMMAND ${ComputeCpp_DEVICE_COMPILER_EXECUTABLE}
+ ${COMPUTECPP_DEVICE_COMPILER_FLAGS}
+ -isystem ${ComputeCpp_INCLUDE_DIRS}
+ -o ${ComputeCpp_STL_CHECK_SRC}.sycl
+ -c ${ComputeCpp_STL_CHECK_SRC}.cpp
+ WORKING_DIRECTORY ${CMAKE_CURRENT_BINARY_DIR}
+ RESULT_VARIABLE ComputeCpp_STL_CHECK_RESULT
+ ERROR_QUIET
+ OUTPUT_QUIET)
+ if(NOT ${ComputeCpp_STL_CHECK_RESULT} EQUAL 0)
+ # Try disabling compiler version checks
+ execute_process(
+ COMMAND ${ComputeCpp_DEVICE_COMPILER_EXECUTABLE}
+ ${COMPUTECPP_DEVICE_COMPILER_FLAGS}
+ -D_ALLOW_COMPILER_AND_STL_VERSION_MISMATCH
+ -isystem ${ComputeCpp_INCLUDE_DIRS}
+ -o ${ComputeCpp_STL_CHECK_SRC}.cpp.sycl
+ -c ${ComputeCpp_STL_CHECK_SRC}.cpp
+ WORKING_DIRECTORY ${CMAKE_CURRENT_BINARY_DIR}
+ RESULT_VARIABLE ComputeCpp_STL_CHECK_RESULT
+ ERROR_QUIET
+ OUTPUT_QUIET)
+ if(NOT ${ComputeCpp_STL_CHECK_RESULT} EQUAL 0)
+ message(STATUS "Device compiler cannot consume hosted STL headers. Using any parts of the STL will likely result in device compiler errors.")
+ else()
+ message(STATUS "Device compiler does not meet certain STL version requirements. Disabling version checks and hoping for the best.")
+ list(APPEND COMPUTECPP_DEVICE_COMPILER_FLAGS -D_ALLOW_COMPILER_AND_STL_VERSION_MISMATCH)
+ endif()
+ endif()
+ file(REMOVE ${CMAKE_CURRENT_BINARY_DIR}/${ComputeCpp_STL_CHECK_SRC}.cpp
+ ${CMAKE_CURRENT_BINARY_DIR}/${ComputeCpp_STL_CHECK_SRC}.cpp.sycl)
+endif(MSVC)
diff --git a/cmake/ComputeCppIRMap.cmake b/cmake/ComputeCppIRMap.cmake
new file mode 100644
index 0000000..942d91d
--- /dev/null
+++ b/cmake/ComputeCppIRMap.cmake
@@ -0,0 +1,18 @@
+cmake_minimum_required(VERSION 3.4.3)
+
+# These should match the types of IR output by compute++
+set(IR_MAP_spir bc)
+set(IR_MAP_spir64 bc)
+set(IR_MAP_spir32 bc)
+set(IR_MAP_spirv spv)
+set(IR_MAP_spirv64 spv)
+set(IR_MAP_spirv32 spv)
+set(IR_MAP_aorta-x86_64 o)
+set(IR_MAP_aorta-aarch64 o)
+set(IR_MAP_aorta-rcar-cve o)
+set(IR_MAP_custom-spir64 bc)
+set(IR_MAP_custom-spir32 bc)
+set(IR_MAP_custom-spirv64 spv)
+set(IR_MAP_custom-spirv32 spv)
+set(IR_MAP_ptx64 s)
+set(IR_MAP_amdgcn s)
diff --git a/cmake/Eigen3Config.cmake.in b/cmake/Eigen3Config.cmake.in
new file mode 100644
index 0000000..96582f5
--- /dev/null
+++ b/cmake/Eigen3Config.cmake.in
@@ -0,0 +1,8 @@
+# This file exports the Eigen3::Eigen CMake target which should be passed to the
+# target_link_libraries command.
+
+@PACKAGE_INIT@
+
+if (NOT TARGET Eigen3::Eigen)
+ include ("${CMAKE_CURRENT_LIST_DIR}/Eigen3Targets.cmake")
+endif (NOT TARGET Eigen3::Eigen)
diff --git a/cmake/EigenConfigureTesting.cmake b/cmake/EigenConfigureTesting.cmake
new file mode 100644
index 0000000..2a1e7ab
--- /dev/null
+++ b/cmake/EigenConfigureTesting.cmake
@@ -0,0 +1,67 @@
+include(EigenTesting)
+include(CheckCXXSourceCompiles)
+
+# configure the "site" and "buildname"
+ei_set_sitename()
+
+# retrieve and store the build string
+ei_set_build_string()
+
+add_custom_target(buildtests)
+add_custom_target(check COMMAND "ctest" ${EIGEN_CTEST_ARGS})
+add_dependencies(check buildtests)
+
+# Convenience target for only building GPU tests.
+add_custom_target(buildtests_gpu)
+add_custom_target(check_gpu COMMAND "ctest" "--output-on-failure"
+ "--no-compress-output"
+ "--build-no-clean"
+ "-T" "test"
+ "-L" "gpu")
+add_dependencies(check_gpu buildtests_gpu)
+
+# check whether /bin/bash exists (disabled as not used anymore)
+# find_file(EIGEN_BIN_BASH_EXISTS "/bin/bash" PATHS "/" NO_DEFAULT_PATH)
+
+# This call activates testing and generates the DartConfiguration.tcl
+include(CTest)
+
+set(EIGEN_TEST_BUILD_FLAGS "" CACHE STRING "Options passed to the build command of unit tests")
+set(EIGEN_DASHBOARD_BUILD_TARGET "buildtests" CACHE STRING "Target to be built in dashboard mode, default is buildtests")
+set(EIGEN_CTEST_ERROR_EXCEPTION "" CACHE STRING "Regular expression for build error messages to be filtered out")
+
+# Overwrite default DartConfiguration.tcl such that ctest can build our unit tests.
+# Recall that our unit tests are not in the "all" target, so we have to explicitly ask ctest to build our custom 'buildtests' target.
+# At this stage, we can also add custom flags to the build tool through the user defined EIGEN_TEST_BUILD_FLAGS variable.
+file(READ "${CMAKE_CURRENT_BINARY_DIR}/DartConfiguration.tcl" EIGEN_DART_CONFIG_FILE)
+# try to grab the default flags
+string(REGEX MATCH "MakeCommand:.*-- (.*)\nDefaultCTestConfigurationType" EIGEN_DUMMY ${EIGEN_DART_CONFIG_FILE})
+if(NOT CMAKE_MATCH_1)
+string(REGEX MATCH "MakeCommand:.*[^c]make (.*)\nDefaultCTestConfigurationType" EIGEN_DUMMY ${EIGEN_DART_CONFIG_FILE})
+endif()
+string(REGEX REPLACE "MakeCommand:.*DefaultCTestConfigurationType" "MakeCommand: ${CMAKE_COMMAND} --build . --target ${EIGEN_DASHBOARD_BUILD_TARGET} --config \"\${CTEST_CONFIGURATION_TYPE}\" -- ${CMAKE_MATCH_1} ${EIGEN_TEST_BUILD_FLAGS}\nDefaultCTestConfigurationType"
+ EIGEN_DART_CONFIG_FILE2 ${EIGEN_DART_CONFIG_FILE})
+file(WRITE "${CMAKE_CURRENT_BINARY_DIR}/DartConfiguration.tcl" ${EIGEN_DART_CONFIG_FILE2})
+
+configure_file(${CMAKE_CURRENT_SOURCE_DIR}/CTestCustom.cmake.in ${CMAKE_BINARY_DIR}/CTestCustom.cmake)
+
+# some documentation of this function would be nice
+ei_init_testing()
+
+# configure Eigen related testing options
+option(EIGEN_NO_ASSERTION_CHECKING "Disable checking of assertions using exceptions" OFF)
+option(EIGEN_DEBUG_ASSERTS "Enable advanced debugging of assertions" OFF)
+
+if(CMAKE_COMPILER_IS_GNUCXX)
+ option(EIGEN_COVERAGE_TESTING "Enable/disable gcov" OFF)
+ if(EIGEN_COVERAGE_TESTING)
+ set(COVERAGE_FLAGS "-fprofile-arcs -ftest-coverage")
+ set(CTEST_CUSTOM_COVERAGE_EXCLUDE "/test/")
+ set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} ${COVERAGE_FLAGS}")
+ endif()
+
+elseif(MSVC)
+ set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} /D_CRT_SECURE_NO_WARNINGS /D_SCL_SECURE_NO_WARNINGS")
+endif()
+
+
diff --git a/cmake/EigenSmokeTestList.cmake b/cmake/EigenSmokeTestList.cmake
new file mode 100644
index 0000000..498d529
--- /dev/null
+++ b/cmake/EigenSmokeTestList.cmake
@@ -0,0 +1,135 @@
+# List of tests that will be build and run during Eigen's smoke testing. If one
+# of these tests doesn't exists or cannot be build with the current configuration
+# it will just be skipped.
+set(ei_smoke_test_list
+ adjoint_1
+ alignedvector3
+ array_cwise_7
+ array_cwise_8
+ array_for_matrix_1
+ array_of_string
+ array_replicate_1
+ array_reverse_1
+ autodiff_1
+ autodiff_scalar_1
+ bandmatrix
+ bdcsvd_9
+ bessel_functions_1
+ bfloat16_float
+ blasutil_1
+ block_5
+ BVH
+ cholesky_1
+ cholmod_support_23
+ cholmod_support_24
+ conservative_resize_1
+ constructor_1
+ corners_1
+ ctorleakmiscmatrices_4
+ dense_storage
+ determinant_1
+ diagonal_1
+ diagonal_2
+ diagonalmatrices_1
+ dynalloc
+ eigensolver_complex_1
+ eigensolver_selfadjoint_8
+ EulerAngles_1
+ exceptions
+ fastmath
+ first_aligned
+ geo_alignedbox_2
+ geo_eulerangles_1
+ geo_homogeneous_1
+ geo_hyperplane_1
+ geo_orthomethods_1
+ geo_parametrizedline_1
+ geo_transformations_7
+ half_float
+ hessenberg_1
+ hessenberg_6qr_10
+ householder_8
+ indexed_view_1
+ inplace_decomposition_1
+ integer_types_1
+ inverse_1
+ is_same_dense
+ jacobi_1
+ jacobisvd_1
+ kronecker_product
+ linearstructure_1
+ mapped_matrix_1
+ mapstaticmethods_1
+ mapstride_1
+ unaryviewstride_1
+ unaryviewstride_2
+ unaryviewstride_3
+ matrix_square_root_1
+ meta
+ minres_2
+ miscmatrices_1
+ mixingtypes_7
+ nestbyvalue
+ nesting_ops_1
+ nomalloc_1
+ nullary_1
+ num_dimensions
+ NumericalDiff
+ numext
+ packetmath
+ permutationmatrices_1
+ polynomialsolver_1
+ prec_inverse_4x4_1
+ product_extra_5
+ product_selfadjoint_1
+ product_small_7
+ product_symm_1
+ product_syrk_1
+ product_trmm_1
+ product_trmv_1
+ product_trsolve_5
+ qr_1
+ qr_colpivoting_7
+ qr_fullpivoting_4
+ rand
+ real_qz_1
+ redux_1
+ ref_1
+ resize
+ rvalue_types_1
+ schur_complex_1
+ schur_real_1
+ selfadjoint_1
+ sizeof
+ sizeoverflow
+ smallvectors
+ sparse_basic_3
+ sparse_block_1
+ sparse_extra_4
+ sparse_permutations_2
+ sparse_product_4
+ sparse_ref_1
+ sparse_solvers_1
+ sparse_vector_1
+ special_functions_1
+ special_numbers_1
+ special_packetmath_1
+ spqr_support_2
+ stable_norm_1
+ stddeque_1
+ stddeque_overload_1
+ stdlist_1
+ stdlist_overload_1
+ stdvector_1
+ stdvector_overload_1
+ stl_iterators_1
+ swap_1
+ symbolic_index_1
+ triangular_1
+ type_aliaslu_9
+ umeyama_3
+ unalignedassert
+ unalignedcount
+ vectorwiseop_1
+ visitor_1
+ vectorization_logic_1)
\ No newline at end of file
diff --git a/cmake/EigenTesting.cmake b/cmake/EigenTesting.cmake
new file mode 100644
index 0000000..1ddaa12
--- /dev/null
+++ b/cmake/EigenTesting.cmake
@@ -0,0 +1,750 @@
+
+macro(ei_add_property prop value)
+ get_property(previous GLOBAL PROPERTY ${prop})
+ if ((NOT previous) OR (previous STREQUAL ""))
+ set_property(GLOBAL PROPERTY ${prop} "${value}")
+ else()
+ set_property(GLOBAL PROPERTY ${prop} "${previous} ${value}")
+ endif()
+endmacro()
+
+#internal. See documentation of ei_add_test for details.
+macro(ei_add_test_internal testname testname_with_suffix)
+ set(targetname ${testname_with_suffix})
+
+ if(EIGEN_ADD_TEST_FILENAME_EXTENSION)
+ set(filename ${testname}.${EIGEN_ADD_TEST_FILENAME_EXTENSION})
+ else()
+ set(filename ${testname}.cpp)
+ endif()
+
+ # Add the current target to the list of subtest targets
+ get_property(EIGEN_SUBTESTS_LIST GLOBAL PROPERTY EIGEN_SUBTESTS_LIST)
+ set(EIGEN_SUBTESTS_LIST "${EIGEN_SUBTESTS_LIST}${targetname}\n")
+ set_property(GLOBAL PROPERTY EIGEN_SUBTESTS_LIST "${EIGEN_SUBTESTS_LIST}")
+
+ set(is_gpu_test OFF)
+ if(EIGEN_ADD_TEST_FILENAME_EXTENSION STREQUAL cu)
+ set(is_gpu_test ON)
+ if(EIGEN_TEST_HIP)
+ hip_reset_flags()
+ hip_add_executable(${targetname} ${filename} HIPCC_OPTIONS -std=c++14)
+ target_compile_definitions(${targetname} PRIVATE -DEIGEN_USE_HIP)
+ set_property(TARGET ${targetname} PROPERTY HIP_ARCHITECTURES gfx900 gfx906 gfx908 gfx90a gfx1030)
+ elseif(EIGEN_TEST_CUDA_CLANG)
+ set_source_files_properties(${filename} PROPERTIES LANGUAGE CXX)
+
+ if(CUDA_64_BIT_DEVICE_CODE AND (EXISTS "${CUDA_TOOLKIT_ROOT_DIR}/lib64"))
+ link_directories("${CUDA_TOOLKIT_ROOT_DIR}/lib64")
+ else()
+ link_directories("${CUDA_TOOLKIT_ROOT_DIR}/lib")
+ endif()
+
+ add_executable(${targetname} ${filename})
+ set(CUDA_CLANG_LINK_LIBRARIES "cudart_static" "cuda" "dl" "pthread")
+ if (CMAKE_SYSTEM_NAME STREQUAL "Linux")
+ set(CUDA_CLANG_LINK_LIBRARIES ${CUDA_CLANG_LINK_LIBRARIES} "rt")
+ endif()
+ target_link_libraries(${targetname} ${CUDA_CLANG_LINK_LIBRARIES})
+ else()
+ cuda_add_executable(${targetname} ${filename})
+ endif()
+ else()
+ add_executable(${targetname} ${filename})
+ endif()
+
+ add_dependencies(buildtests ${targetname})
+
+ if (is_gpu_test)
+ add_dependencies(buildtests_gpu ${targetname})
+ endif()
+
+ if(EIGEN_NO_ASSERTION_CHECKING)
+ target_compile_definitions(${targetname} PRIVATE EIGEN_NO_ASSERTION_CHECKING=1)
+ else()
+ if(EIGEN_DEBUG_ASSERTS)
+ target_compile_definitions(${targetname} PRIVATE EIGEN_DEBUG_ASSERTS=1)
+ endif()
+ endif()
+
+ target_compile_definitions(${targetname} PRIVATE EIGEN_TEST_MAX_SIZE=${EIGEN_TEST_MAX_SIZE})
+
+ if(MSVC)
+ target_compile_options(${targetname} PRIVATE "/bigobj")
+ endif()
+
+ # let the user pass flags.
+ if(${ARGC} GREATER 2)
+ target_compile_options(${targetname} PRIVATE ${ARGV2})
+ endif()
+
+ if(EIGEN_TEST_CUSTOM_CXX_FLAGS)
+ target_compile_options(${targetname} PRIVATE ${EIGEN_TEST_CUSTOM_CXX_FLAGS})
+ endif()
+
+ if(EIGEN_STANDARD_LIBRARIES_TO_LINK_TO)
+ target_link_libraries(${targetname} ${EIGEN_STANDARD_LIBRARIES_TO_LINK_TO})
+ endif()
+ if(EXTERNAL_LIBS)
+ target_link_libraries(${targetname} ${EXTERNAL_LIBS})
+ endif()
+ if(EIGEN_TEST_CUSTOM_LINKER_FLAGS)
+ target_link_libraries(${targetname} ${EIGEN_TEST_CUSTOM_LINKER_FLAGS})
+ endif()
+
+ if(${ARGC} GREATER 3)
+ set(libs_to_link ${ARGV3})
+ # it could be that some cmake module provides a bad library string " " (just spaces),
+ # and that severely breaks target_link_libraries ("can't link to -l-lstdc++" errors).
+ # so we check for strings containing only spaces.
+ string(STRIP "${libs_to_link}" libs_to_link_stripped)
+ string(LENGTH "${libs_to_link_stripped}" libs_to_link_stripped_length)
+ if(${libs_to_link_stripped_length} GREATER 0)
+ # notice: no double quotes around ${libs_to_link} here. It may be a list.
+ target_link_libraries(${targetname} ${libs_to_link})
+ endif()
+ endif()
+
+ add_test(${testname_with_suffix} "${targetname}")
+
+ # Specify target and test labels according to EIGEN_CURRENT_SUBPROJECT
+ get_property(current_subproject GLOBAL PROPERTY EIGEN_CURRENT_SUBPROJECT)
+ if ((current_subproject) AND (NOT (current_subproject STREQUAL "")))
+ set_property(TARGET ${targetname} PROPERTY LABELS "Build${current_subproject}")
+ add_dependencies("Build${current_subproject}" ${targetname})
+ set_property(TEST ${testname_with_suffix} PROPERTY LABELS "${current_subproject}")
+ endif()
+ if (is_gpu_test)
+ # Add gpu tag for testing only GPU tests.
+ set_property(TEST ${testname_with_suffix} APPEND PROPERTY LABELS "gpu")
+ endif()
+
+ if(EIGEN_SYCL)
+ # Force include of the SYCL file at the end to avoid errors.
+ set_property(TARGET ${targetname} PROPERTY COMPUTECPP_INCLUDE_AFTER 1)
+ # Link against pthread and add sycl to target
+ set(THREADS_PREFER_PTHREAD_FLAG ON)
+ find_package(Threads REQUIRED)
+ target_link_libraries(${targetname} Threads::Threads)
+ add_sycl_to_target(TARGET ${targetname} SOURCES ${filename})
+ endif(EIGEN_SYCL)
+endmacro(ei_add_test_internal)
+# Macro to add a test
+#
+# the unique mandatory parameter testname must correspond to a file
+# <testname>.cpp which follows this pattern:
+#
+# #include "main.h"
+# void test_<testname>() { ... }
+#
+# Depending on the contents of that file, this macro can have 2 behaviors,
+# see below.
+#
+# The optional 2nd parameter is libraries to link to.
+#
+# A. Default behavior
+#
+# this macro adds an executable <testname> as well as a ctest test
+# named <testname> too.
+#
+# On platforms with bash simply run:
+# "ctest -V" or "ctest -V -R <testname>"
+# On other platform use ctest as usual
+#
+# B. Multi-part behavior
+#
+# If the source file matches the regexp
+# CALL_SUBTEST_[0-9]+|EIGEN_TEST_PART_[0-9]+
+# then it is interpreted as a multi-part test. The behavior then depends on the
+# CMake option EIGEN_SPLIT_LARGE_TESTS, which is ON by default.
+#
+# If EIGEN_SPLIT_LARGE_TESTS is OFF, the behavior is the same as in A (the multi-part
+# aspect is ignored).
+#
+# If EIGEN_SPLIT_LARGE_TESTS is ON, the test is split into multiple executables
+# test_<testname>_<N>
+# where N runs from 1 to the greatest occurrence found in the source file. Each of these
+# executables is built passing -DEIGEN_TEST_PART_N. This allows to split large tests
+# into smaller executables.
+#
+# Moreover, targets <testname> are still generated, they
+# have the effect of building all the parts of the test.
+#
+# Again, ctest -R allows to run all matching tests.
+macro(ei_add_test testname)
+ get_property(EIGEN_TESTS_LIST GLOBAL PROPERTY EIGEN_TESTS_LIST)
+ set(EIGEN_TESTS_LIST "${EIGEN_TESTS_LIST}${testname}\n")
+ set_property(GLOBAL PROPERTY EIGEN_TESTS_LIST "${EIGEN_TESTS_LIST}")
+
+ if(EIGEN_ADD_TEST_FILENAME_EXTENSION)
+ set(filename ${testname}.${EIGEN_ADD_TEST_FILENAME_EXTENSION})
+ else()
+ set(filename ${testname}.cpp)
+ endif()
+
+ file(READ "${filename}" test_source)
+ string(REGEX MATCHALL "CALL_SUBTEST_[0-9]+|EIGEN_TEST_PART_[0-9]+|EIGEN_SUFFIXES(;[0-9]+)+"
+ occurrences "${test_source}")
+ string(REGEX REPLACE "CALL_SUBTEST_|EIGEN_TEST_PART_|EIGEN_SUFFIXES" "" suffixes "${occurrences}")
+ list(REMOVE_DUPLICATES suffixes)
+ set(explicit_suffixes "")
+ if( (NOT EIGEN_SPLIT_LARGE_TESTS) AND suffixes)
+ # Check whether we have EIGEN_TEST_PART_* statements, in which case we likely must enforce splitting.
+ # For instance, indexed_view activate a different c++ version for each part.
+ string(REGEX MATCHALL "EIGEN_TEST_PART_[0-9]+" occurrences "${test_source}")
+ string(REGEX REPLACE "EIGEN_TEST_PART_" "" explicit_suffixes "${occurrences}")
+ list(REMOVE_DUPLICATES explicit_suffixes)
+ endif()
+ if( (EIGEN_SPLIT_LARGE_TESTS AND suffixes) OR explicit_suffixes)
+ add_custom_target(${testname})
+ foreach(suffix ${suffixes})
+ ei_add_test_internal(${testname} ${testname}_${suffix} "${ARGV1}" "${ARGV2}")
+ add_dependencies(${testname} ${testname}_${suffix})
+ target_compile_definitions(${testname}_${suffix} PRIVATE -DEIGEN_TEST_PART_${suffix}=1)
+ endforeach()
+ else()
+ ei_add_test_internal(${testname} ${testname} "${ARGV1}" "${ARGV2}")
+ target_compile_definitions(${testname} PRIVATE -DEIGEN_TEST_PART_ALL=1)
+ endif()
+endmacro()
+
+# adds a failtest, i.e. a test that succeed if the program fails to compile
+# note that the test runner for these is CMake itself, when passed -DEIGEN_FAILTEST=ON
+# so here we're just running CMake commands immediately, we're not adding any targets.
+macro(ei_add_failtest testname)
+
+ set(test_target_ok ${testname}_ok)
+ set(test_target_ko ${testname}_ko)
+
+ # Add executables
+ add_executable(${test_target_ok} ${testname}.cpp)
+ add_executable(${test_target_ko} ${testname}.cpp)
+
+ # Remove them from the normal build process
+ set_target_properties(${test_target_ok} ${test_target_ko} PROPERTIES
+ EXCLUDE_FROM_ALL TRUE
+ EXCLUDE_FROM_DEFAULT_BUILD TRUE)
+
+ # Configure the failing test
+ target_compile_definitions(${test_target_ko} PRIVATE EIGEN_SHOULD_FAIL_TO_BUILD)
+
+ # Add the tests to ctest.
+ add_test(NAME ${test_target_ok}
+ COMMAND ${CMAKE_COMMAND} --build . --target ${test_target_ok} --config $<CONFIGURATION>
+ WORKING_DIRECTORY ${CMAKE_BINARY_DIR})
+ add_test(NAME ${test_target_ko}
+ COMMAND ${CMAKE_COMMAND} --build . --target ${test_target_ko} --config $<CONFIGURATION>
+ WORKING_DIRECTORY ${CMAKE_BINARY_DIR})
+
+ # Expect the second test to fail
+ set_tests_properties(${test_target_ko} PROPERTIES WILL_FAIL TRUE)
+endmacro()
+
+# print a summary of the different options
+macro(ei_testing_print_summary)
+ message(STATUS "************************************************************")
+ message(STATUS "*** Eigen's unit tests configuration summary ***")
+ message(STATUS "************************************************************")
+ message(STATUS "")
+ message(STATUS "Build type: ${CMAKE_BUILD_TYPE}")
+ message(STATUS "Build site: ${SITE}")
+ message(STATUS "Build string: ${BUILDNAME}")
+ get_property(EIGEN_TESTING_SUMMARY GLOBAL PROPERTY EIGEN_TESTING_SUMMARY)
+ get_property(EIGEN_TESTED_BACKENDS GLOBAL PROPERTY EIGEN_TESTED_BACKENDS)
+ get_property(EIGEN_MISSING_BACKENDS GLOBAL PROPERTY EIGEN_MISSING_BACKENDS)
+ message(STATUS "Enabled backends: ${EIGEN_TESTED_BACKENDS}")
+ message(STATUS "Disabled backends: ${EIGEN_MISSING_BACKENDS}")
+
+ if(EIGEN_DEFAULT_TO_ROW_MAJOR)
+ message(STATUS "Default order: Row-major")
+ else()
+ message(STATUS "Default order: Column-major")
+ endif()
+
+ if(EIGEN_TEST_NO_EXPLICIT_ALIGNMENT)
+ message(STATUS "Explicit alignment (hence vectorization) disabled")
+ elseif(EIGEN_TEST_NO_EXPLICIT_VECTORIZATION)
+ message(STATUS "Explicit vectorization disabled (alignment kept enabled)")
+ else()
+
+ message(STATUS "Maximal matrix/vector size: ${EIGEN_TEST_MAX_SIZE}")
+
+ if(EIGEN_TEST_SSE2)
+ message(STATUS "SSE2: ON")
+ else()
+ message(STATUS "SSE2: Using architecture defaults")
+ endif()
+
+ if(EIGEN_TEST_SSE3)
+ message(STATUS "SSE3: ON")
+ else()
+ message(STATUS "SSE3: Using architecture defaults")
+ endif()
+
+ if(EIGEN_TEST_SSSE3)
+ message(STATUS "SSSE3: ON")
+ else()
+ message(STATUS "SSSE3: Using architecture defaults")
+ endif()
+
+ if(EIGEN_TEST_SSE4_1)
+ message(STATUS "SSE4.1: ON")
+ else()
+ message(STATUS "SSE4.1: Using architecture defaults")
+ endif()
+
+ if(EIGEN_TEST_SSE4_2)
+ message(STATUS "SSE4.2: ON")
+ else()
+ message(STATUS "SSE4.2: Using architecture defaults")
+ endif()
+
+ if(EIGEN_TEST_AVX)
+ message(STATUS "AVX: ON")
+ else()
+ message(STATUS "AVX: Using architecture defaults")
+ endif()
+
+ if(EIGEN_TEST_AVX2)
+ message(STATUS "AVX2: ON")
+ else()
+ message(STATUS "AVX2: Using architecture defaults")
+ endif()
+
+ if(EIGEN_TEST_FMA)
+ message(STATUS "FMA: ON")
+ else()
+ message(STATUS "FMA: Using architecture defaults")
+ endif()
+
+ if(EIGEN_TEST_AVX512)
+ message(STATUS "AVX512: ON")
+ else()
+ message(STATUS "AVX512: Using architecture defaults")
+ endif()
+
+ if(EIGEN_TEST_AVX512DQ)
+ message(STATUS "AVX512DQ: ON")
+ else()
+ message(STATUS "AVX512DQ: Using architecture defaults")
+ endif()
+
+ if(EIGEN_TEST_ALTIVEC)
+ message(STATUS "Altivec: ON")
+ else()
+ message(STATUS "Altivec: Using architecture defaults")
+ endif()
+
+ if(EIGEN_TEST_VSX)
+ message(STATUS "VSX: ON")
+ else()
+ message(STATUS "VSX: Using architecture defaults")
+ endif()
+
+ if(EIGEN_TEST_MSA)
+ message(STATUS "MIPS MSA: ON")
+ else()
+ message(STATUS "MIPS MSA: Using architecture defaults")
+ endif()
+
+ if(EIGEN_TEST_NEON)
+ message(STATUS "ARM NEON: ON")
+ else()
+ message(STATUS "ARM NEON: Using architecture defaults")
+ endif()
+
+ if(EIGEN_TEST_NEON64)
+ message(STATUS "ARMv8 NEON: ON")
+ else()
+ message(STATUS "ARMv8 NEON: Using architecture defaults")
+ endif()
+
+ if(EIGEN_TEST_ZVECTOR)
+ message(STATUS "S390X ZVECTOR: ON")
+ else()
+ message(STATUS "S390X ZVECTOR: Using architecture defaults")
+ endif()
+
+ if(EIGEN_TEST_SYCL)
+ if(EIGEN_SYCL_TRISYCL)
+ message(STATUS "SYCL: ON (using triSYCL)")
+ else()
+ message(STATUS "SYCL: ON (using computeCPP)")
+ endif()
+ else()
+ message(STATUS "SYCL: OFF")
+ endif()
+ if(EIGEN_TEST_CUDA)
+ if(EIGEN_TEST_CUDA_CLANG)
+ message(STATUS "CUDA: ON (using clang)")
+ else()
+ message(STATUS "CUDA: ON (using nvcc)")
+ endif()
+ else()
+ message(STATUS "CUDA: OFF")
+ endif()
+ if(EIGEN_TEST_HIP)
+ message(STATUS "HIP: ON (using hipcc)")
+ else()
+ message(STATUS "HIP: OFF")
+ endif()
+
+ endif() # vectorization / alignment options
+
+ message(STATUS "\n${EIGEN_TESTING_SUMMARY}")
+
+ message(STATUS "************************************************************")
+endmacro()
+
+macro(ei_init_testing)
+ define_property(GLOBAL PROPERTY EIGEN_CURRENT_SUBPROJECT BRIEF_DOCS " " FULL_DOCS " ")
+ define_property(GLOBAL PROPERTY EIGEN_TESTED_BACKENDS BRIEF_DOCS " " FULL_DOCS " ")
+ define_property(GLOBAL PROPERTY EIGEN_MISSING_BACKENDS BRIEF_DOCS " " FULL_DOCS " ")
+ define_property(GLOBAL PROPERTY EIGEN_TESTING_SUMMARY BRIEF_DOCS " " FULL_DOCS " ")
+ define_property(GLOBAL PROPERTY EIGEN_TESTS_LIST BRIEF_DOCS " " FULL_DOCS " ")
+ define_property(GLOBAL PROPERTY EIGEN_SUBTESTS_LIST BRIEF_DOCS " " FULL_DOCS " ")
+
+ set_property(GLOBAL PROPERTY EIGEN_TESTED_BACKENDS "")
+ set_property(GLOBAL PROPERTY EIGEN_MISSING_BACKENDS "")
+ set_property(GLOBAL PROPERTY EIGEN_TESTING_SUMMARY "")
+ set_property(GLOBAL PROPERTY EIGEN_TESTS_LIST "")
+ set_property(GLOBAL PROPERTY EIGEN_SUBTESTS_LIST "")
+
+ define_property(GLOBAL PROPERTY EIGEN_FAILTEST_FAILURE_COUNT BRIEF_DOCS " " FULL_DOCS " ")
+ define_property(GLOBAL PROPERTY EIGEN_FAILTEST_COUNT BRIEF_DOCS " " FULL_DOCS " ")
+
+ set_property(GLOBAL PROPERTY EIGEN_FAILTEST_FAILURE_COUNT "0")
+ set_property(GLOBAL PROPERTY EIGEN_FAILTEST_COUNT "0")
+
+ # uncomment anytime you change the ei_get_compilerver_from_cxx_version_string macro
+ # ei_test_get_compilerver_from_cxx_version_string()
+endmacro()
+
+macro(ei_set_sitename)
+ # if the sitename is not yet set, try to set it
+ if(NOT ${SITE} OR ${SITE} STREQUAL "")
+ set(eigen_computername $ENV{COMPUTERNAME})
+ set(eigen_hostname $ENV{HOSTNAME})
+ if(eigen_hostname)
+ set(SITE ${eigen_hostname})
+ elseif(eigen_computername)
+ set(SITE ${eigen_computername})
+ endif()
+ endif()
+ # in case it is already set, enforce lower case
+ if(SITE)
+ string(TOLOWER ${SITE} SITE)
+ endif()
+endmacro()
+
+macro(ei_get_compilerver VAR)
+ if(MSVC)
+ set(${VAR} "${CMAKE_CXX_COMPILER_VERSION}")
+ elseif(${CMAKE_CXX_COMPILER_ID} MATCHES "PGI")
+ set(${VAR} "${CMAKE_CXX_COMPILER_ID}-${CMAKE_CXX_COMPILER_VERSION}")
+ else()
+ # on all other system we rely on ${CMAKE_CXX_COMPILER}
+ # supporting a "--version" or "/version" flag
+
+ if(WIN32 AND ${CMAKE_CXX_COMPILER_ID} EQUAL "Intel")
+ set(EIGEN_CXX_FLAG_VERSION "/version")
+ else()
+ set(EIGEN_CXX_FLAG_VERSION "--version")
+ endif()
+
+ execute_process(COMMAND ${CMAKE_CXX_COMPILER} ${EIGEN_CXX_FLAG_VERSION}
+ OUTPUT_VARIABLE eigen_cxx_compiler_version_string OUTPUT_STRIP_TRAILING_WHITESPACE)
+ string(REGEX REPLACE "^[ \n\r]+" "" eigen_cxx_compiler_version_string ${eigen_cxx_compiler_version_string})
+ string(REGEX REPLACE "[\n\r].*" "" eigen_cxx_compiler_version_string ${eigen_cxx_compiler_version_string})
+
+ ei_get_compilerver_from_cxx_version_string("${eigen_cxx_compiler_version_string}" CNAME CVER)
+ set(${VAR} "${CNAME}-${CVER}")
+
+ endif()
+endmacro()
+
+# Extract compiler name and version from a raw version string
+# WARNING: if you edit this macro, then please test it by uncommenting
+# the testing macro call in ei_init_testing() of the EigenTesting.cmake file.
+# See also the ei_test_get_compilerver_from_cxx_version_string macro at the end
+# of the file
+macro(ei_get_compilerver_from_cxx_version_string VERSTRING CNAME CVER)
+ # extract possible compiler names
+ string(REGEX MATCH "g\\+\\+" ei_has_gpp ${VERSTRING})
+ string(REGEX MATCH "llvm|LLVM" ei_has_llvm ${VERSTRING})
+ string(REGEX MATCH "gcc|GCC" ei_has_gcc ${VERSTRING})
+ string(REGEX MATCH "icpc|ICC" ei_has_icpc ${VERSTRING})
+ string(REGEX MATCH "clang|CLANG" ei_has_clang ${VERSTRING})
+ string(REGEX MATCH "mingw32" ei_has_mingw ${VERSTRING})
+
+ # combine them
+ if((ei_has_llvm) AND (ei_has_gpp OR ei_has_gcc))
+ set(${CNAME} "llvm-g++")
+ elseif((ei_has_llvm) AND (ei_has_clang))
+ set(${CNAME} "llvm-clang++")
+ elseif(ei_has_clang)
+ set(${CNAME} "clang++")
+ elseif ((ei_has_mingw) AND (ei_has_gpp OR ei_has_gcc))
+ set(${CNAME} "mingw32-g++")
+ elseif(ei_has_icpc)
+ set(${CNAME} "icpc")
+ elseif(ei_has_gpp OR ei_has_gcc)
+ set(${CNAME} "g++")
+ else()
+ set(${CNAME} "_")
+ endif()
+
+ # extract possible version numbers
+ # first try to extract 3 isolated numbers:
+ string(REGEX MATCH " [0-9]+\\.[0-9]+\\.[0-9]+" eicver ${VERSTRING})
+ if(NOT eicver)
+ # try to extract 2 isolated ones:
+ string(REGEX MATCH " [0-9]+\\.[0-9]+" eicver ${VERSTRING})
+ if(NOT eicver)
+ # try to extract 3:
+ string(REGEX MATCH "[^0-9][0-9]+\\.[0-9]+\\.[0-9]+" eicver ${VERSTRING})
+ if(NOT eicver)
+ # try to extract 2:
+ string(REGEX MATCH "[^0-9][0-9]+\\.[0-9]+" eicver ${VERSTRING})
+ if (NOT eicver AND ei_has_mingw)
+ # try to extract 1 number plus suffix:
+ string(REGEX MATCH "[^0-9][0-9]+-win32" eicver ${VERSTRING})
+ endif()
+ endif()
+ endif()
+ endif()
+
+ if (NOT eicver)
+ set(eicver " _")
+ endif()
+
+ string(REGEX REPLACE ".(.*)" "\\1" ${CVER} ${eicver})
+
+endmacro()
+
+macro(ei_get_cxxflags VAR)
+ set(${VAR} "")
+ ei_is_64bit_env(IS_64BIT_ENV)
+ if(EIGEN_TEST_NEON)
+ set(${VAR} NEON)
+ elseif(EIGEN_TEST_NEON64)
+ set(${VAR} NEON)
+ elseif(EIGEN_TEST_ZVECTOR)
+ set(${VAR} ZVECTOR)
+ elseif(EIGEN_TEST_VSX)
+ set(${VAR} VSX)
+ elseif(EIGEN_TEST_ALTIVEC)
+ set(${VAR} ALVEC)
+ elseif(EIGEN_TEST_FMA)
+ set(${VAR} FMA)
+ elseif(EIGEN_TEST_AVX)
+ set(${VAR} AVX)
+ elseif(EIGEN_TEST_SSE4_2)
+ set(${VAR} SSE42)
+ elseif(EIGEN_TEST_SSE4_1)
+ set(${VAR} SSE41)
+ elseif(EIGEN_TEST_SSSE3)
+ set(${VAR} SSSE3)
+ elseif(EIGEN_TEST_SSE3)
+ set(${VAR} SSE3)
+ elseif(EIGEN_TEST_SSE2 OR IS_64BIT_ENV)
+ set(${VAR} SSE2)
+ elseif(EIGEN_TEST_MSA)
+ set(${VAR} MSA)
+ endif()
+
+ if(EIGEN_TEST_OPENMP)
+ if (${VAR} STREQUAL "")
+ set(${VAR} OMP)
+ else()
+ set(${VAR} ${${VAR}}-OMP)
+ endif()
+ endif()
+
+ if(EIGEN_DEFAULT_TO_ROW_MAJOR)
+ if (${VAR} STREQUAL "")
+ set(${VAR} ROW)
+ else()
+ set(${VAR} ${${VAR}}-ROWMAJ)
+ endif()
+ endif()
+endmacro()
+
+macro(ei_set_build_string)
+ ei_get_compilerver(LOCAL_COMPILER_VERSION)
+ ei_get_cxxflags(LOCAL_COMPILER_FLAGS)
+
+ set(TMP_BUILD_STRING ${CMAKE_SYSTEM}-${LOCAL_COMPILER_VERSION})
+
+ if (NOT ${LOCAL_COMPILER_FLAGS} STREQUAL "")
+ set(TMP_BUILD_STRING ${TMP_BUILD_STRING}-${LOCAL_COMPILER_FLAGS})
+ endif()
+
+ if(EIGEN_TEST_EXTERNAL_BLAS)
+ set(TMP_BUILD_STRING ${TMP_BUILD_STRING}-external_blas)
+ endif()
+
+ ei_is_64bit_env(IS_64BIT_ENV)
+ if(NOT IS_64BIT_ENV)
+ set(TMP_BUILD_STRING ${TMP_BUILD_STRING}-32bit)
+ else()
+ set(TMP_BUILD_STRING ${TMP_BUILD_STRING}-64bit)
+ endif()
+
+ if(EIGEN_BUILD_STRING_SUFFIX)
+ set(TMP_BUILD_STRING ${TMP_BUILD_STRING}-${EIGEN_BUILD_STRING_SUFFIX})
+ endif()
+
+ string(TOLOWER ${TMP_BUILD_STRING} BUILDNAME)
+endmacro()
+
+macro(ei_is_64bit_env VAR)
+ if(CMAKE_SIZEOF_VOID_P EQUAL 8)
+ set(${VAR} 1)
+ elseif(CMAKE_SIZEOF_VOID_P EQUAL 4)
+ set(${VAR} 0)
+ else()
+ message(WARNING "Unsupported pointer size. Please contact the authors.")
+ endif()
+endmacro()
+
+
+# helper macro for testing ei_get_compilerver_from_cxx_version_string
+# STR: raw version string
+# REFNAME: expected compiler name
+# REFVER: expected compiler version
+macro(ei_test1_get_compilerver_from_cxx_version_string STR REFNAME REFVER)
+ ei_get_compilerver_from_cxx_version_string(${STR} CNAME CVER)
+ if((NOT ${REFNAME} STREQUAL ${CNAME}) OR (NOT ${REFVER} STREQUAL ${CVER}))
+ message("STATUS ei_get_compilerver_from_cxx_version_string error:")
+ message("Expected \"${REFNAME}-${REFVER}\", got \"${CNAME}-${CVER}\"")
+ endif()
+endmacro()
+
+# macro for testing ei_get_compilerver_from_cxx_version_string
+# feel free to add more version strings
+macro(ei_test_get_compilerver_from_cxx_version_string)
+ ei_test1_get_compilerver_from_cxx_version_string("g++ (SUSE Linux) 4.5.3 20110428 [gcc-4_5-branch revision 173117]" "g++" "4.5.3")
+ ei_test1_get_compilerver_from_cxx_version_string("c++ (GCC) 4.5.1 20100924 (Red Hat 4.5.1-4)" "g++" "4.5.1")
+ ei_test1_get_compilerver_from_cxx_version_string("icpc (ICC) 11.0 20081105" "icpc" "11.0")
+ ei_test1_get_compilerver_from_cxx_version_string("g++-3.4 (GCC) 3.4.6" "g++" "3.4.6")
+ ei_test1_get_compilerver_from_cxx_version_string("SUSE Linux clang version 3.0 (branches/release_30 145598) (based on LLVM 3.0)" "llvm-clang++" "3.0")
+ ei_test1_get_compilerver_from_cxx_version_string("icpc (ICC) 12.0.5 20110719" "icpc" "12.0.5")
+ ei_test1_get_compilerver_from_cxx_version_string("Apple clang version 2.1 (tags/Apple/clang-163.7.1) (based on LLVM 3.0svn)" "llvm-clang++" "2.1")
+ ei_test1_get_compilerver_from_cxx_version_string("i686-apple-darwin11-llvm-g++-4.2 (GCC) 4.2.1 (Based on Apple Inc. build 5658) (LLVM build 2335.15.00)" "llvm-g++" "4.2.1")
+ ei_test1_get_compilerver_from_cxx_version_string("g++-mp-4.4 (GCC) 4.4.6" "g++" "4.4.6")
+ ei_test1_get_compilerver_from_cxx_version_string("g++-mp-4.4 (GCC) 2011" "g++" "4.4")
+ ei_test1_get_compilerver_from_cxx_version_string("x86_64-w64-mingw32-g++ (GCC) 10-win32 20210110" "mingw32-g++" "10-win32")
+endmacro()
+
+# Split all tests listed in EIGEN_TESTS_LIST into num_splits many targets
+# named buildtestspartN with N = { 0, ..., num_splits-1}.
+#
+# The intention behind the existence of this macro is the size of Eigen's
+# testsuite. Together with the relatively big compile-times building all tests
+# can take a substantial amount of time depending on the available hardware.
+#
+# The last buildtestspartN target will build possible remaining tests.
+#
+# An example:
+#
+# EIGEN_TESTS_LIST= [ test1, test2, test3, test4, test5, test6, test7 ]
+#
+# A call to ei_split_testsuite(3) creates the following targets with dependencies
+#
+# Target Dependencies
+# ------ ------------
+# buildtestspart0 test1, test2
+# buildtestspart1 test3, test4
+# buildtestspart2 test5, test6, test7
+#
+macro(ei_split_testsuite num_splits)
+ get_property(EIGEN_TESTS_LIST GLOBAL PROPERTY EIGEN_TESTS_LIST)
+
+ # Translate EIGEN_TESTS_LIST into a CMake list
+ string(REGEX REPLACE "\n" " " EIGEN_TESTS_LIST "${EIGEN_TESTS_LIST}")
+ set(EIGEN_TESTS_LIST "${EIGEN_TESTS_LIST}")
+ separate_arguments(EIGEN_TESTS_LIST)
+
+ set(eigen_test_count "0")
+ foreach(t IN ITEMS ${EIGEN_TESTS_LIST})
+ math(EXPR eigen_test_count "${eigen_test_count}+1")
+ endforeach()
+
+ # Get number of tests per target
+ math(EXPR num_tests_per_target "${eigen_test_count}/${num_splits} - ${eigen_test_count}/${num_splits} % 1")
+
+ set(test_idx "0")
+ math(EXPR target_bound "${num_splits}-1")
+ foreach(part RANGE "0" "${target_bound}")
+ # Create target
+ set(current_target "buildtestspart${part}")
+ add_custom_target("${current_target}")
+ math(EXPR upper_bound "${test_idx} + ${num_tests_per_target} - 1")
+ foreach(test_idx RANGE "${test_idx}" "${upper_bound}")
+ list(GET EIGEN_TESTS_LIST "${test_idx}" curr_test)
+ add_dependencies("${current_target}" "${curr_test}")
+ endforeach()
+ math(EXPR test_idx "${test_idx} + ${num_tests_per_target}")
+ endforeach()
+
+ # Handle the possibly remaining tests
+ math(EXPR test_idx "${num_splits} * ${num_tests_per_target}")
+ math(EXPR target_bound "${eigen_test_count} - 1")
+ foreach(test_idx RANGE "${test_idx}" "${target_bound}")
+ list(GET EIGEN_TESTS_LIST "${test_idx}" curr_test)
+ add_dependencies("${current_target}" "${curr_test}")
+ endforeach()
+endmacro(ei_split_testsuite num_splits)
+
+# Defines the custom command buildsmoketests to build a number of tests
+# specified in smoke_test_list.
+#
+# Test in smoke_test_list can be either test targets (e.g. packetmath) or
+# subtests targets (e.g. packetmath_2). If any of the test are not available
+# in the current configuration they are just skipped.
+#
+# All tests added via this macro are labeled with the smoketest label. This
+# allows running smoketests only using ctest.
+#
+# Smoke tests are intended to be run before the whole test suite is invoked,
+# e.g., to smoke test patches.
+macro(ei_add_smoke_tests smoke_test_list)
+ # Set the build target to build smoketests
+ set(buildtarget "buildsmoketests")
+ add_custom_target("${buildtarget}")
+
+ # Get list of all tests and translate it into a CMake list
+ get_property(EIGEN_TESTS_LIST GLOBAL PROPERTY EIGEN_TESTS_LIST)
+ string(REGEX REPLACE "\n" " " EIGEN_TESTS_LIST "${EIGEN_TESTS_LIST}")
+ set(EIGEN_TESTS_LIST "${EIGEN_TESTS_LIST}")
+ separate_arguments(EIGEN_TESTS_LIST)
+
+ # Check if the test in smoke_test_list is a currently valid test target
+ foreach(test IN ITEMS ${smoke_test_list})
+ # Add tests in smoke_test_list to our smoke test target but only if the test
+ # is currently available, i.e., is in EIGEN_SUBTESTS_LIST
+ if ("${test}" IN_LIST EIGEN_TESTS_LIST)
+ add_dependencies("${buildtarget}" "${test}")
+ # In the case of a test we match all subtests
+ set(ctest_regex "${ctest_regex}^${test}_[0-9]+$$|")
+ endif()
+ endforeach()
+
+ # Get list of all subtests and translate it into a CMake list
+ get_property(EIGEN_SUBTESTS_LIST GLOBAL PROPERTY EIGEN_SUBTESTS_LIST)
+ string(REGEX REPLACE "\n" " " EIGEN_SUBTESTS_LIST "${EIGEN_SUBTESTS_LIST}")
+ set(EIGEN_SUBTESTS_LIST "${EIGEN_SUBTESTS_LIST}")
+ separate_arguments(EIGEN_SUBTESTS_LIST)
+
+ # Check if the test in smoke_test_list is a currently valid subtest target
+ foreach(test IN ITEMS ${smoke_test_list})
+ # Add tests in smoke_test_list to our smoke test target but only if the test
+ # is currently available, i.e., is in EIGEN_SUBTESTS_LIST
+ if ("${test}" IN_LIST EIGEN_SUBTESTS_LIST)
+ add_dependencies("${buildtarget}" "${test}")
+ # Add label smoketest to be able to run smoketests using ctest
+ set_property(TEST ${test} APPEND PROPERTY LABELS "smoketest")
+ endif()
+ endforeach()
+endmacro(ei_add_smoke_tests)
diff --git a/cmake/EigenUninstall.cmake b/cmake/EigenUninstall.cmake
new file mode 100644
index 0000000..5e63c98
--- /dev/null
+++ b/cmake/EigenUninstall.cmake
@@ -0,0 +1,40 @@
+################ CMake Uninstall Template #######################
+# CMake Template file for uninstallation of files
+# mentioned in 'install_manifest.txt'
+#
+# Used by uinstall target
+#################################################################
+
+set(MANIFEST "${CMAKE_CURRENT_BINARY_DIR}/install_manifest.txt")
+
+if(EXISTS ${MANIFEST})
+ message(STATUS "============== Uninstalling Eigen ===================")
+
+ file(STRINGS ${MANIFEST} files)
+ foreach(file ${files})
+ if(EXISTS ${file})
+ message(STATUS "Removing file: '${file}'")
+
+ execute_process(
+ COMMAND ${CMAKE_COMMAND} -E remove ${file}
+ OUTPUT_VARIABLE rm_out
+ RESULT_VARIABLE rm_retval
+ )
+
+ if(NOT "${rm_retval}" STREQUAL 0)
+ message(FATAL_ERROR "Failed to remove file: '${file}'.")
+ endif()
+ else()
+ message(STATUS "File '${file}' does not exist.")
+ endif()
+ endforeach()
+
+ message(STATUS "========== Finished Uninstalling Eigen ==============")
+else()
+ message(STATUS "Cannot find install manifest: '${MANIFEST}'")
+ message(STATUS "Probably make install has not been performed")
+ message(STATUS " or install_manifest.txt has been deleted.")
+endif()
+
+
+
diff --git a/cmake/FindAccelerate.cmake b/cmake/FindAccelerate.cmake
new file mode 100644
index 0000000..787c31c
--- /dev/null
+++ b/cmake/FindAccelerate.cmake
@@ -0,0 +1,28 @@
+if (Accelerate_INCLUDES AND Accelerate_LIBRARIES)
+ set(Accelerate_FIND_QUIETLY TRUE)
+endif ()
+
+find_path(Accelerate_INCLUDES
+ NAMES
+ Accelerate.h
+ PATHS $ENV{ACCELERATEDIR}
+)
+
+find_library(Accelerate_LIBRARIES Accelerate PATHS $ENV{ACCELERATEDIR})
+
+include(FindPackageHandleStandardArgs)
+find_package_handle_standard_args(Accelerate DEFAULT_MSG
+ Accelerate_INCLUDES Accelerate_LIBRARIES)
+
+if (Accelerate_FOUND)
+ get_filename_component(Accelerate_PARENTDIR ${Accelerate_INCLUDES} DIRECTORY)
+
+ file(GLOB_RECURSE SparseHeader ${Accelerate_PARENTDIR}/Sparse.h)
+
+ if ("${SparseHeader}" STREQUAL "")
+ message(STATUS "Accelerate sparse matrix support was not found. Accelerate has been disabled.")
+ set(Accelerate_FOUND FALSE)
+ endif ()
+endif ()
+
+mark_as_advanced(Accelerate_INCLUDES Accelerate_LIBRARIES)
diff --git a/cmake/FindAdolc.cmake b/cmake/FindAdolc.cmake
new file mode 100644
index 0000000..13c59fc
--- /dev/null
+++ b/cmake/FindAdolc.cmake
@@ -0,0 +1,20 @@
+
+if (ADOLC_INCLUDES AND ADOLC_LIBRARIES)
+ set(ADOLC_FIND_QUIETLY TRUE)
+endif ()
+
+find_path(ADOLC_INCLUDES
+ NAMES adolc/adtl.h
+ PATHS $ENV{ADOLCDIR} $ENV{ADOLCDIR}/include ${INCLUDE_INSTALL_DIR}
+)
+
+find_library(ADOLC_LIBRARIES
+ adolc
+ PATHS $ENV{ADOLCDIR} ${LIB_INSTALL_DIR}
+ PATH_SUFFIXES lib lib64)
+
+include(FindPackageHandleStandardArgs)
+find_package_handle_standard_args(Adolc DEFAULT_MSG
+ ADOLC_INCLUDES ADOLC_LIBRARIES)
+
+mark_as_advanced(ADOLC_INCLUDES ADOLC_LIBRARIES)
diff --git a/cmake/FindBLASEXT.cmake b/cmake/FindBLASEXT.cmake
new file mode 100644
index 0000000..69a9418
--- /dev/null
+++ b/cmake/FindBLASEXT.cmake
@@ -0,0 +1,384 @@
+###
+#
+# @copyright (c) 2009-2014 The University of Tennessee and The University
+# of Tennessee Research Foundation.
+# All rights reserved.
+# @copyright (c) 2012-2016 Inria. All rights reserved.
+# @copyright (c) 2012-2014 Bordeaux INP, CNRS (LaBRI UMR 5800), Inria, Univ. Bordeaux. All rights reserved.
+#
+###
+#
+# - Find BLAS EXTENDED for MORSE projects: find include dirs and libraries
+#
+# This module allows to find BLAS libraries by calling the official FindBLAS module
+# and handles the creation of different library lists whether the user wishes to link
+# with a sequential BLAS or a multihreaded (BLAS_SEQ_LIBRARIES and BLAS_PAR_LIBRARIES).
+# BLAS is detected with a FindBLAS call then if the BLAS vendor is Intel10_64lp, ACML
+# or IBMESSLMT then the module attempts to find the corresponding multithreaded libraries.
+#
+# The following variables have been added to manage links with sequential or multithreaded
+# versions:
+# BLAS_INCLUDE_DIRS - BLAS include directories
+# BLAS_LIBRARY_DIRS - Link directories for BLAS libraries
+# BLAS_SEQ_LIBRARIES - BLAS component libraries to be linked (sequential)
+# BLAS_PAR_LIBRARIES - BLAS component libraries to be linked (multithreaded)
+
+#=============================================================================
+# Copyright 2012-2013 Inria
+# Copyright 2012-2013 Emmanuel Agullo
+# Copyright 2012-2013 Mathieu Faverge
+# Copyright 2012 Cedric Castagnede
+# Copyright 2013-2016 Florent Pruvost
+#
+# Distributed under the OSI-approved BSD License (the "License");
+# see accompanying file MORSE-Copyright.txt for details.
+#
+# This software is distributed WITHOUT ANY WARRANTY; without even the
+# implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.
+# See the License for more information.
+#=============================================================================
+# (To distribute this file outside of Morse, substitute the full
+# License text for the above reference.)
+
+# macro to factorize this call
+include(CMakeFindDependencyMacro)
+macro(find_package_blas)
+ if(BLASEXT_FIND_REQUIRED)
+ if(BLASEXT_FIND_QUIETLY)
+ find_dependency(BLAS REQUIRED QUIET)
+ else()
+ find_dependency(BLAS REQUIRED)
+ endif()
+ else()
+ if(BLASEXT_FIND_QUIETLY)
+ find_dependency(BLAS QUIET)
+ else()
+ find_dependency(BLAS)
+ endif()
+ endif()
+endmacro()
+
+# add a cache variable to let the user specify the BLAS vendor
+set(BLA_VENDOR "" CACHE STRING "list of possible BLAS vendor:
+ Open, Eigen, Goto, ATLAS PhiPACK, CXML, DXML, SunPerf, SCSL, SGIMATH, IBMESSL, IBMESSLMT,
+ Intel10_32 (intel mkl v10 32 bit),
+ Intel10_64lp (intel mkl v10 64 bit, lp thread model, lp64 model),
+ Intel10_64lp_seq (intel mkl v10 64 bit, sequential code, lp64 model),
+ Intel( older versions of mkl 32 and 64 bit),
+ ACML, ACML_MP, ACML_GPU, Apple, NAS, Generic")
+
+if(NOT BLASEXT_FIND_QUIETLY)
+ message(STATUS "In FindBLASEXT")
+ message(STATUS "If you want to force the use of one specific library, "
+ "\n please specify the BLAS vendor by setting -DBLA_VENDOR=blas_vendor_name"
+ "\n at cmake configure.")
+ message(STATUS "List of possible BLAS vendor: Goto, ATLAS PhiPACK, CXML, "
+ "\n DXML, SunPerf, SCSL, SGIMATH, IBMESSL, IBMESSLMT, Intel10_32 (intel mkl v10 32 bit),"
+ "\n Intel10_64lp (intel mkl v10 64 bit, lp thread model, lp64 model),"
+ "\n Intel10_64lp_seq (intel mkl v10 64 bit, sequential code, lp64 model),"
+ "\n Intel( older versions of mkl 32 and 64 bit),"
+ "\n ACML, ACML_MP, ACML_GPU, Apple, NAS, Generic")
+endif()
+
+if (NOT BLAS_FOUND)
+ # First try to detect two cases:
+ # 1: only SEQ libs are handled
+ # 2: both SEQ and PAR libs are handled
+ find_package_blas()
+endif ()
+
+# detect the cases where SEQ and PAR libs are handled
+if(BLA_VENDOR STREQUAL "All" AND
+ (BLAS_mkl_core_LIBRARY OR BLAS_mkl_core_dll_LIBRARY)
+ )
+ set(BLA_VENDOR "Intel")
+ if(BLAS_mkl_intel_LIBRARY)
+ set(BLA_VENDOR "Intel10_32")
+ endif()
+ if(BLAS_mkl_intel_lp64_LIBRARY)
+ set(BLA_VENDOR "Intel10_64lp")
+ endif()
+ if(NOT BLASEXT_FIND_QUIETLY)
+ message(STATUS "A BLAS library has been found (${BLAS_LIBRARIES}) but we"
+ "\n have also potentially detected some multithreaded BLAS libraries from the MKL."
+ "\n We try to find both libraries lists (Sequential/Multithreaded).")
+ endif()
+ set(BLAS_FOUND "")
+elseif(BLA_VENDOR STREQUAL "All" AND BLAS_acml_LIBRARY)
+ set(BLA_VENDOR "ACML")
+ if(NOT BLASEXT_FIND_QUIETLY)
+ message(STATUS "A BLAS library has been found (${BLAS_LIBRARIES}) but we"
+ "\n have also potentially detected some multithreaded BLAS libraries from the ACML."
+ "\n We try to find both libraries lists (Sequential/Multithreaded).")
+ endif()
+ set(BLAS_FOUND "")
+elseif(BLA_VENDOR STREQUAL "All" AND BLAS_essl_LIBRARY)
+ set(BLA_VENDOR "IBMESSL")
+ if(NOT BLASEXT_FIND_QUIETLY)
+ message(STATUS "A BLAS library has been found (${BLAS_LIBRARIES}) but we"
+ "\n have also potentially detected some multithreaded BLAS libraries from the ESSL."
+ "\n We try to find both libraries lists (Sequential/Multithreaded).")
+ endif()
+ set(BLAS_FOUND "")
+endif()
+
+# Intel case
+if(BLA_VENDOR MATCHES "Intel*")
+
+ ###
+ # look for include path if the BLAS vendor is Intel
+ ###
+
+ # gather system include paths
+ unset(_inc_env)
+ if(WIN32)
+ string(REPLACE ":" ";" _inc_env "$ENV{INCLUDE}")
+ else()
+ string(REPLACE ":" ";" _path_env "$ENV{INCLUDE}")
+ list(APPEND _inc_env "${_path_env}")
+ string(REPLACE ":" ";" _path_env "$ENV{C_INCLUDE_PATH}")
+ list(APPEND _inc_env "${_path_env}")
+ string(REPLACE ":" ";" _path_env "$ENV{CPATH}")
+ list(APPEND _inc_env "${_path_env}")
+ string(REPLACE ":" ";" _path_env "$ENV{INCLUDE_PATH}")
+ list(APPEND _inc_env "${_path_env}")
+ endif()
+ list(APPEND _inc_env "${CMAKE_PLATFORM_IMPLICIT_INCLUDE_DIRECTORIES}")
+ list(APPEND _inc_env "${CMAKE_C_IMPLICIT_INCLUDE_DIRECTORIES}")
+ set(ENV_MKLROOT "$ENV{MKLROOT}")
+ if (ENV_MKLROOT)
+ list(APPEND _inc_env "${ENV_MKLROOT}/include")
+ endif()
+ list(REMOVE_DUPLICATES _inc_env)
+
+ # find mkl.h inside known include paths
+ set(BLAS_mkl.h_INCLUDE_DIRS "BLAS_mkl.h_INCLUDE_DIRS-NOTFOUND")
+ if(BLAS_INCDIR)
+ set(BLAS_mkl.h_INCLUDE_DIRS "BLAS_mkl.h_INCLUDE_DIRS-NOTFOUND")
+ find_path(BLAS_mkl.h_INCLUDE_DIRS
+ NAMES mkl.h
+ HINTS ${BLAS_INCDIR})
+ else()
+ if(BLAS_DIR)
+ set(BLAS_mkl.h_INCLUDE_DIRS "BLAS_mkl.h_INCLUDE_DIRS-NOTFOUND")
+ find_path(BLAS_mkl.h_INCLUDE_DIRS
+ NAMES mkl.h
+ HINTS ${BLAS_DIR}
+ PATH_SUFFIXES include)
+ else()
+ set(BLAS_mkl.h_INCLUDE_DIRS "BLAS_mkl.h_INCLUDE_DIRS-NOTFOUND")
+ find_path(BLAS_mkl.h_INCLUDE_DIRS
+ NAMES mkl.h
+ HINTS ${_inc_env})
+ endif()
+ endif()
+ mark_as_advanced(BLAS_mkl.h_INCLUDE_DIRS)
+ ## Print status if not found
+ ## -------------------------
+ #if (NOT BLAS_mkl.h_INCLUDE_DIRS AND MORSE_VERBOSE)
+ # Print_Find_Header_Status(blas mkl.h)
+ #endif ()
+ set(BLAS_INCLUDE_DIRS "")
+ if(BLAS_mkl.h_INCLUDE_DIRS)
+ list(APPEND BLAS_INCLUDE_DIRS "${BLAS_mkl.h_INCLUDE_DIRS}" )
+ endif()
+
+ ###
+ # look for libs
+ ###
+ # if Intel 10 64 bit -> look for sequential and multithreaded versions
+ if(BLA_VENDOR MATCHES "Intel10_64lp*")
+
+ ## look for the sequential version
+ set(BLA_VENDOR "Intel10_64lp_seq")
+ if(NOT BLASEXT_FIND_QUIETLY)
+ message(STATUS "Look for the sequential version Intel10_64lp_seq")
+ endif()
+ find_package_blas()
+ if(BLAS_FOUND)
+ set(BLAS_SEQ_LIBRARIES "${BLAS_LIBRARIES}")
+ else()
+ set(BLAS_SEQ_LIBRARIES "${BLAS_SEQ_LIBRARIES-NOTFOUND}")
+ endif()
+
+ ## look for the multithreaded version
+ set(BLA_VENDOR "Intel10_64lp")
+ if(NOT BLASEXT_FIND_QUIETLY)
+ message(STATUS "Look for the multithreaded version Intel10_64lp")
+ endif()
+ find_package_blas()
+ if(BLAS_FOUND)
+ set(BLAS_PAR_LIBRARIES "${BLAS_LIBRARIES}")
+ else()
+ set(BLAS_PAR_LIBRARIES "${BLAS_PAR_LIBRARIES-NOTFOUND}")
+ endif()
+
+ else()
+
+ if(BLAS_FOUND)
+ set(BLAS_SEQ_LIBRARIES "${BLAS_LIBRARIES}")
+ else()
+ set(BLAS_SEQ_LIBRARIES "${BLAS_SEQ_LIBRARIES-NOTFOUND}")
+ endif()
+
+ endif()
+
+ # ACML case
+elseif(BLA_VENDOR MATCHES "ACML*")
+
+ ## look for the sequential version
+ set(BLA_VENDOR "ACML")
+ find_package_blas()
+ if(BLAS_FOUND)
+ set(BLAS_SEQ_LIBRARIES "${BLAS_LIBRARIES}")
+ else()
+ set(BLAS_SEQ_LIBRARIES "${BLAS_SEQ_LIBRARIES-NOTFOUND}")
+ endif()
+
+ ## look for the multithreaded version
+ set(BLA_VENDOR "ACML_MP")
+ find_package_blas()
+ if(BLAS_FOUND)
+ set(BLAS_PAR_LIBRARIES "${BLAS_LIBRARIES}")
+ else()
+ set(BLAS_PAR_LIBRARIES "${BLAS_PAR_LIBRARIES-NOTFOUND}")
+ endif()
+
+ # IBMESSL case
+elseif(BLA_VENDOR MATCHES "IBMESSL*")
+
+ ## look for the sequential version
+ set(BLA_VENDOR "IBMESSL")
+ find_package_blas()
+ if(BLAS_FOUND)
+ set(BLAS_SEQ_LIBRARIES "${BLAS_LIBRARIES}")
+ else()
+ set(BLAS_SEQ_LIBRARIES "${BLAS_SEQ_LIBRARIES-NOTFOUND}")
+ endif()
+
+ ## look for the multithreaded version
+ set(BLA_VENDOR "IBMESSLMT")
+ find_package_blas()
+ if(BLAS_FOUND)
+ set(BLAS_PAR_LIBRARIES "${BLAS_LIBRARIES}")
+ else()
+ set(BLAS_PAR_LIBRARIES "${BLAS_PAR_LIBRARIES-NOTFOUND}")
+ endif()
+
+else()
+
+ if(BLAS_FOUND)
+ # define the SEQ libs as the BLAS_LIBRARIES
+ set(BLAS_SEQ_LIBRARIES "${BLAS_LIBRARIES}")
+ else()
+ set(BLAS_SEQ_LIBRARIES "${BLAS_SEQ_LIBRARIES-NOTFOUND}")
+ endif()
+ set(BLAS_PAR_LIBRARIES "${BLAS_PAR_LIBRARIES-NOTFOUND}")
+
+endif()
+
+
+if(BLAS_SEQ_LIBRARIES)
+ set(BLAS_LIBRARIES "${BLAS_SEQ_LIBRARIES}")
+endif()
+
+# extract libs paths
+# remark: because it is not given by find_package(BLAS)
+set(BLAS_LIBRARY_DIRS "")
+string(REPLACE " " ";" BLAS_LIBRARIES "${BLAS_LIBRARIES}")
+foreach(blas_lib ${BLAS_LIBRARIES})
+ if (EXISTS "${blas_lib}")
+ get_filename_component(a_blas_lib_dir "${blas_lib}" PATH)
+ list(APPEND BLAS_LIBRARY_DIRS "${a_blas_lib_dir}" )
+ else()
+ string(REPLACE "-L" "" blas_lib "${blas_lib}")
+ if (EXISTS "${blas_lib}")
+ list(APPEND BLAS_LIBRARY_DIRS "${blas_lib}" )
+ else()
+ get_filename_component(a_blas_lib_dir "${blas_lib}" PATH)
+ if (EXISTS "${a_blas_lib_dir}")
+ list(APPEND BLAS_LIBRARY_DIRS "${a_blas_lib_dir}" )
+ endif()
+ endif()
+ endif()
+endforeach()
+if (BLAS_LIBRARY_DIRS)
+ list(REMOVE_DUPLICATES BLAS_LIBRARY_DIRS)
+endif ()
+
+# check that BLAS has been found
+# ---------------------------------
+include(FindPackageHandleStandardArgs)
+if(BLA_VENDOR MATCHES "Intel*")
+ if(BLA_VENDOR MATCHES "Intel10_64lp*")
+ if(NOT BLASEXT_FIND_QUIETLY)
+ message(STATUS "BLAS found is Intel MKL:"
+ "\n we manage two lists of libs, one sequential and one parallel if found"
+ "\n (see BLAS_SEQ_LIBRARIES and BLAS_PAR_LIBRARIES)")
+ message(STATUS "BLAS sequential libraries stored in BLAS_SEQ_LIBRARIES")
+ endif()
+ find_package_handle_standard_args(BLASEXT DEFAULT_MSG
+ BLAS_SEQ_LIBRARIES
+ BLAS_LIBRARY_DIRS
+ BLAS_INCLUDE_DIRS)
+ if(BLAS_PAR_LIBRARIES)
+ if(NOT BLASEXT_FIND_QUIETLY)
+ message(STATUS "BLAS parallel libraries stored in BLAS_PAR_LIBRARIES")
+ endif()
+ find_package_handle_standard_args(BLASEXT DEFAULT_MSG
+ BLAS_PAR_LIBRARIES)
+ endif()
+ else()
+ if(NOT BLASEXT_FIND_QUIETLY)
+ message(STATUS "BLAS sequential libraries stored in BLAS_SEQ_LIBRARIES")
+ endif()
+ find_package_handle_standard_args(BLASEXT DEFAULT_MSG
+ BLAS_SEQ_LIBRARIES
+ BLAS_LIBRARY_DIRS
+ BLAS_INCLUDE_DIRS)
+ endif()
+elseif(BLA_VENDOR MATCHES "ACML*")
+ if(NOT BLASEXT_FIND_QUIETLY)
+ message(STATUS "BLAS found is ACML:"
+ "\n we manage two lists of libs, one sequential and one parallel if found"
+ "\n (see BLAS_SEQ_LIBRARIES and BLAS_PAR_LIBRARIES)")
+ message(STATUS "BLAS sequential libraries stored in BLAS_SEQ_LIBRARIES")
+ endif()
+ find_package_handle_standard_args(BLASEXT DEFAULT_MSG
+ BLAS_SEQ_LIBRARIES
+ BLAS_LIBRARY_DIRS)
+ if(BLAS_PAR_LIBRARIES)
+ if(NOT BLASEXT_FIND_QUIETLY)
+ message(STATUS "BLAS parallel libraries stored in BLAS_PAR_LIBRARIES")
+ endif()
+ find_package_handle_standard_args(BLASEXT DEFAULT_MSG
+ BLAS_PAR_LIBRARIES)
+ endif()
+elseif(BLA_VENDOR MATCHES "IBMESSL*")
+ if(NOT BLASEXT_FIND_QUIETLY)
+ message(STATUS "BLAS found is ESSL:"
+ "\n we manage two lists of libs, one sequential and one parallel if found"
+ "\n (see BLAS_SEQ_LIBRARIES and BLAS_PAR_LIBRARIES)")
+ message(STATUS "BLAS sequential libraries stored in BLAS_SEQ_LIBRARIES")
+ endif()
+ find_package_handle_standard_args(BLASEXT DEFAULT_MSG
+ BLAS_SEQ_LIBRARIES
+ BLAS_LIBRARY_DIRS)
+ if(BLAS_PAR_LIBRARIES)
+ if(NOT BLASEXT_FIND_QUIETLY)
+ message(STATUS "BLAS parallel libraries stored in BLAS_PAR_LIBRARIES")
+ endif()
+ find_package_handle_standard_args(BLASEXT DEFAULT_MSG
+ BLAS_PAR_LIBRARIES)
+ endif()
+else()
+ if(NOT BLASEXT_FIND_QUIETLY)
+ message(STATUS "BLAS sequential libraries stored in BLAS_SEQ_LIBRARIES")
+ endif()
+ find_package_handle_standard_args(BLASEXT DEFAULT_MSG
+ BLAS_SEQ_LIBRARIES
+ BLAS_LIBRARY_DIRS)
+endif()
+
+# Callers expect BLAS_FOUND to be set as well.
+set(BLAS_FOUND BLASEXT_FOUND)
diff --git a/cmake/FindCHOLMOD.cmake b/cmake/FindCHOLMOD.cmake
new file mode 100644
index 0000000..e470cb2
--- /dev/null
+++ b/cmake/FindCHOLMOD.cmake
@@ -0,0 +1,89 @@
+# CHOLMOD lib usually requires linking to a blas and lapack library.
+# It is up to the user of this module to find a BLAS and link to it.
+
+if (CHOLMOD_INCLUDES AND CHOLMOD_LIBRARIES)
+ set(CHOLMOD_FIND_QUIETLY TRUE)
+endif ()
+
+find_path(CHOLMOD_INCLUDES
+ NAMES
+ cholmod.h
+ PATHS
+ $ENV{CHOLMODDIR}
+ ${INCLUDE_INSTALL_DIR}
+ PATH_SUFFIXES
+ suitesparse
+ ufsparse
+)
+
+find_library(CHOLMOD_LIBRARIES cholmod PATHS $ENV{CHOLMODDIR} ${LIB_INSTALL_DIR})
+
+if(CHOLMOD_LIBRARIES)
+
+ get_filename_component(CHOLMOD_LIBDIR ${CHOLMOD_LIBRARIES} PATH)
+
+ find_library(AMD_LIBRARY amd PATHS ${CHOLMOD_LIBDIR} $ENV{CHOLMODDIR} ${LIB_INSTALL_DIR})
+ if (AMD_LIBRARY)
+ set(CHOLMOD_LIBRARIES ${CHOLMOD_LIBRARIES} ${AMD_LIBRARY})
+ else ()
+ set(CHOLMOD_LIBRARIES FALSE)
+ endif ()
+
+endif()
+
+if(CHOLMOD_LIBRARIES)
+
+ find_library(COLAMD_LIBRARY colamd PATHS ${CHOLMOD_LIBDIR} $ENV{CHOLMODDIR} ${LIB_INSTALL_DIR})
+ if (COLAMD_LIBRARY)
+ set(CHOLMOD_LIBRARIES ${CHOLMOD_LIBRARIES} ${COLAMD_LIBRARY})
+ else ()
+ set(CHOLMOD_LIBRARIES FALSE)
+ endif ()
+
+endif()
+
+if(CHOLMOD_LIBRARIES)
+
+ find_library(CAMD_LIBRARY camd PATHS ${CHOLMOD_LIBDIR} $ENV{CHOLMODDIR} ${LIB_INSTALL_DIR})
+ if (CAMD_LIBRARY)
+ set(CHOLMOD_LIBRARIES ${CHOLMOD_LIBRARIES} ${CAMD_LIBRARY})
+ else ()
+ set(CHOLMOD_LIBRARIES FALSE)
+ endif ()
+
+endif()
+
+if(CHOLMOD_LIBRARIES)
+
+ find_library(CCOLAMD_LIBRARY ccolamd PATHS ${CHOLMOD_LIBDIR} $ENV{CHOLMODDIR} ${LIB_INSTALL_DIR})
+ if (CCOLAMD_LIBRARY)
+ set(CHOLMOD_LIBRARIES ${CHOLMOD_LIBRARIES} ${CCOLAMD_LIBRARY})
+ else ()
+ set(CHOLMOD_LIBRARIES FALSE)
+ endif ()
+
+endif()
+
+if(CHOLMOD_LIBRARIES)
+
+ find_library(CHOLMOD_METIS_LIBRARY metis PATHS ${CHOLMOD_LIBDIR} $ENV{CHOLMODDIR} ${LIB_INSTALL_DIR})
+ if (CHOLMOD_METIS_LIBRARY)
+ set(CHOLMOD_LIBRARIES ${CHOLMOD_LIBRARIES} ${CHOLMOD_METIS_LIBRARY})
+ endif ()
+
+endif()
+
+if(CHOLMOD_LIBRARIES)
+
+ find_library(SUITESPARSE_LIBRARY SuiteSparse PATHS ${CHOLMOD_LIBDIR} $ENV{CHOLMODDIR} ${LIB_INSTALL_DIR})
+ if (SUITESPARSE_LIBRARY)
+ set(CHOLMOD_LIBRARIES ${CHOLMOD_LIBRARIES} ${SUITESPARSE_LIBRARY})
+ endif ()
+
+endif()
+
+include(FindPackageHandleStandardArgs)
+find_package_handle_standard_args(CHOLMOD DEFAULT_MSG
+ CHOLMOD_INCLUDES CHOLMOD_LIBRARIES)
+
+mark_as_advanced(CHOLMOD_INCLUDES CHOLMOD_LIBRARIES AMD_LIBRARY COLAMD_LIBRARY SUITESPARSE_LIBRARY CAMD_LIBRARY CCOLAMD_LIBRARY CHOLMOD_METIS_LIBRARY)
diff --git a/cmake/FindCLANG_FORMAT.cmake b/cmake/FindCLANG_FORMAT.cmake
new file mode 100644
index 0000000..e00f19f
--- /dev/null
+++ b/cmake/FindCLANG_FORMAT.cmake
@@ -0,0 +1,61 @@
+
+
+# Find clang-format
+#
+# CLANG_FORMAT_EXECUTABLE - Path to clang-format executable
+# CLANG_FORMAT_FOUND - True if the clang-format executable was found.
+# CLANG_FORMAT_VERSION - The version of clang-format found
+#
+# Copyright 2009-2020 The VOTCA Development Team (http://www.votca.org)
+#
+# Licensed under the Mozilla Public License Version 2.0 (the "License");
+# you may not use this file except in compliance with the License.
+# You may obtain a copy of the License at
+#
+# https://www.mozilla.org/en-US/MPL/2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+#
+
+find_program(CLANG_FORMAT_EXECUTABLE
+ NAMES
+ clang-format-9
+ clang-format
+ clang-format-11
+ clang-format-10
+ clang-format-8
+ clang-format-7
+
+ DOC "clang-format executable")
+mark_as_advanced(CLANG_FORMAT_EXECUTABLE)
+
+# Extract version from command "clang-format -version"
+if(CLANG_FORMAT_EXECUTABLE)
+ execute_process(COMMAND ${CLANG_FORMAT_EXECUTABLE} -version
+ OUTPUT_VARIABLE clang_format_version
+ ERROR_QUIET OUTPUT_STRIP_TRAILING_WHITESPACE)
+
+ if(clang_format_version MATCHES "^.*clang-format version .*")
+ # clang_format_version sample: "clang-format version 3.9.1-4ubuntu3~16.04.1
+ # (tags/RELEASE_391/rc2)"
+ string(REGEX
+ REPLACE "^.*clang-format version ([.0-9]+).*"
+ "\\1"
+ CLANG_FORMAT_VERSION
+ "${clang_format_version}")
+ # CLANG_FORMAT_VERSION sample: "3.9.1"
+ else()
+ set(CLANG_FORMAT_VERSION 0.0)
+ endif()
+else()
+ set(CLANG_FORMAT_VERSION 0.0)
+endif()
+
+include(FindPackageHandleStandardArgs)
+# handle the QUIETLY and REQUIRED arguments and set CLANG_FORMAT_FOUND to TRUE
+# if all listed variables are TRUE
+find_package_handle_standard_args(CLANG_FORMAT REQUIRED_VARS CLANG_FORMAT_EXECUTABLE VERSION_VAR CLANG_FORMAT_VERSION)
diff --git a/cmake/FindComputeCpp.cmake b/cmake/FindComputeCpp.cmake
new file mode 100644
index 0000000..e200522
--- /dev/null
+++ b/cmake/FindComputeCpp.cmake
@@ -0,0 +1,455 @@
+#.rst:
+# FindComputeCpp
+#---------------
+#
+# Copyright 2016-2018 Codeplay Software Ltd.
+#
+# Licensed under the Apache License, Version 2.0 (the "License");
+# you may not use these files except in compliance with the License.
+# You may obtain a copy of the License at
+#
+# http://www.apache.org/licenses/LICENSE-2.0
+#
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+
+#########################
+# FindComputeCpp.cmake
+#########################
+#
+# Tools for finding and building with ComputeCpp.
+#
+# User must define ComputeCpp_DIR pointing to the ComputeCpp
+# installation.
+#
+# Latest version of this file can be found at:
+# https://github.com/codeplaysoftware/computecpp-sdk
+
+cmake_minimum_required(VERSION 3.4.3)
+include(FindPackageHandleStandardArgs)
+include(ComputeCppIRMap)
+
+set(COMPUTECPP_USER_FLAGS "" CACHE STRING "User flags for compute++")
+separate_arguments(COMPUTECPP_USER_FLAGS)
+mark_as_advanced(COMPUTECPP_USER_FLAGS)
+
+set(COMPUTECPP_BITCODE "spir64" CACHE STRING
+ "Bitcode type to use as SYCL target in compute++")
+mark_as_advanced(COMPUTECPP_BITCODE)
+
+include(CMakeFindDependencyMacro)
+find_dependency(OpenCL REQUIRED)
+
+# Find ComputeCpp package
+
+if(DEFINED ComputeCpp_DIR)
+ set(computecpp_find_hint ${ComputeCpp_DIR})
+elseif(DEFINED ENV{COMPUTECPP_DIR})
+ set(computecpp_find_hint $ENV{COMPUTECPP_DIR})
+endif()
+
+# Used for running executables on the host
+set(computecpp_host_find_hint ${computecpp_find_hint})
+
+if(CMAKE_CROSSCOMPILING)
+ # ComputeCpp_HOST_DIR is used to find executables that are run on the host
+ if(DEFINED ComputeCpp_HOST_DIR)
+ set(computecpp_host_find_hint ${ComputeCpp_HOST_DIR})
+ elseif(DEFINED ENV{COMPUTECPP_HOST_DIR})
+ set(computecpp_host_find_hint $ENV{COMPUTECPP_HOST_DIR})
+ endif()
+endif()
+
+find_program(ComputeCpp_DEVICE_COMPILER_EXECUTABLE compute++
+ HINTS ${computecpp_host_find_hint}
+ PATH_SUFFIXES bin
+ NO_SYSTEM_ENVIRONMENT_PATH)
+
+find_program(ComputeCpp_INFO_EXECUTABLE computecpp_info
+ HINTS ${computecpp_host_find_hint}
+ PATH_SUFFIXES bin
+ NO_SYSTEM_ENVIRONMENT_PATH)
+
+find_library(COMPUTECPP_RUNTIME_LIBRARY
+ NAMES ComputeCpp ComputeCpp_vs2015
+ HINTS ${computecpp_find_hint}
+ PATH_SUFFIXES lib
+ DOC "ComputeCpp Runtime Library")
+
+find_library(COMPUTECPP_RUNTIME_LIBRARY_DEBUG
+ NAMES ComputeCpp_d ComputeCpp ComputeCpp_vs2015_d
+ HINTS ${computecpp_find_hint}
+ PATH_SUFFIXES lib
+ DOC "ComputeCpp Debug Runtime Library")
+
+find_path(ComputeCpp_INCLUDE_DIRS
+ NAMES "CL/sycl.hpp"
+ HINTS ${computecpp_find_hint}/include
+ DOC "The ComputeCpp include directory")
+get_filename_component(ComputeCpp_INCLUDE_DIRS ${ComputeCpp_INCLUDE_DIRS} ABSOLUTE)
+
+get_filename_component(computecpp_canonical_root_dir "${ComputeCpp_INCLUDE_DIRS}/.." ABSOLUTE)
+set(ComputeCpp_ROOT_DIR "${computecpp_canonical_root_dir}" CACHE PATH
+ "The root of the ComputeCpp install")
+
+if(NOT ComputeCpp_INFO_EXECUTABLE)
+ message(WARNING "Can't find computecpp_info - check ComputeCpp_DIR")
+else()
+ execute_process(COMMAND ${ComputeCpp_INFO_EXECUTABLE} "--dump-version"
+ OUTPUT_VARIABLE ComputeCpp_VERSION
+ RESULT_VARIABLE ComputeCpp_INFO_EXECUTABLE_RESULT OUTPUT_STRIP_TRAILING_WHITESPACE)
+ if(NOT ComputeCpp_INFO_EXECUTABLE_RESULT EQUAL "0")
+ message(WARNING "Package version - Error obtaining version!")
+ endif()
+
+ execute_process(COMMAND ${ComputeCpp_INFO_EXECUTABLE} "--dump-is-supported"
+ OUTPUT_VARIABLE COMPUTECPP_PLATFORM_IS_SUPPORTED
+ RESULT_VARIABLE ComputeCpp_INFO_EXECUTABLE_RESULT OUTPUT_STRIP_TRAILING_WHITESPACE)
+ if(NOT ComputeCpp_INFO_EXECUTABLE_RESULT EQUAL "0")
+ message(WARNING "platform - Error checking platform support!")
+ else()
+ mark_as_advanced(COMPUTECPP_PLATFORM_IS_SUPPORTED)
+ if (COMPUTECPP_PLATFORM_IS_SUPPORTED)
+ message(STATUS "platform - your system can support ComputeCpp")
+ else()
+ message(STATUS "platform - your system is not officially supported")
+ endif()
+ endif()
+endif()
+
+find_package_handle_standard_args(ComputeCpp
+ REQUIRED_VARS ComputeCpp_ROOT_DIR
+ ComputeCpp_DEVICE_COMPILER_EXECUTABLE
+ ComputeCpp_INFO_EXECUTABLE
+ COMPUTECPP_RUNTIME_LIBRARY
+ COMPUTECPP_RUNTIME_LIBRARY_DEBUG
+ ComputeCpp_INCLUDE_DIRS
+ VERSION_VAR ComputeCpp_VERSION)
+mark_as_advanced(ComputeCpp_ROOT_DIR
+ ComputeCpp_DEVICE_COMPILER_EXECUTABLE
+ ComputeCpp_INFO_EXECUTABLE
+ COMPUTECPP_RUNTIME_LIBRARY
+ COMPUTECPP_RUNTIME_LIBRARY_DEBUG
+ ComputeCpp_INCLUDE_DIRS
+ ComputeCpp_VERSION)
+
+if(NOT ComputeCpp_FOUND)
+ return()
+endif()
+
+list(APPEND COMPUTECPP_DEVICE_COMPILER_FLAGS -O2 -mllvm -inline-threshold=1000 -intelspirmetadata)
+mark_as_advanced(COMPUTECPP_DEVICE_COMPILER_FLAGS)
+
+if(CMAKE_CROSSCOMPILING)
+ if(NOT COMPUTECPP_DONT_USE_TOOLCHAIN)
+ list(APPEND COMPUTECPP_DEVICE_COMPILER_FLAGS --gcc-toolchain=${COMPUTECPP_TOOLCHAIN_DIR})
+ endif()
+ list(APPEND COMPUTECPP_DEVICE_COMPILER_FLAGS --sysroot=${COMPUTECPP_SYSROOT_DIR})
+ list(APPEND COMPUTECPP_DEVICE_COMPILER_FLAGS -target ${COMPUTECPP_TARGET_TRIPLE})
+endif()
+
+list(APPEND COMPUTECPP_DEVICE_COMPILER_FLAGS -sycl-target ${COMPUTECPP_BITCODE})
+message(STATUS "compute++ flags - ${COMPUTECPP_DEVICE_COMPILER_FLAGS}")
+
+include(ComputeCppCompilerChecks)
+
+if(NOT TARGET OpenCL::OpenCL)
+ add_library(OpenCL::OpenCL UNKNOWN IMPORTED)
+ set_target_properties(OpenCL::OpenCL PROPERTIES
+ IMPORTED_LOCATION "${OpenCL_LIBRARIES}"
+ INTERFACE_INCLUDE_DIRECTORIES "${OpenCL_INCLUDE_DIRS}"
+ )
+endif()
+
+if(NOT TARGET ComputeCpp::ComputeCpp)
+ add_library(ComputeCpp::ComputeCpp UNKNOWN IMPORTED)
+ set_target_properties(ComputeCpp::ComputeCpp PROPERTIES
+ IMPORTED_LOCATION_DEBUG "${COMPUTECPP_RUNTIME_LIBRARY_DEBUG}"
+ IMPORTED_LOCATION_RELWITHDEBINFO "${COMPUTECPP_RUNTIME_LIBRARY}"
+ IMPORTED_LOCATION "${COMPUTECPP_RUNTIME_LIBRARY}"
+ INTERFACE_INCLUDE_DIRECTORIES "${ComputeCpp_INCLUDE_DIRS}"
+ INTERFACE_LINK_LIBRARIES "OpenCL::OpenCL"
+ )
+endif()
+
+# This property allows targets to specify that their sources should be
+# compiled with the integration header included after the user's
+# sources, not before (e.g. when an enum is used in a kernel name, this
+# is not technically valid SYCL code but can work with ComputeCpp)
+define_property(
+ TARGET PROPERTY COMPUTECPP_INCLUDE_AFTER
+ BRIEF_DOCS "Include integration header after user source"
+ FULL_DOCS "Changes compiler arguments such that the source file is
+ actually the integration header, and the .cpp file is included on
+ the command line so that it is seen by the compiler first. Enables
+ non-standards-conformant SYCL code to compile with ComputeCpp."
+)
+define_property(
+ TARGET PROPERTY INTERFACE_COMPUTECPP_FLAGS
+ BRIEF_DOCS "Interface compile flags to provide compute++"
+ FULL_DOCS "Set additional compile flags to pass to compute++ when compiling
+ any target which links to this one."
+)
+define_property(
+ SOURCE PROPERTY COMPUTECPP_SOURCE_FLAGS
+ BRIEF_DOCS "Source file compile flags for compute++"
+ FULL_DOCS "Set additional compile flags for compiling the SYCL integration
+ header for the given source file."
+)
+
+####################
+# __build_ir
+####################
+#
+# Adds a custom target for running compute++ and adding a dependency for the
+# resulting integration header and kernel binary.
+#
+# TARGET : Name of the target.
+# SOURCE : Source file to be compiled.
+# COUNTER : Counter included in name of custom target. Different counter
+# values prevent duplicated names of custom target when source files with
+# the same name, but located in different directories, are used for the
+# same target.
+#
+function(__build_ir)
+ set(options)
+ set(one_value_args
+ TARGET
+ SOURCE
+ COUNTER
+ )
+ set(multi_value_args)
+ cmake_parse_arguments(SDK_BUILD_IR
+ "${options}"
+ "${one_value_args}"
+ "${multi_value_args}"
+ ${ARGN}
+ )
+ get_filename_component(sourceFileName ${SDK_BUILD_IR_SOURCE} NAME)
+
+ # Set the path to the integration header.
+ # The .sycl filename must depend on the target so that different targets
+ # using the same source file will be generated with a different rule.
+ set(baseSyclName ${CMAKE_CURRENT_BINARY_DIR}/${SDK_BUILD_IR_TARGET}_${sourceFileName})
+ set(outputSyclFile ${baseSyclName}.sycl)
+ set(outputDeviceFile ${baseSyclName}.${IR_MAP_${COMPUTECPP_BITCODE}})
+ set(depFileName ${baseSyclName}.sycl.d)
+
+ set(include_directories "$<TARGET_PROPERTY:${SDK_BUILD_IR_TARGET},INCLUDE_DIRECTORIES>")
+ set(compile_definitions "$<TARGET_PROPERTY:${SDK_BUILD_IR_TARGET},COMPILE_DEFINITIONS>")
+ set(generated_include_directories
+ $<$<BOOL:${include_directories}>:-I\"$<JOIN:${include_directories},\"\t-I\">\">)
+ set(generated_compile_definitions
+ $<$<BOOL:${compile_definitions}>:-D$<JOIN:${compile_definitions},\t-D>>)
+
+ # Obtain language standard of the file
+ set(device_compiler_cxx_standard)
+ get_target_property(targetCxxStandard ${SDK_BUILD_IR_TARGET} CXX_STANDARD)
+ if (targetCxxStandard MATCHES 17)
+ set(device_compiler_cxx_standard "-std=c++1z")
+ elseif (targetCxxStandard MATCHES 14)
+ set(device_compiler_cxx_standard "-std=c++14")
+ elseif (targetCxxStandard MATCHES 11)
+ set(device_compiler_cxx_standard "-std=c++11")
+ elseif (targetCxxStandard MATCHES 98)
+ message(FATAL_ERROR "SYCL applications cannot be compiled using C++98")
+ else ()
+ set(device_compiler_cxx_standard "")
+ endif()
+
+ get_property(source_compile_flags
+ SOURCE ${SDK_BUILD_IR_SOURCE}
+ PROPERTY COMPUTECPP_SOURCE_FLAGS
+ )
+ separate_arguments(source_compile_flags)
+ if(source_compile_flags)
+ list(APPEND computecpp_source_flags ${source_compile_flags})
+ endif()
+
+ list(APPEND COMPUTECPP_DEVICE_COMPILER_FLAGS
+ ${device_compiler_cxx_standard}
+ ${COMPUTECPP_USER_FLAGS}
+ ${computecpp_source_flags}
+ )
+
+ set(ir_dependencies ${SDK_BUILD_IR_SOURCE})
+ get_target_property(target_libraries ${SDK_BUILD_IR_TARGET} LINK_LIBRARIES)
+ if(target_libraries)
+ foreach(library ${target_libraries})
+ if(TARGET ${library})
+ list(APPEND ir_dependencies ${library})
+ endif()
+ endforeach()
+ endif()
+
+ # Depfile support was only added in CMake 3.7
+ # CMake throws an error if it is unsupported by the generator (i. e. not ninja)
+ if((NOT CMAKE_VERSION VERSION_LESS 3.7.0) AND
+ CMAKE_GENERATOR MATCHES "Ninja")
+ file(RELATIVE_PATH relOutputFile ${CMAKE_BINARY_DIR} ${outputDeviceFile})
+ set(generate_depfile -MMD -MF ${depFileName} -MT ${relOutputFile})
+ set(enable_depfile DEPFILE ${depFileName})
+ endif()
+
+ # Add custom command for running compute++
+ add_custom_command(
+ OUTPUT ${outputDeviceFile} ${outputSyclFile}
+ COMMAND ${ComputeCpp_DEVICE_COMPILER_EXECUTABLE}
+ ${COMPUTECPP_DEVICE_COMPILER_FLAGS}
+ ${generated_include_directories}
+ ${generated_compile_definitions}
+ -sycl-ih ${outputSyclFile}
+ -o ${outputDeviceFile}
+ -c ${SDK_BUILD_IR_SOURCE}
+ ${generate_depfile}
+ DEPENDS ${ir_dependencies}
+ IMPLICIT_DEPENDS CXX ${SDK_BUILD_IR_SOURCE}
+ ${enable_depfile}
+ WORKING_DIRECTORY ${CMAKE_CURRENT_BINARY_DIR}
+ COMMENT "Building ComputeCpp integration header file ${outputSyclFile}")
+
+ # Name: (user-defined name)_(source file)_(counter)_ih
+ set(headerTargetName
+ ${SDK_BUILD_IR_TARGET}_${sourceFileName}_${SDK_BUILD_IR_COUNTER}_ih)
+
+ if(NOT MSVC)
+ # Add a custom target for the generated integration header
+ add_custom_target(${headerTargetName} DEPENDS ${outputDeviceFile} ${outputSyclFile})
+ add_dependencies(${SDK_BUILD_IR_TARGET} ${headerTargetName})
+ endif()
+
+ # This property can be set on a per-target basis to indicate that the
+ # integration header should appear after the main source listing
+ get_target_property(includeAfter ${SDK_ADD_SYCL_TARGET} COMPUTECPP_INCLUDE_AFTER)
+
+ if(includeAfter)
+ # Change the source file to the integration header - e.g.
+ # g++ -c source_file_name.cpp.sycl
+ get_target_property(current_sources ${SDK_BUILD_IR_TARGET} SOURCES)
+ # Remove absolute path to source file
+ list(REMOVE_ITEM current_sources ${SDK_BUILD_IR_SOURCE})
+ # Remove relative path to source file
+ string(REPLACE "${CMAKE_CURRENT_SOURCE_DIR}/" ""
+ rel_source_file ${SDK_BUILD_IR_SOURCE}
+ )
+ list(REMOVE_ITEM current_sources ${rel_source_file})
+ # Add SYCL header to source list
+ list(APPEND current_sources ${outputSyclFile})
+ set_property(TARGET ${SDK_BUILD_IR_TARGET}
+ PROPERTY SOURCES ${current_sources})
+ # CMake/gcc don't know what language a .sycl file is, so tell them
+ set_property(SOURCE ${outputSyclFile} PROPERTY LANGUAGE CXX)
+ set(includedFile ${SDK_BUILD_IR_SOURCE})
+ set(cppFile ${outputSyclFile})
+ else()
+ set_property(SOURCE ${outputSyclFile} PROPERTY HEADER_FILE_ONLY ON)
+ set(includedFile ${outputSyclFile})
+ set(cppFile ${SDK_BUILD_IR_SOURCE})
+ endif()
+
+ # Force inclusion of the integration header for the host compiler
+ if(MSVC)
+ # Group SYCL files inside Visual Studio
+ source_group("SYCL" FILES ${outputSyclFile})
+
+ if(includeAfter)
+ # Allow the source file to be edited using Visual Studio.
+ # It will be added as a header file so it won't be compiled.
+ set_property(SOURCE ${SDK_BUILD_IR_SOURCE} PROPERTY HEADER_FILE_ONLY true)
+ endif()
+
+ # Add both source and the sycl files to the VS solution.
+ target_sources(${SDK_BUILD_IR_TARGET} PUBLIC ${SDK_BUILD_IR_SOURCE} ${outputSyclFile})
+
+ set(forceIncludeFlags "/FI${includedFile} /TP")
+ else()
+ set(forceIncludeFlags "-include ${includedFile} -x c++")
+ endif()
+
+ set_property(
+ SOURCE ${cppFile}
+ APPEND_STRING PROPERTY COMPILE_FLAGS "${forceIncludeFlags}"
+ )
+
+endfunction(__build_ir)
+
+#######################
+# add_sycl_to_target
+#######################
+#
+# Adds a SYCL compilation custom command associated with an existing
+# target and sets a dependency on that new command.
+#
+# TARGET : Name of the target to add SYCL to.
+# SOURCES : Source files to be compiled for SYCL.
+#
+function(add_sycl_to_target)
+ set(options)
+ set(one_value_args
+ TARGET
+ )
+ set(multi_value_args
+ SOURCES
+ )
+ cmake_parse_arguments(SDK_ADD_SYCL
+ "${options}"
+ "${one_value_args}"
+ "${multi_value_args}"
+ ${ARGN}
+ )
+
+ set_target_properties(${SDK_ADD_SYCL_TARGET} PROPERTIES LINKER_LANGUAGE CXX)
+
+ # If the CXX compiler is set to compute++ enable the driver.
+ get_filename_component(cmakeCxxCompilerFileName "${CMAKE_CXX_COMPILER}" NAME)
+ if("${cmakeCxxCompilerFileName}" STREQUAL "compute++")
+ if(MSVC)
+ message(FATAL_ERROR "The compiler driver is not supported by this system,
+ revert the CXX compiler to your default host compiler.")
+ endif()
+
+ get_target_property(includeAfter ${SDK_ADD_SYCL_TARGET} COMPUTECPP_INCLUDE_AFTER)
+ if(includeAfter)
+ list(APPEND COMPUTECPP_USER_FLAGS -fsycl-ih-last)
+ endif()
+ list(INSERT COMPUTECPP_DEVICE_COMPILER_FLAGS 0 -sycl-driver)
+ # Prepend COMPUTECPP_DEVICE_COMPILER_FLAGS and append COMPUTECPP_USER_FLAGS
+ foreach(prop COMPILE_OPTIONS INTERFACE_COMPILE_OPTIONS)
+ get_target_property(target_compile_options ${SDK_ADD_SYCL_TARGET} ${prop})
+ if(NOT target_compile_options)
+ set(target_compile_options "")
+ endif()
+ set_property(
+ TARGET ${SDK_ADD_SYCL_TARGET}
+ PROPERTY ${prop}
+ ${COMPUTECPP_DEVICE_COMPILER_FLAGS}
+ ${target_compile_options}
+ ${COMPUTECPP_USER_FLAGS}
+ )
+ endforeach()
+ else()
+ set(fileCounter 0)
+ list(INSERT COMPUTECPP_DEVICE_COMPILER_FLAGS 0 -sycl)
+ # Add custom target to run compute++ and generate the integration header
+ foreach(sourceFile ${SDK_ADD_SYCL_SOURCES})
+ if(NOT IS_ABSOLUTE ${sourceFile})
+ set(sourceFile "${CMAKE_CURRENT_SOURCE_DIR}/${sourceFile}")
+ endif()
+ __build_ir(
+ TARGET ${SDK_ADD_SYCL_TARGET}
+ SOURCE ${sourceFile}
+ COUNTER ${fileCounter}
+ )
+ MATH(EXPR fileCounter "${fileCounter} + 1")
+ endforeach()
+ endif()
+
+ set_property(TARGET ${SDK_ADD_SYCL_TARGET}
+ APPEND PROPERTY LINK_LIBRARIES ComputeCpp::ComputeCpp)
+ set_property(TARGET ${SDK_ADD_SYCL_TARGET}
+ APPEND PROPERTY INTERFACE_LINK_LIBRARIES ComputeCpp::ComputeCpp)
+endfunction(add_sycl_to_target)
diff --git a/cmake/FindFFTW.cmake b/cmake/FindFFTW.cmake
new file mode 100644
index 0000000..ed55c5f
--- /dev/null
+++ b/cmake/FindFFTW.cmake
@@ -0,0 +1,120 @@
+# - Find the FFTW library
+#
+# Usage:
+# find_package(FFTW [REQUIRED] [QUIET] )
+#
+# It sets the following variables:
+# FFTW_FOUND ... true if fftw is found on the system
+# FFTW_LIBRARIES ... full path to fftw library
+# FFTW_INCLUDES ... fftw include directory
+#
+# The following variables will be checked by the function
+# FFTW_USE_STATIC_LIBS ... if true, only static libraries are found
+# FFTW_ROOT ... if set, the libraries are exclusively searched
+# under this path
+# FFTW_LIBRARY ... fftw library to use
+# FFTW_INCLUDE_DIR ... fftw include directory
+#
+
+#If environment variable FFTWDIR is specified, it has same effect as FFTW_ROOT
+if( NOT FFTW_ROOT AND ENV{FFTWDIR} )
+ set( FFTW_ROOT $ENV{FFTWDIR} )
+endif()
+
+# Check if we can use PkgConfig
+include(CMakeFindDependencyMacro)
+find_dependency(PkgConfig)
+
+#Determine from PKG
+if( PKG_CONFIG_FOUND AND NOT FFTW_ROOT )
+ pkg_check_modules( PKG_FFTW QUIET "fftw3" )
+endif()
+
+#Check whether to search static or dynamic libs
+set( CMAKE_FIND_LIBRARY_SUFFIXES_SAV ${CMAKE_FIND_LIBRARY_SUFFIXES} )
+
+if( ${FFTW_USE_STATIC_LIBS} )
+ set( CMAKE_FIND_LIBRARY_SUFFIXES ${CMAKE_STATIC_LIBRARY_SUFFIX} )
+else()
+ set( CMAKE_FIND_LIBRARY_SUFFIXES ${CMAKE_SHARED_LIBRARY_SUFFIX} )
+endif()
+
+if( FFTW_ROOT )
+
+ #find libs
+ find_library(
+ FFTW_LIB
+ NAMES "fftw3"
+ PATHS ${FFTW_ROOT}
+ PATH_SUFFIXES "lib" "lib64"
+ NO_DEFAULT_PATH
+ )
+
+ find_library(
+ FFTWF_LIB
+ NAMES "fftw3f"
+ PATHS ${FFTW_ROOT}
+ PATH_SUFFIXES "lib" "lib64"
+ NO_DEFAULT_PATH
+ )
+
+ find_library(
+ FFTWL_LIB
+ NAMES "fftw3l"
+ PATHS ${FFTW_ROOT}
+ PATH_SUFFIXES "lib" "lib64"
+ NO_DEFAULT_PATH
+ )
+
+ #find includes
+ find_path(
+ FFTW_INCLUDES
+ NAMES "fftw3.h"
+ PATHS ${FFTW_ROOT}
+ PATH_SUFFIXES "include"
+ NO_DEFAULT_PATH
+ )
+
+else()
+
+ find_library(
+ FFTW_LIB
+ NAMES "fftw3"
+ PATHS ${PKG_FFTW_LIBRARY_DIRS} ${LIB_INSTALL_DIR}
+ )
+
+ find_library(
+ FFTWF_LIB
+ NAMES "fftw3f"
+ PATHS ${PKG_FFTW_LIBRARY_DIRS} ${LIB_INSTALL_DIR}
+ )
+
+
+ find_library(
+ FFTWL_LIB
+ NAMES "fftw3l"
+ PATHS ${PKG_FFTW_LIBRARY_DIRS} ${LIB_INSTALL_DIR}
+ )
+
+ find_path(
+ FFTW_INCLUDES
+ NAMES "fftw3.h"
+ PATHS ${PKG_FFTW_INCLUDE_DIRS} ${INCLUDE_INSTALL_DIR}
+ )
+
+endif()
+
+set(FFTW_LIBRARIES ${FFTW_LIB} ${FFTWF_LIB})
+
+if(FFTWL_LIB)
+ set(FFTW_LIBRARIES ${FFTW_LIBRARIES} ${FFTWL_LIB})
+endif()
+
+set( CMAKE_FIND_LIBRARY_SUFFIXES ${CMAKE_FIND_LIBRARY_SUFFIXES_SAV} )
+
+include(FindPackageHandleStandardArgs)
+find_package_handle_standard_args(FFTW DEFAULT_MSG
+ FFTW_INCLUDES FFTW_LIBRARIES)
+
+mark_as_advanced(FFTW_INCLUDES FFTW_LIBRARIES FFTW_LIB FFTWF_LIB FFTWL_LIB)
+
diff --git a/cmake/FindGMP.cmake b/cmake/FindGMP.cmake
new file mode 100644
index 0000000..c41eedc
--- /dev/null
+++ b/cmake/FindGMP.cmake
@@ -0,0 +1,21 @@
+# Try to find the GNU Multiple Precision Arithmetic Library (GMP)
+# See http://gmplib.org/
+
+if (GMP_INCLUDES AND GMP_LIBRARIES)
+ set(GMP_FIND_QUIETLY TRUE)
+endif ()
+
+find_path(GMP_INCLUDES
+ NAMES
+ gmp.h
+ PATHS
+ $ENV{GMPDIR}
+ ${INCLUDE_INSTALL_DIR}
+)
+
+find_library(GMP_LIBRARIES gmp PATHS $ENV{GMPDIR} ${LIB_INSTALL_DIR})
+
+include(FindPackageHandleStandardArgs)
+find_package_handle_standard_args(GMP DEFAULT_MSG
+ GMP_INCLUDES GMP_LIBRARIES)
+mark_as_advanced(GMP_INCLUDES GMP_LIBRARIES)
diff --git a/cmake/FindGoogleHash.cmake b/cmake/FindGoogleHash.cmake
new file mode 100644
index 0000000..481eb4d
--- /dev/null
+++ b/cmake/FindGoogleHash.cmake
@@ -0,0 +1,23 @@
+
+if (GOOGLEHASH_INCLUDES AND GOOGLEHASH_LIBRARIES)
+ set(GOOGLEHASH_FIND_QUIETLY TRUE)
+endif ()
+
+find_path(GOOGLEHASH_INCLUDES
+ NAMES
+ google/dense_hash_map
+ PATHS
+ ${INCLUDE_INSTALL_DIR}
+)
+
+if(GOOGLEHASH_INCLUDES)
+ # let's make sure it compiles with the current compiler
+ file(WRITE ${CMAKE_BINARY_DIR}/googlehash_test.cpp
+ "#include <google/sparse_hash_map>\n#include <google/dense_hash_map>\nint main(int argc, char** argv) { google::dense_hash_map<int,float> a; google::sparse_hash_map<int,float> b; return 0;}\n")
+ try_compile(GOOGLEHASH_COMPILE ${CMAKE_BINARY_DIR} ${CMAKE_BINARY_DIR}/googlehash_test.cpp OUTPUT_VARIABLE GOOGLEHASH_COMPILE_RESULT)
+endif()
+
+include(FindPackageHandleStandardArgs)
+find_package_handle_standard_args(GoogleHash DEFAULT_MSG GOOGLEHASH_INCLUDES GOOGLEHASH_COMPILE)
+
+mark_as_advanced(GOOGLEHASH_INCLUDES)
diff --git a/cmake/FindHWLOC.cmake b/cmake/FindHWLOC.cmake
new file mode 100644
index 0000000..522f521
--- /dev/null
+++ b/cmake/FindHWLOC.cmake
@@ -0,0 +1,332 @@
+###
+#
+# @copyright (c) 2009-2014 The University of Tennessee and The University
+# of Tennessee Research Foundation.
+# All rights reserved.
+# @copyright (c) 2012-2014 Inria. All rights reserved.
+# @copyright (c) 2012-2014 Bordeaux INP, CNRS (LaBRI UMR 5800), Inria, Univ. Bordeaux. All rights reserved.
+#
+###
+#
+# - Find HWLOC include dirs and libraries
+# Use this module by invoking find_package with the form:
+# find_package(HWLOC
+# [REQUIRED]) # Fail with error if hwloc is not found
+#
+# This module finds headers and hwloc library.
+# Results are reported in variables:
+# HWLOC_FOUND - True if headers and requested libraries were found
+# HWLOC_INCLUDE_DIRS - hwloc include directories
+# HWLOC_LIBRARY_DIRS - Link directories for hwloc libraries
+# HWLOC_LIBRARIES - hwloc component libraries to be linked
+#
+# The user can give specific paths where to find the libraries adding cmake
+# options at configure (ex: cmake path/to/project -DHWLOC_DIR=path/to/hwloc):
+# HWLOC_DIR - Where to find the base directory of hwloc
+# HWLOC_INCDIR - Where to find the header files
+# HWLOC_LIBDIR - Where to find the library files
+# The module can also look for the following environment variables if paths
+# are not given as cmake variable: HWLOC_DIR, HWLOC_INCDIR, HWLOC_LIBDIR
+
+#=============================================================================
+# Copyright 2012-2013 Inria
+# Copyright 2012-2013 Emmanuel Agullo
+# Copyright 2012-2013 Mathieu Faverge
+# Copyright 2012 Cedric Castagnede
+# Copyright 2013 Florent Pruvost
+#
+# Distributed under the OSI-approved BSD License (the "License");
+# see accompanying file MORSE-Copyright.txt for details.
+#
+# This software is distributed WITHOUT ANY WARRANTY; without even the
+# implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.
+# See the License for more information.
+#=============================================================================
+# (To distribute this file outside of Morse, substitute the full
+# License text for the above reference.)
+
+include(CheckStructHasMember)
+include(CheckCSourceCompiles)
+
+if (NOT HWLOC_FOUND)
+ set(HWLOC_DIR "" CACHE PATH "Installation directory of HWLOC library")
+ if (NOT HWLOC_FIND_QUIETLY)
+ message(STATUS "A cache variable, namely HWLOC_DIR, has been set to specify the install directory of HWLOC")
+ endif()
+endif()
+
+set(ENV_HWLOC_DIR "$ENV{HWLOC_DIR}")
+set(ENV_HWLOC_INCDIR "$ENV{HWLOC_INCDIR}")
+set(ENV_HWLOC_LIBDIR "$ENV{HWLOC_LIBDIR}")
+set(HWLOC_GIVEN_BY_USER "FALSE")
+if ( HWLOC_DIR OR ( HWLOC_INCDIR AND HWLOC_LIBDIR) OR ENV_HWLOC_DIR OR (ENV_HWLOC_INCDIR AND ENV_HWLOC_LIBDIR) )
+ set(HWLOC_GIVEN_BY_USER "TRUE")
+endif()
+
+# Optionally use pkg-config to detect include/library dirs (if pkg-config is available)
+# -------------------------------------------------------------------------------------
+include(CMakeFindDependencyMacro)
+# include(FindPkgConfig)
+find_dependency(PkgConfig QUIET)
+if( PKG_CONFIG_EXECUTABLE AND NOT HWLOC_GIVEN_BY_USER )
+
+ pkg_search_module(HWLOC hwloc)
+ if (NOT HWLOC_FIND_QUIETLY)
+ if (HWLOC_FOUND AND HWLOC_LIBRARIES)
+ message(STATUS "Looking for HWLOC - found using PkgConfig")
+ #if(NOT HWLOC_INCLUDE_DIRS)
+ # message("${Magenta}HWLOC_INCLUDE_DIRS is empty using PkgConfig."
+ # "Perhaps the path to hwloc headers is already present in your"
+ # "C(PLUS)_INCLUDE_PATH environment variable.${ColourReset}")
+ #endif()
+ else()
+ message(STATUS "${Magenta}Looking for HWLOC - not found using PkgConfig."
+ "\n Perhaps you should add the directory containing hwloc.pc to"
+ "\n the PKG_CONFIG_PATH environment variable.${ColourReset}")
+ endif()
+ endif()
+
+endif()
+
+if( (NOT PKG_CONFIG_EXECUTABLE) OR (PKG_CONFIG_EXECUTABLE AND NOT HWLOC_FOUND) OR (HWLOC_GIVEN_BY_USER) )
+
+ if (NOT HWLOC_FIND_QUIETLY)
+ message(STATUS "Looking for HWLOC - PkgConfig not used")
+ endif()
+
+ # Looking for include
+ # -------------------
+
+ # Add system include paths to search include
+ # ------------------------------------------
+ unset(_inc_env)
+ if(ENV_HWLOC_INCDIR)
+ list(APPEND _inc_env "${ENV_HWLOC_INCDIR}")
+ elseif(ENV_HWLOC_DIR)
+ list(APPEND _inc_env "${ENV_HWLOC_DIR}")
+ list(APPEND _inc_env "${ENV_HWLOC_DIR}/include")
+ list(APPEND _inc_env "${ENV_HWLOC_DIR}/include/hwloc")
+ else()
+ if(WIN32)
+ string(REPLACE ":" ";" _inc_env "$ENV{INCLUDE}")
+ else()
+ string(REPLACE ":" ";" _path_env "$ENV{INCLUDE}")
+ list(APPEND _inc_env "${_path_env}")
+ string(REPLACE ":" ";" _path_env "$ENV{C_INCLUDE_PATH}")
+ list(APPEND _inc_env "${_path_env}")
+ string(REPLACE ":" ";" _path_env "$ENV{CPATH}")
+ list(APPEND _inc_env "${_path_env}")
+ string(REPLACE ":" ";" _path_env "$ENV{INCLUDE_PATH}")
+ list(APPEND _inc_env "${_path_env}")
+ endif()
+ endif()
+ list(APPEND _inc_env "${CMAKE_PLATFORM_IMPLICIT_INCLUDE_DIRECTORIES}")
+ list(APPEND _inc_env "${CMAKE_C_IMPLICIT_INCLUDE_DIRECTORIES}")
+ list(REMOVE_DUPLICATES _inc_env)
+
+ # set paths where to look for
+ set(PATH_TO_LOOK_FOR "${_inc_env}")
+
+ # Try to find the hwloc header in the given paths
+ # -------------------------------------------------
+ # call cmake macro to find the header path
+ if(HWLOC_INCDIR)
+ set(HWLOC_hwloc.h_DIRS "HWLOC_hwloc.h_DIRS-NOTFOUND")
+ find_path(HWLOC_hwloc.h_DIRS
+ NAMES hwloc.h
+ HINTS ${HWLOC_INCDIR})
+ else()
+ if(HWLOC_DIR)
+ set(HWLOC_hwloc.h_DIRS "HWLOC_hwloc.h_DIRS-NOTFOUND")
+ find_path(HWLOC_hwloc.h_DIRS
+ NAMES hwloc.h
+ HINTS ${HWLOC_DIR}
+ PATH_SUFFIXES "include" "include/hwloc")
+ else()
+ set(HWLOC_hwloc.h_DIRS "HWLOC_hwloc.h_DIRS-NOTFOUND")
+ find_path(HWLOC_hwloc.h_DIRS
+ NAMES hwloc.h
+ HINTS ${PATH_TO_LOOK_FOR}
+ PATH_SUFFIXES "hwloc")
+ endif()
+ endif()
+ mark_as_advanced(HWLOC_hwloc.h_DIRS)
+
+ # Add path to cmake variable
+ # ------------------------------------
+ if (HWLOC_hwloc.h_DIRS)
+ set(HWLOC_INCLUDE_DIRS "${HWLOC_hwloc.h_DIRS}")
+ else ()
+ set(HWLOC_INCLUDE_DIRS "HWLOC_INCLUDE_DIRS-NOTFOUND")
+ if(NOT HWLOC_FIND_QUIETLY)
+ message(STATUS "Looking for hwloc -- hwloc.h not found")
+ endif()
+ endif ()
+
+ if (HWLOC_INCLUDE_DIRS)
+ list(REMOVE_DUPLICATES HWLOC_INCLUDE_DIRS)
+ endif ()
+
+
+ # Looking for lib
+ # ---------------
+
+ # Add system library paths to search lib
+ # --------------------------------------
+ unset(_lib_env)
+ if(ENV_HWLOC_LIBDIR)
+ list(APPEND _lib_env "${ENV_HWLOC_LIBDIR}")
+ elseif(ENV_HWLOC_DIR)
+ list(APPEND _lib_env "${ENV_HWLOC_DIR}")
+ list(APPEND _lib_env "${ENV_HWLOC_DIR}/lib")
+ else()
+ if(WIN32)
+ string(REPLACE ":" ";" _lib_env "$ENV{LIB}")
+ else()
+ if(APPLE)
+ string(REPLACE ":" ";" _lib_env "$ENV{DYLD_LIBRARY_PATH}")
+ else()
+ string(REPLACE ":" ";" _lib_env "$ENV{LD_LIBRARY_PATH}")
+ endif()
+ list(APPEND _lib_env "${CMAKE_PLATFORM_IMPLICIT_LINK_DIRECTORIES}")
+ list(APPEND _lib_env "${CMAKE_C_IMPLICIT_LINK_DIRECTORIES}")
+ endif()
+ endif()
+ list(REMOVE_DUPLICATES _lib_env)
+
+ # set paths where to look for
+ set(PATH_TO_LOOK_FOR "${_lib_env}")
+
+ # Try to find the hwloc lib in the given paths
+ # ----------------------------------------------
+
+ # call cmake macro to find the lib path
+ if(HWLOC_LIBDIR)
+ set(HWLOC_hwloc_LIBRARY "HWLOC_hwloc_LIBRARY-NOTFOUND")
+ find_library(HWLOC_hwloc_LIBRARY
+ NAMES hwloc
+ HINTS ${HWLOC_LIBDIR})
+ else()
+ if(HWLOC_DIR)
+ set(HWLOC_hwloc_LIBRARY "HWLOC_hwloc_LIBRARY-NOTFOUND")
+ find_library(HWLOC_hwloc_LIBRARY
+ NAMES hwloc
+ HINTS ${HWLOC_DIR}
+ PATH_SUFFIXES lib lib32 lib64)
+ else()
+ set(HWLOC_hwloc_LIBRARY "HWLOC_hwloc_LIBRARY-NOTFOUND")
+ find_library(HWLOC_hwloc_LIBRARY
+ NAMES hwloc
+ HINTS ${PATH_TO_LOOK_FOR})
+ endif()
+ endif()
+ mark_as_advanced(HWLOC_hwloc_LIBRARY)
+
+ # If found, add path to cmake variable
+ # ------------------------------------
+ if (HWLOC_hwloc_LIBRARY)
+ get_filename_component(hwloc_lib_path ${HWLOC_hwloc_LIBRARY} PATH)
+ # set cmake variables (respects naming convention)
+ set(HWLOC_LIBRARIES "${HWLOC_hwloc_LIBRARY}")
+ set(HWLOC_LIBRARY_DIRS "${hwloc_lib_path}")
+ else ()
+ set(HWLOC_LIBRARIES "HWLOC_LIBRARIES-NOTFOUND")
+ set(HWLOC_LIBRARY_DIRS "HWLOC_LIBRARY_DIRS-NOTFOUND")
+ if(NOT HWLOC_FIND_QUIETLY)
+ message(STATUS "Looking for hwloc -- lib hwloc not found")
+ endif()
+ endif ()
+
+ if (HWLOC_LIBRARY_DIRS)
+ list(REMOVE_DUPLICATES HWLOC_LIBRARY_DIRS)
+ endif ()
+
+ # check a function to validate the find
+ if(HWLOC_LIBRARIES)
+
+ set(REQUIRED_INCDIRS)
+ set(REQUIRED_LIBDIRS)
+ set(REQUIRED_LIBS)
+
+ # HWLOC
+ if (HWLOC_INCLUDE_DIRS)
+ set(REQUIRED_INCDIRS "${HWLOC_INCLUDE_DIRS}")
+ endif()
+ if (HWLOC_LIBRARY_DIRS)
+ set(REQUIRED_LIBDIRS "${HWLOC_LIBRARY_DIRS}")
+ endif()
+ set(REQUIRED_LIBS "${HWLOC_LIBRARIES}")
+
+ # set required libraries for link
+ set(CMAKE_REQUIRED_INCLUDES "${REQUIRED_INCDIRS}")
+ set(CMAKE_REQUIRED_LIBRARIES)
+ foreach(lib_dir ${REQUIRED_LIBDIRS})
+ list(APPEND CMAKE_REQUIRED_LIBRARIES "-L${lib_dir}")
+ endforeach()
+ list(APPEND CMAKE_REQUIRED_LIBRARIES "${REQUIRED_LIBS}")
+ string(REGEX REPLACE "^ -" "-" CMAKE_REQUIRED_LIBRARIES "${CMAKE_REQUIRED_LIBRARIES}")
+
+ # test link
+ unset(HWLOC_WORKS CACHE)
+ include(CheckFunctionExists)
+ check_function_exists(hwloc_topology_init HWLOC_WORKS)
+ mark_as_advanced(HWLOC_WORKS)
+
+ if(NOT HWLOC_WORKS)
+ if(NOT HWLOC_FIND_QUIETLY)
+ message(STATUS "Looking for hwloc : test of hwloc_topology_init with hwloc library fails")
+ message(STATUS "CMAKE_REQUIRED_LIBRARIES: ${CMAKE_REQUIRED_LIBRARIES}")
+ message(STATUS "CMAKE_REQUIRED_INCLUDES: ${CMAKE_REQUIRED_INCLUDES}")
+ message(STATUS "Check in CMakeFiles/CMakeError.log to figure out why it fails")
+ endif()
+ endif()
+ set(CMAKE_REQUIRED_INCLUDES)
+ set(CMAKE_REQUIRED_FLAGS)
+ set(CMAKE_REQUIRED_LIBRARIES)
+ endif()
+
+endif()
+
+if (HWLOC_LIBRARIES)
+ if (HWLOC_LIBRARY_DIRS)
+ list(GET HWLOC_LIBRARY_DIRS 0 first_lib_path)
+ else()
+ list(GET HWLOC_LIBRARIES 0 first_lib)
+ get_filename_component(first_lib_path "${first_lib}" PATH)
+ endif()
+ if (${first_lib_path} MATCHES "/lib(32|64)?$")
+ string(REGEX REPLACE "/lib(32|64)?$" "" not_cached_dir "${first_lib_path}")
+ set(HWLOC_DIR_FOUND "${not_cached_dir}" CACHE PATH "Installation directory of HWLOC library" FORCE)
+ else()
+ set(HWLOC_DIR_FOUND "${first_lib_path}" CACHE PATH "Installation directory of HWLOC library" FORCE)
+ endif()
+endif()
+mark_as_advanced(HWLOC_DIR)
+mark_as_advanced(HWLOC_DIR_FOUND)
+
+# check that HWLOC has been found
+# -------------------------------
+include(FindPackageHandleStandardArgs)
+if (PKG_CONFIG_EXECUTABLE AND HWLOC_FOUND)
+ find_package_handle_standard_args(HWLOC DEFAULT_MSG
+ HWLOC_LIBRARIES)
+else()
+ find_package_handle_standard_args(HWLOC DEFAULT_MSG
+ HWLOC_LIBRARIES
+ HWLOC_WORKS)
+endif()
+
+if (HWLOC_FOUND)
+ set(HWLOC_SAVE_CMAKE_REQUIRED_INCLUDES ${CMAKE_REQUIRED_INCLUDES})
+ list(APPEND CMAKE_REQUIRED_INCLUDES ${HWLOC_INCLUDE_DIRS})
+
+ # test headers to guess the version
+ check_struct_has_member( "struct hwloc_obj" parent hwloc.h HAVE_HWLOC_PARENT_MEMBER )
+ check_struct_has_member( "struct hwloc_cache_attr_s" size hwloc.h HAVE_HWLOC_CACHE_ATTR )
+ check_c_source_compiles( "#include <hwloc.h>
+ int main(void) { hwloc_obj_t o; o->type = HWLOC_OBJ_PU; return 0;}" HAVE_HWLOC_OBJ_PU)
+ include(CheckLibraryExists)
+ check_library_exists(${HWLOC_LIBRARIES} hwloc_bitmap_free "" HAVE_HWLOC_BITMAP)
+
+ set(CMAKE_REQUIRED_INCLUDES ${HWLOC_SAVE_CMAKE_REQUIRED_INCLUDES})
+endif()
diff --git a/cmake/FindKLU.cmake b/cmake/FindKLU.cmake
new file mode 100644
index 0000000..6217d14
--- /dev/null
+++ b/cmake/FindKLU.cmake
@@ -0,0 +1,48 @@
+# KLU lib usually requires linking to a blas library.
+# It is up to the user of this module to find a BLAS and link to it.
+
+if (KLU_INCLUDES AND KLU_LIBRARIES)
+ set(KLU_FIND_QUIETLY TRUE)
+endif ()
+
+find_path(KLU_INCLUDES
+ NAMES
+ klu.h
+ PATHS
+ $ENV{KLUDIR}
+ ${INCLUDE_INSTALL_DIR}
+ PATH_SUFFIXES
+ suitesparse
+ ufsparse
+)
+
+find_library(KLU_LIBRARIES klu PATHS $ENV{KLUDIR} ${LIB_INSTALL_DIR})
+
+if(KLU_LIBRARIES)
+
+ if(NOT KLU_LIBDIR)
+ get_filename_component(KLU_LIBDIR ${KLU_LIBRARIES} PATH)
+ endif()
+
+ find_library(COLAMD_LIBRARY colamd PATHS ${KLU_LIBDIR} $ENV{KLUDIR} ${LIB_INSTALL_DIR})
+ if(COLAMD_LIBRARY)
+ set(KLU_LIBRARIES ${KLU_LIBRARIES} ${COLAMD_LIBRARY})
+ endif ()
+
+ find_library(AMD_LIBRARY amd PATHS ${KLU_LIBDIR} $ENV{KLUDIR} ${LIB_INSTALL_DIR})
+ if(AMD_LIBRARY)
+ set(KLU_LIBRARIES ${KLU_LIBRARIES} ${AMD_LIBRARY})
+ endif ()
+
+ find_library(BTF_LIBRARY btf PATHS $ENV{KLU_LIBDIR} $ENV{KLUDIR} ${LIB_INSTALL_DIR})
+ if(BTF_LIBRARY)
+ set(KLU_LIBRARIES ${KLU_LIBRARIES} ${BTF_LIBRARY})
+ endif()
+
+endif()
+
+include(FindPackageHandleStandardArgs)
+find_package_handle_standard_args(KLU DEFAULT_MSG
+ KLU_INCLUDES KLU_LIBRARIES)
+
+mark_as_advanced(KLU_INCLUDES KLU_LIBRARIES AMD_LIBRARY COLAMD_LIBRARY BTF_LIBRARY)
diff --git a/cmake/FindMPFR.cmake b/cmake/FindMPFR.cmake
new file mode 100644
index 0000000..d8da9d6
--- /dev/null
+++ b/cmake/FindMPFR.cmake
@@ -0,0 +1,83 @@
+# Try to find the MPFR library
+# See http://www.mpfr.org/
+#
+# This module supports requiring a minimum version, e.g. you can do
+# find_package(MPFR 2.3.0)
+# to require version 2.3.0 to newer of MPFR.
+#
+# Once done this will define
+#
+# MPFR_FOUND - system has MPFR lib with correct version
+# MPFR_INCLUDES - the MPFR include directory
+# MPFR_LIBRARIES - the MPFR library
+# MPFR_VERSION - MPFR version
+
+# Copyright (c) 2006, 2007 Montel Laurent, <montel@kde.org>
+# Copyright (c) 2008, 2009 Gael Guennebaud, <g.gael@free.fr>
+# Copyright (c) 2010 Jitse Niesen, <jitse@maths.leeds.ac.uk>
+# Redistribution and use is allowed according to the terms of the BSD license.
+
+# Set MPFR_INCLUDES
+
+find_path(MPFR_INCLUDES
+ NAMES
+ mpfr.h
+ PATHS
+ $ENV{GMPDIR}
+ ${INCLUDE_INSTALL_DIR}
+)
+
+# Set MPFR_FIND_VERSION to 1.0.0 if no minimum version is specified
+
+if(NOT MPFR_FIND_VERSION)
+ if(NOT MPFR_FIND_VERSION_MAJOR)
+ set(MPFR_FIND_VERSION_MAJOR 1)
+ endif()
+ if(NOT MPFR_FIND_VERSION_MINOR)
+ set(MPFR_FIND_VERSION_MINOR 0)
+ endif()
+ if(NOT MPFR_FIND_VERSION_PATCH)
+ set(MPFR_FIND_VERSION_PATCH 0)
+ endif()
+
+ set(MPFR_FIND_VERSION "${MPFR_FIND_VERSION_MAJOR}.${MPFR_FIND_VERSION_MINOR}.${MPFR_FIND_VERSION_PATCH}")
+endif()
+
+
+if(MPFR_INCLUDES)
+
+ # Set MPFR_VERSION
+
+ file(READ "${MPFR_INCLUDES}/mpfr.h" _mpfr_version_header)
+
+ string(REGEX MATCH "define[ \t]+MPFR_VERSION_MAJOR[ \t]+([0-9]+)" _mpfr_major_version_match "${_mpfr_version_header}")
+ set(MPFR_MAJOR_VERSION "${CMAKE_MATCH_1}")
+ string(REGEX MATCH "define[ \t]+MPFR_VERSION_MINOR[ \t]+([0-9]+)" _mpfr_minor_version_match "${_mpfr_version_header}")
+ set(MPFR_MINOR_VERSION "${CMAKE_MATCH_1}")
+ string(REGEX MATCH "define[ \t]+MPFR_VERSION_PATCHLEVEL[ \t]+([0-9]+)" _mpfr_patchlevel_version_match "${_mpfr_version_header}")
+ set(MPFR_PATCHLEVEL_VERSION "${CMAKE_MATCH_1}")
+
+ set(MPFR_VERSION ${MPFR_MAJOR_VERSION}.${MPFR_MINOR_VERSION}.${MPFR_PATCHLEVEL_VERSION})
+
+ # Check whether found version exceeds minimum version
+
+ if(${MPFR_VERSION} VERSION_LESS ${MPFR_FIND_VERSION})
+ set(MPFR_VERSION_OK FALSE)
+ message(STATUS "MPFR version ${MPFR_VERSION} found in ${MPFR_INCLUDES}, "
+ "but at least version ${MPFR_FIND_VERSION} is required")
+ else()
+ set(MPFR_VERSION_OK TRUE)
+ endif()
+
+endif()
+
+# Set MPFR_LIBRARIES
+
+find_library(MPFR_LIBRARIES mpfr PATHS $ENV{GMPDIR} ${LIB_INSTALL_DIR})
+
+# Epilogue
+
+include(FindPackageHandleStandardArgs)
+find_package_handle_standard_args(MPFR DEFAULT_MSG
+ MPFR_INCLUDES MPFR_LIBRARIES MPFR_VERSION_OK)
+mark_as_advanced(MPFR_INCLUDES MPFR_LIBRARIES)
diff --git a/cmake/FindMPREAL.cmake b/cmake/FindMPREAL.cmake
new file mode 100644
index 0000000..947a1ce
--- /dev/null
+++ b/cmake/FindMPREAL.cmake
@@ -0,0 +1,103 @@
+# Try to find the MPFR C++ (MPREAL) library
+# See http://www.holoborodko.com/pavel/mpreal/
+#
+# This module supports requiring a minimum version, e.g. you can do
+# find_package(MPREAL 1.8.6)
+# to require version 1.8.6 or newer of MPREAL C++.
+#
+# Once done this will define
+#
+# MPREAL_FOUND - system has MPREAL lib with correct version
+# MPREAL_INCLUDES - MPREAL required include directories
+# MPREAL_LIBRARIES - MPREAL required libraries
+# MPREAL_VERSION - MPREAL version
+
+# Copyright (c) 2020 The Eigen Authors.
+# Redistribution and use is allowed according to the terms of the BSD license.
+
+include(CMakeFindDependencyMacro)
+find_dependency(MPFR)
+find_dependency(GMP)
+
+# Set MPREAL_INCLUDES
+find_path(MPREAL_INCLUDES
+ NAMES
+ mpreal.h
+ PATHS
+ $ENV{GMPDIR}
+ ${INCLUDE_INSTALL_DIR}
+)
+
+# Set MPREAL_FIND_VERSION to 1.0.0 if no minimum version is specified
+
+if(NOT MPREAL_FIND_VERSION)
+ if(NOT MPREAL_FIND_VERSION_MAJOR)
+ set(MPREAL_FIND_VERSION_MAJOR 1)
+ endif()
+ if(NOT MPREAL_FIND_VERSION_MINOR)
+ set(MPREAL_FIND_VERSION_MINOR 0)
+ endif()
+ if(NOT MPREAL_FIND_VERSION_PATCH)
+ set(MPREAL_FIND_VERSION_PATCH 0)
+ endif()
+
+ set(MPREAL_FIND_VERSION "${MPREAL_FIND_VERSION_MAJOR}.${MPREAL_FIND_VERSION_MINOR}.${MPREAL_FIND_VERSION_PATCH}")
+endif()
+
+# Check bugs
+# - https://github.com/advanpix/mpreal/issues/7
+# - https://github.com/advanpix/mpreal/issues/9
+set(MPREAL_TEST_PROGRAM "
+#include <mpreal.h>
+#include <algorithm>
+int main(int argc, char** argv) {
+ const mpfr::mpreal one = 1.0;
+ const mpfr::mpreal zero = 0.0;
+ using namespace std;
+ const mpfr::mpreal smaller = min(one, zero);
+ return 0;
+}")
+
+if(MPREAL_INCLUDES)
+
+ # Set MPREAL_VERSION
+
+ file(READ "${MPREAL_INCLUDES}/mpreal.h" _mpreal_version_header)
+
+ string(REGEX MATCH "define[ \t]+MPREAL_VERSION_MAJOR[ \t]+([0-9]+)" _mpreal_major_version_match "${_mpreal_version_header}")
+ set(MPREAL_MAJOR_VERSION "${CMAKE_MATCH_1}")
+ string(REGEX MATCH "define[ \t]+MPREAL_VERSION_MINOR[ \t]+([0-9]+)" _mpreal_minor_version_match "${_mpreal_version_header}")
+ set(MPREAL_MINOR_VERSION "${CMAKE_MATCH_1}")
+ string(REGEX MATCH "define[ \t]+MPREAL_VERSION_PATCHLEVEL[ \t]+([0-9]+)" _mpreal_patchlevel_version_match "${_mpreal_version_header}")
+ set(MPREAL_PATCHLEVEL_VERSION "${CMAKE_MATCH_1}")
+
+ set(MPREAL_VERSION ${MPREAL_MAJOR_VERSION}.${MPREAL_MINOR_VERSION}.${MPREAL_PATCHLEVEL_VERSION})
+
+ # Check whether found version exceeds minimum version
+
+ if(${MPREAL_VERSION} VERSION_LESS ${MPREAL_FIND_VERSION})
+ set(MPREAL_VERSION_OK FALSE)
+ message(STATUS "MPREAL version ${MPREAL_VERSION} found in ${MPREAL_INCLUDES}, "
+ "but at least version ${MPREAL_FIND_VERSION} is required")
+ else()
+ set(MPREAL_VERSION_OK TRUE)
+
+ list(APPEND MPREAL_INCLUDES "${MPFR_INCLUDES}" "${GMP_INCLUDES}")
+ list(REMOVE_DUPLICATES MPREAL_INCLUDES)
+
+ list(APPEND MPREAL_LIBRARIES "${MPFR_LIBRARIES}" "${GMP_LIBRARIES}")
+ list(REMOVE_DUPLICATES MPREAL_LIBRARIES)
+
+ # Make sure it compiles with the current compiler.
+ unset(MPREAL_WORKS CACHE)
+ include(CheckCXXSourceCompiles)
+ set(CMAKE_REQUIRED_INCLUDES "${MPREAL_INCLUDES}")
+ set(CMAKE_REQUIRED_LIBRARIES "${MPREAL_LIBRARIES}")
+ check_cxx_source_compiles("${MPREAL_TEST_PROGRAM}" MPREAL_WORKS)
+ endif()
+endif()
+
+include(FindPackageHandleStandardArgs)
+find_package_handle_standard_args(MPREAL DEFAULT_MSG
+ MPREAL_INCLUDES MPREAL_VERSION_OK MPREAL_WORKS)
+mark_as_advanced(MPREAL_INCLUDES)
diff --git a/cmake/FindMetis.cmake b/cmake/FindMetis.cmake
new file mode 100644
index 0000000..747f882
--- /dev/null
+++ b/cmake/FindMetis.cmake
@@ -0,0 +1,265 @@
+###
+#
+# @copyright (c) 2009-2014 The University of Tennessee and The University
+# of Tennessee Research Foundation.
+# All rights reserved.
+# @copyright (c) 2012-2014 Inria. All rights reserved.
+# @copyright (c) 2012-2014 Bordeaux INP, CNRS (LaBRI UMR 5800), Inria, Univ. Bordeaux. All rights reserved.
+#
+###
+#
+# - Find METIS include dirs and libraries
+# Use this module by invoking find_package with the form:
+# find_package(METIS
+# [REQUIRED] # Fail with error if metis is not found
+# )
+#
+# This module finds headers and metis library.
+# Results are reported in variables:
+# METIS_FOUND - True if headers and requested libraries were found
+# METIS_INCLUDE_DIRS - metis include directories
+# METIS_LIBRARY_DIRS - Link directories for metis libraries
+# METIS_LIBRARIES - metis component libraries to be linked
+#
+# The user can give specific paths where to find the libraries adding cmake
+# options at configure (ex: cmake path/to/project -DMETIS_DIR=path/to/metis):
+# METIS_DIR - Where to find the base directory of metis
+# METIS_INCDIR - Where to find the header files
+# METIS_LIBDIR - Where to find the library files
+# The module can also look for the following environment variables if paths
+# are not given as cmake variable: METIS_DIR, METIS_INCDIR, METIS_LIBDIR
+
+#=============================================================================
+# Copyright 2012-2013 Inria
+# Copyright 2012-2013 Emmanuel Agullo
+# Copyright 2012-2013 Mathieu Faverge
+# Copyright 2012 Cedric Castagnede
+# Copyright 2013 Florent Pruvost
+#
+# Distributed under the OSI-approved BSD License (the "License");
+# see accompanying file MORSE-Copyright.txt for details.
+#
+# This software is distributed WITHOUT ANY WARRANTY; without even the
+# implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.
+# See the License for more information.
+#=============================================================================
+# (To distribute this file outside of Morse, substitute the full
+# License text for the above reference.)
+
+if (NOT METIS_FOUND)
+ set(METIS_DIR "" CACHE PATH "Installation directory of METIS library")
+ if (NOT METIS_FIND_QUIETLY)
+ message(STATUS "A cache variable, namely METIS_DIR, has been set to specify the install directory of METIS")
+ endif()
+endif()
+
+# Looking for include
+# -------------------
+
+# Add system include paths to search include
+# ------------------------------------------
+unset(_inc_env)
+set(ENV_METIS_DIR "$ENV{METIS_DIR}")
+set(ENV_METIS_INCDIR "$ENV{METIS_INCDIR}")
+if(ENV_METIS_INCDIR)
+ list(APPEND _inc_env "${ENV_METIS_INCDIR}")
+elseif(ENV_METIS_DIR)
+ list(APPEND _inc_env "${ENV_METIS_DIR}")
+ list(APPEND _inc_env "${ENV_METIS_DIR}/include")
+ list(APPEND _inc_env "${ENV_METIS_DIR}/include/metis")
+else()
+ if(WIN32)
+ string(REPLACE ":" ";" _inc_env "$ENV{INCLUDE}")
+ else()
+ string(REPLACE ":" ";" _path_env "$ENV{INCLUDE}")
+ list(APPEND _inc_env "${_path_env}")
+ string(REPLACE ":" ";" _path_env "$ENV{C_INCLUDE_PATH}")
+ list(APPEND _inc_env "${_path_env}")
+ string(REPLACE ":" ";" _path_env "$ENV{CPATH}")
+ list(APPEND _inc_env "${_path_env}")
+ string(REPLACE ":" ";" _path_env "$ENV{INCLUDE_PATH}")
+ list(APPEND _inc_env "${_path_env}")
+ endif()
+endif()
+list(APPEND _inc_env "${CMAKE_PLATFORM_IMPLICIT_INCLUDE_DIRECTORIES}")
+list(APPEND _inc_env "${CMAKE_C_IMPLICIT_INCLUDE_DIRECTORIES}")
+list(REMOVE_DUPLICATES _inc_env)
+
+
+# Try to find the metis header in the given paths
+# -------------------------------------------------
+# call cmake macro to find the header path
+if(METIS_INCDIR)
+ set(METIS_metis.h_DIRS "METIS_metis.h_DIRS-NOTFOUND")
+ find_path(METIS_metis.h_DIRS
+ NAMES metis.h
+ HINTS ${METIS_INCDIR})
+else()
+ if(METIS_DIR)
+ set(METIS_metis.h_DIRS "METIS_metis.h_DIRS-NOTFOUND")
+ find_path(METIS_metis.h_DIRS
+ NAMES metis.h
+ HINTS ${METIS_DIR}
+ PATH_SUFFIXES "include" "include/metis")
+ else()
+ set(METIS_metis.h_DIRS "METIS_metis.h_DIRS-NOTFOUND")
+ find_path(METIS_metis.h_DIRS
+ NAMES metis.h
+ HINTS ${_inc_env})
+ endif()
+endif()
+mark_as_advanced(METIS_metis.h_DIRS)
+
+
+# If found, add path to cmake variable
+# ------------------------------------
+if (METIS_metis.h_DIRS)
+ set(METIS_INCLUDE_DIRS "${METIS_metis.h_DIRS}")
+else ()
+ set(METIS_INCLUDE_DIRS "METIS_INCLUDE_DIRS-NOTFOUND")
+ if(NOT METIS_FIND_QUIETLY)
+ message(STATUS "Looking for metis -- metis.h not found")
+ endif()
+endif()
+
+
+# Looking for lib
+# ---------------
+
+# Add system library paths to search lib
+# --------------------------------------
+unset(_lib_env)
+set(ENV_METIS_LIBDIR "$ENV{METIS_LIBDIR}")
+if(ENV_METIS_LIBDIR)
+ list(APPEND _lib_env "${ENV_METIS_LIBDIR}")
+elseif(ENV_METIS_DIR)
+ list(APPEND _lib_env "${ENV_METIS_DIR}")
+ list(APPEND _lib_env "${ENV_METIS_DIR}/lib")
+else()
+ if(WIN32)
+ string(REPLACE ":" ";" _lib_env "$ENV{LIB}")
+ else()
+ if(APPLE)
+ string(REPLACE ":" ";" _lib_env "$ENV{DYLD_LIBRARY_PATH}")
+ else()
+ string(REPLACE ":" ";" _lib_env "$ENV{LD_LIBRARY_PATH}")
+ endif()
+ list(APPEND _lib_env "${CMAKE_PLATFORM_IMPLICIT_LINK_DIRECTORIES}")
+ list(APPEND _lib_env "${CMAKE_C_IMPLICIT_LINK_DIRECTORIES}")
+ endif()
+endif()
+list(REMOVE_DUPLICATES _lib_env)
+
+# Try to find the metis lib in the given paths
+# ----------------------------------------------
+# call cmake macro to find the lib path
+if(METIS_LIBDIR)
+ set(METIS_metis_LIBRARY "METIS_metis_LIBRARY-NOTFOUND")
+ find_library(METIS_metis_LIBRARY
+ NAMES metis
+ HINTS ${METIS_LIBDIR})
+else()
+ if(METIS_DIR)
+ set(METIS_metis_LIBRARY "METIS_metis_LIBRARY-NOTFOUND")
+ find_library(METIS_metis_LIBRARY
+ NAMES metis
+ HINTS ${METIS_DIR}
+ PATH_SUFFIXES lib lib32 lib64)
+ else()
+ set(METIS_metis_LIBRARY "METIS_metis_LIBRARY-NOTFOUND")
+ find_library(METIS_metis_LIBRARY
+ NAMES metis
+ HINTS ${_lib_env})
+ endif()
+endif()
+mark_as_advanced(METIS_metis_LIBRARY)
+
+
+# If found, add path to cmake variable
+# ------------------------------------
+if (METIS_metis_LIBRARY)
+ get_filename_component(metis_lib_path "${METIS_metis_LIBRARY}" PATH)
+ # set cmake variables
+ set(METIS_LIBRARIES "${METIS_metis_LIBRARY}")
+ set(METIS_LIBRARY_DIRS "${metis_lib_path}")
+else ()
+ set(METIS_LIBRARIES "METIS_LIBRARIES-NOTFOUND")
+ set(METIS_LIBRARY_DIRS "METIS_LIBRARY_DIRS-NOTFOUND")
+ if(NOT METIS_FIND_QUIETLY)
+ message(STATUS "Looking for metis -- lib metis not found")
+ endif()
+endif ()
+
+# check a function to validate the find
+if(METIS_LIBRARIES)
+
+ set(REQUIRED_INCDIRS)
+ set(REQUIRED_LIBDIRS)
+ set(REQUIRED_LIBS)
+
+ # METIS
+ if (METIS_INCLUDE_DIRS)
+ set(REQUIRED_INCDIRS "${METIS_INCLUDE_DIRS}")
+ endif()
+ if (METIS_LIBRARY_DIRS)
+ set(REQUIRED_LIBDIRS "${METIS_LIBRARY_DIRS}")
+ endif()
+ set(REQUIRED_LIBS "${METIS_LIBRARIES}")
+ # m
+ find_library(M_LIBRARY NAMES m)
+ mark_as_advanced(M_LIBRARY)
+ if(M_LIBRARY)
+ list(APPEND REQUIRED_LIBS "-lm")
+ endif()
+
+ # set required libraries for link
+ set(CMAKE_REQUIRED_INCLUDES "${REQUIRED_INCDIRS}")
+ set(CMAKE_REQUIRED_LIBRARIES)
+ foreach(lib_dir ${REQUIRED_LIBDIRS})
+ list(APPEND CMAKE_REQUIRED_LIBRARIES "-L${lib_dir}")
+ endforeach()
+ list(APPEND CMAKE_REQUIRED_LIBRARIES "${REQUIRED_LIBS}")
+ string(REGEX REPLACE "^ -" "-" CMAKE_REQUIRED_LIBRARIES "${CMAKE_REQUIRED_LIBRARIES}")
+
+ # test link
+ unset(METIS_WORKS CACHE)
+ include(CheckFunctionExists)
+ check_function_exists(METIS_NodeND METIS_WORKS)
+ mark_as_advanced(METIS_WORKS)
+
+ if(NOT METIS_WORKS)
+ if(NOT METIS_FIND_QUIETLY)
+ message(STATUS "Looking for METIS : test of METIS_NodeND with METIS library fails")
+ message(STATUS "CMAKE_REQUIRED_LIBRARIES: ${CMAKE_REQUIRED_LIBRARIES}")
+ message(STATUS "CMAKE_REQUIRED_INCLUDES: ${CMAKE_REQUIRED_INCLUDES}")
+ message(STATUS "Check in CMakeFiles/CMakeError.log to figure out why it fails")
+ endif()
+ endif()
+ set(CMAKE_REQUIRED_INCLUDES)
+ set(CMAKE_REQUIRED_FLAGS)
+ set(CMAKE_REQUIRED_LIBRARIES)
+endif()
+
+if (METIS_LIBRARIES)
+ list(GET METIS_LIBRARIES 0 first_lib)
+ get_filename_component(first_lib_path "${first_lib}" PATH)
+ if (${first_lib_path} MATCHES "/lib(32|64)?$")
+ string(REGEX REPLACE "/lib(32|64)?$" "" not_cached_dir "${first_lib_path}")
+ set(METIS_DIR_FOUND "${not_cached_dir}" CACHE PATH "Installation directory of METIS library" FORCE)
+ else()
+ set(METIS_DIR_FOUND "${first_lib_path}" CACHE PATH "Installation directory of METIS library" FORCE)
+ endif()
+endif()
+mark_as_advanced(METIS_DIR)
+mark_as_advanced(METIS_DIR_FOUND)
+
+# check that METIS has been found
+# ---------------------------------
+include(FindPackageHandleStandardArgs)
+find_package_handle_standard_args(METIS DEFAULT_MSG
+ METIS_LIBRARIES
+ METIS_WORKS
+ METIS_INCLUDE_DIRS)
+#
+# TODO: Add possibility to check for specific functions in the library
+#
diff --git a/cmake/FindPASTIX.cmake b/cmake/FindPASTIX.cmake
new file mode 100644
index 0000000..db1427b
--- /dev/null
+++ b/cmake/FindPASTIX.cmake
@@ -0,0 +1,704 @@
+###
+#
+# @copyright (c) 2009-2014 The University of Tennessee and The University
+# of Tennessee Research Foundation.
+# All rights reserved.
+# @copyright (c) 2012-2014 Inria. All rights reserved.
+# @copyright (c) 2012-2014 Bordeaux INP, CNRS (LaBRI UMR 5800), Inria, Univ. Bordeaux. All rights reserved.
+#
+###
+#
+# - Find PASTIX include dirs and libraries
+# Use this module by invoking find_package with the form:
+# find_package(PASTIX
+# [REQUIRED] # Fail with error if pastix is not found
+# [COMPONENTS <comp1> <comp2> ...] # dependencies
+# )
+#
+# PASTIX depends on the following libraries:
+# - Threads, m, rt
+# - MPI
+# - HWLOC
+# - BLAS
+#
+# COMPONENTS are optional libraries PASTIX could be linked with,
+# Use it to drive detection of a specific compilation chain
+# COMPONENTS can be some of the following:
+# - MPI: to activate detection of the parallel MPI version (default)
+# it looks for Threads, HWLOC, BLAS, MPI and ScaLAPACK libraries
+# - SEQ: to activate detection of the sequential version (exclude MPI version)
+# - STARPU: to activate detection of StarPU version
+# it looks for MPI version of StarPU (default behaviour)
+# if SEQ and STARPU are given, it looks for a StarPU without MPI
+# - STARPU_CUDA: to activate detection of StarPU with CUDA
+# - STARPU_FXT: to activate detection of StarPU with FxT
+# - SCOTCH: to activate detection of PASTIX linked with SCOTCH
+# - PTSCOTCH: to activate detection of PASTIX linked with SCOTCH
+# - METIS: to activate detection of PASTIX linked with SCOTCH
+#
+# This module finds headers and pastix library.
+# Results are reported in variables:
+# PASTIX_FOUND - True if headers and requested libraries were found
+# PASTIX_LINKER_FLAGS - list of required linker flags (excluding -l and -L)
+# PASTIX_INCLUDE_DIRS - pastix include directories
+# PASTIX_LIBRARY_DIRS - Link directories for pastix libraries
+# PASTIX_LIBRARIES - pastix libraries
+# PASTIX_INCLUDE_DIRS_DEP - pastix + dependencies include directories
+# PASTIX_LIBRARY_DIRS_DEP - pastix + dependencies link directories
+# PASTIX_LIBRARIES_DEP - pastix libraries + dependencies
+#
+# The user can give specific paths where to find the libraries adding cmake
+# options at configure (ex: cmake path/to/project -DPASTIX_DIR=path/to/pastix):
+# PASTIX_DIR - Where to find the base directory of pastix
+# PASTIX_INCDIR - Where to find the header files
+# PASTIX_LIBDIR - Where to find the library files
+# The module can also look for the following environment variables if paths
+# are not given as cmake variable: PASTIX_DIR, PASTIX_INCDIR, PASTIX_LIBDIR
+
+#=============================================================================
+# Copyright 2012-2013 Inria
+# Copyright 2012-2013 Emmanuel Agullo
+# Copyright 2012-2013 Mathieu Faverge
+# Copyright 2012 Cedric Castagnede
+# Copyright 2013 Florent Pruvost
+#
+# Distributed under the OSI-approved BSD License (the "License");
+# see accompanying file MORSE-Copyright.txt for details.
+#
+# This software is distributed WITHOUT ANY WARRANTY; without even the
+# implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.
+# See the License for more information.
+#=============================================================================
+# (To distribute this file outside of Morse, substitute the full
+# License text for the above reference.)
+
+
+if (NOT PASTIX_FOUND)
+ set(PASTIX_DIR "" CACHE PATH "Installation directory of PASTIX library")
+ if (NOT PASTIX_FIND_QUIETLY)
+ message(STATUS "A cache variable, namely PASTIX_DIR, has been set to specify the install directory of PASTIX")
+ endif()
+endif()
+
+# Set the version to find
+set(PASTIX_LOOK_FOR_MPI ON)
+set(PASTIX_LOOK_FOR_SEQ OFF)
+set(PASTIX_LOOK_FOR_STARPU OFF)
+set(PASTIX_LOOK_FOR_STARPU_CUDA OFF)
+set(PASTIX_LOOK_FOR_STARPU_FXT OFF)
+set(PASTIX_LOOK_FOR_SCOTCH ON)
+set(PASTIX_LOOK_FOR_PTSCOTCH OFF)
+set(PASTIX_LOOK_FOR_METIS OFF)
+
+if( PASTIX_FIND_COMPONENTS )
+ foreach( component ${PASTIX_FIND_COMPONENTS} )
+ if (${component} STREQUAL "SEQ")
+ # means we look for the sequential version of PaStiX (without MPI)
+ set(PASTIX_LOOK_FOR_SEQ ON)
+ set(PASTIX_LOOK_FOR_MPI OFF)
+ endif()
+ if (${component} STREQUAL "MPI")
+ # means we look for the MPI version of PaStiX (default)
+ set(PASTIX_LOOK_FOR_SEQ OFF)
+ set(PASTIX_LOOK_FOR_MPI ON)
+ endif()
+ if (${component} STREQUAL "STARPU")
+ # means we look for PaStiX with StarPU
+ set(PASTIX_LOOK_FOR_STARPU ON)
+ endif()
+ if (${component} STREQUAL "STARPU_CUDA")
+ # means we look for PaStiX with StarPU + CUDA
+ set(PASTIX_LOOK_FOR_STARPU ON)
+ set(PASTIX_LOOK_FOR_STARPU_CUDA ON)
+ endif()
+ if (${component} STREQUAL "STARPU_FXT")
+ # means we look for PaStiX with StarPU + FxT
+ set(PASTIX_LOOK_FOR_STARPU_FXT ON)
+ endif()
+ if (${component} STREQUAL "SCOTCH")
+ set(PASTIX_LOOK_FOR_SCOTCH ON)
+ endif()
+ if (${component} STREQUAL "PTSCOTCH")
+ set(PASTIX_LOOK_FOR_PTSCOTCH ON)
+ endif()
+ if (${component} STREQUAL "METIS")
+ set(PASTIX_LOOK_FOR_METIS ON)
+ endif()
+ endforeach()
+endif()
+
+# Dependencies detection
+# ----------------------
+
+
+# Required dependencies
+# ---------------------
+include(CMakeFindDependencyMacro)
+if (NOT PASTIX_FIND_QUIETLY)
+ message(STATUS "Looking for PASTIX - Try to detect pthread")
+endif()
+if (PASTIX_FIND_REQUIRED)
+ find_dependency(Threads REQUIRED QUIET)
+else()
+ find_dependency(Threads QUIET)
+endif()
+set(PASTIX_EXTRA_LIBRARIES "")
+if( THREADS_FOUND )
+ list(APPEND PASTIX_EXTRA_LIBRARIES ${CMAKE_THREAD_LIBS_INIT})
+endif ()
+
+# Add math library to the list of extra
+# it normally exists on all common systems provided with a C compiler
+if (NOT PASTIX_FIND_QUIETLY)
+ message(STATUS "Looking for PASTIX - Try to detect libm")
+endif()
+set(PASTIX_M_LIBRARIES "")
+if(UNIX OR WIN32)
+ find_library(
+ PASTIX_M_m_LIBRARY
+ NAMES m
+ )
+ mark_as_advanced(PASTIX_M_m_LIBRARY)
+ if (PASTIX_M_m_LIBRARY)
+ list(APPEND PASTIX_M_LIBRARIES "${PASTIX_M_m_LIBRARY}")
+ list(APPEND PASTIX_EXTRA_LIBRARIES "${PASTIX_M_m_LIBRARY}")
+ else()
+ if (PASTIX_FIND_REQUIRED)
+ message(FATAL_ERROR "Could NOT find libm on your system."
+ "Are you sure to a have a C compiler installed?")
+ endif()
+ endif()
+endif()
+
+# Try to find librt (libposix4 - POSIX.1b Realtime Extensions library)
+# on Unix systems except Apple ones because it does not exist on it
+if (NOT PASTIX_FIND_QUIETLY)
+ message(STATUS "Looking for PASTIX - Try to detect librt")
+endif()
+set(PASTIX_RT_LIBRARIES "")
+if(UNIX AND NOT APPLE)
+ find_library(
+ PASTIX_RT_rt_LIBRARY
+ NAMES rt
+ )
+ mark_as_advanced(PASTIX_RT_rt_LIBRARY)
+ if (PASTIX_RT_rt_LIBRARY)
+ list(APPEND PASTIX_RT_LIBRARIES "${PASTIX_RT_rt_LIBRARY}")
+ list(APPEND PASTIX_EXTRA_LIBRARIES "${PASTIX_RT_rt_LIBRARY}")
+ else()
+ if (PASTIX_FIND_REQUIRED)
+ message(FATAL_ERROR "Could NOT find librt on your system")
+ endif()
+ endif()
+endif()
+
+# PASTIX depends on HWLOC
+#------------------------
+if (NOT PASTIX_FIND_QUIETLY)
+ message(STATUS "Looking for PASTIX - Try to detect HWLOC")
+endif()
+if (PASTIX_FIND_REQUIRED)
+ find_dependency(HWLOC REQUIRED QUIET)
+else()
+ find_dependency(HWLOC QUIET)
+endif()
+
+# PASTIX depends on BLAS
+#-----------------------
+if (NOT PASTIX_FIND_QUIETLY)
+ message(STATUS "Looking for PASTIX - Try to detect BLAS")
+endif()
+if (PASTIX_FIND_REQUIRED)
+ find_dependency(BLASEXT REQUIRED QUIET)
+else()
+ find_dependency(BLASEXT QUIET)
+endif()
+
+# Optional dependencies
+# ---------------------
+
+# PASTIX may depend on MPI
+#-------------------------
+if (NOT MPI_FOUND AND PASTIX_LOOK_FOR_MPI)
+ if (NOT PASTIX_FIND_QUIETLY)
+ message(STATUS "Looking for PASTIX - Try to detect MPI")
+ endif()
+ # allows to use an external mpi compilation by setting compilers with
+ # -DMPI_C_COMPILER=path/to/mpicc -DMPI_Fortran_COMPILER=path/to/mpif90
+ # at cmake configure
+ if(NOT MPI_C_COMPILER)
+ set(MPI_C_COMPILER mpicc)
+ endif()
+ if (PASTIX_FIND_REQUIRED AND PASTIX_FIND_REQUIRED_MPI)
+ find_dependency(MPI REQUIRED QUIET)
+ else()
+ find_dependency(MPI QUIET)
+ endif()
+ if (MPI_FOUND)
+ mark_as_advanced(MPI_LIBRARY)
+ mark_as_advanced(MPI_EXTRA_LIBRARY)
+ endif()
+endif ()
+
+# PASTIX may depend on STARPU
+#----------------------------
+if( NOT STARPU_FOUND AND PASTIX_LOOK_FOR_STARPU)
+
+ if (NOT PASTIX_FIND_QUIETLY)
+ message(STATUS "Looking for PASTIX - Try to detect StarPU")
+ endif()
+
+ set(PASTIX_STARPU_VERSION "1.1" CACHE STRING "oldest STARPU version desired")
+
+ # create list of components in order to make a single call to find_package(starpu...)
+ # we explicitly need a StarPU version built with hwloc
+ set(STARPU_COMPONENT_LIST "HWLOC")
+
+ # StarPU may depend on MPI
+ # allows to use an external mpi compilation by setting compilers with
+ # -DMPI_C_COMPILER=path/to/mpicc -DMPI_Fortran_COMPILER=path/to/mpif90
+ # at cmake configure
+ if (PASTIX_LOOK_FOR_MPI)
+ if(NOT MPI_C_COMPILER)
+ set(MPI_C_COMPILER mpicc)
+ endif()
+ list(APPEND STARPU_COMPONENT_LIST "MPI")
+ endif()
+ if (PASTIX_LOOK_FOR_STARPU_CUDA)
+ list(APPEND STARPU_COMPONENT_LIST "CUDA")
+ endif()
+ if (PASTIX_LOOK_FOR_STARPU_FXT)
+ list(APPEND STARPU_COMPONENT_LIST "FXT")
+ endif()
+ # set the list of optional dependencies we may discover
+ if (PASTIX_FIND_REQUIRED AND PASTIX_FIND_REQUIRED_STARPU)
+ find_dependency(STARPU ${PASTIX_STARPU_VERSION} REQUIRED
+ COMPONENTS ${STARPU_COMPONENT_LIST})
+ else()
+ find_dependency(STARPU ${PASTIX_STARPU_VERSION}
+ COMPONENTS ${STARPU_COMPONENT_LIST})
+ endif()
+
+endif()
+
+# PASTIX may depends on SCOTCH
+#-----------------------------
+if (NOT SCOTCH_FOUND AND PASTIX_LOOK_FOR_SCOTCH)
+ if (NOT PASTIX_FIND_QUIETLY)
+ message(STATUS "Looking for PASTIX - Try to detect SCOTCH")
+ endif()
+ if (PASTIX_FIND_REQUIRED AND PASTIX_FIND_REQUIRED_SCOTCH)
+ find_dependency(SCOTCH REQUIRED QUIET)
+ else()
+ find_dependency(SCOTCH QUIET)
+ endif()
+endif()
+
+# PASTIX may depends on PTSCOTCH
+#-------------------------------
+if (NOT PTSCOTCH_FOUND AND PASTIX_LOOK_FOR_PTSCOTCH)
+ if (NOT PASTIX_FIND_QUIETLY)
+ message(STATUS "Looking for PASTIX - Try to detect PTSCOTCH")
+ endif()
+ if (PASTIX_FIND_REQUIRED AND PASTIX_FIND_REQUIRED_PTSCOTCH)
+ find_dependency(PTSCOTCH REQUIRED QUIET)
+ else()
+ find_dependency(PTSCOTCH QUIET)
+ endif()
+endif()
+
+# PASTIX may depends on METIS
+#----------------------------
+if (NOT METIS_FOUND AND PASTIX_LOOK_FOR_METIS)
+ if (NOT PASTIX_FIND_QUIETLY)
+ message(STATUS "Looking for PASTIX - Try to detect METIS")
+ endif()
+ if (PASTIX_FIND_REQUIRED AND PASTIX_FIND_REQUIRED_METIS)
+ find_dependency(METIS REQUIRED QUIET)
+ else()
+ find_dependency(METIS QUIET)
+ endif()
+endif()
+
+# Error if pastix required and no partitioning lib found
+if (PASTIX_FIND_REQUIRED AND NOT SCOTCH_FOUND AND NOT PTSCOTCH_FOUND AND NOT METIS_FOUND)
+ message(FATAL_ERROR "Could NOT find any partitioning library on your system"
+ " (install scotch, ptscotch or metis)")
+endif()
+
+
+# Looking for PaStiX
+# ------------------
+
+# Looking for include
+# -------------------
+
+# Add system include paths to search include
+# ------------------------------------------
+unset(_inc_env)
+set(ENV_PASTIX_DIR "$ENV{PASTIX_DIR}")
+set(ENV_PASTIX_INCDIR "$ENV{PASTIX_INCDIR}")
+if(ENV_PASTIX_INCDIR)
+ list(APPEND _inc_env "${ENV_PASTIX_INCDIR}")
+elseif(ENV_PASTIX_DIR)
+ list(APPEND _inc_env "${ENV_PASTIX_DIR}")
+ list(APPEND _inc_env "${ENV_PASTIX_DIR}/include")
+ list(APPEND _inc_env "${ENV_PASTIX_DIR}/include/pastix")
+else()
+ if(WIN32)
+ string(REPLACE ":" ";" _inc_env "$ENV{INCLUDE}")
+ else()
+ string(REPLACE ":" ";" _path_env "$ENV{INCLUDE}")
+ list(APPEND _inc_env "${_path_env}")
+ string(REPLACE ":" ";" _path_env "$ENV{C_INCLUDE_PATH}")
+ list(APPEND _inc_env "${_path_env}")
+ string(REPLACE ":" ";" _path_env "$ENV{CPATH}")
+ list(APPEND _inc_env "${_path_env}")
+ string(REPLACE ":" ";" _path_env "$ENV{INCLUDE_PATH}")
+ list(APPEND _inc_env "${_path_env}")
+ endif()
+endif()
+list(APPEND _inc_env "${CMAKE_PLATFORM_IMPLICIT_INCLUDE_DIRECTORIES}")
+list(APPEND _inc_env "${CMAKE_C_IMPLICIT_INCLUDE_DIRECTORIES}")
+list(REMOVE_DUPLICATES _inc_env)
+
+
+# Try to find the pastix header in the given paths
+# ---------------------------------------------------
+# call cmake macro to find the header path
+if(PASTIX_INCDIR)
+ set(PASTIX_pastix.h_DIRS "PASTIX_pastix.h_DIRS-NOTFOUND")
+ find_path(PASTIX_pastix.h_DIRS
+ NAMES pastix.h
+ HINTS ${PASTIX_INCDIR})
+else()
+ if(PASTIX_DIR)
+ set(PASTIX_pastix.h_DIRS "PASTIX_pastix.h_DIRS-NOTFOUND")
+ find_path(PASTIX_pastix.h_DIRS
+ NAMES pastix.h
+ HINTS ${PASTIX_DIR}
+ PATH_SUFFIXES "include" "include/pastix")
+ else()
+ set(PASTIX_pastix.h_DIRS "PASTIX_pastix.h_DIRS-NOTFOUND")
+ find_path(PASTIX_pastix.h_DIRS
+ NAMES pastix.h
+ HINTS ${_inc_env}
+ PATH_SUFFIXES "pastix")
+ endif()
+endif()
+mark_as_advanced(PASTIX_pastix.h_DIRS)
+
+# If found, add path to cmake variable
+# ------------------------------------
+if (PASTIX_pastix.h_DIRS)
+ set(PASTIX_INCLUDE_DIRS "${PASTIX_pastix.h_DIRS}")
+else ()
+ set(PASTIX_INCLUDE_DIRS "PASTIX_INCLUDE_DIRS-NOTFOUND")
+ if(NOT PASTIX_FIND_QUIETLY)
+ message(STATUS "Looking for pastix -- pastix.h not found")
+ endif()
+endif()
+
+
+# Looking for lib
+# ---------------
+
+# Add system library paths to search lib
+# --------------------------------------
+unset(_lib_env)
+set(ENV_PASTIX_LIBDIR "$ENV{PASTIX_LIBDIR}")
+if(ENV_PASTIX_LIBDIR)
+ list(APPEND _lib_env "${ENV_PASTIX_LIBDIR}")
+elseif(ENV_PASTIX_DIR)
+ list(APPEND _lib_env "${ENV_PASTIX_DIR}")
+ list(APPEND _lib_env "${ENV_PASTIX_DIR}/lib")
+else()
+ if(WIN32)
+ string(REPLACE ":" ";" _lib_env "$ENV{LIB}")
+ else()
+ if(APPLE)
+ string(REPLACE ":" ";" _lib_env "$ENV{DYLD_LIBRARY_PATH}")
+ else()
+ string(REPLACE ":" ";" _lib_env "$ENV{LD_LIBRARY_PATH}")
+ endif()
+ list(APPEND _lib_env "${CMAKE_PLATFORM_IMPLICIT_LINK_DIRECTORIES}")
+ list(APPEND _lib_env "${CMAKE_C_IMPLICIT_LINK_DIRECTORIES}")
+ endif()
+endif()
+list(REMOVE_DUPLICATES _lib_env)
+
+# Try to find the pastix lib in the given paths
+# ------------------------------------------------
+
+# create list of libs to find
+set(PASTIX_libs_to_find "pastix_murge;pastix")
+
+# call cmake macro to find the lib path
+if(PASTIX_LIBDIR)
+ foreach(pastix_lib ${PASTIX_libs_to_find})
+ set(PASTIX_${pastix_lib}_LIBRARY "PASTIX_${pastix_lib}_LIBRARY-NOTFOUND")
+ find_library(PASTIX_${pastix_lib}_LIBRARY
+ NAMES ${pastix_lib}
+ HINTS ${PASTIX_LIBDIR})
+ endforeach()
+else()
+ if(PASTIX_DIR)
+ foreach(pastix_lib ${PASTIX_libs_to_find})
+ set(PASTIX_${pastix_lib}_LIBRARY "PASTIX_${pastix_lib}_LIBRARY-NOTFOUND")
+ find_library(PASTIX_${pastix_lib}_LIBRARY
+ NAMES ${pastix_lib}
+ HINTS ${PASTIX_DIR}
+ PATH_SUFFIXES lib lib32 lib64)
+ endforeach()
+ else()
+ foreach(pastix_lib ${PASTIX_libs_to_find})
+ set(PASTIX_${pastix_lib}_LIBRARY "PASTIX_${pastix_lib}_LIBRARY-NOTFOUND")
+ find_library(PASTIX_${pastix_lib}_LIBRARY
+ NAMES ${pastix_lib}
+ HINTS ${_lib_env})
+ endforeach()
+ endif()
+endif()
+
+# If found, add path to cmake variable
+# ------------------------------------
+foreach(pastix_lib ${PASTIX_libs_to_find})
+
+ get_filename_component(${pastix_lib}_lib_path ${PASTIX_${pastix_lib}_LIBRARY} PATH)
+ # set cmake variables (respects naming convention)
+ if (PASTIX_LIBRARIES)
+ list(APPEND PASTIX_LIBRARIES "${PASTIX_${pastix_lib}_LIBRARY}")
+ else()
+ set(PASTIX_LIBRARIES "${PASTIX_${pastix_lib}_LIBRARY}")
+ endif()
+ if (PASTIX_LIBRARY_DIRS)
+ list(APPEND PASTIX_LIBRARY_DIRS "${${pastix_lib}_lib_path}")
+ else()
+ set(PASTIX_LIBRARY_DIRS "${${pastix_lib}_lib_path}")
+ endif()
+ mark_as_advanced(PASTIX_${pastix_lib}_LIBRARY)
+
+endforeach()
+
+# check a function to validate the find
+if(PASTIX_LIBRARIES)
+
+ set(REQUIRED_LDFLAGS)
+ set(REQUIRED_INCDIRS)
+ set(REQUIRED_LIBDIRS)
+ set(REQUIRED_LIBS)
+
+ # PASTIX
+ if (PASTIX_INCLUDE_DIRS)
+ set(REQUIRED_INCDIRS "${PASTIX_INCLUDE_DIRS}")
+ endif()
+ foreach(libdir ${PASTIX_LIBRARY_DIRS})
+ if (libdir)
+ list(APPEND REQUIRED_LIBDIRS "${libdir}")
+ endif()
+ endforeach()
+ set(REQUIRED_LIBS "${PASTIX_LIBRARIES}")
+ # STARPU
+ if (PASTIX_LOOK_FOR_STARPU AND STARPU_FOUND)
+ if (STARPU_INCLUDE_DIRS_DEP)
+ list(APPEND REQUIRED_INCDIRS "${STARPU_INCLUDE_DIRS_DEP}")
+ elseif (STARPU_INCLUDE_DIRS)
+ list(APPEND REQUIRED_INCDIRS "${STARPU_INCLUDE_DIRS}")
+ endif()
+ if(STARPU_LIBRARY_DIRS_DEP)
+ list(APPEND REQUIRED_LIBDIRS "${STARPU_LIBRARY_DIRS_DEP}")
+ elseif(STARPU_LIBRARY_DIRS)
+ list(APPEND REQUIRED_LIBDIRS "${STARPU_LIBRARY_DIRS}")
+ endif()
+ if (STARPU_LIBRARIES_DEP)
+ list(APPEND REQUIRED_LIBS "${STARPU_LIBRARIES_DEP}")
+ elseif (STARPU_LIBRARIES)
+ foreach(lib ${STARPU_LIBRARIES})
+ if (EXISTS ${lib} OR ${lib} MATCHES "^-")
+ list(APPEND REQUIRED_LIBS "${lib}")
+ else()
+ list(APPEND REQUIRED_LIBS "-l${lib}")
+ endif()
+ endforeach()
+ endif()
+ endif()
+ # CUDA
+ if (PASTIX_LOOK_FOR_STARPU_CUDA AND CUDA_FOUND)
+ if (CUDA_INCLUDE_DIRS)
+ list(APPEND REQUIRED_INCDIRS "${CUDA_INCLUDE_DIRS}")
+ endif()
+ foreach(libdir ${CUDA_LIBRARY_DIRS})
+ if (libdir)
+ list(APPEND REQUIRED_LIBDIRS "${libdir}")
+ endif()
+ endforeach()
+ list(APPEND REQUIRED_LIBS "${CUDA_CUBLAS_LIBRARIES};${CUDA_LIBRARIES}")
+ endif()
+ # MPI
+ if (PASTIX_LOOK_FOR_MPI AND MPI_FOUND)
+ if (MPI_C_INCLUDE_PATH)
+ list(APPEND REQUIRED_INCDIRS "${MPI_C_INCLUDE_PATH}")
+ endif()
+ if (MPI_C_LINK_FLAGS)
+ if (${MPI_C_LINK_FLAGS} MATCHES " -")
+ string(REGEX REPLACE " -" "-" MPI_C_LINK_FLAGS ${MPI_C_LINK_FLAGS})
+ endif()
+ list(APPEND REQUIRED_LDFLAGS "${MPI_C_LINK_FLAGS}")
+ endif()
+ list(APPEND REQUIRED_LIBS "${MPI_C_LIBRARIES}")
+ endif()
+ # HWLOC
+ if (HWLOC_FOUND)
+ if (HWLOC_INCLUDE_DIRS)
+ list(APPEND REQUIRED_INCDIRS "${HWLOC_INCLUDE_DIRS}")
+ endif()
+ foreach(libdir ${HWLOC_LIBRARY_DIRS})
+ if (libdir)
+ list(APPEND REQUIRED_LIBDIRS "${libdir}")
+ endif()
+ endforeach()
+ foreach(lib ${HWLOC_LIBRARIES})
+ if (EXISTS ${lib} OR ${lib} MATCHES "^-")
+ list(APPEND REQUIRED_LIBS "${lib}")
+ else()
+ list(APPEND REQUIRED_LIBS "-l${lib}")
+ endif()
+ endforeach()
+ endif()
+ # BLAS
+ if (BLAS_FOUND)
+ if (BLAS_INCLUDE_DIRS)
+ list(APPEND REQUIRED_INCDIRS "${BLAS_INCLUDE_DIRS}")
+ endif()
+ foreach(libdir ${BLAS_LIBRARY_DIRS})
+ if (libdir)
+ list(APPEND REQUIRED_LIBDIRS "${libdir}")
+ endif()
+ endforeach()
+ list(APPEND REQUIRED_LIBS "${BLAS_LIBRARIES}")
+ if (BLAS_LINKER_FLAGS)
+ list(APPEND REQUIRED_LDFLAGS "${BLAS_LINKER_FLAGS}")
+ endif()
+ endif()
+ # SCOTCH
+ if (PASTIX_LOOK_FOR_SCOTCH AND SCOTCH_FOUND)
+ if (SCOTCH_INCLUDE_DIRS)
+ list(APPEND REQUIRED_INCDIRS "${SCOTCH_INCLUDE_DIRS}")
+ endif()
+ foreach(libdir ${SCOTCH_LIBRARY_DIRS})
+ if (libdir)
+ list(APPEND REQUIRED_LIBDIRS "${libdir}")
+ endif()
+ endforeach()
+ list(APPEND REQUIRED_LIBS "${SCOTCH_LIBRARIES}")
+ endif()
+ # PTSCOTCH
+ if (PASTIX_LOOK_FOR_PTSCOTCH AND PTSCOTCH_FOUND)
+ if (PTSCOTCH_INCLUDE_DIRS)
+ list(APPEND REQUIRED_INCDIRS "${PTSCOTCH_INCLUDE_DIRS}")
+ endif()
+ foreach(libdir ${PTSCOTCH_LIBRARY_DIRS})
+ if (libdir)
+ list(APPEND REQUIRED_LIBDIRS "${libdir}")
+ endif()
+ endforeach()
+ list(APPEND REQUIRED_LIBS "${PTSCOTCH_LIBRARIES}")
+ endif()
+ # METIS
+ if (PASTIX_LOOK_FOR_METIS AND METIS_FOUND)
+ if (METIS_INCLUDE_DIRS)
+ list(APPEND REQUIRED_INCDIRS "${METIS_INCLUDE_DIRS}")
+ endif()
+ foreach(libdir ${METIS_LIBRARY_DIRS})
+ if (libdir)
+ list(APPEND REQUIRED_LIBDIRS "${libdir}")
+ endif()
+ endforeach()
+ list(APPEND REQUIRED_LIBS "${METIS_LIBRARIES}")
+ endif()
+ # Fortran
+ if (CMAKE_C_COMPILER_ID MATCHES "GNU")
+ find_library(
+ FORTRAN_gfortran_LIBRARY
+ NAMES gfortran
+ HINTS ${_lib_env}
+ )
+ mark_as_advanced(FORTRAN_gfortran_LIBRARY)
+ if (FORTRAN_gfortran_LIBRARY)
+ list(APPEND REQUIRED_LIBS "${FORTRAN_gfortran_LIBRARY}")
+ endif()
+ elseif (CMAKE_C_COMPILER_ID MATCHES "Intel")
+ find_library(
+ FORTRAN_ifcore_LIBRARY
+ NAMES ifcore
+ HINTS ${_lib_env}
+ )
+ mark_as_advanced(FORTRAN_ifcore_LIBRARY)
+ if (FORTRAN_ifcore_LIBRARY)
+ list(APPEND REQUIRED_LIBS "${FORTRAN_ifcore_LIBRARY}")
+ endif()
+ endif()
+ # EXTRA LIBS such that pthread, m, rt
+ list(APPEND REQUIRED_LIBS ${PASTIX_EXTRA_LIBRARIES})
+
+ # set required libraries for link
+ set(CMAKE_REQUIRED_INCLUDES "${REQUIRED_INCDIRS}")
+ set(CMAKE_REQUIRED_LIBRARIES)
+ list(APPEND CMAKE_REQUIRED_LIBRARIES "${REQUIRED_LDFLAGS}")
+ foreach(lib_dir ${REQUIRED_LIBDIRS})
+ list(APPEND CMAKE_REQUIRED_LIBRARIES "-L${lib_dir}")
+ endforeach()
+ list(APPEND CMAKE_REQUIRED_LIBRARIES "${REQUIRED_LIBS}")
+ list(APPEND CMAKE_REQUIRED_FLAGS "${REQUIRED_FLAGS}")
+ string(REGEX REPLACE "^ -" "-" CMAKE_REQUIRED_LIBRARIES "${CMAKE_REQUIRED_LIBRARIES}")
+
+ # test link
+ unset(PASTIX_WORKS CACHE)
+ include(CheckFunctionExists)
+ check_function_exists(pastix PASTIX_WORKS)
+ mark_as_advanced(PASTIX_WORKS)
+
+ if(PASTIX_WORKS)
+ # save link with dependencies
+ set(PASTIX_LIBRARIES_DEP "${REQUIRED_LIBS}")
+ set(PASTIX_LIBRARY_DIRS_DEP "${REQUIRED_LIBDIRS}")
+ set(PASTIX_INCLUDE_DIRS_DEP "${REQUIRED_INCDIRS}")
+ set(PASTIX_LINKER_FLAGS "${REQUIRED_LDFLAGS}")
+ list(REMOVE_DUPLICATES PASTIX_LIBRARY_DIRS_DEP)
+ list(REMOVE_DUPLICATES PASTIX_INCLUDE_DIRS_DEP)
+ list(REMOVE_DUPLICATES PASTIX_LINKER_FLAGS)
+ else()
+ if(NOT PASTIX_FIND_QUIETLY)
+ message(STATUS "Looking for PASTIX : test of pastix() fails")
+ message(STATUS "CMAKE_REQUIRED_LIBRARIES: ${CMAKE_REQUIRED_LIBRARIES}")
+ message(STATUS "CMAKE_REQUIRED_INCLUDES: ${CMAKE_REQUIRED_INCLUDES}")
+ message(STATUS "Check in CMakeFiles/CMakeError.log to figure out why it fails")
+ message(STATUS "Maybe PASTIX is linked with specific libraries. "
+ "Have you tried with COMPONENTS (MPI/SEQ, STARPU, STARPU_CUDA, SCOTCH, PTSCOTCH, METIS)? "
+ "See the explanation in FindPASTIX.cmake.")
+ endif()
+ endif()
+ set(CMAKE_REQUIRED_INCLUDES)
+ set(CMAKE_REQUIRED_FLAGS)
+ set(CMAKE_REQUIRED_LIBRARIES)
+endif()
+
+if (PASTIX_LIBRARIES)
+ list(GET PASTIX_LIBRARIES 0 first_lib)
+ get_filename_component(first_lib_path "${first_lib}" PATH)
+ if (${first_lib_path} MATCHES "/lib(32|64)?$")
+ string(REGEX REPLACE "/lib(32|64)?$" "" not_cached_dir "${first_lib_path}")
+ set(PASTIX_DIR_FOUND "${not_cached_dir}" CACHE PATH "Installation directory of PASTIX library" FORCE)
+ else()
+ set(PASTIX_DIR_FOUND "${first_lib_path}" CACHE PATH "Installation directory of PASTIX library" FORCE)
+ endif()
+endif()
+mark_as_advanced(PASTIX_DIR)
+mark_as_advanced(PASTIX_DIR_FOUND)
+
+# check that PASTIX has been found
+# ---------------------------------
+include(FindPackageHandleStandardArgs)
+find_package_handle_standard_args(PASTIX DEFAULT_MSG
+ PASTIX_LIBRARIES
+ PASTIX_WORKS)
diff --git a/cmake/FindPTSCOTCH.cmake b/cmake/FindPTSCOTCH.cmake
new file mode 100644
index 0000000..6ccc743
--- /dev/null
+++ b/cmake/FindPTSCOTCH.cmake
@@ -0,0 +1,422 @@
+###
+#
+# @copyright (c) 2009-2014 The University of Tennessee and The University
+# of Tennessee Research Foundation.
+# All rights reserved.
+# @copyright (c) 2012-2016 Inria. All rights reserved.
+# @copyright (c) 2012-2014 Bordeaux INP, CNRS (LaBRI UMR 5800), Inria, Univ. Bordeaux. All rights reserved.
+#
+###
+#
+# - Find PTSCOTCH include dirs and libraries
+# Use this module by invoking find_package with the form:
+# find_package(PTSCOTCH
+# [REQUIRED] # Fail with error if ptscotch is not found
+# [COMPONENTS <comp1> <comp2> ...] # dependencies
+# )
+#
+# PTSCOTCH depends on the following libraries:
+# - Threads
+# - MPI
+#
+# COMPONENTS can be some of the following:
+# - ESMUMPS: to activate detection of PT-Scotch with the esmumps interface
+#
+# This module finds headers and ptscotch library.
+# Results are reported in variables:
+# PTSCOTCH_FOUND - True if headers and requested libraries were found
+# PTSCOTCH_LINKER_FLAGS - list of required linker flags (excluding -l and -L)
+# PTSCOTCH_INCLUDE_DIRS - ptscotch include directories
+# PTSCOTCH_LIBRARY_DIRS - Link directories for ptscotch libraries
+# PTSCOTCH_LIBRARIES - ptscotch component libraries to be linked
+# PTSCOTCH_INCLUDE_DIRS_DEP - ptscotch + dependencies include directories
+# PTSCOTCH_LIBRARY_DIRS_DEP - ptscotch + dependencies link directories
+# PTSCOTCH_LIBRARIES_DEP - ptscotch libraries + dependencies
+# PTSCOTCH_INTSIZE - Number of octets occupied by a SCOTCH_Num
+#
+# The user can give specific paths where to find the libraries adding cmake
+# options at configure (ex: cmake path/to/project -DPTSCOTCH=path/to/ptscotch):
+# PTSCOTCH_DIR - Where to find the base directory of ptscotch
+# PTSCOTCH_INCDIR - Where to find the header files
+# PTSCOTCH_LIBDIR - Where to find the library files
+# The module can also look for the following environment variables if paths
+# are not given as cmake variable: PTSCOTCH_DIR, PTSCOTCH_INCDIR, PTSCOTCH_LIBDIR
+
+#=============================================================================
+# Copyright 2012-2013 Inria
+# Copyright 2012-2013 Emmanuel Agullo
+# Copyright 2012-2013 Mathieu Faverge
+# Copyright 2012 Cedric Castagnede
+# Copyright 2013-2016 Florent Pruvost
+#
+# Distributed under the OSI-approved BSD License (the "License");
+# see accompanying file MORSE-Copyright.txt for details.
+#
+# This software is distributed WITHOUT ANY WARRANTY; without even the
+# implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.
+# See the License for more information.
+#=============================================================================
+# (To distribute this file outside of Morse, substitute the full
+# License text for the above reference.)
+
+if (NOT PTSCOTCH_FOUND)
+ set(PTSCOTCH_DIR "" CACHE PATH "Installation directory of PTSCOTCH library")
+ if (NOT PTSCOTCH_FIND_QUIETLY)
+ message(STATUS "A cache variable, namely PTSCOTCH_DIR, has been set to specify the install directory of PTSCOTCH")
+ endif()
+endif()
+
+# Set the version to find
+set(PTSCOTCH_LOOK_FOR_ESMUMPS OFF)
+
+if( PTSCOTCH_FIND_COMPONENTS )
+ foreach( component ${PTSCOTCH_FIND_COMPONENTS} )
+ if (${component} STREQUAL "ESMUMPS")
+ # means we look for esmumps library
+ set(PTSCOTCH_LOOK_FOR_ESMUMPS ON)
+ endif()
+ endforeach()
+endif()
+
+# PTSCOTCH depends on Threads, try to find it
+include(CMakeFindDependencyMacro)
+if (NOT THREADS_FOUND)
+ if (PTSCOTCH_FIND_REQUIRED)
+ find_dependency(Threads REQUIRED)
+ else()
+ find_dependency(Threads)
+ endif()
+endif()
+
+# PTSCOTCH depends on MPI, try to find it
+if (NOT MPI_FOUND)
+ if (PTSCOTCH_FIND_REQUIRED)
+ find_dependency(MPI REQUIRED)
+ else()
+ find_dependency(MPI)
+ endif()
+endif()
+
+# Looking for include
+# -------------------
+
+# Add system include paths to search include
+# ------------------------------------------
+unset(_inc_env)
+set(ENV_PTSCOTCH_DIR "$ENV{PTSCOTCH_DIR}")
+set(ENV_PTSCOTCH_INCDIR "$ENV{PTSCOTCH_INCDIR}")
+if(ENV_PTSCOTCH_INCDIR)
+ list(APPEND _inc_env "${ENV_PTSCOTCH_INCDIR}")
+elseif(ENV_PTSCOTCH_DIR)
+ list(APPEND _inc_env "${ENV_PTSCOTCH_DIR}")
+ list(APPEND _inc_env "${ENV_PTSCOTCH_DIR}/include")
+ list(APPEND _inc_env "${ENV_PTSCOTCH_DIR}/include/ptscotch")
+else()
+ if(WIN32)
+ string(REPLACE ":" ";" _inc_env "$ENV{INCLUDE}")
+ else()
+ string(REPLACE ":" ";" _path_env "$ENV{INCLUDE}")
+ list(APPEND _inc_env "${_path_env}")
+ string(REPLACE ":" ";" _path_env "$ENV{C_INCLUDE_PATH}")
+ list(APPEND _inc_env "${_path_env}")
+ string(REPLACE ":" ";" _path_env "$ENV{CPATH}")
+ list(APPEND _inc_env "${_path_env}")
+ string(REPLACE ":" ";" _path_env "$ENV{INCLUDE_PATH}")
+ list(APPEND _inc_env "${_path_env}")
+ endif()
+endif()
+list(APPEND _inc_env "${CMAKE_PLATFORM_IMPLICIT_INCLUDE_DIRECTORIES}")
+list(APPEND _inc_env "${CMAKE_C_IMPLICIT_INCLUDE_DIRECTORIES}")
+list(REMOVE_DUPLICATES _inc_env)
+
+
+# Try to find the ptscotch header in the given paths
+# -------------------------------------------------
+
+set(PTSCOTCH_hdrs_to_find "ptscotch.h;scotch.h")
+
+# call cmake macro to find the header path
+if(PTSCOTCH_INCDIR)
+ foreach(ptscotch_hdr ${PTSCOTCH_hdrs_to_find})
+ set(PTSCOTCH_${ptscotch_hdr}_DIRS "PTSCOTCH_${ptscotch_hdr}_DIRS-NOTFOUND")
+ find_path(PTSCOTCH_${ptscotch_hdr}_DIRS
+ NAMES ${ptscotch_hdr}
+ HINTS ${PTSCOTCH_INCDIR})
+ mark_as_advanced(PTSCOTCH_${ptscotch_hdr}_DIRS)
+ endforeach()
+else()
+ if(PTSCOTCH_DIR)
+ foreach(ptscotch_hdr ${PTSCOTCH_hdrs_to_find})
+ set(PTSCOTCH_${ptscotch_hdr}_DIRS "PTSCOTCH_${ptscotch_hdr}_DIRS-NOTFOUND")
+ find_path(PTSCOTCH_${ptscotch_hdr}_DIRS
+ NAMES ${ptscotch_hdr}
+ HINTS ${PTSCOTCH_DIR}
+ PATH_SUFFIXES "include" "include/scotch")
+ mark_as_advanced(PTSCOTCH_${ptscotch_hdr}_DIRS)
+ endforeach()
+ else()
+ foreach(ptscotch_hdr ${PTSCOTCH_hdrs_to_find})
+ set(PTSCOTCH_${ptscotch_hdr}_DIRS "PTSCOTCH_${ptscotch_hdr}_DIRS-NOTFOUND")
+ find_path(PTSCOTCH_${ptscotch_hdr}_DIRS
+ NAMES ${ptscotch_hdr}
+ HINTS ${_inc_env}
+ PATH_SUFFIXES "scotch")
+ mark_as_advanced(PTSCOTCH_${ptscotch_hdr}_DIRS)
+ endforeach()
+ endif()
+endif()
+
+# If found, add path to cmake variable
+# ------------------------------------
+foreach(ptscotch_hdr ${PTSCOTCH_hdrs_to_find})
+ if (PTSCOTCH_${ptscotch_hdr}_DIRS)
+ list(APPEND PTSCOTCH_INCLUDE_DIRS "${PTSCOTCH_${ptscotch_hdr}_DIRS}")
+ else ()
+ if (NOT PTSCOTCH_FIND_QUIETLY)
+ message(STATUS "Looking for ptscotch -- ${ptscotch_hdr} not found")
+ endif()
+ endif()
+endforeach()
+list(REMOVE_DUPLICATES PTSCOTCH_INCLUDE_DIRS)
+
+# Looking for lib
+# ---------------
+
+# Add system library paths to search lib
+# --------------------------------------
+unset(_lib_env)
+set(ENV_PTSCOTCH_LIBDIR "$ENV{PTSCOTCH_LIBDIR}")
+if(ENV_PTSCOTCH_LIBDIR)
+ list(APPEND _lib_env "${ENV_PTSCOTCH_LIBDIR}")
+elseif(ENV_PTSCOTCH_DIR)
+ list(APPEND _lib_env "${ENV_PTSCOTCH_DIR}")
+ list(APPEND _lib_env "${ENV_PTSCOTCH_DIR}/lib")
+else()
+ if(WIN32)
+ string(REPLACE ":" ";" _lib_env "$ENV{LIB}")
+ else()
+ if(APPLE)
+ string(REPLACE ":" ";" _lib_env "$ENV{DYLD_LIBRARY_PATH}")
+ else()
+ string(REPLACE ":" ";" _lib_env "$ENV{LD_LIBRARY_PATH}")
+ endif()
+ list(APPEND _lib_env "${CMAKE_PLATFORM_IMPLICIT_LINK_DIRECTORIES}")
+ list(APPEND _lib_env "${CMAKE_C_IMPLICIT_LINK_DIRECTORIES}")
+ endif()
+endif()
+list(REMOVE_DUPLICATES _lib_env)
+
+# Try to find the ptscotch lib in the given paths
+# ----------------------------------------------
+
+set(PTSCOTCH_libs_to_find "ptscotch;ptscotcherr")
+if (PTSCOTCH_LOOK_FOR_ESMUMPS)
+ list(INSERT PTSCOTCH_libs_to_find 0 "ptesmumps")
+ list(APPEND PTSCOTCH_libs_to_find "esmumps" )
+endif()
+list(APPEND PTSCOTCH_libs_to_find "scotch;scotcherr")
+
+# call cmake macro to find the lib path
+if(PTSCOTCH_LIBDIR)
+ foreach(ptscotch_lib ${PTSCOTCH_libs_to_find})
+ set(PTSCOTCH_${ptscotch_lib}_LIBRARY "PTSCOTCH_${ptscotch_lib}_LIBRARY-NOTFOUND")
+ find_library(PTSCOTCH_${ptscotch_lib}_LIBRARY
+ NAMES ${ptscotch_lib}
+ HINTS ${PTSCOTCH_LIBDIR})
+ endforeach()
+else()
+ if(PTSCOTCH_DIR)
+ foreach(ptscotch_lib ${PTSCOTCH_libs_to_find})
+ set(PTSCOTCH_${ptscotch_lib}_LIBRARY "PTSCOTCH_${ptscotch_lib}_LIBRARY-NOTFOUND")
+ find_library(PTSCOTCH_${ptscotch_lib}_LIBRARY
+ NAMES ${ptscotch_lib}
+ HINTS ${PTSCOTCH_DIR}
+ PATH_SUFFIXES lib lib32 lib64)
+ endforeach()
+ else()
+ foreach(ptscotch_lib ${PTSCOTCH_libs_to_find})
+ set(PTSCOTCH_${ptscotch_lib}_LIBRARY "PTSCOTCH_${ptscotch_lib}_LIBRARY-NOTFOUND")
+ find_library(PTSCOTCH_${ptscotch_lib}_LIBRARY
+ NAMES ${ptscotch_lib}
+ HINTS ${_lib_env})
+ endforeach()
+ endif()
+endif()
+
+set(PTSCOTCH_LIBRARIES "")
+set(PTSCOTCH_LIBRARY_DIRS "")
+# If found, add path to cmake variable
+# ------------------------------------
+foreach(ptscotch_lib ${PTSCOTCH_libs_to_find})
+
+ if (PTSCOTCH_${ptscotch_lib}_LIBRARY)
+ get_filename_component(${ptscotch_lib}_lib_path "${PTSCOTCH_${ptscotch_lib}_LIBRARY}" PATH)
+ # set cmake variables
+ list(APPEND PTSCOTCH_LIBRARIES "${PTSCOTCH_${ptscotch_lib}_LIBRARY}")
+ list(APPEND PTSCOTCH_LIBRARY_DIRS "${${ptscotch_lib}_lib_path}")
+ else ()
+ if (NOT PTSCOTCH_FIND_QUIETLY)
+ message(STATUS "Looking for ptscotch -- lib ${ptscotch_lib} not found")
+ endif()
+ endif ()
+
+ mark_as_advanced(PTSCOTCH_${ptscotch_lib}_LIBRARY)
+
+endforeach()
+list(REMOVE_DUPLICATES PTSCOTCH_LIBRARY_DIRS)
+
+# check a function to validate the find
+if(PTSCOTCH_LIBRARIES)
+
+ set(REQUIRED_LDFLAGS)
+ set(REQUIRED_INCDIRS)
+ set(REQUIRED_LIBDIRS)
+ set(REQUIRED_LIBS)
+
+ # PTSCOTCH
+ if (PTSCOTCH_INCLUDE_DIRS)
+ set(REQUIRED_INCDIRS "${PTSCOTCH_INCLUDE_DIRS}")
+ endif()
+ if (PTSCOTCH_LIBRARY_DIRS)
+ set(REQUIRED_LIBDIRS "${PTSCOTCH_LIBRARY_DIRS}")
+ endif()
+ set(REQUIRED_LIBS "${PTSCOTCH_LIBRARIES}")
+ # MPI
+ if (MPI_FOUND)
+ if (MPI_C_INCLUDE_PATH)
+ list(APPEND CMAKE_REQUIRED_INCLUDES "${MPI_C_INCLUDE_PATH}")
+ endif()
+ if (MPI_C_LINK_FLAGS)
+ if (${MPI_C_LINK_FLAGS} MATCHES " -")
+ string(REGEX REPLACE " -" "-" MPI_C_LINK_FLAGS ${MPI_C_LINK_FLAGS})
+ endif()
+ list(APPEND REQUIRED_LDFLAGS "${MPI_C_LINK_FLAGS}")
+ endif()
+ list(APPEND REQUIRED_LIBS "${MPI_C_LIBRARIES}")
+ endif()
+ # THREADS
+ if(CMAKE_THREAD_LIBS_INIT)
+ list(APPEND REQUIRED_LIBS "${CMAKE_THREAD_LIBS_INIT}")
+ endif()
+ set(Z_LIBRARY "Z_LIBRARY-NOTFOUND")
+ find_library(Z_LIBRARY NAMES z)
+ mark_as_advanced(Z_LIBRARY)
+ if(Z_LIBRARY)
+ list(APPEND REQUIRED_LIBS "-lz")
+ endif()
+ set(M_LIBRARY "M_LIBRARY-NOTFOUND")
+ find_library(M_LIBRARY NAMES m)
+ mark_as_advanced(M_LIBRARY)
+ if(M_LIBRARY)
+ list(APPEND REQUIRED_LIBS "-lm")
+ endif()
+ set(RT_LIBRARY "RT_LIBRARY-NOTFOUND")
+ find_library(RT_LIBRARY NAMES rt)
+ mark_as_advanced(RT_LIBRARY)
+ if(RT_LIBRARY)
+ list(APPEND REQUIRED_LIBS "-lrt")
+ endif()
+
+ # set required libraries for link
+ set(CMAKE_REQUIRED_INCLUDES "${REQUIRED_INCDIRS}")
+ set(CMAKE_REQUIRED_LIBRARIES)
+ list(APPEND CMAKE_REQUIRED_LIBRARIES "${REQUIRED_LDFLAGS}")
+ foreach(lib_dir ${REQUIRED_LIBDIRS})
+ list(APPEND CMAKE_REQUIRED_LIBRARIES "-L${lib_dir}")
+ endforeach()
+ list(APPEND CMAKE_REQUIRED_LIBRARIES "${REQUIRED_LIBS}")
+ list(APPEND CMAKE_REQUIRED_FLAGS "${REQUIRED_FLAGS}")
+ string(REGEX REPLACE "^ -" "-" CMAKE_REQUIRED_LIBRARIES "${CMAKE_REQUIRED_LIBRARIES}")
+
+ # test link
+ unset(PTSCOTCH_WORKS CACHE)
+ include(CheckFunctionExists)
+ check_function_exists(SCOTCH_dgraphInit PTSCOTCH_WORKS)
+ mark_as_advanced(PTSCOTCH_WORKS)
+
+ if(PTSCOTCH_WORKS)
+ # save link with dependencies
+ set(PTSCOTCH_LIBRARIES_DEP "${REQUIRED_LIBS}")
+ set(PTSCOTCH_LIBRARY_DIRS_DEP "${REQUIRED_LIBDIRS}")
+ set(PTSCOTCH_INCLUDE_DIRS_DEP "${REQUIRED_INCDIRS}")
+ set(PTSCOTCH_LINKER_FLAGS "${REQUIRED_LDFLAGS}")
+ list(REMOVE_DUPLICATES PTSCOTCH_LIBRARY_DIRS_DEP)
+ list(REMOVE_DUPLICATES PTSCOTCH_INCLUDE_DIRS_DEP)
+ list(REMOVE_DUPLICATES PTSCOTCH_LINKER_FLAGS)
+ else()
+ if(NOT PTSCOTCH_FIND_QUIETLY)
+ message(STATUS "Looking for PTSCOTCH : test of SCOTCH_dgraphInit with PTSCOTCH library fails")
+ message(STATUS "CMAKE_REQUIRED_LIBRARIES: ${CMAKE_REQUIRED_LIBRARIES}")
+ message(STATUS "CMAKE_REQUIRED_INCLUDES: ${CMAKE_REQUIRED_INCLUDES}")
+ message(STATUS "Check in CMakeFiles/CMakeError.log to figure out why it fails")
+ endif()
+ endif()
+ set(CMAKE_REQUIRED_INCLUDES)
+ set(CMAKE_REQUIRED_FLAGS)
+ set(CMAKE_REQUIRED_LIBRARIES)
+endif()
+
+if (PTSCOTCH_LIBRARIES)
+ list(GET PTSCOTCH_LIBRARIES 0 first_lib)
+ get_filename_component(first_lib_path "${first_lib}" PATH)
+ if (${first_lib_path} MATCHES "/lib(32|64)?$")
+ string(REGEX REPLACE "/lib(32|64)?$" "" not_cached_dir "${first_lib_path}")
+ set(PTSCOTCH_DIR_FOUND "${not_cached_dir}" CACHE PATH "Installation directory of PTSCOTCH library" FORCE)
+ else()
+ set(PTSCOTCH_DIR_FOUND "${first_lib_path}" CACHE PATH "Installation directory of PTSCOTCH library" FORCE)
+ endif()
+endif()
+mark_as_advanced(PTSCOTCH_DIR)
+mark_as_advanced(PTSCOTCH_DIR_FOUND)
+
+# Check the size of SCOTCH_Num
+# ---------------------------------
+set(CMAKE_REQUIRED_INCLUDES ${PTSCOTCH_INCLUDE_DIRS})
+
+include(CheckCSourceRuns)
+#stdio.h and stdint.h should be included by scotch.h directly
+set(PTSCOTCH_C_TEST_SCOTCH_Num_4 "
+#include <stdio.h>
+#include <stdint.h>
+#include <ptscotch.h>
+int main(int argc, char **argv) {
+ if (sizeof(SCOTCH_Num) == 4)
+ return 0;
+ else
+ return 1;
+}
+")
+
+set(PTSCOTCH_C_TEST_SCOTCH_Num_8 "
+#include <stdio.h>
+#include <stdint.h>
+#include <ptscotch.h>
+int main(int argc, char **argv) {
+ if (sizeof(SCOTCH_Num) == 8)
+ return 0;
+ else
+ return 1;
+}
+")
+check_c_source_runs("${PTSCOTCH_C_TEST_SCOTCH_Num_4}" PTSCOTCH_Num_4)
+if(NOT PTSCOTCH_Num_4)
+ check_c_source_runs("${PTSCOTCH_C_TEST_SCOTCH_Num_8}" PTSCOTCH_Num_8)
+ if(NOT PTSCOTCH_Num_8)
+ set(PTSCOTCH_INTSIZE -1)
+ else()
+ set(PTSCOTCH_INTSIZE 8)
+ endif()
+else()
+ set(PTSCOTCH_INTSIZE 4)
+endif()
+set(CMAKE_REQUIRED_INCLUDES "")
+
+# check that PTSCOTCH has been found
+# ---------------------------------
+include(FindPackageHandleStandardArgs)
+find_package_handle_standard_args(PTSCOTCH DEFAULT_MSG
+ PTSCOTCH_LIBRARIES
+ PTSCOTCH_WORKS)
+#
+# TODO: Add possibility to check for specific functions in the library
+#
diff --git a/cmake/FindSCOTCH.cmake b/cmake/FindSCOTCH.cmake
new file mode 100644
index 0000000..11b971a
--- /dev/null
+++ b/cmake/FindSCOTCH.cmake
@@ -0,0 +1,370 @@
+###
+#
+# @copyright (c) 2009-2014 The University of Tennessee and The University
+# of Tennessee Research Foundation.
+# All rights reserved.
+# @copyright (c) 2012-2014 Inria. All rights reserved.
+# @copyright (c) 2012-2014 Bordeaux INP, CNRS (LaBRI UMR 5800), Inria, Univ. Bordeaux. All rights reserved.
+#
+###
+#
+# - Find SCOTCH include dirs and libraries
+# Use this module by invoking find_package with the form:
+# find_package(SCOTCH
+# [REQUIRED] # Fail with error if scotch is not found
+# [COMPONENTS <comp1> <comp2> ...] # dependencies
+# )
+#
+# COMPONENTS can be some of the following:
+# - ESMUMPS: to activate detection of Scotch with the esmumps interface
+#
+# This module finds headers and scotch library.
+# Results are reported in variables:
+# SCOTCH_FOUND - True if headers and requested libraries were found
+# SCOTCH_INCLUDE_DIRS - scotch include directories
+# SCOTCH_LIBRARY_DIRS - Link directories for scotch libraries
+# SCOTCH_LIBRARIES - scotch component libraries to be linked
+# SCOTCH_INTSIZE - Number of octets occupied by a SCOTCH_Num
+#
+# The user can give specific paths where to find the libraries adding cmake
+# options at configure (ex: cmake path/to/project -DSCOTCH=path/to/scotch):
+# SCOTCH_DIR - Where to find the base directory of scotch
+# SCOTCH_INCDIR - Where to find the header files
+# SCOTCH_LIBDIR - Where to find the library files
+# The module can also look for the following environment variables if paths
+# are not given as cmake variable: SCOTCH_DIR, SCOTCH_INCDIR, SCOTCH_LIBDIR
+
+#=============================================================================
+# Copyright 2012-2013 Inria
+# Copyright 2012-2013 Emmanuel Agullo
+# Copyright 2012-2013 Mathieu Faverge
+# Copyright 2012 Cedric Castagnede
+# Copyright 2013 Florent Pruvost
+#
+# Distributed under the OSI-approved BSD License (the "License");
+# see accompanying file MORSE-Copyright.txt for details.
+#
+# This software is distributed WITHOUT ANY WARRANTY; without even the
+# implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.
+# See the License for more information.
+#=============================================================================
+# (To distribute this file outside of Morse, substitute the full
+# License text for the above reference.)
+
+if (NOT SCOTCH_FOUND)
+ set(SCOTCH_DIR "" CACHE PATH "Installation directory of SCOTCH library")
+ if (NOT SCOTCH_FIND_QUIETLY)
+ message(STATUS "A cache variable, namely SCOTCH_DIR, has been set to specify the install directory of SCOTCH")
+ endif()
+endif()
+
+# Set the version to find
+set(SCOTCH_LOOK_FOR_ESMUMPS OFF)
+
+if( SCOTCH_FIND_COMPONENTS )
+ foreach( component ${SCOTCH_FIND_COMPONENTS} )
+ if (${component} STREQUAL "ESMUMPS")
+ # means we look for esmumps library
+ set(SCOTCH_LOOK_FOR_ESMUMPS ON)
+ endif()
+ endforeach()
+endif()
+
+# SCOTCH may depend on Threads, try to find it
+include(CMakeFindDependencyMacro)
+if (NOT THREADS_FOUND)
+ if (SCOTCH_FIND_REQUIRED)
+ find_dependency(Threads REQUIRED)
+ else()
+ find_dependency(Threads)
+ endif()
+endif()
+
+# Looking for include
+# -------------------
+
+# Add system include paths to search include
+# ------------------------------------------
+unset(_inc_env)
+set(ENV_SCOTCH_DIR "$ENV{SCOTCH_DIR}")
+set(ENV_SCOTCH_INCDIR "$ENV{SCOTCH_INCDIR}")
+if(ENV_SCOTCH_INCDIR)
+ list(APPEND _inc_env "${ENV_SCOTCH_INCDIR}")
+elseif(ENV_SCOTCH_DIR)
+ list(APPEND _inc_env "${ENV_SCOTCH_DIR}")
+ list(APPEND _inc_env "${ENV_SCOTCH_DIR}/include")
+ list(APPEND _inc_env "${ENV_SCOTCH_DIR}/include/scotch")
+else()
+ if(WIN32)
+ string(REPLACE ":" ";" _inc_env "$ENV{INCLUDE}")
+ else()
+ string(REPLACE ":" ";" _path_env "$ENV{INCLUDE}")
+ list(APPEND _inc_env "${_path_env}")
+ string(REPLACE ":" ";" _path_env "$ENV{C_INCLUDE_PATH}")
+ list(APPEND _inc_env "${_path_env}")
+ string(REPLACE ":" ";" _path_env "$ENV{CPATH}")
+ list(APPEND _inc_env "${_path_env}")
+ string(REPLACE ":" ";" _path_env "$ENV{INCLUDE_PATH}")
+ list(APPEND _inc_env "${_path_env}")
+ endif()
+endif()
+list(APPEND _inc_env "${CMAKE_PLATFORM_IMPLICIT_INCLUDE_DIRECTORIES}")
+list(APPEND _inc_env "${CMAKE_C_IMPLICIT_INCLUDE_DIRECTORIES}")
+list(REMOVE_DUPLICATES _inc_env)
+
+
+# Try to find the scotch header in the given paths
+# -------------------------------------------------
+# call cmake macro to find the header path
+if(SCOTCH_INCDIR)
+ set(SCOTCH_scotch.h_DIRS "SCOTCH_scotch.h_DIRS-NOTFOUND")
+ find_path(SCOTCH_scotch.h_DIRS
+ NAMES scotch.h
+ HINTS ${SCOTCH_INCDIR})
+else()
+ if(SCOTCH_DIR)
+ set(SCOTCH_scotch.h_DIRS "SCOTCH_scotch.h_DIRS-NOTFOUND")
+ find_path(SCOTCH_scotch.h_DIRS
+ NAMES scotch.h
+ HINTS ${SCOTCH_DIR}
+ PATH_SUFFIXES "include" "include/scotch")
+ else()
+ set(SCOTCH_scotch.h_DIRS "SCOTCH_scotch.h_DIRS-NOTFOUND")
+ find_path(SCOTCH_scotch.h_DIRS
+ NAMES scotch.h
+ HINTS ${_inc_env}
+ PATH_SUFFIXES "scotch")
+ endif()
+endif()
+mark_as_advanced(SCOTCH_scotch.h_DIRS)
+
+# If found, add path to cmake variable
+# ------------------------------------
+if (SCOTCH_scotch.h_DIRS)
+ set(SCOTCH_INCLUDE_DIRS "${SCOTCH_scotch.h_DIRS}")
+else ()
+ set(SCOTCH_INCLUDE_DIRS "SCOTCH_INCLUDE_DIRS-NOTFOUND")
+ if (NOT SCOTCH_FIND_QUIETLY)
+ message(STATUS "Looking for scotch -- scotch.h not found")
+ endif()
+endif()
+list(REMOVE_DUPLICATES SCOTCH_INCLUDE_DIRS)
+
+# Looking for lib
+# ---------------
+
+# Add system library paths to search lib
+# --------------------------------------
+unset(_lib_env)
+set(ENV_SCOTCH_LIBDIR "$ENV{SCOTCH_LIBDIR}")
+if(ENV_SCOTCH_LIBDIR)
+ list(APPEND _lib_env "${ENV_SCOTCH_LIBDIR}")
+elseif(ENV_SCOTCH_DIR)
+ list(APPEND _lib_env "${ENV_SCOTCH_DIR}")
+ list(APPEND _lib_env "${ENV_SCOTCH_DIR}/lib")
+else()
+ if(WIN32)
+ string(REPLACE ":" ";" _lib_env "$ENV{LIB}")
+ else()
+ if(APPLE)
+ string(REPLACE ":" ";" _lib_env "$ENV{DYLD_LIBRARY_PATH}")
+ else()
+ string(REPLACE ":" ";" _lib_env "$ENV{LD_LIBRARY_PATH}")
+ endif()
+ list(APPEND _lib_env "${CMAKE_PLATFORM_IMPLICIT_LINK_DIRECTORIES}")
+ list(APPEND _lib_env "${CMAKE_C_IMPLICIT_LINK_DIRECTORIES}")
+ endif()
+endif()
+list(REMOVE_DUPLICATES _lib_env)
+
+# Try to find the scotch lib in the given paths
+# ----------------------------------------------
+
+set(SCOTCH_libs_to_find "scotch;scotcherrexit")
+if (SCOTCH_LOOK_FOR_ESMUMPS)
+ list(INSERT SCOTCH_libs_to_find 0 "esmumps")
+endif()
+
+# call cmake macro to find the lib path
+if(SCOTCH_LIBDIR)
+ foreach(scotch_lib ${SCOTCH_libs_to_find})
+ set(SCOTCH_${scotch_lib}_LIBRARY "SCOTCH_${scotch_lib}_LIBRARY-NOTFOUND")
+ find_library(SCOTCH_${scotch_lib}_LIBRARY
+ NAMES ${scotch_lib}
+ HINTS ${SCOTCH_LIBDIR})
+ endforeach()
+else()
+ if(SCOTCH_DIR)
+ foreach(scotch_lib ${SCOTCH_libs_to_find})
+ set(SCOTCH_${scotch_lib}_LIBRARY "SCOTCH_${scotch_lib}_LIBRARY-NOTFOUND")
+ find_library(SCOTCH_${scotch_lib}_LIBRARY
+ NAMES ${scotch_lib}
+ HINTS ${SCOTCH_DIR}
+ PATH_SUFFIXES lib lib32 lib64)
+ endforeach()
+ else()
+ foreach(scotch_lib ${SCOTCH_libs_to_find})
+ set(SCOTCH_${scotch_lib}_LIBRARY "SCOTCH_${scotch_lib}_LIBRARY-NOTFOUND")
+ find_library(SCOTCH_${scotch_lib}_LIBRARY
+ NAMES ${scotch_lib}
+ HINTS ${_lib_env})
+ endforeach()
+ endif()
+endif()
+
+set(SCOTCH_LIBRARIES "")
+set(SCOTCH_LIBRARY_DIRS "")
+# If found, add path to cmake variable
+# ------------------------------------
+foreach(scotch_lib ${SCOTCH_libs_to_find})
+
+ if (SCOTCH_${scotch_lib}_LIBRARY)
+ get_filename_component(${scotch_lib}_lib_path "${SCOTCH_${scotch_lib}_LIBRARY}" PATH)
+ # set cmake variables
+ list(APPEND SCOTCH_LIBRARIES "${SCOTCH_${scotch_lib}_LIBRARY}")
+ list(APPEND SCOTCH_LIBRARY_DIRS "${${scotch_lib}_lib_path}")
+ else ()
+ list(APPEND SCOTCH_LIBRARIES "${SCOTCH_${scotch_lib}_LIBRARY}")
+ if (NOT SCOTCH_FIND_QUIETLY)
+ message(STATUS "Looking for scotch -- lib ${scotch_lib} not found")
+ endif()
+ endif ()
+
+ mark_as_advanced(SCOTCH_${scotch_lib}_LIBRARY)
+
+endforeach()
+list(REMOVE_DUPLICATES SCOTCH_LIBRARY_DIRS)
+
+# check a function to validate the find
+if(SCOTCH_LIBRARIES)
+
+ set(REQUIRED_INCDIRS)
+ set(REQUIRED_LIBDIRS)
+ set(REQUIRED_LIBS)
+
+ # SCOTCH
+ if (SCOTCH_INCLUDE_DIRS)
+ set(REQUIRED_INCDIRS "${SCOTCH_INCLUDE_DIRS}")
+ endif()
+ if (SCOTCH_LIBRARY_DIRS)
+ set(REQUIRED_LIBDIRS "${SCOTCH_LIBRARY_DIRS}")
+ endif()
+ set(REQUIRED_LIBS "${SCOTCH_LIBRARIES}")
+ # THREADS
+ if(CMAKE_THREAD_LIBS_INIT)
+ list(APPEND REQUIRED_LIBS "${CMAKE_THREAD_LIBS_INIT}")
+ endif()
+ set(Z_LIBRARY "Z_LIBRARY-NOTFOUND")
+ find_library(Z_LIBRARY NAMES z)
+ mark_as_advanced(Z_LIBRARY)
+ if(Z_LIBRARY)
+ list(APPEND REQUIRED_LIBS "-lz")
+ endif()
+ set(M_LIBRARY "M_LIBRARY-NOTFOUND")
+ find_library(M_LIBRARY NAMES m)
+ mark_as_advanced(M_LIBRARY)
+ if(M_LIBRARY)
+ list(APPEND REQUIRED_LIBS "-lm")
+ endif()
+ set(RT_LIBRARY "RT_LIBRARY-NOTFOUND")
+ find_library(RT_LIBRARY NAMES rt)
+ mark_as_advanced(RT_LIBRARY)
+ if(RT_LIBRARY)
+ list(APPEND REQUIRED_LIBS "-lrt")
+ endif()
+
+ # set required libraries for link
+ set(CMAKE_REQUIRED_INCLUDES "${REQUIRED_INCDIRS}")
+ set(CMAKE_REQUIRED_LIBRARIES)
+ foreach(lib_dir ${REQUIRED_LIBDIRS})
+ list(APPEND CMAKE_REQUIRED_LIBRARIES "-L${lib_dir}")
+ endforeach()
+ list(APPEND CMAKE_REQUIRED_LIBRARIES "${REQUIRED_LIBS}")
+ string(REGEX REPLACE "^ -" "-" CMAKE_REQUIRED_LIBRARIES "${CMAKE_REQUIRED_LIBRARIES}")
+
+ # test link
+ unset(SCOTCH_WORKS CACHE)
+ include(CheckFunctionExists)
+ check_function_exists(SCOTCH_graphInit SCOTCH_WORKS)
+ mark_as_advanced(SCOTCH_WORKS)
+
+ if(SCOTCH_WORKS)
+ # save link with dependencies
+ set(SCOTCH_LIBRARIES "${REQUIRED_LIBS}")
+ else()
+ if(NOT SCOTCH_FIND_QUIETLY)
+ message(STATUS "Looking for SCOTCH : test of SCOTCH_graphInit with SCOTCH library fails")
+ message(STATUS "CMAKE_REQUIRED_LIBRARIES: ${CMAKE_REQUIRED_LIBRARIES}")
+ message(STATUS "CMAKE_REQUIRED_INCLUDES: ${CMAKE_REQUIRED_INCLUDES}")
+ message(STATUS "Check in CMakeFiles/CMakeError.log to figure out why it fails")
+ endif()
+ endif()
+ set(CMAKE_REQUIRED_INCLUDES)
+ set(CMAKE_REQUIRED_FLAGS)
+ set(CMAKE_REQUIRED_LIBRARIES)
+endif()
+
+if (SCOTCH_LIBRARIES)
+ list(GET SCOTCH_LIBRARIES 0 first_lib)
+ get_filename_component(first_lib_path "${first_lib}" PATH)
+ if (${first_lib_path} MATCHES "/lib(32|64)?$")
+ string(REGEX REPLACE "/lib(32|64)?$" "" not_cached_dir "${first_lib_path}")
+ set(SCOTCH_DIR_FOUND "${not_cached_dir}" CACHE PATH "Installation directory of SCOTCH library" FORCE)
+ else()
+ set(SCOTCH_DIR_FOUND "${first_lib_path}" CACHE PATH "Installation directory of SCOTCH library" FORCE)
+ endif()
+endif()
+mark_as_advanced(SCOTCH_DIR)
+mark_as_advanced(SCOTCH_DIR_FOUND)
+
+# Check the size of SCOTCH_Num
+# ---------------------------------
+set(CMAKE_REQUIRED_INCLUDES ${SCOTCH_INCLUDE_DIRS})
+
+include(CheckCSourceRuns)
+#stdio.h and stdint.h should be included by scotch.h directly
+set(SCOTCH_C_TEST_SCOTCH_Num_4 "
+#include <stdio.h>
+#include <stdint.h>
+#include <scotch.h>
+int main(int argc, char **argv) {
+ if (sizeof(SCOTCH_Num) == 4)
+ return 0;
+ else
+ return 1;
+}
+")
+
+set(SCOTCH_C_TEST_SCOTCH_Num_8 "
+#include <stdio.h>
+#include <stdint.h>
+#include <scotch.h>
+int main(int argc, char **argv) {
+ if (sizeof(SCOTCH_Num) == 8)
+ return 0;
+ else
+ return 1;
+}
+")
+check_c_source_runs("${SCOTCH_C_TEST_SCOTCH_Num_4}" SCOTCH_Num_4)
+if(NOT SCOTCH_Num_4)
+ check_c_source_runs("${SCOTCH_C_TEST_SCOTCH_Num_8}" SCOTCH_Num_8)
+ if(NOT SCOTCH_Num_8)
+ set(SCOTCH_INTSIZE -1)
+ else()
+ set(SCOTCH_INTSIZE 8)
+ endif()
+else()
+ set(SCOTCH_INTSIZE 4)
+endif()
+set(CMAKE_REQUIRED_INCLUDES "")
+
+# check that SCOTCH has been found
+# ---------------------------------
+include(FindPackageHandleStandardArgs)
+find_package_handle_standard_args(SCOTCH DEFAULT_MSG
+ SCOTCH_LIBRARIES
+ SCOTCH_WORKS)
+#
+# TODO: Add possibility to check for specific functions in the library
+#
diff --git a/cmake/FindSPQR.cmake b/cmake/FindSPQR.cmake
new file mode 100644
index 0000000..d6fb2e1
--- /dev/null
+++ b/cmake/FindSPQR.cmake
@@ -0,0 +1,41 @@
+# SPQR lib usually requires linking to a blas and lapack library.
+# It is up to the user of this module to find a BLAS and link to it.
+
+# SPQR lib requires Cholmod, colamd and amd as well.
+# FindCholmod.cmake can be used to find those packages before finding spqr
+
+if (SPQR_INCLUDES AND SPQR_LIBRARIES)
+ set(SPQR_FIND_QUIETLY TRUE)
+endif ()
+
+find_path(SPQR_INCLUDES
+ NAMES
+ SuiteSparseQR.hpp
+ PATHS
+ $ENV{SPQRDIR}
+ ${INCLUDE_INSTALL_DIR}
+ PATH_SUFFIXES
+ suitesparse
+ ufsparse
+)
+
+find_library(SPQR_LIBRARIES spqr $ENV{SPQRDIR} ${LIB_INSTALL_DIR})
+
+if(SPQR_LIBRARIES)
+
+ find_library(SUITESPARSE_LIBRARY SuiteSparse PATHS $ENV{SPQRDIR} ${LIB_INSTALL_DIR})
+ if (SUITESPARSE_LIBRARY)
+ set(SPQR_LIBRARIES ${SPQR_LIBRARIES} ${SUITESPARSE_LIBRARY})
+ endif()
+
+ find_library(CHOLMOD_LIBRARY cholmod PATHS $ENV{UMFPACK_LIBDIR} $ENV{UMFPACKDIR} ${LIB_INSTALL_DIR})
+ if(CHOLMOD_LIBRARY)
+ set(SPQR_LIBRARIES ${SPQR_LIBRARIES} ${CHOLMOD_LIBRARY})
+ endif()
+
+endif()
+
+include(FindPackageHandleStandardArgs)
+find_package_handle_standard_args(SPQR DEFAULT_MSG SPQR_INCLUDES SPQR_LIBRARIES)
+
+mark_as_advanced(SPQR_INCLUDES SPQR_LIBRARIES)
\ No newline at end of file
diff --git a/cmake/FindStandardMathLibrary.cmake b/cmake/FindStandardMathLibrary.cmake
new file mode 100644
index 0000000..1d1e5b3
--- /dev/null
+++ b/cmake/FindStandardMathLibrary.cmake
@@ -0,0 +1,70 @@
+# - Try to find how to link to the standard math library, if anything at all is needed to do.
+# On most platforms this is automatic, but for example it's not automatic on QNX.
+#
+# Once done this will define
+#
+# STANDARD_MATH_LIBRARY_FOUND - we found how to successfully link to the standard math library
+# STANDARD_MATH_LIBRARY - the name of the standard library that one has to link to.
+# -- this will be left empty if it's automatic (most platforms).
+# -- this will be set to "m" on platforms where one must explicitly
+# pass the "-lm" linker flag.
+#
+# Copyright (c) 2010 Benoit Jacob <jacob.benoit.1@gmail.com>
+# 2020 Susi Lehtola <susi.lehtola@gmail.com>
+# Redistribution and use is allowed according to the terms of the 2-clause BSD license.
+
+
+include(CheckCXXSourceCompiles)
+
+# a little test program for c++ math functions.
+# notice the std:: is required on some platforms such as QNX
+# notice the (void) is required if -Wall (-Wunused-value) is added to CMAKE_CXX_FLAG
+
+# We read in the arguments from standard input to avoid the compiler optimizing away the calls
+set(find_standard_math_library_test_program
+"
+#include<cmath>
+int main(int argc, char **){
+ return int(std::sin(double(argc)) + std::log(double(argc)));
+}")
+
+# first try compiling/linking the test program without any linker flags
+
+set(CMAKE_REQUIRED_FLAGS "")
+set(CMAKE_REQUIRED_LIBRARIES "")
+CHECK_CXX_SOURCE_COMPILES(
+ "${find_standard_math_library_test_program}"
+ standard_math_library_linked_to_automatically
+)
+
+if(standard_math_library_linked_to_automatically)
+
+ # the test program linked successfully without any linker flag.
+ set(STANDARD_MATH_LIBRARY "")
+ set(STANDARD_MATH_LIBRARY_FOUND TRUE)
+
+else()
+
+ # the test program did not link successfully without any linker flag.
+ # This is a very uncommon case that so far we only saw on QNX. The next try is the
+ # standard name 'm' for the standard math library.
+
+ set(CMAKE_REQUIRED_LIBRARIES "m")
+ CHECK_CXX_SOURCE_COMPILES(
+ "${find_standard_math_library_test_program}"
+ standard_math_library_linked_to_as_m)
+
+ if(standard_math_library_linked_to_as_m)
+
+ # the test program linked successfully when linking to the 'm' library
+ set(STANDARD_MATH_LIBRARY "m")
+ set(STANDARD_MATH_LIBRARY_FOUND TRUE)
+
+ else()
+
+ # the test program still doesn't link successfully
+ set(STANDARD_MATH_LIBRARY_FOUND FALSE)
+
+ endif()
+
+endif()
diff --git a/cmake/FindSuperLU.cmake b/cmake/FindSuperLU.cmake
new file mode 100644
index 0000000..4b779f5
--- /dev/null
+++ b/cmake/FindSuperLU.cmake
@@ -0,0 +1,97 @@
+
+# Umfpack lib usually requires linking to a blas library.
+# It is up to the user of this module to find a BLAS and link to it.
+
+if (SUPERLU_INCLUDES AND SUPERLU_LIBRARIES)
+ set(SUPERLU_FIND_QUIETLY TRUE)
+endif ()
+
+find_path(SUPERLU_INCLUDES
+ NAMES
+ supermatrix.h
+ PATHS
+ $ENV{SUPERLUDIR}
+ ${INCLUDE_INSTALL_DIR}
+ PATH_SUFFIXES
+ superlu
+ SRC
+)
+
+find_library(SUPERLU_LIBRARIES
+ NAMES "superlu_5.2.1" "superlu_5.2" "superlu_5.1.1" "superlu_5.1" "superlu_5.0" "superlu_4.3" "superlu_4.2" "superlu_4.1" "superlu_4.0" "superlu_3.1" "superlu_3.0" "superlu"
+ PATHS $ENV{SUPERLUDIR} ${LIB_INSTALL_DIR}
+ PATH_SUFFIXES lib)
+
+if(SUPERLU_INCLUDES AND SUPERLU_LIBRARIES)
+
+include(CheckCXXSourceCompiles)
+include(CMakePushCheckState)
+cmake_push_check_state()
+
+set(CMAKE_REQUIRED_INCLUDES ${CMAKE_REQUIRED_INCLUDES} ${SUPERLU_INCLUDES})
+
+# check whether struct mem_usage_t is globally defined
+check_cxx_source_compiles("
+typedef int int_t;
+#include <supermatrix.h>
+#include <slu_util.h>
+int main() {
+ mem_usage_t mem;
+ return 0;
+}"
+SUPERLU_HAS_GLOBAL_MEM_USAGE_T)
+
+
+check_cxx_source_compiles("
+typedef int int_t;
+#include <supermatrix.h>
+#include <superlu_enum_consts.h>
+int main() {
+ return SLU_SINGLE;
+}"
+SUPERLU_HAS_CLEAN_ENUMS)
+
+check_cxx_source_compiles("
+typedef int int_t;
+#include <supermatrix.h>
+#include <slu_util.h>
+int main(void)
+{
+ GlobalLU_t glu;
+ return 0;
+}"
+SUPERLU_HAS_GLOBALLU_T)
+
+if(SUPERLU_HAS_GLOBALLU_T)
+ # at least 5.0
+ set(SUPERLU_VERSION_VAR "5.0")
+elseif(SUPERLU_HAS_CLEAN_ENUMS)
+ # at least 4.3
+ set(SUPERLU_VERSION_VAR "4.3")
+elseif(SUPERLU_HAS_GLOBAL_MEM_USAGE_T)
+ # at least 4.0
+ set(SUPERLU_VERSION_VAR "4.0")
+else()
+ set(SUPERLU_VERSION_VAR "3.0")
+endif()
+
+cmake_pop_check_state()
+
+if(SuperLU_FIND_VERSION)
+ if(${SUPERLU_VERSION_VAR} VERSION_LESS ${SuperLU_FIND_VERSION})
+ set(SUPERLU_VERSION_OK FALSE)
+ else()
+ set(SUPERLU_VERSION_OK TRUE)
+ endif()
+else()
+ set(SUPERLU_VERSION_OK TRUE)
+endif()
+
+endif()
+
+include(FindPackageHandleStandardArgs)
+find_package_handle_standard_args(SuperLU
+ REQUIRED_VARS SUPERLU_INCLUDES SUPERLU_LIBRARIES SUPERLU_VERSION_OK
+ VERSION_VAR SUPERLU_VERSION_VAR)
+
+mark_as_advanced(SUPERLU_INCLUDES SUPERLU_LIBRARIES)
diff --git a/cmake/FindTriSYCL.cmake b/cmake/FindTriSYCL.cmake
new file mode 100644
index 0000000..8104239
--- /dev/null
+++ b/cmake/FindTriSYCL.cmake
@@ -0,0 +1,173 @@
+#.rst:
+# FindTriSYCL
+#---------------
+#
+# TODO : insert Copyright and licence
+
+#########################
+# FindTriSYCL.cmake
+#########################
+#
+# Tools for finding and building with TriSYCL.
+#
+# User must define TRISYCL_INCLUDE_DIR pointing to the triSYCL
+# include directory.
+#
+# Latest version of this file can be found at:
+# https://github.com/triSYCL/triSYCL
+
+# Requite CMake version 3.5 or higher
+cmake_minimum_required (VERSION 3.5)
+
+# Check that a supported host compiler can be found
+if(CMAKE_COMPILER_IS_GNUCXX)
+ # Require at least gcc 5.4
+ if (CMAKE_CXX_COMPILER_VERSION VERSION_LESS 5.4)
+ message(FATAL_ERROR
+ "host compiler - Not found! (gcc version must be at least 5.4)")
+ else()
+ message(STATUS "host compiler - gcc ${CMAKE_CXX_COMPILER_VERSION}")
+ endif()
+elseif ("${CMAKE_CXX_COMPILER_ID}" STREQUAL "Clang")
+ # Require at least clang 3.9
+ if (${CMAKE_CXX_COMPILER_VERSION} VERSION_LESS 3.9)
+ message(FATAL_ERROR
+ "host compiler - Not found! (clang version must be at least 3.9)")
+ else()
+ message(STATUS "host compiler - clang ${CMAKE_CXX_COMPILER_VERSION}")
+ endif()
+else()
+ message(WARNING
+ "host compiler - Not found! (triSYCL supports GCC and Clang)")
+endif()
+
+#triSYCL options
+option(TRISYCL_OPENMP "triSYCL multi-threading with OpenMP" ON)
+option(TRISYCL_OPENCL "triSYCL OpenCL interoperability mode" OFF)
+option(TRISYCL_NO_ASYNC "triSYCL use synchronous kernel execution" OFF)
+option(TRISYCL_DEBUG "triSCYL use debug mode" OFF)
+option(TRISYCL_DEBUG_STRUCTORS "triSYCL trace of object lifetimes" OFF)
+option(TRISYCL_TRACE_KERNEL "triSYCL trace of kernel execution" OFF)
+
+mark_as_advanced(TRISYCL_OPENMP)
+mark_as_advanced(TRISYCL_OPENCL)
+mark_as_advanced(TRISYCL_NO_ASYNC)
+mark_as_advanced(TRISYCL_DEBUG)
+mark_as_advanced(TRISYCL_DEBUG_STRUCTORS)
+mark_as_advanced(TRISYCL_TRACE_KERNEL)
+
+#triSYCL definitions
+set(CL_SYCL_LANGUAGE_VERSION 220 CACHE STRING
+ "Host language version to be used by trisYCL (default is: 220)")
+set(TRISYCL_CL_LANGUAGE_VERSION 220 CACHE STRING
+ "Device language version to be used by trisYCL (default is: 220)")
+# triSYCL now requires c++17
+set(CMAKE_CXX_STANDARD 17)
+set(CXX_STANDARD_REQUIRED ON)
+
+
+# Find OpenCL package
+include(CMakeFindDependencyMacro)
+if(TRISYCL_OPENCL)
+ find_dependency(OpenCL REQUIRED)
+ if(UNIX)
+ set(BOOST_COMPUTE_INCPATH /usr/include/compute CACHE PATH
+ "Path to Boost.Compute headers (default is: /usr/include/compute)")
+ endif()
+endif()
+
+# Find OpenMP package
+if(TRISYCL_OPENMP)
+ find_dependency(OpenMP REQUIRED)
+endif()
+
+# Find Boost
+find_dependency(Boost 1.58 REQUIRED COMPONENTS chrono log)
+
+# If debug or trace we need boost log
+if(TRISYCL_DEBUG OR TRISYCL_DEBUG_STRUCTORS OR TRISYCL_TRACE_KERNEL)
+ set(LOG_NEEDED ON)
+else()
+ set(LOG_NEEDED OFF)
+endif()
+
+find_dependency(Threads REQUIRED)
+
+# Find triSYCL directory
+if (TRISYCL_INCLUDES AND TRISYCL_LIBRARIES)
+ set(TRISYCL_FIND_QUIETLY TRUE)
+endif ()
+
+find_path(TRISYCL_INCLUDE_DIR
+ NAMES sycl.hpp
+ PATHS $ENV{TRISYCLDIR} $ENV{TRISYCLDIR}/include ${INCLUDE_INSTALL_DIR}
+ PATH_SUFFIXES triSYCL
+)
+
+include(FindPackageHandleStandardArgs)
+find_package_handle_standard_args(TriSYCL DEFAULT_MSG
+ TRISYCL_INCLUDE_DIR)
+
+if(NOT TRISYCL_INCLUDE_DIR)
+ message(FATAL_ERROR
+ "triSYCL include directory - Not found! (please set TRISYCL_INCLUDE_DIR")
+else()
+ message(STATUS "triSYCL include directory - Found ${TRISYCL_INCLUDE_DIR}")
+endif()
+
+include(CMakeParseArguments)
+#######################
+# add_sycl_to_target
+#######################
+function(add_sycl_to_target)
+ set(options)
+ set(one_value_args
+ TARGET
+ )
+ set(multi_value_args
+ SOURCES
+ )
+ cmake_parse_arguments(ADD_SYCL_ARGS
+ "${options}"
+ "${one_value_args}"
+ "${multi_value_args}"
+ ${ARGN}
+ )
+
+ # Add include directories to the "#include <>" paths
+ target_include_directories (${ADD_SYCL_ARGS_TARGET} PUBLIC
+ ${TRISYCL_INCLUDE_DIR}
+ ${Boost_INCLUDE_DIRS}
+ $<$<BOOL:${TRISYCL_OPENCL}>:${OpenCL_INCLUDE_DIRS}>
+ $<$<BOOL:${TRISYCL_OPENCL}>:${BOOST_COMPUTE_INCPATH}>)
+
+ # Link dependencies
+ target_link_libraries(${ADD_SYCL_ARGS_TARGET}
+ $<$<BOOL:${TRISYCL_OPENCL}>:${OpenCL_LIBRARIES}>
+ Threads::Threads
+ $<$<BOOL:${LOG_NEEDED}>:Boost::log>
+ Boost::chrono)
+
+ # Compile definitions
+ target_compile_definitions(${ADD_SYCL_ARGS_TARGET} PUBLIC
+ EIGEN_SYCL_TRISYCL
+ $<$<BOOL:${TRISYCL_NO_ASYNC}>:TRISYCL_NO_ASYNC>
+ $<$<BOOL:${TRISYCL_OPENCL}>:TRISYCL_OPENCL>
+ $<$<BOOL:${TRISYCL_DEBUG}>:TRISYCL_DEBUG>
+ $<$<BOOL:${TRISYCL_DEBUG_STRUCTORS}>:TRISYCL_DEBUG_STRUCTORS>
+ $<$<BOOL:${TRISYCL_TRACE_KERNEL}>:TRISYCL_TRACE_KERNEL>
+ $<$<BOOL:${LOG_NEEDED}>:BOOST_LOG_DYN_LINK>)
+
+ # C++ and OpenMP requirements
+ target_compile_options(${ADD_SYCL_ARGS_TARGET} PUBLIC
+ ${TRISYCL_COMPILE_OPTIONS}
+ $<$<BOOL:${TRISYCL_OPENMP}>:${OpenMP_CXX_FLAGS}>)
+
+ if(${TRISYCL_OPENMP} AND (NOT WIN32))
+ # Does not support generator expressions
+ set_target_properties(${ADD_SYCL_ARGS_TARGET}
+ PROPERTIES
+ LINK_FLAGS ${OpenMP_CXX_FLAGS})
+ endif()
+
+endfunction()
diff --git a/cmake/FindUMFPACK.cmake b/cmake/FindUMFPACK.cmake
new file mode 100644
index 0000000..91cf637
--- /dev/null
+++ b/cmake/FindUMFPACK.cmake
@@ -0,0 +1,53 @@
+# Umfpack lib usually requires linking to a blas library.
+# It is up to the user of this module to find a BLAS and link to it.
+
+if (UMFPACK_INCLUDES AND UMFPACK_LIBRARIES)
+ set(UMFPACK_FIND_QUIETLY TRUE)
+endif ()
+
+find_path(UMFPACK_INCLUDES
+ NAMES
+ umfpack.h
+ PATHS
+ $ENV{UMFPACKDIR}
+ ${INCLUDE_INSTALL_DIR}
+ PATH_SUFFIXES
+ suitesparse
+ ufsparse
+)
+
+find_library(UMFPACK_LIBRARIES umfpack PATHS $ENV{UMFPACKDIR} ${LIB_INSTALL_DIR})
+
+if(UMFPACK_LIBRARIES)
+
+ if(NOT UMFPACK_LIBDIR)
+ get_filename_component(UMFPACK_LIBDIR ${UMFPACK_LIBRARIES} PATH)
+ endif()
+
+ find_library(COLAMD_LIBRARY colamd PATHS ${UMFPACK_LIBDIR} $ENV{UMFPACKDIR} ${LIB_INSTALL_DIR})
+ if(COLAMD_LIBRARY)
+ set(UMFPACK_LIBRARIES ${UMFPACK_LIBRARIES} ${COLAMD_LIBRARY})
+ endif ()
+
+ find_library(AMD_LIBRARY amd PATHS ${UMFPACK_LIBDIR} $ENV{UMFPACKDIR} ${LIB_INSTALL_DIR})
+ if(AMD_LIBRARY)
+ set(UMFPACK_LIBRARIES ${UMFPACK_LIBRARIES} ${AMD_LIBRARY})
+ endif ()
+
+ find_library(SUITESPARSE_LIBRARY SuiteSparse PATHS ${UMFPACK_LIBDIR} $ENV{UMFPACKDIR} ${LIB_INSTALL_DIR})
+ if(SUITESPARSE_LIBRARY)
+ set(UMFPACK_LIBRARIES ${UMFPACK_LIBRARIES} ${SUITESPARSE_LIBRARY})
+ endif ()
+
+ find_library(CHOLMOD_LIBRARY cholmod PATHS $ENV{UMFPACK_LIBDIR} $ENV{UMFPACKDIR} ${LIB_INSTALL_DIR})
+ if(CHOLMOD_LIBRARY)
+ set(UMFPACK_LIBRARIES ${UMFPACK_LIBRARIES} ${CHOLMOD_LIBRARY})
+ endif()
+
+endif()
+
+include(FindPackageHandleStandardArgs)
+find_package_handle_standard_args(UMFPACK DEFAULT_MSG
+ UMFPACK_INCLUDES UMFPACK_LIBRARIES)
+
+mark_as_advanced(UMFPACK_INCLUDES UMFPACK_LIBRARIES AMD_LIBRARY COLAMD_LIBRARY CHOLMOD_LIBRARY SUITESPARSE_LIBRARY)
diff --git a/cmake/RegexUtils.cmake b/cmake/RegexUtils.cmake
new file mode 100644
index 0000000..f0a1524
--- /dev/null
+++ b/cmake/RegexUtils.cmake
@@ -0,0 +1,19 @@
+function(escape_string_as_regex _str_out _str_in)
+ string(REGEX REPLACE "\\\\" "\\\\\\\\" FILETEST2 "${_str_in}")
+ string(REGEX REPLACE "([.$+*?|-])" "\\\\\\1" FILETEST2 "${FILETEST2}")
+ string(REGEX REPLACE "\\^" "\\\\^" FILETEST2 "${FILETEST2}")
+ string(REGEX REPLACE "\\(" "\\\\(" FILETEST2 "${FILETEST2}")
+ string(REGEX REPLACE "\\)" "\\\\)" FILETEST2 "${FILETEST2}")
+ string(REGEX REPLACE "\\[" "\\\\[" FILETEST2 "${FILETEST2}")
+ string(REGEX REPLACE "\\]" "\\\\]" FILETEST2 "${FILETEST2}")
+ set(${_str_out} "${FILETEST2}" PARENT_SCOPE)
+endfunction()
+
+function(test_escape_string_as_regex)
+ set(test1 "\\.^$-+*()[]?|")
+ escape_string_as_regex(test2 "${test1}")
+ set(testRef "\\\\\\.\\^\\$\\-\\+\\*\\(\\)\\[\\]\\?\\|")
+ if(NOT test2 STREQUAL testRef)
+ message("Error in the escape_string_for_regex function : \n ${test1} was escaped as ${test2}, should be ${testRef}")
+ endif()
+endfunction()
\ No newline at end of file
diff --git a/debug/gdb/__init__.py b/debug/gdb/__init__.py
new file mode 100644
index 0000000..bb7b160
--- /dev/null
+++ b/debug/gdb/__init__.py
@@ -0,0 +1 @@
+# Intentionally empty
diff --git a/debug/gdb/printers.py b/debug/gdb/printers.py
new file mode 100644
index 0000000..2c3fccf
--- /dev/null
+++ b/debug/gdb/printers.py
@@ -0,0 +1,338 @@
+# -*- coding: utf-8 -*-
+# This file is part of Eigen, a lightweight C++ template library
+# for linear algebra.
+#
+# Copyright (C) 2009 Benjamin Schindler <bschindler@inf.ethz.ch>
+#
+# This Source Code Form is subject to the terms of the Mozilla Public
+# License, v. 2.0. If a copy of the MPL was not distributed with this
+# file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+# Pretty printers for Eigen::Matrix
+# This is still pretty basic as the python extension to gdb is still pretty basic.
+# It cannot handle complex eigen types and it doesn't support many of the other eigen types
+# This code supports fixed size as well as dynamic size matrices
+
+# To use it:
+#
+# * Create a directory and put the file as well as an empty __init__.py in
+# that directory.
+# * Create a ~/.gdbinit file, that contains the following:
+# python
+# import sys
+# sys.path.insert(0, '/path/to/eigen/printer/directory')
+# from printers import register_eigen_printers
+# register_eigen_printers(None)
+# end
+
+import gdb
+import re
+from bisect import bisect_left
+
+
+# Basic row/column iteration code for use with Sparse and Dense matrices
+class _MatrixEntryIterator(object):
+
+ def __init__(self, rows, cols, row_major):
+ self.rows = rows
+ self.cols = cols
+ self.currentRow = 0
+ self.currentCol = 0
+ self.rowMajor = row_major
+
+ def __iter__(self):
+ return self
+
+ def next(self):
+ return self.__next__() # Python 2.x compatibility
+
+ def __next__(self):
+ row = self.currentRow
+ col = self.currentCol
+ if self.rowMajor == 0:
+ if self.currentCol >= self.cols:
+ raise StopIteration
+
+ self.currentRow += 1
+ if self.currentRow >= self.rows:
+ self.currentRow = 0
+ self.currentCol += 1
+ else:
+ if self.currentRow >= self.rows:
+ raise StopIteration
+
+ self.currentCol += 1
+ if self.currentCol >= self.cols:
+ self.currentCol = 0
+ self.currentRow += 1
+
+ return row, col
+
+
+class EigenMatrixPrinter:
+ """Print Eigen Matrix or Array of some kind"""
+
+ def __init__(self, variety, val):
+ """Extract all the necessary information"""
+
+ # Save the variety (presumably "Matrix" or "Array") for later usage
+ self.variety = variety
+
+ # The gdb extension does not support value template arguments - need to extract them by hand
+ typeinfo = val.type
+ if typeinfo.code == gdb.TYPE_CODE_REF:
+ typeinfo = typeinfo.target()
+ self.type = typeinfo.unqualified().strip_typedefs()
+ tag = self.type.tag
+ regex = re.compile('<.*>')
+ m = regex.findall(tag)[0][1:-1]
+ template_params = m.split(',')
+ template_params = [x.replace(" ", "") for x in template_params]
+
+ if template_params[1] in ['-0x00000000000000001', '-0x000000001', '-1']:
+ self.rows = val['m_storage']['m_rows']
+ else:
+ self.rows = int(template_params[1])
+
+ if template_params[2] in ['-0x00000000000000001', '-0x000000001', '-1']:
+ self.cols = val['m_storage']['m_cols']
+ else:
+ self.cols = int(template_params[2])
+
+ self.options = 0 # default value
+ if len(template_params) > 3:
+ self.options = template_params[3]
+
+ self.rowMajor = (int(self.options) & 0x1)
+
+ self.innerType = self.type.template_argument(0)
+
+ self.val = val
+
+ # Fixed size matrices have a struct as their storage, so we need to walk through this
+ self.data = self.val['m_storage']['m_data']
+ if self.data.type.code == gdb.TYPE_CODE_STRUCT:
+ self.data = self.data['array']
+ self.data = self.data.cast(self.innerType.pointer())
+
+ class _Iterator(_MatrixEntryIterator):
+ def __init__(self, rows, cols, data_ptr, row_major):
+ super(EigenMatrixPrinter._Iterator, self).__init__(rows, cols, row_major)
+
+ self.dataPtr = data_ptr
+
+ def __next__(self):
+ row, col = super(EigenMatrixPrinter._Iterator, self).__next__()
+
+ item = self.dataPtr.dereference()
+ self.dataPtr += 1
+ if self.cols == 1: # if it's a column vector
+ return '[%d]' % (row,), item
+ elif self.rows == 1: # if it's a row vector
+ return '[%d]' % (col,), item
+ return '[%d,%d]' % (row, col), item
+
+ def children(self):
+ return self._Iterator(self.rows, self.cols, self.data, self.rowMajor)
+
+ def to_string(self):
+ return "Eigen::%s<%s,%d,%d,%s> (data ptr: %s)" % (
+ self.variety, self.innerType, self.rows, self.cols,
+ "RowMajor" if self.rowMajor else "ColMajor", self.data)
+
+
+class EigenSparseMatrixPrinter:
+ """Print an Eigen SparseMatrix"""
+
+ def __init__(self, val):
+ """Extract all the necessary information"""
+
+ typeinfo = val.type
+ if typeinfo.code == gdb.TYPE_CODE_REF:
+ typeinfo = typeinfo.target()
+ self.type = typeinfo.unqualified().strip_typedefs()
+ tag = self.type.tag
+ regex = re.compile('<.*>')
+ m = regex.findall(tag)[0][1:-1]
+ template_params = m.split(',')
+ template_params = [x.replace(" ", "") for x in template_params]
+
+ self.options = 0
+ if len(template_params) > 1:
+ self.options = template_params[1]
+
+ self.rowMajor = (int(self.options) & 0x1)
+
+ self.innerType = self.type.template_argument(0)
+
+ self.val = val
+
+ self.data = self.val['m_data']
+ self.data = self.data.cast(self.innerType.pointer())
+
+ class _Iterator(_MatrixEntryIterator):
+ def __init__(self, rows, cols, val, row_major):
+ super(EigenSparseMatrixPrinter._Iterator, self).__init__(rows, cols, row_major)
+
+ self.val = val
+
+ def __next__(self):
+ row, col = super(EigenSparseMatrixPrinter._Iterator, self).__next__()
+
+ # repeat calculations from SparseMatrix.h:
+ outer = row if self.rowMajor else col
+ inner = col if self.rowMajor else row
+ start = self.val['m_outerIndex'][outer]
+ end = (
+ (start + self.val['m_innerNonZeros'][outer])
+ if self.val['m_innerNonZeros'] else self.val['m_outerIndex'][outer+1]
+ )
+
+ # and from CompressedStorage.h:
+ data = self.val['m_data']
+ if start >= end:
+ item = 0
+ elif (end > start) and (inner == data['m_indices'][end-1]):
+ item = data['m_values'][end-1]
+ else:
+ # create Python index list from the target range within m_indices
+ indices = [data['m_indices'][x] for x in range(int(start), int(end)-1)]
+ # find the index with binary search
+ idx = int(start) + bisect_left(indices, inner)
+ if idx < end and data['m_indices'][idx] == inner:
+ item = data['m_values'][idx]
+ else:
+ item = 0
+
+ return '[%d,%d]' % (row, col), item
+
+ def children(self):
+ if self.data:
+ return self._Iterator(self.rows(), self.cols(), self.val, self.rowMajor)
+
+ return iter([]) # empty matrix, for now
+
+ def rows(self):
+ return self.val['m_outerSize'] if self.rowMajor else self.val['m_innerSize']
+
+ def cols(self):
+ return self.val['m_innerSize'] if self.rowMajor else self.val['m_outerSize']
+
+ def to_string(self):
+
+ if self.data:
+ status = ("not compressed" if self.val['m_innerNonZeros'] else "compressed")
+ else:
+ status = "empty"
+ dimensions = "%d x %d" % (self.rows(), self.cols())
+ layout = "row" if self.rowMajor else "column"
+
+ return "Eigen::SparseMatrix<%s>, %s, %s major, %s" % (
+ self.innerType, dimensions, layout, status)
+
+
+class EigenQuaternionPrinter:
+ """Print an Eigen Quaternion"""
+
+ def __init__(self, val):
+ """Extract all the necessary information"""
+ # The gdb extension does not support value template arguments - need to extract them by hand
+ typeinfo = val.type
+ if typeinfo.code == gdb.TYPE_CODE_REF:
+ typeinfo = typeinfo.target()
+ self.type = typeinfo.unqualified().strip_typedefs()
+ self.innerType = self.type.template_argument(0)
+ self.val = val
+
+ # Quaternions have a struct as their storage, so we need to walk through this
+ self.data = self.val['m_coeffs']['m_storage']['m_data']['array']
+ self.data = self.data.cast(self.innerType.pointer())
+
+ class _Iterator:
+ def __init__(self, data_ptr):
+ self.dataPtr = data_ptr
+ self.currentElement = 0
+ self.elementNames = ['x', 'y', 'z', 'w']
+
+ def __iter__(self):
+ return self
+
+ def next(self):
+ return self.__next__() # Python 2.x compatibility
+
+ def __next__(self):
+ element = self.currentElement
+
+ if self.currentElement >= 4: # there are 4 elements in a quaternion
+ raise StopIteration
+
+ self.currentElement += 1
+
+ item = self.dataPtr.dereference()
+ self.dataPtr += 1
+ return '[%s]' % (self.elementNames[element],), item
+
+ def children(self):
+ return self._Iterator(self.data)
+
+ def to_string(self):
+ return "Eigen::Quaternion<%s> (data ptr: %s)" % (self.innerType, self.data)
+
+
+def cast_eigen_block_to_matrix(val):
+ # Get the type of the variable (and convert to a string)
+ # Example: 'const Eigen::Block<Eigen::Block<Eigen::Matrix<double, -1, -1, 0, -1, -1>, -1, -1, false> const, -1, -1, false>'
+ val_type = str(val.type)
+
+ # Extract the Eigen::Matrix type from the Block:
+ # From the previous example: Eigen::Matrix<double, -1, -1, 0, -1, -1>
+ begin = val_type.find('Eigen::Matrix<')
+ end = val_type.find('>', begin) + 1
+
+ # Convert the Eigen::Block to an Eigen::Matrix
+ return val.cast(gdb.lookup_type(val_type[begin:end]))
+
+
+def build_eigen_dictionary():
+ pretty_printers_dict[re.compile('^Eigen::Quaternion<.*>$')] = lambda val: EigenQuaternionPrinter(val)
+ pretty_printers_dict[re.compile('^Eigen::Matrix<.*>$')] = lambda val: EigenMatrixPrinter("Matrix", val)
+ pretty_printers_dict[re.compile('^Eigen::Block<.*>$')] =\
+ lambda val: EigenMatrixPrinter("Matrix", cast_eigen_block_to_matrix(val))
+ pretty_printers_dict[re.compile('^Eigen::VectorBlock<.*>$')] =\
+ lambda val: EigenMatrixPrinter("Matrix", cast_eigen_block_to_matrix(val))
+ pretty_printers_dict[re.compile('^Eigen::SparseMatrix<.*>$')] = lambda val: EigenSparseMatrixPrinter(val)
+ pretty_printers_dict[re.compile('^Eigen::Array<.*>$')] = lambda val: EigenMatrixPrinter("Array", val)
+
+
+def register_eigen_printers(obj):
+ """Register eigen pretty-printers with objfile Obj"""
+
+ if obj is None:
+ obj = gdb
+ obj.pretty_printers.append(lookup_function)
+
+
+def lookup_function(val):
+ """Look-up and return a pretty-printer that can print val."""
+
+ typeinfo = val.type
+
+ if typeinfo.code == gdb.TYPE_CODE_REF:
+ typeinfo = typeinfo.target()
+
+ typeinfo = typeinfo.unqualified().strip_typedefs()
+
+ typename = typeinfo.tag
+ if typename is None:
+ return None
+
+ for function in pretty_printers_dict:
+ if function.search(typename):
+ return pretty_printers_dict[function](val)
+
+ return None
+
+
+pretty_printers_dict = {}
+
+build_eigen_dictionary()
diff --git a/debug/lldb/eigenlldb.py b/debug/lldb/eigenlldb.py
new file mode 100644
index 0000000..d9b5d06
--- /dev/null
+++ b/debug/lldb/eigenlldb.py
@@ -0,0 +1,234 @@
+# -*- coding: utf-8 -*-
+# This file is part of Eigen, a lightweight C++ template library
+# for linear algebra.
+#
+# Copyright (C) 2021 Huang, Zhaoquan <zhaoquan2008@hotmail.com>
+#
+# This Source Code Form is subject to the terms of the Mozilla Public
+# License, v. 2.0. If a copy of the MPL was not distributed with this
+# file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+# Pretty printers for Eigen::Matrix to use with LLDB debugger
+#
+# Usage:
+# 1. Add the following line (change it according to the path to this file)
+# to the file ~/.lldbinit (create one if it doesn't exist):
+# `command script import /path/to/eigenlldb.py`
+# 2. Inspect the variables in LLDB command line
+# `frame variable`
+
+import lldb
+from typing import List
+import bisect
+
+
+def __lldb_init_module(debugger, internal_dict):
+ debugger.HandleCommand("type synthetic add -x Eigen::Matrix<.*> --python-class eigenlldb.EigenMatrixChildProvider")
+ debugger.HandleCommand(
+ "type synthetic add -x Eigen::SparseMatrix<.*> --python-class eigenlldb.EigenSparseMatrixChildProvider")
+
+
+class EigenMatrixChildProvider:
+ _valobj: lldb.SBValue
+ _scalar_type: lldb.SBType
+ _scalar_size: int
+ _rows_compile_time: int
+ _cols_compile_time: int
+ _row_major: bool
+ _fixed_storage: bool
+
+ def __init__(self, valobj, internal_dict):
+ self._valobj = valobj
+ valtype = valobj.GetType().GetCanonicalType()
+
+ scalar_type = valtype.GetTemplateArgumentType(0)
+ if not scalar_type.IsValid():
+ # In the case that scalar_type is invalid on LLDB 9.0 on Windows with CLion
+ storage = valobj.GetChildMemberWithName("m_storage")
+ data = storage.GetChildMemberWithName("m_data")
+ data_type = data.GetType()
+ if data_type.IsPointerType():
+ scalar_type = data.GetType().GetPointeeType()
+ else:
+ scalar_type = data.GetChildMemberWithName("array").GetType().GetArrayElementType()
+ self._scalar_type = scalar_type
+ self._scalar_size = self._scalar_type.GetByteSize()
+
+ name = valtype.GetName()
+ template_begin = name.find("<")
+ template_end = name.find(">")
+ template_args = name[(template_begin + 1):template_end].split(",")
+ self._rows_compile_time = int(template_args[1])
+ self._cols_compile_time = int(template_args[2])
+ self._row_major = (int(template_args[3]) & 1) != 0
+
+ max_rows = int(template_args[4])
+ max_cols = int(template_args[5])
+ self._fixed_storage = (max_rows != -1 and max_cols != -1)
+
+ def num_children(self):
+ return self._cols() * self._rows()
+
+ def get_child_index(self, name):
+ pass
+
+ def get_child_at_index(self, index):
+ storage = self._valobj.GetChildMemberWithName("m_storage")
+ data = storage.GetChildMemberWithName("m_data")
+ offset = self._scalar_size * index
+
+ if self._row_major:
+ row = index // self._cols()
+ col = index % self._cols()
+ else:
+ row = index % self._rows()
+ col = index // self._rows()
+ if self._fixed_storage:
+ data = data.GetChildMemberWithName("array")
+ if self._cols() == 1:
+ name = '[{}]'.format(row)
+ elif self._rows() == 1:
+ name = '[{}]'.format(col)
+ else:
+ name = '[{},{}]'.format(row, col)
+ return data.CreateChildAtOffset(
+ name, offset, self._scalar_type
+ )
+
+ def _cols(self):
+ if self._cols_compile_time == -1:
+ storage = self._valobj.GetChildMemberWithName("m_storage")
+ cols = storage.GetChildMemberWithName("m_cols")
+ return cols.GetValueAsUnsigned()
+ else:
+ return self._cols_compile_time
+
+ def _rows(self):
+ if self._rows_compile_time == -1:
+ storage = self._valobj.GetChildMemberWithName("m_storage")
+ rows = storage.GetChildMemberWithName("m_rows")
+ return rows.GetValueAsUnsigned()
+ else:
+ return self._rows_compile_time
+
+
+class EigenSparseMatrixChildProvider:
+ _valobj: lldb.SBValue
+ _scalar_type: lldb.SBType
+ _scalar_size: int
+ _index_type: lldb.SBType
+ _index_size: int
+ _row_major: bool
+
+ _outer_size: int
+ _nnz: int
+ _values: lldb.SBValue
+ _inner_indices: lldb.SBValue
+ _outer_starts: lldb.SBValue
+ _inner_nnzs: lldb.SBValue
+ _compressed: bool
+
+ # Index of the first synthetic child under each outer index
+ _child_indices: List[int]
+
+ def __init__(self, valobj, internal_dict):
+ self._valobj = valobj
+ valtype = valobj.GetType().GetCanonicalType()
+ scalar_type = valtype.GetTemplateArgumentType(0)
+ if not scalar_type.IsValid():
+ # In the case that scalar_type is invalid on LLDB 9.0 on Windows with CLion
+ data = valobj.GetChildMemberWithName("m_data")
+ values = data.GetChildMemberWithName("m_values")
+ scalar_type = values.GetType().GetPointeeType()
+ self._scalar_type = scalar_type
+ self._scalar_size = scalar_type.GetByteSize()
+
+ index_type = valtype.GetTemplateArgumentType(2)
+ if not index_type.IsValid():
+ # In the case that scalar_type is invalid on LLDB 9.0 on Windows with CLion
+ outer_starts = valobj.GetChildMemberWithName("m_outerIndex")
+ index_type = outer_starts.GetType().GetPointeeType()
+ self._index_type = index_type
+ self._index_size = index_type.GetByteSize()
+
+ name = valtype.GetName()
+ template_begin = name.find("<")
+ template_end = name.find(">")
+ template_args = name[(template_begin + 1):template_end].split(",")
+ self._row_major = (int(template_args[1]) & 1) != 0
+
+ def num_children(self):
+ return self._nnz + 2
+
+ def get_child_index(self, name):
+ pass
+
+ def get_child_at_index(self, index):
+ if index == 0:
+ name = "rows" if self._row_major else "cols"
+ return self._valobj.GetChildMemberWithName("m_outerSize") \
+ .CreateChildAtOffset(name, 0, self._index_type)
+ elif index == 1:
+ name = "cols" if self._row_major else "rows"
+ return self._valobj.GetChildMemberWithName("m_innerSize") \
+ .CreateChildAtOffset(name, 0, self._index_type)
+ else:
+ index = index - 2
+ outer_index = bisect.bisect_right(self._child_indices, index) - 1
+ total_nnzs = self._child_indices[outer_index]
+ if self._compressed:
+ item_index = index
+ inner_index = self._inner_indices \
+ .CreateChildAtOffset("", item_index * self._index_size, self._index_type) \
+ .GetValueAsUnsigned()
+ return self._values \
+ .CreateChildAtOffset(self._child_name(outer_index, inner_index),
+ item_index * self._scalar_size,
+ self._scalar_type)
+ else:
+ index_begin = self._outer_starts \
+ .CreateChildAtOffset("", outer_index * self._index_size, self._index_type) \
+ .GetValueAsUnsigned()
+ item_index = index - total_nnzs + index_begin
+ inner_index = self._inner_indices \
+ .CreateChildAtOffset("", item_index * self._index_size, self._index_type) \
+ .GetValueAsUnsigned()
+ return self._values \
+ .CreateChildAtOffset(self._child_name(outer_index, inner_index),
+ item_index * self._scalar_size,
+ self._scalar_type)
+
+ def update(self):
+ valobj = self._valobj
+ self._outer_size = valobj.GetChildMemberWithName("m_outerSize").GetValueAsUnsigned()
+ data = valobj.GetChildMemberWithName("m_data")
+ self._values = data.GetChildMemberWithName("m_values")
+ self._inner_indices = data.GetChildMemberWithName("m_indices")
+ self._outer_starts = valobj.GetChildMemberWithName("m_outerIndex")
+ self._inner_nnzs = valobj.GetChildMemberWithName("m_innerNonZeros")
+
+ self._compressed = self._inner_nnzs.GetValueAsUnsigned() == 0
+
+ total_nnzs = 0
+ child_indices = [0]
+ for outer_index in range(self._outer_size):
+ if self._compressed:
+ index_end = self._outer_starts \
+ .CreateChildAtOffset("", (outer_index + 1) * self._index_size, self._index_type) \
+ .GetValueAsUnsigned()
+ total_nnzs = index_end
+ child_indices.append(total_nnzs)
+ else:
+ nnzs = self._inner_nnzs \
+ .CreateChildAtOffset("", outer_index * self._index_size, self._index_type) \
+ .GetValueAsUnsigned()
+ total_nnzs = total_nnzs + nnzs
+ child_indices.append(total_nnzs)
+ self._child_indices = child_indices
+ self._nnz = total_nnzs
+
+ def _child_name(self, outer_index, inner_index):
+ if self._row_major:
+ return "[{0},{1}]".format(outer_index, inner_index)
+ else:
+ return "[{1},{0}]".format(outer_index, inner_index)
diff --git a/debug/msvc/eigen.natvis b/debug/msvc/eigen.natvis
new file mode 100644
index 0000000..22cf346
--- /dev/null
+++ b/debug/msvc/eigen.natvis
@@ -0,0 +1,235 @@
+<?xml version="1.0" encoding="utf-8"?>
+
+<AutoVisualizer xmlns="http://schemas.microsoft.com/vstudio/debugger/natvis/2010">
+
+ <!-- Fixed x Fixed Matrix -->
+ <Type Name="Eigen::Matrix<*,*,*,*,*,*>">
+ <AlternativeType Name="Eigen::Array<*,-1,-1,*,*,*>"/>
+ <DisplayString>[{$T2}, {$T3}] (fixed matrix)</DisplayString>
+ <Expand>
+ <ArrayItems Condition="Flags%2"> <!-- row major layout -->
+ <Rank>2</Rank>
+ <Size>$i==0 ? $T2 : $T3</Size>
+ <ValuePointer>m_storage.m_data.array</ValuePointer>
+ </ArrayItems>
+ <ArrayItems Condition="!(Flags%2)"> <!-- column major layout -->
+ <Direction>Backward</Direction>
+ <Rank>2</Rank>
+ <Size>$i==0 ? $T2 : $T3</Size>
+ <ValuePointer>m_storage.m_data.array</ValuePointer>
+ </ArrayItems>
+ </Expand>
+ </Type>
+
+ <!-- 2 x 2 Matrix -->
+ <Type Name="Eigen::Matrix<*,2,2,*,*,*>">
+ <AlternativeType Name="Eigen::Array<*,2,2,*,*,*>"/>
+ <DisplayString>[2, 2] (fixed matrix)</DisplayString>
+ <Expand>
+ <Synthetic Name="[row 0]" Condition="Flags%2">
+ <DisplayString>({m_storage.m_data.array[0]}, {m_storage.m_data.array[1]})</DisplayString>
+ </Synthetic>
+ <Synthetic Name="[row 0]" Condition="!(Flags%2)">
+ <DisplayString>({m_storage.m_data.array[0]}, {m_storage.m_data.array[2]})</DisplayString>
+ </Synthetic>
+ <Synthetic Name="[row 1]" Condition="Flags%2">
+ <DisplayString>({m_storage.m_data.array[2]}, {m_storage.m_data.array[3]})</DisplayString>
+ </Synthetic>
+ <Synthetic Name="[row 1]" Condition="!(Flags%2)">
+ <DisplayString>({m_storage.m_data.array[1]}, {m_storage.m_data.array[3]})</DisplayString>
+ </Synthetic>
+ </Expand>
+ </Type>
+
+ <!-- 3 x 3 Matrix -->
+ <Type Name="Eigen::Matrix<*,3,3,*,*,*>">
+ <AlternativeType Name="Eigen::Array<*,3,3,*,*,*>"/>
+ <DisplayString>[3, 3] (fixed matrix)</DisplayString>
+ <Expand>
+ <Synthetic Name="[row 0]" Condition="Flags%2">
+ <DisplayString>({m_storage.m_data.array[0]}, {m_storage.m_data.array[1]}, {m_storage.m_data.array[2]})</DisplayString>
+ </Synthetic>
+ <Synthetic Name="[row 0]" Condition="!(Flags%2)">
+ <DisplayString>({m_storage.m_data.array[0]}, {m_storage.m_data.array[3]}, {m_storage.m_data.array[6]})</DisplayString>
+ </Synthetic>
+ <Synthetic Name="[row 1]" Condition="Flags%2">
+ <DisplayString>({m_storage.m_data.array[3]}, {m_storage.m_data.array[4]}, {m_storage.m_data.array[5]})</DisplayString>
+ </Synthetic>
+ <Synthetic Name="[row 1]" Condition="!(Flags%2)">
+ <DisplayString>({m_storage.m_data.array[1]}, {m_storage.m_data.array[4]}, {m_storage.m_data.array[7]})</DisplayString>
+ </Synthetic>
+ <Synthetic Name="[row 2]" Condition="Flags%2">
+ <DisplayString>({m_storage.m_data.array[6]}, {m_storage.m_data.array[7]}, {m_storage.m_data.array[8]})</DisplayString>
+ </Synthetic>
+ <Synthetic Name="[row 2]" Condition="!(Flags%2)">
+ <DisplayString>({m_storage.m_data.array[2]}, {m_storage.m_data.array[5]}, {m_storage.m_data.array[8]})</DisplayString>
+ </Synthetic>
+ </Expand>
+ </Type>
+
+ <!-- 4 x 4 Matrix -->
+ <Type Name="Eigen::Matrix<*,4,4,*,*,*>">
+ <AlternativeType Name="Eigen::Array<*,4,4,*,*,*>"/>
+ <DisplayString>[4, 4] (fixed matrix)</DisplayString>
+ <Expand>
+ <Synthetic Name="[row 0]" Condition="Flags%2">
+ <DisplayString>({m_storage.m_data.array[0]}, {m_storage.m_data.array[1]}, {m_storage.m_data.array[2]}, {m_storage.m_data.array[3]})</DisplayString>
+ </Synthetic>
+ <Synthetic Name="[row 0]" Condition="!(Flags%2)">
+ <DisplayString>({m_storage.m_data.array[0]}, {m_storage.m_data.array[4]}, {m_storage.m_data.array[8]}, {m_storage.m_data.array[12]})</DisplayString>
+ </Synthetic>
+ <Synthetic Name="[row 1]" Condition="Flags%2">
+ <DisplayString>({m_storage.m_data.array[4]}, {m_storage.m_data.array[5]}, {m_storage.m_data.array[6]}, {m_storage.m_data.array[7]})</DisplayString>
+ </Synthetic>
+ <Synthetic Name="[row 1]" Condition="!(Flags%2)">
+ <DisplayString>({m_storage.m_data.array[1]}, {m_storage.m_data.array[5]}, {m_storage.m_data.array[9]}, {m_storage.m_data.array[13]})</DisplayString>
+ </Synthetic>
+ <Synthetic Name="[row 2]" Condition="Flags%2">
+ <DisplayString>({m_storage.m_data.array[8]}, {m_storage.m_data.array[9]}, {m_storage.m_data.array[10]}, {m_storage.m_data.array[11]})</DisplayString>
+ </Synthetic>
+ <Synthetic Name="[row 2]" Condition="!(Flags%2)">
+ <DisplayString>({m_storage.m_data.array[2]}, {m_storage.m_data.array[6]}, {m_storage.m_data.array[10]}, {m_storage.m_data.array[14]})</DisplayString>
+ </Synthetic>
+ <Synthetic Name="[row 3]" Condition="Flags%2">
+ <DisplayString>({m_storage.m_data.array[12]}, {m_storage.m_data.array[13]}, {m_storage.m_data.array[14]}, {m_storage.m_data.array[15]})</DisplayString>
+ </Synthetic>
+ <Synthetic Name="[row 3]" Condition="!(Flags%2)">
+ <DisplayString>({m_storage.m_data.array[3]}, {m_storage.m_data.array[7]}, {m_storage.m_data.array[11]}, {m_storage.m_data.array[15]})</DisplayString>
+ </Synthetic>
+ </Expand>
+ </Type>
+
+ <!-- Dynamic x Dynamic Matrix -->
+ <Type Name="Eigen::Matrix<*,-1,-1,*,*,*>">
+ <AlternativeType Name="Eigen::Array<*,-1,-1,*,*,*>"/>
+ <DisplayString Condition="m_storage.m_data == 0">empty</DisplayString>
+ <DisplayString Condition="m_storage.m_data != 0">[{m_storage.m_rows}, {m_storage.m_cols}] (dynamic matrix)</DisplayString>
+ <Expand>
+ <ArrayItems Condition="Flags%2"> <!-- row major layout -->
+ <Rank>2</Rank>
+ <Size>$i==0 ? m_storage.m_rows : m_storage.m_cols</Size>
+ <ValuePointer>m_storage.m_data</ValuePointer>
+ </ArrayItems>
+ <ArrayItems Condition="!(Flags%2)"> <!-- column major layout -->
+ <Direction>Backward</Direction>
+ <Rank>2</Rank>
+ <Size>$i==0 ? m_storage.m_rows : m_storage.m_cols</Size>
+ <ValuePointer>m_storage.m_data</ValuePointer>
+ </ArrayItems>
+ </Expand>
+ </Type>
+
+ <!-- Fixed x Dynamic Matrix -->
+ <Type Name="Eigen::Matrix<*,*,-1,*,*,*>">
+ <AlternativeType Name="Eigen::Array<*,*,-1,*,*,*>"/>
+ <DisplayString Condition="m_storage.m_data == 0">empty</DisplayString>
+ <DisplayString Condition="m_storage.m_data != 0">[{$T2}, {m_storage.m_cols}] (dynamic column matrix)</DisplayString>
+ <Expand>
+ <ArrayItems Condition="Flags%2"> <!-- row major layout -->
+ <Rank>2</Rank>
+ <Size>$i==0 ? $T2 : m_storage.m_cols</Size>
+ <ValuePointer>m_storage.m_data</ValuePointer>
+ </ArrayItems>
+ <ArrayItems Condition="!(Flags%2)"> <!-- column major layout -->
+ <Direction>Backward</Direction>
+ <Rank>2</Rank>
+ <Size>$i==0 ? $T2 : m_storage.m_cols</Size>
+ <ValuePointer>m_storage.m_data</ValuePointer>
+ </ArrayItems>
+ </Expand>
+ </Type>
+
+ <!-- Dynamic x Fixed Matrix -->
+ <Type Name="Eigen::Matrix<*,-1,*,*,*,*>">
+ <AlternativeType Name="Eigen::Array<*,-1,*,*,*,*>"/>
+ <DisplayString Condition="m_storage.m_data == 0">empty</DisplayString>
+ <DisplayString Condition="m_storage.m_data != 0">[{m_storage.m_rows}, {$T2}] (dynamic row matrix)</DisplayString>
+ <Expand>
+ <ArrayItems Condition="Flags%2"> <!-- row major layout -->
+ <Rank>2</Rank>
+ <Size>$i==0 ? m_storage.m_rows : $T2</Size>
+ <ValuePointer>m_storage.m_data</ValuePointer>
+ </ArrayItems>
+ <ArrayItems Condition="!(Flags%2)"> <!-- column major layout -->
+ <Direction>Backward</Direction>
+ <Rank>2</Rank>
+ <Size>$i==0 ? m_storage.m_rows : $T2</Size>
+ <ValuePointer>m_storage.m_data</ValuePointer>
+ </ArrayItems>
+ </Expand>
+ </Type>
+
+ <!-- Dynamic Column Vector -->
+ <Type Name="Eigen::Matrix<*,1,-1,*,*,*>">
+ <AlternativeType Name="Eigen::Array<*,1,-1,*,*,*>"/>
+ <DisplayString Condition="m_storage.m_data == 0">empty</DisplayString>
+ <DisplayString Condition="m_storage.m_data != 0">[{m_storage.m_cols}] (dynamic column vector)</DisplayString>
+ <Expand>
+ <Item Name="[size]">m_storage.m_cols</Item>
+ <ArrayItems>
+ <Size>m_storage.m_cols</Size>
+ <ValuePointer>m_storage.m_data</ValuePointer>
+ </ArrayItems>
+ </Expand>
+ </Type>
+
+ <!-- Dynamic Row Vector -->
+ <Type Name="Eigen::Matrix<*,-1,1,*,*,*>">
+ <AlternativeType Name="Eigen::Array<*,-1,1,*,*,*>"/>
+ <DisplayString Condition="m_storage.m_data == 0">empty</DisplayString>
+ <DisplayString Condition="m_storage.m_data != 0">[{m_storage.m_rows}] (dynamic row vector)</DisplayString>
+ <Expand>
+ <Item Name="[size]">m_storage.m_rows</Item>
+ <ArrayItems>
+ <Size>m_storage.m_rows</Size>
+ <ValuePointer>m_storage.m_data</ValuePointer>
+ </ArrayItems>
+ </Expand>
+ </Type>
+
+ <!-- Fixed Vector -->
+ <Type Name="Eigen::Matrix<*,1,1,*,*,*>">
+ <AlternativeType Name="Eigen::Array<*,1,1,*,*,*>"/>
+ <DisplayString>[1] ({m_storage.m_data.array[0]})</DisplayString>
+ <Expand>
+ <Item Name="[x]">m_storage.m_data.array[0]</Item>
+ </Expand>
+ </Type>
+
+ <Type Name="Eigen::Matrix<*,2,1,*,*,*>">
+ <AlternativeType Name="Eigen::Matrix<*,1,2,*,*,*>"/>
+ <AlternativeType Name="Eigen::Array<*,2,1,*,*,*>"/>
+ <AlternativeType Name="Eigen::Array<*,1,2,*,*,*>"/>
+ <DisplayString>[2] ({m_storage.m_data.array[0]}, {m_storage.m_data.array[1]})</DisplayString>
+ <Expand>
+ <Item Name="[x]">m_storage.m_data.array[0]</Item>
+ <Item Name="[y]">m_storage.m_data.array[1]</Item>
+ </Expand>
+ </Type>
+
+ <Type Name="Eigen::Matrix<*,3,1,*,*,*>">
+ <AlternativeType Name="Eigen::Matrix<*,1,3,*,*,*>"/>
+ <AlternativeType Name="Eigen::Array<*,3,1,*,*,*>"/>
+ <AlternativeType Name="Eigen::Array<*,1,3,*,*,*>"/>
+ <DisplayString>[3] ({m_storage.m_data.array[0]}, {m_storage.m_data.array[1]}, {m_storage.m_data.array[2]})</DisplayString>
+ <Expand>
+ <Item Name="[x]">m_storage.m_data.array[0]</Item>
+ <Item Name="[y]">m_storage.m_data.array[1]</Item>
+ <Item Name="[z]">m_storage.m_data.array[2]</Item>
+ </Expand>
+ </Type>
+
+ <Type Name="Eigen::Matrix<*,4,1,*,*,*>">
+ <AlternativeType Name="Eigen::Matrix<*,1,4,*,*,*>"/>
+ <AlternativeType Name="Eigen::Array<*,4,1,*,*,*>"/>
+ <AlternativeType Name="Eigen::Array<*,1,4,*,*,*>"/>
+ <DisplayString>[4] ({m_storage.m_data.array[0]}, {m_storage.m_data.array[1]}, {m_storage.m_data.array[2]}, {m_storage.m_data.array[3]})</DisplayString>
+ <Expand>
+ <Item Name="[x]">m_storage.m_data.array[0]</Item>
+ <Item Name="[y]">m_storage.m_data.array[1]</Item>
+ <Item Name="[z]">m_storage.m_data.array[2]</Item>
+ <Item Name="[w]">m_storage.m_data.array[3]</Item>
+ </Expand>
+ </Type>
+
+</AutoVisualizer>
diff --git a/debug/msvc/eigen_autoexp_part.dat b/debug/msvc/eigen_autoexp_part.dat
new file mode 100644
index 0000000..273c10d
--- /dev/null
+++ b/debug/msvc/eigen_autoexp_part.dat
@@ -0,0 +1,295 @@
+; ***************************************************************
+; * Eigen Visualizer
+; *
+; * Author: Hauke Heibel <hauke.heibel@gmail.com>
+; *
+; * Support the enhanced debugging of the following Eigen
+; * types (*: any, +:fixed dimension) :
+; *
+; * - Eigen::Matrix<*,4,1,*,*,*> and Eigen::Matrix<*,1,4,*,*,*>
+; * - Eigen::Matrix<*,3,1,*,*,*> and Eigen::Matrix<*,1,3,*,*,*>
+; * - Eigen::Matrix<*,2,1,*,*,*> and Eigen::Matrix<*,1,2,*,*,*>
+; * - Eigen::Matrix<*,-1,-1,*,*,*>
+; * - Eigen::Matrix<*,+,-1,*,*,*>
+; * - Eigen::Matrix<*,-1,+,*,*,*>
+; * - Eigen::Matrix<*,+,+,*,*,*>
+; *
+; * Matrices are displayed properly independently of the memory
+; * alignment (RowMajor vs. ColMajor).
+; *
+; * This file is distributed WITHOUT ANY WARRANTY. Please ensure
+; * that your original autoexp.dat file is copied to a safe
+; * place before proceeding with its modification.
+; ***************************************************************
+
+[Visualizer]
+
+; Fixed size 4-vectors
+Eigen::Matrix<*,4,1,*,*,*>|Eigen::Matrix<*,1,4,*,*,*>{
+ children
+ (
+ #(
+ [internals]: [$c,!],
+ x : ($c.m_storage.m_data.array)[0],
+ y : ($c.m_storage.m_data.array)[1],
+ z : ($c.m_storage.m_data.array)[2],
+ w : ($c.m_storage.m_data.array)[3]
+ )
+ )
+
+ preview
+ (
+ #(
+ "[",
+ 4,
+ "](",
+ #array(expr: $e.m_storage.m_data.array[$i], size: 4),
+ ")"
+ )
+ )
+}
+
+; Fixed size 3-vectors
+Eigen::Matrix<*,3,1,*,*,*>|Eigen::Matrix<*,1,3,*,*,*>{
+ children
+ (
+ #(
+ [internals]: [$c,!],
+ x : ($c.m_storage.m_data.array)[0],
+ y : ($c.m_storage.m_data.array)[1],
+ z : ($c.m_storage.m_data.array)[2]
+ )
+ )
+
+ preview
+ (
+ #(
+ "[",
+ 3,
+ "](",
+ #array(expr: $e.m_storage.m_data.array[$i], size: 3),
+ ")"
+ )
+ )
+}
+
+; Fixed size 2-vectors
+Eigen::Matrix<*,2,1,*,*,*>|Eigen::Matrix<*,1,2,*,*,*>{
+ children
+ (
+ #(
+ [internals]: [$c,!],
+ x : ($c.m_storage.m_data.array)[0],
+ y : ($c.m_storage.m_data.array)[1]
+ )
+ )
+
+ preview
+ (
+ #(
+ "[",
+ 2,
+ "](",
+ #array(expr: $e.m_storage.m_data.array[$i], size: 2),
+ ")"
+ )
+ )
+}
+
+; Fixed size 1-vectors
+Eigen::Matrix<*,1,1,*,*,*>|Eigen::Matrix<*,1,1,*,*,*>{
+ children
+ (
+ #(
+ [internals]: [$c,!],
+ x : ($c.m_storage.m_data.array)[0]
+ )
+ )
+
+ preview
+ (
+ #(
+ "[",
+ 1,
+ "](",
+ #array(expr: $e.m_storage.m_data.array[$i], size: 1),
+ ")"
+ )
+ )
+}
+
+; Dynamic matrices (ColMajor and RowMajor support)
+Eigen::Matrix<*,-1,-1,*,*,*>{
+ children
+ (
+ #(
+ [internals]: [$c,!],
+ rows: $c.m_storage.m_rows,
+ cols: $c.m_storage.m_cols,
+ ; Check for RowMajorBit
+ #if ($c.Flags & 0x1) (
+ #array(
+ rank: 2,
+ base: 0,
+ expr: ($c.m_storage.m_data)[($i % $c.m_storage.m_rows)*$c.m_storage.m_cols + (($i- $i % $c.m_storage.m_rows)/$c.m_storage.m_rows)],
+ size: ($r==1)*$c.m_storage.m_rows+($r==0)*$c.m_storage.m_cols
+ )
+ ) #else (
+ #array(
+ rank: 2,
+ base: 0,
+ expr: ($c.m_storage.m_data)[$i],
+ size: ($r==1)*$c.m_storage.m_rows+($r==0)*$c.m_storage.m_cols
+ )
+ )
+ )
+ )
+
+ preview
+ (
+ #(
+ "[",
+ $c.m_storage.m_rows,
+ ",",
+ $c.m_storage.m_cols,
+ "](",
+ #array(
+ expr : [($c.m_storage.m_data)[$i],g],
+ size : $c.m_storage.m_rows*$c.m_storage.m_cols
+ ),
+ ")"
+ )
+ )
+}
+
+; Fixed rows, dynamic columns matrix (ColMajor and RowMajor support)
+Eigen::Matrix<*,*,-1,*,*,*>{
+ children
+ (
+ #(
+ [internals]: [$c,!],
+ rows: $c.RowsAtCompileTime,
+ cols: $c.m_storage.m_cols,
+ ; Check for RowMajorBit
+ #if ($c.Flags & 0x1) (
+ #array(
+ rank: 2,
+ base: 0,
+ expr: ($c.m_storage.m_data)[($i % $c.RowsAtCompileTime)*$c.m_storage.m_cols + (($i- $i % $c.RowsAtCompileTime)/$c.RowsAtCompileTime)],
+ size: ($r==1)*$c.RowsAtCompileTime+($r==0)*$c.m_storage.m_cols
+ )
+ ) #else (
+ #array(
+ rank: 2,
+ base: 0,
+ expr: ($c.m_storage.m_data)[$i],
+ size: ($r==1)*$c.RowsAtCompileTime+($r==0)*$c.m_storage.m_cols
+ )
+ )
+ )
+ )
+
+ preview
+ (
+ #(
+ "[",
+ $c.RowsAtCompileTime,
+ ",",
+ $c.m_storage.m_cols,
+ "](",
+ #array(
+ expr : [($c.m_storage.m_data)[$i],g],
+ size : $c.RowsAtCompileTime*$c.m_storage.m_cols
+ ),
+ ")"
+ )
+ )
+}
+
+; Dynamic rows, fixed columns matrix (ColMajor and RowMajor support)
+Eigen::Matrix<*,-1,*,*,*,*>{
+ children
+ (
+ #(
+ [internals]: [$c,!],
+ rows: $c.m_storage.m_rows,
+ cols: $c.ColsAtCompileTime,
+ ; Check for RowMajorBit
+ #if ($c.Flags & 0x1) (
+ #array(
+ rank: 2,
+ base: 0,
+ expr: ($c.m_storage.m_data)[($i % $c.m_storage.m_rows)*$c.ColsAtCompileTime + (($i- $i % $c.m_storage.m_rows)/$c.m_storage.m_rows)],
+ size: ($r==1)*$c.m_storage.m_rows+($r==0)*$c.ColsAtCompileTime
+ )
+ ) #else (
+ #array(
+ rank: 2,
+ base: 0,
+ expr: ($c.m_storage.m_data)[$i],
+ size: ($r==1)*$c.m_storage.m_rows+($r==0)*$c.ColsAtCompileTime
+ )
+ )
+ )
+ )
+
+ preview
+ (
+ #(
+ "[",
+ $c.m_storage.m_rows,
+ ",",
+ $c.ColsAtCompileTime,
+ "](",
+ #array(
+ expr : [($c.m_storage.m_data)[$i],g],
+ size : $c.m_storage.m_rows*$c.ColsAtCompileTime
+ ),
+ ")"
+ )
+ )
+}
+
+; Fixed size matrix (ColMajor and RowMajor support)
+Eigen::Matrix<*,*,*,*,*,*>{
+ children
+ (
+ #(
+ [internals]: [$c,!],
+ rows: $c.RowsAtCompileTime,
+ cols: $c.ColsAtCompileTime,
+ ; Check for RowMajorBit
+ #if ($c.Flags & 0x1) (
+ #array(
+ rank: 2,
+ base: 0,
+ expr: ($c.m_storage.m_data.array)[($i % $c.RowsAtCompileTime)*$c.ColsAtCompileTime + (($i- $i % $c.RowsAtCompileTime)/$c.RowsAtCompileTime)],
+ size: ($r==1)*$c.RowsAtCompileTime+($r==0)*$c.ColsAtCompileTime
+ )
+ ) #else (
+ #array(
+ rank: 2,
+ base: 0,
+ expr: ($c.m_storage.m_data.array)[$i],
+ size: ($r==1)*$c.RowsAtCompileTime+($r==0)*$c.ColsAtCompileTime
+ )
+ )
+ )
+ )
+
+ preview
+ (
+ #(
+ "[",
+ $c.RowsAtCompileTime,
+ ",",
+ $c.ColsAtCompileTime,
+ "](",
+ #array(
+ expr : [($c.m_storage.m_data.array)[$i],g],
+ size : $c.RowsAtCompileTime*$c.ColsAtCompileTime
+ ),
+ ")"
+ )
+ )
+}
diff --git a/demos/CMakeLists.txt b/demos/CMakeLists.txt
new file mode 100644
index 0000000..deb560f
--- /dev/null
+++ b/demos/CMakeLists.txt
@@ -0,0 +1,13 @@
+project(EigenDemos)
+
+add_custom_target(demos)
+
+if(NOT EIGEN_TEST_NOQT)
+ find_package(Qt4)
+ if(QT4_FOUND)
+ add_subdirectory(mandelbrot)
+ add_subdirectory(opengl)
+ else()
+ message(STATUS "Qt4 not found, so disabling the mandelbrot and opengl demos")
+ endif()
+endif()
diff --git a/demos/mandelbrot/CMakeLists.txt b/demos/mandelbrot/CMakeLists.txt
new file mode 100644
index 0000000..ae6001d
--- /dev/null
+++ b/demos/mandelbrot/CMakeLists.txt
@@ -0,0 +1,21 @@
+find_package(Qt4 REQUIRED)
+
+set(CMAKE_INCLUDE_CURRENT_DIR ON)
+
+if (CMAKE_COMPILER_IS_GNUCXX)
+ set ( CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -O2")
+ add_definitions ( "-DNDEBUG" )
+endif ()
+
+include_directories( ${QT_INCLUDE_DIR} )
+
+set(mandelbrot_SRCS
+ mandelbrot.cpp
+)
+
+qt4_automoc(${mandelbrot_SRCS})
+
+add_executable(mandelbrot ${mandelbrot_SRCS})
+add_dependencies(demos mandelbrot)
+
+target_link_libraries(mandelbrot ${QT_QTCORE_LIBRARY} ${QT_QTGUI_LIBRARY})
diff --git a/demos/mandelbrot/README b/demos/mandelbrot/README
new file mode 100644
index 0000000..a451d65
--- /dev/null
+++ b/demos/mandelbrot/README
@@ -0,0 +1,10 @@
+*** Mandelbrot demo ***
+
+Controls:
+* Left mouse button to center view at a point.
+* Drag vertically with left mouse button to zoom in and out.
+
+Be sure to enable SSE2 or AltiVec to improve performance.
+
+The number of iterations, and the choice between single and double precision, are
+determined at runtime depending on the zoom level.
diff --git a/demos/mandelbrot/mandelbrot.cpp b/demos/mandelbrot/mandelbrot.cpp
new file mode 100644
index 0000000..5d575d5
--- /dev/null
+++ b/demos/mandelbrot/mandelbrot.cpp
@@ -0,0 +1,213 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "mandelbrot.h"
+#include <iostream>
+#include<QtGui/QPainter>
+#include<QtGui/QImage>
+#include<QtGui/QMouseEvent>
+#include<QtCore/QTime>
+
+void MandelbrotWidget::resizeEvent(QResizeEvent *)
+{
+ if(size < width() * height())
+ {
+ std::cout << "reallocate buffer" << std::endl;
+ size = width() * height();
+ if(buffer) delete[]buffer;
+ buffer = new unsigned char[4*size];
+ }
+}
+
+template<typename T> struct iters_before_test { enum { ret = 8 }; };
+template<> struct iters_before_test<double> { enum { ret = 16 }; };
+
+template<typename Real> void MandelbrotThread::render(int img_width, int img_height)
+{
+ enum { packetSize = Eigen::internal::packet_traits<Real>::size }; // number of reals in a Packet
+ typedef Eigen::Array<Real, packetSize, 1> Packet; // wrap a Packet as a vector
+
+ enum { iters_before_test = iters_before_test<Real>::ret };
+ max_iter = (max_iter / iters_before_test) * iters_before_test;
+ const int alignedWidth = (img_width/packetSize)*packetSize;
+ unsigned char *const buffer = widget->buffer;
+ const double xradius = widget->xradius;
+ const double yradius = xradius * img_height / img_width;
+ const int threadcount = widget->threadcount;
+ typedef Eigen::Array<Real, 2, 1> Vector2;
+ Vector2 start(widget->center.x() - widget->xradius, widget->center.y() - yradius);
+ Vector2 step(2*widget->xradius/img_width, 2*yradius/img_height);
+ total_iter = 0;
+
+ for(int y = id; y < img_height; y += threadcount)
+ {
+ int pix = y * img_width;
+
+ // for each pixel, we're going to do the iteration z := z^2 + c where z and c are complex numbers,
+ // starting with z = c = complex coord of the pixel. pzi and pzr denote the real and imaginary parts of z.
+ // pci and pcr denote the real and imaginary parts of c.
+
+ Packet pzi_start, pci_start;
+ for(int i = 0; i < packetSize; i++) pzi_start[i] = pci_start[i] = start.y() + y * step.y();
+
+ for(int x = 0; x < alignedWidth; x += packetSize, pix += packetSize)
+ {
+ Packet pcr, pci = pci_start, pzr, pzi = pzi_start, pzr_buf;
+ for(int i = 0; i < packetSize; i++) pzr[i] = pcr[i] = start.x() + (x+i) * step.x();
+
+ // do the iterations. Every iters_before_test iterations we check for divergence,
+ // in which case we can stop iterating.
+ int j = 0;
+ typedef Eigen::Matrix<int, packetSize, 1> Packeti;
+ Packeti pix_iter = Packeti::Zero(), // number of iteration per pixel in the packet
+ pix_dont_diverge; // whether or not each pixel has already diverged
+ do
+ {
+ for(int i = 0; i < iters_before_test/4; i++) // peel the inner loop by 4
+ {
+# define ITERATE \
+ pzr_buf = pzr; \
+ pzr = pzr.square(); \
+ pzr -= pzi.square(); \
+ pzr += pcr; \
+ pzi = (2*pzr_buf)*pzi; \
+ pzi += pci;
+ ITERATE ITERATE ITERATE ITERATE
+ }
+ pix_dont_diverge = ((pzr.square() + pzi.square())
+ .eval() // temporary fix as what follows is not yet vectorized by Eigen
+ <= Packet::Constant(4))
+ // the 4 here is not a magic value, it's a math fact that if
+ // the square modulus is >4 then divergence is inevitable.
+ .template cast<int>();
+ pix_iter += iters_before_test * pix_dont_diverge;
+ j++;
+ total_iter += iters_before_test * packetSize;
+ }
+ while(j < max_iter/iters_before_test && pix_dont_diverge.any()); // any() is not yet vectorized by Eigen
+
+ // compute pixel colors
+ for(int i = 0; i < packetSize; i++)
+ {
+ buffer[4*(pix+i)] = 255*pix_iter[i]/max_iter;
+ buffer[4*(pix+i)+1] = 0;
+ buffer[4*(pix+i)+2] = 0;
+ }
+ }
+
+ // if the width is not a multiple of packetSize, fill the remainder in black
+ for(int x = alignedWidth; x < img_width; x++, pix++)
+ buffer[4*pix] = buffer[4*pix+1] = buffer[4*pix+2] = 0;
+ }
+ return;
+}
+
+void MandelbrotThread::run()
+{
+ setTerminationEnabled(true);
+ double resolution = widget->xradius*2/widget->width();
+ max_iter = 128;
+ if(resolution < 1e-4f) max_iter += 128 * ( - 4 - std::log10(resolution));
+ int img_width = widget->width()/widget->draft;
+ int img_height = widget->height()/widget->draft;
+ single_precision = resolution > 1e-7f;
+
+ if(single_precision)
+ render<float>(img_width, img_height);
+ else
+ render<double>(img_width, img_height);
+}
+
+void MandelbrotWidget::paintEvent(QPaintEvent *)
+{
+ static float max_speed = 0;
+ long long total_iter = 0;
+
+ QTime time;
+ time.start();
+ for(int th = 0; th < threadcount; th++)
+ threads[th]->start(QThread::LowPriority);
+ for(int th = 0; th < threadcount; th++)
+ {
+ threads[th]->wait();
+ total_iter += threads[th]->total_iter;
+ }
+ int elapsed = time.elapsed();
+
+ if(draft == 1)
+ {
+ float speed = elapsed ? float(total_iter)*1000/elapsed : 0;
+ max_speed = std::max(max_speed, speed);
+ std::cout << threadcount << " threads, "
+ << elapsed << " ms, "
+ << speed << " iters/s (max " << max_speed << ")" << std::endl;
+ int packetSize = threads[0]->single_precision
+ ? int(Eigen::internal::packet_traits<float>::size)
+ : int(Eigen::internal::packet_traits<double>::size);
+ setWindowTitle(QString("resolution ")+QString::number(xradius*2/width(), 'e', 2)
+ +QString(", %1 iterations per pixel, ").arg(threads[0]->max_iter)
+ +(threads[0]->single_precision ? QString("single ") : QString("double "))
+ +QString("precision, ")
+ +(packetSize==1 ? QString("no vectorization")
+ : QString("vectorized (%1 per packet)").arg(packetSize)));
+ }
+
+ QImage image(buffer, width()/draft, height()/draft, QImage::Format_RGB32);
+ QPainter painter(this);
+ painter.drawImage(QPoint(0, 0), image.scaled(width(), height()));
+
+ if(draft>1)
+ {
+ draft /= 2;
+ setWindowTitle(QString("recomputing at 1/%1 resolution...").arg(draft));
+ update();
+ }
+}
+
+void MandelbrotWidget::mousePressEvent(QMouseEvent *event)
+{
+ if( event->buttons() & Qt::LeftButton )
+ {
+ lastpos = event->pos();
+ double yradius = xradius * height() / width();
+ center = Eigen::Vector2d(center.x() + (event->pos().x() - width()/2) * xradius * 2 / width(),
+ center.y() + (event->pos().y() - height()/2) * yradius * 2 / height());
+ draft = 16;
+ for(int th = 0; th < threadcount; th++)
+ threads[th]->terminate();
+ update();
+ }
+}
+
+void MandelbrotWidget::mouseMoveEvent(QMouseEvent *event)
+{
+ QPoint delta = event->pos() - lastpos;
+ lastpos = event->pos();
+ if( event->buttons() & Qt::LeftButton )
+ {
+ double t = 1 + 5 * double(delta.y()) / height();
+ if(t < 0.5) t = 0.5;
+ if(t > 2) t = 2;
+ xradius *= t;
+ draft = 16;
+ for(int th = 0; th < threadcount; th++)
+ threads[th]->terminate();
+ update();
+ }
+}
+
+int main(int argc, char *argv[])
+{
+ QApplication app(argc, argv);
+ MandelbrotWidget w;
+ w.show();
+ return app.exec();
+}
+
+#include "mandelbrot.moc"
diff --git a/demos/mandelbrot/mandelbrot.h b/demos/mandelbrot/mandelbrot.h
new file mode 100644
index 0000000..a687fd0
--- /dev/null
+++ b/demos/mandelbrot/mandelbrot.h
@@ -0,0 +1,71 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef MANDELBROT_H
+#define MANDELBROT_H
+
+#include <Eigen/Core>
+#include <QtGui/QApplication>
+#include <QtGui/QWidget>
+#include <QtCore/QThread>
+
+class MandelbrotWidget;
+
+class MandelbrotThread : public QThread
+{
+ friend class MandelbrotWidget;
+ MandelbrotWidget *widget;
+ long long total_iter;
+ int id, max_iter;
+ bool single_precision;
+
+ public:
+ MandelbrotThread(MandelbrotWidget *w, int i) : widget(w), id(i) {}
+ void run();
+ template<typename Real> void render(int img_width, int img_height);
+};
+
+class MandelbrotWidget : public QWidget
+{
+ Q_OBJECT
+
+ friend class MandelbrotThread;
+ Eigen::Vector2d center;
+ double xradius;
+ int size;
+ unsigned char *buffer;
+ QPoint lastpos;
+ int draft;
+ MandelbrotThread **threads;
+ int threadcount;
+
+ protected:
+ void resizeEvent(QResizeEvent *);
+ void paintEvent(QPaintEvent *);
+ void mousePressEvent(QMouseEvent *event);
+ void mouseMoveEvent(QMouseEvent *event);
+
+ public:
+ MandelbrotWidget() : QWidget(), center(0,0), xradius(2),
+ size(0), buffer(0), draft(16)
+ {
+ setAutoFillBackground(false);
+ threadcount = QThread::idealThreadCount();
+ threads = new MandelbrotThread*[threadcount];
+ for(int th = 0; th < threadcount; th++) threads[th] = new MandelbrotThread(this, th);
+ }
+ ~MandelbrotWidget()
+ {
+ if(buffer) delete[]buffer;
+ for(int th = 0; th < threadcount; th++) delete threads[th];
+ delete[] threads;
+ }
+};
+
+#endif // MANDELBROT_H
diff --git a/demos/mix_eigen_and_c/README b/demos/mix_eigen_and_c/README
new file mode 100644
index 0000000..d9cc927
--- /dev/null
+++ b/demos/mix_eigen_and_c/README
@@ -0,0 +1,9 @@
+This is an example of how one can wrap some of Eigen into a C library.
+
+To try this with GCC, do:
+
+ g++ -c binary_library.cpp -O2 -msse2 -I ../..
+ gcc example.c binary_library.o -o example -lstdc++
+ ./example
+
+TODO: add CMakeLists, add more explanations here
diff --git a/demos/mix_eigen_and_c/binary_library.cpp b/demos/mix_eigen_and_c/binary_library.cpp
new file mode 100644
index 0000000..15a2d03
--- /dev/null
+++ b/demos/mix_eigen_and_c/binary_library.cpp
@@ -0,0 +1,185 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+// This C++ file compiles to binary code that can be linked to by your C program,
+// thanks to the extern "C" syntax used in the declarations in binary_library.h.
+
+#include "binary_library.h"
+
+#include <Eigen/Core>
+
+using namespace Eigen;
+
+/************************* pointer conversion methods **********************************************/
+
+////// class MatrixXd //////
+
+inline MatrixXd& c_to_eigen(C_MatrixXd* ptr)
+{
+ return *reinterpret_cast<MatrixXd*>(ptr);
+}
+
+inline const MatrixXd& c_to_eigen(const C_MatrixXd* ptr)
+{
+ return *reinterpret_cast<const MatrixXd*>(ptr);
+}
+
+inline C_MatrixXd* eigen_to_c(MatrixXd& ref)
+{
+ return reinterpret_cast<C_MatrixXd*>(&ref);
+}
+
+inline const C_MatrixXd* eigen_to_c(const MatrixXd& ref)
+{
+ return reinterpret_cast<const C_MatrixXd*>(&ref);
+}
+
+////// class Map<MatrixXd> //////
+
+inline Map<MatrixXd>& c_to_eigen(C_Map_MatrixXd* ptr)
+{
+ return *reinterpret_cast<Map<MatrixXd>*>(ptr);
+}
+
+inline const Map<MatrixXd>& c_to_eigen(const C_Map_MatrixXd* ptr)
+{
+ return *reinterpret_cast<const Map<MatrixXd>*>(ptr);
+}
+
+inline C_Map_MatrixXd* eigen_to_c(Map<MatrixXd>& ref)
+{
+ return reinterpret_cast<C_Map_MatrixXd*>(&ref);
+}
+
+inline const C_Map_MatrixXd* eigen_to_c(const Map<MatrixXd>& ref)
+{
+ return reinterpret_cast<const C_Map_MatrixXd*>(&ref);
+}
+
+
+/************************* implementation of classes **********************************************/
+
+
+////// class MatrixXd //////
+
+
+C_MatrixXd* MatrixXd_new(int rows, int cols)
+{
+ return eigen_to_c(*new MatrixXd(rows,cols));
+}
+
+void MatrixXd_delete(C_MatrixXd *m)
+{
+ delete &c_to_eigen(m);
+}
+
+double* MatrixXd_data(C_MatrixXd *m)
+{
+ return c_to_eigen(m).data();
+}
+
+void MatrixXd_set_zero(C_MatrixXd *m)
+{
+ c_to_eigen(m).setZero();
+}
+
+void MatrixXd_resize(C_MatrixXd *m, int rows, int cols)
+{
+ c_to_eigen(m).resize(rows,cols);
+}
+
+void MatrixXd_copy(C_MatrixXd *dst, const C_MatrixXd *src)
+{
+ c_to_eigen(dst) = c_to_eigen(src);
+}
+
+void MatrixXd_copy_map(C_MatrixXd *dst, const C_Map_MatrixXd *src)
+{
+ c_to_eigen(dst) = c_to_eigen(src);
+}
+
+void MatrixXd_set_coeff(C_MatrixXd *m, int i, int j, double coeff)
+{
+ c_to_eigen(m)(i,j) = coeff;
+}
+
+double MatrixXd_get_coeff(const C_MatrixXd *m, int i, int j)
+{
+ return c_to_eigen(m)(i,j);
+}
+
+void MatrixXd_print(const C_MatrixXd *m)
+{
+ std::cout << c_to_eigen(m) << std::endl;
+}
+
+void MatrixXd_multiply(const C_MatrixXd *m1, const C_MatrixXd *m2, C_MatrixXd *result)
+{
+ c_to_eigen(result) = c_to_eigen(m1) * c_to_eigen(m2);
+}
+
+void MatrixXd_add(const C_MatrixXd *m1, const C_MatrixXd *m2, C_MatrixXd *result)
+{
+ c_to_eigen(result) = c_to_eigen(m1) + c_to_eigen(m2);
+}
+
+
+
+////// class Map_MatrixXd //////
+
+
+C_Map_MatrixXd* Map_MatrixXd_new(double *array, int rows, int cols)
+{
+ return eigen_to_c(*new Map<MatrixXd>(array,rows,cols));
+}
+
+void Map_MatrixXd_delete(C_Map_MatrixXd *m)
+{
+ delete &c_to_eigen(m);
+}
+
+void Map_MatrixXd_set_zero(C_Map_MatrixXd *m)
+{
+ c_to_eigen(m).setZero();
+}
+
+void Map_MatrixXd_copy(C_Map_MatrixXd *dst, const C_Map_MatrixXd *src)
+{
+ c_to_eigen(dst) = c_to_eigen(src);
+}
+
+void Map_MatrixXd_copy_matrix(C_Map_MatrixXd *dst, const C_MatrixXd *src)
+{
+ c_to_eigen(dst) = c_to_eigen(src);
+}
+
+void Map_MatrixXd_set_coeff(C_Map_MatrixXd *m, int i, int j, double coeff)
+{
+ c_to_eigen(m)(i,j) = coeff;
+}
+
+double Map_MatrixXd_get_coeff(const C_Map_MatrixXd *m, int i, int j)
+{
+ return c_to_eigen(m)(i,j);
+}
+
+void Map_MatrixXd_print(const C_Map_MatrixXd *m)
+{
+ std::cout << c_to_eigen(m) << std::endl;
+}
+
+void Map_MatrixXd_multiply(const C_Map_MatrixXd *m1, const C_Map_MatrixXd *m2, C_Map_MatrixXd *result)
+{
+ c_to_eigen(result) = c_to_eigen(m1) * c_to_eigen(m2);
+}
+
+void Map_MatrixXd_add(const C_Map_MatrixXd *m1, const C_Map_MatrixXd *m2, C_Map_MatrixXd *result)
+{
+ c_to_eigen(result) = c_to_eigen(m1) + c_to_eigen(m2);
+}
diff --git a/demos/mix_eigen_and_c/binary_library.h b/demos/mix_eigen_and_c/binary_library.h
new file mode 100644
index 0000000..9b63fac
--- /dev/null
+++ b/demos/mix_eigen_and_c/binary_library.h
@@ -0,0 +1,71 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+// This is a pure C header, no C++ here.
+// The functions declared here will be implemented in C++ but
+// we don't have to know, because thanks to the extern "C" syntax,
+// they will be compiled to C object code.
+
+#ifdef __cplusplus
+extern "C"
+{
+#endif
+
+ // just dummy empty structs to give different pointer types,
+ // instead of using void* which would be type unsafe
+ struct C_MatrixXd {};
+ struct C_Map_MatrixXd {};
+
+ // the C_MatrixXd class, wraps some of the functionality
+ // of Eigen::MatrixXd.
+ struct C_MatrixXd* MatrixXd_new(int rows, int cols);
+ void MatrixXd_delete (struct C_MatrixXd *m);
+ double* MatrixXd_data (struct C_MatrixXd *m);
+ void MatrixXd_set_zero (struct C_MatrixXd *m);
+ void MatrixXd_resize (struct C_MatrixXd *m, int rows, int cols);
+ void MatrixXd_copy (struct C_MatrixXd *dst,
+ const struct C_MatrixXd *src);
+ void MatrixXd_copy_map (struct C_MatrixXd *dst,
+ const struct C_Map_MatrixXd *src);
+ void MatrixXd_set_coeff (struct C_MatrixXd *m,
+ int i, int j, double coeff);
+ double MatrixXd_get_coeff (const struct C_MatrixXd *m,
+ int i, int j);
+ void MatrixXd_print (const struct C_MatrixXd *m);
+ void MatrixXd_add (const struct C_MatrixXd *m1,
+ const struct C_MatrixXd *m2,
+ struct C_MatrixXd *result);
+ void MatrixXd_multiply (const struct C_MatrixXd *m1,
+ const struct C_MatrixXd *m2,
+ struct C_MatrixXd *result);
+
+ // the C_Map_MatrixXd class, wraps some of the functionality
+ // of Eigen::Map<MatrixXd>
+ struct C_Map_MatrixXd* Map_MatrixXd_new(double *array, int rows, int cols);
+ void Map_MatrixXd_delete (struct C_Map_MatrixXd *m);
+ void Map_MatrixXd_set_zero (struct C_Map_MatrixXd *m);
+ void Map_MatrixXd_copy (struct C_Map_MatrixXd *dst,
+ const struct C_Map_MatrixXd *src);
+ void Map_MatrixXd_copy_matrix(struct C_Map_MatrixXd *dst,
+ const struct C_MatrixXd *src);
+ void Map_MatrixXd_set_coeff (struct C_Map_MatrixXd *m,
+ int i, int j, double coeff);
+ double Map_MatrixXd_get_coeff (const struct C_Map_MatrixXd *m,
+ int i, int j);
+ void Map_MatrixXd_print (const struct C_Map_MatrixXd *m);
+ void Map_MatrixXd_add (const struct C_Map_MatrixXd *m1,
+ const struct C_Map_MatrixXd *m2,
+ struct C_Map_MatrixXd *result);
+ void Map_MatrixXd_multiply (const struct C_Map_MatrixXd *m1,
+ const struct C_Map_MatrixXd *m2,
+ struct C_Map_MatrixXd *result);
+
+#ifdef __cplusplus
+} // end extern "C"
+#endif
diff --git a/demos/mix_eigen_and_c/example.c b/demos/mix_eigen_and_c/example.c
new file mode 100644
index 0000000..508eb54
--- /dev/null
+++ b/demos/mix_eigen_and_c/example.c
@@ -0,0 +1,65 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "binary_library.h"
+#include "stdio.h"
+
+void demo_MatrixXd()
+{
+ struct C_MatrixXd *matrix1, *matrix2, *result;
+ printf("*** demo_MatrixXd ***\n");
+
+ matrix1 = MatrixXd_new(3, 3);
+ MatrixXd_set_zero(matrix1);
+ MatrixXd_set_coeff(matrix1, 0, 1, 2.5);
+ MatrixXd_set_coeff(matrix1, 1, 0, 1.4);
+ printf("Here is matrix1:\n");
+ MatrixXd_print(matrix1);
+
+ matrix2 = MatrixXd_new(3, 3);
+ MatrixXd_multiply(matrix1, matrix1, matrix2);
+ printf("Here is matrix1*matrix1:\n");
+ MatrixXd_print(matrix2);
+
+ MatrixXd_delete(matrix1);
+ MatrixXd_delete(matrix2);
+}
+
+// this helper function takes a plain C array and prints it in one line
+void print_array(double *array, int n)
+{
+ struct C_Map_MatrixXd *m = Map_MatrixXd_new(array, 1, n);
+ Map_MatrixXd_print(m);
+ Map_MatrixXd_delete(m);
+}
+
+void demo_Map_MatrixXd()
+{
+ struct C_Map_MatrixXd *map;
+ double array[5];
+ int i;
+ printf("*** demo_Map_MatrixXd ***\n");
+
+ for(i = 0; i < 5; ++i) array[i] = i;
+ printf("Initially, the array is:\n");
+ print_array(array, 5);
+
+ map = Map_MatrixXd_new(array, 5, 1);
+ Map_MatrixXd_add(map, map, map);
+ Map_MatrixXd_delete(map);
+
+ printf("Now the array is:\n");
+ print_array(array, 5);
+}
+
+int main()
+{
+ demo_MatrixXd();
+ demo_Map_MatrixXd();
+}
diff --git a/demos/opengl/CMakeLists.txt b/demos/opengl/CMakeLists.txt
new file mode 100644
index 0000000..299aa44
--- /dev/null
+++ b/demos/opengl/CMakeLists.txt
@@ -0,0 +1,28 @@
+find_package(Qt4)
+find_package(OpenGL)
+
+if(QT4_FOUND AND OPENGL_FOUND)
+
+ set(QT_USE_QTOPENGL TRUE)
+ include(${QT_USE_FILE})
+
+ set(CMAKE_INCLUDE_CURRENT_DIR ON)
+
+ include_directories( ${QT_INCLUDE_DIR} )
+
+ set(quaternion_demo_SRCS gpuhelper.cpp icosphere.cpp camera.cpp trackball.cpp quaternion_demo.cpp)
+
+ qt4_automoc(${quaternion_demo_SRCS})
+
+ add_executable(quaternion_demo ${quaternion_demo_SRCS})
+ add_dependencies(demos quaternion_demo)
+
+ target_link_libraries(quaternion_demo
+ ${QT_QTCORE_LIBRARY} ${QT_QTGUI_LIBRARY}
+ ${QT_QTOPENGL_LIBRARY} ${OPENGL_LIBRARIES} )
+
+else()
+
+ message(STATUS "OpenGL demo disabled because Qt4 and/or OpenGL have not been found.")
+
+endif()
\ No newline at end of file
diff --git a/demos/opengl/README b/demos/opengl/README
new file mode 100644
index 0000000..8fb1649
--- /dev/null
+++ b/demos/opengl/README
@@ -0,0 +1,13 @@
+
+Navigation:
+ left button: rotate around the target
+ middle button: zoom
+ left button + ctrl quake rotate (rotate around camera position)
+ middle button + ctrl walk (progress along camera's z direction)
+ left button: pan (translate in the XY camera's plane)
+
+R : move the camera to initial position
+A : start/stop animation
+C : clear the animation
+G : add a key frame
+
diff --git a/demos/opengl/camera.cpp b/demos/opengl/camera.cpp
new file mode 100644
index 0000000..8a2344c
--- /dev/null
+++ b/demos/opengl/camera.cpp
@@ -0,0 +1,264 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "camera.h"
+
+#include "gpuhelper.h"
+#include <GL/glu.h>
+
+#include "Eigen/LU"
+using namespace Eigen;
+
+Camera::Camera()
+ : mViewIsUptodate(false), mProjIsUptodate(false)
+{
+ mViewMatrix.setIdentity();
+
+ mFovY = M_PI/3.;
+ mNearDist = 1.;
+ mFarDist = 50000.;
+
+ mVpX = 0;
+ mVpY = 0;
+
+ setPosition(Vector3f::Constant(100.));
+ setTarget(Vector3f::Zero());
+}
+
+Camera& Camera::operator=(const Camera& other)
+{
+ mViewIsUptodate = false;
+ mProjIsUptodate = false;
+
+ mVpX = other.mVpX;
+ mVpY = other.mVpY;
+ mVpWidth = other.mVpWidth;
+ mVpHeight = other.mVpHeight;
+
+ mTarget = other.mTarget;
+ mFovY = other.mFovY;
+ mNearDist = other.mNearDist;
+ mFarDist = other.mFarDist;
+
+ mViewMatrix = other.mViewMatrix;
+ mProjectionMatrix = other.mProjectionMatrix;
+
+ return *this;
+}
+
+Camera::Camera(const Camera& other)
+{
+ *this = other;
+}
+
+Camera::~Camera()
+{
+}
+
+
+void Camera::setViewport(uint offsetx, uint offsety, uint width, uint height)
+{
+ mVpX = offsetx;
+ mVpY = offsety;
+ mVpWidth = width;
+ mVpHeight = height;
+
+ mProjIsUptodate = false;
+}
+
+void Camera::setViewport(uint width, uint height)
+{
+ mVpWidth = width;
+ mVpHeight = height;
+
+ mProjIsUptodate = false;
+}
+
+void Camera::setFovY(float value)
+{
+ mFovY = value;
+ mProjIsUptodate = false;
+}
+
+Vector3f Camera::direction(void) const
+{
+ return - (orientation() * Vector3f::UnitZ());
+}
+Vector3f Camera::up(void) const
+{
+ return orientation() * Vector3f::UnitY();
+}
+Vector3f Camera::right(void) const
+{
+ return orientation() * Vector3f::UnitX();
+}
+
+void Camera::setDirection(const Vector3f& newDirection)
+{
+ // TODO implement it computing the rotation between newDirection and current dir ?
+ Vector3f up = this->up();
+
+ Matrix3f camAxes;
+
+ camAxes.col(2) = (-newDirection).normalized();
+ camAxes.col(0) = up.cross( camAxes.col(2) ).normalized();
+ camAxes.col(1) = camAxes.col(2).cross( camAxes.col(0) ).normalized();
+ setOrientation(Quaternionf(camAxes));
+
+ mViewIsUptodate = false;
+}
+
+void Camera::setTarget(const Vector3f& target)
+{
+ mTarget = target;
+ if (!mTarget.isApprox(position()))
+ {
+ Vector3f newDirection = mTarget - position();
+ setDirection(newDirection.normalized());
+ }
+}
+
+void Camera::setPosition(const Vector3f& p)
+{
+ mFrame.position = p;
+ mViewIsUptodate = false;
+}
+
+void Camera::setOrientation(const Quaternionf& q)
+{
+ mFrame.orientation = q;
+ mViewIsUptodate = false;
+}
+
+void Camera::setFrame(const Frame& f)
+{
+ mFrame = f;
+ mViewIsUptodate = false;
+}
+
+void Camera::rotateAroundTarget(const Quaternionf& q)
+{
+ Matrix4f mrot, mt, mtm;
+
+ // update the transform matrix
+ updateViewMatrix();
+ Vector3f t = mViewMatrix * mTarget;
+
+ mViewMatrix = Translation3f(t)
+ * q
+ * Translation3f(-t)
+ * mViewMatrix;
+
+ Quaternionf qa(mViewMatrix.linear());
+ qa = qa.conjugate();
+ setOrientation(qa);
+ setPosition(- (qa * mViewMatrix.translation()) );
+
+ mViewIsUptodate = true;
+}
+
+void Camera::localRotate(const Quaternionf& q)
+{
+ float dist = (position() - mTarget).norm();
+ setOrientation(orientation() * q);
+ mTarget = position() + dist * direction();
+ mViewIsUptodate = false;
+}
+
+void Camera::zoom(float d)
+{
+ float dist = (position() - mTarget).norm();
+ if(dist > d)
+ {
+ setPosition(position() + direction() * d);
+ mViewIsUptodate = false;
+ }
+}
+
+void Camera::localTranslate(const Vector3f& t)
+{
+ Vector3f trans = orientation() * t;
+ setPosition( position() + trans );
+ setTarget( mTarget + trans );
+
+ mViewIsUptodate = false;
+}
+
+void Camera::updateViewMatrix(void) const
+{
+ if(!mViewIsUptodate)
+ {
+ Quaternionf q = orientation().conjugate();
+ mViewMatrix.linear() = q.toRotationMatrix();
+ mViewMatrix.translation() = - (mViewMatrix.linear() * position());
+
+ mViewIsUptodate = true;
+ }
+}
+
+const Affine3f& Camera::viewMatrix(void) const
+{
+ updateViewMatrix();
+ return mViewMatrix;
+}
+
+void Camera::updateProjectionMatrix(void) const
+{
+ if(!mProjIsUptodate)
+ {
+ mProjectionMatrix.setIdentity();
+ float aspect = float(mVpWidth)/float(mVpHeight);
+ float theta = mFovY*0.5;
+ float range = mFarDist - mNearDist;
+ float invtan = 1./tan(theta);
+
+ mProjectionMatrix(0,0) = invtan / aspect;
+ mProjectionMatrix(1,1) = invtan;
+ mProjectionMatrix(2,2) = -(mNearDist + mFarDist) / range;
+ mProjectionMatrix(3,2) = -1;
+ mProjectionMatrix(2,3) = -2 * mNearDist * mFarDist / range;
+ mProjectionMatrix(3,3) = 0;
+
+ mProjIsUptodate = true;
+ }
+}
+
+const Matrix4f& Camera::projectionMatrix(void) const
+{
+ updateProjectionMatrix();
+ return mProjectionMatrix;
+}
+
+void Camera::activateGL(void)
+{
+ glViewport(vpX(), vpY(), vpWidth(), vpHeight());
+ gpu.loadMatrix(projectionMatrix(),GL_PROJECTION);
+ gpu.loadMatrix(viewMatrix().matrix(),GL_MODELVIEW);
+}
+
+
+Vector3f Camera::unProject(const Vector2f& uv, float depth) const
+{
+ Matrix4f inv = mViewMatrix.inverse().matrix();
+ return unProject(uv, depth, inv);
+}
+
+Vector3f Camera::unProject(const Vector2f& uv, float depth, const Matrix4f& invModelview) const
+{
+ updateViewMatrix();
+ updateProjectionMatrix();
+
+ Vector3f a(2.*uv.x()/float(mVpWidth)-1., 2.*uv.y()/float(mVpHeight)-1., 1.);
+ a.x() *= depth/mProjectionMatrix(0,0);
+ a.y() *= depth/mProjectionMatrix(1,1);
+ a.z() = -depth;
+ // FIXME /\/|
+ Vector4f b = invModelview * Vector4f(a.x(), a.y(), a.z(), 1.);
+ return Vector3f(b.x(), b.y(), b.z());
+}
diff --git a/demos/opengl/camera.h b/demos/opengl/camera.h
new file mode 100644
index 0000000..15714d2
--- /dev/null
+++ b/demos/opengl/camera.h
@@ -0,0 +1,118 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_CAMERA_H
+#define EIGEN_CAMERA_H
+
+#include <Eigen/Geometry>
+#include <QObject>
+// #include <frame.h>
+
+class Frame
+{
+ public:
+ EIGEN_MAKE_ALIGNED_OPERATOR_NEW
+
+ inline Frame(const Eigen::Vector3f& pos = Eigen::Vector3f::Zero(),
+ const Eigen::Quaternionf& o = Eigen::Quaternionf())
+ : orientation(o), position(pos)
+ {}
+ Frame lerp(float alpha, const Frame& other) const
+ {
+ return Frame((1.f-alpha)*position + alpha * other.position,
+ orientation.slerp(alpha,other.orientation));
+ }
+
+ Eigen::Quaternionf orientation;
+ Eigen::Vector3f position;
+};
+
+class Camera
+{
+ public:
+ EIGEN_MAKE_ALIGNED_OPERATOR_NEW
+
+ Camera(void);
+
+ Camera(const Camera& other);
+
+ virtual ~Camera();
+
+ Camera& operator=(const Camera& other);
+
+ void setViewport(uint offsetx, uint offsety, uint width, uint height);
+ void setViewport(uint width, uint height);
+
+ inline uint vpX(void) const { return mVpX; }
+ inline uint vpY(void) const { return mVpY; }
+ inline uint vpWidth(void) const { return mVpWidth; }
+ inline uint vpHeight(void) const { return mVpHeight; }
+
+ inline float fovY(void) const { return mFovY; }
+ void setFovY(float value);
+
+ void setPosition(const Eigen::Vector3f& pos);
+ inline const Eigen::Vector3f& position(void) const { return mFrame.position; }
+
+ void setOrientation(const Eigen::Quaternionf& q);
+ inline const Eigen::Quaternionf& orientation(void) const { return mFrame.orientation; }
+
+ void setFrame(const Frame& f);
+ const Frame& frame(void) const { return mFrame; }
+
+ void setDirection(const Eigen::Vector3f& newDirection);
+ Eigen::Vector3f direction(void) const;
+ void setUp(const Eigen::Vector3f& vectorUp);
+ Eigen::Vector3f up(void) const;
+ Eigen::Vector3f right(void) const;
+
+ void setTarget(const Eigen::Vector3f& target);
+ inline const Eigen::Vector3f& target(void) { return mTarget; }
+
+ const Eigen::Affine3f& viewMatrix(void) const;
+ const Eigen::Matrix4f& projectionMatrix(void) const;
+
+ void rotateAroundTarget(const Eigen::Quaternionf& q);
+ void localRotate(const Eigen::Quaternionf& q);
+ void zoom(float d);
+
+ void localTranslate(const Eigen::Vector3f& t);
+
+ /** Setup OpenGL matrices and viewport */
+ void activateGL(void);
+
+ Eigen::Vector3f unProject(const Eigen::Vector2f& uv, float depth, const Eigen::Matrix4f& invModelview) const;
+ Eigen::Vector3f unProject(const Eigen::Vector2f& uv, float depth) const;
+
+ protected:
+ void updateViewMatrix(void) const;
+ void updateProjectionMatrix(void) const;
+
+ protected:
+
+ uint mVpX, mVpY;
+ uint mVpWidth, mVpHeight;
+
+ Frame mFrame;
+
+ mutable Eigen::Affine3f mViewMatrix;
+ mutable Eigen::Matrix4f mProjectionMatrix;
+
+ mutable bool mViewIsUptodate;
+ mutable bool mProjIsUptodate;
+
+ // used by rotateAroundTarget
+ Eigen::Vector3f mTarget;
+
+ float mFovY;
+ float mNearDist;
+ float mFarDist;
+};
+
+#endif // EIGEN_CAMERA_H
diff --git a/demos/opengl/gpuhelper.cpp b/demos/opengl/gpuhelper.cpp
new file mode 100644
index 0000000..fd236b1
--- /dev/null
+++ b/demos/opengl/gpuhelper.cpp
@@ -0,0 +1,126 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "gpuhelper.h"
+#include "icosphere.h"
+#include <GL/glu.h>
+// PLEASE don't look at this old code... ;)
+
+#include <fstream>
+#include <algorithm>
+
+GpuHelper gpu;
+
+GpuHelper::GpuHelper()
+{
+ mVpWidth = mVpHeight = 0;
+ mCurrentMatrixTarget = 0;
+ mInitialized = false;
+}
+
+GpuHelper::~GpuHelper()
+{
+}
+
+void GpuHelper::pushProjectionMode2D(ProjectionMode2D pm)
+{
+ // switch to 2D projection
+ pushMatrix(Matrix4f::Identity(),GL_PROJECTION);
+
+ if(pm==PM_Normalized)
+ {
+ //glOrtho(-1., 1., -1., 1., 0., 1.);
+ }
+ else if(pm==PM_Viewport)
+ {
+ GLint vp[4];
+ glGetIntegerv(GL_VIEWPORT, vp);
+ glOrtho(0., vp[2], 0., vp[3], -1., 1.);
+ }
+
+ pushMatrix(Matrix4f::Identity(),GL_MODELVIEW);
+}
+
+void GpuHelper::popProjectionMode2D(void)
+{
+ popMatrix(GL_PROJECTION);
+ popMatrix(GL_MODELVIEW);
+}
+
+void GpuHelper::drawVector(const Vector3f& position, const Vector3f& vec, const Color& color, float aspect /* = 50.*/)
+{
+ static GLUquadricObj *cylindre = gluNewQuadric();
+ glColor4fv(color.data());
+ float length = vec.norm();
+ pushMatrix(GL_MODELVIEW);
+ glTranslatef(position.x(), position.y(), position.z());
+ Vector3f ax = Matrix3f::Identity().col(2).cross(vec);
+ ax.normalize();
+ Vector3f tmp = vec;
+ tmp.normalize();
+ float angle = 180.f/M_PI * acos(tmp.z());
+ if (angle>1e-3)
+ glRotatef(angle, ax.x(), ax.y(), ax.z());
+ gluCylinder(cylindre, length/aspect, length/aspect, 0.8*length, 10, 10);
+ glTranslatef(0.0,0.0,0.8*length);
+ gluCylinder(cylindre, 2.0*length/aspect, 0.0, 0.2*length, 10, 10);
+
+ popMatrix(GL_MODELVIEW);
+}
+
+void GpuHelper::drawVectorBox(const Vector3f& position, const Vector3f& vec, const Color& color, float aspect)
+{
+ static GLUquadricObj *cylindre = gluNewQuadric();
+ glColor4fv(color.data());
+ float length = vec.norm();
+ pushMatrix(GL_MODELVIEW);
+ glTranslatef(position.x(), position.y(), position.z());
+ Vector3f ax = Matrix3f::Identity().col(2).cross(vec);
+ ax.normalize();
+ Vector3f tmp = vec;
+ tmp.normalize();
+ float angle = 180.f/M_PI * acos(tmp.z());
+ if (angle>1e-3)
+ glRotatef(angle, ax.x(), ax.y(), ax.z());
+ gluCylinder(cylindre, length/aspect, length/aspect, 0.8*length, 10, 10);
+ glTranslatef(0.0,0.0,0.8*length);
+ glScalef(4.0*length/aspect,4.0*length/aspect,4.0*length/aspect);
+ drawUnitCube();
+ popMatrix(GL_MODELVIEW);
+}
+
+void GpuHelper::drawUnitCube(void)
+{
+ static float vertices[][3] = {
+ {-0.5,-0.5,-0.5},
+ { 0.5,-0.5,-0.5},
+ {-0.5, 0.5,-0.5},
+ { 0.5, 0.5,-0.5},
+ {-0.5,-0.5, 0.5},
+ { 0.5,-0.5, 0.5},
+ {-0.5, 0.5, 0.5},
+ { 0.5, 0.5, 0.5}};
+
+ glBegin(GL_QUADS);
+ glNormal3f(0,0,-1); glVertex3fv(vertices[0]); glVertex3fv(vertices[2]); glVertex3fv(vertices[3]); glVertex3fv(vertices[1]);
+ glNormal3f(0,0, 1); glVertex3fv(vertices[4]); glVertex3fv(vertices[5]); glVertex3fv(vertices[7]); glVertex3fv(vertices[6]);
+ glNormal3f(0,-1,0); glVertex3fv(vertices[0]); glVertex3fv(vertices[1]); glVertex3fv(vertices[5]); glVertex3fv(vertices[4]);
+ glNormal3f(0, 1,0); glVertex3fv(vertices[2]); glVertex3fv(vertices[6]); glVertex3fv(vertices[7]); glVertex3fv(vertices[3]);
+ glNormal3f(-1,0,0); glVertex3fv(vertices[0]); glVertex3fv(vertices[4]); glVertex3fv(vertices[6]); glVertex3fv(vertices[2]);
+ glNormal3f( 1,0,0); glVertex3fv(vertices[1]); glVertex3fv(vertices[3]); glVertex3fv(vertices[7]); glVertex3fv(vertices[5]);
+ glEnd();
+}
+
+void GpuHelper::drawUnitSphere(int level)
+{
+ static IcoSphere sphere;
+ sphere.draw(level);
+}
+
+
diff --git a/demos/opengl/gpuhelper.h b/demos/opengl/gpuhelper.h
new file mode 100644
index 0000000..880e9a5
--- /dev/null
+++ b/demos/opengl/gpuhelper.h
@@ -0,0 +1,207 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_GPUHELPER_H
+#define EIGEN_GPUHELPER_H
+
+#include <Eigen/Geometry>
+#include <GL/gl.h>
+#include <vector>
+
+using namespace Eigen;
+
+typedef Vector4f Color;
+
+class GpuHelper
+{
+ public:
+
+ GpuHelper();
+
+ ~GpuHelper();
+
+ enum ProjectionMode2D { PM_Normalized = 1, PM_Viewport = 2 };
+ void pushProjectionMode2D(ProjectionMode2D pm);
+ void popProjectionMode2D();
+
+ /** Multiply the OpenGL matrix \a matrixTarget by the matrix \a mat.
+ Essentially, this helper function automatically calls glMatrixMode(matrixTarget) if required
+ and does a proper call to the right glMultMatrix*() function according to the scalar type
+ and storage order.
+ \warning glMatrixMode() must never be called directly. If you are unsure, use forceMatrixMode().
+ \sa Matrix, loadMatrix(), forceMatrixMode()
+ */
+ template<typename Scalar, int Flags_>
+ void multMatrix(const Matrix<Scalar,4,4, Flags_, 4,4>& mat, GLenum matrixTarget);
+
+ /** Load the matrix \a mat to the OpenGL matrix \a matrixTarget.
+ Essentially, this helper function automatically calls glMatrixMode(matrixTarget) if required
+ and does a proper call to the right glLoadMatrix*() or glLoadIdentity() function according to the scalar type
+ and storage order.
+ \warning glMatrixMode() must never be called directly. If you are unsure, use forceMatrixMode().
+ \sa Matrix, multMatrix(), forceMatrixMode()
+ */
+ template<typename Scalar, int Flags_>
+ void loadMatrix(const Eigen::Matrix<Scalar,4,4, Flags_, 4,4>& mat, GLenum matrixTarget);
+
+ template<typename Scalar, typename Derived>
+ void loadMatrix(
+ const Eigen::CwiseNullaryOp<Eigen::internal::scalar_identity_op<Scalar>,Derived>&,
+ GLenum matrixTarget);
+
+ /** Make the matrix \a matrixTarget the current OpenGL matrix target.
+ Call this function before loadMatrix() or multMatrix() if you cannot guarantee that glMatrixMode()
+ has never been called after the last loadMatrix() or multMatrix() calls.
+ \todo provides a debug mode checking the sanity of the cached matrix mode.
+ */
+ inline void forceMatrixTarget(GLenum matrixTarget) {glMatrixMode(mCurrentMatrixTarget=matrixTarget);}
+
+ inline void setMatrixTarget(GLenum matrixTarget);
+
+ /** Push the OpenGL matrix \a matrixTarget and load \a mat.
+ */
+ template<typename Scalar, int Flags_>
+ inline void pushMatrix(const Matrix<Scalar,4,4, Flags_, 4,4>& mat, GLenum matrixTarget);
+
+ template<typename Scalar, typename Derived>
+ void pushMatrix(
+ const Eigen::CwiseNullaryOp<Eigen::internal::scalar_identity_op<Scalar>,Derived>&,
+ GLenum matrixTarget);
+
+ /** Push and clone the OpenGL matrix \a matrixTarget
+ */
+ inline void pushMatrix(GLenum matrixTarget);
+
+ /** Pop the OpenGL matrix \a matrixTarget
+ */
+ inline void popMatrix(GLenum matrixTarget);
+
+ void drawVector(const Vector3f& position, const Vector3f& vec, const Color& color, float aspect = 50.);
+ void drawVectorBox(const Vector3f& position, const Vector3f& vec, const Color& color, float aspect = 50.);
+ void drawUnitCube(void);
+ void drawUnitSphere(int level=0);
+
+ /// draw the \a nofElement first elements
+ inline void draw(GLenum mode, uint nofElement);
+
+ /// draw a range of elements
+ inline void draw(GLenum mode, uint start, uint end);
+
+ /// draw an indexed subset
+ inline void draw(GLenum mode, const std::vector<uint>* pIndexes);
+
+protected:
+
+ void update(void);
+
+ GLuint mColorBufferId;
+ int mVpWidth, mVpHeight;
+ GLenum mCurrentMatrixTarget;
+ bool mInitialized;
+};
+
+/** Singleton shortcut
+*/
+extern GpuHelper gpu;
+
+
+/** \internal
+*/
+template<bool RowMajor, int Flags_> struct GlMatrixHelper;
+
+template<int Flags_> struct GlMatrixHelper<false,Flags_>
+{
+ static void loadMatrix(const Matrix<float, 4,4, Flags_, 4,4>& mat) { glLoadMatrixf(mat.data()); }
+ static void loadMatrix(const Matrix<double,4,4, Flags_, 4,4>& mat) { glLoadMatrixd(mat.data()); }
+ static void multMatrix(const Matrix<float, 4,4, Flags_, 4,4>& mat) { glMultMatrixf(mat.data()); }
+ static void multMatrix(const Matrix<double,4,4, Flags_, 4,4>& mat) { glMultMatrixd(mat.data()); }
+};
+
+template<int Flags_> struct GlMatrixHelper<true,Flags_>
+{
+ static void loadMatrix(const Matrix<float, 4,4, Flags_, 4,4>& mat) { glLoadMatrixf(mat.transpose().eval().data()); }
+ static void loadMatrix(const Matrix<double,4,4, Flags_, 4,4>& mat) { glLoadMatrixd(mat.transpose().eval().data()); }
+ static void multMatrix(const Matrix<float, 4,4, Flags_, 4,4>& mat) { glMultMatrixf(mat.transpose().eval().data()); }
+ static void multMatrix(const Matrix<double,4,4, Flags_, 4,4>& mat) { glMultMatrixd(mat.transpose().eval().data()); }
+};
+
+inline void GpuHelper::setMatrixTarget(GLenum matrixTarget)
+{
+ if (matrixTarget != mCurrentMatrixTarget)
+ glMatrixMode(mCurrentMatrixTarget=matrixTarget);
+}
+
+template<typename Scalar, int Flags_>
+void GpuHelper::multMatrix(const Matrix<Scalar,4,4, Flags_, 4,4>& mat, GLenum matrixTarget)
+{
+ setMatrixTarget(matrixTarget);
+ GlMatrixHelper<Flags_&Eigen::RowMajorBit, Flags_>::multMatrix(mat);
+}
+
+template<typename Scalar, typename Derived>
+void GpuHelper::loadMatrix(
+ const Eigen::CwiseNullaryOp<Eigen::internal::scalar_identity_op<Scalar>,Derived>&,
+ GLenum matrixTarget)
+{
+ setMatrixTarget(matrixTarget);
+ glLoadIdentity();
+}
+
+template<typename Scalar, int Flags_>
+void GpuHelper::loadMatrix(const Eigen::Matrix<Scalar,4,4, Flags_, 4,4>& mat, GLenum matrixTarget)
+{
+ setMatrixTarget(matrixTarget);
+ GlMatrixHelper<(Flags_&Eigen::RowMajorBit)!=0, Flags_>::loadMatrix(mat);
+}
+
+inline void GpuHelper::pushMatrix(GLenum matrixTarget)
+{
+ setMatrixTarget(matrixTarget);
+ glPushMatrix();
+}
+
+template<typename Scalar, int Flags_>
+inline void GpuHelper::pushMatrix(const Matrix<Scalar,4,4, Flags_, 4,4>& mat, GLenum matrixTarget)
+{
+ pushMatrix(matrixTarget);
+ GlMatrixHelper<Flags_&Eigen::RowMajorBit,Flags_>::loadMatrix(mat);
+}
+
+template<typename Scalar, typename Derived>
+void GpuHelper::pushMatrix(
+ const Eigen::CwiseNullaryOp<Eigen::internal::scalar_identity_op<Scalar>,Derived>&,
+ GLenum matrixTarget)
+{
+ pushMatrix(matrixTarget);
+ glLoadIdentity();
+}
+
+inline void GpuHelper::popMatrix(GLenum matrixTarget)
+{
+ setMatrixTarget(matrixTarget);
+ glPopMatrix();
+}
+
+inline void GpuHelper::draw(GLenum mode, uint nofElement)
+{
+ glDrawArrays(mode, 0, nofElement);
+}
+
+
+inline void GpuHelper::draw(GLenum mode, const std::vector<uint>* pIndexes)
+{
+ glDrawElements(mode, pIndexes->size(), GL_UNSIGNED_INT, &(pIndexes->front()));
+}
+
+inline void GpuHelper::draw(GLenum mode, uint start, uint end)
+{
+ glDrawArrays(mode, start, end-start);
+}
+
+#endif // EIGEN_GPUHELPER_H
diff --git a/demos/opengl/icosphere.cpp b/demos/opengl/icosphere.cpp
new file mode 100644
index 0000000..39444cb
--- /dev/null
+++ b/demos/opengl/icosphere.cpp
@@ -0,0 +1,120 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "icosphere.h"
+
+#include <GL/gl.h>
+#include <map>
+
+using namespace Eigen;
+
+//--------------------------------------------------------------------------------
+// icosahedron data
+//--------------------------------------------------------------------------------
+#define X .525731112119133606
+#define Z .850650808352039932
+
+static GLfloat vdata[12][3] = {
+ {-X, 0.0, Z}, {X, 0.0, Z}, {-X, 0.0, -Z}, {X, 0.0, -Z},
+ {0.0, Z, X}, {0.0, Z, -X}, {0.0, -Z, X}, {0.0, -Z, -X},
+ {Z, X, 0.0}, {-Z, X, 0.0}, {Z, -X, 0.0}, {-Z, -X, 0.0}
+};
+
+static GLint tindices[20][3] = {
+ {0,4,1}, {0,9,4}, {9,5,4}, {4,5,8}, {4,8,1},
+ {8,10,1}, {8,3,10}, {5,3,8}, {5,2,3}, {2,7,3},
+ {7,10,3}, {7,6,10}, {7,11,6}, {11,0,6}, {0,1,6},
+ {6,1,10}, {9,0,11}, {9,11,2}, {9,2,5}, {7,2,11} };
+//--------------------------------------------------------------------------------
+
+IcoSphere::IcoSphere(unsigned int levels)
+{
+ // init with an icosahedron
+ for (int i = 0; i < 12; i++)
+ mVertices.push_back(Map<Vector3f>(vdata[i]));
+ mIndices.push_back(new std::vector<int>);
+ std::vector<int>& indices = *mIndices.back();
+ for (int i = 0; i < 20; i++)
+ {
+ for (int k = 0; k < 3; k++)
+ indices.push_back(tindices[i][k]);
+ }
+ mListIds.push_back(0);
+
+ while(mIndices.size()<levels)
+ _subdivide();
+}
+
+const std::vector<int>& IcoSphere::indices(int level) const
+{
+ while (level>=int(mIndices.size()))
+ const_cast<IcoSphere*>(this)->_subdivide();
+ return *mIndices[level];
+}
+
+void IcoSphere::_subdivide(void)
+{
+ typedef unsigned long long Key;
+ std::map<Key,int> edgeMap;
+ const std::vector<int>& indices = *mIndices.back();
+ mIndices.push_back(new std::vector<int>);
+ std::vector<int>& refinedIndices = *mIndices.back();
+ int end = indices.size();
+ for (int i=0; i<end; i+=3)
+ {
+ int ids0[3], // indices of outer vertices
+ ids1[3]; // indices of edge vertices
+ for (int k=0; k<3; ++k)
+ {
+ int k1 = (k+1)%3;
+ int e0 = indices[i+k];
+ int e1 = indices[i+k1];
+ ids0[k] = e0;
+ if (e1>e0)
+ std::swap(e0,e1);
+ Key edgeKey = Key(e0) | (Key(e1)<<32);
+ std::map<Key,int>::iterator it = edgeMap.find(edgeKey);
+ if (it==edgeMap.end())
+ {
+ ids1[k] = mVertices.size();
+ edgeMap[edgeKey] = ids1[k];
+ mVertices.push_back( (mVertices[e0]+mVertices[e1]).normalized() );
+ }
+ else
+ ids1[k] = it->second;
+ }
+ refinedIndices.push_back(ids0[0]); refinedIndices.push_back(ids1[0]); refinedIndices.push_back(ids1[2]);
+ refinedIndices.push_back(ids0[1]); refinedIndices.push_back(ids1[1]); refinedIndices.push_back(ids1[0]);
+ refinedIndices.push_back(ids0[2]); refinedIndices.push_back(ids1[2]); refinedIndices.push_back(ids1[1]);
+ refinedIndices.push_back(ids1[0]); refinedIndices.push_back(ids1[1]); refinedIndices.push_back(ids1[2]);
+ }
+ mListIds.push_back(0);
+}
+
+void IcoSphere::draw(int level)
+{
+ while (level>=int(mIndices.size()))
+ const_cast<IcoSphere*>(this)->_subdivide();
+ if (mListIds[level]==0)
+ {
+ mListIds[level] = glGenLists(1);
+ glNewList(mListIds[level], GL_COMPILE);
+ glVertexPointer(3, GL_FLOAT, 0, mVertices[0].data());
+ glNormalPointer(GL_FLOAT, 0, mVertices[0].data());
+ glEnableClientState(GL_VERTEX_ARRAY);
+ glEnableClientState(GL_NORMAL_ARRAY);
+ glDrawElements(GL_TRIANGLES, mIndices[level]->size(), GL_UNSIGNED_INT, &(mIndices[level]->at(0)));
+ glDisableClientState(GL_VERTEX_ARRAY);
+ glDisableClientState(GL_NORMAL_ARRAY);
+ glEndList();
+ }
+ glCallList(mListIds[level]);
+}
+
+
diff --git a/demos/opengl/icosphere.h b/demos/opengl/icosphere.h
new file mode 100644
index 0000000..b0210ed
--- /dev/null
+++ b/demos/opengl/icosphere.h
@@ -0,0 +1,30 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_ICOSPHERE_H
+#define EIGEN_ICOSPHERE_H
+
+#include <Eigen/Core>
+#include <vector>
+
+class IcoSphere
+{
+ public:
+ IcoSphere(unsigned int levels=1);
+ const std::vector<Eigen::Vector3f>& vertices() const { return mVertices; }
+ const std::vector<int>& indices(int level) const;
+ void draw(int level);
+ protected:
+ void _subdivide();
+ std::vector<Eigen::Vector3f> mVertices;
+ std::vector<std::vector<int>*> mIndices;
+ std::vector<int> mListIds;
+};
+
+#endif // EIGEN_ICOSPHERE_H
diff --git a/demos/opengl/quaternion_demo.cpp b/demos/opengl/quaternion_demo.cpp
new file mode 100644
index 0000000..531448d
--- /dev/null
+++ b/demos/opengl/quaternion_demo.cpp
@@ -0,0 +1,656 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "quaternion_demo.h"
+#include "icosphere.h"
+
+#include <Eigen/Geometry>
+#include <Eigen/QR>
+#include <Eigen/LU>
+
+#include <iostream>
+#include <QEvent>
+#include <QMouseEvent>
+#include <QInputDialog>
+#include <QGridLayout>
+#include <QButtonGroup>
+#include <QRadioButton>
+#include <QDockWidget>
+#include <QPushButton>
+#include <QGroupBox>
+
+using namespace Eigen;
+
+class FancySpheres
+{
+ public:
+ EIGEN_MAKE_ALIGNED_OPERATOR_NEW
+
+ FancySpheres()
+ {
+ const int levels = 4;
+ const float scale = 0.33;
+ float radius = 100;
+ std::vector<int> parents;
+
+ // leval 0
+ mCenters.push_back(Vector3f::Zero());
+ parents.push_back(-1);
+ mRadii.push_back(radius);
+
+ // generate level 1 using icosphere vertices
+ radius *= 0.45;
+ {
+ float dist = mRadii[0]*0.9;
+ for (int i=0; i<12; ++i)
+ {
+ mCenters.push_back(mIcoSphere.vertices()[i] * dist);
+ mRadii.push_back(radius);
+ parents.push_back(0);
+ }
+ }
+
+ static const float angles [10] = {
+ 0, 0,
+ M_PI, 0.*M_PI,
+ M_PI, 0.5*M_PI,
+ M_PI, 1.*M_PI,
+ M_PI, 1.5*M_PI
+ };
+
+ // generate other levels
+ int start = 1;
+ for (int l=1; l<levels; l++)
+ {
+ radius *= scale;
+ int end = mCenters.size();
+ for (int i=start; i<end; ++i)
+ {
+ Vector3f c = mCenters[i];
+ Vector3f ax0 = (c - mCenters[parents[i]]).normalized();
+ Vector3f ax1 = ax0.unitOrthogonal();
+ Quaternionf q;
+ q.setFromTwoVectors(Vector3f::UnitZ(), ax0);
+ Affine3f t = Translation3f(c) * q * Scaling(mRadii[i]+radius);
+ for (int j=0; j<5; ++j)
+ {
+ Vector3f newC = c + ( (AngleAxisf(angles[j*2+1], ax0)
+ * AngleAxisf(angles[j*2+0] * (l==1 ? 0.35 : 0.5), ax1)) * ax0)
+ * (mRadii[i] + radius*0.8);
+ mCenters.push_back(newC);
+ mRadii.push_back(radius);
+ parents.push_back(i);
+ }
+ }
+ start = end;
+ }
+ }
+
+ void draw()
+ {
+ int end = mCenters.size();
+ glEnable(GL_NORMALIZE);
+ for (int i=0; i<end; ++i)
+ {
+ Affine3f t = Translation3f(mCenters[i]) * Scaling(mRadii[i]);
+ gpu.pushMatrix(GL_MODELVIEW);
+ gpu.multMatrix(t.matrix(),GL_MODELVIEW);
+ mIcoSphere.draw(2);
+ gpu.popMatrix(GL_MODELVIEW);
+ }
+ glDisable(GL_NORMALIZE);
+ }
+ protected:
+ std::vector<Vector3f> mCenters;
+ std::vector<float> mRadii;
+ IcoSphere mIcoSphere;
+};
+
+
+// generic linear interpolation method
+template<typename T> T lerp(float t, const T& a, const T& b)
+{
+ return a*(1-t) + b*t;
+}
+
+// quaternion slerp
+template<> Quaternionf lerp(float t, const Quaternionf& a, const Quaternionf& b)
+{ return a.slerp(t,b); }
+
+// linear interpolation of a frame using the type OrientationType
+// to perform the interpolation of the orientations
+template<typename OrientationType>
+inline static Frame lerpFrame(float alpha, const Frame& a, const Frame& b)
+{
+ return Frame(lerp(alpha,a.position,b.position),
+ Quaternionf(lerp(alpha,OrientationType(a.orientation),OrientationType(b.orientation))));
+}
+
+template<typename Scalar_> class EulerAngles
+{
+public:
+ enum { Dim = 3 };
+ typedef Scalar_ Scalar;
+ typedef Matrix<Scalar,3,3> Matrix3;
+ typedef Matrix<Scalar,3,1> Vector3;
+ typedef Quaternion<Scalar> QuaternionType;
+
+protected:
+
+ Vector3 m_angles;
+
+public:
+
+ EulerAngles() {}
+ inline EulerAngles(Scalar a0, Scalar a1, Scalar a2) : m_angles(a0, a1, a2) {}
+ inline EulerAngles(const QuaternionType& q) { *this = q; }
+
+ const Vector3& coeffs() const { return m_angles; }
+ Vector3& coeffs() { return m_angles; }
+
+ EulerAngles& operator=(const QuaternionType& q)
+ {
+ Matrix3 m = q.toRotationMatrix();
+ return *this = m;
+ }
+
+ EulerAngles& operator=(const Matrix3& m)
+ {
+ // mat = cy*cz -cy*sz sy
+ // cz*sx*sy+cx*sz cx*cz-sx*sy*sz -cy*sx
+ // -cx*cz*sy+sx*sz cz*sx+cx*sy*sz cx*cy
+ m_angles.coeffRef(1) = std::asin(m.coeff(0,2));
+ m_angles.coeffRef(0) = std::atan2(-m.coeff(1,2),m.coeff(2,2));
+ m_angles.coeffRef(2) = std::atan2(-m.coeff(0,1),m.coeff(0,0));
+ return *this;
+ }
+
+ Matrix3 toRotationMatrix(void) const
+ {
+ Vector3 c = m_angles.array().cos();
+ Vector3 s = m_angles.array().sin();
+ Matrix3 res;
+ res << c.y()*c.z(), -c.y()*s.z(), s.y(),
+ c.z()*s.x()*s.y()+c.x()*s.z(), c.x()*c.z()-s.x()*s.y()*s.z(), -c.y()*s.x(),
+ -c.x()*c.z()*s.y()+s.x()*s.z(), c.z()*s.x()+c.x()*s.y()*s.z(), c.x()*c.y();
+ return res;
+ }
+
+ operator QuaternionType() { return QuaternionType(toRotationMatrix()); }
+};
+
+// Euler angles slerp
+template<> EulerAngles<float> lerp(float t, const EulerAngles<float>& a, const EulerAngles<float>& b)
+{
+ EulerAngles<float> res;
+ res.coeffs() = lerp(t, a.coeffs(), b.coeffs());
+ return res;
+}
+
+
+RenderingWidget::RenderingWidget()
+{
+ mAnimate = false;
+ mCurrentTrackingMode = TM_NO_TRACK;
+ mNavMode = NavTurnAround;
+ mLerpMode = LerpQuaternion;
+ mRotationMode = RotationStable;
+ mTrackball.setCamera(&mCamera);
+
+ // required to capture key press events
+ setFocusPolicy(Qt::ClickFocus);
+}
+
+void RenderingWidget::grabFrame(void)
+{
+ // ask user for a time
+ bool ok = false;
+ double t = 0;
+ if (!m_timeline.empty())
+ t = (--m_timeline.end())->first + 1.;
+ t = QInputDialog::getDouble(this, "Eigen's RenderingWidget", "time value: ",
+ t, 0, 1e3, 1, &ok);
+ if (ok)
+ {
+ Frame aux;
+ aux.orientation = mCamera.viewMatrix().linear();
+ aux.position = mCamera.viewMatrix().translation();
+ m_timeline[t] = aux;
+ }
+}
+
+void RenderingWidget::drawScene()
+{
+ static FancySpheres sFancySpheres;
+ float length = 50;
+ gpu.drawVector(Vector3f::Zero(), length*Vector3f::UnitX(), Color(1,0,0,1));
+ gpu.drawVector(Vector3f::Zero(), length*Vector3f::UnitY(), Color(0,1,0,1));
+ gpu.drawVector(Vector3f::Zero(), length*Vector3f::UnitZ(), Color(0,0,1,1));
+
+ // draw the fractal object
+ float sqrt3 = std::sqrt(3.);
+ glLightfv(GL_LIGHT0, GL_AMBIENT, Vector4f(0.5,0.5,0.5,1).data());
+ glLightfv(GL_LIGHT0, GL_DIFFUSE, Vector4f(0.5,1,0.5,1).data());
+ glLightfv(GL_LIGHT0, GL_SPECULAR, Vector4f(1,1,1,1).data());
+ glLightfv(GL_LIGHT0, GL_POSITION, Vector4f(-sqrt3,-sqrt3,sqrt3,0).data());
+
+ glLightfv(GL_LIGHT1, GL_AMBIENT, Vector4f(0,0,0,1).data());
+ glLightfv(GL_LIGHT1, GL_DIFFUSE, Vector4f(1,0.5,0.5,1).data());
+ glLightfv(GL_LIGHT1, GL_SPECULAR, Vector4f(1,1,1,1).data());
+ glLightfv(GL_LIGHT1, GL_POSITION, Vector4f(-sqrt3,sqrt3,-sqrt3,0).data());
+
+ glMaterialfv(GL_FRONT_AND_BACK, GL_AMBIENT, Vector4f(0.7, 0.7, 0.7, 1).data());
+ glMaterialfv(GL_FRONT_AND_BACK, GL_DIFFUSE, Vector4f(0.8, 0.75, 0.6, 1).data());
+ glMaterialfv(GL_FRONT_AND_BACK, GL_SPECULAR, Vector4f(1, 1, 1, 1).data());
+ glMaterialf(GL_FRONT_AND_BACK, GL_SHININESS, 64);
+
+ glEnable(GL_LIGHTING);
+ glEnable(GL_LIGHT0);
+ glEnable(GL_LIGHT1);
+
+ sFancySpheres.draw();
+ glVertexPointer(3, GL_FLOAT, 0, mVertices[0].data());
+ glNormalPointer(GL_FLOAT, 0, mNormals[0].data());
+ glEnableClientState(GL_VERTEX_ARRAY);
+ glEnableClientState(GL_NORMAL_ARRAY);
+ glDrawArrays(GL_TRIANGLES, 0, mVertices.size());
+ glDisableClientState(GL_VERTEX_ARRAY);
+ glDisableClientState(GL_NORMAL_ARRAY);
+
+ glDisable(GL_LIGHTING);
+}
+
+void RenderingWidget::animate()
+{
+ m_alpha += double(m_timer.interval()) * 1e-3;
+
+ TimeLine::const_iterator hi = m_timeline.upper_bound(m_alpha);
+ TimeLine::const_iterator lo = hi;
+ --lo;
+
+ Frame currentFrame;
+
+ if(hi==m_timeline.end())
+ {
+ // end
+ currentFrame = lo->second;
+ stopAnimation();
+ }
+ else if(hi==m_timeline.begin())
+ {
+ // start
+ currentFrame = hi->second;
+ }
+ else
+ {
+ float s = (m_alpha - lo->first)/(hi->first - lo->first);
+ if (mLerpMode==LerpEulerAngles)
+ currentFrame = ::lerpFrame<EulerAngles<float> >(s, lo->second, hi->second);
+ else if (mLerpMode==LerpQuaternion)
+ currentFrame = ::lerpFrame<Eigen::Quaternionf>(s, lo->second, hi->second);
+ else
+ {
+ std::cerr << "Invalid rotation interpolation mode (abort)\n";
+ exit(2);
+ }
+ currentFrame.orientation.coeffs().normalize();
+ }
+
+ currentFrame.orientation = currentFrame.orientation.inverse();
+ currentFrame.position = - (currentFrame.orientation * currentFrame.position);
+ mCamera.setFrame(currentFrame);
+
+ updateGL();
+}
+
+void RenderingWidget::keyPressEvent(QKeyEvent * e)
+{
+ switch(e->key())
+ {
+ case Qt::Key_Up:
+ mCamera.zoom(2);
+ break;
+ case Qt::Key_Down:
+ mCamera.zoom(-2);
+ break;
+ // add a frame
+ case Qt::Key_G:
+ grabFrame();
+ break;
+ // clear the time line
+ case Qt::Key_C:
+ m_timeline.clear();
+ break;
+ // move the camera to initial pos
+ case Qt::Key_R:
+ resetCamera();
+ break;
+ // start/stop the animation
+ case Qt::Key_A:
+ if (mAnimate)
+ {
+ stopAnimation();
+ }
+ else
+ {
+ m_alpha = 0;
+ connect(&m_timer, SIGNAL(timeout()), this, SLOT(animate()));
+ m_timer.start(1000/30);
+ mAnimate = true;
+ }
+ break;
+ default:
+ break;
+ }
+
+ updateGL();
+}
+
+void RenderingWidget::stopAnimation()
+{
+ disconnect(&m_timer, SIGNAL(timeout()), this, SLOT(animate()));
+ m_timer.stop();
+ mAnimate = false;
+ m_alpha = 0;
+}
+
+void RenderingWidget::mousePressEvent(QMouseEvent* e)
+{
+ mMouseCoords = Vector2i(e->pos().x(), e->pos().y());
+ bool fly = (mNavMode==NavFly) || (e->modifiers()&Qt::ControlModifier);
+ switch(e->button())
+ {
+ case Qt::LeftButton:
+ if(fly)
+ {
+ mCurrentTrackingMode = TM_LOCAL_ROTATE;
+ mTrackball.start(Trackball::Local);
+ }
+ else
+ {
+ mCurrentTrackingMode = TM_ROTATE_AROUND;
+ mTrackball.start(Trackball::Around);
+ }
+ mTrackball.track(mMouseCoords);
+ break;
+ case Qt::MidButton:
+ if(fly)
+ mCurrentTrackingMode = TM_FLY_Z;
+ else
+ mCurrentTrackingMode = TM_ZOOM;
+ break;
+ case Qt::RightButton:
+ mCurrentTrackingMode = TM_FLY_PAN;
+ break;
+ default:
+ break;
+ }
+}
+void RenderingWidget::mouseReleaseEvent(QMouseEvent*)
+{
+ mCurrentTrackingMode = TM_NO_TRACK;
+ updateGL();
+}
+
+void RenderingWidget::mouseMoveEvent(QMouseEvent* e)
+{
+ // tracking
+ if(mCurrentTrackingMode != TM_NO_TRACK)
+ {
+ float dx = float(e->x() - mMouseCoords.x()) / float(mCamera.vpWidth());
+ float dy = - float(e->y() - mMouseCoords.y()) / float(mCamera.vpHeight());
+
+ // speedup the transformations
+ if(e->modifiers() & Qt::ShiftModifier)
+ {
+ dx *= 10.;
+ dy *= 10.;
+ }
+
+ switch(mCurrentTrackingMode)
+ {
+ case TM_ROTATE_AROUND:
+ case TM_LOCAL_ROTATE:
+ if (mRotationMode==RotationStable)
+ {
+ // use the stable trackball implementation mapping
+ // the 2D coordinates to 3D points on a sphere.
+ mTrackball.track(Vector2i(e->pos().x(), e->pos().y()));
+ }
+ else
+ {
+ // standard approach mapping the x and y displacements as rotations
+ // around the camera's X and Y axes.
+ Quaternionf q = AngleAxisf( dx*M_PI, Vector3f::UnitY())
+ * AngleAxisf(-dy*M_PI, Vector3f::UnitX());
+ if (mCurrentTrackingMode==TM_LOCAL_ROTATE)
+ mCamera.localRotate(q);
+ else
+ mCamera.rotateAroundTarget(q);
+ }
+ break;
+ case TM_ZOOM :
+ mCamera.zoom(dy*100);
+ break;
+ case TM_FLY_Z :
+ mCamera.localTranslate(Vector3f(0, 0, -dy*200));
+ break;
+ case TM_FLY_PAN :
+ mCamera.localTranslate(Vector3f(dx*200, dy*200, 0));
+ break;
+ default:
+ break;
+ }
+
+ updateGL();
+ }
+
+ mMouseCoords = Vector2i(e->pos().x(), e->pos().y());
+}
+
+void RenderingWidget::paintGL()
+{
+ glEnable(GL_DEPTH_TEST);
+ glDisable(GL_CULL_FACE);
+ glPolygonMode(GL_FRONT_AND_BACK,GL_FILL);
+ glDisable(GL_COLOR_MATERIAL);
+ glDisable(GL_BLEND);
+ glDisable(GL_ALPHA_TEST);
+ glDisable(GL_TEXTURE_1D);
+ glDisable(GL_TEXTURE_2D);
+ glDisable(GL_TEXTURE_3D);
+
+ // Clear buffers
+ glClear(GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT);
+
+ mCamera.activateGL();
+
+ drawScene();
+}
+
+void RenderingWidget::initializeGL()
+{
+ glClearColor(1., 1., 1., 0.);
+ glLightModeli(GL_LIGHT_MODEL_LOCAL_VIEWER, 1);
+ glDepthMask(GL_TRUE);
+ glColorMask(GL_TRUE, GL_TRUE, GL_TRUE, GL_TRUE);
+
+ mCamera.setPosition(Vector3f(-200, -200, -200));
+ mCamera.setTarget(Vector3f(0, 0, 0));
+ mInitFrame.orientation = mCamera.orientation().inverse();
+ mInitFrame.position = mCamera.viewMatrix().translation();
+}
+
+void RenderingWidget::resizeGL(int width, int height)
+{
+ mCamera.setViewport(width,height);
+}
+
+void RenderingWidget::setNavMode(int m)
+{
+ mNavMode = NavMode(m);
+}
+
+void RenderingWidget::setLerpMode(int m)
+{
+ mLerpMode = LerpMode(m);
+}
+
+void RenderingWidget::setRotationMode(int m)
+{
+ mRotationMode = RotationMode(m);
+}
+
+void RenderingWidget::resetCamera()
+{
+ if (mAnimate)
+ stopAnimation();
+ m_timeline.clear();
+ Frame aux0 = mCamera.frame();
+ aux0.orientation = aux0.orientation.inverse();
+ aux0.position = mCamera.viewMatrix().translation();
+ m_timeline[0] = aux0;
+
+ Vector3f currentTarget = mCamera.target();
+ mCamera.setTarget(Vector3f::Zero());
+
+ // compute the rotation duration to move the camera to the target
+ Frame aux1 = mCamera.frame();
+ aux1.orientation = aux1.orientation.inverse();
+ aux1.position = mCamera.viewMatrix().translation();
+ float duration = aux0.orientation.angularDistance(aux1.orientation) * 0.9;
+ if (duration<0.1) duration = 0.1;
+
+ // put the camera at that time step:
+ aux1 = aux0.lerp(duration/2,mInitFrame);
+ // and make it look at the target again
+ aux1.orientation = aux1.orientation.inverse();
+ aux1.position = - (aux1.orientation * aux1.position);
+ mCamera.setFrame(aux1);
+ mCamera.setTarget(Vector3f::Zero());
+
+ // add this camera keyframe
+ aux1.orientation = aux1.orientation.inverse();
+ aux1.position = mCamera.viewMatrix().translation();
+ m_timeline[duration] = aux1;
+
+ m_timeline[2] = mInitFrame;
+ m_alpha = 0;
+ animate();
+ connect(&m_timer, SIGNAL(timeout()), this, SLOT(animate()));
+ m_timer.start(1000/30);
+ mAnimate = true;
+}
+
+QWidget* RenderingWidget::createNavigationControlWidget()
+{
+ QWidget* panel = new QWidget();
+ QVBoxLayout* layout = new QVBoxLayout();
+
+ {
+ QPushButton* but = new QPushButton("reset");
+ but->setToolTip("move the camera to initial position (with animation)");
+ layout->addWidget(but);
+ connect(but, SIGNAL(clicked()), this, SLOT(resetCamera()));
+ }
+ {
+ // navigation mode
+ QGroupBox* box = new QGroupBox("navigation mode");
+ QVBoxLayout* boxLayout = new QVBoxLayout;
+ QButtonGroup* group = new QButtonGroup(panel);
+ QRadioButton* but;
+ but = new QRadioButton("turn around");
+ but->setToolTip("look around an object");
+ group->addButton(but, NavTurnAround);
+ boxLayout->addWidget(but);
+ but = new QRadioButton("fly");
+ but->setToolTip("free navigation like a spaceship\n(this mode can also be enabled pressing the \"shift\" key)");
+ group->addButton(but, NavFly);
+ boxLayout->addWidget(but);
+ group->button(mNavMode)->setChecked(true);
+ connect(group, SIGNAL(buttonClicked(int)), this, SLOT(setNavMode(int)));
+ box->setLayout(boxLayout);
+ layout->addWidget(box);
+ }
+ {
+ // track ball, rotation mode
+ QGroupBox* box = new QGroupBox("rotation mode");
+ QVBoxLayout* boxLayout = new QVBoxLayout;
+ QButtonGroup* group = new QButtonGroup(panel);
+ QRadioButton* but;
+ but = new QRadioButton("stable trackball");
+ group->addButton(but, RotationStable);
+ boxLayout->addWidget(but);
+ but->setToolTip("use the stable trackball implementation mapping\nthe 2D coordinates to 3D points on a sphere");
+ but = new QRadioButton("standard rotation");
+ group->addButton(but, RotationStandard);
+ boxLayout->addWidget(but);
+ but->setToolTip("standard approach mapping the x and y displacements\nas rotations around the camera's X and Y axes");
+ group->button(mRotationMode)->setChecked(true);
+ connect(group, SIGNAL(buttonClicked(int)), this, SLOT(setRotationMode(int)));
+ box->setLayout(boxLayout);
+ layout->addWidget(box);
+ }
+ {
+ // interpolation mode
+ QGroupBox* box = new QGroupBox("spherical interpolation");
+ QVBoxLayout* boxLayout = new QVBoxLayout;
+ QButtonGroup* group = new QButtonGroup(panel);
+ QRadioButton* but;
+ but = new QRadioButton("quaternion slerp");
+ group->addButton(but, LerpQuaternion);
+ boxLayout->addWidget(but);
+ but->setToolTip("use quaternion spherical interpolation\nto interpolate orientations");
+ but = new QRadioButton("euler angles");
+ group->addButton(but, LerpEulerAngles);
+ boxLayout->addWidget(but);
+ but->setToolTip("use Euler angles to interpolate orientations");
+ group->button(mNavMode)->setChecked(true);
+ connect(group, SIGNAL(buttonClicked(int)), this, SLOT(setLerpMode(int)));
+ box->setLayout(boxLayout);
+ layout->addWidget(box);
+ }
+ layout->addItem(new QSpacerItem(0,0,QSizePolicy::Minimum,QSizePolicy::Expanding));
+ panel->setLayout(layout);
+ return panel;
+}
+
+QuaternionDemo::QuaternionDemo()
+{
+ mRenderingWidget = new RenderingWidget();
+ setCentralWidget(mRenderingWidget);
+
+ QDockWidget* panel = new QDockWidget("navigation", this);
+ panel->setAllowedAreas((QFlags<Qt::DockWidgetArea>)(Qt::RightDockWidgetArea | Qt::LeftDockWidgetArea));
+ addDockWidget(Qt::RightDockWidgetArea, panel);
+ panel->setWidget(mRenderingWidget->createNavigationControlWidget());
+}
+
+int main(int argc, char *argv[])
+{
+ std::cout << "Navigation:\n";
+ std::cout << " left button: rotate around the target\n";
+ std::cout << " middle button: zoom\n";
+ std::cout << " left button + ctrl quake rotate (rotate around camera position)\n";
+ std::cout << " middle button + ctrl walk (progress along camera's z direction)\n";
+ std::cout << " left button: pan (translate in the XY camera's plane)\n\n";
+ std::cout << "R : move the camera to initial position\n";
+ std::cout << "A : start/stop animation\n";
+ std::cout << "C : clear the animation\n";
+ std::cout << "G : add a key frame\n";
+
+ QApplication app(argc, argv);
+ QuaternionDemo demo;
+ demo.resize(600,500);
+ demo.show();
+ return app.exec();
+}
+
+#include "quaternion_demo.moc"
+
diff --git a/demos/opengl/quaternion_demo.h b/demos/opengl/quaternion_demo.h
new file mode 100644
index 0000000..dbff46c
--- /dev/null
+++ b/demos/opengl/quaternion_demo.h
@@ -0,0 +1,114 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_QUATERNION_DEMO_H
+#define EIGEN_QUATERNION_DEMO_H
+
+#include "gpuhelper.h"
+#include "camera.h"
+#include "trackball.h"
+#include <map>
+#include <QTimer>
+#include <QtGui/QApplication>
+#include <QtOpenGL/QGLWidget>
+#include <QtGui/QMainWindow>
+
+class RenderingWidget : public QGLWidget
+{
+ Q_OBJECT
+
+ typedef std::map<float,Frame> TimeLine;
+ TimeLine m_timeline;
+ Frame lerpFrame(float t);
+
+ Frame mInitFrame;
+ bool mAnimate;
+ float m_alpha;
+
+ enum TrackMode {
+ TM_NO_TRACK=0, TM_ROTATE_AROUND, TM_ZOOM,
+ TM_LOCAL_ROTATE, TM_FLY_Z, TM_FLY_PAN
+ };
+
+ enum NavMode {
+ NavTurnAround,
+ NavFly
+ };
+
+ enum LerpMode {
+ LerpQuaternion,
+ LerpEulerAngles
+ };
+
+ enum RotationMode {
+ RotationStable,
+ RotationStandard
+ };
+
+ Camera mCamera;
+ TrackMode mCurrentTrackingMode;
+ NavMode mNavMode;
+ LerpMode mLerpMode;
+ RotationMode mRotationMode;
+ Vector2i mMouseCoords;
+ Trackball mTrackball;
+
+ QTimer m_timer;
+
+ void setupCamera();
+
+ std::vector<Vector3f> mVertices;
+ std::vector<Vector3f> mNormals;
+ std::vector<int> mIndices;
+
+ protected slots:
+
+ virtual void animate(void);
+ virtual void drawScene(void);
+
+ virtual void grabFrame(void);
+ virtual void stopAnimation();
+
+ virtual void setNavMode(int);
+ virtual void setLerpMode(int);
+ virtual void setRotationMode(int);
+ virtual void resetCamera();
+
+ protected:
+
+ virtual void initializeGL();
+ virtual void resizeGL(int width, int height);
+ virtual void paintGL();
+
+ //--------------------------------------------------------------------------------
+ virtual void mousePressEvent(QMouseEvent * e);
+ virtual void mouseReleaseEvent(QMouseEvent * e);
+ virtual void mouseMoveEvent(QMouseEvent * e);
+ virtual void keyPressEvent(QKeyEvent * e);
+ //--------------------------------------------------------------------------------
+
+ public:
+ EIGEN_MAKE_ALIGNED_OPERATOR_NEW
+
+ RenderingWidget();
+ ~RenderingWidget() { }
+
+ QWidget* createNavigationControlWidget();
+};
+
+class QuaternionDemo : public QMainWindow
+{
+ Q_OBJECT
+ public:
+ QuaternionDemo();
+ protected:
+ RenderingWidget* mRenderingWidget;
+};
+
+#endif // EIGEN_QUATERNION_DEMO_H
diff --git a/demos/opengl/trackball.cpp b/demos/opengl/trackball.cpp
new file mode 100644
index 0000000..7c2da8e
--- /dev/null
+++ b/demos/opengl/trackball.cpp
@@ -0,0 +1,59 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "trackball.h"
+#include "camera.h"
+
+using namespace Eigen;
+
+void Trackball::track(const Vector2i& point2D)
+{
+ if (mpCamera==0)
+ return;
+ Vector3f newPoint3D;
+ bool newPointOk = mapToSphere(point2D, newPoint3D);
+
+ if (mLastPointOk && newPointOk)
+ {
+ Vector3f axis = mLastPoint3D.cross(newPoint3D).normalized();
+ float cos_angle = mLastPoint3D.dot(newPoint3D);
+ if ( std::abs(cos_angle) < 1.0 )
+ {
+ float angle = 2. * acos(cos_angle);
+ if (mMode==Around)
+ mpCamera->rotateAroundTarget(Quaternionf(AngleAxisf(angle, axis)));
+ else
+ mpCamera->localRotate(Quaternionf(AngleAxisf(-angle, axis)));
+ }
+ }
+
+ mLastPoint3D = newPoint3D;
+ mLastPointOk = newPointOk;
+}
+
+bool Trackball::mapToSphere(const Vector2i& p2, Vector3f& v3)
+{
+ if ((p2.x() >= 0) && (p2.x() <= int(mpCamera->vpWidth())) &&
+ (p2.y() >= 0) && (p2.y() <= int(mpCamera->vpHeight())) )
+ {
+ double x = (double)(p2.x() - 0.5*mpCamera->vpWidth()) / (double)mpCamera->vpWidth();
+ double y = (double)(0.5*mpCamera->vpHeight() - p2.y()) / (double)mpCamera->vpHeight();
+ double sinx = sin(M_PI * x * 0.5);
+ double siny = sin(M_PI * y * 0.5);
+ double sinx2siny2 = sinx * sinx + siny * siny;
+
+ v3.x() = sinx;
+ v3.y() = siny;
+ v3.z() = sinx2siny2 < 1.0 ? sqrt(1.0 - sinx2siny2) : 0.0;
+
+ return true;
+ }
+ else
+ return false;
+}
diff --git a/demos/opengl/trackball.h b/demos/opengl/trackball.h
new file mode 100644
index 0000000..1ea842f
--- /dev/null
+++ b/demos/opengl/trackball.h
@@ -0,0 +1,42 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_TRACKBALL_H
+#define EIGEN_TRACKBALL_H
+
+#include <Eigen/Geometry>
+
+class Camera;
+
+class Trackball
+{
+ public:
+
+ enum Mode {Around, Local};
+
+ Trackball() : mpCamera(0) {}
+
+ void start(Mode m = Around) { mMode = m; mLastPointOk = false; }
+
+ void setCamera(Camera* pCam) { mpCamera = pCam; }
+
+ void track(const Eigen::Vector2i& newPoint2D);
+
+ protected:
+
+ bool mapToSphere( const Eigen::Vector2i& p2, Eigen::Vector3f& v3);
+
+ Camera* mpCamera;
+ Eigen::Vector3f mLastPoint3D;
+ Mode mMode;
+ bool mLastPointOk;
+
+};
+
+#endif // EIGEN_TRACKBALL_H
diff --git a/doc/AsciiQuickReference.txt b/doc/AsciiQuickReference.txt
new file mode 100644
index 0000000..18b4446
--- /dev/null
+++ b/doc/AsciiQuickReference.txt
@@ -0,0 +1,226 @@
+// A simple quickref for Eigen. Add anything that's missing.
+// Main author: Keir Mierle
+
+#include <Eigen/Dense>
+
+Matrix<double, 3, 3> A; // Fixed rows and cols. Same as Matrix3d.
+Matrix<double, 3, Dynamic> B; // Fixed rows, dynamic cols.
+Matrix<double, Dynamic, Dynamic> C; // Full dynamic. Same as MatrixXd.
+Matrix<double, 3, 3, RowMajor> E; // Row major; default is column-major.
+Matrix3f P, Q, R; // 3x3 float matrix.
+Vector3f x, y, z; // 3x1 float matrix.
+RowVector3f a, b, c; // 1x3 float matrix.
+VectorXd v; // Dynamic column vector of doubles
+double s;
+
+// Basic usage
+// Eigen // Matlab // comments
+x.size() // length(x) // vector size
+C.rows() // size(C,1) // number of rows
+C.cols() // size(C,2) // number of columns
+x(i) // x(i+1) // Matlab is 1-based
+C(i,j) // C(i+1,j+1) //
+
+A.resize(4, 4); // Runtime error if assertions are on.
+B.resize(4, 9); // Runtime error if assertions are on.
+A.resize(3, 3); // Ok; size didn't change.
+B.resize(3, 9); // Ok; only dynamic cols changed.
+
+A << 1, 2, 3, // Initialize A. The elements can also be
+ 4, 5, 6, // matrices, which are stacked along cols
+ 7, 8, 9; // and then the rows are stacked.
+B << A, A, A; // B is three horizontally stacked A's.
+A.fill(10); // Fill A with all 10's.
+
+// Eigen // Matlab
+MatrixXd::Identity(rows,cols) // eye(rows,cols)
+C.setIdentity(rows,cols) // C = eye(rows,cols)
+MatrixXd::Zero(rows,cols) // zeros(rows,cols)
+C.setZero(rows,cols) // C = zeros(rows,cols)
+MatrixXd::Ones(rows,cols) // ones(rows,cols)
+C.setOnes(rows,cols) // C = ones(rows,cols)
+MatrixXd::Random(rows,cols) // rand(rows,cols)*2-1 // MatrixXd::Random returns uniform random numbers in (-1, 1).
+C.setRandom(rows,cols) // C = rand(rows,cols)*2-1
+VectorXd::LinSpaced(size,low,high) // linspace(low,high,size)'
+v.setLinSpaced(size,low,high) // v = linspace(low,high,size)'
+VectorXi::LinSpaced(((hi-low)/step)+1, // low:step:hi
+ low,low+step*(size-1)) //
+
+
+// Matrix slicing and blocks. All expressions listed here are read/write.
+// Templated size versions are faster. Note that Matlab is 1-based (a size N
+// vector is x(1)...x(N)).
+/******************************************************************************/
+/* PLEASE HELP US IMPROVING THIS SECTION */
+/* Eigen 3.4 supports a much improved API for sub-matrices, including, */
+/* slicing and indexing from arrays: */
+/* http://eigen.tuxfamily.org/dox-devel/group__TutorialSlicingIndexing.html */
+/******************************************************************************/
+// Eigen // Matlab
+x.head(n) // x(1:n)
+x.head<n>() // x(1:n)
+x.tail(n) // x(end - n + 1: end)
+x.tail<n>() // x(end - n + 1: end)
+x.segment(i, n) // x(i+1 : i+n)
+x.segment<n>(i) // x(i+1 : i+n)
+P.block(i, j, rows, cols) // P(i+1 : i+rows, j+1 : j+cols)
+P.block<rows, cols>(i, j) // P(i+1 : i+rows, j+1 : j+cols)
+P.row(i) // P(i+1, :)
+P.col(j) // P(:, j+1)
+P.leftCols<cols>() // P(:, 1:cols)
+P.leftCols(cols) // P(:, 1:cols)
+P.middleCols<cols>(j) // P(:, j+1:j+cols)
+P.middleCols(j, cols) // P(:, j+1:j+cols)
+P.rightCols<cols>() // P(:, end-cols+1:end)
+P.rightCols(cols) // P(:, end-cols+1:end)
+P.topRows<rows>() // P(1:rows, :)
+P.topRows(rows) // P(1:rows, :)
+P.middleRows<rows>(i) // P(i+1:i+rows, :)
+P.middleRows(i, rows) // P(i+1:i+rows, :)
+P.bottomRows<rows>() // P(end-rows+1:end, :)
+P.bottomRows(rows) // P(end-rows+1:end, :)
+P.topLeftCorner(rows, cols) // P(1:rows, 1:cols)
+P.topRightCorner(rows, cols) // P(1:rows, end-cols+1:end)
+P.bottomLeftCorner(rows, cols) // P(end-rows+1:end, 1:cols)
+P.bottomRightCorner(rows, cols) // P(end-rows+1:end, end-cols+1:end)
+P.topLeftCorner<rows,cols>() // P(1:rows, 1:cols)
+P.topRightCorner<rows,cols>() // P(1:rows, end-cols+1:end)
+P.bottomLeftCorner<rows,cols>() // P(end-rows+1:end, 1:cols)
+P.bottomRightCorner<rows,cols>() // P(end-rows+1:end, end-cols+1:end)
+
+// Of particular note is Eigen's swap function which is highly optimized.
+// Eigen // Matlab
+R.row(i) = P.col(j); // R(i, :) = P(:, j)
+R.col(j1).swap(mat1.col(j2)); // R(:, [j1 j2]) = R(:, [j2, j1])
+
+// Views, transpose, etc;
+/******************************************************************************/
+/* PLEASE HELP US IMPROVING THIS SECTION */
+/* Eigen 3.4 supports a new API for reshaping: */
+/* http://eigen.tuxfamily.org/dox-devel/group__TutorialReshape.html */
+/******************************************************************************/
+// Eigen // Matlab
+R.adjoint() // R'
+R.transpose() // R.' or conj(R') // Read-write
+R.diagonal() // diag(R) // Read-write
+x.asDiagonal() // diag(x)
+R.transpose().colwise().reverse() // rot90(R) // Read-write
+R.rowwise().reverse() // fliplr(R)
+R.colwise().reverse() // flipud(R)
+R.replicate(i,j) // repmat(P,i,j)
+
+
+// All the same as Matlab, but matlab doesn't have *= style operators.
+// Matrix-vector. Matrix-matrix. Matrix-scalar.
+y = M*x; R = P*Q; R = P*s;
+a = b*M; R = P - Q; R = s*P;
+a *= M; R = P + Q; R = P/s;
+ R *= Q; R = s*P;
+ R += Q; R *= s;
+ R -= Q; R /= s;
+
+// Vectorized operations on each element independently
+// Eigen // Matlab
+R = P.cwiseProduct(Q); // R = P .* Q
+R = P.array() * s.array(); // R = P .* s
+R = P.cwiseQuotient(Q); // R = P ./ Q
+R = P.array() / Q.array(); // R = P ./ Q
+R = P.array() + s.array(); // R = P + s
+R = P.array() - s.array(); // R = P - s
+R.array() += s; // R = R + s
+R.array() -= s; // R = R - s
+R.array() < Q.array(); // R < Q
+R.array() <= Q.array(); // R <= Q
+R.cwiseInverse(); // 1 ./ P
+R.array().inverse(); // 1 ./ P
+R.array().sin() // sin(P)
+R.array().cos() // cos(P)
+R.array().pow(s) // P .^ s
+R.array().square() // P .^ 2
+R.array().cube() // P .^ 3
+R.cwiseSqrt() // sqrt(P)
+R.array().sqrt() // sqrt(P)
+R.array().exp() // exp(P)
+R.array().log() // log(P)
+R.cwiseMax(P) // max(R, P)
+R.array().max(P.array()) // max(R, P)
+R.cwiseMin(P) // min(R, P)
+R.array().min(P.array()) // min(R, P)
+R.cwiseAbs() // abs(P)
+R.array().abs() // abs(P)
+R.cwiseAbs2() // abs(P.^2)
+R.array().abs2() // abs(P.^2)
+(R.array() < s).select(P,Q ); // (R < s ? P : Q)
+R = (Q.array()==0).select(P,R) // R(Q==0) = P(Q==0)
+R = P.unaryExpr(ptr_fun(func)) // R = arrayfun(func, P) // with: scalar func(const scalar &x);
+
+
+// Reductions.
+int r, c;
+// Eigen // Matlab
+R.minCoeff() // min(R(:))
+R.maxCoeff() // max(R(:))
+s = R.minCoeff(&r, &c) // [s, i] = min(R(:)); [r, c] = ind2sub(size(R), i);
+s = R.maxCoeff(&r, &c) // [s, i] = max(R(:)); [r, c] = ind2sub(size(R), i);
+R.sum() // sum(R(:))
+R.colwise().sum() // sum(R)
+R.rowwise().sum() // sum(R, 2) or sum(R')'
+R.prod() // prod(R(:))
+R.colwise().prod() // prod(R)
+R.rowwise().prod() // prod(R, 2) or prod(R')'
+R.trace() // trace(R)
+R.all() // all(R(:))
+R.colwise().all() // all(R)
+R.rowwise().all() // all(R, 2)
+R.any() // any(R(:))
+R.colwise().any() // any(R)
+R.rowwise().any() // any(R, 2)
+
+// Dot products, norms, etc.
+// Eigen // Matlab
+x.norm() // norm(x). Note that norm(R) doesn't work in Eigen.
+x.squaredNorm() // dot(x, x) Note the equivalence is not true for complex
+x.dot(y) // dot(x, y)
+x.cross(y) // cross(x, y) Requires #include <Eigen/Geometry>
+
+//// Type conversion
+// Eigen // Matlab
+A.cast<double>(); // double(A)
+A.cast<float>(); // single(A)
+A.cast<int>(); // int32(A)
+A.real(); // real(A)
+A.imag(); // imag(A)
+// if the original type equals destination type, no work is done
+
+// Note that for most operations Eigen requires all operands to have the same type:
+MatrixXf F = MatrixXf::Zero(3,3);
+A += F; // illegal in Eigen. In Matlab A = A+F is allowed
+A += F.cast<double>(); // F converted to double and then added (generally, conversion happens on-the-fly)
+
+// Eigen can map existing memory into Eigen matrices.
+float array[3];
+Vector3f::Map(array).fill(10); // create a temporary Map over array and sets entries to 10
+int data[4] = {1, 2, 3, 4};
+Matrix2i mat2x2(data); // copies data into mat2x2
+Matrix2i::Map(data) = 2*mat2x2; // overwrite elements of data with 2*mat2x2
+MatrixXi::Map(data, 2, 2) += mat2x2; // adds mat2x2 to elements of data (alternative syntax if size is not know at compile time)
+
+// Solve Ax = b. Result stored in x. Matlab: x = A \ b.
+x = A.ldlt().solve(b)); // A sym. p.s.d. #include <Eigen/Cholesky>
+x = A.llt() .solve(b)); // A sym. p.d. #include <Eigen/Cholesky>
+x = A.lu() .solve(b)); // Stable and fast. #include <Eigen/LU>
+x = A.qr() .solve(b)); // No pivoting. #include <Eigen/QR>
+x = A.svd() .solve(b)); // Stable, slowest. #include <Eigen/SVD>
+// .ldlt() -> .matrixL() and .matrixD()
+// .llt() -> .matrixL()
+// .lu() -> .matrixL() and .matrixU()
+// .qr() -> .matrixQ() and .matrixR()
+// .svd() -> .matrixU(), .singularValues(), and .matrixV()
+
+// Eigenvalue problems
+// Eigen // Matlab
+A.eigenvalues(); // eig(A);
+EigenSolver<Matrix3d> eig(A); // [vec val] = eig(A)
+eig.eigenvalues(); // diag(val)
+eig.eigenvectors(); // vec
+// For self-adjoint matrices use SelfAdjointEigenSolver<>
diff --git a/doc/B01_Experimental.dox b/doc/B01_Experimental.dox
new file mode 100644
index 0000000..e1f031d
--- /dev/null
+++ b/doc/B01_Experimental.dox
@@ -0,0 +1,52 @@
+namespace Eigen {
+
+/** \page Experimental Experimental parts of Eigen
+
+\eigenAutoToc
+
+\section Experimental_summary Summary
+
+With the 2.0 release, Eigen's API is, to a large extent, stable. However, we wish to retain the freedom to make API incompatible changes. To that effect, we call many parts of Eigen "experimental" which means that they are not subject to API stability guarantee.
+
+Our goal is that for the 2.1 release (expected in July 2009) most of these parts become API-stable too.
+
+We are aware that API stability is a major concern for our users. That's why it's a priority for us to reach it, but at the same time we're being serious about not calling Eigen API-stable too early.
+
+Experimental features may at any time:
+\li be removed;
+\li be subject to an API incompatible change;
+\li introduce API or ABI incompatible changes in your own code if you let them affect your API or ABI.
+
+\section Experimental_modules Experimental modules
+
+The following modules are considered entirely experimental, and we make no firm API stability guarantee about them for the time being:
+\li SVD
+\li QR
+\li Cholesky
+\li Sparse
+\li Geometry (this one should be mostly stable, but it's a little too early to make a formal guarantee)
+
+\section Experimental_core Experimental parts of the Core module
+
+In the Core module, the only classes subject to ABI stability guarantee (meaning that you can use it for data members in your public ABI) is:
+\li Matrix
+\li Map
+
+All other classes offer no ABI guarantee, e.g. the layout of their data can be changed.
+
+The only classes subject to (even partial) API stability guarantee (meaning that you can safely construct and use objects) are:
+\li MatrixBase : partial API stability (see below)
+\li Matrix : full API stability (except for experimental stuff inherited from MatrixBase)
+\li Map : full API stability (except for experimental stuff inherited from MatrixBase)
+
+All other classes offer no direct API guarantee, e.g. their methods can be changed; however notice that most classes inherit MatrixBase and that this is where most of their API comes from -- so in practice most of the API is stable.
+
+A few MatrixBase methods are considered experimental, hence not part of any API stability guarantee:
+\li all methods documented as internal
+\li all methods hidden in the Doxygen documentation
+\li all methods marked as experimental
+\li all methods defined in experimental modules
+
+*/
+
+}
diff --git a/doc/CMakeLists.txt b/doc/CMakeLists.txt
new file mode 100644
index 0000000..e7eaa4b
--- /dev/null
+++ b/doc/CMakeLists.txt
@@ -0,0 +1,119 @@
+project(EigenDoc)
+
+set_directory_properties(PROPERTIES EXCLUDE_FROM_ALL TRUE)
+
+project(EigenDoc)
+
+if(CMAKE_COMPILER_IS_GNUCXX)
+ if(CMAKE_SYSTEM_NAME MATCHES Linux)
+ set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -O1 -g1")
+ endif()
+endif()
+
+option(EIGEN_INTERNAL_DOCUMENTATION "Build internal documentation" OFF)
+option(EIGEN_DOC_USE_MATHJAX "Use MathJax for rendering math in HTML docs" ON)
+
+# Set some Doxygen flags
+set(EIGEN_DOXY_PROJECT_NAME "Eigen")
+set(EIGEN_DOXY_OUTPUT_DIRECTORY_SUFFIX "")
+set(EIGEN_DOXY_INPUT "\"${Eigen_SOURCE_DIR}/Eigen\" \"${Eigen_SOURCE_DIR}/doc\"")
+set(EIGEN_DOXY_HTML_COLORSTYLE_HUE "220")
+set(EIGEN_DOXY_TAGFILES "")
+
+if(EIGEN_INTERNAL_DOCUMENTATION)
+ set(EIGEN_DOXY_INTERNAL "YES")
+else()
+ set(EIGEN_DOXY_INTERNAL "NO")
+endif()
+
+if (EIGEN_DOC_USE_MATHJAX)
+ set(EIGEN_DOXY_USE_MATHJAX "YES")
+else ()
+ set(EIGEN_DOXY_USE_MATHJAX "NO")
+endif()
+
+configure_file(
+ ${CMAKE_CURRENT_SOURCE_DIR}/Doxyfile.in
+ ${CMAKE_CURRENT_BINARY_DIR}/Doxyfile
+)
+
+set(EIGEN_DOXY_PROJECT_NAME "Eigen-unsupported")
+set(EIGEN_DOXY_OUTPUT_DIRECTORY_SUFFIX "/unsupported")
+set(EIGEN_DOXY_INPUT "\"${Eigen_SOURCE_DIR}/unsupported/Eigen\" \"${Eigen_SOURCE_DIR}/unsupported/doc\"")
+set(EIGEN_DOXY_HTML_COLORSTYLE_HUE "0")
+set(EIGEN_DOXY_TAGFILES "\"${Eigen_BINARY_DIR}/doc/Eigen.doxytags=..\"")
+#set(EIGEN_DOXY_TAGFILES "")
+
+configure_file(
+ ${CMAKE_CURRENT_SOURCE_DIR}/Doxyfile.in
+ ${CMAKE_CURRENT_BINARY_DIR}/Doxyfile-unsupported
+)
+
+configure_file(
+ ${CMAKE_CURRENT_SOURCE_DIR}/eigendoxy_header.html.in
+ ${CMAKE_CURRENT_BINARY_DIR}/eigendoxy_header.html
+)
+
+configure_file(
+ ${CMAKE_CURRENT_SOURCE_DIR}/eigendoxy_footer.html.in
+ ${CMAKE_CURRENT_BINARY_DIR}/eigendoxy_footer.html
+)
+
+configure_file(
+ ${CMAKE_CURRENT_SOURCE_DIR}/eigendoxy_layout.xml.in
+ ${CMAKE_CURRENT_BINARY_DIR}/eigendoxy_layout.xml
+)
+
+configure_file(
+ ${Eigen_SOURCE_DIR}/unsupported/doc/eigendoxy_layout.xml.in
+ ${Eigen_BINARY_DIR}/doc/unsupported/eigendoxy_layout.xml
+)
+
+set(examples_targets "")
+set(snippets_targets "")
+
+add_definitions("-DEIGEN_MAKING_DOCS")
+add_custom_target(all_examples)
+
+add_subdirectory(examples)
+add_subdirectory(special_examples)
+add_subdirectory(snippets)
+
+add_custom_target(
+ doc-eigen-prerequisites
+ ALL
+ COMMAND ${CMAKE_COMMAND} -E make_directory ${CMAKE_CURRENT_BINARY_DIR}/html/
+ COMMAND ${CMAKE_COMMAND} -E copy ${CMAKE_CURRENT_SOURCE_DIR}/eigen_navtree_hacks.js ${CMAKE_CURRENT_BINARY_DIR}/html/
+ COMMAND ${CMAKE_COMMAND} -E copy ${CMAKE_CURRENT_SOURCE_DIR}/Eigen_Silly_Professor_64x64.png ${CMAKE_CURRENT_BINARY_DIR}/html/
+ COMMAND ${CMAKE_COMMAND} -E copy ${CMAKE_CURRENT_SOURCE_DIR}/ftv2pnode.png ${CMAKE_CURRENT_BINARY_DIR}/html/
+ COMMAND ${CMAKE_COMMAND} -E copy ${CMAKE_CURRENT_SOURCE_DIR}/ftv2node.png ${CMAKE_CURRENT_BINARY_DIR}/html/
+ COMMAND ${CMAKE_COMMAND} -E copy ${CMAKE_CURRENT_SOURCE_DIR}/AsciiQuickReference.txt ${CMAKE_CURRENT_BINARY_DIR}/html/
+ WORKING_DIRECTORY ${CMAKE_CURRENT_BINARY_DIR}
+)
+
+add_custom_target(
+ doc-unsupported-prerequisites
+ ALL
+ COMMAND ${CMAKE_COMMAND} -E make_directory ${Eigen_BINARY_DIR}/doc/html/unsupported
+ COMMAND ${CMAKE_COMMAND} -E copy ${CMAKE_CURRENT_SOURCE_DIR}/eigen_navtree_hacks.js ${CMAKE_CURRENT_BINARY_DIR}/html/unsupported/
+ COMMAND ${CMAKE_COMMAND} -E copy ${CMAKE_CURRENT_SOURCE_DIR}/Eigen_Silly_Professor_64x64.png ${CMAKE_CURRENT_BINARY_DIR}/html/unsupported/
+ COMMAND ${CMAKE_COMMAND} -E copy ${CMAKE_CURRENT_SOURCE_DIR}/ftv2pnode.png ${CMAKE_CURRENT_BINARY_DIR}/html/unsupported/
+ COMMAND ${CMAKE_COMMAND} -E copy ${CMAKE_CURRENT_SOURCE_DIR}/ftv2node.png ${CMAKE_CURRENT_BINARY_DIR}/html/unsupported/
+ WORKING_DIRECTORY ${Eigen_BINARY_DIR}/doc
+)
+
+add_dependencies(doc-eigen-prerequisites all_snippets all_examples)
+add_dependencies(doc-unsupported-prerequisites unsupported_snippets unsupported_examples)
+
+add_custom_target(doc ALL
+ COMMAND doxygen
+ COMMAND doxygen Doxyfile-unsupported
+ COMMAND ${CMAKE_COMMAND} -E copy ${Eigen_BINARY_DIR}/doc/html/group__TopicUnalignedArrayAssert.html ${Eigen_BINARY_DIR}/doc/html/TopicUnalignedArrayAssert.html
+ COMMAND ${CMAKE_COMMAND} -E rename html eigen-doc
+ COMMAND ${CMAKE_COMMAND} -E remove eigen-doc/eigen-doc.tgz eigen-doc/unsupported/_formulas.log eigen-doc/_formulas.log
+ COMMAND ${CMAKE_COMMAND} -E tar cfz eigen-doc.tgz eigen-doc
+ COMMAND ${CMAKE_COMMAND} -E rename eigen-doc.tgz eigen-doc/eigen-doc.tgz
+ COMMAND ${CMAKE_COMMAND} -E rename eigen-doc html
+ WORKING_DIRECTORY ${Eigen_BINARY_DIR}/doc)
+
+add_dependencies(doc doc-eigen-prerequisites doc-unsupported-prerequisites)
diff --git a/doc/ClassHierarchy.dox b/doc/ClassHierarchy.dox
new file mode 100644
index 0000000..468e60a
--- /dev/null
+++ b/doc/ClassHierarchy.dox
@@ -0,0 +1,129 @@
+namespace Eigen {
+
+/** \page TopicClassHierarchy The class hierarchy
+
+This page explains the design of the core classes in Eigen's class hierarchy and how they fit together. Casual
+users probably need not concern themselves with these details, but it may be useful for both advanced users
+and Eigen developers.
+
+\eigenAutoToc
+
+
+\section TopicClassHierarchyPrinciples Principles
+
+Eigen's class hierarchy is designed so that virtual functions are avoided where their overhead would
+significantly impair performance. Instead, Eigen achieves polymorphism with the Curiously Recurring Template
+Pattern (CRTP). In this pattern, the base class (for instance, \c MatrixBase) is in fact a template class, and
+the derived class (for instance, \c Matrix) inherits the base class with the derived class itself as a
+template argument (in this case, \c Matrix inherits from \c MatrixBase<Matrix>). This allows Eigen to
+resolve the polymorphic function calls at compile time.
+
+In addition, the design avoids multiple inheritance. One reason for this is that in our experience, some
+compilers (like MSVC) fail to perform empty base class optimization, which is crucial for our fixed-size
+types.
+
+
+\section TopicClassHierarchyCoreClasses The core classes
+
+These are the classes that you need to know about if you want to write functions that accept or return Eigen
+objects.
+
+ - Matrix means plain dense matrix. If \c m is a \c %Matrix, then, for instance, \c m+m is no longer a
+ \c %Matrix, it is a "matrix expression".
+ - MatrixBase means dense matrix expression. This means that a \c %MatrixBase is something that can be
+ added, matrix-multiplied, LU-decomposed, QR-decomposed... All matrix expression classes, including
+ \c %Matrix itself, inherit \c %MatrixBase.
+ - Array means plain dense array. If \c x is an \c %Array, then, for instance, \c x+x is no longer an
+ \c %Array, it is an "array expression".
+ - ArrayBase means dense array expression. This means that an \c %ArrayBase is something that can be
+ added, array-multiplied, and on which you can perform all sorts of array operations... All array
+ expression classes, including \c %Array itself, inherit \c %ArrayBase.
+ - DenseBase means dense (matrix or array) expression. Both \c %ArrayBase and \c %MatrixBase inherit
+ \c %DenseBase. \c %DenseBase is where all the methods go that apply to dense expressions regardless of
+ whether they are matrix or array expressions. For example, the \link DenseBase::block() block(...) \endlink
+ methods are in \c %DenseBase.
+
+\section TopicClassHierarchyBaseClasses Base classes
+
+These classes serve as base classes for the five core classes mentioned above. They are more internal and so
+less interesting for users of the Eigen library.
+
+ - PlainObjectBase means dense (matrix or array) plain object, i.e. something that stores its own dense
+ array of coefficients. This is where, for instance, the \link PlainObjectBase::resize() resize() \endlink
+ methods go. \c %PlainObjectBase is inherited by \c %Matrix and by \c %Array. But above, we said that
+ \c %Matrix inherits \c %MatrixBase and \c %Array inherits \c %ArrayBase. So does that mean multiple
+ inheritance? No, because \c %PlainObjectBase \e itself inherits \c %MatrixBase or \c %ArrayBase depending
+ on whether we are in the matrix or array case. When we said above that \c %Matrix inherited
+ \c %MatrixBase, we omitted to say it does so indirectly via \c %PlainObjectBase. Same for \c %Array.
+ - DenseCoeffsBase means something that has dense coefficient accessors. It is a base class for
+ \c %DenseBase. The reason for \c %DenseCoeffsBase to exist is that the set of available coefficient
+ accessors is very different depending on whether a dense expression has direct memory access or not (the
+ \c DirectAccessBit flag). For example, if \c x is a plain matrix, then \c x has direct access, and
+ \c x.transpose() and \c x.block(...) also have direct access, because their coefficients can be read right
+ off memory, but for example, \c x+x does not have direct memory access, because obtaining any of its
+ coefficients requires a computation (an addition), it can't be just read off memory.
+ - EigenBase means anything that can be evaluated into a plain dense matrix or array (even if that would
+ be a bad idea). \c %EigenBase is really the absolute base class for anything that remotely looks like a
+ matrix or array. It is a base class for \c %DenseCoeffsBase, so it sits below all our dense class
+ hierarchy, but it is not limited to dense expressions. For example, \c %EigenBase is also inherited by
+ diagonal matrices, sparse matrices, etc...
+
+
+\section TopicClassHierarchyInheritanceDiagrams Inheritance diagrams
+
+The inheritance diagram for Matrix looks as follows:
+
+<pre>
+EigenBase<%Matrix>
+ <-- DenseCoeffsBase<%Matrix> (direct access case)
+ <-- DenseBase<%Matrix>
+ <-- MatrixBase<%Matrix>
+ <-- PlainObjectBase<%Matrix> (matrix case)
+ <-- Matrix
+</pre>
+
+The inheritance diagram for Array looks as follows:
+
+<pre>
+EigenBase<%Array>
+ <-- DenseCoeffsBase<%Array> (direct access case)
+ <-- DenseBase<%Array>
+ <-- ArrayBase<%Array>
+ <-- PlainObjectBase<%Array> (array case)
+ <-- Array
+</pre>
+
+The inheritance diagram for some other matrix expression class, here denoted by \c SomeMatrixXpr, looks as
+follows:
+
+<pre>
+EigenBase<SomeMatrixXpr>
+ <-- DenseCoeffsBase<SomeMatrixXpr> (direct access or no direct access case)
+ <-- DenseBase<SomeMatrixXpr>
+ <-- MatrixBase<SomeMatrixXpr>
+ <-- SomeMatrixXpr
+</pre>
+
+The inheritance diagram for some other array expression class, here denoted by \c SomeArrayXpr, looks as
+follows:
+
+<pre>
+EigenBase<SomeArrayXpr>
+ <-- DenseCoeffsBase<SomeArrayXpr> (direct access or no direct access case)
+ <-- DenseBase<SomeArrayXpr>
+ <-- ArrayBase<SomeArrayXpr>
+ <-- SomeArrayXpr
+</pre>
+
+Finally, consider an example of something that is not a dense expression, for instance a diagonal matrix. The
+corresponding inheritance diagram is:
+
+<pre>
+EigenBase<%DiagonalMatrix>
+ <-- DiagonalBase<%DiagonalMatrix>
+ <-- DiagonalMatrix
+</pre>
+
+
+*/
+}
diff --git a/doc/CoeffwiseMathFunctionsTable.dox b/doc/CoeffwiseMathFunctionsTable.dox
new file mode 100644
index 0000000..3f5c564
--- /dev/null
+++ b/doc/CoeffwiseMathFunctionsTable.dox
@@ -0,0 +1,600 @@
+namespace Eigen {
+
+/** \eigenManualPage CoeffwiseMathFunctions Catalog of coefficient-wise math functions
+
+
+<!-- <span style="font-size:300%; color:red; font-weight: 900;">!WORK IN PROGRESS!</span> -->
+
+This table presents a catalog of the coefficient-wise math functions supported by %Eigen.
+In this table, \c a, \c b, refer to Array objects or expressions, and \c m refers to a linear algebra Matrix/Vector object. Standard scalar types are abbreviated as follows:
+ - \c int: \c i32
+ - \c float: \c f
+ - \c double: \c d
+ - \c std::complex<float>: \c cf
+ - \c std::complex<double>: \c cd
+
+For each row, the first column list the equivalent calls for arrays, and matrices when supported. Of course, all functions are available for matrices by first casting it as an array: \c m.array().
+
+The third column gives some hints in the underlying scalar implementation. In most cases, %Eigen does not implement itself the math function but relies on the STL for standard scalar types, or user-provided functions for custom scalar types.
+For instance, some simply calls the respective function of the STL while preserving <a href="http://en.cppreference.com/w/cpp/language/adl">argument-dependent lookup</a> for custom types.
+The following:
+\code
+using std::foo;
+foo(a[i]);
+\endcode
+means that the STL's function \c std::foo will be potentially called if it is compatible with the underlying scalar type. If not, then the user must ensure that an overload of the function foo is available for the given scalar type (usually defined in the same namespace as the given scalar type).
+This also means that, unless specified, if the function \c std::foo is available only in some recent c++ versions (e.g., c++11), then the respective %Eigen's function/method will be usable on standard types only if the compiler support the required c++ version.
+
+<table class="manual-hl">
+<tr>
+<th>API</th><th>Description</th><th>Default scalar implementation</th><th>SIMD</th>
+</tr>
+<tr><td colspan="4"></td></tr>
+<tr><th colspan="4">Basic operations</th></tr>
+<tr>
+ <td class="code">
+ \anchor cwisetable_abs
+ a.\link ArrayBase::abs abs\endlink(); \n
+ \link Eigen::abs abs\endlink(a); \n
+ m.\link MatrixBase::cwiseAbs cwiseAbs\endlink();
+ </td>
+ <td>absolute value (\f$ |a_i| \f$) </td>
+ <td class="code">
+ using <a href="http://en.cppreference.com/w/cpp/numeric/math/fabs">std::abs</a>; \n
+ abs(a[i]);
+ </td>
+ <td>SSE2, AVX (i32,f,d)</td>
+</tr>
+<tr>
+ <td class="code">
+ \anchor cwisetable_inverse
+ a.\link ArrayBase::inverse inverse\endlink(); \n
+ \link Eigen::inverse inverse\endlink(a); \n
+ m.\link MatrixBase::cwiseInverse cwiseInverse\endlink();
+ </td>
+ <td>inverse value (\f$ 1/a_i \f$) </td>
+ <td class="code">
+ 1/a[i];
+ </td>
+ <td>All engines (f,d,fc,fd)</td>
+</tr>
+<tr>
+ <td class="code">
+ \anchor cwisetable_conj
+ a.\link ArrayBase::conjugate conjugate\endlink(); \n
+ \link Eigen::conj conj\endlink(a); \n
+ m.\link MatrixBase::conjugate conjugate\endlink();
+ </td>
+ <td><a href="https://en.wikipedia.org/wiki/Complex_conjugate">complex conjugate</a> (\f$ \bar{a_i} \f$),\n
+ no-op for real </td>
+ <td class="code">
+ using <a href="http://en.cppreference.com/w/cpp/numeric/complex/conj">std::conj</a>; \n
+ conj(a[i]);
+ </td>
+ <td>All engines (fc,fd)</td>
+</tr>
+<tr>
+ <td class="code">
+ \anchor cwisetable_arg
+ a.\link ArrayBase::arg arg\endlink(); \n
+ \link Eigen::arg arg\endlink(a); \n
+ m.\link MatrixBase::cwiseArg cwiseArg\endlink();
+ </td>
+ <td>phase angle of complex number</td>
+ <td class="code">
+ using <a href="http://en.cppreference.com/w/cpp/numeric/complex/arg">std::arg</a>; \n
+ arg(a[i]);
+ </td>
+ <td>All engines (fc,fd)</td>
+</tr>
+<tr>
+<th colspan="4">Exponential functions</th>
+</tr>
+<tr>
+ <td class="code">
+ \anchor cwisetable_exp
+ a.\link ArrayBase::exp exp\endlink(); \n
+ \link Eigen::exp exp\endlink(a);
+ </td>
+ <td>\f$ e \f$ raised to the given power (\f$ e^{a_i} \f$) </td>
+ <td class="code">
+ using <a href="http://en.cppreference.com/w/cpp/numeric/math/exp">std::exp</a>; \n
+ exp(a[i]);
+ </td>
+ <td>SSE2, AVX (f,d)</td>
+</tr>
+<tr>
+ <td class="code">
+ \anchor cwisetable_log
+ a.\link ArrayBase::log log\endlink(); \n
+ \link Eigen::log log\endlink(a);
+ </td>
+ <td>natural (base \f$ e \f$) logarithm (\f$ \ln({a_i}) \f$)</td>
+ <td class="code">
+ using <a href="http://en.cppreference.com/w/cpp/numeric/math/log">std::log</a>; \n
+ log(a[i]);
+ </td>
+ <td>SSE2, AVX (f)</td>
+</tr>
+<tr>
+ <td class="code">
+ \anchor cwisetable_log1p
+ a.\link ArrayBase::log1p log1p\endlink(); \n
+ \link Eigen::log1p log1p\endlink(a);
+ </td>
+ <td>natural (base \f$ e \f$) logarithm of 1 plus \n the given number (\f$ \ln({1+a_i}) \f$)</td>
+ <td>built-in generic implementation based on \c log,\n
+ plus \c using <a href="http://en.cppreference.com/w/cpp/numeric/math/log1p">\c std::log1p </a>; \cpp11</td>
+ <td></td>
+</tr>
+<tr>
+ <td class="code">
+ \anchor cwisetable_log10
+ a.\link ArrayBase::log10 log10\endlink(); \n
+ \link Eigen::log10 log10\endlink(a);
+ </td>
+ <td>base 10 logarithm (\f$ \log_{10}({a_i}) \f$)</td>
+ <td class="code">
+ using <a href="http://en.cppreference.com/w/cpp/numeric/math/log10">std::log10</a>; \n
+ log10(a[i]);
+ </td>
+ <td></td>
+</tr>
+<tr>
+<th colspan="4">Power functions</th>
+</tr>
+<tr>
+ <td class="code">
+ \anchor cwisetable_pow
+ a.\link ArrayBase::pow pow\endlink(b); \n
+ \link ArrayBase::pow(const Eigen::ArrayBase< Derived > &x, const Eigen::ArrayBase< ExponentDerived > &exponents) pow\endlink(a,b);
+ </td>
+ <!-- For some reason Doxygen thinks that pow is in ArrayBase namespace -->
+ <td>raises a number to the given power (\f$ a_i ^ {b_i} \f$) \n \c a and \c b can be either an array or scalar.</td>
+ <td class="code">
+ using <a href="http://en.cppreference.com/w/cpp/numeric/math/pow">std::pow</a>; \n
+ pow(a[i],b[i]);\n
+ (plus builtin for integer types)</td>
+ <td></td>
+</tr>
+<tr>
+ <td class="code">
+ \anchor cwisetable_sqrt
+ a.\link ArrayBase::sqrt sqrt\endlink(); \n
+ \link Eigen::sqrt sqrt\endlink(a);\n
+ m.\link MatrixBase::cwiseSqrt cwiseSqrt\endlink();
+ </td>
+ <td>computes square root (\f$ \sqrt a_i \f$)</td>
+ <td class="code">
+ using <a href="http://en.cppreference.com/w/cpp/numeric/math/sqrt">std::sqrt</a>; \n
+ sqrt(a[i]);</td>
+ <td>SSE2, AVX (f,d)</td>
+</tr>
+<tr>
+ <td class="code">
+ \anchor cwisetable_rsqrt
+ a.\link ArrayBase::rsqrt rsqrt\endlink(); \n
+ \link Eigen::rsqrt rsqrt\endlink(a);
+ </td>
+ <td><a href="https://en.wikipedia.org/wiki/Fast_inverse_square_root">reciprocal square root</a> (\f$ 1/{\sqrt a_i} \f$)</td>
+ <td class="code">
+ using <a href="http://en.cppreference.com/w/cpp/numeric/math/sqrt">std::sqrt</a>; \n
+ 1/sqrt(a[i]); \n
+ </td>
+ <td>SSE2, AVX, AltiVec, ZVector (f,d)\n
+ (approx + 1 Newton iteration)</td>
+</tr>
+<tr>
+ <td class="code">
+ \anchor cwisetable_square
+ a.\link ArrayBase::square square\endlink(); \n
+ \link Eigen::square square\endlink(a);
+ </td>
+ <td>computes square power (\f$ a_i^2 \f$)</td>
+ <td class="code">
+ a[i]*a[i]</td>
+ <td>All (i32,f,d,cf,cd)</td>
+</tr>
+<tr>
+ <td class="code">
+ \anchor cwisetable_cube
+ a.\link ArrayBase::cube cube\endlink(); \n
+ \link Eigen::cube cube\endlink(a);
+ </td>
+ <td>computes cubic power (\f$ a_i^3 \f$)</td>
+ <td class="code">
+ a[i]*a[i]*a[i]</td>
+ <td>All (i32,f,d,cf,cd)</td>
+</tr>
+<tr>
+ <td class="code">
+ \anchor cwisetable_abs2
+ a.\link ArrayBase::abs2 abs2\endlink(); \n
+ \link Eigen::abs2 abs2\endlink(a);\n
+ m.\link MatrixBase::cwiseAbs2 cwiseAbs2\endlink();
+ </td>
+ <td>computes the squared absolute value (\f$ |a_i|^2 \f$)</td>
+ <td class="code">
+ real: a[i]*a[i] \n
+ complex: real(a[i])*real(a[i]) \n
+ + imag(a[i])*imag(a[i])</td>
+ <td>All (i32,f,d)</td>
+</tr>
+<tr>
+<th colspan="4">Trigonometric functions</th>
+</tr>
+<tr>
+ <td class="code">
+ \anchor cwisetable_sin
+ a.\link ArrayBase::sin sin\endlink(); \n
+ \link Eigen::sin sin\endlink(a);
+ </td>
+ <td>computes sine</td>
+ <td class="code">
+ using <a href="http://en.cppreference.com/w/cpp/numeric/math/sin">std::sin</a>; \n
+ sin(a[i]);</td>
+ <td>SSE2, AVX (f)</td>
+</tr>
+<tr>
+ <td class="code">
+ \anchor cwisetable_cos
+ a.\link ArrayBase::cos cos\endlink(); \n
+ \link Eigen::cos cos\endlink(a);
+ </td>
+ <td>computes cosine</td>
+ <td class="code">
+ using <a href="http://en.cppreference.com/w/cpp/numeric/math/cos">std::cos</a>; \n
+ cos(a[i]);</td>
+ <td>SSE2, AVX (f)</td>
+</tr>
+<tr>
+ <td class="code">
+ \anchor cwisetable_tan
+ a.\link ArrayBase::tan tan\endlink(); \n
+ \link Eigen::tan tan\endlink(a);
+ </td>
+ <td>computes tangent</td>
+ <td class="code">
+ using <a href="http://en.cppreference.com/w/cpp/numeric/math/tan">std::tan</a>; \n
+ tan(a[i]);</td>
+ <td></td>
+</tr>
+<tr>
+ <td class="code">
+ \anchor cwisetable_asin
+ a.\link ArrayBase::asin asin\endlink(); \n
+ \link Eigen::asin asin\endlink(a);
+ </td>
+ <td>computes arc sine (\f$ \sin^{-1} a_i \f$)</td>
+ <td class="code">
+ using <a href="http://en.cppreference.com/w/cpp/numeric/math/asin">std::asin</a>; \n
+ asin(a[i]);</td>
+ <td></td>
+</tr>
+<tr>
+ <td class="code">
+ \anchor cwisetable_acos
+ a.\link ArrayBase::acos acos\endlink(); \n
+ \link Eigen::acos acos\endlink(a);
+ </td>
+ <td>computes arc cosine (\f$ \cos^{-1} a_i \f$)</td>
+ <td class="code">
+ using <a href="http://en.cppreference.com/w/cpp/numeric/math/acos">std::acos</a>; \n
+ acos(a[i]);</td>
+ <td></td>
+</tr>
+<tr>
+ <td class="code">
+ \anchor cwisetable_atan
+ a.\link ArrayBase::atan atan\endlink(); \n
+ \link Eigen::atan atan\endlink(a);
+ </td>
+ <td>computes arc tangent (\f$ \tan^{-1} a_i \f$)</td>
+ <td class="code">
+ using <a href="http://en.cppreference.com/w/cpp/numeric/math/atan">std::atan</a>; \n
+ atan(a[i]);</td>
+ <td></td>
+</tr>
+<tr>
+<th colspan="4">Hyperbolic functions</th>
+</tr>
+<tr>
+ <td class="code">
+ \anchor cwisetable_sinh
+ a.\link ArrayBase::sinh sinh\endlink(); \n
+ \link Eigen::sinh sinh\endlink(a);
+ </td>
+ <td>computes hyperbolic sine</td>
+ <td class="code">
+ using <a href="http://en.cppreference.com/w/cpp/numeric/math/sinh">std::sinh</a>; \n
+ sinh(a[i]);</td>
+ <td></td>
+</tr>
+<tr>
+ <td class="code">
+ \anchor cwisetable_cosh
+ a.\link ArrayBase::cosh cohs\endlink(); \n
+ \link Eigen::cosh cosh\endlink(a);
+ </td>
+ <td>computes hyperbolic cosine</td>
+ <td class="code">
+ using <a href="http://en.cppreference.com/w/cpp/numeric/math/cosh">std::cosh</a>; \n
+ cosh(a[i]);</td>
+ <td></td>
+</tr>
+<tr>
+ <td class="code">
+ \anchor cwisetable_tanh
+ a.\link ArrayBase::tanh tanh\endlink(); \n
+ \link Eigen::tanh tanh\endlink(a);
+ </td>
+ <td>computes hyperbolic tangent</td>
+ <td class="code">
+ using <a href="http://en.cppreference.com/w/cpp/numeric/math/tanh">std::tanh</a>; \n
+ tanh(a[i]);</td>
+ <td></td>
+</tr>
+<tr>
+ <td class="code">
+ \anchor cwisetable_asinh
+ a.\link ArrayBase::asinh asinh\endlink(); \n
+ \link Eigen::asinh asinh\endlink(a);
+ </td>
+ <td>computes inverse hyperbolic sine</td>
+ <td class="code">
+ using <a href="http://en.cppreference.com/w/cpp/numeric/math/asinh">std::asinh</a>; \n
+ asinh(a[i]);</td>
+ <td></td>
+</tr>
+<tr>
+ <td class="code">
+ \anchor cwisetable_acosh
+ a.\link ArrayBase::acosh cohs\endlink(); \n
+ \link Eigen::acosh acosh\endlink(a);
+ </td>
+ <td>computes hyperbolic cosine</td>
+ <td class="code">
+ using <a href="http://en.cppreference.com/w/cpp/numeric/math/acosh">std::acosh</a>; \n
+ acosh(a[i]);</td>
+ <td></td>
+</tr>
+<tr>
+ <td class="code">
+ \anchor cwisetable_atanh
+ a.\link ArrayBase::atanh atanh\endlink(); \n
+ \link Eigen::atanh atanh\endlink(a);
+ </td>
+ <td>computes hyperbolic tangent</td>
+ <td class="code">
+ using <a href="http://en.cppreference.com/w/cpp/numeric/math/atanh">std::atanh</a>; \n
+ atanh(a[i]);</td>
+ <td></td>
+</tr>
+<tr>
+<th colspan="4">Nearest integer floating point operations</th>
+</tr>
+<tr>
+ <td class="code">
+ \anchor cwisetable_ceil
+ a.\link ArrayBase::ceil ceil\endlink(); \n
+ \link Eigen::ceil ceil\endlink(a);
+ </td>
+ <td>nearest integer not less than the given value</td>
+ <td class="code">
+ using <a href="http://en.cppreference.com/w/cpp/numeric/math/ceil">std::ceil</a>; \n
+ ceil(a[i]);</td>
+ <td>SSE4,AVX,ZVector (f,d)</td>
+</tr>
+<tr>
+ <td class="code">
+ \anchor cwisetable_floor
+ a.\link ArrayBase::floor floor\endlink(); \n
+ \link Eigen::floor floor\endlink(a);
+ </td>
+ <td>nearest integer not greater than the given value</td>
+ <td class="code">
+ using <a href="http://en.cppreference.com/w/cpp/numeric/math/floor">std::floor</a>; \n
+ floor(a[i]);</td>
+ <td>SSE4,AVX,ZVector (f,d)</td>
+</tr>
+<tr>
+ <td class="code">
+ \anchor cwisetable_round
+ a.\link ArrayBase::round round\endlink(); \n
+ \link Eigen::round round\endlink(a);
+ </td>
+ <td>nearest integer, \n rounding away from zero in halfway cases</td>
+ <td>built-in generic implementation \n based on \c floor and \c ceil,\n
+ plus \c using <a href="http://en.cppreference.com/w/cpp/numeric/math/round">\c std::round </a>; \cpp11</td>
+ <td>SSE4,AVX,ZVector (f,d)</td>
+</tr>
+<tr>
+ <td class="code">
+ \anchor cwisetable_rint
+ a.\link ArrayBase::rint rint\endlink(); \n
+ \link Eigen::rint rint\endlink(a);
+ </td>
+ <td>nearest integer, \n rounding to nearest even in halfway cases</td>
+ <td>built-in generic implementation using <a href="http://en.cppreference.com/w/cpp/numeric/math/rint">\c std::rint </a>; \cpp11
+ or <a href="http://en.cppreference.com/w/c/numeric/math/rint">\c rintf </a>; </td>
+ <td>SSE4,AVX (f,d)</td>
+</tr>
+<tr>
+<th colspan="4">Floating point manipulation functions</th>
+</tr>
+<tr>
+<th colspan="4">Classification and comparison</th>
+</tr>
+<tr>
+ <td class="code">
+ \anchor cwisetable_isfinite
+ a.\link ArrayBase::isFinite isFinite\endlink(); \n
+ \link Eigen::isfinite isfinite\endlink(a);
+ </td>
+ <td>checks if the given number has finite value</td>
+ <td>built-in generic implementation,\n
+ plus \c using <a href="http://en.cppreference.com/w/cpp/numeric/math/isfinite">\c std::isfinite </a>; \cpp11</td>
+ <td></td>
+</tr>
+<tr>
+ <td class="code">
+ \anchor cwisetable_isinf
+ a.\link ArrayBase::isInf isInf\endlink(); \n
+ \link Eigen::isinf isinf\endlink(a);
+ </td>
+ <td>checks if the given number is infinite</td>
+ <td>built-in generic implementation,\n
+ plus \c using <a href="http://en.cppreference.com/w/cpp/numeric/math/isinf">\c std::isinf </a>; \cpp11</td>
+ <td></td>
+</tr>
+<tr>
+ <td class="code">
+ \anchor cwisetable_isnan
+ a.\link ArrayBase::isNaN isNaN\endlink(); \n
+ \link Eigen::isnan isnan\endlink(a);
+ </td>
+ <td>checks if the given number is not a number</td>
+ <td>built-in generic implementation,\n
+ plus \c using <a href="http://en.cppreference.com/w/cpp/numeric/math/isnan">\c std::isnan </a>; \cpp11</td>
+ <td></td>
+</tr>
+<tr>
+<th colspan="4">Error and gamma functions</th>
+</tr>
+<tr> <td colspan="4"> Require \c \#include \c <unsupported/Eigen/SpecialFunctions> </td></tr>
+<tr>
+ <td class="code">
+ \anchor cwisetable_erf
+ a.\link ArrayBase::erf erf\endlink(); \n
+ \link Eigen::erf erf\endlink(a);
+ </td>
+ <td>error function</td>
+ <td class="code">
+ using <a href="http://en.cppreference.com/w/cpp/numeric/math/erf">std::erf</a>; \cpp11 \n
+ erf(a[i]);
+ </td>
+ <td></td>
+</tr>
+<tr>
+ <td class="code">
+ \anchor cwisetable_erfc
+ a.\link ArrayBase::erfc erfc\endlink(); \n
+ \link Eigen::erfc erfc\endlink(a);
+ </td>
+ <td>complementary error function</td>
+ <td class="code">
+ using <a href="http://en.cppreference.com/w/cpp/numeric/math/erfc">std::erfc</a>; \cpp11 \n
+ erfc(a[i]);
+ </td>
+ <td></td>
+</tr>
+<tr>
+ <td class="code">
+ \anchor cwisetable_lgamma
+ a.\link ArrayBase::lgamma lgamma\endlink(); \n
+ \link Eigen::lgamma lgamma\endlink(a);
+ </td>
+ <td>natural logarithm of the gamma function</td>
+ <td class="code">
+ using <a href="http://en.cppreference.com/w/cpp/numeric/math/lgamma">std::lgamma</a>; \cpp11 \n
+ lgamma(a[i]);
+ </td>
+ <td></td>
+</tr>
+<tr>
+ <td class="code">
+ \anchor cwisetable_digamma
+ a.\link ArrayBase::digamma digamma\endlink(); \n
+ \link Eigen::digamma digamma\endlink(a);
+ </td>
+ <td><a href="https://en.wikipedia.org/wiki/Digamma_function">logarithmic derivative of the gamma function</a></td>
+ <td>
+ built-in for float and double
+ </td>
+ <td></td>
+</tr>
+<tr>
+ <td class="code">
+ \anchor cwisetable_igamma
+ \link Eigen::igamma igamma\endlink(a,x);
+ </td>
+ <td><a href="https://en.wikipedia.org/wiki/Incomplete_gamma_function">lower incomplete gamma integral</a>
+ \n \f$ \gamma(a_i,x_i)= \frac{1}{|a_i|} \int_{0}^{x_i}e^{\text{-}t} t^{a_i-1} \mathrm{d} t \f$</td>
+ <td>
+ built-in for float and double,\n but requires \cpp11
+ </td>
+ <td></td>
+</tr>
+<tr>
+ <td class="code">
+ \anchor cwisetable_igammac
+ \link Eigen::igammac igammac\endlink(a,x);
+ </td>
+ <td><a href="https://en.wikipedia.org/wiki/Incomplete_gamma_function">upper incomplete gamma integral</a>
+ \n \f$ \Gamma(a_i,x_i) = \frac{1}{|a_i|} \int_{x_i}^{\infty}e^{\text{-}t} t^{a_i-1} \mathrm{d} t \f$</td>
+ <td>
+ built-in for float and double,\n but requires \cpp11
+ </td>
+ <td></td>
+</tr>
+<tr>
+<th colspan="4">Special functions</th>
+</tr>
+<tr> <td colspan="4"> Require \c \#include \c <unsupported/Eigen/SpecialFunctions> </td></tr>
+<tr>
+ <td class="code">
+ \anchor cwisetable_polygamma
+ \link Eigen::polygamma polygamma\endlink(n,x);
+ </td>
+ <td><a href="https://en.wikipedia.org/wiki/Polygamma_function">n-th derivative of digamma at x</a></td>
+ <td>
+ built-in generic based on\n <a href="#cwisetable_lgamma">\c lgamma </a>,
+ <a href="#cwisetable_digamma"> \c digamma </a>
+ and <a href="#cwisetable_zeta">\c zeta </a>.
+ </td>
+ <td></td>
+</tr>
+<tr>
+ <td class="code">
+ \anchor cwisetable_betainc
+ \link Eigen::betainc betainc\endlink(a,b,x);
+ </td>
+ <td><a href="https://en.wikipedia.org/wiki/Beta_function#Incomplete_beta_function">Incomplete beta function</a></td>
+ <td>
+ built-in for float and double,\n but requires \cpp11
+ </td>
+ <td></td>
+</tr>
+<tr>
+ <td class="code">
+ \anchor cwisetable_zeta
+ \link Eigen::zeta zeta\endlink(a,b); \n
+ a.\link ArrayBase::zeta zeta\endlink(b);
+ </td>
+ <td><a href="https://en.wikipedia.org/wiki/Hurwitz_zeta_function">Hurwitz zeta function</a>
+ \n \f$ \zeta(a_i,b_i)=\sum_{k=0}^{\infty}(b_i+k)^{\text{-}a_i} \f$</td>
+ <td>
+ built-in for float and double
+ </td>
+ <td></td>
+</tr>
+<tr>
+ <td class="code">
+ \anchor cwisetable_ndtri
+ a.\link ArrayBase::ndtri ndtri\endlink(); \n
+ \link Eigen::ndtri ndtri\endlink(a);
+ </td>
+ <td>Inverse of the CDF of the Normal distribution function</td>
+ <td>
+ built-in for float and double
+ </td>
+ <td></td>
+</tr>
+<tr><td colspan="4"></td></tr>
+</table>
+
+\n
+
+*/
+
+}
diff --git a/doc/CustomizingEigen_CustomScalar.dox b/doc/CustomizingEigen_CustomScalar.dox
new file mode 100644
index 0000000..24e5f56
--- /dev/null
+++ b/doc/CustomizingEigen_CustomScalar.dox
@@ -0,0 +1,120 @@
+namespace Eigen {
+
+/** \page TopicCustomizing_CustomScalar Using custom scalar types
+\anchor user_defined_scalars
+
+By default, Eigen currently supports standard floating-point types (\c float, \c double, \c std::complex<float>, \c std::complex<double>, \c long \c double), as well as all native integer types (e.g., \c int, \c unsigned \c int, \c short, etc.), and \c bool.
+On x86-64 systems, \c long \c double permits to locally enforces the use of x87 registers with extended accuracy (in comparison to SSE).
+
+In order to add support for a custom type \c T you need:
+-# make sure the common operator (+,-,*,/,etc.) are supported by the type \c T
+-# add a specialization of struct Eigen::NumTraits<T> (see \ref NumTraits)
+-# define the math functions that makes sense for your type. This includes standard ones like sqrt, pow, sin, tan, conj, real, imag, etc, as well as abs2 which is Eigen specific.
+ (see the file Eigen/src/Core/MathFunctions.h)
+
+The math function should be defined in the same namespace than \c T, or in the \c std namespace though that second approach is not recommended.
+
+Here is a concrete example adding support for the Adolc's \c adouble type. <a href="https://projects.coin-or.org/ADOL-C">Adolc</a> is an automatic differentiation library. The type \c adouble is basically a real value tracking the values of any number of partial derivatives.
+
+\code
+#ifndef ADOLCSUPPORT_H
+#define ADOLCSUPPORT_H
+
+#define ADOLC_TAPELESS
+#include <adolc/adouble.h>
+#include <Eigen/Core>
+
+namespace Eigen {
+
+template<> struct NumTraits<adtl::adouble>
+ : NumTraits<double> // permits to get the epsilon, dummy_precision, lowest, highest functions
+{
+ typedef adtl::adouble Real;
+ typedef adtl::adouble NonInteger;
+ typedef adtl::adouble Nested;
+
+ enum {
+ IsComplex = 0,
+ IsInteger = 0,
+ IsSigned = 1,
+ RequireInitialization = 1,
+ ReadCost = 1,
+ AddCost = 3,
+ MulCost = 3
+ };
+};
+
+}
+
+namespace adtl {
+
+inline const adouble& conj(const adouble& x) { return x; }
+inline const adouble& real(const adouble& x) { return x; }
+inline adouble imag(const adouble&) { return 0.; }
+inline adouble abs(const adouble& x) { return fabs(x); }
+inline adouble abs2(const adouble& x) { return x*x; }
+
+}
+
+#endif // ADOLCSUPPORT_H
+\endcode
+
+This other example adds support for the \c mpq_class type from <a href="https://gmplib.org/">GMP</a>. It shows in particular how to change the way Eigen picks the best pivot during LU factorization. It selects the coefficient with the highest score, where the score is by default the absolute value of a number, but we can define a different score, for instance to prefer pivots with a more compact representation (this is an example, not a recommendation). Note that the scores should always be non-negative and only zero is allowed to have a score of zero. Also, this can interact badly with thresholds for inexact scalar types.
+
+\code
+#include <gmpxx.h>
+#include <Eigen/Core>
+#include <boost/operators.hpp>
+
+namespace Eigen {
+ template<> struct NumTraits<mpq_class> : GenericNumTraits<mpq_class>
+ {
+ typedef mpq_class Real;
+ typedef mpq_class NonInteger;
+ typedef mpq_class Nested;
+
+ static inline Real epsilon() { return 0; }
+ static inline Real dummy_precision() { return 0; }
+ static inline int digits10() { return 0; }
+
+ enum {
+ IsInteger = 0,
+ IsSigned = 1,
+ IsComplex = 0,
+ RequireInitialization = 1,
+ ReadCost = 6,
+ AddCost = 150,
+ MulCost = 100
+ };
+ };
+
+ namespace internal {
+
+ template<> struct scalar_score_coeff_op<mpq_class> {
+ struct result_type : boost::totally_ordered1<result_type> {
+ std::size_t len;
+ result_type(int i = 0) : len(i) {} // Eigen uses Score(0) and Score()
+ result_type(mpq_class const& q) :
+ len(mpz_size(q.get_num_mpz_t())+
+ mpz_size(q.get_den_mpz_t())-1) {}
+ friend bool operator<(result_type x, result_type y) {
+ // 0 is the worst possible pivot
+ if (x.len == 0) return y.len > 0;
+ if (y.len == 0) return false;
+ // Prefer a pivot with a small representation
+ return x.len > y.len;
+ }
+ friend bool operator==(result_type x, result_type y) {
+ // Only used to test if the score is 0
+ return x.len == y.len;
+ }
+ };
+ result_type operator()(mpq_class const& x) const { return x; }
+ };
+ }
+}
+\endcode
+
+*/
+
+}
diff --git a/doc/CustomizingEigen_InheritingMatrix.dox b/doc/CustomizingEigen_InheritingMatrix.dox
new file mode 100644
index 0000000..b21e554
--- /dev/null
+++ b/doc/CustomizingEigen_InheritingMatrix.dox
@@ -0,0 +1,34 @@
+namespace Eigen {
+
+/** \page TopicCustomizing_InheritingMatrix Inheriting from Matrix
+
+Before inheriting from Matrix, be really, I mean REALLY, sure that using
+EIGEN_MATRIX_PLUGIN is not what you really want (see previous section).
+If you just need to add few members to Matrix, this is the way to go.
+
+An example of when you actually need to inherit Matrix, is when you
+have several layers of heritage such as
+MyVerySpecificVector1, MyVerySpecificVector2 -> MyVector1 -> Matrix and
+MyVerySpecificVector3, MyVerySpecificVector4 -> MyVector2 -> Matrix.
+
+In order for your object to work within the %Eigen framework, you need to
+define a few members in your inherited class.
+
+Here is a minimalistic example:
+
+\include CustomizingEigen_Inheritance.cpp
+
+Output: \verbinclude CustomizingEigen_Inheritance.out
+
+This is the kind of error you can get if you don't provide those methods
+\verbatim
+error: no match for ‘operator=’ in ‘v = Eigen::operator*(
+const Eigen::MatrixBase<Eigen::Matrix<double, -0x000000001, 1, 0, -0x000000001, 1> >::Scalar&,
+const Eigen::MatrixBase<Eigen::Matrix<double, -0x000000001, 1> >::StorageBaseType&)
+(((const Eigen::MatrixBase<Eigen::Matrix<double, -0x000000001, 1> >::StorageBaseType&)
+((const Eigen::MatrixBase<Eigen::Matrix<double, -0x000000001, 1> >::StorageBaseType*)(& v))))’
+\endverbatim
+
+*/
+
+}
diff --git a/doc/CustomizingEigen_NullaryExpr.dox b/doc/CustomizingEigen_NullaryExpr.dox
new file mode 100644
index 0000000..37c8dcd
--- /dev/null
+++ b/doc/CustomizingEigen_NullaryExpr.dox
@@ -0,0 +1,86 @@
+namespace Eigen {
+
+/** \page TopicCustomizing_NullaryExpr Matrix manipulation via nullary-expressions
+
+
+The main purpose of the class CwiseNullaryOp is to define \em procedural matrices such as constant or random matrices as returned by the Ones(), Zero(), Constant(), Identity() and Random() methods.
+Nevertheless, with some imagination it is possible to accomplish very sophisticated matrix manipulation with minimal efforts such that \ref TopicNewExpressionType "implementing new expression" is rarely needed.
+
+\section NullaryExpr_Circulant Example 1: circulant matrix
+
+To explore these possibilities let us start with the \em circulant example of the \ref TopicNewExpressionType "implementing new expression" topic.
+Let us recall that a circulant matrix is a matrix where each column is the same as the
+column to the left, except that it is cyclically shifted downwards.
+For example, here is a 4-by-4 circulant matrix:
+\f[ \begin{bmatrix}
+ 1 & 8 & 4 & 2 \\
+ 2 & 1 & 8 & 4 \\
+ 4 & 2 & 1 & 8 \\
+ 8 & 4 & 2 & 1
+\end{bmatrix} \f]
+A circulant matrix is uniquely determined by its first column. We wish
+to write a function \c makeCirculant which, given the first column,
+returns an expression representing the circulant matrix.
+
+For this exercise, the return type of \c makeCirculant will be a CwiseNullaryOp that we need to instantiate with:
+1 - a proper \c circulant_functor storing the input vector and implementing the adequate coefficient accessor \c operator(i,j)
+2 - a template instantiation of class Matrix conveying compile-time information such as the scalar type, sizes, and preferred storage layout.
+
+Calling \c ArgType the type of the input vector, we can construct the equivalent squared Matrix type as follows:
+
+\snippet make_circulant2.cpp square
+
+This little helper structure will help us to implement our \c makeCirculant function as follows:
+
+\snippet make_circulant2.cpp makeCirculant
+
+As usual, our function takes as argument a \c MatrixBase (see this \ref TopicFunctionTakingEigenTypes "page" for more details).
+Then, the CwiseNullaryOp object is constructed through the DenseBase::NullaryExpr static method with the adequate runtime sizes.
+
+Then, we need to implement our \c circulant_functor, which is a straightforward exercise:
+
+\snippet make_circulant2.cpp circulant_func
+
+We are now all set to try our new feature:
+
+\snippet make_circulant2.cpp main
+
+
+If all the fragments are combined, the following output is produced,
+showing that the program works as expected:
+
+\include make_circulant2.out
+
+This implementation of \c makeCirculant is much simpler than \ref TopicNewExpressionType "defining a new expression" from scratch.
+
+
+\section NullaryExpr_Indexing Example 2: indexing rows and columns
+
+The goal here is to mimic MatLab's ability to index a matrix through two vectors of indices referencing the rows and columns to be picked respectively, like this:
+
+\snippet nullary_indexing.out main1
+
+To this end, let us first write a nullary-functor storing references to the input matrix and to the two arrays of indices, and implementing the required \c operator()(i,j):
+
+\snippet nullary_indexing.cpp functor
+
+Then, let's create an \c indexing(A,rows,cols) function creating the nullary expression:
+
+\snippet nullary_indexing.cpp function
+
+Finally, here is an example of how this function can be used:
+
+\snippet nullary_indexing.cpp main1
+
+This straightforward implementation is already quite powerful as the row or column index arrays can also be expressions to perform offsetting, modulo, striding, reverse, etc.
+
+\snippet nullary_indexing.cpp main2
+
+and the output is:
+
+\snippet nullary_indexing.out main2
+
+*/
+
+}
+
diff --git a/doc/CustomizingEigen_Plugins.dox b/doc/CustomizingEigen_Plugins.dox
new file mode 100644
index 0000000..d88f240
--- /dev/null
+++ b/doc/CustomizingEigen_Plugins.dox
@@ -0,0 +1,69 @@
+namespace Eigen {
+
+/** \page TopicCustomizing_Plugins Extending MatrixBase (and other classes)
+
+In this section we will see how to add custom methods to MatrixBase. Since all expressions and matrix types inherit MatrixBase, adding a method to MatrixBase make it immediately available to all expressions ! A typical use case is, for instance, to make Eigen compatible with another API.
+
+You certainly know that in C++ it is not possible to add methods to an existing class. So how that's possible ? Here the trick is to include in the declaration of MatrixBase a file defined by the preprocessor token \c EIGEN_MATRIXBASE_PLUGIN:
+\code
+class MatrixBase {
+ // ...
+ #ifdef EIGEN_MATRIXBASE_PLUGIN
+ #include EIGEN_MATRIXBASE_PLUGIN
+ #endif
+};
+\endcode
+Therefore to extend MatrixBase with your own methods you just have to create a file with your method declaration and define EIGEN_MATRIXBASE_PLUGIN before you include any Eigen's header file.
+
+You can extend many of the other classes used in Eigen by defining similarly named preprocessor symbols. For instance, define \c EIGEN_ARRAYBASE_PLUGIN if you want to extend the ArrayBase class. A full list of classes that can be extended in this way and the corresponding preprocessor symbols can be found on our page \ref TopicPreprocessorDirectives.
+
+Here is an example of an extension file for adding methods to MatrixBase: \n
+\b MatrixBaseAddons.h
+\code
+inline Scalar at(uint i, uint j) const { return this->operator()(i,j); }
+inline Scalar& at(uint i, uint j) { return this->operator()(i,j); }
+inline Scalar at(uint i) const { return this->operator[](i); }
+inline Scalar& at(uint i) { return this->operator[](i); }
+
+inline RealScalar squaredLength() const { return squaredNorm(); }
+inline RealScalar length() const { return norm(); }
+inline RealScalar invLength(void) const { return fast_inv_sqrt(squaredNorm()); }
+
+template<typename OtherDerived>
+inline Scalar squaredDistanceTo(const MatrixBase<OtherDerived>& other) const
+{ return (derived() - other.derived()).squaredNorm(); }
+
+template<typename OtherDerived>
+inline RealScalar distanceTo(const MatrixBase<OtherDerived>& other) const
+{ return internal::sqrt(derived().squaredDistanceTo(other)); }
+
+inline void scaleTo(RealScalar l) { RealScalar vl = norm(); if (vl>1e-9) derived() *= (l/vl); }
+
+inline Transpose<Derived> transposed() {return this->transpose();}
+inline const Transpose<Derived> transposed() const {return this->transpose();}
+
+inline uint minComponentId(void) const { int i; this->minCoeff(&i); return i; }
+inline uint maxComponentId(void) const { int i; this->maxCoeff(&i); return i; }
+
+template<typename OtherDerived>
+void makeFloor(const MatrixBase<OtherDerived>& other) { derived() = derived().cwiseMin(other.derived()); }
+template<typename OtherDerived>
+void makeCeil(const MatrixBase<OtherDerived>& other) { derived() = derived().cwiseMax(other.derived()); }
+
+const CwiseBinaryOp<internal::scalar_sum_op<Scalar>, const Derived, const ConstantReturnType>
+operator+(const Scalar& scalar) const
+{ return CwiseBinaryOp<internal::scalar_sum_op<Scalar>, const Derived, const ConstantReturnType>(derived(), Constant(rows(),cols(),scalar)); }
+
+friend const CwiseBinaryOp<internal::scalar_sum_op<Scalar>, const ConstantReturnType, Derived>
+operator+(const Scalar& scalar, const MatrixBase<Derived>& mat)
+{ return CwiseBinaryOp<internal::scalar_sum_op<Scalar>, const ConstantReturnType, Derived>(Constant(rows(),cols(),scalar), mat.derived()); }
+\endcode
+
+Then one can the following declaration in the config.h or whatever prerequisites header file of his project:
+\code
+#define EIGEN_MATRIXBASE_PLUGIN "MatrixBaseAddons.h"
+\endcode
+
+*/
+
+}
diff --git a/doc/DenseDecompositionBenchmark.dox b/doc/DenseDecompositionBenchmark.dox
new file mode 100644
index 0000000..8f9570b
--- /dev/null
+++ b/doc/DenseDecompositionBenchmark.dox
@@ -0,0 +1,42 @@
+namespace Eigen {
+
+/** \eigenManualPage DenseDecompositionBenchmark Benchmark of dense decompositions
+
+This page presents a speed comparison of the dense matrix decompositions offered by %Eigen for a wide range of square matrices and overconstrained problems.
+
+For a more general overview on the features and numerical robustness of linear solvers and decompositions, check this \link TopicLinearAlgebraDecompositions table \endlink.
+
+This benchmark has been run on a laptop equipped with an Intel core i7 \@ 2,6 GHz, and compiled with clang with \b AVX and \b FMA instruction sets enabled but without multi-threading.
+It uses \b single \b precision \b float numbers. For double, you can get a good estimate by multiplying the timings by a factor 2.
+
+The square matrices are symmetric, and for the overconstrained matrices, the reported timmings include the cost to compute the symmetric covariance matrix \f$ A^T A \f$ for the first four solvers based on Cholesky and LU, as denoted by the \b * symbol (top-right corner part of the table).
+Timings are in \b milliseconds, and factors are relative to the LLT decomposition which is the fastest but also the least general and robust.
+
+<table class="manual">
+<tr><th>solver/size</th>
+ <th>8x8</th> <th>100x100</th> <th>1000x1000</th> <th>4000x4000</th> <th>10000x8</th> <th>10000x100</th> <th>10000x1000</th> <th>10000x4000</th></tr>
+<tr><td>LLT</td><td>0.05</td><td>0.42</td><td>5.83</td><td>374.55</td><td>6.79 <sup><a href="#note_ls">*</a></sup></td><td>30.15 <sup><a href="#note_ls">*</a></sup></td><td>236.34 <sup><a href="#note_ls">*</a></sup></td><td>3847.17 <sup><a href="#note_ls">*</a></sup></td></tr>
+<tr class="alt"><td>LDLT</td><td>0.07 (x1.3)</td><td>0.65 (x1.5)</td><td>26.86 (x4.6)</td><td>2361.18 (x6.3)</td><td>6.81 (x1) <sup><a href="#note_ls">*</a></sup></td><td>31.91 (x1.1) <sup><a href="#note_ls">*</a></sup></td><td>252.61 (x1.1) <sup><a href="#note_ls">*</a></sup></td><td>5807.66 (x1.5) <sup><a href="#note_ls">*</a></sup></td></tr>
+<tr><td>PartialPivLU</td><td>0.08 (x1.5)</td><td>0.69 (x1.6)</td><td>15.63 (x2.7)</td><td>709.32 (x1.9)</td><td>6.81 (x1) <sup><a href="#note_ls">*</a></sup></td><td>31.32 (x1) <sup><a href="#note_ls">*</a></sup></td><td>241.68 (x1) <sup><a href="#note_ls">*</a></sup></td><td>4270.48 (x1.1) <sup><a href="#note_ls">*</a></sup></td></tr>
+<tr class="alt"><td>FullPivLU</td><td>0.1 (x1.9)</td><td>4.48 (x10.6)</td><td>281.33 (x48.2)</td><td>-</td><td>6.83 (x1) <sup><a href="#note_ls">*</a></sup></td><td>32.67 (x1.1) <sup><a href="#note_ls">*</a></sup></td><td>498.25 (x2.1) <sup><a href="#note_ls">*</a></sup></td><td>-</td></tr>
+<tr><td>HouseholderQR</td><td>0.19 (x3.5)</td><td>2.18 (x5.2)</td><td>23.42 (x4)</td><td>1337.52 (x3.6)</td><td>34.26 (x5)</td><td>129.01 (x4.3)</td><td>377.37 (x1.6)</td><td>4839.1 (x1.3)</td></tr>
+<tr class="alt"><td>ColPivHouseholderQR</td><td>0.23 (x4.3)</td><td>2.23 (x5.3)</td><td>103.34 (x17.7)</td><td>9987.16 (x26.7)</td><td>36.05 (x5.3)</td><td>163.18 (x5.4)</td><td>2354.08 (x10)</td><td>37860.5 (x9.8)</td></tr>
+<tr><td>CompleteOrthogonalDecomposition</td><td>0.23 (x4.3)</td><td>2.22 (x5.2)</td><td>99.44 (x17.1)</td><td>10555.3 (x28.2)</td><td>35.75 (x5.3)</td><td>169.39 (x5.6)</td><td>2150.56 (x9.1)</td><td>36981.8 (x9.6)</td></tr>
+<tr class="alt"><td>FullPivHouseholderQR</td><td>0.23 (x4.3)</td><td>4.64 (x11)</td><td>289.1 (x49.6)</td><td>-</td><td>69.38 (x10.2)</td><td>446.73 (x14.8)</td><td>4852.12 (x20.5)</td><td>-</td></tr>
+<tr><td>JacobiSVD</td><td>1.01 (x18.6)</td><td>71.43 (x168.4)</td><td>-</td><td>-</td><td>113.81 (x16.7)</td><td>1179.66 (x39.1)</td><td>-</td><td>-</td></tr>
+<tr class="alt"><td>BDCSVD</td><td>1.07 (x19.7)</td><td>21.83 (x51.5)</td><td>331.77 (x56.9)</td><td>18587.9 (x49.6)</td><td>110.53 (x16.3)</td><td>397.67 (x13.2)</td><td>2975 (x12.6)</td><td>48593.2 (x12.6)</td></tr>
+</table>
+
+<a name="note_ls">\b *: </a> This decomposition do not support direct least-square solving for over-constrained problems, and the reported timing include the cost to form the symmetric covariance matrix \f$ A^T A \f$.
+
+\b Observations:
+ + LLT is always the fastest solvers.
+ + For largely over-constrained problems, the cost of Cholesky/LU decompositions is dominated by the computation of the symmetric covariance matrix.
+ + For large problem sizes, only the decomposition implementing a cache-friendly blocking strategy scale well. Those include LLT, PartialPivLU, HouseholderQR, and BDCSVD. This explain why for a 4k x 4k matrix, HouseholderQR is faster than LDLT. In the future, LDLT and ColPivHouseholderQR will also implement blocking strategies.
+ + CompleteOrthogonalDecomposition is based on ColPivHouseholderQR and they thus achieve the same level of performance.
+
+The above table has been generated by the <a href="https://gitlab.com/libeigen/eigen/raw/master/bench/dense_solvers.cpp">bench/dense_solvers.cpp</a> file, feel-free to hack it to generate a table matching your hardware, compiler, and favorite problem sizes.
+
+*/
+
+}
diff --git a/doc/Doxyfile.in b/doc/Doxyfile.in
new file mode 100644
index 0000000..d0e96fa
--- /dev/null
+++ b/doc/Doxyfile.in
@@ -0,0 +1,1913 @@
+# Doxyfile 1.8.1.1
+
+# This file describes the settings to be used by the documentation system
+# doxygen (www.doxygen.org) for a project.
+#
+# All text after a hash (#) is considered a comment and will be ignored.
+# The format is:
+# TAG = value [value, ...]
+# For lists items can also be appended using:
+# TAG += value [value, ...]
+# Values that contain spaces should be placed between quotes (" ").
+
+#---------------------------------------------------------------------------
+# Project related configuration options
+#---------------------------------------------------------------------------
+
+# This tag specifies the encoding used for all characters in the config file
+# that follow. The default is UTF-8 which is also the encoding used for all
+# text before the first occurrence of this tag. Doxygen uses libiconv (or the
+# iconv built into libc) for the transcoding. See
+# http://www.gnu.org/software/libiconv for the list of possible encodings.
+
+DOXYFILE_ENCODING = UTF-8
+
+# The PROJECT_NAME tag is a single word (or sequence of words) that should
+# identify the project. Note that if you do not use Doxywizard you need
+# to put quotes around the project name if it contains spaces.
+
+PROJECT_NAME = ${EIGEN_DOXY_PROJECT_NAME}
+
+# The PROJECT_NUMBER tag can be used to enter a project or revision number.
+# This could be handy for archiving the generated documentation or
+# if some version control system is used.
+
+# EIGEN_VERSION is set in the root CMakeLists.txt
+
+PROJECT_NUMBER = "${EIGEN_VERSION}"
+
+# Using the PROJECT_BRIEF tag one can provide an optional one line description
+# for a project that appears at the top of each page and should give viewer
+# a quick idea about the purpose of the project. Keep the description short.
+
+PROJECT_BRIEF =
+
+# With the PROJECT_LOGO tag one can specify an logo or icon that is
+# included in the documentation. The maximum height of the logo should not
+# exceed 55 pixels and the maximum width should not exceed 200 pixels.
+# Doxygen will copy the logo to the output directory.
+
+PROJECT_LOGO = "${Eigen_SOURCE_DIR}/doc/Eigen_Silly_Professor_64x64.png"
+
+# The OUTPUT_DIRECTORY tag is used to specify the (relative or absolute)
+# base path where the generated documentation will be put.
+# If a relative path is entered, it will be relative to the location
+# where doxygen was started. If left blank the current directory will be used.
+
+OUTPUT_DIRECTORY = "${Eigen_BINARY_DIR}/doc${EIGEN_DOXY_OUTPUT_DIRECTORY_SUFFIX}"
+
+# If the CREATE_SUBDIRS tag is set to YES, then doxygen will create
+# 4096 sub-directories (in 2 levels) under the output directory of each output
+# format and will distribute the generated files over these directories.
+# Enabling this option can be useful when feeding doxygen a huge amount of
+# source files, where putting all generated files in the same directory would
+# otherwise cause performance problems for the file system.
+
+CREATE_SUBDIRS = NO
+
+# The OUTPUT_LANGUAGE tag is used to specify the language in which all
+# documentation generated by doxygen is written. Doxygen will use this
+# information to generate all constant output in the proper language.
+# The default language is English, other supported languages are:
+# Afrikaans, Arabic, Brazilian, Catalan, Chinese, Chinese-Traditional,
+# Croatian, Czech, Danish, Dutch, Esperanto, Farsi, Finnish, French, German,
+# Greek, Hungarian, Italian, Japanese, Japanese-en (Japanese with English
+# messages), Korean, Korean-en, Lithuanian, Norwegian, Macedonian, Persian,
+# Polish, Portuguese, Romanian, Russian, Serbian, Serbian-Cyrillic, Slovak,
+# Slovene, Spanish, Swedish, Ukrainian, and Vietnamese.
+
+OUTPUT_LANGUAGE = English
+
+# If the BRIEF_MEMBER_DESC tag is set to YES (the default) Doxygen will
+# include brief member descriptions after the members that are listed in
+# the file and class documentation (similar to JavaDoc).
+# Set to NO to disable this.
+
+BRIEF_MEMBER_DESC = YES
+
+# If the REPEAT_BRIEF tag is set to YES (the default) Doxygen will prepend
+# the brief description of a member or function before the detailed description.
+# Note: if both HIDE_UNDOC_MEMBERS and BRIEF_MEMBER_DESC are set to NO, the
+# brief descriptions will be completely suppressed.
+
+REPEAT_BRIEF = YES
+
+# This tag implements a quasi-intelligent brief description abbreviator
+# that is used to form the text in various listings. Each string
+# in this list, if found as the leading text of the brief description, will be
+# stripped from the text and the result after processing the whole list, is
+# used as the annotated text. Otherwise, the brief description is used as-is.
+# If left blank, the following values are used ("$name" is automatically
+# replaced with the name of the entity): "The $name class" "The $name widget"
+# "The $name file" "is" "provides" "specifies" "contains"
+# "represents" "a" "an" "the"
+
+ABBREVIATE_BRIEF = "The $name class" \
+ "The $name widget" \
+ "The $name file" \
+ is \
+ provides \
+ specifies \
+ contains \
+ represents \
+ a \
+ an \
+ the
+
+# If the ALWAYS_DETAILED_SEC and REPEAT_BRIEF tags are both set to YES then
+# Doxygen will generate a detailed section even if there is only a brief
+# description.
+
+ALWAYS_DETAILED_SEC = NO
+
+# If the INLINE_INHERITED_MEMB tag is set to YES, doxygen will show all
+# inherited members of a class in the documentation of that class as if those
+# members were ordinary class members. Constructors, destructors and assignment
+# operators of the base classes will not be shown.
+
+INLINE_INHERITED_MEMB = NO
+
+# If the FULL_PATH_NAMES tag is set to YES then Doxygen will prepend the full
+# path before files name in the file list and in the header files. If set
+# to NO the shortest path that makes the file name unique will be used.
+
+FULL_PATH_NAMES = NO
+
+# If the FULL_PATH_NAMES tag is set to YES then the STRIP_FROM_PATH tag
+# can be used to strip a user-defined part of the path. Stripping is
+# only done if one of the specified strings matches the left-hand part of
+# the path. The tag can be used to show relative paths in the file list.
+# If left blank the directory from which doxygen is run is used as the
+# path to strip.
+
+STRIP_FROM_PATH =
+
+# The STRIP_FROM_INC_PATH tag can be used to strip a user-defined part of
+# the path mentioned in the documentation of a class, which tells
+# the reader which header file to include in order to use a class.
+# If left blank only the name of the header file containing the class
+# definition is used. Otherwise one should specify the include paths that
+# are normally passed to the compiler using the -I flag.
+
+STRIP_FROM_INC_PATH =
+
+# If the SHORT_NAMES tag is set to YES, doxygen will generate much shorter
+# (but less readable) file names. This can be useful if your file system
+# doesn't support long names like on DOS, Mac, or CD-ROM.
+
+SHORT_NAMES = NO
+
+# If the JAVADOC_AUTOBRIEF tag is set to YES then Doxygen
+# will interpret the first line (until the first dot) of a JavaDoc-style
+# comment as the brief description. If set to NO, the JavaDoc
+# comments will behave just like regular Qt-style comments
+# (thus requiring an explicit @brief command for a brief description.)
+
+JAVADOC_AUTOBRIEF = NO
+
+# If the QT_AUTOBRIEF tag is set to YES then Doxygen will
+# interpret the first line (until the first dot) of a Qt-style
+# comment as the brief description. If set to NO, the comments
+# will behave just like regular Qt-style comments (thus requiring
+# an explicit \brief command for a brief description.)
+
+QT_AUTOBRIEF = NO
+
+# The MULTILINE_CPP_IS_BRIEF tag can be set to YES to make Doxygen
+# treat a multi-line C++ special comment block (i.e. a block of //! or ///
+# comments) as a brief description. This used to be the default behaviour.
+# The new default is to treat a multi-line C++ comment block as a detailed
+# description. Set this tag to YES if you prefer the old behaviour instead.
+
+MULTILINE_CPP_IS_BRIEF = NO
+
+# If the INHERIT_DOCS tag is set to YES (the default) then an undocumented
+# member inherits the documentation from any documented member that it
+# re-implements.
+
+INHERIT_DOCS = YES
+
+# If the SEPARATE_MEMBER_PAGES tag is set to YES, then doxygen will produce
+# a new page for each member. If set to NO, the documentation of a member will
+# be part of the file/class/namespace that contains it.
+
+SEPARATE_MEMBER_PAGES = NO
+
+# The TAB_SIZE tag can be used to set the number of spaces in a tab.
+# Doxygen uses this value to replace tabs by spaces in code fragments.
+
+TAB_SIZE = 8
+
+# This tag can be used to specify a number of aliases that acts
+# as commands in the documentation. An alias has the form "name=value".
+# For example adding "sideeffect=\par Side Effects:\n" will allow you to
+# put the command \sideeffect (or @sideeffect) in the documentation, which
+# will result in a user-defined paragraph with heading "Side Effects:".
+# You can put \n's in the value part of an alias to insert newlines.
+
+ALIASES = "only_for_vectors=This is only for vectors (either row-vectors or column-vectors), i.e. matrices which are known at compile-time to have either one row or one column." \
+ "not_reentrant=\warning This function is not re-entrant." \
+ "array_module=This is defined in the %Array module. \code #include <Eigen/Array> \endcode" \
+ "cholesky_module=This is defined in the %Cholesky module. \code #include <Eigen/Cholesky> \endcode" \
+ "eigenvalues_module=This is defined in the %Eigenvalues module. \code #include <Eigen/Eigenvalues> \endcode" \
+ "geometry_module=This is defined in the %Geometry module. \code #include <Eigen/Geometry> \endcode" \
+ "householder_module=This is defined in the %Householder module. \code #include <Eigen/Householder> \endcode" \
+ "jacobi_module=This is defined in the %Jacobi module. \code #include <Eigen/Jacobi> \endcode" \
+ "lu_module=This is defined in the %LU module. \code #include <Eigen/LU> \endcode" \
+ "qr_module=This is defined in the %QR module. \code #include <Eigen/QR> \endcode" \
+ "svd_module=This is defined in the %SVD module. \code #include <Eigen/SVD> \endcode" \
+ "specialfunctions_module=This is defined in the \b unsupported SpecialFunctions module. \code #include <Eigen/SpecialFunctions> \endcode" \
+ "label=\bug" \
+ "matrixworld=<a href='#matrixonly' style='color:green;text-decoration: none;'>*</a>" \
+ "arrayworld=<a href='#arrayonly' style='color:blue;text-decoration: none;'>*</a>" \
+ "note_about_arbitrary_choice_of_solution=If there exists more than one solution, this method will arbitrarily choose one." \
+ "note_about_using_kernel_to_study_multiple_solutions=If you need a complete analysis of the space of solutions, take the one solution obtained by this method and add to it elements of the kernel, as determined by kernel()." \
+ "note_about_checking_solutions=This method just tries to find as good a solution as possible. If you want to check whether a solution exists or if it is accurate, just call this function to get a result and then compute the error of this result, or use MatrixBase::isApprox() directly, for instance like this: \code bool a_solution_exists = (A*result).isApprox(b, precision); \endcode This method avoids dividing by zero, so that the non-existence of a solution doesn't by itself mean that you'll get \c inf or \c nan values." \
+ "note_try_to_help_rvo=This function returns the result by value. In order to make that efficient, it is implemented as just a return statement using a special constructor, hopefully allowing the compiler to perform a RVO (return value optimization)." \
+ "nonstableyet=\warning This is not considered to be part of the stable public API yet. Changes may happen in future releases. See \ref Experimental \"Experimental parts of Eigen\"" \
+ "implsparsesolverconcept=This class follows the \link TutorialSparseSolverConcept sparse solver concept \endlink." \
+ "blank= " \
+ "cpp11=<span class='cpp11'>[c++11]</span>" \
+ "cpp14=<span class='cpp14'>[c++14]</span>" \
+ "cpp17=<span class='cpp17'>[c++17]</span>" \
+ "newin{1}=<span class='newin3x'>New in %Eigen \1.</span>"
+
+
+ALIASES += "eigenAutoToc= "
+ALIASES += "eigenManualPage=\defgroup"
+
+# This tag can be used to specify a number of word-keyword mappings (TCL only).
+# A mapping has the form "name=value". For example adding
+# "class=itcl::class" will allow you to use the command class in the
+# itcl::class meaning.
+
+TCL_SUBST =
+
+# Set the OPTIMIZE_OUTPUT_FOR_C tag to YES if your project consists of C
+# sources only. Doxygen will then generate output that is more tailored for C.
+# For instance, some of the names that are used will be different. The list
+# of all members will be omitted, etc.
+
+OPTIMIZE_OUTPUT_FOR_C = NO
+
+# Set the OPTIMIZE_OUTPUT_JAVA tag to YES if your project consists of Java
+# sources only. Doxygen will then generate output that is more tailored for
+# Java. For instance, namespaces will be presented as packages, qualified
+# scopes will look different, etc.
+
+OPTIMIZE_OUTPUT_JAVA = NO
+
+# Set the OPTIMIZE_FOR_FORTRAN tag to YES if your project consists of Fortran
+# sources only. Doxygen will then generate output that is more tailored for
+# Fortran.
+
+OPTIMIZE_FOR_FORTRAN = NO
+
+# Set the OPTIMIZE_OUTPUT_VHDL tag to YES if your project consists of VHDL
+# sources. Doxygen will then generate output that is tailored for
+# VHDL.
+
+OPTIMIZE_OUTPUT_VHDL = NO
+
+# Doxygen selects the parser to use depending on the extension of the files it
+# parses. With this tag you can assign which parser to use for a given extension.
+# Doxygen has a built-in mapping, but you can override or extend it using this
+# tag. The format is ext=language, where ext is a file extension, and language
+# is one of the parsers supported by doxygen: IDL, Java, Javascript, CSharp, C,
+# C++, D, PHP, Objective-C, Python, Fortran, VHDL, C, C++. For instance to make
+# doxygen treat .inc files as Fortran files (default is PHP), and .f files as C
+# (default is Fortran), use: inc=Fortran f=C. Note that for custom extensions
+# you also need to set FILE_PATTERNS otherwise the files are not read by doxygen.
+
+EXTENSION_MAPPING = .h=C++ no_extension=C++
+
+# If MARKDOWN_SUPPORT is enabled (the default) then doxygen pre-processes all
+# comments according to the Markdown format, which allows for more readable
+# documentation. See http://daringfireball.net/projects/markdown/ for details.
+# The output of markdown processing is further processed by doxygen, so you
+# can mix doxygen, HTML, and XML commands with Markdown formatting.
+# Disable only in case of backward compatibilities issues.
+
+MARKDOWN_SUPPORT = YES
+
+# If you use STL classes (i.e. std::string, std::vector, etc.) but do not want
+# to include (a tag file for) the STL sources as input, then you should
+# set this tag to YES in order to let doxygen match functions declarations and
+# definitions whose arguments contain STL classes (e.g. func(std::string); v.s.
+# func(std::string) {}). This also makes the inheritance and collaboration
+# diagrams that involve STL classes more complete and accurate.
+
+BUILTIN_STL_SUPPORT = NO
+
+# If you use Microsoft's C++/CLI language, you should set this option to YES to
+# enable parsing support.
+
+CPP_CLI_SUPPORT = NO
+
+# Set the SIP_SUPPORT tag to YES if your project consists of sip sources only.
+# Doxygen will parse them like normal C++ but will assume all classes use public
+# instead of private inheritance when no explicit protection keyword is present.
+
+SIP_SUPPORT = NO
+
+# For Microsoft's IDL there are propget and propput attributes to indicate getter
+# and setter methods for a property. Setting this option to YES (the default)
+# will make doxygen replace the get and set methods by a property in the
+# documentation. This will only work if the methods are indeed getting or
+# setting a simple type. If this is not the case, or you want to show the
+# methods anyway, you should set this option to NO.
+
+IDL_PROPERTY_SUPPORT = YES
+
+# If member grouping is used in the documentation and the DISTRIBUTE_GROUP_DOC
+# tag is set to YES, then doxygen will reuse the documentation of the first
+# member in the group (if any) for the other members of the group. By default
+# all members of a group must be documented explicitly.
+
+DISTRIBUTE_GROUP_DOC = YES
+
+# Set the SUBGROUPING tag to YES (the default) to allow class member groups of
+# the same type (for instance a group of public functions) to be put as a
+# subgroup of that type (e.g. under the Public Functions section). Set it to
+# NO to prevent subgrouping. Alternatively, this can be done per class using
+# the \nosubgrouping command.
+
+SUBGROUPING = YES
+
+# When the INLINE_GROUPED_CLASSES tag is set to YES, classes, structs and
+# unions are shown inside the group in which they are included (e.g. using
+# @ingroup) instead of on a separate page (for HTML and Man pages) or
+# section (for LaTeX and RTF).
+
+INLINE_GROUPED_CLASSES = NO
+
+# When the INLINE_SIMPLE_STRUCTS tag is set to YES, structs, classes, and
+# unions with only public data fields will be shown inline in the documentation
+# of the scope in which they are defined (i.e. file, namespace, or group
+# documentation), provided this scope is documented. If set to NO (the default),
+# structs, classes, and unions are shown on a separate page (for HTML and Man
+# pages) or section (for LaTeX and RTF).
+
+INLINE_SIMPLE_STRUCTS = NO
+
+# When TYPEDEF_HIDES_STRUCT is enabled, a typedef of a struct, union, or enum
+# is documented as struct, union, or enum with the name of the typedef. So
+# typedef struct TypeS {} TypeT, will appear in the documentation as a struct
+# with name TypeT. When disabled the typedef will appear as a member of a file,
+# namespace, or class. And the struct will be named TypeS. This can typically
+# be useful for C code in case the coding convention dictates that all compound
+# types are typedef'ed and only the typedef is referenced, never the tag name.
+
+TYPEDEF_HIDES_STRUCT = NO
+
+# The SYMBOL_CACHE_SIZE determines the size of the internal cache use to
+# determine which symbols to keep in memory and which to flush to disk.
+# When the cache is full, less often used symbols will be written to disk.
+# For small to medium size projects (<1000 input files) the default value is
+# probably good enough. For larger projects a too small cache size can cause
+# doxygen to be busy swapping symbols to and from disk most of the time
+# causing a significant performance penalty.
+# If the system has enough physical memory increasing the cache will improve the
+# performance by keeping more symbols in memory. Note that the value works on
+# a logarithmic scale so increasing the size by one will roughly double the
+# memory usage. The cache size is given by this formula:
+# 2^(16+SYMBOL_CACHE_SIZE). The valid range is 0..9, the default is 0,
+# corresponding to a cache size of 2^16 = 65536 symbols.
+
+# SYMBOL_CACHE_SIZE = 0
+
+# Similar to the SYMBOL_CACHE_SIZE the size of the symbol lookup cache can be
+# set using LOOKUP_CACHE_SIZE. This cache is used to resolve symbols given
+# their name and scope. Since this can be an expensive process and often the
+# same symbol appear multiple times in the code, doxygen keeps a cache of
+# pre-resolved symbols. If the cache is too small doxygen will become slower.
+# If the cache is too large, memory is wasted. The cache size is given by this
+# formula: 2^(16+LOOKUP_CACHE_SIZE). The valid range is 0..9, the default is 0,
+# corresponding to a cache size of 2^16 = 65536 symbols.
+
+LOOKUP_CACHE_SIZE = 0
+
+#---------------------------------------------------------------------------
+# Build related configuration options
+#---------------------------------------------------------------------------
+
+# If the EXTRACT_ALL tag is set to YES doxygen will assume all entities in
+# documentation are documented, even if no documentation was available.
+# Private class members and static file members will be hidden unless
+# the EXTRACT_PRIVATE and EXTRACT_STATIC tags are set to YES
+
+EXTRACT_ALL = NO
+
+# If the EXTRACT_PRIVATE tag is set to YES all private members of a class
+# will be included in the documentation.
+
+EXTRACT_PRIVATE = NO
+
+# If the EXTRACT_PACKAGE tag is set to YES all members with package or internal scope will be included in the documentation.
+
+EXTRACT_PACKAGE = NO
+
+# If the EXTRACT_STATIC tag is set to YES all static members of a file
+# will be included in the documentation.
+
+EXTRACT_STATIC = YES
+
+# If the EXTRACT_LOCAL_CLASSES tag is set to YES classes (and structs)
+# defined locally in source files will be included in the documentation.
+# If set to NO only classes defined in header files are included.
+
+EXTRACT_LOCAL_CLASSES = NO
+
+# This flag is only useful for Objective-C code. When set to YES local
+# methods, which are defined in the implementation section but not in
+# the interface are included in the documentation.
+# If set to NO (the default) only methods in the interface are included.
+
+EXTRACT_LOCAL_METHODS = NO
+
+# If this flag is set to YES, the members of anonymous namespaces will be
+# extracted and appear in the documentation as a namespace called
+# 'anonymous_namespace{file}', where file will be replaced with the base
+# name of the file that contains the anonymous namespace. By default
+# anonymous namespaces are hidden.
+
+EXTRACT_ANON_NSPACES = NO
+
+# If the HIDE_UNDOC_MEMBERS tag is set to YES, Doxygen will hide all
+# undocumented members of documented classes, files or namespaces.
+# If set to NO (the default) these members will be included in the
+# various overviews, but no documentation section is generated.
+# This option has no effect if EXTRACT_ALL is enabled.
+
+HIDE_UNDOC_MEMBERS = YES
+
+# If the HIDE_UNDOC_CLASSES tag is set to YES, Doxygen will hide all
+# undocumented classes that are normally visible in the class hierarchy.
+# If set to NO (the default) these classes will be included in the various
+# overviews. This option has no effect if EXTRACT_ALL is enabled.
+
+HIDE_UNDOC_CLASSES = YES
+
+# If the HIDE_FRIEND_COMPOUNDS tag is set to YES, Doxygen will hide all
+# friend (class|struct|union) declarations.
+# If set to NO (the default) these declarations will be included in the
+# documentation.
+
+HIDE_FRIEND_COMPOUNDS = YES
+
+# If the HIDE_IN_BODY_DOCS tag is set to YES, Doxygen will hide any
+# documentation blocks found inside the body of a function.
+# If set to NO (the default) these blocks will be appended to the
+# function's detailed documentation block.
+
+HIDE_IN_BODY_DOCS = NO
+
+# The INTERNAL_DOCS tag determines if documentation
+# that is typed after a \internal command is included. If the tag is set
+# to NO (the default) then the documentation will be excluded.
+# Set it to YES to include the internal documentation.
+
+INTERNAL_DOCS = ${EIGEN_DOXY_INTERNAL}
+
+# If the CASE_SENSE_NAMES tag is set to NO then Doxygen will only generate
+# file names in lower-case letters. If set to YES upper-case letters are also
+# allowed. This is useful if you have classes or files whose names only differ
+# in case and if your file system supports case sensitive file names. Windows
+# and Mac users are advised to set this option to NO.
+
+CASE_SENSE_NAMES = YES
+
+# If the HIDE_SCOPE_NAMES tag is set to NO (the default) then Doxygen
+# will show members with their full class and namespace scopes in the
+# documentation. If set to YES the scope will be hidden.
+
+HIDE_SCOPE_NAMES = NO
+
+# If the SHOW_INCLUDE_FILES tag is set to YES (the default) then Doxygen
+# will put a list of the files that are included by a file in the documentation
+# of that file.
+
+SHOW_INCLUDE_FILES = ${EIGEN_DOXY_INTERNAL}
+
+# If the FORCE_LOCAL_INCLUDES tag is set to YES then Doxygen
+# will list include files with double quotes in the documentation
+# rather than with sharp brackets.
+
+FORCE_LOCAL_INCLUDES = NO
+
+# If the INLINE_INFO tag is set to YES (the default) then a tag [inline]
+# is inserted in the documentation for inline members.
+
+INLINE_INFO = YES
+
+# If the SORT_MEMBER_DOCS tag is set to YES (the default) then doxygen
+# will sort the (detailed) documentation of file and class members
+# alphabetically by member name. If set to NO the members will appear in
+# declaration order.
+
+SORT_MEMBER_DOCS = YES
+
+# If the SORT_BRIEF_DOCS tag is set to YES then doxygen will sort the
+# brief documentation of file, namespace and class members alphabetically
+# by member name. If set to NO (the default) the members will appear in
+# declaration order.
+
+SORT_BRIEF_DOCS = YES
+
+# If the SORT_MEMBERS_CTORS_1ST tag is set to YES then doxygen
+# will sort the (brief and detailed) documentation of class members so that
+# constructors and destructors are listed first. If set to NO (the default)
+# the constructors will appear in the respective orders defined by
+# SORT_MEMBER_DOCS and SORT_BRIEF_DOCS.
+# This tag will be ignored for brief docs if SORT_BRIEF_DOCS is set to NO
+# and ignored for detailed docs if SORT_MEMBER_DOCS is set to NO.
+
+SORT_MEMBERS_CTORS_1ST = NO
+
+# If the SORT_GROUP_NAMES tag is set to YES then doxygen will sort the
+# hierarchy of group names into alphabetical order. If set to NO (the default)
+# the group names will appear in their defined order.
+
+SORT_GROUP_NAMES = NO
+
+# If the SORT_BY_SCOPE_NAME tag is set to YES, the class list will be
+# sorted by fully-qualified names, including namespaces. If set to
+# NO (the default), the class list will be sorted only by class name,
+# not including the namespace part.
+# Note: This option is not very useful if HIDE_SCOPE_NAMES is set to YES.
+# Note: This option applies only to the class list, not to the
+# alphabetical list.
+
+SORT_BY_SCOPE_NAME = NO
+
+# If the STRICT_PROTO_MATCHING option is enabled and doxygen fails to
+# do proper type resolution of all parameters of a function it will reject a
+# match between the prototype and the implementation of a member function even
+# if there is only one candidate or it is obvious which candidate to choose
+# by doing a simple string match. By disabling STRICT_PROTO_MATCHING doxygen
+# will still accept a match between prototype and implementation in such cases.
+
+STRICT_PROTO_MATCHING = NO
+
+# The GENERATE_TODOLIST tag can be used to enable (YES) or
+# disable (NO) the todo list. This list is created by putting \todo
+# commands in the documentation.
+
+GENERATE_TODOLIST = ${EIGEN_DOXY_INTERNAL}
+
+# The GENERATE_TESTLIST tag can be used to enable (YES) or
+# disable (NO) the test list. This list is created by putting \test
+# commands in the documentation.
+
+GENERATE_TESTLIST = NO
+
+# The GENERATE_BUGLIST tag can be used to enable (YES) or
+# disable (NO) the bug list. This list is created by putting \bug
+# commands in the documentation.
+
+GENERATE_BUGLIST = ${EIGEN_DOXY_INTERNAL}
+
+# The GENERATE_DEPRECATEDLIST tag can be used to enable (YES) or
+# disable (NO) the deprecated list. This list is created by putting
+# \deprecated commands in the documentation.
+
+GENERATE_DEPRECATEDLIST= YES
+
+# The ENABLED_SECTIONS tag can be used to enable conditional
+# documentation sections, marked by \if sectionname ... \endif.
+
+ENABLED_SECTIONS =
+
+# The MAX_INITIALIZER_LINES tag determines the maximum number of lines
+# the initial value of a variable or macro consists of for it to appear in
+# the documentation. If the initializer consists of more lines than specified
+# here it will be hidden. Use a value of 0 to hide initializers completely.
+# The appearance of the initializer of individual variables and macros in the
+# documentation can be controlled using \showinitializer or \hideinitializer
+# command in the documentation regardless of this setting.
+
+MAX_INITIALIZER_LINES = 0
+
+# Set the SHOW_USED_FILES tag to NO to disable the list of files generated
+# at the bottom of the documentation of classes and structs. If set to YES the
+# list will mention the files that were used to generate the documentation.
+
+SHOW_USED_FILES = YES
+
+# Set the SHOW_FILES tag to NO to disable the generation of the Files page.
+# This will remove the Files entry from the Quick Index and from the
+# Folder Tree View (if specified). The default is YES.
+
+SHOW_FILES = YES
+
+# Set the SHOW_NAMESPACES tag to NO to disable the generation of the
+# Namespaces page.
+# This will remove the Namespaces entry from the Quick Index
+# and from the Folder Tree View (if specified). The default is YES.
+
+SHOW_NAMESPACES = NO
+
+# The FILE_VERSION_FILTER tag can be used to specify a program or script that
+# doxygen should invoke to get the current version for each file (typically from
+# the version control system). Doxygen will invoke the program by executing (via
+# popen()) the command <command> <input-file>, where <command> is the value of
+# the FILE_VERSION_FILTER tag, and <input-file> is the name of an input file
+# provided by doxygen. Whatever the program writes to standard output
+# is used as the file version. See the manual for examples.
+
+FILE_VERSION_FILTER =
+
+# The LAYOUT_FILE tag can be used to specify a layout file which will be parsed
+# by doxygen. The layout file controls the global structure of the generated
+# output files in an output format independent way. To create the layout file
+# that represents doxygen's defaults, run doxygen with the -l option.
+# You can optionally specify a file name after the option, if omitted
+# DoxygenLayout.xml will be used as the name of the layout file.
+
+LAYOUT_FILE = "${Eigen_BINARY_DIR}/doc${EIGEN_DOXY_OUTPUT_DIRECTORY_SUFFIX}/eigendoxy_layout.xml"
+
+# The CITE_BIB_FILES tag can be used to specify one or more bib files
+# containing the references data. This must be a list of .bib files. The
+# .bib extension is automatically appended if omitted. Using this command
+# requires the bibtex tool to be installed. See also
+# http://en.wikipedia.org/wiki/BibTeX for more info. For LaTeX the style
+# of the bibliography can be controlled using LATEX_BIB_STYLE. To use this
+# feature you need bibtex and perl available in the search path.
+
+CITE_BIB_FILES =
+
+#---------------------------------------------------------------------------
+# configuration options related to warning and progress messages
+#---------------------------------------------------------------------------
+
+# The QUIET tag can be used to turn on/off the messages that are generated
+# by doxygen. Possible values are YES and NO. If left blank NO is used.
+
+QUIET = NO
+
+# The WARNINGS tag can be used to turn on/off the warning messages that are
+# generated by doxygen. Possible values are YES and NO. If left blank
+# NO is used.
+
+WARNINGS = YES
+
+# If WARN_IF_UNDOCUMENTED is set to YES, then doxygen will generate warnings
+# for undocumented members. If EXTRACT_ALL is set to YES then this flag will
+# automatically be disabled.
+
+WARN_IF_UNDOCUMENTED = NO
+
+# If WARN_IF_DOC_ERROR is set to YES, doxygen will generate warnings for
+# potential errors in the documentation, such as not documenting some
+# parameters in a documented function, or documenting parameters that
+# don't exist or using markup commands wrongly.
+
+WARN_IF_DOC_ERROR = YES
+
+# The WARN_NO_PARAMDOC option can be enabled to get warnings for
+# functions that are documented, but have no documentation for their parameters
+# or return value. If set to NO (the default) doxygen will only warn about
+# wrong or incomplete parameter documentation, but not about the absence of
+# documentation.
+
+WARN_NO_PARAMDOC = NO
+
+# The WARN_FORMAT tag determines the format of the warning messages that
+# doxygen can produce. The string should contain the $file, $line, and $text
+# tags, which will be replaced by the file and line number from which the
+# warning originated and the warning text. Optionally the format may contain
+# $version, which will be replaced by the version of the file (if it could
+# be obtained via FILE_VERSION_FILTER)
+
+WARN_FORMAT = "$file:$line: $text"
+
+# The WARN_LOGFILE tag can be used to specify a file to which warning
+# and error messages should be written. If left blank the output is written
+# to stderr.
+
+WARN_LOGFILE =
+
+#---------------------------------------------------------------------------
+# configuration options related to the input files
+#---------------------------------------------------------------------------
+
+# The INPUT tag can be used to specify the files and/or directories that contain
+# documented source files. You may enter file names like "myfile.cpp" or
+# directories like "/usr/src/myproject". Separate the files or directories
+# with spaces.
+
+INPUT = ${EIGEN_DOXY_INPUT}
+
+# This tag can be used to specify the character encoding of the source files
+# that doxygen parses. Internally doxygen uses the UTF-8 encoding, which is
+# also the default input encoding. Doxygen uses libiconv (or the iconv built
+# into libc) for the transcoding. See http://www.gnu.org/software/libiconv for
+# the list of possible encodings.
+
+INPUT_ENCODING = UTF-8
+
+# If the value of the INPUT tag contains directories, you can use the
+# FILE_PATTERNS tag to specify one or more wildcard pattern (like *.cpp
+# and *.h) to filter out the source-files in the directories. If left
+# blank the following patterns are tested:
+# *.c *.cc *.cxx *.cpp *.c++ *.d *.java *.ii *.ixx *.ipp *.i++ *.inl *.h *.hh
+# *.hxx *.hpp *.h++ *.idl *.odl *.cs *.php *.php3 *.inc *.m *.mm *.dox *.py
+# *.f90 *.f *.for *.vhd *.vhdl
+
+FILE_PATTERNS = *
+
+# The RECURSIVE tag can be used to turn specify whether or not subdirectories
+# should be searched for input files as well. Possible values are YES and NO.
+# If left blank NO is used.
+
+RECURSIVE = YES
+
+# The EXCLUDE tag can be used to specify files and/or directories that should be
+# excluded from the INPUT source files. This way you can easily exclude a
+# subdirectory from a directory tree whose root is specified with the INPUT tag.
+# Note that relative paths are relative to the directory from which doxygen is
+# run.
+
+EXCLUDE = "${Eigen_SOURCE_DIR}/Eigen/src/Core/products" \
+ "${Eigen_SOURCE_DIR}/Eigen/Eigen2Support" \
+ "${Eigen_SOURCE_DIR}/Eigen/src/Eigen2Support" \
+ "${Eigen_SOURCE_DIR}/doc/examples" \
+ "${Eigen_SOURCE_DIR}/doc/special_examples" \
+ "${Eigen_SOURCE_DIR}/doc/snippets" \
+ "${Eigen_SOURCE_DIR}/unsupported/doc/examples" \
+ "${Eigen_SOURCE_DIR}/unsupported/doc/snippets"
+
+# Forward declarations of class templates cause the title of the main page for
+# the class template to not contain the template signature. This only happens
+# when the \class command is used to document the class. Possibly caused
+# by https://github.com/doxygen/doxygen/issues/7698. Confirmed fixed by
+# doxygen release 1.8.19.
+
+EXCLUDE += "${Eigen_SOURCE_DIR}/Eigen/src/Core/util/ForwardDeclarations.h"
+
+# The EXCLUDE_SYMLINKS tag can be used to select whether or not files or
+# directories that are symbolic links (a Unix file system feature) are excluded
+# from the input.
+
+EXCLUDE_SYMLINKS = NO
+
+# If the value of the INPUT tag contains directories, you can use the
+# EXCLUDE_PATTERNS tag to specify one or more wildcard patterns to exclude
+# certain files from those directories. Note that the wildcards are matched
+# against the file with absolute path, so to exclude all test directories
+# for example use the pattern */test/*
+
+EXCLUDE_PATTERNS = CMake* \
+ *.txt \
+ *.sh \
+ *.orig \
+ *.diff \
+ diff \
+ *~ \
+ *. \
+ *.sln \
+ *.sdf \
+ *.tmp \
+ *.vcxproj \
+ *.filters \
+ *.user \
+ *.suo
+
+# The EXCLUDE_SYMBOLS tag can be used to specify one or more symbol names
+# (namespaces, classes, functions, etc.) that should be excluded from the
+# output. The symbol name can be a fully qualified name, a word, or if the
+# wildcard * is used, a substring. Examples: ANamespace, AClass,
+# AClass::ANamespace, ANamespace::*Test
+
+EXCLUDE_SYMBOLS = internal::* \
+ Flagged* \
+ *InnerIterator* \
+ DenseStorage<* \
+
+
+# The EXAMPLE_PATH tag can be used to specify one or more files or
+# directories that contain example code fragments that are included (see
+# the \include command).
+
+EXAMPLE_PATH = "${Eigen_SOURCE_DIR}/doc/snippets" \
+ "${Eigen_BINARY_DIR}/doc/snippets" \
+ "${Eigen_SOURCE_DIR}/doc/examples" \
+ "${Eigen_BINARY_DIR}/doc/examples" \
+ "${Eigen_SOURCE_DIR}/doc/special_examples" \
+ "${Eigen_BINARY_DIR}/doc/special_examples" \
+ "${Eigen_SOURCE_DIR}/unsupported/doc/snippets" \
+ "${Eigen_BINARY_DIR}/unsupported/doc/snippets" \
+ "${Eigen_SOURCE_DIR}/unsupported/doc/examples" \
+ "${Eigen_BINARY_DIR}/unsupported/doc/examples"
+
+# If the value of the EXAMPLE_PATH tag contains directories, you can use the
+# EXAMPLE_PATTERNS tag to specify one or more wildcard pattern (like *.cpp
+# and *.h) to filter out the source-files in the directories. If left
+# blank all files are included.
+
+EXAMPLE_PATTERNS = *
+
+# If the EXAMPLE_RECURSIVE tag is set to YES then subdirectories will be
+# searched for input files to be used with the \include or \dontinclude
+# commands irrespective of the value of the RECURSIVE tag.
+# Possible values are YES and NO. If left blank NO is used.
+
+EXAMPLE_RECURSIVE = NO
+
+# The IMAGE_PATH tag can be used to specify one or more files or
+# directories that contain image that are included in the documentation (see
+# the \image command).
+
+IMAGE_PATH = ${Eigen_BINARY_DIR}/doc/html
+
+# The INPUT_FILTER tag can be used to specify a program that doxygen should
+# invoke to filter for each input file. Doxygen will invoke the filter program
+# by executing (via popen()) the command <filter> <input-file>, where <filter>
+# is the value of the INPUT_FILTER tag, and <input-file> is the name of an
+# input file. Doxygen will then use the output that the filter program writes
+# to standard output.
+# If FILTER_PATTERNS is specified, this tag will be
+# ignored.
+
+INPUT_FILTER =
+
+# The FILTER_PATTERNS tag can be used to specify filters on a per file pattern
+# basis.
+# Doxygen will compare the file name with each pattern and apply the
+# filter if there is a match.
+# The filters are a list of the form:
+# pattern=filter (like *.cpp=my_cpp_filter). See INPUT_FILTER for further
+# info on how filters are used. If FILTER_PATTERNS is empty or if
+# non of the patterns match the file name, INPUT_FILTER is applied.
+
+FILTER_PATTERNS =
+
+# If the FILTER_SOURCE_FILES tag is set to YES, the input filter (if set using
+# INPUT_FILTER) will be used to filter the input files when producing source
+# files to browse (i.e. when SOURCE_BROWSER is set to YES).
+
+FILTER_SOURCE_FILES = NO
+
+# The FILTER_SOURCE_PATTERNS tag can be used to specify source filters per file
+# pattern. A pattern will override the setting for FILTER_PATTERN (if any)
+# and it is also possible to disable source filtering for a specific pattern
+# using *.ext= (so without naming a filter). This option only has effect when
+# FILTER_SOURCE_FILES is enabled.
+
+FILTER_SOURCE_PATTERNS =
+
+#---------------------------------------------------------------------------
+# configuration options related to source browsing
+#---------------------------------------------------------------------------
+
+# If the SOURCE_BROWSER tag is set to YES then a list of source files will
+# be generated. Documented entities will be cross-referenced with these sources.
+# Note: To get rid of all source code in the generated output, make sure also
+# VERBATIM_HEADERS is set to NO.
+
+SOURCE_BROWSER = NO
+
+# Setting the INLINE_SOURCES tag to YES will include the body
+# of functions and classes directly in the documentation.
+
+INLINE_SOURCES = NO
+
+# Setting the STRIP_CODE_COMMENTS tag to YES (the default) will instruct
+# doxygen to hide any special comment blocks from generated source code
+# fragments. Normal C, C++ and Fortran comments will always remain visible.
+
+STRIP_CODE_COMMENTS = YES
+
+# If the REFERENCED_BY_RELATION tag is set to YES
+# then for each documented function all documented
+# functions referencing it will be listed.
+
+REFERENCED_BY_RELATION = NO
+
+# If the REFERENCES_RELATION tag is set to YES
+# then for each documented function all documented entities
+# called/used by that function will be listed.
+
+REFERENCES_RELATION = NO
+
+# If the REFERENCES_LINK_SOURCE tag is set to YES (the default)
+# and SOURCE_BROWSER tag is set to YES, then the hyperlinks from
+# functions in REFERENCES_RELATION and REFERENCED_BY_RELATION lists will
+# link to the source code.
+# Otherwise they will link to the documentation.
+
+REFERENCES_LINK_SOURCE = YES
+
+# If the USE_HTAGS tag is set to YES then the references to source code
+# will point to the HTML generated by the htags(1) tool instead of doxygen
+# built-in source browser. The htags tool is part of GNU's global source
+# tagging system (see http://www.gnu.org/software/global/global.html). You
+# will need version 4.8.6 or higher.
+
+USE_HTAGS = NO
+
+# If the VERBATIM_HEADERS tag is set to YES (the default) then Doxygen
+# will generate a verbatim copy of the header file for each class for
+# which an include is specified. Set to NO to disable this.
+
+VERBATIM_HEADERS = YES
+
+#---------------------------------------------------------------------------
+# configuration options related to the alphabetical class index
+#---------------------------------------------------------------------------
+
+# If the ALPHABETICAL_INDEX tag is set to YES, an alphabetical index
+# of all compounds will be generated. Enable this if the project
+# contains a lot of classes, structs, unions or interfaces.
+
+ALPHABETICAL_INDEX = NO
+
+# If the alphabetical index is enabled (see ALPHABETICAL_INDEX) then
+# the COLS_IN_ALPHA_INDEX tag can be used to specify the number of columns
+# in which this list will be split (can be a number in the range [1..20])
+
+COLS_IN_ALPHA_INDEX = 5
+
+# In case all classes in a project start with a common prefix, all
+# classes will be put under the same header in the alphabetical index.
+# The IGNORE_PREFIX tag can be used to specify one or more prefixes that
+# should be ignored while generating the index headers.
+
+IGNORE_PREFIX =
+
+#---------------------------------------------------------------------------
+# configuration options related to the HTML output
+#---------------------------------------------------------------------------
+
+# If the GENERATE_HTML tag is set to YES (the default) Doxygen will
+# generate HTML output.
+
+GENERATE_HTML = YES
+
+# The HTML_OUTPUT tag is used to specify where the HTML docs will be put.
+# If a relative path is entered the value of OUTPUT_DIRECTORY will be
+# put in front of it. If left blank `html' will be used as the default path.
+
+HTML_OUTPUT = "${Eigen_BINARY_DIR}/doc/html${EIGEN_DOXY_OUTPUT_DIRECTORY_SUFFIX}"
+
+# The HTML_FILE_EXTENSION tag can be used to specify the file extension for
+# each generated HTML page (for example: .htm,.php,.asp). If it is left blank
+# doxygen will generate files with .html extension.
+
+HTML_FILE_EXTENSION = .html
+
+# The HTML_HEADER tag can be used to specify a personal HTML header for
+# each generated HTML page. If it is left blank doxygen will generate a
+# standard header. Note that when using a custom header you are responsible
+# for the proper inclusion of any scripts and style sheets that doxygen
+# needs, which is dependent on the configuration options used.
+# It is advised to generate a default header using "doxygen -w html
+# header.html footer.html stylesheet.css YourConfigFile" and then modify
+# that header. Note that the header is subject to change so you typically
+# have to redo this when upgrading to a newer version of doxygen or when
+# changing the value of configuration settings such as GENERATE_TREEVIEW!
+
+HTML_HEADER = "${Eigen_BINARY_DIR}/doc/eigendoxy_header.html"
+
+# The HTML_FOOTER tag can be used to specify a personal HTML footer for
+# each generated HTML page. If it is left blank doxygen will generate a
+# standard footer.
+
+HTML_FOOTER = "${Eigen_BINARY_DIR}/doc/eigendoxy_footer.html"
+
+# The HTML_STYLESHEET tag can be used to specify a user-defined cascading
+# style sheet that is used by each HTML page. It can be used to
+# fine-tune the look of the HTML output. If the tag is left blank doxygen
+# will generate a default style sheet. Note that doxygen will try to copy
+# the style sheet file to the HTML output directory, so don't put your own
+# style sheet in the HTML output directory as well, or it will be erased!
+
+HTML_STYLESHEET =
+
+# The HTML_EXTRA_FILES tag can be used to specify one or more extra images or
+# other source files which should be copied to the HTML output directory. Note
+# that these files will be copied to the base HTML output directory. Use the
+# $relpath$ marker in the HTML_HEADER and/or HTML_FOOTER files to load these
+# files. In the HTML_STYLESHEET file, use the file name only. Also note that
+# the files will be copied as-is; there are no commands or markers available.
+
+HTML_EXTRA_FILES = "${Eigen_SOURCE_DIR}/doc/eigendoxy.css"
+
+# The HTML_COLORSTYLE_HUE tag controls the color of the HTML output.
+# Doxygen will adjust the colors in the style sheet and background images
+# according to this color. Hue is specified as an angle on a colorwheel,
+# see http://en.wikipedia.org/wiki/Hue for more information.
+# For instance the value 0 represents red, 60 is yellow, 120 is green,
+# 180 is cyan, 240 is blue, 300 purple, and 360 is red again.
+# The allowed range is 0 to 359.
+# The default is 220.
+
+HTML_COLORSTYLE_HUE = ${EIGEN_DOXY_HTML_COLORSTYLE_HUE}
+
+# The HTML_COLORSTYLE_SAT tag controls the purity (or saturation) of
+# the colors in the HTML output. For a value of 0 the output will use
+# grayscales only. A value of 255 will produce the most vivid colors.
+
+HTML_COLORSTYLE_SAT = 100
+
+# The HTML_COLORSTYLE_GAMMA tag controls the gamma correction applied to
+# the luminance component of the colors in the HTML output. Values below
+# 100 gradually make the output lighter, whereas values above 100 make
+# the output darker. The value divided by 100 is the actual gamma applied,
+# so 80 represents a gamma of 0.8, The value 220 represents a gamma of 2.2,
+# and 100 does not change the gamma.
+
+HTML_COLORSTYLE_GAMMA = 80
+
+# If the HTML_TIMESTAMP tag is set to YES then the footer of each generated HTML
+# page will contain the date and time when the page was generated. Setting
+# this to NO can help when comparing the output of multiple runs.
+
+HTML_TIMESTAMP = YES
+
+# If the HTML_DYNAMIC_SECTIONS tag is set to YES then the generated HTML
+# documentation will contain sections that can be hidden and shown after the
+# page has loaded.
+
+HTML_DYNAMIC_SECTIONS = YES
+
+# With HTML_INDEX_NUM_ENTRIES one can control the preferred number of
+# entries shown in the various tree structured indices initially; the user
+# can expand and collapse entries dynamically later on. Doxygen will expand
+# the tree to such a level that at most the specified number of entries are
+# visible (unless a fully collapsed tree already exceeds this amount).
+# So setting the number of entries 1 will produce a full collapsed tree by
+# default. 0 is a special value representing an infinite number of entries
+# and will result in a full expanded tree by default.
+
+HTML_INDEX_NUM_ENTRIES = 100
+
+# If the GENERATE_DOCSET tag is set to YES, additional index files
+# will be generated that can be used as input for Apple's Xcode 3
+# integrated development environment, introduced with OSX 10.5 (Leopard).
+# To create a documentation set, doxygen will generate a Makefile in the
+# HTML output directory. Running make will produce the docset in that
+# directory and running "make install" will install the docset in
+# ~/Library/Developer/Shared/Documentation/DocSets so that Xcode will find
+# it at startup.
+# See http://developer.apple.com/tools/creatingdocsetswithdoxygen.html
+# for more information.
+
+GENERATE_DOCSET = NO
+
+# When GENERATE_DOCSET tag is set to YES, this tag determines the name of the
+# feed. A documentation feed provides an umbrella under which multiple
+# documentation sets from a single provider (such as a company or product suite)
+# can be grouped.
+
+DOCSET_FEEDNAME = "Doxygen generated docs"
+
+# When GENERATE_DOCSET tag is set to YES, this tag specifies a string that
+# should uniquely identify the documentation set bundle. This should be a
+# reverse domain-name style string, e.g. com.mycompany.MyDocSet. Doxygen
+# will append .docset to the name.
+
+DOCSET_BUNDLE_ID = org.doxygen.Project
+
+# When GENERATE_PUBLISHER_ID tag specifies a string that should uniquely identify
+# the documentation publisher. This should be a reverse domain-name style
+# string, e.g. com.mycompany.MyDocSet.documentation.
+
+DOCSET_PUBLISHER_ID = org.doxygen.Publisher
+
+# The GENERATE_PUBLISHER_NAME tag identifies the documentation publisher.
+
+DOCSET_PUBLISHER_NAME = Publisher
+
+# If the GENERATE_HTMLHELP tag is set to YES, additional index files
+# will be generated that can be used as input for tools like the
+# Microsoft HTML help workshop to generate a compiled HTML help file (.chm)
+# of the generated HTML documentation.
+
+GENERATE_HTMLHELP = NO
+
+# If the GENERATE_HTMLHELP tag is set to YES, the CHM_FILE tag can
+# be used to specify the file name of the resulting .chm file. You
+# can add a path in front of the file if the result should not be
+# written to the html output directory.
+
+CHM_FILE =
+
+# If the GENERATE_HTMLHELP tag is set to YES, the HHC_LOCATION tag can
+# be used to specify the location (absolute path including file name) of
+# the HTML help compiler (hhc.exe). If non-empty doxygen will try to run
+# the HTML help compiler on the generated index.hhp.
+
+HHC_LOCATION =
+
+# If the GENERATE_HTMLHELP tag is set to YES, the GENERATE_CHI flag
+# controls if a separate .chi index file is generated (YES) or that
+# it should be included in the master .chm file (NO).
+
+GENERATE_CHI = NO
+
+# If the GENERATE_HTMLHELP tag is set to YES, the CHM_INDEX_ENCODING
+# is used to encode HtmlHelp index (hhk), content (hhc) and project file
+# content.
+
+CHM_INDEX_ENCODING =
+
+# If the GENERATE_HTMLHELP tag is set to YES, the BINARY_TOC flag
+# controls whether a binary table of contents is generated (YES) or a
+# normal table of contents (NO) in the .chm file.
+
+BINARY_TOC = NO
+
+# The TOC_EXPAND flag can be set to YES to add extra items for group members
+# to the contents of the HTML help documentation and to the tree view.
+
+TOC_EXPAND = NO
+
+# If the GENERATE_QHP tag is set to YES and both QHP_NAMESPACE and
+# QHP_VIRTUAL_FOLDER are set, an additional index file will be generated
+# that can be used as input for Qt's qhelpgenerator to generate a
+# Qt Compressed Help (.qch) of the generated HTML documentation.
+
+GENERATE_QHP = NO
+
+# If the QHG_LOCATION tag is specified, the QCH_FILE tag can
+# be used to specify the file name of the resulting .qch file.
+# The path specified is relative to the HTML output folder.
+
+QCH_FILE =
+
+# The QHP_NAMESPACE tag specifies the namespace to use when generating
+# Qt Help Project output. For more information please see
+# http://doc.trolltech.com/qthelpproject.html#namespace
+
+QHP_NAMESPACE = org.doxygen.Project
+
+# The QHP_VIRTUAL_FOLDER tag specifies the namespace to use when generating
+# Qt Help Project output. For more information please see
+# http://doc.trolltech.com/qthelpproject.html#virtual-folders
+
+QHP_VIRTUAL_FOLDER = doc
+
+# If QHP_CUST_FILTER_NAME is set, it specifies the name of a custom filter to
+# add. For more information please see
+# http://doc.trolltech.com/qthelpproject.html#custom-filters
+
+QHP_CUST_FILTER_NAME =
+
+# The QHP_CUST_FILT_ATTRS tag specifies the list of the attributes of the
+# custom filter to add. For more information please see
+# <a href="http://doc.trolltech.com/qthelpproject.html#custom-filters">
+# Qt Help Project / Custom Filters</a>.
+
+QHP_CUST_FILTER_ATTRS =
+
+# The QHP_SECT_FILTER_ATTRS tag specifies the list of the attributes this
+# project's
+# filter section matches.
+# <a href="http://doc.trolltech.com/qthelpproject.html#filter-attributes">
+# Qt Help Project / Filter Attributes</a>.
+
+QHP_SECT_FILTER_ATTRS =
+
+# If the GENERATE_QHP tag is set to YES, the QHG_LOCATION tag can
+# be used to specify the location of Qt's qhelpgenerator.
+# If non-empty doxygen will try to run qhelpgenerator on the generated
+# .qhp file.
+
+QHG_LOCATION =
+
+# If the GENERATE_ECLIPSEHELP tag is set to YES, additional index files
+# will be generated, which together with the HTML files, form an Eclipse help
+# plugin. To install this plugin and make it available under the help contents
+# menu in Eclipse, the contents of the directory containing the HTML and XML
+# files needs to be copied into the plugins directory of eclipse. The name of
+# the directory within the plugins directory should be the same as
+# the ECLIPSE_DOC_ID value. After copying Eclipse needs to be restarted before
+# the help appears.
+
+GENERATE_ECLIPSEHELP = NO
+
+# A unique identifier for the eclipse help plugin. When installing the plugin
+# the directory name containing the HTML and XML files should also have
+# this name.
+
+ECLIPSE_DOC_ID = org.doxygen.Project
+
+# The DISABLE_INDEX tag can be used to turn on/off the condensed index (tabs)
+# at top of each HTML page. The value NO (the default) enables the index and
+# the value YES disables it. Since the tabs have the same information as the
+# navigation tree you can set this option to NO if you already set
+# GENERATE_TREEVIEW to YES.
+
+DISABLE_INDEX = YES
+
+# The GENERATE_TREEVIEW tag is used to specify whether a tree-like index
+# structure should be generated to display hierarchical information.
+# If the tag value is set to YES, a side panel will be generated
+# containing a tree-like index structure (just like the one that
+# is generated for HTML Help). For this to work a browser that supports
+# JavaScript, DHTML, CSS and frames is required (i.e. any modern browser).
+# Windows users are probably better off using the HTML help feature.
+# Since the tree basically has the same information as the tab index you
+# could consider to set DISABLE_INDEX to NO when enabling this option.
+
+GENERATE_TREEVIEW = YES
+
+# The ENUM_VALUES_PER_LINE tag can be used to set the number of enum values
+# (range [0,1..20]) that doxygen will group on one line in the generated HTML
+# documentation. Note that a value of 0 will completely suppress the enum
+# values from appearing in the overview section.
+
+ENUM_VALUES_PER_LINE = 1
+
+# If the treeview is enabled (see GENERATE_TREEVIEW) then this tag can be
+# used to set the initial width (in pixels) of the frame in which the tree
+# is shown.
+
+TREEVIEW_WIDTH = 250
+
+# When the EXT_LINKS_IN_WINDOW option is set to YES doxygen will open
+# links to external symbols imported via tag files in a separate window.
+
+EXT_LINKS_IN_WINDOW = NO
+
+# Use this tag to change the font size of Latex formulas included
+# as images in the HTML documentation. The default is 10. Note that
+# when you change the font size after a successful doxygen run you need
+# to manually remove any form_*.png images from the HTML output directory
+# to force them to be regenerated.
+
+FORMULA_FONTSIZE = 12
+
+# Use the FORMULA_TRANPARENT tag to determine whether or not the images
+# generated for formulas are transparent PNGs. Transparent PNGs are
+# not supported properly for IE 6.0, but are supported on all modern browsers.
+# Note that when changing this option you need to delete any form_*.png files
+# in the HTML output before the changes have effect.
+
+FORMULA_TRANSPARENT = YES
+
+# Enable the USE_MATHJAX option to render LaTeX formulas using MathJax
+# (see http://www.mathjax.org) which uses client side Javascript for the
+# rendering instead of using prerendered bitmaps. Use this if you do not
+# have LaTeX installed or if you want to formulas look prettier in the HTML
+# output. When enabled you may also need to install MathJax separately and
+# configure the path to it using the MATHJAX_RELPATH option.
+
+USE_MATHJAX = @EIGEN_DOXY_USE_MATHJAX@
+
+# When MathJax is enabled you need to specify the location relative to the
+# HTML output directory using the MATHJAX_RELPATH option. The destination
+# directory should contain the MathJax.js script. For instance, if the mathjax
+# directory is located at the same level as the HTML output directory, then
+# MATHJAX_RELPATH should be ../mathjax. The default value points to
+# the MathJax Content Delivery Network so you can quickly see the result without
+# installing MathJax.
+# However, it is strongly recommended to install a local
+# copy of MathJax from http://www.mathjax.org before deployment.
+
+MATHJAX_RELPATH = https://cdn.mathjax.org/mathjax/latest
+
+# The MATHJAX_EXTENSIONS tag can be used to specify one or MathJax extension
+# names that should be enabled during MathJax rendering.
+
+MATHJAX_EXTENSIONS = TeX/AMSmath TeX/AMSsymbols
+
+# When the SEARCHENGINE tag is enabled doxygen will generate a search box
+# for the HTML output. The underlying search engine uses javascript
+# and DHTML and should work on any modern browser. Note that when using
+# HTML help (GENERATE_HTMLHELP), Qt help (GENERATE_QHP), or docsets
+# (GENERATE_DOCSET) there is already a search function so this one should
+# typically be disabled. For large projects the javascript based search engine
+# can be slow, then enabling SERVER_BASED_SEARCH may provide a better solution.
+
+SEARCHENGINE = YES
+
+# When the SERVER_BASED_SEARCH tag is enabled the search engine will be
+# implemented using a PHP enabled web server instead of at the web client
+# using Javascript. Doxygen will generate the search PHP script and index
+# file to put on the web server. The advantage of the server
+# based approach is that it scales better to large projects and allows
+# full text search. The disadvantages are that it is more difficult to setup
+# and does not have live searching capabilities.
+
+SERVER_BASED_SEARCH = NO
+
+#---------------------------------------------------------------------------
+# configuration options related to the LaTeX output
+#---------------------------------------------------------------------------
+
+# If the GENERATE_LATEX tag is set to YES (the default) Doxygen will
+# generate Latex output.
+
+GENERATE_LATEX = NO
+
+# The LATEX_OUTPUT tag is used to specify where the LaTeX docs will be put.
+# If a relative path is entered the value of OUTPUT_DIRECTORY will be
+# put in front of it. If left blank `latex' will be used as the default path.
+
+LATEX_OUTPUT = latex
+
+# The LATEX_CMD_NAME tag can be used to specify the LaTeX command name to be
+# invoked. If left blank `latex' will be used as the default command name.
+# Note that when enabling USE_PDFLATEX this option is only used for
+# generating bitmaps for formulas in the HTML output, but not in the
+# Makefile that is written to the output directory.
+
+LATEX_CMD_NAME = latex
+
+# The MAKEINDEX_CMD_NAME tag can be used to specify the command name to
+# generate index for LaTeX. If left blank `makeindex' will be used as the
+# default command name.
+
+MAKEINDEX_CMD_NAME = makeindex
+
+# If the COMPACT_LATEX tag is set to YES Doxygen generates more compact
+# LaTeX documents. This may be useful for small projects and may help to
+# save some trees in general.
+
+COMPACT_LATEX = NO
+
+# The PAPER_TYPE tag can be used to set the paper type that is used
+# by the printer. Possible values are: a4, letter, legal and
+# executive. If left blank a4wide will be used.
+
+PAPER_TYPE = a4wide
+
+# The EXTRA_PACKAGES tag can be to specify one or more names of LaTeX
+# packages that should be included in the LaTeX output.
+
+EXTRA_PACKAGES = amssymb \
+ amsmath
+
+# The LATEX_HEADER tag can be used to specify a personal LaTeX header for
+# the generated latex document. The header should contain everything until
+# the first chapter. If it is left blank doxygen will generate a
+# standard header. Notice: only use this tag if you know what you are doing!
+
+LATEX_HEADER =
+
+# The LATEX_FOOTER tag can be used to specify a personal LaTeX footer for
+# the generated latex document. The footer should contain everything after
+# the last chapter. If it is left blank doxygen will generate a
+# standard footer. Notice: only use this tag if you know what you are doing!
+
+LATEX_FOOTER =
+
+# If the PDF_HYPERLINKS tag is set to YES, the LaTeX that is generated
+# is prepared for conversion to pdf (using ps2pdf). The pdf file will
+# contain links (just like the HTML output) instead of page references
+# This makes the output suitable for online browsing using a pdf viewer.
+
+PDF_HYPERLINKS = NO
+
+# If the USE_PDFLATEX tag is set to YES, pdflatex will be used instead of
+# plain latex in the generated Makefile. Set this option to YES to get a
+# higher quality PDF documentation.
+
+USE_PDFLATEX = NO
+
+# If the LATEX_BATCHMODE tag is set to YES, doxygen will add the \\batchmode.
+# command to the generated LaTeX files. This will instruct LaTeX to keep
+# running if errors occur, instead of asking the user for help.
+# This option is also used when generating formulas in HTML.
+
+LATEX_BATCHMODE = NO
+
+# If LATEX_HIDE_INDICES is set to YES then doxygen will not
+# include the index chapters (such as File Index, Compound Index, etc.)
+# in the output.
+
+LATEX_HIDE_INDICES = NO
+
+# If LATEX_SOURCE_CODE is set to YES then doxygen will include
+# source code with syntax highlighting in the LaTeX output.
+# Note that which sources are shown also depends on other settings
+# such as SOURCE_BROWSER.
+
+LATEX_SOURCE_CODE = NO
+
+# The LATEX_BIB_STYLE tag can be used to specify the style to use for the
+# bibliography, e.g. plainnat, or ieeetr. The default style is "plain". See
+# http://en.wikipedia.org/wiki/BibTeX for more info.
+
+LATEX_BIB_STYLE = plain
+
+#---------------------------------------------------------------------------
+# configuration options related to the RTF output
+#---------------------------------------------------------------------------
+
+# If the GENERATE_RTF tag is set to YES Doxygen will generate RTF output
+# The RTF output is optimized for Word 97 and may not look very pretty with
+# other RTF readers or editors.
+
+GENERATE_RTF = NO
+
+# The RTF_OUTPUT tag is used to specify where the RTF docs will be put.
+# If a relative path is entered the value of OUTPUT_DIRECTORY will be
+# put in front of it. If left blank `rtf' will be used as the default path.
+
+RTF_OUTPUT = rtf
+
+# If the COMPACT_RTF tag is set to YES Doxygen generates more compact
+# RTF documents. This may be useful for small projects and may help to
+# save some trees in general.
+
+COMPACT_RTF = NO
+
+# If the RTF_HYPERLINKS tag is set to YES, the RTF that is generated
+# will contain hyperlink fields. The RTF file will
+# contain links (just like the HTML output) instead of page references.
+# This makes the output suitable for online browsing using WORD or other
+# programs which support those fields.
+# Note: wordpad (write) and others do not support links.
+
+RTF_HYPERLINKS = NO
+
+# Load style sheet definitions from file. Syntax is similar to doxygen's
+# config file, i.e. a series of assignments. You only have to provide
+# replacements, missing definitions are set to their default value.
+
+RTF_STYLESHEET_FILE =
+
+# Set optional variables used in the generation of an rtf document.
+# Syntax is similar to doxygen's config file.
+
+RTF_EXTENSIONS_FILE =
+
+#---------------------------------------------------------------------------
+# configuration options related to the man page output
+#---------------------------------------------------------------------------
+
+# If the GENERATE_MAN tag is set to YES (the default) Doxygen will
+# generate man pages
+
+GENERATE_MAN = NO
+
+# The MAN_OUTPUT tag is used to specify where the man pages will be put.
+# If a relative path is entered the value of OUTPUT_DIRECTORY will be
+# put in front of it. If left blank `man' will be used as the default path.
+
+MAN_OUTPUT = man
+
+# The MAN_EXTENSION tag determines the extension that is added to
+# the generated man pages (default is the subroutine's section .3)
+
+MAN_EXTENSION = .3
+
+# If the MAN_LINKS tag is set to YES and Doxygen generates man output,
+# then it will generate one additional man file for each entity
+# documented in the real man page(s). These additional files
+# only source the real man page, but without them the man command
+# would be unable to find the correct page. The default is NO.
+
+MAN_LINKS = NO
+
+#---------------------------------------------------------------------------
+# configuration options related to the XML output
+#---------------------------------------------------------------------------
+
+# If the GENERATE_XML tag is set to YES Doxygen will
+# generate an XML file that captures the structure of
+# the code including all documentation.
+
+GENERATE_XML = NO
+
+# The XML_OUTPUT tag is used to specify where the XML pages will be put.
+# If a relative path is entered the value of OUTPUT_DIRECTORY will be
+# put in front of it. If left blank `xml' will be used as the default path.
+
+XML_OUTPUT = xml
+
+# The XML_SCHEMA tag can be used to specify an XML schema,
+# which can be used by a validating XML parser to check the
+# syntax of the XML files.
+
+# XML_SCHEMA =
+
+# The XML_DTD tag can be used to specify an XML DTD,
+# which can be used by a validating XML parser to check the
+# syntax of the XML files.
+
+# XML_DTD =
+
+# If the XML_PROGRAMLISTING tag is set to YES Doxygen will
+# dump the program listings (including syntax highlighting
+# and cross-referencing information) to the XML output. Note that
+# enabling this will significantly increase the size of the XML output.
+
+XML_PROGRAMLISTING = YES
+
+#---------------------------------------------------------------------------
+# configuration options for the AutoGen Definitions output
+#---------------------------------------------------------------------------
+
+# If the GENERATE_AUTOGEN_DEF tag is set to YES Doxygen will
+# generate an AutoGen Definitions (see autogen.sf.net) file
+# that captures the structure of the code including all
+# documentation. Note that this feature is still experimental
+# and incomplete at the moment.
+
+GENERATE_AUTOGEN_DEF = NO
+
+#---------------------------------------------------------------------------
+# configuration options related to the Perl module output
+#---------------------------------------------------------------------------
+
+# If the GENERATE_PERLMOD tag is set to YES Doxygen will
+# generate a Perl module file that captures the structure of
+# the code including all documentation. Note that this
+# feature is still experimental and incomplete at the
+# moment.
+
+GENERATE_PERLMOD = NO
+
+# If the PERLMOD_LATEX tag is set to YES Doxygen will generate
+# the necessary Makefile rules, Perl scripts and LaTeX code to be able
+# to generate PDF and DVI output from the Perl module output.
+
+PERLMOD_LATEX = NO
+
+# If the PERLMOD_PRETTY tag is set to YES the Perl module output will be
+# nicely formatted so it can be parsed by a human reader.
+# This is useful
+# if you want to understand what is going on.
+# On the other hand, if this
+# tag is set to NO the size of the Perl module output will be much smaller
+# and Perl will parse it just the same.
+
+PERLMOD_PRETTY = YES
+
+# The names of the make variables in the generated doxyrules.make file
+# are prefixed with the string contained in PERLMOD_MAKEVAR_PREFIX.
+# This is useful so different doxyrules.make files included by the same
+# Makefile don't overwrite each other's variables.
+
+PERLMOD_MAKEVAR_PREFIX =
+
+#---------------------------------------------------------------------------
+# Configuration options related to the preprocessor
+#---------------------------------------------------------------------------
+
+# If the ENABLE_PREPROCESSING tag is set to YES (the default) Doxygen will
+# evaluate all C-preprocessor directives found in the sources and include
+# files.
+
+ENABLE_PREPROCESSING = YES
+
+# If the MACRO_EXPANSION tag is set to YES Doxygen will expand all macro
+# names in the source code. If set to NO (the default) only conditional
+# compilation will be performed. Macro expansion can be done in a controlled
+# way by setting EXPAND_ONLY_PREDEF to YES.
+
+MACRO_EXPANSION = YES
+
+# If the EXPAND_ONLY_PREDEF and MACRO_EXPANSION tags are both set to YES
+# then the macro expansion is limited to the macros specified with the
+# PREDEFINED and EXPAND_AS_DEFINED tags.
+
+EXPAND_ONLY_PREDEF = YES
+
+# If the SEARCH_INCLUDES tag is set to YES (the default) the includes files
+# pointed to by INCLUDE_PATH will be searched when a #include is found.
+
+SEARCH_INCLUDES = YES
+
+# The INCLUDE_PATH tag can be used to specify one or more directories that
+# contain include files that are not input files but should be processed by
+# the preprocessor.
+
+INCLUDE_PATH = "${Eigen_SOURCE_DIR}/Eigen/src/plugins"
+
+# You can use the INCLUDE_FILE_PATTERNS tag to specify one or more wildcard
+# patterns (like *.h and *.hpp) to filter out the header-files in the
+# directories. If left blank, the patterns specified with FILE_PATTERNS will
+# be used.
+
+INCLUDE_FILE_PATTERNS =
+
+# The PREDEFINED tag can be used to specify one or more macro names that
+# are defined before the preprocessor is started (similar to the -D option of
+# gcc). The argument of the tag is a list of macros of the form: name
+# or name=definition (no spaces). If the definition and the = are
+# omitted =1 is assumed. To prevent a macro definition from being
+# undefined via #undef or recursively expanded use the := operator
+# instead of the = operator.
+
+PREDEFINED = EIGEN_EMPTY_STRUCT \
+ EIGEN_PARSED_BY_DOXYGEN \
+ EIGEN_VECTORIZE \
+ EIGEN_QT_SUPPORT \
+ EIGEN_STRONG_INLINE=inline \
+ EIGEN_DEVICE_FUNC= \
+ "EIGEN_MAKE_CWISE_BINARY_OP(METHOD,FUNCTOR)=template<typename OtherDerived> const CwiseBinaryOp<FUNCTOR<Scalar>, const Derived, const OtherDerived> METHOD(const EIGEN_CURRENT_STORAGE_BASE_CLASS<OtherDerived> &other) const;" \
+ "EIGEN_CWISE_PRODUCT_RETURN_TYPE(LHS,RHS)=CwiseBinaryOp<internal::scalar_product_op<LHS::Scalar,RHS::Scalar>, const LHS, const RHS>"\
+ "EIGEN_CAT2(a,b)= a ## b"\
+ "EIGEN_CAT(a,b)=EIGEN_CAT2(a,b)"\
+ "EIGEN_CWISE_BINARY_RETURN_TYPE(LHS,RHS,OPNAME)=CwiseBinaryOp<EIGEN_CAT(EIGEN_CAT(internal::scalar_,OPNAME),_op)<LHS::Scalar, RHS::Scalar>, const LHS, const RHS>"\
+ "EIGEN_ALIGN_TO_BOUNDARY(x)="\
+ DOXCOMMA=,
+
+
+# If the MACRO_EXPANSION and EXPAND_ONLY_PREDEF tags are set to YES then
+# this tag can be used to specify a list of macro names that should be expanded.
+# The macro definition that is found in the sources will be used.
+# Use the PREDEFINED tag if you want to use a different macro definition that
+# overrules the definition found in the source code.
+
+EXPAND_AS_DEFINED = EIGEN_MAKE_TYPEDEFS \
+ EIGEN_MAKE_FIXED_TYPEDEFS \
+ EIGEN_MAKE_TYPEDEFS_ALL_SIZES \
+ EIGEN_MAKE_ARRAY_TYPEDEFS \
+ EIGEN_MAKE_ARRAY_FIXED_TYPEDEFS \
+ EIGEN_MAKE_ARRAY_TYPEDEFS_ALL_SIZES \
+ EIGEN_CWISE_UNOP_RETURN_TYPE \
+ EIGEN_CWISE_BINOP_RETURN_TYPE \
+ EIGEN_CURRENT_STORAGE_BASE_CLASS \
+ EIGEN_MATHFUNC_IMPL \
+ _EIGEN_GENERIC_PUBLIC_INTERFACE \
+ EIGEN_ARRAY_DECLARE_GLOBAL_UNARY \
+ EIGEN_EMPTY \
+ EIGEN_EULER_ANGLES_TYPEDEFS \
+ EIGEN_EULER_ANGLES_SINGLE_TYPEDEF \
+ EIGEN_EULER_SYSTEM_TYPEDEF \
+ EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY \
+ EIGEN_MATRIX_FUNCTION \
+ EIGEN_MATRIX_FUNCTION_1 \
+ EIGEN_DOC_UNARY_ADDONS \
+ EIGEN_DOC_BLOCK_ADDONS_NOT_INNER_PANEL \
+ EIGEN_DOC_BLOCK_ADDONS_INNER_PANEL_IF
+
+
+# If the SKIP_FUNCTION_MACROS tag is set to YES (the default) then
+# doxygen's preprocessor will remove all references to function-like macros
+# that are alone on a line, have an all uppercase name, and do not end with a
+# semicolon, because these will confuse the parser if not removed.
+
+SKIP_FUNCTION_MACROS = YES
+
+#---------------------------------------------------------------------------
+# Configuration::additions related to external references
+#---------------------------------------------------------------------------
+
+# The TAGFILES option can be used to specify one or more tagfiles. For each
+# tag file the location of the external documentation should be added. The
+# format of a tag file without this location is as follows:
+#
+# TAGFILES = file1 file2 ...
+# Adding location for the tag files is done as follows:
+#
+# TAGFILES = file1=loc1 "file2 = loc2" ...
+# where "loc1" and "loc2" can be relative or absolute paths
+# or URLs. Note that each tag file must have a unique name (where the name does
+# NOT include the path). If a tag file is not located in the directory in which
+# doxygen is run, you must also specify the path to the tagfile here.
+
+TAGFILES = ${EIGEN_DOXY_TAGFILES}
+# "${Eigen_BINARY_DIR}/doc/eigen-unsupported.doxytags =unsupported"
+
+# When a file name is specified after GENERATE_TAGFILE, doxygen will create
+# a tag file that is based on the input files it reads.
+
+GENERATE_TAGFILE = "${Eigen_BINARY_DIR}/doc/${EIGEN_DOXY_PROJECT_NAME}.doxytags"
+
+# If the ALLEXTERNALS tag is set to YES all external classes will be listed
+# in the class index. If set to NO only the inherited external classes
+# will be listed.
+
+ALLEXTERNALS = NO
+
+# If the EXTERNAL_GROUPS tag is set to YES all external groups will be listed
+# in the modules index. If set to NO, only the current project's groups will
+# be listed.
+
+EXTERNAL_GROUPS = NO
+
+# The PERL_PATH should be the absolute path and name of the perl script
+# interpreter (i.e. the result of `which perl').
+
+PERL_PATH = /usr/bin/perl
+
+#---------------------------------------------------------------------------
+# Configuration options related to the dot tool
+#---------------------------------------------------------------------------
+
+# If the CLASS_DIAGRAMS tag is set to YES (the default) Doxygen will
+# generate a inheritance diagram (in HTML, RTF and LaTeX) for classes with base
+# or super classes. Setting the tag to NO turns the diagrams off. Note that
+# this option also works with HAVE_DOT disabled, but it is recommended to
+# install and use dot, since it yields more powerful graphs.
+
+CLASS_DIAGRAMS = YES
+
+# You can define message sequence charts within doxygen comments using the \msc
+# command. Doxygen will then run the mscgen tool (see
+# http://www.mcternan.me.uk/mscgen/) to produce the chart and insert it in the
+# documentation. The MSCGEN_PATH tag allows you to specify the directory where
+# the mscgen tool resides. If left empty the tool is assumed to be found in the
+# default search path.
+
+MSCGEN_PATH =
+
+# If set to YES, the inheritance and collaboration graphs will hide
+# inheritance and usage relations if the target is undocumented
+# or is not a class.
+
+HIDE_UNDOC_RELATIONS = NO
+
+# If you set the HAVE_DOT tag to YES then doxygen will assume the dot tool is
+# available from the path. This tool is part of Graphviz, a graph visualization
+# toolkit from AT&T and Lucent Bell Labs. The other options in this section
+# have no effect if this option is set to NO (the default)
+
+HAVE_DOT = YES
+
+# The DOT_NUM_THREADS specifies the number of dot invocations doxygen is
+# allowed to run in parallel. When set to 0 (the default) doxygen will
+# base this on the number of processors available in the system. You can set it
+# explicitly to a value larger than 0 to get control over the balance
+# between CPU load and processing speed.
+
+DOT_NUM_THREADS = 0
+
+# By default doxygen will use the Helvetica font for all dot files that
+# doxygen generates. When you want a differently looking font you can specify
+# the font name using DOT_FONTNAME. You need to make sure dot is able to find
+# the font, which can be done by putting it in a standard location or by setting
+# the DOTFONTPATH environment variable or by setting DOT_FONTPATH to the
+# directory containing the font.
+
+DOT_FONTNAME =
+
+# The DOT_FONTSIZE tag can be used to set the size of the font of dot graphs.
+# The default size is 10pt.
+
+DOT_FONTSIZE = 10
+
+# By default doxygen will tell dot to use the Helvetica font.
+# If you specify a different font using DOT_FONTNAME you can use DOT_FONTPATH to
+# set the path where dot can find it.
+
+DOT_FONTPATH =
+
+# If the CLASS_GRAPH and HAVE_DOT tags are set to YES then doxygen
+# will generate a graph for each documented class showing the direct and
+# indirect inheritance relations. Setting this tag to YES will force the
+# CLASS_DIAGRAMS tag to NO.
+
+CLASS_GRAPH = YES
+
+# If the COLLABORATION_GRAPH and HAVE_DOT tags are set to YES then doxygen
+# will generate a graph for each documented class showing the direct and
+# indirect implementation dependencies (inheritance, containment, and
+# class references variables) of the class with other documented classes.
+
+COLLABORATION_GRAPH = NO
+
+# If the GROUP_GRAPHS and HAVE_DOT tags are set to YES then doxygen
+# will generate a graph for groups, showing the direct groups dependencies
+
+GROUP_GRAPHS = NO
+
+# If the UML_LOOK tag is set to YES doxygen will generate inheritance and
+# collaboration diagrams in a style similar to the OMG's Unified Modeling
+# Language.
+
+UML_LOOK = YES
+
+# If the UML_LOOK tag is enabled, the fields and methods are shown inside
+# the class node. If there are many fields or methods and many nodes the
+# graph may become too big to be useful. The UML_LIMIT_NUM_FIELDS
+# threshold limits the number of items for each type to make the size more
+# manageable. Set this to 0 for no limit. Note that the threshold may be
+# exceeded by 50% before the limit is enforced.
+
+UML_LIMIT_NUM_FIELDS = 10
+
+# If set to YES, the inheritance and collaboration graphs will show the
+# relations between templates and their instances.
+
+TEMPLATE_RELATIONS = NO
+
+# If the ENABLE_PREPROCESSING, SEARCH_INCLUDES, INCLUDE_GRAPH, and HAVE_DOT
+# tags are set to YES then doxygen will generate a graph for each documented
+# file showing the direct and indirect include dependencies of the file with
+# other documented files.
+
+INCLUDE_GRAPH = NO
+
+# If the ENABLE_PREPROCESSING, SEARCH_INCLUDES, INCLUDED_BY_GRAPH, and
+# HAVE_DOT tags are set to YES then doxygen will generate a graph for each
+# documented header file showing the documented files that directly or
+# indirectly include this file.
+
+INCLUDED_BY_GRAPH = NO
+
+# If the CALL_GRAPH and HAVE_DOT options are set to YES then
+# doxygen will generate a call dependency graph for every global function
+# or class method. Note that enabling this option will significantly increase
+# the time of a run. So in most cases it will be better to enable call graphs
+# for selected functions only using the \callgraph command.
+
+CALL_GRAPH = NO
+
+# If the CALLER_GRAPH and HAVE_DOT tags are set to YES then
+# doxygen will generate a caller dependency graph for every global function
+# or class method. Note that enabling this option will significantly increase
+# the time of a run. So in most cases it will be better to enable caller
+# graphs for selected functions only using the \callergraph command.
+
+CALLER_GRAPH = NO
+
+# If the GRAPHICAL_HIERARCHY and HAVE_DOT tags are set to YES then doxygen
+# will generate a graphical hierarchy of all classes instead of a textual one.
+
+GRAPHICAL_HIERARCHY = NO
+
+# If the DIRECTORY_GRAPH and HAVE_DOT tags are set to YES
+# then doxygen will show the dependencies a directory has on other directories
+# in a graphical way. The dependency relations are determined by the #include
+# relations between the files in the directories.
+
+DIRECTORY_GRAPH = NO
+
+# The DOT_IMAGE_FORMAT tag can be used to set the image format of the images
+# generated by dot. Possible values are svg, png, jpg, or gif.
+# If left blank png will be used. If you choose svg you need to set
+# HTML_FILE_EXTENSION to xhtml in order to make the SVG files
+# visible in IE 9+ (other browsers do not have this requirement).
+
+DOT_IMAGE_FORMAT = png
+
+# If DOT_IMAGE_FORMAT is set to svg, then this option can be set to YES to
+# enable generation of interactive SVG images that allow zooming and panning.
+# Note that this requires a modern browser other than Internet Explorer.
+# Tested and working are Firefox, Chrome, Safari, and Opera. For IE 9+ you
+# need to set HTML_FILE_EXTENSION to xhtml in order to make the SVG files
+# visible. Older versions of IE do not have SVG support.
+
+INTERACTIVE_SVG = NO
+
+# The tag DOT_PATH can be used to specify the path where the dot tool can be
+# found. If left blank, it is assumed the dot tool can be found in the path.
+
+DOT_PATH =
+
+# The DOTFILE_DIRS tag can be used to specify one or more directories that
+# contain dot files that are included in the documentation (see the
+# \dotfile command).
+
+DOTFILE_DIRS =
+
+# The MSCFILE_DIRS tag can be used to specify one or more directories that
+# contain msc files that are included in the documentation (see the
+# \mscfile command).
+
+MSCFILE_DIRS =
+
+# The DOT_GRAPH_MAX_NODES tag can be used to set the maximum number of
+# nodes that will be shown in the graph. If the number of nodes in a graph
+# becomes larger than this value, doxygen will truncate the graph, which is
+# visualized by representing a node as a red box. Note that doxygen if the
+# number of direct children of the root node in a graph is already larger than
+# DOT_GRAPH_MAX_NODES then the graph will not be shown at all. Also note
+# that the size of a graph can be further restricted by MAX_DOT_GRAPH_DEPTH.
+
+DOT_GRAPH_MAX_NODES = 50
+
+# The MAX_DOT_GRAPH_DEPTH tag can be used to set the maximum depth of the
+# graphs generated by dot. A depth value of 3 means that only nodes reachable
+# from the root by following a path via at most 3 edges will be shown. Nodes
+# that lay further from the root node will be omitted. Note that setting this
+# option to 1 or 2 may greatly reduce the computation time needed for large
+# code bases. Also note that the size of a graph can be further restricted by
+# DOT_GRAPH_MAX_NODES. Using a depth of 0 means no depth restriction.
+
+MAX_DOT_GRAPH_DEPTH = 0
+
+# Set the DOT_TRANSPARENT tag to YES to generate images with a transparent
+# background. This is disabled by default, because dot on Windows does not
+# seem to support this out of the box. Warning: Depending on the platform used,
+# enabling this option may lead to badly anti-aliased labels on the edges of
+# a graph (i.e. they become hard to read).
+
+DOT_TRANSPARENT = NO
+
+# Set the DOT_MULTI_TARGETS tag to YES allow dot to generate multiple output
+# files in one run (i.e. multiple -o and -T options on the command line). This
+# makes dot run faster, but since only newer versions of dot (>1.8.10)
+# support this, this feature is disabled by default.
+
+DOT_MULTI_TARGETS = NO
+
+# If the GENERATE_LEGEND tag is set to YES (the default) Doxygen will
+# generate a legend page explaining the meaning of the various boxes and
+# arrows in the dot generated graphs.
+
+GENERATE_LEGEND = YES
+
+# If the DOT_CLEANUP tag is set to YES (the default) Doxygen will
+# remove the intermediate dot files that are used to generate
+# the various graphs.
+
+DOT_CLEANUP = YES
diff --git a/doc/Eigen_Silly_Professor_64x64.png b/doc/Eigen_Silly_Professor_64x64.png
new file mode 100644
index 0000000..079d45b
--- /dev/null
+++ b/doc/Eigen_Silly_Professor_64x64.png
Binary files differ
diff --git a/doc/FixedSizeVectorizable.dox b/doc/FixedSizeVectorizable.dox
new file mode 100644
index 0000000..0012465
--- /dev/null
+++ b/doc/FixedSizeVectorizable.dox
@@ -0,0 +1,38 @@
+namespace Eigen {
+
+/** \eigenManualPage TopicFixedSizeVectorizable Fixed-size vectorizable %Eigen objects
+
+The goal of this page is to explain what we mean by "fixed-size vectorizable".
+
+\section FixedSizeVectorizable_summary Executive Summary
+
+An Eigen object is called "fixed-size vectorizable" if it has fixed size and that size is a multiple of 16 bytes.
+
+Examples include:
+\li Eigen::Vector2d
+\li Eigen::Vector4d
+\li Eigen::Vector4f
+\li Eigen::Matrix2d
+\li Eigen::Matrix2f
+\li Eigen::Matrix4d
+\li Eigen::Matrix4f
+\li Eigen::Affine3d
+\li Eigen::Affine3f
+\li Eigen::Quaterniond
+\li Eigen::Quaternionf
+
+\section FixedSizeVectorizable_explanation Explanation
+
+First, "fixed-size" should be clear: an %Eigen object has fixed size if its number of rows and its number of columns are fixed at compile-time. So for example \ref Matrix3f has fixed size, but \ref MatrixXf doesn't (the opposite of fixed-size is dynamic-size).
+
+The array of coefficients of a fixed-size %Eigen object is a plain "static array", it is not dynamically allocated. For example, the data behind a \ref Matrix4f is just a "float array[16]".
+
+Fixed-size objects are typically very small, which means that we want to handle them with zero runtime overhead -- both in terms of memory usage and of speed.
+
+Now, vectorization works with 128-bit packets (e.g., SSE, AltiVec, NEON), 256-bit packets (e.g., AVX), or 512-bit packets (e.g., AVX512). Moreover, for performance reasons, these packets are most efficiently read and written if they have the same alignment as the packet size, that is 16 bytes, 32 bytes, and 64 bytes respectively.
+
+So it turns out that the best way that fixed-size %Eigen objects can be vectorized, is if their size is a multiple of 16 bytes (or more). %Eigen will then request 16-byte alignment (or more) for these objects, and henceforth rely on these objects being aligned to achieve maximal efficiency.
+
+*/
+
+}
diff --git a/doc/FunctionsTakingEigenTypes.dox b/doc/FunctionsTakingEigenTypes.dox
new file mode 100644
index 0000000..6b4e492
--- /dev/null
+++ b/doc/FunctionsTakingEigenTypes.dox
@@ -0,0 +1,217 @@
+namespace Eigen {
+
+/** \page TopicFunctionTakingEigenTypes Writing Functions Taking %Eigen Types as Parameters
+
+%Eigen's use of expression templates results in potentially every expression being of a different type. If you pass such an expression to a function taking a parameter of type Matrix, your expression will implicitly be evaluated into a temporary Matrix, which will then be passed to the function. This means that you lose the benefit of expression templates. Concretely, this has two drawbacks:
+ \li The evaluation into a temporary may be useless and inefficient;
+ \li This only allows the function to read from the expression, not to write to it.
+
+Fortunately, all this myriad of expression types have in common that they all inherit a few common, templated base classes. By letting your function take templated parameters of these base types, you can let them play nicely with %Eigen's expression templates.
+
+\eigenAutoToc
+
+\section TopicFirstExamples Some First Examples
+
+This section will provide simple examples for different types of objects %Eigen is offering. Before starting with the actual examples, we need to recapitulate which base objects we can work with (see also \ref TopicClassHierarchy).
+
+ \li MatrixBase: The common base class for all dense matrix expressions (as opposed to array expressions, as opposed to sparse and special matrix classes). Use it in functions that are meant to work only on dense matrices.
+ \li ArrayBase: The common base class for all dense array expressions (as opposed to matrix expressions, etc). Use it in functions that are meant to work only on arrays.
+ \li DenseBase: The common base class for all dense matrix expression, that is, the base class for both \c MatrixBase and \c ArrayBase. It can be used in functions that are meant to work on both matrices and arrays.
+ \li EigenBase: The base class unifying all types of objects that can be evaluated into dense matrices or arrays, for example special matrix classes such as diagonal matrices, permutation matrices, etc. It can be used in functions that are meant to work on any such general type.
+
+<b> %EigenBase Example </b><br/><br/>
+Prints the dimensions of the most generic object present in %Eigen. It could be any matrix expressions, any dense or sparse matrix and any array.
+<table class="example">
+<tr><th>Example:</th><th>Output:</th></tr>
+<tr><td>
+\include function_taking_eigenbase.cpp
+</td>
+<td>
+\verbinclude function_taking_eigenbase.out
+</td></tr></table>
+<b> %DenseBase Example </b><br/><br/>
+Prints a sub-block of the dense expression. Accepts any dense matrix or array expression, but no sparse objects and no special matrix classes such as DiagonalMatrix.
+\code
+template <typename Derived>
+void print_block(const DenseBase<Derived>& b, int x, int y, int r, int c)
+{
+ std::cout << "block: " << b.block(x,y,r,c) << std::endl;
+}
+\endcode
+<b> %ArrayBase Example </b><br/><br/>
+Prints the maximum coefficient of the array or array-expression.
+\code
+template <typename Derived>
+void print_max_coeff(const ArrayBase<Derived> &a)
+{
+ std::cout << "max: " << a.maxCoeff() << std::endl;
+}
+\endcode
+<b> %MatrixBase Example </b><br/><br/>
+Prints the inverse condition number of the given matrix or matrix-expression.
+\code
+template <typename Derived>
+void print_inv_cond(const MatrixBase<Derived>& a)
+{
+ const typename JacobiSVD<typename Derived::PlainObject>::SingularValuesType&
+ sing_vals = a.jacobiSvd().singularValues();
+ std::cout << "inv cond: " << sing_vals(sing_vals.size()-1) / sing_vals(0) << std::endl;
+}
+\endcode
+<b> Multiple templated arguments example </b><br/><br/>
+Calculate the Euclidean distance between two points.
+\code
+template <typename DerivedA,typename DerivedB>
+typename DerivedA::Scalar squaredist(const MatrixBase<DerivedA>& p1,const MatrixBase<DerivedB>& p2)
+{
+ return (p1-p2).squaredNorm();
+}
+\endcode
+Notice that we used two template parameters, one per argument. This permits the function to handle inputs of different types, e.g.,
+\code
+squaredist(v1,2*v2)
+\endcode
+where the first argument \c v1 is a vector and the second argument \c 2*v2 is an expression.
+<br/><br/>
+
+These examples are just intended to give the reader a first impression of how functions can be written which take a plain and constant Matrix or Array argument. They are also intended to give the reader an idea about the most common base classes being the optimal candidates for functions. In the next section we will look in more detail at an example and the different ways it can be implemented, while discussing each implementation's problems and advantages. For the discussion below, Matrix and Array as well as MatrixBase and ArrayBase can be exchanged and all arguments still hold.
+
+
+\section TopicUsingRefClass How to write generic, but non-templated function?
+
+In all the previous examples, the functions had to be template functions. This approach allows to write very generic code, but it is often desirable to write non templated functions and still keep some level of genericity to avoid stupid copies of the arguments. The typical example is to write functions accepting both a MatrixXf or a block of a MatrixXf. This is exactly the purpose of the Ref class. Here is a simple example:
+
+<table class="example">
+<tr><th>Example:</th><th>Output:</th></tr>
+<tr><td>
+\include function_taking_ref.cpp
+</td>
+<td>
+\verbinclude function_taking_ref.out
+</td></tr></table>
+In the first two calls to inv_cond, no copy occur because the memory layout of the arguments matches the memory layout accepted by Ref<MatrixXf>. However, in the last call, we have a generic expression that will be automatically evaluated into a temporary MatrixXf by the Ref<> object.
+
+A Ref object can also be writable. Here is an example of a function computing the covariance matrix of two input matrices where each row is an observation:
+\code
+void cov(const Ref<const MatrixXf> x, const Ref<const MatrixXf> y, Ref<MatrixXf> C)
+{
+ const float num_observations = static_cast<float>(x.rows());
+ const RowVectorXf x_mean = x.colwise().sum() / num_observations;
+ const RowVectorXf y_mean = y.colwise().sum() / num_observations;
+ C = (x.rowwise() - x_mean).transpose() * (y.rowwise() - y_mean) / num_observations;
+}
+\endcode
+and here are two examples calling cov without any copy:
+\code
+MatrixXf m1, m2, m3
+cov(m1, m2, m3);
+cov(m1.leftCols<3>(), m2.leftCols<3>(), m3.topLeftCorner<3,3>());
+\endcode
+The Ref<> class has two other optional template arguments allowing to control the kind of memory layout that can be accepted without any copy. See the class Ref documentation for the details.
+
+\section TopicPlainFunctionsWorking In which cases do functions taking plain Matrix or Array arguments work?
+
+Without using template functions, and without the Ref class, a naive implementation of the previous cov function might look like this
+\code
+MatrixXf cov(const MatrixXf& x, const MatrixXf& y)
+{
+ const float num_observations = static_cast<float>(x.rows());
+ const RowVectorXf x_mean = x.colwise().sum() / num_observations;
+ const RowVectorXf y_mean = y.colwise().sum() / num_observations;
+ return (x.rowwise() - x_mean).transpose() * (y.rowwise() - y_mean) / num_observations;
+}
+\endcode
+and contrary to what one might think at first, this implementation is fine unless you require a generic implementation that works with double matrices too and unless you do not care about temporary objects. Why is that the case? Where are temporaries involved? How can code as given below compile?
+\code
+MatrixXf x,y,z;
+MatrixXf C = cov(x,y+z);
+\endcode
+In this special case, the example is fine and will be working because both parameters are declared as \e const references. The compiler creates a temporary and evaluates the expression x+z into this temporary. Once the function is processed, the temporary is released and the result is assigned to C.
+
+\b Note: Functions taking \e const references to Matrix (or Array) can process expressions at the cost of temporaries.
+
+
+\section TopicPlainFunctionsFailing In which cases do functions taking a plain Matrix or Array argument fail?
+
+Here, we consider a slightly modified version of the function given above. This time, we do not want to return the result but pass an additional non-const parameter which allows us to store the result. A first naive implementation might look as follows.
+\code
+// Note: This code is flawed!
+void cov(const MatrixXf& x, const MatrixXf& y, MatrixXf& C)
+{
+ const float num_observations = static_cast<float>(x.rows());
+ const RowVectorXf x_mean = x.colwise().sum() / num_observations;
+ const RowVectorXf y_mean = y.colwise().sum() / num_observations;
+ C = (x.rowwise() - x_mean).transpose() * (y.rowwise() - y_mean) / num_observations;
+}
+\endcode
+When trying to execute the following code
+\code
+MatrixXf C = MatrixXf::Zero(3,6);
+cov(x,y, C.block(0,0,3,3));
+\endcode
+the compiler will fail, because it is not possible to convert the expression returned by \c MatrixXf::block() into a non-const \c MatrixXf&. This is the case because the compiler wants to protect you from writing your result to a temporary object. In this special case this protection is not intended -- we want to write to a temporary object. So how can we overcome this problem?
+
+The solution which is preferred at the moment is based on a little \em hack. One needs to pass a const reference to the matrix and internally the constness needs to be cast away. The correct implementation for C98 compliant compilers would be
+\code
+template <typename Derived, typename OtherDerived>
+void cov(const MatrixBase<Derived>& x, const MatrixBase<Derived>& y, MatrixBase<OtherDerived> const & C)
+{
+ typedef typename Derived::Scalar Scalar;
+ typedef typename internal::plain_row_type<Derived>::type RowVectorType;
+
+ const Scalar num_observations = static_cast<Scalar>(x.rows());
+
+ const RowVectorType x_mean = x.colwise().sum() / num_observations;
+ const RowVectorType y_mean = y.colwise().sum() / num_observations;
+
+ const_cast< MatrixBase<OtherDerived>& >(C) =
+ (x.rowwise() - x_mean).transpose() * (y.rowwise() - y_mean) / num_observations;
+}
+\endcode
+The implementation above does now not only work with temporary expressions but it also allows to use the function with matrices of arbitrary floating point scalar types.
+
+\b Note: The const cast hack will only work with templated functions. It will not work with the MatrixXf implementation because it is not possible to cast a Block expression to a Matrix reference!
+
+
+
+\section TopicResizingInGenericImplementations How to resize matrices in generic implementations?
+
+One might think we are done now, right? This is not completely true because in order for our covariance function to be generically applicable, we want the following code to work
+\code
+MatrixXf x = MatrixXf::Random(100,3);
+MatrixXf y = MatrixXf::Random(100,3);
+MatrixXf C;
+cov(x, y, C);
+\endcode
+This is not the case anymore, when we are using an implementation taking MatrixBase as a parameter. In general, %Eigen supports automatic resizing but it is not possible to do so on expressions. Why should resizing of a matrix Block be allowed? It is a reference to a sub-matrix and we definitely don't want to resize that. So how can we incorporate resizing if we cannot resize on MatrixBase? The solution is to resize the derived object as in this implementation.
+\code
+template <typename Derived, typename OtherDerived>
+void cov(const MatrixBase<Derived>& x, const MatrixBase<Derived>& y, MatrixBase<OtherDerived> const & C_)
+{
+ typedef typename Derived::Scalar Scalar;
+ typedef typename internal::plain_row_type<Derived>::type RowVectorType;
+
+ const Scalar num_observations = static_cast<Scalar>(x.rows());
+
+ const RowVectorType x_mean = x.colwise().sum() / num_observations;
+ const RowVectorType y_mean = y.colwise().sum() / num_observations;
+
+ MatrixBase<OtherDerived>& C = const_cast< MatrixBase<OtherDerived>& >(C_);
+
+ C.derived().resize(x.cols(),x.cols()); // resize the derived object
+ C = (x.rowwise() - x_mean).transpose() * (y.rowwise() - y_mean) / num_observations;
+}
+\endcode
+This implementation is now working for parameters being expressions and for parameters being matrices and having the wrong size. Resizing the expressions does not do any harm in this case unless they actually require resizing. That means, passing an expression with the wrong dimensions will result in a run-time error (in debug mode only) while passing expressions of the correct size will just work fine.
+
+\b Note: In the above discussion the terms Matrix and Array and MatrixBase and ArrayBase can be exchanged and all arguments still hold.
+
+\section TopicSummary Summary
+
+ - To summarize, the implementation of functions taking non-writable (const referenced) objects is not a big issue and does not lead to problematic situations in terms of compiling and running your program. However, a naive implementation is likely to introduce unnecessary temporary objects in your code. In order to avoid evaluating parameters into temporaries, pass them as (const) references to MatrixBase or ArrayBase (so templatize your function).
+
+ - Functions taking writable (non-const) parameters must take const references and cast away constness within the function body.
+
+ - Functions that take as parameters MatrixBase (or ArrayBase) objects, and potentially need to resize them (in the case where they are resizable), must call resize() on the derived class, as returned by derived().
+*/
+}
diff --git a/doc/HiPerformance.dox b/doc/HiPerformance.dox
new file mode 100644
index 0000000..9cee335
--- /dev/null
+++ b/doc/HiPerformance.dox
@@ -0,0 +1,128 @@
+
+namespace Eigen {
+
+/** \page TopicWritingEfficientProductExpression Writing efficient matrix product expressions
+
+In general achieving good performance with Eigen does no require any special effort:
+simply write your expressions in the most high level way. This is especially true
+for small fixed size matrices. For large matrices, however, it might be useful to
+take some care when writing your expressions in order to minimize useless evaluations
+and optimize the performance.
+In this page we will give a brief overview of the Eigen's internal mechanism to simplify
+and evaluate complex product expressions, and discuss the current limitations.
+In particular we will focus on expressions matching level 2 and 3 BLAS routines, i.e,
+all kind of matrix products and triangular solvers.
+
+Indeed, in Eigen we have implemented a set of highly optimized routines which are very similar
+to BLAS's ones. Unlike BLAS, those routines are made available to user via a high level and
+natural API. Each of these routines can compute in a single evaluation a wide variety of expressions.
+Given an expression, the challenge is then to map it to a minimal set of routines.
+As explained latter, this mechanism has some limitations, and knowing them will allow
+you to write faster code by making your expressions more Eigen friendly.
+
+\section GEMM General Matrix-Matrix product (GEMM)
+
+Let's start with the most common primitive: the matrix product of general dense matrices.
+In the BLAS world this corresponds to the GEMM routine. Our equivalent primitive can
+perform the following operation:
+\f$ C.noalias() += \alpha op1(A) op2(B) \f$
+where A, B, and C are column and/or row major matrices (or sub-matrices),
+alpha is a scalar value, and op1, op2 can be transpose, adjoint, conjugate, or the identity.
+When Eigen detects a matrix product, it analyzes both sides of the product to extract a
+unique scalar factor alpha, and for each side, its effective storage order, shape, and conjugation states.
+More precisely each side is simplified by iteratively removing trivial expressions such as scalar multiple,
+negation and conjugation. Transpose and Block expressions are not evaluated and they only modify the storage order
+and shape. All other expressions are immediately evaluated.
+For instance, the following expression:
+\code m1.noalias() -= s4 * (s1 * m2.adjoint() * (-(s3*m3).conjugate()*s2)) \endcode
+is automatically simplified to:
+\code m1.noalias() += (s1*s2*conj(s3)*s4) * m2.adjoint() * m3.conjugate() \endcode
+which exactly matches our GEMM routine.
+
+\subsection GEMM_Limitations Limitations
+Unfortunately, this simplification mechanism is not perfect yet and not all expressions which could be
+handled by a single GEMM-like call are correctly detected.
+<table class="manual" style="width:100%">
+<tr>
+<th>Not optimal expression</th>
+<th>Evaluated as</th>
+<th>Optimal version (single evaluation)</th>
+<th>Comments</th>
+</tr>
+<tr>
+<td>\code
+m1 += m2 * m3; \endcode</td>
+<td>\code
+temp = m2 * m3;
+m1 += temp; \endcode</td>
+<td>\code
+m1.noalias() += m2 * m3; \endcode</td>
+<td>Use .noalias() to tell Eigen the result and right-hand-sides do not alias.
+ Otherwise the product m2 * m3 is evaluated into a temporary.</td>
+</tr>
+<tr class="alt">
+<td></td>
+<td></td>
+<td>\code
+m1.noalias() += s1 * (m2 * m3); \endcode</td>
+<td>This is a special feature of Eigen. Here the product between a scalar
+ and a matrix product does not evaluate the matrix product but instead it
+ returns a matrix product expression tracking the scalar scaling factor. <br>
+ Without this optimization, the matrix product would be evaluated into a
+ temporary as in the next example.</td>
+</tr>
+<tr>
+<td>\code
+m1.noalias() += (m2 * m3).adjoint(); \endcode</td>
+<td>\code
+temp = m2 * m3;
+m1 += temp.adjoint(); \endcode</td>
+<td>\code
+m1.noalias() += m3.adjoint()
+* * m2.adjoint(); \endcode</td>
+<td>This is because the product expression has the EvalBeforeNesting bit which
+ enforces the evaluation of the product by the Tranpose expression.</td>
+</tr>
+<tr class="alt">
+<td>\code
+m1 = m1 + m2 * m3; \endcode</td>
+<td>\code
+temp = m2 * m3;
+m1 = m1 + temp; \endcode</td>
+<td>\code m1.noalias() += m2 * m3; \endcode</td>
+<td>Here there is no way to detect at compile time that the two m1 are the same,
+ and so the matrix product will be immediately evaluated.</td>
+</tr>
+<tr>
+<td>\code
+m1.noalias() = m4 + m2 * m3; \endcode</td>
+<td>\code
+temp = m2 * m3;
+m1 = m4 + temp; \endcode</td>
+<td>\code
+m1 = m4;
+m1.noalias() += m2 * m3; \endcode</td>
+<td>First of all, here the .noalias() in the first expression is useless because
+ m2*m3 will be evaluated anyway. However, note how this expression can be rewritten
+ so that no temporary is required. (tip: for very small fixed size matrix
+ it is slightly better to rewrite it like this: m1.noalias() = m2 * m3; m1 += m4;</td>
+</tr>
+<tr class="alt">
+<td>\code
+m1.noalias() += (s1*m2).block(..) * m3; \endcode</td>
+<td>\code
+temp = (s1*m2).block(..);
+m1 += temp * m3; \endcode</td>
+<td>\code
+m1.noalias() += s1 * m2.block(..) * m3; \endcode</td>
+<td>This is because our expression analyzer is currently not able to extract trivial
+ expressions nested in a Block expression. Therefore the nested scalar
+ multiple cannot be properly extracted.</td>
+</tr>
+</table>
+
+Of course all these remarks hold for all other kind of products involving triangular or selfadjoint matrices.
+
+*/
+
+}
diff --git a/doc/InplaceDecomposition.dox b/doc/InplaceDecomposition.dox
new file mode 100644
index 0000000..cb1c6d4
--- /dev/null
+++ b/doc/InplaceDecomposition.dox
@@ -0,0 +1,115 @@
+namespace Eigen {
+
+/** \eigenManualPage InplaceDecomposition Inplace matrix decompositions
+
+Starting from %Eigen 3.3, the LU, Cholesky, and QR decompositions can operate \em inplace, that is, directly within the given input matrix.
+This feature is especially useful when dealing with huge matrices, and or when the available memory is very limited (embedded systems).
+
+To this end, the respective decomposition class must be instantiated with a Ref<> matrix type, and the decomposition object must be constructed with the input matrix as argument. As an example, let us consider an inplace LU decomposition with partial pivoting.
+
+Let's start with the basic inclusions, and declaration of a 2x2 matrix \c A:
+
+<table class="example">
+<tr><th>code</th><th>output</th></tr>
+<tr>
+ <td>\snippet TutorialInplaceLU.cpp init
+ </td>
+ <td>\snippet TutorialInplaceLU.out init
+ </td>
+</tr>
+</table>
+
+No surprise here! Then, let's declare our inplace LU object \c lu, and check the content of the matrix \c A:
+
+<table class="example">
+<tr>
+ <td>\snippet TutorialInplaceLU.cpp declaration
+ </td>
+ <td>\snippet TutorialInplaceLU.out declaration
+ </td>
+</tr>
+</table>
+
+Here, the \c lu object computes and stores the \c L and \c U factors within the memory held by the matrix \c A.
+The coefficients of \c A have thus been destroyed during the factorization, and replaced by the L and U factors as one can verify:
+
+<table class="example">
+<tr>
+ <td>\snippet TutorialInplaceLU.cpp matrixLU
+ </td>
+ <td>\snippet TutorialInplaceLU.out matrixLU
+ </td>
+</tr>
+</table>
+
+Then, one can use the \c lu object as usual, for instance to solve the Ax=b problem:
+<table class="example">
+<tr>
+ <td>\snippet TutorialInplaceLU.cpp solve
+ </td>
+ <td>\snippet TutorialInplaceLU.out solve
+ </td>
+</tr>
+</table>
+
+Here, since the content of the original matrix \c A has been lost, we had to declared a new matrix \c A0 to verify the result.
+
+Since the memory is shared between \c A and \c lu, modifying the matrix \c A will make \c lu invalid.
+This can easily be verified by modifying the content of \c A and trying to solve the initial problem again:
+
+<table class="example">
+<tr>
+ <td>\snippet TutorialInplaceLU.cpp modifyA
+ </td>
+ <td>\snippet TutorialInplaceLU.out modifyA
+ </td>
+</tr>
+</table>
+
+Note that there is no shared pointer under the hood, it is the \b responsibility \b of \b the \b user to keep the input matrix \c A in life as long as \c lu is living.
+
+If one wants to update the factorization with the modified A, one has to call the compute method as usual:
+<table class="example">
+<tr>
+ <td>\snippet TutorialInplaceLU.cpp recompute
+ </td>
+ <td>\snippet TutorialInplaceLU.out recompute
+ </td>
+</tr>
+</table>
+
+Note that calling compute does not change the memory which is referenced by the \c lu object. Therefore, if the compute method is called with another matrix \c A1 different than \c A, then the content of \c A1 won't be modified. This is still the content of \c A that will be used to store the L and U factors of the matrix \c A1.
+This can easily be verified as follows:
+<table class="example">
+<tr>
+ <td>\snippet TutorialInplaceLU.cpp recompute_bis0
+ </td>
+ <td>\snippet TutorialInplaceLU.out recompute_bis0
+ </td>
+</tr>
+</table>
+The matrix \c A1 is unchanged, and one can thus solve A1*x=b, and directly check the residual without any copy of \c A1:
+<table class="example">
+<tr>
+ <td>\snippet TutorialInplaceLU.cpp recompute_bis1
+ </td>
+ <td>\snippet TutorialInplaceLU.out recompute_bis1
+ </td>
+</tr>
+</table>
+
+
+Here is the list of matrix decompositions supporting this inplace mechanism:
+
+- class LLT
+- class LDLT
+- class PartialPivLU
+- class FullPivLU
+- class HouseholderQR
+- class ColPivHouseholderQR
+- class FullPivHouseholderQR
+- class CompleteOrthogonalDecomposition
+
+*/
+
+}
\ No newline at end of file
diff --git a/doc/InsideEigenExample.dox b/doc/InsideEigenExample.dox
new file mode 100644
index 0000000..4af185d
--- /dev/null
+++ b/doc/InsideEigenExample.dox
@@ -0,0 +1,500 @@
+namespace Eigen {
+
+/** \page TopicInsideEigenExample What happens inside Eigen, on a simple example
+
+\eigenAutoToc
+
+<hr>
+
+
+Consider the following example program:
+
+\code
+#include<Eigen/Core>
+
+int main()
+{
+ int size = 50;
+ // VectorXf is a vector of floats, with dynamic size.
+ Eigen::VectorXf u(size), v(size), w(size);
+ u = v + w;
+}
+\endcode
+
+The goal of this page is to understand how Eigen compiles it, assuming that SSE2 vectorization is enabled (GCC option -msse2).
+
+\section WhyInteresting Why it's interesting
+
+Maybe you think, that the above example program is so simple, that compiling it shouldn't involve anything interesting. So before starting, let us explain what is nontrivial in compiling it correctly -- that is, producing optimized code -- so that the complexity of Eigen, that we'll explain here, is really useful.
+
+Look at the line of code
+\code
+ u = v + w; // (*)
+\endcode
+
+The first important thing about compiling it, is that the arrays should be traversed only once, like
+\code
+ for(int i = 0; i < size; i++) u[i] = v[i] + w[i];
+\endcode
+The problem is that if we make a naive C++ library where the VectorXf class has an operator+ returning a VectorXf, then the line of code (*) will amount to:
+\code
+ VectorXf tmp = v + w;
+ VectorXf u = tmp;
+\endcode
+Obviously, the introduction of the temporary \a tmp here is useless. It has a very bad effect on performance, first because the creation of \a tmp requires a dynamic memory allocation in this context, and second as there are now two for loops:
+\code
+ for(int i = 0; i < size; i++) tmp[i] = v[i] + w[i];
+ for(int i = 0; i < size; i++) u[i] = tmp[i];
+\endcode
+Traversing the arrays twice instead of once is terrible for performance, as it means that we do many redundant memory accesses.
+
+The second important thing about compiling the above program, is to make correct use of SSE2 instructions. Notice that Eigen also supports AltiVec and that all the discussion that we make here applies also to AltiVec.
+
+SSE2, like AltiVec, is a set of instructions allowing to perform computations on packets of 128 bits at once. Since a float is 32 bits, this means that SSE2 instructions can handle 4 floats at once. This means that, if correctly used, they can make our computation go up to 4x faster.
+
+However, in the above program, we have chosen size=50, so our vectors consist of 50 float's, and 50 is not a multiple of 4. This means that we cannot hope to do all of that computation using SSE2 instructions. The second best thing, to which we should aim, is to handle the 48 first coefficients with SSE2 instructions, since 48 is the biggest multiple of 4 below 50, and then handle separately, without SSE2, the 49th and 50th coefficients. Something like this:
+
+\code
+ for(int i = 0; i < 4*(size/4); i+=4) u.packet(i) = v.packet(i) + w.packet(i);
+ for(int i = 4*(size/4); i < size; i++) u[i] = v[i] + w[i];
+\endcode
+
+So let us look line by line at our example program, and let's follow Eigen as it compiles it.
+
+\section ConstructingVectors Constructing vectors
+
+Let's analyze the first line:
+
+\code
+ Eigen::VectorXf u(size), v(size), w(size);
+\endcode
+
+First of all, VectorXf is the following typedef:
+\code
+ typedef Matrix<float, Dynamic, 1> VectorXf;
+\endcode
+
+The class template Matrix is declared in src/Core/util/ForwardDeclarations.h with 6 template parameters, but the last 3 are automatically determined by the first 3. So you don't need to worry about them for now. Here, Matrix\<float, Dynamic, 1\> means a matrix of floats, with a dynamic number of rows and 1 column.
+
+The Matrix class inherits a base class, MatrixBase. Don't worry about it, for now it suffices to say that MatrixBase is what unifies matrices/vectors and all the expressions types -- more on that below.
+
+When we do
+\code
+ Eigen::VectorXf u(size);
+\endcode
+the constructor that is called is Matrix::Matrix(int), in src/Core/Matrix.h. Besides some assertions, all it does is to construct the \a m_storage member, which is of type DenseStorage\<float, Dynamic, Dynamic, 1\>.
+
+You may wonder, isn't it overengineering to have the storage in a separate class? The reason is that the Matrix class template covers all kinds of matrices and vector: both fixed-size and dynamic-size. The storage method is not the same in these two cases. For fixed-size, the matrix coefficients are stored as a plain member array. For dynamic-size, the coefficients will be stored as a pointer to a dynamically-allocated array. Because of this, we need to abstract storage away from the Matrix class. That's DenseStorage.
+
+Let's look at this constructor, in src/Core/DenseStorage.h. You can see that there are many partial template specializations of DenseStorages here, treating separately the cases where dimensions are Dynamic or fixed at compile-time. The partial specialization that we are looking at is:
+\code
+template<typename T, int Cols_> class DenseStorage<T, Dynamic, Dynamic, Cols_>
+\endcode
+
+Here, the constructor called is DenseStorage::DenseStorage(int size, int rows, int columns)
+with size=50, rows=50, columns=1.
+
+Here is this constructor:
+\code
+inline DenseStorage(int size, int rows, int) : m_data(internal::aligned_new<T>(size)), m_rows(rows) {}
+\endcode
+
+Here, the \a m_data member is the actual array of coefficients of the matrix. As you see, it is dynamically allocated. Rather than calling new[] or malloc(), as you can see, we have our own internal::aligned_new defined in src/Core/util/Memory.h. What it does is that if vectorization is enabled, then it uses a platform-specific call to allocate a 128-bit-aligned array, as that is very useful for vectorization with both SSE2 and AltiVec. If vectorization is disabled, it amounts to the standard new[].
+
+As you can see, the constructor also sets the \a m_rows member to \a size. Notice that there is no \a m_columns member: indeed, in this partial specialization of DenseStorage, we know the number of columns at compile-time, since the Cols_ template parameter is different from Dynamic. Namely, in our case, Cols_ is 1, which is to say that our vector is just a matrix with 1 column. Hence, there is no need to store the number of columns as a runtime variable.
+
+When you call VectorXf::data() to get the pointer to the array of coefficients, it returns DenseStorage::data() which returns the \a m_data member.
+
+When you call VectorXf::size() to get the size of the vector, this is actually a method in the base class MatrixBase. It determines that the vector is a column-vector, since ColsAtCompileTime==1 (this comes from the template parameters in the typedef VectorXf). It deduces that the size is the number of rows, so it returns VectorXf::rows(), which returns DenseStorage::rows(), which returns the \a m_rows member, which was set to \a size by the constructor.
+
+\section ConstructionOfSumXpr Construction of the sum expression
+
+Now that our vectors are constructed, let's move on to the next line:
+
+\code
+u = v + w;
+\endcode
+
+The executive summary is that operator+ returns a "sum of vectors" expression, but doesn't actually perform the computation. It is the operator=, whose call occurs thereafter, that does the computation.
+
+Let us now see what Eigen does when it sees this:
+
+\code
+v + w
+\endcode
+
+Here, v and w are of type VectorXf, which is a typedef for a specialization of Matrix (as we explained above), which is a subclass of MatrixBase. So what is being called is
+
+\code
+MatrixBase::operator+(const MatrixBase&)
+\endcode
+
+The return type of this operator is
+\code
+CwiseBinaryOp<internal::scalar_sum_op<float>, VectorXf, VectorXf>
+\endcode
+The CwiseBinaryOp class is our first encounter with an expression template. As we said, the operator+ doesn't by itself perform any computation, it just returns an abstract "sum of vectors" expression. Since there are also "difference of vectors" and "coefficient-wise product of vectors" expressions, we unify them all as "coefficient-wise binary operations", which we abbreviate as "CwiseBinaryOp". "Coefficient-wise" means that the operations is performed coefficient by coefficient. "binary" means that there are two operands -- we are adding two vectors with one another.
+
+Now you might ask, what if we did something like
+
+\code
+v + w + u;
+\endcode
+
+The first v + w would return a CwiseBinaryOp as above, so in order for this to compile, we'd need to define an operator+ also in the class CwiseBinaryOp... at this point it starts looking like a nightmare: are we going to have to define all operators in each of the expression classes (as you guessed, CwiseBinaryOp is only one of many) ? This looks like a dead end!
+
+The solution is that CwiseBinaryOp itself, as well as Matrix and all the other expression types, is a subclass of MatrixBase. So it is enough to define once and for all the operators in class MatrixBase.
+
+Since MatrixBase is the common base class of different subclasses, the aspects that depend on the subclass must be abstracted from MatrixBase. This is called polymorphism.
+
+The classical approach to polymorphism in C++ is by means of virtual functions. This is dynamic polymorphism. Here we don't want dynamic polymorphism because the whole design of Eigen is based around the assumption that all the complexity, all the abstraction, gets resolved at compile-time. This is crucial: if the abstraction can't get resolved at compile-time, Eigen's compile-time optimization mechanisms become useless, not to mention that if that abstraction has to be resolved at runtime it'll incur an overhead by itself.
+
+Here, what we want is to have a single class MatrixBase as the base of many subclasses, in such a way that each MatrixBase object (be it a matrix, or vector, or any kind of expression) knows at compile-time (as opposed to run-time) of which particular subclass it is an object (i.e. whether it is a matrix, or an expression, and what kind of expression).
+
+The solution is the <a href="http://en.wikipedia.org/wiki/Curiously_Recurring_Template_Pattern">Curiously Recurring Template Pattern</a>. Let's do the break now. Hopefully you can read this wikipedia page during the break if needed, but it won't be allowed during the exam.
+
+In short, MatrixBase takes a template parameter \a Derived. Whenever we define a subclass Subclass, we actually make Subclass inherit MatrixBase\<Subclass\>. The point is that different subclasses inherit different MatrixBase types. Thanks to this, whenever we have an object of a subclass, and we call on it some MatrixBase method, we still remember even from inside the MatrixBase method which particular subclass we're talking about.
+
+This means that we can put almost all the methods and operators in the base class MatrixBase, and have only the bare minimum in the subclasses. If you look at the subclasses in Eigen, like for instance the CwiseBinaryOp class, they have very few methods. There are coeff() and sometimes coeffRef() methods for access to the coefficients, there are rows() and cols() methods returning the number of rows and columns, but there isn't much more than that. All the meat is in MatrixBase, so it only needs to be coded once for all kinds of expressions, matrices, and vectors.
+
+So let's end this digression and come back to the piece of code from our example program that we were currently analyzing,
+
+\code
+v + w
+\endcode
+
+Now that MatrixBase is a good friend, let's write fully the prototype of the operator+ that gets called here (this code is from src/Core/MatrixBase.h):
+
+\code
+template<typename Derived>
+class MatrixBase
+{
+ // ...
+
+ template<typename OtherDerived>
+ const CwiseBinaryOp<internal::scalar_sum_op<typename internal::traits<Derived>::Scalar>, Derived, OtherDerived>
+ operator+(const MatrixBase<OtherDerived> &other) const;
+
+ // ...
+};
+\endcode
+
+Here of course, \a Derived and \a OtherDerived are VectorXf.
+
+As we said, CwiseBinaryOp is also used for other operations such as substration, so it takes another template parameter determining the operation that will be applied to coefficients. This template parameter is a functor, that is, a class in which we have an operator() so it behaves like a function. Here, the functor used is internal::scalar_sum_op. It is defined in src/Core/Functors.h.
+
+Let us now explain the internal::traits here. The internal::scalar_sum_op class takes one template parameter: the type of the numbers to handle. Here of course we want to pass the scalar type (a.k.a. numeric type) of VectorXf, which is \c float. How do we determine which is the scalar type of \a Derived ? Throughout Eigen, all matrix and expression types define a typedef \a Scalar which gives its scalar type. For example, VectorXf::Scalar is a typedef for \c float. So here, if life was easy, we could find the numeric type of \a Derived as just
+\code
+typename Derived::Scalar
+\endcode
+Unfortunately, we can't do that here, as the compiler would complain that the type Derived hasn't yet been defined. So we use a workaround: in src/Core/util/ForwardDeclarations.h, we declared (not defined!) all our subclasses, like Matrix, and we also declared the following class template:
+\code
+template<typename T> struct internal::traits;
+\endcode
+In src/Core/Matrix.h, right \em before the definition of class Matrix, we define a partial specialization of internal::traits for T=Matrix\<any template parameters\>. In this specialization of internal::traits, we define the Scalar typedef. So when we actually define Matrix, it is legal to refer to "typename internal::traits\<Matrix\>::Scalar".
+
+Anyway, we have declared our operator+. In our case, where \a Derived and \a OtherDerived are VectorXf, the above declaration amounts to:
+\code
+class MatrixBase<VectorXf>
+{
+ // ...
+
+ const CwiseBinaryOp<internal::scalar_sum_op<float>, VectorXf, VectorXf>
+ operator+(const MatrixBase<VectorXf> &other) const;
+
+ // ...
+};
+\endcode
+
+Let's now jump to src/Core/CwiseBinaryOp.h to see how it is defined. As you can see there, all it does is to return a CwiseBinaryOp object, and this object is just storing references to the left-hand-side and right-hand-side expressions -- here, these are the vectors \a v and \a w. Well, the CwiseBinaryOp object is also storing an instance of the (empty) functor class, but you shouldn't worry about it as that is a minor implementation detail.
+
+Thus, the operator+ hasn't performed any actual computation. To summarize, the operation \a v + \a w just returned an object of type CwiseBinaryOp which did nothing else than just storing references to \a v and \a w.
+
+\section Assignment The assignment
+
+<div class="warningbox">
+<strong>PLEASE HELP US IMPROVING THIS SECTION.</strong>
+This page reflects how %Eigen worked until 3.2, but since %Eigen 3.3 the assignment is more sophisticated as it involves an Assignment expression, and the creation of so called evaluator which are responsible for the evaluation of each kind of expressions.
+</div>
+
+At this point, the expression \a v + \a w has finished evaluating, so, in the process of compiling the line of code
+\code
+u = v + w;
+\endcode
+we now enter the operator=.
+
+What operator= is being called here? The vector u is an object of class VectorXf, i.e. Matrix. In src/Core/Matrix.h, inside the definition of class Matrix, we see this:
+\code
+ template<typename OtherDerived>
+ inline Matrix& operator=(const MatrixBase<OtherDerived>& other)
+ {
+ eigen_assert(m_storage.data()!=0 && "you cannot use operator= with a non initialized matrix (instead use set()");
+ return Base::operator=(other.derived());
+ }
+\endcode
+Here, Base is a typedef for MatrixBase\<Matrix\>. So, what is being called is the operator= of MatrixBase. Let's see its prototype in src/Core/MatrixBase.h:
+\code
+ template<typename OtherDerived>
+ Derived& operator=(const MatrixBase<OtherDerived>& other);
+\endcode
+Here, \a Derived is VectorXf (since u is a VectorXf) and \a OtherDerived is CwiseBinaryOp. More specifically, as explained in the previous section, \a OtherDerived is:
+\code
+CwiseBinaryOp<internal::scalar_sum_op<float>, VectorXf, VectorXf>
+\endcode
+So the full prototype of the operator= being called is:
+\code
+VectorXf& MatrixBase<VectorXf>::operator=(const MatrixBase<CwiseBinaryOp<internal::scalar_sum_op<float>, VectorXf, VectorXf> > & other);
+\endcode
+This operator= literally reads "copying a sum of two VectorXf's into another VectorXf".
+
+Let's now look at the implementation of this operator=. It resides in the file src/Core/Assign.h.
+
+What we can see there is:
+\code
+template<typename Derived>
+template<typename OtherDerived>
+inline Derived& MatrixBase<Derived>
+ ::operator=(const MatrixBase<OtherDerived>& other)
+{
+ return internal::assign_selector<Derived,OtherDerived>::run(derived(), other.derived());
+}
+\endcode
+
+OK so our next task is to understand internal::assign_selector :)
+
+Here is its declaration (all that is still in the same file src/Core/Assign.h)
+\code
+template<typename Derived, typename OtherDerived,
+ bool EvalBeforeAssigning = int(OtherDerived::Flags) & EvalBeforeAssigningBit,
+ bool NeedToTranspose = Derived::IsVectorAtCompileTime
+ && OtherDerived::IsVectorAtCompileTime
+ && int(Derived::RowsAtCompileTime) == int(OtherDerived::ColsAtCompileTime)
+ && int(Derived::ColsAtCompileTime) == int(OtherDerived::RowsAtCompileTime)
+ && int(Derived::SizeAtCompileTime) != 1>
+struct internal::assign_selector;
+\endcode
+
+So internal::assign_selector takes 4 template parameters, but the 2 last ones are automatically determined by the 2 first ones.
+
+EvalBeforeAssigning is here to enforce the EvalBeforeAssigningBit. As explained <a href="TopicLazyEvaluation.html">here</a>, certain expressions have this flag which makes them automatically evaluate into temporaries before assigning them to another expression. This is the case of the Product expression, in order to avoid strange aliasing effects when doing "m = m * m;" However, of course here our CwiseBinaryOp expression doesn't have the EvalBeforeAssigningBit: we said since the beginning that we didn't want a temporary to be introduced here. So if you go to src/Core/CwiseBinaryOp.h, you'll see that the Flags in internal::traits\<CwiseBinaryOp\> don't include the EvalBeforeAssigningBit. The Flags member of CwiseBinaryOp is then imported from the internal::traits by the EIGEN_GENERIC_PUBLIC_INTERFACE macro. Anyway, here the template parameter EvalBeforeAssigning has the value \c false.
+
+NeedToTranspose is here for the case where the user wants to copy a row-vector into a column-vector. We allow this as a special exception to the general rule that in assignments we require the dimesions to match. Anyway, here both the left-hand and right-hand sides are column vectors, in the sense that ColsAtCompileTime is equal to 1. So NeedToTranspose is \c false too.
+
+So, here we are in the partial specialization:
+\code
+internal::assign_selector<Derived, OtherDerived, false, false>
+\endcode
+
+Here's how it is defined:
+\code
+template<typename Derived, typename OtherDerived>
+struct internal::assign_selector<Derived,OtherDerived,false,false> {
+ static Derived& run(Derived& dst, const OtherDerived& other) { return dst.lazyAssign(other.derived()); }
+};
+\endcode
+
+OK so now our next job is to understand how lazyAssign works :)
+
+\code
+template<typename Derived>
+template<typename OtherDerived>
+inline Derived& MatrixBase<Derived>
+ ::lazyAssign(const MatrixBase<OtherDerived>& other)
+{
+ EIGEN_STATIC_ASSERT_SAME_MATRIX_SIZE(Derived,OtherDerived)
+ eigen_assert(rows() == other.rows() && cols() == other.cols());
+ internal::assign_impl<Derived, OtherDerived>::run(derived(),other.derived());
+ return derived();
+}
+\endcode
+
+What do we see here? Some assertions, and then the only interesting line is:
+\code
+ internal::assign_impl<Derived, OtherDerived>::run(derived(),other.derived());
+\endcode
+
+OK so now we want to know what is inside internal::assign_impl.
+
+Here is its declaration:
+\code
+template<typename Derived1, typename Derived2,
+ int Vectorization = internal::assign_traits<Derived1, Derived2>::Vectorization,
+ int Unrolling = internal::assign_traits<Derived1, Derived2>::Unrolling>
+struct internal::assign_impl;
+\endcode
+Again, internal::assign_selector takes 4 template parameters, but the 2 last ones are automatically determined by the 2 first ones.
+
+These two parameters \a Vectorization and \a Unrolling are determined by a helper class internal::assign_traits. Its job is to determine which vectorization strategy to use (that is \a Vectorization) and which unrolling strategy to use (that is \a Unrolling).
+
+We'll not enter into the details of how these strategies are chosen (this is in the implementation of internal::assign_traits at the top of the same file). Let's just say that here \a Vectorization has the value \a LinearVectorization, and \a Unrolling has the value \a NoUnrolling (the latter is obvious since our vectors have dynamic size so there's no way to unroll the loop at compile-time).
+
+So the partial specialization of internal::assign_impl that we're looking at is:
+\code
+internal::assign_impl<Derived1, Derived2, LinearVectorization, NoUnrolling>
+\endcode
+
+Here is how it's defined:
+\code
+template<typename Derived1, typename Derived2>
+struct internal::assign_impl<Derived1, Derived2, LinearVectorization, NoUnrolling>
+{
+ static void run(Derived1 &dst, const Derived2 &src)
+ {
+ const int size = dst.size();
+ const int packetSize = internal::packet_traits<typename Derived1::Scalar>::size;
+ const int alignedStart = internal::assign_traits<Derived1,Derived2>::DstIsAligned ? 0
+ : internal::first_aligned(&dst.coeffRef(0), size);
+ const int alignedEnd = alignedStart + ((size-alignedStart)/packetSize)*packetSize;
+
+ for(int index = 0; index < alignedStart; index++)
+ dst.copyCoeff(index, src);
+
+ for(int index = alignedStart; index < alignedEnd; index += packetSize)
+ {
+ dst.template copyPacket<Derived2, Aligned, internal::assign_traits<Derived1,Derived2>::SrcAlignment>(index, src);
+ }
+
+ for(int index = alignedEnd; index < size; index++)
+ dst.copyCoeff(index, src);
+ }
+};
+\endcode
+
+Here's how it works. \a LinearVectorization means that the left-hand and right-hand side expression can be accessed linearly i.e. you can refer to their coefficients by one integer \a index, as opposed to having to refer to its coefficients by two integers \a row, \a column.
+
+As we said at the beginning, vectorization works with blocks of 4 floats. Here, \a PacketSize is 4.
+
+There are two potential problems that we need to deal with:
+\li first, vectorization works much better if the packets are 128-bit-aligned. This is especially important for write access. So when writing to the coefficients of \a dst, we want to group these coefficients by packets of 4 such that each of these packets is 128-bit-aligned. In general, this requires to skip a few coefficients at the beginning of \a dst. This is the purpose of \a alignedStart. We then copy these first few coefficients one by one, not by packets. However, in our case, the \a dst expression is a VectorXf and remember that in the construction of the vectors we allocated aligned arrays. Thanks to \a DstIsAligned, Eigen remembers that without having to do any runtime check, so \a alignedStart is zero and this part is avoided altogether.
+\li second, the number of coefficients to copy is not in general a multiple of \a packetSize. Here, there are 50 coefficients to copy and \a packetSize is 4. So we'll have to copy the last 2 coefficients one by one, not by packets. Here, \a alignedEnd is 48.
+
+Now come the actual loops.
+
+First, the vectorized part: the 48 first coefficients out of 50 will be copied by packets of 4:
+\code
+ for(int index = alignedStart; index < alignedEnd; index += packetSize)
+ {
+ dst.template copyPacket<Derived2, Aligned, internal::assign_traits<Derived1,Derived2>::SrcAlignment>(index, src);
+ }
+\endcode
+
+What is copyPacket? It is defined in src/Core/Coeffs.h:
+\code
+template<typename Derived>
+template<typename OtherDerived, int StoreMode, int LoadMode>
+inline void MatrixBase<Derived>::copyPacket(int index, const MatrixBase<OtherDerived>& other)
+{
+ eigen_internal_assert(index >= 0 && index < size());
+ derived().template writePacket<StoreMode>(index,
+ other.derived().template packet<LoadMode>(index));
+}
+\endcode
+
+OK, what are writePacket() and packet() here?
+
+First, writePacket() here is a method on the left-hand side VectorXf. So we go to src/Core/Matrix.h to look at its definition:
+\code
+template<int StoreMode>
+inline void writePacket(int index, const PacketScalar& x)
+{
+ internal::pstoret<Scalar, PacketScalar, StoreMode>(m_storage.data() + index, x);
+}
+\endcode
+Here, \a StoreMode is \a #Aligned, indicating that we are doing a 128-bit-aligned write access, \a PacketScalar is a type representing a "SSE packet of 4 floats" and internal::pstoret is a function writing such a packet in memory. Their definitions are architecture-specific, we find them in src/Core/arch/SSE/PacketMath.h:
+
+The line in src/Core/arch/SSE/PacketMath.h that determines the PacketScalar type (via a typedef in Matrix.h) is:
+\code
+template<> struct internal::packet_traits<float> { typedef __m128 type; enum {size=4}; };
+\endcode
+Here, __m128 is a SSE-specific type. Notice that the enum \a size here is what was used to define \a packetSize above.
+
+And here is the implementation of internal::pstoret:
+\code
+template<> inline void internal::pstore(float* to, const __m128& from) { _mm_store_ps(to, from); }
+\endcode
+Here, __mm_store_ps is a SSE-specific intrinsic function, representing a single SSE instruction. The difference between internal::pstore and internal::pstoret is that internal::pstoret is a dispatcher handling both the aligned and unaligned cases, you find its definition in src/Core/GenericPacketMath.h:
+\code
+template<typename Scalar, typename Packet, int LoadMode>
+inline void internal::pstoret(Scalar* to, const Packet& from)
+{
+ if(LoadMode == Aligned)
+ internal::pstore(to, from);
+ else
+ internal::pstoreu(to, from);
+}
+\endcode
+
+OK, that explains how writePacket() works. Now let's look into the packet() call. Remember that we are analyzing this line of code inside copyPacket():
+\code
+derived().template writePacket<StoreMode>(index,
+ other.derived().template packet<LoadMode>(index));
+\endcode
+
+Here, \a other is our sum expression \a v + \a w. The .derived() is just casting from MatrixBase to the subclass which here is CwiseBinaryOp. So let's go to src/Core/CwiseBinaryOp.h:
+\code
+class CwiseBinaryOp
+{
+ // ...
+ template<int LoadMode>
+ inline PacketScalar packet(int index) const
+ {
+ return m_functor.packetOp(m_lhs.template packet<LoadMode>(index), m_rhs.template packet<LoadMode>(index));
+ }
+};
+\endcode
+Here, \a m_lhs is the vector \a v, and \a m_rhs is the vector \a w. So the packet() function here is Matrix::packet(). The template parameter \a LoadMode is \a #Aligned. So we're looking at
+\code
+class Matrix
+{
+ // ...
+ template<int LoadMode>
+ inline PacketScalar packet(int index) const
+ {
+ return internal::ploadt<Scalar, LoadMode>(m_storage.data() + index);
+ }
+};
+\endcode
+We let you look up the definition of internal::ploadt in GenericPacketMath.h and the internal::pload in src/Core/arch/SSE/PacketMath.h. It is very similar to the above for internal::pstore.
+
+Let's go back to CwiseBinaryOp::packet(). Once the packets from the vectors \a v and \a w have been returned, what does this function do? It calls m_functor.packetOp() on them. What is m_functor? Here we must remember what particular template specialization of CwiseBinaryOp we're dealing with:
+\code
+CwiseBinaryOp<internal::scalar_sum_op<float>, VectorXf, VectorXf>
+\endcode
+So m_functor is an object of the empty class internal::scalar_sum_op<float>. As we mentioned above, don't worry about why we constructed an object of this empty class at all -- it's an implementation detail, the point is that some other functors need to store member data.
+
+Anyway, internal::scalar_sum_op is defined in src/Core/Functors.h:
+\code
+template<typename Scalar> struct internal::scalar_sum_op EIGEN_EMPTY_STRUCT {
+ inline const Scalar operator() (const Scalar& a, const Scalar& b) const { return a + b; }
+ template<typename PacketScalar>
+ inline const PacketScalar packetOp(const PacketScalar& a, const PacketScalar& b) const
+ { return internal::padd(a,b); }
+};
+\endcode
+As you can see, all what packetOp() does is to call internal::padd on the two packets. Here is the definition of internal::padd from src/Core/arch/SSE/PacketMath.h:
+\code
+template<> inline __m128 internal::padd(const __m128& a, const __m128& b) { return _mm_add_ps(a,b); }
+\endcode
+Here, _mm_add_ps is a SSE-specific intrinsic function, representing a single SSE instruction.
+
+To summarize, the loop
+\code
+ for(int index = alignedStart; index < alignedEnd; index += packetSize)
+ {
+ dst.template copyPacket<Derived2, Aligned, internal::assign_traits<Derived1,Derived2>::SrcAlignment>(index, src);
+ }
+\endcode
+has been compiled to the following code: for \a index going from 0 to the 11 ( = 48/4 - 1), read the i-th packet (of 4 floats) from the vector v and the i-th packet from the vector w using two __mm_load_ps SSE instructions, then add them together using a __mm_add_ps instruction, then store the result using a __mm_store_ps instruction.
+
+There remains the second loop handling the last few (here, the last 2) coefficients:
+\code
+ for(int index = alignedEnd; index < size; index++)
+ dst.copyCoeff(index, src);
+\endcode
+However, it works just like the one we just explained, it is just simpler because there is no SSE vectorization involved here. copyPacket() becomes copyCoeff(), packet() becomes coeff(), writePacket() becomes coeffRef(). If you followed us this far, you can probably understand this part by yourself.
+
+We see that all the C++ abstraction of Eigen goes away during compilation and that we indeed are precisely controlling which assembly instructions we emit. Such is the beauty of C++! Since we have such precise control over the emitted assembly instructions, but such complex logic to choose the right instructions, we can say that Eigen really behaves like an optimizing compiler. If you prefer, you could say that Eigen behaves like a script for the compiler. In a sense, C++ template metaprogramming is scripting the compiler -- and it's been shown that this scripting language is Turing-complete. See <a href="http://en.wikipedia.org/wiki/Template_metaprogramming"> Wikipedia</a>.
+
+*/
+
+}
diff --git a/doc/LeastSquares.dox b/doc/LeastSquares.dox
new file mode 100644
index 0000000..ddbf38d
--- /dev/null
+++ b/doc/LeastSquares.dox
@@ -0,0 +1,75 @@
+namespace Eigen {
+
+/** \eigenManualPage LeastSquares Solving linear least squares systems
+
+This page describes how to solve linear least squares systems using %Eigen. An overdetermined system
+of equations, say \a Ax = \a b, has no solutions. In this case, it makes sense to search for the
+vector \a x which is closest to being a solution, in the sense that the difference \a Ax - \a b is
+as small as possible. This \a x is called the least square solution (if the Euclidean norm is used).
+
+The three methods discussed on this page are the SVD decomposition, the QR decomposition and normal
+equations. Of these, the SVD decomposition is generally the most accurate but the slowest, normal
+equations is the fastest but least accurate, and the QR decomposition is in between.
+
+\eigenAutoToc
+
+
+\section LeastSquaresSVD Using the SVD decomposition
+
+The \link BDCSVD::solve() solve() \endlink method in the BDCSVD class can be directly used to
+solve linear squares systems. It is not enough to compute only the singular values (the default for
+this class); you also need the singular vectors but the thin SVD decomposition suffices for
+computing least squares solutions:
+
+<table class="example">
+<tr><th>Example:</th><th>Output:</th></tr>
+<tr>
+ <td>\include TutorialLinAlgSVDSolve.cpp </td>
+ <td>\verbinclude TutorialLinAlgSVDSolve.out </td>
+</tr>
+</table>
+
+This is example from the page \link TutorialLinearAlgebra Linear algebra and decompositions \endlink.
+If you just need to solve the least squares problem, but are not interested in the SVD per se, a
+faster alternative method is CompleteOrthogonalDecomposition.
+
+
+\section LeastSquaresQR Using the QR decomposition
+
+The solve() method in QR decomposition classes also computes the least squares solution. There are
+three QR decomposition classes: HouseholderQR (no pivoting, fast but unstable if your matrix is
+not rull rank), ColPivHouseholderQR (column pivoting, thus a bit slower but more stable) and
+FullPivHouseholderQR (full pivoting, so slowest and slightly more stable than ColPivHouseholderQR).
+Here is an example with column pivoting:
+
+<table class="example">
+<tr><th>Example:</th><th>Output:</th></tr>
+<tr>
+ <td>\include LeastSquaresQR.cpp </td>
+ <td>\verbinclude LeastSquaresQR.out </td>
+</tr>
+</table>
+
+
+\section LeastSquaresNormalEquations Using normal equations
+
+Finding the least squares solution of \a Ax = \a b is equivalent to solving the normal equation
+<i>A</i><sup>T</sup><i>Ax</i> = <i>A</i><sup>T</sup><i>b</i>. This leads to the following code
+
+<table class="example">
+<tr><th>Example:</th><th>Output:</th></tr>
+<tr>
+ <td>\include LeastSquaresNormalEquations.cpp </td>
+ <td>\verbinclude LeastSquaresNormalEquations.out </td>
+</tr>
+</table>
+
+This method is usually the fastest, especially when \a A is "tall and skinny". However, if the
+matrix \a A is even mildly ill-conditioned, this is not a good method, because the condition number
+of <i>A</i><sup>T</sup><i>A</i> is the square of the condition number of \a A. This means that you
+lose roughly twice as many digits of accuracy using the normal equation, compared to the more stable
+methods mentioned above.
+
+*/
+
+}
\ No newline at end of file
diff --git a/doc/Manual.dox b/doc/Manual.dox
new file mode 100644
index 0000000..84f0db6
--- /dev/null
+++ b/doc/Manual.dox
@@ -0,0 +1,192 @@
+
+// This file strutures pages and modules into a convenient hierarchical structure.
+
+namespace Eigen {
+
+/** \page UserManual_CustomizingEigen Extending/Customizing Eigen
+ %Eigen can be extended in several ways, for instance, by defining global methods, by inserting custom methods within main %Eigen's classes through the \ref TopicCustomizing_Plugins "plugin" mechanism, by adding support to \ref TopicCustomizing_CustomScalar "custom scalar types" etc. See below for the respective sub-topics.
+ - \subpage TopicCustomizing_Plugins
+ - \subpage TopicCustomizing_InheritingMatrix
+ - \subpage TopicCustomizing_CustomScalar
+ - \subpage TopicCustomizing_NullaryExpr
+ - \subpage TopicNewExpressionType
+ \sa \ref TopicPreprocessorDirectives
+*/
+
+
+/** \page UserManual_Generalities General topics
+ - \subpage TopicFunctionTakingEigenTypes
+ - \subpage TopicPreprocessorDirectives
+ - \subpage TopicAssertions
+ - \subpage TopicMultiThreading
+ - \subpage TopicUsingBlasLapack
+ - \subpage TopicUsingIntelMKL
+ - \subpage TopicCUDA
+ - \subpage TopicPitfalls
+ - \subpage TopicTemplateKeyword
+ - \subpage UserManual_UnderstandingEigen
+ - \subpage TopicCMakeGuide
+*/
+
+/** \page UserManual_UnderstandingEigen Understanding Eigen
+ - \subpage TopicInsideEigenExample
+ - \subpage TopicClassHierarchy
+ - \subpage TopicLazyEvaluation
+*/
+
+/** \page UnclassifiedPages Unclassified pages
+ - \subpage TopicResizing
+ - \subpage TopicVectorization
+ - \subpage TopicEigenExpressionTemplates
+ - \subpage TopicScalarTypes
+ - \subpage GettingStarted
+ - \subpage TutorialSparse_example_details
+ - \subpage TopicWritingEfficientProductExpression
+ - \subpage Experimental
+*/
+
+
+/** \defgroup Support_modules Support modules
+ * Category of modules which add support for external libraries.
+ */
+
+
+/** \defgroup DenseMatrixManipulation_chapter Dense matrix and array manipulation */
+/** \defgroup DenseMatrixManipulation_Alignement Alignment issues */
+/** \defgroup DenseMatrixManipulation_Reference Reference */
+
+/** \addtogroup TutorialMatrixClass
+ \ingroup DenseMatrixManipulation_chapter */
+/** \addtogroup TutorialMatrixArithmetic
+ \ingroup DenseMatrixManipulation_chapter */
+/** \addtogroup TutorialArrayClass
+ \ingroup DenseMatrixManipulation_chapter */
+/** \addtogroup TutorialBlockOperations
+ \ingroup DenseMatrixManipulation_chapter */
+/** \addtogroup TutorialSlicingIndexing
+ \ingroup DenseMatrixManipulation_chapter */
+/** \addtogroup TutorialAdvancedInitialization
+ \ingroup DenseMatrixManipulation_chapter */
+/** \addtogroup TutorialReductionsVisitorsBroadcasting
+ \ingroup DenseMatrixManipulation_chapter */
+/** \addtogroup TutorialReshape
+ \ingroup DenseMatrixManipulation_chapter */
+/** \addtogroup TutorialSTL
+ \ingroup DenseMatrixManipulation_chapter */
+/** \addtogroup TutorialMapClass
+ \ingroup DenseMatrixManipulation_chapter */
+/** \addtogroup TopicAliasing
+ \ingroup DenseMatrixManipulation_chapter */
+/** \addtogroup TopicStorageOrders
+ \ingroup DenseMatrixManipulation_chapter */
+
+/** \addtogroup DenseMatrixManipulation_Alignement
+ \ingroup DenseMatrixManipulation_chapter */
+/** \addtogroup TopicUnalignedArrayAssert
+ \ingroup DenseMatrixManipulation_Alignement */
+/** \addtogroup TopicFixedSizeVectorizable
+ \ingroup DenseMatrixManipulation_Alignement */
+/** \addtogroup TopicStructHavingEigenMembers
+ \ingroup DenseMatrixManipulation_Alignement */
+/** \addtogroup TopicStlContainers
+ \ingroup DenseMatrixManipulation_Alignement */
+/** \addtogroup TopicPassingByValue
+ \ingroup DenseMatrixManipulation_Alignement */
+/** \addtogroup TopicWrongStackAlignment
+ \ingroup DenseMatrixManipulation_Alignement */
+
+/** \addtogroup DenseMatrixManipulation_Reference
+ \ingroup DenseMatrixManipulation_chapter */
+/** \addtogroup Core_Module
+ \ingroup DenseMatrixManipulation_Reference */
+/** \addtogroup Jacobi_Module
+ \ingroup DenseMatrixManipulation_Reference */
+/** \addtogroup Householder_Module
+ \ingroup DenseMatrixManipulation_Reference */
+
+/** \addtogroup CoeffwiseMathFunctions
+ \ingroup DenseMatrixManipulation_chapter */
+
+/** \addtogroup QuickRefPage
+ \ingroup DenseMatrixManipulation_chapter */
+
+
+/** \defgroup DenseLinearSolvers_chapter Dense linear problems and decompositions */
+/** \defgroup DenseLinearSolvers_Reference Reference */
+
+/** \addtogroup TutorialLinearAlgebra
+ \ingroup DenseLinearSolvers_chapter */
+/** \addtogroup TopicLinearAlgebraDecompositions
+ \ingroup DenseLinearSolvers_chapter */
+/** \addtogroup LeastSquares
+ \ingroup DenseLinearSolvers_chapter */
+/** \addtogroup InplaceDecomposition
+ \ingroup DenseLinearSolvers_chapter */
+/** \addtogroup DenseDecompositionBenchmark
+ \ingroup DenseLinearSolvers_chapter */
+
+/** \addtogroup DenseLinearSolvers_Reference
+ \ingroup DenseLinearSolvers_chapter */
+/** \addtogroup Cholesky_Module
+ \ingroup DenseLinearSolvers_Reference */
+/** \addtogroup LU_Module
+ \ingroup DenseLinearSolvers_Reference */
+/** \addtogroup QR_Module
+ \ingroup DenseLinearSolvers_Reference */
+/** \addtogroup SVD_Module
+ \ingroup DenseLinearSolvers_Reference*/
+/** \addtogroup Eigenvalues_Module
+ \ingroup DenseLinearSolvers_Reference */
+
+
+
+
+/** \defgroup Sparse_chapter Sparse linear algebra */
+/** \defgroup Sparse_Reference Reference */
+
+/** \addtogroup TutorialSparse
+ \ingroup Sparse_chapter */
+/** \addtogroup TopicSparseSystems
+ \ingroup Sparse_chapter */
+/** \addtogroup MatrixfreeSolverExample
+ \ingroup Sparse_chapter */
+
+/** \addtogroup Sparse_Reference
+ \ingroup Sparse_chapter */
+/** \addtogroup SparseCore_Module
+ \ingroup Sparse_Reference */
+/** \addtogroup OrderingMethods_Module
+ \ingroup Sparse_Reference */
+/** \addtogroup SparseCholesky_Module
+ \ingroup Sparse_Reference */
+/** \addtogroup SparseLU_Module
+ \ingroup Sparse_Reference */
+/** \addtogroup SparseQR_Module
+ \ingroup Sparse_Reference */
+/** \addtogroup IterativeLinearSolvers_Module
+ \ingroup Sparse_Reference */
+/** \addtogroup Sparse_Module
+ \ingroup Sparse_Reference */
+/** \addtogroup Support_modules
+ \ingroup Sparse_Reference */
+
+/** \addtogroup SparseQuickRefPage
+ \ingroup Sparse_chapter */
+
+
+/** \defgroup Geometry_chapter Geometry */
+/** \defgroup Geometry_Reference Reference */
+
+/** \addtogroup TutorialGeometry
+ \ingroup Geometry_chapter */
+
+/** \addtogroup Geometry_Reference
+ \ingroup Geometry_chapter */
+/** \addtogroup Geometry_Module
+ \ingroup Geometry_Reference */
+/** \addtogroup Splines_Module
+ \ingroup Geometry_Reference */
+
+/** \internal \brief Namespace containing low-level routines from the %Eigen library. */
+namespace internal {}
+}
diff --git a/doc/MatrixfreeSolverExample.dox b/doc/MatrixfreeSolverExample.dox
new file mode 100644
index 0000000..3efa292
--- /dev/null
+++ b/doc/MatrixfreeSolverExample.dox
@@ -0,0 +1,20 @@
+
+namespace Eigen {
+
+/**
+
+\eigenManualPage MatrixfreeSolverExample Matrix-free solvers
+
+Iterative solvers such as ConjugateGradient and BiCGSTAB can be used in a matrix free context. To this end, user must provide a wrapper class inheriting EigenBase<> and implementing the following methods:
+ - \c Index \c rows() and \c Index \c cols(): returns number of rows and columns respectively
+ - \c operator* with your type and an %Eigen dense column vector (its actual implementation goes in a specialization of the internal::generic_product_impl class)
+
+\c Eigen::internal::traits<> must also be specialized for the wrapper type.
+
+Here is a complete example wrapping an Eigen::SparseMatrix:
+\include matrixfree_cg.cpp
+Output: \verbinclude matrixfree_cg.out
+
+*/
+
+}
\ No newline at end of file
diff --git a/doc/NewExpressionType.dox b/doc/NewExpressionType.dox
new file mode 100644
index 0000000..c2f2433
--- /dev/null
+++ b/doc/NewExpressionType.dox
@@ -0,0 +1,143 @@
+namespace Eigen {
+
+/** \page TopicNewExpressionType Adding a new expression type
+
+<!--<span style="font-size:130%; color:red; font-weight: 900;"></span>-->
+\warning
+Disclaimer: this page is tailored to very advanced users who are not afraid of dealing with some %Eigen's internal aspects.
+In most cases, a custom expression can be avoided by either using custom \ref MatrixBase::unaryExpr "unary" or \ref MatrixBase::binaryExpr "binary" functors,
+while extremely complex matrix manipulations can be achieved by a nullary functors as described in the \ref TopicCustomizing_NullaryExpr "previous page".
+
+This page describes with the help of an example how to implement a new
+light-weight expression type in %Eigen. This consists of three parts:
+the expression type itself, a traits class containing compile-time
+information about the expression, and the evaluator class which is
+used to evaluate the expression to a matrix.
+
+\b TO \b DO: Write a page explaining the design, with details on
+vectorization etc., and refer to that page here.
+
+
+\eigenAutoToc
+
+\section TopicSetting The setting
+
+A circulant matrix is a matrix where each column is the same as the
+column to the left, except that it is cyclically shifted downwards.
+For example, here is a 4-by-4 circulant matrix:
+\f[ \begin{bmatrix}
+ 1 & 8 & 4 & 2 \\
+ 2 & 1 & 8 & 4 \\
+ 4 & 2 & 1 & 8 \\
+ 8 & 4 & 2 & 1
+\end{bmatrix} \f]
+A circulant matrix is uniquely determined by its first column. We wish
+to write a function \c makeCirculant which, given the first column,
+returns an expression representing the circulant matrix.
+
+For simplicity, we restrict the \c makeCirculant function to dense
+matrices. It may make sense to also allow arrays, or sparse matrices,
+but we will not do so here. We also do not want to support
+vectorization.
+
+
+\section TopicPreamble Getting started
+
+We will present the file implementing the \c makeCirculant function
+part by part. We start by including the appropriate header files and
+forward declaring the expression class, which we will call
+\c Circulant. The \c makeCirculant function will return an object of
+this type. The class \c Circulant is in fact a class template; the
+template argument \c ArgType refers to the type of the vector passed
+to the \c makeCirculant function.
+
+\include make_circulant.cpp.preamble
+
+
+\section TopicTraits The traits class
+
+For every expression class \c X, there should be a traits class
+\c Traits<X> in the \c Eigen::internal namespace containing
+information about \c X known as compile time.
+
+As explained in \ref TopicSetting, we designed the \c Circulant
+expression class to refer to dense matrices. The entries of the
+circulant matrix have the same type as the entries of the vector
+passed to the \c makeCirculant function. The type used to index the
+entries is also the same. Again for simplicity, we will only return
+column-major matrices. Finally, the circulant matrix is a square
+matrix (number of rows equals number of columns), and the number of
+rows equals the number of rows of the column vector passed to the
+\c makeCirculant function. If this is a dynamic-size vector, then the
+size of the circulant matrix is not known at compile-time.
+
+This leads to the following code:
+
+\include make_circulant.cpp.traits
+
+
+\section TopicExpression The expression class
+
+The next step is to define the expression class itself. In our case,
+we want to inherit from \c MatrixBase in order to expose the interface
+for dense matrices. In the constructor, we check that we are passed a
+column vector (see \ref TopicAssertions) and we store the vector from
+which we are going to build the circulant matrix in the member
+variable \c m_arg. Finally, the expression class should compute the
+size of the corresponding circulant matrix. As explained above, this
+is a square matrix with as many columns as the vector used to
+construct the matrix.
+
+\b TO \b DO: What about the \c Nested typedef? It seems to be
+necessary; is this only temporary?
+
+\include make_circulant.cpp.expression
+
+
+\section TopicEvaluator The evaluator
+
+The last big fragment implements the evaluator for the \c Circulant
+expression. The evaluator computes the entries of the circulant
+matrix; this is done in the \c .coeff() member function. The entries
+are computed by finding the corresponding entry of the vector from
+which the circulant matrix is constructed. Getting this entry may
+actually be non-trivial when the circulant matrix is constructed from
+a vector which is given by a complicated expression, so we use the
+evaluator which corresponds to the vector.
+
+The \c CoeffReadCost constant records the cost of computing an entry
+of the circulant matrix; we ignore the index computation and say that
+this is the same as the cost of computing an entry of the vector from
+which the circulant matrix is constructed.
+
+In the constructor, we save the evaluator for the column vector which
+defined the circulant matrix. We also save the size of that vector;
+remember that we can query an expression object to find the size but
+not the evaluator.
+
+\include make_circulant.cpp.evaluator
+
+
+\section TopicEntry The entry point
+
+After all this, the \c makeCirculant function is very simple. It
+simply creates an expression object and returns it.
+
+\include make_circulant.cpp.entry
+
+
+\section TopicMain A simple main function for testing
+
+Finally, a short \c main function that shows how the \c makeCirculant
+function can be called.
+
+\include make_circulant.cpp.main
+
+If all the fragments are combined, the following output is produced,
+showing that the program works as expected:
+
+\include make_circulant.out
+
+*/
+}
+
diff --git a/doc/Overview.dox b/doc/Overview.dox
new file mode 100644
index 0000000..43a1287
--- /dev/null
+++ b/doc/Overview.dox
@@ -0,0 +1,28 @@
+namespace Eigen {
+
+/** \mainpage notitle
+
+This is the API documentation for Eigen3. You can <a href="eigen-doc.tgz">download</a> it as a tgz archive for offline reading.
+
+For a first contact with Eigen, the best place is to have a look at the \link GettingStarted getting started \endlink page that show you how to write and compile your first program with Eigen.
+
+Then, the \b quick \b reference \b pages give you a quite complete description of the API in a very condensed format that is specially useful to recall the syntax of a particular feature, or to have a quick look at the API. They currently cover the two following feature sets, and more will come in the future:
+ - \link QuickRefPage [QuickRef] Dense matrix and array manipulations \endlink
+ - \link SparseQuickRefPage [QuickRef] Sparse linear algebra \endlink
+
+You're a MatLab user? There is also a <a href="AsciiQuickReference.txt">short ASCII reference</a> with Matlab translations.
+
+The \b main \b documentation is organized into \em chapters covering different domains of features.
+They are themselves composed of \em user \em manual pages describing the different features in a comprehensive way, and \em reference pages that gives you access to the API documentation through the related Eigen's \em modules and \em classes.
+
+Under the \subpage UserManual_CustomizingEigen section, you will find discussions and examples on extending %Eigen's features and supporting custom scalar types.
+
+Under the \subpage UserManual_Generalities section, you will find documentation on more general topics such as preprocessor directives, controlling assertions, multi-threading, MKL support, some Eigen's internal insights, and much more...
+
+Finally, do not miss the search engine, useful to quickly get to the documentation of a given class or function.
+
+Want more? Checkout the <a href="unsupported/index.html">\em unsupported \em modules </a> documentation.
+
+*/
+
+}
diff --git a/doc/PassingByValue.dox b/doc/PassingByValue.dox
new file mode 100644
index 0000000..9254fe6
--- /dev/null
+++ b/doc/PassingByValue.dox
@@ -0,0 +1,40 @@
+namespace Eigen {
+
+/** \eigenManualPage TopicPassingByValue Passing Eigen objects by value to functions
+
+Passing objects by value is almost always a very bad idea in C++, as this means useless copies, and one should pass them by reference instead.
+
+With %Eigen, this is even more important: passing \ref TopicFixedSizeVectorizable "fixed-size vectorizable Eigen objects" by value is not only inefficient, it can be illegal or make your program crash! And the reason is that these %Eigen objects have alignment modifiers that aren't respected when they are passed by value.
+
+For example, a function like this, where \c v is passed by value:
+
+\code
+void my_function(Eigen::Vector2d v);
+\endcode
+
+needs to be rewritten as follows, passing \c v by const reference:
+
+\code
+void my_function(const Eigen::Vector2d& v);
+\endcode
+
+Likewise if you have a class having an %Eigen object as member:
+
+\code
+struct Foo
+{
+ Eigen::Vector2d v;
+};
+void my_function(Foo v);
+\endcode
+
+This function also needs to be rewritten like this:
+\code
+void my_function(const Foo& v);
+\endcode
+
+Note that on the other hand, there is no problem with functions that return objects by value.
+
+*/
+
+}
diff --git a/doc/Pitfalls.dox b/doc/Pitfalls.dox
new file mode 100644
index 0000000..85282bd
--- /dev/null
+++ b/doc/Pitfalls.dox
@@ -0,0 +1,149 @@
+namespace Eigen {
+
+/** \page TopicPitfalls Common pitfalls
+
+
+\section TopicPitfalls_template_keyword Compilation error with template methods
+
+See this \link TopicTemplateKeyword page \endlink.
+
+
+\section TopicPitfalls_aliasing Aliasing
+
+Don't miss this \link TopicAliasing page \endlink on aliasing,
+especially if you got wrong results in statements where the destination appears on the right hand side of the expression.
+
+
+\section TopicPitfalls_alignment_issue Alignment Issues (runtime assertion)
+
+%Eigen does explicit vectorization, and while that is appreciated by many users, that also leads to some issues in special situations where data alignment is compromised.
+Indeed, prior to C++17, C++ does not have quite good enough support for explicit data alignment.
+In that case your program hits an assertion failure (that is, a "controlled crash") with a message that tells you to consult this page:
+\code
+http://eigen.tuxfamily.org/dox/group__TopicUnalignedArrayAssert.html
+\endcode
+Have a look at \link TopicUnalignedArrayAssert it \endlink and see for yourself if that's something that you can cope with.
+It contains detailed information about how to deal with each known cause for that issue.
+
+Now what if you don't care about vectorization and so don't want to be annoyed with these alignment issues? Then read \link getrid how to get rid of them \endlink.
+
+
+\section TopicPitfalls_auto_keyword C++11 and the auto keyword
+
+In short: do not use the auto keywords with %Eigen's expressions, unless you are 100% sure about what you are doing. In particular, do not use the auto keyword as a replacement for a \c Matrix<> type. Here is an example:
+
+\code
+MatrixXd A, B;
+auto C = A*B;
+for(...) { ... w = C * v; ...}
+\endcode
+
+In this example, the type of C is not a \c MatrixXd but an abstract expression representing a matrix product and storing references to \c A and \c B.
+Therefore, the product of \c A*B will be carried out multiple times, once per iteration of the for loop.
+Moreover, if the coefficients of `A` or `B` change during the iteration, then `C` will evaluate to different values as in the following example:
+
+\code
+MatrixXd A = ..., B = ...;
+auto C = A*B;
+MatrixXd R1 = C;
+A = ...;
+MatrixXd R2 = C;
+\endcode
+for which we end up with `R1` ≠ `R2`.
+
+
+Here is another example leading to a segfault:
+\code
+auto C = ((A+B).eval()).transpose();
+// do something with C
+\endcode
+The problem is that \c eval() returns a temporary object (in this case a \c MatrixXd) which is then referenced by the \c Transpose<> expression.
+However, this temporary is deleted right after the first line, and then the \c C expression references a dead object.
+One possible fix consists in applying \c eval() on the whole expression:
+\code
+auto C = (A+B).transpose().eval();
+\endcode
+
+The same issue might occur when sub expressions are automatically evaluated by %Eigen as in the following example:
+\code
+VectorXd u, v;
+auto C = u + (A*v).normalized();
+// do something with C
+\endcode
+Here the \c normalized() method has to evaluate the expensive product \c A*v to avoid evaluating it twice.
+Again, one possible fix is to call \c .eval() on the whole expression:
+\code
+auto C = (u + (A*v).normalized()).eval();
+\endcode
+In this case, \c C will be a regular \c VectorXd object.
+Note that DenseBase::eval() is smart enough to avoid copies when the underlying expression is already a plain \c Matrix<>.
+
+
+\section TopicPitfalls_header_issues Header Issues (failure to compile)
+
+With all libraries, one must check the documentation for which header to include.
+The same is true with %Eigen, but slightly worse: with %Eigen, a method in a class may require an additional \c \#include over what the class itself requires!
+For example, if you want to use the \c cross() method on a vector (it computes a cross-product) then you need to:
+\code
+#include<Eigen/Geometry>
+\endcode
+We try to always document this, but do tell us if we forgot an occurrence.
+
+
+\section TopicPitfalls_ternary_operator Ternary operator
+
+In short: avoid the use of the ternary operator <code>(COND ? THEN : ELSE)</code> with %Eigen's expressions for the \c THEN and \c ELSE statements.
+To see why, let's consider the following example:
+\code
+Vector3f A;
+A << 1, 2, 3;
+Vector3f B = ((1 < 0) ? (A.reverse()) : A);
+\endcode
+This example will return <code>B = 3, 2, 1</code>. Do you see why?
+The reason is that in c++ the type of the \c ELSE statement is inferred from the type of the \c THEN expression such that both match.
+Since \c THEN is a <code>Reverse<Vector3f></code>, the \c ELSE statement A is converted to a <code>Reverse<Vector3f></code>, and the compiler thus generates:
+\code
+Vector3f B = ((1 < 0) ? (A.reverse()) : Reverse<Vector3f>(A));
+\endcode
+In this very particular case, a workaround would be to call A.reverse().eval() for the \c THEN statement, but the safest and fastest is really to avoid this ternary operator with %Eigen's expressions and use a if/else construct.
+
+
+\section TopicPitfalls_pass_by_value Pass-by-value
+
+If you don't know why passing-by-value is wrong with %Eigen, read this \link TopicPassingByValue page \endlink first.
+
+While you may be extremely careful and use care to make sure that all of your code that explicitly uses %Eigen types is pass-by-reference you have to watch out for templates which define the argument types at compile time.
+
+If a template has a function that takes arguments pass-by-value, and the relevant template parameter ends up being an %Eigen type, then you will of course have the same alignment problems that you would in an explicitly defined function passing %Eigen types by reference.
+
+Using %Eigen types with other third party libraries or even the STL can present the same problem.
+<code>boost::bind</code> for example uses pass-by-value to store arguments in the returned functor.
+This will of course be a problem.
+
+There are at least two ways around this:
+ - If the value you are passing is guaranteed to be around for the life of the functor, you can use boost::ref() to wrap the value as you pass it to boost::bind. Generally this is not a solution for values on the stack as if the functor ever gets passed to a lower or independent scope, the object may be gone by the time it's attempted to be used.
+ - The other option is to make your functions take a reference counted pointer like boost::shared_ptr as the argument. This avoids needing to worry about managing the lifetime of the object being passed.
+
+
+\section TopicPitfalls_matrix_bool Matrices with boolean coefficients
+
+The current behaviour of using \c Matrix with boolean coefficients is inconsistent and likely to change in future versions of Eigen, so please use it carefully!
+
+A simple example for such an inconsistency is
+
+\code
+template<int Size>
+void foo() {
+ Eigen::Matrix<bool, Size, Size> A, B, C;
+ A.setOnes();
+ B.setOnes();
+
+ C = A * B - A * B;
+ std::cout << C << "\n";
+}
+\endcode
+
+since calling \c foo<3>() prints the zero matrix while calling \c foo<10>() prints the identity matrix.
+
+*/
+}
diff --git a/doc/PreprocessorDirectives.dox b/doc/PreprocessorDirectives.dox
new file mode 100644
index 0000000..d6024dc
--- /dev/null
+++ b/doc/PreprocessorDirectives.dox
@@ -0,0 +1,168 @@
+namespace Eigen {
+
+/** \page TopicPreprocessorDirectives Preprocessor directives
+
+You can control some aspects of %Eigen by defining the preprocessor tokens using \c \#define. These macros
+should be defined before any %Eigen headers are included. Often they are best set in the project options.
+
+This page lists the preprocessor tokens recognized by %Eigen.
+
+\eigenAutoToc
+
+
+\section TopicPreprocessorDirectivesMajor Macros with major effects
+
+These macros have a major effect and typically break the API (Application Programming Interface) and/or the
+ABI (Application Binary Interface). This can be rather dangerous: if parts of your program are compiled with
+one option, and other parts (or libraries that you use) are compiled with another option, your program may
+fail to link or exhibit subtle bugs. Nevertheless, these options can be useful for people who know what they
+are doing.
+
+ - \b EIGEN2_SUPPORT and \b EIGEN2_SUPPORT_STAGEnn_xxx are disabled starting from the 3.3 release.
+ Defining one of these will raise a compile-error. If you need to compile Eigen2 code,
+ <a href="http://eigen.tuxfamily.org/index.php?title=Eigen2">check this site</a>.
+ - \b EIGEN_DEFAULT_DENSE_INDEX_TYPE - the type for column and row indices in matrices, vectors and array
+ (DenseBase::Index). Set to \c std::ptrdiff_t by default.
+ - \b EIGEN_DEFAULT_IO_FORMAT - the IOFormat to use when printing a matrix if no %IOFormat is specified.
+ Defaults to the %IOFormat constructed by the default constructor IOFormat::IOFormat().
+ - \b EIGEN_INITIALIZE_MATRICES_BY_ZERO - if defined, all entries of newly constructed matrices and arrays are
+ initialized to zero, as are new entries in matrices and arrays after resizing. Not defined by default.
+ \warning The unary (resp. binary) constructor of \c 1x1 (resp. \c 2x1 or \c 1x2) fixed size matrices is
+ always interpreted as an initialization constructor where the argument(s) are the coefficient values
+ and not the sizes. For instance, \code Vector2d v(2,1); \endcode will create a vector with coeficients [2,1],
+ and \b not a \c 2x1 vector initialized with zeros (i.e., [0,0]). If such cases might occur, then it is
+ recommended to use the default constructor with a explicit call to resize:
+ \code
+ Matrix<?,SizeAtCompileTime,1> v;
+ v.resize(size);
+ Matrix<?,RowsAtCompileTime,ColsAtCompileTime> m;
+ m.resize(rows,cols);
+ \endcode
+ - \b EIGEN_INITIALIZE_MATRICES_BY_NAN - if defined, all entries of newly constructed matrices and arrays are
+ initialized to NaN, as are new entries in matrices and arrays after resizing. This option is especially
+ useful for debugging purpose, though a memory tool like <a href="http://valgrind.org/">valgrind</a> is
+ preferable. Not defined by default.
+ \warning See the documentation of \c EIGEN_INITIALIZE_MATRICES_BY_ZERO for a discussion on a limitations
+ of these macros when applied to \c 1x1, \c 1x2, and \c 2x1 fixed-size matrices.
+ - \b EIGEN_NO_AUTOMATIC_RESIZING - if defined, the matrices (or arrays) on both sides of an assignment
+ <tt>a = b</tt> have to be of the same size; otherwise, %Eigen automatically resizes \c a so that it is of
+ the correct size. Not defined by default.
+
+
+\section TopicPreprocessorDirectivesCppVersion C++ standard features
+
+By default, %Eigen strive to automatically detect and enable language features at compile-time based on
+the information provided by the compiler.
+
+ - \b EIGEN_MAX_CPP_VER - disables usage of C++ features requiring a version greater than EIGEN_MAX_CPP_VER.
+ Possible values are: 14, 17, etc. If not defined (the default), %Eigen enables all features supported
+ by the compiler.
+
+Individual features can be explicitly enabled or disabled by defining the following token to 0 or 1 respectively.
+For instance, one might limit the C++ version to C++14 by defining EIGEN_MAX_CPP_VER=14, but still enable C99 math
+functions by defining EIGEN_HAS_C99_MATH=1.
+
+ - \b EIGEN_HAS_C99_MATH - controls the usage of C99 math functions such as erf, erfc, lgamma, etc.
+ - \b EIGEN_HAS_STD_RESULT_OF - defines whether std::result_of is supported
+ - \b EIGEN_NO_IO - Disables any usage and support for `<iostreams>`.
+
+\section TopicPreprocessorDirectivesAssertions Assertions
+
+The %Eigen library contains many assertions to guard against programming errors, both at compile time and at
+run time. However, these assertions do cost time and can thus be turned off.
+
+ - \b EIGEN_NO_DEBUG - disables %Eigen's assertions if defined. Not defined by default, unless the
+ \c NDEBUG macro is defined (this is a standard C++ macro which disables all asserts).
+ - \b EIGEN_NO_STATIC_ASSERT - if defined, compile-time static assertions are replaced by runtime assertions;
+ this saves compilation time. Not defined by default.
+ - \b eigen_assert - macro with one argument that is used inside %Eigen for assertions. By default, it is
+ basically defined to be \c assert, which aborts the program if the assertion is violated. Redefine this
+ macro if you want to do something else, like throwing an exception.
+ - \b EIGEN_MPL2_ONLY - disable non MPL2 compatible features, or in other words disable the features which
+ are still under the LGPL.
+
+
+\section TopicPreprocessorDirectivesPerformance Alignment, vectorization and performance tweaking
+
+ - \b \c EIGEN_MALLOC_ALREADY_ALIGNED - Can be set to 0 or 1 to tell whether default system \c malloc already
+ returns aligned buffers. In not defined, then this information is automatically deduced from the compiler
+ and system preprocessor tokens.
+ - \b \c EIGEN_MAX_ALIGN_BYTES - Must be a power of two, or 0. Defines an upper bound on the memory boundary in bytes on which dynamically and statically allocated data may be aligned by %Eigen. If not defined, a default value is automatically computed based on architecture, compiler, and OS.
+ This option is typically used to enforce binary compatibility between code/libraries compiled with different SIMD options. For instance, one may compile AVX code and enforce ABI compatibility with existing SSE code by defining \c EIGEN_MAX_ALIGN_BYTES=16. In the other way round, since by default AVX implies 32 bytes alignment for best performance, one can compile SSE code to be ABI compatible with AVX code by defining \c EIGEN_MAX_ALIGN_BYTES=32.
+ - \b \c EIGEN_MAX_STATIC_ALIGN_BYTES - Same as \c EIGEN_MAX_ALIGN_BYTES but for statically allocated data only. By default, if only \c EIGEN_MAX_ALIGN_BYTES is defined, then \c EIGEN_MAX_STATIC_ALIGN_BYTES == \c EIGEN_MAX_ALIGN_BYTES, otherwise a default value is automatically computed based on architecture, compiler, and OS (can be smaller than the default value of EIGEN_MAX_ALIGN_BYTES on architectures that do not support stack alignment).
+ Let us emphasize that \c EIGEN_MAX_*_ALIGN_BYTES define only a desirable upper bound. In practice data is aligned to largest power-of-two common divisor of \c EIGEN_MAX_STATIC_ALIGN_BYTES and the size of the data, such that memory is not wasted.
+ - \b \c EIGEN_DONT_PARALLELIZE - if defined, this disables multi-threading. This is only relevant if you enabled OpenMP.
+ See \ref TopicMultiThreading for details.
+ - \b \c EIGEN_DONT_VECTORIZE - disables explicit vectorization when defined. Not defined by default, unless
+ alignment is disabled by %Eigen's platform test or the user defining \c EIGEN_DONT_ALIGN.
+ - \b \c EIGEN_UNALIGNED_VECTORIZE - disables/enables vectorization with unaligned stores. Default is 1 (enabled).
+ If set to 0 (disabled), then expression for which the destination cannot be aligned are not vectorized (e.g., unaligned
+ small fixed size vectors or matrices)
+ - \b \c EIGEN_FAST_MATH - enables some optimizations which might affect the accuracy of the result. This currently
+ enables the SSE vectorization of sin() and cos(), and speedups sqrt() for single precision. Defined to 1 by default.
+ Define it to 0 to disable.
+ - \b \c EIGEN_UNROLLING_LIMIT - defines the size of a loop to enable meta unrolling. Set it to zero to disable
+ unrolling. The size of a loop here is expressed in %Eigen's own notion of "number of FLOPS", it does not
+ correspond to the number of iterations or the number of instructions. The default is value 110.
+ - \b \c EIGEN_STACK_ALLOCATION_LIMIT - defines the maximum bytes for a buffer to be allocated on the stack. For internal
+ temporary buffers, dynamic memory allocation is employed as a fall back. For fixed-size matrices or arrays, exceeding
+ this threshold raises a compile time assertion. Use 0 to set no limit. Default is 128 KB.
+ - \b \c EIGEN_NO_CUDA - disables CUDA support when defined. Might be useful in .cu files for which Eigen is used on the host only,
+ and never called from device code.
+ - \b \c EIGEN_STRONG_INLINE - This macro is used to qualify critical functions and methods that we expect the compiler to inline.
+ By default it is defined to \c __forceinline for MSVC and ICC, and to \c inline for other compilers. A tipical usage is to
+ define it to \c inline for MSVC users wanting faster compilation times, at the risk of performance degradations in some rare
+ cases for which MSVC inliner fails to do a good job.
+ - \b \c EIGEN_DEFAULT_L1_CACHE_SIZE - Sets the default L1 cache size that is used in Eigen's GEBP kernel when the correct cache size cannot be determined at runtime.
+ - \b \c EIGEN_DEFAULT_L2_CACHE_SIZE - Sets the default L2 cache size that is used in Eigen's GEBP kernel when the correct cache size cannot be determined at runtime.
+ - \b \c EIGEN_DEFAULT_L3_CACHE_SIZE - Sets the default L3 cache size that is used in Eigen's GEBP kernel when the correct cache size cannot be determined at runtime.
+
+ - \b \c EIGEN_DONT_ALIGN - Deprecated, it is a synonym for \c EIGEN_MAX_ALIGN_BYTES=0. It disables alignment completely. %Eigen will not try to align its objects and does not expect that any objects passed to it are aligned. This will turn off vectorization if \b \c EIGEN_UNALIGNED_VECTORIZE=1. Not defined by default.
+ - \b \c EIGEN_DONT_ALIGN_STATICALLY - Deprecated, it is a synonym for \c EIGEN_MAX_STATIC_ALIGN_BYTES=0. It disables alignment of arrays on the stack. Not defined by default, unless \c EIGEN_DONT_ALIGN is defined.
+ - \b \c EIGEN_ALTIVEC_ENABLE_MMA_DYNAMIC_DISPATCH - Controls whether to use Eigen's dynamic dispatching for Altivec MMA or not.
+ - \b \c EIGEN_ALTIVEC_DISABLE_MMA - Overrides the usage of Altivec MMA instructions.
+ - \b \c EIGEN_ALTIVEC_USE_CUSTOM_PACK - Controls whether to use Eigen's custom packing for Altivec or not.
+
+
+\section TopicPreprocessorDirectivesPlugins Plugins
+
+It is possible to add new methods to many fundamental classes in %Eigen by writing a plugin. As explained in
+the section \ref TopicCustomizing_Plugins, the plugin is specified by defining a \c EIGEN_xxx_PLUGIN macro. The
+following macros are supported; none of them are defined by default.
+
+ - \b EIGEN_ARRAY_PLUGIN - filename of plugin for extending the Array class.
+ - \b EIGEN_ARRAYBASE_PLUGIN - filename of plugin for extending the ArrayBase class.
+ - \b EIGEN_CWISE_PLUGIN - filename of plugin for extending the Cwise class.
+ - \b EIGEN_DENSEBASE_PLUGIN - filename of plugin for extending the DenseBase class.
+ - \b EIGEN_DYNAMICSPARSEMATRIX_PLUGIN - filename of plugin for extending the DynamicSparseMatrix class.
+ - \b EIGEN_FUNCTORS_PLUGIN - filename of plugin for adding new functors and specializations of functor_traits.
+ - \b EIGEN_MAPBASE_PLUGIN - filename of plugin for extending the MapBase class.
+ - \b EIGEN_MATRIX_PLUGIN - filename of plugin for extending the Matrix class.
+ - \b EIGEN_MATRIXBASE_PLUGIN - filename of plugin for extending the MatrixBase class.
+ - \b EIGEN_PLAINOBJECTBASE_PLUGIN - filename of plugin for extending the PlainObjectBase class.
+ - \b EIGEN_QUATERNION_PLUGIN - filename of plugin for extending the Quaternion class.
+ - \b EIGEN_QUATERNIONBASE_PLUGIN - filename of plugin for extending the QuaternionBase class.
+ - \b EIGEN_SPARSEMATRIX_PLUGIN - filename of plugin for extending the SparseMatrix class.
+ - \b EIGEN_SPARSEMATRIXBASE_PLUGIN - filename of plugin for extending the SparseMatrixBase class.
+ - \b EIGEN_SPARSEVECTOR_PLUGIN - filename of plugin for extending the SparseVector class.
+ - \b EIGEN_TRANSFORM_PLUGIN - filename of plugin for extending the Transform class.
+ - \b EIGEN_VECTORWISEOP_PLUGIN - filename of plugin for extending the VectorwiseOp class.
+
+\section TopicPreprocessorDirectivesDevelopers Macros for Eigen developers
+
+These macros are mainly meant for people developing %Eigen and for testing purposes. Even though, they might be useful for power users and the curious for debugging and testing purpose, they \b should \b not \b be \b used by real-word code.
+
+ - \b EIGEN_DEFAULT_TO_ROW_MAJOR - when defined, the default storage order for matrices becomes row-major
+ instead of column-major. Not defined by default.
+ - \b EIGEN_INTERNAL_DEBUGGING - if defined, enables assertions in %Eigen's internal routines. This is useful
+ for debugging %Eigen itself. Not defined by default.
+ - \b EIGEN_NO_MALLOC - if defined, any request from inside the %Eigen to allocate memory from the heap
+ results in an assertion failure. This is useful to check that some routine does not allocate memory
+ dynamically. Not defined by default.
+ - \b EIGEN_RUNTIME_NO_MALLOC - if defined, a new switch is introduced which can be turned on and off by
+ calling <tt>set_is_malloc_allowed(bool)</tt>. If malloc is not allowed and %Eigen tries to allocate memory
+ dynamically anyway, an assertion failure results. Not defined by default.
+
+*/
+
+}
diff --git a/doc/QuickReference.dox b/doc/QuickReference.dox
new file mode 100644
index 0000000..c5dfce4
--- /dev/null
+++ b/doc/QuickReference.dox
@@ -0,0 +1,805 @@
+namespace Eigen {
+
+/** \eigenManualPage QuickRefPage Quick reference guide
+
+\eigenAutoToc
+
+<hr>
+
+<a href="#" class="top">top</a>
+\section QuickRef_Headers Modules and Header files
+
+The Eigen library is divided in a Core module and several additional modules. Each module has a corresponding header file which has to be included in order to use the module. The \c %Dense and \c Eigen header files are provided to conveniently gain access to several modules at once.
+
+<table class="manual">
+<tr><th>Module</th><th>Header file</th><th>Contents</th></tr>
+<tr ><td>\link Core_Module Core \endlink</td><td>\code#include <Eigen/Core>\endcode</td><td>Matrix and Array classes, basic linear algebra (including triangular and selfadjoint products), array manipulation</td></tr>
+<tr class="alt"><td>\link Geometry_Module Geometry \endlink</td><td>\code#include <Eigen/Geometry>\endcode</td><td>Transform, Translation, Scaling, Rotation2D and 3D rotations (Quaternion, AngleAxis)</td></tr>
+<tr ><td>\link LU_Module LU \endlink</td><td>\code#include <Eigen/LU>\endcode</td><td>Inverse, determinant, LU decompositions with solver (FullPivLU, PartialPivLU)</td></tr>
+<tr class="alt"><td>\link Cholesky_Module Cholesky \endlink</td><td>\code#include <Eigen/Cholesky>\endcode</td><td>LLT and LDLT Cholesky factorization with solver</td></tr>
+<tr ><td>\link Householder_Module Householder \endlink</td><td>\code#include <Eigen/Householder>\endcode</td><td>Householder transformations; this module is used by several linear algebra modules</td></tr>
+<tr class="alt"><td>\link SVD_Module SVD \endlink</td><td>\code#include <Eigen/SVD>\endcode</td><td>SVD decompositions with least-squares solver (JacobiSVD, BDCSVD)</td></tr>
+<tr ><td>\link QR_Module QR \endlink</td><td>\code#include <Eigen/QR>\endcode</td><td>QR decomposition with solver (HouseholderQR, ColPivHouseholderQR, FullPivHouseholderQR)</td></tr>
+<tr class="alt"><td>\link Eigenvalues_Module Eigenvalues \endlink</td><td>\code#include <Eigen/Eigenvalues>\endcode</td><td>Eigenvalue, eigenvector decompositions (EigenSolver, SelfAdjointEigenSolver, ComplexEigenSolver)</td></tr>
+<tr ><td>\link Sparse_Module Sparse \endlink</td><td>\code#include <Eigen/Sparse>\endcode</td><td>%Sparse matrix storage and related basic linear algebra (SparseMatrix, SparseVector) \n (see \ref SparseQuickRefPage for details on sparse modules)</td></tr>
+<tr class="alt"><td></td><td>\code#include <Eigen/Dense>\endcode</td><td>Includes Core, Geometry, LU, Cholesky, SVD, QR, and Eigenvalues header files</td></tr>
+<tr ><td></td><td>\code#include <Eigen/Eigen>\endcode</td><td>Includes %Dense and %Sparse header files (the whole Eigen library)</td></tr>
+</table>
+
+<a href="#" class="top">top</a>
+\section QuickRef_Types Array, matrix and vector types
+
+
+\b Recall: Eigen provides two kinds of dense objects: mathematical matrices and vectors which are both represented by the template class Matrix, and general 1D and 2D arrays represented by the template class Array:
+\code
+typedef Matrix<Scalar, RowsAtCompileTime, ColsAtCompileTime, Options> MyMatrixType;
+typedef Array<Scalar, RowsAtCompileTime, ColsAtCompileTime, Options> MyArrayType;
+\endcode
+
+\li \c Scalar is the scalar type of the coefficients (e.g., \c float, \c double, \c bool, \c int, etc.).
+\li \c RowsAtCompileTime and \c ColsAtCompileTime are the number of rows and columns of the matrix as known at compile-time or \c Dynamic.
+\li \c Options can be \c ColMajor or \c RowMajor, default is \c ColMajor. (see class Matrix for more options)
+
+All combinations are allowed: you can have a matrix with a fixed number of rows and a dynamic number of columns, etc. The following are all valid:
+\code
+Matrix<double, 6, Dynamic> // Dynamic number of columns (heap allocation)
+Matrix<double, Dynamic, 2> // Dynamic number of rows (heap allocation)
+Matrix<double, Dynamic, Dynamic, RowMajor> // Fully dynamic, row major (heap allocation)
+Matrix<double, 13, 3> // Fully fixed (usually allocated on stack)
+\endcode
+
+In most cases, you can simply use one of the convenience typedefs for \ref matrixtypedefs "matrices" and \ref arraytypedefs "arrays". Some examples:
+<table class="example">
+<tr><th>Matrices</th><th>Arrays</th></tr>
+<tr><td>\code
+Matrix<float,Dynamic,Dynamic> <=> MatrixXf
+Matrix<double,Dynamic,1> <=> VectorXd
+Matrix<int,1,Dynamic> <=> RowVectorXi
+Matrix<float,3,3> <=> Matrix3f
+Matrix<float,4,1> <=> Vector4f
+\endcode</td><td>\code
+Array<float,Dynamic,Dynamic> <=> ArrayXXf
+Array<double,Dynamic,1> <=> ArrayXd
+Array<int,1,Dynamic> <=> RowArrayXi
+Array<float,3,3> <=> Array33f
+Array<float,4,1> <=> Array4f
+\endcode</td></tr>
+</table>
+
+Conversion between the matrix and array worlds:
+\code
+Array44f a1, a2;
+Matrix4f m1, m2;
+m1 = a1 * a2; // coeffwise product, implicit conversion from array to matrix.
+a1 = m1 * m2; // matrix product, implicit conversion from matrix to array.
+a2 = a1 + m1.array(); // mixing array and matrix is forbidden
+m2 = a1.matrix() + m1; // and explicit conversion is required.
+ArrayWrapper<Matrix4f> m1a(m1); // m1a is an alias for m1.array(), they share the same coefficients
+MatrixWrapper<Array44f> a1m(a1);
+\endcode
+
+In the rest of this document we will use the following symbols to emphasize the features which are specifics to a given kind of object:
+\li <a name="matrixonly"></a>\matrixworld linear algebra matrix and vector only
+\li <a name="arrayonly"></a>\arrayworld array objects only
+
+\subsection QuickRef_Basics Basic matrix manipulation
+
+<table class="manual">
+<tr><th></th><th>1D objects</th><th>2D objects</th><th>Notes</th></tr>
+<tr><td>Constructors</td>
+<td>\code
+Vector4d v4;
+Vector2f v1(x, y);
+Array3i v2(x, y, z);
+Vector4d v3(x, y, z, w);
+
+VectorXf v5; // empty object
+ArrayXf v6(size);
+\endcode</td><td>\code
+Matrix4f m1;
+
+
+
+
+MatrixXf m5; // empty object
+MatrixXf m6(nb_rows, nb_columns);
+\endcode</td><td class="note">
+By default, the coefficients \n are left uninitialized</td></tr>
+<tr class="alt"><td>Comma initializer</td>
+<td>\code
+Vector3f v1; v1 << x, y, z;
+ArrayXf v2(4); v2 << 1, 2, 3, 4;
+
+\endcode</td><td>\code
+Matrix3f m1; m1 << 1, 2, 3,
+ 4, 5, 6,
+ 7, 8, 9;
+\endcode</td><td></td></tr>
+
+<tr><td>Comma initializer (bis)</td>
+<td colspan="2">
+\include Tutorial_commainit_02.cpp
+</td>
+<td>
+output:
+\verbinclude Tutorial_commainit_02.out
+</td>
+</tr>
+
+<tr class="alt"><td>Runtime info</td>
+<td>\code
+vector.size();
+
+vector.innerStride();
+vector.data();
+\endcode</td><td>\code
+matrix.rows(); matrix.cols();
+matrix.innerSize(); matrix.outerSize();
+matrix.innerStride(); matrix.outerStride();
+matrix.data();
+\endcode</td><td class="note">Inner/Outer* are storage order dependent</td></tr>
+<tr><td>Compile-time info</td>
+<td colspan="2">\code
+ObjectType::Scalar ObjectType::RowsAtCompileTime
+ObjectType::RealScalar ObjectType::ColsAtCompileTime
+ObjectType::Index ObjectType::SizeAtCompileTime
+\endcode</td><td></td></tr>
+<tr class="alt"><td>Resizing</td>
+<td>\code
+vector.resize(size);
+
+
+vector.resizeLike(other_vector);
+vector.conservativeResize(size);
+\endcode</td><td>\code
+matrix.resize(nb_rows, nb_cols);
+matrix.resize(Eigen::NoChange, nb_cols);
+matrix.resize(nb_rows, Eigen::NoChange);
+matrix.resizeLike(other_matrix);
+matrix.conservativeResize(nb_rows, nb_cols);
+\endcode</td><td class="note">no-op if the new sizes match,<br/>otherwise data are lost<br/><br/>resizing with data preservation</td></tr>
+
+<tr><td>Coeff access with \n range checking</td>
+<td>\code
+vector(i) vector.x()
+vector[i] vector.y()
+ vector.z()
+ vector.w()
+\endcode</td><td>\code
+matrix(i,j)
+\endcode</td><td class="note">Range checking is disabled if \n NDEBUG or EIGEN_NO_DEBUG is defined</td></tr>
+
+<tr class="alt"><td>Coeff access without \n range checking</td>
+<td>\code
+vector.coeff(i)
+vector.coeffRef(i)
+\endcode</td><td>\code
+matrix.coeff(i,j)
+matrix.coeffRef(i,j)
+\endcode</td><td></td></tr>
+
+<tr><td>Assignment/copy</td>
+<td colspan="2">\code
+object = expression;
+object_of_float = expression_of_double.cast<float>();
+\endcode</td><td class="note">the destination is automatically resized (if possible)</td></tr>
+
+</table>
+
+\subsection QuickRef_PredefMat Predefined Matrices
+
+<table class="manual">
+<tr>
+ <th>Fixed-size matrix or vector</th>
+ <th>Dynamic-size matrix</th>
+ <th>Dynamic-size vector</th>
+</tr>
+<tr style="border-bottom-style: none;">
+ <td>
+\code
+typedef {Matrix3f|Array33f} FixedXD;
+FixedXD x;
+
+x = FixedXD::Zero();
+x = FixedXD::Ones();
+x = FixedXD::Constant(value);
+x = FixedXD::Random();
+x = FixedXD::LinSpaced(size, low, high);
+
+x.setZero();
+x.setOnes();
+x.setConstant(value);
+x.setRandom();
+x.setLinSpaced(size, low, high);
+\endcode
+ </td>
+ <td>
+\code
+typedef {MatrixXf|ArrayXXf} Dynamic2D;
+Dynamic2D x;
+
+x = Dynamic2D::Zero(rows, cols);
+x = Dynamic2D::Ones(rows, cols);
+x = Dynamic2D::Constant(rows, cols, value);
+x = Dynamic2D::Random(rows, cols);
+N/A
+
+x.setZero(rows, cols);
+x.setOnes(rows, cols);
+x.setConstant(rows, cols, value);
+x.setRandom(rows, cols);
+N/A
+\endcode
+ </td>
+ <td>
+\code
+typedef {VectorXf|ArrayXf} Dynamic1D;
+Dynamic1D x;
+
+x = Dynamic1D::Zero(size);
+x = Dynamic1D::Ones(size);
+x = Dynamic1D::Constant(size, value);
+x = Dynamic1D::Random(size);
+x = Dynamic1D::LinSpaced(size, low, high);
+
+x.setZero(size);
+x.setOnes(size);
+x.setConstant(size, value);
+x.setRandom(size);
+x.setLinSpaced(size, low, high);
+\endcode
+ </td>
+</tr>
+
+<tr><td colspan="3">Identity and \link MatrixBase::Unit basis vectors \endlink \matrixworld</td></tr>
+<tr style="border-bottom-style: none;">
+ <td>
+\code
+x = FixedXD::Identity();
+x.setIdentity();
+
+Vector3f::UnitX() // 1 0 0
+Vector3f::UnitY() // 0 1 0
+Vector3f::UnitZ() // 0 0 1
+Vector4f::Unit(i)
+x.setUnit(i);
+\endcode
+ </td>
+ <td>
+\code
+x = Dynamic2D::Identity(rows, cols);
+x.setIdentity(rows, cols);
+
+
+
+N/A
+\endcode
+ </td>
+ <td>\code
+N/A
+
+
+VectorXf::Unit(size,i)
+x.setUnit(size,i);
+VectorXf::Unit(4,1) == Vector4f(0,1,0,0)
+ == Vector4f::UnitY()
+\endcode
+ </td>
+</tr>
+</table>
+
+Note that it is allowed to call any of the \c set* functions to a dynamic-sized vector or matrix without passing new sizes.
+For instance:
+\code
+MatrixXi M(3,3);
+M.setIdentity();
+\endcode
+
+\subsection QuickRef_Map Mapping external arrays
+
+<table class="manual">
+<tr>
+<td>Contiguous \n memory</td>
+<td>\code
+float data[] = {1,2,3,4};
+Map<Vector3f> v1(data); // uses v1 as a Vector3f object
+Map<ArrayXf> v2(data,3); // uses v2 as a ArrayXf object
+Map<Array22f> m1(data); // uses m1 as a Array22f object
+Map<MatrixXf> m2(data,2,2); // uses m2 as a MatrixXf object
+\endcode</td>
+</tr>
+<tr>
+<td>Typical usage \n of strides</td>
+<td>\code
+float data[] = {1,2,3,4,5,6,7,8,9};
+Map<VectorXf,0,InnerStride<2> > v1(data,3); // = [1,3,5]
+Map<VectorXf,0,InnerStride<> > v2(data,3,InnerStride<>(3)); // = [1,4,7]
+Map<MatrixXf,0,OuterStride<3> > m2(data,2,3); // both lines |1,4,7|
+Map<MatrixXf,0,OuterStride<> > m1(data,2,3,OuterStride<>(3)); // are equal to: |2,5,8|
+\endcode</td>
+</tr>
+</table>
+
+
+<a href="#" class="top">top</a>
+\section QuickRef_ArithmeticOperators Arithmetic Operators
+
+<table class="manual">
+<tr><td>
+add \n subtract</td><td>\code
+mat3 = mat1 + mat2; mat3 += mat1;
+mat3 = mat1 - mat2; mat3 -= mat1;\endcode
+</td></tr>
+<tr class="alt"><td>
+scalar product</td><td>\code
+mat3 = mat1 * s1; mat3 *= s1; mat3 = s1 * mat1;
+mat3 = mat1 / s1; mat3 /= s1;\endcode
+</td></tr>
+<tr><td>
+matrix/vector \n products \matrixworld</td><td>\code
+col2 = mat1 * col1;
+row2 = row1 * mat1; row1 *= mat1;
+mat3 = mat1 * mat2; mat3 *= mat1; \endcode
+</td></tr>
+<tr class="alt"><td>
+transposition \n adjoint \matrixworld</td><td>\code
+mat1 = mat2.transpose(); mat1.transposeInPlace();
+mat1 = mat2.adjoint(); mat1.adjointInPlace();
+\endcode
+</td></tr>
+<tr><td>
+\link MatrixBase::dot dot \endlink product \n inner product \matrixworld</td><td>\code
+scalar = vec1.dot(vec2);
+scalar = col1.adjoint() * col2;
+scalar = (col1.adjoint() * col2).value();\endcode
+</td></tr>
+<tr class="alt"><td>
+outer product \matrixworld</td><td>\code
+mat = col1 * col2.transpose();\endcode
+</td></tr>
+
+<tr><td>
+\link MatrixBase::norm() norm \endlink \n \link MatrixBase::normalized() normalization \endlink \matrixworld</td><td>\code
+scalar = vec1.norm(); scalar = vec1.squaredNorm()
+vec2 = vec1.normalized(); vec1.normalize(); // inplace \endcode
+</td></tr>
+
+<tr class="alt"><td>
+\link MatrixBase::cross() cross product \endlink \matrixworld</td><td>\code
+#include <Eigen/Geometry>
+vec3 = vec1.cross(vec2);\endcode</td></tr>
+</table>
+
+<a href="#" class="top">top</a>
+\section QuickRef_Coeffwise Coefficient-wise \& Array operators
+
+In addition to the aforementioned operators, Eigen supports numerous coefficient-wise operator and functions.
+Most of them unambiguously makes sense in array-world\arrayworld. The following operators are readily available for arrays,
+or available through .array() for vectors and matrices:
+
+<table class="manual">
+<tr><td>Arithmetic operators</td><td>\code
+array1 * array2 array1 / array2 array1 *= array2 array1 /= array2
+array1 + scalar array1 - scalar array1 += scalar array1 -= scalar
+\endcode</td></tr>
+<tr><td>Comparisons</td><td>\code
+array1 < array2 array1 > array2 array1 < scalar array1 > scalar
+array1 <= array2 array1 >= array2 array1 <= scalar array1 >= scalar
+array1 == array2 array1 != array2 array1 == scalar array1 != scalar
+array1.min(array2) array1.max(array2) array1.min(scalar) array1.max(scalar)
+\endcode</td></tr>
+<tr><td>Trigo, power, and \n misc functions \n and the STL-like variants</td><td>\code
+array1.abs2()
+array1.abs() abs(array1)
+array1.sqrt() sqrt(array1)
+array1.log() log(array1)
+array1.log10() log10(array1)
+array1.exp() exp(array1)
+array1.pow(array2) pow(array1,array2)
+array1.pow(scalar) pow(array1,scalar)
+ pow(scalar,array2)
+array1.square()
+array1.cube()
+array1.inverse()
+
+array1.sin() sin(array1)
+array1.cos() cos(array1)
+array1.tan() tan(array1)
+array1.asin() asin(array1)
+array1.acos() acos(array1)
+array1.atan() atan(array1)
+array1.sinh() sinh(array1)
+array1.cosh() cosh(array1)
+array1.tanh() tanh(array1)
+array1.arg() arg(array1)
+
+array1.floor() floor(array1)
+array1.ceil() ceil(array1)
+array1.round() round(aray1)
+
+array1.isFinite() isfinite(array1)
+array1.isInf() isinf(array1)
+array1.isNaN() isnan(array1)
+\endcode
+</td></tr>
+</table>
+
+
+The following coefficient-wise operators are available for all kind of expressions (matrices, vectors, and arrays), and for both real or complex scalar types:
+
+<table class="manual">
+<tr><th>Eigen's API</th><th>STL-like APIs\arrayworld </th><th>Comments</th></tr>
+<tr><td>\code
+mat1.real()
+mat1.imag()
+mat1.conjugate()
+\endcode
+</td><td>\code
+real(array1)
+imag(array1)
+conj(array1)
+\endcode
+</td><td>
+\code
+ // read-write, no-op for real expressions
+ // read-only for real, read-write for complexes
+ // no-op for real expressions
+\endcode
+</td></tr>
+</table>
+
+Some coefficient-wise operators are readily available for for matrices and vectors through the following cwise* methods:
+<table class="manual">
+<tr><th>Matrix API \matrixworld</th><th>Via Array conversions</th></tr>
+<tr><td>\code
+mat1.cwiseMin(mat2) mat1.cwiseMin(scalar)
+mat1.cwiseMax(mat2) mat1.cwiseMax(scalar)
+mat1.cwiseAbs2()
+mat1.cwiseAbs()
+mat1.cwiseSqrt()
+mat1.cwiseInverse()
+mat1.cwiseProduct(mat2)
+mat1.cwiseQuotient(mat2)
+mat1.cwiseEqual(mat2) mat1.cwiseEqual(scalar)
+mat1.cwiseNotEqual(mat2)
+\endcode
+</td><td>\code
+mat1.array().min(mat2.array()) mat1.array().min(scalar)
+mat1.array().max(mat2.array()) mat1.array().max(scalar)
+mat1.array().abs2()
+mat1.array().abs()
+mat1.array().sqrt()
+mat1.array().inverse()
+mat1.array() * mat2.array()
+mat1.array() / mat2.array()
+mat1.array() == mat2.array() mat1.array() == scalar
+mat1.array() != mat2.array()
+\endcode</td></tr>
+</table>
+The main difference between the two API is that the one based on cwise* methods returns an expression in the matrix world,
+while the second one (based on .array()) returns an array expression.
+Recall that .array() has no cost, it only changes the available API and interpretation of the data.
+
+It is also very simple to apply any user defined function \c foo using DenseBase::unaryExpr together with <a href="http://en.cppreference.com/w/cpp/utility/functional/ptr_fun">std::ptr_fun</a> (c++03, deprecated or removed in newer C++ versions), <a href="http://en.cppreference.com/w/cpp/utility/functional/ref">std::ref</a> (c++11), or <a href="http://en.cppreference.com/w/cpp/language/lambda">lambdas</a> (c++11):
+\code
+mat1.unaryExpr(std::ptr_fun(foo));
+mat1.unaryExpr(std::ref(foo));
+mat1.unaryExpr([](double x) { return foo(x); });
+\endcode
+
+Please note that it's not possible to pass a raw function pointer to \c unaryExpr, so please warp it as shown above.
+
+<a href="#" class="top">top</a>
+\section QuickRef_Reductions Reductions
+
+Eigen provides several reduction methods such as:
+\link DenseBase::minCoeff() minCoeff() \endlink, \link DenseBase::maxCoeff() maxCoeff() \endlink,
+\link DenseBase::sum() sum() \endlink, \link DenseBase::prod() prod() \endlink,
+\link MatrixBase::trace() trace() \endlink \matrixworld,
+\link MatrixBase::norm() norm() \endlink \matrixworld, \link MatrixBase::squaredNorm() squaredNorm() \endlink \matrixworld,
+\link DenseBase::all() all() \endlink, and \link DenseBase::any() any() \endlink.
+All reduction operations can be done matrix-wise,
+\link DenseBase::colwise() column-wise \endlink or
+\link DenseBase::rowwise() row-wise \endlink. Usage example:
+<table class="manual">
+<tr><td rowspan="3" style="border-right-style:dashed;vertical-align:middle">\code
+ 5 3 1
+mat = 2 7 8
+ 9 4 6 \endcode
+</td> <td>\code mat.minCoeff(); \endcode</td><td>\code 1 \endcode</td></tr>
+<tr class="alt"><td>\code mat.colwise().minCoeff(); \endcode</td><td>\code 2 3 1 \endcode</td></tr>
+<tr style="vertical-align:middle"><td>\code mat.rowwise().minCoeff(); \endcode</td><td>\code
+1
+2
+4
+\endcode</td></tr>
+</table>
+
+Special versions of \link DenseBase::minCoeff(IndexType*,IndexType*) const minCoeff \endlink and \link DenseBase::maxCoeff(IndexType*,IndexType*) const maxCoeff \endlink:
+\code
+int i, j;
+s = vector.minCoeff(&i); // s == vector[i]
+s = matrix.maxCoeff(&i, &j); // s == matrix(i,j)
+\endcode
+Typical use cases of all() and any():
+\code
+if((array1 > 0).all()) ... // if all coefficients of array1 are greater than 0 ...
+if((array1 < array2).any()) ... // if there exist a pair i,j such that array1(i,j) < array2(i,j) ...
+\endcode
+
+
+<a href="#" class="top">top</a>\section QuickRef_Blocks Sub-matrices
+
+<div class="warningbox">
+<strong>PLEASE HELP US IMPROVING THIS SECTION.</strong>
+%Eigen 3.4 supports a much improved API for sub-matrices, including,
+slicing and indexing from arrays: \ref TutorialSlicingIndexing
+</div>
+
+Read-write access to a \link DenseBase::col(Index) column \endlink
+or a \link DenseBase::row(Index) row \endlink of a matrix (or array):
+\code
+mat1.row(i) = mat2.col(j);
+mat1.col(j1).swap(mat1.col(j2));
+\endcode
+
+Read-write access to sub-vectors:
+<table class="manual">
+<tr>
+<th>Default versions</th>
+<th>Optimized versions when the size \n is known at compile time</th></tr>
+<th></th>
+
+<tr><td>\code vec1.head(n)\endcode</td><td>\code vec1.head<n>()\endcode</td><td>the first \c n coeffs </td></tr>
+<tr><td>\code vec1.tail(n)\endcode</td><td>\code vec1.tail<n>()\endcode</td><td>the last \c n coeffs </td></tr>
+<tr><td>\code vec1.segment(pos,n)\endcode</td><td>\code vec1.segment<n>(pos)\endcode</td>
+ <td>the \c n coeffs in the \n range [\c pos : \c pos + \c n - 1]</td></tr>
+<tr class="alt"><td colspan="3">
+
+Read-write access to sub-matrices:</td></tr>
+<tr>
+ <td>\code mat1.block(i,j,rows,cols)\endcode
+ \link DenseBase::block(Index,Index,Index,Index) (more) \endlink</td>
+ <td>\code mat1.block<rows,cols>(i,j)\endcode
+ \link DenseBase::block(Index,Index) (more) \endlink</td>
+ <td>the \c rows x \c cols sub-matrix \n starting from position (\c i,\c j)</td></tr>
+<tr><td>\code
+ mat1.topLeftCorner(rows,cols)
+ mat1.topRightCorner(rows,cols)
+ mat1.bottomLeftCorner(rows,cols)
+ mat1.bottomRightCorner(rows,cols)\endcode
+ <td>\code
+ mat1.topLeftCorner<rows,cols>()
+ mat1.topRightCorner<rows,cols>()
+ mat1.bottomLeftCorner<rows,cols>()
+ mat1.bottomRightCorner<rows,cols>()\endcode
+ <td>the \c rows x \c cols sub-matrix \n taken in one of the four corners</td></tr>
+ <tr><td>\code
+ mat1.topRows(rows)
+ mat1.bottomRows(rows)
+ mat1.leftCols(cols)
+ mat1.rightCols(cols)\endcode
+ <td>\code
+ mat1.topRows<rows>()
+ mat1.bottomRows<rows>()
+ mat1.leftCols<cols>()
+ mat1.rightCols<cols>()\endcode
+ <td>specialized versions of block() \n when the block fit two corners</td></tr>
+</table>
+
+
+
+<a href="#" class="top">top</a>\section QuickRef_Misc Miscellaneous operations
+
+<div class="warningbox">
+<strong>PLEASE HELP US IMPROVING THIS SECTION.</strong>
+%Eigen 3.4 supports a new API for reshaping: \ref TutorialReshape
+</div>
+
+\subsection QuickRef_Reverse Reverse
+Vectors, rows, and/or columns of a matrix can be reversed (see DenseBase::reverse(), DenseBase::reverseInPlace(), VectorwiseOp::reverse()).
+\code
+vec.reverse() mat.colwise().reverse() mat.rowwise().reverse()
+vec.reverseInPlace()
+\endcode
+
+\subsection QuickRef_Replicate Replicate
+Vectors, matrices, rows, and/or columns can be replicated in any direction (see DenseBase::replicate(), VectorwiseOp::replicate())
+\code
+vec.replicate(times) vec.replicate<Times>
+mat.replicate(vertical_times, horizontal_times) mat.replicate<VerticalTimes, HorizontalTimes>()
+mat.colwise().replicate(vertical_times, horizontal_times) mat.colwise().replicate<VerticalTimes, HorizontalTimes>()
+mat.rowwise().replicate(vertical_times, horizontal_times) mat.rowwise().replicate<VerticalTimes, HorizontalTimes>()
+\endcode
+
+
+<a href="#" class="top">top</a>\section QuickRef_DiagTriSymm Diagonal, Triangular, and Self-adjoint matrices
+(matrix world \matrixworld)
+
+\subsection QuickRef_Diagonal Diagonal matrices
+
+<table class="example">
+<tr><th>Operation</th><th>Code</th></tr>
+<tr><td>
+view a vector \link MatrixBase::asDiagonal() as a diagonal matrix \endlink \n </td><td>\code
+mat1 = vec1.asDiagonal();\endcode
+</td></tr>
+<tr><td>
+Declare a diagonal matrix</td><td>\code
+DiagonalMatrix<Scalar,SizeAtCompileTime> diag1(size);
+diag1.diagonal() = vector;\endcode
+</td></tr>
+<tr><td>Access the \link MatrixBase::diagonal() diagonal \endlink and \link MatrixBase::diagonal(Index) super/sub diagonals \endlink of a matrix as a vector (read/write)</td>
+ <td>\code
+vec1 = mat1.diagonal(); mat1.diagonal() = vec1; // main diagonal
+vec1 = mat1.diagonal(+n); mat1.diagonal(+n) = vec1; // n-th super diagonal
+vec1 = mat1.diagonal(-n); mat1.diagonal(-n) = vec1; // n-th sub diagonal
+vec1 = mat1.diagonal<1>(); mat1.diagonal<1>() = vec1; // first super diagonal
+vec1 = mat1.diagonal<-2>(); mat1.diagonal<-2>() = vec1; // second sub diagonal
+\endcode</td>
+</tr>
+
+<tr><td>Optimized products and inverse</td>
+ <td>\code
+mat3 = scalar * diag1 * mat1;
+mat3 += scalar * mat1 * vec1.asDiagonal();
+mat3 = vec1.asDiagonal().inverse() * mat1
+mat3 = mat1 * diag1.inverse()
+\endcode</td>
+</tr>
+
+</table>
+
+\subsection QuickRef_TriangularView Triangular views
+
+TriangularView gives a view on a triangular part of a dense matrix and allows to perform optimized operations on it. The opposite triangular part is never referenced and can be used to store other information.
+
+\note The .triangularView() template member function requires the \c template keyword if it is used on an
+object of a type that depends on a template parameter; see \ref TopicTemplateKeyword for details.
+
+<table class="example">
+<tr><th>Operation</th><th>Code</th></tr>
+<tr><td>
+Reference to a triangular with optional \n
+unit or null diagonal (read/write):
+</td><td>\code
+m.triangularView<Xxx>()
+\endcode \n
+\c Xxx = ::Upper, ::Lower, ::StrictlyUpper, ::StrictlyLower, ::UnitUpper, ::UnitLower
+</td></tr>
+<tr><td>
+Writing to a specific triangular part:\n (only the referenced triangular part is evaluated)
+</td><td>\code
+m1.triangularView<Eigen::Lower>() = m2 + m3 \endcode
+</td></tr>
+<tr><td>
+Conversion to a dense matrix setting the opposite triangular part to zero:
+</td><td>\code
+m2 = m1.triangularView<Eigen::UnitUpper>()\endcode
+</td></tr>
+<tr><td>
+Products:
+</td><td>\code
+m3 += s1 * m1.adjoint().triangularView<Eigen::UnitUpper>() * m2
+m3 -= s1 * m2.conjugate() * m1.adjoint().triangularView<Eigen::Lower>() \endcode
+</td></tr>
+<tr><td>
+Solving linear equations:\n
+\f$ M_2 := L_1^{-1} M_2 \f$ \n
+\f$ M_3 := {L_1^*}^{-1} M_3 \f$ \n
+\f$ M_4 := M_4 U_1^{-1} \f$
+</td><td>\n \code
+L1.triangularView<Eigen::UnitLower>().solveInPlace(M2)
+L1.triangularView<Eigen::Lower>().adjoint().solveInPlace(M3)
+U1.triangularView<Eigen::Upper>().solveInPlace<OnTheRight>(M4)\endcode
+</td></tr>
+</table>
+
+\subsection QuickRef_SelfadjointMatrix Symmetric/selfadjoint views
+
+Just as for triangular matrix, you can reference any triangular part of a square matrix to see it as a selfadjoint
+matrix and perform special and optimized operations. Again the opposite triangular part is never referenced and can be
+used to store other information.
+
+\note The .selfadjointView() template member function requires the \c template keyword if it is used on an
+object of a type that depends on a template parameter; see \ref TopicTemplateKeyword for details.
+
+<table class="example">
+<tr><th>Operation</th><th>Code</th></tr>
+<tr><td>
+Conversion to a dense matrix:
+</td><td>\code
+m2 = m.selfadjointView<Eigen::Lower>();\endcode
+</td></tr>
+<tr><td>
+Product with another general matrix or vector:
+</td><td>\code
+m3 = s1 * m1.conjugate().selfadjointView<Eigen::Upper>() * m3;
+m3 -= s1 * m3.adjoint() * m1.selfadjointView<Eigen::Lower>();\endcode
+</td></tr>
+<tr><td>
+Rank 1 and rank K update: \n
+\f$ upper(M_1) \mathrel{{+}{=}} s_1 M_2 M_2^* \f$ \n
+\f$ lower(M_1) \mathbin{{-}{=}} M_2^* M_2 \f$
+</td><td>\n \code
+M1.selfadjointView<Eigen::Upper>().rankUpdate(M2,s1);
+M1.selfadjointView<Eigen::Lower>().rankUpdate(M2.adjoint(),-1); \endcode
+</td></tr>
+<tr><td>
+Rank 2 update: (\f$ M \mathrel{{+}{=}} s u v^* + s v u^* \f$)
+</td><td>\code
+M.selfadjointView<Eigen::Upper>().rankUpdate(u,v,s);
+\endcode
+</td></tr>
+<tr><td>
+Solving linear equations:\n(\f$ M_2 := M_1^{-1} M_2 \f$)
+</td><td>\code
+// via a standard Cholesky factorization
+m2 = m1.selfadjointView<Eigen::Upper>().llt().solve(m2);
+// via a Cholesky factorization with pivoting
+m2 = m1.selfadjointView<Eigen::Lower>().ldlt().solve(m2);
+\endcode
+</td></tr>
+</table>
+
+*/
+
+/*
+<table class="tutorial_code">
+<tr><td>
+\link MatrixBase::asDiagonal() make a diagonal matrix \endlink \n from a vector </td><td>\code
+mat1 = vec1.asDiagonal();\endcode
+</td></tr>
+<tr><td>
+Declare a diagonal matrix</td><td>\code
+DiagonalMatrix<Scalar,SizeAtCompileTime> diag1(size);
+diag1.diagonal() = vector;\endcode
+</td></tr>
+<tr><td>Access \link MatrixBase::diagonal() the diagonal and super/sub diagonals of a matrix \endlink as a vector (read/write)</td>
+ <td>\code
+vec1 = mat1.diagonal(); mat1.diagonal() = vec1; // main diagonal
+vec1 = mat1.diagonal(+n); mat1.diagonal(+n) = vec1; // n-th super diagonal
+vec1 = mat1.diagonal(-n); mat1.diagonal(-n) = vec1; // n-th sub diagonal
+vec1 = mat1.diagonal<1>(); mat1.diagonal<1>() = vec1; // first super diagonal
+vec1 = mat1.diagonal<-2>(); mat1.diagonal<-2>() = vec1; // second sub diagonal
+\endcode</td>
+</tr>
+
+<tr><td>View on a triangular part of a matrix (read/write)</td>
+ <td>\code
+mat2 = mat1.triangularView<Xxx>();
+// Xxx = Upper, Lower, StrictlyUpper, StrictlyLower, UnitUpper, UnitLower
+mat1.triangularView<Upper>() = mat2 + mat3; // only the upper part is evaluated and referenced
+\endcode</td></tr>
+
+<tr><td>View a triangular part as a symmetric/self-adjoint matrix (read/write)</td>
+ <td>\code
+mat2 = mat1.selfadjointView<Xxx>(); // Xxx = Upper or Lower
+mat1.selfadjointView<Upper>() = mat2 + mat2.adjoint(); // evaluated and write to the upper triangular part only
+\endcode</td></tr>
+
+</table>
+
+Optimized products:
+\code
+mat3 += scalar * vec1.asDiagonal() * mat1
+mat3 += scalar * mat1 * vec1.asDiagonal()
+mat3.noalias() += scalar * mat1.triangularView<Xxx>() * mat2
+mat3.noalias() += scalar * mat2 * mat1.triangularView<Xxx>()
+mat3.noalias() += scalar * mat1.selfadjointView<Upper or Lower>() * mat2
+mat3.noalias() += scalar * mat2 * mat1.selfadjointView<Upper or Lower>()
+mat1.selfadjointView<Upper or Lower>().rankUpdate(mat2);
+mat1.selfadjointView<Upper or Lower>().rankUpdate(mat2.adjoint(), scalar);
+\endcode
+
+Inverse products: (all are optimized)
+\code
+mat3 = vec1.asDiagonal().inverse() * mat1
+mat3 = mat1 * diag1.inverse()
+mat1.triangularView<Xxx>().solveInPlace(mat2)
+mat1.triangularView<Xxx>().solveInPlace<OnTheRight>(mat2)
+mat2 = mat1.selfadjointView<Upper or Lower>().llt().solve(mat2)
+\endcode
+
+*/
+}
diff --git a/doc/QuickStartGuide.dox b/doc/QuickStartGuide.dox
new file mode 100644
index 0000000..0372694
--- /dev/null
+++ b/doc/QuickStartGuide.dox
@@ -0,0 +1,100 @@
+namespace Eigen {
+
+/** \page GettingStarted Getting started
+
+\eigenAutoToc
+
+This is a very short guide on how to get started with Eigen. It has a dual purpose. It serves as a minimal introduction to the Eigen library for people who want to start coding as soon as possible. You can also read this page as the first part of the Tutorial, which explains the library in more detail; in this case you will continue with \ref TutorialMatrixClass.
+
+\section GettingStartedInstallation How to "install" Eigen?
+
+In order to use Eigen, you just need to download and extract Eigen's source code (see <a href="http://eigen.tuxfamily.org/index.php?title=Main_Page#Download">the wiki</a> for download instructions). In fact, the header files in the \c Eigen subdirectory are the only files required to compile programs using Eigen. The header files are the same for all platforms. It is not necessary to use CMake or install anything.
+
+
+\section GettingStartedFirstProgram A simple first program
+
+Here is a rather simple program to get you started.
+
+\include QuickStart_example.cpp
+
+We will explain the program after telling you how to compile it.
+
+
+\section GettingStartedCompiling Compiling and running your first program
+
+There is no library to link to. The only thing that you need to keep in mind when compiling the above program is that the compiler must be able to find the Eigen header files. The directory in which you placed Eigen's source code must be in the include path. With GCC you use the \c -I option to achieve this, so you can compile the program with a command like this:
+
+\code g++ -I /path/to/eigen/ my_program.cpp -o my_program \endcode
+
+On Linux or Mac OS X, another option is to symlink or copy the Eigen folder into \c /usr/local/include/. This way, you can compile the program with:
+
+\code g++ my_program.cpp -o my_program \endcode
+
+When you run the program, it produces the following output:
+
+\include QuickStart_example.out
+
+
+\section GettingStartedExplanation Explanation of the first program
+
+The Eigen header files define many types, but for simple applications it may be enough to use only the \c MatrixXd type. This represents a matrix of arbitrary size (hence the \c X in \c MatrixXd), in which every entry is a \c double (hence the \c d in \c MatrixXd). See the \ref QuickRef_Types "quick reference guide" for an overview of the different types you can use to represent a matrix.
+
+The \c Eigen/Dense header file defines all member functions for the MatrixXd type and related types (see also the \ref QuickRef_Headers "table of header files"). All classes and functions defined in this header file (and other Eigen header files) are in the \c Eigen namespace.
+
+The first line of the \c main function declares a variable of type \c MatrixXd and specifies that it is a matrix with 2 rows and 2 columns (the entries are not initialized). The statement <tt>m(0,0) = 3</tt> sets the entry in the top-left corner to 3. You need to use round parentheses to refer to entries in the matrix. As usual in computer science, the index of the first index is 0, as opposed to the convention in mathematics that the first index is 1.
+
+The following three statements sets the other three entries. The final line outputs the matrix \c m to the standard output stream.
+
+
+\section GettingStartedExample2 Example 2: Matrices and vectors
+
+Here is another example, which combines matrices with vectors. Concentrate on the left-hand program for now; we will talk about the right-hand program later.
+
+<table class="manual">
+<tr><th>Size set at run time:</th><th>Size set at compile time:</th></tr>
+<tr><td>
+\include QuickStart_example2_dynamic.cpp
+</td>
+<td>
+\include QuickStart_example2_fixed.cpp
+</td></tr></table>
+
+The output is as follows:
+
+\include QuickStart_example2_dynamic.out
+
+
+\section GettingStartedExplanation2 Explanation of the second example
+
+The second example starts by declaring a 3-by-3 matrix \c m which is initialized using the \link DenseBase::Random(Index,Index) Random() \endlink method with random values between -1 and 1. The next line applies a linear mapping such that the values are between 10 and 110. The function call \link DenseBase::Constant(Index,Index,const Scalar&) MatrixXd::Constant\endlink(3,3,1.2) returns a 3-by-3 matrix expression having all coefficients equal to 1.2. The rest is standard arithmetic.
+
+The next line of the \c main function introduces a new type: \c VectorXd. This represents a (column) vector of arbitrary size. Here, the vector \c v is created to contain \c 3 coefficients which are left uninitialized. The one but last line uses the so-called comma-initializer, explained in \ref TutorialAdvancedInitialization, to set all coefficients of the vector \c v to be as follows:
+
+\f[
+v =
+\begin{bmatrix}
+ 1 \\
+ 2 \\
+ 3
+\end{bmatrix}.
+\f]
+
+The final line of the program multiplies the matrix \c m with the vector \c v and outputs the result.
+
+Now look back at the second example program. We presented two versions of it. In the version in the left column, the matrix is of type \c MatrixXd which represents matrices of arbitrary size. The version in the right column is similar, except that the matrix is of type \c Matrix3d, which represents matrices of a fixed size (here 3-by-3). Because the type already encodes the size of the matrix, it is not necessary to specify the size in the constructor; compare <tt>MatrixXd m(3,3)</tt> with <tt>Matrix3d m</tt>. Similarly, we have \c VectorXd on the left (arbitrary size) versus \c Vector3d on the right (fixed size). Note that here the coefficients of vector \c v are directly set in the constructor, though the same syntax of the left example could be used too.
+
+The use of fixed-size matrices and vectors has two advantages. The compiler emits better (faster) code because it knows the size of the matrices and vectors. Specifying the size in the type also allows for more rigorous checking at compile-time. For instance, the compiler will complain if you try to multiply a \c Matrix4d (a 4-by-4 matrix) with a \c Vector3d (a vector of size 3). However, the use of many types increases compilation time and the size of the executable. The size of the matrix may also not be known at compile-time. A rule of thumb is to use fixed-size matrices for size 4-by-4 and smaller.
+
+
+\section GettingStartedConclusion Where to go from here?
+
+It's worth taking the time to read the \ref TutorialMatrixClass "long tutorial".
+
+However if you think you don't need it, you can directly use the classes documentation and our \ref QuickRefPage.
+
+\li \b Next: \ref TutorialMatrixClass
+
+*/
+
+}
+
diff --git a/doc/SparseLinearSystems.dox b/doc/SparseLinearSystems.dox
new file mode 100644
index 0000000..0135ee2
--- /dev/null
+++ b/doc/SparseLinearSystems.dox
@@ -0,0 +1,228 @@
+namespace Eigen {
+/** \eigenManualPage TopicSparseSystems Solving Sparse Linear Systems
+In Eigen, there are several methods available to solve linear systems when the coefficient matrix is sparse. Because of the special representation of this class of matrices, special care should be taken in order to get a good performance. See \ref TutorialSparse for a detailed introduction about sparse matrices in Eigen. This page lists the sparse solvers available in Eigen. The main steps that are common to all these linear solvers are introduced as well. Depending on the properties of the matrix, the desired accuracy, the end-user is able to tune those steps in order to improve the performance of its code. Note that it is not required to know deeply what's hiding behind these steps: the last section presents a benchmark routine that can be easily used to get an insight on the performance of all the available solvers.
+
+\eigenAutoToc
+
+\section TutorialSparseSolverList List of sparse solvers
+
+%Eigen currently provides a wide set of built-in solvers, as well as wrappers to external solver libraries.
+They are summarized in the following tables:
+
+\subsection TutorialSparseSolverList_Direct Built-in direct solvers
+
+<table class="manual">
+<tr><th>Class</th><th>Solver kind</th><th>Matrix kind</th><th>Features related to performance</th>
+ <th class="width20em"><p>Notes</p></th></tr>
+
+<tr><td>SimplicialLLT \n <tt>\#include<Eigen/\link SparseCholesky_Module SparseCholesky\endlink></tt></td><td>Direct LLt factorization</td><td>SPD</td><td>Fill-in reducing</td>
+ <td>SimplicialLDLT is often preferable</td></tr>
+
+<tr><td>SimplicialLDLT \n <tt>\#include<Eigen/\link SparseCholesky_Module SparseCholesky\endlink></tt></td><td>Direct LDLt factorization</td><td>SPD</td><td>Fill-in reducing</td>
+ <td>Recommended for very sparse and not too large problems (e.g., 2D Poisson eq.)</td></tr>
+
+<tr><td>SparseLU \n <tt>\#include<Eigen/\link SparseLU_Module SparseLU\endlink></tt></td> <td>LU factorization </td>
+ <td>Square </td><td>Fill-in reducing, Leverage fast dense algebra</td>
+ <td>optimized for small and large problems with irregular patterns </td></tr>
+
+<tr><td>SparseQR \n <tt>\#include<Eigen/\link SparseQR_Module SparseQR\endlink></tt></td> <td> QR factorization</td>
+ <td>Any, rectangular</td><td> Fill-in reducing</td>
+ <td>recommended for least-square problems, has a basic rank-revealing feature</td></tr>
+ </table>
+
+\subsection TutorialSparseSolverList_Iterative Built-in iterative solvers
+
+<table class="manual">
+<tr><th>Class</th><th>Solver kind</th><th>Matrix kind</th><th>Supported preconditioners, [default]</th>
+ <th class="width20em"><p>Notes</p></th></tr>
+
+<tr><td>ConjugateGradient \n <tt>\#include<Eigen/\link IterativeLinearSolvers_Module IterativeLinearSolvers\endlink></tt></td> <td>Classic iterative CG</td><td>SPD</td>
+ <td>IdentityPreconditioner, [DiagonalPreconditioner], IncompleteCholesky</td>
+ <td>Recommended for large symmetric problems (e.g., 3D Poisson eq.)</td></tr>
+
+<tr><td>LeastSquaresConjugateGradient \n <tt>\#include<Eigen/\link IterativeLinearSolvers_Module IterativeLinearSolvers\endlink></tt></td><td>CG for rectangular least-square problem</td><td>Rectangular</td>
+ <td>IdentityPreconditioner, [LeastSquareDiagonalPreconditioner]</td>
+ <td>Solve for min |Ax-b|^2 without forming A'A</td></tr>
+
+<tr><td>BiCGSTAB \n <tt>\#include<Eigen/\link IterativeLinearSolvers_Module IterativeLinearSolvers\endlink></tt></td><td>Iterative stabilized bi-conjugate gradient</td><td>Square</td>
+ <td>IdentityPreconditioner, [DiagonalPreconditioner], IncompleteLUT</td>
+ <td>To speedup the convergence, try it with the \ref IncompleteLUT preconditioner.</td></tr>
+</table>
+
+\subsection TutorialSparseSolverList_Wrapper Wrappers to external solvers
+
+<table class="manual">
+<tr><th>Class</th><th>Module</th><th>Solver kind</th><th>Matrix kind</th><th>Features related to performance</th>
+ <th>Dependencies,License</th><th class="width20em"><p>Notes</p></th></tr>
+<tr><td>PastixLLT \n PastixLDLT \n PastixLU</td><td>\link PaStiXSupport_Module PaStiXSupport \endlink</td><td>Direct LLt, LDLt, LU factorizations</td><td>SPD \n SPD \n Square</td><td>Fill-in reducing, Leverage fast dense algebra, Multithreading</td>
+ <td>Requires the <a href="http://pastix.gforge.inria.fr">PaStiX</a> package, \b CeCILL-C </td>
+ <td>optimized for tough problems and symmetric patterns</td></tr>
+<tr><td>CholmodSupernodalLLT</td><td>\link CholmodSupport_Module CholmodSupport \endlink</td><td>Direct LLt factorization</td><td>SPD</td><td>Fill-in reducing, Leverage fast dense algebra</td>
+ <td>Requires the <a href="http://www.suitesparse.com">SuiteSparse</a> package, \b GPL </td>
+ <td></td></tr>
+<tr><td>UmfPackLU</td><td>\link UmfPackSupport_Module UmfPackSupport \endlink</td><td>Direct LU factorization</td><td>Square</td><td>Fill-in reducing, Leverage fast dense algebra</td>
+ <td>Requires the <a href="http://www.suitesparse.com">SuiteSparse</a> package, \b GPL </td>
+ <td></td></tr>
+<tr><td>KLU</td><td>\link KLUSupport_Module KLUSupport \endlink</td><td>Direct LU factorization</td><td>Square</td><td>Fill-in reducing, suitted for circuit simulation</td>
+ <td>Requires the <a href="http://www.suitesparse.com">SuiteSparse</a> package, \b GPL </td>
+ <td></td></tr>
+<tr><td>SuperLU</td><td>\link SuperLUSupport_Module SuperLUSupport \endlink</td><td>Direct LU factorization</td><td>Square</td><td>Fill-in reducing, Leverage fast dense algebra</td>
+ <td>Requires the <a href="http://crd-legacy.lbl.gov/~xiaoye/SuperLU/">SuperLU</a> library, (BSD-like)</td>
+ <td></td></tr>
+<tr><td>SPQR</td><td>\link SPQRSupport_Module SPQRSupport \endlink </td> <td> QR factorization </td>
+ <td> Any, rectangular</td><td>fill-in reducing, multithreaded, fast dense algebra</td>
+ <td> requires the <a href="http://www.suitesparse.com">SuiteSparse</a> package, \b GPL </td><td>recommended for linear least-squares problems, has a rank-revealing feature</tr>
+<tr><td>PardisoLLT \n PardisoLDLT \n PardisoLU</td><td>\link PardisoSupport_Module PardisoSupport \endlink</td><td>Direct LLt, LDLt, LU factorizations</td><td>SPD \n SPD \n Square</td><td>Fill-in reducing, Leverage fast dense algebra, Multithreading</td>
+ <td>Requires the <a href="http://eigen.tuxfamily.org/Counter/redirect_to_mkl.php">Intel MKL</a> package, \b Proprietary </td>
+ <td>optimized for tough problems patterns, see also \link TopicUsingIntelMKL using MKL with Eigen \endlink</td></tr>
+<tr><td>AccelerateLLT \n AccelerateLDLT \n AccelerateQR</td><td>\link AccelerateSupport_Module AccelerateSupport \endlink</td><td>Direct LLt, LDLt, QR factorizations</td><td>SPD \n SPD \n Rectangular</td><td>Fill-in reducing, Leverage fast dense algebra, Multithreading</td>
+ <td>Requires the <a href="https://developer.apple.com/documentation/accelerate">Apple Accelerate</a> package, \b Proprietary </td>
+ <td></td></tr>
+</table>
+
+Here \c SPD means symmetric positive definite.
+
+\section TutorialSparseSolverConcept Sparse solver concept
+
+All these solvers follow the same general concept.
+Here is a typical and general example:
+\code
+#include <Eigen/RequiredModuleName>
+// ...
+SparseMatrix<double> A;
+// fill A
+VectorXd b, x;
+// fill b
+// solve Ax = b
+SolverClassName<SparseMatrix<double> > solver;
+solver.compute(A);
+if(solver.info()!=Success) {
+ // decomposition failed
+ return;
+}
+x = solver.solve(b);
+if(solver.info()!=Success) {
+ // solving failed
+ return;
+}
+// solve for another right hand side:
+x1 = solver.solve(b1);
+\endcode
+
+For \c SPD solvers, a second optional template argument allows to specify which triangular part have to be used, e.g.:
+
+\code
+#include <Eigen/IterativeLinearSolvers>
+
+ConjugateGradient<SparseMatrix<double>, Eigen::Upper> solver;
+x = solver.compute(A).solve(b);
+\endcode
+In the above example, only the upper triangular part of the input matrix A is considered for solving. The opposite triangle might either be empty or contain arbitrary values.
+
+In the case where multiple problems with the same sparsity pattern have to be solved, then the "compute" step can be decomposed as follow:
+\code
+SolverClassName<SparseMatrix<double> > solver;
+solver.analyzePattern(A); // for this step the numerical values of A are not used
+solver.factorize(A);
+x1 = solver.solve(b1);
+x2 = solver.solve(b2);
+...
+A = ...; // modify the values of the nonzeros of A, the nonzeros pattern must stay unchanged
+solver.factorize(A);
+x1 = solver.solve(b1);
+x2 = solver.solve(b2);
+...
+\endcode
+The `compute()` method is equivalent to calling both `analyzePattern()` and `factorize()`.
+
+Each solver provides some specific features, such as determinant, access to the factors, controls of the iterations, and so on.
+More details are available in the documentations of the respective classes.
+
+Finally, most of the iterative solvers, can also be used in a \b matrix-free context, see the following \link MatrixfreeSolverExample example \endlink.
+
+\section TheSparseCompute The Compute Step
+In the `compute()` function, the matrix is generally factorized: LLT for self-adjoint matrices, LDLT for general hermitian matrices, LU for non hermitian matrices and QR for rectangular matrices. These are the results of using direct solvers. For this class of solvers precisely, the compute step is further subdivided into `analyzePattern()` and `factorize()`.
+
+The goal of `analyzePattern()` is to reorder the nonzero elements of the matrix, such that the factorization step creates less fill-in. This step exploits only the structure of the matrix. Hence, the results of this step can be used for other linear systems where the matrix has the same structure. Note however that sometimes, some external solvers (like SuperLU) require that the values of the matrix are set in this step, for instance to equilibrate the rows and columns of the matrix. In this situation, the results of this step should not be used with other matrices.
+
+Eigen provides a limited set of methods to reorder the matrix in this step, either built-in (COLAMD, AMD) or external (METIS). These methods are set in template parameter list of the solver :
+\code
+DirectSolverClassName<SparseMatrix<double>, OrderingMethod<IndexType> > solver;
+\endcode
+
+See the \link OrderingMethods_Module OrderingMethods module \endlink for the list of available methods and the associated options.
+
+In `factorize()`, the factors of the coefficient matrix are computed. This step should be called each time the values of the matrix change. However, the structural pattern of the matrix should not change between multiple calls.
+
+For iterative solvers, the compute step is used to eventually setup a preconditioner. For instance, with the ILUT preconditioner, the incomplete factors L and U are computed in this step. Remember that, basically, the goal of the preconditioner is to speedup the convergence of an iterative method by solving a modified linear system where the coefficient matrix has more clustered eigenvalues. For real problems, an iterative solver should always be used with a preconditioner. In Eigen, a preconditioner is selected by simply adding it as a template parameter to the iterative solver object.
+\code
+IterativeSolverClassName<SparseMatrix<double>, PreconditionerName<SparseMatrix<double> > solver;
+\endcode
+The member function `preconditioner()` returns a read-write reference to the preconditioner
+ to directly interact with it. See the \link IterativeLinearSolvers_Module Iterative solvers module \endlink and the documentation of each class for the list of available methods.
+
+\section TheSparseSolve The Solve step
+The `solve()` function computes the solution of the linear systems with one or many right hand sides.
+\code
+X = solver.solve(B);
+\endcode
+Here, B can be a vector or a matrix where the columns form the different right hand sides. `The solve()` function can be called several times as well, for instance when all the right hand sides are not available at once.
+\code
+x1 = solver.solve(b1);
+// Get the second right hand side b2
+x2 = solver.solve(b2);
+// ...
+\endcode
+For direct methods, the solution are computed at the machine precision. Sometimes, the solution need not be too accurate. In this case, the iterative methods are more suitable and the desired accuracy can be set before the solve step using \b setTolerance(). For all the available functions, please, refer to the documentation of the \link IterativeLinearSolvers_Module Iterative solvers module \endlink.
+
+\section BenchmarkRoutine
+Most of the time, all you need is to know how much time it will take to solve your system, and hopefully, what is the most suitable solver. In Eigen, we provide a benchmark routine that can be used for this purpose. It is very easy to use. In the build directory, navigate to `bench/spbench` and compile the routine by typing `make spbenchsolver`. Run it with `--help` option to get the list of all available options. Basically, the matrices to test should be in <a href="http://math.nist.gov/MatrixMarket/formats.html">MatrixMarket Coordinate format</a>, and the routine returns the statistics from all available solvers in Eigen.
+
+To export your matrices and right-hand-side vectors in the matrix-market format, you can the the unsupported SparseExtra module:
+\code
+#include <unsupported/Eigen/SparseExtra>
+...
+Eigen::saveMarket(A, "filename.mtx");
+Eigen::saveMarket(A, "filename_SPD.mtx", Eigen::Symmetric); // if A is symmetric-positive-definite
+Eigen::saveMarketVector(B, "filename_b.mtx");
+\endcode
+
+The following table gives an example of XML statistics from several Eigen built-in and external solvers.
+<TABLE border="1">
+ <TR><TH>Matrix <TH> N <TH> NNZ <TH> <TH > UMFPACK <TH > SUPERLU <TH > PASTIX LU <TH >BiCGSTAB <TH > BiCGSTAB+ILUT <TH >GMRES+ILUT<TH > LDLT <TH> CHOLMOD LDLT <TH > PASTIX LDLT <TH > LLT <TH > CHOLMOD SP LLT <TH > CHOLMOD LLT <TH > PASTIX LLT <TH> CG</TR>
+<TR><TH rowspan="4">vector_graphics <TD rowspan="4"> 12855 <TD rowspan="4"> 72069 <TH>Compute Time <TD>0.0254549<TD>0.0215677<TD>0.0701827<TD>0.000153388<TD>0.0140107<TD>0.0153709<TD>0.0101601<TD style="background-color:red">0.00930502<TD>0.0649689
+<TR><TH>Solve Time <TD>0.00337835<TD>0.000951826<TD>0.00484373<TD>0.0374886<TD>0.0046445<TD>0.00847754<TD>0.000541813<TD style="background-color:red">0.000293696<TD>0.00485376
+<TR><TH>Total Time <TD>0.0288333<TD>0.0225195<TD>0.0750265<TD>0.037642<TD>0.0186552<TD>0.0238484<TD>0.0107019<TD style="background-color:red">0.00959871<TD>0.0698227
+<TR><TH>Error(Iter) <TD> 1.299e-16 <TD> 2.04207e-16 <TD> 4.83393e-15 <TD> 3.94856e-11 (80) <TD> 1.03861e-12 (3) <TD> 5.81088e-14 (6) <TD> 1.97578e-16 <TD> 1.83927e-16 <TD> 4.24115e-15
+<TR><TH rowspan="4">poisson_SPD <TD rowspan="4"> 19788 <TD rowspan="4"> 308232 <TH>Compute Time <TD>0.425026<TD>1.82378<TD>0.617367<TD>0.000478921<TD>1.34001<TD>1.33471<TD>0.796419<TD>0.857573<TD>0.473007<TD>0.814826<TD style="background-color:red">0.184719<TD>0.861555<TD>0.470559<TD>0.000458188
+<TR><TH>Solve Time <TD>0.0280053<TD>0.0194402<TD>0.0268747<TD>0.249437<TD>0.0548444<TD>0.0926991<TD>0.00850204<TD>0.0053171<TD>0.0258932<TD>0.00874603<TD style="background-color:red">0.00578155<TD>0.00530361<TD>0.0248942<TD>0.239093
+<TR><TH>Total Time <TD>0.453031<TD>1.84322<TD>0.644241<TD>0.249916<TD>1.39486<TD>1.42741<TD>0.804921<TD>0.862891<TD>0.4989<TD>0.823572<TD style="background-color:red">0.190501<TD>0.866859<TD>0.495453<TD>0.239551
+<TR><TH>Error(Iter) <TD> 4.67146e-16 <TD> 1.068e-15 <TD> 1.3397e-15 <TD> 6.29233e-11 (201) <TD> 3.68527e-11 (6) <TD> 3.3168e-15 (16) <TD> 1.86376e-15 <TD> 1.31518e-16 <TD> 1.42593e-15 <TD> 3.45361e-15 <TD> 3.14575e-16 <TD> 2.21723e-15 <TD> 7.21058e-16 <TD> 9.06435e-12 (261)
+<TR><TH rowspan="4">sherman2 <TD rowspan="4"> 1080 <TD rowspan="4"> 23094 <TH>Compute Time <TD style="background-color:red">0.00631754<TD>0.015052<TD>0.0247514 <TD> -<TD>0.0214425<TD>0.0217988
+<TR><TH>Solve Time <TD style="background-color:red">0.000478424<TD>0.000337998<TD>0.0010291 <TD> -<TD>0.00243152<TD>0.00246152
+<TR><TH>Total Time <TD style="background-color:red">0.00679597<TD>0.01539<TD>0.0257805 <TD> -<TD>0.023874<TD>0.0242603
+<TR><TH>Error(Iter) <TD> 1.83099e-15 <TD> 8.19351e-15 <TD> 2.625e-14 <TD> 1.3678e+69 (1080) <TD> 4.1911e-12 (7) <TD> 5.0299e-13 (12)
+<TR><TH rowspan="4">bcsstk01_SPD <TD rowspan="4"> 48 <TD rowspan="4"> 400 <TH>Compute Time <TD>0.000169079<TD>0.00010789<TD>0.000572538<TD>1.425e-06<TD>9.1612e-05<TD>8.3985e-05<TD style="background-color:red">5.6489e-05<TD>7.0913e-05<TD>0.000468251<TD>5.7389e-05<TD>8.0212e-05<TD>5.8394e-05<TD>0.000463017<TD>1.333e-06
+<TR><TH>Solve Time <TD>1.2288e-05<TD>1.1124e-05<TD>0.000286387<TD>8.5896e-05<TD>1.6381e-05<TD>1.6984e-05<TD style="background-color:red">3.095e-06<TD>4.115e-06<TD>0.000325438<TD>3.504e-06<TD>7.369e-06<TD>3.454e-06<TD>0.000294095<TD>6.0516e-05
+<TR><TH>Total Time <TD>0.000181367<TD>0.000119014<TD>0.000858925<TD>8.7321e-05<TD>0.000107993<TD>0.000100969<TD style="background-color:red">5.9584e-05<TD>7.5028e-05<TD>0.000793689<TD>6.0893e-05<TD>8.7581e-05<TD>6.1848e-05<TD>0.000757112<TD>6.1849e-05
+<TR><TH>Error(Iter) <TD> 1.03474e-16 <TD> 2.23046e-16 <TD> 2.01273e-16 <TD> 4.87455e-07 (48) <TD> 1.03553e-16 (2) <TD> 3.55965e-16 (2) <TD> 2.48189e-16 <TD> 1.88808e-16 <TD> 1.97976e-16 <TD> 2.37248e-16 <TD> 1.82701e-16 <TD> 2.71474e-16 <TD> 2.11322e-16 <TD> 3.547e-09 (48)
+<TR><TH rowspan="4">sherman1 <TD rowspan="4"> 1000 <TD rowspan="4"> 3750 <TH>Compute Time <TD>0.00228805<TD>0.00209231<TD>0.00528268<TD>9.846e-06<TD>0.00163522<TD>0.00162155<TD>0.000789259<TD style="background-color:red">0.000804495<TD>0.00438269
+<TR><TH>Solve Time <TD>0.000213788<TD>9.7983e-05<TD>0.000938831<TD>0.00629835<TD>0.000361764<TD>0.00078794<TD>4.3989e-05<TD style="background-color:red">2.5331e-05<TD>0.000917166
+<TR><TH>Total Time <TD>0.00250184<TD>0.00219029<TD>0.00622151<TD>0.0063082<TD>0.00199698<TD>0.00240949<TD>0.000833248<TD style="background-color:red">0.000829826<TD>0.00529986
+<TR><TH>Error(Iter) <TD> 1.16839e-16 <TD> 2.25968e-16 <TD> 2.59116e-16 <TD> 3.76779e-11 (248) <TD> 4.13343e-11 (4) <TD> 2.22347e-14 (10) <TD> 2.05861e-16 <TD> 1.83555e-16 <TD> 1.02917e-15
+<TR><TH rowspan="4">young1c <TD rowspan="4"> 841 <TD rowspan="4"> 4089 <TH>Compute Time <TD>0.00235843<TD style="background-color:red">0.00217228<TD>0.00568075<TD>1.2735e-05<TD>0.00264866<TD>0.00258236
+<TR><TH>Solve Time <TD>0.000329599<TD style="background-color:red">0.000168634<TD>0.00080118<TD>0.0534738<TD>0.00187193<TD>0.00450211
+<TR><TH>Total Time <TD>0.00268803<TD style="background-color:red">0.00234091<TD>0.00648193<TD>0.0534865<TD>0.00452059<TD>0.00708447
+<TR><TH>Error(Iter) <TD> 1.27029e-16 <TD> 2.81321e-16 <TD> 5.0492e-15 <TD> 8.0507e-11 (706) <TD> 3.00447e-12 (8) <TD> 1.46532e-12 (16)
+<TR><TH rowspan="4">mhd1280b <TD rowspan="4"> 1280 <TD rowspan="4"> 22778 <TH>Compute Time <TD>0.00234898<TD>0.00207079<TD>0.00570918<TD>2.5976e-05<TD>0.00302563<TD>0.00298036<TD>0.00144525<TD style="background-color:red">0.000919922<TD>0.00426444
+<TR><TH>Solve Time <TD>0.00103392<TD>0.000211911<TD>0.00105<TD>0.0110432<TD>0.000628287<TD>0.00392089<TD>0.000138303<TD style="background-color:red">6.2446e-05<TD>0.00097564
+<TR><TH>Total Time <TD>0.0033829<TD>0.0022827<TD>0.00675918<TD>0.0110692<TD>0.00365392<TD>0.00690124<TD>0.00158355<TD style="background-color:red">0.000982368<TD>0.00524008
+<TR><TH>Error(Iter) <TD> 1.32953e-16 <TD> 3.08646e-16 <TD> 6.734e-16 <TD> 8.83132e-11 (40) <TD> 1.51153e-16 (1) <TD> 6.08556e-16 (8) <TD> 1.89264e-16 <TD> 1.97477e-16 <TD> 6.68126e-09
+<TR><TH rowspan="4">crashbasis <TD rowspan="4"> 160000 <TD rowspan="4"> 1750416 <TH>Compute Time <TD>3.2019<TD>5.7892<TD>15.7573<TD style="background-color:red">0.00383515<TD>3.1006<TD>3.09921
+<TR><TH>Solve Time <TD>0.261915<TD>0.106225<TD>0.402141<TD style="background-color:red">1.49089<TD>0.24888<TD>0.443673
+<TR><TH>Total Time <TD>3.46381<TD>5.89542<TD>16.1594<TD style="background-color:red">1.49473<TD>3.34948<TD>3.54288
+<TR><TH>Error(Iter) <TD> 1.76348e-16 <TD> 4.58395e-16 <TD> 1.67982e-14 <TD> 8.64144e-11 (61) <TD> 8.5996e-12 (2) <TD> 6.04042e-14 (5)
+
+</TABLE>
+*/
+}
diff --git a/doc/SparseQuickReference.dox b/doc/SparseQuickReference.dox
new file mode 100644
index 0000000..b8264a4
--- /dev/null
+++ b/doc/SparseQuickReference.dox
@@ -0,0 +1,272 @@
+namespace Eigen {
+/** \eigenManualPage SparseQuickRefPage Quick reference guide for sparse matrices
+\eigenAutoToc
+
+<hr>
+
+In this page, we give a quick summary of the main operations available for sparse matrices in the class SparseMatrix. First, it is recommended to read the introductory tutorial at \ref TutorialSparse. The important point to have in mind when working on sparse matrices is how they are stored :
+i.e either row major or column major. The default is column major. Most arithmetic operations on sparse matrices will assert that they have the same storage order.
+
+\section SparseMatrixInit Sparse Matrix Initialization
+<table class="manual">
+<tr><th> Category </th> <th> Operations</th> <th>Notes</th></tr>
+<tr><td>Constructor</td>
+<td>
+\code
+ SparseMatrix<double> sm1(1000,1000);
+ SparseMatrix<std::complex<double>,RowMajor> sm2;
+\endcode
+</td> <td> Default is ColMajor</td> </tr>
+<tr class="alt">
+<td> Resize/Reserve</td>
+<td>
+ \code
+ sm1.resize(m,n); // Change sm1 to a m x n matrix.
+ sm1.reserve(nnz); // Allocate room for nnz nonzeros elements.
+ \endcode
+</td>
+<td> Note that when calling reserve(), it is not required that nnz is the exact number of nonzero elements in the final matrix. However, an exact estimation will avoid multiple reallocations during the insertion phase. </td>
+</tr>
+<tr>
+<td> Assignment </td>
+<td>
+\code
+ SparseMatrix<double,Colmajor> sm1;
+ // Initialize sm2 with sm1.
+ SparseMatrix<double,Rowmajor> sm2(sm1), sm3;
+ // Assignment and evaluations modify the storage order.
+ sm3 = sm1;
+ \endcode
+</td>
+<td> The copy constructor can be used to convert from a storage order to another</td>
+</tr>
+<tr class="alt">
+<td> Element-wise Insertion</td>
+<td>
+\code
+// Insert a new element;
+ sm1.insert(i, j) = v_ij;
+
+// Update the value v_ij
+ sm1.coeffRef(i,j) = v_ij;
+ sm1.coeffRef(i,j) += v_ij;
+ sm1.coeffRef(i,j) -= v_ij;
+\endcode
+</td>
+<td> insert() assumes that the element does not already exist; otherwise, use coeffRef()</td>
+</tr>
+<tr>
+<td> Batch insertion</td>
+<td>
+\code
+ std::vector< Eigen::Triplet<double> > tripletList;
+ tripletList.reserve(estimation_of_entries);
+ // -- Fill tripletList with nonzero elements...
+ sm1.setFromTriplets(TripletList.begin(), TripletList.end());
+\endcode
+</td>
+<td>A complete example is available at \link TutorialSparseFilling Triplet Insertion \endlink.</td>
+</tr>
+<tr class="alt">
+<td> Constant or Random Insertion</td>
+<td>
+\code
+sm1.setZero();
+\endcode
+</td>
+<td>Remove all non-zero coefficients</td>
+</tr>
+</table>
+
+
+\section SparseBasicInfos Matrix properties
+Beyond the basic functions rows() and cols(), there are some useful functions that are available to easily get some information from the matrix.
+<table class="manual">
+<tr>
+ <td> \code
+ sm1.rows(); // Number of rows
+ sm1.cols(); // Number of columns
+ sm1.nonZeros(); // Number of non zero values
+ sm1.outerSize(); // Number of columns (resp. rows) for a column major (resp. row major )
+ sm1.innerSize(); // Number of rows (resp. columns) for a row major (resp. column major)
+ sm1.norm(); // Euclidian norm of the matrix
+ sm1.squaredNorm(); // Squared norm of the matrix
+ sm1.blueNorm();
+ sm1.isVector(); // Check if sm1 is a sparse vector or a sparse matrix
+ sm1.isCompressed(); // Check if sm1 is in compressed form
+ ...
+ \endcode </td>
+</tr>
+</table>
+
+\section SparseBasicOps Arithmetic operations
+It is easy to perform arithmetic operations on sparse matrices provided that the dimensions are adequate and that the matrices have the same storage order. Note that the evaluation can always be done in a matrix with a different storage order. In the following, \b sm denotes a sparse matrix, \b dm a dense matrix and \b dv a dense vector.
+<table class="manual">
+<tr><th> Operations </th> <th> Code </th> <th> Notes </th></tr>
+
+<tr>
+ <td> add subtract </td>
+ <td> \code
+ sm3 = sm1 + sm2;
+ sm3 = sm1 - sm2;
+ sm2 += sm1;
+ sm2 -= sm1; \endcode
+ </td>
+ <td>
+ sm1 and sm2 should have the same storage order
+ </td>
+</tr>
+
+<tr class="alt"><td>
+ scalar product</td><td>\code
+ sm3 = sm1 * s1; sm3 *= s1;
+ sm3 = s1 * sm1 + s2 * sm2; sm3 /= s1;\endcode
+ </td>
+ <td>
+ Many combinations are possible if the dimensions and the storage order agree.
+</tr>
+
+<tr>
+ <td> %Sparse %Product </td>
+ <td> \code
+ sm3 = sm1 * sm2;
+ dm2 = sm1 * dm1;
+ dv2 = sm1 * dv1;
+ \endcode </td>
+ <td>
+ </td>
+</tr>
+
+<tr class='alt'>
+ <td> transposition, adjoint</td>
+ <td> \code
+ sm2 = sm1.transpose();
+ sm2 = sm1.adjoint();
+ \endcode </td>
+ <td>
+ Note that the transposition change the storage order. There is no support for transposeInPlace().
+ </td>
+</tr>
+<tr>
+<td> Permutation </td>
+<td>
+\code
+perm.indices(); // Reference to the vector of indices
+sm1.twistedBy(perm); // Permute rows and columns
+sm2 = sm1 * perm; // Permute the columns
+sm2 = perm * sm1; // Permute the columns
+\endcode
+</td>
+<td>
+
+</td>
+</tr>
+<tr>
+ <td>
+ Component-wise ops
+ </td>
+ <td>\code
+ sm1.cwiseProduct(sm2);
+ sm1.cwiseQuotient(sm2);
+ sm1.cwiseMin(sm2);
+ sm1.cwiseMax(sm2);
+ sm1.cwiseAbs();
+ sm1.cwiseSqrt();
+ \endcode</td>
+ <td>
+ sm1 and sm2 should have the same storage order
+ </td>
+</tr>
+</table>
+
+\section sparseotherops Other supported operations
+<table class="manual">
+<tr><th style="min-width:initial"> Code </th> <th> Notes</th> </tr>
+<tr><td colspan="2">Sub-matrices</td></tr>
+<tr>
+<td>
+\code
+ sm1.block(startRow, startCol, rows, cols);
+ sm1.block(startRow, startCol);
+ sm1.topLeftCorner(rows, cols);
+ sm1.topRightCorner(rows, cols);
+ sm1.bottomLeftCorner( rows, cols);
+ sm1.bottomRightCorner( rows, cols);
+ \endcode
+</td><td>
+Contrary to dense matrices, here <strong>all these methods are read-only</strong>.\n
+See \ref TutorialSparse_SubMatrices and below for read-write sub-matrices.
+</td>
+</tr>
+<tr class="alt"><td colspan="2"> Range </td></tr>
+<tr class="alt">
+<td>
+\code
+ sm1.innerVector(outer); // RW
+ sm1.innerVectors(start, size); // RW
+ sm1.leftCols(size); // RW
+ sm2.rightCols(size); // RO because sm2 is row-major
+ sm1.middleRows(start, numRows); // RO because sm1 is column-major
+ sm1.middleCols(start, numCols); // RW
+ sm1.col(j); // RW
+\endcode
+</td>
+<td>
+A inner vector is either a row (for row-major) or a column (for column-major).\n
+As stated earlier, for a read-write sub-matrix (RW), the evaluation can be done in a matrix with different storage order.
+</td>
+</tr>
+<tr><td colspan="2"> Triangular and selfadjoint views</td></tr>
+<tr>
+<td>
+\code
+ sm2 = sm1.triangularview<Lower>();
+ sm2 = sm1.selfadjointview<Lower>();
+\endcode
+</td>
+<td> Several combination between triangular views and blocks views are possible
+\code
+ \endcode </td>
+</tr>
+<tr class="alt"><td colspan="2">Triangular solve </td></tr>
+<tr class="alt">
+<td>
+\code
+ dv2 = sm1.triangularView<Upper>().solve(dv1);
+ dv2 = sm1.topLeftCorner(size, size)
+ .triangularView<Lower>().solve(dv1);
+\endcode
+</td>
+<td> For general sparse solve, Use any suitable module described at \ref TopicSparseSystems </td>
+</tr>
+<tr><td colspan="2"> Low-level API</td></tr>
+<tr>
+<td>
+\code
+sm1.valuePtr(); // Pointer to the values
+sm1.innerIndexPtr(); // Pointer to the indices.
+sm1.outerIndexPtr(); // Pointer to the beginning of each inner vector
+\endcode
+</td>
+<td>
+If the matrix is not in compressed form, `makeCompressed()` should be called before.\n
+Note that these functions are mostly provided for interoperability purposes with external libraries.\n
+A better access to the values of the matrix is done by using the InnerIterator class as described in \link TutorialSparse the Tutorial Sparse \endlink section</td>
+</tr>
+<tr class="alt"><td colspan="2">Mapping external buffers</td></tr>
+<tr class="alt">
+<td>
+\code
+int outerIndexPtr[cols+1];
+int innerIndices[nnz];
+double values[nnz];
+Map<SparseMatrix<double> > sm1(rows,cols,nnz,outerIndexPtr, // read-write
+ innerIndices,values);
+Map<const SparseMatrix<double> > sm2(...); // read-only
+\endcode
+</td>
+<td>As for dense matrices, class Map<SparseMatrixType> can be used to see external buffers as an %Eigen's SparseMatrix object. </td>
+</tr>
+</table>
+*/
+}
diff --git a/doc/StlContainers.dox b/doc/StlContainers.dox
new file mode 100644
index 0000000..0342573
--- /dev/null
+++ b/doc/StlContainers.dox
@@ -0,0 +1,73 @@
+namespace Eigen {
+
+/** \eigenManualPage TopicStlContainers Using STL Containers with Eigen
+
+\eigenAutoToc
+
+\section StlContainers_summary Executive summary
+
+If you're compiling in \cpp17 mode only with a sufficiently recent compiler (e.g., GCC>=7, clang>=5, MSVC>=19.12), then everything is taken care by the compiler and you can stop reading.
+
+Otherwise, using STL containers on \ref TopicFixedSizeVectorizable "fixed-size vectorizable Eigen types", or classes having members of such types, requires the use of an over-aligned allocator.
+That is, an allocator capable of allocating buffers with 16, 32, or even 64 bytes alignment.
+%Eigen does provide one ready for use: aligned_allocator.
+
+Prior to \cpp11, if you want to use the `std::vector` container, then you also have to <code> \#include <Eigen/StdVector> </code>.
+
+These issues arise only with \ref TopicFixedSizeVectorizable "fixed-size vectorizable Eigen types" and \ref TopicStructHavingEigenMembers "structures having such Eigen objects as member".
+For other %Eigen types, such as Vector3f or MatrixXd, no special care is needed when using STL containers.
+
+\section allocator Using an aligned allocator
+
+STL containers take an optional template parameter, the allocator type. When using STL containers on \ref TopicFixedSizeVectorizable "fixed-size vectorizable Eigen types", you need tell the container to use an allocator that will always allocate memory at 16-byte-aligned (or more) locations. Fortunately, %Eigen does provide such an allocator: Eigen::aligned_allocator.
+
+For example, instead of
+\code
+std::map<int, Eigen::Vector4d>
+\endcode
+you need to use
+\code
+std::map<int, Eigen::Vector4d, std::less<int>,
+ Eigen::aligned_allocator<std::pair<const int, Eigen::Vector4d> > >
+\endcode
+Note that the third parameter `std::less<int>` is just the default value, but we have to include it because we want to specify the fourth parameter, which is the allocator type.
+
+\section StlContainers_vector The case of std::vector
+
+This section is for c++98/03 users only. \cpp11 (or above) users can stop reading here.
+
+So in c++98/03, the situation with `std::vector` is more complicated because of a bug in the standard (explanation below).
+To workaround the issue, we had to specialize it for the Eigen::aligned_allocator type.
+In practice you \b must use the Eigen::aligned_allocator (not another aligned allocator), \b and \#include <Eigen/StdVector>.
+
+Here is an example:
+\code
+#include<Eigen/StdVector>
+/* ... */
+std::vector<Eigen::Vector4f,Eigen::aligned_allocator<Eigen::Vector4f> >
+\endcode
+
+<span class="note">\b Explanation: The `resize()` method of `std::vector` takes a `value_type` argument (defaulting to `value_type()`). So with `std::vector<Eigen::Vector4d>`, some Eigen::Vector4d objects will be passed by value, which discards any alignment modifiers, so a Eigen::Vector4d can be created at an unaligned location.
+In order to avoid that, the only solution we saw was to specialize `std::vector` to make it work on a slight modification of, here, Eigen::Vector4d, that is able to deal properly with this situation.
+</span>
+
+\subsection vector_spec An alternative - specializing std::vector for Eigen types
+
+As an alternative to the recommended approach described above, you have the option to specialize std::vector for Eigen types requiring alignment.
+The advantage is that you won't need to declare std::vector all over with Eigen::aligned_allocator. One drawback on the other hand side is that
+the specialization needs to be defined before all code pieces in which e.g. `std::vector<Vector2d>` is used. Otherwise, without knowing the specialization
+the compiler will compile that particular instance with the default `std::allocator` and you program is most likely to crash.
+
+Here is an example:
+\code
+#include<Eigen/StdVector>
+/* ... */
+EIGEN_DEFINE_STL_VECTOR_SPECIALIZATION(Matrix2d)
+std::vector<Eigen::Vector2d>
+\endcode
+
+
+
+*/
+
+}
diff --git a/doc/StorageOrders.dox b/doc/StorageOrders.dox
new file mode 100644
index 0000000..6164531
--- /dev/null
+++ b/doc/StorageOrders.dox
@@ -0,0 +1,86 @@
+namespace Eigen {
+
+/** \eigenManualPage TopicStorageOrders Storage orders
+
+There are two different storage orders for matrices and two-dimensional arrays: column-major and row-major.
+This page explains these storage orders and how to specify which one should be used.
+
+\eigenAutoToc
+
+
+\section TopicStorageOrdersIntro Column-major and row-major storage
+
+The entries of a matrix form a two-dimensional grid. However, when the matrix is stored in memory, the entries
+have to somehow be laid out linearly. There are two main ways to do this, by row and by column.
+
+We say that a matrix is stored in \b row-major order if it is stored row by row. The entire first row is
+stored first, followed by the entire second row, and so on. Consider for example the matrix
+
+\f[
+A = \begin{bmatrix}
+8 & 2 & 2 & 9 \\
+9 & 1 & 4 & 4 \\
+3 & 5 & 4 & 5
+\end{bmatrix}.
+\f]
+
+If this matrix is stored in row-major order, then the entries are laid out in memory as follows:
+
+\code 8 2 2 9 9 1 4 4 3 5 4 5 \endcode
+
+On the other hand, a matrix is stored in \b column-major order if it is stored column by column, starting with
+the entire first column, followed by the entire second column, and so on. If the above matrix is stored in
+column-major order, it is laid out as follows:
+
+\code 8 9 3 2 1 5 2 4 4 9 4 5 \endcode
+
+This example is illustrated by the following Eigen code. It uses the PlainObjectBase::data() function, which
+returns a pointer to the memory location of the first entry of the matrix.
+
+<table class="example">
+<tr><th>Example</th><th>Output</th></tr>
+<tr><td>
+\include TopicStorageOrders_example.cpp
+</td>
+<td>
+\verbinclude TopicStorageOrders_example.out
+</td></tr></table>
+
+
+\section TopicStorageOrdersInEigen Storage orders in Eigen
+
+The storage order of a matrix or a two-dimensional array can be set by specifying the \c Options template
+parameter for Matrix or Array. As \ref TutorialMatrixClass explains, the %Matrix class template has six
+template parameters, of which three are compulsory (\c Scalar, \c RowsAtCompileTime and \c ColsAtCompileTime)
+and three are optional (\c Options, \c MaxRowsAtCompileTime and \c MaxColsAtCompileTime). If the \c Options
+parameter is set to \c RowMajor, then the matrix or array is stored in row-major order; if it is set to
+\c ColMajor, then it is stored in column-major order. This mechanism is used in the above Eigen program to
+specify the storage order.
+
+If the storage order is not specified, then Eigen defaults to storing the entry in column-major. This is also
+the case if one of the convenience typedefs (\c Matrix3f, \c ArrayXXd, etc.) is used.
+
+Matrices and arrays using one storage order can be assigned to matrices and arrays using the other storage
+order, as happens in the above program when \c Arowmajor is initialized using \c Acolmajor. Eigen will reorder
+the entries automatically. More generally, row-major and column-major matrices can be mixed in an expression
+as we want.
+
+
+\section TopicStorageOrdersWhich Which storage order to choose?
+
+So, which storage order should you use in your program? There is no simple answer to this question; it depends
+on your application. Here are some points to keep in mind:
+
+ - Your users may expect you to use a specific storage order. Alternatively, you may use other libraries than
+ Eigen, and these other libraries may expect a certain storage order. In these cases it may be easiest and
+ fastest to use this storage order in your whole program.
+ - Algorithms that traverse a matrix row by row will go faster when the matrix is stored in row-major order
+ because of better data locality. Similarly, column-by-column traversal is faster for column-major
+ matrices. It may be worthwhile to experiment a bit to find out what is faster for your particular
+ application.
+ - The default in Eigen is column-major. Naturally, most of the development and testing of the Eigen library
+ is thus done with column-major matrices. This means that, even though we aim to support column-major and
+ row-major storage orders transparently, the Eigen library may well work best with column-major matrices.
+
+*/
+}
diff --git a/doc/StructHavingEigenMembers.dox b/doc/StructHavingEigenMembers.dox
new file mode 100644
index 0000000..4c97093
--- /dev/null
+++ b/doc/StructHavingEigenMembers.dox
@@ -0,0 +1,203 @@
+namespace Eigen {
+
+/** \eigenManualPage TopicStructHavingEigenMembers Structures Having Eigen Members
+
+\eigenAutoToc
+
+\section StructHavingEigenMembers_summary Executive Summary
+
+
+If you define a structure having members of \ref TopicFixedSizeVectorizable "fixed-size vectorizable Eigen types", you must ensure that calling operator new on it allocates properly aligned buffers.
+If you're compiling in \cpp17 mode only with a sufficiently recent compiler (e.g., GCC>=7, clang>=5, MSVC>=19.12), then everything is taken care by the compiler and you can stop reading.
+
+Otherwise, you have to overload its `operator new` so that it generates properly aligned pointers (e.g., 32-bytes-aligned for Vector4d and AVX).
+Fortunately, %Eigen provides you with a macro `EIGEN_MAKE_ALIGNED_OPERATOR_NEW` that does that for you.
+
+\section StructHavingEigenMembers_what What kind of code needs to be changed?
+
+The kind of code that needs to be changed is this:
+
+\code
+class Foo
+{
+ ...
+ Eigen::Vector2d v;
+ ...
+};
+
+...
+
+Foo *foo = new Foo;
+\endcode
+
+In other words: you have a class that has as a member a \ref TopicFixedSizeVectorizable "fixed-size vectorizable Eigen object", and then you dynamically create an object of that class.
+
+\section StructHavingEigenMembers_how How should such code be modified?
+
+Very easy, you just need to put a `EIGEN_MAKE_ALIGNED_OPERATOR_NEW` macro in a public part of your class, like this:
+
+\code
+class Foo
+{
+ ...
+ Eigen::Vector4d v;
+ ...
+public:
+ EIGEN_MAKE_ALIGNED_OPERATOR_NEW
+};
+
+...
+
+Foo *foo = new Foo;
+\endcode
+
+This macro makes `new Foo` always return an aligned pointer.
+
+In \cpp17, this macro is empty.
+
+If this approach is too intrusive, see also the \ref StructHavingEigenMembers_othersolutions "other solutions".
+
+\section StructHavingEigenMembers_why Why is this needed?
+
+OK let's say that your code looks like this:
+
+\code
+class Foo
+{
+ ...
+ Eigen::Vector4d v;
+ ...
+};
+
+...
+
+Foo *foo = new Foo;
+\endcode
+
+A Eigen::Vector4d consists of 4 doubles, which is 256 bits.
+This is exactly the size of an AVX register, which makes it possible to use AVX for all sorts of operations on this vector.
+But AVX instructions (at least the ones that %Eigen uses, which are the fast ones) require 256-bit alignment.
+Otherwise you get a segmentation fault.
+
+For this reason, %Eigen takes care by itself to require 256-bit alignment for Eigen::Vector4d, by doing two things:
+\li %Eigen requires 256-bit alignment for the Eigen::Vector4d's array (of 4 doubles). This is done with the <a href="https://en.cppreference.com/w/cpp/keyword/alignas">alignas</a> keyword.
+\li %Eigen overloads the `operator new` of Eigen::Vector4d so it will always return 256-bit aligned pointers. (removed in \cpp17)
+
+Thus, normally, you don't have to worry about anything, %Eigen handles alignment of operator new for you...
+
+... except in one case. When you have a `class Foo` like above, and you dynamically allocate a new `Foo` as above, then, since `Foo` doesn't have aligned `operator new`, the returned pointer foo is not necessarily 256-bit aligned.
+
+The alignment attribute of the member `v` is then relative to the start of the class `Foo`. If the `foo` pointer wasn't aligned, then `foo->v` won't be aligned either!
+
+The solution is to let `class Foo` have an aligned `operator new`, as we showed in the previous section.
+
+This explanation also holds for SSE/NEON/MSA/Altivec/VSX targets, which require 16-bytes alignment, and AVX512 which requires 64-bytes alignment for fixed-size objects multiple of 64 bytes (e.g., Eigen::Matrix4d).
+
+\section StructHavingEigenMembers_movetotop Should I then put all the members of Eigen types at the beginning of my class?
+
+That's not required. Since %Eigen takes care of declaring adequate alignment, all members that need it are automatically aligned relatively to the class. So code like this works fine:
+
+\code
+class Foo
+{
+ double x;
+ Eigen::Vector4d v;
+public:
+ EIGEN_MAKE_ALIGNED_OPERATOR_NEW
+};
+\endcode
+
+That said, as usual, it is recommended to sort the members so that alignment does not waste memory.
+In the above example, with AVX, the compiler will have to reserve 24 empty bytes between `x` and `v`.
+
+
+\section StructHavingEigenMembers_dynamicsize What about dynamic-size matrices and vectors?
+
+Dynamic-size matrices and vectors, such as Eigen::VectorXd, allocate dynamically their own array of coefficients, so they take care of requiring absolute alignment automatically. So they don't cause this issue. The issue discussed here is only with \ref TopicFixedSizeVectorizable "fixed-size vectorizable matrices and vectors".
+
+
+\section StructHavingEigenMembers_bugineigen So is this a bug in Eigen?
+
+No, it's not our bug. It's more like an inherent problem of the c++ language specification that has been solved in c++17 through the feature known as <a href="http://wg21.link/p0035r4">dynamic memory allocation for over-aligned data</a>.
+
+
+\section StructHavingEigenMembers_conditional What if I want to do this conditionally (depending on template parameters) ?
+
+For this situation, we offer the macro `EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF(NeedsToAlign)`.
+It will generate aligned operators like `EIGEN_MAKE_ALIGNED_OPERATOR_NEW` if `NeedsToAlign` is true.
+It will generate operators with the default alignment if `NeedsToAlign` is false.
+In \cpp17, this macro is empty.
+
+Example:
+
+\code
+template<int n> class Foo
+{
+ typedef Eigen::Matrix<float,n,1> Vector;
+ enum { NeedsToAlign = (sizeof(Vector)%16)==0 };
+ ...
+ Vector v;
+ ...
+public:
+ EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF(NeedsToAlign)
+};
+
+...
+
+Foo<4> *foo4 = new Foo<4>; // foo4 is guaranteed to be 128bit-aligned
+Foo<3> *foo3 = new Foo<3>; // foo3 has only the system default alignment guarantee
+\endcode
+
+
+\section StructHavingEigenMembers_othersolutions Other solutions
+
+In case putting the `EIGEN_MAKE_ALIGNED_OPERATOR_NEW` macro everywhere is too intrusive, there exists at least two other solutions.
+
+\subsection othersolutions1 Disabling alignment
+
+The first is to disable alignment requirement for the fixed size members:
+\code
+class Foo
+{
+ ...
+ Eigen::Matrix<double,4,1,Eigen::DontAlign> v;
+ ...
+};
+\endcode
+This `v` is fully compatible with aligned Eigen::Vector4d.
+This has only for effect to make load/stores to `v` more expensive (usually slightly, but that's hardware dependent).
+
+
+\subsection othersolutions2 Private structure
+
+The second consist in storing the fixed-size objects into a private struct which will be dynamically allocated at the construction time of the main object:
+
+\code
+struct Foo_d
+{
+ EIGEN_MAKE_ALIGNED_OPERATOR_NEW
+ Vector4d v;
+ ...
+};
+
+
+struct Foo {
+ Foo() { init_d(); }
+ ~Foo() { delete d; }
+ void bar()
+ {
+ // use d->v instead of v
+ ...
+ }
+private:
+ void init_d() { d = new Foo_d; }
+ Foo_d* d;
+};
+\endcode
+
+The clear advantage here is that the class `Foo` remains unchanged regarding alignment issues.
+The drawback is that an additional heap allocation will be required whatsoever.
+
+*/
+
+}
diff --git a/doc/TemplateKeyword.dox b/doc/TemplateKeyword.dox
new file mode 100644
index 0000000..fbf2c70
--- /dev/null
+++ b/doc/TemplateKeyword.dox
@@ -0,0 +1,133 @@
+namespace Eigen {
+
+/** \page TopicTemplateKeyword The template and typename keywords in C++
+
+There are two uses for the \c template and \c typename keywords in C++. One of them is fairly well known
+amongst programmers: to define templates. The other use is more obscure: to specify that an expression refers
+to a template function or a type. This regularly trips up programmers that use the %Eigen library, often
+leading to error messages from the compiler that are difficult to understand, such as "expected expression" or
+"no match for operator<".
+
+\eigenAutoToc
+
+
+\section TopicTemplateKeywordToDefineTemplates Using the template and typename keywords to define templates
+
+The \c template and \c typename keywords are routinely used to define templates. This is not the topic of this
+page as we assume that the reader is aware of this (otherwise consult a C++ book). The following example
+should illustrate this use of the \c template keyword.
+
+\code
+template <typename T>
+bool isPositive(T x)
+{
+ return x > 0;
+}
+\endcode
+
+We could just as well have written <tt>template <class T></tt>; the keywords \c typename and \c class have the
+same meaning in this context.
+
+
+\section TopicTemplateKeywordExample An example showing the second use of the template keyword
+
+Let us illustrate the second use of the \c template keyword with an example. Suppose we want to write a
+function which copies all entries in the upper triangular part of a matrix into another matrix, while keeping
+the lower triangular part unchanged. A straightforward implementation would be as follows:
+
+<table class="example">
+<tr><th>Example:</th><th>Output:</th></tr>
+<tr><td>
+\include TemplateKeyword_simple.cpp
+</td>
+<td>
+\verbinclude TemplateKeyword_simple.out
+</td></tr></table>
+
+That works fine, but it is not very flexible. First, it only works with dynamic-size matrices of
+single-precision floats; the function \c copyUpperTriangularPart() does not accept static-size matrices or
+matrices with double-precision numbers. Second, if you use an expression such as
+<tt>mat.topLeftCorner(3,3)</tt> as the parameter \c src, then this is copied into a temporary variable of type
+MatrixXf; this copy can be avoided.
+
+As explained in \ref TopicFunctionTakingEigenTypes, both issues can be resolved by making
+\c copyUpperTriangularPart() accept any object of type MatrixBase. This leads to the following code:
+
+<table class="example">
+<tr><th>Example:</th><th>Output:</th></tr>
+<tr><td>
+\include TemplateKeyword_flexible.cpp
+</td>
+<td>
+\verbinclude TemplateKeyword_flexible.out
+</td></tr></table>
+
+The one line in the body of the function \c copyUpperTriangularPart() shows the second, more obscure use of
+the \c template keyword in C++. Even though it may look strange, the \c template keywords are necessary
+according to the standard. Without it, the compiler may reject the code with an error message like "no match
+for operator<".
+
+
+\section TopicTemplateKeywordExplanation Explanation
+
+The reason that the \c template keyword is necessary in the last example has to do with the rules for how
+templates are supposed to be compiled in C++. The compiler has to check the code for correct syntax at the
+point where the template is defined, without knowing the actual value of the template arguments (\c Derived1
+and \c Derived2 in the example). That means that the compiler cannot know that <tt>dst.triangularView</tt> is
+a member template and that the following < symbol is part of the delimiter for the template
+parameter. Another possibility would be that <tt>dst.triangularView</tt> is a member variable with the <
+symbol referring to the <tt>operator<()</tt> function. In fact, the compiler should choose the second
+possibility, according to the standard. If <tt>dst.triangularView</tt> is a member template (as in our case),
+the programmer should specify this explicitly with the \c template keyword and write <tt>dst.template
+triangularView</tt>.
+
+The precise rules are rather complicated, but ignoring some subtleties we can summarize them as follows:
+- A <em>dependent name</em> is name that depends (directly or indirectly) on a template parameter. In the
+ example, \c dst is a dependent name because it is of type <tt>MatrixBase<Derived1></tt> which depends
+ on the template parameter \c Derived1.
+- If the code contains either one of the constructs <tt>xxx.yyy</tt> or <tt>xxx->yyy</tt> and \c xxx is a
+ dependent name and \c yyy refers to a member template, then the \c template keyword must be used before
+ \c yyy, leading to <tt>xxx.template yyy</tt> or <tt>xxx->template yyy</tt>.
+- If the code contains the construct <tt>xxx::yyy</tt> and \c xxx is a dependent name and \c yyy refers to a
+ member typedef, then the \c typename keyword must be used before the whole construct, leading to
+ <tt>typename xxx::yyy</tt>.
+
+As an example where the \c typename keyword is required, consider the following code in \ref TutorialSparse
+for iterating over the non-zero entries of a sparse matrix type:
+
+\code
+SparseMatrixType mat(rows,cols);
+for (int k=0; k<mat.outerSize(); ++k)
+ for (SparseMatrixType::InnerIterator it(mat,k); it; ++it)
+ {
+ /* ... */
+ }
+\endcode
+
+If \c SparseMatrixType depends on a template parameter, then the \c typename keyword is required:
+
+\code
+template <typename T>
+void iterateOverSparseMatrix(const SparseMatrix<T>& mat;
+{
+ for (int k=0; k<m1.outerSize(); ++k)
+ for (typename SparseMatrix<T>::InnerIterator it(mat,k); it; ++it)
+ {
+ /* ... */
+ }
+}
+\endcode
+
+
+\section TopicTemplateKeywordResources Resources for further reading
+
+For more information and a fuller explanation of this topic, the reader may consult the following sources:
+- The book "C++ Template Metaprogramming" by David Abrahams and Aleksey Gurtovoy contains a very good
+ explanation in Appendix B ("The typename and template Keywords") which formed the basis for this page.
+- http://pages.cs.wisc.edu/~driscoll/typename.html
+- http://www.parashift.com/c++-faq-lite/templates.html#faq-35.18
+- http://www.comeaucomputing.com/techtalk/templates/#templateprefix
+- http://www.comeaucomputing.com/techtalk/templates/#typename
+
+*/
+}
diff --git a/doc/TopicAliasing.dox b/doc/TopicAliasing.dox
new file mode 100644
index 0000000..a8f1644
--- /dev/null
+++ b/doc/TopicAliasing.dox
@@ -0,0 +1,237 @@
+namespace Eigen {
+
+/** \eigenManualPage TopicAliasing Aliasing
+
+In %Eigen, aliasing refers to assignment statement in which the same matrix (or array or vector) appears on the
+left and on the right of the assignment operators. Statements like <tt>mat = 2 * mat;</tt> or <tt>mat =
+mat.transpose();</tt> exhibit aliasing. The aliasing in the first example is harmless, but the aliasing in the
+second example leads to unexpected results. This page explains what aliasing is, when it is harmful, and what
+to do about it.
+
+\eigenAutoToc
+
+
+\section TopicAliasingExamples Examples
+
+Here is a simple example exhibiting aliasing:
+
+<table class="example">
+<tr><th>Example</th><th>Output</th></tr>
+<tr><td>
+\include TopicAliasing_block.cpp
+</td>
+<td>
+\verbinclude TopicAliasing_block.out
+</td></tr></table>
+
+The output is not what one would expect. The problem is the assignment
+\code
+mat.bottomRightCorner(2,2) = mat.topLeftCorner(2,2);
+\endcode
+This assignment exhibits aliasing: the coefficient \c mat(1,1) appears both in the block
+<tt>mat.bottomRightCorner(2,2)</tt> on the left-hand side of the assignment and the block
+<tt>mat.topLeftCorner(2,2)</tt> on the right-hand side. After the assignment, the (2,2) entry in the bottom
+right corner should have the value of \c mat(1,1) before the assignment, which is 5. However, the output shows
+that \c mat(2,2) is actually 1. The problem is that %Eigen uses lazy evaluation (see
+\ref TopicEigenExpressionTemplates) for <tt>mat.topLeftCorner(2,2)</tt>. The result is similar to
+\code
+mat(1,1) = mat(0,0);
+mat(1,2) = mat(0,1);
+mat(2,1) = mat(1,0);
+mat(2,2) = mat(1,1);
+\endcode
+Thus, \c mat(2,2) is assigned the \e new value of \c mat(1,1) instead of the old value. The next section
+explains how to solve this problem by calling \link DenseBase::eval() eval()\endlink.
+
+Aliasing occurs more naturally when trying to shrink a matrix. For example, the expressions <tt>vec =
+vec.head(n)</tt> and <tt>mat = mat.block(i,j,r,c)</tt> exhibit aliasing.
+
+In general, aliasing cannot be detected at compile time: if \c mat in the first example were a bit bigger,
+then the blocks would not overlap, and there would be no aliasing problem. However, %Eigen does detect some
+instances of aliasing, albeit at run time. The following example exhibiting aliasing was mentioned in \ref
+TutorialMatrixArithmetic :
+
+<table class="example">
+<tr><th>Example</th><th>Output</th></tr>
+<tr><td>
+\include tut_arithmetic_transpose_aliasing.cpp
+</td>
+<td>
+\verbinclude tut_arithmetic_transpose_aliasing.out
+</td></tr></table>
+
+Again, the output shows the aliasing issue. However, by default %Eigen uses a run-time assertion to detect this
+and exits with a message like
+
+\verbatim
+void Eigen::DenseBase<Derived>::checkTransposeAliasing(const OtherDerived&) const
+[with OtherDerived = Eigen::Transpose<Eigen::Matrix<int, 2, 2, 0, 2, 2> >, Derived = Eigen::Matrix<int, 2, 2, 0, 2, 2>]:
+Assertion `(!internal::check_transpose_aliasing_selector<Scalar,internal::blas_traits<Derived>::IsTransposed,OtherDerived>::run(internal::extract_data(derived()), other))
+&& "aliasing detected during transposition, use transposeInPlace() or evaluate the rhs into a temporary using .eval()"' failed.
+\endverbatim
+
+The user can turn %Eigen's run-time assertions like the one to detect this aliasing problem off by defining the
+EIGEN_NO_DEBUG macro, and the above program was compiled with this macro turned off in order to illustrate the
+aliasing problem. See \ref TopicAssertions for more information about %Eigen's run-time assertions.
+
+
+\section TopicAliasingSolution Resolving aliasing issues
+
+If you understand the cause of the aliasing issue, then it is obvious what must happen to solve it: %Eigen has
+to evaluate the right-hand side fully into a temporary matrix/array and then assign it to the left-hand
+side. The function \link DenseBase::eval() eval() \endlink does precisely that.
+
+For example, here is the corrected version of the first example above:
+
+<table class="example">
+<tr><th>Example</th><th>Output</th></tr>
+<tr><td>
+\include TopicAliasing_block_correct.cpp
+</td>
+<td>
+\verbinclude TopicAliasing_block_correct.out
+</td></tr></table>
+
+Now, \c mat(2,2) equals 5 after the assignment, as it should be.
+
+The same solution also works for the second example, with the transpose: simply replace the line
+<tt>a = a.transpose();</tt> with <tt>a = a.transpose().eval();</tt>. However, in this common case there is a
+better solution. %Eigen provides the special-purpose function
+\link DenseBase::transposeInPlace() transposeInPlace() \endlink which replaces a matrix by its transpose.
+This is shown below:
+
+<table class="example">
+<tr><th>Example</th><th>Output</th></tr>
+<tr><td>
+\include tut_arithmetic_transpose_inplace.cpp
+</td>
+<td>
+\verbinclude tut_arithmetic_transpose_inplace.out
+</td></tr></table>
+
+If an xxxInPlace() function is available, then it is best to use it, because it indicates more clearly what you
+are doing. This may also allow %Eigen to optimize more aggressively. These are some of the xxxInPlace()
+functions provided:
+
+<table class="manual">
+<tr><th>Original function</th><th>In-place function</th></tr>
+<tr> <td> MatrixBase::adjoint() </td> <td> MatrixBase::adjointInPlace() </td> </tr>
+<tr class="alt"> <td> DenseBase::reverse() </td> <td> DenseBase::reverseInPlace() </td> </tr>
+<tr> <td> LDLT::solve() </td> <td> LDLT::solveInPlace() </td> </tr>
+<tr class="alt"> <td> LLT::solve() </td> <td> LLT::solveInPlace() </td> </tr>
+<tr> <td> TriangularView::solve() </td> <td> TriangularView::solveInPlace() </td> </tr>
+<tr class="alt"> <td> DenseBase::transpose() </td> <td> DenseBase::transposeInPlace() </td> </tr>
+</table>
+
+In the special case where a matrix or vector is shrunk using an expression like <tt>vec = vec.head(n)</tt>,
+you can use \link PlainObjectBase::conservativeResize() conservativeResize() \endlink.
+
+
+\section TopicAliasingCwise Aliasing and component-wise operations
+
+As explained above, it may be dangerous if the same matrix or array occurs on both the left-hand side and the
+right-hand side of an assignment operator, and it is then often necessary to evaluate the right-hand side
+explicitly. However, applying component-wise operations (such as matrix addition, scalar multiplication and
+array multiplication) is safe.
+
+The following example has only component-wise operations. Thus, there is no need for \link DenseBase::eval()
+eval() \endlink even though the same matrix appears on both sides of the assignments.
+
+<table class="example">
+<tr><th>Example</th><th>Output</th></tr>
+<tr><td>
+\include TopicAliasing_cwise.cpp
+</td>
+<td>
+\verbinclude TopicAliasing_cwise.out
+</td></tr></table>
+
+In general, an assignment is safe if the (i,j) entry of the expression on the right-hand side depends only on
+the (i,j) entry of the matrix or array on the left-hand side and not on any other entries. In that case it is
+not necessary to evaluate the right-hand side explicitly.
+
+
+\section TopicAliasingMatrixMult Aliasing and matrix multiplication
+
+Matrix multiplication is the only operation in %Eigen that assumes aliasing by default, <strong>under the
+condition that the destination matrix is not resized</strong>.
+Thus, if \c matA is a \b squared matrix, then the statement <tt>matA = matA * matA;</tt> is safe.
+All other operations in %Eigen assume that there are no aliasing problems,
+either because the result is assigned to a different matrix or because it is a component-wise operation.
+
+<table class="example">
+<tr><th>Example</th><th>Output</th></tr>
+<tr><td>
+\include TopicAliasing_mult1.cpp
+</td>
+<td>
+\verbinclude TopicAliasing_mult1.out
+</td></tr></table>
+
+However, this comes at a price. When executing the expression <tt>matA = matA * matA</tt>, %Eigen evaluates the
+product in a temporary matrix which is assigned to \c matA after the computation. This is fine. But %Eigen does
+the same when the product is assigned to a different matrix (e.g., <tt>matB = matA * matA</tt>). In that case,
+it is more efficient to evaluate the product directly into \c matB instead of evaluating it first into a
+temporary matrix and copying that matrix to \c matB.
+
+The user can indicate with the \link MatrixBase::noalias() noalias()\endlink function that there is no
+aliasing, as follows: <tt>matB.noalias() = matA * matA</tt>. This allows %Eigen to evaluate the matrix product
+<tt>matA * matA</tt> directly into \c matB.
+
+<table class="example">
+<tr><th>Example</th><th>Output</th></tr>
+<tr><td>
+\include TopicAliasing_mult2.cpp
+</td>
+<td>
+\verbinclude TopicAliasing_mult2.out
+</td></tr></table>
+
+Of course, you should not use \c noalias() when there is in fact aliasing taking place. If you do, then you
+may get wrong results:
+
+<table class="example">
+<tr><th>Example</th><th>Output</th></tr>
+<tr><td>
+\include TopicAliasing_mult3.cpp
+</td>
+<td>
+\verbinclude TopicAliasing_mult3.out
+</td></tr></table>
+
+Moreover, starting in Eigen 3.3, aliasing is \b not assumed if the destination matrix is resized and the product is not directly assigned to the destination.
+Therefore, the following example is also wrong:
+
+<table class="example">
+<tr><th>Example</th><th>Output</th></tr>
+<tr><td>
+\include TopicAliasing_mult4.cpp
+</td>
+<td>
+\verbinclude TopicAliasing_mult4.out
+</td></tr></table>
+
+As for any aliasing issue, you can resolve it by explicitly evaluating the expression prior to assignment:
+<table class="example">
+<tr><th>Example</th><th>Output</th></tr>
+<tr><td>
+\include TopicAliasing_mult5.cpp
+</td>
+<td>
+\verbinclude TopicAliasing_mult5.out
+</td></tr></table>
+
+\section TopicAliasingSummary Summary
+
+Aliasing occurs when the same matrix or array coefficients appear both on the left- and the right-hand side of
+an assignment operator.
+ - Aliasing is harmless with coefficient-wise computations; this includes scalar multiplication and matrix or
+ array addition.
+ - When you multiply two matrices, %Eigen assumes that aliasing occurs. If you know that there is no aliasing,
+ then you can use \link MatrixBase::noalias() noalias()\endlink.
+ - In all other situations, %Eigen assumes that there is no aliasing issue and thus gives the wrong result if
+ aliasing does in fact occur. To prevent this, you have to use \link DenseBase::eval() eval() \endlink or
+ one of the xxxInPlace() functions.
+
+*/
+}
diff --git a/doc/TopicAssertions.dox b/doc/TopicAssertions.dox
new file mode 100644
index 0000000..c8b4d84
--- /dev/null
+++ b/doc/TopicAssertions.dox
@@ -0,0 +1,108 @@
+namespace Eigen {
+
+/** \page TopicAssertions Assertions
+
+\eigenAutoToc
+
+\section PlainAssert Assertions
+
+The macro eigen_assert is defined to be \c eigen_plain_assert by default. We use eigen_plain_assert instead of \c assert to work around a known bug for GCC <= 4.3. Basically, eigen_plain_assert \a is \c assert.
+
+\subsection RedefineAssert Redefining assertions
+
+Both eigen_assert and eigen_plain_assert are defined in Macros.h. Defining eigen_assert indirectly gives you a chance to change its behavior. You can redefine this macro if you want to do something else such as throwing an exception, and fall back to its default behavior with eigen_plain_assert. The code below tells Eigen to throw an std::runtime_error:
+
+\code
+#include <stdexcept>
+#undef eigen_assert
+#define eigen_assert(x) \
+ if (!(x)) { throw (std::runtime_error("Put your message here")); }
+\endcode
+
+\subsection DisableAssert Disabling assertions
+
+Assertions cost run time and can be turned off. You can suppress eigen_assert by defining \c EIGEN_NO_DEBUG \b before including Eigen headers. \c EIGEN_NO_DEBUG is undefined by default unless \c NDEBUG is defined.
+
+\section StaticAssert Static assertions
+
+Static assertions are not standardized until C++11. However, in the Eigen library, there are many conditions can and should be detectedat compile time. For instance, we use static assertions to prevent the code below from compiling.
+
+\code
+Matrix3d() + Matrix4d(); // adding matrices of different sizes
+Matrix4cd() * Vector3cd(); // invalid product known at compile time
+\endcode
+
+Static assertions are defined in StaticAssert.h. If there is native static_assert, we use it. Otherwise, we have implemented an assertion macro that can show a limited range of messages.
+
+One can easily come up with static assertions without messages, such as:
+
+\code
+#define STATIC_ASSERT(x) \
+ switch(0) { case 0: case x:; }
+\endcode
+
+However, the example above obviously cannot tell why the assertion failed. Therefore, we define a \c struct in namespace Eigen::internal to handle available messages.
+
+\code
+template<bool condition>
+struct static_assertion {};
+
+template<>
+struct static_assertion<true>
+{
+ enum {
+ YOU_TRIED_CALLING_A_VECTOR_METHOD_ON_A_MATRIX,
+ YOU_MIXED_VECTORS_OF_DIFFERENT_SIZES,
+ // see StaticAssert.h for all enums.
+ };
+};
+\endcode
+
+And then, we define EIGEN_STATIC_ASSERT(CONDITION,MSG) to access Eigen::internal::static_assertion<bool(CONDITION)>::MSG. If the condition evaluates into \c false, your compiler displays a lot of messages explaining there is no MSG in static_assert<false>. Nevertheless, this is \a not in what we are interested. As you can see, all members of static_assert<true> are ALL_CAPS_AND_THEY_ARE_SHOUTING.
+
+\warning
+When using this macro, MSG should be a member of static_assertion<true>, or the static assertion \b always fails.
+Currently, it can only be used in function scope.
+
+\subsection DerivedStaticAssert Derived static assertions
+
+There are other macros derived from EIGEN_STATIC_ASSERT to enhance readability. Their names are self-explanatory.
+
+- \b EIGEN_STATIC_ASSERT_FIXED_SIZE(TYPE) - passes if \a TYPE is fixed size.
+- \b EIGEN_STATIC_ASSERT_DYNAMIC_SIZE(TYPE) - passes if \a TYPE is dynamic size.
+- \b EIGEN_STATIC_ASSERT_LVALUE(Derived) - failes if \a Derived is read-only.
+- \b EIGEN_STATIC_ASSERT_ARRAYXPR(Derived) - passes if \a Derived is an array expression.
+- <b>EIGEN_STATIC_ASSERT_SAME_XPR_KIND(Derived1, Derived2)</b> - failes if the two expressions are an array one and a matrix one.
+
+Because Eigen handles both fixed-size and dynamic-size expressions, some conditions cannot be clearly determined at compile time. We classify them into strict assertions and permissive assertions.
+
+\subsubsection StrictAssertions Strict assertions
+
+These assertions fail if the condition <b>may not</b> be met. For example, MatrixXd may not be a vector, so it fails EIGEN_STATIC_ASSERT_VECTOR_ONLY.
+
+- \b EIGEN_STATIC_ASSERT_VECTOR_ONLY(TYPE) - passes if \a TYPE must be a vector type.
+- <b>EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(TYPE, SIZE)</b> - passes if \a TYPE must be a vector of the given size.
+- <b>EIGEN_STATIC_ASSERT_MATRIX_SPECIFIC_SIZE(TYPE, ROWS, COLS)</b> - passes if \a TYPE must be a matrix with given rows and columns.
+
+\subsubsection PermissiveAssertions Permissive assertions
+
+These assertions fail if the condition \b cannot be met. For example, MatrixXd and Matrix4d may have the same size, so they pass EIGEN_STATIC_ASSERT_SAME_MATRIX_SIZE.
+
+- \b EIGEN_STATIC_ASSERT_SAME_VECTOR_SIZE(TYPE0,TYPE1) - fails if the two vector expression types must have different sizes.
+- \b EIGEN_STATIC_ASSERT_SAME_MATRIX_SIZE(TYPE0,TYPE1) - fails if the two matrix expression types must have different sizes.
+- \b EIGEN_STATIC_ASSERT_SIZE_1x1(TYPE) - fails if \a TYPE cannot be an 1x1 expression.
+
+See StaticAssert.h for details such as what messages they throw.
+
+\subsection DisableStaticAssert Disabling static assertions
+
+If \c EIGEN_NO_STATIC_ASSERT is defined, static assertions turn into <tt>eigen_assert</tt>'s, working like:
+
+\code
+#define EIGEN_STATIC_ASSERT(CONDITION,MSG) eigen_assert((CONDITION) && #MSG);
+\endcode
+
+This saves compile time but consumes more run time. \c EIGEN_NO_STATIC_ASSERT is undefined by default.
+
+*/
+}
diff --git a/doc/TopicCMakeGuide.dox b/doc/TopicCMakeGuide.dox
new file mode 100644
index 0000000..cf767d0
--- /dev/null
+++ b/doc/TopicCMakeGuide.dox
@@ -0,0 +1,56 @@
+namespace Eigen {
+
+/**
+
+\page TopicCMakeGuide Using %Eigen in CMake Projects
+
+%Eigen provides native CMake support which allows the library to be easily
+used in CMake projects.
+
+\note %CMake 3.0 (or later) is required to enable this functionality.
+
+%Eigen exports a CMake target called `Eigen3::Eigen` which can be imported
+using the `find_package` CMake command and used by calling
+`target_link_libraries` as in the following example:
+\code{.cmake}
+cmake_minimum_required (VERSION 3.0)
+project (myproject)
+
+find_package (Eigen3 3.3 REQUIRED NO_MODULE)
+
+add_executable (example example.cpp)
+target_link_libraries (example Eigen3::Eigen)
+\endcode
+
+The above code snippet must be placed in a file called `CMakeLists.txt` alongside
+`example.cpp`. After running
+\code{.sh}
+$ cmake path-to-example-directory
+\endcode
+CMake will produce project files that generate an executable called `example`
+which requires at least version 3.3 of %Eigen. Here, `path-to-example-directory`
+is the path to the directory that contains both `CMakeLists.txt` and
+`example.cpp`.
+
+Do not forget to set the <a href="https://cmake.org/cmake/help/v3.7/variable/CMAKE_PREFIX_PATH.html">\c CMAKE_PREFIX_PATH </a> variable if Eigen is not installed in a default location or if you want to pick a specific version. For instance:
+\code{.sh}
+$ cmake path-to-example-directory -DCMAKE_PREFIX_PATH=$HOME/mypackages
+\endcode
+An alternative is to set the \c Eigen3_DIR cmake's variable to the respective path containing the \c Eigen3*.cmake files. For instance:
+\code{.sh}
+$ cmake path-to-example-directory -DEigen3_DIR=$HOME/mypackages/share/eigen3/cmake/
+\endcode
+
+If the `REQUIRED` option is omitted when locating %Eigen using
+`find_package`, one can check whether the package was found as follows:
+\code{.cmake}
+find_package (Eigen3 3.3 NO_MODULE)
+
+if (TARGET Eigen3::Eigen)
+ # Use the imported target
+endif (TARGET Eigen3::Eigen)
+\endcode
+
+*/
+
+}
diff --git a/doc/TopicEigenExpressionTemplates.dox b/doc/TopicEigenExpressionTemplates.dox
new file mode 100644
index 0000000..b31fd47
--- /dev/null
+++ b/doc/TopicEigenExpressionTemplates.dox
@@ -0,0 +1,12 @@
+namespace Eigen {
+
+/** \page TopicEigenExpressionTemplates Expression templates in Eigen
+
+
+TODO: write this dox page!
+
+Is linked from the tutorial on arithmetic ops.
+
+*/
+
+}
diff --git a/doc/TopicLazyEvaluation.dox b/doc/TopicLazyEvaluation.dox
new file mode 100644
index 0000000..d2a704f
--- /dev/null
+++ b/doc/TopicLazyEvaluation.dox
@@ -0,0 +1,97 @@
+namespace Eigen {
+
+/** \page TopicLazyEvaluation Lazy Evaluation and Aliasing
+
+Executive summary: %Eigen has intelligent compile-time mechanisms to enable lazy evaluation and removing temporaries where appropriate.
+It will handle aliasing automatically in most cases, for example with matrix products. The automatic behavior can be overridden
+manually by using the MatrixBase::eval() and MatrixBase::noalias() methods.
+
+When you write a line of code involving a complex expression such as
+
+\code mat1 = mat2 + mat3 * (mat4 + mat5);
+\endcode
+
+%Eigen determines automatically, for each sub-expression, whether to evaluate it into a temporary variable. Indeed, in certain cases it is better to evaluate a sub-expression into a temporary variable, while in other cases it is better to avoid that.
+
+A traditional math library without expression templates always evaluates all sub-expressions into temporaries. So with this code,
+
+\code vec1 = vec2 + vec3;
+\endcode
+
+a traditional library would evaluate \c vec2 + vec3 into a temporary \c vec4 and then copy \c vec4 into \c vec1. This is of course inefficient: the arrays are traversed twice, so there are a lot of useless load/store operations.
+
+Expression-templates-based libraries can avoid evaluating sub-expressions into temporaries, which in many cases results in large speed improvements.
+This is called <i>lazy evaluation</i> as an expression is getting evaluated as late as possible.
+In %Eigen <b>all expressions are lazy-evaluated</b>.
+More precisely, an expression starts to be evaluated once it is assigned to a matrix.
+Until then nothing happens beyond constructing the abstract expression tree.
+In contrast to most other expression-templates-based libraries, however, <b>%Eigen might choose to evaluate some sub-expressions into temporaries</b>.
+There are two reasons for that: first, pure lazy evaluation is not always a good choice for performance; second, pure lazy evaluation can be very dangerous, for example with matrix products: doing <tt>mat = mat*mat</tt> gives a wrong result if the matrix product is directly evaluated within the destination matrix, because of the way matrix product works.
+
+For these reasons, %Eigen has intelligent compile-time mechanisms to determine automatically which sub-expression should be evaluated into a temporary variable.
+
+So in the basic example,
+
+\code mat1 = mat2 + mat3;
+\endcode
+
+%Eigen chooses not to introduce any temporary. Thus the arrays are traversed only once, producing optimized code.
+If you really want to force immediate evaluation, use \link MatrixBase::eval() eval()\endlink:
+
+\code mat1 = (mat2 + mat3).eval();
+\endcode
+
+Here is now a more involved example:
+
+\code mat1 = -mat2 + mat3 + 5 * mat4;
+\endcode
+
+Here again %Eigen won't introduce any temporary, thus producing a single <b>fused</b> evaluation loop, which is clearly the correct choice.
+
+\section TopicLazyEvaluationWhichExpr Which sub-expressions are evaluated into temporaries?
+
+The default evaluation strategy is to fuse the operations in a single loop, and %Eigen will choose it except in a few circumstances.
+
+<b>The first circumstance</b> in which %Eigen chooses to evaluate a sub-expression is when it sees an assignment <tt>a = b;</tt> and the expression \c b has the evaluate-before-assigning \link flags flag\endlink.
+The most important example of such an expression is the \link Product matrix product expression\endlink. For example, when you do
+
+\code mat = mat * mat;
+\endcode
+
+%Eigen will evaluate <tt>mat * mat</tt> into a temporary matrix, and then copies it into the original \c mat.
+This guarantees a correct result as we saw above that lazy evaluation gives wrong results with matrix products.
+It also doesn't cost much, as the cost of the matrix product itself is much higher.
+Note that this temporary is introduced at evaluation time only, that is, within operator= in this example.
+The expression <tt>mat * mat</tt> still return a abstract product type.
+
+What if you know that the result does no alias the operand of the product and want to force lazy evaluation? Then use \link MatrixBase::noalias() .noalias()\endlink instead. Here is an example:
+
+\code mat1.noalias() = mat2 * mat2;
+\endcode
+
+Here, since we know that mat2 is not the same matrix as mat1, we know that lazy evaluation is not dangerous, so we may force lazy evaluation. Concretely, the effect of noalias() here is to bypass the evaluate-before-assigning \link flags flag\endlink.
+
+<b>The second circumstance</b> in which %Eigen chooses to evaluate a sub-expression, is when it sees a nested expression such as <tt>a + b</tt> where \c b is already an expression having the evaluate-before-nesting \link flags flag\endlink.
+Again, the most important example of such an expression is the \link Product matrix product expression\endlink.
+For example, when you do
+
+\code mat1 = mat2 * mat3 + mat4 * mat5;
+\endcode
+
+the products <tt>mat2 * mat3</tt> and <tt>mat4 * mat5</tt> gets evaluated separately into temporary matrices before being summed up in <tt>mat1</tt>.
+Indeed, to be efficient matrix products need to be evaluated within a destination matrix at hand, and not as simple "dot products".
+For small matrices, however, you might want to enforce a "dot-product" based lazy evaluation with lazyProduct().
+Again, it is important to understand that those temporaries are created at evaluation time only, that is in operator =.
+See TopicPitfalls_auto_keyword for common pitfalls regarding this remark.
+
+<b>The third circumstance</b> in which %Eigen chooses to evaluate a sub-expression, is when its cost model shows that the total cost of an operation is reduced if a sub-expression gets evaluated into a temporary.
+Indeed, in certain cases, an intermediate result is sufficiently costly to compute and is reused sufficiently many times, that is worth "caching". Here is an example:
+
+\code mat1 = mat2 * (mat3 + mat4);
+\endcode
+
+Here, provided the matrices have at least 2 rows and 2 columns, each coefficient of the expression <tt>mat3 + mat4</tt> is going to be used several times in the matrix product. Instead of computing the sum every time, it is much better to compute it once and store it in a temporary variable. %Eigen understands this and evaluates <tt>mat3 + mat4</tt> into a temporary variable before evaluating the product.
+
+*/
+
+}
diff --git a/doc/TopicLinearAlgebraDecompositions.dox b/doc/TopicLinearAlgebraDecompositions.dox
new file mode 100644
index 0000000..8598ce6
--- /dev/null
+++ b/doc/TopicLinearAlgebraDecompositions.dox
@@ -0,0 +1,287 @@
+namespace Eigen {
+
+/** \eigenManualPage TopicLinearAlgebraDecompositions Catalogue of dense decompositions
+
+This page presents a catalogue of the dense matrix decompositions offered by Eigen.
+For an introduction on linear solvers and decompositions, check this \link TutorialLinearAlgebra page \endlink.
+To get an overview of the true relative speed of the different decompositions, check this \link DenseDecompositionBenchmark benchmark \endlink.
+
+\section TopicLinAlgBigTable Catalogue of decompositions offered by Eigen
+
+<table class="manual-vl">
+ <tr>
+ <th class="meta"></th>
+ <th class="meta" colspan="5">Generic information, not Eigen-specific</th>
+ <th class="meta" colspan="3">Eigen-specific</th>
+ </tr>
+
+ <tr>
+ <th>Decomposition</th>
+ <th>Requirements on the matrix</th>
+ <th>Speed</th>
+ <th>Algorithm reliability and accuracy</th>
+ <th>Rank-revealing</th>
+ <th>Allows to compute (besides linear solving)</th>
+ <th>Linear solver provided by Eigen</th>
+ <th>Maturity of Eigen's implementation</th>
+ <th>Optimizations</th>
+ </tr>
+
+ <tr>
+ <td>PartialPivLU</td>
+ <td>Invertible</td>
+ <td>Fast</td>
+ <td>Depends on condition number</td>
+ <td>-</td>
+ <td>-</td>
+ <td>Yes</td>
+ <td>Excellent</td>
+ <td>Blocking, Implicit MT</td>
+ </tr>
+
+ <tr class="alt">
+ <td>FullPivLU</td>
+ <td>-</td>
+ <td>Slow</td>
+ <td>Proven</td>
+ <td>Yes</td>
+ <td>-</td>
+ <td>Yes</td>
+ <td>Excellent</td>
+ <td>-</td>
+ </tr>
+
+ <tr>
+ <td>HouseholderQR</td>
+ <td>-</td>
+ <td>Fast</td>
+ <td>Depends on condition number</td>
+ <td>-</td>
+ <td>Orthogonalization</td>
+ <td>Yes</td>
+ <td>Excellent</td>
+ <td>Blocking</td>
+ </tr>
+
+ <tr class="alt">
+ <td>ColPivHouseholderQR</td>
+ <td>-</td>
+ <td>Fast</td>
+ <td>Good</td>
+ <td>Yes</td>
+ <td>Orthogonalization</td>
+ <td>Yes</td>
+ <td>Excellent</td>
+ <td><em>-</em></td>
+ </tr>
+
+ <tr>
+ <td>FullPivHouseholderQR</td>
+ <td>-</td>
+ <td>Slow</td>
+ <td>Proven</td>
+ <td>Yes</td>
+ <td>Orthogonalization</td>
+ <td>Yes</td>
+ <td>Average</td>
+ <td>-</td>
+ </tr>
+
+ <tr class="alt">
+ <td>CompleteOrthogonalDecomposition</td>
+ <td>-</td>
+ <td>Fast</td>
+ <td>Good</td>
+ <td>Yes</td>
+ <td>Orthogonalization</td>
+ <td>Yes</td>
+ <td>Excellent</td>
+ <td><em>-</em></td>
+ </tr>
+
+ <tr>
+ <td>LLT</td>
+ <td>Positive definite</td>
+ <td>Very fast</td>
+ <td>Depends on condition number</td>
+ <td>-</td>
+ <td>-</td>
+ <td>Yes</td>
+ <td>Excellent</td>
+ <td>Blocking</td>
+ </tr>
+
+ <tr class="alt">
+ <td>LDLT</td>
+ <td>Positive or negative semidefinite<sup><a href="#note1">1</a></sup></td>
+ <td>Very fast</td>
+ <td>Good</td>
+ <td>-</td>
+ <td>-</td>
+ <td>Yes</td>
+ <td>Excellent</td>
+ <td><em>Soon: blocking</em></td>
+ </tr>
+
+ <tr><th class="inter" colspan="9">\n Singular values and eigenvalues decompositions</th></tr>
+
+ <tr>
+ <td>BDCSVD (divide \& conquer)</td>
+ <td>-</td>
+ <td>One of the fastest SVD algorithms</td>
+ <td>Excellent</td>
+ <td>Yes</td>
+ <td>Singular values/vectors, least squares</td>
+ <td>Yes (and does least squares)</td>
+ <td>Excellent</td>
+ <td>Blocked bidiagonalization</td>
+ </tr>
+
+ <tr>
+ <td>JacobiSVD (two-sided)</td>
+ <td>-</td>
+ <td>Slow (but fast for small matrices)</td>
+ <td>Proven<sup><a href="#note3">3</a></sup></td>
+ <td>Yes</td>
+ <td>Singular values/vectors, least squares</td>
+ <td>Yes (and does least squares)</td>
+ <td>Excellent</td>
+ <td>R-SVD</td>
+ </tr>
+
+ <tr class="alt">
+ <td>SelfAdjointEigenSolver</td>
+ <td>Self-adjoint</td>
+ <td>Fast-average<sup><a href="#note2">2</a></sup></td>
+ <td>Good</td>
+ <td>Yes</td>
+ <td>Eigenvalues/vectors</td>
+ <td>-</td>
+ <td>Excellent</td>
+ <td><em>Closed forms for 2x2 and 3x3</em></td>
+ </tr>
+
+ <tr>
+ <td>ComplexEigenSolver</td>
+ <td>Square</td>
+ <td>Slow-very slow<sup><a href="#note2">2</a></sup></td>
+ <td>Depends on condition number</td>
+ <td>Yes</td>
+ <td>Eigenvalues/vectors</td>
+ <td>-</td>
+ <td>Average</td>
+ <td>-</td>
+ </tr>
+
+ <tr class="alt">
+ <td>EigenSolver</td>
+ <td>Square and real</td>
+ <td>Average-slow<sup><a href="#note2">2</a></sup></td>
+ <td>Depends on condition number</td>
+ <td>Yes</td>
+ <td>Eigenvalues/vectors</td>
+ <td>-</td>
+ <td>Average</td>
+ <td>-</td>
+ </tr>
+
+ <tr>
+ <td>GeneralizedSelfAdjointEigenSolver</td>
+ <td>Square</td>
+ <td>Fast-average<sup><a href="#note2">2</a></sup></td>
+ <td>Depends on condition number</td>
+ <td>-</td>
+ <td>Generalized eigenvalues/vectors</td>
+ <td>-</td>
+ <td>Good</td>
+ <td>-</td>
+ </tr>
+
+ <tr><th class="inter" colspan="9">\n Helper decompositions</th></tr>
+
+ <tr>
+ <td>RealSchur</td>
+ <td>Square and real</td>
+ <td>Average-slow<sup><a href="#note2">2</a></sup></td>
+ <td>Depends on condition number</td>
+ <td>Yes</td>
+ <td>-</td>
+ <td>-</td>
+ <td>Average</td>
+ <td>-</td>
+ </tr>
+
+ <tr class="alt">
+ <td>ComplexSchur</td>
+ <td>Square</td>
+ <td>Slow-very slow<sup><a href="#note2">2</a></sup></td>
+ <td>Depends on condition number</td>
+ <td>Yes</td>
+ <td>-</td>
+ <td>-</td>
+ <td>Average</td>
+ <td>-</td>
+ </tr>
+
+ <tr class="alt">
+ <td>Tridiagonalization</td>
+ <td>Self-adjoint</td>
+ <td>Fast</td>
+ <td>Good</td>
+ <td>-</td>
+ <td>-</td>
+ <td>-</td>
+ <td>Good</td>
+ <td><em>Soon: blocking</em></td>
+ </tr>
+
+ <tr>
+ <td>HessenbergDecomposition</td>
+ <td>Square</td>
+ <td>Average</td>
+ <td>Good</td>
+ <td>-</td>
+ <td>-</td>
+ <td>-</td>
+ <td>Good</td>
+ <td><em>Soon: blocking</em></td>
+ </tr>
+
+</table>
+
+\b Notes:
+<ul>
+<li><a name="note1">\b 1: </a>There exist two variants of the LDLT algorithm. Eigen's one produces a pure diagonal D matrix, and therefore it cannot handle indefinite matrices, unlike Lapack's one which produces a block diagonal D matrix.</li>
+<li><a name="note2">\b 2: </a>Eigenvalues, SVD and Schur decompositions rely on iterative algorithms. Their convergence speed depends on how well the eigenvalues are separated.</li>
+<li><a name="note3">\b 3: </a>Our JacobiSVD is two-sided, making for proven and optimal precision for square matrices. For non-square matrices, we have to use a QR preconditioner first. The default choice, ColPivHouseholderQR, is already very reliable, but if you want it to be proven, use FullPivHouseholderQR instead.
+</ul>
+
+\section TopicLinAlgTerminology Terminology
+
+<dl>
+ <dt><b>Selfadjoint</b></dt>
+ <dd>For a real matrix, selfadjoint is a synonym for symmetric. For a complex matrix, selfadjoint is a synonym for \em hermitian.
+ More generally, a matrix \f$ A \f$ is selfadjoint if and only if it is equal to its adjoint \f$ A^* \f$. The adjoint is also called the \em conjugate \em transpose. </dd>
+ <dt><b>Positive/negative definite</b></dt>
+ <dd>A selfadjoint matrix \f$ A \f$ is positive definite if \f$ v^* A v > 0 \f$ for any non zero vector \f$ v \f$.
+ In the same vein, it is negative definite if \f$ v^* A v < 0 \f$ for any non zero vector \f$ v \f$ </dd>
+ <dt><b>Positive/negative semidefinite</b></dt>
+ <dd>A selfadjoint matrix \f$ A \f$ is positive semi-definite if \f$ v^* A v \ge 0 \f$ for any non zero vector \f$ v \f$.
+ In the same vein, it is negative semi-definite if \f$ v^* A v \le 0 \f$ for any non zero vector \f$ v \f$ </dd>
+
+ <dt><b>Blocking</b></dt>
+ <dd>Means the algorithm can work per block, whence guaranteeing a good scaling of the performance for large matrices.</dd>
+ <dt><b>Implicit Multi Threading (MT)</b></dt>
+ <dd>Means the algorithm can take advantage of multicore processors via OpenMP. "Implicit" means the algorithm itself is not parallelized, but that it relies on parallelized matrix-matrix product routines.</dd>
+ <dt><b>Explicit Multi Threading (MT)</b></dt>
+ <dd>Means the algorithm is explicitly parallelized to take advantage of multicore processors via OpenMP.</dd>
+ <dt><b>Meta-unroller</b></dt>
+ <dd>Means the algorithm is automatically and explicitly unrolled for very small fixed size matrices.</dd>
+ <dt><b></b></dt>
+ <dd></dd>
+</dl>
+
+
+*/
+
+}
diff --git a/doc/TopicMultithreading.dox b/doc/TopicMultithreading.dox
new file mode 100644
index 0000000..7a8ff30
--- /dev/null
+++ b/doc/TopicMultithreading.dox
@@ -0,0 +1,67 @@
+namespace Eigen {
+
+/** \page TopicMultiThreading Eigen and multi-threading
+
+\section TopicMultiThreading_MakingEigenMT Make Eigen run in parallel
+
+Some %Eigen's algorithms can exploit the multiple cores present in your hardware.
+To this end, it is enough to enable OpenMP on your compiler, for instance:
+ - GCC: \c -fopenmp
+ - ICC: \c -openmp
+ - MSVC: check the respective option in the build properties.
+
+You can control the number of threads that will be used using either the OpenMP API or %Eigen's API using the following priority:
+\code
+ OMP_NUM_THREADS=n ./my_program
+ omp_set_num_threads(n);
+ Eigen::setNbThreads(n);
+\endcode
+Unless `setNbThreads` has been called, %Eigen uses the number of threads specified by OpenMP.
+You can restore this behavior by calling `setNbThreads(0);`.
+You can query the number of threads that will be used with:
+\code
+n = Eigen::nbThreads( );
+\endcode
+You can disable %Eigen's multi threading at compile time by defining the \link TopicPreprocessorDirectivesPerformance EIGEN_DONT_PARALLELIZE \endlink preprocessor token.
+
+Currently, the following algorithms can make use of multi-threading:
+ - general dense matrix - matrix products
+ - PartialPivLU
+ - row-major-sparse * dense vector/matrix products
+ - ConjugateGradient with \c Lower|Upper as the \c UpLo template parameter.
+ - BiCGSTAB with a row-major sparse matrix format.
+ - LeastSquaresConjugateGradient
+
+\warning On most OS it is <strong>very important</strong> to limit the number of threads to the number of physical cores, otherwise significant slowdowns are expected, especially for operations involving dense matrices.
+
+Indeed, the principle of hyper-threading is to run multiple threads (in most cases 2) on a single core in an interleaved manner.
+However, %Eigen's matrix-matrix product kernel is fully optimized and already exploits nearly 100% of the CPU capacity.
+Consequently, there is no room for running multiple such threads on a single core, and the performance would drops significantly because of cache pollution and other sources of overheads.
+At this stage of reading you're probably wondering why %Eigen does not limit itself to the number of physical cores?
+This is simply because OpenMP does not allow to know the number of physical cores, and thus %Eigen will launch as many threads as <i>cores</i> reported by OpenMP.
+
+\section TopicMultiThreading_UsingEigenWithMT Using Eigen in a multi-threaded application
+
+In the case your own application is multithreaded, and multiple threads make calls to %Eigen, then you have to initialize %Eigen by calling the following routine \b before creating the threads:
+\code
+#include <Eigen/Core>
+
+int main(int argc, char** argv)
+{
+ Eigen::initParallel();
+
+ ...
+}
+\endcode
+
+\note With %Eigen 3.3, and a fully C++11 compliant compiler (i.e., <a href="http://en.cppreference.com/w/cpp/language/storage_duration#Static_local_variables">thread-safe static local variable initialization</a>), then calling \c initParallel() is optional.
+
+\warning Note that all functions generating random matrices are \b not re-entrant nor thread-safe. Those include DenseBase::Random(), and DenseBase::setRandom() despite a call to `Eigen::initParallel()`. This is because these functions are based on `std::rand` which is not re-entrant.
+For thread-safe random generator, we recommend the use of c++11 random generators (\link DenseBase::NullaryExpr(Index, const CustomNullaryOp&) example \endlink) or `boost::random`.
+
+In the case your application is parallelized with OpenMP, you might want to disable %Eigen's own parallelization as detailed in the previous section.
+
+\warning Using OpenMP with custom scalar types that might throw exceptions can lead to unexpected behaviour in the event of throwing.
+*/
+
+}
diff --git a/doc/TopicResizing.dox b/doc/TopicResizing.dox
new file mode 100644
index 0000000..c323e17
--- /dev/null
+++ b/doc/TopicResizing.dox
@@ -0,0 +1,11 @@
+namespace Eigen {
+
+/** \page TopicResizing Resizing
+
+
+TODO: write this dox page!
+
+Is linked from the tutorial on the Matrix class.
+
+*/
+}
diff --git a/doc/TopicScalarTypes.dox b/doc/TopicScalarTypes.dox
new file mode 100644
index 0000000..2ff03c1
--- /dev/null
+++ b/doc/TopicScalarTypes.dox
@@ -0,0 +1,12 @@
+namespace Eigen {
+
+/** \page TopicScalarTypes Scalar types
+
+
+TODO: write this dox page!
+
+Is linked from the tutorial on the Matrix class.
+
+*/
+
+}
diff --git a/doc/TopicVectorization.dox b/doc/TopicVectorization.dox
new file mode 100644
index 0000000..274d045
--- /dev/null
+++ b/doc/TopicVectorization.dox
@@ -0,0 +1,9 @@
+namespace Eigen {
+
+/** \page TopicVectorization Vectorization
+
+
+TODO: write this dox page!
+
+*/
+}
diff --git a/doc/TutorialAdvancedInitialization.dox b/doc/TutorialAdvancedInitialization.dox
new file mode 100644
index 0000000..50374d0
--- /dev/null
+++ b/doc/TutorialAdvancedInitialization.dox
@@ -0,0 +1,162 @@
+namespace Eigen {
+
+/** \eigenManualPage TutorialAdvancedInitialization Advanced initialization
+
+This page discusses several advanced methods for initializing matrices. It gives more details on the
+comma-initializer, which was introduced before. It also explains how to get special matrices such as the
+identity matrix and the zero matrix.
+
+\eigenAutoToc
+
+\section TutorialAdvancedInitializationCommaInitializer The comma initializer
+
+Eigen offers a comma initializer syntax which allows the user to easily set all the coefficients of a matrix,
+vector or array. Simply list the coefficients, starting at the top-left corner and moving from left to right
+and from the top to the bottom. The size of the object needs to be specified beforehand. If you list too few
+or too many coefficients, Eigen will complain.
+
+<table class="example">
+<tr><th>Example:</th><th>Output:</th></tr>
+<tr><td>
+\include Tutorial_commainit_01.cpp
+</td>
+<td>
+\verbinclude Tutorial_commainit_01.out
+</td></tr></table>
+
+Moreover, the elements of the initialization list may themselves be vectors or matrices. A common use is
+to join vectors or matrices together. For example, here is how to join two row vectors together. Remember
+that you have to set the size before you can use the comma initializer.
+
+<table class="example">
+<tr><th>Example:</th><th>Output:</th></tr>
+<tr><td>
+\include Tutorial_AdvancedInitialization_Join.cpp
+</td>
+<td>
+\verbinclude Tutorial_AdvancedInitialization_Join.out
+</td></tr></table>
+
+We can use the same technique to initialize matrices with a block structure.
+
+<table class="example">
+<tr><th>Example:</th><th>Output:</th></tr>
+<tr><td>
+\include Tutorial_AdvancedInitialization_Block.cpp
+</td>
+<td>
+\verbinclude Tutorial_AdvancedInitialization_Block.out
+</td></tr></table>
+
+The comma initializer can also be used to fill block expressions such as <tt>m.row(i)</tt>. Here is a more
+complicated way to get the same result as in the first example above:
+
+<table class="example">
+<tr><th>Example:</th><th>Output:</th></tr>
+<tr><td>
+\include Tutorial_commainit_01b.cpp
+</td>
+<td>
+\verbinclude Tutorial_commainit_01b.out
+</td></tr></table>
+
+
+\section TutorialAdvancedInitializationSpecialMatrices Special matrices and arrays
+
+The Matrix and Array classes have static methods like \link DenseBase::Zero() Zero()\endlink, which can be
+used to initialize all coefficients to zero. There are three variants. The first variant takes no arguments
+and can only be used for fixed-size objects. If you want to initialize a dynamic-size object to zero, you need
+to specify the size. Thus, the second variant requires one argument and can be used for one-dimensional
+dynamic-size objects, while the third variant requires two arguments and can be used for two-dimensional
+objects. All three variants are illustrated in the following example:
+
+<table class="example">
+<tr><th>Example:</th><th>Output:</th></tr>
+<tr><td>
+\include Tutorial_AdvancedInitialization_Zero.cpp
+</td>
+<td>
+\verbinclude Tutorial_AdvancedInitialization_Zero.out
+</td></tr></table>
+
+Similarly, the static method \link DenseBase::Constant() Constant\endlink(value) sets all coefficients to \c value.
+If the size of the object needs to be specified, the additional arguments go before the \c value
+argument, as in <tt>MatrixXd::Constant(rows, cols, value)</tt>. The method \link DenseBase::Random() Random()
+\endlink fills the matrix or array with random coefficients. The identity matrix can be obtained by calling
+\link MatrixBase::Identity() Identity()\endlink; this method is only available for Matrix, not for Array,
+because "identity matrix" is a linear algebra concept. The method
+\link DenseBase::LinSpaced LinSpaced\endlink(size, low, high) is only available for vectors and
+one-dimensional arrays; it yields a vector of the specified size whose coefficients are equally spaced between
+\c low and \c high. The method \c LinSpaced() is illustrated in the following example, which prints a table
+with angles in degrees, the corresponding angle in radians, and their sine and cosine.
+
+<table class="example">
+<tr><th>Example:</th><th>Output:</th></tr>
+<tr><td>
+\include Tutorial_AdvancedInitialization_LinSpaced.cpp
+</td>
+<td>
+\verbinclude Tutorial_AdvancedInitialization_LinSpaced.out
+</td></tr></table>
+
+This example shows that objects like the ones returned by LinSpaced() can be assigned to variables (and
+expressions). Eigen defines utility functions like \link DenseBase::setZero() setZero()\endlink,
+\link MatrixBase::setIdentity() \endlink and \link DenseBase::setLinSpaced() \endlink to do this
+conveniently. The following example contrasts three ways to construct the matrix
+\f$ J = \bigl[ \begin{smallmatrix} O & I \\ I & O \end{smallmatrix} \bigr] \f$: using static methods and
+assignment, using static methods and the comma-initializer, or using the setXxx() methods.
+
+<table class="example">
+<tr><th>Example:</th><th>Output:</th></tr>
+<tr><td>
+\include Tutorial_AdvancedInitialization_ThreeWays.cpp
+</td>
+<td>
+\verbinclude Tutorial_AdvancedInitialization_ThreeWays.out
+</td></tr></table>
+
+A summary of all pre-defined matrix, vector and array objects can be found in the \ref QuickRefPage.
+
+
+\section TutorialAdvancedInitializationTemporaryObjects Usage as temporary objects
+
+As shown above, static methods as Zero() and Constant() can be used to initialize variables at the time of
+declaration or at the right-hand side of an assignment operator. You can think of these methods as returning a
+matrix or array; in fact, they return so-called \ref TopicEigenExpressionTemplates "expression objects" which
+evaluate to a matrix or array when needed, so that this syntax does not incur any overhead.
+
+These expressions can also be used as a temporary object. The second example in
+the \ref GettingStarted guide, which we reproduce here, already illustrates this.
+
+<table class="example">
+<tr><th>Example:</th><th>Output:</th></tr>
+<tr><td>
+\include QuickStart_example2_dynamic.cpp
+</td>
+<td>
+\verbinclude QuickStart_example2_dynamic.out
+</td></tr></table>
+
+The expression <tt>m + MatrixXf::Constant(3,3,1.2)</tt> constructs the 3-by-3 matrix expression with all its coefficients
+equal to 1.2 plus the corresponding coefficient of \a m.
+
+The comma-initializer, too, can also be used to construct temporary objects. The following example constructs a random
+matrix of size 2-by-3, and then multiplies this matrix on the left with
+\f$ \bigl[ \begin{smallmatrix} 0 & 1 \\ 1 & 0 \end{smallmatrix} \bigr] \f$.
+
+<table class="example">
+<tr><th>Example:</th><th>Output:</th></tr>
+<tr><td>
+\include Tutorial_AdvancedInitialization_CommaTemporary.cpp
+</td>
+<td>
+\verbinclude Tutorial_AdvancedInitialization_CommaTemporary.out
+</td></tr></table>
+
+The \link CommaInitializer::finished() finished() \endlink method is necessary here to get the actual matrix
+object once the comma initialization of our temporary submatrix is done.
+
+
+*/
+
+}
diff --git a/doc/TutorialArrayClass.dox b/doc/TutorialArrayClass.dox
new file mode 100644
index 0000000..f6f3510
--- /dev/null
+++ b/doc/TutorialArrayClass.dox
@@ -0,0 +1,192 @@
+namespace Eigen {
+
+/** \eigenManualPage TutorialArrayClass The Array class and coefficient-wise operations
+
+This page aims to provide an overview and explanations on how to use
+Eigen's Array class.
+
+\eigenAutoToc
+
+\section TutorialArrayClassIntro What is the Array class?
+
+The Array class provides general-purpose arrays, as opposed to the Matrix class which
+is intended for linear algebra. Furthermore, the Array class provides an easy way to
+perform coefficient-wise operations, which might not have a linear algebraic meaning,
+such as adding a constant to every coefficient in the array or multiplying two arrays coefficient-wise.
+
+
+\section TutorialArrayClassTypes Array types
+Array is a class template taking the same template parameters as Matrix.
+As with Matrix, the first three template parameters are mandatory:
+\code
+Array<typename Scalar, int RowsAtCompileTime, int ColsAtCompileTime>
+\endcode
+The last three template parameters are optional. Since this is exactly the same as for Matrix,
+we won't explain it again here and just refer to \ref TutorialMatrixClass.
+
+Eigen also provides typedefs for some common cases, in a way that is similar to the Matrix typedefs
+but with some slight differences, as the word "array" is used for both 1-dimensional and 2-dimensional arrays.
+We adopt the convention that typedefs of the form ArrayNt stand for 1-dimensional arrays, where N and t are
+the size and the scalar type, as in the Matrix typedefs explained on \ref TutorialMatrixClass "this page". For 2-dimensional arrays, we
+use typedefs of the form ArrayNNt. Some examples are shown in the following table:
+
+<table class="manual">
+ <tr>
+ <th>Type </th>
+ <th>Typedef </th>
+ </tr>
+ <tr>
+ <td> \code Array<float,Dynamic,1> \endcode </td>
+ <td> \code ArrayXf \endcode </td>
+ </tr>
+ <tr>
+ <td> \code Array<float,3,1> \endcode </td>
+ <td> \code Array3f \endcode </td>
+ </tr>
+ <tr>
+ <td> \code Array<double,Dynamic,Dynamic> \endcode </td>
+ <td> \code ArrayXXd \endcode </td>
+ </tr>
+ <tr>
+ <td> \code Array<double,3,3> \endcode </td>
+ <td> \code Array33d \endcode </td>
+ </tr>
+</table>
+
+
+\section TutorialArrayClassAccess Accessing values inside an Array
+
+The parenthesis operator is overloaded to provide write and read access to the coefficients of an array, just as with matrices.
+Furthermore, the \c << operator can be used to initialize arrays (via the comma initializer) or to print them.
+
+<table class="example">
+<tr><th>Example:</th><th>Output:</th></tr>
+<tr><td>
+\include Tutorial_ArrayClass_accessors.cpp
+</td>
+<td>
+\verbinclude Tutorial_ArrayClass_accessors.out
+</td></tr></table>
+
+For more information about the comma initializer, see \ref TutorialAdvancedInitialization.
+
+
+\section TutorialArrayClassAddSub Addition and subtraction
+
+Adding and subtracting two arrays is the same as for matrices.
+The operation is valid if both arrays have the same size, and the addition or subtraction is done coefficient-wise.
+
+Arrays also support expressions of the form <tt>array + scalar</tt> which add a scalar to each coefficient in the array.
+This provides a functionality that is not directly available for Matrix objects.
+
+<table class="example">
+<tr><th>Example:</th><th>Output:</th></tr>
+<tr><td>
+\include Tutorial_ArrayClass_addition.cpp
+</td>
+<td>
+\verbinclude Tutorial_ArrayClass_addition.out
+</td></tr></table>
+
+
+\section TutorialArrayClassMult Array multiplication
+
+First of all, of course you can multiply an array by a scalar, this works in the same way as matrices. Where arrays
+are fundamentally different from matrices, is when you multiply two together. Matrices interpret
+multiplication as matrix product and arrays interpret multiplication as coefficient-wise product. Thus, two
+arrays can be multiplied if and only if they have the same dimensions.
+
+<table class="example">
+<tr><th>Example:</th><th>Output:</th></tr>
+<tr><td>
+\include Tutorial_ArrayClass_mult.cpp
+</td>
+<td>
+\verbinclude Tutorial_ArrayClass_mult.out
+</td></tr></table>
+
+
+\section TutorialArrayClassCwiseOther Other coefficient-wise operations
+
+The Array class defines other coefficient-wise operations besides the addition, subtraction and multiplication
+operators described above. For example, the \link ArrayBase::abs() .abs() \endlink method takes the absolute
+value of each coefficient, while \link ArrayBase::sqrt() .sqrt() \endlink computes the square root of the
+coefficients. If you have two arrays of the same size, you can call \link ArrayBase::min(const Eigen::ArrayBase<OtherDerived>&) const .min(.) \endlink to
+construct the array whose coefficients are the minimum of the corresponding coefficients of the two given
+arrays. These operations are illustrated in the following example.
+
+<table class="example">
+<tr><th>Example:</th><th>Output:</th></tr>
+<tr><td>
+\include Tutorial_ArrayClass_cwise_other.cpp
+</td>
+<td>
+\verbinclude Tutorial_ArrayClass_cwise_other.out
+</td></tr></table>
+
+More coefficient-wise operations can be found in the \ref QuickRefPage.
+
+
+\section TutorialArrayClassConvert Converting between array and matrix expressions
+
+When should you use objects of the Matrix class and when should you use objects of the Array class? You cannot
+apply Matrix operations on arrays, or Array operations on matrices. Thus, if you need to do linear algebraic
+operations such as matrix multiplication, then you should use matrices; if you need to do coefficient-wise
+operations, then you should use arrays. However, sometimes it is not that simple, but you need to use both
+Matrix and Array operations. In that case, you need to convert a matrix to an array or reversely. This gives
+access to all operations regardless of the choice of declaring objects as arrays or as matrices.
+
+\link MatrixBase Matrix expressions \endlink have an \link MatrixBase::array() .array() \endlink method that
+'converts' them into \link ArrayBase array expressions\endlink, so that coefficient-wise operations
+can be applied easily. Conversely, \link ArrayBase array expressions \endlink
+have a \link ArrayBase::matrix() .matrix() \endlink method. As with all Eigen expression abstractions,
+this doesn't have any runtime cost (provided that you let your compiler optimize).
+Both \link MatrixBase::array() .array() \endlink and \link ArrayBase::matrix() .matrix() \endlink
+can be used as rvalues and as lvalues.
+
+Mixing matrices and arrays in an expression is forbidden with Eigen. For instance, you cannot add a matrix and
+array directly; the operands of a \c + operator should either both be matrices or both be arrays. However,
+it is easy to convert from one to the other with \link MatrixBase::array() .array() \endlink and
+\link ArrayBase::matrix() .matrix()\endlink. The exception to this rule is the assignment operator: it is
+allowed to assign a matrix expression to an array variable, or to assign an array expression to a matrix
+variable.
+
+The following example shows how to use array operations on a Matrix object by employing the
+\link MatrixBase::array() .array() \endlink method. For example, the statement
+<tt>result = m.array() * n.array()</tt> takes two matrices \c m and \c n, converts them both to an array, uses
+* to multiply them coefficient-wise and assigns the result to the matrix variable \c result (this is legal
+because Eigen allows assigning array expressions to matrix variables).
+
+As a matter of fact, this usage case is so common that Eigen provides a \link MatrixBase::cwiseProduct const
+.cwiseProduct(.) \endlink method for matrices to compute the coefficient-wise product. This is also shown in
+the example program.
+
+<table class="example">
+<tr><th>Example:</th><th>Output:</th></tr>
+<tr><td>
+\include Tutorial_ArrayClass_interop_matrix.cpp
+</td>
+<td>
+\verbinclude Tutorial_ArrayClass_interop_matrix.out
+</td></tr></table>
+
+Similarly, if \c array1 and \c array2 are arrays, then the expression <tt>array1.matrix() * array2.matrix()</tt>
+computes their matrix product.
+
+Here is a more advanced example. The expression <tt>(m.array() + 4).matrix() * m</tt> adds 4 to every
+coefficient in the matrix \c m and then computes the matrix product of the result with \c m. Similarly, the
+expression <tt>(m.array() * n.array()).matrix() * m</tt> computes the coefficient-wise product of the matrices
+\c m and \c n and then the matrix product of the result with \c m.
+
+<table class="example">
+<tr><th>Example:</th><th>Output:</th></tr>
+<tr><td>
+\include Tutorial_ArrayClass_interop.cpp
+</td>
+<td>
+\verbinclude Tutorial_ArrayClass_interop.out
+</td></tr></table>
+
+*/
+
+}
diff --git a/doc/TutorialBlockOperations.dox b/doc/TutorialBlockOperations.dox
new file mode 100644
index 0000000..df27748
--- /dev/null
+++ b/doc/TutorialBlockOperations.dox
@@ -0,0 +1,242 @@
+namespace Eigen {
+
+/** \eigenManualPage TutorialBlockOperations Block operations
+
+This page explains the essentials of block operations.
+A block is a rectangular part of a matrix or array. Blocks expressions can be used both
+as rvalues and as lvalues. As usual with Eigen expressions, this abstraction has zero runtime cost
+provided that you let your compiler optimize.
+
+\eigenAutoToc
+
+\section TutorialBlockOperationsUsing Using block operations
+
+The most general block operation in Eigen is called \link DenseBase::block() .block() \endlink.
+There are two versions, whose syntax is as follows:
+
+<table class="manual">
+<tr><th>\b %Block \b operation</td>
+<th>Version constructing a \n dynamic-size block expression</th>
+<th>Version constructing a \n fixed-size block expression</th></tr>
+<tr><td>%Block of size <tt>(p,q)</tt>, starting at <tt>(i,j)</tt></td>
+ <td>\code
+matrix.block(i,j,p,q);\endcode </td>
+ <td>\code
+matrix.block<p,q>(i,j);\endcode </td>
+</tr>
+</table>
+
+As always in Eigen, indices start at 0.
+
+Both versions can be used on fixed-size and dynamic-size matrices and arrays.
+These two expressions are semantically equivalent.
+The only difference is that the fixed-size version will typically give you faster code if the block size is small,
+but requires this size to be known at compile time.
+
+The following program uses the dynamic-size and fixed-size versions to print the values of several blocks inside a
+matrix.
+
+<table class="example">
+<tr><th>Example:</th><th>Output:</th></tr>
+<tr><td>
+\include Tutorial_BlockOperations_print_block.cpp
+</td>
+<td>
+\verbinclude Tutorial_BlockOperations_print_block.out
+</td></tr></table>
+
+In the above example the \link DenseBase::block() .block() \endlink function was employed as a \em rvalue, i.e.
+it was only read from. However, blocks can also be used as \em lvalues, meaning that you can assign to a block.
+
+This is illustrated in the following example. This example also demonstrates blocks in arrays, which works exactly like the above-demonstrated blocks in matrices.
+
+<table class="example">
+<tr><th>Example:</th><th>Output:</th></tr>
+<tr><td>
+\include Tutorial_BlockOperations_block_assignment.cpp
+</td>
+<td>
+\verbinclude Tutorial_BlockOperations_block_assignment.out
+</td></tr></table>
+
+While the \link DenseBase::block() .block() \endlink method can be used for any block operation, there are
+other methods for special cases, providing more specialized API and/or better performance. On the topic of performance, all what
+matters is that you give Eigen as much information as possible at compile time. For example, if your block is a single whole column in a matrix,
+using the specialized \link DenseBase::col() .col() \endlink function described below lets Eigen know that, which can give it optimization opportunities.
+
+The rest of this page describes these specialized methods.
+
+\section TutorialBlockOperationsSyntaxColumnRows Columns and rows
+
+Individual columns and rows are special cases of blocks. Eigen provides methods to easily address them:
+\link DenseBase::col() .col() \endlink and \link DenseBase::row() .row()\endlink.
+
+<table class="manual">
+<tr><th>%Block operation</th>
+<th>Method</th>
+<tr><td>i<sup>th</sup> row
+ \link DenseBase::row() * \endlink</td>
+ <td>\code
+matrix.row(i);\endcode </td>
+</tr>
+<tr><td>j<sup>th</sup> column
+ \link DenseBase::col() * \endlink</td>
+ <td>\code
+matrix.col(j);\endcode </td>
+</tr>
+</table>
+
+The argument for \p col() and \p row() is the index of the column or row to be accessed. As always in Eigen, indices start at 0.
+
+<table class="example">
+<tr><th>Example:</th><th>Output:</th></tr>
+<tr><td>
+\include Tutorial_BlockOperations_colrow.cpp
+</td>
+<td>
+\verbinclude Tutorial_BlockOperations_colrow.out
+</td></tr></table>
+
+That example also demonstrates that block expressions (here columns) can be used in arithmetic like any other expression.
+
+
+\section TutorialBlockOperationsSyntaxCorners Corner-related operations
+
+Eigen also provides special methods for blocks that are flushed against one of the corners or sides of a
+matrix or array. For instance, \link DenseBase::topLeftCorner() .topLeftCorner() \endlink can be used to refer
+to a block in the top-left corner of a matrix.
+
+The different possibilities are summarized in the following table:
+
+<table class="manual">
+<tr><th>%Block \b operation</td>
+<th>Version constructing a \n dynamic-size block expression</th>
+<th>Version constructing a \n fixed-size block expression</th></tr>
+<tr><td>Top-left p by q block \link DenseBase::topLeftCorner() * \endlink</td>
+ <td>\code
+matrix.topLeftCorner(p,q);\endcode </td>
+ <td>\code
+matrix.topLeftCorner<p,q>();\endcode </td>
+</tr>
+<tr><td>Bottom-left p by q block
+ \link DenseBase::bottomLeftCorner() * \endlink</td>
+ <td>\code
+matrix.bottomLeftCorner(p,q);\endcode </td>
+ <td>\code
+matrix.bottomLeftCorner<p,q>();\endcode </td>
+</tr>
+<tr><td>Top-right p by q block
+ \link DenseBase::topRightCorner() * \endlink</td>
+ <td>\code
+matrix.topRightCorner(p,q);\endcode </td>
+ <td>\code
+matrix.topRightCorner<p,q>();\endcode </td>
+</tr>
+<tr><td>Bottom-right p by q block
+ \link DenseBase::bottomRightCorner() * \endlink</td>
+ <td>\code
+matrix.bottomRightCorner(p,q);\endcode </td>
+ <td>\code
+matrix.bottomRightCorner<p,q>();\endcode </td>
+</tr>
+<tr><td>%Block containing the first q rows
+ \link DenseBase::topRows() * \endlink</td>
+ <td>\code
+matrix.topRows(q);\endcode </td>
+ <td>\code
+matrix.topRows<q>();\endcode </td>
+</tr>
+<tr><td>%Block containing the last q rows
+ \link DenseBase::bottomRows() * \endlink</td>
+ <td>\code
+matrix.bottomRows(q);\endcode </td>
+ <td>\code
+matrix.bottomRows<q>();\endcode </td>
+</tr>
+<tr><td>%Block containing the first p columns
+ \link DenseBase::leftCols() * \endlink</td>
+ <td>\code
+matrix.leftCols(p);\endcode </td>
+ <td>\code
+matrix.leftCols<p>();\endcode </td>
+</tr>
+<tr><td>%Block containing the last q columns
+ \link DenseBase::rightCols() * \endlink</td>
+ <td>\code
+matrix.rightCols(q);\endcode </td>
+ <td>\code
+matrix.rightCols<q>();\endcode </td>
+</tr>
+<tr><td>%Block containing the q columns starting from i
+ \link DenseBase::middleCols() * \endlink</td>
+ <td>\code
+matrix.middleCols(i,q);\endcode </td>
+ <td>\code
+matrix.middleCols<q>(i);\endcode </td>
+</tr>
+<tr><td>%Block containing the q rows starting from i
+ \link DenseBase::middleRows() * \endlink</td>
+ <td>\code
+matrix.middleRows(i,q);\endcode </td>
+ <td>\code
+matrix.middleRows<q>(i);\endcode </td>
+</tr>
+</table>
+
+Here is a simple example illustrating the use of the operations presented above:
+
+<table class="example">
+<tr><th>Example:</th><th>Output:</th></tr>
+<tr><td>
+\include Tutorial_BlockOperations_corner.cpp
+</td>
+<td>
+\verbinclude Tutorial_BlockOperations_corner.out
+</td></tr></table>
+
+
+\section TutorialBlockOperationsSyntaxVectors Block operations for vectors
+
+Eigen also provides a set of block operations designed specifically for the special case of vectors and one-dimensional arrays:
+
+<table class="manual">
+<tr><th> %Block operation</th>
+<th>Version constructing a \n dynamic-size block expression</th>
+<th>Version constructing a \n fixed-size block expression</th></tr>
+<tr><td>%Block containing the first \p n elements
+ \link DenseBase::head() * \endlink</td>
+ <td>\code
+vector.head(n);\endcode </td>
+ <td>\code
+vector.head<n>();\endcode </td>
+</tr>
+<tr><td>%Block containing the last \p n elements
+ \link DenseBase::tail() * \endlink</td>
+ <td>\code
+vector.tail(n);\endcode </td>
+ <td>\code
+vector.tail<n>();\endcode </td>
+</tr>
+<tr><td>%Block containing \p n elements, starting at position \p i
+ \link DenseBase::segment() * \endlink</td>
+ <td>\code
+vector.segment(i,n);\endcode </td>
+ <td>\code
+vector.segment<n>(i);\endcode </td>
+</tr>
+</table>
+
+
+An example is presented below:
+<table class="example">
+<tr><th>Example:</th><th>Output:</th></tr>
+<tr><td>
+\include Tutorial_BlockOperations_vector.cpp
+</td>
+<td>
+\verbinclude Tutorial_BlockOperations_vector.out
+</td></tr></table>
+
+*/
+
+}
diff --git a/doc/TutorialGeometry.dox b/doc/TutorialGeometry.dox
new file mode 100644
index 0000000..1d214f3
--- /dev/null
+++ b/doc/TutorialGeometry.dox
@@ -0,0 +1,242 @@
+namespace Eigen {
+
+/** \eigenManualPage TutorialGeometry Space transformations
+
+In this page, we will introduce the many possibilities offered by the \ref Geometry_Module "geometry module" to deal with 2D and 3D rotations and projective or affine transformations.
+
+\eigenAutoToc
+
+Eigen's Geometry module provides two different kinds of geometric transformations:
+ - Abstract transformations, such as rotations (represented by \ref AngleAxis "angle and axis" or by a \ref Quaternion "quaternion"), \ref Translation "translations", \ref Scaling "scalings". These transformations are NOT represented as matrices, but you can nevertheless mix them with matrices and vectors in expressions, and convert them to matrices if you wish.
+ - Projective or affine transformation matrices: see the Transform class. These are really matrices.
+
+\note If you are working with OpenGL 4x4 matrices then Affine3f and Affine3d are what you want. Since Eigen defaults to column-major storage, you can directly use the Transform::data() method to pass your transformation matrix to OpenGL.
+
+You can construct a Transform from an abstract transformation, like this:
+\code
+ Transform t(AngleAxis(angle,axis));
+\endcode
+or like this:
+\code
+ Transform t;
+ t = AngleAxis(angle,axis);
+\endcode
+But note that unfortunately, because of how C++ works, you can \b not do this:
+\code
+ Transform t = AngleAxis(angle,axis);
+\endcode
+<span class="note">\b Explanation: In the C++ language, this would require Transform to have a non-explicit conversion constructor from AngleAxis, but we really don't want to allow implicit casting here.
+</span>
+
+\section TutorialGeoElementaryTransformations Transformation types
+
+<table class="manual">
+<tr><th>Transformation type</th><th>Typical initialization code</th></tr>
+<tr><td>
+\ref Rotation2D "2D rotation" from an angle</td><td>\code
+Rotation2D<float> rot2(angle_in_radian);\endcode</td></tr>
+<tr class="alt"><td>
+3D rotation as an \ref AngleAxis "angle + axis"</td><td>\code
+AngleAxis<float> aa(angle_in_radian, Vector3f(ax,ay,az));\endcode
+<span class="note">The axis vector must be normalized.</span></td></tr>
+<tr><td>
+3D rotation as a \ref Quaternion "quaternion"</td><td>\code
+Quaternion<float> q; q = AngleAxis<float>(angle_in_radian, axis);\endcode</td></tr>
+<tr class="alt"><td>
+N-D Scaling</td><td>\code
+Scaling(sx, sy)
+Scaling(sx, sy, sz)
+Scaling(s)
+Scaling(vecN)\endcode</td></tr>
+<tr><td>
+N-D Translation</td><td>\code
+Translation<float,2>(tx, ty)
+Translation<float,3>(tx, ty, tz)
+Translation<float,N>(s)
+Translation<float,N>(vecN)\endcode</td></tr>
+<tr class="alt"><td>
+N-D \ref TutorialGeoTransform "Affine transformation"</td><td>\code
+Transform<float,N,Affine> t = concatenation_of_any_transformations;
+Transform<float,3,Affine> t = Translation3f(p) * AngleAxisf(a,axis) * Scaling(s);\endcode</td></tr>
+<tr><td>
+N-D Linear transformations \n
+<em class=note>(pure rotations, \n scaling, etc.)</em></td><td>\code
+Matrix<float,N> t = concatenation_of_rotations_and_scalings;
+Matrix<float,2> t = Rotation2Df(a) * Scaling(s);
+Matrix<float,3> t = AngleAxisf(a,axis) * Scaling(s);\endcode</td></tr>
+</table>
+
+<strong>Notes on rotations</strong>\n To transform more than a single vector the preferred
+representations are rotation matrices, while for other usages Quaternion is the
+representation of choice as they are compact, fast and stable. Finally Rotation2D and
+AngleAxis are mainly convenient types to create other rotation objects.
+
+<strong>Notes on Translation and Scaling</strong>\n Like AngleAxis, these classes were
+designed to simplify the creation/initialization of linear (Matrix) and affine (Transform)
+transformations. Nevertheless, unlike AngleAxis which is inefficient to use, these classes
+might still be interesting to write generic and efficient algorithms taking as input any
+kind of transformations.
+
+Any of the above transformation types can be converted to any other types of the same nature,
+or to a more generic type. Here are some additional examples:
+<table class="manual">
+<tr><td>\code
+Rotation2Df r; r = Matrix2f(..); // assumes a pure rotation matrix
+AngleAxisf aa; aa = Quaternionf(..);
+AngleAxisf aa; aa = Matrix3f(..); // assumes a pure rotation matrix
+Matrix2f m; m = Rotation2Df(..);
+Matrix3f m; m = Quaternionf(..); Matrix3f m; m = Scaling(..);
+Affine3f m; m = AngleAxis3f(..); Affine3f m; m = Scaling(..);
+Affine3f m; m = Translation3f(..); Affine3f m; m = Matrix3f(..);
+\endcode</td></tr>
+</table>
+
+
+<a href="#" class="top">top</a>\section TutorialGeoCommontransformationAPI Common API across transformation types
+
+To some extent, Eigen's \ref Geometry_Module "geometry module" allows you to write
+generic algorithms working on any kind of transformation representations:
+<table class="manual">
+<tr><td>
+Concatenation of two transformations</td><td>\code
+gen1 * gen2;\endcode</td></tr>
+<tr class="alt"><td>Apply the transformation to a vector</td><td>\code
+vec2 = gen1 * vec1;\endcode</td></tr>
+<tr><td>Get the inverse of the transformation</td><td>\code
+gen2 = gen1.inverse();\endcode</td></tr>
+<tr class="alt"><td>Spherical interpolation \n (Rotation2D and Quaternion only)</td><td>\code
+rot3 = rot1.slerp(alpha,rot2);\endcode</td></tr>
+</table>
+
+
+
+<a href="#" class="top">top</a>\section TutorialGeoTransform Affine transformations
+Generic affine transformations are represented by the Transform class which internally
+is a (Dim+1)^2 matrix. In Eigen we have chosen to not distinghish between points and
+vectors such that all points are actually represented by displacement vectors from the
+origin ( \f$ \mathbf{p} \equiv \mathbf{p}-0 \f$ ). With that in mind, real points and
+vector distinguish when the transformation is applied.
+<table class="manual">
+<tr><td>
+Apply the transformation to a \b point </td><td>\code
+VectorNf p1, p2;
+p2 = t * p1;\endcode</td></tr>
+<tr class="alt"><td>
+Apply the transformation to a \b vector </td><td>\code
+VectorNf vec1, vec2;
+vec2 = t.linear() * vec1;\endcode</td></tr>
+<tr><td>
+Apply a \em general transformation \n to a \b normal \b vector \n
+</td><td>\code
+VectorNf n1, n2;
+MatrixNf normalMatrix = t.linear().inverse().transpose();
+n2 = (normalMatrix * n1).normalized();\endcode</td></tr>
+<tr><td colspan="2">(See subject 5.27 of this <a href="http://www.faqs.org/faqs/graphics/algorithms-faq">faq</a> for the explanations)</td></tr>
+<tr class="alt"><td>
+Apply a transformation with \em pure \em rotation \n to a \b normal \b vector
+(no scaling, no shear)</td><td>\code
+n2 = t.linear() * n1;\endcode</td></tr>
+<tr><td>
+OpenGL compatibility \b 3D </td><td>\code
+glLoadMatrixf(t.data());\endcode</td></tr>
+<tr class="alt"><td>
+OpenGL compatibility \b 2D </td><td>\code
+Affine3f aux(Affine3f::Identity());
+aux.linear().topLeftCorner<2,2>() = t.linear();
+aux.translation().start<2>() = t.translation();
+glLoadMatrixf(aux.data());\endcode</td></tr>
+</table>
+
+\b Component \b accessors
+<table class="manual">
+<tr><td>
+full read-write access to the internal matrix</td><td>\code
+t.matrix() = matN1xN1; // N1 means N+1
+matN1xN1 = t.matrix();
+\endcode</td></tr>
+<tr class="alt"><td>
+coefficient accessors</td><td>\code
+t(i,j) = scalar; <=> t.matrix()(i,j) = scalar;
+scalar = t(i,j); <=> scalar = t.matrix()(i,j);
+\endcode</td></tr>
+<tr><td>
+translation part</td><td>\code
+t.translation() = vecN;
+vecN = t.translation();
+\endcode</td></tr>
+<tr class="alt"><td>
+linear part</td><td>\code
+t.linear() = matNxN;
+matNxN = t.linear();
+\endcode</td></tr>
+<tr><td>
+extract the rotation matrix</td><td>\code
+matNxN = t.rotation();
+\endcode</td></tr>
+</table>
+
+
+\b Transformation \b creation \n
+While transformation objects can be created and updated concatenating elementary transformations,
+the Transform class also features a procedural API:
+<table class="manual">
+<tr><th></th><th>procedural API</th><th>equivalent natural API </th></tr>
+<tr><td>Translation</td><td>\code
+t.translate(Vector_(tx,ty,..));
+t.pretranslate(Vector_(tx,ty,..));
+\endcode</td><td>\code
+t *= Translation_(tx,ty,..);
+t = Translation_(tx,ty,..) * t;
+\endcode</td></tr>
+<tr class="alt"><td>\b Rotation \n <em class="note">In 2D and for the procedural API, any_rotation can also \n be an angle in radian</em></td><td>\code
+t.rotate(any_rotation);
+t.prerotate(any_rotation);
+\endcode</td><td>\code
+t *= any_rotation;
+t = any_rotation * t;
+\endcode</td></tr>
+<tr><td>Scaling</td><td>\code
+t.scale(Vector_(sx,sy,..));
+t.scale(s);
+t.prescale(Vector_(sx,sy,..));
+t.prescale(s);
+\endcode</td><td>\code
+t *= Scaling(sx,sy,..);
+t *= Scaling(s);
+t = Scaling(sx,sy,..) * t;
+t = Scaling(s) * t;
+\endcode</td></tr>
+<tr class="alt"><td>Shear transformation \n ( \b 2D \b only ! )</td><td>\code
+t.shear(sx,sy);
+t.preshear(sx,sy);
+\endcode</td><td></td></tr>
+</table>
+
+Note that in both API, any many transformations can be concatenated in a single expression as shown in the two following equivalent examples:
+<table class="manual">
+<tr><td>\code
+t.pretranslate(..).rotate(..).translate(..).scale(..);
+\endcode</td></tr>
+<tr><td>\code
+t = Translation_(..) * t * RotationType(..) * Translation_(..) * Scaling(..);
+\endcode</td></tr>
+</table>
+
+
+
+<a href="#" class="top">top</a>\section TutorialGeoEulerAngles Euler angles
+<table class="manual">
+<tr><td style="max-width:30em;">
+Euler angles might be convenient to create rotation objects.
+On the other hand, since there exist 24 different conventions, they are pretty confusing to use. This example shows how
+to create a rotation matrix according to the 2-1-2 convention.</td><td>\code
+Matrix3f m;
+m = AngleAxisf(angle1, Vector3f::UnitZ())
+ * * AngleAxisf(angle2, Vector3f::UnitY())
+ * * AngleAxisf(angle3, Vector3f::UnitZ());
+\endcode</td></tr>
+</table>
+
+*/
+
+}
diff --git a/doc/TutorialLinearAlgebra.dox b/doc/TutorialLinearAlgebra.dox
new file mode 100644
index 0000000..8042fca
--- /dev/null
+++ b/doc/TutorialLinearAlgebra.dox
@@ -0,0 +1,299 @@
+namespace Eigen {
+
+/** \eigenManualPage TutorialLinearAlgebra Linear algebra and decompositions
+
+This page explains how to solve linear systems, compute various decompositions such as LU,
+QR, %SVD, eigendecompositions... After reading this page, don't miss our
+\link TopicLinearAlgebraDecompositions catalogue \endlink of dense matrix decompositions.
+
+\eigenAutoToc
+
+\section TutorialLinAlgBasicSolve Basic linear solving
+
+\b The \b problem: You have a system of equations, that you have written as a single matrix equation
+ \f[ Ax \: = \: b \f]
+Where \a A and \a b are matrices (\a b could be a vector, as a special case). You want to find a solution \a x.
+
+\b The \b solution: You can choose between various decompositions, depending on the properties of your matrix \a A,
+and depending on whether you favor speed or accuracy. However, let's start with an example that works in all cases,
+and is a good compromise:
+<table class="example">
+<tr><th>Example:</th><th>Output:</th></tr>
+<tr>
+ <td>\include TutorialLinAlgExSolveColPivHouseholderQR.cpp </td>
+ <td>\verbinclude TutorialLinAlgExSolveColPivHouseholderQR.out </td>
+</tr>
+</table>
+
+In this example, the colPivHouseholderQr() method returns an object of class ColPivHouseholderQR. Since here the
+matrix is of type Matrix3f, this line could have been replaced by:
+\code
+ColPivHouseholderQR<Matrix3f> dec(A);
+Vector3f x = dec.solve(b);
+\endcode
+
+Here, ColPivHouseholderQR is a QR decomposition with column pivoting. It's a good compromise for this tutorial, as it
+works for all matrices while being quite fast. Here is a table of some other decompositions that you can choose from,
+depending on your matrix, the problem you are trying to solve, and the trade-off you want to make:
+
+<table class="manual">
+ <tr>
+ <th>Decomposition</th>
+ <th>Method</th>
+ <th>Requirements<br/>on the matrix</th>
+ <th>Speed<br/> (small-to-medium)</th>
+ <th>Speed<br/> (large)</th>
+ <th>Accuracy</th>
+ </tr>
+ <tr>
+ <td>PartialPivLU</td>
+ <td>partialPivLu()</td>
+ <td>Invertible</td>
+ <td>++</td>
+ <td>++</td>
+ <td>+</td>
+ </tr>
+ <tr class="alt">
+ <td>FullPivLU</td>
+ <td>fullPivLu()</td>
+ <td>None</td>
+ <td>-</td>
+ <td>- -</td>
+ <td>+++</td>
+ </tr>
+ <tr>
+ <td>HouseholderQR</td>
+ <td>householderQr()</td>
+ <td>None</td>
+ <td>++</td>
+ <td>++</td>
+ <td>+</td>
+ </tr>
+ <tr class="alt">
+ <td>ColPivHouseholderQR</td>
+ <td>colPivHouseholderQr()</td>
+ <td>None</td>
+ <td>+</td>
+ <td>-</td>
+ <td>+++</td>
+ </tr>
+ <tr>
+ <td>FullPivHouseholderQR</td>
+ <td>fullPivHouseholderQr()</td>
+ <td>None</td>
+ <td>-</td>
+ <td>- -</td>
+ <td>+++</td>
+ </tr>
+ <tr class="alt">
+ <td>CompleteOrthogonalDecomposition</td>
+ <td>completeOrthogonalDecomposition()</td>
+ <td>None</td>
+ <td>+</td>
+ <td>-</td>
+ <td>+++</td>
+ </tr>
+ <tr class="alt">
+ <td>LLT</td>
+ <td>llt()</td>
+ <td>Positive definite</td>
+ <td>+++</td>
+ <td>+++</td>
+ <td>+</td>
+ </tr>
+ <tr>
+ <td>LDLT</td>
+ <td>ldlt()</td>
+ <td>Positive or negative<br/> semidefinite</td>
+ <td>+++</td>
+ <td>+</td>
+ <td>++</td>
+ </tr>
+ <tr class="alt">
+ <td>BDCSVD</td>
+ <td>bdcSvd()</td>
+ <td>None</td>
+ <td>-</td>
+ <td>-</td>
+ <td>+++</td>
+ </tr>
+ <tr class="alt">
+ <td>JacobiSVD</td>
+ <td>jacobiSvd()</td>
+ <td>None</td>
+ <td>-</td>
+ <td>- - -</td>
+ <td>+++</td>
+ </tr>
+</table>
+To get an overview of the true relative speed of the different decompositions, check this \link DenseDecompositionBenchmark benchmark \endlink.
+
+All of these decompositions offer a solve() method that works as in the above example.
+
+If you know more about the properties of your matrix, you can use the above table to select the best method.
+For example, a good choice for solving linear systems with a non-symmetric matrix of full rank is PartialPivLU.
+If you know that your matrix is also symmetric and positive definite, the above table says that
+a very good choice is the LLT or LDLT decomposition. Here's an example, also demonstrating that using a general
+matrix (not a vector) as right hand side is possible:
+
+<table class="example">
+<tr><th>Example:</th><th>Output:</th></tr>
+<tr>
+ <td>\include TutorialLinAlgExSolveLDLT.cpp </td>
+ <td>\verbinclude TutorialLinAlgExSolveLDLT.out </td>
+</tr>
+</table>
+
+For a \ref TopicLinearAlgebraDecompositions "much more complete table" comparing all decompositions supported by Eigen (notice that Eigen
+supports many other decompositions), see our special page on
+\ref TopicLinearAlgebraDecompositions "this topic".
+
+
+\section TutorialLinAlgLeastsquares Least squares solving
+
+The most general and accurate method to solve under- or over-determined linear systems
+in the least squares sense, is the SVD decomposition. Eigen provides two implementations.
+The recommended one is the BDCSVD class, which scales well for large problems
+and automatically falls back to the JacobiSVD class for smaller problems.
+For both classes, their solve() method solved the linear system in the least-squares
+sense.
+
+Here is an example:
+<table class="example">
+<tr><th>Example:</th><th>Output:</th></tr>
+<tr>
+ <td>\include TutorialLinAlgSVDSolve.cpp </td>
+ <td>\verbinclude TutorialLinAlgSVDSolve.out </td>
+</tr>
+</table>
+
+An alternative to the SVD, which is usually faster and about as accurate, is CompleteOrthogonalDecomposition.
+
+Again, if you know more about the problem, the table above contains methods that are potentially faster.
+If your matrix is full rank, HouseHolderQR is the method of choice. If your matrix is full rank and well conditioned,
+using the Cholesky decomposition (LLT) on the matrix of the normal equations can be faster still.
+Our page on \link LeastSquares least squares solving \endlink has more details.
+
+
+\section TutorialLinAlgSolutionExists Checking if a matrix is singular
+
+Only you know what error margin you want to allow for a solution to be considered valid.
+So Eigen lets you do this computation for yourself, if you want to, as in this example:
+
+<table class="example">
+<tr><th>Example:</th><th>Output:</th></tr>
+<tr>
+ <td>\include TutorialLinAlgExComputeSolveError.cpp </td>
+ <td>\verbinclude TutorialLinAlgExComputeSolveError.out </td>
+</tr>
+</table>
+
+\section TutorialLinAlgEigensolving Computing eigenvalues and eigenvectors
+
+You need an eigendecomposition here, see available such decompositions on \ref TopicLinearAlgebraDecompositions "this page".
+Make sure to check if your matrix is self-adjoint, as is often the case in these problems. Here's an example using
+SelfAdjointEigenSolver, it could easily be adapted to general matrices using EigenSolver or ComplexEigenSolver.
+
+The computation of eigenvalues and eigenvectors does not necessarily converge, but such failure to converge is
+very rare. The call to info() is to check for this possibility.
+
+<table class="example">
+<tr><th>Example:</th><th>Output:</th></tr>
+<tr>
+ <td>\include TutorialLinAlgSelfAdjointEigenSolver.cpp </td>
+ <td>\verbinclude TutorialLinAlgSelfAdjointEigenSolver.out </td>
+</tr>
+</table>
+
+\section TutorialLinAlgInverse Computing inverse and determinant
+
+First of all, make sure that you really want this. While inverse and determinant are fundamental mathematical concepts,
+in \em numerical linear algebra they are not as useful as in pure mathematics. Inverse computations are often
+advantageously replaced by solve() operations, and the determinant is often \em not a good way of checking if a matrix
+is invertible.
+
+However, for \em very \em small matrices, the above may not be true, and inverse and determinant can be very useful.
+
+While certain decompositions, such as PartialPivLU and FullPivLU, offer inverse() and determinant() methods, you can also
+call inverse() and determinant() directly on a matrix. If your matrix is of a very small fixed size (at most 4x4) this
+allows Eigen to avoid performing a LU decomposition, and instead use formulas that are more efficient on such small matrices.
+
+Here is an example:
+<table class="example">
+<tr><th>Example:</th><th>Output:</th></tr>
+<tr>
+ <td>\include TutorialLinAlgInverseDeterminant.cpp </td>
+ <td>\verbinclude TutorialLinAlgInverseDeterminant.out </td>
+</tr>
+</table>
+
+\section TutorialLinAlgSeparateComputation Separating the computation from the construction
+
+In the above examples, the decomposition was computed at the same time that the decomposition object was constructed.
+There are however situations where you might want to separate these two things, for example if you don't know,
+at the time of the construction, the matrix that you will want to decompose; or if you want to reuse an existing
+decomposition object.
+
+What makes this possible is that:
+\li all decompositions have a default constructor,
+\li all decompositions have a compute(matrix) method that does the computation, and that may be called again
+ on an already-computed decomposition, reinitializing it.
+
+For example:
+
+<table class="example">
+<tr><th>Example:</th><th>Output:</th></tr>
+<tr>
+ <td>\include TutorialLinAlgComputeTwice.cpp </td>
+ <td>\verbinclude TutorialLinAlgComputeTwice.out </td>
+</tr>
+</table>
+
+Finally, you can tell the decomposition constructor to preallocate storage for decomposing matrices of a given size,
+so that when you subsequently decompose such matrices, no dynamic memory allocation is performed (of course, if you
+are using fixed-size matrices, no dynamic memory allocation happens at all). This is done by just
+passing the size to the decomposition constructor, as in this example:
+\code
+HouseholderQR<MatrixXf> qr(50,50);
+MatrixXf A = MatrixXf::Random(50,50);
+qr.compute(A); // no dynamic memory allocation
+\endcode
+
+\section TutorialLinAlgRankRevealing Rank-revealing decompositions
+
+Certain decompositions are rank-revealing, i.e. are able to compute the rank of a matrix. These are typically
+also the decompositions that behave best in the face of a non-full-rank matrix (which in the square case means a
+singular matrix). On \ref TopicLinearAlgebraDecompositions "this table" you can see for all our decompositions
+whether they are rank-revealing or not.
+
+Rank-revealing decompositions offer at least a rank() method. They can also offer convenience methods such as isInvertible(),
+and some are also providing methods to compute the kernel (null-space) and image (column-space) of the matrix, as is the
+case with FullPivLU:
+
+<table class="example">
+<tr><th>Example:</th><th>Output:</th></tr>
+<tr>
+ <td>\include TutorialLinAlgRankRevealing.cpp </td>
+ <td>\verbinclude TutorialLinAlgRankRevealing.out </td>
+</tr>
+</table>
+
+Of course, any rank computation depends on the choice of an arbitrary threshold, since practically no
+floating-point matrix is \em exactly rank-deficient. Eigen picks a sensible default threshold, which depends
+on the decomposition but is typically the diagonal size times machine epsilon. While this is the best default we
+could pick, only you know what is the right threshold for your application. You can set this by calling setThreshold()
+on your decomposition object before calling rank() or any other method that needs to use such a threshold.
+The decomposition itself, i.e. the compute() method, is independent of the threshold. You don't need to recompute the
+decomposition after you've changed the threshold.
+
+<table class="example">
+<tr><th>Example:</th><th>Output:</th></tr>
+<tr>
+ <td>\include TutorialLinAlgSetThreshold.cpp </td>
+ <td>\verbinclude TutorialLinAlgSetThreshold.out </td>
+</tr>
+</table>
+
+*/
+
+}
diff --git a/doc/TutorialMapClass.dox b/doc/TutorialMapClass.dox
new file mode 100644
index 0000000..caa2539
--- /dev/null
+++ b/doc/TutorialMapClass.dox
@@ -0,0 +1,86 @@
+namespace Eigen {
+
+/** \eigenManualPage TutorialMapClass Interfacing with raw buffers: the Map class
+
+This page explains how to work with "raw" C/C++ arrays.
+This can be useful in a variety of contexts, particularly when "importing" vectors and matrices from other libraries into %Eigen.
+
+\eigenAutoToc
+
+\section TutorialMapIntroduction Introduction
+
+Occasionally you may have a pre-defined array of numbers that you want to use within %Eigen as a vector or matrix. While one option is to make a copy of the data, most commonly you probably want to re-use this memory as an %Eigen type. Fortunately, this is very easy with the Map class.
+
+\section TutorialMapTypes Map types and declaring Map variables
+
+A Map object has a type defined by its %Eigen equivalent:
+\code
+Map<Matrix<typename Scalar, int RowsAtCompileTime, int ColsAtCompileTime> >
+\endcode
+Note that, in this default case, a Map requires just a single template parameter.
+
+To construct a Map variable, you need two other pieces of information: a pointer to the region of memory defining the array of coefficients, and the desired shape of the matrix or vector. For example, to define a matrix of \c float with sizes determined at compile time, you might do the following:
+\code
+Map<MatrixXf> mf(pf,rows,columns);
+\endcode
+where \c pf is a \c float \c * pointing to the array of memory. A fixed-size read-only vector of integers might be declared as
+\code
+Map<const Vector4i> mi(pi);
+\endcode
+where \c pi is an \c int \c *. In this case the size does not have to be passed to the constructor, because it is already specified by the Matrix/Array type.
+
+Note that Map does not have a default constructor; you \em must pass a pointer to initialize the object. However, you can work around this requirement (see \ref TutorialMapPlacementNew).
+
+Map is flexible enough to accommodate a variety of different data representations. There are two other (optional) template parameters:
+\code
+Map<typename MatrixType,
+ int MapOptions,
+ typename StrideType>
+\endcode
+\li \c MapOptions specifies whether the pointer is \c #Aligned, or \c #Unaligned. The default is \c #Unaligned.
+\li \c StrideType allows you to specify a custom layout for the memory array, using the Stride class. One example would be to specify that the data array is organized in row-major format:
+<table class="example">
+<tr><th>Example:</th><th>Output:</th></tr>
+<tr>
+<td>\include Tutorial_Map_rowmajor.cpp </td>
+<td>\verbinclude Tutorial_Map_rowmajor.out </td>
+</table>
+However, Stride is even more flexible than this; for details, see the documentation for the Map and Stride classes.
+
+\section TutorialMapUsing Using Map variables
+
+You can use a Map object just like any other %Eigen type:
+<table class="example">
+<tr><th>Example:</th><th>Output:</th></tr>
+<tr>
+<td>\include Tutorial_Map_using.cpp </td>
+<td>\verbinclude Tutorial_Map_using.out </td>
+</table>
+
+All %Eigen functions are written to accept Map objects just like other %Eigen types. However, when writing your own functions taking %Eigen types, this does \em not happen automatically: a Map type is not identical to its Dense equivalent. See \ref TopicFunctionTakingEigenTypes for details.
+
+\section TutorialMapPlacementNew Changing the mapped array
+
+It is possible to change the array of a Map object after declaration, using the C++ "placement new" syntax:
+<table class="example">
+<tr><th>Example:</th><th>Output:</th></tr>
+<tr>
+<td>\include Map_placement_new.cpp </td>
+<td>\verbinclude Map_placement_new.out </td>
+</table>
+Despite appearances, this does not invoke the memory allocator, because the syntax specifies the location for storing the result.
+
+This syntax makes it possible to declare a Map object without first knowing the mapped array's location in memory:
+\code
+Map<Matrix3f> A(NULL); // don't try to use this matrix yet!
+VectorXf b(n_matrices);
+for (int i = 0; i < n_matrices; i++)
+{
+ new (&A) Map<Matrix3f>(get_matrix_pointer(i));
+ b(i) = A.trace();
+}
+\endcode
+
+*/
+
+}
diff --git a/doc/TutorialMatrixArithmetic.dox b/doc/TutorialMatrixArithmetic.dox
new file mode 100644
index 0000000..5fc569a
--- /dev/null
+++ b/doc/TutorialMatrixArithmetic.dox
@@ -0,0 +1,214 @@
+namespace Eigen {
+
+/** \eigenManualPage TutorialMatrixArithmetic Matrix and vector arithmetic
+
+This page aims to provide an overview and some details on how to perform arithmetic
+between matrices, vectors and scalars with Eigen.
+
+\eigenAutoToc
+
+\section TutorialArithmeticIntroduction Introduction
+
+Eigen offers matrix/vector arithmetic operations either through overloads of common C++ arithmetic operators such as +, -, *,
+or through special methods such as dot(), cross(), etc.
+For the Matrix class (matrices and vectors), operators are only overloaded to support
+linear-algebraic operations. For example, \c matrix1 \c * \c matrix2 means matrix-matrix product,
+and \c vector \c + \c scalar is just not allowed. If you want to perform all kinds of array operations,
+not linear algebra, see the \ref TutorialArrayClass "next page".
+
+\section TutorialArithmeticAddSub Addition and subtraction
+
+The left hand side and right hand side must, of course, have the same numbers of rows and of columns. They must
+also have the same \c Scalar type, as Eigen doesn't do automatic type promotion. The operators at hand here are:
+\li binary operator + as in \c a+b
+\li binary operator - as in \c a-b
+\li unary operator - as in \c -a
+\li compound operator += as in \c a+=b
+\li compound operator -= as in \c a-=b
+
+<table class="example">
+<tr><th>Example:</th><th>Output:</th></tr>
+<tr><td>
+\include tut_arithmetic_add_sub.cpp
+</td>
+<td>
+\verbinclude tut_arithmetic_add_sub.out
+</td></tr></table>
+
+\section TutorialArithmeticScalarMulDiv Scalar multiplication and division
+
+Multiplication and division by a scalar is very simple too. The operators at hand here are:
+\li binary operator * as in \c matrix*scalar
+\li binary operator * as in \c scalar*matrix
+\li binary operator / as in \c matrix/scalar
+\li compound operator *= as in \c matrix*=scalar
+\li compound operator /= as in \c matrix/=scalar
+
+<table class="example">
+<tr><th>Example:</th><th>Output:</th></tr>
+<tr><td>
+\include tut_arithmetic_scalar_mul_div.cpp
+</td>
+<td>
+\verbinclude tut_arithmetic_scalar_mul_div.out
+</td></tr></table>
+
+
+\section TutorialArithmeticMentionXprTemplates A note about expression templates
+
+This is an advanced topic that we explain on \ref TopicEigenExpressionTemplates "this page",
+but it is useful to just mention it now. In Eigen, arithmetic operators such as \c operator+ don't
+perform any computation by themselves, they just return an "expression object" describing the computation to be
+performed. The actual computation happens later, when the whole expression is evaluated, typically in \c operator=.
+While this might sound heavy, any modern optimizing compiler is able to optimize away that abstraction and
+the result is perfectly optimized code. For example, when you do:
+\code
+VectorXf a(50), b(50), c(50), d(50);
+...
+a = 3*b + 4*c + 5*d;
+\endcode
+Eigen compiles it to just one for loop, so that the arrays are traversed only once. Simplifying (e.g. ignoring
+SIMD optimizations), this loop looks like this:
+\code
+for(int i = 0; i < 50; ++i)
+ a[i] = 3*b[i] + 4*c[i] + 5*d[i];
+\endcode
+Thus, you should not be afraid of using relatively large arithmetic expressions with Eigen: it only gives Eigen
+more opportunities for optimization.
+
+\section TutorialArithmeticTranspose Transposition and conjugation
+
+The transpose \f$ a^T \f$, conjugate \f$ \bar{a} \f$, and adjoint (i.e., conjugate transpose) \f$ a^* \f$ of a matrix or vector \f$ a \f$ are obtained by the member functions \link DenseBase::transpose() transpose()\endlink, \link MatrixBase::conjugate() conjugate()\endlink, and \link MatrixBase::adjoint() adjoint()\endlink, respectively.
+
+<table class="example">
+<tr><th>Example:</th><th>Output:</th></tr>
+<tr><td>
+\include tut_arithmetic_transpose_conjugate.cpp
+</td>
+<td>
+\verbinclude tut_arithmetic_transpose_conjugate.out
+</td></tr></table>
+
+For real matrices, \c conjugate() is a no-operation, and so \c adjoint() is equivalent to \c transpose().
+
+As for basic arithmetic operators, \c transpose() and \c adjoint() simply return a proxy object without doing the actual transposition. If you do <tt>b = a.transpose()</tt>, then the transpose is evaluated at the same time as the result is written into \c b. However, there is a complication here. If you do <tt>a = a.transpose()</tt>, then Eigen starts writing the result into \c a before the evaluation of the transpose is finished. Therefore, the instruction <tt>a = a.transpose()</tt> does not replace \c a with its transpose, as one would expect:
+<table class="example">
+<tr><th>Example:</th><th>Output:</th></tr>
+<tr><td>
+\include tut_arithmetic_transpose_aliasing.cpp
+</td>
+<td>
+\verbinclude tut_arithmetic_transpose_aliasing.out
+</td></tr></table>
+This is the so-called \ref TopicAliasing "aliasing issue". In "debug mode", i.e., when \ref TopicAssertions "assertions" have not been disabled, such common pitfalls are automatically detected.
+
+For \em in-place transposition, as for instance in <tt>a = a.transpose()</tt>, simply use the \link DenseBase::transposeInPlace() transposeInPlace()\endlink function:
+<table class="example">
+<tr><th>Example:</th><th>Output:</th></tr>
+<tr><td>
+\include tut_arithmetic_transpose_inplace.cpp
+</td>
+<td>
+\verbinclude tut_arithmetic_transpose_inplace.out
+</td></tr></table>
+There is also the \link MatrixBase::adjointInPlace() adjointInPlace()\endlink function for complex matrices.
+
+\section TutorialArithmeticMatrixMul Matrix-matrix and matrix-vector multiplication
+
+Matrix-matrix multiplication is again done with \c operator*. Since vectors are a special
+case of matrices, they are implicitly handled there too, so matrix-vector product is really just a special
+case of matrix-matrix product, and so is vector-vector outer product. Thus, all these cases are handled by just
+two operators:
+\li binary operator * as in \c a*b
+\li compound operator *= as in \c a*=b (this multiplies on the right: \c a*=b is equivalent to <tt>a = a*b</tt>)
+
+<table class="example">
+<tr><th>Example:</th><th>Output:</th></tr>
+<tr><td>
+\include tut_arithmetic_matrix_mul.cpp
+</td>
+<td>
+\verbinclude tut_arithmetic_matrix_mul.out
+</td></tr></table>
+
+Note: if you read the above paragraph on expression templates and are worried that doing \c m=m*m might cause
+aliasing issues, be reassured for now: Eigen treats matrix multiplication as a special case and takes care of
+introducing a temporary here, so it will compile \c m=m*m as:
+\code
+tmp = m*m;
+m = tmp;
+\endcode
+If you know your matrix product can be safely evaluated into the destination matrix without aliasing issue, then you can use the \link MatrixBase::noalias() noalias()\endlink function to avoid the temporary, e.g.:
+\code
+c.noalias() += a * b;
+\endcode
+For more details on this topic, see the page on \ref TopicAliasing "aliasing".
+
+\b Note: for BLAS users worried about performance, expressions such as <tt>c.noalias() -= 2 * a.adjoint() * b;</tt> are fully optimized and trigger a single gemm-like function call.
+
+\section TutorialArithmeticDotAndCross Dot product and cross product
+
+For dot product and cross product, you need the \link MatrixBase::dot() dot()\endlink and \link MatrixBase::cross() cross()\endlink methods. Of course, the dot product can also be obtained as a 1x1 matrix as u.adjoint()*v.
+<table class="example">
+<tr><th>Example:</th><th>Output:</th></tr>
+<tr><td>
+\include tut_arithmetic_dot_cross.cpp
+</td>
+<td>
+\verbinclude tut_arithmetic_dot_cross.out
+</td></tr></table>
+
+Remember that cross product is only for vectors of size 3. Dot product is for vectors of any sizes.
+When using complex numbers, Eigen's dot product is conjugate-linear in the first variable and linear in the
+second variable.
+
+\section TutorialArithmeticRedux Basic arithmetic reduction operations
+Eigen also provides some reduction operations to reduce a given matrix or vector to a single value such as the sum (computed by \link DenseBase::sum() sum()\endlink), product (\link DenseBase::prod() prod()\endlink), or the maximum (\link DenseBase::maxCoeff() maxCoeff()\endlink) and minimum (\link DenseBase::minCoeff() minCoeff()\endlink) of all its coefficients.
+
+<table class="example">
+<tr><th>Example:</th><th>Output:</th></tr>
+<tr><td>
+\include tut_arithmetic_redux_basic.cpp
+</td>
+<td>
+\verbinclude tut_arithmetic_redux_basic.out
+</td></tr></table>
+
+The \em trace of a matrix, as returned by the function \link MatrixBase::trace() trace()\endlink, is the sum of the diagonal coefficients and can also be computed as efficiently using <tt>a.diagonal().sum()</tt>, as we will see later on.
+
+There also exist variants of the \c minCoeff and \c maxCoeff functions returning the coordinates of the respective coefficient via the arguments:
+
+<table class="example">
+<tr><th>Example:</th><th>Output:</th></tr>
+<tr><td>
+\include tut_arithmetic_redux_minmax.cpp
+</td>
+<td>
+\verbinclude tut_arithmetic_redux_minmax.out
+</td></tr></table>
+
+
+\section TutorialArithmeticValidity Validity of operations
+Eigen checks the validity of the operations that you perform. When possible,
+it checks them at compile time, producing compilation errors. These error messages can be long and ugly,
+but Eigen writes the important message in UPPERCASE_LETTERS_SO_IT_STANDS_OUT. For example:
+\code
+ Matrix3f m;
+ Vector4f v;
+ v = m*v; // Compile-time error: YOU_MIXED_MATRICES_OF_DIFFERENT_SIZES
+\endcode
+
+Of course, in many cases, for example when checking dynamic sizes, the check cannot be performed at compile time.
+Eigen then uses runtime assertions. This means that the program will abort with an error message when executing an illegal operation if it is run in "debug mode", and it will probably crash if assertions are turned off.
+
+\code
+ MatrixXf m(3,3);
+ VectorXf v(4);
+ v = m * v; // Run-time assertion failure here: "invalid matrix product"
+\endcode
+
+For more details on this topic, see \ref TopicAssertions "this page".
+
+*/
+
+}
diff --git a/doc/TutorialMatrixClass.dox b/doc/TutorialMatrixClass.dox
new file mode 100644
index 0000000..e4e4f98
--- /dev/null
+++ b/doc/TutorialMatrixClass.dox
@@ -0,0 +1,295 @@
+namespace Eigen {
+
+/** \eigenManualPage TutorialMatrixClass The Matrix class
+
+\eigenAutoToc
+
+In Eigen, all matrices and vectors are objects of the Matrix template class.
+Vectors are just a special case of matrices, with either 1 row or 1 column.
+
+\section TutorialMatrixFirst3Params The first three template parameters of Matrix
+
+The Matrix class takes six template parameters, but for now it's enough to
+learn about the first three first parameters. The three remaining parameters have default
+values, which for now we will leave untouched, and which we
+\ref TutorialMatrixOptTemplParams "discuss below".
+
+The three mandatory template parameters of Matrix are:
+\code
+Matrix<typename Scalar, int RowsAtCompileTime, int ColsAtCompileTime>
+\endcode
+\li \c Scalar is the scalar type, i.e. the type of the coefficients.
+ That is, if you want a matrix of floats, choose \c float here.
+ See \ref TopicScalarTypes "Scalar types" for a list of all supported
+ scalar types and for how to extend support to new types.
+\li \c RowsAtCompileTime and \c ColsAtCompileTime are the number of rows
+ and columns of the matrix as known at compile time (see
+ \ref TutorialMatrixDynamic "below" for what to do if the number is not
+ known at compile time).
+
+We offer a lot of convenience typedefs to cover the usual cases. For example, \c Matrix4f is
+a 4x4 matrix of floats. Here is how it is defined by Eigen:
+\code
+typedef Matrix<float, 4, 4> Matrix4f;
+\endcode
+We discuss \ref TutorialMatrixTypedefs "below" these convenience typedefs.
+
+\section TutorialMatrixVectors Vectors
+
+As mentioned above, in Eigen, vectors are just a special case of
+matrices, with either 1 row or 1 column. The case where they have 1 column is the most common;
+such vectors are called column-vectors, often abbreviated as just vectors. In the other case
+where they have 1 row, they are called row-vectors.
+
+For example, the convenience typedef \c Vector3f is a (column) vector of 3 floats. It is defined as follows by Eigen:
+\code
+typedef Matrix<float, 3, 1> Vector3f;
+\endcode
+We also offer convenience typedefs for row-vectors, for example:
+\code
+typedef Matrix<int, 1, 2> RowVector2i;
+\endcode
+
+\section TutorialMatrixDynamic The special value Dynamic
+
+Of course, Eigen is not limited to matrices whose dimensions are known at compile time.
+The \c RowsAtCompileTime and \c ColsAtCompileTime template parameters can take the special
+value \c Dynamic which indicates that the size is unknown at compile time, so must
+be handled as a run-time variable. In Eigen terminology, such a size is referred to as a
+\em dynamic \em size; while a size that is known at compile time is called a
+\em fixed \em size. For example, the convenience typedef \c MatrixXd, meaning
+a matrix of doubles with dynamic size, is defined as follows:
+\code
+typedef Matrix<double, Dynamic, Dynamic> MatrixXd;
+\endcode
+And similarly, we define a self-explanatory typedef \c VectorXi as follows:
+\code
+typedef Matrix<int, Dynamic, 1> VectorXi;
+\endcode
+You can perfectly have e.g. a fixed number of rows with a dynamic number of columns, as in:
+\code
+Matrix<float, 3, Dynamic>
+\endcode
+
+\section TutorialMatrixConstructors Constructors
+
+A default constructor is always available, never performs any dynamic memory allocation, and never initializes the matrix coefficients. You can do:
+\code
+Matrix3f a;
+MatrixXf b;
+\endcode
+Here,
+\li \c a is a 3-by-3 matrix, with a plain float[9] array of uninitialized coefficients,
+\li \c b is a dynamic-size matrix whose size is currently 0-by-0, and whose array of
+coefficients hasn't yet been allocated at all.
+
+Constructors taking sizes are also available. For matrices, the number of rows is always passed first.
+For vectors, just pass the vector size. They allocate the array of coefficients
+with the given size, but don't initialize the coefficients themselves:
+\code
+MatrixXf a(10,15);
+VectorXf b(30);
+\endcode
+Here,
+\li \c a is a 10x15 dynamic-size matrix, with allocated but currently uninitialized coefficients.
+\li \c b is a dynamic-size vector of size 30, with allocated but currently uninitialized coefficients.
+
+In order to offer a uniform API across fixed-size and dynamic-size matrices, it is legal to use these
+constructors on fixed-size matrices, even if passing the sizes is useless in this case. So this is legal:
+\code
+Matrix3f a(3,3);
+\endcode
+and is a no-operation.
+
+Matrices and vectors can also be initialized from lists of coefficients.
+Prior to C++11, this feature is limited to small fixed-size column or vectors up to size 4:
+\code
+Vector2d a(5.0, 6.0);
+Vector3d b(5.0, 6.0, 7.0);
+Vector4d c(5.0, 6.0, 7.0, 8.0);
+\endcode
+
+If C++11 is enabled, fixed-size column or row vectors of arbitrary size can be initialized by passing an arbitrary number of coefficients:
+\code
+Vector2i a(1, 2); // A column-vector containing the elements {1, 2}
+Matrix<int, 5, 1> b {1, 2, 3, 4, 5}; // A column-vector containing the elements {1, 2, 3, 4, 5}
+Matrix<int, 1, 5> c = {1, 2, 3, 4, 5}; // A row-vector containing the elements {1, 2, 3, 4, 5}
+\endcode
+
+In the general case of matrices and vectors with either fixed or runtime sizes,
+coefficients have to be grouped by rows and passed as an initializer list of initializer list (\link Matrix::Matrix(const std::initializer_list<std::initializer_list<Scalar>>&) details \endlink):
+\code
+MatrixXi a { // construct a 2x2 matrix
+ {1, 2}, // first row
+ {3, 4} // second row
+};
+Matrix<double, 2, 3> b {
+ {2, 3, 4},
+ {5, 6, 7},
+};
+\endcode
+
+For column or row vectors, implicit transposition is allowed.
+This means that a column vector can be initialized from a single row:
+\code
+VectorXd a {{1.5, 2.5, 3.5}}; // A column-vector with 3 coefficients
+RowVectorXd b {{1.0, 2.0, 3.0, 4.0}}; // A row-vector with 4 coefficients
+\endcode
+
+\section TutorialMatrixCoeffAccessors Coefficient accessors
+
+The primary coefficient accessors and mutators in Eigen are the overloaded parenthesis operators.
+For matrices, the row index is always passed first. For vectors, just pass one index.
+The numbering starts at 0. This example is self-explanatory:
+
+<table class="example">
+<tr><th>Example:</th><th>Output:</th></tr>
+<tr><td>
+\include tut_matrix_coefficient_accessors.cpp
+</td>
+<td>
+\verbinclude tut_matrix_coefficient_accessors.out
+</td></tr></table>
+
+Note that the syntax `m(index)`
+is not restricted to vectors, it is also available for general matrices, meaning index-based access
+in the array of coefficients. This however depends on the matrix's storage order. All Eigen matrices default to
+column-major storage order, but this can be changed to row-major, see \ref TopicStorageOrders "Storage orders".
+
+The `operator[]` is also overloaded for index-based access in vectors, but keep in mind that C++ doesn't allow `operator[]` to
+take more than one argument. We restrict `operator[]` to vectors, because an awkwardness in the C++ language
+would make `matrix[i,j]` compile to the same thing as `matrix[j]`!
+
+\section TutorialMatrixCommaInitializer Comma-initialization
+
+%Matrix and vector coefficients can be conveniently set using the so-called \em comma-initializer syntax.
+For now, it is enough to know this example:
+
+<table class="example">
+<tr><th>Example:</th><th>Output:</th></tr>
+<tr>
+<td>\include Tutorial_commainit_01.cpp </td>
+<td>\verbinclude Tutorial_commainit_01.out </td>
+</tr></table>
+
+
+The right-hand side can also contain matrix expressions as discussed in \ref TutorialAdvancedInitialization "this page".
+
+\section TutorialMatrixSizesResizing Resizing
+
+The current size of a matrix can be retrieved by \link EigenBase::rows() rows()\endlink, \link EigenBase::cols() cols() \endlink and \link EigenBase::size() size()\endlink. These methods return the number of rows, the number of columns and the number of coefficients, respectively. Resizing a dynamic-size matrix is done by the \link PlainObjectBase::resize(Index,Index) resize() \endlink method.
+
+<table class="example">
+<tr><th>Example:</th><th>Output:</th></tr>
+<tr>
+<td>\include tut_matrix_resize.cpp </td>
+<td>\verbinclude tut_matrix_resize.out </td>
+</tr></table>
+
+The `resize()` method is a no-operation if the actual matrix size doesn't change; otherwise it is destructive: the values of the coefficients may change.
+If you want a conservative variant of `resize()` which does not change the coefficients, use \link PlainObjectBase::conservativeResize() conservativeResize()\endlink, see \ref TopicResizing "this page" for more details.
+
+All these methods are still available on fixed-size matrices, for the sake of API uniformity. Of course, you can't actually
+resize a fixed-size matrix. Trying to change a fixed size to an actually different value will trigger an assertion failure;
+but the following code is legal:
+
+<table class="example">
+<tr><th>Example:</th><th>Output:</th></tr>
+<tr>
+<td>\include tut_matrix_resize_fixed_size.cpp </td>
+<td>\verbinclude tut_matrix_resize_fixed_size.out </td>
+</tr></table>
+
+
+\section TutorialMatrixAssignment Assignment and resizing
+
+Assignment is the action of copying a matrix into another, using \c operator=. Eigen resizes the matrix on the left-hand side automatically so that it matches the size of the matrix on the right-hand size. For example:
+
+<table class="example">
+<tr><th>Example:</th><th>Output:</th></tr>
+<tr>
+<td>\include tut_matrix_assignment_resizing.cpp </td>
+<td>\verbinclude tut_matrix_assignment_resizing.out </td>
+</tr></table>
+
+Of course, if the left-hand side is of fixed size, resizing it is not allowed.
+
+If you do not want this automatic resizing to happen (for example for debugging purposes), you can disable it, see
+\ref TopicResizing "this page".
+
+
+\section TutorialMatrixFixedVsDynamic Fixed vs. Dynamic size
+
+When should one use fixed sizes (e.g. \c Matrix4f), and when should one prefer dynamic sizes (e.g. \c MatrixXf)?
+The simple answer is: use fixed
+sizes for very small sizes where you can, and use dynamic sizes for larger sizes or where you have to. For small sizes,
+especially for sizes smaller than (roughly) 16, using fixed sizes is hugely beneficial
+to performance, as it allows Eigen to avoid dynamic memory allocation and to unroll
+loops. Internally, a fixed-size Eigen matrix is just a plain array, i.e. doing
+\code Matrix4f mymatrix; \endcode
+really amounts to just doing
+\code float mymatrix[16]; \endcode
+so this really has zero runtime cost. By contrast, the array of a dynamic-size matrix
+is always allocated on the heap, so doing
+\code MatrixXf mymatrix(rows,columns); \endcode
+amounts to doing
+\code float *mymatrix = new float[rows*columns]; \endcode
+and in addition to that, the \c MatrixXf object stores its number of rows and columns as
+member variables.
+
+The limitation of using fixed sizes, of course, is that this is only possible
+when you know the sizes at compile time. Also, for large enough sizes, say for sizes
+greater than (roughly) 32, the performance benefit of using fixed sizes becomes negligible.
+Worse, trying to create a very large matrix using fixed sizes inside a function could result in a
+stack overflow, since Eigen will try to allocate the array automatically as a local variable, and
+this is normally done on the stack.
+Finally, depending on circumstances, Eigen can also be more aggressive trying to vectorize
+(use SIMD instructions) when dynamic sizes are used, see \ref TopicVectorization "Vectorization".
+
+\section TutorialMatrixOptTemplParams Optional template parameters
+
+We mentioned at the beginning of this page that the Matrix class takes six template parameters,
+but so far we only discussed the first three. The remaining three parameters are optional. Here is
+the complete list of template parameters:
+\code
+Matrix<typename Scalar,
+ int RowsAtCompileTime,
+ int ColsAtCompileTime,
+ int Options = 0,
+ int MaxRowsAtCompileTime = RowsAtCompileTime,
+ int MaxColsAtCompileTime = ColsAtCompileTime>
+\endcode
+\li \c Options is a bit field. Here, we discuss only one bit: \c RowMajor. It specifies that the matrices
+ of this type use row-major storage order; by default, the storage order is column-major. See the page on
+ \ref TopicStorageOrders "storage orders". For example, this type means row-major 3x3 matrices:
+ \code
+ Matrix<float, 3, 3, RowMajor>
+ \endcode
+\li \c MaxRowsAtCompileTime and \c MaxColsAtCompileTime are useful when you want to specify that, even though
+ the exact sizes of your matrices are not known at compile time, a fixed upper bound is known at
+ compile time. The biggest reason why you might want to do that is to avoid dynamic memory allocation.
+ For example the following matrix type uses a plain array of 12 floats, without dynamic memory allocation:
+ \code
+ Matrix<float, Dynamic, Dynamic, 0, 3, 4>
+ \endcode
+
+\section TutorialMatrixTypedefs Convenience typedefs
+
+Eigen defines the following Matrix typedefs:
+\li \c MatrixNt for `Matrix<type, N, N>`. For example, \c MatrixXi for `Matrix<int, Dynamic, Dynamic>`.
+\li \c MatrixXNt for `Matrix<type, Dynamic, N>`. For example, \c MatrixX3i for `Matrix<int, Dynamic, 3>`.
+\li \c MatrixNXt for `Matrix<type, N, Dynamic>`. For example, \c Matrix4Xd for `Matrix<d, 4, Dynamic>`.
+\li \c VectorNt for `Matrix<type, N, 1>`. For example, \c Vector2f for `Matrix<float, 2, 1>`.
+\li \c RowVectorNt for `Matrix<type, 1, N>`. For example, \c RowVector3d for `Matrix<double, 1, 3>`.
+
+Where:
+\li \c N can be any one of \c 2, \c 3, \c 4, or \c X (meaning \c Dynamic).
+\li \c t can be any one of \c i (meaning \c int), \c f (meaning \c float), \c d (meaning \c double),
+ \c cf (meaning `complex<float>`), or \c cd (meaning `complex<double>`). The fact that `typedef`s are only
+ defined for these five types doesn't mean that they are the only supported scalar types. For example,
+ all standard integer types are supported, see \ref TopicScalarTypes "Scalar types".
+
+
+*/
+
+}
diff --git a/doc/TutorialReductionsVisitorsBroadcasting.dox b/doc/TutorialReductionsVisitorsBroadcasting.dox
new file mode 100644
index 0000000..f5322b4
--- /dev/null
+++ b/doc/TutorialReductionsVisitorsBroadcasting.dox
@@ -0,0 +1,266 @@
+namespace Eigen {
+
+/** \eigenManualPage TutorialReductionsVisitorsBroadcasting Reductions, visitors and broadcasting
+
+This page explains Eigen's reductions, visitors and broadcasting and how they are used with
+\link MatrixBase matrices \endlink and \link ArrayBase arrays \endlink.
+
+\eigenAutoToc
+
+\section TutorialReductionsVisitorsBroadcastingReductions Reductions
+In Eigen, a reduction is a function taking a matrix or array, and returning a single
+scalar value. One of the most used reductions is \link DenseBase::sum() .sum() \endlink,
+returning the sum of all the coefficients inside a given matrix or array.
+
+<table class="example">
+<tr><th>Example:</th><th>Output:</th></tr>
+<tr><td>
+\include tut_arithmetic_redux_basic.cpp
+</td>
+<td>
+\verbinclude tut_arithmetic_redux_basic.out
+</td></tr></table>
+
+The \em trace of a matrix, as returned by the function \c trace(), is the sum of the diagonal coefficients and can equivalently be computed <tt>a.diagonal().sum()</tt>.
+
+
+\subsection TutorialReductionsVisitorsBroadcastingReductionsNorm Norm computations
+
+The (Euclidean a.k.a. \f$\ell^2\f$) squared norm of a vector can be obtained \link MatrixBase::squaredNorm() squaredNorm() \endlink. It is equal to the dot product of the vector by itself, and equivalently to the sum of squared absolute values of its coefficients.
+
+Eigen also provides the \link MatrixBase::norm() norm() \endlink method, which returns the square root of \link MatrixBase::squaredNorm() squaredNorm() \endlink.
+
+These operations can also operate on matrices; in that case, a n-by-p matrix is seen as a vector of size (n*p), so for example the \link MatrixBase::norm() norm() \endlink method returns the "Frobenius" or "Hilbert-Schmidt" norm. We refrain from speaking of the \f$\ell^2\f$ norm of a matrix because that can mean different things.
+
+If you want other coefficient-wise \f$\ell^p\f$ norms, use the \link MatrixBase::lpNorm lpNorm<p>() \endlink method. The template parameter \a p can take the special value \a Infinity if you want the \f$\ell^\infty\f$ norm, which is the maximum of the absolute values of the coefficients.
+
+The following example demonstrates these methods.
+
+<table class="example">
+<tr><th>Example:</th><th>Output:</th></tr>
+<tr><td>
+\include Tutorial_ReductionsVisitorsBroadcasting_reductions_norm.cpp
+</td>
+<td>
+\verbinclude Tutorial_ReductionsVisitorsBroadcasting_reductions_norm.out
+</td></tr></table>
+
+\b Operator \b norm: The 1-norm and \f$\infty\f$-norm <a href="https://en.wikipedia.org/wiki/Operator_norm">matrix operator norms</a> can easily be computed as follows:
+<table class="example">
+<tr><th>Example:</th><th>Output:</th></tr>
+<tr><td>
+\include Tutorial_ReductionsVisitorsBroadcasting_reductions_operatornorm.cpp
+</td>
+<td>
+\verbinclude Tutorial_ReductionsVisitorsBroadcasting_reductions_operatornorm.out
+</td></tr></table>
+See below for more explanations on the syntax of these expressions.
+
+\subsection TutorialReductionsVisitorsBroadcastingReductionsBool Boolean reductions
+
+The following reductions operate on boolean values:
+ - \link DenseBase::all() all() \endlink returns \b true if all of the coefficients in a given Matrix or Array evaluate to \b true .
+ - \link DenseBase::any() any() \endlink returns \b true if at least one of the coefficients in a given Matrix or Array evaluates to \b true .
+ - \link DenseBase::count() count() \endlink returns the number of coefficients in a given Matrix or Array that evaluate to \b true.
+
+These are typically used in conjunction with the coefficient-wise comparison and equality operators provided by Array. For instance, <tt>array > 0</tt> is an %Array of the same size as \c array , with \b true at those positions where the corresponding coefficient of \c array is positive. Thus, <tt>(array > 0).all()</tt> tests whether all coefficients of \c array are positive. This can be seen in the following example:
+
+<table class="example">
+<tr><th>Example:</th><th>Output:</th></tr>
+<tr><td>
+\include Tutorial_ReductionsVisitorsBroadcasting_reductions_bool.cpp
+</td>
+<td>
+\verbinclude Tutorial_ReductionsVisitorsBroadcasting_reductions_bool.out
+</td></tr></table>
+
+\subsection TutorialReductionsVisitorsBroadcastingReductionsUserdefined User defined reductions
+
+TODO
+
+In the meantime you can have a look at the DenseBase::redux() function.
+
+\section TutorialReductionsVisitorsBroadcastingVisitors Visitors
+Visitors are useful when one wants to obtain the location of a coefficient inside
+a Matrix or Array. The simplest examples are
+\link MatrixBase::maxCoeff() maxCoeff(&x,&y) \endlink and
+\link MatrixBase::minCoeff() minCoeff(&x,&y)\endlink, which can be used to find
+the location of the greatest or smallest coefficient in a Matrix or
+Array.
+
+The arguments passed to a visitor are pointers to the variables where the
+row and column position are to be stored. These variables should be of type
+\link Eigen::Index Index \endlink, as shown below:
+
+<table class="example">
+<tr><th>Example:</th><th>Output:</th></tr>
+<tr><td>
+\include Tutorial_ReductionsVisitorsBroadcasting_visitors.cpp
+</td>
+<td>
+\verbinclude Tutorial_ReductionsVisitorsBroadcasting_visitors.out
+</td></tr></table>
+
+Both functions also return the value of the minimum or maximum coefficient.
+
+\section TutorialReductionsVisitorsBroadcastingPartialReductions Partial reductions
+Partial reductions are reductions that can operate column- or row-wise on a Matrix or
+Array, applying the reduction operation on each column or row and
+returning a column or row vector with the corresponding values. Partial reductions are applied
+with \link DenseBase::colwise() colwise() \endlink or \link DenseBase::rowwise() rowwise() \endlink.
+
+A simple example is obtaining the maximum of the elements
+in each column in a given matrix, storing the result in a row vector:
+
+<table class="example">
+<tr><th>Example:</th><th>Output:</th></tr>
+<tr><td>
+\include Tutorial_ReductionsVisitorsBroadcasting_colwise.cpp
+</td>
+<td>
+\verbinclude Tutorial_ReductionsVisitorsBroadcasting_colwise.out
+</td></tr></table>
+
+The same operation can be performed row-wise:
+
+<table class="example">
+<tr><th>Example:</th><th>Output:</th></tr>
+<tr><td>
+\include Tutorial_ReductionsVisitorsBroadcasting_rowwise.cpp
+</td>
+<td>
+\verbinclude Tutorial_ReductionsVisitorsBroadcasting_rowwise.out
+</td></tr></table>
+
+<b>Note that column-wise operations return a row vector, while row-wise operations return a column vector.</b>
+
+\subsection TutorialReductionsVisitorsBroadcastingPartialReductionsCombined Combining partial reductions with other operations
+It is also possible to use the result of a partial reduction to do further processing.
+Here is another example that finds the column whose sum of elements is the maximum
+ within a matrix. With column-wise partial reductions this can be coded as:
+
+<table class="example">
+<tr><th>Example:</th><th>Output:</th></tr>
+<tr><td>
+\include Tutorial_ReductionsVisitorsBroadcasting_maxnorm.cpp
+</td>
+<td>
+\verbinclude Tutorial_ReductionsVisitorsBroadcasting_maxnorm.out
+</td></tr></table>
+
+The previous example applies the \link DenseBase::sum() sum() \endlink reduction on each column
+though the \link DenseBase::colwise() colwise() \endlink visitor, obtaining a new matrix whose
+size is 1x4.
+
+Therefore, if
+\f[
+\mbox{m} = \begin{bmatrix} 1 & 2 & 6 & 9 \\
+ 3 & 1 & 7 & 2 \end{bmatrix}
+\f]
+
+then
+
+\f[
+\mbox{m.colwise().sum()} = \begin{bmatrix} 4 & 3 & 13 & 11 \end{bmatrix}
+\f]
+
+The \link DenseBase::maxCoeff() maxCoeff() \endlink reduction is finally applied
+to obtain the column index where the maximum sum is found,
+which is the column index 2 (third column) in this case.
+
+
+\section TutorialReductionsVisitorsBroadcastingBroadcasting Broadcasting
+The concept behind broadcasting is similar to partial reductions, with the difference that broadcasting
+constructs an expression where a vector (column or row) is interpreted as a matrix by replicating it in
+one direction.
+
+A simple example is to add a certain column vector to each column in a matrix.
+This can be accomplished with:
+
+<table class="example">
+<tr><th>Example:</th><th>Output:</th></tr>
+<tr><td>
+\include Tutorial_ReductionsVisitorsBroadcasting_broadcast_simple.cpp
+</td>
+<td>
+\verbinclude Tutorial_ReductionsVisitorsBroadcasting_broadcast_simple.out
+</td></tr></table>
+
+We can interpret the instruction <tt>mat.colwise() += v</tt> in two equivalent ways. It adds the vector \c v
+to every column of the matrix. Alternatively, it can be interpreted as repeating the vector \c v four times to
+form a four-by-two matrix which is then added to \c mat:
+\f[
+\begin{bmatrix} 1 & 2 & 6 & 9 \\ 3 & 1 & 7 & 2 \end{bmatrix}
++ \begin{bmatrix} 0 & 0 & 0 & 0 \\ 1 & 1 & 1 & 1 \end{bmatrix}
+= \begin{bmatrix} 1 & 2 & 6 & 9 \\ 4 & 2 & 8 & 3 \end{bmatrix}.
+\f]
+The operators <tt>-=</tt>, <tt>+</tt> and <tt>-</tt> can also be used column-wise and row-wise. On arrays, we
+can also use the operators <tt>*=</tt>, <tt>/=</tt>, <tt>*</tt> and <tt>/</tt> to perform coefficient-wise
+multiplication and division column-wise or row-wise. These operators are not available on matrices because it
+is not clear what they would do. If you want multiply column 0 of a matrix \c mat with \c v(0), column 1 with
+\c v(1), and so on, then use <tt>mat = mat * v.asDiagonal()</tt>.
+
+It is important to point out that the vector to be added column-wise or row-wise must be of type Vector,
+and cannot be a Matrix. If this is not met then you will get compile-time error. This also means that
+broadcasting operations can only be applied with an object of type Vector, when operating with Matrix.
+The same applies for the Array class, where the equivalent for VectorXf is ArrayXf. As always, you should
+not mix arrays and matrices in the same expression.
+
+To perform the same operation row-wise we can do:
+
+<table class="example">
+<tr><th>Example:</th><th>Output:</th></tr>
+<tr><td>
+\include Tutorial_ReductionsVisitorsBroadcasting_broadcast_simple_rowwise.cpp
+</td>
+<td>
+\verbinclude Tutorial_ReductionsVisitorsBroadcasting_broadcast_simple_rowwise.out
+</td></tr></table>
+
+\subsection TutorialReductionsVisitorsBroadcastingBroadcastingCombined Combining broadcasting with other operations
+Broadcasting can also be combined with other operations, such as Matrix or Array operations,
+reductions and partial reductions.
+
+Now that broadcasting, reductions and partial reductions have been introduced, we can dive into a more advanced example that finds
+the nearest neighbour of a vector <tt>v</tt> within the columns of matrix <tt>m</tt>. The Euclidean distance will be used in this example,
+computing the squared Euclidean distance with the partial reduction named \link MatrixBase::squaredNorm() squaredNorm() \endlink:
+
+<table class="example">
+<tr><th>Example:</th><th>Output:</th></tr>
+<tr><td>
+\include Tutorial_ReductionsVisitorsBroadcasting_broadcast_1nn.cpp
+</td>
+<td>
+\verbinclude Tutorial_ReductionsVisitorsBroadcasting_broadcast_1nn.out
+</td></tr></table>
+
+The line that does the job is
+\code
+ (m.colwise() - v).colwise().squaredNorm().minCoeff(&index);
+\endcode
+
+We will go step by step to understand what is happening:
+
+ - <tt>m.colwise() - v</tt> is a broadcasting operation, subtracting <tt>v</tt> from each column in <tt>m</tt>. The result of this operation
+is a new matrix whose size is the same as matrix <tt>m</tt>: \f[
+ \mbox{m.colwise() - v} =
+ \begin{bmatrix}
+ -1 & 21 & 4 & 7 \\
+ 0 & 8 & 4 & -1
+ \end{bmatrix}
+\f]
+
+ - <tt>(m.colwise() - v).colwise().squaredNorm()</tt> is a partial reduction, computing the squared norm column-wise. The result of
+this operation is a row vector where each coefficient is the squared Euclidean distance between each column in <tt>m</tt> and <tt>v</tt>: \f[
+ \mbox{(m.colwise() - v).colwise().squaredNorm()} =
+ \begin{bmatrix}
+ 1 & 505 & 32 & 50
+ \end{bmatrix}
+\f]
+
+ - Finally, <tt>minCoeff(&index)</tt> is used to obtain the index of the column in <tt>m</tt> that is closest to <tt>v</tt> in terms of Euclidean
+distance.
+
+*/
+
+}
diff --git a/doc/TutorialReshape.dox b/doc/TutorialReshape.dox
new file mode 100644
index 0000000..07e5c3c
--- /dev/null
+++ b/doc/TutorialReshape.dox
@@ -0,0 +1,82 @@
+namespace Eigen {
+
+/** \eigenManualPage TutorialReshape Reshape
+
+Since the version 3.4, %Eigen exposes convenient methods to reshape a matrix to another matrix of different sizes or vector.
+All cases are handled via the `DenseBase::reshaped(NRowsType,NColsType)` and `DenseBase::reshaped()` functions.
+Those functions do not perform in-place reshaping, but instead return a <i> view </i> on the input expression.
+
+\eigenAutoToc
+
+\section TutorialReshapeMat2Mat Reshaped 2D views
+
+The more general reshaping transformation is handled via: `reshaped(nrows,ncols)`.
+Here is an example reshaping a 4x4 matrix to a 2x8 one:
+
+<table class="example">
+<tr><th>Example:</th><th>Output:</th></tr>
+<tr><td>
+\include MatrixBase_reshaped_int_int.cpp
+</td>
+<td>
+\verbinclude MatrixBase_reshaped_int_int.out
+</td></tr></table>
+
+By default, the input coefficients are always interpreted in column-major order regardless of the storage order of the input expression.
+For more control on ordering, compile-time sizes, and automatic size deduction, please see de documentation of `DenseBase::reshaped(NRowsType,NColsType)` that contains all the details with many examples.
+
+
+\section TutorialReshapeMat2Vec 1D linear views
+
+A very common usage of reshaping is to create a 1D linear view over a given 2D matrix or expression.
+In this case, sizes can be deduced and thus omitted as in the following example:
+
+<table class="example">
+<tr><th>Example:</th></tr>
+<tr><td>
+\include MatrixBase_reshaped_to_vector.cpp
+</td></tr>
+<tr><th>Output:</th></tr>
+<tr><td>
+\verbinclude MatrixBase_reshaped_to_vector.out
+</td></tr></table>
+
+This shortcut always returns a column vector and by default input coefficients are always interpreted in column-major order.
+Again, see the documentation of DenseBase::reshaped() for more control on the ordering.
+
+\section TutorialReshapeInPlace
+
+The above examples create reshaped views, but what about reshaping inplace a given matrix?
+Of course this task in only conceivable for matrix and arrays having runtime dimensions.
+In many cases, this can be accomplished via PlainObjectBase::resize(Index,Index):
+
+<table class="example">
+<tr><th>Example:</th></tr>
+<tr><td>
+\include Tutorial_reshaped_vs_resize_1.cpp
+</td></tr>
+<tr><th>Output:</th></tr>
+<tr><td>
+\verbinclude Tutorial_reshaped_vs_resize_1.out
+</td></tr></table>
+
+However beware that unlike \c reshaped, the result of \c resize depends on the input storage order.
+It thus behaves similarly to `reshaped<AutoOrder>`:
+
+<table class="example">
+<tr><th>Example:</th></tr>
+<tr><td>
+\include Tutorial_reshaped_vs_resize_2.cpp
+</td></tr>
+<tr><th>Output:</th></tr>
+<tr><td>
+\verbinclude Tutorial_reshaped_vs_resize_2.out
+</td></tr></table>
+
+Finally, assigning a reshaped matrix to itself is currently not supported and will result to undefined-behavior because of \link TopicAliasing aliasing \endlink.
+The following is forbidden: \code A = A.reshaped(2,8); \endcode
+This is OK: \code A = A.reshaped(2,8).eval(); \endcode
+
+*/
+
+}
diff --git a/doc/TutorialSTL.dox b/doc/TutorialSTL.dox
new file mode 100644
index 0000000..9a825bc
--- /dev/null
+++ b/doc/TutorialSTL.dox
@@ -0,0 +1,66 @@
+namespace Eigen {
+
+/** \eigenManualPage TutorialSTL STL iterators and algorithms
+
+Since the version 3.4, %Eigen's dense matrices and arrays provide STL compatible iterators.
+As demonstrated below, this makes them naturally compatible with range-for-loops and STL's algorithms.
+
+\eigenAutoToc
+
+\section TutorialSTLVectors Iterating over 1D arrays and vectors
+
+Any dense 1D expressions exposes the pair of `begin()/end()` methods to iterate over them.
+
+This directly enables c++11 range for loops:
+<table class="example">
+<tr><th>Example:</th><th>Output:</th></tr>
+<tr><td>
+\include Tutorial_range_for_loop_1d_cxx11.cpp
+</td>
+<td>
+\verbinclude Tutorial_range_for_loop_1d_cxx11.out
+</td></tr></table>
+
+One dimensional expressions can also easily be passed to STL algorithms:
+<table class="example">
+<tr><th>Example:</th><th>Output:</th></tr>
+<tr><td>
+\include Tutorial_std_sort.cpp
+</td>
+<td>
+\verbinclude Tutorial_std_sort.out
+</td></tr></table>
+
+Similar to `std::vector`, 1D expressions also exposes the pair of `cbegin()/cend()` methods to conveniently get const iterators on non-const object.
+
+\section TutorialSTLMatrices Iterating over coefficients of 2D arrays and matrices
+
+STL iterators are intrinsically designed to iterate over 1D structures.
+This is why `begin()/end()` methods are disabled for 2D expressions.
+Iterating over all coefficients of a 2D expressions is still easily accomplished by creating a 1D linear view through `reshaped()`:
+<table class="example">
+<tr><th>Example:</th><th>Output:</th></tr>
+<tr><td>
+\include Tutorial_range_for_loop_2d_cxx11.cpp
+</td>
+<td>
+\verbinclude Tutorial_range_for_loop_2d_cxx11.out
+</td></tr></table>
+
+\section TutorialSTLRowsColumns Iterating over rows or columns of 2D arrays and matrices
+
+It is also possible to get iterators over rows or columns of 2D expressions.
+Those are available through the `rowwise()` and `colwise()` proxies.
+Here is an example sorting each row of a matrix:
+<table class="example">
+<tr><th>Example:</th><th>Output:</th></tr>
+<tr><td>
+\include Tutorial_std_sort_rows_cxx11.cpp
+</td>
+<td>
+\verbinclude Tutorial_std_sort_rows_cxx11.out
+</td></tr></table>
+
+*/
+
+}
diff --git a/doc/TutorialSlicingIndexing.dox b/doc/TutorialSlicingIndexing.dox
new file mode 100644
index 0000000..8b067df
--- /dev/null
+++ b/doc/TutorialSlicingIndexing.dox
@@ -0,0 +1,245 @@
+namespace Eigen {
+
+/** \eigenManualPage TutorialSlicingIndexing Slicing and Indexing
+
+This page presents the numerous possibilities offered by `operator()` to index sub-set of rows and columns.
+This API has been introduced in %Eigen 3.4.
+It supports all the feature proposed by the \link TutorialBlockOperations block API \endlink, and much more.
+In particular, it supports \b slicing that consists in taking a set of rows, columns, or elements, uniformly spaced within a matrix or indexed from an array of indices.
+
+\eigenAutoToc
+
+\section TutorialSlicingOverview Overview
+
+All the aforementioned operations are handled through the generic DenseBase::operator()(const RowIndices&, const ColIndices&) method.
+Each argument can be:
+ - An integer indexing a single row or column, including symbolic indices.
+ - The symbol Eigen::all representing the whole set of respective rows or columns in increasing order.
+ - An ArithmeticSequence as constructed by the Eigen::seq, Eigen::seqN, or Eigen::placeholders::lastN functions.
+ - Any 1D vector/array of integers including %Eigen's vector/array, expressions, std::vector, std::array, as well as plain C arrays: `int[N]`.
+
+More generally, it can accepts any object exposing the following two member functions:
+ \code
+ <integral type> operator[](<integral type>) const;
+ <integral type> size() const;
+ \endcode
+where `<integral type>` stands for any integer type compatible with Eigen::Index (i.e. `std::ptrdiff_t`).
+
+\section TutorialSlicingBasic Basic slicing
+
+Taking a set of rows, columns, or elements, uniformly spaced within a matrix or vector is achieved through the Eigen::seq or Eigen::seqN functions where "seq" stands for arithmetic sequence. Their signatures are summarized below:
+
+<table class="manual">
+<tr>
+ <th>function</th>
+ <th>description</th>
+ <th>example</th>
+</tr>
+<tr>
+ <td>\code seq(firstIdx,lastIdx) \endcode</td>
+ <td>represents the sequence of integers ranging from \c firstIdx to \c lastIdx</td>
+ <td>\code seq(2,5) <=> {2,3,4,5} \endcode</td>
+</tr>
+<tr>
+ <td>\code seq(firstIdx,lastIdx,incr) \endcode</td>
+ <td>same but using the increment \c incr to advance from one index to the next</td>
+ <td>\code seq(2,8,2) <=> {2,4,6,8} \endcode</td>
+</tr>
+<tr>
+ <td>\code seqN(firstIdx,size) \endcode</td>
+ <td>represents the sequence of \c size integers starting from \c firstIdx</td>
+ <td>\code seqN(2,5) <=> {2,3,4,5,6} \endcode</td>
+</tr>
+<tr>
+ <td>\code seqN(firstIdx,size,incr) \endcode</td>
+ <td>same but using the increment \c incr to advance from one index to the next</td>
+ <td>\code seqN(2,3,3) <=> {2,5,8} \endcode</td>
+</tr>
+</table>
+
+The \c firstIdx and \c lastIdx parameters can also be defined with the help of the Eigen::last symbol representing the index of the last row, column or element of the underlying matrix/vector once the arithmetic sequence is passed to it through operator().
+Here are some examples for a 2D array/matrix \c A and a 1D array/vector \c v.
+<table class="manual">
+<tr>
+ <th>Intent</th>
+ <th>Code</th>
+ <th>Block-API equivalence</th>
+</tr>
+<tr>
+ <td>Bottom-left corner starting at row \c i with \c n columns</td>
+ <td>\code A(seq(i,last), seqN(0,n)) \endcode</td>
+ <td>\code A.bottomLeftCorner(A.rows()-i,n) \endcode</td>
+</tr>
+<tr>
+ <td>%Block starting at \c i,j having \c m rows, and \c n columns</td>
+ <td>\code A(seqN(i,m), seqN(i,n)) \endcode</td>
+ <td>\code A.block(i,j,m,n) \endcode</td>
+</tr>
+<tr>
+ <td>%Block starting at \c i0,j0 and ending at \c i1,j1</td>
+ <td>\code A(seq(i0,i1), seq(j0,j1) \endcode</td>
+ <td>\code A.block(i0,j0,i1-i0+1,j1-j0+1) \endcode</td>
+</tr>
+<tr>
+ <td>Even columns of A</td>
+ <td>\code A(all, seq(0,last,2)) \endcode</td>
+ <td></td>
+</tr>
+<tr>
+ <td>First \c n odd rows A</td>
+ <td>\code A(seqN(1,n,2), all) \endcode</td>
+ <td></td>
+</tr>
+<tr>
+ <td>The last past one column</td>
+ <td>\code A(all, last-1) \endcode</td>
+ <td>\code A.col(A.cols()-2) \endcode</td>
+</tr>
+<tr>
+ <td>The middle row</td>
+ <td>\code A(last/2,all) \endcode</td>
+ <td>\code A.row((A.rows()-1)/2) \endcode</td>
+</tr>
+<tr>
+ <td>Last elements of v starting at i</td>
+ <td>\code v(seq(i,last)) \endcode</td>
+ <td>\code v.tail(v.size()-i) \endcode</td>
+</tr>
+<tr>
+ <td>Last \c n elements of v</td>
+ <td>\code v(seq(last+1-n,last)) \endcode</td>
+ <td>\code v.tail(n) \endcode</td>
+</tr>
+</table>
+
+As seen in the last example, referencing the <i> last n </i> elements (or rows/columns) is a bit cumbersome to write.
+This becomes even more tricky and error prone with a non-default increment.
+Here comes \link Eigen::placeholders::lastN(SizeType) Eigen::placeholders::lastN(size) \endlink, and
+\link Eigen::placeholders::lastN(SizeType,IncrType) Eigen::placeholders::lastN(size,incr) \endlink:
+
+<table class="manual">
+<tr>
+ <th>Intent</th>
+ <th>Code</th>
+ <th>Block-API equivalence</th>
+</tr>
+<tr>
+ <td>Last \c n elements of v</td>
+ <td>\code v(lastN(n)) \endcode</td>
+ <td>\code v.tail(n) \endcode</td>
+</tr>
+<tr>
+ <td>Bottom-right corner of A of size \c m times \c n</td>
+ <td>\code A(lastN(m), lastN(n)) \endcode</td>
+ <td>\code A.bottomRightCorner(m,n) \endcode</td>
+</tr>
+<tr>
+ <td>Bottom-right corner of A of size \c m times \c n</td>
+ <td>\code A(lastN(m), lastN(n)) \endcode</td>
+ <td>\code A.bottomRightCorner(m,n) \endcode</td>
+</tr>
+<tr>
+ <td>Last \c n columns taking 1 column over 3</td>
+ <td>\code A(all, lastN(n,3)) \endcode</td>
+ <td></td>
+</tr>
+</table>
+
+\section TutorialSlicingFixed Compile time size and increment
+
+In terms of performance, %Eigen and the compiler can take advantage of compile-time size and increment.
+To this end, you can enforce compile-time parameters using Eigen::fix<val>.
+Such compile-time value can be combined with the Eigen::last symbol:
+\code v(seq(last-fix<7>, last-fix<2>))
+\endcode
+In this example %Eigen knowns at compile-time that the returned expression has 6 elements.
+It is equivalent to:
+\code v(seqN(last-7, fix<6>))
+\endcode
+
+We can revisit the <i>even columns of A</i> example as follows:
+\code A(all, seq(0,last,fix<2>))
+\endcode
+
+
+\section TutorialSlicingReverse Reverse order
+
+Row/column indices can also be enumerated in decreasing order using a negative increment.
+For instance, one over two columns of A from the column 20 to 10:
+\code A(all, seq(20, 10, fix<-2>))
+\endcode
+The last \c n rows starting from the last one:
+\code A(seqN(last, n, fix<-1>), all)
+\endcode
+You can also use the ArithmeticSequence::reverse() method to reverse its order.
+The previous example can thus also be written as:
+\code A(lastN(n).reverse(), all)
+\endcode
+
+
+\section TutorialSlicingArray Array of indices
+
+The generic `operator()` can also takes as input an arbitrary list of row or column indices stored as either an `ArrayXi`, a `std::vector<int>`, `std::array<int,N>`, etc.
+
+<table class="example">
+<tr><th>Example:</th><th>Output:</th></tr>
+<tr><td>
+\include Slicing_stdvector_cxx11.cpp
+</td>
+<td>
+\verbinclude Slicing_stdvector_cxx11.out
+</td></tr></table>
+
+You can also directly pass a static array:
+<table class="example">
+<tr><th>Example:</th><th>Output:</th></tr>
+<tr><td>
+\include Slicing_rawarray_cxx11.cpp
+</td>
+<td>
+\verbinclude Slicing_rawarray_cxx11.out
+</td></tr></table>
+
+or expressions:
+<table class="example">
+<tr><th>Example:</th><th>Output:</th></tr>
+<tr><td>
+\include Slicing_arrayexpr.cpp
+</td>
+<td>
+\verbinclude Slicing_arrayexpr.out
+</td></tr></table>
+
+When passing an object with a compile-time size such as `Array4i`, `std::array<int,N>`, or a static array, then the returned expression also exhibit compile-time dimensions.
+
+\section TutorialSlicingCustomArray Custom index list
+
+More generally, `operator()` can accept as inputs any object \c ind of type \c T compatible with:
+\code
+Index s = ind.size(); or Index s = size(ind);
+Index i;
+i = ind[i];
+\endcode
+
+This means you can easily build your own fancy sequence generator and pass it to `operator()`.
+Here is an example enlarging a given matrix while padding the additional first rows and columns through repetition:
+
+<table class="example">
+<tr><th>Example:</th><th>Output:</th></tr>
+<tr><td>
+\include Slicing_custom_padding_cxx11.cpp
+</td>
+<td>
+\verbinclude Slicing_custom_padding_cxx11.out
+</td></tr></table>
+
+<br>
+
+*/
+
+/*
+TODO add:
+so_repeat_inner.cpp
+so_repeleme.cpp
+*/
+}
diff --git a/doc/TutorialSparse.dox b/doc/TutorialSparse.dox
new file mode 100644
index 0000000..a00bacd
--- /dev/null
+++ b/doc/TutorialSparse.dox
@@ -0,0 +1,365 @@
+namespace Eigen {
+
+/** \eigenManualPage TutorialSparse Sparse matrix manipulations
+
+\eigenAutoToc
+
+Manipulating and solving sparse problems involves various modules which are summarized below:
+
+<table class="manual">
+<tr><th>Module</th><th>Header file</th><th>Contents</th></tr>
+<tr><td>\link SparseCore_Module SparseCore \endlink</td><td>\code#include <Eigen/SparseCore>\endcode</td><td>SparseMatrix and SparseVector classes, matrix assembly, basic sparse linear algebra (including sparse triangular solvers)</td></tr>
+<tr><td>\link SparseCholesky_Module SparseCholesky \endlink</td><td>\code#include <Eigen/SparseCholesky>\endcode</td><td>Direct sparse LLT and LDLT Cholesky factorization to solve sparse self-adjoint positive definite problems</td></tr>
+<tr><td>\link SparseLU_Module SparseLU \endlink</td><td>\code #include<Eigen/SparseLU> \endcode</td>
+<td>%Sparse LU factorization to solve general square sparse systems</td></tr>
+<tr><td>\link SparseQR_Module SparseQR \endlink</td><td>\code #include<Eigen/SparseQR>\endcode </td><td>%Sparse QR factorization for solving sparse linear least-squares problems</td></tr>
+<tr><td>\link IterativeLinearSolvers_Module IterativeLinearSolvers \endlink</td><td>\code#include <Eigen/IterativeLinearSolvers>\endcode</td><td>Iterative solvers to solve large general linear square problems (including self-adjoint positive definite problems)</td></tr>
+<tr><td>\link Sparse_Module Sparse \endlink</td><td>\code#include <Eigen/Sparse>\endcode</td><td>Includes all the above modules</td></tr>
+</table>
+
+\section TutorialSparseIntro Sparse matrix format
+
+In many applications (e.g., finite element methods) it is common to deal with very large matrices where only a few coefficients are different from zero. In such cases, memory consumption can be reduced and performance increased by using a specialized representation storing only the nonzero coefficients. Such a matrix is called a sparse matrix.
+
+\b The \b %SparseMatrix \b class
+
+The class SparseMatrix is the main sparse matrix representation of Eigen's sparse module; it offers high performance and low memory usage.
+It implements a more versatile variant of the widely-used Compressed Column (or Row) Storage scheme.
+It consists of four compact arrays:
+ - \c Values: stores the coefficient values of the non-zeros.
+ - \c InnerIndices: stores the row (resp. column) indices of the non-zeros.
+ - \c OuterStarts: stores for each column (resp. row) the index of the first non-zero in the previous two arrays.
+ - \c InnerNNZs: stores the number of non-zeros of each column (resp. row).
+The word \c inner refers to an \em inner \em vector that is a column for a column-major matrix, or a row for a row-major matrix.
+The word \c outer refers to the other direction.
+
+This storage scheme is better explained on an example. The following matrix
+<table class="manual">
+<tr><td> 0</td><td>3</td><td> 0</td><td>0</td><td> 0</td></tr>
+<tr><td>22</td><td>0</td><td> 0</td><td>0</td><td>17</td></tr>
+<tr><td> 7</td><td>5</td><td> 0</td><td>1</td><td> 0</td></tr>
+<tr><td> 0</td><td>0</td><td> 0</td><td>0</td><td> 0</td></tr>
+<tr><td> 0</td><td>0</td><td>14</td><td>0</td><td> 8</td></tr>
+</table>
+
+and one of its possible sparse, \b column \b major representation:
+<table class="manual">
+<tr><td>Values:</td> <td>22</td><td>7</td><td>_</td><td>3</td><td>5</td><td>_</td><td>14</td><td>_</td><td>1</td><td>_</td><td>17</td><td>8</td></tr>
+<tr><td>InnerIndices:</td> <td> 1</td><td>2</td><td>_</td><td>0</td><td>2</td><td>_</td><td>4</td><td>_</td><td>2</td><td>_</td><td> 1</td><td>4</td></tr>
+</table>
+<table class="manual">
+<tr><td>OuterStarts:</td><td>0</td><td>3</td><td>5</td><td>8</td><td>10</td><td>\em 12 </td></tr>
+<tr><td>InnerNNZs:</td> <td>2</td><td>2</td><td>1</td><td>1</td><td> 2</td><td></td></tr>
+</table>
+
+Currently the elements of a given inner vector are guaranteed to be always sorted by increasing inner indices.
+The \c "_" indicates available free space to quickly insert new elements.
+Assuming no reallocation is needed, the insertion of a random element is therefore in `O(nnz_j)` where `nnz_j` is the number of nonzeros of the respective inner vector.
+On the other hand, inserting elements with increasing inner indices in a given inner vector is much more efficient since this only requires to increase the respective \c InnerNNZs entry that is a `O(1)` operation.
+
+The case where no empty space is available is a special case, and is referred as the \em compressed mode.
+It corresponds to the widely used Compressed Column (or Row) Storage schemes (CCS or CRS).
+Any SparseMatrix can be turned to this form by calling the SparseMatrix::makeCompressed() function.
+In this case, one can remark that the \c InnerNNZs array is redundant with \c OuterStarts because we have the equality: `InnerNNZs[j] == OuterStarts[j+1] - OuterStarts[j]`.
+Therefore, in practice a call to SparseMatrix::makeCompressed() frees this buffer.
+
+It is worth noting that most of our wrappers to external libraries requires compressed matrices as inputs.
+
+The results of %Eigen's operations always produces \b compressed sparse matrices.
+On the other hand, the insertion of a new element into a SparseMatrix converts this later to the \b uncompressed mode.
+
+Here is the previous matrix represented in compressed mode:
+<table class="manual">
+<tr><td>Values:</td> <td>22</td><td>7</td><td>3</td><td>5</td><td>14</td><td>1</td><td>17</td><td>8</td></tr>
+<tr><td>InnerIndices:</td> <td> 1</td><td>2</td><td>0</td><td>2</td><td> 4</td><td>2</td><td> 1</td><td>4</td></tr>
+</table>
+<table class="manual">
+<tr><td>OuterStarts:</td><td>0</td><td>2</td><td>4</td><td>5</td><td>6</td><td>\em 8 </td></tr>
+</table>
+
+A SparseVector is a special case of a SparseMatrix where only the \c Values and \c InnerIndices arrays are stored.
+There is no notion of compressed/uncompressed mode for a SparseVector.
+
+
+\section TutorialSparseExample First example
+
+Before describing each individual class, let's start with the following typical example: solving the Laplace equation \f$ \Delta u = 0 \f$ on a regular 2D grid using a finite difference scheme and Dirichlet boundary conditions.
+Such problem can be mathematically expressed as a linear problem of the form \f$ Ax=b \f$ where \f$ x \f$ is the vector of \c m unknowns (in our case, the values of the pixels), \f$ b \f$ is the right hand side vector resulting from the boundary conditions, and \f$ A \f$ is an \f$ m \times m \f$ matrix containing only a few non-zero elements resulting from the discretization of the Laplacian operator.
+
+<table class="manual">
+<tr><td>
+\include Tutorial_sparse_example.cpp
+</td>
+<td>
+\image html Tutorial_sparse_example.jpeg
+</td></tr></table>
+
+In this example, we start by defining a column-major sparse matrix type of double \c SparseMatrix<double>, and a triplet list of the same scalar type \c Triplet<double>. A triplet is a simple object representing a non-zero entry as the triplet: \c row index, \c column index, \c value.
+
+In the main function, we declare a list \c coefficients of triplets (as a std vector) and the right hand side vector \f$ b \f$ which are filled by the \a buildProblem function.
+The raw and flat list of non-zero entries is then converted to a true SparseMatrix object \c A.
+Note that the elements of the list do not have to be sorted, and possible duplicate entries will be summed up.
+
+The last step consists of effectively solving the assembled problem.
+Since the resulting matrix \c A is symmetric by construction, we can perform a direct Cholesky factorization via the SimplicialLDLT class which behaves like its LDLT counterpart for dense objects.
+
+The resulting vector \c x contains the pixel values as a 1D array which is saved to a jpeg file shown on the right of the code above.
+
+Describing the \a buildProblem and \a save functions is out of the scope of this tutorial. They are given \ref TutorialSparse_example_details "here" for the curious and reproducibility purpose.
+
+
+
+
+\section TutorialSparseSparseMatrix The SparseMatrix class
+
+\b %Matrix \b and \b vector \b properties \n
+
+The SparseMatrix and SparseVector classes take three template arguments:
+ * the scalar type (e.g., double)
+ * the storage order (ColMajor or RowMajor, the default is ColMajor)
+ * the inner index type (default is \c int).
+
+As for dense Matrix objects, constructors takes the size of the object.
+Here are some examples:
+
+\code
+SparseMatrix<std::complex<float> > mat(1000,2000); // declares a 1000x2000 column-major compressed sparse matrix of complex<float>
+SparseMatrix<double,RowMajor> mat(1000,2000); // declares a 1000x2000 row-major compressed sparse matrix of double
+SparseVector<std::complex<float> > vec(1000); // declares a column sparse vector of complex<float> of size 1000
+SparseVector<double,RowMajor> vec(1000); // declares a row sparse vector of double of size 1000
+\endcode
+
+In the rest of the tutorial, \c mat and \c vec represent any sparse-matrix and sparse-vector objects, respectively.
+
+The dimensions of a matrix can be queried using the following functions:
+<table class="manual">
+<tr><td>Standard \n dimensions</td><td>\code
+mat.rows()
+mat.cols()\endcode</td>
+<td>\code
+vec.size() \endcode</td>
+</tr>
+<tr><td>Sizes along the \n inner/outer dimensions</td><td>\code
+mat.innerSize()
+mat.outerSize()\endcode</td>
+<td></td>
+</tr>
+<tr><td>Number of non \n zero coefficients</td><td>\code
+mat.nonZeros() \endcode</td>
+<td>\code
+vec.nonZeros() \endcode</td></tr>
+</table>
+
+
+\b Iterating \b over \b the \b nonzero \b coefficients \n
+
+Random access to the elements of a sparse object can be done through the \c coeffRef(i,j) function.
+However, this function involves a quite expensive binary search.
+In most cases, one only wants to iterate over the non-zeros elements. This is achieved by a standard loop over the outer dimension, and then by iterating over the non-zeros of the current inner vector via an InnerIterator. Thus, the non-zero entries have to be visited in the same order than the storage order.
+Here is an example:
+<table class="manual">
+<tr><td>
+\code
+SparseMatrix<double> mat(rows,cols);
+for (int k=0; k<mat.outerSize(); ++k)
+ for (SparseMatrix<double>::InnerIterator it(mat,k); it; ++it)
+ {
+ it.value();
+ it.row(); // row index
+ it.col(); // col index (here it is equal to k)
+ it.index(); // inner index, here it is equal to it.row()
+ }
+\endcode
+</td><td>
+\code
+SparseVector<double> vec(size);
+for (SparseVector<double>::InnerIterator it(vec); it; ++it)
+{
+ it.value(); // == vec[ it.index() ]
+ it.index();
+}
+\endcode
+</td></tr>
+</table>
+For a writable expression, the referenced value can be modified using the valueRef() function.
+If the type of the sparse matrix or vector depends on a template parameter, then the \c typename keyword is
+required to indicate that \c InnerIterator denotes a type; see \ref TopicTemplateKeyword for details.
+
+
+\section TutorialSparseFilling Filling a sparse matrix
+
+Because of the special storage scheme of a SparseMatrix, special care has to be taken when adding new nonzero entries.
+For instance, the cost of a single purely random insertion into a SparseMatrix is \c O(nnz), where \c nnz is the current number of non-zero coefficients.
+
+The simplest way to create a sparse matrix while guaranteeing good performance is thus to first build a list of so-called \em triplets, and then convert it to a SparseMatrix.
+
+Here is a typical usage example:
+\code
+typedef Eigen::Triplet<double> T;
+std::vector<T> tripletList;
+tripletList.reserve(estimation_of_entries);
+for(...)
+{
+ // ...
+ tripletList.push_back(T(i,j,v_ij));
+}
+SparseMatrixType mat(rows,cols);
+mat.setFromTriplets(tripletList.begin(), tripletList.end());
+// mat is ready to go!
+\endcode
+The \c std::vector of triplets might contain the elements in arbitrary order, and might even contain duplicated elements that will be summed up by setFromTriplets().
+See the SparseMatrix::setFromTriplets() function and class Triplet for more details.
+
+
+In some cases, however, slightly higher performance, and lower memory consumption can be reached by directly inserting the non-zeros into the destination matrix.
+A typical scenario of this approach is illustrated below:
+\code
+1: SparseMatrix<double> mat(rows,cols); // default is column major
+2: mat.reserve(VectorXi::Constant(cols,6));
+3: for each i,j such that v_ij != 0
+4: mat.insert(i,j) = v_ij; // alternative: mat.coeffRef(i,j) += v_ij;
+5: mat.makeCompressed(); // optional
+\endcode
+
+- The key ingredient here is the line 2 where we reserve room for 6 non-zeros per column. In many cases, the number of non-zeros per column or row can easily be known in advance. If it varies significantly for each inner vector, then it is possible to specify a reserve size for each inner vector by providing a vector object with an `operator[](int j)` returning the reserve size of the \c j-th inner vector (e.g., via a `VectorXi` or `std::vector<int>`). If only a rought estimate of the number of nonzeros per inner-vector can be obtained, it is highly recommended to overestimate it rather than the opposite. If this line is omitted, then the first insertion of a new element will reserve room for 2 elements per inner vector.
+- The line 4 performs a sorted insertion. In this example, the ideal case is when the \c j-th column is not full and contains non-zeros whose inner-indices are smaller than \c i. In this case, this operation boils down to trivial O(1) operation.
+- When calling `insert(i,j)` the element `i`, `j` must not already exists, otherwise use the `coeffRef(i,j)` method that will allow to, e.g., accumulate values. This method first performs a binary search and finally calls `insert(i,j)` if the element does not already exist. It is more flexible than `insert()` but also more costly.
+- The line 5 suppresses the remaining empty space and transforms the matrix into a compressed column storage.
+
+
+
+\section TutorialSparseFeatureSet Supported operators and functions
+
+Because of their special storage format, sparse matrices cannot offer the same level of flexibility than dense matrices.
+In Eigen's sparse module we chose to expose only the subset of the dense matrix API which can be efficiently implemented.
+In the following \em sm denotes a sparse matrix, \em sv a sparse vector, \em dm a dense matrix, and \em dv a dense vector.
+
+\subsection TutorialSparse_BasicOps Basic operations
+
+%Sparse expressions support most of the unary and binary coefficient wise operations:
+\code
+sm1.real() sm1.imag() -sm1 0.5*sm1
+sm1+sm2 sm1-sm2 sm1.cwiseProduct(sm2)
+\endcode
+However, <strong>a strong restriction is that the storage orders must match</strong>. For instance, in the following example:
+\code
+sm4 = sm1 + sm2 + sm3;
+\endcode
+sm1, sm2, and sm3 must all be row-major or all column-major.
+On the other hand, there is no restriction on the target matrix sm4.
+For instance, this means that for computing \f$ A^T + A \f$, the matrix \f$ A^T \f$ must be evaluated into a temporary matrix of compatible storage order:
+\code
+SparseMatrix<double> A, B;
+B = SparseMatrix<double>(A.transpose()) + A;
+\endcode
+
+Binary coefficient wise operators can also mix sparse and dense expressions:
+\code
+sm2 = sm1.cwiseProduct(dm1);
+dm2 = sm1 + dm1;
+dm2 = dm1 - sm1;
+\endcode
+Performance-wise, the adding/subtracting sparse and dense matrices is better performed in two steps. For instance, instead of doing `dm2 = sm1 + dm1`, better write:
+\code
+dm2 = dm1;
+dm2 += sm1;
+\endcode
+This version has the advantage to fully exploit the higher performance of dense storage (no indirection, SIMD, etc.), and to pay the cost of slow sparse evaluation on the few non-zeros of the sparse matrix only.
+
+
+%Sparse expressions also support transposition:
+\code
+sm1 = sm2.transpose();
+sm1 = sm2.adjoint();
+\endcode
+However, there is no `transposeInPlace()` method.
+
+
+\subsection TutorialSparse_Products Matrix products
+
+%Eigen supports various kind of sparse matrix products which are summarize below:
+ - \b sparse-dense:
+ \code
+dv2 = sm1 * dv1;
+dm2 = dm1 * sm1.adjoint();
+dm2 = 2. * sm1 * dm1;
+ \endcode
+ - \b symmetric \b sparse-dense. The product of a sparse symmetric matrix with a dense matrix (or vector) can also be optimized by specifying the symmetry with `selfadjointView()`:
+ \code
+dm2 = sm1.selfadjointView<>() * dm1; // if all coefficients of sm1 are stored
+dm2 = sm1.selfadjointView<Upper>() * dm1; // if only the upper part of sm1 is stored
+dm2 = sm1.selfadjointView<Lower>() * dm1; // if only the lower part of sm1 is stored
+ \endcode
+ - \b sparse-sparse. For sparse-sparse products, two different algorithms are available. The default one is conservative and preserve the explicit zeros that might appear:
+ \code
+sm3 = sm1 * sm2;
+sm3 = 4 * sm1.adjoint() * sm2;
+ \endcode
+ The second algorithm prunes on the fly the explicit zeros, or the values smaller than a given threshold. It is enabled and controlled through the `prune()` functions:
+ \code
+sm3 = (sm1 * sm2).pruned(); // removes numerical zeros
+sm3 = (sm1 * sm2).pruned(ref); // removes elements much smaller than ref
+sm3 = (sm1 * sm2).pruned(ref,epsilon); // removes elements smaller than ref*epsilon
+ \endcode
+
+ - \b permutations. Finally, permutations can be applied to sparse matrices too:
+ \code
+PermutationMatrix<Dynamic,Dynamic> P = ...;
+sm2 = P * sm1;
+sm2 = sm1 * P.inverse();
+sm2 = sm1.transpose() * P;
+ \endcode
+
+
+\subsection TutorialSparse_SubMatrices Block operations
+
+Regarding read-access, sparse matrices expose the same API than for dense matrices to access to sub-matrices such as blocks, columns, and rows. See \ref TutorialBlockOperations for a detailed introduction.
+However, for performance reasons, writing to a sub-sparse-matrix is much more limited, and currently only contiguous sets of columns (resp. rows) of a column-major (resp. row-major) SparseMatrix are writable. Moreover, this information has to be known at compile-time, leaving out methods such as `block(...)` and `corner*(...)`. The available API for write-access to a SparseMatrix are summarized below:
+\code
+SparseMatrix<double,ColMajor> sm1;
+sm1.col(j) = ...;
+sm1.leftCols(ncols) = ...;
+sm1.middleCols(j,ncols) = ...;
+sm1.rightCols(ncols) = ...;
+
+SparseMatrix<double,RowMajor> sm2;
+sm2.row(i) = ...;
+sm2.topRows(nrows) = ...;
+sm2.middleRows(i,nrows) = ...;
+sm2.bottomRows(nrows) = ...;
+\endcode
+
+In addition, sparse matrices expose the `SparseMatrixBase::innerVector()` and `SparseMatrixBase::innerVectors()` methods, which are aliases to the `col`/`middleCols` methods for a column-major storage, and to the `row`/`middleRows` methods for a row-major storage.
+
+\subsection TutorialSparse_TriangularSelfadjoint Triangular and selfadjoint views
+
+Just as with dense matrices, the `triangularView()` function can be used to address a triangular part of the matrix, and perform triangular solves with a dense right hand side:
+\code
+dm2 = sm1.triangularView<Lower>(dm1);
+dv2 = sm1.transpose().triangularView<Upper>(dv1);
+\endcode
+
+The `selfadjointView()` function permits various operations:
+ - optimized sparse-dense matrix products:
+ \code
+dm2 = sm1.selfadjointView<>() * dm1; // if all coefficients of sm1 are stored
+dm2 = sm1.selfadjointView<Upper>() * dm1; // if only the upper part of sm1 is stored
+dm2 = sm1.selfadjointView<Lower>() * dm1; // if only the lower part of sm1 is stored
+ \endcode
+ - copy of triangular parts:
+ \code
+sm2 = sm1.selfadjointView<Upper>(); // makes a full selfadjoint matrix from the upper triangular part
+sm2.selfadjointView<Lower>() = sm1.selfadjointView<Upper>(); // copies the upper triangular part to the lower triangular part
+ \endcode
+ - application of symmetric permutations:
+ \code
+PermutationMatrix<Dynamic,Dynamic> P = ...;
+sm2 = A.selfadjointView<Upper>().twistedBy(P); // compute P S P' from the upper triangular part of A, and make it a full matrix
+sm2.selfadjointView<Lower>() = A.selfadjointView<Lower>().twistedBy(P); // compute P S P' from the lower triangular part of A, and then only compute the lower part
+ \endcode
+
+Please, refer to the \link SparseQuickRefPage Quick Reference \endlink guide for the list of supported operations. The list of linear solvers available is \link TopicSparseSystems here. \endlink
+
+*/
+
+}
diff --git a/doc/TutorialSparse_example_details.dox b/doc/TutorialSparse_example_details.dox
new file mode 100644
index 0000000..0438da8
--- /dev/null
+++ b/doc/TutorialSparse_example_details.dox
@@ -0,0 +1,4 @@
+/**
+\page TutorialSparse_example_details
+\include Tutorial_sparse_example_details.cpp
+*/
diff --git a/doc/UnalignedArrayAssert.dox b/doc/UnalignedArrayAssert.dox
new file mode 100644
index 0000000..410c8a5
--- /dev/null
+++ b/doc/UnalignedArrayAssert.dox
@@ -0,0 +1,133 @@
+namespace Eigen {
+
+/** \eigenManualPage TopicUnalignedArrayAssert Explanation of the assertion on unaligned arrays
+
+Hello! You are seeing this webpage because your program terminated on an assertion failure like this one:
+<pre>
+my_program: path/to/eigen/Eigen/src/Core/DenseStorage.h:44:
+Eigen::internal::matrix_array<T, Size, MatrixOptions, Align>::internal::matrix_array()
+[with T = double, int Size = 2, int MatrixOptions = 2, bool Align = true]:
+Assertion `(reinterpret_cast<size_t>(array) & (sizemask)) == 0 && "this assertion
+is explained here: http://eigen.tuxfamily.org/dox-devel/group__TopicUnalignedArrayAssert.html
+**** READ THIS WEB PAGE !!! ****"' failed.
+</pre>
+
+There are 4 known causes for this issue.
+If you can target \cpp17 only with a recent compiler (e.g., GCC>=7, clang>=5, MSVC>=19.12), then you're lucky: enabling c++17 should be enough (if not, please <a href="http://eigen.tuxfamily.org/bz/">report</a> to us).
+Otherwise, please read on to understand those issues and learn how to fix them.
+
+\eigenAutoToc
+
+\section where Where in my own code is the cause of the problem?
+
+First of all, you need to find out where in your own code this assertion was triggered from. At first glance, the error message doesn't look helpful, as it refers to a file inside Eigen! However, since your program crashed, if you can reproduce the crash, you can get a backtrace using any debugger. For example, if you're using GCC, you can use the GDB debugger as follows:
+\code
+$ gdb ./my_program # Start GDB on your program
+> run # Start running your program
+... # Now reproduce the crash!
+> bt # Obtain the backtrace
+\endcode
+Now that you know precisely where in your own code the problem is happening, read on to understand what you need to change.
+
+\section c1 Cause 1: Structures having Eigen objects as members
+
+If you have code like this,
+
+\code
+class Foo
+{
+ //...
+ Eigen::Vector4d v;
+ //...
+};
+//...
+Foo *foo = new Foo;
+\endcode
+
+then you need to read this separate page: \ref TopicStructHavingEigenMembers "Structures Having Eigen Members".
+
+Note that here, Eigen::Vector4d is only used as an example, more generally the issue arises for all \ref TopicFixedSizeVectorizable "fixed-size vectorizable Eigen types".
+
+\section c2 Cause 2: STL Containers or manual memory allocation
+
+If you use STL Containers such as std::vector, std::map, ..., with %Eigen objects, or with classes containing %Eigen objects, like this,
+
+\code
+std::vector<Eigen::Matrix2d> my_vector;
+struct my_class { ... Eigen::Matrix2d m; ... };
+std::map<int, my_class> my_map;
+\endcode
+
+then you need to read this separate page: \ref TopicStlContainers "Using STL Containers with Eigen".
+
+Note that here, Eigen::Matrix2d is only used as an example, more generally the issue arises for all \ref TopicFixedSizeVectorizable "fixed-size vectorizable Eigen types" and \ref TopicStructHavingEigenMembers "structures having such Eigen objects as member".
+
+The same issue will be exhibited by any classes/functions by-passing operator new to allocate memory, that is, by performing custom memory allocation followed by calls to the placement new operator. This is for instance typically the case of \c `std::make_shared` or `std::allocate_shared` for which is the solution is to use an \ref aligned_allocator "aligned allocator" as detailed in the \ref TopicStlContainers "solution for STL containers".
+
+\section c3 Cause 3: Passing Eigen objects by value
+
+If some function in your code is getting an %Eigen object passed by value, like this,
+
+\code
+void func(Eigen::Vector4d v);
+\endcode
+
+then you need to read this separate page: \ref TopicPassingByValue "Passing Eigen objects by value to functions".
+
+Note that here, Eigen::Vector4d is only used as an example, more generally the issue arises for all \ref TopicFixedSizeVectorizable "fixed-size vectorizable Eigen types".
+
+\section c4 Cause 4: Compiler making a wrong assumption on stack alignment (for instance GCC on Windows)
+
+This is a must-read for people using GCC on Windows (like MinGW or TDM-GCC). If you have this assertion failure in an innocent function declaring a local variable like this:
+
+\code
+void foo()
+{
+ Eigen::Quaternionf q;
+ //...
+}
+\endcode
+
+then you need to read this separate page: \ref TopicWrongStackAlignment "Compiler making a wrong assumption on stack alignment".
+
+Note that here, Eigen::Quaternionf is only used as an example, more generally the issue arises for all \ref TopicFixedSizeVectorizable "fixed-size vectorizable Eigen types".
+
+
+\section explanation General explanation of this assertion
+
+\ref TopicFixedSizeVectorizable "Fixed-size vectorizable Eigen objects" must absolutely be created at properly aligned locations, otherwise SIMD instructions addressing them will crash.
+For instance, SSE/NEON/MSA/Altivec/VSX targets will require 16-byte-alignment, whereas AVX and AVX512 targets may require up to 32 and 64 byte alignment respectively.
+
+%Eigen normally takes care of these alignment issues for you, by setting an alignment attribute on them and by overloading their `operator new`.
+
+However there are a few corner cases where these alignment settings get overridden: they are the possible causes for this assertion.
+
+\section getrid I don't care about optimal vectorization, how do I get rid of that stuff?
+
+Three possibilities:
+<ul>
+ <li>Use the \c DontAlign option to Matrix, Array, Quaternion, etc. objects that gives you trouble. This way %Eigen won't try to over-align them, and thus won"t assume any special alignment. On the down side, you will pay the cost of unaligned loads/stores for them, but on modern CPUs, the overhead is either null or marginal. See \link StructHavingEigenMembers_othersolutions here \endlink for an example.</li>
+ <li>Define \link TopicPreprocessorDirectivesPerformance EIGEN_MAX_STATIC_ALIGN_BYTES \endlink to 0. That disables all 16-byte (and above) static alignment code, while keeping 16-byte (or above) heap alignment. This has the effect of
+ vectorizing fixed-size objects (like Matrix4d) through unaligned stores (as controlled by \link TopicPreprocessorDirectivesPerformance EIGEN_UNALIGNED_VECTORIZE \endlink), while keeping unchanged the vectorization of dynamic-size objects
+ (like MatrixXd). On 64 bytes systems, you might also define it 16 to disable only 32 and 64 bytes of over-alignment. But do note that this breaks ABI compatibility with the default behavior of static alignment.</li>
+ <li>Or define both \link TopicPreprocessorDirectivesPerformance EIGEN_DONT_VECTORIZE \endlink and `EIGEN_DISABLE_UNALIGNED_ARRAY_ASSERT`. This keeps the
+ 16-byte (or above) alignment code and thus preserves ABI compatibility, but completely disables vectorization.</li>
+</ul>
+
+If you want to know why defining `EIGEN_DONT_VECTORIZE` does not by itself disable 16-byte (or above) alignment and the assertion, here's the explanation:
+
+It doesn't disable the assertion, because otherwise code that runs fine without vectorization would suddenly crash when enabling vectorization.
+It doesn't disable 16-byte (or above) alignment, because that would mean that vectorized and non-vectorized code are not mutually ABI-compatible. This ABI compatibility is very important, even for people who develop only an in-house application, as for instance one may want to have in the same application a vectorized path and a non-vectorized path.
+
+\section checkmycode How can I check my code is safe regarding alignment issues?
+
+Unfortunately, there is no possibility in c++ to detect any of the aforementioned shortcoming at compile time (though static analyzers are becoming more and more powerful and could detect some of them).
+Even at runtime, all we can do is to catch invalid unaligned allocation and trigger the explicit assertion mentioned at the beginning of this page.
+Therefore, if your program runs fine on a given system with some given compilation flags, then this does not guarantee that your code is safe. For instance, on most 64 bits systems buffer are aligned on 16 bytes boundary and so, if you do not enable AVX instruction set, then your code will run fine. On the other hand, the same code may assert if moving to a more exotic platform, or enabling AVX instructions that required 32 bytes alignment by default.
+
+The situation is not hopeless though. Assuming your code is well covered by unit test, then you can check its alignment safety by linking it to a custom malloc library returning 8 bytes aligned buffers only. This way all alignment shortcomings should pop-up. To this end, you must also compile your program with \link TopicPreprocessorDirectivesPerformance EIGEN_MALLOC_ALREADY_ALIGNED=0 \endlink.
+
+
+*/
+
+}
diff --git a/doc/UsingBlasLapackBackends.dox b/doc/UsingBlasLapackBackends.dox
new file mode 100644
index 0000000..4572820
--- /dev/null
+++ b/doc/UsingBlasLapackBackends.dox
@@ -0,0 +1,133 @@
+/*
+ Copyright (c) 2011, Intel Corporation. All rights reserved.
+ Copyright (C) 2011-2016 Gael Guennebaud <gael.guennebaud@inria.fr>
+
+ Redistribution and use in source and binary forms, with or without modification,
+ are permitted provided that the following conditions are met:
+
+ * Redistributions of source code must retain the above copyright notice, this
+ list of conditions and the following disclaimer.
+ * Redistributions in binary form must reproduce the above copyright notice,
+ this list of conditions and the following disclaimer in the documentation
+ and/or other materials provided with the distribution.
+ * Neither the name of Intel Corporation nor the names of its contributors may
+ be used to endorse or promote products derived from this software without
+ specific prior written permission.
+
+ THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
+ ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
+ WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
+ DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR
+ ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
+ (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
+ LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON
+ ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
+ (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
+ SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+
+ ********************************************************************************
+ * Content : Documentation on the use of BLAS/LAPACK libraries through Eigen
+ ********************************************************************************
+*/
+
+namespace Eigen {
+
+/** \page TopicUsingBlasLapack Using BLAS/LAPACK from %Eigen
+
+
+Since %Eigen version 3.3 and later, any F77 compatible BLAS or LAPACK libraries can be used as backends for dense matrix products and dense matrix decompositions.
+For instance, one can use <a href="http://eigen.tuxfamily.org/Counter/redirect_to_mkl.php">Intel® MKL</a>, Apple's Accelerate framework on OSX, <a href="http://www.openblas.net/">OpenBLAS</a>, <a href="http://www.netlib.org/lapack">Netlib LAPACK</a>, etc.
+
+Do not miss this \link TopicUsingIntelMKL page \endlink for further discussions on the specific use of Intel® MKL (also includes VML, PARDISO, etc.)
+
+In order to use an external BLAS and/or LAPACK library, you must link you own application to the respective libraries and their dependencies.
+For LAPACK, you must also link to the standard <a href="http://www.netlib.org/lapack/lapacke.html">Lapacke</a> library, which is used as a convenient think layer between %Eigen's C++ code and LAPACK F77 interface. Then you must activate their usage by defining one or multiple of the following macros (\b before including any %Eigen's header):
+
+\note For Mac users, in order to use the lapack version shipped with the Accelerate framework, you also need the lapacke library.
+Using <a href="https://www.macports.org/">MacPorts</a>, this is as easy as:
+\code
+sudo port install lapack
+\endcode
+and then use the following link flags: \c -framework \c Accelerate \c /opt/local/lib/lapack/liblapacke.dylib
+
+<table class="manual">
+<tr><td>\c EIGEN_USE_BLAS </td><td>Enables the use of external BLAS level 2 and 3 routines (compatible with any F77 BLAS interface)</td></tr>
+<tr class="alt"><td>\c EIGEN_USE_LAPACKE </td><td>Enables the use of external Lapack routines via the <a href="http://www.netlib.org/lapack/lapacke.html">Lapacke</a> C interface to Lapack (compatible with any F77 LAPACK interface)</td></tr>
+<tr><td>\c EIGEN_USE_LAPACKE_STRICT </td><td>Same as \c EIGEN_USE_LAPACKE but algorithms of lower numerical robustness are disabled. \n This currently concerns only JacobiSVD which otherwise would be replaced by \c gesvd that is less robust than Jacobi rotations.</td></tr>
+</table>
+
+When doing so, a number of %Eigen's algorithms are silently substituted with calls to BLAS or LAPACK routines.
+These substitutions apply only for \b Dynamic \b or \b large enough objects with one of the following four standard scalar types: \c float, \c double, \c complex<float>, and \c complex<double>.
+Operations on other scalar types or mixing reals and complexes will continue to use the built-in algorithms.
+
+The breadth of %Eigen functionality that can be substituted is listed in the table below.
+<table class="manual">
+<tr><th>Functional domain</th><th>Code example</th><th>BLAS/LAPACK routines</th></tr>
+<tr><td>Matrix-matrix operations \n \c EIGEN_USE_BLAS </td><td>\code
+m1*m2.transpose();
+m1.selfadjointView<Lower>()*m2;
+m1*m2.triangularView<Upper>();
+m1.selfadjointView<Lower>().rankUpdate(m2,1.0);
+\endcode</td><td>\code
+?gemm
+?symm/?hemm
+?trmm
+dsyrk/ssyrk
+\endcode</td></tr>
+<tr class="alt"><td>Matrix-vector operations \n \c EIGEN_USE_BLAS </td><td>\code
+m1.adjoint()*b;
+m1.selfadjointView<Lower>()*b;
+m1.triangularView<Upper>()*b;
+\endcode</td><td>\code
+?gemv
+?symv/?hemv
+?trmv
+\endcode</td></tr>
+<tr><td>LU decomposition \n \c EIGEN_USE_LAPACKE \n \c EIGEN_USE_LAPACKE_STRICT </td><td>\code
+v1 = m1.lu().solve(v2);
+\endcode</td><td>\code
+?getrf
+\endcode</td></tr>
+<tr class="alt"><td>Cholesky decomposition \n \c EIGEN_USE_LAPACKE \n \c EIGEN_USE_LAPACKE_STRICT </td><td>\code
+v1 = m2.selfadjointView<Upper>().llt().solve(v2);
+\endcode</td><td>\code
+?potrf
+\endcode</td></tr>
+<tr><td>QR decomposition \n \c EIGEN_USE_LAPACKE \n \c EIGEN_USE_LAPACKE_STRICT </td><td>\code
+m1.householderQr();
+m1.colPivHouseholderQr();
+\endcode</td><td>\code
+?geqrf
+?geqp3
+\endcode</td></tr>
+<tr class="alt"><td>Singular value decomposition \n \c EIGEN_USE_LAPACKE </td><td>\code
+JacobiSVD<MatrixXd, ComputeThinV> svd;
+svd.compute(m1);
+\endcode</td><td>\code
+?gesvd
+\endcode</td></tr>
+<tr><td>Eigen-value decompositions \n \c EIGEN_USE_LAPACKE \n \c EIGEN_USE_LAPACKE_STRICT </td><td>\code
+EigenSolver<MatrixXd> es(m1);
+ComplexEigenSolver<MatrixXcd> ces(m1);
+SelfAdjointEigenSolver<MatrixXd> saes(m1+m1.transpose());
+GeneralizedSelfAdjointEigenSolver<MatrixXd>
+ gsaes(m1+m1.transpose(),m2+m2.transpose());
+\endcode</td><td>\code
+?gees
+?gees
+?syev/?heev
+?syev/?heev,
+?potrf
+\endcode</td></tr>
+<tr class="alt"><td>Schur decomposition \n \c EIGEN_USE_LAPACKE \n \c EIGEN_USE_LAPACKE_STRICT </td><td>\code
+RealSchur<MatrixXd> schurR(m1);
+ComplexSchur<MatrixXcd> schurC(m1);
+\endcode</td><td>\code
+?gees
+\endcode</td></tr>
+</table>
+In the examples, m1 and m2 are dense matrices and v1 and v2 are dense vectors.
+
+*/
+
+}
diff --git a/doc/UsingIntelMKL.dox b/doc/UsingIntelMKL.dox
new file mode 100644
index 0000000..fc35c3c
--- /dev/null
+++ b/doc/UsingIntelMKL.dox
@@ -0,0 +1,113 @@
+/*
+ Copyright (c) 2011, Intel Corporation. All rights reserved.
+ Copyright (C) 2011 Gael Guennebaud <gael.guennebaud@inria.fr>
+
+ Redistribution and use in source and binary forms, with or without modification,
+ are permitted provided that the following conditions are met:
+
+ * Redistributions of source code must retain the above copyright notice, this
+ list of conditions and the following disclaimer.
+ * Redistributions in binary form must reproduce the above copyright notice,
+ this list of conditions and the following disclaimer in the documentation
+ and/or other materials provided with the distribution.
+ * Neither the name of Intel Corporation nor the names of its contributors may
+ be used to endorse or promote products derived from this software without
+ specific prior written permission.
+
+ THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
+ ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
+ WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
+ DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR
+ ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
+ (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
+ LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON
+ ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
+ (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
+ SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+
+ ********************************************************************************
+ * Content : Documentation on the use of Intel MKL through Eigen
+ ********************************************************************************
+*/
+
+namespace Eigen {
+
+/** \page TopicUsingIntelMKL Using Intel® MKL from %Eigen
+
+<!-- \section TopicUsingIntelMKL_Intro Eigen and Intel® Math Kernel Library (Intel® MKL) -->
+
+Since %Eigen version 3.1 and later, users can benefit from built-in Intel® Math Kernel Library (MKL) optimizations with an installed copy of Intel MKL 10.3 (or later).
+
+<a href="http://eigen.tuxfamily.org/Counter/redirect_to_mkl.php"> Intel MKL </a> provides highly optimized multi-threaded mathematical routines for x86-compatible architectures.
+Intel MKL is available on Linux, Mac and Windows for both Intel64 and IA32 architectures.
+
+\note
+Intel® MKL is a proprietary software and it is the responsibility of users to buy or register for community (free) Intel MKL licenses for their products. Moreover, the license of the user product has to allow linking to proprietary software that excludes any unmodified versions of the GPL.
+
+Using Intel MKL through %Eigen is easy:
+-# define the \c EIGEN_USE_MKL_ALL macro before including any %Eigen's header
+-# link your program to MKL libraries (see the <a href="http://software.intel.com/en-us/articles/intel-mkl-link-line-advisor/">MKL linking advisor</a>)
+-# on a 64bits system, you must use the LP64 interface (not the ILP64 one)
+
+When doing so, a number of %Eigen's algorithms are silently substituted with calls to Intel MKL routines.
+These substitutions apply only for \b Dynamic \b or \b large enough objects with one of the following four standard scalar types: \c float, \c double, \c complex<float>, and \c complex<double>.
+Operations on other scalar types or mixing reals and complexes will continue to use the built-in algorithms.
+
+In addition you can choose which parts will be substituted by defining one or multiple of the following macros:
+
+<table class="manual">
+<tr><td>\c EIGEN_USE_BLAS </td><td>Enables the use of external BLAS level 2 and 3 routines</td></tr>
+<tr class="alt"><td>\c EIGEN_USE_LAPACKE </td><td>Enables the use of external Lapack routines via the <a href="http://www.netlib.org/lapack/lapacke.html">Lapacke</a> C interface to Lapack</td></tr>
+<tr><td>\c EIGEN_USE_LAPACKE_STRICT </td><td>Same as \c EIGEN_USE_LAPACKE but algorithm of lower robustness are disabled. \n This currently concerns only JacobiSVD which otherwise would be replaced by \c gesvd that is less robust than Jacobi rotations.</td></tr>
+<tr class="alt"><td>\c EIGEN_USE_MKL_VML </td><td>Enables the use of Intel VML (vector operations)</td></tr>
+<tr><td>\c EIGEN_USE_MKL_ALL </td><td>Defines \c EIGEN_USE_BLAS, \c EIGEN_USE_LAPACKE, and \c EIGEN_USE_MKL_VML </td></tr>
+</table>
+
+The \c EIGEN_USE_BLAS and \c EIGEN_USE_LAPACKE* macros can be combined with \c EIGEN_USE_MKL to explicitly tell Eigen that the underlying BLAS/Lapack implementation is Intel MKL.
+The main effect is to enable MKL direct call feature (\c MKL_DIRECT_CALL).
+This may help to increase performance of some MKL BLAS (?GEMM, ?GEMV, ?TRSM, ?AXPY and ?DOT) and LAPACK (LU, Cholesky and QR) routines for very small matrices.
+MKL direct call can be disabled by defining \c EIGEN_MKL_NO_DIRECT_CALL.
+
+
+Note that the BLAS and LAPACKE backends can be enabled for any F77 compatible BLAS and LAPACK libraries. See this \link TopicUsingBlasLapack page \endlink for the details.
+
+Finally, the PARDISO sparse solver shipped with Intel MKL can be used through the \ref PardisoLU, \ref PardisoLLT and \ref PardisoLDLT classes of the \ref PardisoSupport_Module.
+
+The following table summarizes the list of functions covered by \c EIGEN_USE_MKL_VML:
+<table class="manual">
+<tr><th>Code example</th><th>MKL routines</th></tr>
+<tr><td>\code
+v2=v1.array().sin();
+v2=v1.array().asin();
+v2=v1.array().cos();
+v2=v1.array().acos();
+v2=v1.array().tan();
+v2=v1.array().exp();
+v2=v1.array().log();
+v2=v1.array().sqrt();
+v2=v1.array().square();
+v2=v1.array().pow(1.5);
+\endcode</td><td>\code
+v?Sin
+v?Asin
+v?Cos
+v?Acos
+v?Tan
+v?Exp
+v?Ln
+v?Sqrt
+v?Sqr
+v?Powx
+\endcode</td></tr>
+</table>
+In the examples, v1 and v2 are dense vectors.
+
+
+\section TopicUsingIntelMKL_Links Links
+- Intel MKL can be purchased and downloaded <a href="http://eigen.tuxfamily.org/Counter/redirect_to_mkl.php">here</a>.
+- Intel MKL is also bundled with <a href="http://software.intel.com/en-us/articles/intel-composer-xe/">Intel Composer XE</a>.
+
+
+*/
+
+}
diff --git a/doc/UsingNVCC.dox b/doc/UsingNVCC.dox
new file mode 100644
index 0000000..36beb2d
--- /dev/null
+++ b/doc/UsingNVCC.dox
@@ -0,0 +1,30 @@
+
+namespace Eigen {
+
+/** \page TopicCUDA Using Eigen in CUDA kernels
+
+Staring from CUDA 5.5 and Eigen 3.3, it is possible to use Eigen's matrices, vectors, and arrays for fixed size within CUDA kernels. This is especially useful when working on numerous but small problems. By default, when Eigen's headers are included within a .cu file compiled by nvcc most Eigen's functions and methods are prefixed by the \c __device__ \c __host__ keywords making them callable from both host and device code.
+This support can be disabled by defining \c EIGEN_NO_CUDA before including any Eigen's header.
+This might be useful to disable some warnings when a .cu file makes use of Eigen on the host side only.
+However, in both cases, host's SIMD vectorization has to be disabled in .cu files.
+It is thus \b strongly \b recommended to properly move all costly host computation from your .cu files to regular .cpp files.
+
+Known issues:
+
+ - \c nvcc with MS Visual Studio does not work (patch welcome)
+
+ - \c nvcc 5.5 with gcc-4.7 (or greater) has issues with the standard \c \<limits\> header file. To workaround this, you can add the following before including any other files:
+ \code
+ // workaround issue between gcc >= 4.7 and cuda 5.5
+ #if (defined __GNUC__) && (__GNUC__>4 || __GNUC_MINOR__>=7)
+ #undef _GLIBCXX_ATOMIC_BUILTINS
+ #undef _GLIBCXX_USE_INT128
+ #endif
+ \endcode
+
+ - On 64bits system Eigen uses \c long \c int as the default type for indexes and sizes. On CUDA device, it would make sense to default to 32 bits \c int.
+ However, to keep host and CUDA code compatible, this cannot be done automatically by %Eigen, and the user is thus required to define \c EIGEN_DEFAULT_DENSE_INDEX_TYPE to \c int throughout his code (or only for CUDA code if there is no interaction between host and CUDA code through %Eigen's object).
+
+*/
+
+}
diff --git a/doc/WrongStackAlignment.dox b/doc/WrongStackAlignment.dox
new file mode 100644
index 0000000..17d5513
--- /dev/null
+++ b/doc/WrongStackAlignment.dox
@@ -0,0 +1,56 @@
+namespace Eigen {
+
+/** \eigenManualPage TopicWrongStackAlignment Compiler making a wrong assumption on stack alignment
+
+<h4>It appears that this was a GCC bug that has been fixed in GCC 4.5.
+If you hit this issue, please upgrade to GCC 4.5 and report to us, so we can update this page.</h4>
+
+This is an issue that, so far, we met only with GCC on Windows: for instance, MinGW and TDM-GCC.
+
+By default, in a function like this,
+
+\code
+void foo()
+{
+ Eigen::Quaternionf q;
+ //...
+}
+\endcode
+
+GCC assumes that the stack is already 16-byte-aligned so that the object \a q will be created at a 16-byte-aligned location. For this reason, it doesn't take any special care to explicitly align the object \a q, as Eigen requires.
+
+The problem is that, in some particular cases, this assumption can be wrong on Windows, where the stack is only guaranteed to have 4-byte alignment. Indeed, even though GCC takes care of aligning the stack in the main function and does its best to keep it aligned, when a function is called from another thread or from a binary compiled with another compiler, the stack alignment can be corrupted. This results in the object 'q' being created at an unaligned location, making your program crash with the \ref TopicUnalignedArrayAssert "assertion on unaligned arrays". So far we found the three following solutions.
+
+
+\section sec_sol1 Local solution
+
+A local solution is to mark such a function with this attribute:
+\code
+__attribute__((force_align_arg_pointer)) void foo()
+{
+ Eigen::Quaternionf q;
+ //...
+}
+\endcode
+Read <a href="http://gcc.gnu.org/onlinedocs/gcc-4.4.0/gcc/Function-Attributes.html#Function-Attributes">this GCC documentation</a> to understand what this does. Of course this should only be done on GCC on Windows, so for portability you'll have to encapsulate this in a macro which you leave empty on other platforms. The advantage of this solution is that you can finely select which function might have a corrupted stack alignment. Of course on the downside this has to be done for every such function, so you may prefer one of the following two global solutions.
+
+
+\section sec_sol2 Global solutions
+
+A global solution is to edit your project so that when compiling with GCC on Windows, you pass this option to GCC:
+\code
+-mincoming-stack-boundary=2
+\endcode
+Explanation: this tells GCC that the stack is only required to be aligned to 2^2=4 bytes, so that GCC now knows that it really must take extra care to honor the 16 byte alignment of \ref TopicFixedSizeVectorizable "fixed-size vectorizable Eigen types" when needed.
+
+Another global solution is to pass this option to gcc:
+\code
+-mstackrealign
+\endcode
+which has the same effect than adding the \c force_align_arg_pointer attribute to all functions.
+
+These global solutions are easy to use, but note that they may slowdown your program because they lead to extra prologue/epilogue instructions for every function.
+
+*/
+
+}
diff --git a/doc/eigen_navtree_hacks.js b/doc/eigen_navtree_hacks.js
new file mode 100644
index 0000000..afb97ed
--- /dev/null
+++ b/doc/eigen_navtree_hacks.js
@@ -0,0 +1,247 @@
+
+// generate a table of contents in the side-nav based on the h1/h2 tags of the current page.
+function generate_autotoc() {
+ var headers = $("h1, h2");
+ if(headers.length > 1) {
+ var toc = $("#side-nav").append('<div id="nav-toc" class="toc"><h3>Table of contents</h3></div>');
+ toc = $("#nav-toc");
+ var footer = $("#nav-path");
+ var footerHeight = footer.height();
+ toc = toc.append('<ul></ul>');
+ toc = toc.find('ul');
+ var indices = new Array();
+ indices[0] = 0;
+ indices[1] = 0;
+
+ var h1counts = $("h1").length;
+ headers.each(function(i) {
+ var current = $(this);
+ var levelTag = current[0].tagName.charAt(1);
+ if(h1counts==0)
+ levelTag--;
+ var cur_id = current.attr("id");
+
+ indices[levelTag-1]+=1;
+ var prefix = indices[0];
+ if (levelTag >1) {
+ prefix+="."+indices[1];
+ }
+
+ // Uncomment to add number prefixes
+ // current.html(prefix + " " + current.html());
+ for(var l = levelTag; l < 2; ++l){
+ indices[l] = 0;
+ }
+
+ if(cur_id == undefined) {
+ current.attr('id', 'title' + i);
+ current.addClass('anchor');
+ toc.append("<li class='level" + levelTag + "'><a id='link" + i + "' href='#title" +
+ i + "' title='" + current.prop("tagName") + "'>" + current.text() + "</a></li>");
+ } else {
+ toc.append("<li class='level" + levelTag + "'><a id='" + cur_id + "' href='#title" +
+ i + "' title='" + current.prop("tagName") + "'>" + current.text() + "</a></li>");
+ }
+ });
+ resizeHeight();
+ }
+}
+
+
+var global_navtree_object;
+
+// Overloaded to remove links to sections/subsections
+function getNode(o, po)
+{
+ po.childrenVisited = true;
+ var l = po.childrenData.length-1;
+ for (var i in po.childrenData) {
+ var nodeData = po.childrenData[i];
+ if((!nodeData[1]) || (nodeData[1].indexOf('#')==-1)) // <- we added this line
+ po.children[i] = newNode(o, po, nodeData[0], nodeData[1], nodeData[2], i==l);
+ }
+}
+
+// Overloaded to adjust the size of the navtree wrt the toc
+function resizeHeight()
+{
+ var header = $("#top");
+ var sidenav = $("#side-nav");
+ var content = $("#doc-content");
+ var navtree = $("#nav-tree");
+ var footer = $("#nav-path");
+ var toc = $("#nav-toc");
+
+ var headerHeight = header.outerHeight();
+ var footerHeight = footer.outerHeight();
+ var tocHeight = toc.height();
+ var windowHeight = $(window).height() - headerHeight - footerHeight;
+ content.css({height:windowHeight + "px"});
+ navtree.css({height:(windowHeight-tocHeight) + "px"});
+ sidenav.css({height:windowHeight + "px"});
+}
+
+// Overloaded to save the root node into global_navtree_object
+function initNavTree(toroot,relpath)
+{
+ var o = new Object();
+ global_navtree_object = o; // <- we added this line
+ o.toroot = toroot;
+ o.node = new Object();
+ o.node.li = document.getElementById("nav-tree-contents");
+ o.node.childrenData = NAVTREE;
+ o.node.children = new Array();
+ o.node.childrenUL = document.createElement("ul");
+ o.node.getChildrenUL = function() { return o.node.childrenUL; };
+ o.node.li.appendChild(o.node.childrenUL);
+ o.node.depth = 0;
+ o.node.relpath = relpath;
+ o.node.expanded = false;
+ o.node.isLast = true;
+ o.node.plus_img = document.createElement("img");
+ o.node.plus_img.src = relpath+"ftv2pnode.png";
+ o.node.plus_img.width = 16;
+ o.node.plus_img.height = 22;
+
+ if (localStorageSupported()) {
+ var navSync = $('#nav-sync');
+ if (cachedLink()) {
+ showSyncOff(navSync,relpath);
+ navSync.removeClass('sync');
+ } else {
+ showSyncOn(navSync,relpath);
+ }
+ navSync.click(function(){ toggleSyncButton(relpath); });
+ }
+
+ navTo(o,toroot,window.location.hash,relpath);
+
+ $(window).bind('hashchange', function(){
+ if (window.location.hash && window.location.hash.length>1){
+ var a;
+ if ($(location).attr('hash')){
+ var clslink=stripPath($(location).attr('pathname'))+':'+
+ $(location).attr('hash').substring(1);
+ a=$('.item a[class$="'+clslink+'"]');
+ }
+ if (a==null || !$(a).parent().parent().hasClass('selected')){
+ $('.item').removeClass('selected');
+ $('.item').removeAttr('id');
+ }
+ var link=stripPath2($(location).attr('pathname'));
+ navTo(o,link,$(location).attr('hash'),relpath);
+ } else if (!animationInProgress) {
+ $('#doc-content').scrollTop(0);
+ $('.item').removeClass('selected');
+ $('.item').removeAttr('id');
+ navTo(o,toroot,window.location.hash,relpath);
+ }
+ })
+
+ $(window).on("load", showRoot);
+}
+
+// return false if the the node has no children at all, or has only section/subsection children
+function checkChildrenData(node) {
+ if (!(typeof(node.childrenData)==='string')) {
+ for (var i in node.childrenData) {
+ var url = node.childrenData[i][1];
+ if(url.indexOf("#")==-1)
+ return true;
+ }
+ return false;
+ }
+ return (node.childrenData);
+}
+
+// Modified to:
+// 1 - remove the root node
+// 2 - remove the section/subsection children
+function createIndent(o,domNode,node,level)
+{
+ var level=-2; // <- we replaced level=-1 by level=-2
+ var n = node;
+ while (n.parentNode) { level++; n=n.parentNode; }
+ if (checkChildrenData(node)) { // <- we modified this line to use checkChildrenData(node) instead of node.childrenData
+ var imgNode = document.createElement("span");
+ imgNode.className = 'arrow';
+ imgNode.style.paddingLeft=(16*level).toString()+'px';
+ imgNode.innerHTML=arrowRight;
+ node.plus_img = imgNode;
+ node.expandToggle = document.createElement("a");
+ node.expandToggle.href = "javascript:void(0)";
+ node.expandToggle.onclick = function() {
+ if (node.expanded) {
+ $(node.getChildrenUL()).slideUp("fast");
+ node.plus_img.innerHTML=arrowRight;
+ node.expanded = false;
+ } else {
+ expandNode(o, node, false, false);
+ }
+ }
+ node.expandToggle.appendChild(imgNode);
+ domNode.appendChild(node.expandToggle);
+ } else {
+ var span = document.createElement("span");
+ span.className = 'arrow';
+ span.style.width = 16*(level+1)+'px';
+ span.innerHTML = ' ';
+ domNode.appendChild(span);
+ }
+}
+
+// Overloaded to automatically expand the selected node
+function selectAndHighlight(hash,n)
+{
+ var a;
+ if (hash) {
+ var link=stripPath($(location).attr('pathname'))+':'+hash.substring(1);
+ a=$('.item a[class$="'+link+'"]');
+ }
+ if (a && a.length) {
+ a.parent().parent().addClass('selected');
+ a.parent().parent().attr('id','selected');
+ highlightAnchor();
+ } else if (n) {
+ $(n.itemDiv).addClass('selected');
+ $(n.itemDiv).attr('id','selected');
+ }
+ if ($('#nav-tree-contents .item:first').hasClass('selected')) {
+ $('#nav-sync').css('top','30px');
+ } else {
+ $('#nav-sync').css('top','5px');
+ }
+ expandNode(global_navtree_object, n, true, true); // <- we added this line
+ showRoot();
+}
+
+
+$(document).ready(function() {
+
+ generate_autotoc();
+
+ (function (){ // wait until the first "selected" element has been created
+ try {
+
+ // this line will triger an exception if there is no #selected element, i.e., before the tree structure is complete.
+ document.getElementById("selected").className = "item selected";
+
+ // ok, the default tree has been created, we can keep going...
+
+ // expand the "Chapters" node
+ if(window.location.href.indexOf('unsupported')==-1)
+ expandNode(global_navtree_object, global_navtree_object.node.children[0].children[2], true, true);
+ else
+ expandNode(global_navtree_object, global_navtree_object.node.children[0].children[1], true, true);
+
+ // Hide the root node "Eigen"
+ $(document.getElementsByClassName('index.html')[0]).parent().parent().css({display:"none"});
+
+ } catch (err) {
+ setTimeout(arguments.callee, 10);
+ }
+ })();
+
+ $(window).on("load", resizeHeight);
+});
+
diff --git a/doc/eigendoxy.css b/doc/eigendoxy.css
new file mode 100644
index 0000000..c746194
--- /dev/null
+++ b/doc/eigendoxy.css
@@ -0,0 +1,233 @@
+
+/******** Eigen specific CSS code ************/
+
+/**** Styles removing elements ****/
+
+/* remove the "modules|classes" link for module pages (they are already in the TOC) */
+div.summary {
+ display:none;
+}
+
+/* remove */
+div.contents hr {
+ display:none;
+}
+
+/**** ****/
+
+p, dl.warning, dl.attention, dl.note
+{
+ max-width:60em;
+ text-align:justify;
+}
+
+li {
+ max-width:55em;
+ text-align:justify;
+}
+
+img {
+ border: 0;
+}
+
+div.fragment {
+ display:table; /* this allows the element to be larger than its parent */
+ padding: 0pt;
+}
+pre.fragment {
+ border: 1px solid #cccccc;
+
+ margin: 2px 0px 2px 0px;
+ padding: 3px 5px 3px 5px;
+}
+
+
+
+/* Common style for all Eigen's tables */
+
+table.example, table.manual, table.manual-vl, table.manual-hl {
+ max-width:100%;
+ border-collapse: collapse;
+ border-style: solid;
+ border-width: 1px;
+ border-color: #cccccc;
+ font-size: 1em;
+
+ box-shadow: 5px 5px 5px rgba(0, 0, 0, 0.15);
+ -moz-box-shadow: 5px 5px 5px rgba(0, 0, 0, 0.15);
+ -webkit-box-shadow: 5px 5px 5px rgba(0, 0, 0, 0.15);
+}
+
+table.example th, table.manual th, table.manual-vl th, table.manual-hl th {
+ padding: 0.5em 0.5em 0.5em 0.5em;
+ text-align: left;
+ padding-right: 1em;
+ color: #555555;
+ background-color: #F4F4E5;
+
+ background-image: -webkit-gradient(linear,center top,center bottom,from(#FFFFFF), color-stop(0.3,#FFFFFF), color-stop(0.30,#FFFFFF), color-stop(0.98,#F4F4E5), to(#ECECDE));
+ background-image: -moz-linear-gradient(center top, #FFFFFF 0%, #FFFFFF 30%, #F4F4E5 98%, #ECECDE);
+ filter: progid:DXImageTransform.Microsoft.gradient(startColorstr='#FFFFFF', endColorstr='#F4F4E5');
+}
+
+table.example td, table.manual td, table.manual-vl td, table.manual-hl td {
+ vertical-align:top;
+ border-width: 1px;
+ border-color: #cccccc;
+}
+
+/* header of headers */
+table th.meta {
+ text-align:center;
+ font-size: 1.2em;
+ background-color:#FFFFFF;
+}
+
+/* intermediate header */
+table th.inter {
+ text-align:left;
+ background-color:#FFFFFF;
+ background-image:none;
+ border-style:solid solid solid solid;
+ border-width: 1px;
+ border-color: #cccccc;
+}
+
+/** class for example / output tables **/
+
+table.example {
+}
+
+table.example th {
+}
+
+table.example td {
+ padding: 0.5em 0.5em 0.5em 0.5em;
+ vertical-align:top;
+}
+
+/* standard class for the manual */
+
+table.manual, table.manual-vl, table.manual-hl {
+ padding: 0.2em 0em 0.5em 0em;
+}
+
+table.manual th, table.manual-vl th, table.manual-hl th {
+ margin: 0em 0em 0.3em 0em;
+}
+
+table.manual td, table.manual-vl td, table.manual-hl td {
+ padding: 0.3em 0.5em 0.3em 0.5em;
+ vertical-align:top;
+ border-width: 1px;
+}
+
+table.manual td.alt, table.manual tr.alt, table.manual-vl td.alt, table.manual-vl tr.alt {
+ background-color: #F4F4E5;
+}
+
+table.manual-vl th, table.manual-vl td, table.manual-vl td.alt {
+ border-color: #cccccc;
+ border-width: 1px;
+ border-style: none solid none solid;
+}
+
+table.manual-vl th.inter {
+ border-style: solid solid solid solid;
+}
+
+table.manual-hl td {
+ border-color: #cccccc;
+ border-width: 1px;
+ border-style: solid none solid none;
+}
+
+table td.code {
+ font-family: monospace;
+}
+
+h2 {
+ margin-top:2em;
+ border-style: none none solid none;
+ border-width: 1px;
+ border-color: #cccccc;
+}
+
+/**** Table of content in the side-nav ****/
+
+
+div.toc {
+ margin:0;
+ padding: 0.3em 0 0 0;
+ width:100%;
+ float: none;
+ border-radius:0px;
+ border-style: solid none none none;
+ max-height:50%;
+ overflow-y: scroll;
+}
+
+div.toc h3 {
+ margin-left: 0.5em;
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+}
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+}
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+ text-align: center;
+}
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+<!-- start footer part -->
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+ <a href="http://www.doxygen.org/index.html">
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+<hr class="footer"/><address class="footer"><small>
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+<meta http-equiv="X-UA-Compatible" content="IE=9"/>
+<meta name="generator" content="Doxygen $doxygenversion"/>
+<meta name="viewport" content="width=device-width, initial-scale=1"/>
+<!--BEGIN PROJECT_NAME--><title>$projectname: $title</title><!--END PROJECT_NAME-->
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+<link href="$relpath^tabs.css" rel="stylesheet" type="text/css"/>
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+$treeview
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+<div id="top"><!-- do not remove this div, it is closed by doxygen! -->
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+<!--BEGIN TITLEAREA-->
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+<table cellspacing="0" cellpadding="0">
+ <tbody>
+ <tr style="height: 56px;">
+ <!--BEGIN PROJECT_LOGO-->
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+ <!--END PROJECT_LOGO-->
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+ <td id="projectalign" style="padding-left: 0.5em;">
+ <div id="projectname"><a href="http://eigen.tuxfamily.org">$projectname</a>
+ <!--BEGIN PROJECT_NUMBER--> <span id="projectnumber">$projectnumber</span><!--END PROJECT_NUMBER-->
+ </div>
+ <!--BEGIN PROJECT_BRIEF--><div id="projectbrief">$projectbrief</div><!--END PROJECT_BRIEF-->
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+ <!--BEGIN PROJECT_BRIEF-->
+ <td id="projectalign" style="padding-left: 0.5em;">
+ <div id="projectbrief">$projectbrief</div>
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+ <!--BEGIN DISABLE_INDEX-->
+ <!--BEGIN SEARCHENGINE-->
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+ <!--END SEARCHENGINE-->
+ <!--END DISABLE_INDEX-->
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+</div>
+<!--END TITLEAREA-->
+<!-- end header part -->
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diff --git a/doc/eigendoxy_layout.xml.in b/doc/eigendoxy_layout.xml.in
new file mode 100644
index 0000000..c14b621
--- /dev/null
+++ b/doc/eigendoxy_layout.xml.in
@@ -0,0 +1,178 @@
+<?xml version="1.0"?>
+<doxygenlayout version="1.0">
+ <!-- Navigation index tabs for HTML output -->
+ <navindex>
+ <tab type="user" url="index.html" title="Overview" />
+ <tab type="user" url="@ref GettingStarted" title="Getting started" />
+ <tab type="modules" visible="yes" title="Chapters" intro=""/>
+ <tab type="mainpage" visible="yes" title=""/>
+ <tab type="classlist" visible="yes" title="" intro=""/>
+<!-- <tab type="classmembers" visible="yes" title="" intro=""/> -->
+ </navindex>
+
+ <!-- Layout definition for a class page -->
+ <class>
+ <briefdescription visible="no"/>
+ <includes visible="$SHOW_INCLUDE_FILES"/>
+ <detaileddescription title=""/>
+ <inheritancegraph visible="$CLASS_GRAPH"/>
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+ <allmemberslink visible="yes"/>
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+ <packagestaticmethods title=""/>
+ <packageattributes title=""/>
+ <packagestaticattributes title=""/>
+ <properties title=""/>
+ <events title=""/>
+ <privatetypes title=""/>
+ <privateslots title=""/>
+ <privatemethods title=""/>
+ <privatestaticmethods title=""/>
+ <privateattributes title=""/>
+ <privatestaticattributes title=""/>
+ <friends title=""/>
+ <related title="" subtitle=""/>
+ <membergroups visible="yes"/>
+ </memberdecl>
+
+ <memberdef>
+ <inlineclasses title=""/>
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+ <authorsection visible="yes"/>
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+
+ <!-- Layout definition for a namespace page -->
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+ <briefdescription visible="yes"/>
+ <memberdecl>
+ <nestednamespaces visible="yes" title=""/>
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+ <authorsection visible="yes"/>
+ </namespace>
+
+ <!-- Layout definition for a file page -->
+ <file>
+ <briefdescription visible="yes"/>
+ <includes visible="$SHOW_INCLUDE_FILES"/>
+ <includegraph visible="$INCLUDE_GRAPH"/>
+ <includedbygraph visible="$INCLUDED_BY_GRAPH"/>
+ <sourcelink visible="yes"/>
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+ <classes visible="yes" title=""/>
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+ </file>
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+ <!-- Layout definition for a group page -->
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+ <briefdescription visible="no"/>
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+ <groupgraph visible="$GROUP_GRAPHS"/>
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+ <dirs visible="yes" title=""/>
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+ </memberdecl>
+
+ <memberdef>
+ <pagedocs/>
+ <inlineclasses title=""/>
+ <defines title=""/>
+ <typedefs title=""/>
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+ <!-- Layout definition for a directory page -->
+ <directory>
+ <briefdescription visible="yes"/>
+ <directorygraph visible="yes"/>
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+ <detaileddescription title=""/>
+ </directory>
+</doxygenlayout>
diff --git a/doc/eigendoxy_tabs.css b/doc/eigendoxy_tabs.css
new file mode 100644
index 0000000..2192056
--- /dev/null
+++ b/doc/eigendoxy_tabs.css
@@ -0,0 +1,59 @@
+.tabs, .tabs2, .tabs3 {
+ background-image: url('tab_b.png');
+ width: 100%;
+ z-index: 101;
+ font-size: 13px;
+}
+
+.tabs2 {
+ font-size: 10px;
+}
+.tabs3 {
+ font-size: 9px;
+}
+
+.tablist {
+ margin: 0;
+ padding: 0;
+ display: table;
+}
+
+.tablist li {
+ float: left;
+ display: table-cell;
+ background-image: url('tab_b.png');
+ line-height: 36px;
+ list-style: none;
+}
+
+.tablist a {
+ display: block;
+ padding: 0 20px;
+ font-weight: bold;
+ background-image:url('tab_s.png');
+ background-repeat:no-repeat;
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+ color: #283A5D;
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+.tabs3 .tablist a {
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+.tablist a:hover {
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+.tablist li.current a {
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diff --git a/doc/examples/.krazy b/doc/examples/.krazy
new file mode 100644
index 0000000..00b9940
--- /dev/null
+++ b/doc/examples/.krazy
@@ -0,0 +1,2 @@
+EXCLUDE copyright
+EXCLUDE license
diff --git a/doc/examples/CMakeLists.txt b/doc/examples/CMakeLists.txt
new file mode 100644
index 0000000..dd49e3c
--- /dev/null
+++ b/doc/examples/CMakeLists.txt
@@ -0,0 +1,16 @@
+file(GLOB examples_SRCS "*.cpp")
+
+foreach(example_src ${examples_SRCS})
+ get_filename_component(example ${example_src} NAME_WE)
+ add_executable(${example} ${example_src})
+ if(EIGEN_STANDARD_LIBRARIES_TO_LINK_TO)
+ target_link_libraries(${example} ${EIGEN_STANDARD_LIBRARIES_TO_LINK_TO})
+ endif()
+ add_custom_command(
+ TARGET ${example}
+ POST_BUILD
+ COMMAND ${example}
+ ARGS >${CMAKE_CURRENT_BINARY_DIR}/${example}.out
+ )
+ add_dependencies(all_examples ${example})
+endforeach()
diff --git a/doc/examples/CustomizingEigen_Inheritance.cpp b/doc/examples/CustomizingEigen_Inheritance.cpp
new file mode 100644
index 0000000..48df64e
--- /dev/null
+++ b/doc/examples/CustomizingEigen_Inheritance.cpp
@@ -0,0 +1,30 @@
+#include <Eigen/Core>
+#include <iostream>
+
+class MyVectorType : public Eigen::VectorXd
+{
+public:
+ MyVectorType(void):Eigen::VectorXd() {}
+
+ // This constructor allows you to construct MyVectorType from Eigen expressions
+ template<typename OtherDerived>
+ MyVectorType(const Eigen::MatrixBase<OtherDerived>& other)
+ : Eigen::VectorXd(other)
+ { }
+
+ // This method allows you to assign Eigen expressions to MyVectorType
+ template<typename OtherDerived>
+ MyVectorType& operator=(const Eigen::MatrixBase <OtherDerived>& other)
+ {
+ this->Eigen::VectorXd::operator=(other);
+ return *this;
+ }
+};
+
+int main()
+{
+ MyVectorType v = MyVectorType::Ones(4);
+ v(2) += 10;
+ v = 2 * v;
+ std::cout << v.transpose() << std::endl;
+}
diff --git a/doc/examples/Cwise_erf.cpp b/doc/examples/Cwise_erf.cpp
new file mode 100644
index 0000000..9ddc57d
--- /dev/null
+++ b/doc/examples/Cwise_erf.cpp
@@ -0,0 +1,8 @@
+#include <Eigen/Core>
+#include <unsupported/Eigen/SpecialFunctions>
+#include <iostream>
+int main()
+{
+ Eigen::Array4d v(-0.5,2,0,-7);
+ std::cout << v.erf() << std::endl;
+}
diff --git a/doc/examples/Cwise_erfc.cpp b/doc/examples/Cwise_erfc.cpp
new file mode 100644
index 0000000..4b7902c
--- /dev/null
+++ b/doc/examples/Cwise_erfc.cpp
@@ -0,0 +1,8 @@
+#include <Eigen/Core>
+#include <unsupported/Eigen/SpecialFunctions>
+#include <iostream>
+int main()
+{
+ Eigen::Array4d v(-0.5,2,0,-7);
+ std::cout << v.erfc() << std::endl;
+}
diff --git a/doc/examples/Cwise_lgamma.cpp b/doc/examples/Cwise_lgamma.cpp
new file mode 100644
index 0000000..f3c9fe6
--- /dev/null
+++ b/doc/examples/Cwise_lgamma.cpp
@@ -0,0 +1,8 @@
+#include <Eigen/Core>
+#include <unsupported/Eigen/SpecialFunctions>
+#include <iostream>
+int main()
+{
+ Eigen::Array4d v(0.5,10,0,-1);
+ std::cout << v.lgamma() << std::endl;
+}
diff --git a/doc/examples/DenseBase_middleCols_int.cpp b/doc/examples/DenseBase_middleCols_int.cpp
new file mode 100644
index 0000000..d05a552
--- /dev/null
+++ b/doc/examples/DenseBase_middleCols_int.cpp
@@ -0,0 +1,12 @@
+#include <Eigen/Core>
+#include <iostream>
+
+int main()
+{
+ int const N = 5;
+ Eigen::MatrixXi A(N,N);
+ A.setRandom();
+ std::cout << "A =\n" << A << '\n' << std::endl;
+ std::cout << "A(1..3,:) =\n" << A.middleCols(1,3) << std::endl;
+ return 0;
+}
diff --git a/doc/examples/DenseBase_middleRows_int.cpp b/doc/examples/DenseBase_middleRows_int.cpp
new file mode 100644
index 0000000..8651629
--- /dev/null
+++ b/doc/examples/DenseBase_middleRows_int.cpp
@@ -0,0 +1,12 @@
+#include <Eigen/Core>
+#include <iostream>
+
+int main()
+{
+ int const N = 5;
+ Eigen::MatrixXi A(N,N);
+ A.setRandom();
+ std::cout << "A =\n" << A << '\n' << std::endl;
+ std::cout << "A(2..3,:) =\n" << A.middleRows(2,2) << std::endl;
+ return 0;
+}
diff --git a/doc/examples/DenseBase_template_int_middleCols.cpp b/doc/examples/DenseBase_template_int_middleCols.cpp
new file mode 100644
index 0000000..caefabf
--- /dev/null
+++ b/doc/examples/DenseBase_template_int_middleCols.cpp
@@ -0,0 +1,12 @@
+#include <Eigen/Core>
+#include <iostream>
+
+int main()
+{
+ int const N = 5;
+ Eigen::MatrixXi A(N,N);
+ A.setRandom();
+ std::cout << "A =\n" << A << '\n' << std::endl;
+ std::cout << "A(:,1..3) =\n" << A.middleCols<3>(1) << std::endl;
+ return 0;
+}
diff --git a/doc/examples/DenseBase_template_int_middleRows.cpp b/doc/examples/DenseBase_template_int_middleRows.cpp
new file mode 100644
index 0000000..ed5b295
--- /dev/null
+++ b/doc/examples/DenseBase_template_int_middleRows.cpp
@@ -0,0 +1,12 @@
+#include <Eigen/Core>
+#include <iostream>
+
+int main()
+{
+ int const N = 5;
+ Eigen::MatrixXi A(N,N);
+ A.setRandom();
+ std::cout << "A =\n" << A << '\n' << std::endl;
+ std::cout << "A(1..3,:) =\n" << A.middleRows<3>(1) << std::endl;
+ return 0;
+}
diff --git a/doc/examples/QuickStart_example.cpp b/doc/examples/QuickStart_example.cpp
new file mode 100644
index 0000000..7238c0c
--- /dev/null
+++ b/doc/examples/QuickStart_example.cpp
@@ -0,0 +1,14 @@
+#include <iostream>
+#include <Eigen/Dense>
+
+using Eigen::MatrixXd;
+
+int main()
+{
+ MatrixXd m(2,2);
+ m(0,0) = 3;
+ m(1,0) = 2.5;
+ m(0,1) = -1;
+ m(1,1) = m(1,0) + m(0,1);
+ std::cout << m << std::endl;
+}
diff --git a/doc/examples/QuickStart_example2_dynamic.cpp b/doc/examples/QuickStart_example2_dynamic.cpp
new file mode 100644
index 0000000..bc8d326
--- /dev/null
+++ b/doc/examples/QuickStart_example2_dynamic.cpp
@@ -0,0 +1,15 @@
+#include <iostream>
+#include <Eigen/Dense>
+
+using Eigen::MatrixXd;
+using Eigen::VectorXd;
+
+int main()
+{
+ MatrixXd m = MatrixXd::Random(3,3);
+ m = (m + MatrixXd::Constant(3,3,1.2)) * 50;
+ std::cout << "m =" << std::endl << m << std::endl;
+ VectorXd v(3);
+ v << 1, 2, 3;
+ std::cout << "m * v =" << std::endl << m * v << std::endl;
+}
diff --git a/doc/examples/QuickStart_example2_fixed.cpp b/doc/examples/QuickStart_example2_fixed.cpp
new file mode 100644
index 0000000..af6f9a9
--- /dev/null
+++ b/doc/examples/QuickStart_example2_fixed.cpp
@@ -0,0 +1,15 @@
+#include <iostream>
+#include <Eigen/Dense>
+
+using Eigen::Matrix3d;
+using Eigen::Vector3d;
+
+int main()
+{
+ Matrix3d m = Matrix3d::Random();
+ m = (m + Matrix3d::Constant(1.2)) * 50;
+ std::cout << "m =" << std::endl << m << std::endl;
+ Vector3d v(1,2,3);
+
+ std::cout << "m * v =" << std::endl << m * v << std::endl;
+}
diff --git a/doc/examples/TemplateKeyword_flexible.cpp b/doc/examples/TemplateKeyword_flexible.cpp
new file mode 100644
index 0000000..efe458b
--- /dev/null
+++ b/doc/examples/TemplateKeyword_flexible.cpp
@@ -0,0 +1,20 @@
+#include <Eigen/Dense>
+#include <iostream>
+
+template <typename Derived1, typename Derived2>
+void copyUpperTriangularPart(Eigen::MatrixBase<Derived1>& dst, const Eigen::MatrixBase<Derived2>& src)
+{
+ /* Note the 'template' keywords in the following line! */
+ dst.template triangularView<Eigen::Upper>() = src.template triangularView<Eigen::Upper>();
+}
+
+int main()
+{
+ Eigen::MatrixXi m1 = Eigen::MatrixXi::Ones(5,5);
+ Eigen::MatrixXi m2 = Eigen::MatrixXi::Random(4,4);
+ std::cout << "m2 before copy:" << std::endl;
+ std::cout << m2 << std::endl << std::endl;
+ copyUpperTriangularPart(m2, m1.topLeftCorner(4,4));
+ std::cout << "m2 after copy:" << std::endl;
+ std::cout << m2 << std::endl << std::endl;
+}
diff --git a/doc/examples/TemplateKeyword_simple.cpp b/doc/examples/TemplateKeyword_simple.cpp
new file mode 100644
index 0000000..6b946ad
--- /dev/null
+++ b/doc/examples/TemplateKeyword_simple.cpp
@@ -0,0 +1,20 @@
+#include <Eigen/Dense>
+#include <iostream>
+
+using Eigen::MatrixXf;
+
+void copyUpperTriangularPart(MatrixXf& dst, const MatrixXf& src)
+{
+ dst.triangularView<Eigen::Upper>() = src.triangularView<Eigen::Upper>();
+}
+
+int main()
+{
+ MatrixXf m1 = MatrixXf::Ones(4,4);
+ MatrixXf m2 = MatrixXf::Random(4,4);
+ std::cout << "m2 before copy:" << std::endl;
+ std::cout << m2 << std::endl << std::endl;
+ copyUpperTriangularPart(m2, m1);
+ std::cout << "m2 after copy:" << std::endl;
+ std::cout << m2 << std::endl << std::endl;
+}
diff --git a/doc/examples/TutorialInplaceLU.cpp b/doc/examples/TutorialInplaceLU.cpp
new file mode 100644
index 0000000..72bead2
--- /dev/null
+++ b/doc/examples/TutorialInplaceLU.cpp
@@ -0,0 +1,57 @@
+#include <iostream>
+struct init {
+ init() { std::cout << "[init]\n"; }
+};
+init init_obj;
+// [init]
+#include <Eigen/Dense>
+
+int main()
+{
+ Eigen::MatrixXd A(2,2);
+ A << 2, -1, 1, 3;
+ std::cout << "Here is the input matrix A before decomposition:\n" << A << "\n";
+ std::cout << "[init]\n";
+
+ std::cout << "[declaration]\n";
+ Eigen::PartialPivLU<Eigen::Ref<Eigen::MatrixXd> > lu(A);
+ std::cout << "Here is the input matrix A after decomposition:\n" << A << "\n";
+ std::cout << "[declaration]\n";
+
+ std::cout << "[matrixLU]\n";
+ std::cout << "Here is the matrix storing the L and U factors:\n" << lu.matrixLU() << "\n";
+ std::cout << "[matrixLU]\n";
+
+ std::cout << "[solve]\n";
+ Eigen::MatrixXd A0(2,2); A0 << 2, -1, 1, 3;
+ Eigen::VectorXd b(2); b << 1, 2;
+ Eigen::VectorXd x = lu.solve(b);
+ std::cout << "Residual: " << (A0 * x - b).norm() << "\n";
+ std::cout << "[solve]\n";
+
+ std::cout << "[modifyA]\n";
+ A << 3, 4, -2, 1;
+ x = lu.solve(b);
+ std::cout << "Residual: " << (A0 * x - b).norm() << "\n";
+ std::cout << "[modifyA]\n";
+
+ std::cout << "[recompute]\n";
+ A0 = A; // save A
+ lu.compute(A);
+ x = lu.solve(b);
+ std::cout << "Residual: " << (A0 * x - b).norm() << "\n";
+ std::cout << "[recompute]\n";
+
+ std::cout << "[recompute_bis0]\n";
+ Eigen::MatrixXd A1(2,2);
+ A1 << 5,-2,3,4;
+ lu.compute(A1);
+ std::cout << "Here is the input matrix A1 after decomposition:\n" << A1 << "\n";
+ std::cout << "[recompute_bis0]\n";
+
+ std::cout << "[recompute_bis1]\n";
+ x = lu.solve(b);
+ std::cout << "Residual: " << (A1 * x - b).norm() << "\n";
+ std::cout << "[recompute_bis1]\n";
+
+}
diff --git a/doc/examples/TutorialLinAlgComputeTwice.cpp b/doc/examples/TutorialLinAlgComputeTwice.cpp
new file mode 100644
index 0000000..a561f08
--- /dev/null
+++ b/doc/examples/TutorialLinAlgComputeTwice.cpp
@@ -0,0 +1,20 @@
+#include <iostream>
+#include <Eigen/Dense>
+
+int main()
+{
+ Eigen::Matrix2f A, b;
+ Eigen::LLT<Eigen::Matrix2f> llt;
+ A << 2, -1, -1, 3;
+ b << 1, 2, 3, 1;
+ std::cout << "Here is the matrix A:\n" << A << std::endl;
+ std::cout << "Here is the right hand side b:\n" << b << std::endl;
+ std::cout << "Computing LLT decomposition..." << std::endl;
+ llt.compute(A);
+ std::cout << "The solution is:\n" << llt.solve(b) << std::endl;
+ A(1,1)++;
+ std::cout << "The matrix A is now:\n" << A << std::endl;
+ std::cout << "Computing LLT decomposition..." << std::endl;
+ llt.compute(A);
+ std::cout << "The solution is now:\n" << llt.solve(b) << std::endl;
+}
diff --git a/doc/examples/TutorialLinAlgExComputeSolveError.cpp b/doc/examples/TutorialLinAlgExComputeSolveError.cpp
new file mode 100644
index 0000000..199f3f5
--- /dev/null
+++ b/doc/examples/TutorialLinAlgExComputeSolveError.cpp
@@ -0,0 +1,13 @@
+#include <iostream>
+#include <Eigen/Dense>
+
+using Eigen::MatrixXd;
+
+int main()
+{
+ MatrixXd A = MatrixXd::Random(100,100);
+ MatrixXd b = MatrixXd::Random(100,50);
+ MatrixXd x = A.fullPivLu().solve(b);
+ double relative_error = (A*x - b).norm() / b.norm(); // norm() is L2 norm
+ std::cout << "The relative error is:\n" << relative_error << std::endl;
+}
diff --git a/doc/examples/TutorialLinAlgExSolveColPivHouseholderQR.cpp b/doc/examples/TutorialLinAlgExSolveColPivHouseholderQR.cpp
new file mode 100644
index 0000000..5ee6b6a
--- /dev/null
+++ b/doc/examples/TutorialLinAlgExSolveColPivHouseholderQR.cpp
@@ -0,0 +1,14 @@
+#include <iostream>
+#include <Eigen/Dense>
+
+int main()
+{
+ Eigen::Matrix3f A;
+ Eigen::Vector3f b;
+ A << 1,2,3, 4,5,6, 7,8,10;
+ b << 3, 3, 4;
+ std::cout << "Here is the matrix A:\n" << A << std::endl;
+ std::cout << "Here is the vector b:\n" << b << std::endl;
+ Eigen::Vector3f x = A.colPivHouseholderQr().solve(b);
+ std::cout << "The solution is:\n" << x << std::endl;
+}
diff --git a/doc/examples/TutorialLinAlgExSolveLDLT.cpp b/doc/examples/TutorialLinAlgExSolveLDLT.cpp
new file mode 100644
index 0000000..82186d4
--- /dev/null
+++ b/doc/examples/TutorialLinAlgExSolveLDLT.cpp
@@ -0,0 +1,13 @@
+#include <iostream>
+#include <Eigen/Dense>
+
+int main()
+{
+ Eigen::Matrix2f A, b;
+ A << 2, -1, -1, 3;
+ b << 1, 2, 3, 1;
+ std::cout << "Here is the matrix A:\n" << A << std::endl;
+ std::cout << "Here is the right hand side b:\n" << b << std::endl;
+ Eigen::Matrix2f x = A.ldlt().solve(b);
+ std::cout << "The solution is:\n" << x << std::endl;
+}
diff --git a/doc/examples/TutorialLinAlgInverseDeterminant.cpp b/doc/examples/TutorialLinAlgInverseDeterminant.cpp
new file mode 100644
index 0000000..b31a92a
--- /dev/null
+++ b/doc/examples/TutorialLinAlgInverseDeterminant.cpp
@@ -0,0 +1,13 @@
+#include <iostream>
+#include <Eigen/Dense>
+
+int main()
+{
+ Eigen::Matrix3f A;
+ A << 1, 2, 1,
+ 2, 1, 0,
+ -1, 1, 2;
+ std::cout << "Here is the matrix A:\n" << A << std::endl;
+ std::cout << "The determinant of A is " << A.determinant() << std::endl;
+ std::cout << "The inverse of A is:\n" << A.inverse() << std::endl;
+}
diff --git a/doc/examples/TutorialLinAlgRankRevealing.cpp b/doc/examples/TutorialLinAlgRankRevealing.cpp
new file mode 100644
index 0000000..fea52ab
--- /dev/null
+++ b/doc/examples/TutorialLinAlgRankRevealing.cpp
@@ -0,0 +1,17 @@
+#include <iostream>
+#include <Eigen/Dense>
+
+int main()
+{
+ Eigen::Matrix3f A;
+ A << 1, 2, 5,
+ 2, 1, 4,
+ 3, 0, 3;
+ std::cout << "Here is the matrix A:\n" << A << std::endl;
+ Eigen::FullPivLU<Eigen::Matrix3f> lu_decomp(A);
+ std::cout << "The rank of A is " << lu_decomp.rank() << std::endl;
+ std::cout << "Here is a matrix whose columns form a basis of the null-space of A:\n"
+ << lu_decomp.kernel() << std::endl;
+ std::cout << "Here is a matrix whose columns form a basis of the column-space of A:\n"
+ << lu_decomp.image(A) << std::endl; // yes, have to pass the original A
+}
diff --git a/doc/examples/TutorialLinAlgSVDSolve.cpp b/doc/examples/TutorialLinAlgSVDSolve.cpp
new file mode 100644
index 0000000..04cbe1b
--- /dev/null
+++ b/doc/examples/TutorialLinAlgSVDSolve.cpp
@@ -0,0 +1,12 @@
+#include <iostream>
+#include <Eigen/Dense>
+
+int main()
+{
+ Eigen::MatrixXf A = Eigen::MatrixXf::Random(3, 2);
+ std::cout << "Here is the matrix A:\n" << A << std::endl;
+ Eigen::VectorXf b = Eigen::VectorXf::Random(3);
+ std::cout << "Here is the right hand side b:\n" << b << std::endl;
+ std::cout << "The least-squares solution is:\n"
+ << A.template bdcSvd<Eigen::ComputeThinU | Eigen::ComputeThinV>().solve(b) << std::endl;
+}
diff --git a/doc/examples/TutorialLinAlgSelfAdjointEigenSolver.cpp b/doc/examples/TutorialLinAlgSelfAdjointEigenSolver.cpp
new file mode 100644
index 0000000..fcf2f33
--- /dev/null
+++ b/doc/examples/TutorialLinAlgSelfAdjointEigenSolver.cpp
@@ -0,0 +1,15 @@
+#include <iostream>
+#include <Eigen/Dense>
+
+int main()
+{
+ Eigen::Matrix2f A;
+ A << 1, 2, 2, 3;
+ std::cout << "Here is the matrix A:\n" << A << std::endl;
+ Eigen::SelfAdjointEigenSolver<Eigen::Matrix2f> eigensolver(A);
+ if (eigensolver.info() != Eigen::Success) abort();
+ std::cout << "The eigenvalues of A are:\n" << eigensolver.eigenvalues() << std::endl;
+ std::cout << "Here's a matrix whose columns are eigenvectors of A \n"
+ << "corresponding to these eigenvalues:\n"
+ << eigensolver.eigenvectors() << std::endl;
+}
diff --git a/doc/examples/TutorialLinAlgSetThreshold.cpp b/doc/examples/TutorialLinAlgSetThreshold.cpp
new file mode 100644
index 0000000..e1335e7
--- /dev/null
+++ b/doc/examples/TutorialLinAlgSetThreshold.cpp
@@ -0,0 +1,13 @@
+#include <iostream>
+#include <Eigen/Dense>
+
+int main()
+{
+ Eigen::Matrix2d A;
+ A << 2, 1,
+ 2, 0.9999999999;
+ Eigen::FullPivLU<Eigen::Matrix2d> lu(A);
+ std::cout << "By default, the rank of A is found to be " << lu.rank() << std::endl;
+ lu.setThreshold(1e-5);
+ std::cout << "With threshold 1e-5, the rank of A is found to be " << lu.rank() << std::endl;
+}
diff --git a/doc/examples/Tutorial_ArrayClass_accessors.cpp b/doc/examples/Tutorial_ArrayClass_accessors.cpp
new file mode 100644
index 0000000..0db52a3
--- /dev/null
+++ b/doc/examples/Tutorial_ArrayClass_accessors.cpp
@@ -0,0 +1,21 @@
+#include <Eigen/Dense>
+#include <iostream>
+
+int main()
+{
+ Eigen::ArrayXXf m(2,2);
+
+ // assign some values coefficient by coefficient
+ m(0,0) = 1.0; m(0,1) = 2.0;
+ m(1,0) = 3.0; m(1,1) = m(0,1) + m(1,0);
+
+ // print values to standard output
+ std::cout << m << std::endl << std::endl;
+
+ // using the comma-initializer is also allowed
+ m << 1.0,2.0,
+ 3.0,4.0;
+
+ // print values to standard output
+ std::cout << m << std::endl;
+}
diff --git a/doc/examples/Tutorial_ArrayClass_addition.cpp b/doc/examples/Tutorial_ArrayClass_addition.cpp
new file mode 100644
index 0000000..4a407a7
--- /dev/null
+++ b/doc/examples/Tutorial_ArrayClass_addition.cpp
@@ -0,0 +1,20 @@
+#include <Eigen/Dense>
+#include <iostream>
+
+int main()
+{
+ Eigen::ArrayXXf a(3,3);
+ Eigen::ArrayXXf b(3,3);
+ a << 1,2,3,
+ 4,5,6,
+ 7,8,9;
+ b << 1,2,3,
+ 1,2,3,
+ 1,2,3;
+
+ // Adding two arrays
+ std::cout << "a + b = " << std::endl << a + b << std::endl << std::endl;
+
+ // Subtracting a scalar from an array
+ std::cout << "a - 2 = " << std::endl << a - 2 << std::endl;
+}
diff --git a/doc/examples/Tutorial_ArrayClass_cwise_other.cpp b/doc/examples/Tutorial_ArrayClass_cwise_other.cpp
new file mode 100644
index 0000000..12483f3
--- /dev/null
+++ b/doc/examples/Tutorial_ArrayClass_cwise_other.cpp
@@ -0,0 +1,16 @@
+#include <Eigen/Dense>
+#include <iostream>
+
+int main()
+{
+ Eigen::ArrayXf a = Eigen::ArrayXf::Random(5);
+ a *= 2;
+ std::cout << "a =" << std::endl
+ << a << std::endl;
+ std::cout << "a.abs() =" << std::endl
+ << a.abs() << std::endl;
+ std::cout << "a.abs().sqrt() =" << std::endl
+ << a.abs().sqrt() << std::endl;
+ std::cout << "a.min(a.abs().sqrt()) =" << std::endl
+ << a.min(a.abs().sqrt()) << std::endl;
+}
diff --git a/doc/examples/Tutorial_ArrayClass_interop.cpp b/doc/examples/Tutorial_ArrayClass_interop.cpp
new file mode 100644
index 0000000..c9a8352
--- /dev/null
+++ b/doc/examples/Tutorial_ArrayClass_interop.cpp
@@ -0,0 +1,21 @@
+#include <Eigen/Dense>
+#include <iostream>
+
+using Eigen::MatrixXf;
+
+int main()
+{
+ MatrixXf m(2,2);
+ MatrixXf n(2,2);
+ MatrixXf result(2,2);
+
+ m << 1,2,
+ 3,4;
+ n << 5,6,
+ 7,8;
+
+ result = (m.array() + 4).matrix() * m;
+ std::cout << "-- Combination 1: --\n" << result << "\n\n";
+ result = (m.array() * n.array()).matrix() * m;
+ std::cout << "-- Combination 2: --\n" << result << "\n\n";
+}
diff --git a/doc/examples/Tutorial_ArrayClass_interop_matrix.cpp b/doc/examples/Tutorial_ArrayClass_interop_matrix.cpp
new file mode 100644
index 0000000..07ec9b0
--- /dev/null
+++ b/doc/examples/Tutorial_ArrayClass_interop_matrix.cpp
@@ -0,0 +1,25 @@
+#include <Eigen/Dense>
+#include <iostream>
+
+using Eigen::MatrixXf;
+
+int main()
+{
+ MatrixXf m(2,2);
+ MatrixXf n(2,2);
+ MatrixXf result(2,2);
+
+ m << 1,2,
+ 3,4;
+ n << 5,6,
+ 7,8;
+
+ result = m * n;
+ std::cout << "-- Matrix m*n: --\n" << result << "\n\n";
+ result = m.array() * n.array();
+ std::cout << "-- Array m*n: --\n" << result << "\n\n";
+ result = m.cwiseProduct(n);
+ std::cout << "-- With cwiseProduct: --\n" << result << "\n\n";
+ result = m.array() + 4;
+ std::cout << "-- Array m + 4: --\n" << result << "\n\n";
+}
diff --git a/doc/examples/Tutorial_ArrayClass_mult.cpp b/doc/examples/Tutorial_ArrayClass_mult.cpp
new file mode 100644
index 0000000..bada36c
--- /dev/null
+++ b/doc/examples/Tutorial_ArrayClass_mult.cpp
@@ -0,0 +1,13 @@
+#include <Eigen/Dense>
+#include <iostream>
+
+int main()
+{
+ Eigen::ArrayXXf a(2,2);
+ Eigen::ArrayXXf b(2,2);
+ a << 1,2,
+ 3,4;
+ b << 5,6,
+ 7,8;
+ std::cout << "a * b = " << std::endl << a * b << std::endl;
+}
diff --git a/doc/examples/Tutorial_BlockOperations_block_assignment.cpp b/doc/examples/Tutorial_BlockOperations_block_assignment.cpp
new file mode 100644
index 0000000..26ad478
--- /dev/null
+++ b/doc/examples/Tutorial_BlockOperations_block_assignment.cpp
@@ -0,0 +1,15 @@
+#include <Eigen/Dense>
+#include <iostream>
+
+int main()
+{
+ Eigen::Array22f m;
+ m << 1,2,
+ 3,4;
+ Eigen::Array44f a = Eigen::Array44f::Constant(0.6);
+ std::cout << "Here is the array a:\n" << a << "\n\n";
+ a.block<2,2>(1,1) = m;
+ std::cout << "Here is now a with m copied into its central 2x2 block:\n" << a << "\n\n";
+ a.block(0,0,2,3) = a.block(2,1,2,3);
+ std::cout << "Here is now a with bottom-right 2x3 block copied into top-left 2x3 block:\n" << a << "\n\n";
+}
diff --git a/doc/examples/Tutorial_BlockOperations_colrow.cpp b/doc/examples/Tutorial_BlockOperations_colrow.cpp
new file mode 100644
index 0000000..2e7eb00
--- /dev/null
+++ b/doc/examples/Tutorial_BlockOperations_colrow.cpp
@@ -0,0 +1,17 @@
+#include <Eigen/Dense>
+#include <iostream>
+
+using namespace std;
+
+int main()
+{
+ Eigen::MatrixXf m(3,3);
+ m << 1,2,3,
+ 4,5,6,
+ 7,8,9;
+ cout << "Here is the matrix m:" << endl << m << endl;
+ cout << "2nd Row: " << m.row(1) << endl;
+ m.col(2) += 3 * m.col(0);
+ cout << "After adding 3 times the first column into the third column, the matrix m is:\n";
+ cout << m << endl;
+}
diff --git a/doc/examples/Tutorial_BlockOperations_corner.cpp b/doc/examples/Tutorial_BlockOperations_corner.cpp
new file mode 100644
index 0000000..3a31507
--- /dev/null
+++ b/doc/examples/Tutorial_BlockOperations_corner.cpp
@@ -0,0 +1,17 @@
+#include <Eigen/Dense>
+#include <iostream>
+
+using namespace std;
+
+int main()
+{
+ Eigen::Matrix4f m;
+ m << 1, 2, 3, 4,
+ 5, 6, 7, 8,
+ 9, 10,11,12,
+ 13,14,15,16;
+ cout << "m.leftCols(2) =" << endl << m.leftCols(2) << endl << endl;
+ cout << "m.bottomRows<2>() =" << endl << m.bottomRows<2>() << endl << endl;
+ m.topLeftCorner(1,3) = m.bottomRightCorner(3,1).transpose();
+ cout << "After assignment, m = " << endl << m << endl;
+}
diff --git a/doc/examples/Tutorial_BlockOperations_print_block.cpp b/doc/examples/Tutorial_BlockOperations_print_block.cpp
new file mode 100644
index 0000000..edea4ae
--- /dev/null
+++ b/doc/examples/Tutorial_BlockOperations_print_block.cpp
@@ -0,0 +1,20 @@
+#include <Eigen/Dense>
+#include <iostream>
+
+using namespace std;
+
+int main()
+{
+ Eigen::MatrixXf m(4,4);
+ m << 1, 2, 3, 4,
+ 5, 6, 7, 8,
+ 9,10,11,12,
+ 13,14,15,16;
+ cout << "Block in the middle" << endl;
+ cout << m.block<2,2>(1,1) << endl << endl;
+ for (int i = 1; i <= 3; ++i)
+ {
+ cout << "Block of size " << i << "x" << i << endl;
+ cout << m.block(0,0,i,i) << endl << endl;
+ }
+}
diff --git a/doc/examples/Tutorial_BlockOperations_vector.cpp b/doc/examples/Tutorial_BlockOperations_vector.cpp
new file mode 100644
index 0000000..4a0b023
--- /dev/null
+++ b/doc/examples/Tutorial_BlockOperations_vector.cpp
@@ -0,0 +1,14 @@
+#include <Eigen/Dense>
+#include <iostream>
+
+using namespace std;
+
+int main()
+{
+ Eigen::ArrayXf v(6);
+ v << 1, 2, 3, 4, 5, 6;
+ cout << "v.head(3) =" << endl << v.head(3) << endl << endl;
+ cout << "v.tail<3>() = " << endl << v.tail<3>() << endl << endl;
+ v.segment(1,4) *= 2;
+ cout << "after 'v.segment(1,4) *= 2', v =" << endl << v << endl;
+}
diff --git a/doc/examples/Tutorial_PartialLU_solve.cpp b/doc/examples/Tutorial_PartialLU_solve.cpp
new file mode 100644
index 0000000..ca72c99
--- /dev/null
+++ b/doc/examples/Tutorial_PartialLU_solve.cpp
@@ -0,0 +1,15 @@
+#include <Eigen/Core>
+#include <Eigen/LU>
+#include <iostream>
+
+int main()
+{
+ Eigen::Matrix3f A;
+ Eigen::Vector3f b;
+ A << 1,2,3, 4,5,6, 7,8,10;
+ b << 3, 3, 4;
+ std::cout << "Here is the matrix A:" << std::endl << A << std::endl;
+ std::cout << "Here is the vector b:" << std::endl << b << std::endl;
+ Eigen::Vector3f x = A.lu().solve(b);
+ std::cout << "The solution is:" << std::endl << x << std::endl;
+}
diff --git a/doc/examples/Tutorial_ReductionsVisitorsBroadcasting_broadcast_1nn.cpp b/doc/examples/Tutorial_ReductionsVisitorsBroadcasting_broadcast_1nn.cpp
new file mode 100644
index 0000000..8ef06be
--- /dev/null
+++ b/doc/examples/Tutorial_ReductionsVisitorsBroadcasting_broadcast_1nn.cpp
@@ -0,0 +1,21 @@
+#include <iostream>
+#include <Eigen/Dense>
+
+int main()
+{
+ Eigen::MatrixXf m(2,4);
+ Eigen::VectorXf v(2);
+
+ m << 1, 23, 6, 9,
+ 3, 11, 7, 2;
+
+ v << 2,
+ 3;
+
+ Eigen::Index index;
+ // find nearest neighbour
+ (m.colwise() - v).colwise().squaredNorm().minCoeff(&index);
+
+ std::cout << "Nearest neighbour is column " << index << ":" << std::endl;
+ std::cout << m.col(index) << std::endl;
+}
diff --git a/doc/examples/Tutorial_ReductionsVisitorsBroadcasting_broadcast_simple.cpp b/doc/examples/Tutorial_ReductionsVisitorsBroadcasting_broadcast_simple.cpp
new file mode 100644
index 0000000..e6c87c6
--- /dev/null
+++ b/doc/examples/Tutorial_ReductionsVisitorsBroadcasting_broadcast_simple.cpp
@@ -0,0 +1,21 @@
+#include <iostream>
+#include <Eigen/Dense>
+
+using namespace std;
+int main()
+{
+ Eigen::MatrixXf mat(2,4);
+ Eigen::VectorXf v(2);
+
+ mat << 1, 2, 6, 9,
+ 3, 1, 7, 2;
+
+ v << 0,
+ 1;
+
+ //add v to each column of m
+ mat.colwise() += v;
+
+ std::cout << "Broadcasting result: " << std::endl;
+ std::cout << mat << std::endl;
+}
diff --git a/doc/examples/Tutorial_ReductionsVisitorsBroadcasting_broadcast_simple_rowwise.cpp b/doc/examples/Tutorial_ReductionsVisitorsBroadcasting_broadcast_simple_rowwise.cpp
new file mode 100644
index 0000000..d87c96a
--- /dev/null
+++ b/doc/examples/Tutorial_ReductionsVisitorsBroadcasting_broadcast_simple_rowwise.cpp
@@ -0,0 +1,20 @@
+#include <iostream>
+#include <Eigen/Dense>
+
+using namespace std;
+int main()
+{
+ Eigen::MatrixXf mat(2,4);
+ Eigen::VectorXf v(4);
+
+ mat << 1, 2, 6, 9,
+ 3, 1, 7, 2;
+
+ v << 0,1,2,3;
+
+ //add v to each row of m
+ mat.rowwise() += v.transpose();
+
+ std::cout << "Broadcasting result: " << std::endl;
+ std::cout << mat << std::endl;
+}
diff --git a/doc/examples/Tutorial_ReductionsVisitorsBroadcasting_colwise.cpp b/doc/examples/Tutorial_ReductionsVisitorsBroadcasting_colwise.cpp
new file mode 100644
index 0000000..df68256
--- /dev/null
+++ b/doc/examples/Tutorial_ReductionsVisitorsBroadcasting_colwise.cpp
@@ -0,0 +1,13 @@
+#include <iostream>
+#include <Eigen/Dense>
+
+using namespace std;
+int main()
+{
+ Eigen::MatrixXf mat(2,4);
+ mat << 1, 2, 6, 9,
+ 3, 1, 7, 2;
+
+ std::cout << "Column's maximum: " << std::endl
+ << mat.colwise().maxCoeff() << std::endl;
+}
diff --git a/doc/examples/Tutorial_ReductionsVisitorsBroadcasting_maxnorm.cpp b/doc/examples/Tutorial_ReductionsVisitorsBroadcasting_maxnorm.cpp
new file mode 100644
index 0000000..b5d88c3
--- /dev/null
+++ b/doc/examples/Tutorial_ReductionsVisitorsBroadcasting_maxnorm.cpp
@@ -0,0 +1,18 @@
+#include <iostream>
+#include <Eigen/Dense>
+
+int main()
+{
+ Eigen::MatrixXf mat(2,4);
+ mat << 1, 2, 6, 9,
+ 3, 1, 7, 2;
+
+ Eigen::Index maxIndex;
+ float maxNorm = mat.colwise().sum().maxCoeff(&maxIndex);
+
+ std::cout << "Maximum sum at position " << maxIndex << std::endl;
+
+ std::cout << "The corresponding vector is: " << std::endl;
+ std::cout << mat.col( maxIndex ) << std::endl;
+ std::cout << "And its sum is is: " << maxNorm << std::endl;
+}
diff --git a/doc/examples/Tutorial_ReductionsVisitorsBroadcasting_reductions_bool.cpp b/doc/examples/Tutorial_ReductionsVisitorsBroadcasting_reductions_bool.cpp
new file mode 100644
index 0000000..7b89bcf
--- /dev/null
+++ b/doc/examples/Tutorial_ReductionsVisitorsBroadcasting_reductions_bool.cpp
@@ -0,0 +1,18 @@
+#include <Eigen/Dense>
+#include <iostream>
+
+int main()
+{
+ Eigen::ArrayXXf a(2,2);
+
+ a << 1,2,
+ 3,4;
+
+ std::cout << "(a > 0).all() = " << (a > 0).all() << std::endl;
+ std::cout << "(a > 0).any() = " << (a > 0).any() << std::endl;
+ std::cout << "(a > 0).count() = " << (a > 0).count() << std::endl;
+ std::cout << std::endl;
+ std::cout << "(a > 2).all() = " << (a > 2).all() << std::endl;
+ std::cout << "(a > 2).any() = " << (a > 2).any() << std::endl;
+ std::cout << "(a > 2).count() = " << (a > 2).count() << std::endl;
+}
diff --git a/doc/examples/Tutorial_ReductionsVisitorsBroadcasting_reductions_norm.cpp b/doc/examples/Tutorial_ReductionsVisitorsBroadcasting_reductions_norm.cpp
new file mode 100644
index 0000000..7519137
--- /dev/null
+++ b/doc/examples/Tutorial_ReductionsVisitorsBroadcasting_reductions_norm.cpp
@@ -0,0 +1,25 @@
+#include <Eigen/Dense>
+#include <iostream>
+
+int main()
+{
+ Eigen::VectorXf v(2);
+ Eigen::MatrixXf m(2,2), n(2,2);
+
+ v << -1,
+ 2;
+
+ m << 1,-2,
+ -3,4;
+
+ std::cout << "v.squaredNorm() = " << v.squaredNorm() << std::endl;
+ std::cout << "v.norm() = " << v.norm() << std::endl;
+ std::cout << "v.lpNorm<1>() = " << v.lpNorm<1>() << std::endl;
+ std::cout << "v.lpNorm<Infinity>() = " << v.lpNorm<Eigen::Infinity>() << std::endl;
+
+ std::cout << std::endl;
+ std::cout << "m.squaredNorm() = " << m.squaredNorm() << std::endl;
+ std::cout << "m.norm() = " << m.norm() << std::endl;
+ std::cout << "m.lpNorm<1>() = " << m.lpNorm<1>() << std::endl;
+ std::cout << "m.lpNorm<Infinity>() = " << m.lpNorm<Eigen::Infinity>() << std::endl;
+}
diff --git a/doc/examples/Tutorial_ReductionsVisitorsBroadcasting_reductions_operatornorm.cpp b/doc/examples/Tutorial_ReductionsVisitorsBroadcasting_reductions_operatornorm.cpp
new file mode 100644
index 0000000..8faa5a1
--- /dev/null
+++ b/doc/examples/Tutorial_ReductionsVisitorsBroadcasting_reductions_operatornorm.cpp
@@ -0,0 +1,15 @@
+#include <Eigen/Dense>
+#include <iostream>
+
+int main()
+{
+ Eigen::MatrixXf m(2,2);
+ m << 1,-2,
+ -3,4;
+
+ std::cout << "1-norm(m) = " << m.cwiseAbs().colwise().sum().maxCoeff()
+ << " == " << m.colwise().lpNorm<1>().maxCoeff() << std::endl;
+
+ std::cout << "infty-norm(m) = " << m.cwiseAbs().rowwise().sum().maxCoeff()
+ << " == " << m.rowwise().lpNorm<1>().maxCoeff() << std::endl;
+}
diff --git a/doc/examples/Tutorial_ReductionsVisitorsBroadcasting_rowwise.cpp b/doc/examples/Tutorial_ReductionsVisitorsBroadcasting_rowwise.cpp
new file mode 100644
index 0000000..80427c9
--- /dev/null
+++ b/doc/examples/Tutorial_ReductionsVisitorsBroadcasting_rowwise.cpp
@@ -0,0 +1,13 @@
+#include <iostream>
+#include <Eigen/Dense>
+
+using namespace std;
+int main()
+{
+ Eigen::MatrixXf mat(2,4);
+ mat << 1, 2, 6, 9,
+ 3, 1, 7, 2;
+
+ std::cout << "Row's maximum: " << std::endl
+ << mat.rowwise().maxCoeff() << std::endl;
+}
diff --git a/doc/examples/Tutorial_ReductionsVisitorsBroadcasting_visitors.cpp b/doc/examples/Tutorial_ReductionsVisitorsBroadcasting_visitors.cpp
new file mode 100644
index 0000000..bd294bd
--- /dev/null
+++ b/doc/examples/Tutorial_ReductionsVisitorsBroadcasting_visitors.cpp
@@ -0,0 +1,23 @@
+#include <iostream>
+#include <Eigen/Dense>
+
+int main()
+{
+ Eigen::MatrixXf m(2,2);
+
+ m << 1, 2,
+ 3, 4;
+
+ //get location of maximum
+ Eigen::Index maxRow, maxCol;
+ float max = m.maxCoeff(&maxRow, &maxCol);
+
+ //get location of minimum
+ Eigen::Index minRow, minCol;
+ float min = m.minCoeff(&minRow, &minCol);
+
+ std::cout << "Max: " << max << ", at: " <<
+ maxRow << "," << maxCol << std::endl;
+ std:: cout << "Min: " << min << ", at: " <<
+ minRow << "," << minCol << std::endl;
+}
diff --git a/doc/examples/Tutorial_simple_example_dynamic_size.cpp b/doc/examples/Tutorial_simple_example_dynamic_size.cpp
new file mode 100644
index 0000000..796bd87
--- /dev/null
+++ b/doc/examples/Tutorial_simple_example_dynamic_size.cpp
@@ -0,0 +1,20 @@
+#include <Eigen/Core>
+#include <iostream>
+
+int main()
+{
+ for (int size=1; size<=4; ++size)
+ {
+ Eigen::MatrixXi m(size,size+1); // a (size)x(size+1)-matrix of int's
+ for (int j=0; j<m.cols(); ++j) // loop over columns
+ for (int i=0; i<m.rows(); ++i) // loop over rows
+ m(i,j) = i+j*size; // to access matrix coefficients,
+ // use operator()(int,int)
+ std::cout << m << "\n\n";
+ }
+
+ Eigen::VectorXf v(4); // a vector of 4 float's
+ // to access vector coefficients, use either operator () or operator []
+ v[0] = 1; v[1] = 2; v(2) = 3; v(3) = 4;
+ std::cout << "\nv:\n" << v << std::endl;
+}
diff --git a/doc/examples/Tutorial_simple_example_fixed_size.cpp b/doc/examples/Tutorial_simple_example_fixed_size.cpp
new file mode 100644
index 0000000..99a974d
--- /dev/null
+++ b/doc/examples/Tutorial_simple_example_fixed_size.cpp
@@ -0,0 +1,13 @@
+#include <Eigen/Core>
+#include <iostream>
+
+int main()
+{
+ Eigen::Matrix3f m3;
+ m3 << 1, 2, 3, 4, 5, 6, 7, 8, 9;
+ Eigen::Matrix4f m4 = Eigen::Matrix4f::Identity();
+ Eigen::Vector4i v4(1, 2, 3, 4);
+
+ std::cout << "m3\n" << m3 << "\nm4:\n"
+ << m4 << "\nv4:\n" << v4 << std::endl;
+}
diff --git a/doc/examples/class_Block.cpp b/doc/examples/class_Block.cpp
new file mode 100644
index 0000000..9ace0da
--- /dev/null
+++ b/doc/examples/class_Block.cpp
@@ -0,0 +1,25 @@
+#include <Eigen/Core>
+#include <iostream>
+
+template<typename Derived>
+Eigen::Block<Derived>
+topLeftCorner(Eigen::MatrixBase<Derived>& m, int rows, int cols)
+{
+ return Eigen::Block<Derived>(m.derived(), 0, 0, rows, cols);
+}
+
+template<typename Derived>
+const Eigen::Block<const Derived>
+topLeftCorner(const Eigen::MatrixBase<Derived>& m, int rows, int cols)
+{
+ return Eigen::Block<const Derived>(m.derived(), 0, 0, rows, cols);
+}
+
+int main(int, char**)
+{
+ Eigen::Matrix4d m = Eigen::Matrix4d::Identity();
+ std::cout << topLeftCorner(4*m, 2, 3) << std::endl; // calls the const version
+ topLeftCorner(m, 2, 3) *= 5; // calls the non-const version
+ std::cout << "Now the matrix m is:" << std::endl << m << std::endl;
+ return 0;
+}
diff --git a/doc/examples/class_CwiseBinaryOp.cpp b/doc/examples/class_CwiseBinaryOp.cpp
new file mode 100644
index 0000000..973befd
--- /dev/null
+++ b/doc/examples/class_CwiseBinaryOp.cpp
@@ -0,0 +1,17 @@
+#include <Eigen/Core>
+#include <iostream>
+
+using Eigen::Matrix4d;
+
+// define a custom template binary functor
+template<typename Scalar> struct MakeComplexOp {
+ typedef std::complex<Scalar> result_type;
+ result_type operator()(const Scalar& a, const Scalar& b) const { return result_type(a,b); }
+};
+
+int main(int, char**)
+{
+ Matrix4d m1 = Matrix4d::Random(), m2 = Matrix4d::Random();
+ std::cout << m1.binaryExpr(m2, MakeComplexOp<double>()) << std::endl;
+ return 0;
+}
diff --git a/doc/examples/class_CwiseUnaryOp.cpp b/doc/examples/class_CwiseUnaryOp.cpp
new file mode 100644
index 0000000..6c65f2e
--- /dev/null
+++ b/doc/examples/class_CwiseUnaryOp.cpp
@@ -0,0 +1,17 @@
+#include <Eigen/Core>
+#include <iostream>
+
+// define a custom template unary functor
+template<typename Scalar>
+struct CwiseClampOp {
+ CwiseClampOp(const Scalar& inf, const Scalar& sup) : m_inf(inf), m_sup(sup) {}
+ const Scalar operator()(const Scalar& x) const { return x<m_inf ? m_inf : (x>m_sup ? m_sup : x); }
+ Scalar m_inf, m_sup;
+};
+
+int main(int, char**)
+{
+ Eigen::Matrix4d m1 = Eigen::Matrix4d::Random();
+ std::cout << m1 << std::endl << "becomes: " << std::endl << m1.unaryExpr(CwiseClampOp<double>(-0.5,0.5)) << std::endl;
+ return 0;
+}
diff --git a/doc/examples/class_CwiseUnaryOp_ptrfun.cpp b/doc/examples/class_CwiseUnaryOp_ptrfun.cpp
new file mode 100644
index 0000000..e97095e
--- /dev/null
+++ b/doc/examples/class_CwiseUnaryOp_ptrfun.cpp
@@ -0,0 +1,18 @@
+#include <Eigen/Core>
+#include <iostream>
+
+// define function to be applied coefficient-wise
+double ramp(double x)
+{
+ if (x > 0)
+ return x;
+ else
+ return 0;
+}
+
+int main(int, char**)
+{
+ Eigen::Matrix4d m1 = Eigen::Matrix4d::Random();
+ std::cout << m1 << std::endl << "becomes: " << std::endl << m1.unaryExpr(std::ptr_fun(ramp)) << std::endl;
+ return 0;
+}
diff --git a/doc/examples/class_FixedBlock.cpp b/doc/examples/class_FixedBlock.cpp
new file mode 100644
index 0000000..4bb2d44
--- /dev/null
+++ b/doc/examples/class_FixedBlock.cpp
@@ -0,0 +1,25 @@
+#include <Eigen/Core>
+#include <iostream>
+
+template<typename Derived>
+Eigen::Block<Derived, 2, 2>
+topLeft2x2Corner(Eigen::MatrixBase<Derived>& m)
+{
+ return Eigen::Block<Derived, 2, 2>(m.derived(), 0, 0);
+}
+
+template<typename Derived>
+const Eigen::Block<const Derived, 2, 2>
+topLeft2x2Corner(const Eigen::MatrixBase<Derived>& m)
+{
+ return Eigen::Block<const Derived, 2, 2>(m.derived(), 0, 0);
+}
+
+int main(int, char**)
+{
+ Eigen::Matrix3d m = Eigen::Matrix3d::Identity();
+ std::cout << topLeft2x2Corner(4*m) << std::endl; // calls the const version
+ topLeft2x2Corner(m) *= 2; // calls the non-const version
+ std::cout << "Now the matrix m is:" << std::endl << m << std::endl;
+ return 0;
+}
diff --git a/doc/examples/class_FixedReshaped.cpp b/doc/examples/class_FixedReshaped.cpp
new file mode 100644
index 0000000..be7069d
--- /dev/null
+++ b/doc/examples/class_FixedReshaped.cpp
@@ -0,0 +1,20 @@
+#include <Eigen/Core>
+#include <iostream>
+
+template<typename Derived>
+Eigen::Reshaped<Derived, 4, 2>
+reshape_helper(Eigen::MatrixBase<Derived>& m)
+{
+ return Eigen::Reshaped<Derived, 4, 2>(m.derived());
+}
+
+int main(int, char**)
+{
+ Eigen::MatrixXd m(2, 4);
+ m << 1, 2, 3, 4,
+ 5, 6, 7, 8;
+ Eigen::MatrixXd n = reshape_helper(m);
+ std::cout << "matrix m is:" << std::endl << m << std::endl;
+ std::cout << "matrix n is:" << std::endl << n << std::endl;
+ return 0;
+}
diff --git a/doc/examples/class_FixedVectorBlock.cpp b/doc/examples/class_FixedVectorBlock.cpp
new file mode 100644
index 0000000..eed3007
--- /dev/null
+++ b/doc/examples/class_FixedVectorBlock.cpp
@@ -0,0 +1,25 @@
+#include <Eigen/Core>
+#include <iostream>
+
+template<typename Derived>
+Eigen::VectorBlock<Derived, 2>
+firstTwo(Eigen::MatrixBase<Derived>& v)
+{
+ return Eigen::VectorBlock<Derived, 2>(v.derived(), 0);
+}
+
+template<typename Derived>
+const Eigen::VectorBlock<const Derived, 2>
+firstTwo(const Eigen::MatrixBase<Derived>& v)
+{
+ return Eigen::VectorBlock<const Derived, 2>(v.derived(), 0);
+}
+
+int main(int, char**)
+{
+ Eigen::Matrix<int,1,6> v; v << 1,2,3,4,5,6;
+ std::cout << firstTwo(4*v) << std::endl; // calls the const version
+ firstTwo(v) *= 2; // calls the non-const version
+ std::cout << "Now the vector v is:" << std::endl << v << std::endl;
+ return 0;
+}
diff --git a/doc/examples/class_Reshaped.cpp b/doc/examples/class_Reshaped.cpp
new file mode 100644
index 0000000..7219853
--- /dev/null
+++ b/doc/examples/class_Reshaped.cpp
@@ -0,0 +1,21 @@
+#include <Eigen/Core>
+#include <iostream>
+
+template<typename Derived>
+const Eigen::Reshaped<const Derived>
+reshape_helper(const Eigen::MatrixBase<Derived>& m, int rows, int cols)
+{
+ return Eigen::Reshaped<const Derived>(m.derived(), rows, cols);
+}
+
+int main(int, char**)
+{
+ Eigen::MatrixXd m(3, 4);
+ m << 1, 4, 7, 10,
+ 2, 5, 8, 11,
+ 3, 6, 9, 12;
+ std::cout << m << std::endl;
+ Eigen::Ref<const Eigen::MatrixXd> n = reshape_helper(m, 2, 6);
+ std::cout << "Matrix m is:" << std::endl << m << std::endl;
+ std::cout << "Matrix n is:" << std::endl << n << std::endl;
+}
diff --git a/doc/examples/class_VectorBlock.cpp b/doc/examples/class_VectorBlock.cpp
new file mode 100644
index 0000000..5cee147
--- /dev/null
+++ b/doc/examples/class_VectorBlock.cpp
@@ -0,0 +1,25 @@
+#include <Eigen/Core>
+#include <iostream>
+
+template<typename Derived>
+Eigen::VectorBlock<Derived>
+segmentFromRange(Eigen::MatrixBase<Derived>& v, int start, int end)
+{
+ return Eigen::VectorBlock<Derived>(v.derived(), start, end-start);
+}
+
+template<typename Derived>
+const Eigen::VectorBlock<const Derived>
+segmentFromRange(const Eigen::MatrixBase<Derived>& v, int start, int end)
+{
+ return Eigen::VectorBlock<const Derived>(v.derived(), start, end-start);
+}
+
+int main(int, char**)
+{
+ Eigen::Matrix<int,1,6> v; v << 1,2,3,4,5,6;
+ std::cout << segmentFromRange(2*v, 2, 4) << std::endl; // calls the const version
+ segmentFromRange(v, 1, 3) *= 5; // calls the non-const version
+ std::cout << "Now the vector v is:" << std::endl << v << std::endl;
+ return 0;
+}
diff --git a/doc/examples/function_taking_eigenbase.cpp b/doc/examples/function_taking_eigenbase.cpp
new file mode 100644
index 0000000..4e1e5a9
--- /dev/null
+++ b/doc/examples/function_taking_eigenbase.cpp
@@ -0,0 +1,17 @@
+#include <iostream>
+#include <Eigen/Core>
+
+template <typename Derived>
+void print_size(const Eigen::EigenBase<Derived>& b)
+{
+ std::cout << "size (rows, cols): " << b.size() << " (" << b.rows()
+ << ", " << b.cols() << ")" << std::endl;
+}
+
+int main()
+{
+ Eigen::Vector3f v;
+ print_size(v);
+ // v.asDiagonal() returns a 3x3 diagonal matrix pseudo-expression
+ print_size(v.asDiagonal());
+}
diff --git a/doc/examples/function_taking_ref.cpp b/doc/examples/function_taking_ref.cpp
new file mode 100644
index 0000000..a837e19
--- /dev/null
+++ b/doc/examples/function_taking_ref.cpp
@@ -0,0 +1,17 @@
+#include <iostream>
+#include <Eigen/SVD>
+
+float inv_cond(const Eigen::Ref<const Eigen::MatrixXf>& a)
+{
+ const Eigen::VectorXf sing_vals = a.jacobiSvd().singularValues();
+ return sing_vals(sing_vals.size()-1) / sing_vals(0);
+}
+
+int main()
+{
+ Eigen::MatrixXf m = Eigen::MatrixXf::Random(4, 4);
+ std::cout << "matrix m:\n" << m << "\n\n";
+ std::cout << "inv_cond(m): " << inv_cond(m) << "\n";
+ std::cout << "inv_cond(m(1:3,1:3)): " << inv_cond(m.topLeftCorner(3,3)) << "\n";
+ std::cout << "inv_cond(m+I): " << inv_cond(m+Eigen::MatrixXf::Identity(4, 4)) << "\n";
+}
diff --git a/doc/examples/make_circulant.cpp b/doc/examples/make_circulant.cpp
new file mode 100644
index 0000000..92e6aaa
--- /dev/null
+++ b/doc/examples/make_circulant.cpp
@@ -0,0 +1,11 @@
+/*
+This program is presented in several fragments in the doc page.
+Every fragment is in its own file; this file simply combines them.
+*/
+
+#include "make_circulant.cpp.preamble"
+#include "make_circulant.cpp.traits"
+#include "make_circulant.cpp.expression"
+#include "make_circulant.cpp.evaluator"
+#include "make_circulant.cpp.entry"
+#include "make_circulant.cpp.main"
diff --git a/doc/examples/make_circulant.cpp.entry b/doc/examples/make_circulant.cpp.entry
new file mode 100644
index 0000000..f9d2eb8
--- /dev/null
+++ b/doc/examples/make_circulant.cpp.entry
@@ -0,0 +1,5 @@
+template <class ArgType>
+Circulant<ArgType> makeCirculant(const Eigen::MatrixBase<ArgType>& arg)
+{
+ return Circulant<ArgType>(arg.derived());
+}
diff --git a/doc/examples/make_circulant.cpp.evaluator b/doc/examples/make_circulant.cpp.evaluator
new file mode 100644
index 0000000..cd461b9
--- /dev/null
+++ b/doc/examples/make_circulant.cpp.evaluator
@@ -0,0 +1,32 @@
+namespace Eigen {
+ namespace internal {
+ template<typename ArgType>
+ struct evaluator<Circulant<ArgType> >
+ : evaluator_base<Circulant<ArgType> >
+ {
+ typedef Circulant<ArgType> XprType;
+ typedef typename nested_eval<ArgType, XprType::ColsAtCompileTime>::type ArgTypeNested;
+ typedef remove_all_t<ArgTypeNested> ArgTypeNestedCleaned;
+ typedef typename XprType::CoeffReturnType CoeffReturnType;
+
+ enum {
+ CoeffReadCost = evaluator<ArgTypeNestedCleaned>::CoeffReadCost,
+ Flags = Eigen::ColMajor
+ };
+
+ evaluator(const XprType& xpr)
+ : m_argImpl(xpr.m_arg), m_rows(xpr.rows())
+ { }
+
+ CoeffReturnType coeff(Index row, Index col) const
+ {
+ Index index = row - col;
+ if (index < 0) index += m_rows;
+ return m_argImpl.coeff(index);
+ }
+
+ evaluator<ArgTypeNestedCleaned> m_argImpl;
+ const Index m_rows;
+ };
+ }
+}
diff --git a/doc/examples/make_circulant.cpp.expression b/doc/examples/make_circulant.cpp.expression
new file mode 100644
index 0000000..380cd44
--- /dev/null
+++ b/doc/examples/make_circulant.cpp.expression
@@ -0,0 +1,20 @@
+template <class ArgType>
+class Circulant : public Eigen::MatrixBase<Circulant<ArgType> >
+{
+public:
+ Circulant(const ArgType& arg)
+ : m_arg(arg)
+ {
+ EIGEN_STATIC_ASSERT(ArgType::ColsAtCompileTime == 1,
+ YOU_TRIED_CALLING_A_VECTOR_METHOD_ON_A_MATRIX);
+ }
+
+ typedef typename Eigen::internal::ref_selector<Circulant>::type Nested;
+
+ typedef Eigen::Index Index;
+ Index rows() const { return m_arg.rows(); }
+ Index cols() const { return m_arg.rows(); }
+
+ typedef typename Eigen::internal::ref_selector<ArgType>::type ArgTypeNested;
+ ArgTypeNested m_arg;
+};
diff --git a/doc/examples/make_circulant.cpp.main b/doc/examples/make_circulant.cpp.main
new file mode 100644
index 0000000..877f97f
--- /dev/null
+++ b/doc/examples/make_circulant.cpp.main
@@ -0,0 +1,8 @@
+int main()
+{
+ Eigen::VectorXd vec(4);
+ vec << 1, 2, 4, 8;
+ Eigen::MatrixXd mat;
+ mat = makeCirculant(vec);
+ std::cout << mat << std::endl;
+}
diff --git a/doc/examples/make_circulant.cpp.preamble b/doc/examples/make_circulant.cpp.preamble
new file mode 100644
index 0000000..e575cce
--- /dev/null
+++ b/doc/examples/make_circulant.cpp.preamble
@@ -0,0 +1,4 @@
+#include <Eigen/Core>
+#include <iostream>
+
+template <class ArgType> class Circulant;
diff --git a/doc/examples/make_circulant.cpp.traits b/doc/examples/make_circulant.cpp.traits
new file mode 100644
index 0000000..4e04535
--- /dev/null
+++ b/doc/examples/make_circulant.cpp.traits
@@ -0,0 +1,19 @@
+namespace Eigen {
+ namespace internal {
+ template <class ArgType>
+ struct traits<Circulant<ArgType> >
+ {
+ typedef Eigen::Dense StorageKind;
+ typedef Eigen::MatrixXpr XprKind;
+ typedef typename ArgType::StorageIndex StorageIndex;
+ typedef typename ArgType::Scalar Scalar;
+ enum {
+ Flags = Eigen::ColMajor,
+ RowsAtCompileTime = ArgType::RowsAtCompileTime,
+ ColsAtCompileTime = ArgType::RowsAtCompileTime,
+ MaxRowsAtCompileTime = ArgType::MaxRowsAtCompileTime,
+ MaxColsAtCompileTime = ArgType::MaxRowsAtCompileTime
+ };
+ };
+ }
+}
diff --git a/doc/examples/make_circulant2.cpp b/doc/examples/make_circulant2.cpp
new file mode 100644
index 0000000..d86a66b
--- /dev/null
+++ b/doc/examples/make_circulant2.cpp
@@ -0,0 +1,50 @@
+#include <Eigen/Core>
+#include <iostream>
+
+// [circulant_func]
+template<class ArgType>
+class circulant_functor {
+ const ArgType &m_vec;
+public:
+ circulant_functor(const ArgType& arg) : m_vec(arg) {}
+
+ const typename ArgType::Scalar& operator() (Eigen::Index row, Eigen::Index col) const {
+ Eigen::Index index = row - col;
+ if (index < 0) index += m_vec.size();
+ return m_vec(index);
+ }
+};
+// [circulant_func]
+
+// [square]
+template<class ArgType>
+struct circulant_helper {
+ typedef Eigen::Matrix<typename ArgType::Scalar,
+ ArgType::SizeAtCompileTime,
+ ArgType::SizeAtCompileTime,
+ Eigen::ColMajor,
+ ArgType::MaxSizeAtCompileTime,
+ ArgType::MaxSizeAtCompileTime> MatrixType;
+};
+// [square]
+
+// [makeCirculant]
+template <class ArgType>
+Eigen::CwiseNullaryOp<circulant_functor<ArgType>, typename circulant_helper<ArgType>::MatrixType>
+makeCirculant(const Eigen::MatrixBase<ArgType>& arg)
+{
+ typedef typename circulant_helper<ArgType>::MatrixType MatrixType;
+ return MatrixType::NullaryExpr(arg.size(), arg.size(), circulant_functor<ArgType>(arg.derived()));
+}
+// [makeCirculant]
+
+// [main]
+int main()
+{
+ Eigen::VectorXd vec(4);
+ vec << 1, 2, 4, 8;
+ Eigen::MatrixXd mat;
+ mat = makeCirculant(vec);
+ std::cout << mat << std::endl;
+}
+// [main]
diff --git a/doc/examples/matrixfree_cg.cpp b/doc/examples/matrixfree_cg.cpp
new file mode 100644
index 0000000..7469938
--- /dev/null
+++ b/doc/examples/matrixfree_cg.cpp
@@ -0,0 +1,129 @@
+#include <iostream>
+#include <Eigen/Core>
+#include <Eigen/Dense>
+#include <Eigen/IterativeLinearSolvers>
+#include <unsupported/Eigen/IterativeSolvers>
+
+class MatrixReplacement;
+using Eigen::SparseMatrix;
+
+namespace Eigen {
+namespace internal {
+ // MatrixReplacement looks-like a SparseMatrix, so let's inherits its traits:
+ template<>
+ struct traits<MatrixReplacement> : public Eigen::internal::traits<Eigen::SparseMatrix<double> >
+ {};
+}
+}
+
+// Example of a matrix-free wrapper from a user type to Eigen's compatible type
+// For the sake of simplicity, this example simply wrap a Eigen::SparseMatrix.
+class MatrixReplacement : public Eigen::EigenBase<MatrixReplacement> {
+public:
+ // Required typedefs, constants, and method:
+ typedef double Scalar;
+ typedef double RealScalar;
+ typedef int StorageIndex;
+ enum {
+ ColsAtCompileTime = Eigen::Dynamic,
+ MaxColsAtCompileTime = Eigen::Dynamic,
+ IsRowMajor = false
+ };
+
+ Index rows() const { return mp_mat->rows(); }
+ Index cols() const { return mp_mat->cols(); }
+
+ template<typename Rhs>
+ Eigen::Product<MatrixReplacement,Rhs,Eigen::AliasFreeProduct> operator*(const Eigen::MatrixBase<Rhs>& x) const {
+ return Eigen::Product<MatrixReplacement,Rhs,Eigen::AliasFreeProduct>(*this, x.derived());
+ }
+
+ // Custom API:
+ MatrixReplacement() : mp_mat(0) {}
+
+ void attachMyMatrix(const SparseMatrix<double> &mat) {
+ mp_mat = &mat;
+ }
+ const SparseMatrix<double> my_matrix() const { return *mp_mat; }
+
+private:
+ const SparseMatrix<double> *mp_mat;
+};
+
+
+// Implementation of MatrixReplacement * Eigen::DenseVector though a specialization of internal::generic_product_impl:
+namespace Eigen {
+namespace internal {
+
+ template<typename Rhs>
+ struct generic_product_impl<MatrixReplacement, Rhs, SparseShape, DenseShape, GemvProduct> // GEMV stands for matrix-vector
+ : generic_product_impl_base<MatrixReplacement,Rhs,generic_product_impl<MatrixReplacement,Rhs> >
+ {
+ typedef typename Product<MatrixReplacement,Rhs>::Scalar Scalar;
+
+ template<typename Dest>
+ static void scaleAndAddTo(Dest& dst, const MatrixReplacement& lhs, const Rhs& rhs, const Scalar& alpha)
+ {
+ // This method should implement "dst += alpha * lhs * rhs" inplace,
+ // however, for iterative solvers, alpha is always equal to 1, so let's not bother about it.
+ assert(alpha==Scalar(1) && "scaling is not implemented");
+ EIGEN_ONLY_USED_FOR_DEBUG(alpha);
+
+ // Here we could simply call dst.noalias() += lhs.my_matrix() * rhs,
+ // but let's do something fancier (and less efficient):
+ for(Index i=0; i<lhs.cols(); ++i)
+ dst += rhs(i) * lhs.my_matrix().col(i);
+ }
+ };
+
+}
+}
+
+int main()
+{
+ int n = 10;
+ Eigen::SparseMatrix<double> S = Eigen::MatrixXd::Random(n,n).sparseView(0.5,1);
+ S = S.transpose()*S;
+
+ MatrixReplacement A;
+ A.attachMyMatrix(S);
+
+ Eigen::VectorXd b(n), x;
+ b.setRandom();
+
+ // Solve Ax = b using various iterative solver with matrix-free version:
+ {
+ Eigen::ConjugateGradient<MatrixReplacement, Eigen::Lower|Eigen::Upper, Eigen::IdentityPreconditioner> cg;
+ cg.compute(A);
+ x = cg.solve(b);
+ std::cout << "CG: #iterations: " << cg.iterations() << ", estimated error: " << cg.error() << std::endl;
+ }
+
+ {
+ Eigen::BiCGSTAB<MatrixReplacement, Eigen::IdentityPreconditioner> bicg;
+ bicg.compute(A);
+ x = bicg.solve(b);
+ std::cout << "BiCGSTAB: #iterations: " << bicg.iterations() << ", estimated error: " << bicg.error() << std::endl;
+ }
+
+ {
+ Eigen::GMRES<MatrixReplacement, Eigen::IdentityPreconditioner> gmres;
+ gmres.compute(A);
+ x = gmres.solve(b);
+ std::cout << "GMRES: #iterations: " << gmres.iterations() << ", estimated error: " << gmres.error() << std::endl;
+ }
+
+ {
+ Eigen::DGMRES<MatrixReplacement, Eigen::IdentityPreconditioner> gmres;
+ gmres.compute(A);
+ x = gmres.solve(b);
+ std::cout << "DGMRES: #iterations: " << gmres.iterations() << ", estimated error: " << gmres.error() << std::endl;
+ }
+
+ {
+ Eigen::MINRES<MatrixReplacement, Eigen::Lower|Eigen::Upper, Eigen::IdentityPreconditioner> minres;
+ minres.compute(A);
+ x = minres.solve(b);
+ std::cout << "MINRES: #iterations: " << minres.iterations() << ", estimated error: " << minres.error() << std::endl;
+ }
+}
diff --git a/doc/examples/nullary_indexing.cpp b/doc/examples/nullary_indexing.cpp
new file mode 100644
index 0000000..38260af
--- /dev/null
+++ b/doc/examples/nullary_indexing.cpp
@@ -0,0 +1,62 @@
+#include <Eigen/Core>
+#include <iostream>
+
+// [functor]
+template<class ArgType, class RowIndexType, class ColIndexType>
+class indexing_functor {
+ const ArgType &m_arg;
+ const RowIndexType &m_rowIndices;
+ const ColIndexType &m_colIndices;
+public:
+ typedef Eigen::Matrix<typename ArgType::Scalar,
+ RowIndexType::SizeAtCompileTime,
+ ColIndexType::SizeAtCompileTime,
+ ArgType::Flags&Eigen::RowMajorBit?Eigen::RowMajor:Eigen::ColMajor,
+ RowIndexType::MaxSizeAtCompileTime,
+ ColIndexType::MaxSizeAtCompileTime> MatrixType;
+
+ indexing_functor(const ArgType& arg, const RowIndexType& row_indices, const ColIndexType& col_indices)
+ : m_arg(arg), m_rowIndices(row_indices), m_colIndices(col_indices)
+ {}
+
+ const typename ArgType::Scalar& operator() (Eigen::Index row, Eigen::Index col) const {
+ return m_arg(m_rowIndices[row], m_colIndices[col]);
+ }
+};
+// [functor]
+
+// [function]
+template <class ArgType, class RowIndexType, class ColIndexType>
+Eigen::CwiseNullaryOp<indexing_functor<ArgType,RowIndexType,ColIndexType>, typename indexing_functor<ArgType,RowIndexType,ColIndexType>::MatrixType>
+mat_indexing(const Eigen::MatrixBase<ArgType>& arg, const RowIndexType& row_indices, const ColIndexType& col_indices)
+{
+ typedef indexing_functor<ArgType,RowIndexType,ColIndexType> Func;
+ typedef typename Func::MatrixType MatrixType;
+ return MatrixType::NullaryExpr(row_indices.size(), col_indices.size(), Func(arg.derived(), row_indices, col_indices));
+}
+// [function]
+
+
+int main()
+{
+ std::cout << "[main1]\n";
+ Eigen::MatrixXi A = Eigen::MatrixXi::Random(4,4);
+ Eigen::Array3i ri(1,2,1);
+ Eigen::ArrayXi ci(6); ci << 3,2,1,0,0,2;
+ Eigen::MatrixXi B = mat_indexing(A, ri, ci);
+ std::cout << "A =" << std::endl;
+ std::cout << A << std::endl << std::endl;
+ std::cout << "A([" << ri.transpose() << "], [" << ci.transpose() << "]) =" << std::endl;
+ std::cout << B << std::endl;
+ std::cout << "[main1]\n";
+
+ std::cout << "[main2]\n";
+ B = mat_indexing(A, ri+1, ci);
+ std::cout << "A(ri+1,ci) =" << std::endl;
+ std::cout << B << std::endl << std::endl;
+ B = mat_indexing(A, Eigen::ArrayXi::LinSpaced(13,0,12).unaryExpr([](int x){return x%4;}), Eigen::ArrayXi::LinSpaced(4,0,3));
+ std::cout << "A(ArrayXi::LinSpaced(13,0,12).unaryExpr([](int x){return x%4;}), ArrayXi::LinSpaced(4,0,3)) =" << std::endl;
+ std::cout << B << std::endl << std::endl;
+ std::cout << "[main2]\n";
+}
+
diff --git a/doc/examples/tut_arithmetic_add_sub.cpp b/doc/examples/tut_arithmetic_add_sub.cpp
new file mode 100644
index 0000000..95162c0
--- /dev/null
+++ b/doc/examples/tut_arithmetic_add_sub.cpp
@@ -0,0 +1,20 @@
+#include <iostream>
+#include <Eigen/Dense>
+
+int main()
+{
+ Eigen::Matrix2d a;
+ a << 1, 2,
+ 3, 4;
+ Eigen::MatrixXd b(2,2);
+ b << 2, 3,
+ 1, 4;
+ std::cout << "a + b =\n" << a + b << std::endl;
+ std::cout << "a - b =\n" << a - b << std::endl;
+ std::cout << "Doing a += b;" << std::endl;
+ a += b;
+ std::cout << "Now a =\n" << a << std::endl;
+ Eigen::Vector3d v(1,2,3);
+ Eigen::Vector3d w(1,0,0);
+ std::cout << "-v + w - v =\n" << -v + w - v << std::endl;
+}
diff --git a/doc/examples/tut_arithmetic_dot_cross.cpp b/doc/examples/tut_arithmetic_dot_cross.cpp
new file mode 100644
index 0000000..5b0fd1e
--- /dev/null
+++ b/doc/examples/tut_arithmetic_dot_cross.cpp
@@ -0,0 +1,13 @@
+#include <iostream>
+#include <Eigen/Dense>
+
+int main()
+{
+ Eigen::Vector3d v(1,2,3);
+ Eigen::Vector3d w(0,1,2);
+
+ std::cout << "Dot product: " << v.dot(w) << std::endl;
+ double dp = v.adjoint()*w; // automatic conversion of the inner product to a scalar
+ std::cout << "Dot product via a matrix product: " << dp << std::endl;
+ std::cout << "Cross product:\n" << v.cross(w) << std::endl;
+}
diff --git a/doc/examples/tut_arithmetic_matrix_mul.cpp b/doc/examples/tut_arithmetic_matrix_mul.cpp
new file mode 100644
index 0000000..c2d5e2d
--- /dev/null
+++ b/doc/examples/tut_arithmetic_matrix_mul.cpp
@@ -0,0 +1,18 @@
+#include <iostream>
+#include <Eigen/Dense>
+
+int main()
+{
+ Eigen::Matrix2d mat;
+ mat << 1, 2,
+ 3, 4;
+ Eigen::Vector2d u(-1,1), v(2,0);
+ std::cout << "Here is mat*mat:\n" << mat*mat << std::endl;
+ std::cout << "Here is mat*u:\n" << mat*u << std::endl;
+ std::cout << "Here is u^T*mat:\n" << u.transpose()*mat << std::endl;
+ std::cout << "Here is u^T*v:\n" << u.transpose()*v << std::endl;
+ std::cout << "Here is u*v^T:\n" << u*v.transpose() << std::endl;
+ std::cout << "Let's multiply mat by itself" << std::endl;
+ mat = mat*mat;
+ std::cout << "Now mat is mat:\n" << mat << std::endl;
+}
diff --git a/doc/examples/tut_arithmetic_redux_basic.cpp b/doc/examples/tut_arithmetic_redux_basic.cpp
new file mode 100644
index 0000000..5632fb5
--- /dev/null
+++ b/doc/examples/tut_arithmetic_redux_basic.cpp
@@ -0,0 +1,16 @@
+#include <iostream>
+#include <Eigen/Dense>
+
+using namespace std;
+int main()
+{
+ Eigen::Matrix2d mat;
+ mat << 1, 2,
+ 3, 4;
+ cout << "Here is mat.sum(): " << mat.sum() << endl;
+ cout << "Here is mat.prod(): " << mat.prod() << endl;
+ cout << "Here is mat.mean(): " << mat.mean() << endl;
+ cout << "Here is mat.minCoeff(): " << mat.minCoeff() << endl;
+ cout << "Here is mat.maxCoeff(): " << mat.maxCoeff() << endl;
+ cout << "Here is mat.trace(): " << mat.trace() << endl;
+}
diff --git a/doc/examples/tut_arithmetic_scalar_mul_div.cpp b/doc/examples/tut_arithmetic_scalar_mul_div.cpp
new file mode 100644
index 0000000..0ba8d6b
--- /dev/null
+++ b/doc/examples/tut_arithmetic_scalar_mul_div.cpp
@@ -0,0 +1,15 @@
+#include <iostream>
+#include <Eigen/Dense>
+
+int main()
+{
+ Eigen::Matrix2d a;
+ a << 1, 2,
+ 3, 4;
+ Eigen::Vector3d v(1,2,3);
+ std::cout << "a * 2.5 =\n" << a * 2.5 << std::endl;
+ std::cout << "0.1 * v =\n" << 0.1 * v << std::endl;
+ std::cout << "Doing v *= 2;" << std::endl;
+ v *= 2;
+ std::cout << "Now v =\n" << v << std::endl;
+}
diff --git a/doc/examples/tut_matrix_coefficient_accessors.cpp b/doc/examples/tut_matrix_coefficient_accessors.cpp
new file mode 100644
index 0000000..040087c
--- /dev/null
+++ b/doc/examples/tut_matrix_coefficient_accessors.cpp
@@ -0,0 +1,16 @@
+#include <iostream>
+#include <Eigen/Dense>
+
+int main()
+{
+ Eigen::MatrixXd m(2,2);
+ m(0,0) = 3;
+ m(1,0) = 2.5;
+ m(0,1) = -1;
+ m(1,1) = m(1,0) + m(0,1);
+ std::cout << "Here is the matrix m:\n" << m << std::endl;
+ Eigen::VectorXd v(2);
+ v(0) = 4;
+ v(1) = v(0) - 1;
+ std::cout << "Here is the vector v:\n" << v << std::endl;
+}
diff --git a/doc/examples/tut_matrix_resize.cpp b/doc/examples/tut_matrix_resize.cpp
new file mode 100644
index 0000000..aa80cf5
--- /dev/null
+++ b/doc/examples/tut_matrix_resize.cpp
@@ -0,0 +1,16 @@
+#include <iostream>
+#include <Eigen/Dense>
+
+int main()
+{
+ Eigen::MatrixXd m(2,5);
+ m.resize(4,3);
+ std::cout << "The matrix m is of size "
+ << m.rows() << "x" << m.cols() << std::endl;
+ std::cout << "It has " << m.size() << " coefficients" << std::endl;
+ Eigen::VectorXd v(2);
+ v.resize(5);
+ std::cout << "The vector v is of size " << v.size() << std::endl;
+ std::cout << "As a matrix, v is of size "
+ << v.rows() << "x" << v.cols() << std::endl;
+}
diff --git a/doc/examples/tut_matrix_resize_fixed_size.cpp b/doc/examples/tut_matrix_resize_fixed_size.cpp
new file mode 100644
index 0000000..3df87d2
--- /dev/null
+++ b/doc/examples/tut_matrix_resize_fixed_size.cpp
@@ -0,0 +1,10 @@
+#include <iostream>
+#include <Eigen/Dense>
+
+int main()
+{
+ Eigen::Matrix4d m;
+ m.resize(4,4); // no operation
+ std::cout << "The matrix m is of size "
+ << m.rows() << "x" << m.cols() << std::endl;
+}
diff --git a/doc/ftv2node.png b/doc/ftv2node.png
new file mode 100644
index 0000000..63c605b
--- /dev/null
+++ b/doc/ftv2node.png
Binary files differ
diff --git a/doc/ftv2pnode.png b/doc/ftv2pnode.png
new file mode 100644
index 0000000..c6ee22f
--- /dev/null
+++ b/doc/ftv2pnode.png
Binary files differ
diff --git a/doc/snippets/.krazy b/doc/snippets/.krazy
new file mode 100644
index 0000000..00b9940
--- /dev/null
+++ b/doc/snippets/.krazy
@@ -0,0 +1,2 @@
+EXCLUDE copyright
+EXCLUDE license
diff --git a/doc/snippets/AngleAxis_mimic_euler.cpp b/doc/snippets/AngleAxis_mimic_euler.cpp
new file mode 100644
index 0000000..456de7f
--- /dev/null
+++ b/doc/snippets/AngleAxis_mimic_euler.cpp
@@ -0,0 +1,5 @@
+Matrix3f m;
+m = AngleAxisf(0.25*M_PI, Vector3f::UnitX())
+ * AngleAxisf(0.5*M_PI, Vector3f::UnitY())
+ * AngleAxisf(0.33*M_PI, Vector3f::UnitZ());
+cout << m << endl << "is unitary: " << m.isUnitary() << endl;
diff --git a/doc/snippets/Array_initializer_list_23_cxx11.cpp b/doc/snippets/Array_initializer_list_23_cxx11.cpp
new file mode 100644
index 0000000..2c2166e
--- /dev/null
+++ b/doc/snippets/Array_initializer_list_23_cxx11.cpp
@@ -0,0 +1,5 @@
+ArrayXXi a {
+ {1, 2, 3},
+ {3, 4, 5}
+};
+cout << a << endl;
diff --git a/doc/snippets/Array_initializer_list_vector_cxx11.cpp b/doc/snippets/Array_initializer_list_vector_cxx11.cpp
new file mode 100644
index 0000000..a668d84
--- /dev/null
+++ b/doc/snippets/Array_initializer_list_vector_cxx11.cpp
@@ -0,0 +1,2 @@
+Array<int, Dynamic, 1> v {{1, 2, 3, 4, 5}};
+cout << v << endl;
diff --git a/doc/snippets/Array_variadic_ctor_cxx11.cpp b/doc/snippets/Array_variadic_ctor_cxx11.cpp
new file mode 100644
index 0000000..0e4ec44
--- /dev/null
+++ b/doc/snippets/Array_variadic_ctor_cxx11.cpp
@@ -0,0 +1,3 @@
+Array<int, 1, 6> a(1, 2, 3, 4, 5, 6);
+Array<int, 3, 1> b {1, 2, 3};
+cout << a << "\n\n" << b << endl;
diff --git a/doc/snippets/BiCGSTAB_simple.cpp b/doc/snippets/BiCGSTAB_simple.cpp
new file mode 100644
index 0000000..8c8829f
--- /dev/null
+++ b/doc/snippets/BiCGSTAB_simple.cpp
@@ -0,0 +1,11 @@
+ int n = 10000;
+ VectorXd x(n), b(n);
+ SparseMatrix<double> A(n,n);
+ /* ... fill A and b ... */
+ BiCGSTAB<SparseMatrix<double> > solver;
+ solver.compute(A);
+ x = solver.solve(b);
+ std::cout << "#iterations: " << solver.iterations() << std::endl;
+ std::cout << "estimated error: " << solver.error() << std::endl;
+ /* ... update b ... */
+ x = solver.solve(b); // solve again
diff --git a/doc/snippets/BiCGSTAB_step_by_step.cpp b/doc/snippets/BiCGSTAB_step_by_step.cpp
new file mode 100644
index 0000000..6c95d5a
--- /dev/null
+++ b/doc/snippets/BiCGSTAB_step_by_step.cpp
@@ -0,0 +1,14 @@
+ int n = 10000;
+ VectorXd x(n), b(n);
+ SparseMatrix<double> A(n,n);
+ /* ... fill A and b ... */
+ BiCGSTAB<SparseMatrix<double> > solver(A);
+ // start from a random solution
+ x = VectorXd::Random(n);
+ solver.setMaxIterations(1);
+ int i = 0;
+ do {
+ x = solver.solveWithGuess(b,x);
+ std::cout << i << " : " << solver.error() << std::endl;
+ ++i;
+ } while (solver.info()!=Success && i<100);
diff --git a/doc/snippets/CMakeLists.txt b/doc/snippets/CMakeLists.txt
new file mode 100644
index 0000000..868d669
--- /dev/null
+++ b/doc/snippets/CMakeLists.txt
@@ -0,0 +1,31 @@
+file(GLOB snippets_SRCS "*.cpp")
+
+add_custom_target(all_snippets)
+
+foreach(snippet_src ${snippets_SRCS})
+ get_filename_component(snippet ${snippet_src} NAME_WE)
+ set(compile_snippet_target compile_${snippet})
+ set(compile_snippet_src ${compile_snippet_target}.cpp)
+
+ file(READ ${snippet_src} snippet_source_code)
+ configure_file(${CMAKE_CURRENT_SOURCE_DIR}/compile_snippet.cpp.in
+ ${CMAKE_CURRENT_BINARY_DIR}/${compile_snippet_src})
+ add_executable(${compile_snippet_target}
+ ${CMAKE_CURRENT_BINARY_DIR}/${compile_snippet_src})
+ if(EIGEN_STANDARD_LIBRARIES_TO_LINK_TO)
+ target_link_libraries(${compile_snippet_target} ${EIGEN_STANDARD_LIBRARIES_TO_LINK_TO})
+ endif()
+
+ if(${snippet_src} MATCHES "deprecated")
+ set_target_properties(${compile_snippet_target} PROPERTIES COMPILE_FLAGS "-DEIGEN_NO_DEPRECATED_WARNING")
+ endif()
+ add_custom_command(
+ TARGET ${compile_snippet_target}
+ POST_BUILD
+ COMMAND ${compile_snippet_target}
+ ARGS >${CMAKE_CURRENT_BINARY_DIR}/${snippet}.out
+ )
+ add_dependencies(all_snippets ${compile_snippet_target})
+ set_source_files_properties(${CMAKE_CURRENT_BINARY_DIR}/${compile_snippet_src}
+ PROPERTIES OBJECT_DEPENDS ${snippet_src})
+endforeach()
diff --git a/doc/snippets/ColPivHouseholderQR_solve.cpp b/doc/snippets/ColPivHouseholderQR_solve.cpp
new file mode 100644
index 0000000..b7b204a
--- /dev/null
+++ b/doc/snippets/ColPivHouseholderQR_solve.cpp
@@ -0,0 +1,8 @@
+Matrix3f m = Matrix3f::Random();
+Matrix3f y = Matrix3f::Random();
+cout << "Here is the matrix m:" << endl << m << endl;
+cout << "Here is the matrix y:" << endl << y << endl;
+Matrix3f x;
+x = m.colPivHouseholderQr().solve(y);
+assert(y.isApprox(m*x));
+cout << "Here is a solution x to the equation mx=y:" << endl << x << endl;
diff --git a/doc/snippets/ComplexEigenSolver_compute.cpp b/doc/snippets/ComplexEigenSolver_compute.cpp
new file mode 100644
index 0000000..11d6bd3
--- /dev/null
+++ b/doc/snippets/ComplexEigenSolver_compute.cpp
@@ -0,0 +1,16 @@
+MatrixXcf A = MatrixXcf::Random(4,4);
+cout << "Here is a random 4x4 matrix, A:" << endl << A << endl << endl;
+
+ComplexEigenSolver<MatrixXcf> ces;
+ces.compute(A);
+cout << "The eigenvalues of A are:" << endl << ces.eigenvalues() << endl;
+cout << "The matrix of eigenvectors, V, is:" << endl << ces.eigenvectors() << endl << endl;
+
+complex<float> lambda = ces.eigenvalues()[0];
+cout << "Consider the first eigenvalue, lambda = " << lambda << endl;
+VectorXcf v = ces.eigenvectors().col(0);
+cout << "If v is the corresponding eigenvector, then lambda * v = " << endl << lambda * v << endl;
+cout << "... and A * v = " << endl << A * v << endl << endl;
+
+cout << "Finally, V * D * V^(-1) = " << endl
+ << ces.eigenvectors() * ces.eigenvalues().asDiagonal() * ces.eigenvectors().inverse() << endl;
diff --git a/doc/snippets/ComplexEigenSolver_eigenvalues.cpp b/doc/snippets/ComplexEigenSolver_eigenvalues.cpp
new file mode 100644
index 0000000..5509bd8
--- /dev/null
+++ b/doc/snippets/ComplexEigenSolver_eigenvalues.cpp
@@ -0,0 +1,4 @@
+MatrixXcf ones = MatrixXcf::Ones(3,3);
+ComplexEigenSolver<MatrixXcf> ces(ones, /* computeEigenvectors = */ false);
+cout << "The eigenvalues of the 3x3 matrix of ones are:"
+ << endl << ces.eigenvalues() << endl;
diff --git a/doc/snippets/ComplexEigenSolver_eigenvectors.cpp b/doc/snippets/ComplexEigenSolver_eigenvectors.cpp
new file mode 100644
index 0000000..adeed9a
--- /dev/null
+++ b/doc/snippets/ComplexEigenSolver_eigenvectors.cpp
@@ -0,0 +1,4 @@
+MatrixXcf ones = MatrixXcf::Ones(3,3);
+ComplexEigenSolver<MatrixXcf> ces(ones);
+cout << "The first eigenvector of the 3x3 matrix of ones is:"
+ << endl << ces.eigenvectors().col(0) << endl;
diff --git a/doc/snippets/ComplexSchur_compute.cpp b/doc/snippets/ComplexSchur_compute.cpp
new file mode 100644
index 0000000..3a51701
--- /dev/null
+++ b/doc/snippets/ComplexSchur_compute.cpp
@@ -0,0 +1,6 @@
+MatrixXcf A = MatrixXcf::Random(4,4);
+ComplexSchur<MatrixXcf> schur(4);
+schur.compute(A);
+cout << "The matrix T in the decomposition of A is:" << endl << schur.matrixT() << endl;
+schur.compute(A.inverse());
+cout << "The matrix T in the decomposition of A^(-1) is:" << endl << schur.matrixT() << endl;
diff --git a/doc/snippets/ComplexSchur_matrixT.cpp b/doc/snippets/ComplexSchur_matrixT.cpp
new file mode 100644
index 0000000..8380571
--- /dev/null
+++ b/doc/snippets/ComplexSchur_matrixT.cpp
@@ -0,0 +1,4 @@
+MatrixXcf A = MatrixXcf::Random(4,4);
+cout << "Here is a random 4x4 matrix, A:" << endl << A << endl << endl;
+ComplexSchur<MatrixXcf> schurOfA(A, false); // false means do not compute U
+cout << "The triangular matrix T is:" << endl << schurOfA.matrixT() << endl;
diff --git a/doc/snippets/ComplexSchur_matrixU.cpp b/doc/snippets/ComplexSchur_matrixU.cpp
new file mode 100644
index 0000000..ba3d9c2
--- /dev/null
+++ b/doc/snippets/ComplexSchur_matrixU.cpp
@@ -0,0 +1,4 @@
+MatrixXcf A = MatrixXcf::Random(4,4);
+cout << "Here is a random 4x4 matrix, A:" << endl << A << endl << endl;
+ComplexSchur<MatrixXcf> schurOfA(A);
+cout << "The unitary matrix U is:" << endl << schurOfA.matrixU() << endl;
diff --git a/doc/snippets/Cwise_abs.cpp b/doc/snippets/Cwise_abs.cpp
new file mode 100644
index 0000000..0aeec3a
--- /dev/null
+++ b/doc/snippets/Cwise_abs.cpp
@@ -0,0 +1,2 @@
+Array3d v(1,-2,-3);
+cout << v.abs() << endl;
diff --git a/doc/snippets/Cwise_abs2.cpp b/doc/snippets/Cwise_abs2.cpp
new file mode 100644
index 0000000..2c4f9b3
--- /dev/null
+++ b/doc/snippets/Cwise_abs2.cpp
@@ -0,0 +1,2 @@
+Array3d v(1,-2,-3);
+cout << v.abs2() << endl;
diff --git a/doc/snippets/Cwise_acos.cpp b/doc/snippets/Cwise_acos.cpp
new file mode 100644
index 0000000..34432cb
--- /dev/null
+++ b/doc/snippets/Cwise_acos.cpp
@@ -0,0 +1,2 @@
+Array3d v(0, sqrt(2.)/2, 1);
+cout << v.acos() << endl;
diff --git a/doc/snippets/Cwise_arg.cpp b/doc/snippets/Cwise_arg.cpp
new file mode 100644
index 0000000..3f45133
--- /dev/null
+++ b/doc/snippets/Cwise_arg.cpp
@@ -0,0 +1,3 @@
+ArrayXcf v = ArrayXcf::Random(3);
+cout << v << endl << endl;
+cout << arg(v) << endl;
diff --git a/doc/snippets/Cwise_array_atan2_array.cpp b/doc/snippets/Cwise_array_atan2_array.cpp
new file mode 100644
index 0000000..ace075a
--- /dev/null
+++ b/doc/snippets/Cwise_array_atan2_array.cpp
@@ -0,0 +1,4 @@
+Array<double,1,3> x(8,-25,3),
+ y(1./3.,0.5,-2.);
+cout << "atan2([" << x << "], [" << y << "]) = " << x.atan2(y) << endl; // using ArrayBase::pow
+cout << "atan2([" << x << "], [" << y << "] = " << atan2(x,y) << endl; // using Eigen::pow
diff --git a/doc/snippets/Cwise_array_power_array.cpp b/doc/snippets/Cwise_array_power_array.cpp
new file mode 100644
index 0000000..432a76e
--- /dev/null
+++ b/doc/snippets/Cwise_array_power_array.cpp
@@ -0,0 +1,4 @@
+Array<double,1,3> x(8,25,3),
+ e(1./3.,0.5,2.);
+cout << "[" << x << "]^[" << e << "] = " << x.pow(e) << endl; // using ArrayBase::pow
+cout << "[" << x << "]^[" << e << "] = " << pow(x,e) << endl; // using Eigen::pow
diff --git a/doc/snippets/Cwise_asin.cpp b/doc/snippets/Cwise_asin.cpp
new file mode 100644
index 0000000..8dad838
--- /dev/null
+++ b/doc/snippets/Cwise_asin.cpp
@@ -0,0 +1,2 @@
+Array3d v(0, sqrt(2.)/2, 1);
+cout << v.asin() << endl;
diff --git a/doc/snippets/Cwise_atan.cpp b/doc/snippets/Cwise_atan.cpp
new file mode 100644
index 0000000..4468447
--- /dev/null
+++ b/doc/snippets/Cwise_atan.cpp
@@ -0,0 +1,2 @@
+ArrayXd v = ArrayXd::LinSpaced(5,0,1);
+cout << v.atan() << endl;
diff --git a/doc/snippets/Cwise_boolean_and.cpp b/doc/snippets/Cwise_boolean_and.cpp
new file mode 100644
index 0000000..df6b60d
--- /dev/null
+++ b/doc/snippets/Cwise_boolean_and.cpp
@@ -0,0 +1,2 @@
+Array3d v(-1,2,1), w(-3,2,3);
+cout << ((v<w) && (v<0)) << endl;
diff --git a/doc/snippets/Cwise_boolean_not.cpp b/doc/snippets/Cwise_boolean_not.cpp
new file mode 100644
index 0000000..40009f1
--- /dev/null
+++ b/doc/snippets/Cwise_boolean_not.cpp
@@ -0,0 +1,5 @@
+Array3d v(1,2,3);
+v(1) *= 0.0/0.0;
+v(2) /= 0.0;
+cout << v << endl << endl;
+cout << !isfinite(v) << endl;
diff --git a/doc/snippets/Cwise_boolean_or.cpp b/doc/snippets/Cwise_boolean_or.cpp
new file mode 100644
index 0000000..83eb006
--- /dev/null
+++ b/doc/snippets/Cwise_boolean_or.cpp
@@ -0,0 +1,2 @@
+Array3d v(-1,2,1), w(-3,2,3);
+cout << ((v<w) || (v<0)) << endl;
diff --git a/doc/snippets/Cwise_boolean_xor.cpp b/doc/snippets/Cwise_boolean_xor.cpp
new file mode 100644
index 0000000..fafbec8
--- /dev/null
+++ b/doc/snippets/Cwise_boolean_xor.cpp
@@ -0,0 +1,2 @@
+Array3d v(-1,2,1), w(-3,2,3);
+cout << ((v<w) ^ (v<0)) << endl;
diff --git a/doc/snippets/Cwise_ceil.cpp b/doc/snippets/Cwise_ceil.cpp
new file mode 100644
index 0000000..76cf661
--- /dev/null
+++ b/doc/snippets/Cwise_ceil.cpp
@@ -0,0 +1,3 @@
+ArrayXd v = ArrayXd::LinSpaced(7,-2,2);
+cout << v << endl << endl;
+cout << ceil(v) << endl;
diff --git a/doc/snippets/Cwise_cos.cpp b/doc/snippets/Cwise_cos.cpp
new file mode 100644
index 0000000..f589f07
--- /dev/null
+++ b/doc/snippets/Cwise_cos.cpp
@@ -0,0 +1,2 @@
+Array3d v(M_PI, M_PI/2, M_PI/3);
+cout << v.cos() << endl;
diff --git a/doc/snippets/Cwise_cosh.cpp b/doc/snippets/Cwise_cosh.cpp
new file mode 100644
index 0000000..80ee75d
--- /dev/null
+++ b/doc/snippets/Cwise_cosh.cpp
@@ -0,0 +1,2 @@
+ArrayXd v = ArrayXd::LinSpaced(5,0,1);
+cout << cosh(v) << endl;
diff --git a/doc/snippets/Cwise_cube.cpp b/doc/snippets/Cwise_cube.cpp
new file mode 100644
index 0000000..85e41dc
--- /dev/null
+++ b/doc/snippets/Cwise_cube.cpp
@@ -0,0 +1,2 @@
+Array3d v(2,3,4);
+cout << v.cube() << endl;
diff --git a/doc/snippets/Cwise_equal_equal.cpp b/doc/snippets/Cwise_equal_equal.cpp
new file mode 100644
index 0000000..0ba96f6
--- /dev/null
+++ b/doc/snippets/Cwise_equal_equal.cpp
@@ -0,0 +1,2 @@
+Array3d v(1,2,3), w(3,2,1);
+cout << (v==w) << endl;
diff --git a/doc/snippets/Cwise_exp.cpp b/doc/snippets/Cwise_exp.cpp
new file mode 100644
index 0000000..db23618
--- /dev/null
+++ b/doc/snippets/Cwise_exp.cpp
@@ -0,0 +1,2 @@
+Array3d v(1,2,3);
+cout << v.exp() << endl;
diff --git a/doc/snippets/Cwise_floor.cpp b/doc/snippets/Cwise_floor.cpp
new file mode 100644
index 0000000..73756b4
--- /dev/null
+++ b/doc/snippets/Cwise_floor.cpp
@@ -0,0 +1,3 @@
+ArrayXd v = ArrayXd::LinSpaced(7,-2,2);
+cout << v << endl << endl;
+cout << floor(v) << endl;
diff --git a/doc/snippets/Cwise_greater.cpp b/doc/snippets/Cwise_greater.cpp
new file mode 100644
index 0000000..40ad029
--- /dev/null
+++ b/doc/snippets/Cwise_greater.cpp
@@ -0,0 +1,2 @@
+Array3d v(1,2,3), w(3,2,1);
+cout << (v>w) << endl;
diff --git a/doc/snippets/Cwise_greater_equal.cpp b/doc/snippets/Cwise_greater_equal.cpp
new file mode 100644
index 0000000..6a08f89
--- /dev/null
+++ b/doc/snippets/Cwise_greater_equal.cpp
@@ -0,0 +1,2 @@
+Array3d v(1,2,3), w(3,2,1);
+cout << (v>=w) << endl;
diff --git a/doc/snippets/Cwise_inverse.cpp b/doc/snippets/Cwise_inverse.cpp
new file mode 100644
index 0000000..3967a7e
--- /dev/null
+++ b/doc/snippets/Cwise_inverse.cpp
@@ -0,0 +1,2 @@
+Array3d v(2,3,4);
+cout << v.inverse() << endl;
diff --git a/doc/snippets/Cwise_isFinite.cpp b/doc/snippets/Cwise_isFinite.cpp
new file mode 100644
index 0000000..1da55fd
--- /dev/null
+++ b/doc/snippets/Cwise_isFinite.cpp
@@ -0,0 +1,5 @@
+Array3d v(1,2,3);
+v(1) *= 0.0/0.0;
+v(2) /= 0.0;
+cout << v << endl << endl;
+cout << isfinite(v) << endl;
diff --git a/doc/snippets/Cwise_isInf.cpp b/doc/snippets/Cwise_isInf.cpp
new file mode 100644
index 0000000..be79308
--- /dev/null
+++ b/doc/snippets/Cwise_isInf.cpp
@@ -0,0 +1,5 @@
+Array3d v(1,2,3);
+v(1) *= 0.0/0.0;
+v(2) /= 0.0;
+cout << v << endl << endl;
+cout << isinf(v) << endl;
diff --git a/doc/snippets/Cwise_isNaN.cpp b/doc/snippets/Cwise_isNaN.cpp
new file mode 100644
index 0000000..7b2a930
--- /dev/null
+++ b/doc/snippets/Cwise_isNaN.cpp
@@ -0,0 +1,5 @@
+Array3d v(1,2,3);
+v(1) *= 0.0/0.0;
+v(2) /= 0.0;
+cout << v << endl << endl;
+cout << isnan(v) << endl;
diff --git a/doc/snippets/Cwise_less.cpp b/doc/snippets/Cwise_less.cpp
new file mode 100644
index 0000000..cafd3b6
--- /dev/null
+++ b/doc/snippets/Cwise_less.cpp
@@ -0,0 +1,2 @@
+Array3d v(1,2,3), w(3,2,1);
+cout << (v<w) << endl;
diff --git a/doc/snippets/Cwise_less_equal.cpp b/doc/snippets/Cwise_less_equal.cpp
new file mode 100644
index 0000000..1600e39
--- /dev/null
+++ b/doc/snippets/Cwise_less_equal.cpp
@@ -0,0 +1,2 @@
+Array3d v(1,2,3), w(3,2,1);
+cout << (v<=w) << endl;
diff --git a/doc/snippets/Cwise_log.cpp b/doc/snippets/Cwise_log.cpp
new file mode 100644
index 0000000..f7aca72
--- /dev/null
+++ b/doc/snippets/Cwise_log.cpp
@@ -0,0 +1,2 @@
+Array3d v(1,2,3);
+cout << v.log() << endl;
diff --git a/doc/snippets/Cwise_log10.cpp b/doc/snippets/Cwise_log10.cpp
new file mode 100644
index 0000000..b7ae4a8
--- /dev/null
+++ b/doc/snippets/Cwise_log10.cpp
@@ -0,0 +1,2 @@
+Array4d v(-1,0,1,2);
+cout << log10(v) << endl;
diff --git a/doc/snippets/Cwise_max.cpp b/doc/snippets/Cwise_max.cpp
new file mode 100644
index 0000000..6602881
--- /dev/null
+++ b/doc/snippets/Cwise_max.cpp
@@ -0,0 +1,2 @@
+Array3d v(2,3,4), w(4,2,3);
+cout << v.max(w) << endl;
diff --git a/doc/snippets/Cwise_min.cpp b/doc/snippets/Cwise_min.cpp
new file mode 100644
index 0000000..1c01c76
--- /dev/null
+++ b/doc/snippets/Cwise_min.cpp
@@ -0,0 +1,2 @@
+Array3d v(2,3,4), w(4,2,3);
+cout << v.min(w) << endl;
diff --git a/doc/snippets/Cwise_minus.cpp b/doc/snippets/Cwise_minus.cpp
new file mode 100644
index 0000000..b89b9fb
--- /dev/null
+++ b/doc/snippets/Cwise_minus.cpp
@@ -0,0 +1,2 @@
+Array3d v(1,2,3);
+cout << v-5 << endl;
diff --git a/doc/snippets/Cwise_minus_equal.cpp b/doc/snippets/Cwise_minus_equal.cpp
new file mode 100644
index 0000000..dfde49d
--- /dev/null
+++ b/doc/snippets/Cwise_minus_equal.cpp
@@ -0,0 +1,3 @@
+Array3d v(1,2,3);
+v -= 5;
+cout << v << endl;
diff --git a/doc/snippets/Cwise_not_equal.cpp b/doc/snippets/Cwise_not_equal.cpp
new file mode 100644
index 0000000..57a407a
--- /dev/null
+++ b/doc/snippets/Cwise_not_equal.cpp
@@ -0,0 +1,2 @@
+Array3d v(1,2,3), w(3,2,1);
+cout << (v!=w) << endl;
diff --git a/doc/snippets/Cwise_plus.cpp b/doc/snippets/Cwise_plus.cpp
new file mode 100644
index 0000000..9d47327
--- /dev/null
+++ b/doc/snippets/Cwise_plus.cpp
@@ -0,0 +1,2 @@
+Array3d v(1,2,3);
+cout << v+5 << endl;
diff --git a/doc/snippets/Cwise_plus_equal.cpp b/doc/snippets/Cwise_plus_equal.cpp
new file mode 100644
index 0000000..d744b1e
--- /dev/null
+++ b/doc/snippets/Cwise_plus_equal.cpp
@@ -0,0 +1,3 @@
+Array3d v(1,2,3);
+v += 5;
+cout << v << endl;
diff --git a/doc/snippets/Cwise_pow.cpp b/doc/snippets/Cwise_pow.cpp
new file mode 100644
index 0000000..a723ed8
--- /dev/null
+++ b/doc/snippets/Cwise_pow.cpp
@@ -0,0 +1,2 @@
+Array3d v(8,27,64);
+cout << v.pow(0.333333) << endl;
diff --git a/doc/snippets/Cwise_product.cpp b/doc/snippets/Cwise_product.cpp
new file mode 100644
index 0000000..714d66d
--- /dev/null
+++ b/doc/snippets/Cwise_product.cpp
@@ -0,0 +1,4 @@
+Array33i a = Array33i::Random(), b = Array33i::Random();
+Array33i c = a * b;
+cout << "a:\n" << a << "\nb:\n" << b << "\nc:\n" << c << endl;
+
diff --git a/doc/snippets/Cwise_quotient.cpp b/doc/snippets/Cwise_quotient.cpp
new file mode 100644
index 0000000..7cb9f7f
--- /dev/null
+++ b/doc/snippets/Cwise_quotient.cpp
@@ -0,0 +1,2 @@
+Array3d v(2,3,4), w(4,2,3);
+cout << v/w << endl;
diff --git a/doc/snippets/Cwise_rint.cpp b/doc/snippets/Cwise_rint.cpp
new file mode 100644
index 0000000..1dc7b2f
--- /dev/null
+++ b/doc/snippets/Cwise_rint.cpp
@@ -0,0 +1,3 @@
+ArrayXd v = ArrayXd::LinSpaced(7,-2,2);
+cout << v << endl << endl;
+cout << rint(v) << endl;
diff --git a/doc/snippets/Cwise_round.cpp b/doc/snippets/Cwise_round.cpp
new file mode 100644
index 0000000..e5c8823
--- /dev/null
+++ b/doc/snippets/Cwise_round.cpp
@@ -0,0 +1,3 @@
+ArrayXd v = ArrayXd::LinSpaced(7,-2,2);
+cout << v << endl << endl;
+cout << round(v) << endl;
diff --git a/doc/snippets/Cwise_scalar_power_array.cpp b/doc/snippets/Cwise_scalar_power_array.cpp
new file mode 100644
index 0000000..c968b2c
--- /dev/null
+++ b/doc/snippets/Cwise_scalar_power_array.cpp
@@ -0,0 +1,2 @@
+Array<double,1,3> e(2,-3,1./3.);
+cout << "10^[" << e << "] = " << pow(10,e) << endl;
diff --git a/doc/snippets/Cwise_sign.cpp b/doc/snippets/Cwise_sign.cpp
new file mode 100644
index 0000000..49920e4
--- /dev/null
+++ b/doc/snippets/Cwise_sign.cpp
@@ -0,0 +1,2 @@
+Array3d v(-3,5,0);
+cout << v.sign() << endl;
diff --git a/doc/snippets/Cwise_sin.cpp b/doc/snippets/Cwise_sin.cpp
new file mode 100644
index 0000000..46fa908
--- /dev/null
+++ b/doc/snippets/Cwise_sin.cpp
@@ -0,0 +1,2 @@
+Array3d v(M_PI, M_PI/2, M_PI/3);
+cout << v.sin() << endl;
diff --git a/doc/snippets/Cwise_sinh.cpp b/doc/snippets/Cwise_sinh.cpp
new file mode 100644
index 0000000..fac9b19
--- /dev/null
+++ b/doc/snippets/Cwise_sinh.cpp
@@ -0,0 +1,2 @@
+ArrayXd v = ArrayXd::LinSpaced(5,0,1);
+cout << sinh(v) << endl;
diff --git a/doc/snippets/Cwise_slash_equal.cpp b/doc/snippets/Cwise_slash_equal.cpp
new file mode 100644
index 0000000..2efd32d
--- /dev/null
+++ b/doc/snippets/Cwise_slash_equal.cpp
@@ -0,0 +1,3 @@
+Array3d v(3,2,4), w(5,4,2);
+v /= w;
+cout << v << endl;
diff --git a/doc/snippets/Cwise_sqrt.cpp b/doc/snippets/Cwise_sqrt.cpp
new file mode 100644
index 0000000..97bafe8
--- /dev/null
+++ b/doc/snippets/Cwise_sqrt.cpp
@@ -0,0 +1,2 @@
+Array3d v(1,2,4);
+cout << v.sqrt() << endl;
diff --git a/doc/snippets/Cwise_square.cpp b/doc/snippets/Cwise_square.cpp
new file mode 100644
index 0000000..f704c5e
--- /dev/null
+++ b/doc/snippets/Cwise_square.cpp
@@ -0,0 +1,2 @@
+Array3d v(2,3,4);
+cout << v.square() << endl;
diff --git a/doc/snippets/Cwise_tan.cpp b/doc/snippets/Cwise_tan.cpp
new file mode 100644
index 0000000..b758ef0
--- /dev/null
+++ b/doc/snippets/Cwise_tan.cpp
@@ -0,0 +1,2 @@
+Array3d v(M_PI, M_PI/2, M_PI/3);
+cout << v.tan() << endl;
diff --git a/doc/snippets/Cwise_tanh.cpp b/doc/snippets/Cwise_tanh.cpp
new file mode 100644
index 0000000..30cd045
--- /dev/null
+++ b/doc/snippets/Cwise_tanh.cpp
@@ -0,0 +1,2 @@
+ArrayXd v = ArrayXd::LinSpaced(5,0,1);
+cout << tanh(v) << endl;
diff --git a/doc/snippets/Cwise_times_equal.cpp b/doc/snippets/Cwise_times_equal.cpp
new file mode 100644
index 0000000..147556c
--- /dev/null
+++ b/doc/snippets/Cwise_times_equal.cpp
@@ -0,0 +1,3 @@
+Array3d v(1,2,3), w(2,3,0);
+v *= w;
+cout << v << endl;
diff --git a/doc/snippets/DenseBase_LinSpaced.cpp b/doc/snippets/DenseBase_LinSpaced.cpp
new file mode 100644
index 0000000..8e54b17
--- /dev/null
+++ b/doc/snippets/DenseBase_LinSpaced.cpp
@@ -0,0 +1,2 @@
+cout << VectorXi::LinSpaced(4,7,10).transpose() << endl;
+cout << VectorXd::LinSpaced(5,0.0,1.0).transpose() << endl;
diff --git a/doc/snippets/DenseBase_LinSpacedInt.cpp b/doc/snippets/DenseBase_LinSpacedInt.cpp
new file mode 100644
index 0000000..0d7ae06
--- /dev/null
+++ b/doc/snippets/DenseBase_LinSpacedInt.cpp
@@ -0,0 +1,8 @@
+cout << "Even spacing inputs:" << endl;
+cout << VectorXi::LinSpaced(8,1,4).transpose() << endl;
+cout << VectorXi::LinSpaced(8,1,8).transpose() << endl;
+cout << VectorXi::LinSpaced(8,1,15).transpose() << endl;
+cout << "Uneven spacing inputs:" << endl;
+cout << VectorXi::LinSpaced(8,1,7).transpose() << endl;
+cout << VectorXi::LinSpaced(8,1,9).transpose() << endl;
+cout << VectorXi::LinSpaced(8,1,16).transpose() << endl;
diff --git a/doc/snippets/DenseBase_LinSpaced_seq_deprecated.cpp b/doc/snippets/DenseBase_LinSpaced_seq_deprecated.cpp
new file mode 100644
index 0000000..f55c508
--- /dev/null
+++ b/doc/snippets/DenseBase_LinSpaced_seq_deprecated.cpp
@@ -0,0 +1,2 @@
+cout << VectorXi::LinSpaced(Sequential,4,7,10).transpose() << endl;
+cout << VectorXd::LinSpaced(Sequential,5,0.0,1.0).transpose() << endl;
diff --git a/doc/snippets/DenseBase_setLinSpaced.cpp b/doc/snippets/DenseBase_setLinSpaced.cpp
new file mode 100644
index 0000000..46054f2
--- /dev/null
+++ b/doc/snippets/DenseBase_setLinSpaced.cpp
@@ -0,0 +1,3 @@
+VectorXf v;
+v.setLinSpaced(5,0.5f,1.5f);
+cout << v << endl;
diff --git a/doc/snippets/DirectionWise_hnormalized.cpp b/doc/snippets/DirectionWise_hnormalized.cpp
new file mode 100644
index 0000000..2451f6e
--- /dev/null
+++ b/doc/snippets/DirectionWise_hnormalized.cpp
@@ -0,0 +1,6 @@
+Matrix4Xd M = Matrix4Xd::Random(4,5);
+Projective3d P(Matrix4d::Random());
+cout << "The matrix M is:" << endl << M << endl << endl;
+cout << "M.colwise().hnormalized():" << endl << M.colwise().hnormalized() << endl << endl;
+cout << "P*M:" << endl << P*M << endl << endl;
+cout << "(P*M).colwise().hnormalized():" << endl << (P*M).colwise().hnormalized() << endl << endl;
diff --git a/doc/snippets/DirectionWise_replicate.cpp b/doc/snippets/DirectionWise_replicate.cpp
new file mode 100644
index 0000000..d92d4a3
--- /dev/null
+++ b/doc/snippets/DirectionWise_replicate.cpp
@@ -0,0 +1,4 @@
+MatrixXi m = MatrixXi::Random(2,3);
+cout << "Here is the matrix m:" << endl << m << endl;
+cout << "m.colwise().replicate<3>() = ..." << endl;
+cout << m.colwise().replicate<3>() << endl;
diff --git a/doc/snippets/DirectionWise_replicate_int.cpp b/doc/snippets/DirectionWise_replicate_int.cpp
new file mode 100644
index 0000000..f9b1b53
--- /dev/null
+++ b/doc/snippets/DirectionWise_replicate_int.cpp
@@ -0,0 +1,4 @@
+Vector3i v = Vector3i::Random();
+cout << "Here is the vector v:" << endl << v << endl;
+cout << "v.rowwise().replicate(5) = ..." << endl;
+cout << v.rowwise().replicate(5) << endl;
diff --git a/doc/snippets/EigenSolver_EigenSolver_MatrixType.cpp b/doc/snippets/EigenSolver_EigenSolver_MatrixType.cpp
new file mode 100644
index 0000000..c1d9fa8
--- /dev/null
+++ b/doc/snippets/EigenSolver_EigenSolver_MatrixType.cpp
@@ -0,0 +1,16 @@
+MatrixXd A = MatrixXd::Random(6,6);
+cout << "Here is a random 6x6 matrix, A:" << endl << A << endl << endl;
+
+EigenSolver<MatrixXd> es(A);
+cout << "The eigenvalues of A are:" << endl << es.eigenvalues() << endl;
+cout << "The matrix of eigenvectors, V, is:" << endl << es.eigenvectors() << endl << endl;
+
+complex<double> lambda = es.eigenvalues()[0];
+cout << "Consider the first eigenvalue, lambda = " << lambda << endl;
+VectorXcd v = es.eigenvectors().col(0);
+cout << "If v is the corresponding eigenvector, then lambda * v = " << endl << lambda * v << endl;
+cout << "... and A * v = " << endl << A.cast<complex<double> >() * v << endl << endl;
+
+MatrixXcd D = es.eigenvalues().asDiagonal();
+MatrixXcd V = es.eigenvectors();
+cout << "Finally, V * D * V^(-1) = " << endl << V * D * V.inverse() << endl;
diff --git a/doc/snippets/EigenSolver_compute.cpp b/doc/snippets/EigenSolver_compute.cpp
new file mode 100644
index 0000000..a5c96e9
--- /dev/null
+++ b/doc/snippets/EigenSolver_compute.cpp
@@ -0,0 +1,6 @@
+EigenSolver<MatrixXf> es;
+MatrixXf A = MatrixXf::Random(4,4);
+es.compute(A, /* computeEigenvectors = */ false);
+cout << "The eigenvalues of A are: " << es.eigenvalues().transpose() << endl;
+es.compute(A + MatrixXf::Identity(4,4), false); // re-use es to compute eigenvalues of A+I
+cout << "The eigenvalues of A+I are: " << es.eigenvalues().transpose() << endl;
diff --git a/doc/snippets/EigenSolver_eigenvalues.cpp b/doc/snippets/EigenSolver_eigenvalues.cpp
new file mode 100644
index 0000000..ed28869
--- /dev/null
+++ b/doc/snippets/EigenSolver_eigenvalues.cpp
@@ -0,0 +1,4 @@
+MatrixXd ones = MatrixXd::Ones(3,3);
+EigenSolver<MatrixXd> es(ones, false);
+cout << "The eigenvalues of the 3x3 matrix of ones are:"
+ << endl << es.eigenvalues() << endl;
diff --git a/doc/snippets/EigenSolver_eigenvectors.cpp b/doc/snippets/EigenSolver_eigenvectors.cpp
new file mode 100644
index 0000000..8355f76
--- /dev/null
+++ b/doc/snippets/EigenSolver_eigenvectors.cpp
@@ -0,0 +1,4 @@
+MatrixXd ones = MatrixXd::Ones(3,3);
+EigenSolver<MatrixXd> es(ones);
+cout << "The first eigenvector of the 3x3 matrix of ones is:"
+ << endl << es.eigenvectors().col(0) << endl;
diff --git a/doc/snippets/EigenSolver_pseudoEigenvectors.cpp b/doc/snippets/EigenSolver_pseudoEigenvectors.cpp
new file mode 100644
index 0000000..85e2569
--- /dev/null
+++ b/doc/snippets/EigenSolver_pseudoEigenvectors.cpp
@@ -0,0 +1,9 @@
+MatrixXd A = MatrixXd::Random(6,6);
+cout << "Here is a random 6x6 matrix, A:" << endl << A << endl << endl;
+
+EigenSolver<MatrixXd> es(A);
+MatrixXd D = es.pseudoEigenvalueMatrix();
+MatrixXd V = es.pseudoEigenvectors();
+cout << "The pseudo-eigenvalue matrix D is:" << endl << D << endl;
+cout << "The pseudo-eigenvector matrix V is:" << endl << V << endl;
+cout << "Finally, V * D * V^(-1) = " << endl << V * D * V.inverse() << endl;
diff --git a/doc/snippets/FullPivHouseholderQR_solve.cpp b/doc/snippets/FullPivHouseholderQR_solve.cpp
new file mode 100644
index 0000000..23bc074
--- /dev/null
+++ b/doc/snippets/FullPivHouseholderQR_solve.cpp
@@ -0,0 +1,8 @@
+Matrix3f m = Matrix3f::Random();
+Matrix3f y = Matrix3f::Random();
+cout << "Here is the matrix m:" << endl << m << endl;
+cout << "Here is the matrix y:" << endl << y << endl;
+Matrix3f x;
+x = m.fullPivHouseholderQr().solve(y);
+assert(y.isApprox(m*x));
+cout << "Here is a solution x to the equation mx=y:" << endl << x << endl;
diff --git a/doc/snippets/FullPivLU_image.cpp b/doc/snippets/FullPivLU_image.cpp
new file mode 100644
index 0000000..817bc1e
--- /dev/null
+++ b/doc/snippets/FullPivLU_image.cpp
@@ -0,0 +1,9 @@
+Matrix3d m;
+m << 1,1,0,
+ 1,3,2,
+ 0,1,1;
+cout << "Here is the matrix m:" << endl << m << endl;
+cout << "Notice that the middle column is the sum of the two others, so the "
+ << "columns are linearly dependent." << endl;
+cout << "Here is a matrix whose columns have the same span but are linearly independent:"
+ << endl << m.fullPivLu().image(m) << endl;
diff --git a/doc/snippets/FullPivLU_kernel.cpp b/doc/snippets/FullPivLU_kernel.cpp
new file mode 100644
index 0000000..7086e01
--- /dev/null
+++ b/doc/snippets/FullPivLU_kernel.cpp
@@ -0,0 +1,7 @@
+MatrixXf m = MatrixXf::Random(3,5);
+cout << "Here is the matrix m:" << endl << m << endl;
+MatrixXf ker = m.fullPivLu().kernel();
+cout << "Here is a matrix whose columns form a basis of the kernel of m:"
+ << endl << ker << endl;
+cout << "By definition of the kernel, m*ker is zero:"
+ << endl << m*ker << endl;
diff --git a/doc/snippets/FullPivLU_solve.cpp b/doc/snippets/FullPivLU_solve.cpp
new file mode 100644
index 0000000..c1f8823
--- /dev/null
+++ b/doc/snippets/FullPivLU_solve.cpp
@@ -0,0 +1,11 @@
+Matrix<float,2,3> m = Matrix<float,2,3>::Random();
+Matrix2f y = Matrix2f::Random();
+cout << "Here is the matrix m:" << endl << m << endl;
+cout << "Here is the matrix y:" << endl << y << endl;
+Matrix<float,3,2> x = m.fullPivLu().solve(y);
+if((m*x).isApprox(y))
+{
+ cout << "Here is a solution x to the equation mx=y:" << endl << x << endl;
+}
+else
+ cout << "The equation mx=y does not have any solution." << endl;
diff --git a/doc/snippets/GeneralizedEigenSolver.cpp b/doc/snippets/GeneralizedEigenSolver.cpp
new file mode 100644
index 0000000..2acda45
--- /dev/null
+++ b/doc/snippets/GeneralizedEigenSolver.cpp
@@ -0,0 +1,7 @@
+GeneralizedEigenSolver<MatrixXf> ges;
+MatrixXf A = MatrixXf::Random(4,4);
+MatrixXf B = MatrixXf::Random(4,4);
+ges.compute(A, B);
+cout << "The (complex) numerators of the generalzied eigenvalues are: " << ges.alphas().transpose() << endl;
+cout << "The (real) denominatore of the generalzied eigenvalues are: " << ges.betas().transpose() << endl;
+cout << "The (complex) generalzied eigenvalues are (alphas./beta): " << ges.eigenvalues().transpose() << endl;
diff --git a/doc/snippets/HessenbergDecomposition_compute.cpp b/doc/snippets/HessenbergDecomposition_compute.cpp
new file mode 100644
index 0000000..50e3783
--- /dev/null
+++ b/doc/snippets/HessenbergDecomposition_compute.cpp
@@ -0,0 +1,6 @@
+MatrixXcf A = MatrixXcf::Random(4,4);
+HessenbergDecomposition<MatrixXcf> hd(4);
+hd.compute(A);
+cout << "The matrix H in the decomposition of A is:" << endl << hd.matrixH() << endl;
+hd.compute(2*A); // re-use hd to compute and store decomposition of 2A
+cout << "The matrix H in the decomposition of 2A is:" << endl << hd.matrixH() << endl;
diff --git a/doc/snippets/HessenbergDecomposition_matrixH.cpp b/doc/snippets/HessenbergDecomposition_matrixH.cpp
new file mode 100644
index 0000000..af01366
--- /dev/null
+++ b/doc/snippets/HessenbergDecomposition_matrixH.cpp
@@ -0,0 +1,8 @@
+Matrix4f A = MatrixXf::Random(4,4);
+cout << "Here is a random 4x4 matrix:" << endl << A << endl;
+HessenbergDecomposition<MatrixXf> hessOfA(A);
+MatrixXf H = hessOfA.matrixH();
+cout << "The Hessenberg matrix H is:" << endl << H << endl;
+MatrixXf Q = hessOfA.matrixQ();
+cout << "The orthogonal matrix Q is:" << endl << Q << endl;
+cout << "Q H Q^T is:" << endl << Q * H * Q.transpose() << endl;
diff --git a/doc/snippets/HessenbergDecomposition_packedMatrix.cpp b/doc/snippets/HessenbergDecomposition_packedMatrix.cpp
new file mode 100644
index 0000000..4fa5957
--- /dev/null
+++ b/doc/snippets/HessenbergDecomposition_packedMatrix.cpp
@@ -0,0 +1,9 @@
+Matrix4d A = Matrix4d::Random(4,4);
+cout << "Here is a random 4x4 matrix:" << endl << A << endl;
+HessenbergDecomposition<Matrix4d> hessOfA(A);
+Matrix4d pm = hessOfA.packedMatrix();
+cout << "The packed matrix M is:" << endl << pm << endl;
+cout << "The upper Hessenberg part corresponds to the matrix H, which is:"
+ << endl << hessOfA.matrixH() << endl;
+Vector3d hc = hessOfA.householderCoefficients();
+cout << "The vector of Householder coefficients is:" << endl << hc << endl;
diff --git a/doc/snippets/HouseholderQR_householderQ.cpp b/doc/snippets/HouseholderQR_householderQ.cpp
new file mode 100644
index 0000000..e859ce5
--- /dev/null
+++ b/doc/snippets/HouseholderQR_householderQ.cpp
@@ -0,0 +1,7 @@
+MatrixXf A(MatrixXf::Random(5,3)), thinQ(MatrixXf::Identity(5,3)), Q;
+A.setRandom();
+HouseholderQR<MatrixXf> qr(A);
+Q = qr.householderQ();
+thinQ = qr.householderQ() * thinQ;
+std::cout << "The complete unitary matrix Q is:\n" << Q << "\n\n";
+std::cout << "The thin matrix Q is:\n" << thinQ << "\n\n";
diff --git a/doc/snippets/HouseholderQR_solve.cpp b/doc/snippets/HouseholderQR_solve.cpp
new file mode 100644
index 0000000..8cce6ce
--- /dev/null
+++ b/doc/snippets/HouseholderQR_solve.cpp
@@ -0,0 +1,9 @@
+typedef Matrix<float,3,3> Matrix3x3;
+Matrix3x3 m = Matrix3x3::Random();
+Matrix3f y = Matrix3f::Random();
+cout << "Here is the matrix m:" << endl << m << endl;
+cout << "Here is the matrix y:" << endl << y << endl;
+Matrix3f x;
+x = m.householderQr().solve(y);
+assert(y.isApprox(m*x));
+cout << "Here is a solution x to the equation mx=y:" << endl << x << endl;
diff --git a/doc/snippets/HouseholderSequence_HouseholderSequence.cpp b/doc/snippets/HouseholderSequence_HouseholderSequence.cpp
new file mode 100644
index 0000000..2632b83
--- /dev/null
+++ b/doc/snippets/HouseholderSequence_HouseholderSequence.cpp
@@ -0,0 +1,31 @@
+Matrix3d v = Matrix3d::Random();
+cout << "The matrix v is:" << endl;
+cout << v << endl;
+
+Vector3d v0(1, v(1,0), v(2,0));
+cout << "The first Householder vector is: v_0 = " << v0.transpose() << endl;
+Vector3d v1(0, 1, v(2,1));
+cout << "The second Householder vector is: v_1 = " << v1.transpose() << endl;
+Vector3d v2(0, 0, 1);
+cout << "The third Householder vector is: v_2 = " << v2.transpose() << endl;
+
+Vector3d h = Vector3d::Random();
+cout << "The Householder coefficients are: h = " << h.transpose() << endl;
+
+Matrix3d H0 = Matrix3d::Identity() - h(0) * v0 * v0.adjoint();
+cout << "The first Householder reflection is represented by H_0 = " << endl;
+cout << H0 << endl;
+Matrix3d H1 = Matrix3d::Identity() - h(1) * v1 * v1.adjoint();
+cout << "The second Householder reflection is represented by H_1 = " << endl;
+cout << H1 << endl;
+Matrix3d H2 = Matrix3d::Identity() - h(2) * v2 * v2.adjoint();
+cout << "The third Householder reflection is represented by H_2 = " << endl;
+cout << H2 << endl;
+cout << "Their product is H_0 H_1 H_2 = " << endl;
+cout << H0 * H1 * H2 << endl;
+
+HouseholderSequence<Matrix3d, Vector3d> hhSeq(v, h);
+Matrix3d hhSeqAsMatrix(hhSeq);
+cout << "If we construct a HouseholderSequence from v and h" << endl;
+cout << "and convert it to a matrix, we get:" << endl;
+cout << hhSeqAsMatrix << endl;
diff --git a/doc/snippets/IOFormat.cpp b/doc/snippets/IOFormat.cpp
new file mode 100644
index 0000000..735f5dd
--- /dev/null
+++ b/doc/snippets/IOFormat.cpp
@@ -0,0 +1,14 @@
+std::string sep = "\n----------------------------------------\n";
+Matrix3d m1;
+m1 << 1.111111, 2, 3.33333, 4, 5, 6, 7, 8.888888, 9;
+
+IOFormat CommaInitFmt(StreamPrecision, DontAlignCols, ", ", ", ", "", "", " << ", ";");
+IOFormat CleanFmt(4, 0, ", ", "\n", "[", "]");
+IOFormat OctaveFmt(StreamPrecision, 0, ", ", ";\n", "", "", "[", "]");
+IOFormat HeavyFmt(FullPrecision, 0, ", ", ";\n", "[", "]", "[", "]");
+
+std::cout << m1 << sep;
+std::cout << m1.format(CommaInitFmt) << sep;
+std::cout << m1.format(CleanFmt) << sep;
+std::cout << m1.format(OctaveFmt) << sep;
+std::cout << m1.format(HeavyFmt) << sep;
diff --git a/doc/snippets/JacobiSVD_basic.cpp b/doc/snippets/JacobiSVD_basic.cpp
new file mode 100644
index 0000000..6c21baf
--- /dev/null
+++ b/doc/snippets/JacobiSVD_basic.cpp
@@ -0,0 +1,9 @@
+MatrixXf m = MatrixXf::Random(3,2);
+cout << "Here is the matrix m:" << endl << m << endl;
+JacobiSVD<MatrixXf, ComputeThinU | ComputeThinV> svd(m);
+cout << "Its singular values are:" << endl << svd.singularValues() << endl;
+cout << "Its left singular vectors are the columns of the thin U matrix:" << endl << svd.matrixU() << endl;
+cout << "Its right singular vectors are the columns of the thin V matrix:" << endl << svd.matrixV() << endl;
+Vector3f rhs(1, 0, 0);
+cout << "Now consider this rhs vector:" << endl << rhs << endl;
+cout << "A least-squares solution of m*x = rhs is:" << endl << svd.solve(rhs) << endl;
diff --git a/doc/snippets/Jacobi_makeGivens.cpp b/doc/snippets/Jacobi_makeGivens.cpp
new file mode 100644
index 0000000..6f8ec05
--- /dev/null
+++ b/doc/snippets/Jacobi_makeGivens.cpp
@@ -0,0 +1,6 @@
+Vector2f v = Vector2f::Random();
+JacobiRotation<float> G;
+G.makeGivens(v.x(), v.y());
+cout << "Here is the vector v:" << endl << v << endl;
+v.applyOnTheLeft(0, 1, G.adjoint());
+cout << "Here is the vector J' * v:" << endl << v << endl;
diff --git a/doc/snippets/Jacobi_makeJacobi.cpp b/doc/snippets/Jacobi_makeJacobi.cpp
new file mode 100644
index 0000000..a86e80a
--- /dev/null
+++ b/doc/snippets/Jacobi_makeJacobi.cpp
@@ -0,0 +1,8 @@
+Matrix2f m = Matrix2f::Random();
+m = (m + m.adjoint()).eval();
+JacobiRotation<float> J;
+J.makeJacobi(m, 0, 1);
+cout << "Here is the matrix m:" << endl << m << endl;
+m.applyOnTheLeft(0, 1, J.adjoint());
+m.applyOnTheRight(0, 1, J);
+cout << "Here is the matrix J' * m * J:" << endl << m << endl;
diff --git a/doc/snippets/LLT_example.cpp b/doc/snippets/LLT_example.cpp
new file mode 100644
index 0000000..46fb407
--- /dev/null
+++ b/doc/snippets/LLT_example.cpp
@@ -0,0 +1,12 @@
+MatrixXd A(3,3);
+A << 4,-1,2, -1,6,0, 2,0,5;
+cout << "The matrix A is" << endl << A << endl;
+
+LLT<MatrixXd> lltOfA(A); // compute the Cholesky decomposition of A
+MatrixXd L = lltOfA.matrixL(); // retrieve factor L in the decomposition
+// The previous two lines can also be written as "L = A.llt().matrixL()"
+
+cout << "The Cholesky factor L is" << endl << L << endl;
+cout << "To check this, let us compute L * L.transpose()" << endl;
+cout << L * L.transpose() << endl;
+cout << "This should equal the matrix A" << endl;
diff --git a/doc/snippets/LLT_solve.cpp b/doc/snippets/LLT_solve.cpp
new file mode 100644
index 0000000..7095d2c
--- /dev/null
+++ b/doc/snippets/LLT_solve.cpp
@@ -0,0 +1,8 @@
+typedef Matrix<float,Dynamic,2> DataMatrix;
+// let's generate some samples on the 3D plane of equation z = 2x+3y (with some noise)
+DataMatrix samples = DataMatrix::Random(12,2);
+VectorXf elevations = 2*samples.col(0) + 3*samples.col(1) + VectorXf::Random(12)*0.1;
+// and let's solve samples * [x y]^T = elevations in least square sense:
+Matrix<float,2,1> xy
+ = (samples.adjoint() * samples).llt().solve((samples.adjoint()*elevations));
+cout << xy << endl;
diff --git a/doc/snippets/LeastSquaresNormalEquations.cpp b/doc/snippets/LeastSquaresNormalEquations.cpp
new file mode 100644
index 0000000..997cf17
--- /dev/null
+++ b/doc/snippets/LeastSquaresNormalEquations.cpp
@@ -0,0 +1,4 @@
+MatrixXf A = MatrixXf::Random(3, 2);
+VectorXf b = VectorXf::Random(3);
+cout << "The solution using normal equations is:\n"
+ << (A.transpose() * A).ldlt().solve(A.transpose() * b) << endl;
diff --git a/doc/snippets/LeastSquaresQR.cpp b/doc/snippets/LeastSquaresQR.cpp
new file mode 100644
index 0000000..6c97045
--- /dev/null
+++ b/doc/snippets/LeastSquaresQR.cpp
@@ -0,0 +1,4 @@
+MatrixXf A = MatrixXf::Random(3, 2);
+VectorXf b = VectorXf::Random(3);
+cout << "The solution using the QR decomposition is:\n"
+ << A.colPivHouseholderQr().solve(b) << endl;
diff --git a/doc/snippets/Map_general_stride.cpp b/doc/snippets/Map_general_stride.cpp
new file mode 100644
index 0000000..0657e7f
--- /dev/null
+++ b/doc/snippets/Map_general_stride.cpp
@@ -0,0 +1,5 @@
+int array[24];
+for(int i = 0; i < 24; ++i) array[i] = i;
+cout << Map<MatrixXi, 0, Stride<Dynamic,2> >
+ (array, 3, 3, Stride<Dynamic,2>(8, 2))
+ << endl;
diff --git a/doc/snippets/Map_inner_stride.cpp b/doc/snippets/Map_inner_stride.cpp
new file mode 100644
index 0000000..d95ae9b
--- /dev/null
+++ b/doc/snippets/Map_inner_stride.cpp
@@ -0,0 +1,5 @@
+int array[12];
+for(int i = 0; i < 12; ++i) array[i] = i;
+cout << Map<VectorXi, 0, InnerStride<2> >
+ (array, 6) // the inner stride has already been passed as template parameter
+ << endl;
diff --git a/doc/snippets/Map_outer_stride.cpp b/doc/snippets/Map_outer_stride.cpp
new file mode 100644
index 0000000..2f6f052
--- /dev/null
+++ b/doc/snippets/Map_outer_stride.cpp
@@ -0,0 +1,3 @@
+int array[12];
+for(int i = 0; i < 12; ++i) array[i] = i;
+cout << Map<MatrixXi, 0, OuterStride<> >(array, 3, 3, OuterStride<>(4)) << endl;
diff --git a/doc/snippets/Map_placement_new.cpp b/doc/snippets/Map_placement_new.cpp
new file mode 100644
index 0000000..83b83a8
--- /dev/null
+++ b/doc/snippets/Map_placement_new.cpp
@@ -0,0 +1,5 @@
+int data[] = {1,2,3,4,5,6,7,8,9};
+Map<RowVectorXi> v(data,4);
+cout << "The mapped vector v is: " << v << "\n";
+new (&v) Map<RowVectorXi>(data+4,5);
+cout << "Now v is: " << v << "\n";
diff --git a/doc/snippets/Map_simple.cpp b/doc/snippets/Map_simple.cpp
new file mode 100644
index 0000000..423bb52
--- /dev/null
+++ b/doc/snippets/Map_simple.cpp
@@ -0,0 +1,3 @@
+int array[9];
+for(int i = 0; i < 9; ++i) array[i] = i;
+cout << Map<Matrix3i>(array) << endl;
diff --git a/doc/snippets/MatrixBase_adjoint.cpp b/doc/snippets/MatrixBase_adjoint.cpp
new file mode 100644
index 0000000..4680d59
--- /dev/null
+++ b/doc/snippets/MatrixBase_adjoint.cpp
@@ -0,0 +1,3 @@
+Matrix2cf m = Matrix2cf::Random();
+cout << "Here is the 2x2 complex matrix m:" << endl << m << endl;
+cout << "Here is the adjoint of m:" << endl << m.adjoint() << endl;
diff --git a/doc/snippets/MatrixBase_all.cpp b/doc/snippets/MatrixBase_all.cpp
new file mode 100644
index 0000000..46f26f1
--- /dev/null
+++ b/doc/snippets/MatrixBase_all.cpp
@@ -0,0 +1,7 @@
+Vector3f boxMin(Vector3f::Zero()), boxMax(Vector3f::Ones());
+Vector3f p0 = Vector3f::Random(), p1 = Vector3f::Random().cwiseAbs();
+// let's check if p0 and p1 are inside the axis aligned box defined by the corners boxMin,boxMax:
+cout << "Is (" << p0.transpose() << ") inside the box: "
+ << ((boxMin.array()<p0.array()).all() && (boxMax.array()>p0.array()).all()) << endl;
+cout << "Is (" << p1.transpose() << ") inside the box: "
+ << ((boxMin.array()<p1.array()).all() && (boxMax.array()>p1.array()).all()) << endl;
diff --git a/doc/snippets/MatrixBase_applyOnTheLeft.cpp b/doc/snippets/MatrixBase_applyOnTheLeft.cpp
new file mode 100644
index 0000000..6398c87
--- /dev/null
+++ b/doc/snippets/MatrixBase_applyOnTheLeft.cpp
@@ -0,0 +1,7 @@
+Matrix3f A = Matrix3f::Random(3,3), B;
+B << 0,1,0,
+ 0,0,1,
+ 1,0,0;
+cout << "At start, A = " << endl << A << endl;
+A.applyOnTheLeft(B);
+cout << "After applyOnTheLeft, A = " << endl << A << endl;
diff --git a/doc/snippets/MatrixBase_applyOnTheRight.cpp b/doc/snippets/MatrixBase_applyOnTheRight.cpp
new file mode 100644
index 0000000..e4b71b2
--- /dev/null
+++ b/doc/snippets/MatrixBase_applyOnTheRight.cpp
@@ -0,0 +1,9 @@
+Matrix3f A = Matrix3f::Random(3,3), B;
+B << 0,1,0,
+ 0,0,1,
+ 1,0,0;
+cout << "At start, A = " << endl << A << endl;
+A *= B;
+cout << "After A *= B, A = " << endl << A << endl;
+A.applyOnTheRight(B); // equivalent to A *= B
+cout << "After applyOnTheRight, A = " << endl << A << endl;
diff --git a/doc/snippets/MatrixBase_array.cpp b/doc/snippets/MatrixBase_array.cpp
new file mode 100644
index 0000000..f215086
--- /dev/null
+++ b/doc/snippets/MatrixBase_array.cpp
@@ -0,0 +1,4 @@
+Vector3d v(1,2,3);
+v.array() += 3;
+v.array() -= 2;
+cout << v << endl;
diff --git a/doc/snippets/MatrixBase_array_const.cpp b/doc/snippets/MatrixBase_array_const.cpp
new file mode 100644
index 0000000..cd3b26a
--- /dev/null
+++ b/doc/snippets/MatrixBase_array_const.cpp
@@ -0,0 +1,4 @@
+Vector3d v(-1,2,-3);
+cout << "the absolute values:" << endl << v.array().abs() << endl;
+cout << "the absolute values plus one:" << endl << v.array().abs()+1 << endl;
+cout << "sum of the squares: " << v.array().square().sum() << endl;
diff --git a/doc/snippets/MatrixBase_asDiagonal.cpp b/doc/snippets/MatrixBase_asDiagonal.cpp
new file mode 100644
index 0000000..b01082d
--- /dev/null
+++ b/doc/snippets/MatrixBase_asDiagonal.cpp
@@ -0,0 +1 @@
+cout << Matrix3i(Vector3i(2,5,6).asDiagonal()) << endl;
diff --git a/doc/snippets/MatrixBase_block_int_int.cpp b/doc/snippets/MatrixBase_block_int_int.cpp
new file mode 100644
index 0000000..f99b6d4
--- /dev/null
+++ b/doc/snippets/MatrixBase_block_int_int.cpp
@@ -0,0 +1,5 @@
+Matrix4i m = Matrix4i::Random();
+cout << "Here is the matrix m:" << endl << m << endl;
+cout << "Here is m.block<2,2>(1,1):" << endl << m.block<2,2>(1,1) << endl;
+m.block<2,2>(1,1).setZero();
+cout << "Now the matrix m is:" << endl << m << endl;
diff --git a/doc/snippets/MatrixBase_block_int_int_int_int.cpp b/doc/snippets/MatrixBase_block_int_int_int_int.cpp
new file mode 100644
index 0000000..7238cbb
--- /dev/null
+++ b/doc/snippets/MatrixBase_block_int_int_int_int.cpp
@@ -0,0 +1,5 @@
+Matrix4i m = Matrix4i::Random();
+cout << "Here is the matrix m:" << endl << m << endl;
+cout << "Here is m.block(1, 1, 2, 2):" << endl << m.block(1, 1, 2, 2) << endl;
+m.block(1, 1, 2, 2).setZero();
+cout << "Now the matrix m is:" << endl << m << endl;
diff --git a/doc/snippets/MatrixBase_bottomLeftCorner_int_int.cpp b/doc/snippets/MatrixBase_bottomLeftCorner_int_int.cpp
new file mode 100644
index 0000000..ebae95e
--- /dev/null
+++ b/doc/snippets/MatrixBase_bottomLeftCorner_int_int.cpp
@@ -0,0 +1,6 @@
+Matrix4i m = Matrix4i::Random();
+cout << "Here is the matrix m:" << endl << m << endl;
+cout << "Here is m.bottomLeftCorner(2, 2):" << endl;
+cout << m.bottomLeftCorner(2, 2) << endl;
+m.bottomLeftCorner(2, 2).setZero();
+cout << "Now the matrix m is:" << endl << m << endl;
diff --git a/doc/snippets/MatrixBase_bottomRightCorner_int_int.cpp b/doc/snippets/MatrixBase_bottomRightCorner_int_int.cpp
new file mode 100644
index 0000000..bf05093
--- /dev/null
+++ b/doc/snippets/MatrixBase_bottomRightCorner_int_int.cpp
@@ -0,0 +1,6 @@
+Matrix4i m = Matrix4i::Random();
+cout << "Here is the matrix m:" << endl << m << endl;
+cout << "Here is m.bottomRightCorner(2, 2):" << endl;
+cout << m.bottomRightCorner(2, 2) << endl;
+m.bottomRightCorner(2, 2).setZero();
+cout << "Now the matrix m is:" << endl << m << endl;
diff --git a/doc/snippets/MatrixBase_bottomRows_int.cpp b/doc/snippets/MatrixBase_bottomRows_int.cpp
new file mode 100644
index 0000000..47ca92e
--- /dev/null
+++ b/doc/snippets/MatrixBase_bottomRows_int.cpp
@@ -0,0 +1,6 @@
+Array44i a = Array44i::Random();
+cout << "Here is the array a:" << endl << a << endl;
+cout << "Here is a.bottomRows(2):" << endl;
+cout << a.bottomRows(2) << endl;
+a.bottomRows(2).setZero();
+cout << "Now the array a is:" << endl << a << endl;
diff --git a/doc/snippets/MatrixBase_cast.cpp b/doc/snippets/MatrixBase_cast.cpp
new file mode 100644
index 0000000..016880b
--- /dev/null
+++ b/doc/snippets/MatrixBase_cast.cpp
@@ -0,0 +1,3 @@
+Matrix2d md = Matrix2d::Identity() * 0.45;
+Matrix2f mf = Matrix2f::Identity();
+cout << md + mf.cast<double>() << endl;
diff --git a/doc/snippets/MatrixBase_col.cpp b/doc/snippets/MatrixBase_col.cpp
new file mode 100644
index 0000000..87c91b1
--- /dev/null
+++ b/doc/snippets/MatrixBase_col.cpp
@@ -0,0 +1,3 @@
+Matrix3d m = Matrix3d::Identity();
+m.col(1) = Vector3d(4,5,6);
+cout << m << endl;
diff --git a/doc/snippets/MatrixBase_colwise.cpp b/doc/snippets/MatrixBase_colwise.cpp
new file mode 100644
index 0000000..a048bef
--- /dev/null
+++ b/doc/snippets/MatrixBase_colwise.cpp
@@ -0,0 +1,5 @@
+Matrix3d m = Matrix3d::Random();
+cout << "Here is the matrix m:" << endl << m << endl;
+cout << "Here is the sum of each column:" << endl << m.colwise().sum() << endl;
+cout << "Here is the maximum absolute value of each column:"
+ << endl << m.cwiseAbs().colwise().maxCoeff() << endl;
diff --git a/doc/snippets/MatrixBase_colwise_iterator_cxx11.cpp b/doc/snippets/MatrixBase_colwise_iterator_cxx11.cpp
new file mode 100644
index 0000000..116063f
--- /dev/null
+++ b/doc/snippets/MatrixBase_colwise_iterator_cxx11.cpp
@@ -0,0 +1,12 @@
+Matrix3i m = Matrix3i::Random();
+cout << "Here is the initial matrix m:" << endl << m << endl;
+int i = -1;
+for(auto c: m.colwise()) {
+ c *= i;
+ ++i;
+}
+cout << "Here is the matrix m after the for-range-loop:" << endl << m << endl;
+auto cols = m.colwise();
+auto it = std::find_if(cols.cbegin(), cols.cend(),
+ [](Matrix3i::ConstColXpr x) { return x.squaredNorm() == 0; });
+cout << "The first empty column is: " << distance(cols.cbegin(),it) << endl;
diff --git a/doc/snippets/MatrixBase_computeInverseAndDetWithCheck.cpp b/doc/snippets/MatrixBase_computeInverseAndDetWithCheck.cpp
new file mode 100644
index 0000000..a7b084f
--- /dev/null
+++ b/doc/snippets/MatrixBase_computeInverseAndDetWithCheck.cpp
@@ -0,0 +1,13 @@
+Matrix3d m = Matrix3d::Random();
+cout << "Here is the matrix m:" << endl << m << endl;
+Matrix3d inverse;
+bool invertible;
+double determinant;
+m.computeInverseAndDetWithCheck(inverse,determinant,invertible);
+cout << "Its determinant is " << determinant << endl;
+if(invertible) {
+ cout << "It is invertible, and its inverse is:" << endl << inverse << endl;
+}
+else {
+ cout << "It is not invertible." << endl;
+}
diff --git a/doc/snippets/MatrixBase_computeInverseWithCheck.cpp b/doc/snippets/MatrixBase_computeInverseWithCheck.cpp
new file mode 100644
index 0000000..873a9f8
--- /dev/null
+++ b/doc/snippets/MatrixBase_computeInverseWithCheck.cpp
@@ -0,0 +1,11 @@
+Matrix3d m = Matrix3d::Random();
+cout << "Here is the matrix m:" << endl << m << endl;
+Matrix3d inverse;
+bool invertible;
+m.computeInverseWithCheck(inverse,invertible);
+if(invertible) {
+ cout << "It is invertible, and its inverse is:" << endl << inverse << endl;
+}
+else {
+ cout << "It is not invertible." << endl;
+}
diff --git a/doc/snippets/MatrixBase_cwiseAbs.cpp b/doc/snippets/MatrixBase_cwiseAbs.cpp
new file mode 100644
index 0000000..28a3160
--- /dev/null
+++ b/doc/snippets/MatrixBase_cwiseAbs.cpp
@@ -0,0 +1,4 @@
+MatrixXd m(2,3);
+m << 2, -4, 6,
+ -5, 1, 0;
+cout << m.cwiseAbs() << endl;
diff --git a/doc/snippets/MatrixBase_cwiseAbs2.cpp b/doc/snippets/MatrixBase_cwiseAbs2.cpp
new file mode 100644
index 0000000..889a2e2
--- /dev/null
+++ b/doc/snippets/MatrixBase_cwiseAbs2.cpp
@@ -0,0 +1,4 @@
+MatrixXd m(2,3);
+m << 2, -4, 6,
+ -5, 1, 0;
+cout << m.cwiseAbs2() << endl;
diff --git a/doc/snippets/MatrixBase_cwiseArg.cpp b/doc/snippets/MatrixBase_cwiseArg.cpp
new file mode 100644
index 0000000..e0857cf
--- /dev/null
+++ b/doc/snippets/MatrixBase_cwiseArg.cpp
@@ -0,0 +1,3 @@
+MatrixXcf v = MatrixXcf::Random(2, 3);
+cout << v << endl << endl;
+cout << v.cwiseArg() << endl;
\ No newline at end of file
diff --git a/doc/snippets/MatrixBase_cwiseEqual.cpp b/doc/snippets/MatrixBase_cwiseEqual.cpp
new file mode 100644
index 0000000..469af64
--- /dev/null
+++ b/doc/snippets/MatrixBase_cwiseEqual.cpp
@@ -0,0 +1,7 @@
+MatrixXi m(2,2);
+m << 1, 0,
+ 1, 1;
+cout << "Comparing m with identity matrix:" << endl;
+cout << m.cwiseEqual(MatrixXi::Identity(2,2)) << endl;
+Index count = m.cwiseEqual(MatrixXi::Identity(2,2)).count();
+cout << "Number of coefficients that are equal: " << count << endl;
diff --git a/doc/snippets/MatrixBase_cwiseInverse.cpp b/doc/snippets/MatrixBase_cwiseInverse.cpp
new file mode 100644
index 0000000..23e08f7
--- /dev/null
+++ b/doc/snippets/MatrixBase_cwiseInverse.cpp
@@ -0,0 +1,4 @@
+MatrixXd m(2,3);
+m << 2, 0.5, 1,
+ 3, 0.25, 1;
+cout << m.cwiseInverse() << endl;
diff --git a/doc/snippets/MatrixBase_cwiseMax.cpp b/doc/snippets/MatrixBase_cwiseMax.cpp
new file mode 100644
index 0000000..3c95681
--- /dev/null
+++ b/doc/snippets/MatrixBase_cwiseMax.cpp
@@ -0,0 +1,2 @@
+Vector3d v(2,3,4), w(4,2,3);
+cout << v.cwiseMax(w) << endl;
diff --git a/doc/snippets/MatrixBase_cwiseMin.cpp b/doc/snippets/MatrixBase_cwiseMin.cpp
new file mode 100644
index 0000000..82fc761
--- /dev/null
+++ b/doc/snippets/MatrixBase_cwiseMin.cpp
@@ -0,0 +1,2 @@
+Vector3d v(2,3,4), w(4,2,3);
+cout << v.cwiseMin(w) << endl;
diff --git a/doc/snippets/MatrixBase_cwiseNotEqual.cpp b/doc/snippets/MatrixBase_cwiseNotEqual.cpp
new file mode 100644
index 0000000..7f0a105
--- /dev/null
+++ b/doc/snippets/MatrixBase_cwiseNotEqual.cpp
@@ -0,0 +1,7 @@
+MatrixXi m(2,2);
+m << 1, 0,
+ 1, 1;
+cout << "Comparing m with identity matrix:" << endl;
+cout << m.cwiseNotEqual(MatrixXi::Identity(2,2)) << endl;
+Index count = m.cwiseNotEqual(MatrixXi::Identity(2,2)).count();
+cout << "Number of coefficients that are not equal: " << count << endl;
diff --git a/doc/snippets/MatrixBase_cwiseProduct.cpp b/doc/snippets/MatrixBase_cwiseProduct.cpp
new file mode 100644
index 0000000..1db3a11
--- /dev/null
+++ b/doc/snippets/MatrixBase_cwiseProduct.cpp
@@ -0,0 +1,4 @@
+Matrix3i a = Matrix3i::Random(), b = Matrix3i::Random();
+Matrix3i c = a.cwiseProduct(b);
+cout << "a:\n" << a << "\nb:\n" << b << "\nc:\n" << c << endl;
+
diff --git a/doc/snippets/MatrixBase_cwiseQuotient.cpp b/doc/snippets/MatrixBase_cwiseQuotient.cpp
new file mode 100644
index 0000000..9691212
--- /dev/null
+++ b/doc/snippets/MatrixBase_cwiseQuotient.cpp
@@ -0,0 +1,2 @@
+Vector3d v(2,3,4), w(4,2,3);
+cout << v.cwiseQuotient(w) << endl;
diff --git a/doc/snippets/MatrixBase_cwiseSign.cpp b/doc/snippets/MatrixBase_cwiseSign.cpp
new file mode 100644
index 0000000..efd7179
--- /dev/null
+++ b/doc/snippets/MatrixBase_cwiseSign.cpp
@@ -0,0 +1,4 @@
+MatrixXd m(2,3);
+m << 2, -4, 6,
+ -5, 1, 0;
+cout << m.cwiseSign() << endl;
diff --git a/doc/snippets/MatrixBase_cwiseSqrt.cpp b/doc/snippets/MatrixBase_cwiseSqrt.cpp
new file mode 100644
index 0000000..4bfd75d
--- /dev/null
+++ b/doc/snippets/MatrixBase_cwiseSqrt.cpp
@@ -0,0 +1,2 @@
+Vector3d v(1,2,4);
+cout << v.cwiseSqrt() << endl;
diff --git a/doc/snippets/MatrixBase_diagonal.cpp b/doc/snippets/MatrixBase_diagonal.cpp
new file mode 100644
index 0000000..cd63413
--- /dev/null
+++ b/doc/snippets/MatrixBase_diagonal.cpp
@@ -0,0 +1,4 @@
+Matrix3i m = Matrix3i::Random();
+cout << "Here is the matrix m:" << endl << m << endl;
+cout << "Here are the coefficients on the main diagonal of m:" << endl
+ << m.diagonal() << endl;
diff --git a/doc/snippets/MatrixBase_diagonal_int.cpp b/doc/snippets/MatrixBase_diagonal_int.cpp
new file mode 100644
index 0000000..7b66abf
--- /dev/null
+++ b/doc/snippets/MatrixBase_diagonal_int.cpp
@@ -0,0 +1,5 @@
+Matrix4i m = Matrix4i::Random();
+cout << "Here is the matrix m:" << endl << m << endl;
+cout << "Here are the coefficients on the 1st super-diagonal and 2nd sub-diagonal of m:" << endl
+ << m.diagonal(1).transpose() << endl
+ << m.diagonal(-2).transpose() << endl;
diff --git a/doc/snippets/MatrixBase_diagonal_template_int.cpp b/doc/snippets/MatrixBase_diagonal_template_int.cpp
new file mode 100644
index 0000000..0e73d1c
--- /dev/null
+++ b/doc/snippets/MatrixBase_diagonal_template_int.cpp
@@ -0,0 +1,5 @@
+Matrix4i m = Matrix4i::Random();
+cout << "Here is the matrix m:" << endl << m << endl;
+cout << "Here are the coefficients on the 1st super-diagonal and 2nd sub-diagonal of m:" << endl
+ << m.diagonal<1>().transpose() << endl
+ << m.diagonal<-2>().transpose() << endl;
diff --git a/doc/snippets/MatrixBase_eigenvalues.cpp b/doc/snippets/MatrixBase_eigenvalues.cpp
new file mode 100644
index 0000000..039f887
--- /dev/null
+++ b/doc/snippets/MatrixBase_eigenvalues.cpp
@@ -0,0 +1,3 @@
+MatrixXd ones = MatrixXd::Ones(3,3);
+VectorXcd eivals = ones.eigenvalues();
+cout << "The eigenvalues of the 3x3 matrix of ones are:" << endl << eivals << endl;
diff --git a/doc/snippets/MatrixBase_end_int.cpp b/doc/snippets/MatrixBase_end_int.cpp
new file mode 100644
index 0000000..03c54a9
--- /dev/null
+++ b/doc/snippets/MatrixBase_end_int.cpp
@@ -0,0 +1,5 @@
+RowVector4i v = RowVector4i::Random();
+cout << "Here is the vector v:" << endl << v << endl;
+cout << "Here is v.tail(2):" << endl << v.tail(2) << endl;
+v.tail(2).setZero();
+cout << "Now the vector v is:" << endl << v << endl;
diff --git a/doc/snippets/MatrixBase_eval.cpp b/doc/snippets/MatrixBase_eval.cpp
new file mode 100644
index 0000000..1df3aa0
--- /dev/null
+++ b/doc/snippets/MatrixBase_eval.cpp
@@ -0,0 +1,12 @@
+Matrix2f M = Matrix2f::Random();
+Matrix2f m;
+m = M;
+cout << "Here is the matrix m:" << endl << m << endl;
+cout << "Now we want to copy a column into a row." << endl;
+cout << "If we do m.col(1) = m.row(0), then m becomes:" << endl;
+m.col(1) = m.row(0);
+cout << m << endl << "which is wrong!" << endl;
+cout << "Now let us instead do m.col(1) = m.row(0).eval(). Then m becomes" << endl;
+m = M;
+m.col(1) = m.row(0).eval();
+cout << m << endl << "which is right." << endl;
diff --git a/doc/snippets/MatrixBase_fixedBlock_int_int.cpp b/doc/snippets/MatrixBase_fixedBlock_int_int.cpp
new file mode 100644
index 0000000..3201127
--- /dev/null
+++ b/doc/snippets/MatrixBase_fixedBlock_int_int.cpp
@@ -0,0 +1,5 @@
+Matrix4d m = Vector4d(1,2,3,4).asDiagonal();
+cout << "Here is the matrix m:" << endl << m << endl;
+cout << "Here is m.fixed<2, 2>(2, 2):" << endl << m.block<2, 2>(2, 2) << endl;
+m.block<2, 2>(2, 0) = m.block<2, 2>(2, 2);
+cout << "Now the matrix m is:" << endl << m << endl;
diff --git a/doc/snippets/MatrixBase_hnormalized.cpp b/doc/snippets/MatrixBase_hnormalized.cpp
new file mode 100644
index 0000000..b714adc
--- /dev/null
+++ b/doc/snippets/MatrixBase_hnormalized.cpp
@@ -0,0 +1,6 @@
+Vector4d v = Vector4d::Random();
+Projective3d P(Matrix4d::Random());
+cout << "v = " << v.transpose() << "]^T" << endl;
+cout << "v.hnormalized() = " << v.hnormalized().transpose() << "]^T" << endl;
+cout << "P*v = " << (P*v).transpose() << "]^T" << endl;
+cout << "(P*v).hnormalized() = " << (P*v).hnormalized().transpose() << "]^T" << endl;
diff --git a/doc/snippets/MatrixBase_homogeneous.cpp b/doc/snippets/MatrixBase_homogeneous.cpp
new file mode 100644
index 0000000..2631960
--- /dev/null
+++ b/doc/snippets/MatrixBase_homogeneous.cpp
@@ -0,0 +1,6 @@
+Vector3d v = Vector3d::Random(), w;
+Projective3d P(Matrix4d::Random());
+cout << "v = [" << v.transpose() << "]^T" << endl;
+cout << "h.homogeneous() = [" << v.homogeneous().transpose() << "]^T" << endl;
+cout << "(P * v.homogeneous()) = [" << (P * v.homogeneous()).transpose() << "]^T" << endl;
+cout << "(P * v.homogeneous()).hnormalized() = [" << (P * v.homogeneous()).eval().hnormalized().transpose() << "]^T" << endl;
diff --git a/doc/snippets/MatrixBase_identity.cpp b/doc/snippets/MatrixBase_identity.cpp
new file mode 100644
index 0000000..b5c1e59
--- /dev/null
+++ b/doc/snippets/MatrixBase_identity.cpp
@@ -0,0 +1 @@
+cout << Matrix<double, 3, 4>::Identity() << endl;
diff --git a/doc/snippets/MatrixBase_identity_int_int.cpp b/doc/snippets/MatrixBase_identity_int_int.cpp
new file mode 100644
index 0000000..918649d
--- /dev/null
+++ b/doc/snippets/MatrixBase_identity_int_int.cpp
@@ -0,0 +1 @@
+cout << MatrixXd::Identity(4, 3) << endl;
diff --git a/doc/snippets/MatrixBase_inverse.cpp b/doc/snippets/MatrixBase_inverse.cpp
new file mode 100644
index 0000000..a56142e
--- /dev/null
+++ b/doc/snippets/MatrixBase_inverse.cpp
@@ -0,0 +1,3 @@
+Matrix3d m = Matrix3d::Random();
+cout << "Here is the matrix m:" << endl << m << endl;
+cout << "Its inverse is:" << endl << m.inverse() << endl;
diff --git a/doc/snippets/MatrixBase_isDiagonal.cpp b/doc/snippets/MatrixBase_isDiagonal.cpp
new file mode 100644
index 0000000..5b1d599
--- /dev/null
+++ b/doc/snippets/MatrixBase_isDiagonal.cpp
@@ -0,0 +1,6 @@
+Matrix3d m = 10000 * Matrix3d::Identity();
+m(0,2) = 1;
+cout << "Here's the matrix m:" << endl << m << endl;
+cout << "m.isDiagonal() returns: " << m.isDiagonal() << endl;
+cout << "m.isDiagonal(1e-3) returns: " << m.isDiagonal(1e-3) << endl;
+
diff --git a/doc/snippets/MatrixBase_isIdentity.cpp b/doc/snippets/MatrixBase_isIdentity.cpp
new file mode 100644
index 0000000..17b756c
--- /dev/null
+++ b/doc/snippets/MatrixBase_isIdentity.cpp
@@ -0,0 +1,5 @@
+Matrix3d m = Matrix3d::Identity();
+m(0,2) = 1e-4;
+cout << "Here's the matrix m:" << endl << m << endl;
+cout << "m.isIdentity() returns: " << m.isIdentity() << endl;
+cout << "m.isIdentity(1e-3) returns: " << m.isIdentity(1e-3) << endl;
diff --git a/doc/snippets/MatrixBase_isOnes.cpp b/doc/snippets/MatrixBase_isOnes.cpp
new file mode 100644
index 0000000..f82f628
--- /dev/null
+++ b/doc/snippets/MatrixBase_isOnes.cpp
@@ -0,0 +1,5 @@
+Matrix3d m = Matrix3d::Ones();
+m(0,2) += 1e-4;
+cout << "Here's the matrix m:" << endl << m << endl;
+cout << "m.isOnes() returns: " << m.isOnes() << endl;
+cout << "m.isOnes(1e-3) returns: " << m.isOnes(1e-3) << endl;
diff --git a/doc/snippets/MatrixBase_isOrthogonal.cpp b/doc/snippets/MatrixBase_isOrthogonal.cpp
new file mode 100644
index 0000000..b22af06
--- /dev/null
+++ b/doc/snippets/MatrixBase_isOrthogonal.cpp
@@ -0,0 +1,6 @@
+Vector3d v(1,0,0);
+Vector3d w(1e-4,0,1);
+cout << "Here's the vector v:" << endl << v << endl;
+cout << "Here's the vector w:" << endl << w << endl;
+cout << "v.isOrthogonal(w) returns: " << v.isOrthogonal(w) << endl;
+cout << "v.isOrthogonal(w,1e-3) returns: " << v.isOrthogonal(w,1e-3) << endl;
diff --git a/doc/snippets/MatrixBase_isUnitary.cpp b/doc/snippets/MatrixBase_isUnitary.cpp
new file mode 100644
index 0000000..3877da3
--- /dev/null
+++ b/doc/snippets/MatrixBase_isUnitary.cpp
@@ -0,0 +1,5 @@
+Matrix3d m = Matrix3d::Identity();
+m(0,2) = 1e-4;
+cout << "Here's the matrix m:" << endl << m << endl;
+cout << "m.isUnitary() returns: " << m.isUnitary() << endl;
+cout << "m.isUnitary(1e-3) returns: " << m.isUnitary(1e-3) << endl;
diff --git a/doc/snippets/MatrixBase_isZero.cpp b/doc/snippets/MatrixBase_isZero.cpp
new file mode 100644
index 0000000..c2cfe22
--- /dev/null
+++ b/doc/snippets/MatrixBase_isZero.cpp
@@ -0,0 +1,5 @@
+Matrix3d m = Matrix3d::Zero();
+m(0,2) = 1e-4;
+cout << "Here's the matrix m:" << endl << m << endl;
+cout << "m.isZero() returns: " << m.isZero() << endl;
+cout << "m.isZero(1e-3) returns: " << m.isZero(1e-3) << endl;
diff --git a/doc/snippets/MatrixBase_leftCols_int.cpp b/doc/snippets/MatrixBase_leftCols_int.cpp
new file mode 100644
index 0000000..6ea984e
--- /dev/null
+++ b/doc/snippets/MatrixBase_leftCols_int.cpp
@@ -0,0 +1,6 @@
+Array44i a = Array44i::Random();
+cout << "Here is the array a:" << endl << a << endl;
+cout << "Here is a.leftCols(2):" << endl;
+cout << a.leftCols(2) << endl;
+a.leftCols(2).setZero();
+cout << "Now the array a is:" << endl << a << endl;
diff --git a/doc/snippets/MatrixBase_noalias.cpp b/doc/snippets/MatrixBase_noalias.cpp
new file mode 100644
index 0000000..3b54a79
--- /dev/null
+++ b/doc/snippets/MatrixBase_noalias.cpp
@@ -0,0 +1,3 @@
+Matrix2d a, b, c; a << 1,2,3,4; b << 5,6,7,8;
+c.noalias() = a * b; // this computes the product directly to c
+cout << c << endl;
diff --git a/doc/snippets/MatrixBase_ones.cpp b/doc/snippets/MatrixBase_ones.cpp
new file mode 100644
index 0000000..02c767c
--- /dev/null
+++ b/doc/snippets/MatrixBase_ones.cpp
@@ -0,0 +1,2 @@
+cout << Matrix2d::Ones() << endl;
+cout << 6 * RowVector4i::Ones() << endl;
diff --git a/doc/snippets/MatrixBase_ones_int.cpp b/doc/snippets/MatrixBase_ones_int.cpp
new file mode 100644
index 0000000..2ef188e
--- /dev/null
+++ b/doc/snippets/MatrixBase_ones_int.cpp
@@ -0,0 +1,2 @@
+cout << 6 * RowVectorXi::Ones(4) << endl;
+cout << VectorXf::Ones(2) << endl;
diff --git a/doc/snippets/MatrixBase_ones_int_int.cpp b/doc/snippets/MatrixBase_ones_int_int.cpp
new file mode 100644
index 0000000..60f5a31
--- /dev/null
+++ b/doc/snippets/MatrixBase_ones_int_int.cpp
@@ -0,0 +1 @@
+cout << MatrixXi::Ones(2,3) << endl;
diff --git a/doc/snippets/MatrixBase_operatorNorm.cpp b/doc/snippets/MatrixBase_operatorNorm.cpp
new file mode 100644
index 0000000..355246f
--- /dev/null
+++ b/doc/snippets/MatrixBase_operatorNorm.cpp
@@ -0,0 +1,3 @@
+MatrixXd ones = MatrixXd::Ones(3,3);
+cout << "The operator norm of the 3x3 matrix of ones is "
+ << ones.operatorNorm() << endl;
diff --git a/doc/snippets/MatrixBase_prod.cpp b/doc/snippets/MatrixBase_prod.cpp
new file mode 100644
index 0000000..d2f27bd
--- /dev/null
+++ b/doc/snippets/MatrixBase_prod.cpp
@@ -0,0 +1,3 @@
+Matrix3d m = Matrix3d::Random();
+cout << "Here is the matrix m:" << endl << m << endl;
+cout << "Here is the product of all the coefficients:" << endl << m.prod() << endl;
diff --git a/doc/snippets/MatrixBase_random.cpp b/doc/snippets/MatrixBase_random.cpp
new file mode 100644
index 0000000..65fc524
--- /dev/null
+++ b/doc/snippets/MatrixBase_random.cpp
@@ -0,0 +1 @@
+cout << 100 * Matrix2i::Random() << endl;
diff --git a/doc/snippets/MatrixBase_random_int.cpp b/doc/snippets/MatrixBase_random_int.cpp
new file mode 100644
index 0000000..f161d03
--- /dev/null
+++ b/doc/snippets/MatrixBase_random_int.cpp
@@ -0,0 +1 @@
+cout << VectorXi::Random(2) << endl;
diff --git a/doc/snippets/MatrixBase_random_int_int.cpp b/doc/snippets/MatrixBase_random_int_int.cpp
new file mode 100644
index 0000000..3f0f7dd
--- /dev/null
+++ b/doc/snippets/MatrixBase_random_int_int.cpp
@@ -0,0 +1 @@
+cout << MatrixXi::Random(2,3) << endl;
diff --git a/doc/snippets/MatrixBase_replicate.cpp b/doc/snippets/MatrixBase_replicate.cpp
new file mode 100644
index 0000000..3ce52bc
--- /dev/null
+++ b/doc/snippets/MatrixBase_replicate.cpp
@@ -0,0 +1,4 @@
+MatrixXi m = MatrixXi::Random(2,3);
+cout << "Here is the matrix m:" << endl << m << endl;
+cout << "m.replicate<3,2>() = ..." << endl;
+cout << m.replicate<3,2>() << endl;
diff --git a/doc/snippets/MatrixBase_replicate_int_int.cpp b/doc/snippets/MatrixBase_replicate_int_int.cpp
new file mode 100644
index 0000000..b1dbc70
--- /dev/null
+++ b/doc/snippets/MatrixBase_replicate_int_int.cpp
@@ -0,0 +1,4 @@
+Vector3i v = Vector3i::Random();
+cout << "Here is the vector v:" << endl << v << endl;
+cout << "v.replicate(2,5) = ..." << endl;
+cout << v.replicate(2,5) << endl;
diff --git a/doc/snippets/MatrixBase_reshaped_auto.cpp b/doc/snippets/MatrixBase_reshaped_auto.cpp
new file mode 100644
index 0000000..59f9d3f
--- /dev/null
+++ b/doc/snippets/MatrixBase_reshaped_auto.cpp
@@ -0,0 +1,4 @@
+Matrix4i m = Matrix4i::Random();
+cout << "Here is the matrix m:" << endl << m << endl;
+cout << "Here is m.reshaped(2, AutoSize):" << endl << m.reshaped(2, AutoSize) << endl;
+cout << "Here is m.reshaped<RowMajor>(AutoSize, fix<8>):" << endl << m.reshaped<RowMajor>(AutoSize, fix<8>) << endl;
diff --git a/doc/snippets/MatrixBase_reshaped_fixed.cpp b/doc/snippets/MatrixBase_reshaped_fixed.cpp
new file mode 100644
index 0000000..3e9e2cf
--- /dev/null
+++ b/doc/snippets/MatrixBase_reshaped_fixed.cpp
@@ -0,0 +1,3 @@
+Matrix4i m = Matrix4i::Random();
+cout << "Here is the matrix m:" << endl << m << endl;
+cout << "Here is m.reshaped(fix<2>,fix<8>):" << endl << m.reshaped(fix<2>,fix<8>) << endl;
diff --git a/doc/snippets/MatrixBase_reshaped_int_int.cpp b/doc/snippets/MatrixBase_reshaped_int_int.cpp
new file mode 100644
index 0000000..af4ca59
--- /dev/null
+++ b/doc/snippets/MatrixBase_reshaped_int_int.cpp
@@ -0,0 +1,3 @@
+Matrix4i m = Matrix4i::Random();
+cout << "Here is the matrix m:" << endl << m << endl;
+cout << "Here is m.reshaped(2, 8):" << endl << m.reshaped(2, 8) << endl;
diff --git a/doc/snippets/MatrixBase_reshaped_to_vector.cpp b/doc/snippets/MatrixBase_reshaped_to_vector.cpp
new file mode 100644
index 0000000..37f65f7
--- /dev/null
+++ b/doc/snippets/MatrixBase_reshaped_to_vector.cpp
@@ -0,0 +1,4 @@
+Matrix4i m = Matrix4i::Random();
+cout << "Here is the matrix m:" << endl << m << endl;
+cout << "Here is m.reshaped().transpose():" << endl << m.reshaped().transpose() << endl;
+cout << "Here is m.reshaped<RowMajor>().transpose(): " << endl << m.reshaped<RowMajor>().transpose() << endl;
diff --git a/doc/snippets/MatrixBase_reverse.cpp b/doc/snippets/MatrixBase_reverse.cpp
new file mode 100644
index 0000000..f545a28
--- /dev/null
+++ b/doc/snippets/MatrixBase_reverse.cpp
@@ -0,0 +1,8 @@
+MatrixXi m = MatrixXi::Random(3,4);
+cout << "Here is the matrix m:" << endl << m << endl;
+cout << "Here is the reverse of m:" << endl << m.reverse() << endl;
+cout << "Here is the coefficient (1,0) in the reverse of m:" << endl
+ << m.reverse()(1,0) << endl;
+cout << "Let us overwrite this coefficient with the value 4." << endl;
+m.reverse()(1,0) = 4;
+cout << "Now the matrix m is:" << endl << m << endl;
diff --git a/doc/snippets/MatrixBase_rightCols_int.cpp b/doc/snippets/MatrixBase_rightCols_int.cpp
new file mode 100644
index 0000000..cb51340
--- /dev/null
+++ b/doc/snippets/MatrixBase_rightCols_int.cpp
@@ -0,0 +1,6 @@
+Array44i a = Array44i::Random();
+cout << "Here is the array a:" << endl << a << endl;
+cout << "Here is a.rightCols(2):" << endl;
+cout << a.rightCols(2) << endl;
+a.rightCols(2).setZero();
+cout << "Now the array a is:" << endl << a << endl;
diff --git a/doc/snippets/MatrixBase_row.cpp b/doc/snippets/MatrixBase_row.cpp
new file mode 100644
index 0000000..b15e626
--- /dev/null
+++ b/doc/snippets/MatrixBase_row.cpp
@@ -0,0 +1,3 @@
+Matrix3d m = Matrix3d::Identity();
+m.row(1) = Vector3d(4,5,6);
+cout << m << endl;
diff --git a/doc/snippets/MatrixBase_rowwise.cpp b/doc/snippets/MatrixBase_rowwise.cpp
new file mode 100644
index 0000000..ae93964
--- /dev/null
+++ b/doc/snippets/MatrixBase_rowwise.cpp
@@ -0,0 +1,5 @@
+Matrix3d m = Matrix3d::Random();
+cout << "Here is the matrix m:" << endl << m << endl;
+cout << "Here is the sum of each row:" << endl << m.rowwise().sum() << endl;
+cout << "Here is the maximum absolute value of each row:"
+ << endl << m.cwiseAbs().rowwise().maxCoeff() << endl;
diff --git a/doc/snippets/MatrixBase_segment_int_int.cpp b/doc/snippets/MatrixBase_segment_int_int.cpp
new file mode 100644
index 0000000..70cd6d2
--- /dev/null
+++ b/doc/snippets/MatrixBase_segment_int_int.cpp
@@ -0,0 +1,5 @@
+RowVector4i v = RowVector4i::Random();
+cout << "Here is the vector v:" << endl << v << endl;
+cout << "Here is v.segment(1, 2):" << endl << v.segment(1, 2) << endl;
+v.segment(1, 2).setZero();
+cout << "Now the vector v is:" << endl << v << endl;
diff --git a/doc/snippets/MatrixBase_select.cpp b/doc/snippets/MatrixBase_select.cpp
new file mode 100644
index 0000000..ae5477f
--- /dev/null
+++ b/doc/snippets/MatrixBase_select.cpp
@@ -0,0 +1,6 @@
+MatrixXi m(3, 3);
+m << 1, 2, 3,
+ 4, 5, 6,
+ 7, 8, 9;
+m = (m.array() >= 5).select(-m, m);
+cout << m << endl;
diff --git a/doc/snippets/MatrixBase_selfadjointView.cpp b/doc/snippets/MatrixBase_selfadjointView.cpp
new file mode 100644
index 0000000..4bd3c7e
--- /dev/null
+++ b/doc/snippets/MatrixBase_selfadjointView.cpp
@@ -0,0 +1,6 @@
+Matrix3i m = Matrix3i::Random();
+cout << "Here is the matrix m:" << endl << m << endl;
+cout << "Here is the symmetric matrix extracted from the upper part of m:" << endl
+ << Matrix3i(m.selfadjointView<Upper>()) << endl;
+cout << "Here is the symmetric matrix extracted from the lower part of m:" << endl
+ << Matrix3i(m.selfadjointView<Lower>()) << endl;
diff --git a/doc/snippets/MatrixBase_set.cpp b/doc/snippets/MatrixBase_set.cpp
new file mode 100644
index 0000000..50ecf5f
--- /dev/null
+++ b/doc/snippets/MatrixBase_set.cpp
@@ -0,0 +1,13 @@
+Matrix3i m1;
+m1 << 1, 2, 3,
+ 4, 5, 6,
+ 7, 8, 9;
+cout << m1 << endl << endl;
+Matrix3i m2 = Matrix3i::Identity();
+m2.block(0,0, 2,2) << 10, 11, 12, 13;
+cout << m2 << endl << endl;
+Vector2i v1;
+v1 << 14, 15;
+m2 << v1.transpose(), 16,
+ v1, m1.block(1,1,2,2);
+cout << m2 << endl;
diff --git a/doc/snippets/MatrixBase_setIdentity.cpp b/doc/snippets/MatrixBase_setIdentity.cpp
new file mode 100644
index 0000000..4fd0aa2
--- /dev/null
+++ b/doc/snippets/MatrixBase_setIdentity.cpp
@@ -0,0 +1,3 @@
+Matrix4i m = Matrix4i::Zero();
+m.block<3,3>(1,0).setIdentity();
+cout << m << endl;
diff --git a/doc/snippets/MatrixBase_setOnes.cpp b/doc/snippets/MatrixBase_setOnes.cpp
new file mode 100644
index 0000000..4cef9c1
--- /dev/null
+++ b/doc/snippets/MatrixBase_setOnes.cpp
@@ -0,0 +1,3 @@
+Matrix4i m = Matrix4i::Random();
+m.row(1).setOnes();
+cout << m << endl;
diff --git a/doc/snippets/MatrixBase_setRandom.cpp b/doc/snippets/MatrixBase_setRandom.cpp
new file mode 100644
index 0000000..e2c257d
--- /dev/null
+++ b/doc/snippets/MatrixBase_setRandom.cpp
@@ -0,0 +1,3 @@
+Matrix4i m = Matrix4i::Zero();
+m.col(1).setRandom();
+cout << m << endl;
diff --git a/doc/snippets/MatrixBase_setZero.cpp b/doc/snippets/MatrixBase_setZero.cpp
new file mode 100644
index 0000000..9b5b958
--- /dev/null
+++ b/doc/snippets/MatrixBase_setZero.cpp
@@ -0,0 +1,3 @@
+Matrix4i m = Matrix4i::Random();
+m.row(1).setZero();
+cout << m << endl;
diff --git a/doc/snippets/MatrixBase_start_int.cpp b/doc/snippets/MatrixBase_start_int.cpp
new file mode 100644
index 0000000..c261d2b
--- /dev/null
+++ b/doc/snippets/MatrixBase_start_int.cpp
@@ -0,0 +1,5 @@
+RowVector4i v = RowVector4i::Random();
+cout << "Here is the vector v:" << endl << v << endl;
+cout << "Here is v.head(2):" << endl << v.head(2) << endl;
+v.head(2).setZero();
+cout << "Now the vector v is:" << endl << v << endl;
diff --git a/doc/snippets/MatrixBase_template_int_bottomRows.cpp b/doc/snippets/MatrixBase_template_int_bottomRows.cpp
new file mode 100644
index 0000000..f9ea892
--- /dev/null
+++ b/doc/snippets/MatrixBase_template_int_bottomRows.cpp
@@ -0,0 +1,6 @@
+Array44i a = Array44i::Random();
+cout << "Here is the array a:" << endl << a << endl;
+cout << "Here is a.bottomRows<2>():" << endl;
+cout << a.bottomRows<2>() << endl;
+a.bottomRows<2>().setZero();
+cout << "Now the array a is:" << endl << a << endl;
diff --git a/doc/snippets/MatrixBase_template_int_end.cpp b/doc/snippets/MatrixBase_template_int_end.cpp
new file mode 100644
index 0000000..f5ccb00
--- /dev/null
+++ b/doc/snippets/MatrixBase_template_int_end.cpp
@@ -0,0 +1,5 @@
+RowVector4i v = RowVector4i::Random();
+cout << "Here is the vector v:" << endl << v << endl;
+cout << "Here is v.tail(2):" << endl << v.tail<2>() << endl;
+v.tail<2>().setZero();
+cout << "Now the vector v is:" << endl << v << endl;
diff --git a/doc/snippets/MatrixBase_template_int_int_block_int_int_int_int.cpp b/doc/snippets/MatrixBase_template_int_int_block_int_int_int_int.cpp
new file mode 100644
index 0000000..4dced03
--- /dev/null
+++ b/doc/snippets/MatrixBase_template_int_int_block_int_int_int_int.cpp
@@ -0,0 +1,5 @@
+Matrix4i m = Matrix4i::Random();
+cout << "Here is the matrix m:" << endl << m << endl;
+cout << "Here is the block:" << endl << m.block<2, Dynamic>(1, 1, 2, 3) << endl;
+m.block<2, Dynamic>(1, 1, 2, 3).setZero();
+cout << "Now the matrix m is:" << endl << m << endl;
diff --git a/doc/snippets/MatrixBase_template_int_int_bottomLeftCorner.cpp b/doc/snippets/MatrixBase_template_int_int_bottomLeftCorner.cpp
new file mode 100644
index 0000000..847892a
--- /dev/null
+++ b/doc/snippets/MatrixBase_template_int_int_bottomLeftCorner.cpp
@@ -0,0 +1,6 @@
+Matrix4i m = Matrix4i::Random();
+cout << "Here is the matrix m:" << endl << m << endl;
+cout << "Here is m.bottomLeftCorner<2,2>():" << endl;
+cout << m.bottomLeftCorner<2,2>() << endl;
+m.bottomLeftCorner<2,2>().setZero();
+cout << "Now the matrix m is:" << endl << m << endl;
diff --git a/doc/snippets/MatrixBase_template_int_int_bottomLeftCorner_int_int.cpp b/doc/snippets/MatrixBase_template_int_int_bottomLeftCorner_int_int.cpp
new file mode 100644
index 0000000..a1edcc8
--- /dev/null
+++ b/doc/snippets/MatrixBase_template_int_int_bottomLeftCorner_int_int.cpp
@@ -0,0 +1,6 @@
+Matrix4i m = Matrix4i::Random();
+cout << "Here is the matrix m:" << endl << m << endl;
+cout << "Here is m.bottomLeftCorner<2,Dynamic>(2,2):" << endl;
+cout << m.bottomLeftCorner<2,Dynamic>(2,2) << endl;
+m.bottomLeftCorner<2,Dynamic>(2,2).setZero();
+cout << "Now the matrix m is:" << endl << m << endl;
diff --git a/doc/snippets/MatrixBase_template_int_int_bottomRightCorner.cpp b/doc/snippets/MatrixBase_template_int_int_bottomRightCorner.cpp
new file mode 100644
index 0000000..abacb01
--- /dev/null
+++ b/doc/snippets/MatrixBase_template_int_int_bottomRightCorner.cpp
@@ -0,0 +1,6 @@
+Matrix4i m = Matrix4i::Random();
+cout << "Here is the matrix m:" << endl << m << endl;
+cout << "Here is m.bottomRightCorner<2,2>():" << endl;
+cout << m.bottomRightCorner<2,2>() << endl;
+m.bottomRightCorner<2,2>().setZero();
+cout << "Now the matrix m is:" << endl << m << endl;
diff --git a/doc/snippets/MatrixBase_template_int_int_bottomRightCorner_int_int.cpp b/doc/snippets/MatrixBase_template_int_int_bottomRightCorner_int_int.cpp
new file mode 100644
index 0000000..a65508f
--- /dev/null
+++ b/doc/snippets/MatrixBase_template_int_int_bottomRightCorner_int_int.cpp
@@ -0,0 +1,6 @@
+Matrix4i m = Matrix4i::Random();
+cout << "Here is the matrix m:" << endl << m << endl;
+cout << "Here is m.bottomRightCorner<2,Dynamic>(2,2):" << endl;
+cout << m.bottomRightCorner<2,Dynamic>(2,2) << endl;
+m.bottomRightCorner<2,Dynamic>(2,2).setZero();
+cout << "Now the matrix m is:" << endl << m << endl;
diff --git a/doc/snippets/MatrixBase_template_int_int_topLeftCorner.cpp b/doc/snippets/MatrixBase_template_int_int_topLeftCorner.cpp
new file mode 100644
index 0000000..1899d90
--- /dev/null
+++ b/doc/snippets/MatrixBase_template_int_int_topLeftCorner.cpp
@@ -0,0 +1,6 @@
+Matrix4i m = Matrix4i::Random();
+cout << "Here is the matrix m:" << endl << m << endl;
+cout << "Here is m.topLeftCorner<2,2>():" << endl;
+cout << m.topLeftCorner<2,2>() << endl;
+m.topLeftCorner<2,2>().setZero();
+cout << "Now the matrix m is:" << endl << m << endl;
diff --git a/doc/snippets/MatrixBase_template_int_int_topLeftCorner_int_int.cpp b/doc/snippets/MatrixBase_template_int_int_topLeftCorner_int_int.cpp
new file mode 100644
index 0000000..fac761f
--- /dev/null
+++ b/doc/snippets/MatrixBase_template_int_int_topLeftCorner_int_int.cpp
@@ -0,0 +1,6 @@
+Matrix4i m = Matrix4i::Random();
+cout << "Here is the matrix m:" << endl << m << endl;
+cout << "Here is m.topLeftCorner<2,Dynamic>(2,2):" << endl;
+cout << m.topLeftCorner<2,Dynamic>(2,2) << endl;
+m.topLeftCorner<2,Dynamic>(2,2).setZero();
+cout << "Now the matrix m is:" << endl << m << endl;
diff --git a/doc/snippets/MatrixBase_template_int_int_topRightCorner.cpp b/doc/snippets/MatrixBase_template_int_int_topRightCorner.cpp
new file mode 100644
index 0000000..c3a1771
--- /dev/null
+++ b/doc/snippets/MatrixBase_template_int_int_topRightCorner.cpp
@@ -0,0 +1,6 @@
+Matrix4i m = Matrix4i::Random();
+cout << "Here is the matrix m:" << endl << m << endl;
+cout << "Here is m.topRightCorner<2,2>():" << endl;
+cout << m.topRightCorner<2,2>() << endl;
+m.topRightCorner<2,2>().setZero();
+cout << "Now the matrix m is:" << endl << m << endl;
diff --git a/doc/snippets/MatrixBase_template_int_int_topRightCorner_int_int.cpp b/doc/snippets/MatrixBase_template_int_int_topRightCorner_int_int.cpp
new file mode 100644
index 0000000..a17acc0
--- /dev/null
+++ b/doc/snippets/MatrixBase_template_int_int_topRightCorner_int_int.cpp
@@ -0,0 +1,6 @@
+Matrix4i m = Matrix4i::Random();
+cout << "Here is the matrix m:" << endl << m << endl;
+cout << "Here is m.topRightCorner<2,Dynamic>(2,2):" << endl;
+cout << m.topRightCorner<2,Dynamic>(2,2) << endl;
+m.topRightCorner<2,Dynamic>(2,2).setZero();
+cout << "Now the matrix m is:" << endl << m << endl;
diff --git a/doc/snippets/MatrixBase_template_int_leftCols.cpp b/doc/snippets/MatrixBase_template_int_leftCols.cpp
new file mode 100644
index 0000000..1c425d9
--- /dev/null
+++ b/doc/snippets/MatrixBase_template_int_leftCols.cpp
@@ -0,0 +1,6 @@
+Array44i a = Array44i::Random();
+cout << "Here is the array a:" << endl << a << endl;
+cout << "Here is a.leftCols<2>():" << endl;
+cout << a.leftCols<2>() << endl;
+a.leftCols<2>().setZero();
+cout << "Now the array a is:" << endl << a << endl;
diff --git a/doc/snippets/MatrixBase_template_int_rightCols.cpp b/doc/snippets/MatrixBase_template_int_rightCols.cpp
new file mode 100644
index 0000000..fc8c0d9
--- /dev/null
+++ b/doc/snippets/MatrixBase_template_int_rightCols.cpp
@@ -0,0 +1,6 @@
+Array44i a = Array44i::Random();
+cout << "Here is the array a:" << endl << a << endl;
+cout << "Here is a.rightCols<2>():" << endl;
+cout << a.rightCols<2>() << endl;
+a.rightCols<2>().setZero();
+cout << "Now the array a is:" << endl << a << endl;
diff --git a/doc/snippets/MatrixBase_template_int_segment.cpp b/doc/snippets/MatrixBase_template_int_segment.cpp
new file mode 100644
index 0000000..e448b40
--- /dev/null
+++ b/doc/snippets/MatrixBase_template_int_segment.cpp
@@ -0,0 +1,5 @@
+RowVector4i v = RowVector4i::Random();
+cout << "Here is the vector v:" << endl << v << endl;
+cout << "Here is v.segment<2>(1):" << endl << v.segment<2>(1) << endl;
+v.segment<2>(2).setZero();
+cout << "Now the vector v is:" << endl << v << endl;
diff --git a/doc/snippets/MatrixBase_template_int_start.cpp b/doc/snippets/MatrixBase_template_int_start.cpp
new file mode 100644
index 0000000..d336b37
--- /dev/null
+++ b/doc/snippets/MatrixBase_template_int_start.cpp
@@ -0,0 +1,5 @@
+RowVector4i v = RowVector4i::Random();
+cout << "Here is the vector v:" << endl << v << endl;
+cout << "Here is v.head(2):" << endl << v.head<2>() << endl;
+v.head<2>().setZero();
+cout << "Now the vector v is:" << endl << v << endl;
diff --git a/doc/snippets/MatrixBase_template_int_topRows.cpp b/doc/snippets/MatrixBase_template_int_topRows.cpp
new file mode 100644
index 0000000..0110251
--- /dev/null
+++ b/doc/snippets/MatrixBase_template_int_topRows.cpp
@@ -0,0 +1,6 @@
+Array44i a = Array44i::Random();
+cout << "Here is the array a:" << endl << a << endl;
+cout << "Here is a.topRows<2>():" << endl;
+cout << a.topRows<2>() << endl;
+a.topRows<2>().setZero();
+cout << "Now the array a is:" << endl << a << endl;
diff --git a/doc/snippets/MatrixBase_topLeftCorner_int_int.cpp b/doc/snippets/MatrixBase_topLeftCorner_int_int.cpp
new file mode 100644
index 0000000..e52cb3b
--- /dev/null
+++ b/doc/snippets/MatrixBase_topLeftCorner_int_int.cpp
@@ -0,0 +1,6 @@
+Matrix4i m = Matrix4i::Random();
+cout << "Here is the matrix m:" << endl << m << endl;
+cout << "Here is m.topLeftCorner(2, 2):" << endl;
+cout << m.topLeftCorner(2, 2) << endl;
+m.topLeftCorner(2, 2).setZero();
+cout << "Now the matrix m is:" << endl << m << endl;
diff --git a/doc/snippets/MatrixBase_topRightCorner_int_int.cpp b/doc/snippets/MatrixBase_topRightCorner_int_int.cpp
new file mode 100644
index 0000000..811fa56
--- /dev/null
+++ b/doc/snippets/MatrixBase_topRightCorner_int_int.cpp
@@ -0,0 +1,6 @@
+Matrix4i m = Matrix4i::Random();
+cout << "Here is the matrix m:" << endl << m << endl;
+cout << "Here is m.topRightCorner(2, 2):" << endl;
+cout << m.topRightCorner(2, 2) << endl;
+m.topRightCorner(2, 2).setZero();
+cout << "Now the matrix m is:" << endl << m << endl;
diff --git a/doc/snippets/MatrixBase_topRows_int.cpp b/doc/snippets/MatrixBase_topRows_int.cpp
new file mode 100644
index 0000000..f2d75f1
--- /dev/null
+++ b/doc/snippets/MatrixBase_topRows_int.cpp
@@ -0,0 +1,6 @@
+Array44i a = Array44i::Random();
+cout << "Here is the array a:" << endl << a << endl;
+cout << "Here is a.topRows(2):" << endl;
+cout << a.topRows(2) << endl;
+a.topRows(2).setZero();
+cout << "Now the array a is:" << endl << a << endl;
diff --git a/doc/snippets/MatrixBase_transpose.cpp b/doc/snippets/MatrixBase_transpose.cpp
new file mode 100644
index 0000000..88eea83
--- /dev/null
+++ b/doc/snippets/MatrixBase_transpose.cpp
@@ -0,0 +1,8 @@
+Matrix2i m = Matrix2i::Random();
+cout << "Here is the matrix m:" << endl << m << endl;
+cout << "Here is the transpose of m:" << endl << m.transpose() << endl;
+cout << "Here is the coefficient (1,0) in the transpose of m:" << endl
+ << m.transpose()(1,0) << endl;
+cout << "Let us overwrite this coefficient with the value 0." << endl;
+m.transpose()(1,0) = 0;
+cout << "Now the matrix m is:" << endl << m << endl;
diff --git a/doc/snippets/MatrixBase_triangularView.cpp b/doc/snippets/MatrixBase_triangularView.cpp
new file mode 100644
index 0000000..03aa303
--- /dev/null
+++ b/doc/snippets/MatrixBase_triangularView.cpp
@@ -0,0 +1,9 @@
+Matrix3i m = Matrix3i::Random();
+cout << "Here is the matrix m:" << endl << m << endl;
+cout << "Here is the upper-triangular matrix extracted from m:" << endl
+ << Matrix3i(m.triangularView<Eigen::Upper>()) << endl;
+cout << "Here is the strictly-upper-triangular matrix extracted from m:" << endl
+ << Matrix3i(m.triangularView<Eigen::StrictlyUpper>()) << endl;
+cout << "Here is the unit-lower-triangular matrix extracted from m:" << endl
+ << Matrix3i(m.triangularView<Eigen::UnitLower>()) << endl;
+// FIXME need to implement output for triangularViews (Bug 885)
diff --git a/doc/snippets/MatrixBase_zero.cpp b/doc/snippets/MatrixBase_zero.cpp
new file mode 100644
index 0000000..6064936
--- /dev/null
+++ b/doc/snippets/MatrixBase_zero.cpp
@@ -0,0 +1,2 @@
+cout << Matrix2d::Zero() << endl;
+cout << RowVector4i::Zero() << endl;
diff --git a/doc/snippets/MatrixBase_zero_int.cpp b/doc/snippets/MatrixBase_zero_int.cpp
new file mode 100644
index 0000000..370a9ba
--- /dev/null
+++ b/doc/snippets/MatrixBase_zero_int.cpp
@@ -0,0 +1,2 @@
+cout << RowVectorXi::Zero(4) << endl;
+cout << VectorXf::Zero(2) << endl;
diff --git a/doc/snippets/MatrixBase_zero_int_int.cpp b/doc/snippets/MatrixBase_zero_int_int.cpp
new file mode 100644
index 0000000..4099c5d
--- /dev/null
+++ b/doc/snippets/MatrixBase_zero_int_int.cpp
@@ -0,0 +1 @@
+cout << MatrixXi::Zero(2,3) << endl;
diff --git a/doc/snippets/Matrix_Map_stride.cpp b/doc/snippets/Matrix_Map_stride.cpp
new file mode 100644
index 0000000..ae42a12
--- /dev/null
+++ b/doc/snippets/Matrix_Map_stride.cpp
@@ -0,0 +1,7 @@
+Matrix4i A;
+A << 1, 2, 3, 4,
+ 5, 6, 7, 8,
+ 9, 10, 11, 12,
+ 13, 14, 15, 16;
+
+std::cout << Matrix2i::Map(&A(1,1),Stride<8,2>()) << std::endl;
diff --git a/doc/snippets/Matrix_initializer_list_23_cxx11.cpp b/doc/snippets/Matrix_initializer_list_23_cxx11.cpp
new file mode 100644
index 0000000..60280ab
--- /dev/null
+++ b/doc/snippets/Matrix_initializer_list_23_cxx11.cpp
@@ -0,0 +1,5 @@
+MatrixXd m {
+ {1, 2, 3},
+ {4, 5, 6}
+};
+cout << m << endl;
diff --git a/doc/snippets/Matrix_initializer_list_vector_cxx11.cpp b/doc/snippets/Matrix_initializer_list_vector_cxx11.cpp
new file mode 100644
index 0000000..325257c
--- /dev/null
+++ b/doc/snippets/Matrix_initializer_list_vector_cxx11.cpp
@@ -0,0 +1,2 @@
+VectorXi v {{1, 2}};
+cout << v << endl;
diff --git a/doc/snippets/Matrix_resize_NoChange_int.cpp b/doc/snippets/Matrix_resize_NoChange_int.cpp
new file mode 100644
index 0000000..acdf18c
--- /dev/null
+++ b/doc/snippets/Matrix_resize_NoChange_int.cpp
@@ -0,0 +1,3 @@
+MatrixXd m(3,4);
+m.resize(NoChange, 5);
+cout << "m: " << m.rows() << " rows, " << m.cols() << " cols" << endl;
diff --git a/doc/snippets/Matrix_resize_int.cpp b/doc/snippets/Matrix_resize_int.cpp
new file mode 100644
index 0000000..044c789
--- /dev/null
+++ b/doc/snippets/Matrix_resize_int.cpp
@@ -0,0 +1,6 @@
+VectorXd v(10);
+v.resize(3);
+RowVector3d w;
+w.resize(3); // this is legal, but has no effect
+cout << "v: " << v.rows() << " rows, " << v.cols() << " cols" << endl;
+cout << "w: " << w.rows() << " rows, " << w.cols() << " cols" << endl;
diff --git a/doc/snippets/Matrix_resize_int_NoChange.cpp b/doc/snippets/Matrix_resize_int_NoChange.cpp
new file mode 100644
index 0000000..5c37c90
--- /dev/null
+++ b/doc/snippets/Matrix_resize_int_NoChange.cpp
@@ -0,0 +1,3 @@
+MatrixXd m(3,4);
+m.resize(5, NoChange);
+cout << "m: " << m.rows() << " rows, " << m.cols() << " cols" << endl;
diff --git a/doc/snippets/Matrix_resize_int_int.cpp b/doc/snippets/Matrix_resize_int_int.cpp
new file mode 100644
index 0000000..bfd4741
--- /dev/null
+++ b/doc/snippets/Matrix_resize_int_int.cpp
@@ -0,0 +1,9 @@
+MatrixXd m(2,3);
+m << 1,2,3,4,5,6;
+cout << "here's the 2x3 matrix m:" << endl << m << endl;
+cout << "let's resize m to 3x2. This is a conservative resizing because 2*3==3*2." << endl;
+m.resize(3,2);
+cout << "here's the 3x2 matrix m:" << endl << m << endl;
+cout << "now let's resize m to size 2x2. This is NOT a conservative resizing, so it becomes uninitialized:" << endl;
+m.resize(2,2);
+cout << m << endl;
diff --git a/doc/snippets/Matrix_setConstant_int.cpp b/doc/snippets/Matrix_setConstant_int.cpp
new file mode 100644
index 0000000..ff5a86c
--- /dev/null
+++ b/doc/snippets/Matrix_setConstant_int.cpp
@@ -0,0 +1,3 @@
+VectorXf v;
+v.setConstant(3, 5);
+cout << v << endl;
diff --git a/doc/snippets/Matrix_setConstant_int_int.cpp b/doc/snippets/Matrix_setConstant_int_int.cpp
new file mode 100644
index 0000000..32b950c
--- /dev/null
+++ b/doc/snippets/Matrix_setConstant_int_int.cpp
@@ -0,0 +1,3 @@
+MatrixXf m;
+m.setConstant(3, 3, 5);
+cout << m << endl;
diff --git a/doc/snippets/Matrix_setIdentity_int_int.cpp b/doc/snippets/Matrix_setIdentity_int_int.cpp
new file mode 100644
index 0000000..a659671
--- /dev/null
+++ b/doc/snippets/Matrix_setIdentity_int_int.cpp
@@ -0,0 +1,3 @@
+MatrixXf m;
+m.setIdentity(3, 3);
+cout << m << endl;
diff --git a/doc/snippets/Matrix_setOnes_int.cpp b/doc/snippets/Matrix_setOnes_int.cpp
new file mode 100644
index 0000000..752cb35
--- /dev/null
+++ b/doc/snippets/Matrix_setOnes_int.cpp
@@ -0,0 +1,3 @@
+VectorXf v;
+v.setOnes(3);
+cout << v << endl;
diff --git a/doc/snippets/Matrix_setOnes_int_int.cpp b/doc/snippets/Matrix_setOnes_int_int.cpp
new file mode 100644
index 0000000..1ffb66b
--- /dev/null
+++ b/doc/snippets/Matrix_setOnes_int_int.cpp
@@ -0,0 +1,3 @@
+MatrixXf m;
+m.setOnes(3, 3);
+cout << m << endl;
diff --git a/doc/snippets/Matrix_setRandom_int.cpp b/doc/snippets/Matrix_setRandom_int.cpp
new file mode 100644
index 0000000..e160dd7
--- /dev/null
+++ b/doc/snippets/Matrix_setRandom_int.cpp
@@ -0,0 +1,3 @@
+VectorXf v;
+v.setRandom(3);
+cout << v << endl;
diff --git a/doc/snippets/Matrix_setRandom_int_int.cpp b/doc/snippets/Matrix_setRandom_int_int.cpp
new file mode 100644
index 0000000..80cda11
--- /dev/null
+++ b/doc/snippets/Matrix_setRandom_int_int.cpp
@@ -0,0 +1,3 @@
+MatrixXf m;
+m.setRandom(3, 3);
+cout << m << endl;
diff --git a/doc/snippets/Matrix_setZero_int.cpp b/doc/snippets/Matrix_setZero_int.cpp
new file mode 100644
index 0000000..0fb16c1
--- /dev/null
+++ b/doc/snippets/Matrix_setZero_int.cpp
@@ -0,0 +1,3 @@
+VectorXf v;
+v.setZero(3);
+cout << v << endl;
diff --git a/doc/snippets/Matrix_setZero_int_int.cpp b/doc/snippets/Matrix_setZero_int_int.cpp
new file mode 100644
index 0000000..ad883b9
--- /dev/null
+++ b/doc/snippets/Matrix_setZero_int_int.cpp
@@ -0,0 +1,3 @@
+MatrixXf m;
+m.setZero(3, 3);
+cout << m << endl;
diff --git a/doc/snippets/Matrix_variadic_ctor_cxx11.cpp b/doc/snippets/Matrix_variadic_ctor_cxx11.cpp
new file mode 100644
index 0000000..06d33f5
--- /dev/null
+++ b/doc/snippets/Matrix_variadic_ctor_cxx11.cpp
@@ -0,0 +1,3 @@
+Matrix<int, 1, 6> a(1, 2, 3, 4, 5, 6);
+Matrix<int, 3, 1> b {1, 2, 3};
+cout << a << "\n\n" << b << endl;
diff --git a/doc/snippets/PartialPivLU_solve.cpp b/doc/snippets/PartialPivLU_solve.cpp
new file mode 100644
index 0000000..fa3570a
--- /dev/null
+++ b/doc/snippets/PartialPivLU_solve.cpp
@@ -0,0 +1,7 @@
+MatrixXd A = MatrixXd::Random(3,3);
+MatrixXd B = MatrixXd::Random(3,2);
+cout << "Here is the invertible matrix A:" << endl << A << endl;
+cout << "Here is the matrix B:" << endl << B << endl;
+MatrixXd X = A.lu().solve(B);
+cout << "Here is the (unique) solution X to the equation AX=B:" << endl << X << endl;
+cout << "Relative error: " << (A*X-B).norm() / B.norm() << endl;
diff --git a/doc/snippets/PartialRedux_count.cpp b/doc/snippets/PartialRedux_count.cpp
new file mode 100644
index 0000000..1c3b3a2
--- /dev/null
+++ b/doc/snippets/PartialRedux_count.cpp
@@ -0,0 +1,5 @@
+Matrix3d m = Matrix3d::Random();
+cout << "Here is the matrix m:" << endl << m << endl;
+Matrix<ptrdiff_t, 3, 1> res = (m.array() >= 0.5).rowwise().count();
+cout << "Here is the count of elements larger or equal than 0.5 of each row:" << endl;
+cout << res << endl;
diff --git a/doc/snippets/PartialRedux_maxCoeff.cpp b/doc/snippets/PartialRedux_maxCoeff.cpp
new file mode 100644
index 0000000..e8fd382
--- /dev/null
+++ b/doc/snippets/PartialRedux_maxCoeff.cpp
@@ -0,0 +1,3 @@
+Matrix3d m = Matrix3d::Random();
+cout << "Here is the matrix m:" << endl << m << endl;
+cout << "Here is the maximum of each column:" << endl << m.colwise().maxCoeff() << endl;
diff --git a/doc/snippets/PartialRedux_minCoeff.cpp b/doc/snippets/PartialRedux_minCoeff.cpp
new file mode 100644
index 0000000..d717bc0
--- /dev/null
+++ b/doc/snippets/PartialRedux_minCoeff.cpp
@@ -0,0 +1,3 @@
+Matrix3d m = Matrix3d::Random();
+cout << "Here is the matrix m:" << endl << m << endl;
+cout << "Here is the minimum of each column:" << endl << m.colwise().minCoeff() << endl;
diff --git a/doc/snippets/PartialRedux_norm.cpp b/doc/snippets/PartialRedux_norm.cpp
new file mode 100644
index 0000000..dbcf290
--- /dev/null
+++ b/doc/snippets/PartialRedux_norm.cpp
@@ -0,0 +1,3 @@
+Matrix3d m = Matrix3d::Random();
+cout << "Here is the matrix m:" << endl << m << endl;
+cout << "Here is the norm of each column:" << endl << m.colwise().norm() << endl;
diff --git a/doc/snippets/PartialRedux_prod.cpp b/doc/snippets/PartialRedux_prod.cpp
new file mode 100644
index 0000000..aacf09c
--- /dev/null
+++ b/doc/snippets/PartialRedux_prod.cpp
@@ -0,0 +1,3 @@
+Matrix3d m = Matrix3d::Random();
+cout << "Here is the matrix m:" << endl << m << endl;
+cout << "Here is the product of each row:" << endl << m.rowwise().prod() << endl;
diff --git a/doc/snippets/PartialRedux_squaredNorm.cpp b/doc/snippets/PartialRedux_squaredNorm.cpp
new file mode 100644
index 0000000..9f3293e
--- /dev/null
+++ b/doc/snippets/PartialRedux_squaredNorm.cpp
@@ -0,0 +1,3 @@
+Matrix3d m = Matrix3d::Random();
+cout << "Here is the matrix m:" << endl << m << endl;
+cout << "Here is the square norm of each row:" << endl << m.rowwise().squaredNorm() << endl;
diff --git a/doc/snippets/PartialRedux_sum.cpp b/doc/snippets/PartialRedux_sum.cpp
new file mode 100644
index 0000000..ec82d3e
--- /dev/null
+++ b/doc/snippets/PartialRedux_sum.cpp
@@ -0,0 +1,3 @@
+Matrix3d m = Matrix3d::Random();
+cout << "Here is the matrix m:" << endl << m << endl;
+cout << "Here is the sum of each row:" << endl << m.rowwise().sum() << endl;
diff --git a/doc/snippets/RealQZ_compute.cpp b/doc/snippets/RealQZ_compute.cpp
new file mode 100644
index 0000000..a18da42
--- /dev/null
+++ b/doc/snippets/RealQZ_compute.cpp
@@ -0,0 +1,17 @@
+MatrixXf A = MatrixXf::Random(4,4);
+MatrixXf B = MatrixXf::Random(4,4);
+RealQZ<MatrixXf> qz(4); // preallocate space for 4x4 matrices
+qz.compute(A,B); // A = Q S Z, B = Q T Z
+
+// print original matrices and result of decomposition
+cout << "A:\n" << A << "\n" << "B:\n" << B << "\n";
+cout << "S:\n" << qz.matrixS() << "\n" << "T:\n" << qz.matrixT() << "\n";
+cout << "Q:\n" << qz.matrixQ() << "\n" << "Z:\n" << qz.matrixZ() << "\n";
+
+// verify precision
+cout << "\nErrors:"
+ << "\n|A-QSZ|: " << (A-qz.matrixQ()*qz.matrixS()*qz.matrixZ()).norm()
+ << ", |B-QTZ|: " << (B-qz.matrixQ()*qz.matrixT()*qz.matrixZ()).norm()
+ << "\n|QQ* - I|: " << (qz.matrixQ()*qz.matrixQ().adjoint() - MatrixXf::Identity(4,4)).norm()
+ << ", |ZZ* - I|: " << (qz.matrixZ()*qz.matrixZ().adjoint() - MatrixXf::Identity(4,4)).norm()
+ << "\n";
diff --git a/doc/snippets/RealSchur_RealSchur_MatrixType.cpp b/doc/snippets/RealSchur_RealSchur_MatrixType.cpp
new file mode 100644
index 0000000..a5530dc
--- /dev/null
+++ b/doc/snippets/RealSchur_RealSchur_MatrixType.cpp
@@ -0,0 +1,10 @@
+MatrixXd A = MatrixXd::Random(6,6);
+cout << "Here is a random 6x6 matrix, A:" << endl << A << endl << endl;
+
+RealSchur<MatrixXd> schur(A);
+cout << "The orthogonal matrix U is:" << endl << schur.matrixU() << endl;
+cout << "The quasi-triangular matrix T is:" << endl << schur.matrixT() << endl << endl;
+
+MatrixXd U = schur.matrixU();
+MatrixXd T = schur.matrixT();
+cout << "U * T * U^T = " << endl << U * T * U.transpose() << endl;
diff --git a/doc/snippets/RealSchur_compute.cpp b/doc/snippets/RealSchur_compute.cpp
new file mode 100644
index 0000000..20c2611
--- /dev/null
+++ b/doc/snippets/RealSchur_compute.cpp
@@ -0,0 +1,6 @@
+MatrixXf A = MatrixXf::Random(4,4);
+RealSchur<MatrixXf> schur(4);
+schur.compute(A, /* computeU = */ false);
+cout << "The matrix T in the decomposition of A is:" << endl << schur.matrixT() << endl;
+schur.compute(A.inverse(), /* computeU = */ false);
+cout << "The matrix T in the decomposition of A^(-1) is:" << endl << schur.matrixT() << endl;
diff --git a/doc/snippets/SelfAdjointEigenSolver_SelfAdjointEigenSolver.cpp b/doc/snippets/SelfAdjointEigenSolver_SelfAdjointEigenSolver.cpp
new file mode 100644
index 0000000..73a7f62
--- /dev/null
+++ b/doc/snippets/SelfAdjointEigenSolver_SelfAdjointEigenSolver.cpp
@@ -0,0 +1,7 @@
+SelfAdjointEigenSolver<Matrix4f> es;
+Matrix4f X = Matrix4f::Random(4,4);
+Matrix4f A = X + X.transpose();
+es.compute(A);
+cout << "The eigenvalues of A are: " << es.eigenvalues().transpose() << endl;
+es.compute(A + Matrix4f::Identity(4,4)); // re-use es to compute eigenvalues of A+I
+cout << "The eigenvalues of A+I are: " << es.eigenvalues().transpose() << endl;
diff --git a/doc/snippets/SelfAdjointEigenSolver_SelfAdjointEigenSolver_MatrixType.cpp b/doc/snippets/SelfAdjointEigenSolver_SelfAdjointEigenSolver_MatrixType.cpp
new file mode 100644
index 0000000..3599b17
--- /dev/null
+++ b/doc/snippets/SelfAdjointEigenSolver_SelfAdjointEigenSolver_MatrixType.cpp
@@ -0,0 +1,17 @@
+MatrixXd X = MatrixXd::Random(5,5);
+MatrixXd A = X + X.transpose();
+cout << "Here is a random symmetric 5x5 matrix, A:" << endl << A << endl << endl;
+
+SelfAdjointEigenSolver<MatrixXd> es(A);
+cout << "The eigenvalues of A are:" << endl << es.eigenvalues() << endl;
+cout << "The matrix of eigenvectors, V, is:" << endl << es.eigenvectors() << endl << endl;
+
+double lambda = es.eigenvalues()[0];
+cout << "Consider the first eigenvalue, lambda = " << lambda << endl;
+VectorXd v = es.eigenvectors().col(0);
+cout << "If v is the corresponding eigenvector, then lambda * v = " << endl << lambda * v << endl;
+cout << "... and A * v = " << endl << A * v << endl << endl;
+
+MatrixXd D = es.eigenvalues().asDiagonal();
+MatrixXd V = es.eigenvectors();
+cout << "Finally, V * D * V^(-1) = " << endl << V * D * V.inverse() << endl;
diff --git a/doc/snippets/SelfAdjointEigenSolver_SelfAdjointEigenSolver_MatrixType2.cpp b/doc/snippets/SelfAdjointEigenSolver_SelfAdjointEigenSolver_MatrixType2.cpp
new file mode 100644
index 0000000..cc0c50e
--- /dev/null
+++ b/doc/snippets/SelfAdjointEigenSolver_SelfAdjointEigenSolver_MatrixType2.cpp
@@ -0,0 +1,16 @@
+MatrixXd X = MatrixXd::Random(5,5);
+MatrixXd A = X + X.transpose();
+cout << "Here is a random symmetric matrix, A:" << endl << A << endl;
+X = MatrixXd::Random(5,5);
+MatrixXd B = X * X.transpose();
+cout << "and a random positive-definite matrix, B:" << endl << B << endl << endl;
+
+GeneralizedSelfAdjointEigenSolver<MatrixXd> es(A,B);
+cout << "The eigenvalues of the pencil (A,B) are:" << endl << es.eigenvalues() << endl;
+cout << "The matrix of eigenvectors, V, is:" << endl << es.eigenvectors() << endl << endl;
+
+double lambda = es.eigenvalues()[0];
+cout << "Consider the first eigenvalue, lambda = " << lambda << endl;
+VectorXd v = es.eigenvectors().col(0);
+cout << "If v is the corresponding eigenvector, then A * v = " << endl << A * v << endl;
+cout << "... and lambda * B * v = " << endl << lambda * B * v << endl << endl;
diff --git a/doc/snippets/SelfAdjointEigenSolver_compute_MatrixType.cpp b/doc/snippets/SelfAdjointEigenSolver_compute_MatrixType.cpp
new file mode 100644
index 0000000..2975cc3
--- /dev/null
+++ b/doc/snippets/SelfAdjointEigenSolver_compute_MatrixType.cpp
@@ -0,0 +1,7 @@
+SelfAdjointEigenSolver<MatrixXf> es(4);
+MatrixXf X = MatrixXf::Random(4,4);
+MatrixXf A = X + X.transpose();
+es.compute(A);
+cout << "The eigenvalues of A are: " << es.eigenvalues().transpose() << endl;
+es.compute(A + MatrixXf::Identity(4,4)); // re-use es to compute eigenvalues of A+I
+cout << "The eigenvalues of A+I are: " << es.eigenvalues().transpose() << endl;
diff --git a/doc/snippets/SelfAdjointEigenSolver_compute_MatrixType2.cpp b/doc/snippets/SelfAdjointEigenSolver_compute_MatrixType2.cpp
new file mode 100644
index 0000000..07c92a1
--- /dev/null
+++ b/doc/snippets/SelfAdjointEigenSolver_compute_MatrixType2.cpp
@@ -0,0 +1,9 @@
+MatrixXd X = MatrixXd::Random(5,5);
+MatrixXd A = X * X.transpose();
+X = MatrixXd::Random(5,5);
+MatrixXd B = X * X.transpose();
+
+GeneralizedSelfAdjointEigenSolver<MatrixXd> es(A,B,EigenvaluesOnly);
+cout << "The eigenvalues of the pencil (A,B) are:" << endl << es.eigenvalues() << endl;
+es.compute(B,A,false);
+cout << "The eigenvalues of the pencil (B,A) are:" << endl << es.eigenvalues() << endl;
diff --git a/doc/snippets/SelfAdjointEigenSolver_eigenvalues.cpp b/doc/snippets/SelfAdjointEigenSolver_eigenvalues.cpp
new file mode 100644
index 0000000..0ff33c6
--- /dev/null
+++ b/doc/snippets/SelfAdjointEigenSolver_eigenvalues.cpp
@@ -0,0 +1,4 @@
+MatrixXd ones = MatrixXd::Ones(3,3);
+SelfAdjointEigenSolver<MatrixXd> es(ones);
+cout << "The eigenvalues of the 3x3 matrix of ones are:"
+ << endl << es.eigenvalues() << endl;
diff --git a/doc/snippets/SelfAdjointEigenSolver_eigenvectors.cpp b/doc/snippets/SelfAdjointEigenSolver_eigenvectors.cpp
new file mode 100644
index 0000000..94b0d6e
--- /dev/null
+++ b/doc/snippets/SelfAdjointEigenSolver_eigenvectors.cpp
@@ -0,0 +1,4 @@
+MatrixXd ones = MatrixXd::Ones(3,3);
+SelfAdjointEigenSolver<MatrixXd> es(ones);
+cout << "The first eigenvector of the 3x3 matrix of ones is:"
+ << endl << es.eigenvectors().col(0) << endl;
diff --git a/doc/snippets/SelfAdjointEigenSolver_operatorInverseSqrt.cpp b/doc/snippets/SelfAdjointEigenSolver_operatorInverseSqrt.cpp
new file mode 100644
index 0000000..114c65f
--- /dev/null
+++ b/doc/snippets/SelfAdjointEigenSolver_operatorInverseSqrt.cpp
@@ -0,0 +1,9 @@
+MatrixXd X = MatrixXd::Random(4,4);
+MatrixXd A = X * X.transpose();
+cout << "Here is a random positive-definite matrix, A:" << endl << A << endl << endl;
+
+SelfAdjointEigenSolver<MatrixXd> es(A);
+cout << "The inverse square root of A is: " << endl;
+cout << es.operatorInverseSqrt() << endl;
+cout << "We can also compute it with operatorSqrt() and inverse(). That yields: " << endl;
+cout << es.operatorSqrt().inverse() << endl;
diff --git a/doc/snippets/SelfAdjointEigenSolver_operatorSqrt.cpp b/doc/snippets/SelfAdjointEigenSolver_operatorSqrt.cpp
new file mode 100644
index 0000000..eeacca7
--- /dev/null
+++ b/doc/snippets/SelfAdjointEigenSolver_operatorSqrt.cpp
@@ -0,0 +1,8 @@
+MatrixXd X = MatrixXd::Random(4,4);
+MatrixXd A = X * X.transpose();
+cout << "Here is a random positive-definite matrix, A:" << endl << A << endl << endl;
+
+SelfAdjointEigenSolver<MatrixXd> es(A);
+MatrixXd sqrtA = es.operatorSqrt();
+cout << "The square root of A is: " << endl << sqrtA << endl;
+cout << "If we square this, we get: " << endl << sqrtA*sqrtA << endl;
diff --git a/doc/snippets/SelfAdjointView_eigenvalues.cpp b/doc/snippets/SelfAdjointView_eigenvalues.cpp
new file mode 100644
index 0000000..be19867
--- /dev/null
+++ b/doc/snippets/SelfAdjointView_eigenvalues.cpp
@@ -0,0 +1,3 @@
+MatrixXd ones = MatrixXd::Ones(3,3);
+VectorXd eivals = ones.selfadjointView<Lower>().eigenvalues();
+cout << "The eigenvalues of the 3x3 matrix of ones are:" << endl << eivals << endl;
diff --git a/doc/snippets/SelfAdjointView_operatorNorm.cpp b/doc/snippets/SelfAdjointView_operatorNorm.cpp
new file mode 100644
index 0000000..f380f55
--- /dev/null
+++ b/doc/snippets/SelfAdjointView_operatorNorm.cpp
@@ -0,0 +1,3 @@
+MatrixXd ones = MatrixXd::Ones(3,3);
+cout << "The operator norm of the 3x3 matrix of ones is "
+ << ones.selfadjointView<Lower>().operatorNorm() << endl;
diff --git a/doc/snippets/Slicing_arrayexpr.cpp b/doc/snippets/Slicing_arrayexpr.cpp
new file mode 100644
index 0000000..6d09980
--- /dev/null
+++ b/doc/snippets/Slicing_arrayexpr.cpp
@@ -0,0 +1,4 @@
+ArrayXi ind(5); ind<<4,2,5,5,3;
+MatrixXi A = MatrixXi::Random(4,6);
+cout << "Initial matrix A:\n" << A << "\n\n";
+cout << "A(all,ind-1):\n" << A(Eigen::placeholders::all,ind-1) << "\n\n";
diff --git a/doc/snippets/Slicing_custom_padding_cxx11.cpp b/doc/snippets/Slicing_custom_padding_cxx11.cpp
new file mode 100644
index 0000000..24db98b
--- /dev/null
+++ b/doc/snippets/Slicing_custom_padding_cxx11.cpp
@@ -0,0 +1,12 @@
+struct pad {
+ Index size() const { return out_size; }
+ Index operator[] (Index i) const { return std::max<Index>(0,i-(out_size-in_size)); }
+ Index in_size, out_size;
+};
+
+Matrix3i A;
+A.reshaped() = VectorXi::LinSpaced(9,1,9);
+cout << "Initial matrix A:\n" << A << "\n\n";
+MatrixXi B(5,5);
+B = A(pad{3,5}, pad{3,5});
+cout << "A(pad{3,N}, pad{3,N}):\n" << B << "\n\n";
diff --git a/doc/snippets/Slicing_rawarray_cxx11.cpp b/doc/snippets/Slicing_rawarray_cxx11.cpp
new file mode 100644
index 0000000..7a3e6e5
--- /dev/null
+++ b/doc/snippets/Slicing_rawarray_cxx11.cpp
@@ -0,0 +1,3 @@
+MatrixXi A = MatrixXi::Random(4,6);
+cout << "Initial matrix A:\n" << A << "\n\n";
+cout << "A(all,{4,2,5,5,3}):\n" << A(Eigen::placeholders::all,{4,2,5,5,3}) << "\n\n";
diff --git a/doc/snippets/Slicing_stdvector_cxx11.cpp b/doc/snippets/Slicing_stdvector_cxx11.cpp
new file mode 100644
index 0000000..74f0727
--- /dev/null
+++ b/doc/snippets/Slicing_stdvector_cxx11.cpp
@@ -0,0 +1,4 @@
+std::vector<int> ind{4,2,5,5,3};
+MatrixXi A = MatrixXi::Random(4,6);
+cout << "Initial matrix A:\n" << A << "\n\n";
+cout << "A(all,ind):\n" << A(Eigen::placeholders::all,ind) << "\n\n";
diff --git a/doc/snippets/SparseMatrix_coeffs.cpp b/doc/snippets/SparseMatrix_coeffs.cpp
new file mode 100644
index 0000000..f71a69b
--- /dev/null
+++ b/doc/snippets/SparseMatrix_coeffs.cpp
@@ -0,0 +1,9 @@
+SparseMatrix<double> A(3,3);
+A.insert(1,2) = 0;
+A.insert(0,1) = 1;
+A.insert(2,0) = 2;
+A.makeCompressed();
+cout << "The matrix A is:" << endl << MatrixXd(A) << endl;
+cout << "it has " << A.nonZeros() << " stored non zero coefficients that are: " << A.coeffs().transpose() << endl;
+A.coeffs() += 10;
+cout << "After adding 10 to every stored non zero coefficient, the matrix A is:" << endl << MatrixXd(A) << endl;
diff --git a/doc/snippets/TopicAliasing_block.cpp b/doc/snippets/TopicAliasing_block.cpp
new file mode 100644
index 0000000..03282f4
--- /dev/null
+++ b/doc/snippets/TopicAliasing_block.cpp
@@ -0,0 +1,7 @@
+MatrixXi mat(3,3);
+mat << 1, 2, 3, 4, 5, 6, 7, 8, 9;
+cout << "Here is the matrix mat:\n" << mat << endl;
+
+// This assignment shows the aliasing problem
+mat.bottomRightCorner(2,2) = mat.topLeftCorner(2,2);
+cout << "After the assignment, mat = \n" << mat << endl;
diff --git a/doc/snippets/TopicAliasing_block_correct.cpp b/doc/snippets/TopicAliasing_block_correct.cpp
new file mode 100644
index 0000000..6fee580
--- /dev/null
+++ b/doc/snippets/TopicAliasing_block_correct.cpp
@@ -0,0 +1,7 @@
+MatrixXi mat(3,3);
+mat << 1, 2, 3, 4, 5, 6, 7, 8, 9;
+cout << "Here is the matrix mat:\n" << mat << endl;
+
+// The eval() solves the aliasing problem
+mat.bottomRightCorner(2,2) = mat.topLeftCorner(2,2).eval();
+cout << "After the assignment, mat = \n" << mat << endl;
diff --git a/doc/snippets/TopicAliasing_cwise.cpp b/doc/snippets/TopicAliasing_cwise.cpp
new file mode 100644
index 0000000..7049f6c
--- /dev/null
+++ b/doc/snippets/TopicAliasing_cwise.cpp
@@ -0,0 +1,20 @@
+MatrixXf mat(2,2);
+mat << 1, 2, 4, 7;
+cout << "Here is the matrix mat:\n" << mat << endl << endl;
+
+mat = 2 * mat;
+cout << "After 'mat = 2 * mat', mat = \n" << mat << endl << endl;
+
+
+mat = mat - MatrixXf::Identity(2,2);
+cout << "After the subtraction, it becomes\n" << mat << endl << endl;
+
+
+ArrayXXf arr = mat;
+arr = arr.square();
+cout << "After squaring, it becomes\n" << arr << endl << endl;
+
+// Combining all operations in one statement:
+mat << 1, 2, 4, 7;
+mat = (2 * mat - MatrixXf::Identity(2,2)).array().square();
+cout << "Doing everything at once yields\n" << mat << endl << endl;
diff --git a/doc/snippets/TopicAliasing_mult1.cpp b/doc/snippets/TopicAliasing_mult1.cpp
new file mode 100644
index 0000000..cd7e900
--- /dev/null
+++ b/doc/snippets/TopicAliasing_mult1.cpp
@@ -0,0 +1,4 @@
+MatrixXf matA(2,2);
+matA << 2, 0, 0, 2;
+matA = matA * matA;
+cout << matA;
diff --git a/doc/snippets/TopicAliasing_mult2.cpp b/doc/snippets/TopicAliasing_mult2.cpp
new file mode 100644
index 0000000..a3ff568
--- /dev/null
+++ b/doc/snippets/TopicAliasing_mult2.cpp
@@ -0,0 +1,10 @@
+MatrixXf matA(2,2), matB(2,2);
+matA << 2, 0, 0, 2;
+
+// Simple but not quite as efficient
+matB = matA * matA;
+cout << matB << endl << endl;
+
+// More complicated but also more efficient
+matB.noalias() = matA * matA;
+cout << matB;
diff --git a/doc/snippets/TopicAliasing_mult3.cpp b/doc/snippets/TopicAliasing_mult3.cpp
new file mode 100644
index 0000000..1d12a6c
--- /dev/null
+++ b/doc/snippets/TopicAliasing_mult3.cpp
@@ -0,0 +1,4 @@
+MatrixXf matA(2,2);
+matA << 2, 0, 0, 2;
+matA.noalias() = matA * matA;
+cout << matA;
diff --git a/doc/snippets/TopicAliasing_mult4.cpp b/doc/snippets/TopicAliasing_mult4.cpp
new file mode 100644
index 0000000..01c1c6d
--- /dev/null
+++ b/doc/snippets/TopicAliasing_mult4.cpp
@@ -0,0 +1,5 @@
+MatrixXf A(2,2), B(3,2);
+B << 2, 0, 0, 3, 1, 1;
+A << 2, 0, 0, -2;
+A = (B * A).cwiseAbs();
+cout << A;
diff --git a/doc/snippets/TopicAliasing_mult5.cpp b/doc/snippets/TopicAliasing_mult5.cpp
new file mode 100644
index 0000000..1a36def
--- /dev/null
+++ b/doc/snippets/TopicAliasing_mult5.cpp
@@ -0,0 +1,5 @@
+MatrixXf A(2,2), B(3,2);
+B << 2, 0, 0, 3, 1, 1;
+A << 2, 0, 0, -2;
+A = (B * A).eval().cwiseAbs();
+cout << A;
diff --git a/doc/snippets/TopicStorageOrders_example.cpp b/doc/snippets/TopicStorageOrders_example.cpp
new file mode 100644
index 0000000..0623ef0
--- /dev/null
+++ b/doc/snippets/TopicStorageOrders_example.cpp
@@ -0,0 +1,18 @@
+Matrix<int, 3, 4, ColMajor> Acolmajor;
+Acolmajor << 8, 2, 2, 9,
+ 9, 1, 4, 4,
+ 3, 5, 4, 5;
+cout << "The matrix A:" << endl;
+cout << Acolmajor << endl << endl;
+
+cout << "In memory (column-major):" << endl;
+for (int i = 0; i < Acolmajor.size(); i++)
+ cout << *(Acolmajor.data() + i) << " ";
+cout << endl << endl;
+
+Matrix<int, 3, 4, RowMajor> Arowmajor = Acolmajor;
+cout << "In memory (row-major):" << endl;
+for (int i = 0; i < Arowmajor.size(); i++)
+ cout << *(Arowmajor.data() + i) << " ";
+cout << endl;
+
diff --git a/doc/snippets/Triangular_solve.cpp b/doc/snippets/Triangular_solve.cpp
new file mode 100644
index 0000000..5484424
--- /dev/null
+++ b/doc/snippets/Triangular_solve.cpp
@@ -0,0 +1,11 @@
+Matrix3d m = Matrix3d::Zero();
+m.triangularView<Eigen::Upper>().setOnes();
+cout << "Here is the matrix m:\n" << m << endl;
+Matrix3d n = Matrix3d::Ones();
+n.triangularView<Eigen::Lower>() *= 2;
+cout << "Here is the matrix n:\n" << n << endl;
+cout << "And now here is m.inverse()*n, taking advantage of the fact that"
+ " m is upper-triangular:\n"
+ << m.triangularView<Eigen::Upper>().solve(n) << endl;
+cout << "And this is n*m.inverse():\n"
+ << m.triangularView<Eigen::Upper>().solve<Eigen::OnTheRight>(n);
diff --git a/doc/snippets/Tridiagonalization_Tridiagonalization_MatrixType.cpp b/doc/snippets/Tridiagonalization_Tridiagonalization_MatrixType.cpp
new file mode 100644
index 0000000..a260124
--- /dev/null
+++ b/doc/snippets/Tridiagonalization_Tridiagonalization_MatrixType.cpp
@@ -0,0 +1,9 @@
+MatrixXd X = MatrixXd::Random(5,5);
+MatrixXd A = X + X.transpose();
+cout << "Here is a random symmetric 5x5 matrix:" << endl << A << endl << endl;
+Tridiagonalization<MatrixXd> triOfA(A);
+MatrixXd Q = triOfA.matrixQ();
+cout << "The orthogonal matrix Q is:" << endl << Q << endl;
+MatrixXd T = triOfA.matrixT();
+cout << "The tridiagonal matrix T is:" << endl << T << endl << endl;
+cout << "Q * T * Q^T = " << endl << Q * T * Q.transpose() << endl;
diff --git a/doc/snippets/Tridiagonalization_compute.cpp b/doc/snippets/Tridiagonalization_compute.cpp
new file mode 100644
index 0000000..0062a99
--- /dev/null
+++ b/doc/snippets/Tridiagonalization_compute.cpp
@@ -0,0 +1,9 @@
+Tridiagonalization<MatrixXf> tri;
+MatrixXf X = MatrixXf::Random(4,4);
+MatrixXf A = X + X.transpose();
+tri.compute(A);
+cout << "The matrix T in the tridiagonal decomposition of A is: " << endl;
+cout << tri.matrixT() << endl;
+tri.compute(2*A); // re-use tri to compute eigenvalues of 2A
+cout << "The matrix T in the tridiagonal decomposition of 2A is: " << endl;
+cout << tri.matrixT() << endl;
diff --git a/doc/snippets/Tridiagonalization_decomposeInPlace.cpp b/doc/snippets/Tridiagonalization_decomposeInPlace.cpp
new file mode 100644
index 0000000..3cdce67
--- /dev/null
+++ b/doc/snippets/Tridiagonalization_decomposeInPlace.cpp
@@ -0,0 +1,11 @@
+MatrixXd X = MatrixXd::Random(5,5);
+MatrixXd A = X + X.transpose();
+cout << "Here is a random symmetric 5x5 matrix:" << endl << A << endl << endl;
+
+VectorXd diag(5);
+VectorXd subdiag(4);
+VectorXd hcoeffs(4); // Scratch space for householder reflector.
+internal::tridiagonalization_inplace(A, diag, subdiag, hcoeffs, true);
+cout << "The orthogonal matrix Q is:" << endl << A << endl;
+cout << "The diagonal of the tridiagonal matrix T is:" << endl << diag << endl;
+cout << "The subdiagonal of the tridiagonal matrix T is:" << endl << subdiag << endl;
diff --git a/doc/snippets/Tridiagonalization_diagonal.cpp b/doc/snippets/Tridiagonalization_diagonal.cpp
new file mode 100644
index 0000000..6eec821
--- /dev/null
+++ b/doc/snippets/Tridiagonalization_diagonal.cpp
@@ -0,0 +1,13 @@
+MatrixXcd X = MatrixXcd::Random(4,4);
+MatrixXcd A = X + X.adjoint();
+cout << "Here is a random self-adjoint 4x4 matrix:" << endl << A << endl << endl;
+
+Tridiagonalization<MatrixXcd> triOfA(A);
+MatrixXd T = triOfA.matrixT();
+cout << "The tridiagonal matrix T is:" << endl << T << endl << endl;
+
+cout << "We can also extract the diagonals of T directly ..." << endl;
+VectorXd diag = triOfA.diagonal();
+cout << "The diagonal is:" << endl << diag << endl;
+VectorXd subdiag = triOfA.subDiagonal();
+cout << "The subdiagonal is:" << endl << subdiag << endl;
diff --git a/doc/snippets/Tridiagonalization_householderCoefficients.cpp b/doc/snippets/Tridiagonalization_householderCoefficients.cpp
new file mode 100644
index 0000000..e5d8728
--- /dev/null
+++ b/doc/snippets/Tridiagonalization_householderCoefficients.cpp
@@ -0,0 +1,6 @@
+Matrix4d X = Matrix4d::Random(4,4);
+Matrix4d A = X + X.transpose();
+cout << "Here is a random symmetric 4x4 matrix:" << endl << A << endl;
+Tridiagonalization<Matrix4d> triOfA(A);
+Vector3d hc = triOfA.householderCoefficients();
+cout << "The vector of Householder coefficients is:" << endl << hc << endl;
diff --git a/doc/snippets/Tridiagonalization_packedMatrix.cpp b/doc/snippets/Tridiagonalization_packedMatrix.cpp
new file mode 100644
index 0000000..0f55d0c
--- /dev/null
+++ b/doc/snippets/Tridiagonalization_packedMatrix.cpp
@@ -0,0 +1,8 @@
+Matrix4d X = Matrix4d::Random(4,4);
+Matrix4d A = X + X.transpose();
+cout << "Here is a random symmetric 4x4 matrix:" << endl << A << endl;
+Tridiagonalization<Matrix4d> triOfA(A);
+Matrix4d pm = triOfA.packedMatrix();
+cout << "The packed matrix M is:" << endl << pm << endl;
+cout << "The diagonal and subdiagonal corresponds to the matrix T, which is:"
+ << endl << triOfA.matrixT() << endl;
diff --git a/doc/snippets/Tutorial_AdvancedInitialization_Block.cpp b/doc/snippets/Tutorial_AdvancedInitialization_Block.cpp
new file mode 100644
index 0000000..96e40ac
--- /dev/null
+++ b/doc/snippets/Tutorial_AdvancedInitialization_Block.cpp
@@ -0,0 +1,5 @@
+MatrixXf matA(2, 2);
+matA << 1, 2, 3, 4;
+MatrixXf matB(4, 4);
+matB << matA, matA/10, matA/10, matA;
+std::cout << matB << std::endl;
diff --git a/doc/snippets/Tutorial_AdvancedInitialization_CommaTemporary.cpp b/doc/snippets/Tutorial_AdvancedInitialization_CommaTemporary.cpp
new file mode 100644
index 0000000..50cff4c
--- /dev/null
+++ b/doc/snippets/Tutorial_AdvancedInitialization_CommaTemporary.cpp
@@ -0,0 +1,4 @@
+MatrixXf mat = MatrixXf::Random(2, 3);
+std::cout << mat << std::endl << std::endl;
+mat = (MatrixXf(2,2) << 0, 1, 1, 0).finished() * mat;
+std::cout << mat << std::endl;
diff --git a/doc/snippets/Tutorial_AdvancedInitialization_Join.cpp b/doc/snippets/Tutorial_AdvancedInitialization_Join.cpp
new file mode 100644
index 0000000..55a2153
--- /dev/null
+++ b/doc/snippets/Tutorial_AdvancedInitialization_Join.cpp
@@ -0,0 +1,11 @@
+RowVectorXd vec1(3);
+vec1 << 1, 2, 3;
+std::cout << "vec1 = " << vec1 << std::endl;
+
+RowVectorXd vec2(4);
+vec2 << 1, 4, 9, 16;
+std::cout << "vec2 = " << vec2 << std::endl;
+
+RowVectorXd joined(7);
+joined << vec1, vec2;
+std::cout << "joined = " << joined << std::endl;
diff --git a/doc/snippets/Tutorial_AdvancedInitialization_LinSpaced.cpp b/doc/snippets/Tutorial_AdvancedInitialization_LinSpaced.cpp
new file mode 100644
index 0000000..c6a73ab
--- /dev/null
+++ b/doc/snippets/Tutorial_AdvancedInitialization_LinSpaced.cpp
@@ -0,0 +1,7 @@
+ArrayXXf table(10, 4);
+table.col(0) = ArrayXf::LinSpaced(10, 0, 90);
+table.col(1) = M_PI / 180 * table.col(0);
+table.col(2) = table.col(1).sin();
+table.col(3) = table.col(1).cos();
+std::cout << " Degrees Radians Sine Cosine\n";
+std::cout << table << std::endl;
diff --git a/doc/snippets/Tutorial_AdvancedInitialization_ThreeWays.cpp b/doc/snippets/Tutorial_AdvancedInitialization_ThreeWays.cpp
new file mode 100644
index 0000000..cb74576
--- /dev/null
+++ b/doc/snippets/Tutorial_AdvancedInitialization_ThreeWays.cpp
@@ -0,0 +1,20 @@
+const int size = 6;
+MatrixXd mat1(size, size);
+mat1.topLeftCorner(size/2, size/2) = MatrixXd::Zero(size/2, size/2);
+mat1.topRightCorner(size/2, size/2) = MatrixXd::Identity(size/2, size/2);
+mat1.bottomLeftCorner(size/2, size/2) = MatrixXd::Identity(size/2, size/2);
+mat1.bottomRightCorner(size/2, size/2) = MatrixXd::Zero(size/2, size/2);
+std::cout << mat1 << std::endl << std::endl;
+
+MatrixXd mat2(size, size);
+mat2.topLeftCorner(size/2, size/2).setZero();
+mat2.topRightCorner(size/2, size/2).setIdentity();
+mat2.bottomLeftCorner(size/2, size/2).setIdentity();
+mat2.bottomRightCorner(size/2, size/2).setZero();
+std::cout << mat2 << std::endl << std::endl;
+
+MatrixXd mat3(size, size);
+mat3 << MatrixXd::Zero(size/2, size/2), MatrixXd::Identity(size/2, size/2),
+ MatrixXd::Identity(size/2, size/2), MatrixXd::Zero(size/2, size/2);
+std::cout << mat3 << std::endl;
+
diff --git a/doc/snippets/Tutorial_AdvancedInitialization_Zero.cpp b/doc/snippets/Tutorial_AdvancedInitialization_Zero.cpp
new file mode 100644
index 0000000..76a36a3
--- /dev/null
+++ b/doc/snippets/Tutorial_AdvancedInitialization_Zero.cpp
@@ -0,0 +1,13 @@
+std::cout << "A fixed-size array:\n";
+Array33f a1 = Array33f::Zero();
+std::cout << a1 << "\n\n";
+
+
+std::cout << "A one-dimensional dynamic-size array:\n";
+ArrayXf a2 = ArrayXf::Zero(3);
+std::cout << a2 << "\n\n";
+
+
+std::cout << "A two-dimensional dynamic-size array:\n";
+ArrayXXf a3 = ArrayXXf::Zero(3, 4);
+std::cout << a3 << "\n";
diff --git a/doc/snippets/Tutorial_Map_rowmajor.cpp b/doc/snippets/Tutorial_Map_rowmajor.cpp
new file mode 100644
index 0000000..fd45ace
--- /dev/null
+++ b/doc/snippets/Tutorial_Map_rowmajor.cpp
@@ -0,0 +1,7 @@
+int array[8];
+for(int i = 0; i < 8; ++i) array[i] = i;
+cout << "Column-major:\n" << Map<Matrix<int,2,4> >(array) << endl;
+cout << "Row-major:\n" << Map<Matrix<int,2,4,RowMajor> >(array) << endl;
+cout << "Row-major using stride:\n" <<
+ Map<Matrix<int,2,4>, Unaligned, Stride<1,4> >(array) << endl;
+
diff --git a/doc/snippets/Tutorial_Map_using.cpp b/doc/snippets/Tutorial_Map_using.cpp
new file mode 100644
index 0000000..e5e499f
--- /dev/null
+++ b/doc/snippets/Tutorial_Map_using.cpp
@@ -0,0 +1,21 @@
+typedef Matrix<float,1,Dynamic> MatrixType;
+typedef Map<MatrixType> MapType;
+typedef Map<const MatrixType> MapTypeConst; // a read-only map
+const int n_dims = 5;
+
+MatrixType m1(n_dims), m2(n_dims);
+m1.setRandom();
+m2.setRandom();
+float *p = &m2(0); // get the address storing the data for m2
+MapType m2map(p,m2.size()); // m2map shares data with m2
+MapTypeConst m2mapconst(p,m2.size()); // a read-only accessor for m2
+
+cout << "m1: " << m1 << endl;
+cout << "m2: " << m2 << endl;
+cout << "Squared euclidean distance: " << (m1-m2).squaredNorm() << endl;
+cout << "Squared euclidean distance, using map: " <<
+ (m1-m2map).squaredNorm() << endl;
+m2map(3) = 7; // this will change m2, since they share the same array
+cout << "Updated m2: " << m2 << endl;
+cout << "m2 coefficient 2, constant accessor: " << m2mapconst(2) << endl;
+/* m2mapconst(2) = 5; */ // this yields a compile-time error
diff --git a/doc/snippets/Tutorial_ReshapeMat2Mat.cpp b/doc/snippets/Tutorial_ReshapeMat2Mat.cpp
new file mode 100644
index 0000000..737afec
--- /dev/null
+++ b/doc/snippets/Tutorial_ReshapeMat2Mat.cpp
@@ -0,0 +1,6 @@
+MatrixXf M1(2,6); // Column-major storage
+M1 << 1, 2, 3, 4, 5, 6,
+ 7, 8, 9, 10, 11, 12;
+
+Map<MatrixXf> M2(M1.data(), 6,2);
+cout << "M2:" << endl << M2 << endl;
diff --git a/doc/snippets/Tutorial_ReshapeMat2Vec.cpp b/doc/snippets/Tutorial_ReshapeMat2Vec.cpp
new file mode 100644
index 0000000..32980a7
--- /dev/null
+++ b/doc/snippets/Tutorial_ReshapeMat2Vec.cpp
@@ -0,0 +1,11 @@
+MatrixXf M1(3,3); // Column-major storage
+M1 << 1, 2, 3,
+ 4, 5, 6,
+ 7, 8, 9;
+
+Map<RowVectorXf> v1(M1.data(), M1.size());
+cout << "v1:" << endl << v1 << endl;
+
+Matrix<float,Dynamic,Dynamic,RowMajor> M2(M1);
+Map<RowVectorXf> v2(M2.data(), M2.size());
+cout << "v2:" << endl << v2 << endl;
diff --git a/doc/snippets/Tutorial_SlicingCol.cpp b/doc/snippets/Tutorial_SlicingCol.cpp
new file mode 100644
index 0000000..695d130
--- /dev/null
+++ b/doc/snippets/Tutorial_SlicingCol.cpp
@@ -0,0 +1,11 @@
+MatrixXf M1 = MatrixXf::Random(3,8);
+cout << "Column major input:" << endl << M1 << "\n";
+Map<MatrixXf,0,OuterStride<> > M2(M1.data(), M1.rows(), (M1.cols()+2)/3, OuterStride<>(M1.outerStride()*3));
+cout << "1 column over 3:" << endl << M2 << "\n";
+
+typedef Matrix<float,Dynamic,Dynamic,RowMajor> RowMajorMatrixXf;
+RowMajorMatrixXf M3(M1);
+cout << "Row major input:" << endl << M3 << "\n";
+Map<RowMajorMatrixXf,0,Stride<Dynamic,3> > M4(M3.data(), M3.rows(), (M3.cols()+2)/3,
+ Stride<Dynamic,3>(M3.outerStride(),3));
+cout << "1 column over 3:" << endl << M4 << "\n";
diff --git a/doc/snippets/Tutorial_SlicingVec.cpp b/doc/snippets/Tutorial_SlicingVec.cpp
new file mode 100644
index 0000000..9b82246
--- /dev/null
+++ b/doc/snippets/Tutorial_SlicingVec.cpp
@@ -0,0 +1,4 @@
+RowVectorXf v = RowVectorXf::LinSpaced(20,0,19);
+cout << "Input:" << endl << v << endl;
+Map<RowVectorXf,0,InnerStride<2> > v2(v.data(), v.size()/2);
+cout << "Even:" << v2 << endl;
diff --git a/doc/snippets/Tutorial_commainit_01.cpp b/doc/snippets/Tutorial_commainit_01.cpp
new file mode 100644
index 0000000..47ba31d
--- /dev/null
+++ b/doc/snippets/Tutorial_commainit_01.cpp
@@ -0,0 +1,5 @@
+Matrix3f m;
+m << 1, 2, 3,
+ 4, 5, 6,
+ 7, 8, 9;
+std::cout << m;
diff --git a/doc/snippets/Tutorial_commainit_01b.cpp b/doc/snippets/Tutorial_commainit_01b.cpp
new file mode 100644
index 0000000..2adb2e2
--- /dev/null
+++ b/doc/snippets/Tutorial_commainit_01b.cpp
@@ -0,0 +1,5 @@
+Matrix3f m;
+m.row(0) << 1, 2, 3;
+m.block(1,0,2,2) << 4, 5, 7, 8;
+m.col(2).tail(2) << 6, 9;
+std::cout << m;
diff --git a/doc/snippets/Tutorial_commainit_02.cpp b/doc/snippets/Tutorial_commainit_02.cpp
new file mode 100644
index 0000000..c960d6a
--- /dev/null
+++ b/doc/snippets/Tutorial_commainit_02.cpp
@@ -0,0 +1,7 @@
+int rows=5, cols=5;
+MatrixXf m(rows,cols);
+m << (Matrix3f() << 1, 2, 3, 4, 5, 6, 7, 8, 9).finished(),
+ MatrixXf::Zero(3,cols-3),
+ MatrixXf::Zero(rows-3,3),
+ MatrixXf::Identity(rows-3,cols-3);
+cout << m;
diff --git a/doc/snippets/Tutorial_range_for_loop_1d_cxx11.cpp b/doc/snippets/Tutorial_range_for_loop_1d_cxx11.cpp
new file mode 100644
index 0000000..e72e715
--- /dev/null
+++ b/doc/snippets/Tutorial_range_for_loop_1d_cxx11.cpp
@@ -0,0 +1,4 @@
+VectorXi v = VectorXi::Random(4);
+cout << "Here is the vector v:\n";
+for(auto x : v) cout << x << " ";
+cout << "\n";
diff --git a/doc/snippets/Tutorial_range_for_loop_2d_cxx11.cpp b/doc/snippets/Tutorial_range_for_loop_2d_cxx11.cpp
new file mode 100644
index 0000000..4a12d26
--- /dev/null
+++ b/doc/snippets/Tutorial_range_for_loop_2d_cxx11.cpp
@@ -0,0 +1,5 @@
+Matrix2i A = Matrix2i::Random();
+cout << "Here are the coeffs of the 2x2 matrix A:\n";
+for(auto x : A.reshaped())
+ cout << x << " ";
+cout << "\n";
diff --git a/doc/snippets/Tutorial_reshaped_vs_resize_1.cpp b/doc/snippets/Tutorial_reshaped_vs_resize_1.cpp
new file mode 100644
index 0000000..e520e8e
--- /dev/null
+++ b/doc/snippets/Tutorial_reshaped_vs_resize_1.cpp
@@ -0,0 +1,5 @@
+MatrixXi m = Matrix4i::Random();
+cout << "Here is the matrix m:" << endl << m << endl;
+cout << "Here is m.reshaped(2, 8):" << endl << m.reshaped(2, 8) << endl;
+m.resize(2,8);
+cout << "Here is the matrix m after m.resize(2,8):" << endl << m << endl;
diff --git a/doc/snippets/Tutorial_reshaped_vs_resize_2.cpp b/doc/snippets/Tutorial_reshaped_vs_resize_2.cpp
new file mode 100644
index 0000000..50dc454
--- /dev/null
+++ b/doc/snippets/Tutorial_reshaped_vs_resize_2.cpp
@@ -0,0 +1,6 @@
+Matrix<int,Dynamic,Dynamic,RowMajor> m = Matrix4i::Random();
+cout << "Here is the matrix m:" << endl << m << endl;
+cout << "Here is m.reshaped(2, 8):" << endl << m.reshaped(2, 8) << endl;
+cout << "Here is m.reshaped<AutoOrder>(2, 8):" << endl << m.reshaped<AutoOrder>(2, 8) << endl;
+m.resize(2,8);
+cout << "Here is the matrix m after m.resize(2,8):" << endl << m << endl;
diff --git a/doc/snippets/Tutorial_solve_matrix_inverse.cpp b/doc/snippets/Tutorial_solve_matrix_inverse.cpp
new file mode 100644
index 0000000..fff3244
--- /dev/null
+++ b/doc/snippets/Tutorial_solve_matrix_inverse.cpp
@@ -0,0 +1,6 @@
+Matrix3f A;
+Vector3f b;
+A << 1,2,3, 4,5,6, 7,8,10;
+b << 3, 3, 4;
+Vector3f x = A.inverse() * b;
+cout << "The solution is:" << endl << x << endl;
diff --git a/doc/snippets/Tutorial_solve_multiple_rhs.cpp b/doc/snippets/Tutorial_solve_multiple_rhs.cpp
new file mode 100644
index 0000000..5411a44
--- /dev/null
+++ b/doc/snippets/Tutorial_solve_multiple_rhs.cpp
@@ -0,0 +1,10 @@
+Matrix3f A(3,3);
+A << 1,2,3, 4,5,6, 7,8,10;
+Matrix<float,3,2> B;
+B << 3,1, 3,1, 4,1;
+Matrix<float,3,2> X;
+X = A.fullPivLu().solve(B);
+cout << "The solution with right-hand side (3,3,4) is:" << endl;
+cout << X.col(0) << endl;
+cout << "The solution with right-hand side (1,1,1) is:" << endl;
+cout << X.col(1) << endl;
diff --git a/doc/snippets/Tutorial_solve_reuse_decomposition.cpp b/doc/snippets/Tutorial_solve_reuse_decomposition.cpp
new file mode 100644
index 0000000..3ca0645
--- /dev/null
+++ b/doc/snippets/Tutorial_solve_reuse_decomposition.cpp
@@ -0,0 +1,13 @@
+Matrix3f A(3,3);
+A << 1,2,3, 4,5,6, 7,8,10;
+PartialPivLU<Matrix3f> luOfA(A); // compute LU decomposition of A
+Vector3f b;
+b << 3,3,4;
+Vector3f x;
+x = luOfA.solve(b);
+cout << "The solution with right-hand side (3,3,4) is:" << endl;
+cout << x << endl;
+b << 1,1,1;
+x = luOfA.solve(b);
+cout << "The solution with right-hand side (1,1,1) is:" << endl;
+cout << x << endl;
diff --git a/doc/snippets/Tutorial_solve_singular.cpp b/doc/snippets/Tutorial_solve_singular.cpp
new file mode 100644
index 0000000..abff1ef
--- /dev/null
+++ b/doc/snippets/Tutorial_solve_singular.cpp
@@ -0,0 +1,9 @@
+Matrix3f A;
+Vector3f b;
+A << 1,2,3, 4,5,6, 7,8,9;
+b << 3, 3, 4;
+cout << "Here is the matrix A:" << endl << A << endl;
+cout << "Here is the vector b:" << endl << b << endl;
+Vector3f x;
+x = A.lu().solve(b);
+cout << "The solution is:" << endl << x << endl;
diff --git a/doc/snippets/Tutorial_solve_triangular.cpp b/doc/snippets/Tutorial_solve_triangular.cpp
new file mode 100644
index 0000000..9d13f22
--- /dev/null
+++ b/doc/snippets/Tutorial_solve_triangular.cpp
@@ -0,0 +1,8 @@
+Matrix3f A;
+Vector3f b;
+A << 1,2,3, 0,5,6, 0,0,10;
+b << 3, 3, 4;
+cout << "Here is the matrix A:" << endl << A << endl;
+cout << "Here is the vector b:" << endl << b << endl;
+Vector3f x = A.triangularView<Upper>().solve(b);
+cout << "The solution is:" << endl << x << endl;
diff --git a/doc/snippets/Tutorial_solve_triangular_inplace.cpp b/doc/snippets/Tutorial_solve_triangular_inplace.cpp
new file mode 100644
index 0000000..16ae633
--- /dev/null
+++ b/doc/snippets/Tutorial_solve_triangular_inplace.cpp
@@ -0,0 +1,6 @@
+Matrix3f A;
+Vector3f b;
+A << 1,2,3, 0,5,6, 0,0,10;
+b << 3, 3, 4;
+A.triangularView<Upper>().solveInPlace(b);
+cout << "The solution is:" << endl << b << endl;
diff --git a/doc/snippets/Tutorial_std_sort.cpp b/doc/snippets/Tutorial_std_sort.cpp
new file mode 100644
index 0000000..cde2a6f
--- /dev/null
+++ b/doc/snippets/Tutorial_std_sort.cpp
@@ -0,0 +1,4 @@
+Array4i v = Array4i::Random().abs();
+cout << "Here is the initial vector v:\n" << v.transpose() << "\n";
+std::sort(v.begin(), v.end());
+cout << "Here is the sorted vector v:\n" << v.transpose() << "\n";
diff --git a/doc/snippets/Tutorial_std_sort_rows_cxx11.cpp b/doc/snippets/Tutorial_std_sort_rows_cxx11.cpp
new file mode 100644
index 0000000..0364160
--- /dev/null
+++ b/doc/snippets/Tutorial_std_sort_rows_cxx11.cpp
@@ -0,0 +1,5 @@
+ArrayXXi A = ArrayXXi::Random(4,4).abs();
+cout << "Here is the initial matrix A:\n" << A << "\n";
+for(auto row : A.rowwise())
+ std::sort(row.begin(), row.end());
+cout << "Here is the sorted matrix A:\n" << A << "\n";
diff --git a/doc/snippets/VectorwiseOp_homogeneous.cpp b/doc/snippets/VectorwiseOp_homogeneous.cpp
new file mode 100644
index 0000000..67cf573
--- /dev/null
+++ b/doc/snippets/VectorwiseOp_homogeneous.cpp
@@ -0,0 +1,6 @@
+Matrix3Xd M = Matrix3Xd::Random(3,5);
+Projective3d P(Matrix4d::Random());
+cout << "The matrix M is:" << endl << M << endl << endl;
+cout << "M.colwise().homogeneous():" << endl << M.colwise().homogeneous() << endl << endl;
+cout << "P * M.colwise().homogeneous():" << endl << P * M.colwise().homogeneous() << endl << endl;
+cout << "P * M.colwise().homogeneous().hnormalized(): " << endl << (P * M.colwise().homogeneous()).colwise().hnormalized() << endl << endl;
diff --git a/doc/snippets/Vectorwise_reverse.cpp b/doc/snippets/Vectorwise_reverse.cpp
new file mode 100644
index 0000000..2f6a350
--- /dev/null
+++ b/doc/snippets/Vectorwise_reverse.cpp
@@ -0,0 +1,10 @@
+MatrixXi m = MatrixXi::Random(3,4);
+cout << "Here is the matrix m:" << endl << m << endl;
+cout << "Here is the rowwise reverse of m:" << endl << m.rowwise().reverse() << endl;
+cout << "Here is the colwise reverse of m:" << endl << m.colwise().reverse() << endl;
+
+cout << "Here is the coefficient (1,0) in the rowise reverse of m:" << endl
+<< m.rowwise().reverse()(1,0) << endl;
+cout << "Let us overwrite this coefficient with the value 4." << endl;
+//m.colwise().reverse()(1,0) = 4;
+cout << "Now the matrix m is:" << endl << m << endl;
diff --git a/doc/snippets/class_FullPivLU.cpp b/doc/snippets/class_FullPivLU.cpp
new file mode 100644
index 0000000..fce7fac
--- /dev/null
+++ b/doc/snippets/class_FullPivLU.cpp
@@ -0,0 +1,16 @@
+typedef Matrix<double, 5, 3> Matrix5x3;
+typedef Matrix<double, 5, 5> Matrix5x5;
+Matrix5x3 m = Matrix5x3::Random();
+cout << "Here is the matrix m:" << endl << m << endl;
+Eigen::FullPivLU<Matrix5x3> lu(m);
+cout << "Here is, up to permutations, its LU decomposition matrix:"
+ << endl << lu.matrixLU() << endl;
+cout << "Here is the L part:" << endl;
+Matrix5x5 l = Matrix5x5::Identity();
+l.block<5,3>(0,0).triangularView<StrictlyLower>() = lu.matrixLU();
+cout << l << endl;
+cout << "Here is the U part:" << endl;
+Matrix5x3 u = lu.matrixLU().triangularView<Upper>();
+cout << u << endl;
+cout << "Let us now reconstruct the original matrix m:" << endl;
+cout << lu.permutationP().inverse() * l * u * lu.permutationQ().inverse() << endl;
diff --git a/doc/snippets/compile_snippet.cpp.in b/doc/snippets/compile_snippet.cpp.in
new file mode 100644
index 0000000..c11457a
--- /dev/null
+++ b/doc/snippets/compile_snippet.cpp.in
@@ -0,0 +1,23 @@
+static bool eigen_did_assert = false;
+#define eigen_assert(X) if(!eigen_did_assert && !(X)){ std::cout << "### Assertion raised in " << __FILE__ << ":" << __LINE__ << ":\n" #X << "\n### The following would happen without assertions:\n"; eigen_did_assert = true;}
+
+#include <iostream>
+#include <Eigen/Eigen>
+
+#ifndef M_PI
+#define M_PI 3.1415926535897932384626433832795
+#endif
+
+
+using namespace Eigen;
+using namespace std;
+
+int main(int, char**)
+{
+ cout.precision(3);
+// intentionally remove indentation of snippet
+{
+${snippet_source_code}
+}
+ return 0;
+}
diff --git a/doc/snippets/tut_arithmetic_redux_minmax.cpp b/doc/snippets/tut_arithmetic_redux_minmax.cpp
new file mode 100644
index 0000000..f4ae7f4
--- /dev/null
+++ b/doc/snippets/tut_arithmetic_redux_minmax.cpp
@@ -0,0 +1,12 @@
+ Matrix3f m = Matrix3f::Random();
+ std::ptrdiff_t i, j;
+ float minOfM = m.minCoeff(&i,&j);
+ cout << "Here is the matrix m:\n" << m << endl;
+ cout << "Its minimum coefficient (" << minOfM
+ << ") is at position (" << i << "," << j << ")\n\n";
+
+ RowVector4i v = RowVector4i::Random();
+ int maxOfV = v.maxCoeff(&i);
+ cout << "Here is the vector v: " << v << endl;
+ cout << "Its maximum coefficient (" << maxOfV
+ << ") is at position " << i << endl;
diff --git a/doc/snippets/tut_arithmetic_transpose_aliasing.cpp b/doc/snippets/tut_arithmetic_transpose_aliasing.cpp
new file mode 100644
index 0000000..f82e6f2
--- /dev/null
+++ b/doc/snippets/tut_arithmetic_transpose_aliasing.cpp
@@ -0,0 +1,5 @@
+Matrix2i a; a << 1, 2, 3, 4;
+cout << "Here is the matrix a:\n" << a << endl;
+
+a = a.transpose(); // !!! do NOT do this !!!
+cout << "and the result of the aliasing effect:\n" << a << endl;
diff --git a/doc/snippets/tut_arithmetic_transpose_conjugate.cpp b/doc/snippets/tut_arithmetic_transpose_conjugate.cpp
new file mode 100644
index 0000000..88496b2
--- /dev/null
+++ b/doc/snippets/tut_arithmetic_transpose_conjugate.cpp
@@ -0,0 +1,12 @@
+MatrixXcf a = MatrixXcf::Random(2,2);
+cout << "Here is the matrix a\n" << a << endl;
+
+cout << "Here is the matrix a^T\n" << a.transpose() << endl;
+
+
+cout << "Here is the conjugate of a\n" << a.conjugate() << endl;
+
+
+cout << "Here is the matrix a^*\n" << a.adjoint() << endl;
+
+
diff --git a/doc/snippets/tut_arithmetic_transpose_inplace.cpp b/doc/snippets/tut_arithmetic_transpose_inplace.cpp
new file mode 100644
index 0000000..5c81c9e
--- /dev/null
+++ b/doc/snippets/tut_arithmetic_transpose_inplace.cpp
@@ -0,0 +1,6 @@
+MatrixXf a(2,3); a << 1, 2, 3, 4, 5, 6;
+cout << "Here is the initial matrix a:\n" << a << endl;
+
+
+a.transposeInPlace();
+cout << "and after being transposed:\n" << a << endl;
diff --git a/doc/snippets/tut_matrix_assignment_resizing.cpp b/doc/snippets/tut_matrix_assignment_resizing.cpp
new file mode 100644
index 0000000..cf18998
--- /dev/null
+++ b/doc/snippets/tut_matrix_assignment_resizing.cpp
@@ -0,0 +1,5 @@
+MatrixXf a(2,2);
+std::cout << "a is of size " << a.rows() << "x" << a.cols() << std::endl;
+MatrixXf b(3,3);
+a = b;
+std::cout << "a is now of size " << a.rows() << "x" << a.cols() << std::endl;
diff --git a/doc/special_examples/CMakeLists.txt b/doc/special_examples/CMakeLists.txt
new file mode 100644
index 0000000..e6407aa
--- /dev/null
+++ b/doc/special_examples/CMakeLists.txt
@@ -0,0 +1,31 @@
+if(NOT EIGEN_TEST_NOQT)
+ find_package(Qt4)
+ if(QT4_FOUND)
+ include(${QT_USE_FILE})
+ endif()
+endif()
+
+if(QT4_FOUND)
+ add_executable(Tutorial_sparse_example Tutorial_sparse_example.cpp Tutorial_sparse_example_details.cpp)
+ target_link_libraries(Tutorial_sparse_example ${EIGEN_STANDARD_LIBRARIES_TO_LINK_TO} ${QT_QTCORE_LIBRARY} ${QT_QTGUI_LIBRARY})
+
+ add_custom_command(
+ TARGET Tutorial_sparse_example
+ POST_BUILD
+ COMMAND ${CMAKE_COMMAND} -E make_directory ${CMAKE_CURRENT_BINARY_DIR}/../html/
+ COMMAND Tutorial_sparse_example ARGS ${CMAKE_CURRENT_BINARY_DIR}/../html/Tutorial_sparse_example.jpeg
+ )
+
+ add_dependencies(all_examples Tutorial_sparse_example)
+endif()
+
+add_executable(random_cpp11 random_cpp11.cpp)
+target_link_libraries(random_cpp11 ${EIGEN_STANDARD_LIBRARIES_TO_LINK_TO})
+add_dependencies(all_examples random_cpp11)
+
+add_custom_command(
+ TARGET random_cpp11
+ POST_BUILD
+ COMMAND random_cpp11
+ ARGS >${CMAKE_CURRENT_BINARY_DIR}/random_cpp11.out
+)
diff --git a/doc/special_examples/Tutorial_sparse_example.cpp b/doc/special_examples/Tutorial_sparse_example.cpp
new file mode 100644
index 0000000..8850db0
--- /dev/null
+++ b/doc/special_examples/Tutorial_sparse_example.cpp
@@ -0,0 +1,38 @@
+#include <Eigen/Sparse>
+#include <vector>
+#include <iostream>
+
+typedef Eigen::SparseMatrix<double> SpMat; // declares a column-major sparse matrix type of double
+typedef Eigen::Triplet<double> T;
+
+void buildProblem(std::vector<T>& coefficients, Eigen::VectorXd& b, int n);
+void saveAsBitmap(const Eigen::VectorXd& x, int n, const char* filename);
+
+int main(int argc, char** argv)
+{
+ if(argc!=2) {
+ std::cerr << "Error: expected one and only one argument.\n";
+ return -1;
+ }
+
+ int n = 300; // size of the image
+ int m = n*n; // number of unknowns (=number of pixels)
+
+ // Assembly:
+ std::vector<T> coefficients; // list of non-zeros coefficients
+ Eigen::VectorXd b(m); // the right hand side-vector resulting from the constraints
+ buildProblem(coefficients, b, n);
+
+ SpMat A(m,m);
+ A.setFromTriplets(coefficients.begin(), coefficients.end());
+
+ // Solving:
+ Eigen::SimplicialCholesky<SpMat> chol(A); // performs a Cholesky factorization of A
+ Eigen::VectorXd x = chol.solve(b); // use the factorization to solve for the given right hand side
+
+ // Export the result to a file:
+ saveAsBitmap(x, n, argv[1]);
+
+ return 0;
+}
+
diff --git a/doc/special_examples/Tutorial_sparse_example_details.cpp b/doc/special_examples/Tutorial_sparse_example_details.cpp
new file mode 100644
index 0000000..bc18b01
--- /dev/null
+++ b/doc/special_examples/Tutorial_sparse_example_details.cpp
@@ -0,0 +1,44 @@
+#include <Eigen/Sparse>
+#include <vector>
+#include <QImage>
+
+typedef Eigen::SparseMatrix<double> SpMat; // declares a column-major sparse matrix type of double
+typedef Eigen::Triplet<double> T;
+
+void insertCoefficient(int id, int i, int j, double w, std::vector<T>& coeffs,
+ Eigen::VectorXd& b, const Eigen::VectorXd& boundary)
+{
+ int n = int(boundary.size());
+ int id1 = i+j*n;
+
+ if(i==-1 || i==n) b(id) -= w * boundary(j); // constrained coefficient
+ else if(j==-1 || j==n) b(id) -= w * boundary(i); // constrained coefficient
+ else coeffs.push_back(T(id,id1,w)); // unknown coefficient
+}
+
+void buildProblem(std::vector<T>& coefficients, Eigen::VectorXd& b, int n)
+{
+ b.setZero();
+ Eigen::ArrayXd boundary = Eigen::ArrayXd::LinSpaced(n, 0,M_PI).sin().pow(2);
+ for(int j=0; j<n; ++j)
+ {
+ for(int i=0; i<n; ++i)
+ {
+ int id = i+j*n;
+ insertCoefficient(id, i-1,j, -1, coefficients, b, boundary);
+ insertCoefficient(id, i+1,j, -1, coefficients, b, boundary);
+ insertCoefficient(id, i,j-1, -1, coefficients, b, boundary);
+ insertCoefficient(id, i,j+1, -1, coefficients, b, boundary);
+ insertCoefficient(id, i,j, 4, coefficients, b, boundary);
+ }
+ }
+}
+
+void saveAsBitmap(const Eigen::VectorXd& x, int n, const char* filename)
+{
+ Eigen::Array<unsigned char,Eigen::Dynamic,Eigen::Dynamic> bits = (x*255).cast<unsigned char>();
+ QImage img(bits.data(), n,n,QImage::Format_Indexed8);
+ img.setColorCount(256);
+ for(int i=0;i<256;i++) img.setColor(i,qRgb(i,i,i));
+ img.save(filename);
+}
diff --git a/doc/special_examples/random_cpp11.cpp b/doc/special_examples/random_cpp11.cpp
new file mode 100644
index 0000000..bd73800
--- /dev/null
+++ b/doc/special_examples/random_cpp11.cpp
@@ -0,0 +1,12 @@
+#include <Eigen/Core>
+#include <iostream>
+#include <random>
+
+int main() {
+ std::default_random_engine generator;
+ std::poisson_distribution<int> distribution(4.1);
+ auto poisson = [&] () {return distribution(generator);};
+
+ Eigen::RowVectorXi v = Eigen::RowVectorXi::NullaryExpr(10, poisson );
+ std::cout << v << "\n";
+}
diff --git a/doc/tutorial.cpp b/doc/tutorial.cpp
new file mode 100644
index 0000000..62be7c2
--- /dev/null
+++ b/doc/tutorial.cpp
@@ -0,0 +1,62 @@
+#include <Eigen/Array>
+
+int main(int argc, char *argv[])
+{
+ std::cout.precision(2);
+
+ // demo static functions
+ Eigen::Matrix3f m3 = Eigen::Matrix3f::Random();
+ Eigen::Matrix4f m4 = Eigen::Matrix4f::Identity();
+
+ std::cout << "*** Step 1 ***\nm3:\n" << m3 << "\nm4:\n" << m4 << std::endl;
+
+ // demo non-static set... functions
+ m4.setZero();
+ m3.diagonal().setOnes();
+
+ std::cout << "*** Step 2 ***\nm3:\n" << m3 << "\nm4:\n" << m4 << std::endl;
+
+ // demo fixed-size block() expression as lvalue and as rvalue
+ m4.block<3,3>(0,1) = m3;
+ m3.row(2) = m4.block<1,3>(2,0);
+
+ std::cout << "*** Step 3 ***\nm3:\n" << m3 << "\nm4:\n" << m4 << std::endl;
+
+ // demo dynamic-size block()
+ {
+ int rows = 3, cols = 3;
+ m4.block(0,1,3,3).setIdentity();
+ std::cout << "*** Step 4 ***\nm4:\n" << m4 << std::endl;
+ }
+
+ // demo vector blocks
+ m4.diagonal().block(1,2).setOnes();
+ std::cout << "*** Step 5 ***\nm4.diagonal():\n" << m4.diagonal() << std::endl;
+ std::cout << "m4.diagonal().start(3)\n" << m4.diagonal().start(3) << std::endl;
+
+ // demo coeff-wise operations
+ m4 = m4.cwise()*m4;
+ m3 = m3.cwise().cos();
+ std::cout << "*** Step 6 ***\nm3:\n" << m3 << "\nm4:\n" << m4 << std::endl;
+
+ // sums of coefficients
+ std::cout << "*** Step 7 ***\n m4.sum(): " << m4.sum() << std::endl;
+ std::cout << "m4.col(2).sum(): " << m4.col(2).sum() << std::endl;
+ std::cout << "m4.colwise().sum():\n" << m4.colwise().sum() << std::endl;
+ std::cout << "m4.rowwise().sum():\n" << m4.rowwise().sum() << std::endl;
+
+ // demo intelligent auto-evaluation
+ m4 = m4 * m4; // auto-evaluates so no aliasing problem (performance penalty is low)
+ Eigen::Matrix4f other = (m4 * m4).lazy(); // forces lazy evaluation
+ m4 = m4 + m4; // here Eigen goes for lazy evaluation, as with most expressions
+ m4 = -m4 + m4 + 5 * m4; // same here, Eigen chooses lazy evaluation for all that.
+ m4 = m4 * (m4 + m4); // here Eigen chooses to first evaluate m4 + m4 into a temporary.
+ // indeed, here it is an optimization to cache this intermediate result.
+ m3 = m3 * m4.block<3,3>(1,1); // here Eigen chooses NOT to evaluate block() into a temporary
+ // because accessing coefficients of that block expression is not more costly than accessing
+ // coefficients of a plain matrix.
+ m4 = m4 * m4.transpose(); // same here, lazy evaluation of the transpose.
+ m4 = m4 * m4.transpose().eval(); // forces immediate evaluation of the transpose
+
+ std::cout << "*** Step 8 ***\nm3:\n" << m3 << "\nm4:\n" << m4 << std::endl;
+}
diff --git a/eigen3.pc.in b/eigen3.pc.in
new file mode 100644
index 0000000..3368a3a
--- /dev/null
+++ b/eigen3.pc.in
@@ -0,0 +1,9 @@
+prefix=@CMAKE_INSTALL_PREFIX@
+exec_prefix=${prefix}
+
+Name: Eigen3
+Description: A C++ template library for linear algebra: vectors, matrices, and related algorithms
+Requires:
+Version: @EIGEN_VERSION_NUMBER@
+Libs:
+Cflags: -I${prefix}/@INCLUDE_INSTALL_DIR@
diff --git a/failtest/CMakeLists.txt b/failtest/CMakeLists.txt
new file mode 100644
index 0000000..2c5fc33
--- /dev/null
+++ b/failtest/CMakeLists.txt
@@ -0,0 +1,66 @@
+
+ei_add_failtest("failtest_sanity_check")
+
+ei_add_failtest("block_nonconst_ctor_on_const_xpr_0")
+ei_add_failtest("block_nonconst_ctor_on_const_xpr_1")
+ei_add_failtest("block_nonconst_ctor_on_const_xpr_2")
+ei_add_failtest("transpose_nonconst_ctor_on_const_xpr")
+ei_add_failtest("diagonal_nonconst_ctor_on_const_xpr")
+ei_add_failtest("cwiseunaryview_nonconst_ctor_on_const_xpr")
+ei_add_failtest("triangularview_nonconst_ctor_on_const_xpr")
+ei_add_failtest("selfadjointview_nonconst_ctor_on_const_xpr")
+
+ei_add_failtest("const_qualified_block_method_retval_0")
+ei_add_failtest("const_qualified_block_method_retval_1")
+ei_add_failtest("const_qualified_transpose_method_retval")
+ei_add_failtest("const_qualified_diagonal_method_retval")
+
+ei_add_failtest("map_nonconst_ctor_on_const_ptr_0")
+ei_add_failtest("map_nonconst_ctor_on_const_ptr_1")
+ei_add_failtest("map_nonconst_ctor_on_const_ptr_2")
+ei_add_failtest("map_nonconst_ctor_on_const_ptr_3")
+ei_add_failtest("map_nonconst_ctor_on_const_ptr_4")
+
+ei_add_failtest("map_on_const_type_actually_const_0")
+ei_add_failtest("map_on_const_type_actually_const_1")
+ei_add_failtest("block_on_const_type_actually_const_0")
+ei_add_failtest("block_on_const_type_actually_const_1")
+ei_add_failtest("transpose_on_const_type_actually_const")
+ei_add_failtest("diagonal_on_const_type_actually_const")
+ei_add_failtest("cwiseunaryview_on_const_type_actually_const")
+ei_add_failtest("triangularview_on_const_type_actually_const")
+ei_add_failtest("selfadjointview_on_const_type_actually_const")
+
+ei_add_failtest("ref_1")
+ei_add_failtest("ref_2")
+ei_add_failtest("ref_3")
+ei_add_failtest("ref_4")
+ei_add_failtest("ref_5")
+
+ei_add_failtest("swap_1")
+ei_add_failtest("swap_2")
+
+ei_add_failtest("ternary_1")
+ei_add_failtest("ternary_2")
+
+ei_add_failtest("sparse_ref_1")
+ei_add_failtest("sparse_ref_2")
+ei_add_failtest("sparse_ref_3")
+ei_add_failtest("sparse_ref_4")
+ei_add_failtest("sparse_ref_5")
+
+ei_add_failtest("sparse_storage_mismatch")
+
+ei_add_failtest("partialpivlu_int")
+ei_add_failtest("fullpivlu_int")
+ei_add_failtest("llt_int")
+ei_add_failtest("ldlt_int")
+ei_add_failtest("qr_int")
+ei_add_failtest("colpivqr_int")
+ei_add_failtest("fullpivqr_int")
+ei_add_failtest("jacobisvd_int")
+ei_add_failtest("bdcsvd_int")
+ei_add_failtest("eigensolver_int")
+ei_add_failtest("eigensolver_cplx")
+ei_add_failtest("initializer_list_1")
+ei_add_failtest("initializer_list_2")
diff --git a/failtest/bdcsvd_int.cpp b/failtest/bdcsvd_int.cpp
new file mode 100644
index 0000000..670752c
--- /dev/null
+++ b/failtest/bdcsvd_int.cpp
@@ -0,0 +1,14 @@
+#include "../Eigen/SVD"
+
+#ifdef EIGEN_SHOULD_FAIL_TO_BUILD
+#define SCALAR int
+#else
+#define SCALAR float
+#endif
+
+using namespace Eigen;
+
+int main()
+{
+ BDCSVD<Matrix<SCALAR,Dynamic,Dynamic> > qr(Matrix<SCALAR,Dynamic,Dynamic>::Random(10,10));
+}
diff --git a/failtest/block_nonconst_ctor_on_const_xpr_0.cpp b/failtest/block_nonconst_ctor_on_const_xpr_0.cpp
new file mode 100644
index 0000000..40b8201
--- /dev/null
+++ b/failtest/block_nonconst_ctor_on_const_xpr_0.cpp
@@ -0,0 +1,15 @@
+#include "../Eigen/Core"
+
+#ifdef EIGEN_SHOULD_FAIL_TO_BUILD
+#define CV_QUALIFIER const
+#else
+#define CV_QUALIFIER
+#endif
+
+using namespace Eigen;
+
+void foo(CV_QUALIFIER Matrix3d &m){
+ Block<Matrix3d,3,3> b(m,0,0);
+}
+
+int main() {}
diff --git a/failtest/block_nonconst_ctor_on_const_xpr_1.cpp b/failtest/block_nonconst_ctor_on_const_xpr_1.cpp
new file mode 100644
index 0000000..ef6d537
--- /dev/null
+++ b/failtest/block_nonconst_ctor_on_const_xpr_1.cpp
@@ -0,0 +1,15 @@
+#include "../Eigen/Core"
+
+#ifdef EIGEN_SHOULD_FAIL_TO_BUILD
+#define CV_QUALIFIER const
+#else
+#define CV_QUALIFIER
+#endif
+
+using namespace Eigen;
+
+void foo(CV_QUALIFIER Matrix3d &m){
+ Block<Matrix3d> b(m,0,0,3,3);
+}
+
+int main() {}
diff --git a/failtest/block_nonconst_ctor_on_const_xpr_2.cpp b/failtest/block_nonconst_ctor_on_const_xpr_2.cpp
new file mode 100644
index 0000000..43f18ae
--- /dev/null
+++ b/failtest/block_nonconst_ctor_on_const_xpr_2.cpp
@@ -0,0 +1,16 @@
+#include "../Eigen/Core"
+
+#ifdef EIGEN_SHOULD_FAIL_TO_BUILD
+#define CV_QUALIFIER const
+#else
+#define CV_QUALIFIER
+#endif
+
+using namespace Eigen;
+
+void foo(CV_QUALIFIER Matrix3d &m){
+ // row/column constructor
+ Block<Matrix3d,3,1> b(m,0);
+}
+
+int main() {}
diff --git a/failtest/block_on_const_type_actually_const_0.cpp b/failtest/block_on_const_type_actually_const_0.cpp
new file mode 100644
index 0000000..009bebe
--- /dev/null
+++ b/failtest/block_on_const_type_actually_const_0.cpp
@@ -0,0 +1,16 @@
+#include "../Eigen/Core"
+
+#ifdef EIGEN_SHOULD_FAIL_TO_BUILD
+#define CV_QUALIFIER const
+#else
+#define CV_QUALIFIER
+#endif
+
+using namespace Eigen;
+
+void foo(){
+ Matrix3f m;
+ Block<CV_QUALIFIER Matrix3f>(m, 0, 0, 3, 3).coeffRef(0, 0) = 1.0f;
+}
+
+int main() {}
diff --git a/failtest/block_on_const_type_actually_const_1.cpp b/failtest/block_on_const_type_actually_const_1.cpp
new file mode 100644
index 0000000..4c3e93f
--- /dev/null
+++ b/failtest/block_on_const_type_actually_const_1.cpp
@@ -0,0 +1,16 @@
+#include "../Eigen/Core"
+
+#ifdef EIGEN_SHOULD_FAIL_TO_BUILD
+#define CV_QUALIFIER const
+#else
+#define CV_QUALIFIER
+#endif
+
+using namespace Eigen;
+
+void foo(){
+ MatrixXf m;
+ Block<CV_QUALIFIER MatrixXf, 3, 3>(m, 0, 0).coeffRef(0, 0) = 1.0f;
+}
+
+int main() {}
diff --git a/failtest/colpivqr_int.cpp b/failtest/colpivqr_int.cpp
new file mode 100644
index 0000000..db11910
--- /dev/null
+++ b/failtest/colpivqr_int.cpp
@@ -0,0 +1,14 @@
+#include "../Eigen/QR"
+
+#ifdef EIGEN_SHOULD_FAIL_TO_BUILD
+#define SCALAR int
+#else
+#define SCALAR float
+#endif
+
+using namespace Eigen;
+
+int main()
+{
+ ColPivHouseholderQR<Matrix<SCALAR,Dynamic,Dynamic> > qr(Matrix<SCALAR,Dynamic,Dynamic>::Random(10,10));
+}
diff --git a/failtest/const_qualified_block_method_retval_0.cpp b/failtest/const_qualified_block_method_retval_0.cpp
new file mode 100644
index 0000000..a6bd5fe
--- /dev/null
+++ b/failtest/const_qualified_block_method_retval_0.cpp
@@ -0,0 +1,15 @@
+#include "../Eigen/Core"
+
+#ifdef EIGEN_SHOULD_FAIL_TO_BUILD
+#define CV_QUALIFIER const
+#else
+#define CV_QUALIFIER
+#endif
+
+using namespace Eigen;
+
+void foo(CV_QUALIFIER Matrix3d &m){
+ Block<Matrix3d,3,3> b(m.block<3,3>(0,0));
+}
+
+int main() {}
diff --git a/failtest/const_qualified_block_method_retval_1.cpp b/failtest/const_qualified_block_method_retval_1.cpp
new file mode 100644
index 0000000..ef40c24
--- /dev/null
+++ b/failtest/const_qualified_block_method_retval_1.cpp
@@ -0,0 +1,15 @@
+#include "../Eigen/Core"
+
+#ifdef EIGEN_SHOULD_FAIL_TO_BUILD
+#define CV_QUALIFIER const
+#else
+#define CV_QUALIFIER
+#endif
+
+using namespace Eigen;
+
+void foo(CV_QUALIFIER Matrix3d &m){
+ Block<Matrix3d> b(m.block(0,0,3,3));
+}
+
+int main() {}
diff --git a/failtest/const_qualified_diagonal_method_retval.cpp b/failtest/const_qualified_diagonal_method_retval.cpp
new file mode 100644
index 0000000..809594a
--- /dev/null
+++ b/failtest/const_qualified_diagonal_method_retval.cpp
@@ -0,0 +1,15 @@
+#include "../Eigen/Core"
+
+#ifdef EIGEN_SHOULD_FAIL_TO_BUILD
+#define CV_QUALIFIER const
+#else
+#define CV_QUALIFIER
+#endif
+
+using namespace Eigen;
+
+void foo(CV_QUALIFIER Matrix3d &m){
+ Diagonal<Matrix3d> b(m.diagonal());
+}
+
+int main() {}
diff --git a/failtest/const_qualified_transpose_method_retval.cpp b/failtest/const_qualified_transpose_method_retval.cpp
new file mode 100644
index 0000000..2d7f19c
--- /dev/null
+++ b/failtest/const_qualified_transpose_method_retval.cpp
@@ -0,0 +1,15 @@
+#include "../Eigen/Core"
+
+#ifdef EIGEN_SHOULD_FAIL_TO_BUILD
+#define CV_QUALIFIER const
+#else
+#define CV_QUALIFIER
+#endif
+
+using namespace Eigen;
+
+void foo(CV_QUALIFIER Matrix3d &m){
+ Transpose<Matrix3d> b(m.transpose());
+}
+
+int main() {}
diff --git a/failtest/cwiseunaryview_nonconst_ctor_on_const_xpr.cpp b/failtest/cwiseunaryview_nonconst_ctor_on_const_xpr.cpp
new file mode 100644
index 0000000..e23cf8f
--- /dev/null
+++ b/failtest/cwiseunaryview_nonconst_ctor_on_const_xpr.cpp
@@ -0,0 +1,15 @@
+#include "../Eigen/Core"
+
+#ifdef EIGEN_SHOULD_FAIL_TO_BUILD
+#define CV_QUALIFIER const
+#else
+#define CV_QUALIFIER
+#endif
+
+using namespace Eigen;
+
+void foo(CV_QUALIFIER Matrix3d &m){
+ CwiseUnaryView<internal::scalar_real_ref_op<double>,Matrix3d> t(m);
+}
+
+int main() {}
diff --git a/failtest/cwiseunaryview_on_const_type_actually_const.cpp b/failtest/cwiseunaryview_on_const_type_actually_const.cpp
new file mode 100644
index 0000000..fcd41df
--- /dev/null
+++ b/failtest/cwiseunaryview_on_const_type_actually_const.cpp
@@ -0,0 +1,16 @@
+#include "../Eigen/Core"
+
+#ifdef EIGEN_SHOULD_FAIL_TO_BUILD
+#define CV_QUALIFIER const
+#else
+#define CV_QUALIFIER
+#endif
+
+using namespace Eigen;
+
+void foo(){
+ MatrixXf m;
+ CwiseUnaryView<internal::scalar_real_ref_op<double>,CV_QUALIFIER MatrixXf>(m).coeffRef(0, 0) = 1.0f;
+}
+
+int main() {}
diff --git a/failtest/diagonal_nonconst_ctor_on_const_xpr.cpp b/failtest/diagonal_nonconst_ctor_on_const_xpr.cpp
new file mode 100644
index 0000000..76398a2
--- /dev/null
+++ b/failtest/diagonal_nonconst_ctor_on_const_xpr.cpp
@@ -0,0 +1,15 @@
+#include "../Eigen/Core"
+
+#ifdef EIGEN_SHOULD_FAIL_TO_BUILD
+#define CV_QUALIFIER const
+#else
+#define CV_QUALIFIER
+#endif
+
+using namespace Eigen;
+
+void foo(CV_QUALIFIER Matrix3d &m){
+ Diagonal<Matrix3d> d(m);
+}
+
+int main() {}
diff --git a/failtest/diagonal_on_const_type_actually_const.cpp b/failtest/diagonal_on_const_type_actually_const.cpp
new file mode 100644
index 0000000..d4b2fd9
--- /dev/null
+++ b/failtest/diagonal_on_const_type_actually_const.cpp
@@ -0,0 +1,16 @@
+#include "../Eigen/Core"
+
+#ifdef EIGEN_SHOULD_FAIL_TO_BUILD
+#define CV_QUALIFIER const
+#else
+#define CV_QUALIFIER
+#endif
+
+using namespace Eigen;
+
+void foo(){
+ MatrixXf m;
+ Diagonal<CV_QUALIFIER MatrixXf>(m).coeffRef(0) = 1.0f;
+}
+
+int main() {}
diff --git a/failtest/eigensolver_cplx.cpp b/failtest/eigensolver_cplx.cpp
new file mode 100644
index 0000000..c2e21e1
--- /dev/null
+++ b/failtest/eigensolver_cplx.cpp
@@ -0,0 +1,14 @@
+#include "../Eigen/Eigenvalues"
+
+#ifdef EIGEN_SHOULD_FAIL_TO_BUILD
+#define SCALAR std::complex<double>
+#else
+#define SCALAR float
+#endif
+
+using namespace Eigen;
+
+int main()
+{
+ EigenSolver<Matrix<SCALAR,Dynamic,Dynamic> > eig(Matrix<SCALAR,Dynamic,Dynamic>::Random(10,10));
+}
diff --git a/failtest/eigensolver_int.cpp b/failtest/eigensolver_int.cpp
new file mode 100644
index 0000000..eda8dc2
--- /dev/null
+++ b/failtest/eigensolver_int.cpp
@@ -0,0 +1,14 @@
+#include "../Eigen/Eigenvalues"
+
+#ifdef EIGEN_SHOULD_FAIL_TO_BUILD
+#define SCALAR int
+#else
+#define SCALAR float
+#endif
+
+using namespace Eigen;
+
+int main()
+{
+ EigenSolver<Matrix<SCALAR,Dynamic,Dynamic> > eig(Matrix<SCALAR,Dynamic,Dynamic>::Random(10,10));
+}
diff --git a/failtest/failtest_sanity_check.cpp b/failtest/failtest_sanity_check.cpp
new file mode 100644
index 0000000..769fa94
--- /dev/null
+++ b/failtest/failtest_sanity_check.cpp
@@ -0,0 +1,5 @@
+#ifdef EIGEN_SHOULD_FAIL_TO_BUILD
+This is just some text that won't compile as a C++ file, as a basic sanity check for failtest.
+#else
+int main() {}
+#endif
diff --git a/failtest/fullpivlu_int.cpp b/failtest/fullpivlu_int.cpp
new file mode 100644
index 0000000..e9d2c6e
--- /dev/null
+++ b/failtest/fullpivlu_int.cpp
@@ -0,0 +1,14 @@
+#include "../Eigen/LU"
+
+#ifdef EIGEN_SHOULD_FAIL_TO_BUILD
+#define SCALAR int
+#else
+#define SCALAR float
+#endif
+
+using namespace Eigen;
+
+int main()
+{
+ FullPivLU<Matrix<SCALAR,Dynamic,Dynamic> > lu(Matrix<SCALAR,Dynamic,Dynamic>::Random(10,10));
+}
diff --git a/failtest/fullpivqr_int.cpp b/failtest/fullpivqr_int.cpp
new file mode 100644
index 0000000..d182a7b
--- /dev/null
+++ b/failtest/fullpivqr_int.cpp
@@ -0,0 +1,14 @@
+#include "../Eigen/QR"
+
+#ifdef EIGEN_SHOULD_FAIL_TO_BUILD
+#define SCALAR int
+#else
+#define SCALAR float
+#endif
+
+using namespace Eigen;
+
+int main()
+{
+ FullPivHouseholderQR<Matrix<SCALAR,Dynamic,Dynamic> > qr(Matrix<SCALAR,Dynamic,Dynamic>::Random(10,10));
+}
diff --git a/failtest/initializer_list_1.cpp b/failtest/initializer_list_1.cpp
new file mode 100644
index 0000000..92dfd1f
--- /dev/null
+++ b/failtest/initializer_list_1.cpp
@@ -0,0 +1,14 @@
+#include "../Eigen/Core"
+
+#ifdef EIGEN_SHOULD_FAIL_TO_BUILD
+#define ROWS Dynamic
+#else
+#define ROWS 3
+#endif
+
+using namespace Eigen;
+
+int main()
+{
+ Matrix<int, ROWS, 1> {1, 2, 3};
+}
diff --git a/failtest/initializer_list_2.cpp b/failtest/initializer_list_2.cpp
new file mode 100644
index 0000000..1996050
--- /dev/null
+++ b/failtest/initializer_list_2.cpp
@@ -0,0 +1,16 @@
+#include "../Eigen/Core"
+
+#ifdef EIGEN_SHOULD_FAIL_TO_BUILD
+#define ROWS Dynamic
+#define COLS Dynamic
+#else
+#define ROWS 3
+#define COLS 1
+#endif
+
+using namespace Eigen;
+
+int main()
+{
+ Matrix<int, ROWS, COLS> {1, 2, 3};
+}
diff --git a/failtest/jacobisvd_int.cpp b/failtest/jacobisvd_int.cpp
new file mode 100644
index 0000000..12790ae
--- /dev/null
+++ b/failtest/jacobisvd_int.cpp
@@ -0,0 +1,14 @@
+#include "../Eigen/SVD"
+
+#ifdef EIGEN_SHOULD_FAIL_TO_BUILD
+#define SCALAR int
+#else
+#define SCALAR float
+#endif
+
+using namespace Eigen;
+
+int main()
+{
+ JacobiSVD<Matrix<SCALAR,Dynamic,Dynamic> > qr(Matrix<SCALAR,Dynamic,Dynamic>::Random(10,10));
+}
diff --git a/failtest/ldlt_int.cpp b/failtest/ldlt_int.cpp
new file mode 100644
index 0000000..243e457
--- /dev/null
+++ b/failtest/ldlt_int.cpp
@@ -0,0 +1,14 @@
+#include "../Eigen/Cholesky"
+
+#ifdef EIGEN_SHOULD_FAIL_TO_BUILD
+#define SCALAR int
+#else
+#define SCALAR float
+#endif
+
+using namespace Eigen;
+
+int main()
+{
+ LDLT<Matrix<SCALAR,Dynamic,Dynamic> > ldlt(Matrix<SCALAR,Dynamic,Dynamic>::Random(10,10));
+}
diff --git a/failtest/llt_int.cpp b/failtest/llt_int.cpp
new file mode 100644
index 0000000..cb02065
--- /dev/null
+++ b/failtest/llt_int.cpp
@@ -0,0 +1,14 @@
+#include "../Eigen/Cholesky"
+
+#ifdef EIGEN_SHOULD_FAIL_TO_BUILD
+#define SCALAR int
+#else
+#define SCALAR float
+#endif
+
+using namespace Eigen;
+
+int main()
+{
+ LLT<Matrix<SCALAR,Dynamic,Dynamic> > llt(Matrix<SCALAR,Dynamic,Dynamic>::Random(10,10));
+}
diff --git a/failtest/map_nonconst_ctor_on_const_ptr_0.cpp b/failtest/map_nonconst_ctor_on_const_ptr_0.cpp
new file mode 100644
index 0000000..d75686f
--- /dev/null
+++ b/failtest/map_nonconst_ctor_on_const_ptr_0.cpp
@@ -0,0 +1,15 @@
+#include "../Eigen/Core"
+
+#ifdef EIGEN_SHOULD_FAIL_TO_BUILD
+#define CV_QUALIFIER const
+#else
+#define CV_QUALIFIER
+#endif
+
+using namespace Eigen;
+
+void foo(CV_QUALIFIER float *ptr){
+ Map<Matrix3f> m(ptr);
+}
+
+int main() {}
diff --git a/failtest/map_nonconst_ctor_on_const_ptr_1.cpp b/failtest/map_nonconst_ctor_on_const_ptr_1.cpp
new file mode 100644
index 0000000..eda134d
--- /dev/null
+++ b/failtest/map_nonconst_ctor_on_const_ptr_1.cpp
@@ -0,0 +1,15 @@
+#include "../Eigen/Core"
+
+#ifdef EIGEN_SHOULD_FAIL_TO_BUILD
+#define CV_QUALIFIER const
+#else
+#define CV_QUALIFIER
+#endif
+
+using namespace Eigen;
+
+void foo(CV_QUALIFIER float *ptr, DenseIndex size){
+ Map<ArrayXf> m(ptr, size);
+}
+
+int main() {}
diff --git a/failtest/map_nonconst_ctor_on_const_ptr_2.cpp b/failtest/map_nonconst_ctor_on_const_ptr_2.cpp
new file mode 100644
index 0000000..06b4b62
--- /dev/null
+++ b/failtest/map_nonconst_ctor_on_const_ptr_2.cpp
@@ -0,0 +1,15 @@
+#include "../Eigen/Core"
+
+#ifdef EIGEN_SHOULD_FAIL_TO_BUILD
+#define CV_QUALIFIER const
+#else
+#define CV_QUALIFIER
+#endif
+
+using namespace Eigen;
+
+void foo(CV_QUALIFIER float *ptr, DenseIndex rows, DenseIndex cols){
+ Map<MatrixXf> m(ptr, rows, cols);
+}
+
+int main() {}
diff --git a/failtest/map_nonconst_ctor_on_const_ptr_3.cpp b/failtest/map_nonconst_ctor_on_const_ptr_3.cpp
new file mode 100644
index 0000000..830f6f0
--- /dev/null
+++ b/failtest/map_nonconst_ctor_on_const_ptr_3.cpp
@@ -0,0 +1,15 @@
+#include "../Eigen/Core"
+
+#ifdef EIGEN_SHOULD_FAIL_TO_BUILD
+#define CV_QUALIFIER const
+#else
+#define CV_QUALIFIER
+#endif
+
+using namespace Eigen;
+
+void foo(CV_QUALIFIER float *ptr, DenseIndex rows, DenseIndex cols){
+ Map<MatrixXf, Aligned, InnerStride<2> > m(ptr, rows, cols, InnerStride<2>());
+}
+
+int main() {}
diff --git a/failtest/map_nonconst_ctor_on_const_ptr_4.cpp b/failtest/map_nonconst_ctor_on_const_ptr_4.cpp
new file mode 100644
index 0000000..c3e8c95
--- /dev/null
+++ b/failtest/map_nonconst_ctor_on_const_ptr_4.cpp
@@ -0,0 +1,15 @@
+#include "../Eigen/Core"
+
+#ifdef EIGEN_SHOULD_FAIL_TO_BUILD
+#define CV_QUALIFIER
+#else
+#define CV_QUALIFIER const
+#endif
+
+using namespace Eigen;
+
+void foo(const float *ptr, DenseIndex rows, DenseIndex cols){
+ Map<CV_QUALIFIER MatrixXf, Unaligned, OuterStride<> > m(ptr, rows, cols, OuterStride<>(2));
+}
+
+int main() {}
diff --git a/failtest/map_on_const_type_actually_const_0.cpp b/failtest/map_on_const_type_actually_const_0.cpp
new file mode 100644
index 0000000..8cb6aa0
--- /dev/null
+++ b/failtest/map_on_const_type_actually_const_0.cpp
@@ -0,0 +1,15 @@
+#include "../Eigen/Core"
+
+#ifdef EIGEN_SHOULD_FAIL_TO_BUILD
+#define CV_QUALIFIER const
+#else
+#define CV_QUALIFIER
+#endif
+
+using namespace Eigen;
+
+void foo(float *ptr){
+ Map<CV_QUALIFIER MatrixXf>(ptr, 1, 1).coeffRef(0,0) = 1.0f;
+}
+
+int main() {}
diff --git a/failtest/map_on_const_type_actually_const_1.cpp b/failtest/map_on_const_type_actually_const_1.cpp
new file mode 100644
index 0000000..04e067c
--- /dev/null
+++ b/failtest/map_on_const_type_actually_const_1.cpp
@@ -0,0 +1,15 @@
+#include "../Eigen/Core"
+
+#ifdef EIGEN_SHOULD_FAIL_TO_BUILD
+#define CV_QUALIFIER const
+#else
+#define CV_QUALIFIER
+#endif
+
+using namespace Eigen;
+
+void foo(float *ptr){
+ Map<CV_QUALIFIER Vector3f>(ptr).coeffRef(0) = 1.0f;
+}
+
+int main() {}
diff --git a/failtest/partialpivlu_int.cpp b/failtest/partialpivlu_int.cpp
new file mode 100644
index 0000000..98ef282
--- /dev/null
+++ b/failtest/partialpivlu_int.cpp
@@ -0,0 +1,14 @@
+#include "../Eigen/LU"
+
+#ifdef EIGEN_SHOULD_FAIL_TO_BUILD
+#define SCALAR int
+#else
+#define SCALAR float
+#endif
+
+using namespace Eigen;
+
+int main()
+{
+ PartialPivLU<Matrix<SCALAR,Dynamic,Dynamic> > lu(Matrix<SCALAR,Dynamic,Dynamic>::Random(10,10));
+}
diff --git a/failtest/qr_int.cpp b/failtest/qr_int.cpp
new file mode 100644
index 0000000..ce200e8
--- /dev/null
+++ b/failtest/qr_int.cpp
@@ -0,0 +1,14 @@
+#include "../Eigen/QR"
+
+#ifdef EIGEN_SHOULD_FAIL_TO_BUILD
+#define SCALAR int
+#else
+#define SCALAR float
+#endif
+
+using namespace Eigen;
+
+int main()
+{
+ HouseholderQR<Matrix<SCALAR,Dynamic,Dynamic> > qr(Matrix<SCALAR,Dynamic,Dynamic>::Random(10,10));
+}
diff --git a/failtest/ref_1.cpp b/failtest/ref_1.cpp
new file mode 100644
index 0000000..8b798d5
--- /dev/null
+++ b/failtest/ref_1.cpp
@@ -0,0 +1,18 @@
+#include "../Eigen/Core"
+
+#ifdef EIGEN_SHOULD_FAIL_TO_BUILD
+#define CV_QUALIFIER const
+#else
+#define CV_QUALIFIER
+#endif
+
+using namespace Eigen;
+
+void call_ref(Ref<VectorXf> a) { }
+
+int main()
+{
+ VectorXf a(10);
+ CV_QUALIFIER VectorXf& ac(a);
+ call_ref(ac);
+}
diff --git a/failtest/ref_2.cpp b/failtest/ref_2.cpp
new file mode 100644
index 0000000..0b779cc
--- /dev/null
+++ b/failtest/ref_2.cpp
@@ -0,0 +1,15 @@
+#include "../Eigen/Core"
+
+using namespace Eigen;
+
+void call_ref(Ref<VectorXf> a) { }
+
+int main()
+{
+ MatrixXf A(10,10);
+#ifdef EIGEN_SHOULD_FAIL_TO_BUILD
+ call_ref(A.row(3));
+#else
+ call_ref(A.col(3));
+#endif
+}
diff --git a/failtest/ref_3.cpp b/failtest/ref_3.cpp
new file mode 100644
index 0000000..f46027d
--- /dev/null
+++ b/failtest/ref_3.cpp
@@ -0,0 +1,15 @@
+#include "../Eigen/Core"
+
+using namespace Eigen;
+
+#ifdef EIGEN_SHOULD_FAIL_TO_BUILD
+void call_ref(Ref<VectorXf> a) { }
+#else
+void call_ref(const Ref<const VectorXf> &a) { }
+#endif
+
+int main()
+{
+ VectorXf a(10);
+ call_ref(a+a);
+}
diff --git a/failtest/ref_4.cpp b/failtest/ref_4.cpp
new file mode 100644
index 0000000..6c11fa4
--- /dev/null
+++ b/failtest/ref_4.cpp
@@ -0,0 +1,15 @@
+#include "../Eigen/Core"
+
+using namespace Eigen;
+
+void call_ref(Ref<MatrixXf,0,OuterStride<> > a) {}
+
+int main()
+{
+ MatrixXf A(10,10);
+#ifdef EIGEN_SHOULD_FAIL_TO_BUILD
+ call_ref(A.transpose());
+#else
+ call_ref(A);
+#endif
+}
diff --git a/failtest/ref_5.cpp b/failtest/ref_5.cpp
new file mode 100644
index 0000000..846d527
--- /dev/null
+++ b/failtest/ref_5.cpp
@@ -0,0 +1,16 @@
+#include "../Eigen/Core"
+
+using namespace Eigen;
+
+void call_ref(Ref<VectorXf> a) { }
+
+int main()
+{
+ VectorXf a(10);
+ DenseBase<VectorXf> &ac(a);
+#ifdef EIGEN_SHOULD_FAIL_TO_BUILD
+ call_ref(ac);
+#else
+ call_ref(ac.derived());
+#endif
+}
diff --git a/failtest/selfadjointview_nonconst_ctor_on_const_xpr.cpp b/failtest/selfadjointview_nonconst_ctor_on_const_xpr.cpp
new file mode 100644
index 0000000..a240f81
--- /dev/null
+++ b/failtest/selfadjointview_nonconst_ctor_on_const_xpr.cpp
@@ -0,0 +1,15 @@
+#include "../Eigen/Core"
+
+#ifdef EIGEN_SHOULD_FAIL_TO_BUILD
+#define CV_QUALIFIER const
+#else
+#define CV_QUALIFIER
+#endif
+
+using namespace Eigen;
+
+void foo(CV_QUALIFIER Matrix3d &m){
+ SelfAdjointView<Matrix3d,Upper> t(m);
+}
+
+int main() {}
diff --git a/failtest/selfadjointview_on_const_type_actually_const.cpp b/failtest/selfadjointview_on_const_type_actually_const.cpp
new file mode 100644
index 0000000..19aaad6
--- /dev/null
+++ b/failtest/selfadjointview_on_const_type_actually_const.cpp
@@ -0,0 +1,16 @@
+#include "../Eigen/Core"
+
+#ifdef EIGEN_SHOULD_FAIL_TO_BUILD
+#define CV_QUALIFIER const
+#else
+#define CV_QUALIFIER
+#endif
+
+using namespace Eigen;
+
+void foo(){
+ MatrixXf m;
+ SelfAdjointView<CV_QUALIFIER MatrixXf,Upper>(m).coeffRef(0, 0) = 1.0f;
+}
+
+int main() {}
diff --git a/failtest/sparse_ref_1.cpp b/failtest/sparse_ref_1.cpp
new file mode 100644
index 0000000..d78d1f9
--- /dev/null
+++ b/failtest/sparse_ref_1.cpp
@@ -0,0 +1,18 @@
+#include "../Eigen/Sparse"
+
+#ifdef EIGEN_SHOULD_FAIL_TO_BUILD
+#define CV_QUALIFIER const
+#else
+#define CV_QUALIFIER
+#endif
+
+using namespace Eigen;
+
+void call_ref(Ref<SparseMatrix<float> > a) { }
+
+int main()
+{
+ SparseMatrix<float> a(10,10);
+ CV_QUALIFIER SparseMatrix<float>& ac(a);
+ call_ref(ac);
+}
diff --git a/failtest/sparse_ref_2.cpp b/failtest/sparse_ref_2.cpp
new file mode 100644
index 0000000..46c9440
--- /dev/null
+++ b/failtest/sparse_ref_2.cpp
@@ -0,0 +1,15 @@
+#include "../Eigen/Sparse"
+
+using namespace Eigen;
+
+void call_ref(Ref<SparseMatrix<float> > a) { }
+
+int main()
+{
+ SparseMatrix<float> A(10,10);
+#ifdef EIGEN_SHOULD_FAIL_TO_BUILD
+ call_ref(A.row(3));
+#else
+ call_ref(A.col(3));
+#endif
+}
diff --git a/failtest/sparse_ref_3.cpp b/failtest/sparse_ref_3.cpp
new file mode 100644
index 0000000..a9949b5
--- /dev/null
+++ b/failtest/sparse_ref_3.cpp
@@ -0,0 +1,15 @@
+#include "../Eigen/Sparse"
+
+using namespace Eigen;
+
+#ifdef EIGEN_SHOULD_FAIL_TO_BUILD
+void call_ref(Ref<SparseMatrix<float> > a) { }
+#else
+void call_ref(const Ref<const SparseMatrix<float> > &a) { }
+#endif
+
+int main()
+{
+ SparseMatrix<float> a(10,10);
+ call_ref(a+a);
+}
diff --git a/failtest/sparse_ref_4.cpp b/failtest/sparse_ref_4.cpp
new file mode 100644
index 0000000..57bb6a1
--- /dev/null
+++ b/failtest/sparse_ref_4.cpp
@@ -0,0 +1,15 @@
+#include "../Eigen/Sparse"
+
+using namespace Eigen;
+
+void call_ref(Ref<SparseMatrix<float> > a) {}
+
+int main()
+{
+ SparseMatrix<float> A(10,10);
+#ifdef EIGEN_SHOULD_FAIL_TO_BUILD
+ call_ref(A.transpose());
+#else
+ call_ref(A);
+#endif
+}
diff --git a/failtest/sparse_ref_5.cpp b/failtest/sparse_ref_5.cpp
new file mode 100644
index 0000000..4478f6f
--- /dev/null
+++ b/failtest/sparse_ref_5.cpp
@@ -0,0 +1,16 @@
+#include "../Eigen/Sparse"
+
+using namespace Eigen;
+
+void call_ref(Ref<SparseMatrix<float> > a) { }
+
+int main()
+{
+ SparseMatrix<float> a(10,10);
+ SparseMatrixBase<SparseMatrix<float> > &ac(a);
+#ifdef EIGEN_SHOULD_FAIL_TO_BUILD
+ call_ref(ac);
+#else
+ call_ref(ac.derived());
+#endif
+}
diff --git a/failtest/sparse_storage_mismatch.cpp b/failtest/sparse_storage_mismatch.cpp
new file mode 100644
index 0000000..51840d4
--- /dev/null
+++ b/failtest/sparse_storage_mismatch.cpp
@@ -0,0 +1,16 @@
+#include "../Eigen/Sparse"
+using namespace Eigen;
+
+typedef SparseMatrix<double,ColMajor> Mat1;
+#ifdef EIGEN_SHOULD_FAIL_TO_BUILD
+typedef SparseMatrix<double,RowMajor> Mat2;
+#else
+typedef SparseMatrix<double,ColMajor> Mat2;
+#endif
+
+int main()
+{
+ Mat1 a(10,10);
+ Mat2 b(10,10);
+ a += b;
+}
diff --git a/failtest/swap_1.cpp b/failtest/swap_1.cpp
new file mode 100644
index 0000000..1063797
--- /dev/null
+++ b/failtest/swap_1.cpp
@@ -0,0 +1,14 @@
+#include "../Eigen/Core"
+
+using namespace Eigen;
+
+int main()
+{
+ VectorXf a(10), b(10);
+#ifdef EIGEN_SHOULD_FAIL_TO_BUILD
+ const DenseBase<VectorXf> &ac(a);
+#else
+ DenseBase<VectorXf> &ac(a);
+#endif
+ b.swap(ac);
+}
diff --git a/failtest/swap_2.cpp b/failtest/swap_2.cpp
new file mode 100644
index 0000000..b386cf4
--- /dev/null
+++ b/failtest/swap_2.cpp
@@ -0,0 +1,14 @@
+#include "../Eigen/Core"
+
+using namespace Eigen;
+
+int main()
+{
+ VectorXf a(10), b(10);
+ VectorXf const &ac(a);
+#ifdef EIGEN_SHOULD_FAIL_TO_BUILD
+ b.swap(ac);
+#else
+ b.swap(ac.const_cast_derived());
+#endif
+}
diff --git a/failtest/ternary_1.cpp b/failtest/ternary_1.cpp
new file mode 100644
index 0000000..b40bcb0
--- /dev/null
+++ b/failtest/ternary_1.cpp
@@ -0,0 +1,13 @@
+#include "../Eigen/Core"
+
+using namespace Eigen;
+
+int main(int argc,char **)
+{
+ VectorXf a(10), b(10);
+#ifdef EIGEN_SHOULD_FAIL_TO_BUILD
+ b = argc>1 ? 2*a : -a;
+#else
+ b = argc>1 ? 2*a : VectorXf(-a);
+#endif
+}
diff --git a/failtest/ternary_2.cpp b/failtest/ternary_2.cpp
new file mode 100644
index 0000000..a46b12b
--- /dev/null
+++ b/failtest/ternary_2.cpp
@@ -0,0 +1,13 @@
+#include "../Eigen/Core"
+
+using namespace Eigen;
+
+int main(int argc,char **)
+{
+ VectorXf a(10), b(10);
+#ifdef EIGEN_SHOULD_FAIL_TO_BUILD
+ b = argc>1 ? 2*a : a+a;
+#else
+ b = argc>1 ? VectorXf(2*a) : VectorXf(a+a);
+#endif
+}
diff --git a/failtest/transpose_nonconst_ctor_on_const_xpr.cpp b/failtest/transpose_nonconst_ctor_on_const_xpr.cpp
new file mode 100644
index 0000000..4223e7f
--- /dev/null
+++ b/failtest/transpose_nonconst_ctor_on_const_xpr.cpp
@@ -0,0 +1,15 @@
+#include "../Eigen/Core"
+
+#ifdef EIGEN_SHOULD_FAIL_TO_BUILD
+#define CV_QUALIFIER const
+#else
+#define CV_QUALIFIER
+#endif
+
+using namespace Eigen;
+
+void foo(CV_QUALIFIER Matrix3d &m){
+ Transpose<Matrix3d> t(m);
+}
+
+int main() {}
diff --git a/failtest/transpose_on_const_type_actually_const.cpp b/failtest/transpose_on_const_type_actually_const.cpp
new file mode 100644
index 0000000..d0b7d0d
--- /dev/null
+++ b/failtest/transpose_on_const_type_actually_const.cpp
@@ -0,0 +1,16 @@
+#include "../Eigen/Core"
+
+#ifdef EIGEN_SHOULD_FAIL_TO_BUILD
+#define CV_QUALIFIER const
+#else
+#define CV_QUALIFIER
+#endif
+
+using namespace Eigen;
+
+void foo(){
+ MatrixXf m;
+ Transpose<CV_QUALIFIER MatrixXf>(m).coeffRef(0, 0) = 1.0f;
+}
+
+int main() {}
diff --git a/failtest/triangularview_nonconst_ctor_on_const_xpr.cpp b/failtest/triangularview_nonconst_ctor_on_const_xpr.cpp
new file mode 100644
index 0000000..807447e
--- /dev/null
+++ b/failtest/triangularview_nonconst_ctor_on_const_xpr.cpp
@@ -0,0 +1,15 @@
+#include "../Eigen/Core"
+
+#ifdef EIGEN_SHOULD_FAIL_TO_BUILD
+#define CV_QUALIFIER const
+#else
+#define CV_QUALIFIER
+#endif
+
+using namespace Eigen;
+
+void foo(CV_QUALIFIER Matrix3d &m){
+ TriangularView<Matrix3d,Upper> t(m);
+}
+
+int main() {}
diff --git a/failtest/triangularview_on_const_type_actually_const.cpp b/failtest/triangularview_on_const_type_actually_const.cpp
new file mode 100644
index 0000000..0a381a6
--- /dev/null
+++ b/failtest/triangularview_on_const_type_actually_const.cpp
@@ -0,0 +1,16 @@
+#include "../Eigen/Core"
+
+#ifdef EIGEN_SHOULD_FAIL_TO_BUILD
+#define CV_QUALIFIER const
+#else
+#define CV_QUALIFIER
+#endif
+
+using namespace Eigen;
+
+void foo(){
+ MatrixXf m;
+ TriangularView<CV_QUALIFIER MatrixXf,Upper>(m).coeffRef(0, 0) = 1.0f;
+}
+
+int main() {}
diff --git a/lapack/CMakeLists.txt b/lapack/CMakeLists.txt
new file mode 100644
index 0000000..8d6d754
--- /dev/null
+++ b/lapack/CMakeLists.txt
@@ -0,0 +1,464 @@
+project(EigenLapack CXX)
+
+if(EIGEN_BUILD_LAPACK AND EIGEN_BUILD_BLAS)
+
+include(CheckLanguage)
+check_language(Fortran)
+if(CMAKE_Fortran_COMPILER)
+ enable_language(Fortran)
+ if("${CMAKE_Fortran_COMPILER_ID}" STREQUAL "GNU")
+ if ("${CMAKE_Fortran_COMPILER_VERSION}" VERSION_GREATER_EQUAL 10.0)
+ # We use an old version of LAPACK with argument type mismatches.
+ # Allow them to compile anyway with newer GNU versions.
+ set(CMAKE_Fortran_FLAGS "${CMAKE_Fortran_FLAGS} -fallow-argument-mismatch")
+ endif()
+ endif()
+ set(EIGEN_Fortran_COMPILER_WORKS ON)
+else()
+ set(EIGEN_Fortran_COMPILER_WORKS OFF)
+endif()
+
+add_custom_target(lapack)
+include_directories(../blas)
+
+set(EigenLapack_SRCS
+single.cpp double.cpp complex_single.cpp complex_double.cpp ../blas/xerbla.cpp
+)
+
+if(EIGEN_Fortran_COMPILER_WORKS)
+
+set(EigenLapack_SRCS ${EigenLapack_SRCS}
+ slarft.f dlarft.f clarft.f zlarft.f
+ slarfb.f dlarfb.f clarfb.f zlarfb.f
+ slarfg.f dlarfg.f clarfg.f zlarfg.f
+ slarf.f dlarf.f clarf.f zlarf.f
+ sladiv.f dladiv.f cladiv.f zladiv.f
+ ilaslr.f iladlr.f ilaclr.f ilazlr.f
+ ilaslc.f iladlc.f ilaclc.f ilazlc.f
+ dlapy2.f dlapy3.f slapy2.f slapy3.f
+ clacgv.f zlacgv.f
+ slamch.f dlamch.f
+ second_NONE.f dsecnd_NONE.f
+)
+
+option(EIGEN_ENABLE_LAPACK_TESTS OFF "Enable the Lapack unit tests")
+
+if(EIGEN_ENABLE_LAPACK_TESTS)
+
+ get_filename_component(eigen_full_path_to_reference_lapack "./reference/" ABSOLUTE)
+ if(NOT EXISTS ${eigen_full_path_to_reference_lapack})
+ # Download lapack and install sources and testing at the right place
+ message(STATUS "Download lapack_addons_3.4.1.tgz...")
+
+ file(DOWNLOAD "http://downloads.tuxfamily.org/eigen/lapack_addons_3.4.1.tgz"
+ "${CMAKE_CURRENT_SOURCE_DIR}/lapack_addons_3.4.1.tgz"
+ INACTIVITY_TIMEOUT 15
+ TIMEOUT 240
+ STATUS download_status
+ EXPECTED_MD5 ab5742640617e3221a873aba44bbdc93
+ SHOW_PROGRESS)
+
+ message(STATUS ${download_status})
+ list(GET download_status 0 download_status_num)
+ set(download_status_num 0)
+ if(download_status_num EQUAL 0)
+ message(STATUS "Setup lapack reference and lapack unit tests")
+ execute_process(COMMAND tar xzf "lapack_addons_3.4.1.tgz" WORKING_DIRECTORY ${CMAKE_CURRENT_SOURCE_DIR})
+ else()
+ message(STATUS "Download of lapack_addons_3.4.1.tgz failed, LAPACK unit tests won't be enabled")
+ set(EIGEN_ENABLE_LAPACK_TESTS false)
+ endif()
+
+ endif()
+
+ get_filename_component(eigen_full_path_to_reference_lapack "./reference/" ABSOLUTE)
+ if(EXISTS ${eigen_full_path_to_reference_lapack})
+ set(EigenLapack_funcfilenames
+ ssyev.f dsyev.f csyev.f zsyev.f
+ spotrf.f dpotrf.f cpotrf.f zpotrf.f
+ spotrs.f dpotrs.f cpotrs.f zpotrs.f
+ sgetrf.f dgetrf.f cgetrf.f zgetrf.f
+ sgetrs.f dgetrs.f cgetrs.f zgetrs.f)
+
+ file(GLOB ReferenceLapack_SRCS0 RELATIVE ${CMAKE_CURRENT_SOURCE_DIR} "reference/*.f")
+ foreach(filename1 IN LISTS ReferenceLapack_SRCS0)
+ string(REPLACE "reference/" "" filename ${filename1})
+ list(FIND EigenLapack_SRCS ${filename} id1)
+ list(FIND EigenLapack_funcfilenames ${filename} id2)
+ if((id1 EQUAL -1) AND (id2 EQUAL -1))
+ set(ReferenceLapack_SRCS ${ReferenceLapack_SRCS} reference/${filename})
+ endif()
+ endforeach()
+ endif()
+
+
+endif()
+
+endif()
+
+set(EIGEN_LAPACK_TARGETS "")
+
+add_library(eigen_lapack_static ${EigenLapack_SRCS} ${ReferenceLapack_SRCS})
+list(APPEND EIGEN_LAPACK_TARGETS eigen_lapack_static)
+
+if (EIGEN_BUILD_SHARED_LIBS)
+ add_library(eigen_lapack SHARED ${EigenLapack_SRCS})
+ list(APPEND EIGEN_LAPACK_TARGETS eigen_lapack)
+ target_link_libraries(eigen_lapack eigen_blas)
+endif()
+
+foreach(target IN LISTS EIGEN_LAPACK_TARGETS)
+ if(EIGEN_STANDARD_LIBRARIES_TO_LINK_TO)
+ target_link_libraries(${target} ${EIGEN_STANDARD_LIBRARIES_TO_LINK_TO})
+ endif()
+ add_dependencies(lapack ${target})
+ install(TARGETS ${target}
+ RUNTIME DESTINATION bin
+ LIBRARY DESTINATION lib
+ ARCHIVE DESTINATION lib)
+endforeach()
+
+
+get_filename_component(eigen_full_path_to_testing_lapack "./testing/" ABSOLUTE)
+if(EXISTS ${eigen_full_path_to_testing_lapack})
+
+ # The following comes from lapack/TESTING/CMakeLists.txt
+ # Get Python
+ find_package(PythonInterp)
+ message(STATUS "Looking for Python found - ${PYTHONINTERP_FOUND}")
+ if (PYTHONINTERP_FOUND)
+ message(STATUS "Using Python version ${PYTHON_VERSION_STRING}")
+ endif()
+
+ set(LAPACK_SOURCE_DIR ${CMAKE_CURRENT_SOURCE_DIR})
+ set(LAPACK_BINARY_DIR ${CMAKE_CURRENT_BINARY_DIR})
+ set(BUILD_SINGLE true)
+ set(BUILD_DOUBLE true)
+ set(BUILD_COMPLEX true)
+ set(BUILD_COMPLEX16E true)
+
+ if(MSVC_VERSION)
+# string(REPLACE "/STACK:10000000" "/STACK:900000000000000000"
+# CMAKE_EXE_LINKER_FLAGS "${CMAKE_EXE_LINKER_FLAGS}")
+ string(REGEX REPLACE "(.*)/STACK:(.*) (.*)" "\\1/STACK:900000000000000000 \\3"
+ CMAKE_EXE_LINKER_FLAGS "${CMAKE_EXE_LINKER_FLAGS}")
+ endif()
+ file(MAKE_DIRECTORY "${LAPACK_BINARY_DIR}/TESTING")
+ add_subdirectory(testing/MATGEN)
+ add_subdirectory(testing/LIN)
+ add_subdirectory(testing/EIG)
+ macro(add_lapack_test output input target)
+ set(TEST_INPUT "${LAPACK_SOURCE_DIR}/testing/${input}")
+ set(TEST_OUTPUT "${LAPACK_BINARY_DIR}/TESTING/${output}")
+ string(REPLACE "." "_" input_name ${input})
+ set(testName "${target}_${input_name}")
+ if(EXISTS "${TEST_INPUT}")
+ add_dependencies(buildtests ${target})
+ add_test(NAME LAPACK-${testName}
+ COMMAND "${CMAKE_COMMAND}"
+ -DTEST=$<TARGET_FILE:${target}>
+ -DINPUT=${TEST_INPUT}
+ -DOUTPUT=${TEST_OUTPUT}
+ -DINTDIR=${CMAKE_CFG_INTDIR}
+ -P "${LAPACK_SOURCE_DIR}/testing/runtest.cmake")
+ endif()
+ endmacro()
+
+ if (BUILD_SINGLE)
+ add_lapack_test(stest.out stest.in xlintsts)
+ #
+ # ======== SINGLE RFP LIN TESTS ========================
+ add_lapack_test(stest_rfp.out stest_rfp.in xlintstrfs)
+ #
+ #
+ # ======== SINGLE EIG TESTS ===========================
+ #
+
+ add_lapack_test(snep.out nep.in xeigtsts)
+
+
+ add_lapack_test(ssep.out sep.in xeigtsts)
+
+
+ add_lapack_test(ssvd.out svd.in xeigtsts)
+
+
+ add_lapack_test(sec.out sec.in xeigtsts)
+
+
+ add_lapack_test(sed.out sed.in xeigtsts)
+
+
+ add_lapack_test(sgg.out sgg.in xeigtsts)
+
+
+ add_lapack_test(sgd.out sgd.in xeigtsts)
+
+
+ add_lapack_test(ssb.out ssb.in xeigtsts)
+
+
+ add_lapack_test(ssg.out ssg.in xeigtsts)
+
+
+ add_lapack_test(sbal.out sbal.in xeigtsts)
+
+
+ add_lapack_test(sbak.out sbak.in xeigtsts)
+
+
+ add_lapack_test(sgbal.out sgbal.in xeigtsts)
+
+
+ add_lapack_test(sgbak.out sgbak.in xeigtsts)
+
+
+ add_lapack_test(sbb.out sbb.in xeigtsts)
+
+
+ add_lapack_test(sglm.out glm.in xeigtsts)
+
+
+ add_lapack_test(sgqr.out gqr.in xeigtsts)
+
+
+ add_lapack_test(sgsv.out gsv.in xeigtsts)
+
+
+ add_lapack_test(scsd.out csd.in xeigtsts)
+
+
+ add_lapack_test(slse.out lse.in xeigtsts)
+ endif()
+
+ if (BUILD_DOUBLE)
+ #
+ # ======== DOUBLE LIN TESTS ===========================
+ add_lapack_test(dtest.out dtest.in xlintstd)
+ #
+ # ======== DOUBLE RFP LIN TESTS ========================
+ add_lapack_test(dtest_rfp.out dtest_rfp.in xlintstrfd)
+ #
+ # ======== DOUBLE EIG TESTS ===========================
+
+ add_lapack_test(dnep.out nep.in xeigtstd)
+
+
+ add_lapack_test(dsep.out sep.in xeigtstd)
+
+
+ add_lapack_test(dsvd.out svd.in xeigtstd)
+
+
+ add_lapack_test(dec.out dec.in xeigtstd)
+
+
+ add_lapack_test(ded.out ded.in xeigtstd)
+
+
+ add_lapack_test(dgg.out dgg.in xeigtstd)
+
+
+ add_lapack_test(dgd.out dgd.in xeigtstd)
+
+
+ add_lapack_test(dsb.out dsb.in xeigtstd)
+
+
+ add_lapack_test(dsg.out dsg.in xeigtstd)
+
+
+ add_lapack_test(dbal.out dbal.in xeigtstd)
+
+
+ add_lapack_test(dbak.out dbak.in xeigtstd)
+
+
+ add_lapack_test(dgbal.out dgbal.in xeigtstd)
+
+
+ add_lapack_test(dgbak.out dgbak.in xeigtstd)
+
+
+ add_lapack_test(dbb.out dbb.in xeigtstd)
+
+
+ add_lapack_test(dglm.out glm.in xeigtstd)
+
+
+ add_lapack_test(dgqr.out gqr.in xeigtstd)
+
+
+ add_lapack_test(dgsv.out gsv.in xeigtstd)
+
+
+ add_lapack_test(dcsd.out csd.in xeigtstd)
+
+
+ add_lapack_test(dlse.out lse.in xeigtstd)
+ endif()
+
+ if (BUILD_COMPLEX)
+ add_lapack_test(ctest.out ctest.in xlintstc)
+ #
+ # ======== COMPLEX RFP LIN TESTS ========================
+ add_lapack_test(ctest_rfp.out ctest_rfp.in xlintstrfc)
+ #
+ # ======== COMPLEX EIG TESTS ===========================
+
+ add_lapack_test(cnep.out nep.in xeigtstc)
+
+
+ add_lapack_test(csep.out sep.in xeigtstc)
+
+
+ add_lapack_test(csvd.out svd.in xeigtstc)
+
+
+ add_lapack_test(cec.out cec.in xeigtstc)
+
+
+ add_lapack_test(ced.out ced.in xeigtstc)
+
+
+ add_lapack_test(cgg.out cgg.in xeigtstc)
+
+
+ add_lapack_test(cgd.out cgd.in xeigtstc)
+
+
+ add_lapack_test(csb.out csb.in xeigtstc)
+
+
+ add_lapack_test(csg.out csg.in xeigtstc)
+
+
+ add_lapack_test(cbal.out cbal.in xeigtstc)
+
+
+ add_lapack_test(cbak.out cbak.in xeigtstc)
+
+
+ add_lapack_test(cgbal.out cgbal.in xeigtstc)
+
+
+ add_lapack_test(cgbak.out cgbak.in xeigtstc)
+
+
+ add_lapack_test(cbb.out cbb.in xeigtstc)
+
+
+ add_lapack_test(cglm.out glm.in xeigtstc)
+
+
+ add_lapack_test(cgqr.out gqr.in xeigtstc)
+
+
+ add_lapack_test(cgsv.out gsv.in xeigtstc)
+
+
+ add_lapack_test(ccsd.out csd.in xeigtstc)
+
+
+ add_lapack_test(clse.out lse.in xeigtstc)
+ endif()
+
+ if (BUILD_COMPLEX16)
+ #
+ # ======== COMPLEX16 LIN TESTS ========================
+ add_lapack_test(ztest.out ztest.in xlintstz)
+ #
+ # ======== COMPLEX16 RFP LIN TESTS ========================
+ add_lapack_test(ztest_rfp.out ztest_rfp.in xlintstrfz)
+ #
+ # ======== COMPLEX16 EIG TESTS ===========================
+
+ add_lapack_test(znep.out nep.in xeigtstz)
+
+
+ add_lapack_test(zsep.out sep.in xeigtstz)
+
+
+ add_lapack_test(zsvd.out svd.in xeigtstz)
+
+
+ add_lapack_test(zec.out zec.in xeigtstz)
+
+
+ add_lapack_test(zed.out zed.in xeigtstz)
+
+
+ add_lapack_test(zgg.out zgg.in xeigtstz)
+
+
+ add_lapack_test(zgd.out zgd.in xeigtstz)
+
+
+ add_lapack_test(zsb.out zsb.in xeigtstz)
+
+
+ add_lapack_test(zsg.out zsg.in xeigtstz)
+
+
+ add_lapack_test(zbal.out zbal.in xeigtstz)
+
+
+ add_lapack_test(zbak.out zbak.in xeigtstz)
+
+
+ add_lapack_test(zgbal.out zgbal.in xeigtstz)
+
+
+ add_lapack_test(zgbak.out zgbak.in xeigtstz)
+
+
+ add_lapack_test(zbb.out zbb.in xeigtstz)
+
+
+ add_lapack_test(zglm.out glm.in xeigtstz)
+
+
+ add_lapack_test(zgqr.out gqr.in xeigtstz)
+
+
+ add_lapack_test(zgsv.out gsv.in xeigtstz)
+
+
+ add_lapack_test(zcsd.out csd.in xeigtstz)
+
+
+ add_lapack_test(zlse.out lse.in xeigtstz)
+ endif()
+
+
+ if (BUILD_SIMPLE)
+ if (BUILD_DOUBLE)
+ #
+ # ======== SINGLE-DOUBLE PROTO LIN TESTS ==============
+ add_lapack_test(dstest.out dstest.in xlintstds)
+ endif()
+ endif()
+
+
+ if (BUILD_COMPLEX)
+ if (BUILD_COMPLEX16)
+ #
+ # ======== COMPLEX-COMPLEX16 LIN TESTS ========================
+ add_lapack_test(zctest.out zctest.in xlintstzc)
+ endif()
+ endif()
+
+ # ==============================================================================
+
+ execute_process(COMMAND ${CMAKE_COMMAND} -E copy ${LAPACK_SOURCE_DIR}/testing/lapack_testing.py ${LAPACK_BINARY_DIR})
+ add_test(
+ NAME LAPACK_Test_Summary
+ WORKING_DIRECTORY ${LAPACK_BINARY_DIR}
+ COMMAND ${PYTHON_EXECUTABLE} "lapack_testing.py"
+ )
+
+endif()
+
+elseif(EIGEN_BUILD_LAPACK AND NOT EIGEN_BUILD_BLAS)
+ message(FATAL_ERROR "EIGEN_BUILD_LAPACK requires EIGEN_BUILD_BLAS")
+endif() #EIGEN_BUILD_LAPACK
diff --git a/lapack/blaswrap.h b/lapack/blaswrap.h
new file mode 100644
index 0000000..4f7c71e
--- /dev/null
+++ b/lapack/blaswrap.h
@@ -0,0 +1,2 @@
+// This is an empty file by design to make the clapack functions in this
+// directory compile without modification.
diff --git a/lapack/cholesky.cpp b/lapack/cholesky.cpp
new file mode 100644
index 0000000..ea3bc12
--- /dev/null
+++ b/lapack/cholesky.cpp
@@ -0,0 +1,72 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2010-2011 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "lapack_common.h"
+#include <Eigen/Cholesky>
+
+// POTRF computes the Cholesky factorization of a real symmetric positive definite matrix A.
+EIGEN_LAPACK_FUNC(potrf,(char* uplo, int *n, RealScalar *pa, int *lda, int *info))
+{
+ *info = 0;
+ if(UPLO(*uplo)==INVALID) *info = -1;
+ else if(*n<0) *info = -2;
+ else if(*lda<std::max(1,*n)) *info = -4;
+ if(*info!=0)
+ {
+ int e = -*info;
+ return xerbla_(SCALAR_SUFFIX_UP"POTRF", &e, 6);
+ }
+
+ Scalar* a = reinterpret_cast<Scalar*>(pa);
+ MatrixType A(a,*n,*n,*lda);
+ int ret;
+ if(UPLO(*uplo)==UP) ret = int(internal::llt_inplace<Scalar, Upper>::blocked(A));
+ else ret = int(internal::llt_inplace<Scalar, Lower>::blocked(A));
+
+ if(ret>=0)
+ *info = ret+1;
+
+ return 0;
+}
+
+// POTRS solves a system of linear equations A*X = B with a symmetric
+// positive definite matrix A using the Cholesky factorization
+// A = U**T*U or A = L*L**T computed by DPOTRF.
+EIGEN_LAPACK_FUNC(potrs,(char* uplo, int *n, int *nrhs, RealScalar *pa, int *lda, RealScalar *pb, int *ldb, int *info))
+{
+ *info = 0;
+ if(UPLO(*uplo)==INVALID) *info = -1;
+ else if(*n<0) *info = -2;
+ else if(*nrhs<0) *info = -3;
+ else if(*lda<std::max(1,*n)) *info = -5;
+ else if(*ldb<std::max(1,*n)) *info = -7;
+ if(*info!=0)
+ {
+ int e = -*info;
+ return xerbla_(SCALAR_SUFFIX_UP"POTRS", &e, 6);
+ }
+
+ Scalar* a = reinterpret_cast<Scalar*>(pa);
+ Scalar* b = reinterpret_cast<Scalar*>(pb);
+ MatrixType A(a,*n,*n,*lda);
+ MatrixType B(b,*n,*nrhs,*ldb);
+
+ if(UPLO(*uplo)==UP)
+ {
+ A.triangularView<Upper>().adjoint().solveInPlace(B);
+ A.triangularView<Upper>().solveInPlace(B);
+ }
+ else
+ {
+ A.triangularView<Lower>().solveInPlace(B);
+ A.triangularView<Lower>().adjoint().solveInPlace(B);
+ }
+
+ return 0;
+}
diff --git a/lapack/cholesky.inc b/lapack/cholesky.inc
new file mode 100644
index 0000000..ea3bc12
--- /dev/null
+++ b/lapack/cholesky.inc
@@ -0,0 +1,72 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2010-2011 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "lapack_common.h"
+#include <Eigen/Cholesky>
+
+// POTRF computes the Cholesky factorization of a real symmetric positive definite matrix A.
+EIGEN_LAPACK_FUNC(potrf,(char* uplo, int *n, RealScalar *pa, int *lda, int *info))
+{
+ *info = 0;
+ if(UPLO(*uplo)==INVALID) *info = -1;
+ else if(*n<0) *info = -2;
+ else if(*lda<std::max(1,*n)) *info = -4;
+ if(*info!=0)
+ {
+ int e = -*info;
+ return xerbla_(SCALAR_SUFFIX_UP"POTRF", &e, 6);
+ }
+
+ Scalar* a = reinterpret_cast<Scalar*>(pa);
+ MatrixType A(a,*n,*n,*lda);
+ int ret;
+ if(UPLO(*uplo)==UP) ret = int(internal::llt_inplace<Scalar, Upper>::blocked(A));
+ else ret = int(internal::llt_inplace<Scalar, Lower>::blocked(A));
+
+ if(ret>=0)
+ *info = ret+1;
+
+ return 0;
+}
+
+// POTRS solves a system of linear equations A*X = B with a symmetric
+// positive definite matrix A using the Cholesky factorization
+// A = U**T*U or A = L*L**T computed by DPOTRF.
+EIGEN_LAPACK_FUNC(potrs,(char* uplo, int *n, int *nrhs, RealScalar *pa, int *lda, RealScalar *pb, int *ldb, int *info))
+{
+ *info = 0;
+ if(UPLO(*uplo)==INVALID) *info = -1;
+ else if(*n<0) *info = -2;
+ else if(*nrhs<0) *info = -3;
+ else if(*lda<std::max(1,*n)) *info = -5;
+ else if(*ldb<std::max(1,*n)) *info = -7;
+ if(*info!=0)
+ {
+ int e = -*info;
+ return xerbla_(SCALAR_SUFFIX_UP"POTRS", &e, 6);
+ }
+
+ Scalar* a = reinterpret_cast<Scalar*>(pa);
+ Scalar* b = reinterpret_cast<Scalar*>(pb);
+ MatrixType A(a,*n,*n,*lda);
+ MatrixType B(b,*n,*nrhs,*ldb);
+
+ if(UPLO(*uplo)==UP)
+ {
+ A.triangularView<Upper>().adjoint().solveInPlace(B);
+ A.triangularView<Upper>().solveInPlace(B);
+ }
+ else
+ {
+ A.triangularView<Lower>().solveInPlace(B);
+ A.triangularView<Lower>().adjoint().solveInPlace(B);
+ }
+
+ return 0;
+}
diff --git a/lapack/clacgv.c b/lapack/clacgv.c
new file mode 100644
index 0000000..31fa8ff
--- /dev/null
+++ b/lapack/clacgv.c
@@ -0,0 +1,95 @@
+/* clacgv.f -- translated by f2c (version 20061008).
+ You must link the resulting object file with libf2c:
+ on Microsoft Windows system, link with libf2c.lib;
+ on Linux or Unix systems, link with .../path/to/libf2c.a -lm
+ or, if you install libf2c.a in a standard place, with -lf2c -lm
+ -- in that order, at the end of the command line, as in
+ cc *.o -lf2c -lm
+ Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
+
+ http://www.netlib.org/f2c/libf2c.zip
+*/
+
+#include "f2c.h"
+#include "blaswrap.h"
+
+/* Subroutine */ int clacgv_(integer *n, complex *x, integer *incx)
+{
+ /* System generated locals */
+ integer i__1, i__2;
+ complex q__1;
+
+ /* Builtin functions */
+ void r_cnjg(complex *, complex *);
+
+ /* Local variables */
+ integer i__, ioff;
+
+
+/* -- LAPACK auxiliary routine (version 3.2) -- */
+/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
+/* November 2006 */
+
+/* .. Scalar Arguments .. */
+/* .. */
+/* .. Array Arguments .. */
+/* .. */
+
+/* Purpose */
+/* ======= */
+
+/* CLACGV conjugates a complex vector of length N. */
+
+/* Arguments */
+/* ========= */
+
+/* N (input) INTEGER */
+/* The length of the vector X. N >= 0. */
+
+/* X (input/output) COMPLEX array, dimension */
+/* (1+(N-1)*abs(INCX)) */
+/* On entry, the vector of length N to be conjugated. */
+/* On exit, X is overwritten with conjg(X). */
+
+/* INCX (input) INTEGER */
+/* The spacing between successive elements of X. */
+
+/* ===================================================================== */
+
+/* .. Local Scalars .. */
+/* .. */
+/* .. Intrinsic Functions .. */
+/* .. */
+/* .. Executable Statements .. */
+
+ /* Parameter adjustments */
+ --x;
+
+ /* Function Body */
+ if (*incx == 1) {
+ i__1 = *n;
+ for (i__ = 1; i__ <= i__1; ++i__) {
+ i__2 = i__;
+ r_cnjg(&q__1, &x[i__]);
+ x[i__2].r = q__1.r, x[i__2].i = q__1.i;
+/* L10: */
+ }
+ } else {
+ ioff = 1;
+ if (*incx < 0) {
+ ioff = 1 - (*n - 1) * *incx;
+ }
+ i__1 = *n;
+ for (i__ = 1; i__ <= i__1; ++i__) {
+ i__2 = ioff;
+ r_cnjg(&q__1, &x[ioff]);
+ x[i__2].r = q__1.r, x[i__2].i = q__1.i;
+ ioff += *incx;
+/* L20: */
+ }
+ }
+ return 0;
+
+/* End of CLACGV */
+
+} /* clacgv_ */
diff --git a/lapack/cladiv.c b/lapack/cladiv.c
new file mode 100644
index 0000000..d10c959
--- /dev/null
+++ b/lapack/cladiv.c
@@ -0,0 +1,74 @@
+/* cladiv.f -- translated by f2c (version 20061008).
+ You must link the resulting object file with libf2c:
+ on Microsoft Windows system, link with libf2c.lib;
+ on Linux or Unix systems, link with .../path/to/libf2c.a -lm
+ or, if you install libf2c.a in a standard place, with -lf2c -lm
+ -- in that order, at the end of the command line, as in
+ cc *.o -lf2c -lm
+ Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
+
+ http://www.netlib.org/f2c/libf2c.zip
+*/
+
+#include "f2c.h"
+#include "blaswrap.h"
+
+/* Complex */ VOID cladiv_(complex * ret_val, complex *x, complex *y)
+{
+ /* System generated locals */
+ real r__1, r__2, r__3, r__4;
+ complex q__1;
+
+ /* Builtin functions */
+ double r_imag(complex *);
+
+ /* Local variables */
+ real zi, zr;
+ extern /* Subroutine */ int sladiv_(real *, real *, real *, real *, real *
+, real *);
+
+
+/* -- LAPACK auxiliary routine (version 3.2) -- */
+/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
+/* November 2006 */
+
+/* .. Scalar Arguments .. */
+/* .. */
+
+/* Purpose */
+/* ======= */
+
+/* CLADIV := X / Y, where X and Y are complex. The computation of X / Y */
+/* will not overflow on an intermediary step unless the results */
+/* overflows. */
+
+/* Arguments */
+/* ========= */
+
+/* X (input) COMPLEX */
+/* Y (input) COMPLEX */
+/* The complex scalars X and Y. */
+
+/* ===================================================================== */
+
+/* .. Local Scalars .. */
+/* .. */
+/* .. External Subroutines .. */
+/* .. */
+/* .. Intrinsic Functions .. */
+/* .. */
+/* .. Executable Statements .. */
+
+ r__1 = x->r;
+ r__2 = r_imag(x);
+ r__3 = y->r;
+ r__4 = r_imag(y);
+ sladiv_(&r__1, &r__2, &r__3, &r__4, &zr, &zi);
+ q__1.r = zr, q__1.i = zi;
+ ret_val->r = q__1.r, ret_val->i = q__1.i;
+
+ return ;
+
+/* End of CLADIV */
+
+} /* cladiv_ */
diff --git a/lapack/clarf.c b/lapack/clarf.c
new file mode 100644
index 0000000..53da4d3
--- /dev/null
+++ b/lapack/clarf.c
@@ -0,0 +1,198 @@
+/* clarf.f -- translated by f2c (version 20061008).
+ You must link the resulting object file with libf2c:
+ on Microsoft Windows system, link with libf2c.lib;
+ on Linux or Unix systems, link with .../path/to/libf2c.a -lm
+ or, if you install libf2c.a in a standard place, with -lf2c -lm
+ -- in that order, at the end of the command line, as in
+ cc *.o -lf2c -lm
+ Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
+
+ http://www.netlib.org/f2c/libf2c.zip
+*/
+
+#include "f2c.h"
+#include "blaswrap.h"
+
+/* Table of constant values */
+
+static complex c_b1 = {1.f,0.f};
+static complex c_b2 = {0.f,0.f};
+static integer c__1 = 1;
+
+/* Subroutine */ int clarf_(char *side, integer *m, integer *n, complex *v,
+ integer *incv, complex *tau, complex *c__, integer *ldc, complex *
+ work)
+{
+ /* System generated locals */
+ integer c_dim1, c_offset, i__1;
+ complex q__1;
+
+ /* Local variables */
+ integer i__;
+ logical applyleft;
+ extern /* Subroutine */ int cgerc_(integer *, integer *, complex *,
+ complex *, integer *, complex *, integer *, complex *, integer *),
+ cgemv_(char *, integer *, integer *, complex *, complex *,
+ integer *, complex *, integer *, complex *, complex *, integer *);
+ extern logical lsame_(char *, char *);
+ integer lastc, lastv;
+ extern integer ilaclc_(integer *, integer *, complex *, integer *),
+ ilaclr_(integer *, integer *, complex *, integer *);
+
+
+/* -- LAPACK auxiliary routine (version 3.2) -- */
+/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
+/* November 2006 */
+
+/* .. Scalar Arguments .. */
+/* .. */
+/* .. Array Arguments .. */
+/* .. */
+
+/* Purpose */
+/* ======= */
+
+/* CLARF applies a complex elementary reflector H to a complex M-by-N */
+/* matrix C, from either the left or the right. H is represented in the */
+/* form */
+
+/* H = I - tau * v * v' */
+
+/* where tau is a complex scalar and v is a complex vector. */
+
+/* If tau = 0, then H is taken to be the unit matrix. */
+
+/* To apply H' (the conjugate transpose of H), supply conjg(tau) instead */
+/* tau. */
+
+/* Arguments */
+/* ========= */
+
+/* SIDE (input) CHARACTER*1 */
+/* = 'L': form H * C */
+/* = 'R': form C * H */
+
+/* M (input) INTEGER */
+/* The number of rows of the matrix C. */
+
+/* N (input) INTEGER */
+/* The number of columns of the matrix C. */
+
+/* V (input) COMPLEX array, dimension */
+/* (1 + (M-1)*abs(INCV)) if SIDE = 'L' */
+/* or (1 + (N-1)*abs(INCV)) if SIDE = 'R' */
+/* The vector v in the representation of H. V is not used if */
+/* TAU = 0. */
+
+/* INCV (input) INTEGER */
+/* The increment between elements of v. INCV <> 0. */
+
+/* TAU (input) COMPLEX */
+/* The value tau in the representation of H. */
+
+/* C (input/output) COMPLEX array, dimension (LDC,N) */
+/* On entry, the M-by-N matrix C. */
+/* On exit, C is overwritten by the matrix H * C if SIDE = 'L', */
+/* or C * H if SIDE = 'R'. */
+
+/* LDC (input) INTEGER */
+/* The leading dimension of the array C. LDC >= max(1,M). */
+
+/* WORK (workspace) COMPLEX array, dimension */
+/* (N) if SIDE = 'L' */
+/* or (M) if SIDE = 'R' */
+
+/* ===================================================================== */
+
+/* .. Parameters .. */
+/* .. */
+/* .. Local Scalars .. */
+/* .. */
+/* .. External Subroutines .. */
+/* .. */
+/* .. External Functions .. */
+/* .. */
+/* .. Executable Statements .. */
+
+ /* Parameter adjustments */
+ --v;
+ c_dim1 = *ldc;
+ c_offset = 1 + c_dim1;
+ c__ -= c_offset;
+ --work;
+
+ /* Function Body */
+ applyleft = lsame_(side, "L");
+ lastv = 0;
+ lastc = 0;
+ if (tau->r != 0.f || tau->i != 0.f) {
+/* Set up variables for scanning V. LASTV begins pointing to the end */
+/* of V. */
+ if (applyleft) {
+ lastv = *m;
+ } else {
+ lastv = *n;
+ }
+ if (*incv > 0) {
+ i__ = (lastv - 1) * *incv + 1;
+ } else {
+ i__ = 1;
+ }
+/* Look for the last non-zero row in V. */
+ for(;;) { /* while(complicated condition) */
+ i__1 = i__;
+ if (!(lastv > 0 && (v[i__1].r == 0.f && v[i__1].i == 0.f)))
+ break;
+ --lastv;
+ i__ -= *incv;
+ }
+ if (applyleft) {
+/* Scan for the last non-zero column in C(1:lastv,:). */
+ lastc = ilaclc_(&lastv, n, &c__[c_offset], ldc);
+ } else {
+/* Scan for the last non-zero row in C(:,1:lastv). */
+ lastc = ilaclr_(m, &lastv, &c__[c_offset], ldc);
+ }
+ }
+/* Note that lastc.eq.0 renders the BLAS operations null; no special */
+/* case is needed at this level. */
+ if (applyleft) {
+
+/* Form H * C */
+
+ if (lastv > 0) {
+
+/* w(1:lastc,1) := C(1:lastv,1:lastc)' * v(1:lastv,1) */
+
+ cgemv_("Conjugate transpose", &lastv, &lastc, &c_b1, &c__[
+ c_offset], ldc, &v[1], incv, &c_b2, &work[1], &c__1);
+
+/* C(1:lastv,1:lastc) := C(...) - v(1:lastv,1) * w(1:lastc,1)' */
+
+ q__1.r = -tau->r, q__1.i = -tau->i;
+ cgerc_(&lastv, &lastc, &q__1, &v[1], incv, &work[1], &c__1, &c__[
+ c_offset], ldc);
+ }
+ } else {
+
+/* Form C * H */
+
+ if (lastv > 0) {
+
+/* w(1:lastc,1) := C(1:lastc,1:lastv) * v(1:lastv,1) */
+
+ cgemv_("No transpose", &lastc, &lastv, &c_b1, &c__[c_offset], ldc,
+ &v[1], incv, &c_b2, &work[1], &c__1);
+
+/* C(1:lastc,1:lastv) := C(...) - w(1:lastc,1) * v(1:lastv,1)' */
+
+ q__1.r = -tau->r, q__1.i = -tau->i;
+ cgerc_(&lastc, &lastv, &q__1, &work[1], &c__1, &v[1], incv, &c__[
+ c_offset], ldc);
+ }
+ }
+ return 0;
+
+/* End of CLARF */
+
+} /* clarf_ */
diff --git a/lapack/clarfb.c b/lapack/clarfb.c
new file mode 100644
index 0000000..6b31aa1
--- /dev/null
+++ b/lapack/clarfb.c
@@ -0,0 +1,837 @@
+/* clarfb.f -- translated by f2c (version 20061008).
+ You must link the resulting object file with libf2c:
+ on Microsoft Windows system, link with libf2c.lib;
+ on Linux or Unix systems, link with .../path/to/libf2c.a -lm
+ or, if you install libf2c.a in a standard place, with -lf2c -lm
+ -- in that order, at the end of the command line, as in
+ cc *.o -lf2c -lm
+ Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
+
+ http://www.netlib.org/f2c/libf2c.zip
+*/
+
+#include "f2c.h"
+#include "blaswrap.h"
+
+/* Table of constant values */
+
+static complex c_b1 = {1.f,0.f};
+static integer c__1 = 1;
+
+/* Subroutine */ int clarfb_(char *side, char *trans, char *direct, char *
+ storev, integer *m, integer *n, integer *k, complex *v, integer *ldv,
+ complex *t, integer *ldt, complex *c__, integer *ldc, complex *work,
+ integer *ldwork)
+{
+ /* System generated locals */
+ integer c_dim1, c_offset, t_dim1, t_offset, v_dim1, v_offset, work_dim1,
+ work_offset, i__1, i__2, i__3, i__4, i__5;
+ complex q__1, q__2;
+
+ /* Builtin functions */
+ void r_cnjg(complex *, complex *);
+
+ /* Local variables */
+ integer i__, j;
+ extern /* Subroutine */ int cgemm_(char *, char *, integer *, integer *,
+ integer *, complex *, complex *, integer *, complex *, integer *,
+ complex *, complex *, integer *);
+ extern logical lsame_(char *, char *);
+ integer lastc;
+ extern /* Subroutine */ int ccopy_(integer *, complex *, integer *,
+ complex *, integer *), ctrmm_(char *, char *, char *, char *,
+ integer *, integer *, complex *, complex *, integer *, complex *,
+ integer *);
+ integer lastv;
+ extern integer ilaclc_(integer *, integer *, complex *, integer *);
+ extern /* Subroutine */ int clacgv_(integer *, complex *, integer *);
+ extern integer ilaclr_(integer *, integer *, complex *, integer *);
+ char transt[1];
+
+
+/* -- LAPACK auxiliary routine (version 3.2) -- */
+/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
+/* November 2006 */
+
+/* .. Scalar Arguments .. */
+/* .. */
+/* .. Array Arguments .. */
+/* .. */
+
+/* Purpose */
+/* ======= */
+
+/* CLARFB applies a complex block reflector H or its transpose H' to a */
+/* complex M-by-N matrix C, from either the left or the right. */
+
+/* Arguments */
+/* ========= */
+
+/* SIDE (input) CHARACTER*1 */
+/* = 'L': apply H or H' from the Left */
+/* = 'R': apply H or H' from the Right */
+
+/* TRANS (input) CHARACTER*1 */
+/* = 'N': apply H (No transpose) */
+/* = 'C': apply H' (Conjugate transpose) */
+
+/* DIRECT (input) CHARACTER*1 */
+/* Indicates how H is formed from a product of elementary */
+/* reflectors */
+/* = 'F': H = H(1) H(2) . . . H(k) (Forward) */
+/* = 'B': H = H(k) . . . H(2) H(1) (Backward) */
+
+/* STOREV (input) CHARACTER*1 */
+/* Indicates how the vectors which define the elementary */
+/* reflectors are stored: */
+/* = 'C': Columnwise */
+/* = 'R': Rowwise */
+
+/* M (input) INTEGER */
+/* The number of rows of the matrix C. */
+
+/* N (input) INTEGER */
+/* The number of columns of the matrix C. */
+
+/* K (input) INTEGER */
+/* The order of the matrix T (= the number of elementary */
+/* reflectors whose product defines the block reflector). */
+
+/* V (input) COMPLEX array, dimension */
+/* (LDV,K) if STOREV = 'C' */
+/* (LDV,M) if STOREV = 'R' and SIDE = 'L' */
+/* (LDV,N) if STOREV = 'R' and SIDE = 'R' */
+/* The matrix V. See further details. */
+
+/* LDV (input) INTEGER */
+/* The leading dimension of the array V. */
+/* If STOREV = 'C' and SIDE = 'L', LDV >= max(1,M); */
+/* if STOREV = 'C' and SIDE = 'R', LDV >= max(1,N); */
+/* if STOREV = 'R', LDV >= K. */
+
+/* T (input) COMPLEX array, dimension (LDT,K) */
+/* The triangular K-by-K matrix T in the representation of the */
+/* block reflector. */
+
+/* LDT (input) INTEGER */
+/* The leading dimension of the array T. LDT >= K. */
+
+/* C (input/output) COMPLEX array, dimension (LDC,N) */
+/* On entry, the M-by-N matrix C. */
+/* On exit, C is overwritten by H*C or H'*C or C*H or C*H'. */
+
+/* LDC (input) INTEGER */
+/* The leading dimension of the array C. LDC >= max(1,M). */
+
+/* WORK (workspace) COMPLEX array, dimension (LDWORK,K) */
+
+/* LDWORK (input) INTEGER */
+/* The leading dimension of the array WORK. */
+/* If SIDE = 'L', LDWORK >= max(1,N); */
+/* if SIDE = 'R', LDWORK >= max(1,M). */
+
+/* ===================================================================== */
+
+/* .. Parameters .. */
+/* .. */
+/* .. Local Scalars .. */
+/* .. */
+/* .. External Functions .. */
+/* .. */
+/* .. External Subroutines .. */
+/* .. */
+/* .. Intrinsic Functions .. */
+/* .. */
+/* .. Executable Statements .. */
+
+/* Quick return if possible */
+
+ /* Parameter adjustments */
+ v_dim1 = *ldv;
+ v_offset = 1 + v_dim1;
+ v -= v_offset;
+ t_dim1 = *ldt;
+ t_offset = 1 + t_dim1;
+ t -= t_offset;
+ c_dim1 = *ldc;
+ c_offset = 1 + c_dim1;
+ c__ -= c_offset;
+ work_dim1 = *ldwork;
+ work_offset = 1 + work_dim1;
+ work -= work_offset;
+
+ /* Function Body */
+ if (*m <= 0 || *n <= 0) {
+ return 0;
+ }
+
+ if (lsame_(trans, "N")) {
+ *(unsigned char *)transt = 'C';
+ } else {
+ *(unsigned char *)transt = 'N';
+ }
+
+ if (lsame_(storev, "C")) {
+
+ if (lsame_(direct, "F")) {
+
+/* Let V = ( V1 ) (first K rows) */
+/* ( V2 ) */
+/* where V1 is unit lower triangular. */
+
+ if (lsame_(side, "L")) {
+
+/* Form H * C or H' * C where C = ( C1 ) */
+/* ( C2 ) */
+
+/* Computing MAX */
+ i__1 = *k, i__2 = ilaclr_(m, k, &v[v_offset], ldv);
+ lastv = max(i__1,i__2);
+ lastc = ilaclc_(&lastv, n, &c__[c_offset], ldc);
+
+/* W := C' * V = (C1'*V1 + C2'*V2) (stored in WORK) */
+
+/* W := C1' */
+
+ i__1 = *k;
+ for (j = 1; j <= i__1; ++j) {
+ ccopy_(&lastc, &c__[j + c_dim1], ldc, &work[j * work_dim1
+ + 1], &c__1);
+ clacgv_(&lastc, &work[j * work_dim1 + 1], &c__1);
+/* L10: */
+ }
+
+/* W := W * V1 */
+
+ ctrmm_("Right", "Lower", "No transpose", "Unit", &lastc, k, &
+ c_b1, &v[v_offset], ldv, &work[work_offset], ldwork);
+ if (lastv > *k) {
+
+/* W := W + C2'*V2 */
+
+ i__1 = lastv - *k;
+ cgemm_("Conjugate transpose", "No transpose", &lastc, k, &
+ i__1, &c_b1, &c__[*k + 1 + c_dim1], ldc, &v[*k +
+ 1 + v_dim1], ldv, &c_b1, &work[work_offset],
+ ldwork);
+ }
+
+/* W := W * T' or W * T */
+
+ ctrmm_("Right", "Upper", transt, "Non-unit", &lastc, k, &c_b1,
+ &t[t_offset], ldt, &work[work_offset], ldwork);
+
+/* C := C - V * W' */
+
+ if (*m > *k) {
+
+/* C2 := C2 - V2 * W' */
+
+ i__1 = lastv - *k;
+ q__1.r = -1.f, q__1.i = -0.f;
+ cgemm_("No transpose", "Conjugate transpose", &i__1, &
+ lastc, k, &q__1, &v[*k + 1 + v_dim1], ldv, &work[
+ work_offset], ldwork, &c_b1, &c__[*k + 1 + c_dim1]
+, ldc);
+ }
+
+/* W := W * V1' */
+
+ ctrmm_("Right", "Lower", "Conjugate transpose", "Unit", &
+ lastc, k, &c_b1, &v[v_offset], ldv, &work[work_offset]
+, ldwork)
+ ;
+
+/* C1 := C1 - W' */
+
+ i__1 = *k;
+ for (j = 1; j <= i__1; ++j) {
+ i__2 = lastc;
+ for (i__ = 1; i__ <= i__2; ++i__) {
+ i__3 = j + i__ * c_dim1;
+ i__4 = j + i__ * c_dim1;
+ r_cnjg(&q__2, &work[i__ + j * work_dim1]);
+ q__1.r = c__[i__4].r - q__2.r, q__1.i = c__[i__4].i -
+ q__2.i;
+ c__[i__3].r = q__1.r, c__[i__3].i = q__1.i;
+/* L20: */
+ }
+/* L30: */
+ }
+
+ } else if (lsame_(side, "R")) {
+
+/* Form C * H or C * H' where C = ( C1 C2 ) */
+
+/* Computing MAX */
+ i__1 = *k, i__2 = ilaclr_(n, k, &v[v_offset], ldv);
+ lastv = max(i__1,i__2);
+ lastc = ilaclr_(m, &lastv, &c__[c_offset], ldc);
+
+/* W := C * V = (C1*V1 + C2*V2) (stored in WORK) */
+
+/* W := C1 */
+
+ i__1 = *k;
+ for (j = 1; j <= i__1; ++j) {
+ ccopy_(&lastc, &c__[j * c_dim1 + 1], &c__1, &work[j *
+ work_dim1 + 1], &c__1);
+/* L40: */
+ }
+
+/* W := W * V1 */
+
+ ctrmm_("Right", "Lower", "No transpose", "Unit", &lastc, k, &
+ c_b1, &v[v_offset], ldv, &work[work_offset], ldwork);
+ if (lastv > *k) {
+
+/* W := W + C2 * V2 */
+
+ i__1 = lastv - *k;
+ cgemm_("No transpose", "No transpose", &lastc, k, &i__1, &
+ c_b1, &c__[(*k + 1) * c_dim1 + 1], ldc, &v[*k + 1
+ + v_dim1], ldv, &c_b1, &work[work_offset], ldwork);
+ }
+
+/* W := W * T or W * T' */
+
+ ctrmm_("Right", "Upper", trans, "Non-unit", &lastc, k, &c_b1,
+ &t[t_offset], ldt, &work[work_offset], ldwork);
+
+/* C := C - W * V' */
+
+ if (lastv > *k) {
+
+/* C2 := C2 - W * V2' */
+
+ i__1 = lastv - *k;
+ q__1.r = -1.f, q__1.i = -0.f;
+ cgemm_("No transpose", "Conjugate transpose", &lastc, &
+ i__1, k, &q__1, &work[work_offset], ldwork, &v[*k
+ + 1 + v_dim1], ldv, &c_b1, &c__[(*k + 1) * c_dim1
+ + 1], ldc);
+ }
+
+/* W := W * V1' */
+
+ ctrmm_("Right", "Lower", "Conjugate transpose", "Unit", &
+ lastc, k, &c_b1, &v[v_offset], ldv, &work[work_offset]
+, ldwork)
+ ;
+
+/* C1 := C1 - W */
+
+ i__1 = *k;
+ for (j = 1; j <= i__1; ++j) {
+ i__2 = lastc;
+ for (i__ = 1; i__ <= i__2; ++i__) {
+ i__3 = i__ + j * c_dim1;
+ i__4 = i__ + j * c_dim1;
+ i__5 = i__ + j * work_dim1;
+ q__1.r = c__[i__4].r - work[i__5].r, q__1.i = c__[
+ i__4].i - work[i__5].i;
+ c__[i__3].r = q__1.r, c__[i__3].i = q__1.i;
+/* L50: */
+ }
+/* L60: */
+ }
+ }
+
+ } else {
+
+/* Let V = ( V1 ) */
+/* ( V2 ) (last K rows) */
+/* where V2 is unit upper triangular. */
+
+ if (lsame_(side, "L")) {
+
+/* Form H * C or H' * C where C = ( C1 ) */
+/* ( C2 ) */
+
+/* Computing MAX */
+ i__1 = *k, i__2 = ilaclr_(m, k, &v[v_offset], ldv);
+ lastv = max(i__1,i__2);
+ lastc = ilaclc_(&lastv, n, &c__[c_offset], ldc);
+
+/* W := C' * V = (C1'*V1 + C2'*V2) (stored in WORK) */
+
+/* W := C2' */
+
+ i__1 = *k;
+ for (j = 1; j <= i__1; ++j) {
+ ccopy_(&lastc, &c__[lastv - *k + j + c_dim1], ldc, &work[
+ j * work_dim1 + 1], &c__1);
+ clacgv_(&lastc, &work[j * work_dim1 + 1], &c__1);
+/* L70: */
+ }
+
+/* W := W * V2 */
+
+ ctrmm_("Right", "Upper", "No transpose", "Unit", &lastc, k, &
+ c_b1, &v[lastv - *k + 1 + v_dim1], ldv, &work[
+ work_offset], ldwork);
+ if (lastv > *k) {
+
+/* W := W + C1'*V1 */
+
+ i__1 = lastv - *k;
+ cgemm_("Conjugate transpose", "No transpose", &lastc, k, &
+ i__1, &c_b1, &c__[c_offset], ldc, &v[v_offset],
+ ldv, &c_b1, &work[work_offset], ldwork);
+ }
+
+/* W := W * T' or W * T */
+
+ ctrmm_("Right", "Lower", transt, "Non-unit", &lastc, k, &c_b1,
+ &t[t_offset], ldt, &work[work_offset], ldwork);
+
+/* C := C - V * W' */
+
+ if (lastv > *k) {
+
+/* C1 := C1 - V1 * W' */
+
+ i__1 = lastv - *k;
+ q__1.r = -1.f, q__1.i = -0.f;
+ cgemm_("No transpose", "Conjugate transpose", &i__1, &
+ lastc, k, &q__1, &v[v_offset], ldv, &work[
+ work_offset], ldwork, &c_b1, &c__[c_offset], ldc);
+ }
+
+/* W := W * V2' */
+
+ ctrmm_("Right", "Upper", "Conjugate transpose", "Unit", &
+ lastc, k, &c_b1, &v[lastv - *k + 1 + v_dim1], ldv, &
+ work[work_offset], ldwork);
+
+/* C2 := C2 - W' */
+
+ i__1 = *k;
+ for (j = 1; j <= i__1; ++j) {
+ i__2 = lastc;
+ for (i__ = 1; i__ <= i__2; ++i__) {
+ i__3 = lastv - *k + j + i__ * c_dim1;
+ i__4 = lastv - *k + j + i__ * c_dim1;
+ r_cnjg(&q__2, &work[i__ + j * work_dim1]);
+ q__1.r = c__[i__4].r - q__2.r, q__1.i = c__[i__4].i -
+ q__2.i;
+ c__[i__3].r = q__1.r, c__[i__3].i = q__1.i;
+/* L80: */
+ }
+/* L90: */
+ }
+
+ } else if (lsame_(side, "R")) {
+
+/* Form C * H or C * H' where C = ( C1 C2 ) */
+
+/* Computing MAX */
+ i__1 = *k, i__2 = ilaclr_(n, k, &v[v_offset], ldv);
+ lastv = max(i__1,i__2);
+ lastc = ilaclr_(m, &lastv, &c__[c_offset], ldc);
+
+/* W := C * V = (C1*V1 + C2*V2) (stored in WORK) */
+
+/* W := C2 */
+
+ i__1 = *k;
+ for (j = 1; j <= i__1; ++j) {
+ ccopy_(&lastc, &c__[(lastv - *k + j) * c_dim1 + 1], &c__1,
+ &work[j * work_dim1 + 1], &c__1);
+/* L100: */
+ }
+
+/* W := W * V2 */
+
+ ctrmm_("Right", "Upper", "No transpose", "Unit", &lastc, k, &
+ c_b1, &v[lastv - *k + 1 + v_dim1], ldv, &work[
+ work_offset], ldwork);
+ if (lastv > *k) {
+
+/* W := W + C1 * V1 */
+
+ i__1 = lastv - *k;
+ cgemm_("No transpose", "No transpose", &lastc, k, &i__1, &
+ c_b1, &c__[c_offset], ldc, &v[v_offset], ldv, &
+ c_b1, &work[work_offset], ldwork);
+ }
+
+/* W := W * T or W * T' */
+
+ ctrmm_("Right", "Lower", trans, "Non-unit", &lastc, k, &c_b1,
+ &t[t_offset], ldt, &work[work_offset], ldwork);
+
+/* C := C - W * V' */
+
+ if (lastv > *k) {
+
+/* C1 := C1 - W * V1' */
+
+ i__1 = lastv - *k;
+ q__1.r = -1.f, q__1.i = -0.f;
+ cgemm_("No transpose", "Conjugate transpose", &lastc, &
+ i__1, k, &q__1, &work[work_offset], ldwork, &v[
+ v_offset], ldv, &c_b1, &c__[c_offset], ldc);
+ }
+
+/* W := W * V2' */
+
+ ctrmm_("Right", "Upper", "Conjugate transpose", "Unit", &
+ lastc, k, &c_b1, &v[lastv - *k + 1 + v_dim1], ldv, &
+ work[work_offset], ldwork);
+
+/* C2 := C2 - W */
+
+ i__1 = *k;
+ for (j = 1; j <= i__1; ++j) {
+ i__2 = lastc;
+ for (i__ = 1; i__ <= i__2; ++i__) {
+ i__3 = i__ + (lastv - *k + j) * c_dim1;
+ i__4 = i__ + (lastv - *k + j) * c_dim1;
+ i__5 = i__ + j * work_dim1;
+ q__1.r = c__[i__4].r - work[i__5].r, q__1.i = c__[
+ i__4].i - work[i__5].i;
+ c__[i__3].r = q__1.r, c__[i__3].i = q__1.i;
+/* L110: */
+ }
+/* L120: */
+ }
+ }
+ }
+
+ } else if (lsame_(storev, "R")) {
+
+ if (lsame_(direct, "F")) {
+
+/* Let V = ( V1 V2 ) (V1: first K columns) */
+/* where V1 is unit upper triangular. */
+
+ if (lsame_(side, "L")) {
+
+/* Form H * C or H' * C where C = ( C1 ) */
+/* ( C2 ) */
+
+/* Computing MAX */
+ i__1 = *k, i__2 = ilaclc_(k, m, &v[v_offset], ldv);
+ lastv = max(i__1,i__2);
+ lastc = ilaclc_(&lastv, n, &c__[c_offset], ldc);
+
+/* W := C' * V' = (C1'*V1' + C2'*V2') (stored in WORK) */
+
+/* W := C1' */
+
+ i__1 = *k;
+ for (j = 1; j <= i__1; ++j) {
+ ccopy_(&lastc, &c__[j + c_dim1], ldc, &work[j * work_dim1
+ + 1], &c__1);
+ clacgv_(&lastc, &work[j * work_dim1 + 1], &c__1);
+/* L130: */
+ }
+
+/* W := W * V1' */
+
+ ctrmm_("Right", "Upper", "Conjugate transpose", "Unit", &
+ lastc, k, &c_b1, &v[v_offset], ldv, &work[work_offset]
+, ldwork)
+ ;
+ if (lastv > *k) {
+
+/* W := W + C2'*V2' */
+
+ i__1 = lastv - *k;
+ cgemm_("Conjugate transpose", "Conjugate transpose", &
+ lastc, k, &i__1, &c_b1, &c__[*k + 1 + c_dim1],
+ ldc, &v[(*k + 1) * v_dim1 + 1], ldv, &c_b1, &work[
+ work_offset], ldwork);
+ }
+
+/* W := W * T' or W * T */
+
+ ctrmm_("Right", "Upper", transt, "Non-unit", &lastc, k, &c_b1,
+ &t[t_offset], ldt, &work[work_offset], ldwork);
+
+/* C := C - V' * W' */
+
+ if (lastv > *k) {
+
+/* C2 := C2 - V2' * W' */
+
+ i__1 = lastv - *k;
+ q__1.r = -1.f, q__1.i = -0.f;
+ cgemm_("Conjugate transpose", "Conjugate transpose", &
+ i__1, &lastc, k, &q__1, &v[(*k + 1) * v_dim1 + 1],
+ ldv, &work[work_offset], ldwork, &c_b1, &c__[*k
+ + 1 + c_dim1], ldc);
+ }
+
+/* W := W * V1 */
+
+ ctrmm_("Right", "Upper", "No transpose", "Unit", &lastc, k, &
+ c_b1, &v[v_offset], ldv, &work[work_offset], ldwork);
+
+/* C1 := C1 - W' */
+
+ i__1 = *k;
+ for (j = 1; j <= i__1; ++j) {
+ i__2 = lastc;
+ for (i__ = 1; i__ <= i__2; ++i__) {
+ i__3 = j + i__ * c_dim1;
+ i__4 = j + i__ * c_dim1;
+ r_cnjg(&q__2, &work[i__ + j * work_dim1]);
+ q__1.r = c__[i__4].r - q__2.r, q__1.i = c__[i__4].i -
+ q__2.i;
+ c__[i__3].r = q__1.r, c__[i__3].i = q__1.i;
+/* L140: */
+ }
+/* L150: */
+ }
+
+ } else if (lsame_(side, "R")) {
+
+/* Form C * H or C * H' where C = ( C1 C2 ) */
+
+/* Computing MAX */
+ i__1 = *k, i__2 = ilaclc_(k, n, &v[v_offset], ldv);
+ lastv = max(i__1,i__2);
+ lastc = ilaclr_(m, &lastv, &c__[c_offset], ldc);
+
+/* W := C * V' = (C1*V1' + C2*V2') (stored in WORK) */
+
+/* W := C1 */
+
+ i__1 = *k;
+ for (j = 1; j <= i__1; ++j) {
+ ccopy_(&lastc, &c__[j * c_dim1 + 1], &c__1, &work[j *
+ work_dim1 + 1], &c__1);
+/* L160: */
+ }
+
+/* W := W * V1' */
+
+ ctrmm_("Right", "Upper", "Conjugate transpose", "Unit", &
+ lastc, k, &c_b1, &v[v_offset], ldv, &work[work_offset]
+, ldwork)
+ ;
+ if (lastv > *k) {
+
+/* W := W + C2 * V2' */
+
+ i__1 = lastv - *k;
+ cgemm_("No transpose", "Conjugate transpose", &lastc, k, &
+ i__1, &c_b1, &c__[(*k + 1) * c_dim1 + 1], ldc, &v[
+ (*k + 1) * v_dim1 + 1], ldv, &c_b1, &work[
+ work_offset], ldwork);
+ }
+
+/* W := W * T or W * T' */
+
+ ctrmm_("Right", "Upper", trans, "Non-unit", &lastc, k, &c_b1,
+ &t[t_offset], ldt, &work[work_offset], ldwork);
+
+/* C := C - W * V */
+
+ if (lastv > *k) {
+
+/* C2 := C2 - W * V2 */
+
+ i__1 = lastv - *k;
+ q__1.r = -1.f, q__1.i = -0.f;
+ cgemm_("No transpose", "No transpose", &lastc, &i__1, k, &
+ q__1, &work[work_offset], ldwork, &v[(*k + 1) *
+ v_dim1 + 1], ldv, &c_b1, &c__[(*k + 1) * c_dim1 +
+ 1], ldc);
+ }
+
+/* W := W * V1 */
+
+ ctrmm_("Right", "Upper", "No transpose", "Unit", &lastc, k, &
+ c_b1, &v[v_offset], ldv, &work[work_offset], ldwork);
+
+/* C1 := C1 - W */
+
+ i__1 = *k;
+ for (j = 1; j <= i__1; ++j) {
+ i__2 = lastc;
+ for (i__ = 1; i__ <= i__2; ++i__) {
+ i__3 = i__ + j * c_dim1;
+ i__4 = i__ + j * c_dim1;
+ i__5 = i__ + j * work_dim1;
+ q__1.r = c__[i__4].r - work[i__5].r, q__1.i = c__[
+ i__4].i - work[i__5].i;
+ c__[i__3].r = q__1.r, c__[i__3].i = q__1.i;
+/* L170: */
+ }
+/* L180: */
+ }
+
+ }
+
+ } else {
+
+/* Let V = ( V1 V2 ) (V2: last K columns) */
+/* where V2 is unit lower triangular. */
+
+ if (lsame_(side, "L")) {
+
+/* Form H * C or H' * C where C = ( C1 ) */
+/* ( C2 ) */
+
+/* Computing MAX */
+ i__1 = *k, i__2 = ilaclc_(k, m, &v[v_offset], ldv);
+ lastv = max(i__1,i__2);
+ lastc = ilaclc_(&lastv, n, &c__[c_offset], ldc);
+
+/* W := C' * V' = (C1'*V1' + C2'*V2') (stored in WORK) */
+
+/* W := C2' */
+
+ i__1 = *k;
+ for (j = 1; j <= i__1; ++j) {
+ ccopy_(&lastc, &c__[lastv - *k + j + c_dim1], ldc, &work[
+ j * work_dim1 + 1], &c__1);
+ clacgv_(&lastc, &work[j * work_dim1 + 1], &c__1);
+/* L190: */
+ }
+
+/* W := W * V2' */
+
+ ctrmm_("Right", "Lower", "Conjugate transpose", "Unit", &
+ lastc, k, &c_b1, &v[(lastv - *k + 1) * v_dim1 + 1],
+ ldv, &work[work_offset], ldwork);
+ if (lastv > *k) {
+
+/* W := W + C1'*V1' */
+
+ i__1 = lastv - *k;
+ cgemm_("Conjugate transpose", "Conjugate transpose", &
+ lastc, k, &i__1, &c_b1, &c__[c_offset], ldc, &v[
+ v_offset], ldv, &c_b1, &work[work_offset], ldwork);
+ }
+
+/* W := W * T' or W * T */
+
+ ctrmm_("Right", "Lower", transt, "Non-unit", &lastc, k, &c_b1,
+ &t[t_offset], ldt, &work[work_offset], ldwork);
+
+/* C := C - V' * W' */
+
+ if (lastv > *k) {
+
+/* C1 := C1 - V1' * W' */
+
+ i__1 = lastv - *k;
+ q__1.r = -1.f, q__1.i = -0.f;
+ cgemm_("Conjugate transpose", "Conjugate transpose", &
+ i__1, &lastc, k, &q__1, &v[v_offset], ldv, &work[
+ work_offset], ldwork, &c_b1, &c__[c_offset], ldc);
+ }
+
+/* W := W * V2 */
+
+ ctrmm_("Right", "Lower", "No transpose", "Unit", &lastc, k, &
+ c_b1, &v[(lastv - *k + 1) * v_dim1 + 1], ldv, &work[
+ work_offset], ldwork);
+
+/* C2 := C2 - W' */
+
+ i__1 = *k;
+ for (j = 1; j <= i__1; ++j) {
+ i__2 = lastc;
+ for (i__ = 1; i__ <= i__2; ++i__) {
+ i__3 = lastv - *k + j + i__ * c_dim1;
+ i__4 = lastv - *k + j + i__ * c_dim1;
+ r_cnjg(&q__2, &work[i__ + j * work_dim1]);
+ q__1.r = c__[i__4].r - q__2.r, q__1.i = c__[i__4].i -
+ q__2.i;
+ c__[i__3].r = q__1.r, c__[i__3].i = q__1.i;
+/* L200: */
+ }
+/* L210: */
+ }
+
+ } else if (lsame_(side, "R")) {
+
+/* Form C * H or C * H' where C = ( C1 C2 ) */
+
+/* Computing MAX */
+ i__1 = *k, i__2 = ilaclc_(k, n, &v[v_offset], ldv);
+ lastv = max(i__1,i__2);
+ lastc = ilaclr_(m, &lastv, &c__[c_offset], ldc);
+
+/* W := C * V' = (C1*V1' + C2*V2') (stored in WORK) */
+
+/* W := C2 */
+
+ i__1 = *k;
+ for (j = 1; j <= i__1; ++j) {
+ ccopy_(&lastc, &c__[(lastv - *k + j) * c_dim1 + 1], &c__1,
+ &work[j * work_dim1 + 1], &c__1);
+/* L220: */
+ }
+
+/* W := W * V2' */
+
+ ctrmm_("Right", "Lower", "Conjugate transpose", "Unit", &
+ lastc, k, &c_b1, &v[(lastv - *k + 1) * v_dim1 + 1],
+ ldv, &work[work_offset], ldwork);
+ if (lastv > *k) {
+
+/* W := W + C1 * V1' */
+
+ i__1 = lastv - *k;
+ cgemm_("No transpose", "Conjugate transpose", &lastc, k, &
+ i__1, &c_b1, &c__[c_offset], ldc, &v[v_offset],
+ ldv, &c_b1, &work[work_offset], ldwork);
+ }
+
+/* W := W * T or W * T' */
+
+ ctrmm_("Right", "Lower", trans, "Non-unit", &lastc, k, &c_b1,
+ &t[t_offset], ldt, &work[work_offset], ldwork);
+
+/* C := C - W * V */
+
+ if (lastv > *k) {
+
+/* C1 := C1 - W * V1 */
+
+ i__1 = lastv - *k;
+ q__1.r = -1.f, q__1.i = -0.f;
+ cgemm_("No transpose", "No transpose", &lastc, &i__1, k, &
+ q__1, &work[work_offset], ldwork, &v[v_offset],
+ ldv, &c_b1, &c__[c_offset], ldc);
+ }
+
+/* W := W * V2 */
+
+ ctrmm_("Right", "Lower", "No transpose", "Unit", &lastc, k, &
+ c_b1, &v[(lastv - *k + 1) * v_dim1 + 1], ldv, &work[
+ work_offset], ldwork);
+
+/* C1 := C1 - W */
+
+ i__1 = *k;
+ for (j = 1; j <= i__1; ++j) {
+ i__2 = lastc;
+ for (i__ = 1; i__ <= i__2; ++i__) {
+ i__3 = i__ + (lastv - *k + j) * c_dim1;
+ i__4 = i__ + (lastv - *k + j) * c_dim1;
+ i__5 = i__ + j * work_dim1;
+ q__1.r = c__[i__4].r - work[i__5].r, q__1.i = c__[
+ i__4].i - work[i__5].i;
+ c__[i__3].r = q__1.r, c__[i__3].i = q__1.i;
+/* L230: */
+ }
+/* L240: */
+ }
+
+ }
+
+ }
+ }
+
+ return 0;
+
+/* End of CLARFB */
+
+} /* clarfb_ */
diff --git a/lapack/clarfg.c b/lapack/clarfg.c
new file mode 100644
index 0000000..2a2c3eb
--- /dev/null
+++ b/lapack/clarfg.c
@@ -0,0 +1,190 @@
+/* clarfg.f -- translated by f2c (version 20061008).
+ You must link the resulting object file with libf2c:
+ on Microsoft Windows system, link with libf2c.lib;
+ on Linux or Unix systems, link with .../path/to/libf2c.a -lm
+ or, if you install libf2c.a in a standard place, with -lf2c -lm
+ -- in that order, at the end of the command line, as in
+ cc *.o -lf2c -lm
+ Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
+
+ http://www.netlib.org/f2c/libf2c.zip
+*/
+
+#include "f2c.h"
+#include "blaswrap.h"
+
+/* Table of constant values */
+
+static complex c_b5 = {1.f,0.f};
+
+/* Subroutine */ int clarfg_(integer *n, complex *alpha, complex *x, integer *
+ incx, complex *tau)
+{
+ /* System generated locals */
+ integer i__1;
+ real r__1, r__2;
+ complex q__1, q__2;
+
+ /* Builtin functions */
+ double r_imag(complex *), r_sign(real *, real *);
+
+ /* Local variables */
+ integer j, knt;
+ real beta;
+ extern /* Subroutine */ int cscal_(integer *, complex *, complex *,
+ integer *);
+ real alphi, alphr, xnorm;
+ extern doublereal scnrm2_(integer *, complex *, integer *), slapy3_(real *
+, real *, real *);
+ extern /* Complex */ VOID cladiv_(complex *, complex *, complex *);
+ extern doublereal slamch_(char *);
+ extern /* Subroutine */ int csscal_(integer *, real *, complex *, integer
+ *);
+ real safmin, rsafmn;
+
+
+/* -- LAPACK auxiliary routine (version 3.2) -- */
+/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
+/* November 2006 */
+
+/* .. Scalar Arguments .. */
+/* .. */
+/* .. Array Arguments .. */
+/* .. */
+
+/* Purpose */
+/* ======= */
+
+/* CLARFG generates a complex elementary reflector H of order n, such */
+/* that */
+
+/* H' * ( alpha ) = ( beta ), H' * H = I. */
+/* ( x ) ( 0 ) */
+
+/* where alpha and beta are scalars, with beta real, and x is an */
+/* (n-1)-element complex vector. H is represented in the form */
+
+/* H = I - tau * ( 1 ) * ( 1 v' ) , */
+/* ( v ) */
+
+/* where tau is a complex scalar and v is a complex (n-1)-element */
+/* vector. Note that H is not hermitian. */
+
+/* If the elements of x are all zero and alpha is real, then tau = 0 */
+/* and H is taken to be the unit matrix. */
+
+/* Otherwise 1 <= real(tau) <= 2 and abs(tau-1) <= 1 . */
+
+/* Arguments */
+/* ========= */
+
+/* N (input) INTEGER */
+/* The order of the elementary reflector. */
+
+/* ALPHA (input/output) COMPLEX */
+/* On entry, the value alpha. */
+/* On exit, it is overwritten with the value beta. */
+
+/* X (input/output) COMPLEX array, dimension */
+/* (1+(N-2)*abs(INCX)) */
+/* On entry, the vector x. */
+/* On exit, it is overwritten with the vector v. */
+
+/* INCX (input) INTEGER */
+/* The increment between elements of X. INCX > 0. */
+
+/* TAU (output) COMPLEX */
+/* The value tau. */
+
+/* ===================================================================== */
+
+/* .. Parameters .. */
+/* .. */
+/* .. Local Scalars .. */
+/* .. */
+/* .. External Functions .. */
+/* .. */
+/* .. Intrinsic Functions .. */
+/* .. */
+/* .. External Subroutines .. */
+/* .. */
+/* .. Executable Statements .. */
+
+ /* Parameter adjustments */
+ --x;
+
+ /* Function Body */
+ if (*n <= 0) {
+ tau->r = 0.f, tau->i = 0.f;
+ return 0;
+ }
+
+ i__1 = *n - 1;
+ xnorm = scnrm2_(&i__1, &x[1], incx);
+ alphr = alpha->r;
+ alphi = r_imag(alpha);
+
+ if (xnorm == 0.f && alphi == 0.f) {
+
+/* H = I */
+
+ tau->r = 0.f, tau->i = 0.f;
+ } else {
+
+/* general case */
+
+ r__1 = slapy3_(&alphr, &alphi, &xnorm);
+ beta = -r_sign(&r__1, &alphr);
+ safmin = slamch_("S") / slamch_("E");
+ rsafmn = 1.f / safmin;
+
+ knt = 0;
+ if (dabs(beta) < safmin) {
+
+/* XNORM, BETA may be inaccurate; scale X and recompute them */
+
+L10:
+ ++knt;
+ i__1 = *n - 1;
+ csscal_(&i__1, &rsafmn, &x[1], incx);
+ beta *= rsafmn;
+ alphi *= rsafmn;
+ alphr *= rsafmn;
+ if (dabs(beta) < safmin) {
+ goto L10;
+ }
+
+/* New BETA is at most 1, at least SAFMIN */
+
+ i__1 = *n - 1;
+ xnorm = scnrm2_(&i__1, &x[1], incx);
+ q__1.r = alphr, q__1.i = alphi;
+ alpha->r = q__1.r, alpha->i = q__1.i;
+ r__1 = slapy3_(&alphr, &alphi, &xnorm);
+ beta = -r_sign(&r__1, &alphr);
+ }
+ r__1 = (beta - alphr) / beta;
+ r__2 = -alphi / beta;
+ q__1.r = r__1, q__1.i = r__2;
+ tau->r = q__1.r, tau->i = q__1.i;
+ q__2.r = alpha->r - beta, q__2.i = alpha->i;
+ cladiv_(&q__1, &c_b5, &q__2);
+ alpha->r = q__1.r, alpha->i = q__1.i;
+ i__1 = *n - 1;
+ cscal_(&i__1, alpha, &x[1], incx);
+
+/* If ALPHA is subnormal, it may lose relative accuracy */
+
+ i__1 = knt;
+ for (j = 1; j <= i__1; ++j) {
+ beta *= safmin;
+/* L20: */
+ }
+ alpha->r = beta, alpha->i = 0.f;
+ }
+
+ return 0;
+
+/* End of CLARFG */
+
+} /* clarfg_ */
diff --git a/lapack/clarft.c b/lapack/clarft.c
new file mode 100644
index 0000000..ca573e4
--- /dev/null
+++ b/lapack/clarft.c
@@ -0,0 +1,361 @@
+/* clarft.f -- translated by f2c (version 20061008).
+ You must link the resulting object file with libf2c:
+ on Microsoft Windows system, link with libf2c.lib;
+ on Linux or Unix systems, link with .../path/to/libf2c.a -lm
+ or, if you install libf2c.a in a standard place, with -lf2c -lm
+ -- in that order, at the end of the command line, as in
+ cc *.o -lf2c -lm
+ Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
+
+ http://www.netlib.org/f2c/libf2c.zip
+*/
+
+#include "f2c.h"
+#include "blaswrap.h"
+
+/* Table of constant values */
+
+static complex c_b2 = {0.f,0.f};
+static integer c__1 = 1;
+
+/* Subroutine */ int clarft_(char *direct, char *storev, integer *n, integer *
+ k, complex *v, integer *ldv, complex *tau, complex *t, integer *ldt)
+{
+ /* System generated locals */
+ integer t_dim1, t_offset, v_dim1, v_offset, i__1, i__2, i__3, i__4;
+ complex q__1;
+
+ /* Local variables */
+ integer i__, j, prevlastv;
+ complex vii;
+ extern /* Subroutine */ int cgemv_(char *, integer *, integer *, complex *
+, complex *, integer *, complex *, integer *, complex *, complex *
+, integer *);
+ extern logical lsame_(char *, char *);
+ integer lastv;
+ extern /* Subroutine */ int ctrmv_(char *, char *, char *, integer *,
+ complex *, integer *, complex *, integer *), clacgv_(integer *, complex *, integer *);
+
+
+/* -- LAPACK auxiliary routine (version 3.2) -- */
+/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
+/* November 2006 */
+
+/* .. Scalar Arguments .. */
+/* .. */
+/* .. Array Arguments .. */
+/* .. */
+
+/* Purpose */
+/* ======= */
+
+/* CLARFT forms the triangular factor T of a complex block reflector H */
+/* of order n, which is defined as a product of k elementary reflectors. */
+
+/* If DIRECT = 'F', H = H(1) H(2) . . . H(k) and T is upper triangular; */
+
+/* If DIRECT = 'B', H = H(k) . . . H(2) H(1) and T is lower triangular. */
+
+/* If STOREV = 'C', the vector which defines the elementary reflector */
+/* H(i) is stored in the i-th column of the array V, and */
+
+/* H = I - V * T * V' */
+
+/* If STOREV = 'R', the vector which defines the elementary reflector */
+/* H(i) is stored in the i-th row of the array V, and */
+
+/* H = I - V' * T * V */
+
+/* Arguments */
+/* ========= */
+
+/* DIRECT (input) CHARACTER*1 */
+/* Specifies the order in which the elementary reflectors are */
+/* multiplied to form the block reflector: */
+/* = 'F': H = H(1) H(2) . . . H(k) (Forward) */
+/* = 'B': H = H(k) . . . H(2) H(1) (Backward) */
+
+/* STOREV (input) CHARACTER*1 */
+/* Specifies how the vectors which define the elementary */
+/* reflectors are stored (see also Further Details): */
+/* = 'C': columnwise */
+/* = 'R': rowwise */
+
+/* N (input) INTEGER */
+/* The order of the block reflector H. N >= 0. */
+
+/* K (input) INTEGER */
+/* The order of the triangular factor T (= the number of */
+/* elementary reflectors). K >= 1. */
+
+/* V (input/output) COMPLEX array, dimension */
+/* (LDV,K) if STOREV = 'C' */
+/* (LDV,N) if STOREV = 'R' */
+/* The matrix V. See further details. */
+
+/* LDV (input) INTEGER */
+/* The leading dimension of the array V. */
+/* If STOREV = 'C', LDV >= max(1,N); if STOREV = 'R', LDV >= K. */
+
+/* TAU (input) COMPLEX array, dimension (K) */
+/* TAU(i) must contain the scalar factor of the elementary */
+/* reflector H(i). */
+
+/* T (output) COMPLEX array, dimension (LDT,K) */
+/* The k by k triangular factor T of the block reflector. */
+/* If DIRECT = 'F', T is upper triangular; if DIRECT = 'B', T is */
+/* lower triangular. The rest of the array is not used. */
+
+/* LDT (input) INTEGER */
+/* The leading dimension of the array T. LDT >= K. */
+
+/* Further Details */
+/* =============== */
+
+/* The shape of the matrix V and the storage of the vectors which define */
+/* the H(i) is best illustrated by the following example with n = 5 and */
+/* k = 3. The elements equal to 1 are not stored; the corresponding */
+/* array elements are modified but restored on exit. The rest of the */
+/* array is not used. */
+
+/* DIRECT = 'F' and STOREV = 'C': DIRECT = 'F' and STOREV = 'R': */
+
+/* V = ( 1 ) V = ( 1 v1 v1 v1 v1 ) */
+/* ( v1 1 ) ( 1 v2 v2 v2 ) */
+/* ( v1 v2 1 ) ( 1 v3 v3 ) */
+/* ( v1 v2 v3 ) */
+/* ( v1 v2 v3 ) */
+
+/* DIRECT = 'B' and STOREV = 'C': DIRECT = 'B' and STOREV = 'R': */
+
+/* V = ( v1 v2 v3 ) V = ( v1 v1 1 ) */
+/* ( v1 v2 v3 ) ( v2 v2 v2 1 ) */
+/* ( 1 v2 v3 ) ( v3 v3 v3 v3 1 ) */
+/* ( 1 v3 ) */
+/* ( 1 ) */
+
+/* ===================================================================== */
+
+/* .. Parameters .. */
+/* .. */
+/* .. Local Scalars .. */
+/* .. */
+/* .. External Subroutines .. */
+/* .. */
+/* .. External Functions .. */
+/* .. */
+/* .. Executable Statements .. */
+
+/* Quick return if possible */
+
+ /* Parameter adjustments */
+ v_dim1 = *ldv;
+ v_offset = 1 + v_dim1;
+ v -= v_offset;
+ --tau;
+ t_dim1 = *ldt;
+ t_offset = 1 + t_dim1;
+ t -= t_offset;
+
+ /* Function Body */
+ if (*n == 0) {
+ return 0;
+ }
+
+ if (lsame_(direct, "F")) {
+ prevlastv = *n;
+ i__1 = *k;
+ for (i__ = 1; i__ <= i__1; ++i__) {
+ prevlastv = max(prevlastv,i__);
+ i__2 = i__;
+ if (tau[i__2].r == 0.f && tau[i__2].i == 0.f) {
+
+/* H(i) = I */
+
+ i__2 = i__;
+ for (j = 1; j <= i__2; ++j) {
+ i__3 = j + i__ * t_dim1;
+ t[i__3].r = 0.f, t[i__3].i = 0.f;
+/* L10: */
+ }
+ } else {
+
+/* general case */
+
+ i__2 = i__ + i__ * v_dim1;
+ vii.r = v[i__2].r, vii.i = v[i__2].i;
+ i__2 = i__ + i__ * v_dim1;
+ v[i__2].r = 1.f, v[i__2].i = 0.f;
+ if (lsame_(storev, "C")) {
+/* Skip any trailing zeros. */
+ i__2 = i__ + 1;
+ for (lastv = *n; lastv >= i__2; --lastv) {
+ i__3 = lastv + i__ * v_dim1;
+ if (v[i__3].r != 0.f || v[i__3].i != 0.f) {
+ break;
+ }
+ }
+ j = min(lastv,prevlastv);
+
+/* T(1:i-1,i) := - tau(i) * V(i:j,1:i-1)' * V(i:j,i) */
+
+ i__2 = j - i__ + 1;
+ i__3 = i__ - 1;
+ i__4 = i__;
+ q__1.r = -tau[i__4].r, q__1.i = -tau[i__4].i;
+ cgemv_("Conjugate transpose", &i__2, &i__3, &q__1, &v[i__
+ + v_dim1], ldv, &v[i__ + i__ * v_dim1], &c__1, &
+ c_b2, &t[i__ * t_dim1 + 1], &c__1);
+ } else {
+/* Skip any trailing zeros. */
+ i__2 = i__ + 1;
+ for (lastv = *n; lastv >= i__2; --lastv) {
+ i__3 = i__ + lastv * v_dim1;
+ if (v[i__3].r != 0.f || v[i__3].i != 0.f) {
+ break;
+ }
+ }
+ j = min(lastv,prevlastv);
+
+/* T(1:i-1,i) := - tau(i) * V(1:i-1,i:j) * V(i,i:j)' */
+
+ if (i__ < j) {
+ i__2 = j - i__;
+ clacgv_(&i__2, &v[i__ + (i__ + 1) * v_dim1], ldv);
+ }
+ i__2 = i__ - 1;
+ i__3 = j - i__ + 1;
+ i__4 = i__;
+ q__1.r = -tau[i__4].r, q__1.i = -tau[i__4].i;
+ cgemv_("No transpose", &i__2, &i__3, &q__1, &v[i__ *
+ v_dim1 + 1], ldv, &v[i__ + i__ * v_dim1], ldv, &
+ c_b2, &t[i__ * t_dim1 + 1], &c__1);
+ if (i__ < j) {
+ i__2 = j - i__;
+ clacgv_(&i__2, &v[i__ + (i__ + 1) * v_dim1], ldv);
+ }
+ }
+ i__2 = i__ + i__ * v_dim1;
+ v[i__2].r = vii.r, v[i__2].i = vii.i;
+
+/* T(1:i-1,i) := T(1:i-1,1:i-1) * T(1:i-1,i) */
+
+ i__2 = i__ - 1;
+ ctrmv_("Upper", "No transpose", "Non-unit", &i__2, &t[
+ t_offset], ldt, &t[i__ * t_dim1 + 1], &c__1);
+ i__2 = i__ + i__ * t_dim1;
+ i__3 = i__;
+ t[i__2].r = tau[i__3].r, t[i__2].i = tau[i__3].i;
+ if (i__ > 1) {
+ prevlastv = max(prevlastv,lastv);
+ } else {
+ prevlastv = lastv;
+ }
+ }
+/* L20: */
+ }
+ } else {
+ prevlastv = 1;
+ for (i__ = *k; i__ >= 1; --i__) {
+ i__1 = i__;
+ if (tau[i__1].r == 0.f && tau[i__1].i == 0.f) {
+
+/* H(i) = I */
+
+ i__1 = *k;
+ for (j = i__; j <= i__1; ++j) {
+ i__2 = j + i__ * t_dim1;
+ t[i__2].r = 0.f, t[i__2].i = 0.f;
+/* L30: */
+ }
+ } else {
+
+/* general case */
+
+ if (i__ < *k) {
+ if (lsame_(storev, "C")) {
+ i__1 = *n - *k + i__ + i__ * v_dim1;
+ vii.r = v[i__1].r, vii.i = v[i__1].i;
+ i__1 = *n - *k + i__ + i__ * v_dim1;
+ v[i__1].r = 1.f, v[i__1].i = 0.f;
+/* Skip any leading zeros. */
+ i__1 = i__ - 1;
+ for (lastv = 1; lastv <= i__1; ++lastv) {
+ i__2 = lastv + i__ * v_dim1;
+ if (v[i__2].r != 0.f || v[i__2].i != 0.f) {
+ break;
+ }
+ }
+ j = max(lastv,prevlastv);
+
+/* T(i+1:k,i) := */
+/* - tau(i) * V(j:n-k+i,i+1:k)' * V(j:n-k+i,i) */
+
+ i__1 = *n - *k + i__ - j + 1;
+ i__2 = *k - i__;
+ i__3 = i__;
+ q__1.r = -tau[i__3].r, q__1.i = -tau[i__3].i;
+ cgemv_("Conjugate transpose", &i__1, &i__2, &q__1, &v[
+ j + (i__ + 1) * v_dim1], ldv, &v[j + i__ *
+ v_dim1], &c__1, &c_b2, &t[i__ + 1 + i__ *
+ t_dim1], &c__1);
+ i__1 = *n - *k + i__ + i__ * v_dim1;
+ v[i__1].r = vii.r, v[i__1].i = vii.i;
+ } else {
+ i__1 = i__ + (*n - *k + i__) * v_dim1;
+ vii.r = v[i__1].r, vii.i = v[i__1].i;
+ i__1 = i__ + (*n - *k + i__) * v_dim1;
+ v[i__1].r = 1.f, v[i__1].i = 0.f;
+/* Skip any leading zeros. */
+ i__1 = i__ - 1;
+ for (lastv = 1; lastv <= i__1; ++lastv) {
+ i__2 = i__ + lastv * v_dim1;
+ if (v[i__2].r != 0.f || v[i__2].i != 0.f) {
+ break;
+ }
+ }
+ j = max(lastv,prevlastv);
+
+/* T(i+1:k,i) := */
+/* - tau(i) * V(i+1:k,j:n-k+i) * V(i,j:n-k+i)' */
+
+ i__1 = *n - *k + i__ - 1 - j + 1;
+ clacgv_(&i__1, &v[i__ + j * v_dim1], ldv);
+ i__1 = *k - i__;
+ i__2 = *n - *k + i__ - j + 1;
+ i__3 = i__;
+ q__1.r = -tau[i__3].r, q__1.i = -tau[i__3].i;
+ cgemv_("No transpose", &i__1, &i__2, &q__1, &v[i__ +
+ 1 + j * v_dim1], ldv, &v[i__ + j * v_dim1],
+ ldv, &c_b2, &t[i__ + 1 + i__ * t_dim1], &c__1);
+ i__1 = *n - *k + i__ - 1 - j + 1;
+ clacgv_(&i__1, &v[i__ + j * v_dim1], ldv);
+ i__1 = i__ + (*n - *k + i__) * v_dim1;
+ v[i__1].r = vii.r, v[i__1].i = vii.i;
+ }
+
+/* T(i+1:k,i) := T(i+1:k,i+1:k) * T(i+1:k,i) */
+
+ i__1 = *k - i__;
+ ctrmv_("Lower", "No transpose", "Non-unit", &i__1, &t[i__
+ + 1 + (i__ + 1) * t_dim1], ldt, &t[i__ + 1 + i__ *
+ t_dim1], &c__1)
+ ;
+ if (i__ > 1) {
+ prevlastv = min(prevlastv,lastv);
+ } else {
+ prevlastv = lastv;
+ }
+ }
+ i__1 = i__ + i__ * t_dim1;
+ i__2 = i__;
+ t[i__1].r = tau[i__2].r, t[i__1].i = tau[i__2].i;
+ }
+/* L40: */
+ }
+ }
+ return 0;
+
+/* End of CLARFT */
+
+} /* clarft_ */
diff --git a/lapack/complex_double.cpp b/lapack/complex_double.cpp
new file mode 100644
index 0000000..492f743
--- /dev/null
+++ b/lapack/complex_double.cpp
@@ -0,0 +1,18 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009-2014 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#define SCALAR std::complex<double>
+#define SCALAR_SUFFIX z
+#define SCALAR_SUFFIX_UP "Z"
+#define REAL_SCALAR_SUFFIX d
+#define ISCOMPLEX 1
+
+#include "cholesky.inc"
+#include "lu.inc"
+#include "svd.inc"
diff --git a/lapack/complex_single.cpp b/lapack/complex_single.cpp
new file mode 100644
index 0000000..cdf989e
--- /dev/null
+++ b/lapack/complex_single.cpp
@@ -0,0 +1,18 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009-2014 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#define SCALAR std::complex<float>
+#define SCALAR_SUFFIX c
+#define SCALAR_SUFFIX_UP "C"
+#define REAL_SCALAR_SUFFIX s
+#define ISCOMPLEX 1
+
+#include "cholesky.inc"
+#include "lu.inc"
+#include "svd.inc"
diff --git a/lapack/dladiv.c b/lapack/dladiv.c
new file mode 100644
index 0000000..20fbe6b
--- /dev/null
+++ b/lapack/dladiv.c
@@ -0,0 +1,78 @@
+/* dladiv.f -- translated by f2c (version 20061008).
+ You must link the resulting object file with libf2c:
+ on Microsoft Windows system, link with libf2c.lib;
+ on Linux or Unix systems, link with .../path/to/libf2c.a -lm
+ or, if you install libf2c.a in a standard place, with -lf2c -lm
+ -- in that order, at the end of the command line, as in
+ cc *.o -lf2c -lm
+ Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
+
+ http://www.netlib.org/f2c/libf2c.zip
+*/
+
+#include "f2c.h"
+#include "blaswrap.h"
+
+/* Subroutine */ int dladiv_(doublereal *a, doublereal *b, doublereal *c__,
+ doublereal *d__, doublereal *p, doublereal *q)
+{
+ doublereal e, f;
+
+
+/* -- LAPACK auxiliary routine (version 3.2) -- */
+/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
+/* November 2006 */
+
+/* .. Scalar Arguments .. */
+/* .. */
+
+/* Purpose */
+/* ======= */
+
+/* DLADIV performs complex division in real arithmetic */
+
+/* a + i*b */
+/* p + i*q = --------- */
+/* c + i*d */
+
+/* The algorithm is due to Robert L. Smith and can be found */
+/* in D. Knuth, The art of Computer Programming, Vol.2, p.195 */
+
+/* Arguments */
+/* ========= */
+
+/* A (input) DOUBLE PRECISION */
+/* B (input) DOUBLE PRECISION */
+/* C (input) DOUBLE PRECISION */
+/* D (input) DOUBLE PRECISION */
+/* The scalars a, b, c, and d in the above expression. */
+
+/* P (output) DOUBLE PRECISION */
+/* Q (output) DOUBLE PRECISION */
+/* The scalars p and q in the above expression. */
+
+/* ===================================================================== */
+
+/* .. Local Scalars .. */
+/* .. */
+/* .. Intrinsic Functions .. */
+/* .. */
+/* .. Executable Statements .. */
+
+ if (abs(*d__) < abs(*c__)) {
+ e = *d__ / *c__;
+ f = *c__ + *d__ * e;
+ *p = (*a + *b * e) / f;
+ *q = (*b - *a * e) / f;
+ } else {
+ e = *c__ / *d__;
+ f = *d__ + *c__ * e;
+ *p = (*b + *a * e) / f;
+ *q = (-(*a) + *b * e) / f;
+ }
+
+ return 0;
+
+/* End of DLADIV */
+
+} /* dladiv_ */
diff --git a/lapack/dlamch.c b/lapack/dlamch.c
new file mode 100644
index 0000000..e224439
--- /dev/null
+++ b/lapack/dlamch.c
@@ -0,0 +1,1001 @@
+/* dlamch.f -- translated by f2c (version 20061008).
+ You must link the resulting object file with libf2c:
+ on Microsoft Windows system, link with libf2c.lib;
+ on Linux or Unix systems, link with .../path/to/libf2c.a -lm
+ or, if you install libf2c.a in a standard place, with -lf2c -lm
+ -- in that order, at the end of the command line, as in
+ cc *.o -lf2c -lm
+ Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
+
+ http://www.netlib.org/f2c/libf2c.zip
+*/
+
+#include "f2c.h"
+#include "blaswrap.h"
+
+/* Table of constant values */
+
+static integer c__1 = 1;
+static doublereal c_b32 = 0.;
+
+doublereal dlamch_(char *cmach)
+{
+ /* Initialized data */
+
+ static logical first = TRUE_;
+
+ /* System generated locals */
+ integer i__1;
+ doublereal ret_val;
+
+ /* Builtin functions */
+ double pow_di(doublereal *, integer *);
+
+ /* Local variables */
+ static doublereal t;
+ integer it;
+ static doublereal rnd, eps, base;
+ integer beta;
+ static doublereal emin, prec, emax;
+ integer imin, imax;
+ logical lrnd = 0;
+ static doublereal rmin, rmax;
+ doublereal rmach = 0;
+ extern logical lsame_(char *, char *);
+ doublereal small;
+ static doublereal sfmin;
+ extern /* Subroutine */ int dlamc2_(integer *, integer *, logical *,
+ doublereal *, integer *, doublereal *, integer *, doublereal *);
+
+
+/* -- LAPACK auxiliary routine (version 3.2) -- */
+/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
+/* November 2006 */
+
+/* .. Scalar Arguments .. */
+/* .. */
+
+/* Purpose */
+/* ======= */
+
+/* DLAMCH determines double precision machine parameters. */
+
+/* Arguments */
+/* ========= */
+
+/* CMACH (input) CHARACTER*1 */
+/* Specifies the value to be returned by DLAMCH: */
+/* = 'E' or 'e', DLAMCH := eps */
+/* = 'S' or 's , DLAMCH := sfmin */
+/* = 'B' or 'b', DLAMCH := base */
+/* = 'P' or 'p', DLAMCH := eps*base */
+/* = 'N' or 'n', DLAMCH := t */
+/* = 'R' or 'r', DLAMCH := rnd */
+/* = 'M' or 'm', DLAMCH := emin */
+/* = 'U' or 'u', DLAMCH := rmin */
+/* = 'L' or 'l', DLAMCH := emax */
+/* = 'O' or 'o', DLAMCH := rmax */
+
+/* where */
+
+/* eps = relative machine precision */
+/* sfmin = safe minimum, such that 1/sfmin does not overflow */
+/* base = base of the machine */
+/* prec = eps*base */
+/* t = number of (base) digits in the mantissa */
+/* rnd = 1.0 when rounding occurs in addition, 0.0 otherwise */
+/* emin = minimum exponent before (gradual) underflow */
+/* rmin = underflow threshold - base**(emin-1) */
+/* emax = largest exponent before overflow */
+/* rmax = overflow threshold - (base**emax)*(1-eps) */
+
+/* ===================================================================== */
+
+/* .. Parameters .. */
+/* .. */
+/* .. Local Scalars .. */
+/* .. */
+/* .. External Functions .. */
+/* .. */
+/* .. External Subroutines .. */
+/* .. */
+/* .. Save statement .. */
+/* .. */
+/* .. Data statements .. */
+/* .. */
+/* .. Executable Statements .. */
+
+ if (first) {
+ dlamc2_(&beta, &it, &lrnd, &eps, &imin, &rmin, &imax, &rmax);
+ base = (doublereal) beta;
+ t = (doublereal) it;
+ if (lrnd) {
+ rnd = 1.;
+ i__1 = 1 - it;
+ eps = pow_di(&base, &i__1) / 2;
+ } else {
+ rnd = 0.;
+ i__1 = 1 - it;
+ eps = pow_di(&base, &i__1);
+ }
+ prec = eps * base;
+ emin = (doublereal) imin;
+ emax = (doublereal) imax;
+ sfmin = rmin;
+ small = 1. / rmax;
+ if (small >= sfmin) {
+
+/* Use SMALL plus a bit, to avoid the possibility of rounding */
+/* causing overflow when computing 1/sfmin. */
+
+ sfmin = small * (eps + 1.);
+ }
+ }
+
+ if (lsame_(cmach, "E")) {
+ rmach = eps;
+ } else if (lsame_(cmach, "S")) {
+ rmach = sfmin;
+ } else if (lsame_(cmach, "B")) {
+ rmach = base;
+ } else if (lsame_(cmach, "P")) {
+ rmach = prec;
+ } else if (lsame_(cmach, "N")) {
+ rmach = t;
+ } else if (lsame_(cmach, "R")) {
+ rmach = rnd;
+ } else if (lsame_(cmach, "M")) {
+ rmach = emin;
+ } else if (lsame_(cmach, "U")) {
+ rmach = rmin;
+ } else if (lsame_(cmach, "L")) {
+ rmach = emax;
+ } else if (lsame_(cmach, "O")) {
+ rmach = rmax;
+ }
+
+ ret_val = rmach;
+ first = FALSE_;
+ return ret_val;
+
+/* End of DLAMCH */
+
+} /* dlamch_ */
+
+
+/* *********************************************************************** */
+
+/* Subroutine */ int dlamc1_(integer *beta, integer *t, logical *rnd, logical
+ *ieee1)
+{
+ /* Initialized data */
+
+ static logical first = TRUE_;
+
+ /* System generated locals */
+ doublereal d__1, d__2;
+
+ /* Local variables */
+ doublereal a, b, c__, f, t1, t2;
+ static integer lt;
+ doublereal one, qtr;
+ static logical lrnd;
+ static integer lbeta;
+ doublereal savec;
+ extern doublereal dlamc3_(doublereal *, doublereal *);
+ static logical lieee1;
+
+
+/* -- LAPACK auxiliary routine (version 3.2) -- */
+/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
+/* November 2006 */
+
+/* .. Scalar Arguments .. */
+/* .. */
+
+/* Purpose */
+/* ======= */
+
+/* DLAMC1 determines the machine parameters given by BETA, T, RND, and */
+/* IEEE1. */
+
+/* Arguments */
+/* ========= */
+
+/* BETA (output) INTEGER */
+/* The base of the machine. */
+
+/* T (output) INTEGER */
+/* The number of ( BETA ) digits in the mantissa. */
+
+/* RND (output) LOGICAL */
+/* Specifies whether proper rounding ( RND = .TRUE. ) or */
+/* chopping ( RND = .FALSE. ) occurs in addition. This may not */
+/* be a reliable guide to the way in which the machine performs */
+/* its arithmetic. */
+
+/* IEEE1 (output) LOGICAL */
+/* Specifies whether rounding appears to be done in the IEEE */
+/* 'round to nearest' style. */
+
+/* Further Details */
+/* =============== */
+
+/* The routine is based on the routine ENVRON by Malcolm and */
+/* incorporates suggestions by Gentleman and Marovich. See */
+
+/* Malcolm M. A. (1972) Algorithms to reveal properties of */
+/* floating-point arithmetic. Comms. of the ACM, 15, 949-951. */
+
+/* Gentleman W. M. and Marovich S. B. (1974) More on algorithms */
+/* that reveal properties of floating point arithmetic units. */
+/* Comms. of the ACM, 17, 276-277. */
+
+/* ===================================================================== */
+
+/* .. Local Scalars .. */
+/* .. */
+/* .. External Functions .. */
+/* .. */
+/* .. Save statement .. */
+/* .. */
+/* .. Data statements .. */
+/* .. */
+/* .. Executable Statements .. */
+
+ if (first) {
+ one = 1.;
+
+/* LBETA, LIEEE1, LT and LRND are the local values of BETA, */
+/* IEEE1, T and RND. */
+
+/* Throughout this routine we use the function DLAMC3 to ensure */
+/* that relevant values are stored and not held in registers, or */
+/* are not affected by optimizers. */
+
+/* Compute a = 2.0**m with the smallest positive integer m such */
+/* that */
+
+/* fl( a + 1.0 ) = a. */
+
+ a = 1.;
+ c__ = 1.;
+
+/* + WHILE( C.EQ.ONE )LOOP */
+L10:
+ if (c__ == one) {
+ a *= 2;
+ c__ = dlamc3_(&a, &one);
+ d__1 = -a;
+ c__ = dlamc3_(&c__, &d__1);
+ goto L10;
+ }
+/* + END WHILE */
+
+/* Now compute b = 2.0**m with the smallest positive integer m */
+/* such that */
+
+/* fl( a + b ) .gt. a. */
+
+ b = 1.;
+ c__ = dlamc3_(&a, &b);
+
+/* + WHILE( C.EQ.A )LOOP */
+L20:
+ if (c__ == a) {
+ b *= 2;
+ c__ = dlamc3_(&a, &b);
+ goto L20;
+ }
+/* + END WHILE */
+
+/* Now compute the base. a and c are neighbouring floating point */
+/* numbers in the interval ( beta**t, beta**( t + 1 ) ) and so */
+/* their difference is beta. Adding 0.25 to c is to ensure that it */
+/* is truncated to beta and not ( beta - 1 ). */
+
+ qtr = one / 4;
+ savec = c__;
+ d__1 = -a;
+ c__ = dlamc3_(&c__, &d__1);
+ lbeta = (integer) (c__ + qtr);
+
+/* Now determine whether rounding or chopping occurs, by adding a */
+/* bit less than beta/2 and a bit more than beta/2 to a. */
+
+ b = (doublereal) lbeta;
+ d__1 = b / 2;
+ d__2 = -b / 100;
+ f = dlamc3_(&d__1, &d__2);
+ c__ = dlamc3_(&f, &a);
+ if (c__ == a) {
+ lrnd = TRUE_;
+ } else {
+ lrnd = FALSE_;
+ }
+ d__1 = b / 2;
+ d__2 = b / 100;
+ f = dlamc3_(&d__1, &d__2);
+ c__ = dlamc3_(&f, &a);
+ if (lrnd && c__ == a) {
+ lrnd = FALSE_;
+ }
+
+/* Try and decide whether rounding is done in the IEEE 'round to */
+/* nearest' style. B/2 is half a unit in the last place of the two */
+/* numbers A and SAVEC. Furthermore, A is even, i.e. has last bit */
+/* zero, and SAVEC is odd. Thus adding B/2 to A should not change */
+/* A, but adding B/2 to SAVEC should change SAVEC. */
+
+ d__1 = b / 2;
+ t1 = dlamc3_(&d__1, &a);
+ d__1 = b / 2;
+ t2 = dlamc3_(&d__1, &savec);
+ lieee1 = t1 == a && t2 > savec && lrnd;
+
+/* Now find the mantissa, t. It should be the integer part of */
+/* log to the base beta of a, however it is safer to determine t */
+/* by powering. So we find t as the smallest positive integer for */
+/* which */
+
+/* fl( beta**t + 1.0 ) = 1.0. */
+
+ lt = 0;
+ a = 1.;
+ c__ = 1.;
+
+/* + WHILE( C.EQ.ONE )LOOP */
+L30:
+ if (c__ == one) {
+ ++lt;
+ a *= lbeta;
+ c__ = dlamc3_(&a, &one);
+ d__1 = -a;
+ c__ = dlamc3_(&c__, &d__1);
+ goto L30;
+ }
+/* + END WHILE */
+
+ }
+
+ *beta = lbeta;
+ *t = lt;
+ *rnd = lrnd;
+ *ieee1 = lieee1;
+ first = FALSE_;
+ return 0;
+
+/* End of DLAMC1 */
+
+} /* dlamc1_ */
+
+
+/* *********************************************************************** */
+
+/* Subroutine */ int dlamc2_(integer *beta, integer *t, logical *rnd,
+ doublereal *eps, integer *emin, doublereal *rmin, integer *emax,
+ doublereal *rmax)
+{
+ /* Initialized data */
+
+ static logical first = TRUE_;
+ static logical iwarn = FALSE_;
+
+ /* Format strings */
+ static char fmt_9999[] = "(//\002 WARNING. The value EMIN may be incorre"
+ "ct:-\002,\002 EMIN = \002,i8,/\002 If, after inspection, the va"
+ "lue EMIN looks\002,\002 acceptable please comment out \002,/\002"
+ " the IF block as marked within the code of routine\002,\002 DLAM"
+ "C2,\002,/\002 otherwise supply EMIN explicitly.\002,/)";
+
+ /* System generated locals */
+ integer i__1;
+ doublereal d__1, d__2, d__3, d__4, d__5;
+
+ /* Builtin functions */
+ double pow_di(doublereal *, integer *);
+ integer s_wsfe(cilist *), do_fio(integer *, char *, ftnlen), e_wsfe(void);
+
+ /* Local variables */
+ doublereal a, b, c__;
+ integer i__;
+ static integer lt;
+ doublereal one, two;
+ logical ieee;
+ doublereal half;
+ logical lrnd = 0;
+ static doublereal leps;
+ doublereal zero;
+ static integer lbeta;
+ doublereal rbase;
+ static integer lemin, lemax;
+ integer gnmin;
+ doublereal small;
+ integer gpmin;
+ doublereal third;
+ static doublereal lrmin, lrmax;
+ doublereal sixth;
+ extern /* Subroutine */ int dlamc1_(integer *, integer *, logical *,
+ logical *);
+ extern doublereal dlamc3_(doublereal *, doublereal *);
+ logical lieee1;
+ extern /* Subroutine */ int dlamc4_(integer *, doublereal *, integer *),
+ dlamc5_(integer *, integer *, integer *, logical *, integer *,
+ doublereal *);
+ integer ngnmin, ngpmin;
+
+ /* Fortran I/O blocks */
+ static cilist io___58 = { 0, 6, 0, fmt_9999, 0 };
+
+
+
+/* -- LAPACK auxiliary routine (version 3.2) -- */
+/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
+/* November 2006 */
+
+/* .. Scalar Arguments .. */
+/* .. */
+
+/* Purpose */
+/* ======= */
+
+/* DLAMC2 determines the machine parameters specified in its argument */
+/* list. */
+
+/* Arguments */
+/* ========= */
+
+/* BETA (output) INTEGER */
+/* The base of the machine. */
+
+/* T (output) INTEGER */
+/* The number of ( BETA ) digits in the mantissa. */
+
+/* RND (output) LOGICAL */
+/* Specifies whether proper rounding ( RND = .TRUE. ) or */
+/* chopping ( RND = .FALSE. ) occurs in addition. This may not */
+/* be a reliable guide to the way in which the machine performs */
+/* its arithmetic. */
+
+/* EPS (output) DOUBLE PRECISION */
+/* The smallest positive number such that */
+
+/* fl( 1.0 - EPS ) .LT. 1.0, */
+
+/* where fl denotes the computed value. */
+
+/* EMIN (output) INTEGER */
+/* The minimum exponent before (gradual) underflow occurs. */
+
+/* RMIN (output) DOUBLE PRECISION */
+/* The smallest normalized number for the machine, given by */
+/* BASE**( EMIN - 1 ), where BASE is the floating point value */
+/* of BETA. */
+
+/* EMAX (output) INTEGER */
+/* The maximum exponent before overflow occurs. */
+
+/* RMAX (output) DOUBLE PRECISION */
+/* The largest positive number for the machine, given by */
+/* BASE**EMAX * ( 1 - EPS ), where BASE is the floating point */
+/* value of BETA. */
+
+/* Further Details */
+/* =============== */
+
+/* The computation of EPS is based on a routine PARANOIA by */
+/* W. Kahan of the University of California at Berkeley. */
+
+/* ===================================================================== */
+
+/* .. Local Scalars .. */
+/* .. */
+/* .. External Functions .. */
+/* .. */
+/* .. External Subroutines .. */
+/* .. */
+/* .. Intrinsic Functions .. */
+/* .. */
+/* .. Save statement .. */
+/* .. */
+/* .. Data statements .. */
+/* .. */
+/* .. Executable Statements .. */
+
+ if (first) {
+ zero = 0.;
+ one = 1.;
+ two = 2.;
+
+/* LBETA, LT, LRND, LEPS, LEMIN and LRMIN are the local values of */
+/* BETA, T, RND, EPS, EMIN and RMIN. */
+
+/* Throughout this routine we use the function DLAMC3 to ensure */
+/* that relevant values are stored and not held in registers, or */
+/* are not affected by optimizers. */
+
+/* DLAMC1 returns the parameters LBETA, LT, LRND and LIEEE1. */
+
+ dlamc1_(&lbeta, <, &lrnd, &lieee1);
+
+/* Start to find EPS. */
+
+ b = (doublereal) lbeta;
+ i__1 = -lt;
+ a = pow_di(&b, &i__1);
+ leps = a;
+
+/* Try some tricks to see whether or not this is the correct EPS. */
+
+ b = two / 3;
+ half = one / 2;
+ d__1 = -half;
+ sixth = dlamc3_(&b, &d__1);
+ third = dlamc3_(&sixth, &sixth);
+ d__1 = -half;
+ b = dlamc3_(&third, &d__1);
+ b = dlamc3_(&b, &sixth);
+ b = abs(b);
+ if (b < leps) {
+ b = leps;
+ }
+
+ leps = 1.;
+
+/* + WHILE( ( LEPS.GT.B ).AND.( B.GT.ZERO ) )LOOP */
+L10:
+ if (leps > b && b > zero) {
+ leps = b;
+ d__1 = half * leps;
+/* Computing 5th power */
+ d__3 = two, d__4 = d__3, d__3 *= d__3;
+/* Computing 2nd power */
+ d__5 = leps;
+ d__2 = d__4 * (d__3 * d__3) * (d__5 * d__5);
+ c__ = dlamc3_(&d__1, &d__2);
+ d__1 = -c__;
+ c__ = dlamc3_(&half, &d__1);
+ b = dlamc3_(&half, &c__);
+ d__1 = -b;
+ c__ = dlamc3_(&half, &d__1);
+ b = dlamc3_(&half, &c__);
+ goto L10;
+ }
+/* + END WHILE */
+
+ if (a < leps) {
+ leps = a;
+ }
+
+/* Computation of EPS complete. */
+
+/* Now find EMIN. Let A = + or - 1, and + or - (1 + BASE**(-3)). */
+/* Keep dividing A by BETA until (gradual) underflow occurs. This */
+/* is detected when we cannot recover the previous A. */
+
+ rbase = one / lbeta;
+ small = one;
+ for (i__ = 1; i__ <= 3; ++i__) {
+ d__1 = small * rbase;
+ small = dlamc3_(&d__1, &zero);
+/* L20: */
+ }
+ a = dlamc3_(&one, &small);
+ dlamc4_(&ngpmin, &one, &lbeta);
+ d__1 = -one;
+ dlamc4_(&ngnmin, &d__1, &lbeta);
+ dlamc4_(&gpmin, &a, &lbeta);
+ d__1 = -a;
+ dlamc4_(&gnmin, &d__1, &lbeta);
+ ieee = FALSE_;
+
+ if (ngpmin == ngnmin && gpmin == gnmin) {
+ if (ngpmin == gpmin) {
+ lemin = ngpmin;
+/* ( Non twos-complement machines, no gradual underflow; */
+/* e.g., VAX ) */
+ } else if (gpmin - ngpmin == 3) {
+ lemin = ngpmin - 1 + lt;
+ ieee = TRUE_;
+/* ( Non twos-complement machines, with gradual underflow; */
+/* e.g., IEEE standard followers ) */
+ } else {
+ lemin = min(ngpmin,gpmin);
+/* ( A guess; no known machine ) */
+ iwarn = TRUE_;
+ }
+
+ } else if (ngpmin == gpmin && ngnmin == gnmin) {
+ if ((i__1 = ngpmin - ngnmin, abs(i__1)) == 1) {
+ lemin = max(ngpmin,ngnmin);
+/* ( Twos-complement machines, no gradual underflow; */
+/* e.g., CYBER 205 ) */
+ } else {
+ lemin = min(ngpmin,ngnmin);
+/* ( A guess; no known machine ) */
+ iwarn = TRUE_;
+ }
+
+ } else if ((i__1 = ngpmin - ngnmin, abs(i__1)) == 1 && gpmin == gnmin)
+ {
+ if (gpmin - min(ngpmin,ngnmin) == 3) {
+ lemin = max(ngpmin,ngnmin) - 1 + lt;
+/* ( Twos-complement machines with gradual underflow; */
+/* no known machine ) */
+ } else {
+ lemin = min(ngpmin,ngnmin);
+/* ( A guess; no known machine ) */
+ iwarn = TRUE_;
+ }
+
+ } else {
+/* Computing MIN */
+ i__1 = min(ngpmin,ngnmin), i__1 = min(i__1,gpmin);
+ lemin = min(i__1,gnmin);
+/* ( A guess; no known machine ) */
+ iwarn = TRUE_;
+ }
+ first = FALSE_;
+/* ** */
+/* Comment out this if block if EMIN is ok */
+ if (iwarn) {
+ first = TRUE_;
+ s_wsfe(&io___58);
+ do_fio(&c__1, (char *)&lemin, (ftnlen)sizeof(integer));
+ e_wsfe();
+ }
+/* ** */
+
+/* Assume IEEE arithmetic if we found denormalised numbers above, */
+/* or if arithmetic seems to round in the IEEE style, determined */
+/* in routine DLAMC1. A true IEEE machine should have both things */
+/* true; however, faulty machines may have one or the other. */
+
+ ieee = ieee || lieee1;
+
+/* Compute RMIN by successive division by BETA. We could compute */
+/* RMIN as BASE**( EMIN - 1 ), but some machines underflow during */
+/* this computation. */
+
+ lrmin = 1.;
+ i__1 = 1 - lemin;
+ for (i__ = 1; i__ <= i__1; ++i__) {
+ d__1 = lrmin * rbase;
+ lrmin = dlamc3_(&d__1, &zero);
+/* L30: */
+ }
+
+/* Finally, call DLAMC5 to compute EMAX and RMAX. */
+
+ dlamc5_(&lbeta, <, &lemin, &ieee, &lemax, &lrmax);
+ }
+
+ *beta = lbeta;
+ *t = lt;
+ *rnd = lrnd;
+ *eps = leps;
+ *emin = lemin;
+ *rmin = lrmin;
+ *emax = lemax;
+ *rmax = lrmax;
+
+ return 0;
+
+
+/* End of DLAMC2 */
+
+} /* dlamc2_ */
+
+
+/* *********************************************************************** */
+
+doublereal dlamc3_(doublereal *a, doublereal *b)
+{
+ /* System generated locals */
+ doublereal ret_val;
+
+
+/* -- LAPACK auxiliary routine (version 3.2) -- */
+/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
+/* November 2006 */
+
+/* .. Scalar Arguments .. */
+/* .. */
+
+/* Purpose */
+/* ======= */
+
+/* DLAMC3 is intended to force A and B to be stored prior to doing */
+/* the addition of A and B , for use in situations where optimizers */
+/* might hold one of these in a register. */
+
+/* Arguments */
+/* ========= */
+
+/* A (input) DOUBLE PRECISION */
+/* B (input) DOUBLE PRECISION */
+/* The values A and B. */
+
+/* ===================================================================== */
+
+/* .. Executable Statements .. */
+
+ ret_val = *a + *b;
+
+ return ret_val;
+
+/* End of DLAMC3 */
+
+} /* dlamc3_ */
+
+
+/* *********************************************************************** */
+
+/* Subroutine */ int dlamc4_(integer *emin, doublereal *start, integer *base)
+{
+ /* System generated locals */
+ integer i__1;
+ doublereal d__1;
+
+ /* Local variables */
+ doublereal a;
+ integer i__;
+ doublereal b1, b2, c1, c2, d1, d2, one, zero, rbase;
+ extern doublereal dlamc3_(doublereal *, doublereal *);
+
+
+/* -- LAPACK auxiliary routine (version 3.2) -- */
+/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
+/* November 2006 */
+
+/* .. Scalar Arguments .. */
+/* .. */
+
+/* Purpose */
+/* ======= */
+
+/* DLAMC4 is a service routine for DLAMC2. */
+
+/* Arguments */
+/* ========= */
+
+/* EMIN (output) INTEGER */
+/* The minimum exponent before (gradual) underflow, computed by */
+/* setting A = START and dividing by BASE until the previous A */
+/* can not be recovered. */
+
+/* START (input) DOUBLE PRECISION */
+/* The starting point for determining EMIN. */
+
+/* BASE (input) INTEGER */
+/* The base of the machine. */
+
+/* ===================================================================== */
+
+/* .. Local Scalars .. */
+/* .. */
+/* .. External Functions .. */
+/* .. */
+/* .. Executable Statements .. */
+
+ a = *start;
+ one = 1.;
+ rbase = one / *base;
+ zero = 0.;
+ *emin = 1;
+ d__1 = a * rbase;
+ b1 = dlamc3_(&d__1, &zero);
+ c1 = a;
+ c2 = a;
+ d1 = a;
+ d2 = a;
+/* + WHILE( ( C1.EQ.A ).AND.( C2.EQ.A ).AND. */
+/* $ ( D1.EQ.A ).AND.( D2.EQ.A ) )LOOP */
+L10:
+ if (c1 == a && c2 == a && d1 == a && d2 == a) {
+ --(*emin);
+ a = b1;
+ d__1 = a / *base;
+ b1 = dlamc3_(&d__1, &zero);
+ d__1 = b1 * *base;
+ c1 = dlamc3_(&d__1, &zero);
+ d1 = zero;
+ i__1 = *base;
+ for (i__ = 1; i__ <= i__1; ++i__) {
+ d1 += b1;
+/* L20: */
+ }
+ d__1 = a * rbase;
+ b2 = dlamc3_(&d__1, &zero);
+ d__1 = b2 / rbase;
+ c2 = dlamc3_(&d__1, &zero);
+ d2 = zero;
+ i__1 = *base;
+ for (i__ = 1; i__ <= i__1; ++i__) {
+ d2 += b2;
+/* L30: */
+ }
+ goto L10;
+ }
+/* + END WHILE */
+
+ return 0;
+
+/* End of DLAMC4 */
+
+} /* dlamc4_ */
+
+
+/* *********************************************************************** */
+
+/* Subroutine */ int dlamc5_(integer *beta, integer *p, integer *emin,
+ logical *ieee, integer *emax, doublereal *rmax)
+{
+ /* System generated locals */
+ integer i__1;
+ doublereal d__1;
+
+ /* Local variables */
+ integer i__;
+ doublereal y, z__;
+ integer try__, lexp;
+ doublereal oldy;
+ integer uexp, nbits;
+ extern doublereal dlamc3_(doublereal *, doublereal *);
+ doublereal recbas;
+ integer exbits, expsum;
+
+
+/* -- LAPACK auxiliary routine (version 3.2) -- */
+/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
+/* November 2006 */
+
+/* .. Scalar Arguments .. */
+/* .. */
+
+/* Purpose */
+/* ======= */
+
+/* DLAMC5 attempts to compute RMAX, the largest machine floating-point */
+/* number, without overflow. It assumes that EMAX + abs(EMIN) sum */
+/* approximately to a power of 2. It will fail on machines where this */
+/* assumption does not hold, for example, the Cyber 205 (EMIN = -28625, */
+/* EMAX = 28718). It will also fail if the value supplied for EMIN is */
+/* too large (i.e. too close to zero), probably with overflow. */
+
+/* Arguments */
+/* ========= */
+
+/* BETA (input) INTEGER */
+/* The base of floating-point arithmetic. */
+
+/* P (input) INTEGER */
+/* The number of base BETA digits in the mantissa of a */
+/* floating-point value. */
+
+/* EMIN (input) INTEGER */
+/* The minimum exponent before (gradual) underflow. */
+
+/* IEEE (input) LOGICAL */
+/* A logical flag specifying whether or not the arithmetic */
+/* system is thought to comply with the IEEE standard. */
+
+/* EMAX (output) INTEGER */
+/* The largest exponent before overflow */
+
+/* RMAX (output) DOUBLE PRECISION */
+/* The largest machine floating-point number. */
+
+/* ===================================================================== */
+
+/* .. Parameters .. */
+/* .. */
+/* .. Local Scalars .. */
+/* .. */
+/* .. External Functions .. */
+/* .. */
+/* .. Intrinsic Functions .. */
+/* .. */
+/* .. Executable Statements .. */
+
+/* First compute LEXP and UEXP, two powers of 2 that bound */
+/* abs(EMIN). We then assume that EMAX + abs(EMIN) will sum */
+/* approximately to the bound that is closest to abs(EMIN). */
+/* (EMAX is the exponent of the required number RMAX). */
+
+ lexp = 1;
+ exbits = 1;
+L10:
+ try__ = lexp << 1;
+ if (try__ <= -(*emin)) {
+ lexp = try__;
+ ++exbits;
+ goto L10;
+ }
+ if (lexp == -(*emin)) {
+ uexp = lexp;
+ } else {
+ uexp = try__;
+ ++exbits;
+ }
+
+/* Now -LEXP is less than or equal to EMIN, and -UEXP is greater */
+/* than or equal to EMIN. EXBITS is the number of bits needed to */
+/* store the exponent. */
+
+ if (uexp + *emin > -lexp - *emin) {
+ expsum = lexp << 1;
+ } else {
+ expsum = uexp << 1;
+ }
+
+/* EXPSUM is the exponent range, approximately equal to */
+/* EMAX - EMIN + 1 . */
+
+ *emax = expsum + *emin - 1;
+ nbits = exbits + 1 + *p;
+
+/* NBITS is the total number of bits needed to store a */
+/* floating-point number. */
+
+ if (nbits % 2 == 1 && *beta == 2) {
+
+/* Either there are an odd number of bits used to store a */
+/* floating-point number, which is unlikely, or some bits are */
+/* not used in the representation of numbers, which is possible, */
+/* (e.g. Cray machines) or the mantissa has an implicit bit, */
+/* (e.g. IEEE machines, Dec Vax machines), which is perhaps the */
+/* most likely. We have to assume the last alternative. */
+/* If this is true, then we need to reduce EMAX by one because */
+/* there must be some way of representing zero in an implicit-bit */
+/* system. On machines like Cray, we are reducing EMAX by one */
+/* unnecessarily. */
+
+ --(*emax);
+ }
+
+ if (*ieee) {
+
+/* Assume we are on an IEEE machine which reserves one exponent */
+/* for infinity and NaN. */
+
+ --(*emax);
+ }
+
+/* Now create RMAX, the largest machine number, which should */
+/* be equal to (1.0 - BETA**(-P)) * BETA**EMAX . */
+
+/* First compute 1.0 - BETA**(-P), being careful that the */
+/* result is less than 1.0 . */
+
+ recbas = 1. / *beta;
+ z__ = *beta - 1.;
+ y = 0.;
+ i__1 = *p;
+ for (i__ = 1; i__ <= i__1; ++i__) {
+ z__ *= recbas;
+ if (y < 1.) {
+ oldy = y;
+ }
+ y = dlamc3_(&y, &z__);
+/* L20: */
+ }
+ if (y >= 1.) {
+ y = oldy;
+ }
+
+/* Now multiply by BETA**EMAX to get RMAX. */
+
+ i__1 = *emax;
+ for (i__ = 1; i__ <= i__1; ++i__) {
+ d__1 = y * *beta;
+ y = dlamc3_(&d__1, &c_b32);
+/* L30: */
+ }
+
+ *rmax = y;
+ return 0;
+
+/* End of DLAMC5 */
+
+} /* dlamc5_ */
diff --git a/lapack/dlapy2.c b/lapack/dlapy2.c
new file mode 100644
index 0000000..6e88cd1
--- /dev/null
+++ b/lapack/dlapy2.c
@@ -0,0 +1,73 @@
+/* dlapy2.f -- translated by f2c (version 20061008).
+ You must link the resulting object file with libf2c:
+ on Microsoft Windows system, link with libf2c.lib;
+ on Linux or Unix systems, link with .../path/to/libf2c.a -lm
+ or, if you install libf2c.a in a standard place, with -lf2c -lm
+ -- in that order, at the end of the command line, as in
+ cc *.o -lf2c -lm
+ Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
+
+ http://www.netlib.org/f2c/libf2c.zip
+*/
+
+#include "f2c.h"
+#include "blaswrap.h"
+
+doublereal dlapy2_(doublereal *x, doublereal *y)
+{
+ /* System generated locals */
+ doublereal ret_val, d__1;
+
+ /* Builtin functions */
+ double sqrt(doublereal);
+
+ /* Local variables */
+ doublereal w, z__, xabs, yabs;
+
+
+/* -- LAPACK auxiliary routine (version 3.2) -- */
+/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
+/* November 2006 */
+
+/* .. Scalar Arguments .. */
+/* .. */
+
+/* Purpose */
+/* ======= */
+
+/* DLAPY2 returns sqrt(x**2+y**2), taking care not to cause unnecessary */
+/* overflow. */
+
+/* Arguments */
+/* ========= */
+
+/* X (input) DOUBLE PRECISION */
+/* Y (input) DOUBLE PRECISION */
+/* X and Y specify the values x and y. */
+
+/* ===================================================================== */
+
+/* .. Parameters .. */
+/* .. */
+/* .. Local Scalars .. */
+/* .. */
+/* .. Intrinsic Functions .. */
+/* .. */
+/* .. Executable Statements .. */
+
+ xabs = abs(*x);
+ yabs = abs(*y);
+ w = max(xabs,yabs);
+ z__ = min(xabs,yabs);
+ if (z__ == 0.) {
+ ret_val = w;
+ } else {
+/* Computing 2nd power */
+ d__1 = z__ / w;
+ ret_val = w * sqrt(d__1 * d__1 + 1.);
+ }
+ return ret_val;
+
+/* End of DLAPY2 */
+
+} /* dlapy2_ */
diff --git a/lapack/dlapy3.c b/lapack/dlapy3.c
new file mode 100644
index 0000000..6aec3d0
--- /dev/null
+++ b/lapack/dlapy3.c
@@ -0,0 +1,83 @@
+/* dlapy3.f -- translated by f2c (version 20061008).
+ You must link the resulting object file with libf2c:
+ on Microsoft Windows system, link with libf2c.lib;
+ on Linux or Unix systems, link with .../path/to/libf2c.a -lm
+ or, if you install libf2c.a in a standard place, with -lf2c -lm
+ -- in that order, at the end of the command line, as in
+ cc *.o -lf2c -lm
+ Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
+
+ http://www.netlib.org/f2c/libf2c.zip
+*/
+
+#include "f2c.h"
+#include "blaswrap.h"
+
+doublereal dlapy3_(doublereal *x, doublereal *y, doublereal *z__)
+{
+ /* System generated locals */
+ doublereal ret_val, d__1, d__2, d__3;
+
+ /* Builtin functions */
+ double sqrt(doublereal);
+
+ /* Local variables */
+ doublereal w, xabs, yabs, zabs;
+
+
+/* -- LAPACK auxiliary routine (version 3.2) -- */
+/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
+/* November 2006 */
+
+/* .. Scalar Arguments .. */
+/* .. */
+
+/* Purpose */
+/* ======= */
+
+/* DLAPY3 returns sqrt(x**2+y**2+z**2), taking care not to cause */
+/* unnecessary overflow. */
+
+/* Arguments */
+/* ========= */
+
+/* X (input) DOUBLE PRECISION */
+/* Y (input) DOUBLE PRECISION */
+/* Z (input) DOUBLE PRECISION */
+/* X, Y and Z specify the values x, y and z. */
+
+/* ===================================================================== */
+
+/* .. Parameters .. */
+/* .. */
+/* .. Local Scalars .. */
+/* .. */
+/* .. Intrinsic Functions .. */
+/* .. */
+/* .. Executable Statements .. */
+
+ xabs = abs(*x);
+ yabs = abs(*y);
+ zabs = abs(*z__);
+/* Computing MAX */
+ d__1 = max(xabs,yabs);
+ w = max(d__1,zabs);
+ if (w == 0.) {
+/* W can be zero for max(0,nan,0) */
+/* adding all three entries together will make sure */
+/* NaN will not disappear. */
+ ret_val = xabs + yabs + zabs;
+ } else {
+/* Computing 2nd power */
+ d__1 = xabs / w;
+/* Computing 2nd power */
+ d__2 = yabs / w;
+/* Computing 2nd power */
+ d__3 = zabs / w;
+ ret_val = w * sqrt(d__1 * d__1 + d__2 * d__2 + d__3 * d__3);
+ }
+ return ret_val;
+
+/* End of DLAPY3 */
+
+} /* dlapy3_ */
diff --git a/lapack/dlarf.c b/lapack/dlarf.c
new file mode 100644
index 0000000..aba8a59
--- /dev/null
+++ b/lapack/dlarf.c
@@ -0,0 +1,193 @@
+/* dlarf.f -- translated by f2c (version 20061008).
+ You must link the resulting object file with libf2c:
+ on Microsoft Windows system, link with libf2c.lib;
+ on Linux or Unix systems, link with .../path/to/libf2c.a -lm
+ or, if you install libf2c.a in a standard place, with -lf2c -lm
+ -- in that order, at the end of the command line, as in
+ cc *.o -lf2c -lm
+ Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
+
+ http://www.netlib.org/f2c/libf2c.zip
+*/
+
+#include "f2c.h"
+#include "blaswrap.h"
+
+/* Table of constant values */
+
+static doublereal c_b4 = 1.;
+static doublereal c_b5 = 0.;
+static integer c__1 = 1;
+
+/* Subroutine */ int dlarf_(char *side, integer *m, integer *n, doublereal *v,
+ integer *incv, doublereal *tau, doublereal *c__, integer *ldc,
+ doublereal *work)
+{
+ /* System generated locals */
+ integer c_dim1, c_offset;
+ doublereal d__1;
+
+ /* Local variables */
+ integer i__;
+ logical applyleft;
+ extern /* Subroutine */ int dger_(integer *, integer *, doublereal *,
+ doublereal *, integer *, doublereal *, integer *, doublereal *,
+ integer *);
+ extern logical lsame_(char *, char *);
+ extern /* Subroutine */ int dgemv_(char *, integer *, integer *,
+ doublereal *, doublereal *, integer *, doublereal *, integer *,
+ doublereal *, doublereal *, integer *);
+ integer lastc, lastv;
+ extern integer iladlc_(integer *, integer *, doublereal *, integer *),
+ iladlr_(integer *, integer *, doublereal *, integer *);
+
+
+/* -- LAPACK auxiliary routine (version 3.2) -- */
+/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
+/* November 2006 */
+
+/* .. Scalar Arguments .. */
+/* .. */
+/* .. Array Arguments .. */
+/* .. */
+
+/* Purpose */
+/* ======= */
+
+/* DLARF applies a real elementary reflector H to a real m by n matrix */
+/* C, from either the left or the right. H is represented in the form */
+
+/* H = I - tau * v * v' */
+
+/* where tau is a real scalar and v is a real vector. */
+
+/* If tau = 0, then H is taken to be the unit matrix. */
+
+/* Arguments */
+/* ========= */
+
+/* SIDE (input) CHARACTER*1 */
+/* = 'L': form H * C */
+/* = 'R': form C * H */
+
+/* M (input) INTEGER */
+/* The number of rows of the matrix C. */
+
+/* N (input) INTEGER */
+/* The number of columns of the matrix C. */
+
+/* V (input) DOUBLE PRECISION array, dimension */
+/* (1 + (M-1)*abs(INCV)) if SIDE = 'L' */
+/* or (1 + (N-1)*abs(INCV)) if SIDE = 'R' */
+/* The vector v in the representation of H. V is not used if */
+/* TAU = 0. */
+
+/* INCV (input) INTEGER */
+/* The increment between elements of v. INCV <> 0. */
+
+/* TAU (input) DOUBLE PRECISION */
+/* The value tau in the representation of H. */
+
+/* C (input/output) DOUBLE PRECISION array, dimension (LDC,N) */
+/* On entry, the m by n matrix C. */
+/* On exit, C is overwritten by the matrix H * C if SIDE = 'L', */
+/* or C * H if SIDE = 'R'. */
+
+/* LDC (input) INTEGER */
+/* The leading dimension of the array C. LDC >= max(1,M). */
+
+/* WORK (workspace) DOUBLE PRECISION array, dimension */
+/* (N) if SIDE = 'L' */
+/* or (M) if SIDE = 'R' */
+
+/* ===================================================================== */
+
+/* .. Parameters .. */
+/* .. */
+/* .. Local Scalars .. */
+/* .. */
+/* .. External Subroutines .. */
+/* .. */
+/* .. External Functions .. */
+/* .. */
+/* .. Executable Statements .. */
+
+ /* Parameter adjustments */
+ --v;
+ c_dim1 = *ldc;
+ c_offset = 1 + c_dim1;
+ c__ -= c_offset;
+ --work;
+
+ /* Function Body */
+ applyleft = lsame_(side, "L");
+ lastv = 0;
+ lastc = 0;
+ if (*tau != 0.) {
+/* Set up variables for scanning V. LASTV begins pointing to the end */
+/* of V. */
+ if (applyleft) {
+ lastv = *m;
+ } else {
+ lastv = *n;
+ }
+ if (*incv > 0) {
+ i__ = (lastv - 1) * *incv + 1;
+ } else {
+ i__ = 1;
+ }
+/* Look for the last non-zero row in V. */
+ while(lastv > 0 && v[i__] == 0.) {
+ --lastv;
+ i__ -= *incv;
+ }
+ if (applyleft) {
+/* Scan for the last non-zero column in C(1:lastv,:). */
+ lastc = iladlc_(&lastv, n, &c__[c_offset], ldc);
+ } else {
+/* Scan for the last non-zero row in C(:,1:lastv). */
+ lastc = iladlr_(m, &lastv, &c__[c_offset], ldc);
+ }
+ }
+/* Note that lastc.eq.0 renders the BLAS operations null; no special */
+/* case is needed at this level. */
+ if (applyleft) {
+
+/* Form H * C */
+
+ if (lastv > 0) {
+
+/* w(1:lastc,1) := C(1:lastv,1:lastc)' * v(1:lastv,1) */
+
+ dgemv_("Transpose", &lastv, &lastc, &c_b4, &c__[c_offset], ldc, &
+ v[1], incv, &c_b5, &work[1], &c__1);
+
+/* C(1:lastv,1:lastc) := C(...) - v(1:lastv,1) * w(1:lastc,1)' */
+
+ d__1 = -(*tau);
+ dger_(&lastv, &lastc, &d__1, &v[1], incv, &work[1], &c__1, &c__[
+ c_offset], ldc);
+ }
+ } else {
+
+/* Form C * H */
+
+ if (lastv > 0) {
+
+/* w(1:lastc,1) := C(1:lastc,1:lastv) * v(1:lastv,1) */
+
+ dgemv_("No transpose", &lastc, &lastv, &c_b4, &c__[c_offset], ldc,
+ &v[1], incv, &c_b5, &work[1], &c__1);
+
+/* C(1:lastc,1:lastv) := C(...) - w(1:lastc,1) * v(1:lastv,1)' */
+
+ d__1 = -(*tau);
+ dger_(&lastc, &lastv, &d__1, &work[1], &c__1, &v[1], incv, &c__[
+ c_offset], ldc);
+ }
+ }
+ return 0;
+
+/* End of DLARF */
+
+} /* dlarf_ */
diff --git a/lapack/dlarfb.c b/lapack/dlarfb.c
new file mode 100644
index 0000000..9833b69
--- /dev/null
+++ b/lapack/dlarfb.c
@@ -0,0 +1,774 @@
+/* dlarfb.f -- translated by f2c (version 20061008).
+ You must link the resulting object file with libf2c:
+ on Microsoft Windows system, link with libf2c.lib;
+ on Linux or Unix systems, link with .../path/to/libf2c.a -lm
+ or, if you install libf2c.a in a standard place, with -lf2c -lm
+ -- in that order, at the end of the command line, as in
+ cc *.o -lf2c -lm
+ Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
+
+ http://www.netlib.org/f2c/libf2c.zip
+*/
+
+#include "f2c.h"
+#include "blaswrap.h"
+
+/* Table of constant values */
+
+static integer c__1 = 1;
+static doublereal c_b14 = 1.;
+static doublereal c_b25 = -1.;
+
+/* Subroutine */ int dlarfb_(char *side, char *trans, char *direct, char *
+ storev, integer *m, integer *n, integer *k, doublereal *v, integer *
+ ldv, doublereal *t, integer *ldt, doublereal *c__, integer *ldc,
+ doublereal *work, integer *ldwork)
+{
+ /* System generated locals */
+ integer c_dim1, c_offset, t_dim1, t_offset, v_dim1, v_offset, work_dim1,
+ work_offset, i__1, i__2;
+
+ /* Local variables */
+ integer i__, j;
+ extern /* Subroutine */ int dgemm_(char *, char *, integer *, integer *,
+ integer *, doublereal *, doublereal *, integer *, doublereal *,
+ integer *, doublereal *, doublereal *, integer *);
+ extern logical lsame_(char *, char *);
+ integer lastc;
+ extern /* Subroutine */ int dcopy_(integer *, doublereal *, integer *,
+ doublereal *, integer *), dtrmm_(char *, char *, char *, char *,
+ integer *, integer *, doublereal *, doublereal *, integer *,
+ doublereal *, integer *);
+ integer lastv;
+ extern integer iladlc_(integer *, integer *, doublereal *, integer *),
+ iladlr_(integer *, integer *, doublereal *, integer *);
+ char transt[1];
+
+
+/* -- LAPACK auxiliary routine (version 3.2) -- */
+/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
+/* November 2006 */
+
+/* .. Scalar Arguments .. */
+/* .. */
+/* .. Array Arguments .. */
+/* .. */
+
+/* Purpose */
+/* ======= */
+
+/* DLARFB applies a real block reflector H or its transpose H' to a */
+/* real m by n matrix C, from either the left or the right. */
+
+/* Arguments */
+/* ========= */
+
+/* SIDE (input) CHARACTER*1 */
+/* = 'L': apply H or H' from the Left */
+/* = 'R': apply H or H' from the Right */
+
+/* TRANS (input) CHARACTER*1 */
+/* = 'N': apply H (No transpose) */
+/* = 'T': apply H' (Transpose) */
+
+/* DIRECT (input) CHARACTER*1 */
+/* Indicates how H is formed from a product of elementary */
+/* reflectors */
+/* = 'F': H = H(1) H(2) . . . H(k) (Forward) */
+/* = 'B': H = H(k) . . . H(2) H(1) (Backward) */
+
+/* STOREV (input) CHARACTER*1 */
+/* Indicates how the vectors which define the elementary */
+/* reflectors are stored: */
+/* = 'C': Columnwise */
+/* = 'R': Rowwise */
+
+/* M (input) INTEGER */
+/* The number of rows of the matrix C. */
+
+/* N (input) INTEGER */
+/* The number of columns of the matrix C. */
+
+/* K (input) INTEGER */
+/* The order of the matrix T (= the number of elementary */
+/* reflectors whose product defines the block reflector). */
+
+/* V (input) DOUBLE PRECISION array, dimension */
+/* (LDV,K) if STOREV = 'C' */
+/* (LDV,M) if STOREV = 'R' and SIDE = 'L' */
+/* (LDV,N) if STOREV = 'R' and SIDE = 'R' */
+/* The matrix V. See further details. */
+
+/* LDV (input) INTEGER */
+/* The leading dimension of the array V. */
+/* If STOREV = 'C' and SIDE = 'L', LDV >= max(1,M); */
+/* if STOREV = 'C' and SIDE = 'R', LDV >= max(1,N); */
+/* if STOREV = 'R', LDV >= K. */
+
+/* T (input) DOUBLE PRECISION array, dimension (LDT,K) */
+/* The triangular k by k matrix T in the representation of the */
+/* block reflector. */
+
+/* LDT (input) INTEGER */
+/* The leading dimension of the array T. LDT >= K. */
+
+/* C (input/output) DOUBLE PRECISION array, dimension (LDC,N) */
+/* On entry, the m by n matrix C. */
+/* On exit, C is overwritten by H*C or H'*C or C*H or C*H'. */
+
+/* LDC (input) INTEGER */
+/* The leading dimension of the array C. LDA >= max(1,M). */
+
+/* WORK (workspace) DOUBLE PRECISION array, dimension (LDWORK,K) */
+
+/* LDWORK (input) INTEGER */
+/* The leading dimension of the array WORK. */
+/* If SIDE = 'L', LDWORK >= max(1,N); */
+/* if SIDE = 'R', LDWORK >= max(1,M). */
+
+/* ===================================================================== */
+
+/* .. Parameters .. */
+/* .. */
+/* .. Local Scalars .. */
+/* .. */
+/* .. External Functions .. */
+/* .. */
+/* .. External Subroutines .. */
+/* .. */
+/* .. Executable Statements .. */
+
+/* Quick return if possible */
+
+ /* Parameter adjustments */
+ v_dim1 = *ldv;
+ v_offset = 1 + v_dim1;
+ v -= v_offset;
+ t_dim1 = *ldt;
+ t_offset = 1 + t_dim1;
+ t -= t_offset;
+ c_dim1 = *ldc;
+ c_offset = 1 + c_dim1;
+ c__ -= c_offset;
+ work_dim1 = *ldwork;
+ work_offset = 1 + work_dim1;
+ work -= work_offset;
+
+ /* Function Body */
+ if (*m <= 0 || *n <= 0) {
+ return 0;
+ }
+
+ if (lsame_(trans, "N")) {
+ *(unsigned char *)transt = 'T';
+ } else {
+ *(unsigned char *)transt = 'N';
+ }
+
+ if (lsame_(storev, "C")) {
+
+ if (lsame_(direct, "F")) {
+
+/* Let V = ( V1 ) (first K rows) */
+/* ( V2 ) */
+/* where V1 is unit lower triangular. */
+
+ if (lsame_(side, "L")) {
+
+/* Form H * C or H' * C where C = ( C1 ) */
+/* ( C2 ) */
+
+/* Computing MAX */
+ i__1 = *k, i__2 = iladlr_(m, k, &v[v_offset], ldv);
+ lastv = max(i__1,i__2);
+ lastc = iladlc_(&lastv, n, &c__[c_offset], ldc);
+
+/* W := C' * V = (C1'*V1 + C2'*V2) (stored in WORK) */
+
+/* W := C1' */
+
+ i__1 = *k;
+ for (j = 1; j <= i__1; ++j) {
+ dcopy_(&lastc, &c__[j + c_dim1], ldc, &work[j * work_dim1
+ + 1], &c__1);
+/* L10: */
+ }
+
+/* W := W * V1 */
+
+ dtrmm_("Right", "Lower", "No transpose", "Unit", &lastc, k, &
+ c_b14, &v[v_offset], ldv, &work[work_offset], ldwork);
+ if (lastv > *k) {
+
+/* W := W + C2'*V2 */
+
+ i__1 = lastv - *k;
+ dgemm_("Transpose", "No transpose", &lastc, k, &i__1, &
+ c_b14, &c__[*k + 1 + c_dim1], ldc, &v[*k + 1 +
+ v_dim1], ldv, &c_b14, &work[work_offset], ldwork);
+ }
+
+/* W := W * T' or W * T */
+
+ dtrmm_("Right", "Upper", transt, "Non-unit", &lastc, k, &
+ c_b14, &t[t_offset], ldt, &work[work_offset], ldwork);
+
+/* C := C - V * W' */
+
+ if (lastv > *k) {
+
+/* C2 := C2 - V2 * W' */
+
+ i__1 = lastv - *k;
+ dgemm_("No transpose", "Transpose", &i__1, &lastc, k, &
+ c_b25, &v[*k + 1 + v_dim1], ldv, &work[
+ work_offset], ldwork, &c_b14, &c__[*k + 1 +
+ c_dim1], ldc);
+ }
+
+/* W := W * V1' */
+
+ dtrmm_("Right", "Lower", "Transpose", "Unit", &lastc, k, &
+ c_b14, &v[v_offset], ldv, &work[work_offset], ldwork);
+
+/* C1 := C1 - W' */
+
+ i__1 = *k;
+ for (j = 1; j <= i__1; ++j) {
+ i__2 = lastc;
+ for (i__ = 1; i__ <= i__2; ++i__) {
+ c__[j + i__ * c_dim1] -= work[i__ + j * work_dim1];
+/* L20: */
+ }
+/* L30: */
+ }
+
+ } else if (lsame_(side, "R")) {
+
+/* Form C * H or C * H' where C = ( C1 C2 ) */
+
+/* Computing MAX */
+ i__1 = *k, i__2 = iladlr_(n, k, &v[v_offset], ldv);
+ lastv = max(i__1,i__2);
+ lastc = iladlr_(m, &lastv, &c__[c_offset], ldc);
+
+/* W := C * V = (C1*V1 + C2*V2) (stored in WORK) */
+
+/* W := C1 */
+
+ i__1 = *k;
+ for (j = 1; j <= i__1; ++j) {
+ dcopy_(&lastc, &c__[j * c_dim1 + 1], &c__1, &work[j *
+ work_dim1 + 1], &c__1);
+/* L40: */
+ }
+
+/* W := W * V1 */
+
+ dtrmm_("Right", "Lower", "No transpose", "Unit", &lastc, k, &
+ c_b14, &v[v_offset], ldv, &work[work_offset], ldwork);
+ if (lastv > *k) {
+
+/* W := W + C2 * V2 */
+
+ i__1 = lastv - *k;
+ dgemm_("No transpose", "No transpose", &lastc, k, &i__1, &
+ c_b14, &c__[(*k + 1) * c_dim1 + 1], ldc, &v[*k +
+ 1 + v_dim1], ldv, &c_b14, &work[work_offset],
+ ldwork);
+ }
+
+/* W := W * T or W * T' */
+
+ dtrmm_("Right", "Upper", trans, "Non-unit", &lastc, k, &c_b14,
+ &t[t_offset], ldt, &work[work_offset], ldwork);
+
+/* C := C - W * V' */
+
+ if (lastv > *k) {
+
+/* C2 := C2 - W * V2' */
+
+ i__1 = lastv - *k;
+ dgemm_("No transpose", "Transpose", &lastc, &i__1, k, &
+ c_b25, &work[work_offset], ldwork, &v[*k + 1 +
+ v_dim1], ldv, &c_b14, &c__[(*k + 1) * c_dim1 + 1],
+ ldc);
+ }
+
+/* W := W * V1' */
+
+ dtrmm_("Right", "Lower", "Transpose", "Unit", &lastc, k, &
+ c_b14, &v[v_offset], ldv, &work[work_offset], ldwork);
+
+/* C1 := C1 - W */
+
+ i__1 = *k;
+ for (j = 1; j <= i__1; ++j) {
+ i__2 = lastc;
+ for (i__ = 1; i__ <= i__2; ++i__) {
+ c__[i__ + j * c_dim1] -= work[i__ + j * work_dim1];
+/* L50: */
+ }
+/* L60: */
+ }
+ }
+
+ } else {
+
+/* Let V = ( V1 ) */
+/* ( V2 ) (last K rows) */
+/* where V2 is unit upper triangular. */
+
+ if (lsame_(side, "L")) {
+
+/* Form H * C or H' * C where C = ( C1 ) */
+/* ( C2 ) */
+
+/* Computing MAX */
+ i__1 = *k, i__2 = iladlr_(m, k, &v[v_offset], ldv);
+ lastv = max(i__1,i__2);
+ lastc = iladlc_(&lastv, n, &c__[c_offset], ldc);
+
+/* W := C' * V = (C1'*V1 + C2'*V2) (stored in WORK) */
+
+/* W := C2' */
+
+ i__1 = *k;
+ for (j = 1; j <= i__1; ++j) {
+ dcopy_(&lastc, &c__[lastv - *k + j + c_dim1], ldc, &work[
+ j * work_dim1 + 1], &c__1);
+/* L70: */
+ }
+
+/* W := W * V2 */
+
+ dtrmm_("Right", "Upper", "No transpose", "Unit", &lastc, k, &
+ c_b14, &v[lastv - *k + 1 + v_dim1], ldv, &work[
+ work_offset], ldwork);
+ if (lastv > *k) {
+
+/* W := W + C1'*V1 */
+
+ i__1 = lastv - *k;
+ dgemm_("Transpose", "No transpose", &lastc, k, &i__1, &
+ c_b14, &c__[c_offset], ldc, &v[v_offset], ldv, &
+ c_b14, &work[work_offset], ldwork);
+ }
+
+/* W := W * T' or W * T */
+
+ dtrmm_("Right", "Lower", transt, "Non-unit", &lastc, k, &
+ c_b14, &t[t_offset], ldt, &work[work_offset], ldwork);
+
+/* C := C - V * W' */
+
+ if (lastv > *k) {
+
+/* C1 := C1 - V1 * W' */
+
+ i__1 = lastv - *k;
+ dgemm_("No transpose", "Transpose", &i__1, &lastc, k, &
+ c_b25, &v[v_offset], ldv, &work[work_offset],
+ ldwork, &c_b14, &c__[c_offset], ldc);
+ }
+
+/* W := W * V2' */
+
+ dtrmm_("Right", "Upper", "Transpose", "Unit", &lastc, k, &
+ c_b14, &v[lastv - *k + 1 + v_dim1], ldv, &work[
+ work_offset], ldwork);
+
+/* C2 := C2 - W' */
+
+ i__1 = *k;
+ for (j = 1; j <= i__1; ++j) {
+ i__2 = lastc;
+ for (i__ = 1; i__ <= i__2; ++i__) {
+ c__[lastv - *k + j + i__ * c_dim1] -= work[i__ + j *
+ work_dim1];
+/* L80: */
+ }
+/* L90: */
+ }
+
+ } else if (lsame_(side, "R")) {
+
+/* Form C * H or C * H' where C = ( C1 C2 ) */
+
+/* Computing MAX */
+ i__1 = *k, i__2 = iladlr_(n, k, &v[v_offset], ldv);
+ lastv = max(i__1,i__2);
+ lastc = iladlr_(m, &lastv, &c__[c_offset], ldc);
+
+/* W := C * V = (C1*V1 + C2*V2) (stored in WORK) */
+
+/* W := C2 */
+
+ i__1 = *k;
+ for (j = 1; j <= i__1; ++j) {
+ dcopy_(&lastc, &c__[(*n - *k + j) * c_dim1 + 1], &c__1, &
+ work[j * work_dim1 + 1], &c__1);
+/* L100: */
+ }
+
+/* W := W * V2 */
+
+ dtrmm_("Right", "Upper", "No transpose", "Unit", &lastc, k, &
+ c_b14, &v[lastv - *k + 1 + v_dim1], ldv, &work[
+ work_offset], ldwork);
+ if (lastv > *k) {
+
+/* W := W + C1 * V1 */
+
+ i__1 = lastv - *k;
+ dgemm_("No transpose", "No transpose", &lastc, k, &i__1, &
+ c_b14, &c__[c_offset], ldc, &v[v_offset], ldv, &
+ c_b14, &work[work_offset], ldwork);
+ }
+
+/* W := W * T or W * T' */
+
+ dtrmm_("Right", "Lower", trans, "Non-unit", &lastc, k, &c_b14,
+ &t[t_offset], ldt, &work[work_offset], ldwork);
+
+/* C := C - W * V' */
+
+ if (lastv > *k) {
+
+/* C1 := C1 - W * V1' */
+
+ i__1 = lastv - *k;
+ dgemm_("No transpose", "Transpose", &lastc, &i__1, k, &
+ c_b25, &work[work_offset], ldwork, &v[v_offset],
+ ldv, &c_b14, &c__[c_offset], ldc);
+ }
+
+/* W := W * V2' */
+
+ dtrmm_("Right", "Upper", "Transpose", "Unit", &lastc, k, &
+ c_b14, &v[lastv - *k + 1 + v_dim1], ldv, &work[
+ work_offset], ldwork);
+
+/* C2 := C2 - W */
+
+ i__1 = *k;
+ for (j = 1; j <= i__1; ++j) {
+ i__2 = lastc;
+ for (i__ = 1; i__ <= i__2; ++i__) {
+ c__[i__ + (lastv - *k + j) * c_dim1] -= work[i__ + j *
+ work_dim1];
+/* L110: */
+ }
+/* L120: */
+ }
+ }
+ }
+
+ } else if (lsame_(storev, "R")) {
+
+ if (lsame_(direct, "F")) {
+
+/* Let V = ( V1 V2 ) (V1: first K columns) */
+/* where V1 is unit upper triangular. */
+
+ if (lsame_(side, "L")) {
+
+/* Form H * C or H' * C where C = ( C1 ) */
+/* ( C2 ) */
+
+/* Computing MAX */
+ i__1 = *k, i__2 = iladlc_(k, m, &v[v_offset], ldv);
+ lastv = max(i__1,i__2);
+ lastc = iladlc_(&lastv, n, &c__[c_offset], ldc);
+
+/* W := C' * V' = (C1'*V1' + C2'*V2') (stored in WORK) */
+
+/* W := C1' */
+
+ i__1 = *k;
+ for (j = 1; j <= i__1; ++j) {
+ dcopy_(&lastc, &c__[j + c_dim1], ldc, &work[j * work_dim1
+ + 1], &c__1);
+/* L130: */
+ }
+
+/* W := W * V1' */
+
+ dtrmm_("Right", "Upper", "Transpose", "Unit", &lastc, k, &
+ c_b14, &v[v_offset], ldv, &work[work_offset], ldwork);
+ if (lastv > *k) {
+
+/* W := W + C2'*V2' */
+
+ i__1 = lastv - *k;
+ dgemm_("Transpose", "Transpose", &lastc, k, &i__1, &c_b14,
+ &c__[*k + 1 + c_dim1], ldc, &v[(*k + 1) * v_dim1
+ + 1], ldv, &c_b14, &work[work_offset], ldwork);
+ }
+
+/* W := W * T' or W * T */
+
+ dtrmm_("Right", "Upper", transt, "Non-unit", &lastc, k, &
+ c_b14, &t[t_offset], ldt, &work[work_offset], ldwork);
+
+/* C := C - V' * W' */
+
+ if (lastv > *k) {
+
+/* C2 := C2 - V2' * W' */
+
+ i__1 = lastv - *k;
+ dgemm_("Transpose", "Transpose", &i__1, &lastc, k, &c_b25,
+ &v[(*k + 1) * v_dim1 + 1], ldv, &work[
+ work_offset], ldwork, &c_b14, &c__[*k + 1 +
+ c_dim1], ldc);
+ }
+
+/* W := W * V1 */
+
+ dtrmm_("Right", "Upper", "No transpose", "Unit", &lastc, k, &
+ c_b14, &v[v_offset], ldv, &work[work_offset], ldwork);
+
+/* C1 := C1 - W' */
+
+ i__1 = *k;
+ for (j = 1; j <= i__1; ++j) {
+ i__2 = lastc;
+ for (i__ = 1; i__ <= i__2; ++i__) {
+ c__[j + i__ * c_dim1] -= work[i__ + j * work_dim1];
+/* L140: */
+ }
+/* L150: */
+ }
+
+ } else if (lsame_(side, "R")) {
+
+/* Form C * H or C * H' where C = ( C1 C2 ) */
+
+/* Computing MAX */
+ i__1 = *k, i__2 = iladlc_(k, n, &v[v_offset], ldv);
+ lastv = max(i__1,i__2);
+ lastc = iladlr_(m, &lastv, &c__[c_offset], ldc);
+
+/* W := C * V' = (C1*V1' + C2*V2') (stored in WORK) */
+
+/* W := C1 */
+
+ i__1 = *k;
+ for (j = 1; j <= i__1; ++j) {
+ dcopy_(&lastc, &c__[j * c_dim1 + 1], &c__1, &work[j *
+ work_dim1 + 1], &c__1);
+/* L160: */
+ }
+
+/* W := W * V1' */
+
+ dtrmm_("Right", "Upper", "Transpose", "Unit", &lastc, k, &
+ c_b14, &v[v_offset], ldv, &work[work_offset], ldwork);
+ if (lastv > *k) {
+
+/* W := W + C2 * V2' */
+
+ i__1 = lastv - *k;
+ dgemm_("No transpose", "Transpose", &lastc, k, &i__1, &
+ c_b14, &c__[(*k + 1) * c_dim1 + 1], ldc, &v[(*k +
+ 1) * v_dim1 + 1], ldv, &c_b14, &work[work_offset],
+ ldwork);
+ }
+
+/* W := W * T or W * T' */
+
+ dtrmm_("Right", "Upper", trans, "Non-unit", &lastc, k, &c_b14,
+ &t[t_offset], ldt, &work[work_offset], ldwork);
+
+/* C := C - W * V */
+
+ if (lastv > *k) {
+
+/* C2 := C2 - W * V2 */
+
+ i__1 = lastv - *k;
+ dgemm_("No transpose", "No transpose", &lastc, &i__1, k, &
+ c_b25, &work[work_offset], ldwork, &v[(*k + 1) *
+ v_dim1 + 1], ldv, &c_b14, &c__[(*k + 1) * c_dim1
+ + 1], ldc);
+ }
+
+/* W := W * V1 */
+
+ dtrmm_("Right", "Upper", "No transpose", "Unit", &lastc, k, &
+ c_b14, &v[v_offset], ldv, &work[work_offset], ldwork);
+
+/* C1 := C1 - W */
+
+ i__1 = *k;
+ for (j = 1; j <= i__1; ++j) {
+ i__2 = lastc;
+ for (i__ = 1; i__ <= i__2; ++i__) {
+ c__[i__ + j * c_dim1] -= work[i__ + j * work_dim1];
+/* L170: */
+ }
+/* L180: */
+ }
+
+ }
+
+ } else {
+
+/* Let V = ( V1 V2 ) (V2: last K columns) */
+/* where V2 is unit lower triangular. */
+
+ if (lsame_(side, "L")) {
+
+/* Form H * C or H' * C where C = ( C1 ) */
+/* ( C2 ) */
+
+/* Computing MAX */
+ i__1 = *k, i__2 = iladlc_(k, m, &v[v_offset], ldv);
+ lastv = max(i__1,i__2);
+ lastc = iladlc_(&lastv, n, &c__[c_offset], ldc);
+
+/* W := C' * V' = (C1'*V1' + C2'*V2') (stored in WORK) */
+
+/* W := C2' */
+
+ i__1 = *k;
+ for (j = 1; j <= i__1; ++j) {
+ dcopy_(&lastc, &c__[lastv - *k + j + c_dim1], ldc, &work[
+ j * work_dim1 + 1], &c__1);
+/* L190: */
+ }
+
+/* W := W * V2' */
+
+ dtrmm_("Right", "Lower", "Transpose", "Unit", &lastc, k, &
+ c_b14, &v[(lastv - *k + 1) * v_dim1 + 1], ldv, &work[
+ work_offset], ldwork);
+ if (lastv > *k) {
+
+/* W := W + C1'*V1' */
+
+ i__1 = lastv - *k;
+ dgemm_("Transpose", "Transpose", &lastc, k, &i__1, &c_b14,
+ &c__[c_offset], ldc, &v[v_offset], ldv, &c_b14, &
+ work[work_offset], ldwork);
+ }
+
+/* W := W * T' or W * T */
+
+ dtrmm_("Right", "Lower", transt, "Non-unit", &lastc, k, &
+ c_b14, &t[t_offset], ldt, &work[work_offset], ldwork);
+
+/* C := C - V' * W' */
+
+ if (lastv > *k) {
+
+/* C1 := C1 - V1' * W' */
+
+ i__1 = lastv - *k;
+ dgemm_("Transpose", "Transpose", &i__1, &lastc, k, &c_b25,
+ &v[v_offset], ldv, &work[work_offset], ldwork, &
+ c_b14, &c__[c_offset], ldc);
+ }
+
+/* W := W * V2 */
+
+ dtrmm_("Right", "Lower", "No transpose", "Unit", &lastc, k, &
+ c_b14, &v[(lastv - *k + 1) * v_dim1 + 1], ldv, &work[
+ work_offset], ldwork);
+
+/* C2 := C2 - W' */
+
+ i__1 = *k;
+ for (j = 1; j <= i__1; ++j) {
+ i__2 = lastc;
+ for (i__ = 1; i__ <= i__2; ++i__) {
+ c__[lastv - *k + j + i__ * c_dim1] -= work[i__ + j *
+ work_dim1];
+/* L200: */
+ }
+/* L210: */
+ }
+
+ } else if (lsame_(side, "R")) {
+
+/* Form C * H or C * H' where C = ( C1 C2 ) */
+
+/* Computing MAX */
+ i__1 = *k, i__2 = iladlc_(k, n, &v[v_offset], ldv);
+ lastv = max(i__1,i__2);
+ lastc = iladlr_(m, &lastv, &c__[c_offset], ldc);
+
+/* W := C * V' = (C1*V1' + C2*V2') (stored in WORK) */
+
+/* W := C2 */
+
+ i__1 = *k;
+ for (j = 1; j <= i__1; ++j) {
+ dcopy_(&lastc, &c__[(lastv - *k + j) * c_dim1 + 1], &c__1,
+ &work[j * work_dim1 + 1], &c__1);
+/* L220: */
+ }
+
+/* W := W * V2' */
+
+ dtrmm_("Right", "Lower", "Transpose", "Unit", &lastc, k, &
+ c_b14, &v[(lastv - *k + 1) * v_dim1 + 1], ldv, &work[
+ work_offset], ldwork);
+ if (lastv > *k) {
+
+/* W := W + C1 * V1' */
+
+ i__1 = lastv - *k;
+ dgemm_("No transpose", "Transpose", &lastc, k, &i__1, &
+ c_b14, &c__[c_offset], ldc, &v[v_offset], ldv, &
+ c_b14, &work[work_offset], ldwork);
+ }
+
+/* W := W * T or W * T' */
+
+ dtrmm_("Right", "Lower", trans, "Non-unit", &lastc, k, &c_b14,
+ &t[t_offset], ldt, &work[work_offset], ldwork);
+
+/* C := C - W * V */
+
+ if (lastv > *k) {
+
+/* C1 := C1 - W * V1 */
+
+ i__1 = lastv - *k;
+ dgemm_("No transpose", "No transpose", &lastc, &i__1, k, &
+ c_b25, &work[work_offset], ldwork, &v[v_offset],
+ ldv, &c_b14, &c__[c_offset], ldc);
+ }
+
+/* W := W * V2 */
+
+ dtrmm_("Right", "Lower", "No transpose", "Unit", &lastc, k, &
+ c_b14, &v[(lastv - *k + 1) * v_dim1 + 1], ldv, &work[
+ work_offset], ldwork);
+
+/* C1 := C1 - W */
+
+ i__1 = *k;
+ for (j = 1; j <= i__1; ++j) {
+ i__2 = lastc;
+ for (i__ = 1; i__ <= i__2; ++i__) {
+ c__[i__ + (lastv - *k + j) * c_dim1] -= work[i__ + j *
+ work_dim1];
+/* L230: */
+ }
+/* L240: */
+ }
+
+ }
+
+ }
+ }
+
+ return 0;
+
+/* End of DLARFB */
+
+} /* dlarfb_ */
diff --git a/lapack/dlarfg.c b/lapack/dlarfg.c
new file mode 100644
index 0000000..2a052ca
--- /dev/null
+++ b/lapack/dlarfg.c
@@ -0,0 +1,170 @@
+/* dlarfg.f -- translated by f2c (version 20061008).
+ You must link the resulting object file with libf2c:
+ on Microsoft Windows system, link with libf2c.lib;
+ on Linux or Unix systems, link with .../path/to/libf2c.a -lm
+ or, if you install libf2c.a in a standard place, with -lf2c -lm
+ -- in that order, at the end of the command line, as in
+ cc *.o -lf2c -lm
+ Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
+
+ http://www.netlib.org/f2c/libf2c.zip
+*/
+
+#include "f2c.h"
+#include "blaswrap.h"
+
+/* Subroutine */ int dlarfg_(integer *n, doublereal *alpha, doublereal *x,
+ integer *incx, doublereal *tau)
+{
+ /* System generated locals */
+ integer i__1;
+ doublereal d__1;
+
+ /* Builtin functions */
+ double d_sign(doublereal *, doublereal *);
+
+ /* Local variables */
+ integer j, knt;
+ doublereal beta;
+ extern doublereal dnrm2_(integer *, doublereal *, integer *);
+ extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *,
+ integer *);
+ doublereal xnorm;
+ extern doublereal dlapy2_(doublereal *, doublereal *), dlamch_(char *);
+ doublereal safmin, rsafmn;
+
+
+/* -- LAPACK auxiliary routine (version 3.2) -- */
+/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
+/* November 2006 */
+
+/* .. Scalar Arguments .. */
+/* .. */
+/* .. Array Arguments .. */
+/* .. */
+
+/* Purpose */
+/* ======= */
+
+/* DLARFG generates a real elementary reflector H of order n, such */
+/* that */
+
+/* H * ( alpha ) = ( beta ), H' * H = I. */
+/* ( x ) ( 0 ) */
+
+/* where alpha and beta are scalars, and x is an (n-1)-element real */
+/* vector. H is represented in the form */
+
+/* H = I - tau * ( 1 ) * ( 1 v' ) , */
+/* ( v ) */
+
+/* where tau is a real scalar and v is a real (n-1)-element */
+/* vector. */
+
+/* If the elements of x are all zero, then tau = 0 and H is taken to be */
+/* the unit matrix. */
+
+/* Otherwise 1 <= tau <= 2. */
+
+/* Arguments */
+/* ========= */
+
+/* N (input) INTEGER */
+/* The order of the elementary reflector. */
+
+/* ALPHA (input/output) DOUBLE PRECISION */
+/* On entry, the value alpha. */
+/* On exit, it is overwritten with the value beta. */
+
+/* X (input/output) DOUBLE PRECISION array, dimension */
+/* (1+(N-2)*abs(INCX)) */
+/* On entry, the vector x. */
+/* On exit, it is overwritten with the vector v. */
+
+/* INCX (input) INTEGER */
+/* The increment between elements of X. INCX > 0. */
+
+/* TAU (output) DOUBLE PRECISION */
+/* The value tau. */
+
+/* ===================================================================== */
+
+/* .. Parameters .. */
+/* .. */
+/* .. Local Scalars .. */
+/* .. */
+/* .. External Functions .. */
+/* .. */
+/* .. Intrinsic Functions .. */
+/* .. */
+/* .. External Subroutines .. */
+/* .. */
+/* .. Executable Statements .. */
+
+ /* Parameter adjustments */
+ --x;
+
+ /* Function Body */
+ if (*n <= 1) {
+ *tau = 0.;
+ return 0;
+ }
+
+ i__1 = *n - 1;
+ xnorm = dnrm2_(&i__1, &x[1], incx);
+
+ if (xnorm == 0.) {
+
+/* H = I */
+
+ *tau = 0.;
+ } else {
+
+/* general case */
+
+ d__1 = dlapy2_(alpha, &xnorm);
+ beta = -d_sign(&d__1, alpha);
+ safmin = dlamch_("S") / dlamch_("E");
+ knt = 0;
+ if (abs(beta) < safmin) {
+
+/* XNORM, BETA may be inaccurate; scale X and recompute them */
+
+ rsafmn = 1. / safmin;
+L10:
+ ++knt;
+ i__1 = *n - 1;
+ dscal_(&i__1, &rsafmn, &x[1], incx);
+ beta *= rsafmn;
+ *alpha *= rsafmn;
+ if (abs(beta) < safmin) {
+ goto L10;
+ }
+
+/* New BETA is at most 1, at least SAFMIN */
+
+ i__1 = *n - 1;
+ xnorm = dnrm2_(&i__1, &x[1], incx);
+ d__1 = dlapy2_(alpha, &xnorm);
+ beta = -d_sign(&d__1, alpha);
+ }
+ *tau = (beta - *alpha) / beta;
+ i__1 = *n - 1;
+ d__1 = 1. / (*alpha - beta);
+ dscal_(&i__1, &d__1, &x[1], incx);
+
+/* If ALPHA is subnormal, it may lose relative accuracy */
+
+ i__1 = knt;
+ for (j = 1; j <= i__1; ++j) {
+ beta *= safmin;
+/* L20: */
+ }
+ *alpha = beta;
+ }
+
+ return 0;
+
+/* End of DLARFG */
+
+} /* dlarfg_ */
diff --git a/lapack/dlarft.c b/lapack/dlarft.c
new file mode 100644
index 0000000..0d4951c
--- /dev/null
+++ b/lapack/dlarft.c
@@ -0,0 +1,325 @@
+/* dlarft.f -- translated by f2c (version 20061008).
+ You must link the resulting object file with libf2c:
+ on Microsoft Windows system, link with libf2c.lib;
+ on Linux or Unix systems, link with .../path/to/libf2c.a -lm
+ or, if you install libf2c.a in a standard place, with -lf2c -lm
+ -- in that order, at the end of the command line, as in
+ cc *.o -lf2c -lm
+ Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
+
+ http://www.netlib.org/f2c/libf2c.zip
+*/
+
+#include "f2c.h"
+#include "blaswrap.h"
+
+/* Table of constant values */
+
+static integer c__1 = 1;
+static doublereal c_b8 = 0.;
+
+/* Subroutine */ int dlarft_(char *direct, char *storev, integer *n, integer *
+ k, doublereal *v, integer *ldv, doublereal *tau, doublereal *t,
+ integer *ldt)
+{
+ /* System generated locals */
+ integer t_dim1, t_offset, v_dim1, v_offset, i__1, i__2, i__3;
+ doublereal d__1;
+
+ /* Local variables */
+ integer i__, j, prevlastv;
+ doublereal vii;
+ extern logical lsame_(char *, char *);
+ extern /* Subroutine */ int dgemv_(char *, integer *, integer *,
+ doublereal *, doublereal *, integer *, doublereal *, integer *,
+ doublereal *, doublereal *, integer *);
+ integer lastv;
+ extern /* Subroutine */ int dtrmv_(char *, char *, char *, integer *,
+ doublereal *, integer *, doublereal *, integer *);
+
+
+/* -- LAPACK auxiliary routine (version 3.2) -- */
+/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
+/* November 2006 */
+
+/* .. Scalar Arguments .. */
+/* .. */
+/* .. Array Arguments .. */
+/* .. */
+
+/* Purpose */
+/* ======= */
+
+/* DLARFT forms the triangular factor T of a real block reflector H */
+/* of order n, which is defined as a product of k elementary reflectors. */
+
+/* If DIRECT = 'F', H = H(1) H(2) . . . H(k) and T is upper triangular; */
+
+/* If DIRECT = 'B', H = H(k) . . . H(2) H(1) and T is lower triangular. */
+
+/* If STOREV = 'C', the vector which defines the elementary reflector */
+/* H(i) is stored in the i-th column of the array V, and */
+
+/* H = I - V * T * V' */
+
+/* If STOREV = 'R', the vector which defines the elementary reflector */
+/* H(i) is stored in the i-th row of the array V, and */
+
+/* H = I - V' * T * V */
+
+/* Arguments */
+/* ========= */
+
+/* DIRECT (input) CHARACTER*1 */
+/* Specifies the order in which the elementary reflectors are */
+/* multiplied to form the block reflector: */
+/* = 'F': H = H(1) H(2) . . . H(k) (Forward) */
+/* = 'B': H = H(k) . . . H(2) H(1) (Backward) */
+
+/* STOREV (input) CHARACTER*1 */
+/* Specifies how the vectors which define the elementary */
+/* reflectors are stored (see also Further Details): */
+/* = 'C': columnwise */
+/* = 'R': rowwise */
+
+/* N (input) INTEGER */
+/* The order of the block reflector H. N >= 0. */
+
+/* K (input) INTEGER */
+/* The order of the triangular factor T (= the number of */
+/* elementary reflectors). K >= 1. */
+
+/* V (input/output) DOUBLE PRECISION array, dimension */
+/* (LDV,K) if STOREV = 'C' */
+/* (LDV,N) if STOREV = 'R' */
+/* The matrix V. See further details. */
+
+/* LDV (input) INTEGER */
+/* The leading dimension of the array V. */
+/* If STOREV = 'C', LDV >= max(1,N); if STOREV = 'R', LDV >= K. */
+
+/* TAU (input) DOUBLE PRECISION array, dimension (K) */
+/* TAU(i) must contain the scalar factor of the elementary */
+/* reflector H(i). */
+
+/* T (output) DOUBLE PRECISION array, dimension (LDT,K) */
+/* The k by k triangular factor T of the block reflector. */
+/* If DIRECT = 'F', T is upper triangular; if DIRECT = 'B', T is */
+/* lower triangular. The rest of the array is not used. */
+
+/* LDT (input) INTEGER */
+/* The leading dimension of the array T. LDT >= K. */
+
+/* Further Details */
+/* =============== */
+
+/* The shape of the matrix V and the storage of the vectors which define */
+/* the H(i) is best illustrated by the following example with n = 5 and */
+/* k = 3. The elements equal to 1 are not stored; the corresponding */
+/* array elements are modified but restored on exit. The rest of the */
+/* array is not used. */
+
+/* DIRECT = 'F' and STOREV = 'C': DIRECT = 'F' and STOREV = 'R': */
+
+/* V = ( 1 ) V = ( 1 v1 v1 v1 v1 ) */
+/* ( v1 1 ) ( 1 v2 v2 v2 ) */
+/* ( v1 v2 1 ) ( 1 v3 v3 ) */
+/* ( v1 v2 v3 ) */
+/* ( v1 v2 v3 ) */
+
+/* DIRECT = 'B' and STOREV = 'C': DIRECT = 'B' and STOREV = 'R': */
+
+/* V = ( v1 v2 v3 ) V = ( v1 v1 1 ) */
+/* ( v1 v2 v3 ) ( v2 v2 v2 1 ) */
+/* ( 1 v2 v3 ) ( v3 v3 v3 v3 1 ) */
+/* ( 1 v3 ) */
+/* ( 1 ) */
+
+/* ===================================================================== */
+
+/* .. Parameters .. */
+/* .. */
+/* .. Local Scalars .. */
+/* .. */
+/* .. External Subroutines .. */
+/* .. */
+/* .. External Functions .. */
+/* .. */
+/* .. Executable Statements .. */
+
+/* Quick return if possible */
+
+ /* Parameter adjustments */
+ v_dim1 = *ldv;
+ v_offset = 1 + v_dim1;
+ v -= v_offset;
+ --tau;
+ t_dim1 = *ldt;
+ t_offset = 1 + t_dim1;
+ t -= t_offset;
+
+ /* Function Body */
+ if (*n == 0) {
+ return 0;
+ }
+
+ if (lsame_(direct, "F")) {
+ prevlastv = *n;
+ i__1 = *k;
+ for (i__ = 1; i__ <= i__1; ++i__) {
+ prevlastv = max(i__,prevlastv);
+ if (tau[i__] == 0.) {
+
+/* H(i) = I */
+
+ i__2 = i__;
+ for (j = 1; j <= i__2; ++j) {
+ t[j + i__ * t_dim1] = 0.;
+/* L10: */
+ }
+ } else {
+
+/* general case */
+
+ vii = v[i__ + i__ * v_dim1];
+ v[i__ + i__ * v_dim1] = 1.;
+ if (lsame_(storev, "C")) {
+/* Skip any trailing zeros. */
+ i__2 = i__ + 1;
+ for (lastv = *n; lastv >= i__2; --lastv) {
+ if (v[lastv + i__ * v_dim1] != 0.) {
+ break;
+ }
+ }
+ j = min(lastv,prevlastv);
+
+/* T(1:i-1,i) := - tau(i) * V(i:j,1:i-1)' * V(i:j,i) */
+
+ i__2 = j - i__ + 1;
+ i__3 = i__ - 1;
+ d__1 = -tau[i__];
+ dgemv_("Transpose", &i__2, &i__3, &d__1, &v[i__ + v_dim1],
+ ldv, &v[i__ + i__ * v_dim1], &c__1, &c_b8, &t[
+ i__ * t_dim1 + 1], &c__1);
+ } else {
+/* Skip any trailing zeros. */
+ i__2 = i__ + 1;
+ for (lastv = *n; lastv >= i__2; --lastv) {
+ if (v[i__ + lastv * v_dim1] != 0.) {
+ break;
+ }
+ }
+ j = min(lastv,prevlastv);
+
+/* T(1:i-1,i) := - tau(i) * V(1:i-1,i:j) * V(i,i:j)' */
+
+ i__2 = i__ - 1;
+ i__3 = j - i__ + 1;
+ d__1 = -tau[i__];
+ dgemv_("No transpose", &i__2, &i__3, &d__1, &v[i__ *
+ v_dim1 + 1], ldv, &v[i__ + i__ * v_dim1], ldv, &
+ c_b8, &t[i__ * t_dim1 + 1], &c__1);
+ }
+ v[i__ + i__ * v_dim1] = vii;
+
+/* T(1:i-1,i) := T(1:i-1,1:i-1) * T(1:i-1,i) */
+
+ i__2 = i__ - 1;
+ dtrmv_("Upper", "No transpose", "Non-unit", &i__2, &t[
+ t_offset], ldt, &t[i__ * t_dim1 + 1], &c__1);
+ t[i__ + i__ * t_dim1] = tau[i__];
+ if (i__ > 1) {
+ prevlastv = max(prevlastv,lastv);
+ } else {
+ prevlastv = lastv;
+ }
+ }
+/* L20: */
+ }
+ } else {
+ prevlastv = 1;
+ for (i__ = *k; i__ >= 1; --i__) {
+ if (tau[i__] == 0.) {
+
+/* H(i) = I */
+
+ i__1 = *k;
+ for (j = i__; j <= i__1; ++j) {
+ t[j + i__ * t_dim1] = 0.;
+/* L30: */
+ }
+ } else {
+
+/* general case */
+
+ if (i__ < *k) {
+ if (lsame_(storev, "C")) {
+ vii = v[*n - *k + i__ + i__ * v_dim1];
+ v[*n - *k + i__ + i__ * v_dim1] = 1.;
+/* Skip any leading zeros. */
+ i__1 = i__ - 1;
+ for (lastv = 1; lastv <= i__1; ++lastv) {
+ if (v[lastv + i__ * v_dim1] != 0.) {
+ break;
+ }
+ }
+ j = max(lastv,prevlastv);
+
+/* T(i+1:k,i) := */
+/* - tau(i) * V(j:n-k+i,i+1:k)' * V(j:n-k+i,i) */
+
+ i__1 = *n - *k + i__ - j + 1;
+ i__2 = *k - i__;
+ d__1 = -tau[i__];
+ dgemv_("Transpose", &i__1, &i__2, &d__1, &v[j + (i__
+ + 1) * v_dim1], ldv, &v[j + i__ * v_dim1], &
+ c__1, &c_b8, &t[i__ + 1 + i__ * t_dim1], &
+ c__1);
+ v[*n - *k + i__ + i__ * v_dim1] = vii;
+ } else {
+ vii = v[i__ + (*n - *k + i__) * v_dim1];
+ v[i__ + (*n - *k + i__) * v_dim1] = 1.;
+/* Skip any leading zeros. */
+ i__1 = i__ - 1;
+ for (lastv = 1; lastv <= i__1; ++lastv) {
+ if (v[i__ + lastv * v_dim1] != 0.) {
+ break;
+ }
+ }
+ j = max(lastv,prevlastv);
+
+/* T(i+1:k,i) := */
+/* - tau(i) * V(i+1:k,j:n-k+i) * V(i,j:n-k+i)' */
+
+ i__1 = *k - i__;
+ i__2 = *n - *k + i__ - j + 1;
+ d__1 = -tau[i__];
+ dgemv_("No transpose", &i__1, &i__2, &d__1, &v[i__ +
+ 1 + j * v_dim1], ldv, &v[i__ + j * v_dim1],
+ ldv, &c_b8, &t[i__ + 1 + i__ * t_dim1], &c__1);
+ v[i__ + (*n - *k + i__) * v_dim1] = vii;
+ }
+
+/* T(i+1:k,i) := T(i+1:k,i+1:k) * T(i+1:k,i) */
+
+ i__1 = *k - i__;
+ dtrmv_("Lower", "No transpose", "Non-unit", &i__1, &t[i__
+ + 1 + (i__ + 1) * t_dim1], ldt, &t[i__ + 1 + i__ *
+ t_dim1], &c__1)
+ ;
+ if (i__ > 1) {
+ prevlastv = min(prevlastv,lastv);
+ } else {
+ prevlastv = lastv;
+ }
+ }
+ t[i__ + i__ * t_dim1] = tau[i__];
+ }
+/* L40: */
+ }
+ }
+ return 0;
+
+/* End of DLARFT */
+
+} /* dlarft_ */
diff --git a/lapack/double.cpp b/lapack/double.cpp
new file mode 100644
index 0000000..afabce3
--- /dev/null
+++ b/lapack/double.cpp
@@ -0,0 +1,18 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009-2014 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#define SCALAR double
+#define SCALAR_SUFFIX d
+#define SCALAR_SUFFIX_UP "D"
+#define ISCOMPLEX 0
+
+#include "cholesky.inc"
+#include "lu.inc"
+#include "eigenvalues.inc"
+#include "svd.inc"
diff --git a/lapack/dsecnd.c b/lapack/dsecnd.c
new file mode 100644
index 0000000..d74f805
--- /dev/null
+++ b/lapack/dsecnd.c
@@ -0,0 +1,18 @@
+#include "blaswrap.h"
+#include "f2c.h"
+#include <sys/times.h>
+#include <sys/types.h>
+#include <time.h>
+
+#ifndef CLK_TCK
+#define CLK_TCK 60
+#endif
+
+doublereal dsecnd_()
+{
+ struct tms rusage;
+
+ times(&rusage);
+ return (doublereal)(rusage.tms_utime) / CLK_TCK;
+
+} /* dsecnd_ */
diff --git a/lapack/eigenvalues.cpp b/lapack/eigenvalues.cpp
new file mode 100644
index 0000000..921c515
--- /dev/null
+++ b/lapack/eigenvalues.cpp
@@ -0,0 +1,62 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2011 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "lapack_common.h"
+#include <Eigen/Eigenvalues>
+
+// computes eigen values and vectors of a general N-by-N matrix A
+EIGEN_LAPACK_FUNC(syev,(char *jobz, char *uplo, int* n, Scalar* a, int *lda, Scalar* w, Scalar* /*work*/, int* lwork, int *info))
+{
+ // TODO exploit the work buffer
+ bool query_size = *lwork==-1;
+
+ *info = 0;
+ if(*jobz!='N' && *jobz!='V') *info = -1;
+ else if(UPLO(*uplo)==INVALID) *info = -2;
+ else if(*n<0) *info = -3;
+ else if(*lda<std::max(1,*n)) *info = -5;
+ else if((!query_size) && *lwork<std::max(1,3**n-1)) *info = -8;
+
+ if(*info!=0)
+ {
+ int e = -*info;
+ return xerbla_(SCALAR_SUFFIX_UP"SYEV ", &e, 6);
+ }
+
+ if(query_size)
+ {
+ *lwork = 0;
+ return 0;
+ }
+
+ if(*n==0)
+ return 0;
+
+ PlainMatrixType mat(*n,*n);
+ if(UPLO(*uplo)==UP) mat = matrix(a,*n,*n,*lda).adjoint();
+ else mat = matrix(a,*n,*n,*lda);
+
+ bool computeVectors = *jobz=='V' || *jobz=='v';
+ SelfAdjointEigenSolver<PlainMatrixType> eig(mat,computeVectors?ComputeEigenvectors:EigenvaluesOnly);
+
+ if(eig.info()==NoConvergence)
+ {
+ make_vector(w,*n).setZero();
+ if(computeVectors)
+ matrix(a,*n,*n,*lda).setIdentity();
+ //*info = 1;
+ return 0;
+ }
+
+ make_vector(w,*n) = eig.eigenvalues();
+ if(computeVectors)
+ matrix(a,*n,*n,*lda) = eig.eigenvectors();
+
+ return 0;
+}
diff --git a/lapack/eigenvalues.inc b/lapack/eigenvalues.inc
new file mode 100644
index 0000000..921c515
--- /dev/null
+++ b/lapack/eigenvalues.inc
@@ -0,0 +1,62 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2011 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "lapack_common.h"
+#include <Eigen/Eigenvalues>
+
+// computes eigen values and vectors of a general N-by-N matrix A
+EIGEN_LAPACK_FUNC(syev,(char *jobz, char *uplo, int* n, Scalar* a, int *lda, Scalar* w, Scalar* /*work*/, int* lwork, int *info))
+{
+ // TODO exploit the work buffer
+ bool query_size = *lwork==-1;
+
+ *info = 0;
+ if(*jobz!='N' && *jobz!='V') *info = -1;
+ else if(UPLO(*uplo)==INVALID) *info = -2;
+ else if(*n<0) *info = -3;
+ else if(*lda<std::max(1,*n)) *info = -5;
+ else if((!query_size) && *lwork<std::max(1,3**n-1)) *info = -8;
+
+ if(*info!=0)
+ {
+ int e = -*info;
+ return xerbla_(SCALAR_SUFFIX_UP"SYEV ", &e, 6);
+ }
+
+ if(query_size)
+ {
+ *lwork = 0;
+ return 0;
+ }
+
+ if(*n==0)
+ return 0;
+
+ PlainMatrixType mat(*n,*n);
+ if(UPLO(*uplo)==UP) mat = matrix(a,*n,*n,*lda).adjoint();
+ else mat = matrix(a,*n,*n,*lda);
+
+ bool computeVectors = *jobz=='V' || *jobz=='v';
+ SelfAdjointEigenSolver<PlainMatrixType> eig(mat,computeVectors?ComputeEigenvectors:EigenvaluesOnly);
+
+ if(eig.info()==NoConvergence)
+ {
+ make_vector(w,*n).setZero();
+ if(computeVectors)
+ matrix(a,*n,*n,*lda).setIdentity();
+ //*info = 1;
+ return 0;
+ }
+
+ make_vector(w,*n) = eig.eigenvalues();
+ if(computeVectors)
+ matrix(a,*n,*n,*lda) = eig.eigenvectors();
+
+ return 0;
+}
diff --git a/lapack/experimental/README.md b/lapack/experimental/README.md
new file mode 100644
index 0000000..86aaace
--- /dev/null
+++ b/lapack/experimental/README.md
@@ -0,0 +1,3 @@
+This directory contains C++11 replacment for the f2c-ed functions in the lapack
+directory. This is a temporary directory, which is being used to develop and
+stage these changes, once this code is upstreamed, it will be deleted.
diff --git a/lapack/experimental/ilaver.cpp b/lapack/experimental/ilaver.cpp
new file mode 100644
index 0000000..ddab5dd
--- /dev/null
+++ b/lapack/experimental/ilaver.cpp
@@ -0,0 +1,11 @@
+#include "../../Eigen/Core"
+
+extern "C" {
+void ilaver_(int* major, int* minor, int* patch);
+}
+
+void ilaver_(int* major, int* minor, int* patch) {
+ *major = EIGEN_WORLD_VERSION;
+ *minor = EIGEN_MAJOR_VERSION;
+ *patch = EIGEN_MINOR_VERSION;
+}
diff --git a/lapack/experimental/ilaxly.cpp b/lapack/experimental/ilaxly.cpp
new file mode 100644
index 0000000..c2e56a2
--- /dev/null
+++ b/lapack/experimental/ilaxly.cpp
@@ -0,0 +1,96 @@
+#include "../../Eigen/Core"
+
+extern "C" {
+int ilaslc_(int *m, int *n, float *a, int *lda);
+int iladlc_(int *m, int *n, double *a, int *lda);
+int ilaclc_(int *m, int *n, std::complex<float> *a, int *lda);
+int ilazlc_(int *m, int *n, std::complex<double> *a, int *lda);
+int ilaslr_(int *m, int *n, float *a, int *lda);
+int iladlr_(int *m, int *n, double *a, int *lda);
+int ilaclr_(int *m, int *n, std::complex<float> *a, int *lda);
+int ilazlr_(int *m, int *n, std::complex<double> *a, int *lda);
+}
+
+using Eigen::ColMajor;
+using Eigen::Dynamic;
+using Eigen::Map;
+using Eigen::Matrix;
+using Eigen::OuterStride;
+
+// Scan a matrix for its last non-zero column.
+template <typename T>
+int ilaxlc(const int m, const int n, T *a, const int lda) {
+ if (n == 0) return 0;
+ using MatrixType =
+ Map<Matrix<T, Dynamic, Dynamic, ColMajor>, 0, OuterStride<>>;
+ MatrixType a_matrix(a, m, n, OuterStride<>(lda));
+
+ // Quick test for the common case where one corner is non-zero.
+ if ((a_matrix(0, n - 1) != T(0)) || (a_matrix(m - 1, n - 1) != T(0))) {
+ return n;
+ }
+
+ // Now scan each column from the end, returning with the first non-zero.
+ int c = n - 1;
+ for (; c >= 0; --c) {
+ if ((a_matrix.array().col(c) != T(0)).any()) {
+ break;
+ }
+ }
+ return c + 1;
+}
+
+int ilaslc_(int *m, int *n, float *a, int *lda) {
+ return ilaxlc(*m, *n, a, *lda);
+}
+
+int iladlc_(int *m, int *n, double *a, int *lda) {
+ return ilaxlc(*m, *n, a, *lda);
+}
+
+int ilaclc_(int *m, int *n, std::complex<float> *a, int *lda) {
+ return ilaxlc(*m, *n, a, *lda);
+}
+
+int ilazlc_(int *m, int *n, std::complex<double> *a, int *lda) {
+ return ilaxlc(*m, *n, a, *lda);
+}
+
+// Scan a matrix for its last non-zero row.
+template <typename T>
+int ilaxlr(const int m, const int n, T *a, const int lda) {
+ if (m == 0) return m;
+ using MatrixType =
+ Map<Matrix<T, Dynamic, Dynamic, ColMajor>, 0, OuterStride<>>;
+ MatrixType a_matrix(a, m, n, OuterStride<>(lda));
+
+ // Quick test for the common case where one corner is non-zero.
+ if ((a_matrix(m - 1, 0) != T(0)) || (a_matrix(m - 1, n - 1) != T(0))) {
+ return m;
+ }
+
+ // Now scan each rowfrom the end, returning with the first non-zero.
+ int r = m - 1;
+ for (; r >= 0; --r) {
+ if ((a_matrix.array().row(r) == T(0)).any()) {
+ break;
+ }
+ }
+ return r + 1;
+}
+
+int ilaslr_(int *m, int *n, float *a, int *lda) {
+ return ilaxlr(*m, *n, a, *lda);
+}
+
+int iladlr_(int *m, int *n, double *a, int *lda) {
+ return ilaxlr(*m, *n, a, *lda);
+}
+
+int ilaclr_(int *m, int *n, std::complex<float> *a, int *lda) {
+ return ilaxlr(*m, *n, a, *lda);
+}
+
+int ilazlr_(int *m, int *n, std::complex<double> *a, int *lda) {
+ return ilaxlr(*m, *n, a, *lda);
+}
diff --git a/lapack/experimental/xlacgv.cpp b/lapack/experimental/xlacgv.cpp
new file mode 100644
index 0000000..d022a3b
--- /dev/null
+++ b/lapack/experimental/xlacgv.cpp
@@ -0,0 +1,27 @@
+#include "../../Eigen/Core"
+
+extern "C" {
+void clacgv_(int *n, std::complex<float> *x, int *incx);
+void zlacgv_(int *n, std::complex<double> *x, int *incx);
+}
+
+using Eigen::Map;
+using Eigen::Matrix;
+using Eigen::Dynamic;
+using Eigen::InnerStride;
+
+// Conjugate the entries of the vector x.
+template <typename T>
+void xlacgv(const int n, T *x, const int incx) {
+ using StridedVector = Map<Matrix<T, Dynamic, 1>, 0, InnerStride<Dynamic>>;
+ StridedVector xvec(x, n, InnerStride<Dynamic>(std::abs(incx)));
+ xvec = xvec.conjugate();
+}
+
+void clacgv_(int *n, std::complex<float> *x, int *incx) {
+ xlacgv(*n, x, *incx);
+}
+
+void zlacgv_(int *n, std::complex<double> *x, int *incx) {
+ xlacgv(*n, x, *incx);
+}
diff --git a/lapack/experimental/xladiv.cpp b/lapack/experimental/xladiv.cpp
new file mode 100644
index 0000000..381950f
--- /dev/null
+++ b/lapack/experimental/xladiv.cpp
@@ -0,0 +1,64 @@
+#include <cmath>
+#include <complex>
+
+extern "C" {
+void sladiv_(float* a, float* b, float* c, float* d, float* p, float* q);
+void dladiv_(double* a, double* b, double* c, double* d, double* p, double* q);
+std::complex<float> cladiv_(std::complex<float>* x, std::complex<float>* y);
+std::complex<double> zladiv_(std::complex<double>* x, std::complex<double>* y);
+}
+
+// This implementation is from pg. 21
+// http://www.open-std.org/jtc1/sc22/wg11/docs/n435.pdf and LLVM's libc++.
+template <typename T>
+void complex_divide(T a, T b, T c, T d, T& x, T& y) {
+ int ilogbw = 0;
+ const T logbw = std::logb(std::fmax(std::abs(c), std::abs(d)));
+ if (std::isfinite(logbw)) {
+ ilogbw = static_cast<int>(logbw);
+ c = scalbn(c, -ilogbw);
+ d = scalbn(d, -ilogbw);
+ }
+ const T denom = c * c + d * d;
+
+ x = scalbn((a * c + b * d) / denom, -ilogbw);
+ y = scalbn((b * c - a * d) / denom, -ilogbw);
+ if (std::isnan(x) && std::isnan(y)) {
+ if ((denom == T(0)) && (!std::isnan(a) || !std::isnan(b))) {
+ x = std::copysign(std::numeric_limits<T>::infinity(), c) * a;
+ y = std::copysign(std::numeric_limits<T>::infinity(), c) * b;
+ } else if ((std::isinf(a) || std::isinf(b)) && std::isfinite(c) &&
+ std::isfinite(d)) {
+ a = std::copysign(std::isinf(a) ? T(1) : T(0), a);
+ b = std::copysign(std::isinf(b) ? T(1) : T(0), b);
+ x = std::numeric_limits<T>::infinity() * (a * c + b * d);
+ y = std::numeric_limits<T>::infinity() * (b * c - a * d);
+ } else if (std::isinf(logbw) && logbw > T(0) && std::isfinite(a) &&
+ std::isfinite(b)) {
+ c = std::copysign(std::isinf(c) ? T(1) : T(0), c);
+ d = std::copysign(std::isinf(d) ? T(1) : T(0), d);
+ x = T(0) * (a * c + b * d);
+ y = T(0) * (b * c - a * d);
+ }
+ }
+}
+
+void sladiv_(float* a, float* b, float* c, float* d, float* p, float* q) {
+ complex_divide(*a, *b, *c, *d, *p, *q);
+}
+
+void dladiv_(double* a, double* b, double* c, double* d, double* p, double* q) {
+ complex_divide(*a, *b, *c, *d, *p, *q);
+}
+
+std::complex<float> cladiv_(std::complex<float>* x, std::complex<float>* y) {
+ float p, q;
+ complex_divide(x->real(), x->imag(), y->real(), y->imag(), p, q);
+ return std::complex<float>(p, q);
+}
+
+std::complex<double> zladiv_(std::complex<double>* x, std::complex<double>* y) {
+ double p, q;
+ complex_divide(x->real(), x->imag(), y->real(), y->imag(), p, q);
+ return std::complex<double>(p, q);
+}
diff --git a/lapack/experimental/xlamch.cpp b/lapack/experimental/xlamch.cpp
new file mode 100644
index 0000000..79efd80
--- /dev/null
+++ b/lapack/experimental/xlamch.cpp
@@ -0,0 +1,89 @@
+#include <limits>
+
+#include "../../Eigen/Core"
+
+extern "C" {
+float slamch_(char* cmach);
+double dlamch_(char* cmach);
+float slamc3_(char* cmach);
+double dlamc3_(char* cmach);
+}
+
+// Determines machine parameters.
+template <typename T>
+T xlamch(const char c) {
+ if (c == 'E' || c == 'e') {
+ // eps = relative machine precision. Looking at
+ // https://gcc.gnu.org/onlinedocs/gfortran/EPSILON.html observe that it is
+ // the smallest number E such that 1 + E > 1. It is NOT the same as
+ // numeric_limits::epsilon, which is the difference between 1 and the
+ // floating point number that succeeds it.
+ return std::numeric_limits<T>::epsilon() / std::numeric_limits<T>::radix;
+ }
+
+ if (c == 'S' || c == 's') {
+ // sfmin = safe minimum, such that 1 / sfmin does not overflow
+ EIGEN_CONSTEXPR T tiny = std::numeric_limits<T>::min();
+ EIGEN_CONSTEXPR T small = T(1) / std::numeric_limits<T>::max();
+ EIGEN_CONSTEXPR T small_scaled =
+ small * (T(1) + std::numeric_limits<T>::epsilon());
+ return (small >= tiny) ? small_scaled : tiny;
+ }
+
+ if (c == 'B' || c == 'b') {
+ // base = base of the machine.
+ return std::numeric_limits<T>::radix;
+ }
+
+ if (c == 'P' || c == 'p') {
+ // prec = eps * base
+ return std::numeric_limits<T>::epsilon();
+ }
+
+ if (c == 'N' || c == 'n') {
+ // t = number of (base) digits in the mantissa
+ return std::numeric_limits<T>::digits;
+ }
+
+ if (c == 'R' || c == 'r') {
+ // rnd = 1.0 when rounding occurs in addition.
+ return 1;
+ }
+
+ if (c == 'M' || c == 'm') {
+ // emin = minimum exponent before (gradual) underflow
+ return std::numeric_limits<T>::min_exponent;
+ }
+
+ if (c == 'U' || c == 'u') {
+ // rmin = underflow threshold - base**(emin-1)
+ return std::numeric_limits<T>::min();
+ }
+
+ if (c == 'L' || c == 'l') {
+ // emax = largest exponent before overflow
+ return std::numeric_limits<T>::max_exponent;
+ }
+ if (c == 'O' || c == 'o') {
+ // rmax = overflow threshold - (base**emax)*(1-eps)
+ return std::numeric_limits<T>::max();
+ }
+
+ return 0;
+}
+
+float slamch_(char* cmach) { return xlamch<float>(*cmach); }
+double dlamch_(char* cmach) { return xlamch<double>(*cmach); }
+
+// xLAMC3 is intended to force A and B to be stored prior to doing
+// the addition of A and B , for use in situations where optimizers
+// might hold one of these in a register.
+float slamc3_(float* a, float* b) {
+ volatile float retval = *a + *b;
+ return retval;
+}
+
+double dlamc3_(double* a, double* b) {
+ volatile double retval = *a + *b;
+ return retval;
+}
diff --git a/lapack/experimental/xlapy2.cpp b/lapack/experimental/xlapy2.cpp
new file mode 100644
index 0000000..5992f9e
--- /dev/null
+++ b/lapack/experimental/xlapy2.cpp
@@ -0,0 +1,24 @@
+#include <algorithm>
+#include <cmath>
+
+extern "C" {
+float slapy2_(float* x, float* y);
+double dlapy2_(double* x, double* y);
+}
+
+// Compute sqrt(x*x + y*y) taking care not to cause unnecessary overflow.
+template <typename T>
+T xlapy2(const T x, const T y) {
+ const T xabs = std::abs(x);
+ const T yabs = std::abs(y);
+ const T w = std::fmax(xabs, yabs);
+ const T z = std::fmin(xabs, yabs);
+ if (z > T(0)) {
+ const T t = z / w;
+ return w * std::sqrt(T(1) + t * t);
+ }
+ return w;
+}
+
+float slapy2_(float* x, float* y) { return xlapy2(*x, *y); }
+double dlapy2_(double* x, double* y) { return xlapy2(*x, *y); }
diff --git a/lapack/experimental/xlapy3.cpp b/lapack/experimental/xlapy3.cpp
new file mode 100644
index 0000000..9c935fa
--- /dev/null
+++ b/lapack/experimental/xlapy3.cpp
@@ -0,0 +1,30 @@
+#include <algorithm>
+#include <cmath>
+
+extern "C" {
+float slapy3_(float* x, float* y, float* z);
+double dlapy3_(double* x, double* y, double* z);
+}
+
+// Compute sqrt(x*x + y*y + z*z) taking care not to cause unnecessary overflow.
+template <typename T>
+T xlapy3(const T x, const T y, const T z) {
+ const T xabs = std::abs(x);
+ const T yabs = std::abs(y);
+ const T zabs = std::abs(z);
+ const T w = std::fmax(std::fmax(xabs, yabs), zabs);
+
+ if (w == T(0)) {
+ // W can be zero for max(0,nan,0) adding all three entries together will
+ // make sure NaN will not disappear.
+ return (xabs + yabs + zabs);
+ }
+
+ const T tx = xabs / w;
+ const T ty = yabs / w;
+ const T tz = zabs / w;
+ return w * std::sqrt(tx * tx + ty * ty + tz * tz);
+}
+
+float slapy3_(float* x, float* y, float* z) { return xlapy3(*x, *y, *z); }
+double dlapy3_(double* x, double* y, double* z) { return xlapy3(*x, *y, *z); }
diff --git a/lapack/experimental/xsecnd.cpp b/lapack/experimental/xsecnd.cpp
new file mode 100644
index 0000000..d9e3879
--- /dev/null
+++ b/lapack/experimental/xsecnd.cpp
@@ -0,0 +1,16 @@
+#include <ctime>
+
+extern "C" {
+float second_();
+double dsecnd_();
+}
+
+// Elapsed CPU Time in seconds.
+float second_(float* x, float* y) {
+ return static_cast<float>(std::clock()) / static_cast<float>(CLOCKS_PER_SEC);
+}
+
+double dsecnd_(double* x, double* y) {
+ return static_cast<double>(std::clock()) /
+ static_cast<double>(CLOCKS_PER_SEC);
+}
diff --git a/lapack/ilaclc.c b/lapack/ilaclc.c
new file mode 100644
index 0000000..98a0519
--- /dev/null
+++ b/lapack/ilaclc.c
@@ -0,0 +1,94 @@
+/* ilaclc.f -- translated by f2c (version 20061008).
+ You must link the resulting object file with libf2c:
+ on Microsoft Windows system, link with libf2c.lib;
+ on Linux or Unix systems, link with .../path/to/libf2c.a -lm
+ or, if you install libf2c.a in a standard place, with -lf2c -lm
+ -- in that order, at the end of the command line, as in
+ cc *.o -lf2c -lm
+ Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
+
+ http://www.netlib.org/f2c/libf2c.zip
+*/
+
+#include "f2c.h"
+#include "blaswrap.h"
+
+integer ilaclc_(integer *m, integer *n, complex *a, integer *lda)
+{
+ /* System generated locals */
+ integer a_dim1, a_offset, ret_val, i__1, i__2;
+
+ /* Local variables */
+ integer i__;
+
+
+/* -- LAPACK auxiliary routine (version 3.2.1) -- */
+
+/* -- April 2009 -- */
+
+/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
+/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
+
+/* .. Scalar Arguments .. */
+/* .. */
+/* .. Array Arguments .. */
+/* .. */
+
+/* Purpose */
+/* ======= */
+
+/* ILACLC scans A for its last non-zero column. */
+
+/* Arguments */
+/* ========= */
+
+/* M (input) INTEGER */
+/* The number of rows of the matrix A. */
+
+/* N (input) INTEGER */
+/* The number of columns of the matrix A. */
+
+/* A (input) COMPLEX array, dimension (LDA,N) */
+/* The m by n matrix A. */
+
+/* LDA (input) INTEGER */
+/* The leading dimension of the array A. LDA >= max(1,M). */
+
+/* ===================================================================== */
+
+/* .. Parameters .. */
+/* .. */
+/* .. Local Scalars .. */
+/* .. */
+/* .. Executable Statements .. */
+
+/* Quick test for the common case where one corner is non-zero. */
+ /* Parameter adjustments */
+ a_dim1 = *lda;
+ a_offset = 1 + a_dim1;
+ a -= a_offset;
+
+ /* Function Body */
+ if (*n == 0) {
+ ret_val = *n;
+ } else /* if(complicated condition) */ {
+ i__1 = *n * a_dim1 + 1;
+ i__2 = *m + *n * a_dim1;
+ if (a[i__1].r != 0.f || a[i__1].i != 0.f || (a[i__2].r != 0.f || a[
+ i__2].i != 0.f)) {
+ ret_val = *n;
+ } else {
+/* Now scan each column from the end, returning with the first non-zero. */
+ for (ret_val = *n; ret_val >= 1; --ret_val) {
+ i__1 = *m;
+ for (i__ = 1; i__ <= i__1; ++i__) {
+ i__2 = i__ + ret_val * a_dim1;
+ if (a[i__2].r != 0.f || a[i__2].i != 0.f) {
+ return ret_val;
+ }
+ }
+ }
+ }
+ }
+ return ret_val;
+} /* ilaclc_ */
diff --git a/lapack/ilaclr.c b/lapack/ilaclr.c
new file mode 100644
index 0000000..b28e22e
--- /dev/null
+++ b/lapack/ilaclr.c
@@ -0,0 +1,96 @@
+/* ilaclr.f -- translated by f2c (version 20061008).
+ You must link the resulting object file with libf2c:
+ on Microsoft Windows system, link with libf2c.lib;
+ on Linux or Unix systems, link with .../path/to/libf2c.a -lm
+ or, if you install libf2c.a in a standard place, with -lf2c -lm
+ -- in that order, at the end of the command line, as in
+ cc *.o -lf2c -lm
+ Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
+
+ http://www.netlib.org/f2c/libf2c.zip
+*/
+
+#include "f2c.h"
+#include "blaswrap.h"
+
+integer ilaclr_(integer *m, integer *n, complex *a, integer *lda)
+{
+ /* System generated locals */
+ integer a_dim1, a_offset, ret_val, i__1, i__2;
+
+ /* Local variables */
+ integer i__, j;
+
+
+/* -- LAPACK auxiliary routine (version 3.2.1) -- */
+
+/* -- April 2009 -- */
+
+/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
+/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
+
+/* .. Scalar Arguments .. */
+/* .. */
+/* .. Array Arguments .. */
+/* .. */
+
+/* Purpose */
+/* ======= */
+
+/* ILACLR scans A for its last non-zero row. */
+
+/* Arguments */
+/* ========= */
+
+/* M (input) INTEGER */
+/* The number of rows of the matrix A. */
+
+/* N (input) INTEGER */
+/* The number of columns of the matrix A. */
+
+/* A (input) COMPLEX array, dimension (LDA,N) */
+/* The m by n matrix A. */
+
+/* LDA (input) INTEGER */
+/* The leading dimension of the array A. LDA >= max(1,M). */
+
+/* ===================================================================== */
+
+/* .. Parameters .. */
+/* .. */
+/* .. Local Scalars .. */
+/* .. */
+/* .. Executable Statements .. */
+
+/* Quick test for the common case where one corner is non-zero. */
+ /* Parameter adjustments */
+ a_dim1 = *lda;
+ a_offset = 1 + a_dim1;
+ a -= a_offset;
+
+ /* Function Body */
+ if (*m == 0) {
+ ret_val = *m;
+ } else /* if(complicated condition) */ {
+ i__1 = *m + a_dim1;
+ i__2 = *m + *n * a_dim1;
+ if (a[i__1].r != 0.f || a[i__1].i != 0.f || (a[i__2].r != 0.f || a[
+ i__2].i != 0.f)) {
+ ret_val = *m;
+ } else {
+/* Scan up each column tracking the last zero row seen. */
+ ret_val = 0;
+ i__1 = *n;
+ for (j = 1; j <= i__1; ++j) {
+ for (i__ = *m; i__ >= 1; --i__) {
+ i__2 = i__ + j * a_dim1;
+ if (a[i__2].r != 0.f || a[i__2].i != 0.f) {
+ break;
+ }
+ }
+ ret_val = max(ret_val,i__);
+ }
+ }
+ }
+ return ret_val;
+} /* ilaclr_ */
diff --git a/lapack/iladlc.c b/lapack/iladlc.c
new file mode 100644
index 0000000..a18f02e
--- /dev/null
+++ b/lapack/iladlc.c
@@ -0,0 +1,88 @@
+/* iladlc.f -- translated by f2c (version 20061008).
+ You must link the resulting object file with libf2c:
+ on Microsoft Windows system, link with libf2c.lib;
+ on Linux or Unix systems, link with .../path/to/libf2c.a -lm
+ or, if you install libf2c.a in a standard place, with -lf2c -lm
+ -- in that order, at the end of the command line, as in
+ cc *.o -lf2c -lm
+ Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
+
+ http://www.netlib.org/f2c/libf2c.zip
+*/
+
+#include "f2c.h"
+#include "blaswrap.h"
+
+integer iladlc_(integer *m, integer *n, doublereal *a, integer *lda)
+{
+ /* System generated locals */
+ integer a_dim1, a_offset, ret_val, i__1;
+
+ /* Local variables */
+ integer i__;
+
+
+/* -- LAPACK auxiliary routine (version 3.2.1) -- */
+
+/* -- April 2009 -- */
+
+/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
+/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
+
+/* .. Scalar Arguments .. */
+/* .. */
+/* .. Array Arguments .. */
+/* .. */
+
+/* Purpose */
+/* ======= */
+
+/* ILADLC scans A for its last non-zero column. */
+
+/* Arguments */
+/* ========= */
+
+/* M (input) INTEGER */
+/* The number of rows of the matrix A. */
+
+/* N (input) INTEGER */
+/* The number of columns of the matrix A. */
+
+/* A (input) DOUBLE PRECISION array, dimension (LDA,N) */
+/* The m by n matrix A. */
+
+/* LDA (input) INTEGER */
+/* The leading dimension of the array A. LDA >= max(1,M). */
+
+/* ===================================================================== */
+
+/* .. Parameters .. */
+/* .. */
+/* .. Local Scalars .. */
+/* .. */
+/* .. Executable Statements .. */
+
+/* Quick test for the common case where one corner is non-zero. */
+ /* Parameter adjustments */
+ a_dim1 = *lda;
+ a_offset = 1 + a_dim1;
+ a -= a_offset;
+
+ /* Function Body */
+ if (*n == 0) {
+ ret_val = *n;
+ } else if (a[*n * a_dim1 + 1] != 0. || a[*m + *n * a_dim1] != 0.) {
+ ret_val = *n;
+ } else {
+/* Now scan each column from the end, returning with the first non-zero. */
+ for (ret_val = *n; ret_val >= 1; --ret_val) {
+ i__1 = *m;
+ for (i__ = 1; i__ <= i__1; ++i__) {
+ if (a[i__ + ret_val * a_dim1] != 0.) {
+ return ret_val;
+ }
+ }
+ }
+ }
+ return ret_val;
+} /* iladlc_ */
diff --git a/lapack/iladlr.c b/lapack/iladlr.c
new file mode 100644
index 0000000..f1626e4
--- /dev/null
+++ b/lapack/iladlr.c
@@ -0,0 +1,90 @@
+/* iladlr.f -- translated by f2c (version 20061008).
+ You must link the resulting object file with libf2c:
+ on Microsoft Windows system, link with libf2c.lib;
+ on Linux or Unix systems, link with .../path/to/libf2c.a -lm
+ or, if you install libf2c.a in a standard place, with -lf2c -lm
+ -- in that order, at the end of the command line, as in
+ cc *.o -lf2c -lm
+ Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
+
+ http://www.netlib.org/f2c/libf2c.zip
+*/
+
+#include "f2c.h"
+#include "blaswrap.h"
+
+integer iladlr_(integer *m, integer *n, doublereal *a, integer *lda)
+{
+ /* System generated locals */
+ integer a_dim1, a_offset, ret_val, i__1;
+
+ /* Local variables */
+ integer i__, j;
+
+
+/* -- LAPACK auxiliary routine (version 3.2.1) -- */
+
+/* -- April 2009 -- */
+
+/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
+/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
+
+/* .. Scalar Arguments .. */
+/* .. */
+/* .. Array Arguments .. */
+/* .. */
+
+/* Purpose */
+/* ======= */
+
+/* ILADLR scans A for its last non-zero row. */
+
+/* Arguments */
+/* ========= */
+
+/* M (input) INTEGER */
+/* The number of rows of the matrix A. */
+
+/* N (input) INTEGER */
+/* The number of columns of the matrix A. */
+
+/* A (input) DOUBLE PRECISION array, dimension (LDA,N) */
+/* The m by n matrix A. */
+
+/* LDA (input) INTEGER */
+/* The leading dimension of the array A. LDA >= max(1,M). */
+
+/* ===================================================================== */
+
+/* .. Parameters .. */
+/* .. */
+/* .. Local Scalars .. */
+/* .. */
+/* .. Executable Statements .. */
+
+/* Quick test for the common case where one corner is non-zero. */
+ /* Parameter adjustments */
+ a_dim1 = *lda;
+ a_offset = 1 + a_dim1;
+ a -= a_offset;
+
+ /* Function Body */
+ if (*m == 0) {
+ ret_val = *m;
+ } else if (a[*m + a_dim1] != 0. || a[*m + *n * a_dim1] != 0.) {
+ ret_val = *m;
+ } else {
+/* Scan up each column tracking the last zero row seen. */
+ ret_val = 0;
+ i__1 = *n;
+ for (j = 1; j <= i__1; ++j) {
+ for (i__ = *m; i__ >= 1; --i__) {
+ if (a[i__ + j * a_dim1] != 0.) {
+ break;
+ }
+ }
+ ret_val = max(ret_val,i__);
+ }
+ }
+ return ret_val;
+} /* iladlr_ */
diff --git a/lapack/ilaslc.c b/lapack/ilaslc.c
new file mode 100644
index 0000000..c877084
--- /dev/null
+++ b/lapack/ilaslc.c
@@ -0,0 +1,88 @@
+/* ilaslc.f -- translated by f2c (version 20061008).
+ You must link the resulting object file with libf2c:
+ on Microsoft Windows system, link with libf2c.lib;
+ on Linux or Unix systems, link with .../path/to/libf2c.a -lm
+ or, if you install libf2c.a in a standard place, with -lf2c -lm
+ -- in that order, at the end of the command line, as in
+ cc *.o -lf2c -lm
+ Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
+
+ http://www.netlib.org/f2c/libf2c.zip
+*/
+
+#include "f2c.h"
+#include "blaswrap.h"
+
+integer ilaslc_(integer *m, integer *n, real *a, integer *lda)
+{
+ /* System generated locals */
+ integer a_dim1, a_offset, ret_val, i__1;
+
+ /* Local variables */
+ integer i__;
+
+
+/* -- LAPACK auxiliary routine (version 3.2.1) -- */
+
+/* -- April 2009 -- */
+
+/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
+/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
+
+/* .. Scalar Arguments .. */
+/* .. */
+/* .. Array Arguments .. */
+/* .. */
+
+/* Purpose */
+/* ======= */
+
+/* ILASLC scans A for its last non-zero column. */
+
+/* Arguments */
+/* ========= */
+
+/* M (input) INTEGER */
+/* The number of rows of the matrix A. */
+
+/* N (input) INTEGER */
+/* The number of columns of the matrix A. */
+
+/* A (input) REAL array, dimension (LDA,N) */
+/* The m by n matrix A. */
+
+/* LDA (input) INTEGER */
+/* The leading dimension of the array A. LDA >= max(1,M). */
+
+/* ===================================================================== */
+
+/* .. Parameters .. */
+/* .. */
+/* .. Local Scalars .. */
+/* .. */
+/* .. Executable Statements .. */
+
+/* Quick test for the common case where one corner is non-zero. */
+ /* Parameter adjustments */
+ a_dim1 = *lda;
+ a_offset = 1 + a_dim1;
+ a -= a_offset;
+
+ /* Function Body */
+ if (*n == 0) {
+ ret_val = *n;
+ } else if (a[*n * a_dim1 + 1] != 0.f || a[*m + *n * a_dim1] != 0.f) {
+ ret_val = *n;
+ } else {
+/* Now scan each column from the end, returning with the first non-zero. */
+ for (ret_val = *n; ret_val >= 1; --ret_val) {
+ i__1 = *m;
+ for (i__ = 1; i__ <= i__1; ++i__) {
+ if (a[i__ + ret_val * a_dim1] != 0.f) {
+ return ret_val;
+ }
+ }
+ }
+ }
+ return ret_val;
+} /* ilaslc_ */
diff --git a/lapack/ilaslr.c b/lapack/ilaslr.c
new file mode 100644
index 0000000..0aaa4a0
--- /dev/null
+++ b/lapack/ilaslr.c
@@ -0,0 +1,90 @@
+/* ilaslr.f -- translated by f2c (version 20061008).
+ You must link the resulting object file with libf2c:
+ on Microsoft Windows system, link with libf2c.lib;
+ on Linux or Unix systems, link with .../path/to/libf2c.a -lm
+ or, if you install libf2c.a in a standard place, with -lf2c -lm
+ -- in that order, at the end of the command line, as in
+ cc *.o -lf2c -lm
+ Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
+
+ http://www.netlib.org/f2c/libf2c.zip
+*/
+
+#include "f2c.h"
+#include "blaswrap.h"
+
+integer ilaslr_(integer *m, integer *n, real *a, integer *lda)
+{
+ /* System generated locals */
+ integer a_dim1, a_offset, ret_val, i__1;
+
+ /* Local variables */
+ integer i__, j;
+
+
+/* -- LAPACK auxiliary routine (version 3.2.1) -- */
+
+/* -- April 2009 -- */
+
+/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
+/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
+
+/* .. Scalar Arguments .. */
+/* .. */
+/* .. Array Arguments .. */
+/* .. */
+
+/* Purpose */
+/* ======= */
+
+/* ILASLR scans A for its last non-zero row. */
+
+/* Arguments */
+/* ========= */
+
+/* M (input) INTEGER */
+/* The number of rows of the matrix A. */
+
+/* N (input) INTEGER */
+/* The number of columns of the matrix A. */
+
+/* A (input) REAL array, dimension (LDA,N) */
+/* The m by n matrix A. */
+
+/* LDA (input) INTEGER */
+/* The leading dimension of the array A. LDA >= max(1,M). */
+
+/* ===================================================================== */
+
+/* .. Parameters .. */
+/* .. */
+/* .. Local Scalars .. */
+/* .. */
+/* .. Executable Statements .. */
+
+/* Quick test for the common case where one corner is non-zero. */
+ /* Parameter adjustments */
+ a_dim1 = *lda;
+ a_offset = 1 + a_dim1;
+ a -= a_offset;
+
+ /* Function Body */
+ if (*m == 0) {
+ ret_val = *m;
+ } else if (a[*m + a_dim1] != 0.f || a[*m + *n * a_dim1] != 0.f) {
+ ret_val = *m;
+ } else {
+/* Scan up each column tracking the last zero row seen. */
+ ret_val = 0;
+ i__1 = *n;
+ for (j = 1; j <= i__1; ++j) {
+ for (i__ = *m; i__ >= 1; --i__) {
+ if (a[i__ + j * a_dim1] != 0.f) {
+ break;
+ }
+ }
+ ret_val = max(ret_val,i__);
+ }
+ }
+ return ret_val;
+} /* ilaslr_ */
diff --git a/lapack/ilazlc.c b/lapack/ilazlc.c
new file mode 100644
index 0000000..2b20f40
--- /dev/null
+++ b/lapack/ilazlc.c
@@ -0,0 +1,94 @@
+/* ilazlc.f -- translated by f2c (version 20061008).
+ You must link the resulting object file with libf2c:
+ on Microsoft Windows system, link with libf2c.lib;
+ on Linux or Unix systems, link with .../path/to/libf2c.a -lm
+ or, if you install libf2c.a in a standard place, with -lf2c -lm
+ -- in that order, at the end of the command line, as in
+ cc *.o -lf2c -lm
+ Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
+
+ http://www.netlib.org/f2c/libf2c.zip
+*/
+
+#include "f2c.h"
+#include "blaswrap.h"
+
+integer ilazlc_(integer *m, integer *n, doublecomplex *a, integer *lda)
+{
+ /* System generated locals */
+ integer a_dim1, a_offset, ret_val, i__1, i__2;
+
+ /* Local variables */
+ integer i__;
+
+
+/* -- LAPACK auxiliary routine (version 3.2.1) -- */
+
+/* -- April 2009 -- */
+
+/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
+/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
+
+/* .. Scalar Arguments .. */
+/* .. */
+/* .. Array Arguments .. */
+/* .. */
+
+/* Purpose */
+/* ======= */
+
+/* ILAZLC scans A for its last non-zero column. */
+
+/* Arguments */
+/* ========= */
+
+/* M (input) INTEGER */
+/* The number of rows of the matrix A. */
+
+/* N (input) INTEGER */
+/* The number of columns of the matrix A. */
+
+/* A (input) COMPLEX*16 array, dimension (LDA,N) */
+/* The m by n matrix A. */
+
+/* LDA (input) INTEGER */
+/* The leading dimension of the array A. LDA >= max(1,M). */
+
+/* ===================================================================== */
+
+/* .. Parameters .. */
+/* .. */
+/* .. Local Scalars .. */
+/* .. */
+/* .. Executable Statements .. */
+
+/* Quick test for the common case where one corner is non-zero. */
+ /* Parameter adjustments */
+ a_dim1 = *lda;
+ a_offset = 1 + a_dim1;
+ a -= a_offset;
+
+ /* Function Body */
+ if (*n == 0) {
+ ret_val = *n;
+ } else /* if(complicated condition) */ {
+ i__1 = *n * a_dim1 + 1;
+ i__2 = *m + *n * a_dim1;
+ if (a[i__1].r != 0. || a[i__1].i != 0. || (a[i__2].r != 0. || a[i__2]
+ .i != 0.)) {
+ ret_val = *n;
+ } else {
+/* Now scan each column from the end, returning with the first non-zero. */
+ for (ret_val = *n; ret_val >= 1; --ret_val) {
+ i__1 = *m;
+ for (i__ = 1; i__ <= i__1; ++i__) {
+ i__2 = i__ + ret_val * a_dim1;
+ if (a[i__2].r != 0. || a[i__2].i != 0.) {
+ return ret_val;
+ }
+ }
+ }
+ }
+ }
+ return ret_val;
+} /* ilazlc_ */
diff --git a/lapack/ilazlr.c b/lapack/ilazlr.c
new file mode 100644
index 0000000..373d077
--- /dev/null
+++ b/lapack/ilazlr.c
@@ -0,0 +1,96 @@
+/* ilazlr.f -- translated by f2c (version 20061008).
+ You must link the resulting object file with libf2c:
+ on Microsoft Windows system, link with libf2c.lib;
+ on Linux or Unix systems, link with .../path/to/libf2c.a -lm
+ or, if you install libf2c.a in a standard place, with -lf2c -lm
+ -- in that order, at the end of the command line, as in
+ cc *.o -lf2c -lm
+ Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
+
+ http://www.netlib.org/f2c/libf2c.zip
+*/
+
+#include "f2c.h"
+#include "blaswrap.h"
+
+integer ilazlr_(integer *m, integer *n, doublecomplex *a, integer *lda)
+{
+ /* System generated locals */
+ integer a_dim1, a_offset, ret_val, i__1, i__2;
+
+ /* Local variables */
+ integer i__, j;
+
+
+/* -- LAPACK auxiliary routine (version 3.2.1) -- */
+
+/* -- April 2009 -- */
+
+/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
+/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
+
+/* .. Scalar Arguments .. */
+/* .. */
+/* .. Array Arguments .. */
+/* .. */
+
+/* Purpose */
+/* ======= */
+
+/* ILAZLR scans A for its last non-zero row. */
+
+/* Arguments */
+/* ========= */
+
+/* M (input) INTEGER */
+/* The number of rows of the matrix A. */
+
+/* N (input) INTEGER */
+/* The number of columns of the matrix A. */
+
+/* A (input) COMPLEX*16 array, dimension (LDA,N) */
+/* The m by n matrix A. */
+
+/* LDA (input) INTEGER */
+/* The leading dimension of the array A. LDA >= max(1,M). */
+
+/* ===================================================================== */
+
+/* .. Parameters .. */
+/* .. */
+/* .. Local Scalars .. */
+/* .. */
+/* .. Executable Statements .. */
+
+/* Quick test for the common case where one corner is non-zero. */
+ /* Parameter adjustments */
+ a_dim1 = *lda;
+ a_offset = 1 + a_dim1;
+ a -= a_offset;
+
+ /* Function Body */
+ if (*m == 0) {
+ ret_val = *m;
+ } else /* if(complicated condition) */ {
+ i__1 = *m + a_dim1;
+ i__2 = *m + *n * a_dim1;
+ if (a[i__1].r != 0. || a[i__1].i != 0. || (a[i__2].r != 0. || a[i__2]
+ .i != 0.)) {
+ ret_val = *m;
+ } else {
+/* Scan up each column tracking the last zero row seen. */
+ ret_val = 0;
+ i__1 = *n;
+ for (j = 1; j <= i__1; ++j) {
+ for (i__ = *m; i__ >= 1; --i__) {
+ i__2 = i__ + j * a_dim1;
+ if (a[i__2].r != 0. || a[i__2].i != 0.) {
+ break;
+ }
+ }
+ ret_val = max(ret_val,i__);
+ }
+ }
+ }
+ return ret_val;
+} /* ilazlr_ */
diff --git a/lapack/lapack_common.h b/lapack/lapack_common.h
new file mode 100644
index 0000000..c872a81
--- /dev/null
+++ b/lapack/lapack_common.h
@@ -0,0 +1,29 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2010-2014 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_LAPACK_COMMON_H
+#define EIGEN_LAPACK_COMMON_H
+
+#include "../blas/common.h"
+#include "../Eigen/src/misc/lapack.h"
+
+#define EIGEN_LAPACK_FUNC(FUNC,ARGLIST) \
+ extern "C" { int EIGEN_BLAS_FUNC(FUNC) ARGLIST; } \
+ int EIGEN_BLAS_FUNC(FUNC) ARGLIST
+
+typedef Eigen::Map<Eigen::Transpositions<Eigen::Dynamic,Eigen::Dynamic,int> > PivotsType;
+
+#if ISCOMPLEX
+#define EIGEN_LAPACK_ARG_IF_COMPLEX(X) X,
+#else
+#define EIGEN_LAPACK_ARG_IF_COMPLEX(X)
+#endif
+
+
+#endif // EIGEN_LAPACK_COMMON_H
diff --git a/lapack/lu.cpp b/lapack/lu.cpp
new file mode 100644
index 0000000..90cebe0
--- /dev/null
+++ b/lapack/lu.cpp
@@ -0,0 +1,89 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2010-2011 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "common.h"
+#include <Eigen/LU>
+
+// computes an LU factorization of a general M-by-N matrix A using partial pivoting with row interchanges
+EIGEN_LAPACK_FUNC(getrf,(int *m, int *n, RealScalar *pa, int *lda, int *ipiv, int *info))
+{
+ *info = 0;
+ if(*m<0) *info = -1;
+ else if(*n<0) *info = -2;
+ else if(*lda<std::max(1,*m)) *info = -4;
+ if(*info!=0)
+ {
+ int e = -*info;
+ return xerbla_(SCALAR_SUFFIX_UP"GETRF", &e, 6);
+ }
+
+ if(*m==0 || *n==0)
+ return 0;
+
+ Scalar* a = reinterpret_cast<Scalar*>(pa);
+ int nb_transpositions;
+ int ret = int(Eigen::internal::partial_lu_impl<Scalar,ColMajor,int>
+ ::blocked_lu(*m, *n, a, *lda, ipiv, nb_transpositions));
+
+ for(int i=0; i<std::min(*m,*n); ++i)
+ ipiv[i]++;
+
+ if(ret>=0)
+ *info = ret+1;
+
+ return 0;
+}
+
+//GETRS solves a system of linear equations
+// A * X = B or A' * X = B
+// with a general N-by-N matrix A using the LU factorization computed by GETRF
+EIGEN_LAPACK_FUNC(getrs,(char *trans, int *n, int *nrhs, RealScalar *pa, int *lda, int *ipiv, RealScalar *pb, int *ldb, int *info))
+{
+ *info = 0;
+ if(OP(*trans)==INVALID) *info = -1;
+ else if(*n<0) *info = -2;
+ else if(*nrhs<0) *info = -3;
+ else if(*lda<std::max(1,*n)) *info = -5;
+ else if(*ldb<std::max(1,*n)) *info = -8;
+ if(*info!=0)
+ {
+ int e = -*info;
+ return xerbla_(SCALAR_SUFFIX_UP"GETRS", &e, 6);
+ }
+
+ Scalar* a = reinterpret_cast<Scalar*>(pa);
+ Scalar* b = reinterpret_cast<Scalar*>(pb);
+ MatrixType lu(a,*n,*n,*lda);
+ MatrixType B(b,*n,*nrhs,*ldb);
+
+ for(int i=0; i<*n; ++i)
+ ipiv[i]--;
+ if(OP(*trans)==NOTR)
+ {
+ B = PivotsType(ipiv,*n) * B;
+ lu.triangularView<UnitLower>().solveInPlace(B);
+ lu.triangularView<Upper>().solveInPlace(B);
+ }
+ else if(OP(*trans)==TR)
+ {
+ lu.triangularView<Upper>().transpose().solveInPlace(B);
+ lu.triangularView<UnitLower>().transpose().solveInPlace(B);
+ B = PivotsType(ipiv,*n).transpose() * B;
+ }
+ else if(OP(*trans)==ADJ)
+ {
+ lu.triangularView<Upper>().adjoint().solveInPlace(B);
+ lu.triangularView<UnitLower>().adjoint().solveInPlace(B);
+ B = PivotsType(ipiv,*n).transpose() * B;
+ }
+ for(int i=0; i<*n; ++i)
+ ipiv[i]++;
+
+ return 0;
+}
diff --git a/lapack/lu.inc b/lapack/lu.inc
new file mode 100644
index 0000000..90cebe0
--- /dev/null
+++ b/lapack/lu.inc
@@ -0,0 +1,89 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2010-2011 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "common.h"
+#include <Eigen/LU>
+
+// computes an LU factorization of a general M-by-N matrix A using partial pivoting with row interchanges
+EIGEN_LAPACK_FUNC(getrf,(int *m, int *n, RealScalar *pa, int *lda, int *ipiv, int *info))
+{
+ *info = 0;
+ if(*m<0) *info = -1;
+ else if(*n<0) *info = -2;
+ else if(*lda<std::max(1,*m)) *info = -4;
+ if(*info!=0)
+ {
+ int e = -*info;
+ return xerbla_(SCALAR_SUFFIX_UP"GETRF", &e, 6);
+ }
+
+ if(*m==0 || *n==0)
+ return 0;
+
+ Scalar* a = reinterpret_cast<Scalar*>(pa);
+ int nb_transpositions;
+ int ret = int(Eigen::internal::partial_lu_impl<Scalar,ColMajor,int>
+ ::blocked_lu(*m, *n, a, *lda, ipiv, nb_transpositions));
+
+ for(int i=0; i<std::min(*m,*n); ++i)
+ ipiv[i]++;
+
+ if(ret>=0)
+ *info = ret+1;
+
+ return 0;
+}
+
+//GETRS solves a system of linear equations
+// A * X = B or A' * X = B
+// with a general N-by-N matrix A using the LU factorization computed by GETRF
+EIGEN_LAPACK_FUNC(getrs,(char *trans, int *n, int *nrhs, RealScalar *pa, int *lda, int *ipiv, RealScalar *pb, int *ldb, int *info))
+{
+ *info = 0;
+ if(OP(*trans)==INVALID) *info = -1;
+ else if(*n<0) *info = -2;
+ else if(*nrhs<0) *info = -3;
+ else if(*lda<std::max(1,*n)) *info = -5;
+ else if(*ldb<std::max(1,*n)) *info = -8;
+ if(*info!=0)
+ {
+ int e = -*info;
+ return xerbla_(SCALAR_SUFFIX_UP"GETRS", &e, 6);
+ }
+
+ Scalar* a = reinterpret_cast<Scalar*>(pa);
+ Scalar* b = reinterpret_cast<Scalar*>(pb);
+ MatrixType lu(a,*n,*n,*lda);
+ MatrixType B(b,*n,*nrhs,*ldb);
+
+ for(int i=0; i<*n; ++i)
+ ipiv[i]--;
+ if(OP(*trans)==NOTR)
+ {
+ B = PivotsType(ipiv,*n) * B;
+ lu.triangularView<UnitLower>().solveInPlace(B);
+ lu.triangularView<Upper>().solveInPlace(B);
+ }
+ else if(OP(*trans)==TR)
+ {
+ lu.triangularView<Upper>().transpose().solveInPlace(B);
+ lu.triangularView<UnitLower>().transpose().solveInPlace(B);
+ B = PivotsType(ipiv,*n).transpose() * B;
+ }
+ else if(OP(*trans)==ADJ)
+ {
+ lu.triangularView<Upper>().adjoint().solveInPlace(B);
+ lu.triangularView<UnitLower>().adjoint().solveInPlace(B);
+ B = PivotsType(ipiv,*n).transpose() * B;
+ }
+ for(int i=0; i<*n; ++i)
+ ipiv[i]++;
+
+ return 0;
+}
diff --git a/lapack/second.c b/lapack/second.c
new file mode 100644
index 0000000..33c7dde
--- /dev/null
+++ b/lapack/second.c
@@ -0,0 +1,17 @@
+#include "f2c.h"
+#include <sys/times.h>
+#include <sys/types.h>
+#include <time.h>
+
+#ifndef CLK_TCK
+#define CLK_TCK 60
+#endif
+
+doublereal second_()
+{
+ struct tms rusage;
+
+ times(&rusage);
+ return (doublereal)(rusage.tms_utime) / CLK_TCK;
+
+} /* second_ */
diff --git a/lapack/single.cpp b/lapack/single.cpp
new file mode 100644
index 0000000..2994436
--- /dev/null
+++ b/lapack/single.cpp
@@ -0,0 +1,18 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009-2014 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#define SCALAR float
+#define SCALAR_SUFFIX s
+#define SCALAR_SUFFIX_UP "S"
+#define ISCOMPLEX 0
+
+#include "cholesky.inc"
+#include "lu.inc"
+#include "eigenvalues.inc"
+#include "svd.inc"
diff --git a/lapack/sladiv.c b/lapack/sladiv.c
new file mode 100644
index 0000000..af4e0c5
--- /dev/null
+++ b/lapack/sladiv.c
@@ -0,0 +1,78 @@
+/* sladiv.f -- translated by f2c (version 20061008).
+ You must link the resulting object file with libf2c:
+ on Microsoft Windows system, link with libf2c.lib;
+ on Linux or Unix systems, link with .../path/to/libf2c.a -lm
+ or, if you install libf2c.a in a standard place, with -lf2c -lm
+ -- in that order, at the end of the command line, as in
+ cc *.o -lf2c -lm
+ Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
+
+ http://www.netlib.org/f2c/libf2c.zip
+*/
+
+#include "f2c.h"
+#include "blaswrap.h"
+
+/* Subroutine */ int sladiv_(real *a, real *b, real *c__, real *d__, real *p,
+ real *q)
+{
+ real e, f;
+
+
+/* -- LAPACK auxiliary routine (version 3.2) -- */
+/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
+/* November 2006 */
+
+/* .. Scalar Arguments .. */
+/* .. */
+
+/* Purpose */
+/* ======= */
+
+/* SLADIV performs complex division in real arithmetic */
+
+/* a + i*b */
+/* p + i*q = --------- */
+/* c + i*d */
+
+/* The algorithm is due to Robert L. Smith and can be found */
+/* in D. Knuth, The art of Computer Programming, Vol.2, p.195 */
+
+/* Arguments */
+/* ========= */
+
+/* A (input) REAL */
+/* B (input) REAL */
+/* C (input) REAL */
+/* D (input) REAL */
+/* The scalars a, b, c, and d in the above expression. */
+
+/* P (output) REAL */
+/* Q (output) REAL */
+/* The scalars p and q in the above expression. */
+
+/* ===================================================================== */
+
+/* .. Local Scalars .. */
+/* .. */
+/* .. Intrinsic Functions .. */
+/* .. */
+/* .. Executable Statements .. */
+
+ if (dabs(*d__) < dabs(*c__)) {
+ e = *d__ / *c__;
+ f = *c__ + *d__ * e;
+ *p = (*a + *b * e) / f;
+ *q = (*b - *a * e) / f;
+ } else {
+ e = *c__ / *d__;
+ f = *d__ + *c__ * e;
+ *p = (*b + *a * e) / f;
+ *q = (-(*a) + *b * e) / f;
+ }
+
+ return 0;
+
+/* End of SLADIV */
+
+} /* sladiv_ */
diff --git a/lapack/slamch.c b/lapack/slamch.c
new file mode 100644
index 0000000..e57b5e5
--- /dev/null
+++ b/lapack/slamch.c
@@ -0,0 +1,1000 @@
+/* slamch.f -- translated by f2c (version 20061008).
+ You must link the resulting object file with libf2c:
+ on Microsoft Windows system, link with libf2c.lib;
+ on Linux or Unix systems, link with .../path/to/libf2c.a -lm
+ or, if you install libf2c.a in a standard place, with -lf2c -lm
+ -- in that order, at the end of the command line, as in
+ cc *.o -lf2c -lm
+ Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
+
+ http://www.netlib.org/f2c/libf2c.zip
+*/
+
+#include "f2c.h"
+#include "blaswrap.h"
+
+/* Table of constant values */
+
+static integer c__1 = 1;
+static real c_b32 = 0.f;
+
+doublereal slamch_(char *cmach)
+{
+ /* Initialized data */
+
+ static logical first = TRUE_;
+
+ /* System generated locals */
+ integer i__1;
+ real ret_val;
+
+ /* Builtin functions */
+ double pow_ri(real *, integer *);
+
+ /* Local variables */
+ static real t;
+ integer it;
+ static real rnd, eps, base;
+ integer beta;
+ static real emin, prec, emax;
+ integer imin, imax;
+ logical lrnd;
+ static real rmin, rmax;
+ real rmach = 0;
+ extern logical lsame_(char *, char *);
+ real small;
+ static real sfmin;
+ extern /* Subroutine */ int slamc2_(integer *, integer *, logical *, real
+ *, integer *, real *, integer *, real *);
+
+
+/* -- LAPACK auxiliary routine (version 3.2) -- */
+/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
+/* November 2006 */
+
+/* .. Scalar Arguments .. */
+/* .. */
+
+/* Purpose */
+/* ======= */
+
+/* SLAMCH determines single precision machine parameters. */
+
+/* Arguments */
+/* ========= */
+
+/* CMACH (input) CHARACTER*1 */
+/* Specifies the value to be returned by SLAMCH: */
+/* = 'E' or 'e', SLAMCH := eps */
+/* = 'S' or 's , SLAMCH := sfmin */
+/* = 'B' or 'b', SLAMCH := base */
+/* = 'P' or 'p', SLAMCH := eps*base */
+/* = 'N' or 'n', SLAMCH := t */
+/* = 'R' or 'r', SLAMCH := rnd */
+/* = 'M' or 'm', SLAMCH := emin */
+/* = 'U' or 'u', SLAMCH := rmin */
+/* = 'L' or 'l', SLAMCH := emax */
+/* = 'O' or 'o', SLAMCH := rmax */
+
+/* where */
+
+/* eps = relative machine precision */
+/* sfmin = safe minimum, such that 1/sfmin does not overflow */
+/* base = base of the machine */
+/* prec = eps*base */
+/* t = number of (base) digits in the mantissa */
+/* rnd = 1.0 when rounding occurs in addition, 0.0 otherwise */
+/* emin = minimum exponent before (gradual) underflow */
+/* rmin = underflow threshold - base**(emin-1) */
+/* emax = largest exponent before overflow */
+/* rmax = overflow threshold - (base**emax)*(1-eps) */
+
+/* ===================================================================== */
+
+/* .. Parameters .. */
+/* .. */
+/* .. Local Scalars .. */
+/* .. */
+/* .. External Functions .. */
+/* .. */
+/* .. External Subroutines .. */
+/* .. */
+/* .. Save statement .. */
+/* .. */
+/* .. Data statements .. */
+/* .. */
+/* .. Executable Statements .. */
+
+ if (first) {
+ slamc2_(&beta, &it, &lrnd, &eps, &imin, &rmin, &imax, &rmax);
+ base = (real) beta;
+ t = (real) it;
+ if (lrnd) {
+ rnd = 1.f;
+ i__1 = 1 - it;
+ eps = pow_ri(&base, &i__1) / 2;
+ } else {
+ rnd = 0.f;
+ i__1 = 1 - it;
+ eps = pow_ri(&base, &i__1);
+ }
+ prec = eps * base;
+ emin = (real) imin;
+ emax = (real) imax;
+ sfmin = rmin;
+ small = 1.f / rmax;
+ if (small >= sfmin) {
+
+/* Use SMALL plus a bit, to avoid the possibility of rounding */
+/* causing overflow when computing 1/sfmin. */
+
+ sfmin = small * (eps + 1.f);
+ }
+ }
+
+ if (lsame_(cmach, "E")) {
+ rmach = eps;
+ } else if (lsame_(cmach, "S")) {
+ rmach = sfmin;
+ } else if (lsame_(cmach, "B")) {
+ rmach = base;
+ } else if (lsame_(cmach, "P")) {
+ rmach = prec;
+ } else if (lsame_(cmach, "N")) {
+ rmach = t;
+ } else if (lsame_(cmach, "R")) {
+ rmach = rnd;
+ } else if (lsame_(cmach, "M")) {
+ rmach = emin;
+ } else if (lsame_(cmach, "U")) {
+ rmach = rmin;
+ } else if (lsame_(cmach, "L")) {
+ rmach = emax;
+ } else if (lsame_(cmach, "O")) {
+ rmach = rmax;
+ }
+
+ ret_val = rmach;
+ first = FALSE_;
+ return ret_val;
+
+/* End of SLAMCH */
+
+} /* slamch_ */
+
+
+/* *********************************************************************** */
+
+/* Subroutine */ int slamc1_(integer *beta, integer *t, logical *rnd, logical
+ *ieee1)
+{
+ /* Initialized data */
+
+ static logical first = TRUE_;
+
+ /* System generated locals */
+ real r__1, r__2;
+
+ /* Local variables */
+ real a, b, c__, f, t1, t2;
+ static integer lt;
+ real one, qtr;
+ static logical lrnd;
+ static integer lbeta;
+ real savec;
+ static logical lieee1;
+ extern doublereal slamc3_(real *, real *);
+
+
+/* -- LAPACK auxiliary routine (version 3.2) -- */
+/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
+/* November 2006 */
+
+/* .. Scalar Arguments .. */
+/* .. */
+
+/* Purpose */
+/* ======= */
+
+/* SLAMC1 determines the machine parameters given by BETA, T, RND, and */
+/* IEEE1. */
+
+/* Arguments */
+/* ========= */
+
+/* BETA (output) INTEGER */
+/* The base of the machine. */
+
+/* T (output) INTEGER */
+/* The number of ( BETA ) digits in the mantissa. */
+
+/* RND (output) LOGICAL */
+/* Specifies whether proper rounding ( RND = .TRUE. ) or */
+/* chopping ( RND = .FALSE. ) occurs in addition. This may not */
+/* be a reliable guide to the way in which the machine performs */
+/* its arithmetic. */
+
+/* IEEE1 (output) LOGICAL */
+/* Specifies whether rounding appears to be done in the IEEE */
+/* 'round to nearest' style. */
+
+/* Further Details */
+/* =============== */
+
+/* The routine is based on the routine ENVRON by Malcolm and */
+/* incorporates suggestions by Gentleman and Marovich. See */
+
+/* Malcolm M. A. (1972) Algorithms to reveal properties of */
+/* floating-point arithmetic. Comms. of the ACM, 15, 949-951. */
+
+/* Gentleman W. M. and Marovich S. B. (1974) More on algorithms */
+/* that reveal properties of floating point arithmetic units. */
+/* Comms. of the ACM, 17, 276-277. */
+
+/* ===================================================================== */
+
+/* .. Local Scalars .. */
+/* .. */
+/* .. External Functions .. */
+/* .. */
+/* .. Save statement .. */
+/* .. */
+/* .. Data statements .. */
+/* .. */
+/* .. Executable Statements .. */
+
+ if (first) {
+ one = 1.f;
+
+/* LBETA, LIEEE1, LT and LRND are the local values of BETA, */
+/* IEEE1, T and RND. */
+
+/* Throughout this routine we use the function SLAMC3 to ensure */
+/* that relevant values are stored and not held in registers, or */
+/* are not affected by optimizers. */
+
+/* Compute a = 2.0**m with the smallest positive integer m such */
+/* that */
+
+/* fl( a + 1.0 ) = a. */
+
+ a = 1.f;
+ c__ = 1.f;
+
+/* + WHILE( C.EQ.ONE )LOOP */
+L10:
+ if (c__ == one) {
+ a *= 2;
+ c__ = slamc3_(&a, &one);
+ r__1 = -a;
+ c__ = slamc3_(&c__, &r__1);
+ goto L10;
+ }
+/* + END WHILE */
+
+/* Now compute b = 2.0**m with the smallest positive integer m */
+/* such that */
+
+/* fl( a + b ) .gt. a. */
+
+ b = 1.f;
+ c__ = slamc3_(&a, &b);
+
+/* + WHILE( C.EQ.A )LOOP */
+L20:
+ if (c__ == a) {
+ b *= 2;
+ c__ = slamc3_(&a, &b);
+ goto L20;
+ }
+/* + END WHILE */
+
+/* Now compute the base. a and c are neighbouring floating point */
+/* numbers in the interval ( beta**t, beta**( t + 1 ) ) and so */
+/* their difference is beta. Adding 0.25 to c is to ensure that it */
+/* is truncated to beta and not ( beta - 1 ). */
+
+ qtr = one / 4;
+ savec = c__;
+ r__1 = -a;
+ c__ = slamc3_(&c__, &r__1);
+ lbeta = c__ + qtr;
+
+/* Now determine whether rounding or chopping occurs, by adding a */
+/* bit less than beta/2 and a bit more than beta/2 to a. */
+
+ b = (real) lbeta;
+ r__1 = b / 2;
+ r__2 = -b / 100;
+ f = slamc3_(&r__1, &r__2);
+ c__ = slamc3_(&f, &a);
+ if (c__ == a) {
+ lrnd = TRUE_;
+ } else {
+ lrnd = FALSE_;
+ }
+ r__1 = b / 2;
+ r__2 = b / 100;
+ f = slamc3_(&r__1, &r__2);
+ c__ = slamc3_(&f, &a);
+ if (lrnd && c__ == a) {
+ lrnd = FALSE_;
+ }
+
+/* Try and decide whether rounding is done in the IEEE 'round to */
+/* nearest' style. B/2 is half a unit in the last place of the two */
+/* numbers A and SAVEC. Furthermore, A is even, i.e. has last bit */
+/* zero, and SAVEC is odd. Thus adding B/2 to A should not change */
+/* A, but adding B/2 to SAVEC should change SAVEC. */
+
+ r__1 = b / 2;
+ t1 = slamc3_(&r__1, &a);
+ r__1 = b / 2;
+ t2 = slamc3_(&r__1, &savec);
+ lieee1 = t1 == a && t2 > savec && lrnd;
+
+/* Now find the mantissa, t. It should be the integer part of */
+/* log to the base beta of a, however it is safer to determine t */
+/* by powering. So we find t as the smallest positive integer for */
+/* which */
+
+/* fl( beta**t + 1.0 ) = 1.0. */
+
+ lt = 0;
+ a = 1.f;
+ c__ = 1.f;
+
+/* + WHILE( C.EQ.ONE )LOOP */
+L30:
+ if (c__ == one) {
+ ++lt;
+ a *= lbeta;
+ c__ = slamc3_(&a, &one);
+ r__1 = -a;
+ c__ = slamc3_(&c__, &r__1);
+ goto L30;
+ }
+/* + END WHILE */
+
+ }
+
+ *beta = lbeta;
+ *t = lt;
+ *rnd = lrnd;
+ *ieee1 = lieee1;
+ first = FALSE_;
+ return 0;
+
+/* End of SLAMC1 */
+
+} /* slamc1_ */
+
+
+/* *********************************************************************** */
+
+/* Subroutine */ int slamc2_(integer *beta, integer *t, logical *rnd, real *
+ eps, integer *emin, real *rmin, integer *emax, real *rmax)
+{
+ /* Initialized data */
+
+ static logical first = TRUE_;
+ static logical iwarn = FALSE_;
+
+ /* Format strings */
+ static char fmt_9999[] = "(//\002 WARNING. The value EMIN may be incorre"
+ "ct:-\002,\002 EMIN = \002,i8,/\002 If, after inspection, the va"
+ "lue EMIN looks\002,\002 acceptable please comment out \002,/\002"
+ " the IF block as marked within the code of routine\002,\002 SLAM"
+ "C2,\002,/\002 otherwise supply EMIN explicitly.\002,/)";
+
+ /* System generated locals */
+ integer i__1;
+ real r__1, r__2, r__3, r__4, r__5;
+
+ /* Builtin functions */
+ double pow_ri(real *, integer *);
+ integer s_wsfe(cilist *), do_fio(integer *, char *, ftnlen), e_wsfe(void);
+
+ /* Local variables */
+ real a, b, c__;
+ integer i__;
+ static integer lt;
+ real one, two;
+ logical ieee;
+ real half;
+ logical lrnd = 0;
+ static real leps;
+ real zero;
+ static integer lbeta;
+ real rbase;
+ static integer lemin, lemax;
+ integer gnmin;
+ real small;
+ integer gpmin;
+ real third;
+ static real lrmin, lrmax;
+ real sixth;
+ logical lieee1;
+ extern /* Subroutine */ int slamc1_(integer *, integer *, logical *,
+ logical *);
+ extern doublereal slamc3_(real *, real *);
+ extern /* Subroutine */ int slamc4_(integer *, real *, integer *),
+ slamc5_(integer *, integer *, integer *, logical *, integer *,
+ real *);
+ integer ngnmin, ngpmin;
+
+ /* Fortran I/O blocks */
+ static cilist io___58 = { 0, 6, 0, fmt_9999, 0 };
+
+
+
+/* -- LAPACK auxiliary routine (version 3.2) -- */
+/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
+/* November 2006 */
+
+/* .. Scalar Arguments .. */
+/* .. */
+
+/* Purpose */
+/* ======= */
+
+/* SLAMC2 determines the machine parameters specified in its argument */
+/* list. */
+
+/* Arguments */
+/* ========= */
+
+/* BETA (output) INTEGER */
+/* The base of the machine. */
+
+/* T (output) INTEGER */
+/* The number of ( BETA ) digits in the mantissa. */
+
+/* RND (output) LOGICAL */
+/* Specifies whether proper rounding ( RND = .TRUE. ) or */
+/* chopping ( RND = .FALSE. ) occurs in addition. This may not */
+/* be a reliable guide to the way in which the machine performs */
+/* its arithmetic. */
+
+/* EPS (output) REAL */
+/* The smallest positive number such that */
+
+/* fl( 1.0 - EPS ) .LT. 1.0, */
+
+/* where fl denotes the computed value. */
+
+/* EMIN (output) INTEGER */
+/* The minimum exponent before (gradual) underflow occurs. */
+
+/* RMIN (output) REAL */
+/* The smallest normalized number for the machine, given by */
+/* BASE**( EMIN - 1 ), where BASE is the floating point value */
+/* of BETA. */
+
+/* EMAX (output) INTEGER */
+/* The maximum exponent before overflow occurs. */
+
+/* RMAX (output) REAL */
+/* The largest positive number for the machine, given by */
+/* BASE**EMAX * ( 1 - EPS ), where BASE is the floating point */
+/* value of BETA. */
+
+/* Further Details */
+/* =============== */
+
+/* The computation of EPS is based on a routine PARANOIA by */
+/* W. Kahan of the University of California at Berkeley. */
+
+/* ===================================================================== */
+
+/* .. Local Scalars .. */
+/* .. */
+/* .. External Functions .. */
+/* .. */
+/* .. External Subroutines .. */
+/* .. */
+/* .. Intrinsic Functions .. */
+/* .. */
+/* .. Save statement .. */
+/* .. */
+/* .. Data statements .. */
+/* .. */
+/* .. Executable Statements .. */
+
+ if (first) {
+ zero = 0.f;
+ one = 1.f;
+ two = 2.f;
+
+/* LBETA, LT, LRND, LEPS, LEMIN and LRMIN are the local values of */
+/* BETA, T, RND, EPS, EMIN and RMIN. */
+
+/* Throughout this routine we use the function SLAMC3 to ensure */
+/* that relevant values are stored and not held in registers, or */
+/* are not affected by optimizers. */
+
+/* SLAMC1 returns the parameters LBETA, LT, LRND and LIEEE1. */
+
+ slamc1_(&lbeta, <, &lrnd, &lieee1);
+
+/* Start to find EPS. */
+
+ b = (real) lbeta;
+ i__1 = -lt;
+ a = pow_ri(&b, &i__1);
+ leps = a;
+
+/* Try some tricks to see whether or not this is the correct EPS. */
+
+ b = two / 3;
+ half = one / 2;
+ r__1 = -half;
+ sixth = slamc3_(&b, &r__1);
+ third = slamc3_(&sixth, &sixth);
+ r__1 = -half;
+ b = slamc3_(&third, &r__1);
+ b = slamc3_(&b, &sixth);
+ b = dabs(b);
+ if (b < leps) {
+ b = leps;
+ }
+
+ leps = 1.f;
+
+/* + WHILE( ( LEPS.GT.B ).AND.( B.GT.ZERO ) )LOOP */
+L10:
+ if (leps > b && b > zero) {
+ leps = b;
+ r__1 = half * leps;
+/* Computing 5th power */
+ r__3 = two, r__4 = r__3, r__3 *= r__3;
+/* Computing 2nd power */
+ r__5 = leps;
+ r__2 = r__4 * (r__3 * r__3) * (r__5 * r__5);
+ c__ = slamc3_(&r__1, &r__2);
+ r__1 = -c__;
+ c__ = slamc3_(&half, &r__1);
+ b = slamc3_(&half, &c__);
+ r__1 = -b;
+ c__ = slamc3_(&half, &r__1);
+ b = slamc3_(&half, &c__);
+ goto L10;
+ }
+/* + END WHILE */
+
+ if (a < leps) {
+ leps = a;
+ }
+
+/* Computation of EPS complete. */
+
+/* Now find EMIN. Let A = + or - 1, and + or - (1 + BASE**(-3)). */
+/* Keep dividing A by BETA until (gradual) underflow occurs. This */
+/* is detected when we cannot recover the previous A. */
+
+ rbase = one / lbeta;
+ small = one;
+ for (i__ = 1; i__ <= 3; ++i__) {
+ r__1 = small * rbase;
+ small = slamc3_(&r__1, &zero);
+/* L20: */
+ }
+ a = slamc3_(&one, &small);
+ slamc4_(&ngpmin, &one, &lbeta);
+ r__1 = -one;
+ slamc4_(&ngnmin, &r__1, &lbeta);
+ slamc4_(&gpmin, &a, &lbeta);
+ r__1 = -a;
+ slamc4_(&gnmin, &r__1, &lbeta);
+ ieee = FALSE_;
+
+ if (ngpmin == ngnmin && gpmin == gnmin) {
+ if (ngpmin == gpmin) {
+ lemin = ngpmin;
+/* ( Non twos-complement machines, no gradual underflow; */
+/* e.g., VAX ) */
+ } else if (gpmin - ngpmin == 3) {
+ lemin = ngpmin - 1 + lt;
+ ieee = TRUE_;
+/* ( Non twos-complement machines, with gradual underflow; */
+/* e.g., IEEE standard followers ) */
+ } else {
+ lemin = min(ngpmin,gpmin);
+/* ( A guess; no known machine ) */
+ iwarn = TRUE_;
+ }
+
+ } else if (ngpmin == gpmin && ngnmin == gnmin) {
+ if ((i__1 = ngpmin - ngnmin, abs(i__1)) == 1) {
+ lemin = max(ngpmin,ngnmin);
+/* ( Twos-complement machines, no gradual underflow; */
+/* e.g., CYBER 205 ) */
+ } else {
+ lemin = min(ngpmin,ngnmin);
+/* ( A guess; no known machine ) */
+ iwarn = TRUE_;
+ }
+
+ } else if ((i__1 = ngpmin - ngnmin, abs(i__1)) == 1 && gpmin == gnmin)
+ {
+ if (gpmin - min(ngpmin,ngnmin) == 3) {
+ lemin = max(ngpmin,ngnmin) - 1 + lt;
+/* ( Twos-complement machines with gradual underflow; */
+/* no known machine ) */
+ } else {
+ lemin = min(ngpmin,ngnmin);
+/* ( A guess; no known machine ) */
+ iwarn = TRUE_;
+ }
+
+ } else {
+/* Computing MIN */
+ i__1 = min(ngpmin,ngnmin), i__1 = min(i__1,gpmin);
+ lemin = min(i__1,gnmin);
+/* ( A guess; no known machine ) */
+ iwarn = TRUE_;
+ }
+ first = FALSE_;
+/* ** */
+/* Comment out this if block if EMIN is ok */
+ if (iwarn) {
+ first = TRUE_;
+ s_wsfe(&io___58);
+ do_fio(&c__1, (char *)&lemin, (ftnlen)sizeof(integer));
+ e_wsfe();
+ }
+/* ** */
+
+/* Assume IEEE arithmetic if we found denormalised numbers above, */
+/* or if arithmetic seems to round in the IEEE style, determined */
+/* in routine SLAMC1. A true IEEE machine should have both things */
+/* true; however, faulty machines may have one or the other. */
+
+ ieee = ieee || lieee1;
+
+/* Compute RMIN by successive division by BETA. We could compute */
+/* RMIN as BASE**( EMIN - 1 ), but some machines underflow during */
+/* this computation. */
+
+ lrmin = 1.f;
+ i__1 = 1 - lemin;
+ for (i__ = 1; i__ <= i__1; ++i__) {
+ r__1 = lrmin * rbase;
+ lrmin = slamc3_(&r__1, &zero);
+/* L30: */
+ }
+
+/* Finally, call SLAMC5 to compute EMAX and RMAX. */
+
+ slamc5_(&lbeta, <, &lemin, &ieee, &lemax, &lrmax);
+ }
+
+ *beta = lbeta;
+ *t = lt;
+ *rnd = lrnd;
+ *eps = leps;
+ *emin = lemin;
+ *rmin = lrmin;
+ *emax = lemax;
+ *rmax = lrmax;
+
+ return 0;
+
+
+/* End of SLAMC2 */
+
+} /* slamc2_ */
+
+
+/* *********************************************************************** */
+
+doublereal slamc3_(real *a, real *b)
+{
+ /* System generated locals */
+ real ret_val;
+
+
+/* -- LAPACK auxiliary routine (version 3.2) -- */
+/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
+/* November 2006 */
+
+/* .. Scalar Arguments .. */
+/* .. */
+
+/* Purpose */
+/* ======= */
+
+/* SLAMC3 is intended to force A and B to be stored prior to doing */
+/* the addition of A and B , for use in situations where optimizers */
+/* might hold one of these in a register. */
+
+/* Arguments */
+/* ========= */
+
+/* A (input) REAL */
+/* B (input) REAL */
+/* The values A and B. */
+
+/* ===================================================================== */
+
+/* .. Executable Statements .. */
+
+ ret_val = *a + *b;
+
+ return ret_val;
+
+/* End of SLAMC3 */
+
+} /* slamc3_ */
+
+
+/* *********************************************************************** */
+
+/* Subroutine */ int slamc4_(integer *emin, real *start, integer *base)
+{
+ /* System generated locals */
+ integer i__1;
+ real r__1;
+
+ /* Local variables */
+ real a;
+ integer i__;
+ real b1, b2, c1, c2, d1, d2, one, zero, rbase;
+ extern doublereal slamc3_(real *, real *);
+
+
+/* -- LAPACK auxiliary routine (version 3.2) -- */
+/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
+/* November 2006 */
+
+/* .. Scalar Arguments .. */
+/* .. */
+
+/* Purpose */
+/* ======= */
+
+/* SLAMC4 is a service routine for SLAMC2. */
+
+/* Arguments */
+/* ========= */
+
+/* EMIN (output) INTEGER */
+/* The minimum exponent before (gradual) underflow, computed by */
+/* setting A = START and dividing by BASE until the previous A */
+/* can not be recovered. */
+
+/* START (input) REAL */
+/* The starting point for determining EMIN. */
+
+/* BASE (input) INTEGER */
+/* The base of the machine. */
+
+/* ===================================================================== */
+
+/* .. Local Scalars .. */
+/* .. */
+/* .. External Functions .. */
+/* .. */
+/* .. Executable Statements .. */
+
+ a = *start;
+ one = 1.f;
+ rbase = one / *base;
+ zero = 0.f;
+ *emin = 1;
+ r__1 = a * rbase;
+ b1 = slamc3_(&r__1, &zero);
+ c1 = a;
+ c2 = a;
+ d1 = a;
+ d2 = a;
+/* + WHILE( ( C1.EQ.A ).AND.( C2.EQ.A ).AND. */
+/* $ ( D1.EQ.A ).AND.( D2.EQ.A ) )LOOP */
+L10:
+ if (c1 == a && c2 == a && d1 == a && d2 == a) {
+ --(*emin);
+ a = b1;
+ r__1 = a / *base;
+ b1 = slamc3_(&r__1, &zero);
+ r__1 = b1 * *base;
+ c1 = slamc3_(&r__1, &zero);
+ d1 = zero;
+ i__1 = *base;
+ for (i__ = 1; i__ <= i__1; ++i__) {
+ d1 += b1;
+/* L20: */
+ }
+ r__1 = a * rbase;
+ b2 = slamc3_(&r__1, &zero);
+ r__1 = b2 / rbase;
+ c2 = slamc3_(&r__1, &zero);
+ d2 = zero;
+ i__1 = *base;
+ for (i__ = 1; i__ <= i__1; ++i__) {
+ d2 += b2;
+/* L30: */
+ }
+ goto L10;
+ }
+/* + END WHILE */
+
+ return 0;
+
+/* End of SLAMC4 */
+
+} /* slamc4_ */
+
+
+/* *********************************************************************** */
+
+/* Subroutine */ int slamc5_(integer *beta, integer *p, integer *emin,
+ logical *ieee, integer *emax, real *rmax)
+{
+ /* System generated locals */
+ integer i__1;
+ real r__1;
+
+ /* Local variables */
+ integer i__;
+ real y, z__;
+ integer try__, lexp;
+ real oldy;
+ integer uexp, nbits;
+ extern doublereal slamc3_(real *, real *);
+ real recbas;
+ integer exbits, expsum;
+
+
+/* -- LAPACK auxiliary routine (version 3.2) -- */
+/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
+/* November 2006 */
+
+/* .. Scalar Arguments .. */
+/* .. */
+
+/* Purpose */
+/* ======= */
+
+/* SLAMC5 attempts to compute RMAX, the largest machine floating-point */
+/* number, without overflow. It assumes that EMAX + abs(EMIN) sum */
+/* approximately to a power of 2. It will fail on machines where this */
+/* assumption does not hold, for example, the Cyber 205 (EMIN = -28625, */
+/* EMAX = 28718). It will also fail if the value supplied for EMIN is */
+/* too large (i.e. too close to zero), probably with overflow. */
+
+/* Arguments */
+/* ========= */
+
+/* BETA (input) INTEGER */
+/* The base of floating-point arithmetic. */
+
+/* P (input) INTEGER */
+/* The number of base BETA digits in the mantissa of a */
+/* floating-point value. */
+
+/* EMIN (input) INTEGER */
+/* The minimum exponent before (gradual) underflow. */
+
+/* IEEE (input) LOGICAL */
+/* A logical flag specifying whether or not the arithmetic */
+/* system is thought to comply with the IEEE standard. */
+
+/* EMAX (output) INTEGER */
+/* The largest exponent before overflow */
+
+/* RMAX (output) REAL */
+/* The largest machine floating-point number. */
+
+/* ===================================================================== */
+
+/* .. Parameters .. */
+/* .. */
+/* .. Local Scalars .. */
+/* .. */
+/* .. External Functions .. */
+/* .. */
+/* .. Intrinsic Functions .. */
+/* .. */
+/* .. Executable Statements .. */
+
+/* First compute LEXP and UEXP, two powers of 2 that bound */
+/* abs(EMIN). We then assume that EMAX + abs(EMIN) will sum */
+/* approximately to the bound that is closest to abs(EMIN). */
+/* (EMAX is the exponent of the required number RMAX). */
+
+ lexp = 1;
+ exbits = 1;
+L10:
+ try__ = lexp << 1;
+ if (try__ <= -(*emin)) {
+ lexp = try__;
+ ++exbits;
+ goto L10;
+ }
+ if (lexp == -(*emin)) {
+ uexp = lexp;
+ } else {
+ uexp = try__;
+ ++exbits;
+ }
+
+/* Now -LEXP is less than or equal to EMIN, and -UEXP is greater */
+/* than or equal to EMIN. EXBITS is the number of bits needed to */
+/* store the exponent. */
+
+ if (uexp + *emin > -lexp - *emin) {
+ expsum = lexp << 1;
+ } else {
+ expsum = uexp << 1;
+ }
+
+/* EXPSUM is the exponent range, approximately equal to */
+/* EMAX - EMIN + 1 . */
+
+ *emax = expsum + *emin - 1;
+ nbits = exbits + 1 + *p;
+
+/* NBITS is the total number of bits needed to store a */
+/* floating-point number. */
+
+ if (nbits % 2 == 1 && *beta == 2) {
+
+/* Either there are an odd number of bits used to store a */
+/* floating-point number, which is unlikely, or some bits are */
+/* not used in the representation of numbers, which is possible, */
+/* (e.g. Cray machines) or the mantissa has an implicit bit, */
+/* (e.g. IEEE machines, Dec Vax machines), which is perhaps the */
+/* most likely. We have to assume the last alternative. */
+/* If this is true, then we need to reduce EMAX by one because */
+/* there must be some way of representing zero in an implicit-bit */
+/* system. On machines like Cray, we are reducing EMAX by one */
+/* unnecessarily. */
+
+ --(*emax);
+ }
+
+ if (*ieee) {
+
+/* Assume we are on an IEEE machine which reserves one exponent */
+/* for infinity and NaN. */
+
+ --(*emax);
+ }
+
+/* Now create RMAX, the largest machine number, which should */
+/* be equal to (1.0 - BETA**(-P)) * BETA**EMAX . */
+
+/* First compute 1.0 - BETA**(-P), being careful that the */
+/* result is less than 1.0 . */
+
+ recbas = 1.f / *beta;
+ z__ = *beta - 1.f;
+ y = 0.f;
+ i__1 = *p;
+ for (i__ = 1; i__ <= i__1; ++i__) {
+ z__ *= recbas;
+ if (y < 1.f) {
+ oldy = y;
+ }
+ y = slamc3_(&y, &z__);
+/* L20: */
+ }
+ if (y >= 1.f) {
+ y = oldy;
+ }
+
+/* Now multiply by BETA**EMAX to get RMAX. */
+
+ i__1 = *emax;
+ for (i__ = 1; i__ <= i__1; ++i__) {
+ r__1 = y * *beta;
+ y = slamc3_(&r__1, &c_b32);
+/* L30: */
+ }
+
+ *rmax = y;
+ return 0;
+
+/* End of SLAMC5 */
+
+} /* slamc5_ */
diff --git a/lapack/slapy2.c b/lapack/slapy2.c
new file mode 100644
index 0000000..e048cac
--- /dev/null
+++ b/lapack/slapy2.c
@@ -0,0 +1,73 @@
+/* slapy2.f -- translated by f2c (version 20061008).
+ You must link the resulting object file with libf2c:
+ on Microsoft Windows system, link with libf2c.lib;
+ on Linux or Unix systems, link with .../path/to/libf2c.a -lm
+ or, if you install libf2c.a in a standard place, with -lf2c -lm
+ -- in that order, at the end of the command line, as in
+ cc *.o -lf2c -lm
+ Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
+
+ http://www.netlib.org/f2c/libf2c.zip
+*/
+
+#include "f2c.h"
+#include "blaswrap.h"
+
+doublereal slapy2_(real *x, real *y)
+{
+ /* System generated locals */
+ real ret_val, r__1;
+
+ /* Builtin functions */
+ double sqrt(doublereal);
+
+ /* Local variables */
+ real w, z__, xabs, yabs;
+
+
+/* -- LAPACK auxiliary routine (version 3.2) -- */
+/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
+/* November 2006 */
+
+/* .. Scalar Arguments .. */
+/* .. */
+
+/* Purpose */
+/* ======= */
+
+/* SLAPY2 returns sqrt(x**2+y**2), taking care not to cause unnecessary */
+/* overflow. */
+
+/* Arguments */
+/* ========= */
+
+/* X (input) REAL */
+/* Y (input) REAL */
+/* X and Y specify the values x and y. */
+
+/* ===================================================================== */
+
+/* .. Parameters .. */
+/* .. */
+/* .. Local Scalars .. */
+/* .. */
+/* .. Intrinsic Functions .. */
+/* .. */
+/* .. Executable Statements .. */
+
+ xabs = dabs(*x);
+ yabs = dabs(*y);
+ w = dmax(xabs,yabs);
+ z__ = dmin(xabs,yabs);
+ if (z__ == 0.f) {
+ ret_val = w;
+ } else {
+/* Computing 2nd power */
+ r__1 = z__ / w;
+ ret_val = w * sqrt(r__1 * r__1 + 1.f);
+ }
+ return ret_val;
+
+/* End of SLAPY2 */
+
+} /* slapy2_ */
diff --git a/lapack/slapy3.c b/lapack/slapy3.c
new file mode 100644
index 0000000..921a2c4
--- /dev/null
+++ b/lapack/slapy3.c
@@ -0,0 +1,83 @@
+/* slapy3.f -- translated by f2c (version 20061008).
+ You must link the resulting object file with libf2c:
+ on Microsoft Windows system, link with libf2c.lib;
+ on Linux or Unix systems, link with .../path/to/libf2c.a -lm
+ or, if you install libf2c.a in a standard place, with -lf2c -lm
+ -- in that order, at the end of the command line, as in
+ cc *.o -lf2c -lm
+ Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
+
+ http://www.netlib.org/f2c/libf2c.zip
+*/
+
+#include "f2c.h"
+#include "blaswrap.h"
+
+doublereal slapy3_(real *x, real *y, real *z__)
+{
+ /* System generated locals */
+ real ret_val, r__1, r__2, r__3;
+
+ /* Builtin functions */
+ double sqrt(doublereal);
+
+ /* Local variables */
+ real w, xabs, yabs, zabs;
+
+
+/* -- LAPACK auxiliary routine (version 3.2) -- */
+/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
+/* November 2006 */
+
+/* .. Scalar Arguments .. */
+/* .. */
+
+/* Purpose */
+/* ======= */
+
+/* SLAPY3 returns sqrt(x**2+y**2+z**2), taking care not to cause */
+/* unnecessary overflow. */
+
+/* Arguments */
+/* ========= */
+
+/* X (input) REAL */
+/* Y (input) REAL */
+/* Z (input) REAL */
+/* X, Y and Z specify the values x, y and z. */
+
+/* ===================================================================== */
+
+/* .. Parameters .. */
+/* .. */
+/* .. Local Scalars .. */
+/* .. */
+/* .. Intrinsic Functions .. */
+/* .. */
+/* .. Executable Statements .. */
+
+ xabs = dabs(*x);
+ yabs = dabs(*y);
+ zabs = dabs(*z__);
+/* Computing MAX */
+ r__1 = max(xabs,yabs);
+ w = dmax(r__1,zabs);
+ if (w == 0.f) {
+/* W can be zero for max(0,nan,0) */
+/* adding all three entries together will make sure */
+/* NaN will not disappear. */
+ ret_val = xabs + yabs + zabs;
+ } else {
+/* Computing 2nd power */
+ r__1 = xabs / w;
+/* Computing 2nd power */
+ r__2 = yabs / w;
+/* Computing 2nd power */
+ r__3 = zabs / w;
+ ret_val = w * sqrt(r__1 * r__1 + r__2 * r__2 + r__3 * r__3);
+ }
+ return ret_val;
+
+/* End of SLAPY3 */
+
+} /* slapy3_ */
diff --git a/lapack/slarf.c b/lapack/slarf.c
new file mode 100644
index 0000000..dbef082
--- /dev/null
+++ b/lapack/slarf.c
@@ -0,0 +1,191 @@
+/* slarf.f -- translated by f2c (version 20061008).
+ You must link the resulting object file with libf2c:
+ on Microsoft Windows system, link with libf2c.lib;
+ on Linux or Unix systems, link with .../path/to/libf2c.a -lm
+ or, if you install libf2c.a in a standard place, with -lf2c -lm
+ -- in that order, at the end of the command line, as in
+ cc *.o -lf2c -lm
+ Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
+
+ http://www.netlib.org/f2c/libf2c.zip
+*/
+
+#include "f2c.h"
+#include "blaswrap.h"
+
+/* Table of constant values */
+
+static real c_b4 = 1.f;
+static real c_b5 = 0.f;
+static integer c__1 = 1;
+
+/* Subroutine */ int slarf_(char *side, integer *m, integer *n, real *v,
+ integer *incv, real *tau, real *c__, integer *ldc, real *work)
+{
+ /* System generated locals */
+ integer c_dim1, c_offset;
+ real r__1;
+
+ /* Local variables */
+ integer i__;
+ logical applyleft;
+ extern /* Subroutine */ int sger_(integer *, integer *, real *, real *,
+ integer *, real *, integer *, real *, integer *);
+ extern logical lsame_(char *, char *);
+ integer lastc;
+ extern /* Subroutine */ int sgemv_(char *, integer *, integer *, real *,
+ real *, integer *, real *, integer *, real *, real *, integer *);
+ integer lastv;
+ extern integer ilaslc_(integer *, integer *, real *, integer *), ilaslr_(
+ integer *, integer *, real *, integer *);
+
+
+/* -- LAPACK auxiliary routine (version 3.2) -- */
+/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
+/* November 2006 */
+
+/* .. Scalar Arguments .. */
+/* .. */
+/* .. Array Arguments .. */
+/* .. */
+
+/* Purpose */
+/* ======= */
+
+/* SLARF applies a real elementary reflector H to a real m by n matrix */
+/* C, from either the left or the right. H is represented in the form */
+
+/* H = I - tau * v * v' */
+
+/* where tau is a real scalar and v is a real vector. */
+
+/* If tau = 0, then H is taken to be the unit matrix. */
+
+/* Arguments */
+/* ========= */
+
+/* SIDE (input) CHARACTER*1 */
+/* = 'L': form H * C */
+/* = 'R': form C * H */
+
+/* M (input) INTEGER */
+/* The number of rows of the matrix C. */
+
+/* N (input) INTEGER */
+/* The number of columns of the matrix C. */
+
+/* V (input) REAL array, dimension */
+/* (1 + (M-1)*abs(INCV)) if SIDE = 'L' */
+/* or (1 + (N-1)*abs(INCV)) if SIDE = 'R' */
+/* The vector v in the representation of H. V is not used if */
+/* TAU = 0. */
+
+/* INCV (input) INTEGER */
+/* The increment between elements of v. INCV <> 0. */
+
+/* TAU (input) REAL */
+/* The value tau in the representation of H. */
+
+/* C (input/output) REAL array, dimension (LDC,N) */
+/* On entry, the m by n matrix C. */
+/* On exit, C is overwritten by the matrix H * C if SIDE = 'L', */
+/* or C * H if SIDE = 'R'. */
+
+/* LDC (input) INTEGER */
+/* The leading dimension of the array C. LDC >= max(1,M). */
+
+/* WORK (workspace) REAL array, dimension */
+/* (N) if SIDE = 'L' */
+/* or (M) if SIDE = 'R' */
+
+/* ===================================================================== */
+
+/* .. Parameters .. */
+/* .. */
+/* .. Local Scalars .. */
+/* .. */
+/* .. External Subroutines .. */
+/* .. */
+/* .. External Functions .. */
+/* .. */
+/* .. Executable Statements .. */
+
+ /* Parameter adjustments */
+ --v;
+ c_dim1 = *ldc;
+ c_offset = 1 + c_dim1;
+ c__ -= c_offset;
+ --work;
+
+ /* Function Body */
+ applyleft = lsame_(side, "L");
+ lastv = 0;
+ lastc = 0;
+ if (*tau != 0.f) {
+/* Set up variables for scanning V. LASTV begins pointing to the end */
+/* of V. */
+ if (applyleft) {
+ lastv = *m;
+ } else {
+ lastv = *n;
+ }
+ if (*incv > 0) {
+ i__ = (lastv - 1) * *incv + 1;
+ } else {
+ i__ = 1;
+ }
+/* Look for the last non-zero row in V. */
+ while(lastv > 0 && v[i__] == 0.f) {
+ --lastv;
+ i__ -= *incv;
+ }
+ if (applyleft) {
+/* Scan for the last non-zero column in C(1:lastv,:). */
+ lastc = ilaslc_(&lastv, n, &c__[c_offset], ldc);
+ } else {
+/* Scan for the last non-zero row in C(:,1:lastv). */
+ lastc = ilaslr_(m, &lastv, &c__[c_offset], ldc);
+ }
+ }
+/* Note that lastc.eq.0 renders the BLAS operations null; no special */
+/* case is needed at this level. */
+ if (applyleft) {
+
+/* Form H * C */
+
+ if (lastv > 0) {
+
+/* w(1:lastc,1) := C(1:lastv,1:lastc)' * v(1:lastv,1) */
+
+ sgemv_("Transpose", &lastv, &lastc, &c_b4, &c__[c_offset], ldc, &
+ v[1], incv, &c_b5, &work[1], &c__1);
+
+/* C(1:lastv,1:lastc) := C(...) - v(1:lastv,1) * w(1:lastc,1)' */
+
+ r__1 = -(*tau);
+ sger_(&lastv, &lastc, &r__1, &v[1], incv, &work[1], &c__1, &c__[
+ c_offset], ldc);
+ }
+ } else {
+
+/* Form C * H */
+
+ if (lastv > 0) {
+
+/* w(1:lastc,1) := C(1:lastc,1:lastv) * v(1:lastv,1) */
+
+ sgemv_("No transpose", &lastc, &lastv, &c_b4, &c__[c_offset], ldc,
+ &v[1], incv, &c_b5, &work[1], &c__1);
+
+/* C(1:lastc,1:lastv) := C(...) - w(1:lastc,1) * v(1:lastv,1)' */
+
+ r__1 = -(*tau);
+ sger_(&lastc, &lastv, &r__1, &work[1], &c__1, &v[1], incv, &c__[
+ c_offset], ldc);
+ }
+ }
+ return 0;
+
+/* End of SLARF */
+
+} /* slarf_ */
diff --git a/lapack/slarfb.c b/lapack/slarfb.c
new file mode 100644
index 0000000..3c8030a
--- /dev/null
+++ b/lapack/slarfb.c
@@ -0,0 +1,773 @@
+/* slarfb.f -- translated by f2c (version 20061008).
+ You must link the resulting object file with libf2c:
+ on Microsoft Windows system, link with libf2c.lib;
+ on Linux or Unix systems, link with .../path/to/libf2c.a -lm
+ or, if you install libf2c.a in a standard place, with -lf2c -lm
+ -- in that order, at the end of the command line, as in
+ cc *.o -lf2c -lm
+ Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
+
+ http://www.netlib.org/f2c/libf2c.zip
+*/
+
+#include "f2c.h"
+#include "blaswrap.h"
+
+/* Table of constant values */
+
+static integer c__1 = 1;
+static real c_b14 = 1.f;
+static real c_b25 = -1.f;
+
+/* Subroutine */ int slarfb_(char *side, char *trans, char *direct, char *
+ storev, integer *m, integer *n, integer *k, real *v, integer *ldv,
+ real *t, integer *ldt, real *c__, integer *ldc, real *work, integer *
+ ldwork)
+{
+ /* System generated locals */
+ integer c_dim1, c_offset, t_dim1, t_offset, v_dim1, v_offset, work_dim1,
+ work_offset, i__1, i__2;
+
+ /* Local variables */
+ integer i__, j;
+ extern logical lsame_(char *, char *);
+ integer lastc;
+ extern /* Subroutine */ int sgemm_(char *, char *, integer *, integer *,
+ integer *, real *, real *, integer *, real *, integer *, real *,
+ real *, integer *);
+ integer lastv;
+ extern /* Subroutine */ int scopy_(integer *, real *, integer *, real *,
+ integer *), strmm_(char *, char *, char *, char *, integer *,
+ integer *, real *, real *, integer *, real *, integer *);
+ extern integer ilaslc_(integer *, integer *, real *, integer *), ilaslr_(
+ integer *, integer *, real *, integer *);
+ char transt[1];
+
+
+/* -- LAPACK auxiliary routine (version 3.2) -- */
+/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
+/* November 2006 */
+
+/* .. Scalar Arguments .. */
+/* .. */
+/* .. Array Arguments .. */
+/* .. */
+
+/* Purpose */
+/* ======= */
+
+/* SLARFB applies a real block reflector H or its transpose H' to a */
+/* real m by n matrix C, from either the left or the right. */
+
+/* Arguments */
+/* ========= */
+
+/* SIDE (input) CHARACTER*1 */
+/* = 'L': apply H or H' from the Left */
+/* = 'R': apply H or H' from the Right */
+
+/* TRANS (input) CHARACTER*1 */
+/* = 'N': apply H (No transpose) */
+/* = 'T': apply H' (Transpose) */
+
+/* DIRECT (input) CHARACTER*1 */
+/* Indicates how H is formed from a product of elementary */
+/* reflectors */
+/* = 'F': H = H(1) H(2) . . . H(k) (Forward) */
+/* = 'B': H = H(k) . . . H(2) H(1) (Backward) */
+
+/* STOREV (input) CHARACTER*1 */
+/* Indicates how the vectors which define the elementary */
+/* reflectors are stored: */
+/* = 'C': Columnwise */
+/* = 'R': Rowwise */
+
+/* M (input) INTEGER */
+/* The number of rows of the matrix C. */
+
+/* N (input) INTEGER */
+/* The number of columns of the matrix C. */
+
+/* K (input) INTEGER */
+/* The order of the matrix T (= the number of elementary */
+/* reflectors whose product defines the block reflector). */
+
+/* V (input) REAL array, dimension */
+/* (LDV,K) if STOREV = 'C' */
+/* (LDV,M) if STOREV = 'R' and SIDE = 'L' */
+/* (LDV,N) if STOREV = 'R' and SIDE = 'R' */
+/* The matrix V. See further details. */
+
+/* LDV (input) INTEGER */
+/* The leading dimension of the array V. */
+/* If STOREV = 'C' and SIDE = 'L', LDV >= max(1,M); */
+/* if STOREV = 'C' and SIDE = 'R', LDV >= max(1,N); */
+/* if STOREV = 'R', LDV >= K. */
+
+/* T (input) REAL array, dimension (LDT,K) */
+/* The triangular k by k matrix T in the representation of the */
+/* block reflector. */
+
+/* LDT (input) INTEGER */
+/* The leading dimension of the array T. LDT >= K. */
+
+/* C (input/output) REAL array, dimension (LDC,N) */
+/* On entry, the m by n matrix C. */
+/* On exit, C is overwritten by H*C or H'*C or C*H or C*H'. */
+
+/* LDC (input) INTEGER */
+/* The leading dimension of the array C. LDA >= max(1,M). */
+
+/* WORK (workspace) REAL array, dimension (LDWORK,K) */
+
+/* LDWORK (input) INTEGER */
+/* The leading dimension of the array WORK. */
+/* If SIDE = 'L', LDWORK >= max(1,N); */
+/* if SIDE = 'R', LDWORK >= max(1,M). */
+
+/* ===================================================================== */
+
+/* .. Parameters .. */
+/* .. */
+/* .. Local Scalars .. */
+/* .. */
+/* .. External Functions .. */
+/* .. */
+/* .. External Subroutines .. */
+/* .. */
+/* .. Executable Statements .. */
+
+/* Quick return if possible */
+
+ /* Parameter adjustments */
+ v_dim1 = *ldv;
+ v_offset = 1 + v_dim1;
+ v -= v_offset;
+ t_dim1 = *ldt;
+ t_offset = 1 + t_dim1;
+ t -= t_offset;
+ c_dim1 = *ldc;
+ c_offset = 1 + c_dim1;
+ c__ -= c_offset;
+ work_dim1 = *ldwork;
+ work_offset = 1 + work_dim1;
+ work -= work_offset;
+
+ /* Function Body */
+ if (*m <= 0 || *n <= 0) {
+ return 0;
+ }
+
+ if (lsame_(trans, "N")) {
+ *(unsigned char *)transt = 'T';
+ } else {
+ *(unsigned char *)transt = 'N';
+ }
+
+ if (lsame_(storev, "C")) {
+
+ if (lsame_(direct, "F")) {
+
+/* Let V = ( V1 ) (first K rows) */
+/* ( V2 ) */
+/* where V1 is unit lower triangular. */
+
+ if (lsame_(side, "L")) {
+
+/* Form H * C or H' * C where C = ( C1 ) */
+/* ( C2 ) */
+
+/* Computing MAX */
+ i__1 = *k, i__2 = ilaslr_(m, k, &v[v_offset], ldv);
+ lastv = max(i__1,i__2);
+ lastc = ilaslc_(&lastv, n, &c__[c_offset], ldc);
+
+/* W := C' * V = (C1'*V1 + C2'*V2) (stored in WORK) */
+
+/* W := C1' */
+
+ i__1 = *k;
+ for (j = 1; j <= i__1; ++j) {
+ scopy_(&lastc, &c__[j + c_dim1], ldc, &work[j * work_dim1
+ + 1], &c__1);
+/* L10: */
+ }
+
+/* W := W * V1 */
+
+ strmm_("Right", "Lower", "No transpose", "Unit", &lastc, k, &
+ c_b14, &v[v_offset], ldv, &work[work_offset], ldwork);
+ if (lastv > *k) {
+
+/* W := W + C2'*V2 */
+
+ i__1 = lastv - *k;
+ sgemm_("Transpose", "No transpose", &lastc, k, &i__1, &
+ c_b14, &c__[*k + 1 + c_dim1], ldc, &v[*k + 1 +
+ v_dim1], ldv, &c_b14, &work[work_offset], ldwork);
+ }
+
+/* W := W * T' or W * T */
+
+ strmm_("Right", "Upper", transt, "Non-unit", &lastc, k, &
+ c_b14, &t[t_offset], ldt, &work[work_offset], ldwork);
+
+/* C := C - V * W' */
+
+ if (lastv > *k) {
+
+/* C2 := C2 - V2 * W' */
+
+ i__1 = lastv - *k;
+ sgemm_("No transpose", "Transpose", &i__1, &lastc, k, &
+ c_b25, &v[*k + 1 + v_dim1], ldv, &work[
+ work_offset], ldwork, &c_b14, &c__[*k + 1 +
+ c_dim1], ldc);
+ }
+
+/* W := W * V1' */
+
+ strmm_("Right", "Lower", "Transpose", "Unit", &lastc, k, &
+ c_b14, &v[v_offset], ldv, &work[work_offset], ldwork);
+
+/* C1 := C1 - W' */
+
+ i__1 = *k;
+ for (j = 1; j <= i__1; ++j) {
+ i__2 = lastc;
+ for (i__ = 1; i__ <= i__2; ++i__) {
+ c__[j + i__ * c_dim1] -= work[i__ + j * work_dim1];
+/* L20: */
+ }
+/* L30: */
+ }
+
+ } else if (lsame_(side, "R")) {
+
+/* Form C * H or C * H' where C = ( C1 C2 ) */
+
+/* Computing MAX */
+ i__1 = *k, i__2 = ilaslr_(n, k, &v[v_offset], ldv);
+ lastv = max(i__1,i__2);
+ lastc = ilaslr_(m, &lastv, &c__[c_offset], ldc);
+
+/* W := C * V = (C1*V1 + C2*V2) (stored in WORK) */
+
+/* W := C1 */
+
+ i__1 = *k;
+ for (j = 1; j <= i__1; ++j) {
+ scopy_(&lastc, &c__[j * c_dim1 + 1], &c__1, &work[j *
+ work_dim1 + 1], &c__1);
+/* L40: */
+ }
+
+/* W := W * V1 */
+
+ strmm_("Right", "Lower", "No transpose", "Unit", &lastc, k, &
+ c_b14, &v[v_offset], ldv, &work[work_offset], ldwork);
+ if (lastv > *k) {
+
+/* W := W + C2 * V2 */
+
+ i__1 = lastv - *k;
+ sgemm_("No transpose", "No transpose", &lastc, k, &i__1, &
+ c_b14, &c__[(*k + 1) * c_dim1 + 1], ldc, &v[*k +
+ 1 + v_dim1], ldv, &c_b14, &work[work_offset],
+ ldwork);
+ }
+
+/* W := W * T or W * T' */
+
+ strmm_("Right", "Upper", trans, "Non-unit", &lastc, k, &c_b14,
+ &t[t_offset], ldt, &work[work_offset], ldwork);
+
+/* C := C - W * V' */
+
+ if (lastv > *k) {
+
+/* C2 := C2 - W * V2' */
+
+ i__1 = lastv - *k;
+ sgemm_("No transpose", "Transpose", &lastc, &i__1, k, &
+ c_b25, &work[work_offset], ldwork, &v[*k + 1 +
+ v_dim1], ldv, &c_b14, &c__[(*k + 1) * c_dim1 + 1],
+ ldc);
+ }
+
+/* W := W * V1' */
+
+ strmm_("Right", "Lower", "Transpose", "Unit", &lastc, k, &
+ c_b14, &v[v_offset], ldv, &work[work_offset], ldwork);
+
+/* C1 := C1 - W */
+
+ i__1 = *k;
+ for (j = 1; j <= i__1; ++j) {
+ i__2 = lastc;
+ for (i__ = 1; i__ <= i__2; ++i__) {
+ c__[i__ + j * c_dim1] -= work[i__ + j * work_dim1];
+/* L50: */
+ }
+/* L60: */
+ }
+ }
+
+ } else {
+
+/* Let V = ( V1 ) */
+/* ( V2 ) (last K rows) */
+/* where V2 is unit upper triangular. */
+
+ if (lsame_(side, "L")) {
+
+/* Form H * C or H' * C where C = ( C1 ) */
+/* ( C2 ) */
+
+/* Computing MAX */
+ i__1 = *k, i__2 = ilaslr_(m, k, &v[v_offset], ldv);
+ lastv = max(i__1,i__2);
+ lastc = ilaslc_(&lastv, n, &c__[c_offset], ldc);
+
+/* W := C' * V = (C1'*V1 + C2'*V2) (stored in WORK) */
+
+/* W := C2' */
+
+ i__1 = *k;
+ for (j = 1; j <= i__1; ++j) {
+ scopy_(&lastc, &c__[lastv - *k + j + c_dim1], ldc, &work[
+ j * work_dim1 + 1], &c__1);
+/* L70: */
+ }
+
+/* W := W * V2 */
+
+ strmm_("Right", "Upper", "No transpose", "Unit", &lastc, k, &
+ c_b14, &v[lastv - *k + 1 + v_dim1], ldv, &work[
+ work_offset], ldwork);
+ if (lastv > *k) {
+
+/* W := W + C1'*V1 */
+
+ i__1 = lastv - *k;
+ sgemm_("Transpose", "No transpose", &lastc, k, &i__1, &
+ c_b14, &c__[c_offset], ldc, &v[v_offset], ldv, &
+ c_b14, &work[work_offset], ldwork);
+ }
+
+/* W := W * T' or W * T */
+
+ strmm_("Right", "Lower", transt, "Non-unit", &lastc, k, &
+ c_b14, &t[t_offset], ldt, &work[work_offset], ldwork);
+
+/* C := C - V * W' */
+
+ if (lastv > *k) {
+
+/* C1 := C1 - V1 * W' */
+
+ i__1 = lastv - *k;
+ sgemm_("No transpose", "Transpose", &i__1, &lastc, k, &
+ c_b25, &v[v_offset], ldv, &work[work_offset],
+ ldwork, &c_b14, &c__[c_offset], ldc);
+ }
+
+/* W := W * V2' */
+
+ strmm_("Right", "Upper", "Transpose", "Unit", &lastc, k, &
+ c_b14, &v[lastv - *k + 1 + v_dim1], ldv, &work[
+ work_offset], ldwork);
+
+/* C2 := C2 - W' */
+
+ i__1 = *k;
+ for (j = 1; j <= i__1; ++j) {
+ i__2 = lastc;
+ for (i__ = 1; i__ <= i__2; ++i__) {
+ c__[lastv - *k + j + i__ * c_dim1] -= work[i__ + j *
+ work_dim1];
+/* L80: */
+ }
+/* L90: */
+ }
+
+ } else if (lsame_(side, "R")) {
+
+/* Form C * H or C * H' where C = ( C1 C2 ) */
+
+/* Computing MAX */
+ i__1 = *k, i__2 = ilaslr_(n, k, &v[v_offset], ldv);
+ lastv = max(i__1,i__2);
+ lastc = ilaslr_(m, &lastv, &c__[c_offset], ldc);
+
+/* W := C * V = (C1*V1 + C2*V2) (stored in WORK) */
+
+/* W := C2 */
+
+ i__1 = *k;
+ for (j = 1; j <= i__1; ++j) {
+ scopy_(&lastc, &c__[(*n - *k + j) * c_dim1 + 1], &c__1, &
+ work[j * work_dim1 + 1], &c__1);
+/* L100: */
+ }
+
+/* W := W * V2 */
+
+ strmm_("Right", "Upper", "No transpose", "Unit", &lastc, k, &
+ c_b14, &v[lastv - *k + 1 + v_dim1], ldv, &work[
+ work_offset], ldwork);
+ if (lastv > *k) {
+
+/* W := W + C1 * V1 */
+
+ i__1 = lastv - *k;
+ sgemm_("No transpose", "No transpose", &lastc, k, &i__1, &
+ c_b14, &c__[c_offset], ldc, &v[v_offset], ldv, &
+ c_b14, &work[work_offset], ldwork);
+ }
+
+/* W := W * T or W * T' */
+
+ strmm_("Right", "Lower", trans, "Non-unit", &lastc, k, &c_b14,
+ &t[t_offset], ldt, &work[work_offset], ldwork);
+
+/* C := C - W * V' */
+
+ if (lastv > *k) {
+
+/* C1 := C1 - W * V1' */
+
+ i__1 = lastv - *k;
+ sgemm_("No transpose", "Transpose", &lastc, &i__1, k, &
+ c_b25, &work[work_offset], ldwork, &v[v_offset],
+ ldv, &c_b14, &c__[c_offset], ldc);
+ }
+
+/* W := W * V2' */
+
+ strmm_("Right", "Upper", "Transpose", "Unit", &lastc, k, &
+ c_b14, &v[lastv - *k + 1 + v_dim1], ldv, &work[
+ work_offset], ldwork);
+
+/* C2 := C2 - W */
+
+ i__1 = *k;
+ for (j = 1; j <= i__1; ++j) {
+ i__2 = lastc;
+ for (i__ = 1; i__ <= i__2; ++i__) {
+ c__[i__ + (lastv - *k + j) * c_dim1] -= work[i__ + j *
+ work_dim1];
+/* L110: */
+ }
+/* L120: */
+ }
+ }
+ }
+
+ } else if (lsame_(storev, "R")) {
+
+ if (lsame_(direct, "F")) {
+
+/* Let V = ( V1 V2 ) (V1: first K columns) */
+/* where V1 is unit upper triangular. */
+
+ if (lsame_(side, "L")) {
+
+/* Form H * C or H' * C where C = ( C1 ) */
+/* ( C2 ) */
+
+/* Computing MAX */
+ i__1 = *k, i__2 = ilaslc_(k, m, &v[v_offset], ldv);
+ lastv = max(i__1,i__2);
+ lastc = ilaslc_(&lastv, n, &c__[c_offset], ldc);
+
+/* W := C' * V' = (C1'*V1' + C2'*V2') (stored in WORK) */
+
+/* W := C1' */
+
+ i__1 = *k;
+ for (j = 1; j <= i__1; ++j) {
+ scopy_(&lastc, &c__[j + c_dim1], ldc, &work[j * work_dim1
+ + 1], &c__1);
+/* L130: */
+ }
+
+/* W := W * V1' */
+
+ strmm_("Right", "Upper", "Transpose", "Unit", &lastc, k, &
+ c_b14, &v[v_offset], ldv, &work[work_offset], ldwork);
+ if (lastv > *k) {
+
+/* W := W + C2'*V2' */
+
+ i__1 = lastv - *k;
+ sgemm_("Transpose", "Transpose", &lastc, k, &i__1, &c_b14,
+ &c__[*k + 1 + c_dim1], ldc, &v[(*k + 1) * v_dim1
+ + 1], ldv, &c_b14, &work[work_offset], ldwork);
+ }
+
+/* W := W * T' or W * T */
+
+ strmm_("Right", "Upper", transt, "Non-unit", &lastc, k, &
+ c_b14, &t[t_offset], ldt, &work[work_offset], ldwork);
+
+/* C := C - V' * W' */
+
+ if (lastv > *k) {
+
+/* C2 := C2 - V2' * W' */
+
+ i__1 = lastv - *k;
+ sgemm_("Transpose", "Transpose", &i__1, &lastc, k, &c_b25,
+ &v[(*k + 1) * v_dim1 + 1], ldv, &work[
+ work_offset], ldwork, &c_b14, &c__[*k + 1 +
+ c_dim1], ldc);
+ }
+
+/* W := W * V1 */
+
+ strmm_("Right", "Upper", "No transpose", "Unit", &lastc, k, &
+ c_b14, &v[v_offset], ldv, &work[work_offset], ldwork);
+
+/* C1 := C1 - W' */
+
+ i__1 = *k;
+ for (j = 1; j <= i__1; ++j) {
+ i__2 = lastc;
+ for (i__ = 1; i__ <= i__2; ++i__) {
+ c__[j + i__ * c_dim1] -= work[i__ + j * work_dim1];
+/* L140: */
+ }
+/* L150: */
+ }
+
+ } else if (lsame_(side, "R")) {
+
+/* Form C * H or C * H' where C = ( C1 C2 ) */
+
+/* Computing MAX */
+ i__1 = *k, i__2 = ilaslc_(k, n, &v[v_offset], ldv);
+ lastv = max(i__1,i__2);
+ lastc = ilaslr_(m, &lastv, &c__[c_offset], ldc);
+
+/* W := C * V' = (C1*V1' + C2*V2') (stored in WORK) */
+
+/* W := C1 */
+
+ i__1 = *k;
+ for (j = 1; j <= i__1; ++j) {
+ scopy_(&lastc, &c__[j * c_dim1 + 1], &c__1, &work[j *
+ work_dim1 + 1], &c__1);
+/* L160: */
+ }
+
+/* W := W * V1' */
+
+ strmm_("Right", "Upper", "Transpose", "Unit", &lastc, k, &
+ c_b14, &v[v_offset], ldv, &work[work_offset], ldwork);
+ if (lastv > *k) {
+
+/* W := W + C2 * V2' */
+
+ i__1 = lastv - *k;
+ sgemm_("No transpose", "Transpose", &lastc, k, &i__1, &
+ c_b14, &c__[(*k + 1) * c_dim1 + 1], ldc, &v[(*k +
+ 1) * v_dim1 + 1], ldv, &c_b14, &work[work_offset],
+ ldwork);
+ }
+
+/* W := W * T or W * T' */
+
+ strmm_("Right", "Upper", trans, "Non-unit", &lastc, k, &c_b14,
+ &t[t_offset], ldt, &work[work_offset], ldwork);
+
+/* C := C - W * V */
+
+ if (lastv > *k) {
+
+/* C2 := C2 - W * V2 */
+
+ i__1 = lastv - *k;
+ sgemm_("No transpose", "No transpose", &lastc, &i__1, k, &
+ c_b25, &work[work_offset], ldwork, &v[(*k + 1) *
+ v_dim1 + 1], ldv, &c_b14, &c__[(*k + 1) * c_dim1
+ + 1], ldc);
+ }
+
+/* W := W * V1 */
+
+ strmm_("Right", "Upper", "No transpose", "Unit", &lastc, k, &
+ c_b14, &v[v_offset], ldv, &work[work_offset], ldwork);
+
+/* C1 := C1 - W */
+
+ i__1 = *k;
+ for (j = 1; j <= i__1; ++j) {
+ i__2 = lastc;
+ for (i__ = 1; i__ <= i__2; ++i__) {
+ c__[i__ + j * c_dim1] -= work[i__ + j * work_dim1];
+/* L170: */
+ }
+/* L180: */
+ }
+
+ }
+
+ } else {
+
+/* Let V = ( V1 V2 ) (V2: last K columns) */
+/* where V2 is unit lower triangular. */
+
+ if (lsame_(side, "L")) {
+
+/* Form H * C or H' * C where C = ( C1 ) */
+/* ( C2 ) */
+
+/* Computing MAX */
+ i__1 = *k, i__2 = ilaslc_(k, m, &v[v_offset], ldv);
+ lastv = max(i__1,i__2);
+ lastc = ilaslc_(&lastv, n, &c__[c_offset], ldc);
+
+/* W := C' * V' = (C1'*V1' + C2'*V2') (stored in WORK) */
+
+/* W := C2' */
+
+ i__1 = *k;
+ for (j = 1; j <= i__1; ++j) {
+ scopy_(&lastc, &c__[lastv - *k + j + c_dim1], ldc, &work[
+ j * work_dim1 + 1], &c__1);
+/* L190: */
+ }
+
+/* W := W * V2' */
+
+ strmm_("Right", "Lower", "Transpose", "Unit", &lastc, k, &
+ c_b14, &v[(lastv - *k + 1) * v_dim1 + 1], ldv, &work[
+ work_offset], ldwork);
+ if (lastv > *k) {
+
+/* W := W + C1'*V1' */
+
+ i__1 = lastv - *k;
+ sgemm_("Transpose", "Transpose", &lastc, k, &i__1, &c_b14,
+ &c__[c_offset], ldc, &v[v_offset], ldv, &c_b14, &
+ work[work_offset], ldwork);
+ }
+
+/* W := W * T' or W * T */
+
+ strmm_("Right", "Lower", transt, "Non-unit", &lastc, k, &
+ c_b14, &t[t_offset], ldt, &work[work_offset], ldwork);
+
+/* C := C - V' * W' */
+
+ if (lastv > *k) {
+
+/* C1 := C1 - V1' * W' */
+
+ i__1 = lastv - *k;
+ sgemm_("Transpose", "Transpose", &i__1, &lastc, k, &c_b25,
+ &v[v_offset], ldv, &work[work_offset], ldwork, &
+ c_b14, &c__[c_offset], ldc);
+ }
+
+/* W := W * V2 */
+
+ strmm_("Right", "Lower", "No transpose", "Unit", &lastc, k, &
+ c_b14, &v[(lastv - *k + 1) * v_dim1 + 1], ldv, &work[
+ work_offset], ldwork);
+
+/* C2 := C2 - W' */
+
+ i__1 = *k;
+ for (j = 1; j <= i__1; ++j) {
+ i__2 = lastc;
+ for (i__ = 1; i__ <= i__2; ++i__) {
+ c__[lastv - *k + j + i__ * c_dim1] -= work[i__ + j *
+ work_dim1];
+/* L200: */
+ }
+/* L210: */
+ }
+
+ } else if (lsame_(side, "R")) {
+
+/* Form C * H or C * H' where C = ( C1 C2 ) */
+
+/* Computing MAX */
+ i__1 = *k, i__2 = ilaslc_(k, n, &v[v_offset], ldv);
+ lastv = max(i__1,i__2);
+ lastc = ilaslr_(m, &lastv, &c__[c_offset], ldc);
+
+/* W := C * V' = (C1*V1' + C2*V2') (stored in WORK) */
+
+/* W := C2 */
+
+ i__1 = *k;
+ for (j = 1; j <= i__1; ++j) {
+ scopy_(&lastc, &c__[(lastv - *k + j) * c_dim1 + 1], &c__1,
+ &work[j * work_dim1 + 1], &c__1);
+/* L220: */
+ }
+
+/* W := W * V2' */
+
+ strmm_("Right", "Lower", "Transpose", "Unit", &lastc, k, &
+ c_b14, &v[(lastv - *k + 1) * v_dim1 + 1], ldv, &work[
+ work_offset], ldwork);
+ if (lastv > *k) {
+
+/* W := W + C1 * V1' */
+
+ i__1 = lastv - *k;
+ sgemm_("No transpose", "Transpose", &lastc, k, &i__1, &
+ c_b14, &c__[c_offset], ldc, &v[v_offset], ldv, &
+ c_b14, &work[work_offset], ldwork);
+ }
+
+/* W := W * T or W * T' */
+
+ strmm_("Right", "Lower", trans, "Non-unit", &lastc, k, &c_b14,
+ &t[t_offset], ldt, &work[work_offset], ldwork);
+
+/* C := C - W * V */
+
+ if (lastv > *k) {
+
+/* C1 := C1 - W * V1 */
+
+ i__1 = lastv - *k;
+ sgemm_("No transpose", "No transpose", &lastc, &i__1, k, &
+ c_b25, &work[work_offset], ldwork, &v[v_offset],
+ ldv, &c_b14, &c__[c_offset], ldc);
+ }
+
+/* W := W * V2 */
+
+ strmm_("Right", "Lower", "No transpose", "Unit", &lastc, k, &
+ c_b14, &v[(lastv - *k + 1) * v_dim1 + 1], ldv, &work[
+ work_offset], ldwork);
+
+/* C1 := C1 - W */
+
+ i__1 = *k;
+ for (j = 1; j <= i__1; ++j) {
+ i__2 = lastc;
+ for (i__ = 1; i__ <= i__2; ++i__) {
+ c__[i__ + (lastv - *k + j) * c_dim1] -= work[i__ + j *
+ work_dim1];
+/* L230: */
+ }
+/* L240: */
+ }
+
+ }
+
+ }
+ }
+
+ return 0;
+
+/* End of SLARFB */
+
+} /* slarfb_ */
diff --git a/lapack/slarfg.c b/lapack/slarfg.c
new file mode 100644
index 0000000..0d31251
--- /dev/null
+++ b/lapack/slarfg.c
@@ -0,0 +1,169 @@
+/* slarfg.f -- translated by f2c (version 20061008).
+ You must link the resulting object file with libf2c:
+ on Microsoft Windows system, link with libf2c.lib;
+ on Linux or Unix systems, link with .../path/to/libf2c.a -lm
+ or, if you install libf2c.a in a standard place, with -lf2c -lm
+ -- in that order, at the end of the command line, as in
+ cc *.o -lf2c -lm
+ Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
+
+ http://www.netlib.org/f2c/libf2c.zip
+*/
+
+#include "f2c.h"
+#include "blaswrap.h"
+
+/* Subroutine */ int slarfg_(integer *n, real *alpha, real *x, integer *incx,
+ real *tau)
+{
+ /* System generated locals */
+ integer i__1;
+ real r__1;
+
+ /* Builtin functions */
+ double r_sign(real *, real *);
+
+ /* Local variables */
+ integer j, knt;
+ real beta;
+ extern doublereal snrm2_(integer *, real *, integer *);
+ extern /* Subroutine */ int sscal_(integer *, real *, real *, integer *);
+ real xnorm;
+ extern doublereal slapy2_(real *, real *), slamch_(char *);
+ real safmin, rsafmn;
+
+
+/* -- LAPACK auxiliary routine (version 3.2) -- */
+/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
+/* November 2006 */
+
+/* .. Scalar Arguments .. */
+/* .. */
+/* .. Array Arguments .. */
+/* .. */
+
+/* Purpose */
+/* ======= */
+
+/* SLARFG generates a real elementary reflector H of order n, such */
+/* that */
+
+/* H * ( alpha ) = ( beta ), H' * H = I. */
+/* ( x ) ( 0 ) */
+
+/* where alpha and beta are scalars, and x is an (n-1)-element real */
+/* vector. H is represented in the form */
+
+/* H = I - tau * ( 1 ) * ( 1 v' ) , */
+/* ( v ) */
+
+/* where tau is a real scalar and v is a real (n-1)-element */
+/* vector. */
+
+/* If the elements of x are all zero, then tau = 0 and H is taken to be */
+/* the unit matrix. */
+
+/* Otherwise 1 <= tau <= 2. */
+
+/* Arguments */
+/* ========= */
+
+/* N (input) INTEGER */
+/* The order of the elementary reflector. */
+
+/* ALPHA (input/output) REAL */
+/* On entry, the value alpha. */
+/* On exit, it is overwritten with the value beta. */
+
+/* X (input/output) REAL array, dimension */
+/* (1+(N-2)*abs(INCX)) */
+/* On entry, the vector x. */
+/* On exit, it is overwritten with the vector v. */
+
+/* INCX (input) INTEGER */
+/* The increment between elements of X. INCX > 0. */
+
+/* TAU (output) REAL */
+/* The value tau. */
+
+/* ===================================================================== */
+
+/* .. Parameters .. */
+/* .. */
+/* .. Local Scalars .. */
+/* .. */
+/* .. External Functions .. */
+/* .. */
+/* .. Intrinsic Functions .. */
+/* .. */
+/* .. External Subroutines .. */
+/* .. */
+/* .. Executable Statements .. */
+
+ /* Parameter adjustments */
+ --x;
+
+ /* Function Body */
+ if (*n <= 1) {
+ *tau = 0.f;
+ return 0;
+ }
+
+ i__1 = *n - 1;
+ xnorm = snrm2_(&i__1, &x[1], incx);
+
+ if (xnorm == 0.f) {
+
+/* H = I */
+
+ *tau = 0.f;
+ } else {
+
+/* general case */
+
+ r__1 = slapy2_(alpha, &xnorm);
+ beta = -r_sign(&r__1, alpha);
+ safmin = slamch_("S") / slamch_("E");
+ knt = 0;
+ if (dabs(beta) < safmin) {
+
+/* XNORM, BETA may be inaccurate; scale X and recompute them */
+
+ rsafmn = 1.f / safmin;
+L10:
+ ++knt;
+ i__1 = *n - 1;
+ sscal_(&i__1, &rsafmn, &x[1], incx);
+ beta *= rsafmn;
+ *alpha *= rsafmn;
+ if (dabs(beta) < safmin) {
+ goto L10;
+ }
+
+/* New BETA is at most 1, at least SAFMIN */
+
+ i__1 = *n - 1;
+ xnorm = snrm2_(&i__1, &x[1], incx);
+ r__1 = slapy2_(alpha, &xnorm);
+ beta = -r_sign(&r__1, alpha);
+ }
+ *tau = (beta - *alpha) / beta;
+ i__1 = *n - 1;
+ r__1 = 1.f / (*alpha - beta);
+ sscal_(&i__1, &r__1, &x[1], incx);
+
+/* If ALPHA is subnormal, it may lose relative accuracy */
+
+ i__1 = knt;
+ for (j = 1; j <= i__1; ++j) {
+ beta *= safmin;
+/* L20: */
+ }
+ *alpha = beta;
+ }
+
+ return 0;
+
+/* End of SLARFG */
+
+} /* slarfg_ */
diff --git a/lapack/slarft.c b/lapack/slarft.c
new file mode 100644
index 0000000..4143ce4
--- /dev/null
+++ b/lapack/slarft.c
@@ -0,0 +1,323 @@
+/* slarft.f -- translated by f2c (version 20061008).
+ You must link the resulting object file with libf2c:
+ on Microsoft Windows system, link with libf2c.lib;
+ on Linux or Unix systems, link with .../path/to/libf2c.a -lm
+ or, if you install libf2c.a in a standard place, with -lf2c -lm
+ -- in that order, at the end of the command line, as in
+ cc *.o -lf2c -lm
+ Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
+
+ http://www.netlib.org/f2c/libf2c.zip
+*/
+
+#include "f2c.h"
+#include "blaswrap.h"
+
+/* Table of constant values */
+
+static integer c__1 = 1;
+static real c_b8 = 0.f;
+
+/* Subroutine */ int slarft_(char *direct, char *storev, integer *n, integer *
+ k, real *v, integer *ldv, real *tau, real *t, integer *ldt)
+{
+ /* System generated locals */
+ integer t_dim1, t_offset, v_dim1, v_offset, i__1, i__2, i__3;
+ real r__1;
+
+ /* Local variables */
+ integer i__, j, prevlastv;
+ real vii;
+ extern logical lsame_(char *, char *);
+ extern /* Subroutine */ int sgemv_(char *, integer *, integer *, real *,
+ real *, integer *, real *, integer *, real *, real *, integer *);
+ integer lastv;
+ extern /* Subroutine */ int strmv_(char *, char *, char *, integer *,
+ real *, integer *, real *, integer *);
+
+
+/* -- LAPACK auxiliary routine (version 3.2) -- */
+/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
+/* November 2006 */
+
+/* .. Scalar Arguments .. */
+/* .. */
+/* .. Array Arguments .. */
+/* .. */
+
+/* Purpose */
+/* ======= */
+
+/* SLARFT forms the triangular factor T of a real block reflector H */
+/* of order n, which is defined as a product of k elementary reflectors. */
+
+/* If DIRECT = 'F', H = H(1) H(2) . . . H(k) and T is upper triangular; */
+
+/* If DIRECT = 'B', H = H(k) . . . H(2) H(1) and T is lower triangular. */
+
+/* If STOREV = 'C', the vector which defines the elementary reflector */
+/* H(i) is stored in the i-th column of the array V, and */
+
+/* H = I - V * T * V' */
+
+/* If STOREV = 'R', the vector which defines the elementary reflector */
+/* H(i) is stored in the i-th row of the array V, and */
+
+/* H = I - V' * T * V */
+
+/* Arguments */
+/* ========= */
+
+/* DIRECT (input) CHARACTER*1 */
+/* Specifies the order in which the elementary reflectors are */
+/* multiplied to form the block reflector: */
+/* = 'F': H = H(1) H(2) . . . H(k) (Forward) */
+/* = 'B': H = H(k) . . . H(2) H(1) (Backward) */
+
+/* STOREV (input) CHARACTER*1 */
+/* Specifies how the vectors which define the elementary */
+/* reflectors are stored (see also Further Details): */
+/* = 'C': columnwise */
+/* = 'R': rowwise */
+
+/* N (input) INTEGER */
+/* The order of the block reflector H. N >= 0. */
+
+/* K (input) INTEGER */
+/* The order of the triangular factor T (= the number of */
+/* elementary reflectors). K >= 1. */
+
+/* V (input/output) REAL array, dimension */
+/* (LDV,K) if STOREV = 'C' */
+/* (LDV,N) if STOREV = 'R' */
+/* The matrix V. See further details. */
+
+/* LDV (input) INTEGER */
+/* The leading dimension of the array V. */
+/* If STOREV = 'C', LDV >= max(1,N); if STOREV = 'R', LDV >= K. */
+
+/* TAU (input) REAL array, dimension (K) */
+/* TAU(i) must contain the scalar factor of the elementary */
+/* reflector H(i). */
+
+/* T (output) REAL array, dimension (LDT,K) */
+/* The k by k triangular factor T of the block reflector. */
+/* If DIRECT = 'F', T is upper triangular; if DIRECT = 'B', T is */
+/* lower triangular. The rest of the array is not used. */
+
+/* LDT (input) INTEGER */
+/* The leading dimension of the array T. LDT >= K. */
+
+/* Further Details */
+/* =============== */
+
+/* The shape of the matrix V and the storage of the vectors which define */
+/* the H(i) is best illustrated by the following example with n = 5 and */
+/* k = 3. The elements equal to 1 are not stored; the corresponding */
+/* array elements are modified but restored on exit. The rest of the */
+/* array is not used. */
+
+/* DIRECT = 'F' and STOREV = 'C': DIRECT = 'F' and STOREV = 'R': */
+
+/* V = ( 1 ) V = ( 1 v1 v1 v1 v1 ) */
+/* ( v1 1 ) ( 1 v2 v2 v2 ) */
+/* ( v1 v2 1 ) ( 1 v3 v3 ) */
+/* ( v1 v2 v3 ) */
+/* ( v1 v2 v3 ) */
+
+/* DIRECT = 'B' and STOREV = 'C': DIRECT = 'B' and STOREV = 'R': */
+
+/* V = ( v1 v2 v3 ) V = ( v1 v1 1 ) */
+/* ( v1 v2 v3 ) ( v2 v2 v2 1 ) */
+/* ( 1 v2 v3 ) ( v3 v3 v3 v3 1 ) */
+/* ( 1 v3 ) */
+/* ( 1 ) */
+
+/* ===================================================================== */
+
+/* .. Parameters .. */
+/* .. */
+/* .. Local Scalars .. */
+/* .. */
+/* .. External Subroutines .. */
+/* .. */
+/* .. External Functions .. */
+/* .. */
+/* .. Executable Statements .. */
+
+/* Quick return if possible */
+
+ /* Parameter adjustments */
+ v_dim1 = *ldv;
+ v_offset = 1 + v_dim1;
+ v -= v_offset;
+ --tau;
+ t_dim1 = *ldt;
+ t_offset = 1 + t_dim1;
+ t -= t_offset;
+
+ /* Function Body */
+ if (*n == 0) {
+ return 0;
+ }
+
+ if (lsame_(direct, "F")) {
+ prevlastv = *n;
+ i__1 = *k;
+ for (i__ = 1; i__ <= i__1; ++i__) {
+ prevlastv = max(i__,prevlastv);
+ if (tau[i__] == 0.f) {
+
+/* H(i) = I */
+
+ i__2 = i__;
+ for (j = 1; j <= i__2; ++j) {
+ t[j + i__ * t_dim1] = 0.f;
+/* L10: */
+ }
+ } else {
+
+/* general case */
+
+ vii = v[i__ + i__ * v_dim1];
+ v[i__ + i__ * v_dim1] = 1.f;
+ if (lsame_(storev, "C")) {
+/* Skip any trailing zeros. */
+ i__2 = i__ + 1;
+ for (lastv = *n; lastv >= i__2; --lastv) {
+ if (v[lastv + i__ * v_dim1] != 0.f) {
+ break;
+ }
+ }
+ j = min(lastv,prevlastv);
+
+/* T(1:i-1,i) := - tau(i) * V(i:j,1:i-1)' * V(i:j,i) */
+
+ i__2 = j - i__ + 1;
+ i__3 = i__ - 1;
+ r__1 = -tau[i__];
+ sgemv_("Transpose", &i__2, &i__3, &r__1, &v[i__ + v_dim1],
+ ldv, &v[i__ + i__ * v_dim1], &c__1, &c_b8, &t[
+ i__ * t_dim1 + 1], &c__1);
+ } else {
+/* Skip any trailing zeros. */
+ i__2 = i__ + 1;
+ for (lastv = *n; lastv >= i__2; --lastv) {
+ if (v[i__ + lastv * v_dim1] != 0.f) {
+ break;
+ }
+ }
+ j = min(lastv,prevlastv);
+
+/* T(1:i-1,i) := - tau(i) * V(1:i-1,i:j) * V(i,i:j)' */
+
+ i__2 = i__ - 1;
+ i__3 = j - i__ + 1;
+ r__1 = -tau[i__];
+ sgemv_("No transpose", &i__2, &i__3, &r__1, &v[i__ *
+ v_dim1 + 1], ldv, &v[i__ + i__ * v_dim1], ldv, &
+ c_b8, &t[i__ * t_dim1 + 1], &c__1);
+ }
+ v[i__ + i__ * v_dim1] = vii;
+
+/* T(1:i-1,i) := T(1:i-1,1:i-1) * T(1:i-1,i) */
+
+ i__2 = i__ - 1;
+ strmv_("Upper", "No transpose", "Non-unit", &i__2, &t[
+ t_offset], ldt, &t[i__ * t_dim1 + 1], &c__1);
+ t[i__ + i__ * t_dim1] = tau[i__];
+ if (i__ > 1) {
+ prevlastv = max(prevlastv,lastv);
+ } else {
+ prevlastv = lastv;
+ }
+ }
+/* L20: */
+ }
+ } else {
+ prevlastv = 1;
+ for (i__ = *k; i__ >= 1; --i__) {
+ if (tau[i__] == 0.f) {
+
+/* H(i) = I */
+
+ i__1 = *k;
+ for (j = i__; j <= i__1; ++j) {
+ t[j + i__ * t_dim1] = 0.f;
+/* L30: */
+ }
+ } else {
+
+/* general case */
+
+ if (i__ < *k) {
+ if (lsame_(storev, "C")) {
+ vii = v[*n - *k + i__ + i__ * v_dim1];
+ v[*n - *k + i__ + i__ * v_dim1] = 1.f;
+/* Skip any leading zeros. */
+ i__1 = i__ - 1;
+ for (lastv = 1; lastv <= i__1; ++lastv) {
+ if (v[lastv + i__ * v_dim1] != 0.f) {
+ break;
+ }
+ }
+ j = max(lastv,prevlastv);
+
+/* T(i+1:k,i) := */
+/* - tau(i) * V(j:n-k+i,i+1:k)' * V(j:n-k+i,i) */
+
+ i__1 = *n - *k + i__ - j + 1;
+ i__2 = *k - i__;
+ r__1 = -tau[i__];
+ sgemv_("Transpose", &i__1, &i__2, &r__1, &v[j + (i__
+ + 1) * v_dim1], ldv, &v[j + i__ * v_dim1], &
+ c__1, &c_b8, &t[i__ + 1 + i__ * t_dim1], &
+ c__1);
+ v[*n - *k + i__ + i__ * v_dim1] = vii;
+ } else {
+ vii = v[i__ + (*n - *k + i__) * v_dim1];
+ v[i__ + (*n - *k + i__) * v_dim1] = 1.f;
+/* Skip any leading zeros. */
+ i__1 = i__ - 1;
+ for (lastv = 1; lastv <= i__1; ++lastv) {
+ if (v[i__ + lastv * v_dim1] != 0.f) {
+ break;
+ }
+ }
+ j = max(lastv,prevlastv);
+
+/* T(i+1:k,i) := */
+/* - tau(i) * V(i+1:k,j:n-k+i) * V(i,j:n-k+i)' */
+
+ i__1 = *k - i__;
+ i__2 = *n - *k + i__ - j + 1;
+ r__1 = -tau[i__];
+ sgemv_("No transpose", &i__1, &i__2, &r__1, &v[i__ +
+ 1 + j * v_dim1], ldv, &v[i__ + j * v_dim1],
+ ldv, &c_b8, &t[i__ + 1 + i__ * t_dim1], &c__1);
+ v[i__ + (*n - *k + i__) * v_dim1] = vii;
+ }
+
+/* T(i+1:k,i) := T(i+1:k,i+1:k) * T(i+1:k,i) */
+
+ i__1 = *k - i__;
+ strmv_("Lower", "No transpose", "Non-unit", &i__1, &t[i__
+ + 1 + (i__ + 1) * t_dim1], ldt, &t[i__ + 1 + i__ *
+ t_dim1], &c__1)
+ ;
+ if (i__ > 1) {
+ prevlastv = min(prevlastv,lastv);
+ } else {
+ prevlastv = lastv;
+ }
+ }
+ t[i__ + i__ * t_dim1] = tau[i__];
+ }
+/* L40: */
+ }
+ }
+ return 0;
+
+/* End of SLARFT */
+
+} /* slarft_ */
diff --git a/lapack/svd.cpp b/lapack/svd.cpp
new file mode 100644
index 0000000..83544cf
--- /dev/null
+++ b/lapack/svd.cpp
@@ -0,0 +1,138 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2014 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "lapack_common.h"
+#include <Eigen/SVD>
+
+// computes the singular values/vectors a general M-by-N matrix A using divide-and-conquer
+EIGEN_LAPACK_FUNC(gesdd,(char *jobz, int *m, int* n, Scalar* a, int *lda, RealScalar *s, Scalar *u, int *ldu, Scalar *vt, int *ldvt, Scalar* /*work*/, int* lwork,
+ EIGEN_LAPACK_ARG_IF_COMPLEX(RealScalar */*rwork*/) int * /*iwork*/, int *info))
+{
+ // TODO exploit the work buffer
+ bool query_size = *lwork==-1;
+ int diag_size = (std::min)(*m,*n);
+
+ *info = 0;
+ if(*jobz!='A' && *jobz!='S' && *jobz!='O' && *jobz!='N') *info = -1;
+ else if(*m<0) *info = -2;
+ else if(*n<0) *info = -3;
+ else if(*lda<std::max(1,*m)) *info = -5;
+ else if(*lda<std::max(1,*m)) *info = -8;
+ else if(*ldu <1 || (*jobz=='A' && *ldu <*m)
+ || (*jobz=='O' && *m<*n && *ldu<*m)) *info = -8;
+ else if(*ldvt<1 || (*jobz=='A' && *ldvt<*n)
+ || (*jobz=='S' && *ldvt<diag_size)
+ || (*jobz=='O' && *m>=*n && *ldvt<*n)) *info = -10;
+
+ if(*info!=0)
+ {
+ int e = -*info;
+ return xerbla_(SCALAR_SUFFIX_UP"GESDD ", &e, 6);
+ }
+
+ if(query_size)
+ {
+ *lwork = 0;
+ return 0;
+ }
+
+ if(*n==0 || *m==0)
+ return 0;
+
+ PlainMatrixType mat(*m,*n);
+ mat = matrix(a,*m,*n,*lda);
+
+ int option = *jobz=='A' ? ComputeFullU|ComputeFullV
+ : *jobz=='S' ? ComputeThinU|ComputeThinV
+ : *jobz=='O' ? ComputeThinU|ComputeThinV
+ : 0;
+
+ BDCSVD<PlainMatrixType> svd(mat,option);
+
+ make_vector(s,diag_size) = svd.singularValues().head(diag_size);
+
+ if(*jobz=='A')
+ {
+ matrix(u,*m,*m,*ldu) = svd.matrixU();
+ matrix(vt,*n,*n,*ldvt) = svd.matrixV().adjoint();
+ }
+ else if(*jobz=='S')
+ {
+ matrix(u,*m,diag_size,*ldu) = svd.matrixU();
+ matrix(vt,diag_size,*n,*ldvt) = svd.matrixV().adjoint();
+ }
+ else if(*jobz=='O' && *m>=*n)
+ {
+ matrix(a,*m,*n,*lda) = svd.matrixU();
+ matrix(vt,*n,*n,*ldvt) = svd.matrixV().adjoint();
+ }
+ else if(*jobz=='O')
+ {
+ matrix(u,*m,*m,*ldu) = svd.matrixU();
+ matrix(a,diag_size,*n,*lda) = svd.matrixV().adjoint();
+ }
+
+ return 0;
+}
+
+// computes the singular values/vectors a general M-by-N matrix A using two sided jacobi algorithm
+EIGEN_LAPACK_FUNC(gesvd,(char *jobu, char *jobv, int *m, int* n, Scalar* a, int *lda, RealScalar *s, Scalar *u, int *ldu, Scalar *vt, int *ldvt, Scalar* /*work*/, int* lwork,
+ EIGEN_LAPACK_ARG_IF_COMPLEX(RealScalar */*rwork*/) int *info))
+{
+ // TODO exploit the work buffer
+ bool query_size = *lwork==-1;
+ int diag_size = (std::min)(*m,*n);
+
+ *info = 0;
+ if( *jobu!='A' && *jobu!='S' && *jobu!='O' && *jobu!='N') *info = -1;
+ else if((*jobv!='A' && *jobv!='S' && *jobv!='O' && *jobv!='N')
+ || (*jobu=='O' && *jobv=='O')) *info = -2;
+ else if(*m<0) *info = -3;
+ else if(*n<0) *info = -4;
+ else if(*lda<std::max(1,*m)) *info = -6;
+ else if(*ldu <1 || ((*jobu=='A' || *jobu=='S') && *ldu<*m)) *info = -9;
+ else if(*ldvt<1 || (*jobv=='A' && *ldvt<*n)
+ || (*jobv=='S' && *ldvt<diag_size)) *info = -11;
+
+ if(*info!=0)
+ {
+ int e = -*info;
+ return xerbla_(SCALAR_SUFFIX_UP"GESVD ", &e, 6);
+ }
+
+ if(query_size)
+ {
+ *lwork = 0;
+ return 0;
+ }
+
+ if(*n==0 || *m==0)
+ return 0;
+
+ PlainMatrixType mat(*m,*n);
+ mat = matrix(a,*m,*n,*lda);
+
+ int option = (*jobu=='A' ? ComputeFullU : *jobu=='S' || *jobu=='O' ? ComputeThinU : 0)
+ | (*jobv=='A' ? ComputeFullV : *jobv=='S' || *jobv=='O' ? ComputeThinV : 0);
+
+ JacobiSVD<PlainMatrixType> svd(mat,option);
+
+ make_vector(s,diag_size) = svd.singularValues().head(diag_size);
+ {
+ if(*jobu=='A') matrix(u,*m,*m,*ldu) = svd.matrixU();
+ else if(*jobu=='S') matrix(u,*m,diag_size,*ldu) = svd.matrixU();
+ else if(*jobu=='O') matrix(a,*m,diag_size,*lda) = svd.matrixU();
+ }
+ {
+ if(*jobv=='A') matrix(vt,*n,*n,*ldvt) = svd.matrixV().adjoint();
+ else if(*jobv=='S') matrix(vt,diag_size,*n,*ldvt) = svd.matrixV().adjoint();
+ else if(*jobv=='O') matrix(a,diag_size,*n,*lda) = svd.matrixV().adjoint();
+ }
+ return 0;
+}
\ No newline at end of file
diff --git a/lapack/svd.inc b/lapack/svd.inc
new file mode 100644
index 0000000..83544cf
--- /dev/null
+++ b/lapack/svd.inc
@@ -0,0 +1,138 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2014 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "lapack_common.h"
+#include <Eigen/SVD>
+
+// computes the singular values/vectors a general M-by-N matrix A using divide-and-conquer
+EIGEN_LAPACK_FUNC(gesdd,(char *jobz, int *m, int* n, Scalar* a, int *lda, RealScalar *s, Scalar *u, int *ldu, Scalar *vt, int *ldvt, Scalar* /*work*/, int* lwork,
+ EIGEN_LAPACK_ARG_IF_COMPLEX(RealScalar */*rwork*/) int * /*iwork*/, int *info))
+{
+ // TODO exploit the work buffer
+ bool query_size = *lwork==-1;
+ int diag_size = (std::min)(*m,*n);
+
+ *info = 0;
+ if(*jobz!='A' && *jobz!='S' && *jobz!='O' && *jobz!='N') *info = -1;
+ else if(*m<0) *info = -2;
+ else if(*n<0) *info = -3;
+ else if(*lda<std::max(1,*m)) *info = -5;
+ else if(*lda<std::max(1,*m)) *info = -8;
+ else if(*ldu <1 || (*jobz=='A' && *ldu <*m)
+ || (*jobz=='O' && *m<*n && *ldu<*m)) *info = -8;
+ else if(*ldvt<1 || (*jobz=='A' && *ldvt<*n)
+ || (*jobz=='S' && *ldvt<diag_size)
+ || (*jobz=='O' && *m>=*n && *ldvt<*n)) *info = -10;
+
+ if(*info!=0)
+ {
+ int e = -*info;
+ return xerbla_(SCALAR_SUFFIX_UP"GESDD ", &e, 6);
+ }
+
+ if(query_size)
+ {
+ *lwork = 0;
+ return 0;
+ }
+
+ if(*n==0 || *m==0)
+ return 0;
+
+ PlainMatrixType mat(*m,*n);
+ mat = matrix(a,*m,*n,*lda);
+
+ int option = *jobz=='A' ? ComputeFullU|ComputeFullV
+ : *jobz=='S' ? ComputeThinU|ComputeThinV
+ : *jobz=='O' ? ComputeThinU|ComputeThinV
+ : 0;
+
+ BDCSVD<PlainMatrixType> svd(mat,option);
+
+ make_vector(s,diag_size) = svd.singularValues().head(diag_size);
+
+ if(*jobz=='A')
+ {
+ matrix(u,*m,*m,*ldu) = svd.matrixU();
+ matrix(vt,*n,*n,*ldvt) = svd.matrixV().adjoint();
+ }
+ else if(*jobz=='S')
+ {
+ matrix(u,*m,diag_size,*ldu) = svd.matrixU();
+ matrix(vt,diag_size,*n,*ldvt) = svd.matrixV().adjoint();
+ }
+ else if(*jobz=='O' && *m>=*n)
+ {
+ matrix(a,*m,*n,*lda) = svd.matrixU();
+ matrix(vt,*n,*n,*ldvt) = svd.matrixV().adjoint();
+ }
+ else if(*jobz=='O')
+ {
+ matrix(u,*m,*m,*ldu) = svd.matrixU();
+ matrix(a,diag_size,*n,*lda) = svd.matrixV().adjoint();
+ }
+
+ return 0;
+}
+
+// computes the singular values/vectors a general M-by-N matrix A using two sided jacobi algorithm
+EIGEN_LAPACK_FUNC(gesvd,(char *jobu, char *jobv, int *m, int* n, Scalar* a, int *lda, RealScalar *s, Scalar *u, int *ldu, Scalar *vt, int *ldvt, Scalar* /*work*/, int* lwork,
+ EIGEN_LAPACK_ARG_IF_COMPLEX(RealScalar */*rwork*/) int *info))
+{
+ // TODO exploit the work buffer
+ bool query_size = *lwork==-1;
+ int diag_size = (std::min)(*m,*n);
+
+ *info = 0;
+ if( *jobu!='A' && *jobu!='S' && *jobu!='O' && *jobu!='N') *info = -1;
+ else if((*jobv!='A' && *jobv!='S' && *jobv!='O' && *jobv!='N')
+ || (*jobu=='O' && *jobv=='O')) *info = -2;
+ else if(*m<0) *info = -3;
+ else if(*n<0) *info = -4;
+ else if(*lda<std::max(1,*m)) *info = -6;
+ else if(*ldu <1 || ((*jobu=='A' || *jobu=='S') && *ldu<*m)) *info = -9;
+ else if(*ldvt<1 || (*jobv=='A' && *ldvt<*n)
+ || (*jobv=='S' && *ldvt<diag_size)) *info = -11;
+
+ if(*info!=0)
+ {
+ int e = -*info;
+ return xerbla_(SCALAR_SUFFIX_UP"GESVD ", &e, 6);
+ }
+
+ if(query_size)
+ {
+ *lwork = 0;
+ return 0;
+ }
+
+ if(*n==0 || *m==0)
+ return 0;
+
+ PlainMatrixType mat(*m,*n);
+ mat = matrix(a,*m,*n,*lda);
+
+ int option = (*jobu=='A' ? ComputeFullU : *jobu=='S' || *jobu=='O' ? ComputeThinU : 0)
+ | (*jobv=='A' ? ComputeFullV : *jobv=='S' || *jobv=='O' ? ComputeThinV : 0);
+
+ JacobiSVD<PlainMatrixType> svd(mat,option);
+
+ make_vector(s,diag_size) = svd.singularValues().head(diag_size);
+ {
+ if(*jobu=='A') matrix(u,*m,*m,*ldu) = svd.matrixU();
+ else if(*jobu=='S') matrix(u,*m,diag_size,*ldu) = svd.matrixU();
+ else if(*jobu=='O') matrix(a,*m,diag_size,*lda) = svd.matrixU();
+ }
+ {
+ if(*jobv=='A') matrix(vt,*n,*n,*ldvt) = svd.matrixV().adjoint();
+ else if(*jobv=='S') matrix(vt,diag_size,*n,*ldvt) = svd.matrixV().adjoint();
+ else if(*jobv=='O') matrix(a,diag_size,*n,*lda) = svd.matrixV().adjoint();
+ }
+ return 0;
+}
\ No newline at end of file
diff --git a/lapack/zlacgv.c b/lapack/zlacgv.c
new file mode 100644
index 0000000..e455696
--- /dev/null
+++ b/lapack/zlacgv.c
@@ -0,0 +1,95 @@
+/* zlacgv.f -- translated by f2c (version 20061008).
+ You must link the resulting object file with libf2c:
+ on Microsoft Windows system, link with libf2c.lib;
+ on Linux or Unix systems, link with .../path/to/libf2c.a -lm
+ or, if you install libf2c.a in a standard place, with -lf2c -lm
+ -- in that order, at the end of the command line, as in
+ cc *.o -lf2c -lm
+ Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
+
+ http://www.netlib.org/f2c/libf2c.zip
+*/
+
+#include "f2c.h"
+#include "blaswrap.h"
+
+/* Subroutine */ int zlacgv_(integer *n, doublecomplex *x, integer *incx)
+{
+ /* System generated locals */
+ integer i__1, i__2;
+ doublecomplex z__1;
+
+ /* Builtin functions */
+ void d_cnjg(doublecomplex *, doublecomplex *);
+
+ /* Local variables */
+ integer i__, ioff;
+
+
+/* -- LAPACK auxiliary routine (version 3.2) -- */
+/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
+/* November 2006 */
+
+/* .. Scalar Arguments .. */
+/* .. */
+/* .. Array Arguments .. */
+/* .. */
+
+/* Purpose */
+/* ======= */
+
+/* ZLACGV conjugates a complex vector of length N. */
+
+/* Arguments */
+/* ========= */
+
+/* N (input) INTEGER */
+/* The length of the vector X. N >= 0. */
+
+/* X (input/output) COMPLEX*16 array, dimension */
+/* (1+(N-1)*abs(INCX)) */
+/* On entry, the vector of length N to be conjugated. */
+/* On exit, X is overwritten with conjg(X). */
+
+/* INCX (input) INTEGER */
+/* The spacing between successive elements of X. */
+
+/* ===================================================================== */
+
+/* .. Local Scalars .. */
+/* .. */
+/* .. Intrinsic Functions .. */
+/* .. */
+/* .. Executable Statements .. */
+
+ /* Parameter adjustments */
+ --x;
+
+ /* Function Body */
+ if (*incx == 1) {
+ i__1 = *n;
+ for (i__ = 1; i__ <= i__1; ++i__) {
+ i__2 = i__;
+ d_cnjg(&z__1, &x[i__]);
+ x[i__2].r = z__1.r, x[i__2].i = z__1.i;
+/* L10: */
+ }
+ } else {
+ ioff = 1;
+ if (*incx < 0) {
+ ioff = 1 - (*n - 1) * *incx;
+ }
+ i__1 = *n;
+ for (i__ = 1; i__ <= i__1; ++i__) {
+ i__2 = ioff;
+ d_cnjg(&z__1, &x[ioff]);
+ x[i__2].r = z__1.r, x[i__2].i = z__1.i;
+ ioff += *incx;
+/* L20: */
+ }
+ }
+ return 0;
+
+/* End of ZLACGV */
+
+} /* zlacgv_ */
diff --git a/lapack/zladiv.c b/lapack/zladiv.c
new file mode 100644
index 0000000..d92be5a
--- /dev/null
+++ b/lapack/zladiv.c
@@ -0,0 +1,75 @@
+/* zladiv.f -- translated by f2c (version 20061008).
+ You must link the resulting object file with libf2c:
+ on Microsoft Windows system, link with libf2c.lib;
+ on Linux or Unix systems, link with .../path/to/libf2c.a -lm
+ or, if you install libf2c.a in a standard place, with -lf2c -lm
+ -- in that order, at the end of the command line, as in
+ cc *.o -lf2c -lm
+ Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
+
+ http://www.netlib.org/f2c/libf2c.zip
+*/
+
+#include "f2c.h"
+#include "blaswrap.h"
+
+/* Double Complex */ VOID zladiv_(doublecomplex * ret_val, doublecomplex *x,
+ doublecomplex *y)
+{
+ /* System generated locals */
+ doublereal d__1, d__2, d__3, d__4;
+ doublecomplex z__1;
+
+ /* Builtin functions */
+ double d_imag(doublecomplex *);
+
+ /* Local variables */
+ doublereal zi, zr;
+ extern /* Subroutine */ int dladiv_(doublereal *, doublereal *,
+ doublereal *, doublereal *, doublereal *, doublereal *);
+
+
+/* -- LAPACK auxiliary routine (version 3.2) -- */
+/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
+/* November 2006 */
+
+/* .. Scalar Arguments .. */
+/* .. */
+
+/* Purpose */
+/* ======= */
+
+/* ZLADIV := X / Y, where X and Y are complex. The computation of X / Y */
+/* will not overflow on an intermediary step unless the results */
+/* overflows. */
+
+/* Arguments */
+/* ========= */
+
+/* X (input) COMPLEX*16 */
+/* Y (input) COMPLEX*16 */
+/* The complex scalars X and Y. */
+
+/* ===================================================================== */
+
+/* .. Local Scalars .. */
+/* .. */
+/* .. External Subroutines .. */
+/* .. */
+/* .. Intrinsic Functions .. */
+/* .. */
+/* .. Executable Statements .. */
+
+ d__1 = x->r;
+ d__2 = d_imag(x);
+ d__3 = y->r;
+ d__4 = d_imag(y);
+ dladiv_(&d__1, &d__2, &d__3, &d__4, &zr, &zi);
+ z__1.r = zr, z__1.i = zi;
+ ret_val->r = z__1.r, ret_val->i = z__1.i;
+
+ return ;
+
+/* End of ZLADIV */
+
+} /* zladiv_ */
diff --git a/lapack/zlarf.c b/lapack/zlarf.c
new file mode 100644
index 0000000..0b8ad02
--- /dev/null
+++ b/lapack/zlarf.c
@@ -0,0 +1,200 @@
+/* zlarf.f -- translated by f2c (version 20061008).
+ You must link the resulting object file with libf2c:
+ on Microsoft Windows system, link with libf2c.lib;
+ on Linux or Unix systems, link with .../path/to/libf2c.a -lm
+ or, if you install libf2c.a in a standard place, with -lf2c -lm
+ -- in that order, at the end of the command line, as in
+ cc *.o -lf2c -lm
+ Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
+
+ http://www.netlib.org/f2c/libf2c.zip
+*/
+
+#include "f2c.h"
+#include "blaswrap.h"
+
+/* Table of constant values */
+
+static doublecomplex c_b1 = {1.,0.};
+static doublecomplex c_b2 = {0.,0.};
+static integer c__1 = 1;
+
+/* Subroutine */ int zlarf_(char *side, integer *m, integer *n, doublecomplex
+ *v, integer *incv, doublecomplex *tau, doublecomplex *c__, integer *
+ ldc, doublecomplex *work)
+{
+ /* System generated locals */
+ integer c_dim1, c_offset, i__1;
+ doublecomplex z__1;
+
+ /* Local variables */
+ integer i__;
+ logical applyleft;
+ extern logical lsame_(char *, char *);
+ integer lastc;
+ extern /* Subroutine */ int zgerc_(integer *, integer *, doublecomplex *,
+ doublecomplex *, integer *, doublecomplex *, integer *,
+ doublecomplex *, integer *), zgemv_(char *, integer *, integer *,
+ doublecomplex *, doublecomplex *, integer *, doublecomplex *,
+ integer *, doublecomplex *, doublecomplex *, integer *);
+ integer lastv;
+ extern integer ilazlc_(integer *, integer *, doublecomplex *, integer *),
+ ilazlr_(integer *, integer *, doublecomplex *, integer *);
+
+
+/* -- LAPACK auxiliary routine (version 3.2) -- */
+/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
+/* November 2006 */
+
+/* .. Scalar Arguments .. */
+/* .. */
+/* .. Array Arguments .. */
+/* .. */
+
+/* Purpose */
+/* ======= */
+
+/* ZLARF applies a complex elementary reflector H to a complex M-by-N */
+/* matrix C, from either the left or the right. H is represented in the */
+/* form */
+
+/* H = I - tau * v * v' */
+
+/* where tau is a complex scalar and v is a complex vector. */
+
+/* If tau = 0, then H is taken to be the unit matrix. */
+
+/* To apply H' (the conjugate transpose of H), supply conjg(tau) instead */
+/* tau. */
+
+/* Arguments */
+/* ========= */
+
+/* SIDE (input) CHARACTER*1 */
+/* = 'L': form H * C */
+/* = 'R': form C * H */
+
+/* M (input) INTEGER */
+/* The number of rows of the matrix C. */
+
+/* N (input) INTEGER */
+/* The number of columns of the matrix C. */
+
+/* V (input) COMPLEX*16 array, dimension */
+/* (1 + (M-1)*abs(INCV)) if SIDE = 'L' */
+/* or (1 + (N-1)*abs(INCV)) if SIDE = 'R' */
+/* The vector v in the representation of H. V is not used if */
+/* TAU = 0. */
+
+/* INCV (input) INTEGER */
+/* The increment between elements of v. INCV <> 0. */
+
+/* TAU (input) COMPLEX*16 */
+/* The value tau in the representation of H. */
+
+/* C (input/output) COMPLEX*16 array, dimension (LDC,N) */
+/* On entry, the M-by-N matrix C. */
+/* On exit, C is overwritten by the matrix H * C if SIDE = 'L', */
+/* or C * H if SIDE = 'R'. */
+
+/* LDC (input) INTEGER */
+/* The leading dimension of the array C. LDC >= max(1,M). */
+
+/* WORK (workspace) COMPLEX*16 array, dimension */
+/* (N) if SIDE = 'L' */
+/* or (M) if SIDE = 'R' */
+
+/* ===================================================================== */
+
+/* .. Parameters .. */
+/* .. */
+/* .. Local Scalars .. */
+/* .. */
+/* .. External Subroutines .. */
+/* .. */
+/* .. External Functions .. */
+/* .. */
+/* .. Executable Statements .. */
+
+ /* Parameter adjustments */
+ --v;
+ c_dim1 = *ldc;
+ c_offset = 1 + c_dim1;
+ c__ -= c_offset;
+ --work;
+
+ /* Function Body */
+ applyleft = lsame_(side, "L");
+ lastv = 0;
+ lastc = 0;
+ if (tau->r != 0. || tau->i != 0.) {
+/* Set up variables for scanning V. LASTV begins pointing to the end */
+/* of V. */
+ if (applyleft) {
+ lastv = *m;
+ } else {
+ lastv = *n;
+ }
+ if (*incv > 0) {
+ i__ = (lastv - 1) * *incv + 1;
+ } else {
+ i__ = 1;
+ }
+/* Look for the last non-zero row in V. */
+ for(;;) { /* while(complicated condition) */
+ i__1 = i__;
+ if (!(lastv > 0 && (v[i__1].r == 0. && v[i__1].i == 0.)))
+ break;
+ --lastv;
+ i__ -= *incv;
+ }
+ if (applyleft) {
+/* Scan for the last non-zero column in C(1:lastv,:). */
+ lastc = ilazlc_(&lastv, n, &c__[c_offset], ldc);
+ } else {
+/* Scan for the last non-zero row in C(:,1:lastv). */
+ lastc = ilazlr_(m, &lastv, &c__[c_offset], ldc);
+ }
+ }
+/* Note that lastc.eq.0 renders the BLAS operations null; no special */
+/* case is needed at this level. */
+ if (applyleft) {
+
+/* Form H * C */
+
+ if (lastv > 0) {
+
+/* w(1:lastc,1) := C(1:lastv,1:lastc)' * v(1:lastv,1) */
+
+ zgemv_("Conjugate transpose", &lastv, &lastc, &c_b1, &c__[
+ c_offset], ldc, &v[1], incv, &c_b2, &work[1], &c__1);
+
+/* C(1:lastv,1:lastc) := C(...) - v(1:lastv,1) * w(1:lastc,1)' */
+
+ z__1.r = -tau->r, z__1.i = -tau->i;
+ zgerc_(&lastv, &lastc, &z__1, &v[1], incv, &work[1], &c__1, &c__[
+ c_offset], ldc);
+ }
+ } else {
+
+/* Form C * H */
+
+ if (lastv > 0) {
+
+/* w(1:lastc,1) := C(1:lastc,1:lastv) * v(1:lastv,1) */
+
+ zgemv_("No transpose", &lastc, &lastv, &c_b1, &c__[c_offset], ldc,
+ &v[1], incv, &c_b2, &work[1], &c__1);
+
+/* C(1:lastc,1:lastv) := C(...) - w(1:lastc,1) * v(1:lastv,1)' */
+
+ z__1.r = -tau->r, z__1.i = -tau->i;
+ zgerc_(&lastc, &lastv, &z__1, &work[1], &c__1, &v[1], incv, &c__[
+ c_offset], ldc);
+ }
+ }
+ return 0;
+
+/* End of ZLARF */
+
+} /* zlarf_ */
diff --git a/lapack/zlarfb.c b/lapack/zlarfb.c
new file mode 100644
index 0000000..cdd584e
--- /dev/null
+++ b/lapack/zlarfb.c
@@ -0,0 +1,839 @@
+/* zlarfb.f -- translated by f2c (version 20061008).
+ You must link the resulting object file with libf2c:
+ on Microsoft Windows system, link with libf2c.lib;
+ on Linux or Unix systems, link with .../path/to/libf2c.a -lm
+ or, if you install libf2c.a in a standard place, with -lf2c -lm
+ -- in that order, at the end of the command line, as in
+ cc *.o -lf2c -lm
+ Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
+
+ http://www.netlib.org/f2c/libf2c.zip
+*/
+
+#include "f2c.h"
+#include "blaswrap.h"
+
+/* Table of constant values */
+
+static doublecomplex c_b1 = {1.,0.};
+static integer c__1 = 1;
+
+/* Subroutine */ int zlarfb_(char *side, char *trans, char *direct, char *
+ storev, integer *m, integer *n, integer *k, doublecomplex *v, integer
+ *ldv, doublecomplex *t, integer *ldt, doublecomplex *c__, integer *
+ ldc, doublecomplex *work, integer *ldwork)
+{
+ /* System generated locals */
+ integer c_dim1, c_offset, t_dim1, t_offset, v_dim1, v_offset, work_dim1,
+ work_offset, i__1, i__2, i__3, i__4, i__5;
+ doublecomplex z__1, z__2;
+
+ /* Builtin functions */
+ void d_cnjg(doublecomplex *, doublecomplex *);
+
+ /* Local variables */
+ integer i__, j;
+ extern logical lsame_(char *, char *);
+ integer lastc;
+ extern /* Subroutine */ int zgemm_(char *, char *, integer *, integer *,
+ integer *, doublecomplex *, doublecomplex *, integer *,
+ doublecomplex *, integer *, doublecomplex *, doublecomplex *,
+ integer *);
+ integer lastv;
+ extern /* Subroutine */ int zcopy_(integer *, doublecomplex *, integer *,
+ doublecomplex *, integer *), ztrmm_(char *, char *, char *, char *
+, integer *, integer *, doublecomplex *, doublecomplex *, integer
+ *, doublecomplex *, integer *);
+ extern integer ilazlc_(integer *, integer *, doublecomplex *, integer *);
+ extern /* Subroutine */ int zlacgv_(integer *, doublecomplex *, integer *)
+ ;
+ extern integer ilazlr_(integer *, integer *, doublecomplex *, integer *);
+ char transt[1];
+
+
+/* -- LAPACK auxiliary routine (version 3.2) -- */
+/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
+/* November 2006 */
+
+/* .. Scalar Arguments .. */
+/* .. */
+/* .. Array Arguments .. */
+/* .. */
+
+/* Purpose */
+/* ======= */
+
+/* ZLARFB applies a complex block reflector H or its transpose H' to a */
+/* complex M-by-N matrix C, from either the left or the right. */
+
+/* Arguments */
+/* ========= */
+
+/* SIDE (input) CHARACTER*1 */
+/* = 'L': apply H or H' from the Left */
+/* = 'R': apply H or H' from the Right */
+
+/* TRANS (input) CHARACTER*1 */
+/* = 'N': apply H (No transpose) */
+/* = 'C': apply H' (Conjugate transpose) */
+
+/* DIRECT (input) CHARACTER*1 */
+/* Indicates how H is formed from a product of elementary */
+/* reflectors */
+/* = 'F': H = H(1) H(2) . . . H(k) (Forward) */
+/* = 'B': H = H(k) . . . H(2) H(1) (Backward) */
+
+/* STOREV (input) CHARACTER*1 */
+/* Indicates how the vectors which define the elementary */
+/* reflectors are stored: */
+/* = 'C': Columnwise */
+/* = 'R': Rowwise */
+
+/* M (input) INTEGER */
+/* The number of rows of the matrix C. */
+
+/* N (input) INTEGER */
+/* The number of columns of the matrix C. */
+
+/* K (input) INTEGER */
+/* The order of the matrix T (= the number of elementary */
+/* reflectors whose product defines the block reflector). */
+
+/* V (input) COMPLEX*16 array, dimension */
+/* (LDV,K) if STOREV = 'C' */
+/* (LDV,M) if STOREV = 'R' and SIDE = 'L' */
+/* (LDV,N) if STOREV = 'R' and SIDE = 'R' */
+/* The matrix V. See further details. */
+
+/* LDV (input) INTEGER */
+/* The leading dimension of the array V. */
+/* If STOREV = 'C' and SIDE = 'L', LDV >= max(1,M); */
+/* if STOREV = 'C' and SIDE = 'R', LDV >= max(1,N); */
+/* if STOREV = 'R', LDV >= K. */
+
+/* T (input) COMPLEX*16 array, dimension (LDT,K) */
+/* The triangular K-by-K matrix T in the representation of the */
+/* block reflector. */
+
+/* LDT (input) INTEGER */
+/* The leading dimension of the array T. LDT >= K. */
+
+/* C (input/output) COMPLEX*16 array, dimension (LDC,N) */
+/* On entry, the M-by-N matrix C. */
+/* On exit, C is overwritten by H*C or H'*C or C*H or C*H'. */
+
+/* LDC (input) INTEGER */
+/* The leading dimension of the array C. LDC >= max(1,M). */
+
+/* WORK (workspace) COMPLEX*16 array, dimension (LDWORK,K) */
+
+/* LDWORK (input) INTEGER */
+/* The leading dimension of the array WORK. */
+/* If SIDE = 'L', LDWORK >= max(1,N); */
+/* if SIDE = 'R', LDWORK >= max(1,M). */
+
+/* ===================================================================== */
+
+/* .. Parameters .. */
+/* .. */
+/* .. Local Scalars .. */
+/* .. */
+/* .. External Functions .. */
+/* .. */
+/* .. External Subroutines .. */
+/* .. */
+/* .. Intrinsic Functions .. */
+/* .. */
+/* .. Executable Statements .. */
+
+/* Quick return if possible */
+
+ /* Parameter adjustments */
+ v_dim1 = *ldv;
+ v_offset = 1 + v_dim1;
+ v -= v_offset;
+ t_dim1 = *ldt;
+ t_offset = 1 + t_dim1;
+ t -= t_offset;
+ c_dim1 = *ldc;
+ c_offset = 1 + c_dim1;
+ c__ -= c_offset;
+ work_dim1 = *ldwork;
+ work_offset = 1 + work_dim1;
+ work -= work_offset;
+
+ /* Function Body */
+ if (*m <= 0 || *n <= 0) {
+ return 0;
+ }
+
+ if (lsame_(trans, "N")) {
+ *(unsigned char *)transt = 'C';
+ } else {
+ *(unsigned char *)transt = 'N';
+ }
+
+ if (lsame_(storev, "C")) {
+
+ if (lsame_(direct, "F")) {
+
+/* Let V = ( V1 ) (first K rows) */
+/* ( V2 ) */
+/* where V1 is unit lower triangular. */
+
+ if (lsame_(side, "L")) {
+
+/* Form H * C or H' * C where C = ( C1 ) */
+/* ( C2 ) */
+
+/* Computing MAX */
+ i__1 = *k, i__2 = ilazlr_(m, k, &v[v_offset], ldv);
+ lastv = max(i__1,i__2);
+ lastc = ilazlc_(&lastv, n, &c__[c_offset], ldc);
+
+/* W := C' * V = (C1'*V1 + C2'*V2) (stored in WORK) */
+
+/* W := C1' */
+
+ i__1 = *k;
+ for (j = 1; j <= i__1; ++j) {
+ zcopy_(&lastc, &c__[j + c_dim1], ldc, &work[j * work_dim1
+ + 1], &c__1);
+ zlacgv_(&lastc, &work[j * work_dim1 + 1], &c__1);
+/* L10: */
+ }
+
+/* W := W * V1 */
+
+ ztrmm_("Right", "Lower", "No transpose", "Unit", &lastc, k, &
+ c_b1, &v[v_offset], ldv, &work[work_offset], ldwork);
+ if (lastv > *k) {
+
+/* W := W + C2'*V2 */
+
+ i__1 = lastv - *k;
+ zgemm_("Conjugate transpose", "No transpose", &lastc, k, &
+ i__1, &c_b1, &c__[*k + 1 + c_dim1], ldc, &v[*k +
+ 1 + v_dim1], ldv, &c_b1, &work[work_offset],
+ ldwork);
+ }
+
+/* W := W * T' or W * T */
+
+ ztrmm_("Right", "Upper", transt, "Non-unit", &lastc, k, &c_b1,
+ &t[t_offset], ldt, &work[work_offset], ldwork);
+
+/* C := C - V * W' */
+
+ if (*m > *k) {
+
+/* C2 := C2 - V2 * W' */
+
+ i__1 = lastv - *k;
+ z__1.r = -1., z__1.i = -0.;
+ zgemm_("No transpose", "Conjugate transpose", &i__1, &
+ lastc, k, &z__1, &v[*k + 1 + v_dim1], ldv, &work[
+ work_offset], ldwork, &c_b1, &c__[*k + 1 + c_dim1]
+, ldc);
+ }
+
+/* W := W * V1' */
+
+ ztrmm_("Right", "Lower", "Conjugate transpose", "Unit", &
+ lastc, k, &c_b1, &v[v_offset], ldv, &work[work_offset]
+, ldwork)
+ ;
+
+/* C1 := C1 - W' */
+
+ i__1 = *k;
+ for (j = 1; j <= i__1; ++j) {
+ i__2 = lastc;
+ for (i__ = 1; i__ <= i__2; ++i__) {
+ i__3 = j + i__ * c_dim1;
+ i__4 = j + i__ * c_dim1;
+ d_cnjg(&z__2, &work[i__ + j * work_dim1]);
+ z__1.r = c__[i__4].r - z__2.r, z__1.i = c__[i__4].i -
+ z__2.i;
+ c__[i__3].r = z__1.r, c__[i__3].i = z__1.i;
+/* L20: */
+ }
+/* L30: */
+ }
+
+ } else if (lsame_(side, "R")) {
+
+/* Form C * H or C * H' where C = ( C1 C2 ) */
+
+/* Computing MAX */
+ i__1 = *k, i__2 = ilazlr_(n, k, &v[v_offset], ldv);
+ lastv = max(i__1,i__2);
+ lastc = ilazlr_(m, &lastv, &c__[c_offset], ldc);
+
+/* W := C * V = (C1*V1 + C2*V2) (stored in WORK) */
+
+/* W := C1 */
+
+ i__1 = *k;
+ for (j = 1; j <= i__1; ++j) {
+ zcopy_(&lastc, &c__[j * c_dim1 + 1], &c__1, &work[j *
+ work_dim1 + 1], &c__1);
+/* L40: */
+ }
+
+/* W := W * V1 */
+
+ ztrmm_("Right", "Lower", "No transpose", "Unit", &lastc, k, &
+ c_b1, &v[v_offset], ldv, &work[work_offset], ldwork);
+ if (lastv > *k) {
+
+/* W := W + C2 * V2 */
+
+ i__1 = lastv - *k;
+ zgemm_("No transpose", "No transpose", &lastc, k, &i__1, &
+ c_b1, &c__[(*k + 1) * c_dim1 + 1], ldc, &v[*k + 1
+ + v_dim1], ldv, &c_b1, &work[work_offset], ldwork);
+ }
+
+/* W := W * T or W * T' */
+
+ ztrmm_("Right", "Upper", trans, "Non-unit", &lastc, k, &c_b1,
+ &t[t_offset], ldt, &work[work_offset], ldwork);
+
+/* C := C - W * V' */
+
+ if (lastv > *k) {
+
+/* C2 := C2 - W * V2' */
+
+ i__1 = lastv - *k;
+ z__1.r = -1., z__1.i = -0.;
+ zgemm_("No transpose", "Conjugate transpose", &lastc, &
+ i__1, k, &z__1, &work[work_offset], ldwork, &v[*k
+ + 1 + v_dim1], ldv, &c_b1, &c__[(*k + 1) * c_dim1
+ + 1], ldc);
+ }
+
+/* W := W * V1' */
+
+ ztrmm_("Right", "Lower", "Conjugate transpose", "Unit", &
+ lastc, k, &c_b1, &v[v_offset], ldv, &work[work_offset]
+, ldwork)
+ ;
+
+/* C1 := C1 - W */
+
+ i__1 = *k;
+ for (j = 1; j <= i__1; ++j) {
+ i__2 = lastc;
+ for (i__ = 1; i__ <= i__2; ++i__) {
+ i__3 = i__ + j * c_dim1;
+ i__4 = i__ + j * c_dim1;
+ i__5 = i__ + j * work_dim1;
+ z__1.r = c__[i__4].r - work[i__5].r, z__1.i = c__[
+ i__4].i - work[i__5].i;
+ c__[i__3].r = z__1.r, c__[i__3].i = z__1.i;
+/* L50: */
+ }
+/* L60: */
+ }
+ }
+
+ } else {
+
+/* Let V = ( V1 ) */
+/* ( V2 ) (last K rows) */
+/* where V2 is unit upper triangular. */
+
+ if (lsame_(side, "L")) {
+
+/* Form H * C or H' * C where C = ( C1 ) */
+/* ( C2 ) */
+
+/* Computing MAX */
+ i__1 = *k, i__2 = ilazlr_(m, k, &v[v_offset], ldv);
+ lastv = max(i__1,i__2);
+ lastc = ilazlc_(&lastv, n, &c__[c_offset], ldc);
+
+/* W := C' * V = (C1'*V1 + C2'*V2) (stored in WORK) */
+
+/* W := C2' */
+
+ i__1 = *k;
+ for (j = 1; j <= i__1; ++j) {
+ zcopy_(&lastc, &c__[lastv - *k + j + c_dim1], ldc, &work[
+ j * work_dim1 + 1], &c__1);
+ zlacgv_(&lastc, &work[j * work_dim1 + 1], &c__1);
+/* L70: */
+ }
+
+/* W := W * V2 */
+
+ ztrmm_("Right", "Upper", "No transpose", "Unit", &lastc, k, &
+ c_b1, &v[lastv - *k + 1 + v_dim1], ldv, &work[
+ work_offset], ldwork);
+ if (lastv > *k) {
+
+/* W := W + C1'*V1 */
+
+ i__1 = lastv - *k;
+ zgemm_("Conjugate transpose", "No transpose", &lastc, k, &
+ i__1, &c_b1, &c__[c_offset], ldc, &v[v_offset],
+ ldv, &c_b1, &work[work_offset], ldwork);
+ }
+
+/* W := W * T' or W * T */
+
+ ztrmm_("Right", "Lower", transt, "Non-unit", &lastc, k, &c_b1,
+ &t[t_offset], ldt, &work[work_offset], ldwork);
+
+/* C := C - V * W' */
+
+ if (lastv > *k) {
+
+/* C1 := C1 - V1 * W' */
+
+ i__1 = lastv - *k;
+ z__1.r = -1., z__1.i = -0.;
+ zgemm_("No transpose", "Conjugate transpose", &i__1, &
+ lastc, k, &z__1, &v[v_offset], ldv, &work[
+ work_offset], ldwork, &c_b1, &c__[c_offset], ldc);
+ }
+
+/* W := W * V2' */
+
+ ztrmm_("Right", "Upper", "Conjugate transpose", "Unit", &
+ lastc, k, &c_b1, &v[lastv - *k + 1 + v_dim1], ldv, &
+ work[work_offset], ldwork);
+
+/* C2 := C2 - W' */
+
+ i__1 = *k;
+ for (j = 1; j <= i__1; ++j) {
+ i__2 = lastc;
+ for (i__ = 1; i__ <= i__2; ++i__) {
+ i__3 = lastv - *k + j + i__ * c_dim1;
+ i__4 = lastv - *k + j + i__ * c_dim1;
+ d_cnjg(&z__2, &work[i__ + j * work_dim1]);
+ z__1.r = c__[i__4].r - z__2.r, z__1.i = c__[i__4].i -
+ z__2.i;
+ c__[i__3].r = z__1.r, c__[i__3].i = z__1.i;
+/* L80: */
+ }
+/* L90: */
+ }
+
+ } else if (lsame_(side, "R")) {
+
+/* Form C * H or C * H' where C = ( C1 C2 ) */
+
+/* Computing MAX */
+ i__1 = *k, i__2 = ilazlr_(n, k, &v[v_offset], ldv);
+ lastv = max(i__1,i__2);
+ lastc = ilazlr_(m, &lastv, &c__[c_offset], ldc);
+
+/* W := C * V = (C1*V1 + C2*V2) (stored in WORK) */
+
+/* W := C2 */
+
+ i__1 = *k;
+ for (j = 1; j <= i__1; ++j) {
+ zcopy_(&lastc, &c__[(lastv - *k + j) * c_dim1 + 1], &c__1,
+ &work[j * work_dim1 + 1], &c__1);
+/* L100: */
+ }
+
+/* W := W * V2 */
+
+ ztrmm_("Right", "Upper", "No transpose", "Unit", &lastc, k, &
+ c_b1, &v[lastv - *k + 1 + v_dim1], ldv, &work[
+ work_offset], ldwork);
+ if (lastv > *k) {
+
+/* W := W + C1 * V1 */
+
+ i__1 = lastv - *k;
+ zgemm_("No transpose", "No transpose", &lastc, k, &i__1, &
+ c_b1, &c__[c_offset], ldc, &v[v_offset], ldv, &
+ c_b1, &work[work_offset], ldwork);
+ }
+
+/* W := W * T or W * T' */
+
+ ztrmm_("Right", "Lower", trans, "Non-unit", &lastc, k, &c_b1,
+ &t[t_offset], ldt, &work[work_offset], ldwork);
+
+/* C := C - W * V' */
+
+ if (lastv > *k) {
+
+/* C1 := C1 - W * V1' */
+
+ i__1 = lastv - *k;
+ z__1.r = -1., z__1.i = -0.;
+ zgemm_("No transpose", "Conjugate transpose", &lastc, &
+ i__1, k, &z__1, &work[work_offset], ldwork, &v[
+ v_offset], ldv, &c_b1, &c__[c_offset], ldc);
+ }
+
+/* W := W * V2' */
+
+ ztrmm_("Right", "Upper", "Conjugate transpose", "Unit", &
+ lastc, k, &c_b1, &v[lastv - *k + 1 + v_dim1], ldv, &
+ work[work_offset], ldwork);
+
+/* C2 := C2 - W */
+
+ i__1 = *k;
+ for (j = 1; j <= i__1; ++j) {
+ i__2 = lastc;
+ for (i__ = 1; i__ <= i__2; ++i__) {
+ i__3 = i__ + (lastv - *k + j) * c_dim1;
+ i__4 = i__ + (lastv - *k + j) * c_dim1;
+ i__5 = i__ + j * work_dim1;
+ z__1.r = c__[i__4].r - work[i__5].r, z__1.i = c__[
+ i__4].i - work[i__5].i;
+ c__[i__3].r = z__1.r, c__[i__3].i = z__1.i;
+/* L110: */
+ }
+/* L120: */
+ }
+ }
+ }
+
+ } else if (lsame_(storev, "R")) {
+
+ if (lsame_(direct, "F")) {
+
+/* Let V = ( V1 V2 ) (V1: first K columns) */
+/* where V1 is unit upper triangular. */
+
+ if (lsame_(side, "L")) {
+
+/* Form H * C or H' * C where C = ( C1 ) */
+/* ( C2 ) */
+
+/* Computing MAX */
+ i__1 = *k, i__2 = ilazlc_(k, m, &v[v_offset], ldv);
+ lastv = max(i__1,i__2);
+ lastc = ilazlc_(&lastv, n, &c__[c_offset], ldc);
+
+/* W := C' * V' = (C1'*V1' + C2'*V2') (stored in WORK) */
+
+/* W := C1' */
+
+ i__1 = *k;
+ for (j = 1; j <= i__1; ++j) {
+ zcopy_(&lastc, &c__[j + c_dim1], ldc, &work[j * work_dim1
+ + 1], &c__1);
+ zlacgv_(&lastc, &work[j * work_dim1 + 1], &c__1);
+/* L130: */
+ }
+
+/* W := W * V1' */
+
+ ztrmm_("Right", "Upper", "Conjugate transpose", "Unit", &
+ lastc, k, &c_b1, &v[v_offset], ldv, &work[work_offset]
+, ldwork)
+ ;
+ if (lastv > *k) {
+
+/* W := W + C2'*V2' */
+
+ i__1 = lastv - *k;
+ zgemm_("Conjugate transpose", "Conjugate transpose", &
+ lastc, k, &i__1, &c_b1, &c__[*k + 1 + c_dim1],
+ ldc, &v[(*k + 1) * v_dim1 + 1], ldv, &c_b1, &work[
+ work_offset], ldwork);
+ }
+
+/* W := W * T' or W * T */
+
+ ztrmm_("Right", "Upper", transt, "Non-unit", &lastc, k, &c_b1,
+ &t[t_offset], ldt, &work[work_offset], ldwork);
+
+/* C := C - V' * W' */
+
+ if (lastv > *k) {
+
+/* C2 := C2 - V2' * W' */
+
+ i__1 = lastv - *k;
+ z__1.r = -1., z__1.i = -0.;
+ zgemm_("Conjugate transpose", "Conjugate transpose", &
+ i__1, &lastc, k, &z__1, &v[(*k + 1) * v_dim1 + 1],
+ ldv, &work[work_offset], ldwork, &c_b1, &c__[*k
+ + 1 + c_dim1], ldc);
+ }
+
+/* W := W * V1 */
+
+ ztrmm_("Right", "Upper", "No transpose", "Unit", &lastc, k, &
+ c_b1, &v[v_offset], ldv, &work[work_offset], ldwork);
+
+/* C1 := C1 - W' */
+
+ i__1 = *k;
+ for (j = 1; j <= i__1; ++j) {
+ i__2 = lastc;
+ for (i__ = 1; i__ <= i__2; ++i__) {
+ i__3 = j + i__ * c_dim1;
+ i__4 = j + i__ * c_dim1;
+ d_cnjg(&z__2, &work[i__ + j * work_dim1]);
+ z__1.r = c__[i__4].r - z__2.r, z__1.i = c__[i__4].i -
+ z__2.i;
+ c__[i__3].r = z__1.r, c__[i__3].i = z__1.i;
+/* L140: */
+ }
+/* L150: */
+ }
+
+ } else if (lsame_(side, "R")) {
+
+/* Form C * H or C * H' where C = ( C1 C2 ) */
+
+/* Computing MAX */
+ i__1 = *k, i__2 = ilazlc_(k, n, &v[v_offset], ldv);
+ lastv = max(i__1,i__2);
+ lastc = ilazlr_(m, &lastv, &c__[c_offset], ldc);
+
+/* W := C * V' = (C1*V1' + C2*V2') (stored in WORK) */
+
+/* W := C1 */
+
+ i__1 = *k;
+ for (j = 1; j <= i__1; ++j) {
+ zcopy_(&lastc, &c__[j * c_dim1 + 1], &c__1, &work[j *
+ work_dim1 + 1], &c__1);
+/* L160: */
+ }
+
+/* W := W * V1' */
+
+ ztrmm_("Right", "Upper", "Conjugate transpose", "Unit", &
+ lastc, k, &c_b1, &v[v_offset], ldv, &work[work_offset]
+, ldwork)
+ ;
+ if (lastv > *k) {
+
+/* W := W + C2 * V2' */
+
+ i__1 = lastv - *k;
+ zgemm_("No transpose", "Conjugate transpose", &lastc, k, &
+ i__1, &c_b1, &c__[(*k + 1) * c_dim1 + 1], ldc, &v[
+ (*k + 1) * v_dim1 + 1], ldv, &c_b1, &work[
+ work_offset], ldwork);
+ }
+
+/* W := W * T or W * T' */
+
+ ztrmm_("Right", "Upper", trans, "Non-unit", &lastc, k, &c_b1,
+ &t[t_offset], ldt, &work[work_offset], ldwork);
+
+/* C := C - W * V */
+
+ if (lastv > *k) {
+
+/* C2 := C2 - W * V2 */
+
+ i__1 = lastv - *k;
+ z__1.r = -1., z__1.i = -0.;
+ zgemm_("No transpose", "No transpose", &lastc, &i__1, k, &
+ z__1, &work[work_offset], ldwork, &v[(*k + 1) *
+ v_dim1 + 1], ldv, &c_b1, &c__[(*k + 1) * c_dim1 +
+ 1], ldc);
+ }
+
+/* W := W * V1 */
+
+ ztrmm_("Right", "Upper", "No transpose", "Unit", &lastc, k, &
+ c_b1, &v[v_offset], ldv, &work[work_offset], ldwork);
+
+/* C1 := C1 - W */
+
+ i__1 = *k;
+ for (j = 1; j <= i__1; ++j) {
+ i__2 = lastc;
+ for (i__ = 1; i__ <= i__2; ++i__) {
+ i__3 = i__ + j * c_dim1;
+ i__4 = i__ + j * c_dim1;
+ i__5 = i__ + j * work_dim1;
+ z__1.r = c__[i__4].r - work[i__5].r, z__1.i = c__[
+ i__4].i - work[i__5].i;
+ c__[i__3].r = z__1.r, c__[i__3].i = z__1.i;
+/* L170: */
+ }
+/* L180: */
+ }
+
+ }
+
+ } else {
+
+/* Let V = ( V1 V2 ) (V2: last K columns) */
+/* where V2 is unit lower triangular. */
+
+ if (lsame_(side, "L")) {
+
+/* Form H * C or H' * C where C = ( C1 ) */
+/* ( C2 ) */
+
+/* Computing MAX */
+ i__1 = *k, i__2 = ilazlc_(k, m, &v[v_offset], ldv);
+ lastv = max(i__1,i__2);
+ lastc = ilazlc_(&lastv, n, &c__[c_offset], ldc);
+
+/* W := C' * V' = (C1'*V1' + C2'*V2') (stored in WORK) */
+
+/* W := C2' */
+
+ i__1 = *k;
+ for (j = 1; j <= i__1; ++j) {
+ zcopy_(&lastc, &c__[lastv - *k + j + c_dim1], ldc, &work[
+ j * work_dim1 + 1], &c__1);
+ zlacgv_(&lastc, &work[j * work_dim1 + 1], &c__1);
+/* L190: */
+ }
+
+/* W := W * V2' */
+
+ ztrmm_("Right", "Lower", "Conjugate transpose", "Unit", &
+ lastc, k, &c_b1, &v[(lastv - *k + 1) * v_dim1 + 1],
+ ldv, &work[work_offset], ldwork);
+ if (lastv > *k) {
+
+/* W := W + C1'*V1' */
+
+ i__1 = lastv - *k;
+ zgemm_("Conjugate transpose", "Conjugate transpose", &
+ lastc, k, &i__1, &c_b1, &c__[c_offset], ldc, &v[
+ v_offset], ldv, &c_b1, &work[work_offset], ldwork);
+ }
+
+/* W := W * T' or W * T */
+
+ ztrmm_("Right", "Lower", transt, "Non-unit", &lastc, k, &c_b1,
+ &t[t_offset], ldt, &work[work_offset], ldwork);
+
+/* C := C - V' * W' */
+
+ if (lastv > *k) {
+
+/* C1 := C1 - V1' * W' */
+
+ i__1 = lastv - *k;
+ z__1.r = -1., z__1.i = -0.;
+ zgemm_("Conjugate transpose", "Conjugate transpose", &
+ i__1, &lastc, k, &z__1, &v[v_offset], ldv, &work[
+ work_offset], ldwork, &c_b1, &c__[c_offset], ldc);
+ }
+
+/* W := W * V2 */
+
+ ztrmm_("Right", "Lower", "No transpose", "Unit", &lastc, k, &
+ c_b1, &v[(lastv - *k + 1) * v_dim1 + 1], ldv, &work[
+ work_offset], ldwork);
+
+/* C2 := C2 - W' */
+
+ i__1 = *k;
+ for (j = 1; j <= i__1; ++j) {
+ i__2 = lastc;
+ for (i__ = 1; i__ <= i__2; ++i__) {
+ i__3 = lastv - *k + j + i__ * c_dim1;
+ i__4 = lastv - *k + j + i__ * c_dim1;
+ d_cnjg(&z__2, &work[i__ + j * work_dim1]);
+ z__1.r = c__[i__4].r - z__2.r, z__1.i = c__[i__4].i -
+ z__2.i;
+ c__[i__3].r = z__1.r, c__[i__3].i = z__1.i;
+/* L200: */
+ }
+/* L210: */
+ }
+
+ } else if (lsame_(side, "R")) {
+
+/* Form C * H or C * H' where C = ( C1 C2 ) */
+
+/* Computing MAX */
+ i__1 = *k, i__2 = ilazlc_(k, n, &v[v_offset], ldv);
+ lastv = max(i__1,i__2);
+ lastc = ilazlr_(m, &lastv, &c__[c_offset], ldc);
+
+/* W := C * V' = (C1*V1' + C2*V2') (stored in WORK) */
+
+/* W := C2 */
+
+ i__1 = *k;
+ for (j = 1; j <= i__1; ++j) {
+ zcopy_(&lastc, &c__[(lastv - *k + j) * c_dim1 + 1], &c__1,
+ &work[j * work_dim1 + 1], &c__1);
+/* L220: */
+ }
+
+/* W := W * V2' */
+
+ ztrmm_("Right", "Lower", "Conjugate transpose", "Unit", &
+ lastc, k, &c_b1, &v[(lastv - *k + 1) * v_dim1 + 1],
+ ldv, &work[work_offset], ldwork);
+ if (lastv > *k) {
+
+/* W := W + C1 * V1' */
+
+ i__1 = lastv - *k;
+ zgemm_("No transpose", "Conjugate transpose", &lastc, k, &
+ i__1, &c_b1, &c__[c_offset], ldc, &v[v_offset],
+ ldv, &c_b1, &work[work_offset], ldwork);
+ }
+
+/* W := W * T or W * T' */
+
+ ztrmm_("Right", "Lower", trans, "Non-unit", &lastc, k, &c_b1,
+ &t[t_offset], ldt, &work[work_offset], ldwork);
+
+/* C := C - W * V */
+
+ if (lastv > *k) {
+
+/* C1 := C1 - W * V1 */
+
+ i__1 = lastv - *k;
+ z__1.r = -1., z__1.i = -0.;
+ zgemm_("No transpose", "No transpose", &lastc, &i__1, k, &
+ z__1, &work[work_offset], ldwork, &v[v_offset],
+ ldv, &c_b1, &c__[c_offset], ldc);
+ }
+
+/* W := W * V2 */
+
+ ztrmm_("Right", "Lower", "No transpose", "Unit", &lastc, k, &
+ c_b1, &v[(lastv - *k + 1) * v_dim1 + 1], ldv, &work[
+ work_offset], ldwork);
+
+/* C1 := C1 - W */
+
+ i__1 = *k;
+ for (j = 1; j <= i__1; ++j) {
+ i__2 = lastc;
+ for (i__ = 1; i__ <= i__2; ++i__) {
+ i__3 = i__ + (lastv - *k + j) * c_dim1;
+ i__4 = i__ + (lastv - *k + j) * c_dim1;
+ i__5 = i__ + j * work_dim1;
+ z__1.r = c__[i__4].r - work[i__5].r, z__1.i = c__[
+ i__4].i - work[i__5].i;
+ c__[i__3].r = z__1.r, c__[i__3].i = z__1.i;
+/* L230: */
+ }
+/* L240: */
+ }
+
+ }
+
+ }
+ }
+
+ return 0;
+
+/* End of ZLARFB */
+
+} /* zlarfb_ */
diff --git a/lapack/zlarfg.c b/lapack/zlarfg.c
new file mode 100644
index 0000000..d18efe5
--- /dev/null
+++ b/lapack/zlarfg.c
@@ -0,0 +1,191 @@
+/* zlarfg.f -- translated by f2c (version 20061008).
+ You must link the resulting object file with libf2c:
+ on Microsoft Windows system, link with libf2c.lib;
+ on Linux or Unix systems, link with .../path/to/libf2c.a -lm
+ or, if you install libf2c.a in a standard place, with -lf2c -lm
+ -- in that order, at the end of the command line, as in
+ cc *.o -lf2c -lm
+ Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
+
+ http://www.netlib.org/f2c/libf2c.zip
+*/
+
+#include "f2c.h"
+#include "blaswrap.h"
+
+/* Table of constant values */
+
+static doublecomplex c_b5 = {1.,0.};
+
+/* Subroutine */ int zlarfg_(integer *n, doublecomplex *alpha, doublecomplex *
+ x, integer *incx, doublecomplex *tau)
+{
+ /* System generated locals */
+ integer i__1;
+ doublereal d__1, d__2;
+ doublecomplex z__1, z__2;
+
+ /* Builtin functions */
+ double d_imag(doublecomplex *), d_sign(doublereal *, doublereal *);
+
+ /* Local variables */
+ integer j, knt;
+ doublereal beta, alphi, alphr;
+ extern /* Subroutine */ int zscal_(integer *, doublecomplex *,
+ doublecomplex *, integer *);
+ doublereal xnorm;
+ extern doublereal dlapy3_(doublereal *, doublereal *, doublereal *),
+ dznrm2_(integer *, doublecomplex *, integer *), dlamch_(char *);
+ doublereal safmin;
+ extern /* Subroutine */ int zdscal_(integer *, doublereal *,
+ doublecomplex *, integer *);
+ doublereal rsafmn;
+ extern /* Double Complex */ VOID zladiv_(doublecomplex *, doublecomplex *,
+ doublecomplex *);
+
+
+/* -- LAPACK auxiliary routine (version 3.2) -- */
+/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
+/* November 2006 */
+
+/* .. Scalar Arguments .. */
+/* .. */
+/* .. Array Arguments .. */
+/* .. */
+
+/* Purpose */
+/* ======= */
+
+/* ZLARFG generates a complex elementary reflector H of order n, such */
+/* that */
+
+/* H' * ( alpha ) = ( beta ), H' * H = I. */
+/* ( x ) ( 0 ) */
+
+/* where alpha and beta are scalars, with beta real, and x is an */
+/* (n-1)-element complex vector. H is represented in the form */
+
+/* H = I - tau * ( 1 ) * ( 1 v' ) , */
+/* ( v ) */
+
+/* where tau is a complex scalar and v is a complex (n-1)-element */
+/* vector. Note that H is not hermitian. */
+
+/* If the elements of x are all zero and alpha is real, then tau = 0 */
+/* and H is taken to be the unit matrix. */
+
+/* Otherwise 1 <= real(tau) <= 2 and abs(tau-1) <= 1 . */
+
+/* Arguments */
+/* ========= */
+
+/* N (input) INTEGER */
+/* The order of the elementary reflector. */
+
+/* ALPHA (input/output) COMPLEX*16 */
+/* On entry, the value alpha. */
+/* On exit, it is overwritten with the value beta. */
+
+/* X (input/output) COMPLEX*16 array, dimension */
+/* (1+(N-2)*abs(INCX)) */
+/* On entry, the vector x. */
+/* On exit, it is overwritten with the vector v. */
+
+/* INCX (input) INTEGER */
+/* The increment between elements of X. INCX > 0. */
+
+/* TAU (output) COMPLEX*16 */
+/* The value tau. */
+
+/* ===================================================================== */
+
+/* .. Parameters .. */
+/* .. */
+/* .. Local Scalars .. */
+/* .. */
+/* .. External Functions .. */
+/* .. */
+/* .. Intrinsic Functions .. */
+/* .. */
+/* .. External Subroutines .. */
+/* .. */
+/* .. Executable Statements .. */
+
+ /* Parameter adjustments */
+ --x;
+
+ /* Function Body */
+ if (*n <= 0) {
+ tau->r = 0., tau->i = 0.;
+ return 0;
+ }
+
+ i__1 = *n - 1;
+ xnorm = dznrm2_(&i__1, &x[1], incx);
+ alphr = alpha->r;
+ alphi = d_imag(alpha);
+
+ if (xnorm == 0. && alphi == 0.) {
+
+/* H = I */
+
+ tau->r = 0., tau->i = 0.;
+ } else {
+
+/* general case */
+
+ d__1 = dlapy3_(&alphr, &alphi, &xnorm);
+ beta = -d_sign(&d__1, &alphr);
+ safmin = dlamch_("S") / dlamch_("E");
+ rsafmn = 1. / safmin;
+
+ knt = 0;
+ if (abs(beta) < safmin) {
+
+/* XNORM, BETA may be inaccurate; scale X and recompute them */
+
+L10:
+ ++knt;
+ i__1 = *n - 1;
+ zdscal_(&i__1, &rsafmn, &x[1], incx);
+ beta *= rsafmn;
+ alphi *= rsafmn;
+ alphr *= rsafmn;
+ if (abs(beta) < safmin) {
+ goto L10;
+ }
+
+/* New BETA is at most 1, at least SAFMIN */
+
+ i__1 = *n - 1;
+ xnorm = dznrm2_(&i__1, &x[1], incx);
+ z__1.r = alphr, z__1.i = alphi;
+ alpha->r = z__1.r, alpha->i = z__1.i;
+ d__1 = dlapy3_(&alphr, &alphi, &xnorm);
+ beta = -d_sign(&d__1, &alphr);
+ }
+ d__1 = (beta - alphr) / beta;
+ d__2 = -alphi / beta;
+ z__1.r = d__1, z__1.i = d__2;
+ tau->r = z__1.r, tau->i = z__1.i;
+ z__2.r = alpha->r - beta, z__2.i = alpha->i;
+ zladiv_(&z__1, &c_b5, &z__2);
+ alpha->r = z__1.r, alpha->i = z__1.i;
+ i__1 = *n - 1;
+ zscal_(&i__1, alpha, &x[1], incx);
+
+/* If ALPHA is subnormal, it may lose relative accuracy */
+
+ i__1 = knt;
+ for (j = 1; j <= i__1; ++j) {
+ beta *= safmin;
+/* L20: */
+ }
+ alpha->r = beta, alpha->i = 0.;
+ }
+
+ return 0;
+
+/* End of ZLARFG */
+
+} /* zlarfg_ */
diff --git a/lapack/zlarft.c b/lapack/zlarft.c
new file mode 100644
index 0000000..b55adc2
--- /dev/null
+++ b/lapack/zlarft.c
@@ -0,0 +1,362 @@
+/* zlarft.f -- translated by f2c (version 20061008).
+ You must link the resulting object file with libf2c:
+ on Microsoft Windows system, link with libf2c.lib;
+ on Linux or Unix systems, link with .../path/to/libf2c.a -lm
+ or, if you install libf2c.a in a standard place, with -lf2c -lm
+ -- in that order, at the end of the command line, as in
+ cc *.o -lf2c -lm
+ Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
+
+ http://www.netlib.org/f2c/libf2c.zip
+*/
+
+#include "f2c.h"
+#include "blaswrap.h"
+
+/* Table of constant values */
+
+static doublecomplex c_b2 = {0.,0.};
+static integer c__1 = 1;
+
+/* Subroutine */ int zlarft_(char *direct, char *storev, integer *n, integer *
+ k, doublecomplex *v, integer *ldv, doublecomplex *tau, doublecomplex *
+ t, integer *ldt)
+{
+ /* System generated locals */
+ integer t_dim1, t_offset, v_dim1, v_offset, i__1, i__2, i__3, i__4;
+ doublecomplex z__1;
+
+ /* Local variables */
+ integer i__, j, prevlastv;
+ doublecomplex vii;
+ extern logical lsame_(char *, char *);
+ extern /* Subroutine */ int zgemv_(char *, integer *, integer *,
+ doublecomplex *, doublecomplex *, integer *, doublecomplex *,
+ integer *, doublecomplex *, doublecomplex *, integer *);
+ integer lastv;
+ extern /* Subroutine */ int ztrmv_(char *, char *, char *, integer *,
+ doublecomplex *, integer *, doublecomplex *, integer *), zlacgv_(integer *, doublecomplex *, integer *);
+
+
+/* -- LAPACK auxiliary routine (version 3.2) -- */
+/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
+/* November 2006 */
+
+/* .. Scalar Arguments .. */
+/* .. */
+/* .. Array Arguments .. */
+/* .. */
+
+/* Purpose */
+/* ======= */
+
+/* ZLARFT forms the triangular factor T of a complex block reflector H */
+/* of order n, which is defined as a product of k elementary reflectors. */
+
+/* If DIRECT = 'F', H = H(1) H(2) . . . H(k) and T is upper triangular; */
+
+/* If DIRECT = 'B', H = H(k) . . . H(2) H(1) and T is lower triangular. */
+
+/* If STOREV = 'C', the vector which defines the elementary reflector */
+/* H(i) is stored in the i-th column of the array V, and */
+
+/* H = I - V * T * V' */
+
+/* If STOREV = 'R', the vector which defines the elementary reflector */
+/* H(i) is stored in the i-th row of the array V, and */
+
+/* H = I - V' * T * V */
+
+/* Arguments */
+/* ========= */
+
+/* DIRECT (input) CHARACTER*1 */
+/* Specifies the order in which the elementary reflectors are */
+/* multiplied to form the block reflector: */
+/* = 'F': H = H(1) H(2) . . . H(k) (Forward) */
+/* = 'B': H = H(k) . . . H(2) H(1) (Backward) */
+
+/* STOREV (input) CHARACTER*1 */
+/* Specifies how the vectors which define the elementary */
+/* reflectors are stored (see also Further Details): */
+/* = 'C': columnwise */
+/* = 'R': rowwise */
+
+/* N (input) INTEGER */
+/* The order of the block reflector H. N >= 0. */
+
+/* K (input) INTEGER */
+/* The order of the triangular factor T (= the number of */
+/* elementary reflectors). K >= 1. */
+
+/* V (input/output) COMPLEX*16 array, dimension */
+/* (LDV,K) if STOREV = 'C' */
+/* (LDV,N) if STOREV = 'R' */
+/* The matrix V. See further details. */
+
+/* LDV (input) INTEGER */
+/* The leading dimension of the array V. */
+/* If STOREV = 'C', LDV >= max(1,N); if STOREV = 'R', LDV >= K. */
+
+/* TAU (input) COMPLEX*16 array, dimension (K) */
+/* TAU(i) must contain the scalar factor of the elementary */
+/* reflector H(i). */
+
+/* T (output) COMPLEX*16 array, dimension (LDT,K) */
+/* The k by k triangular factor T of the block reflector. */
+/* If DIRECT = 'F', T is upper triangular; if DIRECT = 'B', T is */
+/* lower triangular. The rest of the array is not used. */
+
+/* LDT (input) INTEGER */
+/* The leading dimension of the array T. LDT >= K. */
+
+/* Further Details */
+/* =============== */
+
+/* The shape of the matrix V and the storage of the vectors which define */
+/* the H(i) is best illustrated by the following example with n = 5 and */
+/* k = 3. The elements equal to 1 are not stored; the corresponding */
+/* array elements are modified but restored on exit. The rest of the */
+/* array is not used. */
+
+/* DIRECT = 'F' and STOREV = 'C': DIRECT = 'F' and STOREV = 'R': */
+
+/* V = ( 1 ) V = ( 1 v1 v1 v1 v1 ) */
+/* ( v1 1 ) ( 1 v2 v2 v2 ) */
+/* ( v1 v2 1 ) ( 1 v3 v3 ) */
+/* ( v1 v2 v3 ) */
+/* ( v1 v2 v3 ) */
+
+/* DIRECT = 'B' and STOREV = 'C': DIRECT = 'B' and STOREV = 'R': */
+
+/* V = ( v1 v2 v3 ) V = ( v1 v1 1 ) */
+/* ( v1 v2 v3 ) ( v2 v2 v2 1 ) */
+/* ( 1 v2 v3 ) ( v3 v3 v3 v3 1 ) */
+/* ( 1 v3 ) */
+/* ( 1 ) */
+
+/* ===================================================================== */
+
+/* .. Parameters .. */
+/* .. */
+/* .. Local Scalars .. */
+/* .. */
+/* .. External Subroutines .. */
+/* .. */
+/* .. External Functions .. */
+/* .. */
+/* .. Executable Statements .. */
+
+/* Quick return if possible */
+
+ /* Parameter adjustments */
+ v_dim1 = *ldv;
+ v_offset = 1 + v_dim1;
+ v -= v_offset;
+ --tau;
+ t_dim1 = *ldt;
+ t_offset = 1 + t_dim1;
+ t -= t_offset;
+
+ /* Function Body */
+ if (*n == 0) {
+ return 0;
+ }
+
+ if (lsame_(direct, "F")) {
+ prevlastv = *n;
+ i__1 = *k;
+ for (i__ = 1; i__ <= i__1; ++i__) {
+ prevlastv = max(prevlastv,i__);
+ i__2 = i__;
+ if (tau[i__2].r == 0. && tau[i__2].i == 0.) {
+
+/* H(i) = I */
+
+ i__2 = i__;
+ for (j = 1; j <= i__2; ++j) {
+ i__3 = j + i__ * t_dim1;
+ t[i__3].r = 0., t[i__3].i = 0.;
+/* L10: */
+ }
+ } else {
+
+/* general case */
+
+ i__2 = i__ + i__ * v_dim1;
+ vii.r = v[i__2].r, vii.i = v[i__2].i;
+ i__2 = i__ + i__ * v_dim1;
+ v[i__2].r = 1., v[i__2].i = 0.;
+ if (lsame_(storev, "C")) {
+/* Skip any trailing zeros. */
+ i__2 = i__ + 1;
+ for (lastv = *n; lastv >= i__2; --lastv) {
+ i__3 = lastv + i__ * v_dim1;
+ if (v[i__3].r != 0. || v[i__3].i != 0.) {
+ break;
+ }
+ }
+ j = min(lastv,prevlastv);
+
+/* T(1:i-1,i) := - tau(i) * V(i:j,1:i-1)' * V(i:j,i) */
+
+ i__2 = j - i__ + 1;
+ i__3 = i__ - 1;
+ i__4 = i__;
+ z__1.r = -tau[i__4].r, z__1.i = -tau[i__4].i;
+ zgemv_("Conjugate transpose", &i__2, &i__3, &z__1, &v[i__
+ + v_dim1], ldv, &v[i__ + i__ * v_dim1], &c__1, &
+ c_b2, &t[i__ * t_dim1 + 1], &c__1);
+ } else {
+/* Skip any trailing zeros. */
+ i__2 = i__ + 1;
+ for (lastv = *n; lastv >= i__2; --lastv) {
+ i__3 = i__ + lastv * v_dim1;
+ if (v[i__3].r != 0. || v[i__3].i != 0.) {
+ break;
+ }
+ }
+ j = min(lastv,prevlastv);
+
+/* T(1:i-1,i) := - tau(i) * V(1:i-1,i:j) * V(i,i:j)' */
+
+ if (i__ < j) {
+ i__2 = j - i__;
+ zlacgv_(&i__2, &v[i__ + (i__ + 1) * v_dim1], ldv);
+ }
+ i__2 = i__ - 1;
+ i__3 = j - i__ + 1;
+ i__4 = i__;
+ z__1.r = -tau[i__4].r, z__1.i = -tau[i__4].i;
+ zgemv_("No transpose", &i__2, &i__3, &z__1, &v[i__ *
+ v_dim1 + 1], ldv, &v[i__ + i__ * v_dim1], ldv, &
+ c_b2, &t[i__ * t_dim1 + 1], &c__1);
+ if (i__ < j) {
+ i__2 = j - i__;
+ zlacgv_(&i__2, &v[i__ + (i__ + 1) * v_dim1], ldv);
+ }
+ }
+ i__2 = i__ + i__ * v_dim1;
+ v[i__2].r = vii.r, v[i__2].i = vii.i;
+
+/* T(1:i-1,i) := T(1:i-1,1:i-1) * T(1:i-1,i) */
+
+ i__2 = i__ - 1;
+ ztrmv_("Upper", "No transpose", "Non-unit", &i__2, &t[
+ t_offset], ldt, &t[i__ * t_dim1 + 1], &c__1);
+ i__2 = i__ + i__ * t_dim1;
+ i__3 = i__;
+ t[i__2].r = tau[i__3].r, t[i__2].i = tau[i__3].i;
+ if (i__ > 1) {
+ prevlastv = max(prevlastv,lastv);
+ } else {
+ prevlastv = lastv;
+ }
+ }
+/* L20: */
+ }
+ } else {
+ prevlastv = 1;
+ for (i__ = *k; i__ >= 1; --i__) {
+ i__1 = i__;
+ if (tau[i__1].r == 0. && tau[i__1].i == 0.) {
+
+/* H(i) = I */
+
+ i__1 = *k;
+ for (j = i__; j <= i__1; ++j) {
+ i__2 = j + i__ * t_dim1;
+ t[i__2].r = 0., t[i__2].i = 0.;
+/* L30: */
+ }
+ } else {
+
+/* general case */
+
+ if (i__ < *k) {
+ if (lsame_(storev, "C")) {
+ i__1 = *n - *k + i__ + i__ * v_dim1;
+ vii.r = v[i__1].r, vii.i = v[i__1].i;
+ i__1 = *n - *k + i__ + i__ * v_dim1;
+ v[i__1].r = 1., v[i__1].i = 0.;
+/* Skip any leading zeros. */
+ i__1 = i__ - 1;
+ for (lastv = 1; lastv <= i__1; ++lastv) {
+ i__2 = lastv + i__ * v_dim1;
+ if (v[i__2].r != 0. || v[i__2].i != 0.) {
+ break;
+ }
+ }
+ j = max(lastv,prevlastv);
+
+/* T(i+1:k,i) := */
+/* - tau(i) * V(j:n-k+i,i+1:k)' * V(j:n-k+i,i) */
+
+ i__1 = *n - *k + i__ - j + 1;
+ i__2 = *k - i__;
+ i__3 = i__;
+ z__1.r = -tau[i__3].r, z__1.i = -tau[i__3].i;
+ zgemv_("Conjugate transpose", &i__1, &i__2, &z__1, &v[
+ j + (i__ + 1) * v_dim1], ldv, &v[j + i__ *
+ v_dim1], &c__1, &c_b2, &t[i__ + 1 + i__ *
+ t_dim1], &c__1);
+ i__1 = *n - *k + i__ + i__ * v_dim1;
+ v[i__1].r = vii.r, v[i__1].i = vii.i;
+ } else {
+ i__1 = i__ + (*n - *k + i__) * v_dim1;
+ vii.r = v[i__1].r, vii.i = v[i__1].i;
+ i__1 = i__ + (*n - *k + i__) * v_dim1;
+ v[i__1].r = 1., v[i__1].i = 0.;
+/* Skip any leading zeros. */
+ i__1 = i__ - 1;
+ for (lastv = 1; lastv <= i__1; ++lastv) {
+ i__2 = i__ + lastv * v_dim1;
+ if (v[i__2].r != 0. || v[i__2].i != 0.) {
+ break;
+ }
+ }
+ j = max(lastv,prevlastv);
+
+/* T(i+1:k,i) := */
+/* - tau(i) * V(i+1:k,j:n-k+i) * V(i,j:n-k+i)' */
+
+ i__1 = *n - *k + i__ - 1 - j + 1;
+ zlacgv_(&i__1, &v[i__ + j * v_dim1], ldv);
+ i__1 = *k - i__;
+ i__2 = *n - *k + i__ - j + 1;
+ i__3 = i__;
+ z__1.r = -tau[i__3].r, z__1.i = -tau[i__3].i;
+ zgemv_("No transpose", &i__1, &i__2, &z__1, &v[i__ +
+ 1 + j * v_dim1], ldv, &v[i__ + j * v_dim1],
+ ldv, &c_b2, &t[i__ + 1 + i__ * t_dim1], &c__1);
+ i__1 = *n - *k + i__ - 1 - j + 1;
+ zlacgv_(&i__1, &v[i__ + j * v_dim1], ldv);
+ i__1 = i__ + (*n - *k + i__) * v_dim1;
+ v[i__1].r = vii.r, v[i__1].i = vii.i;
+ }
+
+/* T(i+1:k,i) := T(i+1:k,i+1:k) * T(i+1:k,i) */
+
+ i__1 = *k - i__;
+ ztrmv_("Lower", "No transpose", "Non-unit", &i__1, &t[i__
+ + 1 + (i__ + 1) * t_dim1], ldt, &t[i__ + 1 + i__ *
+ t_dim1], &c__1)
+ ;
+ if (i__ > 1) {
+ prevlastv = min(prevlastv,lastv);
+ } else {
+ prevlastv = lastv;
+ }
+ }
+ i__1 = i__ + i__ * t_dim1;
+ i__2 = i__;
+ t[i__1].r = tau[i__2].r, t[i__1].i = tau[i__2].i;
+ }
+/* L40: */
+ }
+ }
+ return 0;
+
+/* End of ZLARFT */
+
+} /* zlarft_ */
diff --git a/scripts/CMakeLists.txt b/scripts/CMakeLists.txt
new file mode 100644
index 0000000..0d9a631
--- /dev/null
+++ b/scripts/CMakeLists.txt
@@ -0,0 +1,6 @@
+get_property(EIGEN_TESTS_LIST GLOBAL PROPERTY EIGEN_TESTS_LIST)
+configure_file(buildtests.in ${CMAKE_BINARY_DIR}/buildtests.sh @ONLY)
+
+configure_file(check.in ${CMAKE_BINARY_DIR}/check.sh COPYONLY)
+configure_file(debug.in ${CMAKE_BINARY_DIR}/debug.sh COPYONLY)
+configure_file(release.in ${CMAKE_BINARY_DIR}/release.sh COPYONLY)
diff --git a/scripts/buildtests.in b/scripts/buildtests.in
new file mode 100755
index 0000000..ab9c18f
--- /dev/null
+++ b/scripts/buildtests.in
@@ -0,0 +1,22 @@
+#!/bin/bash
+
+if [[ $# != 1 || $1 == *help ]]
+then
+ echo "usage: $0 regexp"
+ echo " Builds tests matching the regexp."
+ echo " The EIGEN_MAKE_ARGS environment variable allows to pass args to 'make'."
+ echo " For example, to launch 5 concurrent builds, use EIGEN_MAKE_ARGS='-j5'"
+ exit 0
+fi
+
+TESTSLIST="@EIGEN_TESTS_LIST@"
+targets_to_make=$(echo "$TESTSLIST" | grep -E "$1" | xargs echo)
+
+if [ -n "${EIGEN_MAKE_ARGS:+x}" ]
+then
+ @CMAKE_MAKE_PROGRAM@ $targets_to_make ${EIGEN_MAKE_ARGS}
+else
+ @CMAKE_MAKE_PROGRAM@ $targets_to_make @EIGEN_TEST_BUILD_FLAGS@
+fi
+exit $?
+
diff --git a/scripts/cdashtesting.cmake.in b/scripts/cdashtesting.cmake.in
new file mode 100644
index 0000000..0bf0fac
--- /dev/null
+++ b/scripts/cdashtesting.cmake.in
@@ -0,0 +1,49 @@
+
+set(CTEST_SOURCE_DIRECTORY "@CMAKE_SOURCE_DIR@")
+set(CTEST_BINARY_DIRECTORY "@CMAKE_BINARY_DIR@")
+set(CTEST_CMAKE_GENERATOR "@CMAKE_GENERATOR@")
+set(CTEST_BUILD_NAME "@BUILDNAME@")
+set(CTEST_SITE "@SITE@")
+
+set(MODEL Experimental)
+if(${CTEST_SCRIPT_ARG} MATCHES Nightly)
+ set(MODEL Nightly)
+elseif(${CTEST_SCRIPT_ARG} MATCHES Continuous)
+ set(MODEL Continuous)
+endif()
+
+find_program(CTEST_GIT_COMMAND NAMES git)
+set(CTEST_UPDATE_COMMAND "${CTEST_GIT_COMMAND}")
+
+ctest_start(${MODEL} ${CTEST_SOURCE_DIRECTORY} ${CTEST_BINARY_DIRECTORY})
+
+ctest_update(SOURCE "${CTEST_SOURCE_DIRECTORY}")
+ctest_submit(PARTS Update Notes)
+
+# to get CTEST_PROJECT_SUBPROJECTS definition:
+include("${CTEST_SOURCE_DIRECTORY}/CTestConfig.cmake")
+
+foreach(subproject ${CTEST_PROJECT_SUBPROJECTS})
+ message("")
+ message("Process ${subproject}")
+
+ set_property(GLOBAL PROPERTY SubProject ${subproject})
+ set_property(GLOBAL PROPERTY Label ${subproject})
+
+ ctest_configure(BUILD ${CTEST_BINARY_DIRECTORY} SOURCE ${CTEST_SOURCE_DIRECTORY} )
+ ctest_submit(PARTS Configure)
+
+ set(CTEST_BUILD_TARGET "Build${subproject}")
+ message("Build ${CTEST_BUILD_TARGET}")
+ ctest_build(BUILD "${CTEST_BINARY_DIRECTORY}" APPEND)
+ # builds target ${CTEST_BUILD_TARGET}
+ ctest_submit(PARTS Build)
+
+ ctest_test(BUILD "${CTEST_BINARY_DIRECTORY}" INCLUDE_LABEL "${subproject}" )
+ # runs only tests that have a LABELS property matching "${subproject}"
+
+ ctest_coverage(BUILD "${CTEST_BINARY_DIRECTORY}" LABELS "${subproject}" )
+
+ ctest_submit(PARTS Test)
+
+endforeach()
diff --git a/scripts/check.in b/scripts/check.in
new file mode 100755
index 0000000..7717e2d
--- /dev/null
+++ b/scripts/check.in
@@ -0,0 +1,21 @@
+#!/bin/bash
+# check : shorthand for make and ctest -R
+
+if [[ $# != 1 || $1 == *help ]]
+then
+ echo "usage: $0 regexp"
+ echo " Builds and runs tests matching the regexp."
+ echo " The EIGEN_MAKE_ARGS environment variable allows to pass args to 'make'."
+ echo " For example, to launch 5 concurrent builds, use EIGEN_MAKE_ARGS='-j5'"
+ echo " The EIGEN_CTEST_ARGS environment variable allows to pass args to 'ctest'."
+ echo " For example, with CTest 2.8, you can use EIGEN_CTEST_ARGS='-j5'."
+ exit 0
+fi
+
+if [ -n "${EIGEN_CTEST_ARGS:+x}" ]
+then
+ ./buildtests.sh "$1" && ctest -R "$1" ${EIGEN_CTEST_ARGS}
+else
+ ./buildtests.sh "$1" && ctest -R "$1"
+fi
+exit $?
diff --git a/scripts/debug.in b/scripts/debug.in
new file mode 100755
index 0000000..d339d3d
--- /dev/null
+++ b/scripts/debug.in
@@ -0,0 +1,3 @@
+#!/bin/sh
+
+cmake -DCMAKE_BUILD_TYPE=Debug .
diff --git a/scripts/eigen_gen_credits.cpp b/scripts/eigen_gen_credits.cpp
new file mode 100644
index 0000000..f2e8163
--- /dev/null
+++ b/scripts/eigen_gen_credits.cpp
@@ -0,0 +1,232 @@
+#include <string>
+#include <sstream>
+#include <iostream>
+#include <fstream>
+#include <iomanip>
+#include <map>
+#include <list>
+
+using namespace std;
+
+// this function takes a line that may contain a name and/or email address,
+// and returns just the name, while fixing the "bad cases".
+std::string contributor_name(const std::string& line)
+{
+ string result;
+
+ // let's first take care of the case of isolated email addresses, like
+ // "user@localhost.localdomain" entries
+ if(line.find("markb@localhost.localdomain") != string::npos)
+ {
+ return "Mark Borgerding";
+ }
+
+ if(line.find("kayhman@contact.intra.cea.fr") != string::npos)
+ {
+ return "Guillaume Saupin";
+ }
+
+ // from there on we assume that we have a entry of the form
+ // either:
+ // Bla bli Blurp
+ // or:
+ // Bla bli Blurp <bblurp@email.com>
+
+ size_t position_of_email_address = line.find_first_of('<');
+ if(position_of_email_address != string::npos)
+ {
+ // there is an e-mail address in <...>.
+
+ // Hauke once committed as "John Smith", fix that.
+ if(line.find("hauke.heibel") != string::npos)
+ result = "Hauke Heibel";
+ else
+ {
+ // just remove the e-mail address
+ result = line.substr(0, position_of_email_address);
+ }
+ }
+ else
+ {
+ // there is no e-mail address in <...>.
+
+ if(line.find("convert-repo") != string::npos)
+ result = "";
+ else
+ result = line;
+ }
+
+ // remove trailing spaces
+ size_t length = result.length();
+ while(length >= 1 && result[length-1] == ' ') result.erase(--length);
+
+ return result;
+}
+
+// parses hg churn output to generate a contributors map.
+map<string,int> contributors_map_from_churn_output(const char *filename)
+{
+ map<string,int> contributors_map;
+
+ string line;
+ ifstream churn_out;
+ churn_out.open(filename, ios::in);
+ while(!getline(churn_out,line).eof())
+ {
+ // remove the histograms "******" that hg churn may draw at the end of some lines
+ size_t first_star = line.find_first_of('*');
+ if(first_star != string::npos) line.erase(first_star);
+
+ // remove trailing spaces
+ size_t length = line.length();
+ while(length >= 1 && line[length-1] == ' ') line.erase(--length);
+
+ // now the last space indicates where the number starts
+ size_t last_space = line.find_last_of(' ');
+
+ // get the number (of changesets or of modified lines for each contributor)
+ int number;
+ istringstream(line.substr(last_space+1)) >> number;
+
+ // get the name of the contributor
+ line.erase(last_space);
+ string name = contributor_name(line);
+
+ map<string,int>::iterator it = contributors_map.find(name);
+ // if new contributor, insert
+ if(it == contributors_map.end())
+ contributors_map.insert(pair<string,int>(name, number));
+ // if duplicate, just add the number
+ else
+ it->second += number;
+ }
+ churn_out.close();
+
+ return contributors_map;
+}
+
+// find the last name, i.e. the last word.
+// for "van den Schbling" types of last names, that's not a problem, that's actually what we want.
+string lastname(const string& name)
+{
+ size_t last_space = name.find_last_of(' ');
+ if(last_space >= name.length()-1) return name;
+ else return name.substr(last_space+1);
+}
+
+struct contributor
+{
+ string name;
+ int changedlines;
+ int changesets;
+ string url;
+ string misc;
+
+ contributor() : changedlines(0), changesets(0) {}
+
+ bool operator < (const contributor& other)
+ {
+ return lastname(name).compare(lastname(other.name)) < 0;
+ }
+};
+
+void add_online_info_into_contributors_list(list<contributor>& contributors_list, const char *filename)
+{
+ string line;
+ ifstream online_info;
+ online_info.open(filename, ios::in);
+ while(!getline(online_info,line).eof())
+ {
+ string hgname, realname, url, misc;
+
+ size_t last_bar = line.find_last_of('|');
+ if(last_bar == string::npos) continue;
+ if(last_bar < line.length())
+ misc = line.substr(last_bar+1);
+ line.erase(last_bar);
+
+ last_bar = line.find_last_of('|');
+ if(last_bar == string::npos) continue;
+ if(last_bar < line.length())
+ url = line.substr(last_bar+1);
+ line.erase(last_bar);
+
+ last_bar = line.find_last_of('|');
+ if(last_bar == string::npos) continue;
+ if(last_bar < line.length())
+ realname = line.substr(last_bar+1);
+ line.erase(last_bar);
+
+ hgname = line;
+
+ // remove the example line
+ if(hgname.find("MercurialName") != string::npos) continue;
+
+ list<contributor>::iterator it;
+ for(it=contributors_list.begin(); it != contributors_list.end() && it->name != hgname; ++it)
+ {}
+
+ if(it == contributors_list.end())
+ {
+ contributor c;
+ c.name = realname;
+ c.url = url;
+ c.misc = misc;
+ contributors_list.push_back(c);
+ }
+ else
+ {
+ it->name = realname;
+ it->url = url;
+ it->misc = misc;
+ }
+ }
+}
+
+int main()
+{
+ // parse the hg churn output files
+ map<string,int> contributors_map_for_changedlines = contributors_map_from_churn_output("churn-changedlines.out");
+ //map<string,int> contributors_map_for_changesets = contributors_map_from_churn_output("churn-changesets.out");
+
+ // merge into the contributors list
+ list<contributor> contributors_list;
+ map<string,int>::iterator it;
+ for(it=contributors_map_for_changedlines.begin(); it != contributors_map_for_changedlines.end(); ++it)
+ {
+ contributor c;
+ c.name = it->first;
+ c.changedlines = it->second;
+ c.changesets = 0; //contributors_map_for_changesets.find(it->first)->second;
+ contributors_list.push_back(c);
+ }
+
+ add_online_info_into_contributors_list(contributors_list, "online-info.out");
+
+ contributors_list.sort();
+
+ cout << "{| cellpadding=\"5\"\n";
+ cout << "!\n";
+ cout << "! Lines changed\n";
+ cout << "!\n";
+
+ list<contributor>::iterator itc;
+ int i = 0;
+ for(itc=contributors_list.begin(); itc != contributors_list.end(); ++itc)
+ {
+ if(itc->name.length() == 0) continue;
+ if(i%2) cout << "|-\n";
+ else cout << "|- style=\"background:#FFFFD0\"\n";
+ if(itc->url.length())
+ cout << "| [" << itc->url << " " << itc->name << "]\n";
+ else
+ cout << "| " << itc->name << "\n";
+ if(itc->changedlines)
+ cout << "| " << itc->changedlines << "\n";
+ else
+ cout << "| (no information)\n";
+ cout << "| " << itc->misc << "\n";
+ i++;
+ }
+ cout << "|}" << endl;
+}
diff --git a/scripts/eigen_gen_docs b/scripts/eigen_gen_docs
new file mode 100644
index 0000000..787dcb3
--- /dev/null
+++ b/scripts/eigen_gen_docs
@@ -0,0 +1,24 @@
+#!/bin/sh
+
+# configuration
+# You should call this script with USER set as you want, else some default
+# will be used
+USER=${USER:-'orzel'}
+UPLOAD_DIR=dox-devel
+
+#ulimit -v 1024000
+
+# step 1 : build
+rm build/doc/html -Rf
+mkdir build -p
+(cd build && cmake .. && make doc) || { echo "make failed"; exit 1; }
+
+#step 2 : upload
+# (the '/' at the end of path is very important, see rsync documentation)
+rsync -az --no-p --delete build/doc/html/ $USER@ssh.tuxfamily.org:eigen/eigen.tuxfamily.org-web/htdocs/$UPLOAD_DIR/ || { echo "upload failed"; exit 1; }
+
+#step 3 : fix the perm
+ssh $USER@ssh.tuxfamily.org "chmod -R g+w /home/eigen/eigen.tuxfamily.org-web/htdocs/$UPLOAD_DIR" || { echo "perm failed"; exit 1; }
+
+echo "Uploaded successfully"
+
diff --git a/scripts/eigen_gen_split_test_help.cmake b/scripts/eigen_gen_split_test_help.cmake
new file mode 100644
index 0000000..e43f5aa
--- /dev/null
+++ b/scripts/eigen_gen_split_test_help.cmake
@@ -0,0 +1,11 @@
+#!cmake -P
+file(WRITE split_test_helper.h "")
+foreach(i RANGE 1 999)
+ file(APPEND split_test_helper.h
+ "#if defined(EIGEN_TEST_PART_${i}) || defined(EIGEN_TEST_PART_ALL)\n"
+ "#define CALL_SUBTEST_${i}(FUNC) CALL_SUBTEST(FUNC)\n"
+ "#else\n"
+ "#define CALL_SUBTEST_${i}(FUNC)\n"
+ "#endif\n\n"
+ )
+endforeach()
\ No newline at end of file
diff --git a/scripts/release.in b/scripts/release.in
new file mode 100755
index 0000000..db2d9d9
--- /dev/null
+++ b/scripts/release.in
@@ -0,0 +1,3 @@
+#!/bin/sh
+
+cmake -DCMAKE_BUILD_TYPE=Release .
diff --git a/scripts/relicense.py b/scripts/relicense.py
new file mode 100644
index 0000000..8a5265f
--- /dev/null
+++ b/scripts/relicense.py
@@ -0,0 +1,69 @@
+# This file is part of Eigen, a lightweight C++ template library
+# for linear algebra.
+#
+# Copyright (C) 2012 Keir Mierle <mierle@gmail.com>
+#
+# This Source Code Form is subject to the terms of the Mozilla
+# Public License v. 2.0. If a copy of the MPL was not distributed
+# with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+#
+# Author: mierle@gmail.com (Keir Mierle)
+#
+# Make the long-awaited conversion to MPL.
+
+lgpl3_header = '''
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+'''
+
+mpl2_header = """
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+"""
+
+import os
+import sys
+
+exclusions = set(['relicense.py'])
+
+def update(text):
+ if text.find(lgpl3_header) == -1:
+ return text, False
+ return text.replace(lgpl3_header, mpl2_header), True
+
+rootdir = sys.argv[1]
+for root, sub_folders, files in os.walk(rootdir):
+ for basename in files:
+ if basename in exclusions:
+ print 'SKIPPED', filename
+ continue
+ filename = os.path.join(root, basename)
+ fo = file(filename)
+ text = fo.read()
+ fo.close()
+
+ text, updated = update(text)
+ if updated:
+ fo = file(filename, "w")
+ fo.write(text)
+ fo.close()
+ print 'UPDATED', filename
+ else:
+ print ' ', filename
diff --git a/signature_of_eigen3_matrix_library b/signature_of_eigen3_matrix_library
new file mode 100644
index 0000000..80aaf46
--- /dev/null
+++ b/signature_of_eigen3_matrix_library
@@ -0,0 +1 @@
+This file is just there as a signature to help identify directories containing Eigen3. When writing a script looking for Eigen3, just look for this file. This is especially useful to help disambiguate with Eigen2...
diff --git a/test/AnnoyingScalar.h b/test/AnnoyingScalar.h
new file mode 100644
index 0000000..4362de2
--- /dev/null
+++ b/test/AnnoyingScalar.h
@@ -0,0 +1,163 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2011-2018 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_TEST_ANNOYING_SCALAR_H
+#define EIGEN_TEST_ANNOYING_SCALAR_H
+
+#include <ostream>
+
+#if EIGEN_COMP_GNUC
+#pragma GCC diagnostic ignored "-Wshadow"
+#endif
+
+#ifndef EIGEN_TEST_ANNOYING_SCALAR_DONT_THROW
+struct my_exception
+{
+ my_exception() {}
+ ~my_exception() {}
+};
+#endif
+
+// An AnnoyingScalar is a pseudo scalar type that:
+// - can randomly through an exception in operator +
+// - randomly allocate on the heap or initialize a reference to itself making it non trivially copyable, nor movable, nor relocatable.
+
+class AnnoyingScalar
+{
+ public:
+ AnnoyingScalar() { init(); *v = 0; }
+ AnnoyingScalar(long double _v) { init(); *v = static_cast<float>(_v); }
+ AnnoyingScalar(double _v) { init(); *v = static_cast<float>(_v); }
+ AnnoyingScalar(float _v) { init(); *v = _v; }
+ AnnoyingScalar(int _v) { init(); *v = static_cast<float>(_v); }
+ AnnoyingScalar(long _v) { init(); *v = static_cast<float>(_v); }
+ AnnoyingScalar(long long _v) { init(); *v = static_cast<float>(_v); }
+ AnnoyingScalar(const AnnoyingScalar& other) { init(); *v = *(other.v); }
+ ~AnnoyingScalar() {
+ if(v!=&data)
+ delete v;
+ instances--;
+ }
+
+ void init() {
+ if(internal::random<bool>())
+ v = new float;
+ else
+ v = &data;
+ instances++;
+ }
+
+ AnnoyingScalar operator+(const AnnoyingScalar& other) const
+ {
+ #ifndef EIGEN_TEST_ANNOYING_SCALAR_DONT_THROW
+ countdown--;
+ if(countdown<=0 && !dont_throw)
+ throw my_exception();
+ #endif
+ return AnnoyingScalar(*v+*other.v);
+ }
+
+ AnnoyingScalar operator-() const
+ { return AnnoyingScalar(-*v); }
+
+ AnnoyingScalar operator-(const AnnoyingScalar& other) const
+ { return AnnoyingScalar(*v-*other.v); }
+
+ AnnoyingScalar operator*(const AnnoyingScalar& other) const
+ { return AnnoyingScalar((*v)*(*other.v)); }
+
+ AnnoyingScalar operator/(const AnnoyingScalar& other) const
+ { return AnnoyingScalar((*v)/(*other.v)); }
+
+ AnnoyingScalar& operator+=(const AnnoyingScalar& other) { *v += *other.v; return *this; }
+ AnnoyingScalar& operator-=(const AnnoyingScalar& other) { *v -= *other.v; return *this; }
+ AnnoyingScalar& operator*=(const AnnoyingScalar& other) { *v *= *other.v; return *this; }
+ AnnoyingScalar& operator/=(const AnnoyingScalar& other) { *v /= *other.v; return *this; }
+ AnnoyingScalar& operator= (const AnnoyingScalar& other) { *v = *other.v; return *this; }
+
+ bool operator==(const AnnoyingScalar& other) const { return numext::equal_strict(*v, *other.v); }
+ bool operator!=(const AnnoyingScalar& other) const { return numext::not_equal_strict(*v, *other.v); }
+ bool operator<=(const AnnoyingScalar& other) const { return *v <= *other.v; }
+ bool operator< (const AnnoyingScalar& other) const { return *v < *other.v; }
+ bool operator>=(const AnnoyingScalar& other) const { return *v >= *other.v; }
+ bool operator> (const AnnoyingScalar& other) const { return *v > *other.v; }
+
+ float* v;
+ float data;
+ static int instances;
+#ifndef EIGEN_TEST_ANNOYING_SCALAR_DONT_THROW
+ static int countdown;
+ static bool dont_throw;
+#endif
+};
+
+AnnoyingScalar real(const AnnoyingScalar &x) { return x; }
+AnnoyingScalar imag(const AnnoyingScalar & ) { return 0; }
+AnnoyingScalar conj(const AnnoyingScalar &x) { return x; }
+AnnoyingScalar sqrt(const AnnoyingScalar &x) { return std::sqrt(*x.v); }
+AnnoyingScalar abs (const AnnoyingScalar &x) { return std::abs(*x.v); }
+AnnoyingScalar cos (const AnnoyingScalar &x) { return std::cos(*x.v); }
+AnnoyingScalar sin (const AnnoyingScalar &x) { return std::sin(*x.v); }
+AnnoyingScalar acos(const AnnoyingScalar &x) { return std::acos(*x.v); }
+AnnoyingScalar atan2(const AnnoyingScalar &y,const AnnoyingScalar &x) { return std::atan2(*y.v,*x.v); }
+
+std::ostream& operator<<(std::ostream& stream,const AnnoyingScalar& x) {
+ stream << (*(x.v));
+ return stream;
+}
+
+int AnnoyingScalar::instances = 0;
+
+#ifndef EIGEN_TEST_ANNOYING_SCALAR_DONT_THROW
+int AnnoyingScalar::countdown = 0;
+bool AnnoyingScalar::dont_throw = false;
+#endif
+
+namespace Eigen {
+template<>
+struct NumTraits<AnnoyingScalar> : NumTraits<float>
+{
+ enum {
+ RequireInitialization = 1,
+ };
+ typedef AnnoyingScalar Real;
+ typedef AnnoyingScalar Nested;
+ typedef AnnoyingScalar Literal;
+ typedef AnnoyingScalar NonInteger;
+};
+
+template<> inline AnnoyingScalar test_precision<AnnoyingScalar>() { return test_precision<float>(); }
+
+namespace numext {
+template<>
+EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
+bool (isfinite)(const AnnoyingScalar& x) {
+ return (numext::isfinite)(*x.v);
+}
+}
+
+namespace internal {
+ template<> EIGEN_STRONG_INLINE double cast(const AnnoyingScalar& x) { return double(*x.v); }
+ template<> EIGEN_STRONG_INLINE float cast(const AnnoyingScalar& x) { return *x.v; }
+}
+} // namespace Eigen
+
+AnnoyingScalar get_test_precision(const AnnoyingScalar&)
+{ return Eigen::test_precision<AnnoyingScalar>(); }
+
+AnnoyingScalar test_relative_error(const AnnoyingScalar &a, const AnnoyingScalar &b)
+{ return test_relative_error(*a.v, *b.v); }
+
+inline bool test_isApprox(const AnnoyingScalar &a, const AnnoyingScalar &b)
+{ return internal::isApprox(*a.v, *b.v, test_precision<float>()); }
+
+inline bool test_isMuchSmallerThan(const AnnoyingScalar &a, const AnnoyingScalar &b)
+{ return test_isMuchSmallerThan(*a.v, *b.v); }
+
+#endif // EIGEN_TEST_ANNOYING_SCALAR_H
diff --git a/test/CMakeLists.txt b/test/CMakeLists.txt
new file mode 100644
index 0000000..8ffa002
--- /dev/null
+++ b/test/CMakeLists.txt
@@ -0,0 +1,484 @@
+# The file split_test_helper.h was generated at first run,
+# it is now included in test/
+if(EXISTS ${CMAKE_CURRENT_BINARY_DIR}/split_test_helper.h)
+ file(REMOVE ${CMAKE_CURRENT_BINARY_DIR}/split_test_helper.h)
+endif()
+
+# check if we have a Fortran compiler
+include(CheckLanguage)
+check_language(Fortran)
+if(CMAKE_Fortran_COMPILER)
+ enable_language(Fortran)
+ set(EIGEN_Fortran_COMPILER_WORKS ON)
+else()
+ set(EIGEN_Fortran_COMPILER_WORKS OFF)
+ # search for a default Lapack library to complete Eigen's one
+ find_package(LAPACK QUIET)
+endif()
+
+# TODO do the same for EXTERNAL_LAPACK
+option(EIGEN_TEST_EXTERNAL_BLAS "Use external BLAS library for testsuite" OFF)
+if(EIGEN_TEST_EXTERNAL_BLAS)
+ find_package(BLAS REQUIRED)
+ message(STATUS "BLAS_COMPILER_FLAGS: ${BLAS_COMPILER_FLAGS}")
+ add_definitions("-DEIGEN_USE_BLAS") # is adding ${BLAS_COMPILER_FLAGS} necessary?
+ list(APPEND EXTERNAL_LIBS "${BLAS_LIBRARIES}")
+endif()
+
+# configure blas/lapack (use Eigen's ones)
+set(EIGEN_BLAS_LIBRARIES eigen_blas)
+set(EIGEN_LAPACK_LIBRARIES eigen_lapack)
+
+set(EIGEN_TEST_MATRIX_DIR "" CACHE STRING "Enable testing of realword sparse matrices contained in the specified path")
+if(EIGEN_TEST_MATRIX_DIR)
+ if(NOT WIN32)
+ message(STATUS "Test realworld sparse matrices: ${EIGEN_TEST_MATRIX_DIR}")
+ add_definitions( -DTEST_REAL_CASES="${EIGEN_TEST_MATRIX_DIR}" )
+ else()
+ message(STATUS "REAL CASES CAN NOT BE CURRENTLY TESTED ON WIN32")
+ endif()
+endif()
+
+set(SPARSE_LIBS " ")
+
+find_package(CHOLMOD)
+if(CHOLMOD_FOUND AND EIGEN_BUILD_BLAS AND EIGEN_BUILD_LAPACK)
+ add_definitions("-DEIGEN_CHOLMOD_SUPPORT")
+ include_directories(${CHOLMOD_INCLUDES})
+ set(SPARSE_LIBS ${SPARSE_LIBS} ${CHOLMOD_LIBRARIES} ${EIGEN_BLAS_LIBRARIES} ${EIGEN_LAPACK_LIBRARIES})
+ set(CHOLMOD_ALL_LIBS ${CHOLMOD_LIBRARIES} ${EIGEN_BLAS_LIBRARIES} ${EIGEN_LAPACK_LIBRARIES})
+ ei_add_property(EIGEN_TESTED_BACKENDS "CHOLMOD, ")
+
+ ei_add_test(cholmod_support "" "${CHOLMOD_ALL_LIBS}")
+else()
+ ei_add_property(EIGEN_MISSING_BACKENDS "CHOLMOD, ")
+endif()
+
+find_package(UMFPACK)
+if(UMFPACK_FOUND AND EIGEN_BUILD_BLAS)
+ add_definitions("-DEIGEN_UMFPACK_SUPPORT")
+ include_directories(${UMFPACK_INCLUDES})
+ set(SPARSE_LIBS ${SPARSE_LIBS} ${UMFPACK_LIBRARIES} ${EIGEN_BLAS_LIBRARIES})
+ set(UMFPACK_ALL_LIBS ${UMFPACK_LIBRARIES} ${EIGEN_BLAS_LIBRARIES})
+ ei_add_property(EIGEN_TESTED_BACKENDS "UMFPACK, ")
+
+ ei_add_test(umfpack_support "" "${UMFPACK_ALL_LIBS}")
+else()
+ ei_add_property(EIGEN_MISSING_BACKENDS "UMFPACK, ")
+endif()
+
+find_package(KLU)
+if(KLU_FOUND AND EIGEN_BUILD_BLAS)
+ add_definitions("-DEIGEN_KLU_SUPPORT")
+ include_directories(${KLU_INCLUDES})
+ set(SPARSE_LIBS ${SPARSE_LIBS} ${KLU_LIBRARIES} ${EIGEN_BLAS_LIBRARIES})
+ set(KLU_ALL_LIBS ${KLU_LIBRARIES} ${EIGEN_BLAS_LIBRARIES})
+ ei_add_property(EIGEN_TESTED_BACKENDS "KLU, ")
+
+ ei_add_test(klu_support "" "${KLU_ALL_LIBS}")
+else()
+ ei_add_property(EIGEN_MISSING_BACKENDS "KLU, ")
+endif()
+
+find_package(SuperLU 4.0)
+if(SuperLU_FOUND AND EIGEN_BUILD_BLAS)
+ add_definitions("-DEIGEN_SUPERLU_SUPPORT")
+ include_directories(${SUPERLU_INCLUDES})
+ set(SPARSE_LIBS ${SPARSE_LIBS} ${SUPERLU_LIBRARIES} ${EIGEN_BLAS_LIBRARIES})
+ set(SUPERLU_ALL_LIBS ${SUPERLU_LIBRARIES} ${EIGEN_BLAS_LIBRARIES})
+ ei_add_property(EIGEN_TESTED_BACKENDS "SuperLU, ")
+
+ ei_add_test(superlu_support "" "${SUPERLU_ALL_LIBS}")
+else()
+ ei_add_property(EIGEN_MISSING_BACKENDS "SuperLU, ")
+endif()
+
+
+find_package(PASTIX QUIET COMPONENTS METIS SEQ)
+# check that the PASTIX found is a version without MPI
+find_path(PASTIX_pastix_nompi.h_INCLUDE_DIRS
+ NAMES pastix_nompi.h
+ HINTS ${PASTIX_INCLUDE_DIRS}
+)
+if (NOT PASTIX_pastix_nompi.h_INCLUDE_DIRS)
+ message(STATUS "A version of Pastix has been found but pastix_nompi.h does not exist in the include directory."
+ " Because Eigen tests require a version without MPI, we disable the Pastix backend.")
+endif()
+if(PASTIX_FOUND AND PASTIX_pastix_nompi.h_INCLUDE_DIRS)
+ add_definitions("-DEIGEN_PASTIX_SUPPORT")
+ include_directories(${PASTIX_INCLUDE_DIRS_DEP})
+ if(SCOTCH_FOUND)
+ include_directories(${SCOTCH_INCLUDE_DIRS})
+ set(PASTIX_LIBRARIES ${PASTIX_LIBRARIES} ${SCOTCH_LIBRARIES})
+ elseif(METIS_FOUND)
+ include_directories(${METIS_INCLUDE_DIRS})
+ set(PASTIX_LIBRARIES ${PASTIX_LIBRARIES} ${METIS_LIBRARIES})
+ else()
+ ei_add_property(EIGEN_MISSING_BACKENDS "PaStiX, ")
+ endif()
+ set(SPARSE_LIBS ${SPARSE_LIBS} ${PASTIX_LIBRARIES_DEP} ${ORDERING_LIBRARIES})
+ set(PASTIX_ALL_LIBS ${PASTIX_LIBRARIES_DEP})
+ ei_add_property(EIGEN_TESTED_BACKENDS "PaStiX, ")
+else()
+ ei_add_property(EIGEN_MISSING_BACKENDS "PaStiX, ")
+endif()
+
+if(METIS_FOUND)
+ add_definitions("-DEIGEN_METIS_SUPPORT")
+ include_directories(${METIS_INCLUDE_DIRS})
+ ei_add_property(EIGEN_TESTED_BACKENDS "METIS, ")
+else()
+ ei_add_property(EIGEN_MISSING_BACKENDS "METIS, ")
+endif()
+
+find_package(SPQR)
+if(SPQR_FOUND AND CHOLMOD_FOUND AND EIGEN_BUILD_BLAS AND EIGEN_BUILD_LAPACK AND (EIGEN_Fortran_COMPILER_WORKS OR LAPACK_FOUND) )
+ add_definitions("-DEIGEN_SPQR_SUPPORT")
+ include_directories(${SPQR_INCLUDES})
+ set(SPQR_ALL_LIBS ${SPQR_LIBRARIES} ${CHOLMOD_LIBRARIES} ${EIGEN_LAPACK_LIBRARIES} ${EIGEN_BLAS_LIBRARIES} ${LAPACK_LIBRARIES})
+ set(SPARSE_LIBS ${SPARSE_LIBS} ${SPQR_ALL_LIBS})
+ ei_add_property(EIGEN_TESTED_BACKENDS "SPQR, ")
+else()
+ ei_add_property(EIGEN_MISSING_BACKENDS "SPQR, ")
+endif()
+
+find_package(Accelerate)
+if(Accelerate_FOUND)
+ add_definitions("-DEIGEN_ACCELERATE_SUPPORT")
+ include_directories(${Accelerate_INCLUDES})
+ set(SPARSE_LIBS ${SPARSE_LIBS} ${Accelerate_LIBRARIES})
+ set(Accelerate_ALL_LIBS ${Accelerate_LIBRARIES})
+ ei_add_property(EIGEN_TESTED_BACKENDS "Accelerate, ")
+else()
+ ei_add_property(EIGEN_MISSING_BACKENDS "Accelerate, ")
+endif()
+
+option(EIGEN_TEST_NOQT "Disable Qt support in unit tests" OFF)
+if(NOT EIGEN_TEST_NOQT)
+ find_package(Qt4)
+ if(QT4_FOUND)
+ include(${QT_USE_FILE})
+ ei_add_property(EIGEN_TESTED_BACKENDS "Qt4 support, ")
+ else()
+ ei_add_property(EIGEN_MISSING_BACKENDS "Qt4 support, ")
+ endif()
+endif()
+
+if(TEST_LIB)
+ add_definitions("-DEIGEN_EXTERN_INSTANTIATIONS=1")
+endif()
+
+set_property(GLOBAL PROPERTY EIGEN_CURRENT_SUBPROJECT "Official")
+add_custom_target(BuildOfficial)
+
+ei_add_test(rand)
+ei_add_test(meta)
+ei_add_test(numext)
+ei_add_test(sizeof)
+ei_add_test(dynalloc)
+ei_add_test(nomalloc)
+ei_add_test(first_aligned)
+ei_add_test(type_alias)
+ei_add_test(nullary)
+ei_add_test(mixingtypes)
+ei_add_test(io)
+ei_add_test(packetmath "-DEIGEN_FAST_MATH=1")
+ei_add_test(vectorization_logic)
+ei_add_test(basicstuff)
+ei_add_test(constructor)
+ei_add_test(linearstructure)
+ei_add_test(integer_types)
+ei_add_test(unalignedcount)
+if(NOT EIGEN_TEST_NO_EXCEPTIONS AND NOT EIGEN_TEST_OPENMP)
+ ei_add_test(exceptions)
+endif()
+ei_add_test(redux)
+ei_add_test(visitor)
+ei_add_test(block)
+ei_add_test(corners)
+ei_add_test(symbolic_index)
+ei_add_test(indexed_view)
+ei_add_test(reshape)
+ei_add_test(swap)
+ei_add_test(resize)
+ei_add_test(conservative_resize)
+ei_add_test(product_small)
+ei_add_test(product_large)
+ei_add_test(product_extra)
+ei_add_test(diagonalmatrices)
+ei_add_test(skew_symmetric_matrix3)
+ei_add_test(adjoint)
+ei_add_test(diagonal)
+ei_add_test(miscmatrices)
+ei_add_test(commainitializer)
+ei_add_test(smallvectors)
+ei_add_test(mapped_matrix)
+ei_add_test(mapstride)
+ei_add_test(unaryviewstride)
+ei_add_test(mapstaticmethods)
+ei_add_test(array_cwise)
+ei_add_test(array_for_matrix)
+ei_add_test(array_replicate)
+ei_add_test(array_reverse)
+ei_add_test(ref)
+ei_add_test(is_same_dense)
+ei_add_test(triangular)
+ei_add_test(selfadjoint)
+ei_add_test(product_selfadjoint)
+ei_add_test(product_symm)
+ei_add_test(product_syrk)
+ei_add_test(product_trmv)
+ei_add_test(product_trmm)
+ei_add_test(product_trsolve)
+ei_add_test(product_mmtr)
+ei_add_test(product_notemporary)
+ei_add_test(stable_norm)
+ei_add_test(permutationmatrices)
+ei_add_test(bandmatrix)
+ei_add_test(cholesky)
+ei_add_test(lu)
+ei_add_test(determinant)
+ei_add_test(inverse)
+ei_add_test(qr)
+ei_add_test(qr_colpivoting)
+ei_add_test(qr_fullpivoting)
+ei_add_test(upperbidiagonalization)
+ei_add_test(hessenberg)
+ei_add_test(schur_real)
+ei_add_test(schur_complex)
+ei_add_test(eigensolver_selfadjoint)
+ei_add_test(eigensolver_generic)
+ei_add_test(eigensolver_complex)
+ei_add_test(real_qz)
+ei_add_test(eigensolver_generalized_real)
+ei_add_test(jacobi)
+ei_add_test(jacobisvd)
+ei_add_test(bdcsvd)
+ei_add_test(householder)
+ei_add_test(geo_orthomethods)
+ei_add_test(geo_quaternion)
+ei_add_test(geo_eulerangles)
+ei_add_test(geo_parametrizedline)
+ei_add_test(geo_alignedbox)
+ei_add_test(geo_hyperplane)
+ei_add_test(geo_transformations)
+ei_add_test(geo_homogeneous)
+ei_add_test(stdvector)
+ei_add_test(stdvector_overload)
+ei_add_test(stdlist)
+ei_add_test(stdlist_overload)
+ei_add_test(stddeque)
+ei_add_test(stddeque_overload)
+ei_add_test(sparse_basic)
+ei_add_test(sparse_block)
+ei_add_test(sparse_vector)
+ei_add_test(sparse_product)
+ei_add_test(sparse_ref)
+ei_add_test(sparse_solvers)
+ei_add_test(sparse_permutations)
+ei_add_test(simplicial_cholesky)
+ei_add_test(conjugate_gradient)
+ei_add_test(incomplete_cholesky)
+ei_add_test(bicgstab)
+ei_add_test(lscg)
+ei_add_test(sparselu)
+ei_add_test(sparseqr)
+ei_add_test(umeyama)
+ei_add_test(nesting_ops "${CMAKE_CXX_FLAGS_DEBUG}")
+ei_add_test(nestbyvalue)
+ei_add_test(zerosized)
+ei_add_test(dontalign)
+ei_add_test(evaluators)
+if(NOT EIGEN_TEST_NO_EXCEPTIONS)
+ ei_add_test(sizeoverflow)
+endif()
+ei_add_test(prec_inverse_4x4)
+ei_add_test(vectorwiseop)
+ei_add_test(special_numbers)
+ei_add_test(rvalue_types)
+ei_add_test(dense_storage)
+ei_add_test(ctorleak)
+ei_add_test(mpl2only)
+ei_add_test(inplace_decomposition)
+ei_add_test(half_float)
+ei_add_test(bfloat16_float)
+ei_add_test(array_of_string)
+ei_add_test(num_dimensions)
+ei_add_test(stl_iterators)
+ei_add_test(blasutil)
+ei_add_test(random_matrix)
+ei_add_test(initializer_list_construction)
+ei_add_test(diagonal_matrix_variadic_ctor)
+ei_add_test(serializer)
+ei_add_test(tuple_test)
+
+add_executable(bug1213 bug1213.cpp bug1213_main.cpp)
+
+check_cxx_compiler_flag("-ffast-math" COMPILER_SUPPORT_FASTMATH)
+if(COMPILER_SUPPORT_FASTMATH)
+ set(EIGEN_FASTMATH_FLAGS "-ffast-math")
+else()
+ check_cxx_compiler_flag("/fp:fast" COMPILER_SUPPORT_FPFAST)
+ if(COMPILER_SUPPORT_FPFAST)
+ set(EIGEN_FASTMATH_FLAGS "/fp:fast")
+ endif()
+endif()
+
+ei_add_test(fastmath "${EIGEN_FASTMATH_FLAGS}")
+
+# # ei_add_test(denseLM)
+
+if(QT4_FOUND)
+ ei_add_test(qtvector "" "${QT_QTCORE_LIBRARY}")
+endif()
+
+if(PARDISO_FOUND)
+ ei_add_test(pardiso_support "" "${PARDISO_ALL_LIBS}")
+endif()
+
+if(PASTIX_FOUND AND (SCOTCH_FOUND OR METIS_FOUND))
+ ei_add_test(pastix_support "" "${PASTIX_ALL_LIBS}")
+endif()
+
+if(SPQR_FOUND AND CHOLMOD_FOUND AND EIGEN_BUILD_BLAS AND EIGEN_BUILD_LAPACK)
+ ei_add_test(spqr_support "" "${SPQR_ALL_LIBS}")
+endif()
+
+if(METIS_FOUND)
+ei_add_test(metis_support "" "${METIS_LIBRARIES}")
+endif()
+
+if(Accelerate_FOUND)
+ ei_add_test(accelerate_support "" "${Accelerate_ALL_LIBS}")
+endif()
+
+string(TOLOWER "${CMAKE_CXX_COMPILER}" cmake_cxx_compiler_tolower)
+if(cmake_cxx_compiler_tolower MATCHES "qcc")
+ set(CXX_IS_QCC "ON")
+endif()
+
+ei_add_property(EIGEN_TESTING_SUMMARY "CXX: ${CMAKE_CXX_COMPILER}\n")
+if(CMAKE_COMPILER_IS_GNUCXX AND NOT CXX_IS_QCC)
+ execute_process(COMMAND ${CMAKE_CXX_COMPILER} --version COMMAND head -n 1 OUTPUT_VARIABLE EIGEN_CXX_VERSION_STRING OUTPUT_STRIP_TRAILING_WHITESPACE)
+ ei_add_property(EIGEN_TESTING_SUMMARY "CXX_VERSION: ${EIGEN_CXX_VERSION_STRING}\n")
+endif()
+ei_add_property(EIGEN_TESTING_SUMMARY "CXX_FLAGS: ${CMAKE_CXX_FLAGS}\n")
+if (EIGEN_TEST_CUSTOM_CXX_FLAGS)
+ ei_add_property(EIGEN_TESTING_SUMMARY "Custom CXX flags: ${EIGEN_TEST_CUSTOM_CXX_FLAGS}\n")
+endif()
+ei_add_property(EIGEN_TESTING_SUMMARY "Sparse lib flags: ${SPARSE_LIBS}\n")
+
+option(EIGEN_TEST_EIGEN2 "Run whole Eigen2 test suite against EIGEN2_SUPPORT" OFF)
+mark_as_advanced(EIGEN_TEST_EIGEN2)
+if(EIGEN_TEST_EIGEN2)
+ message(WARNING "The Eigen2 test suite has been removed")
+endif()
+
+# boost MP unit test
+find_package(Boost 1.53.0)
+if(Boost_FOUND)
+ include_directories(${Boost_INCLUDE_DIRS})
+ ei_add_test(boostmultiprec "" "${Boost_LIBRARIES}")
+ ei_add_property(EIGEN_TESTED_BACKENDS "Boost.Multiprecision, ")
+else()
+ ei_add_property(EIGEN_MISSING_BACKENDS "Boost.Multiprecision, ")
+endif()
+
+
+# CUDA unit tests
+option(EIGEN_TEST_CUDA "Enable CUDA support in unit tests" OFF)
+option(EIGEN_TEST_CUDA_CLANG "Use clang instead of nvcc to compile the CUDA tests" OFF)
+
+if(EIGEN_TEST_CUDA_CLANG AND NOT CMAKE_CXX_COMPILER MATCHES "clang")
+ message(WARNING "EIGEN_TEST_CUDA_CLANG is set, but CMAKE_CXX_COMPILER does not appear to be clang.")
+endif()
+
+find_package(CUDA 9.0)
+if(CUDA_FOUND AND EIGEN_TEST_CUDA)
+ # Make sure to compile without the -pedantic, -Wundef, -Wnon-virtual-dtor
+ # and -fno-check-new flags since they trigger thousands of compilation warnings
+ # in the CUDA runtime
+ string(REPLACE "-pedantic" "" CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS}")
+ string(REPLACE "-Wundef" "" CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS}")
+ string(REPLACE "-Wnon-virtual-dtor" "" CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS}")
+ string(REPLACE "-fno-check-new" "" CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS}")
+
+ if(EIGEN_TEST_CUDA_CLANG)
+ string(APPEND CMAKE_CXX_FLAGS " --cuda-path=${CUDA_TOOLKIT_ROOT_DIR}")
+ foreach(GPU IN LISTS EIGEN_CUDA_COMPUTE_ARCH)
+ string(APPEND CMAKE_CXX_FLAGS " --cuda-gpu-arch=sm_${GPU}")
+ endforeach()
+ string(APPEND CMAKE_CXX_FLAGS " ${EIGEN_CUDA_CXX_FLAGS}")
+ else()
+ set(CUDA_PROPAGATE_HOST_FLAGS OFF)
+ set(NVCC_ARCH_FLAGS)
+ # Define an -arch=sm_<arch>, otherwise if GPU does not exactly match one of
+ # those in the arch list for -gencode, the kernels will fail to run with
+ # cudaErrorNoKernelImageForDevice
+ # This can happen with newer cards (e.g. sm_75) and compiling with older
+ # versions of nvcc (e.g. 9.2) that do not support their specific arch.
+ list(LENGTH EIGEN_CUDA_COMPUTE_ARCH EIGEN_CUDA_COMPUTE_ARCH_SIZE)
+ if(EIGEN_CUDA_COMPUTE_ARCH_SIZE)
+ list(GET EIGEN_CUDA_COMPUTE_ARCH 0 EIGEN_CUDA_COMPUTE_DEFAULT)
+ set(NVCC_ARCH_FLAGS " -arch=sm_${EIGEN_CUDA_COMPUTE_DEFAULT}")
+ endif()
+ foreach(ARCH IN LISTS EIGEN_CUDA_COMPUTE_ARCH)
+ string(APPEND NVCC_ARCH_FLAGS " -gencode arch=compute_${ARCH},code=sm_${ARCH}")
+ endforeach()
+ set(CUDA_NVCC_FLAGS "--expt-relaxed-constexpr -Xcudafe \"--display_error_number\" ${NVCC_ARCH_FLAGS} ${CUDA_NVCC_FLAGS} ${EIGEN_CUDA_CXX_FLAGS}")
+ cuda_include_directories("${CMAKE_CURRENT_BINARY_DIR}" "${CUDA_TOOLKIT_ROOT_DIR}/include")
+ endif()
+
+ set(EIGEN_ADD_TEST_FILENAME_EXTENSION "cu")
+
+ ei_add_test(gpu_example)
+ ei_add_test(gpu_basic)
+
+ unset(EIGEN_ADD_TEST_FILENAME_EXTENSION)
+
+endif()
+
+
+# HIP unit tests
+option(EIGEN_TEST_HIP "Add HIP support." OFF)
+if (EIGEN_TEST_HIP)
+
+ set(HIP_PATH "/opt/rocm/hip" CACHE STRING "Path to the HIP installation.")
+
+ if (EXISTS ${HIP_PATH})
+
+ list(APPEND CMAKE_MODULE_PATH ${HIP_PATH}/cmake)
+
+ find_package(HIP REQUIRED)
+ if (HIP_FOUND)
+
+ execute_process(COMMAND ${HIP_PATH}/bin/hipconfig --platform OUTPUT_VARIABLE HIP_PLATFORM)
+
+ if ((${HIP_PLATFORM} STREQUAL "hcc") OR (${HIP_PLATFORM} STREQUAL "amd"))
+
+ include_directories(${HIP_PATH}/include)
+
+ set(EIGEN_ADD_TEST_FILENAME_EXTENSION "cu")
+ ei_add_test(gpu_basic)
+ ei_add_test(gpu_example)
+ unset(EIGEN_ADD_TEST_FILENAME_EXTENSION)
+
+ elseif ((${HIP_PLATFORM} STREQUAL "nvcc") OR (${HIP_PLATFORM} STREQUAL "nvidia"))
+ message(FATAL_ERROR "HIP_PLATFORM = nvcc is not supported within Eigen")
+ else ()
+ message(FATAL_ERROR "Unknown HIP_PLATFORM = ${HIP_PLATFORM}")
+ endif()
+ endif()
+ else ()
+ message(FATAL_ERROR "EIGEN_TEST_HIP is ON, but the specified HIP_PATH (${HIP_PATH}) does not exist")
+ endif()
+endif()
+
+cmake_dependent_option(EIGEN_TEST_BUILD_DOCUMENTATION "Test building the doxygen documentation" OFF "EIGEN_BUILD_DOC" OFF)
+if(EIGEN_TEST_BUILD_DOCUMENTATION)
+ add_dependencies(buildtests doc)
+endif()
+
+# Register all smoke tests
+include("EigenSmokeTestList")
+ei_add_smoke_tests("${ei_smoke_test_list}")
diff --git a/test/MovableScalar.h b/test/MovableScalar.h
new file mode 100644
index 0000000..6a90d03
--- /dev/null
+++ b/test/MovableScalar.h
@@ -0,0 +1,35 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2020 Sebastien Boisvert <seb@boisvert.info>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_MISC_MOVABLE_SCALAR_H
+#define EIGEN_MISC_MOVABLE_SCALAR_H
+
+#include <vector>
+
+namespace Eigen
+{
+template <typename Scalar, typename Base = std::vector<Scalar>>
+struct MovableScalar : public Base
+{
+ MovableScalar() = default;
+ ~MovableScalar() = default;
+ MovableScalar(const MovableScalar&) = default;
+ MovableScalar(MovableScalar&& other) = default;
+ MovableScalar& operator=(const MovableScalar&) = default;
+ MovableScalar& operator=(MovableScalar&& other) = default;
+ MovableScalar(Scalar scalar) : Base(100, scalar) {}
+
+ operator Scalar() const { return this->size() > 0 ? this->back() : Scalar(); }
+};
+
+template<> struct NumTraits<MovableScalar<float>> : GenericNumTraits<float> {};
+}
+
+#endif
+
diff --git a/test/OffByOneScalar.h b/test/OffByOneScalar.h
new file mode 100644
index 0000000..c0371a6
--- /dev/null
+++ b/test/OffByOneScalar.h
@@ -0,0 +1,28 @@
+
+// A Scalar with internal representation T+1 so that zero is internally
+// represented by T(1). This is used to test memory fill.
+//
+template<typename T>
+class OffByOneScalar {
+ public:
+ OffByOneScalar() : val_(1) {}
+ OffByOneScalar(const OffByOneScalar& other) {
+ *this = other;
+ }
+ OffByOneScalar& operator=(const OffByOneScalar& other) {
+ val_ = other.val_;
+ return *this;
+ }
+
+ OffByOneScalar(T val) : val_(val + 1) {}
+ OffByOneScalar& operator=(T val) {
+ val_ = val + 1;
+ }
+
+ operator T() const {
+ return val_ - 1;
+ }
+
+ private:
+ T val_;
+};
diff --git a/test/SafeScalar.h b/test/SafeScalar.h
new file mode 100644
index 0000000..c5cb757
--- /dev/null
+++ b/test/SafeScalar.h
@@ -0,0 +1,30 @@
+
+// A Scalar that asserts for uninitialized access.
+template<typename T>
+class SafeScalar {
+ public:
+ SafeScalar() : initialized_(false) {}
+ SafeScalar(const SafeScalar& other) {
+ *this = other;
+ }
+ SafeScalar& operator=(const SafeScalar& other) {
+ val_ = T(other);
+ initialized_ = true;
+ return *this;
+ }
+
+ SafeScalar(T val) : val_(val), initialized_(true) {}
+ SafeScalar& operator=(T val) {
+ val_ = val;
+ initialized_ = true;
+ }
+
+ operator T() const {
+ VERIFY(initialized_ && "Uninitialized access.");
+ return val_;
+ }
+
+ private:
+ T val_;
+ bool initialized_;
+};
diff --git a/test/accelerate_support.cpp b/test/accelerate_support.cpp
new file mode 100644
index 0000000..ac4be61
--- /dev/null
+++ b/test/accelerate_support.cpp
@@ -0,0 +1,176 @@
+#define EIGEN_NO_DEBUG_SMALL_PRODUCT_BLOCKS
+#include "sparse_solver.h"
+
+#if defined(DEBUG)
+#undef DEBUG
+#endif
+
+#include <Eigen/AccelerateSupport>
+
+template<typename MatrixType,typename DenseMat>
+int generate_sparse_rectangular_problem(MatrixType& A, DenseMat& dA, int maxRows = 300, int maxCols = 300)
+{
+ typedef typename MatrixType::Scalar Scalar;
+ int rows = internal::random<int>(1, maxRows);
+ int cols = internal::random<int>(1, maxCols);
+ double density = (std::max)(8.0 / (rows * cols), 0.01);
+
+ A.resize(rows,cols);
+ dA.resize(rows,cols);
+ initSparse<Scalar>(density, dA, A, ForceNonZeroDiag);
+ A.makeCompressed();
+ return rows;
+}
+
+template<typename MatrixType,typename DenseMat>
+int generate_sparse_square_symmetric_problem(MatrixType& A, DenseMat& dA, int maxSize = 300)
+{
+ typedef typename MatrixType::Scalar Scalar;
+ int rows = internal::random<int>(1, maxSize);
+ int cols = rows;
+ double density = (std::max)(8.0 / (rows * cols), 0.01);
+
+ A.resize(rows,cols);
+ dA.resize(rows,cols);
+ initSparse<Scalar>(density, dA, A, ForceNonZeroDiag);
+ dA = dA * dA.transpose();
+ A = A * A.transpose();
+ A.makeCompressed();
+ return rows;
+}
+
+template<typename Scalar, typename Solver> void test_accelerate_ldlt()
+{
+ typedef SparseMatrix<Scalar> MatrixType;
+ typedef Matrix<Scalar,Dynamic,1> DenseVector;
+
+ MatrixType A;
+ Matrix<Scalar,Dynamic,Dynamic> dA;
+
+ generate_sparse_square_symmetric_problem(A, dA);
+
+ DenseVector b = DenseVector::Random(A.rows());
+
+ Solver solver;
+ solver.compute(A);
+
+ if (solver.info() != Success)
+ {
+ std::cerr << "sparse LDLT factorization failed\n";
+ exit(0);
+ return;
+ }
+
+ DenseVector x = solver.solve(b);
+
+ if (solver.info() != Success)
+ {
+ std::cerr << "sparse LDLT factorization failed\n";
+ exit(0);
+ return;
+ }
+
+ //Compare with a dense solver
+ DenseVector refX = dA.ldlt().solve(b);
+ VERIFY((A * x).isApprox(A * refX, test_precision<Scalar>()));
+}
+
+template<typename Scalar, typename Solver> void test_accelerate_llt()
+{
+ typedef SparseMatrix<Scalar> MatrixType;
+ typedef Matrix<Scalar,Dynamic,1> DenseVector;
+
+ MatrixType A;
+ Matrix<Scalar,Dynamic,Dynamic> dA;
+
+ generate_sparse_square_symmetric_problem(A, dA);
+
+ DenseVector b = DenseVector::Random(A.rows());
+
+ Solver solver;
+ solver.compute(A);
+
+ if (solver.info() != Success)
+ {
+ std::cerr << "sparse LLT factorization failed\n";
+ exit(0);
+ return;
+ }
+
+ DenseVector x = solver.solve(b);
+
+ if (solver.info() != Success)
+ {
+ std::cerr << "sparse LLT factorization failed\n";
+ exit(0);
+ return;
+ }
+
+ //Compare with a dense solver
+ DenseVector refX = dA.llt().solve(b);
+ VERIFY((A * x).isApprox(A * refX, test_precision<Scalar>()));
+}
+
+template<typename Scalar, typename Solver> void test_accelerate_qr()
+{
+ typedef SparseMatrix<Scalar> MatrixType;
+ typedef Matrix<Scalar,Dynamic,1> DenseVector;
+
+ MatrixType A;
+ Matrix<Scalar,Dynamic,Dynamic> dA;
+
+ generate_sparse_rectangular_problem(A, dA);
+
+ DenseVector b = DenseVector::Random(A.rows());
+
+ Solver solver;
+ solver.compute(A);
+
+ if (solver.info() != Success)
+ {
+ std::cerr << "sparse QR factorization failed\n";
+ exit(0);
+ return;
+ }
+
+ DenseVector x = solver.solve(b);
+
+ if (solver.info() != Success)
+ {
+ std::cerr << "sparse QR factorization failed\n";
+ exit(0);
+ return;
+ }
+
+ //Compare with a dense solver
+ DenseVector refX = dA.colPivHouseholderQr().solve(b);
+ VERIFY((A * x).isApprox(A * refX, test_precision<Scalar>()));
+}
+
+template<typename Scalar>
+void run_tests()
+{
+ typedef SparseMatrix<Scalar> MatrixType;
+
+ test_accelerate_ldlt<Scalar, AccelerateLDLT<MatrixType, Lower> >();
+ test_accelerate_ldlt<Scalar, AccelerateLDLTUnpivoted<MatrixType, Lower> >();
+ test_accelerate_ldlt<Scalar, AccelerateLDLTSBK<MatrixType, Lower> >();
+ test_accelerate_ldlt<Scalar, AccelerateLDLTTPP<MatrixType, Lower> >();
+
+ test_accelerate_ldlt<Scalar, AccelerateLDLT<MatrixType, Upper> >();
+ test_accelerate_ldlt<Scalar, AccelerateLDLTUnpivoted<MatrixType, Upper> >();
+ test_accelerate_ldlt<Scalar, AccelerateLDLTSBK<MatrixType, Upper> >();
+ test_accelerate_ldlt<Scalar, AccelerateLDLTTPP<MatrixType, Upper> >();
+
+ test_accelerate_llt<Scalar, AccelerateLLT<MatrixType, Lower> >();
+
+ test_accelerate_llt<Scalar, AccelerateLLT<MatrixType, Upper> >();
+
+ test_accelerate_qr<Scalar, AccelerateQR<MatrixType> >();
+}
+
+EIGEN_DECLARE_TEST(accelerate_support)
+{
+ CALL_SUBTEST_1(run_tests<float>());
+ CALL_SUBTEST_2(run_tests<double>());
+}
diff --git a/test/adjoint.cpp b/test/adjoint.cpp
new file mode 100644
index 0000000..210a4d9
--- /dev/null
+++ b/test/adjoint.cpp
@@ -0,0 +1,233 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "main.h"
+
+template<bool IsInteger> struct adjoint_specific;
+
+template<> struct adjoint_specific<true> {
+ template<typename Vec, typename Mat, typename Scalar>
+ static void run(const Vec& v1, const Vec& v2, Vec& v3, const Mat& square, Scalar s1, Scalar s2) {
+ VERIFY(test_isApproxWithRef((s1 * v1 + s2 * v2).dot(v3), numext::conj(s1) * v1.dot(v3) + numext::conj(s2) * v2.dot(v3), 0));
+ VERIFY(test_isApproxWithRef(v3.dot(s1 * v1 + s2 * v2), s1*v3.dot(v1)+s2*v3.dot(v2), 0));
+
+ // check compatibility of dot and adjoint
+ VERIFY(test_isApproxWithRef(v1.dot(square * v2), (square.adjoint() * v1).dot(v2), 0));
+ }
+};
+
+template<> struct adjoint_specific<false> {
+ template<typename Vec, typename Mat, typename Scalar>
+ static void run(const Vec& v1, const Vec& v2, Vec& v3, const Mat& square, Scalar s1, Scalar s2) {
+ typedef typename NumTraits<Scalar>::Real RealScalar;
+ using std::abs;
+
+ RealScalar ref = NumTraits<Scalar>::IsInteger ? RealScalar(0) : (std::max)((s1 * v1 + s2 * v2).norm(),v3.norm());
+ VERIFY(test_isApproxWithRef((s1 * v1 + s2 * v2).dot(v3), numext::conj(s1) * v1.dot(v3) + numext::conj(s2) * v2.dot(v3), ref));
+ VERIFY(test_isApproxWithRef(v3.dot(s1 * v1 + s2 * v2), s1*v3.dot(v1)+s2*v3.dot(v2), ref));
+
+ VERIFY_IS_APPROX(v1.squaredNorm(), v1.norm() * v1.norm());
+ // check normalized() and normalize()
+ VERIFY_IS_APPROX(v1, v1.norm() * v1.normalized());
+ v3 = v1;
+ v3.normalize();
+ VERIFY_IS_APPROX(v1, v1.norm() * v3);
+ VERIFY_IS_APPROX(v3, v1.normalized());
+ VERIFY_IS_APPROX(v3.norm(), RealScalar(1));
+
+ // check null inputs
+ VERIFY_IS_APPROX((v1*0).normalized(), (v1*0));
+#if (!EIGEN_ARCH_i386) || defined(EIGEN_VECTORIZE)
+ RealScalar very_small = (std::numeric_limits<RealScalar>::min)();
+ VERIFY( numext::is_exactly_zero((v1*very_small).norm()) );
+ VERIFY_IS_APPROX((v1*very_small).normalized(), (v1*very_small));
+ v3 = v1*very_small;
+ v3.normalize();
+ VERIFY_IS_APPROX(v3, (v1*very_small));
+#endif
+
+ // check compatibility of dot and adjoint
+ ref = NumTraits<Scalar>::IsInteger ? 0 : (std::max)((std::max)(v1.norm(),v2.norm()),(std::max)((square * v2).norm(),(square.adjoint() * v1).norm()));
+ VERIFY(internal::isMuchSmallerThan(abs(v1.dot(square * v2) - (square.adjoint() * v1).dot(v2)), ref, test_precision<Scalar>()));
+
+ // check that Random().normalized() works: tricky as the random xpr must be evaluated by
+ // normalized() in order to produce a consistent result.
+ VERIFY_IS_APPROX(Vec::Random(v1.size()).normalized().norm(), RealScalar(1));
+ }
+};
+
+template<typename MatrixType, typename Scalar = typename MatrixType::Scalar>
+MatrixType RandomMatrix(int rows, int cols, Scalar min, Scalar max) {
+ MatrixType M = MatrixType(rows, cols);
+ for (int i=0; i<rows; ++i) {
+ for (int j=0; j<cols; ++j) {
+ M(i, j) = Eigen::internal::random<Scalar>(min, max);
+ }
+ }
+ return M;
+}
+
+template<typename MatrixType> void adjoint(const MatrixType& m)
+{
+ /* this test covers the following files:
+ Transpose.h Conjugate.h Dot.h
+ */
+ using std::abs;
+ typedef typename MatrixType::Scalar Scalar;
+ typedef typename NumTraits<Scalar>::Real RealScalar;
+ typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> VectorType;
+ typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime> SquareMatrixType;
+ const Index PacketSize = internal::packet_traits<Scalar>::size;
+
+ Index rows = m.rows();
+ Index cols = m.cols();
+
+ // Avoid integer overflow by limiting input values.
+ RealScalar rmin = static_cast<RealScalar>(NumTraits<Scalar>::IsInteger ? NumTraits<Scalar>::IsSigned ? -100 : 0 : -1);
+ RealScalar rmax = static_cast<RealScalar>(NumTraits<Scalar>::IsInteger ? 100 : 1);
+
+ MatrixType m1 = RandomMatrix<MatrixType>(rows, cols, rmin, rmax),
+ m2 = RandomMatrix<MatrixType>(rows, cols, rmin, rmax),
+ m3(rows, cols),
+ square = RandomMatrix<SquareMatrixType>(rows, rows, rmin, rmax);
+ VectorType v1 = RandomMatrix<VectorType>(rows, 1, rmin, rmax),
+ v2 = RandomMatrix<VectorType>(rows, 1, rmin, rmax),
+ v3 = RandomMatrix<VectorType>(rows, 1, rmin, rmax),
+ vzero = VectorType::Zero(rows);
+
+ Scalar s1 = internal::random<Scalar>(rmin, rmax),
+ s2 = internal::random<Scalar>(rmin, rmax);
+
+ // check basic compatibility of adjoint, transpose, conjugate
+ VERIFY_IS_APPROX(m1.transpose().conjugate().adjoint(), m1);
+ VERIFY_IS_APPROX(m1.adjoint().conjugate().transpose(), m1);
+
+ // check multiplicative behavior
+ VERIFY_IS_APPROX((m1.adjoint() * m2).adjoint(), m2.adjoint() * m1);
+ VERIFY_IS_APPROX((s1 * m1).adjoint(), numext::conj(s1) * m1.adjoint());
+
+ // check basic properties of dot, squaredNorm
+ VERIFY_IS_APPROX(numext::conj(v1.dot(v2)), v2.dot(v1));
+ VERIFY_IS_APPROX(numext::real(v1.dot(v1)), v1.squaredNorm());
+
+ adjoint_specific<NumTraits<Scalar>::IsInteger>::run(v1, v2, v3, square, s1, s2);
+
+ VERIFY_IS_MUCH_SMALLER_THAN(abs(vzero.dot(v1)), static_cast<RealScalar>(1));
+
+ // like in testBasicStuff, test operator() to check const-qualification
+ Index r = internal::random<Index>(0, rows-1),
+ c = internal::random<Index>(0, cols-1);
+ VERIFY_IS_APPROX(m1.conjugate()(r,c), numext::conj(m1(r,c)));
+ VERIFY_IS_APPROX(m1.adjoint()(c,r), numext::conj(m1(r,c)));
+
+ // check inplace transpose
+ m3 = m1;
+ m3.transposeInPlace();
+ VERIFY_IS_APPROX(m3,m1.transpose());
+ m3.transposeInPlace();
+ VERIFY_IS_APPROX(m3,m1);
+
+ if(PacketSize<m3.rows() && PacketSize<m3.cols())
+ {
+ m3 = m1;
+ Index i = internal::random<Index>(0,m3.rows()-PacketSize);
+ Index j = internal::random<Index>(0,m3.cols()-PacketSize);
+ m3.template block<PacketSize,PacketSize>(i,j).transposeInPlace();
+ VERIFY_IS_APPROX( (m3.template block<PacketSize,PacketSize>(i,j)), (m1.template block<PacketSize,PacketSize>(i,j).transpose()) );
+ m3.template block<PacketSize,PacketSize>(i,j).transposeInPlace();
+ VERIFY_IS_APPROX(m3,m1);
+ }
+
+ // check inplace adjoint
+ m3 = m1;
+ m3.adjointInPlace();
+ VERIFY_IS_APPROX(m3,m1.adjoint());
+ m3.transposeInPlace();
+ VERIFY_IS_APPROX(m3,m1.conjugate());
+
+ // check mixed dot product
+ typedef Matrix<RealScalar, MatrixType::RowsAtCompileTime, 1> RealVectorType;
+ RealVectorType rv1 = RandomMatrix<RealVectorType>(rows, 1, rmin, rmax);
+
+ VERIFY_IS_APPROX(v1.dot(rv1.template cast<Scalar>()), v1.dot(rv1));
+ VERIFY_IS_APPROX(rv1.template cast<Scalar>().dot(v1), rv1.dot(v1));
+
+ VERIFY( is_same_type(m1,m1.template conjugateIf<false>()) );
+ VERIFY( is_same_type(m1.conjugate(),m1.template conjugateIf<true>()) );
+}
+
+template<int>
+void adjoint_extra()
+{
+ MatrixXcf a(10,10), b(10,10);
+ VERIFY_RAISES_ASSERT(a = a.transpose());
+ VERIFY_RAISES_ASSERT(a = a.transpose() + b);
+ VERIFY_RAISES_ASSERT(a = b + a.transpose());
+ VERIFY_RAISES_ASSERT(a = a.conjugate().transpose());
+ VERIFY_RAISES_ASSERT(a = a.adjoint());
+ VERIFY_RAISES_ASSERT(a = a.adjoint() + b);
+ VERIFY_RAISES_ASSERT(a = b + a.adjoint());
+
+ // no assertion should be triggered for these cases:
+ a.transpose() = a.transpose();
+ a.transpose() += a.transpose();
+ a.transpose() += a.transpose() + b;
+ a.transpose() = a.adjoint();
+ a.transpose() += a.adjoint();
+ a.transpose() += a.adjoint() + b;
+
+ // regression tests for check_for_aliasing
+ MatrixXd c(10,10);
+ c = 1.0 * MatrixXd::Ones(10,10) + c;
+ c = MatrixXd::Ones(10,10) * 1.0 + c;
+ c = c + MatrixXd::Ones(10,10) .cwiseProduct( MatrixXd::Zero(10,10) );
+ c = MatrixXd::Ones(10,10) * MatrixXd::Zero(10,10);
+
+ // regression for bug 1646
+ for (int j = 0; j < 10; ++j) {
+ c.col(j).head(j) = c.row(j).head(j);
+ }
+
+ for (int j = 0; j < 10; ++j) {
+ c.col(j) = c.row(j);
+ }
+
+ a.conservativeResize(1,1);
+ a = a.transpose();
+
+ a.conservativeResize(0,0);
+ a = a.transpose();
+}
+
+EIGEN_DECLARE_TEST(adjoint)
+{
+ for(int i = 0; i < g_repeat; i++) {
+ CALL_SUBTEST_1( adjoint(Matrix<float, 1, 1>()) );
+ CALL_SUBTEST_2( adjoint(Matrix3d()) );
+ CALL_SUBTEST_3( adjoint(Matrix4f()) );
+
+ CALL_SUBTEST_4( adjoint(MatrixXcf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE/2), internal::random<int>(1,EIGEN_TEST_MAX_SIZE/2))) );
+ CALL_SUBTEST_5( adjoint(MatrixXi(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
+ CALL_SUBTEST_6( adjoint(MatrixXf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
+
+ // Complement for 128 bits vectorization:
+ CALL_SUBTEST_8( adjoint(Matrix2d()) );
+ CALL_SUBTEST_9( adjoint(Matrix<int,4,4>()) );
+
+ // 256 bits vectorization:
+ CALL_SUBTEST_10( adjoint(Matrix<float,8,8>()) );
+ CALL_SUBTEST_11( adjoint(Matrix<double,4,4>()) );
+ CALL_SUBTEST_12( adjoint(Matrix<int,8,8>()) );
+ }
+ // test a large static matrix only once
+ CALL_SUBTEST_7( adjoint(Matrix<float, 100, 100>()) );
+
+ CALL_SUBTEST_13( adjoint_extra<0>() );
+}
+
diff --git a/test/array_cwise.cpp b/test/array_cwise.cpp
new file mode 100644
index 0000000..a7e0ff4
--- /dev/null
+++ b/test/array_cwise.cpp
@@ -0,0 +1,909 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include <vector>
+#include "main.h"
+
+template <typename Scalar>
+std::vector<Scalar> special_values() {
+ const Scalar zero = Scalar(0);
+ const Scalar eps = Eigen::NumTraits<Scalar>::epsilon();
+ const Scalar one = Scalar(1);
+ const Scalar two = Scalar(2);
+ const Scalar three = Scalar(3);
+ const Scalar sqrt_half = Scalar(std::sqrt(0.5));
+ const Scalar sqrt2 = Scalar(std::sqrt(2));
+ const Scalar inf = Eigen::NumTraits<Scalar>::infinity();
+ const Scalar nan = Eigen::NumTraits<Scalar>::quiet_NaN();
+ const Scalar denorm_min = std::numeric_limits<Scalar>::denorm_min();
+ const Scalar min = (std::numeric_limits<Scalar>::min)();
+ const Scalar max = (std::numeric_limits<Scalar>::max)();
+ const Scalar max_exp = (static_cast<Scalar>(int(Eigen::NumTraits<Scalar>::max_exponent())) * Scalar(EIGEN_LN2)) / eps;
+
+ return {zero, denorm_min, min, eps, sqrt_half, one, sqrt2, two, three, max_exp, max, inf, nan};
+}
+
+template<typename Scalar>
+void special_value_pairs(Array<Scalar, Dynamic, Dynamic>& x,
+ Array<Scalar, Dynamic, Dynamic>& y) {
+ std::vector<Scalar> abs_vals = special_values<Scalar>();
+ const int abs_cases = abs_vals.size();
+ const int num_cases = 2*abs_cases * 2*abs_cases;
+ // ensure both vectorized and non-vectorized paths taken
+ const int num_repeats = 2 * internal::packet_traits<Scalar>::size + 1;
+ x.resize(num_repeats, num_cases);
+ y.resize(num_repeats, num_cases);
+ int count = 0;
+ for (int i = 0; i < abs_cases; ++i) {
+ const Scalar abs_x = abs_vals[i];
+ for (int sign_x = 0; sign_x < 2; ++sign_x) {
+ Scalar x_case = sign_x == 0 ? -abs_x : abs_x;
+ for (int j = 0; j < abs_cases; ++j) {
+ const Scalar abs_y = abs_vals[j];
+ for (int sign_y = 0; sign_y < 2; ++sign_y) {
+ Scalar y_case = sign_y == 0 ? -abs_y : abs_y;
+ for (int repeat = 0; repeat < num_repeats; ++repeat) {
+ x(repeat, count) = x_case;
+ y(repeat, count) = y_case;
+ }
+ ++count;
+ }
+ }
+ }
+ }
+}
+
+template <typename Scalar, typename Fn, typename RefFn>
+void binary_op_test(std::string name, Fn fun, RefFn ref) {
+ const Scalar tol = test_precision<Scalar>();
+ Array<Scalar, Dynamic, Dynamic> x;
+ Array<Scalar, Dynamic, Dynamic> y;
+ special_value_pairs(x, y);
+
+ Array<Scalar, Dynamic, Dynamic> actual = fun(x, y);
+ bool all_pass = true;
+ for (int i = 0; i < x.rows(); ++i) {
+ for (int j = 0; j < x.cols(); ++j) {
+ Scalar e = static_cast<Scalar>(ref(x(i,j), y(i,j)));
+ Scalar a = actual(i, j);
+ bool success = (a==e) || ((numext::isfinite)(e) && internal::isApprox(a, e, tol)) || ((numext::isnan)(a) && (numext::isnan)(e));
+ all_pass &= success;
+ if (!success) {
+ std::cout << name << "(" << x(i,j) << "," << y(i,j) << ") = " << a << " != " << e << std::endl;
+ }
+ }
+ }
+ VERIFY(all_pass);
+}
+
+template <typename Scalar>
+void binary_ops_test() {
+ binary_op_test<Scalar>("pow",
+ [](auto x, auto y) { return Eigen::pow(x, y); },
+ [](auto x, auto y) { return std::pow(x, y); });
+ binary_op_test<Scalar>("atan2",
+ [](auto x, auto y) { return Eigen::atan2(x, y); },
+ [](auto x, auto y) { return std::atan2(x, y); });
+}
+
+template <typename Scalar>
+void pow_scalar_exponent_test() {
+ using Int_t = typename internal::make_integer<Scalar>::type;
+ const Scalar tol = test_precision<Scalar>();
+
+ std::vector<Scalar> abs_vals = special_values<Scalar>();
+ const int num_vals = abs_vals.size();
+ Map<Array<Scalar, Dynamic, 1>> bases(abs_vals.data(), num_vals);
+
+ bool all_pass = true;
+ for (Scalar abs_exponent : abs_vals) {
+ for (Scalar exponent : {-abs_exponent, abs_exponent}) {
+ // test integer exponent code path
+ bool exponent_is_integer = (numext::isfinite)(exponent) && (numext::round(exponent) == exponent) &&
+ (numext::abs(exponent) < static_cast<Scalar>(NumTraits<Int_t>::highest()));
+ if (exponent_is_integer) {
+ Int_t exponent_as_int = static_cast<Int_t>(exponent);
+ Array<Scalar, Dynamic, 1> eigenPow = bases.pow(exponent_as_int);
+ for (int j = 0; j < num_vals; j++) {
+ Scalar e = static_cast<Scalar>(std::pow(bases(j), exponent));
+ Scalar a = eigenPow(j);
+ bool success = (a == e) || ((numext::isfinite)(e) && internal::isApprox(a, e, tol)) ||
+ ((numext::isnan)(a) && (numext::isnan)(e));
+ all_pass &= success;
+ if (!success) {
+ std::cout << "pow(" << bases(j) << "," << exponent << ") = " << a << " != " << e << std::endl;
+ }
+ }
+ } else {
+ // test floating point exponent code path
+ Array<Scalar, Dynamic, 1> eigenPow = bases.pow(exponent);
+ for (int j = 0; j < num_vals; j++) {
+ Scalar e = static_cast<Scalar>(std::pow(bases(j), exponent));
+ Scalar a = eigenPow(j);
+ bool success = (a == e) || ((numext::isfinite)(e) && internal::isApprox(a, e, tol)) ||
+ ((numext::isnan)(a) && (numext::isnan)(e));
+ all_pass &= success;
+ if (!success) {
+ std::cout << "pow(" << bases(j) << "," << exponent << ") = " << a << " != " << e << std::endl;
+ }
+ }
+ }
+ }
+ }
+ VERIFY(all_pass);
+}
+
+template <typename Scalar, typename ScalarExponent>
+Scalar calc_overflow_threshold(const ScalarExponent exponent) {
+ EIGEN_USING_STD(exp2);
+ EIGEN_USING_STD(log2);
+ EIGEN_STATIC_ASSERT((NumTraits<Scalar>::digits() < 2 * NumTraits<double>::digits()), BASE_TYPE_IS_TOO_BIG);
+
+ if (exponent < 2)
+ return NumTraits<Scalar>::highest();
+ else {
+ // base^e <= highest ==> base <= 2^(log2(highest)/e)
+ // For floating-point types, consider the bound for integer values that can be reproduced exactly = 2 ^ digits
+ double highest_bits = numext::mini(static_cast<double>(NumTraits<Scalar>::digits()),
+ static_cast<double>(log2(NumTraits<Scalar>::highest())));
+ return static_cast<Scalar>(
+ numext::floor(exp2(highest_bits / static_cast<double>(exponent))));
+ }
+}
+
+template <typename Base, typename Exponent, bool ExpIsInteger = NumTraits<Exponent>::IsInteger>
+struct ref_pow {
+ static Base run(Base base, Exponent exponent) {
+ EIGEN_USING_STD(pow);
+ return pow(base, static_cast<Base>(exponent));
+ }
+};
+
+template <typename Base, typename Exponent>
+struct ref_pow<Base, Exponent, true> {
+ static Base run(Base base, Exponent exponent) {
+ EIGEN_USING_STD(pow);
+ return pow(base, exponent);
+ }
+};
+
+template <typename Base, typename Exponent>
+void test_exponent(Exponent exponent) {
+ const Base max_abs_bases = static_cast<Base>(10000);
+ // avoid integer overflow in Base type
+ Base threshold = calc_overflow_threshold<Base, Exponent>(numext::abs(exponent));
+ // avoid numbers that can't be verified with std::pow
+ double double_threshold = calc_overflow_threshold<double, Exponent>(numext::abs(exponent));
+ // use the lesser of these two thresholds
+ Base testing_threshold =
+ static_cast<double>(threshold) < double_threshold ? threshold : static_cast<Base>(double_threshold);
+ // test both vectorized and non-vectorized code paths
+ const Index array_size = 2 * internal::packet_traits<Base>::size + 1;
+
+ Base max_base = numext::mini(testing_threshold, max_abs_bases);
+ Base min_base = NumTraits<Base>::IsSigned ? -max_base : Base(0);
+
+ ArrayX<Base> x(array_size), y(array_size);
+ bool all_pass = true;
+ for (Base base = min_base; base <= max_base; base++) {
+ if (exponent < 0 && base == 0) continue;
+ x.setConstant(base);
+ y = x.pow(exponent);
+ for (Base a : y) {
+ Base e = ref_pow<Base, Exponent>::run(base, exponent);
+ bool pass = (a == e);
+ if (!NumTraits<Base>::IsInteger) {
+ pass = pass || (((numext::isfinite)(e) && internal::isApprox(a, e)) ||
+ ((numext::isnan)(a) && (numext::isnan)(e)));
+ }
+ all_pass &= pass;
+ if (!pass) {
+ std::cout << "pow(" << base << "," << exponent << ") = " << a << " != " << e << std::endl;
+ }
+ }
+ }
+ VERIFY(all_pass);
+}
+
+template <typename Base, typename Exponent>
+void unary_pow_test() {
+ Exponent max_exponent = static_cast<Exponent>(NumTraits<Base>::digits());
+ Exponent min_exponent = static_cast<Exponent>(NumTraits<Exponent>::IsSigned ? -max_exponent : 0);
+
+ for (Exponent exponent = min_exponent; exponent < max_exponent; ++exponent) {
+ test_exponent<Base, Exponent>(exponent);
+ }
+};
+
+void mixed_pow_test() {
+ // The following cases will test promoting a smaller exponent type
+ // to a wider base type.
+ unary_pow_test<double, int>();
+ unary_pow_test<double, float>();
+ unary_pow_test<float, half>();
+ unary_pow_test<double, half>();
+ unary_pow_test<float, bfloat16>();
+ unary_pow_test<double, bfloat16>();
+
+ // Although in the following cases the exponent cannot be represented exactly
+ // in the base type, we do not perform a conversion, but implement
+ // the operation using repeated squaring.
+ unary_pow_test<float, int>();
+ unary_pow_test<double, long long>();
+
+ // The following cases will test promoting a wider exponent type
+ // to a narrower base type. This should compile but generate a
+ // deprecation warning:
+ unary_pow_test<float, double>();
+}
+
+void int_pow_test() {
+ unary_pow_test<int, int>();
+ unary_pow_test<unsigned int, unsigned int>();
+ unary_pow_test<long long, long long>();
+ unary_pow_test<unsigned long long, unsigned long long>();
+
+ // Although in the following cases the exponent cannot be represented exactly
+ // in the base type, we do not perform a conversion, but implement the
+ // operation using repeated squaring.
+ unary_pow_test<long long, int>();
+ unary_pow_test<int, unsigned int>();
+ unary_pow_test<unsigned int, int>();
+ unary_pow_test<long long, unsigned long long>();
+ unary_pow_test<unsigned long long, long long>();
+ unary_pow_test<long long, int>();
+}
+
+template<typename ArrayType> void array(const ArrayType& m)
+{
+ typedef typename ArrayType::Scalar Scalar;
+ typedef typename ArrayType::RealScalar RealScalar;
+ typedef Array<Scalar, ArrayType::RowsAtCompileTime, 1> ColVectorType;
+ typedef Array<Scalar, 1, ArrayType::ColsAtCompileTime> RowVectorType;
+
+ Index rows = m.rows();
+ Index cols = m.cols();
+
+ ArrayType m1 = ArrayType::Random(rows, cols);
+ if (NumTraits<RealScalar>::IsInteger && NumTraits<RealScalar>::IsSigned
+ && !NumTraits<Scalar>::IsComplex) {
+ // Here we cap the size of the values in m1 such that pow(3)/cube()
+ // doesn't overflow and result in undefined behavior. Notice that because
+ // pow(int, int) promotes its inputs and output to double (according to
+ // the C++ standard), we have to make sure that the result fits in 53 bits
+ // for int64,
+ RealScalar max_val =
+ numext::mini(RealScalar(std::cbrt(NumTraits<RealScalar>::highest())),
+ RealScalar(std::cbrt(1LL << 53)))/2;
+ m1.array() = (m1.abs().array() <= max_val).select(m1, Scalar(max_val));
+ }
+ ArrayType m2 = ArrayType::Random(rows, cols),
+ m3(rows, cols);
+ ArrayType m4 = m1; // copy constructor
+ VERIFY_IS_APPROX(m1, m4);
+
+ ColVectorType cv1 = ColVectorType::Random(rows);
+ RowVectorType rv1 = RowVectorType::Random(cols);
+
+ Scalar s1 = internal::random<Scalar>(),
+ s2 = internal::random<Scalar>();
+
+ // scalar addition
+ VERIFY_IS_APPROX(m1 + s1, s1 + m1);
+ VERIFY_IS_APPROX(m1 + s1, ArrayType::Constant(rows,cols,s1) + m1);
+ VERIFY_IS_APPROX(s1 - m1, (-m1)+s1 );
+ VERIFY_IS_APPROX(m1 - s1, m1 - ArrayType::Constant(rows,cols,s1));
+ VERIFY_IS_APPROX(s1 - m1, ArrayType::Constant(rows,cols,s1) - m1);
+ VERIFY_IS_APPROX((m1*Scalar(2)) - s2, (m1+m1) - ArrayType::Constant(rows,cols,s2) );
+ m3 = m1;
+ m3 += s2;
+ VERIFY_IS_APPROX(m3, m1 + s2);
+ m3 = m1;
+ m3 -= s1;
+ VERIFY_IS_APPROX(m3, m1 - s1);
+
+ // scalar operators via Maps
+ m3 = m1; m4 = m1;
+ ArrayType::Map(m4.data(), m4.rows(), m4.cols()) -= ArrayType::Map(m2.data(), m2.rows(), m2.cols());
+ VERIFY_IS_APPROX(m4, m3 - m2);
+
+ m3 = m1; m4 = m1;
+ ArrayType::Map(m4.data(), m4.rows(), m4.cols()) += ArrayType::Map(m2.data(), m2.rows(), m2.cols());
+ VERIFY_IS_APPROX(m4, m3 + m2);
+
+ m3 = m1; m4 = m1;
+ ArrayType::Map(m4.data(), m4.rows(), m4.cols()) *= ArrayType::Map(m2.data(), m2.rows(), m2.cols());
+ VERIFY_IS_APPROX(m4, m3 * m2);
+
+ m3 = m1; m4 = m1;
+ m2 = ArrayType::Random(rows,cols);
+ m2 = (m2==0).select(1,m2);
+ ArrayType::Map(m4.data(), m4.rows(), m4.cols()) /= ArrayType::Map(m2.data(), m2.rows(), m2.cols());
+ VERIFY_IS_APPROX(m4, m3 / m2);
+
+ // reductions
+ VERIFY_IS_APPROX(m1.abs().colwise().sum().sum(), m1.abs().sum());
+ VERIFY_IS_APPROX(m1.abs().rowwise().sum().sum(), m1.abs().sum());
+ using std::abs;
+ VERIFY_IS_MUCH_SMALLER_THAN(abs(m1.colwise().sum().sum() - m1.sum()), m1.abs().sum());
+ VERIFY_IS_MUCH_SMALLER_THAN(abs(m1.rowwise().sum().sum() - m1.sum()), m1.abs().sum());
+ if (!internal::isMuchSmallerThan(abs(m1.sum() - (m1+m2).sum()), m1.abs().sum(), test_precision<Scalar>()))
+ VERIFY_IS_NOT_APPROX(((m1+m2).rowwise().sum()).sum(), m1.sum());
+ VERIFY_IS_APPROX(m1.colwise().sum(), m1.colwise().redux(internal::scalar_sum_op<Scalar,Scalar>()));
+
+ // vector-wise ops
+ m3 = m1;
+ VERIFY_IS_APPROX(m3.colwise() += cv1, m1.colwise() + cv1);
+ m3 = m1;
+ VERIFY_IS_APPROX(m3.colwise() -= cv1, m1.colwise() - cv1);
+ m3 = m1;
+ VERIFY_IS_APPROX(m3.rowwise() += rv1, m1.rowwise() + rv1);
+ m3 = m1;
+ VERIFY_IS_APPROX(m3.rowwise() -= rv1, m1.rowwise() - rv1);
+
+ // Conversion from scalar
+ VERIFY_IS_APPROX((m3 = s1), ArrayType::Constant(rows,cols,s1));
+ VERIFY_IS_APPROX((m3 = 1), ArrayType::Constant(rows,cols,1));
+ VERIFY_IS_APPROX((m3.topLeftCorner(rows,cols) = 1), ArrayType::Constant(rows,cols,1));
+ typedef Array<Scalar,
+ ArrayType::RowsAtCompileTime==Dynamic?2:ArrayType::RowsAtCompileTime,
+ ArrayType::ColsAtCompileTime==Dynamic?2:ArrayType::ColsAtCompileTime,
+ ArrayType::Options> FixedArrayType;
+ {
+ FixedArrayType f1(s1);
+ VERIFY_IS_APPROX(f1, FixedArrayType::Constant(s1));
+ FixedArrayType f2(numext::real(s1));
+ VERIFY_IS_APPROX(f2, FixedArrayType::Constant(numext::real(s1)));
+ FixedArrayType f3((int)100*numext::real(s1));
+ VERIFY_IS_APPROX(f3, FixedArrayType::Constant((int)100*numext::real(s1)));
+ f1.setRandom();
+ FixedArrayType f4(f1.data());
+ VERIFY_IS_APPROX(f4, f1);
+ }
+ {
+ FixedArrayType f1{s1};
+ VERIFY_IS_APPROX(f1, FixedArrayType::Constant(s1));
+ FixedArrayType f2{numext::real(s1)};
+ VERIFY_IS_APPROX(f2, FixedArrayType::Constant(numext::real(s1)));
+ FixedArrayType f3{(int)100*numext::real(s1)};
+ VERIFY_IS_APPROX(f3, FixedArrayType::Constant((int)100*numext::real(s1)));
+ f1.setRandom();
+ FixedArrayType f4{f1.data()};
+ VERIFY_IS_APPROX(f4, f1);
+ }
+
+ // pow
+ VERIFY_IS_APPROX(m1.pow(2), m1.square());
+ VERIFY_IS_APPROX(pow(m1,2), m1.square());
+ VERIFY_IS_APPROX(m1.pow(3), m1.cube());
+ VERIFY_IS_APPROX(pow(m1,3), m1.cube());
+ VERIFY_IS_APPROX((-m1).pow(3), -m1.cube());
+ VERIFY_IS_APPROX(pow(2*m1,3), 8*m1.cube());
+ ArrayType exponents = ArrayType::Constant(rows, cols, RealScalar(2));
+ VERIFY_IS_APPROX(Eigen::pow(m1,exponents), m1.square());
+ VERIFY_IS_APPROX(m1.pow(exponents), m1.square());
+ VERIFY_IS_APPROX(Eigen::pow(2*m1,exponents), 4*m1.square());
+ VERIFY_IS_APPROX((2*m1).pow(exponents), 4*m1.square());
+ VERIFY_IS_APPROX(Eigen::pow(m1,2*exponents), m1.square().square());
+ VERIFY_IS_APPROX(m1.pow(2*exponents), m1.square().square());
+ VERIFY_IS_APPROX(Eigen::pow(m1(0,0), exponents), ArrayType::Constant(rows,cols,m1(0,0)*m1(0,0)));
+
+ // Check possible conflicts with 1D ctor
+ typedef Array<Scalar, Dynamic, 1> OneDArrayType;
+ {
+ OneDArrayType o1(rows);
+ VERIFY(o1.size()==rows);
+ OneDArrayType o2(static_cast<int>(rows));
+ VERIFY(o2.size()==rows);
+ }
+ {
+ OneDArrayType o1{rows};
+ VERIFY(o1.size()==rows);
+ OneDArrayType o4{int(rows)};
+ VERIFY(o4.size()==rows);
+ }
+ // Check possible conflicts with 2D ctor
+ typedef Array<Scalar, Dynamic, Dynamic> TwoDArrayType;
+ typedef Array<Scalar, 2, 1> ArrayType2;
+ {
+ TwoDArrayType o1(rows,cols);
+ VERIFY(o1.rows()==rows);
+ VERIFY(o1.cols()==cols);
+ TwoDArrayType o2(static_cast<int>(rows),static_cast<int>(cols));
+ VERIFY(o2.rows()==rows);
+ VERIFY(o2.cols()==cols);
+
+ ArrayType2 o3(rows,cols);
+ VERIFY(o3(0)==Scalar(rows) && o3(1)==Scalar(cols));
+ ArrayType2 o4(static_cast<int>(rows),static_cast<int>(cols));
+ VERIFY(o4(0)==Scalar(rows) && o4(1)==Scalar(cols));
+ }
+ {
+ TwoDArrayType o1{rows,cols};
+ VERIFY(o1.rows()==rows);
+ VERIFY(o1.cols()==cols);
+ TwoDArrayType o2{int(rows),int(cols)};
+ VERIFY(o2.rows()==rows);
+ VERIFY(o2.cols()==cols);
+
+ ArrayType2 o3{rows,cols};
+ VERIFY(o3(0)==Scalar(rows) && o3(1)==Scalar(cols));
+ ArrayType2 o4{int(rows),int(cols)};
+ VERIFY(o4(0)==Scalar(rows) && o4(1)==Scalar(cols));
+ }
+}
+
+template<typename ArrayType> void comparisons(const ArrayType& m)
+{
+ using std::abs;
+ typedef typename ArrayType::Scalar Scalar;
+ typedef typename NumTraits<Scalar>::Real RealScalar;
+
+ Index rows = m.rows();
+ Index cols = m.cols();
+
+ Index r = internal::random<Index>(0, rows-1),
+ c = internal::random<Index>(0, cols-1);
+
+ ArrayType m1 = ArrayType::Random(rows, cols),
+ m2 = ArrayType::Random(rows, cols),
+ m3(rows, cols),
+ m4 = m1;
+
+ m4 = (m4.abs()==Scalar(0)).select(1,m4);
+
+ VERIFY(((m1 + Scalar(1)) > m1).all());
+ VERIFY(((m1 - Scalar(1)) < m1).all());
+ if (rows*cols>1)
+ {
+ m3 = m1;
+ m3(r,c) += 1;
+ VERIFY(! (m1 < m3).all() );
+ VERIFY(! (m1 > m3).all() );
+ }
+ VERIFY(!(m1 > m2 && m1 < m2).any());
+ VERIFY((m1 <= m2 || m1 >= m2).all());
+
+ // comparisons array to scalar
+ VERIFY( (m1 != (m1(r,c)+1) ).any() );
+ VERIFY( (m1 > (m1(r,c)-1) ).any() );
+ VERIFY( (m1 < (m1(r,c)+1) ).any() );
+ VERIFY( (m1 == m1(r,c) ).any() );
+
+ // comparisons scalar to array
+ VERIFY( ( (m1(r,c)+1) != m1).any() );
+ VERIFY( ( (m1(r,c)-1) < m1).any() );
+ VERIFY( ( (m1(r,c)+1) > m1).any() );
+ VERIFY( ( m1(r,c) == m1).any() );
+
+ // test Select
+ VERIFY_IS_APPROX( (m1<m2).select(m1,m2), m1.cwiseMin(m2) );
+ VERIFY_IS_APPROX( (m1>m2).select(m1,m2), m1.cwiseMax(m2) );
+ Scalar mid = (m1.cwiseAbs().minCoeff() + m1.cwiseAbs().maxCoeff())/Scalar(2);
+ for (int j=0; j<cols; ++j)
+ for (int i=0; i<rows; ++i)
+ m3(i,j) = abs(m1(i,j))<mid ? 0 : m1(i,j);
+ VERIFY_IS_APPROX( (m1.abs()<ArrayType::Constant(rows,cols,mid))
+ .select(ArrayType::Zero(rows,cols),m1), m3);
+ // shorter versions:
+ VERIFY_IS_APPROX( (m1.abs()<ArrayType::Constant(rows,cols,mid))
+ .select(0,m1), m3);
+ VERIFY_IS_APPROX( (m1.abs()>=ArrayType::Constant(rows,cols,mid))
+ .select(m1,0), m3);
+ // even shorter version:
+ VERIFY_IS_APPROX( (m1.abs()<mid).select(0,m1), m3);
+
+ // count
+ VERIFY(((m1.abs()+1)>RealScalar(0.1)).count() == rows*cols);
+
+ // and/or
+ VERIFY( (m1<RealScalar(0) && m1>RealScalar(0)).count() == 0);
+ VERIFY( (m1<RealScalar(0) || m1>=RealScalar(0)).count() == rows*cols);
+ RealScalar a = m1.abs().mean();
+ VERIFY( (m1<-a || m1>a).count() == (m1.abs()>a).count());
+
+ typedef Array<Index, Dynamic, 1> ArrayOfIndices;
+
+ // TODO allows colwise/rowwise for array
+ VERIFY_IS_APPROX(((m1.abs()+1)>RealScalar(0.1)).colwise().count(), ArrayOfIndices::Constant(cols,rows).transpose());
+ VERIFY_IS_APPROX(((m1.abs()+1)>RealScalar(0.1)).rowwise().count(), ArrayOfIndices::Constant(rows, cols));
+}
+
+template<typename ArrayType> void array_real(const ArrayType& m)
+{
+ using std::abs;
+ using std::sqrt;
+ typedef typename ArrayType::Scalar Scalar;
+ typedef typename NumTraits<Scalar>::Real RealScalar;
+
+ Index rows = m.rows();
+ Index cols = m.cols();
+
+ ArrayType m1 = ArrayType::Random(rows, cols),
+ m2 = ArrayType::Random(rows, cols),
+ m3(rows, cols),
+ m4 = m1;
+
+ m4 = (m4.abs()==Scalar(0)).select(Scalar(1),m4);
+
+ Scalar s1 = internal::random<Scalar>();
+
+ // these tests are mostly to check possible compilation issues with free-functions.
+ VERIFY_IS_APPROX(m1.sin(), sin(m1));
+ VERIFY_IS_APPROX(m1.cos(), cos(m1));
+ VERIFY_IS_APPROX(m1.tan(), tan(m1));
+ VERIFY_IS_APPROX(m1.asin(), asin(m1));
+ VERIFY_IS_APPROX(m1.acos(), acos(m1));
+ VERIFY_IS_APPROX(m1.atan(), atan(m1));
+ VERIFY_IS_APPROX(m1.sinh(), sinh(m1));
+ VERIFY_IS_APPROX(m1.cosh(), cosh(m1));
+ VERIFY_IS_APPROX(m1.tanh(), tanh(m1));
+ VERIFY_IS_APPROX(m1.atan2(m2), atan2(m1,m2));
+
+ VERIFY_IS_APPROX(m1.tanh().atanh(), atanh(tanh(m1)));
+ VERIFY_IS_APPROX(m1.sinh().asinh(), asinh(sinh(m1)));
+ VERIFY_IS_APPROX(m1.cosh().acosh(), acosh(cosh(m1)));
+ VERIFY_IS_APPROX(m1.logistic(), logistic(m1));
+
+ VERIFY_IS_APPROX(m1.arg(), arg(m1));
+ VERIFY_IS_APPROX(m1.round(), round(m1));
+ VERIFY_IS_APPROX(m1.rint(), rint(m1));
+ VERIFY_IS_APPROX(m1.floor(), floor(m1));
+ VERIFY_IS_APPROX(m1.ceil(), ceil(m1));
+ VERIFY((m1.isNaN() == (Eigen::isnan)(m1)).all());
+ VERIFY((m1.isInf() == (Eigen::isinf)(m1)).all());
+ VERIFY((m1.isFinite() == (Eigen::isfinite)(m1)).all());
+ VERIFY_IS_APPROX(m4.inverse(), inverse(m4));
+ VERIFY_IS_APPROX(m1.abs(), abs(m1));
+ VERIFY_IS_APPROX(m1.abs2(), abs2(m1));
+ VERIFY_IS_APPROX(m1.square(), square(m1));
+ VERIFY_IS_APPROX(m1.cube(), cube(m1));
+ VERIFY_IS_APPROX(cos(m1+RealScalar(3)*m2), cos((m1+RealScalar(3)*m2).eval()));
+ VERIFY_IS_APPROX(m1.sign(), sign(m1));
+ VERIFY((m1.sqrt().sign().isNaN() == (Eigen::isnan)(sign(sqrt(m1)))).all());
+
+ // avoid inf and NaNs so verification doesn't fail
+ m3 = m4.abs();
+ VERIFY_IS_APPROX(m3.sqrt(), sqrt(abs(m3)));
+ VERIFY_IS_APPROX(m3.rsqrt(), Scalar(1)/sqrt(abs(m3)));
+ VERIFY_IS_APPROX(rsqrt(m3), Scalar(1)/sqrt(abs(m3)));
+ VERIFY_IS_APPROX(m3.log(), log(m3));
+ VERIFY_IS_APPROX(m3.log1p(), log1p(m3));
+ VERIFY_IS_APPROX(m3.log10(), log10(m3));
+ VERIFY_IS_APPROX(m3.log2(), log2(m3));
+
+
+ VERIFY((!(m1>m2) == (m1<=m2)).all());
+
+ VERIFY_IS_APPROX(sin(m1.asin()), m1);
+ VERIFY_IS_APPROX(cos(m1.acos()), m1);
+ VERIFY_IS_APPROX(tan(m1.atan()), m1);
+ VERIFY_IS_APPROX(sinh(m1), Scalar(0.5)*(exp(m1)-exp(-m1)));
+ VERIFY_IS_APPROX(cosh(m1), Scalar(0.5)*(exp(m1)+exp(-m1)));
+ VERIFY_IS_APPROX(tanh(m1), (Scalar(0.5)*(exp(m1)-exp(-m1)))/(Scalar(0.5)*(exp(m1)+exp(-m1))));
+ VERIFY_IS_APPROX(logistic(m1), (Scalar(1)/(Scalar(1)+exp(-m1))));
+ VERIFY_IS_APPROX(arg(m1), ((m1<Scalar(0)).template cast<Scalar>())*Scalar(std::acos(Scalar(-1))));
+ VERIFY((round(m1) <= ceil(m1) && round(m1) >= floor(m1)).all());
+ VERIFY((rint(m1) <= ceil(m1) && rint(m1) >= floor(m1)).all());
+ VERIFY(((ceil(m1) - round(m1)) <= Scalar(0.5) || (round(m1) - floor(m1)) <= Scalar(0.5)).all());
+ VERIFY(((ceil(m1) - round(m1)) <= Scalar(1.0) && (round(m1) - floor(m1)) <= Scalar(1.0)).all());
+ VERIFY(((ceil(m1) - rint(m1)) <= Scalar(0.5) || (rint(m1) - floor(m1)) <= Scalar(0.5)).all());
+ VERIFY(((ceil(m1) - rint(m1)) <= Scalar(1.0) && (rint(m1) - floor(m1)) <= Scalar(1.0)).all());
+ VERIFY((Eigen::isnan)((m1*Scalar(0))/Scalar(0)).all());
+ VERIFY((Eigen::isinf)(m4/Scalar(0)).all());
+ VERIFY(((Eigen::isfinite)(m1) && (!(Eigen::isfinite)(m1*Scalar(0)/Scalar(0))) && (!(Eigen::isfinite)(m4/Scalar(0)))).all());
+ VERIFY_IS_APPROX(inverse(inverse(m4)),m4);
+ VERIFY((abs(m1) == m1 || abs(m1) == -m1).all());
+ VERIFY_IS_APPROX(m3, sqrt(abs2(m3)));
+ VERIFY_IS_APPROX(m1.absolute_difference(m2), (m1 > m2).select(m1 - m2, m2 - m1));
+ VERIFY_IS_APPROX( m1.sign(), -(-m1).sign() );
+ VERIFY_IS_APPROX( m1*m1.sign(),m1.abs());
+ VERIFY_IS_APPROX(m1.sign() * m1.abs(), m1);
+
+ ArrayType tmp = m1.atan2(m2);
+ for (Index i = 0; i < tmp.size(); ++i) {
+ Scalar actual = tmp.array()(i);
+ Scalar expected = atan2(m1.array()(i), m2.array()(i));
+ VERIFY_IS_APPROX(actual, expected);
+ }
+
+ VERIFY_IS_APPROX(numext::abs2(numext::real(m1)) + numext::abs2(numext::imag(m1)), numext::abs2(m1));
+ VERIFY_IS_APPROX(numext::abs2(Eigen::real(m1)) + numext::abs2(Eigen::imag(m1)), numext::abs2(m1));
+ if(!NumTraits<Scalar>::IsComplex)
+ VERIFY_IS_APPROX(numext::real(m1), m1);
+
+ // shift argument of logarithm so that it is not zero
+ Scalar smallNumber = NumTraits<Scalar>::dummy_precision();
+ VERIFY_IS_APPROX((m3 + smallNumber).log() , log(abs(m3) + smallNumber));
+ VERIFY_IS_APPROX((m3 + smallNumber + Scalar(1)).log() , log1p(abs(m3) + smallNumber));
+
+ VERIFY_IS_APPROX(m1.exp() * m2.exp(), exp(m1+m2));
+ VERIFY_IS_APPROX(m1.exp(), exp(m1));
+ VERIFY_IS_APPROX(m1.exp() / m2.exp(),(m1-m2).exp());
+
+ VERIFY_IS_APPROX(m1.expm1(), expm1(m1));
+ VERIFY_IS_APPROX((m3 + smallNumber).exp() - Scalar(1), expm1(abs(m3) + smallNumber));
+
+ VERIFY_IS_APPROX(m3.pow(RealScalar(0.5)), m3.sqrt());
+ VERIFY_IS_APPROX(pow(m3,RealScalar(0.5)), m3.sqrt());
+
+ VERIFY_IS_APPROX(m3.pow(RealScalar(-0.5)), m3.rsqrt());
+ VERIFY_IS_APPROX(pow(m3,RealScalar(-0.5)), m3.rsqrt());
+
+ // Avoid inf and NaN.
+ m3 = (m1.square()<NumTraits<Scalar>::epsilon()).select(Scalar(1),m3);
+ VERIFY_IS_APPROX(m3.pow(RealScalar(-2)), m3.square().inverse());
+
+ // Test pow and atan2 on special IEEE values.
+ binary_ops_test<Scalar>();
+ pow_scalar_exponent_test<Scalar>();
+
+ VERIFY_IS_APPROX(log10(m3), log(m3)/numext::log(Scalar(10)));
+ VERIFY_IS_APPROX(log2(m3), log(m3)/numext::log(Scalar(2)));
+
+ // scalar by array division
+ const RealScalar tiny = sqrt(std::numeric_limits<RealScalar>::epsilon());
+ s1 += Scalar(tiny);
+ m1 += ArrayType::Constant(rows,cols,Scalar(tiny));
+ VERIFY_IS_CWISE_APPROX(s1/m1, s1 * m1.inverse());
+
+ // check inplace transpose
+ m3 = m1;
+ m3.transposeInPlace();
+ VERIFY_IS_APPROX(m3, m1.transpose());
+ m3.transposeInPlace();
+ VERIFY_IS_APPROX(m3, m1);
+}
+
+
+template<typename ArrayType> void array_complex(const ArrayType& m)
+{
+ typedef typename ArrayType::Scalar Scalar;
+ typedef typename NumTraits<Scalar>::Real RealScalar;
+
+ Index rows = m.rows();
+ Index cols = m.cols();
+
+ ArrayType m1 = ArrayType::Random(rows, cols),
+ m2(rows, cols),
+ m4 = m1;
+
+ m4.real() = (m4.real().abs()==RealScalar(0)).select(RealScalar(1),m4.real());
+ m4.imag() = (m4.imag().abs()==RealScalar(0)).select(RealScalar(1),m4.imag());
+
+ Array<RealScalar, -1, -1> m3(rows, cols);
+
+ for (Index i = 0; i < m.rows(); ++i)
+ for (Index j = 0; j < m.cols(); ++j)
+ m2(i,j) = sqrt(m1(i,j));
+
+ // these tests are mostly to check possible compilation issues with free-functions.
+ VERIFY_IS_APPROX(m1.sin(), sin(m1));
+ VERIFY_IS_APPROX(m1.cos(), cos(m1));
+ VERIFY_IS_APPROX(m1.tan(), tan(m1));
+ VERIFY_IS_APPROX(m1.sinh(), sinh(m1));
+ VERIFY_IS_APPROX(m1.cosh(), cosh(m1));
+ VERIFY_IS_APPROX(m1.tanh(), tanh(m1));
+ VERIFY_IS_APPROX(m1.logistic(), logistic(m1));
+ VERIFY_IS_APPROX(m1.arg(), arg(m1));
+ VERIFY((m1.isNaN() == (Eigen::isnan)(m1)).all());
+ VERIFY((m1.isInf() == (Eigen::isinf)(m1)).all());
+ VERIFY((m1.isFinite() == (Eigen::isfinite)(m1)).all());
+ VERIFY_IS_APPROX(m4.inverse(), inverse(m4));
+ VERIFY_IS_APPROX(m1.log(), log(m1));
+ VERIFY_IS_APPROX(m1.log10(), log10(m1));
+ VERIFY_IS_APPROX(m1.log2(), log2(m1));
+ VERIFY_IS_APPROX(m1.abs(), abs(m1));
+ VERIFY_IS_APPROX(m1.abs2(), abs2(m1));
+ VERIFY_IS_APPROX(m1.sqrt(), sqrt(m1));
+ VERIFY_IS_APPROX(m1.square(), square(m1));
+ VERIFY_IS_APPROX(m1.cube(), cube(m1));
+ VERIFY_IS_APPROX(cos(m1+RealScalar(3)*m2), cos((m1+RealScalar(3)*m2).eval()));
+ VERIFY_IS_APPROX(m1.sign(), sign(m1));
+
+ VERIFY_IS_APPROX(m1.exp() * m2.exp(), exp(m1+m2));
+ VERIFY_IS_APPROX(m1.exp(), exp(m1));
+ VERIFY_IS_APPROX(m1.exp() / m2.exp(),(m1-m2).exp());
+
+ VERIFY_IS_APPROX(m1.expm1(), expm1(m1));
+ VERIFY_IS_APPROX(expm1(m1), exp(m1) - 1.);
+ // Check for larger magnitude complex numbers that expm1 matches exp - 1.
+ VERIFY_IS_APPROX(expm1(10. * m1), exp(10. * m1) - 1.);
+
+ VERIFY_IS_APPROX(sinh(m1), 0.5*(exp(m1)-exp(-m1)));
+ VERIFY_IS_APPROX(cosh(m1), 0.5*(exp(m1)+exp(-m1)));
+ VERIFY_IS_APPROX(tanh(m1), (0.5*(exp(m1)-exp(-m1)))/(0.5*(exp(m1)+exp(-m1))));
+ VERIFY_IS_APPROX(logistic(m1), (1.0/(1.0 + exp(-m1))));
+
+ for (Index i = 0; i < m.rows(); ++i)
+ for (Index j = 0; j < m.cols(); ++j)
+ m3(i,j) = std::atan2(m1(i,j).imag(), m1(i,j).real());
+ VERIFY_IS_APPROX(arg(m1), m3);
+
+ std::complex<RealScalar> zero(0.0,0.0);
+ VERIFY((Eigen::isnan)(m1*zero/zero).all());
+#if EIGEN_COMP_MSVC
+ // msvc complex division is not robust
+ VERIFY((Eigen::isinf)(m4/RealScalar(0)).all());
+#else
+#if EIGEN_COMP_CLANG
+ // clang's complex division is notoriously broken too
+ if((numext::isinf)(m4(0,0)/RealScalar(0))) {
+#endif
+ VERIFY((Eigen::isinf)(m4/zero).all());
+#if EIGEN_COMP_CLANG
+ }
+ else
+ {
+ VERIFY((Eigen::isinf)(m4.real()/zero.real()).all());
+ }
+#endif
+#endif // MSVC
+
+ VERIFY(((Eigen::isfinite)(m1) && (!(Eigen::isfinite)(m1*zero/zero)) && (!(Eigen::isfinite)(m1/zero))).all());
+
+ VERIFY_IS_APPROX(inverse(inverse(m4)),m4);
+ VERIFY_IS_APPROX(conj(m1.conjugate()), m1);
+ VERIFY_IS_APPROX(abs(m1), sqrt(square(m1.real())+square(m1.imag())));
+ VERIFY_IS_APPROX(abs(m1), sqrt(abs2(m1)));
+ VERIFY_IS_APPROX(log10(m1), log(m1)/log(10));
+ VERIFY_IS_APPROX(log2(m1), log(m1)/log(2));
+
+ VERIFY_IS_APPROX( m1.sign(), -(-m1).sign() );
+ VERIFY_IS_APPROX( m1.sign() * m1.abs(), m1);
+
+ // scalar by array division
+ Scalar s1 = internal::random<Scalar>();
+ const RealScalar tiny = std::sqrt(std::numeric_limits<RealScalar>::epsilon());
+ s1 += Scalar(tiny);
+ m1 += ArrayType::Constant(rows,cols,Scalar(tiny));
+ VERIFY_IS_APPROX(s1/m1, s1 * m1.inverse());
+
+ // check inplace transpose
+ m2 = m1;
+ m2.transposeInPlace();
+ VERIFY_IS_APPROX(m2, m1.transpose());
+ m2.transposeInPlace();
+ VERIFY_IS_APPROX(m2, m1);
+ // Check vectorized inplace transpose.
+ ArrayType m5 = ArrayType::Random(131, 131);
+ ArrayType m6 = m5;
+ m6.transposeInPlace();
+ VERIFY_IS_APPROX(m6, m5.transpose());
+}
+
+template<typename ArrayType> void min_max(const ArrayType& m)
+{
+ typedef typename ArrayType::Scalar Scalar;
+
+ Index rows = m.rows();
+ Index cols = m.cols();
+
+ ArrayType m1 = ArrayType::Random(rows, cols);
+
+ // min/max with array
+ Scalar maxM1 = m1.maxCoeff();
+ Scalar minM1 = m1.minCoeff();
+
+ VERIFY_IS_APPROX(ArrayType::Constant(rows,cols, minM1), (m1.min)(ArrayType::Constant(rows,cols, minM1)));
+ VERIFY_IS_APPROX(m1, (m1.min)(ArrayType::Constant(rows,cols, maxM1)));
+
+ VERIFY_IS_APPROX(ArrayType::Constant(rows,cols, maxM1), (m1.max)(ArrayType::Constant(rows,cols, maxM1)));
+ VERIFY_IS_APPROX(m1, (m1.max)(ArrayType::Constant(rows,cols, minM1)));
+
+ // min/max with scalar input
+ VERIFY_IS_APPROX(ArrayType::Constant(rows,cols, minM1), (m1.min)( minM1));
+ VERIFY_IS_APPROX(m1, (m1.min)( maxM1));
+
+ VERIFY_IS_APPROX(ArrayType::Constant(rows,cols, maxM1), (m1.max)( maxM1));
+ VERIFY_IS_APPROX(m1, (m1.max)( minM1));
+
+
+ // min/max with various NaN propagation options.
+ if (m1.size() > 1 && !NumTraits<Scalar>::IsInteger) {
+ m1(0,0) = NumTraits<Scalar>::quiet_NaN();
+ maxM1 = m1.template maxCoeff<PropagateNaN>();
+ minM1 = m1.template minCoeff<PropagateNaN>();
+ VERIFY((numext::isnan)(maxM1));
+ VERIFY((numext::isnan)(minM1));
+
+ maxM1 = m1.template maxCoeff<PropagateNumbers>();
+ minM1 = m1.template minCoeff<PropagateNumbers>();
+ VERIFY(!(numext::isnan)(maxM1));
+ VERIFY(!(numext::isnan)(minM1));
+ }
+}
+
+template<int N>
+struct shift_left {
+ template<typename Scalar>
+ Scalar operator()(const Scalar& v) const {
+ return v << N;
+ }
+};
+
+template<int N>
+struct arithmetic_shift_right {
+ template<typename Scalar>
+ Scalar operator()(const Scalar& v) const {
+ return v >> N;
+ }
+};
+
+template<typename ArrayType> void array_integer(const ArrayType& m)
+{
+ Index rows = m.rows();
+ Index cols = m.cols();
+
+ ArrayType m1 = ArrayType::Random(rows, cols),
+ m2(rows, cols);
+
+ m2 = m1.template shiftLeft<2>();
+ VERIFY( (m2 == m1.unaryExpr(shift_left<2>())).all() );
+ m2 = m1.template shiftLeft<9>();
+ VERIFY( (m2 == m1.unaryExpr(shift_left<9>())).all() );
+
+ m2 = m1.template shiftRight<2>();
+ VERIFY( (m2 == m1.unaryExpr(arithmetic_shift_right<2>())).all() );
+ m2 = m1.template shiftRight<9>();
+ VERIFY( (m2 == m1.unaryExpr(arithmetic_shift_right<9>())).all() );
+}
+
+EIGEN_DECLARE_TEST(array_cwise)
+{
+ for(int i = 0; i < g_repeat; i++) {
+ CALL_SUBTEST_1( array(Array<float, 1, 1>()) );
+ CALL_SUBTEST_2( array(Array22f()) );
+ CALL_SUBTEST_3( array(Array44d()) );
+ CALL_SUBTEST_4( array(ArrayXXcf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
+ CALL_SUBTEST_5( array(ArrayXXf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
+ CALL_SUBTEST_6( array(ArrayXXi(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
+ CALL_SUBTEST_6( array(Array<Index,Dynamic,Dynamic>(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
+ CALL_SUBTEST_6( array_integer(ArrayXXi(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
+ CALL_SUBTEST_6( array_integer(Array<Index,Dynamic,Dynamic>(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
+ }
+ for(int i = 0; i < g_repeat; i++) {
+ CALL_SUBTEST_1( comparisons(Array<float, 1, 1>()) );
+ CALL_SUBTEST_2( comparisons(Array22f()) );
+ CALL_SUBTEST_3( comparisons(Array44d()) );
+ CALL_SUBTEST_5( comparisons(ArrayXXf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
+ CALL_SUBTEST_6( comparisons(ArrayXXi(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
+ }
+ for(int i = 0; i < g_repeat; i++) {
+ CALL_SUBTEST_1( min_max(Array<float, 1, 1>()) );
+ CALL_SUBTEST_2( min_max(Array22f()) );
+ CALL_SUBTEST_3( min_max(Array44d()) );
+ CALL_SUBTEST_5( min_max(ArrayXXf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
+ CALL_SUBTEST_6( min_max(ArrayXXi(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
+ }
+ for(int i = 0; i < g_repeat; i++) {
+ CALL_SUBTEST_1( array_real(Array<float, 1, 1>()) );
+ CALL_SUBTEST_2( array_real(Array22f()) );
+ CALL_SUBTEST_3( array_real(Array44d()) );
+ CALL_SUBTEST_5( array_real(ArrayXXf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
+ CALL_SUBTEST_7( array_real(Array<Eigen::half, 32, 32>()) );
+ CALL_SUBTEST_8( array_real(Array<Eigen::bfloat16, 32, 32>()) );
+ }
+ for(int i = 0; i < g_repeat; i++) {
+ CALL_SUBTEST_4( array_complex(ArrayXXcf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
+ }
+
+ for(int i = 0; i < g_repeat; i++) {
+ CALL_SUBTEST_6( int_pow_test() );
+ CALL_SUBTEST_7( mixed_pow_test() );
+ }
+
+ VERIFY((internal::is_same< internal::global_math_functions_filtering_base<int>::type, int >::value));
+ VERIFY((internal::is_same< internal::global_math_functions_filtering_base<float>::type, float >::value));
+ VERIFY((internal::is_same< internal::global_math_functions_filtering_base<Array2i>::type, ArrayBase<Array2i> >::value));
+ typedef CwiseUnaryOp<internal::scalar_abs_op<double>, ArrayXd > Xpr;
+ VERIFY((internal::is_same< internal::global_math_functions_filtering_base<Xpr>::type,
+ ArrayBase<Xpr>
+ >::value));
+}
diff --git a/test/array_for_matrix.cpp b/test/array_for_matrix.cpp
new file mode 100644
index 0000000..06e04a2
--- /dev/null
+++ b/test/array_for_matrix.cpp
@@ -0,0 +1,341 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "main.h"
+
+template<typename MatrixType> void array_for_matrix(const MatrixType& m)
+{
+ typedef typename MatrixType::Scalar Scalar;
+ typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> ColVectorType;
+ typedef Matrix<Scalar, 1, MatrixType::ColsAtCompileTime> RowVectorType;
+
+ Index rows = m.rows();
+ Index cols = m.cols();
+
+ MatrixType m1 = MatrixType::Random(rows, cols),
+ m2 = MatrixType::Random(rows, cols),
+ m3(rows, cols);
+
+ ColVectorType cv1 = ColVectorType::Random(rows);
+ RowVectorType rv1 = RowVectorType::Random(cols);
+
+ Scalar s1 = internal::random<Scalar>(),
+ s2 = internal::random<Scalar>();
+
+ // scalar addition
+ VERIFY_IS_APPROX(m1.array() + s1, s1 + m1.array());
+ VERIFY_IS_APPROX((m1.array() + s1).matrix(), MatrixType::Constant(rows,cols,s1) + m1);
+ VERIFY_IS_APPROX(((m1*Scalar(2)).array() - s2).matrix(), (m1+m1) - MatrixType::Constant(rows,cols,s2) );
+ m3 = m1;
+ m3.array() += s2;
+ VERIFY_IS_APPROX(m3, (m1.array() + s2).matrix());
+ m3 = m1;
+ m3.array() -= s1;
+ VERIFY_IS_APPROX(m3, (m1.array() - s1).matrix());
+
+ // reductions
+ VERIFY_IS_MUCH_SMALLER_THAN(m1.colwise().sum().sum() - m1.sum(), m1.squaredNorm());
+ VERIFY_IS_MUCH_SMALLER_THAN(m1.rowwise().sum().sum() - m1.sum(), m1.squaredNorm());
+ VERIFY_IS_MUCH_SMALLER_THAN(m1.colwise().sum() + m2.colwise().sum() - (m1+m2).colwise().sum(), (m1+m2).squaredNorm());
+ VERIFY_IS_MUCH_SMALLER_THAN(m1.rowwise().sum() - m2.rowwise().sum() - (m1-m2).rowwise().sum(), (m1-m2).squaredNorm());
+ VERIFY_IS_APPROX(m1.colwise().sum(), m1.colwise().redux(internal::scalar_sum_op<Scalar,Scalar>()));
+
+ // vector-wise ops
+ m3 = m1;
+ VERIFY_IS_APPROX(m3.colwise() += cv1, m1.colwise() + cv1);
+ m3 = m1;
+ VERIFY_IS_APPROX(m3.colwise() -= cv1, m1.colwise() - cv1);
+ m3 = m1;
+ VERIFY_IS_APPROX(m3.rowwise() += rv1, m1.rowwise() + rv1);
+ m3 = m1;
+ VERIFY_IS_APPROX(m3.rowwise() -= rv1, m1.rowwise() - rv1);
+
+ // empty objects
+ VERIFY_IS_APPROX((m1.template block<0,Dynamic>(0,0,0,cols).colwise().sum()), RowVectorType::Zero(cols));
+ VERIFY_IS_APPROX((m1.template block<Dynamic,0>(0,0,rows,0).rowwise().sum()), ColVectorType::Zero(rows));
+ VERIFY_IS_APPROX((m1.template block<0,Dynamic>(0,0,0,cols).colwise().prod()), RowVectorType::Ones(cols));
+ VERIFY_IS_APPROX((m1.template block<Dynamic,0>(0,0,rows,0).rowwise().prod()), ColVectorType::Ones(rows));
+
+ VERIFY_IS_APPROX(m1.block(0,0,0,cols).colwise().sum(), RowVectorType::Zero(cols));
+ VERIFY_IS_APPROX(m1.block(0,0,rows,0).rowwise().sum(), ColVectorType::Zero(rows));
+ VERIFY_IS_APPROX(m1.block(0,0,0,cols).colwise().prod(), RowVectorType::Ones(cols));
+ VERIFY_IS_APPROX(m1.block(0,0,rows,0).rowwise().prod(), ColVectorType::Ones(rows));
+
+ // verify the const accessors exist
+ const Scalar& ref_m1 = m.matrix().array().coeffRef(0);
+ const Scalar& ref_m2 = m.matrix().array().coeffRef(0,0);
+ const Scalar& ref_a1 = m.array().matrix().coeffRef(0);
+ const Scalar& ref_a2 = m.array().matrix().coeffRef(0,0);
+ VERIFY(&ref_a1 == &ref_m1);
+ VERIFY(&ref_a2 == &ref_m2);
+
+ // Check write accessors:
+ m1.array().coeffRef(0,0) = 1;
+ VERIFY_IS_APPROX(m1(0,0),Scalar(1));
+ m1.array()(0,0) = 2;
+ VERIFY_IS_APPROX(m1(0,0),Scalar(2));
+ m1.array().matrix().coeffRef(0,0) = 3;
+ VERIFY_IS_APPROX(m1(0,0),Scalar(3));
+ m1.array().matrix()(0,0) = 4;
+ VERIFY_IS_APPROX(m1(0,0),Scalar(4));
+}
+
+template<typename MatrixType> void comparisons(const MatrixType& m)
+{
+ using std::abs;
+ typedef typename MatrixType::Scalar Scalar;
+ typedef typename NumTraits<Scalar>::Real RealScalar;
+
+ Index rows = m.rows();
+ Index cols = m.cols();
+
+ Index r = internal::random<Index>(0, rows-1),
+ c = internal::random<Index>(0, cols-1);
+
+ MatrixType m1 = MatrixType::Random(rows, cols),
+ m2 = MatrixType::Random(rows, cols),
+ m3(rows, cols);
+
+ VERIFY(((m1.array() + Scalar(1)) > m1.array()).all());
+ VERIFY(((m1.array() - Scalar(1)) < m1.array()).all());
+ if (rows*cols>1)
+ {
+ m3 = m1;
+ m3(r,c) += 1;
+ VERIFY(! (m1.array() < m3.array()).all() );
+ VERIFY(! (m1.array() > m3.array()).all() );
+ }
+
+ // comparisons to scalar
+ VERIFY( (m1.array() != (m1(r,c)+1) ).any() );
+ VERIFY( (m1.array() > (m1(r,c)-1) ).any() );
+ VERIFY( (m1.array() < (m1(r,c)+1) ).any() );
+ VERIFY( (m1.array() == m1(r,c) ).any() );
+ VERIFY( m1.cwiseEqual(m1(r,c)).any() );
+
+ // test Select
+ VERIFY_IS_APPROX( (m1.array()<m2.array()).select(m1,m2), m1.cwiseMin(m2) );
+ VERIFY_IS_APPROX( (m1.array()>m2.array()).select(m1,m2), m1.cwiseMax(m2) );
+ Scalar mid = (m1.cwiseAbs().minCoeff() + m1.cwiseAbs().maxCoeff())/Scalar(2);
+ for (int j=0; j<cols; ++j)
+ for (int i=0; i<rows; ++i)
+ m3(i,j) = abs(m1(i,j))<mid ? 0 : m1(i,j);
+ VERIFY_IS_APPROX( (m1.array().abs()<MatrixType::Constant(rows,cols,mid).array())
+ .select(MatrixType::Zero(rows,cols),m1), m3);
+ // shorter versions:
+ VERIFY_IS_APPROX( (m1.array().abs()<MatrixType::Constant(rows,cols,mid).array())
+ .select(0,m1), m3);
+ VERIFY_IS_APPROX( (m1.array().abs()>=MatrixType::Constant(rows,cols,mid).array())
+ .select(m1,0), m3);
+ // even shorter version:
+ VERIFY_IS_APPROX( (m1.array().abs()<mid).select(0,m1), m3);
+
+ // count
+ VERIFY(((m1.array().abs()+1)>RealScalar(0.1)).count() == rows*cols);
+
+ // and/or
+ VERIFY( ((m1.array()<RealScalar(0)).matrix() && (m1.array()>RealScalar(0)).matrix()).count() == 0);
+ VERIFY( ((m1.array()<RealScalar(0)).matrix() || (m1.array()>=RealScalar(0)).matrix()).count() == rows*cols);
+ RealScalar a = m1.cwiseAbs().mean();
+ VERIFY( ((m1.array()<-a).matrix() || (m1.array()>a).matrix()).count() == (m1.cwiseAbs().array()>a).count());
+
+ typedef Matrix<Index, Dynamic, 1> VectorOfIndices;
+
+ // TODO allows colwise/rowwise for array
+ VERIFY_IS_APPROX(((m1.array().abs()+1)>RealScalar(0.1)).matrix().colwise().count(), VectorOfIndices::Constant(cols,rows).transpose());
+ VERIFY_IS_APPROX(((m1.array().abs()+1)>RealScalar(0.1)).matrix().rowwise().count(), VectorOfIndices::Constant(rows, cols));
+}
+
+template<typename VectorType> void lpNorm(const VectorType& v)
+{
+ using std::sqrt;
+ typedef typename VectorType::RealScalar RealScalar;
+ VectorType u = VectorType::Random(v.size());
+
+ if(v.size()==0)
+ {
+ VERIFY_IS_APPROX(u.template lpNorm<Infinity>(), RealScalar(0));
+ VERIFY_IS_APPROX(u.template lpNorm<1>(), RealScalar(0));
+ VERIFY_IS_APPROX(u.template lpNorm<2>(), RealScalar(0));
+ VERIFY_IS_APPROX(u.template lpNorm<5>(), RealScalar(0));
+ }
+ else
+ {
+ VERIFY_IS_APPROX(u.template lpNorm<Infinity>(), u.cwiseAbs().maxCoeff());
+ }
+
+ VERIFY_IS_APPROX(u.template lpNorm<1>(), u.cwiseAbs().sum());
+ VERIFY_IS_APPROX(u.template lpNorm<2>(), sqrt(u.array().abs().square().sum()));
+ VERIFY_IS_APPROX(numext::pow(u.template lpNorm<5>(), typename VectorType::RealScalar(5)), u.array().abs().pow(5).sum());
+}
+
+template<typename MatrixType> void cwise_min_max(const MatrixType& m)
+{
+ typedef typename MatrixType::Scalar Scalar;
+
+ Index rows = m.rows();
+ Index cols = m.cols();
+
+ MatrixType m1 = MatrixType::Random(rows, cols);
+
+ // min/max with array
+ Scalar maxM1 = m1.maxCoeff();
+ Scalar minM1 = m1.minCoeff();
+
+ VERIFY_IS_APPROX(MatrixType::Constant(rows,cols, minM1), m1.cwiseMin(MatrixType::Constant(rows,cols, minM1)));
+ VERIFY_IS_APPROX(m1, m1.cwiseMin(MatrixType::Constant(rows,cols, maxM1)));
+
+ VERIFY_IS_APPROX(MatrixType::Constant(rows,cols, maxM1), m1.cwiseMax(MatrixType::Constant(rows,cols, maxM1)));
+ VERIFY_IS_APPROX(m1, m1.cwiseMax(MatrixType::Constant(rows,cols, minM1)));
+
+ // min/max with scalar input
+ VERIFY_IS_APPROX(MatrixType::Constant(rows,cols, minM1), m1.cwiseMin( minM1));
+ VERIFY_IS_APPROX(m1, m1.cwiseMin(maxM1));
+ VERIFY_IS_APPROX(-m1, (-m1).cwiseMin(-minM1));
+ VERIFY_IS_APPROX(-m1.array(), ((-m1).array().min)( -minM1));
+
+ VERIFY_IS_APPROX(MatrixType::Constant(rows,cols, maxM1), m1.cwiseMax( maxM1));
+ VERIFY_IS_APPROX(m1, m1.cwiseMax(minM1));
+ VERIFY_IS_APPROX(-m1, (-m1).cwiseMax(-maxM1));
+ VERIFY_IS_APPROX(-m1.array(), ((-m1).array().max)(-maxM1));
+
+ VERIFY_IS_APPROX(MatrixType::Constant(rows,cols, minM1).array(), (m1.array().min)( minM1));
+ VERIFY_IS_APPROX(m1.array(), (m1.array().min)( maxM1));
+
+ VERIFY_IS_APPROX(MatrixType::Constant(rows,cols, maxM1).array(), (m1.array().max)( maxM1));
+ VERIFY_IS_APPROX(m1.array(), (m1.array().max)( minM1));
+
+ // Test NaN propagation for min/max.
+ if (!NumTraits<Scalar>::IsInteger) {
+ m1(0,0) = NumTraits<Scalar>::quiet_NaN();
+ // Elementwise.
+ VERIFY((numext::isnan)(m1.template cwiseMax<PropagateNaN>(MatrixType::Constant(rows,cols, Scalar(1)))(0,0)));
+ VERIFY((numext::isnan)(m1.template cwiseMin<PropagateNaN>(MatrixType::Constant(rows,cols, Scalar(1)))(0,0)));
+ VERIFY(!(numext::isnan)(m1.template cwiseMax<PropagateNumbers>(MatrixType::Constant(rows,cols, Scalar(1)))(0,0)));
+ VERIFY(!(numext::isnan)(m1.template cwiseMin<PropagateNumbers>(MatrixType::Constant(rows,cols, Scalar(1)))(0,0)));
+ VERIFY((numext::isnan)(m1.template cwiseMax<PropagateNaN>(Scalar(1))(0,0)));
+ VERIFY((numext::isnan)(m1.template cwiseMin<PropagateNaN>(Scalar(1))(0,0)));
+ VERIFY(!(numext::isnan)(m1.template cwiseMax<PropagateNumbers>(Scalar(1))(0,0)));
+ VERIFY(!(numext::isnan)(m1.template cwiseMin<PropagateNumbers>(Scalar(1))(0,0)));
+
+
+ VERIFY((numext::isnan)(m1.array().template max<PropagateNaN>(MatrixType::Constant(rows,cols, Scalar(1)).array())(0,0)));
+ VERIFY((numext::isnan)(m1.array().template min<PropagateNaN>(MatrixType::Constant(rows,cols, Scalar(1)).array())(0,0)));
+ VERIFY(!(numext::isnan)(m1.array().template max<PropagateNumbers>(MatrixType::Constant(rows,cols, Scalar(1)).array())(0,0)));
+ VERIFY(!(numext::isnan)(m1.array().template min<PropagateNumbers>(MatrixType::Constant(rows,cols, Scalar(1)).array())(0,0)));
+ VERIFY((numext::isnan)(m1.array().template max<PropagateNaN>(Scalar(1))(0,0)));
+ VERIFY((numext::isnan)(m1.array().template min<PropagateNaN>(Scalar(1))(0,0)));
+ VERIFY(!(numext::isnan)(m1.array().template max<PropagateNumbers>(Scalar(1))(0,0)));
+ VERIFY(!(numext::isnan)(m1.array().template min<PropagateNumbers>(Scalar(1))(0,0)));
+
+ // Reductions.
+ VERIFY((numext::isnan)(m1.template maxCoeff<PropagateNaN>()));
+ VERIFY((numext::isnan)(m1.template minCoeff<PropagateNaN>()));
+ if (m1.size() > 1) {
+ VERIFY(!(numext::isnan)(m1.template maxCoeff<PropagateNumbers>()));
+ VERIFY(!(numext::isnan)(m1.template minCoeff<PropagateNumbers>()));
+ } else {
+ VERIFY((numext::isnan)(m1.template maxCoeff<PropagateNumbers>()));
+ VERIFY((numext::isnan)(m1.template minCoeff<PropagateNumbers>()));
+ }
+ }
+}
+
+template<typename MatrixTraits> void resize(const MatrixTraits& t)
+{
+ typedef typename MatrixTraits::Scalar Scalar;
+ typedef Matrix<Scalar,Dynamic,Dynamic> MatrixType;
+ typedef Array<Scalar,Dynamic,Dynamic> Array2DType;
+ typedef Matrix<Scalar,Dynamic,1> VectorType;
+ typedef Array<Scalar,Dynamic,1> Array1DType;
+
+ Index rows = t.rows(), cols = t.cols();
+
+ MatrixType m(rows,cols);
+ VectorType v(rows);
+ Array2DType a2(rows,cols);
+ Array1DType a1(rows);
+
+ m.array().resize(rows+1,cols+1);
+ VERIFY(m.rows()==rows+1 && m.cols()==cols+1);
+ a2.matrix().resize(rows+1,cols+1);
+ VERIFY(a2.rows()==rows+1 && a2.cols()==cols+1);
+ v.array().resize(cols);
+ VERIFY(v.size()==cols);
+ a1.matrix().resize(cols);
+ VERIFY(a1.size()==cols);
+}
+
+template<int>
+void regression_bug_654()
+{
+ ArrayXf a = RowVectorXf(3);
+ VectorXf v = Array<float,1,Dynamic>(3);
+}
+
+// Check propagation of LvalueBit through Array/Matrix-Wrapper
+template<int>
+void regrrssion_bug_1410()
+{
+ const Matrix4i M;
+ const Array4i A;
+ ArrayWrapper<const Matrix4i> MA = M.array();
+ MA.row(0);
+ MatrixWrapper<const Array4i> AM = A.matrix();
+ AM.row(0);
+
+ VERIFY((internal::traits<ArrayWrapper<const Matrix4i> >::Flags&LvalueBit)==0);
+ VERIFY((internal::traits<MatrixWrapper<const Array4i> >::Flags&LvalueBit)==0);
+
+ VERIFY((internal::traits<ArrayWrapper<Matrix4i> >::Flags&LvalueBit)==LvalueBit);
+ VERIFY((internal::traits<MatrixWrapper<Array4i> >::Flags&LvalueBit)==LvalueBit);
+}
+
+EIGEN_DECLARE_TEST(array_for_matrix)
+{
+ for(int i = 0; i < g_repeat; i++) {
+ CALL_SUBTEST_1( array_for_matrix(Matrix<float, 1, 1>()) );
+ CALL_SUBTEST_2( array_for_matrix(Matrix2f()) );
+ CALL_SUBTEST_3( array_for_matrix(Matrix4d()) );
+ CALL_SUBTEST_4( array_for_matrix(MatrixXcf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
+ CALL_SUBTEST_5( array_for_matrix(MatrixXf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
+ CALL_SUBTEST_6( array_for_matrix(MatrixXi(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
+ }
+ for(int i = 0; i < g_repeat; i++) {
+ CALL_SUBTEST_1( comparisons(Matrix<float, 1, 1>()) );
+ CALL_SUBTEST_2( comparisons(Matrix2f()) );
+ CALL_SUBTEST_3( comparisons(Matrix4d()) );
+ CALL_SUBTEST_5( comparisons(MatrixXf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
+ CALL_SUBTEST_6( comparisons(MatrixXi(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
+ }
+ for(int i = 0; i < g_repeat; i++) {
+ CALL_SUBTEST_1( cwise_min_max(Matrix<float, 1, 1>()) );
+ CALL_SUBTEST_2( cwise_min_max(Matrix2f()) );
+ CALL_SUBTEST_3( cwise_min_max(Matrix4d()) );
+ CALL_SUBTEST_5( cwise_min_max(MatrixXf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
+ CALL_SUBTEST_6( cwise_min_max(MatrixXi(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
+ }
+ for(int i = 0; i < g_repeat; i++) {
+ CALL_SUBTEST_1( lpNorm(Matrix<float, 1, 1>()) );
+ CALL_SUBTEST_2( lpNorm(Vector2f()) );
+ CALL_SUBTEST_7( lpNorm(Vector3d()) );
+ CALL_SUBTEST_8( lpNorm(Vector4f()) );
+ CALL_SUBTEST_5( lpNorm(VectorXf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
+ CALL_SUBTEST_4( lpNorm(VectorXcf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
+ }
+ CALL_SUBTEST_5( lpNorm(VectorXf(0)) );
+ CALL_SUBTEST_4( lpNorm(VectorXcf(0)) );
+ for(int i = 0; i < g_repeat; i++) {
+ CALL_SUBTEST_4( resize(MatrixXcf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
+ CALL_SUBTEST_5( resize(MatrixXf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
+ CALL_SUBTEST_6( resize(MatrixXi(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
+ }
+ CALL_SUBTEST_6( regression_bug_654<0>() );
+ CALL_SUBTEST_6( regrrssion_bug_1410<0>() );
+}
diff --git a/test/array_of_string.cpp b/test/array_of_string.cpp
new file mode 100644
index 0000000..23e5152
--- /dev/null
+++ b/test/array_of_string.cpp
@@ -0,0 +1,32 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2016 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "main.h"
+
+EIGEN_DECLARE_TEST(array_of_string)
+{
+ typedef Array<std::string,1,Dynamic> ArrayXs;
+ ArrayXs a1(3), a2(3), a3(3), a3ref(3);
+ a1 << "one", "two", "three";
+ a2 << "1", "2", "3";
+ a3ref << "one (1)", "two (2)", "three (3)";
+ std::stringstream s1;
+ s1 << a1;
+ VERIFY_IS_EQUAL(s1.str(), std::string(" one two three"));
+ a3 = a1 + std::string(" (") + a2 + std::string(")");
+ VERIFY((a3==a3ref).all());
+
+ a3 = a1;
+ a3 += std::string(" (") + a2 + std::string(")");
+ VERIFY((a3==a3ref).all());
+
+ a1.swap(a3);
+ VERIFY((a1==a3ref).all());
+ VERIFY((a3!=a3ref).all());
+}
diff --git a/test/array_replicate.cpp b/test/array_replicate.cpp
new file mode 100644
index 0000000..057c3c7
--- /dev/null
+++ b/test/array_replicate.cpp
@@ -0,0 +1,81 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "main.h"
+
+template<typename MatrixType> void replicate(const MatrixType& m)
+{
+ /* this test covers the following files:
+ Replicate.cpp
+ */
+ typedef typename MatrixType::Scalar Scalar;
+ typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> VectorType;
+ typedef Matrix<Scalar, Dynamic, Dynamic> MatrixX;
+ typedef Matrix<Scalar, Dynamic, 1> VectorX;
+
+ Index rows = m.rows();
+ Index cols = m.cols();
+
+ MatrixType m1 = MatrixType::Random(rows, cols),
+ m2 = MatrixType::Random(rows, cols);
+
+ VectorType v1 = VectorType::Random(rows);
+
+ MatrixX x1, x2;
+ VectorX vx1;
+
+ int f1 = internal::random<int>(1,10),
+ f2 = internal::random<int>(1,10);
+
+ x1.resize(rows*f1,cols*f2);
+ for(int j=0; j<f2; j++)
+ for(int i=0; i<f1; i++)
+ x1.block(i*rows,j*cols,rows,cols) = m1;
+ VERIFY_IS_APPROX(x1, m1.replicate(f1,f2));
+
+ x2.resize(2*rows,3*cols);
+ x2 << m2, m2, m2,
+ m2, m2, m2;
+ VERIFY_IS_APPROX(x2, (m2.template replicate<2,3>()));
+
+ x2.resize(rows,3*cols);
+ x2 << m2, m2, m2;
+ VERIFY_IS_APPROX(x2, (m2.template replicate<1,3>()));
+
+ vx1.resize(3*rows,cols);
+ vx1 << m2, m2, m2;
+ VERIFY_IS_APPROX(vx1+vx1, vx1+(m2.template replicate<3,1>()));
+
+ vx1=m2+(m2.colwise().replicate(1));
+
+ if(m2.cols()==1)
+ VERIFY_IS_APPROX(m2.coeff(0), (m2.template replicate<3,1>().coeff(m2.rows())));
+
+ x2.resize(rows,f1);
+ for (int j=0; j<f1; ++j)
+ x2.col(j) = v1;
+ VERIFY_IS_APPROX(x2, v1.rowwise().replicate(f1));
+
+ vx1.resize(rows*f2);
+ for (int j=0; j<f2; ++j)
+ vx1.segment(j*rows,rows) = v1;
+ VERIFY_IS_APPROX(vx1, v1.colwise().replicate(f2));
+}
+
+EIGEN_DECLARE_TEST(array_replicate)
+{
+ for(int i = 0; i < g_repeat; i++) {
+ CALL_SUBTEST_1( replicate(Matrix<float, 1, 1>()) );
+ CALL_SUBTEST_2( replicate(Vector2f()) );
+ CALL_SUBTEST_3( replicate(Vector3d()) );
+ CALL_SUBTEST_4( replicate(Vector4f()) );
+ CALL_SUBTEST_5( replicate(VectorXf(16)) );
+ CALL_SUBTEST_6( replicate(VectorXcd(10)) );
+ }
+}
diff --git a/test/array_reverse.cpp b/test/array_reverse.cpp
new file mode 100644
index 0000000..c77528a
--- /dev/null
+++ b/test/array_reverse.cpp
@@ -0,0 +1,204 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+// Copyright (C) 2009 Ricard Marxer <email@ricardmarxer.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "main.h"
+#include <iostream>
+
+using namespace std;
+
+template<typename MatrixType> void reverse(const MatrixType& m)
+{
+ typedef typename MatrixType::Scalar Scalar;
+ typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> VectorType;
+
+ Index rows = m.rows();
+ Index cols = m.cols();
+
+ // this test relies a lot on Random.h, and there's not much more that we can do
+ // to test it, hence I consider that we will have tested Random.h
+ MatrixType m1 = MatrixType::Random(rows, cols), m2;
+ VectorType v1 = VectorType::Random(rows);
+
+ MatrixType m1_r = m1.reverse();
+ // Verify that MatrixBase::reverse() works
+ for ( int i = 0; i < rows; i++ ) {
+ for ( int j = 0; j < cols; j++ ) {
+ VERIFY_IS_APPROX(m1_r(i, j), m1(rows - 1 - i, cols - 1 - j));
+ }
+ }
+
+ Reverse<MatrixType> m1_rd(m1);
+ // Verify that a Reverse default (in both directions) of an expression works
+ for ( int i = 0; i < rows; i++ ) {
+ for ( int j = 0; j < cols; j++ ) {
+ VERIFY_IS_APPROX(m1_rd(i, j), m1(rows - 1 - i, cols - 1 - j));
+ }
+ }
+
+ Reverse<MatrixType, BothDirections> m1_rb(m1);
+ // Verify that a Reverse in both directions of an expression works
+ for ( int i = 0; i < rows; i++ ) {
+ for ( int j = 0; j < cols; j++ ) {
+ VERIFY_IS_APPROX(m1_rb(i, j), m1(rows - 1 - i, cols - 1 - j));
+ }
+ }
+
+ Reverse<MatrixType, Vertical> m1_rv(m1);
+ // Verify that a Reverse in the vertical directions of an expression works
+ for ( int i = 0; i < rows; i++ ) {
+ for ( int j = 0; j < cols; j++ ) {
+ VERIFY_IS_APPROX(m1_rv(i, j), m1(rows - 1 - i, j));
+ }
+ }
+
+ Reverse<MatrixType, Horizontal> m1_rh(m1);
+ // Verify that a Reverse in the horizontal directions of an expression works
+ for ( int i = 0; i < rows; i++ ) {
+ for ( int j = 0; j < cols; j++ ) {
+ VERIFY_IS_APPROX(m1_rh(i, j), m1(i, cols - 1 - j));
+ }
+ }
+
+ VectorType v1_r = v1.reverse();
+ // Verify that a VectorType::reverse() of an expression works
+ for ( int i = 0; i < rows; i++ ) {
+ VERIFY_IS_APPROX(v1_r(i), v1(rows - 1 - i));
+ }
+
+ MatrixType m1_cr = m1.colwise().reverse();
+ // Verify that PartialRedux::reverse() works (for colwise())
+ for ( int i = 0; i < rows; i++ ) {
+ for ( int j = 0; j < cols; j++ ) {
+ VERIFY_IS_APPROX(m1_cr(i, j), m1(rows - 1 - i, j));
+ }
+ }
+
+ MatrixType m1_rr = m1.rowwise().reverse();
+ // Verify that PartialRedux::reverse() works (for rowwise())
+ for ( int i = 0; i < rows; i++ ) {
+ for ( int j = 0; j < cols; j++ ) {
+ VERIFY_IS_APPROX(m1_rr(i, j), m1(i, cols - 1 - j));
+ }
+ }
+
+ Scalar x = internal::random<Scalar>();
+
+ Index r = internal::random<Index>(0, rows-1),
+ c = internal::random<Index>(0, cols-1);
+
+ m1.reverse()(r, c) = x;
+ VERIFY_IS_APPROX(x, m1(rows - 1 - r, cols - 1 - c));
+
+ m2 = m1;
+ m2.reverseInPlace();
+ VERIFY_IS_APPROX(m2,m1.reverse().eval());
+
+ m2 = m1;
+ m2.col(0).reverseInPlace();
+ VERIFY_IS_APPROX(m2.col(0),m1.col(0).reverse().eval());
+
+ m2 = m1;
+ m2.row(0).reverseInPlace();
+ VERIFY_IS_APPROX(m2.row(0),m1.row(0).reverse().eval());
+
+ m2 = m1;
+ m2.rowwise().reverseInPlace();
+ VERIFY_IS_APPROX(m2,m1.rowwise().reverse().eval());
+
+ m2 = m1;
+ m2.colwise().reverseInPlace();
+ VERIFY_IS_APPROX(m2,m1.colwise().reverse().eval());
+
+ m1.colwise().reverse()(r, c) = x;
+ VERIFY_IS_APPROX(x, m1(rows - 1 - r, c));
+
+ m1.rowwise().reverse()(r, c) = x;
+ VERIFY_IS_APPROX(x, m1(r, cols - 1 - c));
+}
+
+template<int>
+void array_reverse_extra()
+{
+ Vector4f x; x << 1, 2, 3, 4;
+ Vector4f y; y << 4, 3, 2, 1;
+ VERIFY(x.reverse()[1] == 3);
+ VERIFY(x.reverse() == y);
+}
+
+// Simpler version of reverseInPlace leveraging a bug
+// in clang 6/7 with -O2 and AVX or AVX512 enabled.
+// This simpler version ensure that the clang bug is not simply hidden
+// through mis-inlining of reverseInPlace or other minor changes.
+template<typename MatrixType>
+EIGEN_DONT_INLINE
+void bug1684_job1(MatrixType& m1, MatrixType& m2)
+{
+ m2 = m1;
+ m2.col(0).swap(m2.col(3));
+ m2.col(1).swap(m2.col(2));
+}
+
+template<typename MatrixType>
+EIGEN_DONT_INLINE
+void bug1684_job2(MatrixType& m1, MatrixType& m2)
+{
+ m2 = m1; // load m1/m2 in AVX registers
+ m1.col(0) = m2.col(3); // perform 128 bits moves
+ m1.col(1) = m2.col(2);
+ m1.col(2) = m2.col(1);
+ m1.col(3) = m2.col(0);
+}
+
+template<typename MatrixType>
+EIGEN_DONT_INLINE
+void bug1684_job3(MatrixType& m1, MatrixType& m2)
+{
+ m2 = m1;
+ Vector4f tmp;
+ tmp = m2.col(0);
+ m2.col(0) = m2.col(3);
+ m2.col(3) = tmp;
+ tmp = m2.col(1);
+ m2.col(1) = m2.col(2);
+ m2.col(2) = tmp;
+
+}
+
+template<int>
+void bug1684()
+{
+ Matrix4f m1 = Matrix4f::Random();
+ Matrix4f m2 = Matrix4f::Random();
+ bug1684_job1(m1,m2);
+ VERIFY_IS_APPROX(m2, m1.rowwise().reverse().eval());
+ bug1684_job2(m1,m2);
+ VERIFY_IS_APPROX(m2, m1.rowwise().reverse().eval());
+ // This one still fail after our swap's workaround,
+ // but I expect users not to implement their own swap.
+ // bug1684_job3(m1,m2);
+ // VERIFY_IS_APPROX(m2, m1.rowwise().reverse().eval());
+}
+
+EIGEN_DECLARE_TEST(array_reverse)
+{
+ for(int i = 0; i < g_repeat; i++) {
+ CALL_SUBTEST_1( reverse(Matrix<float, 1, 1>()) );
+ CALL_SUBTEST_2( reverse(Matrix2f()) );
+ CALL_SUBTEST_3( reverse(Matrix4f()) );
+ CALL_SUBTEST_4( reverse(Matrix4d()) );
+ CALL_SUBTEST_5( reverse(MatrixXcf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
+ CALL_SUBTEST_6( reverse(MatrixXi(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
+ CALL_SUBTEST_7( reverse(MatrixXcd(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
+ CALL_SUBTEST_8( reverse(Matrix<float, 100, 100>()) );
+ CALL_SUBTEST_9( reverse(Matrix<float,Dynamic,Dynamic,RowMajor>(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
+ CALL_SUBTEST_3( bug1684<0>() );
+ }
+ CALL_SUBTEST_3( array_reverse_extra<0>() );
+}
diff --git a/test/bandmatrix.cpp b/test/bandmatrix.cpp
new file mode 100644
index 0000000..66a1b0d
--- /dev/null
+++ b/test/bandmatrix.cpp
@@ -0,0 +1,71 @@
+// This file is triangularView of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "main.h"
+
+template<typename MatrixType> void bandmatrix(const MatrixType& _m)
+{
+ typedef typename MatrixType::Scalar Scalar;
+ typedef typename NumTraits<Scalar>::Real RealScalar;
+ typedef Matrix<Scalar,Dynamic,Dynamic> DenseMatrixType;
+
+ Index rows = _m.rows();
+ Index cols = _m.cols();
+ Index supers = _m.supers();
+ Index subs = _m.subs();
+
+ MatrixType m(rows,cols,supers,subs);
+
+ DenseMatrixType dm1(rows,cols);
+ dm1.setZero();
+
+ m.diagonal().setConstant(123);
+ dm1.diagonal().setConstant(123);
+ for (int i=1; i<=m.supers();++i)
+ {
+ m.diagonal(i).setConstant(static_cast<RealScalar>(i));
+ dm1.diagonal(i).setConstant(static_cast<RealScalar>(i));
+ }
+ for (int i=1; i<=m.subs();++i)
+ {
+ m.diagonal(-i).setConstant(-static_cast<RealScalar>(i));
+ dm1.diagonal(-i).setConstant(-static_cast<RealScalar>(i));
+ }
+ //std::cerr << m.m_data << "\n\n" << m.toDense() << "\n\n" << dm1 << "\n\n\n\n";
+ VERIFY_IS_APPROX(dm1,m.toDenseMatrix());
+
+ for (int i=0; i<cols; ++i)
+ {
+ m.col(i).setConstant(static_cast<RealScalar>(i+1));
+ dm1.col(i).setConstant(static_cast<RealScalar>(i+1));
+ }
+ Index d = (std::min)(rows,cols);
+ Index a = std::max<Index>(0,cols-d-supers);
+ Index b = std::max<Index>(0,rows-d-subs);
+ if(a>0) dm1.block(0,d+supers,rows,a).setZero();
+ dm1.block(0,supers+1,cols-supers-1-a,cols-supers-1-a).template triangularView<Upper>().setZero();
+ dm1.block(subs+1,0,rows-subs-1-b,rows-subs-1-b).template triangularView<Lower>().setZero();
+ if(b>0) dm1.block(d+subs,0,b,cols).setZero();
+ //std::cerr << m.m_data << "\n\n" << m.toDense() << "\n\n" << dm1 << "\n\n";
+ VERIFY_IS_APPROX(dm1,m.toDenseMatrix());
+
+}
+
+using Eigen::internal::BandMatrix;
+
+EIGEN_DECLARE_TEST(bandmatrix)
+{
+ for(int i = 0; i < 10*g_repeat ; i++) {
+ Index rows = internal::random<Index>(1,10);
+ Index cols = internal::random<Index>(1,10);
+ Index sups = internal::random<Index>(0,cols-1);
+ Index subs = internal::random<Index>(0,rows-1);
+ CALL_SUBTEST(bandmatrix(BandMatrix<float>(rows,cols,sups,subs)) );
+ }
+}
diff --git a/test/basicstuff.cpp b/test/basicstuff.cpp
new file mode 100644
index 0000000..47dfc04
--- /dev/null
+++ b/test/basicstuff.cpp
@@ -0,0 +1,358 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "main.h"
+#include "random_without_cast_overflow.h"
+
+template <typename MatrixType>
+std::enable_if_t<(MatrixType::RowsAtCompileTime==1 || MatrixType::ColsAtCompileTime==1),void>
+check_index(const MatrixType& m) {
+ VERIFY_RAISES_ASSERT(m[0]);
+ VERIFY_RAISES_ASSERT((m+m)[0]);
+}
+
+template <typename MatrixType>
+std::enable_if_t<!(MatrixType::RowsAtCompileTime==1 || MatrixType::ColsAtCompileTime==1),void>
+check_index(const MatrixType& /*unused*/) {}
+
+template<typename MatrixType> void basicStuff(const MatrixType& m)
+{
+ typedef typename MatrixType::Scalar Scalar;
+ typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> VectorType;
+ typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime> SquareMatrixType;
+
+ Index rows = m.rows();
+ Index cols = m.cols();
+
+ // this test relies a lot on Random.h, and there's not much more that we can do
+ // to test it, hence I consider that we will have tested Random.h
+ MatrixType m1 = MatrixType::Random(rows, cols),
+ m2 = MatrixType::Random(rows, cols),
+ m3(rows, cols),
+ mzero = MatrixType::Zero(rows, cols),
+ square = Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime>::Random(rows, rows);
+ VectorType v1 = VectorType::Random(rows),
+ vzero = VectorType::Zero(rows);
+ SquareMatrixType sm1 = SquareMatrixType::Random(rows,rows), sm2(rows,rows);
+
+ Scalar x = 0;
+ while(x == Scalar(0)) x = internal::random<Scalar>();
+
+ Index r = internal::random<Index>(0, rows-1),
+ c = internal::random<Index>(0, cols-1);
+
+ m1.coeffRef(r,c) = x;
+ VERIFY_IS_APPROX(x, m1.coeff(r,c));
+ m1(r,c) = x;
+ VERIFY_IS_APPROX(x, m1(r,c));
+ v1.coeffRef(r) = x;
+ VERIFY_IS_APPROX(x, v1.coeff(r));
+ v1(r) = x;
+ VERIFY_IS_APPROX(x, v1(r));
+ v1[r] = x;
+ VERIFY_IS_APPROX(x, v1[r]);
+
+ // test fetching with various index types.
+ Index r1 = internal::random<Index>(0, numext::mini(Index(127),rows-1));
+ x = v1(static_cast<char>(r1));
+ x = v1(static_cast<signed char>(r1));
+ x = v1(static_cast<unsigned char>(r1));
+ x = v1(static_cast<signed short>(r1));
+ x = v1(static_cast<unsigned short>(r1));
+ x = v1(static_cast<signed int>(r1));
+ x = v1(static_cast<unsigned int>(r1));
+ x = v1(static_cast<signed long>(r1));
+ x = v1(static_cast<unsigned long>(r1));
+ x = v1(static_cast<long long int>(r1));
+ x = v1(static_cast<unsigned long long int>(r1));
+
+ VERIFY_IS_APPROX( v1, v1);
+ VERIFY_IS_NOT_APPROX( v1, 2*v1);
+ VERIFY_IS_MUCH_SMALLER_THAN( vzero, v1);
+ VERIFY_IS_MUCH_SMALLER_THAN( vzero, v1.squaredNorm());
+ VERIFY_IS_NOT_MUCH_SMALLER_THAN(v1, v1);
+ VERIFY_IS_APPROX( vzero, v1-v1);
+ VERIFY_IS_APPROX( m1, m1);
+ VERIFY_IS_NOT_APPROX( m1, 2*m1);
+ VERIFY_IS_MUCH_SMALLER_THAN( mzero, m1);
+ VERIFY_IS_NOT_MUCH_SMALLER_THAN(m1, m1);
+ VERIFY_IS_APPROX( mzero, m1-m1);
+
+ // always test operator() on each read-only expression class,
+ // in order to check const-qualifiers.
+ // indeed, if an expression class (here Zero) is meant to be read-only,
+ // hence has no _write() method, the corresponding MatrixBase method (here zero())
+ // should return a const-qualified object so that it is the const-qualified
+ // operator() that gets called, which in turn calls _read().
+ VERIFY_IS_MUCH_SMALLER_THAN(MatrixType::Zero(rows,cols)(r,c), static_cast<Scalar>(1));
+
+ // now test copying a row-vector into a (column-)vector and conversely.
+ square.col(r) = square.row(r).eval();
+ Matrix<Scalar, 1, MatrixType::RowsAtCompileTime> rv(rows);
+ Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> cv(rows);
+ rv = square.row(r);
+ cv = square.col(r);
+
+ VERIFY_IS_APPROX(rv, cv.transpose());
+
+ if(cols!=1 && rows!=1 && MatrixType::SizeAtCompileTime!=Dynamic)
+ {
+ VERIFY_RAISES_ASSERT(m1 = (m2.block(0,0, rows-1, cols-1)));
+ }
+
+ if(cols!=1 && rows!=1)
+ {
+ check_index(m1);
+ }
+
+ VERIFY_IS_APPROX(m3 = m1,m1);
+ MatrixType m4;
+ VERIFY_IS_APPROX(m4 = m1,m1);
+
+ m3.real() = m1.real();
+ VERIFY_IS_APPROX(static_cast<const MatrixType&>(m3).real(), static_cast<const MatrixType&>(m1).real());
+ VERIFY_IS_APPROX(static_cast<const MatrixType&>(m3).real(), m1.real());
+
+ // check == / != operators
+ VERIFY(m1==m1);
+ VERIFY(m1!=m2);
+ VERIFY(!(m1==m2));
+ VERIFY(!(m1!=m1));
+ m1 = m2;
+ VERIFY(m1==m2);
+ VERIFY(!(m1!=m2));
+
+ // check automatic transposition
+ sm2.setZero();
+ for(Index i=0;i<rows;++i)
+ sm2.col(i) = sm1.row(i);
+ VERIFY_IS_APPROX(sm2,sm1.transpose());
+
+ sm2.setZero();
+ for(Index i=0;i<rows;++i)
+ sm2.col(i).noalias() = sm1.row(i);
+ VERIFY_IS_APPROX(sm2,sm1.transpose());
+
+ sm2.setZero();
+ for(Index i=0;i<rows;++i)
+ sm2.col(i).noalias() += sm1.row(i);
+ VERIFY_IS_APPROX(sm2,sm1.transpose());
+
+ sm2.setZero();
+ for(Index i=0;i<rows;++i)
+ sm2.col(i).noalias() -= sm1.row(i);
+ VERIFY_IS_APPROX(sm2,-sm1.transpose());
+
+ // check ternary usage
+ {
+ bool b = internal::random<int>(0,10)>5;
+ m3 = b ? m1 : m2;
+ if(b) VERIFY_IS_APPROX(m3,m1);
+ else VERIFY_IS_APPROX(m3,m2);
+ m3 = b ? -m1 : m2;
+ if(b) VERIFY_IS_APPROX(m3,-m1);
+ else VERIFY_IS_APPROX(m3,m2);
+ m3 = b ? m1 : -m2;
+ if(b) VERIFY_IS_APPROX(m3,m1);
+ else VERIFY_IS_APPROX(m3,-m2);
+ }
+}
+
+template<typename MatrixType> void basicStuffComplex(const MatrixType& m)
+{
+ typedef typename MatrixType::Scalar Scalar;
+ typedef typename NumTraits<Scalar>::Real RealScalar;
+ typedef Matrix<RealScalar, MatrixType::RowsAtCompileTime, MatrixType::ColsAtCompileTime> RealMatrixType;
+
+ Index rows = m.rows();
+ Index cols = m.cols();
+
+ Scalar s1 = internal::random<Scalar>(),
+ s2 = internal::random<Scalar>();
+
+ VERIFY(numext::real(s1)==numext::real_ref(s1));
+ VERIFY(numext::imag(s1)==numext::imag_ref(s1));
+ numext::real_ref(s1) = numext::real(s2);
+ numext::imag_ref(s1) = numext::imag(s2);
+ VERIFY(internal::isApprox(s1, s2, NumTraits<RealScalar>::epsilon()));
+ // extended precision in Intel FPUs means that s1 == s2 in the line above is not guaranteed.
+
+ RealMatrixType rm1 = RealMatrixType::Random(rows,cols),
+ rm2 = RealMatrixType::Random(rows,cols);
+ MatrixType cm(rows,cols);
+ cm.real() = rm1;
+ cm.imag() = rm2;
+ VERIFY_IS_APPROX(static_cast<const MatrixType&>(cm).real(), rm1);
+ VERIFY_IS_APPROX(static_cast<const MatrixType&>(cm).imag(), rm2);
+ rm1.setZero();
+ rm2.setZero();
+ rm1 = cm.real();
+ rm2 = cm.imag();
+ VERIFY_IS_APPROX(static_cast<const MatrixType&>(cm).real(), rm1);
+ VERIFY_IS_APPROX(static_cast<const MatrixType&>(cm).imag(), rm2);
+ cm.real().setZero();
+ VERIFY(static_cast<const MatrixType&>(cm).real().isZero());
+ VERIFY(!static_cast<const MatrixType&>(cm).imag().isZero());
+}
+
+template<typename SrcScalar, typename TgtScalar>
+struct casting_test {
+ static void run() {
+ Matrix<SrcScalar,4,4> m;
+ for (int i=0; i<m.rows(); ++i) {
+ for (int j=0; j<m.cols(); ++j) {
+ m(i, j) = internal::random_without_cast_overflow<SrcScalar,TgtScalar>::value();
+ }
+ }
+ Matrix<TgtScalar,4,4> n = m.template cast<TgtScalar>();
+ for (int i=0; i<m.rows(); ++i) {
+ for (int j=0; j<m.cols(); ++j) {
+ VERIFY_IS_APPROX(n(i, j), (internal::cast<SrcScalar,TgtScalar>(m(i, j))));
+ }
+ }
+ }
+};
+
+template<typename SrcScalar, typename EnableIf = void>
+struct casting_test_runner {
+ static void run() {
+ casting_test<SrcScalar, bool>::run();
+ casting_test<SrcScalar, int8_t>::run();
+ casting_test<SrcScalar, uint8_t>::run();
+ casting_test<SrcScalar, int16_t>::run();
+ casting_test<SrcScalar, uint16_t>::run();
+ casting_test<SrcScalar, int32_t>::run();
+ casting_test<SrcScalar, uint32_t>::run();
+ casting_test<SrcScalar, int64_t>::run();
+ casting_test<SrcScalar, uint64_t>::run();
+ casting_test<SrcScalar, half>::run();
+ casting_test<SrcScalar, bfloat16>::run();
+ casting_test<SrcScalar, float>::run();
+ casting_test<SrcScalar, double>::run();
+ casting_test<SrcScalar, std::complex<float> >::run();
+ casting_test<SrcScalar, std::complex<double> >::run();
+ }
+};
+
+template<typename SrcScalar>
+struct casting_test_runner<SrcScalar, std::enable_if_t<(NumTraits<SrcScalar>::IsComplex)>>
+{
+ static void run() {
+ // Only a few casts from std::complex<T> are defined.
+ casting_test<SrcScalar, half>::run();
+ casting_test<SrcScalar, bfloat16>::run();
+ casting_test<SrcScalar, std::complex<float> >::run();
+ casting_test<SrcScalar, std::complex<double> >::run();
+ }
+};
+
+void casting_all() {
+ casting_test_runner<bool>::run();
+ casting_test_runner<int8_t>::run();
+ casting_test_runner<uint8_t>::run();
+ casting_test_runner<int16_t>::run();
+ casting_test_runner<uint16_t>::run();
+ casting_test_runner<int32_t>::run();
+ casting_test_runner<uint32_t>::run();
+ casting_test_runner<int64_t>::run();
+ casting_test_runner<uint64_t>::run();
+ casting_test_runner<half>::run();
+ casting_test_runner<bfloat16>::run();
+ casting_test_runner<float>::run();
+ casting_test_runner<double>::run();
+ casting_test_runner<std::complex<float> >::run();
+ casting_test_runner<std::complex<double> >::run();
+}
+
+template <typename Scalar>
+void fixedSizeMatrixConstruction()
+{
+ Scalar raw[4];
+ for(int k=0; k<4; ++k)
+ raw[k] = internal::random<Scalar>();
+
+ {
+ Matrix<Scalar,4,1> m(raw);
+ Array<Scalar,4,1> a(raw);
+ for(int k=0; k<4; ++k) VERIFY(m(k) == raw[k]);
+ for(int k=0; k<4; ++k) VERIFY(a(k) == raw[k]);
+ VERIFY_IS_EQUAL(m,(Matrix<Scalar,4,1>(raw[0],raw[1],raw[2],raw[3])));
+ VERIFY((a==(Array<Scalar,4,1>(raw[0],raw[1],raw[2],raw[3]))).all());
+ }
+ {
+ Matrix<Scalar,3,1> m(raw);
+ Array<Scalar,3,1> a(raw);
+ for(int k=0; k<3; ++k) VERIFY(m(k) == raw[k]);
+ for(int k=0; k<3; ++k) VERIFY(a(k) == raw[k]);
+ VERIFY_IS_EQUAL(m,(Matrix<Scalar,3,1>(raw[0],raw[1],raw[2])));
+ VERIFY((a==Array<Scalar,3,1>(raw[0],raw[1],raw[2])).all());
+ }
+ {
+ Matrix<Scalar,2,1> m(raw), m2( (DenseIndex(raw[0])), (DenseIndex(raw[1])) );
+ Array<Scalar,2,1> a(raw), a2( (DenseIndex(raw[0])), (DenseIndex(raw[1])) );
+ for(int k=0; k<2; ++k) VERIFY(m(k) == raw[k]);
+ for(int k=0; k<2; ++k) VERIFY(a(k) == raw[k]);
+ VERIFY_IS_EQUAL(m,(Matrix<Scalar,2,1>(raw[0],raw[1])));
+ VERIFY((a==Array<Scalar,2,1>(raw[0],raw[1])).all());
+ for(int k=0; k<2; ++k) VERIFY(m2(k) == DenseIndex(raw[k]));
+ for(int k=0; k<2; ++k) VERIFY(a2(k) == DenseIndex(raw[k]));
+ }
+ {
+ Matrix<Scalar,1,2> m(raw),
+ m2( (DenseIndex(raw[0])), (DenseIndex(raw[1])) ),
+ m3( (int(raw[0])), (int(raw[1])) ),
+ m4( (float(raw[0])), (float(raw[1])) );
+ Array<Scalar,1,2> a(raw), a2( (DenseIndex(raw[0])), (DenseIndex(raw[1])) );
+ for(int k=0; k<2; ++k) VERIFY(m(k) == raw[k]);
+ for(int k=0; k<2; ++k) VERIFY(a(k) == raw[k]);
+ VERIFY_IS_EQUAL(m,(Matrix<Scalar,1,2>(raw[0],raw[1])));
+ VERIFY((a==Array<Scalar,1,2>(raw[0],raw[1])).all());
+ for(int k=0; k<2; ++k) VERIFY(m2(k) == DenseIndex(raw[k]));
+ for(int k=0; k<2; ++k) VERIFY(a2(k) == DenseIndex(raw[k]));
+ for(int k=0; k<2; ++k) VERIFY(m3(k) == int(raw[k]));
+ for(int k=0; k<2; ++k) VERIFY((m4(k)) == Scalar(float(raw[k])));
+ }
+ {
+ Matrix<Scalar,1,1> m(raw), m1(raw[0]), m2( (DenseIndex(raw[0])) ), m3( (int(raw[0])) );
+ Array<Scalar,1,1> a(raw), a1(raw[0]), a2( (DenseIndex(raw[0])) );
+ VERIFY(m(0) == raw[0]);
+ VERIFY(a(0) == raw[0]);
+ VERIFY(m1(0) == raw[0]);
+ VERIFY(a1(0) == raw[0]);
+ VERIFY(m2(0) == DenseIndex(raw[0]));
+ VERIFY(a2(0) == DenseIndex(raw[0]));
+ VERIFY(m3(0) == int(raw[0]));
+ VERIFY_IS_EQUAL(m,(Matrix<Scalar,1,1>(raw[0])));
+ VERIFY((a==Array<Scalar,1,1>(raw[0])).all());
+ }
+}
+
+EIGEN_DECLARE_TEST(basicstuff)
+{
+ for(int i = 0; i < g_repeat; i++) {
+ CALL_SUBTEST_1( basicStuff(Matrix<float, 1, 1>()) );
+ CALL_SUBTEST_2( basicStuff(Matrix4d()) );
+ CALL_SUBTEST_3( basicStuff(MatrixXcf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
+ CALL_SUBTEST_4( basicStuff(MatrixXi(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
+ CALL_SUBTEST_5( basicStuff(MatrixXcd(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
+ CALL_SUBTEST_6( basicStuff(Matrix<float, 100, 100>()) );
+ CALL_SUBTEST_7( basicStuff(Matrix<long double,Dynamic,Dynamic>(internal::random<int>(1,EIGEN_TEST_MAX_SIZE),internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
+ CALL_SUBTEST_8( casting_all() );
+
+ CALL_SUBTEST_3( basicStuffComplex(MatrixXcf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
+ CALL_SUBTEST_5( basicStuffComplex(MatrixXcd(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
+ }
+
+ CALL_SUBTEST_1(fixedSizeMatrixConstruction<unsigned char>());
+ CALL_SUBTEST_1(fixedSizeMatrixConstruction<float>());
+ CALL_SUBTEST_1(fixedSizeMatrixConstruction<double>());
+ CALL_SUBTEST_1(fixedSizeMatrixConstruction<int>());
+ CALL_SUBTEST_1(fixedSizeMatrixConstruction<long int>());
+ CALL_SUBTEST_1(fixedSizeMatrixConstruction<std::ptrdiff_t>());
+}
diff --git a/test/bdcsvd.cpp b/test/bdcsvd.cpp
new file mode 100644
index 0000000..539494b
--- /dev/null
+++ b/test/bdcsvd.cpp
@@ -0,0 +1,181 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2013 Gauthier Brun <brun.gauthier@gmail.com>
+// Copyright (C) 2013 Nicolas Carre <nicolas.carre@ensimag.fr>
+// Copyright (C) 2013 Jean Ceccato <jean.ceccato@ensimag.fr>
+// Copyright (C) 2013 Pierre Zoppitelli <pierre.zoppitelli@ensimag.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/
+
+// We explicitly disable deprecated declarations for this set of tests
+// because we purposely verify assertions for the deprecated SVD runtime
+// option behavior.
+#if defined(__GNUC__)
+#pragma GCC diagnostic ignored "-Wdeprecated-declarations"
+#elif defined(_MSC_VER)
+#pragma warning( disable : 4996 )
+#endif
+
+// discard stack allocation as that too bypasses malloc
+#define EIGEN_STACK_ALLOCATION_LIMIT 0
+#define EIGEN_RUNTIME_NO_MALLOC
+
+#include "main.h"
+#include <Eigen/SVD>
+
+#define SVD_DEFAULT(M) BDCSVD<M>
+#define SVD_FOR_MIN_NORM(M) BDCSVD<M>
+#define SVD_STATIC_OPTIONS(M, O) BDCSVD<M, O>
+#include "svd_common.h"
+
+template<typename MatrixType>
+void bdcsvd_method()
+{
+ enum { Size = MatrixType::RowsAtCompileTime };
+ typedef typename MatrixType::RealScalar RealScalar;
+ typedef Matrix<RealScalar, Size, 1> RealVecType;
+ MatrixType m = MatrixType::Identity();
+ VERIFY_IS_APPROX(m.bdcSvd().singularValues(), RealVecType::Ones());
+ VERIFY_RAISES_ASSERT(m.bdcSvd().matrixU());
+ VERIFY_RAISES_ASSERT(m.bdcSvd().matrixV());
+
+ // Deprecated behavior.
+ VERIFY_IS_APPROX(m.bdcSvd(ComputeFullU|ComputeFullV).solve(m), m);
+ VERIFY_IS_APPROX(m.bdcSvd(ComputeFullU|ComputeFullV).transpose().solve(m), m);
+ VERIFY_IS_APPROX(m.bdcSvd(ComputeFullU|ComputeFullV).adjoint().solve(m), m);
+ VERIFY_IS_APPROX(m.template bdcSvd<DisableQRDecomposition>(ComputeFullU|ComputeFullV).solve(m), m);
+ VERIFY_IS_APPROX(m.template bdcSvd<DisableQRDecomposition>(ComputeFullU|ComputeFullV).transpose().solve(m), m);
+ VERIFY_IS_APPROX(m.template bdcSvd<DisableQRDecomposition>(ComputeFullU|ComputeFullV).adjoint().solve(m), m);
+
+ VERIFY_IS_APPROX(m.template bdcSvd<ComputeFullU | ComputeFullV>().solve(m), m);
+ VERIFY_IS_APPROX(m.template bdcSvd<ComputeFullU | ComputeFullV>().transpose().solve(m), m);
+ VERIFY_IS_APPROX(m.template bdcSvd<ComputeFullU | ComputeFullV>().adjoint().solve(m), m);
+
+ VERIFY_IS_APPROX(m.template bdcSvd<ComputeFullU | ComputeFullV | DisableQRDecomposition>().solve(m), m);
+ VERIFY_IS_APPROX(m.template bdcSvd<ComputeFullU | ComputeFullV | DisableQRDecomposition>().transpose().solve(m), m);
+ VERIFY_IS_APPROX(m.template bdcSvd<ComputeFullU | ComputeFullV | DisableQRDecomposition>().adjoint().solve(m), m);
+}
+
+// compare the Singular values returned with Jacobi and Bdc
+template <typename MatrixType>
+void compare_bdc_jacobi(const MatrixType& a = MatrixType(), int algoswap = 16, bool random = true) {
+ MatrixType m = random ? MatrixType::Random(a.rows(), a.cols()) : a;
+
+ BDCSVD<MatrixType> bdc_svd(m.rows(), m.cols());
+ bdc_svd.setSwitchSize(algoswap);
+ bdc_svd.compute(m);
+
+ JacobiSVD<MatrixType> jacobi_svd(m);
+ VERIFY_IS_APPROX(bdc_svd.singularValues(), jacobi_svd.singularValues());
+}
+
+// Verifies total deflation is **not** triggered.
+void compare_bdc_jacobi_instance(bool structure_as_m, int algoswap = 16)
+{
+ MatrixXd m(4, 3);
+ if (structure_as_m) {
+ // The first 3 rows are the reduced form of Matrix 1 as shown below, and it
+ // has nonzero elements in the first column and diagonals only.
+ m << 1.056293, 0, 0,
+ -0.336468, 0.907359, 0,
+ -1.566245, 0, 0.149150,
+ -0.1, 0, 0;
+ } else {
+ // Matrix 1.
+ m << 0.882336, 18.3914, -26.7921,
+ -5.58135, 17.1931, -24.0892,
+ -20.794, 8.68496, -4.83103,
+ -8.4981, -10.5451, 23.9072;
+ }
+ compare_bdc_jacobi(m, algoswap, false);
+}
+
+template <typename MatrixType>
+void bdcsvd_all_options(const MatrixType& input = MatrixType()) {
+ MatrixType m(input.rows(), input.cols());
+ svd_fill_random(m);
+ svd_option_checks<MatrixType, 0>(m);
+}
+
+template <typename MatrixType>
+void bdcsvd_verify_assert(const MatrixType& input = MatrixType()) {
+ svd_verify_assert<MatrixType>(input);
+ svd_verify_constructor_options_assert<BDCSVD<MatrixType>>(input);
+}
+
+EIGEN_DECLARE_TEST(bdcsvd)
+{
+ CALL_SUBTEST_1((bdcsvd_verify_assert<Matrix3f>()));
+ CALL_SUBTEST_1((bdcsvd_verify_assert<Matrix4d>()));
+ CALL_SUBTEST_2((bdcsvd_verify_assert<Matrix<float, 10, 7>>()));
+ CALL_SUBTEST_2((bdcsvd_verify_assert<Matrix<float, 7, 10>>()));
+ CALL_SUBTEST_3((bdcsvd_verify_assert<Matrix<std::complex<double>, 6, 9>>()));
+
+ CALL_SUBTEST_4((svd_all_trivial_2x2(bdcsvd_all_options<Matrix2cd>)));
+ CALL_SUBTEST_5((svd_all_trivial_2x2(bdcsvd_all_options<Matrix2d>)));
+
+ for (int i = 0; i < g_repeat; i++) {
+ int r = internal::random<int>(1, EIGEN_TEST_MAX_SIZE/2),
+ c = internal::random<int>(1, EIGEN_TEST_MAX_SIZE/2);
+
+ TEST_SET_BUT_UNUSED_VARIABLE(r)
+ TEST_SET_BUT_UNUSED_VARIABLE(c)
+
+ CALL_SUBTEST_6((compare_bdc_jacobi<MatrixXf>(MatrixXf(r, c))));
+ CALL_SUBTEST_7((compare_bdc_jacobi<MatrixXd>(MatrixXd(r, c))));
+ CALL_SUBTEST_8((compare_bdc_jacobi<MatrixXcd>(MatrixXcd(r, c))));
+ // Test on inf/nan matrix
+ CALL_SUBTEST_9((svd_inf_nan<MatrixXf>()));
+ CALL_SUBTEST_10((svd_inf_nan<MatrixXd>()));
+
+ // Verify some computations using all combinations of the Options template parameter.
+ CALL_SUBTEST_11((bdcsvd_all_options<Matrix3f>()));
+ CALL_SUBTEST_12((bdcsvd_all_options<Matrix<float, 2, 3>>()));
+ CALL_SUBTEST_13((bdcsvd_all_options<MatrixXd>(MatrixXd(20, 17))));
+ CALL_SUBTEST_14((bdcsvd_all_options<MatrixXd>(MatrixXd(17, 20))));
+ CALL_SUBTEST_15((bdcsvd_all_options<Matrix<double, Dynamic, 15>>(Matrix<double, Dynamic, 15>(r, 15))));
+ CALL_SUBTEST_16((bdcsvd_all_options<Matrix<double, 13, Dynamic>>(Matrix<double, 13, Dynamic>(13, c))));
+ CALL_SUBTEST_17((bdcsvd_all_options<MatrixXf>(MatrixXf(r, c))));
+ CALL_SUBTEST_18((bdcsvd_all_options<MatrixXcd>(MatrixXcd(r, c))));
+ CALL_SUBTEST_19((bdcsvd_all_options<MatrixXd>(MatrixXd(r, c))));
+ CALL_SUBTEST_20((bdcsvd_all_options<Matrix<double, Dynamic, Dynamic, RowMajor>>(Matrix<double, Dynamic, Dynamic, RowMajor>(20, 27))));
+ CALL_SUBTEST_21((bdcsvd_all_options<Matrix<double, Dynamic, Dynamic, RowMajor>>(Matrix<double, Dynamic, Dynamic, RowMajor>(27, 20))));
+
+ CALL_SUBTEST_22((
+ svd_check_max_size_matrix<Matrix<float, Dynamic, Dynamic, ColMajor, 20, 35>, ColPivHouseholderQRPreconditioner>(
+ r, c)));
+ CALL_SUBTEST_22(
+ (svd_check_max_size_matrix<Matrix<float, Dynamic, Dynamic, ColMajor, 35, 20>, HouseholderQRPreconditioner>(r,
+ c)));
+ CALL_SUBTEST_22((
+ svd_check_max_size_matrix<Matrix<float, Dynamic, Dynamic, RowMajor, 20, 35>, ColPivHouseholderQRPreconditioner>(
+ r, c)));
+ CALL_SUBTEST_22(
+ (svd_check_max_size_matrix<Matrix<float, Dynamic, Dynamic, RowMajor, 35, 20>, HouseholderQRPreconditioner>(r,
+ c)));
+ }
+
+ // test matrixbase method
+ CALL_SUBTEST_23(( bdcsvd_method<Matrix2cd>() ));
+ CALL_SUBTEST_23(( bdcsvd_method<Matrix3f>() ));
+
+ // Test problem size constructors
+ CALL_SUBTEST_24( BDCSVD<MatrixXf>(10,10) );
+
+ // Check that preallocation avoids subsequent mallocs
+ // Disabled because not supported by BDCSVD
+ // CALL_SUBTEST_9( svd_preallocate<void>() );
+
+ CALL_SUBTEST_25( svd_underoverflow<void>() );
+
+ // Without total deflation issues.
+ CALL_SUBTEST_26(( compare_bdc_jacobi_instance(true) ));
+ CALL_SUBTEST_26(( compare_bdc_jacobi_instance(false) ));
+
+ // With total deflation issues before, when it shouldn't be triggered.
+ CALL_SUBTEST_27(( compare_bdc_jacobi_instance(true, 3) ));
+ CALL_SUBTEST_27(( compare_bdc_jacobi_instance(false, 3) ));
+}
diff --git a/test/bfloat16_float.cpp b/test/bfloat16_float.cpp
new file mode 100644
index 0000000..b2a22ce
--- /dev/null
+++ b/test/bfloat16_float.cpp
@@ -0,0 +1,378 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include <sstream>
+#include <memory>
+#include <math.h>
+
+#include "main.h"
+
+#include <Eigen/src/Core/arch/Default/BFloat16.h>
+
+#define VERIFY_BFLOAT16_BITS_EQUAL(h, bits) \
+ VERIFY_IS_EQUAL((numext::bit_cast<numext::uint16_t>(h)), (static_cast<numext::uint16_t>(bits)))
+
+// Make sure it's possible to forward declare Eigen::bfloat16
+namespace Eigen {
+struct bfloat16;
+}
+
+using Eigen::bfloat16;
+
+float BinaryToFloat(uint32_t sign, uint32_t exponent, uint32_t high_mantissa,
+ uint32_t low_mantissa) {
+ float dest;
+ uint32_t src = (sign << 31) + (exponent << 23) + (high_mantissa << 16) + low_mantissa;
+ memcpy(static_cast<void*>(&dest),
+ static_cast<const void*>(&src), sizeof(dest));
+ return dest;
+}
+
+template<typename T>
+ void test_roundtrip() {
+ // Representable T round trip via bfloat16
+ VERIFY_IS_EQUAL((internal::cast<bfloat16,T>(internal::cast<T,bfloat16>(-std::numeric_limits<T>::infinity()))), -std::numeric_limits<T>::infinity());
+ VERIFY_IS_EQUAL((internal::cast<bfloat16,T>(internal::cast<T,bfloat16>(std::numeric_limits<T>::infinity()))), std::numeric_limits<T>::infinity());
+ VERIFY_IS_EQUAL((internal::cast<bfloat16,T>(internal::cast<T,bfloat16>(T(-1.0)))), T(-1.0));
+ VERIFY_IS_EQUAL((internal::cast<bfloat16,T>(internal::cast<T,bfloat16>(T(-0.5)))), T(-0.5));
+ VERIFY_IS_EQUAL((internal::cast<bfloat16,T>(internal::cast<T,bfloat16>(T(-0.0)))), T(-0.0));
+ VERIFY_IS_EQUAL((internal::cast<bfloat16,T>(internal::cast<T,bfloat16>(T(1.0)))), T(1.0));
+ VERIFY_IS_EQUAL((internal::cast<bfloat16,T>(internal::cast<T,bfloat16>(T(0.5)))), T(0.5));
+ VERIFY_IS_EQUAL((internal::cast<bfloat16,T>(internal::cast<T,bfloat16>(T(0.0)))), T(0.0));
+}
+
+void test_conversion()
+{
+ using Eigen::bfloat16_impl::__bfloat16_raw;
+
+ // Round-trip casts
+ VERIFY_IS_EQUAL(
+ numext::bit_cast<bfloat16>(numext::bit_cast<numext::uint16_t>(bfloat16(1.0f))),
+ bfloat16(1.0f));
+ VERIFY_IS_EQUAL(
+ numext::bit_cast<bfloat16>(numext::bit_cast<numext::uint16_t>(bfloat16(0.5f))),
+ bfloat16(0.5f));
+ VERIFY_IS_EQUAL(
+ numext::bit_cast<bfloat16>(numext::bit_cast<numext::uint16_t>(bfloat16(-0.33333f))),
+ bfloat16(-0.33333f));
+ VERIFY_IS_EQUAL(
+ numext::bit_cast<bfloat16>(numext::bit_cast<numext::uint16_t>(bfloat16(0.0f))),
+ bfloat16(0.0f));
+
+ // Conversion from float.
+ VERIFY_BFLOAT16_BITS_EQUAL(bfloat16(1.0f), 0x3f80);
+ VERIFY_BFLOAT16_BITS_EQUAL(bfloat16(0.5f), 0x3f00);
+ VERIFY_BFLOAT16_BITS_EQUAL(bfloat16(0.33333f), 0x3eab);
+ VERIFY_BFLOAT16_BITS_EQUAL(bfloat16(3.38e38f), 0x7f7e);
+ VERIFY_BFLOAT16_BITS_EQUAL(bfloat16(3.40e38f), 0x7f80); // Becomes infinity.
+
+ // Verify round-to-nearest-even behavior.
+ float val1 = static_cast<float>(bfloat16(__bfloat16_raw(0x3c00)));
+ float val2 = static_cast<float>(bfloat16(__bfloat16_raw(0x3c01)));
+ float val3 = static_cast<float>(bfloat16(__bfloat16_raw(0x3c02)));
+ VERIFY_BFLOAT16_BITS_EQUAL(bfloat16(0.5f * (val1 + val2)), 0x3c00);
+ VERIFY_BFLOAT16_BITS_EQUAL(bfloat16(0.5f * (val2 + val3)), 0x3c02);
+
+ // Conversion from int.
+ VERIFY_BFLOAT16_BITS_EQUAL(bfloat16(-1), 0xbf80);
+ VERIFY_BFLOAT16_BITS_EQUAL(bfloat16(0), 0x0000);
+ VERIFY_BFLOAT16_BITS_EQUAL(bfloat16(1), 0x3f80);
+ VERIFY_BFLOAT16_BITS_EQUAL(bfloat16(2), 0x4000);
+ VERIFY_BFLOAT16_BITS_EQUAL(bfloat16(3), 0x4040);
+ VERIFY_BFLOAT16_BITS_EQUAL(bfloat16(12), 0x4140);
+
+ // Conversion from bool.
+ VERIFY_BFLOAT16_BITS_EQUAL(bfloat16(false), 0x0000);
+ VERIFY_BFLOAT16_BITS_EQUAL(bfloat16(true), 0x3f80);
+
+ // Conversion to bool
+ VERIFY_IS_EQUAL(static_cast<bool>(bfloat16(3)), true);
+ VERIFY_IS_EQUAL(static_cast<bool>(bfloat16(0.33333f)), true);
+ VERIFY_IS_EQUAL(bfloat16(-0.0), false);
+ VERIFY_IS_EQUAL(static_cast<bool>(bfloat16(0.0)), false);
+
+ // Explicit conversion to float.
+ VERIFY_IS_EQUAL(static_cast<float>(bfloat16(__bfloat16_raw(0x0000))), 0.0f);
+ VERIFY_IS_EQUAL(static_cast<float>(bfloat16(__bfloat16_raw(0x3f80))), 1.0f);
+
+ // Implicit conversion to float
+ VERIFY_IS_EQUAL(bfloat16(__bfloat16_raw(0x0000)), 0.0f);
+ VERIFY_IS_EQUAL(bfloat16(__bfloat16_raw(0x3f80)), 1.0f);
+
+ // Zero representations
+ VERIFY_IS_EQUAL(bfloat16(0.0f), bfloat16(0.0f));
+ VERIFY_IS_EQUAL(bfloat16(-0.0f), bfloat16(0.0f));
+ VERIFY_IS_EQUAL(bfloat16(-0.0f), bfloat16(-0.0f));
+ VERIFY_BFLOAT16_BITS_EQUAL(bfloat16(0.0f), 0x0000);
+ VERIFY_BFLOAT16_BITS_EQUAL(bfloat16(-0.0f), 0x8000);
+
+ // Default is zero
+ VERIFY_IS_EQUAL(static_cast<float>(bfloat16()), 0.0f);
+
+ // Representable floats round trip via bfloat16
+ test_roundtrip<float>();
+ test_roundtrip<double>();
+ test_roundtrip<std::complex<float> >();
+ test_roundtrip<std::complex<double> >();
+
+ // Conversion
+ Array<float,1,100> a;
+ for (int i = 0; i < 100; i++) a(i) = i + 1.25;
+ Array<bfloat16,1,100> b = a.cast<bfloat16>();
+ Array<float,1,100> c = b.cast<float>();
+ for (int i = 0; i < 100; ++i) {
+ VERIFY_LE(numext::abs(c(i) - a(i)), a(i) / 128);
+ }
+
+ // Epsilon
+ VERIFY_LE(1.0f, static_cast<float>((std::numeric_limits<bfloat16>::epsilon)() + bfloat16(1.0f)));
+ VERIFY_IS_EQUAL(1.0f, static_cast<float>((std::numeric_limits<bfloat16>::epsilon)() / bfloat16(2.0f) + bfloat16(1.0f)));
+
+ // Negate
+ VERIFY_IS_EQUAL(static_cast<float>(-bfloat16(3.0f)), -3.0f);
+ VERIFY_IS_EQUAL(static_cast<float>(-bfloat16(-4.5f)), 4.5f);
+
+
+#if !EIGEN_COMP_MSVC
+ // Visual Studio errors out on divisions by 0
+ VERIFY((numext::isnan)(static_cast<float>(bfloat16(0.0 / 0.0))));
+ VERIFY((numext::isinf)(static_cast<float>(bfloat16(1.0 / 0.0))));
+ VERIFY((numext::isinf)(static_cast<float>(bfloat16(-1.0 / 0.0))));
+
+ // Visual Studio errors out on divisions by 0
+ VERIFY((numext::isnan)(bfloat16(0.0 / 0.0)));
+ VERIFY((numext::isinf)(bfloat16(1.0 / 0.0)));
+ VERIFY((numext::isinf)(bfloat16(-1.0 / 0.0)));
+#endif
+
+ // NaNs and infinities.
+ VERIFY(!(numext::isinf)(static_cast<float>(bfloat16(3.38e38f)))); // Largest finite number.
+ VERIFY(!(numext::isnan)(static_cast<float>(bfloat16(0.0f))));
+ VERIFY((numext::isinf)(static_cast<float>(bfloat16(__bfloat16_raw(0xff80)))));
+ VERIFY((numext::isnan)(static_cast<float>(bfloat16(__bfloat16_raw(0xffc0)))));
+ VERIFY((numext::isinf)(static_cast<float>(bfloat16(__bfloat16_raw(0x7f80)))));
+ VERIFY((numext::isnan)(static_cast<float>(bfloat16(__bfloat16_raw(0x7fc0)))));
+
+ // Exactly same checks as above, just directly on the bfloat16 representation.
+ VERIFY(!(numext::isinf)(bfloat16(__bfloat16_raw(0x7bff))));
+ VERIFY(!(numext::isnan)(bfloat16(__bfloat16_raw(0x0000))));
+ VERIFY((numext::isinf)(bfloat16(__bfloat16_raw(0xff80))));
+ VERIFY((numext::isnan)(bfloat16(__bfloat16_raw(0xffc0))));
+ VERIFY((numext::isinf)(bfloat16(__bfloat16_raw(0x7f80))));
+ VERIFY((numext::isnan)(bfloat16(__bfloat16_raw(0x7fc0))));
+
+ VERIFY_BFLOAT16_BITS_EQUAL(bfloat16(BinaryToFloat(0x0, 0xff, 0x40, 0x0)), 0x7fc0);
+ VERIFY_BFLOAT16_BITS_EQUAL(bfloat16(BinaryToFloat(0x1, 0xff, 0x40, 0x0)), 0xffc0);
+}
+
+void test_numtraits()
+{
+ std::cout << "epsilon = " << NumTraits<bfloat16>::epsilon() << " (0x" << std::hex << numext::bit_cast<numext::uint16_t>(NumTraits<bfloat16>::epsilon()) << ")" << std::endl;
+ std::cout << "highest = " << NumTraits<bfloat16>::highest() << " (0x" << std::hex << numext::bit_cast<numext::uint16_t>(NumTraits<bfloat16>::highest()) << ")" << std::endl;
+ std::cout << "lowest = " << NumTraits<bfloat16>::lowest() << " (0x" << std::hex << numext::bit_cast<numext::uint16_t>(NumTraits<bfloat16>::lowest()) << ")" << std::endl;
+ std::cout << "min = " << (std::numeric_limits<bfloat16>::min)() << " (0x" << std::hex << numext::bit_cast<numext::uint16_t>((std::numeric_limits<bfloat16>::min)()) << ")" << std::endl;
+ std::cout << "denorm min = " << (std::numeric_limits<bfloat16>::denorm_min)() << " (0x" << std::hex << numext::bit_cast<numext::uint16_t>((std::numeric_limits<bfloat16>::denorm_min)()) << ")" << std::endl;
+ std::cout << "infinity = " << NumTraits<bfloat16>::infinity() << " (0x" << std::hex << numext::bit_cast<numext::uint16_t>(NumTraits<bfloat16>::infinity()) << ")" << std::endl;
+ std::cout << "quiet nan = " << NumTraits<bfloat16>::quiet_NaN() << " (0x" << std::hex << numext::bit_cast<numext::uint16_t>(NumTraits<bfloat16>::quiet_NaN()) << ")" << std::endl;
+ std::cout << "signaling nan = " << std::numeric_limits<bfloat16>::signaling_NaN() << " (0x" << std::hex << numext::bit_cast<numext::uint16_t>(std::numeric_limits<bfloat16>::signaling_NaN()) << ")" << std::endl;
+
+ VERIFY(NumTraits<bfloat16>::IsSigned);
+
+ VERIFY_IS_EQUAL(
+ numext::bit_cast<numext::uint16_t>(std::numeric_limits<bfloat16>::infinity()),
+ numext::bit_cast<numext::uint16_t>(bfloat16(std::numeric_limits<float>::infinity())) );
+ // There is no guarantee that casting a 32-bit NaN to bfloat16 has a precise
+ // bit pattern. We test that it is in fact a NaN, then test the signaling
+ // bit (msb of significand is 1 for quiet, 0 for signaling).
+ const numext::uint16_t BFLOAT16_QUIET_BIT = 0x0040;
+ VERIFY(
+ (numext::isnan)(std::numeric_limits<bfloat16>::quiet_NaN())
+ && (numext::isnan)(bfloat16(std::numeric_limits<float>::quiet_NaN()))
+ && ((numext::bit_cast<numext::uint16_t>(std::numeric_limits<bfloat16>::quiet_NaN()) & BFLOAT16_QUIET_BIT) > 0)
+ && ((numext::bit_cast<numext::uint16_t>(bfloat16(std::numeric_limits<float>::quiet_NaN())) & BFLOAT16_QUIET_BIT) > 0) );
+ // After a cast to bfloat16, a signaling NaN may become non-signaling. Thus,
+ // we check that both are NaN, and that only the `numeric_limits` version is
+ // signaling.
+ VERIFY(
+ (numext::isnan)(std::numeric_limits<bfloat16>::signaling_NaN())
+ && (numext::isnan)(bfloat16(std::numeric_limits<float>::signaling_NaN()))
+ && ((numext::bit_cast<numext::uint16_t>(std::numeric_limits<bfloat16>::signaling_NaN()) & BFLOAT16_QUIET_BIT) == 0) );
+
+ VERIFY( (std::numeric_limits<bfloat16>::min)() > bfloat16(0.f) );
+ VERIFY( (std::numeric_limits<bfloat16>::denorm_min)() > bfloat16(0.f) );
+ VERIFY_IS_EQUAL( (std::numeric_limits<bfloat16>::denorm_min)()/bfloat16(2), bfloat16(0.f) );
+}
+
+void test_arithmetic()
+{
+ VERIFY_IS_EQUAL(static_cast<float>(bfloat16(2) + bfloat16(2)), 4.f);
+ VERIFY_IS_EQUAL(static_cast<float>(bfloat16(2) + bfloat16(-2)), 0.f);
+ VERIFY_IS_APPROX(static_cast<float>(bfloat16(0.33333f) + bfloat16(0.66667f)), 1.0f);
+ VERIFY_IS_EQUAL(static_cast<float>(bfloat16(2.0f) * bfloat16(-5.5f)), -11.0f);
+ VERIFY_IS_APPROX(static_cast<float>(bfloat16(1.0f) / bfloat16(3.0f)), 0.3339f);
+ VERIFY_IS_EQUAL(static_cast<float>(-bfloat16(4096.0f)), -4096.0f);
+ VERIFY_IS_EQUAL(static_cast<float>(-bfloat16(-4096.0f)), 4096.0f);
+}
+
+void test_comparison()
+{
+ VERIFY(bfloat16(1.0f) > bfloat16(0.5f));
+ VERIFY(bfloat16(0.5f) < bfloat16(1.0f));
+ VERIFY(!(bfloat16(1.0f) < bfloat16(0.5f)));
+ VERIFY(!(bfloat16(0.5f) > bfloat16(1.0f)));
+
+ VERIFY(!(bfloat16(4.0f) > bfloat16(4.0f)));
+ VERIFY(!(bfloat16(4.0f) < bfloat16(4.0f)));
+
+ VERIFY(!(bfloat16(0.0f) < bfloat16(-0.0f)));
+ VERIFY(!(bfloat16(-0.0f) < bfloat16(0.0f)));
+ VERIFY(!(bfloat16(0.0f) > bfloat16(-0.0f)));
+ VERIFY(!(bfloat16(-0.0f) > bfloat16(0.0f)));
+
+ VERIFY(bfloat16(0.2f) > bfloat16(-1.0f));
+ VERIFY(bfloat16(-1.0f) < bfloat16(0.2f));
+ VERIFY(bfloat16(-16.0f) < bfloat16(-15.0f));
+
+ VERIFY(bfloat16(1.0f) == bfloat16(1.0f));
+ VERIFY(bfloat16(1.0f) != bfloat16(2.0f));
+
+ // Comparisons with NaNs and infinities.
+#if !EIGEN_COMP_MSVC
+ // Visual Studio errors out on divisions by 0
+ VERIFY(!(bfloat16(0.0 / 0.0) == bfloat16(0.0 / 0.0)));
+ VERIFY(bfloat16(0.0 / 0.0) != bfloat16(0.0 / 0.0));
+
+ VERIFY(!(bfloat16(1.0) == bfloat16(0.0 / 0.0)));
+ VERIFY(!(bfloat16(1.0) < bfloat16(0.0 / 0.0)));
+ VERIFY(!(bfloat16(1.0) > bfloat16(0.0 / 0.0)));
+ VERIFY(bfloat16(1.0) != bfloat16(0.0 / 0.0));
+
+ VERIFY(bfloat16(1.0) < bfloat16(1.0 / 0.0));
+ VERIFY(bfloat16(1.0) > bfloat16(-1.0 / 0.0));
+#endif
+}
+
+void test_basic_functions()
+{
+ VERIFY_IS_EQUAL(static_cast<float>(numext::abs(bfloat16(3.5f))), 3.5f);
+ VERIFY_IS_EQUAL(static_cast<float>(abs(bfloat16(3.5f))), 3.5f);
+ VERIFY_IS_EQUAL(static_cast<float>(numext::abs(bfloat16(-3.5f))), 3.5f);
+ VERIFY_IS_EQUAL(static_cast<float>(abs(bfloat16(-3.5f))), 3.5f);
+
+ VERIFY_IS_EQUAL(static_cast<float>(numext::floor(bfloat16(3.5f))), 3.0f);
+ VERIFY_IS_EQUAL(static_cast<float>(floor(bfloat16(3.5f))), 3.0f);
+ VERIFY_IS_EQUAL(static_cast<float>(numext::floor(bfloat16(-3.5f))), -4.0f);
+ VERIFY_IS_EQUAL(static_cast<float>(floor(bfloat16(-3.5f))), -4.0f);
+
+ VERIFY_IS_EQUAL(static_cast<float>(numext::ceil(bfloat16(3.5f))), 4.0f);
+ VERIFY_IS_EQUAL(static_cast<float>(ceil(bfloat16(3.5f))), 4.0f);
+ VERIFY_IS_EQUAL(static_cast<float>(numext::ceil(bfloat16(-3.5f))), -3.0f);
+ VERIFY_IS_EQUAL(static_cast<float>(ceil(bfloat16(-3.5f))), -3.0f);
+
+ VERIFY_IS_APPROX(static_cast<float>(numext::sqrt(bfloat16(0.0f))), 0.0f);
+ VERIFY_IS_APPROX(static_cast<float>(sqrt(bfloat16(0.0f))), 0.0f);
+ VERIFY_IS_APPROX(static_cast<float>(numext::sqrt(bfloat16(4.0f))), 2.0f);
+ VERIFY_IS_APPROX(static_cast<float>(sqrt(bfloat16(4.0f))), 2.0f);
+
+ VERIFY_IS_APPROX(static_cast<float>(numext::pow(bfloat16(0.0f), bfloat16(1.0f))), 0.0f);
+ VERIFY_IS_APPROX(static_cast<float>(pow(bfloat16(0.0f), bfloat16(1.0f))), 0.0f);
+ VERIFY_IS_APPROX(static_cast<float>(numext::pow(bfloat16(2.0f), bfloat16(2.0f))), 4.0f);
+ VERIFY_IS_APPROX(static_cast<float>(pow(bfloat16(2.0f), bfloat16(2.0f))), 4.0f);
+
+ VERIFY_IS_EQUAL(static_cast<float>(numext::exp(bfloat16(0.0f))), 1.0f);
+ VERIFY_IS_EQUAL(static_cast<float>(exp(bfloat16(0.0f))), 1.0f);
+ VERIFY_IS_APPROX(static_cast<float>(numext::exp(bfloat16(EIGEN_PI))), 20.f + static_cast<float>(EIGEN_PI));
+ VERIFY_IS_APPROX(static_cast<float>(exp(bfloat16(EIGEN_PI))), 20.f + static_cast<float>(EIGEN_PI));
+
+ VERIFY_IS_EQUAL(static_cast<float>(numext::expm1(bfloat16(0.0f))), 0.0f);
+ VERIFY_IS_EQUAL(static_cast<float>(expm1(bfloat16(0.0f))), 0.0f);
+ VERIFY_IS_APPROX(static_cast<float>(numext::expm1(bfloat16(2.0f))), 6.375f);
+ VERIFY_IS_APPROX(static_cast<float>(expm1(bfloat16(2.0f))), 6.375f);
+
+ VERIFY_IS_EQUAL(static_cast<float>(numext::log(bfloat16(1.0f))), 0.0f);
+ VERIFY_IS_EQUAL(static_cast<float>(log(bfloat16(1.0f))), 0.0f);
+ VERIFY_IS_APPROX(static_cast<float>(numext::log(bfloat16(10.0f))), 2.296875f);
+ VERIFY_IS_APPROX(static_cast<float>(log(bfloat16(10.0f))), 2.296875f);
+
+ VERIFY_IS_EQUAL(static_cast<float>(numext::log1p(bfloat16(0.0f))), 0.0f);
+ VERIFY_IS_EQUAL(static_cast<float>(log1p(bfloat16(0.0f))), 0.0f);
+ VERIFY_IS_APPROX(static_cast<float>(numext::log1p(bfloat16(10.0f))), 2.390625f);
+ VERIFY_IS_APPROX(static_cast<float>(log1p(bfloat16(10.0f))), 2.390625f);
+}
+
+void test_trigonometric_functions()
+{
+ VERIFY_IS_APPROX(numext::cos(bfloat16(0.0f)), bfloat16(cosf(0.0f)));
+ VERIFY_IS_APPROX(cos(bfloat16(0.0f)), bfloat16(cosf(0.0f)));
+ VERIFY_IS_APPROX(numext::cos(bfloat16(EIGEN_PI)), bfloat16(cosf(EIGEN_PI)));
+ // VERIFY_IS_APPROX(numext::cos(bfloat16(EIGEN_PI/2)), bfloat16(cosf(EIGEN_PI/2)));
+ // VERIFY_IS_APPROX(numext::cos(bfloat16(3*EIGEN_PI/2)), bfloat16(cosf(3*EIGEN_PI/2)));
+ VERIFY_IS_APPROX(numext::cos(bfloat16(3.5f)), bfloat16(cosf(3.5f)));
+
+ VERIFY_IS_APPROX(numext::sin(bfloat16(0.0f)), bfloat16(sinf(0.0f)));
+ VERIFY_IS_APPROX(sin(bfloat16(0.0f)), bfloat16(sinf(0.0f)));
+ // VERIFY_IS_APPROX(numext::sin(bfloat16(EIGEN_PI)), bfloat16(sinf(EIGEN_PI)));
+ VERIFY_IS_APPROX(numext::sin(bfloat16(EIGEN_PI/2)), bfloat16(sinf(EIGEN_PI/2)));
+ VERIFY_IS_APPROX(numext::sin(bfloat16(3*EIGEN_PI/2)), bfloat16(sinf(3*EIGEN_PI/2)));
+ VERIFY_IS_APPROX(numext::sin(bfloat16(3.5f)), bfloat16(sinf(3.5f)));
+
+ VERIFY_IS_APPROX(numext::tan(bfloat16(0.0f)), bfloat16(tanf(0.0f)));
+ VERIFY_IS_APPROX(tan(bfloat16(0.0f)), bfloat16(tanf(0.0f)));
+ // VERIFY_IS_APPROX(numext::tan(bfloat16(EIGEN_PI)), bfloat16(tanf(EIGEN_PI)));
+ // VERIFY_IS_APPROX(numext::tan(bfloat16(EIGEN_PI/2)), bfloat16(tanf(EIGEN_PI/2)));
+ // VERIFY_IS_APPROX(numext::tan(bfloat16(3*EIGEN_PI/2)), bfloat16(tanf(3*EIGEN_PI/2)));
+ VERIFY_IS_APPROX(numext::tan(bfloat16(3.5f)), bfloat16(tanf(3.5f)));
+}
+
+void test_array()
+{
+ typedef Array<bfloat16,1,Dynamic> ArrayXh;
+ Index size = internal::random<Index>(1,10);
+ Index i = internal::random<Index>(0,size-1);
+ ArrayXh a1 = ArrayXh::Random(size), a2 = ArrayXh::Random(size);
+ VERIFY_IS_APPROX( a1+a1, bfloat16(2)*a1 );
+ VERIFY( (a1.abs() >= bfloat16(0)).all() );
+ VERIFY_IS_APPROX( (a1*a1).sqrt(), a1.abs() );
+
+ VERIFY( ((a1.min)(a2) <= (a1.max)(a2)).all() );
+ a1(i) = bfloat16(-10.);
+ VERIFY_IS_EQUAL( a1.minCoeff(), bfloat16(-10.) );
+ a1(i) = bfloat16(10.);
+ VERIFY_IS_EQUAL( a1.maxCoeff(), bfloat16(10.) );
+
+ std::stringstream ss;
+ ss << a1;
+}
+
+void test_product()
+{
+ typedef Matrix<bfloat16,Dynamic,Dynamic> MatrixXh;
+ Index rows = internal::random<Index>(1,EIGEN_TEST_MAX_SIZE);
+ Index cols = internal::random<Index>(1,EIGEN_TEST_MAX_SIZE);
+ Index depth = internal::random<Index>(1,EIGEN_TEST_MAX_SIZE);
+ MatrixXh Ah = MatrixXh::Random(rows,depth);
+ MatrixXh Bh = MatrixXh::Random(depth,cols);
+ MatrixXh Ch = MatrixXh::Random(rows,cols);
+ MatrixXf Af = Ah.cast<float>();
+ MatrixXf Bf = Bh.cast<float>();
+ MatrixXf Cf = Ch.cast<float>();
+ VERIFY_IS_APPROX(Ch.noalias()+=Ah*Bh, (Cf.noalias()+=Af*Bf).cast<bfloat16>());
+}
+
+EIGEN_DECLARE_TEST(bfloat16_float)
+{
+ CALL_SUBTEST(test_numtraits());
+ for(int i = 0; i < g_repeat; i++) {
+ CALL_SUBTEST(test_conversion());
+ CALL_SUBTEST(test_arithmetic());
+ CALL_SUBTEST(test_comparison());
+ CALL_SUBTEST(test_basic_functions());
+ CALL_SUBTEST(test_trigonometric_functions());
+ CALL_SUBTEST(test_array());
+ CALL_SUBTEST(test_product());
+ }
+}
diff --git a/test/bicgstab.cpp b/test/bicgstab.cpp
new file mode 100644
index 0000000..59c4b50
--- /dev/null
+++ b/test/bicgstab.cpp
@@ -0,0 +1,34 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2011 Gael Guennebaud <g.gael@free.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "sparse_solver.h"
+#include <Eigen/IterativeLinearSolvers>
+
+template<typename T, typename I_> void test_bicgstab_T()
+{
+ BiCGSTAB<SparseMatrix<T,0,I_>, DiagonalPreconditioner<T> > bicgstab_colmajor_diag;
+ BiCGSTAB<SparseMatrix<T,0,I_>, IdentityPreconditioner > bicgstab_colmajor_I;
+ BiCGSTAB<SparseMatrix<T,0,I_>, IncompleteLUT<T,I_> > bicgstab_colmajor_ilut;
+ //BiCGSTAB<SparseMatrix<T>, SSORPreconditioner<T> > bicgstab_colmajor_ssor;
+
+ bicgstab_colmajor_diag.setTolerance(NumTraits<T>::epsilon()*4);
+ bicgstab_colmajor_ilut.setTolerance(NumTraits<T>::epsilon()*4);
+
+ CALL_SUBTEST( check_sparse_square_solving(bicgstab_colmajor_diag) );
+// CALL_SUBTEST( check_sparse_square_solving(bicgstab_colmajor_I) );
+ CALL_SUBTEST( check_sparse_square_solving(bicgstab_colmajor_ilut) );
+ //CALL_SUBTEST( check_sparse_square_solving(bicgstab_colmajor_ssor) );
+}
+
+EIGEN_DECLARE_TEST(bicgstab)
+{
+ CALL_SUBTEST_1((test_bicgstab_T<double,int>()) );
+ CALL_SUBTEST_2((test_bicgstab_T<std::complex<double>, int>()));
+ CALL_SUBTEST_3((test_bicgstab_T<double,long int>()));
+}
diff --git a/test/blasutil.cpp b/test/blasutil.cpp
new file mode 100644
index 0000000..ee98df4
--- /dev/null
+++ b/test/blasutil.cpp
@@ -0,0 +1,205 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2020 Everton Constantino <everton.constantino@ibm.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/
+
+#include "main.h"
+
+// Disable "ignoring attributes on template argument"
+// for packet_traits<Packet*>
+// => The only workaround would be to wrap _m128 and the likes
+// within wrappers.
+#if EIGEN_GNUC_AT_LEAST(6,0)
+ #pragma GCC diagnostic ignored "-Wignored-attributes"
+#endif
+
+#define GET(i,j) (StorageOrder == RowMajor ? (i)*stride + (j) : (i) + (j)*stride)
+#define SCATTER(i,j,k) (StorageOrder == RowMajor ? ((i)+(k))*stride + (j) : (i) + ((j)+(k))*stride)
+
+template<typename Scalar, typename Packet>
+void compare(const Packet& a, const Packet& b)
+{
+ int pktsz = internal::packet_traits<Scalar>::size;
+ Scalar *buffA = new Scalar[pktsz];
+ Scalar *buffB = new Scalar[pktsz];
+
+ internal::pstoreu<Scalar, Packet>(buffA, a);
+ internal::pstoreu<Scalar, Packet>(buffB, b);
+
+ for(int i = 0; i < pktsz; i++)
+ {
+ VERIFY_IS_EQUAL(buffA[i], buffB[i]);
+ }
+
+ delete[] buffA;
+ delete[] buffB;
+}
+
+template<typename Scalar, int StorageOrder, int n>
+struct PacketBlockSet
+{
+ typedef typename internal::packet_traits<Scalar>::type Packet;
+
+ void setPacketBlock(internal::PacketBlock<Packet,n>& block, Scalar value)
+ {
+ for(int idx = 0; idx < n; idx++)
+ {
+ block.packet[idx] = internal::pset1<Packet>(value);
+ }
+ }
+
+ void comparePacketBlock(Scalar *data, int i, int j, int stride, internal::PacketBlock<Packet, n>& block)
+ {
+ for(int idx = 0; idx < n; idx++)
+ {
+ Packet line = internal::ploadu<Packet>(data + SCATTER(i,j,idx));
+ compare<Scalar, Packet>(block.packet[idx], line);
+ }
+ }
+};
+
+template<typename Scalar, int StorageOrder, int BlockSize>
+void run_bdmp_spec_1()
+{
+ typedef internal::blas_data_mapper<Scalar, int, StorageOrder> BlasDataMapper;
+ int packetSize = internal::packet_traits<Scalar>::size;
+ int minSize = std::max<int>(packetSize, BlockSize);
+ typedef typename internal::packet_traits<Scalar>::type Packet;
+
+ int szm = internal::random<int>(minSize,500), szn = internal::random<int>(minSize,500);
+ int stride = StorageOrder == RowMajor ? szn : szm;
+ Scalar *d = new Scalar[szn*szm];
+
+ // Initializing with random entries
+ for(int i = 0; i < szm*szn; i++)
+ {
+ d[i] = internal::random<Scalar>(static_cast<Scalar>(3), static_cast<Scalar>(10));
+ }
+
+ BlasDataMapper bdm(d, stride);
+
+ // Testing operator()
+ for(int i = 0; i < szm; i++)
+ {
+ for(int j = 0; j < szn; j++)
+ {
+ VERIFY_IS_EQUAL(d[GET(i,j)], bdm(i,j));
+ }
+ }
+
+ // Testing getSubMapper and getLinearMapper
+ int i0 = internal::random<int>(0,szm-2);
+ int j0 = internal::random<int>(0,szn-2);
+ for(int i = i0; i < szm; i++)
+ {
+ for(int j = j0; j < szn; j++)
+ {
+ const BlasDataMapper& bdmSM = bdm.getSubMapper(i0,j0);
+ const internal::BlasLinearMapper<Scalar, int, 0>& bdmLM = bdm.getLinearMapper(i0,j0);
+
+ Scalar v = bdmSM(i - i0, j - j0);
+ Scalar vd = d[GET(i,j)];
+ VERIFY_IS_EQUAL(vd, v);
+ VERIFY_IS_EQUAL(vd, bdmLM(GET(i-i0, j-j0)));
+ }
+ }
+
+ // Testing loadPacket
+ for(int i = 0; i < szm - minSize; i++)
+ {
+ for(int j = 0; j < szn - minSize; j++)
+ {
+ Packet pktBDM = bdm.template loadPacket<Packet>(i,j);
+ Packet pktD = internal::ploadu<Packet>(d + GET(i,j));
+
+ compare<Scalar, Packet>(pktBDM, pktD);
+ }
+ }
+
+ // Testing gatherPacket
+ Scalar *buff = new Scalar[packetSize];
+ for(int i = 0; i < szm - minSize; i++)
+ {
+ for(int j = 0; j < szn - minSize; j++)
+ {
+ Packet p = bdm.template gatherPacket<Packet>(i,j);
+ internal::pstoreu<Scalar, Packet>(buff, p);
+
+ for(int k = 0; k < packetSize; k++)
+ {
+ VERIFY_IS_EQUAL(d[SCATTER(i,j,k)], buff[k]);
+ }
+
+ }
+ }
+ delete[] buff;
+
+ // Testing scatterPacket
+ for(int i = 0; i < szm - minSize; i++)
+ {
+ for(int j = 0; j < szn - minSize; j++)
+ {
+ Packet p = internal::pset1<Packet>(static_cast<Scalar>(1));
+ bdm.template scatterPacket<Packet>(i,j,p);
+ for(int k = 0; k < packetSize; k++)
+ {
+ VERIFY_IS_EQUAL(d[SCATTER(i,j,k)], static_cast<Scalar>(1));
+ }
+ }
+ }
+
+ //Testing storePacketBlock
+ internal::PacketBlock<Packet, BlockSize> block;
+
+ PacketBlockSet<Scalar, StorageOrder, BlockSize> pbs;
+ pbs.setPacketBlock(block, static_cast<Scalar>(2));
+
+ for(int i = 0; i < szm - minSize; i++)
+ {
+ for(int j = 0; j < szn - minSize; j++)
+ {
+ bdm.template storePacketBlock<Packet, BlockSize>(i, j, block);
+
+ pbs.comparePacketBlock(d, i, j, stride, block);
+ }
+ }
+
+ delete[] d;
+}
+
+template<typename Scalar>
+void run_test()
+{
+ run_bdmp_spec_1<Scalar, RowMajor, 1>();
+ run_bdmp_spec_1<Scalar, ColMajor, 1>();
+ run_bdmp_spec_1<Scalar, RowMajor, 2>();
+ run_bdmp_spec_1<Scalar, ColMajor, 2>();
+ run_bdmp_spec_1<Scalar, RowMajor, 4>();
+ run_bdmp_spec_1<Scalar, ColMajor, 4>();
+ run_bdmp_spec_1<Scalar, RowMajor, 8>();
+ run_bdmp_spec_1<Scalar, ColMajor, 8>();
+ run_bdmp_spec_1<Scalar, RowMajor, 16>();
+ run_bdmp_spec_1<Scalar, ColMajor, 16>();
+}
+
+EIGEN_DECLARE_TEST(blasutil)
+{
+ for(int i = 0; i < g_repeat; i++)
+ {
+ CALL_SUBTEST_1(run_test<numext::int8_t>());
+ CALL_SUBTEST_2(run_test<numext::int16_t>());
+ CALL_SUBTEST_3(run_test<numext::int32_t>());
+
+// TODO: Replace this by a call to numext::int64_t as soon as we have a way to
+// detect the typedef for int64_t on all platforms
+ CALL_SUBTEST_4(run_test<signed long long>());
+ CALL_SUBTEST_5(run_test<float_t>());
+ CALL_SUBTEST_6(run_test<double_t>());
+ CALL_SUBTEST_7(run_test<std::complex<float> >());
+ CALL_SUBTEST_8(run_test<std::complex<double> >());
+ }
+}
diff --git a/test/block.cpp b/test/block.cpp
new file mode 100644
index 0000000..f8583c3
--- /dev/null
+++ b/test/block.cpp
@@ -0,0 +1,329 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2006-2010 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "main.h"
+
+template<typename MatrixType, typename Index, typename Scalar>
+std::enable_if_t<!NumTraits<typename MatrixType::Scalar>::IsComplex,typename MatrixType::Scalar>
+block_real_only(const MatrixType &m1, Index r1, Index r2, Index c1, Index c2, const Scalar& s1) {
+ // check cwise-Functions:
+ VERIFY_IS_APPROX(m1.row(r1).cwiseMax(s1), m1.cwiseMax(s1).row(r1));
+ VERIFY_IS_APPROX(m1.col(c1).cwiseMin(s1), m1.cwiseMin(s1).col(c1));
+
+ VERIFY_IS_APPROX(m1.block(r1,c1,r2-r1+1,c2-c1+1).cwiseMin(s1), m1.cwiseMin(s1).block(r1,c1,r2-r1+1,c2-c1+1));
+ VERIFY_IS_APPROX(m1.block(r1,c1,r2-r1+1,c2-c1+1).cwiseMax(s1), m1.cwiseMax(s1).block(r1,c1,r2-r1+1,c2-c1+1));
+
+ return Scalar(0);
+}
+
+template<typename MatrixType, typename Index, typename Scalar>
+std::enable_if_t<NumTraits<typename MatrixType::Scalar>::IsComplex,typename MatrixType::Scalar>
+block_real_only(const MatrixType &, Index, Index, Index, Index, const Scalar&) {
+ return Scalar(0);
+}
+
+// Check at compile-time that T1==T2, and at runtime-time that a==b
+template<typename T1,typename T2>
+std::enable_if_t<internal::is_same<T1,T2>::value,bool>
+is_same_block(const T1& a, const T2& b)
+{
+ return a.isApprox(b);
+}
+
+template <typename MatrixType>
+std::enable_if_t<((MatrixType::Flags&RowMajorBit)==0),void>
+check_left_top(const MatrixType& m, Index r, Index c,
+ Index rows, Index /*unused*/) {
+ VERIFY_IS_EQUAL(m.leftCols(c).coeff(r+c*rows), m(r,c));
+}
+
+template <typename MatrixType>
+std::enable_if_t<((MatrixType::Flags&RowMajorBit)!=0),void>
+check_left_top(const MatrixType& m, Index r, Index c,
+ Index /*unused*/, Index cols) {
+ VERIFY_IS_EQUAL(m.topRows(r).coeff(c+r*cols), m(r,c));
+}
+
+template<typename MatrixType> void block(const MatrixType& m)
+{
+ typedef typename MatrixType::Scalar Scalar;
+ typedef typename MatrixType::RealScalar RealScalar;
+ typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> VectorType;
+ typedef Matrix<Scalar, 1, MatrixType::ColsAtCompileTime> RowVectorType;
+ typedef Matrix<Scalar, Dynamic, Dynamic, MatrixType::IsRowMajor?RowMajor:ColMajor> DynamicMatrixType;
+ typedef Matrix<Scalar, Dynamic, 1> DynamicVectorType;
+
+ Index rows = m.rows();
+ Index cols = m.cols();
+
+ MatrixType m1 = MatrixType::Random(rows, cols),
+ m1_copy = m1,
+ m2 = MatrixType::Random(rows, cols),
+ m3(rows, cols),
+ ones = MatrixType::Ones(rows, cols);
+ VectorType v1 = VectorType::Random(rows);
+
+ Scalar s1 = internal::random<Scalar>();
+
+ Index r1 = internal::random<Index>(0,rows-1);
+ Index r2 = internal::random<Index>(r1,rows-1);
+ Index c1 = internal::random<Index>(0,cols-1);
+ Index c2 = internal::random<Index>(c1,cols-1);
+
+ block_real_only(m1, r1, r2, c1, c1, s1);
+
+ //check row() and col()
+ VERIFY_IS_EQUAL(m1.col(c1).transpose(), m1.transpose().row(c1));
+ //check operator(), both constant and non-constant, on row() and col()
+ m1 = m1_copy;
+ m1.row(r1) += s1 * m1_copy.row(r2);
+ VERIFY_IS_APPROX(m1.row(r1), m1_copy.row(r1) + s1 * m1_copy.row(r2));
+ // check nested block xpr on lhs
+ m1.row(r1).row(0) += s1 * m1_copy.row(r2);
+ VERIFY_IS_APPROX(m1.row(r1), m1_copy.row(r1) + Scalar(2) * s1 * m1_copy.row(r2));
+ m1 = m1_copy;
+ m1.col(c1) += s1 * m1_copy.col(c2);
+ VERIFY_IS_APPROX(m1.col(c1), m1_copy.col(c1) + s1 * m1_copy.col(c2));
+ m1.col(c1).col(0) += s1 * m1_copy.col(c2);
+ VERIFY_IS_APPROX(m1.col(c1), m1_copy.col(c1) + Scalar(2) * s1 * m1_copy.col(c2));
+
+ check_left_top(m1,r1,c1,rows,cols);
+
+ //check block()
+ Matrix<Scalar,Dynamic,Dynamic> b1(1,1); b1(0,0) = m1(r1,c1);
+
+ RowVectorType br1(m1.block(r1,0,1,cols));
+ VectorType bc1(m1.block(0,c1,rows,1));
+ VERIFY_IS_EQUAL(b1, m1.block(r1,c1,1,1));
+ VERIFY_IS_EQUAL(m1.row(r1), br1);
+ VERIFY_IS_EQUAL(m1.col(c1), bc1);
+ //check operator(), both constant and non-constant, on block()
+ m1.block(r1,c1,r2-r1+1,c2-c1+1) = s1 * m2.block(0, 0, r2-r1+1,c2-c1+1);
+ m1.block(r1,c1,r2-r1+1,c2-c1+1)(r2-r1,c2-c1) = m2.block(0, 0, r2-r1+1,c2-c1+1)(0,0);
+
+ const Index BlockRows = 2;
+ const Index BlockCols = 5;
+
+ if (rows>=5 && cols>=8)
+ {
+ // test fixed block() as lvalue
+ m1.template block<BlockRows,BlockCols>(1,1) *= s1;
+ // test operator() on fixed block() both as constant and non-constant
+ m1.template block<BlockRows,BlockCols>(1,1)(0, 3) = m1.template block<2,5>(1,1)(1,2);
+ // check that fixed block() and block() agree
+ Matrix<Scalar,Dynamic,Dynamic> b = m1.template block<BlockRows,BlockCols>(3,3);
+ VERIFY_IS_EQUAL(b, m1.block(3,3,BlockRows,BlockCols));
+
+ // same tests with mixed fixed/dynamic size
+ m1.template block<BlockRows,Dynamic>(1,1,BlockRows,BlockCols) *= s1;
+ m1.template block<BlockRows,Dynamic>(1,1,BlockRows,BlockCols)(0,3) = m1.template block<2,5>(1,1)(1,2);
+ Matrix<Scalar,Dynamic,Dynamic> b2 = m1.template block<Dynamic,BlockCols>(3,3,2,5);
+ VERIFY_IS_EQUAL(b2, m1.block(3,3,BlockRows,BlockCols));
+
+ VERIFY(is_same_block(m1.block(3,3,BlockRows,BlockCols), m1.block(3,3,fix<Dynamic>(BlockRows),fix<Dynamic>(BlockCols))));
+ VERIFY(is_same_block(m1.template block<BlockRows,Dynamic>(1,1,BlockRows,BlockCols), m1.block(1,1,fix<BlockRows>,BlockCols)));
+ VERIFY(is_same_block(m1.template block<BlockRows,BlockCols>(1,1,BlockRows,BlockCols), m1.block(1,1,fix<BlockRows>(),fix<BlockCols>)));
+ VERIFY(is_same_block(m1.template block<BlockRows,BlockCols>(1,1,BlockRows,BlockCols), m1.block(1,1,fix<BlockRows>,fix<BlockCols>(BlockCols))));
+ }
+
+ if (rows>2)
+ {
+ // test sub vectors
+ VERIFY_IS_EQUAL(v1.template head<2>(), v1.block(0,0,2,1));
+ VERIFY_IS_EQUAL(v1.template head<2>(), v1.head(2));
+ VERIFY_IS_EQUAL(v1.template head<2>(), v1.segment(0,2));
+ VERIFY_IS_EQUAL(v1.template head<2>(), v1.template segment<2>(0));
+ Index i = rows-2;
+ VERIFY_IS_EQUAL(v1.template tail<2>(), v1.block(i,0,2,1));
+ VERIFY_IS_EQUAL(v1.template tail<2>(), v1.tail(2));
+ VERIFY_IS_EQUAL(v1.template tail<2>(), v1.segment(i,2));
+ VERIFY_IS_EQUAL(v1.template tail<2>(), v1.template segment<2>(i));
+ i = internal::random<Index>(0,rows-2);
+ VERIFY_IS_EQUAL(v1.segment(i,2), v1.template segment<2>(i));
+ }
+
+ // stress some basic stuffs with block matrices
+ VERIFY_IS_EQUAL(numext::real(ones.col(c1).sum()), RealScalar(rows));
+ VERIFY_IS_EQUAL(numext::real(ones.row(r1).sum()), RealScalar(cols));
+
+ VERIFY_IS_EQUAL(numext::real(ones.col(c1).dot(ones.col(c2))), RealScalar(rows));
+ VERIFY_IS_EQUAL(numext::real(ones.row(r1).dot(ones.row(r2))), RealScalar(cols));
+
+ // check that linear acccessors works on blocks
+ m1 = m1_copy;
+
+ // now test some block-inside-of-block.
+
+ // expressions with direct access
+ VERIFY_IS_EQUAL( (m1.block(r1,c1,rows-r1,cols-c1).block(r2-r1,c2-c1,rows-r2,cols-c2)) , (m1.block(r2,c2,rows-r2,cols-c2)) );
+ VERIFY_IS_EQUAL( (m1.block(r1,c1,r2-r1+1,c2-c1+1).row(0)) , (m1.row(r1).segment(c1,c2-c1+1)) );
+ VERIFY_IS_EQUAL( (m1.block(r1,c1,r2-r1+1,c2-c1+1).col(0)) , (m1.col(c1).segment(r1,r2-r1+1)) );
+ VERIFY_IS_EQUAL( (m1.block(r1,c1,r2-r1+1,c2-c1+1).transpose().col(0)) , (m1.row(r1).segment(c1,c2-c1+1)).transpose() );
+ VERIFY_IS_EQUAL( (m1.transpose().block(c1,r1,c2-c1+1,r2-r1+1).col(0)) , (m1.row(r1).segment(c1,c2-c1+1)).transpose() );
+
+ // expressions without direct access
+ VERIFY_IS_APPROX( ((m1+m2).block(r1,c1,rows-r1,cols-c1).block(r2-r1,c2-c1,rows-r2,cols-c2)) , ((m1+m2).block(r2,c2,rows-r2,cols-c2)) );
+ VERIFY_IS_APPROX( ((m1+m2).block(r1,c1,r2-r1+1,c2-c1+1).row(0)) , ((m1+m2).row(r1).segment(c1,c2-c1+1)) );
+ VERIFY_IS_APPROX( ((m1+m2).block(r1,c1,r2-r1+1,c2-c1+1).row(0)) , ((m1+m2).eval().row(r1).segment(c1,c2-c1+1)) );
+ VERIFY_IS_APPROX( ((m1+m2).block(r1,c1,r2-r1+1,c2-c1+1).col(0)) , ((m1+m2).col(c1).segment(r1,r2-r1+1)) );
+ VERIFY_IS_APPROX( ((m1+m2).block(r1,c1,r2-r1+1,c2-c1+1).transpose().col(0)) , ((m1+m2).row(r1).segment(c1,c2-c1+1)).transpose() );
+ VERIFY_IS_APPROX( ((m1+m2).transpose().block(c1,r1,c2-c1+1,r2-r1+1).col(0)) , ((m1+m2).row(r1).segment(c1,c2-c1+1)).transpose() );
+ VERIFY_IS_APPROX( ((m1+m2).template block<Dynamic,1>(r1,c1,r2-r1+1,1)) , ((m1+m2).eval().col(c1).eval().segment(r1,r2-r1+1)) );
+ VERIFY_IS_APPROX( ((m1+m2).template block<1,Dynamic>(r1,c1,1,c2-c1+1)) , ((m1+m2).eval().row(r1).eval().segment(c1,c2-c1+1)) );
+ VERIFY_IS_APPROX( ((m1+m2).transpose().template block<1,Dynamic>(c1,r1,1,r2-r1+1)) , ((m1+m2).eval().col(c1).eval().segment(r1,r2-r1+1)).transpose() );
+ VERIFY_IS_APPROX( (m1+m2).row(r1).eval(), (m1+m2).eval().row(r1) );
+ VERIFY_IS_APPROX( (m1+m2).adjoint().col(r1).eval(), (m1+m2).adjoint().eval().col(r1) );
+ VERIFY_IS_APPROX( (m1+m2).adjoint().row(c1).eval(), (m1+m2).adjoint().eval().row(c1) );
+ VERIFY_IS_APPROX( (m1*1).row(r1).segment(c1,c2-c1+1).eval(), m1.row(r1).eval().segment(c1,c2-c1+1).eval() );
+ VERIFY_IS_APPROX( m1.col(c1).reverse().segment(r1,r2-r1+1).eval(),m1.col(c1).reverse().eval().segment(r1,r2-r1+1).eval() );
+
+ VERIFY_IS_APPROX( (m1*1).topRows(r1), m1.topRows(r1) );
+ VERIFY_IS_APPROX( (m1*1).leftCols(c1), m1.leftCols(c1) );
+ VERIFY_IS_APPROX( (m1*1).transpose().topRows(c1), m1.transpose().topRows(c1) );
+ VERIFY_IS_APPROX( (m1*1).transpose().leftCols(r1), m1.transpose().leftCols(r1) );
+ VERIFY_IS_APPROX( (m1*1).transpose().middleRows(c1,c2-c1+1), m1.transpose().middleRows(c1,c2-c1+1) );
+ VERIFY_IS_APPROX( (m1*1).transpose().middleCols(r1,r2-r1+1), m1.transpose().middleCols(r1,r2-r1+1) );
+
+ // evaluation into plain matrices from expressions with direct access (stress MapBase)
+ DynamicMatrixType dm;
+ DynamicVectorType dv;
+ dm.setZero();
+ dm = m1.block(r1,c1,rows-r1,cols-c1).block(r2-r1,c2-c1,rows-r2,cols-c2);
+ VERIFY_IS_EQUAL(dm, (m1.block(r2,c2,rows-r2,cols-c2)));
+ dm.setZero();
+ dv.setZero();
+ dm = m1.block(r1,c1,r2-r1+1,c2-c1+1).row(0).transpose();
+ dv = m1.row(r1).segment(c1,c2-c1+1);
+ VERIFY_IS_EQUAL(dv, dm);
+ dm.setZero();
+ dv.setZero();
+ dm = m1.col(c1).segment(r1,r2-r1+1);
+ dv = m1.block(r1,c1,r2-r1+1,c2-c1+1).col(0);
+ VERIFY_IS_EQUAL(dv, dm);
+ dm.setZero();
+ dv.setZero();
+ dm = m1.block(r1,c1,r2-r1+1,c2-c1+1).transpose().col(0);
+ dv = m1.row(r1).segment(c1,c2-c1+1);
+ VERIFY_IS_EQUAL(dv, dm);
+ dm.setZero();
+ dv.setZero();
+ dm = m1.row(r1).segment(c1,c2-c1+1).transpose();
+ dv = m1.transpose().block(c1,r1,c2-c1+1,r2-r1+1).col(0);
+ VERIFY_IS_EQUAL(dv, dm);
+
+ VERIFY_IS_EQUAL( (m1.template block<Dynamic,1>(1,0,0,1)), m1.block(1,0,0,1));
+ VERIFY_IS_EQUAL( (m1.template block<1,Dynamic>(0,1,1,0)), m1.block(0,1,1,0));
+ VERIFY_IS_EQUAL( ((m1*1).template block<Dynamic,1>(1,0,0,1)), m1.block(1,0,0,1));
+ VERIFY_IS_EQUAL( ((m1*1).template block<1,Dynamic>(0,1,1,0)), m1.block(0,1,1,0));
+
+ VERIFY_IS_EQUAL( m1.template subVector<Horizontal>(r1), m1.row(r1) );
+ VERIFY_IS_APPROX( (m1+m1).template subVector<Horizontal>(r1), (m1+m1).row(r1) );
+ VERIFY_IS_EQUAL( m1.template subVector<Vertical>(c1), m1.col(c1) );
+ VERIFY_IS_APPROX( (m1+m1).template subVector<Vertical>(c1), (m1+m1).col(c1) );
+ VERIFY_IS_EQUAL( m1.template subVectors<Horizontal>(), m1.rows() );
+ VERIFY_IS_EQUAL( m1.template subVectors<Vertical>(), m1.cols() );
+
+ if (rows>=2 || cols>=2) {
+ VERIFY_IS_EQUAL( int(m1.middleCols(0,0).IsRowMajor), int(m1.IsRowMajor) );
+ VERIFY_IS_EQUAL( m1.middleCols(0,0).outerSize(), m1.IsRowMajor ? rows : 0);
+ VERIFY_IS_EQUAL( m1.middleCols(0,0).innerSize(), m1.IsRowMajor ? 0 : rows);
+
+ VERIFY_IS_EQUAL( int(m1.middleRows(0,0).IsRowMajor), int(m1.IsRowMajor) );
+ VERIFY_IS_EQUAL( m1.middleRows(0,0).outerSize(), m1.IsRowMajor ? 0 : cols);
+ VERIFY_IS_EQUAL( m1.middleRows(0,0).innerSize(), m1.IsRowMajor ? cols : 0);
+ }
+}
+
+
+
+template<typename MatrixType>
+std::enable_if_t<MatrixType::IsVectorAtCompileTime,void>
+compare_using_data_and_stride(const MatrixType& m)
+{
+ Index rows = m.rows();
+ Index cols = m.cols();
+ Index size = m.size();
+ Index innerStride = m.innerStride();
+ Index rowStride = m.rowStride();
+ Index colStride = m.colStride();
+ const typename MatrixType::Scalar* data = m.data();
+
+ for(int j=0;j<cols;++j)
+ for(int i=0;i<rows;++i)
+ VERIFY(m.coeff(i,j) == data[i*rowStride + j*colStride]);
+
+ VERIFY(innerStride == int((&m.coeff(1))-(&m.coeff(0))));
+ for (int i=0;i<size;++i)
+ VERIFY(m.coeff(i) == data[i*innerStride]);
+}
+
+template<typename MatrixType>
+std::enable_if_t<!MatrixType::IsVectorAtCompileTime,void>
+compare_using_data_and_stride(const MatrixType& m)
+{
+ Index rows = m.rows();
+ Index cols = m.cols();
+ Index innerStride = m.innerStride();
+ Index outerStride = m.outerStride();
+ Index rowStride = m.rowStride();
+ Index colStride = m.colStride();
+ const typename MatrixType::Scalar* data = m.data();
+
+ for(int j=0;j<cols;++j)
+ for(int i=0;i<rows;++i)
+ VERIFY(m.coeff(i,j) == data[i*rowStride + j*colStride]);
+
+ for(int j=0;j<cols;++j)
+ for(int i=0;i<rows;++i)
+ VERIFY(m.coeff(i,j) == data[(MatrixType::Flags&RowMajorBit)
+ ? i*outerStride + j*innerStride
+ : j*outerStride + i*innerStride]);
+}
+
+template<typename MatrixType>
+void data_and_stride(const MatrixType& m)
+{
+ Index rows = m.rows();
+ Index cols = m.cols();
+
+ Index r1 = internal::random<Index>(0,rows-1);
+ Index r2 = internal::random<Index>(r1,rows-1);
+ Index c1 = internal::random<Index>(0,cols-1);
+ Index c2 = internal::random<Index>(c1,cols-1);
+
+ MatrixType m1 = MatrixType::Random(rows, cols);
+ compare_using_data_and_stride(m1.block(r1, c1, r2-r1+1, c2-c1+1));
+ compare_using_data_and_stride(m1.transpose().block(c1, r1, c2-c1+1, r2-r1+1));
+ compare_using_data_and_stride(m1.row(r1));
+ compare_using_data_and_stride(m1.col(c1));
+ compare_using_data_and_stride(m1.row(r1).transpose());
+ compare_using_data_and_stride(m1.col(c1).transpose());
+}
+
+EIGEN_DECLARE_TEST(block)
+{
+ for(int i = 0; i < g_repeat; i++) {
+ CALL_SUBTEST_1( block(Matrix<float, 1, 1>()) );
+ CALL_SUBTEST_1( block(Matrix<float, 1, Dynamic>(internal::random(2,50))) );
+ CALL_SUBTEST_1( block(Matrix<float, Dynamic, 1>(internal::random(2,50))) );
+ CALL_SUBTEST_2( block(Matrix4d()) );
+ CALL_SUBTEST_3( block(MatrixXcf(internal::random(2,50), internal::random(2,50))) );
+ CALL_SUBTEST_4( block(MatrixXi(internal::random(2,50), internal::random(2,50))) );
+ CALL_SUBTEST_5( block(MatrixXcd(internal::random(2,50), internal::random(2,50))) );
+ CALL_SUBTEST_6( block(MatrixXf(internal::random(2,50), internal::random(2,50))) );
+ CALL_SUBTEST_7( block(Matrix<int,Dynamic,Dynamic,RowMajor>(internal::random(2,50), internal::random(2,50))) );
+
+ CALL_SUBTEST_8( block(Matrix<float,Dynamic,4>(3, 4)) );
+
+#ifndef EIGEN_DEFAULT_TO_ROW_MAJOR
+ CALL_SUBTEST_6( data_and_stride(MatrixXf(internal::random(5,50), internal::random(5,50))) );
+ CALL_SUBTEST_7( data_and_stride(Matrix<int,Dynamic,Dynamic,RowMajor>(internal::random(5,50), internal::random(5,50))) );
+#endif
+ }
+}
diff --git a/test/boostmultiprec.cpp b/test/boostmultiprec.cpp
new file mode 100644
index 0000000..e2fc9a8
--- /dev/null
+++ b/test/boostmultiprec.cpp
@@ -0,0 +1,207 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2016 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include <sstream>
+
+#ifdef EIGEN_TEST_MAX_SIZE
+#undef EIGEN_TEST_MAX_SIZE
+#endif
+
+#define EIGEN_TEST_MAX_SIZE 50
+
+#ifdef EIGEN_TEST_PART_1
+#include "cholesky.cpp"
+#endif
+
+#ifdef EIGEN_TEST_PART_2
+#include "lu.cpp"
+#endif
+
+#ifdef EIGEN_TEST_PART_3
+#include "qr.cpp"
+#endif
+
+#ifdef EIGEN_TEST_PART_4
+#include "qr_colpivoting.cpp"
+#endif
+
+#ifdef EIGEN_TEST_PART_5
+#include "qr_fullpivoting.cpp"
+#endif
+
+#ifdef EIGEN_TEST_PART_6
+#include "eigensolver_selfadjoint.cpp"
+#endif
+
+#ifdef EIGEN_TEST_PART_7
+#include "eigensolver_generic.cpp"
+#endif
+
+#ifdef EIGEN_TEST_PART_8
+#include "eigensolver_generalized_real.cpp"
+#endif
+
+#ifdef EIGEN_TEST_PART_9
+#include "jacobisvd.cpp"
+#endif
+
+#ifdef EIGEN_TEST_PART_10
+#include "bdcsvd.cpp"
+#endif
+
+#ifdef EIGEN_TEST_PART_11
+#include "simplicial_cholesky.cpp"
+#endif
+
+#include <Eigen/Dense>
+
+#undef min
+#undef max
+#undef isnan
+#undef isinf
+#undef isfinite
+#undef I
+
+#include <boost/serialization/nvp.hpp>
+#include <boost/multiprecision/cpp_dec_float.hpp>
+#include <boost/multiprecision/number.hpp>
+#include <boost/math/special_functions.hpp>
+#include <boost/math/complex.hpp>
+
+typedef boost::multiprecision::number<boost::multiprecision::cpp_dec_float<100>, boost::multiprecision::et_on> Real;
+
+namespace Eigen {
+ template<> struct NumTraits<Real> : GenericNumTraits<Real> {
+ static inline Real dummy_precision() { return 1e-50; }
+ };
+
+ template<typename T1,typename T2,typename T3,typename T4,typename T5>
+ struct NumTraits<boost::multiprecision::detail::expression<T1,T2,T3,T4,T5> > : NumTraits<Real> {};
+
+ template<>
+ Real test_precision<Real>() { return 1e-50; }
+
+ // needed in C++93 mode where number does not support explicit cast.
+ namespace internal {
+ template<typename NewType>
+ struct cast_impl<Real,NewType> {
+ static inline NewType run(const Real& x) {
+ return x.template convert_to<NewType>();
+ }
+ };
+
+ template<>
+ struct cast_impl<Real,std::complex<Real> > {
+ static inline std::complex<Real> run(const Real& x) {
+ return std::complex<Real>(x);
+ }
+ };
+ }
+}
+
+namespace boost {
+namespace multiprecision {
+ // to make ADL works as expected:
+ using boost::math::isfinite;
+ using boost::math::isnan;
+ using boost::math::isinf;
+ using boost::math::copysign;
+ using boost::math::hypot;
+
+ // The following is needed for std::complex<Real>:
+ Real fabs(const Real& a) { return abs EIGEN_NOT_A_MACRO (a); }
+ Real fmax(const Real& a, const Real& b) { using std::max; return max(a,b); }
+
+ // some specialization for the unit tests:
+ inline bool test_isMuchSmallerThan(const Real& a, const Real& b) {
+ return internal::isMuchSmallerThan(a, b, test_precision<Real>());
+ }
+
+ inline bool test_isApprox(const Real& a, const Real& b) {
+ return internal::isApprox(a, b, test_precision<Real>());
+ }
+
+ inline bool test_isApproxOrLessThan(const Real& a, const Real& b) {
+ return internal::isApproxOrLessThan(a, b, test_precision<Real>());
+ }
+
+ Real get_test_precision(const Real&) {
+ return test_precision<Real>();
+ }
+
+ Real test_relative_error(const Real &a, const Real &b) {
+ using Eigen::numext::abs2;
+ return sqrt(abs2<Real>(a-b)/Eigen::numext::mini<Real>(abs2(a),abs2(b)));
+ }
+}
+}
+
+namespace Eigen {
+
+}
+
+EIGEN_DECLARE_TEST(boostmultiprec)
+{
+ typedef Matrix<Real,Dynamic,Dynamic> Mat;
+ typedef Matrix<std::complex<Real>,Dynamic,Dynamic> MatC;
+
+ std::cout << "NumTraits<Real>::epsilon() = " << NumTraits<Real>::epsilon() << std::endl;
+ std::cout << "NumTraits<Real>::dummy_precision() = " << NumTraits<Real>::dummy_precision() << std::endl;
+ std::cout << "NumTraits<Real>::lowest() = " << NumTraits<Real>::lowest() << std::endl;
+ std::cout << "NumTraits<Real>::highest() = " << NumTraits<Real>::highest() << std::endl;
+ std::cout << "NumTraits<Real>::digits10() = " << NumTraits<Real>::digits10() << std::endl;
+
+ // check stream output
+ {
+ Mat A(10,10);
+ A.setRandom();
+ std::stringstream ss;
+ ss << A;
+ }
+ {
+ MatC A(10,10);
+ A.setRandom();
+ std::stringstream ss;
+ ss << A;
+ }
+
+ for(int i = 0; i < g_repeat; i++) {
+ int s = internal::random<int>(1,EIGEN_TEST_MAX_SIZE);
+
+ CALL_SUBTEST_1( cholesky(Mat(s,s)) );
+
+ CALL_SUBTEST_2( lu_non_invertible<Mat>() );
+ CALL_SUBTEST_2( lu_invertible<Mat>() );
+ CALL_SUBTEST_2( lu_non_invertible<MatC>() );
+ CALL_SUBTEST_2( lu_invertible<MatC>() );
+
+ CALL_SUBTEST_3( qr(Mat(internal::random<int>(1,EIGEN_TEST_MAX_SIZE),internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
+ CALL_SUBTEST_3( qr_invertible<Mat>() );
+
+ CALL_SUBTEST_4( qr<Mat>() );
+ CALL_SUBTEST_4( cod<Mat>() );
+ CALL_SUBTEST_4( qr_invertible<Mat>() );
+
+ CALL_SUBTEST_5( qr<Mat>() );
+ CALL_SUBTEST_5( qr_invertible<Mat>() );
+
+ CALL_SUBTEST_6( selfadjointeigensolver(Mat(s,s)) );
+
+ CALL_SUBTEST_7( eigensolver(Mat(s,s)) );
+
+ CALL_SUBTEST_8( generalized_eigensolver_real(Mat(s,s)) );
+
+ TEST_SET_BUT_UNUSED_VARIABLE(s)
+ }
+
+ CALL_SUBTEST_9(( jacobisvd_all_options(Mat(internal::random<int>(EIGEN_TEST_MAX_SIZE/4, EIGEN_TEST_MAX_SIZE), internal::random<int>(EIGEN_TEST_MAX_SIZE/4, EIGEN_TEST_MAX_SIZE/2))) ));
+ CALL_SUBTEST_10(( bdcsvd_all_options(Mat(internal::random<int>(EIGEN_TEST_MAX_SIZE/4, EIGEN_TEST_MAX_SIZE), internal::random<int>(EIGEN_TEST_MAX_SIZE/4, EIGEN_TEST_MAX_SIZE/2))) ));
+
+ CALL_SUBTEST_11(( test_simplicial_cholesky_T<Real,int,ColMajor>() ));
+}
diff --git a/test/bug1213.cpp b/test/bug1213.cpp
new file mode 100644
index 0000000..581760c
--- /dev/null
+++ b/test/bug1213.cpp
@@ -0,0 +1,13 @@
+
+// This anonymous enum is essential to trigger the linking issue
+enum {
+ Foo
+};
+
+#include "bug1213.h"
+
+bool bug1213_1(const Eigen::Vector3f& x)
+{
+ return bug1213_2(x);
+}
+
diff --git a/test/bug1213.h b/test/bug1213.h
new file mode 100644
index 0000000..040e5a4
--- /dev/null
+++ b/test/bug1213.h
@@ -0,0 +1,8 @@
+
+#include <Eigen/Core>
+
+template<typename T, int dim>
+bool bug1213_2(const Eigen::Matrix<T,dim,1>& x);
+
+bool bug1213_1(const Eigen::Vector3f& x);
+
diff --git a/test/bug1213_main.cpp b/test/bug1213_main.cpp
new file mode 100644
index 0000000..4802c00
--- /dev/null
+++ b/test/bug1213_main.cpp
@@ -0,0 +1,18 @@
+
+// This is a regression unit regarding a weird linking issue with gcc.
+
+#include "bug1213.h"
+
+int main()
+{
+ return 0;
+}
+
+
+template<typename T, int dim>
+bool bug1213_2(const Eigen::Matrix<T,dim,1>& )
+{
+ return true;
+}
+
+template bool bug1213_2<float,3>(const Eigen::Vector3f&);
diff --git a/test/cholesky.cpp b/test/cholesky.cpp
new file mode 100644
index 0000000..0b1a7b4
--- /dev/null
+++ b/test/cholesky.cpp
@@ -0,0 +1,532 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#define TEST_ENABLE_TEMPORARY_TRACKING
+
+#include "main.h"
+#include <Eigen/Cholesky>
+#include <Eigen/QR>
+#include "solverbase.h"
+
+template<typename MatrixType, int UpLo>
+typename MatrixType::RealScalar matrix_l1_norm(const MatrixType& m) {
+ if(m.cols()==0) return typename MatrixType::RealScalar(0);
+ MatrixType symm = m.template selfadjointView<UpLo>();
+ return symm.cwiseAbs().colwise().sum().maxCoeff();
+}
+
+template<typename MatrixType,template <typename,int> class CholType> void test_chol_update(const MatrixType& symm)
+{
+ typedef typename MatrixType::Scalar Scalar;
+ typedef typename MatrixType::RealScalar RealScalar;
+ typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> VectorType;
+
+ MatrixType symmLo = symm.template triangularView<Lower>();
+ MatrixType symmUp = symm.template triangularView<Upper>();
+ MatrixType symmCpy = symm;
+
+ CholType<MatrixType,Lower> chollo(symmLo);
+ CholType<MatrixType,Upper> cholup(symmUp);
+
+ for (int k=0; k<10; ++k)
+ {
+ VectorType vec = VectorType::Random(symm.rows());
+ RealScalar sigma = internal::random<RealScalar>();
+ symmCpy += sigma * vec * vec.adjoint();
+
+ // we are doing some downdates, so it might be the case that the matrix is not SPD anymore
+ CholType<MatrixType,Lower> chol(symmCpy);
+ if(chol.info()!=Success)
+ break;
+
+ chollo.rankUpdate(vec, sigma);
+ VERIFY_IS_APPROX(symmCpy, chollo.reconstructedMatrix());
+
+ cholup.rankUpdate(vec, sigma);
+ VERIFY_IS_APPROX(symmCpy, cholup.reconstructedMatrix());
+ }
+}
+
+template<typename MatrixType> void cholesky(const MatrixType& m)
+{
+ /* this test covers the following files:
+ LLT.h LDLT.h
+ */
+ Index rows = m.rows();
+ Index cols = m.cols();
+
+ typedef typename MatrixType::Scalar Scalar;
+ typedef typename NumTraits<Scalar>::Real RealScalar;
+ typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime> SquareMatrixType;
+ typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> VectorType;
+
+ MatrixType a0 = MatrixType::Random(rows,cols);
+ VectorType vecB = VectorType::Random(rows), vecX(rows);
+ MatrixType matB = MatrixType::Random(rows,cols), matX(rows,cols);
+ SquareMatrixType symm = a0 * a0.adjoint();
+ // let's make sure the matrix is not singular or near singular
+ for (int k=0; k<3; ++k)
+ {
+ MatrixType a1 = MatrixType::Random(rows,cols);
+ symm += a1 * a1.adjoint();
+ }
+
+ {
+ STATIC_CHECK(( internal::is_same<typename LLT<MatrixType,Lower>::StorageIndex,int>::value ));
+ STATIC_CHECK(( internal::is_same<typename LLT<MatrixType,Upper>::StorageIndex,int>::value ));
+
+ SquareMatrixType symmUp = symm.template triangularView<Upper>();
+ SquareMatrixType symmLo = symm.template triangularView<Lower>();
+
+ LLT<SquareMatrixType,Lower> chollo(symmLo);
+ VERIFY_IS_APPROX(symm, chollo.reconstructedMatrix());
+
+ check_solverbase<VectorType, VectorType>(symm, chollo, rows, rows, 1);
+ check_solverbase<MatrixType, MatrixType>(symm, chollo, rows, cols, rows);
+
+ const MatrixType symmLo_inverse = chollo.solve(MatrixType::Identity(rows,cols));
+ RealScalar rcond = (RealScalar(1) / matrix_l1_norm<MatrixType, Lower>(symmLo)) /
+ matrix_l1_norm<MatrixType, Lower>(symmLo_inverse);
+ RealScalar rcond_est = chollo.rcond();
+ // Verify that the estimated condition number is within a factor of 10 of the
+ // truth.
+ VERIFY(rcond_est >= rcond / 10 && rcond_est <= rcond * 10);
+
+ // test the upper mode
+ LLT<SquareMatrixType,Upper> cholup(symmUp);
+ VERIFY_IS_APPROX(symm, cholup.reconstructedMatrix());
+ vecX = cholup.solve(vecB);
+ VERIFY_IS_APPROX(symm * vecX, vecB);
+ matX = cholup.solve(matB);
+ VERIFY_IS_APPROX(symm * matX, matB);
+
+ // Verify that the estimated condition number is within a factor of 10 of the
+ // truth.
+ const MatrixType symmUp_inverse = cholup.solve(MatrixType::Identity(rows,cols));
+ rcond = (RealScalar(1) / matrix_l1_norm<MatrixType, Upper>(symmUp)) /
+ matrix_l1_norm<MatrixType, Upper>(symmUp_inverse);
+ rcond_est = cholup.rcond();
+ VERIFY(rcond_est >= rcond / 10 && rcond_est <= rcond * 10);
+
+
+ MatrixType neg = -symmLo;
+ chollo.compute(neg);
+ VERIFY(neg.size()==0 || chollo.info()==NumericalIssue);
+
+ VERIFY_IS_APPROX(MatrixType(chollo.matrixL().transpose().conjugate()), MatrixType(chollo.matrixU()));
+ VERIFY_IS_APPROX(MatrixType(chollo.matrixU().transpose().conjugate()), MatrixType(chollo.matrixL()));
+ VERIFY_IS_APPROX(MatrixType(cholup.matrixL().transpose().conjugate()), MatrixType(cholup.matrixU()));
+ VERIFY_IS_APPROX(MatrixType(cholup.matrixU().transpose().conjugate()), MatrixType(cholup.matrixL()));
+
+ // test some special use cases of SelfCwiseBinaryOp:
+ MatrixType m1 = MatrixType::Random(rows,cols), m2(rows,cols);
+ m2 = m1;
+ m2 += symmLo.template selfadjointView<Lower>().llt().solve(matB);
+ VERIFY_IS_APPROX(m2, m1 + symmLo.template selfadjointView<Lower>().llt().solve(matB));
+ m2 = m1;
+ m2 -= symmLo.template selfadjointView<Lower>().llt().solve(matB);
+ VERIFY_IS_APPROX(m2, m1 - symmLo.template selfadjointView<Lower>().llt().solve(matB));
+ m2 = m1;
+ m2.noalias() += symmLo.template selfadjointView<Lower>().llt().solve(matB);
+ VERIFY_IS_APPROX(m2, m1 + symmLo.template selfadjointView<Lower>().llt().solve(matB));
+ m2 = m1;
+ m2.noalias() -= symmLo.template selfadjointView<Lower>().llt().solve(matB);
+ VERIFY_IS_APPROX(m2, m1 - symmLo.template selfadjointView<Lower>().llt().solve(matB));
+ }
+
+ // LDLT
+ {
+ STATIC_CHECK(( internal::is_same<typename LDLT<MatrixType,Lower>::StorageIndex,int>::value ));
+ STATIC_CHECK(( internal::is_same<typename LDLT<MatrixType,Upper>::StorageIndex,int>::value ));
+
+ int sign = internal::random<int>()%2 ? 1 : -1;
+
+ if(sign == -1)
+ {
+ symm = -symm; // test a negative matrix
+ }
+
+ SquareMatrixType symmUp = symm.template triangularView<Upper>();
+ SquareMatrixType symmLo = symm.template triangularView<Lower>();
+
+ LDLT<SquareMatrixType,Lower> ldltlo(symmLo);
+ VERIFY(ldltlo.info()==Success);
+ VERIFY_IS_APPROX(symm, ldltlo.reconstructedMatrix());
+
+ check_solverbase<VectorType, VectorType>(symm, ldltlo, rows, rows, 1);
+ check_solverbase<MatrixType, MatrixType>(symm, ldltlo, rows, cols, rows);
+
+ const MatrixType symmLo_inverse = ldltlo.solve(MatrixType::Identity(rows,cols));
+ RealScalar rcond = (RealScalar(1) / matrix_l1_norm<MatrixType, Lower>(symmLo)) /
+ matrix_l1_norm<MatrixType, Lower>(symmLo_inverse);
+ RealScalar rcond_est = ldltlo.rcond();
+ // Verify that the estimated condition number is within a factor of 10 of the
+ // truth.
+ VERIFY(rcond_est >= rcond / 10 && rcond_est <= rcond * 10);
+
+
+ LDLT<SquareMatrixType,Upper> ldltup(symmUp);
+ VERIFY(ldltup.info()==Success);
+ VERIFY_IS_APPROX(symm, ldltup.reconstructedMatrix());
+ vecX = ldltup.solve(vecB);
+ VERIFY_IS_APPROX(symm * vecX, vecB);
+ matX = ldltup.solve(matB);
+ VERIFY_IS_APPROX(symm * matX, matB);
+
+ // Verify that the estimated condition number is within a factor of 10 of the
+ // truth.
+ const MatrixType symmUp_inverse = ldltup.solve(MatrixType::Identity(rows,cols));
+ rcond = (RealScalar(1) / matrix_l1_norm<MatrixType, Upper>(symmUp)) /
+ matrix_l1_norm<MatrixType, Upper>(symmUp_inverse);
+ rcond_est = ldltup.rcond();
+ VERIFY(rcond_est >= rcond / 10 && rcond_est <= rcond * 10);
+
+ VERIFY_IS_APPROX(MatrixType(ldltlo.matrixL().transpose().conjugate()), MatrixType(ldltlo.matrixU()));
+ VERIFY_IS_APPROX(MatrixType(ldltlo.matrixU().transpose().conjugate()), MatrixType(ldltlo.matrixL()));
+ VERIFY_IS_APPROX(MatrixType(ldltup.matrixL().transpose().conjugate()), MatrixType(ldltup.matrixU()));
+ VERIFY_IS_APPROX(MatrixType(ldltup.matrixU().transpose().conjugate()), MatrixType(ldltup.matrixL()));
+
+ if(MatrixType::RowsAtCompileTime==Dynamic)
+ {
+ // note : each inplace permutation requires a small temporary vector (mask)
+
+ // check inplace solve
+ matX = matB;
+ VERIFY_EVALUATION_COUNT(matX = ldltlo.solve(matX), 0);
+ VERIFY_IS_APPROX(matX, ldltlo.solve(matB).eval());
+
+
+ matX = matB;
+ VERIFY_EVALUATION_COUNT(matX = ldltup.solve(matX), 0);
+ VERIFY_IS_APPROX(matX, ldltup.solve(matB).eval());
+ }
+
+ // restore
+ if(sign == -1)
+ symm = -symm;
+
+ // check matrices coming from linear constraints with Lagrange multipliers
+ if(rows>=3)
+ {
+ SquareMatrixType A = symm;
+ Index c = internal::random<Index>(0,rows-2);
+ A.bottomRightCorner(c,c).setZero();
+ // Make sure a solution exists:
+ vecX.setRandom();
+ vecB = A * vecX;
+ vecX.setZero();
+ ldltlo.compute(A);
+ VERIFY_IS_APPROX(A, ldltlo.reconstructedMatrix());
+ vecX = ldltlo.solve(vecB);
+ VERIFY_IS_APPROX(A * vecX, vecB);
+ }
+
+ // check non-full rank matrices
+ if(rows>=3)
+ {
+ Index r = internal::random<Index>(1,rows-1);
+ Matrix<Scalar,Dynamic,Dynamic> a = Matrix<Scalar,Dynamic,Dynamic>::Random(rows,r);
+ SquareMatrixType A = a * a.adjoint();
+ // Make sure a solution exists:
+ vecX.setRandom();
+ vecB = A * vecX;
+ vecX.setZero();
+ ldltlo.compute(A);
+ VERIFY_IS_APPROX(A, ldltlo.reconstructedMatrix());
+ vecX = ldltlo.solve(vecB);
+ VERIFY_IS_APPROX(A * vecX, vecB);
+ }
+
+ // check matrices with a wide spectrum
+ if(rows>=3)
+ {
+ using std::pow;
+ using std::sqrt;
+ RealScalar s = (std::min)(16,std::numeric_limits<RealScalar>::max_exponent10/8);
+ Matrix<Scalar,Dynamic,Dynamic> a = Matrix<Scalar,Dynamic,Dynamic>::Random(rows,rows);
+ Matrix<RealScalar,Dynamic,1> d = Matrix<RealScalar,Dynamic,1>::Random(rows);
+ for(Index k=0; k<rows; ++k)
+ d(k) = d(k)*pow(RealScalar(10),internal::random<RealScalar>(-s,s));
+ SquareMatrixType A = a * d.asDiagonal() * a.adjoint();
+ // Make sure a solution exists:
+ vecX.setRandom();
+ vecB = A * vecX;
+ vecX.setZero();
+ ldltlo.compute(A);
+ VERIFY_IS_APPROX(A, ldltlo.reconstructedMatrix());
+ vecX = ldltlo.solve(vecB);
+
+ if(ldltlo.vectorD().real().cwiseAbs().minCoeff()>RealScalar(0))
+ {
+ VERIFY_IS_APPROX(A * vecX,vecB);
+ }
+ else
+ {
+ RealScalar large_tol = sqrt(test_precision<RealScalar>());
+ VERIFY((A * vecX).isApprox(vecB, large_tol));
+
+ ++g_test_level;
+ VERIFY_IS_APPROX(A * vecX,vecB);
+ --g_test_level;
+ }
+ }
+ }
+
+ // update/downdate
+ CALL_SUBTEST(( test_chol_update<SquareMatrixType,LLT>(symm) ));
+ CALL_SUBTEST(( test_chol_update<SquareMatrixType,LDLT>(symm) ));
+}
+
+template<typename MatrixType> void cholesky_cplx(const MatrixType& m)
+{
+ // classic test
+ cholesky(m);
+
+ // test mixing real/scalar types
+
+ Index rows = m.rows();
+ Index cols = m.cols();
+
+ typedef typename MatrixType::Scalar Scalar;
+ typedef typename NumTraits<Scalar>::Real RealScalar;
+ typedef Matrix<RealScalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime> RealMatrixType;
+ typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> VectorType;
+
+ RealMatrixType a0 = RealMatrixType::Random(rows,cols);
+ VectorType vecB = VectorType::Random(rows), vecX(rows);
+ MatrixType matB = MatrixType::Random(rows,cols), matX(rows,cols);
+ RealMatrixType symm = a0 * a0.adjoint();
+ // let's make sure the matrix is not singular or near singular
+ for (int k=0; k<3; ++k)
+ {
+ RealMatrixType a1 = RealMatrixType::Random(rows,cols);
+ symm += a1 * a1.adjoint();
+ }
+
+ {
+ RealMatrixType symmLo = symm.template triangularView<Lower>();
+
+ LLT<RealMatrixType,Lower> chollo(symmLo);
+ VERIFY_IS_APPROX(symm, chollo.reconstructedMatrix());
+
+ check_solverbase<VectorType, VectorType>(symm, chollo, rows, rows, 1);
+ //check_solverbase<MatrixType, MatrixType>(symm, chollo, rows, cols, rows);
+ }
+
+ // LDLT
+ {
+ int sign = internal::random<int>()%2 ? 1 : -1;
+
+ if(sign == -1)
+ {
+ symm = -symm; // test a negative matrix
+ }
+
+ RealMatrixType symmLo = symm.template triangularView<Lower>();
+
+ LDLT<RealMatrixType,Lower> ldltlo(symmLo);
+ VERIFY(ldltlo.info()==Success);
+ VERIFY_IS_APPROX(symm, ldltlo.reconstructedMatrix());
+
+ check_solverbase<VectorType, VectorType>(symm, ldltlo, rows, rows, 1);
+ //check_solverbase<MatrixType, MatrixType>(symm, ldltlo, rows, cols, rows);
+ }
+}
+
+// regression test for bug 241
+template<typename MatrixType> void cholesky_bug241(const MatrixType& m)
+{
+ eigen_assert(m.rows() == 2 && m.cols() == 2);
+
+ typedef typename MatrixType::Scalar Scalar;
+ typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> VectorType;
+
+ MatrixType matA;
+ matA << 1, 1, 1, 1;
+ VectorType vecB;
+ vecB << 1, 1;
+ VectorType vecX = matA.ldlt().solve(vecB);
+ VERIFY_IS_APPROX(matA * vecX, vecB);
+}
+
+// LDLT is not guaranteed to work for indefinite matrices, but happens to work fine if matrix is diagonal.
+// This test checks that LDLT reports correctly that matrix is indefinite.
+// See http://forum.kde.org/viewtopic.php?f=74&t=106942 and bug 736
+template<typename MatrixType> void cholesky_definiteness(const MatrixType& m)
+{
+ eigen_assert(m.rows() == 2 && m.cols() == 2);
+ MatrixType mat;
+ LDLT<MatrixType> ldlt(2);
+
+ {
+ mat << 1, 0, 0, -1;
+ ldlt.compute(mat);
+ VERIFY(ldlt.info()==Success);
+ VERIFY(!ldlt.isNegative());
+ VERIFY(!ldlt.isPositive());
+ VERIFY_IS_APPROX(mat,ldlt.reconstructedMatrix());
+ }
+ {
+ mat << 1, 2, 2, 1;
+ ldlt.compute(mat);
+ VERIFY(ldlt.info()==Success);
+ VERIFY(!ldlt.isNegative());
+ VERIFY(!ldlt.isPositive());
+ VERIFY_IS_APPROX(mat,ldlt.reconstructedMatrix());
+ }
+ {
+ mat << 0, 0, 0, 0;
+ ldlt.compute(mat);
+ VERIFY(ldlt.info()==Success);
+ VERIFY(ldlt.isNegative());
+ VERIFY(ldlt.isPositive());
+ VERIFY_IS_APPROX(mat,ldlt.reconstructedMatrix());
+ }
+ {
+ mat << 0, 0, 0, 1;
+ ldlt.compute(mat);
+ VERIFY(ldlt.info()==Success);
+ VERIFY(!ldlt.isNegative());
+ VERIFY(ldlt.isPositive());
+ VERIFY_IS_APPROX(mat,ldlt.reconstructedMatrix());
+ }
+ {
+ mat << -1, 0, 0, 0;
+ ldlt.compute(mat);
+ VERIFY(ldlt.info()==Success);
+ VERIFY(ldlt.isNegative());
+ VERIFY(!ldlt.isPositive());
+ VERIFY_IS_APPROX(mat,ldlt.reconstructedMatrix());
+ }
+}
+
+template<typename>
+void cholesky_faillure_cases()
+{
+ MatrixXd mat;
+ LDLT<MatrixXd> ldlt;
+
+ {
+ mat.resize(2,2);
+ mat << 0, 1, 1, 0;
+ ldlt.compute(mat);
+ VERIFY_IS_NOT_APPROX(mat,ldlt.reconstructedMatrix());
+ VERIFY(ldlt.info()==NumericalIssue);
+ }
+#if (!EIGEN_ARCH_i386) || defined(EIGEN_VECTORIZE_SSE2)
+ {
+ mat.resize(3,3);
+ mat << -1, -3, 3,
+ -3, -8.9999999999999999999, 1,
+ 3, 1, 0;
+ ldlt.compute(mat);
+ VERIFY(ldlt.info()==NumericalIssue);
+ VERIFY_IS_NOT_APPROX(mat,ldlt.reconstructedMatrix());
+ }
+#endif
+ {
+ mat.resize(3,3);
+ mat << 1, 2, 3,
+ 2, 4, 1,
+ 3, 1, 0;
+ ldlt.compute(mat);
+ VERIFY(ldlt.info()==NumericalIssue);
+ VERIFY_IS_NOT_APPROX(mat,ldlt.reconstructedMatrix());
+ }
+
+ {
+ mat.resize(8,8);
+ mat << 0.1, 0, -0.1, 0, 0, 0, 1, 0,
+ 0, 4.24667, 0, 2.00333, 0, 0, 0, 0,
+ -0.1, 0, 0.2, 0, -0.1, 0, 0, 0,
+ 0, 2.00333, 0, 8.49333, 0, 2.00333, 0, 0,
+ 0, 0, -0.1, 0, 0.1, 0, 0, 1,
+ 0, 0, 0, 2.00333, 0, 4.24667, 0, 0,
+ 1, 0, 0, 0, 0, 0, 0, 0,
+ 0, 0, 0, 0, 1, 0, 0, 0;
+ ldlt.compute(mat);
+ VERIFY(ldlt.info()==NumericalIssue);
+ VERIFY_IS_NOT_APPROX(mat,ldlt.reconstructedMatrix());
+ }
+
+ // bug 1479
+ {
+ mat.resize(4,4);
+ mat << 1, 2, 0, 1,
+ 2, 4, 0, 2,
+ 0, 0, 0, 1,
+ 1, 2, 1, 1;
+ ldlt.compute(mat);
+ VERIFY(ldlt.info()==NumericalIssue);
+ VERIFY_IS_NOT_APPROX(mat,ldlt.reconstructedMatrix());
+ }
+}
+
+template<typename MatrixType> void cholesky_verify_assert()
+{
+ MatrixType tmp;
+
+ LLT<MatrixType> llt;
+ VERIFY_RAISES_ASSERT(llt.matrixL())
+ VERIFY_RAISES_ASSERT(llt.matrixU())
+ VERIFY_RAISES_ASSERT(llt.solve(tmp))
+ VERIFY_RAISES_ASSERT(llt.transpose().solve(tmp))
+ VERIFY_RAISES_ASSERT(llt.adjoint().solve(tmp))
+ VERIFY_RAISES_ASSERT(llt.solveInPlace(tmp))
+
+ LDLT<MatrixType> ldlt;
+ VERIFY_RAISES_ASSERT(ldlt.matrixL())
+ VERIFY_RAISES_ASSERT(ldlt.transpositionsP())
+ VERIFY_RAISES_ASSERT(ldlt.vectorD())
+ VERIFY_RAISES_ASSERT(ldlt.isPositive())
+ VERIFY_RAISES_ASSERT(ldlt.isNegative())
+ VERIFY_RAISES_ASSERT(ldlt.solve(tmp))
+ VERIFY_RAISES_ASSERT(ldlt.transpose().solve(tmp))
+ VERIFY_RAISES_ASSERT(ldlt.adjoint().solve(tmp))
+ VERIFY_RAISES_ASSERT(ldlt.solveInPlace(tmp))
+}
+
+EIGEN_DECLARE_TEST(cholesky)
+{
+ int s = 0;
+ for(int i = 0; i < g_repeat; i++) {
+ CALL_SUBTEST_1( cholesky(Matrix<double,1,1>()) );
+ CALL_SUBTEST_3( cholesky(Matrix2d()) );
+ CALL_SUBTEST_3( cholesky_bug241(Matrix2d()) );
+ CALL_SUBTEST_3( cholesky_definiteness(Matrix2d()) );
+ CALL_SUBTEST_4( cholesky(Matrix3f()) );
+ CALL_SUBTEST_5( cholesky(Matrix4d()) );
+
+ s = internal::random<int>(1,EIGEN_TEST_MAX_SIZE);
+ CALL_SUBTEST_2( cholesky(MatrixXd(s,s)) );
+ TEST_SET_BUT_UNUSED_VARIABLE(s)
+
+ s = internal::random<int>(1,EIGEN_TEST_MAX_SIZE/2);
+ CALL_SUBTEST_6( cholesky_cplx(MatrixXcd(s,s)) );
+ TEST_SET_BUT_UNUSED_VARIABLE(s)
+ }
+ // empty matrix, regression test for Bug 785:
+ CALL_SUBTEST_2( cholesky(MatrixXd(0,0)) );
+
+ // This does not work yet:
+ // CALL_SUBTEST_2( cholesky(Matrix<double,0,0>()) );
+
+ CALL_SUBTEST_4( cholesky_verify_assert<Matrix3f>() );
+ CALL_SUBTEST_7( cholesky_verify_assert<Matrix3d>() );
+ CALL_SUBTEST_8( cholesky_verify_assert<MatrixXf>() );
+ CALL_SUBTEST_2( cholesky_verify_assert<MatrixXd>() );
+
+ // Test problem size constructors
+ CALL_SUBTEST_9( LLT<MatrixXf>(10) );
+ CALL_SUBTEST_9( LDLT<MatrixXf>(10) );
+
+ CALL_SUBTEST_2( cholesky_faillure_cases<void>() );
+
+ TEST_SET_BUT_UNUSED_VARIABLE(nb_temporaries)
+}
diff --git a/test/cholmod_support.cpp b/test/cholmod_support.cpp
new file mode 100644
index 0000000..89b9cf4
--- /dev/null
+++ b/test/cholmod_support.cpp
@@ -0,0 +1,69 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2011 Gael Guennebaud <g.gael@free.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#define EIGEN_NO_DEBUG_SMALL_PRODUCT_BLOCKS
+#include "sparse_solver.h"
+
+#include <Eigen/CholmodSupport>
+
+template<typename SparseType> void test_cholmod_ST()
+{
+ CholmodDecomposition<SparseType, Lower> g_chol_colmajor_lower; g_chol_colmajor_lower.setMode(CholmodSupernodalLLt);
+ CholmodDecomposition<SparseType, Upper> g_chol_colmajor_upper; g_chol_colmajor_upper.setMode(CholmodSupernodalLLt);
+ CholmodDecomposition<SparseType, Lower> g_llt_colmajor_lower; g_llt_colmajor_lower.setMode(CholmodSimplicialLLt);
+ CholmodDecomposition<SparseType, Upper> g_llt_colmajor_upper; g_llt_colmajor_upper.setMode(CholmodSimplicialLLt);
+ CholmodDecomposition<SparseType, Lower> g_ldlt_colmajor_lower; g_ldlt_colmajor_lower.setMode(CholmodLDLt);
+ CholmodDecomposition<SparseType, Upper> g_ldlt_colmajor_upper; g_ldlt_colmajor_upper.setMode(CholmodLDLt);
+
+ CholmodSupernodalLLT<SparseType, Lower> chol_colmajor_lower;
+ CholmodSupernodalLLT<SparseType, Upper> chol_colmajor_upper;
+ CholmodSimplicialLLT<SparseType, Lower> llt_colmajor_lower;
+ CholmodSimplicialLLT<SparseType, Upper> llt_colmajor_upper;
+ CholmodSimplicialLDLT<SparseType, Lower> ldlt_colmajor_lower;
+ CholmodSimplicialLDLT<SparseType, Upper> ldlt_colmajor_upper;
+
+ check_sparse_spd_solving(g_chol_colmajor_lower);
+ check_sparse_spd_solving(g_chol_colmajor_upper);
+ check_sparse_spd_solving(g_llt_colmajor_lower);
+ check_sparse_spd_solving(g_llt_colmajor_upper);
+ check_sparse_spd_solving(g_ldlt_colmajor_lower);
+ check_sparse_spd_solving(g_ldlt_colmajor_upper);
+
+ check_sparse_spd_solving(chol_colmajor_lower);
+ check_sparse_spd_solving(chol_colmajor_upper);
+ check_sparse_spd_solving(llt_colmajor_lower);
+ check_sparse_spd_solving(llt_colmajor_upper);
+ check_sparse_spd_solving(ldlt_colmajor_lower);
+ check_sparse_spd_solving(ldlt_colmajor_upper);
+
+ check_sparse_spd_determinant(chol_colmajor_lower);
+ check_sparse_spd_determinant(chol_colmajor_upper);
+ check_sparse_spd_determinant(llt_colmajor_lower);
+ check_sparse_spd_determinant(llt_colmajor_upper);
+ check_sparse_spd_determinant(ldlt_colmajor_lower);
+ check_sparse_spd_determinant(ldlt_colmajor_upper);
+}
+
+template<typename T, int flags, typename IdxType> void test_cholmod_T()
+{
+ test_cholmod_ST<SparseMatrix<T, flags, IdxType> >();
+}
+
+EIGEN_DECLARE_TEST(cholmod_support)
+{
+ CALL_SUBTEST_11( (test_cholmod_T<double , ColMajor, int >()) );
+ CALL_SUBTEST_12( (test_cholmod_T<double , ColMajor, long>()) );
+ CALL_SUBTEST_13( (test_cholmod_T<double , RowMajor, int >()) );
+ CALL_SUBTEST_14( (test_cholmod_T<double , RowMajor, long>()) );
+ CALL_SUBTEST_21( (test_cholmod_T<std::complex<double>, ColMajor, int >()) );
+ CALL_SUBTEST_22( (test_cholmod_T<std::complex<double>, ColMajor, long>()) );
+ // TODO complex row-major matrices do not work at the moment:
+ // CALL_SUBTEST_23( (test_cholmod_T<std::complex<double>, RowMajor, int >()) );
+ // CALL_SUBTEST_24( (test_cholmod_T<std::complex<double>, RowMajor, long>()) );
+}
diff --git a/test/commainitializer.cpp b/test/commainitializer.cpp
new file mode 100644
index 0000000..eb275be
--- /dev/null
+++ b/test/commainitializer.cpp
@@ -0,0 +1,118 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "main.h"
+
+
+template<int M1, int M2, int N1, int N2>
+void test_blocks()
+{
+ Matrix<int, M1+M2, N1+N2> m_fixed;
+ MatrixXi m_dynamic(M1+M2, N1+N2);
+
+ Matrix<int, M1, N1> mat11; mat11.setRandom();
+ Matrix<int, M1, N2> mat12; mat12.setRandom();
+ Matrix<int, M2, N1> mat21; mat21.setRandom();
+ Matrix<int, M2, N2> mat22; mat22.setRandom();
+
+ MatrixXi matx11 = mat11, matx12 = mat12, matx21 = mat21, matx22 = mat22;
+
+ {
+ VERIFY_IS_EQUAL((m_fixed << mat11, mat12, mat21, matx22).finished(), (m_dynamic << mat11, matx12, mat21, matx22).finished());
+ VERIFY_IS_EQUAL((m_fixed.template topLeftCorner<M1,N1>()), mat11);
+ VERIFY_IS_EQUAL((m_fixed.template topRightCorner<M1,N2>()), mat12);
+ VERIFY_IS_EQUAL((m_fixed.template bottomLeftCorner<M2,N1>()), mat21);
+ VERIFY_IS_EQUAL((m_fixed.template bottomRightCorner<M2,N2>()), mat22);
+ VERIFY_IS_EQUAL((m_fixed << mat12, mat11, matx21, mat22).finished(), (m_dynamic << mat12, matx11, matx21, mat22).finished());
+ }
+
+ if(N1 > 0)
+ {
+ if(M1 > 0)
+ {
+ VERIFY_RAISES_ASSERT((m_fixed << mat11, mat12, mat11, mat21, mat22));
+ }
+ if(M2 > 0)
+ {
+ VERIFY_RAISES_ASSERT((m_fixed << mat11, mat12, mat21, mat21, mat22));
+ }
+ }
+ else
+ {
+ // allow insertion of zero-column blocks:
+ VERIFY_IS_EQUAL((m_fixed << mat11, mat12, mat11, mat11, mat21, mat21, mat22).finished(), (m_dynamic << mat12, mat22).finished());
+ }
+ if(M1 != M2)
+ {
+ VERIFY_RAISES_ASSERT((m_fixed << mat11, mat21, mat12, mat22));
+ }
+}
+
+
+template<int depth, int N=0>
+struct test_block_recursion
+{
+ static void run()
+ {
+ test_block_recursion<depth-1, N>::run();
+ test_block_recursion<depth-1, N + (1 << (depth-1))>::run();
+ }
+};
+
+template<int N>
+struct test_block_recursion<0,N>
+{
+ static void run() {
+ test_blocks<(N>>6)&3, (N>>4)&3, (N>>2)&3, N & 3>();
+ }
+};
+
+void test_basics() {
+ Matrix3d m3;
+ Matrix4d m4;
+
+ VERIFY_RAISES_ASSERT( (m3 << 1, 2, 3, 4, 5, 6, 7, 8) );
+
+ #ifndef _MSC_VER
+ VERIFY_RAISES_ASSERT( (m3 << 1, 2, 3, 4, 5, 6, 7, 8, 9, 10) );
+ #endif
+
+ double data[] = {1, 2, 3, 4, 5, 6, 7, 8, 9};
+ Matrix3d ref = Map<Matrix<double,3,3,RowMajor> >(data);
+
+ m3 = Matrix3d::Random();
+ m3 << 1, 2, 3, 4, 5, 6, 7, 8, 9;
+ VERIFY_IS_APPROX(m3, ref );
+
+ Vector3d vec[3];
+ vec[0] << 1, 4, 7;
+ vec[1] << 2, 5, 8;
+ vec[2] << 3, 6, 9;
+ m3 = Matrix3d::Random();
+ m3 << vec[0], vec[1], vec[2];
+ VERIFY_IS_APPROX(m3, ref);
+
+ vec[0] << 1, 2, 3;
+ vec[1] << 4, 5, 6;
+ vec[2] << 7, 8, 9;
+ m3 = Matrix3d::Random();
+ m3 << vec[0].transpose(),
+ 4, 5, 6,
+ vec[2].transpose();
+ VERIFY_IS_APPROX(m3, ref);
+}
+
+EIGEN_DECLARE_TEST(commainitializer)
+{
+
+ CALL_SUBTEST_1(test_basics());
+
+ // recursively test all block-sizes from 0 to 3:
+ CALL_SUBTEST_2(test_block_recursion<8>::run());
+}
diff --git a/test/conjugate_gradient.cpp b/test/conjugate_gradient.cpp
new file mode 100644
index 0000000..b076a12
--- /dev/null
+++ b/test/conjugate_gradient.cpp
@@ -0,0 +1,34 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2011 Gael Guennebaud <g.gael@free.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "sparse_solver.h"
+#include <Eigen/IterativeLinearSolvers>
+
+template<typename T, typename I_> void test_conjugate_gradient_T()
+{
+ typedef SparseMatrix<T,0,I_> SparseMatrixType;
+ ConjugateGradient<SparseMatrixType, Lower > cg_colmajor_lower_diag;
+ ConjugateGradient<SparseMatrixType, Upper > cg_colmajor_upper_diag;
+ ConjugateGradient<SparseMatrixType, Lower|Upper> cg_colmajor_loup_diag;
+ ConjugateGradient<SparseMatrixType, Lower, IdentityPreconditioner> cg_colmajor_lower_I;
+ ConjugateGradient<SparseMatrixType, Upper, IdentityPreconditioner> cg_colmajor_upper_I;
+
+ CALL_SUBTEST( check_sparse_spd_solving(cg_colmajor_lower_diag) );
+ CALL_SUBTEST( check_sparse_spd_solving(cg_colmajor_upper_diag) );
+ CALL_SUBTEST( check_sparse_spd_solving(cg_colmajor_loup_diag) );
+ CALL_SUBTEST( check_sparse_spd_solving(cg_colmajor_lower_I) );
+ CALL_SUBTEST( check_sparse_spd_solving(cg_colmajor_upper_I) );
+}
+
+EIGEN_DECLARE_TEST(conjugate_gradient)
+{
+ CALL_SUBTEST_1(( test_conjugate_gradient_T<double,int>() ));
+ CALL_SUBTEST_2(( test_conjugate_gradient_T<std::complex<double>, int>() ));
+ CALL_SUBTEST_3(( test_conjugate_gradient_T<double,long int>() ));
+}
diff --git a/test/conservative_resize.cpp b/test/conservative_resize.cpp
new file mode 100644
index 0000000..d48eb12
--- /dev/null
+++ b/test/conservative_resize.cpp
@@ -0,0 +1,167 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009 Hauke Heibel <hauke.heibel@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "main.h"
+
+#include <Eigen/Core>
+#include "AnnoyingScalar.h"
+
+using namespace Eigen;
+
+template <typename Scalar, int Storage>
+void run_matrix_tests()
+{
+ typedef Matrix<Scalar, Eigen::Dynamic, Eigen::Dynamic, Storage> MatrixType;
+
+ MatrixType m, n;
+
+ // boundary cases ...
+ m = n = MatrixType::Random(50,50);
+ m.conservativeResize(1,50);
+ VERIFY_IS_APPROX(m, n.block(0,0,1,50));
+
+ m = n = MatrixType::Random(50,50);
+ m.conservativeResize(50,1);
+ VERIFY_IS_APPROX(m, n.block(0,0,50,1));
+
+ m = n = MatrixType::Random(50,50);
+ m.conservativeResize(50,50);
+ VERIFY_IS_APPROX(m, n.block(0,0,50,50));
+
+ // random shrinking ...
+ for (int i=0; i<25; ++i)
+ {
+ const Index rows = internal::random<Index>(1,50);
+ const Index cols = internal::random<Index>(1,50);
+ m = n = MatrixType::Random(50,50);
+ m.conservativeResize(rows,cols);
+ VERIFY_IS_APPROX(m, n.block(0,0,rows,cols));
+ }
+
+ // random growing with zeroing ...
+ for (int i=0; i<25; ++i)
+ {
+ const Index rows = internal::random<Index>(50,75);
+ const Index cols = internal::random<Index>(50,75);
+ m = n = MatrixType::Random(50,50);
+ m.conservativeResizeLike(MatrixType::Zero(rows,cols));
+ VERIFY_IS_APPROX(m.block(0,0,n.rows(),n.cols()), n);
+ VERIFY( rows<=50 || m.block(50,0,rows-50,cols).sum() == Scalar(0) );
+ VERIFY( cols<=50 || m.block(0,50,rows,cols-50).sum() == Scalar(0) );
+ }
+}
+
+template <typename Scalar>
+void run_vector_tests()
+{
+ typedef Matrix<Scalar, 1, Eigen::Dynamic> VectorType;
+
+ VectorType m, n;
+
+ // boundary cases ...
+ m = n = VectorType::Random(50);
+ m.conservativeResize(1);
+ VERIFY_IS_APPROX(m, n.segment(0,1));
+
+ m = n = VectorType::Random(50);
+ m.conservativeResize(50);
+ VERIFY_IS_APPROX(m, n.segment(0,50));
+
+ m = n = VectorType::Random(50);
+ m.conservativeResize(m.rows(),1);
+ VERIFY_IS_APPROX(m, n.segment(0,1));
+
+ m = n = VectorType::Random(50);
+ m.conservativeResize(m.rows(),50);
+ VERIFY_IS_APPROX(m, n.segment(0,50));
+
+ // random shrinking ...
+ for (int i=0; i<50; ++i)
+ {
+ const int size = internal::random<int>(1,50);
+ m = n = VectorType::Random(50);
+ m.conservativeResize(size);
+ VERIFY_IS_APPROX(m, n.segment(0,size));
+
+ m = n = VectorType::Random(50);
+ m.conservativeResize(m.rows(), size);
+ VERIFY_IS_APPROX(m, n.segment(0,size));
+ }
+
+ // random growing with zeroing ...
+ for (int i=0; i<50; ++i)
+ {
+ const int size = internal::random<int>(50,100);
+ m = n = VectorType::Random(50);
+ m.conservativeResizeLike(VectorType::Zero(size));
+ VERIFY_IS_APPROX(m.segment(0,50), n);
+ VERIFY( size<=50 || m.segment(50,size-50).sum() == Scalar(0) );
+
+ m = n = VectorType::Random(50);
+ m.conservativeResizeLike(Matrix<Scalar,Dynamic,Dynamic>::Zero(1,size));
+ VERIFY_IS_APPROX(m.segment(0,50), n);
+ VERIFY( size<=50 || m.segment(50,size-50).sum() == Scalar(0) );
+ }
+}
+
+// Basic memory leak check with a non-copyable scalar type
+template<int> void noncopyable()
+{
+ typedef Eigen::Matrix<AnnoyingScalar,Dynamic,1> VectorType;
+ typedef Eigen::Matrix<AnnoyingScalar,Dynamic,Dynamic> MatrixType;
+
+ {
+#ifndef EIGEN_TEST_ANNOYING_SCALAR_DONT_THROW
+ AnnoyingScalar::dont_throw = true;
+#endif
+ int n = 50;
+ VectorType v0(n), v1(n);
+ MatrixType m0(n,n), m1(n,n), m2(n,n);
+ v0.setOnes(); v1.setOnes();
+ m0.setOnes(); m1.setOnes(); m2.setOnes();
+ VERIFY(m0==m1);
+ m0.conservativeResize(2*n,2*n);
+ VERIFY(m0.topLeftCorner(n,n) == m1);
+
+ VERIFY(v0.head(n) == v1);
+ v0.conservativeResize(2*n);
+ VERIFY(v0.head(n) == v1);
+ }
+ VERIFY(AnnoyingScalar::instances==0 && "global memory leak detected in noncopyable");
+}
+
+EIGEN_DECLARE_TEST(conservative_resize)
+{
+ for(int i=0; i<g_repeat; ++i)
+ {
+ CALL_SUBTEST_1((run_matrix_tests<int, Eigen::RowMajor>()));
+ CALL_SUBTEST_1((run_matrix_tests<int, Eigen::ColMajor>()));
+ CALL_SUBTEST_2((run_matrix_tests<float, Eigen::RowMajor>()));
+ CALL_SUBTEST_2((run_matrix_tests<float, Eigen::ColMajor>()));
+ CALL_SUBTEST_3((run_matrix_tests<double, Eigen::RowMajor>()));
+ CALL_SUBTEST_3((run_matrix_tests<double, Eigen::ColMajor>()));
+ CALL_SUBTEST_4((run_matrix_tests<std::complex<float>, Eigen::RowMajor>()));
+ CALL_SUBTEST_4((run_matrix_tests<std::complex<float>, Eigen::ColMajor>()));
+ CALL_SUBTEST_5((run_matrix_tests<std::complex<double>, Eigen::RowMajor>()));
+ CALL_SUBTEST_5((run_matrix_tests<std::complex<double>, Eigen::ColMajor>()));
+ CALL_SUBTEST_1((run_matrix_tests<int, Eigen::RowMajor | Eigen::DontAlign>()));
+
+ CALL_SUBTEST_1((run_vector_tests<int>()));
+ CALL_SUBTEST_2((run_vector_tests<float>()));
+ CALL_SUBTEST_3((run_vector_tests<double>()));
+ CALL_SUBTEST_4((run_vector_tests<std::complex<float> >()));
+ CALL_SUBTEST_5((run_vector_tests<std::complex<double> >()));
+
+#ifndef EIGEN_TEST_ANNOYING_SCALAR_DONT_THROW
+ AnnoyingScalar::dont_throw = true;
+#endif
+ CALL_SUBTEST_6(( run_vector_tests<AnnoyingScalar>() ));
+ CALL_SUBTEST_6(( noncopyable<0>() ));
+ }
+}
diff --git a/test/constructor.cpp b/test/constructor.cpp
new file mode 100644
index 0000000..ffd5e80
--- /dev/null
+++ b/test/constructor.cpp
@@ -0,0 +1,98 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2017 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+
+#define TEST_ENABLE_TEMPORARY_TRACKING
+
+#include "main.h"
+
+template<typename MatrixType> struct Wrapper
+{
+ MatrixType m_mat;
+ inline Wrapper(const MatrixType &x) : m_mat(x) {}
+ inline operator const MatrixType& () const { return m_mat; }
+ inline operator MatrixType& () { return m_mat; }
+};
+
+enum my_sizes { M = 12, N = 7};
+
+template<typename MatrixType> void ctor_init1(const MatrixType& m)
+{
+ // Check logic in PlainObjectBase::_init1
+ Index rows = m.rows();
+ Index cols = m.cols();
+
+ MatrixType m0 = MatrixType::Random(rows,cols);
+
+ VERIFY_EVALUATION_COUNT( MatrixType m1(m0), 1);
+ VERIFY_EVALUATION_COUNT( MatrixType m2(m0+m0), 1);
+ VERIFY_EVALUATION_COUNT( MatrixType m2(m0.block(0,0,rows,cols)) , 1);
+
+ Wrapper<MatrixType> wrapper(m0);
+ VERIFY_EVALUATION_COUNT( MatrixType m3(wrapper) , 1);
+}
+
+
+EIGEN_DECLARE_TEST(constructor)
+{
+ for(int i = 0; i < g_repeat; i++) {
+ CALL_SUBTEST_1( ctor_init1(Matrix<float, 1, 1>()) );
+ CALL_SUBTEST_1( ctor_init1(Matrix4d()) );
+ CALL_SUBTEST_1( ctor_init1(MatrixXcf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
+ CALL_SUBTEST_1( ctor_init1(MatrixXi(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
+ }
+ {
+ Matrix<Index,1,1> a(123);
+ VERIFY_IS_EQUAL(a[0], 123);
+ }
+ {
+ Matrix<Index,1,1> a(123.0);
+ VERIFY_IS_EQUAL(a[0], 123);
+ }
+ {
+ Matrix<float,1,1> a(123);
+ VERIFY_IS_EQUAL(a[0], 123.f);
+ }
+ {
+ Array<Index,1,1> a(123);
+ VERIFY_IS_EQUAL(a[0], 123);
+ }
+ {
+ Array<Index,1,1> a(123.0);
+ VERIFY_IS_EQUAL(a[0], 123);
+ }
+ {
+ Array<float,1,1> a(123);
+ VERIFY_IS_EQUAL(a[0], 123.f);
+ }
+ {
+ Array<Index,3,3> a(123);
+ VERIFY_IS_EQUAL(a(4), 123);
+ }
+ {
+ Array<Index,3,3> a(123.0);
+ VERIFY_IS_EQUAL(a(4), 123);
+ }
+ {
+ Array<float,3,3> a(123);
+ VERIFY_IS_EQUAL(a(4), 123.f);
+ }
+ {
+ MatrixXi m1(M,N);
+ VERIFY_IS_EQUAL(m1.rows(),M);
+ VERIFY_IS_EQUAL(m1.cols(),N);
+ ArrayXXi a1(M,N);
+ VERIFY_IS_EQUAL(a1.rows(),M);
+ VERIFY_IS_EQUAL(a1.cols(),N);
+ VectorXi v1(M);
+ VERIFY_IS_EQUAL(v1.size(),M);
+ ArrayXi a2(M);
+ VERIFY_IS_EQUAL(a2.size(),M);
+ }
+}
diff --git a/test/corners.cpp b/test/corners.cpp
new file mode 100644
index 0000000..73342a8
--- /dev/null
+++ b/test/corners.cpp
@@ -0,0 +1,117 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2006-2010 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "main.h"
+
+#define COMPARE_CORNER(A,B) \
+ VERIFY_IS_EQUAL(matrix.A, matrix.B); \
+ VERIFY_IS_EQUAL(const_matrix.A, const_matrix.B);
+
+template<typename MatrixType> void corners(const MatrixType& m)
+{
+ Index rows = m.rows();
+ Index cols = m.cols();
+
+ Index r = internal::random<Index>(1,rows);
+ Index c = internal::random<Index>(1,cols);
+
+ MatrixType matrix = MatrixType::Random(rows,cols);
+ const MatrixType const_matrix = MatrixType::Random(rows,cols);
+
+ COMPARE_CORNER(topLeftCorner(r,c), block(0,0,r,c));
+ COMPARE_CORNER(topRightCorner(r,c), block(0,cols-c,r,c));
+ COMPARE_CORNER(bottomLeftCorner(r,c), block(rows-r,0,r,c));
+ COMPARE_CORNER(bottomRightCorner(r,c), block(rows-r,cols-c,r,c));
+
+ Index sr = internal::random<Index>(1,rows) - 1;
+ Index nr = internal::random<Index>(1,rows-sr);
+ Index sc = internal::random<Index>(1,cols) - 1;
+ Index nc = internal::random<Index>(1,cols-sc);
+
+ COMPARE_CORNER(topRows(r), block(0,0,r,cols));
+ COMPARE_CORNER(middleRows(sr,nr), block(sr,0,nr,cols));
+ COMPARE_CORNER(bottomRows(r), block(rows-r,0,r,cols));
+ COMPARE_CORNER(leftCols(c), block(0,0,rows,c));
+ COMPARE_CORNER(middleCols(sc,nc), block(0,sc,rows,nc));
+ COMPARE_CORNER(rightCols(c), block(0,cols-c,rows,c));
+}
+
+template<typename MatrixType, int CRows, int CCols, int SRows, int SCols> void corners_fixedsize()
+{
+ MatrixType matrix = MatrixType::Random();
+ const MatrixType const_matrix = MatrixType::Random();
+
+ enum {
+ rows = MatrixType::RowsAtCompileTime,
+ cols = MatrixType::ColsAtCompileTime,
+ r = CRows,
+ c = CCols,
+ sr = SRows,
+ sc = SCols
+ };
+
+ VERIFY_IS_EQUAL((matrix.template topLeftCorner<r,c>()), (matrix.template block<r,c>(0,0)));
+ VERIFY_IS_EQUAL((matrix.template topRightCorner<r,c>()), (matrix.template block<r,c>(0,cols-c)));
+ VERIFY_IS_EQUAL((matrix.template bottomLeftCorner<r,c>()), (matrix.template block<r,c>(rows-r,0)));
+ VERIFY_IS_EQUAL((matrix.template bottomRightCorner<r,c>()), (matrix.template block<r,c>(rows-r,cols-c)));
+
+ VERIFY_IS_EQUAL((matrix.template topLeftCorner<r,c>()), (matrix.template topLeftCorner<r,Dynamic>(r,c)));
+ VERIFY_IS_EQUAL((matrix.template topRightCorner<r,c>()), (matrix.template topRightCorner<r,Dynamic>(r,c)));
+ VERIFY_IS_EQUAL((matrix.template bottomLeftCorner<r,c>()), (matrix.template bottomLeftCorner<r,Dynamic>(r,c)));
+ VERIFY_IS_EQUAL((matrix.template bottomRightCorner<r,c>()), (matrix.template bottomRightCorner<r,Dynamic>(r,c)));
+
+ VERIFY_IS_EQUAL((matrix.template topLeftCorner<r,c>()), (matrix.template topLeftCorner<Dynamic,c>(r,c)));
+ VERIFY_IS_EQUAL((matrix.template topRightCorner<r,c>()), (matrix.template topRightCorner<Dynamic,c>(r,c)));
+ VERIFY_IS_EQUAL((matrix.template bottomLeftCorner<r,c>()), (matrix.template bottomLeftCorner<Dynamic,c>(r,c)));
+ VERIFY_IS_EQUAL((matrix.template bottomRightCorner<r,c>()), (matrix.template bottomRightCorner<Dynamic,c>(r,c)));
+
+ VERIFY_IS_EQUAL((matrix.template topRows<r>()), (matrix.template block<r,cols>(0,0)));
+ VERIFY_IS_EQUAL((matrix.template middleRows<r>(sr)), (matrix.template block<r,cols>(sr,0)));
+ VERIFY_IS_EQUAL((matrix.template bottomRows<r>()), (matrix.template block<r,cols>(rows-r,0)));
+ VERIFY_IS_EQUAL((matrix.template leftCols<c>()), (matrix.template block<rows,c>(0,0)));
+ VERIFY_IS_EQUAL((matrix.template middleCols<c>(sc)), (matrix.template block<rows,c>(0,sc)));
+ VERIFY_IS_EQUAL((matrix.template rightCols<c>()), (matrix.template block<rows,c>(0,cols-c)));
+
+ VERIFY_IS_EQUAL((const_matrix.template topLeftCorner<r,c>()), (const_matrix.template block<r,c>(0,0)));
+ VERIFY_IS_EQUAL((const_matrix.template topRightCorner<r,c>()), (const_matrix.template block<r,c>(0,cols-c)));
+ VERIFY_IS_EQUAL((const_matrix.template bottomLeftCorner<r,c>()), (const_matrix.template block<r,c>(rows-r,0)));
+ VERIFY_IS_EQUAL((const_matrix.template bottomRightCorner<r,c>()), (const_matrix.template block<r,c>(rows-r,cols-c)));
+
+ VERIFY_IS_EQUAL((const_matrix.template topLeftCorner<r,c>()), (const_matrix.template topLeftCorner<r,Dynamic>(r,c)));
+ VERIFY_IS_EQUAL((const_matrix.template topRightCorner<r,c>()), (const_matrix.template topRightCorner<r,Dynamic>(r,c)));
+ VERIFY_IS_EQUAL((const_matrix.template bottomLeftCorner<r,c>()), (const_matrix.template bottomLeftCorner<r,Dynamic>(r,c)));
+ VERIFY_IS_EQUAL((const_matrix.template bottomRightCorner<r,c>()), (const_matrix.template bottomRightCorner<r,Dynamic>(r,c)));
+
+ VERIFY_IS_EQUAL((const_matrix.template topLeftCorner<r,c>()), (const_matrix.template topLeftCorner<Dynamic,c>(r,c)));
+ VERIFY_IS_EQUAL((const_matrix.template topRightCorner<r,c>()), (const_matrix.template topRightCorner<Dynamic,c>(r,c)));
+ VERIFY_IS_EQUAL((const_matrix.template bottomLeftCorner<r,c>()), (const_matrix.template bottomLeftCorner<Dynamic,c>(r,c)));
+ VERIFY_IS_EQUAL((const_matrix.template bottomRightCorner<r,c>()), (const_matrix.template bottomRightCorner<Dynamic,c>(r,c)));
+
+ VERIFY_IS_EQUAL((const_matrix.template topRows<r>()), (const_matrix.template block<r,cols>(0,0)));
+ VERIFY_IS_EQUAL((const_matrix.template middleRows<r>(sr)), (const_matrix.template block<r,cols>(sr,0)));
+ VERIFY_IS_EQUAL((const_matrix.template bottomRows<r>()), (const_matrix.template block<r,cols>(rows-r,0)));
+ VERIFY_IS_EQUAL((const_matrix.template leftCols<c>()), (const_matrix.template block<rows,c>(0,0)));
+ VERIFY_IS_EQUAL((const_matrix.template middleCols<c>(sc)), (const_matrix.template block<rows,c>(0,sc)));
+ VERIFY_IS_EQUAL((const_matrix.template rightCols<c>()), (const_matrix.template block<rows,c>(0,cols-c)));
+}
+
+EIGEN_DECLARE_TEST(corners)
+{
+ for(int i = 0; i < g_repeat; i++) {
+ CALL_SUBTEST_1( corners(Matrix<float, 1, 1>()) );
+ CALL_SUBTEST_2( corners(Matrix4d()) );
+ CALL_SUBTEST_3( corners(Matrix<int,10,12>()) );
+ CALL_SUBTEST_4( corners(MatrixXcf(5, 7)) );
+ CALL_SUBTEST_5( corners(MatrixXf(21, 20)) );
+
+ CALL_SUBTEST_1(( corners_fixedsize<Matrix<float, 1, 1>, 1, 1, 0, 0>() ));
+ CALL_SUBTEST_2(( corners_fixedsize<Matrix4d,2,2,1,1>() ));
+ CALL_SUBTEST_3(( corners_fixedsize<Matrix<int,10,12>,4,7,5,2>() ));
+ }
+}
diff --git a/test/ctorleak.cpp b/test/ctorleak.cpp
new file mode 100644
index 0000000..7390417
--- /dev/null
+++ b/test/ctorleak.cpp
@@ -0,0 +1,81 @@
+#include "main.h"
+
+#include <exception> // std::exception
+
+struct Foo
+{
+ static Index object_count;
+ static Index object_limit;
+ int dummy;
+
+ Foo() : dummy(0)
+ {
+#ifdef EIGEN_EXCEPTIONS
+ // TODO: Is this the correct way to handle this?
+ if (Foo::object_count > Foo::object_limit) { std::cout << "\nThrow!\n"; throw Foo::Fail(); }
+#endif
+ std::cout << '+';
+ ++Foo::object_count;
+ }
+
+ ~Foo()
+ {
+ std::cout << '-';
+ --Foo::object_count;
+ }
+
+ class Fail : public std::exception {};
+};
+
+Index Foo::object_count = 0;
+Index Foo::object_limit = 0;
+
+#undef EIGEN_TEST_MAX_SIZE
+#define EIGEN_TEST_MAX_SIZE 3
+
+EIGEN_DECLARE_TEST(ctorleak)
+{
+ typedef Matrix<Foo, Dynamic, Dynamic> MatrixX;
+ typedef Matrix<Foo, Dynamic, 1> VectorX;
+
+ Foo::object_count = 0;
+ for(int i = 0; i < g_repeat; i++) {
+ Index rows = internal::random<Index>(2,EIGEN_TEST_MAX_SIZE), cols = internal::random<Index>(2,EIGEN_TEST_MAX_SIZE);
+ Foo::object_limit = rows*cols;
+ {
+ MatrixX r(rows, cols);
+ Foo::object_limit = r.size()+internal::random<Index>(0, rows*cols - 2);
+ std::cout << "object_limit =" << Foo::object_limit << std::endl;
+#ifdef EIGEN_EXCEPTIONS
+ try
+ {
+#endif
+ if(internal::random<bool>()) {
+ std::cout << "\nMatrixX m(" << rows << ", " << cols << ");\n";
+ MatrixX m(rows, cols);
+ }
+ else {
+ std::cout << "\nMatrixX m(r);\n";
+ MatrixX m(r);
+ }
+#ifdef EIGEN_EXCEPTIONS
+ VERIFY(false); // not reached if exceptions are enabled
+ }
+ catch (const Foo::Fail&) { /* ignore */ }
+#endif
+ }
+ VERIFY_IS_EQUAL(Index(0), Foo::object_count);
+
+ {
+ Foo::object_limit = (rows+1)*(cols+1);
+ MatrixX A(rows, cols);
+ VERIFY_IS_EQUAL(Foo::object_count, rows*cols);
+ VectorX v=A.row(0);
+ VERIFY_IS_EQUAL(Foo::object_count, (rows+1)*cols);
+ v = A.col(0);
+ VERIFY_IS_EQUAL(Foo::object_count, rows*(cols+1));
+ }
+ VERIFY_IS_EQUAL(Index(0), Foo::object_count);
+ }
+ std::cout << "\n";
+}
diff --git a/test/denseLM.cpp b/test/denseLM.cpp
new file mode 100644
index 0000000..afb8004
--- /dev/null
+++ b/test/denseLM.cpp
@@ -0,0 +1,190 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2012 Desire Nuentsa <desire.nuentsa_wakam@inria.fr>
+// Copyright (C) 2012 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include <iostream>
+#include <fstream>
+#include <iomanip>
+
+#include "main.h"
+#include <Eigen/LevenbergMarquardt>
+using namespace std;
+using namespace Eigen;
+
+template<typename Scalar>
+struct DenseLM : DenseFunctor<Scalar>
+{
+ typedef DenseFunctor<Scalar> Base;
+ typedef typename Base::JacobianType JacobianType;
+ typedef Matrix<Scalar,Dynamic,1> VectorType;
+
+ DenseLM(int n, int m) : DenseFunctor<Scalar>(n,m)
+ { }
+
+ VectorType model(const VectorType& uv, VectorType& x)
+ {
+ VectorType y; // Should change to use expression template
+ int m = Base::values();
+ int n = Base::inputs();
+ eigen_assert(uv.size()%2 == 0);
+ eigen_assert(uv.size() == n);
+ eigen_assert(x.size() == m);
+ y.setZero(m);
+ int half = n/2;
+ VectorBlock<const VectorType> u(uv, 0, half);
+ VectorBlock<const VectorType> v(uv, half, half);
+ for (int j = 0; j < m; j++)
+ {
+ for (int i = 0; i < half; i++)
+ y(j) += u(i)*std::exp(-(x(j)-i)*(x(j)-i)/(v(i)*v(i)));
+ }
+ return y;
+
+ }
+ void initPoints(VectorType& uv_ref, VectorType& x)
+ {
+ m_x = x;
+ m_y = this->model(uv_ref, x);
+ }
+
+ int operator()(const VectorType& uv, VectorType& fvec)
+ {
+
+ int m = Base::values();
+ int n = Base::inputs();
+ eigen_assert(uv.size()%2 == 0);
+ eigen_assert(uv.size() == n);
+ eigen_assert(fvec.size() == m);
+ int half = n/2;
+ VectorBlock<const VectorType> u(uv, 0, half);
+ VectorBlock<const VectorType> v(uv, half, half);
+ for (int j = 0; j < m; j++)
+ {
+ fvec(j) = m_y(j);
+ for (int i = 0; i < half; i++)
+ {
+ fvec(j) -= u(i) *std::exp(-(m_x(j)-i)*(m_x(j)-i)/(v(i)*v(i)));
+ }
+ }
+
+ return 0;
+ }
+ int df(const VectorType& uv, JacobianType& fjac)
+ {
+ int m = Base::values();
+ int n = Base::inputs();
+ eigen_assert(n == uv.size());
+ eigen_assert(fjac.rows() == m);
+ eigen_assert(fjac.cols() == n);
+ int half = n/2;
+ VectorBlock<const VectorType> u(uv, 0, half);
+ VectorBlock<const VectorType> v(uv, half, half);
+ for (int j = 0; j < m; j++)
+ {
+ for (int i = 0; i < half; i++)
+ {
+ fjac.coeffRef(j,i) = -std::exp(-(m_x(j)-i)*(m_x(j)-i)/(v(i)*v(i)));
+ fjac.coeffRef(j,i+half) = -2.*u(i)*(m_x(j)-i)*(m_x(j)-i)/(std::pow(v(i),3)) * std::exp(-(m_x(j)-i)*(m_x(j)-i)/(v(i)*v(i)));
+ }
+ }
+ return 0;
+ }
+ VectorType m_x, m_y; //Data Points
+};
+
+template<typename FunctorType, typename VectorType>
+int test_minimizeLM(FunctorType& functor, VectorType& uv)
+{
+ LevenbergMarquardt<FunctorType> lm(functor);
+ LevenbergMarquardtSpace::Status info;
+
+ info = lm.minimize(uv);
+
+ VERIFY_IS_EQUAL(info, 1);
+ //FIXME Check other parameters
+ return info;
+}
+
+template<typename FunctorType, typename VectorType>
+int test_lmder(FunctorType& functor, VectorType& uv)
+{
+ typedef typename VectorType::Scalar Scalar;
+ LevenbergMarquardtSpace::Status info;
+ LevenbergMarquardt<FunctorType> lm(functor);
+ info = lm.lmder1(uv);
+
+ VERIFY_IS_EQUAL(info, 1);
+ //FIXME Check other parameters
+ return info;
+}
+
+template<typename FunctorType, typename VectorType>
+int test_minimizeSteps(FunctorType& functor, VectorType& uv)
+{
+ LevenbergMarquardtSpace::Status info;
+ LevenbergMarquardt<FunctorType> lm(functor);
+ info = lm.minimizeInit(uv);
+ if (info==LevenbergMarquardtSpace::ImproperInputParameters)
+ return info;
+ do
+ {
+ info = lm.minimizeOneStep(uv);
+ } while (info==LevenbergMarquardtSpace::Running);
+
+ VERIFY_IS_EQUAL(info, 1);
+ //FIXME Check other parameters
+ return info;
+}
+
+template<typename T>
+void test_denseLM_T()
+{
+ typedef Matrix<T,Dynamic,1> VectorType;
+
+ int inputs = 10;
+ int values = 1000;
+ DenseLM<T> dense_gaussian(inputs, values);
+ VectorType uv(inputs),uv_ref(inputs);
+ VectorType x(values);
+
+ // Generate the reference solution
+ uv_ref << -2, 1, 4 ,8, 6, 1.8, 1.2, 1.1, 1.9 , 3;
+
+ //Generate the reference data points
+ x.setRandom();
+ x = 10*x;
+ x.array() += 10;
+ dense_gaussian.initPoints(uv_ref, x);
+
+ // Generate the initial parameters
+ VectorBlock<VectorType> u(uv, 0, inputs/2);
+ VectorBlock<VectorType> v(uv, inputs/2, inputs/2);
+
+ // Solve the optimization problem
+
+ //Solve in one go
+ u.setOnes(); v.setOnes();
+ test_minimizeLM(dense_gaussian, uv);
+
+ //Solve until the machine precision
+ u.setOnes(); v.setOnes();
+ test_lmder(dense_gaussian, uv);
+
+ // Solve step by step
+ v.setOnes(); u.setOnes();
+ test_minimizeSteps(dense_gaussian, uv);
+
+}
+
+EIGEN_DECLARE_TEST(denseLM)
+{
+ CALL_SUBTEST_2(test_denseLM_T<double>());
+
+ // CALL_SUBTEST_2(test_sparseLM_T<std::complex<double>());
+}
diff --git a/test/dense_storage.cpp b/test/dense_storage.cpp
new file mode 100644
index 0000000..ec78f01
--- /dev/null
+++ b/test/dense_storage.cpp
@@ -0,0 +1,185 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2013 Hauke Heibel <hauke.heibel@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "main.h"
+#include "AnnoyingScalar.h"
+#include "SafeScalar.h"
+
+#include <Eigen/Core>
+
+using DenseStorageD3x3 = Eigen::DenseStorage<double, 3, 3, 3, 3>;
+static_assert(std::is_trivially_move_constructible<DenseStorageD3x3>::value, "DenseStorage not trivially_move_constructible");
+static_assert(std::is_trivially_move_assignable<DenseStorageD3x3>::value, "DenseStorage not trivially_move_assignable");
+#if !defined(EIGEN_DENSE_STORAGE_CTOR_PLUGIN)
+static_assert(std::is_trivially_copy_constructible<DenseStorageD3x3>::value, "DenseStorage not trivially_copy_constructible");
+static_assert(std::is_trivially_copy_assignable<DenseStorageD3x3>::value, "DenseStorage not trivially_copy_assignable");
+static_assert(std::is_trivially_copyable<DenseStorageD3x3>::value, "DenseStorage not trivially_copyable");
+#endif
+
+template <typename T, int Size, int Rows, int Cols>
+void dense_storage_copy(int rows, int cols)
+{
+ typedef DenseStorage<T, Size, Rows, Cols, 0> DenseStorageType;
+
+ const int size = rows*cols;
+ DenseStorageType reference(size, rows, cols);
+ T* raw_reference = reference.data();
+ for (int i=0; i<size; ++i)
+ raw_reference[i] = static_cast<T>(i);
+
+ DenseStorageType copied_reference(reference);
+ const T* raw_copied_reference = copied_reference.data();
+ for (int i=0; i<size; ++i)
+ VERIFY_IS_EQUAL(raw_reference[i], raw_copied_reference[i]);
+}
+
+template <typename T, int Size, int Rows, int Cols>
+void dense_storage_assignment(int rows, int cols)
+{
+ typedef DenseStorage<T, Size, Rows, Cols, 0> DenseStorageType;
+
+ const int size = rows*cols;
+ DenseStorageType reference(size, rows, cols);
+ T* raw_reference = reference.data();
+ for (int i=0; i<size; ++i)
+ raw_reference[i] = static_cast<T>(i);
+
+ DenseStorageType copied_reference;
+ copied_reference = reference;
+ const T* raw_copied_reference = copied_reference.data();
+ for (int i=0; i<size; ++i)
+ VERIFY_IS_EQUAL(raw_reference[i], raw_copied_reference[i]);
+}
+
+template <typename T, int Size, int Rows, int Cols>
+void dense_storage_swap(int rows0, int cols0, int rows1, int cols1)
+{
+ typedef DenseStorage<T, Size, Rows, Cols, 0> DenseStorageType;
+
+ const int size0 = rows0*cols0;
+ DenseStorageType a(size0, rows0, cols0);
+ for (int i=0; i<size0; ++i) {
+ a.data()[i] = static_cast<T>(i);
+ }
+
+ const int size1 = rows1*cols1;
+ DenseStorageType b(size1, rows1, cols1);
+ for (int i=0; i<size1; ++i) {
+ b.data()[i] = static_cast<T>(-i);
+ }
+
+ a.swap(b);
+
+ for (int i=0; i<size0; ++i) {
+ VERIFY_IS_EQUAL(b.data()[i], static_cast<T>(i));
+ }
+
+ for (int i=0; i<size1; ++i) {
+ VERIFY_IS_EQUAL(a.data()[i], static_cast<T>(-i));
+ }
+}
+
+template<typename T, int Size, std::size_t Alignment>
+void dense_storage_alignment()
+{
+ struct alignas(Alignment) Empty1 {};
+ VERIFY_IS_EQUAL(std::alignment_of<Empty1>::value, Alignment);
+
+ struct EIGEN_ALIGN_TO_BOUNDARY(Alignment) Empty2 {};
+ VERIFY_IS_EQUAL(std::alignment_of<Empty2>::value, Alignment);
+
+ struct Nested1 { EIGEN_ALIGN_TO_BOUNDARY(Alignment) T data[Size]; };
+ VERIFY_IS_EQUAL(std::alignment_of<Nested1>::value, Alignment);
+
+ VERIFY_IS_EQUAL( (std::alignment_of<internal::plain_array<T,Size,AutoAlign,Alignment> >::value), Alignment);
+
+ const std::size_t default_alignment = internal::compute_default_alignment<T,Size>::value;
+ if (default_alignment > 0) {
+ VERIFY_IS_EQUAL( (std::alignment_of<DenseStorage<T,Size,1,1,AutoAlign> >::value), default_alignment);
+ VERIFY_IS_EQUAL( (std::alignment_of<Matrix<T,Size,1,AutoAlign> >::value), default_alignment);
+ struct Nested2 { Matrix<T,Size,1,AutoAlign> mat; };
+ VERIFY_IS_EQUAL(std::alignment_of<Nested2>::value, default_alignment);
+ }
+}
+
+template<typename T>
+void dense_storage_tests() {
+ // Dynamic Storage.
+ dense_storage_copy<T,Dynamic,Dynamic,Dynamic>(4, 3);
+ dense_storage_copy<T,Dynamic,Dynamic,3>(4, 3);
+ dense_storage_copy<T,Dynamic,4,Dynamic>(4, 3);
+ // Fixed Storage.
+ dense_storage_copy<T,12,4,3>(4, 3);
+ dense_storage_copy<T,12,Dynamic,Dynamic>(4, 3);
+ dense_storage_copy<T,12,4,Dynamic>(4, 3);
+ dense_storage_copy<T,12,Dynamic,3>(4, 3);
+ // Fixed Storage with Uninitialized Elements.
+ dense_storage_copy<T,18,Dynamic,Dynamic>(4, 3);
+ dense_storage_copy<T,18,4,Dynamic>(4, 3);
+ dense_storage_copy<T,18,Dynamic,3>(4, 3);
+
+ // Dynamic Storage.
+ dense_storage_assignment<T,Dynamic,Dynamic,Dynamic>(4, 3);
+ dense_storage_assignment<T,Dynamic,Dynamic,3>(4, 3);
+ dense_storage_assignment<T,Dynamic,4,Dynamic>(4, 3);
+ // Fixed Storage.
+ dense_storage_assignment<T,12,4,3>(4, 3);
+ dense_storage_assignment<T,12,Dynamic,Dynamic>(4, 3);
+ dense_storage_assignment<T,12,4,Dynamic>(4, 3);
+ dense_storage_assignment<T,12,Dynamic,3>(4, 3);
+ // Fixed Storage with Uninitialized Elements.
+ dense_storage_assignment<T,18,Dynamic,Dynamic>(4, 3);
+ dense_storage_assignment<T,18,4,Dynamic>(4, 3);
+ dense_storage_assignment<T,18,Dynamic,3>(4, 3);
+
+ // Dynamic Storage.
+ dense_storage_swap<T,Dynamic,Dynamic,Dynamic>(4, 3, 4, 3);
+ dense_storage_swap<T,Dynamic,Dynamic,Dynamic>(4, 3, 2, 1);
+ dense_storage_swap<T,Dynamic,Dynamic,Dynamic>(2, 1, 4, 3);
+ dense_storage_swap<T,Dynamic,Dynamic,3>(4, 3, 4, 3);
+ dense_storage_swap<T,Dynamic,Dynamic,3>(4, 3, 2, 3);
+ dense_storage_swap<T,Dynamic,Dynamic,3>(2, 3, 4, 3);
+ dense_storage_swap<T,Dynamic,4,Dynamic>(4, 3, 4, 3);
+ dense_storage_swap<T,Dynamic,4,Dynamic>(4, 3, 4, 1);
+ dense_storage_swap<T,Dynamic,4,Dynamic>(4, 1, 4, 3);
+ // Fixed Storage.
+ dense_storage_swap<T,12,4,3>(4, 3, 4, 3);
+ dense_storage_swap<T,12,Dynamic,Dynamic>(4, 3, 4, 3);
+ dense_storage_swap<T,12,Dynamic,Dynamic>(4, 3, 2, 1);
+ dense_storage_swap<T,12,Dynamic,Dynamic>(2, 1, 4, 3);
+ dense_storage_swap<T,12,4,Dynamic>(4, 3, 4, 3);
+ dense_storage_swap<T,12,4,Dynamic>(4, 3, 4, 1);
+ dense_storage_swap<T,12,4,Dynamic>(4, 1, 4, 3);
+ dense_storage_swap<T,12,Dynamic,3>(4, 3, 4, 3);
+ dense_storage_swap<T,12,Dynamic,3>(4, 3, 2, 3);
+ dense_storage_swap<T,12,Dynamic,3>(2, 3, 4, 3);
+ // Fixed Storage with Uninitialized Elements.
+ dense_storage_swap<T,18,Dynamic,Dynamic>(4, 3, 4, 3);
+ dense_storage_swap<T,18,Dynamic,Dynamic>(4, 3, 2, 1);
+ dense_storage_swap<T,18,Dynamic,Dynamic>(2, 1, 4, 3);
+ dense_storage_swap<T,18,4,Dynamic>(4, 3, 4, 3);
+ dense_storage_swap<T,18,4,Dynamic>(4, 3, 4, 1);
+ dense_storage_swap<T,18,4,Dynamic>(4, 1, 4, 3);
+ dense_storage_swap<T,18,Dynamic,3>(4, 3, 4, 3);
+ dense_storage_swap<T,18,Dynamic,3>(4, 3, 2, 3);
+ dense_storage_swap<T,18,Dynamic,3>(2, 3, 4, 3);
+
+ dense_storage_alignment<T,16,8>();
+ dense_storage_alignment<T,16,16>();
+ dense_storage_alignment<T,16,32>();
+ dense_storage_alignment<T,16,64>();
+}
+
+EIGEN_DECLARE_TEST(dense_storage)
+{
+ dense_storage_tests<int>();
+ dense_storage_tests<float>();
+ dense_storage_tests<SafeScalar<float> >();
+ dense_storage_tests<AnnoyingScalar>();
+}
diff --git a/test/determinant.cpp b/test/determinant.cpp
new file mode 100644
index 0000000..7dd33c3
--- /dev/null
+++ b/test/determinant.cpp
@@ -0,0 +1,66 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "main.h"
+#include <Eigen/LU>
+
+template<typename MatrixType> void determinant(const MatrixType& m)
+{
+ /* this test covers the following files:
+ Determinant.h
+ */
+ Index size = m.rows();
+
+ MatrixType m1(size, size), m2(size, size);
+ m1.setRandom();
+ m2.setRandom();
+ typedef typename MatrixType::Scalar Scalar;
+ Scalar x = internal::random<Scalar>();
+ VERIFY_IS_APPROX(MatrixType::Identity(size, size).determinant(), Scalar(1));
+ VERIFY_IS_APPROX((m1*m2).eval().determinant(), m1.determinant() * m2.determinant());
+ if(size==1) return;
+ Index i = internal::random<Index>(0, size-1);
+ Index j;
+ do {
+ j = internal::random<Index>(0, size-1);
+ } while(j==i);
+ m2 = m1;
+ m2.row(i).swap(m2.row(j));
+ VERIFY_IS_APPROX(m2.determinant(), -m1.determinant());
+ m2 = m1;
+ m2.col(i).swap(m2.col(j));
+ VERIFY_IS_APPROX(m2.determinant(), -m1.determinant());
+ VERIFY_IS_APPROX(m2.determinant(), m2.transpose().determinant());
+ VERIFY_IS_APPROX(numext::conj(m2.determinant()), m2.adjoint().determinant());
+ m2 = m1;
+ m2.row(i) += x*m2.row(j);
+ VERIFY_IS_APPROX(m2.determinant(), m1.determinant());
+ m2 = m1;
+ m2.row(i) *= x;
+ VERIFY_IS_APPROX(m2.determinant(), m1.determinant() * x);
+
+ // check empty matrix
+ VERIFY_IS_APPROX(m2.block(0,0,0,0).determinant(), Scalar(1));
+}
+
+EIGEN_DECLARE_TEST(determinant)
+{
+ for(int i = 0; i < g_repeat; i++) {
+ int s = 0;
+ CALL_SUBTEST_1( determinant(Matrix<float, 1, 1>()) );
+ CALL_SUBTEST_2( determinant(Matrix<double, 2, 2>()) );
+ CALL_SUBTEST_3( determinant(Matrix<double, 3, 3>()) );
+ CALL_SUBTEST_4( determinant(Matrix<double, 4, 4>()) );
+ CALL_SUBTEST_5( determinant(Matrix<std::complex<double>, 10, 10>()) );
+ s = internal::random<int>(1,EIGEN_TEST_MAX_SIZE/4);
+ CALL_SUBTEST_6( determinant(MatrixXd(s, s)) );
+ TEST_SET_BUT_UNUSED_VARIABLE(s)
+ }
+}
diff --git a/test/diagonal.cpp b/test/diagonal.cpp
new file mode 100644
index 0000000..4e8c4b3
--- /dev/null
+++ b/test/diagonal.cpp
@@ -0,0 +1,105 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2006-2010 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "main.h"
+
+template<typename MatrixType> void diagonal(const MatrixType& m)
+{
+ typedef typename MatrixType::Scalar Scalar;
+
+ Index rows = m.rows();
+ Index cols = m.cols();
+
+ MatrixType m1 = MatrixType::Random(rows, cols),
+ m2 = MatrixType::Random(rows, cols);
+
+ Scalar s1 = internal::random<Scalar>();
+
+ //check diagonal()
+ VERIFY_IS_APPROX(m1.diagonal(), m1.transpose().diagonal());
+ m2.diagonal() = 2 * m1.diagonal();
+ m2.diagonal()[0] *= 3;
+
+ if (rows>2)
+ {
+ enum {
+ N1 = MatrixType::RowsAtCompileTime>2 ? 2 : 0,
+ N2 = MatrixType::RowsAtCompileTime>1 ? -1 : 0
+ };
+
+ // check sub/super diagonal
+ if(MatrixType::SizeAtCompileTime!=Dynamic)
+ {
+ VERIFY(m1.template diagonal<N1>().RowsAtCompileTime == m1.diagonal(N1).size());
+ VERIFY(m1.template diagonal<N2>().RowsAtCompileTime == m1.diagonal(N2).size());
+ }
+
+ m2.template diagonal<N1>() = 2 * m1.template diagonal<N1>();
+ VERIFY_IS_APPROX(m2.template diagonal<N1>(), static_cast<Scalar>(2) * m1.diagonal(N1));
+ m2.template diagonal<N1>()[0] *= 3;
+ VERIFY_IS_APPROX(m2.template diagonal<N1>()[0], static_cast<Scalar>(6) * m1.template diagonal<N1>()[0]);
+
+
+ m2.template diagonal<N2>() = 2 * m1.template diagonal<N2>();
+ m2.template diagonal<N2>()[0] *= 3;
+ VERIFY_IS_APPROX(m2.template diagonal<N2>()[0], static_cast<Scalar>(6) * m1.template diagonal<N2>()[0]);
+
+ m2.diagonal(N1) = 2 * m1.diagonal(N1);
+ VERIFY_IS_APPROX(m2.template diagonal<N1>(), static_cast<Scalar>(2) * m1.diagonal(N1));
+ m2.diagonal(N1)[0] *= 3;
+ VERIFY_IS_APPROX(m2.diagonal(N1)[0], static_cast<Scalar>(6) * m1.diagonal(N1)[0]);
+
+ m2.diagonal(N2) = 2 * m1.diagonal(N2);
+ VERIFY_IS_APPROX(m2.template diagonal<N2>(), static_cast<Scalar>(2) * m1.diagonal(N2));
+ m2.diagonal(N2)[0] *= 3;
+ VERIFY_IS_APPROX(m2.diagonal(N2)[0], static_cast<Scalar>(6) * m1.diagonal(N2)[0]);
+
+ m2.diagonal(N2).x() = s1;
+ VERIFY_IS_APPROX(m2.diagonal(N2).x(), s1);
+ m2.diagonal(N2).coeffRef(0) = Scalar(2)*s1;
+ VERIFY_IS_APPROX(m2.diagonal(N2).coeff(0), Scalar(2)*s1);
+ }
+
+ VERIFY( m1.diagonal( cols).size()==0 );
+ VERIFY( m1.diagonal(-rows).size()==0 );
+}
+
+template<typename MatrixType> void diagonal_assert(const MatrixType& m) {
+ Index rows = m.rows();
+ Index cols = m.cols();
+
+ MatrixType m1 = MatrixType::Random(rows, cols);
+
+ if (rows>=2 && cols>=2)
+ {
+ VERIFY_RAISES_ASSERT( m1 += m1.diagonal() );
+ VERIFY_RAISES_ASSERT( m1 -= m1.diagonal() );
+ VERIFY_RAISES_ASSERT( m1.array() *= m1.diagonal().array() );
+ VERIFY_RAISES_ASSERT( m1.array() /= m1.diagonal().array() );
+ }
+
+ VERIFY_RAISES_ASSERT( m1.diagonal(cols+1) );
+ VERIFY_RAISES_ASSERT( m1.diagonal(-(rows+1)) );
+}
+
+EIGEN_DECLARE_TEST(diagonal)
+{
+ for(int i = 0; i < g_repeat; i++) {
+ CALL_SUBTEST_1( diagonal(Matrix<float, 1, 1>()) );
+ CALL_SUBTEST_1( diagonal(Matrix<float, 4, 9>()) );
+ CALL_SUBTEST_1( diagonal(Matrix<float, 7, 3>()) );
+ CALL_SUBTEST_2( diagonal(Matrix4d()) );
+ CALL_SUBTEST_2( diagonal(MatrixXcf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
+ CALL_SUBTEST_2( diagonal(MatrixXi(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
+ CALL_SUBTEST_2( diagonal(MatrixXcd(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
+ CALL_SUBTEST_1( diagonal(MatrixXf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
+ CALL_SUBTEST_1( diagonal(Matrix<float,Dynamic,4>(3, 4)) );
+ CALL_SUBTEST_1( diagonal_assert(MatrixXf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
+ }
+}
diff --git a/test/diagonal_matrix_variadic_ctor.cpp b/test/diagonal_matrix_variadic_ctor.cpp
new file mode 100644
index 0000000..db56539
--- /dev/null
+++ b/test/diagonal_matrix_variadic_ctor.cpp
@@ -0,0 +1,153 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2019 David Tellenbach <david.tellenbach@tellnotes.org>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "main.h"
+
+#define VERIFY_IMPLICIT_CONVERSION_3(DIAGTYPE, V0, V1, V2) \
+ DIAGTYPE d(V0, V1, V2); \
+ DIAGTYPE::DenseMatrixType Dense = d.toDenseMatrix(); \
+ VERIFY_IS_APPROX(Dense(0, 0), (Scalar)V0); \
+ VERIFY_IS_APPROX(Dense(1, 1), (Scalar)V1); \
+ VERIFY_IS_APPROX(Dense(2, 2), (Scalar)V2);
+
+#define VERIFY_IMPLICIT_CONVERSION_4(DIAGTYPE, V0, V1, V2, V3) \
+ DIAGTYPE d(V0, V1, V2, V3); \
+ DIAGTYPE::DenseMatrixType Dense = d.toDenseMatrix(); \
+ VERIFY_IS_APPROX(Dense(0, 0), (Scalar)V0); \
+ VERIFY_IS_APPROX(Dense(1, 1), (Scalar)V1); \
+ VERIFY_IS_APPROX(Dense(2, 2), (Scalar)V2); \
+ VERIFY_IS_APPROX(Dense(3, 3), (Scalar)V3);
+
+#define VERIFY_IMPLICIT_CONVERSION_5(DIAGTYPE, V0, V1, V2, V3, V4) \
+ DIAGTYPE d(V0, V1, V2, V3, V4); \
+ DIAGTYPE::DenseMatrixType Dense = d.toDenseMatrix(); \
+ VERIFY_IS_APPROX(Dense(0, 0), (Scalar)V0); \
+ VERIFY_IS_APPROX(Dense(1, 1), (Scalar)V1); \
+ VERIFY_IS_APPROX(Dense(2, 2), (Scalar)V2); \
+ VERIFY_IS_APPROX(Dense(3, 3), (Scalar)V3); \
+ VERIFY_IS_APPROX(Dense(4, 4), (Scalar)V4);
+
+template<typename Scalar>
+void constructorTest()
+{
+ typedef DiagonalMatrix<Scalar, 0> DiagonalMatrix0;
+ typedef DiagonalMatrix<Scalar, 3> DiagonalMatrix3;
+ typedef DiagonalMatrix<Scalar, 4> DiagonalMatrix4;
+ typedef DiagonalMatrix<Scalar, Dynamic> DiagonalMatrixX;
+
+ Scalar raw[7];
+ for (int k = 0; k < 7; ++k) raw[k] = internal::random<Scalar>();
+
+ // Fixed-sized matrices
+ {
+ DiagonalMatrix0 a {{}};
+ VERIFY(a.rows() == 0);
+ VERIFY(a.cols() == 0);
+ typename DiagonalMatrix0::DenseMatrixType m = a.toDenseMatrix();
+ for (Index k = 0; k < a.rows(); ++k) VERIFY(m(k, k) == raw[k]);
+ }
+ {
+ DiagonalMatrix3 a {{raw[0], raw[1], raw[2]}};
+ VERIFY(a.rows() == 3);
+ VERIFY(a.cols() == 3);
+ typename DiagonalMatrix3::DenseMatrixType m = a.toDenseMatrix();
+ for (Index k = 0; k < a.rows(); ++k) VERIFY(m(k, k) == raw[k]);
+ }
+ {
+ DiagonalMatrix4 a {{raw[0], raw[1], raw[2], raw[3]}};
+ VERIFY(a.rows() == 4);
+ VERIFY(a.cols() == 4);
+ typename DiagonalMatrix4::DenseMatrixType m = a.toDenseMatrix();
+ for (Index k = 0; k < a.rows(); ++k) VERIFY(m(k, k) == raw[k]);
+ }
+
+ // dynamically sized matrices
+ {
+ DiagonalMatrixX a{{}};
+ VERIFY(a.rows() == 0);
+ VERIFY(a.rows() == 0);
+ typename DiagonalMatrixX::DenseMatrixType m = a.toDenseMatrix();
+ for (Index k = 0; k < a.rows(); ++k) VERIFY(m(k, k) == raw[k]);
+ }
+ {
+ DiagonalMatrixX a{{raw[0], raw[1], raw[2], raw[3], raw[4], raw[5], raw[6]}};
+ VERIFY(a.rows() == 7);
+ VERIFY(a.rows() == 7);
+ typename DiagonalMatrixX::DenseMatrixType m = a.toDenseMatrix();
+ for (Index k = 0; k < a.rows(); ++k) VERIFY(m(k, k) == raw[k]);
+ }
+}
+
+template<>
+void constructorTest<float>()
+{
+ typedef float Scalar;
+
+ typedef DiagonalMatrix<Scalar, 0> DiagonalMatrix0;
+ typedef DiagonalMatrix<Scalar, 3> DiagonalMatrix3;
+ typedef DiagonalMatrix<Scalar, 4> DiagonalMatrix4;
+ typedef DiagonalMatrix<Scalar, 5> DiagonalMatrix5;
+ typedef DiagonalMatrix<Scalar, Dynamic> DiagonalMatrixX;
+
+ Scalar raw[7];
+ for (int k = 0; k < 7; ++k) raw[k] = internal::random<Scalar>();
+
+ // Fixed-sized matrices
+ {
+ DiagonalMatrix0 a {{}};
+ VERIFY(a.rows() == 0);
+ VERIFY(a.cols() == 0);
+ typename DiagonalMatrix0::DenseMatrixType m = a.toDenseMatrix();
+ for (Index k = 0; k < a.rows(); ++k) VERIFY(m(k, k) == raw[k]);
+ }
+ {
+ DiagonalMatrix3 a {{raw[0], raw[1], raw[2]}};
+ VERIFY(a.rows() == 3);
+ VERIFY(a.cols() == 3);
+ typename DiagonalMatrix3::DenseMatrixType m = a.toDenseMatrix();
+ for (Index k = 0; k < a.rows(); ++k) VERIFY(m(k, k) == raw[k]);
+ }
+ {
+ DiagonalMatrix4 a {{raw[0], raw[1], raw[2], raw[3]}};
+ VERIFY(a.rows() == 4);
+ VERIFY(a.cols() == 4);
+ typename DiagonalMatrix4::DenseMatrixType m = a.toDenseMatrix();
+ for (Index k = 0; k < a.rows(); ++k) VERIFY(m(k, k) == raw[k]);
+ }
+
+ // dynamically sized matrices
+ {
+ DiagonalMatrixX a{{}};
+ VERIFY(a.rows() == 0);
+ VERIFY(a.rows() == 0);
+ typename DiagonalMatrixX::DenseMatrixType m = a.toDenseMatrix();
+ for (Index k = 0; k < a.rows(); ++k) VERIFY(m(k, k) == raw[k]);
+ }
+ {
+ DiagonalMatrixX a{{raw[0], raw[1], raw[2], raw[3], raw[4], raw[5], raw[6]}};
+ VERIFY(a.rows() == 7);
+ VERIFY(a.rows() == 7);
+ typename DiagonalMatrixX::DenseMatrixType m = a.toDenseMatrix();
+ for (Index k = 0; k < a.rows(); ++k) VERIFY(m(k, k) == raw[k]);
+ }
+ { VERIFY_IMPLICIT_CONVERSION_3(DiagonalMatrix3, 1.2647, 2.56f, -3); }
+ { VERIFY_IMPLICIT_CONVERSION_4(DiagonalMatrix4, 1.2647, 2.56f, -3, 3.23f); }
+ { VERIFY_IMPLICIT_CONVERSION_5(DiagonalMatrix5, 1.2647, 2.56f, -3, 3.23f, 2); }
+}
+
+EIGEN_DECLARE_TEST(diagonal_matrix_variadic_ctor)
+{
+ CALL_SUBTEST_2(constructorTest<unsigned char>());
+ CALL_SUBTEST_2(constructorTest<float>());
+ CALL_SUBTEST_2(constructorTest<Index>());
+ CALL_SUBTEST_2(constructorTest<int>());
+ CALL_SUBTEST_2(constructorTest<long int>());
+ CALL_SUBTEST_2(constructorTest<std::ptrdiff_t>());
+ CALL_SUBTEST_2(constructorTest<std::complex<double>>());
+}
diff --git a/test/diagonalmatrices.cpp b/test/diagonalmatrices.cpp
new file mode 100644
index 0000000..15492a7
--- /dev/null
+++ b/test/diagonalmatrices.cpp
@@ -0,0 +1,199 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+
+// discard stack allocation as that too bypasses malloc
+#define EIGEN_STACK_ALLOCATION_LIMIT 0
+// heap allocation will raise an assert if enabled at runtime
+#define EIGEN_RUNTIME_NO_MALLOC
+
+#include "main.h"
+using namespace std;
+template<typename MatrixType> void diagonalmatrices(const MatrixType& m)
+{
+ typedef typename MatrixType::Scalar Scalar;
+ enum { Rows = MatrixType::RowsAtCompileTime, Cols = MatrixType::ColsAtCompileTime };
+ typedef Matrix<Scalar, Rows, 1> VectorType;
+ typedef Matrix<Scalar, 1, Cols> RowVectorType;
+ typedef Matrix<Scalar, Rows, Rows> SquareMatrixType;
+ typedef Matrix<Scalar, Dynamic, Dynamic> DynMatrixType;
+ typedef DiagonalMatrix<Scalar, Rows> LeftDiagonalMatrix;
+ typedef DiagonalMatrix<Scalar, Cols> RightDiagonalMatrix;
+ typedef Matrix<Scalar, Rows==Dynamic?Dynamic:2*Rows, Cols==Dynamic?Dynamic:2*Cols> BigMatrix;
+ Index rows = m.rows();
+ Index cols = m.cols();
+
+ MatrixType m1 = MatrixType::Random(rows, cols),
+ m2 = MatrixType::Random(rows, cols);
+ VectorType v1 = VectorType::Random(rows),
+ v2 = VectorType::Random(rows);
+ RowVectorType rv1 = RowVectorType::Random(cols),
+ rv2 = RowVectorType::Random(cols);
+
+ LeftDiagonalMatrix ldm1(v1), ldm2(v2);
+ RightDiagonalMatrix rdm1(rv1), rdm2(rv2);
+
+ Scalar s1 = internal::random<Scalar>();
+
+ SquareMatrixType sq_m1 (v1.asDiagonal());
+ VERIFY_IS_APPROX(sq_m1, v1.asDiagonal().toDenseMatrix());
+ sq_m1 = v1.asDiagonal();
+ VERIFY_IS_APPROX(sq_m1, v1.asDiagonal().toDenseMatrix());
+ SquareMatrixType sq_m2 = v1.asDiagonal();
+ VERIFY_IS_APPROX(sq_m1, sq_m2);
+
+ ldm1 = v1.asDiagonal();
+ LeftDiagonalMatrix ldm3(v1);
+ VERIFY_IS_APPROX(ldm1.diagonal(), ldm3.diagonal());
+ LeftDiagonalMatrix ldm4 = v1.asDiagonal();
+ VERIFY_IS_APPROX(ldm1.diagonal(), ldm4.diagonal());
+
+ sq_m1.block(0,0,rows,rows) = ldm1;
+ VERIFY_IS_APPROX(sq_m1, ldm1.toDenseMatrix());
+ sq_m1.transpose() = ldm1;
+ VERIFY_IS_APPROX(sq_m1, ldm1.toDenseMatrix());
+
+ Index i = internal::random<Index>(0, rows-1);
+ Index j = internal::random<Index>(0, cols-1);
+
+ internal::set_is_malloc_allowed(false);
+ VERIFY_IS_APPROX( ((ldm1 * m1)(i,j)) , ldm1.diagonal()(i) * m1(i,j) );
+ VERIFY_IS_APPROX( ((ldm1 * (m1+m2))(i,j)) , ldm1.diagonal()(i) * (m1+m2)(i,j) );
+ VERIFY_IS_APPROX( ((m1 * rdm1)(i,j)) , rdm1.diagonal()(j) * m1(i,j) );
+ VERIFY_IS_APPROX( ((v1.asDiagonal() * m1)(i,j)) , v1(i) * m1(i,j) );
+ VERIFY_IS_APPROX( ((m1 * rv1.asDiagonal())(i,j)) , rv1(j) * m1(i,j) );
+ VERIFY_IS_APPROX( (((v1+v2).asDiagonal() * m1)(i,j)) , (v1+v2)(i) * m1(i,j) );
+ VERIFY_IS_APPROX( (((v1+v2).asDiagonal() * (m1+m2))(i,j)) , (v1+v2)(i) * (m1+m2)(i,j) );
+ VERIFY_IS_APPROX( ((m1 * (rv1+rv2).asDiagonal())(i,j)) , (rv1+rv2)(j) * m1(i,j) );
+ VERIFY_IS_APPROX( (((m1+m2) * (rv1+rv2).asDiagonal())(i,j)) , (rv1+rv2)(j) * (m1+m2)(i,j) );
+ VERIFY_IS_APPROX( (ldm1 * ldm1).diagonal()(i), ldm1.diagonal()(i) * ldm1.diagonal()(i) );
+ VERIFY_IS_APPROX( (ldm1 * ldm1 * m1)(i, j), ldm1.diagonal()(i) * ldm1.diagonal()(i) * m1(i, j) );
+ VERIFY_IS_APPROX( ((v1.asDiagonal() * v1.asDiagonal()).diagonal()(i)), v1(i) * v1(i) );
+ internal::set_is_malloc_allowed(true);
+
+ if(rows>1)
+ {
+ DynMatrixType tmp = m1.topRows(rows/2), res;
+ VERIFY_IS_APPROX( (res = m1.topRows(rows/2) * rv1.asDiagonal()), tmp * rv1.asDiagonal() );
+ VERIFY_IS_APPROX( (res = v1.head(rows/2).asDiagonal()*m1.topRows(rows/2)), v1.head(rows/2).asDiagonal()*tmp );
+ }
+
+ BigMatrix big;
+ big.setZero(2*rows, 2*cols);
+
+ big.block(i,j,rows,cols) = m1;
+ big.block(i,j,rows,cols) = v1.asDiagonal() * big.block(i,j,rows,cols);
+
+ VERIFY_IS_APPROX((big.block(i,j,rows,cols)) , v1.asDiagonal() * m1 );
+
+ big.block(i,j,rows,cols) = m1;
+ big.block(i,j,rows,cols) = big.block(i,j,rows,cols) * rv1.asDiagonal();
+ VERIFY_IS_APPROX((big.block(i,j,rows,cols)) , m1 * rv1.asDiagonal() );
+
+ // products do not allocate memory
+ MatrixType res(rows, cols);
+ internal::set_is_malloc_allowed(false);
+ res.noalias() = ldm1 * m1;
+ res.noalias() = m1 * rdm1;
+ res.noalias() = ldm1 * m1 * rdm1;
+ res.noalias() = LeftDiagonalMatrix::Identity(rows) * m1 * RightDiagonalMatrix::Zero(cols);
+ internal::set_is_malloc_allowed(true);
+
+ // scalar multiple
+ VERIFY_IS_APPROX(LeftDiagonalMatrix(ldm1*s1).diagonal(), ldm1.diagonal() * s1);
+ VERIFY_IS_APPROX(LeftDiagonalMatrix(s1*ldm1).diagonal(), s1 * ldm1.diagonal());
+
+ VERIFY_IS_APPROX(m1 * (rdm1 * s1), (m1 * rdm1) * s1);
+ VERIFY_IS_APPROX(m1 * (s1 * rdm1), (m1 * rdm1) * s1);
+
+ // Diagonal to dense
+ sq_m1.setRandom();
+ sq_m2 = sq_m1;
+ VERIFY_IS_APPROX( (sq_m1 += (s1*v1).asDiagonal()), sq_m2 += (s1*v1).asDiagonal().toDenseMatrix() );
+ VERIFY_IS_APPROX( (sq_m1 -= (s1*v1).asDiagonal()), sq_m2 -= (s1*v1).asDiagonal().toDenseMatrix() );
+ VERIFY_IS_APPROX( (sq_m1 = (s1*v1).asDiagonal()), (s1*v1).asDiagonal().toDenseMatrix() );
+
+ sq_m1.setRandom();
+ sq_m2 = v1.asDiagonal();
+ sq_m2 = sq_m1 * sq_m2;
+ VERIFY_IS_APPROX( (sq_m1*v1.asDiagonal()).col(i), sq_m2.col(i) );
+ VERIFY_IS_APPROX( (sq_m1*v1.asDiagonal()).row(i), sq_m2.row(i) );
+
+ sq_m1 = v1.asDiagonal();
+ sq_m2 = v2.asDiagonal();
+ SquareMatrixType sq_m3 = v1.asDiagonal();
+ VERIFY_IS_APPROX( sq_m3 = v1.asDiagonal() + v2.asDiagonal(), sq_m1 + sq_m2);
+ VERIFY_IS_APPROX( sq_m3 = v1.asDiagonal() - v2.asDiagonal(), sq_m1 - sq_m2);
+ VERIFY_IS_APPROX( sq_m3 = v1.asDiagonal() - 2*v2.asDiagonal() + v1.asDiagonal(), sq_m1 - 2*sq_m2 + sq_m1);
+
+ // Zero and Identity
+ LeftDiagonalMatrix zero = LeftDiagonalMatrix::Zero(rows);
+ LeftDiagonalMatrix identity = LeftDiagonalMatrix::Identity(rows);
+ VERIFY_IS_APPROX(identity.diagonal().sum(), Scalar(rows));
+ VERIFY_IS_APPROX(zero.diagonal().sum(), Scalar(0));
+ VERIFY_IS_APPROX((zero + 2 * LeftDiagonalMatrix::Identity(rows)).diagonal().sum(), Scalar(2 * rows));
+}
+
+template<typename MatrixType> void as_scalar_product(const MatrixType& m)
+{
+ typedef typename MatrixType::Scalar Scalar;
+ typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> VectorType;
+ typedef Matrix<Scalar, Dynamic, Dynamic> DynMatrixType;
+ typedef Matrix<Scalar, Dynamic, 1> DynVectorType;
+ typedef Matrix<Scalar, 1, Dynamic> DynRowVectorType;
+
+ Index rows = m.rows();
+ Index depth = internal::random<Index>(1,EIGEN_TEST_MAX_SIZE);
+
+ VectorType v1 = VectorType::Random(rows);
+ DynVectorType dv1 = DynVectorType::Random(depth);
+ DynRowVectorType drv1 = DynRowVectorType::Random(depth);
+ DynMatrixType dm1 = dv1;
+ DynMatrixType drm1 = drv1;
+
+ Scalar s = v1(0);
+
+ VERIFY_IS_APPROX( v1.asDiagonal() * drv1, s*drv1 );
+ VERIFY_IS_APPROX( dv1 * v1.asDiagonal(), dv1*s );
+
+ VERIFY_IS_APPROX( v1.asDiagonal() * drm1, s*drm1 );
+ VERIFY_IS_APPROX( dm1 * v1.asDiagonal(), dm1*s );
+}
+
+template<int>
+void bug987()
+{
+ Matrix3Xd points = Matrix3Xd::Random(3, 3);
+ Vector2d diag = Vector2d::Random();
+ Matrix2Xd tmp1 = points.topRows<2>(), res1, res2;
+ VERIFY_IS_APPROX( res1 = diag.asDiagonal() * points.topRows<2>(), res2 = diag.asDiagonal() * tmp1 );
+ Matrix2d tmp2 = points.topLeftCorner<2,2>();
+ VERIFY_IS_APPROX(( res1 = points.topLeftCorner<2,2>()*diag.asDiagonal()) , res2 = tmp2*diag.asDiagonal() );
+}
+
+EIGEN_DECLARE_TEST(diagonalmatrices)
+{
+ for(int i = 0; i < g_repeat; i++) {
+ CALL_SUBTEST_1( diagonalmatrices(Matrix<float, 1, 1>()) );
+ CALL_SUBTEST_1( as_scalar_product(Matrix<float, 1, 1>()) );
+
+ CALL_SUBTEST_2( diagonalmatrices(Matrix3f()) );
+ CALL_SUBTEST_3( diagonalmatrices(Matrix<double,3,3,RowMajor>()) );
+ CALL_SUBTEST_4( diagonalmatrices(Matrix4d()) );
+ CALL_SUBTEST_5( diagonalmatrices(Matrix<float,4,4,RowMajor>()) );
+ CALL_SUBTEST_6( diagonalmatrices(MatrixXcf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
+ CALL_SUBTEST_6( as_scalar_product(MatrixXcf(1,1)) );
+ CALL_SUBTEST_7( diagonalmatrices(MatrixXi(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
+ CALL_SUBTEST_8( diagonalmatrices(Matrix<double,Dynamic,Dynamic,RowMajor>(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
+ CALL_SUBTEST_9( diagonalmatrices(MatrixXf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
+ CALL_SUBTEST_9( diagonalmatrices(MatrixXf(1,1)) );
+ CALL_SUBTEST_9( as_scalar_product(MatrixXf(1,1)) );
+ }
+ CALL_SUBTEST_10( bug987<0>() );
+}
diff --git a/test/dontalign.cpp b/test/dontalign.cpp
new file mode 100644
index 0000000..2e4102b
--- /dev/null
+++ b/test/dontalign.cpp
@@ -0,0 +1,62 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2011 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#if defined EIGEN_TEST_PART_1 || defined EIGEN_TEST_PART_2 || defined EIGEN_TEST_PART_3 || defined EIGEN_TEST_PART_4
+#define EIGEN_DONT_ALIGN
+#elif defined EIGEN_TEST_PART_5 || defined EIGEN_TEST_PART_6 || defined EIGEN_TEST_PART_7 || defined EIGEN_TEST_PART_8
+#define EIGEN_DONT_ALIGN_STATICALLY
+#endif
+
+#include "main.h"
+#include <Eigen/Dense>
+
+template<typename MatrixType>
+void dontalign(const MatrixType& m)
+{
+ typedef typename MatrixType::Scalar Scalar;
+ typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> VectorType;
+ typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime> SquareMatrixType;
+
+ Index rows = m.rows();
+ Index cols = m.cols();
+
+ MatrixType a = MatrixType::Random(rows,cols);
+ SquareMatrixType square = SquareMatrixType::Random(rows,rows);
+ VectorType v = VectorType::Random(rows);
+
+ VERIFY_IS_APPROX(v, square * square.colPivHouseholderQr().solve(v));
+ square = square.inverse().eval();
+ a = square * a;
+ square = square*square;
+ v = square * v;
+ v = a.adjoint() * v;
+ VERIFY(square.determinant() != Scalar(0));
+
+ // bug 219: MapAligned() was giving an assert with EIGEN_DONT_ALIGN, because Map Flags were miscomputed
+ Scalar* array = internal::aligned_new<Scalar>(rows);
+ v = VectorType::MapAligned(array, rows);
+ internal::aligned_delete(array, rows);
+}
+
+EIGEN_DECLARE_TEST(dontalign)
+{
+#if defined EIGEN_TEST_PART_1 || defined EIGEN_TEST_PART_5
+ dontalign(Matrix3d());
+ dontalign(Matrix4f());
+#elif defined EIGEN_TEST_PART_2 || defined EIGEN_TEST_PART_6
+ dontalign(Matrix3cd());
+ dontalign(Matrix4cf());
+#elif defined EIGEN_TEST_PART_3 || defined EIGEN_TEST_PART_7
+ dontalign(Matrix<float, 32, 32>());
+ dontalign(Matrix<std::complex<float>, 32, 32>());
+#elif defined EIGEN_TEST_PART_4 || defined EIGEN_TEST_PART_8
+ dontalign(MatrixXd(32, 32));
+ dontalign(MatrixXcf(32, 32));
+#endif
+}
diff --git a/test/dynalloc.cpp b/test/dynalloc.cpp
new file mode 100644
index 0000000..cdc10ee
--- /dev/null
+++ b/test/dynalloc.cpp
@@ -0,0 +1,180 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "main.h"
+
+#if EIGEN_MAX_ALIGN_BYTES>0
+#define ALIGNMENT EIGEN_MAX_ALIGN_BYTES
+#else
+#define ALIGNMENT 1
+#endif
+
+typedef Matrix<float,16,1> Vector16f;
+typedef Matrix<float,8,1> Vector8f;
+
+void check_handmade_aligned_malloc()
+{
+ // Hand-make alignment needs at least sizeof(void*) to store the offset.
+ constexpr int alignment = (std::max<int>)(EIGEN_DEFAULT_ALIGN_BYTES, sizeof(void*));
+
+ for(int i = 1; i < 1000; i++)
+ {
+ char *p = (char*)internal::handmade_aligned_malloc(i, alignment);
+ VERIFY(internal::UIntPtr(p)%ALIGNMENT==0);
+ // if the buffer is wrongly allocated this will give a bad write --> check with valgrind
+ for(int j = 0; j < i; j++) p[j]=0;
+ internal::handmade_aligned_free(p);
+ }
+}
+
+void check_aligned_malloc()
+{
+ for(int i = ALIGNMENT; i < 1000; i++)
+ {
+ char *p = (char*)internal::aligned_malloc(i);
+ VERIFY(internal::UIntPtr(p)%ALIGNMENT==0);
+ // if the buffer is wrongly allocated this will give a bad write --> check with valgrind
+ for(int j = 0; j < i; j++) p[j]=0;
+ internal::aligned_free(p);
+ }
+}
+
+void check_aligned_new()
+{
+ for(int i = ALIGNMENT; i < 1000; i++)
+ {
+ float *p = internal::aligned_new<float>(i);
+ VERIFY(internal::UIntPtr(p)%ALIGNMENT==0);
+ // if the buffer is wrongly allocated this will give a bad write --> check with valgrind
+ for(int j = 0; j < i; j++) p[j]=0;
+ internal::aligned_delete(p,i);
+ }
+}
+
+void check_aligned_stack_alloc()
+{
+ for(int i = ALIGNMENT; i < 400; i++)
+ {
+ ei_declare_aligned_stack_constructed_variable(float,p,i,0);
+ VERIFY(internal::UIntPtr(p)%ALIGNMENT==0);
+ // if the buffer is wrongly allocated this will give a bad write --> check with valgrind
+ for(int j = 0; j < i; j++) p[j]=0;
+ }
+}
+
+
+// test compilation with both a struct and a class...
+struct MyStruct
+{
+ EIGEN_MAKE_ALIGNED_OPERATOR_NEW
+ char dummychar;
+ Vector16f avec;
+};
+
+class MyClassA
+{
+ public:
+ EIGEN_MAKE_ALIGNED_OPERATOR_NEW
+ char dummychar;
+ Vector16f avec;
+};
+
+template<typename T> void check_dynaligned()
+{
+ // TODO have to be updated once we support multiple alignment values
+ if(T::SizeAtCompileTime % ALIGNMENT == 0)
+ {
+ T* obj = new T;
+ VERIFY(T::NeedsToAlign==1);
+ VERIFY(internal::UIntPtr(obj)%ALIGNMENT==0);
+ delete obj;
+ }
+}
+
+template<typename T> void check_custom_new_delete()
+{
+ {
+ T* t = new T;
+ delete t;
+ }
+
+ {
+ std::size_t N = internal::random<std::size_t>(1,10);
+ T* t = new T[N];
+ delete[] t;
+ }
+
+#if EIGEN_MAX_ALIGN_BYTES>0 && (!EIGEN_HAS_CXX17_OVERALIGN)
+ {
+ T* t = static_cast<T *>((T::operator new)(sizeof(T)));
+ (T::operator delete)(t, sizeof(T));
+ }
+
+ {
+ T* t = static_cast<T *>((T::operator new)(sizeof(T)));
+ (T::operator delete)(t);
+ }
+#endif
+}
+
+EIGEN_DECLARE_TEST(dynalloc)
+{
+ // low level dynamic memory allocation
+ CALL_SUBTEST(check_handmade_aligned_malloc());
+ CALL_SUBTEST(check_aligned_malloc());
+ CALL_SUBTEST(check_aligned_new());
+ CALL_SUBTEST(check_aligned_stack_alloc());
+
+ for (int i=0; i<g_repeat*100; ++i)
+ {
+ CALL_SUBTEST( check_custom_new_delete<Vector4f>() );
+ CALL_SUBTEST( check_custom_new_delete<Vector2f>() );
+ CALL_SUBTEST( check_custom_new_delete<Matrix4f>() );
+ CALL_SUBTEST( check_custom_new_delete<MatrixXi>() );
+ }
+
+ // check static allocation, who knows ?
+ #if EIGEN_MAX_STATIC_ALIGN_BYTES
+ for (int i=0; i<g_repeat*100; ++i)
+ {
+ CALL_SUBTEST(check_dynaligned<Vector4f>() );
+ CALL_SUBTEST(check_dynaligned<Vector2d>() );
+ CALL_SUBTEST(check_dynaligned<Matrix4f>() );
+ CALL_SUBTEST(check_dynaligned<Vector4d>() );
+ CALL_SUBTEST(check_dynaligned<Vector4i>() );
+ CALL_SUBTEST(check_dynaligned<Vector8f>() );
+ CALL_SUBTEST(check_dynaligned<Vector16f>() );
+ }
+
+ {
+ MyStruct foo0; VERIFY(internal::UIntPtr(foo0.avec.data())%ALIGNMENT==0);
+ MyClassA fooA; VERIFY(internal::UIntPtr(fooA.avec.data())%ALIGNMENT==0);
+ }
+
+ // dynamic allocation, single object
+ for (int i=0; i<g_repeat*100; ++i)
+ {
+ MyStruct *foo0 = new MyStruct(); VERIFY(internal::UIntPtr(foo0->avec.data())%ALIGNMENT==0);
+ MyClassA *fooA = new MyClassA(); VERIFY(internal::UIntPtr(fooA->avec.data())%ALIGNMENT==0);
+ delete foo0;
+ delete fooA;
+ }
+
+ // dynamic allocation, array
+ const int N = 10;
+ for (int i=0; i<g_repeat*100; ++i)
+ {
+ MyStruct *foo0 = new MyStruct[N]; VERIFY(internal::UIntPtr(foo0->avec.data())%ALIGNMENT==0);
+ MyClassA *fooA = new MyClassA[N]; VERIFY(internal::UIntPtr(fooA->avec.data())%ALIGNMENT==0);
+ delete[] foo0;
+ delete[] fooA;
+ }
+ #endif
+
+}
diff --git a/test/eigen2support.cpp b/test/eigen2support.cpp
new file mode 100644
index 0000000..49d7328
--- /dev/null
+++ b/test/eigen2support.cpp
@@ -0,0 +1,65 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#define EIGEN2_SUPPORT
+
+#include "main.h"
+
+template<typename MatrixType> void eigen2support(const MatrixType& m)
+{
+ typedef typename MatrixType::Scalar Scalar;
+
+ Index rows = m.rows();
+ Index cols = m.cols();
+
+ MatrixType m1 = MatrixType::Random(rows, cols),
+ m3(rows, cols);
+
+ Scalar s1 = internal::random<Scalar>(),
+ s2 = internal::random<Scalar>();
+
+ // scalar addition
+ VERIFY_IS_APPROX(m1.cwise() + s1, s1 + m1.cwise());
+ VERIFY_IS_APPROX(m1.cwise() + s1, MatrixType::Constant(rows,cols,s1) + m1);
+ VERIFY_IS_APPROX((m1*Scalar(2)).cwise() - s2, (m1+m1) - MatrixType::Constant(rows,cols,s2) );
+ m3 = m1;
+ m3.cwise() += s2;
+ VERIFY_IS_APPROX(m3, m1.cwise() + s2);
+ m3 = m1;
+ m3.cwise() -= s1;
+ VERIFY_IS_APPROX(m3, m1.cwise() - s1);
+
+ VERIFY_IS_EQUAL((m1.corner(TopLeft,1,1)), (m1.block(0,0,1,1)));
+ VERIFY_IS_EQUAL((m1.template corner<1,1>(TopLeft)), (m1.template block<1,1>(0,0)));
+ VERIFY_IS_EQUAL((m1.col(0).start(1)), (m1.col(0).segment(0,1)));
+ VERIFY_IS_EQUAL((m1.col(0).template start<1>()), (m1.col(0).segment(0,1)));
+ VERIFY_IS_EQUAL((m1.col(0).end(1)), (m1.col(0).segment(rows-1,1)));
+ VERIFY_IS_EQUAL((m1.col(0).template end<1>()), (m1.col(0).segment(rows-1,1)));
+
+ using std::cos;
+ using numext::real;
+ using numext::abs2;
+ VERIFY_IS_EQUAL(ei_cos(s1), cos(s1));
+ VERIFY_IS_EQUAL(ei_real(s1), real(s1));
+ VERIFY_IS_EQUAL(ei_abs2(s1), abs2(s1));
+
+ m1.minor(0,0);
+}
+
+EIGEN_DECLARE_TEST(eigen2support)
+{
+ for(int i = 0; i < g_repeat; i++) {
+ CALL_SUBTEST_1( eigen2support(Matrix<double,1,1>()) );
+ CALL_SUBTEST_2( eigen2support(MatrixXd(1,1)) );
+ CALL_SUBTEST_4( eigen2support(Matrix3f()) );
+ CALL_SUBTEST_5( eigen2support(Matrix4d()) );
+ CALL_SUBTEST_2( eigen2support(MatrixXf(200,200)) );
+ CALL_SUBTEST_6( eigen2support(MatrixXcd(100,100)) );
+ }
+}
diff --git a/test/eigensolver_complex.cpp b/test/eigensolver_complex.cpp
new file mode 100644
index 0000000..c5373f4
--- /dev/null
+++ b/test/eigensolver_complex.cpp
@@ -0,0 +1,176 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2010 Jitse Niesen <jitse@maths.leeds.ac.uk>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "main.h"
+#include <limits>
+#include <Eigen/Eigenvalues>
+#include <Eigen/LU>
+
+template<typename MatrixType> bool find_pivot(typename MatrixType::Scalar tol, MatrixType &diffs, Index col=0)
+{
+ bool match = diffs.diagonal().sum() <= tol;
+ if(match || col==diffs.cols())
+ {
+ return match;
+ }
+ else
+ {
+ Index n = diffs.cols();
+ std::vector<std::pair<Index,Index> > transpositions;
+ for(Index i=col; i<n; ++i)
+ {
+ Index best_index(0);
+ if(diffs.col(col).segment(col,n-i).minCoeff(&best_index) > tol)
+ break;
+
+ best_index += col;
+
+ diffs.row(col).swap(diffs.row(best_index));
+ if(find_pivot(tol,diffs,col+1)) return true;
+ diffs.row(col).swap(diffs.row(best_index));
+
+ // move current pivot to the end
+ diffs.row(n-(i-col)-1).swap(diffs.row(best_index));
+ transpositions.push_back(std::pair<Index,Index>(n-(i-col)-1,best_index));
+ }
+ // restore
+ for(Index k=transpositions.size()-1; k>=0; --k)
+ diffs.row(transpositions[k].first).swap(diffs.row(transpositions[k].second));
+ }
+ return false;
+}
+
+/* Check that two column vectors are approximately equal up to permutations.
+ * Initially, this method checked that the k-th power sums are equal for all k = 1, ..., vec1.rows(),
+ * however this strategy is numerically inacurate because of numerical cancellation issues.
+ */
+template<typename VectorType>
+void verify_is_approx_upto_permutation(const VectorType& vec1, const VectorType& vec2)
+{
+ typedef typename VectorType::Scalar Scalar;
+ typedef typename NumTraits<Scalar>::Real RealScalar;
+
+ VERIFY(vec1.cols() == 1);
+ VERIFY(vec2.cols() == 1);
+ VERIFY(vec1.rows() == vec2.rows());
+
+ Index n = vec1.rows();
+ RealScalar tol = test_precision<RealScalar>()*test_precision<RealScalar>()*numext::maxi(vec1.squaredNorm(),vec2.squaredNorm());
+ Matrix<RealScalar,Dynamic,Dynamic> diffs = (vec1.rowwise().replicate(n) - vec2.rowwise().replicate(n).transpose()).cwiseAbs2();
+
+ VERIFY( find_pivot(tol, diffs) );
+}
+
+
+template<typename MatrixType> void eigensolver(const MatrixType& m)
+{
+ /* this test covers the following files:
+ ComplexEigenSolver.h, and indirectly ComplexSchur.h
+ */
+ Index rows = m.rows();
+ Index cols = m.cols();
+
+ typedef typename MatrixType::Scalar Scalar;
+ typedef typename NumTraits<Scalar>::Real RealScalar;
+
+ MatrixType a = MatrixType::Random(rows,cols);
+ MatrixType symmA = a.adjoint() * a;
+
+ ComplexEigenSolver<MatrixType> ei0(symmA);
+ VERIFY_IS_EQUAL(ei0.info(), Success);
+ VERIFY_IS_APPROX(symmA * ei0.eigenvectors(), ei0.eigenvectors() * ei0.eigenvalues().asDiagonal());
+
+ ComplexEigenSolver<MatrixType> ei1(a);
+ VERIFY_IS_EQUAL(ei1.info(), Success);
+ VERIFY_IS_APPROX(a * ei1.eigenvectors(), ei1.eigenvectors() * ei1.eigenvalues().asDiagonal());
+ // Note: If MatrixType is real then a.eigenvalues() uses EigenSolver and thus
+ // another algorithm so results may differ slightly
+ verify_is_approx_upto_permutation(a.eigenvalues(), ei1.eigenvalues());
+
+ ComplexEigenSolver<MatrixType> ei2;
+ ei2.setMaxIterations(ComplexSchur<MatrixType>::m_maxIterationsPerRow * rows).compute(a);
+ VERIFY_IS_EQUAL(ei2.info(), Success);
+ VERIFY_IS_EQUAL(ei2.eigenvectors(), ei1.eigenvectors());
+ VERIFY_IS_EQUAL(ei2.eigenvalues(), ei1.eigenvalues());
+ if (rows > 2) {
+ ei2.setMaxIterations(1).compute(a);
+ VERIFY_IS_EQUAL(ei2.info(), NoConvergence);
+ VERIFY_IS_EQUAL(ei2.getMaxIterations(), 1);
+ }
+
+ ComplexEigenSolver<MatrixType> eiNoEivecs(a, false);
+ VERIFY_IS_EQUAL(eiNoEivecs.info(), Success);
+ VERIFY_IS_APPROX(ei1.eigenvalues(), eiNoEivecs.eigenvalues());
+
+ // Regression test for issue #66
+ MatrixType z = MatrixType::Zero(rows,cols);
+ ComplexEigenSolver<MatrixType> eiz(z);
+ VERIFY((eiz.eigenvalues().cwiseEqual(0)).all());
+
+ MatrixType id = MatrixType::Identity(rows, cols);
+ VERIFY_IS_APPROX(id.operatorNorm(), RealScalar(1));
+
+ if (rows > 1 && rows < 20)
+ {
+ // Test matrix with NaN
+ a(0,0) = std::numeric_limits<typename MatrixType::RealScalar>::quiet_NaN();
+ ComplexEigenSolver<MatrixType> eiNaN(a);
+ VERIFY_IS_EQUAL(eiNaN.info(), NoConvergence);
+ }
+
+ // regression test for bug 1098
+ {
+ ComplexEigenSolver<MatrixType> eig(a.adjoint() * a);
+ eig.compute(a.adjoint() * a);
+ }
+
+ // regression test for bug 478
+ {
+ a.setZero();
+ ComplexEigenSolver<MatrixType> ei3(a);
+ VERIFY_IS_EQUAL(ei3.info(), Success);
+ VERIFY_IS_MUCH_SMALLER_THAN(ei3.eigenvalues().norm(),RealScalar(1));
+ VERIFY((ei3.eigenvectors().transpose()*ei3.eigenvectors().transpose()).eval().isIdentity());
+ }
+}
+
+template<typename MatrixType> void eigensolver_verify_assert(const MatrixType& m)
+{
+ ComplexEigenSolver<MatrixType> eig;
+ VERIFY_RAISES_ASSERT(eig.eigenvectors());
+ VERIFY_RAISES_ASSERT(eig.eigenvalues());
+
+ MatrixType a = MatrixType::Random(m.rows(),m.cols());
+ eig.compute(a, false);
+ VERIFY_RAISES_ASSERT(eig.eigenvectors());
+}
+
+EIGEN_DECLARE_TEST(eigensolver_complex)
+{
+ int s = 0;
+ for(int i = 0; i < g_repeat; i++) {
+ CALL_SUBTEST_1( eigensolver(Matrix4cf()) );
+ s = internal::random<int>(1,EIGEN_TEST_MAX_SIZE/4);
+ CALL_SUBTEST_2( eigensolver(MatrixXcd(s,s)) );
+ CALL_SUBTEST_3( eigensolver(Matrix<std::complex<float>, 1, 1>()) );
+ CALL_SUBTEST_4( eigensolver(Matrix3f()) );
+ TEST_SET_BUT_UNUSED_VARIABLE(s)
+ }
+ CALL_SUBTEST_1( eigensolver_verify_assert(Matrix4cf()) );
+ s = internal::random<int>(1,EIGEN_TEST_MAX_SIZE/4);
+ CALL_SUBTEST_2( eigensolver_verify_assert(MatrixXcd(s,s)) );
+ CALL_SUBTEST_3( eigensolver_verify_assert(Matrix<std::complex<float>, 1, 1>()) );
+ CALL_SUBTEST_4( eigensolver_verify_assert(Matrix3f()) );
+
+ // Test problem size constructors
+ CALL_SUBTEST_5(ComplexEigenSolver<MatrixXf> tmp(s));
+
+ TEST_SET_BUT_UNUSED_VARIABLE(s)
+}
diff --git a/test/eigensolver_generalized_real.cpp b/test/eigensolver_generalized_real.cpp
new file mode 100644
index 0000000..a0c99b1
--- /dev/null
+++ b/test/eigensolver_generalized_real.cpp
@@ -0,0 +1,140 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2012-2016 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#define EIGEN_RUNTIME_NO_MALLOC
+#include "main.h"
+#include <limits>
+#include <Eigen/Eigenvalues>
+#include <Eigen/LU>
+
+template<typename MatrixType> void generalized_eigensolver_real(const MatrixType& m)
+{
+ /* this test covers the following files:
+ GeneralizedEigenSolver.h
+ */
+ Index rows = m.rows();
+ Index cols = m.cols();
+
+ typedef typename MatrixType::Scalar Scalar;
+ typedef std::complex<Scalar> ComplexScalar;
+ typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> VectorType;
+
+ MatrixType a = MatrixType::Random(rows,cols);
+ MatrixType b = MatrixType::Random(rows,cols);
+ MatrixType a1 = MatrixType::Random(rows,cols);
+ MatrixType b1 = MatrixType::Random(rows,cols);
+ MatrixType spdA = a.adjoint() * a + a1.adjoint() * a1;
+ MatrixType spdB = b.adjoint() * b + b1.adjoint() * b1;
+
+ // lets compare to GeneralizedSelfAdjointEigenSolver
+ {
+ GeneralizedSelfAdjointEigenSolver<MatrixType> symmEig(spdA, spdB);
+ GeneralizedEigenSolver<MatrixType> eig(spdA, spdB);
+
+ VERIFY_IS_EQUAL(eig.eigenvalues().imag().cwiseAbs().maxCoeff(), 0);
+
+ VectorType realEigenvalues = eig.eigenvalues().real();
+ std::sort(realEigenvalues.data(), realEigenvalues.data()+realEigenvalues.size());
+ VERIFY_IS_APPROX(realEigenvalues, symmEig.eigenvalues());
+
+ // check eigenvectors
+ typename GeneralizedEigenSolver<MatrixType>::EigenvectorsType D = eig.eigenvalues().asDiagonal();
+ typename GeneralizedEigenSolver<MatrixType>::EigenvectorsType V = eig.eigenvectors();
+ VERIFY_IS_APPROX(spdA*V, spdB*V*D);
+ }
+
+ // non symmetric case:
+ {
+ GeneralizedEigenSolver<MatrixType> eig(rows);
+ // TODO enable full-prealocation of required memory, this probably requires an in-place mode for HessenbergDecomposition
+ //Eigen::internal::set_is_malloc_allowed(false);
+ eig.compute(a,b);
+ //Eigen::internal::set_is_malloc_allowed(true);
+ for(Index k=0; k<cols; ++k)
+ {
+ Matrix<ComplexScalar,Dynamic,Dynamic> tmp = (eig.betas()(k)*a).template cast<ComplexScalar>() - eig.alphas()(k)*b;
+ if(tmp.size()>1 && tmp.norm()>(std::numeric_limits<Scalar>::min)())
+ tmp /= tmp.norm();
+ VERIFY_IS_MUCH_SMALLER_THAN( std::abs(tmp.determinant()), Scalar(1) );
+ }
+ // check eigenvectors
+ typename GeneralizedEigenSolver<MatrixType>::EigenvectorsType D = eig.eigenvalues().asDiagonal();
+ typename GeneralizedEigenSolver<MatrixType>::EigenvectorsType V = eig.eigenvectors();
+ VERIFY_IS_APPROX(a*V, b*V*D);
+ }
+
+ // regression test for bug 1098
+ {
+ GeneralizedSelfAdjointEigenSolver<MatrixType> eig1(a.adjoint() * a,b.adjoint() * b);
+ eig1.compute(a.adjoint() * a,b.adjoint() * b);
+ GeneralizedEigenSolver<MatrixType> eig2(a.adjoint() * a,b.adjoint() * b);
+ eig2.compute(a.adjoint() * a,b.adjoint() * b);
+ }
+
+ // check without eigenvectors
+ {
+ GeneralizedEigenSolver<MatrixType> eig1(spdA, spdB, true);
+ GeneralizedEigenSolver<MatrixType> eig2(spdA, spdB, false);
+ VERIFY_IS_APPROX(eig1.eigenvalues(), eig2.eigenvalues());
+ }
+}
+
+template<typename MatrixType>
+void generalized_eigensolver_assert() {
+ GeneralizedEigenSolver<MatrixType> eig;
+ // all raise assert if uninitialized
+ VERIFY_RAISES_ASSERT(eig.info());
+ VERIFY_RAISES_ASSERT(eig.eigenvectors());
+ VERIFY_RAISES_ASSERT(eig.eigenvalues());
+ VERIFY_RAISES_ASSERT(eig.alphas());
+ VERIFY_RAISES_ASSERT(eig.betas());
+
+ // none raise assert after compute called
+ eig.compute(MatrixType::Random(20, 20), MatrixType::Random(20, 20));
+ VERIFY(eig.info() == Success);
+ eig.eigenvectors();
+ eig.eigenvalues();
+ eig.alphas();
+ eig.betas();
+
+ // eigenvectors() raises assert, if eigenvectors were not requested
+ eig.compute(MatrixType::Random(20, 20), MatrixType::Random(20, 20), false);
+ VERIFY(eig.info() == Success);
+ VERIFY_RAISES_ASSERT(eig.eigenvectors());
+ eig.eigenvalues();
+ eig.alphas();
+ eig.betas();
+
+ // all except info raise assert if realQZ did not converge
+ eig.setMaxIterations(0); // force real QZ to fail.
+ eig.compute(MatrixType::Random(20, 20), MatrixType::Random(20, 20));
+ VERIFY(eig.info() == NoConvergence);
+ VERIFY_RAISES_ASSERT(eig.eigenvectors());
+ VERIFY_RAISES_ASSERT(eig.eigenvalues());
+ VERIFY_RAISES_ASSERT(eig.alphas());
+ VERIFY_RAISES_ASSERT(eig.betas());
+}
+
+EIGEN_DECLARE_TEST(eigensolver_generalized_real)
+{
+ for(int i = 0; i < g_repeat; i++) {
+ int s = 0;
+ CALL_SUBTEST_1( generalized_eigensolver_real(Matrix4f()) );
+ s = internal::random<int>(1,EIGEN_TEST_MAX_SIZE/4);
+ CALL_SUBTEST_2( generalized_eigensolver_real(MatrixXd(s,s)) );
+
+ // some trivial but implementation-wise special cases
+ CALL_SUBTEST_2( generalized_eigensolver_real(MatrixXd(1,1)) );
+ CALL_SUBTEST_2( generalized_eigensolver_real(MatrixXd(2,2)) );
+ CALL_SUBTEST_3( generalized_eigensolver_real(Matrix<double,1,1>()) );
+ CALL_SUBTEST_4( generalized_eigensolver_real(Matrix2d()) );
+ CALL_SUBTEST_5( generalized_eigensolver_assert<MatrixXd>() );
+ TEST_SET_BUT_UNUSED_VARIABLE(s)
+ }
+}
diff --git a/test/eigensolver_generic.cpp b/test/eigensolver_generic.cpp
new file mode 100644
index 0000000..7adb986
--- /dev/null
+++ b/test/eigensolver_generic.cpp
@@ -0,0 +1,247 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2010,2012 Jitse Niesen <jitse@maths.leeds.ac.uk>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "main.h"
+#include <limits>
+#include <Eigen/Eigenvalues>
+
+template<typename EigType,typename MatType>
+void check_eigensolver_for_given_mat(const EigType &eig, const MatType& a)
+{
+ typedef typename NumTraits<typename MatType::Scalar>::Real RealScalar;
+ typedef Matrix<RealScalar, MatType::RowsAtCompileTime, 1> RealVectorType;
+ typedef typename std::complex<RealScalar> Complex;
+ Index n = a.rows();
+ VERIFY_IS_EQUAL(eig.info(), Success);
+ VERIFY_IS_APPROX(a * eig.pseudoEigenvectors(), eig.pseudoEigenvectors() * eig.pseudoEigenvalueMatrix());
+ VERIFY_IS_APPROX(a.template cast<Complex>() * eig.eigenvectors(),
+ eig.eigenvectors() * eig.eigenvalues().asDiagonal());
+ VERIFY_IS_APPROX(eig.eigenvectors().colwise().norm(), RealVectorType::Ones(n).transpose());
+ VERIFY_IS_APPROX(a.eigenvalues(), eig.eigenvalues());
+}
+
+template<typename MatrixType> void eigensolver(const MatrixType& m)
+{
+ /* this test covers the following files:
+ EigenSolver.h
+ */
+ Index rows = m.rows();
+ Index cols = m.cols();
+
+ typedef typename MatrixType::Scalar Scalar;
+ typedef typename NumTraits<Scalar>::Real RealScalar;
+ typedef typename std::complex<RealScalar> Complex;
+
+ MatrixType a = MatrixType::Random(rows,cols);
+ MatrixType a1 = MatrixType::Random(rows,cols);
+ MatrixType symmA = a.adjoint() * a + a1.adjoint() * a1;
+
+ EigenSolver<MatrixType> ei0(symmA);
+ VERIFY_IS_EQUAL(ei0.info(), Success);
+ VERIFY_IS_APPROX(symmA * ei0.pseudoEigenvectors(), ei0.pseudoEigenvectors() * ei0.pseudoEigenvalueMatrix());
+ VERIFY_IS_APPROX((symmA.template cast<Complex>()) * (ei0.pseudoEigenvectors().template cast<Complex>()),
+ (ei0.pseudoEigenvectors().template cast<Complex>()) * (ei0.eigenvalues().asDiagonal()));
+
+ EigenSolver<MatrixType> ei1(a);
+ CALL_SUBTEST( check_eigensolver_for_given_mat(ei1,a) );
+
+ EigenSolver<MatrixType> ei2;
+ ei2.setMaxIterations(RealSchur<MatrixType>::m_maxIterationsPerRow * rows).compute(a);
+ VERIFY_IS_EQUAL(ei2.info(), Success);
+ VERIFY_IS_EQUAL(ei2.eigenvectors(), ei1.eigenvectors());
+ VERIFY_IS_EQUAL(ei2.eigenvalues(), ei1.eigenvalues());
+ if (rows > 2) {
+ ei2.setMaxIterations(1).compute(a);
+ VERIFY_IS_EQUAL(ei2.info(), NoConvergence);
+ VERIFY_IS_EQUAL(ei2.getMaxIterations(), 1);
+ }
+
+ EigenSolver<MatrixType> eiNoEivecs(a, false);
+ VERIFY_IS_EQUAL(eiNoEivecs.info(), Success);
+ VERIFY_IS_APPROX(ei1.eigenvalues(), eiNoEivecs.eigenvalues());
+ VERIFY_IS_APPROX(ei1.pseudoEigenvalueMatrix(), eiNoEivecs.pseudoEigenvalueMatrix());
+
+ MatrixType id = MatrixType::Identity(rows, cols);
+ VERIFY_IS_APPROX(id.operatorNorm(), RealScalar(1));
+
+ if (rows > 2 && rows < 20)
+ {
+ // Test matrix with NaN
+ a(0,0) = std::numeric_limits<typename MatrixType::RealScalar>::quiet_NaN();
+ EigenSolver<MatrixType> eiNaN(a);
+ VERIFY_IS_NOT_EQUAL(eiNaN.info(), Success);
+ }
+
+ // regression test for bug 1098
+ {
+ EigenSolver<MatrixType> eig(a.adjoint() * a);
+ eig.compute(a.adjoint() * a);
+ }
+
+ // regression test for bug 478
+ {
+ a.setZero();
+ EigenSolver<MatrixType> ei3(a);
+ VERIFY_IS_EQUAL(ei3.info(), Success);
+ VERIFY_IS_MUCH_SMALLER_THAN(ei3.eigenvalues().norm(),RealScalar(1));
+ VERIFY((ei3.eigenvectors().transpose()*ei3.eigenvectors().transpose()).eval().isIdentity());
+ }
+}
+
+template<typename MatrixType> void eigensolver_verify_assert(const MatrixType& m)
+{
+ EigenSolver<MatrixType> eig;
+ VERIFY_RAISES_ASSERT(eig.eigenvectors());
+ VERIFY_RAISES_ASSERT(eig.pseudoEigenvectors());
+ VERIFY_RAISES_ASSERT(eig.pseudoEigenvalueMatrix());
+ VERIFY_RAISES_ASSERT(eig.eigenvalues());
+
+ MatrixType a = MatrixType::Random(m.rows(),m.cols());
+ eig.compute(a, false);
+ VERIFY_RAISES_ASSERT(eig.eigenvectors());
+ VERIFY_RAISES_ASSERT(eig.pseudoEigenvectors());
+}
+
+
+template<typename CoeffType>
+Matrix<typename CoeffType::Scalar,Dynamic,Dynamic>
+make_companion(const CoeffType& coeffs)
+{
+ Index n = coeffs.size()-1;
+ Matrix<typename CoeffType::Scalar,Dynamic,Dynamic> res(n,n);
+ res.setZero();
+ res.row(0) = -coeffs.tail(n) / coeffs(0);
+ res.diagonal(-1).setOnes();
+ return res;
+}
+
+template<int>
+void eigensolver_generic_extra()
+{
+ {
+ // regression test for bug 793
+ MatrixXd a(3,3);
+ a << 0, 0, 1,
+ 1, 1, 1,
+ 1, 1e+200, 1;
+ Eigen::EigenSolver<MatrixXd> eig(a);
+ double scale = 1e-200; // scale to avoid overflow during the comparisons
+ VERIFY_IS_APPROX(a * eig.pseudoEigenvectors()*scale, eig.pseudoEigenvectors() * eig.pseudoEigenvalueMatrix()*scale);
+ VERIFY_IS_APPROX(a * eig.eigenvectors()*scale, eig.eigenvectors() * eig.eigenvalues().asDiagonal()*scale);
+ }
+ {
+ // check a case where all eigenvalues are null.
+ MatrixXd a(2,2);
+ a << 1, 1,
+ -1, -1;
+ Eigen::EigenSolver<MatrixXd> eig(a);
+ VERIFY_IS_APPROX(eig.pseudoEigenvectors().squaredNorm(), 2.);
+ VERIFY_IS_APPROX((a * eig.pseudoEigenvectors()).norm()+1., 1.);
+ VERIFY_IS_APPROX((eig.pseudoEigenvectors() * eig.pseudoEigenvalueMatrix()).norm()+1., 1.);
+ VERIFY_IS_APPROX((a * eig.eigenvectors()).norm()+1., 1.);
+ VERIFY_IS_APPROX((eig.eigenvectors() * eig.eigenvalues().asDiagonal()).norm()+1., 1.);
+ }
+
+ // regression test for bug 933
+ {
+ {
+ VectorXd coeffs(5); coeffs << 1, -3, -175, -225, 2250;
+ MatrixXd C = make_companion(coeffs);
+ EigenSolver<MatrixXd> eig(C);
+ CALL_SUBTEST( check_eigensolver_for_given_mat(eig,C) );
+ }
+ {
+ // this test is tricky because it requires high accuracy in smallest eigenvalues
+ VectorXd coeffs(5); coeffs << 6.154671e-15, -1.003870e-10, -9.819570e-01, 3.995715e+03, 2.211511e+08;
+ MatrixXd C = make_companion(coeffs);
+ EigenSolver<MatrixXd> eig(C);
+ CALL_SUBTEST( check_eigensolver_for_given_mat(eig,C) );
+ Index n = C.rows();
+ for(Index i=0;i<n;++i)
+ {
+ typedef std::complex<double> Complex;
+ MatrixXcd ac = C.cast<Complex>();
+ ac.diagonal().array() -= eig.eigenvalues()(i);
+ VectorXd sv = ac.jacobiSvd().singularValues();
+ // comparing to sv(0) is not enough here to catch the "bug",
+ // the hard-coded 1.0 is important!
+ VERIFY_IS_MUCH_SMALLER_THAN(sv(n-1), 1.0);
+ }
+ }
+ }
+ // regression test for bug 1557
+ {
+ // this test is interesting because it contains zeros on the diagonal.
+ MatrixXd A_bug1557(3,3);
+ A_bug1557 << 0, 0, 0, 1, 0, 0.5887907064808635127, 0, 1, 0;
+ EigenSolver<MatrixXd> eig(A_bug1557);
+ CALL_SUBTEST( check_eigensolver_for_given_mat(eig,A_bug1557) );
+ }
+
+ // regression test for bug 1174
+ {
+ Index n = 12;
+ MatrixXf A_bug1174(n,n);
+ A_bug1174 << 262144, 0, 0, 262144, 786432, 0, 0, 0, 0, 0, 0, 786432,
+ 262144, 0, 0, 262144, 786432, 0, 0, 0, 0, 0, 0, 786432,
+ 262144, 0, 0, 262144, 786432, 0, 0, 0, 0, 0, 0, 786432,
+ 262144, 0, 0, 262144, 786432, 0, 0, 0, 0, 0, 0, 786432,
+ 0, 262144, 262144, 0, 0, 262144, 262144, 262144, 262144, 262144, 262144, 0,
+ 0, 262144, 262144, 0, 0, 262144, 262144, 262144, 262144, 262144, 262144, 0,
+ 0, 262144, 262144, 0, 0, 262144, 262144, 262144, 262144, 262144, 262144, 0,
+ 0, 262144, 262144, 0, 0, 262144, 262144, 262144, 262144, 262144, 262144, 0,
+ 0, 262144, 262144, 0, 0, 262144, 262144, 262144, 262144, 262144, 262144, 0,
+ 0, 262144, 262144, 0, 0, 262144, 262144, 262144, 262144, 262144, 262144, 0,
+ 0, 262144, 262144, 0, 0, 262144, 262144, 262144, 262144, 262144, 262144, 0,
+ 0, 262144, 262144, 0, 0, 262144, 262144, 262144, 262144, 262144, 262144, 0;
+ EigenSolver<MatrixXf> eig(A_bug1174);
+ CALL_SUBTEST( check_eigensolver_for_given_mat(eig,A_bug1174) );
+ }
+}
+
+EIGEN_DECLARE_TEST(eigensolver_generic)
+{
+ int s = 0;
+ for(int i = 0; i < g_repeat; i++) {
+ CALL_SUBTEST_1( eigensolver(Matrix4f()) );
+ s = internal::random<int>(1,EIGEN_TEST_MAX_SIZE/4);
+ CALL_SUBTEST_2( eigensolver(MatrixXd(s,s)) );
+ TEST_SET_BUT_UNUSED_VARIABLE(s)
+
+ // some trivial but implementation-wise tricky cases
+ CALL_SUBTEST_2( eigensolver(MatrixXd(1,1)) );
+ CALL_SUBTEST_2( eigensolver(MatrixXd(2,2)) );
+ CALL_SUBTEST_3( eigensolver(Matrix<double,1,1>()) );
+ CALL_SUBTEST_4( eigensolver(Matrix2d()) );
+ }
+
+ CALL_SUBTEST_1( eigensolver_verify_assert(Matrix4f()) );
+ s = internal::random<int>(1,EIGEN_TEST_MAX_SIZE/4);
+ CALL_SUBTEST_2( eigensolver_verify_assert(MatrixXd(s,s)) );
+ CALL_SUBTEST_3( eigensolver_verify_assert(Matrix<double,1,1>()) );
+ CALL_SUBTEST_4( eigensolver_verify_assert(Matrix2d()) );
+
+ // Test problem size constructors
+ CALL_SUBTEST_5(EigenSolver<MatrixXf> tmp(s));
+
+ // regression test for bug 410
+ CALL_SUBTEST_2(
+ {
+ MatrixXd A(1,1);
+ A(0,0) = std::sqrt(-1.); // is Not-a-Number
+ Eigen::EigenSolver<MatrixXd> solver(A);
+ VERIFY_IS_EQUAL(solver.info(), NumericalIssue);
+ }
+ );
+
+ CALL_SUBTEST_2( eigensolver_generic_extra<0>() );
+
+ TEST_SET_BUT_UNUSED_VARIABLE(s)
+}
diff --git a/test/eigensolver_selfadjoint.cpp b/test/eigensolver_selfadjoint.cpp
new file mode 100644
index 0000000..0fb2f4d
--- /dev/null
+++ b/test/eigensolver_selfadjoint.cpp
@@ -0,0 +1,281 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2010 Jitse Niesen <jitse@maths.leeds.ac.uk>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "main.h"
+#include "svd_fill.h"
+#include <limits>
+#include <Eigen/Eigenvalues>
+#include <Eigen/SparseCore>
+
+
+template<typename MatrixType> void selfadjointeigensolver_essential_check(const MatrixType& m)
+{
+ typedef typename MatrixType::Scalar Scalar;
+ typedef typename NumTraits<Scalar>::Real RealScalar;
+ RealScalar eival_eps = numext::mini<RealScalar>(test_precision<RealScalar>(), NumTraits<Scalar>::dummy_precision()*20000);
+
+ SelfAdjointEigenSolver<MatrixType> eiSymm(m);
+ VERIFY_IS_EQUAL(eiSymm.info(), Success);
+
+ RealScalar scaling = m.cwiseAbs().maxCoeff();
+
+ if(scaling<(std::numeric_limits<RealScalar>::min)())
+ {
+ VERIFY(eiSymm.eigenvalues().cwiseAbs().maxCoeff() <= (std::numeric_limits<RealScalar>::min)());
+ }
+ else
+ {
+ VERIFY_IS_APPROX((m.template selfadjointView<Lower>() * eiSymm.eigenvectors())/scaling,
+ (eiSymm.eigenvectors() * eiSymm.eigenvalues().asDiagonal())/scaling);
+ }
+ VERIFY_IS_APPROX(m.template selfadjointView<Lower>().eigenvalues(), eiSymm.eigenvalues());
+ VERIFY_IS_UNITARY(eiSymm.eigenvectors());
+
+ if(m.cols()<=4)
+ {
+ SelfAdjointEigenSolver<MatrixType> eiDirect;
+ eiDirect.computeDirect(m);
+ VERIFY_IS_EQUAL(eiDirect.info(), Success);
+ if(! eiSymm.eigenvalues().isApprox(eiDirect.eigenvalues(), eival_eps) )
+ {
+ std::cerr << "reference eigenvalues: " << eiSymm.eigenvalues().transpose() << "\n"
+ << "obtained eigenvalues: " << eiDirect.eigenvalues().transpose() << "\n"
+ << "diff: " << (eiSymm.eigenvalues()-eiDirect.eigenvalues()).transpose() << "\n"
+ << "error (eps): " << (eiSymm.eigenvalues()-eiDirect.eigenvalues()).norm() / eiSymm.eigenvalues().norm() << " (" << eival_eps << ")\n";
+ }
+ if(scaling<(std::numeric_limits<RealScalar>::min)())
+ {
+ VERIFY(eiDirect.eigenvalues().cwiseAbs().maxCoeff() <= (std::numeric_limits<RealScalar>::min)());
+ }
+ else
+ {
+ VERIFY_IS_APPROX(eiSymm.eigenvalues()/scaling, eiDirect.eigenvalues()/scaling);
+ VERIFY_IS_APPROX((m.template selfadjointView<Lower>() * eiDirect.eigenvectors())/scaling,
+ (eiDirect.eigenvectors() * eiDirect.eigenvalues().asDiagonal())/scaling);
+ VERIFY_IS_APPROX(m.template selfadjointView<Lower>().eigenvalues()/scaling, eiDirect.eigenvalues()/scaling);
+ }
+
+ VERIFY_IS_UNITARY(eiDirect.eigenvectors());
+ }
+}
+
+template<typename MatrixType> void selfadjointeigensolver(const MatrixType& m)
+{
+ /* this test covers the following files:
+ EigenSolver.h, SelfAdjointEigenSolver.h (and indirectly: Tridiagonalization.h)
+ */
+ Index rows = m.rows();
+ Index cols = m.cols();
+
+ typedef typename MatrixType::Scalar Scalar;
+ typedef typename NumTraits<Scalar>::Real RealScalar;
+
+ RealScalar largerEps = 10*test_precision<RealScalar>();
+
+ MatrixType a = MatrixType::Random(rows,cols);
+ MatrixType a1 = MatrixType::Random(rows,cols);
+ MatrixType symmA = a.adjoint() * a + a1.adjoint() * a1;
+ MatrixType symmC = symmA;
+
+ svd_fill_random(symmA,Symmetric);
+
+ symmA.template triangularView<StrictlyUpper>().setZero();
+ symmC.template triangularView<StrictlyUpper>().setZero();
+
+ MatrixType b = MatrixType::Random(rows,cols);
+ MatrixType b1 = MatrixType::Random(rows,cols);
+ MatrixType symmB = b.adjoint() * b + b1.adjoint() * b1;
+ symmB.template triangularView<StrictlyUpper>().setZero();
+
+ CALL_SUBTEST( selfadjointeigensolver_essential_check(symmA) );
+
+ SelfAdjointEigenSolver<MatrixType> eiSymm(symmA);
+ // generalized eigen pb
+ GeneralizedSelfAdjointEigenSolver<MatrixType> eiSymmGen(symmC, symmB);
+
+ SelfAdjointEigenSolver<MatrixType> eiSymmNoEivecs(symmA, false);
+ VERIFY_IS_EQUAL(eiSymmNoEivecs.info(), Success);
+ VERIFY_IS_APPROX(eiSymm.eigenvalues(), eiSymmNoEivecs.eigenvalues());
+
+ // generalized eigen problem Ax = lBx
+ eiSymmGen.compute(symmC, symmB,Ax_lBx);
+ VERIFY_IS_EQUAL(eiSymmGen.info(), Success);
+ VERIFY((symmC.template selfadjointView<Lower>() * eiSymmGen.eigenvectors()).isApprox(
+ symmB.template selfadjointView<Lower>() * (eiSymmGen.eigenvectors() * eiSymmGen.eigenvalues().asDiagonal()), largerEps));
+
+ // generalized eigen problem BAx = lx
+ eiSymmGen.compute(symmC, symmB,BAx_lx);
+ VERIFY_IS_EQUAL(eiSymmGen.info(), Success);
+ VERIFY((symmB.template selfadjointView<Lower>() * (symmC.template selfadjointView<Lower>() * eiSymmGen.eigenvectors())).isApprox(
+ (eiSymmGen.eigenvectors() * eiSymmGen.eigenvalues().asDiagonal()), largerEps));
+
+ // generalized eigen problem ABx = lx
+ eiSymmGen.compute(symmC, symmB,ABx_lx);
+ VERIFY_IS_EQUAL(eiSymmGen.info(), Success);
+ VERIFY((symmC.template selfadjointView<Lower>() * (symmB.template selfadjointView<Lower>() * eiSymmGen.eigenvectors())).isApprox(
+ (eiSymmGen.eigenvectors() * eiSymmGen.eigenvalues().asDiagonal()), largerEps));
+
+
+ eiSymm.compute(symmC);
+ MatrixType sqrtSymmA = eiSymm.operatorSqrt();
+ VERIFY_IS_APPROX(MatrixType(symmC.template selfadjointView<Lower>()), sqrtSymmA*sqrtSymmA);
+ VERIFY_IS_APPROX(sqrtSymmA, symmC.template selfadjointView<Lower>()*eiSymm.operatorInverseSqrt());
+
+ MatrixType id = MatrixType::Identity(rows, cols);
+ VERIFY_IS_APPROX(id.template selfadjointView<Lower>().operatorNorm(), RealScalar(1));
+
+ SelfAdjointEigenSolver<MatrixType> eiSymmUninitialized;
+ VERIFY_RAISES_ASSERT(eiSymmUninitialized.info());
+ VERIFY_RAISES_ASSERT(eiSymmUninitialized.eigenvalues());
+ VERIFY_RAISES_ASSERT(eiSymmUninitialized.eigenvectors());
+ VERIFY_RAISES_ASSERT(eiSymmUninitialized.operatorSqrt());
+ VERIFY_RAISES_ASSERT(eiSymmUninitialized.operatorInverseSqrt());
+
+ eiSymmUninitialized.compute(symmA, false);
+ VERIFY_RAISES_ASSERT(eiSymmUninitialized.eigenvectors());
+ VERIFY_RAISES_ASSERT(eiSymmUninitialized.operatorSqrt());
+ VERIFY_RAISES_ASSERT(eiSymmUninitialized.operatorInverseSqrt());
+
+ // test Tridiagonalization's methods
+ Tridiagonalization<MatrixType> tridiag(symmC);
+ VERIFY_IS_APPROX(tridiag.diagonal(), tridiag.matrixT().diagonal());
+ VERIFY_IS_APPROX(tridiag.subDiagonal(), tridiag.matrixT().template diagonal<-1>());
+ Matrix<RealScalar,Dynamic,Dynamic> T = tridiag.matrixT();
+ if(rows>1 && cols>1) {
+ // FIXME check that upper and lower part are 0:
+ //VERIFY(T.topRightCorner(rows-2, cols-2).template triangularView<Upper>().isZero());
+ }
+ VERIFY_IS_APPROX(tridiag.diagonal(), T.diagonal());
+ VERIFY_IS_APPROX(tridiag.subDiagonal(), T.template diagonal<1>());
+ VERIFY_IS_APPROX(MatrixType(symmC.template selfadjointView<Lower>()), tridiag.matrixQ() * tridiag.matrixT().eval() * MatrixType(tridiag.matrixQ()).adjoint());
+ VERIFY_IS_APPROX(MatrixType(symmC.template selfadjointView<Lower>()), tridiag.matrixQ() * tridiag.matrixT() * tridiag.matrixQ().adjoint());
+
+ // Test computation of eigenvalues from tridiagonal matrix
+ if(rows > 1)
+ {
+ SelfAdjointEigenSolver<MatrixType> eiSymmTridiag;
+ eiSymmTridiag.computeFromTridiagonal(tridiag.matrixT().diagonal(), tridiag.matrixT().diagonal(-1), ComputeEigenvectors);
+ VERIFY_IS_APPROX(eiSymm.eigenvalues(), eiSymmTridiag.eigenvalues());
+ VERIFY_IS_APPROX(tridiag.matrixT(), eiSymmTridiag.eigenvectors().real() * eiSymmTridiag.eigenvalues().asDiagonal() * eiSymmTridiag.eigenvectors().real().transpose());
+ }
+
+ if (rows > 1 && rows < 20)
+ {
+ // Test matrix with NaN
+ symmC(0,0) = std::numeric_limits<typename MatrixType::RealScalar>::quiet_NaN();
+ SelfAdjointEigenSolver<MatrixType> eiSymmNaN(symmC);
+ VERIFY_IS_EQUAL(eiSymmNaN.info(), NoConvergence);
+ }
+
+ // regression test for bug 1098
+ {
+ SelfAdjointEigenSolver<MatrixType> eig(a.adjoint() * a);
+ eig.compute(a.adjoint() * a);
+ }
+
+ // regression test for bug 478
+ {
+ a.setZero();
+ SelfAdjointEigenSolver<MatrixType> ei3(a);
+ VERIFY_IS_EQUAL(ei3.info(), Success);
+ VERIFY_IS_MUCH_SMALLER_THAN(ei3.eigenvalues().norm(),RealScalar(1));
+ VERIFY((ei3.eigenvectors().transpose()*ei3.eigenvectors().transpose()).eval().isIdentity());
+ }
+}
+
+template<int>
+void bug_854()
+{
+ Matrix3d m;
+ m << 850.961, 51.966, 0,
+ 51.966, 254.841, 0,
+ 0, 0, 0;
+ selfadjointeigensolver_essential_check(m);
+}
+
+template<int>
+void bug_1014()
+{
+ Matrix3d m;
+ m << 0.11111111111111114658, 0, 0,
+ 0, 0.11111111111111109107, 0,
+ 0, 0, 0.11111111111111107719;
+ selfadjointeigensolver_essential_check(m);
+}
+
+template<int>
+void bug_1225()
+{
+ Matrix3d m1, m2;
+ m1.setRandom();
+ m1 = m1*m1.transpose();
+ m2 = m1.triangularView<Upper>();
+ SelfAdjointEigenSolver<Matrix3d> eig1(m1);
+ SelfAdjointEigenSolver<Matrix3d> eig2(m2.selfadjointView<Upper>());
+ VERIFY_IS_APPROX(eig1.eigenvalues(), eig2.eigenvalues());
+}
+
+template<int>
+void bug_1204()
+{
+ SparseMatrix<double> A(2,2);
+ A.setIdentity();
+ SelfAdjointEigenSolver<Eigen::SparseMatrix<double> > eig(A);
+}
+
+EIGEN_DECLARE_TEST(eigensolver_selfadjoint)
+{
+ int s = 0;
+ for(int i = 0; i < g_repeat; i++) {
+
+ // trivial test for 1x1 matrices:
+ CALL_SUBTEST_1( selfadjointeigensolver(Matrix<float, 1, 1>()));
+ CALL_SUBTEST_1( selfadjointeigensolver(Matrix<double, 1, 1>()));
+ CALL_SUBTEST_1( selfadjointeigensolver(Matrix<std::complex<double>, 1, 1>()));
+
+ // very important to test 3x3 and 2x2 matrices since we provide special paths for them
+ CALL_SUBTEST_12( selfadjointeigensolver(Matrix2f()) );
+ CALL_SUBTEST_12( selfadjointeigensolver(Matrix2d()) );
+ CALL_SUBTEST_12( selfadjointeigensolver(Matrix2cd()) );
+ CALL_SUBTEST_13( selfadjointeigensolver(Matrix3f()) );
+ CALL_SUBTEST_13( selfadjointeigensolver(Matrix3d()) );
+ CALL_SUBTEST_13( selfadjointeigensolver(Matrix3cd()) );
+ CALL_SUBTEST_2( selfadjointeigensolver(Matrix4d()) );
+ CALL_SUBTEST_2( selfadjointeigensolver(Matrix4cd()) );
+
+ s = internal::random<int>(1,EIGEN_TEST_MAX_SIZE/4);
+ CALL_SUBTEST_3( selfadjointeigensolver(MatrixXf(s,s)) );
+ CALL_SUBTEST_4( selfadjointeigensolver(MatrixXd(s,s)) );
+ CALL_SUBTEST_5( selfadjointeigensolver(MatrixXcd(s,s)) );
+ CALL_SUBTEST_9( selfadjointeigensolver(Matrix<std::complex<double>,Dynamic,Dynamic,RowMajor>(s,s)) );
+ TEST_SET_BUT_UNUSED_VARIABLE(s)
+
+ // some trivial but implementation-wise tricky cases
+ CALL_SUBTEST_4( selfadjointeigensolver(MatrixXd(1,1)) );
+ CALL_SUBTEST_4( selfadjointeigensolver(MatrixXd(2,2)) );
+ CALL_SUBTEST_5( selfadjointeigensolver(MatrixXcd(1,1)) );
+ CALL_SUBTEST_5( selfadjointeigensolver(MatrixXcd(2,2)) );
+ CALL_SUBTEST_6( selfadjointeigensolver(Matrix<double,1,1>()) );
+ CALL_SUBTEST_7( selfadjointeigensolver(Matrix<double,2,2>()) );
+ }
+
+ CALL_SUBTEST_13( bug_854<0>() );
+ CALL_SUBTEST_13( bug_1014<0>() );
+ CALL_SUBTEST_13( bug_1204<0>() );
+ CALL_SUBTEST_13( bug_1225<0>() );
+
+ // Test problem size constructors
+ s = internal::random<int>(1,EIGEN_TEST_MAX_SIZE/4);
+ CALL_SUBTEST_8(SelfAdjointEigenSolver<MatrixXf> tmp1(s));
+ CALL_SUBTEST_8(Tridiagonalization<MatrixXf> tmp2(s));
+
+ TEST_SET_BUT_UNUSED_VARIABLE(s)
+}
+
diff --git a/test/evaluator_common.h b/test/evaluator_common.h
new file mode 100644
index 0000000..e69de29
--- /dev/null
+++ b/test/evaluator_common.h
diff --git a/test/evaluators.cpp b/test/evaluators.cpp
new file mode 100644
index 0000000..95bfb45
--- /dev/null
+++ b/test/evaluators.cpp
@@ -0,0 +1,527 @@
+
+#include "main.h"
+
+namespace Eigen {
+
+ template<typename Lhs,typename Rhs>
+ const Product<Lhs,Rhs>
+ prod(const Lhs& lhs, const Rhs& rhs)
+ {
+ return Product<Lhs,Rhs>(lhs,rhs);
+ }
+
+ template<typename Lhs,typename Rhs>
+ const Product<Lhs,Rhs,LazyProduct>
+ lazyprod(const Lhs& lhs, const Rhs& rhs)
+ {
+ return Product<Lhs,Rhs,LazyProduct>(lhs,rhs);
+ }
+
+ template<typename DstXprType, typename SrcXprType>
+ EIGEN_STRONG_INLINE
+ DstXprType& copy_using_evaluator(const EigenBase<DstXprType> &dst, const SrcXprType &src)
+ {
+ call_assignment(dst.const_cast_derived(), src.derived(), internal::assign_op<typename DstXprType::Scalar,typename SrcXprType::Scalar>());
+ return dst.const_cast_derived();
+ }
+
+ template<typename DstXprType, template <typename> class StorageBase, typename SrcXprType>
+ EIGEN_STRONG_INLINE
+ const DstXprType& copy_using_evaluator(const NoAlias<DstXprType, StorageBase>& dst, const SrcXprType &src)
+ {
+ call_assignment(dst, src.derived(), internal::assign_op<typename DstXprType::Scalar,typename SrcXprType::Scalar>());
+ return dst.expression();
+ }
+
+ template<typename DstXprType, typename SrcXprType>
+ EIGEN_STRONG_INLINE
+ DstXprType& copy_using_evaluator(const PlainObjectBase<DstXprType> &dst, const SrcXprType &src)
+ {
+ #ifdef EIGEN_NO_AUTOMATIC_RESIZING
+ eigen_assert((dst.size()==0 || (IsVectorAtCompileTime ? (dst.size() == src.size())
+ : (dst.rows() == src.rows() && dst.cols() == src.cols())))
+ && "Size mismatch. Automatic resizing is disabled because EIGEN_NO_AUTOMATIC_RESIZING is defined");
+ #else
+ dst.const_cast_derived().resizeLike(src.derived());
+ #endif
+
+ call_assignment(dst.const_cast_derived(), src.derived(), internal::assign_op<typename DstXprType::Scalar,typename SrcXprType::Scalar>());
+ return dst.const_cast_derived();
+ }
+
+ template<typename DstXprType, typename SrcXprType>
+ void add_assign_using_evaluator(const DstXprType& dst, const SrcXprType& src)
+ {
+ typedef typename DstXprType::Scalar Scalar;
+ call_assignment(const_cast<DstXprType&>(dst), src.derived(), internal::add_assign_op<Scalar,typename SrcXprType::Scalar>());
+ }
+
+ template<typename DstXprType, typename SrcXprType>
+ void subtract_assign_using_evaluator(const DstXprType& dst, const SrcXprType& src)
+ {
+ typedef typename DstXprType::Scalar Scalar;
+ call_assignment(const_cast<DstXprType&>(dst), src.derived(), internal::sub_assign_op<Scalar,typename SrcXprType::Scalar>());
+ }
+
+ template<typename DstXprType, typename SrcXprType>
+ void multiply_assign_using_evaluator(const DstXprType& dst, const SrcXprType& src)
+ {
+ typedef typename DstXprType::Scalar Scalar;
+ call_assignment(dst.const_cast_derived(), src.derived(), internal::mul_assign_op<Scalar,typename SrcXprType::Scalar>());
+ }
+
+ template<typename DstXprType, typename SrcXprType>
+ void divide_assign_using_evaluator(const DstXprType& dst, const SrcXprType& src)
+ {
+ typedef typename DstXprType::Scalar Scalar;
+ call_assignment(dst.const_cast_derived(), src.derived(), internal::div_assign_op<Scalar,typename SrcXprType::Scalar>());
+ }
+
+ template<typename DstXprType, typename SrcXprType>
+ void swap_using_evaluator(const DstXprType& dst, const SrcXprType& src)
+ {
+ typedef typename DstXprType::Scalar Scalar;
+ call_assignment(dst.const_cast_derived(), src.const_cast_derived(), internal::swap_assign_op<Scalar>());
+ }
+
+ namespace internal {
+ template<typename Dst, template <typename> class StorageBase, typename Src, typename Func>
+ EIGEN_DEVICE_FUNC void call_assignment(const NoAlias<Dst,StorageBase>& dst, const Src& src, const Func& func)
+ {
+ call_assignment_no_alias(dst.expression(), src, func);
+ }
+
+ template<typename Dst, template <typename> class StorageBase, typename Src, typename Func>
+ EIGEN_DEVICE_FUNC void call_restricted_packet_assignment(const NoAlias<Dst,StorageBase>& dst, const Src& src, const Func& func)
+ {
+ call_restricted_packet_assignment_no_alias(dst.expression(), src, func);
+ }
+ }
+
+}
+
+template<typename XprType> long get_cost(const XprType& ) { return Eigen::internal::evaluator<XprType>::CoeffReadCost; }
+
+using namespace std;
+
+#define VERIFY_IS_APPROX_EVALUATOR(DEST,EXPR) VERIFY_IS_APPROX(copy_using_evaluator(DEST,(EXPR)), (EXPR).eval());
+#define VERIFY_IS_APPROX_EVALUATOR2(DEST,EXPR,REF) VERIFY_IS_APPROX(copy_using_evaluator(DEST,(EXPR)), (REF).eval());
+
+EIGEN_DECLARE_TEST(evaluators)
+{
+ // Testing Matrix evaluator and Transpose
+ Vector2d v = Vector2d::Random();
+ const Vector2d v_const(v);
+ Vector2d v2;
+ RowVector2d w;
+
+ VERIFY_IS_APPROX_EVALUATOR(v2, v);
+ VERIFY_IS_APPROX_EVALUATOR(v2, v_const);
+
+ // Testing Transpose
+ VERIFY_IS_APPROX_EVALUATOR(w, v.transpose()); // Transpose as rvalue
+ VERIFY_IS_APPROX_EVALUATOR(w, v_const.transpose());
+
+ copy_using_evaluator(w.transpose(), v); // Transpose as lvalue
+ VERIFY_IS_APPROX(w,v.transpose().eval());
+
+ copy_using_evaluator(w.transpose(), v_const);
+ VERIFY_IS_APPROX(w,v_const.transpose().eval());
+
+ // Testing Array evaluator
+ {
+ ArrayXXf a(2,3);
+ ArrayXXf b(3,2);
+ a << 1,2,3, 4,5,6;
+ const ArrayXXf a_const(a);
+
+ VERIFY_IS_APPROX_EVALUATOR(b, a.transpose());
+
+ VERIFY_IS_APPROX_EVALUATOR(b, a_const.transpose());
+
+ // Testing CwiseNullaryOp evaluator
+ copy_using_evaluator(w, RowVector2d::Random());
+ VERIFY((w.array() >= -1).all() && (w.array() <= 1).all()); // not easy to test ...
+
+ VERIFY_IS_APPROX_EVALUATOR(w, RowVector2d::Zero());
+
+ VERIFY_IS_APPROX_EVALUATOR(w, RowVector2d::Constant(3));
+
+ // mix CwiseNullaryOp and transpose
+ VERIFY_IS_APPROX_EVALUATOR(w, Vector2d::Zero().transpose());
+ }
+
+ {
+ // test product expressions
+ int s = internal::random<int>(1,100);
+ MatrixXf a(s,s), b(s,s), c(s,s), d(s,s);
+ a.setRandom();
+ b.setRandom();
+ c.setRandom();
+ d.setRandom();
+ VERIFY_IS_APPROX_EVALUATOR(d, (a + b));
+ VERIFY_IS_APPROX_EVALUATOR(d, (a + b).transpose());
+ VERIFY_IS_APPROX_EVALUATOR2(d, prod(a,b), a*b);
+ VERIFY_IS_APPROX_EVALUATOR2(d.noalias(), prod(a,b), a*b);
+ VERIFY_IS_APPROX_EVALUATOR2(d, prod(a,b) + c, a*b + c);
+ VERIFY_IS_APPROX_EVALUATOR2(d, s * prod(a,b), s * a*b);
+ VERIFY_IS_APPROX_EVALUATOR2(d, prod(a,b).transpose(), (a*b).transpose());
+ VERIFY_IS_APPROX_EVALUATOR2(d, prod(a,b) + prod(b,c), a*b + b*c);
+
+ // check that prod works even with aliasing present
+ c = a*a;
+ copy_using_evaluator(a, prod(a,a));
+ VERIFY_IS_APPROX(a,c);
+
+ // check compound assignment of products
+ d = c;
+ add_assign_using_evaluator(c.noalias(), prod(a,b));
+ d.noalias() += a*b;
+ VERIFY_IS_APPROX(c, d);
+
+ d = c;
+ subtract_assign_using_evaluator(c.noalias(), prod(a,b));
+ d.noalias() -= a*b;
+ VERIFY_IS_APPROX(c, d);
+ }
+
+ {
+ // test product with all possible sizes
+ int s = internal::random<int>(1,100);
+ Matrix<float, 1, 1> m11, res11; m11.setRandom(1,1);
+ Matrix<float, 1, 4> m14, res14; m14.setRandom(1,4);
+ Matrix<float, 1,Dynamic> m1X, res1X; m1X.setRandom(1,s);
+ Matrix<float, 4, 1> m41, res41; m41.setRandom(4,1);
+ Matrix<float, 4, 4> m44, res44; m44.setRandom(4,4);
+ Matrix<float, 4,Dynamic> m4X, res4X; m4X.setRandom(4,s);
+ Matrix<float,Dynamic, 1> mX1, resX1; mX1.setRandom(s,1);
+ Matrix<float,Dynamic, 4> mX4, resX4; mX4.setRandom(s,4);
+ Matrix<float,Dynamic,Dynamic> mXX, resXX; mXX.setRandom(s,s);
+
+ VERIFY_IS_APPROX_EVALUATOR2(res11, prod(m11,m11), m11*m11);
+ VERIFY_IS_APPROX_EVALUATOR2(res11, prod(m14,m41), m14*m41);
+ VERIFY_IS_APPROX_EVALUATOR2(res11, prod(m1X,mX1), m1X*mX1);
+ VERIFY_IS_APPROX_EVALUATOR2(res14, prod(m11,m14), m11*m14);
+ VERIFY_IS_APPROX_EVALUATOR2(res14, prod(m14,m44), m14*m44);
+ VERIFY_IS_APPROX_EVALUATOR2(res14, prod(m1X,mX4), m1X*mX4);
+ VERIFY_IS_APPROX_EVALUATOR2(res1X, prod(m11,m1X), m11*m1X);
+ VERIFY_IS_APPROX_EVALUATOR2(res1X, prod(m14,m4X), m14*m4X);
+ VERIFY_IS_APPROX_EVALUATOR2(res1X, prod(m1X,mXX), m1X*mXX);
+ VERIFY_IS_APPROX_EVALUATOR2(res41, prod(m41,m11), m41*m11);
+ VERIFY_IS_APPROX_EVALUATOR2(res41, prod(m44,m41), m44*m41);
+ VERIFY_IS_APPROX_EVALUATOR2(res41, prod(m4X,mX1), m4X*mX1);
+ VERIFY_IS_APPROX_EVALUATOR2(res44, prod(m41,m14), m41*m14);
+ VERIFY_IS_APPROX_EVALUATOR2(res44, prod(m44,m44), m44*m44);
+ VERIFY_IS_APPROX_EVALUATOR2(res44, prod(m4X,mX4), m4X*mX4);
+ VERIFY_IS_APPROX_EVALUATOR2(res4X, prod(m41,m1X), m41*m1X);
+ VERIFY_IS_APPROX_EVALUATOR2(res4X, prod(m44,m4X), m44*m4X);
+ VERIFY_IS_APPROX_EVALUATOR2(res4X, prod(m4X,mXX), m4X*mXX);
+ VERIFY_IS_APPROX_EVALUATOR2(resX1, prod(mX1,m11), mX1*m11);
+ VERIFY_IS_APPROX_EVALUATOR2(resX1, prod(mX4,m41), mX4*m41);
+ VERIFY_IS_APPROX_EVALUATOR2(resX1, prod(mXX,mX1), mXX*mX1);
+ VERIFY_IS_APPROX_EVALUATOR2(resX4, prod(mX1,m14), mX1*m14);
+ VERIFY_IS_APPROX_EVALUATOR2(resX4, prod(mX4,m44), mX4*m44);
+ VERIFY_IS_APPROX_EVALUATOR2(resX4, prod(mXX,mX4), mXX*mX4);
+ VERIFY_IS_APPROX_EVALUATOR2(resXX, prod(mX1,m1X), mX1*m1X);
+ VERIFY_IS_APPROX_EVALUATOR2(resXX, prod(mX4,m4X), mX4*m4X);
+ VERIFY_IS_APPROX_EVALUATOR2(resXX, prod(mXX,mXX), mXX*mXX);
+ }
+
+ {
+ ArrayXXf a(2,3);
+ ArrayXXf b(3,2);
+ a << 1,2,3, 4,5,6;
+ const ArrayXXf a_const(a);
+
+ // this does not work because Random is eval-before-nested:
+ // copy_using_evaluator(w, Vector2d::Random().transpose());
+
+ // test CwiseUnaryOp
+ VERIFY_IS_APPROX_EVALUATOR(v2, 3 * v);
+ VERIFY_IS_APPROX_EVALUATOR(w, (3 * v).transpose());
+ VERIFY_IS_APPROX_EVALUATOR(b, (a + 3).transpose());
+ VERIFY_IS_APPROX_EVALUATOR(b, (2 * a_const + 3).transpose());
+
+ // test CwiseBinaryOp
+ VERIFY_IS_APPROX_EVALUATOR(v2, v + Vector2d::Ones());
+ VERIFY_IS_APPROX_EVALUATOR(w, (v + Vector2d::Ones()).transpose().cwiseProduct(RowVector2d::Constant(3)));
+
+ // dynamic matrices and arrays
+ MatrixXd mat1(6,6), mat2(6,6);
+ VERIFY_IS_APPROX_EVALUATOR(mat1, MatrixXd::Identity(6,6));
+ VERIFY_IS_APPROX_EVALUATOR(mat2, mat1);
+ copy_using_evaluator(mat2.transpose(), mat1);
+ VERIFY_IS_APPROX(mat2.transpose(), mat1);
+
+ ArrayXXd arr1(6,6), arr2(6,6);
+ VERIFY_IS_APPROX_EVALUATOR(arr1, ArrayXXd::Constant(6,6, 3.0));
+ VERIFY_IS_APPROX_EVALUATOR(arr2, arr1);
+
+ // test automatic resizing
+ mat2.resize(3,3);
+ VERIFY_IS_APPROX_EVALUATOR(mat2, mat1);
+ arr2.resize(9,9);
+ VERIFY_IS_APPROX_EVALUATOR(arr2, arr1);
+
+ // test direct traversal
+ Matrix3f m3;
+ Array33f a3;
+ VERIFY_IS_APPROX_EVALUATOR(m3, Matrix3f::Identity()); // matrix, nullary
+ // TODO: find a way to test direct traversal with array
+ VERIFY_IS_APPROX_EVALUATOR(m3.transpose(), Matrix3f::Identity().transpose()); // transpose
+ VERIFY_IS_APPROX_EVALUATOR(m3, 2 * Matrix3f::Identity()); // unary
+ VERIFY_IS_APPROX_EVALUATOR(m3, Matrix3f::Identity() + Matrix3f::Zero()); // binary
+ VERIFY_IS_APPROX_EVALUATOR(m3.block(0,0,2,2), Matrix3f::Identity().block(1,1,2,2)); // block
+
+ // test linear traversal
+ VERIFY_IS_APPROX_EVALUATOR(m3, Matrix3f::Zero()); // matrix, nullary
+ VERIFY_IS_APPROX_EVALUATOR(a3, Array33f::Zero()); // array
+ VERIFY_IS_APPROX_EVALUATOR(m3.transpose(), Matrix3f::Zero().transpose()); // transpose
+ VERIFY_IS_APPROX_EVALUATOR(m3, 2 * Matrix3f::Zero()); // unary
+ VERIFY_IS_APPROX_EVALUATOR(m3, Matrix3f::Zero() + m3); // binary
+
+ // test inner vectorization
+ Matrix4f m4, m4src = Matrix4f::Random();
+ Array44f a4, a4src = Matrix4f::Random();
+ VERIFY_IS_APPROX_EVALUATOR(m4, m4src); // matrix
+ VERIFY_IS_APPROX_EVALUATOR(a4, a4src); // array
+ VERIFY_IS_APPROX_EVALUATOR(m4.transpose(), m4src.transpose()); // transpose
+ // TODO: find out why Matrix4f::Zero() does not allow inner vectorization
+ VERIFY_IS_APPROX_EVALUATOR(m4, 2 * m4src); // unary
+ VERIFY_IS_APPROX_EVALUATOR(m4, m4src + m4src); // binary
+
+ // test linear vectorization
+ MatrixXf mX(6,6), mXsrc = MatrixXf::Random(6,6);
+ ArrayXXf aX(6,6), aXsrc = ArrayXXf::Random(6,6);
+ VERIFY_IS_APPROX_EVALUATOR(mX, mXsrc); // matrix
+ VERIFY_IS_APPROX_EVALUATOR(aX, aXsrc); // array
+ VERIFY_IS_APPROX_EVALUATOR(mX.transpose(), mXsrc.transpose()); // transpose
+ VERIFY_IS_APPROX_EVALUATOR(mX, MatrixXf::Zero(6,6)); // nullary
+ VERIFY_IS_APPROX_EVALUATOR(mX, 2 * mXsrc); // unary
+ VERIFY_IS_APPROX_EVALUATOR(mX, mXsrc + mXsrc); // binary
+
+ // test blocks and slice vectorization
+ VERIFY_IS_APPROX_EVALUATOR(m4, (mXsrc.block<4,4>(1,0)));
+ VERIFY_IS_APPROX_EVALUATOR(aX, ArrayXXf::Constant(10, 10, 3.0).block(2, 3, 6, 6));
+
+ Matrix4f m4ref = m4;
+ copy_using_evaluator(m4.block(1, 1, 2, 3), m3.bottomRows(2));
+ m4ref.block(1, 1, 2, 3) = m3.bottomRows(2);
+ VERIFY_IS_APPROX(m4, m4ref);
+
+ mX.setIdentity(20,20);
+ MatrixXf mXref = MatrixXf::Identity(20,20);
+ mXsrc = MatrixXf::Random(9,12);
+ copy_using_evaluator(mX.block(4, 4, 9, 12), mXsrc);
+ mXref.block(4, 4, 9, 12) = mXsrc;
+ VERIFY_IS_APPROX(mX, mXref);
+
+ // test Map
+ const float raw[3] = {1,2,3};
+ float buffer[3] = {0,0,0};
+ Vector3f v3;
+ Array3f a3f;
+ VERIFY_IS_APPROX_EVALUATOR(v3, Map<const Vector3f>(raw));
+ VERIFY_IS_APPROX_EVALUATOR(a3f, Map<const Array3f>(raw));
+ Vector3f::Map(buffer) = 2*v3;
+ VERIFY(buffer[0] == 2);
+ VERIFY(buffer[1] == 4);
+ VERIFY(buffer[2] == 6);
+
+ // test CwiseUnaryView
+ mat1.setRandom();
+ mat2.setIdentity();
+ MatrixXcd matXcd(6,6), matXcd_ref(6,6);
+ copy_using_evaluator(matXcd.real(), mat1);
+ copy_using_evaluator(matXcd.imag(), mat2);
+ matXcd_ref.real() = mat1;
+ matXcd_ref.imag() = mat2;
+ VERIFY_IS_APPROX(matXcd, matXcd_ref);
+
+ // test Select
+ VERIFY_IS_APPROX_EVALUATOR(aX, (aXsrc > 0).select(aXsrc, -aXsrc));
+
+ // test Replicate
+ mXsrc = MatrixXf::Random(6, 6);
+ VectorXf vX = VectorXf::Random(6);
+ mX.resize(6, 6);
+ VERIFY_IS_APPROX_EVALUATOR(mX, mXsrc.colwise() + vX);
+ matXcd.resize(12, 12);
+ VERIFY_IS_APPROX_EVALUATOR(matXcd, matXcd_ref.replicate(2,2));
+ VERIFY_IS_APPROX_EVALUATOR(matXcd, (matXcd_ref.replicate<2,2>()));
+
+ // test partial reductions
+ VectorXd vec1(6);
+ VERIFY_IS_APPROX_EVALUATOR(vec1, mat1.rowwise().sum());
+ VERIFY_IS_APPROX_EVALUATOR(vec1, mat1.colwise().sum().transpose());
+
+ // test MatrixWrapper and ArrayWrapper
+ mat1.setRandom(6,6);
+ arr1.setRandom(6,6);
+ VERIFY_IS_APPROX_EVALUATOR(mat2, arr1.matrix());
+ VERIFY_IS_APPROX_EVALUATOR(arr2, mat1.array());
+ VERIFY_IS_APPROX_EVALUATOR(mat2, (arr1 + 2).matrix());
+ VERIFY_IS_APPROX_EVALUATOR(arr2, mat1.array() + 2);
+ mat2.array() = arr1 * arr1;
+ VERIFY_IS_APPROX(mat2, (arr1 * arr1).matrix());
+ arr2.matrix() = MatrixXd::Identity(6,6);
+ VERIFY_IS_APPROX(arr2, MatrixXd::Identity(6,6).array());
+
+ // test Reverse
+ VERIFY_IS_APPROX_EVALUATOR(arr2, arr1.reverse());
+ VERIFY_IS_APPROX_EVALUATOR(arr2, arr1.colwise().reverse());
+ VERIFY_IS_APPROX_EVALUATOR(arr2, arr1.rowwise().reverse());
+ arr2.reverse() = arr1;
+ VERIFY_IS_APPROX(arr2, arr1.reverse());
+ mat2.array() = mat1.array().reverse();
+ VERIFY_IS_APPROX(mat2.array(), mat1.array().reverse());
+
+ // test Diagonal
+ VERIFY_IS_APPROX_EVALUATOR(vec1, mat1.diagonal());
+ vec1.resize(5);
+ VERIFY_IS_APPROX_EVALUATOR(vec1, mat1.diagonal(1));
+ VERIFY_IS_APPROX_EVALUATOR(vec1, mat1.diagonal<-1>());
+ vec1.setRandom();
+
+ mat2 = mat1;
+ copy_using_evaluator(mat1.diagonal(1), vec1);
+ mat2.diagonal(1) = vec1;
+ VERIFY_IS_APPROX(mat1, mat2);
+
+ copy_using_evaluator(mat1.diagonal<-1>(), mat1.diagonal(1));
+ mat2.diagonal<-1>() = mat2.diagonal(1);
+ VERIFY_IS_APPROX(mat1, mat2);
+ }
+
+ {
+ // test swapping
+ MatrixXd mat1, mat2, mat1ref, mat2ref;
+ mat1ref = mat1 = MatrixXd::Random(6, 6);
+ mat2ref = mat2 = 2 * mat1 + MatrixXd::Identity(6, 6);
+ swap_using_evaluator(mat1, mat2);
+ mat1ref.swap(mat2ref);
+ VERIFY_IS_APPROX(mat1, mat1ref);
+ VERIFY_IS_APPROX(mat2, mat2ref);
+
+ swap_using_evaluator(mat1.block(0, 0, 3, 3), mat2.block(3, 3, 3, 3));
+ mat1ref.block(0, 0, 3, 3).swap(mat2ref.block(3, 3, 3, 3));
+ VERIFY_IS_APPROX(mat1, mat1ref);
+ VERIFY_IS_APPROX(mat2, mat2ref);
+
+ swap_using_evaluator(mat1.row(2), mat2.col(3).transpose());
+ mat1.row(2).swap(mat2.col(3).transpose());
+ VERIFY_IS_APPROX(mat1, mat1ref);
+ VERIFY_IS_APPROX(mat2, mat2ref);
+ }
+
+ {
+ // test compound assignment
+ const Matrix4d mat_const = Matrix4d::Random();
+ Matrix4d mat, mat_ref;
+ mat = mat_ref = Matrix4d::Identity();
+ add_assign_using_evaluator(mat, mat_const);
+ mat_ref += mat_const;
+ VERIFY_IS_APPROX(mat, mat_ref);
+
+ subtract_assign_using_evaluator(mat.row(1), 2*mat.row(2));
+ mat_ref.row(1) -= 2*mat_ref.row(2);
+ VERIFY_IS_APPROX(mat, mat_ref);
+
+ const ArrayXXf arr_const = ArrayXXf::Random(5,3);
+ ArrayXXf arr, arr_ref;
+ arr = arr_ref = ArrayXXf::Constant(5, 3, 0.5);
+ multiply_assign_using_evaluator(arr, arr_const);
+ arr_ref *= arr_const;
+ VERIFY_IS_APPROX(arr, arr_ref);
+
+ divide_assign_using_evaluator(arr.row(1), arr.row(2) + 1);
+ arr_ref.row(1) /= (arr_ref.row(2) + 1);
+ VERIFY_IS_APPROX(arr, arr_ref);
+ }
+
+ {
+ // test triangular shapes
+ MatrixXd A = MatrixXd::Random(6,6), B(6,6), C(6,6), D(6,6);
+ A.setRandom();B.setRandom();
+ VERIFY_IS_APPROX_EVALUATOR2(B, A.triangularView<Upper>(), MatrixXd(A.triangularView<Upper>()));
+
+ A.setRandom();B.setRandom();
+ VERIFY_IS_APPROX_EVALUATOR2(B, A.triangularView<UnitLower>(), MatrixXd(A.triangularView<UnitLower>()));
+
+ A.setRandom();B.setRandom();
+ VERIFY_IS_APPROX_EVALUATOR2(B, A.triangularView<UnitUpper>(), MatrixXd(A.triangularView<UnitUpper>()));
+
+ A.setRandom();B.setRandom();
+ C = B; C.triangularView<Upper>() = A;
+ copy_using_evaluator(B.triangularView<Upper>(), A);
+ VERIFY(B.isApprox(C) && "copy_using_evaluator(B.triangularView<Upper>(), A)");
+
+ A.setRandom();B.setRandom();
+ C = B; C.triangularView<Lower>() = A.triangularView<Lower>();
+ copy_using_evaluator(B.triangularView<Lower>(), A.triangularView<Lower>());
+ VERIFY(B.isApprox(C) && "copy_using_evaluator(B.triangularView<Lower>(), A.triangularView<Lower>())");
+
+
+ A.setRandom();B.setRandom();
+ C = B; C.triangularView<Lower>() = A.triangularView<Upper>().transpose();
+ copy_using_evaluator(B.triangularView<Lower>(), A.triangularView<Upper>().transpose());
+ VERIFY(B.isApprox(C) && "copy_using_evaluator(B.triangularView<Lower>(), A.triangularView<Lower>().transpose())");
+
+
+ A.setRandom();B.setRandom(); C = B; D = A;
+ C.triangularView<Upper>().swap(D.triangularView<Upper>());
+ swap_using_evaluator(B.triangularView<Upper>(), A.triangularView<Upper>());
+ VERIFY(B.isApprox(C) && "swap_using_evaluator(B.triangularView<Upper>(), A.triangularView<Upper>())");
+
+
+ VERIFY_IS_APPROX_EVALUATOR2(B, prod(A.triangularView<Upper>(),A), MatrixXd(A.triangularView<Upper>()*A));
+
+ VERIFY_IS_APPROX_EVALUATOR2(B, prod(A.selfadjointView<Upper>(),A), MatrixXd(A.selfadjointView<Upper>()*A));
+ }
+
+ {
+ // test diagonal shapes
+ VectorXd d = VectorXd::Random(6);
+ MatrixXd A = MatrixXd::Random(6,6), B(6,6);
+ A.setRandom();B.setRandom();
+
+ VERIFY_IS_APPROX_EVALUATOR2(B, lazyprod(d.asDiagonal(),A), MatrixXd(d.asDiagonal()*A));
+ VERIFY_IS_APPROX_EVALUATOR2(B, lazyprod(A,d.asDiagonal()), MatrixXd(A*d.asDiagonal()));
+ }
+
+ {
+ // test CoeffReadCost
+ Matrix4d a, b;
+ VERIFY_IS_EQUAL( get_cost(a), 1 );
+ VERIFY_IS_EQUAL( get_cost(a+b), 3);
+ VERIFY_IS_EQUAL( get_cost(2*a+b), 4);
+ VERIFY_IS_EQUAL( get_cost(a*b), 1);
+ VERIFY_IS_EQUAL( get_cost(a.lazyProduct(b)), 15);
+ VERIFY_IS_EQUAL( get_cost(a*(a*b)), 1);
+ VERIFY_IS_EQUAL( get_cost(a.lazyProduct(a*b)), 15);
+ VERIFY_IS_EQUAL( get_cost(a*(a+b)), 1);
+ VERIFY_IS_EQUAL( get_cost(a.lazyProduct(a+b)), 15);
+ }
+
+ // regression test for PR 544 and bug 1622 (introduced in #71609c4)
+ {
+ // test restricted_packet_assignment with an unaligned destination
+ const size_t M = 2;
+ const size_t K = 2;
+ const size_t N = 5;
+ float *destMem = new float[(M*N) + 1];
+ // In case of no alignment, avoid division by zero.
+ constexpr int alignment = (std::max<int>)(EIGEN_MAX_ALIGN_BYTES, 1);
+ float *dest = (internal::UIntPtr(destMem)%alignment) == 0 ? destMem+1 : destMem;
+
+ const Matrix<float, Dynamic, Dynamic, RowMajor> a = Matrix<float, Dynamic, Dynamic, RowMajor>::Random(M, K);
+ const Matrix<float, Dynamic, Dynamic, RowMajor> b = Matrix<float, Dynamic, Dynamic, RowMajor>::Random(K, N);
+
+ Map<Matrix<float, Dynamic, Dynamic, RowMajor> > z(dest, M, N);;
+ Product<Matrix<float, Dynamic, Dynamic, RowMajor>, Matrix<float, Dynamic, Dynamic, RowMajor>, LazyProduct> tmp(a,b);
+ internal::call_restricted_packet_assignment(z.noalias(), tmp.derived(), internal::assign_op<float, float>());
+
+ VERIFY_IS_APPROX(z, a*b);
+ delete[] destMem;
+ }
+}
diff --git a/test/exceptions.cpp b/test/exceptions.cpp
new file mode 100644
index 0000000..3d93060
--- /dev/null
+++ b/test/exceptions.cpp
@@ -0,0 +1,49 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2011 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+
+// Various sanity tests with exceptions and non trivially copyable scalar type.
+// - no memory leak when a custom scalar type trow an exceptions
+// - todo: complete the list of tests!
+
+#define EIGEN_STACK_ALLOCATION_LIMIT 100000000
+
+#include "main.h"
+#include "AnnoyingScalar.h"
+
+#define CHECK_MEMLEAK(OP) { \
+ AnnoyingScalar::countdown = 100; \
+ int before = AnnoyingScalar::instances; \
+ bool exception_thrown = false; \
+ try { OP; } \
+ catch (my_exception) { \
+ exception_thrown = true; \
+ VERIFY(AnnoyingScalar::instances==before && "memory leak detected in " && EIGEN_MAKESTRING(OP)); \
+ } \
+ VERIFY( (AnnoyingScalar::dont_throw) || (exception_thrown && " no exception thrown in " && EIGEN_MAKESTRING(OP)) ); \
+ }
+
+EIGEN_DECLARE_TEST(exceptions)
+{
+ typedef Eigen::Matrix<AnnoyingScalar,Dynamic,1> VectorType;
+ typedef Eigen::Matrix<AnnoyingScalar,Dynamic,Dynamic> MatrixType;
+
+ {
+ AnnoyingScalar::dont_throw = false;
+ int n = 50;
+ VectorType v0(n), v1(n);
+ MatrixType m0(n,n), m1(n,n), m2(n,n);
+ v0.setOnes(); v1.setOnes();
+ m0.setOnes(); m1.setOnes(); m2.setOnes();
+ CHECK_MEMLEAK(v0 = m0 * m1 * v1);
+ CHECK_MEMLEAK(m2 = m0 * m1 * m2);
+ CHECK_MEMLEAK((v0+v1).dot(v0+v1));
+ }
+ VERIFY(AnnoyingScalar::instances==0 && "global memory leak detected in " && EIGEN_MAKESTRING(OP));
+}
diff --git a/test/fastmath.cpp b/test/fastmath.cpp
new file mode 100644
index 0000000..00a1a59
--- /dev/null
+++ b/test/fastmath.cpp
@@ -0,0 +1,99 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2015 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "main.h"
+
+void check(bool b, bool ref)
+{
+ std::cout << b;
+ if(b==ref)
+ std::cout << " OK ";
+ else
+ std::cout << " BAD ";
+}
+
+#if EIGEN_COMP_MSVC && EIGEN_COMP_MSVC < 1800
+namespace std {
+ template<typename T> bool (isfinite)(T x) { return _finite(x); }
+ template<typename T> bool (isnan)(T x) { return _isnan(x); }
+ template<typename T> bool (isinf)(T x) { return _fpclass(x)==_FPCLASS_NINF || _fpclass(x)==_FPCLASS_PINF; }
+}
+#endif
+
+template<typename T>
+void check_inf_nan(bool dryrun) {
+ Matrix<T,Dynamic,1> m(10);
+ m.setRandom();
+ m(3) = std::numeric_limits<T>::quiet_NaN();
+
+ if(dryrun)
+ {
+ std::cout << "std::isfinite(" << m(3) << ") = "; check((std::isfinite)(m(3)),false); std::cout << " ; numext::isfinite = "; check((numext::isfinite)(m(3)), false); std::cout << "\n";
+ std::cout << "std::isinf(" << m(3) << ") = "; check((std::isinf)(m(3)),false); std::cout << " ; numext::isinf = "; check((numext::isinf)(m(3)), false); std::cout << "\n";
+ std::cout << "std::isnan(" << m(3) << ") = "; check((std::isnan)(m(3)),true); std::cout << " ; numext::isnan = "; check((numext::isnan)(m(3)), true); std::cout << "\n";
+ std::cout << "allFinite: "; check(m.allFinite(), 0); std::cout << "\n";
+ std::cout << "hasNaN: "; check(m.hasNaN(), 1); std::cout << "\n";
+ std::cout << "\n";
+ }
+ else
+ {
+ if( (std::isfinite)(m(3))) g_test_level=1; VERIFY( !(numext::isfinite)(m(3)) ); g_test_level=0;
+ if( (std::isinf) (m(3))) g_test_level=1; VERIFY( !(numext::isinf)(m(3)) ); g_test_level=0;
+ if(!(std::isnan) (m(3))) g_test_level=1; VERIFY( (numext::isnan)(m(3)) ); g_test_level=0;
+ if( (std::isfinite)(m(3))) g_test_level=1; VERIFY( !m.allFinite() ); g_test_level=0;
+ if(!(std::isnan) (m(3))) g_test_level=1; VERIFY( m.hasNaN() ); g_test_level=0;
+ }
+ T hidden_zero = (std::numeric_limits<T>::min)()*(std::numeric_limits<T>::min)();
+ m(4) /= hidden_zero;
+ if(dryrun)
+ {
+ std::cout << "std::isfinite(" << m(4) << ") = "; check((std::isfinite)(m(4)),false); std::cout << " ; numext::isfinite = "; check((numext::isfinite)(m(4)), false); std::cout << "\n";
+ std::cout << "std::isinf(" << m(4) << ") = "; check((std::isinf)(m(4)),true); std::cout << " ; numext::isinf = "; check((numext::isinf)(m(4)), true); std::cout << "\n";
+ std::cout << "std::isnan(" << m(4) << ") = "; check((std::isnan)(m(4)),false); std::cout << " ; numext::isnan = "; check((numext::isnan)(m(4)), false); std::cout << "\n";
+ std::cout << "allFinite: "; check(m.allFinite(), 0); std::cout << "\n";
+ std::cout << "hasNaN: "; check(m.hasNaN(), 1); std::cout << "\n";
+ std::cout << "\n";
+ }
+ else
+ {
+ if( (std::isfinite)(m(3))) g_test_level=1; VERIFY( !(numext::isfinite)(m(4)) ); g_test_level=0;
+ if(!(std::isinf) (m(3))) g_test_level=1; VERIFY( (numext::isinf)(m(4)) ); g_test_level=0;
+ if( (std::isnan) (m(3))) g_test_level=1; VERIFY( !(numext::isnan)(m(4)) ); g_test_level=0;
+ if( (std::isfinite)(m(3))) g_test_level=1; VERIFY( !m.allFinite() ); g_test_level=0;
+ if(!(std::isnan) (m(3))) g_test_level=1; VERIFY( m.hasNaN() ); g_test_level=0;
+ }
+ m(3) = 0;
+ if(dryrun)
+ {
+ std::cout << "std::isfinite(" << m(3) << ") = "; check((std::isfinite)(m(3)),true); std::cout << " ; numext::isfinite = "; check((numext::isfinite)(m(3)), true); std::cout << "\n";
+ std::cout << "std::isinf(" << m(3) << ") = "; check((std::isinf)(m(3)),false); std::cout << " ; numext::isinf = "; check((numext::isinf)(m(3)), false); std::cout << "\n";
+ std::cout << "std::isnan(" << m(3) << ") = "; check((std::isnan)(m(3)),false); std::cout << " ; numext::isnan = "; check((numext::isnan)(m(3)), false); std::cout << "\n";
+ std::cout << "allFinite: "; check(m.allFinite(), 0); std::cout << "\n";
+ std::cout << "hasNaN: "; check(m.hasNaN(), 0); std::cout << "\n";
+ std::cout << "\n\n";
+ }
+ else
+ {
+ if(!(std::isfinite)(m(3))) g_test_level=1; VERIFY( (numext::isfinite)(m(3)) ); g_test_level=0;
+ if( (std::isinf) (m(3))) g_test_level=1; VERIFY( !(numext::isinf)(m(3)) ); g_test_level=0;
+ if( (std::isnan) (m(3))) g_test_level=1; VERIFY( !(numext::isnan)(m(3)) ); g_test_level=0;
+ if( (std::isfinite)(m(3))) g_test_level=1; VERIFY( !m.allFinite() ); g_test_level=0;
+ if( (std::isnan) (m(3))) g_test_level=1; VERIFY( !m.hasNaN() ); g_test_level=0;
+ }
+}
+
+EIGEN_DECLARE_TEST(fastmath) {
+ std::cout << "*** float *** \n\n"; check_inf_nan<float>(true);
+ std::cout << "*** double ***\n\n"; check_inf_nan<double>(true);
+ std::cout << "*** long double *** \n\n"; check_inf_nan<long double>(true);
+
+ check_inf_nan<float>(false);
+ check_inf_nan<double>(false);
+ check_inf_nan<long double>(false);
+}
diff --git a/test/first_aligned.cpp b/test/first_aligned.cpp
new file mode 100644
index 0000000..ed99450
--- /dev/null
+++ b/test/first_aligned.cpp
@@ -0,0 +1,51 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "main.h"
+
+template<typename Scalar>
+void test_first_aligned_helper(Scalar *array, int size)
+{
+ const int packet_size = sizeof(Scalar) * internal::packet_traits<Scalar>::size;
+ VERIFY(((size_t(array) + sizeof(Scalar) * internal::first_default_aligned(array, size)) % packet_size) == 0);
+}
+
+template<typename Scalar>
+void test_none_aligned_helper(Scalar *array, int size)
+{
+ EIGEN_UNUSED_VARIABLE(array);
+ EIGEN_UNUSED_VARIABLE(size);
+ VERIFY(internal::packet_traits<Scalar>::size == 1 || internal::first_default_aligned(array, size) == size);
+}
+
+struct some_non_vectorizable_type { float x; };
+
+EIGEN_DECLARE_TEST(first_aligned)
+{
+ EIGEN_ALIGN16 float array_float[100];
+ test_first_aligned_helper(array_float, 50);
+ test_first_aligned_helper(array_float+1, 50);
+ test_first_aligned_helper(array_float+2, 50);
+ test_first_aligned_helper(array_float+3, 50);
+ test_first_aligned_helper(array_float+4, 50);
+ test_first_aligned_helper(array_float+5, 50);
+
+ EIGEN_ALIGN16 double array_double[100];
+ test_first_aligned_helper(array_double, 50);
+ test_first_aligned_helper(array_double+1, 50);
+ test_first_aligned_helper(array_double+2, 50);
+
+ double *array_double_plus_4_bytes = (double*)(internal::UIntPtr(array_double)+4);
+ test_none_aligned_helper(array_double_plus_4_bytes, 50);
+ test_none_aligned_helper(array_double_plus_4_bytes+1, 50);
+
+ some_non_vectorizable_type array_nonvec[100];
+ test_first_aligned_helper(array_nonvec, 100);
+ test_none_aligned_helper(array_nonvec, 100);
+}
diff --git a/test/geo_alignedbox.cpp b/test/geo_alignedbox.cpp
new file mode 100644
index 0000000..e4dab32
--- /dev/null
+++ b/test/geo_alignedbox.cpp
@@ -0,0 +1,531 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "main.h"
+#include <Eigen/Geometry>
+
+using namespace std;
+
+// NOTE the following workaround was needed on some 32 bits builds to kill extra precision of x87 registers.
+// It seems that it is not needed anymore, but let's keep it here, just in case...
+
+template<typename T> EIGEN_DONT_INLINE
+void kill_extra_precision(T& /* x */) {
+ // This one worked but triggered a warning:
+ /* eigen_assert((void*)(&x) != (void*)0); */
+ // An alternative could be:
+ /* volatile T tmp = x; */
+ /* x = tmp; */
+}
+
+
+template<typename BoxType> void alignedbox(const BoxType& box)
+{
+ /* this test covers the following files:
+ AlignedBox.h
+ */
+ typedef typename BoxType::Scalar Scalar;
+ typedef NumTraits<Scalar> ScalarTraits;
+ typedef typename ScalarTraits::Real RealScalar;
+ typedef Matrix<Scalar, BoxType::AmbientDimAtCompileTime, 1> VectorType;
+
+ const Index dim = box.dim();
+
+ VectorType p0 = VectorType::Random(dim);
+ VectorType p1 = VectorType::Random(dim);
+ while( p1 == p0 ){
+ p1 = VectorType::Random(dim); }
+ RealScalar s1 = internal::random<RealScalar>(0,1);
+
+ BoxType b0(dim);
+ BoxType b1(VectorType::Random(dim),VectorType::Random(dim));
+ BoxType b2;
+
+ kill_extra_precision(b1);
+ kill_extra_precision(p0);
+ kill_extra_precision(p1);
+
+ b0.extend(p0);
+ b0.extend(p1);
+ VERIFY(b0.contains(p0*s1+(Scalar(1)-s1)*p1));
+ VERIFY(b0.contains(b0.center()));
+ VERIFY_IS_APPROX(b0.center(),(p0+p1)/Scalar(2));
+
+ (b2 = b0).extend(b1);
+ VERIFY(b2.contains(b0));
+ VERIFY(b2.contains(b1));
+ VERIFY_IS_APPROX(b2.clamp(b0), b0);
+
+ // intersection
+ BoxType box1(VectorType::Random(dim));
+ box1.extend(VectorType::Random(dim));
+ BoxType box2(VectorType::Random(dim));
+ box2.extend(VectorType::Random(dim));
+
+ VERIFY(box1.intersects(box2) == !box1.intersection(box2).isEmpty());
+
+ // alignment -- make sure there is no memory alignment assertion
+ BoxType *bp0 = new BoxType(dim);
+ BoxType *bp1 = new BoxType(dim);
+ bp0->extend(*bp1);
+ delete bp0;
+ delete bp1;
+
+ // sampling
+ for( int i=0; i<10; ++i )
+ {
+ VectorType r = b0.sample();
+ VERIFY(b0.contains(r));
+ }
+
+}
+
+template<typename BoxType> void alignedboxTranslatable(const BoxType& box)
+{
+ typedef typename BoxType::Scalar Scalar;
+ typedef Matrix<Scalar, BoxType::AmbientDimAtCompileTime, 1> VectorType;
+ typedef Transform<Scalar, BoxType::AmbientDimAtCompileTime, Isometry> IsometryTransform;
+ typedef Transform<Scalar, BoxType::AmbientDimAtCompileTime, Affine> AffineTransform;
+
+ alignedbox(box);
+
+ const VectorType Ones = VectorType::Ones();
+ const VectorType UnitX = VectorType::UnitX();
+ const Index dim = box.dim();
+
+ // box((-1, -1, -1), (1, 1, 1))
+ BoxType a(-Ones, Ones);
+
+ VERIFY_IS_APPROX(a.sizes(), Ones * Scalar(2));
+
+ BoxType b = a;
+ VectorType translate = Ones;
+ translate[0] = Scalar(2);
+ b.translate(translate);
+ // translate by (2, 1, 1) -> box((1, 0, 0), (3, 2, 2))
+
+ VERIFY_IS_APPROX(b.sizes(), Ones * Scalar(2));
+ VERIFY_IS_APPROX((b.min)(), UnitX);
+ VERIFY_IS_APPROX((b.max)(), Ones * Scalar(2) + UnitX);
+
+ // Test transform
+
+ IsometryTransform tf = IsometryTransform::Identity();
+ tf.translation() = -translate;
+
+ BoxType c = b.transformed(tf);
+ // translate by (-2, -1, -1) -> box((-1, -1, -1), (1, 1, 1))
+ VERIFY_IS_APPROX(c.sizes(), a.sizes());
+ VERIFY_IS_APPROX((c.min)(), (a.min)());
+ VERIFY_IS_APPROX((c.max)(), (a.max)());
+
+ c.transform(tf);
+ // translate by (-2, -1, -1) -> box((-3, -2, -2), (-1, 0, 0))
+ VERIFY_IS_APPROX(c.sizes(), a.sizes());
+ VERIFY_IS_APPROX((c.min)(), Ones * Scalar(-2) - UnitX);
+ VERIFY_IS_APPROX((c.max)(), -UnitX);
+
+ // Scaling
+
+ AffineTransform atf = AffineTransform::Identity();
+ atf.scale(Scalar(3));
+ c.transform(atf);
+ // scale by 3 -> box((-9, -6, -6), (-3, 0, 0))
+ VERIFY_IS_APPROX(c.sizes(), Scalar(3) * a.sizes());
+ VERIFY_IS_APPROX((c.min)(), Ones * Scalar(-6) - UnitX * Scalar(3));
+ VERIFY_IS_APPROX((c.max)(), UnitX * Scalar(-3));
+
+ atf = AffineTransform::Identity();
+ atf.scale(Scalar(-3));
+ c.transform(atf);
+ // scale by -3 -> box((27, 18, 18), (9, 0, 0))
+ VERIFY_IS_APPROX(c.sizes(), Scalar(9) * a.sizes());
+ VERIFY_IS_APPROX((c.min)(), UnitX * Scalar(9));
+ VERIFY_IS_APPROX((c.max)(), Ones * Scalar(18) + UnitX * Scalar(9));
+
+ // Check identity transform within numerical precision.
+ BoxType transformedC = c.transformed(IsometryTransform::Identity());
+ VERIFY_IS_APPROX(transformedC, c);
+
+ for (size_t i = 0; i < 10; ++i)
+ {
+ VectorType minCorner;
+ VectorType maxCorner;
+ for (Index d = 0; d < dim; ++d)
+ {
+ minCorner[d] = internal::random<Scalar>(-10,10);
+ maxCorner[d] = minCorner[d] + internal::random<Scalar>(0, 10);
+ }
+
+ c = BoxType(minCorner, maxCorner);
+
+ translate = VectorType::Random();
+ c.translate(translate);
+
+ VERIFY_IS_APPROX((c.min)(), minCorner + translate);
+ VERIFY_IS_APPROX((c.max)(), maxCorner + translate);
+ }
+}
+
+template<typename Scalar, typename Rotation>
+Rotation rotate2D(Scalar angle) {
+ return Rotation2D<Scalar>(angle);
+}
+
+template<typename Scalar, typename Rotation>
+Rotation rotate2DIntegral(typename NumTraits<Scalar>::NonInteger angle) {
+ typedef typename NumTraits<Scalar>::NonInteger NonInteger;
+ return Rotation2D<NonInteger>(angle).toRotationMatrix().
+ template cast<Scalar>();
+}
+
+template<typename Scalar, typename Rotation>
+Rotation rotate3DZAxis(Scalar angle) {
+ return AngleAxis<Scalar>(angle, Matrix<Scalar, 3, 1>(0, 0, 1));
+}
+
+template<typename Scalar, typename Rotation>
+Rotation rotate3DZAxisIntegral(typename NumTraits<Scalar>::NonInteger angle) {
+ typedef typename NumTraits<Scalar>::NonInteger NonInteger;
+ return AngleAxis<NonInteger>(angle, Matrix<NonInteger, 3, 1>(0, 0, 1)).
+ toRotationMatrix().template cast<Scalar>();
+}
+
+template<typename Scalar, typename Rotation>
+Rotation rotate4DZWAxis(Scalar angle) {
+ Rotation result = Matrix<Scalar, 4, 4>::Identity();
+ result.block(0, 0, 3, 3) = rotate3DZAxis<Scalar, AngleAxisd>(angle).toRotationMatrix();
+ return result;
+}
+
+template <typename MatrixType>
+MatrixType randomRotationMatrix()
+{
+ // algorithm from
+ // https://www.isprs-ann-photogramm-remote-sens-spatial-inf-sci.net/III-7/103/2016/isprs-annals-III-7-103-2016.pdf
+ const MatrixType rand = MatrixType::Random();
+ const MatrixType q = rand.householderQr().householderQ();
+ const JacobiSVD<MatrixType, ComputeFullU | ComputeFullV> svd(q);
+ const typename MatrixType::Scalar det = (svd.matrixU() * svd.matrixV().transpose()).determinant();
+ MatrixType diag = rand.Identity();
+ diag(MatrixType::RowsAtCompileTime - 1, MatrixType::ColsAtCompileTime - 1) = det;
+ const MatrixType rotation = svd.matrixU() * diag * svd.matrixV().transpose();
+ return rotation;
+}
+
+template <typename Scalar, int Dim>
+Matrix<Scalar, Dim, (1<<Dim)> boxGetCorners(const Matrix<Scalar, Dim, 1>& min_, const Matrix<Scalar, Dim, 1>& max_)
+{
+ Matrix<Scalar, Dim, (1<<Dim) > result;
+ for(Index i=0; i<(1<<Dim); ++i)
+ {
+ for(Index j=0; j<Dim; ++j)
+ result(j,i) = (i & (1<<j)) ? min_(j) : max_(j);
+ }
+ return result;
+}
+
+template<typename BoxType, typename Rotation> void alignedboxRotatable(
+ const BoxType& box,
+ Rotation (*rotate)(typename NumTraits<typename BoxType::Scalar>::NonInteger /*_angle*/))
+{
+ alignedboxTranslatable(box);
+
+ typedef typename BoxType::Scalar Scalar;
+ typedef typename NumTraits<Scalar>::NonInteger NonInteger;
+ typedef Matrix<Scalar, BoxType::AmbientDimAtCompileTime, 1> VectorType;
+ typedef Transform<Scalar, BoxType::AmbientDimAtCompileTime, Isometry> IsometryTransform;
+ typedef Transform<Scalar, BoxType::AmbientDimAtCompileTime, Affine> AffineTransform;
+
+ const VectorType Zero = VectorType::Zero();
+ const VectorType Ones = VectorType::Ones();
+ const VectorType UnitX = VectorType::UnitX();
+ const VectorType UnitY = VectorType::UnitY();
+ // this is vector (0, 0, -1, -1, -1, ...), i.e. with zeros at first and second dimensions
+ const VectorType UnitZ = Ones - UnitX - UnitY;
+
+ // in this kind of comments the 3D case values will be illustrated
+ // box((-1, -1, -1), (1, 1, 1))
+ BoxType a(-Ones, Ones);
+
+ // to allow templating this test for both 2D and 3D cases, we always set all
+ // but the first coordinate to the same value; so basically 3D case works as
+ // if you were looking at the scene from top
+
+ VectorType minPoint = -2 * Ones;
+ minPoint[0] = -3;
+ VectorType maxPoint = Zero;
+ maxPoint[0] = -1;
+ BoxType c(minPoint, maxPoint);
+ // box((-3, -2, -2), (-1, 0, 0))
+
+ IsometryTransform tf2 = IsometryTransform::Identity();
+ // for some weird reason the following statement has to be put separate from
+ // the following rotate call, otherwise precision problems arise...
+ Rotation rot = rotate(NonInteger(EIGEN_PI));
+ tf2.rotate(rot);
+
+ c.transform(tf2);
+ // rotate by 180 deg around origin -> box((1, 0, -2), (3, 2, 0))
+
+ VERIFY_IS_APPROX(c.sizes(), a.sizes());
+ VERIFY_IS_APPROX((c.min)(), UnitX - UnitZ * Scalar(2));
+ VERIFY_IS_APPROX((c.max)(), UnitX * Scalar(3) + UnitY * Scalar(2));
+
+ rot = rotate(NonInteger(EIGEN_PI / 2));
+ tf2.setIdentity();
+ tf2.rotate(rot);
+
+ c.transform(tf2);
+ // rotate by 90 deg around origin -> box((-2, 1, -2), (0, 3, 0))
+
+ VERIFY_IS_APPROX(c.sizes(), a.sizes());
+ VERIFY_IS_APPROX((c.min)(), Ones * Scalar(-2) + UnitY * Scalar(3));
+ VERIFY_IS_APPROX((c.max)(), UnitY * Scalar(3));
+
+ // box((-1, -1, -1), (1, 1, 1))
+ AffineTransform atf = AffineTransform::Identity();
+ atf.linearExt()(0, 1) = Scalar(1);
+ c = BoxType(-Ones, Ones);
+ c.transform(atf);
+ // 45 deg shear in x direction -> box((-2, -1, -1), (2, 1, 1))
+
+ VERIFY_IS_APPROX(c.sizes(), Ones * Scalar(2) + UnitX * Scalar(2));
+ VERIFY_IS_APPROX((c.min)(), -Ones - UnitX);
+ VERIFY_IS_APPROX((c.max)(), Ones + UnitX);
+}
+
+template<typename BoxType, typename Rotation> void alignedboxNonIntegralRotatable(
+ const BoxType& box,
+ Rotation (*rotate)(typename NumTraits<typename BoxType::Scalar>::NonInteger /*_angle*/))
+{
+ alignedboxRotatable(box, rotate);
+
+ typedef typename BoxType::Scalar Scalar;
+ typedef typename NumTraits<Scalar>::NonInteger NonInteger;
+ enum { Dim = BoxType::AmbientDimAtCompileTime };
+ typedef Matrix<Scalar, Dim, 1> VectorType;
+ typedef Matrix<Scalar, Dim, (1 << Dim)> CornersType;
+ typedef Transform<Scalar, Dim, Isometry> IsometryTransform;
+ typedef Transform<Scalar, Dim, Affine> AffineTransform;
+
+ const Index dim = box.dim();
+ const VectorType Zero = VectorType::Zero();
+ const VectorType Ones = VectorType::Ones();
+
+ VectorType minPoint = -2 * Ones;
+ minPoint[1] = 1;
+ VectorType maxPoint = Zero;
+ maxPoint[1] = 3;
+ BoxType c(minPoint, maxPoint);
+ // ((-2, 1, -2), (0, 3, 0))
+
+ VectorType cornerBL = (c.min)();
+ VectorType cornerTR = (c.max)();
+ VectorType cornerBR = (c.min)(); cornerBR[0] = cornerTR[0];
+ VectorType cornerTL = (c.max)(); cornerTL[0] = cornerBL[0];
+
+ NonInteger angle = NonInteger(EIGEN_PI/3);
+ Rotation rot = rotate(angle);
+ IsometryTransform tf2;
+ tf2.setIdentity();
+ tf2.rotate(rot);
+
+ c.transform(tf2);
+ // rotate by 60 deg -> box((-3.59, -1.23, -2), (-0.86, 1.5, 0))
+
+ cornerBL = tf2 * cornerBL;
+ cornerBR = tf2 * cornerBR;
+ cornerTL = tf2 * cornerTL;
+ cornerTR = tf2 * cornerTR;
+
+ VectorType minCorner = Ones * Scalar(-2);
+ VectorType maxCorner = Zero;
+ minCorner[0] = (min)((min)(cornerBL[0], cornerBR[0]), (min)(cornerTL[0], cornerTR[0]));
+ maxCorner[0] = (max)((max)(cornerBL[0], cornerBR[0]), (max)(cornerTL[0], cornerTR[0]));
+ minCorner[1] = (min)((min)(cornerBL[1], cornerBR[1]), (min)(cornerTL[1], cornerTR[1]));
+ maxCorner[1] = (max)((max)(cornerBL[1], cornerBR[1]), (max)(cornerTL[1], cornerTR[1]));
+
+ for (Index d = 2; d < dim; ++d)
+ VERIFY_IS_APPROX(c.sizes()[d], Scalar(2));
+
+ VERIFY_IS_APPROX((c.min)(), minCorner);
+ VERIFY_IS_APPROX((c.max)(), maxCorner);
+
+ VectorType minCornerValue = Ones * Scalar(-2);
+ VectorType maxCornerValue = Zero;
+ minCornerValue[0] = Scalar(Scalar(-sqrt(2*2 + 3*3)) * Scalar(cos(Scalar(atan(2.0/3.0)) - angle/2)));
+ minCornerValue[1] = Scalar(Scalar(-sqrt(1*1 + 2*2)) * Scalar(sin(Scalar(atan(2.0/1.0)) - angle/2)));
+ maxCornerValue[0] = Scalar(-sin(angle));
+ maxCornerValue[1] = Scalar(3 * cos(angle));
+ VERIFY_IS_APPROX((c.min)(), minCornerValue);
+ VERIFY_IS_APPROX((c.max)(), maxCornerValue);
+
+ // randomized test - translate and rotate the box and compare to a box made of transformed vertices
+ for (size_t i = 0; i < 10; ++i)
+ {
+ for (Index d = 0; d < dim; ++d)
+ {
+ minCorner[d] = internal::random<Scalar>(-10,10);
+ maxCorner[d] = minCorner[d] + internal::random<Scalar>(0, 10);
+ }
+
+ c = BoxType(minCorner, maxCorner);
+
+ CornersType corners = boxGetCorners(minCorner, maxCorner);
+
+ typename AffineTransform::LinearMatrixType rotation =
+ randomRotationMatrix<typename AffineTransform::LinearMatrixType>();
+
+ tf2.setIdentity();
+ tf2.rotate(rotation);
+ tf2.translate(VectorType::Random());
+
+ c.transform(tf2);
+ corners = tf2 * corners;
+
+ minCorner = corners.rowwise().minCoeff();
+ maxCorner = corners.rowwise().maxCoeff();
+
+ VERIFY_IS_APPROX((c.min)(), minCorner);
+ VERIFY_IS_APPROX((c.max)(), maxCorner);
+ }
+
+ // randomized test - transform the box with a random affine matrix and compare to a box made of transformed vertices
+ for (size_t i = 0; i < 10; ++i)
+ {
+ for (Index d = 0; d < dim; ++d)
+ {
+ minCorner[d] = internal::random<Scalar>(-10,10);
+ maxCorner[d] = minCorner[d] + internal::random<Scalar>(0, 10);
+ }
+
+ c = BoxType(minCorner, maxCorner);
+
+ CornersType corners = boxGetCorners(minCorner, maxCorner);
+
+ AffineTransform atf = AffineTransform::Identity();
+ atf.linearExt() = AffineTransform::LinearPart::Random();
+ atf.translate(VectorType::Random());
+
+ c.transform(atf);
+ corners = atf * corners;
+
+ minCorner = corners.rowwise().minCoeff();
+ maxCorner = corners.rowwise().maxCoeff();
+
+ VERIFY_IS_APPROX((c.min)(), minCorner);
+ VERIFY_IS_APPROX((c.max)(), maxCorner);
+ }
+}
+
+template<typename BoxType>
+void alignedboxCastTests(const BoxType& box)
+{
+ // casting
+ typedef typename BoxType::Scalar Scalar;
+ typedef Matrix<Scalar, BoxType::AmbientDimAtCompileTime, 1> VectorType;
+
+ const Index dim = box.dim();
+
+ VectorType p0 = VectorType::Random(dim);
+ VectorType p1 = VectorType::Random(dim);
+
+ BoxType b0(dim);
+
+ b0.extend(p0);
+ b0.extend(p1);
+
+ const int Dim = BoxType::AmbientDimAtCompileTime;
+ typedef typename GetDifferentType<Scalar>::type OtherScalar;
+ AlignedBox<OtherScalar,Dim> hp1f = b0.template cast<OtherScalar>();
+ VERIFY_IS_APPROX(hp1f.template cast<Scalar>(),b0);
+ AlignedBox<Scalar,Dim> hp1d = b0.template cast<Scalar>();
+ VERIFY_IS_APPROX(hp1d.template cast<Scalar>(),b0);
+}
+
+
+void specificTest1()
+{
+ Vector2f m; m << -1.0f, -2.0f;
+ Vector2f M; M << 1.0f, 5.0f;
+
+ typedef AlignedBox2f BoxType;
+ BoxType box( m, M );
+
+ Vector2f sides = M-m;
+ VERIFY_IS_APPROX(sides, box.sizes() );
+ VERIFY_IS_APPROX(sides[1], box.sizes()[1] );
+ VERIFY_IS_APPROX(sides[1], box.sizes().maxCoeff() );
+ VERIFY_IS_APPROX(sides[0], box.sizes().minCoeff() );
+
+ VERIFY_IS_APPROX( 14.0f, box.volume() );
+ VERIFY_IS_APPROX( 53.0f, box.diagonal().squaredNorm() );
+ VERIFY_IS_APPROX( std::sqrt( 53.0f ), box.diagonal().norm() );
+
+ VERIFY_IS_APPROX( m, box.corner( BoxType::BottomLeft ) );
+ VERIFY_IS_APPROX( M, box.corner( BoxType::TopRight ) );
+ Vector2f bottomRight; bottomRight << M[0], m[1];
+ Vector2f topLeft; topLeft << m[0], M[1];
+ VERIFY_IS_APPROX( bottomRight, box.corner( BoxType::BottomRight ) );
+ VERIFY_IS_APPROX( topLeft, box.corner( BoxType::TopLeft ) );
+}
+
+
+void specificTest2()
+{
+ Vector3i m; m << -1, -2, 0;
+ Vector3i M; M << 1, 5, 3;
+
+ typedef AlignedBox3i BoxType;
+ BoxType box( m, M );
+
+ Vector3i sides = M-m;
+ VERIFY_IS_APPROX(sides, box.sizes() );
+ VERIFY_IS_APPROX(sides[1], box.sizes()[1] );
+ VERIFY_IS_APPROX(sides[1], box.sizes().maxCoeff() );
+ VERIFY_IS_APPROX(sides[0], box.sizes().minCoeff() );
+
+ VERIFY_IS_APPROX( 42, box.volume() );
+ VERIFY_IS_APPROX( 62, box.diagonal().squaredNorm() );
+
+ VERIFY_IS_APPROX( m, box.corner( BoxType::BottomLeftFloor ) );
+ VERIFY_IS_APPROX( M, box.corner( BoxType::TopRightCeil ) );
+ Vector3i bottomRightFloor; bottomRightFloor << M[0], m[1], m[2];
+ Vector3i topLeftFloor; topLeftFloor << m[0], M[1], m[2];
+ VERIFY_IS_APPROX( bottomRightFloor, box.corner( BoxType::BottomRightFloor ) );
+ VERIFY_IS_APPROX( topLeftFloor, box.corner( BoxType::TopLeftFloor ) );
+}
+
+
+EIGEN_DECLARE_TEST(geo_alignedbox)
+{
+ for(int i = 0; i < g_repeat; i++)
+ {
+ CALL_SUBTEST_1( (alignedboxNonIntegralRotatable<AlignedBox2f, Rotation2Df>(AlignedBox2f(), &rotate2D)) );
+ CALL_SUBTEST_2( alignedboxCastTests(AlignedBox2f()) );
+
+ CALL_SUBTEST_3( (alignedboxNonIntegralRotatable<AlignedBox3f, AngleAxisf>(AlignedBox3f(), &rotate3DZAxis)) );
+ CALL_SUBTEST_4( alignedboxCastTests(AlignedBox3f()) );
+
+ CALL_SUBTEST_5( (alignedboxNonIntegralRotatable<AlignedBox4d, Matrix4d>(AlignedBox4d(), &rotate4DZWAxis)) );
+ CALL_SUBTEST_6( alignedboxCastTests(AlignedBox4d()) );
+
+ CALL_SUBTEST_7( alignedboxTranslatable(AlignedBox1d()) );
+ CALL_SUBTEST_8( alignedboxCastTests(AlignedBox1d()) );
+
+ CALL_SUBTEST_9( alignedboxTranslatable(AlignedBox1i()) );
+ CALL_SUBTEST_10( (alignedboxRotatable<AlignedBox2i, Matrix2i>(AlignedBox2i(), &rotate2DIntegral<int, Matrix2i>)) );
+ CALL_SUBTEST_11( (alignedboxRotatable<AlignedBox3i, Matrix3i>(AlignedBox3i(), &rotate3DZAxisIntegral<int, Matrix3i>)) );
+
+ CALL_SUBTEST_14( alignedbox(AlignedBox<double,Dynamic>(4)) );
+ }
+ CALL_SUBTEST_12( specificTest1() );
+ CALL_SUBTEST_13( specificTest2() );
+}
diff --git a/test/geo_eulerangles.cpp b/test/geo_eulerangles.cpp
new file mode 100644
index 0000000..bea2419
--- /dev/null
+++ b/test/geo_eulerangles.cpp
@@ -0,0 +1,112 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2012 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "main.h"
+#include <Eigen/Geometry>
+#include <Eigen/LU>
+#include <Eigen/SVD>
+
+
+template<typename Scalar>
+void verify_euler(const Matrix<Scalar,3,1>& ea, int i, int j, int k)
+{
+ typedef Matrix<Scalar,3,3> Matrix3;
+ typedef Matrix<Scalar,3,1> Vector3;
+ typedef AngleAxis<Scalar> AngleAxisx;
+ using std::abs;
+ Matrix3 m(AngleAxisx(ea[0], Vector3::Unit(i)) * AngleAxisx(ea[1], Vector3::Unit(j)) * AngleAxisx(ea[2], Vector3::Unit(k)));
+ Vector3 eabis = m.eulerAngles(i, j, k);
+ Matrix3 mbis(AngleAxisx(eabis[0], Vector3::Unit(i)) * AngleAxisx(eabis[1], Vector3::Unit(j)) * AngleAxisx(eabis[2], Vector3::Unit(k)));
+ VERIFY_IS_APPROX(m, mbis);
+ /* If I==K, and ea[1]==0, then there no unique solution. */
+ /* The remark apply in the case where I!=K, and |ea[1]| is close to pi/2. */
+ if((i!=k || !numext::is_exactly_zero(ea[1])) && (i == k || !internal::isApprox(abs(ea[1]), Scalar(EIGEN_PI / 2), test_precision<Scalar>())) )
+ VERIFY((ea-eabis).norm() <= test_precision<Scalar>());
+
+ // approx_or_less_than does not work for 0
+ VERIFY(0 < eabis[0] || test_isMuchSmallerThan(eabis[0], Scalar(1)));
+ VERIFY_IS_APPROX_OR_LESS_THAN(eabis[0], Scalar(EIGEN_PI));
+ VERIFY_IS_APPROX_OR_LESS_THAN(-Scalar(EIGEN_PI), eabis[1]);
+ VERIFY_IS_APPROX_OR_LESS_THAN(eabis[1], Scalar(EIGEN_PI));
+ VERIFY_IS_APPROX_OR_LESS_THAN(-Scalar(EIGEN_PI), eabis[2]);
+ VERIFY_IS_APPROX_OR_LESS_THAN(eabis[2], Scalar(EIGEN_PI));
+}
+
+template<typename Scalar> void check_all_var(const Matrix<Scalar,3,1>& ea)
+{
+ verify_euler(ea, 0,1,2);
+ verify_euler(ea, 0,1,0);
+ verify_euler(ea, 0,2,1);
+ verify_euler(ea, 0,2,0);
+
+ verify_euler(ea, 1,2,0);
+ verify_euler(ea, 1,2,1);
+ verify_euler(ea, 1,0,2);
+ verify_euler(ea, 1,0,1);
+
+ verify_euler(ea, 2,0,1);
+ verify_euler(ea, 2,0,2);
+ verify_euler(ea, 2,1,0);
+ verify_euler(ea, 2,1,2);
+}
+
+template<typename Scalar> void eulerangles()
+{
+ typedef Matrix<Scalar,3,3> Matrix3;
+ typedef Matrix<Scalar,3,1> Vector3;
+ typedef Array<Scalar,3,1> Array3;
+ typedef Quaternion<Scalar> Quaternionx;
+ typedef AngleAxis<Scalar> AngleAxisx;
+
+ Scalar a = internal::random<Scalar>(-Scalar(EIGEN_PI), Scalar(EIGEN_PI));
+ Quaternionx q1;
+ q1 = AngleAxisx(a, Vector3::Random().normalized());
+ Matrix3 m;
+ m = q1;
+
+ Vector3 ea = m.eulerAngles(0,1,2);
+ check_all_var(ea);
+ ea = m.eulerAngles(0,1,0);
+ check_all_var(ea);
+
+ // Check with purely random Quaternion:
+ q1.coeffs() = Quaternionx::Coefficients::Random().normalized();
+ m = q1;
+ ea = m.eulerAngles(0,1,2);
+ check_all_var(ea);
+ ea = m.eulerAngles(0,1,0);
+ check_all_var(ea);
+
+ // Check with random angles in range [0:pi]x[-pi:pi]x[-pi:pi].
+ ea = (Array3::Random() + Array3(1,0,0))*Scalar(EIGEN_PI)*Array3(0.5,1,1);
+ check_all_var(ea);
+
+ ea[2] = ea[0] = internal::random<Scalar>(0,Scalar(EIGEN_PI));
+ check_all_var(ea);
+
+ ea[0] = ea[1] = internal::random<Scalar>(0,Scalar(EIGEN_PI));
+ check_all_var(ea);
+
+ ea[1] = 0;
+ check_all_var(ea);
+
+ ea.head(2).setZero();
+ check_all_var(ea);
+
+ ea.setZero();
+ check_all_var(ea);
+}
+
+EIGEN_DECLARE_TEST(geo_eulerangles)
+{
+ for(int i = 0; i < g_repeat; i++) {
+ CALL_SUBTEST_1( eulerangles<float>() );
+ CALL_SUBTEST_2( eulerangles<double>() );
+ }
+}
diff --git a/test/geo_homogeneous.cpp b/test/geo_homogeneous.cpp
new file mode 100644
index 0000000..9aebe62
--- /dev/null
+++ b/test/geo_homogeneous.cpp
@@ -0,0 +1,125 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "main.h"
+#include <Eigen/Geometry>
+
+template<typename Scalar,int Size> void homogeneous(void)
+{
+ /* this test covers the following files:
+ Homogeneous.h
+ */
+
+ typedef Matrix<Scalar,Size,Size> MatrixType;
+ typedef Matrix<Scalar,Size,1, ColMajor> VectorType;
+
+ typedef Matrix<Scalar,Size+1,Size> HMatrixType;
+ typedef Matrix<Scalar,Size+1,1> HVectorType;
+
+ typedef Matrix<Scalar,Size,Size+1> T1MatrixType;
+ typedef Matrix<Scalar,Size+1,Size+1> T2MatrixType;
+ typedef Matrix<Scalar,Size+1,Size> T3MatrixType;
+
+ VectorType v0 = VectorType::Random(),
+ ones = VectorType::Ones();
+
+ HVectorType hv0 = HVectorType::Random();
+
+ MatrixType m0 = MatrixType::Random();
+
+ HMatrixType hm0 = HMatrixType::Random();
+
+ hv0 << v0, 1;
+ VERIFY_IS_APPROX(v0.homogeneous(), hv0);
+ VERIFY_IS_APPROX(v0, hv0.hnormalized());
+
+ VERIFY_IS_APPROX(v0.homogeneous().sum(), hv0.sum());
+ VERIFY_IS_APPROX(v0.homogeneous().minCoeff(), hv0.minCoeff());
+ VERIFY_IS_APPROX(v0.homogeneous().maxCoeff(), hv0.maxCoeff());
+
+ hm0 << m0, ones.transpose();
+ VERIFY_IS_APPROX(m0.colwise().homogeneous(), hm0);
+ VERIFY_IS_APPROX(m0, hm0.colwise().hnormalized());
+ hm0.row(Size-1).setRandom();
+ for(int j=0; j<Size; ++j)
+ m0.col(j) = hm0.col(j).head(Size) / hm0(Size,j);
+ VERIFY_IS_APPROX(m0, hm0.colwise().hnormalized());
+
+ T1MatrixType t1 = T1MatrixType::Random();
+ VERIFY_IS_APPROX(t1 * (v0.homogeneous().eval()), t1 * v0.homogeneous());
+ VERIFY_IS_APPROX(t1 * (m0.colwise().homogeneous().eval()), t1 * m0.colwise().homogeneous());
+
+ T2MatrixType t2 = T2MatrixType::Random();
+ VERIFY_IS_APPROX(t2 * (v0.homogeneous().eval()), t2 * v0.homogeneous());
+ VERIFY_IS_APPROX(t2 * (m0.colwise().homogeneous().eval()), t2 * m0.colwise().homogeneous());
+ VERIFY_IS_APPROX(t2 * (v0.homogeneous().asDiagonal()), t2 * hv0.asDiagonal());
+ VERIFY_IS_APPROX((v0.homogeneous().asDiagonal()) * t2, hv0.asDiagonal() * t2);
+
+ VERIFY_IS_APPROX((v0.transpose().rowwise().homogeneous().eval()) * t2,
+ v0.transpose().rowwise().homogeneous() * t2);
+ VERIFY_IS_APPROX((m0.transpose().rowwise().homogeneous().eval()) * t2,
+ m0.transpose().rowwise().homogeneous() * t2);
+
+ T3MatrixType t3 = T3MatrixType::Random();
+ VERIFY_IS_APPROX((v0.transpose().rowwise().homogeneous().eval()) * t3,
+ v0.transpose().rowwise().homogeneous() * t3);
+ VERIFY_IS_APPROX((m0.transpose().rowwise().homogeneous().eval()) * t3,
+ m0.transpose().rowwise().homogeneous() * t3);
+
+ // test product with a Transform object
+ Transform<Scalar, Size, Affine> aff;
+ Transform<Scalar, Size, AffineCompact> caff;
+ Transform<Scalar, Size, Projective> proj;
+ Matrix<Scalar, Size, Dynamic> pts;
+ Matrix<Scalar, Size+1, Dynamic> pts1, pts2;
+
+ aff.affine().setRandom();
+ proj = caff = aff;
+ pts.setRandom(Size,internal::random<int>(1,20));
+
+ pts1 = pts.colwise().homogeneous();
+ VERIFY_IS_APPROX(aff * pts.colwise().homogeneous(), (aff * pts1).colwise().hnormalized());
+ VERIFY_IS_APPROX(caff * pts.colwise().homogeneous(), (caff * pts1).colwise().hnormalized());
+ VERIFY_IS_APPROX(proj * pts.colwise().homogeneous(), (proj * pts1));
+
+ VERIFY_IS_APPROX((aff * pts1).colwise().hnormalized(), aff * pts);
+ VERIFY_IS_APPROX((caff * pts1).colwise().hnormalized(), caff * pts);
+
+ pts2 = pts1;
+ pts2.row(Size).setRandom();
+ VERIFY_IS_APPROX((aff * pts2).colwise().hnormalized(), aff * pts2.colwise().hnormalized());
+ VERIFY_IS_APPROX((caff * pts2).colwise().hnormalized(), caff * pts2.colwise().hnormalized());
+ VERIFY_IS_APPROX((proj * pts2).colwise().hnormalized(), (proj * pts2.colwise().hnormalized().colwise().homogeneous()).colwise().hnormalized());
+
+ // Test combination of homogeneous
+
+ VERIFY_IS_APPROX( (t2 * v0.homogeneous()).hnormalized(),
+ (t2.template topLeftCorner<Size,Size>() * v0 + t2.template topRightCorner<Size,1>())
+ / ((t2.template bottomLeftCorner<1,Size>()*v0).value() + t2(Size,Size)) );
+
+ VERIFY_IS_APPROX( (t2 * pts.colwise().homogeneous()).colwise().hnormalized(),
+ (Matrix<Scalar, Size+1, Dynamic>(t2 * pts1).colwise().hnormalized()) );
+
+ VERIFY_IS_APPROX( (t2 .lazyProduct( v0.homogeneous() )).hnormalized(), (t2 * v0.homogeneous()).hnormalized() );
+ VERIFY_IS_APPROX( (t2 .lazyProduct ( pts.colwise().homogeneous() )).colwise().hnormalized(), (t2 * pts1).colwise().hnormalized() );
+
+ VERIFY_IS_APPROX( (v0.transpose().homogeneous() .lazyProduct( t2 )).hnormalized(), (v0.transpose().homogeneous()*t2).hnormalized() );
+ VERIFY_IS_APPROX( (pts.transpose().rowwise().homogeneous() .lazyProduct( t2 )).rowwise().hnormalized(), (pts1.transpose()*t2).rowwise().hnormalized() );
+
+ VERIFY_IS_APPROX( (t2.template triangularView<Lower>() * v0.homogeneous()).eval(), (t2.template triangularView<Lower>()*hv0) );
+}
+
+EIGEN_DECLARE_TEST(geo_homogeneous)
+{
+ for(int i = 0; i < g_repeat; i++) {
+ CALL_SUBTEST_1(( homogeneous<float,1>() ));
+ CALL_SUBTEST_2(( homogeneous<double,3>() ));
+ CALL_SUBTEST_3(( homogeneous<double,8>() ));
+ }
+}
diff --git a/test/geo_hyperplane.cpp b/test/geo_hyperplane.cpp
new file mode 100644
index 0000000..44b2f2a
--- /dev/null
+++ b/test/geo_hyperplane.cpp
@@ -0,0 +1,192 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "main.h"
+#include <Eigen/Geometry>
+#include <Eigen/LU>
+#include <Eigen/QR>
+
+template<typename HyperplaneType> void hyperplane(const HyperplaneType& _plane)
+{
+ /* this test covers the following files:
+ Hyperplane.h
+ */
+ using std::abs;
+ const Index dim = _plane.dim();
+ enum { Options = HyperplaneType::Options };
+ typedef typename HyperplaneType::Scalar Scalar;
+ typedef typename HyperplaneType::RealScalar RealScalar;
+ typedef Matrix<Scalar, HyperplaneType::AmbientDimAtCompileTime, 1> VectorType;
+ typedef Matrix<Scalar, HyperplaneType::AmbientDimAtCompileTime,
+ HyperplaneType::AmbientDimAtCompileTime> MatrixType;
+
+ VectorType p0 = VectorType::Random(dim);
+ VectorType p1 = VectorType::Random(dim);
+
+ VectorType n0 = VectorType::Random(dim).normalized();
+ VectorType n1 = VectorType::Random(dim).normalized();
+
+ HyperplaneType pl0(n0, p0);
+ HyperplaneType pl1(n1, p1);
+ HyperplaneType pl2 = pl1;
+
+ Scalar s0 = internal::random<Scalar>();
+ Scalar s1 = internal::random<Scalar>();
+
+ VERIFY_IS_APPROX( n1.dot(n1), Scalar(1) );
+
+ VERIFY_IS_MUCH_SMALLER_THAN( pl0.absDistance(p0), Scalar(1) );
+ if(numext::abs2(s0)>RealScalar(1e-6))
+ VERIFY_IS_APPROX( pl1.signedDistance(p1 + n1 * s0), s0);
+ else
+ VERIFY_IS_MUCH_SMALLER_THAN( abs(pl1.signedDistance(p1 + n1 * s0) - s0), Scalar(1) );
+ VERIFY_IS_MUCH_SMALLER_THAN( pl1.signedDistance(pl1.projection(p0)), Scalar(1) );
+ VERIFY_IS_MUCH_SMALLER_THAN( pl1.absDistance(p1 + pl1.normal().unitOrthogonal() * s1), Scalar(1) );
+
+ // transform
+ if (!NumTraits<Scalar>::IsComplex)
+ {
+ MatrixType rot = MatrixType::Random(dim,dim).householderQr().householderQ();
+ DiagonalMatrix<Scalar,HyperplaneType::AmbientDimAtCompileTime> scaling(VectorType::Random());
+ Translation<Scalar,HyperplaneType::AmbientDimAtCompileTime> translation(VectorType::Random());
+
+ while(scaling.diagonal().cwiseAbs().minCoeff()<RealScalar(1e-4)) scaling.diagonal() = VectorType::Random();
+
+ pl2 = pl1;
+ VERIFY_IS_MUCH_SMALLER_THAN( pl2.transform(rot).absDistance(rot * p1), Scalar(1) );
+ pl2 = pl1;
+ VERIFY_IS_MUCH_SMALLER_THAN( pl2.transform(rot,Isometry).absDistance(rot * p1), Scalar(1) );
+ pl2 = pl1;
+ VERIFY_IS_MUCH_SMALLER_THAN( pl2.transform(rot*scaling).absDistance((rot*scaling) * p1), Scalar(1) );
+ VERIFY_IS_APPROX( pl2.normal().norm(), RealScalar(1) );
+ pl2 = pl1;
+ VERIFY_IS_MUCH_SMALLER_THAN( pl2.transform(rot*scaling*translation)
+ .absDistance((rot*scaling*translation) * p1), Scalar(1) );
+ VERIFY_IS_APPROX( pl2.normal().norm(), RealScalar(1) );
+ pl2 = pl1;
+ VERIFY_IS_MUCH_SMALLER_THAN( pl2.transform(rot*translation,Isometry)
+ .absDistance((rot*translation) * p1), Scalar(1) );
+ VERIFY_IS_APPROX( pl2.normal().norm(), RealScalar(1) );
+ }
+
+ // casting
+ const int Dim = HyperplaneType::AmbientDimAtCompileTime;
+ typedef typename GetDifferentType<Scalar>::type OtherScalar;
+ Hyperplane<OtherScalar,Dim,Options> hp1f = pl1.template cast<OtherScalar>();
+ VERIFY_IS_APPROX(hp1f.template cast<Scalar>(),pl1);
+ Hyperplane<Scalar,Dim,Options> hp1d = pl1.template cast<Scalar>();
+ VERIFY_IS_APPROX(hp1d.template cast<Scalar>(),pl1);
+}
+
+template<typename Scalar> void lines()
+{
+ using std::abs;
+ typedef Hyperplane<Scalar, 2> HLine;
+ typedef ParametrizedLine<Scalar, 2> PLine;
+ typedef Matrix<Scalar,2,1> Vector;
+ typedef Matrix<Scalar,3,1> CoeffsType;
+
+ for(int i = 0; i < 10; i++)
+ {
+ Vector center = Vector::Random();
+ Vector u = Vector::Random();
+ Vector v = Vector::Random();
+ Scalar a = internal::random<Scalar>();
+ while (abs(a-1) < Scalar(1e-4)) a = internal::random<Scalar>();
+ while (u.norm() < Scalar(1e-4)) u = Vector::Random();
+ while (v.norm() < Scalar(1e-4)) v = Vector::Random();
+
+ HLine line_u = HLine::Through(center + u, center + a*u);
+ HLine line_v = HLine::Through(center + v, center + a*v);
+
+ // the line equations should be normalized so that a^2+b^2=1
+ VERIFY_IS_APPROX(line_u.normal().norm(), Scalar(1));
+ VERIFY_IS_APPROX(line_v.normal().norm(), Scalar(1));
+
+ Vector result = line_u.intersection(line_v);
+
+ // the lines should intersect at the point we called "center"
+ if(abs(a-1) > Scalar(1e-2) && abs(v.normalized().dot(u.normalized()))<Scalar(0.9))
+ VERIFY_IS_APPROX(result, center);
+
+ // check conversions between two types of lines
+ PLine pl(line_u); // gcc 3.3 will crash if we don't name this variable.
+ HLine line_u2(pl);
+ CoeffsType converted_coeffs = line_u2.coeffs();
+ if(line_u2.normal().dot(line_u.normal())<Scalar(0))
+ converted_coeffs = -line_u2.coeffs();
+ VERIFY(line_u.coeffs().isApprox(converted_coeffs));
+ }
+}
+
+template<typename Scalar> void planes()
+{
+ using std::abs;
+ typedef Hyperplane<Scalar, 3> Plane;
+ typedef Matrix<Scalar,3,1> Vector;
+
+ for(int i = 0; i < 10; i++)
+ {
+ Vector v0 = Vector::Random();
+ Vector v1(v0), v2(v0);
+ if(internal::random<double>(0,1)>0.25)
+ v1 += Vector::Random();
+ if(internal::random<double>(0,1)>0.25)
+ v2 += v1 * std::pow(internal::random<Scalar>(0,1),internal::random<int>(1,16));
+ if(internal::random<double>(0,1)>0.25)
+ v2 += Vector::Random() * std::pow(internal::random<Scalar>(0,1),internal::random<int>(1,16));
+
+ Plane p0 = Plane::Through(v0, v1, v2);
+
+ VERIFY_IS_APPROX(p0.normal().norm(), Scalar(1));
+ VERIFY_IS_MUCH_SMALLER_THAN(p0.absDistance(v0), Scalar(1));
+ VERIFY_IS_MUCH_SMALLER_THAN(p0.absDistance(v1), Scalar(1));
+ VERIFY_IS_MUCH_SMALLER_THAN(p0.absDistance(v2), Scalar(1));
+ }
+}
+
+template<typename Scalar> void hyperplane_alignment()
+{
+ typedef Hyperplane<Scalar,3,AutoAlign> Plane3a;
+ typedef Hyperplane<Scalar,3,DontAlign> Plane3u;
+
+ EIGEN_ALIGN_MAX Scalar array1[4];
+ EIGEN_ALIGN_MAX Scalar array2[4];
+ EIGEN_ALIGN_MAX Scalar array3[4+1];
+ Scalar* array3u = array3+1;
+
+ Plane3a *p1 = ::new(reinterpret_cast<void*>(array1)) Plane3a;
+ Plane3u *p2 = ::new(reinterpret_cast<void*>(array2)) Plane3u;
+ Plane3u *p3 = ::new(reinterpret_cast<void*>(array3u)) Plane3u;
+
+ p1->coeffs().setRandom();
+ *p2 = *p1;
+ *p3 = *p1;
+
+ VERIFY_IS_APPROX(p1->coeffs(), p2->coeffs());
+ VERIFY_IS_APPROX(p1->coeffs(), p3->coeffs());
+}
+
+
+EIGEN_DECLARE_TEST(geo_hyperplane)
+{
+ for(int i = 0; i < g_repeat; i++) {
+ CALL_SUBTEST_1( hyperplane(Hyperplane<float,2>()) );
+ CALL_SUBTEST_2( hyperplane(Hyperplane<float,3>()) );
+ CALL_SUBTEST_2( hyperplane(Hyperplane<float,3,DontAlign>()) );
+ CALL_SUBTEST_2( hyperplane_alignment<float>() );
+ CALL_SUBTEST_3( hyperplane(Hyperplane<double,4>()) );
+ CALL_SUBTEST_4( hyperplane(Hyperplane<std::complex<double>,5>()) );
+ CALL_SUBTEST_1( lines<float>() );
+ CALL_SUBTEST_3( lines<double>() );
+ CALL_SUBTEST_2( planes<float>() );
+ CALL_SUBTEST_5( planes<double>() );
+ }
+}
diff --git a/test/geo_orthomethods.cpp b/test/geo_orthomethods.cpp
new file mode 100644
index 0000000..5f7ddb9
--- /dev/null
+++ b/test/geo_orthomethods.cpp
@@ -0,0 +1,134 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "main.h"
+#include <Eigen/Geometry>
+#include <Eigen/LU>
+#include <Eigen/SVD>
+
+/* this test covers the following files:
+ Geometry/OrthoMethods.h
+*/
+
+template<typename Scalar> void orthomethods_3()
+{
+ typedef typename NumTraits<Scalar>::Real RealScalar;
+ typedef Matrix<Scalar,3,3> Matrix3;
+ typedef Matrix<Scalar,3,1> Vector3;
+
+ typedef Matrix<Scalar,4,1> Vector4;
+
+ Vector3 v0 = Vector3::Random(),
+ v1 = Vector3::Random(),
+ v2 = Vector3::Random();
+
+ // cross product
+ VERIFY_IS_MUCH_SMALLER_THAN(v1.cross(v2).dot(v1), Scalar(1));
+ VERIFY_IS_MUCH_SMALLER_THAN(v1.dot(v1.cross(v2)), Scalar(1));
+ VERIFY_IS_MUCH_SMALLER_THAN(v1.cross(v2).dot(v2), Scalar(1));
+ VERIFY_IS_MUCH_SMALLER_THAN(v2.dot(v1.cross(v2)), Scalar(1));
+ VERIFY_IS_MUCH_SMALLER_THAN(v1.cross(Vector3::Random()).dot(v1), Scalar(1));
+ Matrix3 mat3;
+ mat3 << v0.normalized(),
+ (v0.cross(v1)).normalized(),
+ (v0.cross(v1).cross(v0)).normalized();
+ VERIFY(mat3.isUnitary());
+
+ mat3.setRandom();
+ VERIFY_IS_APPROX(v0.cross(mat3*v1), -(mat3*v1).cross(v0));
+ VERIFY_IS_APPROX(v0.cross(mat3.lazyProduct(v1)), -(mat3.lazyProduct(v1)).cross(v0));
+
+ // colwise/rowwise cross product
+ mat3.setRandom();
+ Vector3 vec3 = Vector3::Random();
+ Matrix3 mcross;
+ int i = internal::random<int>(0,2);
+ mcross = mat3.colwise().cross(vec3);
+ VERIFY_IS_APPROX(mcross.col(i), mat3.col(i).cross(vec3));
+
+ VERIFY_IS_MUCH_SMALLER_THAN((mat3.adjoint() * mat3.colwise().cross(vec3)).diagonal().cwiseAbs().sum(), Scalar(1));
+ VERIFY_IS_MUCH_SMALLER_THAN((mat3.adjoint() * mat3.colwise().cross(Vector3::Random())).diagonal().cwiseAbs().sum(), Scalar(1));
+
+ VERIFY_IS_MUCH_SMALLER_THAN((vec3.adjoint() * mat3.colwise().cross(vec3)).cwiseAbs().sum(), Scalar(1));
+ VERIFY_IS_MUCH_SMALLER_THAN((vec3.adjoint() * Matrix3::Random().colwise().cross(vec3)).cwiseAbs().sum(), Scalar(1));
+
+ mcross = mat3.rowwise().cross(vec3);
+ VERIFY_IS_APPROX(mcross.row(i), mat3.row(i).cross(vec3));
+
+ // cross3
+ Vector4 v40 = Vector4::Random(),
+ v41 = Vector4::Random(),
+ v42 = Vector4::Random();
+ v40.w() = v41.w() = v42.w() = 0;
+ v42.template head<3>() = v40.template head<3>().cross(v41.template head<3>());
+ VERIFY_IS_APPROX(v40.cross3(v41), v42);
+ VERIFY_IS_MUCH_SMALLER_THAN(v40.cross3(Vector4::Random()).dot(v40), Scalar(1));
+
+ // check mixed product
+ typedef Matrix<RealScalar, 3, 1> RealVector3;
+ RealVector3 rv1 = RealVector3::Random();
+ v2 = rv1.template cast<Scalar>();
+ VERIFY_IS_APPROX(v1.cross(v2), v1.cross(rv1));
+ VERIFY_IS_APPROX(v2.cross(v1), rv1.cross(v1));
+}
+
+template<typename Scalar, int Size> void orthomethods(int size=Size)
+{
+ typedef typename NumTraits<Scalar>::Real RealScalar;
+ typedef Matrix<Scalar,Size,1> VectorType;
+ typedef Matrix<Scalar,3,Size> Matrix3N;
+ typedef Matrix<Scalar,Size,3> MatrixN3;
+ typedef Matrix<Scalar,3,1> Vector3;
+
+ VectorType v0 = VectorType::Random(size);
+
+ // unitOrthogonal
+ VERIFY_IS_MUCH_SMALLER_THAN(v0.unitOrthogonal().dot(v0), Scalar(1));
+ VERIFY_IS_APPROX(v0.unitOrthogonal().norm(), RealScalar(1));
+
+ if (size>=3)
+ {
+ v0.template head<2>().setZero();
+ v0.tail(size-2).setRandom();
+
+ VERIFY_IS_MUCH_SMALLER_THAN(v0.unitOrthogonal().dot(v0), Scalar(1));
+ VERIFY_IS_APPROX(v0.unitOrthogonal().norm(), RealScalar(1));
+ }
+
+ // colwise/rowwise cross product
+ Vector3 vec3 = Vector3::Random();
+ int i = internal::random<int>(0,size-1);
+
+ Matrix3N mat3N(3,size), mcross3N(3,size);
+ mat3N.setRandom();
+ mcross3N = mat3N.colwise().cross(vec3);
+ VERIFY_IS_APPROX(mcross3N.col(i), mat3N.col(i).cross(vec3));
+
+ MatrixN3 matN3(size,3), mcrossN3(size,3);
+ matN3.setRandom();
+ mcrossN3 = matN3.rowwise().cross(vec3);
+ VERIFY_IS_APPROX(mcrossN3.row(i), matN3.row(i).cross(vec3));
+}
+
+EIGEN_DECLARE_TEST(geo_orthomethods)
+{
+ for(int i = 0; i < g_repeat; i++) {
+ CALL_SUBTEST_1( orthomethods_3<float>() );
+ CALL_SUBTEST_2( orthomethods_3<double>() );
+ CALL_SUBTEST_4( orthomethods_3<std::complex<double> >() );
+ CALL_SUBTEST_1( (orthomethods<float,2>()) );
+ CALL_SUBTEST_2( (orthomethods<double,2>()) );
+ CALL_SUBTEST_1( (orthomethods<float,3>()) );
+ CALL_SUBTEST_2( (orthomethods<double,3>()) );
+ CALL_SUBTEST_3( (orthomethods<float,7>()) );
+ CALL_SUBTEST_4( (orthomethods<std::complex<double>,8>()) );
+ CALL_SUBTEST_5( (orthomethods<float,Dynamic>(36)) );
+ CALL_SUBTEST_6( (orthomethods<double,Dynamic>(35)) );
+ }
+}
diff --git a/test/geo_parametrizedline.cpp b/test/geo_parametrizedline.cpp
new file mode 100644
index 0000000..e4b194a
--- /dev/null
+++ b/test/geo_parametrizedline.cpp
@@ -0,0 +1,125 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "main.h"
+#include <Eigen/Geometry>
+#include <Eigen/LU>
+#include <Eigen/QR>
+
+template<typename LineType> void parametrizedline(const LineType& _line)
+{
+ /* this test covers the following files:
+ ParametrizedLine.h
+ */
+ using std::abs;
+ const Index dim = _line.dim();
+ typedef typename LineType::Scalar Scalar;
+ typedef typename NumTraits<Scalar>::Real RealScalar;
+ typedef Matrix<Scalar, LineType::AmbientDimAtCompileTime, 1> VectorType;
+ typedef Hyperplane<Scalar,LineType::AmbientDimAtCompileTime> HyperplaneType;
+ typedef Matrix<Scalar, HyperplaneType::AmbientDimAtCompileTime,
+ HyperplaneType::AmbientDimAtCompileTime> MatrixType;
+
+ VectorType p0 = VectorType::Random(dim);
+ VectorType p1 = VectorType::Random(dim);
+
+ VectorType d0 = VectorType::Random(dim).normalized();
+
+ LineType l0(p0, d0);
+
+ Scalar s0 = internal::random<Scalar>();
+ Scalar s1 = abs(internal::random<Scalar>());
+
+ VERIFY_IS_MUCH_SMALLER_THAN( l0.distance(p0), RealScalar(1) );
+ VERIFY_IS_MUCH_SMALLER_THAN( l0.distance(p0+s0*d0), RealScalar(1) );
+ VERIFY_IS_APPROX( (l0.projection(p1)-p1).norm(), l0.distance(p1) );
+ VERIFY_IS_MUCH_SMALLER_THAN( l0.distance(l0.projection(p1)), RealScalar(1) );
+ VERIFY_IS_APPROX( Scalar(l0.distance((p0+s0*d0) + d0.unitOrthogonal() * s1)), s1 );
+
+ // casting
+ const int Dim = LineType::AmbientDimAtCompileTime;
+ typedef typename GetDifferentType<Scalar>::type OtherScalar;
+ ParametrizedLine<OtherScalar,Dim> hp1f = l0.template cast<OtherScalar>();
+ VERIFY_IS_APPROX(hp1f.template cast<Scalar>(),l0);
+ ParametrizedLine<Scalar,Dim> hp1d = l0.template cast<Scalar>();
+ VERIFY_IS_APPROX(hp1d.template cast<Scalar>(),l0);
+
+ // intersections
+ VectorType p2 = VectorType::Random(dim);
+ VectorType n2 = VectorType::Random(dim).normalized();
+ HyperplaneType hp(p2,n2);
+ Scalar t = l0.intersectionParameter(hp);
+ VectorType pi = l0.pointAt(t);
+ VERIFY_IS_MUCH_SMALLER_THAN(hp.signedDistance(pi), RealScalar(1));
+ VERIFY_IS_MUCH_SMALLER_THAN(l0.distance(pi), RealScalar(1));
+ VERIFY_IS_APPROX(l0.intersectionPoint(hp), pi);
+
+ // transform
+ if (!NumTraits<Scalar>::IsComplex)
+ {
+ MatrixType rot = MatrixType::Random(dim,dim).householderQr().householderQ();
+ DiagonalMatrix<Scalar,LineType::AmbientDimAtCompileTime> scaling(VectorType::Random());
+ Translation<Scalar,LineType::AmbientDimAtCompileTime> translation(VectorType::Random());
+
+ while(scaling.diagonal().cwiseAbs().minCoeff()<RealScalar(1e-4)) scaling.diagonal() = VectorType::Random();
+
+ LineType l1 = l0;
+ VectorType p3 = l0.pointAt(Scalar(1));
+ VERIFY_IS_MUCH_SMALLER_THAN( l1.transform(rot).distance(rot * p3), Scalar(1) );
+ l1 = l0;
+ VERIFY_IS_MUCH_SMALLER_THAN( l1.transform(rot,Isometry).distance(rot * p3), Scalar(1) );
+ l1 = l0;
+ VERIFY_IS_MUCH_SMALLER_THAN( l1.transform(rot*scaling).distance((rot*scaling) * p3), Scalar(1) );
+ l1 = l0;
+ VERIFY_IS_MUCH_SMALLER_THAN( l1.transform(rot*scaling*translation)
+ .distance((rot*scaling*translation) * p3), Scalar(1) );
+ l1 = l0;
+ VERIFY_IS_MUCH_SMALLER_THAN( l1.transform(rot*translation,Isometry)
+ .distance((rot*translation) * p3), Scalar(1) );
+ }
+
+}
+
+template<typename Scalar> void parametrizedline_alignment()
+{
+ typedef ParametrizedLine<Scalar,4,AutoAlign> Line4a;
+ typedef ParametrizedLine<Scalar,4,DontAlign> Line4u;
+
+ EIGEN_ALIGN_MAX Scalar array1[16];
+ EIGEN_ALIGN_MAX Scalar array2[16];
+ EIGEN_ALIGN_MAX Scalar array3[16+1];
+ Scalar* array3u = array3+1;
+
+ Line4a *p1 = ::new(reinterpret_cast<void*>(array1)) Line4a;
+ Line4u *p2 = ::new(reinterpret_cast<void*>(array2)) Line4u;
+ Line4u *p3 = ::new(reinterpret_cast<void*>(array3u)) Line4u;
+
+ p1->origin().setRandom();
+ p1->direction().setRandom();
+ *p2 = *p1;
+ *p3 = *p1;
+
+ VERIFY_IS_APPROX(p1->origin(), p2->origin());
+ VERIFY_IS_APPROX(p1->origin(), p3->origin());
+ VERIFY_IS_APPROX(p1->direction(), p2->direction());
+ VERIFY_IS_APPROX(p1->direction(), p3->direction());
+}
+
+EIGEN_DECLARE_TEST(geo_parametrizedline)
+{
+ for(int i = 0; i < g_repeat; i++) {
+ CALL_SUBTEST_1( parametrizedline(ParametrizedLine<float,2>()) );
+ CALL_SUBTEST_2( parametrizedline(ParametrizedLine<float,3>()) );
+ CALL_SUBTEST_2( parametrizedline_alignment<float>() );
+ CALL_SUBTEST_3( parametrizedline(ParametrizedLine<double,4>()) );
+ CALL_SUBTEST_3( parametrizedline_alignment<double>() );
+ CALL_SUBTEST_4( parametrizedline(ParametrizedLine<std::complex<double>,5>()) );
+ }
+}
diff --git a/test/geo_quaternion.cpp b/test/geo_quaternion.cpp
new file mode 100644
index 0000000..a821cf2
--- /dev/null
+++ b/test/geo_quaternion.cpp
@@ -0,0 +1,328 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2009 Mathieu Gautier <mathieu.gautier@cea.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "main.h"
+#include <Eigen/Geometry>
+#include <Eigen/LU>
+#include <Eigen/SVD>
+#include "AnnoyingScalar.h"
+
+template<typename T> T bounded_acos(T v)
+{
+ using std::acos;
+ using std::min;
+ using std::max;
+ return acos((max)(T(-1),(min)(v,T(1))));
+}
+
+template<typename QuatType> void check_slerp(const QuatType& q0, const QuatType& q1)
+{
+ using std::abs;
+ typedef typename QuatType::Scalar Scalar;
+ typedef AngleAxis<Scalar> AA;
+
+ Scalar largeEps = test_precision<Scalar>();
+
+ Scalar theta_tot = AA(q1*q0.inverse()).angle();
+ if(theta_tot>Scalar(EIGEN_PI))
+ theta_tot = Scalar(2.)*Scalar(EIGEN_PI)-theta_tot;
+ for(Scalar t=0; t<=Scalar(1.001); t+=Scalar(0.1))
+ {
+ QuatType q = q0.slerp(t,q1);
+ Scalar theta = AA(q*q0.inverse()).angle();
+ VERIFY(abs(q.norm() - 1) < largeEps);
+ if(theta_tot==0) VERIFY(theta_tot==0);
+ else VERIFY(abs(theta - t * theta_tot) < largeEps);
+ }
+}
+
+template<typename Scalar, int Options> void quaternion(void)
+{
+ /* this test covers the following files:
+ Quaternion.h
+ */
+ using std::abs;
+ typedef Matrix<Scalar,3,1> Vector3;
+ typedef Matrix<Scalar,3,3> Matrix3;
+ typedef Quaternion<Scalar,Options> Quaternionx;
+ typedef AngleAxis<Scalar> AngleAxisx;
+
+ Scalar largeEps = test_precision<Scalar>();
+ if (internal::is_same<Scalar,float>::value)
+ largeEps = Scalar(1e-3);
+
+ Scalar eps = internal::random<Scalar>() * Scalar(1e-2);
+
+ Vector3 v0 = Vector3::Random(),
+ v1 = Vector3::Random(),
+ v2 = Vector3::Random(),
+ v3 = Vector3::Random();
+
+ Scalar a = internal::random<Scalar>(-Scalar(EIGEN_PI), Scalar(EIGEN_PI)),
+ b = internal::random<Scalar>(-Scalar(EIGEN_PI), Scalar(EIGEN_PI));
+
+ // Quaternion: Identity(), setIdentity();
+ Quaternionx q1, q2;
+ q2.setIdentity();
+ VERIFY_IS_APPROX(Quaternionx(Quaternionx::Identity()).coeffs(), q2.coeffs());
+ q1.coeffs().setRandom();
+ VERIFY_IS_APPROX(q1.coeffs(), (q1*q2).coeffs());
+
+#ifndef EIGEN_NO_IO
+ // Printing
+ std::ostringstream ss;
+ ss << q2;
+ VERIFY(ss.str() == "0i + 0j + 0k + 1");
+#endif
+
+ // concatenation
+ q1 *= q2;
+
+ q1 = AngleAxisx(a, v0.normalized());
+ q2 = AngleAxisx(a, v1.normalized());
+
+ // angular distance
+ Scalar refangle = abs(AngleAxisx(q1.inverse()*q2).angle());
+ if (refangle>Scalar(EIGEN_PI))
+ refangle = Scalar(2)*Scalar(EIGEN_PI) - refangle;
+
+ if((q1.coeffs()-q2.coeffs()).norm() > Scalar(10)*largeEps)
+ {
+ VERIFY_IS_MUCH_SMALLER_THAN(abs(q1.angularDistance(q2) - refangle), Scalar(1));
+ }
+
+ // rotation matrix conversion
+ VERIFY_IS_APPROX(q1 * v2, q1.toRotationMatrix() * v2);
+ VERIFY_IS_APPROX(q1 * q2 * v2,
+ q1.toRotationMatrix() * q2.toRotationMatrix() * v2);
+
+ VERIFY( (q2*q1).isApprox(q1*q2, largeEps)
+ || !(q2 * q1 * v2).isApprox(q1.toRotationMatrix() * q2.toRotationMatrix() * v2));
+
+ q2 = q1.toRotationMatrix();
+ VERIFY_IS_APPROX(q1*v1,q2*v1);
+
+ Matrix3 rot1(q1);
+ VERIFY_IS_APPROX(q1*v1,rot1*v1);
+ Quaternionx q3(rot1.transpose()*rot1);
+ VERIFY_IS_APPROX(q3*v1,v1);
+
+
+ // angle-axis conversion
+ AngleAxisx aa = AngleAxisx(q1);
+ VERIFY_IS_APPROX(q1 * v1, Quaternionx(aa) * v1);
+
+ // Do not execute the test if the rotation angle is almost zero, or
+ // the rotation axis and v1 are almost parallel.
+ if (abs(aa.angle()) > Scalar(5)*test_precision<Scalar>()
+ && (aa.axis() - v1.normalized()).norm() < Scalar(1.99)
+ && (aa.axis() + v1.normalized()).norm() < Scalar(1.99))
+ {
+ VERIFY_IS_NOT_APPROX(q1 * v1, Quaternionx(AngleAxisx(aa.angle()*2,aa.axis())) * v1);
+ }
+
+ // from two vector creation
+ VERIFY_IS_APPROX( v2.normalized(),(q2.setFromTwoVectors(v1, v2)*v1).normalized());
+ VERIFY_IS_APPROX( v1.normalized(),(q2.setFromTwoVectors(v1, v1)*v1).normalized());
+ VERIFY_IS_APPROX(-v1.normalized(),(q2.setFromTwoVectors(v1,-v1)*v1).normalized());
+ if (internal::is_same<Scalar,double>::value)
+ {
+ v3 = (v1.array()+eps).matrix();
+ VERIFY_IS_APPROX( v3.normalized(),(q2.setFromTwoVectors(v1, v3)*v1).normalized());
+ VERIFY_IS_APPROX(-v3.normalized(),(q2.setFromTwoVectors(v1,-v3)*v1).normalized());
+ }
+
+ // from two vector creation static function
+ VERIFY_IS_APPROX( v2.normalized(),(Quaternionx::FromTwoVectors(v1, v2)*v1).normalized());
+ VERIFY_IS_APPROX( v1.normalized(),(Quaternionx::FromTwoVectors(v1, v1)*v1).normalized());
+ VERIFY_IS_APPROX(-v1.normalized(),(Quaternionx::FromTwoVectors(v1,-v1)*v1).normalized());
+ if (internal::is_same<Scalar,double>::value)
+ {
+ v3 = (v1.array()+eps).matrix();
+ VERIFY_IS_APPROX( v3.normalized(),(Quaternionx::FromTwoVectors(v1, v3)*v1).normalized());
+ VERIFY_IS_APPROX(-v3.normalized(),(Quaternionx::FromTwoVectors(v1,-v3)*v1).normalized());
+ }
+
+ // inverse and conjugate
+ VERIFY_IS_APPROX(q1 * (q1.inverse() * v1), v1);
+ VERIFY_IS_APPROX(q1 * (q1.conjugate() * v1), v1);
+
+ // test casting
+ Quaternion<float> q1f = q1.template cast<float>();
+ VERIFY_IS_APPROX(q1f.template cast<Scalar>(),q1);
+ Quaternion<double> q1d = q1.template cast<double>();
+ VERIFY_IS_APPROX(q1d.template cast<Scalar>(),q1);
+
+ // test bug 369 - improper alignment.
+ Quaternionx *q = new Quaternionx;
+ delete q;
+
+ q1 = Quaternionx::UnitRandom();
+ q2 = Quaternionx::UnitRandom();
+ check_slerp(q1,q2);
+
+ q1 = AngleAxisx(b, v1.normalized());
+ q2 = AngleAxisx(b+Scalar(EIGEN_PI), v1.normalized());
+ check_slerp(q1,q2);
+
+ q1 = AngleAxisx(b, v1.normalized());
+ q2 = AngleAxisx(-b, -v1.normalized());
+ check_slerp(q1,q2);
+
+ q1 = Quaternionx::UnitRandom();
+ q2.coeffs() = -q1.coeffs();
+ check_slerp(q1,q2);
+}
+
+template<typename Scalar> void mapQuaternion(void){
+ typedef Map<Quaternion<Scalar>, Aligned> MQuaternionA;
+ typedef Map<const Quaternion<Scalar>, Aligned> MCQuaternionA;
+ typedef Map<Quaternion<Scalar> > MQuaternionUA;
+ typedef Map<const Quaternion<Scalar> > MCQuaternionUA;
+ typedef Quaternion<Scalar> Quaternionx;
+ typedef Matrix<Scalar,3,1> Vector3;
+ typedef AngleAxis<Scalar> AngleAxisx;
+
+ Vector3 v0 = Vector3::Random(),
+ v1 = Vector3::Random();
+ Scalar a = internal::random<Scalar>(-Scalar(EIGEN_PI), Scalar(EIGEN_PI));
+
+ EIGEN_ALIGN_MAX Scalar array1[4];
+ EIGEN_ALIGN_MAX Scalar array2[4];
+ EIGEN_ALIGN_MAX Scalar array3[4+1];
+ Scalar* array3unaligned = array3+1;
+
+ MQuaternionA mq1(array1);
+ MCQuaternionA mcq1(array1);
+ MQuaternionA mq2(array2);
+ MQuaternionUA mq3(array3unaligned);
+ MCQuaternionUA mcq3(array3unaligned);
+
+// std::cerr << array1 << " " << array2 << " " << array3 << "\n";
+ mq1 = AngleAxisx(a, v0.normalized());
+ mq2 = mq1;
+ mq3 = mq1;
+
+ Quaternionx q1 = mq1;
+ Quaternionx q2 = mq2;
+ Quaternionx q3 = mq3;
+ Quaternionx q4 = MCQuaternionUA(array3unaligned);
+
+ VERIFY_IS_APPROX(q1.coeffs(), q2.coeffs());
+ VERIFY_IS_APPROX(q1.coeffs(), q3.coeffs());
+ VERIFY_IS_APPROX(q4.coeffs(), q3.coeffs());
+
+ VERIFY_IS_APPROX(mq1 * (mq1.inverse() * v1), v1);
+ VERIFY_IS_APPROX(mq1 * (mq1.conjugate() * v1), v1);
+
+ VERIFY_IS_APPROX(mcq1 * (mcq1.inverse() * v1), v1);
+ VERIFY_IS_APPROX(mcq1 * (mcq1.conjugate() * v1), v1);
+
+ VERIFY_IS_APPROX(mq3 * (mq3.inverse() * v1), v1);
+ VERIFY_IS_APPROX(mq3 * (mq3.conjugate() * v1), v1);
+
+ VERIFY_IS_APPROX(mcq3 * (mcq3.inverse() * v1), v1);
+ VERIFY_IS_APPROX(mcq3 * (mcq3.conjugate() * v1), v1);
+
+ VERIFY_IS_APPROX(mq1*mq2, q1*q2);
+ VERIFY_IS_APPROX(mq3*mq2, q3*q2);
+ VERIFY_IS_APPROX(mcq1*mq2, q1*q2);
+ VERIFY_IS_APPROX(mcq3*mq2, q3*q2);
+
+ // Bug 1461, compilation issue with Map<const Quat>::w(), and other reference/constness checks:
+ VERIFY_IS_APPROX(mcq3.coeffs().x() + mcq3.coeffs().y() + mcq3.coeffs().z() + mcq3.coeffs().w(), mcq3.coeffs().sum());
+ VERIFY_IS_APPROX(mcq3.x() + mcq3.y() + mcq3.z() + mcq3.w(), mcq3.coeffs().sum());
+ mq3.w() = 1;
+ const Quaternionx& cq3(q3);
+ VERIFY( &cq3.x() == &q3.x() );
+ const MQuaternionUA& cmq3(mq3);
+ VERIFY( &cmq3.x() == &mq3.x() );
+ // FIXME the following should be ok. The problem is that currently the LValueBit flag
+ // is used to determine whether we can return a coeff by reference or not, which is not enough for Map<const ...>.
+ //const MCQuaternionUA& cmcq3(mcq3);
+ //VERIFY( &cmcq3.x() == &mcq3.x() );
+
+ // test cast
+ {
+ Quaternion<float> q1f = mq1.template cast<float>();
+ VERIFY_IS_APPROX(q1f.template cast<Scalar>(),mq1);
+ Quaternion<double> q1d = mq1.template cast<double>();
+ VERIFY_IS_APPROX(q1d.template cast<Scalar>(),mq1);
+ }
+}
+
+template<typename Scalar> void quaternionAlignment(void){
+ typedef Quaternion<Scalar,AutoAlign> QuaternionA;
+ typedef Quaternion<Scalar,DontAlign> QuaternionUA;
+
+ EIGEN_ALIGN_MAX Scalar array1[4];
+ EIGEN_ALIGN_MAX Scalar array2[4];
+ EIGEN_ALIGN_MAX Scalar array3[4+1];
+ Scalar* arrayunaligned = array3+1;
+
+ QuaternionA *q1 = ::new(reinterpret_cast<void*>(array1)) QuaternionA;
+ QuaternionUA *q2 = ::new(reinterpret_cast<void*>(array2)) QuaternionUA;
+ QuaternionUA *q3 = ::new(reinterpret_cast<void*>(arrayunaligned)) QuaternionUA;
+
+ q1->coeffs().setRandom();
+ *q2 = *q1;
+ *q3 = *q1;
+
+ VERIFY_IS_APPROX(q1->coeffs(), q2->coeffs());
+ VERIFY_IS_APPROX(q1->coeffs(), q3->coeffs());
+}
+
+template<typename PlainObjectType> void check_const_correctness(const PlainObjectType&)
+{
+ // there's a lot that we can't test here while still having this test compile!
+ // the only possible approach would be to run a script trying to compile stuff and checking that it fails.
+ // CMake can help with that.
+
+ // verify that map-to-const don't have LvalueBit
+ typedef std::add_const_t<PlainObjectType> ConstPlainObjectType;
+ VERIFY( !(internal::traits<Map<ConstPlainObjectType> >::Flags & LvalueBit) );
+ VERIFY( !(internal::traits<Map<ConstPlainObjectType, Aligned> >::Flags & LvalueBit) );
+ VERIFY( !(Map<ConstPlainObjectType>::Flags & LvalueBit) );
+ VERIFY( !(Map<ConstPlainObjectType, Aligned>::Flags & LvalueBit) );
+}
+
+// Regression for bug 1573
+struct MovableClass {
+ // The following line is a workaround for gcc 4.7 and 4.8 (see bug 1573 comments).
+ static_assert(std::is_nothrow_move_constructible<Quaternionf>::value,"");
+ MovableClass() = default;
+ MovableClass(const MovableClass&) = default;
+ MovableClass(MovableClass&&) noexcept = default;
+ MovableClass& operator=(const MovableClass&) = default;
+ MovableClass& operator=(MovableClass&&) = default;
+ Quaternionf m_quat;
+};
+
+EIGEN_DECLARE_TEST(geo_quaternion)
+{
+ for(int i = 0; i < g_repeat; i++) {
+ CALL_SUBTEST_1(( quaternion<float,AutoAlign>() ));
+ CALL_SUBTEST_1( check_const_correctness(Quaternionf()) );
+ CALL_SUBTEST_1(( quaternion<float,DontAlign>() ));
+ CALL_SUBTEST_1(( quaternionAlignment<float>() ));
+ CALL_SUBTEST_1( mapQuaternion<float>() );
+
+ CALL_SUBTEST_2(( quaternion<double,AutoAlign>() ));
+ CALL_SUBTEST_2( check_const_correctness(Quaterniond()) );
+ CALL_SUBTEST_2(( quaternion<double,DontAlign>() ));
+ CALL_SUBTEST_2(( quaternionAlignment<double>() ));
+ CALL_SUBTEST_2( mapQuaternion<double>() );
+
+#ifndef EIGEN_TEST_ANNOYING_SCALAR_DONT_THROW
+ AnnoyingScalar::dont_throw = true;
+#endif
+ CALL_SUBTEST_3(( quaternion<AnnoyingScalar,AutoAlign>() ));
+ }
+}
diff --git a/test/geo_transformations.cpp b/test/geo_transformations.cpp
new file mode 100644
index 0000000..72c6eda
--- /dev/null
+++ b/test/geo_transformations.cpp
@@ -0,0 +1,731 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "main.h"
+#include <Eigen/Geometry>
+#include <Eigen/LU>
+#include <Eigen/SVD>
+
+template<typename T>
+Matrix<T,2,1> angleToVec(T a)
+{
+ return Matrix<T,2,1>(std::cos(a), std::sin(a));
+}
+
+// This permits to workaround a bug in clang/llvm code generation.
+template<typename T>
+EIGEN_DONT_INLINE
+void dont_over_optimize(T& x) { volatile typename T::Scalar tmp = x(0); x(0) = tmp; }
+
+template<typename Scalar, int Mode, int Options> void non_projective_only()
+{
+ /* this test covers the following files:
+ Cross.h Quaternion.h, Transform.cpp
+ */
+ typedef Matrix<Scalar,3,1> Vector3;
+ typedef Quaternion<Scalar> Quaternionx;
+ typedef AngleAxis<Scalar> AngleAxisx;
+ typedef Transform<Scalar,3,Mode,Options> Transform3;
+ typedef DiagonalMatrix<Scalar,3> AlignedScaling3;
+ typedef Translation<Scalar,3> Translation3;
+
+ Vector3 v0 = Vector3::Random(),
+ v1 = Vector3::Random();
+
+ Transform3 t0, t1, t2;
+
+ Scalar a = internal::random<Scalar>(-Scalar(EIGEN_PI), Scalar(EIGEN_PI));
+
+ Quaternionx q1, q2;
+
+ q1 = AngleAxisx(a, v0.normalized());
+
+ t0 = Transform3::Identity();
+ VERIFY_IS_APPROX(t0.matrix(), Transform3::MatrixType::Identity());
+
+ t0.linear() = q1.toRotationMatrix();
+
+ v0 << 50, 2, 1;
+ t0.scale(v0);
+
+ VERIFY_IS_APPROX( (t0 * Vector3(1,0,0)).template head<3>().norm(), v0.x());
+
+ t0.setIdentity();
+ t1.setIdentity();
+ v1 << 1, 2, 3;
+ t0.linear() = q1.toRotationMatrix();
+ t0.pretranslate(v0);
+ t0.scale(v1);
+ t1.linear() = q1.conjugate().toRotationMatrix();
+ t1.prescale(v1.cwiseInverse());
+ t1.translate(-v0);
+
+ VERIFY((t0 * t1).matrix().isIdentity(test_precision<Scalar>()));
+
+ t1.fromPositionOrientationScale(v0, q1, v1);
+ VERIFY_IS_APPROX(t1.matrix(), t0.matrix());
+ VERIFY_IS_APPROX(t1*v1, t0*v1);
+
+ // translation * vector
+ t0.setIdentity();
+ t0.translate(v0);
+ VERIFY_IS_APPROX((t0 * v1).template head<3>(), Translation3(v0) * v1);
+
+ // AlignedScaling * vector
+ t0.setIdentity();
+ t0.scale(v0);
+ VERIFY_IS_APPROX((t0 * v1).template head<3>(), AlignedScaling3(v0) * v1);
+}
+
+template<typename Scalar, int Mode, int Options> void transformations()
+{
+ /* this test covers the following files:
+ Cross.h Quaternion.h, Transform.cpp
+ */
+ using std::cos;
+ using std::abs;
+ typedef Matrix<Scalar,3,3> Matrix3;
+ typedef Matrix<Scalar,4,4> Matrix4;
+ typedef Matrix<Scalar,2,1> Vector2;
+ typedef Matrix<Scalar,3,1> Vector3;
+ typedef Matrix<Scalar,4,1> Vector4;
+ typedef Quaternion<Scalar> Quaternionx;
+ typedef AngleAxis<Scalar> AngleAxisx;
+ typedef Transform<Scalar,2,Mode,Options> Transform2;
+ typedef Transform<Scalar,3,Mode,Options> Transform3;
+ typedef typename Transform3::MatrixType MatrixType;
+ typedef DiagonalMatrix<Scalar,3> AlignedScaling3;
+ typedef Translation<Scalar,2> Translation2;
+ typedef Translation<Scalar,3> Translation3;
+
+ Vector3 v0 = Vector3::Random(),
+ v1 = Vector3::Random();
+ Matrix3 matrot1, m;
+
+ Scalar a = internal::random<Scalar>(-Scalar(EIGEN_PI), Scalar(EIGEN_PI));
+ Scalar s0 = internal::random<Scalar>(), s1 = internal::random<Scalar>();
+
+ while(v0.norm() < test_precision<Scalar>()) v0 = Vector3::Random();
+ while(v1.norm() < test_precision<Scalar>()) v1 = Vector3::Random();
+
+ VERIFY_IS_APPROX(v0, AngleAxisx(a, v0.normalized()) * v0);
+ VERIFY_IS_APPROX(-v0, AngleAxisx(Scalar(EIGEN_PI), v0.unitOrthogonal()) * v0);
+ if(abs(cos(a)) > test_precision<Scalar>())
+ {
+ VERIFY_IS_APPROX(cos(a)*v0.squaredNorm(), v0.dot(AngleAxisx(a, v0.unitOrthogonal()) * v0));
+ }
+ m = AngleAxisx(a, v0.normalized()).toRotationMatrix().adjoint();
+ VERIFY_IS_APPROX(Matrix3::Identity(), m * AngleAxisx(a, v0.normalized()));
+ VERIFY_IS_APPROX(Matrix3::Identity(), AngleAxisx(a, v0.normalized()) * m);
+
+ Quaternionx q1, q2;
+ q1 = AngleAxisx(a, v0.normalized());
+ q2 = AngleAxisx(a, v1.normalized());
+
+ // rotation matrix conversion
+ matrot1 = AngleAxisx(Scalar(0.1), Vector3::UnitX())
+ * AngleAxisx(Scalar(0.2), Vector3::UnitY())
+ * AngleAxisx(Scalar(0.3), Vector3::UnitZ());
+ VERIFY_IS_APPROX(matrot1 * v1,
+ AngleAxisx(Scalar(0.1), Vector3(1,0,0)).toRotationMatrix()
+ * (AngleAxisx(Scalar(0.2), Vector3(0,1,0)).toRotationMatrix()
+ * (AngleAxisx(Scalar(0.3), Vector3(0,0,1)).toRotationMatrix() * v1)));
+
+ // angle-axis conversion
+ AngleAxisx aa = AngleAxisx(q1);
+ VERIFY_IS_APPROX(q1 * v1, Quaternionx(aa) * v1);
+
+ // The following test is stable only if 2*angle != angle and v1 is not colinear with axis
+ if( (abs(aa.angle()) > test_precision<Scalar>()) && (abs(aa.axis().dot(v1.normalized()))<(Scalar(1)-Scalar(4)*test_precision<Scalar>())) )
+ {
+ VERIFY( !(q1 * v1).isApprox(Quaternionx(AngleAxisx(aa.angle()*2,aa.axis())) * v1) );
+ }
+
+ aa.fromRotationMatrix(aa.toRotationMatrix());
+ VERIFY_IS_APPROX(q1 * v1, Quaternionx(aa) * v1);
+ // The following test is stable only if 2*angle != angle and v1 is not colinear with axis
+ if( (abs(aa.angle()) > test_precision<Scalar>()) && (abs(aa.axis().dot(v1.normalized()))<(Scalar(1)-Scalar(4)*test_precision<Scalar>())) )
+ {
+ VERIFY( !(q1 * v1).isApprox(Quaternionx(AngleAxisx(aa.angle()*2,aa.axis())) * v1) );
+ }
+
+ // AngleAxis
+ VERIFY_IS_APPROX(AngleAxisx(a,v1.normalized()).toRotationMatrix(),
+ Quaternionx(AngleAxisx(a,v1.normalized())).toRotationMatrix());
+
+ AngleAxisx aa1;
+ m = q1.toRotationMatrix();
+ aa1 = m;
+ VERIFY_IS_APPROX(AngleAxisx(m).toRotationMatrix(),
+ Quaternionx(m).toRotationMatrix());
+
+ // Transform
+ // TODO complete the tests !
+ a = 0;
+ while (abs(a)<Scalar(0.1))
+ a = internal::random<Scalar>(-Scalar(0.4)*Scalar(EIGEN_PI), Scalar(0.4)*Scalar(EIGEN_PI));
+ q1 = AngleAxisx(a, v0.normalized());
+ Transform3 t0, t1, t2;
+
+ // first test setIdentity() and Identity()
+ t0.setIdentity();
+ VERIFY_IS_APPROX(t0.matrix(), Transform3::MatrixType::Identity());
+ t0.matrix().setZero();
+ t0 = Transform3::Identity();
+ VERIFY_IS_APPROX(t0.matrix(), Transform3::MatrixType::Identity());
+
+ t0.setIdentity();
+ t1.setIdentity();
+ v1 << 1, 2, 3;
+ t0.linear() = q1.toRotationMatrix();
+ t0.pretranslate(v0);
+ t0.scale(v1);
+ t1.linear() = q1.conjugate().toRotationMatrix();
+ t1.prescale(v1.cwiseInverse());
+ t1.translate(-v0);
+
+ VERIFY((t0 * t1).matrix().isIdentity(test_precision<Scalar>()));
+
+ t1.fromPositionOrientationScale(v0, q1, v1);
+ VERIFY_IS_APPROX(t1.matrix(), t0.matrix());
+
+ t0.setIdentity(); t0.scale(v0).rotate(q1.toRotationMatrix());
+ t1.setIdentity(); t1.scale(v0).rotate(q1);
+ VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
+
+ t0.setIdentity(); t0.scale(v0).rotate(AngleAxisx(q1));
+ VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
+
+ VERIFY_IS_APPROX(t0.scale(a).matrix(), t1.scale(Vector3::Constant(a)).matrix());
+ VERIFY_IS_APPROX(t0.prescale(a).matrix(), t1.prescale(Vector3::Constant(a)).matrix());
+
+ // More transform constructors, operator=, operator*=
+
+ Matrix3 mat3 = Matrix3::Random();
+ Matrix4 mat4;
+ mat4 << mat3 , Vector3::Zero() , Vector4::Zero().transpose();
+ Transform3 tmat3(mat3), tmat4(mat4);
+ if(Mode!=int(AffineCompact))
+ tmat4.matrix()(3,3) = Scalar(1);
+ VERIFY_IS_APPROX(tmat3.matrix(), tmat4.matrix());
+
+ Scalar a3 = internal::random<Scalar>(-Scalar(EIGEN_PI), Scalar(EIGEN_PI));
+ Vector3 v3 = Vector3::Random().normalized();
+ AngleAxisx aa3(a3, v3);
+ Transform3 t3(aa3);
+ Transform3 t4;
+ t4 = aa3;
+ VERIFY_IS_APPROX(t3.matrix(), t4.matrix());
+ t4.rotate(AngleAxisx(-a3,v3));
+ VERIFY_IS_APPROX(t4.matrix(), MatrixType::Identity());
+ t4 *= aa3;
+ VERIFY_IS_APPROX(t3.matrix(), t4.matrix());
+
+ do {
+ v3 = Vector3::Random();
+ dont_over_optimize(v3);
+ } while (v3.cwiseAbs().minCoeff()<NumTraits<Scalar>::epsilon());
+ Translation3 tv3(v3);
+ Transform3 t5(tv3);
+ t4 = tv3;
+ VERIFY_IS_APPROX(t5.matrix(), t4.matrix());
+ t4.translate((-v3).eval());
+ VERIFY_IS_APPROX(t4.matrix(), MatrixType::Identity());
+ t4 *= tv3;
+ VERIFY_IS_APPROX(t5.matrix(), t4.matrix());
+
+ AlignedScaling3 sv3(v3);
+ Transform3 t6(sv3);
+ t4 = sv3;
+ VERIFY_IS_APPROX(t6.matrix(), t4.matrix());
+ t4.scale(v3.cwiseInverse());
+ VERIFY_IS_APPROX(t4.matrix(), MatrixType::Identity());
+ t4 *= sv3;
+ VERIFY_IS_APPROX(t6.matrix(), t4.matrix());
+
+ // matrix * transform
+ VERIFY_IS_APPROX((t3.matrix()*t4).matrix(), (t3*t4).matrix());
+
+ // chained Transform product
+ VERIFY_IS_APPROX(((t3*t4)*t5).matrix(), (t3*(t4*t5)).matrix());
+
+ // check that Transform product doesn't have aliasing problems
+ t5 = t4;
+ t5 = t5*t5;
+ VERIFY_IS_APPROX(t5, t4*t4);
+
+ // 2D transformation
+ Transform2 t20, t21;
+ Vector2 v20 = Vector2::Random();
+ Vector2 v21 = Vector2::Random();
+ for (int k=0; k<2; ++k)
+ if (abs(v21[k])<Scalar(1e-3)) v21[k] = Scalar(1e-3);
+ t21.setIdentity();
+ t21.linear() = Rotation2D<Scalar>(a).toRotationMatrix();
+ VERIFY_IS_APPROX(t20.fromPositionOrientationScale(v20,a,v21).matrix(),
+ t21.pretranslate(v20).scale(v21).matrix());
+
+ t21.setIdentity();
+ t21.linear() = Rotation2D<Scalar>(-a).toRotationMatrix();
+ VERIFY( (t20.fromPositionOrientationScale(v20,a,v21)
+ * (t21.prescale(v21.cwiseInverse()).translate(-v20))).matrix().isIdentity(test_precision<Scalar>()) );
+
+ // Transform - new API
+ // 3D
+ t0.setIdentity();
+ t0.rotate(q1).scale(v0).translate(v0);
+ // mat * aligned scaling and mat * translation
+ t1 = (Matrix3(q1) * AlignedScaling3(v0)) * Translation3(v0);
+ VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
+ t1 = (Matrix3(q1) * Eigen::Scaling(v0)) * Translation3(v0);
+ VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
+ t1 = (q1 * Eigen::Scaling(v0)) * Translation3(v0);
+ VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
+ // mat * transformation and aligned scaling * translation
+ t1 = Matrix3(q1) * (AlignedScaling3(v0) * Translation3(v0));
+ VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
+
+
+ t0.setIdentity();
+ t0.scale(s0).translate(v0);
+ t1 = Eigen::Scaling(s0) * Translation3(v0);
+ VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
+ t0.prescale(s0);
+ t1 = Eigen::Scaling(s0) * t1;
+ VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
+
+ t0 = t3;
+ t0.scale(s0);
+ t1 = t3 * Eigen::Scaling(s0,s0,s0);
+ VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
+ t0.prescale(s0);
+ t1 = Eigen::Scaling(s0,s0,s0) * t1;
+ VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
+
+ t0 = t3;
+ t0.scale(s0);
+ t1 = t3 * Eigen::Scaling(s0);
+ VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
+ t0.prescale(s0);
+ t1 = Eigen::Scaling(s0) * t1;
+ VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
+
+ t0.setIdentity();
+ t0.prerotate(q1).prescale(v0).pretranslate(v0);
+ // translation * aligned scaling and transformation * mat
+ t1 = (Translation3(v0) * AlignedScaling3(v0)) * Transform3(q1);
+ VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
+ // scaling * mat and translation * mat
+ t1 = Translation3(v0) * (AlignedScaling3(v0) * Transform3(q1));
+ VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
+
+ t0.setIdentity();
+ t0.scale(v0).translate(v0).rotate(q1);
+ // translation * mat and aligned scaling * transformation
+ t1 = AlignedScaling3(v0) * (Translation3(v0) * Transform3(q1));
+ VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
+ // transformation * aligned scaling
+ t0.scale(v0);
+ t1 *= AlignedScaling3(v0);
+ VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
+ t1 = AlignedScaling3(v0) * (Translation3(v0) * Transform3(q1));
+ t1 = t1 * v0.asDiagonal();
+ VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
+ // transformation * translation
+ t0.translate(v0);
+ t1 = t1 * Translation3(v0);
+ VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
+ // translation * transformation
+ t0.pretranslate(v0);
+ t1 = Translation3(v0) * t1;
+ VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
+
+ // transform * quaternion
+ t0.rotate(q1);
+ t1 = t1 * q1;
+ VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
+
+ // translation * quaternion
+ t0.translate(v1).rotate(q1);
+ t1 = t1 * (Translation3(v1) * q1);
+ VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
+
+ // aligned scaling * quaternion
+ t0.scale(v1).rotate(q1);
+ t1 = t1 * (AlignedScaling3(v1) * q1);
+ VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
+
+ // quaternion * transform
+ t0.prerotate(q1);
+ t1 = q1 * t1;
+ VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
+
+ // quaternion * translation
+ t0.rotate(q1).translate(v1);
+ t1 = t1 * (q1 * Translation3(v1));
+ VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
+
+ // quaternion * aligned scaling
+ t0.rotate(q1).scale(v1);
+ t1 = t1 * (q1 * AlignedScaling3(v1));
+ VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
+
+ // test transform inversion
+ t0.setIdentity();
+ t0.translate(v0);
+ do {
+ t0.linear().setRandom();
+ } while(t0.linear().jacobiSvd().singularValues()(2)<test_precision<Scalar>());
+ Matrix4 t044 = Matrix4::Zero();
+ t044(3,3) = 1;
+ t044.block(0,0,t0.matrix().rows(),4) = t0.matrix();
+ VERIFY_IS_APPROX(t0.inverse(Affine).matrix(), t044.inverse().block(0,0,t0.matrix().rows(),4));
+ t0.setIdentity();
+ t0.translate(v0).rotate(q1);
+ t044 = Matrix4::Zero();
+ t044(3,3) = 1;
+ t044.block(0,0,t0.matrix().rows(),4) = t0.matrix();
+ VERIFY_IS_APPROX(t0.inverse(Isometry).matrix(), t044.inverse().block(0,0,t0.matrix().rows(),4));
+
+ Matrix3 mat_rotation, mat_scaling;
+ t0.setIdentity();
+ t0.translate(v0).rotate(q1).scale(v1);
+ t0.computeRotationScaling(&mat_rotation, &mat_scaling);
+ VERIFY_IS_APPROX(t0.linear(), mat_rotation * mat_scaling);
+ VERIFY_IS_APPROX(mat_rotation*mat_rotation.adjoint(), Matrix3::Identity());
+ VERIFY_IS_APPROX(mat_rotation.determinant(), Scalar(1));
+ t0.computeScalingRotation(&mat_scaling, &mat_rotation);
+ VERIFY_IS_APPROX(t0.linear(), mat_scaling * mat_rotation);
+ VERIFY_IS_APPROX(mat_rotation*mat_rotation.adjoint(), Matrix3::Identity());
+ VERIFY_IS_APPROX(mat_rotation.determinant(), Scalar(1));
+
+ // test casting
+ Transform<float,3,Mode> t1f = t1.template cast<float>();
+ VERIFY_IS_APPROX(t1f.template cast<Scalar>(),t1);
+ Transform<double,3,Mode> t1d = t1.template cast<double>();
+ VERIFY_IS_APPROX(t1d.template cast<Scalar>(),t1);
+
+ Translation3 tr1(v0);
+ Translation<float,3> tr1f = tr1.template cast<float>();
+ VERIFY_IS_APPROX(tr1f.template cast<Scalar>(),tr1);
+ Translation<double,3> tr1d = tr1.template cast<double>();
+ VERIFY_IS_APPROX(tr1d.template cast<Scalar>(),tr1);
+
+ AngleAxis<float> aa1f = aa1.template cast<float>();
+ VERIFY_IS_APPROX(aa1f.template cast<Scalar>(),aa1);
+ AngleAxis<double> aa1d = aa1.template cast<double>();
+ VERIFY_IS_APPROX(aa1d.template cast<Scalar>(),aa1);
+
+ Rotation2D<Scalar> r2d1(internal::random<Scalar>());
+ Rotation2D<float> r2d1f = r2d1.template cast<float>();
+ VERIFY_IS_APPROX(r2d1f.template cast<Scalar>(),r2d1);
+ Rotation2D<double> r2d1d = r2d1.template cast<double>();
+ VERIFY_IS_APPROX(r2d1d.template cast<Scalar>(),r2d1);
+
+ for(int k=0; k<100; ++k)
+ {
+ Scalar angle = internal::random<Scalar>(-100,100);
+ Rotation2D<Scalar> rot2(angle);
+ VERIFY( rot2.smallestPositiveAngle() >= 0 );
+ VERIFY( rot2.smallestPositiveAngle() <= Scalar(2)*Scalar(EIGEN_PI) );
+ VERIFY_IS_APPROX( angleToVec(rot2.smallestPositiveAngle()), angleToVec(rot2.angle()) );
+
+ VERIFY( rot2.smallestAngle() >= -Scalar(EIGEN_PI) );
+ VERIFY( rot2.smallestAngle() <= Scalar(EIGEN_PI) );
+ VERIFY_IS_APPROX( angleToVec(rot2.smallestAngle()), angleToVec(rot2.angle()) );
+
+ Matrix<Scalar,2,2> rot2_as_mat(rot2);
+ Rotation2D<Scalar> rot3(rot2_as_mat);
+ VERIFY_IS_APPROX( angleToVec(rot2.smallestAngle()), angleToVec(rot3.angle()) );
+ }
+
+ s0 = internal::random<Scalar>(-100,100);
+ s1 = internal::random<Scalar>(-100,100);
+ Rotation2D<Scalar> R0(s0), R1(s1);
+
+ t20 = Translation2(v20) * (R0 * Eigen::Scaling(s0));
+ t21 = Translation2(v20) * R0 * Eigen::Scaling(s0);
+ VERIFY_IS_APPROX(t20,t21);
+
+ t20 = Translation2(v20) * (R0 * R0.inverse() * Eigen::Scaling(s0));
+ t21 = Translation2(v20) * Eigen::Scaling(s0);
+ VERIFY_IS_APPROX(t20,t21);
+
+ VERIFY_IS_APPROX(s0, (R0.slerp(0, R1)).angle());
+ VERIFY_IS_APPROX( angleToVec(R1.smallestPositiveAngle()), angleToVec((R0.slerp(1, R1)).smallestPositiveAngle()) );
+ VERIFY_IS_APPROX(R0.smallestPositiveAngle(), (R0.slerp(0.5, R0)).smallestPositiveAngle());
+
+ if(std::cos(s0)>0)
+ VERIFY_IS_MUCH_SMALLER_THAN((R0.slerp(0.5, R0.inverse())).smallestAngle(), Scalar(1));
+ else
+ VERIFY_IS_APPROX(Scalar(EIGEN_PI), (R0.slerp(0.5, R0.inverse())).smallestPositiveAngle());
+
+ // Check path length
+ Scalar l = 0;
+ int path_steps = 100;
+ for(int k=0; k<path_steps; ++k)
+ {
+ Scalar a1 = R0.slerp(Scalar(k)/Scalar(path_steps), R1).angle();
+ Scalar a2 = R0.slerp(Scalar(k+1)/Scalar(path_steps), R1).angle();
+ l += std::abs(a2-a1);
+ }
+ VERIFY(l<=Scalar(EIGEN_PI)*(Scalar(1)+NumTraits<Scalar>::epsilon()*Scalar(path_steps/2)));
+
+ // check basic features
+ {
+ Rotation2D<Scalar> r1; // default ctor
+ r1 = Rotation2D<Scalar>(s0); // copy assignment
+ VERIFY_IS_APPROX(r1.angle(),s0);
+ Rotation2D<Scalar> r2(r1); // copy ctor
+ VERIFY_IS_APPROX(r2.angle(),s0);
+ }
+
+ {
+ Transform3 t32(Matrix4::Random()), t33, t34;
+ t34 = t33 = t32;
+ t32.scale(v0);
+ t33*=AlignedScaling3(v0);
+ VERIFY_IS_APPROX(t32.matrix(), t33.matrix());
+ t33 = t34 * AlignedScaling3(v0);
+ VERIFY_IS_APPROX(t32.matrix(), t33.matrix());
+ }
+
+}
+
+template<typename A1, typename A2, typename P, typename Q, typename V, typename H>
+void transform_associativity_left(const A1& a1, const A2& a2, const P& p, const Q& q, const V& v, const H& h)
+{
+ VERIFY_IS_APPROX( q*(a1*v), (q*a1)*v );
+ VERIFY_IS_APPROX( q*(a2*v), (q*a2)*v );
+ VERIFY_IS_APPROX( q*(p*h).hnormalized(), ((q*p)*h).hnormalized() );
+}
+
+template<typename A1, typename A2, typename P, typename Q, typename V, typename H>
+void transform_associativity2(const A1& a1, const A2& a2, const P& p, const Q& q, const V& v, const H& h)
+{
+ VERIFY_IS_APPROX( a1*(q*v), (a1*q)*v );
+ VERIFY_IS_APPROX( a2*(q*v), (a2*q)*v );
+ VERIFY_IS_APPROX( p *(q*v).homogeneous(), (p *q)*v.homogeneous() );
+
+ transform_associativity_left(a1, a2,p, q, v, h);
+}
+
+template<typename Scalar, int Dim, int Options,typename RotationType>
+void transform_associativity(const RotationType& R)
+{
+ typedef Matrix<Scalar,Dim,1> VectorType;
+ typedef Matrix<Scalar,Dim+1,1> HVectorType;
+ typedef Matrix<Scalar,Dim,Dim> LinearType;
+ typedef Matrix<Scalar,Dim+1,Dim+1> MatrixType;
+ typedef Transform<Scalar,Dim,AffineCompact,Options> AffineCompactType;
+ typedef Transform<Scalar,Dim,Affine,Options> AffineType;
+ typedef Transform<Scalar,Dim,Projective,Options> ProjectiveType;
+ typedef DiagonalMatrix<Scalar,Dim> ScalingType;
+ typedef Translation<Scalar,Dim> TranslationType;
+
+ AffineCompactType A1c; A1c.matrix().setRandom();
+ AffineCompactType A2c; A2c.matrix().setRandom();
+ AffineType A1(A1c);
+ AffineType A2(A2c);
+ ProjectiveType P1; P1.matrix().setRandom();
+ VectorType v1 = VectorType::Random();
+ VectorType v2 = VectorType::Random();
+ HVectorType h1 = HVectorType::Random();
+ Scalar s1 = internal::random<Scalar>();
+ LinearType L = LinearType::Random();
+ MatrixType M = MatrixType::Random();
+
+ CALL_SUBTEST( transform_associativity2(A1c, A1, P1, A2, v2, h1) );
+ CALL_SUBTEST( transform_associativity2(A1c, A1, P1, A2c, v2, h1) );
+ CALL_SUBTEST( transform_associativity2(A1c, A1, P1, v1.asDiagonal(), v2, h1) );
+ CALL_SUBTEST( transform_associativity2(A1c, A1, P1, ScalingType(v1), v2, h1) );
+ CALL_SUBTEST( transform_associativity2(A1c, A1, P1, Scaling(v1), v2, h1) );
+ CALL_SUBTEST( transform_associativity2(A1c, A1, P1, Scaling(s1), v2, h1) );
+ CALL_SUBTEST( transform_associativity2(A1c, A1, P1, TranslationType(v1), v2, h1) );
+ CALL_SUBTEST( transform_associativity_left(A1c, A1, P1, L, v2, h1) );
+ CALL_SUBTEST( transform_associativity2(A1c, A1, P1, R, v2, h1) );
+
+ VERIFY_IS_APPROX( A1*(M*h1), (A1*M)*h1 );
+ VERIFY_IS_APPROX( A1c*(M*h1), (A1c*M)*h1 );
+ VERIFY_IS_APPROX( P1*(M*h1), (P1*M)*h1 );
+
+ VERIFY_IS_APPROX( M*(A1*h1), (M*A1)*h1 );
+ VERIFY_IS_APPROX( M*(A1c*h1), (M*A1c)*h1 );
+ VERIFY_IS_APPROX( M*(P1*h1), ((M*P1)*h1) );
+}
+
+template<typename Scalar> void transform_alignment()
+{
+ typedef Transform<Scalar,3,Projective,AutoAlign> Projective3a;
+ typedef Transform<Scalar,3,Projective,DontAlign> Projective3u;
+
+ EIGEN_ALIGN_MAX Scalar array1[16];
+ EIGEN_ALIGN_MAX Scalar array2[16];
+ EIGEN_ALIGN_MAX Scalar array3[16+1];
+ Scalar* array3u = array3+1;
+
+ Projective3a *p1 = ::new(reinterpret_cast<void*>(array1)) Projective3a;
+ Projective3u *p2 = ::new(reinterpret_cast<void*>(array2)) Projective3u;
+ Projective3u *p3 = ::new(reinterpret_cast<void*>(array3u)) Projective3u;
+
+ p1->matrix().setRandom();
+ *p2 = *p1;
+ *p3 = *p1;
+
+ VERIFY_IS_APPROX(p1->matrix(), p2->matrix());
+ VERIFY_IS_APPROX(p1->matrix(), p3->matrix());
+
+ VERIFY_IS_APPROX( (*p1) * (*p1), (*p2)*(*p3));
+}
+
+template<typename Scalar, int Dim, int Options> void transform_products()
+{
+ typedef Matrix<Scalar,Dim+1,Dim+1> Mat;
+ typedef Transform<Scalar,Dim,Projective,Options> Proj;
+ typedef Transform<Scalar,Dim,Affine,Options> Aff;
+ typedef Transform<Scalar,Dim,AffineCompact,Options> AffC;
+
+ Proj p; p.matrix().setRandom();
+ Aff a; a.linear().setRandom(); a.translation().setRandom();
+ AffC ac = a;
+
+ Mat p_m(p.matrix()), a_m(a.matrix());
+
+ VERIFY_IS_APPROX((p*p).matrix(), p_m*p_m);
+ VERIFY_IS_APPROX((a*a).matrix(), a_m*a_m);
+ VERIFY_IS_APPROX((p*a).matrix(), p_m*a_m);
+ VERIFY_IS_APPROX((a*p).matrix(), a_m*p_m);
+ VERIFY_IS_APPROX((ac*a).matrix(), a_m*a_m);
+ VERIFY_IS_APPROX((a*ac).matrix(), a_m*a_m);
+ VERIFY_IS_APPROX((p*ac).matrix(), p_m*a_m);
+ VERIFY_IS_APPROX((ac*p).matrix(), a_m*p_m);
+}
+
+template<typename Scalar, int Mode, int Options> void transformations_no_scale()
+{
+ /* this test covers the following files:
+ Cross.h Quaternion.h, Transform.h
+ */
+ typedef Matrix<Scalar,3,1> Vector3;
+ typedef Matrix<Scalar,4,1> Vector4;
+ typedef Quaternion<Scalar> Quaternionx;
+ typedef AngleAxis<Scalar> AngleAxisx;
+ typedef Transform<Scalar,3,Mode,Options> Transform3;
+ typedef Translation<Scalar,3> Translation3;
+ typedef Matrix<Scalar,4,4> Matrix4;
+
+ Vector3 v0 = Vector3::Random(),
+ v1 = Vector3::Random();
+
+ Transform3 t0, t1, t2;
+
+ Scalar a = internal::random<Scalar>(-Scalar(EIGEN_PI), Scalar(EIGEN_PI));
+
+ Quaternionx q1, q2;
+
+ q1 = AngleAxisx(a, v0.normalized());
+
+ t0 = Transform3::Identity();
+ VERIFY_IS_APPROX(t0.matrix(), Transform3::MatrixType::Identity());
+
+ t0.setIdentity();
+ t1.setIdentity();
+ v1 = Vector3::Ones();
+ t0.linear() = q1.toRotationMatrix();
+ t0.pretranslate(v0);
+ t1.linear() = q1.conjugate().toRotationMatrix();
+ t1.translate(-v0);
+
+ VERIFY((t0 * t1).matrix().isIdentity(test_precision<Scalar>()));
+
+ t1.fromPositionOrientationScale(v0, q1, v1);
+ VERIFY_IS_APPROX(t1.matrix(), t0.matrix());
+ VERIFY_IS_APPROX(t1*v1, t0*v1);
+
+ // translation * vector
+ t0.setIdentity();
+ t0.translate(v0);
+ VERIFY_IS_APPROX((t0 * v1).template head<3>(), Translation3(v0) * v1);
+
+ // Conversion to matrix.
+ Transform3 t3;
+ t3.linear() = q1.toRotationMatrix();
+ t3.translation() = v1;
+ Matrix4 m3 = t3.matrix();
+ VERIFY((m3 * m3.inverse()).isIdentity(test_precision<Scalar>()));
+ // Verify implicit last row is initialized.
+ VERIFY_IS_APPROX(Vector4(m3.row(3)), Vector4(0.0, 0.0, 0.0, 1.0));
+
+ VERIFY_IS_APPROX(t3.rotation(), t3.linear());
+ if(Mode==Isometry)
+ VERIFY(t3.rotation().data()==t3.linear().data());
+}
+
+template<typename Scalar, int Mode, int Options> void transformations_computed_scaling_continuity()
+{
+ typedef Matrix<Scalar, 3, 1> Vector3;
+ typedef Transform<Scalar, 3, Mode, Options> Transform3;
+ typedef Matrix<Scalar, 3, 3> Matrix3;
+
+ // Given: two transforms that differ by '2*eps'.
+ Scalar eps(1e-3);
+ Vector3 v0 = Vector3::Random().normalized(),
+ v1 = Vector3::Random().normalized(),
+ v3 = Vector3::Random().normalized();
+ Transform3 t0, t1;
+ // The interesting case is when their determinants have different signs.
+ Matrix3 rank2 = 50 * v0 * v0.adjoint() + 20 * v1 * v1.adjoint();
+ t0.linear() = rank2 + eps * v3 * v3.adjoint();
+ t1.linear() = rank2 - eps * v3 * v3.adjoint();
+
+ // When: computing the rotation-scaling parts
+ Matrix3 r0, s0, r1, s1;
+ t0.computeRotationScaling(&r0, &s0);
+ t1.computeRotationScaling(&r1, &s1);
+
+ // Then: the scaling parts should differ by no more than '2*eps'.
+ const Scalar c(2.1); // 2 + room for rounding errors
+ VERIFY((s0 - s1).norm() < c * eps);
+}
+
+EIGEN_DECLARE_TEST(geo_transformations)
+{
+ for(int i = 0; i < g_repeat; i++) {
+ CALL_SUBTEST_1(( transformations<double,Affine,AutoAlign>() ));
+ CALL_SUBTEST_1(( non_projective_only<double,Affine,AutoAlign>() ));
+ CALL_SUBTEST_1(( transformations_computed_scaling_continuity<double,Affine,AutoAlign>() ));
+
+ CALL_SUBTEST_2(( transformations<float,AffineCompact,AutoAlign>() ));
+ CALL_SUBTEST_2(( non_projective_only<float,AffineCompact,AutoAlign>() ));
+ CALL_SUBTEST_2(( transform_alignment<float>() ));
+
+ CALL_SUBTEST_3(( transformations<double,Projective,AutoAlign>() ));
+ CALL_SUBTEST_3(( transformations<double,Projective,DontAlign>() ));
+ CALL_SUBTEST_3(( transform_alignment<double>() ));
+
+ CALL_SUBTEST_4(( transformations<float,Affine,RowMajor|AutoAlign>() ));
+ CALL_SUBTEST_4(( non_projective_only<float,Affine,RowMajor>() ));
+
+ CALL_SUBTEST_5(( transformations<double,AffineCompact,RowMajor|AutoAlign>() ));
+ CALL_SUBTEST_5(( non_projective_only<double,AffineCompact,RowMajor>() ));
+
+ CALL_SUBTEST_6(( transformations<double,Projective,RowMajor|AutoAlign>() ));
+ CALL_SUBTEST_6(( transformations<double,Projective,RowMajor|DontAlign>() ));
+
+
+ CALL_SUBTEST_7(( transform_products<double,3,RowMajor|AutoAlign>() ));
+ CALL_SUBTEST_7(( transform_products<float,2,AutoAlign>() ));
+
+ CALL_SUBTEST_8(( transform_associativity<double,2,ColMajor>(Rotation2D<double>(internal::random<double>()*double(EIGEN_PI))) ));
+ CALL_SUBTEST_8(( transform_associativity<double,3,ColMajor>(Quaterniond::UnitRandom()) ));
+
+ CALL_SUBTEST_9(( transformations_no_scale<double,Affine,AutoAlign>() ));
+ CALL_SUBTEST_9(( transformations_no_scale<double,Isometry,AutoAlign>() ));
+ }
+}
diff --git a/test/gpu_basic.cu b/test/gpu_basic.cu
new file mode 100644
index 0000000..e424a93
--- /dev/null
+++ b/test/gpu_basic.cu
@@ -0,0 +1,465 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2015-2016 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+// workaround issue between gcc >= 4.7 and cuda 5.5
+#if (defined __GNUC__) && (__GNUC__>4 || __GNUC_MINOR__>=7)
+ #undef _GLIBCXX_ATOMIC_BUILTINS
+ #undef _GLIBCXX_USE_INT128
+#endif
+
+#define EIGEN_TEST_NO_LONGDOUBLE
+#define EIGEN_DEFAULT_DENSE_INDEX_TYPE int
+
+#include "main.h"
+#include "gpu_common.h"
+
+// Check that dense modules can be properly parsed by nvcc
+#include <Eigen/Dense>
+
+// struct Foo{
+// EIGEN_DEVICE_FUNC
+// void operator()(int i, const float* mats, float* vecs) const {
+// using namespace Eigen;
+// // Matrix3f M(data);
+// // Vector3f x(data+9);
+// // Map<Vector3f>(data+9) = M.inverse() * x;
+// Matrix3f M(mats+i/16);
+// Vector3f x(vecs+i*3);
+// // using std::min;
+// // using std::sqrt;
+// Map<Vector3f>(vecs+i*3) << x.minCoeff(), 1, 2;// / x.dot(x);//(M.inverse() * x) / x.x();
+// //x = x*2 + x.y() * x + x * x.maxCoeff() - x / x.sum();
+// }
+// };
+
+template<typename T>
+struct coeff_wise {
+ EIGEN_DEVICE_FUNC
+ void operator()(int i, const typename T::Scalar* in, typename T::Scalar* out) const
+ {
+ using namespace Eigen;
+ T x1(in+i);
+ T x2(in+i+1);
+ T x3(in+i+2);
+ Map<T> res(out+i*T::MaxSizeAtCompileTime);
+
+ res.array() += (in[0] * x1 + x2).array() * x3.array();
+ }
+};
+
+template<typename T>
+struct complex_sqrt {
+ EIGEN_DEVICE_FUNC
+ void operator()(int i, const typename T::Scalar* in, typename T::Scalar* out) const
+ {
+ using namespace Eigen;
+ typedef typename T::Scalar ComplexType;
+ typedef typename T::Scalar::value_type ValueType;
+ const int num_special_inputs = 18;
+
+ if (i == 0) {
+ const ValueType nan = std::numeric_limits<ValueType>::quiet_NaN();
+ typedef Eigen::Vector<ComplexType, num_special_inputs> SpecialInputs;
+ SpecialInputs special_in;
+ special_in.setZero();
+ int idx = 0;
+ special_in[idx++] = ComplexType(0, 0);
+ special_in[idx++] = ComplexType(-0, 0);
+ special_in[idx++] = ComplexType(0, -0);
+ special_in[idx++] = ComplexType(-0, -0);
+ // GCC's fallback sqrt implementation fails for inf inputs.
+ // It is called when _GLIBCXX_USE_C99_COMPLEX is false or if
+ // clang includes the GCC header (which temporarily disables
+ // _GLIBCXX_USE_C99_COMPLEX)
+ #if !defined(_GLIBCXX_COMPLEX) || \
+ (_GLIBCXX_USE_C99_COMPLEX && !defined(__CLANG_CUDA_WRAPPERS_COMPLEX))
+ const ValueType inf = std::numeric_limits<ValueType>::infinity();
+ special_in[idx++] = ComplexType(1.0, inf);
+ special_in[idx++] = ComplexType(nan, inf);
+ special_in[idx++] = ComplexType(1.0, -inf);
+ special_in[idx++] = ComplexType(nan, -inf);
+ special_in[idx++] = ComplexType(-inf, 1.0);
+ special_in[idx++] = ComplexType(inf, 1.0);
+ special_in[idx++] = ComplexType(-inf, -1.0);
+ special_in[idx++] = ComplexType(inf, -1.0);
+ special_in[idx++] = ComplexType(-inf, nan);
+ special_in[idx++] = ComplexType(inf, nan);
+ #endif
+ special_in[idx++] = ComplexType(1.0, nan);
+ special_in[idx++] = ComplexType(nan, 1.0);
+ special_in[idx++] = ComplexType(nan, -1.0);
+ special_in[idx++] = ComplexType(nan, nan);
+
+ Map<SpecialInputs> special_out(out);
+ special_out = special_in.cwiseSqrt();
+ }
+
+ T x1(in + i);
+ Map<T> res(out + num_special_inputs + i*T::MaxSizeAtCompileTime);
+ res = x1.cwiseSqrt();
+ }
+};
+
+template<typename T>
+struct complex_operators {
+ EIGEN_DEVICE_FUNC
+ void operator()(int i, const typename T::Scalar* in, typename T::Scalar* out) const
+ {
+ using namespace Eigen;
+ typedef typename T::Scalar ComplexType;
+ typedef typename T::Scalar::value_type ValueType;
+ const int num_scalar_operators = 24;
+ const int num_vector_operators = 23; // no unary + operator.
+ int out_idx = i * (num_scalar_operators + num_vector_operators * T::MaxSizeAtCompileTime);
+
+ // Scalar operators.
+ const ComplexType a = in[i];
+ const ComplexType b = in[i + 1];
+
+ out[out_idx++] = +a;
+ out[out_idx++] = -a;
+
+ out[out_idx++] = a + b;
+ out[out_idx++] = a + numext::real(b);
+ out[out_idx++] = numext::real(a) + b;
+ out[out_idx++] = a - b;
+ out[out_idx++] = a - numext::real(b);
+ out[out_idx++] = numext::real(a) - b;
+ out[out_idx++] = a * b;
+ out[out_idx++] = a * numext::real(b);
+ out[out_idx++] = numext::real(a) * b;
+ out[out_idx++] = a / b;
+ out[out_idx++] = a / numext::real(b);
+ out[out_idx++] = numext::real(a) / b;
+
+#if !defined(EIGEN_COMP_MSVC)
+ out[out_idx] = a; out[out_idx++] += b;
+ out[out_idx] = a; out[out_idx++] -= b;
+ out[out_idx] = a; out[out_idx++] *= b;
+ out[out_idx] = a; out[out_idx++] /= b;
+#endif
+
+ const ComplexType true_value = ComplexType(ValueType(1), ValueType(0));
+ const ComplexType false_value = ComplexType(ValueType(0), ValueType(0));
+ out[out_idx++] = (a == b ? true_value : false_value);
+ out[out_idx++] = (a == numext::real(b) ? true_value : false_value);
+ out[out_idx++] = (numext::real(a) == b ? true_value : false_value);
+ out[out_idx++] = (a != b ? true_value : false_value);
+ out[out_idx++] = (a != numext::real(b) ? true_value : false_value);
+ out[out_idx++] = (numext::real(a) != b ? true_value : false_value);
+
+ // Vector versions.
+ T x1(in + i);
+ T x2(in + i + 1);
+ const int res_size = T::MaxSizeAtCompileTime * num_scalar_operators;
+ const int size = T::MaxSizeAtCompileTime;
+ int block_idx = 0;
+
+ Map<VectorX<ComplexType>> res(out + out_idx, res_size);
+ res.segment(block_idx, size) = -x1;
+ block_idx += size;
+
+ res.segment(block_idx, size) = x1 + x2;
+ block_idx += size;
+ res.segment(block_idx, size) = x1 + x2.real();
+ block_idx += size;
+ res.segment(block_idx, size) = x1.real() + x2;
+ block_idx += size;
+ res.segment(block_idx, size) = x1 - x2;
+ block_idx += size;
+ res.segment(block_idx, size) = x1 - x2.real();
+ block_idx += size;
+ res.segment(block_idx, size) = x1.real() - x2;
+ block_idx += size;
+ res.segment(block_idx, size) = x1.array() * x2.array();
+ block_idx += size;
+ res.segment(block_idx, size) = x1.array() * x2.real().array();
+ block_idx += size;
+ res.segment(block_idx, size) = x1.real().array() * x2.array();
+ block_idx += size;
+ res.segment(block_idx, size) = x1.array() / x2.array();
+ block_idx += size;
+ res.segment(block_idx, size) = x1.array() / x2.real().array();
+ block_idx += size;
+ res.segment(block_idx, size) = x1.real().array() / x2.array();
+ block_idx += size;
+
+#if !defined(EIGEN_COMP_MSVC)
+ res.segment(block_idx, size) = x1; res.segment(block_idx, size) += x2;
+ block_idx += size;
+ res.segment(block_idx, size) = x1; res.segment(block_idx, size) -= x2;
+ block_idx += size;
+ res.segment(block_idx, size) = x1; res.segment(block_idx, size).array() *= x2.array();
+ block_idx += size;
+ res.segment(block_idx, size) = x1; res.segment(block_idx, size).array() /= x2.array();
+ block_idx += size;
+#endif
+
+ const T true_vector = T::Constant(true_value);
+ const T false_vector = T::Constant(false_value);
+ res.segment(block_idx, size) = (x1 == x2 ? true_vector : false_vector);
+ block_idx += size;
+ // Mixing types in equality comparison does not work.
+ // res.segment(block_idx, size) = (x1 == x2.real() ? true_vector : false_vector);
+ // block_idx += size;
+ // res.segment(block_idx, size) = (x1.real() == x2 ? true_vector : false_vector);
+ // block_idx += size;
+ res.segment(block_idx, size) = (x1 != x2 ? true_vector : false_vector);
+ block_idx += size;
+ // res.segment(block_idx, size) = (x1 != x2.real() ? true_vector : false_vector);
+ // block_idx += size;
+ // res.segment(block_idx, size) = (x1.real() != x2 ? true_vector : false_vector);
+ // block_idx += size;
+ }
+};
+
+template<typename T>
+struct replicate {
+ EIGEN_DEVICE_FUNC
+ void operator()(int i, const typename T::Scalar* in, typename T::Scalar* out) const
+ {
+ using namespace Eigen;
+ T x1(in+i);
+ int step = x1.size() * 4;
+ int stride = 3 * step;
+
+ typedef Map<Array<typename T::Scalar,Dynamic,Dynamic> > MapType;
+ MapType(out+i*stride+0*step, x1.rows()*2, x1.cols()*2) = x1.replicate(2,2);
+ MapType(out+i*stride+1*step, x1.rows()*3, x1.cols()) = in[i] * x1.colwise().replicate(3);
+ MapType(out+i*stride+2*step, x1.rows(), x1.cols()*3) = in[i] * x1.rowwise().replicate(3);
+ }
+};
+
+template<typename T>
+struct alloc_new_delete {
+ EIGEN_DEVICE_FUNC
+ void operator()(int i, const typename T::Scalar* in, typename T::Scalar* out) const
+ {
+ int offset = 2*i*T::MaxSizeAtCompileTime;
+ T* x = new T(in + offset);
+ Eigen::Map<T> u(out + offset);
+ u = *x;
+ delete x;
+
+ offset += T::MaxSizeAtCompileTime;
+ T* y = new T[1];
+ y[0] = T(in + offset);
+ Eigen::Map<T> v(out + offset);
+ v = y[0];
+ delete[] y;
+ }
+};
+
+template<typename T>
+struct redux {
+ EIGEN_DEVICE_FUNC
+ void operator()(int i, const typename T::Scalar* in, typename T::Scalar* out) const
+ {
+ using namespace Eigen;
+ int N = 10;
+ T x1(in+i);
+ out[i*N+0] = x1.minCoeff();
+ out[i*N+1] = x1.maxCoeff();
+ out[i*N+2] = x1.sum();
+ out[i*N+3] = x1.prod();
+ out[i*N+4] = x1.matrix().squaredNorm();
+ out[i*N+5] = x1.matrix().norm();
+ out[i*N+6] = x1.colwise().sum().maxCoeff();
+ out[i*N+7] = x1.rowwise().maxCoeff().sum();
+ out[i*N+8] = x1.matrix().colwise().squaredNorm().sum();
+ }
+};
+
+template<typename T1, typename T2>
+struct prod_test {
+ EIGEN_DEVICE_FUNC
+ void operator()(int i, const typename T1::Scalar* in, typename T1::Scalar* out) const
+ {
+ using namespace Eigen;
+ typedef Matrix<typename T1::Scalar, T1::RowsAtCompileTime, T2::ColsAtCompileTime> T3;
+ T1 x1(in+i);
+ T2 x2(in+i+1);
+ Map<T3> res(out+i*T3::MaxSizeAtCompileTime);
+ res += in[i] * x1 * x2;
+ }
+};
+
+template<typename T1, typename T2>
+struct diagonal {
+ EIGEN_DEVICE_FUNC
+ void operator()(int i, const typename T1::Scalar* in, typename T1::Scalar* out) const
+ {
+ using namespace Eigen;
+ T1 x1(in+i);
+ Map<T2> res(out+i*T2::MaxSizeAtCompileTime);
+ res += x1.diagonal();
+ }
+};
+
+template<typename T>
+struct eigenvalues_direct {
+ EIGEN_DEVICE_FUNC
+ void operator()(int i, const typename T::Scalar* in, typename T::Scalar* out) const
+ {
+ using namespace Eigen;
+ typedef Matrix<typename T::Scalar, T::RowsAtCompileTime, 1> Vec;
+ T M(in+i);
+ Map<Vec> res(out+i*Vec::MaxSizeAtCompileTime);
+ T A = M*M.adjoint();
+ SelfAdjointEigenSolver<T> eig;
+ eig.computeDirect(A);
+ res = eig.eigenvalues();
+ }
+};
+
+template<typename T>
+struct eigenvalues {
+ EIGEN_DEVICE_FUNC
+ void operator()(int i, const typename T::Scalar* in, typename T::Scalar* out) const
+ {
+ using namespace Eigen;
+ typedef Matrix<typename T::Scalar, T::RowsAtCompileTime, 1> Vec;
+ T M(in+i);
+ Map<Vec> res(out+i*Vec::MaxSizeAtCompileTime);
+ T A = M*M.adjoint();
+ SelfAdjointEigenSolver<T> eig;
+ eig.compute(A);
+ res = eig.eigenvalues();
+ }
+};
+
+template<typename T>
+struct matrix_inverse {
+ EIGEN_DEVICE_FUNC
+ void operator()(int i, const typename T::Scalar* in, typename T::Scalar* out) const
+ {
+ using namespace Eigen;
+ T M(in+i);
+ Map<T> res(out+i*T::MaxSizeAtCompileTime);
+ res = M.inverse();
+ }
+};
+
+template<typename T>
+struct numeric_limits_test {
+ EIGEN_DEVICE_FUNC
+ void operator()(int i, const typename T::Scalar* in, typename T::Scalar* out) const
+ {
+ EIGEN_UNUSED_VARIABLE(in)
+ int out_idx = i * 5;
+ out[out_idx++] = numext::numeric_limits<float>::epsilon();
+ out[out_idx++] = (numext::numeric_limits<float>::max)();
+ out[out_idx++] = (numext::numeric_limits<float>::min)();
+ out[out_idx++] = numext::numeric_limits<float>::infinity();
+ out[out_idx++] = numext::numeric_limits<float>::quiet_NaN();
+ }
+};
+
+template<typename Type1, typename Type2>
+bool verifyIsApproxWithInfsNans(const Type1& a, const Type2& b, typename Type1::Scalar* = 0) // Enabled for Eigen's type only
+{
+ if (a.rows() != b.rows()) {
+ return false;
+ }
+ if (a.cols() != b.cols()) {
+ return false;
+ }
+ for (Index r = 0; r < a.rows(); ++r) {
+ for (Index c = 0; c < a.cols(); ++c) {
+ if (a(r, c) != b(r, c)
+ && !((numext::isnan)(a(r, c)) && (numext::isnan)(b(r, c)))
+ && !test_isApprox(a(r, c), b(r, c))) {
+ return false;
+ }
+ }
+ }
+ return true;
+}
+
+template<typename Kernel, typename Input, typename Output>
+void test_with_infs_nans(const Kernel& ker, int n, const Input& in, Output& out)
+{
+ Output out_ref, out_gpu;
+ #if !defined(EIGEN_GPU_COMPILE_PHASE)
+ out_ref = out_gpu = out;
+ #else
+ EIGEN_UNUSED_VARIABLE(in);
+ EIGEN_UNUSED_VARIABLE(out);
+ #endif
+ run_on_cpu (ker, n, in, out_ref);
+ run_on_gpu(ker, n, in, out_gpu);
+ #if !defined(EIGEN_GPU_COMPILE_PHASE)
+ verifyIsApproxWithInfsNans(out_ref, out_gpu);
+ #endif
+}
+
+EIGEN_DECLARE_TEST(gpu_basic)
+{
+ ei_test_init_gpu();
+
+ int nthreads = 100;
+ Eigen::VectorXf in, out;
+ Eigen::VectorXcf cfin, cfout;
+
+ #if !defined(EIGEN_GPU_COMPILE_PHASE)
+ int data_size = nthreads * 512;
+ in.setRandom(data_size);
+ out.setConstant(data_size, -1);
+ cfin.setRandom(data_size);
+ cfout.setConstant(data_size, -1);
+ #endif
+
+ CALL_SUBTEST( run_and_compare_to_gpu(coeff_wise<Vector3f>(), nthreads, in, out) );
+ CALL_SUBTEST( run_and_compare_to_gpu(coeff_wise<Array44f>(), nthreads, in, out) );
+
+#if !defined(EIGEN_USE_HIP)
+ // FIXME
+ // These subtests result in a compile failure on the HIP platform
+ //
+ // eigen-upstream/Eigen/src/Core/Replicate.h:61:65: error:
+ // base class 'internal::dense_xpr_base<Replicate<Array<float, 4, 1, 0, 4, 1>, -1, -1> >::type'
+ // (aka 'ArrayBase<Eigen::Replicate<Eigen::Array<float, 4, 1, 0, 4, 1>, -1, -1> >') has protected default constructor
+ CALL_SUBTEST( run_and_compare_to_gpu(replicate<Array4f>(), nthreads, in, out) );
+ CALL_SUBTEST( run_and_compare_to_gpu(replicate<Array33f>(), nthreads, in, out) );
+
+ // HIP does not support new/delete on device.
+ CALL_SUBTEST( run_and_compare_to_gpu(alloc_new_delete<Vector3f>(), nthreads, in, out) );
+#endif
+
+ CALL_SUBTEST( run_and_compare_to_gpu(redux<Array4f>(), nthreads, in, out) );
+ CALL_SUBTEST( run_and_compare_to_gpu(redux<Matrix3f>(), nthreads, in, out) );
+
+ CALL_SUBTEST( run_and_compare_to_gpu(prod_test<Matrix3f,Matrix3f>(), nthreads, in, out) );
+ CALL_SUBTEST( run_and_compare_to_gpu(prod_test<Matrix4f,Vector4f>(), nthreads, in, out) );
+
+ CALL_SUBTEST( run_and_compare_to_gpu(diagonal<Matrix3f,Vector3f>(), nthreads, in, out) );
+ CALL_SUBTEST( run_and_compare_to_gpu(diagonal<Matrix4f,Vector4f>(), nthreads, in, out) );
+
+ CALL_SUBTEST( run_and_compare_to_gpu(matrix_inverse<Matrix2f>(), nthreads, in, out) );
+ CALL_SUBTEST( run_and_compare_to_gpu(matrix_inverse<Matrix3f>(), nthreads, in, out) );
+ CALL_SUBTEST( run_and_compare_to_gpu(matrix_inverse<Matrix4f>(), nthreads, in, out) );
+
+ CALL_SUBTEST( run_and_compare_to_gpu(eigenvalues_direct<Matrix3f>(), nthreads, in, out) );
+ CALL_SUBTEST( run_and_compare_to_gpu(eigenvalues_direct<Matrix2f>(), nthreads, in, out) );
+
+ // Test std::complex.
+ CALL_SUBTEST( run_and_compare_to_gpu(complex_operators<Vector3cf>(), nthreads, cfin, cfout) );
+ CALL_SUBTEST( test_with_infs_nans(complex_sqrt<Vector3cf>(), nthreads, cfin, cfout) );
+
+ // numeric_limits
+ CALL_SUBTEST( test_with_infs_nans(numeric_limits_test<Vector3f>(), 1, in, out) );
+
+#if defined(__NVCC__)
+ // FIXME
+ // These subtests compiles only with nvcc and fail with HIPCC and clang-cuda
+ CALL_SUBTEST( run_and_compare_to_gpu(eigenvalues<Matrix4f>(), nthreads, in, out) );
+ typedef Matrix<float,6,6> Matrix6f;
+ CALL_SUBTEST( run_and_compare_to_gpu(eigenvalues<Matrix6f>(), nthreads, in, out) );
+#endif
+}
diff --git a/test/gpu_common.h b/test/gpu_common.h
new file mode 100644
index 0000000..c37eaa1
--- /dev/null
+++ b/test/gpu_common.h
@@ -0,0 +1,176 @@
+#ifndef EIGEN_TEST_GPU_COMMON_H
+#define EIGEN_TEST_GPU_COMMON_H
+
+#ifdef EIGEN_USE_HIP
+ #include <hip/hip_runtime.h>
+ #include <hip/hip_runtime_api.h>
+#else
+ #include <cuda.h>
+ #include <cuda_runtime.h>
+ #include <cuda_runtime_api.h>
+#endif
+
+#include <iostream>
+
+#define EIGEN_USE_GPU
+#include <unsupported/Eigen/CXX11/src/Tensor/TensorGpuHipCudaDefines.h>
+
+#if !defined(__CUDACC__) && !defined(__HIPCC__)
+dim3 threadIdx, blockDim, blockIdx;
+#endif
+
+template<typename Kernel, typename Input, typename Output>
+void run_on_cpu(const Kernel& ker, int n, const Input& in, Output& out)
+{
+ for(int i=0; i<n; i++)
+ ker(i, in.data(), out.data());
+}
+
+
+template<typename Kernel, typename Input, typename Output>
+__global__
+EIGEN_HIP_LAUNCH_BOUNDS_1024
+void run_on_gpu_meta_kernel(const Kernel ker, int n, const Input* in, Output* out)
+{
+ int i = threadIdx.x + blockIdx.x*blockDim.x;
+ if(i<n) {
+ ker(i, in, out);
+ }
+}
+
+
+template<typename Kernel, typename Input, typename Output>
+void run_on_gpu(const Kernel& ker, int n, const Input& in, Output& out)
+{
+ typename Input::Scalar* d_in;
+ typename Output::Scalar* d_out;
+ std::ptrdiff_t in_bytes = in.size() * sizeof(typename Input::Scalar);
+ std::ptrdiff_t out_bytes = out.size() * sizeof(typename Output::Scalar);
+
+ gpuMalloc((void**)(&d_in), in_bytes);
+ gpuMalloc((void**)(&d_out), out_bytes);
+
+ gpuMemcpy(d_in, in.data(), in_bytes, gpuMemcpyHostToDevice);
+ gpuMemcpy(d_out, out.data(), out_bytes, gpuMemcpyHostToDevice);
+
+ // Simple and non-optimal 1D mapping assuming n is not too large
+ // That's only for unit testing!
+ dim3 Blocks(128);
+ dim3 Grids( (n+int(Blocks.x)-1)/int(Blocks.x) );
+
+ gpuDeviceSynchronize();
+
+#ifdef EIGEN_USE_HIP
+ hipLaunchKernelGGL(HIP_KERNEL_NAME(run_on_gpu_meta_kernel<Kernel,
+ typename std::decay<decltype(*d_in)>::type,
+ typename std::decay<decltype(*d_out)>::type>),
+ dim3(Grids), dim3(Blocks), 0, 0, ker, n, d_in, d_out);
+#else
+ run_on_gpu_meta_kernel<<<Grids,Blocks>>>(ker, n, d_in, d_out);
+#endif
+ // Pre-launch errors.
+ gpuError_t err = gpuGetLastError();
+ if (err != gpuSuccess) {
+ printf("%s: %s\n", gpuGetErrorName(err), gpuGetErrorString(err));
+ gpu_assert(false);
+ }
+
+ // Kernel execution errors.
+ err = gpuDeviceSynchronize();
+ if (err != gpuSuccess) {
+ printf("%s: %s\n", gpuGetErrorName(err), gpuGetErrorString(err));
+ gpu_assert(false);
+ }
+
+
+ // check inputs have not been modified
+ gpuMemcpy(const_cast<typename Input::Scalar*>(in.data()), d_in, in_bytes, gpuMemcpyDeviceToHost);
+ gpuMemcpy(out.data(), d_out, out_bytes, gpuMemcpyDeviceToHost);
+
+ gpuFree(d_in);
+ gpuFree(d_out);
+}
+
+
+template<typename Kernel, typename Input, typename Output>
+void run_and_compare_to_gpu(const Kernel& ker, int n, const Input& in, Output& out)
+{
+ Input in_ref, in_gpu;
+ Output out_ref, out_gpu;
+ #if !defined(EIGEN_GPU_COMPILE_PHASE)
+ in_ref = in_gpu = in;
+ out_ref = out_gpu = out;
+ #else
+ EIGEN_UNUSED_VARIABLE(in);
+ EIGEN_UNUSED_VARIABLE(out);
+ #endif
+ run_on_cpu (ker, n, in_ref, out_ref);
+ run_on_gpu(ker, n, in_gpu, out_gpu);
+ #if !defined(EIGEN_GPU_COMPILE_PHASE)
+ VERIFY_IS_APPROX(in_ref, in_gpu);
+ VERIFY_IS_APPROX(out_ref, out_gpu);
+ #endif
+}
+
+struct compile_time_device_info {
+ EIGEN_DEVICE_FUNC
+ void operator()(int i, const int* /*in*/, int* info) const
+ {
+ if (i == 0) {
+ EIGEN_UNUSED_VARIABLE(info)
+ #if defined(__CUDA_ARCH__)
+ info[0] = int(__CUDA_ARCH__ +0);
+ #endif
+ #if defined(EIGEN_HIP_DEVICE_COMPILE)
+ info[1] = int(EIGEN_HIP_DEVICE_COMPILE +0);
+ #endif
+ }
+ }
+};
+
+void ei_test_init_gpu()
+{
+ int device = 0;
+ gpuDeviceProp_t deviceProp;
+ gpuGetDeviceProperties(&deviceProp, device);
+
+ ArrayXi dummy(1), info(10);
+ info = -1;
+ run_on_gpu(compile_time_device_info(),10,dummy,info);
+
+
+ std::cout << "GPU compile-time info:\n";
+
+ #ifdef EIGEN_CUDACC
+ std::cout << " EIGEN_CUDACC: " << int(EIGEN_CUDACC) << "\n";
+ #endif
+
+ #ifdef EIGEN_CUDA_SDK_VER
+ std::cout << " EIGEN_CUDA_SDK_VER: " << int(EIGEN_CUDA_SDK_VER) << "\n";
+ #endif
+
+ #ifdef EIGEN_COMP_NVCC
+ std::cout << " EIGEN_COMP_NVCC: " << int(EIGEN_COMP_NVCC) << "\n";
+ #endif
+
+ #ifdef EIGEN_HIPCC
+ std::cout << " EIGEN_HIPCC: " << int(EIGEN_HIPCC) << "\n";
+ #endif
+
+ std::cout << " EIGEN_CUDA_ARCH: " << info[0] << "\n";
+ std::cout << " EIGEN_HIP_DEVICE_COMPILE: " << info[1] << "\n";
+
+ std::cout << "GPU device info:\n";
+ std::cout << " name: " << deviceProp.name << "\n";
+ std::cout << " capability: " << deviceProp.major << "." << deviceProp.minor << "\n";
+ std::cout << " multiProcessorCount: " << deviceProp.multiProcessorCount << "\n";
+ std::cout << " maxThreadsPerMultiProcessor: " << deviceProp.maxThreadsPerMultiProcessor << "\n";
+ std::cout << " warpSize: " << deviceProp.warpSize << "\n";
+ std::cout << " regsPerBlock: " << deviceProp.regsPerBlock << "\n";
+ std::cout << " concurrentKernels: " << deviceProp.concurrentKernels << "\n";
+ std::cout << " clockRate: " << deviceProp.clockRate << "\n";
+ std::cout << " canMapHostMemory: " << deviceProp.canMapHostMemory << "\n";
+ std::cout << " computeMode: " << deviceProp.computeMode << "\n";
+}
+
+#endif // EIGEN_TEST_GPU_COMMON_H
diff --git a/test/gpu_example.cu b/test/gpu_example.cu
new file mode 100644
index 0000000..a69f5ea
--- /dev/null
+++ b/test/gpu_example.cu
@@ -0,0 +1,129 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2021 The Eigen Team.
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+// The following is an example GPU test.
+
+#include "main.h" // Include the main test utilities.
+
+// Define a kernel functor.
+//
+// The kernel must be a POD type and implement operator().
+struct AddKernel {
+ // Parameters must be POD or serializable Eigen types (e.g. Matrix,
+ // Array). The return value must be a POD or serializable value type.
+ template<typename Type1, typename Type2, typename Type3>
+ EIGEN_DEVICE_FUNC
+ Type3 operator()(const Type1& A, const Type2& B, Type3& C) const {
+ C = A + B; // Populate output parameter.
+ Type3 D = A + B; // Populate return value.
+ return D;
+ }
+};
+
+// Define a sub-test that uses the kernel.
+template <typename T>
+void test_add(const T& type) {
+ const Index rows = type.rows();
+ const Index cols = type.cols();
+
+ // Create random inputs.
+ const T A = T::Random(rows, cols);
+ const T B = T::Random(rows, cols);
+ T C; // Output parameter.
+
+ // Create kernel.
+ AddKernel add_kernel;
+
+ // Run add_kernel(A, B, C) via run(...).
+ // This will run on the GPU if using a GPU compiler, or CPU otherwise,
+ // facilitating generic tests that can run on either.
+ T D = run(add_kernel, A, B, C);
+
+ // Check that both output parameter and return value are correctly populated.
+ const T expected = A + B;
+ VERIFY_IS_CWISE_EQUAL(C, expected);
+ VERIFY_IS_CWISE_EQUAL(D, expected);
+
+ // In a GPU-only test, we can verify that the CPU and GPU produce the
+ // same results.
+ T C_cpu, C_gpu;
+ T D_cpu = run_on_cpu(add_kernel, A, B, C_cpu); // Runs on CPU.
+ T D_gpu = run_on_gpu(add_kernel, A, B, C_gpu); // Runs on GPU.
+ VERIFY_IS_CWISE_EQUAL(C_cpu, C_gpu);
+ VERIFY_IS_CWISE_EQUAL(D_cpu, D_gpu);
+};
+
+struct MultiplyKernel {
+ template<typename Type1, typename Type2, typename Type3>
+ EIGEN_DEVICE_FUNC
+ Type3 operator()(const Type1& A, const Type2& B, Type3& C) const {
+ C = A * B;
+ return A * B;
+ }
+};
+
+template <typename T1, typename T2, typename T3>
+void test_multiply(const T1& type1, const T2& type2, const T3& type3) {
+ const T1 A = T1::Random(type1.rows(), type1.cols());
+ const T2 B = T2::Random(type2.rows(), type2.cols());
+ T3 C;
+
+ MultiplyKernel multiply_kernel;
+
+ // The run(...) family of functions uses a memory buffer to transfer data back
+ // and forth to and from the device. The size of this buffer is estimated
+ // from the size of all input parameters. If the estimated buffer size is
+ // not sufficient for transferring outputs from device-to-host, then an
+ // explicit buffer size needs to be specified.
+
+ // 2 outputs of size (A * B). For each matrix output, the buffer will store
+ // the number of rows, columns, and the data.
+ size_t buffer_capacity_hint = 2 * ( // 2 output parameters
+ 2 * sizeof(typename T3::Index) // # Rows, # Cols
+ + A.rows() * B.cols() * sizeof(typename T3::Scalar)); // Output data
+
+ T3 D = run_with_hint(buffer_capacity_hint, multiply_kernel, A, B, C);
+
+ const T3 expected = A * B;
+ VERIFY_IS_CWISE_APPROX(C, expected);
+ VERIFY_IS_CWISE_APPROX(D, expected);
+
+ T3 C_cpu, C_gpu;
+ T3 D_cpu = run_on_cpu(multiply_kernel, A, B, C_cpu);
+ T3 D_gpu = run_on_gpu_with_hint(buffer_capacity_hint,
+ multiply_kernel, A, B, C_gpu);
+ VERIFY_IS_CWISE_APPROX(C_cpu, C_gpu);
+ VERIFY_IS_CWISE_APPROX(D_cpu, D_gpu);
+}
+
+// Declare the test fixture.
+EIGEN_DECLARE_TEST(gpu_example)
+{
+ // For the number of repeats, call the desired subtests.
+ for(int i = 0; i < g_repeat; i++) {
+ // Call subtests with different sized/typed inputs.
+ CALL_SUBTEST( test_add(Eigen::Vector3f()) );
+ CALL_SUBTEST( test_add(Eigen::Matrix3d()) );
+ CALL_SUBTEST( test_add(Eigen::MatrixX<int>(10, 10)) );
+
+ CALL_SUBTEST( test_add(Eigen::Array44f()) );
+ CALL_SUBTEST( test_add(Eigen::ArrayXd(20)) );
+ CALL_SUBTEST( test_add(Eigen::ArrayXXi(13, 17)) );
+
+ CALL_SUBTEST( test_multiply(Eigen::Matrix3d(),
+ Eigen::Matrix3d(),
+ Eigen::Matrix3d()) );
+ CALL_SUBTEST( test_multiply(Eigen::MatrixX<int>(10, 10),
+ Eigen::MatrixX<int>(10, 10),
+ Eigen::MatrixX<int>()) );
+ CALL_SUBTEST( test_multiply(Eigen::MatrixXf(12, 1),
+ Eigen::MatrixXf(1, 32),
+ Eigen::MatrixXf()) );
+ }
+}
diff --git a/test/gpu_test_helper.h b/test/gpu_test_helper.h
new file mode 100644
index 0000000..0942466
--- /dev/null
+++ b/test/gpu_test_helper.h
@@ -0,0 +1,476 @@
+#ifndef GPU_TEST_HELPER_H
+#define GPU_TEST_HELPER_H
+
+#include <Eigen/Core>
+
+#ifdef EIGEN_GPUCC
+#define EIGEN_USE_GPU
+#include "../unsupported/Eigen/CXX11/src/Tensor/TensorGpuHipCudaDefines.h"
+#endif // EIGEN_GPUCC
+
+// std::tuple cannot be used on device, and there is a bug in cuda < 9.2 that
+// doesn't allow std::tuple to compile for host code either. In these cases,
+// use our custom implementation.
+#if defined(EIGEN_GPU_COMPILE_PHASE) || (defined(EIGEN_CUDACC) && EIGEN_CUDA_SDK_VER < 92000)
+#define EIGEN_USE_CUSTOM_TUPLE 1
+#else
+#define EIGEN_USE_CUSTOM_TUPLE 0
+#endif
+
+#if EIGEN_USE_CUSTOM_TUPLE
+#include "../Eigen/src/Core/arch/GPU/Tuple.h"
+#else
+#include <tuple>
+#endif
+namespace Eigen {
+
+namespace internal {
+
+// Note: cannot re-use tuple_impl, since that will cause havoc for
+// tuple_test.
+namespace test_detail {
+// Use std::tuple on CPU, otherwise use the GPU-specific versions.
+#if !EIGEN_USE_CUSTOM_TUPLE
+using std::tuple;
+using std::get;
+using std::make_tuple;
+using std::tie;
+#else
+using tuple_impl::tuple;
+using tuple_impl::get;
+using tuple_impl::make_tuple;
+using tuple_impl::tie;
+#endif
+#undef EIGEN_USE_CUSTOM_TUPLE
+} // namespace test_detail
+
+template<size_t N, size_t Idx, typename OutputIndexSequence, typename... Ts>
+struct extract_output_indices_helper;
+
+/**
+ * Extracts a set of indices corresponding to non-const l-value reference
+ * output types.
+ *
+ * \internal
+ * \tparam N the number of types {T1, Ts...}.
+ * \tparam Idx the "index" to append if T1 is an output type.
+ * \tparam OutputIndices the current set of output indices.
+ * \tparam T1 the next type to consider, with index Idx.
+ * \tparam Ts the remaining types.
+ */
+template<size_t N, size_t Idx, size_t... OutputIndices, typename T1, typename... Ts>
+struct extract_output_indices_helper<N, Idx, std::index_sequence<OutputIndices...>, T1, Ts...> {
+ using type = typename
+ extract_output_indices_helper<
+ N - 1, Idx + 1,
+ typename std::conditional<
+ // If is a non-const l-value reference, append index.
+ std::is_lvalue_reference<T1>::value
+ && !std::is_const<std::remove_reference_t<T1>>::value,
+ std::index_sequence<OutputIndices..., Idx>,
+ std::index_sequence<OutputIndices...> >::type,
+ Ts...>::type;
+};
+
+// Base case.
+template<size_t Idx, size_t... OutputIndices>
+struct extract_output_indices_helper<0, Idx, std::index_sequence<OutputIndices...> > {
+ using type = std::index_sequence<OutputIndices...>;
+};
+
+// Extracts a set of indices into Types... that correspond to non-const
+// l-value references.
+template<typename... Types>
+using extract_output_indices = typename extract_output_indices_helper<sizeof...(Types), 0, std::index_sequence<>, Types...>::type;
+
+// Helper struct for dealing with Generic functors that may return void.
+struct void_helper {
+ struct Void {};
+
+ // Converts void -> Void, T otherwise.
+ template<typename T>
+ using ReturnType = typename std::conditional<std::is_same<T, void>::value, Void, T>::type;
+
+ // Non-void return value.
+ template<typename Func, typename... Args>
+ static EIGEN_ALWAYS_INLINE EIGEN_DEVICE_FUNC
+ auto call(Func&& func, Args&&... args) ->
+ std::enable_if_t<!std::is_same<decltype(func(args...)), void>::value,
+ decltype(func(args...))> {
+ return func(std::forward<Args>(args)...);
+ }
+
+ // Void return value.
+ template<typename Func, typename... Args>
+ static EIGEN_ALWAYS_INLINE EIGEN_DEVICE_FUNC
+ auto call(Func&& func, Args&&... args) ->
+ std::enable_if_t<std::is_same<decltype(func(args...)), void>::value,
+ Void> {
+ func(std::forward<Args>(args)...);
+ return Void{};
+ }
+
+ // Restores the original return type, Void -> void, T otherwise.
+ template<typename T>
+ static EIGEN_ALWAYS_INLINE EIGEN_DEVICE_FUNC
+ std::enable_if_t<!std::is_same<typename std::decay<T>::type, Void>::value, T>
+ restore(T&& val) {
+ return val;
+ }
+
+ // Void case.
+ template<typename T = void>
+ static EIGEN_ALWAYS_INLINE EIGEN_DEVICE_FUNC
+ void restore(const Void&) {}
+};
+
+// Runs a kernel via serialized buffer. Does this by deserializing the buffer
+// to construct the arguments, calling the kernel, then re-serialing the outputs.
+// The buffer contains
+// [ input_buffer_size, args ]
+// After the kernel call, it is then populated with
+// [ output_buffer_size, output_parameters, return_value ]
+// If the output_buffer_size exceeds the buffer's capacity, then only the
+// output_buffer_size is populated.
+template<typename Kernel, typename... Args, size_t... Indices, size_t... OutputIndices>
+EIGEN_DEVICE_FUNC
+void run_serialized(std::index_sequence<Indices...>, std::index_sequence<OutputIndices...>,
+ Kernel kernel, uint8_t* buffer, size_t capacity) {
+ using test_detail::get;
+ using test_detail::make_tuple;
+ using test_detail::tuple;
+ // Deserialize input size and inputs.
+ size_t input_size;
+ const uint8_t* read_ptr = buffer;
+ const uint8_t* read_end = buffer + capacity;
+ read_ptr = Eigen::deserialize(read_ptr, read_end, input_size);
+ // Create value-type instances to populate.
+ auto args = make_tuple(typename std::decay<Args>::type{}...);
+ EIGEN_UNUSED_VARIABLE(args) // Avoid NVCC compile warning.
+ // NVCC 9.1 requires us to spell out the template parameters explicitly.
+ read_ptr = Eigen::deserialize(read_ptr, read_end, get<Indices, typename std::decay<Args>::type...>(args)...);
+
+ // Call function, with void->Void conversion so we are guaranteed a complete
+ // output type.
+ auto result = void_helper::call(kernel, get<Indices, typename std::decay<Args>::type...>(args)...);
+
+ // Determine required output size.
+ size_t output_size = Eigen::serialize_size(capacity);
+ output_size += Eigen::serialize_size(get<OutputIndices, typename std::decay<Args>::type...>(args)...);
+ output_size += Eigen::serialize_size(result);
+
+ // Always serialize required buffer size.
+ uint8_t* write_ptr = buffer;
+ uint8_t* write_end = buffer + capacity;
+ write_ptr = Eigen::serialize(write_ptr, write_end, output_size);
+ // Null `write_ptr` can be safely passed along.
+ // Serialize outputs if they fit in the buffer.
+ if (output_size <= capacity) {
+ // Collect outputs and result.
+ write_ptr = Eigen::serialize(write_ptr, write_end, get<OutputIndices, typename std::decay<Args>::type...>(args)...);
+ write_ptr = Eigen::serialize(write_ptr, write_end, result);
+ }
+}
+
+template<typename Kernel, typename... Args>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+void run_serialized(Kernel kernel, uint8_t* buffer, size_t capacity) {
+ run_serialized<Kernel, Args...> (std::make_index_sequence<sizeof...(Args)>{},
+ extract_output_indices<Args...>{},
+ kernel, buffer, capacity);
+}
+
+#ifdef EIGEN_GPUCC
+
+// Checks for GPU errors and asserts / prints the error message.
+#define GPU_CHECK(expr) \
+do { \
+ gpuError_t err = expr; \
+ if (err != gpuSuccess) { \
+ printf("%s: %s\n", gpuGetErrorName(err), gpuGetErrorString(err)); \
+ gpu_assert(false); \
+ } \
+} while(0)
+
+// Calls run_serialized on the GPU.
+template<typename Kernel, typename... Args>
+__global__
+EIGEN_HIP_LAUNCH_BOUNDS_1024
+void run_serialized_on_gpu_meta_kernel(const Kernel kernel, uint8_t* buffer, size_t capacity) {
+ run_serialized<Kernel, Args...>(kernel, buffer, capacity);
+}
+
+// Runs kernel(args...) on the GPU via the serialization mechanism.
+//
+// Note: this may end up calling the kernel multiple times if the initial output
+// buffer is not large enough to hold the outputs.
+template<typename Kernel, typename... Args, size_t... Indices, size_t... OutputIndices>
+auto run_serialized_on_gpu(size_t buffer_capacity_hint,
+ std::index_sequence<Indices...>,
+ std::index_sequence<OutputIndices...>,
+ Kernel kernel, Args&&... args) -> decltype(kernel(args...)) {
+ // Compute the required serialization buffer capacity.
+ // Round up input size to next power of two to give a little extra room
+ // for outputs.
+ size_t input_data_size = sizeof(size_t) + Eigen::serialize_size(args...);
+
+ size_t capacity;
+ if (buffer_capacity_hint == 0) {
+ // Estimate as the power of two larger than the total input size.
+ capacity = sizeof(size_t);
+ while (capacity <= input_data_size) {
+ capacity *= 2;
+ }
+ } else {
+ // Use the larger of the hint and the total input size.
+ // Add sizeof(size_t) to the hint to account for storing the buffer capacity
+ // itself so the user doesn't need to think about this.
+ capacity = std::max<size_t>(buffer_capacity_hint + sizeof(size_t),
+ input_data_size);
+ }
+ std::vector<uint8_t> buffer(capacity);
+
+ uint8_t* host_data = nullptr;
+ uint8_t* host_data_end = nullptr;
+ uint8_t* host_ptr = nullptr;
+ uint8_t* device_data = nullptr;
+ size_t output_data_size = 0;
+
+ // Allocate buffers and copy input data.
+ capacity = std::max<size_t>(capacity, output_data_size);
+ buffer.resize(capacity);
+ host_data = buffer.data();
+ host_data_end = buffer.data() + capacity;
+ host_ptr = Eigen::serialize(host_data, host_data_end, input_data_size);
+ host_ptr = Eigen::serialize(host_ptr, host_data_end, args...);
+
+ // Copy inputs to host.
+ gpuMalloc((void**)(&device_data), capacity);
+ gpuMemcpy(device_data, buffer.data(), input_data_size, gpuMemcpyHostToDevice);
+ GPU_CHECK(gpuDeviceSynchronize());
+
+ // Run kernel.
+ #ifdef EIGEN_USE_HIP
+ hipLaunchKernelGGL(
+ HIP_KERNEL_NAME(run_serialized_on_gpu_meta_kernel<Kernel, Args...>),
+ 1, 1, 0, 0, kernel, device_data, capacity);
+ #else
+ run_serialized_on_gpu_meta_kernel<Kernel, Args...><<<1,1>>>(
+ kernel, device_data, capacity);
+ #endif
+ // Check pre-launch and kernel execution errors.
+ GPU_CHECK(gpuGetLastError());
+ GPU_CHECK(gpuDeviceSynchronize());
+ // Copy back new output to host.
+ gpuMemcpy(host_data, device_data, capacity, gpuMemcpyDeviceToHost);
+ gpuFree(device_data);
+ GPU_CHECK(gpuDeviceSynchronize());
+
+ // Determine output buffer size.
+ const uint8_t* c_host_ptr = Eigen::deserialize(host_data, host_data_end, output_data_size);
+ // If the output doesn't fit in the buffer, spit out warning and fail.
+ if (output_data_size > capacity) {
+ std::cerr << "The serialized output does not fit in the output buffer, "
+ << output_data_size << " vs capacity " << capacity << "."
+ << std::endl
+ << "Try specifying a minimum buffer capacity: " << std::endl
+ << " run_with_hint(" << output_data_size << ", ...)"
+ << std::endl;
+ VERIFY(false);
+ }
+
+ // Deserialize outputs.
+ auto args_tuple = test_detail::tie(args...);
+ EIGEN_UNUSED_VARIABLE(args_tuple) // Avoid NVCC compile warning.
+ c_host_ptr = Eigen::deserialize(c_host_ptr, host_data_end, test_detail::get<OutputIndices, Args&...>(args_tuple)...);
+
+ // Maybe deserialize return value, properly handling void.
+ typename void_helper::ReturnType<decltype(kernel(args...))> result;
+ c_host_ptr = Eigen::deserialize(c_host_ptr, host_data_end, result);
+ return void_helper::restore(result);
+}
+
+#endif // EIGEN_GPUCC
+
+} // namespace internal
+
+/**
+ * Runs a kernel on the CPU, returning the results.
+ * \param kernel kernel to run.
+ * \param args ... input arguments.
+ * \return kernel(args...).
+ */
+template<typename Kernel, typename... Args>
+auto run_on_cpu(Kernel kernel, Args&&... args) -> decltype(kernel(args...)){
+ return kernel(std::forward<Args>(args)...);
+}
+
+#ifdef EIGEN_GPUCC
+
+/**
+ * Runs a kernel on the GPU, returning the results.
+ *
+ * The kernel must be able to be passed directly as an input to a global
+ * function (i.e. empty or POD). Its inputs must be "Serializable" so we
+ * can transfer them to the device, and the output must be a Serializable value
+ * type so it can be transferred back from the device.
+ *
+ * \param kernel kernel to run.
+ * \param args ... input arguments, must be "Serializable".
+ * \return kernel(args...).
+ */
+template<typename Kernel, typename... Args>
+auto run_on_gpu(Kernel kernel, Args&&... args) -> decltype(kernel(args...)){
+ return internal::run_serialized_on_gpu<Kernel, Args...>(
+ /*buffer_capacity_hint=*/ 0,
+ std::make_index_sequence<sizeof...(Args)>{},
+ internal::extract_output_indices<Args...>{},
+ kernel, std::forward<Args>(args)...);
+}
+
+/**
+ * Runs a kernel on the GPU, returning the results.
+ *
+ * This version allows specifying a minimum buffer capacity size required for
+ * serializing the puts to transfer results from device to host. Use this when
+ * `run_on_gpu(...)` fails to determine an appropriate capacity by default.
+ *
+ * \param buffer_capacity_hint minimum required buffer size for serializing
+ * outputs.
+ * \param kernel kernel to run.
+ * \param args ... input arguments, must be "Serializable".
+ * \return kernel(args...).
+ * \sa run_on_gpu
+ */
+template<typename Kernel, typename... Args>
+auto run_on_gpu_with_hint(size_t buffer_capacity_hint,
+ Kernel kernel, Args&&... args) -> decltype(kernel(args...)){
+ return internal::run_serialized_on_gpu<Kernel, Args...>(
+ buffer_capacity_hint,
+ std::make_index_sequence<sizeof...(Args)>{},
+ internal::extract_output_indices<Args...>{},
+ kernel, std::forward<Args>(args)...);
+}
+
+/**
+ * Kernel for determining basic Eigen compile-time information
+ * (i.e. the cuda/hip arch)
+ */
+struct CompileTimeDeviceInfoKernel {
+ struct Info {
+ int cuda;
+ int hip;
+ };
+
+ EIGEN_DEVICE_FUNC
+ Info operator()() const
+ {
+ Info info = {-1, -1};
+ #if defined(__CUDA_ARCH__)
+ info.cuda = static_cast<int>(__CUDA_ARCH__ +0);
+ #endif
+ #if defined(EIGEN_HIP_DEVICE_COMPILE)
+ info.hip = static_cast<int>(EIGEN_HIP_DEVICE_COMPILE +0);
+ #endif
+ return info;
+ }
+};
+
+/**
+ * Queries and prints the compile-time and runtime GPU info.
+ */
+void print_gpu_device_info()
+{
+ int device = 0;
+ gpuDeviceProp_t deviceProp;
+ gpuGetDeviceProperties(&deviceProp, device);
+
+ auto info = run_on_gpu(CompileTimeDeviceInfoKernel());
+
+ std::cout << "GPU compile-time info:\n";
+
+ #ifdef EIGEN_CUDACC
+ std::cout << " EIGEN_CUDACC: " << int(EIGEN_CUDACC) << std::endl;
+ #endif
+
+ #ifdef EIGEN_CUDA_SDK_VER
+ std::cout << " EIGEN_CUDA_SDK_VER: " << int(EIGEN_CUDA_SDK_VER) << std::endl;
+ #endif
+
+ #ifdef EIGEN_COMP_NVCC
+ std::cout << " EIGEN_COMP_NVCC: " << int(EIGEN_COMP_NVCC) << std::endl;
+ #endif
+
+ #ifdef EIGEN_HIPCC
+ std::cout << " EIGEN_HIPCC: " << int(EIGEN_HIPCC) << std::endl;
+ #endif
+
+ std::cout << " EIGEN_CUDA_ARCH: " << info.cuda << std::endl;
+ std::cout << " EIGEN_HIP_DEVICE_COMPILE: " << info.hip << std::endl;
+
+ std::cout << "GPU device info:\n";
+ std::cout << " name: " << deviceProp.name << std::endl;
+ std::cout << " capability: " << deviceProp.major << "." << deviceProp.minor << std::endl;
+ std::cout << " multiProcessorCount: " << deviceProp.multiProcessorCount << std::endl;
+ std::cout << " maxThreadsPerMultiProcessor: " << deviceProp.maxThreadsPerMultiProcessor << std::endl;
+ std::cout << " warpSize: " << deviceProp.warpSize << std::endl;
+ std::cout << " regsPerBlock: " << deviceProp.regsPerBlock << std::endl;
+ std::cout << " concurrentKernels: " << deviceProp.concurrentKernels << std::endl;
+ std::cout << " clockRate: " << deviceProp.clockRate << std::endl;
+ std::cout << " canMapHostMemory: " << deviceProp.canMapHostMemory << std::endl;
+ std::cout << " computeMode: " << deviceProp.computeMode << std::endl;
+}
+
+#endif // EIGEN_GPUCC
+
+/**
+ * Runs a kernel on the GPU (if EIGEN_GPUCC), or CPU otherwise.
+ *
+ * This is to better support creating generic tests.
+ *
+ * The kernel must be able to be passed directly as an input to a global
+ * function (i.e. empty or POD). Its inputs must be "Serializable" so we
+ * can transfer them to the device, and the output must be a Serializable value
+ * type so it can be transferred back from the device.
+ *
+ * \param kernel kernel to run.
+ * \param args ... input arguments, must be "Serializable".
+ * \return kernel(args...).
+ */
+template<typename Kernel, typename... Args>
+auto run(Kernel kernel, Args&&... args) -> decltype(kernel(args...)){
+#ifdef EIGEN_GPUCC
+ return run_on_gpu(kernel, std::forward<Args>(args)...);
+#else
+ return run_on_cpu(kernel, std::forward<Args>(args)...);
+#endif
+}
+
+/**
+ * Runs a kernel on the GPU (if EIGEN_GPUCC), or CPU otherwise.
+ *
+ * This version allows specifying a minimum buffer capacity size required for
+ * serializing the puts to transfer results from device to host. Use this when
+ * `run(...)` fails to determine an appropriate capacity by default.
+ *
+ * \param buffer_capacity_hint minimum required buffer size for serializing
+ * outputs.
+ * \param kernel kernel to run.
+ * \param args ... input arguments, must be "Serializable".
+ * \return kernel(args...).
+ * \sa run
+ */
+template<typename Kernel, typename... Args>
+auto run_with_hint(size_t buffer_capacity_hint,
+ Kernel kernel, Args&&... args) -> decltype(kernel(args...)){
+#ifdef EIGEN_GPUCC
+ return run_on_gpu_with_hint(buffer_capacity_hint, kernel, std::forward<Args>(args)...);
+#else
+ EIGEN_UNUSED_VARIABLE(buffer_capacity_hint)
+ return run_on_cpu(kernel, std::forward<Args>(args)...);
+#endif
+}
+
+} // namespace Eigen
+
+#endif // GPU_TEST_HELPER_H
diff --git a/test/half_float.cpp b/test/half_float.cpp
new file mode 100644
index 0000000..00a8b48
--- /dev/null
+++ b/test/half_float.cpp
@@ -0,0 +1,358 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include <sstream>
+
+#include "main.h"
+
+#include <Eigen/src/Core/arch/Default/Half.h>
+
+#define VERIFY_HALF_BITS_EQUAL(h, bits) \
+ VERIFY_IS_EQUAL((numext::bit_cast<numext::uint16_t>(h)), (static_cast<numext::uint16_t>(bits)))
+
+// Make sure it's possible to forward declare Eigen::half
+namespace Eigen {
+struct half;
+}
+
+using Eigen::half;
+
+void test_conversion()
+{
+ using Eigen::half_impl::__half_raw;
+
+ // Round-trip bit-cast with uint16.
+ VERIFY_IS_EQUAL(
+ numext::bit_cast<half>(numext::bit_cast<numext::uint16_t>(half(1.0f))),
+ half(1.0f));
+ VERIFY_IS_EQUAL(
+ numext::bit_cast<half>(numext::bit_cast<numext::uint16_t>(half(0.5f))),
+ half(0.5f));
+ VERIFY_IS_EQUAL(
+ numext::bit_cast<half>(numext::bit_cast<numext::uint16_t>(half(-0.33333f))),
+ half(-0.33333f));
+ VERIFY_IS_EQUAL(
+ numext::bit_cast<half>(numext::bit_cast<numext::uint16_t>(half(0.0f))),
+ half(0.0f));
+
+ // Conversion from float.
+ VERIFY_HALF_BITS_EQUAL(half(1.0f), 0x3c00);
+ VERIFY_HALF_BITS_EQUAL(half(0.5f), 0x3800);
+ VERIFY_HALF_BITS_EQUAL(half(0.33333f), 0x3555);
+ VERIFY_HALF_BITS_EQUAL(half(0.0f), 0x0000);
+ VERIFY_HALF_BITS_EQUAL(half(-0.0f), 0x8000);
+ VERIFY_HALF_BITS_EQUAL(half(65504.0f), 0x7bff);
+ VERIFY_HALF_BITS_EQUAL(half(65536.0f), 0x7c00); // Becomes infinity.
+
+ // Denormals.
+ VERIFY_HALF_BITS_EQUAL(half(-5.96046e-08f), 0x8001);
+ VERIFY_HALF_BITS_EQUAL(half(5.96046e-08f), 0x0001);
+ VERIFY_HALF_BITS_EQUAL(half(1.19209e-07f), 0x0002);
+
+ // Verify round-to-nearest-even behavior.
+ float val1 = float(half(__half_raw(0x3c00)));
+ float val2 = float(half(__half_raw(0x3c01)));
+ float val3 = float(half(__half_raw(0x3c02)));
+ VERIFY_HALF_BITS_EQUAL(half(0.5f * (val1 + val2)), 0x3c00);
+ VERIFY_HALF_BITS_EQUAL(half(0.5f * (val2 + val3)), 0x3c02);
+
+ // Conversion from int.
+ VERIFY_HALF_BITS_EQUAL(half(-1), 0xbc00);
+ VERIFY_HALF_BITS_EQUAL(half(0), 0x0000);
+ VERIFY_HALF_BITS_EQUAL(half(1), 0x3c00);
+ VERIFY_HALF_BITS_EQUAL(half(2), 0x4000);
+ VERIFY_HALF_BITS_EQUAL(half(3), 0x4200);
+
+ // Conversion from bool.
+ VERIFY_HALF_BITS_EQUAL(half(false), 0x0000);
+ VERIFY_HALF_BITS_EQUAL(half(true), 0x3c00);
+
+ // Conversion to float.
+ VERIFY_IS_EQUAL(float(half(__half_raw(0x0000))), 0.0f);
+ VERIFY_IS_EQUAL(float(half(__half_raw(0x3c00))), 1.0f);
+
+ // Denormals.
+ VERIFY_IS_APPROX(float(half(__half_raw(0x8001))), -5.96046e-08f);
+ VERIFY_IS_APPROX(float(half(__half_raw(0x0001))), 5.96046e-08f);
+ VERIFY_IS_APPROX(float(half(__half_raw(0x0002))), 1.19209e-07f);
+
+ // NaNs and infinities.
+ VERIFY(!(numext::isinf)(float(half(65504.0f)))); // Largest finite number.
+ VERIFY(!(numext::isnan)(float(half(0.0f))));
+ VERIFY((numext::isinf)(float(half(__half_raw(0xfc00)))));
+ VERIFY((numext::isnan)(float(half(__half_raw(0xfc01)))));
+ VERIFY((numext::isinf)(float(half(__half_raw(0x7c00)))));
+ VERIFY((numext::isnan)(float(half(__half_raw(0x7c01)))));
+
+#if !EIGEN_COMP_MSVC
+ // Visual Studio errors out on divisions by 0
+ VERIFY((numext::isnan)(float(half(0.0 / 0.0))));
+ VERIFY((numext::isinf)(float(half(1.0 / 0.0))));
+ VERIFY((numext::isinf)(float(half(-1.0 / 0.0))));
+#endif
+
+ // Exactly same checks as above, just directly on the half representation.
+ VERIFY(!(numext::isinf)(half(__half_raw(0x7bff))));
+ VERIFY(!(numext::isnan)(half(__half_raw(0x0000))));
+ VERIFY((numext::isinf)(half(__half_raw(0xfc00))));
+ VERIFY((numext::isnan)(half(__half_raw(0xfc01))));
+ VERIFY((numext::isinf)(half(__half_raw(0x7c00))));
+ VERIFY((numext::isnan)(half(__half_raw(0x7c01))));
+
+#if !EIGEN_COMP_MSVC
+ // Visual Studio errors out on divisions by 0
+ VERIFY((numext::isnan)(half(0.0 / 0.0)));
+ VERIFY((numext::isinf)(half(1.0 / 0.0)));
+ VERIFY((numext::isinf)(half(-1.0 / 0.0)));
+#endif
+
+ // Conversion to bool
+ VERIFY(!static_cast<bool>(half(0.0)));
+ VERIFY(!static_cast<bool>(half(-0.0)));
+ VERIFY(static_cast<bool>(half(__half_raw(0x7bff))));
+ VERIFY(static_cast<bool>(half(-0.33333)));
+ VERIFY(static_cast<bool>(half(1.0)));
+ VERIFY(static_cast<bool>(half(-1.0)));
+ VERIFY(static_cast<bool>(half(-5.96046e-08f)));
+}
+
+void test_numtraits()
+{
+ std::cout << "epsilon = " << NumTraits<half>::epsilon() << " (0x" << std::hex << numext::bit_cast<numext::uint16_t>(NumTraits<half>::epsilon()) << ")" << std::endl;
+ std::cout << "highest = " << NumTraits<half>::highest() << " (0x" << std::hex << numext::bit_cast<numext::uint16_t>(NumTraits<half>::highest()) << ")" << std::endl;
+ std::cout << "lowest = " << NumTraits<half>::lowest() << " (0x" << std::hex << numext::bit_cast<numext::uint16_t>(NumTraits<half>::lowest()) << ")" << std::endl;
+ std::cout << "min = " << (std::numeric_limits<half>::min)() << " (0x" << std::hex << numext::bit_cast<numext::uint16_t>(half((std::numeric_limits<half>::min)())) << ")" << std::endl;
+ std::cout << "denorm min = " << (std::numeric_limits<half>::denorm_min)() << " (0x" << std::hex << numext::bit_cast<numext::uint16_t>(half((std::numeric_limits<half>::denorm_min)())) << ")" << std::endl;
+ std::cout << "infinity = " << NumTraits<half>::infinity() << " (0x" << std::hex << numext::bit_cast<numext::uint16_t>(NumTraits<half>::infinity()) << ")" << std::endl;
+ std::cout << "quiet nan = " << NumTraits<half>::quiet_NaN() << " (0x" << std::hex << numext::bit_cast<numext::uint16_t>(NumTraits<half>::quiet_NaN()) << ")" << std::endl;
+ std::cout << "signaling nan = " << std::numeric_limits<half>::signaling_NaN() << " (0x" << std::hex << numext::bit_cast<numext::uint16_t>(std::numeric_limits<half>::signaling_NaN()) << ")" << std::endl;
+
+ VERIFY(NumTraits<half>::IsSigned);
+
+ VERIFY_IS_EQUAL(
+ numext::bit_cast<numext::uint16_t>(std::numeric_limits<half>::infinity()),
+ numext::bit_cast<numext::uint16_t>(half(std::numeric_limits<float>::infinity())) );
+ // There is no guarantee that casting a 32-bit NaN to 16-bit has a precise
+ // bit pattern. We test that it is in fact a NaN, then test the signaling
+ // bit (msb of significand is 1 for quiet, 0 for signaling).
+ const numext::uint16_t HALF_QUIET_BIT = 0x0200;
+ VERIFY(
+ (numext::isnan)(std::numeric_limits<half>::quiet_NaN())
+ && (numext::isnan)(half(std::numeric_limits<float>::quiet_NaN()))
+ && ((numext::bit_cast<numext::uint16_t>(std::numeric_limits<half>::quiet_NaN()) & HALF_QUIET_BIT) > 0)
+ && ((numext::bit_cast<numext::uint16_t>(half(std::numeric_limits<float>::quiet_NaN())) & HALF_QUIET_BIT) > 0) );
+ // After a cast to half, a signaling NaN may become non-signaling
+ // (e.g. in the case of casting float to native __fp16). Thus, we check that
+ // both are NaN, and that only the `numeric_limits` version is signaling.
+ VERIFY(
+ (numext::isnan)(std::numeric_limits<half>::signaling_NaN())
+ && (numext::isnan)(half(std::numeric_limits<float>::signaling_NaN()))
+ && ((numext::bit_cast<numext::uint16_t>(std::numeric_limits<half>::signaling_NaN()) & HALF_QUIET_BIT) == 0) );
+
+ VERIFY( (std::numeric_limits<half>::min)() > half(0.f) );
+ VERIFY( (std::numeric_limits<half>::denorm_min)() > half(0.f) );
+ VERIFY( (std::numeric_limits<half>::min)()/half(2) > half(0.f) );
+ VERIFY_IS_EQUAL( (std::numeric_limits<half>::denorm_min)()/half(2), half(0.f) );
+
+ // Test to see that we are able to link against the symbols for digits and
+ // digits10.
+ volatile const int& digits10 = std::numeric_limits<half>::digits10;
+ volatile const int& digits = std::numeric_limits<half>::digits;
+ VERIFY( (digits10) != (digits) );
+}
+
+void test_arithmetic()
+{
+ VERIFY_IS_EQUAL(float(half(2) + half(2)), 4);
+ VERIFY_IS_EQUAL(float(half(2) + half(-2)), 0);
+ VERIFY_IS_APPROX(float(half(0.33333f) + half(0.66667f)), 1.0f);
+ VERIFY_IS_EQUAL(float(half(2.0f) * half(-5.5f)), -11.0f);
+ VERIFY_IS_APPROX(float(half(1.0f) / half(3.0f)), 0.33333f);
+ VERIFY_IS_EQUAL(float(-half(4096.0f)), -4096.0f);
+ VERIFY_IS_EQUAL(float(-half(-4096.0f)), 4096.0f);
+
+ half x(3);
+ half y = ++x;
+ VERIFY_IS_EQUAL(x, half(4));
+ VERIFY_IS_EQUAL(y, half(4));
+ y = --x;
+ VERIFY_IS_EQUAL(x, half(3));
+ VERIFY_IS_EQUAL(y, half(3));
+ y = x++;
+ VERIFY_IS_EQUAL(x, half(4));
+ VERIFY_IS_EQUAL(y, half(3));
+ y = x--;
+ VERIFY_IS_EQUAL(x, half(3));
+ VERIFY_IS_EQUAL(y, half(4));
+}
+
+void test_comparison()
+{
+ VERIFY(half(1.0f) > half(0.5f));
+ VERIFY(half(0.5f) < half(1.0f));
+ VERIFY(!(half(1.0f) < half(0.5f)));
+ VERIFY(!(half(0.5f) > half(1.0f)));
+
+ VERIFY(!(half(4.0f) > half(4.0f)));
+ VERIFY(!(half(4.0f) < half(4.0f)));
+
+ VERIFY(!(half(0.0f) < half(-0.0f)));
+ VERIFY(!(half(-0.0f) < half(0.0f)));
+ VERIFY(!(half(0.0f) > half(-0.0f)));
+ VERIFY(!(half(-0.0f) > half(0.0f)));
+
+ VERIFY(half(0.2f) > half(-1.0f));
+ VERIFY(half(-1.0f) < half(0.2f));
+ VERIFY(half(-16.0f) < half(-15.0f));
+
+ VERIFY(half(1.0f) == half(1.0f));
+ VERIFY(half(1.0f) != half(2.0f));
+
+ // Comparisons with NaNs and infinities.
+#if !EIGEN_COMP_MSVC
+ // Visual Studio errors out on divisions by 0
+ VERIFY(!(half(0.0 / 0.0) == half(0.0 / 0.0)));
+ VERIFY(half(0.0 / 0.0) != half(0.0 / 0.0));
+
+ VERIFY(!(half(1.0) == half(0.0 / 0.0)));
+ VERIFY(!(half(1.0) < half(0.0 / 0.0)));
+ VERIFY(!(half(1.0) > half(0.0 / 0.0)));
+ VERIFY(half(1.0) != half(0.0 / 0.0));
+
+ VERIFY(half(1.0) < half(1.0 / 0.0));
+ VERIFY(half(1.0) > half(-1.0 / 0.0));
+#endif
+}
+
+void test_basic_functions()
+{
+ constexpr float PI = static_cast<float>(EIGEN_PI);
+
+ VERIFY_IS_EQUAL(float(numext::abs(half(3.5f))), 3.5f);
+ VERIFY_IS_EQUAL(float(abs(half(3.5f))), 3.5f);
+ VERIFY_IS_EQUAL(float(numext::abs(half(-3.5f))), 3.5f);
+ VERIFY_IS_EQUAL(float(abs(half(-3.5f))), 3.5f);
+
+ VERIFY_IS_EQUAL(float(numext::floor(half(3.5f))), 3.0f);
+ VERIFY_IS_EQUAL(float(floor(half(3.5f))), 3.0f);
+ VERIFY_IS_EQUAL(float(numext::floor(half(-3.5f))), -4.0f);
+ VERIFY_IS_EQUAL(float(floor(half(-3.5f))), -4.0f);
+
+ VERIFY_IS_EQUAL(float(numext::ceil(half(3.5f))), 4.0f);
+ VERIFY_IS_EQUAL(float(ceil(half(3.5f))), 4.0f);
+ VERIFY_IS_EQUAL(float(numext::ceil(half(-3.5f))), -3.0f);
+ VERIFY_IS_EQUAL(float(ceil(half(-3.5f))), -3.0f);
+
+ VERIFY_IS_APPROX(float(numext::sqrt(half(0.0f))), 0.0f);
+ VERIFY_IS_APPROX(float(sqrt(half(0.0f))), 0.0f);
+ VERIFY_IS_APPROX(float(numext::sqrt(half(4.0f))), 2.0f);
+ VERIFY_IS_APPROX(float(sqrt(half(4.0f))), 2.0f);
+
+ VERIFY_IS_APPROX(float(numext::pow(half(0.0f), half(1.0f))), 0.0f);
+ VERIFY_IS_APPROX(float(pow(half(0.0f), half(1.0f))), 0.0f);
+ VERIFY_IS_APPROX(float(numext::pow(half(2.0f), half(2.0f))), 4.0f);
+ VERIFY_IS_APPROX(float(pow(half(2.0f), half(2.0f))), 4.0f);
+
+ VERIFY_IS_EQUAL(float(numext::exp(half(0.0f))), 1.0f);
+ VERIFY_IS_EQUAL(float(exp(half(0.0f))), 1.0f);
+ VERIFY_IS_APPROX(float(numext::exp(half(PI))), 20.f + PI);
+ VERIFY_IS_APPROX(float(exp(half(PI))), 20.f + PI);
+
+ VERIFY_IS_EQUAL(float(numext::expm1(half(0.0f))), 0.0f);
+ VERIFY_IS_EQUAL(float(expm1(half(0.0f))), 0.0f);
+ VERIFY_IS_APPROX(float(numext::expm1(half(2.0f))), 6.3890561f);
+ VERIFY_IS_APPROX(float(expm1(half(2.0f))), 6.3890561f);
+
+ VERIFY_IS_EQUAL(float(numext::log(half(1.0f))), 0.0f);
+ VERIFY_IS_EQUAL(float(log(half(1.0f))), 0.0f);
+ VERIFY_IS_APPROX(float(numext::log(half(10.0f))), 2.30273f);
+ VERIFY_IS_APPROX(float(log(half(10.0f))), 2.30273f);
+
+ VERIFY_IS_EQUAL(float(numext::log1p(half(0.0f))), 0.0f);
+ VERIFY_IS_EQUAL(float(log1p(half(0.0f))), 0.0f);
+ VERIFY_IS_APPROX(float(numext::log1p(half(10.0f))), 2.3978953f);
+ VERIFY_IS_APPROX(float(log1p(half(10.0f))), 2.3978953f);
+
+ VERIFY_IS_APPROX(numext::fmod(half(5.3f), half(2.0f)), half(1.3f));
+ VERIFY_IS_APPROX(fmod(half(5.3f), half(2.0f)), half(1.3f));
+ VERIFY_IS_APPROX(numext::fmod(half(-18.5f), half(-4.2f)), half(-1.7f));
+ VERIFY_IS_APPROX(fmod(half(-18.5f), half(-4.2f)), half(-1.7f));
+}
+
+void test_trigonometric_functions()
+{
+ constexpr float PI = static_cast<float>(EIGEN_PI);
+ VERIFY_IS_APPROX(numext::cos(half(0.0f)), half(cosf(0.0f)));
+ VERIFY_IS_APPROX(cos(half(0.0f)), half(cosf(0.0f)));
+ VERIFY_IS_APPROX(numext::cos(half(PI)), half(cosf(PI)));
+ // VERIFY_IS_APPROX(numext::cos(half(PI/2)), half(cosf(PI/2)));
+ // VERIFY_IS_APPROX(numext::cos(half(3*PI/2)), half(cosf(3*PI/2)));
+ VERIFY_IS_APPROX(numext::cos(half(3.5f)), half(cosf(3.5f)));
+
+ VERIFY_IS_APPROX(numext::sin(half(0.0f)), half(sinf(0.0f)));
+ VERIFY_IS_APPROX(sin(half(0.0f)), half(sinf(0.0f)));
+ // VERIFY_IS_APPROX(numext::sin(half(PI)), half(sinf(PI)));
+ VERIFY_IS_APPROX(numext::sin(half(PI/2)), half(sinf(PI/2)));
+ VERIFY_IS_APPROX(numext::sin(half(3*PI/2)), half(sinf(3*PI/2)));
+ VERIFY_IS_APPROX(numext::sin(half(3.5f)), half(sinf(3.5f)));
+
+ VERIFY_IS_APPROX(numext::tan(half(0.0f)), half(tanf(0.0f)));
+ VERIFY_IS_APPROX(tan(half(0.0f)), half(tanf(0.0f)));
+ // VERIFY_IS_APPROX(numext::tan(half(PI)), half(tanf(PI)));
+ // VERIFY_IS_APPROX(numext::tan(half(PI/2)), half(tanf(PI/2)));
+ //VERIFY_IS_APPROX(numext::tan(half(3*PI/2)), half(tanf(3*PI/2)));
+ VERIFY_IS_APPROX(numext::tan(half(3.5f)), half(tanf(3.5f)));
+}
+
+void test_array()
+{
+ typedef Array<half,1,Dynamic> ArrayXh;
+ Index size = internal::random<Index>(1,10);
+ Index i = internal::random<Index>(0,size-1);
+ ArrayXh a1 = ArrayXh::Random(size), a2 = ArrayXh::Random(size);
+ VERIFY_IS_APPROX( a1+a1, half(2)*a1 );
+ VERIFY( (a1.abs() >= half(0)).all() );
+ VERIFY_IS_APPROX( (a1*a1).sqrt(), a1.abs() );
+
+ VERIFY( ((a1.min)(a2) <= (a1.max)(a2)).all() );
+ a1(i) = half(-10.);
+ VERIFY_IS_EQUAL( a1.minCoeff(), half(-10.) );
+ a1(i) = half(10.);
+ VERIFY_IS_EQUAL( a1.maxCoeff(), half(10.) );
+
+ std::stringstream ss;
+ ss << a1;
+}
+
+void test_product()
+{
+ typedef Matrix<half,Dynamic,Dynamic> MatrixXh;
+ Index rows = internal::random<Index>(1,EIGEN_TEST_MAX_SIZE);
+ Index cols = internal::random<Index>(1,EIGEN_TEST_MAX_SIZE);
+ Index depth = internal::random<Index>(1,EIGEN_TEST_MAX_SIZE);
+ MatrixXh Ah = MatrixXh::Random(rows,depth);
+ MatrixXh Bh = MatrixXh::Random(depth,cols);
+ MatrixXh Ch = MatrixXh::Random(rows,cols);
+ MatrixXf Af = Ah.cast<float>();
+ MatrixXf Bf = Bh.cast<float>();
+ MatrixXf Cf = Ch.cast<float>();
+ VERIFY_IS_APPROX(Ch.noalias()+=Ah*Bh, (Cf.noalias()+=Af*Bf).cast<half>());
+}
+
+EIGEN_DECLARE_TEST(half_float)
+{
+ CALL_SUBTEST(test_numtraits());
+ for(int i = 0; i < g_repeat; i++) {
+ CALL_SUBTEST(test_conversion());
+ CALL_SUBTEST(test_arithmetic());
+ CALL_SUBTEST(test_comparison());
+ CALL_SUBTEST(test_basic_functions());
+ CALL_SUBTEST(test_trigonometric_functions());
+ CALL_SUBTEST(test_array());
+ CALL_SUBTEST(test_product());
+ }
+}
diff --git a/test/hessenberg.cpp b/test/hessenberg.cpp
new file mode 100644
index 0000000..0e1b009
--- /dev/null
+++ b/test/hessenberg.cpp
@@ -0,0 +1,62 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2010 Jitse Niesen <jitse@maths.leeds.ac.uk>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "main.h"
+#include <Eigen/Eigenvalues>
+
+template<typename Scalar,int Size> void hessenberg(int size = Size)
+{
+ typedef Matrix<Scalar,Size,Size> MatrixType;
+
+ // Test basic functionality: A = U H U* and H is Hessenberg
+ for(int counter = 0; counter < g_repeat; ++counter) {
+ MatrixType m = MatrixType::Random(size,size);
+ HessenbergDecomposition<MatrixType> hess(m);
+ MatrixType Q = hess.matrixQ();
+ MatrixType H = hess.matrixH();
+ VERIFY_IS_APPROX(m, Q * H * Q.adjoint());
+ for(int row = 2; row < size; ++row) {
+ for(int col = 0; col < row-1; ++col) {
+ VERIFY(H(row,col) == (typename MatrixType::Scalar)0);
+ }
+ }
+ }
+
+ // Test whether compute() and constructor returns same result
+ MatrixType A = MatrixType::Random(size, size);
+ HessenbergDecomposition<MatrixType> cs1;
+ cs1.compute(A);
+ HessenbergDecomposition<MatrixType> cs2(A);
+ VERIFY_IS_EQUAL(cs1.matrixH().eval(), cs2.matrixH().eval());
+ MatrixType cs1Q = cs1.matrixQ();
+ MatrixType cs2Q = cs2.matrixQ();
+ VERIFY_IS_EQUAL(cs1Q, cs2Q);
+
+ // Test assertions for when used uninitialized
+ HessenbergDecomposition<MatrixType> hessUninitialized;
+ VERIFY_RAISES_ASSERT( hessUninitialized.matrixH() );
+ VERIFY_RAISES_ASSERT( hessUninitialized.matrixQ() );
+ VERIFY_RAISES_ASSERT( hessUninitialized.householderCoefficients() );
+ VERIFY_RAISES_ASSERT( hessUninitialized.packedMatrix() );
+
+ // TODO: Add tests for packedMatrix() and householderCoefficients()
+}
+
+EIGEN_DECLARE_TEST(hessenberg)
+{
+ CALL_SUBTEST_1(( hessenberg<std::complex<double>,1>() ));
+ CALL_SUBTEST_2(( hessenberg<std::complex<double>,2>() ));
+ CALL_SUBTEST_3(( hessenberg<std::complex<float>,4>() ));
+ CALL_SUBTEST_4(( hessenberg<float,Dynamic>(internal::random<int>(1,EIGEN_TEST_MAX_SIZE)) ));
+ CALL_SUBTEST_5(( hessenberg<std::complex<double>,Dynamic>(internal::random<int>(1,EIGEN_TEST_MAX_SIZE)) ));
+
+ // Test problem size constructors
+ CALL_SUBTEST_6(HessenbergDecomposition<MatrixXf>(10));
+}
diff --git a/test/householder.cpp b/test/householder.cpp
new file mode 100644
index 0000000..3a3d047
--- /dev/null
+++ b/test/householder.cpp
@@ -0,0 +1,235 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009-2010 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "main.h"
+#include <Eigen/QR>
+
+template<typename MatrixType> void householder(const MatrixType& m)
+{
+ static bool even = true;
+ even = !even;
+ /* this test covers the following files:
+ Householder.h
+ */
+ Index rows = m.rows();
+ Index cols = m.cols();
+
+ typedef typename MatrixType::Scalar Scalar;
+ typedef typename NumTraits<Scalar>::Real RealScalar;
+ typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> VectorType;
+ typedef Matrix<Scalar, internal::decrement_size<MatrixType::RowsAtCompileTime>::ret, 1> EssentialVectorType;
+ typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime> SquareMatrixType;
+ typedef Matrix<Scalar, Dynamic, MatrixType::ColsAtCompileTime> HBlockMatrixType;
+ typedef Matrix<Scalar, Dynamic, 1> HCoeffsVectorType;
+
+ typedef Matrix<Scalar, MatrixType::ColsAtCompileTime, MatrixType::RowsAtCompileTime> TMatrixType;
+
+ Matrix<Scalar, internal::max_size_prefer_dynamic(MatrixType::RowsAtCompileTime,MatrixType::ColsAtCompileTime), 1> _tmp((std::max)(rows,cols));
+ Scalar* tmp = &_tmp.coeffRef(0,0);
+
+ Scalar beta;
+ RealScalar alpha;
+ EssentialVectorType essential;
+
+ VectorType v1 = VectorType::Random(rows), v2;
+ v2 = v1;
+ v1.makeHouseholder(essential, beta, alpha);
+ v1.applyHouseholderOnTheLeft(essential,beta,tmp);
+ VERIFY_IS_APPROX(v1.norm(), v2.norm());
+ if(rows>=2) VERIFY_IS_MUCH_SMALLER_THAN(v1.tail(rows-1).norm(), v1.norm());
+ v1 = VectorType::Random(rows);
+ v2 = v1;
+ v1.applyHouseholderOnTheLeft(essential,beta,tmp);
+ VERIFY_IS_APPROX(v1.norm(), v2.norm());
+
+ // reconstruct householder matrix:
+ SquareMatrixType id, H1, H2;
+ id.setIdentity(rows, rows);
+ H1 = H2 = id;
+ VectorType vv(rows);
+ vv << Scalar(1), essential;
+ H1.applyHouseholderOnTheLeft(essential, beta, tmp);
+ H2.applyHouseholderOnTheRight(essential, beta, tmp);
+ VERIFY_IS_APPROX(H1, H2);
+ VERIFY_IS_APPROX(H1, id - beta * vv*vv.adjoint());
+
+ MatrixType m1(rows, cols),
+ m2(rows, cols);
+
+ v1 = VectorType::Random(rows);
+ if(even) v1.tail(rows-1).setZero();
+ m1.colwise() = v1;
+ m2 = m1;
+ m1.col(0).makeHouseholder(essential, beta, alpha);
+ m1.applyHouseholderOnTheLeft(essential,beta,tmp);
+ VERIFY_IS_APPROX(m1.norm(), m2.norm());
+ if(rows>=2) VERIFY_IS_MUCH_SMALLER_THAN(m1.block(1,0,rows-1,cols).norm(), m1.norm());
+ VERIFY_IS_MUCH_SMALLER_THAN(numext::imag(m1(0,0)), numext::real(m1(0,0)));
+ VERIFY_IS_APPROX(numext::real(m1(0,0)), alpha);
+
+ v1 = VectorType::Random(rows);
+ if(even) v1.tail(rows-1).setZero();
+ SquareMatrixType m3(rows,rows), m4(rows,rows);
+ m3.rowwise() = v1.transpose();
+ m4 = m3;
+ m3.row(0).makeHouseholder(essential, beta, alpha);
+ m3.applyHouseholderOnTheRight(essential.conjugate(),beta,tmp);
+ VERIFY_IS_APPROX(m3.norm(), m4.norm());
+ if(rows>=2) VERIFY_IS_MUCH_SMALLER_THAN(m3.block(0,1,rows,rows-1).norm(), m3.norm());
+ VERIFY_IS_MUCH_SMALLER_THAN(numext::imag(m3(0,0)), numext::real(m3(0,0)));
+ VERIFY_IS_APPROX(numext::real(m3(0,0)), alpha);
+
+ // test householder sequence on the left with a shift
+
+ Index shift = internal::random<Index>(0, std::max<Index>(rows-2,0));
+ Index brows = rows - shift;
+ m1.setRandom(rows, cols);
+ HBlockMatrixType hbm = m1.block(shift,0,brows,cols);
+ HouseholderQR<HBlockMatrixType> qr(hbm);
+ m2 = m1;
+ m2.block(shift,0,brows,cols) = qr.matrixQR();
+ HCoeffsVectorType hc = qr.hCoeffs().conjugate();
+ HouseholderSequence<MatrixType, HCoeffsVectorType> hseq(m2, hc);
+ hseq.setLength(hc.size()).setShift(shift);
+ VERIFY(hseq.length() == hc.size());
+ VERIFY(hseq.shift() == shift);
+
+ MatrixType m5 = m2;
+ m5.block(shift,0,brows,cols).template triangularView<StrictlyLower>().setZero();
+ VERIFY_IS_APPROX(hseq * m5, m1); // test applying hseq directly
+ m3 = hseq;
+ VERIFY_IS_APPROX(m3 * m5, m1); // test evaluating hseq to a dense matrix, then applying
+
+ SquareMatrixType hseq_mat = hseq;
+ SquareMatrixType hseq_mat_conj = hseq.conjugate();
+ SquareMatrixType hseq_mat_adj = hseq.adjoint();
+ SquareMatrixType hseq_mat_trans = hseq.transpose();
+ SquareMatrixType m6 = SquareMatrixType::Random(rows, rows);
+ VERIFY_IS_APPROX(hseq_mat.adjoint(), hseq_mat_adj);
+ VERIFY_IS_APPROX(hseq_mat.conjugate(), hseq_mat_conj);
+ VERIFY_IS_APPROX(hseq_mat.transpose(), hseq_mat_trans);
+ VERIFY_IS_APPROX(hseq * m6, hseq_mat * m6);
+ VERIFY_IS_APPROX(hseq.adjoint() * m6, hseq_mat_adj * m6);
+ VERIFY_IS_APPROX(hseq.conjugate() * m6, hseq_mat_conj * m6);
+ VERIFY_IS_APPROX(hseq.transpose() * m6, hseq_mat_trans * m6);
+ VERIFY_IS_APPROX(m6 * hseq, m6 * hseq_mat);
+ VERIFY_IS_APPROX(m6 * hseq.adjoint(), m6 * hseq_mat_adj);
+ VERIFY_IS_APPROX(m6 * hseq.conjugate(), m6 * hseq_mat_conj);
+ VERIFY_IS_APPROX(m6 * hseq.transpose(), m6 * hseq_mat_trans);
+
+ // test householder sequence on the right with a shift
+
+ TMatrixType tm2 = m2.transpose();
+ HouseholderSequence<TMatrixType, HCoeffsVectorType, OnTheRight> rhseq(tm2, hc);
+ rhseq.setLength(hc.size()).setShift(shift);
+ VERIFY_IS_APPROX(rhseq * m5, m1); // test applying rhseq directly
+ m3 = rhseq;
+ VERIFY_IS_APPROX(m3 * m5, m1); // test evaluating rhseq to a dense matrix, then applying
+}
+
+
+template <typename MatrixType>
+void householder_update(const MatrixType& m) {
+ // This test is covering the internal::householder_qr_inplace_update function.
+ // At time of writing, there is not public API that exposes this update behavior directly,
+ // so we are testing the internal implementation.
+
+ const Index rows = m.rows();
+ const Index cols = m.cols();
+
+ typedef typename MatrixType::Scalar Scalar;
+ typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> VectorType;
+ typedef Matrix<Scalar, Dynamic, 1> HCoeffsVectorType;
+ typedef Matrix<Scalar, Dynamic, Dynamic> MatrixX;
+ typedef Matrix<Scalar, Dynamic, 1> VectorX;
+
+ VectorX tmpOwner(cols);
+ Scalar* tmp = tmpOwner.data();
+
+ // The matrix to factorize.
+ const MatrixType A = MatrixType::Random(rows, cols);
+
+ // matQR and hCoeffs will hold the factorization of A,
+ // built by a sequence of calls to `update`.
+ MatrixType matQR(rows, cols);
+ HCoeffsVectorType hCoeffs(cols);
+
+ // householder_qr_inplace_update should be able to build a QR factorization one column at a time.
+ // We verify this by starting with an empty factorization and 'updating' one column at a time.
+ // After each call to update, we should have a QR factorization of the columns presented so far.
+
+ const Index size = (std::min)(rows, cols); // QR can only go up to 'size' b/c that's full rank.
+ for (Index k = 0; k != size; ++k)
+ {
+ // Make a copy of the column to prevent any possibility of 'leaking' other parts of A.
+ const VectorType newColumn = A.col(k);
+ internal::householder_qr_inplace_update(matQR, hCoeffs, newColumn, k, tmp);
+
+ // Verify Property:
+ // matQR.leftCols(k+1) and hCoeffs.head(k+1) hold
+ // a QR factorization of A.leftCols(k+1).
+ // This is the fundamental guarantee of householder_qr_inplace_update.
+ {
+ const MatrixX matQR_k = matQR.leftCols(k + 1);
+ const VectorX hCoeffs_k = hCoeffs.head(k + 1);
+ MatrixX R = matQR_k.template triangularView<Upper>();
+ MatrixX QxR = householderSequence(matQR_k, hCoeffs_k.conjugate()) * R;
+ VERIFY_IS_APPROX(QxR, A.leftCols(k + 1));
+ }
+
+ // Verify Property:
+ // A sequence of calls to 'householder_qr_inplace_update'
+ // should produce the same result as 'householder_qr_inplace_unblocked'.
+ // This is a property of the current implementation.
+ // If these implementations diverge in the future,
+ // then simply delete the test of this property.
+ {
+ MatrixX QR_at_once = A.leftCols(k + 1);
+ VectorX hCoeffs_at_once(k + 1);
+ internal::householder_qr_inplace_unblocked(QR_at_once, hCoeffs_at_once, tmp);
+ VERIFY_IS_APPROX(QR_at_once, matQR.leftCols(k + 1));
+ VERIFY_IS_APPROX(hCoeffs_at_once, hCoeffs.head(k + 1));
+ }
+ }
+
+ // Verify Property:
+ // We can go back and update any column to have a new value,
+ // and get a QR factorization of the columns up to that one.
+ {
+ const Index k = internal::random<Index>(0, size - 1);
+ VectorType newColumn = VectorType::Random(rows);
+ internal::householder_qr_inplace_update(matQR, hCoeffs, newColumn, k, tmp);
+
+ const MatrixX matQR_k = matQR.leftCols(k + 1);
+ const VectorX hCoeffs_k = hCoeffs.head(k + 1);
+ MatrixX R = matQR_k.template triangularView<Upper>();
+ MatrixX QxR = householderSequence(matQR_k, hCoeffs_k.conjugate()) * R;
+ VERIFY_IS_APPROX(QxR.leftCols(k), A.leftCols(k));
+ VERIFY_IS_APPROX(QxR.col(k), newColumn);
+ }
+}
+
+
+EIGEN_DECLARE_TEST(householder)
+{
+ for(int i = 0; i < g_repeat; i++) {
+ CALL_SUBTEST_1( householder(Matrix<double,2,2>()) );
+ CALL_SUBTEST_2( householder(Matrix<float,2,3>()) );
+ CALL_SUBTEST_3( householder(Matrix<double,3,5>()) );
+ CALL_SUBTEST_4( householder(Matrix<float,4,4>()) );
+ CALL_SUBTEST_5( householder(MatrixXd(internal::random<int>(1,EIGEN_TEST_MAX_SIZE),internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
+ CALL_SUBTEST_6( householder(MatrixXcf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE),internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
+ CALL_SUBTEST_7( householder(MatrixXf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE),internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
+ CALL_SUBTEST_8( householder(Matrix<double,1,1>()) );
+
+ CALL_SUBTEST_9( householder_update(Matrix<double, 3, 5>()) );
+ CALL_SUBTEST_9( householder_update(Matrix<float, 4, 2>()) );
+ CALL_SUBTEST_9( householder_update(MatrixXcf(internal::random<Index>(1,EIGEN_TEST_MAX_SIZE), internal::random<Index>(1,EIGEN_TEST_MAX_SIZE))) );
+ }
+}
diff --git a/test/incomplete_cholesky.cpp b/test/incomplete_cholesky.cpp
new file mode 100644
index 0000000..ecc17f5
--- /dev/null
+++ b/test/incomplete_cholesky.cpp
@@ -0,0 +1,69 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2015-2016 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+// #define EIGEN_DONT_VECTORIZE
+// #define EIGEN_MAX_ALIGN_BYTES 0
+#include "sparse_solver.h"
+#include <Eigen/IterativeLinearSolvers>
+#include <unsupported/Eigen/IterativeSolvers>
+
+template<typename T, typename I_> void test_incomplete_cholesky_T()
+{
+ typedef SparseMatrix<T,0,I_> SparseMatrixType;
+ ConjugateGradient<SparseMatrixType, Lower, IncompleteCholesky<T, Lower, AMDOrdering<I_> > > cg_illt_lower_amd;
+ ConjugateGradient<SparseMatrixType, Lower, IncompleteCholesky<T, Lower, NaturalOrdering<I_> > > cg_illt_lower_nat;
+ ConjugateGradient<SparseMatrixType, Upper, IncompleteCholesky<T, Upper, AMDOrdering<I_> > > cg_illt_upper_amd;
+ ConjugateGradient<SparseMatrixType, Upper, IncompleteCholesky<T, Upper, NaturalOrdering<I_> > > cg_illt_upper_nat;
+ ConjugateGradient<SparseMatrixType, Upper|Lower, IncompleteCholesky<T, Lower, AMDOrdering<I_> > > cg_illt_uplo_amd;
+
+
+ CALL_SUBTEST( check_sparse_spd_solving(cg_illt_lower_amd) );
+ CALL_SUBTEST( check_sparse_spd_solving(cg_illt_lower_nat) );
+ CALL_SUBTEST( check_sparse_spd_solving(cg_illt_upper_amd) );
+ CALL_SUBTEST( check_sparse_spd_solving(cg_illt_upper_nat) );
+ CALL_SUBTEST( check_sparse_spd_solving(cg_illt_uplo_amd) );
+}
+
+template<int>
+void bug1150()
+{
+ // regression for bug 1150
+ for(int N = 1; N<20; ++N)
+ {
+ Eigen::MatrixXd b( N, N );
+ b.setOnes();
+
+ Eigen::SparseMatrix<double> m( N, N );
+ m.reserve(Eigen::VectorXi::Constant(N,4));
+ for( int i = 0; i < N; ++i )
+ {
+ m.insert( i, i ) = 1;
+ m.coeffRef( i, i / 2 ) = 2;
+ m.coeffRef( i, i / 3 ) = 2;
+ m.coeffRef( i, i / 4 ) = 2;
+ }
+
+ Eigen::SparseMatrix<double> A;
+ A = m * m.transpose();
+
+ Eigen::ConjugateGradient<Eigen::SparseMatrix<double>,
+ Eigen::Lower | Eigen::Upper,
+ Eigen::IncompleteCholesky<double> > solver( A );
+ VERIFY(solver.preconditioner().info() == Eigen::Success);
+ VERIFY(solver.info() == Eigen::Success);
+ }
+}
+
+EIGEN_DECLARE_TEST(incomplete_cholesky)
+{
+ CALL_SUBTEST_1(( test_incomplete_cholesky_T<double,int>() ));
+ CALL_SUBTEST_2(( test_incomplete_cholesky_T<std::complex<double>, int>() ));
+ CALL_SUBTEST_3(( test_incomplete_cholesky_T<double,long int>() ));
+
+ CALL_SUBTEST_1(( bug1150<0>() ));
+}
diff --git a/test/indexed_view.cpp b/test/indexed_view.cpp
new file mode 100644
index 0000000..d149960
--- /dev/null
+++ b/test/indexed_view.cpp
@@ -0,0 +1,440 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2017 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include <valarray>
+#include <vector>
+#include "main.h"
+
+using Eigen::placeholders::all;
+using Eigen::placeholders::last;
+using Eigen::placeholders::lastp1;
+using Eigen::placeholders::lastN;
+#include <array>
+
+typedef std::pair<Index,Index> IndexPair;
+
+int encode(Index i, Index j) {
+ return int(i*100 + j);
+}
+
+IndexPair decode(Index ij) {
+ return IndexPair(ij / 100, ij % 100);
+}
+
+template<typename T>
+bool match(const T& xpr, std::string ref, std::string str_xpr = "") {
+ EIGEN_UNUSED_VARIABLE(str_xpr);
+ std::stringstream str;
+ str << xpr;
+ if(!(str.str() == ref))
+ std::cout << str_xpr << "\n" << xpr << "\n\n";
+ return str.str() == ref;
+}
+
+#define MATCH(X,R) match(X, R, #X)
+
+template<typename T1,typename T2>
+std::enable_if_t<internal::is_same<T1,T2>::value,bool>
+is_same_eq(const T1& a, const T2& b)
+{
+ return (a == b).all();
+}
+
+template<typename T1,typename T2>
+bool is_same_seq(const T1& a, const T2& b)
+{
+ bool ok = a.first()==b.first() && a.size() == b.size() && Index(a.incrObject())==Index(b.incrObject());;
+ if(!ok)
+ {
+ std::cerr << "seqN(" << a.first() << ", " << a.size() << ", " << Index(a.incrObject()) << ") != ";
+ std::cerr << "seqN(" << b.first() << ", " << b.size() << ", " << Index(b.incrObject()) << ")\n";
+ }
+ return ok;
+}
+
+template<typename T1,typename T2>
+std::enable_if_t<internal::is_same<T1,T2>::value,bool>
+is_same_seq_type(const T1& a, const T2& b)
+{
+ return is_same_seq(a,b);
+}
+
+
+
+#define VERIFY_EQ_INT(A,B) VERIFY_IS_APPROX(int(A),int(B))
+
+// C++03 does not allow local or unnamed enums as index
+enum DummyEnum { XX=0, YY=1 };
+
+void check_indexed_view()
+{
+ Index n = 10;
+
+ ArrayXd a = ArrayXd::LinSpaced(n,0,n-1);
+ Array<double,1,Dynamic> b = a.transpose();
+
+ ArrayXXi A = ArrayXXi::NullaryExpr(n,n, std::ref(encode));
+
+ for(Index i=0; i<n; ++i)
+ for(Index j=0; j<n; ++j)
+ VERIFY( decode(A(i,j)) == IndexPair(i,j) );
+
+ Array4i eii(4); eii << 3, 1, 6, 5;
+ std::valarray<int> vali(4); Map<ArrayXi>(&vali[0],4) = eii;
+ std::vector<int> veci(4); Map<ArrayXi>(veci.data(),4) = eii;
+
+ VERIFY( MATCH( A(3, seq(9,3,-1)),
+ "309 308 307 306 305 304 303")
+ );
+
+ VERIFY( MATCH( A(seqN(2,5), seq(9,3,-1)),
+ "209 208 207 206 205 204 203\n"
+ "309 308 307 306 305 304 303\n"
+ "409 408 407 406 405 404 403\n"
+ "509 508 507 506 505 504 503\n"
+ "609 608 607 606 605 604 603")
+ );
+
+ VERIFY( MATCH( A(seqN(2,5), 5),
+ "205\n"
+ "305\n"
+ "405\n"
+ "505\n"
+ "605")
+ );
+
+ VERIFY( MATCH( A(seqN(last,5,-1), seq(2,last)),
+ "902 903 904 905 906 907 908 909\n"
+ "802 803 804 805 806 807 808 809\n"
+ "702 703 704 705 706 707 708 709\n"
+ "602 603 604 605 606 607 608 609\n"
+ "502 503 504 505 506 507 508 509")
+ );
+
+ VERIFY( MATCH( A(eii, veci),
+ "303 301 306 305\n"
+ "103 101 106 105\n"
+ "603 601 606 605\n"
+ "503 501 506 505")
+ );
+
+ VERIFY( MATCH( A(eii, all),
+ "300 301 302 303 304 305 306 307 308 309\n"
+ "100 101 102 103 104 105 106 107 108 109\n"
+ "600 601 602 603 604 605 606 607 608 609\n"
+ "500 501 502 503 504 505 506 507 508 509")
+ );
+
+ // take row number 3, and repeat it 5 times
+ VERIFY( MATCH( A(seqN(3,5,0), all),
+ "300 301 302 303 304 305 306 307 308 309\n"
+ "300 301 302 303 304 305 306 307 308 309\n"
+ "300 301 302 303 304 305 306 307 308 309\n"
+ "300 301 302 303 304 305 306 307 308 309\n"
+ "300 301 302 303 304 305 306 307 308 309")
+ );
+
+ VERIFY( MATCH( a(seqN(3,3),0), "3\n4\n5" ) );
+ VERIFY( MATCH( a(seq(3,5)), "3\n4\n5" ) );
+ VERIFY( MATCH( a(seqN(3,3,1)), "3\n4\n5" ) );
+ VERIFY( MATCH( a(seqN(5,3,-1)), "5\n4\n3" ) );
+
+ VERIFY( MATCH( b(0,seqN(3,3)), "3 4 5" ) );
+ VERIFY( MATCH( b(seq(3,5)), "3 4 5" ) );
+ VERIFY( MATCH( b(seqN(3,3,1)), "3 4 5" ) );
+ VERIFY( MATCH( b(seqN(5,3,-1)), "5 4 3" ) );
+
+ VERIFY( MATCH( b(all), "0 1 2 3 4 5 6 7 8 9" ) );
+ VERIFY( MATCH( b(eii), "3 1 6 5" ) );
+
+ Array44i B;
+ B.setRandom();
+ VERIFY( (A(seqN(2,5), 5)).ColsAtCompileTime == 1);
+ VERIFY( (A(seqN(2,5), 5)).RowsAtCompileTime == Dynamic);
+ VERIFY_EQ_INT( (A(seqN(2,5), 5)).InnerStrideAtCompileTime , A.InnerStrideAtCompileTime);
+ VERIFY_EQ_INT( (A(seqN(2,5), 5)).OuterStrideAtCompileTime , A.col(5).OuterStrideAtCompileTime);
+
+ VERIFY_EQ_INT( (A(5,seqN(2,5))).InnerStrideAtCompileTime , A.row(5).InnerStrideAtCompileTime);
+ VERIFY_EQ_INT( (A(5,seqN(2,5))).OuterStrideAtCompileTime , A.row(5).OuterStrideAtCompileTime);
+ VERIFY_EQ_INT( (B(1,seqN(1,2))).InnerStrideAtCompileTime , B.row(1).InnerStrideAtCompileTime);
+ VERIFY_EQ_INT( (B(1,seqN(1,2))).OuterStrideAtCompileTime , B.row(1).OuterStrideAtCompileTime);
+
+ VERIFY_EQ_INT( (A(seqN(2,5), seq(1,3))).InnerStrideAtCompileTime , A.InnerStrideAtCompileTime);
+ VERIFY_EQ_INT( (A(seqN(2,5), seq(1,3))).OuterStrideAtCompileTime , A.OuterStrideAtCompileTime);
+ VERIFY_EQ_INT( (B(seqN(1,2), seq(1,3))).InnerStrideAtCompileTime , B.InnerStrideAtCompileTime);
+ VERIFY_EQ_INT( (B(seqN(1,2), seq(1,3))).OuterStrideAtCompileTime , B.OuterStrideAtCompileTime);
+ VERIFY_EQ_INT( (A(seqN(2,5,2), seq(1,3,2))).InnerStrideAtCompileTime , Dynamic);
+ VERIFY_EQ_INT( (A(seqN(2,5,2), seq(1,3,2))).OuterStrideAtCompileTime , Dynamic);
+ VERIFY_EQ_INT( (A(seqN(2,5,fix<2>), seq(1,3,fix<3>))).InnerStrideAtCompileTime , 2);
+ VERIFY_EQ_INT( (A(seqN(2,5,fix<2>), seq(1,3,fix<3>))).OuterStrideAtCompileTime , Dynamic);
+ VERIFY_EQ_INT( (B(seqN(1,2,fix<2>), seq(1,3,fix<3>))).InnerStrideAtCompileTime , 2);
+ VERIFY_EQ_INT( (B(seqN(1,2,fix<2>), seq(1,3,fix<3>))).OuterStrideAtCompileTime , 3*4);
+
+ VERIFY_EQ_INT( (A(seqN(2,fix<5>), seqN(1,fix<3>))).RowsAtCompileTime, 5);
+ VERIFY_EQ_INT( (A(seqN(2,fix<5>), seqN(1,fix<3>))).ColsAtCompileTime, 3);
+ VERIFY_EQ_INT( (A(seqN(2,fix<5>(5)), seqN(1,fix<3>(3)))).RowsAtCompileTime, 5);
+ VERIFY_EQ_INT( (A(seqN(2,fix<5>(5)), seqN(1,fix<3>(3)))).ColsAtCompileTime, 3);
+ VERIFY_EQ_INT( (A(seqN(2,fix<Dynamic>(5)), seqN(1,fix<Dynamic>(3)))).RowsAtCompileTime, Dynamic);
+ VERIFY_EQ_INT( (A(seqN(2,fix<Dynamic>(5)), seqN(1,fix<Dynamic>(3)))).ColsAtCompileTime, Dynamic);
+ VERIFY_EQ_INT( (A(seqN(2,fix<Dynamic>(5)), seqN(1,fix<Dynamic>(3)))).rows(), 5);
+ VERIFY_EQ_INT( (A(seqN(2,fix<Dynamic>(5)), seqN(1,fix<Dynamic>(3)))).cols(), 3);
+
+ VERIFY( is_same_seq_type( seqN(2,5,fix<-1>), seqN(2,5,fix<-1>(-1)) ) );
+ VERIFY( is_same_seq_type( seqN(2,5), seqN(2,5,fix<1>(1)) ) );
+ VERIFY( is_same_seq_type( seqN(2,5,3), seqN(2,5,fix<DynamicIndex>(3)) ) );
+ VERIFY( is_same_seq_type( seq(2,7,fix<3>), seqN(2,2,fix<3>) ) );
+ VERIFY( is_same_seq_type( seqN(2,fix<Dynamic>(5),3), seqN(2,5,fix<DynamicIndex>(3)) ) );
+ VERIFY( is_same_seq_type( seqN(2,fix<5>(5),fix<-2>), seqN(2,fix<5>,fix<-2>()) ) );
+
+ VERIFY( is_same_seq_type( seq(2,fix<5>), seqN(2,4) ) );
+ VERIFY( is_same_seq_type( seq(fix<2>,fix<5>), seqN(fix<2>,fix<4>) ) );
+ VERIFY( is_same_seq( seqN(2,std::integral_constant<int,5>(),std::integral_constant<int,-2>()), seqN(2,fix<5>,fix<-2>()) ) );
+ VERIFY( is_same_seq( seq(std::integral_constant<int,1>(),std::integral_constant<int,5>(),std::integral_constant<int,2>()),
+ seq(fix<1>,fix<5>,fix<2>()) ) );
+ VERIFY( is_same_seq_type( seqN(2,std::integral_constant<int,5>(),std::integral_constant<int,-2>()), seqN(2,fix<5>,fix<-2>()) ) );
+ VERIFY( is_same_seq_type( seq(std::integral_constant<int,1>(),std::integral_constant<int,5>(),std::integral_constant<int,2>()),
+ seq(fix<1>,fix<5>,fix<2>()) ) );
+
+ VERIFY( is_same_seq_type( seqN(2,std::integral_constant<int,5>()), seqN(2,fix<5>) ) );
+ VERIFY( is_same_seq_type( seq(std::integral_constant<int,1>(),std::integral_constant<int,5>()), seq(fix<1>,fix<5>) ) );
+
+ VERIFY( (A(seqN(2,fix<5>), 5)).RowsAtCompileTime == 5);
+ VERIFY( (A(4, all)).ColsAtCompileTime == Dynamic);
+ VERIFY( (A(4, all)).RowsAtCompileTime == 1);
+ VERIFY( (B(1, all)).ColsAtCompileTime == 4);
+ VERIFY( (B(1, all)).RowsAtCompileTime == 1);
+ VERIFY( (B(all,1)).ColsAtCompileTime == 1);
+ VERIFY( (B(all,1)).RowsAtCompileTime == 4);
+
+ VERIFY(int( (A(all, eii)).ColsAtCompileTime) == int(eii.SizeAtCompileTime));
+ VERIFY_EQ_INT( (A(eii, eii)).Flags&DirectAccessBit, (unsigned int)(0));
+ VERIFY_EQ_INT( (A(eii, eii)).InnerStrideAtCompileTime, 0);
+ VERIFY_EQ_INT( (A(eii, eii)).OuterStrideAtCompileTime, 0);
+
+ VERIFY_IS_APPROX( A(seq(n-1,2,-2), seqN(n-1-6,3,-1)), A(seq(last,2,fix<-2>), seqN(last-6,3,fix<-1>)) );
+
+ VERIFY_IS_APPROX( A(seq(n-1,2,-2), seqN(n-1-6,4)), A(seq(last,2,-2), seqN(last-6,4)) );
+ VERIFY_IS_APPROX( A(seq(n-1-6,n-1-2), seqN(n-1-6,4)), A(seq(last-6,last-2), seqN(6+last-6-6,4)) );
+ VERIFY_IS_APPROX( A(seq((n-1)/2,(n)/2+3), seqN(2,4)), A(seq(last/2,(last+1)/2+3), seqN(last+2-last,4)) );
+ VERIFY_IS_APPROX( A(seq(n-2,2,-2), seqN(n-8,4)), A(seq(lastp1-2,2,-2), seqN(lastp1-8,4)) );
+
+ // Check all combinations of seq:
+ VERIFY_IS_APPROX( A(seq(1,n-1-2,2), seq(1,n-1-2,2)), A(seq(1,last-2,2), seq(1,last-2,fix<2>)) );
+ VERIFY_IS_APPROX( A(seq(n-1-5,n-1-2,2), seq(n-1-5,n-1-2,2)), A(seq(last-5,last-2,2), seq(last-5,last-2,fix<2>)) );
+ VERIFY_IS_APPROX( A(seq(n-1-5,7,2), seq(n-1-5,7,2)), A(seq(last-5,7,2), seq(last-5,7,fix<2>)) );
+ VERIFY_IS_APPROX( A(seq(1,n-1-2), seq(n-1-5,7)), A(seq(1,last-2), seq(last-5,7)) );
+ VERIFY_IS_APPROX( A(seq(n-1-5,n-1-2), seq(n-1-5,n-1-2)), A(seq(last-5,last-2), seq(last-5,last-2)) );
+
+ VERIFY_IS_APPROX( A.col(A.cols()-1), A(all,last) );
+ VERIFY_IS_APPROX( A(A.rows()-2, A.cols()/2), A(last-1, lastp1/2) );
+ VERIFY_IS_APPROX( a(a.size()-2), a(last-1) );
+ VERIFY_IS_APPROX( a(a.size()/2), a((last+1)/2) );
+
+ // Check fall-back to Block
+ {
+ VERIFY( is_same_eq(A.col(0), A(all,0)) );
+ VERIFY( is_same_eq(A.row(0), A(0,all)) );
+ VERIFY( is_same_eq(A.block(0,0,2,2), A(seqN(0,2),seq(0,1))) );
+ VERIFY( is_same_eq(A.middleRows(2,4), A(seqN(2,4),all)) );
+ VERIFY( is_same_eq(A.middleCols(2,4), A(all,seqN(2,4))) );
+
+ VERIFY( is_same_eq(A.col(A.cols()-1), A(all,last)) );
+
+ const ArrayXXi& cA(A);
+ VERIFY( is_same_eq(cA.col(0), cA(all,0)) );
+ VERIFY( is_same_eq(cA.row(0), cA(0,all)) );
+ VERIFY( is_same_eq(cA.block(0,0,2,2), cA(seqN(0,2),seq(0,1))) );
+ VERIFY( is_same_eq(cA.middleRows(2,4), cA(seqN(2,4),all)) );
+ VERIFY( is_same_eq(cA.middleCols(2,4), cA(all,seqN(2,4))) );
+
+ VERIFY( is_same_eq(a.head(4), a(seq(0,3))) );
+ VERIFY( is_same_eq(a.tail(4), a(seqN(last-3,4))) );
+ VERIFY( is_same_eq(a.tail(4), a(seq(lastp1-4,last))) );
+ VERIFY( is_same_eq(a.segment<4>(3), a(seqN(3,fix<4>))) );
+ }
+
+ ArrayXXi A1=A, A2 = ArrayXXi::Random(4,4);
+ ArrayXi range25(4); range25 << 3,2,4,5;
+ A1(seqN(3,4),seq(2,5)) = A2;
+ VERIFY_IS_APPROX( A1.block(3,2,4,4), A2 );
+ A1 = A;
+ A2.setOnes();
+ A1(seq(6,3,-1),range25) = A2;
+ VERIFY_IS_APPROX( A1.block(3,2,4,4), A2 );
+
+ // check reverse
+ {
+ VERIFY( is_same_seq_type( seq(3,7).reverse(), seqN(7,5,fix<-1>) ) );
+ VERIFY( is_same_seq_type( seq(7,3,fix<-2>).reverse(), seqN(3,3,fix<2>) ) );
+ VERIFY_IS_APPROX( a(seqN(2,last/2).reverse()), a(seqN(2+(last/2-1)*1,last/2,fix<-1>)) );
+ VERIFY_IS_APPROX( a(seqN(last/2,fix<4>).reverse()),a(seqN(last/2,fix<4>)).reverse() );
+ VERIFY_IS_APPROX( A(seq(last-5,last-1,2).reverse(), seqN(last-3,3,fix<-2>).reverse()),
+ A(seq(last-5,last-1,2), seqN(last-3,3,fix<-2>)).reverse() );
+ }
+
+ // check lastN
+ VERIFY_IS_APPROX( a(lastN(3)), a.tail(3) );
+ VERIFY( MATCH( a(lastN(3)), "7\n8\n9" ) );
+ VERIFY_IS_APPROX( a(lastN(fix<3>())), a.tail<3>() );
+ VERIFY( MATCH( a(lastN(3,2)), "5\n7\n9" ) );
+ VERIFY( MATCH( a(lastN(3,fix<2>())), "5\n7\n9" ) );
+ VERIFY( a(lastN(fix<3>())).SizeAtCompileTime == 3 );
+
+ VERIFY( (A(all, std::array<int,4>{{1,3,2,4}})).ColsAtCompileTime == 4);
+
+ VERIFY_IS_APPROX( (A(std::array<int,3>{{1,3,5}}, std::array<int,4>{{9,6,3,0}})), A(seqN(1,3,2), seqN(9,4,-3)) );
+
+ VERIFY_IS_APPROX( A({3, 1, 6, 5}, all), A(std::array<int,4>{{3, 1, 6, 5}}, all) );
+ VERIFY_IS_APPROX( A(all,{3, 1, 6, 5}), A(all,std::array<int,4>{{3, 1, 6, 5}}) );
+ VERIFY_IS_APPROX( A({1,3,5},{3, 1, 6, 5}), A(std::array<int,3>{{1,3,5}},std::array<int,4>{{3, 1, 6, 5}}) );
+
+ VERIFY_IS_EQUAL( A({1,3,5},{3, 1, 6, 5}).RowsAtCompileTime, 3 );
+ VERIFY_IS_EQUAL( A({1,3,5},{3, 1, 6, 5}).ColsAtCompileTime, 4 );
+
+ VERIFY_IS_APPROX( a({3, 1, 6, 5}), a(std::array<int,4>{{3, 1, 6, 5}}) );
+ VERIFY_IS_EQUAL( a({1,3,5}).SizeAtCompileTime, 3 );
+
+ VERIFY_IS_APPROX( b({3, 1, 6, 5}), b(std::array<int,4>{{3, 1, 6, 5}}) );
+ VERIFY_IS_EQUAL( b({1,3,5}).SizeAtCompileTime, 3 );
+
+ // check mat(i,j) with weird types for i and j
+ {
+ VERIFY_IS_APPROX( A(B.RowsAtCompileTime-1, 1), A(3,1) );
+ VERIFY_IS_APPROX( A(B.RowsAtCompileTime, 1), A(4,1) );
+ VERIFY_IS_APPROX( A(B.RowsAtCompileTime-1, B.ColsAtCompileTime-1), A(3,3) );
+ VERIFY_IS_APPROX( A(B.RowsAtCompileTime, B.ColsAtCompileTime), A(4,4) );
+ const Index I_ = 3, J_ = 4;
+ VERIFY_IS_APPROX( A(I_,J_), A(3,4) );
+ }
+
+ // check extended block API
+ {
+ VERIFY( is_same_eq( A.block<3,4>(1,1), A.block(1,1,fix<3>,fix<4>)) );
+ VERIFY( is_same_eq( A.block<3,4>(1,1,3,4), A.block(1,1,fix<3>(),fix<4>(4))) );
+ VERIFY( is_same_eq( A.block<3,Dynamic>(1,1,3,4), A.block(1,1,fix<3>,4)) );
+ VERIFY( is_same_eq( A.block<Dynamic,4>(1,1,3,4), A.block(1,1,fix<Dynamic>(3),fix<4>)) );
+ VERIFY( is_same_eq( A.block(1,1,3,4), A.block(1,1,fix<Dynamic>(3),fix<Dynamic>(4))) );
+
+ VERIFY( is_same_eq( A.topLeftCorner<3,4>(), A.topLeftCorner(fix<3>,fix<4>)) );
+ VERIFY( is_same_eq( A.bottomLeftCorner<3,4>(), A.bottomLeftCorner(fix<3>,fix<4>)) );
+ VERIFY( is_same_eq( A.bottomRightCorner<3,4>(), A.bottomRightCorner(fix<3>,fix<4>)) );
+ VERIFY( is_same_eq( A.topRightCorner<3,4>(), A.topRightCorner(fix<3>,fix<4>)) );
+
+ VERIFY( is_same_eq( A.leftCols<3>(), A.leftCols(fix<3>)) );
+ VERIFY( is_same_eq( A.rightCols<3>(), A.rightCols(fix<3>)) );
+ VERIFY( is_same_eq( A.middleCols<3>(1), A.middleCols(1,fix<3>)) );
+
+ VERIFY( is_same_eq( A.topRows<3>(), A.topRows(fix<3>)) );
+ VERIFY( is_same_eq( A.bottomRows<3>(), A.bottomRows(fix<3>)) );
+ VERIFY( is_same_eq( A.middleRows<3>(1), A.middleRows(1,fix<3>)) );
+
+ VERIFY( is_same_eq( a.segment<3>(1), a.segment(1,fix<3>)) );
+ VERIFY( is_same_eq( a.head<3>(), a.head(fix<3>)) );
+ VERIFY( is_same_eq( a.tail<3>(), a.tail(fix<3>)) );
+
+ const ArrayXXi& cA(A);
+ VERIFY( is_same_eq( cA.block<Dynamic,4>(1,1,3,4), cA.block(1,1,fix<Dynamic>(3),fix<4>)) );
+
+ VERIFY( is_same_eq( cA.topLeftCorner<3,4>(), cA.topLeftCorner(fix<3>,fix<4>)) );
+ VERIFY( is_same_eq( cA.bottomLeftCorner<3,4>(), cA.bottomLeftCorner(fix<3>,fix<4>)) );
+ VERIFY( is_same_eq( cA.bottomRightCorner<3,4>(), cA.bottomRightCorner(fix<3>,fix<4>)) );
+ VERIFY( is_same_eq( cA.topRightCorner<3,4>(), cA.topRightCorner(fix<3>,fix<4>)) );
+
+ VERIFY( is_same_eq( cA.leftCols<3>(), cA.leftCols(fix<3>)) );
+ VERIFY( is_same_eq( cA.rightCols<3>(), cA.rightCols(fix<3>)) );
+ VERIFY( is_same_eq( cA.middleCols<3>(1), cA.middleCols(1,fix<3>)) );
+
+ VERIFY( is_same_eq( cA.topRows<3>(), cA.topRows(fix<3>)) );
+ VERIFY( is_same_eq( cA.bottomRows<3>(), cA.bottomRows(fix<3>)) );
+ VERIFY( is_same_eq( cA.middleRows<3>(1), cA.middleRows(1,fix<3>)) );
+ }
+
+ // Check compilation of enums as index type:
+ a(XX) = 1;
+ A(XX,YY) = 1;
+ // Anonymous enums only work with C++11
+ enum { X=0, Y=1 };
+ a(X) = 1;
+ A(X,Y) = 1;
+ A(XX,Y) = 1;
+ A(X,YY) = 1;
+
+ // Check compilation of varying integer types as index types:
+ Index i = n/2;
+ short i_short(i);
+ std::size_t i_sizet(i);
+ VERIFY_IS_EQUAL( a(i), a.coeff(i_short) );
+ VERIFY_IS_EQUAL( a(i), a.coeff(i_sizet) );
+
+ VERIFY_IS_EQUAL( A(i,i), A.coeff(i_short, i_short) );
+ VERIFY_IS_EQUAL( A(i,i), A.coeff(i_short, i) );
+ VERIFY_IS_EQUAL( A(i,i), A.coeff(i, i_short) );
+ VERIFY_IS_EQUAL( A(i,i), A.coeff(i, i_sizet) );
+ VERIFY_IS_EQUAL( A(i,i), A.coeff(i_sizet, i) );
+ VERIFY_IS_EQUAL( A(i,i), A.coeff(i_sizet, i_short) );
+ VERIFY_IS_EQUAL( A(i,i), A.coeff(5, i_sizet) );
+
+ // Regression test for Max{Rows,Cols}AtCompileTime
+ {
+ Matrix3i A3 = Matrix3i::Random();
+ ArrayXi ind(5); ind << 1,1,1,1,1;
+ VERIFY_IS_EQUAL( A3(ind,ind).eval(), MatrixXi::Constant(5,5,A3(1,1)) );
+ }
+
+ // Regression for bug 1736
+ {
+ VERIFY_IS_APPROX(A(all, eii).col(0).eval(), A.col(eii(0)));
+ A(all, eii).col(0) = A.col(eii(0));
+ }
+
+ // bug 1815: IndexedView should allow linear access
+ {
+ VERIFY( MATCH( b(eii)(0), "3" ) );
+ VERIFY( MATCH( a(eii)(0), "3" ) );
+ VERIFY( MATCH( A(1,eii)(0), "103"));
+ VERIFY( MATCH( A(eii,1)(0), "301"));
+ VERIFY( MATCH( A(1,all)(1), "101"));
+ VERIFY( MATCH( A(all,1)(1), "101"));
+ }
+
+ // bug #2375: indexing over matrices of dim >128 should compile on gcc
+ {
+ Matrix<double, 513, 3> large_mat = Matrix<double, 513, 3>::Random();
+ std::array<int, 2> test_indices = {0, 1};
+ Matrix<double, 513, 2> thin_slice = large_mat(all, test_indices);
+ for(int col = 0; col < int(test_indices.size()); ++col)
+ for(int row = 0; row < large_mat.rows(); ++row)
+ VERIFY_IS_EQUAL( thin_slice(row, col), large_mat(row, col) );
+ }
+
+ //Bug IndexView with a single static row should be RowMajor:
+ {
+ // A(1, seq(0,2,1)).cwiseAbs().colwise().replicate(2).eval();
+ STATIC_CHECK(( (internal::evaluator<decltype( A(1,seq(0,2,1)) )>::Flags & RowMajorBit) == RowMajorBit ));
+ }
+
+}
+
+EIGEN_DECLARE_TEST(indexed_view)
+{
+// for(int i = 0; i < g_repeat; i++) {
+ CALL_SUBTEST_1( check_indexed_view() );
+// }
+
+ // static checks of some internals:
+ STATIC_CHECK(( internal::is_valid_index_type<int>::value ));
+ STATIC_CHECK(( internal::is_valid_index_type<unsigned int>::value ));
+ STATIC_CHECK(( internal::is_valid_index_type<short>::value ));
+ STATIC_CHECK(( internal::is_valid_index_type<std::ptrdiff_t>::value ));
+ STATIC_CHECK(( internal::is_valid_index_type<std::size_t>::value ));
+ STATIC_CHECK(( !internal::valid_indexed_view_overload<int,int>::value ));
+ STATIC_CHECK(( !internal::valid_indexed_view_overload<int,std::ptrdiff_t>::value ));
+ STATIC_CHECK(( !internal::valid_indexed_view_overload<std::ptrdiff_t,int>::value ));
+ STATIC_CHECK(( !internal::valid_indexed_view_overload<std::size_t,int>::value ));
+}
diff --git a/test/initializer_list_construction.cpp b/test/initializer_list_construction.cpp
new file mode 100644
index 0000000..b576ec2
--- /dev/null
+++ b/test/initializer_list_construction.cpp
@@ -0,0 +1,380 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2019 David Tellenbach <david.tellenbach@tellnotes.org>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#if defined(__GNUC__) && __GNUC__ >= 10
+// GCC 10+ has a bug for unsigned char that thinks we're writing past the
+// end of an array when compiled with -O3. This warning is not triggered for
+// any other types, nor for other compilers, nor for other optimization levels.
+#pragma GCC diagnostic ignored "-Wstringop-overflow"
+#endif
+
+#include "main.h"
+
+template<typename Scalar, bool is_integer = NumTraits<Scalar>::IsInteger>
+struct TestMethodDispatching {
+ static void run() {}
+};
+
+template<typename Scalar>
+struct TestMethodDispatching<Scalar, 1> {
+ static void run()
+ {
+ {
+ Matrix<Scalar, Dynamic, Dynamic> m {3, 4};
+ Array<Scalar, Dynamic, Dynamic> a {3, 4};
+ VERIFY(m.rows() == 3);
+ VERIFY(m.cols() == 4);
+ VERIFY(a.rows() == 3);
+ VERIFY(a.cols() == 4);
+ }
+ {
+ Matrix<Scalar, 1, 2> m {3, 4};
+ Array<Scalar, 1, 2> a {3, 4};
+ VERIFY(m(0) == 3);
+ VERIFY(m(1) == 4);
+ VERIFY(a(0) == 3);
+ VERIFY(a(1) == 4);
+ }
+ {
+ Matrix<Scalar, 2, 1> m {3, 4};
+ Array<Scalar, 2, 1> a {3, 4};
+ VERIFY(m(0) == 3);
+ VERIFY(m(1) == 4);
+ VERIFY(a(0) == 3);
+ VERIFY(a(1) == 4);
+ }
+ }
+};
+
+template<typename Vec4, typename Vec5> void fixedsizeVariadicVectorConstruction2()
+{
+ {
+ Vec4 ref = Vec4::Random();
+ Vec4 v{ ref[0], ref[1], ref[2], ref[3] };
+ VERIFY_IS_APPROX(v, ref);
+ VERIFY_IS_APPROX(v, (Vec4( ref[0], ref[1], ref[2], ref[3] )));
+ VERIFY_IS_APPROX(v, (Vec4({ref[0], ref[1], ref[2], ref[3]})));
+
+ Vec4 v2 = { ref[0], ref[1], ref[2], ref[3] };
+ VERIFY_IS_APPROX(v2, ref);
+ }
+ {
+ Vec5 ref = Vec5::Random();
+ Vec5 v{ ref[0], ref[1], ref[2], ref[3], ref[4] };
+ VERIFY_IS_APPROX(v, ref);
+ VERIFY_IS_APPROX(v, (Vec5( ref[0], ref[1], ref[2], ref[3], ref[4] )));
+ VERIFY_IS_APPROX(v, (Vec5({ref[0], ref[1], ref[2], ref[3], ref[4]})));
+
+ Vec5 v2 = { ref[0], ref[1], ref[2], ref[3], ref[4] };
+ VERIFY_IS_APPROX(v2, ref);
+ }
+}
+
+#define CHECK_MIXSCALAR_V5_APPROX(V, A0, A1, A2, A3, A4) { \
+ VERIFY_IS_APPROX(V[0], Scalar(A0) ); \
+ VERIFY_IS_APPROX(V[1], Scalar(A1) ); \
+ VERIFY_IS_APPROX(V[2], Scalar(A2) ); \
+ VERIFY_IS_APPROX(V[3], Scalar(A3) ); \
+ VERIFY_IS_APPROX(V[4], Scalar(A4) ); \
+}
+
+#define CHECK_MIXSCALAR_V5(VEC5, A0, A1, A2, A3, A4) { \
+ typedef VEC5::Scalar Scalar; \
+ VEC5 v = { A0 , A1 , A2 , A3 , A4 }; \
+ CHECK_MIXSCALAR_V5_APPROX(v, A0 , A1 , A2 , A3 , A4); \
+}
+
+template<int> void fixedsizeVariadicVectorConstruction3()
+{
+ typedef Matrix<double,5,1> Vec5;
+ typedef Array<float,5,1> Arr5;
+ CHECK_MIXSCALAR_V5(Vec5, 1, 2., -3, 4.121, 5.53252);
+ CHECK_MIXSCALAR_V5(Arr5, 1, 2., 3.12f, 4.121, 5.53252);
+}
+
+template<typename Scalar> void fixedsizeVariadicVectorConstruction()
+{
+ CALL_SUBTEST(( fixedsizeVariadicVectorConstruction2<Matrix<Scalar,4,1>, Matrix<Scalar,5,1> >() ));
+ CALL_SUBTEST(( fixedsizeVariadicVectorConstruction2<Matrix<Scalar,1,4>, Matrix<Scalar,1,5> >() ));
+ CALL_SUBTEST(( fixedsizeVariadicVectorConstruction2<Array<Scalar,4,1>, Array<Scalar,5,1> >() ));
+ CALL_SUBTEST(( fixedsizeVariadicVectorConstruction2<Array<Scalar,1,4>, Array<Scalar,1,5> >() ));
+}
+
+
+template<typename Scalar> void initializerListVectorConstruction()
+{
+ Scalar raw[4];
+ for(int k = 0; k < 4; ++k) {
+ raw[k] = internal::random<Scalar>();
+ }
+ {
+ Matrix<Scalar, 4, 1> m { {raw[0]}, {raw[1]},{raw[2]},{raw[3]} };
+ Array<Scalar, 4, 1> a { {raw[0]}, {raw[1]}, {raw[2]}, {raw[3]} };
+ for(int k = 0; k < 4; ++k) {
+ VERIFY(m(k) == raw[k]);
+ }
+ for(int k = 0; k < 4; ++k) {
+ VERIFY(a(k) == raw[k]);
+ }
+ VERIFY_IS_EQUAL(m, (Matrix<Scalar,4,1>({ {raw[0]}, {raw[1]}, {raw[2]}, {raw[3]} })));
+ VERIFY((a == (Array<Scalar,4,1>({ {raw[0]}, {raw[1]}, {raw[2]}, {raw[3]} }))).all());
+ }
+ {
+ Matrix<Scalar, 1, 4> m { {raw[0], raw[1], raw[2], raw[3]} };
+ Array<Scalar, 1, 4> a { {raw[0], raw[1], raw[2], raw[3]} };
+ for(int k = 0; k < 4; ++k) {
+ VERIFY(m(k) == raw[k]);
+ }
+ for(int k = 0; k < 4; ++k) {
+ VERIFY(a(k) == raw[k]);
+ }
+ VERIFY_IS_EQUAL(m, (Matrix<Scalar, 1, 4>({{raw[0],raw[1],raw[2],raw[3]}})));
+ VERIFY((a == (Array<Scalar, 1, 4>({{raw[0],raw[1],raw[2],raw[3]}}))).all());
+ }
+ {
+ Matrix<Scalar, 4, Dynamic> m { {raw[0]}, {raw[1]}, {raw[2]}, {raw[3]} };
+ Array<Scalar, 4, Dynamic> a { {raw[0]}, {raw[1]}, {raw[2]}, {raw[3]} };
+ for(int k=0; k < 4; ++k) {
+ VERIFY(m(k) == raw[k]);
+ }
+ for(int k=0; k < 4; ++k) {
+ VERIFY(a(k) == raw[k]);
+ }
+ VERIFY_IS_EQUAL(m, (Matrix<Scalar, 4, Dynamic>({ {raw[0]}, {raw[1]}, {raw[2]}, {raw[3]} })));
+ VERIFY((a == (Array<Scalar, 4, Dynamic>({ {raw[0]}, {raw[1]}, {raw[2]}, {raw[3]} }))).all());
+ }
+ {
+ Matrix<Scalar, Dynamic, 4> m {{raw[0],raw[1],raw[2],raw[3]}};
+ Array<Scalar, Dynamic, 4> a {{raw[0],raw[1],raw[2],raw[3]}};
+ for(int k=0; k < 4; ++k) {
+ VERIFY(m(k) == raw[k]);
+ }
+ for(int k=0; k < 4; ++k) {
+ VERIFY(a(k) == raw[k]);
+ }
+ VERIFY_IS_EQUAL(m, (Matrix<Scalar, Dynamic, 4>({{raw[0],raw[1],raw[2],raw[3]}})));
+ VERIFY((a == (Array<Scalar, Dynamic, 4>({{raw[0],raw[1],raw[2],raw[3]}}))).all());
+ }
+}
+
+template<typename Scalar> void initializerListMatrixConstruction()
+{
+ const Index RowsAtCompileTime = 5;
+ const Index ColsAtCompileTime = 4;
+ const Index SizeAtCompileTime = RowsAtCompileTime * ColsAtCompileTime;
+
+ Scalar raw[SizeAtCompileTime];
+ for (int i = 0; i < SizeAtCompileTime; ++i) {
+ raw[i] = internal::random<Scalar>();
+ }
+ {
+ Matrix<Scalar, Dynamic, Dynamic> m {};
+ VERIFY(m.cols() == 0);
+ VERIFY(m.rows() == 0);
+ VERIFY_IS_EQUAL(m, (Matrix<Scalar, Dynamic, Dynamic>()));
+ }
+ {
+ Matrix<Scalar, 5, 4> m {
+ {raw[0], raw[1], raw[2], raw[3]},
+ {raw[4], raw[5], raw[6], raw[7]},
+ {raw[8], raw[9], raw[10], raw[11]},
+ {raw[12], raw[13], raw[14], raw[15]},
+ {raw[16], raw[17], raw[18], raw[19]}
+ };
+
+ Matrix<Scalar, 5, 4> m2;
+ m2 << raw[0], raw[1], raw[2], raw[3],
+ raw[4], raw[5], raw[6], raw[7],
+ raw[8], raw[9], raw[10], raw[11],
+ raw[12], raw[13], raw[14], raw[15],
+ raw[16], raw[17], raw[18], raw[19];
+
+ int k = 0;
+ for(int i = 0; i < RowsAtCompileTime; ++i) {
+ for (int j = 0; j < ColsAtCompileTime; ++j) {
+ VERIFY(m(i, j) == raw[k]);
+ ++k;
+ }
+ }
+ VERIFY_IS_EQUAL(m, m2);
+ }
+ {
+ Matrix<Scalar, Dynamic, Dynamic> m{
+ {raw[0], raw[1], raw[2], raw[3]},
+ {raw[4], raw[5], raw[6], raw[7]},
+ {raw[8], raw[9], raw[10], raw[11]},
+ {raw[12], raw[13], raw[14], raw[15]},
+ {raw[16], raw[17], raw[18], raw[19]}
+ };
+
+ VERIFY(m.cols() == 4);
+ VERIFY(m.rows() == 5);
+ int k = 0;
+ for(int i = 0; i < RowsAtCompileTime; ++i) {
+ for (int j = 0; j < ColsAtCompileTime; ++j) {
+ VERIFY(m(i, j) == raw[k]);
+ ++k;
+ }
+ }
+
+ Matrix<Scalar, Dynamic, Dynamic> m2(RowsAtCompileTime, ColsAtCompileTime);
+ k = 0;
+ for(int i = 0; i < RowsAtCompileTime; ++i) {
+ for (int j = 0; j < ColsAtCompileTime; ++j) {
+ m2(i, j) = raw[k];
+ ++k;
+ }
+ }
+ VERIFY_IS_EQUAL(m, m2);
+ }
+}
+
+template<typename Scalar> void initializerListArrayConstruction()
+{
+ const Index RowsAtCompileTime = 5;
+ const Index ColsAtCompileTime = 4;
+ const Index SizeAtCompileTime = RowsAtCompileTime * ColsAtCompileTime;
+
+ Scalar raw[SizeAtCompileTime];
+ for (int i = 0; i < SizeAtCompileTime; ++i) {
+ raw[i] = internal::random<Scalar>();
+ }
+ {
+ Array<Scalar, Dynamic, Dynamic> a {};
+ VERIFY(a.cols() == 0);
+ VERIFY(a.rows() == 0);
+ }
+ {
+ Array<Scalar, 5, 4> m {
+ {raw[0], raw[1], raw[2], raw[3]},
+ {raw[4], raw[5], raw[6], raw[7]},
+ {raw[8], raw[9], raw[10], raw[11]},
+ {raw[12], raw[13], raw[14], raw[15]},
+ {raw[16], raw[17], raw[18], raw[19]}
+ };
+
+ Array<Scalar, 5, 4> m2;
+ m2 << raw[0], raw[1], raw[2], raw[3],
+ raw[4], raw[5], raw[6], raw[7],
+ raw[8], raw[9], raw[10], raw[11],
+ raw[12], raw[13], raw[14], raw[15],
+ raw[16], raw[17], raw[18], raw[19];
+
+ int k = 0;
+ for(int i = 0; i < RowsAtCompileTime; ++i) {
+ for (int j = 0; j < ColsAtCompileTime; ++j) {
+ VERIFY(m(i, j) == raw[k]);
+ ++k;
+ }
+ }
+ VERIFY_IS_APPROX(m, m2);
+ }
+ {
+ Array<Scalar, Dynamic, Dynamic> m {
+ {raw[0], raw[1], raw[2], raw[3]},
+ {raw[4], raw[5], raw[6], raw[7]},
+ {raw[8], raw[9], raw[10], raw[11]},
+ {raw[12], raw[13], raw[14], raw[15]},
+ {raw[16], raw[17], raw[18], raw[19]}
+ };
+
+ VERIFY(m.cols() == 4);
+ VERIFY(m.rows() == 5);
+ int k = 0;
+ for(int i = 0; i < RowsAtCompileTime; ++i) {
+ for (int j = 0; j < ColsAtCompileTime; ++j) {
+ VERIFY(m(i, j) == raw[k]);
+ ++k;
+ }
+ }
+
+ Array<Scalar, Dynamic, Dynamic> m2(RowsAtCompileTime, ColsAtCompileTime);
+ k = 0;
+ for(int i = 0; i < RowsAtCompileTime; ++i) {
+ for (int j = 0; j < ColsAtCompileTime; ++j) {
+ m2(i, j) = raw[k];
+ ++k;
+ }
+ }
+ VERIFY_IS_APPROX(m, m2);
+ }
+}
+
+template<typename Scalar> void dynamicVectorConstruction()
+{
+ const Index size = 4;
+ Scalar raw[size];
+ for (int i = 0; i < size; ++i) {
+ raw[i] = internal::random<Scalar>();
+ }
+
+ typedef Matrix<Scalar, Dynamic, 1> VectorX;
+
+ {
+ VectorX v {{raw[0], raw[1], raw[2], raw[3]}};
+ for (int i = 0; i < size; ++i) {
+ VERIFY(v(i) == raw[i]);
+ }
+ VERIFY(v.rows() == size);
+ VERIFY(v.cols() == 1);
+ VERIFY_IS_EQUAL(v, (VectorX {{raw[0], raw[1], raw[2], raw[3]}}));
+ }
+}
+
+EIGEN_DECLARE_TEST(initializer_list_construction)
+{
+ CALL_SUBTEST_1(initializerListVectorConstruction<unsigned char>());
+ CALL_SUBTEST_1(initializerListVectorConstruction<float>());
+ CALL_SUBTEST_1(initializerListVectorConstruction<double>());
+ CALL_SUBTEST_1(initializerListVectorConstruction<int>());
+ CALL_SUBTEST_1(initializerListVectorConstruction<long int>());
+ CALL_SUBTEST_1(initializerListVectorConstruction<std::ptrdiff_t>());
+ CALL_SUBTEST_1(initializerListVectorConstruction<std::complex<double>>());
+ CALL_SUBTEST_1(initializerListVectorConstruction<std::complex<float>>());
+
+ CALL_SUBTEST_2(initializerListMatrixConstruction<unsigned char>());
+ CALL_SUBTEST_2(initializerListMatrixConstruction<float>());
+ CALL_SUBTEST_2(initializerListMatrixConstruction<double>());
+ CALL_SUBTEST_2(initializerListMatrixConstruction<int>());
+ CALL_SUBTEST_2(initializerListMatrixConstruction<long int>());
+ CALL_SUBTEST_2(initializerListMatrixConstruction<std::ptrdiff_t>());
+ CALL_SUBTEST_2(initializerListMatrixConstruction<std::complex<double>>());
+ CALL_SUBTEST_2(initializerListMatrixConstruction<std::complex<float>>());
+
+ CALL_SUBTEST_3(initializerListArrayConstruction<unsigned char>());
+ CALL_SUBTEST_3(initializerListArrayConstruction<float>());
+ CALL_SUBTEST_3(initializerListArrayConstruction<double>());
+ CALL_SUBTEST_3(initializerListArrayConstruction<int>());
+ CALL_SUBTEST_3(initializerListArrayConstruction<long int>());
+ CALL_SUBTEST_3(initializerListArrayConstruction<std::ptrdiff_t>());
+ CALL_SUBTEST_3(initializerListArrayConstruction<std::complex<double>>());
+ CALL_SUBTEST_3(initializerListArrayConstruction<std::complex<float>>());
+
+ CALL_SUBTEST_4(fixedsizeVariadicVectorConstruction<unsigned char>());
+ CALL_SUBTEST_4(fixedsizeVariadicVectorConstruction<float>());
+ CALL_SUBTEST_4(fixedsizeVariadicVectorConstruction<double>());
+ CALL_SUBTEST_4(fixedsizeVariadicVectorConstruction<int>());
+ CALL_SUBTEST_4(fixedsizeVariadicVectorConstruction<long int>());
+ CALL_SUBTEST_4(fixedsizeVariadicVectorConstruction<std::ptrdiff_t>());
+ CALL_SUBTEST_4(fixedsizeVariadicVectorConstruction<std::complex<double>>());
+ CALL_SUBTEST_4(fixedsizeVariadicVectorConstruction<std::complex<float>>());
+ CALL_SUBTEST_4(fixedsizeVariadicVectorConstruction3<0>());
+
+ CALL_SUBTEST_5(TestMethodDispatching<int>::run());
+ CALL_SUBTEST_5(TestMethodDispatching<long int>::run());
+
+ CALL_SUBTEST_6(dynamicVectorConstruction<unsigned char>());
+ CALL_SUBTEST_6(dynamicVectorConstruction<float>());
+ CALL_SUBTEST_6(dynamicVectorConstruction<double>());
+ CALL_SUBTEST_6(dynamicVectorConstruction<int>());
+ CALL_SUBTEST_6(dynamicVectorConstruction<long int>());
+ CALL_SUBTEST_6(dynamicVectorConstruction<std::ptrdiff_t>());
+ CALL_SUBTEST_6(dynamicVectorConstruction<std::complex<double>>());
+ CALL_SUBTEST_6(dynamicVectorConstruction<std::complex<float>>());
+}
diff --git a/test/inplace_decomposition.cpp b/test/inplace_decomposition.cpp
new file mode 100644
index 0000000..e3aa995
--- /dev/null
+++ b/test/inplace_decomposition.cpp
@@ -0,0 +1,110 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2016 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "main.h"
+#include <Eigen/LU>
+#include <Eigen/Cholesky>
+#include <Eigen/QR>
+
+// This file test inplace decomposition through Ref<>, as supported by Cholesky, LU, and QR decompositions.
+
+template<typename DecType,typename MatrixType> void inplace(bool square = false, bool SPD = false)
+{
+ typedef typename MatrixType::Scalar Scalar;
+ typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> RhsType;
+ typedef Matrix<Scalar, MatrixType::ColsAtCompileTime, 1> ResType;
+
+ Index rows = MatrixType::RowsAtCompileTime==Dynamic ? internal::random<Index>(2,EIGEN_TEST_MAX_SIZE/2) : Index(MatrixType::RowsAtCompileTime);
+ Index cols = MatrixType::ColsAtCompileTime==Dynamic ? (square?rows:internal::random<Index>(2,rows)) : Index(MatrixType::ColsAtCompileTime);
+
+ MatrixType A = MatrixType::Random(rows,cols);
+ RhsType b = RhsType::Random(rows);
+ ResType x(cols);
+
+ if(SPD)
+ {
+ assert(square);
+ A.topRows(cols) = A.topRows(cols).adjoint() * A.topRows(cols);
+ A.diagonal().array() += 1e-3;
+ }
+
+ MatrixType A0 = A;
+ MatrixType A1 = A;
+
+ DecType dec(A);
+
+ // Check that the content of A has been modified
+ VERIFY_IS_NOT_APPROX( A, A0 );
+
+ // Check that the decomposition is correct:
+ if(rows==cols)
+ {
+ VERIFY_IS_APPROX( A0 * (x = dec.solve(b)), b );
+ }
+ else
+ {
+ VERIFY_IS_APPROX( A0.transpose() * A0 * (x = dec.solve(b)), A0.transpose() * b );
+ }
+
+ // Check that modifying A breaks the current dec:
+ A.setRandom();
+ if(rows==cols)
+ {
+ VERIFY_IS_NOT_APPROX( A0 * (x = dec.solve(b)), b );
+ }
+ else
+ {
+ VERIFY_IS_NOT_APPROX( A0.transpose() * A0 * (x = dec.solve(b)), A0.transpose() * b );
+ }
+
+ // Check that calling compute(A1) does not modify A1:
+ A = A0;
+ dec.compute(A1);
+ VERIFY_IS_EQUAL(A0,A1);
+ VERIFY_IS_NOT_APPROX( A, A0 );
+ if(rows==cols)
+ {
+ VERIFY_IS_APPROX( A0 * (x = dec.solve(b)), b );
+ }
+ else
+ {
+ VERIFY_IS_APPROX( A0.transpose() * A0 * (x = dec.solve(b)), A0.transpose() * b );
+ }
+}
+
+
+EIGEN_DECLARE_TEST(inplace_decomposition)
+{
+ EIGEN_UNUSED typedef Matrix<double,4,3> Matrix43d;
+ for(int i = 0; i < g_repeat; i++) {
+ CALL_SUBTEST_1(( inplace<LLT<Ref<MatrixXd> >, MatrixXd>(true,true) ));
+ CALL_SUBTEST_1(( inplace<LLT<Ref<Matrix4d> >, Matrix4d>(true,true) ));
+
+ CALL_SUBTEST_2(( inplace<LDLT<Ref<MatrixXd> >, MatrixXd>(true,true) ));
+ CALL_SUBTEST_2(( inplace<LDLT<Ref<Matrix4d> >, Matrix4d>(true,true) ));
+
+ CALL_SUBTEST_3(( inplace<PartialPivLU<Ref<MatrixXd> >, MatrixXd>(true,false) ));
+ CALL_SUBTEST_3(( inplace<PartialPivLU<Ref<Matrix4d> >, Matrix4d>(true,false) ));
+
+ CALL_SUBTEST_4(( inplace<FullPivLU<Ref<MatrixXd> >, MatrixXd>(true,false) ));
+ CALL_SUBTEST_4(( inplace<FullPivLU<Ref<Matrix4d> >, Matrix4d>(true,false) ));
+
+ CALL_SUBTEST_5(( inplace<HouseholderQR<Ref<MatrixXd> >, MatrixXd>(false,false) ));
+ CALL_SUBTEST_5(( inplace<HouseholderQR<Ref<Matrix43d> >, Matrix43d>(false,false) ));
+
+ CALL_SUBTEST_6(( inplace<ColPivHouseholderQR<Ref<MatrixXd> >, MatrixXd>(false,false) ));
+ CALL_SUBTEST_6(( inplace<ColPivHouseholderQR<Ref<Matrix43d> >, Matrix43d>(false,false) ));
+
+ CALL_SUBTEST_7(( inplace<FullPivHouseholderQR<Ref<MatrixXd> >, MatrixXd>(false,false) ));
+ CALL_SUBTEST_7(( inplace<FullPivHouseholderQR<Ref<Matrix43d> >, Matrix43d>(false,false) ));
+
+ CALL_SUBTEST_8(( inplace<CompleteOrthogonalDecomposition<Ref<MatrixXd> >, MatrixXd>(false,false) ));
+ CALL_SUBTEST_8(( inplace<CompleteOrthogonalDecomposition<Ref<Matrix43d> >, Matrix43d>(false,false) ));
+ }
+}
diff --git a/test/integer_types.cpp b/test/integer_types.cpp
new file mode 100644
index 0000000..1322527
--- /dev/null
+++ b/test/integer_types.cpp
@@ -0,0 +1,169 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2010 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "main.h"
+
+#undef VERIFY_IS_APPROX
+#define VERIFY_IS_APPROX(a, b) VERIFY((a)==(b));
+#undef VERIFY_IS_NOT_APPROX
+#define VERIFY_IS_NOT_APPROX(a, b) VERIFY((a)!=(b));
+
+template<typename MatrixType> void signed_integer_type_tests(const MatrixType& m)
+{
+ typedef typename MatrixType::Scalar Scalar;
+
+ enum { is_signed = (Scalar(-1) > Scalar(0)) ? 0 : 1 };
+ VERIFY(is_signed == 1);
+
+ Index rows = m.rows();
+ Index cols = m.cols();
+
+ MatrixType m1(rows, cols),
+ m2 = MatrixType::Random(rows, cols),
+ mzero = MatrixType::Zero(rows, cols);
+
+ do {
+ m1 = MatrixType::Random(rows, cols);
+ } while(m1 == mzero || m1 == m2);
+
+ // check linear structure
+
+ Scalar s1;
+ do {
+ s1 = internal::random<Scalar>();
+ } while(s1 == 0);
+
+ VERIFY_IS_EQUAL(-(-m1), m1);
+ VERIFY_IS_EQUAL(-m2+m1+m2, m1);
+ VERIFY_IS_EQUAL((-m1+m2)*s1, -s1*m1+s1*m2);
+}
+
+template<typename MatrixType> void integer_type_tests(const MatrixType& m)
+{
+ typedef typename MatrixType::Scalar Scalar;
+
+ VERIFY(NumTraits<Scalar>::IsInteger);
+ enum { is_signed = (Scalar(-1) > Scalar(0)) ? 0 : 1 };
+ VERIFY(int(NumTraits<Scalar>::IsSigned) == is_signed);
+
+ typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> VectorType;
+
+ Index rows = m.rows();
+ Index cols = m.cols();
+
+ // this test relies a lot on Random.h, and there's not much more that we can do
+ // to test it, hence I consider that we will have tested Random.h
+ MatrixType m1(rows, cols),
+ m2 = MatrixType::Random(rows, cols),
+ m3(rows, cols),
+ mzero = MatrixType::Zero(rows, cols);
+
+ typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime> SquareMatrixType;
+ SquareMatrixType identity = SquareMatrixType::Identity(rows, rows),
+ square = SquareMatrixType::Random(rows, rows);
+ VectorType v1(rows),
+ v2 = VectorType::Random(rows),
+ vzero = VectorType::Zero(rows);
+
+ do {
+ m1 = MatrixType::Random(rows, cols);
+ } while(m1 == mzero || m1 == m2);
+
+ do {
+ v1 = VectorType::Random(rows);
+ } while(v1 == vzero || v1 == v2);
+
+ VERIFY_IS_APPROX( v1, v1);
+ VERIFY_IS_NOT_APPROX( v1, 2*v1);
+ VERIFY_IS_APPROX( vzero, v1-v1);
+ VERIFY_IS_APPROX( m1, m1);
+ VERIFY_IS_NOT_APPROX( m1, 2*m1);
+ VERIFY_IS_APPROX( mzero, m1-m1);
+
+ VERIFY_IS_APPROX(m3 = m1,m1);
+ MatrixType m4;
+ VERIFY_IS_APPROX(m4 = m1,m1);
+
+ m3.real() = m1.real();
+ VERIFY_IS_APPROX(static_cast<const MatrixType&>(m3).real(), static_cast<const MatrixType&>(m1).real());
+ VERIFY_IS_APPROX(static_cast<const MatrixType&>(m3).real(), m1.real());
+
+ // check == / != operators
+ VERIFY(m1==m1);
+ VERIFY(m1!=m2);
+ VERIFY(!(m1==m2));
+ VERIFY(!(m1!=m1));
+ m1 = m2;
+ VERIFY(m1==m2);
+ VERIFY(!(m1!=m2));
+
+ // check linear structure
+
+ Scalar s1;
+ do {
+ s1 = internal::random<Scalar>();
+ } while(s1 == 0);
+
+ VERIFY_IS_EQUAL(m1+m1, 2*m1);
+ VERIFY_IS_EQUAL(m1+m2-m1, m2);
+ VERIFY_IS_EQUAL(m1*s1, s1*m1);
+ VERIFY_IS_EQUAL((m1+m2)*s1, s1*m1+s1*m2);
+ m3 = m2; m3 += m1;
+ VERIFY_IS_EQUAL(m3, m1+m2);
+ m3 = m2; m3 -= m1;
+ VERIFY_IS_EQUAL(m3, m2-m1);
+ m3 = m2; m3 *= s1;
+ VERIFY_IS_EQUAL(m3, s1*m2);
+
+ // check matrix product.
+
+ VERIFY_IS_APPROX(identity * m1, m1);
+ VERIFY_IS_APPROX(square * (m1 + m2), square * m1 + square * m2);
+ VERIFY_IS_APPROX((m1 + m2).transpose() * square, m1.transpose() * square + m2.transpose() * square);
+ VERIFY_IS_APPROX((m1 * m2.transpose()) * m1, m1 * (m2.transpose() * m1));
+}
+
+template<int>
+void integer_types_extra()
+{
+ VERIFY_IS_EQUAL(int(internal::scalar_div_cost<int>::value), 8);
+ VERIFY_IS_EQUAL(int(internal::scalar_div_cost<unsigned int>::value), 8);
+ if(sizeof(long)>sizeof(int)) {
+ VERIFY(int(internal::scalar_div_cost<long>::value) > int(internal::scalar_div_cost<int>::value));
+ VERIFY(int(internal::scalar_div_cost<unsigned long>::value) > int(internal::scalar_div_cost<int>::value));
+ }
+}
+
+EIGEN_DECLARE_TEST(integer_types)
+{
+ for(int i = 0; i < g_repeat; i++) {
+ CALL_SUBTEST_1( integer_type_tests(Matrix<unsigned int, 1, 1>()) );
+ CALL_SUBTEST_1( integer_type_tests(Matrix<unsigned long, 3, 4>()) );
+
+ CALL_SUBTEST_2( integer_type_tests(Matrix<long, 2, 2>()) );
+ CALL_SUBTEST_2( signed_integer_type_tests(Matrix<long, 2, 2>()) );
+
+ CALL_SUBTEST_3( integer_type_tests(Matrix<char, 2, Dynamic>(2, 10)) );
+ CALL_SUBTEST_3( signed_integer_type_tests(Matrix<signed char, 2, Dynamic>(2, 10)) );
+
+ CALL_SUBTEST_4( integer_type_tests(Matrix<unsigned char, 3, 3>()) );
+ CALL_SUBTEST_4( integer_type_tests(Matrix<unsigned char, Dynamic, Dynamic>(20, 20)) );
+
+ CALL_SUBTEST_5( integer_type_tests(Matrix<short, Dynamic, 4>(7, 4)) );
+ CALL_SUBTEST_5( signed_integer_type_tests(Matrix<short, Dynamic, 4>(7, 4)) );
+
+ CALL_SUBTEST_6( integer_type_tests(Matrix<unsigned short, 4, 4>()) );
+
+ CALL_SUBTEST_7( integer_type_tests(Matrix<long long, 11, 13>()) );
+ CALL_SUBTEST_7( signed_integer_type_tests(Matrix<long long, 11, 13>()) );
+
+ CALL_SUBTEST_8( integer_type_tests(Matrix<unsigned long long, Dynamic, 5>(1, 5)) );
+ }
+ CALL_SUBTEST_9( integer_types_extra<0>() );
+}
diff --git a/test/inverse.cpp b/test/inverse.cpp
new file mode 100644
index 0000000..2748c38
--- /dev/null
+++ b/test/inverse.cpp
@@ -0,0 +1,150 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "main.h"
+#include <Eigen/LU>
+
+template<typename MatrixType>
+void inverse_for_fixed_size(const MatrixType&, std::enable_if_t<MatrixType::SizeAtCompileTime==Dynamic>* = 0)
+{
+}
+
+template<typename MatrixType>
+void inverse_for_fixed_size(const MatrixType& m1, std::enable_if_t<MatrixType::SizeAtCompileTime!=Dynamic>* = 0)
+{
+ using std::abs;
+
+ MatrixType m2, identity = MatrixType::Identity();
+
+ typedef typename MatrixType::Scalar Scalar;
+ typedef typename NumTraits<Scalar>::Real RealScalar;
+ typedef Matrix<Scalar, MatrixType::ColsAtCompileTime, 1> VectorType;
+
+ //computeInverseAndDetWithCheck tests
+ //First: an invertible matrix
+ bool invertible;
+ Scalar det;
+
+ m2.setZero();
+ m1.computeInverseAndDetWithCheck(m2, det, invertible);
+ VERIFY(invertible);
+ VERIFY_IS_APPROX(identity, m1*m2);
+ VERIFY_IS_APPROX(det, m1.determinant());
+
+ m2.setZero();
+ m1.computeInverseWithCheck(m2, invertible);
+ VERIFY(invertible);
+ VERIFY_IS_APPROX(identity, m1*m2);
+
+ //Second: a rank one matrix (not invertible, except for 1x1 matrices)
+ VectorType v3 = VectorType::Random();
+ MatrixType m3 = v3*v3.transpose(), m4;
+ m3.computeInverseAndDetWithCheck(m4, det, invertible);
+ VERIFY( m1.rows()==1 ? invertible : !invertible );
+ VERIFY_IS_MUCH_SMALLER_THAN(abs(det-m3.determinant()), RealScalar(1));
+ m3.computeInverseWithCheck(m4, invertible);
+ VERIFY( m1.rows()==1 ? invertible : !invertible );
+
+ // check with submatrices
+ {
+ Matrix<Scalar, MatrixType::RowsAtCompileTime+1, MatrixType::RowsAtCompileTime+1, MatrixType::Options> m5;
+ m5.setRandom();
+ m5.topLeftCorner(m1.rows(),m1.rows()) = m1;
+ m2 = m5.template topLeftCorner<MatrixType::RowsAtCompileTime,MatrixType::ColsAtCompileTime>().inverse();
+ VERIFY_IS_APPROX( (m5.template topLeftCorner<MatrixType::RowsAtCompileTime,MatrixType::ColsAtCompileTime>()), m2.inverse() );
+ }
+}
+
+template<typename MatrixType> void inverse(const MatrixType& m)
+{
+ /* this test covers the following files:
+ Inverse.h
+ */
+ Index rows = m.rows();
+ Index cols = m.cols();
+
+ typedef typename MatrixType::Scalar Scalar;
+
+ MatrixType m1(rows, cols),
+ m2(rows, cols),
+ identity = MatrixType::Identity(rows, rows);
+ createRandomPIMatrixOfRank(rows,rows,rows,m1);
+ m2 = m1.inverse();
+ VERIFY_IS_APPROX(m1, m2.inverse() );
+
+ VERIFY_IS_APPROX((Scalar(2)*m2).inverse(), m2.inverse()*Scalar(0.5));
+
+ VERIFY_IS_APPROX(identity, m1.inverse() * m1 );
+ VERIFY_IS_APPROX(identity, m1 * m1.inverse() );
+
+ VERIFY_IS_APPROX(m1, m1.inverse().inverse() );
+
+ // since for the general case we implement separately row-major and col-major, test that
+ VERIFY_IS_APPROX(MatrixType(m1.transpose().inverse()), MatrixType(m1.inverse().transpose()));
+
+ inverse_for_fixed_size(m1);
+
+ // check in-place inversion
+ if(MatrixType::RowsAtCompileTime>=2 && MatrixType::RowsAtCompileTime<=4)
+ {
+ // in-place is forbidden
+ VERIFY_RAISES_ASSERT(m1 = m1.inverse());
+ }
+ else
+ {
+ m2 = m1.inverse();
+ m1 = m1.inverse();
+ VERIFY_IS_APPROX(m1,m2);
+ }
+}
+
+template<typename Scalar>
+void inverse_zerosized()
+{
+ Matrix<Scalar,Dynamic,Dynamic> A(0,0);
+ {
+ Matrix<Scalar,0,1> b, x;
+ x = A.inverse() * b;
+ }
+ {
+ Matrix<Scalar,Dynamic,Dynamic> b(0,1), x;
+ x = A.inverse() * b;
+ VERIFY_IS_EQUAL(x.rows(), 0);
+ VERIFY_IS_EQUAL(x.cols(), 1);
+ }
+}
+
+EIGEN_DECLARE_TEST(inverse)
+{
+ int s = 0;
+ for(int i = 0; i < g_repeat; i++) {
+ CALL_SUBTEST_1( inverse(Matrix<double,1,1>()) );
+ CALL_SUBTEST_2( inverse(Matrix2d()) );
+ CALL_SUBTEST_3( inverse(Matrix3f()) );
+ CALL_SUBTEST_4( inverse(Matrix4f()) );
+ CALL_SUBTEST_4( inverse(Matrix<float,4,4,DontAlign>()) );
+
+ s = internal::random<int>(50,320);
+ CALL_SUBTEST_5( inverse(MatrixXf(s,s)) );
+ TEST_SET_BUT_UNUSED_VARIABLE(s)
+ CALL_SUBTEST_5( inverse_zerosized<float>() );
+ CALL_SUBTEST_5( inverse(MatrixXf(0, 0)) );
+ CALL_SUBTEST_5( inverse(MatrixXf(1, 1)) );
+
+ s = internal::random<int>(25,100);
+ CALL_SUBTEST_6( inverse(MatrixXcd(s,s)) );
+ TEST_SET_BUT_UNUSED_VARIABLE(s)
+
+ CALL_SUBTEST_7( inverse(Matrix4d()) );
+ CALL_SUBTEST_7( inverse(Matrix<double,4,4,DontAlign>()) );
+
+ CALL_SUBTEST_8( inverse(Matrix4cd()) );
+ }
+}
diff --git a/test/io.cpp b/test/io.cpp
new file mode 100644
index 0000000..aa14e76
--- /dev/null
+++ b/test/io.cpp
@@ -0,0 +1,71 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2019 Joel Holdsworth <joel.holdsworth@vcatechnology.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include <sstream>
+
+#include "main.h"
+
+template<typename Scalar>
+struct check_ostream_impl
+{
+ static void run()
+ {
+ const Array<Scalar,1,1> array(123);
+ std::ostringstream ss;
+ ss << array;
+ VERIFY(ss.str() == "123");
+
+ check_ostream_impl< std::complex<Scalar> >::run();
+ };
+};
+
+template<>
+struct check_ostream_impl<bool>
+{
+ static void run()
+ {
+ const Array<bool,1,2> array(1, 0);
+ std::ostringstream ss;
+ ss << array;
+ VERIFY(ss.str() == "1 0");
+ };
+};
+
+template<typename Scalar>
+struct check_ostream_impl< std::complex<Scalar> >
+{
+ static void run()
+ {
+ const Array<std::complex<Scalar>,1,1> array(std::complex<Scalar>(12, 34));
+ std::ostringstream ss;
+ ss << array;
+ VERIFY(ss.str() == "(12,34)");
+ };
+};
+
+template<typename Scalar>
+static void check_ostream()
+{
+ check_ostream_impl<Scalar>::run();
+}
+
+EIGEN_DECLARE_TEST(rand)
+{
+ CALL_SUBTEST(check_ostream<bool>());
+ CALL_SUBTEST(check_ostream<float>());
+ CALL_SUBTEST(check_ostream<double>());
+ CALL_SUBTEST(check_ostream<Eigen::numext::int8_t>());
+ CALL_SUBTEST(check_ostream<Eigen::numext::uint8_t>());
+ CALL_SUBTEST(check_ostream<Eigen::numext::int16_t>());
+ CALL_SUBTEST(check_ostream<Eigen::numext::uint16_t>());
+ CALL_SUBTEST(check_ostream<Eigen::numext::int32_t>());
+ CALL_SUBTEST(check_ostream<Eigen::numext::uint32_t>());
+ CALL_SUBTEST(check_ostream<Eigen::numext::int64_t>());
+ CALL_SUBTEST(check_ostream<Eigen::numext::uint64_t>());
+}
diff --git a/test/is_same_dense.cpp b/test/is_same_dense.cpp
new file mode 100644
index 0000000..23dd806
--- /dev/null
+++ b/test/is_same_dense.cpp
@@ -0,0 +1,41 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2015 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "main.h"
+
+using internal::is_same_dense;
+
+EIGEN_DECLARE_TEST(is_same_dense)
+{
+ typedef Matrix<double,Dynamic,Dynamic,ColMajor> ColMatrixXd;
+ typedef Matrix<std::complex<double>,Dynamic,Dynamic,ColMajor> ColMatrixXcd;
+ ColMatrixXd m1(10,10);
+ ColMatrixXcd m2(10,10);
+ Ref<ColMatrixXd> ref_m1(m1);
+ Ref<ColMatrixXd,0, Stride<Dynamic,Dynamic> > ref_m2_real(m2.real());
+ Ref<const ColMatrixXd> const_ref_m1(m1);
+
+ VERIFY(is_same_dense(m1,m1));
+ VERIFY(is_same_dense(m1,ref_m1));
+ VERIFY(is_same_dense(const_ref_m1,m1));
+ VERIFY(is_same_dense(const_ref_m1,ref_m1));
+
+ VERIFY(is_same_dense(m1.block(0,0,m1.rows(),m1.cols()),m1));
+ VERIFY(!is_same_dense(m1.row(0),m1.col(0)));
+
+ Ref<const ColMatrixXd> const_ref_m1_row(m1.row(1));
+ VERIFY(!is_same_dense(m1.row(1),const_ref_m1_row));
+
+ Ref<const ColMatrixXd> const_ref_m1_col(m1.col(1));
+ VERIFY(is_same_dense(m1.col(1),const_ref_m1_col));
+
+
+ VERIFY(!is_same_dense(m1, ref_m2_real));
+ VERIFY(!is_same_dense(m2, ref_m2_real));
+}
diff --git a/test/jacobi.cpp b/test/jacobi.cpp
new file mode 100644
index 0000000..273b94d
--- /dev/null
+++ b/test/jacobi.cpp
@@ -0,0 +1,85 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2009 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "main.h"
+#include <Eigen/SVD>
+
+template<typename MatrixType, typename JacobiScalar>
+void jacobi(const MatrixType& m = MatrixType())
+{
+ Index rows = m.rows();
+ Index cols = m.cols();
+
+ enum {
+ RowsAtCompileTime = MatrixType::RowsAtCompileTime,
+ ColsAtCompileTime = MatrixType::ColsAtCompileTime
+ };
+
+ typedef Matrix<JacobiScalar, 2, 1> JacobiVector;
+
+ const MatrixType a(MatrixType::Random(rows, cols));
+
+ JacobiVector v = JacobiVector::Random().normalized();
+ JacobiScalar c = v.x(), s = v.y();
+ JacobiRotation<JacobiScalar> rot(c, s);
+
+ {
+ Index p = internal::random<Index>(0, rows-1);
+ Index q;
+ do {
+ q = internal::random<Index>(0, rows-1);
+ } while (q == p);
+
+ MatrixType b = a;
+ b.applyOnTheLeft(p, q, rot);
+ VERIFY_IS_APPROX(b.row(p), c * a.row(p) + numext::conj(s) * a.row(q));
+ VERIFY_IS_APPROX(b.row(q), -s * a.row(p) + numext::conj(c) * a.row(q));
+ }
+
+ {
+ Index p = internal::random<Index>(0, cols-1);
+ Index q;
+ do {
+ q = internal::random<Index>(0, cols-1);
+ } while (q == p);
+
+ MatrixType b = a;
+ b.applyOnTheRight(p, q, rot);
+ VERIFY_IS_APPROX(b.col(p), c * a.col(p) - s * a.col(q));
+ VERIFY_IS_APPROX(b.col(q), numext::conj(s) * a.col(p) + numext::conj(c) * a.col(q));
+ }
+}
+
+EIGEN_DECLARE_TEST(jacobi)
+{
+ for(int i = 0; i < g_repeat; i++) {
+ CALL_SUBTEST_1(( jacobi<Matrix3f, float>() ));
+ CALL_SUBTEST_2(( jacobi<Matrix4d, double>() ));
+ CALL_SUBTEST_3(( jacobi<Matrix4cf, float>() ));
+ CALL_SUBTEST_3(( jacobi<Matrix4cf, std::complex<float> >() ));
+
+ CALL_SUBTEST_1(( jacobi<Matrix<float, 3, 3, RowMajor>, float>() ));
+ CALL_SUBTEST_2(( jacobi<Matrix<double, 4, 4, RowMajor>, double>() ));
+ CALL_SUBTEST_3(( jacobi<Matrix<std::complex<float>, 4, 4, RowMajor>, float>() ));
+ CALL_SUBTEST_3(( jacobi<Matrix<std::complex<float>, 4, 4, RowMajor>, std::complex<float> >() ));
+
+ int r = internal::random<int>(2, internal::random<int>(1,EIGEN_TEST_MAX_SIZE)/2),
+ c = internal::random<int>(2, internal::random<int>(1,EIGEN_TEST_MAX_SIZE)/2);
+ CALL_SUBTEST_4(( jacobi<MatrixXf, float>(MatrixXf(r,c)) ));
+ CALL_SUBTEST_5(( jacobi<MatrixXcd, double>(MatrixXcd(r,c)) ));
+ CALL_SUBTEST_5(( jacobi<MatrixXcd, std::complex<double> >(MatrixXcd(r,c)) ));
+ // complex<float> is really important to test as it is the only way to cover conjugation issues in certain unaligned paths
+ CALL_SUBTEST_6(( jacobi<MatrixXcf, float>(MatrixXcf(r,c)) ));
+ CALL_SUBTEST_6(( jacobi<MatrixXcf, std::complex<float> >(MatrixXcf(r,c)) ));
+
+ TEST_SET_BUT_UNUSED_VARIABLE(r);
+ TEST_SET_BUT_UNUSED_VARIABLE(c);
+ }
+}
diff --git a/test/jacobisvd.cpp b/test/jacobisvd.cpp
new file mode 100644
index 0000000..daf24a7
--- /dev/null
+++ b/test/jacobisvd.cpp
@@ -0,0 +1,196 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2014 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2009 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+// We explicitly disable deprecated declarations for this set of tests
+// because we purposely verify assertions for the deprecated SVD runtime
+// option behavior.
+#if defined(__GNUC__)
+#pragma GCC diagnostic ignored "-Wdeprecated-declarations"
+#elif defined(_MSC_VER)
+#pragma warning( disable : 4996 )
+#endif
+
+// discard stack allocation as that too bypasses malloc
+#define EIGEN_STACK_ALLOCATION_LIMIT 0
+#define EIGEN_RUNTIME_NO_MALLOC
+#include "main.h"
+#include <Eigen/SVD>
+
+#define SVD_DEFAULT(M) JacobiSVD<M>
+#define SVD_FOR_MIN_NORM(M) JacobiSVD<M,ColPivHouseholderQRPreconditioner>
+#define SVD_STATIC_OPTIONS(M, O) JacobiSVD<M, O>
+#include "svd_common.h"
+
+template<typename MatrixType>
+void jacobisvd_method()
+{
+ enum { Size = MatrixType::RowsAtCompileTime };
+ typedef typename MatrixType::RealScalar RealScalar;
+ typedef Matrix<RealScalar, Size, 1> RealVecType;
+ MatrixType m = MatrixType::Identity();
+ VERIFY_IS_APPROX(m.jacobiSvd().singularValues(), RealVecType::Ones());
+ VERIFY_RAISES_ASSERT(m.jacobiSvd().matrixU());
+ VERIFY_RAISES_ASSERT(m.jacobiSvd().matrixV());
+ VERIFY_IS_APPROX(m.template jacobiSvd<ComputeFullU | ComputeFullV>().solve(m), m);
+ VERIFY_IS_APPROX(m.template jacobiSvd<ComputeFullU | ComputeFullV>().transpose().solve(m), m);
+ VERIFY_IS_APPROX(m.template jacobiSvd<ComputeFullU | ComputeFullV>().adjoint().solve(m), m);
+
+ // Deprecated behavior.
+ VERIFY_IS_APPROX(m.jacobiSvd(ComputeFullU|ComputeFullV).solve(m), m);
+ VERIFY_IS_APPROX(m.jacobiSvd(ComputeFullU|ComputeFullV).transpose().solve(m), m);
+ VERIFY_IS_APPROX(m.jacobiSvd(ComputeFullU|ComputeFullV).adjoint().solve(m), m);
+}
+
+template <typename MatrixType>
+void jacobisvd_all_options(const MatrixType& input = MatrixType()) {
+ MatrixType m(input.rows(), input.cols());
+ svd_fill_random(m);
+ svd_option_checks<MatrixType, 0>(m);
+ svd_option_checks<MatrixType, ColPivHouseholderQRPreconditioner>(m);
+ svd_option_checks<MatrixType, HouseholderQRPreconditioner>(m);
+ svd_option_checks_full_only<MatrixType, FullPivHouseholderQRPreconditioner>(
+ m); // FullPiv only used when computing full unitaries
+}
+
+template <typename MatrixType>
+void jacobisvd_verify_assert(const MatrixType& m = MatrixType()) {
+ svd_verify_assert<MatrixType, 0>(m);
+ svd_verify_assert<MatrixType, ColPivHouseholderQRPreconditioner>(m);
+ svd_verify_assert<MatrixType, HouseholderQRPreconditioner>(m);
+ svd_verify_assert_full_only<MatrixType, FullPivHouseholderQRPreconditioner>(m);
+
+ svd_verify_constructor_options_assert<JacobiSVD<MatrixType>>(m);
+ svd_verify_constructor_options_assert<JacobiSVD<MatrixType, ColPivHouseholderQRPreconditioner>>(m);
+ svd_verify_constructor_options_assert<JacobiSVD<MatrixType, HouseholderQRPreconditioner>>(m);
+ svd_verify_constructor_options_assert<JacobiSVD<MatrixType, FullPivHouseholderQRPreconditioner>>(m, true);
+}
+
+template <typename MatrixType>
+void jacobisvd_verify_inputs(const MatrixType& m = MatrixType()) {
+ // check defaults
+ typedef JacobiSVD<MatrixType> DefaultSVD;
+ DefaultSVD defaultSvd(m);
+ VERIFY((int)DefaultSVD::QRPreconditioner == (int)ColPivHouseholderQRPreconditioner);
+ VERIFY(!defaultSvd.computeU());
+ VERIFY(!defaultSvd.computeV());
+
+ // ColPivHouseholderQR is always default in presence of other options.
+ VERIFY(((int)JacobiSVD<MatrixType, ComputeThinU>::QRPreconditioner == (int)ColPivHouseholderQRPreconditioner));
+ VERIFY(((int)JacobiSVD<MatrixType, ComputeThinV>::QRPreconditioner == (int)ColPivHouseholderQRPreconditioner));
+ VERIFY(((int)JacobiSVD<MatrixType, ComputeThinU | ComputeThinV>::QRPreconditioner ==
+ (int)ColPivHouseholderQRPreconditioner));
+ VERIFY(((int)JacobiSVD<MatrixType, ComputeFullU | ComputeFullV>::QRPreconditioner ==
+ (int)ColPivHouseholderQRPreconditioner));
+ VERIFY(((int)JacobiSVD<MatrixType, ComputeThinU | ComputeFullV>::QRPreconditioner ==
+ (int)ColPivHouseholderQRPreconditioner));
+ VERIFY(((int)JacobiSVD<MatrixType, ComputeFullU | ComputeThinV>::QRPreconditioner ==
+ (int)ColPivHouseholderQRPreconditioner));
+}
+
+namespace Foo {
+// older compiler require a default constructor for Bar
+// cf: https://stackoverflow.com/questions/7411515/
+class Bar {public: Bar() {}};
+bool operator<(const Bar&, const Bar&) { return true; }
+}
+// regression test for a very strange MSVC issue for which simply
+// including SVDBase.h messes up with std::max and custom scalar type
+void msvc_workaround()
+{
+ const Foo::Bar a;
+ const Foo::Bar b;
+ const Foo::Bar c = std::max EIGEN_NOT_A_MACRO (a,b);
+ EIGEN_UNUSED_VARIABLE(c)
+}
+
+EIGEN_DECLARE_TEST(jacobisvd)
+{
+ CALL_SUBTEST_1((jacobisvd_verify_inputs<Matrix4d>()));
+ CALL_SUBTEST_1((jacobisvd_verify_inputs(Matrix<float, 5, Dynamic>(5, 6))));
+ CALL_SUBTEST_1((jacobisvd_verify_inputs<Matrix<std::complex<double>, 7, 5>>()));
+
+ CALL_SUBTEST_2((jacobisvd_verify_assert<Matrix3f>()));
+ CALL_SUBTEST_2((jacobisvd_verify_assert<Matrix4d>()));
+ CALL_SUBTEST_2((jacobisvd_verify_assert<Matrix<float, 10, 12>>()));
+ CALL_SUBTEST_2((jacobisvd_verify_assert<Matrix<float, 12, 10>>()));
+ CALL_SUBTEST_2((jacobisvd_verify_assert<MatrixXf>(MatrixXf(10, 12))));
+ CALL_SUBTEST_2((jacobisvd_verify_assert<MatrixXcd>(MatrixXcd(7, 5))));
+
+ CALL_SUBTEST_3(svd_all_trivial_2x2(jacobisvd_all_options<Matrix2cd>));
+ CALL_SUBTEST_4(svd_all_trivial_2x2(jacobisvd_all_options<Matrix2d>));
+
+ for (int i = 0; i < g_repeat; i++) {
+ int r = internal::random<int>(1, 30),
+ c = internal::random<int>(1, 30);
+
+ TEST_SET_BUT_UNUSED_VARIABLE(r)
+ TEST_SET_BUT_UNUSED_VARIABLE(c)
+
+ CALL_SUBTEST_5((jacobisvd_all_options<Matrix3f>()));
+ CALL_SUBTEST_6((jacobisvd_all_options<Matrix4d>()));
+ CALL_SUBTEST_7((jacobisvd_all_options<Matrix<float, 2, 3>>()));
+ CALL_SUBTEST_8((jacobisvd_all_options<Matrix<double, 4, 7>>()));
+ CALL_SUBTEST_9((jacobisvd_all_options<Matrix<double, 7, 4>>()));
+ CALL_SUBTEST_10((jacobisvd_all_options<Matrix<double, Dynamic, 5>>(Matrix<double, Dynamic, 5>(r, 5))));
+ CALL_SUBTEST_11((jacobisvd_all_options<Matrix<double, 5, Dynamic>>(Matrix<double, 5, Dynamic>(5, c))));
+ CALL_SUBTEST_12((jacobisvd_all_options<MatrixXf>(MatrixXf(r, c))));
+ CALL_SUBTEST_13((jacobisvd_all_options<MatrixXcd>(MatrixXcd(r, c))));
+ CALL_SUBTEST_14((jacobisvd_all_options<MatrixXd>(MatrixXd(r, c))));
+ CALL_SUBTEST_15((jacobisvd_all_options<Matrix<double, 5, 7, RowMajor>>()));
+ CALL_SUBTEST_16((jacobisvd_all_options<Matrix<double, 7, 5, RowMajor>>()));
+
+ MatrixXcd noQRTest = MatrixXcd(r, r);
+ svd_fill_random(noQRTest);
+ CALL_SUBTEST_17((svd_option_checks<MatrixXcd, NoQRPreconditioner>(noQRTest)));
+
+ CALL_SUBTEST_18((
+ svd_check_max_size_matrix<Matrix<float, Dynamic, Dynamic, ColMajor, 13, 15>, ColPivHouseholderQRPreconditioner>(
+ r, c)));
+ CALL_SUBTEST_18(
+ (svd_check_max_size_matrix<Matrix<float, Dynamic, Dynamic, ColMajor, 15, 13>, HouseholderQRPreconditioner>(r,
+ c)));
+ CALL_SUBTEST_18((
+ svd_check_max_size_matrix<Matrix<float, Dynamic, Dynamic, RowMajor, 13, 15>, ColPivHouseholderQRPreconditioner>(
+ r, c)));
+ CALL_SUBTEST_18(
+ (svd_check_max_size_matrix<Matrix<float, Dynamic, Dynamic, RowMajor, 15, 13>, HouseholderQRPreconditioner>(r,
+ c)));
+
+ // Test on inf/nan matrix
+ CALL_SUBTEST_19((svd_inf_nan<MatrixXf>()));
+ CALL_SUBTEST_19((svd_inf_nan<MatrixXd>()));
+
+ CALL_SUBTEST_20((jacobisvd_verify_assert<Matrix<double, 6, 1>>()));
+ CALL_SUBTEST_20((jacobisvd_verify_assert<Matrix<double, 1, 6>>()));
+ CALL_SUBTEST_20((jacobisvd_verify_assert<Matrix<double, Dynamic, 1>>(Matrix<double, Dynamic, 1>(r))));
+ CALL_SUBTEST_20((jacobisvd_verify_assert<Matrix<double, 1, Dynamic>>(Matrix<double, 1, Dynamic>(c))));
+ }
+
+ CALL_SUBTEST_21((jacobisvd_all_options<MatrixXd>(
+ MatrixXd(internal::random<int>(EIGEN_TEST_MAX_SIZE / 4, EIGEN_TEST_MAX_SIZE / 2),
+ internal::random<int>(EIGEN_TEST_MAX_SIZE / 4, EIGEN_TEST_MAX_SIZE / 2)))));
+ CALL_SUBTEST_22((jacobisvd_all_options<MatrixXcd>(
+ MatrixXcd(internal::random<int>(EIGEN_TEST_MAX_SIZE / 4, EIGEN_TEST_MAX_SIZE / 3),
+ internal::random<int>(EIGEN_TEST_MAX_SIZE / 4, EIGEN_TEST_MAX_SIZE / 3)))));
+
+ // test matrixbase method
+ CALL_SUBTEST_23(( jacobisvd_method<Matrix2cd>() ));
+ CALL_SUBTEST_23(( jacobisvd_method<Matrix3f>() ));
+
+ // Test problem size constructors
+ CALL_SUBTEST_24( JacobiSVD<MatrixXf>(10,10) );
+
+ // Check that preallocation avoids subsequent mallocs
+ CALL_SUBTEST_25( svd_preallocate<void>() );
+
+ CALL_SUBTEST_26( svd_underoverflow<void>() );
+
+ msvc_workaround();
+}
diff --git a/test/klu_support.cpp b/test/klu_support.cpp
new file mode 100644
index 0000000..f806ad5
--- /dev/null
+++ b/test/klu_support.cpp
@@ -0,0 +1,32 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2011 Gael Guennebaud <g.gael@free.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#define EIGEN_NO_DEBUG_SMALL_PRODUCT_BLOCKS
+#include "sparse_solver.h"
+
+#include <Eigen/KLUSupport>
+
+template<typename T> void test_klu_support_T()
+{
+ KLU<SparseMatrix<T, ColMajor> > klu_colmajor;
+ KLU<SparseMatrix<T, RowMajor> > klu_rowmajor;
+
+ check_sparse_square_solving(klu_colmajor);
+ check_sparse_square_solving(klu_rowmajor);
+
+ //check_sparse_square_determinant(umfpack_colmajor);
+ //check_sparse_square_determinant(umfpack_rowmajor);
+}
+
+EIGEN_DECLARE_TEST(klu_support)
+{
+ CALL_SUBTEST_1(test_klu_support_T<double>());
+ CALL_SUBTEST_2(test_klu_support_T<std::complex<double> >());
+}
+
diff --git a/test/linearstructure.cpp b/test/linearstructure.cpp
new file mode 100644
index 0000000..46ee516
--- /dev/null
+++ b/test/linearstructure.cpp
@@ -0,0 +1,147 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+// Copyright (C) 2014 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+static bool g_called;
+#define EIGEN_SCALAR_BINARY_OP_PLUGIN { g_called |= (!internal::is_same<LhsScalar,RhsScalar>::value); }
+
+#include "main.h"
+
+template<typename MatrixType> void linearStructure(const MatrixType& m)
+{
+ using std::abs;
+ /* this test covers the following files:
+ CwiseUnaryOp.h, CwiseBinaryOp.h, SelfCwiseBinaryOp.h
+ */
+ typedef typename MatrixType::Scalar Scalar;
+ typedef typename MatrixType::RealScalar RealScalar;
+
+ Index rows = m.rows();
+ Index cols = m.cols();
+
+ // this test relies a lot on Random.h, and there's not much more that we can do
+ // to test it, hence I consider that we will have tested Random.h
+ MatrixType m1 = MatrixType::Random(rows, cols),
+ m2 = MatrixType::Random(rows, cols),
+ m3(rows, cols);
+
+ Scalar s1 = internal::random<Scalar>();
+ while (abs(s1)<RealScalar(1e-3)) s1 = internal::random<Scalar>();
+
+ Index r = internal::random<Index>(0, rows-1),
+ c = internal::random<Index>(0, cols-1);
+
+ VERIFY_IS_APPROX(-(-m1), m1);
+ VERIFY_IS_APPROX(m1+m1, 2*m1);
+ VERIFY_IS_APPROX(m1+m2-m1, m2);
+ VERIFY_IS_APPROX(-m2+m1+m2, m1);
+ VERIFY_IS_APPROX(m1*s1, s1*m1);
+ VERIFY_IS_APPROX((m1+m2)*s1, s1*m1+s1*m2);
+ VERIFY_IS_APPROX((-m1+m2)*s1, -s1*m1+s1*m2);
+ m3 = m2; m3 += m1;
+ VERIFY_IS_APPROX(m3, m1+m2);
+ m3 = m2; m3 -= m1;
+ VERIFY_IS_APPROX(m3, m2-m1);
+ m3 = m2; m3 *= s1;
+ VERIFY_IS_APPROX(m3, s1*m2);
+ if(!NumTraits<Scalar>::IsInteger)
+ {
+ m3 = m2; m3 /= s1;
+ VERIFY_IS_APPROX(m3, m2/s1);
+ }
+
+ // again, test operator() to check const-qualification
+ VERIFY_IS_APPROX((-m1)(r,c), -(m1(r,c)));
+ VERIFY_IS_APPROX((m1-m2)(r,c), (m1(r,c))-(m2(r,c)));
+ VERIFY_IS_APPROX((m1+m2)(r,c), (m1(r,c))+(m2(r,c)));
+ VERIFY_IS_APPROX((s1*m1)(r,c), s1*(m1(r,c)));
+ VERIFY_IS_APPROX((m1*s1)(r,c), (m1(r,c))*s1);
+ if(!NumTraits<Scalar>::IsInteger)
+ VERIFY_IS_APPROX((m1/s1)(r,c), (m1(r,c))/s1);
+
+ // use .block to disable vectorization and compare to the vectorized version
+ VERIFY_IS_APPROX(m1+m1.block(0,0,rows,cols), m1+m1);
+ VERIFY_IS_APPROX(m1.cwiseProduct(m1.block(0,0,rows,cols)), m1.cwiseProduct(m1));
+ VERIFY_IS_APPROX(m1 - m1.block(0,0,rows,cols), m1 - m1);
+ VERIFY_IS_APPROX(m1.block(0,0,rows,cols) * s1, m1 * s1);
+}
+
+// Make sure that complex * real and real * complex are properly optimized
+template<typename MatrixType> void real_complex(DenseIndex rows = MatrixType::RowsAtCompileTime, DenseIndex cols = MatrixType::ColsAtCompileTime)
+{
+ typedef typename MatrixType::Scalar Scalar;
+ typedef typename MatrixType::RealScalar RealScalar;
+
+ RealScalar s = internal::random<RealScalar>();
+ MatrixType m1 = MatrixType::Random(rows, cols);
+
+ g_called = false;
+ VERIFY_IS_APPROX(s*m1, Scalar(s)*m1);
+ VERIFY(g_called && "real * matrix<complex> not properly optimized");
+
+ g_called = false;
+ VERIFY_IS_APPROX(m1*s, m1*Scalar(s));
+ VERIFY(g_called && "matrix<complex> * real not properly optimized");
+
+ g_called = false;
+ VERIFY_IS_APPROX(m1/s, m1/Scalar(s));
+ VERIFY(g_called && "matrix<complex> / real not properly optimized");
+
+ g_called = false;
+ VERIFY_IS_APPROX(s+m1.array(), Scalar(s)+m1.array());
+ VERIFY(g_called && "real + matrix<complex> not properly optimized");
+
+ g_called = false;
+ VERIFY_IS_APPROX(m1.array()+s, m1.array()+Scalar(s));
+ VERIFY(g_called && "matrix<complex> + real not properly optimized");
+
+ g_called = false;
+ VERIFY_IS_APPROX(s-m1.array(), Scalar(s)-m1.array());
+ VERIFY(g_called && "real - matrix<complex> not properly optimized");
+
+ g_called = false;
+ VERIFY_IS_APPROX(m1.array()-s, m1.array()-Scalar(s));
+ VERIFY(g_called && "matrix<complex> - real not properly optimized");
+}
+
+template<int>
+void linearstructure_overflow()
+{
+ // make sure that /=scalar and /scalar do not overflow
+ // rational: 1.0/4.94e-320 overflow, but m/4.94e-320 should not
+ Matrix4d m2, m3;
+ m3 = m2 = Matrix4d::Random()*1e-20;
+ m2 = m2 / 4.9e-320;
+ VERIFY_IS_APPROX(m2.cwiseQuotient(m2), Matrix4d::Ones());
+ m3 /= 4.9e-320;
+ VERIFY_IS_APPROX(m3.cwiseQuotient(m3), Matrix4d::Ones());
+}
+
+EIGEN_DECLARE_TEST(linearstructure)
+{
+ g_called = true;
+ VERIFY(g_called); // avoid `unneeded-internal-declaration` warning.
+ for(int i = 0; i < g_repeat; i++) {
+ CALL_SUBTEST_1( linearStructure(Matrix<float, 1, 1>()) );
+ CALL_SUBTEST_2( linearStructure(Matrix2f()) );
+ CALL_SUBTEST_3( linearStructure(Vector3d()) );
+ CALL_SUBTEST_4( linearStructure(Matrix4d()) );
+ CALL_SUBTEST_5( linearStructure(MatrixXcf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE/2), internal::random<int>(1,EIGEN_TEST_MAX_SIZE/2))) );
+ CALL_SUBTEST_6( linearStructure(MatrixXf (internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
+ CALL_SUBTEST_7( linearStructure(MatrixXi (internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
+ CALL_SUBTEST_8( linearStructure(MatrixXcd(internal::random<int>(1,EIGEN_TEST_MAX_SIZE/2), internal::random<int>(1,EIGEN_TEST_MAX_SIZE/2))) );
+ CALL_SUBTEST_9( linearStructure(ArrayXXf (internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
+ CALL_SUBTEST_10( linearStructure(ArrayXXcf (internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
+
+ CALL_SUBTEST_11( real_complex<Matrix4cd>() );
+ CALL_SUBTEST_11( real_complex<MatrixXcf>(10,10) );
+ CALL_SUBTEST_11( real_complex<ArrayXXcf>(10,10) );
+ }
+ CALL_SUBTEST_4( linearstructure_overflow<0>() );
+}
diff --git a/test/lscg.cpp b/test/lscg.cpp
new file mode 100644
index 0000000..feb2347
--- /dev/null
+++ b/test/lscg.cpp
@@ -0,0 +1,37 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2011 Gael Guennebaud <g.gael@free.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "sparse_solver.h"
+#include <Eigen/IterativeLinearSolvers>
+
+template<typename T> void test_lscg_T()
+{
+ LeastSquaresConjugateGradient<SparseMatrix<T> > lscg_colmajor_diag;
+ LeastSquaresConjugateGradient<SparseMatrix<T>, IdentityPreconditioner> lscg_colmajor_I;
+ LeastSquaresConjugateGradient<SparseMatrix<T,RowMajor> > lscg_rowmajor_diag;
+ LeastSquaresConjugateGradient<SparseMatrix<T,RowMajor>, IdentityPreconditioner> lscg_rowmajor_I;
+
+ CALL_SUBTEST( check_sparse_square_solving(lscg_colmajor_diag) );
+ CALL_SUBTEST( check_sparse_square_solving(lscg_colmajor_I) );
+
+ CALL_SUBTEST( check_sparse_leastsquare_solving(lscg_colmajor_diag) );
+ CALL_SUBTEST( check_sparse_leastsquare_solving(lscg_colmajor_I) );
+
+ CALL_SUBTEST( check_sparse_square_solving(lscg_rowmajor_diag) );
+ CALL_SUBTEST( check_sparse_square_solving(lscg_rowmajor_I) );
+
+ CALL_SUBTEST( check_sparse_leastsquare_solving(lscg_rowmajor_diag) );
+ CALL_SUBTEST( check_sparse_leastsquare_solving(lscg_rowmajor_I) );
+}
+
+EIGEN_DECLARE_TEST(lscg)
+{
+ CALL_SUBTEST_1(test_lscg_T<double>());
+ CALL_SUBTEST_2(test_lscg_T<std::complex<double> >());
+}
diff --git a/test/lu.cpp b/test/lu.cpp
new file mode 100644
index 0000000..1bbadcb
--- /dev/null
+++ b/test/lu.cpp
@@ -0,0 +1,252 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2009 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "main.h"
+#include <Eigen/LU>
+#include "solverbase.h"
+using namespace std;
+
+template<typename MatrixType>
+typename MatrixType::RealScalar matrix_l1_norm(const MatrixType& m) {
+ return m.cwiseAbs().colwise().sum().maxCoeff();
+}
+
+template<typename MatrixType> void lu_non_invertible()
+{
+ STATIC_CHECK(( internal::is_same<typename FullPivLU<MatrixType>::StorageIndex,int>::value ));
+
+ typedef typename MatrixType::RealScalar RealScalar;
+ /* this test covers the following files:
+ LU.h
+ */
+ Index rows, cols, cols2;
+ if(MatrixType::RowsAtCompileTime==Dynamic)
+ {
+ rows = internal::random<Index>(2,EIGEN_TEST_MAX_SIZE);
+ }
+ else
+ {
+ rows = MatrixType::RowsAtCompileTime;
+ }
+ if(MatrixType::ColsAtCompileTime==Dynamic)
+ {
+ cols = internal::random<Index>(2,EIGEN_TEST_MAX_SIZE);
+ cols2 = internal::random<int>(2,EIGEN_TEST_MAX_SIZE);
+ }
+ else
+ {
+ cols2 = cols = MatrixType::ColsAtCompileTime;
+ }
+
+ enum {
+ RowsAtCompileTime = MatrixType::RowsAtCompileTime,
+ ColsAtCompileTime = MatrixType::ColsAtCompileTime
+ };
+ typedef typename internal::kernel_retval_base<FullPivLU<MatrixType> >::ReturnType KernelMatrixType;
+ typedef typename internal::image_retval_base<FullPivLU<MatrixType> >::ReturnType ImageMatrixType;
+ typedef Matrix<typename MatrixType::Scalar, ColsAtCompileTime, ColsAtCompileTime>
+ CMatrixType;
+ typedef Matrix<typename MatrixType::Scalar, RowsAtCompileTime, RowsAtCompileTime>
+ RMatrixType;
+
+ Index rank = internal::random<Index>(1, (std::min)(rows, cols)-1);
+
+ // The image of the zero matrix should consist of a single (zero) column vector
+ VERIFY((MatrixType::Zero(rows,cols).fullPivLu().image(MatrixType::Zero(rows,cols)).cols() == 1));
+
+ // The kernel of the zero matrix is the entire space, and thus is an invertible matrix of dimensions cols.
+ KernelMatrixType kernel = MatrixType::Zero(rows,cols).fullPivLu().kernel();
+ VERIFY((kernel.fullPivLu().isInvertible()));
+
+ MatrixType m1(rows, cols), m3(rows, cols2);
+ CMatrixType m2(cols, cols2);
+ createRandomPIMatrixOfRank(rank, rows, cols, m1);
+
+ FullPivLU<MatrixType> lu;
+
+ // The special value 0.01 below works well in tests. Keep in mind that we're only computing the rank
+ // of singular values are either 0 or 1.
+ // So it's not clear at all that the epsilon should play any role there.
+ lu.setThreshold(RealScalar(0.01));
+ lu.compute(m1);
+
+ MatrixType u(rows,cols);
+ u = lu.matrixLU().template triangularView<Upper>();
+ RMatrixType l = RMatrixType::Identity(rows,rows);
+ l.block(0,0,rows,(std::min)(rows,cols)).template triangularView<StrictlyLower>()
+ = lu.matrixLU().block(0,0,rows,(std::min)(rows,cols));
+
+ VERIFY_IS_APPROX(lu.permutationP() * m1 * lu.permutationQ(), l*u);
+
+ KernelMatrixType m1kernel = lu.kernel();
+ ImageMatrixType m1image = lu.image(m1);
+
+ VERIFY_IS_APPROX(m1, lu.reconstructedMatrix());
+ VERIFY(rank == lu.rank());
+ VERIFY(cols - lu.rank() == lu.dimensionOfKernel());
+ VERIFY(!lu.isInjective());
+ VERIFY(!lu.isInvertible());
+ VERIFY(!lu.isSurjective());
+ VERIFY_IS_MUCH_SMALLER_THAN((m1 * m1kernel), m1);
+ VERIFY(m1image.fullPivLu().rank() == rank);
+ VERIFY_IS_APPROX(m1 * m1.adjoint() * m1image, m1image);
+
+ check_solverbase<CMatrixType, MatrixType>(m1, lu, rows, cols, cols2);
+
+ m2 = CMatrixType::Random(cols,cols2);
+ m3 = m1*m2;
+ m2 = CMatrixType::Random(cols,cols2);
+ // test that the code, which does resize(), may be applied to an xpr
+ m2.block(0,0,m2.rows(),m2.cols()) = lu.solve(m3);
+ VERIFY_IS_APPROX(m3, m1*m2);
+}
+
+template<typename MatrixType> void lu_invertible()
+{
+ /* this test covers the following files:
+ FullPivLU.h
+ */
+ typedef typename NumTraits<typename MatrixType::Scalar>::Real RealScalar;
+ Index size = MatrixType::RowsAtCompileTime;
+ if( size==Dynamic)
+ size = internal::random<Index>(1,EIGEN_TEST_MAX_SIZE);
+
+ MatrixType m1(size, size), m2(size, size), m3(size, size);
+ FullPivLU<MatrixType> lu;
+ lu.setThreshold(RealScalar(0.01));
+ do {
+ m1 = MatrixType::Random(size,size);
+ lu.compute(m1);
+ } while(!lu.isInvertible());
+
+ VERIFY_IS_APPROX(m1, lu.reconstructedMatrix());
+ VERIFY(0 == lu.dimensionOfKernel());
+ VERIFY(lu.kernel().cols() == 1); // the kernel() should consist of a single (zero) column vector
+ VERIFY(size == lu.rank());
+ VERIFY(lu.isInjective());
+ VERIFY(lu.isSurjective());
+ VERIFY(lu.isInvertible());
+ VERIFY(lu.image(m1).fullPivLu().isInvertible());
+
+ check_solverbase<MatrixType, MatrixType>(m1, lu, size, size, size);
+
+ MatrixType m1_inverse = lu.inverse();
+ m3 = MatrixType::Random(size,size);
+ m2 = lu.solve(m3);
+ VERIFY_IS_APPROX(m2, m1_inverse*m3);
+
+ RealScalar rcond = (RealScalar(1) / matrix_l1_norm(m1)) / matrix_l1_norm(m1_inverse);
+ const RealScalar rcond_est = lu.rcond();
+ // Verify that the estimated condition number is within a factor of 10 of the
+ // truth.
+ VERIFY(rcond_est > rcond / 10 && rcond_est < rcond * 10);
+
+ // Regression test for Bug 302
+ MatrixType m4 = MatrixType::Random(size,size);
+ VERIFY_IS_APPROX(lu.solve(m3*m4), lu.solve(m3)*m4);
+}
+
+template<typename MatrixType> void lu_partial_piv(Index size = MatrixType::ColsAtCompileTime)
+{
+ /* this test covers the following files:
+ PartialPivLU.h
+ */
+ typedef typename NumTraits<typename MatrixType::Scalar>::Real RealScalar;
+
+ MatrixType m1(size, size), m2(size, size), m3(size, size);
+ m1.setRandom();
+ PartialPivLU<MatrixType> plu(m1);
+
+ STATIC_CHECK(( internal::is_same<typename PartialPivLU<MatrixType>::StorageIndex,int>::value ));
+
+ VERIFY_IS_APPROX(m1, plu.reconstructedMatrix());
+
+ check_solverbase<MatrixType, MatrixType>(m1, plu, size, size, size);
+
+ MatrixType m1_inverse = plu.inverse();
+ m3 = MatrixType::Random(size,size);
+ m2 = plu.solve(m3);
+ VERIFY_IS_APPROX(m2, m1_inverse*m3);
+
+ RealScalar rcond = (RealScalar(1) / matrix_l1_norm(m1)) / matrix_l1_norm(m1_inverse);
+ const RealScalar rcond_est = plu.rcond();
+ // Verify that the estimate is within a factor of 10 of the truth.
+ VERIFY(rcond_est > rcond / 10 && rcond_est < rcond * 10);
+}
+
+template<typename MatrixType> void lu_verify_assert()
+{
+ MatrixType tmp;
+
+ FullPivLU<MatrixType> lu;
+ VERIFY_RAISES_ASSERT(lu.matrixLU())
+ VERIFY_RAISES_ASSERT(lu.permutationP())
+ VERIFY_RAISES_ASSERT(lu.permutationQ())
+ VERIFY_RAISES_ASSERT(lu.kernel())
+ VERIFY_RAISES_ASSERT(lu.image(tmp))
+ VERIFY_RAISES_ASSERT(lu.solve(tmp))
+ VERIFY_RAISES_ASSERT(lu.transpose().solve(tmp))
+ VERIFY_RAISES_ASSERT(lu.adjoint().solve(tmp))
+ VERIFY_RAISES_ASSERT(lu.determinant())
+ VERIFY_RAISES_ASSERT(lu.rank())
+ VERIFY_RAISES_ASSERT(lu.dimensionOfKernel())
+ VERIFY_RAISES_ASSERT(lu.isInjective())
+ VERIFY_RAISES_ASSERT(lu.isSurjective())
+ VERIFY_RAISES_ASSERT(lu.isInvertible())
+ VERIFY_RAISES_ASSERT(lu.inverse())
+
+ PartialPivLU<MatrixType> plu;
+ VERIFY_RAISES_ASSERT(plu.matrixLU())
+ VERIFY_RAISES_ASSERT(plu.permutationP())
+ VERIFY_RAISES_ASSERT(plu.solve(tmp))
+ VERIFY_RAISES_ASSERT(plu.transpose().solve(tmp))
+ VERIFY_RAISES_ASSERT(plu.adjoint().solve(tmp))
+ VERIFY_RAISES_ASSERT(plu.determinant())
+ VERIFY_RAISES_ASSERT(plu.inverse())
+}
+
+EIGEN_DECLARE_TEST(lu)
+{
+ for(int i = 0; i < g_repeat; i++) {
+ CALL_SUBTEST_1( lu_non_invertible<Matrix3f>() );
+ CALL_SUBTEST_1( lu_invertible<Matrix3f>() );
+ CALL_SUBTEST_1( lu_verify_assert<Matrix3f>() );
+ CALL_SUBTEST_1( lu_partial_piv<Matrix3f>() );
+
+ CALL_SUBTEST_2( (lu_non_invertible<Matrix<double, 4, 6> >()) );
+ CALL_SUBTEST_2( (lu_verify_assert<Matrix<double, 4, 6> >()) );
+ CALL_SUBTEST_2( lu_partial_piv<Matrix2d>() );
+ CALL_SUBTEST_2( lu_partial_piv<Matrix4d>() );
+ CALL_SUBTEST_2( (lu_partial_piv<Matrix<double,6,6> >()) );
+
+ CALL_SUBTEST_3( lu_non_invertible<MatrixXf>() );
+ CALL_SUBTEST_3( lu_invertible<MatrixXf>() );
+ CALL_SUBTEST_3( lu_verify_assert<MatrixXf>() );
+
+ CALL_SUBTEST_4( lu_non_invertible<MatrixXd>() );
+ CALL_SUBTEST_4( lu_invertible<MatrixXd>() );
+ CALL_SUBTEST_4( lu_partial_piv<MatrixXd>(internal::random<int>(1,EIGEN_TEST_MAX_SIZE)) );
+ CALL_SUBTEST_4( lu_verify_assert<MatrixXd>() );
+
+ CALL_SUBTEST_5( lu_non_invertible<MatrixXcf>() );
+ CALL_SUBTEST_5( lu_invertible<MatrixXcf>() );
+ CALL_SUBTEST_5( lu_verify_assert<MatrixXcf>() );
+
+ CALL_SUBTEST_6( lu_non_invertible<MatrixXcd>() );
+ CALL_SUBTEST_6( lu_invertible<MatrixXcd>() );
+ CALL_SUBTEST_6( lu_partial_piv<MatrixXcd>(internal::random<int>(1,EIGEN_TEST_MAX_SIZE)) );
+ CALL_SUBTEST_6( lu_verify_assert<MatrixXcd>() );
+
+ CALL_SUBTEST_7(( lu_non_invertible<Matrix<float,Dynamic,16> >() ));
+
+ // Test problem size constructors
+ CALL_SUBTEST_9( PartialPivLU<MatrixXf>(10) );
+ CALL_SUBTEST_9( FullPivLU<MatrixXf>(10, 20); );
+ }
+}
diff --git a/test/main.h b/test/main.h
new file mode 100644
index 0000000..884b6c3
--- /dev/null
+++ b/test/main.h
@@ -0,0 +1,871 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include <cstdlib>
+#include <cerrno>
+#include <ctime>
+#include <iostream>
+#include <fstream>
+#include <string>
+#include <sstream>
+#include <vector>
+#include <typeinfo>
+#include <functional>
+
+// The following includes of STL headers have to be done _before_ the
+// definition of macros min() and max(). The reason is that many STL
+// implementations will not work properly as the min and max symbols collide
+// with the STL functions std::min() and std::max(). The STL headers may check
+// for the macro definition of min/max and issue a warning or undefine the
+// macros.
+//
+// Still, Windows defines min() and max() in windef.h as part of the regular
+// Windows system interfaces and many other Windows APIs depend on these
+// macros being available. To prevent the macro expansion of min/max and to
+// make Eigen compatible with the Windows environment all function calls of
+// std::min() and std::max() have to be written with parenthesis around the
+// function name.
+//
+// All STL headers used by Eigen should be included here. Because main.h is
+// included before any Eigen header and because the STL headers are guarded
+// against multiple inclusions, no STL header will see our own min/max macro
+// definitions.
+#include <limits>
+#include <algorithm>
+// Disable ICC's std::complex operator specializations so we can use our own.
+#define _OVERRIDE_COMPLEX_SPECIALIZATION_ 1
+#include <complex>
+#include <deque>
+#include <queue>
+#include <cassert>
+#include <list>
+#if __cplusplus >= 201103L || (defined(_MSVC_LANG) && _MSVC_LANG >= 201103L)
+#include <random>
+#include <chrono>
+#ifdef EIGEN_USE_THREADS
+#include <future>
+#endif
+#endif
+#if __cplusplus > 201703L
+// libstdc++ 9's <memory> indirectly uses max() via <bit>.
+// libstdc++ 10's <memory> indirectly uses max() via ranges headers.
+#include <memory>
+// libstdc++ 11's <thread> indirectly uses max() via semaphore headers.
+#include <thread>
+#endif
+
+// Configure GPU.
+#if defined(EIGEN_USE_HIP)
+ #if defined(__HIPCC__) && !defined(EIGEN_NO_HIP)
+ #define EIGEN_HIPCC __HIPCC__
+ #include <hip/hip_runtime.h>
+ #include <hip/hip_runtime_api.h>
+ #endif
+#elif defined(__CUDACC__) && !defined(EIGEN_NO_CUDA)
+ #define EIGEN_CUDACC __CUDACC__
+ #include <cuda.h>
+ #include <cuda_runtime.h>
+ #include <cuda_runtime_api.h>
+ #if CUDA_VERSION >= 7050
+ #include <cuda_fp16.h>
+ #endif
+#endif
+
+#if defined(EIGEN_CUDACC) || defined(EIGEN_HIPCC)
+ #define EIGEN_TEST_NO_LONGDOUBLE
+ #define EIGEN_DEFAULT_DENSE_INDEX_TYPE int
+#endif
+
+// To test that all calls from Eigen code to std::min() and std::max() are
+// protected by parenthesis against macro expansion, the min()/max() macros
+// are defined here and any not-parenthesized min/max call will cause a
+// compiler error.
+#if !defined(__HIPCC__) && !defined(EIGEN_USE_SYCL) && !defined(EIGEN_POCKETFFT_DEFAULT)
+ //
+ // HIP header files include the following files
+ // <thread>
+ // <regex>
+ // <unordered_map>
+ // which seem to contain not-parenthesized calls to "max"/"min", triggering the following check and causing the compile to fail
+ //
+ // Including those header files before the following macro definition for "min" / "max", only partially resolves the issue
+ // This is because other HIP header files also define "isnan" / "isinf" / "isfinite" functions, which are needed in other
+ // headers.
+ //
+ // So instead choosing to simply disable this check for HIP
+ //
+ #define min(A,B) please_protect_your_min_with_parentheses
+ #define max(A,B) please_protect_your_max_with_parentheses
+ #define isnan(X) please_protect_your_isnan_with_parentheses
+ #define isinf(X) please_protect_your_isinf_with_parentheses
+ #define isfinite(X) please_protect_your_isfinite_with_parentheses
+#endif
+
+
+// test possible conflicts
+struct real {};
+struct imag {};
+
+#ifdef M_PI
+#undef M_PI
+#endif
+#define M_PI please_use_EIGEN_PI_instead_of_M_PI
+
+#define FORBIDDEN_IDENTIFIER (this_identifier_is_forbidden_to_avoid_clashes) this_identifier_is_forbidden_to_avoid_clashes
+// B0 is defined in POSIX header termios.h
+#define B0 FORBIDDEN_IDENTIFIER
+// `I` may be defined by complex.h:
+#define I FORBIDDEN_IDENTIFIER
+
+// Unit tests calling Eigen's blas library must preserve the default blocking size
+// to avoid troubles.
+#ifndef EIGEN_NO_DEBUG_SMALL_PRODUCT_BLOCKS
+#define EIGEN_DEBUG_SMALL_PRODUCT_BLOCKS
+#endif
+
+// shuts down ICC's remark #593: variable "XXX" was set but never used
+#define TEST_SET_BUT_UNUSED_VARIABLE(X) EIGEN_UNUSED_VARIABLE(X)
+
+#ifdef TEST_ENABLE_TEMPORARY_TRACKING
+
+static long int nb_temporaries;
+static long int nb_temporaries_on_assert = -1;
+
+inline void on_temporary_creation(long int size) {
+ // here's a great place to set a breakpoint when debugging failures in this test!
+ if(size!=0) nb_temporaries++;
+ if(nb_temporaries_on_assert>0) assert(nb_temporaries<nb_temporaries_on_assert);
+}
+
+#define EIGEN_DENSE_STORAGE_CTOR_PLUGIN { on_temporary_creation(size); }
+
+#define VERIFY_EVALUATION_COUNT(XPR,N) {\
+ nb_temporaries = 0; \
+ XPR; \
+ if(nb_temporaries!=(N)) { std::cerr << "nb_temporaries == " << nb_temporaries << "\n"; }\
+ VERIFY( (#XPR) && nb_temporaries==(N) ); \
+ }
+
+#endif
+
+#include "split_test_helper.h"
+
+#ifdef NDEBUG
+#undef NDEBUG
+#endif
+
+// On windows CE, NDEBUG is automatically defined <assert.h> if NDEBUG is not defined.
+#ifndef DEBUG
+#define DEBUG
+#endif
+
+// bounds integer values for AltiVec
+#if defined(__ALTIVEC__) || defined(__VSX__)
+#define EIGEN_MAKING_DOCS
+#endif
+
+#define DEFAULT_REPEAT 10
+
+namespace Eigen
+{
+ static std::vector<std::string> g_test_stack;
+ // level == 0 <=> abort if test fail
+ // level >= 1 <=> warning message to std::cerr if test fail
+ static int g_test_level = 0;
+ static int g_repeat = 1;
+ static unsigned int g_seed = 0;
+ static bool g_has_set_repeat = false, g_has_set_seed = false;
+
+ class EigenTest
+ {
+ public:
+ EigenTest() : m_func(0) {}
+ EigenTest(const char* a_name, void (*func)(void))
+ : m_name(a_name), m_func(func)
+ {
+ get_registered_tests().push_back(this);
+ }
+ const std::string& name() const { return m_name; }
+ void operator()() const { m_func(); }
+
+ static const std::vector<EigenTest*>& all() { return get_registered_tests(); }
+ protected:
+ static std::vector<EigenTest*>& get_registered_tests()
+ {
+ static std::vector<EigenTest*>* ms_registered_tests = new std::vector<EigenTest*>();
+ return *ms_registered_tests;
+ }
+ std::string m_name;
+ void (*m_func)(void);
+ };
+
+ // Declare and register a test, e.g.:
+ // EIGEN_DECLARE_TEST(mytest) { ... }
+ // will create a function:
+ // void test_mytest() { ... }
+ // that will be automatically called.
+ #define EIGEN_DECLARE_TEST(X) \
+ void EIGEN_CAT(test_,X) (); \
+ static EigenTest EIGEN_CAT(test_handler_,X) (EIGEN_MAKESTRING(X), & EIGEN_CAT(test_,X)); \
+ void EIGEN_CAT(test_,X) ()
+}
+
+#define TRACK std::cerr << __FILE__ << " " << __LINE__ << std::endl
+// #define TRACK while()
+
+#define EIGEN_DEFAULT_IO_FORMAT IOFormat(4, 0, " ", "\n", "", "", "", "")
+
+#if (defined(_CPPUNWIND) || defined(__EXCEPTIONS)) && !defined(__CUDA_ARCH__) && !defined(__HIP_DEVICE_COMPILE__) && !defined(__SYCL_DEVICE_ONLY__)
+ #define EIGEN_EXCEPTIONS
+#endif
+
+#ifndef EIGEN_NO_ASSERTION_CHECKING
+
+ namespace Eigen
+ {
+ static const bool should_raise_an_assert = false;
+
+ // Used to avoid to raise two exceptions at a time in which
+ // case the exception is not properly caught.
+ // This may happen when a second exceptions is triggered in a destructor.
+ static bool no_more_assert = false;
+ static bool report_on_cerr_on_assert_failure = true;
+
+ struct eigen_assert_exception
+ {
+ eigen_assert_exception(void) {}
+ ~eigen_assert_exception() { Eigen::no_more_assert = false; }
+ };
+
+ struct eigen_static_assert_exception
+ {
+ eigen_static_assert_exception(void) {}
+ ~eigen_static_assert_exception() { Eigen::no_more_assert = false; }
+ };
+ }
+ // If EIGEN_DEBUG_ASSERTS is defined and if no assertion is triggered while
+ // one should have been, then the list of executed assertions is printed out.
+ //
+ // EIGEN_DEBUG_ASSERTS is not enabled by default as it
+ // significantly increases the compilation time
+ // and might even introduce side effects that would hide
+ // some memory errors.
+ #ifdef EIGEN_DEBUG_ASSERTS
+
+ namespace Eigen
+ {
+ namespace internal
+ {
+ static bool push_assert = false;
+ }
+ static std::vector<std::string> eigen_assert_list;
+ }
+ #define eigen_assert(a) \
+ if( (!(a)) && (!no_more_assert) ) \
+ { \
+ if(report_on_cerr_on_assert_failure) \
+ std::cerr << #a << " " __FILE__ << "(" << __LINE__ << ")\n"; \
+ Eigen::no_more_assert = true; \
+ EIGEN_THROW_X(Eigen::eigen_assert_exception()); \
+ } \
+ else if (Eigen::internal::push_assert) \
+ { \
+ eigen_assert_list.push_back(std::string(EIGEN_MAKESTRING(__FILE__) " (" EIGEN_MAKESTRING(__LINE__) ") : " #a) ); \
+ }
+
+ #ifdef EIGEN_EXCEPTIONS
+ #define VERIFY_RAISES_ASSERT(a) \
+ { \
+ Eigen::no_more_assert = false; \
+ Eigen::eigen_assert_list.clear(); \
+ Eigen::internal::push_assert = true; \
+ Eigen::report_on_cerr_on_assert_failure = false; \
+ try { \
+ a; \
+ std::cerr << "One of the following asserts should have been triggered:\n"; \
+ for (uint ai=0 ; ai<eigen_assert_list.size() ; ++ai) \
+ std::cerr << " " << eigen_assert_list[ai] << "\n"; \
+ VERIFY(Eigen::should_raise_an_assert && # a); \
+ } catch (Eigen::eigen_assert_exception) { \
+ Eigen::internal::push_assert = false; VERIFY(true); \
+ } \
+ Eigen::report_on_cerr_on_assert_failure = true; \
+ Eigen::internal::push_assert = false; \
+ }
+ #endif //EIGEN_EXCEPTIONS
+
+ #elif !defined(__CUDACC__) && !defined(__HIPCC__) && !defined(SYCL_DEVICE_ONLY) // EIGEN_DEBUG_ASSERTS
+ #define eigen_assert(a) \
+ if( (!(a)) && (!no_more_assert) ) \
+ { \
+ Eigen::no_more_assert = true; \
+ if(report_on_cerr_on_assert_failure) \
+ eigen_plain_assert(a); \
+ else \
+ EIGEN_THROW_X(Eigen::eigen_assert_exception()); \
+ }
+
+ #ifdef EIGEN_EXCEPTIONS
+ #define VERIFY_RAISES_ASSERT(a) { \
+ Eigen::no_more_assert = false; \
+ Eigen::report_on_cerr_on_assert_failure = false; \
+ try { \
+ a; \
+ VERIFY(Eigen::should_raise_an_assert && # a); \
+ } \
+ catch (Eigen::eigen_assert_exception&) { VERIFY(true); } \
+ Eigen::report_on_cerr_on_assert_failure = true; \
+ }
+ #endif // EIGEN_EXCEPTIONS
+ #endif // EIGEN_DEBUG_ASSERTS
+
+#ifndef VERIFY_RAISES_ASSERT
+ #define VERIFY_RAISES_ASSERT(a) \
+ std::cout << "Can't VERIFY_RAISES_ASSERT( " #a " ) with exceptions disabled\n";
+#endif
+
+ #if !defined(__CUDACC__) && !defined(__HIPCC__) && !defined(SYCL_DEVICE_ONLY)
+ #define EIGEN_USE_CUSTOM_ASSERT
+ #endif
+
+#else // EIGEN_NO_ASSERTION_CHECKING
+
+ #define VERIFY_RAISES_ASSERT(a) {}
+
+#endif // EIGEN_NO_ASSERTION_CHECKING
+
+#define EIGEN_INTERNAL_DEBUGGING
+#include <Eigen/QR> // required for createRandomPIMatrixOfRank and generateRandomMatrixSvs
+
+inline void verify_impl(bool condition, const char *testname, const char *file, int line, const char *condition_as_string)
+{
+ if (!condition)
+ {
+ if(Eigen::g_test_level>0)
+ std::cerr << "WARNING: ";
+ std::cerr << "Test " << testname << " failed in " << file << " (" << line << ")"
+ << std::endl << " " << condition_as_string << std::endl;
+ std::cerr << "Stack:\n";
+ const int test_stack_size = static_cast<int>(Eigen::g_test_stack.size());
+ for(int i=test_stack_size-1; i>=0; --i)
+ std::cerr << " - " << Eigen::g_test_stack[i] << "\n";
+ std::cerr << "\n";
+ if(Eigen::g_test_level==0)
+ abort();
+ }
+}
+
+#define VERIFY(a) ::verify_impl(a, g_test_stack.back().c_str(), __FILE__, __LINE__, EIGEN_MAKESTRING(a))
+
+#define VERIFY_GE(a, b) ::verify_impl(a >= b, g_test_stack.back().c_str(), __FILE__, __LINE__, EIGEN_MAKESTRING(a >= b))
+#define VERIFY_LE(a, b) ::verify_impl(a <= b, g_test_stack.back().c_str(), __FILE__, __LINE__, EIGEN_MAKESTRING(a <= b))
+
+
+#define VERIFY_IS_EQUAL(a, b) VERIFY(test_is_equal(a, b, true))
+#define VERIFY_IS_NOT_EQUAL(a, b) VERIFY(test_is_equal(a, b, false))
+#define VERIFY_IS_APPROX(a, b) VERIFY(verifyIsApprox(a, b))
+#define VERIFY_IS_NOT_APPROX(a, b) VERIFY(!test_isApprox(a, b))
+#define VERIFY_IS_MUCH_SMALLER_THAN(a, b) VERIFY(test_isMuchSmallerThan(a, b))
+#define VERIFY_IS_NOT_MUCH_SMALLER_THAN(a, b) VERIFY(!test_isMuchSmallerThan(a, b))
+#define VERIFY_IS_APPROX_OR_LESS_THAN(a, b) VERIFY(test_isApproxOrLessThan(a, b))
+#define VERIFY_IS_NOT_APPROX_OR_LESS_THAN(a, b) VERIFY(!test_isApproxOrLessThan(a, b))
+#define VERIFY_IS_CWISE_EQUAL(a, b) VERIFY(verifyIsCwiseApprox(a, b, true))
+#define VERIFY_IS_CWISE_APPROX(a, b) VERIFY(verifyIsCwiseApprox(a, b, false))
+
+#define VERIFY_IS_UNITARY(a) VERIFY(test_isUnitary(a))
+
+#define STATIC_CHECK(COND) EIGEN_STATIC_ASSERT( (COND) , EIGEN_INTERNAL_ERROR_PLEASE_FILE_A_BUG_REPORT )
+
+#define CALL_SUBTEST(FUNC) do { \
+ g_test_stack.push_back(EIGEN_MAKESTRING(FUNC)); \
+ FUNC; \
+ g_test_stack.pop_back(); \
+ } while (0)
+
+
+// Forward declarations to avoid ICC warnings
+#if EIGEN_COMP_ICC
+
+template<typename T> std::string type_name();
+
+namespace Eigen {
+
+template<typename T, typename U>
+bool test_is_equal(const T& actual, const U& expected, bool expect_equal=true);
+
+} // end namespace Eigen
+
+#endif // EIGEN_COMP_ICC
+
+
+namespace Eigen {
+
+template<typename T1,typename T2>
+std::enable_if_t<internal::is_same<T1,T2>::value,bool>
+is_same_type(const T1&, const T2&)
+{
+ return true;
+}
+
+template<typename T> inline typename NumTraits<T>::Real test_precision() { return NumTraits<T>::dummy_precision(); }
+template<> inline float test_precision<float>() { return 1e-3f; }
+template<> inline double test_precision<double>() { return 1e-6; }
+template<> inline long double test_precision<long double>() { return 1e-6l; }
+template<> inline float test_precision<std::complex<float> >() { return test_precision<float>(); }
+template<> inline double test_precision<std::complex<double> >() { return test_precision<double>(); }
+template<> inline long double test_precision<std::complex<long double> >() { return test_precision<long double>(); }
+
+#define EIGEN_TEST_SCALAR_TEST_OVERLOAD(TYPE) \
+ inline bool test_isApprox(TYPE a, TYPE b) \
+ { return numext::equal_strict(a, b) || \
+ ((numext::isnan)(a) && (numext::isnan)(b)) || \
+ (internal::isApprox(a, b, test_precision<TYPE>())); } \
+ inline bool test_isCwiseApprox(TYPE a, TYPE b, bool exact) \
+ { return numext::equal_strict(a, b) || \
+ ((numext::isnan)(a) && (numext::isnan)(b)) || \
+ (!exact && internal::isApprox(a, b, test_precision<TYPE>())); } \
+ inline bool test_isMuchSmallerThan(TYPE a, TYPE b) \
+ { return internal::isMuchSmallerThan(a, b, test_precision<TYPE>()); } \
+ inline bool test_isApproxOrLessThan(TYPE a, TYPE b) \
+ { return internal::isApproxOrLessThan(a, b, test_precision<TYPE>()); }
+
+EIGEN_TEST_SCALAR_TEST_OVERLOAD(short)
+EIGEN_TEST_SCALAR_TEST_OVERLOAD(unsigned short)
+EIGEN_TEST_SCALAR_TEST_OVERLOAD(int)
+EIGEN_TEST_SCALAR_TEST_OVERLOAD(unsigned int)
+EIGEN_TEST_SCALAR_TEST_OVERLOAD(long)
+EIGEN_TEST_SCALAR_TEST_OVERLOAD(unsigned long)
+EIGEN_TEST_SCALAR_TEST_OVERLOAD(long long)
+EIGEN_TEST_SCALAR_TEST_OVERLOAD(unsigned long long)
+EIGEN_TEST_SCALAR_TEST_OVERLOAD(float)
+EIGEN_TEST_SCALAR_TEST_OVERLOAD(double)
+EIGEN_TEST_SCALAR_TEST_OVERLOAD(half)
+EIGEN_TEST_SCALAR_TEST_OVERLOAD(bfloat16)
+
+#undef EIGEN_TEST_SCALAR_TEST_OVERLOAD
+
+#ifndef EIGEN_TEST_NO_COMPLEX
+inline bool test_isApprox(const std::complex<float>& a, const std::complex<float>& b)
+{ return internal::isApprox(a, b, test_precision<std::complex<float> >()); }
+inline bool test_isMuchSmallerThan(const std::complex<float>& a, const std::complex<float>& b)
+{ return internal::isMuchSmallerThan(a, b, test_precision<std::complex<float> >()); }
+
+inline bool test_isApprox(const std::complex<double>& a, const std::complex<double>& b)
+{ return internal::isApprox(a, b, test_precision<std::complex<double> >()); }
+inline bool test_isMuchSmallerThan(const std::complex<double>& a, const std::complex<double>& b)
+{ return internal::isMuchSmallerThan(a, b, test_precision<std::complex<double> >()); }
+
+#ifndef EIGEN_TEST_NO_LONGDOUBLE
+inline bool test_isApprox(const std::complex<long double>& a, const std::complex<long double>& b)
+{ return internal::isApprox(a, b, test_precision<std::complex<long double> >()); }
+inline bool test_isMuchSmallerThan(const std::complex<long double>& a, const std::complex<long double>& b)
+{ return internal::isMuchSmallerThan(a, b, test_precision<std::complex<long double> >()); }
+#endif
+#endif
+
+#ifndef EIGEN_TEST_NO_LONGDOUBLE
+inline bool test_isApprox(const long double& a, const long double& b)
+{
+ bool ret = internal::isApprox(a, b, test_precision<long double>());
+ if (!ret) std::cerr
+ << std::endl << " actual = " << a
+ << std::endl << " expected = " << b << std::endl << std::endl;
+ return ret;
+}
+
+inline bool test_isMuchSmallerThan(const long double& a, const long double& b)
+{ return internal::isMuchSmallerThan(a, b, test_precision<long double>()); }
+inline bool test_isApproxOrLessThan(const long double& a, const long double& b)
+{ return internal::isApproxOrLessThan(a, b, test_precision<long double>()); }
+#endif // EIGEN_TEST_NO_LONGDOUBLE
+
+// test_relative_error returns the relative difference between a and b as a real scalar as used in isApprox.
+template<typename T1,typename T2>
+typename NumTraits<typename T1::RealScalar>::NonInteger test_relative_error(const EigenBase<T1> &a, const EigenBase<T2> &b)
+{
+ using std::sqrt;
+ typedef typename NumTraits<typename T1::RealScalar>::NonInteger RealScalar;
+ typename internal::nested_eval<T1,2>::type ea(a.derived());
+ typename internal::nested_eval<T2,2>::type eb(b.derived());
+ return sqrt(RealScalar((ea-eb).cwiseAbs2().sum()) / RealScalar((std::min)(eb.cwiseAbs2().sum(),ea.cwiseAbs2().sum())));
+}
+
+template<typename T1,typename T2>
+typename T1::RealScalar test_relative_error(const T1 &a, const T2 &b, const typename T1::Coefficients* = 0)
+{
+ return test_relative_error(a.coeffs(), b.coeffs());
+}
+
+template<typename T1,typename T2>
+typename T1::Scalar test_relative_error(const T1 &a, const T2 &b, const typename T1::MatrixType* = 0)
+{
+ return test_relative_error(a.matrix(), b.matrix());
+}
+
+template<typename S, int D>
+S test_relative_error(const Translation<S,D> &a, const Translation<S,D> &b)
+{
+ return test_relative_error(a.vector(), b.vector());
+}
+
+template <typename S, int D, int O>
+S test_relative_error(const ParametrizedLine<S,D,O> &a, const ParametrizedLine<S,D,O> &b)
+{
+ return (std::max)(test_relative_error(a.origin(), b.origin()), test_relative_error(a.origin(), b.origin()));
+}
+
+template <typename S, int D>
+S test_relative_error(const AlignedBox<S,D> &a, const AlignedBox<S,D> &b)
+{
+ return (std::max)(test_relative_error((a.min)(), (b.min)()), test_relative_error((a.max)(), (b.max)()));
+}
+
+template<typename Derived> class SparseMatrixBase;
+template<typename T1,typename T2>
+typename T1::RealScalar test_relative_error(const MatrixBase<T1> &a, const SparseMatrixBase<T2> &b)
+{
+ return test_relative_error(a,b.toDense());
+}
+
+template<typename Derived> class SparseMatrixBase;
+template<typename T1,typename T2>
+typename T1::RealScalar test_relative_error(const SparseMatrixBase<T1> &a, const MatrixBase<T2> &b)
+{
+ return test_relative_error(a.toDense(),b);
+}
+
+template<typename Derived> class SparseMatrixBase;
+template<typename T1,typename T2>
+typename T1::RealScalar test_relative_error(const SparseMatrixBase<T1> &a, const SparseMatrixBase<T2> &b)
+{
+ return test_relative_error(a.toDense(),b.toDense());
+}
+
+template<typename T1,typename T2>
+typename NumTraits<typename NumTraits<T1>::Real>::NonInteger test_relative_error(const T1 &a, const T2 &b, std::enable_if_t<internal::is_arithmetic<typename NumTraits<T1>::Real>::value, T1>* = 0)
+{
+ typedef typename NumTraits<typename NumTraits<T1>::Real>::NonInteger RealScalar;
+ return numext::sqrt(RealScalar(numext::abs2(a-b))/(numext::mini)(RealScalar(numext::abs2(a)),RealScalar(numext::abs2(b))));
+}
+
+template<typename T>
+T test_relative_error(const Rotation2D<T> &a, const Rotation2D<T> &b)
+{
+ return test_relative_error(a.angle(), b.angle());
+}
+
+template<typename T>
+T test_relative_error(const AngleAxis<T> &a, const AngleAxis<T> &b)
+{
+ return (std::max)(test_relative_error(a.angle(), b.angle()), test_relative_error(a.axis(), b.axis()));
+}
+
+template<typename Type1, typename Type2>
+inline bool test_isApprox(const Type1& a, const Type2& b, typename Type1::Scalar* = 0) // Enabled for Eigen's type only
+{
+ return a.isApprox(b, test_precision<typename Type1::Scalar>());
+}
+
+// get_test_precision is a small wrapper to test_precision allowing to return the scalar precision for either scalars or expressions
+template<typename T>
+typename NumTraits<typename T::Scalar>::Real get_test_precision(const T&, const typename T::Scalar* = 0)
+{
+ return test_precision<typename NumTraits<typename T::Scalar>::Real>();
+}
+
+template<typename T>
+typename NumTraits<T>::Real get_test_precision(const T&,std::enable_if_t<internal::is_arithmetic<typename NumTraits<T>::Real>::value, T>* = 0)
+{
+ return test_precision<typename NumTraits<T>::Real>();
+}
+
+// verifyIsApprox is a wrapper to test_isApprox that outputs the relative difference magnitude if the test fails.
+template<typename Type1, typename Type2>
+inline bool verifyIsApprox(const Type1& a, const Type2& b)
+{
+ bool ret = test_isApprox(a,b);
+ if(!ret)
+ {
+ std::cerr << "Difference too large wrt tolerance " << get_test_precision(a) << ", relative error is: " << test_relative_error(a,b) << std::endl;
+ }
+ return ret;
+}
+
+// verifyIsCwiseApprox is a wrapper to test_isCwiseApprox that outputs the relative difference magnitude if the test fails.
+template<typename Type1, typename Type2>
+inline bool verifyIsCwiseApprox(const Type1& a, const Type2& b, bool exact)
+{
+ bool ret = test_isCwiseApprox(a,b,exact);
+ if(!ret) {
+ if (exact) {
+ std::cerr << "Values are not an exact match";
+ } else {
+ std::cerr << "Difference too large wrt tolerance " << get_test_precision(a);
+ }
+ std::cerr << ", relative error is: " << test_relative_error(a,b) << std::endl;
+ }
+ return ret;
+}
+
+// The idea behind this function is to compare the two scalars a and b where
+// the scalar ref is a hint about the expected order of magnitude of a and b.
+// WARNING: the scalar a and b must be positive
+// Therefore, if for some reason a and b are very small compared to ref,
+// we won't issue a false negative.
+// This test could be: abs(a-b) <= eps * ref
+// However, it seems that simply comparing a+ref and b+ref is more sensitive to true error.
+template<typename Scalar,typename ScalarRef>
+inline bool test_isApproxWithRef(const Scalar& a, const Scalar& b, const ScalarRef& ref)
+{
+ return test_isApprox(a+ref, b+ref);
+}
+
+template<typename Derived1, typename Derived2>
+inline bool test_isMuchSmallerThan(const MatrixBase<Derived1>& m1,
+ const MatrixBase<Derived2>& m2)
+{
+ return m1.isMuchSmallerThan(m2, test_precision<typename internal::traits<Derived1>::Scalar>());
+}
+
+template<typename Derived>
+inline bool test_isMuchSmallerThan(const MatrixBase<Derived>& m,
+ const typename NumTraits<typename internal::traits<Derived>::Scalar>::Real& s)
+{
+ return m.isMuchSmallerThan(s, test_precision<typename internal::traits<Derived>::Scalar>());
+}
+
+template<typename Derived>
+inline bool test_isUnitary(const MatrixBase<Derived>& m)
+{
+ return m.isUnitary(test_precision<typename internal::traits<Derived>::Scalar>());
+}
+
+// Checks component-wise, works with infs and nans.
+template<typename Derived1, typename Derived2>
+bool test_isCwiseApprox(const DenseBase<Derived1>& m1,
+ const DenseBase<Derived2>& m2,
+ bool exact) {
+ if (m1.rows() != m2.rows()) {
+ return false;
+ }
+ if (m1.cols() != m2.cols()) {
+ return false;
+ }
+ for (Index r = 0; r < m1.rows(); ++r) {
+ for (Index c = 0; c < m1.cols(); ++c) {
+ if (m1(r, c) != m2(r, c)
+ && !((numext::isnan)(m1(r, c)) && (numext::isnan)(m2(r, c)))
+ && (exact || !test_isApprox(m1(r, c), m2(r, c)))) {
+ return false;
+ }
+ }
+ }
+ return true;
+}
+
+template<typename T, typename U>
+bool test_is_equal(const T& actual, const U& expected, bool expect_equal)
+{
+ if (numext::equal_strict(actual, expected) == expect_equal)
+ return true;
+ // false:
+ std::cerr
+ << "\n actual = " << actual
+ << "\n expected " << (expect_equal ? "= " : "!=") << expected << "\n\n";
+ return false;
+}
+
+
+
+/**
+ * Check if number is "not a number" (NaN).
+ *
+ * @tparam T input type
+ * @param x input value
+ * @return true, if input value is "not a number" (NaN)
+ */
+template<typename T> bool isNotNaN(const T& x)
+{
+ return x==x;
+}
+
+/**
+ * Check if number is plus infinity.
+ *
+ * @tparam T input type
+ * @param x input value
+ * @return true, if input value is plus infinity
+ */
+template<typename T> bool isPlusInf(const T& x)
+{
+ return x > NumTraits<T>::highest();
+}
+
+/**
+ * Check if number is minus infinity.
+ *
+ * @tparam T input type
+ * @param x input value
+ * @return true, if input value is minus infinity
+ */
+template<typename T> bool isMinusInf(const T& x)
+{
+ return x < NumTraits<T>::lowest();
+}
+
+} // end namespace Eigen
+
+
+#include "random_matrix_helper.h"
+
+
+template<typename T> struct GetDifferentType;
+
+template<> struct GetDifferentType<float> { typedef double type; };
+template<> struct GetDifferentType<double> { typedef float type; };
+template<typename T> struct GetDifferentType<std::complex<T> >
+{ typedef std::complex<typename GetDifferentType<T>::type> type; };
+
+template<typename T> std::string type_name() { return "other"; }
+template<> std::string type_name<float>() { return "float"; }
+template<> std::string type_name<double>() { return "double"; }
+template<> std::string type_name<long double>() { return "long double"; }
+template<> std::string type_name<int>() { return "int"; }
+template<> std::string type_name<std::complex<float> >() { return "complex<float>"; }
+template<> std::string type_name<std::complex<double> >() { return "complex<double>"; }
+template<> std::string type_name<std::complex<long double> >() { return "complex<long double>"; }
+template<> std::string type_name<std::complex<int> >() { return "complex<int>"; }
+
+using namespace Eigen;
+
+/**
+ * Set number of repetitions for unit test from input string.
+ *
+ * @param str input string
+ */
+inline void set_repeat_from_string(const char *str)
+{
+ errno = 0;
+ g_repeat = int(strtoul(str, 0, 10));
+ if(errno || g_repeat <= 0)
+ {
+ std::cout << "Invalid repeat value " << str << std::endl;
+ exit(EXIT_FAILURE);
+ }
+ g_has_set_repeat = true;
+}
+
+/**
+ * Set seed for randomized unit tests from input string.
+ *
+ * @param str input string
+ */
+inline void set_seed_from_string(const char *str)
+{
+ errno = 0;
+ g_seed = int(strtoul(str, 0, 10));
+ if(errno || g_seed == 0)
+ {
+ std::cout << "Invalid seed value " << str << std::endl;
+ exit(EXIT_FAILURE);
+ }
+ g_has_set_seed = true;
+}
+
+int main(int argc, char *argv[])
+{
+ g_has_set_repeat = false;
+ g_has_set_seed = false;
+ bool need_help = false;
+
+ for(int i = 1; i < argc; i++)
+ {
+ if(argv[i][0] == 'r')
+ {
+ if(g_has_set_repeat)
+ {
+ std::cout << "Argument " << argv[i] << " conflicting with a former argument" << std::endl;
+ return 1;
+ }
+ set_repeat_from_string(argv[i]+1);
+ }
+ else if(argv[i][0] == 's')
+ {
+ if(g_has_set_seed)
+ {
+ std::cout << "Argument " << argv[i] << " conflicting with a former argument" << std::endl;
+ return 1;
+ }
+ set_seed_from_string(argv[i]+1);
+ }
+ else
+ {
+ need_help = true;
+ }
+ }
+
+ if(need_help)
+ {
+ std::cout << "This test application takes the following optional arguments:" << std::endl;
+ std::cout << " rN Repeat each test N times (default: " << DEFAULT_REPEAT << ")" << std::endl;
+ std::cout << " sN Use N as seed for random numbers (default: based on current time)" << std::endl;
+ std::cout << std::endl;
+ std::cout << "If defined, the environment variables EIGEN_REPEAT and EIGEN_SEED" << std::endl;
+ std::cout << "will be used as default values for these parameters." << std::endl;
+ return 1;
+ }
+
+ char *env_EIGEN_REPEAT = getenv("EIGEN_REPEAT");
+ if(!g_has_set_repeat && env_EIGEN_REPEAT)
+ set_repeat_from_string(env_EIGEN_REPEAT);
+ char *env_EIGEN_SEED = getenv("EIGEN_SEED");
+ if(!g_has_set_seed && env_EIGEN_SEED)
+ set_seed_from_string(env_EIGEN_SEED);
+
+ if(!g_has_set_seed) g_seed = (unsigned int) time(NULL);
+ if(!g_has_set_repeat) g_repeat = DEFAULT_REPEAT;
+
+ std::cout << "Initializing random number generator with seed " << g_seed << std::endl;
+ std::stringstream ss;
+ ss << "Seed: " << g_seed;
+ g_test_stack.push_back(ss.str());
+ srand(g_seed);
+ std::cout << "Repeating each test " << g_repeat << " times" << std::endl;
+
+ VERIFY(EigenTest::all().size()>0);
+
+ for(std::size_t i=0; i<EigenTest::all().size(); ++i)
+ {
+ const EigenTest& current_test = *EigenTest::all()[i];
+ Eigen::g_test_stack.push_back(current_test.name());
+ current_test();
+ Eigen::g_test_stack.pop_back();
+ }
+
+ return 0;
+}
+
+// These warning are disabled here such that they are still ON when parsing Eigen's header files.
+#if defined __INTEL_COMPILER
+ // remark #383: value copied to temporary, reference to temporary used
+ // -> this warning is raised even for legal usage as: g_test_stack.push_back("foo"); where g_test_stack is a std::vector<std::string>
+ // remark #1418: external function definition with no prior declaration
+ // -> this warning is raised for all our test functions. Declaring them static would fix the issue.
+ // warning #279: controlling expression is constant
+ // remark #1572: floating-point equality and inequality comparisons are unreliable
+ #pragma warning disable 279 383 1418 1572
+#endif
+
+#ifdef _MSC_VER
+ // 4503 - decorated name length exceeded, name was truncated
+ #pragma warning( disable : 4503)
+#endif
+
+#include "gpu_test_helper.h"
diff --git a/test/mapped_matrix.cpp b/test/mapped_matrix.cpp
new file mode 100644
index 0000000..1dd6959
--- /dev/null
+++ b/test/mapped_matrix.cpp
@@ -0,0 +1,209 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2006-2010 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "main.h"
+
+#define EIGEN_TESTMAP_MAX_SIZE 256
+
+template<typename VectorType> void map_class_vector(const VectorType& m)
+{
+ typedef typename VectorType::Scalar Scalar;
+
+ Index size = m.size();
+
+ Scalar* array1 = internal::aligned_new<Scalar>(size);
+ Scalar* array2 = internal::aligned_new<Scalar>(size);
+ Scalar* array3 = new Scalar[size+1];
+ // In case of no alignment, avoid division by zero.
+ constexpr int alignment = (std::max<int>)(EIGEN_MAX_ALIGN_BYTES, 1);
+ Scalar* array3unaligned = (internal::UIntPtr(array3)%alignment) == 0 ? array3+1 : array3;
+ Scalar array4[EIGEN_TESTMAP_MAX_SIZE];
+
+ Map<VectorType, AlignedMax>(array1, size) = VectorType::Random(size);
+ Map<VectorType, AlignedMax>(array2, size) = Map<VectorType,AlignedMax>(array1, size);
+ Map<VectorType>(array3unaligned, size) = Map<VectorType>(array1, size);
+ Map<VectorType>(array4, size) = Map<VectorType,AlignedMax>(array1, size);
+ VectorType ma1 = Map<VectorType, AlignedMax>(array1, size);
+ VectorType ma2 = Map<VectorType, AlignedMax>(array2, size);
+ VectorType ma3 = Map<VectorType>(array3unaligned, size);
+ VectorType ma4 = Map<VectorType>(array4, size);
+ VERIFY_IS_EQUAL(ma1, ma2);
+ VERIFY_IS_EQUAL(ma1, ma3);
+ VERIFY_IS_EQUAL(ma1, ma4);
+ #ifdef EIGEN_VECTORIZE
+ if(internal::packet_traits<Scalar>::Vectorizable && size>=AlignedMax)
+ VERIFY_RAISES_ASSERT((Map<VectorType,AlignedMax>(array3unaligned, size)))
+ #endif
+
+ internal::aligned_delete(array1, size);
+ internal::aligned_delete(array2, size);
+ delete[] array3;
+}
+
+template<typename MatrixType> void map_class_matrix(const MatrixType& m)
+{
+ typedef typename MatrixType::Scalar Scalar;
+
+ Index rows = m.rows(), cols = m.cols(), size = rows*cols;
+ Scalar s1 = internal::random<Scalar>();
+
+ // array1 and array2 -> aligned heap allocation
+ Scalar* array1 = internal::aligned_new<Scalar>(size);
+ for(int i = 0; i < size; i++) array1[i] = Scalar(1);
+ Scalar* array2 = internal::aligned_new<Scalar>(size);
+ for(int i = 0; i < size; i++) array2[i] = Scalar(1);
+ // array3unaligned -> unaligned pointer to heap
+ Scalar* array3 = new Scalar[size+1];
+ Index sizep1 = size + 1; // <- without this temporary MSVC 2103 generates bad code
+ for(Index i = 0; i < sizep1; i++) array3[i] = Scalar(1);
+ // In case of no alignment, avoid division by zero.
+ constexpr int alignment = (std::max<int>)(EIGEN_MAX_ALIGN_BYTES, 1);
+ Scalar* array3unaligned = (internal::UIntPtr(array3)%alignment) == 0 ? array3+1 : array3;
+ Scalar array4[256];
+ if(size<=256)
+ for(int i = 0; i < size; i++) array4[i] = Scalar(1);
+
+ Map<MatrixType> map1(array1, rows, cols);
+ Map<MatrixType, AlignedMax> map2(array2, rows, cols);
+ Map<MatrixType> map3(array3unaligned, rows, cols);
+ Map<MatrixType> map4(array4, rows, cols);
+
+ VERIFY_IS_EQUAL(map1, MatrixType::Ones(rows,cols));
+ VERIFY_IS_EQUAL(map2, MatrixType::Ones(rows,cols));
+ VERIFY_IS_EQUAL(map3, MatrixType::Ones(rows,cols));
+ map1 = MatrixType::Random(rows,cols);
+ map2 = map1;
+ map3 = map1;
+ MatrixType ma1 = map1;
+ MatrixType ma2 = map2;
+ MatrixType ma3 = map3;
+ VERIFY_IS_EQUAL(map1, map2);
+ VERIFY_IS_EQUAL(map1, map3);
+ VERIFY_IS_EQUAL(ma1, ma2);
+ VERIFY_IS_EQUAL(ma1, ma3);
+ VERIFY_IS_EQUAL(ma1, map3);
+
+ VERIFY_IS_APPROX(s1*map1, s1*map2);
+ VERIFY_IS_APPROX(s1*ma1, s1*ma2);
+ VERIFY_IS_EQUAL(s1*ma1, s1*ma3);
+ VERIFY_IS_APPROX(s1*map1, s1*map3);
+
+ map2 *= s1;
+ map3 *= s1;
+ VERIFY_IS_APPROX(s1*map1, map2);
+ VERIFY_IS_APPROX(s1*map1, map3);
+
+ if(size<=256)
+ {
+ VERIFY_IS_EQUAL(map4, MatrixType::Ones(rows,cols));
+ map4 = map1;
+ MatrixType ma4 = map4;
+ VERIFY_IS_EQUAL(map1, map4);
+ VERIFY_IS_EQUAL(ma1, map4);
+ VERIFY_IS_EQUAL(ma1, ma4);
+ VERIFY_IS_APPROX(s1*map1, s1*map4);
+
+ map4 *= s1;
+ VERIFY_IS_APPROX(s1*map1, map4);
+ }
+
+ internal::aligned_delete(array1, size);
+ internal::aligned_delete(array2, size);
+ delete[] array3;
+}
+
+template<typename VectorType> void map_static_methods(const VectorType& m)
+{
+ typedef typename VectorType::Scalar Scalar;
+
+ Index size = m.size();
+
+ Scalar* array1 = internal::aligned_new<Scalar>(size);
+ Scalar* array2 = internal::aligned_new<Scalar>(size);
+ Scalar* array3 = new Scalar[size+1];
+ // In case of no alignment, avoid division by zero.
+ constexpr int alignment = (std::max<int>)(EIGEN_MAX_ALIGN_BYTES, 1);
+ Scalar* array3unaligned = (internal::UIntPtr(array3)%alignment) == 0 ? array3+1 : array3;
+
+ VectorType::MapAligned(array1, size) = VectorType::Random(size);
+ VectorType::Map(array2, size) = VectorType::Map(array1, size);
+ VectorType::Map(array3unaligned, size) = VectorType::Map(array1, size);
+ VectorType ma1 = VectorType::Map(array1, size);
+ VectorType ma2 = VectorType::MapAligned(array2, size);
+ VectorType ma3 = VectorType::Map(array3unaligned, size);
+ VERIFY_IS_EQUAL(ma1, ma2);
+ VERIFY_IS_EQUAL(ma1, ma3);
+
+ internal::aligned_delete(array1, size);
+ internal::aligned_delete(array2, size);
+ delete[] array3;
+}
+
+template<typename PlainObjectType> void check_const_correctness(const PlainObjectType&)
+{
+ // there's a lot that we can't test here while still having this test compile!
+ // the only possible approach would be to run a script trying to compile stuff and checking that it fails.
+ // CMake can help with that.
+
+ // verify that map-to-const don't have LvalueBit
+ typedef std::add_const_t<PlainObjectType> ConstPlainObjectType;
+ VERIFY( !(internal::traits<Map<ConstPlainObjectType> >::Flags & LvalueBit) );
+ VERIFY( !(internal::traits<Map<ConstPlainObjectType, AlignedMax> >::Flags & LvalueBit) );
+ VERIFY( !(Map<ConstPlainObjectType>::Flags & LvalueBit) );
+ VERIFY( !(Map<ConstPlainObjectType, AlignedMax>::Flags & LvalueBit) );
+}
+
+template<typename Scalar>
+void map_not_aligned_on_scalar()
+{
+ typedef Matrix<Scalar,Dynamic,Dynamic> MatrixType;
+ Index size = 11;
+ Scalar* array1 = internal::aligned_new<Scalar>((size+1)*(size+1)+1);
+ Scalar* array2 = reinterpret_cast<Scalar*>(sizeof(Scalar)/2+std::size_t(array1));
+ Map<MatrixType,0,OuterStride<> > map2(array2, size, size, OuterStride<>(size+1));
+ MatrixType m2 = MatrixType::Random(size,size);
+ map2 = m2;
+ VERIFY_IS_EQUAL(m2, map2);
+
+ typedef Matrix<Scalar,Dynamic,1> VectorType;
+ Map<VectorType> map3(array2, size);
+ MatrixType v3 = VectorType::Random(size);
+ map3 = v3;
+ VERIFY_IS_EQUAL(v3, map3);
+
+ internal::aligned_delete(array1, (size+1)*(size+1)+1);
+}
+
+EIGEN_DECLARE_TEST(mapped_matrix)
+{
+ for(int i = 0; i < g_repeat; i++) {
+ CALL_SUBTEST_1( map_class_vector(Matrix<float, 1, 1>()) );
+ CALL_SUBTEST_1( check_const_correctness(Matrix<float, 1, 1>()) );
+ CALL_SUBTEST_2( map_class_vector(Vector4d()) );
+ CALL_SUBTEST_2( map_class_vector(VectorXd(13)) );
+ CALL_SUBTEST_2( check_const_correctness(Matrix4d()) );
+ CALL_SUBTEST_3( map_class_vector(RowVector4f()) );
+ CALL_SUBTEST_4( map_class_vector(VectorXcf(8)) );
+ CALL_SUBTEST_5( map_class_vector(VectorXi(12)) );
+ CALL_SUBTEST_5( check_const_correctness(VectorXi(12)) );
+
+ CALL_SUBTEST_1( map_class_matrix(Matrix<float, 1, 1>()) );
+ CALL_SUBTEST_2( map_class_matrix(Matrix4d()) );
+ CALL_SUBTEST_11( map_class_matrix(Matrix<float,3,5>()) );
+ CALL_SUBTEST_4( map_class_matrix(MatrixXcf(internal::random<int>(1,10),internal::random<int>(1,10))) );
+ CALL_SUBTEST_5( map_class_matrix(MatrixXi(internal::random<int>(1,10),internal::random<int>(1,10))) );
+
+ CALL_SUBTEST_6( map_static_methods(Matrix<double, 1, 1>()) );
+ CALL_SUBTEST_7( map_static_methods(Vector3f()) );
+ CALL_SUBTEST_8( map_static_methods(RowVector3d()) );
+ CALL_SUBTEST_9( map_static_methods(VectorXcd(8)) );
+ CALL_SUBTEST_10( map_static_methods(VectorXf(12)) );
+ CALL_SUBTEST_11( map_not_aligned_on_scalar<double>() );
+ }
+}
diff --git a/test/mapstaticmethods.cpp b/test/mapstaticmethods.cpp
new file mode 100644
index 0000000..d0128ba
--- /dev/null
+++ b/test/mapstaticmethods.cpp
@@ -0,0 +1,177 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2011 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "main.h"
+
+// GCC<=4.8 has spurious shadow warnings, because `ptr` re-appears inside template instantiations
+// workaround: put these in an anonymous namespace
+namespace {
+float *ptr;
+const float *const_ptr;
+}
+
+template<typename PlainObjectType,
+ bool IsDynamicSize = PlainObjectType::SizeAtCompileTime == Dynamic,
+ bool IsVector = PlainObjectType::IsVectorAtCompileTime
+>
+struct mapstaticmethods_impl {};
+
+template<typename PlainObjectType, bool IsVector>
+struct mapstaticmethods_impl<PlainObjectType, false, IsVector>
+{
+ static void run(const PlainObjectType& m)
+ {
+ mapstaticmethods_impl<PlainObjectType, true, IsVector>::run(m);
+
+ int i = internal::random<int>(2,5), j = internal::random<int>(2,5);
+
+ PlainObjectType::Map(ptr).setZero();
+ PlainObjectType::MapAligned(ptr).setZero();
+ PlainObjectType::Map(const_ptr).sum();
+ PlainObjectType::MapAligned(const_ptr).sum();
+
+ PlainObjectType::Map(ptr, InnerStride<>(i)).setZero();
+ PlainObjectType::MapAligned(ptr, InnerStride<>(i)).setZero();
+ PlainObjectType::Map(const_ptr, InnerStride<>(i)).sum();
+ PlainObjectType::MapAligned(const_ptr, InnerStride<>(i)).sum();
+
+ PlainObjectType::Map(ptr, InnerStride<2>()).setZero();
+ PlainObjectType::MapAligned(ptr, InnerStride<3>()).setZero();
+ PlainObjectType::Map(const_ptr, InnerStride<4>()).sum();
+ PlainObjectType::MapAligned(const_ptr, InnerStride<5>()).sum();
+
+ PlainObjectType::Map(ptr, OuterStride<>(i)).setZero();
+ PlainObjectType::MapAligned(ptr, OuterStride<>(i)).setZero();
+ PlainObjectType::Map(const_ptr, OuterStride<>(i)).sum();
+ PlainObjectType::MapAligned(const_ptr, OuterStride<>(i)).sum();
+
+ PlainObjectType::Map(ptr, OuterStride<2>()).setZero();
+ PlainObjectType::MapAligned(ptr, OuterStride<3>()).setZero();
+ PlainObjectType::Map(const_ptr, OuterStride<4>()).sum();
+ PlainObjectType::MapAligned(const_ptr, OuterStride<5>()).sum();
+
+ PlainObjectType::Map(ptr, Stride<Dynamic, Dynamic>(i,j)).setZero();
+ PlainObjectType::MapAligned(ptr, Stride<2,Dynamic>(2,i)).setZero();
+ PlainObjectType::Map(const_ptr, Stride<Dynamic,3>(i,3)).sum();
+ PlainObjectType::MapAligned(const_ptr, Stride<Dynamic, Dynamic>(i,j)).sum();
+
+ PlainObjectType::Map(ptr, Stride<2,3>()).setZero();
+ PlainObjectType::MapAligned(ptr, Stride<3,4>()).setZero();
+ PlainObjectType::Map(const_ptr, Stride<2,4>()).sum();
+ PlainObjectType::MapAligned(const_ptr, Stride<5,3>()).sum();
+ }
+};
+
+template<typename PlainObjectType>
+struct mapstaticmethods_impl<PlainObjectType, true, false>
+{
+ static void run(const PlainObjectType& m)
+ {
+ Index rows = m.rows(), cols = m.cols();
+
+ int i = internal::random<int>(2,5), j = internal::random<int>(2,5);
+
+ PlainObjectType::Map(ptr, rows, cols).setZero();
+ PlainObjectType::MapAligned(ptr, rows, cols).setZero();
+ PlainObjectType::Map(const_ptr, rows, cols).sum();
+ PlainObjectType::MapAligned(const_ptr, rows, cols).sum();
+
+ PlainObjectType::Map(ptr, rows, cols, InnerStride<>(i)).setZero();
+ PlainObjectType::MapAligned(ptr, rows, cols, InnerStride<>(i)).setZero();
+ PlainObjectType::Map(const_ptr, rows, cols, InnerStride<>(i)).sum();
+ PlainObjectType::MapAligned(const_ptr, rows, cols, InnerStride<>(i)).sum();
+
+ PlainObjectType::Map(ptr, rows, cols, InnerStride<2>()).setZero();
+ PlainObjectType::MapAligned(ptr, rows, cols, InnerStride<3>()).setZero();
+ PlainObjectType::Map(const_ptr, rows, cols, InnerStride<4>()).sum();
+ PlainObjectType::MapAligned(const_ptr, rows, cols, InnerStride<5>()).sum();
+
+ PlainObjectType::Map(ptr, rows, cols, OuterStride<>(i)).setZero();
+ PlainObjectType::MapAligned(ptr, rows, cols, OuterStride<>(i)).setZero();
+ PlainObjectType::Map(const_ptr, rows, cols, OuterStride<>(i)).sum();
+ PlainObjectType::MapAligned(const_ptr, rows, cols, OuterStride<>(i)).sum();
+
+ PlainObjectType::Map(ptr, rows, cols, OuterStride<2>()).setZero();
+ PlainObjectType::MapAligned(ptr, rows, cols, OuterStride<3>()).setZero();
+ PlainObjectType::Map(const_ptr, rows, cols, OuterStride<4>()).sum();
+ PlainObjectType::MapAligned(const_ptr, rows, cols, OuterStride<5>()).sum();
+
+ PlainObjectType::Map(ptr, rows, cols, Stride<Dynamic, Dynamic>(i,j)).setZero();
+ PlainObjectType::MapAligned(ptr, rows, cols, Stride<2,Dynamic>(2,i)).setZero();
+ PlainObjectType::Map(const_ptr, rows, cols, Stride<Dynamic,3>(i,3)).sum();
+ PlainObjectType::MapAligned(const_ptr, rows, cols, Stride<Dynamic, Dynamic>(i,j)).sum();
+
+ PlainObjectType::Map(ptr, rows, cols, Stride<2,3>()).setZero();
+ PlainObjectType::MapAligned(ptr, rows, cols, Stride<3,4>()).setZero();
+ PlainObjectType::Map(const_ptr, rows, cols, Stride<2,4>()).sum();
+ PlainObjectType::MapAligned(const_ptr, rows, cols, Stride<5,3>()).sum();
+ }
+};
+
+template<typename PlainObjectType>
+struct mapstaticmethods_impl<PlainObjectType, true, true>
+{
+ static void run(const PlainObjectType& v)
+ {
+ Index size = v.size();
+
+ int i = internal::random<int>(2,5);
+
+ PlainObjectType::Map(ptr, size).setZero();
+ PlainObjectType::MapAligned(ptr, size).setZero();
+ PlainObjectType::Map(const_ptr, size).sum();
+ PlainObjectType::MapAligned(const_ptr, size).sum();
+
+ PlainObjectType::Map(ptr, size, InnerStride<>(i)).setZero();
+ PlainObjectType::MapAligned(ptr, size, InnerStride<>(i)).setZero();
+ PlainObjectType::Map(const_ptr, size, InnerStride<>(i)).sum();
+ PlainObjectType::MapAligned(const_ptr, size, InnerStride<>(i)).sum();
+
+ PlainObjectType::Map(ptr, size, InnerStride<2>()).setZero();
+ PlainObjectType::MapAligned(ptr, size, InnerStride<3>()).setZero();
+ PlainObjectType::Map(const_ptr, size, InnerStride<4>()).sum();
+ PlainObjectType::MapAligned(const_ptr, size, InnerStride<5>()).sum();
+ }
+};
+
+template<typename PlainObjectType>
+void mapstaticmethods(const PlainObjectType& m)
+{
+ mapstaticmethods_impl<PlainObjectType>::run(m);
+ VERIFY(true); // just to avoid 'unused function' warning
+}
+
+EIGEN_DECLARE_TEST(mapstaticmethods)
+{
+ ptr = internal::aligned_new<float>(1000);
+ for(int i = 0; i < 1000; i++) ptr[i] = float(i);
+
+ const_ptr = ptr;
+
+ CALL_SUBTEST_1(( mapstaticmethods(Matrix<float, 1, 1>()) ));
+ CALL_SUBTEST_1(( mapstaticmethods(Vector2f()) ));
+ CALL_SUBTEST_2(( mapstaticmethods(Vector3f()) ));
+ CALL_SUBTEST_2(( mapstaticmethods(Matrix2f()) ));
+ CALL_SUBTEST_3(( mapstaticmethods(Matrix4f()) ));
+ CALL_SUBTEST_3(( mapstaticmethods(Array4f()) ));
+ CALL_SUBTEST_4(( mapstaticmethods(Array3f()) ));
+ CALL_SUBTEST_4(( mapstaticmethods(Array33f()) ));
+ CALL_SUBTEST_5(( mapstaticmethods(Array44f()) ));
+ CALL_SUBTEST_5(( mapstaticmethods(VectorXf(1)) ));
+ CALL_SUBTEST_5(( mapstaticmethods(VectorXf(8)) ));
+ CALL_SUBTEST_6(( mapstaticmethods(MatrixXf(1,1)) ));
+ CALL_SUBTEST_6(( mapstaticmethods(MatrixXf(5,7)) ));
+ CALL_SUBTEST_7(( mapstaticmethods(ArrayXf(1)) ));
+ CALL_SUBTEST_7(( mapstaticmethods(ArrayXf(5)) ));
+ CALL_SUBTEST_8(( mapstaticmethods(ArrayXXf(1,1)) ));
+ CALL_SUBTEST_8(( mapstaticmethods(ArrayXXf(8,6)) ));
+
+ internal::aligned_delete(ptr, 1000);
+}
+
diff --git a/test/mapstride.cpp b/test/mapstride.cpp
new file mode 100644
index 0000000..42ceb0c
--- /dev/null
+++ b/test/mapstride.cpp
@@ -0,0 +1,263 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2010 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "main.h"
+
+template<int Alignment,typename VectorType> void map_class_vector(const VectorType& m)
+{
+ typedef typename VectorType::Scalar Scalar;
+
+ Index size = m.size();
+
+ VectorType v = VectorType::Random(size);
+
+ Index arraysize = 3*size;
+
+ Scalar* a_array = internal::aligned_new<Scalar>(arraysize+1);
+ Scalar* array = a_array;
+ if(Alignment!=Aligned)
+ array = (Scalar*)(internal::IntPtr(a_array) + (internal::packet_traits<Scalar>::AlignedOnScalar?sizeof(Scalar):sizeof(typename NumTraits<Scalar>::Real)));
+
+ {
+ Map<VectorType, Alignment, InnerStride<3> > map(array, size);
+ map = v;
+ for(int i = 0; i < size; ++i)
+ {
+ VERIFY_IS_EQUAL(array[3*i], v[i]);
+ VERIFY_IS_EQUAL(map[i], v[i]);
+ }
+ }
+
+ {
+ Map<VectorType, Unaligned, InnerStride<Dynamic> > map(array, size, InnerStride<Dynamic>(2));
+ map = v;
+ for(int i = 0; i < size; ++i)
+ {
+ VERIFY_IS_EQUAL(array[2*i], v[i]);
+ VERIFY_IS_EQUAL(map[i], v[i]);
+ }
+ }
+
+ internal::aligned_delete(a_array, arraysize+1);
+}
+
+template<int Alignment,typename MatrixType> void map_class_matrix(const MatrixType& _m)
+{
+ typedef typename MatrixType::Scalar Scalar;
+
+ Index rows = _m.rows(), cols = _m.cols();
+
+ MatrixType m = MatrixType::Random(rows,cols);
+ Scalar s1 = internal::random<Scalar>();
+
+ Index arraysize = 4*(rows+4)*(cols+4);
+
+ Scalar* a_array1 = internal::aligned_new<Scalar>(arraysize+1);
+ Scalar* array1 = a_array1;
+ if(Alignment!=Aligned)
+ array1 = (Scalar*)(internal::IntPtr(a_array1) + (internal::packet_traits<Scalar>::AlignedOnScalar?sizeof(Scalar):sizeof(typename NumTraits<Scalar>::Real)));
+
+ Scalar a_array2[256];
+ Scalar* array2 = a_array2;
+ if(Alignment!=Aligned) {
+ array2 = (Scalar*)(internal::IntPtr(a_array2) + (internal::packet_traits<Scalar>::AlignedOnScalar?sizeof(Scalar):sizeof(typename NumTraits<Scalar>::Real)));
+ } else {
+ // In case there is no alignment, default to pointing to the start.
+ constexpr int alignment = (std::max<int>)(EIGEN_MAX_ALIGN_BYTES, 1);
+ array2 = (Scalar*)(((internal::UIntPtr(a_array2)+alignment-1)/alignment)*alignment);
+ }
+ Index maxsize2 = a_array2 - array2 + 256;
+
+ // test no inner stride and some dynamic outer stride
+ for(int k=0; k<2; ++k)
+ {
+ if(k==1 && (m.innerSize()+1)*m.outerSize() > maxsize2)
+ break;
+ Scalar* array = (k==0 ? array1 : array2);
+
+ Map<MatrixType, Alignment, OuterStride<Dynamic> > map(array, rows, cols, OuterStride<Dynamic>(m.innerSize()+1));
+ map = m;
+ VERIFY(map.outerStride() == map.innerSize()+1);
+ for(int i = 0; i < m.outerSize(); ++i)
+ for(int j = 0; j < m.innerSize(); ++j)
+ {
+ VERIFY_IS_EQUAL(array[map.outerStride()*i+j], m.coeffByOuterInner(i,j));
+ VERIFY_IS_EQUAL(map.coeffByOuterInner(i,j), m.coeffByOuterInner(i,j));
+ }
+ VERIFY_IS_APPROX(s1*map,s1*m);
+ map *= s1;
+ VERIFY_IS_APPROX(map,s1*m);
+ }
+
+ // test no inner stride and an outer stride of +4. This is quite important as for fixed-size matrices,
+ // this allows to hit the special case where it's vectorizable.
+ for(int k=0; k<2; ++k)
+ {
+ if(k==1 && (m.innerSize()+4)*m.outerSize() > maxsize2)
+ break;
+ Scalar* array = (k==0 ? array1 : array2);
+
+ enum {
+ InnerSize = MatrixType::InnerSizeAtCompileTime,
+ OuterStrideAtCompileTime = InnerSize==Dynamic ? Dynamic : InnerSize+4
+ };
+ Map<MatrixType, Alignment, OuterStride<OuterStrideAtCompileTime> >
+ map(array, rows, cols, OuterStride<OuterStrideAtCompileTime>(m.innerSize()+4));
+ map = m;
+ VERIFY(map.outerStride() == map.innerSize()+4);
+ for(int i = 0; i < m.outerSize(); ++i)
+ for(int j = 0; j < m.innerSize(); ++j)
+ {
+ VERIFY_IS_EQUAL(array[map.outerStride()*i+j], m.coeffByOuterInner(i,j));
+ VERIFY_IS_EQUAL(map.coeffByOuterInner(i,j), m.coeffByOuterInner(i,j));
+ }
+ VERIFY_IS_APPROX(s1*map,s1*m);
+ map *= s1;
+ VERIFY_IS_APPROX(map,s1*m);
+ }
+
+ // test both inner stride and outer stride
+ for(int k=0; k<2; ++k)
+ {
+ if(k==1 && (2*m.innerSize()+1)*(m.outerSize()*2) > maxsize2)
+ break;
+ Scalar* array = (k==0 ? array1 : array2);
+
+ Map<MatrixType, Alignment, Stride<Dynamic,Dynamic> > map(array, rows, cols, Stride<Dynamic,Dynamic>(2*m.innerSize()+1, 2));
+ map = m;
+ VERIFY(map.outerStride() == 2*map.innerSize()+1);
+ VERIFY(map.innerStride() == 2);
+ for(int i = 0; i < m.outerSize(); ++i)
+ for(int j = 0; j < m.innerSize(); ++j)
+ {
+ VERIFY_IS_EQUAL(array[map.outerStride()*i+map.innerStride()*j], m.coeffByOuterInner(i,j));
+ VERIFY_IS_EQUAL(map.coeffByOuterInner(i,j), m.coeffByOuterInner(i,j));
+ }
+ VERIFY_IS_APPROX(s1*map,s1*m);
+ map *= s1;
+ VERIFY_IS_APPROX(map,s1*m);
+ }
+
+ // test inner stride and no outer stride
+ for(int k=0; k<2; ++k)
+ {
+ if(k==1 && (m.innerSize()*2)*m.outerSize() > maxsize2)
+ break;
+ Scalar* array = (k==0 ? array1 : array2);
+
+ Map<MatrixType, Alignment, InnerStride<Dynamic> > map(array, rows, cols, InnerStride<Dynamic>(2));
+ map = m;
+ VERIFY(map.outerStride() == map.innerSize()*2);
+ for(int i = 0; i < m.outerSize(); ++i)
+ for(int j = 0; j < m.innerSize(); ++j)
+ {
+ VERIFY_IS_EQUAL(array[map.innerSize()*i*2+j*2], m.coeffByOuterInner(i,j));
+ VERIFY_IS_EQUAL(map.coeffByOuterInner(i,j), m.coeffByOuterInner(i,j));
+ }
+ VERIFY_IS_APPROX(s1*map,s1*m);
+ map *= s1;
+ VERIFY_IS_APPROX(map,s1*m);
+ }
+
+ // test negative strides
+ {
+ Matrix<Scalar,Dynamic,1>::Map(a_array1, arraysize+1).setRandom();
+ Index outerstride = m.innerSize()+4;
+ Scalar* array = array1;
+
+ {
+ Map<MatrixType, Alignment, OuterStride<> > map1(array, rows, cols, OuterStride<>( outerstride));
+ Map<MatrixType, Unaligned, OuterStride<> > map2(array+(m.outerSize()-1)*outerstride, rows, cols, OuterStride<>(-outerstride));
+ if(MatrixType::IsRowMajor) VERIFY_IS_APPROX(map1.colwise().reverse(), map2);
+ else VERIFY_IS_APPROX(map1.rowwise().reverse(), map2);
+ }
+
+ {
+ Map<MatrixType, Alignment, OuterStride<> > map1(array, rows, cols, OuterStride<>( outerstride));
+ Map<MatrixType, Unaligned, Stride<Dynamic,Dynamic> > map2(array+(m.outerSize()-1)*outerstride+m.innerSize()-1, rows, cols, Stride<Dynamic,Dynamic>(-outerstride,-1));
+ VERIFY_IS_APPROX(map1.reverse(), map2);
+ }
+
+ {
+ Map<MatrixType, Alignment, OuterStride<> > map1(array, rows, cols, OuterStride<>( outerstride));
+ Map<MatrixType, Unaligned, Stride<Dynamic,-1> > map2(array+(m.outerSize()-1)*outerstride+m.innerSize()-1, rows, cols, Stride<Dynamic,-1>(-outerstride,-1));
+ VERIFY_IS_APPROX(map1.reverse(), map2);
+ }
+ }
+
+ internal::aligned_delete(a_array1, arraysize+1);
+}
+
+// Additional tests for inner-stride but no outer-stride
+template<int>
+void bug1453()
+{
+ const int data[] = {0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31};
+ typedef Matrix<int,Dynamic,Dynamic,RowMajor> RowMatrixXi;
+ typedef Matrix<int,2,3,ColMajor> ColMatrix23i;
+ typedef Matrix<int,3,2,ColMajor> ColMatrix32i;
+ typedef Matrix<int,2,3,RowMajor> RowMatrix23i;
+ typedef Matrix<int,3,2,RowMajor> RowMatrix32i;
+
+ VERIFY_IS_APPROX(MatrixXi::Map(data, 2, 3, InnerStride<2>()), MatrixXi::Map(data, 2, 3, Stride<4,2>()));
+ VERIFY_IS_APPROX(MatrixXi::Map(data, 2, 3, InnerStride<>(2)), MatrixXi::Map(data, 2, 3, Stride<4,2>()));
+ VERIFY_IS_APPROX(MatrixXi::Map(data, 3, 2, InnerStride<2>()), MatrixXi::Map(data, 3, 2, Stride<6,2>()));
+ VERIFY_IS_APPROX(MatrixXi::Map(data, 3, 2, InnerStride<>(2)), MatrixXi::Map(data, 3, 2, Stride<6,2>()));
+
+ VERIFY_IS_APPROX(RowMatrixXi::Map(data, 2, 3, InnerStride<2>()), RowMatrixXi::Map(data, 2, 3, Stride<6,2>()));
+ VERIFY_IS_APPROX(RowMatrixXi::Map(data, 2, 3, InnerStride<>(2)), RowMatrixXi::Map(data, 2, 3, Stride<6,2>()));
+ VERIFY_IS_APPROX(RowMatrixXi::Map(data, 3, 2, InnerStride<2>()), RowMatrixXi::Map(data, 3, 2, Stride<4,2>()));
+ VERIFY_IS_APPROX(RowMatrixXi::Map(data, 3, 2, InnerStride<>(2)), RowMatrixXi::Map(data, 3, 2, Stride<4,2>()));
+
+ VERIFY_IS_APPROX(ColMatrix23i::Map(data, InnerStride<2>()), MatrixXi::Map(data, 2, 3, Stride<4,2>()));
+ VERIFY_IS_APPROX(ColMatrix23i::Map(data, InnerStride<>(2)), MatrixXi::Map(data, 2, 3, Stride<4,2>()));
+ VERIFY_IS_APPROX(ColMatrix32i::Map(data, InnerStride<2>()), MatrixXi::Map(data, 3, 2, Stride<6,2>()));
+ VERIFY_IS_APPROX(ColMatrix32i::Map(data, InnerStride<>(2)), MatrixXi::Map(data, 3, 2, Stride<6,2>()));
+
+ VERIFY_IS_APPROX(RowMatrix23i::Map(data, InnerStride<2>()), RowMatrixXi::Map(data, 2, 3, Stride<6,2>()));
+ VERIFY_IS_APPROX(RowMatrix23i::Map(data, InnerStride<>(2)), RowMatrixXi::Map(data, 2, 3, Stride<6,2>()));
+ VERIFY_IS_APPROX(RowMatrix32i::Map(data, InnerStride<2>()), RowMatrixXi::Map(data, 3, 2, Stride<4,2>()));
+ VERIFY_IS_APPROX(RowMatrix32i::Map(data, InnerStride<>(2)), RowMatrixXi::Map(data, 3, 2, Stride<4,2>()));
+}
+
+EIGEN_DECLARE_TEST(mapstride)
+{
+ for(int i = 0; i < g_repeat; i++) {
+ int maxn = 3;
+ CALL_SUBTEST_1( map_class_vector<Aligned>(Matrix<float, 1, 1>()) );
+ CALL_SUBTEST_1( map_class_vector<Unaligned>(Matrix<float, 1, 1>()) );
+ CALL_SUBTEST_2( map_class_vector<Aligned>(Vector4d()) );
+ CALL_SUBTEST_2( map_class_vector<Unaligned>(Vector4d()) );
+ CALL_SUBTEST_3( map_class_vector<Aligned>(RowVector4f()) );
+ CALL_SUBTEST_3( map_class_vector<Unaligned>(RowVector4f()) );
+ CALL_SUBTEST_4( map_class_vector<Aligned>(VectorXcf(internal::random<int>(1,maxn))) );
+ CALL_SUBTEST_4( map_class_vector<Unaligned>(VectorXcf(internal::random<int>(1,maxn))) );
+ CALL_SUBTEST_5( map_class_vector<Aligned>(VectorXi(internal::random<int>(1,maxn))) );
+ CALL_SUBTEST_5( map_class_vector<Unaligned>(VectorXi(internal::random<int>(1,maxn))) );
+
+ CALL_SUBTEST_1( map_class_matrix<Aligned>(Matrix<float, 1, 1>()) );
+ CALL_SUBTEST_1( map_class_matrix<Unaligned>(Matrix<float, 1, 1>()) );
+ CALL_SUBTEST_2( map_class_matrix<Aligned>(Matrix4d()) );
+ CALL_SUBTEST_2( map_class_matrix<Unaligned>(Matrix4d()) );
+ CALL_SUBTEST_3( map_class_matrix<Aligned>(Matrix<float,3,5>()) );
+ CALL_SUBTEST_3( map_class_matrix<Unaligned>(Matrix<float,3,5>()) );
+ CALL_SUBTEST_3( map_class_matrix<Aligned>(Matrix<float,4,8>()) );
+ CALL_SUBTEST_3( map_class_matrix<Unaligned>(Matrix<float,4,8>()) );
+ CALL_SUBTEST_4( map_class_matrix<Aligned>(MatrixXcf(internal::random<int>(1,maxn),internal::random<int>(1,maxn))) );
+ CALL_SUBTEST_4( map_class_matrix<Unaligned>(MatrixXcf(internal::random<int>(1,maxn),internal::random<int>(1,maxn))) );
+ CALL_SUBTEST_5( map_class_matrix<Aligned>(MatrixXi(internal::random<int>(1,maxn),internal::random<int>(1,maxn))) );
+ CALL_SUBTEST_5( map_class_matrix<Unaligned>(MatrixXi(internal::random<int>(1,maxn),internal::random<int>(1,maxn))) );
+ CALL_SUBTEST_6( map_class_matrix<Aligned>(MatrixXcd(internal::random<int>(1,maxn),internal::random<int>(1,maxn))) );
+ CALL_SUBTEST_6( map_class_matrix<Unaligned>(MatrixXcd(internal::random<int>(1,maxn),internal::random<int>(1,maxn))) );
+
+ CALL_SUBTEST_5( bug1453<0>() );
+
+ TEST_SET_BUT_UNUSED_VARIABLE(maxn);
+ }
+}
diff --git a/test/meta.cpp b/test/meta.cpp
new file mode 100644
index 0000000..cac7af1
--- /dev/null
+++ b/test/meta.cpp
@@ -0,0 +1,133 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "main.h"
+
+template<typename From, typename To>
+bool check_is_convertible(const From&, const To&)
+{
+ return internal::is_convertible<From,To>::value;
+}
+
+struct FooReturnType {
+ typedef int ReturnType;
+};
+
+struct MyInterface {
+ virtual void func() = 0;
+ virtual ~MyInterface() {}
+};
+struct MyImpl : public MyInterface {
+ void func() {}
+};
+
+EIGEN_DECLARE_TEST(meta)
+{
+ VERIFY(( internal::is_same<float,float>::value));
+ VERIFY((!internal::is_same<float,double>::value));
+ VERIFY((!internal::is_same<float,float&>::value));
+ VERIFY((!internal::is_same<float,const float&>::value));
+
+ VERIFY(( internal::is_same<float,internal::remove_all_t<const float&> >::value));
+ VERIFY(( internal::is_same<float,internal::remove_all_t<const float*> >::value));
+ VERIFY(( internal::is_same<float,internal::remove_all_t<const float*&> >::value));
+ VERIFY(( internal::is_same<float,internal::remove_all_t<float**> >::value));
+ VERIFY(( internal::is_same<float,internal::remove_all_t<float**&> >::value));
+ VERIFY(( internal::is_same<float,internal::remove_all_t<float* const *&> >::value));
+ VERIFY(( internal::is_same<float,internal::remove_all_t<float* const> >::value));
+
+ // test add_const_on_value_type
+ VERIFY(( internal::is_same< internal::add_const_on_value_type_t<float&>, float const& >::value));
+ VERIFY(( internal::is_same< internal::add_const_on_value_type_t<float*>, float const* >::value));
+
+ VERIFY(( internal::is_same< internal::add_const_on_value_type_t<float>, const float >::value));
+ VERIFY(( internal::is_same< internal::add_const_on_value_type_t<const float>, const float >::value));
+
+ VERIFY(( internal::is_same< internal::add_const_on_value_type_t<const float* const>, const float* const>::value));
+ VERIFY(( internal::is_same< internal::add_const_on_value_type_t<float* const>, const float* const>::value));
+
+ // is_convertible
+ STATIC_CHECK(( internal::is_convertible<float,double>::value ));
+ STATIC_CHECK(( internal::is_convertible<int,double>::value ));
+ STATIC_CHECK(( internal::is_convertible<int, short>::value ));
+ STATIC_CHECK(( internal::is_convertible<short, int>::value ));
+ STATIC_CHECK(( internal::is_convertible<double,int>::value ));
+ STATIC_CHECK(( internal::is_convertible<double,std::complex<double> >::value ));
+ STATIC_CHECK((!internal::is_convertible<std::complex<double>,double>::value ));
+ STATIC_CHECK(( internal::is_convertible<Array33f,Matrix3f>::value ));
+ STATIC_CHECK(( internal::is_convertible<Matrix3f&,Matrix3f>::value ));
+ STATIC_CHECK(( internal::is_convertible<Matrix3f&,Matrix3f&>::value ));
+ STATIC_CHECK(( internal::is_convertible<Matrix3f&,const Matrix3f&>::value ));
+ STATIC_CHECK(( internal::is_convertible<const Matrix3f&,Matrix3f>::value ));
+ STATIC_CHECK(( internal::is_convertible<const Matrix3f&,const Matrix3f&>::value ));
+ STATIC_CHECK((!internal::is_convertible<const Matrix3f&,Matrix3f&>::value ));
+ STATIC_CHECK((!internal::is_convertible<const Matrix3f,Matrix3f&>::value ));
+ STATIC_CHECK(!( internal::is_convertible<Matrix3f,Matrix3f&>::value ));
+
+ STATIC_CHECK(!( internal::is_convertible<int,int&>::value ));
+ STATIC_CHECK(( internal::is_convertible<const int,const int& >::value ));
+
+ //STATIC_CHECK((!internal::is_convertible<Matrix3f,Matrix3d>::value )); //does not even compile because the conversion is prevented by a static assertion
+ STATIC_CHECK((!internal::is_convertible<Array33f,int>::value ));
+ STATIC_CHECK((!internal::is_convertible<MatrixXf,float>::value ));
+ {
+ float f = 0.0f;
+ MatrixXf A, B;
+ VectorXf a, b;
+ VERIFY(( check_is_convertible(a.dot(b), f) ));
+ VERIFY(( check_is_convertible(a.transpose()*b, f) ));
+ VERIFY((!check_is_convertible(A*B, f) ));
+ VERIFY(( check_is_convertible(A*B, A) ));
+ }
+
+ #if (EIGEN_COMP_GNUC && EIGEN_COMP_GNUC <= 99) \
+ || (EIGEN_COMP_CLANG && EIGEN_COMP_CLANG <= 909) \
+ || (EIGEN_COMP_MSVC && EIGEN_COMP_MSVC <=1914)
+ // See http://eigen.tuxfamily.org/bz/show_bug.cgi?id=1752,
+ // basically, a fix in the c++ standard breaks our c++98 implementation
+ // of is_convertible for abstract classes.
+ // So the following tests are expected to fail with recent compilers.
+
+ STATIC_CHECK(( !internal::is_convertible<MyInterface, MyImpl>::value ));
+ STATIC_CHECK(( !internal::is_convertible<MyImpl, MyInterface>::value ));
+ STATIC_CHECK(( internal::is_convertible<MyImpl, const MyInterface&>::value ));
+
+ #endif
+
+ {
+ int i = 0;
+ VERIFY(( check_is_convertible(fix<3>(), i) ));
+ VERIFY((!check_is_convertible(i, fix<DynamicIndex>()) ));
+ }
+
+
+ VERIFY(( internal::has_ReturnType<FooReturnType>::value ));
+ VERIFY(( internal::has_ReturnType<ScalarBinaryOpTraits<int,int> >::value ));
+ VERIFY(( !internal::has_ReturnType<MatrixXf>::value ));
+ VERIFY(( !internal::has_ReturnType<int>::value ));
+
+ VERIFY(internal::meta_sqrt<1>::ret == 1);
+ #define VERIFY_META_SQRT(X) VERIFY(internal::meta_sqrt<X>::ret == int(std::sqrt(double(X))))
+ VERIFY_META_SQRT(2);
+ VERIFY_META_SQRT(3);
+ VERIFY_META_SQRT(4);
+ VERIFY_META_SQRT(5);
+ VERIFY_META_SQRT(6);
+ VERIFY_META_SQRT(8);
+ VERIFY_META_SQRT(9);
+ VERIFY_META_SQRT(15);
+ VERIFY_META_SQRT(16);
+ VERIFY_META_SQRT(17);
+ VERIFY_META_SQRT(255);
+ VERIFY_META_SQRT(256);
+ VERIFY_META_SQRT(257);
+ VERIFY_META_SQRT(1023);
+ VERIFY_META_SQRT(1024);
+ VERIFY_META_SQRT(1025);
+}
diff --git a/test/metis_support.cpp b/test/metis_support.cpp
new file mode 100644
index 0000000..b490dac
--- /dev/null
+++ b/test/metis_support.cpp
@@ -0,0 +1,25 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2012 Désiré Nuentsa-Wakam <desire.nuentsa_wakam@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "sparse_solver.h"
+#include <Eigen/SparseLU>
+#include <Eigen/MetisSupport>
+#include <unsupported/Eigen/SparseExtra>
+
+template<typename T> void test_metis_T()
+{
+ SparseLU<SparseMatrix<T, ColMajor>, MetisOrdering<int> > sparselu_metis;
+
+ check_sparse_square_solving(sparselu_metis);
+}
+
+EIGEN_DECLARE_TEST(metis_support)
+{
+ CALL_SUBTEST_1(test_metis_T<double>());
+}
diff --git a/test/miscmatrices.cpp b/test/miscmatrices.cpp
new file mode 100644
index 0000000..e71712f
--- /dev/null
+++ b/test/miscmatrices.cpp
@@ -0,0 +1,46 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "main.h"
+
+template<typename MatrixType> void miscMatrices(const MatrixType& m)
+{
+ /* this test covers the following files:
+ DiagonalMatrix.h Ones.h
+ */
+ typedef typename MatrixType::Scalar Scalar;
+ typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> VectorType;
+ Index rows = m.rows();
+ Index cols = m.cols();
+
+ Index r = internal::random<Index>(0, rows-1), r2 = internal::random<Index>(0, rows-1), c = internal::random<Index>(0, cols-1);
+ VERIFY_IS_APPROX(MatrixType::Ones(rows,cols)(r,c), static_cast<Scalar>(1));
+ MatrixType m1 = MatrixType::Ones(rows,cols);
+ VERIFY_IS_APPROX(m1(r,c), static_cast<Scalar>(1));
+ VectorType v1 = VectorType::Random(rows);
+ v1[0];
+ Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime>
+ square(v1.asDiagonal());
+ if(r==r2) VERIFY_IS_APPROX(square(r,r2), v1[r]);
+ else VERIFY_IS_MUCH_SMALLER_THAN(square(r,r2), static_cast<Scalar>(1));
+ square = MatrixType::Zero(rows, rows);
+ square.diagonal() = VectorType::Ones(rows);
+ VERIFY_IS_APPROX(square, MatrixType::Identity(rows, rows));
+}
+
+EIGEN_DECLARE_TEST(miscmatrices)
+{
+ for(int i = 0; i < g_repeat; i++) {
+ CALL_SUBTEST_1( miscMatrices(Matrix<float, 1, 1>()) );
+ CALL_SUBTEST_2( miscMatrices(Matrix4d()) );
+ CALL_SUBTEST_3( miscMatrices(MatrixXcf(3, 3)) );
+ CALL_SUBTEST_4( miscMatrices(MatrixXi(8, 12)) );
+ CALL_SUBTEST_5( miscMatrices(MatrixXcd(20, 20)) );
+ }
+}
diff --git a/test/mixingtypes.cpp b/test/mixingtypes.cpp
new file mode 100644
index 0000000..fe760b7
--- /dev/null
+++ b/test/mixingtypes.cpp
@@ -0,0 +1,299 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2015 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#if defined(EIGEN_TEST_PART_7)
+
+// ignore double-promotion diagnostic for clang and gcc, if we check for static assertion anyway:
+// TODO do the same for MSVC?
+#if defined(__clang__)
+# if (__clang_major__ * 100 + __clang_minor__) >= 308
+# pragma clang diagnostic ignored "-Wdouble-promotion"
+# endif
+#elif defined(__GNUC__)
+ // TODO is there a minimal GCC version for this? At least g++-4.7 seems to be fine with this.
+# pragma GCC diagnostic ignored "-Wdouble-promotion"
+#endif
+
+#endif
+
+
+
+#if defined(EIGEN_TEST_PART_1) || defined(EIGEN_TEST_PART_2) || defined(EIGEN_TEST_PART_3)
+
+#ifndef EIGEN_DONT_VECTORIZE
+#define EIGEN_DONT_VECTORIZE
+#endif
+
+#endif
+
+static bool g_called;
+#define EIGEN_SCALAR_BINARY_OP_PLUGIN { g_called |= (!internal::is_same<LhsScalar,RhsScalar>::value); }
+
+#include "main.h"
+
+using namespace std;
+
+#define VERIFY_MIX_SCALAR(XPR,REF) \
+ g_called = false; \
+ VERIFY_IS_APPROX(XPR,REF); \
+ VERIFY( g_called && #XPR" not properly optimized");
+
+template<int SizeAtCompileType> void mixingtypes(int size = SizeAtCompileType)
+{
+ typedef std::complex<float> CF;
+ typedef std::complex<double> CD;
+ typedef Matrix<float, SizeAtCompileType, SizeAtCompileType> Mat_f;
+ typedef Matrix<double, SizeAtCompileType, SizeAtCompileType> Mat_d;
+ typedef Matrix<std::complex<float>, SizeAtCompileType, SizeAtCompileType> Mat_cf;
+ typedef Matrix<std::complex<double>, SizeAtCompileType, SizeAtCompileType> Mat_cd;
+ typedef Matrix<float, SizeAtCompileType, 1> Vec_f;
+ typedef Matrix<double, SizeAtCompileType, 1> Vec_d;
+ typedef Matrix<std::complex<float>, SizeAtCompileType, 1> Vec_cf;
+ typedef Matrix<std::complex<double>, SizeAtCompileType, 1> Vec_cd;
+
+ Mat_f mf = Mat_f::Random(size,size);
+ Mat_d md = mf.template cast<double>();
+ //Mat_d rd = md;
+ Mat_cf mcf = Mat_cf::Random(size,size);
+ Mat_cd mcd = mcf.template cast<complex<double> >();
+ Mat_cd rcd = mcd;
+ Vec_f vf = Vec_f::Random(size,1);
+ Vec_d vd = vf.template cast<double>();
+ Vec_cf vcf = Vec_cf::Random(size,1);
+ Vec_cd vcd = vcf.template cast<complex<double> >();
+ float sf = internal::random<float>();
+ double sd = internal::random<double>();
+ complex<float> scf = internal::random<complex<float> >();
+ complex<double> scd = internal::random<complex<double> >();
+
+ mf+mf;
+
+ float epsf = std::sqrt(std::numeric_limits<float> ::min EIGEN_EMPTY ());
+ double epsd = std::sqrt(std::numeric_limits<double>::min EIGEN_EMPTY ());
+
+ while(std::abs(sf )<epsf) sf = internal::random<float>();
+ while(std::abs(sd )<epsd) sd = internal::random<double>();
+ while(std::abs(scf)<epsf) scf = internal::random<CF>();
+ while(std::abs(scd)<epsd) scd = internal::random<CD>();
+
+ // check scalar products
+ VERIFY_MIX_SCALAR(vcf * sf , vcf * complex<float>(sf));
+ VERIFY_MIX_SCALAR(sd * vcd , complex<double>(sd) * vcd);
+ VERIFY_MIX_SCALAR(vf * scf , vf.template cast<complex<float> >() * scf);
+ VERIFY_MIX_SCALAR(scd * vd , scd * vd.template cast<complex<double> >());
+
+ VERIFY_MIX_SCALAR(vcf * 2 , vcf * complex<float>(2));
+ VERIFY_MIX_SCALAR(vcf * 2.1 , vcf * complex<float>(2.1));
+ VERIFY_MIX_SCALAR(2 * vcf, vcf * complex<float>(2));
+ VERIFY_MIX_SCALAR(2.1 * vcf , vcf * complex<float>(2.1));
+
+ // check scalar quotients
+ VERIFY_MIX_SCALAR(vcf / sf , vcf / complex<float>(sf));
+ VERIFY_MIX_SCALAR(vf / scf , vf.template cast<complex<float> >() / scf);
+ VERIFY_MIX_SCALAR(vf.array() / scf, vf.template cast<complex<float> >().array() / scf);
+ VERIFY_MIX_SCALAR(scd / vd.array() , scd / vd.template cast<complex<double> >().array());
+
+ // check scalar increment
+ VERIFY_MIX_SCALAR(vcf.array() + sf , vcf.array() + complex<float>(sf));
+ VERIFY_MIX_SCALAR(sd + vcd.array(), complex<double>(sd) + vcd.array());
+ VERIFY_MIX_SCALAR(vf.array() + scf, vf.template cast<complex<float> >().array() + scf);
+ VERIFY_MIX_SCALAR(scd + vd.array() , scd + vd.template cast<complex<double> >().array());
+
+ // check scalar subtractions
+ VERIFY_MIX_SCALAR(vcf.array() - sf , vcf.array() - complex<float>(sf));
+ VERIFY_MIX_SCALAR(sd - vcd.array(), complex<double>(sd) - vcd.array());
+ VERIFY_MIX_SCALAR(vf.array() - scf, vf.template cast<complex<float> >().array() - scf);
+ VERIFY_MIX_SCALAR(scd - vd.array() , scd - vd.template cast<complex<double> >().array());
+
+ // check scalar powers
+ // NOTE: scalar exponents use a unary op.
+ VERIFY_IS_APPROX( pow(vcf.array(), sf), Eigen::pow(vcf.array(), complex<float>(sf)) );
+ VERIFY_IS_APPROX( vcf.array().pow(sf) , Eigen::pow(vcf.array(), complex<float>(sf)) );
+ VERIFY_MIX_SCALAR( pow(sd, vcd.array()), Eigen::pow(complex<double>(sd), vcd.array()) );
+ VERIFY_IS_APPROX( Eigen::pow(vf.array(), scf), Eigen::pow(vf.template cast<complex<float> >().array(), scf) );
+ VERIFY_IS_APPROX( vf.array().pow(scf) , Eigen::pow(vf.template cast<complex<float> >().array(), scf) );
+ VERIFY_MIX_SCALAR( Eigen::pow(scd, vd.array()), Eigen::pow(scd, vd.template cast<complex<double> >().array()) );
+
+ // check dot product
+ vf.dot(vf);
+ VERIFY_IS_APPROX(vcf.dot(vf), vcf.dot(vf.template cast<complex<float> >()));
+
+ // check diagonal product
+ VERIFY_IS_APPROX(vf.asDiagonal() * mcf, vf.template cast<complex<float> >().asDiagonal() * mcf);
+ VERIFY_IS_APPROX(vcd.asDiagonal() * md, vcd.asDiagonal() * md.template cast<complex<double> >());
+ VERIFY_IS_APPROX(mcf * vf.asDiagonal(), mcf * vf.template cast<complex<float> >().asDiagonal());
+ VERIFY_IS_APPROX(md * vcd.asDiagonal(), md.template cast<complex<double> >() * vcd.asDiagonal());
+
+ // check inner product
+ VERIFY_IS_APPROX((vf.transpose() * vcf).value(), (vf.template cast<complex<float> >().transpose() * vcf).value());
+
+ // check outer product
+ VERIFY_IS_APPROX((vf * vcf.transpose()).eval(), (vf.template cast<complex<float> >() * vcf.transpose()).eval());
+
+ // coeff wise product
+
+ VERIFY_IS_APPROX((vf * vcf.transpose()).eval(), (vf.template cast<complex<float> >() * vcf.transpose()).eval());
+
+ Mat_cd mcd2 = mcd;
+ VERIFY_IS_APPROX(mcd.array() *= md.array(), mcd2.array() *= md.array().template cast<std::complex<double> >());
+
+ // check matrix-matrix products
+ VERIFY_IS_APPROX(sd*md*mcd, (sd*md).template cast<CD>().eval()*mcd);
+ VERIFY_IS_APPROX(sd*mcd*md, sd*mcd*md.template cast<CD>());
+ VERIFY_IS_APPROX(scd*md*mcd, scd*md.template cast<CD>().eval()*mcd);
+ VERIFY_IS_APPROX(scd*mcd*md, scd*mcd*md.template cast<CD>());
+
+ VERIFY_IS_APPROX(sf*mf*mcf, sf*mf.template cast<CF>()*mcf);
+ VERIFY_IS_APPROX(sf*mcf*mf, sf*mcf*mf.template cast<CF>());
+ VERIFY_IS_APPROX(scf*mf*mcf, scf*mf.template cast<CF>()*mcf);
+ VERIFY_IS_APPROX(scf*mcf*mf, scf*mcf*mf.template cast<CF>());
+
+ VERIFY_IS_APPROX(sd*md.adjoint()*mcd, (sd*md).template cast<CD>().eval().adjoint()*mcd);
+ VERIFY_IS_APPROX(sd*mcd.adjoint()*md, sd*mcd.adjoint()*md.template cast<CD>());
+ VERIFY_IS_APPROX(sd*md.adjoint()*mcd.adjoint(), (sd*md).template cast<CD>().eval().adjoint()*mcd.adjoint());
+ VERIFY_IS_APPROX(sd*mcd.adjoint()*md.adjoint(), sd*mcd.adjoint()*md.template cast<CD>().adjoint());
+ VERIFY_IS_APPROX(sd*md*mcd.adjoint(), (sd*md).template cast<CD>().eval()*mcd.adjoint());
+ VERIFY_IS_APPROX(sd*mcd*md.adjoint(), sd*mcd*md.template cast<CD>().adjoint());
+
+ VERIFY_IS_APPROX(sf*mf.adjoint()*mcf, (sf*mf).template cast<CF>().eval().adjoint()*mcf);
+ VERIFY_IS_APPROX(sf*mcf.adjoint()*mf, sf*mcf.adjoint()*mf.template cast<CF>());
+ VERIFY_IS_APPROX(sf*mf.adjoint()*mcf.adjoint(), (sf*mf).template cast<CF>().eval().adjoint()*mcf.adjoint());
+ VERIFY_IS_APPROX(sf*mcf.adjoint()*mf.adjoint(), sf*mcf.adjoint()*mf.template cast<CF>().adjoint());
+ VERIFY_IS_APPROX(sf*mf*mcf.adjoint(), (sf*mf).template cast<CF>().eval()*mcf.adjoint());
+ VERIFY_IS_APPROX(sf*mcf*mf.adjoint(), sf*mcf*mf.template cast<CF>().adjoint());
+
+ VERIFY_IS_APPROX(sf*mf*vcf, (sf*mf).template cast<CF>().eval()*vcf);
+ VERIFY_IS_APPROX(scf*mf*vcf,(scf*mf.template cast<CF>()).eval()*vcf);
+ VERIFY_IS_APPROX(sf*mcf*vf, sf*mcf*vf.template cast<CF>());
+ VERIFY_IS_APPROX(scf*mcf*vf,scf*mcf*vf.template cast<CF>());
+
+ VERIFY_IS_APPROX(sf*vcf.adjoint()*mf, sf*vcf.adjoint()*mf.template cast<CF>().eval());
+ VERIFY_IS_APPROX(scf*vcf.adjoint()*mf, scf*vcf.adjoint()*mf.template cast<CF>().eval());
+ VERIFY_IS_APPROX(sf*vf.adjoint()*mcf, sf*vf.adjoint().template cast<CF>().eval()*mcf);
+ VERIFY_IS_APPROX(scf*vf.adjoint()*mcf, scf*vf.adjoint().template cast<CF>().eval()*mcf);
+
+ VERIFY_IS_APPROX(sd*md*vcd, (sd*md).template cast<CD>().eval()*vcd);
+ VERIFY_IS_APPROX(scd*md*vcd,(scd*md.template cast<CD>()).eval()*vcd);
+ VERIFY_IS_APPROX(sd*mcd*vd, sd*mcd*vd.template cast<CD>().eval());
+ VERIFY_IS_APPROX(scd*mcd*vd,scd*mcd*vd.template cast<CD>().eval());
+
+ VERIFY_IS_APPROX(sd*vcd.adjoint()*md, sd*vcd.adjoint()*md.template cast<CD>().eval());
+ VERIFY_IS_APPROX(scd*vcd.adjoint()*md, scd*vcd.adjoint()*md.template cast<CD>().eval());
+ VERIFY_IS_APPROX(sd*vd.adjoint()*mcd, sd*vd.adjoint().template cast<CD>().eval()*mcd);
+ VERIFY_IS_APPROX(scd*vd.adjoint()*mcd, scd*vd.adjoint().template cast<CD>().eval()*mcd);
+
+ VERIFY_IS_APPROX( sd*vcd.adjoint()*md.template triangularView<Upper>(), sd*vcd.adjoint()*md.template cast<CD>().eval().template triangularView<Upper>());
+ VERIFY_IS_APPROX(scd*vcd.adjoint()*md.template triangularView<Lower>(), scd*vcd.adjoint()*md.template cast<CD>().eval().template triangularView<Lower>());
+ VERIFY_IS_APPROX( sd*vcd.adjoint()*md.transpose().template triangularView<Upper>(), sd*vcd.adjoint()*md.transpose().template cast<CD>().eval().template triangularView<Upper>());
+ VERIFY_IS_APPROX(scd*vcd.adjoint()*md.transpose().template triangularView<Lower>(), scd*vcd.adjoint()*md.transpose().template cast<CD>().eval().template triangularView<Lower>());
+ VERIFY_IS_APPROX( sd*vd.adjoint()*mcd.template triangularView<Lower>(), sd*vd.adjoint().template cast<CD>().eval()*mcd.template triangularView<Lower>());
+ VERIFY_IS_APPROX(scd*vd.adjoint()*mcd.template triangularView<Upper>(), scd*vd.adjoint().template cast<CD>().eval()*mcd.template triangularView<Upper>());
+ VERIFY_IS_APPROX( sd*vd.adjoint()*mcd.transpose().template triangularView<Lower>(), sd*vd.adjoint().template cast<CD>().eval()*mcd.transpose().template triangularView<Lower>());
+ VERIFY_IS_APPROX(scd*vd.adjoint()*mcd.transpose().template triangularView<Upper>(), scd*vd.adjoint().template cast<CD>().eval()*mcd.transpose().template triangularView<Upper>());
+
+ // Not supported yet: trmm
+// VERIFY_IS_APPROX(sd*mcd*md.template triangularView<Lower>(), sd*mcd*md.template cast<CD>().eval().template triangularView<Lower>());
+// VERIFY_IS_APPROX(scd*mcd*md.template triangularView<Upper>(), scd*mcd*md.template cast<CD>().eval().template triangularView<Upper>());
+// VERIFY_IS_APPROX(sd*md*mcd.template triangularView<Lower>(), sd*md.template cast<CD>().eval()*mcd.template triangularView<Lower>());
+// VERIFY_IS_APPROX(scd*md*mcd.template triangularView<Upper>(), scd*md.template cast<CD>().eval()*mcd.template triangularView<Upper>());
+
+ // Not supported yet: symv
+// VERIFY_IS_APPROX(sd*vcd.adjoint()*md.template selfadjointView<Upper>(), sd*vcd.adjoint()*md.template cast<CD>().eval().template selfadjointView<Upper>());
+// VERIFY_IS_APPROX(scd*vcd.adjoint()*md.template selfadjointView<Lower>(), scd*vcd.adjoint()*md.template cast<CD>().eval().template selfadjointView<Lower>());
+// VERIFY_IS_APPROX(sd*vd.adjoint()*mcd.template selfadjointView<Lower>(), sd*vd.adjoint().template cast<CD>().eval()*mcd.template selfadjointView<Lower>());
+// VERIFY_IS_APPROX(scd*vd.adjoint()*mcd.template selfadjointView<Upper>(), scd*vd.adjoint().template cast<CD>().eval()*mcd.template selfadjointView<Upper>());
+
+ // Not supported yet: symm
+// VERIFY_IS_APPROX(sd*vcd.adjoint()*md.template selfadjointView<Upper>(), sd*vcd.adjoint()*md.template cast<CD>().eval().template selfadjointView<Upper>());
+// VERIFY_IS_APPROX(scd*vcd.adjoint()*md.template selfadjointView<Upper>(), scd*vcd.adjoint()*md.template cast<CD>().eval().template selfadjointView<Upper>());
+// VERIFY_IS_APPROX(sd*vd.adjoint()*mcd.template selfadjointView<Upper>(), sd*vd.adjoint().template cast<CD>().eval()*mcd.template selfadjointView<Upper>());
+// VERIFY_IS_APPROX(scd*vd.adjoint()*mcd.template selfadjointView<Upper>(), scd*vd.adjoint().template cast<CD>().eval()*mcd.template selfadjointView<Upper>());
+
+ rcd.setZero();
+ VERIFY_IS_APPROX(Mat_cd(rcd.template triangularView<Upper>() = sd * mcd * md),
+ Mat_cd((sd * mcd * md.template cast<CD>().eval()).template triangularView<Upper>()));
+ VERIFY_IS_APPROX(Mat_cd(rcd.template triangularView<Upper>() = sd * md * mcd),
+ Mat_cd((sd * md.template cast<CD>().eval() * mcd).template triangularView<Upper>()));
+ VERIFY_IS_APPROX(Mat_cd(rcd.template triangularView<Upper>() = scd * mcd * md),
+ Mat_cd((scd * mcd * md.template cast<CD>().eval()).template triangularView<Upper>()));
+ VERIFY_IS_APPROX(Mat_cd(rcd.template triangularView<Upper>() = scd * md * mcd),
+ Mat_cd((scd * md.template cast<CD>().eval() * mcd).template triangularView<Upper>()));
+
+
+ VERIFY_IS_APPROX( md.array() * mcd.array(), md.template cast<CD>().eval().array() * mcd.array() );
+ VERIFY_IS_APPROX( mcd.array() * md.array(), mcd.array() * md.template cast<CD>().eval().array() );
+
+ VERIFY_IS_APPROX( md.array() + mcd.array(), md.template cast<CD>().eval().array() + mcd.array() );
+ VERIFY_IS_APPROX( mcd.array() + md.array(), mcd.array() + md.template cast<CD>().eval().array() );
+
+ VERIFY_IS_APPROX( md.array() - mcd.array(), md.template cast<CD>().eval().array() - mcd.array() );
+ VERIFY_IS_APPROX( mcd.array() - md.array(), mcd.array() - md.template cast<CD>().eval().array() );
+
+ if(mcd.array().abs().minCoeff()>epsd)
+ {
+ VERIFY_IS_APPROX( md.array() / mcd.array(), md.template cast<CD>().eval().array() / mcd.array() );
+ }
+ if(md.array().abs().minCoeff()>epsd)
+ {
+ VERIFY_IS_APPROX( mcd.array() / md.array(), mcd.array() / md.template cast<CD>().eval().array() );
+ }
+
+ if(md.array().abs().minCoeff()>epsd || mcd.array().abs().minCoeff()>epsd)
+ {
+ VERIFY_IS_APPROX( md.array().pow(mcd.array()), md.template cast<CD>().eval().array().pow(mcd.array()) );
+ VERIFY_IS_APPROX( mcd.array().pow(md.array()), mcd.array().pow(md.template cast<CD>().eval().array()) );
+
+ VERIFY_IS_APPROX( pow(md.array(),mcd.array()), md.template cast<CD>().eval().array().pow(mcd.array()) );
+ VERIFY_IS_APPROX( pow(mcd.array(),md.array()), mcd.array().pow(md.template cast<CD>().eval().array()) );
+ }
+
+ rcd = mcd;
+ VERIFY_IS_APPROX( rcd = md, md.template cast<CD>().eval() );
+ rcd = mcd;
+ VERIFY_IS_APPROX( rcd += md, mcd + md.template cast<CD>().eval() );
+ rcd = mcd;
+ VERIFY_IS_APPROX( rcd -= md, mcd - md.template cast<CD>().eval() );
+ rcd = mcd;
+ VERIFY_IS_APPROX( rcd.array() *= md.array(), mcd.array() * md.template cast<CD>().eval().array() );
+ rcd = mcd;
+ if(md.array().abs().minCoeff()>epsd)
+ {
+ VERIFY_IS_APPROX( rcd.array() /= md.array(), mcd.array() / md.template cast<CD>().eval().array() );
+ }
+
+ rcd = mcd;
+ VERIFY_IS_APPROX( rcd.noalias() += md + mcd*md, mcd + (md.template cast<CD>().eval()) + mcd*(md.template cast<CD>().eval()));
+
+ VERIFY_IS_APPROX( rcd.noalias() = md*md, ((md*md).eval().template cast<CD>()) );
+ rcd = mcd;
+ VERIFY_IS_APPROX( rcd.noalias() += md*md, mcd + ((md*md).eval().template cast<CD>()) );
+ rcd = mcd;
+ VERIFY_IS_APPROX( rcd.noalias() -= md*md, mcd - ((md*md).eval().template cast<CD>()) );
+
+ VERIFY_IS_APPROX( rcd.noalias() = mcd + md*md, mcd + ((md*md).eval().template cast<CD>()) );
+ rcd = mcd;
+ VERIFY_IS_APPROX( rcd.noalias() += mcd + md*md, mcd + mcd + ((md*md).eval().template cast<CD>()) );
+ rcd = mcd;
+ VERIFY_IS_APPROX( rcd.noalias() -= mcd + md*md, - ((md*md).eval().template cast<CD>()) );
+}
+
+EIGEN_DECLARE_TEST(mixingtypes)
+{
+ g_called = false; // Silence -Wunneeded-internal-declaration.
+ for(int i = 0; i < g_repeat; i++) {
+ CALL_SUBTEST_1(mixingtypes<3>());
+ CALL_SUBTEST_2(mixingtypes<4>());
+ CALL_SUBTEST_3(mixingtypes<Dynamic>(internal::random<int>(1,EIGEN_TEST_MAX_SIZE)));
+
+ CALL_SUBTEST_4(mixingtypes<3>());
+ CALL_SUBTEST_5(mixingtypes<4>());
+ CALL_SUBTEST_6(mixingtypes<Dynamic>(internal::random<int>(1,EIGEN_TEST_MAX_SIZE)));
+ }
+}
diff --git a/test/mpl2only.cpp b/test/mpl2only.cpp
new file mode 100644
index 0000000..296350d
--- /dev/null
+++ b/test/mpl2only.cpp
@@ -0,0 +1,24 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2015 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_MPL2_ONLY
+#define EIGEN_MPL2_ONLY
+#endif
+#include <Eigen/Dense>
+#include <Eigen/SparseCore>
+#include <Eigen/SparseLU>
+#include <Eigen/SparseQR>
+#include <Eigen/Sparse>
+#include <Eigen/IterativeLinearSolvers>
+#include <Eigen/Eigen>
+
+int main()
+{
+ return 0;
+}
diff --git a/test/nestbyvalue.cpp b/test/nestbyvalue.cpp
new file mode 100644
index 0000000..3a86bea
--- /dev/null
+++ b/test/nestbyvalue.cpp
@@ -0,0 +1,37 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2019 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#define TEST_ENABLE_TEMPORARY_TRACKING
+
+#include "main.h"
+
+typedef NestByValue<MatrixXd> CpyMatrixXd;
+typedef CwiseBinaryOp<internal::scalar_sum_op<double,double>,const CpyMatrixXd,const CpyMatrixXd> XprType;
+
+XprType get_xpr_with_temps(const MatrixXd& a)
+{
+ MatrixXd t1 = a.rowwise().reverse();
+ MatrixXd t2 = a+a;
+ return t1.nestByValue() + t2.nestByValue();
+}
+
+EIGEN_DECLARE_TEST(nestbyvalue)
+{
+ for(int i = 0; i < g_repeat; i++) {
+ Index rows = internal::random<Index>(1,EIGEN_TEST_MAX_SIZE);
+ Index cols = internal::random<Index>(1,EIGEN_TEST_MAX_SIZE);
+ MatrixXd a = MatrixXd::Random(rows,cols);
+ nb_temporaries = 0;
+ XprType x = get_xpr_with_temps(a);
+ VERIFY_IS_EQUAL(nb_temporaries,6);
+ MatrixXd b = x;
+ VERIFY_IS_EQUAL(nb_temporaries,6+1);
+ VERIFY_IS_APPROX(b, a.rowwise().reverse().eval() + (a+a).eval());
+ }
+}
diff --git a/test/nesting_ops.cpp b/test/nesting_ops.cpp
new file mode 100644
index 0000000..1350994
--- /dev/null
+++ b/test/nesting_ops.cpp
@@ -0,0 +1,107 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2010 Hauke Heibel <hauke.heibel@gmail.com>
+// Copyright (C) 2015 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#define TEST_ENABLE_TEMPORARY_TRACKING
+
+#include "main.h"
+
+template <int N, typename XprType>
+void use_n_times(const XprType &xpr)
+{
+ typename internal::nested_eval<XprType,N>::type mat(xpr);
+ typename XprType::PlainObject res(mat.rows(), mat.cols());
+ nb_temporaries--; // remove res
+ res.setZero();
+ for(int i=0; i<N; ++i)
+ res += mat;
+}
+
+template <int N, typename ReferenceType, typename XprType>
+bool verify_eval_type(const XprType &, const ReferenceType&)
+{
+ typedef typename internal::nested_eval<XprType,N>::type EvalType;
+ return internal::is_same<internal::remove_all_t<EvalType>, internal::remove_all_t<ReferenceType>>::value;
+}
+
+template <typename MatrixType> void run_nesting_ops_1(const MatrixType& _m)
+{
+ typename internal::nested_eval<MatrixType,2>::type m(_m);
+
+ // Make really sure that we are in debug mode!
+ VERIFY_RAISES_ASSERT(eigen_assert(false));
+
+ // The only intention of these tests is to ensure that this code does
+ // not trigger any asserts or segmentation faults... more to come.
+ VERIFY_IS_APPROX( (m.transpose() * m).diagonal().sum(), (m.transpose() * m).diagonal().sum() );
+ VERIFY_IS_APPROX( (m.transpose() * m).diagonal().array().abs().sum(), (m.transpose() * m).diagonal().array().abs().sum() );
+
+ VERIFY_IS_APPROX( (m.transpose() * m).array().abs().sum(), (m.transpose() * m).array().abs().sum() );
+}
+
+template <typename MatrixType> void run_nesting_ops_2(const MatrixType& _m)
+{
+ typedef typename MatrixType::Scalar Scalar;
+ Index rows = _m.rows();
+ Index cols = _m.cols();
+ MatrixType m1 = MatrixType::Random(rows,cols);
+ Matrix<Scalar,MatrixType::RowsAtCompileTime,MatrixType::ColsAtCompileTime,ColMajor> m2;
+
+ if((MatrixType::SizeAtCompileTime==Dynamic))
+ {
+ VERIFY_EVALUATION_COUNT( use_n_times<1>(m1 + m1*m1), 1 );
+ VERIFY_EVALUATION_COUNT( use_n_times<10>(m1 + m1*m1), 1 );
+
+ VERIFY_EVALUATION_COUNT( use_n_times<1>(m1.template triangularView<Lower>().solve(m1.col(0))), 1 );
+ VERIFY_EVALUATION_COUNT( use_n_times<10>(m1.template triangularView<Lower>().solve(m1.col(0))), 1 );
+
+ VERIFY_EVALUATION_COUNT( use_n_times<1>(Scalar(2)*m1.template triangularView<Lower>().solve(m1.col(0))), 2 ); // FIXME could be one by applying the scaling in-place on the solve result
+ VERIFY_EVALUATION_COUNT( use_n_times<1>(m1.col(0)+m1.template triangularView<Lower>().solve(m1.col(0))), 2 ); // FIXME could be one by adding m1.col() inplace
+ VERIFY_EVALUATION_COUNT( use_n_times<10>(m1.col(0)+m1.template triangularView<Lower>().solve(m1.col(0))), 2 );
+ }
+
+ {
+ VERIFY( verify_eval_type<10>(m1, m1) );
+ if(!NumTraits<Scalar>::IsComplex)
+ {
+ VERIFY( verify_eval_type<3>(2*m1, 2*m1) );
+ VERIFY( verify_eval_type<4>(2*m1, m1) );
+ }
+ else
+ {
+ VERIFY( verify_eval_type<2>(2*m1, 2*m1) );
+ VERIFY( verify_eval_type<3>(2*m1, m1) );
+ }
+ VERIFY( verify_eval_type<2>(m1+m1, m1+m1) );
+ VERIFY( verify_eval_type<3>(m1+m1, m1) );
+ VERIFY( verify_eval_type<1>(m1*m1.transpose(), m2) );
+ VERIFY( verify_eval_type<1>(m1*(m1+m1).transpose(), m2) );
+ VERIFY( verify_eval_type<2>(m1*m1.transpose(), m2) );
+ VERIFY( verify_eval_type<1>(m1+m1*m1, m1) );
+
+ VERIFY( verify_eval_type<1>(m1.template triangularView<Lower>().solve(m1), m1) );
+ VERIFY( verify_eval_type<1>(m1+m1.template triangularView<Lower>().solve(m1), m1) );
+ }
+}
+
+
+EIGEN_DECLARE_TEST(nesting_ops)
+{
+ CALL_SUBTEST_1(run_nesting_ops_1(MatrixXf::Random(25,25)));
+ CALL_SUBTEST_2(run_nesting_ops_1(MatrixXcd::Random(25,25)));
+ CALL_SUBTEST_3(run_nesting_ops_1(Matrix4f::Random()));
+ CALL_SUBTEST_4(run_nesting_ops_1(Matrix2d::Random()));
+
+ Index s = internal::random<int>(1,EIGEN_TEST_MAX_SIZE);
+ CALL_SUBTEST_1( run_nesting_ops_2(MatrixXf(s,s)) );
+ CALL_SUBTEST_2( run_nesting_ops_2(MatrixXcd(s,s)) );
+ CALL_SUBTEST_3( run_nesting_ops_2(Matrix4f()) );
+ CALL_SUBTEST_4( run_nesting_ops_2(Matrix2d()) );
+ TEST_SET_BUT_UNUSED_VARIABLE(s)
+}
diff --git a/test/nomalloc.cpp b/test/nomalloc.cpp
new file mode 100644
index 0000000..689a4cc
--- /dev/null
+++ b/test/nomalloc.cpp
@@ -0,0 +1,228 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+// discard stack allocation as that too bypasses malloc
+#define EIGEN_STACK_ALLOCATION_LIMIT 0
+// heap allocation will raise an assert if enabled at runtime
+#define EIGEN_RUNTIME_NO_MALLOC
+
+#include "main.h"
+#include <Eigen/Cholesky>
+#include <Eigen/Eigenvalues>
+#include <Eigen/LU>
+#include <Eigen/QR>
+#include <Eigen/SVD>
+
+template<typename MatrixType> void nomalloc(const MatrixType& m)
+{
+ /* this test check no dynamic memory allocation are issued with fixed-size matrices
+ */
+ typedef typename MatrixType::Scalar Scalar;
+
+ Index rows = m.rows();
+ Index cols = m.cols();
+
+ MatrixType m1 = MatrixType::Random(rows, cols),
+ m2 = MatrixType::Random(rows, cols),
+ m3(rows, cols);
+
+ Scalar s1 = internal::random<Scalar>();
+
+ Index r = internal::random<Index>(0, rows-1),
+ c = internal::random<Index>(0, cols-1);
+
+ VERIFY_IS_APPROX((m1+m2)*s1, s1*m1+s1*m2);
+ VERIFY_IS_APPROX((m1+m2)(r,c), (m1(r,c))+(m2(r,c)));
+ VERIFY_IS_APPROX(m1.cwiseProduct(m1.block(0,0,rows,cols)), (m1.array()*m1.array()).matrix());
+ VERIFY_IS_APPROX((m1*m1.transpose())*m2, m1*(m1.transpose()*m2));
+
+ m2.col(0).noalias() = m1 * m1.col(0);
+ m2.col(0).noalias() -= m1.adjoint() * m1.col(0);
+ m2.col(0).noalias() -= m1 * m1.row(0).adjoint();
+ m2.col(0).noalias() -= m1.adjoint() * m1.row(0).adjoint();
+
+ m2.row(0).noalias() = m1.row(0) * m1;
+ m2.row(0).noalias() -= m1.row(0) * m1.adjoint();
+ m2.row(0).noalias() -= m1.col(0).adjoint() * m1;
+ m2.row(0).noalias() -= m1.col(0).adjoint() * m1.adjoint();
+ VERIFY_IS_APPROX(m2,m2);
+
+ m2.col(0).noalias() = m1.template triangularView<Upper>() * m1.col(0);
+ m2.col(0).noalias() -= m1.adjoint().template triangularView<Upper>() * m1.col(0);
+ m2.col(0).noalias() -= m1.template triangularView<Upper>() * m1.row(0).adjoint();
+ m2.col(0).noalias() -= m1.adjoint().template triangularView<Upper>() * m1.row(0).adjoint();
+
+ m2.row(0).noalias() = m1.row(0) * m1.template triangularView<Upper>();
+ m2.row(0).noalias() -= m1.row(0) * m1.adjoint().template triangularView<Upper>();
+ m2.row(0).noalias() -= m1.col(0).adjoint() * m1.template triangularView<Upper>();
+ m2.row(0).noalias() -= m1.col(0).adjoint() * m1.adjoint().template triangularView<Upper>();
+ VERIFY_IS_APPROX(m2,m2);
+
+ m2.col(0).noalias() = m1.template selfadjointView<Upper>() * m1.col(0);
+ m2.col(0).noalias() -= m1.adjoint().template selfadjointView<Upper>() * m1.col(0);
+ m2.col(0).noalias() -= m1.template selfadjointView<Upper>() * m1.row(0).adjoint();
+ m2.col(0).noalias() -= m1.adjoint().template selfadjointView<Upper>() * m1.row(0).adjoint();
+
+ m2.row(0).noalias() = m1.row(0) * m1.template selfadjointView<Upper>();
+ m2.row(0).noalias() -= m1.row(0) * m1.adjoint().template selfadjointView<Upper>();
+ m2.row(0).noalias() -= m1.col(0).adjoint() * m1.template selfadjointView<Upper>();
+ m2.row(0).noalias() -= m1.col(0).adjoint() * m1.adjoint().template selfadjointView<Upper>();
+ VERIFY_IS_APPROX(m2,m2);
+
+ m2.template selfadjointView<Lower>().rankUpdate(m1.col(0),-1);
+ m2.template selfadjointView<Upper>().rankUpdate(m1.row(0),-1);
+ m2.template selfadjointView<Lower>().rankUpdate(m1.col(0), m1.col(0)); // rank-2
+
+ // The following fancy matrix-matrix products are not safe yet regarding static allocation
+ m2.template selfadjointView<Lower>().rankUpdate(m1);
+ m2 += m2.template triangularView<Upper>() * m1;
+ m2.template triangularView<Upper>() = m2 * m2;
+ m1 += m1.template selfadjointView<Lower>() * m2;
+ VERIFY_IS_APPROX(m2,m2);
+}
+
+template<typename Scalar>
+void ctms_decompositions()
+{
+ const int maxSize = 16;
+ const int size = 12;
+
+ typedef Eigen::Matrix<Scalar,
+ Eigen::Dynamic, Eigen::Dynamic,
+ 0,
+ maxSize, maxSize> Matrix;
+
+ typedef Eigen::Matrix<Scalar,
+ Eigen::Dynamic, 1,
+ 0,
+ maxSize, 1> Vector;
+
+ typedef Eigen::Matrix<std::complex<Scalar>,
+ Eigen::Dynamic, Eigen::Dynamic,
+ 0,
+ maxSize, maxSize> ComplexMatrix;
+
+ const Matrix A(Matrix::Random(size, size)), B(Matrix::Random(size, size));
+ Matrix X(size,size);
+ const ComplexMatrix complexA(ComplexMatrix::Random(size, size));
+ const Matrix saA = A.adjoint() * A;
+ const Vector b(Vector::Random(size));
+ Vector x(size);
+
+ // Cholesky module
+ Eigen::LLT<Matrix> LLT; LLT.compute(A);
+ X = LLT.solve(B);
+ x = LLT.solve(b);
+ Eigen::LDLT<Matrix> LDLT; LDLT.compute(A);
+ X = LDLT.solve(B);
+ x = LDLT.solve(b);
+
+ // Eigenvalues module
+ Eigen::HessenbergDecomposition<ComplexMatrix> hessDecomp; hessDecomp.compute(complexA);
+ Eigen::ComplexSchur<ComplexMatrix> cSchur(size); cSchur.compute(complexA);
+ Eigen::ComplexEigenSolver<ComplexMatrix> cEigSolver; cEigSolver.compute(complexA);
+ Eigen::EigenSolver<Matrix> eigSolver; eigSolver.compute(A);
+ Eigen::SelfAdjointEigenSolver<Matrix> saEigSolver(size); saEigSolver.compute(saA);
+ Eigen::Tridiagonalization<Matrix> tridiag; tridiag.compute(saA);
+
+ // LU module
+ Eigen::PartialPivLU<Matrix> ppLU; ppLU.compute(A);
+ X = ppLU.solve(B);
+ x = ppLU.solve(b);
+ Eigen::FullPivLU<Matrix> fpLU; fpLU.compute(A);
+ X = fpLU.solve(B);
+ x = fpLU.solve(b);
+
+ // QR module
+ Eigen::HouseholderQR<Matrix> hQR; hQR.compute(A);
+ X = hQR.solve(B);
+ x = hQR.solve(b);
+ Eigen::ColPivHouseholderQR<Matrix> cpQR; cpQR.compute(A);
+ X = cpQR.solve(B);
+ x = cpQR.solve(b);
+ Eigen::FullPivHouseholderQR<Matrix> fpQR; fpQR.compute(A);
+ // FIXME X = fpQR.solve(B);
+ x = fpQR.solve(b);
+
+ // SVD module
+ Eigen::JacobiSVD<Matrix, ComputeFullU | ComputeFullV> jSVD; jSVD.compute(A);
+}
+
+void test_zerosized() {
+ // default constructors:
+ Eigen::MatrixXd A;
+ Eigen::VectorXd v;
+ // explicit zero-sized:
+ Eigen::ArrayXXd A0(0,0);
+ Eigen::ArrayXd v0(0);
+
+ // assigning empty objects to each other:
+ A=A0;
+ v=v0;
+}
+
+template<typename MatrixType> void test_reference(const MatrixType& m) {
+ typedef typename MatrixType::Scalar Scalar;
+ enum { Flag = MatrixType::IsRowMajor ? Eigen::RowMajor : Eigen::ColMajor};
+ enum { TransposeFlag = !MatrixType::IsRowMajor ? Eigen::RowMajor : Eigen::ColMajor};
+ Index rows = m.rows(), cols=m.cols();
+ typedef Eigen::Matrix<Scalar, Eigen::Dynamic, Eigen::Dynamic, Flag > MatrixX;
+ typedef Eigen::Matrix<Scalar, Eigen::Dynamic, Eigen::Dynamic, TransposeFlag> MatrixXT;
+ // Dynamic reference:
+ typedef Eigen::Ref<const MatrixX > Ref;
+ typedef Eigen::Ref<const MatrixXT > RefT;
+
+ Ref r1(m);
+ Ref r2(m.block(rows/3, cols/4, rows/2, cols/2));
+ RefT r3(m.transpose());
+ RefT r4(m.topLeftCorner(rows/2, cols/2).transpose());
+
+ VERIFY_RAISES_ASSERT(RefT r5(m));
+ VERIFY_RAISES_ASSERT(Ref r6(m.transpose()));
+ VERIFY_RAISES_ASSERT(Ref r7(Scalar(2) * m));
+
+ // Copy constructors shall also never malloc
+ Ref r8 = r1;
+ RefT r9 = r3;
+
+ // Initializing from a compatible Ref shall also never malloc
+ Eigen::Ref<const MatrixX, Unaligned, Stride<Dynamic, Dynamic> > r10=r8, r11=m;
+
+ // Initializing from an incompatible Ref will malloc:
+ typedef Eigen::Ref<const MatrixX, Aligned> RefAligned;
+ VERIFY_RAISES_ASSERT(RefAligned r12=r10);
+ VERIFY_RAISES_ASSERT(Ref r13=r10); // r10 has more dynamic strides
+
+}
+
+EIGEN_DECLARE_TEST(nomalloc)
+{
+ // create some dynamic objects
+ Eigen::MatrixXd M1 = MatrixXd::Random(3,3);
+ Ref<const MatrixXd> R1 = 2.0*M1; // Ref requires temporary
+
+ // from here on prohibit malloc:
+ Eigen::internal::set_is_malloc_allowed(false);
+
+ // check that our operator new is indeed called:
+ VERIFY_RAISES_ASSERT(MatrixXd dummy(MatrixXd::Random(3,3)));
+ CALL_SUBTEST_1(nomalloc(Matrix<float, 1, 1>()) );
+ CALL_SUBTEST_2(nomalloc(Matrix4d()) );
+ CALL_SUBTEST_3(nomalloc(Matrix<float,32,32>()) );
+
+ // Check decomposition modules with dynamic matrices that have a known compile-time max size (ctms)
+ CALL_SUBTEST_4(ctms_decompositions<float>());
+
+ CALL_SUBTEST_5(test_zerosized());
+
+ CALL_SUBTEST_6(test_reference(Matrix<float,32,32>()));
+ CALL_SUBTEST_7(test_reference(R1));
+ CALL_SUBTEST_8(Ref<MatrixXd> R2 = M1.topRows<2>(); test_reference(R2));
+}
diff --git a/test/nullary.cpp b/test/nullary.cpp
new file mode 100644
index 0000000..2c4d938
--- /dev/null
+++ b/test/nullary.cpp
@@ -0,0 +1,337 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2010-2011 Jitse Niesen <jitse@maths.leeds.ac.uk>
+// Copyright (C) 2016 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "main.h"
+
+template<typename MatrixType>
+bool equalsIdentity(const MatrixType& A)
+{
+ bool offDiagOK = true;
+ for (Index i = 0; i < A.rows(); ++i) {
+ for (Index j = i+1; j < A.cols(); ++j) {
+ offDiagOK = offDiagOK && numext::is_exactly_zero(A(i, j));
+ }
+ }
+ for (Index i = 0; i < A.rows(); ++i) {
+ for (Index j = 0; j < (std::min)(i, A.cols()); ++j) {
+ offDiagOK = offDiagOK && numext::is_exactly_zero(A(i, j));
+ }
+ }
+
+ bool diagOK = (A.diagonal().array() == 1).all();
+ return offDiagOK && diagOK;
+}
+
+template<typename VectorType>
+void check_extremity_accuracy(const VectorType &v, const typename VectorType::Scalar &low, const typename VectorType::Scalar &high)
+{
+ typedef typename VectorType::Scalar Scalar;
+ typedef typename VectorType::RealScalar RealScalar;
+
+ RealScalar prec = internal::is_same<RealScalar,float>::value ? NumTraits<RealScalar>::dummy_precision()*10 : NumTraits<RealScalar>::dummy_precision()/10;
+ Index size = v.size();
+
+ if(size<20)
+ return;
+
+ for (int i=0; i<size; ++i)
+ {
+ if(i<5 || i>size-6)
+ {
+ Scalar ref = (low*RealScalar(size-i-1))/RealScalar(size-1) + (high*RealScalar(i))/RealScalar(size-1);
+ if(std::abs(ref)>1)
+ {
+ if(!internal::isApprox(v(i), ref, prec))
+ std::cout << v(i) << " != " << ref << " ; relative error: " << std::abs((v(i)-ref)/ref) << " ; required precision: " << prec << " ; range: " << low << "," << high << " ; i: " << i << "\n";
+ VERIFY(internal::isApprox(v(i), (low*RealScalar(size-i-1))/RealScalar(size-1) + (high*RealScalar(i))/RealScalar(size-1), prec));
+ }
+ }
+ }
+}
+
+template<typename VectorType>
+void testVectorType(const VectorType& base)
+{
+ typedef typename VectorType::Scalar Scalar;
+ typedef typename VectorType::RealScalar RealScalar;
+
+ const Index size = base.size();
+
+ Scalar high = internal::random<Scalar>(-500,500);
+ Scalar low = (size == 1 ? high : internal::random<Scalar>(-500,500));
+ if (numext::real(low)>numext::real(high)) std::swap(low,high);
+
+ // check low==high
+ if(internal::random<float>(0.f,1.f)<0.05f)
+ low = high;
+ // check abs(low) >> abs(high)
+ else if(size>2 && std::numeric_limits<RealScalar>::max_exponent10>0 && internal::random<float>(0.f,1.f)<0.1f)
+ low = -internal::random<Scalar>(1,2) * RealScalar(std::pow(RealScalar(10),std::numeric_limits<RealScalar>::max_exponent10/2));
+
+ const Scalar step = ((size == 1) ? 1 : (high-low)/RealScalar(size-1));
+
+ // check whether the result yields what we expect it to do
+ VectorType m(base);
+ m.setLinSpaced(size,low,high);
+
+ if(!NumTraits<Scalar>::IsInteger)
+ {
+ VectorType n(size);
+ for (int i=0; i<size; ++i)
+ n(i) = low+RealScalar(i)*step;
+ VERIFY_IS_APPROX(m,n);
+
+ CALL_SUBTEST( check_extremity_accuracy(m, low, high) );
+ }
+
+ RealScalar range_length = numext::real(high-low);
+ if((!NumTraits<Scalar>::IsInteger) || (range_length>=size && (Index(range_length)%(size-1))==0) || (Index(range_length+1)<size && (size%Index(range_length+1))==0))
+ {
+ VectorType n(size);
+ if((!NumTraits<Scalar>::IsInteger) || (range_length>=size))
+ for (int i=0; i<size; ++i)
+ n(i) = size==1 ? low : (low + ((high-low)*Scalar(i))/RealScalar(size-1));
+ else
+ for (int i=0; i<size; ++i)
+ n(i) = size==1 ? low : low + Scalar((double(range_length+1)*double(i))/double(size));
+ VERIFY_IS_APPROX(m,n);
+
+ // random access version
+ m = VectorType::LinSpaced(size,low,high);
+ VERIFY_IS_APPROX(m,n);
+ VERIFY( internal::isApprox(m(m.size()-1),high) );
+ VERIFY( size==1 || internal::isApprox(m(0),low) );
+ VERIFY_IS_EQUAL(m(m.size()-1) , high);
+ if(!NumTraits<Scalar>::IsInteger)
+ CALL_SUBTEST( check_extremity_accuracy(m, low, high) );
+ }
+
+ VERIFY( numext::real(m(m.size()-1)) <= numext::real(high) );
+ VERIFY( (m.array().real() <= numext::real(high)).all() );
+ VERIFY( (m.array().real() >= numext::real(low)).all() );
+
+
+ VERIFY( numext::real(m(m.size()-1)) >= numext::real(low) );
+ if(size>=1)
+ {
+ VERIFY( internal::isApprox(m(0),low) );
+ VERIFY_IS_EQUAL(m(0) , low);
+ }
+
+ // check whether everything works with row and col major vectors
+ Matrix<Scalar,Dynamic,1> row_vector(size);
+ Matrix<Scalar,1,Dynamic> col_vector(size);
+ row_vector.setLinSpaced(size,low,high);
+ col_vector.setLinSpaced(size,low,high);
+ // when using the extended precision (e.g., FPU) the relative error might exceed 1 bit
+ // when computing the squared sum in isApprox, thus the 2x factor.
+ VERIFY( row_vector.isApprox(col_vector.transpose(), RealScalar(2)*NumTraits<Scalar>::epsilon()));
+
+ Matrix<Scalar,Dynamic,1> size_changer(size+50);
+ size_changer.setLinSpaced(size,low,high);
+ VERIFY( size_changer.size() == size );
+
+ typedef Matrix<Scalar,1,1> ScalarMatrix;
+ ScalarMatrix scalar;
+ scalar.setLinSpaced(1,low,high);
+ VERIFY_IS_APPROX( scalar, ScalarMatrix::Constant(high) );
+ VERIFY_IS_APPROX( ScalarMatrix::LinSpaced(1,low,high), ScalarMatrix::Constant(high) );
+
+ // regression test for bug 526 (linear vectorized transversal)
+ if (size > 1 && (!NumTraits<Scalar>::IsInteger)) {
+ m.tail(size-1).setLinSpaced(low, high);
+ VERIFY_IS_APPROX(m(size-1), high);
+ }
+
+ // regression test for bug 1383 (LinSpaced with empty size/range)
+ {
+ Index n0 = VectorType::SizeAtCompileTime==Dynamic ? 0 : VectorType::SizeAtCompileTime;
+ low = internal::random<Scalar>();
+ m = VectorType::LinSpaced(n0,low,low-RealScalar(1));
+ VERIFY(m.size()==n0);
+
+ if(VectorType::SizeAtCompileTime==Dynamic)
+ {
+ VERIFY_IS_EQUAL(VectorType::LinSpaced(n0,0,Scalar(n0-1)).sum(),Scalar(0));
+ VERIFY_IS_EQUAL(VectorType::LinSpaced(n0,low,low-RealScalar(1)).sum(),Scalar(0));
+ }
+
+ m.setLinSpaced(n0,0,Scalar(n0-1));
+ VERIFY(m.size()==n0);
+ m.setLinSpaced(n0,low,low-RealScalar(1));
+ VERIFY(m.size()==n0);
+
+ // empty range only:
+ VERIFY_IS_APPROX(VectorType::LinSpaced(size,low,low),VectorType::Constant(size,low));
+ m.setLinSpaced(size,low,low);
+ VERIFY_IS_APPROX(m,VectorType::Constant(size,low));
+
+ if(NumTraits<Scalar>::IsInteger)
+ {
+ VERIFY_IS_APPROX( VectorType::LinSpaced(size,low,low+Scalar(size-1)), VectorType::LinSpaced(size,low+Scalar(size-1),low).reverse() );
+
+ if(VectorType::SizeAtCompileTime==Dynamic)
+ {
+ // Check negative multiplicator path:
+ for(Index k=1; k<5; ++k)
+ VERIFY_IS_APPROX( VectorType::LinSpaced(size,low,low+Scalar((size-1)*k)), VectorType::LinSpaced(size,low+Scalar((size-1)*k),low).reverse() );
+ // Check negative divisor path:
+ for(Index k=1; k<5; ++k)
+ VERIFY_IS_APPROX( VectorType::LinSpaced(size*k,low,low+Scalar(size-1)), VectorType::LinSpaced(size*k,low+Scalar(size-1),low).reverse() );
+ }
+ }
+ }
+
+ // test setUnit()
+ if(m.size()>0)
+ {
+ for(Index k=0; k<10; ++k)
+ {
+ Index i = internal::random<Index>(0,m.size()-1);
+ m.setUnit(i);
+ VERIFY_IS_APPROX( m, VectorType::Unit(m.size(), i) );
+ }
+ if(VectorType::SizeAtCompileTime==Dynamic)
+ {
+ Index i = internal::random<Index>(0,2*m.size()-1);
+ m.setUnit(2*m.size(),i);
+ VERIFY_IS_APPROX( m, VectorType::Unit(m.size(),i) );
+ }
+ }
+
+}
+
+template<typename MatrixType>
+void testMatrixType(const MatrixType& m)
+{
+ using std::abs;
+ const Index rows = m.rows();
+ const Index cols = m.cols();
+ typedef typename MatrixType::Scalar Scalar;
+ typedef typename MatrixType::RealScalar RealScalar;
+
+ Scalar s1;
+ do {
+ s1 = internal::random<Scalar>();
+ } while(abs(s1)<RealScalar(1e-5) && (!NumTraits<Scalar>::IsInteger));
+
+ MatrixType A;
+ A.setIdentity(rows, cols);
+ VERIFY(equalsIdentity(A));
+ VERIFY(equalsIdentity(MatrixType::Identity(rows, cols)));
+
+
+ A = MatrixType::Constant(rows,cols,s1);
+ Index i = internal::random<Index>(0,rows-1);
+ Index j = internal::random<Index>(0,cols-1);
+ VERIFY_IS_APPROX( MatrixType::Constant(rows,cols,s1)(i,j), s1 );
+ VERIFY_IS_APPROX( MatrixType::Constant(rows,cols,s1).coeff(i,j), s1 );
+ VERIFY_IS_APPROX( A(i,j), s1 );
+}
+
+template<int>
+void bug79()
+{
+ // Assignment of a RowVectorXd to a MatrixXd (regression test for bug #79).
+ VERIFY( (MatrixXd(RowVectorXd::LinSpaced(3, 0, 1)) - RowVector3d(0, 0.5, 1)).norm() < std::numeric_limits<double>::epsilon() );
+}
+
+template<int>
+void bug1630()
+{
+ Array4d x4 = Array4d::LinSpaced(0.0, 1.0);
+ Array3d x3(Array4d::LinSpaced(0.0, 1.0).head(3));
+ VERIFY_IS_APPROX(x4.head(3), x3);
+}
+
+template<int>
+void nullary_overflow()
+{
+ // Check possible overflow issue
+ int n = 60000;
+ ArrayXi a1(n), a2(n);
+ a1.setLinSpaced(n, 0, n-1);
+ for(int i=0; i<n; ++i)
+ a2(i) = i;
+ VERIFY_IS_APPROX(a1,a2);
+}
+
+template<int>
+void nullary_internal_logic()
+{
+ // check some internal logic
+ VERIFY(( internal::has_nullary_operator<internal::scalar_constant_op<double> >::value ));
+ VERIFY(( !internal::has_unary_operator<internal::scalar_constant_op<double> >::value ));
+ VERIFY(( !internal::has_binary_operator<internal::scalar_constant_op<double> >::value ));
+ VERIFY(( internal::functor_has_linear_access<internal::scalar_constant_op<double> >::ret ));
+
+ VERIFY(( !internal::has_nullary_operator<internal::scalar_identity_op<double> >::value ));
+ VERIFY(( !internal::has_unary_operator<internal::scalar_identity_op<double> >::value ));
+ VERIFY(( internal::has_binary_operator<internal::scalar_identity_op<double> >::value ));
+ VERIFY(( !internal::functor_has_linear_access<internal::scalar_identity_op<double> >::ret ));
+
+ VERIFY(( !internal::has_nullary_operator<internal::linspaced_op<float> >::value ));
+ VERIFY(( internal::has_unary_operator<internal::linspaced_op<float> >::value ));
+ VERIFY(( !internal::has_binary_operator<internal::linspaced_op<float> >::value ));
+ VERIFY(( internal::functor_has_linear_access<internal::linspaced_op<float> >::ret ));
+
+ // Regression unit test for a weird MSVC bug.
+ // Search "nullary_wrapper_workaround_msvc" in CoreEvaluators.h for the details.
+ // See also traits<Ref>::match.
+ {
+ MatrixXf A = MatrixXf::Random(3,3);
+ Ref<const MatrixXf> R = 2.0*A;
+ VERIFY_IS_APPROX(R, A+A);
+
+ Ref<const MatrixXf> R1 = MatrixXf::Random(3,3)+A;
+
+ VectorXi V = VectorXi::Random(3);
+ Ref<const VectorXi> R2 = VectorXi::LinSpaced(3,1,3)+V;
+ VERIFY_IS_APPROX(R2, V+Vector3i(1,2,3));
+
+ VERIFY(( internal::has_nullary_operator<internal::scalar_constant_op<float> >::value ));
+ VERIFY(( !internal::has_unary_operator<internal::scalar_constant_op<float> >::value ));
+ VERIFY(( !internal::has_binary_operator<internal::scalar_constant_op<float> >::value ));
+ VERIFY(( internal::functor_has_linear_access<internal::scalar_constant_op<float> >::ret ));
+
+ VERIFY(( !internal::has_nullary_operator<internal::linspaced_op<int> >::value ));
+ VERIFY(( internal::has_unary_operator<internal::linspaced_op<int> >::value ));
+ VERIFY(( !internal::has_binary_operator<internal::linspaced_op<int> >::value ));
+ VERIFY(( internal::functor_has_linear_access<internal::linspaced_op<int> >::ret ));
+ }
+}
+
+EIGEN_DECLARE_TEST(nullary)
+{
+ CALL_SUBTEST_1( testMatrixType(Matrix2d()) );
+ CALL_SUBTEST_2( testMatrixType(MatrixXcf(internal::random<int>(1,300),internal::random<int>(1,300))) );
+ CALL_SUBTEST_3( testMatrixType(MatrixXf(internal::random<int>(1,300),internal::random<int>(1,300))) );
+
+ for(int i = 0; i < g_repeat*10; i++) {
+ CALL_SUBTEST_3( testVectorType(VectorXcd(internal::random<int>(1,30000))) );
+ CALL_SUBTEST_4( testVectorType(VectorXd(internal::random<int>(1,30000))) );
+ CALL_SUBTEST_5( testVectorType(Vector4d()) ); // regression test for bug 232
+ CALL_SUBTEST_6( testVectorType(Vector3d()) );
+ CALL_SUBTEST_7( testVectorType(VectorXf(internal::random<int>(1,30000))) );
+ CALL_SUBTEST_8( testVectorType(Vector3f()) );
+ CALL_SUBTEST_8( testVectorType(Vector4f()) );
+ CALL_SUBTEST_8( testVectorType(Matrix<float,8,1>()) );
+ CALL_SUBTEST_8( testVectorType(Matrix<float,1,1>()) );
+
+ CALL_SUBTEST_9( testVectorType(VectorXi(internal::random<int>(1,10))) );
+ CALL_SUBTEST_9( testVectorType(VectorXi(internal::random<int>(9,300))) );
+ CALL_SUBTEST_9( testVectorType(Matrix<int,1,1>()) );
+ }
+
+ CALL_SUBTEST_6( bug79<0>() );
+ CALL_SUBTEST_6( bug1630<0>() );
+ CALL_SUBTEST_9( nullary_overflow<0>() );
+ CALL_SUBTEST_10( nullary_internal_logic<0>() );
+}
diff --git a/test/num_dimensions.cpp b/test/num_dimensions.cpp
new file mode 100644
index 0000000..528c8f6
--- /dev/null
+++ b/test/num_dimensions.cpp
@@ -0,0 +1,84 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2018 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "main.h"
+#include <Eigen/SparseCore>
+
+template<int ExpectedDim,typename Xpr>
+void check_dim(const Xpr& ) {
+ STATIC_CHECK( Xpr::NumDimensions == ExpectedDim );
+}
+
+template<template <typename,int,int> class Object>
+void map_num_dimensions()
+{
+ typedef Object<double, 1, 1> ArrayScalarType;
+ typedef Object<double, 2, 1> ArrayVectorType;
+ typedef Object<double, 1, 2> TransposeArrayVectorType;
+ typedef Object<double, 2, 2> ArrayType;
+ typedef Object<double, Eigen::Dynamic, 1> DynamicArrayVectorType;
+ typedef Object<double, 1, Eigen::Dynamic> DynamicTransposeArrayVectorType;
+ typedef Object<double, Eigen::Dynamic, Eigen::Dynamic> DynamicArrayType;
+
+ STATIC_CHECK(ArrayScalarType::NumDimensions == 0);
+ STATIC_CHECK(ArrayVectorType::NumDimensions == 1);
+ STATIC_CHECK(TransposeArrayVectorType::NumDimensions == 1);
+ STATIC_CHECK(ArrayType::NumDimensions == 2);
+ STATIC_CHECK(DynamicArrayVectorType::NumDimensions == 1);
+ STATIC_CHECK(DynamicTransposeArrayVectorType::NumDimensions == 1);
+ STATIC_CHECK(DynamicArrayType::NumDimensions == 2);
+
+ typedef Eigen::Map<ArrayScalarType> ArrayScalarMap;
+ typedef Eigen::Map<ArrayVectorType> ArrayVectorMap;
+ typedef Eigen::Map<TransposeArrayVectorType> TransposeArrayVectorMap;
+ typedef Eigen::Map<ArrayType> ArrayMap;
+ typedef Eigen::Map<DynamicArrayVectorType> DynamicArrayVectorMap;
+ typedef Eigen::Map<DynamicTransposeArrayVectorType> DynamicTransposeArrayVectorMap;
+ typedef Eigen::Map<DynamicArrayType> DynamicArrayMap;
+
+ STATIC_CHECK(ArrayScalarMap::NumDimensions == 0);
+ STATIC_CHECK(ArrayVectorMap::NumDimensions == 1);
+ STATIC_CHECK(TransposeArrayVectorMap::NumDimensions == 1);
+ STATIC_CHECK(ArrayMap::NumDimensions == 2);
+ STATIC_CHECK(DynamicArrayVectorMap::NumDimensions == 1);
+ STATIC_CHECK(DynamicTransposeArrayVectorMap::NumDimensions == 1);
+ STATIC_CHECK(DynamicArrayMap::NumDimensions == 2);
+}
+
+template<typename Scalar, int Rows, int Cols>
+using TArray = Array<Scalar,Rows,Cols>;
+
+template<typename Scalar, int Rows, int Cols>
+using TMatrix = Matrix<Scalar,Rows,Cols>;
+
+EIGEN_DECLARE_TEST(num_dimensions)
+{
+ int n = 10;
+ ArrayXXd A(n,n);
+ CALL_SUBTEST( check_dim<2>(A) );
+ CALL_SUBTEST( check_dim<2>(A.block(1,1,2,2)) );
+ CALL_SUBTEST( check_dim<1>(A.col(1)) );
+ CALL_SUBTEST( check_dim<1>(A.row(1)) );
+
+ MatrixXd M(n,n);
+ CALL_SUBTEST( check_dim<0>(M.row(1)*M.col(1)) );
+
+ SparseMatrix<double> S(n,n);
+ CALL_SUBTEST( check_dim<2>(S) );
+ CALL_SUBTEST( check_dim<2>(S.block(1,1,2,2)) );
+ CALL_SUBTEST( check_dim<1>(S.col(1)) );
+ CALL_SUBTEST( check_dim<1>(S.row(1)) );
+
+ SparseVector<double> s(n);
+ CALL_SUBTEST( check_dim<1>(s) );
+ CALL_SUBTEST( check_dim<1>(s.head(2)) );
+
+ CALL_SUBTEST( map_num_dimensions<TArray>() );
+ CALL_SUBTEST( map_num_dimensions<TMatrix>() );
+}
diff --git a/test/numext.cpp b/test/numext.cpp
new file mode 100644
index 0000000..ee879c9
--- /dev/null
+++ b/test/numext.cpp
@@ -0,0 +1,275 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2017 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "main.h"
+
+template<typename T, typename U>
+bool check_if_equal_or_nans(const T& actual, const U& expected) {
+ return (numext::equal_strict(actual, expected) || ((numext::isnan)(actual) && (numext::isnan)(expected)));
+}
+
+template<typename T, typename U>
+bool check_if_equal_or_nans(const std::complex<T>& actual, const std::complex<U>& expected) {
+ return check_if_equal_or_nans(numext::real(actual), numext::real(expected))
+ && check_if_equal_or_nans(numext::imag(actual), numext::imag(expected));
+}
+
+template<typename T, typename U>
+bool test_is_equal_or_nans(const T& actual, const U& expected)
+{
+ if (check_if_equal_or_nans(actual, expected)) {
+ return true;
+ }
+
+ // false:
+ std::cerr
+ << "\n actual = " << actual
+ << "\n expected = " << expected << "\n\n";
+ return false;
+}
+
+#define VERIFY_IS_EQUAL_OR_NANS(a, b) VERIFY(test_is_equal_or_nans(a, b))
+
+template<typename T>
+void check_abs() {
+ typedef typename NumTraits<T>::Real Real;
+ Real zero(0);
+
+ if(NumTraits<T>::IsSigned)
+ VERIFY_IS_EQUAL(numext::abs(-T(1)), T(1));
+ VERIFY_IS_EQUAL(numext::abs(T(0)), T(0));
+ VERIFY_IS_EQUAL(numext::abs(T(1)), T(1));
+
+ for(int k=0; k<100; ++k)
+ {
+ T x = internal::random<T>();
+ if(!internal::is_same<T,bool>::value)
+ x = x/Real(2);
+ if(NumTraits<T>::IsSigned)
+ {
+ VERIFY_IS_EQUAL(numext::abs(x), numext::abs(-x));
+ VERIFY( numext::abs(-x) >= zero );
+ }
+ VERIFY( numext::abs(x) >= zero );
+ VERIFY_IS_APPROX( numext::abs2(x), numext::abs2(numext::abs(x)) );
+ }
+}
+
+template<typename T>
+void check_arg() {
+ typedef typename NumTraits<T>::Real Real;
+ VERIFY_IS_EQUAL(numext::abs(T(0)), T(0));
+ VERIFY_IS_EQUAL(numext::abs(T(1)), T(1));
+
+ for(int k=0; k<100; ++k)
+ {
+ T x = internal::random<T>();
+ Real y = numext::arg(x);
+ VERIFY_IS_APPROX( y, std::arg(x) );
+ }
+}
+
+template<typename T>
+struct check_sqrt_impl {
+ static void run() {
+ for (int i=0; i<1000; ++i) {
+ const T x = numext::abs(internal::random<T>());
+ const T sqrtx = numext::sqrt(x);
+ VERIFY_IS_APPROX(sqrtx*sqrtx, x);
+ }
+
+ // Corner cases.
+ const T zero = T(0);
+ const T one = T(1);
+ const T inf = std::numeric_limits<T>::infinity();
+ const T nan = std::numeric_limits<T>::quiet_NaN();
+ VERIFY_IS_EQUAL(numext::sqrt(zero), zero);
+ VERIFY_IS_EQUAL(numext::sqrt(inf), inf);
+ VERIFY((numext::isnan)(numext::sqrt(nan)));
+ VERIFY((numext::isnan)(numext::sqrt(-one)));
+ }
+};
+
+template<typename T>
+struct check_sqrt_impl<std::complex<T> > {
+ static void run() {
+ typedef typename std::complex<T> ComplexT;
+
+ for (int i=0; i<1000; ++i) {
+ const ComplexT x = internal::random<ComplexT>();
+ const ComplexT sqrtx = numext::sqrt(x);
+ VERIFY_IS_APPROX(sqrtx*sqrtx, x);
+ }
+
+ // Corner cases.
+ const T zero = T(0);
+ const T one = T(1);
+ const T inf = std::numeric_limits<T>::infinity();
+ const T nan = std::numeric_limits<T>::quiet_NaN();
+
+ // Set of corner cases from https://en.cppreference.com/w/cpp/numeric/complex/sqrt
+ const int kNumCorners = 20;
+ const ComplexT corners[kNumCorners][2] = {
+ {ComplexT(zero, zero), ComplexT(zero, zero)},
+ {ComplexT(-zero, zero), ComplexT(zero, zero)},
+ {ComplexT(zero, -zero), ComplexT(zero, zero)},
+ {ComplexT(-zero, -zero), ComplexT(zero, zero)},
+ {ComplexT(one, inf), ComplexT(inf, inf)},
+ {ComplexT(nan, inf), ComplexT(inf, inf)},
+ {ComplexT(one, -inf), ComplexT(inf, -inf)},
+ {ComplexT(nan, -inf), ComplexT(inf, -inf)},
+ {ComplexT(-inf, one), ComplexT(zero, inf)},
+ {ComplexT(inf, one), ComplexT(inf, zero)},
+ {ComplexT(-inf, -one), ComplexT(zero, -inf)},
+ {ComplexT(inf, -one), ComplexT(inf, -zero)},
+ {ComplexT(-inf, nan), ComplexT(nan, inf)},
+ {ComplexT(inf, nan), ComplexT(inf, nan)},
+ {ComplexT(zero, nan), ComplexT(nan, nan)},
+ {ComplexT(one, nan), ComplexT(nan, nan)},
+ {ComplexT(nan, zero), ComplexT(nan, nan)},
+ {ComplexT(nan, one), ComplexT(nan, nan)},
+ {ComplexT(nan, -one), ComplexT(nan, nan)},
+ {ComplexT(nan, nan), ComplexT(nan, nan)},
+ };
+
+ for (int i=0; i<kNumCorners; ++i) {
+ const ComplexT& x = corners[i][0];
+ const ComplexT sqrtx = corners[i][1];
+ VERIFY_IS_EQUAL_OR_NANS(numext::sqrt(x), sqrtx);
+ }
+ }
+};
+
+template<typename T>
+void check_sqrt() {
+ check_sqrt_impl<T>::run();
+}
+
+template<typename T>
+struct check_rsqrt_impl {
+ static void run() {
+ const T zero = T(0);
+ const T one = T(1);
+ const T inf = std::numeric_limits<T>::infinity();
+ const T nan = std::numeric_limits<T>::quiet_NaN();
+
+ for (int i=0; i<1000; ++i) {
+ const T x = numext::abs(internal::random<T>());
+ const T rsqrtx = numext::rsqrt(x);
+ const T invx = one / x;
+ VERIFY_IS_APPROX(rsqrtx*rsqrtx, invx);
+ }
+
+ // Corner cases.
+ VERIFY_IS_EQUAL(numext::rsqrt(zero), inf);
+ VERIFY_IS_EQUAL(numext::rsqrt(inf), zero);
+ VERIFY((numext::isnan)(numext::rsqrt(nan)));
+ VERIFY((numext::isnan)(numext::rsqrt(-one)));
+ }
+};
+
+template<typename T>
+struct check_rsqrt_impl<std::complex<T> > {
+ static void run() {
+ typedef typename std::complex<T> ComplexT;
+ const T zero = T(0);
+ const T one = T(1);
+ const T inf = std::numeric_limits<T>::infinity();
+ const T nan = std::numeric_limits<T>::quiet_NaN();
+
+ for (int i=0; i<1000; ++i) {
+ const ComplexT x = internal::random<ComplexT>();
+ const ComplexT invx = ComplexT(one, zero) / x;
+ const ComplexT rsqrtx = numext::rsqrt(x);
+ VERIFY_IS_APPROX(rsqrtx*rsqrtx, invx);
+ }
+
+ // GCC and MSVC differ in their treatment of 1/(0 + 0i)
+ // GCC/clang = (inf, nan)
+ // MSVC = (nan, nan)
+ // and 1 / (x + inf i)
+ // GCC/clang = (0, 0)
+ // MSVC = (nan, nan)
+ #if (EIGEN_COMP_GNUC)
+ {
+ const int kNumCorners = 20;
+ const ComplexT corners[kNumCorners][2] = {
+ // Only consistent across GCC, clang
+ {ComplexT(zero, zero), ComplexT(zero, zero)},
+ {ComplexT(-zero, zero), ComplexT(zero, zero)},
+ {ComplexT(zero, -zero), ComplexT(zero, zero)},
+ {ComplexT(-zero, -zero), ComplexT(zero, zero)},
+ {ComplexT(one, inf), ComplexT(inf, inf)},
+ {ComplexT(nan, inf), ComplexT(inf, inf)},
+ {ComplexT(one, -inf), ComplexT(inf, -inf)},
+ {ComplexT(nan, -inf), ComplexT(inf, -inf)},
+ // Consistent across GCC, clang, MSVC
+ {ComplexT(-inf, one), ComplexT(zero, inf)},
+ {ComplexT(inf, one), ComplexT(inf, zero)},
+ {ComplexT(-inf, -one), ComplexT(zero, -inf)},
+ {ComplexT(inf, -one), ComplexT(inf, -zero)},
+ {ComplexT(-inf, nan), ComplexT(nan, inf)},
+ {ComplexT(inf, nan), ComplexT(inf, nan)},
+ {ComplexT(zero, nan), ComplexT(nan, nan)},
+ {ComplexT(one, nan), ComplexT(nan, nan)},
+ {ComplexT(nan, zero), ComplexT(nan, nan)},
+ {ComplexT(nan, one), ComplexT(nan, nan)},
+ {ComplexT(nan, -one), ComplexT(nan, nan)},
+ {ComplexT(nan, nan), ComplexT(nan, nan)},
+ };
+
+ for (int i=0; i<kNumCorners; ++i) {
+ const ComplexT& x = corners[i][0];
+ const ComplexT rsqrtx = ComplexT(one, zero) / corners[i][1];
+ VERIFY_IS_EQUAL_OR_NANS(numext::rsqrt(x), rsqrtx);
+ }
+ }
+ #endif
+ }
+};
+
+template<typename T>
+void check_rsqrt() {
+ check_rsqrt_impl<T>::run();
+}
+
+EIGEN_DECLARE_TEST(numext) {
+ for(int k=0; k<g_repeat; ++k)
+ {
+ CALL_SUBTEST( check_abs<bool>() );
+ CALL_SUBTEST( check_abs<signed char>() );
+ CALL_SUBTEST( check_abs<unsigned char>() );
+ CALL_SUBTEST( check_abs<short>() );
+ CALL_SUBTEST( check_abs<unsigned short>() );
+ CALL_SUBTEST( check_abs<int>() );
+ CALL_SUBTEST( check_abs<unsigned int>() );
+ CALL_SUBTEST( check_abs<long>() );
+ CALL_SUBTEST( check_abs<unsigned long>() );
+ CALL_SUBTEST( check_abs<half>() );
+ CALL_SUBTEST( check_abs<bfloat16>() );
+ CALL_SUBTEST( check_abs<float>() );
+ CALL_SUBTEST( check_abs<double>() );
+ CALL_SUBTEST( check_abs<long double>() );
+ CALL_SUBTEST( check_abs<std::complex<float> >() );
+ CALL_SUBTEST( check_abs<std::complex<double> >() );
+
+ CALL_SUBTEST( check_arg<std::complex<float> >() );
+ CALL_SUBTEST( check_arg<std::complex<double> >() );
+
+ CALL_SUBTEST( check_sqrt<float>() );
+ CALL_SUBTEST( check_sqrt<double>() );
+ CALL_SUBTEST( check_sqrt<std::complex<float> >() );
+ CALL_SUBTEST( check_sqrt<std::complex<double> >() );
+
+ CALL_SUBTEST( check_rsqrt<float>() );
+ CALL_SUBTEST( check_rsqrt<double>() );
+ CALL_SUBTEST( check_rsqrt<std::complex<float> >() );
+ CALL_SUBTEST( check_rsqrt<std::complex<double> >() );
+ }
+}
diff --git a/test/packetmath.cpp b/test/packetmath.cpp
new file mode 100644
index 0000000..d7c7c9c
--- /dev/null
+++ b/test/packetmath.cpp
@@ -0,0 +1,1505 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "packetmath_test_shared.h"
+#include "random_without_cast_overflow.h"
+
+template <typename T>
+inline T REF_ADD(const T& a, const T& b) {
+ return a + b;
+}
+template <typename T>
+inline T REF_SUB(const T& a, const T& b) {
+ return a - b;
+}
+template <typename T>
+inline T REF_MUL(const T& a, const T& b) {
+ return a * b;
+}
+template <typename T>
+inline T REF_MADD(const T& a, const T& b, const T& c) {
+ return a * b + c;
+}
+template <typename T>
+inline T REF_MSUB(const T& a, const T& b, const T& c) {
+ return a * b - c;
+}
+template <typename T>
+inline T REF_NMADD(const T& a, const T& b, const T& c) {
+ return (-a * b) + c;
+}
+template <typename T>
+inline T REF_NMSUB(const T& a, const T& b, const T& c) {
+ return (-a * b) - c;
+}
+template <typename T>
+inline T REF_DIV(const T& a, const T& b) {
+ return a / b;
+}
+template <typename T>
+inline T REF_RECIPROCAL(const T& a) {
+ return T(1) / a;
+}
+template <typename T>
+inline T REF_ABS_DIFF(const T& a, const T& b) {
+ return a > b ? a - b : b - a;
+}
+
+// Specializations for bool.
+template <>
+inline bool REF_ADD(const bool& a, const bool& b) {
+ return a || b;
+}
+template <>
+inline bool REF_SUB(const bool& a, const bool& b) {
+ return a ^ b;
+}
+template <>
+inline bool REF_MUL(const bool& a, const bool& b) {
+ return a && b;
+}
+template <>
+inline bool REF_MADD(const bool& a, const bool& b, const bool& c) {
+ return (a && b) || c;
+}
+
+template <typename T>
+inline T REF_FREXP(const T& x, T& exp) {
+ int iexp = 0;
+ EIGEN_USING_STD(frexp)
+ const T out = static_cast<T>(frexp(x, &iexp));
+ exp = static_cast<T>(iexp);
+
+ // The exponent value is unspecified if the input is inf or NaN, but MSVC
+ // seems to set it to 1. We need to set it back to zero for consistency.
+ if (!(numext::isfinite)(x)) {
+ exp = T(0);
+ }
+ return out;
+}
+
+template <typename T>
+inline T REF_LDEXP(const T& x, const T& exp) {
+ EIGEN_USING_STD(ldexp)
+ return static_cast<T>(ldexp(x, static_cast<int>(exp)));
+}
+
+// Uses pcast to cast from one array to another.
+template <typename SrcPacket, typename TgtPacket, int SrcCoeffRatio, int TgtCoeffRatio>
+struct pcast_array;
+
+template <typename SrcPacket, typename TgtPacket, int TgtCoeffRatio>
+struct pcast_array<SrcPacket, TgtPacket, 1, TgtCoeffRatio> {
+ typedef typename internal::unpacket_traits<SrcPacket>::type SrcScalar;
+ typedef typename internal::unpacket_traits<TgtPacket>::type TgtScalar;
+ static void cast(const SrcScalar* src, size_t size, TgtScalar* dst) {
+ static const int SrcPacketSize = internal::unpacket_traits<SrcPacket>::size;
+ static const int TgtPacketSize = internal::unpacket_traits<TgtPacket>::size;
+ size_t i;
+ for (i = 0; i < size && i + SrcPacketSize <= size; i += TgtPacketSize) {
+ internal::pstoreu(dst + i, internal::pcast<SrcPacket, TgtPacket>(internal::ploadu<SrcPacket>(src + i)));
+ }
+ // Leftovers that cannot be loaded into a packet.
+ for (; i < size; ++i) {
+ dst[i] = static_cast<TgtScalar>(src[i]);
+ }
+ }
+};
+
+template <typename SrcPacket, typename TgtPacket>
+struct pcast_array<SrcPacket, TgtPacket, 2, 1> {
+ static void cast(const typename internal::unpacket_traits<SrcPacket>::type* src, size_t size,
+ typename internal::unpacket_traits<TgtPacket>::type* dst) {
+ static const int SrcPacketSize = internal::unpacket_traits<SrcPacket>::size;
+ static const int TgtPacketSize = internal::unpacket_traits<TgtPacket>::size;
+ for (size_t i = 0; i < size; i += TgtPacketSize) {
+ SrcPacket a = internal::ploadu<SrcPacket>(src + i);
+ SrcPacket b = internal::ploadu<SrcPacket>(src + i + SrcPacketSize);
+ internal::pstoreu(dst + i, internal::pcast<SrcPacket, TgtPacket>(a, b));
+ }
+ }
+};
+
+template <typename SrcPacket, typename TgtPacket>
+struct pcast_array<SrcPacket, TgtPacket, 4, 1> {
+ static void cast(const typename internal::unpacket_traits<SrcPacket>::type* src, size_t size,
+ typename internal::unpacket_traits<TgtPacket>::type* dst) {
+ static const int SrcPacketSize = internal::unpacket_traits<SrcPacket>::size;
+ static const int TgtPacketSize = internal::unpacket_traits<TgtPacket>::size;
+ for (size_t i = 0; i < size; i += TgtPacketSize) {
+ SrcPacket a = internal::ploadu<SrcPacket>(src + i);
+ SrcPacket b = internal::ploadu<SrcPacket>(src + i + SrcPacketSize);
+ SrcPacket c = internal::ploadu<SrcPacket>(src + i + 2 * SrcPacketSize);
+ SrcPacket d = internal::ploadu<SrcPacket>(src + i + 3 * SrcPacketSize);
+ internal::pstoreu(dst + i, internal::pcast<SrcPacket, TgtPacket>(a, b, c, d));
+ }
+ }
+};
+
+template <typename SrcPacket, typename TgtPacket>
+struct pcast_array<SrcPacket, TgtPacket, 8, 1> {
+ static void cast(const typename internal::unpacket_traits<SrcPacket>::type* src, size_t size,
+ typename internal::unpacket_traits<TgtPacket>::type* dst) {
+ static const int SrcPacketSize = internal::unpacket_traits<SrcPacket>::size;
+ static const int TgtPacketSize = internal::unpacket_traits<TgtPacket>::size;
+ for (size_t i = 0; i < size; i += TgtPacketSize) {
+ SrcPacket a = internal::ploadu<SrcPacket>(src + i);
+ SrcPacket b = internal::ploadu<SrcPacket>(src + i + SrcPacketSize);
+ SrcPacket c = internal::ploadu<SrcPacket>(src + i + 2 * SrcPacketSize);
+ SrcPacket d = internal::ploadu<SrcPacket>(src + i + 3 * SrcPacketSize);
+ SrcPacket e = internal::ploadu<SrcPacket>(src + i + 4 * SrcPacketSize);
+ SrcPacket f = internal::ploadu<SrcPacket>(src + i + 5 * SrcPacketSize);
+ SrcPacket g = internal::ploadu<SrcPacket>(src + i + 6 * SrcPacketSize);
+ SrcPacket h = internal::ploadu<SrcPacket>(src + i + 7 * SrcPacketSize);
+ internal::pstoreu(dst + i, internal::pcast<SrcPacket, TgtPacket>(a, b, c, d, e, f, g, h));
+ }
+ }
+};
+
+template <typename SrcPacket, typename TgtPacket, int SrcCoeffRatio, int TgtCoeffRatio, bool CanCast = false>
+struct test_cast_helper;
+
+template <typename SrcPacket, typename TgtPacket, int SrcCoeffRatio, int TgtCoeffRatio>
+struct test_cast_helper<SrcPacket, TgtPacket, SrcCoeffRatio, TgtCoeffRatio, false> {
+ static void run() {}
+};
+
+template <typename SrcPacket, typename TgtPacket, int SrcCoeffRatio, int TgtCoeffRatio>
+struct test_cast_helper<SrcPacket, TgtPacket, SrcCoeffRatio, TgtCoeffRatio, true> {
+ static void run() {
+ typedef typename internal::unpacket_traits<SrcPacket>::type SrcScalar;
+ typedef typename internal::unpacket_traits<TgtPacket>::type TgtScalar;
+ static const int SrcPacketSize = internal::unpacket_traits<SrcPacket>::size;
+ static const int TgtPacketSize = internal::unpacket_traits<TgtPacket>::size;
+ static const int BlockSize = SrcPacketSize * SrcCoeffRatio;
+ eigen_assert(BlockSize == TgtPacketSize * TgtCoeffRatio && "Packet sizes and cast ratios are mismatched.");
+
+ static const int DataSize = 10 * BlockSize;
+ EIGEN_ALIGN_MAX SrcScalar data1[DataSize];
+ EIGEN_ALIGN_MAX TgtScalar data2[DataSize];
+ EIGEN_ALIGN_MAX TgtScalar ref[DataSize];
+
+ // Construct a packet of scalars that will not overflow when casting
+ for (int i = 0; i < DataSize; ++i) {
+ data1[i] = internal::random_without_cast_overflow<SrcScalar, TgtScalar>::value();
+ }
+
+ for (int i = 0; i < DataSize; ++i) {
+ ref[i] = static_cast<const TgtScalar>(data1[i]);
+ }
+
+ pcast_array<SrcPacket, TgtPacket, SrcCoeffRatio, TgtCoeffRatio>::cast(data1, DataSize, data2);
+
+ VERIFY(test::areApprox(ref, data2, DataSize) && "internal::pcast<>");
+ }
+};
+
+template <typename SrcPacket, typename TgtPacket>
+struct test_cast {
+ static void run() {
+ typedef typename internal::unpacket_traits<SrcPacket>::type SrcScalar;
+ typedef typename internal::unpacket_traits<TgtPacket>::type TgtScalar;
+ typedef typename internal::type_casting_traits<SrcScalar, TgtScalar> TypeCastingTraits;
+ static const int SrcCoeffRatio = TypeCastingTraits::SrcCoeffRatio;
+ static const int TgtCoeffRatio = TypeCastingTraits::TgtCoeffRatio;
+ static const int SrcPacketSize = internal::unpacket_traits<SrcPacket>::size;
+ static const int TgtPacketSize = internal::unpacket_traits<TgtPacket>::size;
+ static const bool HasCast =
+ internal::unpacket_traits<SrcPacket>::vectorizable && internal::unpacket_traits<TgtPacket>::vectorizable &&
+ TypeCastingTraits::VectorizedCast && (SrcPacketSize * SrcCoeffRatio == TgtPacketSize * TgtCoeffRatio);
+ test_cast_helper<SrcPacket, TgtPacket, SrcCoeffRatio, TgtCoeffRatio, HasCast>::run();
+ }
+};
+
+template <typename SrcPacket, typename TgtScalar,
+ typename TgtPacket = typename internal::packet_traits<TgtScalar>::type,
+ bool Vectorized = internal::packet_traits<TgtScalar>::Vectorizable,
+ bool HasHalf = !internal::is_same<typename internal::unpacket_traits<TgtPacket>::half, TgtPacket>::value>
+struct test_cast_runner;
+
+template <typename SrcPacket, typename TgtScalar, typename TgtPacket>
+struct test_cast_runner<SrcPacket, TgtScalar, TgtPacket, true, false> {
+ static void run() { test_cast<SrcPacket, TgtPacket>::run(); }
+};
+
+template <typename SrcPacket, typename TgtScalar, typename TgtPacket>
+struct test_cast_runner<SrcPacket, TgtScalar, TgtPacket, true, true> {
+ static void run() {
+ test_cast<SrcPacket, TgtPacket>::run();
+ test_cast_runner<SrcPacket, TgtScalar, typename internal::unpacket_traits<TgtPacket>::half>::run();
+ }
+};
+
+template <typename SrcPacket, typename TgtScalar, typename TgtPacket>
+struct test_cast_runner<SrcPacket, TgtScalar, TgtPacket, false, false> {
+ static void run() {}
+};
+
+template <typename Scalar, typename Packet, typename EnableIf = void>
+struct packetmath_pcast_ops_runner {
+ static void run() {
+ test_cast_runner<Packet, float>::run();
+ test_cast_runner<Packet, double>::run();
+ test_cast_runner<Packet, int8_t>::run();
+ test_cast_runner<Packet, uint8_t>::run();
+ test_cast_runner<Packet, int16_t>::run();
+ test_cast_runner<Packet, uint16_t>::run();
+ test_cast_runner<Packet, int32_t>::run();
+ test_cast_runner<Packet, uint32_t>::run();
+ test_cast_runner<Packet, int64_t>::run();
+ test_cast_runner<Packet, uint64_t>::run();
+ test_cast_runner<Packet, bool>::run();
+ test_cast_runner<Packet, std::complex<float> >::run();
+ test_cast_runner<Packet, std::complex<double> >::run();
+ test_cast_runner<Packet, half>::run();
+ test_cast_runner<Packet, bfloat16>::run();
+ }
+};
+
+// Only some types support cast from std::complex<>.
+template <typename Scalar, typename Packet>
+struct packetmath_pcast_ops_runner<Scalar, Packet, std::enable_if_t<NumTraits<Scalar>::IsComplex>> {
+ static void run() {
+ test_cast_runner<Packet, std::complex<float> >::run();
+ test_cast_runner<Packet, std::complex<double> >::run();
+ test_cast_runner<Packet, half>::run();
+ test_cast_runner<Packet, bfloat16>::run();
+ }
+};
+
+template <typename Scalar, typename Packet>
+void packetmath_boolean_mask_ops() {
+ const int PacketSize = internal::unpacket_traits<Packet>::size;
+ const int size = 2 * PacketSize;
+ EIGEN_ALIGN_MAX Scalar data1[size];
+ EIGEN_ALIGN_MAX Scalar data2[size];
+ EIGEN_ALIGN_MAX Scalar ref[size];
+
+ for (int i = 0; i < size; ++i) {
+ data1[i] = internal::random<Scalar>();
+ }
+ CHECK_CWISE1(internal::ptrue, internal::ptrue);
+ CHECK_CWISE2_IF(true, internal::pandnot, internal::pandnot);
+ for (int i = 0; i < PacketSize; ++i) {
+ data1[i] = Scalar(i);
+ data1[i + PacketSize] = internal::random<bool>() ? data1[i] : Scalar(0);
+ }
+
+ CHECK_CWISE2_IF(true, internal::pcmp_eq, internal::pcmp_eq);
+
+ //Test (-0) == (0) for signed operations
+ for (int i = 0; i < PacketSize; ++i) {
+ data1[i] = Scalar(-0.0);
+ data1[i + PacketSize] = internal::random<bool>() ? data1[i] : Scalar(0);
+ }
+ CHECK_CWISE2_IF(true, internal::pcmp_eq, internal::pcmp_eq);
+
+ //Test NaN
+ for (int i = 0; i < PacketSize; ++i) {
+ data1[i] = NumTraits<Scalar>::quiet_NaN();
+ data1[i + PacketSize] = internal::random<bool>() ? data1[i] : Scalar(0);
+ }
+ CHECK_CWISE2_IF(true, internal::pcmp_eq, internal::pcmp_eq);
+}
+
+template <typename Scalar, typename Packet>
+void packetmath_boolean_mask_ops_real() {
+ const int PacketSize = internal::unpacket_traits<Packet>::size;
+ const int size = 2 * PacketSize;
+ EIGEN_ALIGN_MAX Scalar data1[size];
+ EIGEN_ALIGN_MAX Scalar data2[size];
+ EIGEN_ALIGN_MAX Scalar ref[size];
+
+ for (int i = 0; i < PacketSize; ++i) {
+ data1[i] = internal::random<Scalar>();
+ data1[i + PacketSize] = internal::random<bool>() ? data1[i] : Scalar(0);
+ }
+
+ CHECK_CWISE2_IF(true, internal::pcmp_lt_or_nan, internal::pcmp_lt_or_nan);
+
+ //Test (-0) <=/< (0) for signed operations
+ for (int i = 0; i < PacketSize; ++i) {
+ data1[i] = Scalar(-0.0);
+ data1[i + PacketSize] = internal::random<bool>() ? data1[i] : Scalar(0);
+ }
+ CHECK_CWISE2_IF(true, internal::pcmp_lt_or_nan, internal::pcmp_lt_or_nan);
+
+ //Test NaN
+ for (int i = 0; i < PacketSize; ++i) {
+ data1[i] = NumTraits<Scalar>::quiet_NaN();
+ data1[i + PacketSize] = internal::random<bool>() ? data1[i] : Scalar(0);
+ }
+ CHECK_CWISE2_IF(true, internal::pcmp_lt_or_nan, internal::pcmp_lt_or_nan);
+}
+
+template <typename Scalar, typename Packet>
+void packetmath_boolean_mask_ops_notcomplex() {
+ const int PacketSize = internal::unpacket_traits<Packet>::size;
+ const int size = 2 * PacketSize;
+ EIGEN_ALIGN_MAX Scalar data1[size];
+ EIGEN_ALIGN_MAX Scalar data2[size];
+ EIGEN_ALIGN_MAX Scalar ref[size];
+
+ for (int i = 0; i < PacketSize; ++i) {
+ data1[i] = internal::random<Scalar>();
+ data1[i + PacketSize] = internal::random<bool>() ? data1[i] : Scalar(0);
+ }
+
+ CHECK_CWISE2_IF(true, internal::pcmp_le, internal::pcmp_le);
+ CHECK_CWISE2_IF(true, internal::pcmp_lt, internal::pcmp_lt);
+
+ //Test (-0) <=/< (0) for signed operations
+ for (int i = 0; i < PacketSize; ++i) {
+ data1[i] = Scalar(-0.0);
+ data1[i + PacketSize] = internal::random<bool>() ? data1[i] : Scalar(0);
+ }
+ CHECK_CWISE2_IF(true, internal::pcmp_le, internal::pcmp_le);
+ CHECK_CWISE2_IF(true, internal::pcmp_lt, internal::pcmp_lt);
+
+ //Test NaN
+ for (int i = 0; i < PacketSize; ++i) {
+ data1[i] = NumTraits<Scalar>::quiet_NaN();
+ data1[i + PacketSize] = internal::random<bool>() ? data1[i] : Scalar(0);
+ }
+ CHECK_CWISE2_IF(true, internal::pcmp_le, internal::pcmp_le);
+ CHECK_CWISE2_IF(true, internal::pcmp_lt, internal::pcmp_lt);
+}
+
+// Packet16b representing bool does not support ptrue, pandnot or pcmp_eq, since the scalar path
+// (for some compilers) compute the bitwise and with 0x1 of the results to keep the value in [0,1].
+template<>
+void packetmath_boolean_mask_ops<bool, internal::packet_traits<bool>::type>() {}
+template<>
+void packetmath_boolean_mask_ops_notcomplex<bool, internal::packet_traits<bool>::type>() {}
+
+template <typename Scalar, typename Packet>
+void packetmath_minus_zero_add() {
+ const int PacketSize = internal::unpacket_traits<Packet>::size;
+ const int size = 2 * PacketSize;
+ EIGEN_ALIGN_MAX Scalar data1[size] = {};
+ EIGEN_ALIGN_MAX Scalar data2[size] = {};
+ EIGEN_ALIGN_MAX Scalar ref[size] = {};
+
+ for (int i = 0; i < PacketSize; ++i) {
+ data1[i] = Scalar(-0.0);
+ data1[i + PacketSize] = Scalar(-0.0);
+ }
+ CHECK_CWISE2_IF(internal::packet_traits<Scalar>::HasAdd, REF_ADD, internal::padd);
+}
+
+// Ensure optimization barrier compiles and doesn't modify contents.
+// Only applies to raw types, so will not work for std::complex, Eigen::half
+// or Eigen::bfloat16. For those you would need to refer to an underlying
+// storage element.
+template<typename Packet, typename EnableIf = void>
+struct eigen_optimization_barrier_test {
+ static void run() {}
+};
+
+template<typename Packet>
+struct eigen_optimization_barrier_test<Packet, std::enable_if_t<
+ !NumTraits<Packet>::IsComplex &&
+ !internal::is_same<Packet, Eigen::half>::value &&
+ !internal::is_same<Packet, Eigen::bfloat16>::value
+ >> {
+ static void run() {
+ typedef typename internal::unpacket_traits<Packet>::type Scalar;
+ Scalar s = internal::random<Scalar>();
+ Packet barrier = internal::pset1<Packet>(s);
+ EIGEN_OPTIMIZATION_BARRIER(barrier);
+ eigen_assert(s == internal::pfirst(barrier) && "EIGEN_OPTIMIZATION_BARRIER");
+ }
+};
+
+template <typename Scalar, typename Packet>
+void packetmath() {
+ typedef internal::packet_traits<Scalar> PacketTraits;
+ const int PacketSize = internal::unpacket_traits<Packet>::size;
+ typedef typename NumTraits<Scalar>::Real RealScalar;
+
+ if (g_first_pass)
+ std::cerr << "=== Testing packet of type '" << typeid(Packet).name() << "' and scalar type '"
+ << typeid(Scalar).name() << "' and size '" << PacketSize << "' ===\n";
+
+ const int max_size = PacketSize > 4 ? PacketSize : 4;
+ const int size = PacketSize * max_size;
+ EIGEN_ALIGN_MAX Scalar data1[size];
+ EIGEN_ALIGN_MAX Scalar data2[size];
+ EIGEN_ALIGN_MAX Scalar data3[size];
+ EIGEN_ALIGN_MAX Scalar ref[size];
+ RealScalar refvalue = RealScalar(0);
+
+ eigen_optimization_barrier_test<Packet>::run();
+ eigen_optimization_barrier_test<Scalar>::run();
+
+ for (int i = 0; i < size; ++i) {
+ data1[i] = internal::random<Scalar>() / RealScalar(PacketSize);
+ data2[i] = internal::random<Scalar>() / RealScalar(PacketSize);
+ refvalue = (std::max)(refvalue, numext::abs(data1[i]));
+ }
+
+ internal::pstore(data2, internal::pload<Packet>(data1));
+ VERIFY(test::areApprox(data1, data2, PacketSize) && "aligned load/store");
+
+ for (int offset = 0; offset < PacketSize; ++offset) {
+ internal::pstore(data2, internal::ploadu<Packet>(data1 + offset));
+ VERIFY(test::areApprox(data1 + offset, data2, PacketSize) && "internal::ploadu");
+ }
+
+ for (int offset = 0; offset < PacketSize; ++offset) {
+ internal::pstoreu(data2 + offset, internal::pload<Packet>(data1));
+ VERIFY(test::areApprox(data1, data2 + offset, PacketSize) && "internal::pstoreu");
+ }
+
+ for (int M = 0; M < PacketSize; ++M) {
+ for (int N = 0; N <= PacketSize; ++N) {
+ for (int j = 0; j < size; ++j) {
+ data1[j] = internal::random<Scalar>() / RealScalar(PacketSize);
+ data2[j] = internal::random<Scalar>() / RealScalar(PacketSize);
+ refvalue = (std::max)(refvalue, numext::abs(data1[j]));
+ }
+
+ if (M == 0) {
+ internal::pstore_partial(data2, internal::pload_partial<Packet>(data1, N), N);
+ VERIFY(test::areApprox(data1, data2, N) && "aligned loadN/storeN");
+
+ for (int offset = 0; offset < PacketSize; ++offset) {
+ internal::pstore_partial(data2, internal::ploadu_partial<Packet>(data1 + offset, N), N);
+ VERIFY(test::areApprox(data1 + offset, data2, N) && "internal::ploadu_partial");
+ }
+
+ for (int offset = 0; offset < PacketSize; ++offset) {
+ internal::pstoreu_partial(data2 + offset, internal::pload_partial<Packet>(data1, N), N);
+ VERIFY(test::areApprox(data1, data2 + offset, N) && "internal::pstoreu_partial");
+ }
+ }
+
+ if (N + M > PacketSize) continue; // Don't read or write past end of Packet
+
+ internal::pstore_partial(data2, internal::pload_partial<Packet>(data1, N, M), N, M);
+ VERIFY(test::areApprox(data1, data2, N) && "aligned offset loadN/storeN");
+ }
+ }
+
+ if (internal::unpacket_traits<Packet>::masked_load_available) {
+ test::packet_helper<internal::unpacket_traits<Packet>::masked_load_available, Packet> h;
+ unsigned long long max_umask = (0x1ull << PacketSize);
+
+ for (int offset = 0; offset < PacketSize; ++offset) {
+ for (unsigned long long umask = 0; umask < max_umask; ++umask) {
+ h.store(data2, h.load(data1 + offset, umask));
+ for (int k = 0; k < PacketSize; ++k) data3[k] = ((umask & (0x1ull << k)) >> k) ? data1[k + offset] : Scalar(0);
+ VERIFY(test::areApprox(data3, data2, PacketSize) && "internal::ploadu masked");
+ }
+ }
+ }
+
+ if (internal::unpacket_traits<Packet>::masked_store_available) {
+ test::packet_helper<internal::unpacket_traits<Packet>::masked_store_available, Packet> h;
+ unsigned long long max_umask = (0x1ull << PacketSize);
+
+ for (int offset = 0; offset < PacketSize; ++offset) {
+ for (unsigned long long umask = 0; umask < max_umask; ++umask) {
+ internal::pstore(data2, internal::pset1<Packet>(Scalar(0)));
+ h.store(data2, h.loadu(data1 + offset), umask);
+ for (int k = 0; k < PacketSize; ++k) data3[k] = ((umask & (0x1ull << k)) >> k) ? data1[k + offset] : Scalar(0);
+ VERIFY(test::areApprox(data3, data2, PacketSize) && "internal::pstoreu masked");
+ }
+ }
+ }
+
+ VERIFY((!PacketTraits::Vectorizable) || PacketTraits::HasAdd);
+ VERIFY((!PacketTraits::Vectorizable) || PacketTraits::HasSub);
+ VERIFY((!PacketTraits::Vectorizable) || PacketTraits::HasMul);
+
+ CHECK_CWISE2_IF(PacketTraits::HasAdd, REF_ADD, internal::padd);
+ CHECK_CWISE2_IF(PacketTraits::HasSub, REF_SUB, internal::psub);
+ CHECK_CWISE2_IF(PacketTraits::HasMul, REF_MUL, internal::pmul);
+ CHECK_CWISE2_IF(PacketTraits::HasDiv, REF_DIV, internal::pdiv);
+
+ CHECK_CWISE1_IF(PacketTraits::HasNegate, internal::negate, internal::pnegate);
+ CHECK_CWISE1_IF(PacketTraits::HasReciprocal, REF_RECIPROCAL, internal::preciprocal);
+ CHECK_CWISE1(numext::conj, internal::pconj);
+ CHECK_CWISE1_IF(PacketTraits::HasSign, numext::sign, internal::psign);
+
+
+ for (int offset = 0; offset < 3; ++offset) {
+ for (int i = 0; i < PacketSize; ++i) ref[i] = data1[offset];
+ internal::pstore(data2, internal::pset1<Packet>(data1[offset]));
+ VERIFY(test::areApprox(ref, data2, PacketSize) && "internal::pset1");
+ }
+
+ {
+ for (int i = 0; i < PacketSize * 4; ++i) ref[i] = data1[i / PacketSize];
+ Packet A0, A1, A2, A3;
+ internal::pbroadcast4<Packet>(data1, A0, A1, A2, A3);
+ internal::pstore(data2 + 0 * PacketSize, A0);
+ internal::pstore(data2 + 1 * PacketSize, A1);
+ internal::pstore(data2 + 2 * PacketSize, A2);
+ internal::pstore(data2 + 3 * PacketSize, A3);
+ VERIFY(test::areApprox(ref, data2, 4 * PacketSize) && "internal::pbroadcast4");
+ }
+
+ {
+ for (int i = 0; i < PacketSize * 2; ++i) ref[i] = data1[i / PacketSize];
+ Packet A0, A1;
+ internal::pbroadcast2<Packet>(data1, A0, A1);
+ internal::pstore(data2 + 0 * PacketSize, A0);
+ internal::pstore(data2 + 1 * PacketSize, A1);
+ VERIFY(test::areApprox(ref, data2, 2 * PacketSize) && "internal::pbroadcast2");
+ }
+
+ VERIFY(internal::isApprox(data1[0], internal::pfirst(internal::pload<Packet>(data1))) && "internal::pfirst");
+
+ if (PacketSize > 1) {
+ // apply different offsets to check that ploaddup is robust to unaligned inputs
+ for (int offset = 0; offset < 4; ++offset) {
+ for (int i = 0; i < PacketSize / 2; ++i) ref[2 * i + 0] = ref[2 * i + 1] = data1[offset + i];
+ internal::pstore(data2, internal::ploaddup<Packet>(data1 + offset));
+ VERIFY(test::areApprox(ref, data2, PacketSize) && "ploaddup");
+ }
+ }
+
+ if (PacketSize > 2) {
+ // apply different offsets to check that ploadquad is robust to unaligned inputs
+ for (int offset = 0; offset < 4; ++offset) {
+ for (int i = 0; i < PacketSize / 4; ++i)
+ ref[4 * i + 0] = ref[4 * i + 1] = ref[4 * i + 2] = ref[4 * i + 3] = data1[offset + i];
+ internal::pstore(data2, internal::ploadquad<Packet>(data1 + offset));
+ VERIFY(test::areApprox(ref, data2, PacketSize) && "ploadquad");
+ }
+ }
+
+ ref[0] = Scalar(0);
+ for (int i = 0; i < PacketSize; ++i) ref[0] += data1[i];
+ VERIFY(test::isApproxAbs(ref[0], internal::predux(internal::pload<Packet>(data1)), refvalue) && "internal::predux");
+
+ if (!internal::is_same<Packet, typename internal::unpacket_traits<Packet>::half>::value) {
+ int HalfPacketSize = PacketSize > 4 ? PacketSize / 2 : PacketSize;
+ for (int i = 0; i < HalfPacketSize; ++i) ref[i] = Scalar(0);
+ for (int i = 0; i < PacketSize; ++i) ref[i % HalfPacketSize] += data1[i];
+ internal::pstore(data2, internal::predux_half_dowto4(internal::pload<Packet>(data1)));
+ VERIFY(test::areApprox(ref, data2, HalfPacketSize) && "internal::predux_half_dowto4");
+ }
+
+ ref[0] = Scalar(1);
+ for (int i = 0; i < PacketSize; ++i) ref[0] = REF_MUL(ref[0], data1[i]);
+ VERIFY(internal::isApprox(ref[0], internal::predux_mul(internal::pload<Packet>(data1))) && "internal::predux_mul");
+
+ for (int i = 0; i < PacketSize; ++i) ref[i] = data1[PacketSize - i - 1];
+ internal::pstore(data2, internal::preverse(internal::pload<Packet>(data1)));
+ VERIFY(test::areApprox(ref, data2, PacketSize) && "internal::preverse");
+
+ internal::PacketBlock<Packet> kernel;
+ for (int i = 0; i < PacketSize; ++i) {
+ kernel.packet[i] = internal::pload<Packet>(data1 + i * PacketSize);
+ }
+ ptranspose(kernel);
+ for (int i = 0; i < PacketSize; ++i) {
+ internal::pstore(data2, kernel.packet[i]);
+ for (int j = 0; j < PacketSize; ++j) {
+ VERIFY(test::isApproxAbs(data2[j], data1[i + j * PacketSize], refvalue) && "ptranspose");
+ }
+ }
+
+ // GeneralBlockPanelKernel also checks PacketBlock<Packet,(PacketSize%4)==0?4:PacketSize>;
+ if (PacketSize > 4 && PacketSize % 4 == 0) {
+ internal::PacketBlock<Packet, PacketSize%4==0?4:PacketSize> kernel2;
+ for (int i = 0; i < 4; ++i) {
+ kernel2.packet[i] = internal::pload<Packet>(data1 + i * PacketSize);
+ }
+ ptranspose(kernel2);
+ int data_counter = 0;
+ for (int i = 0; i < PacketSize; ++i) {
+ for (int j = 0; j < 4; ++j) {
+ data2[data_counter++] = data1[j*PacketSize + i];
+ }
+ }
+ for (int i = 0; i < 4; ++i) {
+ internal::pstore(data3, kernel2.packet[i]);
+ for (int j = 0; j < PacketSize; ++j) {
+ VERIFY(test::isApproxAbs(data3[j], data2[i*PacketSize + j], refvalue) && "ptranspose");
+ }
+ }
+ }
+
+ if (PacketTraits::HasBlend) {
+ Packet thenPacket = internal::pload<Packet>(data1);
+ Packet elsePacket = internal::pload<Packet>(data2);
+ EIGEN_ALIGN_MAX internal::Selector<PacketSize> selector;
+ for (int i = 0; i < PacketSize; ++i) {
+ selector.select[i] = i;
+ }
+
+ Packet blend = internal::pblend(selector, thenPacket, elsePacket);
+ EIGEN_ALIGN_MAX Scalar result[size];
+ internal::pstore(result, blend);
+ for (int i = 0; i < PacketSize; ++i) {
+ VERIFY(test::isApproxAbs(result[i], (selector.select[i] ? data1[i] : data2[i]), refvalue));
+ }
+ }
+
+ {
+ for (int i = 0; i < PacketSize; ++i) {
+ // "if" mask
+ unsigned char v = internal::random<bool>() ? 0xff : 0;
+ char* bytes = (char*)(data1 + i);
+ for (int k = 0; k < int(sizeof(Scalar)); ++k) {
+ bytes[k] = v;
+ }
+ // "then" packet
+ data1[i + PacketSize] = internal::random<Scalar>();
+ // "else" packet
+ data1[i + 2 * PacketSize] = internal::random<Scalar>();
+ }
+ CHECK_CWISE3_IF(true, internal::pselect, internal::pselect);
+ }
+
+ for (int i = 0; i < size; ++i) {
+ data1[i] = internal::random<Scalar>();
+ }
+ CHECK_CWISE1(internal::pzero, internal::pzero);
+ CHECK_CWISE2_IF(true, internal::por, internal::por);
+ CHECK_CWISE2_IF(true, internal::pxor, internal::pxor);
+ CHECK_CWISE2_IF(true, internal::pand, internal::pand);
+
+ packetmath_boolean_mask_ops<Scalar, Packet>();
+ packetmath_pcast_ops_runner<Scalar, Packet>::run();
+ packetmath_minus_zero_add<Scalar, Packet>();
+
+ for (int i = 0; i < size; ++i) {
+ data1[i] = numext::abs(internal::random<Scalar>());
+ }
+ CHECK_CWISE1_IF(PacketTraits::HasSqrt, numext::sqrt, internal::psqrt);
+ CHECK_CWISE1_IF(PacketTraits::HasRsqrt, numext::rsqrt, internal::prsqrt);
+ CHECK_CWISE3_IF(true, REF_MADD, internal::pmadd);
+ if (!std::is_same<Scalar, bool>::value && NumTraits<Scalar>::IsSigned) {
+ CHECK_CWISE3_IF(true, REF_NMSUB, internal::pnmsub);
+ }
+
+ // For pmsub, pnmadd, the values can cancel each other to become near zero,
+ // which can lead to very flaky tests. Here we ensure the signs are such that
+ // they do not cancel.
+ for (int i = 0; i < PacketSize; ++i) {
+ data1[i] = numext::abs(internal::random<Scalar>());
+ data1[i + PacketSize] = numext::abs(internal::random<Scalar>());
+ data1[i + 2 * PacketSize] = -numext::abs(internal::random<Scalar>());
+ }
+ if (!std::is_same<Scalar, bool>::value && NumTraits<Scalar>::IsSigned) {
+ CHECK_CWISE3_IF(true, REF_MSUB, internal::pmsub);
+ CHECK_CWISE3_IF(true, REF_NMADD, internal::pnmadd);
+ }
+}
+
+// Notice that this definition works for complex types as well.
+// c++11 has std::log2 for real, but not for complex types.
+template <typename Scalar>
+Scalar log2(Scalar x) {
+ return Scalar(EIGEN_LOG2E) * std::log(x);
+}
+
+// Create a functor out of a function so it can be passed (with overloads)
+// to another function as an input argument.
+#define CREATE_FUNCTOR(Name, Func) \
+struct Name { \
+ template<typename T> \
+ T operator()(const T& val) const { \
+ return Func(val); \
+ } \
+}
+
+CREATE_FUNCTOR(psqrt_functor, internal::psqrt);
+CREATE_FUNCTOR(prsqrt_functor, internal::prsqrt);
+
+// TODO(rmlarsen): Run this test for more functions.
+template <bool Cond, typename Scalar, typename Packet, typename RefFunctorT, typename FunctorT>
+void packetmath_test_IEEE_corner_cases(const RefFunctorT& ref_fun,
+ const FunctorT& fun) {
+ const int PacketSize = internal::unpacket_traits<Packet>::size;
+ const Scalar norm_min = (std::numeric_limits<Scalar>::min)();
+ const Scalar norm_max = (std::numeric_limits<Scalar>::max)();
+
+ constexpr int size = PacketSize * 2;
+ EIGEN_ALIGN_MAX Scalar data1[size];
+ EIGEN_ALIGN_MAX Scalar data2[size];
+ EIGEN_ALIGN_MAX Scalar ref[size];
+ for (int i = 0; i < size; ++i) {
+ data1[i] = data2[i] = ref[i] = Scalar(0);
+ }
+
+ // Test for subnormals.
+ if (Cond && std::numeric_limits<Scalar>::has_denorm == std::denorm_present) {
+
+ for (int scale = 1; scale < 5; ++scale) {
+ // When EIGEN_FAST_MATH is 1 we relax the conditions slightly, and allow the function
+ // to return the same value for subnormals as the reference would return for zero with
+ // the same sign as the input.
+ #if EIGEN_FAST_MATH
+ data1[0] = Scalar(scale) * std::numeric_limits<Scalar>::denorm_min();
+ data1[1] = -data1[0];
+ test::packet_helper<Cond, Packet> h;
+ h.store(data2, fun(h.load(data1)));
+ for (int i=0; i < PacketSize; ++i) {
+ const Scalar ref_zero = ref_fun(data1[i] < 0 ? -Scalar(0) : Scalar(0));
+ const Scalar ref_val = ref_fun(data1[i]);
+ VERIFY(((std::isnan)(data2[i]) && (std::isnan)(ref_val)) || data2[i] == ref_zero ||
+ verifyIsApprox(data2[i], ref_val));
+ }
+ #else
+ CHECK_CWISE1_IF(Cond, ref_fun, fun);
+ #endif
+ }
+ }
+
+ // Test for smallest normalized floats.
+ data1[0] = norm_min;
+ data1[1] = -data1[0];
+ CHECK_CWISE1_IF(Cond, ref_fun, fun);
+
+ // Test for largest floats.
+ data1[0] = norm_max;
+ data1[1] = -data1[0];
+ CHECK_CWISE1_IF(Cond, ref_fun, fun);
+
+ // Test for zeros.
+ data1[0] = Scalar(0.0);
+ data1[1] = -data1[0];
+ CHECK_CWISE1_IF(Cond, ref_fun, fun);
+
+ // Test for infinities.
+ data1[0] = NumTraits<Scalar>::infinity();
+ data1[1] = -data1[0];
+ CHECK_CWISE1_IF(Cond, ref_fun, fun);
+
+ // Test for quiet NaNs.
+ data1[0] = std::numeric_limits<Scalar>::quiet_NaN();
+ data1[1] = -std::numeric_limits<Scalar>::quiet_NaN();
+ CHECK_CWISE1_IF(Cond, ref_fun, fun);
+}
+
+template <typename Scalar, typename Packet>
+void packetmath_real() {
+ typedef internal::packet_traits<Scalar> PacketTraits;
+ const int PacketSize = internal::unpacket_traits<Packet>::size;
+
+ const int size = PacketSize * 4;
+ EIGEN_ALIGN_MAX Scalar data1[PacketSize * 4];
+ EIGEN_ALIGN_MAX Scalar data2[PacketSize * 4];
+ EIGEN_ALIGN_MAX Scalar ref[PacketSize * 4];
+
+ for (int i = 0; i < size; ++i) {
+ data1[i] = Scalar(internal::random<double>(0, 1) * std::pow(10., internal::random<double>(-6, 6)));
+ data2[i] = Scalar(internal::random<double>(0, 1) * std::pow(10., internal::random<double>(-6, 6)));
+ }
+
+ if (internal::random<float>(0, 1) < 0.1f) data1[internal::random<int>(0, PacketSize)] = Scalar(0);
+
+ CHECK_CWISE1_IF(PacketTraits::HasLog, std::log, internal::plog);
+ CHECK_CWISE1_IF(PacketTraits::HasLog, log2, internal::plog2);
+ CHECK_CWISE1_IF(PacketTraits::HasRsqrt, numext::rsqrt, internal::prsqrt);
+
+ for (int i = 0; i < size; ++i) {
+ data1[i] = Scalar(internal::random<double>(-1, 1) * std::pow(10., internal::random<double>(-3, 3)));
+ data2[i] = Scalar(internal::random<double>(-1, 1) * std::pow(10., internal::random<double>(-3, 3)));
+ }
+ CHECK_CWISE1_IF(PacketTraits::HasSin, std::sin, internal::psin);
+ CHECK_CWISE1_IF(PacketTraits::HasCos, std::cos, internal::pcos);
+ CHECK_CWISE1_IF(PacketTraits::HasTan, std::tan, internal::ptan);
+
+ CHECK_CWISE1_EXACT_IF(PacketTraits::HasRound, numext::round, internal::pround);
+ CHECK_CWISE1_EXACT_IF(PacketTraits::HasCeil, numext::ceil, internal::pceil);
+ CHECK_CWISE1_EXACT_IF(PacketTraits::HasFloor, numext::floor, internal::pfloor);
+ CHECK_CWISE1_EXACT_IF(PacketTraits::HasRint, numext::rint, internal::print);
+ CHECK_CWISE1_IF(PacketTraits::HasSign, numext::sign, internal::psign);
+
+ packetmath_boolean_mask_ops_real<Scalar,Packet>();
+
+ // Rounding edge cases.
+ if (PacketTraits::HasRound || PacketTraits::HasCeil || PacketTraits::HasFloor || PacketTraits::HasRint) {
+ typedef typename internal::make_integer<Scalar>::type IntType;
+ // Start with values that cannot fit inside an integer, work down to less than one.
+ Scalar val = numext::mini(
+ Scalar(2) * static_cast<Scalar>(NumTraits<IntType>::highest()),
+ NumTraits<Scalar>::highest());
+ std::vector<Scalar> values;
+ while (val > Scalar(0.25)) {
+ // Cover both even and odd, positive and negative cases.
+ values.push_back(val);
+ values.push_back(val + Scalar(0.3));
+ values.push_back(val + Scalar(0.5));
+ values.push_back(val + Scalar(0.8));
+ values.push_back(val + Scalar(1));
+ values.push_back(val + Scalar(1.3));
+ values.push_back(val + Scalar(1.5));
+ values.push_back(val + Scalar(1.8));
+ values.push_back(-val);
+ values.push_back(-val - Scalar(0.3));
+ values.push_back(-val - Scalar(0.5));
+ values.push_back(-val - Scalar(0.8));
+ values.push_back(-val - Scalar(1));
+ values.push_back(-val - Scalar(1.3));
+ values.push_back(-val - Scalar(1.5));
+ values.push_back(-val - Scalar(1.8));
+ values.push_back(Scalar(-1.5) + val); // Bug 1785.
+ val = val / Scalar(2);
+ }
+ values.push_back(NumTraits<Scalar>::infinity());
+ values.push_back(-NumTraits<Scalar>::infinity());
+ values.push_back(NumTraits<Scalar>::quiet_NaN());
+
+ for (size_t k=0; k<values.size(); ++k) {
+ data1[0] = values[k];
+ CHECK_CWISE1_EXACT_IF(PacketTraits::HasRound, numext::round, internal::pround);
+ CHECK_CWISE1_EXACT_IF(PacketTraits::HasCeil, numext::ceil, internal::pceil);
+ CHECK_CWISE1_EXACT_IF(PacketTraits::HasFloor, numext::floor, internal::pfloor);
+ CHECK_CWISE1_EXACT_IF(PacketTraits::HasRint, numext::rint, internal::print);
+ }
+ }
+
+ for (int i = 0; i < size; ++i) {
+ data1[i] = Scalar(internal::random<double>(-1, 1));
+ data2[i] = Scalar(internal::random<double>(-1, 1));
+ }
+ CHECK_CWISE1_IF(PacketTraits::HasASin, std::asin, internal::pasin);
+ CHECK_CWISE1_IF(PacketTraits::HasACos, std::acos, internal::pacos);
+
+ for (int i = 0; i < size; ++i) {
+ data1[i] = Scalar(internal::random<double>(-87, 88));
+ data2[i] = Scalar(internal::random<double>(-87, 88));
+ data1[0] = -NumTraits<Scalar>::infinity();
+ }
+ CHECK_CWISE1_IF(PacketTraits::HasExp, std::exp, internal::pexp);
+
+ CHECK_CWISE1_BYREF1_IF(PacketTraits::HasExp, REF_FREXP, internal::pfrexp);
+ if (PacketTraits::HasExp) {
+ // Check denormals:
+ for (int j=0; j<3; ++j) {
+ data1[0] = Scalar(std::ldexp(1, NumTraits<Scalar>::min_exponent()-j));
+ CHECK_CWISE1_BYREF1_IF(PacketTraits::HasExp, REF_FREXP, internal::pfrexp);
+ data1[0] = -data1[0];
+ CHECK_CWISE1_BYREF1_IF(PacketTraits::HasExp, REF_FREXP, internal::pfrexp);
+ }
+
+ // zero
+ data1[0] = Scalar(0);
+ CHECK_CWISE1_BYREF1_IF(PacketTraits::HasExp, REF_FREXP, internal::pfrexp);
+
+ // inf and NaN only compare output fraction, not exponent.
+ test::packet_helper<PacketTraits::HasExp,Packet> h;
+ Packet pout;
+ Scalar sout;
+ Scalar special[] = { NumTraits<Scalar>::infinity(),
+ -NumTraits<Scalar>::infinity(),
+ NumTraits<Scalar>::quiet_NaN()};
+ for (int i=0; i<3; ++i) {
+ data1[0] = special[i];
+ ref[0] = Scalar(REF_FREXP(data1[0], ref[PacketSize]));
+ h.store(data2, internal::pfrexp(h.load(data1), h.forward_reference(pout, sout)));
+ VERIFY(test::areApprox(ref, data2, 1) && "internal::pfrexp");
+ }
+ }
+
+ for (int i = 0; i < PacketSize; ++i) {
+ data1[i] = Scalar(internal::random<double>(-1, 1));
+ data2[i] = Scalar(internal::random<double>(-1, 1));
+ }
+ for (int i = 0; i < PacketSize; ++i) {
+ data1[i+PacketSize] = Scalar(internal::random<int>(-4, 4));
+ data2[i+PacketSize] = Scalar(internal::random<double>(-4, 4));
+ }
+ CHECK_CWISE2_IF(PacketTraits::HasExp, REF_LDEXP, internal::pldexp);
+ if (PacketTraits::HasExp) {
+ data1[0] = Scalar(-1);
+ // underflow to zero
+ data1[PacketSize] = Scalar(NumTraits<Scalar>::min_exponent()-55);
+ CHECK_CWISE2_IF(PacketTraits::HasExp, REF_LDEXP, internal::pldexp);
+ // overflow to inf
+ data1[PacketSize] = Scalar(NumTraits<Scalar>::max_exponent()+10);
+ CHECK_CWISE2_IF(PacketTraits::HasExp, REF_LDEXP, internal::pldexp);
+ // NaN stays NaN
+ data1[0] = NumTraits<Scalar>::quiet_NaN();
+ CHECK_CWISE2_IF(PacketTraits::HasExp, REF_LDEXP, internal::pldexp);
+ VERIFY((numext::isnan)(data2[0]));
+ // inf stays inf
+ data1[0] = NumTraits<Scalar>::infinity();
+ data1[PacketSize] = Scalar(NumTraits<Scalar>::min_exponent()-10);
+ CHECK_CWISE2_IF(PacketTraits::HasExp, REF_LDEXP, internal::pldexp);
+ // zero stays zero
+ data1[0] = Scalar(0);
+ data1[PacketSize] = Scalar(NumTraits<Scalar>::max_exponent()+10);
+ CHECK_CWISE2_IF(PacketTraits::HasExp, REF_LDEXP, internal::pldexp);
+ // Small number big exponent.
+ data1[0] = Scalar(std::ldexp(Scalar(1.0), NumTraits<Scalar>::min_exponent()-1));
+ data1[PacketSize] = Scalar(-NumTraits<Scalar>::min_exponent()
+ +NumTraits<Scalar>::max_exponent());
+ CHECK_CWISE2_IF(PacketTraits::HasExp, REF_LDEXP, internal::pldexp);
+ // Big number small exponent.
+ data1[0] = Scalar(std::ldexp(Scalar(1.0), NumTraits<Scalar>::max_exponent()-1));
+ data1[PacketSize] = Scalar(+NumTraits<Scalar>::min_exponent()
+ -NumTraits<Scalar>::max_exponent());
+ CHECK_CWISE2_IF(PacketTraits::HasExp, REF_LDEXP, internal::pldexp);
+ }
+
+ for (int i = 0; i < size; ++i) {
+ data1[i] = Scalar(internal::random<double>(-1, 1) * std::pow(10., internal::random<double>(-6, 6)));
+ data2[i] = Scalar(internal::random<double>(-1, 1) * std::pow(10., internal::random<double>(-6, 6)));
+ }
+ data1[0] = Scalar(1e-20);
+ CHECK_CWISE1_IF(PacketTraits::HasTanh, std::tanh, internal::ptanh);
+ if (PacketTraits::HasExp && PacketSize >= 2) {
+ const Scalar small = NumTraits<Scalar>::epsilon();
+ data1[0] = NumTraits<Scalar>::quiet_NaN();
+ data1[1] = small;
+ test::packet_helper<PacketTraits::HasExp, Packet> h;
+ h.store(data2, internal::pexp(h.load(data1)));
+ VERIFY((numext::isnan)(data2[0]));
+ // TODO(rmlarsen): Re-enable for bfloat16.
+ if (!internal::is_same<Scalar, bfloat16>::value) {
+ VERIFY_IS_APPROX(std::exp(small), data2[1]);
+ }
+
+ data1[0] = -small;
+ data1[1] = Scalar(0);
+ h.store(data2, internal::pexp(h.load(data1)));
+ // TODO(rmlarsen): Re-enable for bfloat16.
+ if (!internal::is_same<Scalar, bfloat16>::value) {
+ VERIFY_IS_APPROX(std::exp(-small), data2[0]);
+ }
+ VERIFY_IS_EQUAL(std::exp(Scalar(0)), data2[1]);
+
+ data1[0] = (std::numeric_limits<Scalar>::min)();
+ data1[1] = -(std::numeric_limits<Scalar>::min)();
+ h.store(data2, internal::pexp(h.load(data1)));
+ VERIFY_IS_APPROX(std::exp((std::numeric_limits<Scalar>::min)()), data2[0]);
+ VERIFY_IS_APPROX(std::exp(-(std::numeric_limits<Scalar>::min)()), data2[1]);
+
+ data1[0] = std::numeric_limits<Scalar>::denorm_min();
+ data1[1] = -std::numeric_limits<Scalar>::denorm_min();
+ h.store(data2, internal::pexp(h.load(data1)));
+ VERIFY_IS_APPROX(std::exp(std::numeric_limits<Scalar>::denorm_min()), data2[0]);
+ VERIFY_IS_APPROX(std::exp(-std::numeric_limits<Scalar>::denorm_min()), data2[1]);
+ }
+
+ if (PacketTraits::HasTanh) {
+ // NOTE this test migh fail with GCC prior to 6.3, see MathFunctionsImpl.h for details.
+ data1[0] = NumTraits<Scalar>::quiet_NaN();
+ test::packet_helper<internal::packet_traits<Scalar>::HasTanh, Packet> h;
+ h.store(data2, internal::ptanh(h.load(data1)));
+ VERIFY((numext::isnan)(data2[0]));
+ }
+
+ if (PacketTraits::HasExp) {
+ internal::scalar_logistic_op<Scalar> logistic;
+ for (int i = 0; i < size; ++i) {
+ data1[i] = Scalar(internal::random<double>(-20, 20));
+ }
+
+ test::packet_helper<PacketTraits::HasExp, Packet> h;
+ h.store(data2, logistic.packetOp(h.load(data1)));
+ for (int i = 0; i < PacketSize; ++i) {
+ VERIFY_IS_APPROX(data2[i], logistic(data1[i]));
+ }
+ }
+
+#if EIGEN_HAS_C99_MATH
+ data1[0] = NumTraits<Scalar>::infinity();
+ data1[1] = Scalar(-1);
+ CHECK_CWISE1_IF(PacketTraits::HasLog1p, std::log1p, internal::plog1p);
+ data1[0] = NumTraits<Scalar>::infinity();
+ data1[1] = -NumTraits<Scalar>::infinity();
+ CHECK_CWISE1_IF(PacketTraits::HasExpm1, std::expm1, internal::pexpm1);
+#endif
+
+ if (PacketSize >= 2) {
+ data1[0] = NumTraits<Scalar>::quiet_NaN();
+ data1[1] = NumTraits<Scalar>::epsilon();
+ if (PacketTraits::HasLog) {
+ test::packet_helper<PacketTraits::HasLog, Packet> h;
+ h.store(data2, internal::plog(h.load(data1)));
+ VERIFY((numext::isnan)(data2[0]));
+ // TODO(cantonios): Re-enable for bfloat16.
+ if (!internal::is_same<Scalar, bfloat16>::value) {
+ VERIFY_IS_APPROX(std::log(data1[1]), data2[1]);
+ }
+
+ data1[0] = -NumTraits<Scalar>::epsilon();
+ data1[1] = Scalar(0);
+ h.store(data2, internal::plog(h.load(data1)));
+ VERIFY((numext::isnan)(data2[0]));
+ VERIFY_IS_EQUAL(std::log(Scalar(0)), data2[1]);
+
+ data1[0] = (std::numeric_limits<Scalar>::min)();
+ data1[1] = -(std::numeric_limits<Scalar>::min)();
+ h.store(data2, internal::plog(h.load(data1)));
+ // TODO(cantonios): Re-enable for bfloat16.
+ if (!internal::is_same<Scalar, bfloat16>::value) {
+ VERIFY_IS_APPROX(std::log((std::numeric_limits<Scalar>::min)()), data2[0]);
+ }
+ VERIFY((numext::isnan)(data2[1]));
+
+ // Note: 32-bit arm always flushes denorms to zero.
+#if !EIGEN_ARCH_ARM
+ if (std::numeric_limits<Scalar>::has_denorm == std::denorm_present) {
+ data1[0] = std::numeric_limits<Scalar>::denorm_min();
+ data1[1] = -std::numeric_limits<Scalar>::denorm_min();
+ h.store(data2, internal::plog(h.load(data1)));
+ // TODO(rmlarsen): Re-enable for bfloat16.
+ if (!internal::is_same<Scalar, bfloat16>::value) {
+ VERIFY_IS_APPROX(std::log(std::numeric_limits<Scalar>::denorm_min()), data2[0]);
+ }
+ VERIFY((numext::isnan)(data2[1]));
+ }
+#endif
+
+ data1[0] = Scalar(-1.0f);
+ h.store(data2, internal::plog(h.load(data1)));
+ VERIFY((numext::isnan)(data2[0]));
+
+ data1[0] = NumTraits<Scalar>::infinity();
+ h.store(data2, internal::plog(h.load(data1)));
+ VERIFY((numext::isinf)(data2[0]));
+ }
+ if (PacketTraits::HasLog1p) {
+ test::packet_helper<PacketTraits::HasLog1p, Packet> h;
+ data1[0] = Scalar(-2);
+ data1[1] = -NumTraits<Scalar>::infinity();
+ h.store(data2, internal::plog1p(h.load(data1)));
+ VERIFY((numext::isnan)(data2[0]));
+ VERIFY((numext::isnan)(data2[1]));
+ }
+
+ packetmath_test_IEEE_corner_cases<PacketTraits::HasSqrt, Scalar, Packet>(numext::sqrt<Scalar>, psqrt_functor());
+ packetmath_test_IEEE_corner_cases<PacketTraits::HasRsqrt, Scalar, Packet>(numext::rsqrt<Scalar>, prsqrt_functor());
+
+ // TODO(rmlarsen): Re-enable for half and bfloat16.
+ if (PacketTraits::HasCos
+ && !internal::is_same<Scalar, half>::value
+ && !internal::is_same<Scalar, bfloat16>::value) {
+ test::packet_helper<PacketTraits::HasCos, Packet> h;
+ for (Scalar k = Scalar(1); k < Scalar(10000) / NumTraits<Scalar>::epsilon(); k *= Scalar(2)) {
+ for (int k1 = 0; k1 <= 1; ++k1) {
+ data1[0] = Scalar((2 * double(k) + k1) * double(EIGEN_PI) / 2 * internal::random<double>(0.8, 1.2));
+ data1[1] = Scalar((2 * double(k) + 2 + k1) * double(EIGEN_PI) / 2 * internal::random<double>(0.8, 1.2));
+ h.store(data2, internal::pcos(h.load(data1)));
+ h.store(data2 + PacketSize, internal::psin(h.load(data1)));
+ VERIFY(data2[0] <= Scalar(1.) && data2[0] >= Scalar(-1.));
+ VERIFY(data2[1] <= Scalar(1.) && data2[1] >= Scalar(-1.));
+ VERIFY(data2[PacketSize + 0] <= Scalar(1.) && data2[PacketSize + 0] >= Scalar(-1.));
+ VERIFY(data2[PacketSize + 1] <= Scalar(1.) && data2[PacketSize + 1] >= Scalar(-1.));
+
+ VERIFY_IS_APPROX(data2[0], std::cos(data1[0]));
+ VERIFY_IS_APPROX(data2[1], std::cos(data1[1]));
+ VERIFY_IS_APPROX(data2[PacketSize + 0], std::sin(data1[0]));
+ VERIFY_IS_APPROX(data2[PacketSize + 1], std::sin(data1[1]));
+
+ VERIFY_IS_APPROX(numext::abs2(data2[0]) + numext::abs2(data2[PacketSize + 0]), Scalar(1));
+ VERIFY_IS_APPROX(numext::abs2(data2[1]) + numext::abs2(data2[PacketSize + 1]), Scalar(1));
+ }
+ }
+
+ data1[0] = NumTraits<Scalar>::infinity();
+ data1[1] = -NumTraits<Scalar>::infinity();
+ h.store(data2, internal::psin(h.load(data1)));
+ VERIFY((numext::isnan)(data2[0]));
+ VERIFY((numext::isnan)(data2[1]));
+
+ h.store(data2, internal::pcos(h.load(data1)));
+ VERIFY((numext::isnan)(data2[0]));
+ VERIFY((numext::isnan)(data2[1]));
+
+ data1[0] = NumTraits<Scalar>::quiet_NaN();
+ h.store(data2, internal::psin(h.load(data1)));
+ VERIFY((numext::isnan)(data2[0]));
+ h.store(data2, internal::pcos(h.load(data1)));
+ VERIFY((numext::isnan)(data2[0]));
+
+ data1[0] = -Scalar(0.);
+ h.store(data2, internal::psin(h.load(data1)));
+ VERIFY(internal::biteq(data2[0], data1[0]));
+ h.store(data2, internal::pcos(h.load(data1)));
+ VERIFY_IS_EQUAL(data2[0], Scalar(1));
+ }
+ }
+ if (PacketTraits::HasReciprocal && PacketSize >= 2) {
+ test::packet_helper<PacketTraits::HasReciprocal, Packet> h;
+ const Scalar inf = NumTraits<Scalar>::infinity();
+ const Scalar zero = Scalar(0);
+ data1[0] = zero;
+ data1[1] = -zero;
+ h.store(data2, internal::preciprocal(h.load(data1)));
+ VERIFY_IS_EQUAL(data2[0], inf);
+ VERIFY_IS_EQUAL(data2[1], -inf);
+
+ data1[0] = inf;
+ data1[1] = -inf;
+ h.store(data2, internal::preciprocal(h.load(data1)));
+ VERIFY_IS_EQUAL(data2[0], zero);
+ VERIFY_IS_EQUAL(data2[1], -zero);
+
+ }
+}
+
+#define CAST_CHECK_CWISE1_IF(COND, REFOP, POP, SCALAR, REFTYPE) if(COND) { \
+ test::packet_helper<COND,Packet> h; \
+ for (int i=0; i<PacketSize; ++i) \
+ ref[i] = SCALAR(REFOP(static_cast<REFTYPE>(data1[i]))); \
+ h.store(data2, POP(h.load(data1))); \
+ VERIFY(test::areApprox(ref, data2, PacketSize) && #POP); \
+}
+
+template <typename Scalar>
+Scalar propagate_nan_max(const Scalar& a, const Scalar& b) {
+ if ((numext::isnan)(a)) return a;
+ if ((numext::isnan)(b)) return b;
+ return (numext::maxi)(a,b);
+}
+
+template <typename Scalar>
+Scalar propagate_nan_min(const Scalar& a, const Scalar& b) {
+ if ((numext::isnan)(a)) return a;
+ if ((numext::isnan)(b)) return b;
+ return (numext::mini)(a,b);
+}
+
+template <typename Scalar>
+Scalar propagate_number_max(const Scalar& a, const Scalar& b) {
+ if ((numext::isnan)(a)) return b;
+ if ((numext::isnan)(b)) return a;
+ return (numext::maxi)(a,b);
+}
+
+template <typename Scalar>
+Scalar propagate_number_min(const Scalar& a, const Scalar& b) {
+ if ((numext::isnan)(a)) return b;
+ if ((numext::isnan)(b)) return a;
+ return (numext::mini)(a,b);
+}
+
+template <typename Scalar, typename Packet>
+void packetmath_notcomplex() {
+ typedef internal::packet_traits<Scalar> PacketTraits;
+ const int PacketSize = internal::unpacket_traits<Packet>::size;
+
+ EIGEN_ALIGN_MAX Scalar data1[PacketSize * 4];
+ EIGEN_ALIGN_MAX Scalar data2[PacketSize * 4];
+ EIGEN_ALIGN_MAX Scalar ref[PacketSize * 4];
+
+ Array<Scalar, Dynamic, 1>::Map(data1, PacketSize * 4).setRandom();
+
+ VERIFY((!PacketTraits::Vectorizable) || PacketTraits::HasMin);
+ VERIFY((!PacketTraits::Vectorizable) || PacketTraits::HasMax);
+
+ CHECK_CWISE2_IF(PacketTraits::HasMin, (std::min), internal::pmin);
+ CHECK_CWISE2_IF(PacketTraits::HasMax, (std::max), internal::pmax);
+
+ CHECK_CWISE2_IF(PacketTraits::HasMin, propagate_number_min, internal::pmin<PropagateNumbers>);
+ CHECK_CWISE2_IF(PacketTraits::HasMax, propagate_number_max, internal::pmax<PropagateNumbers>);
+ CHECK_CWISE1(numext::abs, internal::pabs);
+ CHECK_CWISE2_IF(PacketTraits::HasAbsDiff, REF_ABS_DIFF, internal::pabsdiff);
+
+ ref[0] = data1[0];
+ for (int i = 0; i < PacketSize; ++i) ref[0] = internal::pmin(ref[0], data1[i]);
+ VERIFY(internal::isApprox(ref[0], internal::predux_min(internal::pload<Packet>(data1))) && "internal::predux_min");
+ ref[0] = data1[0];
+ for (int i = 0; i < PacketSize; ++i) ref[0] = internal::pmax(ref[0], data1[i]);
+ VERIFY(internal::isApprox(ref[0], internal::predux_max(internal::pload<Packet>(data1))) && "internal::predux_max");
+
+ for (int i = 0; i < PacketSize; ++i) ref[i] = data1[0] + Scalar(i);
+ internal::pstore(data2, internal::plset<Packet>(data1[0]));
+ VERIFY(test::areApprox(ref, data2, PacketSize) && "internal::plset");
+
+ {
+ unsigned char* data1_bits = reinterpret_cast<unsigned char*>(data1);
+ // predux_all - not needed yet
+ // for (unsigned int i=0; i<PacketSize*sizeof(Scalar); ++i) data1_bits[i] = 0xff;
+ // VERIFY(internal::predux_all(internal::pload<Packet>(data1)) && "internal::predux_all(1111)");
+ // for(int k=0; k<PacketSize; ++k)
+ // {
+ // for (unsigned int i=0; i<sizeof(Scalar); ++i) data1_bits[k*sizeof(Scalar)+i] = 0x0;
+ // VERIFY( (!internal::predux_all(internal::pload<Packet>(data1))) && "internal::predux_all(0101)");
+ // for (unsigned int i=0; i<sizeof(Scalar); ++i) data1_bits[k*sizeof(Scalar)+i] = 0xff;
+ // }
+
+ // predux_any
+ for (unsigned int i = 0; i < PacketSize * sizeof(Scalar); ++i) data1_bits[i] = 0x0;
+ VERIFY((!internal::predux_any(internal::pload<Packet>(data1))) && "internal::predux_any(0000)");
+ for (int k = 0; k < PacketSize; ++k) {
+ for (unsigned int i = 0; i < sizeof(Scalar); ++i) data1_bits[k * sizeof(Scalar) + i] = 0xff;
+ VERIFY(internal::predux_any(internal::pload<Packet>(data1)) && "internal::predux_any(0101)");
+ for (unsigned int i = 0; i < sizeof(Scalar); ++i) data1_bits[k * sizeof(Scalar) + i] = 0x00;
+ }
+ }
+
+
+ // Test NaN propagation.
+ if (!NumTraits<Scalar>::IsInteger) {
+ // Test reductions with no NaNs.
+ ref[0] = data1[0];
+ for (int i = 0; i < PacketSize; ++i) ref[0] = internal::pmin<PropagateNumbers>(ref[0], data1[i]);
+ VERIFY(internal::isApprox(ref[0], internal::predux_min<PropagateNumbers>(internal::pload<Packet>(data1))) && "internal::predux_min<PropagateNumbers>");
+ ref[0] = data1[0];
+ for (int i = 0; i < PacketSize; ++i) ref[0] = internal::pmin<PropagateNaN>(ref[0], data1[i]);
+ VERIFY(internal::isApprox(ref[0], internal::predux_min<PropagateNaN>(internal::pload<Packet>(data1))) && "internal::predux_min<PropagateNaN>");
+ ref[0] = data1[0];
+ for (int i = 0; i < PacketSize; ++i) ref[0] = internal::pmax<PropagateNumbers>(ref[0], data1[i]);
+ VERIFY(internal::isApprox(ref[0], internal::predux_max<PropagateNumbers>(internal::pload<Packet>(data1))) && "internal::predux_max<PropagateNumbers>");
+ ref[0] = data1[0];
+ for (int i = 0; i < PacketSize; ++i) ref[0] = internal::pmax<PropagateNaN>(ref[0], data1[i]);
+ VERIFY(internal::isApprox(ref[0], internal::predux_max<PropagateNaN>(internal::pload<Packet>(data1))) && "internal::predux_max<PropagateNumbers>");
+ // A single NaN.
+ const size_t index = std::numeric_limits<size_t>::quiet_NaN() % PacketSize;
+ data1[index] = NumTraits<Scalar>::quiet_NaN();
+ VERIFY(PacketSize==1 || !(numext::isnan)(internal::predux_min<PropagateNumbers>(internal::pload<Packet>(data1))));
+ VERIFY((numext::isnan)(internal::predux_min<PropagateNaN>(internal::pload<Packet>(data1))));
+ VERIFY(PacketSize==1 || !(numext::isnan)(internal::predux_max<PropagateNumbers>(internal::pload<Packet>(data1))));
+ VERIFY((numext::isnan)(internal::predux_max<PropagateNaN>(internal::pload<Packet>(data1))));
+ // All NaNs.
+ for (int i = 0; i < 4 * PacketSize; ++i) data1[i] = NumTraits<Scalar>::quiet_NaN();
+ VERIFY((numext::isnan)(internal::predux_min<PropagateNumbers>(internal::pload<Packet>(data1))));
+ VERIFY((numext::isnan)(internal::predux_min<PropagateNaN>(internal::pload<Packet>(data1))));
+ VERIFY((numext::isnan)(internal::predux_max<PropagateNumbers>(internal::pload<Packet>(data1))));
+ VERIFY((numext::isnan)(internal::predux_max<PropagateNaN>(internal::pload<Packet>(data1))));
+
+ // Test NaN propagation for coefficient-wise min and max.
+ for (int i = 0; i < PacketSize; ++i) {
+ data1[i] = internal::random<bool>() ? NumTraits<Scalar>::quiet_NaN() : Scalar(0);
+ data1[i + PacketSize] = internal::random<bool>() ? NumTraits<Scalar>::quiet_NaN() : Scalar(0);
+ }
+ // Note: NaN propagation is implementation defined for pmin/pmax, so we do not test it here.
+ CHECK_CWISE2_IF(PacketTraits::HasMin, propagate_number_min, (internal::pmin<PropagateNumbers>));
+ CHECK_CWISE2_IF(PacketTraits::HasMax, propagate_number_max, internal::pmax<PropagateNumbers>);
+ CHECK_CWISE2_IF(PacketTraits::HasMin, propagate_nan_min, (internal::pmin<PropagateNaN>));
+ CHECK_CWISE2_IF(PacketTraits::HasMax, propagate_nan_max, internal::pmax<PropagateNaN>);
+ }
+
+ packetmath_boolean_mask_ops_notcomplex<Scalar, Packet>();
+}
+
+template <typename Scalar, typename Packet, bool ConjLhs, bool ConjRhs>
+void test_conj_helper(Scalar* data1, Scalar* data2, Scalar* ref, Scalar* pval) {
+ const int PacketSize = internal::unpacket_traits<Packet>::size;
+
+ internal::conj_if<ConjLhs> cj0;
+ internal::conj_if<ConjRhs> cj1;
+ internal::conj_helper<Scalar, Scalar, ConjLhs, ConjRhs> cj;
+ internal::conj_helper<Packet, Packet, ConjLhs, ConjRhs> pcj;
+
+ for (int i = 0; i < PacketSize; ++i) {
+ ref[i] = cj0(data1[i]) * cj1(data2[i]);
+ VERIFY(internal::isApprox(ref[i], cj.pmul(data1[i], data2[i])) && "conj_helper pmul");
+ }
+ internal::pstore(pval, pcj.pmul(internal::pload<Packet>(data1), internal::pload<Packet>(data2)));
+ VERIFY(test::areApprox(ref, pval, PacketSize) && "conj_helper pmul");
+
+ for (int i = 0; i < PacketSize; ++i) {
+ Scalar tmp = ref[i];
+ ref[i] += cj0(data1[i]) * cj1(data2[i]);
+ VERIFY(internal::isApprox(ref[i], cj.pmadd(data1[i], data2[i], tmp)) && "conj_helper pmadd");
+ }
+ internal::pstore(
+ pval, pcj.pmadd(internal::pload<Packet>(data1), internal::pload<Packet>(data2), internal::pload<Packet>(pval)));
+ VERIFY(test::areApprox(ref, pval, PacketSize) && "conj_helper pmadd");
+}
+
+template <typename Scalar, typename Packet>
+void packetmath_complex() {
+ typedef internal::packet_traits<Scalar> PacketTraits;
+ typedef typename Scalar::value_type RealScalar;
+ const int PacketSize = internal::unpacket_traits<Packet>::size;
+
+ const int size = PacketSize * 4;
+ EIGEN_ALIGN_MAX Scalar data1[PacketSize * 4];
+ EIGEN_ALIGN_MAX Scalar data2[PacketSize * 4];
+ EIGEN_ALIGN_MAX Scalar ref[PacketSize * 4];
+ EIGEN_ALIGN_MAX Scalar pval[PacketSize * 4];
+
+ for (int i = 0; i < size; ++i) {
+ data1[i] = internal::random<Scalar>() * Scalar(1e2);
+ data2[i] = internal::random<Scalar>() * Scalar(1e2);
+ }
+
+ test_conj_helper<Scalar, Packet, false, false>(data1, data2, ref, pval);
+ test_conj_helper<Scalar, Packet, false, true>(data1, data2, ref, pval);
+ test_conj_helper<Scalar, Packet, true, false>(data1, data2, ref, pval);
+ test_conj_helper<Scalar, Packet, true, true>(data1, data2, ref, pval);
+
+ // Test pcplxflip.
+ {
+ for (int i = 0; i < PacketSize; ++i) ref[i] = Scalar(std::imag(data1[i]), std::real(data1[i]));
+ internal::pstore(pval, internal::pcplxflip(internal::pload<Packet>(data1)));
+ VERIFY(test::areApprox(ref, pval, PacketSize) && "pcplxflip");
+ }
+
+ if (PacketTraits::HasSqrt) {
+ for (int i = 0; i < size; ++i) {
+ data1[i] = Scalar(internal::random<RealScalar>(), internal::random<RealScalar>());
+ }
+ CHECK_CWISE1_N(numext::sqrt, internal::psqrt, size);
+ CHECK_CWISE1_IF(PacketTraits::HasSign, numext::sign, internal::psign);
+
+ // Test misc. corner cases.
+ const RealScalar zero = RealScalar(0);
+ const RealScalar one = RealScalar(1);
+ const RealScalar inf = std::numeric_limits<RealScalar>::infinity();
+ const RealScalar nan = std::numeric_limits<RealScalar>::quiet_NaN();
+ data1[0] = Scalar(zero, zero);
+ data1[1] = Scalar(-zero, zero);
+ data1[2] = Scalar(one, zero);
+ data1[3] = Scalar(zero, one);
+ CHECK_CWISE1_N(numext::sqrt, internal::psqrt, 4);
+ data1[0] = Scalar(-one, zero);
+ data1[1] = Scalar(zero, -one);
+ data1[2] = Scalar(one, one);
+ data1[3] = Scalar(-one, -one);
+ CHECK_CWISE1_N(numext::sqrt, internal::psqrt, 4);
+ data1[0] = Scalar(inf, zero);
+ data1[1] = Scalar(zero, inf);
+ data1[2] = Scalar(-inf, zero);
+ data1[3] = Scalar(zero, -inf);
+ CHECK_CWISE1_N(numext::sqrt, internal::psqrt, 4);
+ data1[0] = Scalar(inf, inf);
+ data1[1] = Scalar(-inf, inf);
+ data1[2] = Scalar(inf, -inf);
+ data1[3] = Scalar(-inf, -inf);
+ CHECK_CWISE1_N(numext::sqrt, internal::psqrt, 4);
+ data1[0] = Scalar(nan, zero);
+ data1[1] = Scalar(zero, nan);
+ data1[2] = Scalar(nan, one);
+ data1[3] = Scalar(one, nan);
+ CHECK_CWISE1_N(numext::sqrt, internal::psqrt, 4);
+ data1[0] = Scalar(nan, nan);
+ data1[1] = Scalar(inf, nan);
+ data1[2] = Scalar(nan, inf);
+ data1[3] = Scalar(-inf, nan);
+ CHECK_CWISE1_N(numext::sqrt, internal::psqrt, 4);
+ }
+}
+
+template <typename Scalar, typename Packet>
+void packetmath_scatter_gather() {
+ typedef typename NumTraits<Scalar>::Real RealScalar;
+ const int PacketSize = internal::unpacket_traits<Packet>::size;
+ EIGEN_ALIGN_MAX Scalar data1[PacketSize];
+ RealScalar refvalue = RealScalar(0);
+ for (int i = 0; i < PacketSize; ++i) {
+ data1[i] = internal::random<Scalar>() / RealScalar(PacketSize);
+ }
+
+ int stride = internal::random<int>(1, 20);
+
+ // Buffer of zeros.
+ EIGEN_ALIGN_MAX Scalar buffer[PacketSize * 20] = {};
+
+ Packet packet = internal::pload<Packet>(data1);
+ internal::pscatter<Scalar, Packet>(buffer, packet, stride);
+
+ for (int i = 0; i < PacketSize * 20; ++i) {
+ if ((i % stride) == 0 && i < stride * PacketSize) {
+ VERIFY(test::isApproxAbs(buffer[i], data1[i / stride], refvalue) && "pscatter");
+ } else {
+ VERIFY(test::isApproxAbs(buffer[i], Scalar(0), refvalue) && "pscatter");
+ }
+ }
+
+ for (int i = 0; i < PacketSize * 7; ++i) {
+ buffer[i] = internal::random<Scalar>() / RealScalar(PacketSize);
+ }
+ packet = internal::pgather<Scalar, Packet>(buffer, 7);
+ internal::pstore(data1, packet);
+ for (int i = 0; i < PacketSize; ++i) {
+ VERIFY(test::isApproxAbs(data1[i], buffer[i * 7], refvalue) && "pgather");
+ }
+
+ for (Index N = 0; N <= PacketSize; ++N) {
+ for (Index i = 0; i < N; ++i) {
+ data1[i] = internal::random<Scalar>() / RealScalar(PacketSize);
+ }
+
+ for (Index i = 0; i < N * 20; ++i) {
+ buffer[i] = Scalar(0);
+ }
+
+ packet = internal::pload_partial<Packet>(data1, N);
+ internal::pscatter_partial<Scalar, Packet>(buffer, packet, stride, N);
+
+ for (Index i = 0; i < N * 20; ++i) {
+ if ((i % stride) == 0 && i < stride * N) {
+ VERIFY(test::isApproxAbs(buffer[i], data1[i / stride], refvalue) && "pscatter_partial");
+ } else {
+ VERIFY(test::isApproxAbs(buffer[i], Scalar(0), refvalue) && "pscatter_partial");
+ }
+ }
+
+ for (Index i = 0; i < N * 7; ++i) {
+ buffer[i] = internal::random<Scalar>() / RealScalar(PacketSize);
+ }
+ packet = internal::pgather_partial<Scalar, Packet>(buffer, 7, N);
+ internal::pstore_partial(data1, packet, N);
+ for (Index i = 0; i < N; ++i) {
+ VERIFY(test::isApproxAbs(data1[i], buffer[i * 7], refvalue) && "pgather_partial");
+ }
+ }
+}
+
+namespace Eigen {
+namespace test {
+
+template <typename Scalar, typename PacketType>
+struct runall<Scalar, PacketType, false, false> { // i.e. float or double
+ static void run() {
+ packetmath<Scalar, PacketType>();
+ packetmath_scatter_gather<Scalar, PacketType>();
+ packetmath_notcomplex<Scalar, PacketType>();
+ packetmath_real<Scalar, PacketType>();
+ }
+};
+
+template <typename Scalar, typename PacketType>
+struct runall<Scalar, PacketType, false, true> { // i.e. int
+ static void run() {
+ packetmath<Scalar, PacketType>();
+ packetmath_scatter_gather<Scalar, PacketType>();
+ packetmath_notcomplex<Scalar, PacketType>();
+ }
+};
+
+template <typename Scalar, typename PacketType>
+struct runall<Scalar, PacketType, true, false> { // i.e. complex
+ static void run() {
+ packetmath<Scalar, PacketType>();
+ packetmath_scatter_gather<Scalar, PacketType>();
+ packetmath_complex<Scalar, PacketType>();
+ }
+};
+
+} // namespace test
+} // namespace Eigen
+
+EIGEN_DECLARE_TEST(packetmath) {
+ g_first_pass = true;
+ for (int i = 0; i < g_repeat; i++) {
+ CALL_SUBTEST_1(test::runner<float>::run());
+ CALL_SUBTEST_2(test::runner<double>::run());
+ CALL_SUBTEST_3(test::runner<int8_t>::run());
+ CALL_SUBTEST_4(test::runner<uint8_t>::run());
+ CALL_SUBTEST_5(test::runner<int16_t>::run());
+ CALL_SUBTEST_6(test::runner<uint16_t>::run());
+ CALL_SUBTEST_7(test::runner<int32_t>::run());
+ CALL_SUBTEST_8(test::runner<uint32_t>::run());
+ CALL_SUBTEST_9(test::runner<int64_t>::run());
+ CALL_SUBTEST_10(test::runner<uint64_t>::run());
+ CALL_SUBTEST_11(test::runner<std::complex<float> >::run());
+ CALL_SUBTEST_12(test::runner<std::complex<double> >::run());
+ CALL_SUBTEST_13(test::runner<half>::run());
+ CALL_SUBTEST_14((packetmath<bool, internal::packet_traits<bool>::type>()));
+ CALL_SUBTEST_15(test::runner<bfloat16>::run());
+ g_first_pass = false;
+ }
+}
diff --git a/test/packetmath_test_shared.h b/test/packetmath_test_shared.h
new file mode 100644
index 0000000..6fc489f
--- /dev/null
+++ b/test/packetmath_test_shared.h
@@ -0,0 +1,278 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "main.h"
+#include <typeinfo>
+
+#if defined __GNUC__ && __GNUC__>=6
+ #pragma GCC diagnostic ignored "-Wignored-attributes"
+#endif
+// using namespace Eigen;
+
+bool g_first_pass = true;
+
+namespace Eigen {
+namespace internal {
+
+template<typename T> T negate(const T& x) { return -x; }
+
+template<typename T>
+Map<const Array<unsigned char,sizeof(T),1> >
+bits(const T& x) {
+ return Map<const Array<unsigned char,sizeof(T),1> >(reinterpret_cast<const unsigned char *>(&x));
+}
+
+// The following implement bitwise operations on floating point types
+template<typename T,typename Bits,typename Func>
+T apply_bit_op(Bits a, Bits b, Func f) {
+ Array<unsigned char,sizeof(T),1> data;
+ T res;
+ for(Index i = 0; i < data.size(); ++i)
+ data[i] = f(a[i], b[i]);
+ // Note: The reinterpret_cast works around GCC's class-memaccess warnings:
+ std::memcpy(reinterpret_cast<unsigned char*>(&res), data.data(), sizeof(T));
+ return res;
+}
+
+#define EIGEN_TEST_MAKE_BITWISE2(OP,FUNC,T) \
+ template<> T EIGEN_CAT(p,OP)(const T& a,const T& b) { \
+ return apply_bit_op<T>(bits(a),bits(b),FUNC); \
+ }
+
+#define EIGEN_TEST_MAKE_BITWISE(OP,FUNC) \
+ EIGEN_TEST_MAKE_BITWISE2(OP,FUNC,float) \
+ EIGEN_TEST_MAKE_BITWISE2(OP,FUNC,double) \
+ EIGEN_TEST_MAKE_BITWISE2(OP,FUNC,half) \
+ EIGEN_TEST_MAKE_BITWISE2(OP,FUNC,bfloat16) \
+ EIGEN_TEST_MAKE_BITWISE2(OP,FUNC,std::complex<float>) \
+ EIGEN_TEST_MAKE_BITWISE2(OP,FUNC,std::complex<double>)
+
+EIGEN_TEST_MAKE_BITWISE(xor,std::bit_xor<unsigned char>())
+EIGEN_TEST_MAKE_BITWISE(and,std::bit_and<unsigned char>())
+EIGEN_TEST_MAKE_BITWISE(or, std::bit_or<unsigned char>())
+struct bit_andnot{
+ template<typename T> T
+ operator()(T a, T b) const { return a & (~b); }
+};
+EIGEN_TEST_MAKE_BITWISE(andnot, bit_andnot())
+template<typename T>
+bool biteq(T a, T b) {
+ return (bits(a) == bits(b)).all();
+}
+
+}
+
+namespace test {
+
+// NOTE: we disable inlining for this function to workaround a GCC issue when using -O3 and the i387 FPU.
+template<typename Scalar> EIGEN_DONT_INLINE
+bool isApproxAbs(const Scalar& a, const Scalar& b, const typename NumTraits<Scalar>::Real& refvalue)
+{
+ return internal::isMuchSmallerThan(a-b, refvalue);
+}
+
+template<typename Scalar>
+inline void print_mismatch(const Scalar* ref, const Scalar* vec, int size) {
+ std::cout << "ref: [" << Map<const Matrix<Scalar,1,Dynamic> >(ref,size) << "]" << " != vec: [" << Map<const Matrix<Scalar,1,Dynamic> >(vec,size) << "]\n";
+}
+
+template<typename Scalar> bool areApproxAbs(const Scalar* a, const Scalar* b, int size, const typename NumTraits<Scalar>::Real& refvalue)
+{
+ for (int i=0; i<size; ++i)
+ {
+ if (!isApproxAbs(a[i],b[i],refvalue))
+ {
+ print_mismatch(a, b, size);
+ std::cout << "Values differ in position " << i << ": " << a[i] << " vs " << b[i] << std::endl;
+ return false;
+ }
+ }
+ return true;
+}
+
+template<typename Scalar> bool areApprox(const Scalar* a, const Scalar* b, int size)
+{
+ for (int i=0; i<size; ++i)
+ {
+ if ( numext::not_equal_strict(a[i], b[i]) && !internal::isApprox(a[i],b[i])
+ && !((numext::isnan)(a[i]) && (numext::isnan)(b[i])) )
+ {
+ print_mismatch(a, b, size);
+ std::cout << "Values differ in position " << i << ": " << a[i] << " vs " << b[i] << std::endl;
+ return false;
+ }
+ }
+ return true;
+}
+
+template<typename Scalar> bool areEqual(const Scalar* a, const Scalar* b, int size)
+{
+ for (int i=0; i<size; ++i)
+ {
+ if ( numext::not_equal_strict(a[i], b[i]) && !((numext::isnan)(a[i]) && (numext::isnan)(b[i])) )
+ {
+ print_mismatch(a, b, size);
+ std::cout << "Values differ in position " << i << ": " << a[i] << " vs " << b[i] << std::endl;
+ return false;
+ }
+ }
+ return true;
+}
+
+#define CHECK_CWISE1(REFOP, POP) { \
+ for (int i=0; i<PacketSize; ++i) \
+ ref[i] = REFOP(data1[i]); \
+ internal::pstore(data2, POP(internal::pload<Packet>(data1))); \
+ VERIFY(test::areApprox(ref, data2, PacketSize) && #POP); \
+}
+
+// Checks component-wise for input of size N. All of data1, data2, and ref
+// should have size at least ceil(N/PacketSize)*PacketSize to avoid memory
+// access errors.
+#define CHECK_CWISE1_N(REFOP, POP, N) { \
+ for (int i=0; i<N; ++i) \
+ ref[i] = REFOP(data1[i]); \
+ for (int j=0; j<N; j+=PacketSize) \
+ internal::pstore(data2 + j, POP(internal::pload<Packet>(data1 + j))); \
+ VERIFY(test::areApprox(ref, data2, N) && #POP); \
+}
+
+template<bool Cond,typename Packet>
+struct packet_helper
+{
+ template<typename T>
+ inline Packet load(const T* from) const { return internal::pload<Packet>(from); }
+
+ template<typename T>
+ inline Packet loadu(const T* from) const { return internal::ploadu<Packet>(from); }
+
+ template<typename T>
+ inline Packet load(const T* from, unsigned long long umask) const { return internal::ploadu<Packet>(from, umask); }
+
+ template<typename T>
+ inline void store(T* to, const Packet& x) const { internal::pstore(to,x); }
+
+ template<typename T>
+ inline void store(T* to, const Packet& x, unsigned long long umask) const { internal::pstoreu(to, x, umask); }
+
+ template<typename T>
+ inline Packet& forward_reference(Packet& packet, T& /*scalar*/) const { return packet; }
+};
+
+template<typename Packet>
+struct packet_helper<false,Packet>
+{
+ template<typename T>
+ inline T load(const T* from) const { return *from; }
+
+ template<typename T>
+ inline T loadu(const T* from) const { return *from; }
+
+ template<typename T>
+ inline T load(const T* from, unsigned long long) const { return *from; }
+
+ template<typename T>
+ inline void store(T* to, const T& x) const { *to = x; }
+
+ template<typename T>
+ inline void store(T* to, const T& x, unsigned long long) const { *to = x; }
+
+ template<typename T>
+ inline T& forward_reference(Packet& /*packet*/, T& scalar) const { return scalar; }
+};
+
+#define CHECK_CWISE1_IF(COND, REFOP, POP) if(COND) { \
+ test::packet_helper<COND,Packet> h; \
+ for (int i=0; i<PacketSize; ++i) \
+ ref[i] = Scalar(REFOP(data1[i])); \
+ h.store(data2, POP(h.load(data1))); \
+ VERIFY(test::areApprox(ref, data2, PacketSize) && #POP); \
+}
+
+#define CHECK_CWISE1_EXACT_IF(COND, REFOP, POP) if(COND) { \
+ test::packet_helper<COND,Packet> h; \
+ for (int i=0; i<PacketSize; ++i) \
+ ref[i] = Scalar(REFOP(data1[i])); \
+ h.store(data2, POP(h.load(data1))); \
+ VERIFY(test::areEqual(ref, data2, PacketSize) && #POP); \
+}
+
+#define CHECK_CWISE2_IF(COND, REFOP, POP) if(COND) { \
+ test::packet_helper<COND,Packet> h; \
+ for (int i=0; i<PacketSize; ++i) \
+ ref[i] = Scalar(REFOP(data1[i], data1[i+PacketSize])); \
+ h.store(data2, POP(h.load(data1),h.load(data1+PacketSize))); \
+ VERIFY(test::areApprox(ref, data2, PacketSize) && #POP); \
+}
+
+// One input, one output by reference.
+#define CHECK_CWISE1_BYREF1_IF(COND, REFOP, POP) if(COND) { \
+ test::packet_helper<COND,Packet> h; \
+ for (int i=0; i<PacketSize; ++i) \
+ ref[i] = Scalar(REFOP(data1[i], ref[i+PacketSize])); \
+ Packet pout; \
+ Scalar sout; \
+ h.store(data2, POP(h.load(data1), h.forward_reference(pout, sout))); \
+ h.store(data2+PacketSize, h.forward_reference(pout, sout)); \
+ VERIFY(test::areApprox(ref, data2, 2 * PacketSize) && #POP); \
+}
+
+#define CHECK_CWISE3_IF(COND, REFOP, POP) if (COND) { \
+ test::packet_helper<COND, Packet> h; \
+ for (int i = 0; i < PacketSize; ++i) \
+ ref[i] = Scalar(REFOP(data1[i], data1[i + PacketSize], \
+ data1[i + 2 * PacketSize])); \
+ h.store(data2, POP(h.load(data1), h.load(data1 + PacketSize), \
+ h.load(data1 + 2 * PacketSize))); \
+ VERIFY(test::areApprox(ref, data2, PacketSize) && #POP); \
+}
+
+// Specialize the runall struct in your test file by defining run().
+template<
+ typename Scalar,
+ typename PacketType,
+ bool IsComplex = NumTraits<Scalar>::IsComplex,
+ bool IsInteger = NumTraits<Scalar>::IsInteger>
+struct runall;
+
+template<
+ typename Scalar,
+ typename PacketType = typename internal::packet_traits<Scalar>::type,
+ bool Vectorized = internal::packet_traits<Scalar>::Vectorizable,
+ bool HasHalf = !internal::is_same<typename internal::unpacket_traits<PacketType>::half,PacketType>::value >
+struct runner;
+
+template<typename Scalar,typename PacketType>
+struct runner<Scalar,PacketType,true,true>
+{
+ static void run() {
+ runall<Scalar,PacketType>::run();
+ runner<Scalar,typename internal::unpacket_traits<PacketType>::half>::run();
+ }
+};
+
+template<typename Scalar,typename PacketType>
+struct runner<Scalar,PacketType,true,false>
+{
+ static void run() {
+ runall<Scalar,PacketType>::run();
+ }
+};
+
+template<typename Scalar,typename PacketType>
+struct runner<Scalar,PacketType,false,false>
+{
+ static void run() {
+ runall<Scalar,PacketType>::run();
+ }
+};
+
+}
+}
diff --git a/test/pardiso_support.cpp b/test/pardiso_support.cpp
new file mode 100644
index 0000000..9c16ded
--- /dev/null
+++ b/test/pardiso_support.cpp
@@ -0,0 +1,29 @@
+/*
+ Intel Copyright (C) ....
+*/
+
+#include "sparse_solver.h"
+#include <Eigen/PardisoSupport>
+
+template<typename T> void test_pardiso_T()
+{
+ PardisoLLT < SparseMatrix<T, RowMajor>, Lower> pardiso_llt_lower;
+ PardisoLLT < SparseMatrix<T, RowMajor>, Upper> pardiso_llt_upper;
+ PardisoLDLT < SparseMatrix<T, RowMajor>, Lower> pardiso_ldlt_lower;
+ PardisoLDLT < SparseMatrix<T, RowMajor>, Upper> pardiso_ldlt_upper;
+ PardisoLU < SparseMatrix<T, RowMajor> > pardiso_lu;
+
+ check_sparse_spd_solving(pardiso_llt_lower);
+ check_sparse_spd_solving(pardiso_llt_upper);
+ check_sparse_spd_solving(pardiso_ldlt_lower);
+ check_sparse_spd_solving(pardiso_ldlt_upper);
+ check_sparse_square_solving(pardiso_lu);
+}
+
+EIGEN_DECLARE_TEST(pardiso_support)
+{
+ CALL_SUBTEST_1(test_pardiso_T<float>());
+ CALL_SUBTEST_2(test_pardiso_T<double>());
+ CALL_SUBTEST_3(test_pardiso_T< std::complex<float> >());
+ CALL_SUBTEST_4(test_pardiso_T< std::complex<double> >());
+}
diff --git a/test/pastix_support.cpp b/test/pastix_support.cpp
new file mode 100644
index 0000000..9b64417
--- /dev/null
+++ b/test/pastix_support.cpp
@@ -0,0 +1,54 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2012 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2012 Désiré Nuentsa-Wakam <desire.nuentsa_wakam@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#define EIGEN_NO_DEBUG_SMALL_PRODUCT_BLOCKS
+#include "sparse_solver.h"
+#include <Eigen/PaStiXSupport>
+#include <unsupported/Eigen/SparseExtra>
+
+
+template<typename T> void test_pastix_T()
+{
+ PastixLLT< SparseMatrix<T, ColMajor>, Eigen::Lower > pastix_llt_lower;
+ PastixLDLT< SparseMatrix<T, ColMajor>, Eigen::Lower > pastix_ldlt_lower;
+ PastixLLT< SparseMatrix<T, ColMajor>, Eigen::Upper > pastix_llt_upper;
+ PastixLDLT< SparseMatrix<T, ColMajor>, Eigen::Upper > pastix_ldlt_upper;
+ PastixLU< SparseMatrix<T, ColMajor> > pastix_lu;
+
+ check_sparse_spd_solving(pastix_llt_lower);
+ check_sparse_spd_solving(pastix_ldlt_lower);
+ check_sparse_spd_solving(pastix_llt_upper);
+ check_sparse_spd_solving(pastix_ldlt_upper);
+ check_sparse_square_solving(pastix_lu);
+
+ // Some compilation check:
+ pastix_llt_lower.iparm();
+ pastix_llt_lower.dparm();
+ pastix_ldlt_lower.iparm();
+ pastix_ldlt_lower.dparm();
+ pastix_lu.iparm();
+ pastix_lu.dparm();
+}
+
+// There is no support for selfadjoint matrices with PaStiX.
+// Complex symmetric matrices should pass though
+template<typename T> void test_pastix_T_LU()
+{
+ PastixLU< SparseMatrix<T, ColMajor> > pastix_lu;
+ check_sparse_square_solving(pastix_lu);
+}
+
+EIGEN_DECLARE_TEST(pastix_support)
+{
+ CALL_SUBTEST_1(test_pastix_T<float>());
+ CALL_SUBTEST_2(test_pastix_T<double>());
+ CALL_SUBTEST_3( (test_pastix_T_LU<std::complex<float> >()) );
+ CALL_SUBTEST_4(test_pastix_T_LU<std::complex<double> >());
+}
diff --git a/test/permutationmatrices.cpp b/test/permutationmatrices.cpp
new file mode 100644
index 0000000..d4b68b2
--- /dev/null
+++ b/test/permutationmatrices.cpp
@@ -0,0 +1,181 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#define TEST_ENABLE_TEMPORARY_TRACKING
+
+#include "main.h"
+
+using namespace std;
+template<typename MatrixType> void permutationmatrices(const MatrixType& m)
+{
+ typedef typename MatrixType::Scalar Scalar;
+ enum { Rows = MatrixType::RowsAtCompileTime, Cols = MatrixType::ColsAtCompileTime,
+ Options = MatrixType::Options };
+ typedef PermutationMatrix<Rows> LeftPermutationType;
+ typedef Transpositions<Rows> LeftTranspositionsType;
+ typedef Matrix<int, Rows, 1> LeftPermutationVectorType;
+ typedef Map<LeftPermutationType> MapLeftPerm;
+ typedef PermutationMatrix<Cols> RightPermutationType;
+ typedef Transpositions<Cols> RightTranspositionsType;
+ typedef Matrix<int, Cols, 1> RightPermutationVectorType;
+ typedef Map<RightPermutationType> MapRightPerm;
+
+ Index rows = m.rows();
+ Index cols = m.cols();
+
+ MatrixType m_original = MatrixType::Random(rows,cols);
+ LeftPermutationVectorType lv;
+ randomPermutationVector(lv, rows);
+ LeftPermutationType lp(lv);
+ RightPermutationVectorType rv;
+ randomPermutationVector(rv, cols);
+ RightPermutationType rp(rv);
+ LeftTranspositionsType lt(lv);
+ RightTranspositionsType rt(rv);
+ MatrixType m_permuted = MatrixType::Random(rows,cols);
+
+ VERIFY_EVALUATION_COUNT(m_permuted = lp * m_original * rp, 1); // 1 temp for sub expression "lp * m_original"
+
+ for (int i=0; i<rows; i++)
+ for (int j=0; j<cols; j++)
+ VERIFY_IS_APPROX(m_permuted(lv(i),j), m_original(i,rv(j)));
+
+ Matrix<Scalar,Rows,Rows> lm(lp);
+ Matrix<Scalar,Cols,Cols> rm(rp);
+
+ VERIFY_IS_APPROX(m_permuted, lm*m_original*rm);
+
+ m_permuted = m_original;
+ VERIFY_EVALUATION_COUNT(m_permuted = lp * m_permuted * rp, 1);
+ VERIFY_IS_APPROX(m_permuted, lm*m_original*rm);
+
+ LeftPermutationType lpi;
+ lpi = lp.inverse();
+ VERIFY_IS_APPROX(lpi*m_permuted,lp.inverse()*m_permuted);
+
+ VERIFY_IS_APPROX(lp.inverse()*m_permuted*rp.inverse(), m_original);
+ VERIFY_IS_APPROX(lv.asPermutation().inverse()*m_permuted*rv.asPermutation().inverse(), m_original);
+ VERIFY_IS_APPROX(MapLeftPerm(lv.data(),lv.size()).inverse()*m_permuted*MapRightPerm(rv.data(),rv.size()).inverse(), m_original);
+
+ VERIFY((lp*lp.inverse()).toDenseMatrix().isIdentity());
+ VERIFY((lv.asPermutation()*lv.asPermutation().inverse()).toDenseMatrix().isIdentity());
+ VERIFY((MapLeftPerm(lv.data(),lv.size())*MapLeftPerm(lv.data(),lv.size()).inverse()).toDenseMatrix().isIdentity());
+
+ LeftPermutationVectorType lv2;
+ randomPermutationVector(lv2, rows);
+ LeftPermutationType lp2(lv2);
+ Matrix<Scalar,Rows,Rows> lm2(lp2);
+ VERIFY_IS_APPROX((lp*lp2).toDenseMatrix().template cast<Scalar>(), lm*lm2);
+ VERIFY_IS_APPROX((lv.asPermutation()*lv2.asPermutation()).toDenseMatrix().template cast<Scalar>(), lm*lm2);
+ VERIFY_IS_APPROX((MapLeftPerm(lv.data(),lv.size())*MapLeftPerm(lv2.data(),lv2.size())).toDenseMatrix().template cast<Scalar>(), lm*lm2);
+
+ LeftPermutationType identityp;
+ identityp.setIdentity(rows);
+ VERIFY_IS_APPROX(m_original, identityp*m_original);
+
+ // check inplace permutations
+ m_permuted = m_original;
+ VERIFY_EVALUATION_COUNT(m_permuted.noalias()= lp.inverse() * m_permuted, 1); // 1 temp to allocate the mask
+ VERIFY_IS_APPROX(m_permuted, lp.inverse()*m_original);
+
+ m_permuted = m_original;
+ VERIFY_EVALUATION_COUNT(m_permuted.noalias() = m_permuted * rp.inverse(), 1); // 1 temp to allocate the mask
+ VERIFY_IS_APPROX(m_permuted, m_original*rp.inverse());
+
+ m_permuted = m_original;
+ VERIFY_EVALUATION_COUNT(m_permuted.noalias() = lp * m_permuted, 1); // 1 temp to allocate the mask
+ VERIFY_IS_APPROX(m_permuted, lp*m_original);
+
+ m_permuted = m_original;
+ VERIFY_EVALUATION_COUNT(m_permuted.noalias() = m_permuted * rp, 1); // 1 temp to allocate the mask
+ VERIFY_IS_APPROX(m_permuted, m_original*rp);
+
+ if(rows>1 && cols>1)
+ {
+ lp2 = lp;
+ Index i = internal::random<Index>(0, rows-1);
+ Index j;
+ do j = internal::random<Index>(0, rows-1); while(j==i);
+ lp2.applyTranspositionOnTheLeft(i, j);
+ lm = lp;
+ lm.row(i).swap(lm.row(j));
+ VERIFY_IS_APPROX(lm, lp2.toDenseMatrix().template cast<Scalar>());
+
+ RightPermutationType rp2 = rp;
+ i = internal::random<Index>(0, cols-1);
+ do j = internal::random<Index>(0, cols-1); while(j==i);
+ rp2.applyTranspositionOnTheRight(i, j);
+ rm = rp;
+ rm.col(i).swap(rm.col(j));
+ VERIFY_IS_APPROX(rm, rp2.toDenseMatrix().template cast<Scalar>());
+ }
+
+ {
+ // simple compilation check
+ Matrix<Scalar, Cols, Cols> A = rp;
+ Matrix<Scalar, Cols, Cols> B = rp.transpose();
+ VERIFY_IS_APPROX(A, B.transpose());
+ }
+
+ m_permuted = m_original;
+ lp = lt;
+ rp = rt;
+ VERIFY_EVALUATION_COUNT(m_permuted = lt * m_permuted * rt, 1);
+ VERIFY_IS_APPROX(m_permuted, lp*m_original*rp.transpose());
+
+ VERIFY_IS_APPROX(lt.inverse()*m_permuted*rt.inverse(), m_original);
+
+ // Check inplace transpositions
+ m_permuted = m_original;
+ VERIFY_IS_APPROX(m_permuted = lt * m_permuted, lp * m_original);
+ m_permuted = m_original;
+ VERIFY_IS_APPROX(m_permuted = lt.inverse() * m_permuted, lp.inverse() * m_original);
+ m_permuted = m_original;
+ VERIFY_IS_APPROX(m_permuted = m_permuted * rt, m_original * rt);
+ m_permuted = m_original;
+ VERIFY_IS_APPROX(m_permuted = m_permuted * rt.inverse(), m_original * rt.inverse());
+}
+
+template<typename T>
+void bug890()
+{
+ typedef Matrix<T, Dynamic, Dynamic> MatrixType;
+ typedef Matrix<T, Dynamic, 1> VectorType;
+ typedef Stride<Dynamic,Dynamic> S;
+ typedef Map<MatrixType, Aligned, S> MapType;
+ typedef PermutationMatrix<Dynamic> Perm;
+
+ VectorType v1(2), v2(2), op(4), rhs(2);
+ v1 << 666,667;
+ op << 1,0,0,1;
+ rhs << 42,42;
+
+ Perm P(2);
+ P.indices() << 1, 0;
+
+ MapType(v1.data(),2,1,S(1,1)) = P * MapType(rhs.data(),2,1,S(1,1));
+ VERIFY_IS_APPROX(v1, (P * rhs).eval());
+
+ MapType(v1.data(),2,1,S(1,1)) = P.inverse() * MapType(rhs.data(),2,1,S(1,1));
+ VERIFY_IS_APPROX(v1, (P.inverse() * rhs).eval());
+}
+
+EIGEN_DECLARE_TEST(permutationmatrices)
+{
+ for(int i = 0; i < g_repeat; i++) {
+ CALL_SUBTEST_1( permutationmatrices(Matrix<float, 1, 1>()) );
+ CALL_SUBTEST_2( permutationmatrices(Matrix3f()) );
+ CALL_SUBTEST_3( permutationmatrices(Matrix<double,3,3,RowMajor>()) );
+ CALL_SUBTEST_4( permutationmatrices(Matrix4d()) );
+ CALL_SUBTEST_5( permutationmatrices(Matrix<double,40,60>()) );
+ CALL_SUBTEST_6( permutationmatrices(Matrix<double,Dynamic,Dynamic,RowMajor>(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
+ CALL_SUBTEST_7( permutationmatrices(MatrixXcf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
+ }
+ CALL_SUBTEST_5( bug890<double>() );
+}
diff --git a/test/prec_inverse_4x4.cpp b/test/prec_inverse_4x4.cpp
new file mode 100644
index 0000000..333322f
--- /dev/null
+++ b/test/prec_inverse_4x4.cpp
@@ -0,0 +1,79 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "main.h"
+#include <Eigen/LU>
+#include <algorithm>
+
+template<typename MatrixType> void inverse_permutation_4x4()
+{
+ Vector4i indices(0,1,2,3);
+ for(int i = 0; i < 24; ++i)
+ {
+ MatrixType m = PermutationMatrix<4>(indices);
+ MatrixType inv = m.inverse();
+ VERIFY_IS_APPROX(m*inv, MatrixType::Identity());
+ std::next_permutation(indices.data(),indices.data()+4);
+ }
+}
+
+template<typename MatrixType> void inverse_general_4x4(int repeat)
+{
+ using std::abs;
+ typedef typename MatrixType::Scalar Scalar;
+ double error_sum = 0., error_max = 0.;
+ for(int i = 0; i < repeat; ++i)
+ {
+ MatrixType m;
+ bool is_invertible;
+ do {
+ m = MatrixType::Random();
+ is_invertible = Eigen::FullPivLU<MatrixType>(m).isInvertible();
+ } while(!is_invertible);
+ MatrixType inv = m.inverse();
+ double error = double( (m*inv-MatrixType::Identity()).norm());
+ error_sum += error;
+ error_max = (std::max)(error_max, error);
+ }
+ std::cerr << "inverse_general_4x4, Scalar = " << type_name<Scalar>() << std::endl;
+ double error_avg = error_sum / repeat;
+ EIGEN_DEBUG_VAR(error_avg);
+ EIGEN_DEBUG_VAR(error_max);
+ // FIXME that 1.25 used to be a 1.0 until the NumTraits changes on 28 April 2010, what's going wrong??
+ // FIXME that 1.25 used to be 1.2 until we tested gcc 4.1 on 30 June 2010 and got 1.21.
+ VERIFY(error_avg < (NumTraits<Scalar>::IsComplex ? 8.0 : 1.25));
+ VERIFY(error_max < (NumTraits<Scalar>::IsComplex ? 64.0 : 20.0));
+
+ {
+ int s = 5;//internal::random<int>(4,10);
+ int i = 0;//internal::random<int>(0,s-4);
+ int j = 0;//internal::random<int>(0,s-4);
+ Matrix<Scalar,5,5> mat(s,s);
+ mat.setRandom();
+ MatrixType submat = mat.template block<4,4>(i,j);
+ MatrixType mat_inv = mat.template block<4,4>(i,j).inverse();
+ VERIFY_IS_APPROX(mat_inv, submat.inverse());
+ mat.template block<4,4>(i,j) = submat.inverse();
+ VERIFY_IS_APPROX(mat_inv, (mat.template block<4,4>(i,j)));
+ }
+}
+
+EIGEN_DECLARE_TEST(prec_inverse_4x4)
+{
+ CALL_SUBTEST_1((inverse_permutation_4x4<Matrix4f>()));
+ CALL_SUBTEST_1(( inverse_general_4x4<Matrix4f>(200000 * g_repeat) ));
+ CALL_SUBTEST_1(( inverse_general_4x4<Matrix<float,4,4,RowMajor> >(200000 * g_repeat) ));
+
+ CALL_SUBTEST_2((inverse_permutation_4x4<Matrix<double,4,4,RowMajor> >()));
+ CALL_SUBTEST_2(( inverse_general_4x4<Matrix<double,4,4,ColMajor> >(200000 * g_repeat) ));
+ CALL_SUBTEST_2(( inverse_general_4x4<Matrix<double,4,4,RowMajor> >(200000 * g_repeat) ));
+
+ CALL_SUBTEST_3((inverse_permutation_4x4<Matrix4cf>()));
+ CALL_SUBTEST_3((inverse_general_4x4<Matrix4cf>(50000 * g_repeat)));
+}
diff --git a/test/product.h b/test/product.h
new file mode 100644
index 0000000..a4d8591
--- /dev/null
+++ b/test/product.h
@@ -0,0 +1,271 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "main.h"
+#include <Eigen/QR>
+
+template<typename Derived1, typename Derived2>
+bool areNotApprox(const MatrixBase<Derived1>& m1, const MatrixBase<Derived2>& m2, typename Derived1::RealScalar epsilon = NumTraits<typename Derived1::RealScalar>::dummy_precision())
+{
+ return !((m1-m2).cwiseAbs2().maxCoeff() < epsilon * epsilon
+ * (std::max)(m1.cwiseAbs2().maxCoeff(), m2.cwiseAbs2().maxCoeff()));
+}
+
+template <typename LhsType, typename RhsType>
+std::enable_if_t<RhsType::SizeAtCompileTime==Dynamic,void>
+check_mismatched_product(LhsType& lhs, const RhsType& rhs) {
+ VERIFY_RAISES_ASSERT(lhs = rhs*rhs);
+}
+
+template <typename LhsType, typename RhsType>
+std::enable_if_t<RhsType::SizeAtCompileTime!=Dynamic,void>
+check_mismatched_product(LhsType& /*unused*/, const RhsType& /*unused*/) {
+}
+
+template<typename MatrixType> void product(const MatrixType& m)
+{
+ /* this test covers the following files:
+ Identity.h Product.h
+ */
+ typedef typename MatrixType::Scalar Scalar;
+ typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> RowVectorType;
+ typedef Matrix<Scalar, MatrixType::ColsAtCompileTime, 1> ColVectorType;
+ typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime> RowSquareMatrixType;
+ typedef Matrix<Scalar, MatrixType::ColsAtCompileTime, MatrixType::ColsAtCompileTime> ColSquareMatrixType;
+ typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::ColsAtCompileTime,
+ MatrixType::Flags&RowMajorBit?ColMajor:RowMajor> OtherMajorMatrixType;
+
+ Index rows = m.rows();
+ Index cols = m.cols();
+
+ // this test relies a lot on Random.h, and there's not much more that we can do
+ // to test it, hence I consider that we will have tested Random.h
+ MatrixType m1 = MatrixType::Random(rows, cols),
+ m2 = MatrixType::Random(rows, cols),
+ m3(rows, cols);
+ RowSquareMatrixType
+ identity = RowSquareMatrixType::Identity(rows, rows),
+ square = RowSquareMatrixType::Random(rows, rows),
+ res = RowSquareMatrixType::Random(rows, rows);
+ ColSquareMatrixType
+ square2 = ColSquareMatrixType::Random(cols, cols),
+ res2 = ColSquareMatrixType::Random(cols, cols);
+ RowVectorType v1 = RowVectorType::Random(rows);
+ ColVectorType vc2 = ColVectorType::Random(cols), vcres(cols);
+ OtherMajorMatrixType tm1 = m1;
+
+ Scalar s1 = internal::random<Scalar>();
+
+ Index r = internal::random<Index>(0, rows-1),
+ c = internal::random<Index>(0, cols-1),
+ c2 = internal::random<Index>(0, cols-1);
+
+ // begin testing Product.h: only associativity for now
+ // (we use Transpose.h but this doesn't count as a test for it)
+ VERIFY_IS_APPROX((m1*m1.transpose())*m2, m1*(m1.transpose()*m2));
+ m3 = m1;
+ m3 *= m1.transpose() * m2;
+ VERIFY_IS_APPROX(m3, m1 * (m1.transpose()*m2));
+ VERIFY_IS_APPROX(m3, m1 * (m1.transpose()*m2));
+
+ // continue testing Product.h: distributivity
+ VERIFY_IS_APPROX(square*(m1 + m2), square*m1+square*m2);
+ VERIFY_IS_APPROX(square*(m1 - m2), square*m1-square*m2);
+
+ // continue testing Product.h: compatibility with ScalarMultiple.h
+ VERIFY_IS_APPROX(s1*(square*m1), (s1*square)*m1);
+ VERIFY_IS_APPROX(s1*(square*m1), square*(m1*s1));
+
+ // test Product.h together with Identity.h
+ VERIFY_IS_APPROX(v1, identity*v1);
+ VERIFY_IS_APPROX(v1.transpose(), v1.transpose() * identity);
+ // again, test operator() to check const-qualification
+ VERIFY_IS_APPROX(MatrixType::Identity(rows, cols)(r,c), static_cast<Scalar>(r==c));
+
+ if (rows!=cols) {
+ check_mismatched_product(m3, m1);
+ }
+
+ // test the previous tests were not screwed up because operator* returns 0
+ // (we use the more accurate default epsilon)
+ if (!NumTraits<Scalar>::IsInteger && (std::min)(rows,cols)>1)
+ {
+ VERIFY(areNotApprox(m1.transpose()*m2,m2.transpose()*m1));
+ }
+
+ // test optimized operator+= path
+ res = square;
+ res.noalias() += m1 * m2.transpose();
+ VERIFY_IS_APPROX(res, square + m1 * m2.transpose());
+ if (!NumTraits<Scalar>::IsInteger && (std::min)(rows,cols)>1)
+ {
+ VERIFY(areNotApprox(res,square + m2 * m1.transpose()));
+ }
+ vcres = vc2;
+ vcres.noalias() += m1.transpose() * v1;
+ VERIFY_IS_APPROX(vcres, vc2 + m1.transpose() * v1);
+
+ // test optimized operator-= path
+ res = square;
+ res.noalias() -= m1 * m2.transpose();
+ VERIFY_IS_APPROX(res, square - (m1 * m2.transpose()));
+ if (!NumTraits<Scalar>::IsInteger && (std::min)(rows,cols)>1)
+ {
+ VERIFY(areNotApprox(res,square - m2 * m1.transpose()));
+ }
+ vcres = vc2;
+ vcres.noalias() -= m1.transpose() * v1;
+ VERIFY_IS_APPROX(vcres, vc2 - m1.transpose() * v1);
+
+ // test scaled products
+ res = square;
+ res.noalias() = s1 * m1 * m2.transpose();
+ VERIFY_IS_APPROX(res, ((s1*m1).eval() * m2.transpose()));
+ res = square;
+ res.noalias() += s1 * m1 * m2.transpose();
+ VERIFY_IS_APPROX(res, square + ((s1*m1).eval() * m2.transpose()));
+ res = square;
+ res.noalias() -= s1 * m1 * m2.transpose();
+ VERIFY_IS_APPROX(res, square - ((s1*m1).eval() * m2.transpose()));
+
+ // test d ?= a+b*c rules
+ res.noalias() = square + m1 * m2.transpose();
+ VERIFY_IS_APPROX(res, square + m1 * m2.transpose());
+ res.noalias() += square + m1 * m2.transpose();
+ VERIFY_IS_APPROX(res, 2*(square + m1 * m2.transpose()));
+ res.noalias() -= square + m1 * m2.transpose();
+ VERIFY_IS_APPROX(res, square + m1 * m2.transpose());
+
+ // test d ?= a-b*c rules
+ res.noalias() = square - m1 * m2.transpose();
+ VERIFY_IS_APPROX(res, square - m1 * m2.transpose());
+ res.noalias() += square - m1 * m2.transpose();
+ VERIFY_IS_APPROX(res, 2*(square - m1 * m2.transpose()));
+ res.noalias() -= square - m1 * m2.transpose();
+ VERIFY_IS_APPROX(res, square - m1 * m2.transpose());
+
+
+ tm1 = m1;
+ VERIFY_IS_APPROX(tm1.transpose() * v1, m1.transpose() * v1);
+ VERIFY_IS_APPROX(v1.transpose() * tm1, v1.transpose() * m1);
+
+ // test submatrix and matrix/vector product
+ for (int i=0; i<rows; ++i)
+ res.row(i) = m1.row(i) * m2.transpose();
+ VERIFY_IS_APPROX(res, m1 * m2.transpose());
+ // the other way round:
+ for (int i=0; i<rows; ++i)
+ res.col(i) = m1 * m2.transpose().col(i);
+ VERIFY_IS_APPROX(res, m1 * m2.transpose());
+
+ res2 = square2;
+ res2.noalias() += m1.transpose() * m2;
+ VERIFY_IS_APPROX(res2, square2 + m1.transpose() * m2);
+ if (!NumTraits<Scalar>::IsInteger && (std::min)(rows,cols)>1)
+ {
+ VERIFY(areNotApprox(res2,square2 + m2.transpose() * m1));
+ }
+
+ VERIFY_IS_APPROX(res.col(r).noalias() = square.adjoint() * square.col(r), (square.adjoint() * square.col(r)).eval());
+ VERIFY_IS_APPROX(res.col(r).noalias() = square * square.col(r), (square * square.col(r)).eval());
+
+ // vector at runtime (see bug 1166)
+ {
+ RowSquareMatrixType ref(square);
+ ColSquareMatrixType ref2(square2);
+ ref = res = square;
+ VERIFY_IS_APPROX(res.block(0,0,1,rows).noalias() = m1.col(0).transpose() * square.transpose(), (ref.row(0) = m1.col(0).transpose() * square.transpose()));
+ VERIFY_IS_APPROX(res.block(0,0,1,rows).noalias() = m1.block(0,0,rows,1).transpose() * square.transpose(), (ref.row(0) = m1.col(0).transpose() * square.transpose()));
+ VERIFY_IS_APPROX(res.block(0,0,1,rows).noalias() = m1.col(0).transpose() * square, (ref.row(0) = m1.col(0).transpose() * square));
+ VERIFY_IS_APPROX(res.block(0,0,1,rows).noalias() = m1.block(0,0,rows,1).transpose() * square, (ref.row(0) = m1.col(0).transpose() * square));
+ ref2 = res2 = square2;
+ VERIFY_IS_APPROX(res2.block(0,0,1,cols).noalias() = m1.row(0) * square2.transpose(), (ref2.row(0) = m1.row(0) * square2.transpose()));
+ VERIFY_IS_APPROX(res2.block(0,0,1,cols).noalias() = m1.block(0,0,1,cols) * square2.transpose(), (ref2.row(0) = m1.row(0) * square2.transpose()));
+ VERIFY_IS_APPROX(res2.block(0,0,1,cols).noalias() = m1.row(0) * square2, (ref2.row(0) = m1.row(0) * square2));
+ VERIFY_IS_APPROX(res2.block(0,0,1,cols).noalias() = m1.block(0,0,1,cols) * square2, (ref2.row(0) = m1.row(0) * square2));
+ }
+
+ // vector.block() (see bug 1283)
+ {
+ RowVectorType w1(rows);
+ VERIFY_IS_APPROX(square * v1.block(0,0,rows,1), square * v1);
+ VERIFY_IS_APPROX(w1.noalias() = square * v1.block(0,0,rows,1), square * v1);
+ VERIFY_IS_APPROX(w1.block(0,0,rows,1).noalias() = square * v1.block(0,0,rows,1), square * v1);
+
+ Matrix<Scalar,1,MatrixType::ColsAtCompileTime> w2(cols);
+ VERIFY_IS_APPROX(vc2.block(0,0,cols,1).transpose() * square2, vc2.transpose() * square2);
+ VERIFY_IS_APPROX(w2.noalias() = vc2.block(0,0,cols,1).transpose() * square2, vc2.transpose() * square2);
+ VERIFY_IS_APPROX(w2.block(0,0,1,cols).noalias() = vc2.block(0,0,cols,1).transpose() * square2, vc2.transpose() * square2);
+
+ vc2 = square2.block(0,0,1,cols).transpose();
+ VERIFY_IS_APPROX(square2.block(0,0,1,cols) * square2, vc2.transpose() * square2);
+ VERIFY_IS_APPROX(w2.noalias() = square2.block(0,0,1,cols) * square2, vc2.transpose() * square2);
+ VERIFY_IS_APPROX(w2.block(0,0,1,cols).noalias() = square2.block(0,0,1,cols) * square2, vc2.transpose() * square2);
+
+ vc2 = square2.block(0,0,cols,1);
+ VERIFY_IS_APPROX(square2.block(0,0,cols,1).transpose() * square2, vc2.transpose() * square2);
+ VERIFY_IS_APPROX(w2.noalias() = square2.block(0,0,cols,1).transpose() * square2, vc2.transpose() * square2);
+ VERIFY_IS_APPROX(w2.block(0,0,1,cols).noalias() = square2.block(0,0,cols,1).transpose() * square2, vc2.transpose() * square2);
+ }
+
+ // inner product
+ {
+ Scalar x = square2.row(c) * square2.col(c2);
+ VERIFY_IS_APPROX(x, square2.row(c).transpose().cwiseProduct(square2.col(c2)).sum());
+ }
+
+ // outer product
+ {
+ VERIFY_IS_APPROX(m1.col(c) * m1.row(r), m1.block(0,c,rows,1) * m1.block(r,0,1,cols));
+ VERIFY_IS_APPROX(m1.row(r).transpose() * m1.col(c).transpose(), m1.block(r,0,1,cols).transpose() * m1.block(0,c,rows,1).transpose());
+ VERIFY_IS_APPROX(m1.block(0,c,rows,1) * m1.row(r), m1.block(0,c,rows,1) * m1.block(r,0,1,cols));
+ VERIFY_IS_APPROX(m1.col(c) * m1.block(r,0,1,cols), m1.block(0,c,rows,1) * m1.block(r,0,1,cols));
+ VERIFY_IS_APPROX(m1.leftCols(1) * m1.row(r), m1.block(0,0,rows,1) * m1.block(r,0,1,cols));
+ VERIFY_IS_APPROX(m1.col(c) * m1.topRows(1), m1.block(0,c,rows,1) * m1.block(0,0,1,cols));
+ }
+
+ // Aliasing
+ {
+ ColVectorType x(cols); x.setRandom();
+ ColVectorType z(x);
+ ColVectorType y(cols); y.setZero();
+ ColSquareMatrixType A(cols,cols); A.setRandom();
+ // CwiseBinaryOp
+ VERIFY_IS_APPROX(x = y + A*x, A*z);
+ x = z;
+ VERIFY_IS_APPROX(x = y - A*x, A*(-z));
+ x = z;
+ // CwiseUnaryOp
+ VERIFY_IS_APPROX(x = Scalar(1.)*(A*x), A*z);
+ }
+
+ // regression for blas_trais
+ {
+ VERIFY_IS_APPROX(square * (square*square).transpose(), square * square.transpose() * square.transpose());
+ VERIFY_IS_APPROX(square * (-(square*square)), -square * square * square);
+ VERIFY_IS_APPROX(square * (s1*(square*square)), s1 * square * square * square);
+ VERIFY_IS_APPROX(square * (square*square).conjugate(), square * square.conjugate() * square.conjugate());
+ }
+
+ // destination with a non-default inner-stride
+ // see bug 1741
+ if(!MatrixType::IsRowMajor)
+ {
+ typedef Matrix<Scalar,Dynamic,Dynamic> MatrixX;
+ MatrixX buffer(2*rows,2*rows);
+ Map<RowSquareMatrixType,0,Stride<Dynamic,2> > map1(buffer.data(),rows,rows,Stride<Dynamic,2>(2*rows,2));
+ buffer.setZero();
+ VERIFY_IS_APPROX(map1 = m1 * m2.transpose(), (m1 * m2.transpose()).eval());
+ buffer.setZero();
+ VERIFY_IS_APPROX(map1.noalias() = m1 * m2.transpose(), (m1 * m2.transpose()).eval());
+ buffer.setZero();
+ VERIFY_IS_APPROX(map1.noalias() += m1 * m2.transpose(), (m1 * m2.transpose()).eval());
+ }
+
+}
diff --git a/test/product_extra.cpp b/test/product_extra.cpp
new file mode 100644
index 0000000..15c6989
--- /dev/null
+++ b/test/product_extra.cpp
@@ -0,0 +1,390 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "main.h"
+
+template<typename MatrixType> void product_extra(const MatrixType& m)
+{
+ typedef typename MatrixType::Scalar Scalar;
+ typedef Matrix<Scalar, 1, Dynamic> RowVectorType;
+ typedef Matrix<Scalar, Dynamic, 1> ColVectorType;
+ typedef Matrix<Scalar, Dynamic, Dynamic,
+ MatrixType::Flags&RowMajorBit> OtherMajorMatrixType;
+
+ Index rows = m.rows();
+ Index cols = m.cols();
+
+ MatrixType m1 = MatrixType::Random(rows, cols),
+ m2 = MatrixType::Random(rows, cols),
+ m3(rows, cols),
+ mzero = MatrixType::Zero(rows, cols),
+ identity = MatrixType::Identity(rows, rows),
+ square = MatrixType::Random(rows, rows),
+ res = MatrixType::Random(rows, rows),
+ square2 = MatrixType::Random(cols, cols),
+ res2 = MatrixType::Random(cols, cols);
+ RowVectorType v1 = RowVectorType::Random(rows), vrres(rows);
+ ColVectorType vc2 = ColVectorType::Random(cols), vcres(cols);
+ OtherMajorMatrixType tm1 = m1;
+
+ Scalar s1 = internal::random<Scalar>(),
+ s2 = internal::random<Scalar>(),
+ s3 = internal::random<Scalar>();
+
+ VERIFY_IS_APPROX(m3.noalias() = m1 * m2.adjoint(), m1 * m2.adjoint().eval());
+ VERIFY_IS_APPROX(m3.noalias() = m1.adjoint() * square.adjoint(), m1.adjoint().eval() * square.adjoint().eval());
+ VERIFY_IS_APPROX(m3.noalias() = m1.adjoint() * m2, m1.adjoint().eval() * m2);
+ VERIFY_IS_APPROX(m3.noalias() = (s1 * m1.adjoint()) * m2, (s1 * m1.adjoint()).eval() * m2);
+ VERIFY_IS_APPROX(m3.noalias() = ((s1 * m1).adjoint()) * m2, (numext::conj(s1) * m1.adjoint()).eval() * m2);
+ VERIFY_IS_APPROX(m3.noalias() = (- m1.adjoint() * s1) * (s3 * m2), (- m1.adjoint() * s1).eval() * (s3 * m2).eval());
+ VERIFY_IS_APPROX(m3.noalias() = (s2 * m1.adjoint() * s1) * m2, (s2 * m1.adjoint() * s1).eval() * m2);
+ VERIFY_IS_APPROX(m3.noalias() = (-m1*s2) * s1*m2.adjoint(), (-m1*s2).eval() * (s1*m2.adjoint()).eval());
+
+ // a very tricky case where a scale factor has to be automatically conjugated:
+ VERIFY_IS_APPROX( m1.adjoint() * (s1*m2).conjugate(), (m1.adjoint()).eval() * ((s1*m2).conjugate()).eval());
+
+
+ // test all possible conjugate combinations for the four matrix-vector product cases:
+
+ VERIFY_IS_APPROX((-m1.conjugate() * s2) * (s1 * vc2),
+ (-m1.conjugate()*s2).eval() * (s1 * vc2).eval());
+ VERIFY_IS_APPROX((-m1 * s2) * (s1 * vc2.conjugate()),
+ (-m1*s2).eval() * (s1 * vc2.conjugate()).eval());
+ VERIFY_IS_APPROX((-m1.conjugate() * s2) * (s1 * vc2.conjugate()),
+ (-m1.conjugate()*s2).eval() * (s1 * vc2.conjugate()).eval());
+
+ VERIFY_IS_APPROX((s1 * vc2.transpose()) * (-m1.adjoint() * s2),
+ (s1 * vc2.transpose()).eval() * (-m1.adjoint()*s2).eval());
+ VERIFY_IS_APPROX((s1 * vc2.adjoint()) * (-m1.transpose() * s2),
+ (s1 * vc2.adjoint()).eval() * (-m1.transpose()*s2).eval());
+ VERIFY_IS_APPROX((s1 * vc2.adjoint()) * (-m1.adjoint() * s2),
+ (s1 * vc2.adjoint()).eval() * (-m1.adjoint()*s2).eval());
+
+ VERIFY_IS_APPROX((-m1.adjoint() * s2) * (s1 * v1.transpose()),
+ (-m1.adjoint()*s2).eval() * (s1 * v1.transpose()).eval());
+ VERIFY_IS_APPROX((-m1.transpose() * s2) * (s1 * v1.adjoint()),
+ (-m1.transpose()*s2).eval() * (s1 * v1.adjoint()).eval());
+ VERIFY_IS_APPROX((-m1.adjoint() * s2) * (s1 * v1.adjoint()),
+ (-m1.adjoint()*s2).eval() * (s1 * v1.adjoint()).eval());
+
+ VERIFY_IS_APPROX((s1 * v1) * (-m1.conjugate() * s2),
+ (s1 * v1).eval() * (-m1.conjugate()*s2).eval());
+ VERIFY_IS_APPROX((s1 * v1.conjugate()) * (-m1 * s2),
+ (s1 * v1.conjugate()).eval() * (-m1*s2).eval());
+ VERIFY_IS_APPROX((s1 * v1.conjugate()) * (-m1.conjugate() * s2),
+ (s1 * v1.conjugate()).eval() * (-m1.conjugate()*s2).eval());
+
+ VERIFY_IS_APPROX((-m1.adjoint() * s2) * (s1 * v1.adjoint()),
+ (-m1.adjoint()*s2).eval() * (s1 * v1.adjoint()).eval());
+
+ // test the vector-matrix product with non aligned starts
+ Index i = internal::random<Index>(0,m1.rows()-2);
+ Index j = internal::random<Index>(0,m1.cols()-2);
+ Index r = internal::random<Index>(1,m1.rows()-i);
+ Index c = internal::random<Index>(1,m1.cols()-j);
+ Index i2 = internal::random<Index>(0,m1.rows()-1);
+ Index j2 = internal::random<Index>(0,m1.cols()-1);
+
+ VERIFY_IS_APPROX(m1.col(j2).adjoint() * m1.block(0,j,m1.rows(),c), m1.col(j2).adjoint().eval() * m1.block(0,j,m1.rows(),c).eval());
+ VERIFY_IS_APPROX(m1.block(i,0,r,m1.cols()) * m1.row(i2).adjoint(), m1.block(i,0,r,m1.cols()).eval() * m1.row(i2).adjoint().eval());
+
+ // test negative strides
+ {
+ Map<MatrixType,Unaligned,Stride<Dynamic,Dynamic> > map1(&m1(rows-1,cols-1), rows, cols, Stride<Dynamic,Dynamic>(-m1.outerStride(),-1));
+ Map<MatrixType,Unaligned,Stride<Dynamic,Dynamic> > map2(&m2(rows-1,cols-1), rows, cols, Stride<Dynamic,Dynamic>(-m2.outerStride(),-1));
+ Map<RowVectorType,Unaligned,InnerStride<-1> > mapv1(&v1(v1.size()-1), v1.size(), InnerStride<-1>(-1));
+ Map<ColVectorType,Unaligned,InnerStride<-1> > mapvc2(&vc2(vc2.size()-1), vc2.size(), InnerStride<-1>(-1));
+ VERIFY_IS_APPROX(MatrixType(map1), m1.reverse());
+ VERIFY_IS_APPROX(MatrixType(map2), m2.reverse());
+ VERIFY_IS_APPROX(m3.noalias() = MatrixType(map1) * MatrixType(map2).adjoint(), m1.reverse() * m2.reverse().adjoint());
+ VERIFY_IS_APPROX(m3.noalias() = map1 * map2.adjoint(), m1.reverse() * m2.reverse().adjoint());
+ VERIFY_IS_APPROX(map1 * vc2, m1.reverse() * vc2);
+ VERIFY_IS_APPROX(m1 * mapvc2, m1 * mapvc2);
+ VERIFY_IS_APPROX(map1.adjoint() * v1.transpose(), m1.adjoint().reverse() * v1.transpose());
+ VERIFY_IS_APPROX(m1.adjoint() * mapv1.transpose(), m1.adjoint() * v1.reverse().transpose());
+ }
+
+ // regression test
+ MatrixType tmp = m1 * m1.adjoint() * s1;
+ VERIFY_IS_APPROX(tmp, m1 * m1.adjoint() * s1);
+
+ // regression test for bug 1343, assignment to arrays
+ Array<Scalar,Dynamic,1> a1 = m1 * vc2;
+ VERIFY_IS_APPROX(a1.matrix(),m1*vc2);
+ Array<Scalar,Dynamic,1> a2 = s1 * (m1 * vc2);
+ VERIFY_IS_APPROX(a2.matrix(),s1*m1*vc2);
+ Array<Scalar,1,Dynamic> a3 = v1 * m1;
+ VERIFY_IS_APPROX(a3.matrix(),v1*m1);
+ Array<Scalar,Dynamic,Dynamic> a4 = m1 * m2.adjoint();
+ VERIFY_IS_APPROX(a4.matrix(),m1*m2.adjoint());
+}
+
+// Regression test for bug reported at http://forum.kde.org/viewtopic.php?f=74&t=96947
+void mat_mat_scalar_scalar_product()
+{
+ Eigen::Matrix2Xd dNdxy(2, 3);
+ dNdxy << -0.5, 0.5, 0,
+ -0.3, 0, 0.3;
+ double det = 6.0, wt = 0.5;
+ VERIFY_IS_APPROX(dNdxy.transpose()*dNdxy*det*wt, det*wt*dNdxy.transpose()*dNdxy);
+}
+
+template <typename MatrixType>
+void zero_sized_objects(const MatrixType& m)
+{
+ typedef typename MatrixType::Scalar Scalar;
+ const int PacketSize = internal::packet_traits<Scalar>::size;
+ const int PacketSize1 = PacketSize>1 ? PacketSize-1 : 1;
+ Index rows = m.rows();
+ Index cols = m.cols();
+
+ {
+ MatrixType res, a(rows,0), b(0,cols);
+ VERIFY_IS_APPROX( (res=a*b), MatrixType::Zero(rows,cols) );
+ VERIFY_IS_APPROX( (res=a*a.transpose()), MatrixType::Zero(rows,rows) );
+ VERIFY_IS_APPROX( (res=b.transpose()*b), MatrixType::Zero(cols,cols) );
+ VERIFY_IS_APPROX( (res=b.transpose()*a.transpose()), MatrixType::Zero(cols,rows) );
+ }
+
+ {
+ MatrixType res, a(rows,cols), b(cols,0);
+ res = a*b;
+ VERIFY(res.rows()==rows && res.cols()==0);
+ b.resize(0,rows);
+ res = b*a;
+ VERIFY(res.rows()==0 && res.cols()==cols);
+ }
+
+ {
+ Matrix<Scalar,PacketSize,0> a;
+ Matrix<Scalar,0,1> b;
+ Matrix<Scalar,PacketSize,1> res;
+ VERIFY_IS_APPROX( (res=a*b), MatrixType::Zero(PacketSize,1) );
+ VERIFY_IS_APPROX( (res=a.lazyProduct(b)), MatrixType::Zero(PacketSize,1) );
+ }
+
+ {
+ Matrix<Scalar,PacketSize1,0> a;
+ Matrix<Scalar,0,1> b;
+ Matrix<Scalar,PacketSize1,1> res;
+ VERIFY_IS_APPROX( (res=a*b), MatrixType::Zero(PacketSize1,1) );
+ VERIFY_IS_APPROX( (res=a.lazyProduct(b)), MatrixType::Zero(PacketSize1,1) );
+ }
+
+ {
+ Matrix<Scalar,PacketSize,Dynamic> a(PacketSize,0);
+ Matrix<Scalar,Dynamic,1> b(0,1);
+ Matrix<Scalar,PacketSize,1> res;
+ VERIFY_IS_APPROX( (res=a*b), MatrixType::Zero(PacketSize,1) );
+ VERIFY_IS_APPROX( (res=a.lazyProduct(b)), MatrixType::Zero(PacketSize,1) );
+ }
+
+ {
+ Matrix<Scalar,PacketSize1,Dynamic> a(PacketSize1,0);
+ Matrix<Scalar,Dynamic,1> b(0,1);
+ Matrix<Scalar,PacketSize1,1> res;
+ VERIFY_IS_APPROX( (res=a*b), MatrixType::Zero(PacketSize1,1) );
+ VERIFY_IS_APPROX( (res=a.lazyProduct(b)), MatrixType::Zero(PacketSize1,1) );
+ }
+}
+
+template<int>
+void bug_127()
+{
+ // Bug 127
+ //
+ // a product of the form lhs*rhs with
+ //
+ // lhs:
+ // rows = 1, cols = 4
+ // RowsAtCompileTime = 1, ColsAtCompileTime = -1
+ // MaxRowsAtCompileTime = 1, MaxColsAtCompileTime = 5
+ //
+ // rhs:
+ // rows = 4, cols = 0
+ // RowsAtCompileTime = -1, ColsAtCompileTime = -1
+ // MaxRowsAtCompileTime = 5, MaxColsAtCompileTime = 1
+ //
+ // was failing on a runtime assertion, because it had been mis-compiled as a dot product because Product.h was using the
+ // max-sizes to detect size 1 indicating vectors, and that didn't account for 0-sized object with max-size 1.
+
+ Matrix<float,1,Dynamic,RowMajor,1,5> a(1,4);
+ Matrix<float,Dynamic,Dynamic,ColMajor,5,1> b(4,0);
+ a*b;
+}
+
+template<int> void bug_817()
+{
+ ArrayXXf B = ArrayXXf::Random(10,10), C;
+ VectorXf x = VectorXf::Random(10);
+ C = (x.transpose()*B.matrix());
+ B = (x.transpose()*B.matrix());
+ VERIFY_IS_APPROX(B,C);
+}
+
+template<int>
+void unaligned_objects()
+{
+ // Regression test for the bug reported here:
+ // http://forum.kde.org/viewtopic.php?f=74&t=107541
+ // Recall the matrix*vector kernel avoid unaligned loads by loading two packets and then reassemble then.
+ // There was a mistake in the computation of the valid range for fully unaligned objects: in some rare cases,
+ // memory was read outside the allocated matrix memory. Though the values were not used, this might raise segfault.
+ for(int m=450;m<460;++m)
+ {
+ for(int n=8;n<12;++n)
+ {
+ MatrixXf M(m, n);
+ VectorXf v1(n), r1(500);
+ RowVectorXf v2(m), r2(16);
+
+ M.setRandom();
+ v1.setRandom();
+ v2.setRandom();
+ for(int o=0; o<4; ++o)
+ {
+ r1.segment(o,m).noalias() = M * v1;
+ VERIFY_IS_APPROX(r1.segment(o,m), M * MatrixXf(v1));
+ r2.segment(o,n).noalias() = v2 * M;
+ VERIFY_IS_APPROX(r2.segment(o,n), MatrixXf(v2) * M);
+ }
+ }
+ }
+}
+
+template<typename T>
+EIGEN_DONT_INLINE
+Index test_compute_block_size(Index m, Index n, Index k)
+{
+ Index mc(m), nc(n), kc(k);
+ internal::computeProductBlockingSizes<T,T>(kc, mc, nc);
+ return kc+mc+nc;
+}
+
+template<typename T>
+Index compute_block_size()
+{
+ Index ret = 0;
+ ret += test_compute_block_size<T>(0,1,1);
+ ret += test_compute_block_size<T>(1,0,1);
+ ret += test_compute_block_size<T>(1,1,0);
+ ret += test_compute_block_size<T>(0,0,1);
+ ret += test_compute_block_size<T>(0,1,0);
+ ret += test_compute_block_size<T>(1,0,0);
+ ret += test_compute_block_size<T>(0,0,0);
+ return ret;
+}
+
+template<typename>
+void aliasing_with_resize()
+{
+ Index m = internal::random<Index>(10,50);
+ Index n = internal::random<Index>(10,50);
+ MatrixXd A, B, C(m,n), D(m,m);
+ VectorXd a, b, c(n);
+ C.setRandom();
+ D.setRandom();
+ c.setRandom();
+ double s = internal::random<double>(1,10);
+
+ A = C;
+ B = A * A.transpose();
+ A = A * A.transpose();
+ VERIFY_IS_APPROX(A,B);
+
+ A = C;
+ B = (A * A.transpose())/s;
+ A = (A * A.transpose())/s;
+ VERIFY_IS_APPROX(A,B);
+
+ A = C;
+ B = (A * A.transpose()) + D;
+ A = (A * A.transpose()) + D;
+ VERIFY_IS_APPROX(A,B);
+
+ A = C;
+ B = D + (A * A.transpose());
+ A = D + (A * A.transpose());
+ VERIFY_IS_APPROX(A,B);
+
+ A = C;
+ B = s * (A * A.transpose());
+ A = s * (A * A.transpose());
+ VERIFY_IS_APPROX(A,B);
+
+ A = C;
+ a = c;
+ b = (A * a)/s;
+ a = (A * a)/s;
+ VERIFY_IS_APPROX(a,b);
+}
+
+template<int>
+void bug_1308()
+{
+ int n = 10;
+ MatrixXd r(n,n);
+ VectorXd v = VectorXd::Random(n);
+ r = v * RowVectorXd::Ones(n);
+ VERIFY_IS_APPROX(r, v.rowwise().replicate(n));
+ r = VectorXd::Ones(n) * v.transpose();
+ VERIFY_IS_APPROX(r, v.rowwise().replicate(n).transpose());
+
+ Matrix4d ones44 = Matrix4d::Ones();
+ Matrix4d m44 = Matrix4d::Ones() * Matrix4d::Ones();
+ VERIFY_IS_APPROX(m44,Matrix4d::Constant(4));
+ VERIFY_IS_APPROX(m44.noalias()=ones44*Matrix4d::Ones(), Matrix4d::Constant(4));
+ VERIFY_IS_APPROX(m44.noalias()=ones44.transpose()*Matrix4d::Ones(), Matrix4d::Constant(4));
+ VERIFY_IS_APPROX(m44.noalias()=Matrix4d::Ones()*ones44, Matrix4d::Constant(4));
+ VERIFY_IS_APPROX(m44.noalias()=Matrix4d::Ones()*ones44.transpose(), Matrix4d::Constant(4));
+
+ typedef Matrix<double,4,4,RowMajor> RMatrix4d;
+ RMatrix4d r44 = Matrix4d::Ones() * Matrix4d::Ones();
+ VERIFY_IS_APPROX(r44,Matrix4d::Constant(4));
+ VERIFY_IS_APPROX(r44.noalias()=ones44*Matrix4d::Ones(), Matrix4d::Constant(4));
+ VERIFY_IS_APPROX(r44.noalias()=ones44.transpose()*Matrix4d::Ones(), Matrix4d::Constant(4));
+ VERIFY_IS_APPROX(r44.noalias()=Matrix4d::Ones()*ones44, Matrix4d::Constant(4));
+ VERIFY_IS_APPROX(r44.noalias()=Matrix4d::Ones()*ones44.transpose(), Matrix4d::Constant(4));
+ VERIFY_IS_APPROX(r44.noalias()=ones44*RMatrix4d::Ones(), Matrix4d::Constant(4));
+ VERIFY_IS_APPROX(r44.noalias()=ones44.transpose()*RMatrix4d::Ones(), Matrix4d::Constant(4));
+ VERIFY_IS_APPROX(r44.noalias()=RMatrix4d::Ones()*ones44, Matrix4d::Constant(4));
+ VERIFY_IS_APPROX(r44.noalias()=RMatrix4d::Ones()*ones44.transpose(), Matrix4d::Constant(4));
+
+// RowVector4d r4;
+ m44.setOnes();
+ r44.setZero();
+ VERIFY_IS_APPROX(r44.noalias() += m44.row(0).transpose() * RowVector4d::Ones(), ones44);
+ r44.setZero();
+ VERIFY_IS_APPROX(r44.noalias() += m44.col(0) * RowVector4d::Ones(), ones44);
+ r44.setZero();
+ VERIFY_IS_APPROX(r44.noalias() += Vector4d::Ones() * m44.row(0), ones44);
+ r44.setZero();
+ VERIFY_IS_APPROX(r44.noalias() += Vector4d::Ones() * m44.col(0).transpose(), ones44);
+}
+
+EIGEN_DECLARE_TEST(product_extra)
+{
+ for(int i = 0; i < g_repeat; i++) {
+ CALL_SUBTEST_1( product_extra(MatrixXf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
+ CALL_SUBTEST_2( product_extra(MatrixXd(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
+ CALL_SUBTEST_2( mat_mat_scalar_scalar_product() );
+ CALL_SUBTEST_3( product_extra(MatrixXcf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE/2), internal::random<int>(1,EIGEN_TEST_MAX_SIZE/2))) );
+ CALL_SUBTEST_4( product_extra(MatrixXcd(internal::random<int>(1,EIGEN_TEST_MAX_SIZE/2), internal::random<int>(1,EIGEN_TEST_MAX_SIZE/2))) );
+ CALL_SUBTEST_1( zero_sized_objects(MatrixXf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
+ }
+ CALL_SUBTEST_5( bug_127<0>() );
+ CALL_SUBTEST_5( bug_817<0>() );
+ CALL_SUBTEST_5( bug_1308<0>() );
+ CALL_SUBTEST_6( unaligned_objects<0>() );
+ CALL_SUBTEST_7( compute_block_size<float>() );
+ CALL_SUBTEST_7( compute_block_size<double>() );
+ CALL_SUBTEST_7( compute_block_size<std::complex<double> >() );
+ CALL_SUBTEST_8( aliasing_with_resize<void>() );
+
+}
diff --git a/test/product_large.cpp b/test/product_large.cpp
new file mode 100644
index 0000000..3d0204b
--- /dev/null
+++ b/test/product_large.cpp
@@ -0,0 +1,131 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "product.h"
+#include <Eigen/LU>
+
+template<typename T>
+void test_aliasing()
+{
+ int rows = internal::random<int>(1,12);
+ int cols = internal::random<int>(1,12);
+ typedef Matrix<T,Dynamic,Dynamic> MatrixType;
+ typedef Matrix<T,Dynamic,1> VectorType;
+ VectorType x(cols); x.setRandom();
+ VectorType z(x);
+ VectorType y(rows); y.setZero();
+ MatrixType A(rows,cols); A.setRandom();
+ // CwiseBinaryOp
+ VERIFY_IS_APPROX(x = y + A*x, A*z); // OK because "y + A*x" is marked as "assume-aliasing"
+ x = z;
+ // CwiseUnaryOp
+ VERIFY_IS_APPROX(x = T(1.)*(A*x), A*z); // OK because 1*(A*x) is replaced by (1*A*x) which is a Product<> expression
+ x = z;
+ // VERIFY_IS_APPROX(x = y-A*x, -A*z); // Not OK in 3.3 because x is resized before A*x gets evaluated
+ x = z;
+}
+
+template<int>
+void product_large_regressions()
+{
+ {
+ // test a specific issue in DiagonalProduct
+ int N = 1000000;
+ VectorXf v = VectorXf::Ones(N);
+ MatrixXf m = MatrixXf::Ones(N,3);
+ m = (v+v).asDiagonal() * m;
+ VERIFY_IS_APPROX(m, MatrixXf::Constant(N,3,2));
+ }
+
+ {
+ // test deferred resizing in Matrix::operator=
+ MatrixXf a = MatrixXf::Random(10,4), b = MatrixXf::Random(4,10), c = a;
+ VERIFY_IS_APPROX((a = a * b), (c * b).eval());
+ }
+
+ {
+ // check the functions to setup blocking sizes compile and do not segfault
+ // FIXME check they do what they are supposed to do !!
+ std::ptrdiff_t l1 = internal::random<int>(10000,20000);
+ std::ptrdiff_t l2 = internal::random<int>(100000,200000);
+ std::ptrdiff_t l3 = internal::random<int>(1000000,2000000);
+ setCpuCacheSizes(l1,l2,l3);
+ VERIFY(l1==l1CacheSize());
+ VERIFY(l2==l2CacheSize());
+ std::ptrdiff_t k1 = internal::random<int>(10,100)*16;
+ std::ptrdiff_t m1 = internal::random<int>(10,100)*16;
+ std::ptrdiff_t n1 = internal::random<int>(10,100)*16;
+ // only makes sure it compiles fine
+ internal::computeProductBlockingSizes<float,float,std::ptrdiff_t>(k1,m1,n1,1);
+ }
+
+ {
+ // test regression in row-vector by matrix (bad Map type)
+ MatrixXf mat1(10,32); mat1.setRandom();
+ MatrixXf mat2(32,32); mat2.setRandom();
+ MatrixXf r1 = mat1.row(2)*mat2.transpose();
+ VERIFY_IS_APPROX(r1, (mat1.row(2)*mat2.transpose()).eval());
+
+ MatrixXf r2 = mat1.row(2)*mat2;
+ VERIFY_IS_APPROX(r2, (mat1.row(2)*mat2).eval());
+ }
+
+ {
+ Eigen::MatrixXd A(10,10), B, C;
+ A.setRandom();
+ C = A;
+ for(int k=0; k<79; ++k)
+ C = C * A;
+ B.noalias() = (((A*A)*(A*A))*((A*A)*(A*A))*((A*A)*(A*A))*((A*A)*(A*A))*((A*A)*(A*A)) * ((A*A)*(A*A))*((A*A)*(A*A))*((A*A)*(A*A))*((A*A)*(A*A))*((A*A)*(A*A)))
+ * (((A*A)*(A*A))*((A*A)*(A*A))*((A*A)*(A*A))*((A*A)*(A*A))*((A*A)*(A*A)) * ((A*A)*(A*A))*((A*A)*(A*A))*((A*A)*(A*A))*((A*A)*(A*A))*((A*A)*(A*A)));
+ VERIFY_IS_APPROX(B,C);
+ }
+}
+
+template<int>
+void bug_1622() {
+ typedef Matrix<double, 2, -1, 0, 2, -1> Mat2X;
+ Mat2X x(2,2); x.setRandom();
+ MatrixXd y(2,2); y.setRandom();
+ const Mat2X K1 = x * y.inverse();
+ const Matrix2d K2 = x * y.inverse();
+ VERIFY_IS_APPROX(K1,K2);
+}
+
+EIGEN_DECLARE_TEST(product_large)
+{
+ for(int i = 0; i < g_repeat; i++) {
+ CALL_SUBTEST_1( product(MatrixXf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
+ CALL_SUBTEST_2( product(MatrixXd(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
+ CALL_SUBTEST_2( product(MatrixXd(internal::random<int>(1,10), internal::random<int>(1,10))) );
+
+ CALL_SUBTEST_3( product(MatrixXi(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
+ CALL_SUBTEST_4( product(MatrixXcf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE/2), internal::random<int>(1,EIGEN_TEST_MAX_SIZE/2))) );
+ CALL_SUBTEST_5( product(Matrix<float,Dynamic,Dynamic,RowMajor>(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
+
+ CALL_SUBTEST_1( test_aliasing<float>() );
+
+ CALL_SUBTEST_6( bug_1622<1>() );
+
+ CALL_SUBTEST_7( product(MatrixXcd(internal::random<int>(1,EIGEN_TEST_MAX_SIZE/2), internal::random<int>(1,EIGEN_TEST_MAX_SIZE/2))) );
+ CALL_SUBTEST_8( product(Matrix<double,Dynamic,Dynamic,RowMajor>(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
+ CALL_SUBTEST_9( product(Matrix<std::complex<float>,Dynamic,Dynamic,RowMajor>(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
+ CALL_SUBTEST_10( product(Matrix<std::complex<double>,Dynamic,Dynamic,RowMajor>(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
+ }
+
+ CALL_SUBTEST_6( product_large_regressions<0>() );
+
+ // Regression test for bug 714:
+#if defined EIGEN_HAS_OPENMP
+ omp_set_dynamic(1);
+ for(int i = 0; i < g_repeat; i++) {
+ CALL_SUBTEST_6( product(Matrix<float,Dynamic,Dynamic>(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
+ }
+#endif
+}
diff --git a/test/product_mmtr.cpp b/test/product_mmtr.cpp
new file mode 100644
index 0000000..8f8c5fe
--- /dev/null
+++ b/test/product_mmtr.cpp
@@ -0,0 +1,106 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2010-2017 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "main.h"
+
+#define CHECK_MMTR(DEST, TRI, OP) { \
+ ref3 = DEST; \
+ ref2 = ref1 = DEST; \
+ DEST.template triangularView<TRI>() OP; \
+ ref1 OP; \
+ ref2.template triangularView<TRI>() \
+ = ref1.template triangularView<TRI>(); \
+ VERIFY_IS_APPROX(DEST,ref2); \
+ \
+ DEST = ref3; \
+ ref3 = ref2; \
+ ref3.diagonal() = DEST.diagonal(); \
+ DEST.template triangularView<TRI|ZeroDiag>() OP; \
+ VERIFY_IS_APPROX(DEST,ref3); \
+ }
+
+template<typename Scalar> void mmtr(int size)
+{
+ typedef Matrix<Scalar,Dynamic,Dynamic,ColMajor> MatrixColMaj;
+ typedef Matrix<Scalar,Dynamic,Dynamic,RowMajor> MatrixRowMaj;
+
+ DenseIndex othersize = internal::random<DenseIndex>(1,200);
+
+ MatrixColMaj matc = MatrixColMaj::Zero(size, size);
+ MatrixRowMaj matr = MatrixRowMaj::Zero(size, size);
+ MatrixColMaj ref1(size, size), ref2(size, size), ref3(size,size);
+
+ MatrixColMaj soc(size,othersize); soc.setRandom();
+ MatrixColMaj osc(othersize,size); osc.setRandom();
+ MatrixRowMaj sor(size,othersize); sor.setRandom();
+ MatrixRowMaj osr(othersize,size); osr.setRandom();
+ MatrixColMaj sqc(size,size); sqc.setRandom();
+ MatrixRowMaj sqr(size,size); sqr.setRandom();
+
+ Scalar s = internal::random<Scalar>();
+
+ CHECK_MMTR(matc, Lower, = s*soc*sor.adjoint());
+ CHECK_MMTR(matc, Upper, = s*(soc*soc.adjoint()));
+ CHECK_MMTR(matr, Lower, = s*soc*soc.adjoint());
+ CHECK_MMTR(matr, Upper, = soc*(s*sor.adjoint()));
+
+ CHECK_MMTR(matc, Lower, += s*soc*soc.adjoint());
+ CHECK_MMTR(matc, Upper, += s*(soc*sor.transpose()));
+ CHECK_MMTR(matr, Lower, += s*sor*soc.adjoint());
+ CHECK_MMTR(matr, Upper, += soc*(s*soc.adjoint()));
+
+ CHECK_MMTR(matc, Lower, -= s*soc*soc.adjoint());
+ CHECK_MMTR(matc, Upper, -= s*(osc.transpose()*osc.conjugate()));
+ CHECK_MMTR(matr, Lower, -= s*soc*soc.adjoint());
+ CHECK_MMTR(matr, Upper, -= soc*(s*soc.adjoint()));
+
+ CHECK_MMTR(matc, Lower, -= s*sqr*sqc.template triangularView<Upper>());
+ CHECK_MMTR(matc, Upper, = s*sqc*sqr.template triangularView<Upper>());
+ CHECK_MMTR(matc, Lower, += s*sqr*sqc.template triangularView<Lower>());
+ CHECK_MMTR(matc, Upper, = s*sqc*sqc.template triangularView<Lower>());
+
+ CHECK_MMTR(matc, Lower, = (s*sqr).template triangularView<Upper>()*sqc);
+ CHECK_MMTR(matc, Upper, -= (s*sqc).template triangularView<Upper>()*sqc);
+ CHECK_MMTR(matc, Lower, = (s*sqr).template triangularView<Lower>()*sqc);
+ CHECK_MMTR(matc, Upper, += (s*sqc).template triangularView<Lower>()*sqc);
+
+ // check aliasing
+ ref2 = ref1 = matc;
+ ref1 = sqc.adjoint() * matc * sqc;
+ ref2.template triangularView<Upper>() = ref1.template triangularView<Upper>();
+ matc.template triangularView<Upper>() = sqc.adjoint() * matc * sqc;
+ VERIFY_IS_APPROX(matc, ref2);
+
+ ref2 = ref1 = matc;
+ ref1 = sqc * matc * sqc.adjoint();
+ ref2.template triangularView<Lower>() = ref1.template triangularView<Lower>();
+ matc.template triangularView<Lower>() = sqc * matc * sqc.adjoint();
+ VERIFY_IS_APPROX(matc, ref2);
+
+ // destination with a non-default inner-stride
+ // see bug 1741
+ {
+ typedef Matrix<Scalar,Dynamic,Dynamic> MatrixX;
+ MatrixX buffer(2*size,2*size);
+ Map<MatrixColMaj,0,Stride<Dynamic,Dynamic> > map1(buffer.data(),size,size,Stride<Dynamic,Dynamic>(2*size,2));
+ buffer.setZero();
+ CHECK_MMTR(map1, Lower, = s*soc*sor.adjoint());
+ }
+}
+
+EIGEN_DECLARE_TEST(product_mmtr)
+{
+ for(int i = 0; i < g_repeat ; i++)
+ {
+ CALL_SUBTEST_1((mmtr<float>(internal::random<int>(1,EIGEN_TEST_MAX_SIZE))));
+ CALL_SUBTEST_2((mmtr<double>(internal::random<int>(1,EIGEN_TEST_MAX_SIZE))));
+ CALL_SUBTEST_3((mmtr<std::complex<float> >(internal::random<int>(1,EIGEN_TEST_MAX_SIZE/2))));
+ CALL_SUBTEST_4((mmtr<std::complex<double> >(internal::random<int>(1,EIGEN_TEST_MAX_SIZE/2))));
+ }
+}
diff --git a/test/product_notemporary.cpp b/test/product_notemporary.cpp
new file mode 100644
index 0000000..20cb7c0
--- /dev/null
+++ b/test/product_notemporary.cpp
@@ -0,0 +1,209 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#define TEST_ENABLE_TEMPORARY_TRACKING
+
+#include "main.h"
+
+template<typename Dst, typename Lhs, typename Rhs>
+void check_scalar_multiple3(Dst &dst, const Lhs& A, const Rhs& B)
+{
+ VERIFY_EVALUATION_COUNT( (dst.noalias() = A * B), 0);
+ VERIFY_IS_APPROX( dst, (A.eval() * B.eval()).eval() );
+ VERIFY_EVALUATION_COUNT( (dst.noalias() += A * B), 0);
+ VERIFY_IS_APPROX( dst, 2*(A.eval() * B.eval()).eval() );
+ VERIFY_EVALUATION_COUNT( (dst.noalias() -= A * B), 0);
+ VERIFY_IS_APPROX( dst, (A.eval() * B.eval()).eval() );
+}
+
+template<typename Dst, typename Lhs, typename Rhs, typename S2>
+void check_scalar_multiple2(Dst &dst, const Lhs& A, const Rhs& B, S2 s2)
+{
+ CALL_SUBTEST( check_scalar_multiple3(dst, A, B) );
+ CALL_SUBTEST( check_scalar_multiple3(dst, A, -B) );
+ CALL_SUBTEST( check_scalar_multiple3(dst, A, s2*B) );
+ CALL_SUBTEST( check_scalar_multiple3(dst, A, B*s2) );
+ CALL_SUBTEST( check_scalar_multiple3(dst, A, (B*s2).conjugate()) );
+}
+
+template<typename Dst, typename Lhs, typename Rhs, typename S1, typename S2>
+void check_scalar_multiple1(Dst &dst, const Lhs& A, const Rhs& B, S1 s1, S2 s2)
+{
+ CALL_SUBTEST( check_scalar_multiple2(dst, A, B, s2) );
+ CALL_SUBTEST( check_scalar_multiple2(dst, -A, B, s2) );
+ CALL_SUBTEST( check_scalar_multiple2(dst, s1*A, B, s2) );
+ CALL_SUBTEST( check_scalar_multiple2(dst, A*s1, B, s2) );
+ CALL_SUBTEST( check_scalar_multiple2(dst, (A*s1).conjugate(), B, s2) );
+}
+
+template<typename MatrixType> void product_notemporary(const MatrixType& m)
+{
+ /* This test checks the number of temporaries created
+ * during the evaluation of a complex expression */
+ typedef typename MatrixType::Scalar Scalar;
+ typedef typename MatrixType::RealScalar RealScalar;
+ typedef Matrix<Scalar, 1, Dynamic> RowVectorType;
+ typedef Matrix<Scalar, Dynamic, 1> ColVectorType;
+ typedef Matrix<Scalar, Dynamic, Dynamic, ColMajor> ColMajorMatrixType;
+ typedef Matrix<Scalar, Dynamic, Dynamic, RowMajor> RowMajorMatrixType;
+
+ Index rows = m.rows();
+ Index cols = m.cols();
+
+ ColMajorMatrixType m1 = MatrixType::Random(rows, cols),
+ m2 = MatrixType::Random(rows, cols),
+ m3(rows, cols);
+ RowVectorType rv1 = RowVectorType::Random(rows), rvres(rows);
+ ColVectorType cv1 = ColVectorType::Random(cols), cvres(cols);
+ RowMajorMatrixType rm3(rows, cols);
+
+ Scalar s1 = internal::random<Scalar>(),
+ s2 = internal::random<Scalar>(),
+ s3 = internal::random<Scalar>();
+
+ Index c0 = internal::random<Index>(4,cols-8),
+ c1 = internal::random<Index>(8,cols-c0),
+ r0 = internal::random<Index>(4,cols-8),
+ r1 = internal::random<Index>(8,rows-r0);
+
+ VERIFY_EVALUATION_COUNT( m3 = (m1 * m2.adjoint()), 1);
+ VERIFY_EVALUATION_COUNT( m3 = (m1 * m2.adjoint()).transpose(), 1);
+ VERIFY_EVALUATION_COUNT( m3.noalias() = m1 * m2.adjoint(), 0);
+
+ VERIFY_EVALUATION_COUNT( m3 = s1 * (m1 * m2.transpose()), 1);
+// VERIFY_EVALUATION_COUNT( m3 = m3 + s1 * (m1 * m2.transpose()), 1);
+ VERIFY_EVALUATION_COUNT( m3.noalias() = s1 * (m1 * m2.transpose()), 0);
+
+ VERIFY_EVALUATION_COUNT( m3 = m3 + (m1 * m2.adjoint()), 1);
+ VERIFY_EVALUATION_COUNT( m3 = m3 - (m1 * m2.adjoint()), 1);
+
+ VERIFY_EVALUATION_COUNT( m3 = m3 + (m1 * m2.adjoint()).transpose(), 1);
+ VERIFY_EVALUATION_COUNT( m3.noalias() = m3 + m1 * m2.transpose(), 0);
+ VERIFY_EVALUATION_COUNT( m3.noalias() += m3 + m1 * m2.transpose(), 0);
+ VERIFY_EVALUATION_COUNT( m3.noalias() -= m3 + m1 * m2.transpose(), 0);
+ VERIFY_EVALUATION_COUNT( m3.noalias() = m3 - m1 * m2.transpose(), 0);
+ VERIFY_EVALUATION_COUNT( m3.noalias() += m3 - m1 * m2.transpose(), 0);
+ VERIFY_EVALUATION_COUNT( m3.noalias() -= m3 - m1 * m2.transpose(), 0);
+
+ VERIFY_EVALUATION_COUNT( m3.noalias() = s1 * m1 * s2 * m2.adjoint(), 0);
+ VERIFY_EVALUATION_COUNT( m3.noalias() = s1 * m1 * s2 * (m1*s3+m2*s2).adjoint(), 1);
+ VERIFY_EVALUATION_COUNT( m3.noalias() = (s1 * m1).adjoint() * s2 * m2, 0);
+ VERIFY_EVALUATION_COUNT( m3.noalias() += s1 * (-m1*s3).adjoint() * (s2 * m2 * s3), 0);
+ VERIFY_EVALUATION_COUNT( m3.noalias() -= s1 * (m1.transpose() * m2), 0);
+
+ VERIFY_EVALUATION_COUNT(( m3.block(r0,r0,r1,r1).noalias() += -m1.block(r0,c0,r1,c1) * (s2*m2.block(r0,c0,r1,c1)).adjoint() ), 0);
+ VERIFY_EVALUATION_COUNT(( m3.block(r0,r0,r1,r1).noalias() -= s1 * m1.block(r0,c0,r1,c1) * m2.block(c0,r0,c1,r1) ), 0);
+
+ // NOTE this is because the Block expression is not handled yet by our expression analyser
+ VERIFY_EVALUATION_COUNT(( m3.block(r0,r0,r1,r1).noalias() = s1 * m1.block(r0,c0,r1,c1) * (s1*m2).block(c0,r0,c1,r1) ), 1);
+
+ VERIFY_EVALUATION_COUNT( m3.noalias() -= (s1 * m1).template triangularView<Lower>() * m2, 0);
+ VERIFY_EVALUATION_COUNT( rm3.noalias() = (s1 * m1.adjoint()).template triangularView<Upper>() * (m2+m2), 1);
+ VERIFY_EVALUATION_COUNT( rm3.noalias() = (s1 * m1.adjoint()).template triangularView<UnitUpper>() * m2.adjoint(), 0);
+
+ VERIFY_EVALUATION_COUNT( m3.template triangularView<Upper>() = (m1 * m2.adjoint()), 0);
+ VERIFY_EVALUATION_COUNT( m3.template triangularView<Upper>() -= (m1 * m2.adjoint()), 0);
+
+ // NOTE this is because the blas_traits require innerstride==1 to avoid a temporary, but that doesn't seem to be actually needed for the triangular products
+ VERIFY_EVALUATION_COUNT( rm3.col(c0).noalias() = (s1 * m1.adjoint()).template triangularView<UnitUpper>() * (s2*m2.row(c0)).adjoint(), 1);
+
+ VERIFY_EVALUATION_COUNT( m1.template triangularView<Lower>().solveInPlace(m3), 0);
+ VERIFY_EVALUATION_COUNT( m1.adjoint().template triangularView<Lower>().solveInPlace(m3.transpose()), 0);
+
+ VERIFY_EVALUATION_COUNT( m3.noalias() -= (s1 * m1).adjoint().template selfadjointView<Lower>() * (-m2*s3).adjoint(), 0);
+ VERIFY_EVALUATION_COUNT( m3.noalias() = s2 * m2.adjoint() * (s1 * m1.adjoint()).template selfadjointView<Upper>(), 0);
+ VERIFY_EVALUATION_COUNT( rm3.noalias() = (s1 * m1.adjoint()).template selfadjointView<Lower>() * m2.adjoint(), 0);
+
+ // NOTE this is because the blas_traits require innerstride==1 to avoid a temporary, but that doesn't seem to be actually needed for the triangular products
+ VERIFY_EVALUATION_COUNT( m3.col(c0).noalias() = (s1 * m1).adjoint().template selfadjointView<Lower>() * (-m2.row(c0)*s3).adjoint(), 1);
+ VERIFY_EVALUATION_COUNT( m3.col(c0).noalias() -= (s1 * m1).adjoint().template selfadjointView<Upper>() * (-m2.row(c0)*s3).adjoint(), 1);
+
+ VERIFY_EVALUATION_COUNT( m3.block(r0,c0,r1,c1).noalias() += m1.block(r0,r0,r1,r1).template selfadjointView<Upper>() * (s1*m2.block(r0,c0,r1,c1)), 0);
+ VERIFY_EVALUATION_COUNT( m3.block(r0,c0,r1,c1).noalias() = m1.block(r0,r0,r1,r1).template selfadjointView<Upper>() * m2.block(r0,c0,r1,c1), 0);
+
+ VERIFY_EVALUATION_COUNT( m3.template selfadjointView<Lower>().rankUpdate(m2.adjoint()), 0);
+
+ // Here we will get 1 temporary for each resize operation of the lhs operator; resize(r1,c1) would lead to zero temporaries
+ m3.resize(1,1);
+ VERIFY_EVALUATION_COUNT( m3.noalias() = m1.block(r0,r0,r1,r1).template selfadjointView<Lower>() * m2.block(r0,c0,r1,c1), 1);
+ m3.resize(1,1);
+ VERIFY_EVALUATION_COUNT( m3.noalias() = m1.block(r0,r0,r1,r1).template triangularView<UnitUpper>() * m2.block(r0,c0,r1,c1), 1);
+
+ // Zero temporaries for lazy products ...
+ m3.setRandom(rows,cols);
+ VERIFY_EVALUATION_COUNT( Scalar tmp = 0; tmp += Scalar(RealScalar(1)) / (m3.transpose().lazyProduct(m3)).diagonal().sum(), 0 );
+ VERIFY_EVALUATION_COUNT( m3.noalias() = m1.conjugate().lazyProduct(m2.conjugate()), 0);
+
+ // ... and even no temporary for even deeply (>=2) nested products
+ VERIFY_EVALUATION_COUNT( Scalar tmp = 0; tmp += Scalar(RealScalar(1)) / (m3.transpose() * m3).diagonal().sum(), 0 );
+ VERIFY_EVALUATION_COUNT( Scalar tmp = 0; tmp += Scalar(RealScalar(1)) / (m3.transpose() * m3).diagonal().array().abs().sum(), 0 );
+
+ // Zero temporaries for ... CoeffBasedProductMode
+ VERIFY_EVALUATION_COUNT( m3.col(0).template head<5>() * m3.col(0).transpose() + m3.col(0).template head<5>() * m3.col(0).transpose(), 0 );
+
+ // Check matrix * vectors
+ VERIFY_EVALUATION_COUNT( cvres.noalias() = m1 * cv1, 0 );
+ VERIFY_EVALUATION_COUNT( cvres.noalias() -= m1 * cv1, 0 );
+ VERIFY_EVALUATION_COUNT( cvres.noalias() -= m1 * m2.col(0), 0 );
+ VERIFY_EVALUATION_COUNT( cvres.noalias() -= m1 * rv1.adjoint(), 0 );
+ VERIFY_EVALUATION_COUNT( cvres.noalias() -= m1 * m2.row(0).transpose(), 0 );
+
+ VERIFY_EVALUATION_COUNT( cvres.noalias() = (m1+m1) * cv1, 0 );
+ VERIFY_EVALUATION_COUNT( cvres.noalias() = (rm3+rm3) * cv1, 0 );
+ VERIFY_EVALUATION_COUNT( cvres.noalias() = (m1+m1) * (m1*cv1), 1 );
+ VERIFY_EVALUATION_COUNT( cvres.noalias() = (rm3+rm3) * (m1*cv1), 1 );
+
+ // Check outer products
+ #ifdef EIGEN_ALLOCA
+ bool temp_via_alloca = m3.rows()*sizeof(Scalar) <= EIGEN_STACK_ALLOCATION_LIMIT;
+ #else
+ bool temp_via_alloca = false;
+ #endif
+ m3 = cv1 * rv1;
+ VERIFY_EVALUATION_COUNT( m3.noalias() = cv1 * rv1, 0 );
+ VERIFY_EVALUATION_COUNT( m3.noalias() = (cv1+cv1) * (rv1+rv1), temp_via_alloca ? 0 : 1 );
+ VERIFY_EVALUATION_COUNT( m3.noalias() = (m1*cv1) * (rv1), 1 );
+ VERIFY_EVALUATION_COUNT( m3.noalias() += (m1*cv1) * (rv1), 1 );
+ rm3 = cv1 * rv1;
+ VERIFY_EVALUATION_COUNT( rm3.noalias() = cv1 * rv1, 0 );
+ VERIFY_EVALUATION_COUNT( rm3.noalias() = (cv1+cv1) * (rv1+rv1), temp_via_alloca ? 0 : 1 );
+ VERIFY_EVALUATION_COUNT( rm3.noalias() = (cv1) * (rv1 * m1), 1 );
+ VERIFY_EVALUATION_COUNT( rm3.noalias() -= (cv1) * (rv1 * m1), 1 );
+ VERIFY_EVALUATION_COUNT( rm3.noalias() = (m1*cv1) * (rv1 * m1), 2 );
+ VERIFY_EVALUATION_COUNT( rm3.noalias() += (m1*cv1) * (rv1 * m1), 2 );
+
+ // Check nested products
+ VERIFY_EVALUATION_COUNT( cvres.noalias() = m1.adjoint() * m1 * cv1, 1 );
+ VERIFY_EVALUATION_COUNT( rvres.noalias() = rv1 * (m1 * m2.adjoint()), 1 );
+
+ // exhaustively check all scalar multiple combinations:
+ {
+ // Generic path:
+ check_scalar_multiple1(m3, m1, m2, s1, s2);
+ // Force fall back to coeff-based:
+ typename ColMajorMatrixType::BlockXpr m3_blck = m3.block(r0,r0,1,1);
+ check_scalar_multiple1(m3_blck, m1.block(r0,c0,1,1), m2.block(c0,r0,1,1), s1, s2);
+ }
+}
+
+EIGEN_DECLARE_TEST(product_notemporary)
+{
+ int s;
+ for(int i = 0; i < g_repeat; i++) {
+ s = internal::random<int>(16,EIGEN_TEST_MAX_SIZE);
+ CALL_SUBTEST_1( product_notemporary(MatrixXf(s, s)) );
+ CALL_SUBTEST_2( product_notemporary(MatrixXd(s, s)) );
+ TEST_SET_BUT_UNUSED_VARIABLE(s)
+
+ s = internal::random<int>(16,EIGEN_TEST_MAX_SIZE/2);
+ CALL_SUBTEST_3( product_notemporary(MatrixXcf(s,s)) );
+ CALL_SUBTEST_4( product_notemporary(MatrixXcd(s,s)) );
+ TEST_SET_BUT_UNUSED_VARIABLE(s)
+ }
+}
diff --git a/test/product_selfadjoint.cpp b/test/product_selfadjoint.cpp
new file mode 100644
index 0000000..bdccd04
--- /dev/null
+++ b/test/product_selfadjoint.cpp
@@ -0,0 +1,86 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "main.h"
+
+template<typename MatrixType> void product_selfadjoint(const MatrixType& m)
+{
+ typedef typename MatrixType::Scalar Scalar;
+ typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> VectorType;
+ typedef Matrix<Scalar, 1, MatrixType::RowsAtCompileTime> RowVectorType;
+
+ typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, Dynamic, RowMajor> RhsMatrixType;
+
+ Index rows = m.rows();
+ Index cols = m.cols();
+
+ MatrixType m1 = MatrixType::Random(rows, cols),
+ m2 = MatrixType::Random(rows, cols),
+ m3;
+ VectorType v1 = VectorType::Random(rows),
+ v2 = VectorType::Random(rows),
+ v3(rows);
+ RowVectorType r1 = RowVectorType::Random(rows),
+ r2 = RowVectorType::Random(rows);
+ RhsMatrixType m4 = RhsMatrixType::Random(rows,10);
+
+ Scalar s1 = internal::random<Scalar>(),
+ s2 = internal::random<Scalar>(),
+ s3 = internal::random<Scalar>();
+
+ m1 = (m1.adjoint() + m1).eval();
+
+ // rank2 update
+ m2 = m1.template triangularView<Lower>();
+ m2.template selfadjointView<Lower>().rankUpdate(v1,v2);
+ VERIFY_IS_APPROX(m2, (m1 + v1 * v2.adjoint()+ v2 * v1.adjoint()).template triangularView<Lower>().toDenseMatrix());
+
+ m2 = m1.template triangularView<Upper>();
+ m2.template selfadjointView<Upper>().rankUpdate(-v1,s2*v2,s3);
+ VERIFY_IS_APPROX(m2, (m1 + (s3*(-v1)*(s2*v2).adjoint()+numext::conj(s3)*(s2*v2)*(-v1).adjoint())).template triangularView<Upper>().toDenseMatrix());
+
+ m2 = m1.template triangularView<Upper>();
+ m2.template selfadjointView<Upper>().rankUpdate(-s2*r1.adjoint(),r2.adjoint()*s3,s1);
+ VERIFY_IS_APPROX(m2, (m1 + s1*(-s2*r1.adjoint())*(r2.adjoint()*s3).adjoint() + numext::conj(s1)*(r2.adjoint()*s3) * (-s2*r1.adjoint()).adjoint()).template triangularView<Upper>().toDenseMatrix());
+
+ if (rows>1)
+ {
+ m2 = m1.template triangularView<Lower>();
+ m2.block(1,1,rows-1,cols-1).template selfadjointView<Lower>().rankUpdate(v1.tail(rows-1),v2.head(cols-1));
+ m3 = m1;
+ m3.block(1,1,rows-1,cols-1) += v1.tail(rows-1) * v2.head(cols-1).adjoint()+ v2.head(cols-1) * v1.tail(rows-1).adjoint();
+ VERIFY_IS_APPROX(m2, m3.template triangularView<Lower>().toDenseMatrix());
+ }
+}
+
+EIGEN_DECLARE_TEST(product_selfadjoint)
+{
+ int s = 0;
+ for(int i = 0; i < g_repeat ; i++) {
+ CALL_SUBTEST_1( product_selfadjoint(Matrix<float, 1, 1>()) );
+ CALL_SUBTEST_2( product_selfadjoint(Matrix<float, 2, 2>()) );
+ CALL_SUBTEST_3( product_selfadjoint(Matrix3d()) );
+
+ s = internal::random<int>(1,EIGEN_TEST_MAX_SIZE/2);
+ CALL_SUBTEST_4( product_selfadjoint(MatrixXcf(s, s)) );
+ TEST_SET_BUT_UNUSED_VARIABLE(s)
+
+ s = internal::random<int>(1,EIGEN_TEST_MAX_SIZE/2);
+ CALL_SUBTEST_5( product_selfadjoint(MatrixXcd(s,s)) );
+ TEST_SET_BUT_UNUSED_VARIABLE(s)
+
+ s = internal::random<int>(1,EIGEN_TEST_MAX_SIZE);
+ CALL_SUBTEST_6( product_selfadjoint(MatrixXd(s,s)) );
+ TEST_SET_BUT_UNUSED_VARIABLE(s)
+
+ s = internal::random<int>(1,EIGEN_TEST_MAX_SIZE);
+ CALL_SUBTEST_7( product_selfadjoint(Matrix<float,Dynamic,Dynamic,RowMajor>(s,s)) );
+ TEST_SET_BUT_UNUSED_VARIABLE(s)
+ }
+}
diff --git a/test/product_small.cpp b/test/product_small.cpp
new file mode 100644
index 0000000..c1d9943
--- /dev/null
+++ b/test/product_small.cpp
@@ -0,0 +1,322 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "product.h"
+#include <Eigen/LU>
+
+// regression test for bug 447
+template<int>
+void product1x1()
+{
+ Matrix<float,1,3> matAstatic;
+ Matrix<float,3,1> matBstatic;
+ matAstatic.setRandom();
+ matBstatic.setRandom();
+ VERIFY_IS_APPROX( (matAstatic * matBstatic).coeff(0,0),
+ matAstatic.cwiseProduct(matBstatic.transpose()).sum() );
+
+ MatrixXf matAdynamic(1,3);
+ MatrixXf matBdynamic(3,1);
+ matAdynamic.setRandom();
+ matBdynamic.setRandom();
+ VERIFY_IS_APPROX( (matAdynamic * matBdynamic).coeff(0,0),
+ matAdynamic.cwiseProduct(matBdynamic.transpose()).sum() );
+}
+
+template<typename TC, typename TA, typename TB>
+const TC& ref_prod(TC &C, const TA &A, const TB &B)
+{
+ for(Index i=0;i<C.rows();++i)
+ for(Index j=0;j<C.cols();++j)
+ for(Index k=0;k<A.cols();++k)
+ C.coeffRef(i,j) += A.coeff(i,k) * B.coeff(k,j);
+ return C;
+}
+
+template<typename T, int Rows, int Cols, int Depth, int OC, int OA, int OB>
+std::enable_if_t<! ( (Rows ==1&&Depth!=1&&OA==ColMajor)
+ || (Depth==1&&Rows !=1&&OA==RowMajor)
+ || (Cols ==1&&Depth!=1&&OB==RowMajor)
+ || (Depth==1&&Cols !=1&&OB==ColMajor)
+ || (Rows ==1&&Cols !=1&&OC==ColMajor)
+ || (Cols ==1&&Rows !=1&&OC==RowMajor)),void>
+test_lazy_single(int rows, int cols, int depth)
+{
+ Matrix<T,Rows,Depth,OA> A(rows,depth); A.setRandom();
+ Matrix<T,Depth,Cols,OB> B(depth,cols); B.setRandom();
+ Matrix<T,Rows,Cols,OC> C(rows,cols); C.setRandom();
+ Matrix<T,Rows,Cols,OC> D(C);
+ VERIFY_IS_APPROX(C+=A.lazyProduct(B), ref_prod(D,A,B));
+}
+
+void test_dynamic_bool()
+{
+ int rows = internal::random<int>(1,64);
+ int cols = internal::random<int>(1,64);
+ int depth = internal::random<int>(1,65);
+
+ typedef Matrix<bool,Dynamic,Dynamic> MatrixX;
+ MatrixX A(rows,depth); A.setRandom();
+ MatrixX B(depth,cols); B.setRandom();
+ MatrixX C(rows,cols); C.setRandom();
+ MatrixX D(C);
+ for(Index i=0;i<C.rows();++i)
+ for(Index j=0;j<C.cols();++j)
+ for(Index k=0;k<A.cols();++k)
+ D.coeffRef(i,j) |= A.coeff(i,k) & B.coeff(k,j);
+ C += A * B;
+ VERIFY_IS_EQUAL(C, D);
+
+ MatrixX E = B.transpose();
+ for(Index i=0;i<B.rows();++i)
+ for(Index j=0;j<B.cols();++j)
+ VERIFY_IS_EQUAL(B(i,j), E(j,i));
+}
+
+template<typename T, int Rows, int Cols, int Depth, int OC, int OA, int OB>
+std::enable_if_t< ( (Rows ==1&&Depth!=1&&OA==ColMajor)
+ || (Depth==1&&Rows !=1&&OA==RowMajor)
+ || (Cols ==1&&Depth!=1&&OB==RowMajor)
+ || (Depth==1&&Cols !=1&&OB==ColMajor)
+ || (Rows ==1&&Cols !=1&&OC==ColMajor)
+ || (Cols ==1&&Rows !=1&&OC==RowMajor)),void>
+test_lazy_single(int, int, int)
+{
+}
+
+template<typename T, int Rows, int Cols, int Depth>
+void test_lazy_all_layout(int rows=Rows, int cols=Cols, int depth=Depth)
+{
+ CALL_SUBTEST(( test_lazy_single<T,Rows,Cols,Depth,ColMajor,ColMajor,ColMajor>(rows,cols,depth) ));
+ CALL_SUBTEST(( test_lazy_single<T,Rows,Cols,Depth,RowMajor,ColMajor,ColMajor>(rows,cols,depth) ));
+ CALL_SUBTEST(( test_lazy_single<T,Rows,Cols,Depth,ColMajor,RowMajor,ColMajor>(rows,cols,depth) ));
+ CALL_SUBTEST(( test_lazy_single<T,Rows,Cols,Depth,RowMajor,RowMajor,ColMajor>(rows,cols,depth) ));
+ CALL_SUBTEST(( test_lazy_single<T,Rows,Cols,Depth,ColMajor,ColMajor,RowMajor>(rows,cols,depth) ));
+ CALL_SUBTEST(( test_lazy_single<T,Rows,Cols,Depth,RowMajor,ColMajor,RowMajor>(rows,cols,depth) ));
+ CALL_SUBTEST(( test_lazy_single<T,Rows,Cols,Depth,ColMajor,RowMajor,RowMajor>(rows,cols,depth) ));
+ CALL_SUBTEST(( test_lazy_single<T,Rows,Cols,Depth,RowMajor,RowMajor,RowMajor>(rows,cols,depth) ));
+}
+
+template<typename T>
+void test_lazy_l1()
+{
+ int rows = internal::random<int>(1,12);
+ int cols = internal::random<int>(1,12);
+ int depth = internal::random<int>(1,12);
+
+ // Inner
+ CALL_SUBTEST(( test_lazy_all_layout<T,1,1,1>() ));
+ CALL_SUBTEST(( test_lazy_all_layout<T,1,1,2>() ));
+ CALL_SUBTEST(( test_lazy_all_layout<T,1,1,3>() ));
+ CALL_SUBTEST(( test_lazy_all_layout<T,1,1,8>() ));
+ CALL_SUBTEST(( test_lazy_all_layout<T,1,1,9>() ));
+ CALL_SUBTEST(( test_lazy_all_layout<T,1,1,-1>(1,1,depth) ));
+
+ // Outer
+ CALL_SUBTEST(( test_lazy_all_layout<T,2,1,1>() ));
+ CALL_SUBTEST(( test_lazy_all_layout<T,1,2,1>() ));
+ CALL_SUBTEST(( test_lazy_all_layout<T,2,2,1>() ));
+ CALL_SUBTEST(( test_lazy_all_layout<T,3,3,1>() ));
+ CALL_SUBTEST(( test_lazy_all_layout<T,4,4,1>() ));
+ CALL_SUBTEST(( test_lazy_all_layout<T,4,8,1>() ));
+ CALL_SUBTEST(( test_lazy_all_layout<T,4,-1,1>(4,cols) ));
+ CALL_SUBTEST(( test_lazy_all_layout<T,7,-1,1>(7,cols) ));
+ CALL_SUBTEST(( test_lazy_all_layout<T,-1,8,1>(rows) ));
+ CALL_SUBTEST(( test_lazy_all_layout<T,-1,3,1>(rows) ));
+ CALL_SUBTEST(( test_lazy_all_layout<T,-1,-1,1>(rows,cols) ));
+}
+
+template<typename T>
+void test_lazy_l2()
+{
+ int rows = internal::random<int>(1,12);
+ int cols = internal::random<int>(1,12);
+ int depth = internal::random<int>(1,12);
+
+ // mat-vec
+ CALL_SUBTEST(( test_lazy_all_layout<T,2,1,2>() ));
+ CALL_SUBTEST(( test_lazy_all_layout<T,2,1,4>() ));
+ CALL_SUBTEST(( test_lazy_all_layout<T,4,1,2>() ));
+ CALL_SUBTEST(( test_lazy_all_layout<T,4,1,4>() ));
+ CALL_SUBTEST(( test_lazy_all_layout<T,5,1,4>() ));
+ CALL_SUBTEST(( test_lazy_all_layout<T,4,1,5>() ));
+ CALL_SUBTEST(( test_lazy_all_layout<T,4,1,6>() ));
+ CALL_SUBTEST(( test_lazy_all_layout<T,6,1,4>() ));
+ CALL_SUBTEST(( test_lazy_all_layout<T,8,1,8>() ));
+ CALL_SUBTEST(( test_lazy_all_layout<T,-1,1,4>(rows) ));
+ CALL_SUBTEST(( test_lazy_all_layout<T,4,1,-1>(4,1,depth) ));
+ CALL_SUBTEST(( test_lazy_all_layout<T,-1,1,-1>(rows,1,depth) ));
+
+ // vec-mat
+ CALL_SUBTEST(( test_lazy_all_layout<T,1,2,2>() ));
+ CALL_SUBTEST(( test_lazy_all_layout<T,1,2,4>() ));
+ CALL_SUBTEST(( test_lazy_all_layout<T,1,4,2>() ));
+ CALL_SUBTEST(( test_lazy_all_layout<T,1,4,4>() ));
+ CALL_SUBTEST(( test_lazy_all_layout<T,1,5,4>() ));
+ CALL_SUBTEST(( test_lazy_all_layout<T,1,4,5>() ));
+ CALL_SUBTEST(( test_lazy_all_layout<T,1,4,6>() ));
+ CALL_SUBTEST(( test_lazy_all_layout<T,1,6,4>() ));
+ CALL_SUBTEST(( test_lazy_all_layout<T,1,8,8>() ));
+ CALL_SUBTEST(( test_lazy_all_layout<T,1,-1, 4>(1,cols) ));
+ CALL_SUBTEST(( test_lazy_all_layout<T,1, 4,-1>(1,4,depth) ));
+ CALL_SUBTEST(( test_lazy_all_layout<T,1,-1,-1>(1,cols,depth) ));
+}
+
+template<typename T>
+void test_lazy_l3()
+{
+ int rows = internal::random<int>(1,12);
+ int cols = internal::random<int>(1,12);
+ int depth = internal::random<int>(1,12);
+ // mat-mat
+ CALL_SUBTEST(( test_lazy_all_layout<T,2,4,2>() ));
+ CALL_SUBTEST(( test_lazy_all_layout<T,2,6,4>() ));
+ CALL_SUBTEST(( test_lazy_all_layout<T,4,3,2>() ));
+ CALL_SUBTEST(( test_lazy_all_layout<T,4,8,4>() ));
+ CALL_SUBTEST(( test_lazy_all_layout<T,5,6,4>() ));
+ CALL_SUBTEST(( test_lazy_all_layout<T,4,2,5>() ));
+ CALL_SUBTEST(( test_lazy_all_layout<T,4,7,6>() ));
+ CALL_SUBTEST(( test_lazy_all_layout<T,6,8,4>() ));
+ CALL_SUBTEST(( test_lazy_all_layout<T,8,3,8>() ));
+ CALL_SUBTEST(( test_lazy_all_layout<T,-1,6,4>(rows) ));
+ CALL_SUBTEST(( test_lazy_all_layout<T,4,3,-1>(4,3,depth) ));
+ CALL_SUBTEST(( test_lazy_all_layout<T,-1,6,-1>(rows,6,depth) ));
+ CALL_SUBTEST(( test_lazy_all_layout<T,8,2,2>() ));
+ CALL_SUBTEST(( test_lazy_all_layout<T,5,2,4>() ));
+ CALL_SUBTEST(( test_lazy_all_layout<T,4,4,2>() ));
+ CALL_SUBTEST(( test_lazy_all_layout<T,8,4,4>() ));
+ CALL_SUBTEST(( test_lazy_all_layout<T,6,5,4>() ));
+ CALL_SUBTEST(( test_lazy_all_layout<T,4,4,5>() ));
+ CALL_SUBTEST(( test_lazy_all_layout<T,3,4,6>() ));
+ CALL_SUBTEST(( test_lazy_all_layout<T,2,6,4>() ));
+ CALL_SUBTEST(( test_lazy_all_layout<T,7,8,8>() ));
+ CALL_SUBTEST(( test_lazy_all_layout<T,8,-1, 4>(8,cols) ));
+ CALL_SUBTEST(( test_lazy_all_layout<T,3, 4,-1>(3,4,depth) ));
+ CALL_SUBTEST(( test_lazy_all_layout<T,4,-1,-1>(4,cols,depth) ));
+}
+
+template<typename T,int N,int M,int K>
+void test_linear_but_not_vectorizable()
+{
+ // Check tricky cases for which the result of the product is a vector and thus must exhibit the LinearBit flag,
+ // but is not vectorizable along the linear dimension.
+ Index n = N==Dynamic ? internal::random<Index>(1,32) : N;
+ Index m = M==Dynamic ? internal::random<Index>(1,32) : M;
+ Index k = K==Dynamic ? internal::random<Index>(1,32) : K;
+
+ {
+ Matrix<T,N,M+1> A; A.setRandom(n,m+1);
+ Matrix<T,M*2,K> B; B.setRandom(m*2,k);
+ Matrix<T,1,K> C;
+ Matrix<T,1,K> R;
+
+ C.noalias() = A.template topLeftCorner<1,M>() * (B.template topRows<M>()+B.template bottomRows<M>());
+ R.noalias() = A.template topLeftCorner<1,M>() * (B.template topRows<M>()+B.template bottomRows<M>()).eval();
+ VERIFY_IS_APPROX(C,R);
+ }
+
+ {
+ Matrix<T,M+1,N,RowMajor> A; A.setRandom(m+1,n);
+ Matrix<T,K,M*2,RowMajor> B; B.setRandom(k,m*2);
+ Matrix<T,K,1> C;
+ Matrix<T,K,1> R;
+
+ C.noalias() = (B.template leftCols<M>()+B.template rightCols<M>()) * A.template topLeftCorner<M,1>();
+ R.noalias() = (B.template leftCols<M>()+B.template rightCols<M>()).eval() * A.template topLeftCorner<M,1>();
+ VERIFY_IS_APPROX(C,R);
+ }
+}
+
+template<int Rows>
+void bug_1311()
+{
+ Matrix< double, Rows, 2 > A; A.setRandom();
+ Vector2d b = Vector2d::Random() ;
+ Matrix<double,Rows,1> res;
+ res.noalias() = 1. * (A * b);
+ VERIFY_IS_APPROX(res, A*b);
+ res.noalias() = 1.*A * b;
+ VERIFY_IS_APPROX(res, A*b);
+ res.noalias() = (1.*A).lazyProduct(b);
+ VERIFY_IS_APPROX(res, A*b);
+ res.noalias() = (1.*A).lazyProduct(1.*b);
+ VERIFY_IS_APPROX(res, A*b);
+ res.noalias() = (A).lazyProduct(1.*b);
+ VERIFY_IS_APPROX(res, A*b);
+}
+
+template<int>
+void product_small_regressions()
+{
+ {
+ // test compilation of (outer_product) * vector
+ Vector3f v = Vector3f::Random();
+ VERIFY_IS_APPROX( (v * v.transpose()) * v, (v * v.transpose()).eval() * v);
+ }
+
+ {
+ // regression test for pull-request #93
+ Eigen::Matrix<double, 1, 1> A; A.setRandom();
+ Eigen::Matrix<double, 18, 1> B; B.setRandom();
+ Eigen::Matrix<double, 1, 18> C; C.setRandom();
+ VERIFY_IS_APPROX(B * A.inverse(), B * A.inverse()[0]);
+ VERIFY_IS_APPROX(A.inverse() * C, A.inverse()[0] * C);
+ }
+
+ {
+ Eigen::Matrix<double, 10, 10> A, B, C;
+ A.setRandom();
+ C = A;
+ for(int k=0; k<79; ++k)
+ C = C * A;
+ B.noalias() = (((A*A)*(A*A))*((A*A)*(A*A))*((A*A)*(A*A))*((A*A)*(A*A))*((A*A)*(A*A)) * ((A*A)*(A*A))*((A*A)*(A*A))*((A*A)*(A*A))*((A*A)*(A*A))*((A*A)*(A*A)))
+ * (((A*A)*(A*A))*((A*A)*(A*A))*((A*A)*(A*A))*((A*A)*(A*A))*((A*A)*(A*A)) * ((A*A)*(A*A))*((A*A)*(A*A))*((A*A)*(A*A))*((A*A)*(A*A))*((A*A)*(A*A)));
+ VERIFY_IS_APPROX(B,C);
+ }
+}
+
+EIGEN_DECLARE_TEST(product_small)
+{
+ for(int i = 0; i < g_repeat; i++) {
+ CALL_SUBTEST_1( product(Matrix<float, 3, 2>()) );
+ CALL_SUBTEST_2( product(Matrix<int, 3, 17>()) );
+ CALL_SUBTEST_8( product(Matrix<double, 3, 17>()) );
+ CALL_SUBTEST_3( product(Matrix3d()) );
+ CALL_SUBTEST_4( product(Matrix4d()) );
+ CALL_SUBTEST_5( product(Matrix4f()) );
+ CALL_SUBTEST_6( product1x1<0>() );
+
+ CALL_SUBTEST_11( test_lazy_l1<float>() );
+ CALL_SUBTEST_12( test_lazy_l2<float>() );
+ CALL_SUBTEST_13( test_lazy_l3<float>() );
+
+ CALL_SUBTEST_21( test_lazy_l1<double>() );
+ CALL_SUBTEST_22( test_lazy_l2<double>() );
+ CALL_SUBTEST_23( test_lazy_l3<double>() );
+
+ CALL_SUBTEST_31( test_lazy_l1<std::complex<float> >() );
+ CALL_SUBTEST_32( test_lazy_l2<std::complex<float> >() );
+ CALL_SUBTEST_33( test_lazy_l3<std::complex<float> >() );
+
+ CALL_SUBTEST_41( test_lazy_l1<std::complex<double> >() );
+ CALL_SUBTEST_42( test_lazy_l2<std::complex<double> >() );
+ CALL_SUBTEST_43( test_lazy_l3<std::complex<double> >() );
+
+ CALL_SUBTEST_7(( test_linear_but_not_vectorizable<float,2,1,Dynamic>() ));
+ CALL_SUBTEST_7(( test_linear_but_not_vectorizable<float,3,1,Dynamic>() ));
+ CALL_SUBTEST_7(( test_linear_but_not_vectorizable<float,2,1,16>() ));
+
+ CALL_SUBTEST_6( bug_1311<3>() );
+ CALL_SUBTEST_6( bug_1311<5>() );
+
+ CALL_SUBTEST_9( test_dynamic_bool() );
+ }
+
+ CALL_SUBTEST_6( product_small_regressions<0>() );
+}
diff --git a/test/product_symm.cpp b/test/product_symm.cpp
new file mode 100644
index 0000000..ea8d4d5
--- /dev/null
+++ b/test/product_symm.cpp
@@ -0,0 +1,125 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "main.h"
+
+template<typename Scalar, int Size, int OtherSize> void symm(int size = Size, int othersize = OtherSize)
+{
+ typedef Matrix<Scalar, Size, Size> MatrixType;
+ typedef Matrix<Scalar, Size, OtherSize> Rhs1;
+ typedef Matrix<Scalar, OtherSize, Size> Rhs2;
+ enum { order = OtherSize==1 ? 0 : RowMajor };
+ typedef Matrix<Scalar, Size, OtherSize,order> Rhs3;
+
+ Index rows = size;
+ Index cols = size;
+
+ MatrixType m1 = MatrixType::Random(rows, cols),
+ m2 = MatrixType::Random(rows, cols), m3;
+
+ m1 = (m1+m1.adjoint()).eval();
+
+ Rhs1 rhs1 = Rhs1::Random(cols, othersize), rhs12(cols, othersize), rhs13(cols, othersize);
+ Rhs2 rhs2 = Rhs2::Random(othersize, rows), rhs22(othersize, rows), rhs23(othersize, rows);
+ Rhs3 rhs3 = Rhs3::Random(cols, othersize), rhs32(cols, othersize), rhs33(cols, othersize);
+
+ Scalar s1 = internal::random<Scalar>(),
+ s2 = internal::random<Scalar>();
+
+ m2 = m1.template triangularView<Lower>();
+ m3 = m2.template selfadjointView<Lower>();
+ VERIFY_IS_EQUAL(m1, m3);
+ VERIFY_IS_APPROX(rhs12 = (s1*m2).template selfadjointView<Lower>() * (s2*rhs1),
+ rhs13 = (s1*m1) * (s2*rhs1));
+
+ VERIFY_IS_APPROX(rhs12 = (s1*m2).transpose().template selfadjointView<Upper>() * (s2*rhs1),
+ rhs13 = (s1*m1.transpose()) * (s2*rhs1));
+
+ VERIFY_IS_APPROX(rhs12 = (s1*m2).template selfadjointView<Lower>().transpose() * (s2*rhs1),
+ rhs13 = (s1*m1.transpose()) * (s2*rhs1));
+
+ VERIFY_IS_APPROX(rhs12 = (s1*m2).conjugate().template selfadjointView<Lower>() * (s2*rhs1),
+ rhs13 = (s1*m1).conjugate() * (s2*rhs1));
+
+ VERIFY_IS_APPROX(rhs12 = (s1*m2).template selfadjointView<Lower>().conjugate() * (s2*rhs1),
+ rhs13 = (s1*m1).conjugate() * (s2*rhs1));
+
+ VERIFY_IS_APPROX(rhs12 = (s1*m2).adjoint().template selfadjointView<Upper>() * (s2*rhs1),
+ rhs13 = (s1*m1).adjoint() * (s2*rhs1));
+
+ VERIFY_IS_APPROX(rhs12 = (s1*m2).template selfadjointView<Lower>().adjoint() * (s2*rhs1),
+ rhs13 = (s1*m1).adjoint() * (s2*rhs1));
+
+ m2 = m1.template triangularView<Upper>(); rhs12.setRandom(); rhs13 = rhs12;
+ m3 = m2.template selfadjointView<Upper>();
+ VERIFY_IS_EQUAL(m1, m3);
+ VERIFY_IS_APPROX(rhs12 += (s1*m2).template selfadjointView<Upper>() * (s2*rhs1),
+ rhs13 += (s1*m1) * (s2*rhs1));
+
+ m2 = m1.template triangularView<Lower>();
+ VERIFY_IS_APPROX(rhs12 = (s1*m2).template selfadjointView<Lower>() * (s2*rhs2.adjoint()),
+ rhs13 = (s1*m1) * (s2*rhs2.adjoint()));
+
+ m2 = m1.template triangularView<Upper>();
+ VERIFY_IS_APPROX(rhs12 = (s1*m2).template selfadjointView<Upper>() * (s2*rhs2.adjoint()),
+ rhs13 = (s1*m1) * (s2*rhs2.adjoint()));
+
+ m2 = m1.template triangularView<Upper>();
+ VERIFY_IS_APPROX(rhs12 = (s1*m2.adjoint()).template selfadjointView<Lower>() * (s2*rhs2.adjoint()),
+ rhs13 = (s1*m1.adjoint()) * (s2*rhs2.adjoint()));
+
+ // test row major = <...>
+ m2 = m1.template triangularView<Lower>(); rhs32.setRandom(); rhs13 = rhs32;
+ VERIFY_IS_APPROX(rhs32.noalias() -= (s1*m2).template selfadjointView<Lower>() * (s2*rhs3),
+ rhs13 -= (s1*m1) * (s2 * rhs3));
+
+ m2 = m1.template triangularView<Upper>();
+ VERIFY_IS_APPROX(rhs32.noalias() = (s1*m2.adjoint()).template selfadjointView<Lower>() * (s2*rhs3).conjugate(),
+ rhs13 = (s1*m1.adjoint()) * (s2*rhs3).conjugate());
+
+
+ m2 = m1.template triangularView<Upper>(); rhs13 = rhs12;
+ VERIFY_IS_APPROX(rhs12.noalias() += s1 * ((m2.adjoint()).template selfadjointView<Lower>() * (s2*rhs3).conjugate()),
+ rhs13 += (s1*m1.adjoint()) * (s2*rhs3).conjugate());
+
+ m2 = m1.template triangularView<Lower>();
+ VERIFY_IS_APPROX(rhs22 = (rhs2) * (m2).template selfadjointView<Lower>(), rhs23 = (rhs2) * (m1));
+ VERIFY_IS_APPROX(rhs22 = (s2*rhs2) * (s1*m2).template selfadjointView<Lower>(), rhs23 = (s2*rhs2) * (s1*m1));
+
+ // destination with a non-default inner-stride
+ // see bug 1741
+ {
+ typedef Matrix<Scalar,Dynamic,Dynamic> MatrixX;
+ MatrixX buffer(2*cols,2*othersize);
+ Map<Rhs1,0,Stride<Dynamic,2> > map1(buffer.data(),cols,othersize,Stride<Dynamic,2>(2*rows,2));
+ buffer.setZero();
+ VERIFY_IS_APPROX( map1.noalias() = (s1*m2).template selfadjointView<Lower>() * (s2*rhs1),
+ rhs13 = (s1*m1) * (s2*rhs1));
+
+ Map<Rhs2,0,Stride<Dynamic,2> > map2(buffer.data(),rhs22.rows(),rhs22.cols(),Stride<Dynamic,2>(2*rhs22.outerStride(),2));
+ buffer.setZero();
+ VERIFY_IS_APPROX(map2 = (rhs2) * (m2).template selfadjointView<Lower>(), rhs23 = (rhs2) * (m1));
+ }
+}
+
+EIGEN_DECLARE_TEST(product_symm)
+{
+ for(int i = 0; i < g_repeat ; i++)
+ {
+ CALL_SUBTEST_1(( symm<float,Dynamic,Dynamic>(internal::random<int>(1,EIGEN_TEST_MAX_SIZE),internal::random<int>(1,EIGEN_TEST_MAX_SIZE)) ));
+ CALL_SUBTEST_2(( symm<double,Dynamic,Dynamic>(internal::random<int>(1,EIGEN_TEST_MAX_SIZE),internal::random<int>(1,EIGEN_TEST_MAX_SIZE)) ));
+ CALL_SUBTEST_3(( symm<std::complex<float>,Dynamic,Dynamic>(internal::random<int>(1,EIGEN_TEST_MAX_SIZE/2),internal::random<int>(1,EIGEN_TEST_MAX_SIZE/2)) ));
+ CALL_SUBTEST_4(( symm<std::complex<double>,Dynamic,Dynamic>(internal::random<int>(1,EIGEN_TEST_MAX_SIZE/2),internal::random<int>(1,EIGEN_TEST_MAX_SIZE/2)) ));
+
+ CALL_SUBTEST_5(( symm<float,Dynamic,1>(internal::random<int>(1,EIGEN_TEST_MAX_SIZE)) ));
+ CALL_SUBTEST_6(( symm<double,Dynamic,1>(internal::random<int>(1,EIGEN_TEST_MAX_SIZE)) ));
+ CALL_SUBTEST_7(( symm<std::complex<float>,Dynamic,1>(internal::random<int>(1,EIGEN_TEST_MAX_SIZE)) ));
+ CALL_SUBTEST_8(( symm<std::complex<double>,Dynamic,1>(internal::random<int>(1,EIGEN_TEST_MAX_SIZE)) ));
+ }
+}
diff --git a/test/product_syrk.cpp b/test/product_syrk.cpp
new file mode 100644
index 0000000..8becd37
--- /dev/null
+++ b/test/product_syrk.cpp
@@ -0,0 +1,146 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "main.h"
+
+template<typename MatrixType> void syrk(const MatrixType& m)
+{
+ typedef typename MatrixType::Scalar Scalar;
+ typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::ColsAtCompileTime, RowMajor> RMatrixType;
+ typedef Matrix<Scalar, MatrixType::ColsAtCompileTime, Dynamic> Rhs1;
+ typedef Matrix<Scalar, Dynamic, MatrixType::RowsAtCompileTime> Rhs2;
+ typedef Matrix<Scalar, MatrixType::ColsAtCompileTime, Dynamic,RowMajor> Rhs3;
+
+ Index rows = m.rows();
+ Index cols = m.cols();
+
+ MatrixType m1 = MatrixType::Random(rows, cols),
+ m2 = MatrixType::Random(rows, cols),
+ m3 = MatrixType::Random(rows, cols);
+ RMatrixType rm2 = MatrixType::Random(rows, cols);
+
+ Rhs1 rhs1 = Rhs1::Random(internal::random<int>(1,320), cols); Rhs1 rhs11 = Rhs1::Random(rhs1.rows(), cols);
+ Rhs2 rhs2 = Rhs2::Random(rows, internal::random<int>(1,320)); Rhs2 rhs22 = Rhs2::Random(rows, rhs2.cols());
+ Rhs3 rhs3 = Rhs3::Random(internal::random<int>(1,320), rows);
+
+ Scalar s1 = internal::random<Scalar>();
+
+ Index c = internal::random<Index>(0,cols-1);
+
+ m2.setZero();
+ VERIFY_IS_APPROX((m2.template selfadjointView<Lower>().rankUpdate(rhs2,s1)._expression()),
+ ((s1 * rhs2 * rhs2.adjoint()).eval().template triangularView<Lower>().toDenseMatrix()));
+ m2.setZero();
+ VERIFY_IS_APPROX(((m2.template triangularView<Lower>() += s1 * rhs2 * rhs22.adjoint()).nestedExpression()),
+ ((s1 * rhs2 * rhs22.adjoint()).eval().template triangularView<Lower>().toDenseMatrix()));
+
+
+ m2.setZero();
+ VERIFY_IS_APPROX(m2.template selfadjointView<Upper>().rankUpdate(rhs2,s1)._expression(),
+ (s1 * rhs2 * rhs2.adjoint()).eval().template triangularView<Upper>().toDenseMatrix());
+ m2.setZero();
+ VERIFY_IS_APPROX((m2.template triangularView<Upper>() += s1 * rhs22 * rhs2.adjoint()).nestedExpression(),
+ (s1 * rhs22 * rhs2.adjoint()).eval().template triangularView<Upper>().toDenseMatrix());
+
+
+ m2.setZero();
+ VERIFY_IS_APPROX(m2.template selfadjointView<Lower>().rankUpdate(rhs1.adjoint(),s1)._expression(),
+ (s1 * rhs1.adjoint() * rhs1).eval().template triangularView<Lower>().toDenseMatrix());
+ m2.setZero();
+ VERIFY_IS_APPROX((m2.template triangularView<Lower>() += s1 * rhs11.adjoint() * rhs1).nestedExpression(),
+ (s1 * rhs11.adjoint() * rhs1).eval().template triangularView<Lower>().toDenseMatrix());
+
+
+ m2.setZero();
+ VERIFY_IS_APPROX(m2.template selfadjointView<Upper>().rankUpdate(rhs1.adjoint(),s1)._expression(),
+ (s1 * rhs1.adjoint() * rhs1).eval().template triangularView<Upper>().toDenseMatrix());
+ VERIFY_IS_APPROX((m2.template triangularView<Upper>() = s1 * rhs1.adjoint() * rhs11).nestedExpression(),
+ (s1 * rhs1.adjoint() * rhs11).eval().template triangularView<Upper>().toDenseMatrix());
+
+
+ m2.setZero();
+ VERIFY_IS_APPROX(m2.template selfadjointView<Lower>().rankUpdate(rhs3.adjoint(),s1)._expression(),
+ (s1 * rhs3.adjoint() * rhs3).eval().template triangularView<Lower>().toDenseMatrix());
+
+ m2.setZero();
+ VERIFY_IS_APPROX(m2.template selfadjointView<Upper>().rankUpdate(rhs3.adjoint(),s1)._expression(),
+ (s1 * rhs3.adjoint() * rhs3).eval().template triangularView<Upper>().toDenseMatrix());
+
+ m2.setZero();
+ VERIFY_IS_APPROX((m2.template selfadjointView<Lower>().rankUpdate(m1.col(c),s1)._expression()),
+ ((s1 * m1.col(c) * m1.col(c).adjoint()).eval().template triangularView<Lower>().toDenseMatrix()));
+
+ m2.setZero();
+ VERIFY_IS_APPROX((m2.template selfadjointView<Upper>().rankUpdate(m1.col(c),s1)._expression()),
+ ((s1 * m1.col(c) * m1.col(c).adjoint()).eval().template triangularView<Upper>().toDenseMatrix()));
+ rm2.setZero();
+ VERIFY_IS_APPROX((rm2.template selfadjointView<Upper>().rankUpdate(m1.col(c),s1)._expression()),
+ ((s1 * m1.col(c) * m1.col(c).adjoint()).eval().template triangularView<Upper>().toDenseMatrix()));
+ m2.setZero();
+ VERIFY_IS_APPROX((m2.template triangularView<Upper>() += s1 * m3.col(c) * m1.col(c).adjoint()).nestedExpression(),
+ ((s1 * m3.col(c) * m1.col(c).adjoint()).eval().template triangularView<Upper>().toDenseMatrix()));
+ rm2.setZero();
+ VERIFY_IS_APPROX((rm2.template triangularView<Upper>() += s1 * m1.col(c) * m3.col(c).adjoint()).nestedExpression(),
+ ((s1 * m1.col(c) * m3.col(c).adjoint()).eval().template triangularView<Upper>().toDenseMatrix()));
+
+ m2.setZero();
+ VERIFY_IS_APPROX((m2.template selfadjointView<Lower>().rankUpdate(m1.col(c).conjugate(),s1)._expression()),
+ ((s1 * m1.col(c).conjugate() * m1.col(c).conjugate().adjoint()).eval().template triangularView<Lower>().toDenseMatrix()));
+
+ m2.setZero();
+ VERIFY_IS_APPROX((m2.template selfadjointView<Upper>().rankUpdate(m1.col(c).conjugate(),s1)._expression()),
+ ((s1 * m1.col(c).conjugate() * m1.col(c).conjugate().adjoint()).eval().template triangularView<Upper>().toDenseMatrix()));
+
+
+ m2.setZero();
+ VERIFY_IS_APPROX((m2.template selfadjointView<Lower>().rankUpdate(m1.row(c),s1)._expression()),
+ ((s1 * m1.row(c).transpose() * m1.row(c).transpose().adjoint()).eval().template triangularView<Lower>().toDenseMatrix()));
+ rm2.setZero();
+ VERIFY_IS_APPROX((rm2.template selfadjointView<Lower>().rankUpdate(m1.row(c),s1)._expression()),
+ ((s1 * m1.row(c).transpose() * m1.row(c).transpose().adjoint()).eval().template triangularView<Lower>().toDenseMatrix()));
+ m2.setZero();
+ VERIFY_IS_APPROX((m2.template triangularView<Lower>() += s1 * m3.row(c).transpose() * m1.row(c).transpose().adjoint()).nestedExpression(),
+ ((s1 * m3.row(c).transpose() * m1.row(c).transpose().adjoint()).eval().template triangularView<Lower>().toDenseMatrix()));
+ rm2.setZero();
+ VERIFY_IS_APPROX((rm2.template triangularView<Lower>() += s1 * m3.row(c).transpose() * m1.row(c).transpose().adjoint()).nestedExpression(),
+ ((s1 * m3.row(c).transpose() * m1.row(c).transpose().adjoint()).eval().template triangularView<Lower>().toDenseMatrix()));
+
+
+ m2.setZero();
+ VERIFY_IS_APPROX((m2.template selfadjointView<Upper>().rankUpdate(m1.row(c).adjoint(),s1)._expression()),
+ ((s1 * m1.row(c).adjoint() * m1.row(c).adjoint().adjoint()).eval().template triangularView<Upper>().toDenseMatrix()));
+
+ // destination with a non-default inner-stride
+ // see bug 1741
+ {
+ typedef Matrix<Scalar,Dynamic,Dynamic> MatrixX;
+ MatrixX buffer(2*rows,2*cols);
+ Map<MatrixType,0,Stride<Dynamic,2> > map1(buffer.data(),rows,cols,Stride<Dynamic,2>(2*rows,2));
+ buffer.setZero();
+ VERIFY_IS_APPROX((map1.template selfadjointView<Lower>().rankUpdate(rhs2,s1)._expression()),
+ ((s1 * rhs2 * rhs2.adjoint()).eval().template triangularView<Lower>().toDenseMatrix()));
+ }
+}
+
+EIGEN_DECLARE_TEST(product_syrk)
+{
+ for(int i = 0; i < g_repeat ; i++)
+ {
+ int s;
+ s = internal::random<int>(1,EIGEN_TEST_MAX_SIZE);
+ CALL_SUBTEST_1( syrk(MatrixXf(s, s)) );
+ CALL_SUBTEST_2( syrk(MatrixXd(s, s)) );
+ TEST_SET_BUT_UNUSED_VARIABLE(s)
+
+ s = internal::random<int>(1,EIGEN_TEST_MAX_SIZE/2);
+ CALL_SUBTEST_3( syrk(MatrixXcf(s, s)) );
+ CALL_SUBTEST_4( syrk(MatrixXcd(s, s)) );
+ TEST_SET_BUT_UNUSED_VARIABLE(s)
+ }
+}
diff --git a/test/product_trmm.cpp b/test/product_trmm.cpp
new file mode 100644
index 0000000..2bb4b9e
--- /dev/null
+++ b/test/product_trmm.cpp
@@ -0,0 +1,137 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "main.h"
+
+template<typename T>
+int get_random_size()
+{
+ const int factor = NumTraits<T>::ReadCost;
+ const int max_test_size = EIGEN_TEST_MAX_SIZE>2*factor ? EIGEN_TEST_MAX_SIZE/factor : EIGEN_TEST_MAX_SIZE;
+ return internal::random<int>(1,max_test_size);
+}
+
+template<typename Scalar, int Mode, int TriOrder, int OtherOrder, int ResOrder, int OtherCols>
+void trmm(int rows=get_random_size<Scalar>(),
+ int cols=get_random_size<Scalar>(),
+ int otherCols = OtherCols==Dynamic?get_random_size<Scalar>():OtherCols)
+{
+ typedef Matrix<Scalar,Dynamic,Dynamic,TriOrder> TriMatrix;
+ typedef Matrix<Scalar,Dynamic,OtherCols,OtherCols==1?ColMajor:OtherOrder> OnTheRight;
+ typedef Matrix<Scalar,OtherCols,Dynamic,OtherCols==1?RowMajor:OtherOrder> OnTheLeft;
+
+ typedef Matrix<Scalar,Dynamic,OtherCols,OtherCols==1?ColMajor:ResOrder> ResXS;
+ typedef Matrix<Scalar,OtherCols,Dynamic,OtherCols==1?RowMajor:ResOrder> ResSX;
+
+ TriMatrix mat(rows,cols), tri(rows,cols), triTr(cols,rows), s1tri(rows,cols), s1triTr(cols,rows);
+
+ OnTheRight ge_right(cols,otherCols);
+ OnTheLeft ge_left(otherCols,rows);
+ ResSX ge_sx, ge_sx_save;
+ ResXS ge_xs, ge_xs_save;
+
+ Scalar s1 = internal::random<Scalar>(),
+ s2 = internal::random<Scalar>();
+
+ mat.setRandom();
+ tri = mat.template triangularView<Mode>();
+ triTr = mat.transpose().template triangularView<Mode>();
+ s1tri = (s1*mat).template triangularView<Mode>();
+ s1triTr = (s1*mat).transpose().template triangularView<Mode>();
+ ge_right.setRandom();
+ ge_left.setRandom();
+
+ VERIFY_IS_APPROX( ge_xs = mat.template triangularView<Mode>() * ge_right, tri * ge_right);
+ VERIFY_IS_APPROX( ge_sx = ge_left * mat.template triangularView<Mode>(), ge_left * tri);
+
+ VERIFY_IS_APPROX( ge_xs.noalias() = mat.template triangularView<Mode>() * ge_right, tri * ge_right);
+ VERIFY_IS_APPROX( ge_sx.noalias() = ge_left * mat.template triangularView<Mode>(), ge_left * tri);
+
+ if((Mode&UnitDiag)==0)
+ VERIFY_IS_APPROX( ge_xs.noalias() = (s1*mat.adjoint()).template triangularView<Mode>() * (s2*ge_left.transpose()), s1*triTr.conjugate() * (s2*ge_left.transpose()));
+
+ VERIFY_IS_APPROX( ge_xs.noalias() = (s1*mat.transpose()).template triangularView<Mode>() * (s2*ge_left.transpose()), s1triTr * (s2*ge_left.transpose()));
+ VERIFY_IS_APPROX( ge_sx.noalias() = (s2*ge_left) * (s1*mat).template triangularView<Mode>(), (s2*ge_left)*s1tri);
+
+ VERIFY_IS_APPROX( ge_sx.noalias() = ge_right.transpose() * mat.adjoint().template triangularView<Mode>(), ge_right.transpose() * triTr.conjugate());
+ VERIFY_IS_APPROX( ge_sx.noalias() = ge_right.adjoint() * mat.adjoint().template triangularView<Mode>(), ge_right.adjoint() * triTr.conjugate());
+
+ ge_xs_save = ge_xs;
+ if((Mode&UnitDiag)==0)
+ VERIFY_IS_APPROX( (ge_xs_save + s1*triTr.conjugate() * (s2*ge_left.adjoint())).eval(), ge_xs.noalias() += (s1*mat.adjoint()).template triangularView<Mode>() * (s2*ge_left.adjoint()) );
+ ge_xs_save = ge_xs;
+ VERIFY_IS_APPROX( (ge_xs_save + s1triTr * (s2*ge_left.adjoint())).eval(), ge_xs.noalias() += (s1*mat.transpose()).template triangularView<Mode>() * (s2*ge_left.adjoint()) );
+ ge_sx.setRandom();
+ ge_sx_save = ge_sx;
+ if((Mode&UnitDiag)==0)
+ VERIFY_IS_APPROX( ge_sx_save - (ge_right.adjoint() * (-s1 * triTr).conjugate()).eval(), ge_sx.noalias() -= (ge_right.adjoint() * (-s1 * mat).adjoint().template triangularView<Mode>()).eval());
+
+ if((Mode&UnitDiag)==0)
+ VERIFY_IS_APPROX( ge_xs = (s1*mat).adjoint().template triangularView<Mode>() * ge_left.adjoint(), numext::conj(s1) * triTr.conjugate() * ge_left.adjoint());
+ VERIFY_IS_APPROX( ge_xs = (s1*mat).transpose().template triangularView<Mode>() * ge_left.adjoint(), s1triTr * ge_left.adjoint());
+
+ // TODO check with sub-matrix expressions ?
+
+ // destination with a non-default inner-stride
+ // see bug 1741
+ {
+ VERIFY_IS_APPROX( ge_xs.noalias() = mat.template triangularView<Mode>() * ge_right, tri * ge_right);
+ typedef Matrix<Scalar,Dynamic,Dynamic> MatrixX;
+ MatrixX buffer(2*ge_xs.rows(),2*ge_xs.cols());
+ Map<ResXS,0,Stride<Dynamic,2> > map1(buffer.data(),ge_xs.rows(),ge_xs.cols(),Stride<Dynamic,2>(2*ge_xs.outerStride(),2));
+ buffer.setZero();
+ VERIFY_IS_APPROX( map1.noalias() = mat.template triangularView<Mode>() * ge_right, tri * ge_right);
+ }
+}
+
+template<typename Scalar, int Mode, int TriOrder>
+void trmv(int rows=get_random_size<Scalar>(), int cols=get_random_size<Scalar>())
+{
+ trmm<Scalar,Mode,TriOrder,ColMajor,ColMajor,1>(rows,cols,1);
+}
+
+template<typename Scalar, int Mode, int TriOrder, int OtherOrder, int ResOrder>
+void trmm(int rows=get_random_size<Scalar>(), int cols=get_random_size<Scalar>(), int otherCols = get_random_size<Scalar>())
+{
+ trmm<Scalar,Mode,TriOrder,OtherOrder,ResOrder,Dynamic>(rows,cols,otherCols);
+}
+
+#define CALL_ALL_ORDERS(NB,SCALAR,MODE) \
+ EIGEN_CAT(CALL_SUBTEST_,NB)((trmm<SCALAR, MODE, ColMajor,ColMajor,ColMajor>())); \
+ EIGEN_CAT(CALL_SUBTEST_,NB)((trmm<SCALAR, MODE, ColMajor,ColMajor,RowMajor>())); \
+ EIGEN_CAT(CALL_SUBTEST_,NB)((trmm<SCALAR, MODE, ColMajor,RowMajor,ColMajor>())); \
+ EIGEN_CAT(CALL_SUBTEST_,NB)((trmm<SCALAR, MODE, ColMajor,RowMajor,RowMajor>())); \
+ EIGEN_CAT(CALL_SUBTEST_,NB)((trmm<SCALAR, MODE, RowMajor,ColMajor,ColMajor>())); \
+ EIGEN_CAT(CALL_SUBTEST_,NB)((trmm<SCALAR, MODE, RowMajor,ColMajor,RowMajor>())); \
+ EIGEN_CAT(CALL_SUBTEST_,NB)((trmm<SCALAR, MODE, RowMajor,RowMajor,ColMajor>())); \
+ EIGEN_CAT(CALL_SUBTEST_,NB)((trmm<SCALAR, MODE, RowMajor,RowMajor,RowMajor>())); \
+ \
+ EIGEN_CAT(CALL_SUBTEST_1,NB)((trmv<SCALAR, MODE, ColMajor>())); \
+ EIGEN_CAT(CALL_SUBTEST_1,NB)((trmv<SCALAR, MODE, RowMajor>()));
+
+
+#define CALL_ALL(NB,SCALAR) \
+ CALL_ALL_ORDERS(EIGEN_CAT(1,NB),SCALAR,Upper) \
+ CALL_ALL_ORDERS(EIGEN_CAT(2,NB),SCALAR,UnitUpper) \
+ CALL_ALL_ORDERS(EIGEN_CAT(3,NB),SCALAR,StrictlyUpper) \
+ CALL_ALL_ORDERS(EIGEN_CAT(1,NB),SCALAR,Lower) \
+ CALL_ALL_ORDERS(EIGEN_CAT(2,NB),SCALAR,UnitLower) \
+ CALL_ALL_ORDERS(EIGEN_CAT(3,NB),SCALAR,StrictlyLower)
+
+
+EIGEN_DECLARE_TEST(product_trmm)
+{
+ for(int i = 0; i < g_repeat ; i++)
+ {
+ CALL_ALL(1,float); // EIGEN_SUFFIXES;11;111;21;121;31;131
+ CALL_ALL(2,double); // EIGEN_SUFFIXES;12;112;22;122;32;132
+ CALL_ALL(3,std::complex<float>); // EIGEN_SUFFIXES;13;113;23;123;33;133
+ CALL_ALL(4,std::complex<double>); // EIGEN_SUFFIXES;14;114;24;124;34;134
+ }
+}
diff --git a/test/product_trmv.cpp b/test/product_trmv.cpp
new file mode 100644
index 0000000..5eb1b5a
--- /dev/null
+++ b/test/product_trmv.cpp
@@ -0,0 +1,90 @@
+// This file is triangularView of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "main.h"
+
+template<typename MatrixType> void trmv(const MatrixType& m)
+{
+ typedef typename MatrixType::Scalar Scalar;
+ typedef typename NumTraits<Scalar>::Real RealScalar;
+ typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> VectorType;
+
+ RealScalar largerEps = 10*test_precision<RealScalar>();
+
+ Index rows = m.rows();
+ Index cols = m.cols();
+
+ MatrixType m1 = MatrixType::Random(rows, cols),
+ m3(rows, cols);
+ VectorType v1 = VectorType::Random(rows);
+
+ Scalar s1 = internal::random<Scalar>();
+
+ m1 = MatrixType::Random(rows, cols);
+
+ // check with a column-major matrix
+ m3 = m1.template triangularView<Eigen::Lower>();
+ VERIFY((m3 * v1).isApprox(m1.template triangularView<Eigen::Lower>() * v1, largerEps));
+ m3 = m1.template triangularView<Eigen::Upper>();
+ VERIFY((m3 * v1).isApprox(m1.template triangularView<Eigen::Upper>() * v1, largerEps));
+ m3 = m1.template triangularView<Eigen::UnitLower>();
+ VERIFY((m3 * v1).isApprox(m1.template triangularView<Eigen::UnitLower>() * v1, largerEps));
+ m3 = m1.template triangularView<Eigen::UnitUpper>();
+ VERIFY((m3 * v1).isApprox(m1.template triangularView<Eigen::UnitUpper>() * v1, largerEps));
+
+ // check conjugated and scalar multiple expressions (col-major)
+ m3 = m1.template triangularView<Eigen::Lower>();
+ VERIFY(((s1*m3).conjugate() * v1).isApprox((s1*m1).conjugate().template triangularView<Eigen::Lower>() * v1, largerEps));
+ m3 = m1.template triangularView<Eigen::Upper>();
+ VERIFY((m3.conjugate() * v1.conjugate()).isApprox(m1.conjugate().template triangularView<Eigen::Upper>() * v1.conjugate(), largerEps));
+
+ // check with a row-major matrix
+ m3 = m1.template triangularView<Eigen::Upper>();
+ VERIFY((m3.transpose() * v1).isApprox(m1.transpose().template triangularView<Eigen::Lower>() * v1, largerEps));
+ m3 = m1.template triangularView<Eigen::Lower>();
+ VERIFY((m3.transpose() * v1).isApprox(m1.transpose().template triangularView<Eigen::Upper>() * v1, largerEps));
+ m3 = m1.template triangularView<Eigen::UnitUpper>();
+ VERIFY((m3.transpose() * v1).isApprox(m1.transpose().template triangularView<Eigen::UnitLower>() * v1, largerEps));
+ m3 = m1.template triangularView<Eigen::UnitLower>();
+ VERIFY((m3.transpose() * v1).isApprox(m1.transpose().template triangularView<Eigen::UnitUpper>() * v1, largerEps));
+
+ // check conjugated and scalar multiple expressions (row-major)
+ m3 = m1.template triangularView<Eigen::Upper>();
+ VERIFY((m3.adjoint() * v1).isApprox(m1.adjoint().template triangularView<Eigen::Lower>() * v1, largerEps));
+ m3 = m1.template triangularView<Eigen::Lower>();
+ VERIFY((m3.adjoint() * (s1*v1.conjugate())).isApprox(m1.adjoint().template triangularView<Eigen::Upper>() * (s1*v1.conjugate()), largerEps));
+ m3 = m1.template triangularView<Eigen::UnitUpper>();
+
+ // check transposed cases:
+ m3 = m1.template triangularView<Eigen::Lower>();
+ VERIFY((v1.transpose() * m3).isApprox(v1.transpose() * m1.template triangularView<Eigen::Lower>(), largerEps));
+ VERIFY((v1.adjoint() * m3).isApprox(v1.adjoint() * m1.template triangularView<Eigen::Lower>(), largerEps));
+ VERIFY((v1.adjoint() * m3.adjoint()).isApprox(v1.adjoint() * m1.template triangularView<Eigen::Lower>().adjoint(), largerEps));
+
+ // TODO check with sub-matrices
+}
+
+EIGEN_DECLARE_TEST(product_trmv)
+{
+ int s = 0;
+ for(int i = 0; i < g_repeat ; i++) {
+ CALL_SUBTEST_1( trmv(Matrix<float, 1, 1>()) );
+ CALL_SUBTEST_2( trmv(Matrix<float, 2, 2>()) );
+ CALL_SUBTEST_3( trmv(Matrix3d()) );
+
+ s = internal::random<int>(1,EIGEN_TEST_MAX_SIZE/2);
+ CALL_SUBTEST_4( trmv(MatrixXcf(s,s)) );
+ CALL_SUBTEST_5( trmv(MatrixXcd(s,s)) );
+ TEST_SET_BUT_UNUSED_VARIABLE(s)
+
+ s = internal::random<int>(1,EIGEN_TEST_MAX_SIZE);
+ CALL_SUBTEST_6( trmv(Matrix<float,Dynamic,Dynamic,RowMajor>(s, s)) );
+ TEST_SET_BUT_UNUSED_VARIABLE(s)
+ }
+}
diff --git a/test/product_trsolve.cpp b/test/product_trsolve.cpp
new file mode 100644
index 0000000..c59748c
--- /dev/null
+++ b/test/product_trsolve.cpp
@@ -0,0 +1,127 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "main.h"
+
+#define VERIFY_TRSM(TRI,XB) { \
+ (XB).setRandom(); ref = (XB); \
+ (TRI).solveInPlace(XB); \
+ VERIFY_IS_APPROX((TRI).toDenseMatrix() * (XB), ref); \
+ (XB).setRandom(); ref = (XB); \
+ (XB) = (TRI).solve(XB); \
+ VERIFY_IS_APPROX((TRI).toDenseMatrix() * (XB), ref); \
+ }
+
+#define VERIFY_TRSM_ONTHERIGHT(TRI,XB) { \
+ (XB).setRandom(); ref = (XB); \
+ (TRI).transpose().template solveInPlace<OnTheRight>(XB.transpose()); \
+ VERIFY_IS_APPROX((XB).transpose() * (TRI).transpose().toDenseMatrix(), ref.transpose()); \
+ (XB).setRandom(); ref = (XB); \
+ (XB).transpose() = (TRI).transpose().template solve<OnTheRight>(XB.transpose()); \
+ VERIFY_IS_APPROX((XB).transpose() * (TRI).transpose().toDenseMatrix(), ref.transpose()); \
+ }
+
+template<typename Scalar,int Size, int Cols> void trsolve(int size=Size,int cols=Cols)
+{
+ typedef typename NumTraits<Scalar>::Real RealScalar;
+
+ Matrix<Scalar,Size,Size,ColMajor> cmLhs(size,size);
+ Matrix<Scalar,Size,Size,RowMajor> rmLhs(size,size);
+
+ enum { colmajor = Size==1 ? RowMajor : ColMajor,
+ rowmajor = Cols==1 ? ColMajor : RowMajor };
+ Matrix<Scalar,Size,Cols,colmajor> cmRhs(size,cols);
+ Matrix<Scalar,Size,Cols,rowmajor> rmRhs(size,cols);
+ Matrix<Scalar,Dynamic,Dynamic,colmajor> ref(size,cols);
+
+ cmLhs.setRandom(); cmLhs *= static_cast<RealScalar>(0.1); cmLhs.diagonal().array() += static_cast<RealScalar>(1);
+ rmLhs.setRandom(); rmLhs *= static_cast<RealScalar>(0.1); rmLhs.diagonal().array() += static_cast<RealScalar>(1);
+
+ VERIFY_TRSM(cmLhs.conjugate().template triangularView<Lower>(), cmRhs);
+ VERIFY_TRSM(cmLhs.adjoint() .template triangularView<Lower>(), cmRhs);
+ VERIFY_TRSM(cmLhs .template triangularView<Upper>(), cmRhs);
+ VERIFY_TRSM(cmLhs .template triangularView<Lower>(), rmRhs);
+ VERIFY_TRSM(cmLhs.conjugate().template triangularView<Upper>(), rmRhs);
+ VERIFY_TRSM(cmLhs.adjoint() .template triangularView<Upper>(), rmRhs);
+
+ VERIFY_TRSM(cmLhs.conjugate().template triangularView<UnitLower>(), cmRhs);
+ VERIFY_TRSM(cmLhs .template triangularView<UnitUpper>(), rmRhs);
+
+ VERIFY_TRSM(rmLhs .template triangularView<Lower>(), cmRhs);
+ VERIFY_TRSM(rmLhs.conjugate().template triangularView<UnitUpper>(), rmRhs);
+
+
+ VERIFY_TRSM_ONTHERIGHT(cmLhs.conjugate().template triangularView<Lower>(), cmRhs);
+ VERIFY_TRSM_ONTHERIGHT(cmLhs .template triangularView<Upper>(), cmRhs);
+ VERIFY_TRSM_ONTHERIGHT(cmLhs .template triangularView<Lower>(), rmRhs);
+ VERIFY_TRSM_ONTHERIGHT(cmLhs.conjugate().template triangularView<Upper>(), rmRhs);
+
+ VERIFY_TRSM_ONTHERIGHT(cmLhs.conjugate().template triangularView<UnitLower>(), cmRhs);
+ VERIFY_TRSM_ONTHERIGHT(cmLhs .template triangularView<UnitUpper>(), rmRhs);
+
+ VERIFY_TRSM_ONTHERIGHT(rmLhs .template triangularView<Lower>(), cmRhs);
+ VERIFY_TRSM_ONTHERIGHT(rmLhs.conjugate().template triangularView<UnitUpper>(), rmRhs);
+
+ int c = internal::random<int>(0,cols-1);
+ VERIFY_TRSM(rmLhs.template triangularView<Lower>(), rmRhs.col(c));
+ VERIFY_TRSM(cmLhs.template triangularView<Lower>(), rmRhs.col(c));
+
+ // destination with a non-default inner-stride
+ // see bug 1741
+ {
+ typedef Matrix<Scalar,Dynamic,Dynamic> MatrixX;
+ MatrixX buffer(2*cmRhs.rows(),2*cmRhs.cols());
+ Map<Matrix<Scalar,Size,Cols,colmajor>,0,Stride<Dynamic,2> > map1(buffer.data(),cmRhs.rows(),cmRhs.cols(),Stride<Dynamic,2>(2*cmRhs.outerStride(),2));
+ Map<Matrix<Scalar,Size,Cols,rowmajor>,0,Stride<Dynamic,2> > map2(buffer.data(),rmRhs.rows(),rmRhs.cols(),Stride<Dynamic,2>(2*rmRhs.outerStride(),2));
+ buffer.setZero();
+ VERIFY_TRSM(cmLhs.conjugate().template triangularView<Lower>(), map1);
+ buffer.setZero();
+ VERIFY_TRSM(cmLhs .template triangularView<Lower>(), map2);
+ }
+
+ if(Size==Dynamic)
+ {
+ cmLhs.resize(0,0);
+ cmRhs.resize(0,cmRhs.cols());
+ Matrix<Scalar,Size,Cols,colmajor> res = cmLhs.template triangularView<Lower>().solve(cmRhs);
+ VERIFY_IS_EQUAL(res.rows(),0);
+ VERIFY_IS_EQUAL(res.cols(),cmRhs.cols());
+ res = cmRhs;
+ cmLhs.template triangularView<Lower>().solveInPlace(res);
+ VERIFY_IS_EQUAL(res.rows(),0);
+ VERIFY_IS_EQUAL(res.cols(),cmRhs.cols());
+ }
+}
+
+EIGEN_DECLARE_TEST(product_trsolve)
+{
+ for(int i = 0; i < g_repeat ; i++)
+ {
+ // matrices
+ CALL_SUBTEST_1((trsolve<float,Dynamic,Dynamic>(internal::random<int>(1,EIGEN_TEST_MAX_SIZE),internal::random<int>(1,EIGEN_TEST_MAX_SIZE))));
+ CALL_SUBTEST_2((trsolve<double,Dynamic,Dynamic>(internal::random<int>(1,EIGEN_TEST_MAX_SIZE),internal::random<int>(1,EIGEN_TEST_MAX_SIZE))));
+ CALL_SUBTEST_3((trsolve<std::complex<float>,Dynamic,Dynamic>(internal::random<int>(1,EIGEN_TEST_MAX_SIZE/2),internal::random<int>(1,EIGEN_TEST_MAX_SIZE/2))));
+ CALL_SUBTEST_4((trsolve<std::complex<double>,Dynamic,Dynamic>(internal::random<int>(1,EIGEN_TEST_MAX_SIZE/2),internal::random<int>(1,EIGEN_TEST_MAX_SIZE/2))));
+
+ // vectors
+ CALL_SUBTEST_5((trsolve<float,Dynamic,1>(internal::random<int>(1,EIGEN_TEST_MAX_SIZE))));
+ CALL_SUBTEST_6((trsolve<double,Dynamic,1>(internal::random<int>(1,EIGEN_TEST_MAX_SIZE))));
+ CALL_SUBTEST_7((trsolve<std::complex<float>,Dynamic,1>(internal::random<int>(1,EIGEN_TEST_MAX_SIZE))));
+ CALL_SUBTEST_8((trsolve<std::complex<double>,Dynamic,1>(internal::random<int>(1,EIGEN_TEST_MAX_SIZE))));
+
+ // meta-unrollers
+ CALL_SUBTEST_9((trsolve<float,4,1>()));
+ CALL_SUBTEST_10((trsolve<double,4,1>()));
+ CALL_SUBTEST_11((trsolve<std::complex<float>,4,1>()));
+ CALL_SUBTEST_12((trsolve<float,1,1>()));
+ CALL_SUBTEST_13((trsolve<float,1,2>()));
+ CALL_SUBTEST_14((trsolve<float,3,1>()));
+
+ }
+}
diff --git a/test/qr.cpp b/test/qr.cpp
new file mode 100644
index 0000000..36f3121
--- /dev/null
+++ b/test/qr.cpp
@@ -0,0 +1,133 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "main.h"
+#include <Eigen/QR>
+#include "solverbase.h"
+
+template<typename MatrixType> void qr(const MatrixType& m)
+{
+ Index rows = m.rows();
+ Index cols = m.cols();
+
+ typedef typename MatrixType::Scalar Scalar;
+ typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime> MatrixQType;
+
+ MatrixType a = MatrixType::Random(rows,cols);
+ HouseholderQR<MatrixType> qrOfA(a);
+
+ MatrixQType q = qrOfA.householderQ();
+ VERIFY_IS_UNITARY(q);
+
+ MatrixType r = qrOfA.matrixQR().template triangularView<Upper>();
+ VERIFY_IS_APPROX(a, qrOfA.householderQ() * r);
+}
+
+template<typename MatrixType, int Cols2> void qr_fixedsize()
+{
+ enum { Rows = MatrixType::RowsAtCompileTime, Cols = MatrixType::ColsAtCompileTime };
+ typedef typename MatrixType::Scalar Scalar;
+ Matrix<Scalar,Rows,Cols> m1 = Matrix<Scalar,Rows,Cols>::Random();
+ HouseholderQR<Matrix<Scalar,Rows,Cols> > qr(m1);
+
+ Matrix<Scalar,Rows,Cols> r = qr.matrixQR();
+ // FIXME need better way to construct trapezoid
+ for(int i = 0; i < Rows; i++) for(int j = 0; j < Cols; j++) if(i>j) r(i,j) = Scalar(0);
+
+ VERIFY_IS_APPROX(m1, qr.householderQ() * r);
+
+ check_solverbase<Matrix<Scalar,Cols,Cols2>, Matrix<Scalar,Rows,Cols2> >(m1, qr, Rows, Cols, Cols2);
+}
+
+template<typename MatrixType> void qr_invertible()
+{
+ using std::log;
+ using std::abs;
+ using std::pow;
+ using std::max;
+ typedef typename NumTraits<typename MatrixType::Scalar>::Real RealScalar;
+ typedef typename MatrixType::Scalar Scalar;
+
+ STATIC_CHECK(( internal::is_same<typename HouseholderQR<MatrixType>::StorageIndex,int>::value ));
+
+ int size = internal::random<int>(10,50);
+
+ MatrixType m1(size, size), m2(size, size), m3(size, size);
+ m1 = MatrixType::Random(size,size);
+
+ if (internal::is_same<RealScalar,float>::value)
+ {
+ // let's build a matrix more stable to inverse
+ MatrixType a = MatrixType::Random(size,size*4);
+ m1 += a * a.adjoint();
+ }
+
+ HouseholderQR<MatrixType> qr(m1);
+
+ check_solverbase<MatrixType, MatrixType>(m1, qr, size, size, size);
+
+ // now construct a matrix with prescribed determinant
+ m1.setZero();
+ for(int i = 0; i < size; i++) m1(i,i) = internal::random<Scalar>();
+ Scalar det = m1.diagonal().prod();
+ RealScalar absdet = abs(det);
+ m3 = qr.householderQ(); // get a unitary
+ m1 = m3 * m1 * m3.adjoint();
+ qr.compute(m1);
+ VERIFY_IS_APPROX(log(absdet), qr.logAbsDeterminant());
+ // This test is tricky if the determinant becomes too small.
+ // Since we generate random numbers with magnitude range [0,1], the average determinant is 0.5^size
+ RealScalar tol = numext::maxi(RealScalar(pow(0.5,size)), numext::maxi<RealScalar>(abs(absdet), abs(qr.absDeterminant())));
+ VERIFY_IS_MUCH_SMALLER_THAN(abs(det - qr.determinant()), tol);
+ VERIFY_IS_MUCH_SMALLER_THAN(abs(absdet - qr.absDeterminant()), tol);
+}
+
+template<typename MatrixType> void qr_verify_assert()
+{
+ MatrixType tmp;
+
+ HouseholderQR<MatrixType> qr;
+ VERIFY_RAISES_ASSERT(qr.matrixQR())
+ VERIFY_RAISES_ASSERT(qr.solve(tmp))
+ VERIFY_RAISES_ASSERT(qr.transpose().solve(tmp))
+ VERIFY_RAISES_ASSERT(qr.adjoint().solve(tmp))
+ VERIFY_RAISES_ASSERT(qr.householderQ())
+ VERIFY_RAISES_ASSERT(qr.determinant())
+ VERIFY_RAISES_ASSERT(qr.absDeterminant())
+ VERIFY_RAISES_ASSERT(qr.logAbsDeterminant())
+}
+
+EIGEN_DECLARE_TEST(qr)
+{
+ for(int i = 0; i < g_repeat; i++) {
+ CALL_SUBTEST_1( qr(MatrixXf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE),internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
+ CALL_SUBTEST_2( qr(MatrixXcd(internal::random<int>(1,EIGEN_TEST_MAX_SIZE/2),internal::random<int>(1,EIGEN_TEST_MAX_SIZE/2))) );
+ CALL_SUBTEST_3(( qr_fixedsize<Matrix<float,3,4>, 2 >() ));
+ CALL_SUBTEST_4(( qr_fixedsize<Matrix<double,6,2>, 4 >() ));
+ CALL_SUBTEST_5(( qr_fixedsize<Matrix<double,2,5>, 7 >() ));
+ CALL_SUBTEST_11( qr(Matrix<float,1,1>()) );
+ }
+
+ for(int i = 0; i < g_repeat; i++) {
+ CALL_SUBTEST_1( qr_invertible<MatrixXf>() );
+ CALL_SUBTEST_6( qr_invertible<MatrixXd>() );
+ CALL_SUBTEST_7( qr_invertible<MatrixXcf>() );
+ CALL_SUBTEST_8( qr_invertible<MatrixXcd>() );
+ }
+
+ CALL_SUBTEST_9(qr_verify_assert<Matrix3f>());
+ CALL_SUBTEST_10(qr_verify_assert<Matrix3d>());
+ CALL_SUBTEST_1(qr_verify_assert<MatrixXf>());
+ CALL_SUBTEST_6(qr_verify_assert<MatrixXd>());
+ CALL_SUBTEST_7(qr_verify_assert<MatrixXcf>());
+ CALL_SUBTEST_8(qr_verify_assert<MatrixXcd>());
+
+ // Test problem size constructors
+ CALL_SUBTEST_12(HouseholderQR<MatrixXf>(10, 20));
+}
diff --git a/test/qr_colpivoting.cpp b/test/qr_colpivoting.cpp
new file mode 100644
index 0000000..4185f51
--- /dev/null
+++ b/test/qr_colpivoting.cpp
@@ -0,0 +1,372 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2009 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "main.h"
+#include <Eigen/QR>
+#include <Eigen/SVD>
+#include "solverbase.h"
+
+template <typename MatrixType>
+void cod() {
+ STATIC_CHECK(( internal::is_same<typename CompleteOrthogonalDecomposition<MatrixType>::StorageIndex,int>::value ));
+
+ Index rows = internal::random<Index>(2, EIGEN_TEST_MAX_SIZE);
+ Index cols = internal::random<Index>(2, EIGEN_TEST_MAX_SIZE);
+ Index cols2 = internal::random<Index>(2, EIGEN_TEST_MAX_SIZE);
+ Index rank = internal::random<Index>(1, (std::min)(rows, cols) - 1);
+
+ typedef typename MatrixType::Scalar Scalar;
+ typedef Matrix<Scalar, MatrixType::RowsAtCompileTime,
+ MatrixType::RowsAtCompileTime>
+ MatrixQType;
+ MatrixType matrix;
+ createRandomPIMatrixOfRank(rank, rows, cols, matrix);
+ CompleteOrthogonalDecomposition<MatrixType> cod(matrix);
+ VERIFY(rank == cod.rank());
+ VERIFY(cols - cod.rank() == cod.dimensionOfKernel());
+ VERIFY(!cod.isInjective());
+ VERIFY(!cod.isInvertible());
+ VERIFY(!cod.isSurjective());
+
+ MatrixQType q = cod.householderQ();
+ VERIFY_IS_UNITARY(q);
+
+ MatrixType z = cod.matrixZ();
+ VERIFY_IS_UNITARY(z);
+
+ MatrixType t;
+ t.setZero(rows, cols);
+ t.topLeftCorner(rank, rank) =
+ cod.matrixT().topLeftCorner(rank, rank).template triangularView<Upper>();
+
+ MatrixType c = q * t * z * cod.colsPermutation().inverse();
+ VERIFY_IS_APPROX(matrix, c);
+
+ check_solverbase<MatrixType, MatrixType>(matrix, cod, rows, cols, cols2);
+
+ // Verify that we get the same minimum-norm solution as the SVD.
+ MatrixType exact_solution = MatrixType::Random(cols, cols2);
+ MatrixType rhs = matrix * exact_solution;
+ MatrixType cod_solution = cod.solve(rhs);
+ JacobiSVD<MatrixType, ComputeThinU | ComputeThinV> svd(matrix);
+ MatrixType svd_solution = svd.solve(rhs);
+ VERIFY_IS_APPROX(cod_solution, svd_solution);
+
+ MatrixType pinv = cod.pseudoInverse();
+ VERIFY_IS_APPROX(cod_solution, pinv * rhs);
+}
+
+template <typename MatrixType, int Cols2>
+void cod_fixedsize() {
+ enum {
+ Rows = MatrixType::RowsAtCompileTime,
+ Cols = MatrixType::ColsAtCompileTime
+ };
+ typedef typename MatrixType::Scalar Scalar;
+ typedef CompleteOrthogonalDecomposition<Matrix<Scalar, Rows, Cols> > COD;
+ int rank = internal::random<int>(1, (std::min)(int(Rows), int(Cols)) - 1);
+ Matrix<Scalar, Rows, Cols> matrix;
+ createRandomPIMatrixOfRank(rank, Rows, Cols, matrix);
+ COD cod(matrix);
+ VERIFY(rank == cod.rank());
+ VERIFY(Cols - cod.rank() == cod.dimensionOfKernel());
+ VERIFY(cod.isInjective() == (rank == Rows));
+ VERIFY(cod.isSurjective() == (rank == Cols));
+ VERIFY(cod.isInvertible() == (cod.isInjective() && cod.isSurjective()));
+
+ check_solverbase<Matrix<Scalar, Cols, Cols2>, Matrix<Scalar, Rows, Cols2> >(matrix, cod, Rows, Cols, Cols2);
+
+ // Verify that we get the same minimum-norm solution as the SVD.
+ Matrix<Scalar, Cols, Cols2> exact_solution;
+ exact_solution.setRandom(Cols, Cols2);
+ Matrix<Scalar, Rows, Cols2> rhs = matrix * exact_solution;
+ Matrix<Scalar, Cols, Cols2> cod_solution = cod.solve(rhs);
+ JacobiSVD<MatrixType, ComputeFullU | ComputeFullV> svd(matrix);
+ Matrix<Scalar, Cols, Cols2> svd_solution = svd.solve(rhs);
+ VERIFY_IS_APPROX(cod_solution, svd_solution);
+
+ typename Inverse<COD>::PlainObject pinv = cod.pseudoInverse();
+ VERIFY_IS_APPROX(cod_solution, pinv * rhs);
+}
+
+template<typename MatrixType> void qr()
+{
+ using std::sqrt;
+
+ STATIC_CHECK(( internal::is_same<typename ColPivHouseholderQR<MatrixType>::StorageIndex,int>::value ));
+
+ Index rows = internal::random<Index>(2,EIGEN_TEST_MAX_SIZE), cols = internal::random<Index>(2,EIGEN_TEST_MAX_SIZE), cols2 = internal::random<Index>(2,EIGEN_TEST_MAX_SIZE);
+ Index rank = internal::random<Index>(1, (std::min)(rows, cols)-1);
+
+ typedef typename MatrixType::Scalar Scalar;
+ typedef typename MatrixType::RealScalar RealScalar;
+ typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime> MatrixQType;
+ MatrixType m1;
+ createRandomPIMatrixOfRank(rank,rows,cols,m1);
+ ColPivHouseholderQR<MatrixType> qr(m1);
+ VERIFY_IS_EQUAL(rank, qr.rank());
+ VERIFY_IS_EQUAL(cols - qr.rank(), qr.dimensionOfKernel());
+ VERIFY(!qr.isInjective());
+ VERIFY(!qr.isInvertible());
+ VERIFY(!qr.isSurjective());
+
+ MatrixQType q = qr.householderQ();
+ VERIFY_IS_UNITARY(q);
+
+ MatrixType r = qr.matrixQR().template triangularView<Upper>();
+ MatrixType c = q * r * qr.colsPermutation().inverse();
+ VERIFY_IS_APPROX(m1, c);
+
+ // Verify that the absolute value of the diagonal elements in R are
+ // non-increasing until they reach the singularity threshold.
+ RealScalar threshold =
+ sqrt(RealScalar(rows)) * numext::abs(r(0, 0)) * NumTraits<Scalar>::epsilon();
+ for (Index i = 0; i < (std::min)(rows, cols) - 1; ++i) {
+ RealScalar x = numext::abs(r(i, i));
+ RealScalar y = numext::abs(r(i + 1, i + 1));
+ if (x < threshold && y < threshold) continue;
+ if (!test_isApproxOrLessThan(y, x)) {
+ for (Index j = 0; j < (std::min)(rows, cols); ++j) {
+ std::cout << "i = " << j << ", |r_ii| = " << numext::abs(r(j, j)) << std::endl;
+ }
+ std::cout << "Failure at i=" << i << ", rank=" << rank
+ << ", threshold=" << threshold << std::endl;
+ }
+ VERIFY_IS_APPROX_OR_LESS_THAN(y, x);
+ }
+
+ check_solverbase<MatrixType, MatrixType>(m1, qr, rows, cols, cols2);
+
+ {
+ MatrixType m2, m3;
+ Index size = rows;
+ do {
+ m1 = MatrixType::Random(size,size);
+ qr.compute(m1);
+ } while(!qr.isInvertible());
+ MatrixType m1_inv = qr.inverse();
+ m3 = m1 * MatrixType::Random(size,cols2);
+ m2 = qr.solve(m3);
+ VERIFY_IS_APPROX(m2, m1_inv*m3);
+ }
+}
+
+template<typename MatrixType, int Cols2> void qr_fixedsize()
+{
+ using std::sqrt;
+ using std::abs;
+ enum { Rows = MatrixType::RowsAtCompileTime, Cols = MatrixType::ColsAtCompileTime };
+ typedef typename MatrixType::Scalar Scalar;
+ typedef typename MatrixType::RealScalar RealScalar;
+ int rank = internal::random<int>(1, (std::min)(int(Rows), int(Cols))-1);
+ Matrix<Scalar,Rows,Cols> m1;
+ createRandomPIMatrixOfRank(rank,Rows,Cols,m1);
+ ColPivHouseholderQR<Matrix<Scalar,Rows,Cols> > qr(m1);
+ VERIFY_IS_EQUAL(rank, qr.rank());
+ VERIFY_IS_EQUAL(Cols - qr.rank(), qr.dimensionOfKernel());
+ VERIFY_IS_EQUAL(qr.isInjective(), (rank == Rows));
+ VERIFY_IS_EQUAL(qr.isSurjective(), (rank == Cols));
+ VERIFY_IS_EQUAL(qr.isInvertible(), (qr.isInjective() && qr.isSurjective()));
+
+ Matrix<Scalar,Rows,Cols> r = qr.matrixQR().template triangularView<Upper>();
+ Matrix<Scalar,Rows,Cols> c = qr.householderQ() * r * qr.colsPermutation().inverse();
+ VERIFY_IS_APPROX(m1, c);
+
+ check_solverbase<Matrix<Scalar,Cols,Cols2>, Matrix<Scalar,Rows,Cols2> >(m1, qr, Rows, Cols, Cols2);
+
+ // Verify that the absolute value of the diagonal elements in R are
+ // non-increasing until they reache the singularity threshold.
+ RealScalar threshold =
+ sqrt(RealScalar(Rows)) * (std::abs)(r(0, 0)) * NumTraits<Scalar>::epsilon();
+ for (Index i = 0; i < (std::min)(int(Rows), int(Cols)) - 1; ++i) {
+ RealScalar x = numext::abs(r(i, i));
+ RealScalar y = numext::abs(r(i + 1, i + 1));
+ if (x < threshold && y < threshold) continue;
+ if (!test_isApproxOrLessThan(y, x)) {
+ for (Index j = 0; j < (std::min)(int(Rows), int(Cols)); ++j) {
+ std::cout << "i = " << j << ", |r_ii| = " << numext::abs(r(j, j)) << std::endl;
+ }
+ std::cout << "Failure at i=" << i << ", rank=" << rank
+ << ", threshold=" << threshold << std::endl;
+ }
+ VERIFY_IS_APPROX_OR_LESS_THAN(y, x);
+ }
+}
+
+// This test is meant to verify that pivots are chosen such that
+// even for a graded matrix, the diagonal of R falls of roughly
+// monotonically until it reaches the threshold for singularity.
+// We use the so-called Kahan matrix, which is a famous counter-example
+// for rank-revealing QR. See
+// http://www.netlib.org/lapack/lawnspdf/lawn176.pdf
+// page 3 for more detail.
+template<typename MatrixType> void qr_kahan_matrix()
+{
+ using std::sqrt;
+ using std::abs;
+ typedef typename MatrixType::Scalar Scalar;
+ typedef typename MatrixType::RealScalar RealScalar;
+
+ Index rows = 300, cols = rows;
+
+ MatrixType m1;
+ m1.setZero(rows,cols);
+ RealScalar s = std::pow(NumTraits<RealScalar>::epsilon(), 1.0 / rows);
+ RealScalar c = std::sqrt(1 - s*s);
+ RealScalar pow_s_i(1.0); // pow(s,i)
+ for (Index i = 0; i < rows; ++i) {
+ m1(i, i) = pow_s_i;
+ m1.row(i).tail(rows - i - 1) = -pow_s_i * c * MatrixType::Ones(1, rows - i - 1);
+ pow_s_i *= s;
+ }
+ m1 = (m1 + m1.transpose()).eval();
+ ColPivHouseholderQR<MatrixType> qr(m1);
+ MatrixType r = qr.matrixQR().template triangularView<Upper>();
+
+ RealScalar threshold =
+ std::sqrt(RealScalar(rows)) * numext::abs(r(0, 0)) * NumTraits<Scalar>::epsilon();
+ for (Index i = 0; i < (std::min)(rows, cols) - 1; ++i) {
+ RealScalar x = numext::abs(r(i, i));
+ RealScalar y = numext::abs(r(i + 1, i + 1));
+ if (x < threshold && y < threshold) continue;
+ if (!test_isApproxOrLessThan(y, x)) {
+ for (Index j = 0; j < (std::min)(rows, cols); ++j) {
+ std::cout << "i = " << j << ", |r_ii| = " << numext::abs(r(j, j)) << std::endl;
+ }
+ std::cout << "Failure at i=" << i << ", rank=" << qr.rank()
+ << ", threshold=" << threshold << std::endl;
+ }
+ VERIFY_IS_APPROX_OR_LESS_THAN(y, x);
+ }
+}
+
+template<typename MatrixType> void qr_invertible()
+{
+ using std::log;
+ using std::abs;
+ typedef typename NumTraits<typename MatrixType::Scalar>::Real RealScalar;
+ typedef typename MatrixType::Scalar Scalar;
+
+ int size = internal::random<int>(10,50);
+
+ MatrixType m1(size, size), m2(size, size), m3(size, size);
+ m1 = MatrixType::Random(size,size);
+
+ if (internal::is_same<RealScalar,float>::value)
+ {
+ // let's build a matrix more stable to inverse
+ MatrixType a = MatrixType::Random(size,size*2);
+ m1 += a * a.adjoint();
+ }
+
+ ColPivHouseholderQR<MatrixType> qr(m1);
+
+ check_solverbase<MatrixType, MatrixType>(m1, qr, size, size, size);
+
+ // now construct a matrix with prescribed determinant
+ m1.setZero();
+ for(int i = 0; i < size; i++) m1(i,i) = internal::random<Scalar>();
+ Scalar det = m1.diagonal().prod();
+ RealScalar absdet = abs(det);
+ m3 = qr.householderQ(); // get a unitary
+ m1 = m3 * m1 * m3.adjoint();
+ qr.compute(m1);
+ VERIFY_IS_APPROX(det, qr.determinant());
+ VERIFY_IS_APPROX(absdet, qr.absDeterminant());
+ VERIFY_IS_APPROX(log(absdet), qr.logAbsDeterminant());
+}
+
+template<typename MatrixType> void qr_verify_assert()
+{
+ MatrixType tmp;
+
+ ColPivHouseholderQR<MatrixType> qr;
+ VERIFY_RAISES_ASSERT(qr.matrixQR())
+ VERIFY_RAISES_ASSERT(qr.solve(tmp))
+ VERIFY_RAISES_ASSERT(qr.transpose().solve(tmp))
+ VERIFY_RAISES_ASSERT(qr.adjoint().solve(tmp))
+ VERIFY_RAISES_ASSERT(qr.householderQ())
+ VERIFY_RAISES_ASSERT(qr.dimensionOfKernel())
+ VERIFY_RAISES_ASSERT(qr.isInjective())
+ VERIFY_RAISES_ASSERT(qr.isSurjective())
+ VERIFY_RAISES_ASSERT(qr.isInvertible())
+ VERIFY_RAISES_ASSERT(qr.inverse())
+ VERIFY_RAISES_ASSERT(qr.determinant())
+ VERIFY_RAISES_ASSERT(qr.absDeterminant())
+ VERIFY_RAISES_ASSERT(qr.logAbsDeterminant())
+}
+
+template<typename MatrixType> void cod_verify_assert()
+{
+ MatrixType tmp;
+
+ CompleteOrthogonalDecomposition<MatrixType> cod;
+ VERIFY_RAISES_ASSERT(cod.matrixQTZ())
+ VERIFY_RAISES_ASSERT(cod.solve(tmp))
+ VERIFY_RAISES_ASSERT(cod.transpose().solve(tmp))
+ VERIFY_RAISES_ASSERT(cod.adjoint().solve(tmp))
+ VERIFY_RAISES_ASSERT(cod.householderQ())
+ VERIFY_RAISES_ASSERT(cod.dimensionOfKernel())
+ VERIFY_RAISES_ASSERT(cod.isInjective())
+ VERIFY_RAISES_ASSERT(cod.isSurjective())
+ VERIFY_RAISES_ASSERT(cod.isInvertible())
+ VERIFY_RAISES_ASSERT(cod.pseudoInverse())
+ VERIFY_RAISES_ASSERT(cod.determinant())
+ VERIFY_RAISES_ASSERT(cod.absDeterminant())
+ VERIFY_RAISES_ASSERT(cod.logAbsDeterminant())
+}
+
+EIGEN_DECLARE_TEST(qr_colpivoting)
+{
+ for(int i = 0; i < g_repeat; i++) {
+ CALL_SUBTEST_1( qr<MatrixXf>() );
+ CALL_SUBTEST_2( qr<MatrixXd>() );
+ CALL_SUBTEST_3( qr<MatrixXcd>() );
+ CALL_SUBTEST_4(( qr_fixedsize<Matrix<float,3,5>, 4 >() ));
+ CALL_SUBTEST_5(( qr_fixedsize<Matrix<double,6,2>, 3 >() ));
+ CALL_SUBTEST_5(( qr_fixedsize<Matrix<double,1,1>, 1 >() ));
+ }
+
+ for(int i = 0; i < g_repeat; i++) {
+ CALL_SUBTEST_1( cod<MatrixXf>() );
+ CALL_SUBTEST_2( cod<MatrixXd>() );
+ CALL_SUBTEST_3( cod<MatrixXcd>() );
+ CALL_SUBTEST_4(( cod_fixedsize<Matrix<float,3,5>, 4 >() ));
+ CALL_SUBTEST_5(( cod_fixedsize<Matrix<double,6,2>, 3 >() ));
+ CALL_SUBTEST_5(( cod_fixedsize<Matrix<double,1,1>, 1 >() ));
+ }
+
+ for(int i = 0; i < g_repeat; i++) {
+ CALL_SUBTEST_1( qr_invertible<MatrixXf>() );
+ CALL_SUBTEST_2( qr_invertible<MatrixXd>() );
+ CALL_SUBTEST_6( qr_invertible<MatrixXcf>() );
+ CALL_SUBTEST_3( qr_invertible<MatrixXcd>() );
+ }
+
+ CALL_SUBTEST_7(qr_verify_assert<Matrix3f>());
+ CALL_SUBTEST_8(qr_verify_assert<Matrix3d>());
+ CALL_SUBTEST_1(qr_verify_assert<MatrixXf>());
+ CALL_SUBTEST_2(qr_verify_assert<MatrixXd>());
+ CALL_SUBTEST_6(qr_verify_assert<MatrixXcf>());
+ CALL_SUBTEST_3(qr_verify_assert<MatrixXcd>());
+
+ CALL_SUBTEST_7(cod_verify_assert<Matrix3f>());
+ CALL_SUBTEST_8(cod_verify_assert<Matrix3d>());
+ CALL_SUBTEST_1(cod_verify_assert<MatrixXf>());
+ CALL_SUBTEST_2(cod_verify_assert<MatrixXd>());
+ CALL_SUBTEST_6(cod_verify_assert<MatrixXcf>());
+ CALL_SUBTEST_3(cod_verify_assert<MatrixXcd>());
+
+ // Test problem size constructors
+ CALL_SUBTEST_9(ColPivHouseholderQR<MatrixXf>(10, 20));
+
+ CALL_SUBTEST_1( qr_kahan_matrix<MatrixXf>() );
+ CALL_SUBTEST_2( qr_kahan_matrix<MatrixXd>() );
+}
diff --git a/test/qr_fullpivoting.cpp b/test/qr_fullpivoting.cpp
new file mode 100644
index 0000000..cca9a8c
--- /dev/null
+++ b/test/qr_fullpivoting.cpp
@@ -0,0 +1,162 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2009 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "main.h"
+#include <Eigen/QR>
+#include "solverbase.h"
+
+template<typename MatrixType> void qr()
+{
+ STATIC_CHECK(( internal::is_same<typename FullPivHouseholderQR<MatrixType>::StorageIndex,int>::value ));
+
+ static const int Rows = MatrixType::RowsAtCompileTime, Cols = MatrixType::ColsAtCompileTime;
+ Index max_size = EIGEN_TEST_MAX_SIZE;
+ Index min_size = numext::maxi(1,EIGEN_TEST_MAX_SIZE/10);
+ Index rows = Rows == Dynamic ? internal::random<Index>(min_size,max_size) : Rows,
+ cols = Cols == Dynamic ? internal::random<Index>(min_size,max_size) : Cols,
+ cols2 = Cols == Dynamic ? internal::random<Index>(min_size,max_size) : Cols,
+ rank = internal::random<Index>(1, (std::min)(rows, cols)-1);
+
+ typedef typename MatrixType::Scalar Scalar;
+ typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime> MatrixQType;
+ MatrixType m1;
+ createRandomPIMatrixOfRank(rank,rows,cols,m1);
+ FullPivHouseholderQR<MatrixType> qr(m1);
+ VERIFY_IS_EQUAL(rank, qr.rank());
+ VERIFY_IS_EQUAL(cols - qr.rank(), qr.dimensionOfKernel());
+ VERIFY(!qr.isInjective());
+ VERIFY(!qr.isInvertible());
+ VERIFY(!qr.isSurjective());
+
+ MatrixType r = qr.matrixQR();
+
+ MatrixQType q = qr.matrixQ();
+ VERIFY_IS_UNITARY(q);
+
+ // FIXME need better way to construct trapezoid
+ for(int i = 0; i < rows; i++) for(int j = 0; j < cols; j++) if(i>j) r(i,j) = Scalar(0);
+
+ MatrixType c = qr.matrixQ() * r * qr.colsPermutation().inverse();
+
+ VERIFY_IS_APPROX(m1, c);
+
+ // stress the ReturnByValue mechanism
+ MatrixType tmp;
+ VERIFY_IS_APPROX(tmp.noalias() = qr.matrixQ() * r, (qr.matrixQ() * r).eval());
+
+ check_solverbase<MatrixType, MatrixType>(m1, qr, rows, cols, cols2);
+
+ {
+ MatrixType m2, m3;
+ Index size = rows;
+ do {
+ m1 = MatrixType::Random(size,size);
+ qr.compute(m1);
+ } while(!qr.isInvertible());
+ MatrixType m1_inv = qr.inverse();
+ m3 = m1 * MatrixType::Random(size,cols2);
+ m2 = qr.solve(m3);
+ VERIFY_IS_APPROX(m2, m1_inv*m3);
+ }
+}
+
+template<typename MatrixType> void qr_invertible()
+{
+ using std::log;
+ using std::abs;
+ typedef typename NumTraits<typename MatrixType::Scalar>::Real RealScalar;
+ typedef typename MatrixType::Scalar Scalar;
+
+ Index max_size = numext::mini(50,EIGEN_TEST_MAX_SIZE);
+ Index min_size = numext::maxi(1,EIGEN_TEST_MAX_SIZE/10);
+ Index size = internal::random<Index>(min_size,max_size);
+
+ MatrixType m1(size, size), m2(size, size), m3(size, size);
+ m1 = MatrixType::Random(size,size);
+
+ if (internal::is_same<RealScalar,float>::value)
+ {
+ // let's build a matrix more stable to inverse
+ MatrixType a = MatrixType::Random(size,size*2);
+ m1 += a * a.adjoint();
+ }
+
+ FullPivHouseholderQR<MatrixType> qr(m1);
+ VERIFY(qr.isInjective());
+ VERIFY(qr.isInvertible());
+ VERIFY(qr.isSurjective());
+
+ check_solverbase<MatrixType, MatrixType>(m1, qr, size, size, size);
+
+ // now construct a matrix with prescribed determinant
+ m1.setZero();
+ for(int i = 0; i < size; i++) m1(i,i) = internal::random<Scalar>();
+ Scalar det = m1.diagonal().prod();
+ RealScalar absdet = abs(det);
+ m3 = qr.matrixQ(); // get a unitary
+ m1 = m3 * m1 * m3.adjoint();
+ qr.compute(m1);
+ VERIFY_IS_APPROX(det, qr.determinant());
+ VERIFY_IS_APPROX(absdet, qr.absDeterminant());
+ VERIFY_IS_APPROX(log(absdet), qr.logAbsDeterminant());
+}
+
+template<typename MatrixType> void qr_verify_assert()
+{
+ MatrixType tmp;
+
+ FullPivHouseholderQR<MatrixType> qr;
+ VERIFY_RAISES_ASSERT(qr.matrixQR())
+ VERIFY_RAISES_ASSERT(qr.solve(tmp))
+ VERIFY_RAISES_ASSERT(qr.transpose().solve(tmp))
+ VERIFY_RAISES_ASSERT(qr.adjoint().solve(tmp))
+ VERIFY_RAISES_ASSERT(qr.matrixQ())
+ VERIFY_RAISES_ASSERT(qr.dimensionOfKernel())
+ VERIFY_RAISES_ASSERT(qr.isInjective())
+ VERIFY_RAISES_ASSERT(qr.isSurjective())
+ VERIFY_RAISES_ASSERT(qr.isInvertible())
+ VERIFY_RAISES_ASSERT(qr.inverse())
+ VERIFY_RAISES_ASSERT(qr.determinant())
+ VERIFY_RAISES_ASSERT(qr.absDeterminant())
+ VERIFY_RAISES_ASSERT(qr.logAbsDeterminant())
+}
+
+EIGEN_DECLARE_TEST(qr_fullpivoting)
+{
+ for(int i = 0; i < 1; i++) {
+ CALL_SUBTEST_5( qr<Matrix3f>() );
+ CALL_SUBTEST_6( qr<Matrix3d>() );
+ CALL_SUBTEST_8( qr<Matrix2f>() );
+ CALL_SUBTEST_1( qr<MatrixXf>() );
+ CALL_SUBTEST_2( qr<MatrixXd>() );
+ CALL_SUBTEST_3( qr<MatrixXcd>() );
+ }
+
+ for(int i = 0; i < g_repeat; i++) {
+ CALL_SUBTEST_1( qr_invertible<MatrixXf>() );
+ CALL_SUBTEST_2( qr_invertible<MatrixXd>() );
+ CALL_SUBTEST_4( qr_invertible<MatrixXcf>() );
+ CALL_SUBTEST_3( qr_invertible<MatrixXcd>() );
+ }
+
+ CALL_SUBTEST_5(qr_verify_assert<Matrix3f>());
+ CALL_SUBTEST_6(qr_verify_assert<Matrix3d>());
+ CALL_SUBTEST_1(qr_verify_assert<MatrixXf>());
+ CALL_SUBTEST_2(qr_verify_assert<MatrixXd>());
+ CALL_SUBTEST_4(qr_verify_assert<MatrixXcf>());
+ CALL_SUBTEST_3(qr_verify_assert<MatrixXcd>());
+
+ // Test problem size constructors
+ CALL_SUBTEST_7(FullPivHouseholderQR<MatrixXf>(10, 20));
+ CALL_SUBTEST_7((FullPivHouseholderQR<Matrix<float,10,20> >(10,20)));
+ CALL_SUBTEST_7((FullPivHouseholderQR<Matrix<float,10,20> >(Matrix<float,10,20>::Random())));
+ CALL_SUBTEST_7((FullPivHouseholderQR<Matrix<float,20,10> >(20,10)));
+ CALL_SUBTEST_7((FullPivHouseholderQR<Matrix<float,20,10> >(Matrix<float,20,10>::Random())));
+}
diff --git a/test/qtvector.cpp b/test/qtvector.cpp
new file mode 100644
index 0000000..4ec79b1
--- /dev/null
+++ b/test/qtvector.cpp
@@ -0,0 +1,156 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#define EIGEN_WORK_AROUND_QT_BUG_CALLING_WRONG_OPERATOR_NEW_FIXED_IN_QT_4_5
+
+#include "main.h"
+#include <QtCore/QVector>
+#include <Eigen/Geometry>
+#include <Eigen/QtAlignedMalloc>
+
+template<typename MatrixType>
+void check_qtvector_matrix(const MatrixType& m)
+{
+ Index rows = m.rows();
+ Index cols = m.cols();
+ MatrixType x = MatrixType::Random(rows,cols), y = MatrixType::Random(rows,cols);
+ QVector<MatrixType> v(10, MatrixType(rows,cols)), w(20, y);
+ for(int i = 0; i < 20; i++)
+ {
+ VERIFY_IS_APPROX(w[i], y);
+ }
+ v[5] = x;
+ w[6] = v[5];
+ VERIFY_IS_APPROX(w[6], v[5]);
+ v = w;
+ for(int i = 0; i < 20; i++)
+ {
+ VERIFY_IS_APPROX(w[i], v[i]);
+ }
+
+ v.resize(21);
+ v[20] = x;
+ VERIFY_IS_APPROX(v[20], x);
+ v.fill(y,22);
+ VERIFY_IS_APPROX(v[21], y);
+ v.push_back(x);
+ VERIFY_IS_APPROX(v[22], x);
+ VERIFY((size_t)&(v[22]) == (size_t)&(v[21]) + sizeof(MatrixType));
+
+ // do a lot of push_back such that the vector gets internally resized
+ // (with memory reallocation)
+ MatrixType* ref = &w[0];
+ for(int i=0; i<30 || ((ref==&w[0]) && i<300); ++i)
+ v.push_back(w[i%w.size()]);
+ for(int i=23; i<v.size(); ++i)
+ {
+ VERIFY(v[i]==w[(i-23)%w.size()]);
+ }
+}
+
+template<typename TransformType>
+void check_qtvector_transform(const TransformType&)
+{
+ typedef typename TransformType::MatrixType MatrixType;
+ TransformType x(MatrixType::Random()), y(MatrixType::Random());
+ QVector<TransformType> v(10), w(20, y);
+ v[5] = x;
+ w[6] = v[5];
+ VERIFY_IS_APPROX(w[6], v[5]);
+ v = w;
+ for(int i = 0; i < 20; i++)
+ {
+ VERIFY_IS_APPROX(w[i], v[i]);
+ }
+
+ v.resize(21);
+ v[20] = x;
+ VERIFY_IS_APPROX(v[20], x);
+ v.fill(y,22);
+ VERIFY_IS_APPROX(v[21], y);
+ v.push_back(x);
+ VERIFY_IS_APPROX(v[22], x);
+ VERIFY((size_t)&(v[22]) == (size_t)&(v[21]) + sizeof(TransformType));
+
+ // do a lot of push_back such that the vector gets internally resized
+ // (with memory reallocation)
+ TransformType* ref = &w[0];
+ for(int i=0; i<30 || ((ref==&w[0]) && i<300); ++i)
+ v.push_back(w[i%w.size()]);
+ for(unsigned int i=23; int(i)<v.size(); ++i)
+ {
+ VERIFY(v[i].matrix()==w[(i-23)%w.size()].matrix());
+ }
+}
+
+template<typename QuaternionType>
+void check_qtvector_quaternion(const QuaternionType&)
+{
+ typedef typename QuaternionType::Coefficients Coefficients;
+ QuaternionType x(Coefficients::Random()), y(Coefficients::Random());
+ QVector<QuaternionType> v(10), w(20, y);
+ v[5] = x;
+ w[6] = v[5];
+ VERIFY_IS_APPROX(w[6], v[5]);
+ v = w;
+ for(int i = 0; i < 20; i++)
+ {
+ VERIFY_IS_APPROX(w[i], v[i]);
+ }
+
+ v.resize(21);
+ v[20] = x;
+ VERIFY_IS_APPROX(v[20], x);
+ v.fill(y,22);
+ VERIFY_IS_APPROX(v[21], y);
+ v.push_back(x);
+ VERIFY_IS_APPROX(v[22], x);
+ VERIFY((size_t)&(v[22]) == (size_t)&(v[21]) + sizeof(QuaternionType));
+
+ // do a lot of push_back such that the vector gets internally resized
+ // (with memory reallocation)
+ QuaternionType* ref = &w[0];
+ for(int i=0; i<30 || ((ref==&w[0]) && i<300); ++i)
+ v.push_back(w[i%w.size()]);
+ for(unsigned int i=23; int(i)<v.size(); ++i)
+ {
+ VERIFY(v[i].coeffs()==w[(i-23)%w.size()].coeffs());
+ }
+}
+
+EIGEN_DECLARE_TEST(qtvector)
+{
+ // some non vectorizable fixed sizes
+ CALL_SUBTEST(check_qtvector_matrix(Vector2f()));
+ CALL_SUBTEST(check_qtvector_matrix(Matrix3f()));
+ CALL_SUBTEST(check_qtvector_matrix(Matrix3d()));
+
+ // some vectorizable fixed sizes
+ CALL_SUBTEST(check_qtvector_matrix(Matrix2f()));
+ CALL_SUBTEST(check_qtvector_matrix(Vector4f()));
+ CALL_SUBTEST(check_qtvector_matrix(Matrix4f()));
+ CALL_SUBTEST(check_qtvector_matrix(Matrix4d()));
+
+ // some dynamic sizes
+ CALL_SUBTEST(check_qtvector_matrix(MatrixXd(1,1)));
+ CALL_SUBTEST(check_qtvector_matrix(VectorXd(20)));
+ CALL_SUBTEST(check_qtvector_matrix(RowVectorXf(20)));
+ CALL_SUBTEST(check_qtvector_matrix(MatrixXcf(10,10)));
+
+ // some Transform
+ CALL_SUBTEST(check_qtvector_transform(Affine2f()));
+ CALL_SUBTEST(check_qtvector_transform(Affine3f()));
+ CALL_SUBTEST(check_qtvector_transform(Affine3d()));
+ //CALL_SUBTEST(check_qtvector_transform(Transform4d()));
+
+ // some Quaternion
+ CALL_SUBTEST(check_qtvector_quaternion(Quaternionf()));
+ CALL_SUBTEST(check_qtvector_quaternion(Quaternionf()));
+}
diff --git a/test/rand.cpp b/test/rand.cpp
new file mode 100644
index 0000000..4d686bf
--- /dev/null
+++ b/test/rand.cpp
@@ -0,0 +1,119 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2015 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "main.h"
+
+typedef long long int64;
+
+template<typename Scalar> Scalar check_in_range(Scalar x, Scalar y)
+{
+ Scalar r = internal::random<Scalar>(x,y);
+ VERIFY(r>=x);
+ if(y>=x)
+ {
+ VERIFY(r<=y);
+ }
+ return r;
+}
+
+template<typename Scalar> void check_all_in_range(Scalar x, Scalar y)
+{
+ Array<int,1,Dynamic> mask(y-x+1);
+ mask.fill(0);
+ long n = (y-x+1)*32;
+ for(long k=0; k<n; ++k)
+ {
+ mask( check_in_range(x,y)-x )++;
+ }
+ for(Index i=0; i<mask.size(); ++i)
+ if(mask(i)==0)
+ std::cout << "WARNING: value " << x+i << " not reached." << std::endl;
+ VERIFY( (mask>0).all() );
+}
+
+template<typename Scalar> void check_histogram(Scalar x, Scalar y, int bins)
+{
+ Array<int,1,Dynamic> hist(bins);
+ hist.fill(0);
+ int f = 100000;
+ int n = bins*f;
+ int64 range = int64(y)-int64(x);
+ int divisor = int((range+1)/bins);
+ assert(((range+1)%bins)==0);
+ for(int k=0; k<n; ++k)
+ {
+ Scalar r = check_in_range(x,y);
+ hist( int((int64(r)-int64(x))/divisor) )++;
+ }
+ VERIFY( (((hist.cast<double>()/double(f))-1.0).abs()<0.03).all() );
+}
+
+EIGEN_DECLARE_TEST(rand)
+{
+ long long_ref = NumTraits<long>::highest()/10;
+ // the minimum guarantees that these conversions are safe
+ auto char_offset = static_cast<signed char>((std::min)(g_repeat, 64));
+ auto short_offset = static_cast<signed short>((std::min)(g_repeat, 8000));
+
+ for(int i = 0; i < g_repeat*10000; i++) {
+ CALL_SUBTEST(check_in_range<float>(10,11));
+ CALL_SUBTEST(check_in_range<float>(1.24234523f,1.24234523f));
+ CALL_SUBTEST(check_in_range<float>(-1,1));
+ CALL_SUBTEST(check_in_range<float>(-1432.2352f,-1432.2352f));
+
+ CALL_SUBTEST(check_in_range<double>(10,11));
+ CALL_SUBTEST(check_in_range<double>(1.24234523,1.24234523));
+ CALL_SUBTEST(check_in_range<double>(-1,1));
+ CALL_SUBTEST(check_in_range<double>(-1432.2352,-1432.2352));
+
+ CALL_SUBTEST(check_in_range<int>(0,-1));
+ CALL_SUBTEST(check_in_range<short>(0,-1));
+ CALL_SUBTEST(check_in_range<long>(0,-1));
+ CALL_SUBTEST(check_in_range<int>(-673456,673456));
+ CALL_SUBTEST(check_in_range<int>(-RAND_MAX+10,RAND_MAX-10));
+ CALL_SUBTEST(check_in_range<short>(-24345,24345));
+ CALL_SUBTEST(check_in_range<long>(-long_ref,long_ref));
+ }
+
+ CALL_SUBTEST(check_all_in_range<signed char>(11,11));
+ CALL_SUBTEST(check_all_in_range<signed char>(11,11+char_offset));
+ CALL_SUBTEST(check_all_in_range<signed char>(-5,5));
+ CALL_SUBTEST(check_all_in_range<signed char>(-11-char_offset,-11));
+ CALL_SUBTEST(check_all_in_range<signed char>(-126,-126+char_offset));
+ CALL_SUBTEST(check_all_in_range<signed char>(126-char_offset,126));
+ CALL_SUBTEST(check_all_in_range<signed char>(-126,126));
+
+ CALL_SUBTEST(check_all_in_range<short>(11,11));
+ CALL_SUBTEST(check_all_in_range<short>(11,11+short_offset));
+ CALL_SUBTEST(check_all_in_range<short>(-5,5));
+ CALL_SUBTEST(check_all_in_range<short>(-11-short_offset,-11));
+ CALL_SUBTEST(check_all_in_range<short>(-24345,-24345+short_offset));
+ CALL_SUBTEST(check_all_in_range<short>(24345,24345+short_offset));
+
+ CALL_SUBTEST(check_all_in_range<int>(11,11));
+ CALL_SUBTEST(check_all_in_range<int>(11,11+g_repeat));
+ CALL_SUBTEST(check_all_in_range<int>(-5,5));
+ CALL_SUBTEST(check_all_in_range<int>(-11-g_repeat,-11));
+ CALL_SUBTEST(check_all_in_range<int>(-673456,-673456+g_repeat));
+ CALL_SUBTEST(check_all_in_range<int>(673456,673456+g_repeat));
+
+ CALL_SUBTEST(check_all_in_range<long>(11,11));
+ CALL_SUBTEST(check_all_in_range<long>(11,11+g_repeat));
+ CALL_SUBTEST(check_all_in_range<long>(-5,5));
+ CALL_SUBTEST(check_all_in_range<long>(-11-g_repeat,-11));
+ CALL_SUBTEST(check_all_in_range<long>(-long_ref,-long_ref+g_repeat));
+ CALL_SUBTEST(check_all_in_range<long>( long_ref, long_ref+g_repeat));
+
+ CALL_SUBTEST(check_histogram<int>(-5,5,11));
+ int bins = 100;
+ CALL_SUBTEST(check_histogram<int>(-3333,-3333+bins*(3333/bins)-1,bins));
+ bins = 1000;
+ CALL_SUBTEST(check_histogram<int>(-RAND_MAX+10,-RAND_MAX+10+bins*(RAND_MAX/bins)-1,bins));
+ CALL_SUBTEST(check_histogram<int>(-RAND_MAX+10,-int64(RAND_MAX)+10+bins*(2*int64(RAND_MAX)/bins)-1,bins));
+}
diff --git a/test/random_matrix.cpp b/test/random_matrix.cpp
new file mode 100644
index 0000000..873845f
--- /dev/null
+++ b/test/random_matrix.cpp
@@ -0,0 +1,136 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2021 Kolja Brix <kolja.brix@rwth-aachen.de>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "main.h"
+#include <Eigen/SVD>
+
+
+template<typename MatrixType>
+void check_generateRandomUnitaryMatrix(const Index dim)
+{
+ const MatrixType Q = generateRandomUnitaryMatrix<MatrixType>(dim);
+
+ // validate dimensions
+ VERIFY_IS_EQUAL(Q.rows(), dim);
+ VERIFY_IS_EQUAL(Q.cols(), dim);
+
+ VERIFY_IS_UNITARY(Q);
+}
+
+template<typename VectorType, typename RealScalarType>
+void check_setupRandomSvs(const Index dim, const RealScalarType max)
+{
+ const VectorType v = setupRandomSvs<VectorType, RealScalarType>(dim, max);
+
+ // validate dimensions
+ VERIFY_IS_EQUAL(v.size(), dim);
+
+ // check entries
+ for(Index i = 0; i < v.size(); ++i)
+ VERIFY_GE(v(i), 0);
+ for(Index i = 0; i < v.size()-1; ++i)
+ VERIFY_GE(v(i), v(i+1));
+}
+
+template<typename VectorType, typename RealScalarType>
+void check_setupRangeSvs(const Index dim, const RealScalarType min, const RealScalarType max)
+{
+ const VectorType v = setupRangeSvs<VectorType, RealScalarType>(dim, min, max);
+
+ // validate dimensions
+ VERIFY_IS_EQUAL(v.size(), dim);
+
+ // check entries
+ if(dim == 1) {
+ VERIFY_IS_APPROX(v(0), min);
+ } else {
+ VERIFY_IS_APPROX(v(0), max);
+ VERIFY_IS_APPROX(v(dim-1), min);
+ }
+ for(Index i = 0; i < v.size()-1; ++i)
+ VERIFY_GE(v(i), v(i+1));
+}
+
+template<typename MatrixType, typename RealScalar, typename RealVectorType>
+void check_generateRandomMatrixSvs(const Index rows, const Index cols, const Index diag_size,
+ const RealScalar min_svs, const RealScalar max_svs)
+{
+ RealVectorType svs = setupRangeSvs<RealVectorType, RealScalar>(diag_size, min_svs, max_svs);
+
+ MatrixType M;
+ generateRandomMatrixSvs(svs, rows, cols, M);
+
+ // validate dimensions
+ VERIFY_IS_EQUAL(M.rows(), rows);
+ VERIFY_IS_EQUAL(M.cols(), cols);
+ VERIFY_IS_EQUAL(svs.size(), diag_size);
+
+ // validate singular values
+ Eigen::JacobiSVD<MatrixType> SVD(M);
+ VERIFY_IS_APPROX(svs, SVD.singularValues());
+}
+
+template<typename MatrixType>
+void check_random_matrix(const MatrixType &m)
+{
+ enum {
+ Rows = MatrixType::RowsAtCompileTime,
+ Cols = MatrixType::ColsAtCompileTime,
+ DiagSize = internal::min_size_prefer_dynamic(Rows, Cols)
+ };
+ typedef typename MatrixType::Scalar Scalar;
+ typedef typename NumTraits<Scalar>::Real RealScalar;
+ typedef Matrix<RealScalar, DiagSize, 1> RealVectorType;
+
+ const Index rows = m.rows(), cols = m.cols();
+ const Index diag_size = (std::min)(rows, cols);
+ const RealScalar min_svs = 1.0, max_svs = 1000.0;
+
+ // check generation of unitary random matrices
+ typedef Matrix<Scalar, Rows, Rows> MatrixAType;
+ typedef Matrix<Scalar, Cols, Cols> MatrixBType;
+ check_generateRandomUnitaryMatrix<MatrixAType>(rows);
+ check_generateRandomUnitaryMatrix<MatrixBType>(cols);
+
+ // test generators for singular values
+ check_setupRandomSvs<RealVectorType, RealScalar>(diag_size, max_svs);
+ check_setupRangeSvs<RealVectorType, RealScalar>(diag_size, min_svs, max_svs);
+
+ // check generation of random matrices
+ check_generateRandomMatrixSvs<MatrixType, RealScalar, RealVectorType>(rows, cols, diag_size, min_svs, max_svs);
+}
+
+EIGEN_DECLARE_TEST(random_matrix)
+{
+ for(int i = 0; i < g_repeat; i++) {
+ CALL_SUBTEST_1(check_random_matrix(Matrix<float, 1, 1>()));
+ CALL_SUBTEST_2(check_random_matrix(Matrix<float, 4, 4>()));
+ CALL_SUBTEST_3(check_random_matrix(Matrix<float, 2, 3>()));
+ CALL_SUBTEST_4(check_random_matrix(Matrix<float, 7, 4>()));
+
+ CALL_SUBTEST_5(check_random_matrix(Matrix<double, 1, 1>()));
+ CALL_SUBTEST_6(check_random_matrix(Matrix<double, 6, 6>()));
+ CALL_SUBTEST_7(check_random_matrix(Matrix<double, 5, 3>()));
+ CALL_SUBTEST_8(check_random_matrix(Matrix<double, 4, 9>()));
+
+ CALL_SUBTEST_9(check_random_matrix(Matrix<std::complex<float>, 12, 12>()));
+ CALL_SUBTEST_10(check_random_matrix(Matrix<std::complex<float>, 7, 14>()));
+ CALL_SUBTEST_11(check_random_matrix(Matrix<std::complex<double>, 15, 11>()));
+ CALL_SUBTEST_12(check_random_matrix(Matrix<std::complex<double>, 6, 9>()));
+
+ CALL_SUBTEST_13(check_random_matrix(
+ MatrixXf(internal::random<int>(1, EIGEN_TEST_MAX_SIZE), internal::random<int>(1, EIGEN_TEST_MAX_SIZE))));
+ CALL_SUBTEST_14(check_random_matrix(
+ MatrixXd(internal::random<int>(1, EIGEN_TEST_MAX_SIZE), internal::random<int>(1, EIGEN_TEST_MAX_SIZE))));
+ CALL_SUBTEST_15(check_random_matrix(
+ MatrixXcf(internal::random<int>(1, EIGEN_TEST_MAX_SIZE), internal::random<int>(1, EIGEN_TEST_MAX_SIZE))));
+ CALL_SUBTEST_16(check_random_matrix(
+ MatrixXcd(internal::random<int>(1, EIGEN_TEST_MAX_SIZE), internal::random<int>(1, EIGEN_TEST_MAX_SIZE))));
+ }
+}
diff --git a/test/random_matrix_helper.h b/test/random_matrix_helper.h
new file mode 100644
index 0000000..733dec5
--- /dev/null
+++ b/test/random_matrix_helper.h
@@ -0,0 +1,256 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2021 Kolja Brix <kolja.brix@rwth-aachen.de>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_RANDOM_MATRIX_HELPER
+#define EIGEN_RANDOM_MATRIX_HELPER
+
+#include <typeinfo>
+#include <Eigen/QR> // required for createRandomPIMatrixOfRank and generateRandomMatrixSvs
+
+
+// Forward declarations to avoid ICC warnings
+#if EIGEN_COMP_ICC
+
+namespace Eigen {
+
+template<typename MatrixType>
+void createRandomPIMatrixOfRank(Index desired_rank, Index rows, Index cols, MatrixType& m);
+
+template<typename PermutationVectorType>
+void randomPermutationVector(PermutationVectorType& v, Index size);
+
+template<typename MatrixType>
+MatrixType generateRandomUnitaryMatrix(const Index dim);
+
+template<typename MatrixType, typename RealScalarVectorType>
+void generateRandomMatrixSvs(const RealScalarVectorType &svs, const Index rows, const Index cols, MatrixType& M);
+
+template<typename VectorType, typename RealScalar>
+VectorType setupRandomSvs(const Index dim, const RealScalar max);
+
+template<typename VectorType, typename RealScalar>
+VectorType setupRangeSvs(const Index dim, const RealScalar min, const RealScalar max);
+
+} // end namespace Eigen
+
+#endif // EIGEN_COMP_ICC
+
+
+
+namespace Eigen {
+
+/**
+ * Creates a random partial isometry matrix of given rank.
+ *
+ * A partial isometry is a matrix all of whose singular values are either 0 or 1.
+ * This is very useful to test rank-revealing algorithms.
+ *
+ * @tparam MatrixType type of random partial isometry matrix
+ * @param desired_rank rank requested for the random partial isometry matrix
+ * @param rows row dimension of requested random partial isometry matrix
+ * @param cols column dimension of requested random partial isometry matrix
+ * @param m random partial isometry matrix
+ */
+template<typename MatrixType>
+void createRandomPIMatrixOfRank(Index desired_rank, Index rows, Index cols, MatrixType& m)
+{
+ typedef typename internal::traits<MatrixType>::Scalar Scalar;
+ enum { Rows = MatrixType::RowsAtCompileTime, Cols = MatrixType::ColsAtCompileTime };
+
+ typedef Matrix<Scalar, Dynamic, 1> VectorType;
+ typedef Matrix<Scalar, Rows, Rows> MatrixAType;
+ typedef Matrix<Scalar, Cols, Cols> MatrixBType;
+
+ if(desired_rank == 0)
+ {
+ m.setZero(rows,cols);
+ return;
+ }
+
+ if(desired_rank == 1)
+ {
+ // here we normalize the vectors to get a partial isometry
+ m = VectorType::Random(rows).normalized() * VectorType::Random(cols).normalized().transpose();
+ return;
+ }
+
+ MatrixAType a = MatrixAType::Random(rows,rows);
+ MatrixType d = MatrixType::Identity(rows,cols);
+ MatrixBType b = MatrixBType::Random(cols,cols);
+
+ // set the diagonal such that only desired_rank non-zero entries remain
+ const Index diag_size = (std::min)(d.rows(),d.cols());
+ if(diag_size != desired_rank)
+ d.diagonal().segment(desired_rank, diag_size-desired_rank) = VectorType::Zero(diag_size-desired_rank);
+
+ HouseholderQR<MatrixAType> qra(a);
+ HouseholderQR<MatrixBType> qrb(b);
+ m = qra.householderQ() * d * qrb.householderQ();
+}
+
+/**
+ * Generate random permutation vector.
+ *
+ * @tparam PermutationVectorType type of vector used to store permutation
+ * @param v permutation vector
+ * @param size length of permutation vector
+ */
+template<typename PermutationVectorType>
+void randomPermutationVector(PermutationVectorType& v, Index size)
+{
+ typedef typename PermutationVectorType::Scalar Scalar;
+ v.resize(size);
+ for(Index i = 0; i < size; ++i) v(i) = Scalar(i);
+ if(size == 1) return;
+ for(Index n = 0; n < 3 * size; ++n)
+ {
+ Index i = internal::random<Index>(0, size-1);
+ Index j;
+ do j = internal::random<Index>(0, size-1); while(j==i);
+ std::swap(v(i), v(j));
+ }
+}
+
+/**
+ * Generate a random unitary matrix of prescribed dimension.
+ *
+ * The algorithm is using a random Householder sequence to produce
+ * a random unitary matrix.
+ *
+ * @tparam MatrixType type of matrix to generate
+ * @param dim row and column dimension of the requested square matrix
+ * @return random unitary matrix
+ */
+template<typename MatrixType>
+MatrixType generateRandomUnitaryMatrix(const Index dim)
+{
+ typedef typename internal::traits<MatrixType>::Scalar Scalar;
+ typedef Matrix<Scalar, Dynamic, 1> VectorType;
+
+ MatrixType v = MatrixType::Identity(dim, dim);
+ VectorType h = VectorType::Zero(dim);
+ for (Index i = 0; i < dim; ++i)
+ {
+ v.col(i).tail(dim - i - 1) = VectorType::Random(dim - i - 1);
+ h(i) = 2 / v.col(i).tail(dim - i).squaredNorm();
+ }
+
+ const Eigen::HouseholderSequence<MatrixType, VectorType> HSeq(v, h);
+ return MatrixType(HSeq);
+}
+
+/**
+ * Generation of random matrix with prescribed singular values.
+ *
+ * We generate random matrices with given singular values by setting up
+ * a singular value decomposition. By choosing the number of zeros as
+ * singular values we can specify the rank of the matrix.
+ * Moreover, we also control its spectral norm, which is the largest
+ * singular value, as well as its condition number with respect to the
+ * l2-norm, which is the quotient of the largest and smallest singular
+ * value.
+ *
+ * Reference: For details on the method see e.g. Section 8.1 (pp. 62 f) in
+ *
+ * C. C. Paige, M. A. Saunders,
+ * LSQR: An algorithm for sparse linear equations and sparse least squares.
+ * ACM Transactions on Mathematical Software 8(1), pp. 43-71, 1982.
+ * https://web.stanford.edu/group/SOL/software/lsqr/lsqr-toms82a.pdf
+ *
+ * and also the LSQR webpage https://web.stanford.edu/group/SOL/software/lsqr/.
+ *
+ * @tparam MatrixType matrix type to generate
+ * @tparam RealScalarVectorType vector type with real entries used for singular values
+ * @param svs vector of desired singular values
+ * @param rows row dimension of requested random matrix
+ * @param cols column dimension of requested random matrix
+ * @param M generated matrix with prescribed singular values
+ */
+template<typename MatrixType, typename RealScalarVectorType>
+void generateRandomMatrixSvs(const RealScalarVectorType &svs, const Index rows, const Index cols, MatrixType& M)
+{
+ enum { Rows = MatrixType::RowsAtCompileTime, Cols = MatrixType::ColsAtCompileTime };
+ typedef typename internal::traits<MatrixType>::Scalar Scalar;
+ typedef Matrix<Scalar, Rows, Rows> MatrixAType;
+ typedef Matrix<Scalar, Cols, Cols> MatrixBType;
+
+ const Index min_dim = (std::min)(rows, cols);
+
+ const MatrixAType U = generateRandomUnitaryMatrix<MatrixAType>(rows);
+ const MatrixBType V = generateRandomUnitaryMatrix<MatrixBType>(cols);
+
+ M = U.block(0, 0, rows, min_dim) * svs.asDiagonal() * V.block(0, 0, cols, min_dim).transpose();
+}
+
+/**
+ * Setup a vector of random singular values with prescribed upper limit.
+ * For use with generateRandomMatrixSvs().
+ *
+ * Singular values are non-negative real values. By convention (to be consistent with
+ * singular value decomposition) we sort them in decreasing order.
+ *
+ * This strategy produces random singular values in the range [0, max], in particular
+ * the singular values can be zero or arbitrarily close to zero.
+ *
+ * @tparam VectorType vector type with real entries used for singular values
+ * @tparam RealScalar data type used for real entry
+ * @param dim number of singular values to generate
+ * @param max upper bound for singular values
+ * @return vector of singular values
+ */
+template<typename VectorType, typename RealScalar>
+VectorType setupRandomSvs(const Index dim, const RealScalar max)
+{
+ VectorType svs = max / RealScalar(2) * (VectorType::Random(dim) + VectorType::Ones(dim));
+ std::sort(svs.begin(), svs.end(), std::greater<RealScalar>());
+ return svs;
+}
+
+/**
+ * Setup a vector of random singular values with prescribed range.
+ * For use with generateRandomMatrixSvs().
+ *
+ * Singular values are non-negative real values. By convention (to be consistent with
+ * singular value decomposition) we sort them in decreasing order.
+ *
+ * For dim > 1 this strategy generates a vector with largest entry max, smallest entry
+ * min, and remaining entries in the range [min, max]. For dim == 1 the only entry is
+ * min.
+ *
+ * @tparam VectorType vector type with real entries used for singular values
+ * @tparam RealScalar data type used for real entry
+ * @param dim number of singular values to generate
+ * @param min smallest singular value to use
+ * @param max largest singular value to use
+ * @return vector of singular values
+ */
+template<typename VectorType, typename RealScalar>
+VectorType setupRangeSvs(const Index dim, const RealScalar min, const RealScalar max)
+{
+ VectorType svs = VectorType::Random(dim);
+ if(dim == 0)
+ return svs;
+ if(dim == 1)
+ {
+ svs(0) = min;
+ return svs;
+ }
+ std::sort(svs.begin(), svs.end(), std::greater<RealScalar>());
+
+ // scale to range [min, max]
+ const RealScalar c_min = svs(dim - 1), c_max = svs(0);
+ svs = (svs - VectorType::Constant(dim, c_min)) / (c_max - c_min);
+ return min * (VectorType::Ones(dim) - svs) + max * svs;
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_RANDOM_MATRIX_HELPER
diff --git a/test/random_without_cast_overflow.h b/test/random_without_cast_overflow.h
new file mode 100644
index 0000000..7f1ea5f
--- /dev/null
+++ b/test/random_without_cast_overflow.h
@@ -0,0 +1,152 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2020 C. Antonio Sanchez <cantonios@google.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+// Utilities for generating random numbers without overflows, which might
+// otherwise result in undefined behavior.
+
+namespace Eigen {
+namespace internal {
+
+// Default implementation assuming SrcScalar fits into TgtScalar.
+template <typename SrcScalar, typename TgtScalar, typename EnableIf = void>
+struct random_without_cast_overflow {
+ static SrcScalar value() { return internal::random<SrcScalar>(); }
+};
+
+// Signed to unsigned integer widening cast.
+template <typename SrcScalar, typename TgtScalar>
+struct random_without_cast_overflow<
+ SrcScalar, TgtScalar,
+ std::enable_if_t<NumTraits<SrcScalar>::IsInteger && NumTraits<TgtScalar>::IsInteger &&
+ !NumTraits<TgtScalar>::IsSigned &&
+ (std::numeric_limits<SrcScalar>::digits < std::numeric_limits<TgtScalar>::digits ||
+ (std::numeric_limits<SrcScalar>::digits == std::numeric_limits<TgtScalar>::digits &&
+ NumTraits<SrcScalar>::IsSigned))>> {
+ static SrcScalar value() {
+ SrcScalar a = internal::random<SrcScalar>();
+ return a < SrcScalar(0) ? -(a + 1) : a;
+ }
+};
+
+// Integer to unsigned narrowing cast.
+template <typename SrcScalar, typename TgtScalar>
+struct random_without_cast_overflow<
+ SrcScalar, TgtScalar,
+ std::enable_if_t<
+ NumTraits<SrcScalar>::IsInteger && NumTraits<TgtScalar>::IsInteger && !NumTraits<SrcScalar>::IsSigned &&
+ (std::numeric_limits<SrcScalar>::digits > std::numeric_limits<TgtScalar>::digits)>> {
+ static SrcScalar value() {
+ TgtScalar b = internal::random<TgtScalar>();
+ return static_cast<SrcScalar>(b < TgtScalar(0) ? -(b + 1) : b);
+ }
+};
+
+// Integer to signed narrowing cast.
+template <typename SrcScalar, typename TgtScalar>
+struct random_without_cast_overflow<
+ SrcScalar, TgtScalar,
+ std::enable_if_t<
+ NumTraits<SrcScalar>::IsInteger && NumTraits<TgtScalar>::IsInteger && NumTraits<SrcScalar>::IsSigned &&
+ (std::numeric_limits<SrcScalar>::digits > std::numeric_limits<TgtScalar>::digits)>> {
+ static SrcScalar value() { return static_cast<SrcScalar>(internal::random<TgtScalar>()); }
+};
+
+// Unsigned to signed integer narrowing cast.
+template <typename SrcScalar, typename TgtScalar>
+struct random_without_cast_overflow<
+ SrcScalar, TgtScalar,
+ std::enable_if_t<NumTraits<SrcScalar>::IsInteger && NumTraits<TgtScalar>::IsInteger &&
+ !NumTraits<SrcScalar>::IsSigned && NumTraits<TgtScalar>::IsSigned &&
+ (std::numeric_limits<SrcScalar>::digits ==
+ std::numeric_limits<TgtScalar>::digits)>> {
+ static SrcScalar value() { return internal::random<SrcScalar>() / 2; }
+};
+
+// Floating-point to integer, full precision.
+template <typename SrcScalar, typename TgtScalar>
+struct random_without_cast_overflow<
+ SrcScalar, TgtScalar,
+ std::enable_if_t<
+ !NumTraits<SrcScalar>::IsInteger && !NumTraits<SrcScalar>::IsComplex && NumTraits<TgtScalar>::IsInteger &&
+ (std::numeric_limits<TgtScalar>::digits <= std::numeric_limits<SrcScalar>::digits)>> {
+ static SrcScalar value() { return static_cast<SrcScalar>(internal::random<TgtScalar>()); }
+};
+
+// Floating-point to integer, narrowing precision.
+template <typename SrcScalar, typename TgtScalar>
+struct random_without_cast_overflow<
+ SrcScalar, TgtScalar,
+ std::enable_if_t<
+ !NumTraits<SrcScalar>::IsInteger && !NumTraits<SrcScalar>::IsComplex && NumTraits<TgtScalar>::IsInteger &&
+ (std::numeric_limits<TgtScalar>::digits > std::numeric_limits<SrcScalar>::digits)>> {
+ static SrcScalar value() {
+ // NOTE: internal::random<T>() is limited by RAND_MAX, so random<int64_t> is always within that range.
+ // This prevents us from simply shifting bits, which would result in only 0 or -1.
+ // Instead, keep least-significant K bits and sign.
+ static const TgtScalar KeepMask = (static_cast<TgtScalar>(1) << std::numeric_limits<SrcScalar>::digits) - 1;
+ const TgtScalar a = internal::random<TgtScalar>();
+ return static_cast<SrcScalar>(a > TgtScalar(0) ? (a & KeepMask) : -(a & KeepMask));
+ }
+};
+
+// Integer to floating-point, re-use above logic.
+template <typename SrcScalar, typename TgtScalar>
+struct random_without_cast_overflow<
+ SrcScalar, TgtScalar,
+ std::enable_if_t<NumTraits<SrcScalar>::IsInteger && !NumTraits<TgtScalar>::IsInteger &&
+ !NumTraits<TgtScalar>::IsComplex>> {
+ static SrcScalar value() {
+ return static_cast<SrcScalar>(random_without_cast_overflow<TgtScalar, SrcScalar>::value());
+ }
+};
+
+// Floating-point narrowing conversion.
+template <typename SrcScalar, typename TgtScalar>
+struct random_without_cast_overflow<
+ SrcScalar, TgtScalar,
+ std::enable_if_t<!NumTraits<SrcScalar>::IsInteger && !NumTraits<SrcScalar>::IsComplex &&
+ !NumTraits<TgtScalar>::IsInteger && !NumTraits<TgtScalar>::IsComplex &&
+ (std::numeric_limits<SrcScalar>::digits >
+ std::numeric_limits<TgtScalar>::digits)>> {
+ static SrcScalar value() { return static_cast<SrcScalar>(internal::random<TgtScalar>()); }
+};
+
+// Complex to non-complex.
+template <typename SrcScalar, typename TgtScalar>
+struct random_without_cast_overflow<
+ SrcScalar, TgtScalar,
+ std::enable_if_t<NumTraits<SrcScalar>::IsComplex && !NumTraits<TgtScalar>::IsComplex>> {
+ typedef typename NumTraits<SrcScalar>::Real SrcReal;
+ static SrcScalar value() { return SrcScalar(random_without_cast_overflow<SrcReal, TgtScalar>::value(), 0); }
+};
+
+// Non-complex to complex.
+template <typename SrcScalar, typename TgtScalar>
+struct random_without_cast_overflow<
+ SrcScalar, TgtScalar,
+ std::enable_if_t<!NumTraits<SrcScalar>::IsComplex && NumTraits<TgtScalar>::IsComplex>> {
+ typedef typename NumTraits<TgtScalar>::Real TgtReal;
+ static SrcScalar value() { return random_without_cast_overflow<SrcScalar, TgtReal>::value(); }
+};
+
+// Complex to complex.
+template <typename SrcScalar, typename TgtScalar>
+struct random_without_cast_overflow<
+ SrcScalar, TgtScalar,
+ std::enable_if_t<NumTraits<SrcScalar>::IsComplex && NumTraits<TgtScalar>::IsComplex>> {
+ typedef typename NumTraits<SrcScalar>::Real SrcReal;
+ typedef typename NumTraits<TgtScalar>::Real TgtReal;
+ static SrcScalar value() {
+ return SrcScalar(random_without_cast_overflow<SrcReal, TgtReal>::value(),
+ random_without_cast_overflow<SrcReal, TgtReal>::value());
+ }
+};
+
+} // namespace internal
+} // namespace Eigen
diff --git a/test/real_qz.cpp b/test/real_qz.cpp
new file mode 100644
index 0000000..ea4a270
--- /dev/null
+++ b/test/real_qz.cpp
@@ -0,0 +1,94 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2012 Alexey Korepanov <kaikaikai@yandex.ru>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#define EIGEN_RUNTIME_NO_MALLOC
+#include "main.h"
+#include <limits>
+#include <Eigen/Eigenvalues>
+
+template<typename MatrixType> void real_qz(const MatrixType& m)
+{
+ /* this test covers the following files:
+ RealQZ.h
+ */
+ using std::abs;
+
+ Index dim = m.cols();
+
+ MatrixType A = MatrixType::Random(dim,dim),
+ B = MatrixType::Random(dim,dim);
+
+
+ // Regression test for bug 985: Randomly set rows or columns to zero
+ Index k=internal::random<Index>(0, dim-1);
+ switch(internal::random<int>(0,10)) {
+ case 0:
+ A.row(k).setZero(); break;
+ case 1:
+ A.col(k).setZero(); break;
+ case 2:
+ B.row(k).setZero(); break;
+ case 3:
+ B.col(k).setZero(); break;
+ default:
+ break;
+ }
+
+ RealQZ<MatrixType> qz(dim);
+ // TODO enable full-prealocation of required memory, this probably requires an in-place mode for HessenbergDecomposition
+ //Eigen::internal::set_is_malloc_allowed(false);
+ qz.compute(A,B);
+ //Eigen::internal::set_is_malloc_allowed(true);
+
+ VERIFY_IS_EQUAL(qz.info(), Success);
+ // check for zeros
+ bool all_zeros = true;
+ for (Index i=0; i<A.cols(); i++)
+ for (Index j=0; j<i; j++) {
+ if (!numext::is_exactly_zero(abs(qz.matrixT()(i, j))))
+ {
+ std::cerr << "Error: T(" << i << "," << j << ") = " << qz.matrixT()(i,j) << std::endl;
+ all_zeros = false;
+ }
+ if (j<i-1 && !numext::is_exactly_zero(abs(qz.matrixS()(i, j))))
+ {
+ std::cerr << "Error: S(" << i << "," << j << ") = " << qz.matrixS()(i,j) << std::endl;
+ all_zeros = false;
+ }
+ if (j==i-1 && j>0 && !numext::is_exactly_zero(abs(qz.matrixS()(i, j))) &&
+ !numext::is_exactly_zero(abs(qz.matrixS()(i - 1, j - 1))))
+ {
+ std::cerr << "Error: S(" << i << "," << j << ") = " << qz.matrixS()(i,j) << " && S(" << i-1 << "," << j-1 << ") = " << qz.matrixS()(i-1,j-1) << std::endl;
+ all_zeros = false;
+ }
+ }
+ VERIFY_IS_EQUAL(all_zeros, true);
+ VERIFY_IS_APPROX(qz.matrixQ()*qz.matrixS()*qz.matrixZ(), A);
+ VERIFY_IS_APPROX(qz.matrixQ()*qz.matrixT()*qz.matrixZ(), B);
+ VERIFY_IS_APPROX(qz.matrixQ()*qz.matrixQ().adjoint(), MatrixType::Identity(dim,dim));
+ VERIFY_IS_APPROX(qz.matrixZ()*qz.matrixZ().adjoint(), MatrixType::Identity(dim,dim));
+}
+
+EIGEN_DECLARE_TEST(real_qz)
+{
+ int s = 0;
+ for(int i = 0; i < g_repeat; i++) {
+ CALL_SUBTEST_1( real_qz(Matrix4f()) );
+ s = internal::random<int>(1,EIGEN_TEST_MAX_SIZE/4);
+ CALL_SUBTEST_2( real_qz(MatrixXd(s,s)) );
+
+ // some trivial but implementation-wise tricky cases
+ CALL_SUBTEST_2( real_qz(MatrixXd(1,1)) );
+ CALL_SUBTEST_2( real_qz(MatrixXd(2,2)) );
+ CALL_SUBTEST_3( real_qz(Matrix<double,1,1>()) );
+ CALL_SUBTEST_4( real_qz(Matrix2d()) );
+ }
+
+ TEST_SET_BUT_UNUSED_VARIABLE(s)
+}
diff --git a/test/redux.cpp b/test/redux.cpp
new file mode 100644
index 0000000..fdbab77
--- /dev/null
+++ b/test/redux.cpp
@@ -0,0 +1,183 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+// Copyright (C) 2015 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#define TEST_ENABLE_TEMPORARY_TRACKING
+#define EIGEN_CACHEFRIENDLY_PRODUCT_THRESHOLD 8
+// ^^ see bug 1449
+
+#include "main.h"
+
+template<typename MatrixType> void matrixRedux(const MatrixType& m)
+{
+ typedef typename MatrixType::Scalar Scalar;
+ typedef typename MatrixType::RealScalar RealScalar;
+
+ Index rows = m.rows();
+ Index cols = m.cols();
+
+ MatrixType m1 = MatrixType::Random(rows, cols);
+
+ // The entries of m1 are uniformly distributed in [0,1], so m1.prod() is very small. This may lead to test
+ // failures if we underflow into denormals. Thus, we scale so that entries are close to 1.
+ MatrixType m1_for_prod = MatrixType::Ones(rows, cols) + RealScalar(0.2) * m1;
+
+ Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime> m2(rows,rows);
+ m2.setRandom();
+
+ VERIFY_IS_MUCH_SMALLER_THAN(MatrixType::Zero(rows, cols).sum(), Scalar(1));
+ VERIFY_IS_APPROX(MatrixType::Ones(rows, cols).sum(), Scalar(float(rows*cols))); // the float() here to shut up excessive MSVC warning about int->complex conversion being lossy
+ Scalar s(0), p(1), minc(numext::real(m1.coeff(0))), maxc(numext::real(m1.coeff(0)));
+ for(int j = 0; j < cols; j++)
+ for(int i = 0; i < rows; i++)
+ {
+ s += m1(i,j);
+ p *= m1_for_prod(i,j);
+ minc = (std::min)(numext::real(minc), numext::real(m1(i,j)));
+ maxc = (std::max)(numext::real(maxc), numext::real(m1(i,j)));
+ }
+ const Scalar mean = s/Scalar(RealScalar(rows*cols));
+
+ VERIFY_IS_APPROX(m1.sum(), s);
+ VERIFY_IS_APPROX(m1.mean(), mean);
+ VERIFY_IS_APPROX(m1_for_prod.prod(), p);
+ VERIFY_IS_APPROX(m1.real().minCoeff(), numext::real(minc));
+ VERIFY_IS_APPROX(m1.real().maxCoeff(), numext::real(maxc));
+
+ // test that partial reduction works if nested expressions is forced to evaluate early
+ VERIFY_IS_APPROX((m1.matrix() * m1.matrix().transpose()) .cwiseProduct(m2.matrix()).rowwise().sum().sum(),
+ (m1.matrix() * m1.matrix().transpose()).eval().cwiseProduct(m2.matrix()).rowwise().sum().sum());
+
+ // test slice vectorization assuming assign is ok
+ Index r0 = internal::random<Index>(0,rows-1);
+ Index c0 = internal::random<Index>(0,cols-1);
+ Index r1 = internal::random<Index>(r0+1,rows)-r0;
+ Index c1 = internal::random<Index>(c0+1,cols)-c0;
+ VERIFY_IS_APPROX(m1.block(r0,c0,r1,c1).sum(), m1.block(r0,c0,r1,c1).eval().sum());
+ VERIFY_IS_APPROX(m1.block(r0,c0,r1,c1).mean(), m1.block(r0,c0,r1,c1).eval().mean());
+ VERIFY_IS_APPROX(m1_for_prod.block(r0,c0,r1,c1).prod(), m1_for_prod.block(r0,c0,r1,c1).eval().prod());
+ VERIFY_IS_APPROX(m1.block(r0,c0,r1,c1).real().minCoeff(), m1.block(r0,c0,r1,c1).real().eval().minCoeff());
+ VERIFY_IS_APPROX(m1.block(r0,c0,r1,c1).real().maxCoeff(), m1.block(r0,c0,r1,c1).real().eval().maxCoeff());
+
+ // regression for bug 1090
+ const int R1 = MatrixType::RowsAtCompileTime>=2 ? MatrixType::RowsAtCompileTime/2 : 6;
+ const int C1 = MatrixType::ColsAtCompileTime>=2 ? MatrixType::ColsAtCompileTime/2 : 6;
+ if(R1<=rows-r0 && C1<=cols-c0)
+ {
+ VERIFY_IS_APPROX( (m1.template block<R1,C1>(r0,c0).sum()), m1.block(r0,c0,R1,C1).sum() );
+ }
+
+ // test empty objects
+ VERIFY_IS_APPROX(m1.block(r0,c0,0,0).sum(), Scalar(0));
+ VERIFY_IS_APPROX(m1.block(r0,c0,0,0).prod(), Scalar(1));
+
+ // test nesting complex expression
+ VERIFY_EVALUATION_COUNT( (m1.matrix()*m1.matrix().transpose()).sum(), (MatrixType::IsVectorAtCompileTime && MatrixType::SizeAtCompileTime!=1 ? 0 : 1) );
+ VERIFY_EVALUATION_COUNT( ((m1.matrix()*m1.matrix().transpose())+m2).sum(),(MatrixType::IsVectorAtCompileTime && MatrixType::SizeAtCompileTime!=1 ? 0 : 1));
+}
+
+template<typename VectorType> void vectorRedux(const VectorType& w)
+{
+ using std::abs;
+ typedef typename VectorType::Scalar Scalar;
+ typedef typename NumTraits<Scalar>::Real RealScalar;
+ Index size = w.size();
+
+ VectorType v = VectorType::Random(size);
+ VectorType v_for_prod = VectorType::Ones(size) + Scalar(0.2) * v; // see comment above declaration of m1_for_prod
+
+ for(int i = 1; i < size; i++)
+ {
+ Scalar s(0), p(1);
+ RealScalar minc(numext::real(v.coeff(0))), maxc(numext::real(v.coeff(0)));
+ for(int j = 0; j < i; j++)
+ {
+ s += v[j];
+ p *= v_for_prod[j];
+ minc = (std::min)(minc, numext::real(v[j]));
+ maxc = (std::max)(maxc, numext::real(v[j]));
+ }
+ VERIFY_IS_MUCH_SMALLER_THAN(abs(s - v.head(i).sum()), Scalar(1));
+ VERIFY_IS_APPROX(p, v_for_prod.head(i).prod());
+ VERIFY_IS_APPROX(minc, v.real().head(i).minCoeff());
+ VERIFY_IS_APPROX(maxc, v.real().head(i).maxCoeff());
+ }
+
+ for(int i = 0; i < size-1; i++)
+ {
+ Scalar s(0), p(1);
+ RealScalar minc(numext::real(v.coeff(i))), maxc(numext::real(v.coeff(i)));
+ for(int j = i; j < size; j++)
+ {
+ s += v[j];
+ p *= v_for_prod[j];
+ minc = (std::min)(minc, numext::real(v[j]));
+ maxc = (std::max)(maxc, numext::real(v[j]));
+ }
+ VERIFY_IS_MUCH_SMALLER_THAN(abs(s - v.tail(size-i).sum()), Scalar(1));
+ VERIFY_IS_APPROX(p, v_for_prod.tail(size-i).prod());
+ VERIFY_IS_APPROX(minc, v.real().tail(size-i).minCoeff());
+ VERIFY_IS_APPROX(maxc, v.real().tail(size-i).maxCoeff());
+ }
+
+ for(int i = 0; i < size/2; i++)
+ {
+ Scalar s(0), p(1);
+ RealScalar minc(numext::real(v.coeff(i))), maxc(numext::real(v.coeff(i)));
+ for(int j = i; j < size-i; j++)
+ {
+ s += v[j];
+ p *= v_for_prod[j];
+ minc = (std::min)(minc, numext::real(v[j]));
+ maxc = (std::max)(maxc, numext::real(v[j]));
+ }
+ VERIFY_IS_MUCH_SMALLER_THAN(abs(s - v.segment(i, size-2*i).sum()), Scalar(1));
+ VERIFY_IS_APPROX(p, v_for_prod.segment(i, size-2*i).prod());
+ VERIFY_IS_APPROX(minc, v.real().segment(i, size-2*i).minCoeff());
+ VERIFY_IS_APPROX(maxc, v.real().segment(i, size-2*i).maxCoeff());
+ }
+
+ // test empty objects
+ VERIFY_IS_APPROX(v.head(0).sum(), Scalar(0));
+ VERIFY_IS_APPROX(v.tail(0).prod(), Scalar(1));
+ VERIFY_RAISES_ASSERT(v.head(0).mean());
+ VERIFY_RAISES_ASSERT(v.head(0).minCoeff());
+ VERIFY_RAISES_ASSERT(v.head(0).maxCoeff());
+}
+
+EIGEN_DECLARE_TEST(redux)
+{
+ // the max size cannot be too large, otherwise reduxion operations obviously generate large errors.
+ int maxsize = (std::min)(100,EIGEN_TEST_MAX_SIZE);
+ TEST_SET_BUT_UNUSED_VARIABLE(maxsize);
+ for(int i = 0; i < g_repeat; i++) {
+ CALL_SUBTEST_1( matrixRedux(Matrix<float, 1, 1>()) );
+ CALL_SUBTEST_1( matrixRedux(Array<float, 1, 1>()) );
+ CALL_SUBTEST_2( matrixRedux(Matrix2f()) );
+ CALL_SUBTEST_2( matrixRedux(Array2f()) );
+ CALL_SUBTEST_2( matrixRedux(Array22f()) );
+ CALL_SUBTEST_3( matrixRedux(Matrix4d()) );
+ CALL_SUBTEST_3( matrixRedux(Array4d()) );
+ CALL_SUBTEST_3( matrixRedux(Array44d()) );
+ CALL_SUBTEST_4( matrixRedux(MatrixXcf(internal::random<int>(1,maxsize), internal::random<int>(1,maxsize))) );
+ CALL_SUBTEST_4( matrixRedux(ArrayXXcf(internal::random<int>(1,maxsize), internal::random<int>(1,maxsize))) );
+ CALL_SUBTEST_5( matrixRedux(MatrixXd (internal::random<int>(1,maxsize), internal::random<int>(1,maxsize))) );
+ CALL_SUBTEST_5( matrixRedux(ArrayXXd (internal::random<int>(1,maxsize), internal::random<int>(1,maxsize))) );
+ CALL_SUBTEST_6( matrixRedux(MatrixXi (internal::random<int>(1,maxsize), internal::random<int>(1,maxsize))) );
+ CALL_SUBTEST_6( matrixRedux(ArrayXXi (internal::random<int>(1,maxsize), internal::random<int>(1,maxsize))) );
+ }
+ for(int i = 0; i < g_repeat; i++) {
+ CALL_SUBTEST_7( vectorRedux(Vector4f()) );
+ CALL_SUBTEST_7( vectorRedux(Array4f()) );
+ CALL_SUBTEST_5( vectorRedux(VectorXd(internal::random<int>(1,maxsize))) );
+ CALL_SUBTEST_5( vectorRedux(ArrayXd(internal::random<int>(1,maxsize))) );
+ CALL_SUBTEST_8( vectorRedux(VectorXf(internal::random<int>(1,maxsize))) );
+ CALL_SUBTEST_8( vectorRedux(ArrayXf(internal::random<int>(1,maxsize))) );
+ }
+}
diff --git a/test/ref.cpp b/test/ref.cpp
new file mode 100644
index 0000000..252bacd
--- /dev/null
+++ b/test/ref.cpp
@@ -0,0 +1,345 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2013 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+// This unit test cannot be easily written to work with EIGEN_DEFAULT_TO_ROW_MAJOR
+#ifdef EIGEN_DEFAULT_TO_ROW_MAJOR
+#undef EIGEN_DEFAULT_TO_ROW_MAJOR
+#endif
+
+#define TEST_ENABLE_TEMPORARY_TRACKING
+#define TEST_CHECK_STATIC_ASSERTIONS
+#include "main.h"
+
+// test Ref.h
+
+// Deal with i387 extended precision
+#if EIGEN_ARCH_i386 && !(EIGEN_ARCH_x86_64)
+
+#if EIGEN_COMP_GNUC_STRICT
+#pragma GCC optimize ("-ffloat-store")
+#else
+#undef VERIFY_IS_EQUAL
+#define VERIFY_IS_EQUAL(X,Y) VERIFY_IS_APPROX(X,Y)
+#endif
+
+#endif
+
+template<typename MatrixType> void ref_matrix(const MatrixType& m)
+{
+ typedef typename MatrixType::Scalar Scalar;
+ typedef typename MatrixType::RealScalar RealScalar;
+ typedef Matrix<Scalar,Dynamic,Dynamic,MatrixType::Options> DynMatrixType;
+ typedef Matrix<RealScalar,Dynamic,Dynamic,MatrixType::Options> RealDynMatrixType;
+
+ typedef Ref<MatrixType> RefMat;
+ typedef Ref<DynMatrixType> RefDynMat;
+ typedef Ref<const DynMatrixType> ConstRefDynMat;
+ typedef Ref<RealDynMatrixType , 0, Stride<Dynamic,Dynamic> > RefRealMatWithStride;
+
+ Index rows = m.rows(), cols = m.cols();
+
+ MatrixType m1 = MatrixType::Random(rows, cols),
+ m2 = m1;
+
+ Index i = internal::random<Index>(0,rows-1);
+ Index j = internal::random<Index>(0,cols-1);
+ Index brows = internal::random<Index>(1,rows-i);
+ Index bcols = internal::random<Index>(1,cols-j);
+
+ RefMat rm0 = m1;
+ VERIFY_IS_EQUAL(rm0, m1);
+ RefDynMat rm1 = m1;
+ VERIFY_IS_EQUAL(rm1, m1);
+ RefDynMat rm2 = m1.block(i,j,brows,bcols);
+ VERIFY_IS_EQUAL(rm2, m1.block(i,j,brows,bcols));
+ rm2.setOnes();
+ m2.block(i,j,brows,bcols).setOnes();
+ VERIFY_IS_EQUAL(m1, m2);
+
+ m2.block(i,j,brows,bcols).setRandom();
+ rm2 = m2.block(i,j,brows,bcols);
+ VERIFY_IS_EQUAL(m1, m2);
+
+ ConstRefDynMat rm3 = m1.block(i,j,brows,bcols);
+ m1.block(i,j,brows,bcols) *= 2;
+ m2.block(i,j,brows,bcols) *= 2;
+ VERIFY_IS_EQUAL(rm3, m2.block(i,j,brows,bcols));
+ RefRealMatWithStride rm4 = m1.real();
+ VERIFY_IS_EQUAL(rm4, m2.real());
+ rm4.array() += 1;
+ m2.real().array() += 1;
+ VERIFY_IS_EQUAL(m1, m2);
+}
+
+template<typename VectorType> void ref_vector(const VectorType& m)
+{
+ typedef typename VectorType::Scalar Scalar;
+ typedef typename VectorType::RealScalar RealScalar;
+ typedef Matrix<Scalar,Dynamic,1,VectorType::Options> DynMatrixType;
+ typedef Matrix<Scalar,Dynamic,Dynamic,ColMajor> MatrixType;
+ typedef Matrix<RealScalar,Dynamic,1,VectorType::Options> RealDynMatrixType;
+
+ typedef Ref<VectorType> RefMat;
+ typedef Ref<DynMatrixType> RefDynMat;
+ typedef Ref<const DynMatrixType> ConstRefDynMat;
+ typedef Ref<RealDynMatrixType , 0, InnerStride<> > RefRealMatWithStride;
+ typedef Ref<DynMatrixType , 0, InnerStride<> > RefMatWithStride;
+
+ Index size = m.size();
+
+ VectorType v1 = VectorType::Random(size),
+ v2 = v1;
+ MatrixType mat1 = MatrixType::Random(size,size),
+ mat2 = mat1,
+ mat3 = MatrixType::Random(size,size);
+
+ Index i = internal::random<Index>(0,size-1);
+ Index bsize = internal::random<Index>(1,size-i);
+
+ { RefMat rm0 = v1; VERIFY_IS_EQUAL(rm0, v1); }
+ { RefMat rm0 = v1.block(0,0,size,1); VERIFY_IS_EQUAL(rm0, v1); }
+ { RefDynMat rv1 = v1; VERIFY_IS_EQUAL(rv1, v1); }
+ { RefDynMat rv1 = v1.block(0,0,size,1); VERIFY_IS_EQUAL(rv1, v1); }
+
+ RefDynMat rv2 = v1.segment(i,bsize);
+ VERIFY_IS_EQUAL(rv2, v1.segment(i,bsize));
+ rv2.setOnes();
+ v2.segment(i,bsize).setOnes();
+ VERIFY_IS_EQUAL(v1, v2);
+
+ v2.segment(i,bsize).setRandom();
+ rv2 = v2.segment(i,bsize);
+ VERIFY_IS_EQUAL(v1, v2);
+
+ ConstRefDynMat rm3 = v1.segment(i,bsize);
+ v1.segment(i,bsize) *= 2;
+ v2.segment(i,bsize) *= 2;
+ VERIFY_IS_EQUAL(rm3, v2.segment(i,bsize));
+
+ RefRealMatWithStride rm4 = v1.real();
+ VERIFY_IS_EQUAL(rm4, v2.real());
+ rm4.array() += 1;
+ v2.real().array() += 1;
+ VERIFY_IS_EQUAL(v1, v2);
+
+ RefMatWithStride rm5 = mat1.row(i).transpose();
+ VERIFY_IS_EQUAL(rm5, mat1.row(i).transpose());
+ rm5.array() += 1;
+ mat2.row(i).array() += 1;
+ VERIFY_IS_EQUAL(mat1, mat2);
+ rm5.noalias() = rm4.transpose() * mat3;
+ mat2.row(i) = v2.real().transpose() * mat3;
+ VERIFY_IS_APPROX(mat1, mat2);
+}
+
+template<typename Scalar, int Rows, int Cols>
+void ref_vector_fixed_sizes()
+{
+ typedef Matrix<Scalar,Rows,Cols,RowMajor> RowMajorMatrixType;
+ typedef Matrix<Scalar,Rows,Cols,ColMajor> ColMajorMatrixType;
+ typedef Matrix<Scalar,1,Cols> RowVectorType;
+ typedef Matrix<Scalar,Rows,1> ColVectorType;
+ typedef Matrix<Scalar,Cols,1> RowVectorTransposeType;
+ typedef Matrix<Scalar,1,Rows> ColVectorTransposeType;
+ typedef Stride<Dynamic, Dynamic> DynamicStride;
+
+ RowMajorMatrixType mr = RowMajorMatrixType::Random();
+ ColMajorMatrixType mc = ColMajorMatrixType::Random();
+
+ Index i = internal::random<Index>(0,Rows-1);
+ Index j = internal::random<Index>(0,Cols-1);
+
+ // Reference ith row.
+ Ref<RowVectorType, 0, DynamicStride> mr_ri = mr.row(i);
+ VERIFY_IS_EQUAL(mr_ri, mr.row(i));
+ Ref<RowVectorType, 0, DynamicStride> mc_ri = mc.row(i);
+ VERIFY_IS_EQUAL(mc_ri, mc.row(i));
+
+ // Reference jth col.
+ Ref<ColVectorType, 0, DynamicStride> mr_cj = mr.col(j);
+ VERIFY_IS_EQUAL(mr_cj, mr.col(j));
+ Ref<ColVectorType, 0, DynamicStride> mc_cj = mc.col(j);
+ VERIFY_IS_EQUAL(mc_cj, mc.col(j));
+
+ // Reference the transpose of row i.
+ Ref<RowVectorTransposeType, 0, DynamicStride> mr_rit = mr.row(i);
+ VERIFY_IS_EQUAL(mr_rit, mr.row(i).transpose());
+ Ref<RowVectorTransposeType, 0, DynamicStride> mc_rit = mc.row(i);
+ VERIFY_IS_EQUAL(mc_rit, mc.row(i).transpose());
+
+ // Reference the transpose of col j.
+ Ref<ColVectorTransposeType, 0, DynamicStride> mr_cjt = mr.col(j);
+ VERIFY_IS_EQUAL(mr_cjt, mr.col(j).transpose());
+ Ref<ColVectorTransposeType, 0, DynamicStride> mc_cjt = mc.col(j);
+ VERIFY_IS_EQUAL(mc_cjt, mc.col(j).transpose());
+
+ // Const references without strides.
+ Ref<const RowVectorType> cmr_ri = mr.row(i);
+ VERIFY_IS_EQUAL(cmr_ri, mr.row(i));
+ Ref<const RowVectorType> cmc_ri = mc.row(i);
+ VERIFY_IS_EQUAL(cmc_ri, mc.row(i));
+
+ Ref<const ColVectorType> cmr_cj = mr.col(j);
+ VERIFY_IS_EQUAL(cmr_cj, mr.col(j));
+ Ref<const ColVectorType> cmc_cj = mc.col(j);
+ VERIFY_IS_EQUAL(cmc_cj, mc.col(j));
+
+ Ref<const RowVectorTransposeType> cmr_rit = mr.row(i);
+ VERIFY_IS_EQUAL(cmr_rit, mr.row(i).transpose());
+ Ref<const RowVectorTransposeType> cmc_rit = mc.row(i);
+ VERIFY_IS_EQUAL(cmc_rit, mc.row(i).transpose());
+
+ Ref<const ColVectorTransposeType> cmr_cjt = mr.col(j);
+ VERIFY_IS_EQUAL(cmr_cjt, mr.col(j).transpose());
+ Ref<const ColVectorTransposeType> cmc_cjt = mc.col(j);
+ VERIFY_IS_EQUAL(cmc_cjt, mc.col(j).transpose());
+}
+
+template<typename PlainObjectType> void check_const_correctness(const PlainObjectType&)
+{
+ // verify that ref-to-const don't have LvalueBit
+ typedef std::add_const_t<PlainObjectType> ConstPlainObjectType;
+ VERIFY( !(internal::traits<Ref<ConstPlainObjectType> >::Flags & LvalueBit) );
+ VERIFY( !(internal::traits<Ref<ConstPlainObjectType, Aligned> >::Flags & LvalueBit) );
+ VERIFY( !(Ref<ConstPlainObjectType>::Flags & LvalueBit) );
+ VERIFY( !(Ref<ConstPlainObjectType, Aligned>::Flags & LvalueBit) );
+}
+
+template<typename B>
+EIGEN_DONT_INLINE void call_ref_1(Ref<VectorXf> a, const B &b) { VERIFY_IS_EQUAL(a,b); }
+template<typename B>
+EIGEN_DONT_INLINE void call_ref_2(const Ref<const VectorXf>& a, const B &b) { VERIFY_IS_EQUAL(a,b); }
+template<typename B>
+EIGEN_DONT_INLINE void call_ref_3(Ref<VectorXf,0,InnerStride<> > a, const B &b) { VERIFY_IS_EQUAL(a,b); }
+template<typename B>
+EIGEN_DONT_INLINE void call_ref_4(const Ref<const VectorXf,0,InnerStride<> >& a, const B &b) { VERIFY_IS_EQUAL(a,b); }
+template<typename B>
+EIGEN_DONT_INLINE void call_ref_5(Ref<MatrixXf,0,OuterStride<> > a, const B &b) { VERIFY_IS_EQUAL(a,b); }
+template<typename B>
+EIGEN_DONT_INLINE void call_ref_6(const Ref<const MatrixXf,0,OuterStride<> >& a, const B &b) { VERIFY_IS_EQUAL(a,b); }
+template<typename B>
+EIGEN_DONT_INLINE void call_ref_7(Ref<Matrix<float,Dynamic,3> > a, const B &b) { VERIFY_IS_EQUAL(a,b); }
+
+void call_ref()
+{
+ VectorXcf ca = VectorXcf::Random(10);
+ VectorXf a = VectorXf::Random(10);
+ RowVectorXf b = RowVectorXf::Random(10);
+ MatrixXf A = MatrixXf::Random(10,10);
+ RowVector3f c = RowVector3f::Random();
+ const VectorXf& ac(a);
+ VectorBlock<VectorXf> ab(a,0,3);
+ const VectorBlock<VectorXf> abc(a,0,3);
+
+
+ VERIFY_EVALUATION_COUNT( call_ref_1(a,a), 0);
+ VERIFY_EVALUATION_COUNT( call_ref_1(b,b.transpose()), 0);
+// call_ref_1(ac,a<c); // does not compile because ac is const
+ VERIFY_EVALUATION_COUNT( call_ref_1(ab,ab), 0);
+ VERIFY_EVALUATION_COUNT( call_ref_1(a.head(4),a.head(4)), 0);
+ VERIFY_EVALUATION_COUNT( call_ref_1(abc,abc), 0);
+ VERIFY_EVALUATION_COUNT( call_ref_1(A.col(3),A.col(3)), 0);
+// call_ref_1(A.row(3),A.row(3)); // does not compile because innerstride!=1
+ VERIFY_EVALUATION_COUNT( call_ref_3(A.row(3),A.row(3).transpose()), 0);
+ VERIFY_EVALUATION_COUNT( call_ref_4(A.row(3),A.row(3).transpose()), 0);
+// call_ref_1(a+a, a+a); // does not compile for obvious reason
+
+ MatrixXf tmp = A*A.col(1);
+ VERIFY_EVALUATION_COUNT( call_ref_2(A*A.col(1), tmp), 1); // evaluated into a temp
+ VERIFY_EVALUATION_COUNT( call_ref_2(ac.head(5),ac.head(5)), 0);
+ VERIFY_EVALUATION_COUNT( call_ref_2(ac,ac), 0);
+ VERIFY_EVALUATION_COUNT( call_ref_2(a,a), 0);
+ VERIFY_EVALUATION_COUNT( call_ref_2(ab,ab), 0);
+ VERIFY_EVALUATION_COUNT( call_ref_2(a.head(4),a.head(4)), 0);
+ tmp = a+a;
+ VERIFY_EVALUATION_COUNT( call_ref_2(a+a,tmp), 1); // evaluated into a temp
+ VERIFY_EVALUATION_COUNT( call_ref_2(ca.imag(),ca.imag()), 1); // evaluated into a temp
+
+ VERIFY_EVALUATION_COUNT( call_ref_4(ac.head(5),ac.head(5)), 0);
+ tmp = a+a;
+ VERIFY_EVALUATION_COUNT( call_ref_4(a+a,tmp), 1); // evaluated into a temp
+ VERIFY_EVALUATION_COUNT( call_ref_4(ca.imag(),ca.imag()), 0);
+
+ VERIFY_EVALUATION_COUNT( call_ref_5(a,a), 0);
+ VERIFY_EVALUATION_COUNT( call_ref_5(a.head(3),a.head(3)), 0);
+ VERIFY_EVALUATION_COUNT( call_ref_5(A,A), 0);
+// call_ref_5(A.transpose(),A.transpose()); // does not compile because storage order does not match
+ VERIFY_EVALUATION_COUNT( call_ref_5(A.block(1,1,2,2),A.block(1,1,2,2)), 0);
+ VERIFY_EVALUATION_COUNT( call_ref_5(b,b), 0); // storage order do not match, but this is a degenerate case that should work
+ VERIFY_EVALUATION_COUNT( call_ref_5(a.row(3),a.row(3)), 0);
+
+ VERIFY_EVALUATION_COUNT( call_ref_6(a,a), 0);
+ VERIFY_EVALUATION_COUNT( call_ref_6(a.head(3),a.head(3)), 0);
+ VERIFY_EVALUATION_COUNT( call_ref_6(A.row(3),A.row(3)), 1); // evaluated into a temp thouth it could be avoided by viewing it as a 1xn matrix
+ tmp = A+A;
+ VERIFY_EVALUATION_COUNT( call_ref_6(A+A,tmp), 1); // evaluated into a temp
+ VERIFY_EVALUATION_COUNT( call_ref_6(A,A), 0);
+ VERIFY_EVALUATION_COUNT( call_ref_6(A.transpose(),A.transpose()), 1); // evaluated into a temp because the storage orders do not match
+ VERIFY_EVALUATION_COUNT( call_ref_6(A.block(1,1,2,2),A.block(1,1,2,2)), 0);
+
+ VERIFY_EVALUATION_COUNT( call_ref_7(c,c), 0);
+}
+
+typedef Matrix<double,Dynamic,Dynamic,RowMajor> RowMatrixXd;
+int test_ref_overload_fun1(Ref<MatrixXd> ) { return 1; }
+int test_ref_overload_fun1(Ref<RowMatrixXd> ) { return 2; }
+int test_ref_overload_fun1(Ref<MatrixXf> ) { return 3; }
+
+int test_ref_overload_fun2(Ref<const MatrixXd> ) { return 4; }
+int test_ref_overload_fun2(Ref<const MatrixXf> ) { return 5; }
+
+void test_ref_ambiguous(const Ref<const ArrayXd> &A, Ref<ArrayXd> B)
+{
+ B = A;
+ B = A - A;
+}
+
+// See also bug 969
+void test_ref_overloads()
+{
+ MatrixXd Ad, Bd;
+ RowMatrixXd rAd, rBd;
+ VERIFY( test_ref_overload_fun1(Ad)==1 );
+ VERIFY( test_ref_overload_fun1(rAd)==2 );
+
+ MatrixXf Af, Bf;
+ VERIFY( test_ref_overload_fun2(Ad)==4 );
+ VERIFY( test_ref_overload_fun2(Ad+Bd)==4 );
+ VERIFY( test_ref_overload_fun2(Af+Bf)==5 );
+
+ ArrayXd A, B;
+ test_ref_ambiguous(A, B);
+}
+
+EIGEN_DECLARE_TEST(ref)
+{
+ for(int i = 0; i < g_repeat; i++) {
+ CALL_SUBTEST_1( ref_vector(Matrix<float, 1, 1>()) );
+ CALL_SUBTEST_1( check_const_correctness(Matrix<float, 1, 1>()) );
+ CALL_SUBTEST_2( ref_vector(Vector4d()) );
+ CALL_SUBTEST_2( check_const_correctness(Matrix4d()) );
+ CALL_SUBTEST_3( ref_vector(Vector4cf()) );
+ CALL_SUBTEST_4( ref_vector(VectorXcf(8)) );
+ CALL_SUBTEST_5( ref_vector(VectorXi(12)) );
+ CALL_SUBTEST_5( check_const_correctness(VectorXi(12)) );
+
+ CALL_SUBTEST_1( ref_matrix(Matrix<float, 1, 1>()) );
+ CALL_SUBTEST_2( ref_matrix(Matrix4d()) );
+ CALL_SUBTEST_1( ref_matrix(Matrix<float,3,5>()) );
+ CALL_SUBTEST_4( ref_matrix(MatrixXcf(internal::random<int>(1,10),internal::random<int>(1,10))) );
+ CALL_SUBTEST_4( ref_matrix(Matrix<std::complex<double>,10,15>()) );
+ CALL_SUBTEST_5( ref_matrix(MatrixXi(internal::random<int>(1,10),internal::random<int>(1,10))) );
+ CALL_SUBTEST_6( call_ref() );
+
+ CALL_SUBTEST_8( (ref_vector_fixed_sizes<float,3,5>()) );
+ CALL_SUBTEST_8( (ref_vector_fixed_sizes<float,15,10>()) );
+ }
+
+ CALL_SUBTEST_7( test_ref_overloads() );
+}
diff --git a/test/reshape.cpp b/test/reshape.cpp
new file mode 100644
index 0000000..d248f01
--- /dev/null
+++ b/test/reshape.cpp
@@ -0,0 +1,219 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2017 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2014 yoco <peter.xiau@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "main.h"
+
+using Eigen::placeholders::last;
+using Eigen::placeholders::all;
+
+template<typename T1,typename T2>
+std::enable_if_t<internal::is_same<T1,T2>::value,bool>
+is_same_eq(const T1& a, const T2& b)
+{
+ return (a.array() == b.array()).all();
+}
+
+template <int Order,typename MatType>
+void check_auto_reshape4x4(MatType m)
+{
+ internal::VariableAndFixedInt<MatType::SizeAtCompileTime==Dynamic?-1: 1> v1( 1);
+ internal::VariableAndFixedInt<MatType::SizeAtCompileTime==Dynamic?-1: 2> v2( 2);
+ internal::VariableAndFixedInt<MatType::SizeAtCompileTime==Dynamic?-1: 4> v4( 4);
+ internal::VariableAndFixedInt<MatType::SizeAtCompileTime==Dynamic?-1: 8> v8( 8);
+ internal::VariableAndFixedInt<MatType::SizeAtCompileTime==Dynamic?-1:16> v16(16);
+
+ VERIFY(is_same_eq(m.template reshaped<Order>( 1, AutoSize), m.template reshaped<Order>( 1, 16)));
+ VERIFY(is_same_eq(m.template reshaped<Order>(AutoSize, 16 ), m.template reshaped<Order>( 1, 16)));
+ VERIFY(is_same_eq(m.template reshaped<Order>( 2, AutoSize), m.template reshaped<Order>( 2, 8)));
+ VERIFY(is_same_eq(m.template reshaped<Order>(AutoSize, 8 ), m.template reshaped<Order>( 2, 8)));
+ VERIFY(is_same_eq(m.template reshaped<Order>( 4, AutoSize), m.template reshaped<Order>( 4, 4)));
+ VERIFY(is_same_eq(m.template reshaped<Order>(AutoSize, 4 ), m.template reshaped<Order>( 4, 4)));
+ VERIFY(is_same_eq(m.template reshaped<Order>( 8, AutoSize), m.template reshaped<Order>( 8, 2)));
+ VERIFY(is_same_eq(m.template reshaped<Order>(AutoSize, 2 ), m.template reshaped<Order>( 8, 2)));
+ VERIFY(is_same_eq(m.template reshaped<Order>(16, AutoSize), m.template reshaped<Order>(16, 1)));
+ VERIFY(is_same_eq(m.template reshaped<Order>(AutoSize, 1 ), m.template reshaped<Order>(16, 1)));
+
+ VERIFY(is_same_eq(m.template reshaped<Order>(fix< 1>, AutoSize), m.template reshaped<Order>(fix< 1>, v16 )));
+ VERIFY(is_same_eq(m.template reshaped<Order>(AutoSize, fix<16> ), m.template reshaped<Order>( v1, fix<16>)));
+ VERIFY(is_same_eq(m.template reshaped<Order>(fix< 2>, AutoSize), m.template reshaped<Order>(fix< 2>, v8 )));
+ VERIFY(is_same_eq(m.template reshaped<Order>(AutoSize, fix< 8> ), m.template reshaped<Order>( v2, fix< 8>)));
+ VERIFY(is_same_eq(m.template reshaped<Order>(fix< 4>, AutoSize), m.template reshaped<Order>(fix< 4>, v4 )));
+ VERIFY(is_same_eq(m.template reshaped<Order>(AutoSize, fix< 4> ), m.template reshaped<Order>( v4, fix< 4>)));
+ VERIFY(is_same_eq(m.template reshaped<Order>(fix< 8>, AutoSize), m.template reshaped<Order>(fix< 8>, v2 )));
+ VERIFY(is_same_eq(m.template reshaped<Order>(AutoSize, fix< 2> ), m.template reshaped<Order>( v8, fix< 2>)));
+ VERIFY(is_same_eq(m.template reshaped<Order>(fix<16>, AutoSize), m.template reshaped<Order>(fix<16>, v1 )));
+ VERIFY(is_same_eq(m.template reshaped<Order>(AutoSize, fix< 1> ), m.template reshaped<Order>(v16, fix< 1>)));
+}
+
+template <typename MatType>
+void check_direct_access_reshape4x4(MatType , internal::FixedInt<RowMajorBit>) {}
+
+template <typename MatType>
+void check_direct_access_reshape4x4(MatType m, internal::FixedInt<0>) {
+ VERIFY_IS_EQUAL(m.reshaped( 1, 16).data(), m.data());
+ VERIFY_IS_EQUAL(m.reshaped( 1, 16).innerStride(), 1);
+
+ VERIFY_IS_EQUAL(m.reshaped( 2, 8).data(), m.data());
+ VERIFY_IS_EQUAL(m.reshaped( 2, 8).innerStride(), 1);
+ VERIFY_IS_EQUAL(m.reshaped( 2, 8).outerStride(), 2);
+}
+
+// just test a 4x4 matrix, enumerate all combination manually
+template <typename MatType>
+void reshape4x4(MatType m)
+{
+ typedef typename MatType::Scalar Scalar;
+
+ internal::VariableAndFixedInt<MatType::SizeAtCompileTime==Dynamic?-1: 1> v1( 1);
+ internal::VariableAndFixedInt<MatType::SizeAtCompileTime==Dynamic?-1: 2> v2( 2);
+ internal::VariableAndFixedInt<MatType::SizeAtCompileTime==Dynamic?-1: 4> v4( 4);
+ internal::VariableAndFixedInt<MatType::SizeAtCompileTime==Dynamic?-1: 8> v8( 8);
+ internal::VariableAndFixedInt<MatType::SizeAtCompileTime==Dynamic?-1:16> v16(16);
+
+ if((MatType::Flags&RowMajorBit)==0)
+ {
+ typedef Map<MatrixXi> MapMat;
+ // dynamic
+ VERIFY_IS_EQUAL((m.reshaped( 1, 16)), MapMat(m.data(), 1, 16));
+ VERIFY_IS_EQUAL((m.reshaped( 2, 8)), MapMat(m.data(), 2, 8));
+ VERIFY_IS_EQUAL((m.reshaped( 4, 4)), MapMat(m.data(), 4, 4));
+ VERIFY_IS_EQUAL((m.reshaped( 8, 2)), MapMat(m.data(), 8, 2));
+ VERIFY_IS_EQUAL((m.reshaped(16, 1)), MapMat(m.data(), 16, 1));
+
+ // static
+ VERIFY_IS_EQUAL(m.reshaped(fix< 1>, fix<16>), MapMat(m.data(), 1, 16));
+ VERIFY_IS_EQUAL(m.reshaped(fix< 2>, fix< 8>), MapMat(m.data(), 2, 8));
+ VERIFY_IS_EQUAL(m.reshaped(fix< 4>, fix< 4>), MapMat(m.data(), 4, 4));
+ VERIFY_IS_EQUAL(m.reshaped(fix< 8>, fix< 2>), MapMat(m.data(), 8, 2));
+ VERIFY_IS_EQUAL(m.reshaped(fix<16>, fix< 1>), MapMat(m.data(), 16, 1));
+
+
+ // reshape chain
+ VERIFY_IS_EQUAL(
+ (m
+ .reshaped( 1, 16)
+ .reshaped(fix< 2>,fix< 8>)
+ .reshaped(16, 1)
+ .reshaped(fix< 8>,fix< 2>)
+ .reshaped( 2, 8)
+ .reshaped(fix< 1>,fix<16>)
+ .reshaped( 4, 4)
+ .reshaped(fix<16>,fix< 1>)
+ .reshaped( 8, 2)
+ .reshaped(fix< 4>,fix< 4>)
+ ),
+ MapMat(m.data(), 4, 4)
+ );
+ }
+
+ VERIFY(is_same_eq(m.reshaped( 1, AutoSize), m.reshaped( 1, 16)));
+ VERIFY(is_same_eq(m.reshaped(AutoSize, 16), m.reshaped( 1, 16)));
+ VERIFY(is_same_eq(m.reshaped( 2, AutoSize), m.reshaped( 2, 8)));
+ VERIFY(is_same_eq(m.reshaped(AutoSize, 8), m.reshaped( 2, 8)));
+ VERIFY(is_same_eq(m.reshaped( 4, AutoSize), m.reshaped( 4, 4)));
+ VERIFY(is_same_eq(m.reshaped(AutoSize, 4), m.reshaped( 4, 4)));
+ VERIFY(is_same_eq(m.reshaped( 8, AutoSize), m.reshaped( 8, 2)));
+ VERIFY(is_same_eq(m.reshaped(AutoSize, 2), m.reshaped( 8, 2)));
+ VERIFY(is_same_eq(m.reshaped(16, AutoSize), m.reshaped(16, 1)));
+ VERIFY(is_same_eq(m.reshaped(AutoSize, 1), m.reshaped(16, 1)));
+
+ VERIFY(is_same_eq(m.reshaped(fix< 1>, AutoSize), m.reshaped(fix< 1>, v16)));
+ VERIFY(is_same_eq(m.reshaped(AutoSize, fix<16>), m.reshaped( v1, fix<16>)));
+ VERIFY(is_same_eq(m.reshaped(fix< 2>, AutoSize), m.reshaped(fix< 2>, v8)));
+ VERIFY(is_same_eq(m.reshaped(AutoSize, fix< 8>), m.reshaped( v2, fix< 8>)));
+ VERIFY(is_same_eq(m.reshaped(fix< 4>, AutoSize), m.reshaped(fix< 4>, v4)));
+ VERIFY(is_same_eq(m.reshaped(AutoSize, fix< 4>), m.reshaped( v4, fix< 4>)));
+ VERIFY(is_same_eq(m.reshaped(fix< 8>, AutoSize), m.reshaped(fix< 8>, v2)));
+ VERIFY(is_same_eq(m.reshaped(AutoSize, fix< 2>), m.reshaped( v8, fix< 2>)));
+ VERIFY(is_same_eq(m.reshaped(fix<16>, AutoSize), m.reshaped(fix<16>, v1)));
+ VERIFY(is_same_eq(m.reshaped(AutoSize, fix< 1>), m.reshaped(v16, fix< 1>)));
+
+ check_auto_reshape4x4<ColMajor> (m);
+ check_auto_reshape4x4<RowMajor> (m);
+ check_auto_reshape4x4<AutoOrder>(m);
+ check_auto_reshape4x4<ColMajor> (m.transpose());
+ check_auto_reshape4x4<ColMajor> (m.transpose());
+ check_auto_reshape4x4<AutoOrder>(m.transpose());
+
+ check_direct_access_reshape4x4(m,fix<MatType::Flags&RowMajorBit>);
+
+ if((MatType::Flags&RowMajorBit)==0)
+ {
+ VERIFY_IS_EQUAL(m.template reshaped<ColMajor>(2,8),m.reshaped(2,8));
+ VERIFY_IS_EQUAL(m.template reshaped<ColMajor>(2,8),m.template reshaped<AutoOrder>(2,8));
+ VERIFY_IS_EQUAL(m.transpose().template reshaped<RowMajor>(2,8),m.transpose().template reshaped<AutoOrder>(2,8));
+ }
+ else
+ {
+ VERIFY_IS_EQUAL(m.template reshaped<ColMajor>(2,8),m.reshaped(2,8));
+ VERIFY_IS_EQUAL(m.template reshaped<RowMajor>(2,8),m.template reshaped<AutoOrder>(2,8));
+ VERIFY_IS_EQUAL(m.transpose().template reshaped<ColMajor>(2,8),m.transpose().template reshaped<AutoOrder>(2,8));
+ VERIFY_IS_EQUAL(m.transpose().reshaped(2,8),m.transpose().template reshaped<AutoOrder>(2,8));
+ }
+
+ MatrixXi m28r1 = m.template reshaped<RowMajor>(2,8);
+ MatrixXi m28r2 = m.transpose().template reshaped<ColMajor>(8,2).transpose();
+ VERIFY_IS_EQUAL( m28r1, m28r2);
+
+ VERIFY(is_same_eq(m.reshaped(v16,fix<1>), m.reshaped()));
+ VERIFY_IS_EQUAL(m.reshaped(16,1).eval(), m.reshaped().eval());
+ VERIFY_IS_EQUAL(m.reshaped(1,16).eval(), m.reshaped().transpose().eval());
+ VERIFY_IS_EQUAL(m.reshaped().reshaped(2,8), m.reshaped(2,8));
+ VERIFY_IS_EQUAL(m.reshaped().reshaped(4,4), m.reshaped(4,4));
+ VERIFY_IS_EQUAL(m.reshaped().reshaped(8,2), m.reshaped(8,2));
+
+ VERIFY_IS_EQUAL(m.reshaped(), m.template reshaped<ColMajor>());
+ VERIFY_IS_EQUAL(m.transpose().reshaped(), m.template reshaped<RowMajor>());
+ VERIFY_IS_EQUAL(m.template reshaped<RowMajor>(AutoSize,fix<1>), m.template reshaped<RowMajor>());
+ VERIFY_IS_EQUAL(m.template reshaped<AutoOrder>(AutoSize,fix<1>), m.template reshaped<AutoOrder>());
+
+ VERIFY(is_same_eq(m.reshaped(AutoSize,fix<1>), m.reshaped()));
+ VERIFY_IS_EQUAL(m.template reshaped<RowMajor>(fix<1>,AutoSize), m.transpose().reshaped().transpose());
+
+ // check assignment
+ {
+ Matrix<Scalar,Dynamic,1> m1x(m.size()); m1x.setRandom();
+ VERIFY_IS_APPROX(m.reshaped() = m1x, m1x);
+ VERIFY_IS_APPROX(m, m1x.reshaped(4,4));
+
+ Matrix<Scalar,Dynamic,Dynamic> m28(2,8); m28.setRandom();
+ VERIFY_IS_APPROX(m.reshaped(2,8) = m28, m28);
+ VERIFY_IS_APPROX(m, m28.reshaped(4,4));
+ VERIFY_IS_APPROX(m.template reshaped<RowMajor>(2,8) = m28, m28);
+
+ Matrix<Scalar,Dynamic,Dynamic> m24(2,4); m24.setRandom();
+ VERIFY_IS_APPROX(m(seq(0,last,2),all).reshaped(2,4) = m24, m24);
+
+ // check constness:
+ m.reshaped(2,8).nestedExpression() = m;
+ }
+}
+
+EIGEN_DECLARE_TEST(reshape)
+{
+ typedef Matrix<int,Dynamic,Dynamic,RowMajor> RowMatrixXi;
+ typedef Matrix<int,4,4,RowMajor> RowMatrix4i;
+ MatrixXi mx = MatrixXi::Random(4, 4);
+ Matrix4i m4 = Matrix4i::Random(4, 4);
+ RowMatrixXi rmx = RowMatrixXi::Random(4, 4);
+ RowMatrix4i rm4 = RowMatrix4i::Random(4, 4);
+
+ // test dynamic-size matrix
+ CALL_SUBTEST(reshape4x4(mx));
+ // test static-size matrix
+ CALL_SUBTEST(reshape4x4(m4));
+ // test dynamic-size const matrix
+ CALL_SUBTEST(reshape4x4(static_cast<const MatrixXi>(mx)));
+ // test static-size const matrix
+ CALL_SUBTEST(reshape4x4(static_cast<const Matrix4i>(m4)));
+
+ CALL_SUBTEST(reshape4x4(rmx));
+ CALL_SUBTEST(reshape4x4(rm4));
+}
diff --git a/test/resize.cpp b/test/resize.cpp
new file mode 100644
index 0000000..646a75b
--- /dev/null
+++ b/test/resize.cpp
@@ -0,0 +1,41 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009 Keir Mierle <mierle@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "main.h"
+
+template<DenseIndex rows, DenseIndex cols>
+void resizeLikeTest()
+{
+ MatrixXf A(rows, cols);
+ MatrixXf B;
+ Matrix<double, rows, cols> C;
+ B.resizeLike(A);
+ C.resizeLike(B); // Shouldn't crash.
+ VERIFY(B.rows() == rows && B.cols() == cols);
+
+ VectorXf x(rows);
+ RowVectorXf y;
+ y.resizeLike(x);
+ VERIFY(y.rows() == 1 && y.cols() == rows);
+
+ y.resize(cols);
+ x.resizeLike(y);
+ VERIFY(x.rows() == cols && x.cols() == 1);
+}
+
+void resizeLikeTest12() { resizeLikeTest<1,2>(); }
+void resizeLikeTest1020() { resizeLikeTest<10,20>(); }
+void resizeLikeTest31() { resizeLikeTest<3,1>(); }
+
+EIGEN_DECLARE_TEST(resize)
+{
+ CALL_SUBTEST(resizeLikeTest12() );
+ CALL_SUBTEST(resizeLikeTest1020() );
+ CALL_SUBTEST(resizeLikeTest31() );
+}
diff --git a/test/rvalue_types.cpp b/test/rvalue_types.cpp
new file mode 100644
index 0000000..9af7c92
--- /dev/null
+++ b/test/rvalue_types.cpp
@@ -0,0 +1,144 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2013 Hauke Heibel <hauke.heibel@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#define EIGEN_RUNTIME_NO_MALLOC
+
+#include "main.h"
+#include "MovableScalar.h"
+#include "SafeScalar.h"
+
+#include <Eigen/Core>
+
+using internal::UIntPtr;
+
+template <typename MatrixType>
+void rvalue_copyassign(const MatrixType& m)
+{
+
+ typedef typename internal::traits<MatrixType>::Scalar Scalar;
+
+ // create a temporary which we are about to destroy by moving
+ MatrixType tmp = m;
+ UIntPtr src_address = reinterpret_cast<UIntPtr>(tmp.data());
+
+ Eigen::internal::set_is_malloc_allowed(false); // moving from an rvalue reference shall never allocate
+ // move the temporary to n
+ MatrixType n = std::move(tmp);
+ UIntPtr dst_address = reinterpret_cast<UIntPtr>(n.data());
+ if (MatrixType::RowsAtCompileTime==Dynamic|| MatrixType::ColsAtCompileTime==Dynamic)
+ {
+ // verify that we actually moved the guts
+ VERIFY_IS_EQUAL(src_address, dst_address);
+ VERIFY_IS_EQUAL(tmp.size(), 0);
+ VERIFY_IS_EQUAL(reinterpret_cast<UIntPtr>(tmp.data()), UIntPtr(0));
+ }
+
+ // verify that the content did not change
+ Scalar abs_diff = (m-n).array().abs().sum();
+ VERIFY_IS_EQUAL(abs_diff, Scalar(0));
+ Eigen::internal::set_is_malloc_allowed(true);
+}
+template<typename TranspositionsType>
+void rvalue_transpositions(Index rows)
+{
+ typedef typename TranspositionsType::IndicesType PermutationVectorType;
+
+ PermutationVectorType vec;
+ randomPermutationVector(vec, rows);
+ TranspositionsType t0(vec);
+
+ Eigen::internal::set_is_malloc_allowed(false); // moving from an rvalue reference shall never allocate
+
+ UIntPtr t0_address = reinterpret_cast<UIntPtr>(t0.indices().data());
+
+ // Move constructors:
+ TranspositionsType t1 = std::move(t0);
+ UIntPtr t1_address = reinterpret_cast<UIntPtr>(t1.indices().data());
+ VERIFY_IS_EQUAL(t0_address, t1_address);
+ // t0 must be de-allocated:
+ VERIFY_IS_EQUAL(t0.size(), 0);
+ VERIFY_IS_EQUAL(reinterpret_cast<UIntPtr>(t0.indices().data()), UIntPtr(0));
+
+
+ // Move assignment:
+ t0 = std::move(t1);
+ t0_address = reinterpret_cast<UIntPtr>(t0.indices().data());
+ VERIFY_IS_EQUAL(t0_address, t1_address);
+ // t1 must be de-allocated:
+ VERIFY_IS_EQUAL(t1.size(), 0);
+ VERIFY_IS_EQUAL(reinterpret_cast<UIntPtr>(t1.indices().data()), UIntPtr(0));
+
+ Eigen::internal::set_is_malloc_allowed(true);
+}
+
+template <typename MatrixType>
+void rvalue_move(const MatrixType& m)
+{
+ // lvalue reference is copied
+ MatrixType b(m);
+ VERIFY_IS_EQUAL(b, m);
+
+ // lvalue reference is copied
+ MatrixType c{m};
+ VERIFY_IS_EQUAL(c, m);
+
+ // lvalue reference is copied
+ MatrixType d = m;
+ VERIFY_IS_EQUAL(d, m);
+
+ // rvalue reference is moved - copy constructor.
+ MatrixType e_src(m);
+ VERIFY_IS_EQUAL(e_src, m);
+ MatrixType e_dst(std::move(e_src));
+ VERIFY_IS_EQUAL(e_dst, m);
+
+ // rvalue reference is moved - copy constructor.
+ MatrixType f_src(m);
+ VERIFY_IS_EQUAL(f_src, m);
+ MatrixType f_dst = std::move(f_src);
+ VERIFY_IS_EQUAL(f_dst, m);
+
+ // rvalue reference is moved - copy assignment.
+ MatrixType g_src(m);
+ VERIFY_IS_EQUAL(g_src, m);
+ MatrixType g_dst;
+ g_dst = std::move(g_src);
+ VERIFY_IS_EQUAL(g_dst, m);
+}
+
+EIGEN_DECLARE_TEST(rvalue_types)
+{
+ for(int i = 0; i < g_repeat; i++) {
+ CALL_SUBTEST_1(rvalue_copyassign( MatrixXf::Random(50,50).eval() ));
+ CALL_SUBTEST_1(rvalue_copyassign( ArrayXXf::Random(50,50).eval() ));
+
+ CALL_SUBTEST_1(rvalue_copyassign( Matrix<float,1,Dynamic>::Random(50).eval() ));
+ CALL_SUBTEST_1(rvalue_copyassign( Array<float,1,Dynamic>::Random(50).eval() ));
+
+ CALL_SUBTEST_1(rvalue_copyassign( Matrix<float,Dynamic,1>::Random(50).eval() ));
+ CALL_SUBTEST_1(rvalue_copyassign( Array<float,Dynamic,1>::Random(50).eval() ));
+
+ CALL_SUBTEST_2(rvalue_copyassign( Array<float,2,1>::Random().eval() ));
+ CALL_SUBTEST_2(rvalue_copyassign( Array<float,3,1>::Random().eval() ));
+ CALL_SUBTEST_2(rvalue_copyassign( Array<float,4,1>::Random().eval() ));
+
+ CALL_SUBTEST_2(rvalue_copyassign( Array<float,2,2>::Random().eval() ));
+ CALL_SUBTEST_2(rvalue_copyassign( Array<float,3,3>::Random().eval() ));
+ CALL_SUBTEST_2(rvalue_copyassign( Array<float,4,4>::Random().eval() ));
+
+ CALL_SUBTEST_3((rvalue_transpositions<PermutationMatrix<Dynamic, Dynamic, int> >(internal::random<int>(1,EIGEN_TEST_MAX_SIZE))));
+ CALL_SUBTEST_3((rvalue_transpositions<PermutationMatrix<Dynamic, Dynamic, Index> >(internal::random<int>(1,EIGEN_TEST_MAX_SIZE))));
+ CALL_SUBTEST_4((rvalue_transpositions<Transpositions<Dynamic, Dynamic, int> >(internal::random<int>(1,EIGEN_TEST_MAX_SIZE))));
+ CALL_SUBTEST_4((rvalue_transpositions<Transpositions<Dynamic, Dynamic, Index> >(internal::random<int>(1,EIGEN_TEST_MAX_SIZE))));
+
+ CALL_SUBTEST_5(rvalue_move(Eigen::Matrix<MovableScalar<float>,1,3>::Random().eval()));
+ CALL_SUBTEST_5(rvalue_move(Eigen::Matrix<SafeScalar<float>,1,3>::Random().eval()));
+ CALL_SUBTEST_5(rvalue_move(Eigen::Matrix<SafeScalar<float>,Eigen::Dynamic,Eigen::Dynamic>::Random(1,3).eval()));
+ }
+}
diff --git a/test/schur_complex.cpp b/test/schur_complex.cpp
new file mode 100644
index 0000000..26acb8c
--- /dev/null
+++ b/test/schur_complex.cpp
@@ -0,0 +1,92 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2010,2012 Jitse Niesen <jitse@maths.leeds.ac.uk>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "main.h"
+#include <limits>
+#include <Eigen/Eigenvalues>
+
+template<typename MatrixType> void schur(int size = MatrixType::ColsAtCompileTime)
+{
+ typedef typename ComplexSchur<MatrixType>::ComplexScalar ComplexScalar;
+ typedef typename ComplexSchur<MatrixType>::ComplexMatrixType ComplexMatrixType;
+
+ // Test basic functionality: T is triangular and A = U T U*
+ for(int counter = 0; counter < g_repeat; ++counter) {
+ MatrixType A = MatrixType::Random(size, size);
+ ComplexSchur<MatrixType> schurOfA(A);
+ VERIFY_IS_EQUAL(schurOfA.info(), Success);
+ ComplexMatrixType U = schurOfA.matrixU();
+ ComplexMatrixType T = schurOfA.matrixT();
+ for(int row = 1; row < size; ++row) {
+ for(int col = 0; col < row; ++col) {
+ VERIFY(T(row,col) == (typename MatrixType::Scalar)0);
+ }
+ }
+ VERIFY_IS_APPROX(A.template cast<ComplexScalar>(), U * T * U.adjoint());
+ }
+
+ // Test asserts when not initialized
+ ComplexSchur<MatrixType> csUninitialized;
+ VERIFY_RAISES_ASSERT(csUninitialized.matrixT());
+ VERIFY_RAISES_ASSERT(csUninitialized.matrixU());
+ VERIFY_RAISES_ASSERT(csUninitialized.info());
+
+ // Test whether compute() and constructor returns same result
+ MatrixType A = MatrixType::Random(size, size);
+ ComplexSchur<MatrixType> cs1;
+ cs1.compute(A);
+ ComplexSchur<MatrixType> cs2(A);
+ VERIFY_IS_EQUAL(cs1.info(), Success);
+ VERIFY_IS_EQUAL(cs2.info(), Success);
+ VERIFY_IS_EQUAL(cs1.matrixT(), cs2.matrixT());
+ VERIFY_IS_EQUAL(cs1.matrixU(), cs2.matrixU());
+
+ // Test maximum number of iterations
+ ComplexSchur<MatrixType> cs3;
+ cs3.setMaxIterations(ComplexSchur<MatrixType>::m_maxIterationsPerRow * size).compute(A);
+ VERIFY_IS_EQUAL(cs3.info(), Success);
+ VERIFY_IS_EQUAL(cs3.matrixT(), cs1.matrixT());
+ VERIFY_IS_EQUAL(cs3.matrixU(), cs1.matrixU());
+ cs3.setMaxIterations(1).compute(A);
+ // The schur decomposition does often converge with a single iteration.
+ // VERIFY_IS_EQUAL(cs3.info(), size > 1 ? NoConvergence : Success);
+ VERIFY_IS_EQUAL(cs3.getMaxIterations(), 1);
+
+ MatrixType Atriangular = A;
+ Atriangular.template triangularView<StrictlyLower>().setZero();
+ cs3.setMaxIterations(1).compute(Atriangular); // triangular matrices do not need any iterations
+ VERIFY_IS_EQUAL(cs3.info(), Success);
+ VERIFY_IS_EQUAL(cs3.matrixT(), Atriangular.template cast<ComplexScalar>());
+ VERIFY_IS_EQUAL(cs3.matrixU(), ComplexMatrixType::Identity(size, size));
+
+ // Test computation of only T, not U
+ ComplexSchur<MatrixType> csOnlyT(A, false);
+ VERIFY_IS_EQUAL(csOnlyT.info(), Success);
+ VERIFY_IS_EQUAL(cs1.matrixT(), csOnlyT.matrixT());
+ VERIFY_RAISES_ASSERT(csOnlyT.matrixU());
+
+ if (size > 1 && size < 20)
+ {
+ // Test matrix with NaN
+ A(0,0) = std::numeric_limits<typename MatrixType::RealScalar>::quiet_NaN();
+ ComplexSchur<MatrixType> csNaN(A);
+ VERIFY_IS_EQUAL(csNaN.info(), NoConvergence);
+ }
+}
+
+EIGEN_DECLARE_TEST(schur_complex)
+{
+ CALL_SUBTEST_1(( schur<Matrix4cd>() ));
+ CALL_SUBTEST_2(( schur<MatrixXcf>(internal::random<int>(1,EIGEN_TEST_MAX_SIZE/4)) ));
+ CALL_SUBTEST_3(( schur<Matrix<std::complex<float>, 1, 1> >() ));
+ CALL_SUBTEST_4(( schur<Matrix<float, 3, 3, Eigen::RowMajor> >() ));
+
+ // Test problem size constructors
+ CALL_SUBTEST_5(ComplexSchur<MatrixXf>(10));
+}
diff --git a/test/schur_real.cpp b/test/schur_real.cpp
new file mode 100644
index 0000000..8b40ddd
--- /dev/null
+++ b/test/schur_real.cpp
@@ -0,0 +1,110 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2010,2012 Jitse Niesen <jitse@maths.leeds.ac.uk>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "main.h"
+#include <limits>
+#include <Eigen/Eigenvalues>
+
+template<typename MatrixType> void verifyIsQuasiTriangular(const MatrixType& T)
+{
+ const Index size = T.cols();
+ typedef typename MatrixType::Scalar Scalar;
+
+ // Check T is lower Hessenberg
+ for(int row = 2; row < size; ++row) {
+ for(int col = 0; col < row - 1; ++col) {
+ VERIFY_IS_EQUAL(T(row,col), Scalar(0));
+ }
+ }
+
+ // Check that any non-zero on the subdiagonal is followed by a zero and is
+ // part of a 2x2 diagonal block with imaginary eigenvalues.
+ for(int row = 1; row < size; ++row) {
+ if (!numext::is_exactly_zero(T(row, row - 1))) {
+ VERIFY(row == size-1 || numext::is_exactly_zero(T(row + 1, row)));
+ Scalar tr = T(row-1,row-1) + T(row,row);
+ Scalar det = T(row-1,row-1) * T(row,row) - T(row-1,row) * T(row,row-1);
+ VERIFY(4 * det > tr * tr);
+ }
+ }
+}
+
+template<typename MatrixType> void schur(int size = MatrixType::ColsAtCompileTime)
+{
+ // Test basic functionality: T is quasi-triangular and A = U T U*
+ for(int counter = 0; counter < g_repeat; ++counter) {
+ MatrixType A = MatrixType::Random(size, size);
+ RealSchur<MatrixType> schurOfA(A);
+ VERIFY_IS_EQUAL(schurOfA.info(), Success);
+ MatrixType U = schurOfA.matrixU();
+ MatrixType T = schurOfA.matrixT();
+ verifyIsQuasiTriangular(T);
+ VERIFY_IS_APPROX(A, U * T * U.transpose());
+ }
+
+ // Test asserts when not initialized
+ RealSchur<MatrixType> rsUninitialized;
+ VERIFY_RAISES_ASSERT(rsUninitialized.matrixT());
+ VERIFY_RAISES_ASSERT(rsUninitialized.matrixU());
+ VERIFY_RAISES_ASSERT(rsUninitialized.info());
+
+ // Test whether compute() and constructor returns same result
+ MatrixType A = MatrixType::Random(size, size);
+ RealSchur<MatrixType> rs1;
+ rs1.compute(A);
+ RealSchur<MatrixType> rs2(A);
+ VERIFY_IS_EQUAL(rs1.info(), Success);
+ VERIFY_IS_EQUAL(rs2.info(), Success);
+ VERIFY_IS_EQUAL(rs1.matrixT(), rs2.matrixT());
+ VERIFY_IS_EQUAL(rs1.matrixU(), rs2.matrixU());
+
+ // Test maximum number of iterations
+ RealSchur<MatrixType> rs3;
+ rs3.setMaxIterations(RealSchur<MatrixType>::m_maxIterationsPerRow * size).compute(A);
+ VERIFY_IS_EQUAL(rs3.info(), Success);
+ VERIFY_IS_EQUAL(rs3.matrixT(), rs1.matrixT());
+ VERIFY_IS_EQUAL(rs3.matrixU(), rs1.matrixU());
+ if (size > 2) {
+ rs3.setMaxIterations(1).compute(A);
+ VERIFY_IS_EQUAL(rs3.info(), NoConvergence);
+ VERIFY_IS_EQUAL(rs3.getMaxIterations(), 1);
+ }
+
+ MatrixType Atriangular = A;
+ Atriangular.template triangularView<StrictlyLower>().setZero();
+ rs3.setMaxIterations(1).compute(Atriangular); // triangular matrices do not need any iterations
+ VERIFY_IS_EQUAL(rs3.info(), Success);
+ VERIFY_IS_APPROX(rs3.matrixT(), Atriangular); // approx because of scaling...
+ VERIFY_IS_EQUAL(rs3.matrixU(), MatrixType::Identity(size, size));
+
+ // Test computation of only T, not U
+ RealSchur<MatrixType> rsOnlyT(A, false);
+ VERIFY_IS_EQUAL(rsOnlyT.info(), Success);
+ VERIFY_IS_EQUAL(rs1.matrixT(), rsOnlyT.matrixT());
+ VERIFY_RAISES_ASSERT(rsOnlyT.matrixU());
+
+ if (size > 2 && size < 20)
+ {
+ // Test matrix with NaN
+ A(0,0) = std::numeric_limits<typename MatrixType::Scalar>::quiet_NaN();
+ RealSchur<MatrixType> rsNaN(A);
+ VERIFY_IS_EQUAL(rsNaN.info(), NoConvergence);
+ }
+}
+
+EIGEN_DECLARE_TEST(schur_real)
+{
+ CALL_SUBTEST_1(( schur<Matrix4f>() ));
+ CALL_SUBTEST_2(( schur<MatrixXd>(internal::random<int>(1,EIGEN_TEST_MAX_SIZE/4)) ));
+ CALL_SUBTEST_3(( schur<Matrix<float, 1, 1> >() ));
+ CALL_SUBTEST_4(( schur<Matrix<double, 3, 3, Eigen::RowMajor> >() ));
+
+ // Test problem size constructors
+ CALL_SUBTEST_5(RealSchur<MatrixXf>(10));
+}
diff --git a/test/selfadjoint.cpp b/test/selfadjoint.cpp
new file mode 100644
index 0000000..74495fb
--- /dev/null
+++ b/test/selfadjoint.cpp
@@ -0,0 +1,72 @@
+// This file is triangularView of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2010 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#define TEST_CHECK_STATIC_ASSERTIONS
+#include "main.h"
+
+// This file tests the basic selfadjointView API,
+// the related products and decompositions are tested in specific files.
+
+template<typename MatrixType> void selfadjoint(const MatrixType& m)
+{
+ typedef typename MatrixType::Scalar Scalar;
+
+ Index rows = m.rows();
+ Index cols = m.cols();
+
+ MatrixType m1 = MatrixType::Random(rows, cols),
+ m2 = MatrixType::Random(rows, cols),
+ m3(rows, cols),
+ m4(rows, cols);
+
+ m1.diagonal() = m1.diagonal().real().template cast<Scalar>();
+
+ // check selfadjoint to dense
+ m3 = m1.template selfadjointView<Upper>();
+ VERIFY_IS_APPROX(MatrixType(m3.template triangularView<Upper>()), MatrixType(m1.template triangularView<Upper>()));
+ VERIFY_IS_APPROX(m3, m3.adjoint());
+
+ m3 = m1.template selfadjointView<Lower>();
+ VERIFY_IS_APPROX(MatrixType(m3.template triangularView<Lower>()), MatrixType(m1.template triangularView<Lower>()));
+ VERIFY_IS_APPROX(m3, m3.adjoint());
+
+ m3 = m1.template selfadjointView<Upper>();
+ m4 = m2;
+ m4 += m1.template selfadjointView<Upper>();
+ VERIFY_IS_APPROX(m4, m2+m3);
+
+ m3 = m1.template selfadjointView<Lower>();
+ m4 = m2;
+ m4 -= m1.template selfadjointView<Lower>();
+ VERIFY_IS_APPROX(m4, m2-m3);
+}
+
+void bug_159()
+{
+ Matrix3d m = Matrix3d::Random().selfadjointView<Lower>();
+ EIGEN_UNUSED_VARIABLE(m)
+}
+
+EIGEN_DECLARE_TEST(selfadjoint)
+{
+ for(int i = 0; i < g_repeat ; i++)
+ {
+ int s = internal::random<int>(1,EIGEN_TEST_MAX_SIZE);
+
+ CALL_SUBTEST_1( selfadjoint(Matrix<float, 1, 1>()) );
+ CALL_SUBTEST_2( selfadjoint(Matrix<float, 2, 2>()) );
+ CALL_SUBTEST_3( selfadjoint(Matrix3cf()) );
+ CALL_SUBTEST_4( selfadjoint(MatrixXcd(s,s)) );
+ CALL_SUBTEST_5( selfadjoint(Matrix<float,Dynamic,Dynamic,RowMajor>(s, s)) );
+
+ TEST_SET_BUT_UNUSED_VARIABLE(s)
+ }
+
+ CALL_SUBTEST_1( bug_159() );
+}
diff --git a/test/serializer.cpp b/test/serializer.cpp
new file mode 100644
index 0000000..76b9083
--- /dev/null
+++ b/test/serializer.cpp
@@ -0,0 +1,168 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2021 The Eigen Team
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "main.h"
+
+#include <vector>
+#include <Eigen/Core>
+
+struct MyPodType {
+ double x;
+ int y;
+ float z;
+};
+
+// Plain-old-data serialization.
+void test_pod_type() {
+ MyPodType initial = {1.3, 17, 1.9f};
+ MyPodType clone = {-1, -1, -1};
+
+ Eigen::Serializer<MyPodType> serializer;
+
+ // Determine required size.
+ size_t buffer_size = serializer.size(initial);
+ VERIFY_IS_EQUAL(buffer_size, sizeof(MyPodType));
+
+ // Serialize.
+ std::vector<uint8_t> buffer(buffer_size);
+ uint8_t* begin = buffer.data();
+ uint8_t* end = buffer.data() + buffer.size();
+ uint8_t* dest = serializer.serialize(begin, end, initial);
+ VERIFY(dest != nullptr);
+ VERIFY_IS_EQUAL(dest - begin, buffer_size);
+
+ // Deserialize.
+ const uint8_t* src = serializer.deserialize(begin, end, clone);
+ VERIFY(src != nullptr);
+ VERIFY_IS_EQUAL(src - begin, buffer_size);
+ VERIFY_IS_EQUAL(clone.x, initial.x);
+ VERIFY_IS_EQUAL(clone.y, initial.y);
+ VERIFY_IS_EQUAL(clone.z, initial.z);
+
+ // Serialize with bounds checking errors.
+ dest = serializer.serialize(begin, end - 1, initial);
+ VERIFY(dest == nullptr);
+ dest = serializer.serialize(begin, begin, initial);
+ VERIFY(dest == nullptr);
+ dest = serializer.serialize(nullptr, nullptr, initial);
+ VERIFY(dest == nullptr);
+
+ // Deserialize with bounds checking errors.
+ src = serializer.deserialize(begin, end - 1, clone);
+ VERIFY(src == nullptr);
+ src = serializer.deserialize(begin, begin, clone);
+ VERIFY(src == nullptr);
+ src = serializer.deserialize(nullptr, nullptr, clone);
+ VERIFY(src == nullptr);
+}
+
+// Matrix, Vector, Array
+template<typename T>
+void test_eigen_type(const T& type) {
+ const Index rows = type.rows();
+ const Index cols = type.cols();
+
+ const T initial = T::Random(rows, cols);
+
+ // Serialize.
+ Eigen::Serializer<T> serializer;
+ size_t buffer_size = serializer.size(initial);
+ std::vector<uint8_t> buffer(buffer_size);
+ uint8_t* begin = buffer.data();
+ uint8_t* end = buffer.data() + buffer.size();
+ uint8_t* dest = serializer.serialize(begin, end, initial);
+ VERIFY(dest != nullptr);
+ VERIFY_IS_EQUAL(dest - begin, buffer_size);
+
+ // Deserialize.
+ T clone;
+ const uint8_t* src = serializer.deserialize(begin, end, clone);
+ VERIFY(src != nullptr);
+ VERIFY_IS_EQUAL(src - begin, buffer_size);
+ VERIFY_IS_CWISE_EQUAL(clone, initial);
+
+ // Serialize with bounds checking errors.
+ dest = serializer.serialize(begin, end - 1, initial);
+ VERIFY(dest == nullptr);
+ dest = serializer.serialize(begin, begin, initial);
+ VERIFY(dest == nullptr);
+ dest = serializer.serialize(nullptr, nullptr, initial);
+ VERIFY(dest == nullptr);
+
+ // Deserialize with bounds checking errors.
+ src = serializer.deserialize(begin, end - 1, clone);
+ VERIFY(src == nullptr);
+ src = serializer.deserialize(begin, begin, clone);
+ VERIFY(src == nullptr);
+ src = serializer.deserialize(nullptr, nullptr, clone);
+ VERIFY(src == nullptr);
+}
+
+// Test a collection of dense types.
+template<typename T1, typename T2, typename T3>
+void test_dense_types(const T1& type1, const T2& type2, const T3& type3) {
+
+ // Make random inputs.
+ const T1 x1 = T1::Random(type1.rows(), type1.cols());
+ const T2 x2 = T2::Random(type2.rows(), type2.cols());
+ const T3 x3 = T3::Random(type3.rows(), type3.cols());
+
+ // Allocate buffer and serialize.
+ size_t buffer_size = Eigen::serialize_size(x1, x2, x3);
+ std::vector<uint8_t> buffer(buffer_size);
+ uint8_t* begin = buffer.data();
+ uint8_t* end = buffer.data() + buffer.size();
+ uint8_t* dest = Eigen::serialize(begin, end, x1, x2, x3);
+ VERIFY(dest != nullptr);
+
+ // Clone everything.
+ T1 y1;
+ T2 y2;
+ T3 y3;
+ const uint8_t* src = Eigen::deserialize(begin, end, y1, y2, y3);
+ VERIFY(src != nullptr);
+
+ // Verify they equal.
+ VERIFY_IS_CWISE_EQUAL(y1, x1);
+ VERIFY_IS_CWISE_EQUAL(y2, x2);
+ VERIFY_IS_CWISE_EQUAL(y3, x3);
+
+ // Serialize everything with bounds checking errors.
+ dest = Eigen::serialize(begin, end - 1, y1, y2, y3);
+ VERIFY(dest == nullptr);
+ dest = Eigen::serialize(begin, begin, y1, y2, y3);
+ VERIFY(dest == nullptr);
+ dest = Eigen::serialize(nullptr, nullptr, y1, y2, y3);
+ VERIFY(dest == nullptr);
+
+ // Deserialize everything with bounds checking errors.
+ src = Eigen::deserialize(begin, end - 1, y1, y2, y3);
+ VERIFY(src == nullptr);
+ src = Eigen::deserialize(begin, begin, y1, y2, y3);
+ VERIFY(src == nullptr);
+ src = Eigen::deserialize(nullptr, nullptr, y1, y2, y3);
+ VERIFY(src == nullptr);
+}
+
+EIGEN_DECLARE_TEST(serializer)
+{
+ CALL_SUBTEST( test_pod_type() );
+
+ for(int i = 0; i < g_repeat; i++) {
+ CALL_SUBTEST( test_eigen_type(Eigen::Array33f()) );
+ CALL_SUBTEST( test_eigen_type(Eigen::ArrayXd(10)) );
+ CALL_SUBTEST( test_eigen_type(Eigen::Vector3f()) );
+ CALL_SUBTEST( test_eigen_type(Eigen::Matrix4d()) );
+ CALL_SUBTEST( test_eigen_type(Eigen::MatrixXd(15, 17)) );
+
+ CALL_SUBTEST( test_dense_types( Eigen::Array33f(),
+ Eigen::ArrayXd(10),
+ Eigen::MatrixXd(15, 17)) );
+ }
+}
diff --git a/test/simplicial_cholesky.cpp b/test/simplicial_cholesky.cpp
new file mode 100644
index 0000000..538d01a
--- /dev/null
+++ b/test/simplicial_cholesky.cpp
@@ -0,0 +1,50 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2011 Gael Guennebaud <g.gael@free.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "sparse_solver.h"
+
+template<typename T, typename I_, int flag> void test_simplicial_cholesky_T()
+{
+ typedef SparseMatrix<T,flag,I_> SparseMatrixType;
+ SimplicialCholesky<SparseMatrixType, Lower> chol_colmajor_lower_amd;
+ SimplicialCholesky<SparseMatrixType, Upper> chol_colmajor_upper_amd;
+ SimplicialLLT< SparseMatrixType, Lower> llt_colmajor_lower_amd;
+ SimplicialLLT< SparseMatrixType, Upper> llt_colmajor_upper_amd;
+ SimplicialLDLT< SparseMatrixType, Lower> ldlt_colmajor_lower_amd;
+ SimplicialLDLT< SparseMatrixType, Upper> ldlt_colmajor_upper_amd;
+ SimplicialLDLT< SparseMatrixType, Lower, NaturalOrdering<I_> > ldlt_colmajor_lower_nat;
+ SimplicialLDLT< SparseMatrixType, Upper, NaturalOrdering<I_> > ldlt_colmajor_upper_nat;
+
+ check_sparse_spd_solving(chol_colmajor_lower_amd);
+ check_sparse_spd_solving(chol_colmajor_upper_amd);
+ check_sparse_spd_solving(llt_colmajor_lower_amd);
+ check_sparse_spd_solving(llt_colmajor_upper_amd);
+ check_sparse_spd_solving(ldlt_colmajor_lower_amd);
+ check_sparse_spd_solving(ldlt_colmajor_upper_amd);
+
+ check_sparse_spd_determinant(chol_colmajor_lower_amd);
+ check_sparse_spd_determinant(chol_colmajor_upper_amd);
+ check_sparse_spd_determinant(llt_colmajor_lower_amd);
+ check_sparse_spd_determinant(llt_colmajor_upper_amd);
+ check_sparse_spd_determinant(ldlt_colmajor_lower_amd);
+ check_sparse_spd_determinant(ldlt_colmajor_upper_amd);
+
+ check_sparse_spd_solving(ldlt_colmajor_lower_nat, (std::min)(300,EIGEN_TEST_MAX_SIZE), 1000);
+ check_sparse_spd_solving(ldlt_colmajor_upper_nat, (std::min)(300,EIGEN_TEST_MAX_SIZE), 1000);
+}
+
+EIGEN_DECLARE_TEST(simplicial_cholesky)
+{
+ CALL_SUBTEST_11(( test_simplicial_cholesky_T<double, int, ColMajor>() ));
+ CALL_SUBTEST_12(( test_simplicial_cholesky_T<std::complex<double>, int, ColMajor>() ));
+ CALL_SUBTEST_13(( test_simplicial_cholesky_T<double, long int, ColMajor>() ));
+ CALL_SUBTEST_21(( test_simplicial_cholesky_T<double, int, RowMajor>() ));
+ CALL_SUBTEST_22(( test_simplicial_cholesky_T<std::complex<double>, int, RowMajor>() ));
+ CALL_SUBTEST_23(( test_simplicial_cholesky_T<double, long int, RowMajor>() ));
+}
diff --git a/test/sizeof.cpp b/test/sizeof.cpp
new file mode 100644
index 0000000..af34e97
--- /dev/null
+++ b/test/sizeof.cpp
@@ -0,0 +1,47 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "main.h"
+
+template<typename MatrixType> void verifySizeOf(const MatrixType&)
+{
+ typedef typename MatrixType::Scalar Scalar;
+ if (MatrixType::RowsAtCompileTime!=Dynamic && MatrixType::ColsAtCompileTime!=Dynamic)
+ VERIFY_IS_EQUAL(std::ptrdiff_t(sizeof(MatrixType)),std::ptrdiff_t(sizeof(Scalar))*std::ptrdiff_t(MatrixType::SizeAtCompileTime));
+ else
+ VERIFY_IS_EQUAL(sizeof(MatrixType),sizeof(Scalar*) + 2 * sizeof(Index));
+}
+
+EIGEN_DECLARE_TEST(sizeof)
+{
+ CALL_SUBTEST(verifySizeOf(Matrix<float, 1, 1>()) );
+ CALL_SUBTEST(verifySizeOf(Array<float, 2, 1>()) );
+ CALL_SUBTEST(verifySizeOf(Array<float, 3, 1>()) );
+ CALL_SUBTEST(verifySizeOf(Array<float, 4, 1>()) );
+ CALL_SUBTEST(verifySizeOf(Array<float, 5, 1>()) );
+ CALL_SUBTEST(verifySizeOf(Array<float, 6, 1>()) );
+ CALL_SUBTEST(verifySizeOf(Array<float, 7, 1>()) );
+ CALL_SUBTEST(verifySizeOf(Array<float, 8, 1>()) );
+ CALL_SUBTEST(verifySizeOf(Array<float, 9, 1>()) );
+ CALL_SUBTEST(verifySizeOf(Array<float, 10, 1>()) );
+ CALL_SUBTEST(verifySizeOf(Array<float, 11, 1>()) );
+ CALL_SUBTEST(verifySizeOf(Array<float, 12, 1>()) );
+ CALL_SUBTEST(verifySizeOf(Vector2d()) );
+ CALL_SUBTEST(verifySizeOf(Vector4f()) );
+ CALL_SUBTEST(verifySizeOf(Matrix4d()) );
+ CALL_SUBTEST(verifySizeOf(Matrix<double, 4, 2>()) );
+ CALL_SUBTEST(verifySizeOf(Matrix<bool, 7, 5>()) );
+ CALL_SUBTEST(verifySizeOf(MatrixXcf(3, 3)) );
+ CALL_SUBTEST(verifySizeOf(MatrixXi(8, 12)) );
+ CALL_SUBTEST(verifySizeOf(MatrixXcd(20, 20)) );
+ CALL_SUBTEST(verifySizeOf(Matrix<float, 100, 100>()) );
+
+ VERIFY(sizeof(std::complex<float>) == 2*sizeof(float));
+ VERIFY(sizeof(std::complex<double>) == 2*sizeof(double));
+}
diff --git a/test/sizeoverflow.cpp b/test/sizeoverflow.cpp
new file mode 100644
index 0000000..4213512
--- /dev/null
+++ b/test/sizeoverflow.cpp
@@ -0,0 +1,64 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2011 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "main.h"
+
+#define VERIFY_THROWS_BADALLOC(a) { \
+ bool threw = false; \
+ try { \
+ a; \
+ } \
+ catch (std::bad_alloc&) { threw = true; } \
+ VERIFY(threw && "should have thrown bad_alloc: " #a); \
+ }
+
+template<typename MatrixType>
+void triggerMatrixBadAlloc(Index rows, Index cols)
+{
+ VERIFY_THROWS_BADALLOC( MatrixType m(rows, cols) );
+ VERIFY_THROWS_BADALLOC( MatrixType m; m.resize(rows, cols) );
+ VERIFY_THROWS_BADALLOC( MatrixType m; m.conservativeResize(rows, cols) );
+}
+
+template<typename VectorType>
+void triggerVectorBadAlloc(Index size)
+{
+ VERIFY_THROWS_BADALLOC( VectorType v(size) );
+ VERIFY_THROWS_BADALLOC( VectorType v; v.resize(size) );
+ VERIFY_THROWS_BADALLOC( VectorType v; v.conservativeResize(size) );
+}
+
+EIGEN_DECLARE_TEST(sizeoverflow)
+{
+ // there are 2 levels of overflow checking. first in PlainObjectBase.h we check for overflow in rows*cols computations.
+ // this is tested in tests of the form times_itself_gives_0 * times_itself_gives_0
+ // Then in Memory.h we check for overflow in size * sizeof(T) computations.
+ // this is tested in tests of the form times_4_gives_0 * sizeof(float)
+
+ size_t times_itself_gives_0 = size_t(1) << (8 * sizeof(Index) / 2);
+ VERIFY(times_itself_gives_0 * times_itself_gives_0 == 0);
+
+ size_t times_4_gives_0 = size_t(1) << (8 * sizeof(Index) - 2);
+ VERIFY(times_4_gives_0 * 4 == 0);
+
+ size_t times_8_gives_0 = size_t(1) << (8 * sizeof(Index) - 3);
+ VERIFY(times_8_gives_0 * 8 == 0);
+
+ triggerMatrixBadAlloc<MatrixXf>(times_itself_gives_0, times_itself_gives_0);
+ triggerMatrixBadAlloc<MatrixXf>(times_itself_gives_0 / 4, times_itself_gives_0);
+ triggerMatrixBadAlloc<MatrixXf>(times_4_gives_0, 1);
+
+ triggerMatrixBadAlloc<MatrixXd>(times_itself_gives_0, times_itself_gives_0);
+ triggerMatrixBadAlloc<MatrixXd>(times_itself_gives_0 / 8, times_itself_gives_0);
+ triggerMatrixBadAlloc<MatrixXd>(times_8_gives_0, 1);
+
+ triggerVectorBadAlloc<VectorXf>(times_4_gives_0);
+
+ triggerVectorBadAlloc<VectorXd>(times_8_gives_0);
+}
diff --git a/test/skew_symmetric_matrix3.cpp b/test/skew_symmetric_matrix3.cpp
new file mode 100644
index 0000000..6dad003
--- /dev/null
+++ b/test/skew_symmetric_matrix3.cpp
@@ -0,0 +1,217 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "main.h"
+#include <Eigen/LU>
+
+namespace {
+template <typename Scalar>
+void constructors() {
+ typedef Matrix<Scalar, 3, 1> Vector;
+ const Vector v = Vector::Random();
+ // l-value
+ const SkewSymmetricMatrix3<Scalar> s1(v);
+ const Vector& v1 = s1.vector();
+ VERIFY_IS_APPROX(v1, v);
+ VERIFY(s1.cols() == 3);
+ VERIFY(s1.rows() == 3);
+
+ // r-value
+ const SkewSymmetricMatrix3<Scalar> s2(std::move(v));
+ VERIFY_IS_APPROX(v1, s2.vector());
+ VERIFY_IS_APPROX(s1.toDenseMatrix(), s2.toDenseMatrix());
+
+ // from scalars
+ SkewSymmetricMatrix3<Scalar> s4(v1(0), v1(1), v1(2));
+ VERIFY_IS_APPROX(v1, s4.vector());
+
+ // constructors with four vectors do not compile
+ // Matrix<Scalar, 4, 1> vector4 = Matrix<Scalar, 4, 1>::Random();
+ // SkewSymmetricMatrix3<Scalar> s5(vector4);
+}
+
+template <typename Scalar>
+void assignments() {
+ typedef Matrix<Scalar, 3, 1> Vector;
+ typedef Matrix<Scalar, 3, 3> SquareMatrix;
+
+ const Vector v = Vector::Random();
+
+ // assign to square matrix
+ SquareMatrix sq;
+ sq = v.asSkewSymmetric();
+ VERIFY(sq.isSkewSymmetric());
+
+ // assign to skew symmetric matrix
+ SkewSymmetricMatrix3<Scalar> sk;
+ sk = v.asSkewSymmetric();
+ VERIFY_IS_APPROX(v, sk.vector());
+}
+
+template <typename Scalar>
+void plusMinus() {
+ typedef Matrix<Scalar, 3, 1> Vector;
+ typedef Matrix<Scalar, 3, 3> SquareMatrix;
+
+ const Vector v1 = Vector::Random();
+ const Vector v2 = Vector::Random();
+
+ SquareMatrix sq1;
+ sq1 = v1.asSkewSymmetric();
+ SquareMatrix sq2;
+ sq2 = v2.asSkewSymmetric();
+
+ SkewSymmetricMatrix3<Scalar> sk1;
+ sk1 = v1.asSkewSymmetric();
+ SkewSymmetricMatrix3<Scalar> sk2;
+ sk2 = v2.asSkewSymmetric();
+
+ VERIFY_IS_APPROX((sk1 + sk2).toDenseMatrix(), sq1 + sq2);
+ VERIFY_IS_APPROX((sk1 - sk2).toDenseMatrix(), sq1 - sq2);
+
+ SquareMatrix sq3 = v1.asSkewSymmetric();
+ VERIFY_IS_APPROX( sq3 = v1.asSkewSymmetric() + v2.asSkewSymmetric(), sq1 + sq2);
+ VERIFY_IS_APPROX( sq3 = v1.asSkewSymmetric() - v2.asSkewSymmetric(), sq1 - sq2);
+ VERIFY_IS_APPROX( sq3 = v1.asSkewSymmetric() - 2*v2.asSkewSymmetric() + v1.asSkewSymmetric(), sq1 - 2*sq2 + sq1);
+
+ VERIFY_IS_APPROX((sk1 + sk1).vector(), 2*v1);
+ VERIFY((sk1 - sk1).vector().isZero());
+ VERIFY((sk1 - sk1).toDenseMatrix().isZero());
+}
+
+
+template <typename Scalar>
+void multiplyScale() {
+ typedef Matrix<Scalar, 3, 1> Vector;
+ typedef Matrix<Scalar, 3, 3> SquareMatrix;
+
+ const Vector v1 = Vector::Random();
+ SquareMatrix sq1;
+ sq1 = v1.asSkewSymmetric();
+ SkewSymmetricMatrix3<Scalar> sk1;
+ sk1 = v1.asSkewSymmetric();
+
+ const Scalar s1 = internal::random<Scalar>();
+ VERIFY_IS_APPROX(SkewSymmetricMatrix3<Scalar>(sk1*s1).vector(), sk1.vector() * s1);
+ VERIFY_IS_APPROX(SkewSymmetricMatrix3<Scalar>(s1*sk1).vector(), s1 * sk1.vector());
+ VERIFY_IS_APPROX(sq1 * (sk1 * s1), (sq1 * sk1) * s1);
+
+ const Vector v2 = Vector::Random();
+ SquareMatrix sq2;
+ sq2 = v2.asSkewSymmetric();
+ SkewSymmetricMatrix3<Scalar> sk2;
+ sk2 = v2.asSkewSymmetric();
+ VERIFY_IS_APPROX(sk1*sk2, sq1*sq2);
+
+ // null space
+ VERIFY((sk1*v1).isZero());
+ VERIFY((sk2*v2).isZero());
+}
+
+template<typename Matrix>
+void skewSymmetricMultiplication(const Matrix& m) {
+ typedef Eigen::Matrix<typename Matrix::Scalar, 3, 1> Vector;
+ const Vector v = Vector::Random();
+ const Matrix m1 = Matrix::Random(m.rows(), m.cols());
+ const SkewSymmetricMatrix3<typename Matrix::Scalar> sk = v.asSkewSymmetric();
+ VERIFY_IS_APPROX(m1.transpose() * (sk * m1), (m1.transpose() * sk) * m1);
+ VERIFY((m1.transpose() * (sk * m1)).isSkewSymmetric());
+}
+
+template <typename Scalar>
+void traceAndDet() {
+ typedef Matrix<Scalar, 3, 1> Vector;
+ const Vector v = Vector::Random();
+ // this does not work, values larger than 1.e-08 can be seen
+ //VERIFY_IS_APPROX(sq.determinant(), static_cast<Scalar>(0));
+ VERIFY_IS_APPROX(v.asSkewSymmetric().determinant(), static_cast<Scalar>(0));
+ VERIFY_IS_APPROX(v.asSkewSymmetric().toDenseMatrix().trace(), static_cast<Scalar>(0));
+}
+
+template <typename Scalar>
+void transpose() {
+ typedef Matrix<Scalar, 3, 1> Vector;
+ const Vector v = Vector::Random();
+ // By definition of a skew symmetric matrix: A^T = -A
+ VERIFY_IS_APPROX(v.asSkewSymmetric().toDenseMatrix().transpose(), v.asSkewSymmetric().transpose().toDenseMatrix());
+ VERIFY_IS_APPROX(v.asSkewSymmetric().transpose().vector(), (-v).asSkewSymmetric().vector());
+}
+
+template <typename Scalar>
+void exponentialIdentity() {
+ typedef Matrix<Scalar, 3, 1> Vector;
+ const Vector v1 = Vector::Zero();
+ VERIFY(v1.asSkewSymmetric().exponential().isIdentity());
+
+ Vector v2 = Vector::Random();
+ v2.normalize();
+ VERIFY((2*EIGEN_PI*v2).asSkewSymmetric().exponential().isIdentity());
+
+ Vector v3;
+ const auto precision = static_cast<Scalar>(1.1)*NumTraits<Scalar>::dummy_precision();
+ v3 << 0, 0, precision;
+ VERIFY(v3.asSkewSymmetric().exponential().isIdentity(precision));
+}
+
+template <typename Scalar>
+void exponentialOrthogonality() {
+ typedef Matrix<Scalar, 3, 1> Vector;
+ typedef Matrix<Scalar, 3, 3> SquareMatrix;
+ const Vector v = Vector::Random();
+ SquareMatrix sq = v.asSkewSymmetric().exponential();
+ VERIFY(sq.isUnitary());
+}
+
+template <typename Scalar>
+void exponentialRotation() {
+ typedef Matrix<Scalar, 3, 1> Vector;
+ typedef Matrix<Scalar, 3, 3> SquareMatrix;
+
+ // rotation axis is invariant
+ const Vector v1 = Vector::Random();
+ const SquareMatrix r1 = v1.asSkewSymmetric().exponential();
+ VERIFY_IS_APPROX(r1*v1, v1);
+
+ // rotate around z-axis
+ Vector v2;
+ v2 << 0, 0, EIGEN_PI;
+ const SquareMatrix r2 = v2.asSkewSymmetric().exponential();
+ VERIFY_IS_APPROX(r2*(Vector() << 1,0,0).finished(), (Vector() << -1,0,0).finished());
+ VERIFY_IS_APPROX(r2*(Vector() << 0,1,0).finished(), (Vector() << 0,-1,0).finished());
+}
+
+
+} // namespace
+
+
+EIGEN_DECLARE_TEST(skew_symmetric_matrix3)
+{
+ for(int i = 0; i < g_repeat; i++) {
+ CALL_SUBTEST_1(constructors<float>());
+ CALL_SUBTEST_1(constructors<double>());
+ CALL_SUBTEST_1(assignments<float>());
+ CALL_SUBTEST_1(assignments<double>());
+
+ CALL_SUBTEST_2(plusMinus<float>());
+ CALL_SUBTEST_2(plusMinus<double>());
+ CALL_SUBTEST_2(multiplyScale<float>());
+ CALL_SUBTEST_2(multiplyScale<double>());
+ CALL_SUBTEST_2(skewSymmetricMultiplication(MatrixXf(3,internal::random<int>(1,EIGEN_TEST_MAX_SIZE))));
+ CALL_SUBTEST_2(skewSymmetricMultiplication(MatrixXd(3,internal::random<int>(1,EIGEN_TEST_MAX_SIZE))));
+ CALL_SUBTEST_2(traceAndDet<float>());
+ CALL_SUBTEST_2(traceAndDet<double>());
+ CALL_SUBTEST_2(transpose<float>());
+ CALL_SUBTEST_2(transpose<double>());
+
+ CALL_SUBTEST_3(exponentialIdentity<float>());
+ CALL_SUBTEST_3(exponentialIdentity<double>());
+ CALL_SUBTEST_3(exponentialOrthogonality<float>());
+ CALL_SUBTEST_3(exponentialOrthogonality<double>());
+ CALL_SUBTEST_3(exponentialRotation<float>());
+ CALL_SUBTEST_3(exponentialRotation<double>());
+ }
+}
diff --git a/test/smallvectors.cpp b/test/smallvectors.cpp
new file mode 100644
index 0000000..d58038f
--- /dev/null
+++ b/test/smallvectors.cpp
@@ -0,0 +1,49 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "main.h"
+
+template<typename Scalar> void smallVectors()
+{
+ typedef Matrix<Scalar, 1, 2> V2;
+ typedef Matrix<Scalar, 3, 1> V3;
+ typedef Matrix<Scalar, 1, 4> V4;
+ typedef Matrix<Scalar, Dynamic, 1> VX;
+ Scalar x1 = internal::random<Scalar>(),
+ x2 = internal::random<Scalar>(),
+ x3 = internal::random<Scalar>(),
+ x4 = internal::random<Scalar>();
+ V2 v2(x1, x2);
+ V3 v3(x1, x2, x3);
+ V4 v4(x1, x2, x3, x4);
+ VERIFY_IS_APPROX(x1, v2.x());
+ VERIFY_IS_APPROX(x1, v3.x());
+ VERIFY_IS_APPROX(x1, v4.x());
+ VERIFY_IS_APPROX(x2, v2.y());
+ VERIFY_IS_APPROX(x2, v3.y());
+ VERIFY_IS_APPROX(x2, v4.y());
+ VERIFY_IS_APPROX(x3, v3.z());
+ VERIFY_IS_APPROX(x3, v4.z());
+ VERIFY_IS_APPROX(x4, v4.w());
+
+ VERIFY_RAISES_ASSERT(V3(2, 1))
+ VERIFY_RAISES_ASSERT(V3(3, 2))
+ VERIFY_RAISES_ASSERT(V4(1, 3))
+ VERIFY_RAISES_ASSERT(V4(2, 4))
+ VERIFY_RAISES_ASSERT(VX(3, 2))
+}
+
+EIGEN_DECLARE_TEST(smallvectors)
+{
+ for(int i = 0; i < g_repeat; i++) {
+ CALL_SUBTEST(smallVectors<int>() );
+ CALL_SUBTEST(smallVectors<float>() );
+ CALL_SUBTEST(smallVectors<double>() );
+ }
+}
diff --git a/test/solverbase.h b/test/solverbase.h
new file mode 100644
index 0000000..ba76ba4
--- /dev/null
+++ b/test/solverbase.h
@@ -0,0 +1,40 @@
+#ifndef TEST_SOLVERBASE_H
+#define TEST_SOLVERBASE_H
+
+template<typename DstType, typename RhsType, typename MatrixType, typename SolverType>
+void check_solverbase(const MatrixType& matrix, const SolverType& solver, Index rows, Index cols, Index cols2)
+{
+ // solve
+ DstType m2 = DstType::Random(cols,cols2);
+ RhsType m3 = matrix*m2;
+ DstType solver_solution = DstType::Random(cols,cols2);
+ solver._solve_impl(m3, solver_solution);
+ VERIFY_IS_APPROX(m3, matrix*solver_solution);
+ solver_solution = DstType::Random(cols,cols2);
+ solver_solution = solver.solve(m3);
+ VERIFY_IS_APPROX(m3, matrix*solver_solution);
+ // test solve with transposed
+ m3 = RhsType::Random(rows,cols2);
+ m2 = matrix.transpose()*m3;
+ RhsType solver_solution2 = RhsType::Random(rows,cols2);
+ solver.template _solve_impl_transposed<false>(m2, solver_solution2);
+ VERIFY_IS_APPROX(m2, matrix.transpose()*solver_solution2);
+ solver_solution2 = RhsType::Random(rows,cols2);
+ solver_solution2 = solver.transpose().solve(m2);
+ VERIFY_IS_APPROX(m2, matrix.transpose()*solver_solution2);
+ // test solve with conjugate transposed
+ m3 = RhsType::Random(rows,cols2);
+ m2 = matrix.adjoint()*m3;
+ solver_solution2 = RhsType::Random(rows,cols2);
+ solver.template _solve_impl_transposed<true>(m2, solver_solution2);
+ VERIFY_IS_APPROX(m2, matrix.adjoint()*solver_solution2);
+ solver_solution2 = RhsType::Random(rows,cols2);
+ solver_solution2 = solver.adjoint().solve(m2);
+ VERIFY_IS_APPROX(m2, matrix.adjoint()*solver_solution2);
+ // test with temporary expression as rhs
+ m2 = DstType::Random(cols,cols2);
+ solver_solution = solver.solve(matrix*m2);
+ VERIFY_IS_APPROX(matrix*m2, matrix*solver_solution);
+}
+
+#endif // TEST_SOLVERBASE_H
diff --git a/test/sparse.h b/test/sparse.h
new file mode 100644
index 0000000..f3e697d
--- /dev/null
+++ b/test/sparse.h
@@ -0,0 +1,157 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2011 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_TESTSPARSE_H
+#define EIGEN_TESTSPARSE_H
+
+#define EIGEN_YES_I_KNOW_SPARSE_MODULE_IS_NOT_STABLE_YET
+
+#include "main.h"
+
+#ifdef min
+#undef min
+#endif
+
+#ifdef max
+#undef max
+#endif
+
+#include <unordered_map>
+#define EIGEN_UNORDERED_MAP_SUPPORT
+
+#include <Eigen/Cholesky>
+#include <Eigen/LU>
+#include <Eigen/Sparse>
+
+enum {
+ ForceNonZeroDiag = 1,
+ MakeLowerTriangular = 2,
+ MakeUpperTriangular = 4,
+ ForceRealDiag = 8
+};
+
+/* Initializes both a sparse and dense matrix with same random values,
+ * and a ratio of \a density non zero entries.
+ * \param flags is a union of ForceNonZeroDiag, MakeLowerTriangular and MakeUpperTriangular
+ * allowing to control the shape of the matrix.
+ * \param zeroCoords and nonzeroCoords allows to get the coordinate lists of the non zero,
+ * and zero coefficients respectively.
+ */
+template<typename Scalar,int Opt1,int Opt2,typename StorageIndex> void
+initSparse(double density,
+ Matrix<Scalar,Dynamic,Dynamic,Opt1>& refMat,
+ SparseMatrix<Scalar,Opt2,StorageIndex>& sparseMat,
+ int flags = 0,
+ std::vector<Matrix<StorageIndex,2,1> >* zeroCoords = 0,
+ std::vector<Matrix<StorageIndex,2,1> >* nonzeroCoords = 0)
+{
+ enum { IsRowMajor = SparseMatrix<Scalar,Opt2,StorageIndex>::IsRowMajor };
+ sparseMat.setZero();
+ //sparseMat.reserve(int(refMat.rows()*refMat.cols()*density));
+ int nnz = static_cast<int>((1.5 * density) * static_cast<double>(IsRowMajor ? refMat.cols() : refMat.rows()));
+ sparseMat.reserve(VectorXi::Constant(IsRowMajor ? refMat.rows() : refMat.cols(), nnz));
+
+ Index insert_count = 0;
+ for(Index j=0; j<sparseMat.outerSize(); j++)
+ {
+ //sparseMat.startVec(j);
+ for(Index i=0; i<sparseMat.innerSize(); i++)
+ {
+ Index ai(i), aj(j);
+ if(IsRowMajor)
+ std::swap(ai,aj);
+ Scalar v = (internal::random<double>(0,1) < density) ? internal::random<Scalar>() : Scalar(0);
+ if ((flags&ForceNonZeroDiag) && (i==j))
+ {
+ // FIXME: the following is too conservative
+ v = internal::random<Scalar>()*Scalar(3.);
+ v = v*v;
+ if(numext::real(v)>0) v += Scalar(5);
+ else v -= Scalar(5);
+ }
+ if ((flags & MakeLowerTriangular) && aj>ai)
+ v = Scalar(0);
+ else if ((flags & MakeUpperTriangular) && aj<ai)
+ v = Scalar(0);
+
+ if ((flags&ForceRealDiag) && (i==j))
+ v = numext::real(v);
+
+ if (!numext::is_exactly_zero(v))
+ {
+ //sparseMat.insertBackByOuterInner(j,i) = v;
+ sparseMat.insertByOuterInner(j,i) = v;
+ ++insert_count;
+ if (nonzeroCoords)
+ nonzeroCoords->push_back(Matrix<StorageIndex,2,1> (ai,aj));
+ }
+ else if (zeroCoords)
+ {
+ zeroCoords->push_back(Matrix<StorageIndex,2,1> (ai,aj));
+ }
+ refMat(ai,aj) = v;
+
+ // make sure we only insert as many as the sparse matrix supports
+ if(insert_count == NumTraits<StorageIndex>::highest()) return;
+ }
+ }
+ //sparseMat.finalize();
+}
+
+template<typename Scalar,int Options,typename Index> void
+initSparse(double density,
+ Matrix<Scalar,Dynamic,1>& refVec,
+ SparseVector<Scalar,Options,Index>& sparseVec,
+ std::vector<int>* zeroCoords = 0,
+ std::vector<int>* nonzeroCoords = 0)
+{
+ sparseVec.reserve(int(refVec.size()*density));
+ sparseVec.setZero();
+ for(int i=0; i<refVec.size(); i++)
+ {
+ Scalar v = (internal::random<double>(0,1) < density) ? internal::random<Scalar>() : Scalar(0);
+ if (!numext::is_exactly_zero(v))
+ {
+ sparseVec.insertBack(i) = v;
+ if (nonzeroCoords)
+ nonzeroCoords->push_back(i);
+ }
+ else if (zeroCoords)
+ zeroCoords->push_back(i);
+ refVec[i] = v;
+ }
+}
+
+template<typename Scalar,int Options,typename Index> void
+initSparse(double density,
+ Matrix<Scalar,1,Dynamic>& refVec,
+ SparseVector<Scalar,Options,Index>& sparseVec,
+ std::vector<int>* zeroCoords = 0,
+ std::vector<int>* nonzeroCoords = 0)
+{
+ sparseVec.reserve(int(refVec.size()*density));
+ sparseVec.setZero();
+ for(int i=0; i<refVec.size(); i++)
+ {
+ Scalar v = (internal::random<double>(0,1) < density) ? internal::random<Scalar>() : Scalar(0);
+ if (v!=Scalar(0))
+ {
+ sparseVec.insertBack(i) = v;
+ if (nonzeroCoords)
+ nonzeroCoords->push_back(i);
+ }
+ else if (zeroCoords)
+ zeroCoords->push_back(i);
+ refVec[i] = v;
+ }
+}
+
+
+#include <unsupported/Eigen/SparseExtra>
+#endif // EIGEN_TESTSPARSE_H
diff --git a/test/sparseLM.cpp b/test/sparseLM.cpp
new file mode 100644
index 0000000..a48fcb6
--- /dev/null
+++ b/test/sparseLM.cpp
@@ -0,0 +1,176 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2012 Desire Nuentsa <desire.nuentsa_wakam@inria.fr>
+// Copyright (C) 2012 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+#include <iostream>
+#include <fstream>
+#include <iomanip>
+
+#include "main.h"
+#include <Eigen/LevenbergMarquardt>
+
+using namespace std;
+using namespace Eigen;
+
+template <typename Scalar>
+struct sparseGaussianTest : SparseFunctor<Scalar, int>
+{
+ typedef Matrix<Scalar,Dynamic,1> VectorType;
+ typedef SparseFunctor<Scalar,int> Base;
+ typedef typename Base::JacobianType JacobianType;
+ sparseGaussianTest(int inputs, int values) : SparseFunctor<Scalar,int>(inputs,values)
+ { }
+
+ VectorType model(const VectorType& uv, VectorType& x)
+ {
+ VectorType y; //Change this to use expression template
+ int m = Base::values();
+ int n = Base::inputs();
+ eigen_assert(uv.size()%2 == 0);
+ eigen_assert(uv.size() == n);
+ eigen_assert(x.size() == m);
+ y.setZero(m);
+ int half = n/2;
+ VectorBlock<const VectorType> u(uv, 0, half);
+ VectorBlock<const VectorType> v(uv, half, half);
+ Scalar coeff;
+ for (int j = 0; j < m; j++)
+ {
+ for (int i = 0; i < half; i++)
+ {
+ coeff = (x(j)-i)/v(i);
+ coeff *= coeff;
+ if (coeff < 1. && coeff > 0.)
+ y(j) += u(i)*std::pow((1-coeff), 2);
+ }
+ }
+ return y;
+ }
+ void initPoints(VectorType& uv_ref, VectorType& x)
+ {
+ m_x = x;
+ m_y = this->model(uv_ref,x);
+ }
+ int operator()(const VectorType& uv, VectorType& fvec)
+ {
+ int m = Base::values();
+ int n = Base::inputs();
+ eigen_assert(uv.size()%2 == 0);
+ eigen_assert(uv.size() == n);
+ int half = n/2;
+ VectorBlock<const VectorType> u(uv, 0, half);
+ VectorBlock<const VectorType> v(uv, half, half);
+ fvec = m_y;
+ Scalar coeff;
+ for (int j = 0; j < m; j++)
+ {
+ for (int i = 0; i < half; i++)
+ {
+ coeff = (m_x(j)-i)/v(i);
+ coeff *= coeff;
+ if (coeff < 1. && coeff > 0.)
+ fvec(j) -= u(i)*std::pow((1-coeff), 2);
+ }
+ }
+ return 0;
+ }
+
+ int df(const VectorType& uv, JacobianType& fjac)
+ {
+ int m = Base::values();
+ int n = Base::inputs();
+ eigen_assert(n == uv.size());
+ eigen_assert(fjac.rows() == m);
+ eigen_assert(fjac.cols() == n);
+ int half = n/2;
+ VectorBlock<const VectorType> u(uv, 0, half);
+ VectorBlock<const VectorType> v(uv, half, half);
+ Scalar coeff;
+
+ //Derivatives with respect to u
+ for (int col = 0; col < half; col++)
+ {
+ for (int row = 0; row < m; row++)
+ {
+ coeff = (m_x(row)-col)/v(col);
+ coeff = coeff*coeff;
+ if(coeff < 1. && coeff > 0.)
+ {
+ fjac.coeffRef(row,col) = -(1-coeff)*(1-coeff);
+ }
+ }
+ }
+ //Derivatives with respect to v
+ for (int col = 0; col < half; col++)
+ {
+ for (int row = 0; row < m; row++)
+ {
+ coeff = (m_x(row)-col)/v(col);
+ coeff = coeff*coeff;
+ if(coeff < 1. && coeff > 0.)
+ {
+ fjac.coeffRef(row,col+half) = -4 * (u(col)/v(col))*coeff*(1-coeff);
+ }
+ }
+ }
+ return 0;
+ }
+
+ VectorType m_x, m_y; //Data points
+};
+
+
+template<typename T>
+void test_sparseLM_T()
+{
+ typedef Matrix<T,Dynamic,1> VectorType;
+
+ int inputs = 10;
+ int values = 2000;
+ sparseGaussianTest<T> sparse_gaussian(inputs, values);
+ VectorType uv(inputs),uv_ref(inputs);
+ VectorType x(values);
+ // Generate the reference solution
+ uv_ref << -2, 1, 4 ,8, 6, 1.8, 1.2, 1.1, 1.9 , 3;
+ //Generate the reference data points
+ x.setRandom();
+ x = 10*x;
+ x.array() += 10;
+ sparse_gaussian.initPoints(uv_ref, x);
+
+
+ // Generate the initial parameters
+ VectorBlock<VectorType> u(uv, 0, inputs/2);
+ VectorBlock<VectorType> v(uv, inputs/2, inputs/2);
+ v.setOnes();
+ //Generate u or Solve for u from v
+ u.setOnes();
+
+ // Solve the optimization problem
+ LevenbergMarquardt<sparseGaussianTest<T> > lm(sparse_gaussian);
+ int info;
+// info = lm.minimize(uv);
+
+ VERIFY_IS_EQUAL(info,1);
+ // Do a step by step solution and save the residual
+ int maxiter = 200;
+ int iter = 0;
+ MatrixXd Err(values, maxiter);
+ MatrixXd Mod(values, maxiter);
+ LevenbergMarquardtSpace::Status status;
+ status = lm.minimizeInit(uv);
+ if (status==LevenbergMarquardtSpace::ImproperInputParameters)
+ return ;
+
+}
+EIGEN_DECLARE_TEST(sparseLM)
+{
+ CALL_SUBTEST_1(test_sparseLM_T<double>());
+
+ // CALL_SUBTEST_2(test_sparseLM_T<std::complex<double>());
+}
diff --git a/test/sparse_basic.cpp b/test/sparse_basic.cpp
new file mode 100644
index 0000000..8694490
--- /dev/null
+++ b/test/sparse_basic.cpp
@@ -0,0 +1,752 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2011 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2008 Daniel Gomez Ferro <dgomezferro@gmail.com>
+// Copyright (C) 2013 Désiré Nuentsa-Wakam <desire.nuentsa_wakam@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_SPARSE_TEST_INCLUDED_FROM_SPARSE_EXTRA
+static long g_realloc_count = 0;
+#define EIGEN_SPARSE_COMPRESSED_STORAGE_REALLOCATE_PLUGIN g_realloc_count++;
+
+static long g_dense_op_sparse_count = 0;
+#define EIGEN_SPARSE_ASSIGNMENT_FROM_DENSE_OP_SPARSE_PLUGIN g_dense_op_sparse_count++;
+#define EIGEN_SPARSE_ASSIGNMENT_FROM_SPARSE_ADD_DENSE_PLUGIN g_dense_op_sparse_count+=10;
+#define EIGEN_SPARSE_ASSIGNMENT_FROM_SPARSE_SUB_DENSE_PLUGIN g_dense_op_sparse_count+=20;
+#endif
+
+#include "sparse.h"
+
+template<typename SparseMatrixType> void sparse_basic(const SparseMatrixType& ref)
+{
+ typedef typename SparseMatrixType::StorageIndex StorageIndex;
+ typedef Matrix<StorageIndex,2,1> Vector2;
+
+ const Index rows = ref.rows();
+ const Index cols = ref.cols();
+ //const Index inner = ref.innerSize();
+ //const Index outer = ref.outerSize();
+
+ typedef typename SparseMatrixType::Scalar Scalar;
+ typedef typename SparseMatrixType::RealScalar RealScalar;
+ enum { Flags = SparseMatrixType::Flags };
+
+ double density = (std::max)(8./(rows*cols), 0.01);
+ typedef Matrix<Scalar,Dynamic,Dynamic> DenseMatrix;
+ typedef Matrix<Scalar,Dynamic,1> DenseVector;
+ Scalar eps = 1e-6;
+
+ Scalar s1 = internal::random<Scalar>();
+ {
+ SparseMatrixType m(rows, cols);
+ DenseMatrix refMat = DenseMatrix::Zero(rows, cols);
+ DenseVector vec1 = DenseVector::Random(rows);
+
+ std::vector<Vector2> zeroCoords;
+ std::vector<Vector2> nonzeroCoords;
+ initSparse<Scalar>(density, refMat, m, 0, &zeroCoords, &nonzeroCoords);
+
+ // test coeff and coeffRef
+ for (std::size_t i=0; i<zeroCoords.size(); ++i)
+ {
+ VERIFY_IS_MUCH_SMALLER_THAN( m.coeff(zeroCoords[i].x(),zeroCoords[i].y()), eps );
+ if(internal::is_same<SparseMatrixType,SparseMatrix<Scalar,Flags> >::value)
+ VERIFY_RAISES_ASSERT( m.coeffRef(zeroCoords[i].x(),zeroCoords[i].y()) = 5 );
+ }
+ VERIFY_IS_APPROX(m, refMat);
+
+ if(!nonzeroCoords.empty()) {
+ m.coeffRef(nonzeroCoords[0].x(), nonzeroCoords[0].y()) = Scalar(5);
+ refMat.coeffRef(nonzeroCoords[0].x(), nonzeroCoords[0].y()) = Scalar(5);
+ }
+
+ VERIFY_IS_APPROX(m, refMat);
+
+ // test assertion
+ VERIFY_RAISES_ASSERT( m.coeffRef(-1,1) = 0 );
+ VERIFY_RAISES_ASSERT( m.coeffRef(0,m.cols()) = 0 );
+ }
+
+ // test insert (inner random)
+ {
+ DenseMatrix m1(rows,cols);
+ m1.setZero();
+ SparseMatrixType m2(rows,cols);
+ bool call_reserve = internal::random<int>()%2;
+ Index nnz = internal::random<int>(1,int(rows)/2);
+ if(call_reserve)
+ {
+ if(internal::random<int>()%2)
+ m2.reserve(VectorXi::Constant(m2.outerSize(), int(nnz)));
+ else
+ m2.reserve(m2.outerSize() * nnz);
+ }
+ g_realloc_count = 0;
+ for (Index j=0; j<cols; ++j)
+ {
+ for (Index k=0; k<nnz; ++k)
+ {
+ Index i = internal::random<Index>(0,rows-1);
+ if (m1.coeff(i,j)==Scalar(0))
+ m2.insert(i,j) = m1(i,j) = internal::random<Scalar>();
+ }
+ }
+
+ if(call_reserve && !SparseMatrixType::IsRowMajor)
+ {
+ VERIFY(g_realloc_count==0);
+ }
+
+ m2.finalize();
+ VERIFY_IS_APPROX(m2,m1);
+ }
+
+ // test insert (fully random)
+ {
+ DenseMatrix m1(rows,cols);
+ m1.setZero();
+ SparseMatrixType m2(rows,cols);
+ if(internal::random<int>()%2)
+ m2.reserve(VectorXi::Constant(m2.outerSize(), 2));
+ for (int k=0; k<rows*cols; ++k)
+ {
+ Index i = internal::random<Index>(0,rows-1);
+ Index j = internal::random<Index>(0,cols-1);
+ if ((m1.coeff(i,j)==Scalar(0)) && (internal::random<int>()%2))
+ m2.insert(i,j) = m1(i,j) = internal::random<Scalar>();
+ else
+ {
+ Scalar v = internal::random<Scalar>();
+ m2.coeffRef(i,j) += v;
+ m1(i,j) += v;
+ }
+ }
+ VERIFY_IS_APPROX(m2,m1);
+ }
+
+ // test insert (un-compressed)
+ for(int mode=0;mode<4;++mode)
+ {
+ DenseMatrix m1(rows,cols);
+ m1.setZero();
+ SparseMatrixType m2(rows,cols);
+ VectorXi r(VectorXi::Constant(m2.outerSize(), ((mode%2)==0) ? int(m2.innerSize()) : std::max<int>(1,int(m2.innerSize())/8)));
+ m2.reserve(r);
+ for (Index k=0; k<rows*cols; ++k)
+ {
+ Index i = internal::random<Index>(0,rows-1);
+ Index j = internal::random<Index>(0,cols-1);
+ if (m1.coeff(i,j)==Scalar(0))
+ m2.insert(i,j) = m1(i,j) = internal::random<Scalar>();
+ if(mode==3)
+ m2.reserve(r);
+ }
+ if(internal::random<int>()%2)
+ m2.makeCompressed();
+ VERIFY_IS_APPROX(m2,m1);
+ }
+
+ // test basic computations
+ {
+ DenseMatrix refM1 = DenseMatrix::Zero(rows, cols);
+ DenseMatrix refM2 = DenseMatrix::Zero(rows, cols);
+ DenseMatrix refM3 = DenseMatrix::Zero(rows, cols);
+ DenseMatrix refM4 = DenseMatrix::Zero(rows, cols);
+ SparseMatrixType m1(rows, cols);
+ SparseMatrixType m2(rows, cols);
+ SparseMatrixType m3(rows, cols);
+ SparseMatrixType m4(rows, cols);
+ initSparse<Scalar>(density, refM1, m1);
+ initSparse<Scalar>(density, refM2, m2);
+ initSparse<Scalar>(density, refM3, m3);
+ initSparse<Scalar>(density, refM4, m4);
+
+ if(internal::random<bool>())
+ m1.makeCompressed();
+
+ Index m1_nnz = m1.nonZeros();
+
+ VERIFY_IS_APPROX(m1*s1, refM1*s1);
+ VERIFY_IS_APPROX(m1+m2, refM1+refM2);
+ VERIFY_IS_APPROX(m1+m2+m3, refM1+refM2+refM3);
+ VERIFY_IS_APPROX(m3.cwiseProduct(m1+m2), refM3.cwiseProduct(refM1+refM2));
+ VERIFY_IS_APPROX(m1*s1-m2, refM1*s1-refM2);
+ VERIFY_IS_APPROX(m4=m1/s1, refM1/s1);
+ VERIFY_IS_EQUAL(m4.nonZeros(), m1_nnz);
+
+ if(SparseMatrixType::IsRowMajor)
+ VERIFY_IS_APPROX(m1.innerVector(0).dot(refM2.row(0)), refM1.row(0).dot(refM2.row(0)));
+ else
+ VERIFY_IS_APPROX(m1.innerVector(0).dot(refM2.col(0)), refM1.col(0).dot(refM2.col(0)));
+
+ DenseVector rv = DenseVector::Random(m1.cols());
+ DenseVector cv = DenseVector::Random(m1.rows());
+ Index r = internal::random<Index>(0,m1.rows()-2);
+ Index c = internal::random<Index>(0,m1.cols()-1);
+ VERIFY_IS_APPROX(( m1.template block<1,Dynamic>(r,0,1,m1.cols()).dot(rv)) , refM1.row(r).dot(rv));
+ VERIFY_IS_APPROX(m1.row(r).dot(rv), refM1.row(r).dot(rv));
+ VERIFY_IS_APPROX(m1.col(c).dot(cv), refM1.col(c).dot(cv));
+
+ VERIFY_IS_APPROX(m1.conjugate(), refM1.conjugate());
+ VERIFY_IS_APPROX(m1.real(), refM1.real());
+
+ refM4.setRandom();
+ // sparse cwise* dense
+ VERIFY_IS_APPROX(m3.cwiseProduct(refM4), refM3.cwiseProduct(refM4));
+ // dense cwise* sparse
+ VERIFY_IS_APPROX(refM4.cwiseProduct(m3), refM4.cwiseProduct(refM3));
+// VERIFY_IS_APPROX(m3.cwise()/refM4, refM3.cwise()/refM4);
+
+ // mixed sparse-dense
+ VERIFY_IS_APPROX(refM4 + m3, refM4 + refM3);
+ VERIFY_IS_APPROX(m3 + refM4, refM3 + refM4);
+ VERIFY_IS_APPROX(refM4 - m3, refM4 - refM3);
+ VERIFY_IS_APPROX(m3 - refM4, refM3 - refM4);
+ VERIFY_IS_APPROX((RealScalar(0.5)*refM4 + RealScalar(0.5)*m3).eval(), RealScalar(0.5)*refM4 + RealScalar(0.5)*refM3);
+ VERIFY_IS_APPROX((RealScalar(0.5)*refM4 + m3*RealScalar(0.5)).eval(), RealScalar(0.5)*refM4 + RealScalar(0.5)*refM3);
+ VERIFY_IS_APPROX((RealScalar(0.5)*refM4 + m3.cwiseProduct(m3)).eval(), RealScalar(0.5)*refM4 + refM3.cwiseProduct(refM3));
+
+ VERIFY_IS_APPROX((RealScalar(0.5)*refM4 + RealScalar(0.5)*m3).eval(), RealScalar(0.5)*refM4 + RealScalar(0.5)*refM3);
+ VERIFY_IS_APPROX((RealScalar(0.5)*refM4 + m3*RealScalar(0.5)).eval(), RealScalar(0.5)*refM4 + RealScalar(0.5)*refM3);
+ VERIFY_IS_APPROX((RealScalar(0.5)*refM4 + (m3+m3)).eval(), RealScalar(0.5)*refM4 + (refM3+refM3));
+ VERIFY_IS_APPROX(((refM3+m3)+RealScalar(0.5)*m3).eval(), RealScalar(0.5)*refM3 + (refM3+refM3));
+ VERIFY_IS_APPROX((RealScalar(0.5)*refM4 + (refM3+m3)).eval(), RealScalar(0.5)*refM4 + (refM3+refM3));
+ VERIFY_IS_APPROX((RealScalar(0.5)*refM4 + (m3+refM3)).eval(), RealScalar(0.5)*refM4 + (refM3+refM3));
+
+
+ VERIFY_IS_APPROX(m1.sum(), refM1.sum());
+
+ m4 = m1; refM4 = m4;
+
+ VERIFY_IS_APPROX(m1*=s1, refM1*=s1);
+ VERIFY_IS_EQUAL(m1.nonZeros(), m1_nnz);
+ VERIFY_IS_APPROX(m1/=s1, refM1/=s1);
+ VERIFY_IS_EQUAL(m1.nonZeros(), m1_nnz);
+
+ VERIFY_IS_APPROX(m1+=m2, refM1+=refM2);
+ VERIFY_IS_APPROX(m1-=m2, refM1-=refM2);
+
+ refM3 = refM1;
+
+ VERIFY_IS_APPROX(refM1+=m2, refM3+=refM2);
+ VERIFY_IS_APPROX(refM1-=m2, refM3-=refM2);
+
+ g_dense_op_sparse_count=0; VERIFY_IS_APPROX(refM1 =m2+refM4, refM3 =refM2+refM4); VERIFY_IS_EQUAL(g_dense_op_sparse_count,10);
+ g_dense_op_sparse_count=0; VERIFY_IS_APPROX(refM1+=m2+refM4, refM3+=refM2+refM4); VERIFY_IS_EQUAL(g_dense_op_sparse_count,1);
+ g_dense_op_sparse_count=0; VERIFY_IS_APPROX(refM1-=m2+refM4, refM3-=refM2+refM4); VERIFY_IS_EQUAL(g_dense_op_sparse_count,1);
+ g_dense_op_sparse_count=0; VERIFY_IS_APPROX(refM1 =refM4+m2, refM3 =refM2+refM4); VERIFY_IS_EQUAL(g_dense_op_sparse_count,1);
+ g_dense_op_sparse_count=0; VERIFY_IS_APPROX(refM1+=refM4+m2, refM3+=refM2+refM4); VERIFY_IS_EQUAL(g_dense_op_sparse_count,1);
+ g_dense_op_sparse_count=0; VERIFY_IS_APPROX(refM1-=refM4+m2, refM3-=refM2+refM4); VERIFY_IS_EQUAL(g_dense_op_sparse_count,1);
+
+ g_dense_op_sparse_count=0; VERIFY_IS_APPROX(refM1 =m2-refM4, refM3 =refM2-refM4); VERIFY_IS_EQUAL(g_dense_op_sparse_count,20);
+ g_dense_op_sparse_count=0; VERIFY_IS_APPROX(refM1+=m2-refM4, refM3+=refM2-refM4); VERIFY_IS_EQUAL(g_dense_op_sparse_count,1);
+ g_dense_op_sparse_count=0; VERIFY_IS_APPROX(refM1-=m2-refM4, refM3-=refM2-refM4); VERIFY_IS_EQUAL(g_dense_op_sparse_count,1);
+ g_dense_op_sparse_count=0; VERIFY_IS_APPROX(refM1 =refM4-m2, refM3 =refM4-refM2); VERIFY_IS_EQUAL(g_dense_op_sparse_count,1);
+ g_dense_op_sparse_count=0; VERIFY_IS_APPROX(refM1+=refM4-m2, refM3+=refM4-refM2); VERIFY_IS_EQUAL(g_dense_op_sparse_count,1);
+ g_dense_op_sparse_count=0; VERIFY_IS_APPROX(refM1-=refM4-m2, refM3-=refM4-refM2); VERIFY_IS_EQUAL(g_dense_op_sparse_count,1);
+ refM3 = m3;
+
+ if (rows>=2 && cols>=2)
+ {
+ VERIFY_RAISES_ASSERT( m1 += m1.innerVector(0) );
+ VERIFY_RAISES_ASSERT( m1 -= m1.innerVector(0) );
+ VERIFY_RAISES_ASSERT( refM1 -= m1.innerVector(0) );
+ VERIFY_RAISES_ASSERT( refM1 += m1.innerVector(0) );
+ }
+ m1 = m4; refM1 = refM4;
+
+ // test aliasing
+ VERIFY_IS_APPROX((m1 = -m1), (refM1 = -refM1));
+ VERIFY_IS_EQUAL(m1.nonZeros(), m1_nnz);
+ m1 = m4; refM1 = refM4;
+ VERIFY_IS_APPROX((m1 = m1.transpose()), (refM1 = refM1.transpose().eval()));
+ VERIFY_IS_EQUAL(m1.nonZeros(), m1_nnz);
+ m1 = m4; refM1 = refM4;
+ VERIFY_IS_APPROX((m1 = -m1.transpose()), (refM1 = -refM1.transpose().eval()));
+ VERIFY_IS_EQUAL(m1.nonZeros(), m1_nnz);
+ m1 = m4; refM1 = refM4;
+ VERIFY_IS_APPROX((m1 += -m1), (refM1 += -refM1));
+ VERIFY_IS_EQUAL(m1.nonZeros(), m1_nnz);
+ m1 = m4; refM1 = refM4;
+
+ if(m1.isCompressed())
+ {
+ VERIFY_IS_APPROX(m1.coeffs().sum(), m1.sum());
+ m1.coeffs() += s1;
+ for(Index j = 0; j<m1.outerSize(); ++j)
+ for(typename SparseMatrixType::InnerIterator it(m1,j); it; ++it)
+ refM1(it.row(), it.col()) += s1;
+ VERIFY_IS_APPROX(m1, refM1);
+ }
+
+ // and/or
+ {
+ typedef SparseMatrix<bool, SparseMatrixType::Options, typename SparseMatrixType::StorageIndex> SpBool;
+ SpBool mb1 = m1.real().template cast<bool>();
+ SpBool mb2 = m2.real().template cast<bool>();
+ VERIFY_IS_EQUAL(mb1.template cast<int>().sum(), refM1.real().template cast<bool>().count());
+ VERIFY_IS_EQUAL((mb1 && mb2).template cast<int>().sum(), (refM1.real().template cast<bool>() && refM2.real().template cast<bool>()).count());
+ VERIFY_IS_EQUAL((mb1 || mb2).template cast<int>().sum(), (refM1.real().template cast<bool>() || refM2.real().template cast<bool>()).count());
+ SpBool mb3 = mb1 && mb2;
+ if(mb1.coeffs().all() && mb2.coeffs().all())
+ {
+ VERIFY_IS_EQUAL(mb3.nonZeros(), (refM1.real().template cast<bool>() && refM2.real().template cast<bool>()).count());
+ }
+ }
+ }
+
+ // test reverse iterators
+ {
+ DenseMatrix refMat2 = DenseMatrix::Zero(rows, cols);
+ SparseMatrixType m2(rows, cols);
+ initSparse<Scalar>(density, refMat2, m2);
+ std::vector<Scalar> ref_value(m2.innerSize());
+ std::vector<Index> ref_index(m2.innerSize());
+ if(internal::random<bool>())
+ m2.makeCompressed();
+ for(Index j = 0; j<m2.outerSize(); ++j)
+ {
+ Index count_forward = 0;
+
+ for(typename SparseMatrixType::InnerIterator it(m2,j); it; ++it)
+ {
+ ref_value[ref_value.size()-1-count_forward] = it.value();
+ ref_index[ref_index.size()-1-count_forward] = it.index();
+ count_forward++;
+ }
+ Index count_reverse = 0;
+ for(typename SparseMatrixType::ReverseInnerIterator it(m2,j); it; --it)
+ {
+ VERIFY_IS_APPROX( std::abs(ref_value[ref_value.size()-count_forward+count_reverse])+1, std::abs(it.value())+1);
+ VERIFY_IS_EQUAL( ref_index[ref_index.size()-count_forward+count_reverse] , it.index());
+ count_reverse++;
+ }
+ VERIFY_IS_EQUAL(count_forward, count_reverse);
+ }
+ }
+
+ // test transpose
+ {
+ DenseMatrix refMat2 = DenseMatrix::Zero(rows, cols);
+ SparseMatrixType m2(rows, cols);
+ initSparse<Scalar>(density, refMat2, m2);
+ VERIFY_IS_APPROX(m2.transpose().eval(), refMat2.transpose().eval());
+ VERIFY_IS_APPROX(m2.transpose(), refMat2.transpose());
+
+ VERIFY_IS_APPROX(SparseMatrixType(m2.adjoint()), refMat2.adjoint());
+
+ // check isApprox handles opposite storage order
+ typename Transpose<SparseMatrixType>::PlainObject m3(m2);
+ VERIFY(m2.isApprox(m3));
+ }
+
+ // test prune
+ {
+ SparseMatrixType m2(rows, cols);
+ DenseMatrix refM2(rows, cols);
+ refM2.setZero();
+ int countFalseNonZero = 0;
+ int countTrueNonZero = 0;
+ m2.reserve(VectorXi::Constant(m2.outerSize(), int(m2.innerSize())));
+ for (Index j=0; j<m2.cols(); ++j)
+ {
+ for (Index i=0; i<m2.rows(); ++i)
+ {
+ float x = internal::random<float>(0,1);
+ if (x<0.1f)
+ {
+ // do nothing
+ }
+ else if (x<0.5f)
+ {
+ countFalseNonZero++;
+ m2.insert(i,j) = Scalar(0);
+ }
+ else
+ {
+ countTrueNonZero++;
+ m2.insert(i,j) = Scalar(1);
+ refM2(i,j) = Scalar(1);
+ }
+ }
+ }
+ if(internal::random<bool>())
+ m2.makeCompressed();
+ VERIFY(countFalseNonZero+countTrueNonZero == m2.nonZeros());
+ if(countTrueNonZero>0)
+ VERIFY_IS_APPROX(m2, refM2);
+ m2.prune(Scalar(1));
+ VERIFY(countTrueNonZero==m2.nonZeros());
+ VERIFY_IS_APPROX(m2, refM2);
+ }
+
+ // test setFromTriplets
+ {
+ typedef Triplet<Scalar,StorageIndex> TripletType;
+ std::vector<TripletType> triplets;
+ Index ntriplets = rows*cols;
+ triplets.reserve(ntriplets);
+ DenseMatrix refMat_sum = DenseMatrix::Zero(rows,cols);
+ DenseMatrix refMat_prod = DenseMatrix::Zero(rows,cols);
+ DenseMatrix refMat_last = DenseMatrix::Zero(rows,cols);
+
+ for(Index i=0;i<ntriplets;++i)
+ {
+ StorageIndex r = internal::random<StorageIndex>(0,StorageIndex(rows-1));
+ StorageIndex c = internal::random<StorageIndex>(0,StorageIndex(cols-1));
+ Scalar v = internal::random<Scalar>();
+ triplets.push_back(TripletType(r,c,v));
+ refMat_sum(r,c) += v;
+ if(std::abs(refMat_prod(r,c))==0)
+ refMat_prod(r,c) = v;
+ else
+ refMat_prod(r,c) *= v;
+ refMat_last(r,c) = v;
+ }
+ SparseMatrixType m(rows,cols);
+ m.setFromTriplets(triplets.begin(), triplets.end());
+ VERIFY_IS_APPROX(m, refMat_sum);
+
+ m.setFromTriplets(triplets.begin(), triplets.end(), std::multiplies<Scalar>());
+ VERIFY_IS_APPROX(m, refMat_prod);
+ m.setFromTriplets(triplets.begin(), triplets.end(), [] (Scalar,Scalar b) { return b; });
+ VERIFY_IS_APPROX(m, refMat_last);
+ }
+
+ // test Map
+ {
+ DenseMatrix refMat2(rows, cols), refMat3(rows, cols);
+ SparseMatrixType m2(rows, cols), m3(rows, cols);
+ initSparse<Scalar>(density, refMat2, m2);
+ initSparse<Scalar>(density, refMat3, m3);
+ {
+ Map<SparseMatrixType> mapMat2(m2.rows(), m2.cols(), m2.nonZeros(), m2.outerIndexPtr(), m2.innerIndexPtr(), m2.valuePtr(), m2.innerNonZeroPtr());
+ Map<SparseMatrixType> mapMat3(m3.rows(), m3.cols(), m3.nonZeros(), m3.outerIndexPtr(), m3.innerIndexPtr(), m3.valuePtr(), m3.innerNonZeroPtr());
+ VERIFY_IS_APPROX(mapMat2+mapMat3, refMat2+refMat3);
+ VERIFY_IS_APPROX(mapMat2+mapMat3, refMat2+refMat3);
+ }
+
+ Index i = internal::random<Index>(0,rows-1);
+ Index j = internal::random<Index>(0,cols-1);
+ m2.coeffRef(i,j) = 123;
+ if(internal::random<bool>())
+ m2.makeCompressed();
+ Map<SparseMatrixType> mapMat2(rows, cols, m2.nonZeros(), m2.outerIndexPtr(), m2.innerIndexPtr(), m2.valuePtr(), m2.innerNonZeroPtr());
+ VERIFY_IS_EQUAL(m2.coeff(i,j),Scalar(123));
+ VERIFY_IS_EQUAL(mapMat2.coeff(i,j),Scalar(123));
+ mapMat2.coeffRef(i,j) = -123;
+ VERIFY_IS_EQUAL(m2.coeff(i,j),Scalar(-123));
+ }
+
+ // test triangularView
+ {
+ DenseMatrix refMat2(rows, cols), refMat3(rows, cols);
+ SparseMatrixType m2(rows, cols), m3(rows, cols);
+ initSparse<Scalar>(density, refMat2, m2);
+ refMat3 = refMat2.template triangularView<Lower>();
+ m3 = m2.template triangularView<Lower>();
+ VERIFY_IS_APPROX(m3, refMat3);
+
+ refMat3 = refMat2.template triangularView<Upper>();
+ m3 = m2.template triangularView<Upper>();
+ VERIFY_IS_APPROX(m3, refMat3);
+
+ {
+ refMat3 = refMat2.template triangularView<UnitUpper>();
+ m3 = m2.template triangularView<UnitUpper>();
+ VERIFY_IS_APPROX(m3, refMat3);
+
+ refMat3 = refMat2.template triangularView<UnitLower>();
+ m3 = m2.template triangularView<UnitLower>();
+ VERIFY_IS_APPROX(m3, refMat3);
+ }
+
+ refMat3 = refMat2.template triangularView<StrictlyUpper>();
+ m3 = m2.template triangularView<StrictlyUpper>();
+ VERIFY_IS_APPROX(m3, refMat3);
+
+ refMat3 = refMat2.template triangularView<StrictlyLower>();
+ m3 = m2.template triangularView<StrictlyLower>();
+ VERIFY_IS_APPROX(m3, refMat3);
+
+ // check sparse-triangular to dense
+ refMat3 = m2.template triangularView<StrictlyUpper>();
+ VERIFY_IS_APPROX(refMat3, DenseMatrix(refMat2.template triangularView<StrictlyUpper>()));
+ }
+
+ // test selfadjointView
+ if(!SparseMatrixType::IsRowMajor)
+ {
+ DenseMatrix refMat2(rows, rows), refMat3(rows, rows);
+ SparseMatrixType m2(rows, rows), m3(rows, rows);
+ initSparse<Scalar>(density, refMat2, m2);
+ refMat3 = refMat2.template selfadjointView<Lower>();
+ m3 = m2.template selfadjointView<Lower>();
+ VERIFY_IS_APPROX(m3, refMat3);
+
+ refMat3 += refMat2.template selfadjointView<Lower>();
+ m3 += m2.template selfadjointView<Lower>();
+ VERIFY_IS_APPROX(m3, refMat3);
+
+ refMat3 -= refMat2.template selfadjointView<Lower>();
+ m3 -= m2.template selfadjointView<Lower>();
+ VERIFY_IS_APPROX(m3, refMat3);
+
+ // selfadjointView only works for square matrices:
+ SparseMatrixType m4(rows, rows+1);
+ VERIFY_RAISES_ASSERT(m4.template selfadjointView<Lower>());
+ VERIFY_RAISES_ASSERT(m4.template selfadjointView<Upper>());
+ }
+
+ // test sparseView
+ {
+ DenseMatrix refMat2 = DenseMatrix::Zero(rows, rows);
+ SparseMatrixType m2(rows, rows);
+ initSparse<Scalar>(density, refMat2, m2);
+ VERIFY_IS_APPROX(m2.eval(), refMat2.sparseView().eval());
+
+ // sparse view on expressions:
+ VERIFY_IS_APPROX((s1*m2).eval(), (s1*refMat2).sparseView().eval());
+ VERIFY_IS_APPROX((m2+m2).eval(), (refMat2+refMat2).sparseView().eval());
+ VERIFY_IS_APPROX((m2*m2).eval(), (refMat2.lazyProduct(refMat2)).sparseView().eval());
+ VERIFY_IS_APPROX((m2*m2).eval(), (refMat2*refMat2).sparseView().eval());
+ }
+
+ // test diagonal
+ {
+ DenseMatrix refMat2 = DenseMatrix::Zero(rows, cols);
+ SparseMatrixType m2(rows, cols);
+ initSparse<Scalar>(density, refMat2, m2);
+ VERIFY_IS_APPROX(m2.diagonal(), refMat2.diagonal().eval());
+ DenseVector d = m2.diagonal();
+ VERIFY_IS_APPROX(d, refMat2.diagonal().eval());
+ d = m2.diagonal().array();
+ VERIFY_IS_APPROX(d, refMat2.diagonal().eval());
+ VERIFY_IS_APPROX(const_cast<const SparseMatrixType&>(m2).diagonal(), refMat2.diagonal().eval());
+
+ initSparse<Scalar>(density, refMat2, m2, ForceNonZeroDiag);
+ m2.diagonal() += refMat2.diagonal();
+ refMat2.diagonal() += refMat2.diagonal();
+ VERIFY_IS_APPROX(m2, refMat2);
+ }
+
+ // test diagonal to sparse
+ {
+ DenseVector d = DenseVector::Random(rows);
+ DenseMatrix refMat2 = d.asDiagonal();
+ SparseMatrixType m2;
+ m2 = d.asDiagonal();
+ VERIFY_IS_APPROX(m2, refMat2);
+ SparseMatrixType m3(d.asDiagonal());
+ VERIFY_IS_APPROX(m3, refMat2);
+ refMat2 += d.asDiagonal();
+ m2 += d.asDiagonal();
+ VERIFY_IS_APPROX(m2, refMat2);
+ m2.setZero(); m2 += d.asDiagonal();
+ refMat2.setZero(); refMat2 += d.asDiagonal();
+ VERIFY_IS_APPROX(m2, refMat2);
+ m2.setZero(); m2 -= d.asDiagonal();
+ refMat2.setZero(); refMat2 -= d.asDiagonal();
+ VERIFY_IS_APPROX(m2, refMat2);
+
+ initSparse<Scalar>(density, refMat2, m2);
+ m2.makeCompressed();
+ m2 += d.asDiagonal();
+ refMat2 += d.asDiagonal();
+ VERIFY_IS_APPROX(m2, refMat2);
+
+ initSparse<Scalar>(density, refMat2, m2);
+ m2.makeCompressed();
+ VectorXi res(rows);
+ for(Index i=0; i<rows; ++i)
+ res(i) = internal::random<int>(0,3);
+ m2.reserve(res);
+ m2 -= d.asDiagonal();
+ refMat2 -= d.asDiagonal();
+ VERIFY_IS_APPROX(m2, refMat2);
+ }
+
+ // test conservative resize
+ {
+ std::vector< std::pair<StorageIndex,StorageIndex> > inc;
+ if(rows > 3 && cols > 2)
+ inc.push_back(std::pair<StorageIndex,StorageIndex>(-3,-2));
+ inc.push_back(std::pair<StorageIndex,StorageIndex>(0,0));
+ inc.push_back(std::pair<StorageIndex,StorageIndex>(3,2));
+ inc.push_back(std::pair<StorageIndex,StorageIndex>(3,0));
+ inc.push_back(std::pair<StorageIndex,StorageIndex>(0,3));
+ inc.push_back(std::pair<StorageIndex,StorageIndex>(0,-1));
+ inc.push_back(std::pair<StorageIndex,StorageIndex>(-1,0));
+ inc.push_back(std::pair<StorageIndex,StorageIndex>(-1,-1));
+
+ for(size_t i = 0; i< inc.size(); i++) {
+ StorageIndex incRows = inc[i].first;
+ StorageIndex incCols = inc[i].second;
+ SparseMatrixType m1(rows, cols);
+ DenseMatrix refMat1 = DenseMatrix::Zero(rows, cols);
+ initSparse<Scalar>(density, refMat1, m1);
+
+ SparseMatrixType m2 = m1;
+ m2.makeCompressed();
+
+ m1.conservativeResize(rows+incRows, cols+incCols);
+ m2.conservativeResize(rows+incRows, cols+incCols);
+ refMat1.conservativeResize(rows+incRows, cols+incCols);
+ if (incRows > 0) refMat1.bottomRows(incRows).setZero();
+ if (incCols > 0) refMat1.rightCols(incCols).setZero();
+
+ VERIFY_IS_APPROX(m1, refMat1);
+ VERIFY_IS_APPROX(m2, refMat1);
+
+ // Insert new values
+ if (incRows > 0)
+ m1.insert(m1.rows()-1, 0) = refMat1(refMat1.rows()-1, 0) = 1;
+ if (incCols > 0)
+ m1.insert(0, m1.cols()-1) = refMat1(0, refMat1.cols()-1) = 1;
+
+ VERIFY_IS_APPROX(m1, refMat1);
+
+
+ }
+ }
+
+ // test Identity matrix
+ {
+ DenseMatrix refMat1 = DenseMatrix::Identity(rows, rows);
+ SparseMatrixType m1(rows, rows);
+ m1.setIdentity();
+ VERIFY_IS_APPROX(m1, refMat1);
+ for(int k=0; k<rows*rows/4; ++k)
+ {
+ Index i = internal::random<Index>(0,rows-1);
+ Index j = internal::random<Index>(0,rows-1);
+ Scalar v = internal::random<Scalar>();
+ m1.coeffRef(i,j) = v;
+ refMat1.coeffRef(i,j) = v;
+ VERIFY_IS_APPROX(m1, refMat1);
+ if(internal::random<Index>(0,10)<2)
+ m1.makeCompressed();
+ }
+ m1.setIdentity();
+ refMat1.setIdentity();
+ VERIFY_IS_APPROX(m1, refMat1);
+ }
+
+ // test array/vector of InnerIterator
+ {
+ typedef typename SparseMatrixType::InnerIterator IteratorType;
+
+ DenseMatrix refMat2 = DenseMatrix::Zero(rows, cols);
+ SparseMatrixType m2(rows, cols);
+ initSparse<Scalar>(density, refMat2, m2);
+ IteratorType static_array[2];
+ static_array[0] = IteratorType(m2,0);
+ static_array[1] = IteratorType(m2,m2.outerSize()-1);
+ VERIFY( static_array[0] || m2.innerVector(static_array[0].outer()).nonZeros() == 0 );
+ VERIFY( static_array[1] || m2.innerVector(static_array[1].outer()).nonZeros() == 0 );
+ if(static_array[0] && static_array[1])
+ {
+ ++(static_array[1]);
+ static_array[1] = IteratorType(m2,0);
+ VERIFY( static_array[1] );
+ VERIFY( static_array[1].index() == static_array[0].index() );
+ VERIFY( static_array[1].outer() == static_array[0].outer() );
+ VERIFY( static_array[1].value() == static_array[0].value() );
+ }
+
+ std::vector<IteratorType> iters(2);
+ iters[0] = IteratorType(m2,0);
+ iters[1] = IteratorType(m2,m2.outerSize()-1);
+ }
+
+ // test reserve with empty rows/columns
+ {
+ SparseMatrixType m1(0,cols);
+ m1.reserve(ArrayXi::Constant(m1.outerSize(),1));
+ SparseMatrixType m2(rows,0);
+ m2.reserve(ArrayXi::Constant(m2.outerSize(),1));
+ }
+}
+
+
+template<typename SparseMatrixType>
+void big_sparse_triplet(Index rows, Index cols, double density) {
+ typedef typename SparseMatrixType::StorageIndex StorageIndex;
+ typedef typename SparseMatrixType::Scalar Scalar;
+ typedef Triplet<Scalar,Index> TripletType;
+ std::vector<TripletType> triplets;
+ double nelements = density * static_cast<double>(rows*cols);
+ VERIFY(nelements>=0 && nelements < static_cast<double>(NumTraits<StorageIndex>::highest()));
+ Index ntriplets = Index(nelements);
+ triplets.reserve(ntriplets);
+ Scalar sum = Scalar(0);
+ for(Index i=0;i<ntriplets;++i)
+ {
+ Index r = internal::random<Index>(0,rows-1);
+ Index c = internal::random<Index>(0,cols-1);
+ // use positive values to prevent numerical cancellation errors in sum
+ Scalar v = numext::abs(internal::random<Scalar>());
+ triplets.push_back(TripletType(r,c,v));
+ sum += v;
+ }
+ SparseMatrixType m(rows,cols);
+ m.setFromTriplets(triplets.begin(), triplets.end());
+ VERIFY(m.nonZeros() <= ntriplets);
+ VERIFY_IS_APPROX(sum, m.sum());
+}
+
+template<int>
+void bug1105()
+{
+ // Regression test for bug 1105
+ int n = Eigen::internal::random<int>(200,600);
+ SparseMatrix<std::complex<double>,0, long> mat(n, n);
+ std::complex<double> val;
+
+ for(int i=0; i<n; ++i)
+ {
+ mat.coeffRef(i, i%(n/10)) = val;
+ VERIFY(mat.data().allocatedSize()<20*n);
+ }
+}
+
+#ifndef EIGEN_SPARSE_TEST_INCLUDED_FROM_SPARSE_EXTRA
+
+EIGEN_DECLARE_TEST(sparse_basic)
+{
+ g_dense_op_sparse_count = 0; // Suppresses compiler warning.
+ for(int i = 0; i < g_repeat; i++) {
+ int r = Eigen::internal::random<int>(1,200), c = Eigen::internal::random<int>(1,200);
+ if(Eigen::internal::random<int>(0,4) == 0) {
+ r = c; // check square matrices in 25% of tries
+ }
+ EIGEN_UNUSED_VARIABLE(r+c);
+ CALL_SUBTEST_1(( sparse_basic(SparseMatrix<double>(1, 1)) ));
+ CALL_SUBTEST_1(( sparse_basic(SparseMatrix<double>(8, 8)) ));
+ CALL_SUBTEST_2(( sparse_basic(SparseMatrix<std::complex<double>, ColMajor>(r, c)) ));
+ CALL_SUBTEST_2(( sparse_basic(SparseMatrix<std::complex<double>, RowMajor>(r, c)) ));
+ CALL_SUBTEST_1(( sparse_basic(SparseMatrix<double>(r, c)) ));
+ CALL_SUBTEST_5(( sparse_basic(SparseMatrix<double,ColMajor,long int>(r, c)) ));
+ CALL_SUBTEST_5(( sparse_basic(SparseMatrix<double,RowMajor,long int>(r, c)) ));
+
+ r = Eigen::internal::random<int>(1,100);
+ c = Eigen::internal::random<int>(1,100);
+ if(Eigen::internal::random<int>(0,4) == 0) {
+ r = c; // check square matrices in 25% of tries
+ }
+
+ CALL_SUBTEST_6(( sparse_basic(SparseMatrix<double,ColMajor,short int>(short(r), short(c))) ));
+ CALL_SUBTEST_6(( sparse_basic(SparseMatrix<double,RowMajor,short int>(short(r), short(c))) ));
+ }
+
+ // Regression test for bug 900: (manually insert higher values here, if you have enough RAM):
+ CALL_SUBTEST_3((big_sparse_triplet<SparseMatrix<float, RowMajor, int> >(10000, 10000, 0.125)));
+ CALL_SUBTEST_4((big_sparse_triplet<SparseMatrix<double, ColMajor, long int> >(10000, 10000, 0.125)));
+
+ CALL_SUBTEST_7( bug1105<0>() );
+}
+#endif
diff --git a/test/sparse_block.cpp b/test/sparse_block.cpp
new file mode 100644
index 0000000..955aa60
--- /dev/null
+++ b/test/sparse_block.cpp
@@ -0,0 +1,342 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2015 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "sparse.h"
+#include "AnnoyingScalar.h"
+
+template<typename T>
+std::enable_if_t<(T::Flags&RowMajorBit)==RowMajorBit, typename T::RowXpr>
+innervec(T& A, Index i)
+{
+ return A.row(i);
+}
+
+template<typename T>
+std::enable_if_t<(T::Flags&RowMajorBit)==0, typename T::ColXpr>
+innervec(T& A, Index i)
+{
+ return A.col(i);
+}
+
+template<typename SparseMatrixType> void sparse_block(const SparseMatrixType& ref)
+{
+ const Index rows = ref.rows();
+ const Index cols = ref.cols();
+ const Index inner = ref.innerSize();
+ const Index outer = ref.outerSize();
+
+ typedef typename SparseMatrixType::Scalar Scalar;
+ typedef typename SparseMatrixType::RealScalar RealScalar;
+ typedef typename SparseMatrixType::StorageIndex StorageIndex;
+
+ double density = (std::max)(8./(rows*cols), 0.01);
+ typedef Matrix<Scalar,Dynamic,Dynamic,SparseMatrixType::IsRowMajor?RowMajor:ColMajor> DenseMatrix;
+ typedef Matrix<Scalar,Dynamic,1> DenseVector;
+ typedef Matrix<Scalar,1,Dynamic> RowDenseVector;
+ typedef SparseVector<Scalar> SparseVectorType;
+
+ Scalar s1 = internal::random<Scalar>();
+ {
+ SparseMatrixType m(rows, cols);
+ DenseMatrix refMat = DenseMatrix::Zero(rows, cols);
+ initSparse<Scalar>(density, refMat, m);
+
+ VERIFY_IS_APPROX(m, refMat);
+
+ // test InnerIterators and Block expressions
+ for (int t=0; t<10; ++t)
+ {
+ Index j = internal::random<Index>(0,cols-2);
+ Index i = internal::random<Index>(0,rows-2);
+ Index w = internal::random<Index>(1,cols-j);
+ Index h = internal::random<Index>(1,rows-i);
+
+ VERIFY_IS_APPROX(m.block(i,j,h,w), refMat.block(i,j,h,w));
+ for(Index c=0; c<w; c++)
+ {
+ VERIFY_IS_APPROX(m.block(i,j,h,w).col(c), refMat.block(i,j,h,w).col(c));
+ for(Index r=0; r<h; r++)
+ {
+ VERIFY_IS_APPROX(m.block(i,j,h,w).col(c).coeff(r), refMat.block(i,j,h,w).col(c).coeff(r));
+ VERIFY_IS_APPROX(m.block(i,j,h,w).coeff(r,c), refMat.block(i,j,h,w).coeff(r,c));
+ }
+ }
+ for(Index r=0; r<h; r++)
+ {
+ VERIFY_IS_APPROX(m.block(i,j,h,w).row(r), refMat.block(i,j,h,w).row(r));
+ for(Index c=0; c<w; c++)
+ {
+ VERIFY_IS_APPROX(m.block(i,j,h,w).row(r).coeff(c), refMat.block(i,j,h,w).row(r).coeff(c));
+ VERIFY_IS_APPROX(m.block(i,j,h,w).coeff(r,c), refMat.block(i,j,h,w).coeff(r,c));
+ }
+ }
+
+ VERIFY_IS_APPROX(m.middleCols(j,w), refMat.middleCols(j,w));
+ VERIFY_IS_APPROX(m.middleRows(i,h), refMat.middleRows(i,h));
+ for(Index r=0; r<h; r++)
+ {
+ VERIFY_IS_APPROX(m.middleCols(j,w).row(r), refMat.middleCols(j,w).row(r));
+ VERIFY_IS_APPROX(m.middleRows(i,h).row(r), refMat.middleRows(i,h).row(r));
+ for(Index c=0; c<w; c++)
+ {
+ VERIFY_IS_APPROX(m.col(c).coeff(r), refMat.col(c).coeff(r));
+ VERIFY_IS_APPROX(m.row(r).coeff(c), refMat.row(r).coeff(c));
+
+ VERIFY_IS_APPROX(m.middleCols(j,w).coeff(r,c), refMat.middleCols(j,w).coeff(r,c));
+ VERIFY_IS_APPROX(m.middleRows(i,h).coeff(r,c), refMat.middleRows(i,h).coeff(r,c));
+ if(!numext::is_exactly_zero(m.middleCols(j, w).coeff(r, c)))
+ {
+ VERIFY_IS_APPROX(m.middleCols(j,w).coeffRef(r,c), refMat.middleCols(j,w).coeff(r,c));
+ }
+ if(!numext::is_exactly_zero(m.middleRows(i, h).coeff(r, c)))
+ {
+ VERIFY_IS_APPROX(m.middleRows(i,h).coeff(r,c), refMat.middleRows(i,h).coeff(r,c));
+ }
+ }
+ }
+ for(Index c=0; c<w; c++)
+ {
+ VERIFY_IS_APPROX(m.middleCols(j,w).col(c), refMat.middleCols(j,w).col(c));
+ VERIFY_IS_APPROX(m.middleRows(i,h).col(c), refMat.middleRows(i,h).col(c));
+ }
+ }
+
+ for(Index c=0; c<cols; c++)
+ {
+ VERIFY_IS_APPROX(m.col(c) + m.col(c), (m + m).col(c));
+ VERIFY_IS_APPROX(m.col(c) + m.col(c), refMat.col(c) + refMat.col(c));
+ }
+
+ for(Index r=0; r<rows; r++)
+ {
+ VERIFY_IS_APPROX(m.row(r) + m.row(r), (m + m).row(r));
+ VERIFY_IS_APPROX(m.row(r) + m.row(r), refMat.row(r) + refMat.row(r));
+ }
+ }
+
+ // test innerVector()
+ {
+ DenseMatrix refMat2 = DenseMatrix::Zero(rows, cols);
+ SparseMatrixType m2(rows, cols);
+ initSparse<Scalar>(density, refMat2, m2);
+ Index j0 = internal::random<Index>(0,outer-1);
+ Index j1 = internal::random<Index>(0,outer-1);
+ Index r0 = internal::random<Index>(0,rows-1);
+ Index c0 = internal::random<Index>(0,cols-1);
+
+ VERIFY_IS_APPROX(m2.innerVector(j0), innervec(refMat2,j0));
+ VERIFY_IS_APPROX(m2.innerVector(j0)+m2.innerVector(j1), innervec(refMat2,j0)+innervec(refMat2,j1));
+
+ m2.innerVector(j0) *= Scalar(2);
+ innervec(refMat2,j0) *= Scalar(2);
+ VERIFY_IS_APPROX(m2, refMat2);
+
+ m2.row(r0) *= Scalar(3);
+ refMat2.row(r0) *= Scalar(3);
+ VERIFY_IS_APPROX(m2, refMat2);
+
+ m2.col(c0) *= Scalar(4);
+ refMat2.col(c0) *= Scalar(4);
+ VERIFY_IS_APPROX(m2, refMat2);
+
+ m2.row(r0) /= Scalar(3);
+ refMat2.row(r0) /= Scalar(3);
+ VERIFY_IS_APPROX(m2, refMat2);
+
+ m2.col(c0) /= Scalar(4);
+ refMat2.col(c0) /= Scalar(4);
+ VERIFY_IS_APPROX(m2, refMat2);
+
+ SparseVectorType v1;
+ VERIFY_IS_APPROX(v1 = m2.col(c0) * 4, refMat2.col(c0)*4);
+ VERIFY_IS_APPROX(v1 = m2.row(r0) * 4, refMat2.row(r0).transpose()*4);
+
+ SparseMatrixType m3(rows,cols);
+ m3.reserve(VectorXi::Constant(outer,int(inner/2)));
+ for(Index j=0; j<outer; ++j)
+ for(Index k=0; k<(std::min)(j,inner); ++k)
+ m3.insertByOuterInner(j,k) = internal::convert_index<StorageIndex>(k+1);
+ for(Index j=0; j<(std::min)(outer, inner); ++j)
+ {
+ VERIFY(j==numext::real(m3.innerVector(j).nonZeros()));
+ if(j>0)
+ VERIFY_IS_EQUAL(RealScalar(j), numext::real(m3.innerVector(j).lastCoeff()));
+ }
+ m3.makeCompressed();
+ for(Index j=0; j<(std::min)(outer, inner); ++j)
+ {
+ VERIFY(j==numext::real(m3.innerVector(j).nonZeros()));
+ if(j>0)
+ VERIFY_IS_EQUAL(RealScalar(j), numext::real(m3.innerVector(j).lastCoeff()));
+ }
+
+ VERIFY(m3.innerVector(j0).nonZeros() == m3.transpose().innerVector(j0).nonZeros());
+
+// m2.innerVector(j0) = 2*m2.innerVector(j1);
+// refMat2.col(j0) = 2*refMat2.col(j1);
+// VERIFY_IS_APPROX(m2, refMat2);
+ }
+
+ // test innerVectors()
+ {
+ DenseMatrix refMat2 = DenseMatrix::Zero(rows, cols);
+ SparseMatrixType m2(rows, cols);
+ initSparse<Scalar>(density, refMat2, m2);
+ if(internal::random<float>(0,1)>0.5f) m2.makeCompressed();
+ Index j0 = internal::random<Index>(0,outer-2);
+ Index j1 = internal::random<Index>(0,outer-2);
+ Index n0 = internal::random<Index>(1,outer-(std::max)(j0,j1));
+ if(SparseMatrixType::IsRowMajor)
+ VERIFY_IS_APPROX(m2.innerVectors(j0,n0), refMat2.block(j0,0,n0,cols));
+ else
+ VERIFY_IS_APPROX(m2.innerVectors(j0,n0), refMat2.block(0,j0,rows,n0));
+ if(SparseMatrixType::IsRowMajor)
+ VERIFY_IS_APPROX(m2.innerVectors(j0,n0)+m2.innerVectors(j1,n0),
+ refMat2.middleRows(j0,n0)+refMat2.middleRows(j1,n0));
+ else
+ VERIFY_IS_APPROX(m2.innerVectors(j0,n0)+m2.innerVectors(j1,n0),
+ refMat2.block(0,j0,rows,n0)+refMat2.block(0,j1,rows,n0));
+
+ VERIFY_IS_APPROX(m2, refMat2);
+
+ VERIFY(m2.innerVectors(j0,n0).nonZeros() == m2.transpose().innerVectors(j0,n0).nonZeros());
+
+ m2.innerVectors(j0,n0) = m2.innerVectors(j0,n0) + m2.innerVectors(j1,n0);
+ if(SparseMatrixType::IsRowMajor)
+ refMat2.middleRows(j0,n0) = (refMat2.middleRows(j0,n0) + refMat2.middleRows(j1,n0)).eval();
+ else
+ refMat2.middleCols(j0,n0) = (refMat2.middleCols(j0,n0) + refMat2.middleCols(j1,n0)).eval();
+
+ VERIFY_IS_APPROX(m2, refMat2);
+ }
+
+ // test generic blocks
+ {
+ DenseMatrix refMat2 = DenseMatrix::Zero(rows, cols);
+ SparseMatrixType m2(rows, cols);
+ initSparse<Scalar>(density, refMat2, m2);
+ Index j0 = internal::random<Index>(0,outer-2);
+ Index j1 = internal::random<Index>(0,outer-2);
+ Index n0 = internal::random<Index>(1,outer-(std::max)(j0,j1));
+ if(SparseMatrixType::IsRowMajor)
+ VERIFY_IS_APPROX(m2.block(j0,0,n0,cols), refMat2.block(j0,0,n0,cols));
+ else
+ VERIFY_IS_APPROX(m2.block(0,j0,rows,n0), refMat2.block(0,j0,rows,n0));
+
+ if(SparseMatrixType::IsRowMajor)
+ VERIFY_IS_APPROX(m2.block(j0,0,n0,cols)+m2.block(j1,0,n0,cols),
+ refMat2.block(j0,0,n0,cols)+refMat2.block(j1,0,n0,cols));
+ else
+ VERIFY_IS_APPROX(m2.block(0,j0,rows,n0)+m2.block(0,j1,rows,n0),
+ refMat2.block(0,j0,rows,n0)+refMat2.block(0,j1,rows,n0));
+
+ Index i = internal::random<Index>(0,m2.outerSize()-1);
+ if(SparseMatrixType::IsRowMajor) {
+ m2.innerVector(i) = m2.innerVector(i) * s1;
+ refMat2.row(i) = refMat2.row(i) * s1;
+ VERIFY_IS_APPROX(m2,refMat2);
+ } else {
+ m2.innerVector(i) = m2.innerVector(i) * s1;
+ refMat2.col(i) = refMat2.col(i) * s1;
+ VERIFY_IS_APPROX(m2,refMat2);
+ }
+
+ Index r0 = internal::random<Index>(0,rows-2);
+ Index c0 = internal::random<Index>(0,cols-2);
+ Index r1 = internal::random<Index>(1,rows-r0);
+ Index c1 = internal::random<Index>(1,cols-c0);
+
+ VERIFY_IS_APPROX(DenseVector(m2.col(c0)), refMat2.col(c0));
+ VERIFY_IS_APPROX(m2.col(c0), refMat2.col(c0));
+
+ VERIFY_IS_APPROX(RowDenseVector(m2.row(r0)), refMat2.row(r0));
+ VERIFY_IS_APPROX(m2.row(r0), refMat2.row(r0));
+
+ VERIFY_IS_APPROX(m2.block(r0,c0,r1,c1), refMat2.block(r0,c0,r1,c1));
+ VERIFY_IS_APPROX((2*m2).block(r0,c0,r1,c1), (2*refMat2).block(r0,c0,r1,c1));
+
+ if(m2.nonZeros()>0)
+ {
+ VERIFY_IS_APPROX(m2, refMat2);
+ SparseMatrixType m3(rows, cols);
+ DenseMatrix refMat3(rows, cols); refMat3.setZero();
+ Index n = internal::random<Index>(1,10);
+ for(Index k=0; k<n; ++k)
+ {
+ Index o1 = internal::random<Index>(0,outer-1);
+ Index o2 = internal::random<Index>(0,outer-1);
+ if(SparseMatrixType::IsRowMajor)
+ {
+ m3.innerVector(o1) = m2.row(o2);
+ refMat3.row(o1) = refMat2.row(o2);
+ }
+ else
+ {
+ m3.innerVector(o1) = m2.col(o2);
+ refMat3.col(o1) = refMat2.col(o2);
+ }
+ if(internal::random<bool>())
+ m3.makeCompressed();
+ }
+ if(m3.nonZeros()>0)
+ VERIFY_IS_APPROX(m3, refMat3);
+ }
+ }
+
+ // Explicit inner iterator.
+ {
+ DenseMatrix refMat2 = DenseMatrix::Zero(rows, cols);
+ SparseMatrixType m2(rows, cols);
+ initSparse<Scalar>(density, refMat2, m2);
+
+ Index j0 =internal::random<Index>(0, outer - 1);
+ auto v = innervec(m2, j0);
+
+ typename decltype(v)::InnerIterator block_iterator(v);
+ typename SparseMatrixType::InnerIterator matrix_iterator(m2, j0);
+ while (block_iterator) {
+ VERIFY_IS_EQUAL(block_iterator.index(), matrix_iterator.index());
+ ++block_iterator;
+ ++matrix_iterator;
+ }
+
+ }
+}
+
+EIGEN_DECLARE_TEST(sparse_block)
+{
+ for(int i = 0; i < g_repeat; i++) {
+ int r = Eigen::internal::random<int>(1,200), c = Eigen::internal::random<int>(1,200);
+ if(Eigen::internal::random<int>(0,4) == 0) {
+ r = c; // check square matrices in 25% of tries
+ }
+ EIGEN_UNUSED_VARIABLE(r+c);
+ CALL_SUBTEST_1(( sparse_block(SparseMatrix<double>(1, 1)) ));
+ CALL_SUBTEST_1(( sparse_block(SparseMatrix<double>(8, 8)) ));
+ CALL_SUBTEST_1(( sparse_block(SparseMatrix<double>(r, c)) ));
+ CALL_SUBTEST_2(( sparse_block(SparseMatrix<std::complex<double>, ColMajor>(r, c)) ));
+ CALL_SUBTEST_2(( sparse_block(SparseMatrix<std::complex<double>, RowMajor>(r, c)) ));
+
+ CALL_SUBTEST_3(( sparse_block(SparseMatrix<double,ColMajor,long int>(r, c)) ));
+ CALL_SUBTEST_3(( sparse_block(SparseMatrix<double,RowMajor,long int>(r, c)) ));
+
+ r = Eigen::internal::random<int>(1,100);
+ c = Eigen::internal::random<int>(1,100);
+ if(Eigen::internal::random<int>(0,4) == 0) {
+ r = c; // check square matrices in 25% of tries
+ }
+
+ CALL_SUBTEST_4(( sparse_block(SparseMatrix<double,ColMajor,short int>(short(r), short(c))) ));
+ CALL_SUBTEST_4(( sparse_block(SparseMatrix<double,RowMajor,short int>(short(r), short(c))) ));
+#ifndef EIGEN_TEST_ANNOYING_SCALAR_DONT_THROW
+ AnnoyingScalar::dont_throw = true;
+#endif
+ CALL_SUBTEST_5(( sparse_block(SparseMatrix<AnnoyingScalar>(r,c)) ));
+ }
+}
diff --git a/test/sparse_permutations.cpp b/test/sparse_permutations.cpp
new file mode 100644
index 0000000..5974c74
--- /dev/null
+++ b/test/sparse_permutations.cpp
@@ -0,0 +1,236 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2011-2015 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+
+static long int nb_transposed_copies;
+#define EIGEN_SPARSE_TRANSPOSED_COPY_PLUGIN {nb_transposed_copies++;}
+#define VERIFY_TRANSPOSITION_COUNT(XPR,N) {\
+ nb_transposed_copies = 0; \
+ XPR; \
+ if(nb_transposed_copies!=N) std::cerr << "nb_transposed_copies == " << nb_transposed_copies << "\n"; \
+ VERIFY( (#XPR) && nb_transposed_copies==N ); \
+ }
+
+#include "sparse.h"
+
+template<typename T>
+bool is_sorted(const T& mat) {
+ for(Index k = 0; k<mat.outerSize(); ++k)
+ {
+ Index prev = -1;
+ for(typename T::InnerIterator it(mat,k); it; ++it)
+ {
+ if(prev>=it.index())
+ return false;
+ prev = it.index();
+ }
+ }
+ return true;
+}
+
+template<typename T>
+typename internal::nested_eval<T,1>::type eval(const T &xpr)
+{
+ VERIFY( int(internal::nested_eval<T,1>::type::Flags&RowMajorBit) == int(internal::evaluator<T>::Flags&RowMajorBit) );
+ return xpr;
+}
+
+template<int OtherStorage, typename SparseMatrixType> void sparse_permutations(const SparseMatrixType& ref)
+{
+ const Index rows = ref.rows();
+ const Index cols = ref.cols();
+ typedef typename SparseMatrixType::Scalar Scalar;
+ typedef typename SparseMatrixType::StorageIndex StorageIndex;
+ typedef SparseMatrix<Scalar, OtherStorage, StorageIndex> OtherSparseMatrixType;
+ typedef Matrix<Scalar,Dynamic,Dynamic> DenseMatrix;
+ typedef Matrix<StorageIndex,Dynamic,1> VectorI;
+// bool IsRowMajor1 = SparseMatrixType::IsRowMajor;
+// bool IsRowMajor2 = OtherSparseMatrixType::IsRowMajor;
+
+ double density = (std::max)(8./static_cast<double>(rows*cols), 0.01);
+
+ SparseMatrixType mat(rows, cols), up(rows,cols), lo(rows,cols);
+ OtherSparseMatrixType res;
+ DenseMatrix mat_d = DenseMatrix::Zero(rows, cols), up_sym_d, lo_sym_d, res_d;
+
+ initSparse<Scalar>(density, mat_d, mat, 0);
+
+ up = mat.template triangularView<Upper>();
+ lo = mat.template triangularView<Lower>();
+
+ up_sym_d = mat_d.template selfadjointView<Upper>();
+ lo_sym_d = mat_d.template selfadjointView<Lower>();
+
+ VERIFY_IS_APPROX(mat, mat_d);
+ VERIFY_IS_APPROX(up, DenseMatrix(mat_d.template triangularView<Upper>()));
+ VERIFY_IS_APPROX(lo, DenseMatrix(mat_d.template triangularView<Lower>()));
+
+ PermutationMatrix<Dynamic> p, p_null;
+ VectorI pi;
+ randomPermutationVector(pi, cols);
+ p.indices() = pi;
+
+ VERIFY( is_sorted( ::eval(mat*p) ));
+ VERIFY( is_sorted( res = mat*p ));
+ VERIFY_TRANSPOSITION_COUNT( ::eval(mat*p), 0);
+ //VERIFY_TRANSPOSITION_COUNT( res = mat*p, IsRowMajor ? 1 : 0 );
+ res_d = mat_d*p;
+ VERIFY(res.isApprox(res_d) && "mat*p");
+
+ VERIFY( is_sorted( ::eval(p*mat) ));
+ VERIFY( is_sorted( res = p*mat ));
+ VERIFY_TRANSPOSITION_COUNT( ::eval(p*mat), 0);
+ res_d = p*mat_d;
+ VERIFY(res.isApprox(res_d) && "p*mat");
+
+ VERIFY( is_sorted( (mat*p).eval() ));
+ VERIFY( is_sorted( res = mat*p.inverse() ));
+ VERIFY_TRANSPOSITION_COUNT( ::eval(mat*p.inverse()), 0);
+ res_d = mat*p.inverse();
+ VERIFY(res.isApprox(res_d) && "mat*inv(p)");
+
+ VERIFY( is_sorted( (p*mat+p*mat).eval() ));
+ VERIFY( is_sorted( res = p.inverse()*mat ));
+ VERIFY_TRANSPOSITION_COUNT( ::eval(p.inverse()*mat), 0);
+ res_d = p.inverse()*mat_d;
+ VERIFY(res.isApprox(res_d) && "inv(p)*mat");
+
+ VERIFY( is_sorted( (p * mat * p.inverse()).eval() ));
+ VERIFY( is_sorted( res = mat.twistedBy(p) ));
+ VERIFY_TRANSPOSITION_COUNT( ::eval(p * mat * p.inverse()), 0);
+ res_d = (p * mat_d) * p.inverse();
+ VERIFY(res.isApprox(res_d) && "p*mat*inv(p)");
+
+
+ VERIFY( is_sorted( res = mat.template selfadjointView<Upper>().twistedBy(p_null) ));
+ res_d = up_sym_d;
+ VERIFY(res.isApprox(res_d) && "full selfadjoint upper to full");
+
+ VERIFY( is_sorted( res = mat.template selfadjointView<Lower>().twistedBy(p_null) ));
+ res_d = lo_sym_d;
+ VERIFY(res.isApprox(res_d) && "full selfadjoint lower to full");
+
+
+ VERIFY( is_sorted( res = up.template selfadjointView<Upper>().twistedBy(p_null) ));
+ res_d = up_sym_d;
+ VERIFY(res.isApprox(res_d) && "upper selfadjoint to full");
+
+ VERIFY( is_sorted( res = lo.template selfadjointView<Lower>().twistedBy(p_null) ));
+ res_d = lo_sym_d;
+ VERIFY(res.isApprox(res_d) && "lower selfadjoint full");
+
+
+ VERIFY( is_sorted( res = mat.template selfadjointView<Upper>() ));
+ res_d = up_sym_d;
+ VERIFY(res.isApprox(res_d) && "full selfadjoint upper to full");
+
+ VERIFY( is_sorted( res = mat.template selfadjointView<Lower>() ));
+ res_d = lo_sym_d;
+ VERIFY(res.isApprox(res_d) && "full selfadjoint lower to full");
+
+ VERIFY( is_sorted( res = up.template selfadjointView<Upper>() ));
+ res_d = up_sym_d;
+ VERIFY(res.isApprox(res_d) && "upper selfadjoint to full");
+
+ VERIFY( is_sorted( res = lo.template selfadjointView<Lower>() ));
+ res_d = lo_sym_d;
+ VERIFY(res.isApprox(res_d) && "lower selfadjoint full");
+
+
+ res.template selfadjointView<Upper>() = mat.template selfadjointView<Upper>();
+ res_d = up_sym_d.template triangularView<Upper>();
+ VERIFY(res.isApprox(res_d) && "full selfadjoint upper to upper");
+
+ res.template selfadjointView<Lower>() = mat.template selfadjointView<Upper>();
+ res_d = up_sym_d.template triangularView<Lower>();
+ VERIFY(res.isApprox(res_d) && "full selfadjoint upper to lower");
+
+ res.template selfadjointView<Upper>() = mat.template selfadjointView<Lower>();
+ res_d = lo_sym_d.template triangularView<Upper>();
+ VERIFY(res.isApprox(res_d) && "full selfadjoint lower to upper");
+
+ res.template selfadjointView<Lower>() = mat.template selfadjointView<Lower>();
+ res_d = lo_sym_d.template triangularView<Lower>();
+ VERIFY(res.isApprox(res_d) && "full selfadjoint lower to lower");
+
+
+
+ res.template selfadjointView<Upper>() = mat.template selfadjointView<Upper>().twistedBy(p);
+ res_d = ((p * up_sym_d) * p.inverse()).eval().template triangularView<Upper>();
+ VERIFY(res.isApprox(res_d) && "full selfadjoint upper twisted to upper");
+
+ res.template selfadjointView<Upper>() = mat.template selfadjointView<Lower>().twistedBy(p);
+ res_d = ((p * lo_sym_d) * p.inverse()).eval().template triangularView<Upper>();
+ VERIFY(res.isApprox(res_d) && "full selfadjoint lower twisted to upper");
+
+ res.template selfadjointView<Lower>() = mat.template selfadjointView<Lower>().twistedBy(p);
+ res_d = ((p * lo_sym_d) * p.inverse()).eval().template triangularView<Lower>();
+ VERIFY(res.isApprox(res_d) && "full selfadjoint lower twisted to lower");
+
+ res.template selfadjointView<Lower>() = mat.template selfadjointView<Upper>().twistedBy(p);
+ res_d = ((p * up_sym_d) * p.inverse()).eval().template triangularView<Lower>();
+ VERIFY(res.isApprox(res_d) && "full selfadjoint upper twisted to lower");
+
+
+ res.template selfadjointView<Upper>() = up.template selfadjointView<Upper>().twistedBy(p);
+ res_d = ((p * up_sym_d) * p.inverse()).eval().template triangularView<Upper>();
+ VERIFY(res.isApprox(res_d) && "upper selfadjoint twisted to upper");
+
+ res.template selfadjointView<Upper>() = lo.template selfadjointView<Lower>().twistedBy(p);
+ res_d = ((p * lo_sym_d) * p.inverse()).eval().template triangularView<Upper>();
+ VERIFY(res.isApprox(res_d) && "lower selfadjoint twisted to upper");
+
+ res.template selfadjointView<Lower>() = lo.template selfadjointView<Lower>().twistedBy(p);
+ res_d = ((p * lo_sym_d) * p.inverse()).eval().template triangularView<Lower>();
+ VERIFY(res.isApprox(res_d) && "lower selfadjoint twisted to lower");
+
+ res.template selfadjointView<Lower>() = up.template selfadjointView<Upper>().twistedBy(p);
+ res_d = ((p * up_sym_d) * p.inverse()).eval().template triangularView<Lower>();
+ VERIFY(res.isApprox(res_d) && "upper selfadjoint twisted to lower");
+
+
+ VERIFY( is_sorted( res = mat.template selfadjointView<Upper>().twistedBy(p) ));
+ res_d = (p * up_sym_d) * p.inverse();
+ VERIFY(res.isApprox(res_d) && "full selfadjoint upper twisted to full");
+
+ VERIFY( is_sorted( res = mat.template selfadjointView<Lower>().twistedBy(p) ));
+ res_d = (p * lo_sym_d) * p.inverse();
+ VERIFY(res.isApprox(res_d) && "full selfadjoint lower twisted to full");
+
+ VERIFY( is_sorted( res = up.template selfadjointView<Upper>().twistedBy(p) ));
+ res_d = (p * up_sym_d) * p.inverse();
+ VERIFY(res.isApprox(res_d) && "upper selfadjoint twisted to full");
+
+ VERIFY( is_sorted( res = lo.template selfadjointView<Lower>().twistedBy(p) ));
+ res_d = (p * lo_sym_d) * p.inverse();
+ VERIFY(res.isApprox(res_d) && "lower selfadjoint twisted to full");
+}
+
+template<typename Scalar> void sparse_permutations_all(int size)
+{
+ CALL_SUBTEST(( sparse_permutations<ColMajor>(SparseMatrix<Scalar, ColMajor>(size,size)) ));
+ CALL_SUBTEST(( sparse_permutations<ColMajor>(SparseMatrix<Scalar, RowMajor>(size,size)) ));
+ CALL_SUBTEST(( sparse_permutations<RowMajor>(SparseMatrix<Scalar, ColMajor>(size,size)) ));
+ CALL_SUBTEST(( sparse_permutations<RowMajor>(SparseMatrix<Scalar, RowMajor>(size,size)) ));
+}
+
+EIGEN_DECLARE_TEST(sparse_permutations)
+{
+ for(int i = 0; i < g_repeat; i++) {
+ int s = Eigen::internal::random<int>(1,50);
+ CALL_SUBTEST_1(( sparse_permutations_all<double>(s) ));
+ CALL_SUBTEST_2(( sparse_permutations_all<std::complex<double> >(s) ));
+ }
+
+ VERIFY((internal::is_same<internal::permutation_matrix_product<SparseMatrix<double>,OnTheRight,false,SparseShape>::ReturnType,
+ internal::nested_eval<Product<SparseMatrix<double>,PermutationMatrix<Dynamic,Dynamic>,AliasFreeProduct>,1>::type>::value));
+
+ VERIFY((internal::is_same<internal::permutation_matrix_product<SparseMatrix<double>,OnTheLeft,false,SparseShape>::ReturnType,
+ internal::nested_eval<Product<PermutationMatrix<Dynamic,Dynamic>,SparseMatrix<double>,AliasFreeProduct>,1>::type>::value));
+}
diff --git a/test/sparse_product.cpp b/test/sparse_product.cpp
new file mode 100644
index 0000000..dbf549a
--- /dev/null
+++ b/test/sparse_product.cpp
@@ -0,0 +1,530 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2011 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#if defined(_MSC_VER) && (_MSC_VER==1800)
+// This unit test takes forever to compile in Release mode with MSVC 2013,
+// multiple hours. So let's switch off optimization for this one.
+#pragma optimize("",off)
+#endif
+
+static long int nb_temporaries;
+
+inline void on_temporary_creation() {
+ // here's a great place to set a breakpoint when debugging failures in this test!
+ nb_temporaries++;
+}
+
+#define EIGEN_SPARSE_CREATE_TEMPORARY_PLUGIN { on_temporary_creation(); }
+
+#include "sparse.h"
+
+#define VERIFY_EVALUATION_COUNT(XPR,N) {\
+ nb_temporaries = 0; \
+ CALL_SUBTEST( XPR ); \
+ if(nb_temporaries!=N) std::cerr << "nb_temporaries == " << nb_temporaries << "\n"; \
+ VERIFY( (#XPR) && nb_temporaries==N ); \
+ }
+
+
+
+template<typename SparseMatrixType> void sparse_product()
+{
+ typedef typename SparseMatrixType::StorageIndex StorageIndex;
+ Index n = 100;
+ const Index rows = internal::random<Index>(1,n);
+ const Index cols = internal::random<Index>(1,n);
+ const Index depth = internal::random<Index>(1,n);
+ typedef typename SparseMatrixType::Scalar Scalar;
+ enum { Flags = SparseMatrixType::Flags };
+
+ double density = (std::max)(8./(rows*cols), 0.2);
+ typedef Matrix<Scalar,Dynamic,Dynamic> DenseMatrix;
+ typedef Matrix<Scalar,Dynamic,1> DenseVector;
+ typedef Matrix<Scalar,1,Dynamic> RowDenseVector;
+ typedef SparseVector<Scalar,0,StorageIndex> ColSpVector;
+ typedef SparseVector<Scalar,RowMajor,StorageIndex> RowSpVector;
+
+ Scalar s1 = internal::random<Scalar>();
+ Scalar s2 = internal::random<Scalar>();
+
+ // test matrix-matrix product
+ {
+ DenseMatrix refMat2 = DenseMatrix::Zero(rows, depth);
+ DenseMatrix refMat2t = DenseMatrix::Zero(depth, rows);
+ DenseMatrix refMat3 = DenseMatrix::Zero(depth, cols);
+ DenseMatrix refMat3t = DenseMatrix::Zero(cols, depth);
+ DenseMatrix refMat4 = DenseMatrix::Zero(rows, cols);
+ DenseMatrix refMat4t = DenseMatrix::Zero(cols, rows);
+ DenseMatrix refMat5 = DenseMatrix::Random(depth, cols);
+ DenseMatrix refMat6 = DenseMatrix::Random(rows, rows);
+ DenseMatrix dm4 = DenseMatrix::Zero(rows, rows);
+// DenseVector dv1 = DenseVector::Random(rows);
+ SparseMatrixType m2 (rows, depth);
+ SparseMatrixType m2t(depth, rows);
+ SparseMatrixType m3 (depth, cols);
+ SparseMatrixType m3t(cols, depth);
+ SparseMatrixType m4 (rows, cols);
+ SparseMatrixType m4t(cols, rows);
+ SparseMatrixType m6(rows, rows);
+ initSparse(density, refMat2, m2);
+ initSparse(density, refMat2t, m2t);
+ initSparse(density, refMat3, m3);
+ initSparse(density, refMat3t, m3t);
+ initSparse(density, refMat4, m4);
+ initSparse(density, refMat4t, m4t);
+ initSparse(density, refMat6, m6);
+
+// int c = internal::random<int>(0,depth-1);
+
+ // sparse * sparse
+ VERIFY_IS_APPROX(m4=m2*m3, refMat4=refMat2*refMat3);
+ VERIFY_IS_APPROX(m4=m2t.transpose()*m3, refMat4=refMat2t.transpose()*refMat3);
+ VERIFY_IS_APPROX(m4=m2t.transpose()*m3t.transpose(), refMat4=refMat2t.transpose()*refMat3t.transpose());
+ VERIFY_IS_APPROX(m4=m2*m3t.transpose(), refMat4=refMat2*refMat3t.transpose());
+
+ VERIFY_IS_APPROX(m4 = m2*m3/s1, refMat4 = refMat2*refMat3/s1);
+ VERIFY_IS_APPROX(m4 = m2*m3*s1, refMat4 = refMat2*refMat3*s1);
+ VERIFY_IS_APPROX(m4 = s2*m2*m3*s1, refMat4 = s2*refMat2*refMat3*s1);
+ VERIFY_IS_APPROX(m4 = (m2+m2)*m3, refMat4 = (refMat2+refMat2)*refMat3);
+ VERIFY_IS_APPROX(m4 = m2*m3.leftCols(cols/2), refMat4 = refMat2*refMat3.leftCols(cols/2));
+ VERIFY_IS_APPROX(m4 = m2*(m3+m3).leftCols(cols/2), refMat4 = refMat2*(refMat3+refMat3).leftCols(cols/2));
+
+ VERIFY_IS_APPROX(m4=(m2*m3).pruned(0), refMat4=refMat2*refMat3);
+ VERIFY_IS_APPROX(m4=(m2t.transpose()*m3).pruned(0), refMat4=refMat2t.transpose()*refMat3);
+ VERIFY_IS_APPROX(m4=(m2t.transpose()*m3t.transpose()).pruned(0), refMat4=refMat2t.transpose()*refMat3t.transpose());
+ VERIFY_IS_APPROX(m4=(m2*m3t.transpose()).pruned(0), refMat4=refMat2*refMat3t.transpose());
+
+#ifndef EIGEN_SPARSE_PRODUCT_IGNORE_TEMPORARY_COUNT
+ // make sure the right product implementation is called:
+ if((!SparseMatrixType::IsRowMajor) && m2.rows()<=m3.cols())
+ {
+ VERIFY_EVALUATION_COUNT(m4 = m2*m3, 2); // 2 for transposing and get a sorted result.
+ VERIFY_EVALUATION_COUNT(m4 = (m2*m3).pruned(0), 1);
+ VERIFY_EVALUATION_COUNT(m4 = (m2*m3).eval().pruned(0), 4);
+ }
+#endif
+
+ // and that pruning is effective:
+ {
+ DenseMatrix Ad(2,2);
+ Ad << -1, 1, 1, 1;
+ SparseMatrixType As(Ad.sparseView()), B(2,2);
+ VERIFY_IS_EQUAL( (As*As.transpose()).eval().nonZeros(), 4);
+ VERIFY_IS_EQUAL( (Ad*Ad.transpose()).eval().sparseView().eval().nonZeros(), 2);
+ VERIFY_IS_EQUAL( (As*As.transpose()).pruned(1e-6).eval().nonZeros(), 2);
+ }
+
+ // dense ?= sparse * sparse
+ VERIFY_IS_APPROX(dm4 =m2*m3, refMat4 =refMat2*refMat3);
+ VERIFY_IS_APPROX(dm4+=m2*m3, refMat4+=refMat2*refMat3);
+ VERIFY_IS_APPROX(dm4-=m2*m3, refMat4-=refMat2*refMat3);
+ VERIFY_IS_APPROX(dm4 =m2t.transpose()*m3, refMat4 =refMat2t.transpose()*refMat3);
+ VERIFY_IS_APPROX(dm4+=m2t.transpose()*m3, refMat4+=refMat2t.transpose()*refMat3);
+ VERIFY_IS_APPROX(dm4-=m2t.transpose()*m3, refMat4-=refMat2t.transpose()*refMat3);
+ VERIFY_IS_APPROX(dm4 =m2t.transpose()*m3t.transpose(), refMat4 =refMat2t.transpose()*refMat3t.transpose());
+ VERIFY_IS_APPROX(dm4+=m2t.transpose()*m3t.transpose(), refMat4+=refMat2t.transpose()*refMat3t.transpose());
+ VERIFY_IS_APPROX(dm4-=m2t.transpose()*m3t.transpose(), refMat4-=refMat2t.transpose()*refMat3t.transpose());
+ VERIFY_IS_APPROX(dm4 =m2*m3t.transpose(), refMat4 =refMat2*refMat3t.transpose());
+ VERIFY_IS_APPROX(dm4+=m2*m3t.transpose(), refMat4+=refMat2*refMat3t.transpose());
+ VERIFY_IS_APPROX(dm4-=m2*m3t.transpose(), refMat4-=refMat2*refMat3t.transpose());
+ VERIFY_IS_APPROX(dm4 = m2*m3*s1, refMat4 = refMat2*refMat3*s1);
+
+ // test aliasing
+ m4 = m2; refMat4 = refMat2;
+ VERIFY_IS_APPROX(m4=m4*m3, refMat4=refMat4*refMat3);
+
+ // sparse * dense matrix
+ VERIFY_IS_APPROX(dm4=m2*refMat3, refMat4=refMat2*refMat3);
+ VERIFY_IS_APPROX(dm4=m2*refMat3t.transpose(), refMat4=refMat2*refMat3t.transpose());
+ VERIFY_IS_APPROX(dm4=m2t.transpose()*refMat3, refMat4=refMat2t.transpose()*refMat3);
+ VERIFY_IS_APPROX(dm4=m2t.transpose()*refMat3t.transpose(), refMat4=refMat2t.transpose()*refMat3t.transpose());
+
+ VERIFY_IS_APPROX(dm4=m2*refMat3, refMat4=refMat2*refMat3);
+ VERIFY_IS_APPROX(dm4=dm4+m2*refMat3, refMat4=refMat4+refMat2*refMat3);
+ VERIFY_IS_APPROX(dm4+=m2*refMat3, refMat4+=refMat2*refMat3);
+ VERIFY_IS_APPROX(dm4-=m2*refMat3, refMat4-=refMat2*refMat3);
+ VERIFY_IS_APPROX(dm4.noalias()+=m2*refMat3, refMat4+=refMat2*refMat3);
+ VERIFY_IS_APPROX(dm4.noalias()-=m2*refMat3, refMat4-=refMat2*refMat3);
+ VERIFY_IS_APPROX(dm4=m2*(refMat3+refMat3), refMat4=refMat2*(refMat3+refMat3));
+ VERIFY_IS_APPROX(dm4=m2t.transpose()*(refMat3+refMat5)*0.5, refMat4=refMat2t.transpose()*(refMat3+refMat5)*0.5);
+
+ // sparse * dense vector
+ VERIFY_IS_APPROX(dm4.col(0)=m2*refMat3.col(0), refMat4.col(0)=refMat2*refMat3.col(0));
+ VERIFY_IS_APPROX(dm4.col(0)=m2*refMat3t.transpose().col(0), refMat4.col(0)=refMat2*refMat3t.transpose().col(0));
+ VERIFY_IS_APPROX(dm4.col(0)=m2t.transpose()*refMat3.col(0), refMat4.col(0)=refMat2t.transpose()*refMat3.col(0));
+ VERIFY_IS_APPROX(dm4.col(0)=m2t.transpose()*refMat3t.transpose().col(0), refMat4.col(0)=refMat2t.transpose()*refMat3t.transpose().col(0));
+
+ // dense * sparse
+ VERIFY_IS_APPROX(dm4=refMat2*m3, refMat4=refMat2*refMat3);
+ VERIFY_IS_APPROX(dm4=dm4+refMat2*m3, refMat4=refMat4+refMat2*refMat3);
+ VERIFY_IS_APPROX(dm4+=refMat2*m3, refMat4+=refMat2*refMat3);
+ VERIFY_IS_APPROX(dm4-=refMat2*m3, refMat4-=refMat2*refMat3);
+ VERIFY_IS_APPROX(dm4.noalias()+=refMat2*m3, refMat4+=refMat2*refMat3);
+ VERIFY_IS_APPROX(dm4.noalias()-=refMat2*m3, refMat4-=refMat2*refMat3);
+ VERIFY_IS_APPROX(dm4=refMat2*m3t.transpose(), refMat4=refMat2*refMat3t.transpose());
+ VERIFY_IS_APPROX(dm4=refMat2t.transpose()*m3, refMat4=refMat2t.transpose()*refMat3);
+ VERIFY_IS_APPROX(dm4=refMat2t.transpose()*m3t.transpose(), refMat4=refMat2t.transpose()*refMat3t.transpose());
+
+ // sparse * dense and dense * sparse outer product
+ {
+ Index c = internal::random<Index>(0,depth-1);
+ Index r = internal::random<Index>(0,rows-1);
+ Index c1 = internal::random<Index>(0,cols-1);
+ Index r1 = internal::random<Index>(0,depth-1);
+ DenseMatrix dm5 = DenseMatrix::Random(depth, cols);
+
+ VERIFY_IS_APPROX( m4=m2.col(c)*dm5.col(c1).transpose(), refMat4=refMat2.col(c)*dm5.col(c1).transpose());
+ VERIFY_IS_EQUAL(m4.nonZeros(), (refMat4.array()!=0).count());
+ VERIFY_IS_APPROX( m4=m2.middleCols(c,1)*dm5.col(c1).transpose(), refMat4=refMat2.col(c)*dm5.col(c1).transpose());
+ VERIFY_IS_EQUAL(m4.nonZeros(), (refMat4.array()!=0).count());
+ VERIFY_IS_APPROX(dm4=m2.col(c)*dm5.col(c1).transpose(), refMat4=refMat2.col(c)*dm5.col(c1).transpose());
+
+ VERIFY_IS_APPROX(m4=dm5.col(c1)*m2.col(c).transpose(), refMat4=dm5.col(c1)*refMat2.col(c).transpose());
+ VERIFY_IS_EQUAL(m4.nonZeros(), (refMat4.array()!=0).count());
+ VERIFY_IS_APPROX(m4=dm5.col(c1)*m2.middleCols(c,1).transpose(), refMat4=dm5.col(c1)*refMat2.col(c).transpose());
+ VERIFY_IS_EQUAL(m4.nonZeros(), (refMat4.array()!=0).count());
+ VERIFY_IS_APPROX(dm4=dm5.col(c1)*m2.col(c).transpose(), refMat4=dm5.col(c1)*refMat2.col(c).transpose());
+
+ VERIFY_IS_APPROX( m4=dm5.row(r1).transpose()*m2.col(c).transpose(), refMat4=dm5.row(r1).transpose()*refMat2.col(c).transpose());
+ VERIFY_IS_EQUAL(m4.nonZeros(), (refMat4.array()!=0).count());
+ VERIFY_IS_APPROX(dm4=dm5.row(r1).transpose()*m2.col(c).transpose(), refMat4=dm5.row(r1).transpose()*refMat2.col(c).transpose());
+
+ VERIFY_IS_APPROX( m4=m2.row(r).transpose()*dm5.col(c1).transpose(), refMat4=refMat2.row(r).transpose()*dm5.col(c1).transpose());
+ VERIFY_IS_EQUAL(m4.nonZeros(), (refMat4.array()!=0).count());
+ VERIFY_IS_APPROX( m4=m2.middleRows(r,1).transpose()*dm5.col(c1).transpose(), refMat4=refMat2.row(r).transpose()*dm5.col(c1).transpose());
+ VERIFY_IS_EQUAL(m4.nonZeros(), (refMat4.array()!=0).count());
+ VERIFY_IS_APPROX(dm4=m2.row(r).transpose()*dm5.col(c1).transpose(), refMat4=refMat2.row(r).transpose()*dm5.col(c1).transpose());
+
+ VERIFY_IS_APPROX( m4=dm5.col(c1)*m2.row(r), refMat4=dm5.col(c1)*refMat2.row(r));
+ VERIFY_IS_EQUAL(m4.nonZeros(), (refMat4.array()!=0).count());
+ VERIFY_IS_APPROX( m4=dm5.col(c1)*m2.middleRows(r,1), refMat4=dm5.col(c1)*refMat2.row(r));
+ VERIFY_IS_EQUAL(m4.nonZeros(), (refMat4.array()!=0).count());
+ VERIFY_IS_APPROX(dm4=dm5.col(c1)*m2.row(r), refMat4=dm5.col(c1)*refMat2.row(r));
+
+ VERIFY_IS_APPROX( m4=dm5.row(r1).transpose()*m2.row(r), refMat4=dm5.row(r1).transpose()*refMat2.row(r));
+ VERIFY_IS_EQUAL(m4.nonZeros(), (refMat4.array()!=0).count());
+ VERIFY_IS_APPROX(dm4=dm5.row(r1).transpose()*m2.row(r), refMat4=dm5.row(r1).transpose()*refMat2.row(r));
+ }
+
+ VERIFY_IS_APPROX(m6=m6*m6, refMat6=refMat6*refMat6);
+
+ // sparse matrix * sparse vector
+ ColSpVector cv0(cols), cv1;
+ DenseVector dcv0(cols), dcv1;
+ initSparse(2*density,dcv0, cv0);
+
+ RowSpVector rv0(depth), rv1;
+ RowDenseVector drv0(depth), drv1(rv1);
+ initSparse(2*density,drv0, rv0);
+
+ VERIFY_IS_APPROX(cv1=m3*cv0, dcv1=refMat3*dcv0);
+ VERIFY_IS_APPROX(rv1=rv0*m3, drv1=drv0*refMat3);
+ VERIFY_IS_APPROX(cv1=m3t.adjoint()*cv0, dcv1=refMat3t.adjoint()*dcv0);
+ VERIFY_IS_APPROX(cv1=rv0*m3, dcv1=drv0*refMat3);
+ VERIFY_IS_APPROX(rv1=m3*cv0, drv1=refMat3*dcv0);
+ }
+
+ // test matrix - diagonal product
+ {
+ DenseMatrix refM2 = DenseMatrix::Zero(rows, cols);
+ DenseMatrix refM3 = DenseMatrix::Zero(rows, cols);
+ DenseMatrix d3 = DenseMatrix::Zero(rows, cols);
+ DiagonalMatrix<Scalar,Dynamic> d1(DenseVector::Random(cols));
+ DiagonalMatrix<Scalar,Dynamic> d2(DenseVector::Random(rows));
+ SparseMatrixType m2(rows, cols);
+ SparseMatrixType m3(rows, cols);
+ initSparse<Scalar>(density, refM2, m2);
+ initSparse<Scalar>(density, refM3, m3);
+ VERIFY_IS_APPROX(m3=m2*d1, refM3=refM2*d1);
+ VERIFY_IS_APPROX(m3=m2.transpose()*d2, refM3=refM2.transpose()*d2);
+ VERIFY_IS_APPROX(m3=d2*m2, refM3=d2*refM2);
+ VERIFY_IS_APPROX(m3=d1*m2.transpose(), refM3=d1*refM2.transpose());
+
+ // also check with a SparseWrapper:
+ DenseVector v1 = DenseVector::Random(cols);
+ DenseVector v2 = DenseVector::Random(rows);
+ DenseVector v3 = DenseVector::Random(rows);
+ VERIFY_IS_APPROX(m3=m2*v1.asDiagonal(), refM3=refM2*v1.asDiagonal());
+ VERIFY_IS_APPROX(m3=m2.transpose()*v2.asDiagonal(), refM3=refM2.transpose()*v2.asDiagonal());
+ VERIFY_IS_APPROX(m3=v2.asDiagonal()*m2, refM3=v2.asDiagonal()*refM2);
+ VERIFY_IS_APPROX(m3=v1.asDiagonal()*m2.transpose(), refM3=v1.asDiagonal()*refM2.transpose());
+
+ VERIFY_IS_APPROX(m3=v2.asDiagonal()*m2*v1.asDiagonal(), refM3=v2.asDiagonal()*refM2*v1.asDiagonal());
+
+ VERIFY_IS_APPROX(v2=m2*v1.asDiagonal()*v1, refM2*v1.asDiagonal()*v1);
+ VERIFY_IS_APPROX(v3=v2.asDiagonal()*m2*v1, v2.asDiagonal()*refM2*v1);
+
+ // evaluate to a dense matrix to check the .row() and .col() iterator functions
+ VERIFY_IS_APPROX(d3=m2*d1, refM3=refM2*d1);
+ VERIFY_IS_APPROX(d3=m2.transpose()*d2, refM3=refM2.transpose()*d2);
+ VERIFY_IS_APPROX(d3=d2*m2, refM3=d2*refM2);
+ VERIFY_IS_APPROX(d3=d1*m2.transpose(), refM3=d1*refM2.transpose());
+ }
+
+ // test self-adjoint and triangular-view products
+ {
+ DenseMatrix b = DenseMatrix::Random(rows, rows);
+ DenseMatrix x = DenseMatrix::Random(rows, rows);
+ DenseMatrix refX = DenseMatrix::Random(rows, rows);
+ DenseMatrix refUp = DenseMatrix::Zero(rows, rows);
+ DenseMatrix refLo = DenseMatrix::Zero(rows, rows);
+ DenseMatrix refS = DenseMatrix::Zero(rows, rows);
+ DenseMatrix refA = DenseMatrix::Zero(rows, rows);
+ SparseMatrixType mUp(rows, rows);
+ SparseMatrixType mLo(rows, rows);
+ SparseMatrixType mS(rows, rows);
+ SparseMatrixType mA(rows, rows);
+ initSparse<Scalar>(density, refA, mA);
+ do {
+ initSparse<Scalar>(density, refUp, mUp, ForceRealDiag|/*ForceNonZeroDiag|*/MakeUpperTriangular);
+ } while (refUp.isZero());
+ refLo = refUp.adjoint();
+ mLo = mUp.adjoint();
+ refS = refUp + refLo;
+ refS.diagonal() *= 0.5;
+ mS = mUp + mLo;
+ // TODO be able to address the diagonal....
+ for (int k=0; k<mS.outerSize(); ++k)
+ for (typename SparseMatrixType::InnerIterator it(mS,k); it; ++it)
+ if (it.index() == k)
+ it.valueRef() *= Scalar(0.5);
+
+ VERIFY_IS_APPROX(refS.adjoint(), refS);
+ VERIFY_IS_APPROX(mS.adjoint(), mS);
+ VERIFY_IS_APPROX(mS, refS);
+ VERIFY_IS_APPROX(x=mS*b, refX=refS*b);
+
+ // sparse selfadjointView with dense matrices
+ VERIFY_IS_APPROX(x=mUp.template selfadjointView<Upper>()*b, refX=refS*b);
+ VERIFY_IS_APPROX(x=mLo.template selfadjointView<Lower>()*b, refX=refS*b);
+ VERIFY_IS_APPROX(x=mS.template selfadjointView<Upper|Lower>()*b, refX=refS*b);
+
+ VERIFY_IS_APPROX(x=b * mUp.template selfadjointView<Upper>(), refX=b*refS);
+ VERIFY_IS_APPROX(x=b * mLo.template selfadjointView<Lower>(), refX=b*refS);
+ VERIFY_IS_APPROX(x=b * mS.template selfadjointView<Upper|Lower>(), refX=b*refS);
+
+ VERIFY_IS_APPROX(x.noalias()+=mUp.template selfadjointView<Upper>()*b, refX+=refS*b);
+ VERIFY_IS_APPROX(x.noalias()-=mLo.template selfadjointView<Lower>()*b, refX-=refS*b);
+ VERIFY_IS_APPROX(x.noalias()+=mS.template selfadjointView<Upper|Lower>()*b, refX+=refS*b);
+
+ // sparse selfadjointView with sparse matrices
+ SparseMatrixType mSres(rows,rows);
+ VERIFY_IS_APPROX(mSres = mLo.template selfadjointView<Lower>()*mS,
+ refX = refLo.template selfadjointView<Lower>()*refS);
+ VERIFY_IS_APPROX(mSres = mS * mLo.template selfadjointView<Lower>(),
+ refX = refS * refLo.template selfadjointView<Lower>());
+
+ // sparse triangularView with dense matrices
+ VERIFY_IS_APPROX(x=mA.template triangularView<Upper>()*b, refX=refA.template triangularView<Upper>()*b);
+ VERIFY_IS_APPROX(x=mA.template triangularView<Lower>()*b, refX=refA.template triangularView<Lower>()*b);
+ VERIFY_IS_APPROX(x=b*mA.template triangularView<Upper>(), refX=b*refA.template triangularView<Upper>());
+ VERIFY_IS_APPROX(x=b*mA.template triangularView<Lower>(), refX=b*refA.template triangularView<Lower>());
+
+ // sparse triangularView with sparse matrices
+ VERIFY_IS_APPROX(mSres = mA.template triangularView<Lower>()*mS, refX = refA.template triangularView<Lower>()*refS);
+ VERIFY_IS_APPROX(mSres = mS * mA.template triangularView<Lower>(), refX = refS * refA.template triangularView<Lower>());
+ VERIFY_IS_APPROX(mSres = mA.template triangularView<Upper>()*mS, refX = refA.template triangularView<Upper>()*refS);
+ VERIFY_IS_APPROX(mSres = mS * mA.template triangularView<Upper>(), refX = refS * refA.template triangularView<Upper>());
+ }
+}
+
+// New test for Bug in SparseTimeDenseProduct
+template<typename SparseMatrixType, typename DenseMatrixType> void sparse_product_regression_test()
+{
+ // This code does not compile with afflicted versions of the bug
+ SparseMatrixType sm1(3,2);
+ DenseMatrixType m2(2,2);
+ sm1.setZero();
+ m2.setZero();
+
+ DenseMatrixType m3 = sm1*m2;
+
+
+ // This code produces a segfault with afflicted versions of another SparseTimeDenseProduct
+ // bug
+
+ SparseMatrixType sm2(20000,2);
+ sm2.setZero();
+ DenseMatrixType m4(sm2*m2);
+
+ VERIFY_IS_APPROX( m4(0,0), 0.0 );
+}
+
+template<typename Scalar>
+void bug_942()
+{
+ typedef Matrix<Scalar, Dynamic, 1> Vector;
+ typedef SparseMatrix<Scalar, ColMajor> ColSpMat;
+ typedef SparseMatrix<Scalar, RowMajor> RowSpMat;
+ ColSpMat cmA(1,1);
+ cmA.insert(0,0) = 1;
+
+ RowSpMat rmA(1,1);
+ rmA.insert(0,0) = 1;
+
+ Vector d(1);
+ d[0] = 2;
+
+ double res = 2;
+
+ VERIFY_IS_APPROX( ( cmA*d.asDiagonal() ).eval().coeff(0,0), res );
+ VERIFY_IS_APPROX( ( d.asDiagonal()*rmA ).eval().coeff(0,0), res );
+ VERIFY_IS_APPROX( ( rmA*d.asDiagonal() ).eval().coeff(0,0), res );
+ VERIFY_IS_APPROX( ( d.asDiagonal()*cmA ).eval().coeff(0,0), res );
+}
+
+template<typename Real>
+void test_mixing_types()
+{
+ typedef std::complex<Real> Cplx;
+ typedef SparseMatrix<Real> SpMatReal;
+ typedef SparseMatrix<Cplx> SpMatCplx;
+ typedef SparseMatrix<Cplx,RowMajor> SpRowMatCplx;
+ typedef Matrix<Real,Dynamic,Dynamic> DenseMatReal;
+ typedef Matrix<Cplx,Dynamic,Dynamic> DenseMatCplx;
+
+ Index n = internal::random<Index>(1,100);
+ double density = (std::max)(8./static_cast<double>(n*n), 0.2);
+
+ SpMatReal sR1(n,n);
+ SpMatCplx sC1(n,n), sC2(n,n), sC3(n,n);
+ SpRowMatCplx sCR(n,n);
+ DenseMatReal dR1(n,n);
+ DenseMatCplx dC1(n,n), dC2(n,n), dC3(n,n);
+
+ initSparse<Real>(density, dR1, sR1);
+ initSparse<Cplx>(density, dC1, sC1);
+ initSparse<Cplx>(density, dC2, sC2);
+
+ VERIFY_IS_APPROX( sC2 = (sR1 * sC1), dC3 = dR1.template cast<Cplx>() * dC1 );
+ VERIFY_IS_APPROX( sC2 = (sC1 * sR1), dC3 = dC1 * dR1.template cast<Cplx>() );
+ VERIFY_IS_APPROX( sC2 = (sR1.transpose() * sC1), dC3 = dR1.template cast<Cplx>().transpose() * dC1 );
+ VERIFY_IS_APPROX( sC2 = (sC1.transpose() * sR1), dC3 = dC1.transpose() * dR1.template cast<Cplx>() );
+ VERIFY_IS_APPROX( sC2 = (sR1 * sC1.transpose()), dC3 = dR1.template cast<Cplx>() * dC1.transpose() );
+ VERIFY_IS_APPROX( sC2 = (sC1 * sR1.transpose()), dC3 = dC1 * dR1.template cast<Cplx>().transpose() );
+ VERIFY_IS_APPROX( sC2 = (sR1.transpose() * sC1.transpose()), dC3 = dR1.template cast<Cplx>().transpose() * dC1.transpose() );
+ VERIFY_IS_APPROX( sC2 = (sC1.transpose() * sR1.transpose()), dC3 = dC1.transpose() * dR1.template cast<Cplx>().transpose() );
+
+ VERIFY_IS_APPROX( sCR = (sR1 * sC1), dC3 = dR1.template cast<Cplx>() * dC1 );
+ VERIFY_IS_APPROX( sCR = (sC1 * sR1), dC3 = dC1 * dR1.template cast<Cplx>() );
+ VERIFY_IS_APPROX( sCR = (sR1.transpose() * sC1), dC3 = dR1.template cast<Cplx>().transpose() * dC1 );
+ VERIFY_IS_APPROX( sCR = (sC1.transpose() * sR1), dC3 = dC1.transpose() * dR1.template cast<Cplx>() );
+ VERIFY_IS_APPROX( sCR = (sR1 * sC1.transpose()), dC3 = dR1.template cast<Cplx>() * dC1.transpose() );
+ VERIFY_IS_APPROX( sCR = (sC1 * sR1.transpose()), dC3 = dC1 * dR1.template cast<Cplx>().transpose() );
+ VERIFY_IS_APPROX( sCR = (sR1.transpose() * sC1.transpose()), dC3 = dR1.template cast<Cplx>().transpose() * dC1.transpose() );
+ VERIFY_IS_APPROX( sCR = (sC1.transpose() * sR1.transpose()), dC3 = dC1.transpose() * dR1.template cast<Cplx>().transpose() );
+
+
+ VERIFY_IS_APPROX( sC2 = (sR1 * sC1).pruned(), dC3 = dR1.template cast<Cplx>() * dC1 );
+ VERIFY_IS_APPROX( sC2 = (sC1 * sR1).pruned(), dC3 = dC1 * dR1.template cast<Cplx>() );
+ VERIFY_IS_APPROX( sC2 = (sR1.transpose() * sC1).pruned(), dC3 = dR1.template cast<Cplx>().transpose() * dC1 );
+ VERIFY_IS_APPROX( sC2 = (sC1.transpose() * sR1).pruned(), dC3 = dC1.transpose() * dR1.template cast<Cplx>() );
+ VERIFY_IS_APPROX( sC2 = (sR1 * sC1.transpose()).pruned(), dC3 = dR1.template cast<Cplx>() * dC1.transpose() );
+ VERIFY_IS_APPROX( sC2 = (sC1 * sR1.transpose()).pruned(), dC3 = dC1 * dR1.template cast<Cplx>().transpose() );
+ VERIFY_IS_APPROX( sC2 = (sR1.transpose() * sC1.transpose()).pruned(), dC3 = dR1.template cast<Cplx>().transpose() * dC1.transpose() );
+ VERIFY_IS_APPROX( sC2 = (sC1.transpose() * sR1.transpose()).pruned(), dC3 = dC1.transpose() * dR1.template cast<Cplx>().transpose() );
+
+ VERIFY_IS_APPROX( sCR = (sR1 * sC1).pruned(), dC3 = dR1.template cast<Cplx>() * dC1 );
+ VERIFY_IS_APPROX( sCR = (sC1 * sR1).pruned(), dC3 = dC1 * dR1.template cast<Cplx>() );
+ VERIFY_IS_APPROX( sCR = (sR1.transpose() * sC1).pruned(), dC3 = dR1.template cast<Cplx>().transpose() * dC1 );
+ VERIFY_IS_APPROX( sCR = (sC1.transpose() * sR1).pruned(), dC3 = dC1.transpose() * dR1.template cast<Cplx>() );
+ VERIFY_IS_APPROX( sCR = (sR1 * sC1.transpose()).pruned(), dC3 = dR1.template cast<Cplx>() * dC1.transpose() );
+ VERIFY_IS_APPROX( sCR = (sC1 * sR1.transpose()).pruned(), dC3 = dC1 * dR1.template cast<Cplx>().transpose() );
+ VERIFY_IS_APPROX( sCR = (sR1.transpose() * sC1.transpose()).pruned(), dC3 = dR1.template cast<Cplx>().transpose() * dC1.transpose() );
+ VERIFY_IS_APPROX( sCR = (sC1.transpose() * sR1.transpose()).pruned(), dC3 = dC1.transpose() * dR1.template cast<Cplx>().transpose() );
+
+
+ VERIFY_IS_APPROX( dC2 = (sR1 * sC1), dC3 = dR1.template cast<Cplx>() * dC1 );
+ VERIFY_IS_APPROX( dC2 = (sC1 * sR1), dC3 = dC1 * dR1.template cast<Cplx>() );
+ VERIFY_IS_APPROX( dC2 = (sR1.transpose() * sC1), dC3 = dR1.template cast<Cplx>().transpose() * dC1 );
+ VERIFY_IS_APPROX( dC2 = (sC1.transpose() * sR1), dC3 = dC1.transpose() * dR1.template cast<Cplx>() );
+ VERIFY_IS_APPROX( dC2 = (sR1 * sC1.transpose()), dC3 = dR1.template cast<Cplx>() * dC1.transpose() );
+ VERIFY_IS_APPROX( dC2 = (sC1 * sR1.transpose()), dC3 = dC1 * dR1.template cast<Cplx>().transpose() );
+ VERIFY_IS_APPROX( dC2 = (sR1.transpose() * sC1.transpose()), dC3 = dR1.template cast<Cplx>().transpose() * dC1.transpose() );
+ VERIFY_IS_APPROX( dC2 = (sC1.transpose() * sR1.transpose()), dC3 = dC1.transpose() * dR1.template cast<Cplx>().transpose() );
+
+
+ VERIFY_IS_APPROX( dC2 = dR1 * sC1, dC3 = dR1.template cast<Cplx>() * sC1 );
+ VERIFY_IS_APPROX( dC2 = sR1 * dC1, dC3 = sR1.template cast<Cplx>() * dC1 );
+ VERIFY_IS_APPROX( dC2 = dC1 * sR1, dC3 = dC1 * sR1.template cast<Cplx>() );
+ VERIFY_IS_APPROX( dC2 = sC1 * dR1, dC3 = sC1 * dR1.template cast<Cplx>() );
+
+ VERIFY_IS_APPROX( dC2 = dR1.row(0) * sC1, dC3 = dR1.template cast<Cplx>().row(0) * sC1 );
+ VERIFY_IS_APPROX( dC2 = sR1 * dC1.col(0), dC3 = sR1.template cast<Cplx>() * dC1.col(0) );
+ VERIFY_IS_APPROX( dC2 = dC1.row(0) * sR1, dC3 = dC1.row(0) * sR1.template cast<Cplx>() );
+ VERIFY_IS_APPROX( dC2 = sC1 * dR1.col(0), dC3 = sC1 * dR1.template cast<Cplx>().col(0) );
+}
+
+// Test mixed storage types
+template<int OrderA, int OrderB, int OrderC>
+void test_mixed_storage_imp() {
+ typedef float Real;
+ typedef Matrix<Real,Dynamic,Dynamic> DenseMat;
+
+ // Case: Large inputs but small result
+ {
+ SparseMatrix<Real, OrderA> A(8, 512);
+ SparseMatrix<Real, OrderB> B(512, 8);
+ DenseMat refA(8, 512);
+ DenseMat refB(512, 8);
+
+ initSparse<Real>(0.1, refA, A);
+ initSparse<Real>(0.1, refB, B);
+
+ SparseMatrix<Real, OrderC, std::int8_t> result;
+ SparseMatrix<Real, OrderC> result_large;
+ DenseMat refResult;
+
+ VERIFY_IS_APPROX( result = (A * B), refResult = refA * refB );
+ }
+
+ // Case: Small input but large result
+ {
+ SparseMatrix<Real, OrderA, std::int8_t> A(127, 8);
+ SparseMatrix<Real, OrderB, std::int8_t> B(8, 127);
+ DenseMat refA(127, 8);
+ DenseMat refB(8, 127);
+
+ initSparse<Real>(0.01, refA, A);
+ initSparse<Real>(0.01, refB, B);
+
+ SparseMatrix<Real, OrderC> result;
+ SparseMatrix<Real, OrderC> result_large;
+ DenseMat refResult;
+
+ VERIFY_IS_APPROX( result = (A * B), refResult = refA * refB );
+ }
+}
+
+void test_mixed_storage() {
+ test_mixed_storage_imp<RowMajor, RowMajor, RowMajor>();
+ test_mixed_storage_imp<RowMajor, RowMajor, ColMajor>();
+ test_mixed_storage_imp<RowMajor, ColMajor, RowMajor>();
+ test_mixed_storage_imp<RowMajor, ColMajor, ColMajor>();
+ test_mixed_storage_imp<ColMajor, RowMajor, RowMajor>();
+ test_mixed_storage_imp<ColMajor, RowMajor, ColMajor>();
+ test_mixed_storage_imp<ColMajor, ColMajor, RowMajor>();
+ test_mixed_storage_imp<ColMajor, ColMajor, ColMajor>();
+}
+
+EIGEN_DECLARE_TEST(sparse_product)
+{
+ for(int i = 0; i < g_repeat; i++) {
+ CALL_SUBTEST_1( (sparse_product<SparseMatrix<double,ColMajor> >()) );
+ CALL_SUBTEST_1( (sparse_product<SparseMatrix<double,RowMajor> >()) );
+ CALL_SUBTEST_1( (bug_942<double>()) );
+ CALL_SUBTEST_2( (sparse_product<SparseMatrix<std::complex<double>, ColMajor > >()) );
+ CALL_SUBTEST_2( (sparse_product<SparseMatrix<std::complex<double>, RowMajor > >()) );
+ CALL_SUBTEST_3( (sparse_product<SparseMatrix<float,ColMajor,long int> >()) );
+ CALL_SUBTEST_4( (sparse_product_regression_test<SparseMatrix<double,RowMajor>, Matrix<double, Dynamic, Dynamic, RowMajor> >()) );
+
+ CALL_SUBTEST_5( (test_mixing_types<float>()) );
+ CALL_SUBTEST_5( (test_mixed_storage()) );
+ }
+}
diff --git a/test/sparse_ref.cpp b/test/sparse_ref.cpp
new file mode 100644
index 0000000..098331e
--- /dev/null
+++ b/test/sparse_ref.cpp
@@ -0,0 +1,139 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2015 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+// This unit test cannot be easily written to work with EIGEN_DEFAULT_TO_ROW_MAJOR
+#ifdef EIGEN_DEFAULT_TO_ROW_MAJOR
+#undef EIGEN_DEFAULT_TO_ROW_MAJOR
+#endif
+
+static long int nb_temporaries;
+
+inline void on_temporary_creation() {
+ // here's a great place to set a breakpoint when debugging failures in this test!
+ nb_temporaries++;
+}
+
+#define EIGEN_SPARSE_CREATE_TEMPORARY_PLUGIN { on_temporary_creation(); }
+
+#include "main.h"
+#include <Eigen/SparseCore>
+
+#define VERIFY_EVALUATION_COUNT(XPR,N) {\
+ nb_temporaries = 0; \
+ CALL_SUBTEST( XPR ); \
+ if(nb_temporaries!=N) std::cerr << "nb_temporaries == " << nb_temporaries << "\n"; \
+ VERIFY( (#XPR) && nb_temporaries==N ); \
+ }
+
+template<typename PlainObjectType> void check_const_correctness(const PlainObjectType&)
+{
+ // verify that ref-to-const don't have LvalueBit
+ typedef std::add_const_t<PlainObjectType> ConstPlainObjectType;
+ VERIFY( !(internal::traits<Ref<ConstPlainObjectType> >::Flags & LvalueBit) );
+ VERIFY( !(internal::traits<Ref<ConstPlainObjectType, Aligned> >::Flags & LvalueBit) );
+ VERIFY( !(Ref<ConstPlainObjectType>::Flags & LvalueBit) );
+ VERIFY( !(Ref<ConstPlainObjectType, Aligned>::Flags & LvalueBit) );
+}
+
+template<typename B>
+EIGEN_DONT_INLINE void call_ref_1(Ref<SparseMatrix<float> > a, const B &b) { VERIFY_IS_EQUAL(a.toDense(),b.toDense()); }
+
+template<typename B>
+EIGEN_DONT_INLINE void call_ref_2(const Ref<const SparseMatrix<float> >& a, const B &b) { VERIFY_IS_EQUAL(a.toDense(),b.toDense()); }
+
+template<typename B>
+EIGEN_DONT_INLINE void call_ref_3(const Ref<const SparseMatrix<float>, StandardCompressedFormat>& a, const B &b) {
+ VERIFY(a.isCompressed());
+ VERIFY_IS_EQUAL(a.toDense(),b.toDense());
+}
+
+template<typename B>
+EIGEN_DONT_INLINE void call_ref_4(Ref<SparseVector<float> > a, const B &b) { VERIFY_IS_EQUAL(a.toDense(),b.toDense()); }
+
+template<typename B>
+EIGEN_DONT_INLINE void call_ref_5(const Ref<const SparseVector<float> >& a, const B &b) { VERIFY_IS_EQUAL(a.toDense(),b.toDense()); }
+
+void call_ref()
+{
+ SparseMatrix<float> A = MatrixXf::Random(10,10).sparseView(0.5,1);
+ SparseMatrix<float,RowMajor> B = MatrixXf::Random(10,10).sparseView(0.5,1);
+ SparseMatrix<float> C = MatrixXf::Random(10,10).sparseView(0.5,1);
+ C.reserve(VectorXi::Constant(C.outerSize(), 2));
+ const SparseMatrix<float>& Ac(A);
+ Block<SparseMatrix<float> > Ab(A,0,1, 3,3);
+ const Block<SparseMatrix<float> > Abc(A,0,1,3,3);
+ SparseVector<float> vc = VectorXf::Random(10).sparseView(0.5,1);
+ SparseVector<float,RowMajor> vr = VectorXf::Random(10).sparseView(0.5,1);
+ SparseMatrix<float> AA = A*A;
+
+
+ VERIFY_EVALUATION_COUNT( call_ref_1(A, A), 0);
+// VERIFY_EVALUATION_COUNT( call_ref_1(Ac, Ac), 0); // does not compile on purpose
+ VERIFY_EVALUATION_COUNT( call_ref_2(A, A), 0);
+ VERIFY_EVALUATION_COUNT( call_ref_3(A, A), 0);
+ VERIFY_EVALUATION_COUNT( call_ref_2(A.transpose(), A.transpose()), 1);
+ VERIFY_EVALUATION_COUNT( call_ref_3(A.transpose(), A.transpose()), 1);
+ VERIFY_EVALUATION_COUNT( call_ref_2(Ac,Ac), 0);
+ VERIFY_EVALUATION_COUNT( call_ref_3(Ac,Ac), 0);
+ VERIFY_EVALUATION_COUNT( call_ref_2(A+A,2*Ac), 1);
+ VERIFY_EVALUATION_COUNT( call_ref_3(A+A,2*Ac), 1);
+ VERIFY_EVALUATION_COUNT( call_ref_2(B, B), 1);
+ VERIFY_EVALUATION_COUNT( call_ref_3(B, B), 1);
+ VERIFY_EVALUATION_COUNT( call_ref_2(B.transpose(), B.transpose()), 0);
+ VERIFY_EVALUATION_COUNT( call_ref_3(B.transpose(), B.transpose()), 0);
+ VERIFY_EVALUATION_COUNT( call_ref_2(A*A, AA), 3);
+ VERIFY_EVALUATION_COUNT( call_ref_3(A*A, AA), 3);
+
+ VERIFY(!C.isCompressed());
+ VERIFY_EVALUATION_COUNT( call_ref_3(C, C), 1);
+
+ Ref<SparseMatrix<float> > Ar(A);
+ VERIFY_IS_APPROX(Ar+Ar, A+A);
+ VERIFY_EVALUATION_COUNT( call_ref_1(Ar, A), 0);
+ VERIFY_EVALUATION_COUNT( call_ref_2(Ar, A), 0);
+
+ Ref<SparseMatrix<float,RowMajor> > Br(B);
+ VERIFY_EVALUATION_COUNT( call_ref_1(Br.transpose(), Br.transpose()), 0);
+ VERIFY_EVALUATION_COUNT( call_ref_2(Br, Br), 1);
+ VERIFY_EVALUATION_COUNT( call_ref_2(Br.transpose(), Br.transpose()), 0);
+
+ Ref<const SparseMatrix<float> > Arc(A);
+// VERIFY_EVALUATION_COUNT( call_ref_1(Arc, Arc), 0); // does not compile on purpose
+ VERIFY_EVALUATION_COUNT( call_ref_2(Arc, Arc), 0);
+
+ VERIFY_EVALUATION_COUNT( call_ref_2(A.middleCols(1,3), A.middleCols(1,3)), 0);
+
+ VERIFY_EVALUATION_COUNT( call_ref_2(A.col(2), A.col(2)), 0);
+ VERIFY_EVALUATION_COUNT( call_ref_2(vc, vc), 0);
+ VERIFY_EVALUATION_COUNT( call_ref_2(vr.transpose(), vr.transpose()), 0);
+ VERIFY_EVALUATION_COUNT( call_ref_2(vr, vr.transpose()), 0);
+
+ VERIFY_EVALUATION_COUNT( call_ref_2(A.block(1,1,3,3), A.block(1,1,3,3)), 1); // should be 0 (allocate starts/nnz only)
+
+ VERIFY_EVALUATION_COUNT( call_ref_4(vc, vc), 0);
+ VERIFY_EVALUATION_COUNT( call_ref_4(vr, vr.transpose()), 0);
+ VERIFY_EVALUATION_COUNT( call_ref_5(vc, vc), 0);
+ VERIFY_EVALUATION_COUNT( call_ref_5(vr, vr.transpose()), 0);
+ VERIFY_EVALUATION_COUNT( call_ref_4(A.col(2), A.col(2)), 0);
+ VERIFY_EVALUATION_COUNT( call_ref_5(A.col(2), A.col(2)), 0);
+ // VERIFY_EVALUATION_COUNT( call_ref_4(A.row(2), A.row(2).transpose()), 1); // does not compile on purpose
+ VERIFY_EVALUATION_COUNT( call_ref_5(A.row(2), A.row(2).transpose()), 1);
+}
+
+EIGEN_DECLARE_TEST(sparse_ref)
+{
+ for(int i = 0; i < g_repeat; i++) {
+ CALL_SUBTEST_1( check_const_correctness(SparseMatrix<float>()) );
+ CALL_SUBTEST_1( check_const_correctness(SparseMatrix<double,RowMajor>()) );
+ CALL_SUBTEST_2( call_ref() );
+
+ CALL_SUBTEST_3( check_const_correctness(SparseVector<float>()) );
+ CALL_SUBTEST_3( check_const_correctness(SparseVector<double,RowMajor>()) );
+ }
+}
diff --git a/test/sparse_solver.h b/test/sparse_solver.h
new file mode 100644
index 0000000..a9b18b8
--- /dev/null
+++ b/test/sparse_solver.h
@@ -0,0 +1,699 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2011 Gael Guennebaud <g.gael@free.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "sparse.h"
+#include <Eigen/SparseCore>
+#include <Eigen/SparseLU>
+#include <sstream>
+
+template<typename Solver, typename Rhs, typename Guess,typename Result>
+void solve_with_guess(IterativeSolverBase<Solver>& solver, const MatrixBase<Rhs>& b, const Guess& g, Result &x) {
+ if(internal::random<bool>())
+ {
+ // With a temporary through evaluator<SolveWithGuess>
+ x = solver.derived().solveWithGuess(b,g) + Result::Zero(x.rows(), x.cols());
+ }
+ else
+ {
+ // direct evaluation within x through Assignment<Result,SolveWithGuess>
+ x = solver.derived().solveWithGuess(b.derived(),g);
+ }
+}
+
+template<typename Solver, typename Rhs, typename Guess,typename Result>
+void solve_with_guess(SparseSolverBase<Solver>& solver, const MatrixBase<Rhs>& b, const Guess& , Result& x) {
+ if(internal::random<bool>())
+ x = solver.derived().solve(b) + Result::Zero(x.rows(), x.cols());
+ else
+ x = solver.derived().solve(b);
+}
+
+template<typename Solver, typename Rhs, typename Guess,typename Result>
+void solve_with_guess(SparseSolverBase<Solver>& solver, const SparseMatrixBase<Rhs>& b, const Guess& , Result& x) {
+ x = solver.derived().solve(b);
+}
+
+template<typename Solver, typename Rhs, typename DenseMat, typename DenseRhs>
+void check_sparse_solving(Solver& solver, const typename Solver::MatrixType& A, const Rhs& b, const DenseMat& dA, const DenseRhs& db)
+{
+ typedef typename Solver::MatrixType Mat;
+ typedef typename Mat::Scalar Scalar;
+ typedef typename Mat::StorageIndex StorageIndex;
+
+ DenseRhs refX = dA.householderQr().solve(db);
+ {
+ Rhs x(A.cols(), b.cols());
+ Rhs oldb = b;
+
+ solver.compute(A);
+ if (solver.info() != Success)
+ {
+ std::cerr << "ERROR | sparse solver testing, factorization failed (" << typeid(Solver).name() << ")\n";
+ VERIFY(solver.info() == Success);
+ }
+ x = solver.solve(b);
+ if (solver.info() != Success)
+ {
+ std::cerr << "WARNING: sparse solver testing: solving failed (" << typeid(Solver).name() << ")\n";
+ // dump call stack:
+ g_test_level++;
+ VERIFY(solver.info() == Success);
+ g_test_level--;
+ return;
+ }
+ VERIFY(oldb.isApprox(b) && "sparse solver testing: the rhs should not be modified!");
+ VERIFY(x.isApprox(refX,test_precision<Scalar>()));
+
+ x.setZero();
+ solve_with_guess(solver, b, x, x);
+ VERIFY(solver.info() == Success && "solving failed when using solve_with_guess API");
+ VERIFY(oldb.isApprox(b) && "sparse solver testing: the rhs should not be modified!");
+ VERIFY(x.isApprox(refX,test_precision<Scalar>()));
+
+ x.setZero();
+ // test the analyze/factorize API
+ solver.analyzePattern(A);
+ solver.factorize(A);
+ VERIFY(solver.info() == Success && "factorization failed when using analyzePattern/factorize API");
+ x = solver.solve(b);
+ VERIFY(solver.info() == Success && "solving failed when using analyzePattern/factorize API");
+ VERIFY(oldb.isApprox(b) && "sparse solver testing: the rhs should not be modified!");
+ VERIFY(x.isApprox(refX,test_precision<Scalar>()));
+
+ x.setZero();
+ // test with Map
+ Map<SparseMatrix<Scalar,Mat::Options,StorageIndex>> Am(A.rows(), A.cols(), A.nonZeros(), const_cast<StorageIndex*>(A.outerIndexPtr()), const_cast<StorageIndex*>(A.innerIndexPtr()), const_cast<Scalar*>(A.valuePtr()));
+ solver.compute(Am);
+ VERIFY(solver.info() == Success && "factorization failed when using Map");
+ DenseRhs dx(refX);
+ dx.setZero();
+ Map<DenseRhs> xm(dx.data(), dx.rows(), dx.cols());
+ Map<const DenseRhs> bm(db.data(), db.rows(), db.cols());
+ xm = solver.solve(bm);
+ VERIFY(solver.info() == Success && "solving failed when using Map");
+ VERIFY(oldb.isApprox(bm) && "sparse solver testing: the rhs should not be modified!");
+ VERIFY(xm.isApprox(refX,test_precision<Scalar>()));
+ }
+
+ // if not too large, do some extra check:
+ if(A.rows()<2000)
+ {
+ // test initialization ctor
+ {
+ Rhs x(b.rows(), b.cols());
+ Solver solver2(A);
+ VERIFY(solver2.info() == Success);
+ x = solver2.solve(b);
+ VERIFY(x.isApprox(refX,test_precision<Scalar>()));
+ }
+
+ // test dense Block as the result and rhs:
+ {
+ DenseRhs x(refX.rows(), refX.cols());
+ DenseRhs oldb(db);
+ x.setZero();
+ x.block(0,0,x.rows(),x.cols()) = solver.solve(db.block(0,0,db.rows(),db.cols()));
+ VERIFY(oldb.isApprox(db) && "sparse solver testing: the rhs should not be modified!");
+ VERIFY(x.isApprox(refX,test_precision<Scalar>()));
+ }
+
+ // test uncompressed inputs
+ {
+ Mat A2 = A;
+ A2.reserve((ArrayXf::Random(A.outerSize())+2).template cast<typename Mat::StorageIndex>().eval());
+ solver.compute(A2);
+ Rhs x = solver.solve(b);
+ VERIFY(x.isApprox(refX,test_precision<Scalar>()));
+ }
+
+ // test expression as input
+ {
+ solver.compute(0.5*(A+A));
+ Rhs x = solver.solve(b);
+ VERIFY(x.isApprox(refX,test_precision<Scalar>()));
+
+ Solver solver2(0.5*(A+A));
+ Rhs x2 = solver2.solve(b);
+ VERIFY(x2.isApprox(refX,test_precision<Scalar>()));
+ }
+ }
+}
+
+// specialization of generic check_sparse_solving for SuperLU in order to also test adjoint and transpose solves
+template<typename Scalar, typename Rhs, typename DenseMat, typename DenseRhs>
+void check_sparse_solving(Eigen::SparseLU<Eigen::SparseMatrix<Scalar> >& solver, const typename Eigen::SparseMatrix<Scalar>& A, const Rhs& b, const DenseMat& dA, const DenseRhs& db)
+{
+ typedef typename Eigen::SparseMatrix<Scalar> Mat;
+ typedef typename Mat::StorageIndex StorageIndex;
+ typedef typename Eigen::SparseLU<Eigen::SparseMatrix<Scalar> > Solver;
+
+ // reference solutions computed by dense QR solver
+ DenseRhs refX1 = dA.householderQr().solve(db); // solution of A x = db
+ DenseRhs refX2 = dA.transpose().householderQr().solve(db); // solution of A^T * x = db (use transposed matrix A^T)
+ DenseRhs refX3 = dA.adjoint().householderQr().solve(db); // solution of A^* * x = db (use adjoint matrix A^*)
+
+
+ {
+ Rhs x1(A.cols(), b.cols());
+ Rhs x2(A.cols(), b.cols());
+ Rhs x3(A.cols(), b.cols());
+ Rhs oldb = b;
+
+ solver.compute(A);
+ if (solver.info() != Success)
+ {
+ std::cerr << "ERROR | sparse solver testing, factorization failed (" << typeid(Solver).name() << ")\n";
+ VERIFY(solver.info() == Success);
+ }
+ x1 = solver.solve(b);
+ if (solver.info() != Success)
+ {
+ std::cerr << "WARNING | sparse solver testing: solving failed (" << typeid(Solver).name() << ")\n";
+ return;
+ }
+ VERIFY(oldb.isApprox(b,0.0) && "sparse solver testing: the rhs should not be modified!");
+ VERIFY(x1.isApprox(refX1,test_precision<Scalar>()));
+
+ // test solve with transposed
+ x2 = solver.transpose().solve(b);
+ VERIFY(oldb.isApprox(b) && "sparse solver testing: the rhs should not be modified!");
+ VERIFY(x2.isApprox(refX2,test_precision<Scalar>()));
+
+
+ // test solve with adjoint
+ //solver.template _solve_impl_transposed<true>(b, x3);
+ x3 = solver.adjoint().solve(b);
+ VERIFY(oldb.isApprox(b,0.0) && "sparse solver testing: the rhs should not be modified!");
+ VERIFY(x3.isApprox(refX3,test_precision<Scalar>()));
+
+ x1.setZero();
+ solve_with_guess(solver, b, x1, x1);
+ VERIFY(solver.info() == Success && "solving failed when using analyzePattern/factorize API");
+ VERIFY(oldb.isApprox(b,0.0) && "sparse solver testing: the rhs should not be modified!");
+ VERIFY(x1.isApprox(refX1,test_precision<Scalar>()));
+
+ x1.setZero();
+ x2.setZero();
+ x3.setZero();
+ // test the analyze/factorize API
+ solver.analyzePattern(A);
+ solver.factorize(A);
+ VERIFY(solver.info() == Success && "factorization failed when using analyzePattern/factorize API");
+ x1 = solver.solve(b);
+ x2 = solver.transpose().solve(b);
+ x3 = solver.adjoint().solve(b);
+
+ VERIFY(solver.info() == Success && "solving failed when using analyzePattern/factorize API");
+ VERIFY(oldb.isApprox(b,0.0) && "sparse solver testing: the rhs should not be modified!");
+ VERIFY(x1.isApprox(refX1,test_precision<Scalar>()));
+ VERIFY(x2.isApprox(refX2,test_precision<Scalar>()));
+ VERIFY(x3.isApprox(refX3,test_precision<Scalar>()));
+
+ x1.setZero();
+ // test with Map
+ Map<SparseMatrix<Scalar,Mat::Options,StorageIndex> > Am(A.rows(), A.cols(), A.nonZeros(), const_cast<StorageIndex*>(A.outerIndexPtr()), const_cast<StorageIndex*>(A.innerIndexPtr()), const_cast<Scalar*>(A.valuePtr()));
+ solver.compute(Am);
+ VERIFY(solver.info() == Success && "factorization failed when using Map");
+ DenseRhs dx(refX1);
+ dx.setZero();
+ Map<DenseRhs> xm(dx.data(), dx.rows(), dx.cols());
+ Map<const DenseRhs> bm(db.data(), db.rows(), db.cols());
+ xm = solver.solve(bm);
+ VERIFY(solver.info() == Success && "solving failed when using Map");
+ VERIFY(oldb.isApprox(bm,0.0) && "sparse solver testing: the rhs should not be modified!");
+ VERIFY(xm.isApprox(refX1,test_precision<Scalar>()));
+ }
+
+ // if not too large, do some extra check:
+ if(A.rows()<2000)
+ {
+ // test initialization ctor
+ {
+ Rhs x(b.rows(), b.cols());
+ Solver solver2(A);
+ VERIFY(solver2.info() == Success);
+ x = solver2.solve(b);
+ VERIFY(x.isApprox(refX1,test_precision<Scalar>()));
+ }
+
+ // test dense Block as the result and rhs:
+ {
+ DenseRhs x(refX1.rows(), refX1.cols());
+ DenseRhs oldb(db);
+ x.setZero();
+ x.block(0,0,x.rows(),x.cols()) = solver.solve(db.block(0,0,db.rows(),db.cols()));
+ VERIFY(oldb.isApprox(db,0.0) && "sparse solver testing: the rhs should not be modified!");
+ VERIFY(x.isApprox(refX1,test_precision<Scalar>()));
+ }
+
+ // test uncompressed inputs
+ {
+ Mat A2 = A;
+ A2.reserve((ArrayXf::Random(A.outerSize())+2).template cast<typename Mat::StorageIndex>().eval());
+ solver.compute(A2);
+ Rhs x = solver.solve(b);
+ VERIFY(x.isApprox(refX1,test_precision<Scalar>()));
+ }
+
+ // test expression as input
+ {
+ solver.compute(0.5*(A+A));
+ Rhs x = solver.solve(b);
+ VERIFY(x.isApprox(refX1,test_precision<Scalar>()));
+
+ Solver solver2(0.5*(A+A));
+ Rhs x2 = solver2.solve(b);
+ VERIFY(x2.isApprox(refX1,test_precision<Scalar>()));
+ }
+ }
+}
+
+
+template<typename Solver, typename Rhs>
+void check_sparse_solving_real_cases(Solver& solver, const typename Solver::MatrixType& A, const Rhs& b, const typename Solver::MatrixType& fullA, const Rhs& refX)
+{
+ typedef typename Solver::MatrixType Mat;
+ typedef typename Mat::Scalar Scalar;
+ typedef typename Mat::RealScalar RealScalar;
+
+ Rhs x(A.cols(), b.cols());
+
+ solver.compute(A);
+ if (solver.info() != Success)
+ {
+ std::cerr << "ERROR | sparse solver testing, factorization failed (" << typeid(Solver).name() << ")\n";
+ VERIFY(solver.info() == Success);
+ }
+ x = solver.solve(b);
+
+ if (solver.info() != Success)
+ {
+ std::cerr << "WARNING | sparse solver testing, solving failed (" << typeid(Solver).name() << ")\n";
+ return;
+ }
+
+ RealScalar res_error = (fullA*x-b).norm()/b.norm();
+ VERIFY( (res_error <= test_precision<Scalar>() ) && "sparse solver failed without noticing it");
+
+
+ if(refX.size() != 0 && (refX - x).norm()/refX.norm() > test_precision<Scalar>())
+ {
+ std::cerr << "WARNING | found solution is different from the provided reference one\n";
+ }
+
+}
+template<typename Solver, typename DenseMat>
+void check_sparse_determinant(Solver& solver, const typename Solver::MatrixType& A, const DenseMat& dA)
+{
+ typedef typename Solver::MatrixType Mat;
+ typedef typename Mat::Scalar Scalar;
+
+ solver.compute(A);
+ if (solver.info() != Success)
+ {
+ std::cerr << "WARNING | sparse solver testing: factorization failed (check_sparse_determinant)\n";
+ return;
+ }
+
+ Scalar refDet = dA.determinant();
+ VERIFY_IS_APPROX(refDet,solver.determinant());
+}
+template<typename Solver, typename DenseMat>
+void check_sparse_abs_determinant(Solver& solver, const typename Solver::MatrixType& A, const DenseMat& dA)
+{
+ using std::abs;
+ typedef typename Solver::MatrixType Mat;
+ typedef typename Mat::Scalar Scalar;
+
+ solver.compute(A);
+ if (solver.info() != Success)
+ {
+ std::cerr << "WARNING | sparse solver testing: factorization failed (check_sparse_abs_determinant)\n";
+ return;
+ }
+
+ Scalar refDet = abs(dA.determinant());
+ VERIFY_IS_APPROX(refDet,solver.absDeterminant());
+}
+
+template<typename Solver, typename DenseMat>
+int generate_sparse_spd_problem(Solver& , typename Solver::MatrixType& A, typename Solver::MatrixType& halfA, DenseMat& dA, int maxSize = 300)
+{
+ typedef typename Solver::MatrixType Mat;
+ typedef typename Mat::Scalar Scalar;
+ typedef Matrix<Scalar,Dynamic,Dynamic> DenseMatrix;
+
+ int size = internal::random<int>(1,maxSize);
+ double density = (std::max)(8./static_cast<double>(size*size), 0.01);
+
+ Mat M(size, size);
+ DenseMatrix dM(size, size);
+
+ initSparse<Scalar>(density, dM, M, ForceNonZeroDiag);
+
+ A = M * M.adjoint();
+ dA = dM * dM.adjoint();
+
+ halfA.resize(size,size);
+ if(Solver::UpLo==(Lower|Upper))
+ halfA = A;
+ else
+ halfA.template selfadjointView<Solver::UpLo>().rankUpdate(M);
+
+ return size;
+}
+
+
+#ifdef TEST_REAL_CASES
+template<typename Scalar>
+inline std::string get_matrixfolder()
+{
+ std::string mat_folder = TEST_REAL_CASES;
+ if( internal::is_same<Scalar, std::complex<float> >::value || internal::is_same<Scalar, std::complex<double> >::value )
+ mat_folder = mat_folder + static_cast<std::string>("/complex/");
+ else
+ mat_folder = mat_folder + static_cast<std::string>("/real/");
+ return mat_folder;
+}
+std::string sym_to_string(int sym)
+{
+ if(sym==Symmetric) return "Symmetric ";
+ if(sym==SPD) return "SPD ";
+ return "";
+}
+template<typename Derived>
+std::string solver_stats(const IterativeSolverBase<Derived> &solver)
+{
+ std::stringstream ss;
+ ss << solver.iterations() << " iters, error: " << solver.error();
+ return ss.str();
+}
+template<typename Derived>
+std::string solver_stats(const SparseSolverBase<Derived> &/*solver*/)
+{
+ return "";
+}
+#endif
+
+template<typename Solver> void check_sparse_spd_solving(Solver& solver, int maxSize = (std::min)(300,EIGEN_TEST_MAX_SIZE), int maxRealWorldSize = 100000)
+{
+ typedef typename Solver::MatrixType Mat;
+ typedef typename Mat::Scalar Scalar;
+ typedef typename Mat::StorageIndex StorageIndex;
+ typedef SparseMatrix<Scalar,ColMajor, StorageIndex> SpMat;
+ typedef SparseVector<Scalar, 0, StorageIndex> SpVec;
+ typedef Matrix<Scalar,Dynamic,Dynamic> DenseMatrix;
+ typedef Matrix<Scalar,Dynamic,1> DenseVector;
+
+ // generate the problem
+ Mat A, halfA;
+ DenseMatrix dA;
+ for (int i = 0; i < g_repeat; i++) {
+ int size = generate_sparse_spd_problem(solver, A, halfA, dA, maxSize);
+
+ // generate the right hand sides
+ int rhsCols = internal::random<int>(1,16);
+ double density = (std::max)(8./static_cast<double>(size*rhsCols), 0.1);
+ SpMat B(size,rhsCols);
+ DenseVector b = DenseVector::Random(size);
+ DenseMatrix dB(size,rhsCols);
+ initSparse<Scalar>(density, dB, B, ForceNonZeroDiag);
+ SpVec c = B.col(0);
+ DenseVector dc = dB.col(0);
+
+ CALL_SUBTEST( check_sparse_solving(solver, A, b, dA, b) );
+ CALL_SUBTEST( check_sparse_solving(solver, halfA, b, dA, b) );
+ CALL_SUBTEST( check_sparse_solving(solver, A, dB, dA, dB) );
+ CALL_SUBTEST( check_sparse_solving(solver, halfA, dB, dA, dB) );
+ CALL_SUBTEST( check_sparse_solving(solver, A, B, dA, dB) );
+ CALL_SUBTEST( check_sparse_solving(solver, halfA, B, dA, dB) );
+ CALL_SUBTEST( check_sparse_solving(solver, A, c, dA, dc) );
+ CALL_SUBTEST( check_sparse_solving(solver, halfA, c, dA, dc) );
+
+ // check only once
+ if(i==0)
+ {
+ b = DenseVector::Zero(size);
+ check_sparse_solving(solver, A, b, dA, b);
+ }
+ }
+
+ // First, get the folder
+#ifdef TEST_REAL_CASES
+ // Test real problems with double precision only
+ if (internal::is_same<typename NumTraits<Scalar>::Real, double>::value)
+ {
+ std::string mat_folder = get_matrixfolder<Scalar>();
+ MatrixMarketIterator<Scalar> it(mat_folder);
+ for (; it; ++it)
+ {
+ if (it.sym() == SPD){
+ A = it.matrix();
+ if(A.diagonal().size() <= maxRealWorldSize)
+ {
+ DenseVector b = it.rhs();
+ DenseVector refX = it.refX();
+ PermutationMatrix<Dynamic, Dynamic, StorageIndex> pnull;
+ halfA.resize(A.rows(), A.cols());
+ if(Solver::UpLo == (Lower|Upper))
+ halfA = A;
+ else
+ halfA.template selfadjointView<Solver::UpLo>() = A.template triangularView<Eigen::Lower>().twistedBy(pnull);
+
+ std::cout << "INFO | Testing " << sym_to_string(it.sym()) << "sparse problem " << it.matname()
+ << " (" << A.rows() << "x" << A.cols() << ") using " << typeid(Solver).name() << "..." << std::endl;
+ CALL_SUBTEST( check_sparse_solving_real_cases(solver, A, b, A, refX) );
+ std::string stats = solver_stats(solver);
+ if(stats.size()>0)
+ std::cout << "INFO | " << stats << std::endl;
+ CALL_SUBTEST( check_sparse_solving_real_cases(solver, halfA, b, A, refX) );
+ }
+ else
+ {
+ std::cout << "INFO | Skip sparse problem \"" << it.matname() << "\" (too large)" << std::endl;
+ }
+ }
+ }
+ }
+#else
+ EIGEN_UNUSED_VARIABLE(maxRealWorldSize);
+#endif
+}
+
+template<typename Solver> void check_sparse_spd_determinant(Solver& solver)
+{
+ typedef typename Solver::MatrixType Mat;
+ typedef typename Mat::Scalar Scalar;
+ typedef Matrix<Scalar,Dynamic,Dynamic> DenseMatrix;
+
+ // generate the problem
+ Mat A, halfA;
+ DenseMatrix dA;
+ generate_sparse_spd_problem(solver, A, halfA, dA, 30);
+
+ for (int i = 0; i < g_repeat; i++) {
+ check_sparse_determinant(solver, A, dA);
+ check_sparse_determinant(solver, halfA, dA );
+ }
+}
+
+template<typename Solver, typename DenseMat>
+Index generate_sparse_square_problem(Solver&, typename Solver::MatrixType& A, DenseMat& dA, int maxSize = 300, int options = ForceNonZeroDiag)
+{
+ typedef typename Solver::MatrixType Mat;
+ typedef typename Mat::Scalar Scalar;
+
+ Index size = internal::random<int>(1,maxSize);
+ double density = (std::max)(8./static_cast<double>(size*size), 0.01);
+
+ A.resize(size,size);
+ dA.resize(size,size);
+
+ initSparse<Scalar>(density, dA, A, options);
+
+ return size;
+}
+
+
+struct prune_column {
+ Index m_col;
+ prune_column(Index col) : m_col(col) {}
+ template<class Scalar>
+ bool operator()(Index, Index col, const Scalar&) const {
+ return col != m_col;
+ }
+};
+
+
+template<typename Solver> void check_sparse_square_solving(Solver& solver, int maxSize = 300, int maxRealWorldSize = 100000, bool checkDeficient = false)
+{
+ typedef typename Solver::MatrixType Mat;
+ typedef typename Mat::Scalar Scalar;
+ typedef SparseMatrix<Scalar,ColMajor, typename Mat::StorageIndex> SpMat;
+ typedef SparseVector<Scalar, 0, typename Mat::StorageIndex> SpVec;
+ typedef Matrix<Scalar,Dynamic,Dynamic> DenseMatrix;
+ typedef Matrix<Scalar,Dynamic,1> DenseVector;
+
+ int rhsCols = internal::random<int>(1,16);
+
+ Mat A;
+ DenseMatrix dA;
+ for (int i = 0; i < g_repeat; i++) {
+ Index size = generate_sparse_square_problem(solver, A, dA, maxSize);
+
+ A.makeCompressed();
+ DenseVector b = DenseVector::Random(size);
+ DenseMatrix dB(size,rhsCols);
+ SpMat B(size,rhsCols);
+ double density = (std::max)(8./double(size*rhsCols), 0.1);
+ initSparse<Scalar>(density, dB, B, ForceNonZeroDiag);
+ B.makeCompressed();
+ SpVec c = B.col(0);
+ DenseVector dc = dB.col(0);
+ CALL_SUBTEST(check_sparse_solving(solver, A, b, dA, b));
+ CALL_SUBTEST(check_sparse_solving(solver, A, dB, dA, dB));
+ CALL_SUBTEST(check_sparse_solving(solver, A, B, dA, dB));
+ CALL_SUBTEST(check_sparse_solving(solver, A, c, dA, dc));
+
+ // check only once
+ if(i==0)
+ {
+ CALL_SUBTEST(b = DenseVector::Zero(size); check_sparse_solving(solver, A, b, dA, b));
+ }
+ // regression test for Bug 792 (structurally rank deficient matrices):
+ if(checkDeficient && size>1) {
+ Index col = internal::random<int>(0,int(size-1));
+ A.prune(prune_column(col));
+ solver.compute(A);
+ VERIFY_IS_EQUAL(solver.info(), NumericalIssue);
+ }
+ }
+
+ // First, get the folder
+#ifdef TEST_REAL_CASES
+ // Test real problems with double precision only
+ if (internal::is_same<typename NumTraits<Scalar>::Real, double>::value)
+ {
+ std::string mat_folder = get_matrixfolder<Scalar>();
+ MatrixMarketIterator<Scalar> it(mat_folder);
+ for (; it; ++it)
+ {
+ A = it.matrix();
+ if(A.diagonal().size() <= maxRealWorldSize)
+ {
+ DenseVector b = it.rhs();
+ DenseVector refX = it.refX();
+ std::cout << "INFO | Testing " << sym_to_string(it.sym()) << "sparse problem " << it.matname()
+ << " (" << A.rows() << "x" << A.cols() << ") using " << typeid(Solver).name() << "..." << std::endl;
+ CALL_SUBTEST(check_sparse_solving_real_cases(solver, A, b, A, refX));
+ std::string stats = solver_stats(solver);
+ if(stats.size()>0)
+ std::cout << "INFO | " << stats << std::endl;
+ }
+ else
+ {
+ std::cout << "INFO | SKIP sparse problem \"" << it.matname() << "\" (too large)" << std::endl;
+ }
+ }
+ }
+#else
+ EIGEN_UNUSED_VARIABLE(maxRealWorldSize);
+#endif
+
+}
+
+template<typename Solver> void check_sparse_square_determinant(Solver& solver)
+{
+ typedef typename Solver::MatrixType Mat;
+ typedef typename Mat::Scalar Scalar;
+ typedef Matrix<Scalar,Dynamic,Dynamic> DenseMatrix;
+
+ for (int i = 0; i < g_repeat; i++) {
+ // generate the problem
+ Mat A;
+ DenseMatrix dA;
+
+ int size = internal::random<int>(1,30);
+ dA.setRandom(size,size);
+
+ dA = (dA.array().abs()<0.3).select(0,dA);
+ dA.diagonal() = (dA.diagonal().array()==0).select(1,dA.diagonal());
+ A = dA.sparseView();
+ A.makeCompressed();
+
+ check_sparse_determinant(solver, A, dA);
+ }
+}
+
+template<typename Solver> void check_sparse_square_abs_determinant(Solver& solver)
+{
+ typedef typename Solver::MatrixType Mat;
+ typedef typename Mat::Scalar Scalar;
+ typedef Matrix<Scalar,Dynamic,Dynamic> DenseMatrix;
+
+ for (int i = 0; i < g_repeat; i++) {
+ // generate the problem
+ Mat A;
+ DenseMatrix dA;
+ generate_sparse_square_problem(solver, A, dA, 30);
+ A.makeCompressed();
+ check_sparse_abs_determinant(solver, A, dA);
+ }
+}
+
+template<typename Solver, typename DenseMat>
+void generate_sparse_leastsquare_problem(Solver&, typename Solver::MatrixType& A, DenseMat& dA, int maxSize = 300, int options = ForceNonZeroDiag)
+{
+ typedef typename Solver::MatrixType Mat;
+ typedef typename Mat::Scalar Scalar;
+
+ int rows = internal::random<int>(1,maxSize);
+ int cols = internal::random<int>(1,rows);
+ double density = (std::max)(8./(rows*cols), 0.01);
+
+ A.resize(rows,cols);
+ dA.resize(rows,cols);
+
+ initSparse<Scalar>(density, dA, A, options);
+}
+
+template<typename Solver> void check_sparse_leastsquare_solving(Solver& solver)
+{
+ typedef typename Solver::MatrixType Mat;
+ typedef typename Mat::Scalar Scalar;
+ typedef SparseMatrix<Scalar,ColMajor, typename Mat::StorageIndex> SpMat;
+ typedef Matrix<Scalar,Dynamic,Dynamic> DenseMatrix;
+ typedef Matrix<Scalar,Dynamic,1> DenseVector;
+
+ int rhsCols = internal::random<int>(1,16);
+
+ Mat A;
+ DenseMatrix dA;
+ for (int i = 0; i < g_repeat; i++) {
+ generate_sparse_leastsquare_problem(solver, A, dA);
+
+ A.makeCompressed();
+ DenseVector b = DenseVector::Random(A.rows());
+ DenseMatrix dB(A.rows(),rhsCols);
+ SpMat B(A.rows(),rhsCols);
+ double density = (std::max)(8./(A.rows()*rhsCols), 0.1);
+ initSparse<Scalar>(density, dB, B, ForceNonZeroDiag);
+ B.makeCompressed();
+ check_sparse_solving(solver, A, b, dA, b);
+ check_sparse_solving(solver, A, dB, dA, dB);
+ check_sparse_solving(solver, A, B, dA, dB);
+
+ // check only once
+ if(i==0)
+ {
+ b = DenseVector::Zero(A.rows());
+ check_sparse_solving(solver, A, b, dA, b);
+ }
+ }
+}
diff --git a/test/sparse_solvers.cpp b/test/sparse_solvers.cpp
new file mode 100644
index 0000000..1f4948a
--- /dev/null
+++ b/test/sparse_solvers.cpp
@@ -0,0 +1,125 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2010 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "sparse.h"
+
+template<typename Scalar> void
+initSPD(double density,
+ Matrix<Scalar,Dynamic,Dynamic>& refMat,
+ SparseMatrix<Scalar>& sparseMat)
+{
+ Matrix<Scalar,Dynamic,Dynamic> aux(refMat.rows(),refMat.cols());
+ initSparse(density,refMat,sparseMat);
+ refMat = refMat * refMat.adjoint();
+ for (int k=0; k<2; ++k)
+ {
+ initSparse(density,aux,sparseMat,ForceNonZeroDiag);
+ refMat += aux * aux.adjoint();
+ }
+ sparseMat.setZero();
+ for (int j=0 ; j<sparseMat.cols(); ++j)
+ for (int i=j ; i<sparseMat.rows(); ++i)
+ if (refMat(i,j)!=Scalar(0))
+ sparseMat.insert(i,j) = refMat(i,j);
+ sparseMat.finalize();
+}
+
+template<typename Scalar> void sparse_solvers(int rows, int cols)
+{
+ double density = (std::max)(8./(rows*cols), 0.01);
+ typedef Matrix<Scalar,Dynamic,Dynamic> DenseMatrix;
+ typedef Matrix<Scalar,Dynamic,1> DenseVector;
+ // Scalar eps = 1e-6;
+
+ DenseVector vec1 = DenseVector::Random(rows);
+
+ std::vector<Vector2i> zeroCoords;
+ std::vector<Vector2i> nonzeroCoords;
+
+ // test triangular solver
+ {
+ DenseVector vec2 = vec1, vec3 = vec1;
+ SparseMatrix<Scalar> m2(rows, cols);
+ DenseMatrix refMat2 = DenseMatrix::Zero(rows, cols);
+
+ // lower - dense
+ initSparse<Scalar>(density, refMat2, m2, ForceNonZeroDiag|MakeLowerTriangular, &zeroCoords, &nonzeroCoords);
+ VERIFY_IS_APPROX(refMat2.template triangularView<Lower>().solve(vec2),
+ m2.template triangularView<Lower>().solve(vec3));
+
+ // upper - dense
+ initSparse<Scalar>(density, refMat2, m2, ForceNonZeroDiag|MakeUpperTriangular, &zeroCoords, &nonzeroCoords);
+ VERIFY_IS_APPROX(refMat2.template triangularView<Upper>().solve(vec2),
+ m2.template triangularView<Upper>().solve(vec3));
+ VERIFY_IS_APPROX(refMat2.conjugate().template triangularView<Upper>().solve(vec2),
+ m2.conjugate().template triangularView<Upper>().solve(vec3));
+ {
+ SparseMatrix<Scalar> cm2(m2);
+ //Index rows, Index cols, Index nnz, Index* outerIndexPtr, Index* innerIndexPtr, Scalar* valuePtr
+ Map<SparseMatrix<Scalar> > mm2(rows, cols, cm2.nonZeros(), cm2.outerIndexPtr(), cm2.innerIndexPtr(), cm2.valuePtr());
+ VERIFY_IS_APPROX(refMat2.conjugate().template triangularView<Upper>().solve(vec2),
+ mm2.conjugate().template triangularView<Upper>().solve(vec3));
+ }
+
+ // lower - transpose
+ initSparse<Scalar>(density, refMat2, m2, ForceNonZeroDiag|MakeLowerTriangular, &zeroCoords, &nonzeroCoords);
+ VERIFY_IS_APPROX(refMat2.transpose().template triangularView<Upper>().solve(vec2),
+ m2.transpose().template triangularView<Upper>().solve(vec3));
+
+ // upper - transpose
+ initSparse<Scalar>(density, refMat2, m2, ForceNonZeroDiag|MakeUpperTriangular, &zeroCoords, &nonzeroCoords);
+ VERIFY_IS_APPROX(refMat2.transpose().template triangularView<Lower>().solve(vec2),
+ m2.transpose().template triangularView<Lower>().solve(vec3));
+
+ SparseMatrix<Scalar> matB(rows, rows);
+ DenseMatrix refMatB = DenseMatrix::Zero(rows, rows);
+
+ // lower - sparse
+ initSparse<Scalar>(density, refMat2, m2, ForceNonZeroDiag|MakeLowerTriangular);
+ initSparse<Scalar>(density, refMatB, matB);
+ refMat2.template triangularView<Lower>().solveInPlace(refMatB);
+ m2.template triangularView<Lower>().solveInPlace(matB);
+ VERIFY_IS_APPROX(matB.toDense(), refMatB);
+
+ // upper - sparse
+ initSparse<Scalar>(density, refMat2, m2, ForceNonZeroDiag|MakeUpperTriangular);
+ initSparse<Scalar>(density, refMatB, matB);
+ refMat2.template triangularView<Upper>().solveInPlace(refMatB);
+ m2.template triangularView<Upper>().solveInPlace(matB);
+ VERIFY_IS_APPROX(matB, refMatB);
+
+ // test deprecated API
+ initSparse<Scalar>(density, refMat2, m2, ForceNonZeroDiag|MakeLowerTriangular, &zeroCoords, &nonzeroCoords);
+ VERIFY_IS_APPROX(refMat2.template triangularView<Lower>().solve(vec2),
+ m2.template triangularView<Lower>().solve(vec3));
+
+ // test empty triangular matrix
+ {
+ m2.resize(0,0);
+ refMatB.resize(0,refMatB.cols());
+ DenseMatrix res = m2.template triangularView<Lower>().solve(refMatB);
+ VERIFY_IS_EQUAL(res.rows(),0);
+ VERIFY_IS_EQUAL(res.cols(),refMatB.cols());
+ res = refMatB;
+ m2.template triangularView<Lower>().solveInPlace(res);
+ VERIFY_IS_EQUAL(res.rows(),0);
+ VERIFY_IS_EQUAL(res.cols(),refMatB.cols());
+ }
+ }
+}
+
+EIGEN_DECLARE_TEST(sparse_solvers)
+{
+ for(int i = 0; i < g_repeat; i++) {
+ CALL_SUBTEST_1(sparse_solvers<double>(8, 8) );
+ int s = internal::random<int>(1,300);
+ CALL_SUBTEST_2(sparse_solvers<std::complex<double> >(s,s) );
+ CALL_SUBTEST_1(sparse_solvers<double>(s,s) );
+ }
+}
diff --git a/test/sparse_vector.cpp b/test/sparse_vector.cpp
new file mode 100644
index 0000000..e1e74f3
--- /dev/null
+++ b/test/sparse_vector.cpp
@@ -0,0 +1,190 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2011 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "sparse.h"
+
+template<typename Scalar,typename StorageIndex> void sparse_vector(int rows, int cols)
+{
+ double densityMat = (std::max)(8./(rows*cols), 0.01);
+ double densityVec = (std::max)(8./(rows), 0.1);
+ typedef Matrix<Scalar,Dynamic,Dynamic> DenseMatrix;
+ typedef Matrix<Scalar,Dynamic,1> DenseVector;
+ typedef SparseVector<Scalar,0,StorageIndex> SparseVectorType;
+ typedef SparseMatrix<Scalar,0,StorageIndex> SparseMatrixType;
+ Scalar eps = 1e-6;
+
+ SparseMatrixType m1(rows,rows);
+ SparseVectorType v1(rows), v2(rows), v3(rows);
+ DenseMatrix refM1 = DenseMatrix::Zero(rows, rows);
+ DenseVector refV1 = DenseVector::Random(rows),
+ refV2 = DenseVector::Random(rows),
+ refV3 = DenseVector::Random(rows);
+
+ std::vector<int> zerocoords, nonzerocoords;
+ initSparse<Scalar>(densityVec, refV1, v1, &zerocoords, &nonzerocoords);
+ initSparse<Scalar>(densityMat, refM1, m1);
+
+ initSparse<Scalar>(densityVec, refV2, v2);
+ initSparse<Scalar>(densityVec, refV3, v3);
+
+ Scalar s1 = internal::random<Scalar>();
+
+ // test coeff and coeffRef
+ for (unsigned int i=0; i<zerocoords.size(); ++i)
+ {
+ VERIFY_IS_MUCH_SMALLER_THAN( v1.coeff(zerocoords[i]), eps );
+ //VERIFY_RAISES_ASSERT( v1.coeffRef(zerocoords[i]) = 5 );
+ }
+ {
+ VERIFY(int(nonzerocoords.size()) == v1.nonZeros());
+ int j=0;
+ for (typename SparseVectorType::InnerIterator it(v1); it; ++it,++j)
+ {
+ VERIFY(nonzerocoords[j]==it.index());
+ VERIFY_IS_EQUAL(it.value(), v1.coeff(it.index()));
+ VERIFY_IS_EQUAL(it.value(), refV1.coeff(it.index()));
+ }
+ }
+ VERIFY_IS_APPROX(v1, refV1);
+
+ // test coeffRef with reallocation
+ {
+ SparseVectorType v4(rows);
+ DenseVector v5 = DenseVector::Zero(rows);
+ for(int k=0; k<rows; ++k)
+ {
+ int i = internal::random<int>(0,rows-1);
+ Scalar v = internal::random<Scalar>();
+ v4.coeffRef(i) += v;
+ v5.coeffRef(i) += v;
+ }
+ VERIFY_IS_APPROX(v4,v5);
+ }
+
+ v1.coeffRef(nonzerocoords[0]) = Scalar(5);
+ refV1.coeffRef(nonzerocoords[0]) = Scalar(5);
+ VERIFY_IS_APPROX(v1, refV1);
+
+ VERIFY_IS_APPROX(v1+v2, refV1+refV2);
+ VERIFY_IS_APPROX(v1+v2+v3, refV1+refV2+refV3);
+
+ VERIFY_IS_APPROX(v1*s1-v2, refV1*s1-refV2);
+
+ VERIFY_IS_APPROX(v1*=s1, refV1*=s1);
+ VERIFY_IS_APPROX(v1/=s1, refV1/=s1);
+
+ VERIFY_IS_APPROX(v1+=v2, refV1+=refV2);
+ VERIFY_IS_APPROX(v1-=v2, refV1-=refV2);
+
+ VERIFY_IS_APPROX(v1.dot(v2), refV1.dot(refV2));
+ VERIFY_IS_APPROX(v1.dot(refV2), refV1.dot(refV2));
+
+ VERIFY_IS_APPROX(m1*v2, refM1*refV2);
+ VERIFY_IS_APPROX(v1.dot(m1*v2), refV1.dot(refM1*refV2));
+ {
+ int i = internal::random<int>(0,rows-1);
+ VERIFY_IS_APPROX(v1.dot(m1.col(i)), refV1.dot(refM1.col(i)));
+ }
+
+
+ VERIFY_IS_APPROX(v1.squaredNorm(), refV1.squaredNorm());
+
+ VERIFY_IS_APPROX(v1.blueNorm(), refV1.blueNorm());
+
+ // test aliasing
+ VERIFY_IS_APPROX((v1 = -v1), (refV1 = -refV1));
+ VERIFY_IS_APPROX((v1 = v1.transpose()), (refV1 = refV1.transpose().eval()));
+ VERIFY_IS_APPROX((v1 += -v1), (refV1 += -refV1));
+
+ // sparse matrix to sparse vector
+ SparseMatrixType mv1;
+ VERIFY_IS_APPROX((mv1=v1),v1);
+ VERIFY_IS_APPROX(mv1,(v1=mv1));
+ VERIFY_IS_APPROX(mv1,(v1=mv1.transpose()));
+
+ // check copy to dense vector with transpose
+ refV3.resize(0);
+ VERIFY_IS_APPROX(refV3 = v1.transpose(),v1.toDense());
+ VERIFY_IS_APPROX(DenseVector(v1),v1.toDense());
+
+ // test conservative resize
+ {
+ std::vector<StorageIndex> inc;
+ if(rows > 3)
+ inc.push_back(-3);
+ inc.push_back(0);
+ inc.push_back(3);
+ inc.push_back(1);
+ inc.push_back(10);
+
+ for(std::size_t i = 0; i< inc.size(); i++) {
+ StorageIndex incRows = inc[i];
+ SparseVectorType vec1(rows);
+ DenseVector refVec1 = DenseVector::Zero(rows);
+ initSparse<Scalar>(densityVec, refVec1, vec1);
+
+ vec1.conservativeResize(rows+incRows);
+ refVec1.conservativeResize(rows+incRows);
+ if (incRows > 0) refVec1.tail(incRows).setZero();
+
+ VERIFY_IS_APPROX(vec1, refVec1);
+
+ // Insert new values
+ if (incRows > 0)
+ vec1.insert(vec1.rows()-1) = refVec1(refVec1.rows()-1) = 1;
+
+ VERIFY_IS_APPROX(vec1, refVec1);
+ }
+ }
+
+}
+void test_pruning() {
+ using SparseVectorType = SparseVector<double, 0, int>;
+
+ SparseVectorType vec;
+ auto init_vec = [&](){;
+ vec.resize(10);
+ vec.insert(3) = 0.1;
+ vec.insert(5) = 1.0;
+ vec.insert(8) = -0.1;
+ vec.insert(9) = -0.2;
+ };
+ init_vec();
+
+ VERIFY_IS_EQUAL(vec.nonZeros(), 4);
+ VERIFY_IS_EQUAL(vec.prune(0.1, 1.0), 2);
+ VERIFY_IS_EQUAL(vec.nonZeros(), 2);
+ VERIFY_IS_EQUAL(vec.coeff(5), 1.0);
+ VERIFY_IS_EQUAL(vec.coeff(9), -0.2);
+
+ init_vec();
+ VERIFY_IS_EQUAL(vec.prune([](double v) { return v >= 0; }), 2);
+ VERIFY_IS_EQUAL(vec.nonZeros(), 2);
+ VERIFY_IS_EQUAL(vec.coeff(3), 0.1);
+ VERIFY_IS_EQUAL(vec.coeff(5), 1.0);
+}
+
+EIGEN_DECLARE_TEST(sparse_vector)
+{
+ for(int i = 0; i < g_repeat; i++) {
+ int r = Eigen::internal::random<int>(1,500), c = Eigen::internal::random<int>(1,500);
+ if(Eigen::internal::random<int>(0,4) == 0) {
+ r = c; // check square matrices in 25% of tries
+ }
+ EIGEN_UNUSED_VARIABLE(r+c);
+
+ CALL_SUBTEST_1(( sparse_vector<double,int>(8, 8) ));
+ CALL_SUBTEST_2(( sparse_vector<std::complex<double>, int>(r, c) ));
+ CALL_SUBTEST_1(( sparse_vector<double,long int>(r, c) ));
+ CALL_SUBTEST_1(( sparse_vector<double,short>(r, c) ));
+ }
+
+ CALL_SUBTEST_1(test_pruning());
+}
+
diff --git a/test/sparselu.cpp b/test/sparselu.cpp
new file mode 100644
index 0000000..84cc6eb
--- /dev/null
+++ b/test/sparselu.cpp
@@ -0,0 +1,45 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2012 Désiré Nuentsa-Wakam <desire.nuentsa_wakam@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+// SparseLU solve does not accept column major matrices for the destination.
+// However, as expected, the generic check_sparse_square_solving routines produces row-major
+// rhs and destination matrices when compiled with EIGEN_DEFAULT_TO_ROW_MAJOR
+
+#ifdef EIGEN_DEFAULT_TO_ROW_MAJOR
+#undef EIGEN_DEFAULT_TO_ROW_MAJOR
+#endif
+
+#include "sparse_solver.h"
+#include <Eigen/SparseLU>
+#include <unsupported/Eigen/SparseExtra>
+
+template<typename T> void test_sparselu_T()
+{
+ SparseLU<SparseMatrix<T, ColMajor> /*, COLAMDOrdering<int>*/ > sparselu_colamd; // COLAMDOrdering is the default
+ SparseLU<SparseMatrix<T, ColMajor>, AMDOrdering<int> > sparselu_amd;
+ SparseLU<SparseMatrix<T, ColMajor, long int>, NaturalOrdering<long int> > sparselu_natural;
+
+ check_sparse_square_solving(sparselu_colamd, 300, 100000, true);
+ check_sparse_square_solving(sparselu_amd, 300, 10000, true);
+ check_sparse_square_solving(sparselu_natural, 300, 2000, true);
+
+ check_sparse_square_abs_determinant(sparselu_colamd);
+ check_sparse_square_abs_determinant(sparselu_amd);
+
+ check_sparse_square_determinant(sparselu_colamd);
+ check_sparse_square_determinant(sparselu_amd);
+}
+
+EIGEN_DECLARE_TEST(sparselu)
+{
+ CALL_SUBTEST_1(test_sparselu_T<float>());
+ CALL_SUBTEST_2(test_sparselu_T<double>());
+ CALL_SUBTEST_3(test_sparselu_T<std::complex<float> >());
+ CALL_SUBTEST_4(test_sparselu_T<std::complex<double> >());
+}
diff --git a/test/sparseqr.cpp b/test/sparseqr.cpp
new file mode 100644
index 0000000..3576cc6
--- /dev/null
+++ b/test/sparseqr.cpp
@@ -0,0 +1,149 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2012 Desire Nuentsa Wakam <desire.nuentsa_wakam@inria.fr>
+// Copyright (C) 2014 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+#include "sparse.h"
+#include <Eigen/SparseQR>
+
+template<typename MatrixType,typename DenseMat>
+int generate_sparse_rectangular_problem(MatrixType& A, DenseMat& dA, int maxRows = 300, int maxCols = 150)
+{
+ eigen_assert(maxRows >= maxCols);
+ typedef typename MatrixType::Scalar Scalar;
+ int rows = internal::random<int>(1,maxRows);
+ int cols = internal::random<int>(1,maxCols);
+ double density = (std::max)(8./(rows*cols), 0.01);
+
+ A.resize(rows,cols);
+ dA.resize(rows,cols);
+ initSparse<Scalar>(density, dA, A,ForceNonZeroDiag);
+ A.makeCompressed();
+ int nop = internal::random<int>(0, internal::random<double>(0,1) > 0.5 ? cols/2 : 0);
+ for(int k=0; k<nop; ++k)
+ {
+ int j0 = internal::random<int>(0,cols-1);
+ int j1 = internal::random<int>(0,cols-1);
+ Scalar s = internal::random<Scalar>();
+ A.col(j0) = s * A.col(j1);
+ dA.col(j0) = s * dA.col(j1);
+ }
+
+// if(rows<cols) {
+// A.conservativeResize(cols,cols);
+// dA.conservativeResize(cols,cols);
+// dA.bottomRows(cols-rows).setZero();
+// }
+
+ return rows;
+}
+
+template<typename Scalar> void test_sparseqr_scalar()
+{
+ typedef typename NumTraits<Scalar>::Real RealScalar;
+ typedef SparseMatrix<Scalar,ColMajor> MatrixType;
+ typedef Matrix<Scalar,Dynamic,Dynamic> DenseMat;
+ typedef Matrix<Scalar,Dynamic,1> DenseVector;
+ MatrixType A;
+ DenseMat dA;
+ DenseVector refX,x,b;
+ SparseQR<MatrixType, COLAMDOrdering<int> > solver;
+ generate_sparse_rectangular_problem(A,dA);
+
+ b = dA * DenseVector::Random(A.cols());
+ solver.compute(A);
+
+ // Q should be MxM
+ VERIFY_IS_EQUAL(solver.matrixQ().rows(), A.rows());
+ VERIFY_IS_EQUAL(solver.matrixQ().cols(), A.rows());
+
+ // R should be MxN
+ VERIFY_IS_EQUAL(solver.matrixR().rows(), A.rows());
+ VERIFY_IS_EQUAL(solver.matrixR().cols(), A.cols());
+
+ // Q and R can be multiplied
+ DenseMat recoveredA = solver.matrixQ()
+ * DenseMat(solver.matrixR().template triangularView<Upper>())
+ * solver.colsPermutation().transpose();
+ VERIFY_IS_EQUAL(recoveredA.rows(), A.rows());
+ VERIFY_IS_EQUAL(recoveredA.cols(), A.cols());
+
+ // and in the full rank case the original matrix is recovered
+ if (solver.rank() == A.cols())
+ {
+ VERIFY_IS_APPROX(A, recoveredA);
+ }
+
+ if(internal::random<float>(0,1)>0.5f)
+ solver.factorize(A); // this checks that calling analyzePattern is not needed if the pattern do not change.
+ if (solver.info() != Success)
+ {
+ std::cerr << "sparse QR factorization failed\n";
+ exit(0);
+ return;
+ }
+ x = solver.solve(b);
+ if (solver.info() != Success)
+ {
+ std::cerr << "sparse QR factorization failed\n";
+ exit(0);
+ return;
+ }
+
+ // Compare with a dense QR solver
+ ColPivHouseholderQR<DenseMat> dqr(dA);
+ refX = dqr.solve(b);
+
+ bool rank_deficient = A.cols()>A.rows() || dqr.rank()<A.cols();
+ if(rank_deficient)
+ {
+ // rank deficient problem -> we might have to increase the threshold
+ // to get a correct solution.
+ RealScalar th = RealScalar(20)*dA.colwise().norm().maxCoeff()*(A.rows()+A.cols()) * NumTraits<RealScalar>::epsilon();
+ for(Index k=0; (k<16) && !test_isApprox(A*x,b); ++k)
+ {
+ th *= RealScalar(10);
+ solver.setPivotThreshold(th);
+ solver.compute(A);
+ x = solver.solve(b);
+ }
+ }
+
+ VERIFY_IS_APPROX(A * x, b);
+
+ // For rank deficient problem, the estimated rank might
+ // be slightly off, so let's only raise a warning in such cases.
+ if(rank_deficient) ++g_test_level;
+ VERIFY_IS_EQUAL(solver.rank(), dqr.rank());
+ if(rank_deficient) --g_test_level;
+
+ if(solver.rank()==A.cols()) // full rank
+ VERIFY_IS_APPROX(x, refX);
+// else
+// VERIFY((dA * refX - b).norm() * 2 > (A * x - b).norm() );
+
+ // Compute explicitly the matrix Q
+ MatrixType Q, QtQ, idM;
+ Q = solver.matrixQ();
+ //Check ||Q' * Q - I ||
+ QtQ = Q * Q.adjoint();
+ idM.resize(Q.rows(), Q.rows()); idM.setIdentity();
+ VERIFY(idM.isApprox(QtQ));
+
+ // Q to dense
+ DenseMat dQ;
+ dQ = solver.matrixQ();
+ VERIFY_IS_APPROX(Q, dQ);
+}
+EIGEN_DECLARE_TEST(sparseqr)
+{
+ for(int i=0; i<g_repeat; ++i)
+ {
+ CALL_SUBTEST_1(test_sparseqr_scalar<double>());
+ CALL_SUBTEST_2(test_sparseqr_scalar<std::complex<double> >());
+ }
+}
+
diff --git a/test/special_numbers.cpp b/test/special_numbers.cpp
new file mode 100644
index 0000000..1e1a636
--- /dev/null
+++ b/test/special_numbers.cpp
@@ -0,0 +1,58 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2013 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "main.h"
+
+template<typename Scalar> void special_numbers()
+{
+ typedef Matrix<Scalar, Dynamic,Dynamic> MatType;
+ int rows = internal::random<int>(1,300);
+ int cols = internal::random<int>(1,300);
+
+ Scalar nan = std::numeric_limits<Scalar>::quiet_NaN();
+ Scalar inf = std::numeric_limits<Scalar>::infinity();
+ Scalar s1 = internal::random<Scalar>();
+
+ MatType m1 = MatType::Random(rows,cols),
+ mnan = MatType::Random(rows,cols),
+ minf = MatType::Random(rows,cols),
+ mboth = MatType::Random(rows,cols);
+
+ int n = internal::random<int>(1,10);
+ for(int k=0; k<n; ++k)
+ {
+ mnan(internal::random<int>(0,rows-1), internal::random<int>(0,cols-1)) = nan;
+ minf(internal::random<int>(0,rows-1), internal::random<int>(0,cols-1)) = inf;
+ }
+ mboth = mnan + minf;
+
+ VERIFY(!m1.hasNaN());
+ VERIFY(m1.allFinite());
+
+ VERIFY(mnan.hasNaN());
+ VERIFY((s1*mnan).hasNaN());
+ VERIFY(!minf.hasNaN());
+ VERIFY(!(2*minf).hasNaN());
+ VERIFY(mboth.hasNaN());
+ VERIFY(mboth.array().hasNaN());
+
+ VERIFY(!mnan.allFinite());
+ VERIFY(!minf.allFinite());
+ VERIFY(!(minf-mboth).allFinite());
+ VERIFY(!mboth.allFinite());
+ VERIFY(!mboth.array().allFinite());
+}
+
+EIGEN_DECLARE_TEST(special_numbers)
+{
+ for(int i = 0; i < 10*g_repeat; i++) {
+ CALL_SUBTEST_1( special_numbers<float>() );
+ CALL_SUBTEST_1( special_numbers<double>() );
+ }
+}
diff --git a/test/split_test_helper.h b/test/split_test_helper.h
new file mode 100644
index 0000000..82e82aa
--- /dev/null
+++ b/test/split_test_helper.h
@@ -0,0 +1,5994 @@
+#if defined(EIGEN_TEST_PART_1) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_1(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_1(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_2) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_2(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_2(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_3) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_3(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_3(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_4) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_4(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_4(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_5) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_5(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_5(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_6) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_6(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_6(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_7) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_7(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_7(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_8) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_8(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_8(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_9) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_9(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_9(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_10) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_10(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_10(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_11) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_11(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_11(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_12) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_12(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_12(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_13) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_13(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_13(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_14) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_14(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_14(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_15) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_15(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_15(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_16) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_16(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_16(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_17) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_17(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_17(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_18) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_18(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_18(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_19) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_19(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_19(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_20) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_20(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_20(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_21) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_21(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_21(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_22) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_22(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_22(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_23) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_23(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_23(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_24) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_24(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_24(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_25) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_25(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_25(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_26) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_26(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_26(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_27) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_27(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_27(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_28) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_28(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_28(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_29) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_29(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_29(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_30) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_30(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_30(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_31) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_31(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_31(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_32) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_32(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_32(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_33) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_33(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_33(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_34) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_34(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_34(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_35) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_35(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_35(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_36) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_36(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_36(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_37) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_37(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_37(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_38) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_38(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_38(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_39) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_39(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_39(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_40) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_40(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_40(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_41) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_41(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_41(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_42) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_42(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_42(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_43) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_43(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_43(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_44) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_44(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_44(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_45) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_45(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_45(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_46) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_46(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_46(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_47) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_47(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_47(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_48) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_48(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_48(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_49) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_49(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_49(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_50) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_50(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_50(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_51) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_51(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_51(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_52) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_52(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_52(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_53) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_53(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_53(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_54) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_54(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_54(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_55) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_55(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_55(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_56) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_56(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_56(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_57) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_57(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_57(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_58) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_58(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_58(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_59) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_59(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_59(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_60) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_60(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_60(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_61) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_61(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_61(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_62) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_62(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_62(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_63) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_63(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_63(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_64) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_64(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_64(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_65) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_65(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_65(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_66) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_66(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_66(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_67) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_67(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_67(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_68) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_68(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_68(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_69) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_69(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_69(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_70) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_70(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_70(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_71) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_71(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_71(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_72) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_72(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_72(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_73) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_73(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_73(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_74) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_74(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_74(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_75) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_75(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_75(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_76) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_76(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_76(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_77) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_77(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_77(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_78) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_78(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_78(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_79) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_79(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_79(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_80) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_80(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_80(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_81) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_81(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_81(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_82) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_82(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_82(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_83) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_83(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_83(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_84) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_84(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_84(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_85) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_85(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_85(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_86) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_86(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_86(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_87) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_87(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_87(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_88) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_88(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_88(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_89) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_89(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_89(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_90) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_90(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_90(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_91) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_91(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_91(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_92) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_92(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_92(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_93) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_93(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_93(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_94) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_94(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_94(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_95) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_95(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_95(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_96) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_96(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_96(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_97) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_97(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_97(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_98) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_98(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_98(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_99) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_99(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_99(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_100) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_100(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_100(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_101) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_101(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_101(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_102) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_102(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_102(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_103) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_103(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_103(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_104) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_104(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_104(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_105) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_105(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_105(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_106) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_106(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_106(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_107) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_107(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_107(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_108) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_108(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_108(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_109) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_109(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_109(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_110) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_110(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_110(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_111) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_111(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_111(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_112) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_112(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_112(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_113) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_113(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_113(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_114) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_114(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_114(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_115) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_115(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_115(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_116) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_116(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_116(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_117) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_117(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_117(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_118) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_118(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_118(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_119) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_119(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_119(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_120) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_120(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_120(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_121) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_121(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_121(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_122) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_122(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_122(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_123) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_123(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_123(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_124) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_124(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_124(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_125) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_125(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_125(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_126) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_126(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_126(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_127) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_127(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_127(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_128) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_128(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_128(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_129) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_129(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_129(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_130) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_130(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_130(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_131) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_131(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_131(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_132) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_132(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_132(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_133) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_133(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_133(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_134) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_134(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_134(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_135) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_135(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_135(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_136) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_136(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_136(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_137) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_137(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_137(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_138) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_138(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_138(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_139) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_139(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_139(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_140) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_140(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_140(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_141) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_141(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_141(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_142) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_142(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_142(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_143) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_143(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_143(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_144) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_144(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_144(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_145) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_145(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_145(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_146) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_146(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_146(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_147) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_147(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_147(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_148) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_148(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_148(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_149) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_149(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_149(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_150) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_150(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_150(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_151) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_151(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_151(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_152) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_152(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_152(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_153) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_153(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_153(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_154) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_154(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_154(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_155) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_155(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_155(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_156) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_156(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_156(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_157) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_157(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_157(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_158) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_158(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_158(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_159) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_159(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_159(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_160) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_160(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_160(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_161) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_161(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_161(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_162) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_162(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_162(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_163) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_163(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_163(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_164) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_164(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_164(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_165) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_165(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_165(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_166) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_166(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_166(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_167) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_167(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_167(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_168) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_168(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_168(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_169) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_169(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_169(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_170) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_170(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_170(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_171) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_171(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_171(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_172) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_172(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_172(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_173) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_173(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_173(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_174) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_174(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_174(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_175) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_175(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_175(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_176) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_176(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_176(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_177) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_177(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_177(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_178) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_178(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_178(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_179) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_179(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_179(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_180) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_180(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_180(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_181) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_181(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_181(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_182) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_182(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_182(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_183) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_183(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_183(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_184) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_184(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_184(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_185) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_185(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_185(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_186) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_186(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_186(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_187) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_187(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_187(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_188) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_188(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_188(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_189) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_189(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_189(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_190) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_190(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_190(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_191) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_191(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_191(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_192) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_192(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_192(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_193) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_193(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_193(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_194) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_194(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_194(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_195) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_195(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_195(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_196) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_196(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_196(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_197) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_197(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_197(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_198) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_198(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_198(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_199) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_199(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_199(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_200) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_200(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_200(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_201) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_201(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_201(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_202) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_202(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_202(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_203) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_203(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_203(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_204) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_204(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_204(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_205) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_205(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_205(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_206) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_206(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_206(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_207) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_207(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_207(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_208) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_208(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_208(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_209) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_209(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_209(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_210) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_210(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_210(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_211) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_211(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_211(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_212) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_212(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_212(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_213) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_213(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_213(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_214) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_214(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_214(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_215) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_215(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_215(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_216) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_216(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_216(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_217) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_217(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_217(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_218) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_218(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_218(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_219) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_219(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_219(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_220) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_220(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_220(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_221) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_221(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_221(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_222) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_222(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_222(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_223) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_223(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_223(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_224) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_224(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_224(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_225) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_225(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_225(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_226) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_226(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_226(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_227) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_227(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_227(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_228) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_228(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_228(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_229) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_229(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_229(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_230) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_230(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_230(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_231) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_231(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_231(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_232) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_232(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_232(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_233) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_233(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_233(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_234) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_234(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_234(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_235) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_235(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_235(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_236) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_236(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_236(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_237) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_237(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_237(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_238) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_238(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_238(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_239) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_239(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_239(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_240) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_240(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_240(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_241) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_241(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_241(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_242) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_242(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_242(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_243) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_243(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_243(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_244) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_244(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_244(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_245) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_245(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_245(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_246) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_246(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_246(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_247) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_247(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_247(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_248) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_248(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_248(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_249) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_249(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_249(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_250) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_250(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_250(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_251) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_251(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_251(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_252) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_252(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_252(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_253) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_253(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_253(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_254) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_254(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_254(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_255) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_255(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_255(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_256) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_256(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_256(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_257) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_257(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_257(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_258) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_258(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_258(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_259) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_259(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_259(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_260) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_260(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_260(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_261) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_261(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_261(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_262) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_262(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_262(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_263) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_263(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_263(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_264) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_264(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_264(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_265) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_265(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_265(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_266) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_266(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_266(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_267) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_267(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_267(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_268) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_268(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_268(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_269) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_269(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_269(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_270) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_270(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_270(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_271) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_271(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_271(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_272) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_272(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_272(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_273) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_273(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_273(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_274) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_274(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_274(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_275) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_275(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_275(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_276) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_276(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_276(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_277) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_277(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_277(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_278) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_278(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_278(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_279) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_279(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_279(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_280) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_280(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_280(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_281) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_281(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_281(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_282) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_282(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_282(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_283) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_283(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_283(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_284) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_284(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_284(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_285) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_285(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_285(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_286) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_286(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_286(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_287) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_287(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_287(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_288) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_288(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_288(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_289) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_289(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_289(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_290) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_290(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_290(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_291) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_291(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_291(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_292) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_292(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_292(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_293) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_293(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_293(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_294) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_294(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_294(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_295) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_295(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_295(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_296) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_296(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_296(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_297) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_297(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_297(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_298) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_298(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_298(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_299) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_299(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_299(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_300) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_300(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_300(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_301) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_301(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_301(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_302) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_302(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_302(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_303) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_303(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_303(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_304) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_304(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_304(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_305) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_305(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_305(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_306) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_306(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_306(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_307) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_307(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_307(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_308) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_308(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_308(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_309) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_309(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_309(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_310) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_310(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_310(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_311) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_311(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_311(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_312) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_312(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_312(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_313) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_313(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_313(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_314) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_314(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_314(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_315) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_315(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_315(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_316) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_316(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_316(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_317) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_317(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_317(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_318) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_318(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_318(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_319) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_319(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_319(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_320) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_320(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_320(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_321) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_321(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_321(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_322) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_322(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_322(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_323) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_323(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_323(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_324) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_324(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_324(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_325) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_325(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_325(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_326) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_326(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_326(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_327) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_327(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_327(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_328) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_328(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_328(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_329) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_329(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_329(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_330) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_330(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_330(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_331) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_331(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_331(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_332) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_332(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_332(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_333) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_333(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_333(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_334) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_334(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_334(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_335) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_335(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_335(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_336) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_336(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_336(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_337) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_337(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_337(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_338) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_338(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_338(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_339) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_339(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_339(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_340) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_340(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_340(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_341) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_341(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_341(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_342) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_342(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_342(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_343) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_343(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_343(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_344) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_344(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_344(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_345) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_345(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_345(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_346) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_346(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_346(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_347) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_347(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_347(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_348) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_348(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_348(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_349) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_349(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_349(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_350) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_350(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_350(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_351) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_351(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_351(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_352) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_352(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_352(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_353) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_353(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_353(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_354) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_354(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_354(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_355) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_355(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_355(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_356) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_356(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_356(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_357) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_357(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_357(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_358) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_358(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_358(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_359) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_359(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_359(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_360) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_360(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_360(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_361) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_361(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_361(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_362) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_362(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_362(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_363) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_363(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_363(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_364) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_364(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_364(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_365) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_365(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_365(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_366) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_366(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_366(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_367) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_367(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_367(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_368) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_368(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_368(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_369) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_369(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_369(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_370) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_370(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_370(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_371) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_371(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_371(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_372) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_372(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_372(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_373) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_373(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_373(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_374) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_374(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_374(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_375) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_375(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_375(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_376) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_376(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_376(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_377) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_377(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_377(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_378) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_378(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_378(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_379) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_379(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_379(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_380) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_380(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_380(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_381) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_381(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_381(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_382) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_382(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_382(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_383) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_383(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_383(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_384) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_384(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_384(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_385) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_385(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_385(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_386) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_386(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_386(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_387) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_387(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_387(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_388) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_388(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_388(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_389) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_389(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_389(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_390) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_390(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_390(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_391) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_391(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_391(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_392) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_392(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_392(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_393) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_393(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_393(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_394) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_394(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_394(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_395) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_395(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_395(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_396) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_396(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_396(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_397) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_397(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_397(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_398) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_398(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_398(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_399) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_399(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_399(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_400) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_400(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_400(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_401) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_401(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_401(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_402) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_402(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_402(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_403) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_403(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_403(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_404) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_404(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_404(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_405) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_405(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_405(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_406) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_406(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_406(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_407) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_407(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_407(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_408) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_408(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_408(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_409) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_409(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_409(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_410) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_410(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_410(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_411) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_411(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_411(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_412) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_412(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_412(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_413) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_413(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_413(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_414) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_414(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_414(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_415) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_415(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_415(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_416) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_416(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_416(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_417) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_417(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_417(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_418) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_418(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_418(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_419) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_419(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_419(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_420) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_420(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_420(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_421) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_421(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_421(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_422) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_422(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_422(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_423) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_423(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_423(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_424) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_424(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_424(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_425) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_425(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_425(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_426) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_426(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_426(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_427) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_427(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_427(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_428) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_428(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_428(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_429) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_429(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_429(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_430) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_430(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_430(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_431) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_431(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_431(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_432) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_432(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_432(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_433) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_433(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_433(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_434) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_434(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_434(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_435) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_435(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_435(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_436) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_436(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_436(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_437) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_437(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_437(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_438) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_438(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_438(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_439) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_439(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_439(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_440) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_440(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_440(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_441) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_441(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_441(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_442) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_442(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_442(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_443) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_443(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_443(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_444) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_444(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_444(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_445) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_445(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_445(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_446) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_446(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_446(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_447) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_447(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_447(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_448) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_448(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_448(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_449) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_449(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_449(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_450) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_450(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_450(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_451) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_451(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_451(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_452) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_452(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_452(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_453) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_453(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_453(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_454) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_454(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_454(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_455) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_455(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_455(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_456) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_456(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_456(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_457) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_457(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_457(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_458) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_458(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_458(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_459) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_459(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_459(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_460) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_460(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_460(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_461) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_461(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_461(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_462) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_462(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_462(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_463) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_463(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_463(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_464) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_464(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_464(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_465) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_465(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_465(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_466) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_466(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_466(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_467) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_467(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_467(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_468) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_468(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_468(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_469) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_469(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_469(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_470) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_470(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_470(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_471) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_471(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_471(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_472) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_472(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_472(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_473) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_473(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_473(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_474) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_474(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_474(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_475) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_475(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_475(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_476) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_476(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_476(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_477) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_477(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_477(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_478) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_478(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_478(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_479) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_479(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_479(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_480) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_480(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_480(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_481) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_481(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_481(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_482) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_482(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_482(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_483) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_483(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_483(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_484) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_484(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_484(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_485) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_485(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_485(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_486) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_486(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_486(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_487) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_487(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_487(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_488) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_488(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_488(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_489) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_489(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_489(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_490) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_490(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_490(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_491) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_491(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_491(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_492) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_492(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_492(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_493) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_493(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_493(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_494) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_494(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_494(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_495) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_495(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_495(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_496) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_496(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_496(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_497) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_497(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_497(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_498) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_498(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_498(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_499) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_499(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_499(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_500) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_500(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_500(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_501) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_501(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_501(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_502) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_502(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_502(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_503) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_503(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_503(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_504) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_504(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_504(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_505) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_505(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_505(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_506) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_506(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_506(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_507) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_507(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_507(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_508) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_508(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_508(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_509) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_509(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_509(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_510) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_510(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_510(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_511) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_511(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_511(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_512) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_512(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_512(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_513) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_513(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_513(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_514) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_514(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_514(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_515) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_515(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_515(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_516) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_516(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_516(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_517) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_517(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_517(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_518) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_518(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_518(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_519) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_519(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_519(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_520) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_520(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_520(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_521) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_521(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_521(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_522) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_522(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_522(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_523) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_523(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_523(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_524) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_524(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_524(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_525) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_525(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_525(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_526) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_526(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_526(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_527) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_527(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_527(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_528) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_528(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_528(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_529) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_529(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_529(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_530) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_530(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_530(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_531) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_531(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_531(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_532) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_532(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_532(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_533) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_533(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_533(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_534) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_534(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_534(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_535) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_535(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_535(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_536) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_536(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_536(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_537) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_537(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_537(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_538) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_538(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_538(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_539) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_539(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_539(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_540) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_540(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_540(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_541) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_541(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_541(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_542) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_542(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_542(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_543) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_543(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_543(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_544) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_544(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_544(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_545) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_545(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_545(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_546) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_546(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_546(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_547) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_547(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_547(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_548) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_548(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_548(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_549) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_549(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_549(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_550) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_550(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_550(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_551) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_551(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_551(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_552) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_552(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_552(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_553) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_553(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_553(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_554) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_554(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_554(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_555) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_555(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_555(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_556) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_556(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_556(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_557) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_557(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_557(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_558) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_558(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_558(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_559) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_559(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_559(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_560) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_560(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_560(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_561) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_561(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_561(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_562) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_562(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_562(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_563) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_563(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_563(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_564) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_564(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_564(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_565) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_565(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_565(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_566) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_566(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_566(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_567) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_567(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_567(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_568) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_568(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_568(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_569) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_569(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_569(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_570) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_570(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_570(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_571) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_571(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_571(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_572) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_572(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_572(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_573) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_573(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_573(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_574) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_574(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_574(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_575) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_575(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_575(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_576) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_576(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_576(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_577) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_577(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_577(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_578) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_578(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_578(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_579) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_579(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_579(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_580) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_580(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_580(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_581) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_581(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_581(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_582) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_582(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_582(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_583) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_583(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_583(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_584) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_584(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_584(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_585) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_585(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_585(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_586) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_586(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_586(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_587) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_587(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_587(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_588) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_588(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_588(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_589) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_589(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_589(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_590) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_590(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_590(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_591) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_591(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_591(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_592) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_592(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_592(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_593) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_593(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_593(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_594) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_594(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_594(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_595) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_595(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_595(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_596) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_596(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_596(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_597) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_597(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_597(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_598) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_598(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_598(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_599) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_599(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_599(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_600) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_600(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_600(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_601) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_601(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_601(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_602) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_602(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_602(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_603) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_603(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_603(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_604) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_604(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_604(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_605) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_605(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_605(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_606) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_606(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_606(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_607) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_607(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_607(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_608) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_608(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_608(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_609) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_609(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_609(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_610) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_610(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_610(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_611) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_611(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_611(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_612) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_612(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_612(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_613) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_613(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_613(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_614) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_614(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_614(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_615) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_615(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_615(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_616) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_616(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_616(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_617) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_617(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_617(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_618) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_618(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_618(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_619) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_619(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_619(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_620) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_620(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_620(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_621) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_621(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_621(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_622) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_622(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_622(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_623) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_623(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_623(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_624) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_624(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_624(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_625) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_625(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_625(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_626) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_626(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_626(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_627) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_627(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_627(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_628) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_628(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_628(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_629) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_629(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_629(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_630) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_630(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_630(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_631) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_631(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_631(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_632) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_632(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_632(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_633) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_633(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_633(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_634) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_634(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_634(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_635) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_635(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_635(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_636) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_636(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_636(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_637) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_637(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_637(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_638) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_638(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_638(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_639) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_639(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_639(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_640) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_640(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_640(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_641) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_641(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_641(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_642) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_642(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_642(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_643) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_643(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_643(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_644) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_644(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_644(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_645) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_645(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_645(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_646) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_646(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_646(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_647) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_647(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_647(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_648) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_648(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_648(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_649) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_649(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_649(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_650) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_650(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_650(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_651) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_651(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_651(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_652) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_652(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_652(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_653) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_653(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_653(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_654) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_654(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_654(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_655) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_655(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_655(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_656) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_656(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_656(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_657) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_657(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_657(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_658) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_658(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_658(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_659) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_659(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_659(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_660) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_660(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_660(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_661) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_661(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_661(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_662) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_662(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_662(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_663) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_663(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_663(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_664) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_664(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_664(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_665) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_665(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_665(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_666) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_666(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_666(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_667) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_667(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_667(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_668) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_668(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_668(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_669) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_669(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_669(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_670) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_670(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_670(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_671) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_671(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_671(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_672) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_672(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_672(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_673) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_673(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_673(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_674) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_674(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_674(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_675) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_675(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_675(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_676) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_676(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_676(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_677) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_677(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_677(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_678) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_678(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_678(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_679) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_679(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_679(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_680) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_680(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_680(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_681) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_681(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_681(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_682) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_682(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_682(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_683) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_683(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_683(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_684) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_684(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_684(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_685) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_685(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_685(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_686) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_686(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_686(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_687) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_687(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_687(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_688) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_688(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_688(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_689) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_689(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_689(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_690) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_690(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_690(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_691) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_691(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_691(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_692) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_692(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_692(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_693) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_693(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_693(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_694) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_694(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_694(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_695) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_695(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_695(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_696) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_696(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_696(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_697) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_697(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_697(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_698) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_698(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_698(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_699) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_699(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_699(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_700) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_700(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_700(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_701) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_701(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_701(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_702) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_702(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_702(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_703) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_703(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_703(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_704) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_704(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_704(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_705) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_705(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_705(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_706) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_706(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_706(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_707) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_707(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_707(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_708) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_708(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_708(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_709) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_709(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_709(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_710) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_710(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_710(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_711) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_711(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_711(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_712) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_712(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_712(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_713) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_713(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_713(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_714) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_714(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_714(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_715) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_715(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_715(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_716) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_716(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_716(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_717) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_717(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_717(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_718) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_718(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_718(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_719) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_719(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_719(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_720) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_720(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_720(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_721) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_721(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_721(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_722) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_722(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_722(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_723) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_723(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_723(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_724) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_724(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_724(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_725) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_725(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_725(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_726) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_726(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_726(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_727) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_727(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_727(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_728) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_728(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_728(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_729) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_729(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_729(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_730) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_730(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_730(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_731) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_731(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_731(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_732) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_732(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_732(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_733) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_733(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_733(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_734) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_734(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_734(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_735) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_735(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_735(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_736) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_736(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_736(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_737) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_737(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_737(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_738) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_738(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_738(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_739) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_739(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_739(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_740) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_740(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_740(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_741) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_741(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_741(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_742) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_742(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_742(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_743) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_743(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_743(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_744) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_744(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_744(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_745) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_745(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_745(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_746) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_746(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_746(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_747) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_747(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_747(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_748) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_748(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_748(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_749) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_749(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_749(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_750) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_750(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_750(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_751) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_751(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_751(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_752) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_752(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_752(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_753) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_753(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_753(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_754) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_754(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_754(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_755) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_755(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_755(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_756) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_756(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_756(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_757) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_757(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_757(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_758) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_758(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_758(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_759) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_759(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_759(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_760) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_760(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_760(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_761) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_761(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_761(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_762) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_762(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_762(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_763) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_763(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_763(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_764) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_764(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_764(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_765) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_765(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_765(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_766) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_766(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_766(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_767) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_767(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_767(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_768) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_768(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_768(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_769) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_769(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_769(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_770) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_770(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_770(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_771) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_771(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_771(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_772) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_772(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_772(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_773) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_773(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_773(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_774) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_774(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_774(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_775) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_775(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_775(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_776) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_776(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_776(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_777) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_777(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_777(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_778) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_778(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_778(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_779) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_779(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_779(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_780) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_780(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_780(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_781) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_781(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_781(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_782) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_782(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_782(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_783) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_783(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_783(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_784) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_784(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_784(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_785) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_785(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_785(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_786) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_786(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_786(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_787) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_787(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_787(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_788) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_788(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_788(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_789) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_789(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_789(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_790) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_790(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_790(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_791) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_791(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_791(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_792) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_792(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_792(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_793) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_793(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_793(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_794) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_794(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_794(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_795) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_795(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_795(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_796) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_796(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_796(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_797) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_797(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_797(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_798) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_798(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_798(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_799) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_799(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_799(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_800) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_800(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_800(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_801) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_801(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_801(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_802) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_802(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_802(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_803) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_803(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_803(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_804) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_804(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_804(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_805) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_805(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_805(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_806) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_806(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_806(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_807) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_807(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_807(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_808) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_808(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_808(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_809) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_809(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_809(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_810) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_810(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_810(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_811) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_811(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_811(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_812) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_812(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_812(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_813) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_813(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_813(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_814) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_814(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_814(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_815) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_815(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_815(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_816) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_816(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_816(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_817) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_817(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_817(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_818) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_818(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_818(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_819) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_819(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_819(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_820) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_820(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_820(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_821) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_821(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_821(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_822) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_822(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_822(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_823) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_823(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_823(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_824) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_824(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_824(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_825) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_825(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_825(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_826) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_826(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_826(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_827) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_827(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_827(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_828) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_828(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_828(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_829) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_829(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_829(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_830) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_830(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_830(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_831) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_831(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_831(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_832) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_832(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_832(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_833) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_833(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_833(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_834) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_834(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_834(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_835) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_835(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_835(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_836) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_836(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_836(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_837) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_837(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_837(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_838) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_838(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_838(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_839) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_839(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_839(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_840) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_840(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_840(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_841) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_841(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_841(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_842) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_842(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_842(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_843) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_843(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_843(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_844) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_844(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_844(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_845) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_845(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_845(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_846) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_846(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_846(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_847) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_847(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_847(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_848) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_848(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_848(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_849) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_849(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_849(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_850) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_850(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_850(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_851) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_851(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_851(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_852) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_852(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_852(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_853) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_853(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_853(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_854) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_854(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_854(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_855) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_855(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_855(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_856) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_856(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_856(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_857) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_857(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_857(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_858) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_858(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_858(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_859) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_859(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_859(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_860) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_860(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_860(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_861) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_861(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_861(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_862) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_862(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_862(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_863) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_863(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_863(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_864) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_864(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_864(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_865) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_865(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_865(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_866) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_866(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_866(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_867) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_867(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_867(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_868) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_868(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_868(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_869) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_869(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_869(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_870) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_870(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_870(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_871) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_871(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_871(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_872) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_872(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_872(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_873) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_873(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_873(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_874) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_874(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_874(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_875) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_875(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_875(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_876) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_876(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_876(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_877) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_877(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_877(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_878) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_878(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_878(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_879) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_879(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_879(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_880) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_880(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_880(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_881) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_881(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_881(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_882) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_882(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_882(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_883) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_883(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_883(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_884) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_884(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_884(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_885) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_885(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_885(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_886) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_886(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_886(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_887) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_887(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_887(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_888) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_888(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_888(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_889) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_889(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_889(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_890) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_890(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_890(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_891) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_891(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_891(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_892) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_892(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_892(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_893) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_893(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_893(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_894) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_894(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_894(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_895) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_895(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_895(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_896) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_896(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_896(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_897) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_897(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_897(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_898) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_898(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_898(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_899) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_899(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_899(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_900) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_900(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_900(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_901) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_901(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_901(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_902) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_902(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_902(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_903) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_903(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_903(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_904) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_904(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_904(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_905) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_905(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_905(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_906) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_906(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_906(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_907) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_907(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_907(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_908) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_908(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_908(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_909) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_909(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_909(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_910) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_910(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_910(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_911) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_911(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_911(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_912) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_912(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_912(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_913) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_913(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_913(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_914) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_914(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_914(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_915) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_915(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_915(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_916) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_916(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_916(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_917) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_917(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_917(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_918) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_918(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_918(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_919) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_919(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_919(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_920) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_920(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_920(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_921) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_921(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_921(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_922) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_922(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_922(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_923) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_923(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_923(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_924) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_924(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_924(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_925) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_925(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_925(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_926) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_926(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_926(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_927) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_927(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_927(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_928) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_928(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_928(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_929) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_929(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_929(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_930) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_930(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_930(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_931) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_931(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_931(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_932) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_932(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_932(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_933) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_933(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_933(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_934) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_934(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_934(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_935) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_935(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_935(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_936) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_936(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_936(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_937) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_937(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_937(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_938) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_938(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_938(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_939) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_939(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_939(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_940) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_940(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_940(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_941) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_941(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_941(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_942) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_942(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_942(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_943) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_943(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_943(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_944) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_944(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_944(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_945) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_945(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_945(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_946) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_946(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_946(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_947) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_947(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_947(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_948) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_948(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_948(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_949) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_949(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_949(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_950) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_950(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_950(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_951) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_951(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_951(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_952) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_952(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_952(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_953) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_953(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_953(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_954) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_954(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_954(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_955) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_955(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_955(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_956) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_956(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_956(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_957) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_957(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_957(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_958) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_958(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_958(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_959) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_959(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_959(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_960) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_960(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_960(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_961) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_961(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_961(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_962) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_962(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_962(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_963) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_963(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_963(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_964) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_964(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_964(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_965) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_965(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_965(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_966) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_966(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_966(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_967) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_967(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_967(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_968) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_968(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_968(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_969) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_969(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_969(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_970) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_970(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_970(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_971) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_971(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_971(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_972) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_972(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_972(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_973) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_973(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_973(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_974) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_974(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_974(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_975) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_975(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_975(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_976) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_976(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_976(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_977) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_977(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_977(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_978) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_978(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_978(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_979) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_979(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_979(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_980) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_980(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_980(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_981) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_981(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_981(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_982) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_982(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_982(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_983) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_983(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_983(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_984) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_984(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_984(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_985) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_985(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_985(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_986) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_986(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_986(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_987) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_987(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_987(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_988) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_988(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_988(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_989) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_989(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_989(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_990) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_990(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_990(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_991) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_991(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_991(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_992) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_992(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_992(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_993) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_993(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_993(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_994) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_994(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_994(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_995) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_995(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_995(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_996) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_996(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_996(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_997) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_997(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_997(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_998) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_998(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_998(FUNC)
+#endif
+
+#if defined(EIGEN_TEST_PART_999) || defined(EIGEN_TEST_PART_ALL)
+#define CALL_SUBTEST_999(FUNC) CALL_SUBTEST(FUNC)
+#else
+#define CALL_SUBTEST_999(FUNC)
+#endif
+
diff --git a/test/spqr_support.cpp b/test/spqr_support.cpp
new file mode 100644
index 0000000..79c2c12
--- /dev/null
+++ b/test/spqr_support.cpp
@@ -0,0 +1,64 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2012 Desire Nuentsa Wakam <desire.nuentsa_wakam@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+
+#define EIGEN_NO_DEBUG_SMALL_PRODUCT_BLOCKS
+#include "sparse.h"
+#include <Eigen/SPQRSupport>
+
+
+template<typename MatrixType,typename DenseMat>
+int generate_sparse_rectangular_problem(MatrixType& A, DenseMat& dA, int maxRows = 300, int maxCols = 300)
+{
+ eigen_assert(maxRows >= maxCols);
+ typedef typename MatrixType::Scalar Scalar;
+ int rows = internal::random<int>(1,maxRows);
+ int cols = internal::random<int>(1,rows);
+ double density = (std::max)(8./(rows*cols), 0.01);
+
+ A.resize(rows,cols);
+ dA.resize(rows,cols);
+ initSparse<Scalar>(density, dA, A,ForceNonZeroDiag);
+ A.makeCompressed();
+ return rows;
+}
+
+template<typename Scalar> void test_spqr_scalar()
+{
+ typedef SparseMatrix<Scalar,ColMajor> MatrixType;
+ MatrixType A;
+ Matrix<Scalar,Dynamic,Dynamic> dA;
+ typedef Matrix<Scalar,Dynamic,1> DenseVector;
+ DenseVector refX,x,b;
+ SPQR<MatrixType> solver;
+ generate_sparse_rectangular_problem(A,dA);
+
+ Index m = A.rows();
+ b = DenseVector::Random(m);
+ solver.compute(A);
+ if (solver.info() != Success)
+ {
+ std::cerr << "sparse QR factorization failed\n";
+ exit(0);
+ return;
+ }
+ x = solver.solve(b);
+ if (solver.info() != Success)
+ {
+ std::cerr << "sparse QR factorization failed\n";
+ exit(0);
+ return;
+ }
+ //Compare with a dense solver
+ refX = dA.colPivHouseholderQr().solve(b);
+ VERIFY(x.isApprox(refX,test_precision<Scalar>()));
+}
+EIGEN_DECLARE_TEST(spqr_support)
+{
+ CALL_SUBTEST_1(test_spqr_scalar<double>());
+ CALL_SUBTEST_2(test_spqr_scalar<std::complex<double> >());
+}
diff --git a/test/stable_norm.cpp b/test/stable_norm.cpp
new file mode 100644
index 0000000..cb8a80c
--- /dev/null
+++ b/test/stable_norm.cpp
@@ -0,0 +1,245 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009-2014 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "main.h"
+
+template<typename T> EIGEN_DONT_INLINE T copy(const T& x)
+{
+ return x;
+}
+
+template<typename MatrixType> void stable_norm(const MatrixType& m)
+{
+ /* this test covers the following files:
+ StableNorm.h
+ */
+ using std::sqrt;
+ using std::abs;
+ typedef typename MatrixType::Scalar Scalar;
+ typedef typename NumTraits<Scalar>::Real RealScalar;
+
+ bool complex_real_product_ok = true;
+
+ // Check the basic machine-dependent constants.
+ {
+ int ibeta, it, iemin, iemax;
+
+ ibeta = std::numeric_limits<RealScalar>::radix; // base for floating-point numbers
+ it = std::numeric_limits<RealScalar>::digits; // number of base-beta digits in mantissa
+ iemin = std::numeric_limits<RealScalar>::min_exponent; // minimum exponent
+ iemax = std::numeric_limits<RealScalar>::max_exponent; // maximum exponent
+
+ VERIFY( (!(iemin > 1 - 2*it || 1+it>iemax || (it==2 && ibeta<5) || (it<=4 && ibeta <= 3 ) || it<2))
+ && "the stable norm algorithm cannot be guaranteed on this computer");
+
+ Scalar inf = std::numeric_limits<RealScalar>::infinity();
+ if(NumTraits<Scalar>::IsComplex && (numext::isnan)(inf*RealScalar(1)) )
+ {
+ complex_real_product_ok = false;
+ static bool first = true;
+ if(first)
+ std::cerr << "WARNING: compiler mess up complex*real product, " << inf << " * " << 1.0 << " = " << inf*RealScalar(1) << std::endl;
+ first = false;
+ }
+ }
+
+
+ Index rows = m.rows();
+ Index cols = m.cols();
+
+ // get a non-zero random factor
+ Scalar factor = internal::random<Scalar>();
+ while(numext::abs2(factor)<RealScalar(1e-4))
+ factor = internal::random<Scalar>();
+ Scalar big = factor * ((std::numeric_limits<RealScalar>::max)() * RealScalar(1e-4));
+
+ factor = internal::random<Scalar>();
+ while(numext::abs2(factor)<RealScalar(1e-4))
+ factor = internal::random<Scalar>();
+ Scalar small = factor * ((std::numeric_limits<RealScalar>::min)() * RealScalar(1e4));
+
+ Scalar one(1);
+
+ MatrixType vzero = MatrixType::Zero(rows, cols),
+ vrand = MatrixType::Random(rows, cols),
+ vbig(rows, cols),
+ vsmall(rows,cols);
+
+ vbig.fill(big);
+ vsmall.fill(small);
+
+ VERIFY_IS_MUCH_SMALLER_THAN(vzero.norm(), static_cast<RealScalar>(1));
+ VERIFY_IS_APPROX(vrand.stableNorm(), vrand.norm());
+ VERIFY_IS_APPROX(vrand.blueNorm(), vrand.norm());
+ VERIFY_IS_APPROX(vrand.hypotNorm(), vrand.norm());
+
+ // test with expressions as input
+ VERIFY_IS_APPROX((one*vrand).stableNorm(), vrand.norm());
+ VERIFY_IS_APPROX((one*vrand).blueNorm(), vrand.norm());
+ VERIFY_IS_APPROX((one*vrand).hypotNorm(), vrand.norm());
+ VERIFY_IS_APPROX((one*vrand+one*vrand-one*vrand).stableNorm(), vrand.norm());
+ VERIFY_IS_APPROX((one*vrand+one*vrand-one*vrand).blueNorm(), vrand.norm());
+ VERIFY_IS_APPROX((one*vrand+one*vrand-one*vrand).hypotNorm(), vrand.norm());
+
+ RealScalar size = static_cast<RealScalar>(m.size());
+
+ // test numext::isfinite
+ VERIFY(!(numext::isfinite)( std::numeric_limits<RealScalar>::infinity()));
+ VERIFY(!(numext::isfinite)(sqrt(-abs(big))));
+
+ // test overflow
+ VERIFY((numext::isfinite)(sqrt(size)*abs(big)));
+ VERIFY_IS_NOT_APPROX(sqrt(copy(vbig.squaredNorm())), abs(sqrt(size)*big)); // here the default norm must fail
+ VERIFY_IS_APPROX(vbig.stableNorm(), sqrt(size)*abs(big));
+ VERIFY_IS_APPROX(vbig.blueNorm(), sqrt(size)*abs(big));
+ VERIFY_IS_APPROX(vbig.hypotNorm(), sqrt(size)*abs(big));
+
+ // test underflow
+ VERIFY((numext::isfinite)(sqrt(size)*abs(small)));
+ VERIFY_IS_NOT_APPROX(sqrt(copy(vsmall.squaredNorm())), abs(sqrt(size)*small)); // here the default norm must fail
+ VERIFY_IS_APPROX(vsmall.stableNorm(), sqrt(size)*abs(small));
+ VERIFY_IS_APPROX(vsmall.blueNorm(), sqrt(size)*abs(small));
+ VERIFY_IS_APPROX(vsmall.hypotNorm(), sqrt(size)*abs(small));
+
+ // Test compilation of cwise() version
+ VERIFY_IS_APPROX(vrand.colwise().stableNorm(), vrand.colwise().norm());
+ VERIFY_IS_APPROX(vrand.colwise().blueNorm(), vrand.colwise().norm());
+ VERIFY_IS_APPROX(vrand.colwise().hypotNorm(), vrand.colwise().norm());
+ VERIFY_IS_APPROX(vrand.rowwise().stableNorm(), vrand.rowwise().norm());
+ VERIFY_IS_APPROX(vrand.rowwise().blueNorm(), vrand.rowwise().norm());
+ VERIFY_IS_APPROX(vrand.rowwise().hypotNorm(), vrand.rowwise().norm());
+
+ // test NaN, +inf, -inf
+ MatrixType v;
+ Index i = internal::random<Index>(0,rows-1);
+ Index j = internal::random<Index>(0,cols-1);
+
+ // NaN
+ {
+ v = vrand;
+ v(i,j) = std::numeric_limits<RealScalar>::quiet_NaN();
+ VERIFY(!(numext::isfinite)(v.squaredNorm())); VERIFY((numext::isnan)(v.squaredNorm()));
+ VERIFY(!(numext::isfinite)(v.norm())); VERIFY((numext::isnan)(v.norm()));
+ VERIFY(!(numext::isfinite)(v.stableNorm())); VERIFY((numext::isnan)(v.stableNorm()));
+ VERIFY(!(numext::isfinite)(v.blueNorm())); VERIFY((numext::isnan)(v.blueNorm()));
+ VERIFY(!(numext::isfinite)(v.hypotNorm())); VERIFY((numext::isnan)(v.hypotNorm()));
+ }
+
+ // +inf
+ {
+ v = vrand;
+ v(i,j) = std::numeric_limits<RealScalar>::infinity();
+ VERIFY(!(numext::isfinite)(v.squaredNorm())); VERIFY(isPlusInf(v.squaredNorm()));
+ VERIFY(!(numext::isfinite)(v.norm())); VERIFY(isPlusInf(v.norm()));
+ VERIFY(!(numext::isfinite)(v.stableNorm()));
+ if(complex_real_product_ok){
+ VERIFY(isPlusInf(v.stableNorm()));
+ }
+ VERIFY(!(numext::isfinite)(v.blueNorm())); VERIFY(isPlusInf(v.blueNorm()));
+ VERIFY(!(numext::isfinite)(v.hypotNorm())); VERIFY(isPlusInf(v.hypotNorm()));
+ }
+
+ // -inf
+ {
+ v = vrand;
+ v(i,j) = -std::numeric_limits<RealScalar>::infinity();
+ VERIFY(!(numext::isfinite)(v.squaredNorm())); VERIFY(isPlusInf(v.squaredNorm()));
+ VERIFY(!(numext::isfinite)(v.norm())); VERIFY(isPlusInf(v.norm()));
+ VERIFY(!(numext::isfinite)(v.stableNorm()));
+ if(complex_real_product_ok) {
+ VERIFY(isPlusInf(v.stableNorm()));
+ }
+ VERIFY(!(numext::isfinite)(v.blueNorm())); VERIFY(isPlusInf(v.blueNorm()));
+ VERIFY(!(numext::isfinite)(v.hypotNorm())); VERIFY(isPlusInf(v.hypotNorm()));
+ }
+
+ // mix
+ {
+ Index i2 = internal::random<Index>(0,rows-1);
+ Index j2 = internal::random<Index>(0,cols-1);
+ v = vrand;
+ v(i,j) = -std::numeric_limits<RealScalar>::infinity();
+ v(i2,j2) = std::numeric_limits<RealScalar>::quiet_NaN();
+ VERIFY(!(numext::isfinite)(v.squaredNorm())); VERIFY((numext::isnan)(v.squaredNorm()));
+ VERIFY(!(numext::isfinite)(v.norm())); VERIFY((numext::isnan)(v.norm()));
+ VERIFY(!(numext::isfinite)(v.stableNorm())); VERIFY((numext::isnan)(v.stableNorm()));
+ VERIFY(!(numext::isfinite)(v.blueNorm())); VERIFY((numext::isnan)(v.blueNorm()));
+ if (i2 != i || j2 != j) {
+ // hypot propagates inf over NaN.
+ VERIFY(!(numext::isfinite)(v.hypotNorm())); VERIFY((numext::isinf)(v.hypotNorm()));
+ } else {
+ // inf is overwritten by NaN, expect norm to be NaN.
+ VERIFY(!(numext::isfinite)(v.hypotNorm())); VERIFY((numext::isnan)(v.hypotNorm()));
+ }
+ }
+
+ // stableNormalize[d]
+ {
+ VERIFY_IS_APPROX(vrand.stableNormalized(), vrand.normalized());
+ MatrixType vcopy(vrand);
+ vcopy.stableNormalize();
+ VERIFY_IS_APPROX(vcopy, vrand.normalized());
+ VERIFY_IS_APPROX((vrand.stableNormalized()).norm(), RealScalar(1));
+ VERIFY_IS_APPROX(vcopy.norm(), RealScalar(1));
+ VERIFY_IS_APPROX((vbig.stableNormalized()).norm(), RealScalar(1));
+ VERIFY_IS_APPROX((vsmall.stableNormalized()).norm(), RealScalar(1));
+ RealScalar big_scaling = ((std::numeric_limits<RealScalar>::max)() * RealScalar(1e-4));
+ VERIFY_IS_APPROX(vbig/big_scaling, (vbig.stableNorm() * vbig.stableNormalized()).eval()/big_scaling);
+ VERIFY_IS_APPROX(vsmall, vsmall.stableNorm() * vsmall.stableNormalized());
+ }
+}
+
+template<typename Scalar>
+void test_hypot()
+{
+ typedef typename NumTraits<Scalar>::Real RealScalar;
+ Scalar factor = internal::random<Scalar>();
+ while(numext::abs2(factor)<RealScalar(1e-4))
+ factor = internal::random<Scalar>();
+ Scalar big = factor * ((std::numeric_limits<RealScalar>::max)() * RealScalar(1e-4));
+
+ factor = internal::random<Scalar>();
+ while(numext::abs2(factor)<RealScalar(1e-4))
+ factor = internal::random<Scalar>();
+ Scalar small = factor * ((std::numeric_limits<RealScalar>::min)() * RealScalar(1e4));
+
+ Scalar one (1),
+ zero (0),
+ sqrt2 (std::sqrt(2)),
+ nan (std::numeric_limits<RealScalar>::quiet_NaN());
+
+ Scalar a = internal::random<Scalar>(-1,1);
+ Scalar b = internal::random<Scalar>(-1,1);
+ VERIFY_IS_APPROX(numext::hypot(a,b),std::sqrt(numext::abs2(a)+numext::abs2(b)));
+ VERIFY_IS_EQUAL(numext::hypot(zero,zero), zero);
+ VERIFY_IS_APPROX(numext::hypot(one, one), sqrt2);
+ VERIFY_IS_APPROX(numext::hypot(big,big), sqrt2*numext::abs(big));
+ VERIFY_IS_APPROX(numext::hypot(small,small), sqrt2*numext::abs(small));
+ VERIFY_IS_APPROX(numext::hypot(small,big), numext::abs(big));
+ VERIFY((numext::isnan)(numext::hypot(nan,a)));
+ VERIFY((numext::isnan)(numext::hypot(a,nan)));
+}
+
+EIGEN_DECLARE_TEST(stable_norm)
+{
+ for(int i = 0; i < g_repeat; i++) {
+ CALL_SUBTEST_3( test_hypot<double>() );
+ CALL_SUBTEST_4( test_hypot<float>() );
+ CALL_SUBTEST_5( test_hypot<std::complex<double> >() );
+ CALL_SUBTEST_6( test_hypot<std::complex<float> >() );
+
+ CALL_SUBTEST_1( stable_norm(Matrix<float, 1, 1>()) );
+ CALL_SUBTEST_2( stable_norm(Vector4d()) );
+ CALL_SUBTEST_3( stable_norm(VectorXd(internal::random<int>(10,2000))) );
+ CALL_SUBTEST_3( stable_norm(MatrixXd(internal::random<int>(10,200), internal::random<int>(10,200))) );
+ CALL_SUBTEST_4( stable_norm(VectorXf(internal::random<int>(10,2000))) );
+ CALL_SUBTEST_5( stable_norm(VectorXcd(internal::random<int>(10,2000))) );
+ CALL_SUBTEST_6( stable_norm(VectorXcf(internal::random<int>(10,2000))) );
+ }
+}
diff --git a/test/stddeque.cpp b/test/stddeque.cpp
new file mode 100644
index 0000000..ea85ea9
--- /dev/null
+++ b/test/stddeque.cpp
@@ -0,0 +1,130 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+// Copyright (C) 2010 Hauke Heibel <hauke.heibel@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "main.h"
+#include <Eigen/StdDeque>
+#include <Eigen/Geometry>
+
+template<typename MatrixType>
+void check_stddeque_matrix(const MatrixType& m)
+{
+ Index rows = m.rows();
+ Index cols = m.cols();
+ MatrixType x = MatrixType::Random(rows,cols), y = MatrixType::Random(rows,cols);
+ std::deque<MatrixType,Eigen::aligned_allocator<MatrixType> > v(10, MatrixType::Zero(rows,cols)), w(20, y);
+ v.front() = x;
+ w.front() = w.back();
+ VERIFY_IS_APPROX(w.front(), w.back());
+ v = w;
+
+ typename std::deque<MatrixType,Eigen::aligned_allocator<MatrixType> >::iterator vi = v.begin();
+ typename std::deque<MatrixType,Eigen::aligned_allocator<MatrixType> >::iterator wi = w.begin();
+ for(int i = 0; i < 20; i++)
+ {
+ VERIFY_IS_APPROX(*vi, *wi);
+ ++vi;
+ ++wi;
+ }
+
+ v.resize(21,MatrixType::Zero(rows,cols));
+ v.back() = x;
+ VERIFY_IS_APPROX(v.back(), x);
+ v.resize(22,y);
+ VERIFY_IS_APPROX(v.back(), y);
+ v.push_back(x);
+ VERIFY_IS_APPROX(v.back(), x);
+}
+
+template<typename TransformType>
+void check_stddeque_transform(const TransformType&)
+{
+ typedef typename TransformType::MatrixType MatrixType;
+ TransformType x(MatrixType::Random()), y(MatrixType::Random()), ti=TransformType::Identity();
+ std::deque<TransformType,Eigen::aligned_allocator<TransformType> > v(10,ti), w(20, y);
+ v.front() = x;
+ w.front() = w.back();
+ VERIFY_IS_APPROX(w.front(), w.back());
+ v = w;
+
+ typename std::deque<TransformType,Eigen::aligned_allocator<TransformType> >::iterator vi = v.begin();
+ typename std::deque<TransformType,Eigen::aligned_allocator<TransformType> >::iterator wi = w.begin();
+ for(int i = 0; i < 20; i++)
+ {
+ VERIFY_IS_APPROX(*vi, *wi);
+ ++vi;
+ ++wi;
+ }
+
+ v.resize(21,ti);
+ v.back() = x;
+ VERIFY_IS_APPROX(v.back(), x);
+ v.resize(22,y);
+ VERIFY_IS_APPROX(v.back(), y);
+ v.push_back(x);
+ VERIFY_IS_APPROX(v.back(), x);
+}
+
+template<typename QuaternionType>
+void check_stddeque_quaternion(const QuaternionType&)
+{
+ typedef typename QuaternionType::Coefficients Coefficients;
+ QuaternionType x(Coefficients::Random()), y(Coefficients::Random()), qi=QuaternionType::Identity();
+ std::deque<QuaternionType,Eigen::aligned_allocator<QuaternionType> > v(10,qi), w(20, y);
+ v.front() = x;
+ w.front() = w.back();
+ VERIFY_IS_APPROX(w.front(), w.back());
+ v = w;
+
+ typename std::deque<QuaternionType,Eigen::aligned_allocator<QuaternionType> >::iterator vi = v.begin();
+ typename std::deque<QuaternionType,Eigen::aligned_allocator<QuaternionType> >::iterator wi = w.begin();
+ for(int i = 0; i < 20; i++)
+ {
+ VERIFY_IS_APPROX(*vi, *wi);
+ ++vi;
+ ++wi;
+ }
+
+ v.resize(21,qi);
+ v.back() = x;
+ VERIFY_IS_APPROX(v.back(), x);
+ v.resize(22,y);
+ VERIFY_IS_APPROX(v.back(), y);
+ v.push_back(x);
+ VERIFY_IS_APPROX(v.back(), x);
+}
+
+EIGEN_DECLARE_TEST(stddeque)
+{
+ // some non vectorizable fixed sizes
+ CALL_SUBTEST_1(check_stddeque_matrix(Vector2f()));
+ CALL_SUBTEST_1(check_stddeque_matrix(Matrix3f()));
+ CALL_SUBTEST_2(check_stddeque_matrix(Matrix3d()));
+
+ // some vectorizable fixed sizes
+ CALL_SUBTEST_1(check_stddeque_matrix(Matrix2f()));
+ CALL_SUBTEST_1(check_stddeque_matrix(Vector4f()));
+ CALL_SUBTEST_1(check_stddeque_matrix(Matrix4f()));
+ CALL_SUBTEST_2(check_stddeque_matrix(Matrix4d()));
+
+ // some dynamic sizes
+ CALL_SUBTEST_3(check_stddeque_matrix(MatrixXd(1,1)));
+ CALL_SUBTEST_3(check_stddeque_matrix(VectorXd(20)));
+ CALL_SUBTEST_3(check_stddeque_matrix(RowVectorXf(20)));
+ CALL_SUBTEST_3(check_stddeque_matrix(MatrixXcf(10,10)));
+
+ // some Transform
+ CALL_SUBTEST_4(check_stddeque_transform(Affine2f()));
+ CALL_SUBTEST_4(check_stddeque_transform(Affine3f()));
+ CALL_SUBTEST_4(check_stddeque_transform(Affine3d()));
+
+ // some Quaternion
+ CALL_SUBTEST_5(check_stddeque_quaternion(Quaternionf()));
+ CALL_SUBTEST_5(check_stddeque_quaternion(Quaterniond()));
+}
diff --git a/test/stddeque_overload.cpp b/test/stddeque_overload.cpp
new file mode 100644
index 0000000..0f59f06
--- /dev/null
+++ b/test/stddeque_overload.cpp
@@ -0,0 +1,158 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+// Copyright (C) 2010 Hauke Heibel <hauke.heibel@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "main.h"
+
+#include <Eigen/StdDeque>
+#include <Eigen/Geometry>
+
+EIGEN_DEFINE_STL_DEQUE_SPECIALIZATION(Vector4f)
+
+EIGEN_DEFINE_STL_DEQUE_SPECIALIZATION(Matrix2f)
+EIGEN_DEFINE_STL_DEQUE_SPECIALIZATION(Matrix4f)
+EIGEN_DEFINE_STL_DEQUE_SPECIALIZATION(Matrix4d)
+
+EIGEN_DEFINE_STL_DEQUE_SPECIALIZATION(Affine3f)
+EIGEN_DEFINE_STL_DEQUE_SPECIALIZATION(Affine3d)
+
+EIGEN_DEFINE_STL_DEQUE_SPECIALIZATION(Quaternionf)
+EIGEN_DEFINE_STL_DEQUE_SPECIALIZATION(Quaterniond)
+
+template<typename MatrixType>
+void check_stddeque_matrix(const MatrixType& m)
+{
+ Index rows = m.rows();
+ Index cols = m.cols();
+ MatrixType x = MatrixType::Random(rows,cols), y = MatrixType::Random(rows,cols);
+ std::deque<MatrixType> v(10, MatrixType::Zero(rows,cols)), w(20, y);
+ v[5] = x;
+ w[6] = v[5];
+ VERIFY_IS_APPROX(w[6], v[5]);
+ v = w;
+ for(int i = 0; i < 20; i++)
+ {
+ VERIFY_IS_APPROX(w[i], v[i]);
+ }
+
+ v.resize(21);
+ v[20] = x;
+ VERIFY_IS_APPROX(v[20], x);
+ v.resize(22,y);
+ VERIFY_IS_APPROX(v[21], y);
+ v.push_back(x);
+ VERIFY_IS_APPROX(v[22], x);
+
+ // do a lot of push_back such that the deque gets internally resized
+ // (with memory reallocation)
+ MatrixType* ref = &w[0];
+ for(int i=0; i<30 || ((ref==&w[0]) && i<300); ++i)
+ v.push_back(w[i%w.size()]);
+ for(unsigned int i=23; i<v.size(); ++i)
+ {
+ VERIFY(v[i]==w[(i-23)%w.size()]);
+ }
+}
+
+template<typename TransformType>
+void check_stddeque_transform(const TransformType&)
+{
+ typedef typename TransformType::MatrixType MatrixType;
+ TransformType x(MatrixType::Random()), y(MatrixType::Random()), ti=TransformType::Identity();
+ std::deque<TransformType> v(10,ti), w(20, y);
+ v[5] = x;
+ w[6] = v[5];
+ VERIFY_IS_APPROX(w[6], v[5]);
+ v = w;
+ for(int i = 0; i < 20; i++)
+ {
+ VERIFY_IS_APPROX(w[i], v[i]);
+ }
+
+ v.resize(21,ti);
+ v[20] = x;
+ VERIFY_IS_APPROX(v[20], x);
+ v.resize(22,y);
+ VERIFY_IS_APPROX(v[21], y);
+ v.push_back(x);
+ VERIFY_IS_APPROX(v[22], x);
+
+ // do a lot of push_back such that the deque gets internally resized
+ // (with memory reallocation)
+ TransformType* ref = &w[0];
+ for(int i=0; i<30 || ((ref==&w[0]) && i<300); ++i)
+ v.push_back(w[i%w.size()]);
+ for(unsigned int i=23; i<v.size(); ++i)
+ {
+ VERIFY(v[i].matrix()==w[(i-23)%w.size()].matrix());
+ }
+}
+
+template<typename QuaternionType>
+void check_stddeque_quaternion(const QuaternionType&)
+{
+ typedef typename QuaternionType::Coefficients Coefficients;
+ QuaternionType x(Coefficients::Random()), y(Coefficients::Random()), qi=QuaternionType::Identity();
+ std::deque<QuaternionType> v(10,qi), w(20, y);
+ v[5] = x;
+ w[6] = v[5];
+ VERIFY_IS_APPROX(w[6], v[5]);
+ v = w;
+ for(int i = 0; i < 20; i++)
+ {
+ VERIFY_IS_APPROX(w[i], v[i]);
+ }
+
+ v.resize(21,qi);
+ v[20] = x;
+ VERIFY_IS_APPROX(v[20], x);
+ v.resize(22,y);
+ VERIFY_IS_APPROX(v[21], y);
+ v.push_back(x);
+ VERIFY_IS_APPROX(v[22], x);
+
+ // do a lot of push_back such that the deque gets internally resized
+ // (with memory reallocation)
+ QuaternionType* ref = &w[0];
+ for(int i=0; i<30 || ((ref==&w[0]) && i<300); ++i)
+ v.push_back(w[i%w.size()]);
+ for(unsigned int i=23; i<v.size(); ++i)
+ {
+ VERIFY(v[i].coeffs()==w[(i-23)%w.size()].coeffs());
+ }
+}
+
+EIGEN_DECLARE_TEST(stddeque_overload)
+{
+ // some non vectorizable fixed sizes
+ CALL_SUBTEST_1(check_stddeque_matrix(Vector2f()));
+ CALL_SUBTEST_1(check_stddeque_matrix(Matrix3f()));
+ CALL_SUBTEST_2(check_stddeque_matrix(Matrix3d()));
+
+ // some vectorizable fixed sizes
+ CALL_SUBTEST_1(check_stddeque_matrix(Matrix2f()));
+ CALL_SUBTEST_1(check_stddeque_matrix(Vector4f()));
+ CALL_SUBTEST_1(check_stddeque_matrix(Matrix4f()));
+ CALL_SUBTEST_2(check_stddeque_matrix(Matrix4d()));
+
+ // some dynamic sizes
+ CALL_SUBTEST_3(check_stddeque_matrix(MatrixXd(1,1)));
+ CALL_SUBTEST_3(check_stddeque_matrix(VectorXd(20)));
+ CALL_SUBTEST_3(check_stddeque_matrix(RowVectorXf(20)));
+ CALL_SUBTEST_3(check_stddeque_matrix(MatrixXcf(10,10)));
+
+ // some Transform
+ CALL_SUBTEST_4(check_stddeque_transform(Affine2f())); // does not need the specialization (2+1)^2 = 9
+ CALL_SUBTEST_4(check_stddeque_transform(Affine3f()));
+ CALL_SUBTEST_4(check_stddeque_transform(Affine3d()));
+
+ // some Quaternion
+ CALL_SUBTEST_5(check_stddeque_quaternion(Quaternionf()));
+ CALL_SUBTEST_5(check_stddeque_quaternion(Quaterniond()));
+}
diff --git a/test/stdlist.cpp b/test/stdlist.cpp
new file mode 100644
index 0000000..1af9e6e
--- /dev/null
+++ b/test/stdlist.cpp
@@ -0,0 +1,130 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+// Copyright (C) 2010 Hauke Heibel <hauke.heibel@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "main.h"
+#include <Eigen/StdList>
+#include <Eigen/Geometry>
+
+template<typename MatrixType>
+void check_stdlist_matrix(const MatrixType& m)
+{
+ Index rows = m.rows();
+ Index cols = m.cols();
+ MatrixType x = MatrixType::Random(rows,cols), y = MatrixType::Random(rows,cols);
+ std::list<MatrixType,Eigen::aligned_allocator<MatrixType> > v(10, MatrixType::Zero(rows,cols)), w(20, y);
+ v.front() = x;
+ w.front() = w.back();
+ VERIFY_IS_APPROX(w.front(), w.back());
+ v = w;
+
+ typename std::list<MatrixType,Eigen::aligned_allocator<MatrixType> >::iterator vi = v.begin();
+ typename std::list<MatrixType,Eigen::aligned_allocator<MatrixType> >::iterator wi = w.begin();
+ for(int i = 0; i < 20; i++)
+ {
+ VERIFY_IS_APPROX(*vi, *wi);
+ ++vi;
+ ++wi;
+ }
+
+ v.resize(21, MatrixType::Zero(rows,cols));
+ v.back() = x;
+ VERIFY_IS_APPROX(v.back(), x);
+ v.resize(22,y);
+ VERIFY_IS_APPROX(v.back(), y);
+ v.push_back(x);
+ VERIFY_IS_APPROX(v.back(), x);
+}
+
+template<typename TransformType>
+void check_stdlist_transform(const TransformType&)
+{
+ typedef typename TransformType::MatrixType MatrixType;
+ TransformType x(MatrixType::Random()), y(MatrixType::Random()), ti=TransformType::Identity();
+ std::list<TransformType,Eigen::aligned_allocator<TransformType> > v(10,ti), w(20, y);
+ v.front() = x;
+ w.front() = w.back();
+ VERIFY_IS_APPROX(w.front(), w.back());
+ v = w;
+
+ typename std::list<TransformType,Eigen::aligned_allocator<TransformType> >::iterator vi = v.begin();
+ typename std::list<TransformType,Eigen::aligned_allocator<TransformType> >::iterator wi = w.begin();
+ for(int i = 0; i < 20; i++)
+ {
+ VERIFY_IS_APPROX(*vi, *wi);
+ ++vi;
+ ++wi;
+ }
+
+ v.resize(21, ti);
+ v.back() = x;
+ VERIFY_IS_APPROX(v.back(), x);
+ v.resize(22,y);
+ VERIFY_IS_APPROX(v.back(), y);
+ v.push_back(x);
+ VERIFY_IS_APPROX(v.back(), x);
+}
+
+template<typename QuaternionType>
+void check_stdlist_quaternion(const QuaternionType&)
+{
+ typedef typename QuaternionType::Coefficients Coefficients;
+ QuaternionType x(Coefficients::Random()), y(Coefficients::Random()), qi=QuaternionType::Identity();
+ std::list<QuaternionType,Eigen::aligned_allocator<QuaternionType> > v(10,qi), w(20, y);
+ v.front() = x;
+ w.front() = w.back();
+ VERIFY_IS_APPROX(w.front(), w.back());
+ v = w;
+
+ typename std::list<QuaternionType,Eigen::aligned_allocator<QuaternionType> >::iterator vi = v.begin();
+ typename std::list<QuaternionType,Eigen::aligned_allocator<QuaternionType> >::iterator wi = w.begin();
+ for(int i = 0; i < 20; i++)
+ {
+ VERIFY_IS_APPROX(*vi, *wi);
+ ++vi;
+ ++wi;
+ }
+
+ v.resize(21,qi);
+ v.back() = x;
+ VERIFY_IS_APPROX(v.back(), x);
+ v.resize(22,y);
+ VERIFY_IS_APPROX(v.back(), y);
+ v.push_back(x);
+ VERIFY_IS_APPROX(v.back(), x);
+}
+
+EIGEN_DECLARE_TEST(stdlist)
+{
+ // some non vectorizable fixed sizes
+ CALL_SUBTEST_1(check_stdlist_matrix(Vector2f()));
+ CALL_SUBTEST_1(check_stdlist_matrix(Matrix3f()));
+ CALL_SUBTEST_2(check_stdlist_matrix(Matrix3d()));
+
+ // some vectorizable fixed sizes
+ CALL_SUBTEST_1(check_stdlist_matrix(Matrix2f()));
+ CALL_SUBTEST_1(check_stdlist_matrix(Vector4f()));
+ CALL_SUBTEST_1(check_stdlist_matrix(Matrix4f()));
+ CALL_SUBTEST_2(check_stdlist_matrix(Matrix4d()));
+
+ // some dynamic sizes
+ CALL_SUBTEST_3(check_stdlist_matrix(MatrixXd(1,1)));
+ CALL_SUBTEST_3(check_stdlist_matrix(VectorXd(20)));
+ CALL_SUBTEST_3(check_stdlist_matrix(RowVectorXf(20)));
+ CALL_SUBTEST_3(check_stdlist_matrix(MatrixXcf(10,10)));
+
+ // some Transform
+ CALL_SUBTEST_4(check_stdlist_transform(Affine2f()));
+ CALL_SUBTEST_4(check_stdlist_transform(Affine3f()));
+ CALL_SUBTEST_4(check_stdlist_transform(Affine3d()));
+
+ // some Quaternion
+ CALL_SUBTEST_5(check_stdlist_quaternion(Quaternionf()));
+ CALL_SUBTEST_5(check_stdlist_quaternion(Quaterniond()));
+}
diff --git a/test/stdlist_overload.cpp b/test/stdlist_overload.cpp
new file mode 100644
index 0000000..a78516e
--- /dev/null
+++ b/test/stdlist_overload.cpp
@@ -0,0 +1,192 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+// Copyright (C) 2010 Hauke Heibel <hauke.heibel@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "main.h"
+
+#include <Eigen/StdList>
+#include <Eigen/Geometry>
+
+EIGEN_DEFINE_STL_LIST_SPECIALIZATION(Vector4f)
+
+EIGEN_DEFINE_STL_LIST_SPECIALIZATION(Matrix2f)
+EIGEN_DEFINE_STL_LIST_SPECIALIZATION(Matrix4f)
+EIGEN_DEFINE_STL_LIST_SPECIALIZATION(Matrix4d)
+
+EIGEN_DEFINE_STL_LIST_SPECIALIZATION(Affine3f)
+EIGEN_DEFINE_STL_LIST_SPECIALIZATION(Affine3d)
+
+EIGEN_DEFINE_STL_LIST_SPECIALIZATION(Quaternionf)
+EIGEN_DEFINE_STL_LIST_SPECIALIZATION(Quaterniond)
+
+template <class Container, class Position>
+typename Container::iterator get(Container & c, Position position)
+{
+ typename Container::iterator it = c.begin();
+ std::advance(it, position);
+ return it;
+}
+
+template <class Container, class Position, class Value>
+void set(Container & c, Position position, const Value & value)
+{
+ typename Container::iterator it = c.begin();
+ std::advance(it, position);
+ *it = value;
+}
+
+template<typename MatrixType>
+void check_stdlist_matrix(const MatrixType& m)
+{
+ Index rows = m.rows();
+ Index cols = m.cols();
+ MatrixType x = MatrixType::Random(rows,cols), y = MatrixType::Random(rows,cols);
+ std::list<MatrixType> v(10, MatrixType::Zero(rows,cols)), w(20, y);
+ typename std::list<MatrixType>::iterator itv = get(v, 5);
+ typename std::list<MatrixType>::iterator itw = get(w, 6);
+ *itv = x;
+ *itw = *itv;
+ VERIFY_IS_APPROX(*itw, *itv);
+ v = w;
+ itv = v.begin();
+ itw = w.begin();
+ for(int i = 0; i < 20; i++)
+ {
+ VERIFY_IS_APPROX(*itw, *itv);
+ ++itv;
+ ++itw;
+ }
+
+ v.resize(21);
+ set(v, 20, x);
+ VERIFY_IS_APPROX(*get(v, 20), x);
+ v.resize(22,y);
+ VERIFY_IS_APPROX(*get(v, 21), y);
+ v.push_back(x);
+ VERIFY_IS_APPROX(*get(v, 22), x);
+
+ // do a lot of push_back such that the list gets internally resized
+ // (with memory reallocation)
+ MatrixType* ref = &(*get(w, 0));
+ for(int i=0; i<30 || ((ref==&(*get(w, 0))) && i<300); ++i)
+ v.push_back(*get(w, i%w.size()));
+ for(unsigned int i=23; i<v.size(); ++i)
+ {
+ VERIFY((*get(v, i))==(*get(w, (i-23)%w.size())));
+ }
+}
+
+template<typename TransformType>
+void check_stdlist_transform(const TransformType&)
+{
+ typedef typename TransformType::MatrixType MatrixType;
+ TransformType x(MatrixType::Random()), y(MatrixType::Random()), ti=TransformType::Identity();
+ std::list<TransformType> v(10,ti), w(20, y);
+ typename std::list<TransformType>::iterator itv = get(v, 5);
+ typename std::list<TransformType>::iterator itw = get(w, 6);
+ *itv = x;
+ *itw = *itv;
+ VERIFY_IS_APPROX(*itw, *itv);
+ v = w;
+ itv = v.begin();
+ itw = w.begin();
+ for(int i = 0; i < 20; i++)
+ {
+ VERIFY_IS_APPROX(*itw, *itv);
+ ++itv;
+ ++itw;
+ }
+
+ v.resize(21, ti);
+ set(v, 20, x);
+ VERIFY_IS_APPROX(*get(v, 20), x);
+ v.resize(22,y);
+ VERIFY_IS_APPROX(*get(v, 21), y);
+ v.push_back(x);
+ VERIFY_IS_APPROX(*get(v, 22), x);
+
+ // do a lot of push_back such that the list gets internally resized
+ // (with memory reallocation)
+ TransformType* ref = &(*get(w, 0));
+ for(int i=0; i<30 || ((ref==&(*get(w, 0))) && i<300); ++i)
+ v.push_back(*get(w, i%w.size()));
+ for(unsigned int i=23; i<v.size(); ++i)
+ {
+ VERIFY(get(v, i)->matrix()==get(w, (i-23)%w.size())->matrix());
+ }
+}
+
+template<typename QuaternionType>
+void check_stdlist_quaternion(const QuaternionType&)
+{
+ typedef typename QuaternionType::Coefficients Coefficients;
+ QuaternionType x(Coefficients::Random()), y(Coefficients::Random()), qi=QuaternionType::Identity();
+ std::list<QuaternionType> v(10,qi), w(20, y);
+ typename std::list<QuaternionType>::iterator itv = get(v, 5);
+ typename std::list<QuaternionType>::iterator itw = get(w, 6);
+ *itv = x;
+ *itw = *itv;
+ VERIFY_IS_APPROX(*itw, *itv);
+ v = w;
+ itv = v.begin();
+ itw = w.begin();
+ for(int i = 0; i < 20; i++)
+ {
+ VERIFY_IS_APPROX(*itw, *itv);
+ ++itv;
+ ++itw;
+ }
+
+ v.resize(21,qi);
+ set(v, 20, x);
+ VERIFY_IS_APPROX(*get(v, 20), x);
+ v.resize(22,y);
+ VERIFY_IS_APPROX(*get(v, 21), y);
+ v.push_back(x);
+ VERIFY_IS_APPROX(*get(v, 22), x);
+
+ // do a lot of push_back such that the list gets internally resized
+ // (with memory reallocation)
+ QuaternionType* ref = &(*get(w, 0));
+ for(int i=0; i<30 || ((ref==&(*get(w, 0))) && i<300); ++i)
+ v.push_back(*get(w, i%w.size()));
+ for(unsigned int i=23; i<v.size(); ++i)
+ {
+ VERIFY(get(v, i)->coeffs()==get(w, (i-23)%w.size())->coeffs());
+ }
+}
+
+EIGEN_DECLARE_TEST(stdlist_overload)
+{
+ // some non vectorizable fixed sizes
+ CALL_SUBTEST_1(check_stdlist_matrix(Vector2f()));
+ CALL_SUBTEST_1(check_stdlist_matrix(Matrix3f()));
+ CALL_SUBTEST_2(check_stdlist_matrix(Matrix3d()));
+
+ // some vectorizable fixed sizes
+ CALL_SUBTEST_1(check_stdlist_matrix(Matrix2f()));
+ CALL_SUBTEST_1(check_stdlist_matrix(Vector4f()));
+ CALL_SUBTEST_1(check_stdlist_matrix(Matrix4f()));
+ CALL_SUBTEST_2(check_stdlist_matrix(Matrix4d()));
+
+ // some dynamic sizes
+ CALL_SUBTEST_3(check_stdlist_matrix(MatrixXd(1,1)));
+ CALL_SUBTEST_3(check_stdlist_matrix(VectorXd(20)));
+ CALL_SUBTEST_3(check_stdlist_matrix(RowVectorXf(20)));
+ CALL_SUBTEST_3(check_stdlist_matrix(MatrixXcf(10,10)));
+
+ // some Transform
+ CALL_SUBTEST_4(check_stdlist_transform(Affine2f())); // does not need the specialization (2+1)^2 = 9
+ CALL_SUBTEST_4(check_stdlist_transform(Affine3f()));
+ CALL_SUBTEST_4(check_stdlist_transform(Affine3d()));
+
+ // some Quaternion
+ CALL_SUBTEST_5(check_stdlist_quaternion(Quaternionf()));
+ CALL_SUBTEST_5(check_stdlist_quaternion(Quaterniond()));
+}
diff --git a/test/stdvector.cpp b/test/stdvector.cpp
new file mode 100644
index 0000000..18de240
--- /dev/null
+++ b/test/stdvector.cpp
@@ -0,0 +1,158 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "main.h"
+#include <Eigen/StdVector>
+#include <Eigen/Geometry>
+
+template<typename MatrixType>
+void check_stdvector_matrix(const MatrixType& m)
+{
+ Index rows = m.rows();
+ Index cols = m.cols();
+ MatrixType x = MatrixType::Random(rows,cols), y = MatrixType::Random(rows,cols);
+ std::vector<MatrixType,Eigen::aligned_allocator<MatrixType> > v(10, MatrixType::Zero(rows,cols)), w(20, y);
+ v[5] = x;
+ w[6] = v[5];
+ VERIFY_IS_APPROX(w[6], v[5]);
+ v = w;
+ for(int i = 0; i < 20; i++)
+ {
+ VERIFY_IS_APPROX(w[i], v[i]);
+ }
+
+ v.resize(21);
+ v[20] = x;
+ VERIFY_IS_APPROX(v[20], x);
+ v.resize(22,y);
+ VERIFY_IS_APPROX(v[21], y);
+ v.push_back(x);
+ VERIFY_IS_APPROX(v[22], x);
+ VERIFY((internal::UIntPtr)&(v[22]) == (internal::UIntPtr)&(v[21]) + sizeof(MatrixType));
+
+ // do a lot of push_back such that the vector gets internally resized
+ // (with memory reallocation)
+ MatrixType* ref = &w[0];
+ for(int i=0; i<30 || ((ref==&w[0]) && i<300); ++i)
+ v.push_back(w[i%w.size()]);
+ for(unsigned int i=23; i<v.size(); ++i)
+ {
+ VERIFY(v[i]==w[(i-23)%w.size()]);
+ }
+}
+
+template<typename TransformType>
+void check_stdvector_transform(const TransformType&)
+{
+ typedef typename TransformType::MatrixType MatrixType;
+ TransformType x(MatrixType::Random()), y(MatrixType::Random());
+ std::vector<TransformType,Eigen::aligned_allocator<TransformType> > v(10), w(20, y);
+ v[5] = x;
+ w[6] = v[5];
+ VERIFY_IS_APPROX(w[6], v[5]);
+ v = w;
+ for(int i = 0; i < 20; i++)
+ {
+ VERIFY_IS_APPROX(w[i], v[i]);
+ }
+
+ v.resize(21);
+ v[20] = x;
+ VERIFY_IS_APPROX(v[20], x);
+ v.resize(22,y);
+ VERIFY_IS_APPROX(v[21], y);
+ v.push_back(x);
+ VERIFY_IS_APPROX(v[22], x);
+ VERIFY((internal::UIntPtr)&(v[22]) == (internal::UIntPtr)&(v[21]) + sizeof(TransformType));
+
+ // do a lot of push_back such that the vector gets internally resized
+ // (with memory reallocation)
+ TransformType* ref = &w[0];
+ for(int i=0; i<30 || ((ref==&w[0]) && i<300); ++i)
+ v.push_back(w[i%w.size()]);
+ for(unsigned int i=23; i<v.size(); ++i)
+ {
+ VERIFY(v[i].matrix()==w[(i-23)%w.size()].matrix());
+ }
+}
+
+template<typename QuaternionType>
+void check_stdvector_quaternion(const QuaternionType&)
+{
+ typedef typename QuaternionType::Coefficients Coefficients;
+ QuaternionType x(Coefficients::Random()), y(Coefficients::Random()), qi=QuaternionType::Identity();
+ std::vector<QuaternionType,Eigen::aligned_allocator<QuaternionType> > v(10,qi), w(20, y);
+ v[5] = x;
+ w[6] = v[5];
+ VERIFY_IS_APPROX(w[6], v[5]);
+ v = w;
+ for(int i = 0; i < 20; i++)
+ {
+ VERIFY_IS_APPROX(w[i], v[i]);
+ }
+
+ v.resize(21);
+ v[20] = x;
+ VERIFY_IS_APPROX(v[20], x);
+ v.resize(22,y);
+ VERIFY_IS_APPROX(v[21], y);
+ v.push_back(x);
+ VERIFY_IS_APPROX(v[22], x);
+ VERIFY((internal::UIntPtr)&(v[22]) == (internal::UIntPtr)&(v[21]) + sizeof(QuaternionType));
+
+ // do a lot of push_back such that the vector gets internally resized
+ // (with memory reallocation)
+ QuaternionType* ref = &w[0];
+ for(int i=0; i<30 || ((ref==&w[0]) && i<300); ++i)
+ v.push_back(w[i%w.size()]);
+ for(unsigned int i=23; i<v.size(); ++i)
+ {
+ VERIFY(v[i].coeffs()==w[(i-23)%w.size()].coeffs());
+ }
+}
+
+// the code below triggered an invalid warning with gcc >= 7
+// eigen/Eigen/src/Core/util/Memory.h:189:12: warning: argument 1 value '18446744073709551612' exceeds maximum object size 9223372036854775807
+// This has been reported to gcc there: https://gcc.gnu.org/bugzilla/show_bug.cgi?id=87544
+void std_vector_gcc_warning()
+{
+ typedef Eigen::Vector3f T;
+ std::vector<T, Eigen::aligned_allocator<T> > v;
+ v.push_back(T());
+}
+
+EIGEN_DECLARE_TEST(stdvector)
+{
+ // some non vectorizable fixed sizes
+ CALL_SUBTEST_1(check_stdvector_matrix(Vector2f()));
+ CALL_SUBTEST_1(check_stdvector_matrix(Matrix3f()));
+ CALL_SUBTEST_2(check_stdvector_matrix(Matrix3d()));
+
+ // some vectorizable fixed sizes
+ CALL_SUBTEST_1(check_stdvector_matrix(Matrix2f()));
+ CALL_SUBTEST_1(check_stdvector_matrix(Vector4f()));
+ CALL_SUBTEST_1(check_stdvector_matrix(Matrix4f()));
+ CALL_SUBTEST_2(check_stdvector_matrix(Matrix4d()));
+
+ // some dynamic sizes
+ CALL_SUBTEST_3(check_stdvector_matrix(MatrixXd(1,1)));
+ CALL_SUBTEST_3(check_stdvector_matrix(VectorXd(20)));
+ CALL_SUBTEST_3(check_stdvector_matrix(RowVectorXf(20)));
+ CALL_SUBTEST_3(check_stdvector_matrix(MatrixXcf(10,10)));
+
+ // some Transform
+ CALL_SUBTEST_4(check_stdvector_transform(Projective2f()));
+ CALL_SUBTEST_4(check_stdvector_transform(Projective3f()));
+ CALL_SUBTEST_4(check_stdvector_transform(Projective3d()));
+ //CALL_SUBTEST(heck_stdvector_transform(Projective4d()));
+
+ // some Quaternion
+ CALL_SUBTEST_5(check_stdvector_quaternion(Quaternionf()));
+ CALL_SUBTEST_5(check_stdvector_quaternion(Quaterniond()));
+}
diff --git a/test/stdvector_overload.cpp b/test/stdvector_overload.cpp
new file mode 100644
index 0000000..da04f8a
--- /dev/null
+++ b/test/stdvector_overload.cpp
@@ -0,0 +1,161 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+// Copyright (C) 2010 Hauke Heibel <hauke.heibel@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "main.h"
+
+#include <Eigen/StdVector>
+#include <Eigen/Geometry>
+
+EIGEN_DEFINE_STL_VECTOR_SPECIALIZATION(Vector4f)
+
+EIGEN_DEFINE_STL_VECTOR_SPECIALIZATION(Matrix2f)
+EIGEN_DEFINE_STL_VECTOR_SPECIALIZATION(Matrix4f)
+EIGEN_DEFINE_STL_VECTOR_SPECIALIZATION(Matrix4d)
+
+EIGEN_DEFINE_STL_VECTOR_SPECIALIZATION(Affine3f)
+EIGEN_DEFINE_STL_VECTOR_SPECIALIZATION(Affine3d)
+
+EIGEN_DEFINE_STL_VECTOR_SPECIALIZATION(Quaternionf)
+EIGEN_DEFINE_STL_VECTOR_SPECIALIZATION(Quaterniond)
+
+template<typename MatrixType>
+void check_stdvector_matrix(const MatrixType& m)
+{
+ Index rows = m.rows();
+ Index cols = m.cols();
+ MatrixType x = MatrixType::Random(rows,cols), y = MatrixType::Random(rows,cols);
+ std::vector<MatrixType> v(10, MatrixType::Zero(rows,cols)), w(20, y);
+ v[5] = x;
+ w[6] = v[5];
+ VERIFY_IS_APPROX(w[6], v[5]);
+ v = w;
+ for(int i = 0; i < 20; i++)
+ {
+ VERIFY_IS_APPROX(w[i], v[i]);
+ }
+
+ v.resize(21);
+ v[20] = x;
+ VERIFY_IS_APPROX(v[20], x);
+ v.resize(22,y);
+ VERIFY_IS_APPROX(v[21], y);
+ v.push_back(x);
+ VERIFY_IS_APPROX(v[22], x);
+ VERIFY((internal::UIntPtr)&(v[22]) == (internal::UIntPtr)&(v[21]) + sizeof(MatrixType));
+
+ // do a lot of push_back such that the vector gets internally resized
+ // (with memory reallocation)
+ MatrixType* ref = &w[0];
+ for(int i=0; i<30 || ((ref==&w[0]) && i<300); ++i)
+ v.push_back(w[i%w.size()]);
+ for(unsigned int i=23; i<v.size(); ++i)
+ {
+ VERIFY(v[i]==w[(i-23)%w.size()]);
+ }
+}
+
+template<typename TransformType>
+void check_stdvector_transform(const TransformType&)
+{
+ typedef typename TransformType::MatrixType MatrixType;
+ TransformType x(MatrixType::Random()), y(MatrixType::Random());
+ std::vector<TransformType> v(10), w(20, y);
+ v[5] = x;
+ w[6] = v[5];
+ VERIFY_IS_APPROX(w[6], v[5]);
+ v = w;
+ for(int i = 0; i < 20; i++)
+ {
+ VERIFY_IS_APPROX(w[i], v[i]);
+ }
+
+ v.resize(21);
+ v[20] = x;
+ VERIFY_IS_APPROX(v[20], x);
+ v.resize(22,y);
+ VERIFY_IS_APPROX(v[21], y);
+ v.push_back(x);
+ VERIFY_IS_APPROX(v[22], x);
+ VERIFY((internal::UIntPtr)&(v[22]) == (internal::UIntPtr)&(v[21]) + sizeof(TransformType));
+
+ // do a lot of push_back such that the vector gets internally resized
+ // (with memory reallocation)
+ TransformType* ref = &w[0];
+ for(int i=0; i<30 || ((ref==&w[0]) && i<300); ++i)
+ v.push_back(w[i%w.size()]);
+ for(unsigned int i=23; i<v.size(); ++i)
+ {
+ VERIFY(v[i].matrix()==w[(i-23)%w.size()].matrix());
+ }
+}
+
+template<typename QuaternionType>
+void check_stdvector_quaternion(const QuaternionType&)
+{
+ typedef typename QuaternionType::Coefficients Coefficients;
+ QuaternionType x(Coefficients::Random()), y(Coefficients::Random()), qi=QuaternionType::Identity();
+ std::vector<QuaternionType> v(10,qi), w(20, y);
+ v[5] = x;
+ w[6] = v[5];
+ VERIFY_IS_APPROX(w[6], v[5]);
+ v = w;
+ for(int i = 0; i < 20; i++)
+ {
+ VERIFY_IS_APPROX(w[i], v[i]);
+ }
+
+ v.resize(21);
+ v[20] = x;
+ VERIFY_IS_APPROX(v[20], x);
+ v.resize(22,y);
+ VERIFY_IS_APPROX(v[21], y);
+ v.push_back(x);
+ VERIFY_IS_APPROX(v[22], x);
+ VERIFY((internal::UIntPtr)&(v[22]) == (internal::UIntPtr)&(v[21]) + sizeof(QuaternionType));
+
+ // do a lot of push_back such that the vector gets internally resized
+ // (with memory reallocation)
+ QuaternionType* ref = &w[0];
+ for(int i=0; i<30 || ((ref==&w[0]) && i<300); ++i)
+ v.push_back(w[i%w.size()]);
+ for(unsigned int i=23; i<v.size(); ++i)
+ {
+ VERIFY(v[i].coeffs()==w[(i-23)%w.size()].coeffs());
+ }
+}
+
+EIGEN_DECLARE_TEST(stdvector_overload)
+{
+ // some non vectorizable fixed sizes
+ CALL_SUBTEST_1(check_stdvector_matrix(Vector2f()));
+ CALL_SUBTEST_1(check_stdvector_matrix(Matrix3f()));
+ CALL_SUBTEST_2(check_stdvector_matrix(Matrix3d()));
+
+ // some vectorizable fixed sizes
+ CALL_SUBTEST_1(check_stdvector_matrix(Matrix2f()));
+ CALL_SUBTEST_1(check_stdvector_matrix(Vector4f()));
+ CALL_SUBTEST_1(check_stdvector_matrix(Matrix4f()));
+ CALL_SUBTEST_2(check_stdvector_matrix(Matrix4d()));
+
+ // some dynamic sizes
+ CALL_SUBTEST_3(check_stdvector_matrix(MatrixXd(1,1)));
+ CALL_SUBTEST_3(check_stdvector_matrix(VectorXd(20)));
+ CALL_SUBTEST_3(check_stdvector_matrix(RowVectorXf(20)));
+ CALL_SUBTEST_3(check_stdvector_matrix(MatrixXcf(10,10)));
+
+ // some Transform
+ CALL_SUBTEST_4(check_stdvector_transform(Affine2f())); // does not need the specialization (2+1)^2 = 9
+ CALL_SUBTEST_4(check_stdvector_transform(Affine3f()));
+ CALL_SUBTEST_4(check_stdvector_transform(Affine3d()));
+
+ // some Quaternion
+ CALL_SUBTEST_5(check_stdvector_quaternion(Quaternionf()));
+ CALL_SUBTEST_5(check_stdvector_quaternion(Quaterniond()));
+}
diff --git a/test/stl_iterators.cpp b/test/stl_iterators.cpp
new file mode 100644
index 0000000..121eb86
--- /dev/null
+++ b/test/stl_iterators.cpp
@@ -0,0 +1,520 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2018-2019 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "main.h"
+#include <iterator>
+#include <numeric>
+
+template< class Iterator >
+std::reverse_iterator<Iterator>
+make_reverse_iterator( Iterator i )
+{
+ return std::reverse_iterator<Iterator>(i);
+}
+
+using std::is_sorted;
+
+template<typename XprType>
+bool is_pointer_based_stl_iterator(const internal::pointer_based_stl_iterator<XprType> &) { return true; }
+
+template<typename XprType>
+bool is_generic_randaccess_stl_iterator(const internal::generic_randaccess_stl_iterator<XprType> &) { return true; }
+
+template<typename Iter>
+bool is_default_constructible_and_assignable(const Iter& it)
+{
+ VERIFY(std::is_default_constructible<Iter>::value);
+ VERIFY(std::is_nothrow_default_constructible<Iter>::value);
+ Iter it2;
+ it2 = it;
+ return (it==it2);
+}
+
+template<typename Xpr>
+void check_begin_end_for_loop(Xpr xpr)
+{
+ const Xpr& cxpr(xpr);
+ Index i = 0;
+
+ i = 0;
+ for(typename Xpr::iterator it = xpr.begin(); it!=xpr.end(); ++it) { VERIFY_IS_EQUAL(*it,xpr[i++]); }
+
+ i = 0;
+ for(typename Xpr::const_iterator it = xpr.cbegin(); it!=xpr.cend(); ++it) { VERIFY_IS_EQUAL(*it,xpr[i++]); }
+
+ i = 0;
+ for(typename Xpr::const_iterator it = cxpr.begin(); it!=cxpr.end(); ++it) { VERIFY_IS_EQUAL(*it,xpr[i++]); }
+
+ i = 0;
+ for(typename Xpr::const_iterator it = xpr.begin(); it!=xpr.end(); ++it) { VERIFY_IS_EQUAL(*it,xpr[i++]); }
+
+ {
+ // simple API check
+ typename Xpr::const_iterator cit = xpr.begin();
+ cit = xpr.cbegin();
+
+ auto tmp1 = xpr.begin();
+ VERIFY(tmp1==xpr.begin());
+ auto tmp2 = xpr.cbegin();
+ VERIFY(tmp2==xpr.cbegin());
+ }
+
+ VERIFY( xpr.end() -xpr.begin() == xpr.size() );
+ VERIFY( xpr.cend()-xpr.begin() == xpr.size() );
+ VERIFY( xpr.end() -xpr.cbegin() == xpr.size() );
+ VERIFY( xpr.cend()-xpr.cbegin() == xpr.size() );
+
+ if(xpr.size()>0) {
+ VERIFY(xpr.begin() != xpr.end());
+ VERIFY(xpr.begin() < xpr.end());
+ VERIFY(xpr.begin() <= xpr.end());
+ VERIFY(!(xpr.begin() == xpr.end()));
+ VERIFY(!(xpr.begin() > xpr.end()));
+ VERIFY(!(xpr.begin() >= xpr.end()));
+
+ VERIFY(xpr.cbegin() != xpr.end());
+ VERIFY(xpr.cbegin() < xpr.end());
+ VERIFY(xpr.cbegin() <= xpr.end());
+ VERIFY(!(xpr.cbegin() == xpr.end()));
+ VERIFY(!(xpr.cbegin() > xpr.end()));
+ VERIFY(!(xpr.cbegin() >= xpr.end()));
+
+ VERIFY(xpr.begin() != xpr.cend());
+ VERIFY(xpr.begin() < xpr.cend());
+ VERIFY(xpr.begin() <= xpr.cend());
+ VERIFY(!(xpr.begin() == xpr.cend()));
+ VERIFY(!(xpr.begin() > xpr.cend()));
+ VERIFY(!(xpr.begin() >= xpr.cend()));
+ }
+}
+
+template<typename Scalar, int Rows, int Cols>
+void test_stl_iterators(int rows=Rows, int cols=Cols)
+{
+ typedef Matrix<Scalar,Rows,1> VectorType;
+ typedef Matrix<Scalar,1,Cols> RowVectorType;
+ typedef Matrix<Scalar,Rows,Cols,ColMajor> ColMatrixType;
+ typedef Matrix<Scalar,Rows,Cols,RowMajor> RowMatrixType;
+ VectorType v = VectorType::Random(rows);
+ const VectorType& cv(v);
+ ColMatrixType A = ColMatrixType::Random(rows,cols);
+ const ColMatrixType& cA(A);
+ RowMatrixType B = RowMatrixType::Random(rows,cols);
+ using Eigen::placeholders::last;
+
+ Index i, j;
+
+ // Verify that iterators are default constructible (See bug #1900)
+ {
+ VERIFY( is_default_constructible_and_assignable(v.begin()));
+ VERIFY( is_default_constructible_and_assignable(v.end()));
+ VERIFY( is_default_constructible_and_assignable(cv.begin()));
+ VERIFY( is_default_constructible_and_assignable(cv.end()));
+
+ VERIFY( is_default_constructible_and_assignable(A.row(0).begin()));
+ VERIFY( is_default_constructible_and_assignable(A.row(0).end()));
+ VERIFY( is_default_constructible_and_assignable(cA.row(0).begin()));
+ VERIFY( is_default_constructible_and_assignable(cA.row(0).end()));
+
+ VERIFY( is_default_constructible_and_assignable(B.row(0).begin()));
+ VERIFY( is_default_constructible_and_assignable(B.row(0).end()));
+ }
+
+ // Check we got a fast pointer-based iterator when expected
+ {
+ VERIFY( is_pointer_based_stl_iterator(v.begin()) );
+ VERIFY( is_pointer_based_stl_iterator(v.end()) );
+ VERIFY( is_pointer_based_stl_iterator(cv.begin()) );
+ VERIFY( is_pointer_based_stl_iterator(cv.end()) );
+
+ j = internal::random<Index>(0,A.cols()-1);
+ VERIFY( is_pointer_based_stl_iterator(A.col(j).begin()) );
+ VERIFY( is_pointer_based_stl_iterator(A.col(j).end()) );
+ VERIFY( is_pointer_based_stl_iterator(cA.col(j).begin()) );
+ VERIFY( is_pointer_based_stl_iterator(cA.col(j).end()) );
+
+ i = internal::random<Index>(0,A.rows()-1);
+ VERIFY( is_pointer_based_stl_iterator(A.row(i).begin()) );
+ VERIFY( is_pointer_based_stl_iterator(A.row(i).end()) );
+ VERIFY( is_pointer_based_stl_iterator(cA.row(i).begin()) );
+ VERIFY( is_pointer_based_stl_iterator(cA.row(i).end()) );
+
+ VERIFY( is_pointer_based_stl_iterator(A.reshaped().begin()) );
+ VERIFY( is_pointer_based_stl_iterator(A.reshaped().end()) );
+ VERIFY( is_pointer_based_stl_iterator(cA.reshaped().begin()) );
+ VERIFY( is_pointer_based_stl_iterator(cA.reshaped().end()) );
+
+ VERIFY( is_pointer_based_stl_iterator(B.template reshaped<AutoOrder>().begin()) );
+ VERIFY( is_pointer_based_stl_iterator(B.template reshaped<AutoOrder>().end()) );
+
+ VERIFY( is_generic_randaccess_stl_iterator(A.template reshaped<RowMajor>().begin()) );
+ VERIFY( is_generic_randaccess_stl_iterator(A.template reshaped<RowMajor>().end()) );
+ }
+
+ {
+ check_begin_end_for_loop(v);
+ check_begin_end_for_loop(A.col(internal::random<Index>(0,A.cols()-1)));
+ check_begin_end_for_loop(A.row(internal::random<Index>(0,A.rows()-1)));
+ check_begin_end_for_loop(v+v);
+ }
+
+ // check swappable
+ {
+ using std::swap;
+ // pointer-based
+ {
+ VectorType v_copy = v;
+ auto a = v.begin();
+ auto b = v.end()-1;
+ swap(a,b);
+ VERIFY_IS_EQUAL(v,v_copy);
+ VERIFY_IS_EQUAL(*b,*v.begin());
+ VERIFY_IS_EQUAL(*b,v(0));
+ VERIFY_IS_EQUAL(*a,v.end()[-1]);
+ VERIFY_IS_EQUAL(*a,v(last));
+ }
+
+ // generic
+ {
+ RowMatrixType B_copy = B;
+ auto Br = B.reshaped();
+ auto a = Br.begin();
+ auto b = Br.end()-1;
+ swap(a,b);
+ VERIFY_IS_EQUAL(B,B_copy);
+ VERIFY_IS_EQUAL(*b,*Br.begin());
+ VERIFY_IS_EQUAL(*b,Br(0));
+ VERIFY_IS_EQUAL(*a,Br.end()[-1]);
+ VERIFY_IS_EQUAL(*a,Br(last));
+ }
+ }
+
+ // check non-const iterator with for-range loops
+ {
+ i = 0;
+ for(auto x : v) { VERIFY_IS_EQUAL(x,v[i++]); }
+
+ j = internal::random<Index>(0,A.cols()-1);
+ i = 0;
+ for(auto x : A.col(j)) { VERIFY_IS_EQUAL(x,A(i++,j)); }
+
+ i = 0;
+ for(auto x : (v+A.col(j))) { VERIFY_IS_APPROX(x,v(i)+A(i,j)); ++i; }
+
+ j = 0;
+ i = internal::random<Index>(0,A.rows()-1);
+ for(auto x : A.row(i)) { VERIFY_IS_EQUAL(x,A(i,j++)); }
+
+ i = 0;
+ for(auto x : A.reshaped()) { VERIFY_IS_EQUAL(x,A(i++)); }
+ }
+
+ // same for const_iterator
+ {
+ i = 0;
+ for(auto x : cv) { VERIFY_IS_EQUAL(x,v[i++]); }
+
+ i = 0;
+ for(auto x : cA.reshaped()) { VERIFY_IS_EQUAL(x,A(i++)); }
+
+ j = 0;
+ i = internal::random<Index>(0,A.rows()-1);
+ for(auto x : cA.row(i)) { VERIFY_IS_EQUAL(x,A(i,j++)); }
+ }
+
+ // check reshaped() on row-major
+ {
+ i = 0;
+ Matrix<Scalar,Dynamic,Dynamic,ColMajor> Bc = B;
+ for(auto x : B.reshaped()) { VERIFY_IS_EQUAL(x,Bc(i++)); }
+ }
+
+ // check write access
+ {
+ VectorType w(v.size());
+ i = 0;
+ for(auto& x : w) { x = v(i++); }
+ VERIFY_IS_EQUAL(v,w);
+ }
+
+ // check for dangling pointers
+ {
+ // no dangling because pointer-based
+ {
+ j = internal::random<Index>(0,A.cols()-1);
+ auto it = A.col(j).begin();
+ for(i=0;i<rows;++i) {
+ VERIFY_IS_EQUAL(it[i],A(i,j));
+ }
+ }
+
+ // no dangling because pointer-based
+ {
+ i = internal::random<Index>(0,A.rows()-1);
+ auto it = A.row(i).begin();
+ for(j=0;j<cols;++j) { VERIFY_IS_EQUAL(it[j],A(i,j)); }
+ }
+
+ {
+ j = internal::random<Index>(0,A.cols()-1);
+ // this would produce a dangling pointer:
+ // auto it = (A+2*A).col(j).begin();
+ // we need to name the temporary expression:
+ auto tmp = (A+2*A).col(j);
+ auto it = tmp.begin();
+ for(i=0;i<rows;++i) {
+ VERIFY_IS_APPROX(it[i],3*A(i,j));
+ }
+ }
+ }
+
+ {
+ // check basic for loop on vector-wise iterators
+ j=0;
+ for (auto it = A.colwise().cbegin(); it != A.colwise().cend(); ++it, ++j) {
+ VERIFY_IS_APPROX( it->coeff(0), A(0,j) );
+ VERIFY_IS_APPROX( (*it).coeff(0), A(0,j) );
+ }
+ j=0;
+ for (auto it = A.colwise().begin(); it != A.colwise().end(); ++it, ++j) {
+ (*it).coeffRef(0) = (*it).coeff(0); // compilation check
+ it->coeffRef(0) = it->coeff(0); // compilation check
+ VERIFY_IS_APPROX( it->coeff(0), A(0,j) );
+ VERIFY_IS_APPROX( (*it).coeff(0), A(0,j) );
+ }
+
+ // check valuetype gives us a copy
+ j=0;
+ for (auto it = A.colwise().cbegin(); it != A.colwise().cend(); ++it, ++j) {
+ typename decltype(it)::value_type tmp = *it;
+ VERIFY_IS_NOT_EQUAL( tmp.data() , it->data() );
+ VERIFY_IS_APPROX( tmp, A.col(j) );
+ }
+ }
+
+ if(rows>=3) {
+ VERIFY_IS_EQUAL((v.begin()+rows/2)[1], v(rows/2+1));
+
+ VERIFY_IS_EQUAL((A.rowwise().begin()+rows/2)[1], A.row(rows/2+1));
+ }
+
+ if(cols>=3) {
+ VERIFY_IS_EQUAL((A.colwise().begin()+cols/2)[1], A.col(cols/2+1));
+ }
+
+ // check std::sort
+ {
+ // first check that is_sorted returns false when required
+ if(rows>=2)
+ {
+ v(1) = v(0)-Scalar(1);
+ VERIFY(!is_sorted(std::begin(v),std::end(v)));
+ }
+
+ // on a vector
+ {
+ std::sort(v.begin(),v.end());
+ VERIFY(is_sorted(v.begin(),v.end()));
+ VERIFY(!::is_sorted(make_reverse_iterator(v.end()),make_reverse_iterator(v.begin())));
+ }
+
+ // on a column of a column-major matrix -> pointer-based iterator and default increment
+ {
+ j = internal::random<Index>(0,A.cols()-1);
+ // std::sort(begin(A.col(j)),end(A.col(j))); // does not compile because this returns const iterators
+ typename ColMatrixType::ColXpr Acol = A.col(j);
+ std::sort(Acol.begin(),Acol.end());
+ VERIFY(is_sorted(Acol.cbegin(),Acol.cend()));
+ A.setRandom();
+
+ std::sort(A.col(j).begin(),A.col(j).end());
+ VERIFY(is_sorted(A.col(j).cbegin(),A.col(j).cend()));
+ A.setRandom();
+ }
+
+ // on a row of a rowmajor matrix -> pointer-based iterator and runtime increment
+ {
+ i = internal::random<Index>(0,A.rows()-1);
+ typename ColMatrixType::RowXpr Arow = A.row(i);
+ VERIFY_IS_EQUAL( std::distance(Arow.begin(),Arow.end()), cols);
+ std::sort(Arow.begin(),Arow.end());
+ VERIFY(is_sorted(Arow.cbegin(),Arow.cend()));
+ A.setRandom();
+
+ std::sort(A.row(i).begin(),A.row(i).end());
+ VERIFY(is_sorted(A.row(i).cbegin(),A.row(i).cend()));
+ A.setRandom();
+ }
+
+ // with a generic iterator
+ {
+ Reshaped<RowMatrixType,RowMatrixType::SizeAtCompileTime,1> B1 = B.reshaped();
+ std::sort(B1.begin(),B1.end());
+ VERIFY(is_sorted(B1.cbegin(),B1.cend()));
+ B.setRandom();
+
+ // assertion because nested expressions are different
+ // std::sort(B.reshaped().begin(),B.reshaped().end());
+ // VERIFY(is_sorted(B.reshaped().cbegin(),B.reshaped().cend()));
+ // B.setRandom();
+ }
+ }
+
+ // check with partial_sum
+ {
+ j = internal::random<Index>(0,A.cols()-1);
+ typename ColMatrixType::ColXpr Acol = A.col(j);
+ std::partial_sum(Acol.begin(), Acol.end(), v.begin());
+ VERIFY_IS_APPROX(v(seq(1,last)), v(seq(0,last-1))+Acol(seq(1,last)));
+
+ // inplace
+ std::partial_sum(Acol.begin(), Acol.end(), Acol.begin());
+ VERIFY_IS_APPROX(v, Acol);
+ }
+
+ // stress random access as required by std::nth_element
+ if(rows>=3)
+ {
+ v.setRandom();
+ VectorType v1 = v;
+ std::sort(v1.begin(),v1.end());
+ std::nth_element(v.begin(), v.begin()+rows/2, v.end());
+ VERIFY_IS_APPROX(v1(rows/2), v(rows/2));
+
+ v.setRandom();
+ v1 = v;
+ std::sort(v1.begin()+rows/2,v1.end());
+ std::nth_element(v.begin()+rows/2, v.begin()+rows/4, v.end());
+ VERIFY_IS_APPROX(v1(rows/4), v(rows/4));
+ }
+
+ // check rows/cols iterators with range-for loops
+ {
+ j = 0;
+ for(auto c : A.colwise()) { VERIFY_IS_APPROX(c.sum(), A.col(j).sum()); ++j; }
+ j = 0;
+ for(auto c : B.colwise()) { VERIFY_IS_APPROX(c.sum(), B.col(j).sum()); ++j; }
+
+ j = 0;
+ for(auto c : B.colwise()) {
+ i = 0;
+ for(auto& x : c) {
+ VERIFY_IS_EQUAL(x, B(i,j));
+ x = A(i,j);
+ ++i;
+ }
+ ++j;
+ }
+ VERIFY_IS_APPROX(A,B);
+ B.setRandom();
+
+ i = 0;
+ for(auto r : A.rowwise()) { VERIFY_IS_APPROX(r.sum(), A.row(i).sum()); ++i; }
+ i = 0;
+ for(auto r : B.rowwise()) { VERIFY_IS_APPROX(r.sum(), B.row(i).sum()); ++i; }
+ }
+
+
+ // check rows/cols iterators with STL algorithms
+ {
+ RowVectorType row = RowVectorType::Random(cols);
+ A.rowwise() = row;
+ VERIFY( std::all_of(A.rowwise().begin(), A.rowwise().end(), [&row](typename ColMatrixType::RowXpr x) { return internal::isApprox(x.squaredNorm(),row.squaredNorm()); }) );
+ VERIFY( std::all_of(A.rowwise().rbegin(), A.rowwise().rend(), [&row](typename ColMatrixType::RowXpr x) { return internal::isApprox(x.squaredNorm(),row.squaredNorm()); }) );
+
+ VectorType col = VectorType::Random(rows);
+ A.colwise() = col;
+ VERIFY( std::all_of(A.colwise().begin(), A.colwise().end(), [&col](typename ColMatrixType::ColXpr x) { return internal::isApprox(x.squaredNorm(),col.squaredNorm()); }) );
+ VERIFY( std::all_of(A.colwise().rbegin(), A.colwise().rend(), [&col](typename ColMatrixType::ColXpr x) { return internal::isApprox(x.squaredNorm(),col.squaredNorm()); }) );
+ VERIFY( std::all_of(A.colwise().cbegin(), A.colwise().cend(), [&col](typename ColMatrixType::ConstColXpr x) { return internal::isApprox(x.squaredNorm(),col.squaredNorm()); }) );
+ VERIFY( std::all_of(A.colwise().crbegin(), A.colwise().crend(), [&col](typename ColMatrixType::ConstColXpr x) { return internal::isApprox(x.squaredNorm(),col.squaredNorm()); }) );
+
+ i = internal::random<Index>(0,A.rows()-1);
+ A.setRandom();
+ A.row(i).setZero();
+ VERIFY_IS_EQUAL(std::find_if(A.rowwise().begin(), A.rowwise().end(), [](typename ColMatrixType::RowXpr x) { return numext::is_exactly_zero(x.squaredNorm()); }) - A.rowwise().begin(), i );
+ VERIFY_IS_EQUAL(std::find_if(A.rowwise().rbegin(), A.rowwise().rend(), [](typename ColMatrixType::RowXpr x) { return numext::is_exactly_zero(x.squaredNorm()); }) - A.rowwise().rbegin(), (A.rows() - 1) - i );
+
+ j = internal::random<Index>(0,A.cols()-1);
+ A.setRandom();
+ A.col(j).setZero();
+ VERIFY_IS_EQUAL(std::find_if(A.colwise().begin(), A.colwise().end(), [](typename ColMatrixType::ColXpr x) { return numext::is_exactly_zero(x.squaredNorm()); }) - A.colwise().begin(), j );
+ VERIFY_IS_EQUAL(std::find_if(A.colwise().rbegin(), A.colwise().rend(), [](typename ColMatrixType::ColXpr x) { return numext::is_exactly_zero(x.squaredNorm()); }) - A.colwise().rbegin(), (A.cols() - 1) - j );
+ }
+
+ {
+ using VecOp = VectorwiseOp<ArrayXXi, 0>;
+ STATIC_CHECK(( internal::is_same<VecOp::const_iterator, decltype(std::declval<const VecOp&>().cbegin())>::value ));
+ STATIC_CHECK(( internal::is_same<VecOp::const_iterator, decltype(std::declval<const VecOp&>().cend ())>::value ));
+ STATIC_CHECK(( internal::is_same<VecOp::const_iterator, decltype(std::cbegin(std::declval<const VecOp&>()))>::value ));
+ STATIC_CHECK(( internal::is_same<VecOp::const_iterator, decltype(std::cend (std::declval<const VecOp&>()))>::value ));
+ }
+}
+
+
+// When the compiler sees expression IsContainerTest<C>(0), if C is an
+// STL-style container class, the first overload of IsContainerTest
+// will be viable (since both C::iterator* and C::const_iterator* are
+// valid types and NULL can be implicitly converted to them). It will
+// be picked over the second overload as 'int' is a perfect match for
+// the type of argument 0. If C::iterator or C::const_iterator is not
+// a valid type, the first overload is not viable, and the second
+// overload will be picked.
+template <class C,
+ class Iterator = decltype(::std::declval<const C&>().begin()),
+ class = decltype(::std::declval<const C&>().end()),
+ class = decltype(++::std::declval<Iterator&>()),
+ class = decltype(*::std::declval<Iterator>()),
+ class = typename C::const_iterator>
+bool IsContainerType(int /* dummy */) { return true; }
+
+template <class C>
+bool IsContainerType(long /* dummy */) { return false; }
+
+template <typename Scalar, int Rows, int Cols>
+void test_stl_container_detection(int rows=Rows, int cols=Cols)
+{
+ typedef Matrix<Scalar,Rows,1> VectorType;
+ typedef Matrix<Scalar,Rows,Cols,ColMajor> ColMatrixType;
+ typedef Matrix<Scalar,Rows,Cols,RowMajor> RowMatrixType;
+
+ ColMatrixType A = ColMatrixType::Random(rows, cols);
+ RowMatrixType B = RowMatrixType::Random(rows, cols);
+
+ Index i = 1;
+
+ using ColMatrixColType = decltype(A.col(i));
+ using ColMatrixRowType = decltype(A.row(i));
+ using RowMatrixColType = decltype(B.col(i));
+ using RowMatrixRowType = decltype(B.row(i));
+
+ // Vector and matrix col/row are valid Stl-style container.
+ VERIFY_IS_EQUAL(IsContainerType<VectorType>(0), true);
+ VERIFY_IS_EQUAL(IsContainerType<ColMatrixColType>(0), true);
+ VERIFY_IS_EQUAL(IsContainerType<ColMatrixRowType>(0), true);
+ VERIFY_IS_EQUAL(IsContainerType<RowMatrixColType>(0), true);
+ VERIFY_IS_EQUAL(IsContainerType<RowMatrixRowType>(0), true);
+
+ // But the matrix itself is not a valid Stl-style container.
+ VERIFY_IS_EQUAL(IsContainerType<ColMatrixType>(0), rows == 1 || cols == 1);
+ VERIFY_IS_EQUAL(IsContainerType<RowMatrixType>(0), rows == 1 || cols == 1);
+}
+
+EIGEN_DECLARE_TEST(stl_iterators)
+{
+ for(int i = 0; i < g_repeat; i++) {
+ CALL_SUBTEST_1(( test_stl_iterators<double,2,3>() ));
+ CALL_SUBTEST_1(( test_stl_iterators<float,7,5>() ));
+ CALL_SUBTEST_1(( test_stl_iterators<int,Dynamic,Dynamic>(internal::random<int>(5,10), internal::random<int>(5,10)) ));
+ CALL_SUBTEST_1(( test_stl_iterators<int,Dynamic,Dynamic>(internal::random<int>(10,200), internal::random<int>(10,200)) ));
+ }
+
+ CALL_SUBTEST_1(( test_stl_container_detection<float,1,1>() ));
+ CALL_SUBTEST_1(( test_stl_container_detection<float,5,5>() ));
+}
diff --git a/test/superlu_support.cpp b/test/superlu_support.cpp
new file mode 100644
index 0000000..55450c8
--- /dev/null
+++ b/test/superlu_support.cpp
@@ -0,0 +1,23 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2011 Gael Guennebaud <g.gael@free.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#define EIGEN_NO_DEBUG_SMALL_PRODUCT_BLOCKS
+#include "sparse_solver.h"
+
+#include <Eigen/SuperLUSupport>
+
+EIGEN_DECLARE_TEST(superlu_support)
+{
+ SuperLU<SparseMatrix<double> > superlu_double_colmajor;
+ SuperLU<SparseMatrix<std::complex<double> > > superlu_cplxdouble_colmajor;
+ CALL_SUBTEST_1( check_sparse_square_solving(superlu_double_colmajor) );
+ CALL_SUBTEST_2( check_sparse_square_solving(superlu_cplxdouble_colmajor) );
+ CALL_SUBTEST_1( check_sparse_square_determinant(superlu_double_colmajor) );
+ CALL_SUBTEST_2( check_sparse_square_determinant(superlu_cplxdouble_colmajor) );
+}
diff --git a/test/svd_common.h b/test/svd_common.h
new file mode 100644
index 0000000..9822595
--- /dev/null
+++ b/test/svd_common.h
@@ -0,0 +1,640 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2014 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2009 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef SVD_DEFAULT
+#error a macro SVD_DEFAULT(MatrixType) must be defined prior to including svd_common.h
+#endif
+
+#ifndef SVD_FOR_MIN_NORM
+#error a macro SVD_FOR_MIN_NORM(MatrixType) must be defined prior to including svd_common.h
+#endif
+
+#ifndef SVD_STATIC_OPTIONS
+#error a macro SVD_STATIC_OPTIONS(MatrixType, Options) must be defined prior to including svd_common.h
+#endif
+
+#include "svd_fill.h"
+#include "solverbase.h"
+
+// Check that the matrix m is properly reconstructed and that the U and V factors are unitary
+// The SVD must have already been computed.
+template<typename SvdType, typename MatrixType>
+void svd_check_full(const MatrixType& m, const SvdType& svd)
+{
+ Index rows = m.rows();
+ Index cols = m.cols();
+
+ enum {
+ RowsAtCompileTime = MatrixType::RowsAtCompileTime,
+ ColsAtCompileTime = MatrixType::ColsAtCompileTime
+ };
+
+ typedef typename MatrixType::Scalar Scalar;
+ typedef typename MatrixType::RealScalar RealScalar;
+ typedef Matrix<Scalar, RowsAtCompileTime, RowsAtCompileTime> MatrixUType;
+ typedef Matrix<Scalar, ColsAtCompileTime, ColsAtCompileTime> MatrixVType;
+
+ MatrixType sigma = MatrixType::Zero(rows,cols);
+ sigma.diagonal() = svd.singularValues().template cast<Scalar>();
+ MatrixUType u = svd.matrixU();
+ MatrixVType v = svd.matrixV();
+ RealScalar scaling = m.cwiseAbs().maxCoeff();
+ if(scaling<(std::numeric_limits<RealScalar>::min)())
+ {
+ VERIFY(sigma.cwiseAbs().maxCoeff() <= (std::numeric_limits<RealScalar>::min)());
+ }
+ else
+ {
+ VERIFY_IS_APPROX(m/scaling, u * (sigma/scaling) * v.adjoint());
+ }
+ VERIFY_IS_UNITARY(u);
+ VERIFY_IS_UNITARY(v);
+}
+
+// Compare partial SVD defined by computationOptions to a full SVD referenceSvd
+template <typename MatrixType, typename SvdType, int Options>
+void svd_compare_to_full(const MatrixType& m, const SvdType& referenceSvd) {
+ typedef typename MatrixType::RealScalar RealScalar;
+ Index rows = m.rows();
+ Index cols = m.cols();
+ Index diagSize = (std::min)(rows, cols);
+ RealScalar prec = test_precision<RealScalar>();
+
+ SVD_STATIC_OPTIONS(MatrixType, Options) svd(m);
+
+ VERIFY_IS_APPROX(svd.singularValues(), referenceSvd.singularValues());
+
+ if (Options & (ComputeFullV | ComputeThinV)) {
+ VERIFY( (svd.matrixV().adjoint()*svd.matrixV()).isIdentity(prec) );
+ VERIFY_IS_APPROX( svd.matrixV().leftCols(diagSize) * svd.singularValues().asDiagonal() * svd.matrixV().leftCols(diagSize).adjoint(),
+ referenceSvd.matrixV().leftCols(diagSize) * referenceSvd.singularValues().asDiagonal() * referenceSvd.matrixV().leftCols(diagSize).adjoint());
+ }
+
+ if (Options & (ComputeFullU | ComputeThinU)) {
+ VERIFY( (svd.matrixU().adjoint()*svd.matrixU()).isIdentity(prec) );
+ VERIFY_IS_APPROX( svd.matrixU().leftCols(diagSize) * svd.singularValues().cwiseAbs2().asDiagonal() * svd.matrixU().leftCols(diagSize).adjoint(),
+ referenceSvd.matrixU().leftCols(diagSize) * referenceSvd.singularValues().cwiseAbs2().asDiagonal() * referenceSvd.matrixU().leftCols(diagSize).adjoint());
+ }
+
+ // The following checks are not critical.
+ // For instance, with Dived&Conquer SVD, if only the factor 'V' is computed then different matrix-matrix product
+ // implementation will be used and the resulting 'V' factor might be significantly different when the SVD
+ // decomposition is not unique, especially with single precision float.
+ ++g_test_level;
+ if (Options & ComputeFullU) VERIFY_IS_APPROX(svd.matrixU(), referenceSvd.matrixU());
+ if (Options & ComputeThinU) VERIFY_IS_APPROX(svd.matrixU(), referenceSvd.matrixU().leftCols(diagSize));
+ if (Options & ComputeFullV) VERIFY_IS_APPROX(svd.matrixV().cwiseAbs(), referenceSvd.matrixV().cwiseAbs());
+ if (Options & ComputeThinV) VERIFY_IS_APPROX(svd.matrixV(), referenceSvd.matrixV().leftCols(diagSize));
+ --g_test_level;
+}
+
+template <typename SvdType, typename MatrixType>
+void svd_least_square(const MatrixType& m) {
+ typedef typename MatrixType::Scalar Scalar;
+ typedef typename MatrixType::RealScalar RealScalar;
+ Index rows = m.rows();
+ Index cols = m.cols();
+
+ enum {
+ RowsAtCompileTime = MatrixType::RowsAtCompileTime,
+ ColsAtCompileTime = MatrixType::ColsAtCompileTime
+ };
+
+ typedef Matrix<Scalar, RowsAtCompileTime, Dynamic> RhsType;
+ typedef Matrix<Scalar, ColsAtCompileTime, Dynamic> SolutionType;
+
+ RhsType rhs = RhsType::Random(rows, internal::random<Index>(1, cols));
+ SvdType svd(m);
+
+ if (internal::is_same<RealScalar, double>::value) svd.setThreshold(RealScalar(1e-8));
+ else if(internal::is_same<RealScalar,float>::value) svd.setThreshold(RealScalar(2e-4));
+
+ SolutionType x = svd.solve(rhs);
+
+ RealScalar residual = (m*x-rhs).norm();
+ RealScalar rhs_norm = rhs.norm();
+ if(!test_isMuchSmallerThan(residual,rhs.norm()))
+ {
+ // ^^^ If the residual is very small, then we have an exact solution, so we are already good.
+
+ // evaluate normal equation which works also for least-squares solutions
+ if(internal::is_same<RealScalar,double>::value || svd.rank()==m.diagonal().size())
+ {
+ using std::sqrt;
+ // This test is not stable with single precision.
+ // This is probably because squaring m signicantly affects the precision.
+ if(internal::is_same<RealScalar,float>::value) ++g_test_level;
+
+ VERIFY_IS_APPROX(m.adjoint()*(m*x),m.adjoint()*rhs);
+
+ if(internal::is_same<RealScalar,float>::value) --g_test_level;
+ }
+
+ // Check that there is no significantly better solution in the neighborhood of x
+ for(Index k=0;k<x.rows();++k)
+ {
+ using std::abs;
+
+ SolutionType y(x);
+ y.row(k) = (RealScalar(1)+2*NumTraits<RealScalar>::epsilon())*x.row(k);
+ RealScalar residual_y = (m*y-rhs).norm();
+ VERIFY( test_isMuchSmallerThan(abs(residual_y-residual), rhs_norm) || residual < residual_y );
+ if(internal::is_same<RealScalar,float>::value) ++g_test_level;
+ VERIFY( test_isApprox(residual_y,residual) || residual < residual_y );
+ if(internal::is_same<RealScalar,float>::value) --g_test_level;
+
+ y.row(k) = (RealScalar(1)-2*NumTraits<RealScalar>::epsilon())*x.row(k);
+ residual_y = (m*y-rhs).norm();
+ VERIFY( test_isMuchSmallerThan(abs(residual_y-residual), rhs_norm) || residual < residual_y );
+ if(internal::is_same<RealScalar,float>::value) ++g_test_level;
+ VERIFY( test_isApprox(residual_y,residual) || residual < residual_y );
+ if(internal::is_same<RealScalar,float>::value) --g_test_level;
+ }
+ }
+}
+
+// check minimal norm solutions, the input matrix m is only used to recover problem size
+template <typename MatrixType, int Options>
+void svd_min_norm(const MatrixType& m) {
+ typedef typename MatrixType::Scalar Scalar;
+ Index cols = m.cols();
+
+ enum {
+ ColsAtCompileTime = MatrixType::ColsAtCompileTime
+ };
+
+ typedef Matrix<Scalar, ColsAtCompileTime, Dynamic> SolutionType;
+
+ // generate a full-rank m x n problem with m<n
+ enum {
+ RankAtCompileTime2 = ColsAtCompileTime==Dynamic ? Dynamic : (ColsAtCompileTime)/2+1,
+ RowsAtCompileTime3 = ColsAtCompileTime==Dynamic ? Dynamic : ColsAtCompileTime+1
+ };
+ typedef Matrix<Scalar, RankAtCompileTime2, ColsAtCompileTime> MatrixType2;
+ typedef Matrix<Scalar, RankAtCompileTime2, 1> RhsType2;
+ typedef Matrix<Scalar, ColsAtCompileTime, RankAtCompileTime2> MatrixType2T;
+ Index rank = RankAtCompileTime2==Dynamic ? internal::random<Index>(1,cols) : Index(RankAtCompileTime2);
+ MatrixType2 m2(rank,cols);
+ int guard = 0;
+ do {
+ m2.setRandom();
+ } while(SVD_FOR_MIN_NORM(MatrixType2)(m2).setThreshold(test_precision<Scalar>()).rank()!=rank && (++guard)<10);
+ VERIFY(guard<10);
+
+ RhsType2 rhs2 = RhsType2::Random(rank);
+ // use QR to find a reference minimal norm solution
+ HouseholderQR<MatrixType2T> qr(m2.adjoint());
+ Matrix<Scalar,Dynamic,1> tmp = qr.matrixQR().topLeftCorner(rank,rank).template triangularView<Upper>().adjoint().solve(rhs2);
+ tmp.conservativeResize(cols);
+ tmp.tail(cols-rank).setZero();
+ SolutionType x21 = qr.householderQ() * tmp;
+ // now check with SVD
+ SVD_STATIC_OPTIONS(MatrixType2, Options) svd2(m2);
+ SolutionType x22 = svd2.solve(rhs2);
+ VERIFY_IS_APPROX(m2*x21, rhs2);
+ VERIFY_IS_APPROX(m2*x22, rhs2);
+ VERIFY_IS_APPROX(x21, x22);
+
+ // Now check with a rank deficient matrix
+ typedef Matrix<Scalar, RowsAtCompileTime3, ColsAtCompileTime> MatrixType3;
+ typedef Matrix<Scalar, RowsAtCompileTime3, 1> RhsType3;
+ Index rows3 = RowsAtCompileTime3==Dynamic ? internal::random<Index>(rank+1,2*cols) : Index(RowsAtCompileTime3);
+ Matrix<Scalar,RowsAtCompileTime3,Dynamic> C = Matrix<Scalar,RowsAtCompileTime3,Dynamic>::Random(rows3,rank);
+ MatrixType3 m3 = C * m2;
+ RhsType3 rhs3 = C * rhs2;
+ SVD_STATIC_OPTIONS(MatrixType3, Options) svd3(m3);
+ SolutionType x3 = svd3.solve(rhs3);
+ VERIFY_IS_APPROX(m3*x3, rhs3);
+ VERIFY_IS_APPROX(m3*x21, rhs3);
+ VERIFY_IS_APPROX(m2*x3, rhs2);
+ VERIFY_IS_APPROX(x21, x3);
+}
+
+template<typename MatrixType, typename SolverType>
+void svd_test_solvers(const MatrixType& m, const SolverType& solver) {
+ Index rows, cols, cols2;
+
+ rows = m.rows();
+ cols = m.cols();
+
+ if(MatrixType::ColsAtCompileTime==Dynamic)
+ {
+ cols2 = internal::random<int>(2,EIGEN_TEST_MAX_SIZE);
+ }
+ else
+ {
+ cols2 = cols;
+ }
+ typedef Matrix<typename MatrixType::Scalar, MatrixType::ColsAtCompileTime, MatrixType::ColsAtCompileTime> CMatrixType;
+ check_solverbase<CMatrixType, MatrixType>(m, solver, rows, cols, cols2);
+}
+
+// work around stupid msvc error when constructing at compile time an expression that involves
+// a division by zero, even if the numeric type has floating point
+template<typename Scalar>
+EIGEN_DONT_INLINE Scalar zero() { return Scalar(0); }
+
+// workaround aggressive optimization in ICC
+template<typename T> EIGEN_DONT_INLINE T sub(T a, T b) { return a - b; }
+
+// This function verifies we don't iterate infinitely on nan/inf values,
+// and that info() returns InvalidInput.
+template <typename MatrixType>
+void svd_inf_nan() {
+ SVD_STATIC_OPTIONS(MatrixType, ComputeFullU | ComputeFullV) svd;
+ typedef typename MatrixType::Scalar Scalar;
+ Scalar some_inf = Scalar(1) / zero<Scalar>();
+ VERIFY(sub(some_inf, some_inf) != sub(some_inf, some_inf));
+ svd.compute(MatrixType::Constant(10, 10, some_inf));
+ VERIFY(svd.info() == InvalidInput);
+
+ Scalar nan = std::numeric_limits<Scalar>::quiet_NaN();
+ VERIFY(nan != nan);
+ svd.compute(MatrixType::Constant(10, 10, nan));
+ VERIFY(svd.info() == InvalidInput);
+
+ MatrixType m = MatrixType::Zero(10,10);
+ m(internal::random<int>(0,9), internal::random<int>(0,9)) = some_inf;
+ svd.compute(m);
+ VERIFY(svd.info() == InvalidInput);
+
+ m = MatrixType::Zero(10,10);
+ m(internal::random<int>(0,9), internal::random<int>(0,9)) = nan;
+ svd.compute(m);
+ VERIFY(svd.info() == InvalidInput);
+
+ // regression test for bug 791
+ m.resize(3,3);
+ m << 0, 2*NumTraits<Scalar>::epsilon(), 0.5,
+ 0, -0.5, 0,
+ nan, 0, 0;
+ svd.compute(m);
+ VERIFY(svd.info() == InvalidInput);
+
+ m.resize(4,4);
+ m << 1, 0, 0, 0,
+ 0, 3, 1, 2e-308,
+ 1, 0, 1, nan,
+ 0, nan, nan, 0;
+ svd.compute(m);
+ VERIFY(svd.info() == InvalidInput);
+}
+
+// Regression test for bug 286: JacobiSVD loops indefinitely with some
+// matrices containing denormal numbers.
+template<typename>
+void svd_underoverflow()
+{
+#if defined __INTEL_COMPILER
+// shut up warning #239: floating point underflow
+#pragma warning push
+#pragma warning disable 239
+#endif
+ Matrix2d M;
+ M << -7.90884e-313, -4.94e-324,
+ 0, 5.60844e-313;
+ SVD_STATIC_OPTIONS(Matrix2d, ComputeFullU | ComputeFullV) svd;
+ svd.compute(M);
+ CALL_SUBTEST( svd_check_full(M,svd) );
+
+ // Check all 2x2 matrices made with the following coefficients:
+ VectorXd value_set(9);
+ value_set << 0, 1, -1, 5.60844e-313, -5.60844e-313, 4.94e-324, -4.94e-324, -4.94e-223, 4.94e-223;
+ Array4i id(0,0,0,0);
+ int k = 0;
+ do
+ {
+ M << value_set(id(0)), value_set(id(1)), value_set(id(2)), value_set(id(3));
+ svd.compute(M);
+ CALL_SUBTEST( svd_check_full(M,svd) );
+
+ id(k)++;
+ if(id(k)>=value_set.size())
+ {
+ while(k<3 && id(k)>=value_set.size()) id(++k)++;
+ id.head(k).setZero();
+ k=0;
+ }
+
+ } while((id<int(value_set.size())).all());
+
+#if defined __INTEL_COMPILER
+#pragma warning pop
+#endif
+
+ // Check for overflow:
+ Matrix3d M3;
+ M3 << 4.4331978442502944e+307, -5.8585363752028680e+307, 6.4527017443412964e+307,
+ 3.7841695601406358e+307, 2.4331702789740617e+306, -3.5235707140272905e+307,
+ -8.7190887618028355e+307, -7.3453213709232193e+307, -2.4367363684472105e+307;
+
+ SVD_STATIC_OPTIONS(Matrix3d, ComputeFullU | ComputeFullV) svd3;
+ svd3.compute(M3); // just check we don't loop indefinitely
+ CALL_SUBTEST( svd_check_full(M3,svd3) );
+}
+
+template <typename MatrixType>
+void svd_all_trivial_2x2(void (*cb)(const MatrixType&)) {
+ MatrixType M;
+ VectorXd value_set(3);
+ value_set << 0, 1, -1;
+ Array4i id(0,0,0,0);
+ int k = 0;
+ do
+ {
+ M << value_set(id(0)), value_set(id(1)), value_set(id(2)), value_set(id(3));
+
+ cb(M);
+
+ id(k)++;
+ if(id(k)>=value_set.size())
+ {
+ while(k<3 && id(k)>=value_set.size()) id(++k)++;
+ id.head(k).setZero();
+ k=0;
+ }
+
+ } while((id<int(value_set.size())).all());
+}
+
+template<typename>
+void svd_preallocate()
+{
+ Vector3f v(3.f, 2.f, 1.f);
+ MatrixXf m = v.asDiagonal();
+
+ internal::set_is_malloc_allowed(false);
+ VERIFY_RAISES_ASSERT(VectorXf tmp(10);)
+ SVD_DEFAULT(MatrixXf) svd;
+ internal::set_is_malloc_allowed(true);
+ svd.compute(m);
+ VERIFY_IS_APPROX(svd.singularValues(), v);
+ VERIFY_RAISES_ASSERT(svd.matrixU());
+ VERIFY_RAISES_ASSERT(svd.matrixV());
+
+ SVD_STATIC_OPTIONS(MatrixXf, ComputeFullU | ComputeFullV) svd2(3, 3);
+ internal::set_is_malloc_allowed(false);
+ svd2.compute(m);
+ internal::set_is_malloc_allowed(true);
+ VERIFY_IS_APPROX(svd2.singularValues(), v);
+ VERIFY_IS_APPROX(svd2.matrixU(), Matrix3f::Identity());
+ VERIFY_IS_APPROX(svd2.matrixV(), Matrix3f::Identity());
+ internal::set_is_malloc_allowed(false);
+ svd2.compute(m);
+ internal::set_is_malloc_allowed(true);
+}
+
+template <typename MatrixType, int QRPreconditioner = 0>
+void svd_verify_assert_full_only(const MatrixType& m = MatrixType()) {
+ enum { RowsAtCompileTime = MatrixType::RowsAtCompileTime };
+
+ typedef Matrix<typename MatrixType::Scalar, RowsAtCompileTime, 1> RhsType;
+ RhsType rhs = RhsType::Zero(m.rows());
+
+ SVD_STATIC_OPTIONS(MatrixType, QRPreconditioner) svd0;
+ VERIFY_RAISES_ASSERT((svd0.matrixU()));
+ VERIFY_RAISES_ASSERT((svd0.singularValues()));
+ VERIFY_RAISES_ASSERT((svd0.matrixV()));
+ VERIFY_RAISES_ASSERT((svd0.solve(rhs)));
+ VERIFY_RAISES_ASSERT((svd0.transpose().solve(rhs)));
+ VERIFY_RAISES_ASSERT((svd0.adjoint().solve(rhs)));
+
+ SVD_STATIC_OPTIONS(MatrixType, QRPreconditioner) svd1(m);
+ VERIFY_RAISES_ASSERT((svd1.matrixU()));
+ VERIFY_RAISES_ASSERT((svd1.matrixV()));
+ VERIFY_RAISES_ASSERT((svd1.solve(rhs)));
+
+ SVD_STATIC_OPTIONS(MatrixType, QRPreconditioner | ComputeFullU) svdFullU(m);
+ VERIFY_RAISES_ASSERT((svdFullU.matrixV()));
+ VERIFY_RAISES_ASSERT((svdFullU.solve(rhs)));
+ SVD_STATIC_OPTIONS(MatrixType, QRPreconditioner | ComputeFullV) svdFullV(m);
+ VERIFY_RAISES_ASSERT((svdFullV.matrixU()));
+ VERIFY_RAISES_ASSERT((svdFullV.solve(rhs)));
+}
+
+template <typename MatrixType, int QRPreconditioner = 0>
+void svd_verify_assert(const MatrixType& m = MatrixType()) {
+ enum { RowsAtCompileTime = MatrixType::RowsAtCompileTime };
+
+ typedef Matrix<typename MatrixType::Scalar, RowsAtCompileTime, 1> RhsType;
+ RhsType rhs = RhsType::Zero(m.rows());
+
+ SVD_STATIC_OPTIONS(MatrixType, QRPreconditioner | ComputeThinU) svdThinU(m);
+ VERIFY_RAISES_ASSERT((svdThinU.matrixV()));
+ VERIFY_RAISES_ASSERT((svdThinU.solve(rhs)));
+ SVD_STATIC_OPTIONS(MatrixType, QRPreconditioner | ComputeThinV) svdThinV(m);
+ VERIFY_RAISES_ASSERT((svdThinV.matrixU()));
+ VERIFY_RAISES_ASSERT((svdThinV.solve(rhs)));
+
+ svd_verify_assert_full_only<MatrixType, QRPreconditioner>(m);
+}
+
+template <typename MatrixType, int Options>
+void svd_compute_checks(const MatrixType& m) {
+ typedef SVD_STATIC_OPTIONS(MatrixType, Options) SVDType;
+
+ enum {
+ RowsAtCompileTime = MatrixType::RowsAtCompileTime,
+ ColsAtCompileTime = MatrixType::ColsAtCompileTime,
+ DiagAtCompileTime = internal::min_size_prefer_dynamic(RowsAtCompileTime, ColsAtCompileTime),
+ MatrixURowsAtCompileTime = SVDType::MatrixUType::RowsAtCompileTime,
+ MatrixUColsAtCompileTime = SVDType::MatrixUType::ColsAtCompileTime,
+ MatrixVRowsAtCompileTime = SVDType::MatrixVType::RowsAtCompileTime,
+ MatrixVColsAtCompileTime = SVDType::MatrixVType::ColsAtCompileTime
+ };
+
+ SVDType staticSvd(m);
+
+ VERIFY(MatrixURowsAtCompileTime == RowsAtCompileTime);
+ VERIFY(MatrixVRowsAtCompileTime == ColsAtCompileTime);
+ if (Options & ComputeThinU) VERIFY(MatrixUColsAtCompileTime == DiagAtCompileTime);
+ if (Options & ComputeFullU) VERIFY(MatrixUColsAtCompileTime == RowsAtCompileTime);
+ if (Options & ComputeThinV) VERIFY(MatrixVColsAtCompileTime == DiagAtCompileTime);
+ if (Options & ComputeFullV) VERIFY(MatrixVColsAtCompileTime == ColsAtCompileTime);
+
+ if (Options & (ComputeThinU | ComputeFullU))
+ VERIFY(staticSvd.computeU());
+ else
+ VERIFY(!staticSvd.computeU());
+ if (Options & (ComputeThinV | ComputeFullV))
+ VERIFY(staticSvd.computeV());
+ else
+ VERIFY(!staticSvd.computeV());
+
+ if (staticSvd.computeU()) VERIFY(staticSvd.matrixU().isUnitary());
+ if (staticSvd.computeV()) VERIFY(staticSvd.matrixV().isUnitary());
+
+ if (staticSvd.computeU() && staticSvd.computeV()) {
+ svd_test_solvers(m, staticSvd);
+ svd_least_square<SVDType, MatrixType>(m);
+ // svd_min_norm generates non-square matrices so it can't be used with NoQRPreconditioner
+ if ((Options & internal::QRPreconditionerBits) != NoQRPreconditioner) svd_min_norm<MatrixType, Options>(m);
+ }
+}
+
+// Deprecated behavior.
+template <typename SvdType, typename MatrixType>
+void svd_check_runtime_options(const MatrixType& m, unsigned int computationOptions) {
+ const bool fixedRowAndThinU = SvdType::RowsAtCompileTime != Dynamic && (computationOptions & ComputeThinU) != 0 && m.cols() < m.rows();
+ const bool fixedColAndThinV = SvdType::ColsAtCompileTime != Dynamic && (computationOptions & ComputeThinV) != 0 && m.rows() < m.cols();
+ if (fixedRowAndThinU || fixedColAndThinV) {
+ VERIFY_RAISES_ASSERT(SvdType svd(m, computationOptions));
+ return;
+ }
+
+ Index diagSize = (std::min)(m.rows(), m.cols());
+
+ SvdType svd(m, computationOptions);
+ if (svd.computeU()) {
+ VERIFY(svd.matrixU().isUnitary());
+ if (computationOptions & ComputeThinU) VERIFY(svd.matrixU().cols() == diagSize);
+ }
+
+ if (svd.computeV()) {
+ VERIFY(svd.matrixV().isUnitary());
+ if (computationOptions & ComputeThinV) VERIFY(svd.matrixV().cols() == diagSize);
+ }
+ if (svd.computeU() && svd.computeV()) {
+ svd_test_solvers(m, svd);
+ svd.matrixU().isUnitary();
+ svd.matrixV().isUnitary();
+ }
+}
+
+template <typename MatrixType, int QRPreconditioner = 0>
+void svd_option_checks(const MatrixType& m) {
+ svd_compute_checks<MatrixType, QRPreconditioner>(m);
+ svd_compute_checks<MatrixType, QRPreconditioner | ComputeThinU>(m);
+ svd_compute_checks<MatrixType, QRPreconditioner | ComputeThinV>(m);
+ svd_compute_checks<MatrixType, QRPreconditioner | ComputeThinU | ComputeThinV>(m);
+
+ svd_compute_checks<MatrixType, QRPreconditioner | ComputeFullU>(m);
+ svd_compute_checks<MatrixType, QRPreconditioner | ComputeFullV>(m);
+ svd_compute_checks<MatrixType, QRPreconditioner | ComputeFullU | ComputeFullV>(m);
+
+ svd_compute_checks<MatrixType, QRPreconditioner | ComputeThinU | ComputeFullV>(m);
+ svd_compute_checks<MatrixType, QRPreconditioner | ComputeFullU | ComputeThinV>(m);
+
+ typedef SVD_STATIC_OPTIONS(MatrixType, QRPreconditioner | ComputeFullU | ComputeFullV) FullSvdType;
+ FullSvdType fullSvd(m);
+ svd_check_full(m, fullSvd);
+ svd_compare_to_full<MatrixType, FullSvdType, QRPreconditioner | ComputeFullU | ComputeFullV>(m, fullSvd);
+
+ // Deprecated behavior.
+ typedef SVD_STATIC_OPTIONS(MatrixType, QRPreconditioner) DynamicSvd;
+ svd_check_runtime_options<DynamicSvd>(m, 0);
+ svd_check_runtime_options<DynamicSvd>(m, ComputeThinU);
+ svd_check_runtime_options<DynamicSvd>(m, ComputeThinV);
+ svd_check_runtime_options<DynamicSvd>(m, ComputeThinU | ComputeThinV);
+
+ svd_check_runtime_options<DynamicSvd>(m, ComputeFullU);
+ svd_check_runtime_options<DynamicSvd>(m, ComputeFullV);
+ svd_check_runtime_options<DynamicSvd>(m, ComputeFullU | ComputeFullV);
+
+ svd_check_runtime_options<DynamicSvd>(m, ComputeThinU | ComputeFullV);
+ svd_check_runtime_options<DynamicSvd>(m, ComputeFullU | ComputeThinV);
+}
+
+template <typename MatrixType, int QRPreconditioner = 0>
+void svd_option_checks_full_only(const MatrixType& m) {
+ svd_compute_checks<MatrixType, QRPreconditioner | ComputeFullU>(m);
+ svd_compute_checks<MatrixType, QRPreconditioner | ComputeFullV>(m);
+ svd_compute_checks<MatrixType, QRPreconditioner | ComputeFullU | ComputeFullV>(m);
+
+ SVD_STATIC_OPTIONS(MatrixType, QRPreconditioner | ComputeFullU | ComputeFullV) fullSvd(m);
+ svd_check_full(m, fullSvd);
+}
+
+template <typename MatrixType, int QRPreconditioner = 0>
+void svd_check_max_size_matrix(int initialRows, int initialCols) {
+ enum {
+ MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime,
+ MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime
+ };
+
+ int rows = MaxRowsAtCompileTime == Dynamic ? initialRows : (std::min)(initialRows, (int)MaxRowsAtCompileTime);
+ int cols = MaxColsAtCompileTime == Dynamic ? initialCols : (std::min)(initialCols, (int)MaxColsAtCompileTime);
+
+ MatrixType m(rows, cols);
+ SVD_STATIC_OPTIONS(MatrixType, QRPreconditioner | ComputeThinU | ComputeThinV) thinSvd(m);
+ SVD_STATIC_OPTIONS(MatrixType, QRPreconditioner | ComputeThinU | ComputeFullV) mixedSvd1(m);
+ SVD_STATIC_OPTIONS(MatrixType, QRPreconditioner | ComputeFullU | ComputeThinV) mixedSvd2(m);
+ SVD_STATIC_OPTIONS(MatrixType, QRPreconditioner | ComputeFullU | ComputeFullV) fullSvd(m);
+
+ MatrixType n(MaxRowsAtCompileTime, MaxColsAtCompileTime);
+ thinSvd.compute(n);
+ mixedSvd1.compute(n);
+ mixedSvd2.compute(n);
+ fullSvd.compute(n);
+
+ MatrixX<typename MatrixType::Scalar> dynamicMatrix(MaxRowsAtCompileTime + 1, MaxColsAtCompileTime + 1);
+
+ VERIFY_RAISES_ASSERT(thinSvd.compute(dynamicMatrix));
+ VERIFY_RAISES_ASSERT(mixedSvd1.compute(dynamicMatrix));
+ VERIFY_RAISES_ASSERT(mixedSvd2.compute(dynamicMatrix));
+ VERIFY_RAISES_ASSERT(fullSvd.compute(dynamicMatrix));
+}
+
+template <typename SvdType, typename MatrixType>
+void svd_verify_constructor_options_assert(const MatrixType& m, bool fullOnly = false) {
+ typedef typename MatrixType::Scalar Scalar;
+ Index rows = m.rows();
+ Index cols = m.cols();
+
+ enum {
+ RowsAtCompileTime = MatrixType::RowsAtCompileTime,
+ ColsAtCompileTime = MatrixType::ColsAtCompileTime
+ };
+
+ typedef Matrix<Scalar, RowsAtCompileTime, 1> RhsType;
+ RhsType rhs(rows);
+ SvdType svd;
+ VERIFY_RAISES_ASSERT(svd.matrixU())
+ VERIFY_RAISES_ASSERT(svd.singularValues())
+ VERIFY_RAISES_ASSERT(svd.matrixV())
+ VERIFY_RAISES_ASSERT(svd.solve(rhs))
+ VERIFY_RAISES_ASSERT(svd.transpose().solve(rhs))
+ VERIFY_RAISES_ASSERT(svd.adjoint().solve(rhs))
+
+ MatrixType a = MatrixType::Zero(rows, cols);
+ SvdType svd2(a, 0);
+ VERIFY_RAISES_ASSERT(svd2.matrixU())
+ VERIFY_RAISES_ASSERT(svd2.matrixV())
+ svd2.singularValues();
+ VERIFY_RAISES_ASSERT(svd2.solve(rhs))
+
+ // Deprecated behavior.
+ SvdType svd3(a, ComputeFullU);
+ svd3.matrixU();
+ VERIFY_RAISES_ASSERT(svd3.matrixV())
+ VERIFY_RAISES_ASSERT(svd3.solve(rhs))
+
+ SvdType svd4(a, ComputeFullV);
+ svd4.matrixV();
+ VERIFY_RAISES_ASSERT(svd4.matrixU())
+ VERIFY_RAISES_ASSERT(svd4.solve(rhs))
+
+ if (!fullOnly && ColsAtCompileTime == Dynamic)
+ {
+ SvdType svd5(a, ComputeThinU);
+ svd5.matrixU();
+ VERIFY_RAISES_ASSERT(svd5.matrixV())
+ VERIFY_RAISES_ASSERT(svd5.solve(rhs))
+
+ SvdType svd6(a, ComputeThinV);
+ svd6.matrixV();
+ VERIFY_RAISES_ASSERT(svd6.matrixU())
+ VERIFY_RAISES_ASSERT(svd6.solve(rhs))
+ }
+}
+
+#undef SVD_DEFAULT
+#undef SVD_FOR_MIN_NORM
+#undef SVD_STATIC_OPTIONS
diff --git a/test/svd_fill.h b/test/svd_fill.h
new file mode 100644
index 0000000..6411f57
--- /dev/null
+++ b/test/svd_fill.h
@@ -0,0 +1,121 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2014-2015 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+template<typename T>
+Array<T,4,1> four_denorms();
+
+template<>
+Array4f four_denorms() { return Array4f(5.60844e-39f, -5.60844e-39f, 4.94e-44f, -4.94e-44f); }
+template<>
+Array4d four_denorms() { return Array4d(5.60844e-313, -5.60844e-313, 4.94e-324, -4.94e-324); }
+template<typename T>
+Array<T,4,1> four_denorms() { return four_denorms<double>().cast<T>(); }
+
+template<typename MatrixType>
+void svd_fill_random(MatrixType &m, int Option = 0)
+{
+ using std::pow;
+ typedef typename MatrixType::Scalar Scalar;
+ typedef typename MatrixType::RealScalar RealScalar;
+ Index diagSize = (std::min)(m.rows(), m.cols());
+ RealScalar s = std::numeric_limits<RealScalar>::max_exponent10/4;
+ s = internal::random<RealScalar>(1,s);
+ Matrix<RealScalar,Dynamic,1> d = Matrix<RealScalar,Dynamic,1>::Random(diagSize);
+ for(Index k=0; k<diagSize; ++k)
+ d(k) = d(k)*pow(RealScalar(10),internal::random<RealScalar>(-s,s));
+
+ bool dup = internal::random<int>(0,10) < 3;
+ bool unit_uv = internal::random<int>(0,10) < (dup?7:3); // if we duplicate some diagonal entries, then increase the chance to preserve them using unitary U and V factors
+
+ // duplicate some singular values
+ if(dup)
+ {
+ Index n = internal::random<Index>(0,d.size()-1);
+ for(Index i=0; i<n; ++i)
+ d(internal::random<Index>(0,d.size()-1)) = d(internal::random<Index>(0,d.size()-1));
+ }
+
+ Matrix<Scalar,Dynamic,Dynamic> U(m.rows(),diagSize);
+ Matrix<Scalar,Dynamic,Dynamic> VT(diagSize,m.cols());
+ if(unit_uv)
+ {
+ // in very rare cases let's try with a pure diagonal matrix
+ if(internal::random<int>(0,10) < 1)
+ {
+ U.setIdentity();
+ VT.setIdentity();
+ }
+ else
+ {
+ createRandomPIMatrixOfRank(diagSize,U.rows(), U.cols(), U);
+ createRandomPIMatrixOfRank(diagSize,VT.rows(), VT.cols(), VT);
+ }
+ }
+ else
+ {
+ U.setRandom();
+ VT.setRandom();
+ }
+
+ Matrix<Scalar,Dynamic,1> samples(9);
+ samples << Scalar(0), four_denorms<RealScalar>(),
+ -RealScalar(1)/NumTraits<RealScalar>::highest(),
+ RealScalar(1)/NumTraits<RealScalar>::highest(),
+ (std::numeric_limits<RealScalar>::min)(),
+ pow((std::numeric_limits<RealScalar>::min)(), RealScalar(0.8));
+
+ if(Option==Symmetric)
+ {
+ m = U * d.asDiagonal() * U.transpose();
+
+ // randomly nullify some rows/columns
+ {
+ Index count = internal::random<Index>(-diagSize,diagSize);
+ for(Index k=0; k<count; ++k)
+ {
+ Index i = internal::random<Index>(0,diagSize-1);
+ m.row(i).setZero();
+ m.col(i).setZero();
+ }
+ if(count<0)
+ // (partly) cancel some coeffs
+ if(!(dup && unit_uv))
+ {
+
+ Index n = internal::random<Index>(0,m.size()-1);
+ for(Index k=0; k<n; ++k)
+ {
+ Index i = internal::random<Index>(0,m.rows()-1);
+ Index j = internal::random<Index>(0,m.cols()-1);
+ m(j,i) = m(i,j) = samples(internal::random<Index>(0,samples.size()-1));
+ if(NumTraits<Scalar>::IsComplex)
+ *(&numext::real_ref(m(j,i))+1) = *(&numext::real_ref(m(i,j))+1) = samples.real()(internal::random<Index>(0,samples.size()-1));
+ }
+ }
+ }
+ }
+ else
+ {
+ m = U * d.asDiagonal() * VT;
+ // (partly) cancel some coeffs
+ if(!(dup && unit_uv))
+ {
+ Index n = internal::random<Index>(0,m.size()-1);
+ for(Index k=0; k<n; ++k)
+ {
+ Index i = internal::random<Index>(0,m.rows()-1);
+ Index j = internal::random<Index>(0,m.cols()-1);
+ m(i,j) = samples(internal::random<Index>(0,samples.size()-1));
+ if(NumTraits<Scalar>::IsComplex)
+ *(&numext::real_ref(m(i,j))+1) = samples.real()(internal::random<Index>(0,samples.size()-1));
+ }
+ }
+ }
+}
+
diff --git a/test/swap.cpp b/test/swap.cpp
new file mode 100644
index 0000000..e8d6881
--- /dev/null
+++ b/test/swap.cpp
@@ -0,0 +1,104 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "main.h"
+
+template<typename T>
+struct other_matrix_type
+{
+ typedef int type;
+};
+
+template<typename Scalar_, int Rows_, int Cols_, int Options_, int MaxRows_, int MaxCols_>
+struct other_matrix_type<Matrix<Scalar_, Rows_, Cols_, Options_, MaxRows_, MaxCols_> >
+{
+ typedef Matrix<Scalar_, Rows_, Cols_, Options_^RowMajor, MaxRows_, MaxCols_> type;
+};
+
+template <typename MatrixType>
+std::enable_if_t<(MatrixType::RowsAtCompileTime==1 || MatrixType::RowsAtCompileTime==Dynamic), void>
+check_row_swap(MatrixType& m1) {
+
+ if (m1.rows() != 1) {
+ // test assertion on mismatching size -- matrix case
+ VERIFY_RAISES_ASSERT(m1.swap(m1.row(0)));
+ // test assertion on mismatching size -- xpr case
+ VERIFY_RAISES_ASSERT(m1.row(0).swap(m1));
+ }
+}
+
+template <typename MatrixType>
+std::enable_if_t<!(MatrixType::RowsAtCompileTime==1 || MatrixType::RowsAtCompileTime==Dynamic), void>
+check_row_swap(MatrixType& /* unused */) {
+}
+
+template<typename MatrixType> void swap(const MatrixType& m)
+{
+ typedef typename other_matrix_type<MatrixType>::type OtherMatrixType;
+ typedef typename MatrixType::Scalar Scalar;
+
+ eigen_assert((!internal::is_same<MatrixType,OtherMatrixType>::value));
+ Index rows = m.rows();
+ Index cols = m.cols();
+
+ // construct 3 matrix guaranteed to be distinct
+ MatrixType m1 = MatrixType::Random(rows,cols);
+ MatrixType m2 = MatrixType::Random(rows,cols) + Scalar(100) * MatrixType::Identity(rows,cols);
+ OtherMatrixType m3 = OtherMatrixType::Random(rows,cols) + Scalar(200) * OtherMatrixType::Identity(rows,cols);
+
+ MatrixType m1_copy = m1;
+ MatrixType m2_copy = m2;
+ OtherMatrixType m3_copy = m3;
+
+ // test swapping 2 matrices of same type
+ Scalar *d1=m1.data(), *d2=m2.data();
+ m1.swap(m2);
+ VERIFY_IS_APPROX(m1,m2_copy);
+ VERIFY_IS_APPROX(m2,m1_copy);
+ if(MatrixType::SizeAtCompileTime==Dynamic)
+ {
+ VERIFY(m1.data()==d2);
+ VERIFY(m2.data()==d1);
+ }
+ m1 = m1_copy;
+ m2 = m2_copy;
+
+ // test swapping 2 matrices of different types
+ m1.swap(m3);
+ VERIFY_IS_APPROX(m1,m3_copy);
+ VERIFY_IS_APPROX(m3,m1_copy);
+ m1 = m1_copy;
+ m3 = m3_copy;
+
+ // test swapping matrix with expression
+ m1.swap(m2.block(0,0,rows,cols));
+ VERIFY_IS_APPROX(m1,m2_copy);
+ VERIFY_IS_APPROX(m2,m1_copy);
+ m1 = m1_copy;
+ m2 = m2_copy;
+
+ // test swapping two expressions of different types
+ m1.transpose().swap(m3.transpose());
+ VERIFY_IS_APPROX(m1,m3_copy);
+ VERIFY_IS_APPROX(m3,m1_copy);
+ m1 = m1_copy;
+ m3 = m3_copy;
+
+ check_row_swap(m1);
+}
+
+EIGEN_DECLARE_TEST(swap)
+{
+ int s = internal::random<int>(1,EIGEN_TEST_MAX_SIZE);
+ CALL_SUBTEST_1( swap(Matrix3f()) ); // fixed size, no vectorization
+ CALL_SUBTEST_2( swap(Matrix4d()) ); // fixed size, possible vectorization
+ CALL_SUBTEST_3( swap(MatrixXd(s,s)) ); // dyn size, no vectorization
+ CALL_SUBTEST_4( swap(MatrixXf(s,s)) ); // dyn size, possible vectorization
+ TEST_SET_BUT_UNUSED_VARIABLE(s)
+}
diff --git a/test/symbolic_index.cpp b/test/symbolic_index.cpp
new file mode 100644
index 0000000..53eb55d
--- /dev/null
+++ b/test/symbolic_index.cpp
@@ -0,0 +1,75 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2017 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "main.h"
+
+using Eigen::placeholders::last;
+using Eigen::placeholders::lastp1;
+using Eigen::placeholders::all;
+
+template<typename T1,typename T2>
+bool is_same_symb(const T1& a, const T2& b, Index size)
+{
+ return a.eval(last=size-1) == b.eval(last=size-1);
+}
+
+template<typename T>
+void check_is_symbolic(const T&) {
+ STATIC_CHECK(( symbolic::is_symbolic<T>::value ))
+}
+
+template<typename T>
+void check_isnot_symbolic(const T&) {
+ STATIC_CHECK(( !symbolic::is_symbolic<T>::value ))
+}
+
+#define VERIFY_EQ_INT(A,B) VERIFY_IS_APPROX(int(A),int(B))
+
+void check_symbolic_index()
+{
+ check_is_symbolic(last);
+ check_is_symbolic(lastp1);
+ check_is_symbolic(last+1);
+ check_is_symbolic(last-lastp1);
+ check_is_symbolic(2*last-lastp1/2);
+ check_isnot_symbolic(fix<3>());
+
+ Index size=100;
+
+ // First, let's check FixedInt arithmetic:
+ VERIFY( is_same_type( (fix<5>()-fix<3>())*fix<9>()/(-fix<3>()), fix<-(5-3)*9/3>() ) );
+ VERIFY( is_same_type( (fix<5>()-fix<3>())*fix<9>()/fix<2>(), fix<(5-3)*9/2>() ) );
+ VERIFY( is_same_type( fix<9>()/fix<2>(), fix<9/2>() ) );
+ VERIFY( is_same_type( fix<9>()%fix<2>(), fix<9%2>() ) );
+ VERIFY( is_same_type( fix<9>()&fix<2>(), fix<9&2>() ) );
+ VERIFY( is_same_type( fix<9>()|fix<2>(), fix<9|2>() ) );
+ VERIFY( is_same_type( fix<9>()/2, int(9/2) ) );
+
+ VERIFY( is_same_symb( lastp1-1, last, size) );
+ VERIFY( is_same_symb( lastp1-fix<1>(), last, size) );
+
+ VERIFY_IS_EQUAL( ( (last*5-2)/3 ).eval(last=size-1), ((size-1)*5-2)/3 );
+ VERIFY_IS_EQUAL( ( (last*fix<5>()-fix<2>())/fix<3>() ).eval(last=size-1), ((size-1)*5-2)/3 );
+ VERIFY_IS_EQUAL( ( -last*lastp1 ).eval(last=size-1), -(size-1)*size );
+ VERIFY_IS_EQUAL( ( lastp1-3*last ).eval(last=size-1), size- 3*(size-1) );
+ VERIFY_IS_EQUAL( ( (lastp1-3*last)/lastp1 ).eval(last=size-1), (size- 3*(size-1))/size );
+
+ {
+ struct x_tag {}; static const symbolic::SymbolExpr<x_tag> x;
+ struct y_tag {}; static const symbolic::SymbolExpr<y_tag> y;
+ struct z_tag {}; static const symbolic::SymbolExpr<z_tag> z;
+
+ VERIFY_IS_APPROX( int(((x+3)/y+z).eval(x=6,y=3,z=-13)), (6+3)/3+(-13) );
+ }
+}
+
+EIGEN_DECLARE_TEST(symbolic_index)
+{
+ CALL_SUBTEST_1( check_symbolic_index() );
+}
diff --git a/test/triangular.cpp b/test/triangular.cpp
new file mode 100644
index 0000000..2259869
--- /dev/null
+++ b/test/triangular.cpp
@@ -0,0 +1,291 @@
+// This file is triangularView of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#if defined(EIGEN_TEST_PART_100) || defined(EIGEN_TEST_PART_ALL)
+# define EIGEN_NO_DEPRECATED_WARNING
+#endif
+
+#include "main.h"
+
+
+template<typename MatrixType> void triangular_deprecated(const MatrixType &m)
+{
+ Index rows = m.rows();
+ Index cols = m.cols();
+ MatrixType m1, m2, m3, m4;
+ m1.setRandom(rows,cols);
+ m2.setRandom(rows,cols);
+ m3 = m1; m4 = m2;
+ // deprecated method:
+ m1.template triangularView<Eigen::Upper>().swap(m2);
+ // use this method instead:
+ m3.template triangularView<Eigen::Upper>().swap(m4.template triangularView<Eigen::Upper>());
+ VERIFY_IS_APPROX(m1,m3);
+ VERIFY_IS_APPROX(m2,m4);
+ // deprecated method:
+ m1.template triangularView<Eigen::Lower>().swap(m4);
+ // use this method instead:
+ m3.template triangularView<Eigen::Lower>().swap(m2.template triangularView<Eigen::Lower>());
+ VERIFY_IS_APPROX(m1,m3);
+ VERIFY_IS_APPROX(m2,m4);
+}
+
+
+template<typename MatrixType> void triangular_square(const MatrixType& m)
+{
+ typedef typename MatrixType::Scalar Scalar;
+ typedef typename NumTraits<Scalar>::Real RealScalar;
+ typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> VectorType;
+
+ RealScalar largerEps = 10*test_precision<RealScalar>();
+
+ Index rows = m.rows();
+ Index cols = m.cols();
+
+ MatrixType m1 = MatrixType::Random(rows, cols),
+ m2 = MatrixType::Random(rows, cols),
+ m3(rows, cols),
+ m4(rows, cols),
+ r1(rows, cols),
+ r2(rows, cols);
+ VectorType v2 = VectorType::Random(rows);
+
+ MatrixType m1up = m1.template triangularView<Upper>();
+ MatrixType m2up = m2.template triangularView<Upper>();
+
+ if (rows*cols>1)
+ {
+ VERIFY(m1up.isUpperTriangular());
+ VERIFY(m2up.transpose().isLowerTriangular());
+ VERIFY(!m2.isLowerTriangular());
+ }
+
+// VERIFY_IS_APPROX(m1up.transpose() * m2, m1.upper().transpose().lower() * m2);
+
+ // test overloaded operator+=
+ r1.setZero();
+ r2.setZero();
+ r1.template triangularView<Upper>() += m1;
+ r2 += m1up;
+ VERIFY_IS_APPROX(r1,r2);
+
+ // test overloaded operator=
+ m1.setZero();
+ m1.template triangularView<Upper>() = m2.transpose() + m2;
+ m3 = m2.transpose() + m2;
+ VERIFY_IS_APPROX(m3.template triangularView<Lower>().transpose().toDenseMatrix(), m1);
+
+ // test overloaded operator=
+ m1.setZero();
+ m1.template triangularView<Lower>() = m2.transpose() + m2;
+ VERIFY_IS_APPROX(m3.template triangularView<Lower>().toDenseMatrix(), m1);
+
+ VERIFY_IS_APPROX(m3.template triangularView<Lower>().conjugate().toDenseMatrix(),
+ m3.conjugate().template triangularView<Lower>().toDenseMatrix());
+
+ m1 = MatrixType::Random(rows, cols);
+ for (int i=0; i<rows; ++i)
+ while (numext::abs2(m1(i,i))<RealScalar(1e-1)) m1(i,i) = internal::random<Scalar>();
+
+ Transpose<MatrixType> trm4(m4);
+ // test back and forward substitution with a vector as the rhs
+ m3 = m1.template triangularView<Upper>();
+ VERIFY(v2.isApprox(m3.adjoint() * (m1.adjoint().template triangularView<Lower>().solve(v2)), largerEps));
+ m3 = m1.template triangularView<Lower>();
+ VERIFY(v2.isApprox(m3.transpose() * (m1.transpose().template triangularView<Upper>().solve(v2)), largerEps));
+ m3 = m1.template triangularView<Upper>();
+ VERIFY(v2.isApprox(m3 * (m1.template triangularView<Upper>().solve(v2)), largerEps));
+ m3 = m1.template triangularView<Lower>();
+ VERIFY(v2.isApprox(m3.conjugate() * (m1.conjugate().template triangularView<Lower>().solve(v2)), largerEps));
+
+ // test back and forward substitution with a matrix as the rhs
+ m3 = m1.template triangularView<Upper>();
+ VERIFY(m2.isApprox(m3.adjoint() * (m1.adjoint().template triangularView<Lower>().solve(m2)), largerEps));
+ m3 = m1.template triangularView<Lower>();
+ VERIFY(m2.isApprox(m3.transpose() * (m1.transpose().template triangularView<Upper>().solve(m2)), largerEps));
+ m3 = m1.template triangularView<Upper>();
+ VERIFY(m2.isApprox(m3 * (m1.template triangularView<Upper>().solve(m2)), largerEps));
+ m3 = m1.template triangularView<Lower>();
+ VERIFY(m2.isApprox(m3.conjugate() * (m1.conjugate().template triangularView<Lower>().solve(m2)), largerEps));
+
+ // check M * inv(L) using in place API
+ m4 = m3;
+ m1.transpose().template triangularView<Eigen::Upper>().solveInPlace(trm4);
+ VERIFY_IS_APPROX(m4 * m1.template triangularView<Eigen::Lower>(), m3);
+
+ // check M * inv(U) using in place API
+ m3 = m1.template triangularView<Upper>();
+ m4 = m3;
+ m3.transpose().template triangularView<Eigen::Lower>().solveInPlace(trm4);
+ VERIFY_IS_APPROX(m4 * m1.template triangularView<Eigen::Upper>(), m3);
+
+ // check solve with unit diagonal
+ m3 = m1.template triangularView<UnitUpper>();
+ VERIFY(m2.isApprox(m3 * (m1.template triangularView<UnitUpper>().solve(m2)), largerEps));
+
+// VERIFY(( m1.template triangularView<Upper>()
+// * m2.template triangularView<Upper>()).isUpperTriangular());
+
+ // test swap
+ m1.setOnes();
+ m2.setZero();
+ m2.template triangularView<Upper>().swap(m1.template triangularView<Eigen::Upper>());
+ m3.setZero();
+ m3.template triangularView<Upper>().setOnes();
+ VERIFY_IS_APPROX(m2,m3);
+
+ m1.setRandom();
+ m3 = m1.template triangularView<Upper>();
+ Matrix<Scalar, MatrixType::ColsAtCompileTime, Dynamic> m5(cols, internal::random<int>(1,20)); m5.setRandom();
+ Matrix<Scalar, Dynamic, MatrixType::RowsAtCompileTime> m6(internal::random<int>(1,20), rows); m6.setRandom();
+ VERIFY_IS_APPROX(m1.template triangularView<Upper>() * m5, m3*m5);
+ VERIFY_IS_APPROX(m6*m1.template triangularView<Upper>(), m6*m3);
+
+ m1up = m1.template triangularView<Upper>();
+ VERIFY_IS_APPROX(m1.template selfadjointView<Upper>().template triangularView<Upper>().toDenseMatrix(), m1up);
+ VERIFY_IS_APPROX(m1up.template selfadjointView<Upper>().template triangularView<Upper>().toDenseMatrix(), m1up);
+ VERIFY_IS_APPROX(m1.template selfadjointView<Upper>().template triangularView<Lower>().toDenseMatrix(), m1up.adjoint());
+ VERIFY_IS_APPROX(m1up.template selfadjointView<Upper>().template triangularView<Lower>().toDenseMatrix(), m1up.adjoint());
+
+ VERIFY_IS_APPROX(m1.template selfadjointView<Upper>().diagonal(), m1.diagonal());
+
+ m3.setRandom();
+ const MatrixType& m3c(m3);
+ VERIFY( is_same_type(m3c.template triangularView<Lower>(),m3.template triangularView<Lower>().template conjugateIf<false>()) );
+ VERIFY( is_same_type(m3c.template triangularView<Lower>().conjugate(),m3.template triangularView<Lower>().template conjugateIf<true>()) );
+ VERIFY_IS_APPROX(m3.template triangularView<Lower>().template conjugateIf<true>().toDenseMatrix(),
+ m3.conjugate().template triangularView<Lower>().toDenseMatrix());
+ VERIFY_IS_APPROX(m3.template triangularView<Lower>().template conjugateIf<false>().toDenseMatrix(),
+ m3.template triangularView<Lower>().toDenseMatrix());
+
+ VERIFY( is_same_type(m3c.template selfadjointView<Lower>(),m3.template selfadjointView<Lower>().template conjugateIf<false>()) );
+ VERIFY( is_same_type(m3c.template selfadjointView<Lower>().conjugate(),m3.template selfadjointView<Lower>().template conjugateIf<true>()) );
+ VERIFY_IS_APPROX(m3.template selfadjointView<Lower>().template conjugateIf<true>().toDenseMatrix(),
+ m3.conjugate().template selfadjointView<Lower>().toDenseMatrix());
+ VERIFY_IS_APPROX(m3.template selfadjointView<Lower>().template conjugateIf<false>().toDenseMatrix(),
+ m3.template selfadjointView<Lower>().toDenseMatrix());
+
+}
+
+
+template<typename MatrixType> void triangular_rect(const MatrixType& m)
+{
+ typedef typename MatrixType::Scalar Scalar;
+ typedef typename NumTraits<Scalar>::Real RealScalar;
+ enum { Rows = MatrixType::RowsAtCompileTime, Cols = MatrixType::ColsAtCompileTime };
+
+ Index rows = m.rows();
+ Index cols = m.cols();
+
+ MatrixType m1 = MatrixType::Random(rows, cols),
+ m2 = MatrixType::Random(rows, cols),
+ m3(rows, cols),
+ m4(rows, cols),
+ r1(rows, cols),
+ r2(rows, cols);
+
+ MatrixType m1up = m1.template triangularView<Upper>();
+ MatrixType m2up = m2.template triangularView<Upper>();
+
+ if (rows>1 && cols>1)
+ {
+ VERIFY(m1up.isUpperTriangular());
+ VERIFY(m2up.transpose().isLowerTriangular());
+ VERIFY(!m2.isLowerTriangular());
+ }
+
+ // test overloaded operator+=
+ r1.setZero();
+ r2.setZero();
+ r1.template triangularView<Upper>() += m1;
+ r2 += m1up;
+ VERIFY_IS_APPROX(r1,r2);
+
+ // test overloaded operator=
+ m1.setZero();
+ m1.template triangularView<Upper>() = 3 * m2;
+ m3 = 3 * m2;
+ VERIFY_IS_APPROX(m3.template triangularView<Upper>().toDenseMatrix(), m1);
+
+
+ m1.setZero();
+ m1.template triangularView<Lower>() = 3 * m2;
+ VERIFY_IS_APPROX(m3.template triangularView<Lower>().toDenseMatrix(), m1);
+
+ m1.setZero();
+ m1.template triangularView<StrictlyUpper>() = 3 * m2;
+ VERIFY_IS_APPROX(m3.template triangularView<StrictlyUpper>().toDenseMatrix(), m1);
+
+
+ m1.setZero();
+ m1.template triangularView<StrictlyLower>() = 3 * m2;
+ VERIFY_IS_APPROX(m3.template triangularView<StrictlyLower>().toDenseMatrix(), m1);
+ m1.setRandom();
+ m2 = m1.template triangularView<Upper>();
+ VERIFY(m2.isUpperTriangular());
+ VERIFY(!m2.isLowerTriangular());
+ m2 = m1.template triangularView<StrictlyUpper>();
+ VERIFY(m2.isUpperTriangular());
+ VERIFY(m2.diagonal().isMuchSmallerThan(RealScalar(1)));
+ m2 = m1.template triangularView<UnitUpper>();
+ VERIFY(m2.isUpperTriangular());
+ m2.diagonal().array() -= Scalar(1);
+ VERIFY(m2.diagonal().isMuchSmallerThan(RealScalar(1)));
+ m2 = m1.template triangularView<Lower>();
+ VERIFY(m2.isLowerTriangular());
+ VERIFY(!m2.isUpperTriangular());
+ m2 = m1.template triangularView<StrictlyLower>();
+ VERIFY(m2.isLowerTriangular());
+ VERIFY(m2.diagonal().isMuchSmallerThan(RealScalar(1)));
+ m2 = m1.template triangularView<UnitLower>();
+ VERIFY(m2.isLowerTriangular());
+ m2.diagonal().array() -= Scalar(1);
+ VERIFY(m2.diagonal().isMuchSmallerThan(RealScalar(1)));
+ // test swap
+ m1.setOnes();
+ m2.setZero();
+ m2.template triangularView<Upper>().swap(m1.template triangularView<Eigen::Upper>());
+ m3.setZero();
+ m3.template triangularView<Upper>().setOnes();
+ VERIFY_IS_APPROX(m2,m3);
+}
+
+void bug_159()
+{
+ Matrix3d m = Matrix3d::Random().triangularView<Lower>();
+ EIGEN_UNUSED_VARIABLE(m)
+}
+
+EIGEN_DECLARE_TEST(triangular)
+{
+ int maxsize = (std::min)(EIGEN_TEST_MAX_SIZE,20);
+ for(int i = 0; i < g_repeat ; i++)
+ {
+ int r = internal::random<int>(2,maxsize); TEST_SET_BUT_UNUSED_VARIABLE(r)
+ int c = internal::random<int>(2,maxsize); TEST_SET_BUT_UNUSED_VARIABLE(c)
+
+ CALL_SUBTEST_1( triangular_square(Matrix<float, 1, 1>()) );
+ CALL_SUBTEST_2( triangular_square(Matrix<float, 2, 2>()) );
+ CALL_SUBTEST_3( triangular_square(Matrix3d()) );
+ CALL_SUBTEST_4( triangular_square(Matrix<std::complex<float>,8, 8>()) );
+ CALL_SUBTEST_5( triangular_square(MatrixXcd(r,r)) );
+ CALL_SUBTEST_6( triangular_square(Matrix<float,Dynamic,Dynamic,RowMajor>(r, r)) );
+
+ CALL_SUBTEST_7( triangular_rect(Matrix<float, 4, 5>()) );
+ CALL_SUBTEST_8( triangular_rect(Matrix<double, 6, 2>()) );
+ CALL_SUBTEST_9( triangular_rect(MatrixXcf(r, c)) );
+ CALL_SUBTEST_5( triangular_rect(MatrixXcd(r, c)) );
+ CALL_SUBTEST_6( triangular_rect(Matrix<float,Dynamic,Dynamic,RowMajor>(r, c)) );
+
+ CALL_SUBTEST_100( triangular_deprecated(Matrix<float, 5, 7>()) );
+ CALL_SUBTEST_100( triangular_deprecated(MatrixXd(r,c)) );
+ }
+
+ CALL_SUBTEST_1( bug_159() );
+}
diff --git a/test/tuple_test.cpp b/test/tuple_test.cpp
new file mode 100644
index 0000000..c3bbe37
--- /dev/null
+++ b/test/tuple_test.cpp
@@ -0,0 +1,123 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2021 The Eigen Team
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "main.h"
+
+#include <Eigen/Core>
+#include <Eigen/src/Core/arch/GPU/Tuple.h>
+
+using namespace Eigen::internal;
+using Eigen::internal::tuple_impl::tuple;
+
+void basic_tuple_test() {
+ // Construction.
+ tuple<> tuple0 {};
+ tuple<int> tuple1 {1};
+ tuple<int, float> tuple2 {3, 5.0f};
+ tuple<int, float, double> tuple3 {7, 11.0f, 13.0};
+ // Default construction.
+ tuple<> tuple0default;
+ EIGEN_UNUSED_VARIABLE(tuple0default)
+ tuple<int> tuple1default;
+ EIGEN_UNUSED_VARIABLE(tuple1default)
+ tuple<int, float> tuple2default;
+ EIGEN_UNUSED_VARIABLE(tuple2default)
+ tuple<int, float, double> tuple3default;
+ EIGEN_UNUSED_VARIABLE(tuple3default)
+
+ // Assignment.
+ tuple<> tuple0b = tuple0;
+ EIGEN_UNUSED_VARIABLE(tuple0b)
+ decltype(tuple1) tuple1b = tuple1;
+ EIGEN_UNUSED_VARIABLE(tuple1b)
+ decltype(tuple2) tuple2b = tuple2;
+ EIGEN_UNUSED_VARIABLE(tuple2b)
+ decltype(tuple3) tuple3b = tuple3;
+ EIGEN_UNUSED_VARIABLE(tuple3b)
+
+ // get.
+ VERIFY_IS_EQUAL(tuple_impl::get<0>(tuple3), 7);
+ VERIFY_IS_EQUAL(tuple_impl::get<1>(tuple3), 11.0f);
+ VERIFY_IS_EQUAL(tuple_impl::get<2>(tuple3), 13.0);
+
+ // tuple_impl::tuple_size.
+ VERIFY_IS_EQUAL(tuple_impl::tuple_size<decltype(tuple0)>::value, size_t(0));
+ VERIFY_IS_EQUAL(tuple_impl::tuple_size<decltype(tuple1)>::value, size_t(1));
+ VERIFY_IS_EQUAL(tuple_impl::tuple_size<decltype(tuple2)>::value, size_t(2));
+ VERIFY_IS_EQUAL(tuple_impl::tuple_size<decltype(tuple3)>::value, size_t(3));
+
+ // tuple_impl::tuple_cat.
+ auto tuple2cat3 = tuple_impl::tuple_cat(tuple2, tuple3);
+ VERIFY_IS_EQUAL(tuple_impl::tuple_size<decltype(tuple2cat3)>::value, size_t(5));
+ VERIFY_IS_EQUAL(tuple_impl::get<1>(tuple2cat3), 5.0f);
+ VERIFY_IS_EQUAL(tuple_impl::get<3>(tuple2cat3), 11.0f);
+ auto tuple3cat0 = tuple_impl::tuple_cat(tuple3, tuple0);
+ VERIFY_IS_EQUAL(tuple_impl::tuple_size<decltype(tuple3cat0)>::value, size_t(3));
+ auto singlecat = tuple_impl::tuple_cat(tuple3);
+ VERIFY_IS_EQUAL(tuple_impl::tuple_size<decltype(singlecat)>::value, size_t(3));
+ auto emptycat = tuple_impl::tuple_cat();
+ VERIFY_IS_EQUAL(tuple_impl::tuple_size<decltype(emptycat)>::value, size_t(0));
+ auto tuple0cat1cat2cat3 = tuple_impl::tuple_cat(tuple0, tuple1, tuple2, tuple3);
+ VERIFY_IS_EQUAL(tuple_impl::tuple_size<decltype(tuple0cat1cat2cat3)>::value, size_t(6));
+
+ // make_tuple.
+ // The tuple types should uses values for the second and fourth parameters.
+ double tmp = 20;
+ auto tuple_make = tuple_impl::make_tuple(int(10), tmp, float(20.0f), tuple0);
+ VERIFY( (std::is_same<decltype(tuple_make), tuple<int, double, float, tuple<> > >::value) );
+ VERIFY_IS_EQUAL(tuple_impl::get<1>(tuple_make), tmp);
+
+ // forward_as_tuple.
+ // The tuple types should uses references for the second and fourth parameters.
+ auto tuple_forward = tuple_impl::forward_as_tuple(int(10), tmp, float(20.0f), tuple0);
+ VERIFY( (std::is_same<decltype(tuple_forward), tuple<int, double&, float, tuple<>& > >::value) );
+ VERIFY_IS_EQUAL(tuple_impl::get<1>(tuple_forward), tmp);
+
+ // tie.
+ auto tuple_tie = tuple_impl::tie(tuple0, tuple1, tuple2, tuple3);
+ VERIFY( (std::is_same<decltype(tuple_tie),
+ tuple<decltype(tuple0)&,
+ decltype(tuple1)&,
+ decltype(tuple2)&,
+ decltype(tuple3)&> >::value) );
+ VERIFY_IS_EQUAL( (tuple_impl::get<1>(tuple_impl::get<2>(tuple_tie))), 5.0f );
+ // Modify value and ensure tuple2 is updated.
+ tuple_impl::get<1>(tuple_impl::get<2>(tuple_tie)) = 10.0f;
+ VERIFY_IS_EQUAL( (tuple_impl::get<1>(tuple2)), 10.0f );
+
+ // Assignment.
+ int x = -1;
+ float y = -1;
+ double z = -1;
+ tuple_impl::tie(x, y, z) = tuple3;
+ VERIFY_IS_EQUAL(x, tuple_impl::get<0>(tuple3));
+ VERIFY_IS_EQUAL(y, tuple_impl::get<1>(tuple3));
+ VERIFY_IS_EQUAL(z, tuple_impl::get<2>(tuple3));
+ tuple<int, float, double> tuple3c(-2, -2.0f, -2.0);
+ tuple3c = std::move(tuple3b);
+ VERIFY_IS_EQUAL(tuple_impl::get<0>(tuple3c), tuple_impl::get<0>(tuple3));
+ VERIFY_IS_EQUAL(tuple_impl::get<1>(tuple3c), tuple_impl::get<1>(tuple3));
+ VERIFY_IS_EQUAL(tuple_impl::get<2>(tuple3c), tuple_impl::get<2>(tuple3));
+}
+
+void eigen_tuple_test() {
+ tuple<Eigen::Matrix3d, Eigen::MatrixXd> tuple;
+ tuple_impl::get<0>(tuple).setRandom();
+ tuple_impl::get<1>(tuple).setRandom(10, 10);
+
+ auto tuple_tie = tuple_impl::tie(tuple_impl::get<0>(tuple), tuple_impl::get<1>(tuple));
+ tuple_impl::get<1>(tuple_tie).setIdentity();
+ VERIFY(tuple_impl::get<1>(tuple).isIdentity());
+}
+
+EIGEN_DECLARE_TEST(tuple)
+{
+ CALL_SUBTEST(basic_tuple_test());
+ CALL_SUBTEST(eigen_tuple_test());
+}
diff --git a/test/type_alias.cpp b/test/type_alias.cpp
new file mode 100644
index 0000000..0a223d9
--- /dev/null
+++ b/test/type_alias.cpp
@@ -0,0 +1,43 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2019 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "main.h"
+
+EIGEN_DECLARE_TEST(type_alias)
+{
+ using namespace internal;
+
+ // To warm up, some basic checks:
+ STATIC_CHECK((is_same<MatrixXd,Matrix<double,Dynamic,Dynamic> >::value));
+ STATIC_CHECK((is_same<Matrix2f,Matrix<float,2,2> >::value));
+ STATIC_CHECK((is_same<Array33i,Array<int,3,3> >::value));
+
+ STATIC_CHECK((is_same<MatrixX<double>, MatrixXd>::value));
+ STATIC_CHECK((is_same<MatrixX<int>, MatrixXi>::value));
+ STATIC_CHECK((is_same<Matrix2<int>, Matrix2i>::value));
+ STATIC_CHECK((is_same<Matrix2X<float>, Matrix2Xf>::value));
+ STATIC_CHECK((is_same<MatrixX4<double>, MatrixX4d>::value));
+ STATIC_CHECK((is_same<VectorX<int>, VectorXi>::value));
+ STATIC_CHECK((is_same<Vector2<float>, Vector2f>::value));
+ STATIC_CHECK((is_same<RowVectorX<int>, RowVectorXi>::value));
+ STATIC_CHECK((is_same<RowVector2<float>, RowVector2f>::value));
+
+ STATIC_CHECK((is_same<ArrayXX<float>, ArrayXXf>::value));
+ STATIC_CHECK((is_same<Array33<int>, Array33i>::value));
+ STATIC_CHECK((is_same<Array2X<float>, Array2Xf>::value));
+ STATIC_CHECK((is_same<ArrayX4<double>, ArrayX4d>::value));
+ STATIC_CHECK((is_same<ArrayX<double>, ArrayXd>::value));
+ STATIC_CHECK((is_same<Array4<double>, Array4d>::value));
+
+ STATIC_CHECK((is_same<Vector<float,3>, Vector3f>::value));
+ STATIC_CHECK((is_same<Vector<int,Dynamic>, VectorXi>::value));
+ STATIC_CHECK((is_same<RowVector<float,3>, RowVector3f>::value));
+ STATIC_CHECK((is_same<RowVector<int,Dynamic>, RowVectorXi>::value));
+
+}
diff --git a/test/umeyama.cpp b/test/umeyama.cpp
new file mode 100644
index 0000000..170c28a
--- /dev/null
+++ b/test/umeyama.cpp
@@ -0,0 +1,183 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009 Hauke Heibel <hauke.heibel@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "main.h"
+
+#include <Eigen/Core>
+#include <Eigen/Geometry>
+
+#include <Eigen/LU> // required for MatrixBase::determinant
+#include <Eigen/SVD> // required for SVD
+
+using namespace Eigen;
+
+// Constructs a random matrix from the unitary group U(size).
+template <typename T>
+Eigen::Matrix<T, Eigen::Dynamic, Eigen::Dynamic> randMatrixUnitary(int size)
+{
+ typedef T Scalar;
+ typedef Eigen::Matrix<Scalar, Eigen::Dynamic, Eigen::Dynamic> MatrixType;
+
+ MatrixType Q;
+
+ int max_tries = 40;
+ bool is_unitary = false;
+
+ while (!is_unitary && max_tries > 0)
+ {
+ // initialize random matrix
+ Q = MatrixType::Random(size, size);
+
+ // orthogonalize columns using the Gram-Schmidt algorithm
+ for (int col = 0; col < size; ++col)
+ {
+ typename MatrixType::ColXpr colVec = Q.col(col);
+ for (int prevCol = 0; prevCol < col; ++prevCol)
+ {
+ typename MatrixType::ColXpr prevColVec = Q.col(prevCol);
+ colVec -= colVec.dot(prevColVec)*prevColVec;
+ }
+ Q.col(col) = colVec.normalized();
+ }
+
+ // this additional orthogonalization is not necessary in theory but should enhance
+ // the numerical orthogonality of the matrix
+ for (int row = 0; row < size; ++row)
+ {
+ typename MatrixType::RowXpr rowVec = Q.row(row);
+ for (int prevRow = 0; prevRow < row; ++prevRow)
+ {
+ typename MatrixType::RowXpr prevRowVec = Q.row(prevRow);
+ rowVec -= rowVec.dot(prevRowVec)*prevRowVec;
+ }
+ Q.row(row) = rowVec.normalized();
+ }
+
+ // final check
+ is_unitary = Q.isUnitary();
+ --max_tries;
+ }
+
+ if (max_tries == 0)
+ eigen_assert(false && "randMatrixUnitary: Could not construct unitary matrix!");
+
+ return Q;
+}
+
+// Constructs a random matrix from the special unitary group SU(size).
+template <typename T>
+Eigen::Matrix<T, Eigen::Dynamic, Eigen::Dynamic> randMatrixSpecialUnitary(int size)
+{
+ typedef T Scalar;
+
+ typedef Eigen::Matrix<Scalar, Eigen::Dynamic, Eigen::Dynamic> MatrixType;
+
+ // initialize unitary matrix
+ MatrixType Q = randMatrixUnitary<Scalar>(size);
+
+ // tweak the first column to make the determinant be 1
+ Q.col(0) *= numext::conj(Q.determinant());
+
+ return Q;
+}
+
+template <typename MatrixType>
+void run_test(int dim, int num_elements)
+{
+ using std::abs;
+ typedef typename internal::traits<MatrixType>::Scalar Scalar;
+ typedef Matrix<Scalar, Eigen::Dynamic, Eigen::Dynamic> MatrixX;
+ typedef Matrix<Scalar, Eigen::Dynamic, 1> VectorX;
+
+ // MUST be positive because in any other case det(cR_t) may become negative for
+ // odd dimensions!
+ const Scalar c = abs(internal::random<Scalar>());
+
+ MatrixX R = randMatrixSpecialUnitary<Scalar>(dim);
+ VectorX t = Scalar(50)*VectorX::Random(dim,1);
+
+ MatrixX cR_t = MatrixX::Identity(dim+1,dim+1);
+ cR_t.block(0,0,dim,dim) = c*R;
+ cR_t.block(0,dim,dim,1) = t;
+
+ MatrixX src = MatrixX::Random(dim+1, num_elements);
+ src.row(dim) = Matrix<Scalar, 1, Dynamic>::Constant(num_elements, Scalar(1));
+
+ MatrixX dst = cR_t*src;
+
+ MatrixX cR_t_umeyama = umeyama(src.block(0,0,dim,num_elements), dst.block(0,0,dim,num_elements));
+
+ const Scalar error = ( cR_t_umeyama*src - dst ).norm() / dst.norm();
+ VERIFY(error < Scalar(40)*std::numeric_limits<Scalar>::epsilon());
+}
+
+template<typename Scalar, int Dimension>
+void run_fixed_size_test(int num_elements)
+{
+ using std::abs;
+ typedef Matrix<Scalar, Dimension+1, Dynamic> MatrixX;
+ typedef Matrix<Scalar, Dimension+1, Dimension+1> HomMatrix;
+ typedef Matrix<Scalar, Dimension, Dimension> FixedMatrix;
+ typedef Matrix<Scalar, Dimension, 1> FixedVector;
+
+ const int dim = Dimension;
+
+ // MUST be positive because in any other case det(cR_t) may become negative for
+ // odd dimensions!
+ // Also if c is to small compared to t.norm(), problem is ill-posed (cf. Bug 744)
+ const Scalar c = internal::random<Scalar>(0.5, 2.0);
+
+ FixedMatrix R = randMatrixSpecialUnitary<Scalar>(dim);
+ FixedVector t = Scalar(32)*FixedVector::Random(dim,1);
+
+ HomMatrix cR_t = HomMatrix::Identity(dim+1,dim+1);
+ cR_t.block(0,0,dim,dim) = c*R;
+ cR_t.block(0,dim,dim,1) = t;
+
+ MatrixX src = MatrixX::Random(dim+1, num_elements);
+ src.row(dim) = Matrix<Scalar, 1, Dynamic>::Constant(num_elements, Scalar(1));
+
+ MatrixX dst = cR_t*src;
+
+ Block<MatrixX, Dimension, Dynamic> src_block(src,0,0,dim,num_elements);
+ Block<MatrixX, Dimension, Dynamic> dst_block(dst,0,0,dim,num_elements);
+
+ HomMatrix cR_t_umeyama = umeyama(src_block, dst_block);
+
+ const Scalar error = ( cR_t_umeyama*src - dst ).squaredNorm();
+
+ VERIFY(error < Scalar(16)*std::numeric_limits<Scalar>::epsilon());
+}
+
+EIGEN_DECLARE_TEST(umeyama)
+{
+ for (int i=0; i<g_repeat; ++i)
+ {
+ const int num_elements = internal::random<int>(40,500);
+
+ // works also for dimensions bigger than 3...
+ for (int dim=2; dim<8; ++dim)
+ {
+ CALL_SUBTEST_1(run_test<MatrixXd>(dim, num_elements));
+ CALL_SUBTEST_2(run_test<MatrixXf>(dim, num_elements));
+ }
+
+ CALL_SUBTEST_3((run_fixed_size_test<float, 2>(num_elements)));
+ CALL_SUBTEST_4((run_fixed_size_test<float, 3>(num_elements)));
+ CALL_SUBTEST_5((run_fixed_size_test<float, 4>(num_elements)));
+
+ CALL_SUBTEST_6((run_fixed_size_test<double, 2>(num_elements)));
+ CALL_SUBTEST_7((run_fixed_size_test<double, 3>(num_elements)));
+ CALL_SUBTEST_8((run_fixed_size_test<double, 4>(num_elements)));
+ }
+
+ // Those two calls don't compile and result in meaningful error messages!
+ // umeyama(MatrixXcf(),MatrixXcf());
+ // umeyama(MatrixXcd(),MatrixXcd());
+}
diff --git a/test/umfpack_support.cpp b/test/umfpack_support.cpp
new file mode 100644
index 0000000..d8f2a6f
--- /dev/null
+++ b/test/umfpack_support.cpp
@@ -0,0 +1,34 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2011 Gael Guennebaud <g.gael@free.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#define EIGEN_NO_DEBUG_SMALL_PRODUCT_BLOCKS
+#include "sparse_solver.h"
+
+#include <Eigen/UmfPackSupport>
+
+template<typename T1, typename T2> void test_umfpack_support_T()
+{
+ UmfPackLU<SparseMatrix<T1, ColMajor, T2> > umfpack_colmajor;
+ UmfPackLU<SparseMatrix<T1, RowMajor, T2> > umfpack_rowmajor;
+
+ check_sparse_square_solving(umfpack_colmajor);
+ check_sparse_square_solving(umfpack_rowmajor);
+
+ check_sparse_square_determinant(umfpack_colmajor);
+ check_sparse_square_determinant(umfpack_rowmajor);
+}
+
+EIGEN_DECLARE_TEST(umfpack_support)
+{
+ CALL_SUBTEST_1((test_umfpack_support_T<double, int>()));
+ CALL_SUBTEST_2((test_umfpack_support_T<std::complex<double>, int>()));
+ CALL_SUBTEST_3((test_umfpack_support_T<double, long >()));
+ CALL_SUBTEST_4((test_umfpack_support_T<std::complex<double>, long>()));
+}
+
diff --git a/test/unalignedcount.cpp b/test/unalignedcount.cpp
new file mode 100644
index 0000000..52cdd9e
--- /dev/null
+++ b/test/unalignedcount.cpp
@@ -0,0 +1,60 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+static int nb_load;
+static int nb_loadu;
+static int nb_store;
+static int nb_storeu;
+
+#define EIGEN_DEBUG_ALIGNED_LOAD { nb_load++; }
+#define EIGEN_DEBUG_UNALIGNED_LOAD { nb_loadu++; }
+#define EIGEN_DEBUG_ALIGNED_STORE { nb_store++; }
+#define EIGEN_DEBUG_UNALIGNED_STORE { nb_storeu++; }
+
+#define VERIFY_ALIGNED_UNALIGNED_COUNT(XPR,AL,UL,AS,US) {\
+ nb_load = nb_loadu = nb_store = nb_storeu = 0; \
+ XPR; \
+ if(!(nb_load==AL && nb_loadu==UL && nb_store==AS && nb_storeu==US)) \
+ std::cerr << " >> " << nb_load << ", " << nb_loadu << ", " << nb_store << ", " << nb_storeu << "\n"; \
+ VERIFY( (#XPR) && nb_load==AL && nb_loadu==UL && nb_store==AS && nb_storeu==US ); \
+ }
+
+
+#include "main.h"
+
+EIGEN_DECLARE_TEST(unalignedcount)
+{
+ #if defined(EIGEN_VECTORIZE_AVX512)
+ VectorXf a(48), b(48);
+ VERIFY_ALIGNED_UNALIGNED_COUNT(a += b, 6, 0, 3, 0);
+ VERIFY_ALIGNED_UNALIGNED_COUNT(a.segment(0,48) += b.segment(0,48), 3, 3, 3, 0);
+ VERIFY_ALIGNED_UNALIGNED_COUNT(a.segment(0,48) -= b.segment(0,48), 3, 3, 3, 0);
+ VERIFY_ALIGNED_UNALIGNED_COUNT(a.segment(0,48) *= 3.5, 3, 0, 3, 0);
+ VERIFY_ALIGNED_UNALIGNED_COUNT(a.segment(0,48) /= 3.5, 3, 0, 3, 0);
+ #elif defined(EIGEN_VECTORIZE_AVX)
+ VectorXf a(40), b(40);
+ VERIFY_ALIGNED_UNALIGNED_COUNT(a += b, 10, 0, 5, 0);
+ VERIFY_ALIGNED_UNALIGNED_COUNT(a.segment(0,40) += b.segment(0,40), 5, 5, 5, 0);
+ VERIFY_ALIGNED_UNALIGNED_COUNT(a.segment(0,40) -= b.segment(0,40), 5, 5, 5, 0);
+ VERIFY_ALIGNED_UNALIGNED_COUNT(a.segment(0,40) *= 3.5, 5, 0, 5, 0);
+ VERIFY_ALIGNED_UNALIGNED_COUNT(a.segment(0,40) /= 3.5, 5, 0, 5, 0);
+ #elif defined(EIGEN_VECTORIZE_SSE)
+ VectorXf a(40), b(40);
+ VERIFY_ALIGNED_UNALIGNED_COUNT(a += b, 20, 0, 10, 0);
+ VERIFY_ALIGNED_UNALIGNED_COUNT(a.segment(0,40) += b.segment(0,40), 10, 10, 10, 0);
+ VERIFY_ALIGNED_UNALIGNED_COUNT(a.segment(0,40) -= b.segment(0,40), 10, 10, 10, 0);
+ VERIFY_ALIGNED_UNALIGNED_COUNT(a.segment(0,40) *= 3.5, 10, 0, 10, 0);
+ VERIFY_ALIGNED_UNALIGNED_COUNT(a.segment(0,40) /= 3.5, 10, 0, 10, 0);
+ #else
+ // The following line is to eliminate "variable not used" warnings
+ nb_load = nb_loadu = nb_store = nb_storeu = 0;
+ int a(0), b(0);
+ VERIFY(a==b);
+ #endif
+}
diff --git a/test/unaryviewstride.cpp b/test/unaryviewstride.cpp
new file mode 100644
index 0000000..03a770b
--- /dev/null
+++ b/test/unaryviewstride.cpp
@@ -0,0 +1,38 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2021 Andrew Johnson <andrew.johnson@arjohnsonau.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "main.h"
+
+template<int OuterStride,int InnerStride,typename VectorType> void unaryview_stride(const VectorType& m)
+{
+ typedef typename VectorType::Scalar Scalar;
+ Index rows = m.rows();
+ Index cols = m.cols();
+ VectorType vec = VectorType::Random(rows, cols);
+
+ struct view_op {
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE const Scalar&
+ operator()(const Scalar& v) const { return v; }
+ };
+
+ CwiseUnaryView<view_op, VectorType, Stride<OuterStride,InnerStride>> vec_view(vec);
+ VERIFY(vec_view.outerStride() == (OuterStride == 0 ? 0 : OuterStride));
+ VERIFY(vec_view.innerStride() == (InnerStride == 0 ? 1 : InnerStride));
+}
+
+EIGEN_DECLARE_TEST(unaryviewstride)
+{
+ CALL_SUBTEST_1(( unaryview_stride<1,2>(MatrixXf()) ));
+ CALL_SUBTEST_1(( unaryview_stride<0,0>(MatrixXf()) ));
+ CALL_SUBTEST_2(( unaryview_stride<1,2>(VectorXf()) ));
+ CALL_SUBTEST_2(( unaryview_stride<0,0>(VectorXf()) ));
+ CALL_SUBTEST_3(( unaryview_stride<1,2>(RowVectorXf()) ));
+ CALL_SUBTEST_3(( unaryview_stride<0,0>(RowVectorXf()) ));
+}
diff --git a/test/upperbidiagonalization.cpp b/test/upperbidiagonalization.cpp
new file mode 100644
index 0000000..945c999
--- /dev/null
+++ b/test/upperbidiagonalization.cpp
@@ -0,0 +1,43 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2010 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "main.h"
+#include <Eigen/SVD>
+
+template<typename MatrixType> void upperbidiag(const MatrixType& m)
+{
+ const Index rows = m.rows();
+ const Index cols = m.cols();
+
+ typedef Matrix<typename MatrixType::RealScalar, MatrixType::RowsAtCompileTime, MatrixType::ColsAtCompileTime> RealMatrixType;
+ typedef Matrix<typename MatrixType::Scalar, MatrixType::ColsAtCompileTime, MatrixType::RowsAtCompileTime> TransposeMatrixType;
+
+ MatrixType a = MatrixType::Random(rows,cols);
+ internal::UpperBidiagonalization<MatrixType> ubd(a);
+ RealMatrixType b(rows, cols);
+ b.setZero();
+ b.block(0,0,cols,cols) = ubd.bidiagonal();
+ MatrixType c = ubd.householderU() * b * ubd.householderV().adjoint();
+ VERIFY_IS_APPROX(a,c);
+ TransposeMatrixType d = ubd.householderV() * b.adjoint() * ubd.householderU().adjoint();
+ VERIFY_IS_APPROX(a.adjoint(),d);
+}
+
+EIGEN_DECLARE_TEST(upperbidiagonalization)
+{
+ for(int i = 0; i < g_repeat; i++) {
+ CALL_SUBTEST_1( upperbidiag(MatrixXf(3,3)) );
+ CALL_SUBTEST_2( upperbidiag(MatrixXd(17,12)) );
+ CALL_SUBTEST_3( upperbidiag(MatrixXcf(20,20)) );
+ CALL_SUBTEST_4( upperbidiag(Matrix<std::complex<double>,Dynamic,Dynamic,RowMajor>(16,15)) );
+ CALL_SUBTEST_5( upperbidiag(Matrix<float,6,4>()) );
+ CALL_SUBTEST_6( upperbidiag(Matrix<float,5,5>()) );
+ CALL_SUBTEST_7( upperbidiag(Matrix<double,4,3>()) );
+ }
+}
diff --git a/test/vectorization_logic.cpp b/test/vectorization_logic.cpp
new file mode 100644
index 0000000..a6441ab
--- /dev/null
+++ b/test/vectorization_logic.cpp
@@ -0,0 +1,433 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2015 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifdef EIGEN_TEST_PART_1
+#define EIGEN_UNALIGNED_VECTORIZE 1
+#endif
+
+#ifdef EIGEN_TEST_PART_2
+#define EIGEN_UNALIGNED_VECTORIZE 0
+#endif
+
+#ifdef EIGEN_DEFAULT_TO_ROW_MAJOR
+#undef EIGEN_DEFAULT_TO_ROW_MAJOR
+#endif
+#define EIGEN_DEBUG_ASSIGN
+#include "main.h"
+#include <typeinfo>
+
+// Disable "ignoring attributes on template argument"
+// for packet_traits<Packet*>
+// => The only workaround would be to wrap _m128 and the likes
+// within wrappers.
+#if EIGEN_GNUC_AT_LEAST(6,0)
+ #pragma GCC diagnostic ignored "-Wignored-attributes"
+#endif
+
+using internal::demangle_flags;
+using internal::demangle_traversal;
+using internal::demangle_unrolling;
+
+template<typename Dst, typename Src>
+bool test_assign(const Dst&, const Src&, int traversal, int unrolling)
+{
+ EIGEN_STATIC_ASSERT_SAME_MATRIX_SIZE(Dst,Src);
+ typedef internal::copy_using_evaluator_traits<internal::evaluator<Dst>,internal::evaluator<Src>, internal::assign_op<typename Dst::Scalar,typename Src::Scalar> > traits;
+ // If traversal or unrolling are negative, ignore.
+ bool res = traversal > -1 ? traits::Traversal==traversal : true;
+ if (unrolling > -1) {
+ if(unrolling==InnerUnrolling+CompleteUnrolling) {
+ res = res && (int(traits::Unrolling)==InnerUnrolling || int(traits::Unrolling)==CompleteUnrolling);
+ } else {
+ res = res && int(traits::Unrolling)==unrolling;
+ }
+ }
+ if(!res)
+ {
+ std::cerr << "Src: " << demangle_flags(Src::Flags) << std::endl;
+ std::cerr << " " << demangle_flags(internal::evaluator<Src>::Flags) << std::endl;
+ std::cerr << "Dst: " << demangle_flags(Dst::Flags) << std::endl;
+ std::cerr << " " << demangle_flags(internal::evaluator<Dst>::Flags) << std::endl;
+ traits::debug();
+ std::cerr << " Expected Traversal == " << demangle_traversal(traversal)
+ << " got " << demangle_traversal(traits::Traversal) << "\n";
+ std::cerr << " Expected Unrolling == " << demangle_unrolling(unrolling)
+ << " got " << demangle_unrolling(traits::Unrolling) << "\n";
+ }
+ return res;
+}
+
+template<typename Dst, typename Src>
+bool test_assign(int traversal, int unrolling)
+{
+ EIGEN_STATIC_ASSERT_SAME_MATRIX_SIZE(Dst,Src);
+ typedef internal::copy_using_evaluator_traits<internal::evaluator<Dst>,internal::evaluator<Src>, internal::assign_op<typename Dst::Scalar,typename Src::Scalar> > traits;
+ bool res = traits::Traversal==traversal && traits::Unrolling==unrolling;
+ if(!res)
+ {
+ std::cerr << "Src: " << demangle_flags(Src::Flags) << std::endl;
+ std::cerr << " " << demangle_flags(internal::evaluator<Src>::Flags) << std::endl;
+ std::cerr << "Dst: " << demangle_flags(Dst::Flags) << std::endl;
+ std::cerr << " " << demangle_flags(internal::evaluator<Dst>::Flags) << std::endl;
+ traits::debug();
+ std::cerr << " Expected Traversal == " << demangle_traversal(traversal)
+ << " got " << demangle_traversal(traits::Traversal) << "\n";
+ std::cerr << " Expected Unrolling == " << demangle_unrolling(unrolling)
+ << " got " << demangle_unrolling(traits::Unrolling) << "\n";
+ }
+ return res;
+}
+
+template<typename Xpr>
+bool test_redux(const Xpr&, int traversal, int unrolling)
+{
+ typedef typename Xpr::Scalar Scalar;
+ typedef internal::redux_traits<internal::scalar_sum_op<Scalar,Scalar>,internal::redux_evaluator<Xpr> > traits;
+
+ bool res = traits::Traversal==traversal && traits::Unrolling==unrolling;
+ if(!res)
+ {
+ std::cerr << demangle_flags(Xpr::Flags) << std::endl;
+ std::cerr << demangle_flags(internal::evaluator<Xpr>::Flags) << std::endl;
+ traits::debug();
+
+ std::cerr << " Expected Traversal == " << demangle_traversal(traversal)
+ << " got " << demangle_traversal(traits::Traversal) << "\n";
+ std::cerr << " Expected Unrolling == " << demangle_unrolling(unrolling)
+ << " got " << demangle_unrolling(traits::Unrolling) << "\n";
+ }
+ return res;
+}
+
+template<typename Scalar, bool Enable = internal::packet_traits<Scalar>::Vectorizable>
+struct vectorization_logic
+{
+ typedef internal::packet_traits<Scalar> PacketTraits;
+
+ typedef typename internal::packet_traits<Scalar>::type PacketType;
+ typedef typename internal::unpacket_traits<PacketType>::half HalfPacketType;
+ enum {
+ PacketSize = internal::unpacket_traits<PacketType>::size,
+ HalfPacketSize = internal::unpacket_traits<HalfPacketType>::size
+ };
+ static void run()
+ {
+
+ typedef Matrix<Scalar,PacketSize,1> Vector1;
+ typedef Matrix<Scalar,Dynamic,1> VectorX;
+ typedef Matrix<Scalar,Dynamic,Dynamic> MatrixXX;
+ typedef Matrix<Scalar,PacketSize,PacketSize> Matrix11;
+ typedef Matrix<Scalar,(Matrix11::Flags&RowMajorBit)?8:2*PacketSize,(Matrix11::Flags&RowMajorBit)?2*PacketSize:8> Matrix22;
+ typedef Matrix<Scalar,(Matrix11::Flags&RowMajorBit)?16:4*PacketSize,(Matrix11::Flags&RowMajorBit)?4*PacketSize:16> Matrix44;
+ typedef Matrix<Scalar,(Matrix11::Flags&RowMajorBit)?16:4*PacketSize,(Matrix11::Flags&RowMajorBit)?4*PacketSize:16,DontAlign|EIGEN_DEFAULT_MATRIX_STORAGE_ORDER_OPTION> Matrix44u;
+ typedef Matrix<Scalar,4*PacketSize,4*PacketSize,ColMajor> Matrix44c;
+ typedef Matrix<Scalar,4*PacketSize,4*PacketSize,RowMajor> Matrix44r;
+
+ typedef Matrix<Scalar,
+ (PacketSize==16 ? 8 : PacketSize==8 ? 4 : PacketSize==4 ? 2 : PacketSize==2 ? 1 : /*PacketSize==1 ?*/ 1),
+ (PacketSize==16 ? 2 : PacketSize==8 ? 2 : PacketSize==4 ? 2 : PacketSize==2 ? 2 : /*PacketSize==1 ?*/ 1)
+ > Matrix1;
+
+ typedef Matrix<Scalar,
+ (PacketSize==16 ? 8 : PacketSize==8 ? 4 : PacketSize==4 ? 2 : PacketSize==2 ? 1 : /*PacketSize==1 ?*/ 1),
+ (PacketSize==16 ? 2 : PacketSize==8 ? 2 : PacketSize==4 ? 2 : PacketSize==2 ? 2 : /*PacketSize==1 ?*/ 1),
+ DontAlign|((Matrix1::Flags&RowMajorBit)?RowMajor:ColMajor)> Matrix1u;
+
+ // this type is made such that it can only be vectorized when viewed as a linear 1D vector
+ typedef Matrix<Scalar,
+ (PacketSize==16 ? 4 : PacketSize==8 ? 4 : PacketSize==4 ? 6 : PacketSize==2 ? ((Matrix11::Flags&RowMajorBit)?2:3) : /*PacketSize==1 ?*/ 1),
+ (PacketSize==16 ? 12 : PacketSize==8 ? 6 : PacketSize==4 ? 2 : PacketSize==2 ? ((Matrix11::Flags&RowMajorBit)?3:2) : /*PacketSize==1 ?*/ 3)
+ > Matrix3;
+
+ #if !EIGEN_GCC_AND_ARCH_DOESNT_WANT_STACK_ALIGNMENT
+ VERIFY(test_assign(Vector1(),Vector1(),
+ InnerVectorizedTraversal,CompleteUnrolling));
+ VERIFY(test_assign(Vector1(),Vector1()+Vector1(),
+ InnerVectorizedTraversal,CompleteUnrolling));
+ VERIFY(test_assign(Vector1(),Vector1().cwiseProduct(Vector1()),
+ InnerVectorizedTraversal,CompleteUnrolling));
+ VERIFY(test_assign(Vector1(),Vector1().template cast<Scalar>(),
+ InnerVectorizedTraversal,CompleteUnrolling));
+
+ VERIFY(test_assign(Matrix44(),Matrix44()+Matrix44(),
+ InnerVectorizedTraversal,InnerUnrolling));
+
+ VERIFY(test_assign(Matrix44u(),Matrix44()+Matrix44(),
+ EIGEN_UNALIGNED_VECTORIZE ? InnerVectorizedTraversal : LinearTraversal,
+ EIGEN_UNALIGNED_VECTORIZE ? InnerUnrolling : NoUnrolling));
+
+ VERIFY(test_assign(Matrix1(),Matrix1()+Matrix1(),
+ (int(Matrix1::InnerSizeAtCompileTime) % int(PacketSize))==0 ? InnerVectorizedTraversal : LinearVectorizedTraversal,
+ CompleteUnrolling));
+
+ VERIFY(test_assign(Matrix1u(),Matrix1()+Matrix1(),
+ EIGEN_UNALIGNED_VECTORIZE ? ((int(Matrix1::InnerSizeAtCompileTime) % int(PacketSize))==0 ? InnerVectorizedTraversal : LinearVectorizedTraversal)
+ : LinearTraversal, CompleteUnrolling));
+
+ VERIFY(test_assign(Matrix44c().col(1),Matrix44c().col(2)+Matrix44c().col(3),
+ InnerVectorizedTraversal,CompleteUnrolling));
+
+ VERIFY(test_assign(Matrix44r().row(2),Matrix44r().row(1)+Matrix44r().row(1),
+ InnerVectorizedTraversal,CompleteUnrolling));
+
+ if(PacketSize>1)
+ {
+ typedef Matrix<Scalar,3,3,ColMajor> Matrix33c;
+ typedef Matrix<Scalar,3,1,ColMajor> Vector3;
+ VERIFY(test_assign(Matrix33c().row(2),Matrix33c().row(1)+Matrix33c().row(1),
+ LinearTraversal,CompleteUnrolling));
+ // Vectorization depends on too many factors - ignore.
+ VERIFY(test_assign(Vector3(),Vector3()+Vector3(), -1, CompleteUnrolling));
+
+ VERIFY(test_assign(Matrix3(),Matrix3().cwiseProduct(Matrix3()),
+ LinearVectorizedTraversal,CompleteUnrolling));
+
+ // Vectorization depends on too many factors - ignore.
+ VERIFY(test_assign(Matrix<Scalar,17,17>(),Matrix<Scalar,17,17>()+Matrix<Scalar,17,17>(),
+ -1, NoUnrolling));
+
+ VERIFY(test_assign(Matrix11(), Matrix11()+Matrix11(),InnerVectorizedTraversal,CompleteUnrolling));
+
+
+ VERIFY(test_assign(Matrix11(),Matrix<Scalar,21,21>().template block<PacketSize,PacketSize>(2,3)+Matrix<Scalar,21,21>().template block<PacketSize,PacketSize>(3,2),
+ (EIGEN_UNALIGNED_VECTORIZE) ? InnerVectorizedTraversal : DefaultTraversal, CompleteUnrolling|InnerUnrolling));
+
+ VERIFY(test_assign(Vector1(),Matrix11()*Vector1(),
+ InnerVectorizedTraversal,CompleteUnrolling));
+
+ VERIFY(test_assign(Matrix11(),Matrix11().lazyProduct(Matrix11()),
+ InnerVectorizedTraversal,InnerUnrolling+CompleteUnrolling));
+ }
+
+ VERIFY(test_redux(Vector1(),
+ LinearVectorizedTraversal,CompleteUnrolling));
+
+ VERIFY(test_redux(Vector1().array()*Vector1().array(),
+ LinearVectorizedTraversal,CompleteUnrolling));
+
+ VERIFY(test_redux((Vector1().array()*Vector1().array()).col(0),
+ LinearVectorizedTraversal,CompleteUnrolling));
+
+ VERIFY(test_redux(Matrix<Scalar,PacketSize,3>(),
+ LinearVectorizedTraversal,CompleteUnrolling));
+
+ VERIFY(test_redux(Matrix3(),
+ LinearVectorizedTraversal,CompleteUnrolling));
+
+ VERIFY(test_redux(Matrix44(),
+ LinearVectorizedTraversal,NoUnrolling));
+
+ if(PacketSize>1) {
+ VERIFY(test_redux(Matrix44().template block<(Matrix1::Flags&RowMajorBit)?4:PacketSize,(Matrix1::Flags&RowMajorBit)?PacketSize:4>(1,2),
+ SliceVectorizedTraversal,CompleteUnrolling));
+
+ VERIFY(test_redux(Matrix44().template block<(Matrix1::Flags&RowMajorBit)?2:PacketSize,(Matrix1::Flags&RowMajorBit)?PacketSize:2>(1,2),
+ DefaultTraversal,CompleteUnrolling));
+ }
+
+ VERIFY(test_redux(Matrix44c().template block<2*PacketSize,1>(1,2),
+ LinearVectorizedTraversal,CompleteUnrolling));
+
+ VERIFY(test_redux(Matrix44r().template block<1,2*PacketSize>(2,1),
+ LinearVectorizedTraversal,CompleteUnrolling));
+
+ VERIFY((test_assign<
+ Map<Matrix22, AlignedMax, OuterStride<3*PacketSize> >,
+ Matrix22
+ >(InnerVectorizedTraversal,CompleteUnrolling)));
+
+ VERIFY((test_assign<
+ Map<Matrix<Scalar, internal::plain_enum_max(2,PacketSize), internal::plain_enum_max(2, PacketSize)>, AlignedMax, InnerStride<3*PacketSize> >,
+ Matrix<Scalar, internal::plain_enum_max(2, PacketSize), internal::plain_enum_max(2, PacketSize)>
+ >(DefaultTraversal,PacketSize>=8?InnerUnrolling:CompleteUnrolling)));
+
+ VERIFY((test_assign(Matrix11(), Matrix<Scalar,PacketSize, internal::plain_enum_min(2, PacketSize)>()*Matrix<Scalar, internal::plain_enum_min(2, PacketSize),PacketSize>(),
+ InnerVectorizedTraversal, CompleteUnrolling)));
+ #endif
+
+ VERIFY(test_assign(MatrixXX(10,10),MatrixXX(20,20).block(10,10,2,3),
+ SliceVectorizedTraversal,NoUnrolling));
+
+ VERIFY(test_redux(VectorX(10),
+ LinearVectorizedTraversal,NoUnrolling));
+ }
+};
+
+template<typename Scalar> struct vectorization_logic<Scalar,false>
+{
+ static void run() {}
+};
+
+template<typename Scalar, bool Enable = !internal::is_same<typename internal::unpacket_traits<typename internal::packet_traits<Scalar>::type>::half,
+ typename internal::packet_traits<Scalar>::type>::value >
+struct vectorization_logic_half
+{
+ typedef internal::packet_traits<Scalar> PacketTraits;
+ typedef typename internal::unpacket_traits<typename internal::packet_traits<Scalar>::type>::half PacketType;
+ enum {
+ PacketSize = internal::unpacket_traits<PacketType>::size
+ };
+ static void run()
+ {
+ // Some half-packets have a byte size < EIGEN_MIN_ALIGN_BYTES (e.g. Packet2f),
+ // which causes many of these tests to fail since they don't vectorize if
+ // EIGEN_UNALIGNED_VECTORIZE is 0 (the matrix is assumed unaligned).
+ // Adjust the matrix sizes to account for these alignment issues.
+ constexpr int PacketBytes = sizeof(Scalar)*PacketSize;
+ constexpr int MinVSize = EIGEN_UNALIGNED_VECTORIZE ? PacketSize
+ : PacketBytes >= EIGEN_MIN_ALIGN_BYTES ? PacketSize
+ : (EIGEN_MIN_ALIGN_BYTES + sizeof(Scalar) - 1) / sizeof(Scalar);
+
+ typedef Matrix<Scalar,MinVSize,1> Vector1;
+ typedef Matrix<Scalar,MinVSize,MinVSize> Matrix11;
+ typedef Matrix<Scalar,5*MinVSize,7,ColMajor> Matrix57;
+ typedef Matrix<Scalar,3*MinVSize,5,ColMajor> Matrix35;
+ typedef Matrix<Scalar,5*MinVSize,7,DontAlign|ColMajor> Matrix57u;
+
+ typedef Matrix<Scalar,
+ (PacketSize==16 ? 8 : PacketSize==8 ? 4 : PacketSize==4 ? 2 : PacketSize==2 ? 1 : /*PacketSize==1 ?*/ 1),
+ (PacketSize==16 ? 2 : PacketSize==8 ? 2 : PacketSize==4 ? 2 : PacketSize==2 ? 2 : /*PacketSize==1 ?*/ 1)
+ > Matrix1;
+
+ typedef Matrix<Scalar,
+ (PacketSize==16 ? 8 : PacketSize==8 ? 4 : PacketSize==4 ? 2 : PacketSize==2 ? 1 : /*PacketSize==1 ?*/ 1),
+ (PacketSize==16 ? 2 : PacketSize==8 ? 2 : PacketSize==4 ? 2 : PacketSize==2 ? 2 : /*PacketSize==1 ?*/ 1),
+ DontAlign|((Matrix1::Flags&RowMajorBit)?RowMajor:ColMajor)> Matrix1u;
+
+ // this type is made such that it can only be vectorized when viewed as a linear 1D vector
+ typedef Matrix<Scalar,
+ (MinVSize==16 ? 4 : MinVSize==8 ? 4 : MinVSize==4 ? 6 : MinVSize==2 ? ((Matrix11::Flags&RowMajorBit)?2:3) : /*PacketSize==1 ?*/ 1),
+ (MinVSize==16 ? 12 : MinVSize==8 ? 6 : MinVSize==4 ? 2 : MinVSize==2 ? ((Matrix11::Flags&RowMajorBit)?3:2) : /*PacketSize==1 ?*/ 3)
+ > Matrix3;
+
+#if !EIGEN_GCC_AND_ARCH_DOESNT_WANT_STACK_ALIGNMENT
+ VERIFY(test_assign(Vector1(),Vector1(),
+ InnerVectorizedTraversal,CompleteUnrolling));
+ VERIFY(test_assign(Vector1(),Vector1()+Vector1(),
+ InnerVectorizedTraversal,CompleteUnrolling));
+ VERIFY(test_assign(Vector1(),Vector1().template segment<MinVSize>(0).derived(),
+ EIGEN_UNALIGNED_VECTORIZE ? InnerVectorizedTraversal : LinearVectorizedTraversal,CompleteUnrolling));
+ VERIFY(test_assign(Vector1(),Scalar(2.1)*Vector1()-Vector1(),
+ InnerVectorizedTraversal,CompleteUnrolling));
+ VERIFY(test_assign(Vector1(),(Scalar(2.1)*Vector1().template segment<MinVSize>(0)-Vector1().template segment<MinVSize>(0)).derived(),
+ EIGEN_UNALIGNED_VECTORIZE ? InnerVectorizedTraversal : LinearVectorizedTraversal,CompleteUnrolling));
+ VERIFY(test_assign(Vector1(),Vector1().cwiseProduct(Vector1()),
+ InnerVectorizedTraversal,CompleteUnrolling));
+ VERIFY(test_assign(Vector1(),Vector1().template cast<Scalar>(),
+ InnerVectorizedTraversal,CompleteUnrolling));
+
+ VERIFY(test_assign(Matrix57(),Matrix57()+Matrix57(),
+ InnerVectorizedTraversal,InnerUnrolling));
+
+ VERIFY(test_assign(Matrix57u(),Matrix57()+Matrix57(),
+ EIGEN_UNALIGNED_VECTORIZE ? InnerVectorizedTraversal : LinearTraversal,
+ EIGEN_UNALIGNED_VECTORIZE ? InnerUnrolling : NoUnrolling));
+
+ VERIFY(test_assign(Matrix1u(),Matrix1()+Matrix1(),
+ EIGEN_UNALIGNED_VECTORIZE ? ((int(Matrix1::InnerSizeAtCompileTime) % int(PacketSize))==0 ? InnerVectorizedTraversal : LinearVectorizedTraversal) : LinearTraversal,CompleteUnrolling));
+
+ if(PacketSize>1)
+ {
+ typedef Matrix<Scalar,3,3,ColMajor> Matrix33c;
+ VERIFY(test_assign(Matrix33c().row(2),Matrix33c().row(1)+Matrix33c().row(1),
+ LinearTraversal,CompleteUnrolling));
+
+ // Unrolling depends on read costs and unroll limits, which vary - ignore.
+ VERIFY(test_assign(Matrix3(),Matrix3().cwiseQuotient(Matrix3()),
+ PacketTraits::HasDiv ? LinearVectorizedTraversal : LinearTraversal, -1));
+
+ VERIFY(test_assign(Matrix<Scalar,17,17>(),Matrix<Scalar,17,17>()+Matrix<Scalar,17,17>(),
+ sizeof(Scalar)==16 ? InnerVectorizedTraversal : (EIGEN_UNALIGNED_VECTORIZE ? LinearVectorizedTraversal : LinearTraversal),
+ NoUnrolling));
+
+ VERIFY(test_assign(Matrix11(),Matrix<Scalar,17,17>().template block<MinVSize,MinVSize>(2,3)+Matrix<Scalar,17,17>().template block<MinVSize,MinVSize>(8,4),
+ EIGEN_UNALIGNED_VECTORIZE ? InnerVectorizedTraversal : DefaultTraversal,InnerUnrolling+CompleteUnrolling));
+
+
+ VERIFY(test_assign(Vector1(),Matrix11()*Vector1(),
+ InnerVectorizedTraversal,CompleteUnrolling));
+
+ VERIFY(test_assign(Matrix11(),Matrix11().lazyProduct(Matrix11()),
+ InnerVectorizedTraversal,InnerUnrolling+CompleteUnrolling));
+ }
+
+ VERIFY(test_redux(Vector1(),
+ LinearVectorizedTraversal,CompleteUnrolling));
+
+ VERIFY(test_redux(Matrix<Scalar,MinVSize,3>(),
+ LinearVectorizedTraversal,CompleteUnrolling));
+
+ VERIFY(test_redux(Matrix3(),
+ LinearVectorizedTraversal,CompleteUnrolling));
+
+ VERIFY(test_redux(Matrix35(),
+ LinearVectorizedTraversal,CompleteUnrolling));
+
+ VERIFY(test_redux(Matrix57().template block<PacketSize==1?2:PacketSize,3>(1,0),
+ SliceVectorizedTraversal,CompleteUnrolling));
+
+ if(PacketSize>1) {
+ VERIFY(test_redux(Matrix57().template block<PacketSize,2>(1,0),
+ DefaultTraversal,CompleteUnrolling));
+ }
+
+ VERIFY((test_assign<
+ Map<Matrix<Scalar, internal::plain_enum_max(2, PacketSize), internal::plain_enum_max(2, PacketSize)>,
+ AlignedMax, InnerStride<3 * PacketSize> >,
+ Matrix<Scalar, internal::plain_enum_max(2, PacketSize), internal::plain_enum_max(2, PacketSize)> >(
+ DefaultTraversal, PacketSize > 4 ? InnerUnrolling : CompleteUnrolling)));
+
+ VERIFY((test_assign(Matrix57(), Matrix<Scalar, 5 * MinVSize, 3>() * Matrix<Scalar, 3, 7>(),
+ InnerVectorizedTraversal, InnerUnrolling + CompleteUnrolling)));
+#endif
+ }
+};
+
+template<typename Scalar> struct vectorization_logic_half<Scalar,false>
+{
+ static void run() {}
+};
+
+EIGEN_DECLARE_TEST(vectorization_logic)
+{
+
+#ifdef EIGEN_VECTORIZE
+
+ CALL_SUBTEST( vectorization_logic<int>::run() );
+ CALL_SUBTEST( vectorization_logic<float>::run() );
+ CALL_SUBTEST( vectorization_logic<double>::run() );
+ CALL_SUBTEST( vectorization_logic<std::complex<float> >::run() );
+ CALL_SUBTEST( vectorization_logic<std::complex<double> >::run() );
+
+ CALL_SUBTEST( vectorization_logic_half<int>::run() );
+ CALL_SUBTEST( vectorization_logic_half<float>::run() );
+ CALL_SUBTEST( vectorization_logic_half<double>::run() );
+ CALL_SUBTEST( vectorization_logic_half<std::complex<float> >::run() );
+ CALL_SUBTEST( vectorization_logic_half<std::complex<double> >::run() );
+
+ if(internal::packet_traits<float>::Vectorizable)
+ {
+ VERIFY(test_assign(Matrix<float,3,3>(),Matrix<float,3,3>()+Matrix<float,3,3>(),
+ EIGEN_UNALIGNED_VECTORIZE ? LinearVectorizedTraversal : LinearTraversal,CompleteUnrolling));
+
+ VERIFY(test_redux(Matrix<float,5,2>(),
+ EIGEN_UNALIGNED_VECTORIZE ? LinearVectorizedTraversal : DefaultTraversal,CompleteUnrolling));
+ }
+
+ if(internal::packet_traits<double>::Vectorizable)
+ {
+ VERIFY(test_assign(Matrix<double,3,3>(),Matrix<double,3,3>()+Matrix<double,3,3>(),
+ EIGEN_UNALIGNED_VECTORIZE ? LinearVectorizedTraversal : LinearTraversal,CompleteUnrolling));
+
+ VERIFY(test_redux(Matrix<double,7,3>(),
+ EIGEN_UNALIGNED_VECTORIZE ? LinearVectorizedTraversal : DefaultTraversal,CompleteUnrolling));
+ }
+#endif // EIGEN_VECTORIZE
+
+}
diff --git a/test/vectorwiseop.cpp b/test/vectorwiseop.cpp
new file mode 100644
index 0000000..4369789
--- /dev/null
+++ b/test/vectorwiseop.cpp
@@ -0,0 +1,238 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2011 Benoit Jacob <jacob.benoit.1@gmail.com>
+// Copyright (C) 2015 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#define TEST_ENABLE_TEMPORARY_TRACKING
+
+#include "main.h"
+
+template<typename ArrayType> void vectorwiseop_array(const ArrayType& m)
+{
+ typedef typename ArrayType::Scalar Scalar;
+ typedef Array<Scalar, ArrayType::RowsAtCompileTime, 1> ColVectorType;
+ typedef Array<Scalar, 1, ArrayType::ColsAtCompileTime> RowVectorType;
+
+ Index rows = m.rows();
+ Index cols = m.cols();
+ Index r = internal::random<Index>(0, rows-1),
+ c = internal::random<Index>(0, cols-1);
+
+ ArrayType m1 = ArrayType::Random(rows, cols),
+ m2(rows, cols),
+ m3(rows, cols);
+
+ ColVectorType colvec = ColVectorType::Random(rows);
+ RowVectorType rowvec = RowVectorType::Random(cols);
+
+ // test addition
+ m2 = m1;
+ m2.colwise() += colvec;
+ VERIFY_IS_APPROX(m2, m1.colwise() + colvec);
+ VERIFY_IS_APPROX(m2.col(c), m1.col(c) + colvec);
+
+ m2 = m1;
+ m2.rowwise() += rowvec;
+ VERIFY_IS_APPROX(m2, m1.rowwise() + rowvec);
+ VERIFY_IS_APPROX(m2.row(r), m1.row(r) + rowvec);
+
+ // test subtraction
+ m2 = m1;
+ m2.colwise() -= colvec;
+ VERIFY_IS_APPROX(m2, m1.colwise() - colvec);
+ VERIFY_IS_APPROX(m2.col(c), m1.col(c) - colvec);
+
+ m2 = m1;
+ m2.rowwise() -= rowvec;
+ VERIFY_IS_APPROX(m2, m1.rowwise() - rowvec);
+ VERIFY_IS_APPROX(m2.row(r), m1.row(r) - rowvec);
+
+ // test multiplication
+ m2 = m1;
+ m2.colwise() *= colvec;
+ VERIFY_IS_APPROX(m2, m1.colwise() * colvec);
+ VERIFY_IS_APPROX(m2.col(c), m1.col(c) * colvec);
+
+ m2 = m1;
+ m2.rowwise() *= rowvec;
+ VERIFY_IS_APPROX(m2, m1.rowwise() * rowvec);
+ VERIFY_IS_APPROX(m2.row(r), m1.row(r) * rowvec);
+
+ // test quotient
+ m2 = m1;
+ m2.colwise() /= colvec;
+ VERIFY_IS_APPROX(m2, m1.colwise() / colvec);
+ VERIFY_IS_APPROX(m2.col(c), m1.col(c) / colvec);
+
+ m2 = m1;
+ m2.rowwise() /= rowvec;
+ VERIFY_IS_APPROX(m2, m1.rowwise() / rowvec);
+ VERIFY_IS_APPROX(m2.row(r), m1.row(r) / rowvec);
+
+ m2 = m1;
+ // yes, there might be an aliasing issue there but ".rowwise() /="
+ // is supposed to evaluate " m2.colwise().sum()" into a temporary to avoid
+ // evaluating the reduction multiple times
+ if(ArrayType::RowsAtCompileTime>2 || ArrayType::RowsAtCompileTime==Dynamic)
+ {
+ m2.rowwise() /= m2.colwise().sum();
+ VERIFY_IS_APPROX(m2, m1.rowwise() / m1.colwise().sum());
+ }
+
+ // all/any
+ Array<bool,Dynamic,Dynamic> mb(rows,cols);
+ mb = (m1.real()<=0.7).colwise().all();
+ VERIFY( (mb.col(c) == (m1.real().col(c)<=0.7).all()).all() );
+ mb = (m1.real()<=0.7).rowwise().all();
+ VERIFY( (mb.row(r) == (m1.real().row(r)<=0.7).all()).all() );
+
+ mb = (m1.real()>=0.7).colwise().any();
+ VERIFY( (mb.col(c) == (m1.real().col(c)>=0.7).any()).all() );
+ mb = (m1.real()>=0.7).rowwise().any();
+ VERIFY( (mb.row(r) == (m1.real().row(r)>=0.7).any()).all() );
+}
+
+template<typename MatrixType> void vectorwiseop_matrix(const MatrixType& m)
+{
+ typedef typename MatrixType::Scalar Scalar;
+ typedef typename NumTraits<Scalar>::Real RealScalar;
+ typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> ColVectorType;
+ typedef Matrix<Scalar, 1, MatrixType::ColsAtCompileTime> RowVectorType;
+ typedef Matrix<RealScalar, MatrixType::RowsAtCompileTime, 1> RealColVectorType;
+ typedef Matrix<RealScalar, 1, MatrixType::ColsAtCompileTime> RealRowVectorType;
+ typedef Matrix<Scalar,Dynamic,Dynamic> MatrixX;
+
+ Index rows = m.rows();
+ Index cols = m.cols();
+ Index r = internal::random<Index>(0, rows-1),
+ c = internal::random<Index>(0, cols-1);
+
+ MatrixType m1 = MatrixType::Random(rows, cols),
+ m2(rows, cols),
+ m3(rows, cols);
+
+ ColVectorType colvec = ColVectorType::Random(rows);
+ RowVectorType rowvec = RowVectorType::Random(cols);
+ RealColVectorType rcres;
+ RealRowVectorType rrres;
+
+ // test broadcast assignment
+ m2 = m1;
+ m2.colwise() = colvec;
+ for(Index j=0; j<cols; ++j)
+ VERIFY_IS_APPROX(m2.col(j), colvec);
+ m2.rowwise() = rowvec;
+ for(Index i=0; i<rows; ++i)
+ VERIFY_IS_APPROX(m2.row(i), rowvec);
+
+ // test addition
+ m2 = m1;
+ m2.colwise() += colvec;
+ VERIFY_IS_APPROX(m2, m1.colwise() + colvec);
+ VERIFY_IS_APPROX(m2.col(c), m1.col(c) + colvec);
+
+ m2 = m1;
+ m2.rowwise() += rowvec;
+ VERIFY_IS_APPROX(m2, m1.rowwise() + rowvec);
+ VERIFY_IS_APPROX(m2.row(r), m1.row(r) + rowvec);
+
+
+ // test subtraction
+ m2 = m1;
+ m2.colwise() -= colvec;
+ VERIFY_IS_APPROX(m2, m1.colwise() - colvec);
+ VERIFY_IS_APPROX(m2.col(c), m1.col(c) - colvec);
+
+ m2 = m1;
+ m2.rowwise() -= rowvec;
+ VERIFY_IS_APPROX(m2, m1.rowwise() - rowvec);
+ VERIFY_IS_APPROX(m2.row(r), m1.row(r) - rowvec);
+
+
+ // ------ partial reductions ------
+
+ #define TEST_PARTIAL_REDUX_BASIC(FUNC,ROW,COL,PREPROCESS) { \
+ ROW = m1 PREPROCESS .colwise().FUNC ; \
+ for(Index k=0; k<cols; ++k) VERIFY_IS_APPROX(ROW(k), m1.col(k) PREPROCESS .FUNC ); \
+ COL = m1 PREPROCESS .rowwise().FUNC ; \
+ for(Index k=0; k<rows; ++k) VERIFY_IS_APPROX(COL(k), m1.row(k) PREPROCESS .FUNC ); \
+ }
+
+ TEST_PARTIAL_REDUX_BASIC(sum(), rowvec,colvec,EIGEN_EMPTY);
+ TEST_PARTIAL_REDUX_BASIC(prod(), rowvec,colvec,EIGEN_EMPTY);
+ TEST_PARTIAL_REDUX_BASIC(mean(), rowvec,colvec,EIGEN_EMPTY);
+ TEST_PARTIAL_REDUX_BASIC(minCoeff(), rrres, rcres, .real());
+ TEST_PARTIAL_REDUX_BASIC(maxCoeff(), rrres, rcres, .real());
+ TEST_PARTIAL_REDUX_BASIC(norm(), rrres, rcres, EIGEN_EMPTY);
+ TEST_PARTIAL_REDUX_BASIC(squaredNorm(),rrres, rcres, EIGEN_EMPTY);
+ TEST_PARTIAL_REDUX_BASIC(redux(internal::scalar_sum_op<Scalar,Scalar>()),rowvec,colvec,EIGEN_EMPTY);
+
+ VERIFY_IS_APPROX(m1.cwiseAbs().colwise().sum(), m1.colwise().template lpNorm<1>());
+ VERIFY_IS_APPROX(m1.cwiseAbs().rowwise().sum(), m1.rowwise().template lpNorm<1>());
+ VERIFY_IS_APPROX(m1.cwiseAbs().colwise().maxCoeff(), m1.colwise().template lpNorm<Infinity>());
+ VERIFY_IS_APPROX(m1.cwiseAbs().rowwise().maxCoeff(), m1.rowwise().template lpNorm<Infinity>());
+
+ // regression for bug 1158
+ VERIFY_IS_APPROX(m1.cwiseAbs().colwise().sum().x(), m1.col(0).cwiseAbs().sum());
+
+ // test normalized
+ m2 = m1.colwise().normalized();
+ VERIFY_IS_APPROX(m2.col(c), m1.col(c).normalized());
+ m2 = m1.rowwise().normalized();
+ VERIFY_IS_APPROX(m2.row(r), m1.row(r).normalized());
+
+ // test normalize
+ m2 = m1;
+ m2.colwise().normalize();
+ VERIFY_IS_APPROX(m2.col(c), m1.col(c).normalized());
+ m2 = m1;
+ m2.rowwise().normalize();
+ VERIFY_IS_APPROX(m2.row(r), m1.row(r).normalized());
+
+ // test with partial reduction of products
+ Matrix<Scalar,MatrixType::RowsAtCompileTime,MatrixType::RowsAtCompileTime> m1m1 = m1 * m1.transpose();
+ VERIFY_IS_APPROX( (m1 * m1.transpose()).colwise().sum(), m1m1.colwise().sum());
+ Matrix<Scalar,1,MatrixType::RowsAtCompileTime> tmp(rows);
+ VERIFY_EVALUATION_COUNT( tmp = (m1 * m1.transpose()).colwise().sum(), 1);
+
+ m2 = m1.rowwise() - (m1.colwise().sum()/RealScalar(m1.rows())).eval();
+ m1 = m1.rowwise() - (m1.colwise().sum()/RealScalar(m1.rows()));
+ VERIFY_IS_APPROX( m1, m2 );
+ VERIFY_EVALUATION_COUNT( m2 = (m1.rowwise() - m1.colwise().sum()/RealScalar(m1.rows())), (MatrixType::RowsAtCompileTime!=1 ? 1 : 0) );
+
+ // test empty expressions
+ VERIFY_IS_APPROX(m1.matrix().middleCols(0,0).rowwise().sum().eval(), MatrixX::Zero(rows,1));
+ VERIFY_IS_APPROX(m1.matrix().middleRows(0,0).colwise().sum().eval(), MatrixX::Zero(1,cols));
+ VERIFY_IS_APPROX(m1.matrix().middleCols(0,fix<0>).rowwise().sum().eval(), MatrixX::Zero(rows,1));
+ VERIFY_IS_APPROX(m1.matrix().middleRows(0,fix<0>).colwise().sum().eval(), MatrixX::Zero(1,cols));
+
+ VERIFY_IS_APPROX(m1.matrix().middleCols(0,0).rowwise().prod().eval(), MatrixX::Ones(rows,1));
+ VERIFY_IS_APPROX(m1.matrix().middleRows(0,0).colwise().prod().eval(), MatrixX::Ones(1,cols));
+ VERIFY_IS_APPROX(m1.matrix().middleCols(0,fix<0>).rowwise().prod().eval(), MatrixX::Ones(rows,1));
+ VERIFY_IS_APPROX(m1.matrix().middleRows(0,fix<0>).colwise().prod().eval(), MatrixX::Ones(1,cols));
+ VERIFY_IS_APPROX(m1.matrix().middleCols(0,0).rowwise().squaredNorm().eval(), MatrixX::Zero(rows,1));
+
+ VERIFY_IS_EQUAL(m1.real().middleRows(0,0).rowwise().maxCoeff().eval().rows(),0);
+ VERIFY_IS_EQUAL(m1.real().middleCols(0,0).colwise().maxCoeff().eval().cols(),0);
+ VERIFY_IS_EQUAL(m1.real().middleRows(0,fix<0>).rowwise().maxCoeff().eval().rows(),0);
+ VERIFY_IS_EQUAL(m1.real().middleCols(0,fix<0>).colwise().maxCoeff().eval().cols(),0);
+}
+
+EIGEN_DECLARE_TEST(vectorwiseop)
+{
+ CALL_SUBTEST_1( vectorwiseop_array(Array22cd()) );
+ CALL_SUBTEST_2( vectorwiseop_array(Array<double, 3, 2>()) );
+ CALL_SUBTEST_3( vectorwiseop_array(ArrayXXf(3, 4)) );
+ CALL_SUBTEST_4( vectorwiseop_matrix(Matrix4cf()) );
+ CALL_SUBTEST_5( vectorwiseop_matrix(Matrix4f()) );
+ CALL_SUBTEST_5( vectorwiseop_matrix(Vector4f()) );
+ CALL_SUBTEST_5( vectorwiseop_matrix(Matrix<float,4,5>()) );
+ CALL_SUBTEST_6( vectorwiseop_matrix(MatrixXd(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
+ CALL_SUBTEST_7( vectorwiseop_matrix(VectorXd(internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
+ CALL_SUBTEST_7( vectorwiseop_matrix(RowVectorXd(internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
+}
diff --git a/test/visitor.cpp b/test/visitor.cpp
new file mode 100644
index 0000000..3b118f9
--- /dev/null
+++ b/test/visitor.cpp
@@ -0,0 +1,339 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "main.h"
+
+template<typename MatrixType> void matrixVisitor(const MatrixType& p)
+{
+ typedef typename MatrixType::Scalar Scalar;
+
+ Index rows = p.rows();
+ Index cols = p.cols();
+
+ // construct a random matrix where all coefficients are different
+ MatrixType m;
+ m = MatrixType::Random(rows, cols);
+ for(Index i = 0; i < m.size(); i++)
+ for(Index i2 = 0; i2 < i; i2++)
+ while(numext::equal_strict(m(i), m(i2))) // yes, strict equality
+ m(i) = internal::random<Scalar>();
+
+ Scalar minc = Scalar(1000), maxc = Scalar(-1000);
+ Index minrow=0,mincol=0,maxrow=0,maxcol=0;
+ for(Index j = 0; j < cols; j++)
+ for(Index i = 0; i < rows; i++)
+ {
+ if(m(i,j) < minc)
+ {
+ minc = m(i,j);
+ minrow = i;
+ mincol = j;
+ }
+ if(m(i,j) > maxc)
+ {
+ maxc = m(i,j);
+ maxrow = i;
+ maxcol = j;
+ }
+ }
+ Index eigen_minrow, eigen_mincol, eigen_maxrow, eigen_maxcol;
+ Scalar eigen_minc, eigen_maxc;
+ eigen_minc = m.minCoeff(&eigen_minrow,&eigen_mincol);
+ eigen_maxc = m.maxCoeff(&eigen_maxrow,&eigen_maxcol);
+ VERIFY(minrow == eigen_minrow);
+ VERIFY(maxrow == eigen_maxrow);
+ VERIFY(mincol == eigen_mincol);
+ VERIFY(maxcol == eigen_maxcol);
+ VERIFY_IS_APPROX(minc, eigen_minc);
+ VERIFY_IS_APPROX(maxc, eigen_maxc);
+ VERIFY_IS_APPROX(minc, m.minCoeff());
+ VERIFY_IS_APPROX(maxc, m.maxCoeff());
+
+ eigen_maxc = (m.adjoint()*m).maxCoeff(&eigen_maxrow,&eigen_maxcol);
+ Index maxrow2=0,maxcol2=0;
+ eigen_maxc = (m.adjoint()*m).eval().maxCoeff(&maxrow2,&maxcol2);
+ VERIFY(maxrow2 == eigen_maxrow);
+ VERIFY(maxcol2 == eigen_maxcol);
+
+ if (!NumTraits<Scalar>::IsInteger && m.size() > 2) {
+ // Test NaN propagation by replacing an element with NaN.
+ bool stop = false;
+ for (Index j = 0; j < cols && !stop; ++j) {
+ for (Index i = 0; i < rows && !stop; ++i) {
+ if (!(j == mincol && i == minrow) &&
+ !(j == maxcol && i == maxrow)) {
+ m(i,j) = NumTraits<Scalar>::quiet_NaN();
+ stop = true;
+ break;
+ }
+ }
+ }
+
+ eigen_minc = m.template minCoeff<PropagateNumbers>(&eigen_minrow, &eigen_mincol);
+ eigen_maxc = m.template maxCoeff<PropagateNumbers>(&eigen_maxrow, &eigen_maxcol);
+ VERIFY(minrow == eigen_minrow);
+ VERIFY(maxrow == eigen_maxrow);
+ VERIFY(mincol == eigen_mincol);
+ VERIFY(maxcol == eigen_maxcol);
+ VERIFY_IS_APPROX(minc, eigen_minc);
+ VERIFY_IS_APPROX(maxc, eigen_maxc);
+ VERIFY_IS_APPROX(minc, m.template minCoeff<PropagateNumbers>());
+ VERIFY_IS_APPROX(maxc, m.template maxCoeff<PropagateNumbers>());
+
+ eigen_minc = m.template minCoeff<PropagateNaN>(&eigen_minrow, &eigen_mincol);
+ eigen_maxc = m.template maxCoeff<PropagateNaN>(&eigen_maxrow, &eigen_maxcol);
+ VERIFY(minrow != eigen_minrow || mincol != eigen_mincol);
+ VERIFY(maxrow != eigen_maxrow || maxcol != eigen_maxcol);
+ VERIFY((numext::isnan)(eigen_minc));
+ VERIFY((numext::isnan)(eigen_maxc));
+ }
+
+}
+
+template<typename VectorType> void vectorVisitor(const VectorType& w)
+{
+ typedef typename VectorType::Scalar Scalar;
+
+ Index size = w.size();
+
+ // construct a random vector where all coefficients are different
+ VectorType v;
+ v = VectorType::Random(size);
+ for(Index i = 0; i < size; i++)
+ for(Index i2 = 0; i2 < i; i2++)
+ while(v(i) == v(i2)) // yes, ==
+ v(i) = internal::random<Scalar>();
+
+ Scalar minc = v(0), maxc = v(0);
+ Index minidx=0, maxidx=0;
+ for(Index i = 0; i < size; i++)
+ {
+ if(v(i) < minc)
+ {
+ minc = v(i);
+ minidx = i;
+ }
+ if(v(i) > maxc)
+ {
+ maxc = v(i);
+ maxidx = i;
+ }
+ }
+ Index eigen_minidx, eigen_maxidx;
+ Scalar eigen_minc, eigen_maxc;
+ eigen_minc = v.minCoeff(&eigen_minidx);
+ eigen_maxc = v.maxCoeff(&eigen_maxidx);
+ VERIFY(minidx == eigen_minidx);
+ VERIFY(maxidx == eigen_maxidx);
+ VERIFY_IS_APPROX(minc, eigen_minc);
+ VERIFY_IS_APPROX(maxc, eigen_maxc);
+ VERIFY_IS_APPROX(minc, v.minCoeff());
+ VERIFY_IS_APPROX(maxc, v.maxCoeff());
+
+ Index idx0 = internal::random<Index>(0,size-1);
+ Index idx1 = eigen_minidx;
+ Index idx2 = eigen_maxidx;
+ VectorType v1(v), v2(v);
+ v1(idx0) = v1(idx1);
+ v2(idx0) = v2(idx2);
+ v1.minCoeff(&eigen_minidx);
+ v2.maxCoeff(&eigen_maxidx);
+ VERIFY(eigen_minidx == (std::min)(idx0,idx1));
+ VERIFY(eigen_maxidx == (std::min)(idx0,idx2));
+
+ if (!NumTraits<Scalar>::IsInteger && size > 2) {
+ // Test NaN propagation by replacing an element with NaN.
+ for (Index i = 0; i < size; ++i) {
+ if (i != minidx && i != maxidx) {
+ v(i) = NumTraits<Scalar>::quiet_NaN();
+ break;
+ }
+ }
+ eigen_minc = v.template minCoeff<PropagateNumbers>(&eigen_minidx);
+ eigen_maxc = v.template maxCoeff<PropagateNumbers>(&eigen_maxidx);
+ VERIFY(minidx == eigen_minidx);
+ VERIFY(maxidx == eigen_maxidx);
+ VERIFY_IS_APPROX(minc, eigen_minc);
+ VERIFY_IS_APPROX(maxc, eigen_maxc);
+ VERIFY_IS_APPROX(minc, v.template minCoeff<PropagateNumbers>());
+ VERIFY_IS_APPROX(maxc, v.template maxCoeff<PropagateNumbers>());
+
+ eigen_minc = v.template minCoeff<PropagateNaN>(&eigen_minidx);
+ eigen_maxc = v.template maxCoeff<PropagateNaN>(&eigen_maxidx);
+ VERIFY(minidx != eigen_minidx);
+ VERIFY(maxidx != eigen_maxidx);
+ VERIFY((numext::isnan)(eigen_minc));
+ VERIFY((numext::isnan)(eigen_maxc));
+ }
+}
+
+template<typename T, bool Vectorizable>
+struct TrackedVisitor {
+ void init(T v, Index i, Index j) { return this->operator()(v,i,j); }
+ void operator()(T v, Index i, Index j) {
+ EIGEN_UNUSED_VARIABLE(v)
+ visited.push_back({i, j});
+ vectorized = false;
+ }
+
+ template<typename Packet>
+ void packet(Packet p, Index i, Index j) {
+ EIGEN_UNUSED_VARIABLE(p)
+ visited.push_back({i, j});
+ vectorized = true;
+ }
+ std::vector<std::pair<int,int>> visited;
+ bool vectorized;
+};
+
+namespace Eigen {
+namespace internal {
+
+template<typename T, bool Vectorizable>
+struct functor_traits<TrackedVisitor<T, Vectorizable> > {
+ enum { PacketAccess = Vectorizable, Cost = 1 };
+};
+
+} // namespace internal
+} // namespace Eigen
+
+void checkOptimalTraversal() {
+
+ // Unrolled - ColMajor.
+ {
+ Eigen::Matrix4f X = Eigen::Matrix4f::Random();
+ TrackedVisitor<double, false> visitor;
+ X.visit(visitor);
+ Index count = 0;
+ for (Index j=0; j<X.cols(); ++j) {
+ for (Index i=0; i<X.rows(); ++i) {
+ VERIFY_IS_EQUAL(visitor.visited[count].first, i);
+ VERIFY_IS_EQUAL(visitor.visited[count].second, j);
+ ++count;
+ }
+ }
+ }
+
+ // Unrolled - RowMajor.
+ using Matrix4fRowMajor = Eigen::Matrix<float, 4, 4, Eigen::RowMajor>;
+ {
+ Matrix4fRowMajor X = Matrix4fRowMajor::Random();
+ TrackedVisitor<double, false> visitor;
+ X.visit(visitor);
+ Index count = 0;
+ for (Index i=0; i<X.rows(); ++i) {
+ for (Index j=0; j<X.cols(); ++j) {
+ VERIFY_IS_EQUAL(visitor.visited[count].first, i);
+ VERIFY_IS_EQUAL(visitor.visited[count].second, j);
+ ++count;
+ }
+ }
+ }
+
+ // Not unrolled - ColMajor
+ {
+ Eigen::MatrixXf X = Eigen::MatrixXf::Random(4, 4);
+ TrackedVisitor<double, false> visitor;
+ X.visit(visitor);
+ Index count = 0;
+ for (Index j=0; j<X.cols(); ++j) {
+ for (Index i=0; i<X.rows(); ++i) {
+ VERIFY_IS_EQUAL(visitor.visited[count].first, i);
+ VERIFY_IS_EQUAL(visitor.visited[count].second, j);
+ ++count;
+ }
+ }
+ }
+
+ // Not unrolled - RowMajor.
+ using MatrixXfRowMajor = Eigen::Matrix<float, Eigen::Dynamic, Eigen::Dynamic, Eigen::RowMajor>;
+ {
+ MatrixXfRowMajor X = MatrixXfRowMajor::Random(4, 4);
+ TrackedVisitor<double, false> visitor;
+ X.visit(visitor);
+ Index count = 0;
+ for (Index i=0; i<X.rows(); ++i) {
+ for (Index j=0; j<X.cols(); ++j) {
+ VERIFY_IS_EQUAL(visitor.visited[count].first, i);
+ VERIFY_IS_EQUAL(visitor.visited[count].second, j);
+ ++count;
+ }
+ }
+ }
+
+ // Vectorized - ColMajor
+ {
+ // Ensure rows/cols is larger than packet size.
+ constexpr int PacketSize = Eigen::internal::packet_traits<float>::size;
+ Eigen::MatrixXf X = Eigen::MatrixXf::Random(4 * PacketSize, 4 * PacketSize);
+ TrackedVisitor<double, true> visitor;
+ X.visit(visitor);
+ Index previ = -1;
+ Index prevj = 0;
+ for (const auto& p : visitor.visited) {
+ Index i = p.first;
+ Index j = p.second;
+ VERIFY(
+ (j == prevj && i == previ + 1) // Advance single element
+ || (j == prevj && i == previ + PacketSize) // Advance packet
+ || (j == prevj + 1 && i == 0) // Advance column
+ );
+ previ = i;
+ prevj = j;
+ }
+ if (Eigen::internal::packet_traits<float>::Vectorizable) {
+ VERIFY(visitor.vectorized);
+ }
+ }
+
+ // Vectorized - RowMajor.
+ {
+ // Ensure rows/cols is larger than packet size.
+ constexpr int PacketSize = Eigen::internal::packet_traits<float>::size;
+ MatrixXfRowMajor X = MatrixXfRowMajor::Random(4 * PacketSize, 4 * PacketSize);
+ TrackedVisitor<double, true> visitor;
+ X.visit(visitor);
+ Index previ = 0;
+ Index prevj = -1;
+ for (const auto& p : visitor.visited) {
+ Index i = p.first;
+ Index j = p.second;
+ VERIFY(
+ (i == previ && j == prevj + 1) // Advance single element
+ || (i == previ && j == prevj + PacketSize) // Advance packet
+ || (i == previ + 1 && j == 0) // Advance row
+ );
+ previ = i;
+ prevj = j;
+ }
+ if (Eigen::internal::packet_traits<float>::Vectorizable) {
+ VERIFY(visitor.vectorized);
+ }
+ }
+}
+
+EIGEN_DECLARE_TEST(visitor)
+{
+ for(int i = 0; i < g_repeat; i++) {
+ CALL_SUBTEST_1( matrixVisitor(Matrix<float, 1, 1>()) );
+ CALL_SUBTEST_2( matrixVisitor(Matrix2f()) );
+ CALL_SUBTEST_3( matrixVisitor(Matrix4d()) );
+ CALL_SUBTEST_4( matrixVisitor(MatrixXd(8, 12)) );
+ CALL_SUBTEST_5( matrixVisitor(Matrix<double,Dynamic,Dynamic,RowMajor>(20, 20)) );
+ CALL_SUBTEST_6( matrixVisitor(MatrixXi(8, 12)) );
+ }
+ for(int i = 0; i < g_repeat; i++) {
+ CALL_SUBTEST_7( vectorVisitor(Vector4f()) );
+ CALL_SUBTEST_7( vectorVisitor(Matrix<int,12,1>()) );
+ CALL_SUBTEST_8( vectorVisitor(VectorXd(10)) );
+ CALL_SUBTEST_9( vectorVisitor(RowVectorXd(10)) );
+ CALL_SUBTEST_10( vectorVisitor(VectorXf(33)) );
+ }
+ CALL_SUBTEST_11(checkOptimalTraversal());
+}
diff --git a/test/zerosized.cpp b/test/zerosized.cpp
new file mode 100644
index 0000000..86aa5eb
--- /dev/null
+++ b/test/zerosized.cpp
@@ -0,0 +1,111 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2011 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "main.h"
+
+
+template<typename MatrixType> void zeroReduction(const MatrixType& m) {
+ // Reductions that must hold for zero sized objects
+ VERIFY(m.all());
+ VERIFY(!m.any());
+ VERIFY(m.prod()==1);
+ VERIFY(m.sum()==0);
+ VERIFY(m.norm()==0);
+ VERIFY(m.squaredNorm()==0);
+ VERIFY(m.count()==0);
+ VERIFY(m.allFinite());
+ VERIFY(!m.hasNaN());
+ VERIFY_RAISES_ASSERT( m.minCoeff() );
+ VERIFY_RAISES_ASSERT( m.maxCoeff() );
+ Index i,j;
+ VERIFY_RAISES_ASSERT( m.minCoeff(&i,&j) );
+ VERIFY_RAISES_ASSERT( m.maxCoeff(&i,&j) );
+ VERIFY_RAISES_ASSERT( m.reshaped().minCoeff(&i) );
+ VERIFY_RAISES_ASSERT( m.reshaped().maxCoeff(&i) );
+}
+
+
+template<typename MatrixType> void zeroSizedMatrix()
+{
+ MatrixType t1;
+ typedef typename MatrixType::Scalar Scalar;
+
+ if (MatrixType::SizeAtCompileTime == Dynamic || MatrixType::SizeAtCompileTime == 0)
+ {
+ zeroReduction(t1);
+ if (MatrixType::RowsAtCompileTime == Dynamic)
+ VERIFY(t1.rows() == 0);
+ if (MatrixType::ColsAtCompileTime == Dynamic)
+ VERIFY(t1.cols() == 0);
+
+ if (MatrixType::RowsAtCompileTime == Dynamic && MatrixType::ColsAtCompileTime == Dynamic)
+ {
+
+ MatrixType t2(0, 0);
+ VERIFY(t2.rows() == 0);
+ VERIFY(t2.cols() == 0);
+
+ zeroReduction(t2);
+ VERIFY(t1==t2);
+ }
+ }
+
+ if(MatrixType::MaxColsAtCompileTime!=0 && MatrixType::MaxRowsAtCompileTime!=0)
+ {
+ Index rows = MatrixType::RowsAtCompileTime==Dynamic ? internal::random<Index>(1,10) : Index(MatrixType::RowsAtCompileTime);
+ Index cols = MatrixType::ColsAtCompileTime==Dynamic ? internal::random<Index>(1,10) : Index(MatrixType::ColsAtCompileTime);
+ MatrixType m(rows,cols);
+ zeroReduction(m.template block<0,MatrixType::ColsAtCompileTime>(0,0,0,cols));
+ zeroReduction(m.template block<MatrixType::RowsAtCompileTime,0>(0,0,rows,0));
+ zeroReduction(m.template block<0,1>(0,0));
+ zeroReduction(m.template block<1,0>(0,0));
+ Matrix<Scalar,Dynamic,Dynamic> prod = m.template block<MatrixType::RowsAtCompileTime,0>(0,0,rows,0) * m.template block<0,MatrixType::ColsAtCompileTime>(0,0,0,cols);
+ VERIFY(prod.rows()==rows && prod.cols()==cols);
+ VERIFY(prod.isZero());
+ prod = m.template block<1,0>(0,0) * m.template block<0,1>(0,0);
+ VERIFY(prod.size()==1);
+ VERIFY(prod.isZero());
+ }
+}
+
+template<typename VectorType> void zeroSizedVector()
+{
+ VectorType t1;
+
+ if (VectorType::SizeAtCompileTime == Dynamic || VectorType::SizeAtCompileTime==0)
+ {
+ zeroReduction(t1);
+ VERIFY(t1.size() == 0);
+ VectorType t2(DenseIndex(0)); // DenseIndex disambiguates with 0-the-null-pointer (error with gcc 4.4 and MSVC8)
+ VERIFY(t2.size() == 0);
+ zeroReduction(t2);
+
+ VERIFY(t1==t2);
+ }
+}
+
+EIGEN_DECLARE_TEST(zerosized)
+{
+ zeroSizedMatrix<Matrix2d>();
+ zeroSizedMatrix<Matrix3i>();
+ zeroSizedMatrix<Matrix<float, 2, Dynamic> >();
+ zeroSizedMatrix<MatrixXf>();
+ zeroSizedMatrix<Matrix<float, 0, 0> >();
+ zeroSizedMatrix<Matrix<float, Dynamic, 0, 0, 0, 0> >();
+ zeroSizedMatrix<Matrix<float, 0, Dynamic, 0, 0, 0> >();
+ zeroSizedMatrix<Matrix<float, Dynamic, Dynamic, 0, 0, 0> >();
+ zeroSizedMatrix<Matrix<float, 0, 4> >();
+ zeroSizedMatrix<Matrix<float, 4, 0> >();
+
+ zeroSizedVector<Vector2d>();
+ zeroSizedVector<Vector3i>();
+ zeroSizedVector<VectorXf>();
+ zeroSizedVector<Matrix<float, 0, 1> >();
+ zeroSizedVector<Matrix<float, 1, 0> >();
+}
diff --git a/unsupported/CMakeLists.txt b/unsupported/CMakeLists.txt
new file mode 100644
index 0000000..67d1f62
--- /dev/null
+++ b/unsupported/CMakeLists.txt
@@ -0,0 +1,11 @@
+add_subdirectory(Eigen)
+if(EIGEN_BUILD_DOC)
+ add_subdirectory(doc EXCLUDE_FROM_ALL)
+endif()
+if(EIGEN_BUILD_TESTING)
+ if(EIGEN_LEAVE_TEST_IN_ALL_TARGET)
+ add_subdirectory(test) # can't do EXCLUDE_FROM_ALL here, breaks CTest
+ else()
+ add_subdirectory(test EXCLUDE_FROM_ALL)
+ endif()
+endif()
diff --git a/unsupported/Eigen/AdolcForward b/unsupported/Eigen/AdolcForward
new file mode 100644
index 0000000..ad05504
--- /dev/null
+++ b/unsupported/Eigen/AdolcForward
@@ -0,0 +1,159 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2009 Gael Guennebaud <g.gael@free.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_ADLOC_FORWARD_MODULE_H
+#define EIGEN_ADLOC_FORWARD_MODULE_H
+
+//--------------------------------------------------------------------------------
+//
+// This file provides support for adolc's adouble type in forward mode.
+// ADOL-C is a C++ automatic differentiation library,
+// see https://projects.coin-or.org/ADOL-C for more information.
+//
+// Note that the maximal number of directions is controlled by
+// the preprocessor token NUMBER_DIRECTIONS. The default is 2.
+//
+//--------------------------------------------------------------------------------
+
+#define ADOLC_TAPELESS
+#ifndef NUMBER_DIRECTIONS
+# define NUMBER_DIRECTIONS 2
+#endif
+#include <adolc/adtl.h>
+
+// adolc defines some very stupid macros:
+#if defined(malloc)
+# undef malloc
+#endif
+
+#if defined(calloc)
+# undef calloc
+#endif
+
+#if defined(realloc)
+# undef realloc
+#endif
+
+#include "../../Eigen/Core"
+
+namespace Eigen {
+
+/**
+ * \defgroup AdolcForward_Module Adolc forward module
+ * This module provides support for adolc's adouble type in forward mode.
+ * ADOL-C is a C++ automatic differentiation library,
+ * see https://projects.coin-or.org/ADOL-C for more information.
+ * It mainly consists in:
+ * - a struct Eigen::NumTraits<adtl::adouble> specialization
+ * - overloads of internal::* math function for adtl::adouble type.
+ *
+ * Note that the maximal number of directions is controlled by
+ * the preprocessor token NUMBER_DIRECTIONS. The default is 2.
+ *
+ * \code
+ * #include <unsupported/Eigen/AdolcSupport>
+ * \endcode
+ */
+ //@{
+
+} // namespace Eigen
+
+// Eigen's require a few additional functions which must be defined in the same namespace
+// than the custom scalar type own namespace
+namespace adtl {
+
+inline const adouble& conj(const adouble& x) { return x; }
+inline const adouble& real(const adouble& x) { return x; }
+inline adouble imag(const adouble&) { return 0.; }
+inline adouble abs(const adouble& x) { return fabs(x); }
+inline adouble abs2(const adouble& x) { return x*x; }
+
+inline bool (isinf)(const adouble& x) { return (Eigen::numext::isinf)(x.getValue()); }
+inline bool (isnan)(const adouble& x) { return (Eigen::numext::isnan)(x.getValue()); }
+
+}
+
+namespace Eigen {
+
+template<> struct NumTraits<adtl::adouble>
+ : NumTraits<double>
+{
+ typedef adtl::adouble Real;
+ typedef adtl::adouble NonInteger;
+ typedef adtl::adouble Nested;
+ enum {
+ IsComplex = 0,
+ IsInteger = 0,
+ IsSigned = 1,
+ RequireInitialization = 1,
+ ReadCost = 1,
+ AddCost = 1,
+ MulCost = 1
+ };
+};
+
+template<typename Functor> class AdolcForwardJacobian : public Functor
+{
+ typedef adtl::adouble ActiveScalar;
+public:
+
+ AdolcForwardJacobian() : Functor() {}
+ AdolcForwardJacobian(const Functor& f) : Functor(f) {}
+
+ // forward constructors
+ template<typename T0>
+ AdolcForwardJacobian(const T0& a0) : Functor(a0) {}
+ template<typename T0, typename T1>
+ AdolcForwardJacobian(const T0& a0, const T1& a1) : Functor(a0, a1) {}
+ template<typename T0, typename T1, typename T2>
+ AdolcForwardJacobian(const T0& a0, const T1& a1, const T1& a2) : Functor(a0, a1, a2) {}
+
+ typedef typename Functor::InputType InputType;
+ typedef typename Functor::ValueType ValueType;
+ typedef typename Functor::JacobianType JacobianType;
+
+ typedef Matrix<ActiveScalar, InputType::SizeAtCompileTime, 1> ActiveInput;
+ typedef Matrix<ActiveScalar, ValueType::SizeAtCompileTime, 1> ActiveValue;
+
+ void operator() (const InputType& x, ValueType* v, JacobianType* _jac) const
+ {
+ eigen_assert(v!=0);
+ if (!_jac)
+ {
+ Functor::operator()(x, v);
+ return;
+ }
+
+ JacobianType& jac = *_jac;
+
+ ActiveInput ax = x.template cast<ActiveScalar>();
+ ActiveValue av(jac.rows());
+
+ for (int j=0; j<jac.cols(); j++)
+ for (int i=0; i<jac.cols(); i++)
+ ax[i].setADValue(j, i==j ? 1 : 0);
+
+ Functor::operator()(ax, &av);
+
+ for (int i=0; i<jac.rows(); i++)
+ {
+ (*v)[i] = av[i].getValue();
+ for (int j=0; j<jac.cols(); j++)
+ jac.coeffRef(i,j) = av[i].getADValue(j);
+ }
+ }
+protected:
+
+};
+
+//@}
+
+}
+
+#endif // EIGEN_ADLOC_FORWARD_MODULE_H
diff --git a/unsupported/Eigen/AlignedVector3 b/unsupported/Eigen/AlignedVector3
new file mode 100644
index 0000000..cf2b9f6
--- /dev/null
+++ b/unsupported/Eigen/AlignedVector3
@@ -0,0 +1,234 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009 Gael Guennebaud <g.gael@free.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_ALIGNED_VECTOR3_MODULE_H
+#define EIGEN_ALIGNED_VECTOR3_MODULE_H
+
+#include "../../Eigen/Geometry"
+
+#include "../../Eigen/src/Core/util/DisableStupidWarnings.h"
+
+namespace Eigen {
+
+/**
+ * \defgroup AlignedVector3_Module Aligned vector3 module
+ *
+ * \code
+ * #include <unsupported/Eigen/AlignedVector3>
+ * \endcode
+ */
+ //@{
+
+
+/** \class AlignedVector3
+ *
+ * \brief A vectorization friendly 3D vector
+ *
+ * This class represents a 3D vector internally using a 4D vector
+ * such that vectorization can be seamlessly enabled. Of course,
+ * the same result can be achieved by directly using a 4D vector.
+ * This class makes this process simpler.
+ *
+ */
+// TODO specialize Cwise
+template<typename Scalar_> class AlignedVector3;
+
+namespace internal {
+template<typename Scalar_> struct traits<AlignedVector3<Scalar_> >
+ : traits<Matrix<Scalar_,3,1,0,4,1> >
+{
+};
+}
+
+template<typename Scalar_> class AlignedVector3
+ : public MatrixBase<AlignedVector3<Scalar_> >
+{
+ typedef Matrix<Scalar_,4,1> CoeffType;
+ CoeffType m_coeffs;
+ public:
+
+ typedef MatrixBase<AlignedVector3<Scalar_> > Base;
+ EIGEN_DENSE_PUBLIC_INTERFACE(AlignedVector3)
+ using Base::operator*;
+
+ inline Index rows() const { return 3; }
+ inline Index cols() const { return 1; }
+
+ Scalar* data() { return m_coeffs.data(); }
+ const Scalar* data() const { return m_coeffs.data(); }
+ Index innerStride() const { return 1; }
+ Index outerStride() const { return 3; }
+
+ inline const Scalar& coeff(Index row, Index col) const
+ { return m_coeffs.coeff(row, col); }
+
+ inline Scalar& coeffRef(Index row, Index col)
+ { return m_coeffs.coeffRef(row, col); }
+
+ inline const Scalar& coeff(Index index) const
+ { return m_coeffs.coeff(index); }
+
+ inline Scalar& coeffRef(Index index)
+ { return m_coeffs.coeffRef(index);}
+
+
+ inline AlignedVector3()
+ {}
+
+ inline AlignedVector3(const Scalar& x, const Scalar& y, const Scalar& z)
+ : m_coeffs(x, y, z, Scalar(0))
+ {}
+
+ inline AlignedVector3(const AlignedVector3& other)
+ : Base(), m_coeffs(other.m_coeffs)
+ {}
+
+ template<typename XprType, int Size=XprType::SizeAtCompileTime>
+ struct generic_assign_selector {};
+
+ template<typename XprType> struct generic_assign_selector<XprType,4>
+ {
+ inline static void run(AlignedVector3& dest, const XprType& src)
+ {
+ dest.m_coeffs = src;
+ }
+ };
+
+ template<typename XprType> struct generic_assign_selector<XprType,3>
+ {
+ inline static void run(AlignedVector3& dest, const XprType& src)
+ {
+ dest.m_coeffs.template head<3>() = src;
+ dest.m_coeffs.w() = Scalar(0);
+ }
+ };
+
+ template<typename Derived>
+ inline AlignedVector3(const MatrixBase<Derived>& other)
+ {
+ generic_assign_selector<Derived>::run(*this,other.derived());
+ }
+
+ inline AlignedVector3& operator=(const AlignedVector3& other)
+ { m_coeffs = other.m_coeffs; return *this; }
+
+ template <typename Derived>
+ inline AlignedVector3& operator=(const MatrixBase<Derived>& other)
+ {
+ generic_assign_selector<Derived>::run(*this,other.derived());
+ return *this;
+ }
+
+ inline AlignedVector3 operator+(const AlignedVector3& other) const
+ { return AlignedVector3(m_coeffs + other.m_coeffs); }
+
+ inline AlignedVector3& operator+=(const AlignedVector3& other)
+ { m_coeffs += other.m_coeffs; return *this; }
+
+ inline AlignedVector3 operator-(const AlignedVector3& other) const
+ { return AlignedVector3(m_coeffs - other.m_coeffs); }
+
+ inline AlignedVector3 operator-() const
+ { return AlignedVector3(-m_coeffs); }
+
+ inline AlignedVector3 operator-=(const AlignedVector3& other)
+ { m_coeffs -= other.m_coeffs; return *this; }
+
+ inline AlignedVector3 operator*(const Scalar& s) const
+ { return AlignedVector3(m_coeffs * s); }
+
+ inline friend AlignedVector3 operator*(const Scalar& s,const AlignedVector3& vec)
+ { return AlignedVector3(s * vec.m_coeffs); }
+
+ inline AlignedVector3& operator*=(const Scalar& s)
+ { m_coeffs *= s; return *this; }
+
+ inline AlignedVector3 operator/(const Scalar& s) const
+ { return AlignedVector3(m_coeffs / s); }
+
+ inline AlignedVector3& operator/=(const Scalar& s)
+ { m_coeffs /= s; return *this; }
+
+ inline Scalar dot(const AlignedVector3& other) const
+ {
+ eigen_assert(m_coeffs.w()==Scalar(0));
+ eigen_assert(other.m_coeffs.w()==Scalar(0));
+ return m_coeffs.dot(other.m_coeffs);
+ }
+
+ inline void normalize()
+ {
+ m_coeffs /= norm();
+ }
+
+ inline AlignedVector3 normalized() const
+ {
+ return AlignedVector3(m_coeffs / norm());
+ }
+
+ inline Scalar sum() const
+ {
+ eigen_assert(m_coeffs.w()==Scalar(0));
+ return m_coeffs.sum();
+ }
+
+ inline Scalar squaredNorm() const
+ {
+ eigen_assert(m_coeffs.w()==Scalar(0));
+ return m_coeffs.squaredNorm();
+ }
+
+ inline Scalar norm() const
+ {
+ using std::sqrt;
+ return sqrt(squaredNorm());
+ }
+
+ inline AlignedVector3 cross(const AlignedVector3& other) const
+ {
+ return AlignedVector3(m_coeffs.cross3(other.m_coeffs));
+ }
+
+ template<typename Derived>
+ inline bool isApprox(const MatrixBase<Derived>& other, const RealScalar& eps=NumTraits<Scalar>::dummy_precision()) const
+ {
+ return m_coeffs.template head<3>().isApprox(other,eps);
+ }
+
+ CoeffType& coeffs() { return m_coeffs; }
+ const CoeffType& coeffs() const { return m_coeffs; }
+};
+
+namespace internal {
+
+template<typename Scalar_>
+struct eval<AlignedVector3<Scalar_>, Dense>
+{
+ typedef const AlignedVector3<Scalar_>& type;
+};
+
+template<typename Scalar>
+struct evaluator<AlignedVector3<Scalar> >
+ : evaluator<Matrix<Scalar,4,1> >
+{
+ typedef AlignedVector3<Scalar> XprType;
+ typedef evaluator<Matrix<Scalar,4,1> > Base;
+
+ evaluator(const XprType &m) : Base(m.coeffs()) {}
+};
+
+}
+
+//@}
+
+}
+
+#include "../../Eigen/src/Core/util/ReenableStupidWarnings.h"
+
+#endif // EIGEN_ALIGNED_VECTOR3_MODULE_H
diff --git a/unsupported/Eigen/ArpackSupport b/unsupported/Eigen/ArpackSupport
new file mode 100644
index 0000000..67c4ac8
--- /dev/null
+++ b/unsupported/Eigen/ArpackSupport
@@ -0,0 +1,30 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_ARPACKSUPPORT_MODULE_H
+#define EIGEN_ARPACKSUPPORT_MODULE_H
+
+#include "../../Eigen/Core"
+
+/** \defgroup ArpackSupport_Module Arpack support module
+ *
+ * This module provides a wrapper to Arpack, a library for sparse eigenvalue decomposition.
+ *
+ * \code
+ * #include <Eigen/ArpackSupport>
+ * \endcode
+ */
+
+#include "../../Eigen/SparseCholesky"
+
+#include "../../Eigen/src/Core/util/DisableStupidWarnings.h"
+#include "src/Eigenvalues/ArpackSelfAdjointEigenSolver.h"
+
+#include "../../Eigen/src/Core/util/ReenableStupidWarnings.h"
+
+#endif // EIGEN_ARPACKSUPPORT_MODULE_H
diff --git a/unsupported/Eigen/AutoDiff b/unsupported/Eigen/AutoDiff
new file mode 100644
index 0000000..62fc0b3
--- /dev/null
+++ b/unsupported/Eigen/AutoDiff
@@ -0,0 +1,48 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2009 Gael Guennebaud <g.gael@free.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_AUTODIFF_MODULE_H
+#define EIGEN_AUTODIFF_MODULE_H
+
+#include "../../Eigen/Core"
+
+namespace Eigen {
+
+/**
+ * \defgroup AutoDiff_Module Auto Diff module
+ *
+ * This module features forward automatic differentation via a simple
+ * templated scalar type wrapper AutoDiffScalar.
+ *
+ * Warning : this should NOT be confused with numerical differentiation, which
+ * is a different method and has its own module in Eigen : \ref NumericalDiff_Module.
+ *
+ * \code
+ * #include <unsupported/Eigen/AutoDiff>
+ * \endcode
+ */
+//@{
+
+}
+#include "../../Eigen/src/Core/util/DisableStupidWarnings.h"
+
+
+#include "src/AutoDiff/AutoDiffScalar.h"
+// #include "src/AutoDiff/AutoDiffVector.h"
+#include "src/AutoDiff/AutoDiffJacobian.h"
+
+#include "../../Eigen/src/Core/util/ReenableStupidWarnings.h"
+
+
+
+namespace Eigen {
+//@}
+}
+
+#endif // EIGEN_AUTODIFF_MODULE_H
diff --git a/unsupported/Eigen/BVH b/unsupported/Eigen/BVH
new file mode 100644
index 0000000..666c983
--- /dev/null
+++ b/unsupported/Eigen/BVH
@@ -0,0 +1,95 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009 Ilya Baran <ibaran@mit.edu>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_BVH_MODULE_H
+#define EIGEN_BVH_MODULE_H
+
+#include "../../Eigen/Core"
+#include "../../Eigen/Geometry"
+#include "../../Eigen/StdVector"
+#include <algorithm>
+#include <queue>
+
+namespace Eigen {
+
+/**
+ * \defgroup BVH_Module BVH module
+ * \brief This module provides generic bounding volume hierarchy algorithms
+ * and reference tree implementations.
+ *
+ *
+ * \code
+ * #include <unsupported/Eigen/BVH>
+ * \endcode
+ *
+ * A bounding volume hierarchy (BVH) can accelerate many geometric queries. This module provides a generic implementation
+ * of the two basic algorithms over a BVH: intersection of a query object against all objects in the hierarchy and minimization
+ * of a function over the objects in the hierarchy. It also provides intersection and minimization over a cartesian product of
+ * two BVH's. A BVH accelerates intersection by using the fact that if a query object does not intersect a volume, then it cannot
+ * intersect any object contained in that volume. Similarly, a BVH accelerates minimization because the minimum of a function
+ * over a volume is no greater than the minimum of a function over any object contained in it.
+ *
+ * Some sample queries that can be written in terms of intersection are:
+ * - Determine all points where a ray intersects a triangle mesh
+ * - Given a set of points, determine which are contained in a query sphere
+ * - Given a set of spheres, determine which contain the query point
+ * - Given a set of disks, determine if any is completely contained in a query rectangle (represent each 2D disk as a point \f$(x,y,r)\f$
+ * in 3D and represent the rectangle as a pyramid based on the original rectangle and shrinking in the \f$r\f$ direction)
+ * - Given a set of points, count how many pairs are \f$d\pm\epsilon\f$ apart (done by looking at the cartesian product of the set
+ * of points with itself)
+ *
+ * Some sample queries that can be written in terms of function minimization over a set of objects are:
+ * - Find the intersection between a ray and a triangle mesh closest to the ray origin (function is infinite off the ray)
+ * - Given a polyline and a query point, determine the closest point on the polyline to the query
+ * - Find the diameter of a point cloud (done by looking at the cartesian product and using negative distance as the function)
+ * - Determine how far two meshes are from colliding (this is also a cartesian product query)
+ *
+ * This implementation decouples the basic algorithms both from the type of hierarchy (and the types of the bounding volumes) and
+ * from the particulars of the query. To enable abstraction from the BVH, the BVH is required to implement a generic mechanism
+ * for traversal. To abstract from the query, the query is responsible for keeping track of results.
+ *
+ * To be used in the algorithms, a hierarchy must implement the following traversal mechanism (see KdBVH for a sample implementation): \code
+ typedef Volume //the type of bounding volume
+ typedef Object //the type of object in the hierarchy
+ typedef Index //a reference to a node in the hierarchy--typically an int or a pointer
+ typedef VolumeIterator //an iterator type over node children--returns Index
+ typedef ObjectIterator //an iterator over object (leaf) children--returns const Object &
+ Index getRootIndex() const //returns the index of the hierarchy root
+ const Volume &getVolume(Index index) const //returns the bounding volume of the node at given index
+ void getChildren(Index index, VolumeIterator &outVBegin, VolumeIterator &outVEnd,
+ ObjectIterator &outOBegin, ObjectIterator &outOEnd) const
+ //getChildren takes a node index and makes [outVBegin, outVEnd) range over its node children
+ //and [outOBegin, outOEnd) range over its object children
+ \endcode
+ *
+ * To use the hierarchy, call BVIntersect or BVMinimize, passing it a BVH (or two, for cartesian product) and a minimizer or intersector.
+ * For an intersection query on a single BVH, the intersector encapsulates the query and must provide two functions:
+ * \code
+ bool intersectVolume(const Volume &volume) //returns true if the query intersects the volume
+ bool intersectObject(const Object &object) //returns true if the intersection search should terminate immediately
+ \endcode
+ * The guarantee that BVIntersect provides is that intersectObject will be called on every object whose bounding volume
+ * intersects the query (but possibly on other objects too) unless the search is terminated prematurely. It is the
+ * responsibility of the intersectObject function to keep track of the results in whatever manner is appropriate.
+ * The cartesian product intersection and the BVMinimize queries are similar--see their individual documentation.
+ *
+ * The following is a simple but complete example for how to use the BVH to accelerate the search for a closest red-blue point pair:
+ * \include BVH_Example.cpp
+ * Output: \verbinclude BVH_Example.out
+ */
+}
+
+//@{
+
+#include "src/BVH/BVAlgorithms.h"
+#include "src/BVH/KdBVH.h"
+
+//@}
+
+#endif // EIGEN_BVH_MODULE_H
diff --git a/unsupported/Eigen/CMakeLists.txt b/unsupported/Eigen/CMakeLists.txt
new file mode 100644
index 0000000..dcf9500
--- /dev/null
+++ b/unsupported/Eigen/CMakeLists.txt
@@ -0,0 +1,33 @@
+set(Eigen_HEADERS
+ AdolcForward
+ AlignedVector3
+ ArpackSupport
+ AutoDiff
+ BVH
+ EulerAngles
+ FFT
+ IterativeSolvers
+ KroneckerProduct
+ LevenbergMarquardt
+ MatrixFunctions
+ MoreVectorization
+ MPRealSupport
+ NNLS
+ NonLinearOptimization
+ NumericalDiff
+ OpenGLSupport
+ Polynomials
+ Skyline
+ SparseExtra
+ SpecialFunctions
+ Splines
+ )
+
+install(FILES
+ ${Eigen_HEADERS}
+ DESTINATION ${INCLUDE_INSTALL_DIR}/unsupported/Eigen COMPONENT Devel
+ )
+
+install(DIRECTORY src DESTINATION ${INCLUDE_INSTALL_DIR}/unsupported/Eigen COMPONENT Devel FILES_MATCHING PATTERN "*.h")
+
+add_subdirectory(CXX11)
diff --git a/unsupported/Eigen/CXX11/CMakeLists.txt b/unsupported/Eigen/CXX11/CMakeLists.txt
new file mode 100644
index 0000000..385ed24
--- /dev/null
+++ b/unsupported/Eigen/CXX11/CMakeLists.txt
@@ -0,0 +1,8 @@
+set(Eigen_CXX11_HEADERS Tensor TensorSymmetry ThreadPool)
+
+install(FILES
+ ${Eigen_CXX11_HEADERS}
+ DESTINATION ${INCLUDE_INSTALL_DIR}/unsupported/Eigen/CXX11 COMPONENT Devel
+ )
+
+install(DIRECTORY src DESTINATION ${INCLUDE_INSTALL_DIR}/unsupported/Eigen/CXX11 COMPONENT Devel FILES_MATCHING PATTERN "*.h")
diff --git a/unsupported/Eigen/CXX11/Tensor b/unsupported/Eigen/CXX11/Tensor
new file mode 100644
index 0000000..18a3961
--- /dev/null
+++ b/unsupported/Eigen/CXX11/Tensor
@@ -0,0 +1,138 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>
+// Copyright (C) 2013 Christian Seiler <christian@iwakd.de>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+//#ifndef EIGEN_CXX11_TENSOR_MODULE_H
+#define EIGEN_CXX11_TENSOR_MODULE_H
+
+#include "Eigen/Core"
+
+#include "unsupported/Eigen/SpecialFunctions"
+
+#include "Eigen/src/Core/util/DisableStupidWarnings.h"
+#include "src/util/CXX11Meta.h"
+#include "src/util/MaxSizeVector.h"
+
+/** \defgroup CXX11_Tensor_Module Tensor Module
+ *
+ * This module provides a Tensor class for storing arbitrarily indexed
+ * objects.
+ *
+ * \code
+ * #include <Eigen/CXX11/Tensor>
+ * \endcode
+ *
+ * Much of the documentation can be found \ref eigen_tensors "here".
+ */
+
+#include <atomic>
+#include <chrono>
+#include <cmath>
+#include <cstddef>
+#include <cstring>
+#include <iterator>
+#include <numeric>
+#include <random>
+#include <thread>
+
+#if defined(EIGEN_USE_THREADS) || defined(EIGEN_USE_SYCL)
+#include "ThreadPool"
+#endif
+
+#ifdef EIGEN_USE_GPU
+ #include <iostream>
+ #if defined(EIGEN_USE_HIP)
+ #include <hip/hip_runtime.h>
+ #else
+ #include <cuda_runtime.h>
+ #endif
+#endif
+
+#include "src/Tensor/TensorMacros.h"
+#include "src/Tensor/TensorForwardDeclarations.h"
+#include "src/Tensor/TensorMeta.h"
+#include "src/Tensor/TensorFunctors.h"
+#include "src/Tensor/TensorCostModel.h"
+#include "src/Tensor/TensorDeviceDefault.h"
+#include "src/Tensor/TensorDeviceThreadPool.h"
+#include "src/Tensor/TensorDeviceGpu.h"
+#ifndef gpu_assert
+#define gpu_assert(x)
+#endif
+#include "src/Tensor/TensorDeviceSycl.h"
+#include "src/Tensor/TensorIndexList.h"
+#include "src/Tensor/TensorDimensionList.h"
+#include "src/Tensor/TensorDimensions.h"
+#include "src/Tensor/TensorInitializer.h"
+#include "src/Tensor/TensorTraits.h"
+#include "src/Tensor/TensorRandom.h"
+#include "src/Tensor/TensorUInt128.h"
+#include "src/Tensor/TensorIntDiv.h"
+#include "src/Tensor/TensorGlobalFunctions.h"
+
+#include "src/Tensor/TensorIO.h"
+
+#include "src/Tensor/TensorBase.h"
+#include "src/Tensor/TensorBlock.h"
+
+#include "src/Tensor/TensorEvaluator.h"
+#include "src/Tensor/TensorExpr.h"
+#include "src/Tensor/TensorReduction.h"
+#include "src/Tensor/TensorReductionGpu.h"
+#include "src/Tensor/TensorArgMax.h"
+#include "src/Tensor/TensorConcatenation.h"
+#include "src/Tensor/TensorContractionMapper.h"
+#include "src/Tensor/TensorContractionBlocking.h"
+#include "src/Tensor/TensorContraction.h"
+#include "src/Tensor/TensorContractionThreadPool.h"
+#include "src/Tensor/TensorContractionGpu.h"
+#include "src/Tensor/TensorConversion.h"
+#include "src/Tensor/TensorConvolution.h"
+#include "src/Tensor/TensorFFT.h"
+#include "src/Tensor/TensorPatch.h"
+#include "src/Tensor/TensorImagePatch.h"
+#include "src/Tensor/TensorVolumePatch.h"
+#include "src/Tensor/TensorBroadcasting.h"
+#include "src/Tensor/TensorChipping.h"
+#include "src/Tensor/TensorInflation.h"
+#include "src/Tensor/TensorLayoutSwap.h"
+#include "src/Tensor/TensorMorphing.h"
+#include "src/Tensor/TensorPadding.h"
+#include "src/Tensor/TensorReverse.h"
+#include "src/Tensor/TensorShuffling.h"
+#include "src/Tensor/TensorStriding.h"
+#include "src/Tensor/TensorCustomOp.h"
+#include "src/Tensor/TensorEvalTo.h"
+#include "src/Tensor/TensorForcedEval.h"
+#include "src/Tensor/TensorGenerator.h"
+#include "src/Tensor/TensorAssign.h"
+#include "src/Tensor/TensorScan.h"
+#include "src/Tensor/TensorTrace.h"
+
+#ifdef EIGEN_USE_SYCL
+#include "src/Tensor/TensorReductionSycl.h"
+#include "src/Tensor/TensorConvolutionSycl.h"
+#include "src/Tensor/TensorContractionSycl.h"
+#include "src/Tensor/TensorScanSycl.h"
+#endif
+
+#include "src/Tensor/TensorExecutor.h"
+#include "src/Tensor/TensorDevice.h"
+
+#include "src/Tensor/TensorStorage.h"
+#include "src/Tensor/Tensor.h"
+#include "src/Tensor/TensorFixedSize.h"
+#include "src/Tensor/TensorMap.h"
+#include "src/Tensor/TensorRef.h"
+
+
+
+#include "../../../Eigen/src/Core/util/ReenableStupidWarnings.h"
+
+//#endif // EIGEN_CXX11_TENSOR_MODULE_H
diff --git a/unsupported/Eigen/CXX11/TensorSymmetry b/unsupported/Eigen/CXX11/TensorSymmetry
new file mode 100644
index 0000000..a5c9609
--- /dev/null
+++ b/unsupported/Eigen/CXX11/TensorSymmetry
@@ -0,0 +1,38 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2013 Christian Seiler <christian@iwakd.de>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_CXX11_TENSORSYMMETRY_MODULE_H
+#define EIGEN_CXX11_TENSORSYMMETRY_MODULE_H
+
+#include "Tensor"
+
+#include "../../../Eigen/src/Core/util/DisableStupidWarnings.h"
+
+#include "src/util/CXX11Meta.h"
+
+/** \defgroup CXX11_TensorSymmetry_Module Tensor Symmetry Module
+ *
+ * This module provides a classes that allow for the definition of
+ * symmetries w.r.t. tensor indices.
+ *
+ * Including this module will implicitly include the Tensor module.
+ *
+ * \code
+ * #include <Eigen/TensorSymmetry>
+ * \endcode
+ */
+
+#include "src/TensorSymmetry/util/TemplateGroupTheory.h"
+#include "src/TensorSymmetry/Symmetry.h"
+#include "src/TensorSymmetry/StaticSymmetry.h"
+#include "src/TensorSymmetry/DynamicSymmetry.h"
+
+#include "../../../Eigen/src/Core/util/ReenableStupidWarnings.h"
+
+#endif // EIGEN_CXX11_TENSORSYMMETRY_MODULE_H
diff --git a/unsupported/Eigen/CXX11/ThreadPool b/unsupported/Eigen/CXX11/ThreadPool
new file mode 100644
index 0000000..ddd6cdc
--- /dev/null
+++ b/unsupported/Eigen/CXX11/ThreadPool
@@ -0,0 +1,95 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2016 Benoit Steiner <benoit.steiner.goog@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_CXX11_THREADPOOL_MODULE_H
+#define EIGEN_CXX11_THREADPOOL_MODULE_H
+
+#include "../../../Eigen/Core"
+
+#include "../../../Eigen/src/Core/util/DisableStupidWarnings.h"
+
+/** \defgroup CXX11_ThreadPool_Module C++11 ThreadPool Module
+ *
+ * This module provides 2 threadpool implementations
+ * - a simple reference implementation
+ * - a faster non blocking implementation
+ *
+ * This module requires C++11.
+ *
+ * \code
+ * #include <Eigen/CXX11/ThreadPool>
+ * \endcode
+ */
+
+
+// The code depends on CXX11, so only include the module if the
+// compiler supports it.
+#include <cstddef>
+#include <cstring>
+#include <time.h>
+
+#include <vector>
+#include <atomic>
+#include <condition_variable>
+#include <deque>
+#include <mutex>
+#include <thread>
+#include <functional>
+#include <memory>
+#include <utility>
+
+// There are non-parenthesized calls to "max" in the <unordered_map> header,
+// which trigger a check in test/main.h causing compilation to fail.
+// We work around the check here by removing the check for max in
+// the case where we have to emulate thread_local.
+#ifdef max
+#undef max
+#endif
+#include <unordered_map>
+
+#include "src/util/CXX11Meta.h"
+#include "src/util/MaxSizeVector.h"
+
+#ifdef EIGEN_USE_CUSTOM_THREAD_POOL
+ #undef EIGEN_MUTEX
+ #define EIGEN_MUTEX std::mutex
+ #undef EIGEN_MUTEX_LOCK
+ #define EIGEN_MUTEX_LOCK std::unique_lock<std::mutex>
+ #undef EIGEN_CONDVAR
+ #define EIGEN_CONDVAR std::condition_variable
+#else
+ // Use tensorflow synchronization primitives.
+ #if !defined(EIGEN_MUTEX) || !defined(EIGEN_MUTEX_LOCK) || !defined(EIGEN_CONDVAR)
+ #include "third_party/tensorflow/tsl/platform/types.h"
+ #include "third_party/tensorflow/tsl/platform/mutex.h"
+ #endif
+ #ifndef EIGEN_MUTEX
+ #define EIGEN_MUTEX ::tsl::mutex
+ #endif
+ #ifndef EIGEN_MUTEX_LOCK
+ #define EIGEN_MUTEX_LOCK ::tsl::mutex_lock
+ #endif
+ #ifndef EIGEN_CONDVAR
+ #define EIGEN_CONDVAR ::tsl::condition_variable
+ #endif
+#endif
+
+#include "src/ThreadPool/ThreadLocal.h"
+#include "src/ThreadPool/ThreadYield.h"
+#include "src/ThreadPool/ThreadCancel.h"
+#include "src/ThreadPool/EventCount.h"
+#include "src/ThreadPool/RunQueue.h"
+#include "src/ThreadPool/ThreadPoolInterface.h"
+#include "src/ThreadPool/ThreadEnvironment.h"
+#include "src/ThreadPool/Barrier.h"
+#include "src/ThreadPool/NonBlockingThreadPool.h"
+
+#include "../../../Eigen/src/Core/util/ReenableStupidWarnings.h"
+
+#endif // EIGEN_CXX11_THREADPOOL_MODULE_H
diff --git a/unsupported/Eigen/CXX11/src/Tensor/InternalHeaderCheck.h b/unsupported/Eigen/CXX11/src/Tensor/InternalHeaderCheck.h
new file mode 100644
index 0000000..9e4c1ed
--- /dev/null
+++ b/unsupported/Eigen/CXX11/src/Tensor/InternalHeaderCheck.h
@@ -0,0 +1,3 @@
+#ifndef EIGEN_CXX11_TENSOR_MODULE_H
+#error "Please include unsupported/Eigen/CXX11/Tensor instead of including headers inside the src directory directly."
+#endif
diff --git a/unsupported/Eigen/CXX11/src/Tensor/README.md b/unsupported/Eigen/CXX11/src/Tensor/README.md
new file mode 100644
index 0000000..e4b5e2e
--- /dev/null
+++ b/unsupported/Eigen/CXX11/src/Tensor/README.md
@@ -0,0 +1,1864 @@
+# Eigen Tensors {#eigen_tensors}
+
+Tensors are multidimensional arrays of elements. Elements are typically scalars,
+but more complex types such as strings are also supported.
+
+## Tensor Classes
+
+You can manipulate a tensor with one of the following classes. They all are in
+the namespace `::Eigen.`
+
+
+### Class Tensor<data_type, rank>
+
+This is the class to use to create a tensor and allocate memory for it. The
+class is templatized with the tensor datatype, such as float or int, and the
+tensor rank. The rank is the number of dimensions, for example rank 2 is a
+matrix.
+
+Tensors of this class are resizable. For example, if you assign a tensor of a
+different size to a Tensor, that tensor is resized to match its new value.
+
+#### Constructor Tensor<data_type, rank>(size0, size1, ...)
+
+Constructor for a Tensor. The constructor must be passed `rank` integers
+indicating the sizes of the instance along each of the the `rank`
+dimensions.
+
+ // Create a tensor of rank 3 of sizes 2, 3, 4. This tensor owns
+ // memory to hold 24 floating point values (24 = 2 x 3 x 4).
+ Tensor<float, 3> t_3d(2, 3, 4);
+
+ // Resize t_3d by assigning a tensor of different sizes, but same rank.
+ t_3d = Tensor<float, 3>(3, 4, 3);
+
+#### Constructor Tensor<data_type, rank>(size_array)
+
+Constructor where the sizes for the constructor are specified as an array of
+values instead of an explicitly list of parameters. The array type to use is
+`Eigen::array<Eigen::Index>`. The array can be constructed automatically
+from an initializer list.
+
+ // Create a tensor of strings of rank 2 with sizes 5, 7.
+ Tensor<string, 2> t_2d({5, 7});
+
+
+### Class TensorFixedSize<data_type, Sizes<size0, size1, ...>>
+
+Class to use for tensors of fixed size, where the size is known at compile
+time. Fixed sized tensors can provide very fast computations because all their
+dimensions are known by the compiler. FixedSize tensors are not resizable.
+
+If the total number of elements in a fixed size tensor is small enough the
+tensor data is held onto the stack and does not cause heap allocation and free.
+
+ // Create a 4 x 3 tensor of floats.
+ TensorFixedSize<float, Sizes<4, 3>> t_4x3;
+
+### Class TensorMap<Tensor<data_type, rank>>
+
+This is the class to use to create a tensor on top of memory allocated and
+owned by another part of your code. It allows to view any piece of allocated
+memory as a Tensor. Instances of this class do not own the memory where the
+data are stored.
+
+A TensorMap is not resizable because it does not own the memory where its data
+are stored.
+
+#### Constructor TensorMap<Tensor<data_type, rank>>(data, size0, size1, ...)
+
+Constructor for a Tensor. The constructor must be passed a pointer to the
+storage for the data, and "rank" size attributes. The storage has to be
+large enough to hold all the data.
+
+ // Map a tensor of ints on top of stack-allocated storage.
+ int storage[128]; // 2 x 4 x 2 x 8 = 128
+ TensorMap<Tensor<int, 4>> t_4d(storage, 2, 4, 2, 8);
+
+ // The same storage can be viewed as a different tensor.
+ // You can also pass the sizes as an array.
+ TensorMap<Tensor<int, 2>> t_2d(storage, 16, 8);
+
+ // You can also map fixed-size tensors. Here we get a 1d view of
+ // the 2d fixed-size tensor.
+ TensorFixedSize<float, Sizes<4, 3>> t_4x3;
+ TensorMap<Tensor<float, 1>> t_12(t_4x3.data(), 12);
+
+
+#### Class TensorRef
+
+See Assigning to a TensorRef below.
+
+## Accessing Tensor Elements
+
+#### <data_type> tensor(index0, index1...)
+
+Return the element at position `(index0, index1...)` in tensor
+`tensor`. You must pass as many parameters as the rank of `tensor`.
+The expression can be used as an l-value to set the value of the element at the
+specified position. The value returned is of the datatype of the tensor.
+
+ // Set the value of the element at position (0, 1, 0);
+ Tensor<float, 3> t_3d(2, 3, 4);
+ t_3d(0, 1, 0) = 12.0f;
+
+ // Initialize all elements to random values.
+ for (int i = 0; i < 2; ++i) {
+ for (int j = 0; j < 3; ++j) {
+ for (int k = 0; k < 4; ++k) {
+ t_3d(i, j, k) = ...some random value...;
+ }
+ }
+ }
+
+ // Print elements of a tensor.
+ for (int i = 0; i < 2; ++i) {
+ LOG(INFO) << t_3d(i, 0, 0);
+ }
+
+
+## TensorLayout
+
+The tensor library supports 2 layouts: `ColMajor` (the default) and
+`RowMajor`.
+
+The layout of a tensor is optionally specified as part of its type. If not
+specified explicitly column major is assumed.
+
+ Tensor<float, 3, ColMajor> col_major; // equivalent to Tensor<float, 3>
+ TensorMap<Tensor<float, 3, RowMajor> > row_major(data, ...);
+
+All the arguments to an expression must use the same layout. Attempting to mix
+different layouts will result in a compilation error.
+
+It is possible to change the layout of a tensor or an expression using the
+`swap_layout()` method. Note that this will also reverse the order of the
+dimensions.
+
+ Tensor<float, 2, ColMajor> col_major(2, 4);
+ Tensor<float, 2, RowMajor> row_major(2, 4);
+
+ Tensor<float, 2> col_major_result = col_major; // ok, layouts match
+ Tensor<float, 2> col_major_result = row_major; // will not compile
+
+ // Simple layout swap
+ col_major_result = row_major.swap_layout();
+ eigen_assert(col_major_result.dimension(0) == 4);
+ eigen_assert(col_major_result.dimension(1) == 2);
+
+ // Swap the layout and preserve the order of the dimensions
+ array<int, 2> shuffle(1, 0);
+ col_major_result = row_major.swap_layout().shuffle(shuffle);
+ eigen_assert(col_major_result.dimension(0) == 2);
+ eigen_assert(col_major_result.dimension(1) == 4);
+
+
+## Tensor Operations
+
+The Eigen Tensor library provides a vast library of operations on Tensors:
+numerical operations such as addition and multiplication, geometry operations
+such as slicing and shuffling, etc. These operations are available as methods
+of the Tensor classes, and in some cases as operator overloads. For example
+the following code computes the elementwise addition of two tensors:
+
+ Tensor<float, 3> t1(2, 3, 4);
+ ...set some values in t1...
+ Tensor<float, 3> t2(2, 3, 4);
+ ...set some values in t2...
+ // Set t3 to the element wise sum of t1 and t2
+ Tensor<float, 3> t3 = t1 + t2;
+
+While the code above looks easy enough, it is important to understand that the
+expression `t1 + t2` is not actually adding the values of the tensors. The
+expression instead constructs a "tensor operator" object of the class
+TensorCwiseBinaryOp<scalar_sum>, which has references to the tensors
+`t1` and `t2`. This is a small C++ object that knows how to add
+`t1` and `t2`. It is only when the value of the expression is assigned
+to the tensor `t3` that the addition is actually performed. Technically,
+this happens through the overloading of `operator=()` in the Tensor class.
+
+This mechanism for computing tensor expressions allows for lazy evaluation and
+optimizations which are what make the tensor library very fast.
+
+Of course, the tensor operators do nest, and the expression `t1 + t2 * 0.3f`
+is actually represented with the (approximate) tree of operators:
+
+ TensorCwiseBinaryOp<scalar_sum>(t1, TensorCwiseUnaryOp<scalar_mul>(t2, 0.3f))
+
+
+### Tensor Operations and C++ "auto"
+
+Because Tensor operations create tensor operators, the C++ `auto` keyword
+does not have its intuitive meaning. Consider these 2 lines of code:
+
+ Tensor<float, 3> t3 = t1 + t2;
+ auto t4 = t1 + t2;
+
+In the first line we allocate the tensor `t3` and it will contain the
+result of the addition of `t1` and `t2`. In the second line, `t4`
+is actually the tree of tensor operators that will compute the addition of
+`t1` and `t2`. In fact, `t4` is *not* a tensor and you cannot get
+the values of its elements:
+
+ Tensor<float, 3> t3 = t1 + t2;
+ cout << t3(0, 0, 0); // OK prints the value of t1(0, 0, 0) + t2(0, 0, 0)
+
+ auto t4 = t1 + t2;
+ cout << t4(0, 0, 0); // Compilation error!
+
+When you use `auto` you do not get a Tensor as a result but instead a
+non-evaluated expression. So only use `auto` to delay evaluation.
+
+Unfortunately, there is no single underlying concrete type for holding
+non-evaluated expressions, hence you have to use auto in the case when you do
+want to hold non-evaluated expressions.
+
+When you need the results of set of tensor computations you have to assign the
+result to a Tensor that will be capable of holding onto them. This can be
+either a normal Tensor, a fixed size Tensor, or a TensorMap on an existing
+piece of memory. All the following will work:
+
+ auto t4 = t1 + t2;
+
+ Tensor<float, 3> result = t4; // Could also be: result(t4);
+ cout << result(0, 0, 0);
+
+ TensorMap<float, 4> result(<a float* with enough space>, <size0>, ...) = t4;
+ cout << result(0, 0, 0);
+
+ TensorFixedSize<float, Sizes<size0, ...>> result = t4;
+ cout << result(0, 0, 0);
+
+Until you need the results, you can keep the operation around, and even reuse
+it for additional operations. As long as you keep the expression as an
+operation, no computation is performed.
+
+ // One way to compute exp((t1 + t2) * 0.2f);
+ auto t3 = t1 + t2;
+ auto t4 = t3 * 0.2f;
+ auto t5 = t4.exp();
+ Tensor<float, 3> result = t5;
+
+ // Another way, exactly as efficient as the previous one:
+ Tensor<float, 3> result = ((t1 + t2) * 0.2f).exp();
+
+### Controlling When Expression are Evaluated
+
+There are several ways to control when expressions are evaluated:
+
+* Assignment to a Tensor, TensorFixedSize, or TensorMap.
+* Use of the eval() method.
+* Assignment to a TensorRef.
+
+#### Assigning to a Tensor, TensorFixedSize, or TensorMap.
+
+The most common way to evaluate an expression is to assign it to a Tensor. In
+the example below, the `auto` declarations make the intermediate values
+"Operations", not Tensors, and do not cause the expressions to be evaluated.
+The assignment to the Tensor `result` causes the evaluation of all the
+operations.
+
+ auto t3 = t1 + t2; // t3 is an Operation.
+ auto t4 = t3 * 0.2f; // t4 is an Operation.
+ auto t5 = t4.exp(); // t5 is an Operation.
+ Tensor<float, 3> result = t5; // The operations are evaluated.
+
+If you know the ranks and sizes of the Operation value you can assign the
+Operation to a TensorFixedSize instead of a Tensor, which is a bit more
+efficient.
+
+ // We know that the result is a 4x4x2 tensor!
+ TensorFixedSize<float, Sizes<4, 4, 2>> result = t5;
+
+Simiarly, assigning an expression to a TensorMap causes its evaluation. Like
+tensors of type TensorFixedSize, TensorMaps cannot be resized so they have to
+have the rank and sizes of the expression that are assigned to them.
+
+#### Calling eval().
+
+When you compute large composite expressions, you sometimes want to tell Eigen
+that an intermediate value in the expression tree is worth evaluating ahead of
+time. This is done by inserting a call to the `eval()` method of the
+expression Operation.
+
+ // The previous example could have been written:
+ Tensor<float, 3> result = ((t1 + t2) * 0.2f).exp();
+
+ // If you want to compute (t1 + t2) once ahead of time you can write:
+ Tensor<float, 3> result = ((t1 + t2).eval() * 0.2f).exp();
+
+Semantically, calling `eval()` is equivalent to materializing the value of
+the expression in a temporary Tensor of the right size. The code above in
+effect does:
+
+ // .eval() knows the size!
+ TensorFixedSize<float, Sizes<4, 4, 2>> tmp = t1 + t2;
+ Tensor<float, 3> result = (tmp * 0.2f).exp();
+
+Note that the return value of `eval()` is itself an Operation, so the
+following code does not do what you may think:
+
+ // Here t3 is an evaluation Operation. t3 has not been evaluated yet.
+ auto t3 = (t1 + t2).eval();
+
+ // You can use t3 in another expression. Still no evaluation.
+ auto t4 = (t3 * 0.2f).exp();
+
+ // The value is evaluated when you assign the Operation to a Tensor, using
+ // an intermediate tensor to represent t3.x
+ Tensor<float, 3> result = t4;
+
+While in the examples above calling `eval()` does not make a difference in
+performance, in other cases it can make a huge difference. In the expression
+below the `broadcast()` expression causes the `X.maximum()` expression
+to be evaluated many times:
+
+ Tensor<...> X ...;
+ Tensor<...> Y = ((X - X.maximum(depth_dim).reshape(dims2d).broadcast(bcast))
+ * beta).exp();
+
+Inserting a call to `eval()` between the `maximum()` and
+`reshape()` calls guarantees that maximum() is only computed once and
+greatly speeds-up execution:
+
+ Tensor<...> Y =
+ ((X - X.maximum(depth_dim).eval().reshape(dims2d).broadcast(bcast))
+ * beta).exp();
+
+In the other example below, the tensor `Y` is both used in the expression
+and its assignment. This is an aliasing problem and if the evaluation is not
+done in the right order Y will be updated incrementally during the evaluation
+resulting in bogus results:
+
+ Tensor<...> Y ...;
+ Y = Y / (Y.sum(depth_dim).reshape(dims2d).broadcast(bcast));
+
+Inserting a call to `eval()` between the `sum()` and `reshape()`
+expressions ensures that the sum is computed before any updates to `Y` are
+done.
+
+ Y = Y / (Y.sum(depth_dim).eval().reshape(dims2d).broadcast(bcast));
+
+Note that an eval around the full right hand side expression is not needed
+because the generated has to compute the i-th value of the right hand side
+before assigning it to the left hand side.
+
+However, if you were assigning the expression value to a shuffle of `Y`
+then you would need to force an eval for correctness by adding an `eval()`
+call for the right hand side:
+
+ Y.shuffle(...) =
+ (Y / (Y.sum(depth_dim).eval().reshape(dims2d).broadcast(bcast))).eval();
+
+
+#### Assigning to a TensorRef.
+
+If you need to access only a few elements from the value of an expression you
+can avoid materializing the value in a full tensor by using a TensorRef.
+
+A TensorRef is a small wrapper class for any Eigen Operation. It provides
+overloads for the `()` operator that let you access individual values in
+the expression. TensorRef is convenient, because the Operation themselves do
+not provide a way to access individual elements.
+
+ // Create a TensorRef for the expression. The expression is not
+ // evaluated yet.
+ TensorRef<Tensor<float, 3> > ref = ((t1 + t2) * 0.2f).exp();
+
+ // Use "ref" to access individual elements. The expression is evaluated
+ // on the fly.
+ float at_0 = ref(0, 0, 0);
+ cout << ref(0, 1, 0);
+
+Only use TensorRef when you need a subset of the values of the expression.
+TensorRef only computes the values you access. However note that if you are
+going to access all the values it will be much faster to materialize the
+results in a Tensor first.
+
+In some cases, if the full Tensor result would be very large, you may save
+memory by accessing it as a TensorRef. But not always. So don't count on it.
+
+
+### Controlling How Expressions Are Evaluated
+
+The tensor library provides several implementations of the various operations
+such as contractions and convolutions. The implementations are optimized for
+different environments: single threaded on CPU, multi threaded on CPU, or on a
+GPU using cuda. Additional implementations may be added later.
+
+You can choose which implementation to use with the `device()` call. If
+you do not choose an implementation explicitly the default implementation that
+uses a single thread on the CPU is used.
+
+The default implementation has been optimized for recent Intel CPUs, taking
+advantage of SSE, AVX, and FMA instructions. Work is ongoing to tune the
+library on ARM CPUs. Note that you need to pass compiler-dependent flags
+to enable the use of SSE, AVX, and other instructions.
+
+For example, the following code adds two tensors using the default
+single-threaded CPU implementation:
+
+ Tensor<float, 2> a(30, 40);
+ Tensor<float, 2> b(30, 40);
+ Tensor<float, 2> c = a + b;
+
+To choose a different implementation you have to insert a `device()` call
+before the assignment of the result. For technical C++ reasons this requires
+that the Tensor for the result be declared on its own. This means that you
+have to know the size of the result.
+
+ Eigen::Tensor<float, 2> c(30, 40);
+ c.device(...) = a + b;
+
+The call to `device()` must be the last call on the left of the operator=.
+
+You must pass to the `device()` call an Eigen device object. There are
+presently three devices you can use: DefaultDevice, ThreadPoolDevice and
+GpuDevice.
+
+
+#### Evaluating With the DefaultDevice
+
+This is exactly the same as not inserting a `device()` call.
+
+ DefaultDevice my_device;
+ c.device(my_device) = a + b;
+
+#### Evaluating with a Thread Pool
+
+ // Create the Eigen ThreadPool
+ Eigen::ThreadPool pool(8 /* number of threads in pool */)
+
+ // Create the Eigen ThreadPoolDevice.
+ Eigen::ThreadPoolDevice my_device(&pool, 4 /* number of threads to use */);
+
+ // Now just use the device when evaluating expressions.
+ Eigen::Tensor<float, 2> c(30, 50);
+ c.device(my_device) = a.contract(b, dot_product_dims);
+
+
+#### Evaluating On GPU
+
+This is presently a bit more complicated than just using a thread pool device.
+You need to create a GPU device but you also need to explicitly allocate the
+memory for tensors with cuda.
+
+
+## API Reference
+
+### Datatypes
+
+In the documentation of the tensor methods and Operation we mention datatypes
+that are tensor-type specific:
+
+#### <Tensor-Type>::Dimensions
+
+Acts like an array of ints. Has an `int size` attribute, and can be
+indexed like an array to access individual values. Used to represent the
+dimensions of a tensor. See `dimensions()`.
+
+#### <Tensor-Type>::Index
+
+Acts like an `int`. Used for indexing tensors along their dimensions. See
+`operator()`, `dimension()`, and `size()`.
+
+#### <Tensor-Type>::Scalar
+
+Represents the datatype of individual tensor elements. For example, for a
+`Tensor<float>`, `Scalar` is the type `float`. See
+`setConstant()`.
+
+#### <Operation>
+
+We use this pseudo type to indicate that a tensor Operation is returned by a
+method. We indicate in the text the type and dimensions of the tensor that the
+Operation returns after evaluation.
+
+The Operation will have to be evaluated, for example by assigning it to a
+tensor, before you can access the values of the resulting tensor. You can also
+access the values through a TensorRef.
+
+
+## Built-in Tensor Methods
+
+These are usual C++ methods that act on tensors immediately. They are not
+Operations which provide delayed evaluation of their results. Unless specified
+otherwise, all the methods listed below are available on all tensor classes:
+Tensor, TensorFixedSize, and TensorMap.
+
+## Metadata
+
+### int NumDimensions
+
+Constant value indicating the number of dimensions of a Tensor. This is also
+known as the tensor "rank".
+
+ Eigen::Tensor<float, 2> a(3, 4);
+ cout << "Dims " << a.NumDimensions;
+ => Dims 2
+
+### Dimensions dimensions()
+
+Returns an array-like object representing the dimensions of the tensor.
+The actual type of the `dimensions()` result is `<Tensor-Type>::``Dimensions`.
+
+ Eigen::Tensor<float, 2> a(3, 4);
+ const Eigen::Tensor<float, 2>::Dimensions& d = a.dimensions();
+ cout << "Dim size: " << d.size << ", dim 0: " << d[0]
+ << ", dim 1: " << d[1];
+ => Dim size: 2, dim 0: 3, dim 1: 4
+
+If you use a C++11 compiler, you can use `auto` to simplify the code:
+
+ const auto& d = a.dimensions();
+ cout << "Dim size: " << d.size << ", dim 0: " << d[0]
+ << ", dim 1: " << d[1];
+ => Dim size: 2, dim 0: 3, dim 1: 4
+
+### Index dimension(Index n)
+
+Returns the n-th dimension of the tensor. The actual type of the
+`dimension()` result is `<Tensor-Type>::``Index`, but you can
+always use it like an int.
+
+ Eigen::Tensor<float, 2> a(3, 4);
+ int dim1 = a.dimension(1);
+ cout << "Dim 1: " << dim1;
+ => Dim 1: 4
+
+### Index size()
+
+Returns the total number of elements in the tensor. This is the product of all
+the tensor dimensions. The actual type of the `size()` result is
+`<Tensor-Type>::``Index`, but you can always use it like an int.
+
+ Eigen::Tensor<float, 2> a(3, 4);
+ cout << "Size: " << a.size();
+ => Size: 12
+
+
+### Getting Dimensions From An Operation
+
+A few operations provide `dimensions()` directly,
+e.g. `TensorReslicingOp`. Most operations defer calculating dimensions
+until the operation is being evaluated. If you need access to the dimensions
+of a deferred operation, you can wrap it in a TensorRef (see Assigning to a
+TensorRef above), which provides `dimensions()` and `dimension()` as
+above.
+
+TensorRef can also wrap the plain Tensor types, so this is a useful idiom in
+templated contexts where the underlying object could be either a raw Tensor
+or some deferred operation (e.g. a slice of a Tensor). In this case, the
+template code can wrap the object in a TensorRef and reason about its
+dimensionality while remaining agnostic to the underlying type.
+
+
+## Constructors
+
+### Tensor
+
+Creates a tensor of the specified size. The number of arguments must be equal
+to the rank of the tensor. The content of the tensor is not initialized.
+
+ Eigen::Tensor<float, 2> a(3, 4);
+ cout << "NumRows: " << a.dimension(0) << " NumCols: " << a.dimension(1) << endl;
+ => NumRows: 3 NumCols: 4
+
+### TensorFixedSize
+
+Creates a tensor of the specified size. The number of arguments in the Sizes<>
+template parameter determines the rank of the tensor. The content of the tensor
+is not initialized.
+
+ Eigen::TensorFixedSize<float, Sizes<3, 4>> a;
+ cout << "Rank: " << a.rank() << endl;
+ => Rank: 2
+ cout << "NumRows: " << a.dimension(0) << " NumCols: " << a.dimension(1) << endl;
+ => NumRows: 3 NumCols: 4
+
+### TensorMap
+
+Creates a tensor mapping an existing array of data. The data must not be freed
+until the TensorMap is discarded, and the size of the data must be large enough
+to accommodate the coefficients of the tensor.
+
+ float data[] = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11};
+ Eigen::TensorMap<Tensor<float, 2>> a(data, 3, 4);
+ cout << "NumRows: " << a.dimension(0) << " NumCols: " << a.dimension(1) << endl;
+ => NumRows: 3 NumCols: 4
+ cout << "a(1, 2): " << a(1, 2) << endl;
+ => a(1, 2): 7
+
+
+## Contents Initialization
+
+When a new Tensor or a new TensorFixedSize are created, memory is allocated to
+hold all the tensor elements, but the memory is not initialized. Similarly,
+when a new TensorMap is created on top of non-initialized memory the memory its
+contents are not initialized.
+
+You can use one of the methods below to initialize the tensor memory. These
+have an immediate effect on the tensor and return the tensor itself as a
+result. These are not tensor Operations which delay evaluation.
+
+### <Tensor-Type> setConstant(const Scalar& val)
+
+Sets all elements of the tensor to the constant value `val`. `Scalar`
+is the type of data stored in the tensor. You can pass any value that is
+convertible to that type.
+
+Returns the tensor itself in case you want to chain another call.
+
+ a.setConstant(12.3f);
+ cout << "Constant: " << endl << a << endl << endl;
+ =>
+ Constant:
+ 12.3 12.3 12.3 12.3
+ 12.3 12.3 12.3 12.3
+ 12.3 12.3 12.3 12.3
+
+Note that `setConstant()` can be used on any tensor where the element type
+has a copy constructor and an `operator=()`:
+
+ Eigen::Tensor<string, 2> a(2, 3);
+ a.setConstant("yolo");
+ cout << "String tensor: " << endl << a << endl << endl;
+ =>
+ String tensor:
+ yolo yolo yolo
+ yolo yolo yolo
+
+
+### <Tensor-Type> setZero()
+
+Fills the tensor with zeros. Equivalent to `setConstant(Scalar(0))`.
+Returns the tensor itself in case you want to chain another call.
+
+ a.setZero();
+ cout << "Zeros: " << endl << a << endl << endl;
+ =>
+ Zeros:
+ 0 0 0 0
+ 0 0 0 0
+ 0 0 0 0
+
+
+### <Tensor-Type> setValues({..initializer_list})
+
+Fills the tensor with explicit values specified in a std::initializer_list.
+The type of the initializer list depends on the type and rank of the tensor.
+
+If the tensor has rank N, the initializer list must be nested N times. The
+most deeply nested lists must contains P scalars of the Tensor type where P is
+the size of the last dimension of the Tensor.
+
+For example, for a `TensorFixedSize<float, 2, 3>` the initializer list must
+contains 2 lists of 3 floats each.
+
+`setValues()` returns the tensor itself in case you want to chain another
+call.
+
+ Eigen::Tensor<float, 2> a(2, 3);
+ a.setValues({{0.0f, 1.0f, 2.0f}, {3.0f, 4.0f, 5.0f}});
+ cout << "a" << endl << a << endl << endl;
+ =>
+ a
+ 0 1 2
+ 3 4 5
+
+If a list is too short, the corresponding elements of the tensor will not be
+changed. This is valid at each level of nesting. For example the following
+code only sets the values of the first row of the tensor.
+
+ Eigen::Tensor<int, 2> a(2, 3);
+ a.setConstant(1000);
+ a.setValues({{10, 20, 30}});
+ cout << "a" << endl << a << endl << endl;
+ =>
+ a
+ 10 20 30
+ 1000 1000 1000
+
+### <Tensor-Type> setRandom()
+
+Fills the tensor with random values. Returns the tensor itself in case you
+want to chain another call.
+
+ a.setRandom();
+ cout << "Random: " << endl << a << endl << endl;
+ =>
+ Random:
+ 0.680375 0.59688 -0.329554 0.10794
+ -0.211234 0.823295 0.536459 -0.0452059
+ 0.566198 -0.604897 -0.444451 0.257742
+
+You can customize `setRandom()` by providing your own random number
+generator as a template argument:
+
+ a.setRandom<MyRandomGenerator>();
+
+Here, `MyRandomGenerator` must be a struct with the following member
+functions, where Scalar and Index are the same as `<Tensor-Type>::``Scalar`
+and `<Tensor-Type>::``Index`.
+
+See `struct UniformRandomGenerator` in TensorFunctors.h for an example.
+
+ // Custom number generator for use with setRandom().
+ struct MyRandomGenerator {
+ // Default and copy constructors. Both are needed
+ MyRandomGenerator() { }
+ MyRandomGenerator(const MyRandomGenerator& ) { }
+
+ // Return a random value to be used. "element_location" is the
+ // location of the entry to set in the tensor, it can typically
+ // be ignored.
+ Scalar operator()(Eigen::DenseIndex element_location,
+ Eigen::DenseIndex /*unused*/ = 0) const {
+ return <randomly generated value of type T>;
+ }
+
+ // Same as above but generates several numbers at a time.
+ typename internal::packet_traits<Scalar>::type packetOp(
+ Eigen::DenseIndex packet_location, Eigen::DenseIndex /*unused*/ = 0) const {
+ return <a packet of randomly generated values>;
+ }
+ };
+
+You can also use one of the 2 random number generators that are part of the
+tensor library:
+* UniformRandomGenerator
+* NormalRandomGenerator
+
+
+## Data Access
+
+The Tensor, TensorFixedSize, and TensorRef classes provide the following
+accessors to access the tensor coefficients:
+
+ const Scalar& operator()(const array<Index, NumIndices>& indices)
+ const Scalar& operator()(Index firstIndex, IndexTypes... otherIndices)
+ Scalar& operator()(const array<Index, NumIndices>& indices)
+ Scalar& operator()(Index firstIndex, IndexTypes... otherIndices)
+
+The number of indices must be equal to the rank of the tensor. Moreover, these
+accessors are not available on tensor expressions. In order to access the
+values of a tensor expression, the expression must either be evaluated or
+wrapped in a TensorRef.
+
+
+### Scalar* data() and const Scalar* data() const
+
+Returns a pointer to the storage for the tensor. The pointer is const if the
+tensor was const. This allows direct access to the data. The layout of the
+data depends on the tensor layout: RowMajor or ColMajor.
+
+This access is usually only needed for special cases, for example when mixing
+Eigen Tensor code with other libraries.
+
+Scalar is the type of data stored in the tensor.
+
+ Eigen::Tensor<float, 2> a(3, 4);
+ float* a_data = a.data();
+ a_data[0] = 123.45f;
+ cout << "a(0, 0): " << a(0, 0);
+ => a(0, 0): 123.45
+
+
+## Tensor Operations
+
+All the methods documented below return non evaluated tensor `Operations`.
+These can be chained: you can apply another Tensor Operation to the value
+returned by the method.
+
+The chain of Operation is evaluated lazily, typically when it is assigned to a
+tensor. See "Controlling when Expression are Evaluated" for more details about
+their evaluation.
+
+### <Operation> constant(const Scalar& val)
+
+Returns a tensor of the same type and dimensions as the original tensor but
+where all elements have the value `val`.
+
+This is useful, for example, when you want to add or subtract a constant from a
+tensor, or multiply every element of a tensor by a scalar.
+
+ Eigen::Tensor<float, 2> a(2, 3);
+ a.setConstant(1.0f);
+ Eigen::Tensor<float, 2> b = a + a.constant(2.0f);
+ Eigen::Tensor<float, 2> c = b * b.constant(0.2f);
+ cout << "a" << endl << a << endl << endl;
+ cout << "b" << endl << b << endl << endl;
+ cout << "c" << endl << c << endl << endl;
+ =>
+ a
+ 1 1 1
+ 1 1 1
+
+ b
+ 3 3 3
+ 3 3 3
+
+ c
+ 0.6 0.6 0.6
+ 0.6 0.6 0.6
+
+### <Operation> random()
+
+Returns a tensor of the same type and dimensions as the current tensor
+but where all elements have random values.
+
+This is for example useful to add random values to an existing tensor.
+The generation of random values can be customized in the same manner
+as for `setRandom()`.
+
+ Eigen::Tensor<float, 2> a(2, 3);
+ a.setConstant(1.0f);
+ Eigen::Tensor<float, 2> b = a + a.random();
+ cout << "a" << endl << a << endl << endl;
+ cout << "b" << endl << b << endl << endl;
+ =>
+ a
+ 1 1 1
+ 1 1 1
+
+ b
+ 1.68038 1.5662 1.82329
+ 0.788766 1.59688 0.395103
+
+
+## Unary Element Wise Operations
+
+All these operations take a single input tensor as argument and return a tensor
+of the same type and dimensions as the tensor to which they are applied. The
+requested operations are applied to each element independently.
+
+### <Operation> operator-()
+
+Returns a tensor of the same type and dimensions as the original tensor
+containing the opposite values of the original tensor.
+
+ Eigen::Tensor<float, 2> a(2, 3);
+ a.setConstant(1.0f);
+ Eigen::Tensor<float, 2> b = -a;
+ cout << "a" << endl << a << endl << endl;
+ cout << "b" << endl << b << endl << endl;
+ =>
+ a
+ 1 1 1
+ 1 1 1
+
+ b
+ -1 -1 -1
+ -1 -1 -1
+
+### <Operation> sqrt()
+
+Returns a tensor of the same type and dimensions as the original tensor
+containing the square roots of the original tensor.
+
+### <Operation> rsqrt()
+
+Returns a tensor of the same type and dimensions as the original tensor
+containing the inverse square roots of the original tensor.
+
+### <Operation> square()
+
+Returns a tensor of the same type and dimensions as the original tensor
+containing the squares of the original tensor values.
+
+### <Operation> inverse()
+
+Returns a tensor of the same type and dimensions as the original tensor
+containing the inverse of the original tensor values.
+
+### <Operation> exp()
+
+Returns a tensor of the same type and dimensions as the original tensor
+containing the exponential of the original tensor.
+
+### <Operation> log()
+
+Returns a tensor of the same type and dimensions as the original tensor
+containing the natural logarithms of the original tensor.
+
+### <Operation> abs()
+
+Returns a tensor of the same type and dimensions as the original tensor
+containing the absolute values of the original tensor.
+
+### <Operation> arg()
+
+Returns a tensor with the same dimensions as the original tensor
+containing the complex argument (phase angle) of the values of the
+original tensor.
+
+### <Operation> real()
+
+Returns a tensor with the same dimensions as the original tensor
+containing the real part of the complex values of the original tensor.
+
+### <Operation> imag()
+
+Returns a tensor with the same dimensions as the orginal tensor
+containing the imaginary part of the complex values of the original
+tensor.
+
+### <Operation> pow(Scalar exponent)
+
+Returns a tensor of the same type and dimensions as the original tensor
+containing the coefficients of the original tensor to the power of the
+exponent.
+
+The type of the exponent, Scalar, is always the same as the type of the
+tensor coefficients. For example, only integer exponents can be used in
+conjuntion with tensors of integer values.
+
+You can use cast() to lift this restriction. For example this computes
+cubic roots of an int Tensor:
+
+ Eigen::Tensor<int, 2> a(2, 3);
+ a.setValues({{0, 1, 8}, {27, 64, 125}});
+ Eigen::Tensor<double, 2> b = a.cast<double>().pow(1.0 / 3.0);
+ cout << "a" << endl << a << endl << endl;
+ cout << "b" << endl << b << endl << endl;
+ =>
+ a
+ 0 1 8
+ 27 64 125
+
+ b
+ 0 1 2
+ 3 4 5
+
+### <Operation> operator * (Scalar scale)
+
+Multiplies all the coefficients of the input tensor by the provided scale.
+
+### <Operation> cwiseMax(Scalar threshold)
+TODO
+
+### <Operation> cwiseMin(Scalar threshold)
+TODO
+
+### <Operation> unaryExpr(const CustomUnaryOp& func)
+TODO
+
+
+## Binary Element Wise Operations
+
+These operations take two input tensors as arguments. The 2 input tensors should
+be of the same type and dimensions. The result is a tensor of the same
+dimensions as the tensors to which they are applied, and unless otherwise
+specified it is also of the same type. The requested operations are applied to
+each pair of elements independently.
+
+### <Operation> operator+(const OtherDerived& other)
+
+Returns a tensor of the same type and dimensions as the input tensors
+containing the coefficient wise sums of the inputs.
+
+### <Operation> operator-(const OtherDerived& other)
+
+Returns a tensor of the same type and dimensions as the input tensors
+containing the coefficient wise differences of the inputs.
+
+### <Operation> operator*(const OtherDerived& other)
+
+Returns a tensor of the same type and dimensions as the input tensors
+containing the coefficient wise products of the inputs.
+
+### <Operation> operator/(const OtherDerived& other)
+
+Returns a tensor of the same type and dimensions as the input tensors
+containing the coefficient wise quotients of the inputs.
+
+This operator is not supported for integer types.
+
+### <Operation> cwiseMax(const OtherDerived& other)
+
+Returns a tensor of the same type and dimensions as the input tensors
+containing the coefficient wise maximums of the inputs.
+
+### <Operation> cwiseMin(const OtherDerived& other)
+
+Returns a tensor of the same type and dimensions as the input tensors
+containing the coefficient wise mimimums of the inputs.
+
+### <Operation> Logical operators
+
+The following logical operators are supported as well:
+
+* operator&&(const OtherDerived& other)
+* operator||(const OtherDerived& other)
+* operator<(const OtherDerived& other)
+* operator<=(const OtherDerived& other)
+* operator>(const OtherDerived& other)
+* operator>=(const OtherDerived& other)
+* operator==(const OtherDerived& other)
+* operator!=(const OtherDerived& other)
+
+They all return a tensor of boolean values.
+
+
+## Selection (select(const ThenDerived& thenTensor, const ElseDerived& elseTensor)
+
+Selection is a coefficient-wise ternary operator that is the tensor equivalent
+to the if-then-else operation.
+
+ Tensor<bool, 3> if = ...;
+ Tensor<float, 3> then = ...;
+ Tensor<float, 3> else = ...;
+ Tensor<float, 3> result = if.select(then, else);
+
+The 3 arguments must be of the same dimensions, which will also be the dimension
+of the result. The 'if' tensor must be of type boolean, the 'then' and the
+'else' tensor must be of the same type, which will also be the type of the
+result.
+
+Each coefficient in the result is equal to the corresponding coefficient in the
+'then' tensor if the corresponding value in the 'if' tensor is true. If not, the
+resulting coefficient will come from the 'else' tensor.
+
+
+## Contraction
+
+Tensor *contractions* are a generalization of the matrix product to the
+multidimensional case.
+
+ // Create 2 matrices using tensors of rank 2
+ Eigen::Tensor<int, 2> a(2, 3);
+ a.setValues({{1, 2, 3}, {6, 5, 4}});
+ Eigen::Tensor<int, 2> b(3, 2);
+ b.setValues({{1, 2}, {4, 5}, {5, 6}});
+
+ // Compute the traditional matrix product
+ Eigen::array<Eigen::IndexPair<int>, 1> product_dims = { Eigen::IndexPair<int>(1, 0) };
+ Eigen::Tensor<int, 2> AB = a.contract(b, product_dims);
+
+ // Compute the product of the transpose of the matrices
+ Eigen::array<Eigen::IndexPair<int>, 1> transposed_product_dims = { Eigen::IndexPair<int>(0, 1) };
+ Eigen::Tensor<int, 2> AtBt = a.contract(b, transposed_product_dims);
+
+ // Contraction to scalar value using a double contraction.
+ // First coordinate of both tensors are contracted as well as both second coordinates, i.e., this computes the sum of the squares of the elements.
+ Eigen::array<Eigen::IndexPair<int>, 2> double_contraction_product_dims = { Eigen::IndexPair<int>(0, 0), Eigen::IndexPair<int>(1, 1) };
+ Eigen::Tensor<int, 0> AdoubleContractedA = a.contract(a, double_contraction_product_dims);
+
+ // Extracting the scalar value of the tensor contraction for further usage
+ int value = AdoubleContractedA(0);
+
+## Reduction Operations
+
+A *Reduction* operation returns a tensor with fewer dimensions than the
+original tensor. The values in the returned tensor are computed by applying a
+*reduction operator* to slices of values from the original tensor. You specify
+the dimensions along which the slices are made.
+
+The Eigen Tensor library provides a set of predefined reduction operators such
+as `maximum()` and `sum()` and lets you define additional operators by
+implementing a few methods from a reductor template.
+
+### Reduction Dimensions
+
+All reduction operations take a single parameter of type
+`<TensorType>::``Dimensions` which can always be specified as an array of
+ints. These are called the "reduction dimensions." The values are the indices
+of the dimensions of the input tensor over which the reduction is done. The
+parameter can have at most as many element as the rank of the input tensor;
+each element must be less than the tensor rank, as it indicates one of the
+dimensions to reduce.
+
+Each dimension of the input tensor should occur at most once in the reduction
+dimensions as the implementation does not remove duplicates.
+
+The order of the values in the reduction dimensions does not affect the
+results, but the code may execute faster if you list the dimensions in
+increasing order.
+
+Example: Reduction along one dimension.
+
+ // Create a tensor of 2 dimensions
+ Eigen::Tensor<int, 2> a(2, 3);
+ a.setValues({{1, 2, 3}, {6, 5, 4}});
+ // Reduce it along the second dimension (1)...
+ Eigen::array<int, 1> dims({1 /* dimension to reduce */});
+ // ...using the "maximum" operator.
+ // The result is a tensor with one dimension. The size of
+ // that dimension is the same as the first (non-reduced) dimension of a.
+ Eigen::Tensor<int, 1> b = a.maximum(dims);
+ cout << "a" << endl << a << endl << endl;
+ cout << "b" << endl << b << endl << endl;
+ =>
+ a
+ 1 2 3
+ 6 5 4
+
+ b
+ 3
+ 6
+
+Example: Reduction along two dimensions.
+
+ Eigen::Tensor<float, 3, Eigen::ColMajor> a(2, 3, 4);
+ a.setValues({{{0.0f, 1.0f, 2.0f, 3.0f},
+ {7.0f, 6.0f, 5.0f, 4.0f},
+ {8.0f, 9.0f, 10.0f, 11.0f}},
+ {{12.0f, 13.0f, 14.0f, 15.0f},
+ {19.0f, 18.0f, 17.0f, 16.0f},
+ {20.0f, 21.0f, 22.0f, 23.0f}}});
+ // The tensor a has 3 dimensions. We reduce along the
+ // first 2, resulting in a tensor with a single dimension
+ // of size 4 (the last dimension of a.)
+ // Note that we pass the array of reduction dimensions
+ // directly to the maximum() call.
+ Eigen::Tensor<float, 1, Eigen::ColMajor> b =
+ a.maximum(Eigen::array<int, 2>({0, 1}));
+ cout << "b" << endl << b << endl << endl;
+ =>
+ b
+ 20
+ 21
+ 22
+ 23
+
+#### Reduction along all dimensions
+
+As a special case, if you pass no parameter to a reduction operation the
+original tensor is reduced along *all* its dimensions. The result is a
+scalar, represented as a zero-dimension tensor.
+
+ Eigen::Tensor<float, 3> a(2, 3, 4);
+ a.setValues({{{0.0f, 1.0f, 2.0f, 3.0f},
+ {7.0f, 6.0f, 5.0f, 4.0f},
+ {8.0f, 9.0f, 10.0f, 11.0f}},
+ {{12.0f, 13.0f, 14.0f, 15.0f},
+ {19.0f, 18.0f, 17.0f, 16.0f},
+ {20.0f, 21.0f, 22.0f, 23.0f}}});
+ // Reduce along all dimensions using the sum() operator.
+ Eigen::Tensor<float, 0> b = a.sum();
+ cout << "b" << endl << b << endl << endl;
+ =>
+ b
+ 276
+
+
+### <Operation> sum(const Dimensions& new_dims)
+### <Operation> sum()
+
+Reduce a tensor using the sum() operator. The resulting values
+are the sum of the reduced values.
+
+### <Operation> mean(const Dimensions& new_dims)
+### <Operation> mean()
+
+Reduce a tensor using the mean() operator. The resulting values
+are the mean of the reduced values.
+
+### <Operation> maximum(const Dimensions& new_dims)
+### <Operation> maximum()
+
+Reduce a tensor using the maximum() operator. The resulting values are the
+largest of the reduced values.
+
+### <Operation> minimum(const Dimensions& new_dims)
+### <Operation> minimum()
+
+Reduce a tensor using the minimum() operator. The resulting values
+are the smallest of the reduced values.
+
+### <Operation> prod(const Dimensions& new_dims)
+### <Operation> prod()
+
+Reduce a tensor using the prod() operator. The resulting values
+are the product of the reduced values.
+
+### <Operation> all(const Dimensions& new_dims)
+### <Operation> all()
+Reduce a tensor using the all() operator. Casts tensor to bool and then checks
+whether all elements are true. Runs through all elements rather than
+short-circuiting, so may be significantly inefficient.
+
+### <Operation> any(const Dimensions& new_dims)
+### <Operation> any()
+Reduce a tensor using the any() operator. Casts tensor to bool and then checks
+whether any element is true. Runs through all elements rather than
+short-circuiting, so may be significantly inefficient.
+
+
+### <Operation> reduce(const Dimensions& new_dims, const Reducer& reducer)
+
+Reduce a tensor using a user-defined reduction operator. See `SumReducer`
+in TensorFunctors.h for information on how to implement a reduction operator.
+
+
+## Trace
+
+A *Trace* operation returns a tensor with fewer dimensions than the original
+tensor. It returns a tensor whose elements are the sum of the elements of the
+original tensor along the main diagonal for a list of specified dimensions, the
+"trace dimensions". Similar to the `Reduction Dimensions`, the trace dimensions
+are passed as an input parameter to the operation, are of type `<TensorType>::``Dimensions`
+, and have the same requirements when passed as an input parameter. In addition,
+the trace dimensions must have the same size.
+
+Example: Trace along 2 dimensions.
+
+ // Create a tensor of 3 dimensions
+ Eigen::Tensor<int, 3> a(2, 2, 3);
+ a.setValues({{{1, 2, 3}, {4, 5, 6}}, {{7, 8, 9}, {10, 11, 12}}});
+ // Specify the dimensions along which the trace will be computed.
+ // In this example, the trace can only be computed along the dimensions
+ // with indices 0 and 1
+ Eigen::array<int, 2> dims({0, 1});
+ // The output tensor contains all but the trace dimensions.
+ Tensor<int, 1> a_trace = a.trace(dims);
+ cout << "a_trace:" << endl;
+ cout << a_trace << endl;
+ =>
+ a_trace:
+ 11
+ 13
+ 15
+
+
+### <Operation> trace(const Dimensions& new_dims)
+### <Operation> trace()
+
+As a special case, if no parameter is passed to the operation, trace is computed
+along *all* dimensions of the input tensor.
+
+Example: Trace along all dimensions.
+
+ // Create a tensor of 3 dimensions, with all dimensions having the same size.
+ Eigen::Tensor<int, 3> a(3, 3, 3);
+ a.setValues({{{1, 2, 3}, {4, 5, 6}, {7, 8, 9}},
+ {{10, 11, 12}, {13, 14, 15}, {16, 17, 18}},
+ {{19, 20, 21}, {22, 23, 24}, {25, 26, 27}}});
+ // Result is a zero dimension tensor
+ Tensor<int, 0> a_trace = a.trace();
+ cout<<"a_trace:"<<endl;
+ cout<<a_trace<<endl;
+ =>
+ a_trace:
+ 42
+
+
+## Scan Operations
+
+A *Scan* operation returns a tensor with the same dimensions as the original
+tensor. The operation performs an inclusive scan along the specified
+axis, which means it computes a running total along the axis for a given
+reduction operation.
+If the reduction operation corresponds to summation, then this computes the
+prefix sum of the tensor along the given axis.
+
+Example:
+dd a comment to this line
+
+ // Create a tensor of 2 dimensions
+ Eigen::Tensor<int, 2> a(2, 3);
+ a.setValues({{1, 2, 3}, {4, 5, 6}});
+ // Scan it along the second dimension (1) using summation
+ Eigen::Tensor<int, 2> b = a.cumsum(1);
+ // The result is a tensor with the same size as the input
+ cout << "a" << endl << a << endl << endl;
+ cout << "b" << endl << b << endl << endl;
+ =>
+ a
+ 1 2 3
+ 4 5 6
+
+ b
+ 1 3 6
+ 4 9 15
+
+### <Operation> cumsum(const Index& axis)
+
+Perform a scan by summing consecutive entries.
+
+### <Operation> cumprod(const Index& axis)
+
+Perform a scan by multiplying consecutive entries.
+
+
+## Convolutions
+
+### <Operation> convolve(const Kernel& kernel, const Dimensions& dims)
+
+Returns a tensor that is the output of the convolution of the input tensor with the kernel,
+along the specified dimensions of the input tensor. The dimension size for dimensions of the output tensor
+which were part of the convolution will be reduced by the formula:
+output_dim_size = input_dim_size - kernel_dim_size + 1 (requires: input_dim_size >= kernel_dim_size).
+The dimension sizes for dimensions that were not part of the convolution will remain the same.
+Performance of the convolution can depend on the length of the stride(s) of the input tensor dimension(s) along which the
+convolution is computed (the first dimension has the shortest stride for ColMajor, whereas RowMajor's shortest stride is
+for the last dimension).
+
+ // Compute convolution along the second and third dimension.
+ Tensor<float, 4, DataLayout> input(3, 3, 7, 11);
+ Tensor<float, 2, DataLayout> kernel(2, 2);
+ Tensor<float, 4, DataLayout> output(3, 2, 6, 11);
+ input.setRandom();
+ kernel.setRandom();
+
+ Eigen::array<ptrdiff_t, 2> dims({1, 2}); // Specify second and third dimension for convolution.
+ output = input.convolve(kernel, dims);
+
+ for (int i = 0; i < 3; ++i) {
+ for (int j = 0; j < 2; ++j) {
+ for (int k = 0; k < 6; ++k) {
+ for (int l = 0; l < 11; ++l) {
+ const float result = output(i,j,k,l);
+ const float expected = input(i,j+0,k+0,l) * kernel(0,0) +
+ input(i,j+1,k+0,l) * kernel(1,0) +
+ input(i,j+0,k+1,l) * kernel(0,1) +
+ input(i,j+1,k+1,l) * kernel(1,1);
+ VERIFY_IS_APPROX(result, expected);
+ }
+ }
+ }
+ }
+
+
+## Geometrical Operations
+
+These operations return a Tensor with different dimensions than the original
+Tensor. They can be used to access slices of tensors, see them with different
+dimensions, or pad tensors with additional data.
+
+### <Operation> reshape(const Dimensions& new_dims)
+
+Returns a view of the input tensor that has been reshaped to the specified
+new dimensions. The argument new_dims is an array of Index values. The
+rank of the resulting tensor is equal to the number of elements in new_dims.
+
+The product of all the sizes in the new dimension array must be equal to
+the number of elements in the input tensor.
+
+ // Increase the rank of the input tensor by introducing a new dimension
+ // of size 1.
+ Tensor<float, 2> input(7, 11);
+ array<int, 3> three_dims{{7, 11, 1}};
+ Tensor<float, 3> result = input.reshape(three_dims);
+
+ // Decrease the rank of the input tensor by merging 2 dimensions;
+ array<int, 1> one_dim{{7 * 11}};
+ Tensor<float, 1> result = input.reshape(one_dim);
+
+This operation does not move any data in the input tensor, so the resulting
+contents of a reshaped Tensor depend on the data layout of the original Tensor.
+
+For example this is what happens when you `reshape()` a 2D ColMajor tensor
+to one dimension:
+
+ Eigen::Tensor<float, 2, Eigen::ColMajor> a(2, 3);
+ a.setValues({{0.0f, 100.0f, 200.0f}, {300.0f, 400.0f, 500.0f}});
+ Eigen::array<Eigen::DenseIndex, 1> one_dim({3 * 2});
+ Eigen::Tensor<float, 1, Eigen::ColMajor> b = a.reshape(one_dim);
+ cout << "b" << endl << b << endl;
+ =>
+ b
+ 0
+ 300
+ 100
+ 400
+ 200
+ 500
+
+This is what happens when the 2D Tensor is RowMajor:
+
+ Eigen::Tensor<float, 2, Eigen::RowMajor> a(2, 3);
+ a.setValues({{0.0f, 100.0f, 200.0f}, {300.0f, 400.0f, 500.0f}});
+ Eigen::array<Eigen::DenseIndex, 1> one_dim({3 * 2});
+ Eigen::Tensor<float, 1, Eigen::RowMajor> b = a.reshape(one_dim);
+ cout << "b" << endl << b << endl;
+ =>
+ b
+ 0
+ 100
+ 200
+ 300
+ 400
+ 500
+
+The reshape operation is a lvalue. In other words, it can be used on the left
+side of the assignment operator.
+
+The previous example can be rewritten as follow:
+
+ Eigen::Tensor<float, 2, Eigen::ColMajor> a(2, 3);
+ a.setValues({{0.0f, 100.0f, 200.0f}, {300.0f, 400.0f, 500.0f}});
+ Eigen::array<Eigen::DenseIndex, 2> two_dim({2, 3});
+ Eigen::Tensor<float, 1, Eigen::ColMajor> b(6);
+ b.reshape(two_dim) = a;
+ cout << "b" << endl << b << endl;
+ =>
+ b
+ 0
+ 300
+ 100
+ 400
+ 200
+ 500
+
+Note that "b" itself was not reshaped but that instead the assignment is done to
+the reshape view of b.
+
+
+### <Operation> shuffle(const Shuffle& shuffle)
+
+Returns a copy of the input tensor whose dimensions have been
+reordered according to the specified permutation. The argument shuffle
+is an array of Index values. Its size is the rank of the input
+tensor. It must contain a permutation of 0, 1, ..., rank - 1. The i-th
+dimension of the output tensor equals to the size of the shuffle[i]-th
+dimension of the input tensor. For example:
+
+ // Shuffle all dimensions to the left by 1.
+ Tensor<float, 3> input(20, 30, 50);
+ // ... set some values in input.
+ Tensor<float, 3> output = input.shuffle({1, 2, 0})
+
+ eigen_assert(output.dimension(0) == 30);
+ eigen_assert(output.dimension(1) == 50);
+ eigen_assert(output.dimension(2) == 20);
+
+Indices into the output tensor are shuffled accordingly to formulate
+indices into the input tensor. For example, one can assert in the above
+code snippet that:
+
+ eigen_assert(output(3, 7, 11) == input(11, 3, 7));
+
+In general, one can assert that
+
+ eigen_assert(output(..., indices[shuffle[i]], ...) ==
+ input(..., indices[i], ...))
+
+The shuffle operation results in a lvalue, which means that it can be assigned
+to. In other words, it can be used on the left side of the assignment operator.
+
+Let's rewrite the previous example to take advantage of this feature:
+
+ // Shuffle all dimensions to the left by 1.
+ Tensor<float, 3> input(20, 30, 50);
+ // ... set some values in input.
+ Tensor<float, 3> output(30, 50, 20);
+ output.shuffle({2, 0, 1}) = input;
+
+
+### <Operation> stride(const Strides& strides)
+
+Returns a view of the input tensor that strides (skips stride-1
+elements) along each of the dimensions. The argument strides is an
+array of Index values. The dimensions of the resulting tensor are
+ceil(input_dimensions[i] / strides[i]).
+
+For example this is what happens when you `stride()` a 2D tensor:
+
+ Eigen::Tensor<int, 2> a(4, 3);
+ a.setValues({{0, 100, 200}, {300, 400, 500}, {600, 700, 800}, {900, 1000, 1100}});
+ Eigen::array<Eigen::DenseIndex, 2> strides({3, 2});
+ Eigen::Tensor<int, 2> b = a.stride(strides);
+ cout << "b" << endl << b << endl;
+ =>
+ b
+ 0 200
+ 900 1100
+
+It is possible to assign a tensor to a stride:
+ Tensor<float, 3> input(20, 30, 50);
+ // ... set some values in input.
+ Tensor<float, 3> output(40, 90, 200);
+ output.stride({2, 3, 4}) = input;
+
+
+### <Operation> slice(const StartIndices& offsets, const Sizes& extents)
+
+Returns a sub-tensor of the given tensor. For each dimension i, the slice is
+made of the coefficients stored between offset[i] and offset[i] + extents[i] in
+the input tensor.
+
+ Eigen::Tensor<int, 2> a(4, 3);
+ a.setValues({{0, 100, 200}, {300, 400, 500},
+ {600, 700, 800}, {900, 1000, 1100}});
+ Eigen::array<Eigen::Index, 2> offsets = {1, 0};
+ Eigen::array<Eigen::Index, 2> extents = {2, 2};
+ Eigen::Tensor<int, 2> slice = a.slice(offsets, extents);
+ cout << "a" << endl << a << endl;
+ =>
+ a
+ 0 100 200
+ 300 400 500
+ 600 700 800
+ 900 1000 1100
+ cout << "slice" << endl << slice << endl;
+ =>
+ slice
+ 300 400
+ 600 700
+
+
+### <Operation> chip(const Index offset, const Index dim)
+
+A chip is a special kind of slice. It is the subtensor at the given offset in
+the dimension dim. The returned tensor has one fewer dimension than the input
+tensor: the dimension dim is removed.
+
+For example, a matrix chip would be either a row or a column of the input
+matrix.
+
+ Eigen::Tensor<int, 2> a(4, 3);
+ a.setValues({{0, 100, 200}, {300, 400, 500},
+ {600, 700, 800}, {900, 1000, 1100}});
+ Eigen::Tensor<int, 1> row_3 = a.chip(2, 0);
+ Eigen::Tensor<int, 1> col_2 = a.chip(1, 1);
+ cout << "a" << endl << a << endl;
+ =>
+ a
+ 0 100 200
+ 300 400 500
+ 600 700 800
+ 900 1000 1100
+ cout << "row_3" << endl << row_3 << endl;
+ =>
+ row_3
+ 600 700 800
+ cout << "col_2" << endl << col_2 << endl;
+ =>
+ col_2
+ 100 400 700 1000
+
+It is possible to assign values to a tensor chip since the chip operation is a
+lvalue. For example:
+
+ Eigen::Tensor<int, 1> a(3);
+ a.setValues({{100, 200, 300}});
+ Eigen::Tensor<int, 2> b(2, 3);
+ b.setZero();
+ b.chip(0, 0) = a;
+ cout << "a" << endl << a << endl;
+ =>
+ a
+ 100
+ 200
+ 300
+ cout << "b" << endl << b << endl;
+ =>
+ b
+ 100 200 300
+ 0 0 0
+
+
+### <Operation> reverse(const ReverseDimensions& reverse)
+
+Returns a view of the input tensor that reverses the order of the coefficients
+along a subset of the dimensions. The argument reverse is an array of boolean
+values that indicates whether or not the order of the coefficients should be
+reversed along each of the dimensions. This operation preserves the dimensions
+of the input tensor.
+
+For example this is what happens when you `reverse()` the first dimension
+of a 2D tensor:
+
+ Eigen::Tensor<int, 2> a(4, 3);
+ a.setValues({{0, 100, 200}, {300, 400, 500},
+ {600, 700, 800}, {900, 1000, 1100}});
+ Eigen::array<bool, 2> reverse({true, false});
+ Eigen::Tensor<int, 2> b = a.reverse(reverse);
+ cout << "a" << endl << a << endl << "b" << endl << b << endl;
+ =>
+ a
+ 0 100 200
+ 300 400 500
+ 600 700 800
+ 900 1000 1100
+ b
+ 900 1000 1100
+ 600 700 800
+ 300 400 500
+ 0 100 200
+
+
+### <Operation> broadcast(const Broadcast& broadcast)
+
+Returns a view of the input tensor in which the input is replicated one to many
+times.
+The broadcast argument specifies how many copies of the input tensor need to be
+made in each of the dimensions.
+
+ Eigen::Tensor<int, 2> a(2, 3);
+ a.setValues({{0, 100, 200}, {300, 400, 500}});
+ Eigen::array<int, 2> bcast({3, 2});
+ Eigen::Tensor<int, 2> b = a.broadcast(bcast);
+ cout << "a" << endl << a << endl << "b" << endl << b << endl;
+ =>
+ a
+ 0 100 200
+ 300 400 500
+ b
+ 0 100 200 0 100 200
+ 300 400 500 300 400 500
+ 0 100 200 0 100 200
+ 300 400 500 300 400 500
+ 0 100 200 0 100 200
+ 300 400 500 300 400 500
+
+### <Operation> concatenate(const OtherDerived& other, Axis axis)
+
+TODO
+
+### <Operation> pad(const PaddingDimensions& padding)
+
+Returns a view of the input tensor in which the input is padded with zeros.
+
+ Eigen::Tensor<int, 2> a(2, 3);
+ a.setValues({{0, 100, 200}, {300, 400, 500}});
+ Eigen::array<pair<int, int>, 2> paddings;
+ paddings[0] = make_pair(0, 1);
+ paddings[1] = make_pair(2, 3);
+ Eigen::Tensor<int, 2> b = a.pad(paddings);
+ cout << "a" << endl << a << endl << "b" << endl << b << endl;
+ =>
+ a
+ 0 100 200
+ 300 400 500
+ b
+ 0 0 0 0
+ 0 0 0 0
+ 0 100 200 0
+ 300 400 500 0
+ 0 0 0 0
+ 0 0 0 0
+ 0 0 0 0
+
+
+### <Operation> extract_patches(const PatchDims& patch_dims)
+
+Returns a tensor of coefficient patches extracted from the input tensor, where
+each patch is of dimension specified by 'patch_dims'. The returned tensor has
+one greater dimension than the input tensor, which is used to index each patch.
+The patch index in the output tensor depends on the data layout of the input
+tensor: the patch index is the last dimension ColMajor layout, and the first
+dimension in RowMajor layout.
+
+For example, given the following input tensor:
+
+ Eigen::Tensor<float, 2, DataLayout> tensor(3,4);
+ tensor.setValues({{0.0f, 1.0f, 2.0f, 3.0f},
+ {4.0f, 5.0f, 6.0f, 7.0f},
+ {8.0f, 9.0f, 10.0f, 11.0f}});
+
+ cout << "tensor: " << endl << tensor << endl;
+ =>
+ tensor:
+ 0 1 2 3
+ 4 5 6 7
+ 8 9 10 11
+
+Six 2x2 patches can be extracted and indexed using the following code:
+
+ Eigen::Tensor<float, 3, DataLayout> patch;
+ Eigen::array<ptrdiff_t, 2> patch_dims;
+ patch_dims[0] = 2;
+ patch_dims[1] = 2;
+ patch = tensor.extract_patches(patch_dims);
+ for (int k = 0; k < 6; ++k) {
+ cout << "patch index: " << k << endl;
+ for (int i = 0; i < 2; ++i) {
+ for (int j = 0; j < 2; ++j) {
+ if (DataLayout == ColMajor) {
+ cout << patch(i, j, k) << " ";
+ } else {
+ cout << patch(k, i, j) << " ";
+ }
+ }
+ cout << endl;
+ }
+ }
+
+This code results in the following output when the data layout is ColMajor:
+
+ patch index: 0
+ 0 1
+ 4 5
+ patch index: 1
+ 4 5
+ 8 9
+ patch index: 2
+ 1 2
+ 5 6
+ patch index: 3
+ 5 6
+ 9 10
+ patch index: 4
+ 2 3
+ 6 7
+ patch index: 5
+ 6 7
+ 10 11
+
+This code results in the following output when the data layout is RowMajor:
+(NOTE: the set of patches is the same as in ColMajor, but are indexed differently).
+
+ patch index: 0
+ 0 1
+ 4 5
+ patch index: 1
+ 1 2
+ 5 6
+ patch index: 2
+ 2 3
+ 6 7
+ patch index: 3
+ 4 5
+ 8 9
+ patch index: 4
+ 5 6
+ 9 10
+ patch index: 5
+ 6 7
+ 10 11
+
+### <Operation> extract_image_patches(const Index patch_rows, const Index patch_cols, const Index row_stride, const Index col_stride, const PaddingType padding_type)
+
+Returns a tensor of coefficient image patches extracted from the input tensor,
+which is expected to have dimensions ordered as follows (depending on the data
+layout of the input tensor, and the number of additional dimensions 'N'):
+
+*) ColMajor
+1st dimension: channels (of size d)
+2nd dimension: rows (of size r)
+3rd dimension: columns (of size c)
+4th-Nth dimension: time (for video) or batch (for bulk processing).
+
+*) RowMajor (reverse order of ColMajor)
+1st-Nth dimension: time (for video) or batch (for bulk processing).
+N+1'th dimension: columns (of size c)
+N+2'th dimension: rows (of size r)
+N+3'th dimension: channels (of size d)
+
+The returned tensor has one greater dimension than the input tensor, which is
+used to index each patch. The patch index in the output tensor depends on the
+data layout of the input tensor: the patch index is the 4'th dimension in
+ColMajor layout, and the 4'th from the last dimension in RowMajor layout.
+
+For example, given the following input tensor with the following dimension
+sizes:
+ *) depth: 2
+ *) rows: 3
+ *) columns: 5
+ *) batch: 7
+
+ Tensor<float, 4> tensor(2,3,5,7);
+ Tensor<float, 4, RowMajor> tensor_row_major = tensor.swap_layout();
+
+2x2 image patches can be extracted and indexed using the following code:
+
+*) 2D patch: ColMajor (patch indexed by second-to-last dimension)
+
+ Tensor<float, 5> twod_patch;
+ twod_patch = tensor.extract_image_patches<2, 2>();
+ // twod_patch.dimension(0) == 2
+ // twod_patch.dimension(1) == 2
+ // twod_patch.dimension(2) == 2
+ // twod_patch.dimension(3) == 3*5
+ // twod_patch.dimension(4) == 7
+
+*) 2D patch: RowMajor (patch indexed by the second dimension)
+
+ Tensor<float, 5, RowMajor> twod_patch_row_major;
+ twod_patch_row_major = tensor_row_major.extract_image_patches<2, 2>();
+ // twod_patch_row_major.dimension(0) == 7
+ // twod_patch_row_major.dimension(1) == 3*5
+ // twod_patch_row_major.dimension(2) == 2
+ // twod_patch_row_major.dimension(3) == 2
+ // twod_patch_row_major.dimension(4) == 2
+
+## Special Operations
+
+### <Operation> cast<T>()
+
+Returns a tensor of type T with the same dimensions as the original tensor.
+The returned tensor contains the values of the original tensor converted to
+type T.
+
+ Eigen::Tensor<float, 2> a(2, 3);
+ Eigen::Tensor<int, 2> b = a.cast<int>();
+
+This can be useful for example if you need to do element-wise division of
+Tensors of integers. This is not currently supported by the Tensor library
+but you can easily cast the tensors to floats to do the division:
+
+ Eigen::Tensor<int, 2> a(2, 3);
+ a.setValues({{0, 1, 2}, {3, 4, 5}});
+ Eigen::Tensor<int, 2> b =
+ (a.cast<float>() / a.constant(2).cast<float>()).cast<int>();
+ cout << "a" << endl << a << endl << endl;
+ cout << "b" << endl << b << endl << endl;
+ =>
+ a
+ 0 1 2
+ 3 4 5
+
+ b
+ 0 0 1
+ 1 2 2
+
+
+### <Operation> eval()
+
+TODO
+
+## Tensor Printing
+Tensors can be printed into a stream object (e.g. `std::cout`) using different formatting options.
+
+ Eigen::Tensor<float, 3> tensor3d = {4, 3, 2};
+ tensor3d.setValues( {{{1, 2}, {3, 4}, {5, 6}}, {{7, 8}, {9, 10}, {11, 12}}, {{13, 14}, {15, 16}, {17, 18}}, {{19, 20}, {21, 22}, {23, 24}}} );
+ std::cout << tensor3d.format(Eigen::TensorIOFormat::Plain()) << std::endl;
+ ==>
+ 1 2
+ 3 4
+ 5 6
+
+ 7 8
+ 9 10
+ 11 12
+
+ 13 14
+ 15 16
+ 17 18
+
+ 19 20
+ 21 22
+ 23 24
+
+
+In the example, we used the predefined format `Eigen::TensorIOFormat::Plain`.
+Here is the list of all predefined formats from which you can choose:
+- `Eigen::TensorIOFormat::Plain()` for a plain output without braces. Different submatrices are separated by a blank line.
+- `Eigen::TensorIOFormat::Numpy()` for numpy-like output.
+- `Eigen::TensorIOFormat::Native()` for a `c++` like output which can be directly copy-pasted to setValues().
+- `Eigen::TensorIOFormat::Legacy()` for a backwards compatible printing of tensors.
+
+If you send the tensor directly to the stream the default format is called which is `Eigen::IOFormats::Plain()`.
+
+You can define your own format by explicitly providing a `Eigen::TensorIOFormat` class instance. Here, you can specify:
+- The overall prefix and suffix with `std::string tenPrefix` and `std::string tenSuffix`
+- The prefix, separator and suffix for each new element, row, matrix, 3d subtensor, ... with `std::vector<std::string> prefix`, `std::vector<std::string> separator` and `std::vector<std::string> suffix`. Note that the first entry in each of the vectors refer to the last dimension of the tensor, e.g. `separator[0]` will be printed between adjacent elements, `separator[1]` will be printed between adjacent matrices, ...
+- `char fill`: character which will be placed if the elements are aligned.
+- `int precision`
+- `int flags`: an OR-ed combination of flags, the default value is 0, the only currently available flag is `Eigen::DontAlignCols` which allows to disable the alignment of columns, resulting in faster code.
+
+## Representation of scalar values
+
+Scalar values are often represented by tensors of size 1 and rank 0.For example
+Tensor<T, N>::maximum() currently returns a Tensor<T, 0>. Similarly, the inner
+product of 2 1d tensors (through contractions) returns a 0d tensor.
+
+## Limitations
+
+* The number of tensor dimensions is currently limited to 250 when using a
+ compiler that supports cxx11. It is limited to only 5 for older compilers.
+* The IndexList class requires a cxx11 compliant compiler. You can use an
+ array of indices instead if you don't have access to a modern compiler.
+* On GPUs only floating point values are properly tested and optimized for.
diff --git a/unsupported/Eigen/CXX11/src/Tensor/Tensor.h b/unsupported/Eigen/CXX11/src/Tensor/Tensor.h
new file mode 100644
index 0000000..b830984
--- /dev/null
+++ b/unsupported/Eigen/CXX11/src/Tensor/Tensor.h
@@ -0,0 +1,465 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>
+// Copyright (C) 2013 Christian Seiler <christian@iwakd.de>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_CXX11_TENSOR_TENSOR_H
+#define EIGEN_CXX11_TENSOR_TENSOR_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+/** \class Tensor
+ * \ingroup CXX11_Tensor_Module
+ *
+ * \brief The tensor class.
+ *
+ * The %Tensor class is the work-horse for all \em dense tensors within Eigen.
+ *
+ * The %Tensor class encompasses only dynamic-size objects so far.
+ *
+ * The first two template parameters are required:
+ * \tparam Scalar_ Numeric type, e.g. float, double, int or `std::complex<float>`.
+ * User defined scalar types are supported as well (see \ref user_defined_scalars "here").
+ * \tparam NumIndices_ Number of indices (i.e. rank of the tensor)
+ *
+ * The remaining template parameters are optional -- in most cases you don't have to worry about them.
+ * \tparam Options_ A combination of either \b #RowMajor or \b #ColMajor, and of either
+ * \b #AutoAlign or \b #DontAlign.
+ * The former controls \ref TopicStorageOrders "storage order", and defaults to column-major. The latter controls alignment, which is required
+ * for vectorization. It defaults to aligning tensors. Note that tensors currently do not support any operations that profit from vectorization.
+ * Support for such operations (i.e. adding two tensors etc.) is planned.
+ *
+ * You can access elements of tensors using normal subscripting:
+ *
+ * \code
+ * Eigen::Tensor<double, 4> t(10, 10, 10, 10);
+ * t(0, 1, 2, 3) = 42.0;
+ * \endcode
+ *
+ * This class can be extended with the help of the plugin mechanism described on the page
+ * \ref TopicCustomizing_Plugins by defining the preprocessor symbol \c EIGEN_TENSOR_PLUGIN,
+ * \c EIGEN_TENSORBASE_PLUGIN, and \c EIGEN_READONLY_TENSORBASE_PLUGIN.
+ *
+ * <i><b>Some notes:</b></i>
+ *
+ * <dl>
+ * <dt><b>Relation to other parts of Eigen:</b></dt>
+ * <dd>The midterm development goal for this class is to have a similar hierarchy as Eigen uses for matrices, so that
+ * taking blocks or using tensors in expressions is easily possible, including an interface with the vector/matrix code
+ * by providing .asMatrix() and .asVector() (or similar) methods for rank 2 and 1 tensors. However, currently, the %Tensor
+ * class does not provide any of these features and is only available as a stand-alone class that just allows for
+ * coefficient access. Also, when fixed-size tensors are implemented, the number of template arguments is likely to
+ * change dramatically.</dd>
+ * </dl>
+ *
+ * \ref TopicStorageOrders
+ */
+
+template<typename Scalar_, int NumIndices_, int Options_, typename IndexType_>
+class Tensor : public TensorBase<Tensor<Scalar_, NumIndices_, Options_, IndexType_> >
+{
+ public:
+ typedef Tensor<Scalar_, NumIndices_, Options_, IndexType_> Self;
+ typedef TensorBase<Tensor<Scalar_, NumIndices_, Options_, IndexType_> > Base;
+ typedef typename Eigen::internal::nested<Self>::type Nested;
+ typedef typename internal::traits<Self>::StorageKind StorageKind;
+ typedef typename internal::traits<Self>::Index Index;
+ typedef Scalar_ Scalar;
+ typedef typename NumTraits<Scalar>::Real RealScalar;
+ typedef typename Base::CoeffReturnType CoeffReturnType;
+
+ enum {
+ IsAligned = (EIGEN_MAX_ALIGN_BYTES>0) && !(Options_&DontAlign),
+ CoordAccess = true,
+ RawAccess = true
+ };
+
+ static constexpr int Layout = Options_ & RowMajor ? RowMajor : ColMajor;
+ static constexpr int Options = Options_;
+ static constexpr int NumIndices = NumIndices_;
+ typedef DSizes<Index, NumIndices_> Dimensions;
+
+ protected:
+ TensorStorage<Scalar, Dimensions, Options> m_storage;
+
+ template<typename CustomIndices>
+ struct isOfNormalIndex{
+ static const bool is_array = internal::is_base_of<array<Index, NumIndices>, CustomIndices>::value;
+ static const bool is_int = NumTraits<CustomIndices>::IsInteger;
+ static const bool value = is_array | is_int;
+ };
+
+ public:
+ // Metadata
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Index rank() const { return NumIndices; }
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Index dimension(std::size_t n) const { return m_storage.dimensions()[n]; }
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Dimensions& dimensions() const { return m_storage.dimensions(); }
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Index size() const { return m_storage.size(); }
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar *data() { return m_storage.data(); }
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar *data() const { return m_storage.data(); }
+
+ // This makes EIGEN_INITIALIZE_COEFFS_IF_THAT_OPTION_IS_ENABLED
+ // work, because that uses base().coeffRef() - and we don't yet
+ // implement a similar class hierarchy
+ inline Self& base() { return *this; }
+ inline const Self& base() const { return *this; }
+
+ template<typename... IndexTypes>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar& coeff(Index firstIndex, Index secondIndex, IndexTypes... otherIndices) const
+ {
+ // The number of indices used to access a tensor coefficient must be equal to the rank of the tensor.
+ EIGEN_STATIC_ASSERT(sizeof...(otherIndices) + 2 == NumIndices, YOU_MADE_A_PROGRAMMING_MISTAKE)
+ return coeff(array<Index, NumIndices>{{firstIndex, secondIndex, otherIndices...}});
+ }
+
+ // normal indices
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar& coeff(const array<Index, NumIndices>& indices) const
+ {
+ eigen_internal_assert(checkIndexRange(indices));
+ return m_storage.data()[linearizedIndex(indices)];
+ }
+
+ // custom indices
+ template<typename CustomIndices,
+ EIGEN_SFINAE_ENABLE_IF( !(isOfNormalIndex<CustomIndices>::value) )
+ >
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar& coeff(CustomIndices& indices) const
+ {
+ return coeff(internal::customIndices2Array<Index,NumIndices>(indices));
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar& coeff() const
+ {
+ EIGEN_STATIC_ASSERT(NumIndices == 0, YOU_MADE_A_PROGRAMMING_MISTAKE);
+ return m_storage.data()[0];
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar& coeff(Index index) const
+ {
+ eigen_internal_assert(index >= 0 && index < size());
+ return m_storage.data()[index];
+ }
+
+ template<typename... IndexTypes>
+ inline Scalar& coeffRef(Index firstIndex, Index secondIndex, IndexTypes... otherIndices)
+ {
+ // The number of indices used to access a tensor coefficient must be equal to the rank of the tensor.
+ EIGEN_STATIC_ASSERT(sizeof...(otherIndices) + 2 == NumIndices, YOU_MADE_A_PROGRAMMING_MISTAKE)
+ return coeffRef(array<Index, NumIndices>{{firstIndex, secondIndex, otherIndices...}});
+ }
+
+ // normal indices
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar& coeffRef(const array<Index, NumIndices>& indices)
+ {
+ eigen_internal_assert(checkIndexRange(indices));
+ return m_storage.data()[linearizedIndex(indices)];
+ }
+
+ // custom indices
+ template<typename CustomIndices,
+ EIGEN_SFINAE_ENABLE_IF( !(isOfNormalIndex<CustomIndices>::value) )
+ >
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar& coeffRef(CustomIndices& indices)
+ {
+ return coeffRef(internal::customIndices2Array<Index,NumIndices>(indices));
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar& coeffRef()
+ {
+ EIGEN_STATIC_ASSERT(NumIndices == 0, YOU_MADE_A_PROGRAMMING_MISTAKE);
+ return m_storage.data()[0];
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar& coeffRef(Index index)
+ {
+ eigen_internal_assert(index >= 0 && index < size());
+ return m_storage.data()[index];
+ }
+
+ template<typename... IndexTypes>
+ inline const Scalar& operator()(Index firstIndex, Index secondIndex, IndexTypes... otherIndices) const
+ {
+ // The number of indices used to access a tensor coefficient must be equal to the rank of the tensor.
+ EIGEN_STATIC_ASSERT(sizeof...(otherIndices) + 2 == NumIndices, YOU_MADE_A_PROGRAMMING_MISTAKE)
+ return this->operator()(array<Index, NumIndices>{{firstIndex, secondIndex, otherIndices...}});
+ }
+
+ // custom indices
+ template<typename CustomIndices,
+ EIGEN_SFINAE_ENABLE_IF( !(isOfNormalIndex<CustomIndices>::value) )
+ >
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar& operator()(CustomIndices& indices) const
+ {
+ return coeff(internal::customIndices2Array<Index,NumIndices>(indices));
+ }
+
+ // normal indices
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar& operator()(const array<Index, NumIndices>& indices) const
+ {
+ return coeff(indices);
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar& operator()(Index index) const
+ {
+ eigen_internal_assert(index >= 0 && index < size());
+ return coeff(index);
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar& operator()() const
+ {
+ EIGEN_STATIC_ASSERT(NumIndices == 0, YOU_MADE_A_PROGRAMMING_MISTAKE);
+ return coeff();
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar& operator[](Index index) const
+ {
+ // The bracket operator is only for vectors, use the parenthesis operator instead.
+ EIGEN_STATIC_ASSERT(NumIndices == 1, YOU_MADE_A_PROGRAMMING_MISTAKE);
+ return coeff(index);
+ }
+
+ template<typename... IndexTypes>
+ inline Scalar& operator()(Index firstIndex, Index secondIndex, IndexTypes... otherIndices)
+ {
+ // The number of indices used to access a tensor coefficient must be equal to the rank of the tensor.
+ EIGEN_STATIC_ASSERT(sizeof...(otherIndices) + 2 == NumIndices, YOU_MADE_A_PROGRAMMING_MISTAKE)
+ return operator()(array<Index, NumIndices>{{firstIndex, secondIndex, otherIndices...}});
+ }
+
+ // normal indices
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar& operator()(const array<Index, NumIndices>& indices)
+ {
+ return coeffRef(indices);
+ }
+
+ // custom indices
+ template<typename CustomIndices,
+ EIGEN_SFINAE_ENABLE_IF( !(isOfNormalIndex<CustomIndices>::value) )
+ >
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar& operator()(CustomIndices& indices)
+ {
+ return coeffRef(internal::customIndices2Array<Index,NumIndices>(indices));
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar& operator()(Index index)
+ {
+ eigen_assert(index >= 0 && index < size());
+ return coeffRef(index);
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar& operator()()
+ {
+ EIGEN_STATIC_ASSERT(NumIndices == 0, YOU_MADE_A_PROGRAMMING_MISTAKE);
+ return coeffRef();
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar& operator[](Index index)
+ {
+ // The bracket operator is only for vectors, use the parenthesis operator instead
+ EIGEN_STATIC_ASSERT(NumIndices == 1, YOU_MADE_A_PROGRAMMING_MISTAKE)
+ return coeffRef(index);
+ }
+
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE Tensor()
+ : m_storage()
+ {
+ }
+
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE Tensor(const Self& other)
+ : Base(other), m_storage(other.m_storage)
+ {
+ }
+
+ template<typename... IndexTypes>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Tensor(Index firstDimension, IndexTypes... otherDimensions)
+ : m_storage(firstDimension, otherDimensions...)
+ {
+ // The number of dimensions used to construct a tensor must be equal to the rank of the tensor.
+ EIGEN_STATIC_ASSERT(sizeof...(otherDimensions) + 1 == NumIndices, YOU_MADE_A_PROGRAMMING_MISTAKE)
+ }
+
+ /** Normal Dimension */
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE explicit Tensor(const array<Index, NumIndices>& dimensions)
+ : m_storage(internal::array_prod(dimensions), dimensions)
+ {
+ EIGEN_INITIALIZE_COEFFS_IF_THAT_OPTION_IS_ENABLED
+ }
+
+ template<typename OtherDerived>
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE Tensor(const TensorBase<OtherDerived, ReadOnlyAccessors>& other)
+ {
+ typedef TensorAssignOp<Tensor, const OtherDerived> Assign;
+ Assign assign(*this, other.derived());
+ resize(TensorEvaluator<const Assign, DefaultDevice>(assign, DefaultDevice()).dimensions());
+ internal::TensorExecutor<const Assign, DefaultDevice>::run(assign, DefaultDevice());
+ }
+
+ template<typename OtherDerived>
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE Tensor(const TensorBase<OtherDerived, WriteAccessors>& other)
+ {
+ typedef TensorAssignOp<Tensor, const OtherDerived> Assign;
+ Assign assign(*this, other.derived());
+ resize(TensorEvaluator<const Assign, DefaultDevice>(assign, DefaultDevice()).dimensions());
+ internal::TensorExecutor<const Assign, DefaultDevice>::run(assign, DefaultDevice());
+ }
+
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE Tensor(Self&& other)
+ : m_storage(std::move(other.m_storage))
+ {
+ }
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE Tensor& operator=(Self&& other)
+ {
+ m_storage = std::move(other.m_storage);
+ return *this;
+ }
+
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE Tensor& operator=(const Tensor& other)
+ {
+ typedef TensorAssignOp<Tensor, const Tensor> Assign;
+ Assign assign(*this, other);
+ resize(TensorEvaluator<const Assign, DefaultDevice>(assign, DefaultDevice()).dimensions());
+ internal::TensorExecutor<const Assign, DefaultDevice>::run(assign, DefaultDevice());
+ return *this;
+ }
+ template<typename OtherDerived>
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE Tensor& operator=(const OtherDerived& other)
+ {
+ typedef TensorAssignOp<Tensor, const OtherDerived> Assign;
+ Assign assign(*this, other);
+ resize(TensorEvaluator<const Assign, DefaultDevice>(assign, DefaultDevice()).dimensions());
+ internal::TensorExecutor<const Assign, DefaultDevice>::run(assign, DefaultDevice());
+ return *this;
+ }
+
+ template<typename... IndexTypes> EIGEN_DEVICE_FUNC
+ void resize(Index firstDimension, IndexTypes... otherDimensions)
+ {
+ // The number of dimensions used to resize a tensor must be equal to the rank of the tensor.
+ EIGEN_STATIC_ASSERT(sizeof...(otherDimensions) + 1 == NumIndices, YOU_MADE_A_PROGRAMMING_MISTAKE)
+ resize(array<Index, NumIndices>{{firstDimension, otherDimensions...}});
+ }
+
+ /** Normal Dimension */
+ EIGEN_DEVICE_FUNC void resize(const array<Index, NumIndices>& dimensions)
+ {
+ int i;
+ Index size = Index(1);
+ for (i = 0; i < NumIndices; i++) {
+ internal::check_rows_cols_for_overflow<Dynamic>::run(size, dimensions[i]);
+ size *= dimensions[i];
+ }
+ #ifdef EIGEN_INITIALIZE_COEFFS
+ bool size_changed = size != this->size();
+ m_storage.resize(size, dimensions);
+ if(size_changed) EIGEN_INITIALIZE_COEFFS_IF_THAT_OPTION_IS_ENABLED
+ #else
+ m_storage.resize(size, dimensions);
+ #endif
+ }
+
+ // Why this overload, DSizes is derived from array ??? //
+ EIGEN_DEVICE_FUNC void resize(const DSizes<Index, NumIndices>& dimensions) {
+ array<Index, NumIndices> dims;
+ for (int i = 0; i < NumIndices; ++i) {
+ dims[i] = dimensions[i];
+ }
+ resize(dims);
+ }
+
+ EIGEN_DEVICE_FUNC
+ void resize()
+ {
+ EIGEN_STATIC_ASSERT(NumIndices == 0, YOU_MADE_A_PROGRAMMING_MISTAKE);
+ // Nothing to do: rank 0 tensors have fixed size
+ }
+
+ template <typename FirstType, typename... OtherTypes>
+ EIGEN_DEVICE_FUNC
+ void resize(const Eigen::IndexList<FirstType, OtherTypes...>& dimensions) {
+ array<Index, NumIndices> dims;
+ for (int i = 0; i < NumIndices; ++i) {
+ dims[i] = static_cast<Index>(dimensions[i]);
+ }
+ resize(dims);
+ }
+
+ /** Custom Dimension */
+ template<typename CustomDimension,
+ EIGEN_SFINAE_ENABLE_IF( !(isOfNormalIndex<CustomDimension>::value) )
+ >
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void resize(CustomDimension& dimensions)
+ {
+ resize(internal::customIndices2Array<Index,NumIndices>(dimensions));
+ }
+
+#ifndef EIGEN_EMULATE_CXX11_META_H
+ template <typename std::ptrdiff_t... Indices>
+ EIGEN_DEVICE_FUNC
+ void resize(const Sizes<Indices...>& dimensions) {
+ array<Index, NumIndices> dims;
+ for (int i = 0; i < NumIndices; ++i) {
+ dims[i] = static_cast<Index>(dimensions[i]);
+ }
+ resize(dims);
+ }
+#else
+ template <std::size_t V1, std::size_t V2, std::size_t V3, std::size_t V4, std::size_t V5>
+ EIGEN_DEVICE_FUNC
+ void resize(const Sizes<V1, V2, V3, V4, V5>& dimensions) {
+ array<Index, NumIndices> dims;
+ for (int i = 0; i < NumIndices; ++i) {
+ dims[i] = static_cast<Index>(dimensions[i]);
+ }
+ resize(dims);
+ }
+#endif
+
+ #ifdef EIGEN_TENSOR_PLUGIN
+ #include EIGEN_TENSOR_PLUGIN
+ #endif
+
+ protected:
+
+ bool checkIndexRange(const array<Index, NumIndices>& indices) const
+ {
+ using internal::array_apply_and_reduce;
+ using internal::array_zip_and_reduce;
+ using internal::greater_equal_zero_op;
+ using internal::logical_and_op;
+ using internal::lesser_op;
+
+ return
+ // check whether the indices are all >= 0
+ array_apply_and_reduce<logical_and_op, greater_equal_zero_op>(indices) &&
+ // check whether the indices fit in the dimensions
+ array_zip_and_reduce<logical_and_op, lesser_op>(indices, m_storage.dimensions());
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Index linearizedIndex(const array<Index, NumIndices>& indices) const
+ {
+ if (Options&RowMajor) {
+ return m_storage.dimensions().IndexOfRowMajor(indices);
+ } else {
+ return m_storage.dimensions().IndexOfColMajor(indices);
+ }
+ }
+};
+
+} // end namespace Eigen
+
+#endif // EIGEN_CXX11_TENSOR_TENSOR_H
diff --git a/unsupported/Eigen/CXX11/src/Tensor/TensorArgMax.h b/unsupported/Eigen/CXX11/src/Tensor/TensorArgMax.h
new file mode 100644
index 0000000..0d60327
--- /dev/null
+++ b/unsupported/Eigen/CXX11/src/Tensor/TensorArgMax.h
@@ -0,0 +1,330 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2015 Eugene Brevdo <ebrevdo@gmail.com>
+// Benoit Steiner <benoit.steiner.goog@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_CXX11_TENSOR_TENSOR_ARG_MAX_H
+#define EIGEN_CXX11_TENSOR_TENSOR_ARG_MAX_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+namespace internal {
+
+/** \class TensorIndexPair
+ * \ingroup CXX11_Tensor_Module
+ *
+ * \brief Tensor + Index Pair class.
+ *
+ *
+ */
+template<typename XprType>
+struct traits<TensorIndexPairOp<XprType> > : public traits<XprType>
+{
+ typedef traits<XprType> XprTraits;
+ typedef typename XprTraits::StorageKind StorageKind;
+ typedef typename XprTraits::Index Index;
+ typedef Pair<Index, typename XprTraits::Scalar> Scalar;
+ typedef typename XprType::Nested Nested;
+ typedef std::remove_reference_t<Nested> Nested_;
+ static constexpr int NumDimensions = XprTraits::NumDimensions;
+ static constexpr int Layout = XprTraits::Layout;
+};
+
+template<typename XprType>
+struct eval<TensorIndexPairOp<XprType>, Eigen::Dense>
+{
+ typedef const TensorIndexPairOp<XprType>EIGEN_DEVICE_REF type;
+};
+
+template<typename XprType>
+struct nested<TensorIndexPairOp<XprType>, 1,
+ typename eval<TensorIndexPairOp<XprType> >::type>
+{
+ typedef TensorIndexPairOp<XprType> type;
+};
+
+} // end namespace internal
+
+template<typename XprType>
+class TensorIndexPairOp : public TensorBase<TensorIndexPairOp<XprType>, ReadOnlyAccessors>
+{
+ public:
+ typedef typename Eigen::internal::traits<TensorIndexPairOp>::Scalar Scalar;
+ typedef typename Eigen::NumTraits<Scalar>::Real RealScalar;
+ typedef typename Eigen::internal::nested<TensorIndexPairOp>::type Nested;
+ typedef typename Eigen::internal::traits<TensorIndexPairOp>::StorageKind StorageKind;
+ typedef typename Eigen::internal::traits<TensorIndexPairOp>::Index Index;
+ typedef Pair<Index, typename XprType::CoeffReturnType> CoeffReturnType;
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorIndexPairOp(const XprType& expr)
+ : m_xpr(expr) {}
+
+ EIGEN_DEVICE_FUNC
+ const internal::remove_all_t<typename XprType::Nested>&
+ expression() const { return m_xpr; }
+
+ protected:
+ typename XprType::Nested m_xpr;
+};
+
+// Eval as rvalue
+template<typename ArgType, typename Device>
+struct TensorEvaluator<const TensorIndexPairOp<ArgType>, Device>
+{
+ typedef TensorIndexPairOp<ArgType> XprType;
+ typedef typename XprType::Index Index;
+ typedef typename XprType::Scalar Scalar;
+ typedef typename XprType::CoeffReturnType CoeffReturnType;
+
+ typedef typename TensorEvaluator<ArgType, Device>::Dimensions Dimensions;
+ static constexpr int NumDims = internal::array_size<Dimensions>::value;
+ typedef StorageMemory<CoeffReturnType, Device> Storage;
+ typedef typename Storage::Type EvaluatorPointerType;
+
+ enum {
+ IsAligned = /*TensorEvaluator<ArgType, Device>::IsAligned*/ false,
+ PacketAccess = /*TensorEvaluator<ArgType, Device>::PacketAccess*/ false,
+ BlockAccess = false,
+ PreferBlockAccess = TensorEvaluator<ArgType, Device>::PreferBlockAccess,
+ CoordAccess = false, // to be implemented
+ RawAccess = false
+ };
+ static constexpr int Layout = TensorEvaluator<ArgType, Device>::Layout;
+
+ //===- Tensor block evaluation strategy (see TensorBlock.h) -------------===//
+ typedef internal::TensorBlockNotImplemented TensorBlock;
+ //===--------------------------------------------------------------------===//
+
+ EIGEN_STRONG_INLINE TensorEvaluator(const XprType& op, const Device& device)
+ : m_impl(op.expression(), device) { }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Dimensions& dimensions() const {
+ return m_impl.dimensions();
+ }
+
+ EIGEN_STRONG_INLINE bool evalSubExprsIfNeeded(EvaluatorPointerType /*data*/) {
+ m_impl.evalSubExprsIfNeeded(NULL);
+ return true;
+ }
+ EIGEN_STRONG_INLINE void cleanup() {
+ m_impl.cleanup();
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE CoeffReturnType coeff(Index index) const
+ {
+ return CoeffReturnType(index, m_impl.coeff(index));
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorOpCost
+ costPerCoeff(bool vectorized) const {
+ return m_impl.costPerCoeff(vectorized) + TensorOpCost(0, 0, 1);
+ }
+
+ EIGEN_DEVICE_FUNC EvaluatorPointerType data() const { return NULL; }
+
+#ifdef EIGEN_USE_SYCL
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void bind(cl::sycl::handler &cgh) const {
+ m_impl.bind(cgh);
+ }
+#endif
+
+ protected:
+ TensorEvaluator<ArgType, Device> m_impl;
+};
+
+namespace internal {
+
+/** \class TensorPairIndex
+ * \ingroup CXX11_Tensor_Module
+ *
+ * \brief Converts to Tensor<Pair<Index, Scalar> > and reduces to Tensor<Index>.
+ *
+ */
+template<typename ReduceOp, typename Dims, typename XprType>
+struct traits<TensorPairReducerOp<ReduceOp, Dims, XprType> > : public traits<XprType>
+{
+ typedef traits<XprType> XprTraits;
+ typedef typename XprTraits::StorageKind StorageKind;
+ typedef typename XprTraits::Index Index;
+ typedef Index Scalar;
+ typedef typename XprType::Nested Nested;
+ typedef std::remove_reference_t<Nested> Nested_;
+ static constexpr int NumDimensions = XprTraits::NumDimensions - array_size<Dims>::value;
+ static constexpr int Layout = XprTraits::Layout;
+};
+
+template<typename ReduceOp, typename Dims, typename XprType>
+struct eval<TensorPairReducerOp<ReduceOp, Dims, XprType>, Eigen::Dense>
+{
+ typedef const TensorPairReducerOp<ReduceOp, Dims, XprType>EIGEN_DEVICE_REF type;
+};
+
+template<typename ReduceOp, typename Dims, typename XprType>
+struct nested<TensorPairReducerOp<ReduceOp, Dims, XprType>, 1,
+ typename eval<TensorPairReducerOp<ReduceOp, Dims, XprType> >::type>
+{
+ typedef TensorPairReducerOp<ReduceOp, Dims, XprType> type;
+};
+
+} // end namespace internal
+
+template<typename ReduceOp, typename Dims, typename XprType>
+class TensorPairReducerOp : public TensorBase<TensorPairReducerOp<ReduceOp, Dims, XprType>, ReadOnlyAccessors>
+{
+ public:
+ typedef typename Eigen::internal::traits<TensorPairReducerOp>::Scalar Scalar;
+ typedef typename Eigen::NumTraits<Scalar>::Real RealScalar;
+ typedef typename Eigen::internal::nested<TensorPairReducerOp>::type Nested;
+ typedef typename Eigen::internal::traits<TensorPairReducerOp>::StorageKind StorageKind;
+ typedef typename Eigen::internal::traits<TensorPairReducerOp>::Index Index;
+ typedef Index CoeffReturnType;
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorPairReducerOp(const XprType& expr,
+ const ReduceOp& reduce_op,
+ const Index return_dim,
+ const Dims& reduce_dims)
+ : m_xpr(expr), m_reduce_op(reduce_op), m_return_dim(return_dim), m_reduce_dims(reduce_dims) {}
+
+ EIGEN_DEVICE_FUNC
+ const internal::remove_all_t<typename XprType::Nested>&
+ expression() const { return m_xpr; }
+
+ EIGEN_DEVICE_FUNC
+ const ReduceOp& reduce_op() const { return m_reduce_op; }
+
+ EIGEN_DEVICE_FUNC
+ const Dims& reduce_dims() const { return m_reduce_dims; }
+
+ EIGEN_DEVICE_FUNC
+ Index return_dim() const { return m_return_dim; }
+
+ protected:
+ typename XprType::Nested m_xpr;
+ const ReduceOp m_reduce_op;
+ const Index m_return_dim;
+ const Dims m_reduce_dims;
+};
+
+// Eval as rvalue
+template<typename ReduceOp, typename Dims, typename ArgType, typename Device>
+struct TensorEvaluator<const TensorPairReducerOp<ReduceOp, Dims, ArgType>, Device>
+{
+ typedef TensorPairReducerOp<ReduceOp, Dims, ArgType> XprType;
+ typedef typename XprType::Index Index;
+ typedef typename XprType::Scalar Scalar;
+ typedef typename XprType::CoeffReturnType CoeffReturnType;
+ typedef typename TensorIndexPairOp<ArgType>::CoeffReturnType PairType;
+ typedef typename TensorEvaluator<const TensorReductionOp<ReduceOp, Dims, const TensorIndexPairOp<ArgType> >, Device>::Dimensions Dimensions;
+ typedef typename TensorEvaluator<const TensorIndexPairOp<ArgType> , Device>::Dimensions InputDimensions;
+ static constexpr int NumDims = internal::array_size<InputDimensions>::value;
+ typedef array<Index, NumDims> StrideDims;
+ typedef StorageMemory<CoeffReturnType, Device> Storage;
+ typedef typename Storage::Type EvaluatorPointerType;
+ typedef StorageMemory<PairType, Device> PairStorageMem;
+
+ enum {
+ IsAligned = /*TensorEvaluator<ArgType, Device>::IsAligned*/ false,
+ PacketAccess = /*TensorEvaluator<ArgType, Device>::PacketAccess*/ false,
+ BlockAccess = false,
+ PreferBlockAccess = TensorEvaluator<ArgType, Device>::PreferBlockAccess,
+ CoordAccess = false, // to be implemented
+ RawAccess = false
+ };
+ static constexpr int Layout = TensorEvaluator<const TensorReductionOp<ReduceOp, Dims, const TensorIndexPairOp<ArgType>>, Device>::Layout;
+ //===- Tensor block evaluation strategy (see TensorBlock.h) -------------===//
+ typedef internal::TensorBlockNotImplemented TensorBlock;
+ //===--------------------------------------------------------------------===//
+
+ EIGEN_STRONG_INLINE TensorEvaluator(const XprType& op, const Device& device)
+ : m_orig_impl(op.expression(), device),
+ m_impl(op.expression().index_pairs().reduce(op.reduce_dims(), op.reduce_op()), device),
+ m_return_dim(op.return_dim())
+ {
+ gen_strides(m_orig_impl.dimensions(), m_strides);
+ if (Layout == static_cast<int>(ColMajor)) {
+ const Index total_size = internal::array_prod(m_orig_impl.dimensions());
+ m_stride_mod = (m_return_dim < NumDims - 1) ? m_strides[m_return_dim + 1] : total_size;
+ } else {
+ const Index total_size = internal::array_prod(m_orig_impl.dimensions());
+ m_stride_mod = (m_return_dim > 0) ? m_strides[m_return_dim - 1] : total_size;
+ }
+ // If m_return_dim is not a valid index, returns 1 or this can crash on Windows.
+ m_stride_div = ((m_return_dim >= 0) &&
+ (m_return_dim < static_cast<Index>(m_strides.size())))
+ ? m_strides[m_return_dim] : 1;
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Dimensions& dimensions() const {
+ return m_impl.dimensions();
+ }
+
+ EIGEN_STRONG_INLINE bool evalSubExprsIfNeeded(EvaluatorPointerType /*data*/) {
+ m_impl.evalSubExprsIfNeeded(NULL);
+ return true;
+ }
+ EIGEN_STRONG_INLINE void cleanup() {
+ m_impl.cleanup();
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE CoeffReturnType coeff(Index index) const {
+ const PairType v = m_impl.coeff(index);
+ return (m_return_dim < 0) ? v.first : (v.first % m_stride_mod) / m_stride_div;
+ }
+
+ EIGEN_DEVICE_FUNC EvaluatorPointerType data() const { return NULL; }
+#ifdef EIGEN_USE_SYCL
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void bind(cl::sycl::handler &cgh) const {
+ m_impl.bind(cgh);
+ m_orig_impl.bind(cgh);
+ }
+#endif
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorOpCost
+ costPerCoeff(bool vectorized) const {
+ const double compute_cost = 1.0 +
+ (m_return_dim < 0 ? 0.0 : (TensorOpCost::ModCost<Index>() + TensorOpCost::DivCost<Index>()));
+ return m_orig_impl.costPerCoeff(vectorized) +
+ m_impl.costPerCoeff(vectorized) + TensorOpCost(0, 0, compute_cost);
+ }
+
+ private:
+ EIGEN_DEVICE_FUNC void gen_strides(const InputDimensions& dims, StrideDims& strides) {
+ if (m_return_dim < 0) {
+ return; // Won't be using the strides.
+ }
+ eigen_assert(m_return_dim < NumDims &&
+ "Asking to convert index to a dimension outside of the rank");
+
+ // Calculate m_stride_div and m_stride_mod, which are used to
+ // calculate the value of an index w.r.t. the m_return_dim.
+ if (Layout == static_cast<int>(ColMajor)) {
+ strides[0] = 1;
+ for (int i = 1; i < NumDims; ++i) {
+ strides[i] = strides[i-1] * dims[i-1];
+ }
+ } else {
+ strides[NumDims-1] = 1;
+ for (int i = NumDims - 2; i >= 0; --i) {
+ strides[i] = strides[i+1] * dims[i+1];
+ }
+ }
+ }
+
+ protected:
+ TensorEvaluator<const TensorIndexPairOp<ArgType>, Device> m_orig_impl;
+ TensorEvaluator<const TensorReductionOp<ReduceOp, Dims, const TensorIndexPairOp<ArgType> >, Device> m_impl;
+ const Index m_return_dim;
+ StrideDims m_strides;
+ Index m_stride_mod;
+ Index m_stride_div;
+};
+
+} // end namespace Eigen
+
+#endif // EIGEN_CXX11_TENSOR_TENSOR_ARG_MAX_H
diff --git a/unsupported/Eigen/CXX11/src/Tensor/TensorAssign.h b/unsupported/Eigen/CXX11/src/Tensor/TensorAssign.h
new file mode 100644
index 0000000..0bd3a00
--- /dev/null
+++ b/unsupported/Eigen/CXX11/src/Tensor/TensorAssign.h
@@ -0,0 +1,249 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_CXX11_TENSOR_TENSOR_ASSIGN_H
+#define EIGEN_CXX11_TENSOR_TENSOR_ASSIGN_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+/** \class TensorAssign
+ * \ingroup CXX11_Tensor_Module
+ *
+ * \brief The tensor assignment class.
+ *
+ * This class is represents the assignment of the values resulting from the evaluation of
+ * the rhs expression to the memory locations denoted by the lhs expression.
+ */
+namespace internal {
+template<typename LhsXprType, typename RhsXprType>
+struct traits<TensorAssignOp<LhsXprType, RhsXprType> >
+{
+ typedef typename LhsXprType::Scalar Scalar;
+ typedef typename traits<LhsXprType>::StorageKind StorageKind;
+ typedef typename promote_index_type<typename traits<LhsXprType>::Index,
+ typename traits<RhsXprType>::Index>::type Index;
+ typedef typename LhsXprType::Nested LhsNested;
+ typedef typename RhsXprType::Nested RhsNested;
+ typedef std::remove_reference_t<LhsNested> LhsNested_;
+ typedef std::remove_reference_t<RhsNested> RhsNested_;
+ static constexpr std::size_t NumDimensions = internal::traits<LhsXprType>::NumDimensions;
+ static constexpr int Layout = internal::traits<LhsXprType>::Layout;
+ typedef typename traits<LhsXprType>::PointerType PointerType;
+
+ enum {
+ Flags = 0
+ };
+};
+
+template<typename LhsXprType, typename RhsXprType>
+struct eval<TensorAssignOp<LhsXprType, RhsXprType>, Eigen::Dense>
+{
+ typedef const TensorAssignOp<LhsXprType, RhsXprType>& type;
+};
+
+template<typename LhsXprType, typename RhsXprType>
+struct nested<TensorAssignOp<LhsXprType, RhsXprType>, 1, typename eval<TensorAssignOp<LhsXprType, RhsXprType> >::type>
+{
+ typedef TensorAssignOp<LhsXprType, RhsXprType> type;
+};
+
+} // end namespace internal
+
+
+
+template<typename LhsXprType, typename RhsXprType>
+class TensorAssignOp : public TensorBase<TensorAssignOp<LhsXprType, RhsXprType> >
+{
+ public:
+ typedef typename Eigen::internal::traits<TensorAssignOp>::Scalar Scalar;
+ typedef typename Eigen::NumTraits<Scalar>::Real RealScalar;
+ typedef typename LhsXprType::CoeffReturnType CoeffReturnType;
+ typedef typename Eigen::internal::nested<TensorAssignOp>::type Nested;
+ typedef typename Eigen::internal::traits<TensorAssignOp>::StorageKind StorageKind;
+ typedef typename Eigen::internal::traits<TensorAssignOp>::Index Index;
+
+ static constexpr int NumDims = Eigen::internal::traits<TensorAssignOp>::NumDimensions;
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorAssignOp(LhsXprType& lhs, const RhsXprType& rhs)
+ : m_lhs_xpr(lhs), m_rhs_xpr(rhs) {}
+
+ /** \returns the nested expressions */
+ EIGEN_DEVICE_FUNC
+ internal::remove_all_t<typename LhsXprType::Nested>&
+ lhsExpression() const { return *((internal::remove_all_t<typename LhsXprType::Nested>*)&m_lhs_xpr); }
+
+ EIGEN_DEVICE_FUNC
+ const internal::remove_all_t<typename RhsXprType::Nested>&
+ rhsExpression() const { return m_rhs_xpr; }
+
+ protected:
+ internal::remove_all_t<typename LhsXprType::Nested>& m_lhs_xpr;
+ const internal::remove_all_t<typename RhsXprType::Nested>& m_rhs_xpr;
+};
+
+
+template<typename LeftArgType, typename RightArgType, typename Device>
+struct TensorEvaluator<const TensorAssignOp<LeftArgType, RightArgType>, Device>
+{
+ typedef TensorAssignOp<LeftArgType, RightArgType> XprType;
+ typedef typename XprType::Index Index;
+ typedef typename XprType::Scalar Scalar;
+ typedef typename XprType::CoeffReturnType CoeffReturnType;
+ typedef typename PacketType<CoeffReturnType, Device>::type PacketReturnType;
+ typedef typename TensorEvaluator<RightArgType, Device>::Dimensions Dimensions;
+ typedef StorageMemory<CoeffReturnType, Device> Storage;
+ typedef typename Storage::Type EvaluatorPointerType;
+
+ static constexpr int PacketSize = PacketType<CoeffReturnType, Device>::size;
+ static constexpr int NumDims = XprType::NumDims;
+ static constexpr int Layout = TensorEvaluator<LeftArgType, Device>::Layout;
+
+ enum {
+ IsAligned = int(TensorEvaluator<LeftArgType, Device>::IsAligned) &
+ int(TensorEvaluator<RightArgType, Device>::IsAligned),
+ PacketAccess = int(TensorEvaluator<LeftArgType, Device>::PacketAccess) &
+ int(TensorEvaluator<RightArgType, Device>::PacketAccess),
+ BlockAccess = int(TensorEvaluator<LeftArgType, Device>::BlockAccess) &
+ int(TensorEvaluator<RightArgType, Device>::BlockAccess),
+ PreferBlockAccess = int(TensorEvaluator<LeftArgType, Device>::PreferBlockAccess) |
+ int(TensorEvaluator<RightArgType, Device>::PreferBlockAccess),
+ RawAccess = TensorEvaluator<LeftArgType, Device>::RawAccess
+ };
+
+ //===- Tensor block evaluation strategy (see TensorBlock.h) -------------===//
+ typedef internal::TensorBlockDescriptor<NumDims, Index> TensorBlockDesc;
+ typedef internal::TensorBlockScratchAllocator<Device> TensorBlockScratch;
+
+ typedef typename TensorEvaluator<const RightArgType, Device>::TensorBlock
+ RightTensorBlock;
+ //===--------------------------------------------------------------------===//
+
+ TensorEvaluator(const XprType& op, const Device& device) :
+ m_leftImpl(op.lhsExpression(), device),
+ m_rightImpl(op.rhsExpression(), device)
+ {
+ EIGEN_STATIC_ASSERT(
+ (static_cast<int>(TensorEvaluator<LeftArgType, Device>::Layout) ==
+ static_cast<int>(TensorEvaluator<RightArgType, Device>::Layout)),
+ YOU_MADE_A_PROGRAMMING_MISTAKE);
+ }
+
+ EIGEN_DEVICE_FUNC const Dimensions& dimensions() const
+ {
+ // The dimensions of the lhs and the rhs tensors should be equal to prevent
+ // overflows and ensure the result is fully initialized.
+ // TODO: use left impl instead if right impl dimensions are known at compile time.
+ return m_rightImpl.dimensions();
+ }
+
+ EIGEN_STRONG_INLINE bool evalSubExprsIfNeeded(EvaluatorPointerType) {
+ eigen_assert(dimensions_match(m_leftImpl.dimensions(), m_rightImpl.dimensions()));
+ m_leftImpl.evalSubExprsIfNeeded(NULL);
+ // If the lhs provides raw access to its storage area (i.e. if m_leftImpl.data() returns a non
+ // null value), attempt to evaluate the rhs expression in place. Returns true iff in place
+ // evaluation isn't supported and the caller still needs to manually assign the values generated
+ // by the rhs to the lhs.
+ return m_rightImpl.evalSubExprsIfNeeded(m_leftImpl.data());
+ }
+
+#ifdef EIGEN_USE_THREADS
+ template <typename EvalSubExprsCallback>
+ EIGEN_STRONG_INLINE void evalSubExprsIfNeededAsync(
+ EvaluatorPointerType, EvalSubExprsCallback done) {
+ m_leftImpl.evalSubExprsIfNeededAsync(nullptr, [this, done](bool) {
+ m_rightImpl.evalSubExprsIfNeededAsync(
+ m_leftImpl.data(), [done](bool need_assign) { done(need_assign); });
+ });
+ }
+#endif // EIGEN_USE_THREADS
+
+ EIGEN_STRONG_INLINE void cleanup() {
+ m_leftImpl.cleanup();
+ m_rightImpl.cleanup();
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void evalScalar(Index i) {
+ m_leftImpl.coeffRef(i) = m_rightImpl.coeff(i);
+ }
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void evalPacket(Index i) {
+
+ const int LhsStoreMode = TensorEvaluator<LeftArgType, Device>::IsAligned ? Aligned : Unaligned;
+ const int RhsLoadMode = TensorEvaluator<RightArgType, Device>::IsAligned ? Aligned : Unaligned;
+ m_leftImpl.template writePacket<LhsStoreMode>(i, m_rightImpl.template packet<RhsLoadMode>(i));
+ }
+ EIGEN_DEVICE_FUNC CoeffReturnType coeff(Index index) const
+ {
+ return m_leftImpl.coeff(index);
+ }
+ template<int LoadMode>
+ EIGEN_DEVICE_FUNC PacketReturnType packet(Index index) const
+ {
+ return m_leftImpl.template packet<LoadMode>(index);
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorOpCost
+ costPerCoeff(bool vectorized) const {
+ // We assume that evalPacket or evalScalar is called to perform the
+ // assignment and account for the cost of the write here, but reduce left
+ // cost by one load because we are using m_leftImpl.coeffRef.
+ TensorOpCost left = m_leftImpl.costPerCoeff(vectorized);
+ return m_rightImpl.costPerCoeff(vectorized) +
+ TensorOpCost(
+ numext::maxi(0.0, left.bytes_loaded() - sizeof(CoeffReturnType)),
+ left.bytes_stored(), left.compute_cycles()) +
+ TensorOpCost(0, sizeof(CoeffReturnType), 0, vectorized, PacketSize);
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ internal::TensorBlockResourceRequirements getResourceRequirements() const {
+ return internal::TensorBlockResourceRequirements::merge(
+ m_leftImpl.getResourceRequirements(),
+ m_rightImpl.getResourceRequirements());
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void evalBlock(
+ TensorBlockDesc& desc, TensorBlockScratch& scratch) {
+ if (TensorEvaluator<LeftArgType, Device>::RawAccess &&
+ m_leftImpl.data() != NULL) {
+ // If destination has raw data access, we pass it as a potential
+ // destination for a block descriptor evaluation.
+ desc.template AddDestinationBuffer<Layout>(
+ /*dst_base=*/m_leftImpl.data() + desc.offset(),
+ /*dst_strides=*/internal::strides<Layout>(m_leftImpl.dimensions()));
+ }
+
+ RightTensorBlock block = m_rightImpl.block(desc, scratch, /*root_of_expr_ast=*/true);
+ // If block was evaluated into a destination, there is no need to do assignment.
+ if (block.kind() != internal::TensorBlockKind::kMaterializedInOutput) {
+ m_leftImpl.writeBlock(desc, block);
+ }
+ block.cleanup();
+ }
+
+#ifdef EIGEN_USE_SYCL
+ // binding placeholder accessors to a command group handler for SYCL
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void bind(cl::sycl::handler &cgh) const {
+ m_leftImpl.bind(cgh);
+ m_rightImpl.bind(cgh);
+ }
+#endif
+
+ EIGEN_DEVICE_FUNC EvaluatorPointerType data() const { return m_leftImpl.data(); }
+
+ private:
+ TensorEvaluator<LeftArgType, Device> m_leftImpl;
+ TensorEvaluator<RightArgType, Device> m_rightImpl;
+};
+
+}
+
+
+#endif // EIGEN_CXX11_TENSOR_TENSOR_ASSIGN_H
diff --git a/unsupported/Eigen/CXX11/src/Tensor/TensorBase.h b/unsupported/Eigen/CXX11/src/Tensor/TensorBase.h
new file mode 100644
index 0000000..a4ac2ad
--- /dev/null
+++ b/unsupported/Eigen/CXX11/src/Tensor/TensorBase.h
@@ -0,0 +1,1197 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_CXX11_TENSOR_TENSOR_BASE_H
+#define EIGEN_CXX11_TENSOR_TENSOR_BASE_H
+
+// clang-format off
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+/** \class TensorBase
+ * \ingroup CXX11_Tensor_Module
+ *
+ * \brief The tensor base class.
+ *
+ * This class is the common parent of the Tensor and TensorMap class, thus
+ * making it possible to use either class interchangeably in expressions.
+ */
+#ifndef EIGEN_PARSED_BY_DOXYGEN
+// FIXME Doxygen does not like the inheritance with different template parameters
+// Since there is no doxygen documentation inside, we disable it for now
+template<typename Derived>
+class TensorBase<Derived, ReadOnlyAccessors>
+{
+ public:
+ typedef internal::traits<Derived> DerivedTraits;
+ typedef typename DerivedTraits::Scalar Scalar;
+ typedef typename DerivedTraits::Index Index;
+ typedef std::remove_const_t<Scalar> CoeffReturnType;
+ static constexpr int NumDimensions = DerivedTraits::NumDimensions;
+
+ // Generic nullary operation support.
+ template <typename CustomNullaryOp> EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE const TensorCwiseNullaryOp<CustomNullaryOp, const Derived>
+ nullaryExpr(const CustomNullaryOp& func) const {
+ return TensorCwiseNullaryOp<CustomNullaryOp, const Derived>(derived(), func);
+ }
+
+ // Coefficient-wise nullary operators
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE const TensorCwiseNullaryOp<internal::scalar_constant_op<Scalar>, const Derived>
+ constant(const Scalar& value) const {
+ return nullaryExpr(internal::scalar_constant_op<Scalar>(value));
+ }
+
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE const TensorCwiseNullaryOp<internal::UniformRandomGenerator<Scalar>, const Derived>
+ random() const {
+ return nullaryExpr(internal::UniformRandomGenerator<Scalar>());
+ }
+ template <typename RandomGenerator> EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE const TensorCwiseNullaryOp<RandomGenerator, const Derived>
+ random(const RandomGenerator& gen = RandomGenerator()) const {
+ return nullaryExpr(gen);
+ }
+
+ // Tensor generation
+ template <typename Generator> EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE const TensorGeneratorOp<Generator, const Derived>
+ generate(const Generator& generator) const {
+ return TensorGeneratorOp<Generator, const Derived>(derived(), generator);
+ }
+
+ // Generic unary operation support.
+ template <typename CustomUnaryOp> EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE const TensorCwiseUnaryOp<CustomUnaryOp, const Derived>
+ unaryExpr(const CustomUnaryOp& func) const {
+ return TensorCwiseUnaryOp<CustomUnaryOp, const Derived>(derived(), func);
+ }
+
+ // Coefficient-wise unary operators
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE const TensorCwiseUnaryOp<internal::scalar_opposite_op<Scalar>, const Derived>
+ operator-() const {
+ return unaryExpr(internal::scalar_opposite_op<Scalar>());
+ }
+
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE const TensorCwiseUnaryOp<internal::scalar_sqrt_op<Scalar>, const Derived>
+ sqrt() const {
+ return unaryExpr(internal::scalar_sqrt_op<Scalar>());
+ }
+
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE const TensorCwiseUnaryOp<internal::scalar_sign_op<Scalar>, const Derived>
+ sign() const {
+ return unaryExpr(internal::scalar_sign_op<Scalar>());
+ }
+
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE const TensorCwiseUnaryOp<internal::scalar_rsqrt_op<Scalar>, const Derived>
+ rsqrt() const {
+ return unaryExpr(internal::scalar_rsqrt_op<Scalar>());
+ }
+
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE const TensorCwiseUnaryOp<internal::scalar_square_op<Scalar>, const Derived>
+ square() const {
+ return unaryExpr(internal::scalar_square_op<Scalar>());
+ }
+
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE const TensorCwiseUnaryOp<internal::scalar_cube_op<Scalar>, const Derived>
+ cube() const {
+ return unaryExpr(internal::scalar_cube_op<Scalar>());
+ }
+
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE const TensorCwiseUnaryOp<internal::scalar_inverse_op<Scalar>, const Derived>
+ inverse() const {
+ return unaryExpr(internal::scalar_inverse_op<Scalar>());
+ }
+
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE const TensorCwiseUnaryOp<internal::scalar_tanh_op<Scalar>, const Derived>
+ tanh() const {
+ return unaryExpr(internal::scalar_tanh_op<Scalar>());
+ }
+
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE const TensorCwiseUnaryOp<internal::scalar_lgamma_op<Scalar>, const Derived>
+ lgamma() const {
+ return unaryExpr(internal::scalar_lgamma_op<Scalar>());
+ }
+
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE const TensorCwiseUnaryOp<internal::scalar_digamma_op<Scalar>, const Derived>
+ digamma() const {
+ return unaryExpr(internal::scalar_digamma_op<Scalar>());
+ }
+
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE const TensorCwiseUnaryOp<internal::scalar_bessel_i0_op<Scalar>, const Derived>
+ bessel_i0() const {
+ return unaryExpr(internal::scalar_bessel_i0_op<Scalar>());
+ }
+
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE const TensorCwiseUnaryOp<internal::scalar_bessel_i0e_op<Scalar>, const Derived>
+ bessel_i0e() const {
+ return unaryExpr(internal::scalar_bessel_i0e_op<Scalar>());
+ }
+
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE const TensorCwiseUnaryOp<internal::scalar_bessel_i1_op<Scalar>, const Derived>
+ bessel_i1() const {
+ return unaryExpr(internal::scalar_bessel_i1_op<Scalar>());
+ }
+
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE const TensorCwiseUnaryOp<internal::scalar_bessel_i1e_op<Scalar>, const Derived>
+ bessel_i1e() const {
+ return unaryExpr(internal::scalar_bessel_i1e_op<Scalar>());
+ }
+
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE const TensorCwiseUnaryOp<internal::scalar_bessel_j0_op<Scalar>, const Derived>
+ bessel_j0() const {
+ return unaryExpr(internal::scalar_bessel_j0_op<Scalar>());
+ }
+
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE const TensorCwiseUnaryOp<internal::scalar_bessel_y0_op<Scalar>, const Derived>
+ bessel_y0() const {
+ return unaryExpr(internal::scalar_bessel_y0_op<Scalar>());
+ }
+
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE const TensorCwiseUnaryOp<internal::scalar_bessel_j1_op<Scalar>, const Derived>
+ bessel_j1() const {
+ return unaryExpr(internal::scalar_bessel_j1_op<Scalar>());
+ }
+
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE const TensorCwiseUnaryOp<internal::scalar_bessel_y1_op<Scalar>, const Derived>
+ bessel_y1() const {
+ return unaryExpr(internal::scalar_bessel_y1_op<Scalar>());
+ }
+
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE const TensorCwiseUnaryOp<internal::scalar_bessel_k0_op<Scalar>, const Derived>
+ bessel_k0() const {
+ return unaryExpr(internal::scalar_bessel_k0_op<Scalar>());
+ }
+
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE const TensorCwiseUnaryOp<internal::scalar_bessel_k0e_op<Scalar>, const Derived>
+ bessel_k0e() const {
+ return unaryExpr(internal::scalar_bessel_k0e_op<Scalar>());
+ }
+
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE const TensorCwiseUnaryOp<internal::scalar_bessel_k1_op<Scalar>, const Derived>
+ bessel_k1() const {
+ return unaryExpr(internal::scalar_bessel_k1_op<Scalar>());
+ }
+
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE const TensorCwiseUnaryOp<internal::scalar_bessel_k1e_op<Scalar>, const Derived>
+ bessel_k1e() const {
+ return unaryExpr(internal::scalar_bessel_k1e_op<Scalar>());
+ }
+
+ // igamma(a = this, x = other)
+ template<typename OtherDerived> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ const TensorCwiseBinaryOp<internal::scalar_igamma_op<Scalar>, const Derived, const OtherDerived>
+ igamma(const OtherDerived& other) const {
+ return binaryExpr(other.derived(), internal::scalar_igamma_op<Scalar>());
+ }
+
+ // igamma_der_a(a = this, x = other)
+ template<typename OtherDerived> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ const TensorCwiseBinaryOp<internal::scalar_igamma_der_a_op<Scalar>, const Derived, const OtherDerived>
+ igamma_der_a(const OtherDerived& other) const {
+ return binaryExpr(other.derived(), internal::scalar_igamma_der_a_op<Scalar>());
+ }
+
+ // gamma_sample_der_alpha(alpha = this, sample = other)
+ template<typename OtherDerived> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ const TensorCwiseBinaryOp<internal::scalar_gamma_sample_der_alpha_op<Scalar>, const Derived, const OtherDerived>
+ gamma_sample_der_alpha(const OtherDerived& other) const {
+ return binaryExpr(other.derived(), internal::scalar_gamma_sample_der_alpha_op<Scalar>());
+ }
+
+ // igammac(a = this, x = other)
+ template<typename OtherDerived> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ const TensorCwiseBinaryOp<internal::scalar_igammac_op<Scalar>, const Derived, const OtherDerived>
+ igammac(const OtherDerived& other) const {
+ return binaryExpr(other.derived(), internal::scalar_igammac_op<Scalar>());
+ }
+
+ // zeta(x = this, q = other)
+ template<typename OtherDerived> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ const TensorCwiseBinaryOp<internal::scalar_zeta_op<Scalar>, const Derived, const OtherDerived>
+ zeta(const OtherDerived& other) const {
+ return binaryExpr(other.derived(), internal::scalar_zeta_op<Scalar>());
+ }
+
+ // polygamma(n = this, x = other)
+ template<typename OtherDerived> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ const TensorCwiseBinaryOp<internal::scalar_polygamma_op<Scalar>, const Derived, const OtherDerived>
+ polygamma(const OtherDerived& other) const {
+ return binaryExpr(other.derived(), internal::scalar_polygamma_op<Scalar>());
+ }
+
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE const TensorCwiseUnaryOp<internal::scalar_erf_op<Scalar>, const Derived>
+ erf() const {
+ return unaryExpr(internal::scalar_erf_op<Scalar>());
+ }
+
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE const TensorCwiseUnaryOp<internal::scalar_erfc_op<Scalar>, const Derived>
+ erfc() const {
+ return unaryExpr(internal::scalar_erfc_op<Scalar>());
+ }
+
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE const TensorCwiseUnaryOp<internal::scalar_ndtri_op<Scalar>, const Derived>
+ ndtri() const {
+ return unaryExpr(internal::scalar_ndtri_op<Scalar>());
+ }
+
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE const TensorCwiseUnaryOp<internal::scalar_logistic_op<Scalar>, const Derived>
+ sigmoid() const {
+ return unaryExpr(internal::scalar_logistic_op<Scalar>());
+ }
+
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE const TensorCwiseUnaryOp<internal::scalar_exp_op<Scalar>, const Derived>
+ exp() const {
+ return unaryExpr(internal::scalar_exp_op<Scalar>());
+ }
+
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE const TensorCwiseUnaryOp<internal::scalar_expm1_op<Scalar>, const Derived>
+ expm1() const {
+ return unaryExpr(internal::scalar_expm1_op<Scalar>());
+ }
+
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE const TensorCwiseUnaryOp<internal::scalar_log_op<Scalar>, const Derived>
+ log() const {
+ return unaryExpr(internal::scalar_log_op<Scalar>());
+ }
+
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE const TensorCwiseUnaryOp<internal::scalar_log1p_op<Scalar>, const Derived>
+ log1p() const {
+ return unaryExpr(internal::scalar_log1p_op<Scalar>());
+ }
+
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE const TensorCwiseUnaryOp<internal::scalar_log2_op<Scalar>, const Derived>
+ log2() const {
+ return unaryExpr(internal::scalar_log2_op<Scalar>());
+ }
+
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE const TensorCwiseUnaryOp<internal::scalar_abs_op<Scalar>, const Derived>
+ abs() const {
+ return unaryExpr(internal::scalar_abs_op<Scalar>());
+ }
+
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE const TensorCwiseUnaryOp<internal::scalar_arg_op<Scalar>, const Derived>
+ arg() const {
+ return unaryExpr(internal::scalar_arg_op<Scalar>());
+ }
+
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE const TensorCwiseUnaryOp<internal::scalar_clamp_op<Scalar>, const Derived>
+ clip(Scalar min, Scalar max) const {
+ return unaryExpr(internal::scalar_clamp_op<Scalar>(min, max));
+ }
+
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE const std::conditional_t<NumTraits<CoeffReturnType>::IsComplex,
+ TensorCwiseUnaryOp<internal::scalar_conjugate_op<Scalar>, const Derived>,
+ Derived>
+ conjugate() const {
+ return choose(Cond<NumTraits<CoeffReturnType>::IsComplex>(), unaryExpr(internal::scalar_conjugate_op<Scalar>()), derived());
+ }
+
+ template<typename ScalarExponent>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const std::enable_if_t<internal::is_arithmetic<typename NumTraits<ScalarExponent>::Real>::value,
+ TensorCwiseUnaryOp<internal::scalar_unary_pow_op<Scalar, ScalarExponent>, const Derived>>
+ pow(ScalarExponent exponent) const
+ {
+ return unaryExpr(internal::scalar_unary_pow_op<Scalar, ScalarExponent>(exponent));
+ }
+
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE const TensorCwiseUnaryOp<internal::scalar_real_op<Scalar>, const Derived>
+ real() const {
+ return unaryExpr(internal::scalar_real_op<Scalar>());
+ }
+
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE const TensorCwiseUnaryOp<internal::scalar_imag_op<Scalar>, const Derived>
+ imag() const {
+ return unaryExpr(internal::scalar_imag_op<Scalar>());
+ }
+
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE const TensorCwiseUnaryOp<internal::bind2nd_op<internal::scalar_sum_op<Scalar,Scalar> >, const Derived>
+ operator+ (Scalar rhs) const {
+ return unaryExpr(internal::bind2nd_op<internal::scalar_sum_op<Scalar,Scalar> >(rhs));
+ }
+
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE friend
+ const TensorCwiseUnaryOp<internal::bind1st_op<internal::scalar_sum_op<Scalar> >, const Derived>
+ operator+ (Scalar lhs, const Derived& rhs) {
+ return rhs.unaryExpr(internal::bind1st_op<internal::scalar_sum_op<Scalar> >(lhs));
+ }
+
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE const TensorCwiseUnaryOp<internal::bind2nd_op<internal::scalar_difference_op<Scalar,Scalar> >, const Derived>
+ operator- (Scalar rhs) const {
+ EIGEN_STATIC_ASSERT((NumTraits<Scalar>::IsSigned || internal::is_same<Scalar, const std::complex<float> >::value), YOU_MADE_A_PROGRAMMING_MISTAKE);
+ return unaryExpr(internal::bind2nd_op<internal::scalar_difference_op<Scalar,Scalar> >(rhs));
+ }
+
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE friend
+ const TensorCwiseUnaryOp<internal::bind1st_op<internal::scalar_difference_op<Scalar> >, const Derived>
+ operator- (Scalar lhs, const Derived& rhs) {
+ return rhs.unaryExpr(internal::bind1st_op<internal::scalar_difference_op<Scalar> >(lhs));
+ }
+
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE const TensorCwiseUnaryOp<internal::bind2nd_op<internal::scalar_product_op<Scalar,Scalar> >, const Derived>
+ operator* (Scalar rhs) const {
+ return unaryExpr(internal::bind2nd_op<internal::scalar_product_op<Scalar,Scalar> >(rhs));
+ }
+
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE friend
+ const TensorCwiseUnaryOp<internal::bind1st_op<internal::scalar_product_op<Scalar> >, const Derived>
+ operator* (Scalar lhs, const Derived& rhs) {
+ return rhs.unaryExpr(internal::bind1st_op<internal::scalar_product_op<Scalar> >(lhs));
+ }
+
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE const TensorCwiseUnaryOp<internal::bind2nd_op<internal::scalar_quotient_op<Scalar,Scalar> >, const Derived>
+ operator/ (Scalar rhs) const {
+ return unaryExpr(internal::bind2nd_op<internal::scalar_quotient_op<Scalar,Scalar> >(rhs));
+ }
+
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE friend
+ const TensorCwiseUnaryOp<internal::bind1st_op<internal::scalar_quotient_op<Scalar> >, const Derived>
+ operator/ (Scalar lhs, const Derived& rhs) {
+ return rhs.unaryExpr(internal::bind1st_op<internal::scalar_quotient_op<Scalar> >(lhs));
+ }
+
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE const TensorCwiseUnaryOp<internal::scalar_mod_op<Scalar>, const Derived>
+ operator% (Scalar rhs) const {
+ EIGEN_STATIC_ASSERT(NumTraits<Scalar>::IsInteger, YOU_MADE_A_PROGRAMMING_MISTAKE_TRY_MOD);
+ return unaryExpr(internal::scalar_mod_op<Scalar>(rhs));
+ }
+
+ template <int NanPropagation=PropagateFast>
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE const TensorCwiseBinaryOp<internal::scalar_max_op<Scalar,Scalar,NanPropagation>, const Derived, const TensorCwiseNullaryOp<internal::scalar_constant_op<Scalar>, const Derived> >
+ cwiseMax(Scalar threshold) const {
+ return cwiseMax<NanPropagation>(constant(threshold));
+ }
+
+ template <int NanPropagation=PropagateFast>
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE const TensorCwiseBinaryOp<internal::scalar_min_op<Scalar,Scalar,NanPropagation>, const Derived, const TensorCwiseNullaryOp<internal::scalar_constant_op<Scalar>, const Derived> >
+ cwiseMin(Scalar threshold) const {
+ return cwiseMin<NanPropagation>(constant(threshold));
+ }
+
+ template<typename NewType>
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE const std::conditional_t<internal::is_same<NewType, CoeffReturnType>::value,
+ Derived,
+ TensorConversionOp<NewType, const Derived> >
+ cast() const {
+ return choose(Cond<internal::is_same<NewType, CoeffReturnType>::value>(), derived(), TensorConversionOp<NewType, const Derived>(derived()));
+ }
+
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE const TensorCwiseUnaryOp<internal::scalar_round_op<Scalar>, const Derived>
+ round() const {
+ return unaryExpr(internal::scalar_round_op<Scalar>());
+ }
+
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE const TensorCwiseUnaryOp<internal::scalar_rint_op<Scalar>, const Derived>
+ rint() const {
+ return unaryExpr(internal::scalar_rint_op<Scalar>());
+ }
+
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE const TensorCwiseUnaryOp<internal::scalar_ceil_op<Scalar>, const Derived>
+ ceil() const {
+ return unaryExpr(internal::scalar_ceil_op<Scalar>());
+ }
+
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE const TensorCwiseUnaryOp<internal::scalar_floor_op<Scalar>, const Derived>
+ floor() const {
+ return unaryExpr(internal::scalar_floor_op<Scalar>());
+ }
+
+ // Generic binary operation support.
+ template <typename CustomBinaryOp, typename OtherDerived> EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE const TensorCwiseBinaryOp<CustomBinaryOp, const Derived, const OtherDerived>
+ binaryExpr(const OtherDerived& other, const CustomBinaryOp& func) const {
+ return TensorCwiseBinaryOp<CustomBinaryOp, const Derived, const OtherDerived>(derived(), other, func);
+ }
+
+ // Coefficient-wise binary operators.
+ template<typename OtherDerived> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ const TensorCwiseBinaryOp<internal::scalar_sum_op<Scalar>, const Derived, const OtherDerived>
+ operator+(const OtherDerived& other) const {
+ return binaryExpr(other.derived(), internal::scalar_sum_op<Scalar>());
+ }
+
+ template<typename OtherDerived> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ const TensorCwiseBinaryOp<internal::scalar_difference_op<Scalar>, const Derived, const OtherDerived>
+ operator-(const OtherDerived& other) const {
+ return binaryExpr(other.derived(), internal::scalar_difference_op<Scalar>());
+ }
+
+ template<typename OtherDerived> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ const TensorCwiseBinaryOp<internal::scalar_product_op<Scalar>, const Derived, const OtherDerived>
+ operator*(const OtherDerived& other) const {
+ return binaryExpr(other.derived(), internal::scalar_product_op<Scalar>());
+ }
+
+ template<typename OtherDerived> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ const TensorCwiseBinaryOp<internal::scalar_quotient_op<Scalar>, const Derived, const OtherDerived>
+ operator/(const OtherDerived& other) const {
+ return binaryExpr(other.derived(), internal::scalar_quotient_op<Scalar>());
+ }
+
+ template<int NaNPropagation=PropagateFast, typename OtherDerived> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ const TensorCwiseBinaryOp<internal::scalar_max_op<Scalar,Scalar, NaNPropagation>, const Derived, const OtherDerived>
+ cwiseMax(const OtherDerived& other) const {
+ return binaryExpr(other.derived(), internal::scalar_max_op<Scalar,Scalar, NaNPropagation>());
+ }
+
+ template<int NaNPropagation=PropagateFast, typename OtherDerived> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ const TensorCwiseBinaryOp<internal::scalar_min_op<Scalar,Scalar, NaNPropagation>, const Derived, const OtherDerived>
+ cwiseMin(const OtherDerived& other) const {
+ return binaryExpr(other.derived(), internal::scalar_min_op<Scalar,Scalar, NaNPropagation>());
+ }
+
+ template<typename OtherDerived> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ const TensorCwiseBinaryOp<internal::scalar_boolean_and_op, const Derived, const OtherDerived>
+ operator&&(const OtherDerived& other) const {
+ return binaryExpr(other.derived(), internal::scalar_boolean_and_op());
+ }
+
+ template<typename OtherDerived> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ const TensorCwiseBinaryOp<internal::scalar_boolean_or_op, const Derived, const OtherDerived>
+ operator||(const OtherDerived& other) const {
+ return binaryExpr(other.derived(), internal::scalar_boolean_or_op());
+ }
+
+ template<typename OtherDerived> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ const TensorCwiseBinaryOp<internal::scalar_boolean_xor_op, const Derived, const OtherDerived>
+ operator^(const OtherDerived& other) const {
+ return binaryExpr(other.derived(), internal::scalar_boolean_xor_op());
+ }
+
+ // Comparisons and tests.
+ template<typename OtherDerived> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ const TensorCwiseBinaryOp<internal::scalar_cmp_op<Scalar, Scalar, internal::cmp_LT>, const Derived, const OtherDerived>
+ operator<(const TensorBase<OtherDerived, ReadOnlyAccessors>& other) const {
+ return binaryExpr(other.derived(), internal::scalar_cmp_op<Scalar, Scalar, internal::cmp_LT>());
+ }
+ template<typename OtherDerived> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ const TensorCwiseBinaryOp<internal::scalar_cmp_op<Scalar, Scalar, internal::cmp_LE>, const Derived, const OtherDerived>
+ operator<=(const TensorBase<OtherDerived, ReadOnlyAccessors>& other) const {
+ return binaryExpr(other.derived(), internal::scalar_cmp_op<Scalar, Scalar, internal::cmp_LE>());
+ }
+ template<typename OtherDerived> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ const TensorCwiseBinaryOp<internal::scalar_cmp_op<Scalar, Scalar, internal::cmp_GT>, const Derived, const OtherDerived>
+ operator>(const TensorBase<OtherDerived, ReadOnlyAccessors>& other) const {
+ return binaryExpr(other.derived(), internal::scalar_cmp_op<Scalar, Scalar, internal::cmp_GT>());
+ }
+ template<typename OtherDerived> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ const TensorCwiseBinaryOp<internal::scalar_cmp_op<Scalar, Scalar, internal::cmp_GE>, const Derived, const OtherDerived>
+ operator>=(const TensorBase<OtherDerived, ReadOnlyAccessors>& other) const {
+ return binaryExpr(other.derived(), internal::scalar_cmp_op<Scalar, Scalar, internal::cmp_GE>());
+ }
+
+ template<typename OtherDerived> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ const TensorCwiseBinaryOp<internal::scalar_cmp_op<Scalar, Scalar, internal::cmp_EQ>, const Derived, const OtherDerived>
+ operator==(const TensorBase<OtherDerived, ReadOnlyAccessors>& other) const {
+ return binaryExpr(other.derived(), internal::scalar_cmp_op<Scalar, Scalar, internal::cmp_EQ>());
+ }
+
+ template<typename OtherDerived> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ const TensorCwiseBinaryOp<internal::scalar_cmp_op<Scalar, Scalar, internal::cmp_NEQ>, const Derived, const OtherDerived>
+ operator!=(const TensorBase<OtherDerived, ReadOnlyAccessors>& other) const {
+ return binaryExpr(other.derived(), internal::scalar_cmp_op<Scalar, Scalar, internal::cmp_NEQ>());
+ }
+
+ // comparisons and tests for Scalars
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE const TensorCwiseBinaryOp<internal::scalar_cmp_op<Scalar, Scalar, internal::cmp_LT>, const Derived, const TensorCwiseNullaryOp<internal::scalar_constant_op<Scalar>, const Derived> >
+ operator<(Scalar threshold) const {
+ return operator<(constant(threshold));
+ }
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE const TensorCwiseBinaryOp<internal::scalar_cmp_op<Scalar, Scalar, internal::cmp_LE>, const Derived, const TensorCwiseNullaryOp<internal::scalar_constant_op<Scalar>, const Derived> >
+ operator<=(Scalar threshold) const {
+ return operator<=(constant(threshold));
+ }
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE const TensorCwiseBinaryOp<internal::scalar_cmp_op<Scalar, Scalar, internal::cmp_GT>, const Derived, const TensorCwiseNullaryOp<internal::scalar_constant_op<Scalar>, const Derived> >
+ operator>(Scalar threshold) const {
+ return operator>(constant(threshold));
+ }
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE const TensorCwiseBinaryOp<internal::scalar_cmp_op<Scalar, Scalar, internal::cmp_GE>, const Derived, const TensorCwiseNullaryOp<internal::scalar_constant_op<Scalar>, const Derived> >
+ operator>=(Scalar threshold) const {
+ return operator>=(constant(threshold));
+ }
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE const TensorCwiseBinaryOp<internal::scalar_cmp_op<Scalar, Scalar, internal::cmp_EQ>, const Derived, const TensorCwiseNullaryOp<internal::scalar_constant_op<Scalar>, const Derived> >
+ operator==(Scalar threshold) const {
+ return operator==(constant(threshold));
+ }
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE const TensorCwiseBinaryOp<internal::scalar_cmp_op<Scalar, Scalar, internal::cmp_NEQ>, const Derived, const TensorCwiseNullaryOp<internal::scalar_constant_op<Scalar>, const Derived> >
+ operator!=(Scalar threshold) const {
+ return operator!=(constant(threshold));
+ }
+
+ // Checks
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE const TensorCwiseUnaryOp<internal::scalar_isnan_op<Scalar>, const Derived>
+ (isnan)() const {
+ return unaryExpr(internal::scalar_isnan_op<Scalar>());
+ }
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE const TensorCwiseUnaryOp<internal::scalar_isinf_op<Scalar>, const Derived>
+ (isinf)() const {
+ return unaryExpr(internal::scalar_isinf_op<Scalar>());
+ }
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE const TensorCwiseUnaryOp<internal::scalar_isfinite_op<Scalar>, const Derived>
+ (isfinite)() const {
+ return unaryExpr(internal::scalar_isfinite_op<Scalar>());
+ }
+
+ // Coefficient-wise ternary operators.
+ template<typename ThenDerived, typename ElseDerived> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ const TensorSelectOp<const Derived, const ThenDerived, const ElseDerived>
+ select(const ThenDerived& thenTensor, const ElseDerived& elseTensor) const {
+ return TensorSelectOp<const Derived, const ThenDerived, const ElseDerived>(derived(), thenTensor.derived(), elseTensor.derived());
+ }
+
+ // Contractions.
+ typedef Eigen::IndexPair<Index> DimensionPair;
+
+ template<typename OtherDerived, typename Dimensions> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ const TensorContractionOp<const Dimensions, const Derived, const OtherDerived, const NoOpOutputKernel>
+ contract(const OtherDerived& other, const Dimensions& dims) const {
+ return TensorContractionOp<const Dimensions, const Derived, const OtherDerived, const NoOpOutputKernel>(derived(), other.derived(), dims);
+ }
+
+ template<typename OtherDerived, typename Dimensions, typename OutputKernel> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ const TensorContractionOp<const Dimensions, const Derived, const OtherDerived, const OutputKernel>
+ contract(const OtherDerived& other, const Dimensions& dims, const OutputKernel& output_kernel) const {
+ return TensorContractionOp<const Dimensions, const Derived, const OtherDerived, const OutputKernel>(derived(), other.derived(), dims, output_kernel);
+ }
+
+ // Convolutions.
+ template<typename KernelDerived, typename Dimensions> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ const TensorConvolutionOp<const Dimensions, const Derived, const KernelDerived>
+ convolve(const KernelDerived& kernel, const Dimensions& dims) const {
+ return TensorConvolutionOp<const Dimensions, const Derived, const KernelDerived>(derived(), kernel.derived(), dims);
+ }
+
+ // Fourier transforms
+ template <int FFTDataType, int FFTDirection, typename FFT> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ const TensorFFTOp<const FFT, const Derived, FFTDataType, FFTDirection>
+ fft(const FFT& dims) const {
+ return TensorFFTOp<const FFT, const Derived, FFTDataType, FFTDirection>(derived(), dims);
+ }
+
+ // Scan.
+ typedef TensorScanOp<internal::SumReducer<CoeffReturnType>, const Derived> TensorScanSumOp;
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ const TensorScanSumOp
+ cumsum(const Index& axis, bool exclusive = false) const {
+ return TensorScanSumOp(derived(), axis, exclusive);
+ }
+
+ typedef TensorScanOp<internal::ProdReducer<CoeffReturnType>, const Derived> TensorScanProdOp;
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ const TensorScanProdOp
+ cumprod(const Index& axis, bool exclusive = false) const {
+ return TensorScanProdOp(derived(), axis, exclusive);
+ }
+
+ template <typename Reducer>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ const TensorScanOp<Reducer, const Derived>
+ scan(const Index& axis, const Reducer& reducer, bool exclusive = false) const {
+ return TensorScanOp<Reducer, const Derived>(derived(), axis, exclusive, reducer);
+ }
+
+ // Reductions.
+ template <typename Dims> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ const TensorReductionOp<internal::SumReducer<CoeffReturnType>, const Dims, const Derived>
+ sum(const Dims& dims) const {
+ return TensorReductionOp<internal::SumReducer<CoeffReturnType>, const Dims, const Derived>(derived(), dims, internal::SumReducer<CoeffReturnType>());
+ }
+
+ const TensorReductionOp<internal::SumReducer<CoeffReturnType>, const DimensionList<Index, NumDimensions>, const Derived>
+ sum() const {
+ DimensionList<Index, NumDimensions> in_dims;
+ return TensorReductionOp<internal::SumReducer<CoeffReturnType>, const DimensionList<Index, NumDimensions>, const Derived>(derived(), in_dims, internal::SumReducer<CoeffReturnType>());
+ }
+
+ template <typename Dims> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ const TensorReductionOp<internal::MeanReducer<CoeffReturnType>, const Dims, const Derived>
+ mean(const Dims& dims) const {
+ return TensorReductionOp<internal::MeanReducer<CoeffReturnType>, const Dims, const Derived>(derived(), dims, internal::MeanReducer<CoeffReturnType>());
+ }
+
+ const TensorReductionOp<internal::MeanReducer<CoeffReturnType>, const DimensionList<Index, NumDimensions>, const Derived>
+ mean() const {
+ DimensionList<Index, NumDimensions> in_dims;
+ return TensorReductionOp<internal::MeanReducer<CoeffReturnType>, const DimensionList<Index, NumDimensions>, const Derived>(derived(), in_dims, internal::MeanReducer<CoeffReturnType>());
+ }
+
+ template <typename Dims> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ const TensorReductionOp<internal::ProdReducer<CoeffReturnType>, const Dims, const Derived>
+ prod(const Dims& dims) const {
+ return TensorReductionOp<internal::ProdReducer<CoeffReturnType>, const Dims, const Derived>(derived(), dims, internal::ProdReducer<CoeffReturnType>());
+ }
+
+ const TensorReductionOp<internal::ProdReducer<CoeffReturnType>, const DimensionList<Index, NumDimensions>, const Derived>
+ prod() const {
+ DimensionList<Index, NumDimensions> in_dims;
+ return TensorReductionOp<internal::ProdReducer<CoeffReturnType>, const DimensionList<Index, NumDimensions>, const Derived>(derived(), in_dims, internal::ProdReducer<CoeffReturnType>());
+ }
+
+ template <typename Dims,int NanPropagation=PropagateFast> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ const TensorReductionOp<internal::MaxReducer<CoeffReturnType,NanPropagation>, const Dims, const Derived>
+ maximum(const Dims& dims) const {
+ return TensorReductionOp<internal::MaxReducer<CoeffReturnType,NanPropagation>, const Dims, const Derived>(derived(), dims, internal::MaxReducer<CoeffReturnType,NanPropagation>());
+ }
+
+ template <int NanPropagation=PropagateFast>
+ const TensorReductionOp<internal::MaxReducer<CoeffReturnType,NanPropagation>, const DimensionList<Index, NumDimensions>, const Derived>
+ maximum() const {
+ DimensionList<Index, NumDimensions> in_dims;
+ return TensorReductionOp<internal::MaxReducer<CoeffReturnType,NanPropagation>, const DimensionList<Index, NumDimensions>, const Derived>(derived(), in_dims, internal::MaxReducer<CoeffReturnType,NanPropagation>());
+ }
+
+ template <typename Dims,int NanPropagation=PropagateFast> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ const TensorReductionOp<internal::MinReducer<CoeffReturnType,NanPropagation>, const Dims, const Derived>
+ minimum(const Dims& dims) const {
+ return TensorReductionOp<internal::MinReducer<CoeffReturnType,NanPropagation>, const Dims, const Derived>(derived(), dims, internal::MinReducer<CoeffReturnType,NanPropagation>());
+ }
+
+ template <int NanPropagation=PropagateFast>
+ const TensorReductionOp<internal::MinReducer<CoeffReturnType,NanPropagation>, const DimensionList<Index, NumDimensions>, const Derived>
+ minimum() const {
+ DimensionList<Index, NumDimensions> in_dims;
+ return TensorReductionOp<internal::MinReducer<CoeffReturnType,NanPropagation>, const DimensionList<Index, NumDimensions>, const Derived>(derived(), in_dims, internal::MinReducer<CoeffReturnType,NanPropagation>());
+ }
+
+ template <typename Dims> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ const TensorReductionOp<internal::AndReducer, const Dims, const std::conditional_t<internal::is_same<bool, CoeffReturnType>::value, Derived, TensorConversionOp<bool, const Derived> > >
+ all(const Dims& dims) const {
+ return cast<bool>().reduce(dims, internal::AndReducer());
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ const TensorReductionOp<internal::AndReducer, const DimensionList<Index, NumDimensions>, const std::conditional_t<internal::is_same<bool, CoeffReturnType>::value, Derived, TensorConversionOp<bool, const Derived> > >
+ all() const {
+ DimensionList<Index, NumDimensions> in_dims;
+ return cast<bool>().reduce(in_dims, internal::AndReducer());
+ }
+
+ template <typename Dims> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ const TensorReductionOp<internal::OrReducer, const Dims, const std::conditional_t<internal::is_same<bool, CoeffReturnType>::value, Derived, TensorConversionOp<bool, const Derived> > >
+ any(const Dims& dims) const {
+ return cast<bool>().reduce(dims, internal::OrReducer());
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ const TensorReductionOp<internal::OrReducer, const DimensionList<Index, NumDimensions>, const std::conditional_t<internal::is_same<bool, CoeffReturnType>::value, Derived, TensorConversionOp<bool, const Derived> > >
+ any() const {
+ DimensionList<Index, NumDimensions> in_dims;
+ return cast<bool>().reduce(in_dims, internal::OrReducer());
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ const TensorPairReducerOp<
+ internal::ArgMaxPairReducer<Pair<Index, CoeffReturnType> >,
+ const array<Index, NumDimensions>, const Derived>
+ argmax() const {
+ array<Index, NumDimensions> in_dims;
+ for (Index d = 0; d < NumDimensions; ++d) in_dims[d] = d;
+ return TensorPairReducerOp<
+ internal::ArgMaxPairReducer<Pair<Index, CoeffReturnType> >,
+ const array<Index, NumDimensions>,
+ const Derived>(derived(), internal::ArgMaxPairReducer<Pair<Index, CoeffReturnType> >(), -1, in_dims);
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ const TensorPairReducerOp<
+ internal::ArgMinPairReducer<Pair<Index, CoeffReturnType> >,
+ const array<Index, NumDimensions>, const Derived>
+ argmin() const {
+ array<Index, NumDimensions> in_dims;
+ for (Index d = 0; d < NumDimensions; ++d) in_dims[d] = d;
+ return TensorPairReducerOp<
+ internal::ArgMinPairReducer<Pair<Index, CoeffReturnType> >,
+ const array<Index, NumDimensions>,
+ const Derived>(derived(), internal::ArgMinPairReducer<Pair<Index, CoeffReturnType> >(), -1, in_dims);
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ const TensorPairReducerOp<
+ internal::ArgMaxPairReducer<Pair<Index, CoeffReturnType> >,
+ const array<Index, 1>, const Derived>
+ argmax(const Index return_dim) const {
+ array<Index, 1> in_dims;
+ in_dims[0] = return_dim;
+ return TensorPairReducerOp<
+ internal::ArgMaxPairReducer<Pair<Index, CoeffReturnType> >,
+ const array<Index, 1>,
+ const Derived>(derived(), internal::ArgMaxPairReducer<Pair<Index, CoeffReturnType> >(), return_dim, in_dims);
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ const TensorPairReducerOp<
+ internal::ArgMinPairReducer<Pair<Index, CoeffReturnType> >,
+ const array<Index, 1>, const Derived>
+ argmin(const Index return_dim) const {
+ array<Index, 1> in_dims;
+ in_dims[0] = return_dim;
+ return TensorPairReducerOp<
+ internal::ArgMinPairReducer<Pair<Index, CoeffReturnType> >,
+ const array<Index, 1>,
+ const Derived>(derived(), internal::ArgMinPairReducer<Pair<Index, CoeffReturnType> >(), return_dim, in_dims);
+ }
+
+ template <typename Reducer, typename Dims> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ const TensorReductionOp<Reducer, const Dims, const Derived>
+ reduce(const Dims& dims, const Reducer& reducer) const {
+ return TensorReductionOp<Reducer, const Dims, const Derived>(derived(), dims, reducer);
+ }
+
+ template <typename Dims> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ const TensorTraceOp<const Dims, const Derived>
+ trace(const Dims& dims) const {
+ return TensorTraceOp<const Dims, const Derived>(derived(), dims);
+ }
+
+ const TensorTraceOp<const DimensionList<Index, NumDimensions>, const Derived>
+ trace() const {
+ DimensionList<Index, NumDimensions> in_dims;
+ return TensorTraceOp<const DimensionList<Index, NumDimensions>, const Derived>(derived(), in_dims);
+ }
+
+ template <typename Broadcast> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ const TensorBroadcastingOp<const Broadcast, const Derived>
+ broadcast(const Broadcast& bcast) const {
+ return TensorBroadcastingOp<const Broadcast, const Derived>(derived(), bcast);
+ }
+
+ template <typename Axis, typename OtherDerived> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ const TensorConcatenationOp<Axis, const Derived, const OtherDerived>
+ concatenate(const OtherDerived& other, Axis axis) const {
+ return TensorConcatenationOp<Axis, const Derived, const OtherDerived>(derived(), other.derived(), axis);
+ }
+
+ template <typename PatchDims> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ const TensorPatchOp<const PatchDims, const Derived>
+ extract_patches(const PatchDims& patch_dims) const {
+ return TensorPatchOp<const PatchDims, const Derived>(derived(), patch_dims);
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ const TensorImagePatchOp<Dynamic, Dynamic, const Derived>
+ extract_image_patches(const Index patch_rows = 1, const Index patch_cols = 1,
+ const Index row_stride = 1, const Index col_stride = 1,
+ const Index in_row_stride = 1, const Index in_col_stride = 1,
+ const PaddingType padding_type = PADDING_SAME, const Scalar padding_value = Scalar(0)) const {
+ return TensorImagePatchOp<Dynamic, Dynamic, const Derived>(derived(), patch_rows, patch_cols, row_stride, col_stride,
+ in_row_stride, in_col_stride, 1, 1, padding_type, padding_value);
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ const TensorImagePatchOp<Dynamic, Dynamic, const Derived>
+ extract_image_patches(const Index patch_rows, const Index patch_cols,
+ const Index row_stride, const Index col_stride,
+ const Index in_row_stride, const Index in_col_stride,
+ const Index row_inflate_stride, const Index col_inflate_stride,
+ const Index padding_top, const Index padding_bottom,
+ const Index padding_left,const Index padding_right,
+ const Scalar padding_value) const {
+ return TensorImagePatchOp<Dynamic, Dynamic, const Derived>(derived(), patch_rows, patch_cols, row_stride, col_stride,
+ in_row_stride, in_col_stride, row_inflate_stride, col_inflate_stride,
+ padding_top, padding_bottom, padding_left, padding_right, padding_value);
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ const TensorVolumePatchOp<Dynamic, Dynamic, Dynamic, const Derived>
+ extract_volume_patches(const Index patch_planes, const Index patch_rows, const Index patch_cols,
+ const Index plane_stride = 1, const Index row_stride = 1, const Index col_stride = 1,
+ const PaddingType padding_type = PADDING_SAME, const Scalar padding_value = Scalar(0)) const {
+ return TensorVolumePatchOp<Dynamic, Dynamic, Dynamic, const Derived>(derived(), patch_planes, patch_rows, patch_cols, plane_stride, row_stride, col_stride, 1, 1, 1, 1, 1, 1, padding_type, padding_value);
+ }
+
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ const TensorVolumePatchOp<Dynamic, Dynamic, Dynamic, const Derived>
+ extract_volume_patches(const Index patch_planes, const Index patch_rows, const Index patch_cols,
+ const Index plane_stride, const Index row_stride, const Index col_stride,
+ const Index plane_inflate_stride, const Index row_inflate_stride, const Index col_inflate_stride,
+ const Index padding_top_z, const Index padding_bottom_z,
+ const Index padding_top, const Index padding_bottom,
+ const Index padding_left, const Index padding_right, const Scalar padding_value = Scalar(0)) const {
+ return TensorVolumePatchOp<Dynamic, Dynamic, Dynamic, const Derived>(derived(), patch_planes, patch_rows, patch_cols, plane_stride, row_stride, col_stride, 1, 1, 1, plane_inflate_stride, row_inflate_stride, col_inflate_stride, padding_top_z, padding_bottom_z, padding_top, padding_bottom, padding_left, padding_right, padding_value);
+ }
+
+ // Morphing operators.
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ const TensorLayoutSwapOp<const Derived>
+ swap_layout() const {
+ return TensorLayoutSwapOp<const Derived>(derived());
+ }
+ template <typename NewDimensions> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ const TensorReshapingOp<const NewDimensions, const Derived>
+ reshape(const NewDimensions& newDimensions) const {
+ return TensorReshapingOp<const NewDimensions, const Derived>(derived(), newDimensions);
+ }
+ template <typename StartIndices, typename Sizes> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ const TensorSlicingOp<const StartIndices, const Sizes, const Derived>
+ slice(const StartIndices& startIndices, const Sizes& sizes) const {
+ return TensorSlicingOp<const StartIndices, const Sizes, const Derived>(derived(), startIndices, sizes);
+ }
+ template <typename StartIndices, typename StopIndices, typename Strides> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ const TensorStridingSlicingOp<const StartIndices, const StopIndices, const Strides, const Derived>
+ stridedSlice(const StartIndices& startIndices, const StopIndices& stopIndices, const Strides& strides) const {
+ return TensorStridingSlicingOp<const StartIndices, const StopIndices, const Strides,
+ const Derived>(derived(), startIndices, stopIndices, strides);
+ }
+ template <Index DimId> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ const TensorChippingOp<DimId, const Derived>
+ chip(const Index offset) const {
+ return TensorChippingOp<DimId, const Derived>(derived(), offset, DimId);
+ }
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ const TensorChippingOp<Dynamic, const Derived>
+ chip(const Index offset, const Index dim) const {
+ return TensorChippingOp<Dynamic, const Derived>(derived(), offset, dim);
+ }
+ template <typename ReverseDimensions> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ const TensorReverseOp<const ReverseDimensions, const Derived>
+ reverse(const ReverseDimensions& rev) const {
+ return TensorReverseOp<const ReverseDimensions, const Derived>(derived(), rev);
+ }
+ template <typename PaddingDimensions> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ const TensorPaddingOp<const PaddingDimensions, const Derived>
+ pad(const PaddingDimensions& padding) const {
+ return TensorPaddingOp<const PaddingDimensions, const Derived>(derived(), padding, internal::scalar_cast_op<int, Scalar>()(0));
+ }
+ template <typename PaddingDimensions> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ const TensorPaddingOp<const PaddingDimensions, const Derived>
+ pad(const PaddingDimensions& padding, const Scalar padding_value) const {
+ return TensorPaddingOp<const PaddingDimensions, const Derived>(derived(), padding, padding_value);
+ }
+ template <typename Shuffle> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ const TensorShufflingOp<const Shuffle, const Derived>
+ shuffle(const Shuffle& shfl) const {
+ return TensorShufflingOp<const Shuffle, const Derived>(derived(), shfl);
+ }
+ template <typename Strides> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ const TensorStridingOp<const Strides, const Derived>
+ stride(const Strides& strides) const {
+ return TensorStridingOp<const Strides, const Derived>(derived(), strides);
+ }
+ template <typename Strides> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ const TensorInflationOp<const Strides, const Derived>
+ inflate(const Strides& strides) const {
+ return TensorInflationOp<const Strides, const Derived>(derived(), strides);
+ }
+
+ // Returns a tensor containing index/value pairs
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ const TensorIndexPairOp<const Derived>
+ index_pairs() const {
+ return TensorIndexPairOp<const Derived>(derived());
+ }
+
+ // Support for custom unary and binary operations
+ template <typename CustomUnaryFunc>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ const TensorCustomUnaryOp<const CustomUnaryFunc, const Derived> customOp(const CustomUnaryFunc& op) const {
+ return TensorCustomUnaryOp<const CustomUnaryFunc, const Derived>(derived(), op);
+ }
+ template <typename OtherDerived, typename CustomBinaryFunc>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ const TensorCustomBinaryOp<const CustomBinaryFunc, const Derived, const OtherDerived> customOp(const OtherDerived& other, const CustomBinaryFunc& op) const {
+ return TensorCustomBinaryOp<const CustomBinaryFunc, const Derived, const OtherDerived>(derived(), other, op);
+ }
+
+ // Force the evaluation of the expression.
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ const TensorForcedEvalOp<const Derived> eval() const {
+ return TensorForcedEvalOp<const Derived>(derived());
+ }
+
+ // Returns a formatted tensor ready for printing to a stream
+ inline const TensorWithFormat<Derived,DerivedTraits::Layout,DerivedTraits::NumDimensions> format(const TensorIOFormat& fmt) const {
+ return TensorWithFormat<Derived,DerivedTraits::Layout,DerivedTraits::NumDimensions>(derived(), fmt);
+ }
+
+ #ifdef EIGEN_READONLY_TENSORBASE_PLUGIN
+ #include EIGEN_READONLY_TENSORBASE_PLUGIN
+ #endif
+
+ protected:
+ template <typename Scalar, int NumIndices, int Options, typename IndexType> friend class Tensor;
+ template <typename Scalar, typename Dimensions, int Option, typename IndexTypes> friend class TensorFixedSize;
+ // the Eigen:: prefix is required to workaround a compilation issue with nvcc 9.0
+ template <typename OtherDerived, int AccessLevel> friend class Eigen::TensorBase;
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE const Derived& derived() const { return *static_cast<const Derived*>(this); }
+};
+
+template<typename Derived, int AccessLevel = internal::accessors_level<Derived>::value>
+class TensorBase : public TensorBase<Derived, ReadOnlyAccessors> {
+ public:
+ typedef TensorBase<Derived, ReadOnlyAccessors> Base;
+ typedef internal::traits<Derived> DerivedTraits;
+ typedef typename DerivedTraits::Scalar Scalar;
+ typedef typename DerivedTraits::Index Index;
+ typedef Scalar CoeffReturnType;
+ static constexpr int NumDimensions = DerivedTraits::NumDimensions;
+
+ template <typename Scalar, int NumIndices, int Options, typename IndexType> friend class Tensor;
+ template <typename Scalar, typename Dimensions, int Option, typename IndexTypes> friend class TensorFixedSize;
+ // the Eigen:: prefix is required to workaround a compilation issue with nvcc 9.0
+ template <typename OtherDerived, int OtherAccessLevel> friend class Eigen::TensorBase;
+
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE Derived& setZero() {
+ return setConstant(Scalar(0));
+ }
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE Derived& setConstant(const Scalar& val) {
+ return derived() = this->constant(val);
+ }
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE Derived& setRandom() {
+ return derived() = this->random();
+ }
+ template <typename RandomGenerator> EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE Derived& setRandom() {
+ return derived() = this->template random<RandomGenerator>();
+ }
+
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE Derived& setValues(
+ const typename internal::Initializer<Derived, NumDimensions>::InitList& vals) {
+ TensorEvaluator<Derived, DefaultDevice> eval(derived(), DefaultDevice());
+ internal::initialize_tensor<Derived, NumDimensions>(eval, vals);
+ return derived();
+ }
+
+ template<typename OtherDerived> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ Derived& operator+=(const OtherDerived& other) {
+ return derived() = derived() + other.derived();
+ }
+ template<typename OtherDerived> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ Derived& operator-=(const OtherDerived& other) {
+ return derived() = derived() - other.derived();
+ }
+ template<typename OtherDerived> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ Derived& operator*=(const OtherDerived& other) {
+ return derived() = derived() * other.derived();
+ }
+ template<typename OtherDerived> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ Derived& operator/=(const OtherDerived& other) {
+ return derived() = derived() / other.derived();
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ const TensorLayoutSwapOp<const Derived>
+ swap_layout() const {
+ return TensorLayoutSwapOp<const Derived>(derived());
+ }
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ TensorLayoutSwapOp<Derived>
+ swap_layout() {
+ return TensorLayoutSwapOp<Derived>(derived());
+ }
+
+ template <typename Axis, typename OtherDerived> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ const TensorConcatenationOp<const Axis, const Derived, const OtherDerived>
+ concatenate(const OtherDerived& other, const Axis& axis) const {
+ return TensorConcatenationOp<const Axis, const Derived, const OtherDerived>(derived(), other, axis);
+ }
+ template <typename Axis, typename OtherDerived> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ TensorConcatenationOp<const Axis, Derived, OtherDerived>
+ concatenate(const OtherDerived& other, const Axis& axis) {
+ return TensorConcatenationOp<const Axis, Derived, OtherDerived>(derived(), other, axis);
+ }
+
+ template <typename NewDimensions> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ const TensorReshapingOp<const NewDimensions, const Derived>
+ reshape(const NewDimensions& newDimensions) const {
+ return TensorReshapingOp<const NewDimensions, const Derived>(derived(), newDimensions);
+ }
+ template <typename NewDimensions> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ TensorReshapingOp<const NewDimensions, Derived>
+ reshape(const NewDimensions& newDimensions) {
+ return TensorReshapingOp<const NewDimensions, Derived>(derived(), newDimensions);
+ }
+
+ template <typename StartIndices, typename Sizes> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ const TensorSlicingOp<const StartIndices, const Sizes, const Derived>
+ slice(const StartIndices& startIndices, const Sizes& sizes) const {
+ return TensorSlicingOp<const StartIndices, const Sizes, const Derived>(derived(), startIndices, sizes);
+ }
+ template <typename StartIndices, typename Sizes> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ TensorSlicingOp<const StartIndices, const Sizes, Derived>
+ slice(const StartIndices& startIndices, const Sizes& sizes) {
+ return TensorSlicingOp<const StartIndices, const Sizes, Derived>(derived(), startIndices, sizes);
+ }
+
+ template <typename StartIndices, typename StopIndices, typename Strides> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ const TensorStridingSlicingOp<const StartIndices, const StopIndices, const Strides, const Derived>
+ stridedSlice(const StartIndices& startIndices, const StopIndices& stopIndices, const Strides& strides) const {
+ return TensorStridingSlicingOp<const StartIndices, const StopIndices, const Strides,
+ const Derived>(derived(), startIndices, stopIndices, strides);
+ }
+ template <typename StartIndices, typename StopIndices, typename Strides> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ TensorStridingSlicingOp<const StartIndices, const StopIndices, const Strides, Derived>
+ stridedSlice(const StartIndices& startIndices, const StopIndices& stopIndices, const Strides& strides) {
+ return TensorStridingSlicingOp<const StartIndices, const StopIndices, const Strides,
+ Derived>(derived(), startIndices, stopIndices, strides);
+ }
+
+ template <DenseIndex DimId> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ const TensorChippingOp<DimId, const Derived>
+ chip(const Index offset) const {
+ return TensorChippingOp<DimId, const Derived>(derived(), offset, DimId);
+ }
+ template <Index DimId> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ TensorChippingOp<DimId, Derived>
+ chip(const Index offset) {
+ return TensorChippingOp<DimId, Derived>(derived(), offset, DimId);
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ const TensorChippingOp<Dynamic, const Derived>
+ chip(const Index offset, const Index dim) const {
+ return TensorChippingOp<Dynamic, const Derived>(derived(), offset, dim);
+ }
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ TensorChippingOp<Dynamic, Derived>
+ chip(const Index offset, const Index dim) {
+ return TensorChippingOp<Dynamic, Derived>(derived(), offset, dim);
+ }
+
+ template <typename ReverseDimensions> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ const TensorReverseOp<const ReverseDimensions, const Derived>
+ reverse(const ReverseDimensions& rev) const {
+ return TensorReverseOp<const ReverseDimensions, const Derived>(derived(), rev);
+ }
+ template <typename ReverseDimensions> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ TensorReverseOp<const ReverseDimensions, Derived>
+ reverse(const ReverseDimensions& rev) {
+ return TensorReverseOp<const ReverseDimensions, Derived>(derived(), rev);
+ }
+
+ template <typename Shuffle> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ const TensorShufflingOp<const Shuffle, const Derived>
+ shuffle(const Shuffle& shfl) const {
+ return TensorShufflingOp<const Shuffle, const Derived>(derived(), shfl);
+ }
+ template <typename Shuffle> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ TensorShufflingOp<const Shuffle, Derived>
+ shuffle(const Shuffle& shfl) {
+ return TensorShufflingOp<const Shuffle, Derived>(derived(), shfl);
+ }
+
+ template <typename Strides> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ const TensorStridingOp<const Strides, const Derived>
+ stride(const Strides& strides) const {
+ return TensorStridingOp<const Strides, const Derived>(derived(), strides);
+ }
+ template <typename Strides> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ TensorStridingOp<const Strides, Derived>
+ stride(const Strides& strides) {
+ return TensorStridingOp<const Strides, Derived>(derived(), strides);
+ }
+
+ // Select the device on which to evaluate the expression.
+ template <typename DeviceType>
+ TensorDevice<Derived, DeviceType> device(const DeviceType& dev) {
+ return TensorDevice<Derived, DeviceType>(dev, derived());
+ }
+
+ // Select the async device on which to evaluate the expression.
+ template <typename DeviceType, typename DoneCallback>
+ TensorAsyncDevice<Derived, DeviceType, DoneCallback> device(const DeviceType& dev, DoneCallback done) {
+ return TensorAsyncDevice<Derived, DeviceType, DoneCallback>(dev, derived(), std::move(done));
+ }
+
+ #ifdef EIGEN_TENSORBASE_PLUGIN
+ #include EIGEN_TENSORBASE_PLUGIN
+ #endif
+
+ protected:
+ EIGEN_DEFAULT_EMPTY_CONSTRUCTOR_AND_DESTRUCTOR(TensorBase)
+ EIGEN_DEFAULT_COPY_CONSTRUCTOR(TensorBase)
+
+ template<typename OtherDerived> EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE Derived& operator=(const OtherDerived& other)
+ {
+ typedef TensorAssignOp<Derived, const OtherDerived> Assign;
+ Assign assign(derived(), other.derived());
+ internal::TensorExecutor<const Assign, DefaultDevice>::run(assign, DefaultDevice());
+ return derived();
+ }
+
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE Derived& derived() { return *static_cast<Derived*>(this); }
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE const Derived& derived() const { return *static_cast<const Derived*>(this); }
+};
+#endif // EIGEN_PARSED_BY_DOXYGEN
+} // end namespace Eigen
+
+#endif // EIGEN_CXX11_TENSOR_TENSOR_BASE_H
diff --git a/unsupported/Eigen/CXX11/src/Tensor/TensorBlock.h b/unsupported/Eigen/CXX11/src/Tensor/TensorBlock.h
new file mode 100644
index 0000000..2e66340
--- /dev/null
+++ b/unsupported/Eigen/CXX11/src/Tensor/TensorBlock.h
@@ -0,0 +1,1561 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_CXX11_TENSOR_TENSOR_BLOCK_H
+#define EIGEN_CXX11_TENSOR_TENSOR_BLOCK_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+namespace internal {
+
+// -------------------------------------------------------------------------- //
+// Forward declarations for templates defined below.
+template <typename Scalar, typename IndexType, int NumDims, int Layout>
+class TensorBlockIO;
+
+// -------------------------------------------------------------------------- //
+// Helper function to compute strides for densely stored buffer of given
+// dimensions.
+
+// TODO(ezhulenev): We compute strides 1000 times in different evaluators, use
+// this function instead everywhere.
+template <int Layout, typename IndexType, int NumDims>
+EIGEN_ALWAYS_INLINE DSizes<IndexType, NumDims> strides(
+ const DSizes<IndexType, NumDims>& dimensions) {
+ DSizes<IndexType, NumDims> strides;
+ if (NumDims == 0) return strides;
+
+ // TODO(ezhulenev): Use templates to unroll this loop (similar to
+ // h_array_reduce in CXX11meta.h)? Benchmark it.
+ if (static_cast<int>(Layout) == static_cast<int>(ColMajor)) {
+ strides[0] = 1;
+ for (int i = 1; i < NumDims; ++i) {
+ strides[i] = strides[i - 1] * dimensions[i - 1];
+ }
+ } else {
+ strides[NumDims - 1] = 1;
+ for (int i = NumDims - 2; i >= 0; --i) {
+ strides[i] = strides[i + 1] * dimensions[i + 1];
+ }
+ }
+
+ return strides;
+}
+
+template <int Layout, typename IndexType, size_t NumDims>
+EIGEN_ALWAYS_INLINE DSizes<IndexType, NumDims> strides(
+ const Eigen::array<IndexType, NumDims>& dimensions) {
+ return strides<Layout>(DSizes<IndexType, NumDims>(dimensions));
+}
+
+template <int Layout, std::ptrdiff_t... Indices>
+EIGEN_STRONG_INLINE DSizes<std::ptrdiff_t, sizeof...(Indices)> strides(
+ const Sizes<Indices...>& sizes) {
+ return strides<Layout>(DSizes<std::ptrdiff_t, sizeof...(Indices)>(sizes));
+}
+
+// -------------------------------------------------------------------------- //
+
+// Tensor block shape type defines what are the shape preference for the blocks
+// extracted from the larger tensor.
+//
+// Example: blocks of 100 elements from the large 100x100 tensor:
+// - tensor: 100x100
+// - target_block_size: 100
+//
+// TensorBlockShapeType:
+// - kUniformAllDims: 100 blocks of size 10x10
+// - kSkewedInnerDims: 100 blocks of size 100x1 (or 1x100 depending on a column
+// or row major layout)
+enum class TensorBlockShapeType { kUniformAllDims, kSkewedInnerDims };
+
+struct TensorBlockResourceRequirements {
+ TensorBlockShapeType shape_type; // target block shape
+ size_t size; // target block size
+ TensorOpCost cost_per_coeff; // cost of computing a single block element
+
+#ifdef EIGEN_HIPCC
+ // For HIPCC, we need to explicitly declare as a "device fun", the constructor
+ // which is implicitly invoked in the "merge" / "any" routines. else HIPCC
+ // errors out complaining about the lack of a matching constructor
+ EIGEN_DEVICE_FUNC
+ TensorBlockResourceRequirements(TensorBlockShapeType shape_type_, size_t size_,
+ TensorOpCost cost_)
+ : shape_type(shape_type_), size(size_), cost_per_coeff(cost_)
+ {}
+#endif
+
+ template <typename Scalar>
+ EIGEN_DEVICE_FUNC static TensorBlockResourceRequirements withShapeAndSize(
+ TensorBlockShapeType shape_type, size_t size_in_bytes,
+ TensorOpCost cost) {
+ const size_t size = numext::maxi(size_t(1), size_in_bytes / sizeof(Scalar));
+ return {shape_type, size, cost};
+ }
+
+ template <typename Scalar>
+ EIGEN_DEVICE_FUNC static TensorBlockResourceRequirements withShapeAndSize(
+ TensorBlockShapeType shape_type, size_t size_in_bytes) {
+ // This default cost per coefficient is valid for most materialized tensor
+ // block evaluation implementations, because they typically just read
+ // coefficients from the underlying tensor storage, and write to the tensor
+ // block buffer (scratch or destination memory, reads and writes have linear
+ // access pattern). We ignore the fixed cost of block evaluation, because in
+ // practice it should negligible.
+ //
+ // Lazy block evaluation adds the cost of calling a functor for each
+ // coefficient.
+ //
+ // All non-trivial block evaluation implementations must provide their own
+ // cost approximation (e.g. shuffling inner dimension has a much higher cost
+ // because it reads memory randomly, although the total number of moved
+ // bytes is the same).
+ return withShapeAndSize<Scalar>(shape_type, size_in_bytes,
+ {/*bytes_loaded=*/sizeof(Scalar),
+ /*bytes_stored=*/sizeof(Scalar),
+ /*compute_cycles=*/0});
+ }
+
+ template <typename Scalar>
+ EIGEN_DEVICE_FUNC static TensorBlockResourceRequirements skewed(
+ size_t size_in_bytes) {
+ return withShapeAndSize<Scalar>(TensorBlockShapeType::kSkewedInnerDims,
+ size_in_bytes);
+ }
+
+ template <typename Scalar>
+ EIGEN_DEVICE_FUNC static TensorBlockResourceRequirements uniform(
+ size_t size_in_bytes) {
+ return withShapeAndSize<Scalar>(TensorBlockShapeType::kUniformAllDims,
+ size_in_bytes);
+ }
+
+ EIGEN_DEVICE_FUNC
+ static EIGEN_STRONG_INLINE TensorBlockResourceRequirements
+ merge(const TensorBlockResourceRequirements& lhs,
+ const TensorBlockResourceRequirements& rhs) {
+ return {merge(lhs.shape_type, rhs.shape_type), // shape_type
+ merge(lhs.size, rhs.size), // size
+ merge(lhs.cost_per_coeff, rhs.cost_per_coeff)}; // cost_per_coeff
+ }
+
+ EIGEN_DEVICE_FUNC TensorBlockResourceRequirements& addCostPerCoeff(
+ TensorOpCost cost) {
+ cost_per_coeff += cost;
+ return *this;
+ }
+
+ // This is a resource requirement that should be returned from expressions
+ // that do not have any block evaluation preference (e.g. default tensor
+ // expression with raw buffer access).
+ EIGEN_DEVICE_FUNC
+ static EIGEN_STRONG_INLINE TensorBlockResourceRequirements any() {
+ return {TensorBlockShapeType::kUniformAllDims, 1, {0, 0, 0}};
+ }
+
+ private:
+ using Requirements = TensorBlockResourceRequirements;
+
+ EIGEN_DEVICE_FUNC
+ static EIGEN_STRONG_INLINE size_t merge(size_t lhs_size, size_t rhs_size) {
+ return numext::maxi(lhs_size, rhs_size);
+ }
+
+ EIGEN_DEVICE_FUNC
+ static EIGEN_STRONG_INLINE TensorBlockShapeType
+ merge(TensorBlockShapeType lhs, TensorBlockShapeType rhs) {
+ return (lhs == TensorBlockShapeType::kSkewedInnerDims ||
+ rhs == TensorBlockShapeType::kSkewedInnerDims)
+ ? TensorBlockShapeType::kSkewedInnerDims
+ : TensorBlockShapeType::kUniformAllDims;
+ }
+
+ EIGEN_DEVICE_FUNC
+ static EIGEN_STRONG_INLINE TensorOpCost merge(TensorOpCost lhs_cost,
+ TensorOpCost rhs_cost) {
+ return lhs_cost + rhs_cost;
+ }
+};
+
+// -------------------------------------------------------------------------- //
+// TensorBlockDescriptor specifies a block offset within a tensor and the block
+// sizes along each of the tensor dimensions.
+
+template <int NumDims, typename IndexType = Eigen::Index>
+class TensorBlockDescriptor {
+ public:
+ typedef DSizes<IndexType, NumDims> Dimensions;
+
+ // If we evaluate a Tensor assignment, and expression on the left, already has
+ // a memory buffer, then we might do performance optimization, and evaluate
+ // the root expression directly into the final output memory. Some time it's
+ // possible to reuse it for materializing subexpressions inside an expression
+ // tree, to to avoid dynamic memory allocation.
+ //
+ // The pointer type of the underlying storage is erased, because passing
+ // Scalar type through all the expression evaluation layers is way too many
+ // templates. In practice destination buffer type should always match the
+ // evaluated expression scalar type.
+ class DestinationBuffer {
+ public:
+ enum DestinationBufferKind : int {
+ // The above explicit specification of "int" as the enum basetype is
+ // needed to get around a HIPCC link error ("the field type is not
+ // amp-compatible")
+ // which is issued for class members with the enum type.
+ // TODO(rocm):
+ // remove the "int" basetype once HIPCC has been fixed to not error out
+ // in the above scenario.
+
+ // Destination buffer is not defined (`m_data` == nullptr).
+ kEmpty,
+
+ // Tensor block defined by an owning tensor block descriptor can fit
+ // contiguously into the destination buffer. In this case it's safe to
+ // materialize tensor block in the destination buffer, wrap it in a
+ // TensorMap, and use to build Eigen expression on top of it.
+ kContiguous,
+
+ // Destination buffer strides do not match strides of the contiguously
+ // stored block, and it's impossible to define a TensorMap over this
+ // buffer. However if we are evaluating a root of an expression tree, we
+ // still can materialize an output into this destination, because we can
+ // guarantee that no one will ever access it through block API.
+ //
+ // In theory it is possible to build valid TensorStriding<TensorMap>
+ // expression on top of this destination buffer, however it has
+ // inefficient coeff/packet access, and defeats the purpose of fast block
+ // evaluation API.
+ kStrided
+ };
+
+ template <typename Scalar>
+ Scalar* data() const {
+ eigen_assert(m_data_type_size == sizeof(Scalar));
+ return static_cast<Scalar*>(m_data);
+ }
+
+ const Dimensions& strides() const { return m_strides; }
+ const DestinationBufferKind& kind() const { return m_kind; }
+
+ private:
+ friend class TensorBlockDescriptor<NumDims, IndexType>;
+
+ DestinationBuffer() : m_data(NULL), m_data_type_size(0), m_kind(kEmpty) {}
+
+ template <typename Scalar>
+ DestinationBuffer(Scalar* data, const Dimensions& strides,
+ DestinationBufferKind kind)
+ : m_data(static_cast<void*>(data)),
+ m_data_type_size(sizeof(Scalar)),
+ m_strides(strides),
+ m_kind(kind) {}
+
+ template <int Layout, typename Scalar>
+ static DestinationBuffer make(const TensorBlockDescriptor& desc,
+ Scalar* data, const Dimensions& strides) {
+ return DestinationBuffer(data, strides, kind<Layout>(desc, strides));
+ }
+
+ template <int Layout>
+ static DestinationBufferKind kind(const TensorBlockDescriptor& desc,
+ const Dimensions& strides) {
+ const Dimensions& desc_dims = desc.dimensions();
+ const Dimensions& desc_strides = internal::strides<Layout>(desc_dims);
+ for (int i = 0; i < NumDims; ++i) {
+ if (desc_dims[i] == 1) continue;
+ if (desc_strides[i] != strides[i]) return kStrided;
+ }
+ return kContiguous;
+ }
+
+ // Storage pointer is type erased, to reduce template bloat, but we still
+ // keep the size of the underlying element type for error checking.
+ void* m_data;
+ size_t m_data_type_size;
+
+ // Destination buffer dimensions always match the dimensions of a tensor
+ // block descriptor it belongs to, however strides might be different.
+ Dimensions m_strides;
+
+ DestinationBufferKind m_kind;
+ };
+
+ TensorBlockDescriptor(const IndexType offset, const Dimensions& dimensions,
+ const DestinationBuffer& destination)
+ : m_offset(offset),
+ m_dimensions(dimensions),
+ m_destination(destination) {}
+
+ TensorBlockDescriptor(const IndexType offset, const Dimensions& dimensions)
+ : m_offset(offset),
+ m_dimensions(dimensions),
+ m_destination(DestinationBuffer()) {}
+
+ IndexType offset() const { return m_offset; }
+ const Dimensions& dimensions() const { return m_dimensions; }
+ IndexType dimension(int index) const { return m_dimensions[index]; }
+ IndexType size() const { return array_prod<IndexType>(m_dimensions); }
+
+ const DestinationBuffer& destination() const { return m_destination; }
+
+ template <int Layout, typename Scalar>
+ void AddDestinationBuffer(Scalar* dst_base, const Dimensions& dst_strides) {
+ eigen_assert(dst_base != NULL);
+ m_destination =
+ DestinationBuffer::template make<Layout>(*this, dst_base, dst_strides);
+ }
+
+ template <int Layout, typename Scalar, typename DstStridesIndexType>
+ void AddDestinationBuffer(
+ Scalar* dst_base,
+ const DSizes<DstStridesIndexType, NumDims>& dst_strides) {
+ // DSizes constructor will do index type promotion if it's safe.
+ AddDestinationBuffer<Layout>(dst_base, Dimensions(dst_strides));
+ }
+
+ TensorBlockDescriptor& DropDestinationBuffer() {
+ m_destination.m_data = NULL;
+ m_destination.m_kind = DestinationBuffer::kEmpty;
+ return *this;
+ }
+
+ bool HasDestinationBuffer() const {
+ return m_destination.kind() != DestinationBuffer::kEmpty;
+ }
+
+ // Returns a copy of `*this` with updated offset.
+ TensorBlockDescriptor WithOffset(IndexType offset) const {
+ return TensorBlockDescriptor(offset, m_dimensions, m_destination);
+ }
+
+ private:
+ // Offset and dimensions are immutable after construction. Block descriptor
+ // can only be mutated by adding or dropping destination.
+ const IndexType m_offset;
+ const Dimensions m_dimensions;
+ DestinationBuffer m_destination;
+};
+
+// -------------------------------------------------------------------------- //
+// TensorBlockMapper is responsible for iterating over the blocks of a tensor.
+
+template <int NumDims, int Layout, typename IndexType = Eigen::Index>
+class TensorBlockMapper {
+ typedef TensorBlockDescriptor<NumDims, IndexType> BlockDescriptor;
+
+ public:
+ typedef DSizes<IndexType, NumDims> Dimensions;
+
+ TensorBlockMapper() = default;
+ TensorBlockMapper(const DSizes<IndexType, NumDims>& dimensions,
+ const TensorBlockResourceRequirements& requirements)
+ : m_tensor_dimensions(dimensions), m_requirements(requirements) {
+ // Compute block dimensions and the total number of blocks.
+ InitializeBlockDimensions();
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE IndexType blockCount() const {
+ return m_total_block_count;
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE IndexType blockTotalSize() const {
+ return m_block_dimensions.TotalSize();
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const DSizes<IndexType, NumDims>&
+ blockDimensions() const {
+ return m_block_dimensions;
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE BlockDescriptor
+ blockDescriptor(IndexType block_index) const {
+ static const bool isColMajor = Layout == static_cast<int>(ColMajor);
+
+ IndexType offset = 0;
+ DSizes<IndexType, NumDims> dimensions;
+
+ if (NumDims == 0) return BlockDescriptor(offset, dimensions);
+
+ // Iterate outer -> inner dimensions.
+ for (int i = NumDims - 1; i >= 0; --i) {
+ const int dim = isColMajor ? i : NumDims - i - 1;
+
+ const IndexType idx = block_index / m_block_strides[dim];
+ block_index -= idx * m_block_strides[dim];
+
+ const IndexType coord = idx * m_block_dimensions[dim];
+ dimensions[dim] = numext::mini(m_tensor_dimensions[dim] - coord,
+ m_block_dimensions[dim]);
+ offset += coord * m_tensor_strides[dim];
+ }
+
+ return {offset, dimensions};
+ }
+
+ private:
+ void InitializeBlockDimensions() {
+ // Requested block shape and size.
+ const TensorBlockShapeType shape_type = m_requirements.shape_type;
+ IndexType target_block_size =
+ numext::maxi<IndexType>(1, static_cast<IndexType>(m_requirements.size));
+
+ IndexType tensor_size = m_tensor_dimensions.TotalSize();
+
+ // Corner case: one of the dimensions is zero. Logic below is too complex
+ // to handle this case on a general basis, just use unit block size.
+ // Note: we must not yield blocks with zero dimensions (recipe for
+ // overflows/underflows, divisions by zero and NaNs later).
+ if (tensor_size == 0) {
+ for (int i = 0; i < NumDims; ++i) {
+ m_block_dimensions[i] = 1;
+ }
+ m_total_block_count = 0;
+ return;
+ }
+
+ // If tensor fits into a target block size, evaluate it as a single block.
+ if (tensor_size <= target_block_size) {
+ m_block_dimensions = m_tensor_dimensions;
+ m_total_block_count = 1;
+ // The only valid block index is `0`, and in this case we do not need
+ // to compute real strides for tensor or blocks (see blockDescriptor).
+ for (int i = 0; i < NumDims; ++i) {
+ m_tensor_strides[i] = 0;
+ m_block_strides[i] = 1;
+ }
+ return;
+ }
+
+ static const bool isColMajor = Layout == static_cast<int>(ColMajor);
+
+ // Block shape skewed towards inner dimension.
+ if (shape_type == TensorBlockShapeType::kSkewedInnerDims) {
+ IndexType coeff_to_allocate = target_block_size;
+
+ for (int i = 0; i < NumDims; ++i) {
+ const int dim = isColMajor ? i : NumDims - i - 1;
+ m_block_dimensions[dim] =
+ numext::mini(coeff_to_allocate, m_tensor_dimensions[dim]);
+ coeff_to_allocate = divup(
+ coeff_to_allocate,
+ numext::maxi(static_cast<IndexType>(1), m_block_dimensions[dim]));
+ }
+ eigen_assert(coeff_to_allocate == 1);
+
+ } else if (shape_type == TensorBlockShapeType::kUniformAllDims) {
+ // Tensor will not fit within 'target_block_size' budget: calculate tensor
+ // block dimension sizes based on "square" dimension size target.
+ const IndexType dim_size_target = convert_index<IndexType>(
+ std::pow(static_cast<float>(target_block_size),
+ 1.0f / static_cast<float>(m_block_dimensions.rank())));
+
+ for (int i = 0; i < NumDims; ++i) {
+ // TODO(andydavis) Adjust the inner most 'block_dim_size' to make it
+ // a multiple of the packet size. Note that reducing
+ // 'block_dim_size' in this manner can increase the number of
+ // blocks, and so will amplify any per-block overhead.
+ m_block_dimensions[i] =
+ numext::mini(dim_size_target, m_tensor_dimensions[i]);
+ }
+
+ // Add any un-allocated coefficients to inner dimension(s).
+ IndexType total_size = m_block_dimensions.TotalSize();
+ for (int i = 0; i < NumDims; ++i) {
+ const int dim = isColMajor ? i : NumDims - i - 1;
+
+ if (m_block_dimensions[dim] < m_tensor_dimensions[dim]) {
+ const IndexType total_size_other_dims =
+ total_size / m_block_dimensions[dim];
+ const IndexType alloc_avail =
+ divup<IndexType>(target_block_size, total_size_other_dims);
+ if (alloc_avail == m_block_dimensions[dim]) {
+ // Insufficient excess coefficients to allocate.
+ break;
+ }
+ m_block_dimensions[dim] =
+ numext::mini(m_tensor_dimensions[dim], alloc_avail);
+ total_size = total_size_other_dims * m_block_dimensions[dim];
+ }
+ }
+
+ } else {
+ eigen_assert(false); // unknown block shape
+ }
+
+ eigen_assert(m_block_dimensions.TotalSize() >=
+ numext::mini<IndexType>(target_block_size,
+ m_tensor_dimensions.TotalSize()));
+
+ // Calculate block counts by dimension and total block count.
+ DSizes<IndexType, NumDims> block_count;
+ for (int i = 0; i < NumDims; ++i) {
+ block_count[i] = divup(m_tensor_dimensions[i], m_block_dimensions[i]);
+ }
+ m_total_block_count = array_prod(block_count);
+
+ // Calculate block strides (used for enumerating blocks).
+ m_tensor_strides = strides<Layout>(m_tensor_dimensions);
+ m_block_strides = strides<Layout>(block_count);
+ }
+
+ DSizes<IndexType, NumDims> m_tensor_dimensions;
+ TensorBlockResourceRequirements m_requirements;
+
+ DSizes<IndexType, NumDims> m_block_dimensions;
+ IndexType m_total_block_count;
+
+ DSizes<IndexType, NumDims> m_tensor_strides;
+ DSizes<IndexType, NumDims> m_block_strides;
+};
+
+// -------------------------------------------------------------------------- //
+// TensorBlockScratchAllocator is responsible for allocating temporary buffers
+// for block evaluation (output or input block materialization). Given that
+// Eigen expression traversal order is deterministic, all temporary allocations
+// are happening in the same order, and usually have exactly the same size.
+// Scratch allocator keeps a trace of all dynamic allocations, and after the
+// first block evaluation is completed, we should be able to reuse all the
+// temporary buffers for the next block evaluation.
+
+template <typename Device>
+class TensorBlockScratchAllocator {
+ public:
+ explicit TensorBlockScratchAllocator(const Device& device)
+ : m_device(device), m_allocation_index(0) {}
+
+ ~TensorBlockScratchAllocator() {
+ for (size_t i = 0; i < m_allocations.size(); ++i) {
+ m_device.deallocate(m_allocations[i].ptr);
+ }
+ }
+
+ void* allocate(size_t size) {
+ // TODO(ezhulenev): Remove when replaced with inlined vector.
+ if (m_allocations.capacity() == 0) m_allocations.reserve(8);
+
+ // Check if we already have an existing allocation att current index.
+ const int num_allocations = static_cast<int>(m_allocations.size());
+ const bool has_allocation = m_allocation_index < num_allocations;
+
+ // Allocation index can't be larger than the number of allocations.
+ eigen_assert(m_allocation_index <= num_allocations);
+
+ // If we have existing allocation, and its size is larger or equal to
+ // requested size, we do nothing.
+
+ // If current allocation can't fit requested size, we deallocate it, and
+ // replace with a larger allocation.
+ if (has_allocation && m_allocations[m_allocation_index].size < size) {
+ m_device.deallocate(m_allocations[m_allocation_index].ptr);
+ m_allocations[m_allocation_index].ptr = m_device.allocate(size);
+ m_allocations[m_allocation_index].size = size;
+ }
+
+ // Make a new allocation if we don't have and existing one.
+ if (!has_allocation) {
+ Allocation allocation;
+ allocation.ptr = m_device.allocate(size);
+ allocation.size = size;
+ m_allocations.push_back(allocation);
+ }
+
+ eigen_assert(m_allocations[m_allocation_index].ptr != NULL);
+ eigen_assert(m_allocations[m_allocation_index].size >= size);
+
+ return m_allocations[m_allocation_index++].ptr;
+ }
+
+ void reset() { m_allocation_index = 0; }
+
+ private:
+ struct Allocation {
+ void* ptr;
+ size_t size;
+ };
+
+ const Device& m_device;
+ int m_allocation_index;
+ // TODO(ezhulenev): This should be an inlined vector.
+ std::vector<Allocation> m_allocations;
+};
+
+// -------------------------------------------------------------------------- //
+// TensorBlockKind represents all possible block kinds, that can be produced by
+// TensorEvaluator::evalBlock function.
+enum TensorBlockKind {
+ // Tensor block that is a lazy expression that must be assigned to a
+ // destination using TensorBlockAssign.
+ kExpr,
+
+ // Tensor block that is a view into a memory buffer owned by an underlying
+ // Tensor expression (e.g. it can be a view into a Tensor buffer).
+ kView,
+
+ // Tensor block that was materialized in a scratch memory buffer, allocated
+ // with TensorBlockScratchAllocator. This block must be copied to a
+ // destination, similar to a block of `kExpr` type.
+ kMaterializedInScratch,
+
+ // Tensor block that was materialized directly into the final output memory
+ // buffer. For example if the left side of an assignment is a Tensor, we can
+ // directly materialize the block in the destination memory.
+ //
+ // If strides in the output buffer do not match tensor block strides, the
+ // Tensor expression will be invalid, and should not be used by
+ // TensorBlockAssign or for constructing another block expression.
+ kMaterializedInOutput
+};
+
+// -------------------------------------------------------------------------- //
+// TensorBlockNotImplemented should be used to defined TensorBlock typedef in
+// TensorEvaluators that do not support block evaluation.
+
+class TensorBlockNotImplemented {
+ public:
+ typedef void XprType;
+};
+
+// -------------------------------------------------------------------------- //
+// XprScalar extracts Scalar type from the Eigen expressions (if expression type
+// is not void). It's required to be able to define lazy block expression for
+// argument types, that do not support block evaluation.
+
+template <typename XprType>
+struct XprScalar {
+ typedef typename XprType::Scalar type;
+};
+template <>
+struct XprScalar<void> {
+ typedef void type;
+};
+
+// -------------------------------------------------------------------------- //
+// TensorMaterializedBlock is a fully evaluated block of the original tensor,
+// and XprType is just a TensorMap over the data. This block type is typically
+// used to materialize blocks of tensor expressions, that can't be efficiently
+// represented as lazy Tensor expressions with fast coeff/packet operations,
+// e.g. we materialize all broadcasts into evaluated blocks.
+//
+// TensorMaterializedBlock does not own its memory buffer, it's either a memory
+// buffer that backs the original expression (e.g. block is just a view into a
+// Tensor), or a memory buffer allocated with scratch allocator, and in this
+// case the scratch allocator will deallocate it at the end of block based
+// expression execution.
+//
+// If the block was evaluated directly into the output buffer, and strides in
+// the output buffer do not match block strides, the TensorMap expression will
+// be invalid, and should never be used in block assignment or any other tensor
+// expression.
+
+template <typename Scalar, int NumDims, int Layout,
+ typename IndexType = Eigen::Index>
+class TensorMaterializedBlock {
+ public:
+ typedef DSizes<IndexType, NumDims> Dimensions;
+ typedef TensorMap<const Tensor<Scalar, NumDims, Layout> > XprType;
+
+ TensorMaterializedBlock(TensorBlockKind kind, const Scalar* data,
+ const Dimensions& dimensions, bool valid_expr = true)
+ : m_kind(kind),
+ m_data(data),
+ m_dimensions(dimensions),
+ m_expr(m_data, m_dimensions),
+ m_valid_expr(valid_expr) {
+ eigen_assert(m_kind == internal::TensorBlockKind::kView ||
+ m_kind == internal::TensorBlockKind::kMaterializedInScratch ||
+ m_kind == internal::TensorBlockKind::kMaterializedInOutput);
+ }
+
+ TensorBlockKind kind() const { return m_kind; }
+ // NOTE(ezhulenev): Returning XprType by value like in other block types
+ // causes asan failures. The theory is that XprType::Nested doesn't work
+ // properly for TensorMap.
+ const XprType& expr() const {
+ eigen_assert(m_valid_expr);
+ return m_expr;
+ }
+ const Scalar* data() const { return m_data; }
+ void cleanup() {}
+
+ typedef internal::TensorBlockDescriptor<NumDims, IndexType> TensorBlockDesc;
+
+ // TensorMaterializedBlock can be backed by different types of storage:
+ //
+ // (1) Contiguous block of memory allocated with scratch allocator.
+ // (2) Contiguous block of memory reused from tensor block descriptor
+ // destination buffer.
+ // (3) Strided block of memory reused from tensor block descriptor
+ // destination buffer.
+ //
+ class Storage {
+ public:
+ Scalar* data() const { return m_data; }
+ const Dimensions& dimensions() const { return m_dimensions; }
+ const Dimensions& strides() const { return m_strides; }
+
+ TensorMaterializedBlock AsTensorMaterializedBlock() const {
+ return TensorMaterializedBlock(
+ m_materialized_in_output
+ ? internal::TensorBlockKind::kMaterializedInOutput
+ : internal::TensorBlockKind::kMaterializedInScratch,
+ m_data, m_dimensions, !m_strided_storage);
+ }
+
+ private:
+ friend class TensorMaterializedBlock<Scalar, NumDims, Layout, IndexType>;
+
+ Storage(Scalar* data, const Dimensions& dimensions,
+ const Dimensions& strides, bool materialized_in_output,
+ bool strided_storage)
+ : m_data(data),
+ m_dimensions(dimensions),
+ m_strides(strides),
+ m_materialized_in_output(materialized_in_output),
+ m_strided_storage(strided_storage) {}
+
+ Scalar* m_data;
+ Dimensions m_dimensions;
+ Dimensions m_strides;
+ bool m_materialized_in_output;
+ bool m_strided_storage;
+ };
+
+ // Creates a storage for materialized block either from the block descriptor
+ // destination buffer, or allocates a new buffer with scratch allocator.
+ template <typename TensorBlockScratch>
+ EIGEN_STRONG_INLINE static Storage prepareStorage(
+ TensorBlockDesc& desc, TensorBlockScratch& scratch,
+ bool allow_strided_storage = false) {
+ // Try to reuse destination as an output block buffer.
+ typedef typename TensorBlockDesc::DestinationBuffer DestinationBuffer;
+
+ if (desc.destination().kind() == DestinationBuffer::kContiguous) {
+ Scalar* buffer = desc.destination().template data<Scalar>();
+ desc.DropDestinationBuffer();
+ return Storage(buffer, desc.dimensions(),
+ internal::strides<Layout>(desc.dimensions()),
+ /*materialized_in_output=*/true,
+ /*strided_storage=*/false);
+
+ } else if (desc.destination().kind() == DestinationBuffer::kStrided &&
+ allow_strided_storage) {
+ Scalar* buffer = desc.destination().template data<Scalar>();
+ desc.DropDestinationBuffer();
+ return Storage(buffer, desc.dimensions(), desc.destination().strides(),
+ /*materialized_in_output=*/true, /*strided_storage=*/true);
+
+ } else {
+ void* mem = scratch.allocate(desc.size() * sizeof(Scalar));
+ return Storage(static_cast<Scalar*>(mem), desc.dimensions(),
+ internal::strides<Layout>(desc.dimensions()),
+ /*materialized_in_output=*/false,
+ /*strided_storage=*/false);
+ }
+ }
+
+ // Creates a materialized block for the given descriptor from a memory buffer.
+ template <typename DataDimensions, typename TensorBlockScratch>
+ EIGEN_STRONG_INLINE static TensorMaterializedBlock materialize(
+ const Scalar* data, const DataDimensions& data_dims,
+ TensorBlockDesc& desc, TensorBlockScratch& scratch) {
+ eigen_assert(array_size<DataDimensions>::value == desc.dimensions().size());
+
+ // If a tensor block dimensions covers a contiguous block of the underlying
+ // memory, we can skip block buffer memory allocation, and construct a block
+ // from existing `data` memory buffer.
+ //
+ // Example: (RowMajor layout)
+ // data_dims: [11, 12, 13, 14]
+ // desc.dimensions(): [1, 1, 3, 14]
+ //
+ // In this case we can construct a TensorBlock starting at
+ // `data + desc.offset()`, with a `desc.dimensions()` block sizes.
+ static const bool is_col_major = Layout == ColMajor;
+
+ // Find out how many inner dimensions have a matching size.
+ int num_matching_inner_dims = 0;
+ for (int i = 0; i < NumDims; ++i) {
+ int dim = is_col_major ? i : NumDims - i - 1;
+ if (data_dims[dim] != desc.dimensions()[dim]) break;
+ ++num_matching_inner_dims;
+ }
+
+ // All the outer dimensions must be of size `1`, except a single dimension
+ // before the matching inner dimension (`3` in the example above).
+ bool can_use_direct_access = true;
+ for (int i = num_matching_inner_dims + 1; i < NumDims; ++i) {
+ int dim = is_col_major ? i : NumDims - i - 1;
+ if (desc.dimension(dim) != 1) {
+ can_use_direct_access = false;
+ break;
+ }
+ }
+
+ if (can_use_direct_access) {
+ const Scalar* block_start = data + desc.offset();
+ return TensorMaterializedBlock(internal::TensorBlockKind::kView,
+ block_start, desc.dimensions());
+
+ } else {
+ // Reuse destination buffer or allocate new buffer with scratch allocator.
+ const Storage storage = prepareStorage(desc, scratch);
+
+ typedef internal::TensorBlockIO<Scalar, IndexType, NumDims, Layout>
+ TensorBlockIO;
+ typedef typename TensorBlockIO::Dst TensorBlockIODst;
+ typedef typename TensorBlockIO::Src TensorBlockIOSrc;
+
+ TensorBlockIOSrc src(internal::strides<Layout>(Dimensions(data_dims)),
+ data, desc.offset());
+ TensorBlockIODst dst(storage.dimensions(), storage.strides(),
+ storage.data());
+
+ TensorBlockIO::Copy(dst, src);
+ return storage.AsTensorMaterializedBlock();
+ }
+ }
+
+ private:
+ TensorBlockKind m_kind;
+ const Scalar* m_data;
+ Dimensions m_dimensions;
+ XprType m_expr;
+ bool m_valid_expr;
+};
+
+// -------------------------------------------------------------------------- //
+// TensorCwiseUnaryBlock is a lazy tensor expression block that applies UnaryOp
+// functor to the blocks produced by the underlying Tensor expression.
+
+template <typename UnaryOp, typename ArgTensorBlock>
+class TensorCwiseUnaryBlock {
+ static constexpr bool NoArgBlockAccess =
+ internal::is_void<typename ArgTensorBlock::XprType>::value;
+
+ public:
+ typedef std::conditional_t<
+ NoArgBlockAccess, void,
+ TensorCwiseUnaryOp<UnaryOp, const typename ArgTensorBlock::XprType> >
+ XprType;
+
+ typedef typename XprScalar<XprType>::type Scalar;
+
+ TensorCwiseUnaryBlock(const ArgTensorBlock& arg_block, const UnaryOp& functor)
+ : m_arg_block(arg_block), m_functor(functor) {}
+
+ TensorBlockKind kind() const { return internal::TensorBlockKind::kExpr; }
+
+ XprType expr() const { return XprType(m_arg_block.expr(), m_functor); }
+ const Scalar* data() const { return NULL; }
+ void cleanup() { m_arg_block.cleanup(); }
+
+ private:
+ ArgTensorBlock m_arg_block;
+ UnaryOp m_functor;
+};
+
+// -------------------------------------------------------------------------- //
+// TensorCwiseUnaryBlock is a lazy tensor expression block that applies BinaryOp
+// functor to the blocks produced by the underlying Tensor expression.
+
+template <typename BinaryOp, typename LhsTensorBlock, typename RhsTensorBlock>
+class TensorCwiseBinaryBlock {
+ static constexpr bool NoArgBlockAccess =
+ internal::is_void<typename LhsTensorBlock::XprType>::value ||
+ internal::is_void<typename RhsTensorBlock::XprType>::value;
+
+ public:
+ typedef std::conditional_t<
+ NoArgBlockAccess, void,
+ TensorCwiseBinaryOp<BinaryOp, const typename LhsTensorBlock::XprType,
+ const typename RhsTensorBlock::XprType> >
+ XprType;
+
+ typedef typename XprScalar<XprType>::type Scalar;
+
+ TensorCwiseBinaryBlock(const LhsTensorBlock& left_block,
+ const RhsTensorBlock& right_block,
+ const BinaryOp& functor)
+ : m_left_block(left_block),
+ m_right_block(right_block),
+ m_functor(functor) {}
+
+ TensorBlockKind kind() const { return internal::TensorBlockKind::kExpr; }
+
+ XprType expr() const {
+ return XprType(m_left_block.expr(), m_right_block.expr(), m_functor);
+ }
+
+ const Scalar* data() const { return NULL; }
+
+ void cleanup() {
+ m_left_block.cleanup();
+ m_right_block.cleanup();
+ }
+
+ private:
+ LhsTensorBlock m_left_block;
+ RhsTensorBlock m_right_block;
+ BinaryOp m_functor;
+};
+
+// -------------------------------------------------------------------------- //
+// TensorUnaryExprBlock is a lazy tensor expression block that can construct
+// an arbitrary tensor expression from a block of the underlying type (this is a
+// generalization of the TensorCwiseUnaryBlock for arbitrary expressions).
+
+template <typename BlockFactory, typename ArgTensorBlock>
+class TensorUnaryExprBlock {
+ typedef typename ArgTensorBlock::XprType ArgXprType;
+ static constexpr bool NoArgBlockAccess = internal::is_void<ArgXprType>::value;
+
+ public:
+ typedef std::conditional_t<
+ NoArgBlockAccess, void,
+ typename BlockFactory::template XprType<ArgXprType>::type> XprType;
+
+ typedef typename XprScalar<XprType>::type Scalar;
+
+ TensorUnaryExprBlock(const ArgTensorBlock& arg_block,
+ const BlockFactory& factory)
+ : m_arg_block(arg_block), m_factory(factory) {}
+
+ TensorBlockKind kind() const { return internal::TensorBlockKind::kExpr; }
+ XprType expr() const { return m_factory.expr(m_arg_block.expr()); }
+ const Scalar* data() const { return NULL; }
+ void cleanup() { m_arg_block.cleanup(); }
+
+ private:
+ ArgTensorBlock m_arg_block;
+ BlockFactory m_factory;
+};
+
+// -------------------------------------------------------------------------- //
+// TensorTernaryExprBlock is a lazy tensor expression block that can construct
+// an arbitrary tensor expression from three blocks of the underlying type.
+
+template <typename BlockFactory, typename Arg1TensorBlock,
+ typename Arg2TensorBlock, typename Arg3TensorBlock>
+class TensorTernaryExprBlock {
+ typedef typename Arg1TensorBlock::XprType Arg1XprType;
+ typedef typename Arg2TensorBlock::XprType Arg2XprType;
+ typedef typename Arg3TensorBlock::XprType Arg3XprType;
+
+ static constexpr bool NoArgBlockAccess = internal::is_void<Arg1XprType>::value ||
+ internal::is_void<Arg2XprType>::value ||
+ internal::is_void<Arg3XprType>::value;
+
+ public:
+ typedef std::conditional_t<
+ NoArgBlockAccess, void,
+ typename BlockFactory::template XprType<Arg1XprType, Arg2XprType,
+ Arg3XprType>::type> XprType;
+
+ typedef typename XprScalar<XprType>::type Scalar;
+
+ TensorTernaryExprBlock(const Arg1TensorBlock& arg1_block,
+ const Arg2TensorBlock& arg2_block,
+ const Arg3TensorBlock& arg3_block,
+ const BlockFactory& factory)
+ : m_arg1_block(arg1_block),
+ m_arg2_block(arg2_block),
+ m_arg3_block(arg3_block),
+ m_factory(factory) {}
+
+ TensorBlockKind kind() const { return internal::TensorBlockKind::kExpr; }
+ XprType expr() const {
+ return m_factory.expr(m_arg1_block.expr(), m_arg2_block.expr(),
+ m_arg3_block.expr());
+ }
+ const Scalar* data() const { return NULL; }
+ void cleanup() {
+ m_arg1_block.cleanup();
+ m_arg2_block.cleanup();
+ m_arg3_block.cleanup();
+ }
+
+ private:
+ Arg1TensorBlock m_arg1_block;
+ Arg2TensorBlock m_arg2_block;
+ Arg3TensorBlock m_arg3_block;
+ BlockFactory m_factory;
+};
+
+// -------------------------------------------------------------------------- //
+// StridedLinearBufferCopy provides a method to copy data between two linear
+// buffers with different strides, with optimized paths for scatter/gather.
+
+template <typename Scalar, typename IndexType>
+class StridedLinearBufferCopy {
+ typedef typename packet_traits<Scalar>::type Packet;
+ enum {
+ Vectorizable = packet_traits<Scalar>::Vectorizable,
+ PacketSize = packet_traits<Scalar>::size
+ };
+
+ public:
+ // Specifying linear copy kind statically gives ~30% speedup for small sizes.
+ enum class Kind {
+ Linear = 0, // src_stride == 1 && dst_stride == 1
+ Scatter = 1, // src_stride == 1 && dst_stride != 1
+ FillLinear = 2, // src_stride == 0 && dst_stride == 1
+ FillScatter = 3, // src_stride == 0 && dst_stride != 1
+ Gather = 4, // dst_stride == 1
+ Random = 5 // everything else
+ };
+
+ struct Dst {
+ Dst(IndexType o, IndexType s, Scalar* d) : offset(o), stride(s), data(d) {}
+
+ IndexType offset;
+ IndexType stride;
+ Scalar* data;
+ };
+
+ struct Src {
+ Src(IndexType o, IndexType s, const Scalar* d)
+ : offset(o), stride(s), data(d) {}
+
+ IndexType offset;
+ IndexType stride;
+ const Scalar* data;
+ };
+
+ template <typename StridedLinearBufferCopy::Kind kind>
+ static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void Run(const Dst& dst,
+ const Src& src,
+ const size_t count) {
+ Run<kind>(count, dst.offset, dst.stride, dst.data, src.offset, src.stride,
+ src.data);
+ }
+
+ private:
+ template <typename StridedLinearBufferCopy::Kind kind>
+ static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void Run(
+ const IndexType count, const IndexType dst_offset,
+ const IndexType dst_stride, Scalar* EIGEN_RESTRICT dst_data,
+ const IndexType src_offset, const IndexType src_stride,
+ const Scalar* EIGEN_RESTRICT src_data) {
+ const Scalar* src = &src_data[src_offset];
+ Scalar* dst = &dst_data[dst_offset];
+
+ if (!Vectorizable) {
+ for (Index i = 0; i < count; ++i) {
+ dst[i * dst_stride] = src[i * src_stride];
+ }
+ return;
+ }
+
+ const IndexType vectorized_size = count - PacketSize;
+ IndexType i = 0;
+
+ if (kind == StridedLinearBufferCopy::Kind::Linear) {
+ // ******************************************************************** //
+ // Linear copy from `src` to `dst`.
+ const IndexType unrolled_size = count - 4 * PacketSize;
+ eigen_assert(src_stride == 1 && dst_stride == 1);
+ for (; i <= unrolled_size; i += 4 * PacketSize) {
+ for (int j = 0; j < 4; ++j) {
+ Packet p = ploadu<Packet>(src + i + j * PacketSize);
+ pstoreu<Scalar, Packet>(dst + i + j * PacketSize, p);
+ }
+ }
+ for (; i <= vectorized_size; i += PacketSize) {
+ Packet p = ploadu<Packet>(src + i);
+ pstoreu<Scalar, Packet>(dst + i, p);
+ }
+ for (; i < count; ++i) {
+ dst[i] = src[i];
+ }
+ // ******************************************************************** //
+ } else if (kind == StridedLinearBufferCopy::Kind::Scatter) {
+ // Scatter from `src` to `dst`.
+ eigen_assert(src_stride == 1 && dst_stride != 1);
+ for (; i <= vectorized_size; i += PacketSize) {
+ Packet p = ploadu<Packet>(src + i);
+ pscatter<Scalar, Packet>(dst + i * dst_stride, p, dst_stride);
+ }
+ for (; i < count; ++i) {
+ dst[i * dst_stride] = src[i];
+ }
+ // ******************************************************************** //
+ } else if (kind == StridedLinearBufferCopy::Kind::FillLinear) {
+ // Fill `dst` with value at `*src`.
+ eigen_assert(src_stride == 0 && dst_stride == 1);
+ const IndexType unrolled_size = count - 4 * PacketSize;
+ Packet p = pload1<Packet>(src);
+ for (; i <= unrolled_size; i += 4 * PacketSize) {
+ for (int j = 0; j < 4; ++j) {
+ pstoreu<Scalar, Packet>(dst + i + j * PacketSize, p);
+ }
+ }
+ for (; i <= vectorized_size; i += PacketSize) {
+ pstoreu<Scalar, Packet>(dst + i, p);
+ }
+ for (; i < count; ++i) {
+ dst[i] = *src;
+ }
+ // ******************************************************************** //
+ } else if (kind == StridedLinearBufferCopy::Kind::FillScatter) {
+ // Scatter `*src` into `dst`.
+ eigen_assert(src_stride == 0 && dst_stride != 1);
+ Packet p = pload1<Packet>(src);
+ for (; i <= vectorized_size; i += PacketSize) {
+ pscatter<Scalar, Packet>(dst + i * dst_stride, p, dst_stride);
+ }
+ for (; i < count; ++i) {
+ dst[i * dst_stride] = *src;
+ }
+ // ******************************************************************** //
+ } else if (kind == StridedLinearBufferCopy::Kind::Gather) {
+ // Gather from `src` into `dst`.
+ eigen_assert(dst_stride == 1);
+ for (; i <= vectorized_size; i += PacketSize) {
+ Packet p = pgather<Scalar, Packet>(src + i * src_stride, src_stride);
+ pstoreu<Scalar, Packet>(dst + i, p);
+ }
+ for (; i < count; ++i) {
+ dst[i] = src[i * src_stride];
+ }
+ // ******************************************************************** //
+ } else if (kind == StridedLinearBufferCopy::Kind::Random) {
+ // Random.
+ for (; i < count; ++i) {
+ dst[i * dst_stride] = src[i * src_stride];
+ }
+ } else {
+ eigen_assert(false);
+ }
+ }
+};
+
+// -------------------------------------------------------------------------- //
+// TensorBlockIO copies data from `src` tensor block, to the `dst` tensor block.
+// It's possible to specify src->dst dimension mapping for the copy operation.
+// Dimensions of `dst` specify how many elements have to be copied, for the
+// `src` we need to know only stride to navigate through source memory buffer.
+
+template <typename Scalar, typename IndexType, int NumDims, int Layout>
+class TensorBlockIO {
+ static constexpr bool IsColMajor = (Layout == ColMajor);
+
+ typedef StridedLinearBufferCopy<Scalar, IndexType> LinCopy;
+
+ public:
+ typedef DSizes<IndexType, NumDims> Dimensions;
+ typedef DSizes<int, NumDims> DimensionsMap;
+
+ struct Dst {
+ Dst(const Dimensions& dst_dims, const Dimensions& dst_strides, Scalar* dst,
+ IndexType dst_offset = 0)
+ : dims(dst_dims), strides(dst_strides), data(dst), offset(dst_offset) {}
+
+ Dimensions dims;
+ Dimensions strides;
+ Scalar* data;
+ IndexType offset;
+ };
+
+ struct Src {
+ Src(const Dimensions& src_strides, const Scalar* src,
+ IndexType src_offset = 0)
+ : strides(src_strides), data(src), offset(src_offset) {}
+
+ Dimensions strides;
+ const Scalar* data;
+ IndexType offset;
+ };
+
+ // Copies data to `dst` from `src`, using provided dimensions mapping:
+ //
+ // src_dimension_index = dst_to_src_dim_map[dst_dimension_index]
+ //
+ // Returns the number of copied elements.
+ static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE IndexType Copy(
+ const Dst& dst, const Src& src, const DimensionsMap& dst_to_src_dim_map) {
+ // Copy single scalar value from `src` to `dst`.
+ if (NumDims == 0) {
+ *(dst.data + dst.offset) = *(src.data + src.offset);
+ return 1;
+ }
+
+ // Both `dst` and `src` must have contiguous innermost dimension. We also
+ // accept the special case with stride '0', because it's used as a trick to
+ // implement broadcasting.
+ {
+ int inner_dim = IsColMajor ? 0 : NumDims - 1;
+ EIGEN_UNUSED_VARIABLE(inner_dim);
+ eigen_assert(dst.strides[inner_dim] == 1 || dst.strides[inner_dim] == 0);
+ eigen_assert(src.strides[inner_dim] == 1 || src.strides[inner_dim] == 0);
+ }
+
+ // Give a shorter name to `dst_to_src_dim_map`.
+ const DimensionsMap& dim_map = dst_to_src_dim_map;
+
+ // Do not squeeze reordered inner dimensions.
+ int num_squeezable_dims = NumSqueezableInnerDims(dim_map);
+
+ // NOTE: We find the innermost dimension (contiguous in memory) in the dst
+ // block, and we write data linearly into that dimension, reading it from
+ // the src. If dimensions are reordered, we might end up reading data from
+ // the src with `stride != 1`.
+ //
+ // NOTE: Random-Read/Linear-Write can be up to ~2X faster than
+ // Linear-Read/Random-Write: https://stackoverflow.com/a/54935680
+
+ // Find the innermost dimension in the dst whose size is not 1. This is the
+ // effective inner dim.
+ int num_size_one_inner_dims = 0;
+ for (int i = 0; i < num_squeezable_dims; ++i) {
+ const int dst_dim = IsColMajor ? i : NumDims - i - 1;
+ if (dst.dims[dst_dim] != 1) break;
+ num_size_one_inner_dims++;
+ }
+
+ // If all dimensions are of size 1, just copy a scalar from `src` to `dst`.
+ if (num_size_one_inner_dims == NumDims) {
+ *(dst.data + dst.offset) = *(src.data + src.offset);
+ return 1;
+ }
+
+ // Outermost dimension in the dst with `stride == 1` (contiguous in memory).
+ const int dst_stride1_dim = IsColMajor
+ ? num_size_one_inner_dims
+ : NumDims - num_size_one_inner_dims - 1;
+
+ // Dimension in the src that corresponds to the dst innermost dimension.
+ const int src_dim_for_dst_stride1_dim =
+ NumDims == 0 ? 1 : dim_map[dst_stride1_dim];
+
+ // Size of the innermost dimension (length of contiguous blocks of memory).
+ IndexType dst_inner_dim_size = NumDims == 0 ? 1 : dst.dims[dst_stride1_dim];
+
+ // Squeeze multiple inner dims into one if they are contiguous in `dst` and
+ // `src` memory, so we can do less linear copy calls.
+ for (int i = num_size_one_inner_dims + 1; i < num_squeezable_dims; ++i) {
+ const int dst_dim = IsColMajor ? i : NumDims - i - 1;
+ const IndexType dst_stride = dst.strides[dst_dim];
+ const IndexType src_stride = src.strides[dim_map[dst_dim]];
+ if (dst_inner_dim_size == dst_stride && dst_stride == src_stride) {
+ dst_inner_dim_size *= dst.dims[dst_dim];
+ ++num_size_one_inner_dims;
+ } else {
+ break;
+ }
+ }
+
+ // Setup strides to read data from `src` and write to `dst`.
+ IndexType input_offset = src.offset;
+ IndexType output_offset = dst.offset;
+ IndexType input_stride =
+ NumDims == 0 ? 1 : src.strides[src_dim_for_dst_stride1_dim];
+ IndexType output_stride = NumDims == 0 ? 1 : dst.strides[dst_stride1_dim];
+
+ const int at_least_1_dim = NumDims <= 1 ? 1 : NumDims - 1;
+ array<BlockIteratorState, at_least_1_dim> it;
+
+ // Initialize block iterator state. Squeeze away any dimension of size 1.
+ int idx = 0; // currently initialized iterator state index
+ for (int i = num_size_one_inner_dims; i < NumDims - 1; ++i) {
+ const int dst_dim = IsColMajor ? i + 1 : NumDims - i - 2;
+ if (dst.dims[dst_dim] == 1) continue;
+
+ it[idx].size = dst.dims[dst_dim];
+ it[idx].input_stride = src.strides[dim_map[dst_dim]];
+ it[idx].output_stride = dst.strides[dst_dim];
+
+ it[idx].input_span = it[idx].input_stride * (it[idx].size - 1);
+ it[idx].output_span = it[idx].output_stride * (it[idx].size - 1);
+
+ idx++;
+ }
+
+ // Iterate copying data from src to dst.
+ const IndexType block_total_size = NumDims == 0 ? 1 : dst.dims.TotalSize();
+
+#define COPY_INNER_DIM(KIND) \
+ IndexType num_copied = 0; \
+ for (num_copied = 0; num_copied < block_total_size; \
+ num_copied += dst_inner_dim_size) { \
+ LinCopy::template Run<KIND>( \
+ typename LinCopy::Dst(output_offset, output_stride, dst.data), \
+ typename LinCopy::Src(input_offset, input_stride, src.data), \
+ dst_inner_dim_size); \
+ \
+ for (int j = 0; j < idx; ++j) { \
+ if (++it[j].count < it[j].size) { \
+ input_offset += it[j].input_stride; \
+ output_offset += it[j].output_stride; \
+ break; \
+ } \
+ it[j].count = 0; \
+ input_offset -= it[j].input_span; \
+ output_offset -= it[j].output_span; \
+ } \
+ } \
+ return num_copied;
+
+ if (input_stride == 1 && output_stride == 1) {
+ COPY_INNER_DIM(LinCopy::Kind::Linear);
+ } else if (input_stride == 1 && output_stride != 1) {
+ COPY_INNER_DIM(LinCopy::Kind::Scatter);
+ } else if (input_stride == 0 && output_stride == 1) {
+ COPY_INNER_DIM(LinCopy::Kind::FillLinear);
+ } else if (input_stride == 0 && output_stride != 1) {
+ COPY_INNER_DIM(LinCopy::Kind::FillScatter);
+ } else if (output_stride == 1) {
+ COPY_INNER_DIM(LinCopy::Kind::Gather);
+ } else {
+ COPY_INNER_DIM(LinCopy::Kind::Random);
+ }
+
+#undef COPY_INNER_DIM
+ }
+
+ // Copy from `src` to `dst` with an identity src->dst dimension map. Returns
+ // the number of copied elements.
+ static EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE IndexType Copy(const Dst& dst,
+ const Src& src) {
+ DimensionsMap dst_to_src_map;
+ for (int i = 0; i < NumDims; ++i) dst_to_src_map[i] = i;
+ return Copy(dst, src, dst_to_src_map);
+ }
+
+ private:
+ struct BlockIteratorState {
+ BlockIteratorState()
+ : size(0),
+ count(0),
+ input_stride(0),
+ output_stride(0),
+ input_span(0),
+ output_span(0) {}
+
+ IndexType size;
+ IndexType count;
+ IndexType input_stride;
+ IndexType output_stride;
+ IndexType input_span;
+ IndexType output_span;
+ };
+
+ // Compute how many inner dimensions it's allowed to squeeze when doing IO
+ // between two tensor blocks. It's safe to squeeze inner dimensions, only
+ // if they are not reordered.
+ static int NumSqueezableInnerDims(const DimensionsMap& dim_map) {
+ int num_squeezable_dims = 0;
+ for (int i = 0; i < NumDims; ++i) {
+ const int dim = IsColMajor ? i : NumDims - i - 1;
+ if (dim_map[dim] != dim) break;
+ num_squeezable_dims++;
+ }
+ return num_squeezable_dims;
+ }
+};
+
+// -------------------------------------------------------------------------- //
+// TensorBlockAssignment assigns a block expression of type `TensorBlockExpr` to
+// a Tensor block defined by `desc`, backed by a memory buffer at `target`.
+//
+// Currently there is no way to write from a Tensor expression to a block of
+// memory, if dimensions are reordered. If you need to do that, you should
+// materialize a Tensor block expression into a memory buffer, and then use
+// TensorBlockIO to copy data between two memory buffers with a custom
+// `target->src` dimension map (see definition above).
+//
+// Also currently the innermost dimension of `target` must have a stride '1'
+// (contiguous in memory). This restriction could be lifted with a `pscatter`,
+// but in practice it's never needed, and there is a similar TensorBlockIO
+// workaround for that.
+//
+// TODO(ezhulenev): TensorBlockAssignment is a special case of TensorBlockIO
+// where `src` is a tensor expression. Explore if it is possible to rewrite IO
+// to use expressions instead of pointers, and after that TensorBlockAssignment
+// will become an alias to IO.
+template <typename Scalar, int NumDims, typename TensorBlockExpr,
+ typename IndexType = Eigen::Index>
+class TensorBlockAssignment {
+ // We will use coeff/packet path to evaluate block expressions.
+ typedef TensorEvaluator<const TensorBlockExpr, DefaultDevice>
+ TensorBlockEvaluator;
+
+ typedef DSizes<IndexType, NumDims> Dimensions;
+
+ enum {
+ Vectorizable = packet_traits<Scalar>::Vectorizable,
+ PacketSize = packet_traits<Scalar>::size
+ };
+
+ template <bool Vectorizable, typename Evaluator>
+ struct InnerDimAssign {
+ EIGEN_ALWAYS_INLINE static void Run(Scalar* target, IndexType count,
+ const Evaluator& eval,
+ IndexType eval_offset) {
+ for (IndexType i = 0; i < count; ++i) {
+ target[i] = eval.coeff(eval_offset + i);
+ }
+ }
+ };
+
+ template <typename Evaluator>
+ struct InnerDimAssign<true, Evaluator> {
+ EIGEN_ALWAYS_INLINE static void Run(Scalar* target, IndexType count,
+ const Evaluator& eval,
+ IndexType eval_offset) {
+ typedef typename packet_traits<Scalar>::type Packet;
+
+ const IndexType unrolled_size = count - 4 * PacketSize;
+ const IndexType vectorized_size = count - PacketSize;
+ IndexType i = 0;
+
+ for (; i <= unrolled_size; i += 4 * PacketSize) {
+ for (int j = 0; j < 4; ++j) {
+ const IndexType idx = eval_offset + i + j * PacketSize;
+ Packet p = eval.template packet<Unaligned>(idx);
+ pstoreu<Scalar>(target + i + j * PacketSize, p);
+ }
+ }
+
+ for (; i <= vectorized_size; i += PacketSize) {
+ Packet p = eval.template packet<Unaligned>(eval_offset + i);
+ pstoreu<Scalar>(target + i, p);
+ }
+
+ for (; i < count; ++i) {
+ target[i] = eval.coeff(eval_offset + i);
+ }
+ }
+ };
+
+ public:
+ struct Target {
+ Target(const Dimensions& target_dims, const Dimensions& target_strides,
+ Scalar* target_data, IndexType target_offset = 0)
+ : dims(target_dims),
+ strides(target_strides),
+ data(target_data),
+ offset(target_offset) {}
+
+ Dimensions dims;
+ Dimensions strides;
+ Scalar* data;
+ IndexType offset;
+ };
+
+ static Target target(const Dimensions& target_dims,
+ const Dimensions& target_strides, Scalar* target_data,
+ IndexType target_offset = 0) {
+ return Target(target_dims, target_strides, target_data, target_offset);
+ }
+
+ template <typename TargetDimsIndexType, typename TargetStridesIndexType>
+ static Target target(
+ const DSizes<TargetDimsIndexType, NumDims>& target_dims,
+ const DSizes<TargetStridesIndexType, NumDims>& target_strides,
+ Scalar* target_data, IndexType target_offset = 0) {
+ // DSizes constructor will do index type promotion if it's safe.
+ return Target(Dimensions(target_dims), Dimensions(target_strides),
+ target_data, target_offset);
+ }
+
+ static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void Run(
+ const Target& target, const TensorBlockExpr& expr) {
+ // Prepare evaluator for block expression.
+ DefaultDevice default_device;
+ TensorBlockEvaluator eval(expr, default_device);
+
+ // Tensor block expression dimension should match destination dimensions.
+ eigen_assert(dimensions_match(target.dims, eval.dimensions()));
+
+ static const int Layout = TensorBlockEvaluator::Layout;
+ static const bool is_col_major = Layout == ColMajor;
+
+ // Initialize output inner dimension size based on a layout.
+ const IndexType output_size = NumDims == 0 ? 1 : target.dims.TotalSize();
+ const int inner_dim_idx = is_col_major ? 0 : NumDims - 1;
+ IndexType output_inner_dim_size = target.dims[inner_dim_idx];
+
+ // Target inner dimension stride must be '1'.
+ eigen_assert(target.strides[inner_dim_idx] == 1);
+
+ // Squeeze multiple inner dims into one if they are contiguous in `target`.
+ IndexType num_squeezed_dims = 0;
+ for (Index i = 1; i < NumDims; ++i) {
+ const Index dim = is_col_major ? i : NumDims - i - 1;
+ const IndexType target_stride = target.strides[dim];
+
+ if (output_inner_dim_size == target_stride) {
+ output_inner_dim_size *= target.dims[dim];
+ num_squeezed_dims++;
+ } else {
+ break;
+ }
+ }
+
+ // Initialize output block iterator state. Dimension in this array are
+ // always in inner_most -> outer_most order (col major layout).
+ array<BlockIteratorState, NumDims> it;
+
+ int idx = 0; // currently initialized iterator state index
+ for (Index i = num_squeezed_dims; i < NumDims - 1; ++i) {
+ const Index dim = is_col_major ? i + 1 : NumDims - i - 2;
+
+ it[idx].count = 0;
+ it[idx].size = target.dims[dim];
+ it[idx].output_stride = target.strides[dim];
+ it[idx].output_span = it[idx].output_stride * (it[idx].size - 1);
+ idx++;
+ }
+
+ // We read block expression from the beginning, and start writing data to
+ // `target` at given offset.
+ IndexType input_offset = 0;
+ IndexType output_offset = target.offset;
+
+ // Iterate copying data from `eval` to `target`.
+ for (IndexType i = 0; i < output_size; i += output_inner_dim_size) {
+ // Assign to `target` at current offset.
+ InnerDimAssign<Vectorizable && TensorBlockEvaluator::PacketAccess,
+ TensorBlockEvaluator>::Run(target.data + output_offset,
+ output_inner_dim_size, eval,
+ input_offset);
+
+ // Move input offset forward by the number of assigned coefficients.
+ input_offset += output_inner_dim_size;
+
+ // Update index.
+ for (int j = 0; j < idx; ++j) {
+ if (++it[j].count < it[j].size) {
+ output_offset += it[j].output_stride;
+ break;
+ }
+ it[j].count = 0;
+ output_offset -= it[j].output_span;
+ }
+ }
+ }
+
+ private:
+ struct BlockIteratorState {
+ BlockIteratorState()
+ : count(0), size(0), output_stride(0), output_span(0) {}
+
+ IndexType count;
+ IndexType size;
+ IndexType output_stride;
+ IndexType output_span;
+ };
+};
+
+// -------------------------------------------------------------------------- //
+
+} // namespace internal
+} // namespace Eigen
+
+#endif // EIGEN_CXX11_TENSOR_TENSOR_BLOCK_H
diff --git a/unsupported/Eigen/CXX11/src/Tensor/TensorBroadcasting.h b/unsupported/Eigen/CXX11/src/Tensor/TensorBroadcasting.h
new file mode 100644
index 0000000..64c39ca
--- /dev/null
+++ b/unsupported/Eigen/CXX11/src/Tensor/TensorBroadcasting.h
@@ -0,0 +1,1087 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_CXX11_TENSOR_TENSOR_BROADCASTING_H
+#define EIGEN_CXX11_TENSOR_TENSOR_BROADCASTING_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+/** \class TensorBroadcasting
+ * \ingroup CXX11_Tensor_Module
+ *
+ * \brief Tensor broadcasting class.
+ *
+ *
+ */
+namespace internal {
+template<typename Broadcast, typename XprType>
+struct traits<TensorBroadcastingOp<Broadcast, XprType> > : public traits<XprType>
+{
+ typedef typename XprType::Scalar Scalar;
+ typedef traits<XprType> XprTraits;
+ typedef typename XprTraits::StorageKind StorageKind;
+ typedef typename XprTraits::Index Index;
+ typedef typename XprType::Nested Nested;
+ typedef std::remove_reference_t<Nested> Nested_;
+ static constexpr int NumDimensions = XprTraits::NumDimensions;
+ static constexpr int Layout = XprTraits::Layout;
+ typedef typename XprTraits::PointerType PointerType;
+};
+
+template<typename Broadcast, typename XprType>
+struct eval<TensorBroadcastingOp<Broadcast, XprType>, Eigen::Dense>
+{
+ typedef const TensorBroadcastingOp<Broadcast, XprType> EIGEN_DEVICE_REF type;
+};
+
+template<typename Broadcast, typename XprType>
+struct nested<TensorBroadcastingOp<Broadcast, XprType>, 1, typename eval<TensorBroadcastingOp<Broadcast, XprType> >::type>
+{
+ typedef TensorBroadcastingOp<Broadcast, XprType> type;
+};
+
+template <typename Dims>
+struct is_input_scalar {
+ static const bool value = false;
+};
+template <>
+struct is_input_scalar<Sizes<> > {
+ static const bool value = true;
+};
+#ifndef EIGEN_EMULATE_CXX11_META_H
+template <typename std::ptrdiff_t... Indices>
+struct is_input_scalar<Sizes<Indices...> > {
+ static const bool value = (Sizes<Indices...>::total_size == 1);
+};
+#endif
+
+} // end namespace internal
+
+
+
+template<typename Broadcast, typename XprType>
+class TensorBroadcastingOp : public TensorBase<TensorBroadcastingOp<Broadcast, XprType>, ReadOnlyAccessors>
+{
+ public:
+ typedef typename Eigen::internal::traits<TensorBroadcastingOp>::Scalar Scalar;
+ typedef typename Eigen::NumTraits<Scalar>::Real RealScalar;
+ typedef typename XprType::CoeffReturnType CoeffReturnType;
+ typedef typename Eigen::internal::nested<TensorBroadcastingOp>::type Nested;
+ typedef typename Eigen::internal::traits<TensorBroadcastingOp>::StorageKind StorageKind;
+ typedef typename Eigen::internal::traits<TensorBroadcastingOp>::Index Index;
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorBroadcastingOp(const XprType& expr, const Broadcast& broadcast)
+ : m_xpr(expr), m_broadcast(broadcast) {}
+
+ EIGEN_DEVICE_FUNC
+ const Broadcast& broadcast() const { return m_broadcast; }
+
+ EIGEN_DEVICE_FUNC
+ const internal::remove_all_t<typename XprType::Nested>&
+ expression() const { return m_xpr; }
+
+ protected:
+ typename XprType::Nested m_xpr;
+ const Broadcast m_broadcast;
+};
+
+
+// Eval as rvalue
+template<typename Broadcast, typename ArgType, typename Device>
+struct TensorEvaluator<const TensorBroadcastingOp<Broadcast, ArgType>, Device>
+{
+ typedef TensorBroadcastingOp<Broadcast, ArgType> XprType;
+ typedef typename XprType::Index Index;
+ static constexpr int NumDims = internal::array_size<typename TensorEvaluator<ArgType, Device>::Dimensions>::value;
+ typedef DSizes<Index, NumDims> Dimensions;
+ typedef typename XprType::Scalar Scalar;
+ typedef typename TensorEvaluator<ArgType, Device>::Dimensions InputDimensions;
+ typedef typename XprType::CoeffReturnType CoeffReturnType;
+ typedef typename PacketType<CoeffReturnType, Device>::type PacketReturnType;
+ static constexpr int PacketSize = PacketType<CoeffReturnType, Device>::size;
+ protected: // all the non-static fields must have the same access control, otherwise the TensorEvaluator won't be standard layout;
+ bool isCopy, nByOne, oneByN;
+ public:
+ typedef StorageMemory<CoeffReturnType, Device> Storage;
+ typedef typename Storage::Type EvaluatorPointerType;
+
+ enum {
+ IsAligned = TensorEvaluator<ArgType, Device>::IsAligned,
+ PacketAccess = TensorEvaluator<ArgType, Device>::PacketAccess,
+ BlockAccess = TensorEvaluator<ArgType, Device>::BlockAccess,
+ PreferBlockAccess = true,
+ RawAccess = false
+ };
+ static constexpr int Layout = TensorEvaluator<ArgType, Device>::Layout;
+
+ typedef std::remove_const_t<Scalar> ScalarNoConst;
+
+ // We do block based broadcasting using a trick with 2x tensor rank and 0
+ // strides. See block method implementation for details.
+ typedef DSizes<Index, 2 * NumDims> BroadcastDimensions;
+
+ //===- Tensor block evaluation strategy (see TensorBlock.h) -------------===//
+ typedef internal::TensorBlockDescriptor<NumDims, Index> TensorBlockDesc;
+ typedef internal::TensorBlockScratchAllocator<Device> TensorBlockScratch;
+
+ typedef typename TensorEvaluator<const ArgType, Device>::TensorBlock
+ ArgTensorBlock;
+
+ typedef typename internal::TensorMaterializedBlock<ScalarNoConst, NumDims,
+ Layout, Index>
+ TensorBlock;
+ //===--------------------------------------------------------------------===//
+
+ EIGEN_STRONG_INLINE TensorEvaluator(const XprType& op, const Device& device)
+ : isCopy(false), nByOne(false), oneByN(false),
+ m_device(device), m_broadcast(op.broadcast()), m_impl(op.expression(), device)
+ {
+
+ // The broadcasting op doesn't change the rank of the tensor. One can't broadcast a scalar
+ // and store the result in a scalar. Instead one should reshape the scalar into a N-D
+ // tensor with N >= 1 of 1 element first and then broadcast.
+ EIGEN_STATIC_ASSERT((NumDims > 0), YOU_MADE_A_PROGRAMMING_MISTAKE);
+ const InputDimensions& input_dims = m_impl.dimensions();
+ isCopy = true;
+ for (int i = 0; i < NumDims; ++i) {
+ eigen_assert(input_dims[i] > 0);
+ m_dimensions[i] = input_dims[i] * m_broadcast[i];
+ if (m_broadcast[i] != 1) {
+ isCopy = false;
+ }
+ }
+
+ if (static_cast<int>(Layout) == static_cast<int>(ColMajor)) {
+ m_inputStrides[0] = 1;
+ m_outputStrides[0] = 1;
+ for (int i = 1; i < NumDims; ++i) {
+ m_inputStrides[i] = m_inputStrides[i-1] * input_dims[i-1];
+ m_outputStrides[i] = m_outputStrides[i-1] * m_dimensions[i-1];
+ }
+ } else {
+ m_inputStrides[NumDims-1] = 1;
+ m_outputStrides[NumDims-1] = 1;
+ for (int i = NumDims-2; i >= 0; --i) {
+ m_inputStrides[i] = m_inputStrides[i+1] * input_dims[i+1];
+ m_outputStrides[i] = m_outputStrides[i+1] * m_dimensions[i+1];
+ }
+ }
+
+ if (input_dims[0] == 1) {
+ oneByN = true;
+ for (int i = 1; i < NumDims; ++i) {
+ if (m_broadcast[i] != 1) {
+ oneByN = false;
+ break;
+ }
+ }
+ } else if (input_dims[NumDims-1] == 1) {
+ nByOne = true;
+ for (int i = 0; i < NumDims-1; ++i) {
+ if (m_broadcast[i] != 1) {
+ nByOne = false;
+ break;
+ }
+ }
+ }
+
+ // Handle special format like NCHW, its input shape is '[1, N..., 1]' and
+ // broadcast shape is '[N, 1..., N]'
+ if (!oneByN && !nByOne) {
+ if (input_dims[0] == 1 && input_dims[NumDims-1] == 1 && NumDims > 2) {
+ nByOne = true;
+ oneByN = true;
+ for (int i = 1; i < NumDims-1; ++i) {
+ if (m_broadcast[i] != 1) {
+ nByOne = false;
+ oneByN = false;
+ break;
+ }
+ }
+ }
+ }
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Dimensions& dimensions() const { return m_dimensions; }
+
+ EIGEN_STRONG_INLINE bool evalSubExprsIfNeeded(EvaluatorPointerType) {
+ m_impl.evalSubExprsIfNeeded(NULL);
+ return true;
+ }
+
+#ifdef EIGEN_USE_THREADS
+ template <typename EvalSubExprsCallback>
+ EIGEN_STRONG_INLINE void evalSubExprsIfNeededAsync(
+ EvaluatorPointerType, EvalSubExprsCallback done) {
+ m_impl.evalSubExprsIfNeededAsync(nullptr, [done](bool) { done(true); });
+ }
+#endif // EIGEN_USE_THREADS
+
+ EIGEN_STRONG_INLINE void cleanup() {
+ m_impl.cleanup();
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE CoeffReturnType coeff(Index index) const
+ {
+ if (internal::is_input_scalar<internal::remove_all_t<InputDimensions>>::value) {
+ return m_impl.coeff(0);
+ }
+
+ if (static_cast<int>(Layout) == static_cast<int>(ColMajor)) {
+ if (isCopy) {
+ return m_impl.coeff(index);
+ } else {
+ return coeffColMajor(index);
+ }
+ } else {
+ if (isCopy) {
+ return m_impl.coeff(index);
+ } else {
+ return coeffRowMajor(index);
+ }
+ }
+ }
+
+ // TODO: attempt to speed this up. The integer divisions and modulo are slow
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Index indexColMajor(Index index) const {
+ Index inputIndex = 0;
+ EIGEN_UNROLL_LOOP
+ for (int i = NumDims - 1; i > 0; --i) {
+ const Index idx = index / m_outputStrides[i];
+ if (internal::index_statically_eq<Broadcast>(i, 1)) {
+ eigen_assert(idx < m_impl.dimensions()[i]);
+ inputIndex += idx * m_inputStrides[i];
+ } else {
+ if (internal::index_statically_eq<InputDimensions>(i, 1)) {
+ eigen_assert(idx % m_impl.dimensions()[i] == 0);
+ } else {
+ inputIndex += (idx % m_impl.dimensions()[i]) * m_inputStrides[i];
+ }
+ }
+ index -= idx * m_outputStrides[i];
+ }
+ if (internal::index_statically_eq<Broadcast>(0, 1)) {
+ eigen_assert(index < m_impl.dimensions()[0]);
+ inputIndex += index;
+ } else {
+ if (internal::index_statically_eq<InputDimensions>(0, 1)) {
+ eigen_assert(index % m_impl.dimensions()[0] == 0);
+ } else {
+ inputIndex += (index % m_impl.dimensions()[0]);
+ }
+ }
+ return inputIndex;
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE CoeffReturnType coeffColMajor(Index index) const
+ {
+ return m_impl.coeff(indexColMajor(index));
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Index indexRowMajor(Index index) const {
+ Index inputIndex = 0;
+ EIGEN_UNROLL_LOOP
+ for (int i = 0; i < NumDims - 1; ++i) {
+ const Index idx = index / m_outputStrides[i];
+ if (internal::index_statically_eq<Broadcast>(i, 1)) {
+ eigen_assert(idx < m_impl.dimensions()[i]);
+ inputIndex += idx * m_inputStrides[i];
+ } else {
+ if (internal::index_statically_eq<InputDimensions>(i, 1)) {
+ eigen_assert(idx % m_impl.dimensions()[i] == 0);
+ } else {
+ inputIndex += (idx % m_impl.dimensions()[i]) * m_inputStrides[i];
+ }
+ }
+ index -= idx * m_outputStrides[i];
+ }
+ if (internal::index_statically_eq<Broadcast>(NumDims - 1, 1)) {
+ eigen_assert(index < m_impl.dimensions()[NumDims - 1]);
+ inputIndex += index;
+ } else {
+ if (internal::index_statically_eq<InputDimensions>(NumDims - 1, 1)) {
+ eigen_assert(index % m_impl.dimensions()[NumDims - 1] == 0);
+ } else {
+ inputIndex += (index % m_impl.dimensions()[NumDims - 1]);
+ }
+ }
+ return inputIndex;
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE CoeffReturnType coeffRowMajor(Index index) const
+ {
+ return m_impl.coeff(indexRowMajor(index));
+ }
+
+ template<int LoadMode>
+ EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE PacketReturnType packet(Index index) const
+ {
+ if (internal::is_input_scalar<internal::remove_all_t<InputDimensions>>::value) {
+ return internal::pset1<PacketReturnType>(m_impl.coeff(0));
+ }
+
+ if (static_cast<int>(Layout) == static_cast<int>(ColMajor)) {
+ if (isCopy) {
+ #ifdef EIGEN_GPU_COMPILE_PHASE
+ // See PR 437: on NVIDIA P100 and K20m we observed a x3-4 speed up by enforcing
+ // unaligned loads here. The reason is unclear though.
+ return m_impl.template packet<Unaligned>(index);
+ #else
+ return m_impl.template packet<LoadMode>(index);
+ #endif
+ } else if (oneByN && !nByOne) {
+ return packetNByOne<LoadMode>(index);
+ } else if (!oneByN && nByOne) {
+ return packetOneByN<LoadMode>(index);
+ } else if (oneByN && nByOne) {
+ return packetOneByNByOne<LoadMode>(index);
+ } else {
+ return packetColMajor<LoadMode>(index);
+ }
+ } else {
+ if (isCopy) {
+ #ifdef EIGEN_GPU_COMPILE_PHASE
+ // See above.
+ return m_impl.template packet<Unaligned>(index);
+ #else
+ return m_impl.template packet<LoadMode>(index);
+ #endif
+ } else if (oneByN && !nByOne) {
+ return packetOneByN<LoadMode>(index);
+ } else if (!oneByN && nByOne) {
+ return packetNByOne<LoadMode>(index);
+ } else if (oneByN && nByOne) {
+ return packetOneByNByOne<LoadMode>(index);
+ } else {
+ return packetRowMajor<LoadMode>(index);
+ }
+ }
+ }
+
+ template<int LoadMode>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE PacketReturnType packetOneByNByOne
+ (Index index) const
+ {
+ eigen_assert(index+PacketSize-1 < dimensions().TotalSize());
+
+ EIGEN_ALIGN_MAX std::remove_const_t<CoeffReturnType> values[PacketSize];
+ Index startDim, endDim;
+ Index inputIndex, outputOffset, batchedIndex;
+
+ if (static_cast<int>(Layout) == static_cast<int>(ColMajor)) {
+ startDim = NumDims - 1;
+ endDim = 1;
+ } else {
+ startDim = 0;
+ endDim = NumDims - 2;
+ }
+
+ batchedIndex = index % m_outputStrides[startDim];
+ inputIndex = batchedIndex / m_outputStrides[endDim];
+ outputOffset = batchedIndex % m_outputStrides[endDim];
+
+ if (outputOffset + PacketSize <= m_outputStrides[endDim]) {
+ values[0] = m_impl.coeff(inputIndex);
+ return internal::pload1<PacketReturnType>(values);
+ } else {
+ EIGEN_UNROLL_LOOP
+ for (int i = 0, cur = 0; i < PacketSize; ++i, ++cur) {
+ if (outputOffset + cur < m_outputStrides[endDim]) {
+ values[i] = m_impl.coeff(inputIndex);
+ } else {
+ ++inputIndex;
+ inputIndex = (inputIndex == m_inputStrides[startDim] ? 0 : inputIndex);
+ values[i] = m_impl.coeff(inputIndex);
+ outputOffset = 0;
+ cur = 0;
+ }
+ }
+ return internal::pload<PacketReturnType>(values);
+ }
+ }
+
+ template<int LoadMode>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE PacketReturnType packetOneByN(Index index) const
+ {
+ // Consider the flattened tensor [v0, ..., vN],
+ // Concatenates m_broadcast[dim] copies,
+ // [v0, ..., vN, v0, ..., vN, ... ]
+ // with dim == NumDims - 1 for col-major, dim == 0 for row-major.
+ eigen_assert(index+PacketSize-1 < dimensions().TotalSize());
+
+ // Size of flattened tensor.
+ const Index M = (static_cast<int>(Layout) == static_cast<int>(ColMajor)) ?
+ m_inputStrides[NumDims - 1] : m_inputStrides[0];
+ Index inputIndex = index % M;
+ if (inputIndex + PacketSize <= M) {
+ return m_impl.template packet<Unaligned>(inputIndex);
+ } else {
+ EIGEN_ALIGN_MAX std::remove_const_t<CoeffReturnType> values[PacketSize];
+ EIGEN_UNROLL_LOOP
+ for (int i = 0; i < PacketSize; ++i) {
+ if (inputIndex > M - 1) {
+ inputIndex = 0;
+ }
+ values[i] = m_impl.coeff(inputIndex++);
+ }
+ return internal::pload<PacketReturnType>(values);
+ }
+ }
+
+ template<int LoadMode>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE PacketReturnType packetNByOne(Index index) const
+ {
+ // Consider the flattened tensor [v0, ..., vN],
+ // Interleaves m_broadcast[dim] copies,
+ // [v0, v0, ..., v1, v1, ..., vN, vN, ... ]
+ // with dim == 0 for col-major, dim == NumDims - 1 for row-major.
+ eigen_assert(index + PacketSize-1 < dimensions().TotalSize());
+
+ const Index M = (static_cast<int>(Layout) == static_cast<int>(ColMajor)) ?
+ m_broadcast[0] : m_broadcast[NumDims - 1];
+
+ Index inputIndex = index / M;
+ Index outputOffset = index % M;
+ if (outputOffset + PacketSize <= M) {
+ return internal::pset1<PacketReturnType>(m_impl.coeff(inputIndex));
+ } else {
+ EIGEN_ALIGN_MAX std::remove_const_t<CoeffReturnType> values[PacketSize];
+ EIGEN_UNROLL_LOOP
+ for (int i = 0; i < PacketSize; ++i) {
+ if (outputOffset < M) {
+ values[i] = m_impl.coeff(inputIndex);
+ ++outputOffset;
+ } else {
+ values[i] = m_impl.coeff(++inputIndex);
+ outputOffset = 1; // Next offset.
+ }
+ }
+ return internal::pload<PacketReturnType>(values);
+ }
+ }
+
+ // Ignore the LoadMode and always use unaligned loads since we can't guarantee
+ // the alignment at compile time.
+ template<int LoadMode>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE PacketReturnType packetColMajor(Index index) const
+ {
+ eigen_assert(index+PacketSize-1 < dimensions().TotalSize());
+
+ const Index originalIndex = index;
+
+ Index inputIndex = 0;
+ EIGEN_UNROLL_LOOP
+ for (int i = NumDims - 1; i > 0; --i) {
+ const Index idx = index / m_outputStrides[i];
+ if (internal::index_statically_eq<Broadcast>(i, 1)) {
+ eigen_assert(idx < m_impl.dimensions()[i]);
+ inputIndex += idx * m_inputStrides[i];
+ } else {
+ if (internal::index_statically_eq<InputDimensions>(i, 1)) {
+ eigen_assert(idx % m_impl.dimensions()[i] == 0);
+ } else {
+ inputIndex += (idx % m_impl.dimensions()[i]) * m_inputStrides[i];
+ }
+ }
+ index -= idx * m_outputStrides[i];
+ }
+ Index innermostLoc;
+ if (internal::index_statically_eq<Broadcast>(0, 1)) {
+ eigen_assert(index < m_impl.dimensions()[0]);
+ innermostLoc = index;
+ } else {
+ if (internal::index_statically_eq<InputDimensions>(0, 1)) {
+ eigen_assert(index % m_impl.dimensions()[0] == 0);
+ innermostLoc = 0;
+ } else {
+ innermostLoc = index % m_impl.dimensions()[0];
+ }
+ }
+ inputIndex += innermostLoc;
+
+ // Todo: this could be extended to the second dimension if we're not
+ // broadcasting alongside the first dimension, and so on.
+ if (innermostLoc + PacketSize <= m_impl.dimensions()[0]) {
+ return m_impl.template packet<Unaligned>(inputIndex);
+ } else {
+ EIGEN_ALIGN_MAX std::remove_const_t<CoeffReturnType> values[PacketSize];
+ values[0] = m_impl.coeff(inputIndex);
+ EIGEN_UNROLL_LOOP
+ for (int i = 1; i < PacketSize; ++i) {
+ if (innermostLoc + i < m_impl.dimensions()[0]) {
+ values[i] = m_impl.coeff(inputIndex+i);
+ } else {
+ values[i] = coeffColMajor(originalIndex+i);
+ }
+ }
+ PacketReturnType rslt = internal::pload<PacketReturnType>(values);
+ return rslt;
+ }
+ }
+
+ template<int LoadMode>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE PacketReturnType packetRowMajor(Index index) const
+ {
+ eigen_assert(index+PacketSize-1 < dimensions().TotalSize());
+
+ const Index originalIndex = index;
+
+ Index inputIndex = 0;
+ EIGEN_UNROLL_LOOP
+ for (int i = 0; i < NumDims - 1; ++i) {
+ const Index idx = index / m_outputStrides[i];
+ if (internal::index_statically_eq<Broadcast>(i, 1)) {
+ eigen_assert(idx < m_impl.dimensions()[i]);
+ inputIndex += idx * m_inputStrides[i];
+ } else {
+ if (internal::index_statically_eq<InputDimensions>(i, 1)) {
+ eigen_assert(idx % m_impl.dimensions()[i] == 0);
+ } else {
+ inputIndex += (idx % m_impl.dimensions()[i]) * m_inputStrides[i];
+ }
+ }
+ index -= idx * m_outputStrides[i];
+ }
+ Index innermostLoc;
+ if (internal::index_statically_eq<Broadcast>(NumDims-1, 1)) {
+ eigen_assert(index < m_impl.dimensions()[NumDims-1]);
+ innermostLoc = index;
+ } else {
+ if (internal::index_statically_eq<InputDimensions>(NumDims-1, 1)) {
+ eigen_assert(index % m_impl.dimensions()[NumDims-1] == 0);
+ innermostLoc = 0;
+ } else {
+ innermostLoc = index % m_impl.dimensions()[NumDims-1];
+ }
+ }
+ inputIndex += innermostLoc;
+
+ // Todo: this could be extended to the second dimension if we're not
+ // broadcasting alongside the first dimension, and so on.
+ if (innermostLoc + PacketSize <= m_impl.dimensions()[NumDims-1]) {
+ return m_impl.template packet<Unaligned>(inputIndex);
+ } else {
+ EIGEN_ALIGN_MAX std::remove_const_t<CoeffReturnType> values[PacketSize];
+ values[0] = m_impl.coeff(inputIndex);
+ EIGEN_UNROLL_LOOP
+ for (int i = 1; i < PacketSize; ++i) {
+ if (innermostLoc + i < m_impl.dimensions()[NumDims-1]) {
+ values[i] = m_impl.coeff(inputIndex+i);
+ } else {
+ values[i] = coeffRowMajor(originalIndex+i);
+ }
+ }
+ PacketReturnType rslt = internal::pload<PacketReturnType>(values);
+ return rslt;
+ }
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorOpCost
+ costPerCoeff(bool vectorized) const {
+ double compute_cost = TensorOpCost::AddCost<Index>();
+ if (!isCopy && NumDims > 0) {
+ EIGEN_UNROLL_LOOP
+ for (int i = NumDims - 1; i > 0; --i) {
+ compute_cost += TensorOpCost::DivCost<Index>();
+ if (internal::index_statically_eq<Broadcast>(i, 1)) {
+ compute_cost +=
+ TensorOpCost::MulCost<Index>() + TensorOpCost::AddCost<Index>();
+ } else {
+ if (!internal::index_statically_eq<InputDimensions>(i, 1)) {
+ compute_cost += TensorOpCost::MulCost<Index>() +
+ TensorOpCost::ModCost<Index>() +
+ TensorOpCost::AddCost<Index>();
+ }
+ }
+ compute_cost +=
+ TensorOpCost::MulCost<Index>() + TensorOpCost::AddCost<Index>();
+ }
+ }
+ return m_impl.costPerCoeff(vectorized) +
+ TensorOpCost(0, 0, compute_cost, vectorized, PacketSize);
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ internal::TensorBlockResourceRequirements getResourceRequirements() const {
+ // TODO(wuke): Targeting L1 size is 30% faster than targeting L{-1} on large
+ // tensors. But this might need further tuning.
+ const size_t target_size = m_device.firstLevelCacheSize();
+ return internal::TensorBlockResourceRequirements::merge(
+ m_impl.getResourceRequirements(),
+ internal::TensorBlockResourceRequirements::skewed<Scalar>(target_size));
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorBlock
+ block(TensorBlockDesc& desc, TensorBlockScratch& scratch,
+ bool /*root_of_expr_ast*/ = false) const {
+ BlockBroadcastingParams params = blockBroadcastingParams(desc);
+
+ if (params.inner_dim_size == 0 || params.bcast_dim_size == 0) {
+ return emptyBlock();
+ }
+
+ // Prepare storage for the materialized broadcasting result.
+ const typename TensorBlock::Storage block_storage =
+ TensorBlock::prepareStorage(desc, scratch);
+ ScalarNoConst* materialized_output = block_storage.data();
+
+ // We potentially will need to materialize input blocks.
+ size_t materialized_input_size = 0;
+ ScalarNoConst* materialized_input = NULL;
+
+ // Initialize block broadcating iterator state for outer dimensions (outer
+ // with regard to bcast dimension). Dimension in this array are always in
+ // inner_most -> outer_most order (col major layout).
+ array<BlockBroadcastingIteratorState, NumDims> it;
+ int idx = 0;
+
+ for (int i = params.inner_dim_count + 1; i < NumDims; ++i) {
+ const Index dim = IsColMajor ? i : NumDims - 1 - i;
+ it[idx].size = params.output_dims[dim];
+ it[idx].count = 0;
+ it[idx].output_stride = m_outputStrides[dim];
+ it[idx].output_span = it[idx].output_stride * (it[idx].size - 1);
+ idx++;
+ }
+
+ // Write output into the beginning of `materialized_output`.
+ Index output_offset = 0;
+
+ // We will fill output block by broadcasting along the bcast dim, and
+ // iterating over outer dimension.
+ const Index output_size = NumDims == 0 ? 1 : params.output_dims.TotalSize();
+
+ for (Index num_output_coeffs = 0; num_output_coeffs < output_size;) {
+ ScalarNoConst* bcast_output = materialized_output + num_output_coeffs;
+ Index bcast_offset = desc.offset() + output_offset;
+
+ // Broadcast along the bcast dimension.
+ num_output_coeffs += BroadcastBlockAlongBcastDim(
+ params, bcast_offset, scratch, bcast_output, &materialized_input,
+ &materialized_input_size);
+
+ // Switch to the next outer dimension.
+ for (int j = 0; j < idx; ++j) {
+ if (++it[j].count < it[j].size) {
+ output_offset += it[j].output_stride;
+ break;
+ }
+ it[j].count = 0;
+ output_offset -= it[j].output_span;
+ }
+ }
+
+ return block_storage.AsTensorMaterializedBlock();
+ }
+
+ EIGEN_DEVICE_FUNC EvaluatorPointerType data() const { return NULL; }
+
+ const TensorEvaluator<ArgType, Device>& impl() const { return m_impl; }
+
+ Broadcast functor() const { return m_broadcast; }
+#ifdef EIGEN_USE_SYCL
+ // binding placeholder accessors to a command group handler for SYCL
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void bind(
+ cl::sycl::handler& cgh) const {
+ m_impl.bind(cgh);
+ }
+#endif
+ private:
+ static constexpr bool IsColMajor =
+ static_cast<int>(Layout) == static_cast<int>(ColMajor);
+
+ // We will build a general case block broadcasting on top of broadcasting
+ // primitive that will do broadcasting only for the inner dimension(s) along
+ // the first dimension smaller than the input size (it's called `bcast_dim`).
+ //
+ // Example:
+ // dim: 0 1 2 (ColMajor)
+ // input size: [9, 3, 6]
+ // block size: [9, 2, 6]
+ //
+ // We will compute broadcasted block by iterating over the outer dimensions
+ // before `bcast_dim` (only dimension `2` in this example) and computing
+ // broadcasts along the `bcast_dim` (dimension `1` in this example).
+
+ // BlockBroadcastingParams holds precomputed parameters for broadcasting a
+ // single block along the broadcasting dimension. Sizes and strides along the
+ // `bcast_dim` might be invalid, they will be adjusted later in
+ // `BroadcastBlockAlongBcastDim`.
+ struct BlockBroadcastingParams {
+ Dimensions input_dims; // input expression dimensions
+ Dimensions output_dims; // output block sizes
+ Dimensions output_strides; // output block strides
+
+ int inner_dim_count; // count inner dimensions matching in size
+ int bcast_dim; // broadcasting dimension index
+ Index bcast_dim_size; // broadcasting dimension size
+ Index inner_dim_size; // inner dimensions size
+
+ // Block sizes and strides for the input block where all dimensions before
+ // `bcast_dim` are equal to `1`.
+ Dimensions input_block_sizes;
+ Dimensions input_block_strides;
+
+ // Block sizes and strides for blocks with extra dimensions and strides `0`.
+ BroadcastDimensions bcast_block_sizes;
+ BroadcastDimensions bcast_block_strides;
+ BroadcastDimensions bcast_input_strides;
+ };
+
+ struct BlockBroadcastingIteratorState {
+ Index size;
+ Index count;
+ Index output_stride;
+ Index output_span;
+ };
+
+ EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE BlockBroadcastingParams
+ blockBroadcastingParams(TensorBlockDesc& desc) const {
+ BlockBroadcastingParams params;
+
+ params.input_dims = Dimensions(m_impl.dimensions());
+
+ // Output block sizes and strides.
+ params.output_dims = desc.dimensions();
+ params.output_strides = internal::strides<Layout>(params.output_dims);
+
+ // Find the broadcasting dimension (first dimension with output size smaller
+ // that the input size).
+ params.bcast_dim = 0;
+ params.bcast_dim_size = 1;
+ params.inner_dim_size = 1;
+
+ // Count the number of inner dimensions that have the same size in the block
+ // and in the broadcast expression.
+ params.inner_dim_count = 0;
+
+ for (int i = 0; i < NumDims; ++i) {
+ const int dim = IsColMajor ? i : NumDims - i - 1;
+
+ if (params.output_dims[dim] == m_dimensions[dim]) {
+ params.inner_dim_size *= params.output_dims[dim];
+ ++params.inner_dim_count;
+ continue;
+ }
+
+ // First non-matching dimension is the broadcasting dimension.
+ eigen_assert(params.output_dims[dim] < m_dimensions[dim]);
+ params.bcast_dim = dim;
+ params.bcast_dim_size = params.output_dims[dim];
+ break;
+ }
+
+ // Calculate the input block size for looking into the input.
+ for (int i = 0; i < params.inner_dim_count; ++i) {
+ const int dim = IsColMajor ? i : NumDims - i - 1;
+ params.input_block_sizes[dim] = params.input_dims[dim];
+ }
+ for (int i = params.inner_dim_count; i < NumDims; ++i) {
+ const int dim = IsColMajor ? i : NumDims - i - 1;
+ params.input_block_sizes[dim] = 1;
+ }
+ params.input_block_strides =
+ internal::strides<Layout>(params.input_block_sizes);
+
+ // Broadcast with the 0-stride trick: Create 1 extra dim for each
+ // broadcast, set the input stride to 0.
+ //
+ // When ColMajor:
+ //
+ // - bcast_block_sizes:
+ // [d_0, b_0, d_1, b_1, ...]
+ //
+ // - bcast_block_strides:
+ // [output_block_strides[0], output_block_strides[0] * d_0,
+ // output_block_strides[1], output_block_strides[1] * d_1,
+ // ...]
+ //
+ // - bcast_input_strides:
+ // [input_block_strides[0], 0,
+ // input_block_strides[1], 0,
+ // ...].
+ //
+ for (int i = 0; i < params.inner_dim_count; ++i) {
+ const int dim = IsColMajor ? i : NumDims - i - 1;
+
+ const int copy_dim = IsColMajor ? 2 * i : 2 * NumDims - 2 * i - 1;
+ const int broadcast_dim = IsColMajor ? copy_dim + 1 : copy_dim - 1;
+
+ params.bcast_block_sizes[copy_dim] = params.input_dims[dim];
+ params.bcast_block_sizes[broadcast_dim] = m_broadcast[dim];
+ params.bcast_block_strides[copy_dim] = params.output_strides[dim];
+ params.bcast_block_strides[broadcast_dim] =
+ params.output_strides[dim] * params.input_dims[dim];
+ params.bcast_input_strides[copy_dim] = params.input_block_strides[dim];
+ params.bcast_input_strides[broadcast_dim] = 0;
+ }
+
+ for (int i = 2 * params.inner_dim_count; i < 2 * NumDims; ++i) {
+ const int dim = IsColMajor ? i : 2 * NumDims - i - 1;
+ params.bcast_block_sizes[dim] = 1;
+ params.bcast_block_strides[dim] = 0;
+ params.bcast_input_strides[dim] = 0;
+ }
+
+ return params;
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorBlock emptyBlock() const {
+ DSizes<Index, NumDims> dimensions;
+ for (int i = 0; i < NumDims; ++i) dimensions[i] = 0;
+ return TensorBlock(internal::TensorBlockKind::kView, NULL, dimensions);
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Index BroadcastBlockAlongBcastDim(
+ BlockBroadcastingParams params, Index bcast_offset,
+ TensorBlockScratch& scratch, ScalarNoConst* materialized_output,
+ ScalarNoConst** materialized_input,
+ size_t* materialized_input_size) const {
+ if (params.bcast_dim_size == 1) {
+ // We just need one block read using the ready-set values above.
+ return BroadcastBlock(
+ params.input_block_sizes, params.input_block_strides,
+ params.bcast_block_sizes, params.bcast_block_strides,
+ params.bcast_input_strides, bcast_offset, 0, scratch,
+ materialized_output, materialized_input, materialized_input_size);
+
+ } else if (params.input_dims[params.bcast_dim] == 1) {
+ // Broadcast bcast dimension (< NumDims) by bcast_dim_size.
+ const int broadcast_bcast_dim =
+ IsColMajor ? 2 * params.inner_dim_count + 1
+ : 2 * NumDims - 2 * params.inner_dim_count - 2;
+
+ params.bcast_block_sizes[broadcast_bcast_dim] = params.bcast_dim_size;
+ params.bcast_input_strides[broadcast_bcast_dim] = 0;
+ params.bcast_block_strides[broadcast_bcast_dim] =
+ params.output_strides[params.bcast_dim];
+
+ return BroadcastBlock(
+ params.input_block_sizes, params.input_block_strides,
+ params.bcast_block_sizes, params.bcast_block_strides,
+ params.bcast_input_strides, bcast_offset, 0, scratch,
+ materialized_output, materialized_input, materialized_input_size);
+
+ } else {
+ // Keep track of the total number of the coefficients written to the
+ // output block.
+ Index num_output_coeffs = 0;
+
+ // The general case. Let's denote the output block as
+ //
+ // x[..., a:a+bcast_dim_size, :, ..., :]
+ //
+ // where a:a+bcast_dim_size is a slice on the bcast_dim dimension
+ // (< NumDims). We need to split the a:a+bcast_dim_size into possibly 3
+ // sub-blocks:
+ //
+ // (1) a:b, where b is the smallest multiple of
+ // input_dims[bcast_dim_start] in [a, a+bcast_dim_size].
+ //
+ // (2) b:c, where c is the largest multiple of input_dims[bcast_dim_start]
+ // in [a, a+bcast_dim_size].
+ //
+ // (3) c:a+bcast_dim_size .
+ //
+ // Or, when b and c do not exist, we just need to process the whole block
+ // together.
+
+ // Find a.
+ const Index bcast_dim_left_index =
+ bcast_offset / m_outputStrides[params.bcast_dim];
+
+ // Find b and c.
+ const Index input_bcast_dim_size = params.input_dims[params.bcast_dim];
+
+ // First multiple after a. This is b when <= bcast_dim_left_index +
+ // bcast_dim_size.
+ const Index first_multiple =
+ divup<Index>(bcast_dim_left_index, input_bcast_dim_size) *
+ input_bcast_dim_size;
+
+ if (first_multiple <= bcast_dim_left_index + params.bcast_dim_size) {
+ // b exists, so does c. Find it.
+ const Index last_multiple =
+ (bcast_dim_left_index + params.bcast_dim_size) /
+ input_bcast_dim_size * input_bcast_dim_size;
+ const int copy_bcast_dim =
+ IsColMajor ? 2 * params.inner_dim_count
+ : 2 * NumDims - 2 * params.inner_dim_count - 1;
+ const int broadcast_bcast_dim =
+ IsColMajor ? 2 * params.inner_dim_count + 1
+ : 2 * NumDims - 2 * params.inner_dim_count - 2;
+
+ if (first_multiple > bcast_dim_left_index) {
+ const Index head_size = first_multiple - bcast_dim_left_index;
+ params.input_block_sizes[params.bcast_dim] = head_size;
+ params.bcast_block_sizes[copy_bcast_dim] = head_size;
+ params.bcast_input_strides[copy_bcast_dim] =
+ params.input_block_strides[params.bcast_dim];
+ params.bcast_block_strides[copy_bcast_dim] =
+ params.output_strides[params.bcast_dim];
+ params.bcast_block_sizes[broadcast_bcast_dim] = 1;
+ params.bcast_input_strides[broadcast_bcast_dim] = 0;
+ params.bcast_block_strides[broadcast_bcast_dim] =
+ params.output_strides[params.bcast_dim] *
+ params.input_dims[params.bcast_dim];
+
+ num_output_coeffs += BroadcastBlock(
+ params.input_block_sizes, params.input_block_strides,
+ params.bcast_block_sizes, params.bcast_block_strides,
+ params.bcast_input_strides, bcast_offset, 0, scratch,
+ materialized_output, materialized_input, materialized_input_size);
+ }
+ if (first_multiple < last_multiple) {
+ params.input_block_sizes[params.bcast_dim] = input_bcast_dim_size;
+ params.bcast_block_sizes[copy_bcast_dim] = input_bcast_dim_size;
+ params.bcast_input_strides[copy_bcast_dim] =
+ params.input_block_strides[params.bcast_dim];
+ params.bcast_block_strides[copy_bcast_dim] =
+ params.output_strides[params.bcast_dim];
+ params.bcast_block_sizes[broadcast_bcast_dim] =
+ (last_multiple - first_multiple) / input_bcast_dim_size;
+ params.bcast_input_strides[broadcast_bcast_dim] = 0;
+ params.bcast_block_strides[broadcast_bcast_dim] =
+ params.output_strides[params.bcast_dim] *
+ params.input_dims[params.bcast_dim];
+ const Index offset = (first_multiple - bcast_dim_left_index) *
+ m_outputStrides[params.bcast_dim];
+
+ num_output_coeffs += BroadcastBlock(
+ params.input_block_sizes, params.input_block_strides,
+ params.bcast_block_sizes, params.bcast_block_strides,
+ params.bcast_input_strides, bcast_offset, offset, scratch,
+ materialized_output, materialized_input, materialized_input_size);
+ }
+ if (last_multiple < bcast_dim_left_index + params.bcast_dim_size) {
+ const Index tail_size =
+ bcast_dim_left_index + params.bcast_dim_size - last_multiple;
+ params.input_block_sizes[params.bcast_dim] = tail_size;
+ params.bcast_block_sizes[copy_bcast_dim] = tail_size;
+ params.bcast_input_strides[copy_bcast_dim] =
+ params.input_block_strides[params.bcast_dim];
+ params.bcast_block_strides[copy_bcast_dim] =
+ params.output_strides[params.bcast_dim];
+ params.bcast_block_sizes[broadcast_bcast_dim] = 1;
+ params.bcast_input_strides[broadcast_bcast_dim] = 0;
+ params.bcast_block_strides[broadcast_bcast_dim] =
+ params.output_strides[params.bcast_dim] *
+ params.input_dims[params.bcast_dim];
+ const Index offset = (last_multiple - bcast_dim_left_index) *
+ m_outputStrides[params.bcast_dim];
+
+ num_output_coeffs += BroadcastBlock(
+ params.input_block_sizes, params.input_block_strides,
+ params.bcast_block_sizes, params.bcast_block_strides,
+ params.bcast_input_strides, bcast_offset, offset, scratch,
+ materialized_output, materialized_input, materialized_input_size);
+ }
+ } else {
+ // b and c do not exist.
+ const int copy_bcast_dim =
+ IsColMajor ? 2 * params.inner_dim_count
+ : 2 * NumDims - 2 * params.inner_dim_count - 1;
+ params.input_block_sizes[params.bcast_dim] = params.bcast_dim_size;
+ params.bcast_block_sizes[copy_bcast_dim] = params.bcast_dim_size;
+ params.bcast_input_strides[copy_bcast_dim] =
+ params.input_block_strides[params.bcast_dim];
+ params.bcast_block_strides[copy_bcast_dim] =
+ params.output_strides[params.bcast_dim];
+
+ num_output_coeffs += BroadcastBlock(
+ params.input_block_sizes, params.input_block_strides,
+ params.bcast_block_sizes, params.bcast_block_strides,
+ params.bcast_input_strides, bcast_offset, 0, scratch,
+ materialized_output, materialized_input, materialized_input_size);
+ }
+
+ return num_output_coeffs;
+ }
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Index BroadcastBlock(
+ const Dimensions& input_block_sizes,
+ const Dimensions& input_block_strides,
+ const BroadcastDimensions& bcast_block_sizes,
+ const BroadcastDimensions& bcast_block_strides,
+ const BroadcastDimensions& bcast_input_strides, Index bcast_offset,
+ Index offset, TensorBlockScratch& scratch,
+ ScalarNoConst* materialized_output, ScalarNoConst** materialized_input,
+ size_t* materialized_input_size) const {
+ // ---------------------------------------------------------------------- //
+ // Tensor block descriptor for reading block from the input.
+ const Index input_offset = bcast_offset + offset;
+ TensorBlockDesc input_desc(
+ IsColMajor ? indexColMajor(input_offset) : indexRowMajor(input_offset),
+ input_block_sizes);
+
+ ArgTensorBlock input_block = m_impl.block(input_desc, scratch);
+
+ // ---------------------------------------------------------------------- //
+ // Materialize input block into a temporary memory buffer only if it's not
+ // already available in the arg block.
+ const ScalarNoConst* input_buffer = NULL;
+
+ if (input_block.data() != NULL) {
+ // Input block already has raw data, there is no need to materialize it.
+ input_buffer = input_block.data();
+
+ } else {
+ // Otherwise we have to do block assignment into a temporary buffer.
+
+ // Maybe reuse previously allocated buffer, or allocate a new one with a
+ // scratch allocator.
+ const size_t input_total_size = input_block_sizes.TotalSize();
+ if (*materialized_input == NULL ||
+ *materialized_input_size < input_total_size) {
+ *materialized_input_size = input_total_size;
+ void* mem = scratch.allocate(*materialized_input_size * sizeof(Scalar));
+ *materialized_input = static_cast<ScalarNoConst*>(mem);
+ }
+
+ typedef internal::TensorBlockAssignment<
+ ScalarNoConst, NumDims, typename ArgTensorBlock::XprType, Index>
+ TensorBlockAssignment;
+
+ TensorBlockAssignment::Run(
+ TensorBlockAssignment::target(input_block_sizes, input_block_strides,
+ *materialized_input),
+ input_block.expr());
+
+ input_buffer = *materialized_input;
+ }
+
+ // ---------------------------------------------------------------------- //
+ // Copy data from materialized input block to the materialized output, using
+ // given broadcast strides (strides with zeroes).
+ typedef internal::TensorBlockIO<ScalarNoConst, Index, 2 * NumDims, Layout>
+ TensorBlockIO;
+
+ typename TensorBlockIO::Src src(bcast_input_strides, input_buffer);
+ typename TensorBlockIO::Dst dst(bcast_block_sizes, bcast_block_strides,
+ materialized_output + offset);
+
+ return TensorBlockIO::Copy(dst, src);
+ }
+
+protected:
+ const Device EIGEN_DEVICE_REF m_device;
+ const std::remove_reference_t<Broadcast> m_broadcast;
+ Dimensions m_dimensions;
+ array<Index, NumDims> m_outputStrides;
+ array<Index, NumDims> m_inputStrides;
+ TensorEvaluator<ArgType, Device> m_impl;
+};
+
+
+} // end namespace Eigen
+
+#endif // EIGEN_CXX11_TENSOR_TENSOR_BROADCASTING_H
diff --git a/unsupported/Eigen/CXX11/src/Tensor/TensorChipping.h b/unsupported/Eigen/CXX11/src/Tensor/TensorChipping.h
new file mode 100644
index 0000000..ef01e30
--- /dev/null
+++ b/unsupported/Eigen/CXX11/src/Tensor/TensorChipping.h
@@ -0,0 +1,517 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_CXX11_TENSOR_TENSOR_CHIPPING_H
+#define EIGEN_CXX11_TENSOR_TENSOR_CHIPPING_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+/** \class TensorKChippingReshaping
+ * \ingroup CXX11_Tensor_Module
+ *
+ * \brief A chip is a thin slice, corresponding to a column or a row in a 2-d tensor.
+ *
+ *
+ */
+
+namespace internal {
+template<DenseIndex DimId, typename XprType>
+struct traits<TensorChippingOp<DimId, XprType> > : public traits<XprType>
+{
+ typedef typename XprType::Scalar Scalar;
+ typedef traits<XprType> XprTraits;
+ typedef typename XprTraits::StorageKind StorageKind;
+ typedef typename XprTraits::Index Index;
+ typedef typename XprType::Nested Nested;
+ typedef std::remove_reference_t<Nested> Nested_;
+ static constexpr int NumDimensions = XprTraits::NumDimensions - 1;
+ static constexpr int Layout = XprTraits::Layout;
+ typedef typename XprTraits::PointerType PointerType;
+};
+
+template<DenseIndex DimId, typename XprType>
+struct eval<TensorChippingOp<DimId, XprType>, Eigen::Dense>
+{
+ typedef const TensorChippingOp<DimId, XprType> EIGEN_DEVICE_REF type;
+};
+
+template<DenseIndex DimId, typename XprType>
+struct nested<TensorChippingOp<DimId, XprType>, 1, typename eval<TensorChippingOp<DimId, XprType> >::type>
+{
+ typedef TensorChippingOp<DimId, XprType> type;
+};
+
+template <DenseIndex DimId>
+struct DimensionId
+{
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE DimensionId(DenseIndex dim) {
+ EIGEN_UNUSED_VARIABLE(dim);
+ eigen_assert(dim == DimId);
+ }
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE DenseIndex actualDim() const {
+ return DimId;
+ }
+};
+template <>
+struct DimensionId<Dynamic>
+{
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE DimensionId(DenseIndex dim) : actual_dim(dim) {
+ eigen_assert(dim >= 0);
+ }
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE DenseIndex actualDim() const {
+ return actual_dim;
+ }
+ private:
+ const DenseIndex actual_dim;
+};
+
+
+} // end namespace internal
+
+
+
+template<DenseIndex DimId, typename XprType>
+class TensorChippingOp : public TensorBase<TensorChippingOp<DimId, XprType> >
+{
+ public:
+ typedef TensorBase<TensorChippingOp<DimId, XprType> > Base;
+ typedef typename Eigen::internal::traits<TensorChippingOp>::Scalar Scalar;
+ typedef typename Eigen::NumTraits<Scalar>::Real RealScalar;
+ typedef typename XprType::CoeffReturnType CoeffReturnType;
+ typedef typename Eigen::internal::nested<TensorChippingOp>::type Nested;
+ typedef typename Eigen::internal::traits<TensorChippingOp>::StorageKind StorageKind;
+ typedef typename Eigen::internal::traits<TensorChippingOp>::Index Index;
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorChippingOp(const XprType& expr, const Index offset, const Index dim)
+ : m_xpr(expr), m_offset(offset), m_dim(dim) {
+ }
+
+ EIGEN_DEVICE_FUNC
+ const Index offset() const { return m_offset; }
+ EIGEN_DEVICE_FUNC
+ const Index dim() const { return m_dim.actualDim(); }
+
+ EIGEN_DEVICE_FUNC
+ const internal::remove_all_t<typename XprType::Nested>&
+ expression() const { return m_xpr; }
+
+ EIGEN_TENSOR_INHERIT_ASSIGNMENT_OPERATORS(TensorChippingOp)
+
+ protected:
+ typename XprType::Nested m_xpr;
+ const Index m_offset;
+ const internal::DimensionId<DimId> m_dim;
+};
+
+
+// Eval as rvalue
+template<DenseIndex DimId, typename ArgType, typename Device>
+struct TensorEvaluator<const TensorChippingOp<DimId, ArgType>, Device>
+{
+ typedef TensorChippingOp<DimId, ArgType> XprType;
+ static constexpr int NumInputDims = internal::array_size<typename TensorEvaluator<ArgType, Device>::Dimensions>::value;
+ static constexpr int NumDims = NumInputDims-1;
+ typedef typename XprType::Index Index;
+ typedef DSizes<Index, NumDims> Dimensions;
+ typedef typename XprType::Scalar Scalar;
+ typedef typename XprType::CoeffReturnType CoeffReturnType;
+ typedef typename PacketType<CoeffReturnType, Device>::type PacketReturnType;
+ static constexpr int PacketSize = PacketType<CoeffReturnType, Device>::size;
+ typedef StorageMemory<CoeffReturnType, Device> Storage;
+ typedef typename Storage::Type EvaluatorPointerType;
+ static constexpr int Layout = TensorEvaluator<ArgType, Device>::Layout;
+
+ enum {
+ // Alignment can't be guaranteed at compile time since it depends on the
+ // slice offsets.
+ IsAligned = false,
+ PacketAccess = TensorEvaluator<ArgType, Device>::PacketAccess,
+ BlockAccess = TensorEvaluator<ArgType, Device>::BlockAccess,
+ // Chipping of outer-most dimension is a trivial operation, because we can
+ // read and write directly from the underlying tensor using single offset.
+ IsOuterChipping = (Layout == ColMajor && DimId == NumInputDims - 1) ||
+ (Layout == RowMajor && DimId == 0),
+ // Chipping inner-most dimension.
+ IsInnerChipping = (Layout == ColMajor && DimId == 0) ||
+ (Layout == RowMajor && DimId == NumInputDims - 1),
+ // Prefer block access if the underlying expression prefers it, otherwise
+ // only if chipping is not trivial.
+ PreferBlockAccess = TensorEvaluator<ArgType, Device>::PreferBlockAccess ||
+ !IsOuterChipping,
+ CoordAccess = false, // to be implemented
+ RawAccess = false
+ };
+
+ typedef std::remove_const_t<Scalar> ScalarNoConst;
+
+ //===- Tensor block evaluation strategy (see TensorBlock.h) -------------===//
+ typedef internal::TensorBlockDescriptor<NumDims, Index> TensorBlockDesc;
+ typedef internal::TensorBlockScratchAllocator<Device> TensorBlockScratch;
+
+ typedef internal::TensorBlockDescriptor<NumInputDims, Index>
+ ArgTensorBlockDesc;
+ typedef typename TensorEvaluator<const ArgType, Device>::TensorBlock
+ ArgTensorBlock;
+
+ typedef typename internal::TensorMaterializedBlock<ScalarNoConst, NumDims,
+ Layout, Index>
+ TensorBlock;
+ //===--------------------------------------------------------------------===//
+
+ EIGEN_STRONG_INLINE TensorEvaluator(const XprType& op, const Device& device)
+ : m_impl(op.expression(), device), m_dim(op.dim()), m_device(device)
+ {
+ EIGEN_STATIC_ASSERT((NumInputDims >= 1), YOU_MADE_A_PROGRAMMING_MISTAKE);
+ eigen_assert(NumInputDims > m_dim.actualDim());
+
+ const typename TensorEvaluator<ArgType, Device>::Dimensions& input_dims = m_impl.dimensions();
+ eigen_assert(op.offset() < input_dims[m_dim.actualDim()]);
+
+ int j = 0;
+ for (int i = 0; i < NumInputDims; ++i) {
+ if (i != m_dim.actualDim()) {
+ m_dimensions[j] = input_dims[i];
+ ++j;
+ }
+ }
+
+ m_stride = 1;
+ m_inputStride = 1;
+ if (static_cast<int>(Layout) == static_cast<int>(ColMajor)) {
+ for (int i = 0; i < m_dim.actualDim(); ++i) {
+ m_stride *= input_dims[i];
+ m_inputStride *= input_dims[i];
+ }
+ } else {
+ for (int i = NumInputDims-1; i > m_dim.actualDim(); --i) {
+ m_stride *= input_dims[i];
+ m_inputStride *= input_dims[i];
+ }
+ }
+ m_inputStride *= input_dims[m_dim.actualDim()];
+ m_inputOffset = m_stride * op.offset();
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Dimensions& dimensions() const { return m_dimensions; }
+
+ EIGEN_STRONG_INLINE bool evalSubExprsIfNeeded(EvaluatorPointerType) {
+ m_impl.evalSubExprsIfNeeded(NULL);
+ return true;
+ }
+
+ EIGEN_STRONG_INLINE void cleanup() {
+ m_impl.cleanup();
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE CoeffReturnType coeff(Index index) const
+ {
+ return m_impl.coeff(srcCoeff(index));
+ }
+
+ template<int LoadMode>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE PacketReturnType packet(Index index) const
+ {
+ eigen_assert(index+PacketSize-1 < dimensions().TotalSize());
+
+ if (isInnerChipping()) {
+ // m_stride is equal to 1, so let's avoid the integer division.
+ eigen_assert(m_stride == 1);
+ Index inputIndex = index * m_inputStride + m_inputOffset;
+ EIGEN_ALIGN_MAX std::remove_const_t<CoeffReturnType> values[PacketSize];
+ EIGEN_UNROLL_LOOP
+ for (int i = 0; i < PacketSize; ++i) {
+ values[i] = m_impl.coeff(inputIndex);
+ inputIndex += m_inputStride;
+ }
+ PacketReturnType rslt = internal::pload<PacketReturnType>(values);
+ return rslt;
+ } else if (isOuterChipping()) {
+ // m_stride is always greater than index, so let's avoid the integer division.
+ eigen_assert(m_stride > index);
+ return m_impl.template packet<LoadMode>(index + m_inputOffset);
+ } else {
+ const Index idx = index / m_stride;
+ const Index rem = index - idx * m_stride;
+ if (rem + PacketSize <= m_stride) {
+ Index inputIndex = idx * m_inputStride + m_inputOffset + rem;
+ return m_impl.template packet<LoadMode>(inputIndex);
+ } else {
+ // Cross the stride boundary. Fallback to slow path.
+ EIGEN_ALIGN_MAX std::remove_const_t<CoeffReturnType> values[PacketSize];
+ EIGEN_UNROLL_LOOP
+ for (int i = 0; i < PacketSize; ++i) {
+ values[i] = coeff(index);
+ ++index;
+ }
+ PacketReturnType rslt = internal::pload<PacketReturnType>(values);
+ return rslt;
+ }
+ }
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorOpCost
+ costPerCoeff(bool vectorized) const {
+ double cost = 0;
+ if ((static_cast<int>(Layout) == static_cast<int>(ColMajor) &&
+ m_dim.actualDim() == 0) ||
+ (static_cast<int>(Layout) == static_cast<int>(RowMajor) &&
+ m_dim.actualDim() == NumInputDims - 1)) {
+ cost += TensorOpCost::MulCost<Index>() + TensorOpCost::AddCost<Index>();
+ } else if ((static_cast<int>(Layout) == static_cast<int>(ColMajor) &&
+ m_dim.actualDim() == NumInputDims - 1) ||
+ (static_cast<int>(Layout) == static_cast<int>(RowMajor) &&
+ m_dim.actualDim() == 0)) {
+ cost += TensorOpCost::AddCost<Index>();
+ } else {
+ cost += 3 * TensorOpCost::MulCost<Index>() + TensorOpCost::DivCost<Index>() +
+ 3 * TensorOpCost::AddCost<Index>();
+ }
+
+ return m_impl.costPerCoeff(vectorized) +
+ TensorOpCost(0, 0, cost, vectorized, PacketSize);
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ internal::TensorBlockResourceRequirements getResourceRequirements() const {
+ const size_t target_size = m_device.lastLevelCacheSize();
+ return internal::TensorBlockResourceRequirements::merge(
+ internal::TensorBlockResourceRequirements::skewed<Scalar>(target_size),
+ m_impl.getResourceRequirements());
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorBlock
+ block(TensorBlockDesc& desc, TensorBlockScratch& scratch,
+ bool root_of_expr_ast = false) const {
+ const Index chip_dim = m_dim.actualDim();
+
+ DSizes<Index, NumInputDims> input_block_dims;
+ for (int i = 0; i < NumInputDims; ++i) {
+ input_block_dims[i]
+ = i < chip_dim ? desc.dimension(i)
+ : i > chip_dim ? desc.dimension(i - 1)
+ : 1;
+ }
+
+ ArgTensorBlockDesc arg_desc(srcCoeff(desc.offset()), input_block_dims);
+
+ // Try to reuse destination buffer for materializing argument block.
+ if (desc.HasDestinationBuffer()) {
+ DSizes<Index, NumInputDims> arg_destination_strides;
+ for (int i = 0; i < NumInputDims; ++i) {
+ arg_destination_strides[i]
+ = i < chip_dim ? desc.destination().strides()[i]
+ : i > chip_dim ? desc.destination().strides()[i - 1]
+ : 0; // for dimensions of size `1` stride should never be used.
+ }
+
+ arg_desc.template AddDestinationBuffer<Layout>(
+ desc.destination().template data<ScalarNoConst>(),
+ arg_destination_strides);
+ }
+
+ ArgTensorBlock arg_block = m_impl.block(arg_desc, scratch, root_of_expr_ast);
+ if (!arg_desc.HasDestinationBuffer()) desc.DropDestinationBuffer();
+
+ if (arg_block.data() != NULL) {
+ // Forward argument block buffer if possible.
+ return TensorBlock(arg_block.kind(), arg_block.data(),
+ desc.dimensions());
+
+ } else {
+ // Assign argument block expression to a buffer.
+
+ // Prepare storage for the materialized chipping result.
+ const typename TensorBlock::Storage block_storage =
+ TensorBlock::prepareStorage(desc, scratch);
+
+ typedef internal::TensorBlockAssignment<
+ ScalarNoConst, NumInputDims, typename ArgTensorBlock::XprType, Index>
+ TensorBlockAssignment;
+
+ TensorBlockAssignment::Run(
+ TensorBlockAssignment::target(
+ arg_desc.dimensions(),
+ internal::strides<Layout>(arg_desc.dimensions()),
+ block_storage.data()),
+ arg_block.expr());
+
+ return block_storage.AsTensorMaterializedBlock();
+ }
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE typename Storage::Type data() const {
+ typename Storage::Type result = constCast(m_impl.data());
+ if (isOuterChipping() && result) {
+ return result + m_inputOffset;
+ } else {
+ return NULL;
+ }
+ }
+#ifdef EIGEN_USE_SYCL
+ // binding placeholder accessors to a command group handler for SYCL
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void bind(cl::sycl::handler &cgh) const {
+ m_impl.bind(cgh);
+ }
+#endif
+
+ protected:
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Index srcCoeff(Index index) const
+ {
+ Index inputIndex;
+ if (isInnerChipping()) {
+ // m_stride is equal to 1, so let's avoid the integer division.
+ eigen_assert(m_stride == 1);
+ inputIndex = index * m_inputStride + m_inputOffset;
+ } else if (isOuterChipping()) {
+ // m_stride is always greater than index, so let's avoid the integer
+ // division.
+ eigen_assert(m_stride > index);
+ inputIndex = index + m_inputOffset;
+ } else {
+ const Index idx = index / m_stride;
+ inputIndex = idx * m_inputStride + m_inputOffset;
+ index -= idx * m_stride;
+ inputIndex += index;
+ }
+ return inputIndex;
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE bool isInnerChipping() const {
+ return IsInnerChipping ||
+ (static_cast<int>(Layout) == ColMajor && m_dim.actualDim() == 0) ||
+ (static_cast<int>(Layout) == RowMajor && m_dim.actualDim() == NumInputDims - 1);
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE bool isOuterChipping() const {
+ return IsOuterChipping ||
+ (static_cast<int>(Layout) == ColMajor && m_dim.actualDim() == NumInputDims-1) ||
+ (static_cast<int>(Layout) == RowMajor && m_dim.actualDim() == 0);
+ }
+
+ Dimensions m_dimensions;
+ Index m_stride;
+ Index m_inputOffset;
+ Index m_inputStride;
+ TensorEvaluator<ArgType, Device> m_impl;
+ const internal::DimensionId<DimId> m_dim;
+ const Device EIGEN_DEVICE_REF m_device;
+};
+
+
+// Eval as lvalue
+template<DenseIndex DimId, typename ArgType, typename Device>
+struct TensorEvaluator<TensorChippingOp<DimId, ArgType>, Device>
+ : public TensorEvaluator<const TensorChippingOp<DimId, ArgType>, Device>
+{
+ typedef TensorEvaluator<const TensorChippingOp<DimId, ArgType>, Device> Base;
+ typedef TensorChippingOp<DimId, ArgType> XprType;
+ static constexpr int NumInputDims = internal::array_size<typename TensorEvaluator<ArgType, Device>::Dimensions>::value;
+ static constexpr int NumDims = NumInputDims-1;
+ typedef typename XprType::Index Index;
+ typedef DSizes<Index, NumDims> Dimensions;
+ typedef typename XprType::Scalar Scalar;
+ typedef typename XprType::CoeffReturnType CoeffReturnType;
+ typedef typename PacketType<CoeffReturnType, Device>::type PacketReturnType;
+ static constexpr int PacketSize = PacketType<CoeffReturnType, Device>::size;
+
+ enum {
+ IsAligned = false,
+ PacketAccess = TensorEvaluator<ArgType, Device>::PacketAccess,
+ BlockAccess = TensorEvaluator<ArgType, Device>::RawAccess,
+ Layout = TensorEvaluator<ArgType, Device>::Layout,
+ RawAccess = false
+ };
+
+ //===- Tensor block evaluation strategy (see TensorBlock.h) -------------===//
+ typedef internal::TensorBlockDescriptor<NumDims, Index> TensorBlockDesc;
+ //===--------------------------------------------------------------------===//
+
+ EIGEN_STRONG_INLINE TensorEvaluator(const XprType& op, const Device& device)
+ : Base(op, device)
+ { }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE CoeffReturnType& coeffRef(Index index)
+ {
+ return this->m_impl.coeffRef(this->srcCoeff(index));
+ }
+
+ template <int StoreMode> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ void writePacket(Index index, const PacketReturnType& x)
+ {
+ if (this->isInnerChipping()) {
+ // m_stride is equal to 1, so let's avoid the integer division.
+ eigen_assert(this->m_stride == 1);
+ EIGEN_ALIGN_MAX std::remove_const_t<CoeffReturnType> values[PacketSize];
+ internal::pstore<CoeffReturnType, PacketReturnType>(values, x);
+ Index inputIndex = index * this->m_inputStride + this->m_inputOffset;
+ EIGEN_UNROLL_LOOP
+ for (int i = 0; i < PacketSize; ++i) {
+ this->m_impl.coeffRef(inputIndex) = values[i];
+ inputIndex += this->m_inputStride;
+ }
+ } else if (this->isOuterChipping()) {
+ // m_stride is always greater than index, so let's avoid the integer division.
+ eigen_assert(this->m_stride > index);
+ this->m_impl.template writePacket<StoreMode>(index + this->m_inputOffset, x);
+ } else {
+ const Index idx = index / this->m_stride;
+ const Index rem = index - idx * this->m_stride;
+ if (rem + PacketSize <= this->m_stride) {
+ const Index inputIndex = idx * this->m_inputStride + this->m_inputOffset + rem;
+ this->m_impl.template writePacket<StoreMode>(inputIndex, x);
+ } else {
+ // Cross stride boundary. Fallback to slow path.
+ EIGEN_ALIGN_MAX std::remove_const_t<CoeffReturnType> values[PacketSize];
+ internal::pstore<CoeffReturnType, PacketReturnType>(values, x);
+ EIGEN_UNROLL_LOOP
+ for (int i = 0; i < PacketSize; ++i) {
+ this->coeffRef(index) = values[i];
+ ++index;
+ }
+ }
+ }
+ }
+
+ template <typename TensorBlock>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void writeBlock(
+ const TensorBlockDesc& desc, const TensorBlock& block) {
+ eigen_assert(this->m_impl.data() != NULL);
+
+ const Index chip_dim = this->m_dim.actualDim();
+
+ DSizes<Index, NumInputDims> input_block_dims;
+ for (int i = 0; i < NumInputDims; ++i) {
+ input_block_dims[i] = i < chip_dim ? desc.dimension(i)
+ : i > chip_dim ? desc.dimension(i - 1)
+ : 1;
+ }
+
+ typedef TensorReshapingOp<const DSizes<Index, NumInputDims>,
+ const typename TensorBlock::XprType>
+ TensorBlockExpr;
+
+ typedef internal::TensorBlockAssignment<Scalar, NumInputDims,
+ TensorBlockExpr, Index>
+ TensorBlockAssign;
+
+ TensorBlockAssign::Run(
+ TensorBlockAssign::target(
+ input_block_dims,
+ internal::strides<Layout>(this->m_impl.dimensions()),
+ this->m_impl.data(), this->srcCoeff(desc.offset())),
+ block.expr().reshape(input_block_dims));
+ }
+};
+
+
+} // end namespace Eigen
+
+#endif // EIGEN_CXX11_TENSOR_TENSOR_CHIPPING_H
diff --git a/unsupported/Eigen/CXX11/src/Tensor/TensorConcatenation.h b/unsupported/Eigen/CXX11/src/Tensor/TensorConcatenation.h
new file mode 100644
index 0000000..073be81
--- /dev/null
+++ b/unsupported/Eigen/CXX11/src/Tensor/TensorConcatenation.h
@@ -0,0 +1,379 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_CXX11_TENSOR_TENSOR_CONCATENATION_H
+#define EIGEN_CXX11_TENSOR_TENSOR_CONCATENATION_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+/** \class TensorConcatenationOp
+ * \ingroup CXX11_Tensor_Module
+ *
+ * \brief Tensor concatenation class.
+ *
+ *
+ */
+namespace internal {
+template<typename Axis, typename LhsXprType, typename RhsXprType>
+struct traits<TensorConcatenationOp<Axis, LhsXprType, RhsXprType> >
+{
+ // Type promotion to handle the case where the types of the lhs and the rhs are different.
+ typedef typename promote_storage_type<typename LhsXprType::Scalar,
+ typename RhsXprType::Scalar>::ret Scalar;
+ typedef typename promote_storage_type<typename traits<LhsXprType>::StorageKind,
+ typename traits<RhsXprType>::StorageKind>::ret StorageKind;
+ typedef typename promote_index_type<typename traits<LhsXprType>::Index,
+ typename traits<RhsXprType>::Index>::type Index;
+ typedef typename LhsXprType::Nested LhsNested;
+ typedef typename RhsXprType::Nested RhsNested;
+ typedef std::remove_reference_t<LhsNested> LhsNested_;
+ typedef std::remove_reference_t<RhsNested> RhsNested_;
+ static constexpr int NumDimensions = traits<LhsXprType>::NumDimensions;
+ static constexpr int Layout = traits<LhsXprType>::Layout;
+ enum { Flags = 0 };
+ typedef std::conditional_t<Pointer_type_promotion<typename LhsXprType::Scalar, Scalar>::val,
+ typename traits<LhsXprType>::PointerType, typename traits<RhsXprType>::PointerType> PointerType;
+};
+
+template<typename Axis, typename LhsXprType, typename RhsXprType>
+struct eval<TensorConcatenationOp<Axis, LhsXprType, RhsXprType>, Eigen::Dense>
+{
+ typedef const TensorConcatenationOp<Axis, LhsXprType, RhsXprType>& type;
+};
+
+template<typename Axis, typename LhsXprType, typename RhsXprType>
+struct nested<TensorConcatenationOp<Axis, LhsXprType, RhsXprType>, 1, typename eval<TensorConcatenationOp<Axis, LhsXprType, RhsXprType> >::type>
+{
+ typedef TensorConcatenationOp<Axis, LhsXprType, RhsXprType> type;
+};
+
+} // end namespace internal
+
+
+template<typename Axis, typename LhsXprType, typename RhsXprType>
+class TensorConcatenationOp : public TensorBase<TensorConcatenationOp<Axis, LhsXprType, RhsXprType>, WriteAccessors>
+{
+ public:
+ typedef TensorBase<TensorConcatenationOp<Axis, LhsXprType, RhsXprType>, WriteAccessors> Base;
+ typedef typename internal::traits<TensorConcatenationOp>::Scalar Scalar;
+ typedef typename internal::traits<TensorConcatenationOp>::StorageKind StorageKind;
+ typedef typename internal::traits<TensorConcatenationOp>::Index Index;
+ typedef typename internal::nested<TensorConcatenationOp>::type Nested;
+ typedef typename internal::promote_storage_type<typename LhsXprType::CoeffReturnType,
+ typename RhsXprType::CoeffReturnType>::ret CoeffReturnType;
+ typedef typename NumTraits<Scalar>::Real RealScalar;
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorConcatenationOp(const LhsXprType& lhs, const RhsXprType& rhs, Axis axis)
+ : m_lhs_xpr(lhs), m_rhs_xpr(rhs), m_axis(axis) {}
+
+ EIGEN_DEVICE_FUNC
+ const internal::remove_all_t<typename LhsXprType::Nested>&
+ lhsExpression() const { return m_lhs_xpr; }
+
+ EIGEN_DEVICE_FUNC
+ const internal::remove_all_t<typename RhsXprType::Nested>&
+ rhsExpression() const { return m_rhs_xpr; }
+
+ EIGEN_DEVICE_FUNC const Axis& axis() const { return m_axis; }
+
+ EIGEN_TENSOR_INHERIT_ASSIGNMENT_OPERATORS(TensorConcatenationOp)
+ protected:
+ typename LhsXprType::Nested m_lhs_xpr;
+ typename RhsXprType::Nested m_rhs_xpr;
+ const Axis m_axis;
+};
+
+
+// Eval as rvalue
+template<typename Axis, typename LeftArgType, typename RightArgType, typename Device>
+struct TensorEvaluator<const TensorConcatenationOp<Axis, LeftArgType, RightArgType>, Device>
+{
+ typedef TensorConcatenationOp<Axis, LeftArgType, RightArgType> XprType;
+ typedef typename XprType::Index Index;
+ static constexpr int NumDims = internal::array_size<typename TensorEvaluator<LeftArgType, Device>::Dimensions>::value;
+ static constexpr int RightNumDims = internal::array_size<typename TensorEvaluator<RightArgType, Device>::Dimensions>::value;
+ typedef DSizes<Index, NumDims> Dimensions;
+ typedef typename XprType::Scalar Scalar;
+ typedef typename XprType::CoeffReturnType CoeffReturnType;
+ typedef typename PacketType<CoeffReturnType, Device>::type PacketReturnType;
+ typedef StorageMemory<CoeffReturnType, Device> Storage;
+ typedef typename Storage::Type EvaluatorPointerType;
+ static constexpr int Layout = TensorEvaluator<LeftArgType, Device>::Layout;
+ enum {
+ IsAligned = false,
+ PacketAccess = TensorEvaluator<LeftArgType, Device>::PacketAccess &&
+ TensorEvaluator<RightArgType, Device>::PacketAccess,
+ BlockAccess = false,
+ PreferBlockAccess = TensorEvaluator<LeftArgType, Device>::PreferBlockAccess ||
+ TensorEvaluator<RightArgType, Device>::PreferBlockAccess,
+ RawAccess = false
+ };
+
+ //===- Tensor block evaluation strategy (see TensorBlock.h) -------------===//
+ typedef internal::TensorBlockNotImplemented TensorBlock;
+ //===--------------------------------------------------------------------===//
+
+ EIGEN_STRONG_INLINE TensorEvaluator(const XprType& op, const Device& device)
+ : m_leftImpl(op.lhsExpression(), device), m_rightImpl(op.rhsExpression(), device), m_axis(op.axis())
+ {
+ EIGEN_STATIC_ASSERT((static_cast<int>(TensorEvaluator<LeftArgType, Device>::Layout) == static_cast<int>(TensorEvaluator<RightArgType, Device>::Layout) || NumDims == 1), YOU_MADE_A_PROGRAMMING_MISTAKE);
+ EIGEN_STATIC_ASSERT((NumDims == RightNumDims), YOU_MADE_A_PROGRAMMING_MISTAKE);
+ EIGEN_STATIC_ASSERT((NumDims > 0), YOU_MADE_A_PROGRAMMING_MISTAKE);
+
+ eigen_assert(0 <= m_axis && m_axis < NumDims);
+ const Dimensions& lhs_dims = m_leftImpl.dimensions();
+ const Dimensions& rhs_dims = m_rightImpl.dimensions();
+ {
+ int i = 0;
+ for (; i < m_axis; ++i) {
+ eigen_assert(lhs_dims[i] > 0);
+ eigen_assert(lhs_dims[i] == rhs_dims[i]);
+ m_dimensions[i] = lhs_dims[i];
+ }
+ eigen_assert(lhs_dims[i] > 0); // Now i == m_axis.
+ eigen_assert(rhs_dims[i] > 0);
+ m_dimensions[i] = lhs_dims[i] + rhs_dims[i];
+ for (++i; i < NumDims; ++i) {
+ eigen_assert(lhs_dims[i] > 0);
+ eigen_assert(lhs_dims[i] == rhs_dims[i]);
+ m_dimensions[i] = lhs_dims[i];
+ }
+ }
+
+ if (static_cast<int>(Layout) == static_cast<int>(ColMajor)) {
+ m_leftStrides[0] = 1;
+ m_rightStrides[0] = 1;
+ m_outputStrides[0] = 1;
+
+ for (int j = 1; j < NumDims; ++j) {
+ m_leftStrides[j] = m_leftStrides[j-1] * lhs_dims[j-1];
+ m_rightStrides[j] = m_rightStrides[j-1] * rhs_dims[j-1];
+ m_outputStrides[j] = m_outputStrides[j-1] * m_dimensions[j-1];
+ }
+ } else {
+ m_leftStrides[NumDims - 1] = 1;
+ m_rightStrides[NumDims - 1] = 1;
+ m_outputStrides[NumDims - 1] = 1;
+
+ for (int j = NumDims - 2; j >= 0; --j) {
+ m_leftStrides[j] = m_leftStrides[j+1] * lhs_dims[j+1];
+ m_rightStrides[j] = m_rightStrides[j+1] * rhs_dims[j+1];
+ m_outputStrides[j] = m_outputStrides[j+1] * m_dimensions[j+1];
+ }
+ }
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Dimensions& dimensions() const { return m_dimensions; }
+
+ // TODO(phli): Add short-circuit memcpy evaluation if underlying data are linear?
+ EIGEN_STRONG_INLINE bool evalSubExprsIfNeeded(EvaluatorPointerType)
+ {
+ m_leftImpl.evalSubExprsIfNeeded(NULL);
+ m_rightImpl.evalSubExprsIfNeeded(NULL);
+ return true;
+ }
+
+ EIGEN_STRONG_INLINE void cleanup()
+ {
+ m_leftImpl.cleanup();
+ m_rightImpl.cleanup();
+ }
+
+ // TODO(phli): attempt to speed this up. The integer divisions and modulo are slow.
+ // See CL/76180724 comments for more ideas.
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE CoeffReturnType coeff(Index index) const
+ {
+ // Collect dimension-wise indices (subs).
+ array<Index, NumDims> subs;
+ if (static_cast<int>(Layout) == static_cast<int>(ColMajor)) {
+ for (int i = NumDims - 1; i > 0; --i) {
+ subs[i] = index / m_outputStrides[i];
+ index -= subs[i] * m_outputStrides[i];
+ }
+ subs[0] = index;
+ } else {
+ for (int i = 0; i < NumDims - 1; ++i) {
+ subs[i] = index / m_outputStrides[i];
+ index -= subs[i] * m_outputStrides[i];
+ }
+ subs[NumDims - 1] = index;
+ }
+
+ const Dimensions& left_dims = m_leftImpl.dimensions();
+ if (subs[m_axis] < left_dims[m_axis]) {
+ Index left_index;
+ if (static_cast<int>(Layout) == static_cast<int>(ColMajor)) {
+ left_index = subs[0];
+ EIGEN_UNROLL_LOOP
+ for (int i = 1; i < NumDims; ++i) {
+ left_index += (subs[i] % left_dims[i]) * m_leftStrides[i];
+ }
+ } else {
+ left_index = subs[NumDims - 1];
+ EIGEN_UNROLL_LOOP
+ for (int i = NumDims - 2; i >= 0; --i) {
+ left_index += (subs[i] % left_dims[i]) * m_leftStrides[i];
+ }
+ }
+ return m_leftImpl.coeff(left_index);
+ } else {
+ subs[m_axis] -= left_dims[m_axis];
+ const Dimensions& right_dims = m_rightImpl.dimensions();
+ Index right_index;
+ if (static_cast<int>(Layout) == static_cast<int>(ColMajor)) {
+ right_index = subs[0];
+ EIGEN_UNROLL_LOOP
+ for (int i = 1; i < NumDims; ++i) {
+ right_index += (subs[i] % right_dims[i]) * m_rightStrides[i];
+ }
+ } else {
+ right_index = subs[NumDims - 1];
+ EIGEN_UNROLL_LOOP
+ for (int i = NumDims - 2; i >= 0; --i) {
+ right_index += (subs[i] % right_dims[i]) * m_rightStrides[i];
+ }
+ }
+ return m_rightImpl.coeff(right_index);
+ }
+ }
+
+ // TODO(phli): Add a real vectorization.
+ template<int LoadMode>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE PacketReturnType packet(Index index) const
+ {
+ const int packetSize = PacketType<CoeffReturnType, Device>::size;
+ EIGEN_STATIC_ASSERT((packetSize > 1), YOU_MADE_A_PROGRAMMING_MISTAKE)
+ eigen_assert(index + packetSize - 1 < dimensions().TotalSize());
+
+ EIGEN_ALIGN_MAX CoeffReturnType values[packetSize];
+ EIGEN_UNROLL_LOOP
+ for (int i = 0; i < packetSize; ++i) {
+ values[i] = coeff(index+i);
+ }
+ PacketReturnType rslt = internal::pload<PacketReturnType>(values);
+ return rslt;
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorOpCost
+ costPerCoeff(bool vectorized) const {
+ const double compute_cost = NumDims * (2 * TensorOpCost::AddCost<Index>() +
+ 2 * TensorOpCost::MulCost<Index>() +
+ TensorOpCost::DivCost<Index>() +
+ TensorOpCost::ModCost<Index>());
+ const double lhs_size = m_leftImpl.dimensions().TotalSize();
+ const double rhs_size = m_rightImpl.dimensions().TotalSize();
+ return (lhs_size / (lhs_size + rhs_size)) *
+ m_leftImpl.costPerCoeff(vectorized) +
+ (rhs_size / (lhs_size + rhs_size)) *
+ m_rightImpl.costPerCoeff(vectorized) +
+ TensorOpCost(0, 0, compute_cost);
+ }
+
+ EIGEN_DEVICE_FUNC EvaluatorPointerType data() const { return NULL; }
+
+ #ifdef EIGEN_USE_SYCL
+ // binding placeholder accessors to a command group handler for SYCL
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void bind(cl::sycl::handler &cgh) const {
+ m_leftImpl.bind(cgh);
+ m_rightImpl.bind(cgh);
+ }
+ #endif
+
+ protected:
+ Dimensions m_dimensions;
+ array<Index, NumDims> m_outputStrides;
+ array<Index, NumDims> m_leftStrides;
+ array<Index, NumDims> m_rightStrides;
+ TensorEvaluator<LeftArgType, Device> m_leftImpl;
+ TensorEvaluator<RightArgType, Device> m_rightImpl;
+ const Axis m_axis;
+};
+
+// Eval as lvalue
+template<typename Axis, typename LeftArgType, typename RightArgType, typename Device>
+ struct TensorEvaluator<TensorConcatenationOp<Axis, LeftArgType, RightArgType>, Device>
+ : public TensorEvaluator<const TensorConcatenationOp<Axis, LeftArgType, RightArgType>, Device>
+{
+ typedef TensorEvaluator<const TensorConcatenationOp<Axis, LeftArgType, RightArgType>, Device> Base;
+ typedef TensorConcatenationOp<Axis, LeftArgType, RightArgType> XprType;
+ typedef typename Base::Dimensions Dimensions;
+ static constexpr int Layout = TensorEvaluator<LeftArgType, Device>::Layout;
+ enum {
+ IsAligned = false,
+ PacketAccess = TensorEvaluator<LeftArgType, Device>::PacketAccess &&
+ TensorEvaluator<RightArgType, Device>::PacketAccess,
+ BlockAccess = false,
+ PreferBlockAccess = TensorEvaluator<LeftArgType, Device>::PreferBlockAccess ||
+ TensorEvaluator<RightArgType, Device>::PreferBlockAccess,
+ RawAccess = false
+ };
+
+ //===- Tensor block evaluation strategy (see TensorBlock.h) -------------===//
+ typedef internal::TensorBlockNotImplemented TensorBlock;
+ //===--------------------------------------------------------------------===//
+
+ EIGEN_STRONG_INLINE TensorEvaluator(XprType& op, const Device& device)
+ : Base(op, device)
+ {
+ EIGEN_STATIC_ASSERT((static_cast<int>(Layout) == static_cast<int>(ColMajor)), YOU_MADE_A_PROGRAMMING_MISTAKE);
+ }
+
+ typedef typename XprType::Index Index;
+ typedef typename XprType::Scalar Scalar;
+ typedef typename XprType::CoeffReturnType CoeffReturnType;
+ typedef typename PacketType<CoeffReturnType, Device>::type PacketReturnType;
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE CoeffReturnType& coeffRef(Index index)
+ {
+ // Collect dimension-wise indices (subs).
+ array<Index, Base::NumDims> subs;
+ for (int i = Base::NumDims - 1; i > 0; --i) {
+ subs[i] = index / this->m_outputStrides[i];
+ index -= subs[i] * this->m_outputStrides[i];
+ }
+ subs[0] = index;
+
+ const Dimensions& left_dims = this->m_leftImpl.dimensions();
+ if (subs[this->m_axis] < left_dims[this->m_axis]) {
+ Index left_index = subs[0];
+ for (int i = 1; i < Base::NumDims; ++i) {
+ left_index += (subs[i] % left_dims[i]) * this->m_leftStrides[i];
+ }
+ return this->m_leftImpl.coeffRef(left_index);
+ } else {
+ subs[this->m_axis] -= left_dims[this->m_axis];
+ const Dimensions& right_dims = this->m_rightImpl.dimensions();
+ Index right_index = subs[0];
+ for (int i = 1; i < Base::NumDims; ++i) {
+ right_index += (subs[i] % right_dims[i]) * this->m_rightStrides[i];
+ }
+ return this->m_rightImpl.coeffRef(right_index);
+ }
+ }
+
+ template <int StoreMode> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ void writePacket(Index index, const PacketReturnType& x)
+ {
+ const int packetSize = PacketType<CoeffReturnType, Device>::size;
+ EIGEN_STATIC_ASSERT((packetSize > 1), YOU_MADE_A_PROGRAMMING_MISTAKE)
+ eigen_assert(index + packetSize - 1 < this->dimensions().TotalSize());
+
+ EIGEN_ALIGN_MAX CoeffReturnType values[packetSize];
+ internal::pstore<CoeffReturnType, PacketReturnType>(values, x);
+ for (int i = 0; i < packetSize; ++i) {
+ coeffRef(index+i) = values[i];
+ }
+ }
+};
+
+} // end namespace Eigen
+
+#endif // EIGEN_CXX11_TENSOR_TENSOR_CONCATENATION_H
diff --git a/unsupported/Eigen/CXX11/src/Tensor/TensorContraction.h b/unsupported/Eigen/CXX11/src/Tensor/TensorContraction.h
new file mode 100644
index 0000000..c629e44
--- /dev/null
+++ b/unsupported/Eigen/CXX11/src/Tensor/TensorContraction.h
@@ -0,0 +1,1021 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_CXX11_TENSOR_TENSOR_CONTRACTION_H
+#define EIGEN_CXX11_TENSOR_TENSOR_CONTRACTION_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+/** \class TensorContraction
+ * \ingroup CXX11_Tensor_Module
+ *
+ * \brief Tensor contraction class.
+ *
+ *
+ */
+namespace internal {
+
+template<typename Dimensions, typename LhsXprType, typename RhsXprType, typename OutputKernelType>
+struct traits<TensorContractionOp<Dimensions, LhsXprType, RhsXprType, OutputKernelType> >
+{
+ // Type promotion to handle the case where the types of the lhs and the rhs are different.
+ typedef typename gebp_traits<std::remove_const_t<typename LhsXprType::Scalar>,
+ std::remove_const_t<typename RhsXprType::Scalar>>::ResScalar Scalar;
+
+ typedef typename promote_storage_type<typename traits<LhsXprType>::StorageKind,
+ typename traits<RhsXprType>::StorageKind>::ret StorageKind;
+ typedef typename promote_index_type<typename traits<LhsXprType>::Index,
+ typename traits<RhsXprType>::Index>::type Index;
+ typedef typename LhsXprType::Nested LhsNested;
+ typedef typename RhsXprType::Nested RhsNested;
+ typedef std::remove_reference_t<LhsNested> LhsNested_;
+ typedef std::remove_reference_t<RhsNested> RhsNested_;
+
+ // From NumDims below.
+ static constexpr int NumDimensions = traits<LhsXprType>::NumDimensions + traits<RhsXprType>::NumDimensions - 2 * array_size<Dimensions>::value;
+ static constexpr int Layout = traits<LhsXprType>::Layout;
+ typedef std::conditional_t<Pointer_type_promotion<typename LhsXprType::Scalar, Scalar>::val,
+ typename traits<LhsXprType>::PointerType,
+ typename traits<RhsXprType>::PointerType>
+ PointerType;
+
+ enum {
+ Flags = 0
+ };
+};
+
+template<typename Dimensions, typename LhsXprType, typename RhsXprType, typename OutputKernelType>
+struct eval<TensorContractionOp<Dimensions, LhsXprType, RhsXprType, OutputKernelType>, Eigen::Dense>
+{
+ typedef const TensorContractionOp<Dimensions, LhsXprType, RhsXprType, OutputKernelType>& type;
+};
+
+template<typename Dimensions, typename LhsXprType, typename RhsXprType, typename OutputKernelType>
+struct nested<TensorContractionOp<Dimensions, LhsXprType, RhsXprType, OutputKernelType>, 1, typename eval<TensorContractionOp<Dimensions, LhsXprType, RhsXprType, OutputKernelType> >::type>
+{
+ typedef TensorContractionOp<Dimensions, LhsXprType, RhsXprType, OutputKernelType> type;
+};
+
+template<typename Indices_, typename LeftArgType_, typename RightArgType_, typename OutputKernelType_, typename Device_>
+struct traits<TensorEvaluator<const TensorContractionOp<Indices_, LeftArgType_, RightArgType_, OutputKernelType_>, Device_> > {
+ typedef Indices_ Indices;
+ typedef LeftArgType_ LeftArgType;
+ typedef RightArgType_ RightArgType;
+ typedef OutputKernelType_ OutputKernelType;
+ typedef Device_ Device;
+
+ // From NumDims below.
+ static constexpr int NumDimensions = traits<LeftArgType_>::NumDimensions + traits<RightArgType_>::NumDimensions - 2 * array_size<Indices_>::value;
+};
+
+// Helper class to allocate and deallocate temporary memory for packed buffers.
+template <typename LhsScalar, typename RhsScalar>
+struct TensorContractionBlockMemAllocator {
+ typedef void* BlockMemHandle;
+
+ template <typename Device>
+ EIGEN_DEVICE_FUNC static BlockMemHandle allocate(Device& d, const Index bm,
+ const Index bk,
+ const Index bn,
+ LhsScalar** lhs_block,
+ RhsScalar** rhs_block) {
+ eigen_assert(lhs_block);
+ eigen_assert(rhs_block);
+ BlockSizes sz = ComputeLhsRhsBlockSizes(bm, bk, bn);
+ char* block_mem = static_cast<char*>(d.allocate(sz.lhs_size + sz.rhs_size));
+ eigen_assert(block_mem);
+ *lhs_block = reinterpret_cast<LhsScalar*>(block_mem);
+ *rhs_block = reinterpret_cast<RhsScalar*>(block_mem + sz.lhs_size);
+ return block_mem;
+ }
+
+ template <typename Device>
+ EIGEN_DEVICE_FUNC static BlockMemHandle allocateSlices(
+ Device& d, const Index bm, const Index bk, const Index bn,
+ const Index num_lhs, const Index num_rhs, const Index num_slices,
+ std::vector<LhsScalar*>* lhs_blocks,
+ std::vector<RhsScalar*>* rhs_blocks) {
+ eigen_assert(num_slices > 0);
+ eigen_assert(num_lhs >= 0 && num_rhs >= 0);
+ eigen_assert(num_lhs == 0 || lhs_blocks);
+ eigen_assert(num_rhs == 0 || rhs_blocks);
+ BlockSizes sz = ComputeLhsRhsBlockSizes(bm, bk, bn);
+ void* block_mem = d.allocate(
+ (num_lhs * sz.lhs_size + num_rhs * sz.rhs_size) * num_slices);
+ eigen_assert(block_mem);
+ char* mem = static_cast<char*>(block_mem);
+
+ for (Index x = 0; x < num_slices; x++) {
+ if (num_lhs > 0) lhs_blocks[x].resize(num_lhs);
+ for (Index m = 0; m < num_lhs; m++) {
+ lhs_blocks[x][m] = reinterpret_cast<LhsScalar*>(mem);
+ mem += sz.lhs_size;
+ }
+ if (num_rhs > 0) rhs_blocks[x].resize(num_rhs);
+ for (Index n = 0; n < num_rhs; n++) {
+ rhs_blocks[x][n] = reinterpret_cast<RhsScalar*>(mem);
+ mem += sz.rhs_size;
+ }
+ }
+
+ return block_mem;
+ }
+
+ template <typename Device>
+ EIGEN_DEVICE_FUNC static void deallocate(Device& d, BlockMemHandle handle) {
+ d.deallocate(handle);
+ }
+
+ private:
+ struct BlockSizes {
+ Index lhs_size;
+ Index rhs_size;
+ };
+ EIGEN_DEVICE_FUNC static BlockSizes ComputeLhsRhsBlockSizes(const Index bm,
+ const Index bk,
+ const Index bn) {
+ Index align = numext::maxi(EIGEN_MAX_ALIGN_BYTES, 1);
+ BlockSizes sz;
+ sz.lhs_size = divup<Index>(bm * bk * sizeof(LhsScalar), align) * align;
+ sz.rhs_size = divup<Index>(bn * bk * sizeof(RhsScalar), align) * align;
+ return sz;
+ }
+};
+
+// WARNING: In this code we assume that Lhs and Rhs tensor expressions are in
+// ColMajor storage order. This property is guaranteed by the
+// TensorContractionOp evaluator. TensorContractionKernel specifies how we pack
+// blocks of Lhs and Rhs tensor expressions, and how we invoke matrix
+// multiplication for these blocks. Default tensor contraction uses
+// gemm_pack_rhs, gemm_pack_lhs and gebp_kernel from Eigen Core (see
+// GeneralBlocPanelKernel.h for details).
+//
+// By specializing contraction kernels we can use other low level libraries to
+// perform matrix multiplication, and still rely on Eigen contraction evaluator.
+// This also includes full support in TensorContractionThreadPool, assuming that
+// underlying gemm do not use it's own threading.
+//
+// - ResScalar/LhsScalar/RhsScalar - scalar type for the result of
+// multiplication, lhs tensor and rhs tensor respectively.
+//
+// - StorageIndex - index type for the tensor expressions. In practice almost
+// always is Eigen::Index.
+//
+// - OutputMapper provides access to the memory of the output matrix. In
+// practice it's always column major blas_data_mapper (it must be of ResScalar
+// type).
+//
+// - LhsMapper/RhsMapper similarly to blas_data_mapper provide a two dimensional
+// view into the Lhs/Rhs tensor expressions. In practice it's
+// TensorContractionInputMapper, or some specialization of it based on the
+// type of tensor expression (e.g. TensorImagePatchOp has optimized input
+// mapper).
+template <typename ResScalar, typename LhsScalar, typename RhsScalar,
+ typename StorageIndex, typename OutputMapper, typename LhsMapper,
+ typename RhsMapper>
+struct TensorContractionKernel {
+ // True if `invoke()` supports `beta` in `C <- alpha * A * B + beta * C`
+ // (otherwise beta should be always equal to 1).
+ enum { HasBeta = false };
+
+ EIGEN_DEVICE_FUNC
+ TensorContractionKernel(StorageIndex m_, StorageIndex k_, StorageIndex n_,
+ StorageIndex bm_, StorageIndex bk_, StorageIndex bn_)
+ : m(m_), k(k_), n(n_), bm(bm_), bk(bk_), bn(bn_) {}
+
+ // Pack blocks of Lhs and Rhs into contiguous blocks in memory.
+ typedef LhsScalar* LhsBlock;
+ typedef RhsScalar* RhsBlock;
+
+ // Packed Lhs/Rhs block memory allocator.
+ typedef TensorContractionBlockMemAllocator<LhsScalar, RhsScalar>
+ BlockMemAllocator;
+ typedef typename BlockMemAllocator::BlockMemHandle BlockMemHandle;
+
+ typedef typename internal::gebp_traits<LhsScalar, RhsScalar> Traits;
+
+ typedef internal::gemm_pack_lhs<
+ LhsScalar, StorageIndex, typename LhsMapper::SubMapper, Traits::mr,
+ Traits::LhsProgress, typename Traits::LhsPacket4Packing, ColMajor>
+ LhsPacker;
+
+ typedef internal::gemm_pack_rhs<RhsScalar, StorageIndex,
+ typename RhsMapper::SubMapper, Traits::nr,
+ ColMajor>
+ RhsPacker;
+
+ typedef internal::gebp_kernel<LhsScalar, RhsScalar, StorageIndex,
+ OutputMapper, Traits::mr, Traits::nr,
+ /*ConjugateLhs*/ false, /*ConjugateRhs*/ false>
+ GebpKernel;
+
+ template <typename Device>
+ EIGEN_DEVICE_FUNC BlockMemHandle allocate(Device& d, LhsBlock* lhs_block,
+ RhsBlock* rhs_block) {
+ return BlockMemAllocator::allocate(d, bm, bk, bn, lhs_block, rhs_block);
+ }
+
+ template <typename Device>
+ EIGEN_DEVICE_FUNC BlockMemHandle allocateSlices(
+ Device& d, const StorageIndex num_lhs, const StorageIndex num_rhs,
+ const StorageIndex num_slices, std::vector<LhsBlock>* lhs_blocks,
+ std::vector<RhsBlock>* rhs_blocks) {
+ return BlockMemAllocator::allocateSlices(
+ d, bm, bk, bn, num_lhs, num_rhs, num_slices, lhs_blocks, rhs_blocks);
+ }
+
+ template <typename Device>
+ EIGEN_DEVICE_FUNC static void deallocate(Device& d, BlockMemHandle handle) {
+ BlockMemAllocator::deallocate(d, handle);
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_DONT_INLINE void packLhs(
+ LhsBlock* lhsBlock, const typename LhsMapper::SubMapper& data_mapper,
+ const StorageIndex depth, const StorageIndex rows) {
+ LhsPacker()(*lhsBlock, data_mapper, depth, rows, /*stride*/ 0,
+ /*offset*/ 0);
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_DONT_INLINE void packRhs(
+ RhsBlock* rhsBlock, const typename RhsMapper::SubMapper& data_mapper,
+ const StorageIndex depth, const StorageIndex cols) {
+ RhsPacker()(*rhsBlock, data_mapper, depth, cols);
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_DONT_INLINE void invoke(
+ const OutputMapper& output_mapper, const LhsBlock& lhsBlock,
+ const RhsBlock& rhsBlock, const StorageIndex rows,
+ const StorageIndex depth, const StorageIndex cols,
+ const ResScalar alpha, const ResScalar beta) {
+ // Default GEBP kernel does not support beta.
+ eigen_assert(beta == ResScalar(1));
+ static const int kComputeStrideFromBlockDimensions = -1;
+ GebpKernel()(output_mapper, lhsBlock, rhsBlock, rows, depth, cols, alpha,
+ /*strideA*/ kComputeStrideFromBlockDimensions,
+ /*strideB*/ kComputeStrideFromBlockDimensions,
+ /*offsetA*/ 0, /*offsetB*/ 0);
+ }
+
+ private:
+ // These are dimensions of the original Tensors, and selected block sizes. The
+ // actual block sizes passed to all function above might be smaller because of
+ // the partial blocks at the end.
+ const StorageIndex m;
+ const StorageIndex k;
+ const StorageIndex n;
+ const StorageIndex bm;
+ const StorageIndex bk;
+ const StorageIndex bn;
+};
+
+} // end namespace internal
+
+// Tensor contraction params that should enable to get from output matrix
+// 2-dimensional coordinates to the output tensor dimensions.
+struct TensorContractionParams {
+ // TensorContraction evaluator assumes that both tensors are in ColMajor
+ // layout, if tensors are in RowMajor evaluator swap lhs with rhs.
+ bool swapped_arguments;
+};
+
+// Output kernel allows to fuse operations into the tensor contraction.
+//
+// Examples:
+// 1. Elementwise Relu transformation following Conv2D.
+// 2. AddBias to the Conv2D output channels dimension.
+//
+// The NoOpOutputKernel implements an output kernel that does absolutely nothing.
+struct NoOpOutputKernel {
+ /**
+ * Tensor contraction evaluator calls this kernel after finishing each block
+ * of output matrix. Output blocks belong to the 2-dimensional output tensor.
+ *
+ * TensorContractionParams contains contraction dimensions information
+ * required to map output 2-d space into the expected output tensor space
+ * (potentially higher dimensional).
+ *
+ * \param[in] output_mapper Access to output tensor memory
+ * \param[in] params Tensor contraction parameters
+ * \param[in] i Index of a first row available through output_mapper
+ * \param[in] j Index of a first column available through output_mapper
+ * \param[in] num_rows Number of available rows
+ * \param[in] num_cols Number of available columns
+ */
+ template <typename Index, typename Scalar>
+ EIGEN_ALWAYS_INLINE void operator()(
+ const internal::blas_data_mapper<Scalar, Index, ColMajor>& output_mapper,
+ const TensorContractionParams& params, Index i,
+ Index j, Index num_rows, Index num_cols) const {
+ EIGEN_UNUSED_VARIABLE(output_mapper);
+ EIGEN_UNUSED_VARIABLE(params);
+ EIGEN_UNUSED_VARIABLE(i);
+ EIGEN_UNUSED_VARIABLE(j);
+ EIGEN_UNUSED_VARIABLE(num_rows);
+ EIGEN_UNUSED_VARIABLE(num_cols);
+ }
+};
+
+template<typename Indices, typename LhsXprType, typename RhsXprType, typename OutputKernelType = const NoOpOutputKernel>
+class TensorContractionOp : public TensorBase<TensorContractionOp<Indices, LhsXprType, RhsXprType, OutputKernelType>, ReadOnlyAccessors>
+{
+ public:
+ typedef typename Eigen::internal::traits<TensorContractionOp>::Scalar Scalar;
+ typedef typename internal::gebp_traits<typename LhsXprType::CoeffReturnType,
+ typename RhsXprType::CoeffReturnType>::ResScalar CoeffReturnType;
+ typedef typename Eigen::internal::nested<TensorContractionOp>::type Nested;
+ typedef typename Eigen::internal::traits<TensorContractionOp>::StorageKind StorageKind;
+ typedef typename Eigen::internal::traits<TensorContractionOp>::Index Index;
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorContractionOp(
+ const LhsXprType& lhs, const RhsXprType& rhs, const Indices& dims,
+ const OutputKernelType& output_kernel = OutputKernelType())
+ : m_lhs_xpr(lhs), m_rhs_xpr(rhs), m_indices(dims),
+ m_output_kernel(output_kernel) {}
+
+ EIGEN_DEVICE_FUNC
+ const Indices& indices() const { return m_indices; }
+
+ /** \returns the nested expressions */
+ EIGEN_DEVICE_FUNC
+ const internal::remove_all_t<typename LhsXprType::Nested>&
+ lhsExpression() const { return m_lhs_xpr; }
+
+ EIGEN_DEVICE_FUNC
+ const internal::remove_all_t<typename RhsXprType::Nested>&
+ rhsExpression() const { return m_rhs_xpr; }
+
+ EIGEN_DEVICE_FUNC
+ const OutputKernelType& outputKernel() const { return m_output_kernel; }
+
+ protected:
+ typename LhsXprType::Nested m_lhs_xpr;
+ typename RhsXprType::Nested m_rhs_xpr;
+ const Indices m_indices;
+ const OutputKernelType m_output_kernel;
+};
+
+
+template<typename Derived>
+struct TensorContractionEvaluatorBase : internal::no_assignment_operator
+{
+ typedef typename internal::traits<Derived>::Indices Indices;
+ typedef typename internal::traits<Derived>::LeftArgType LeftArgType;
+ typedef typename internal::traits<Derived>::RightArgType RightArgType;
+ typedef typename internal::traits<Derived>::OutputKernelType OutputKernelType;
+ typedef typename internal::traits<Derived>::Device Device;
+
+ typedef TensorContractionOp<Indices, LeftArgType, RightArgType, OutputKernelType> XprType;
+ typedef std::remove_const_t<typename XprType::Scalar> Scalar;
+ typedef typename XprType::Index Index;
+ typedef typename XprType::CoeffReturnType CoeffReturnType;
+ typedef typename PacketType<CoeffReturnType, Device>::type PacketReturnType;
+ typedef StorageMemory<Scalar, Device> Storage;
+ typedef typename Storage::Type EvaluatorPointerType;
+
+ static constexpr int Layout = TensorEvaluator<LeftArgType, Device>::Layout;
+ enum {
+ IsAligned = true,
+ PacketAccess = (PacketType<CoeffReturnType, Device>::size > 1),
+ BlockAccess = false,
+ PreferBlockAccess = false,
+ CoordAccess = false, // to be implemented
+ RawAccess = true
+ };
+
+ //===- Tensor block evaluation strategy (see TensorBlock.h) -------------===//
+ typedef internal::TensorBlockNotImplemented TensorBlock;
+ //===--------------------------------------------------------------------===//
+
+ // Most of the code is assuming that both input tensors are ColMajor. If the
+ // inputs are RowMajor, we will "cheat" by swapping the LHS and RHS:
+ // If we want to compute A * B = C, where A is LHS and B is RHS, the code
+ // will pretend B is LHS and A is RHS.
+ typedef std::conditional_t<
+ static_cast<int>(Layout) == static_cast<int>(ColMajor), LeftArgType, RightArgType> EvalLeftArgType;
+ typedef std::conditional_t<
+ static_cast<int>(Layout) == static_cast<int>(ColMajor), RightArgType, LeftArgType> EvalRightArgType;
+
+ typedef TensorEvaluator<EvalLeftArgType, Device> LeftEvaluatorType;
+ typedef TensorEvaluator<EvalRightArgType, Device> RightEvaluatorType;
+
+ static constexpr int LDims =
+ internal::array_size<typename TensorEvaluator<EvalLeftArgType, Device>::Dimensions>::value;
+ static constexpr int RDims =
+ internal::array_size<typename TensorEvaluator<EvalRightArgType, Device>::Dimensions>::value;
+ static constexpr int ContractDims = internal::array_size<Indices>::value;
+ static constexpr int NumDims = LDims + RDims - 2 * ContractDims;
+
+ typedef array<Index, ContractDims> contract_t;
+ typedef array<Index, LDims - ContractDims> left_nocontract_t;
+ typedef array<Index, RDims - ContractDims> right_nocontract_t;
+
+ typedef DSizes<Index, NumDims> Dimensions;
+
+ EIGEN_STRONG_INLINE
+ TensorContractionEvaluatorBase(const XprType& op, const Device& device)
+ : m_leftImpl(choose(Cond<static_cast<int>(Layout) == static_cast<int>(ColMajor)>(),
+ op.lhsExpression(), op.rhsExpression()), device),
+ m_rightImpl(choose(Cond<static_cast<int>(Layout) == static_cast<int>(ColMajor)>(),
+ op.rhsExpression(), op.lhsExpression()), device),
+ m_device(device),
+ m_output_kernel(op.outputKernel()),
+ m_result(NULL) {
+ EIGEN_STATIC_ASSERT((static_cast<int>(TensorEvaluator<LeftArgType, Device>::Layout) ==
+ static_cast<int>(TensorEvaluator<RightArgType, Device>::Layout)),
+ YOU_MADE_A_PROGRAMMING_MISTAKE);
+
+
+ DSizes<Index, LDims> eval_left_dims;
+ DSizes<Index, RDims> eval_right_dims;
+ array<IndexPair<Index>, ContractDims> eval_op_indices;
+ if (static_cast<int>(Layout) == static_cast<int>(ColMajor)) {
+ // For ColMajor, we keep using the existing dimensions
+ for (int i = 0; i < LDims; i++) {
+ eval_left_dims[i] = m_leftImpl.dimensions()[i];
+ }
+ for (int i = 0; i < RDims; i++) {
+ eval_right_dims[i] = m_rightImpl.dimensions()[i];
+ }
+ // We keep the pairs of contracting indices.
+ for (int i = 0; i < ContractDims; i++) {
+ eval_op_indices[i].first = op.indices()[i].first;
+ eval_op_indices[i].second = op.indices()[i].second;
+ }
+ } else {
+ // For RowMajor, we need to reverse the existing dimensions
+ for (int i = 0; i < LDims; i++) {
+ eval_left_dims[i] = m_leftImpl.dimensions()[LDims - i - 1];
+ }
+ for (int i = 0; i < RDims; i++) {
+ eval_right_dims[i] = m_rightImpl.dimensions()[RDims - i - 1];
+ }
+ // We need to flip all the pairs of contracting indices as well as
+ // reversing the dimensions.
+ for (int i = 0; i < ContractDims; i++) {
+ eval_op_indices[i].first = LDims - 1 - op.indices()[ContractDims - 1 - i].second;
+ eval_op_indices[i].second = RDims - 1 - op.indices()[ContractDims - 1 - i].first;
+ }
+ }
+
+ // Check for duplicate axes and make sure the first index in eval_op_indices
+ // is increasing. Using O(n^2) sorting is OK since ContractDims is small
+ for (int i = 0; i < ContractDims; i++) {
+ for (int j = i + 1; j < ContractDims; j++) {
+ eigen_assert(eval_op_indices[j].first != eval_op_indices[i].first &&
+ eval_op_indices[j].second != eval_op_indices[i].second &&
+ "contraction axes should be unique");
+ if (eval_op_indices[j].first < eval_op_indices[i].first) {
+ numext::swap(eval_op_indices[j], eval_op_indices[i]);
+ }
+ }
+ }
+
+ array<Index, LDims> lhs_strides;
+ lhs_strides[0] = 1;
+ for (int i = 0; i < LDims-1; ++i) {
+ lhs_strides[i+1] = lhs_strides[i] * eval_left_dims[i];
+ }
+
+ array<Index, RDims> rhs_strides;
+ rhs_strides[0] = 1;
+ for (int i = 0; i < RDims-1; ++i) {
+ rhs_strides[i+1] = rhs_strides[i] * eval_right_dims[i];
+ }
+
+ if (m_i_strides.size() > 0) m_i_strides[0] = 1;
+ if (m_j_strides.size() > 0) m_j_strides[0] = 1;
+ if (m_k_strides.size() > 0) m_k_strides[0] = 1;
+
+ m_i_size = 1;
+ m_j_size = 1;
+ m_k_size = 1;
+
+ // To compute the dimension, we simply concatenate the non-contracting
+ // dimensions of the left and then the right tensor. Additionally, we also
+ // compute the strides corresponding to the left non-contracting
+ // dimensions and right non-contracting dimensions.
+ m_lhs_inner_dim_contiguous = true;
+ int dim_idx = 0;
+ Index nocontract_idx = 0;
+
+ for (int i = 0; i < LDims; i++) {
+ // find if we are contracting on index i of left tensor
+ bool contracting = false;
+ for (int j = 0; j < ContractDims; j++) {
+ if (eval_op_indices[j].first == i) {
+ contracting = true;
+ break;
+ }
+ }
+ if (!contracting) {
+ // add dimension size to output dimensions
+ m_dimensions[dim_idx] = eval_left_dims[i];
+ m_left_nocontract_strides[nocontract_idx] = lhs_strides[i];
+ if (dim_idx != i) {
+ m_lhs_inner_dim_contiguous = false;
+ }
+ if (nocontract_idx+1 < internal::array_size<left_nocontract_t>::value) {
+ m_i_strides[nocontract_idx+1] =
+ m_i_strides[nocontract_idx] * eval_left_dims[i];
+ } else {
+ m_i_size = m_i_strides[nocontract_idx] * eval_left_dims[i];
+ }
+ dim_idx++;
+ nocontract_idx++;
+ }
+ }
+
+ nocontract_idx = 0;
+ for (int i = 0; i < RDims; i++) {
+ bool contracting = false;
+ // find if we are contracting on index i of right tensor
+ for (int j = 0; j < ContractDims; j++) {
+ if (eval_op_indices[j].second == i) {
+ contracting = true;
+ break;
+ }
+ }
+ if (!contracting) {
+ m_dimensions[dim_idx] = eval_right_dims[i];
+ if (nocontract_idx+1 < internal::array_size<right_nocontract_t>::value) {
+ m_j_strides[nocontract_idx+1] =
+ m_j_strides[nocontract_idx] * eval_right_dims[i];
+ } else {
+ m_j_size = m_j_strides[nocontract_idx] * eval_right_dims[i];
+ }
+ m_right_nocontract_strides[nocontract_idx] = rhs_strides[i];
+ dim_idx++;
+ nocontract_idx++;
+ }
+ }
+
+ // Now compute the strides corresponding to the contracting dimensions. We
+ // assumed above that non-contracting axes are represented in the same order
+ // in the matrix as they are in the tensor. This is not the case for
+ // contracting axes. As the contracting axes must be of the same size in
+ // each tensor, we'll only look at the first tensor here.
+ m_rhs_inner_dim_contiguous = true;
+ m_rhs_inner_dim_reordered = false;
+ for (int i = 0; i < ContractDims; i++) {
+ Index left = eval_op_indices[i].first;
+ Index right = eval_op_indices[i].second;
+
+ Index size = eval_left_dims[left];
+ eigen_assert(size == eval_right_dims[right] &&
+ "Contraction axes must be same size");
+
+ if (i+1 < static_cast<int>(internal::array_size<contract_t>::value)) {
+ m_k_strides[i+1] = m_k_strides[i] * size;
+ } else {
+ m_k_size = m_k_strides[i] * size;
+ }
+ m_left_contracting_strides[i] = lhs_strides[left];
+ m_right_contracting_strides[i] = rhs_strides[right];
+
+ if (i > 0 && right < eval_op_indices[i-1].second) {
+ m_rhs_inner_dim_reordered = true;
+ }
+ if (right != i) {
+ m_rhs_inner_dim_contiguous = false;
+ }
+ }
+
+ // If the layout is RowMajor, we need to reverse the m_dimensions
+ if (static_cast<int>(Layout) == static_cast<int>(RowMajor)) {
+ for (int i = 0, j = NumDims - 1; i < j; i++, j--) {
+ numext::swap(m_dimensions[i], m_dimensions[j]);
+ }
+ }
+
+ // A set of parameters that will allow output kernel to get from output
+ // tensor dimensions (i, j) into the original tensor dimensions.
+ // TODO(ezhulenev): Add parameters required to infer output tensor index for
+ // more complex contractions than 2x2 on internal dimension.
+ m_tensor_contraction_params.swapped_arguments = static_cast<int>(Layout) == RowMajor;
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Dimensions& dimensions() const { return m_dimensions; }
+
+ EIGEN_STRONG_INLINE bool evalSubExprsIfNeeded(EvaluatorPointerType data) {
+ m_leftImpl.evalSubExprsIfNeeded(NULL);
+ m_rightImpl.evalSubExprsIfNeeded(NULL);
+ if (data) {
+ evalTo(data);
+ return false;
+ } else {
+ m_result = static_cast<EvaluatorPointerType>(m_device.allocate(dimensions().TotalSize() * sizeof(Scalar)));
+ evalTo(m_result);
+ return true;
+ }
+ }
+
+#ifdef EIGEN_USE_THREADS
+ template <typename EvalSubExprsCallback>
+ EIGEN_STRONG_INLINE void evalSubExprsIfNeededAsync(
+ EvaluatorPointerType dest, EvalSubExprsCallback done) {
+ m_leftImpl.evalSubExprsIfNeededAsync(nullptr, [this, done, dest](bool) {
+ m_rightImpl.evalSubExprsIfNeededAsync(nullptr, [this, done, dest](bool) {
+ if (dest) {
+ evalToAsync(dest, [done]() { done(false); });
+ } else {
+ m_result = static_cast<EvaluatorPointerType>(
+ m_device.allocate(dimensions().TotalSize() * sizeof(Scalar)));
+ evalToAsync(m_result, [done]() { done(true); });
+ }
+ });
+ });
+ }
+#endif // EIGEN_USE_THREADS
+
+#ifndef TENSOR_CONTRACTION_DISPATCH
+#define TENSOR_CONTRACTION_DISPATCH(METHOD, ALIGNMENT, ARGS) \
+ if (this->m_lhs_inner_dim_contiguous) { \
+ if (this->m_rhs_inner_dim_contiguous) { \
+ if (this->m_rhs_inner_dim_reordered) { \
+ METHOD<true, true, true, ALIGNMENT> ARGS; \
+ } else { \
+ METHOD<true, true, false, ALIGNMENT> ARGS; \
+ } \
+ } else { \
+ if (this->m_rhs_inner_dim_reordered) { \
+ METHOD<true, false, true, ALIGNMENT> ARGS; \
+ } else { \
+ METHOD<true, false, false, ALIGNMENT> ARGS; \
+ } \
+ } \
+ } else { \
+ if (this->m_rhs_inner_dim_contiguous) { \
+ if (this->m_rhs_inner_dim_reordered) { \
+ METHOD<false, true, true, ALIGNMENT> ARGS; \
+ } else { \
+ METHOD<false, true, false, ALIGNMENT> ARGS; \
+ } \
+ } else { \
+ if (this->m_rhs_inner_dim_reordered) { \
+ METHOD<false, false, true, ALIGNMENT> ARGS; \
+ } else { \
+ METHOD<false, false, false, ALIGNMENT> ARGS; \
+ } \
+ } \
+ }
+#endif
+
+#ifndef TENSOR_CONTRACTION_ASYNC_DISPATCH
+#define TENSOR_CONTRACTION_ASYNC_DISPATCH(METHOD, DONE, ALIGNMENT, ARGS, FN) \
+ if (this->m_lhs_inner_dim_contiguous) { \
+ if (this->m_rhs_inner_dim_contiguous) { \
+ if (this->m_rhs_inner_dim_reordered) { \
+ (new METHOD<DONE, true, true, true, ALIGNMENT> ARGS)->FN; \
+ } else { \
+ (new METHOD<DONE, true, true, false, ALIGNMENT> ARGS)->FN; \
+ } \
+ } else { \
+ if (this->m_rhs_inner_dim_reordered) { \
+ (new METHOD<DONE, true, false, true, ALIGNMENT> ARGS)->FN; \
+ } else { \
+ (new METHOD<DONE, true, false, false, ALIGNMENT> ARGS)->FN; \
+ } \
+ } \
+ } else { \
+ if (this->m_rhs_inner_dim_contiguous) { \
+ if (this->m_rhs_inner_dim_reordered) { \
+ (new METHOD<DONE, false, true, true, ALIGNMENT> ARGS)->FN; \
+ } else { \
+ (new METHOD<DONE, false, true, false, ALIGNMENT> ARGS)->FN; \
+ } \
+ } else { \
+ if (this->m_rhs_inner_dim_reordered) { \
+ (new METHOD<DONE, false, false, true, ALIGNMENT> ARGS)->FN; \
+ } else { \
+ (new METHOD<DONE, false, false, false, ALIGNMENT> ARGS)->FN; \
+ } \
+ } \
+ }
+#endif
+
+ EIGEN_DEVICE_FUNC void evalTo(Scalar* buffer) const {
+ static_cast<const Derived*>(this)->template evalProduct<Unaligned>(buffer);
+ }
+
+#ifdef EIGEN_USE_THREADS
+ template <typename EvalToCallback>
+ void evalToAsync(Scalar* buffer, EvalToCallback done) const {
+ static_cast<const Derived*>(this)
+ ->template evalProductAsync<EvalToCallback, Unaligned>(buffer,
+ std::move(done));
+ }
+#endif // EIGEN_USE_THREADS
+
+ template <bool lhs_inner_dim_contiguous, bool rhs_inner_dim_contiguous,
+ bool rhs_inner_dim_reordered, int Alignment>
+ void evalProductSequential(Scalar* buffer) const {
+ if (this->m_j_size == 1) {
+ this->template evalGemv<lhs_inner_dim_contiguous,
+ rhs_inner_dim_contiguous, rhs_inner_dim_reordered,
+ Alignment>(buffer);
+ } else {
+ this->template evalGemm<lhs_inner_dim_contiguous, rhs_inner_dim_contiguous,
+ rhs_inner_dim_reordered, Alignment>(buffer);
+ }
+ }
+
+ template <bool lhs_inner_dim_contiguous, bool rhs_inner_dim_contiguous, bool rhs_inner_dim_reordered, int Alignment>
+ #if !defined(EIGEN_HIPCC)
+ EIGEN_DEVICE_FUNC
+ #endif
+ void evalGemv(Scalar* buffer) const {
+ const Index rows = m_i_size;
+ const Index cols = m_k_size;
+
+ typedef std::remove_const_t<typename EvalLeftArgType::Scalar> LhsScalar;
+ typedef std::remove_const_t<typename EvalRightArgType::Scalar> RhsScalar;
+ typedef TensorEvaluator<EvalLeftArgType, Device> LeftEvaluator;
+ typedef TensorEvaluator<EvalRightArgType, Device> RightEvaluator;
+ const Index lhs_packet_size = internal::unpacket_traits<typename LeftEvaluator::PacketReturnType>::size;
+ const Index rhs_packet_size = internal::unpacket_traits<typename RightEvaluator::PacketReturnType>::size;
+ const int lhs_alignment = LeftEvaluator::IsAligned ? Aligned : Unaligned;
+ const int rhs_alignment = RightEvaluator::IsAligned ? Aligned : Unaligned;
+ typedef internal::TensorContractionInputMapper<LhsScalar, Index, internal::Lhs,
+ LeftEvaluator, left_nocontract_t,
+ contract_t, lhs_packet_size,
+ lhs_inner_dim_contiguous,
+ false, lhs_alignment> LhsMapper;
+
+ typedef internal::TensorContractionInputMapper<RhsScalar, Index, internal::Rhs,
+ RightEvaluator, right_nocontract_t,
+ contract_t, rhs_packet_size,
+ rhs_inner_dim_contiguous,
+ rhs_inner_dim_reordered, rhs_alignment> RhsMapper;
+
+ LhsMapper lhs(m_leftImpl, m_left_nocontract_strides, m_i_strides,
+ m_left_contracting_strides, m_k_strides);
+ RhsMapper rhs(m_rightImpl, m_right_nocontract_strides, m_j_strides,
+ m_right_contracting_strides, m_k_strides);
+
+ const Scalar alpha(1);
+ const Index resIncr(1);
+
+ // zero out the result buffer (which must be of size at least rows * sizeof(Scalar)
+ m_device.fill(buffer, buffer + rows, Scalar(0));
+
+ internal::general_matrix_vector_product<Index,LhsScalar,LhsMapper,ColMajor,false,RhsScalar,RhsMapper,false>::run(
+ rows, cols, lhs, rhs,
+ buffer, resIncr, alpha);
+
+ typedef internal::blas_data_mapper<Scalar, Index, ColMajor> OutputMapper;
+ m_output_kernel(OutputMapper(buffer, rows), m_tensor_contraction_params,
+ static_cast<Index>(0), static_cast<Index>(0), rows,
+ static_cast<Index>(1));
+ }
+
+ template <bool lhs_inner_dim_contiguous, bool rhs_inner_dim_contiguous, bool rhs_inner_dim_reordered, int Alignment>
+ #if !defined(EIGEN_HIPCC)
+ EIGEN_DEVICE_FUNC
+ #endif
+ void evalGemm(Scalar* buffer) const {
+ // columns in left side, rows in right side
+ const Index k = this->m_k_size;
+ this->template evalGemmPartial<lhs_inner_dim_contiguous,
+ rhs_inner_dim_contiguous,
+ rhs_inner_dim_reordered,
+ Alignment, true>(buffer, 0, k, 1);
+ }
+
+ template <bool lhs_inner_dim_contiguous, bool rhs_inner_dim_contiguous,
+ bool rhs_inner_dim_reordered, int Alignment>
+ EIGEN_DEVICE_FUNC void evalGemmPartialWithoutOutputKernel(
+ Scalar* buffer, Index k_start, Index k_end, int num_threads) const {
+ evalGemmPartial<lhs_inner_dim_contiguous, rhs_inner_dim_contiguous,
+ rhs_inner_dim_reordered, Alignment,
+ /*use_output_kernel*/ false>(buffer, k_start, k_end,
+ num_threads);
+ }
+
+ template <bool lhs_inner_dim_contiguous, bool rhs_inner_dim_contiguous, bool rhs_inner_dim_reordered, int Alignment, bool use_output_kernel>
+ EIGEN_DEVICE_FUNC void evalGemmPartial(Scalar* buffer, Index k_start, Index k_end, int num_threads) const {
+ eigen_assert(k_end >= k_start && k_start >= 0 && k_end <= this->m_k_size);
+ // columns in slice on left side, rows on right side
+ const Index k_slice = k_end - k_start;
+
+ // rows in left side
+ const Index m = this->m_i_size;
+
+ // columns in right side
+ const Index n = this->m_j_size;
+
+ // define data mappers for Lhs and Rhs
+ typedef std::remove_const_t<typename EvalLeftArgType::Scalar> LhsScalar;
+ typedef std::remove_const_t<typename EvalRightArgType::Scalar> RhsScalar;
+
+ typedef TensorEvaluator<EvalLeftArgType, Device> LeftEvaluator;
+ typedef TensorEvaluator<EvalRightArgType, Device> RightEvaluator;
+
+ const Index lhs_packet_size = internal::unpacket_traits<typename LeftEvaluator::PacketReturnType>::size;
+ const Index rhs_packet_size = internal::unpacket_traits<typename RightEvaluator::PacketReturnType>::size;
+
+ typedef internal::TensorContractionInputMapper<LhsScalar, Index, internal::Lhs,
+ LeftEvaluator, left_nocontract_t,
+ contract_t, lhs_packet_size,
+ lhs_inner_dim_contiguous,
+ false, Unaligned> LhsMapper;
+
+ typedef internal::TensorContractionInputMapper<RhsScalar, Index, internal::Rhs,
+ RightEvaluator, right_nocontract_t,
+ contract_t, rhs_packet_size,
+ rhs_inner_dim_contiguous,
+ rhs_inner_dim_reordered, Unaligned> RhsMapper;
+
+ typedef internal::blas_data_mapper<Scalar, Index, ColMajor> OutputMapper;
+
+ typedef internal::TensorContractionKernel<
+ Scalar, LhsScalar, RhsScalar, Index, OutputMapper, LhsMapper, RhsMapper>
+ TensorContractionKernel;
+
+ // initialize data mappers
+ LhsMapper lhs(this->m_leftImpl, this->m_left_nocontract_strides, this->m_i_strides,
+ this->m_left_contracting_strides, this->m_k_strides);
+
+ RhsMapper rhs(this->m_rightImpl, this->m_right_nocontract_strides, this->m_j_strides,
+ this->m_right_contracting_strides, this->m_k_strides);
+
+ OutputMapper output(buffer, m);
+
+ // Sizes of the blocks to load in cache. See the Goto paper for details.
+ internal::TensorContractionBlocking<Scalar, LhsScalar, RhsScalar,
+ Index, internal::ShardByCol>
+ blocking(k_slice, m, n, num_threads);
+ const Index kc = blocking.kc();
+ const Index mc = numext::mini(m, blocking.mc());
+ const Index nc = numext::mini(n, blocking.nc());
+
+ typedef typename TensorContractionKernel::LhsBlock LhsBlock;
+ typedef typename TensorContractionKernel::RhsBlock RhsBlock;
+
+ LhsBlock blockA;
+ RhsBlock blockB;
+
+ TensorContractionKernel kernel(m, k_slice, n, mc, kc, nc);
+
+ typedef typename TensorContractionKernel::BlockMemHandle BlockMemHandle;
+ const BlockMemHandle packed_mem =
+ kernel.allocate(this->m_device, &blockA, &blockB);
+
+ // If a contraction kernel does not support beta, explicitly initialize
+ // output buffer with zeroes.
+ if (!TensorContractionKernel::HasBeta) {
+ this->m_device.fill(buffer, buffer + m * n, Scalar(0));
+ }
+
+ for(Index i2=0; i2<m; i2+=mc)
+ {
+ const Index actual_mc = numext::mini(i2+mc,m)-i2;
+ for (Index k2 = k_start; k2 < k_end; k2 += kc) {
+ // make sure we don't overshoot right edge of left matrix, then pack vertical panel
+ const Index actual_kc = numext::mini(k2 + kc, k_end) - k2;
+ kernel.packLhs(&blockA, lhs.getSubMapper(i2, k2), actual_kc, actual_mc);
+
+ // If kernel supports beta, there is no need to initialize output
+ // buffer with zeroes.
+ const Scalar alpha = Scalar(1);
+ const Scalar beta = (TensorContractionKernel::HasBeta && k2 == k_start)
+ ? Scalar(0)
+ : Scalar(1);
+
+ // series of horizontal blocks
+ for (Index j2 = 0; j2 < n; j2 += nc) {
+ // make sure we don't overshoot right edge of right matrix, then pack block
+ const Index actual_nc = numext::mini(j2 + nc, n) - j2;
+ kernel.packRhs(&blockB, rhs.getSubMapper(k2, j2), actual_kc,
+ actual_nc);
+
+ // call gebp (matrix kernel)
+ // The parameters here are copied from Eigen's GEMM implementation
+ const OutputMapper output_mapper = output.getSubMapper(i2, j2);
+ kernel.invoke(output_mapper, blockA, blockB, actual_mc, actual_kc,
+ actual_nc, alpha, beta);
+
+ // We are done with this [i2, j2] output block.
+ if (use_output_kernel && k2 + kc >= k_end) {
+ m_output_kernel(output_mapper, m_tensor_contraction_params, i2, j2,
+ actual_mc, actual_nc);
+ }
+ }
+ }
+ }
+
+ kernel.deallocate(this->m_device, packed_mem);
+ }
+
+ EIGEN_STRONG_INLINE void cleanup() {
+ m_leftImpl.cleanup();
+ m_rightImpl.cleanup();
+
+ if (m_result != NULL) {
+ m_device.deallocate(m_result);
+ m_result = NULL;
+ }
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE CoeffReturnType coeff(Index index) const {
+ return m_result[index];
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorOpCost costPerCoeff(bool) const {
+ return TensorOpCost(sizeof(CoeffReturnType), 0, 0);
+ }
+
+ template<int LoadMode>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE PacketReturnType packet(Index index) const {
+ return internal::ploadt<PacketReturnType, LoadMode>(m_result + index);
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE EvaluatorPointerType data() const { return m_result; }
+
+protected:
+ Dimensions m_dimensions;
+
+ contract_t m_k_strides;
+ contract_t m_left_contracting_strides;
+ contract_t m_right_contracting_strides;
+
+ bool m_lhs_inner_dim_contiguous;
+ bool m_rhs_inner_dim_contiguous;
+ bool m_rhs_inner_dim_reordered;
+
+ left_nocontract_t m_i_strides;
+ right_nocontract_t m_j_strides;
+ left_nocontract_t m_left_nocontract_strides;
+ right_nocontract_t m_right_nocontract_strides;
+
+ Index m_i_size;
+ Index m_j_size;
+ Index m_k_size;
+
+ TensorContractionParams m_tensor_contraction_params;
+
+ TensorEvaluator<EvalLeftArgType, Device> m_leftImpl;
+ TensorEvaluator<EvalRightArgType, Device> m_rightImpl;
+ const Device EIGEN_DEVICE_REF m_device;
+ OutputKernelType m_output_kernel;
+ EvaluatorPointerType m_result;
+};
+
+
+// evaluator for default device
+template<typename Indices, typename LeftArgType, typename RightArgType, typename OutputKernelType, typename Device>
+struct TensorEvaluator<const TensorContractionOp<Indices, LeftArgType, RightArgType, OutputKernelType>, Device> :
+ public TensorContractionEvaluatorBase<
+ TensorEvaluator<const TensorContractionOp<Indices, LeftArgType, RightArgType, OutputKernelType>, Device> > {
+ typedef TensorEvaluator<const TensorContractionOp<Indices, LeftArgType, RightArgType, OutputKernelType>, Device> Self;
+ typedef TensorContractionEvaluatorBase<Self> Base;
+
+ typedef TensorContractionOp<Indices, LeftArgType, RightArgType, OutputKernelType> XprType;
+ typedef std::remove_const_t<typename XprType::Scalar> Scalar;
+ typedef typename XprType::Index Index;
+ typedef typename XprType::CoeffReturnType CoeffReturnType;
+ typedef typename PacketType<CoeffReturnType, Device>::type PacketReturnType;
+
+ static constexpr int Layout = TensorEvaluator<LeftArgType, Device>::Layout;
+
+ // Most of the code is assuming that both input tensors are ColMajor. If the
+ // inputs are RowMajor, we will "cheat" by swapping the LHS and RHS:
+ // If we want to compute A * B = C, where A is LHS and B is RHS, the code
+ // will pretend B is LHS and A is RHS.
+ typedef std::conditional_t<Layout == static_cast<int>(ColMajor), LeftArgType, RightArgType> EvalLeftArgType;
+ typedef std::conditional_t<Layout == static_cast<int>(ColMajor), RightArgType, LeftArgType> EvalRightArgType;
+
+ static constexpr int LDims =
+ internal::array_size<typename TensorEvaluator<EvalLeftArgType, Device>::Dimensions>::value;
+ static constexpr int RDims =
+ internal::array_size<typename TensorEvaluator<EvalRightArgType, Device>::Dimensions>::value;
+ static constexpr int ContractDims = internal::array_size<Indices>::value;
+
+ typedef array<Index, ContractDims> contract_t;
+ typedef array<Index, LDims - ContractDims> left_nocontract_t;
+ typedef array<Index, RDims - ContractDims> right_nocontract_t;
+
+ static constexpr int NumDims = LDims + RDims - 2 * ContractDims;
+
+ // Could we use NumDimensions here?
+ typedef DSizes<Index, NumDims> Dimensions;
+
+ TensorEvaluator(const XprType& op, const Device& device) :
+ Base(op, device) { }
+
+ template <int Alignment>
+ void evalProduct(Scalar* buffer) const {
+ TENSOR_CONTRACTION_DISPATCH(this->template evalProductSequential, Alignment, (buffer));
+ }
+};
+
+} // end namespace Eigen
+
+#endif // EIGEN_CXX11_TENSOR_TENSOR_CONTRACTION_H
diff --git a/unsupported/Eigen/CXX11/src/Tensor/TensorContractionBlocking.h b/unsupported/Eigen/CXX11/src/Tensor/TensorContractionBlocking.h
new file mode 100644
index 0000000..60748cc
--- /dev/null
+++ b/unsupported/Eigen/CXX11/src/Tensor/TensorContractionBlocking.h
@@ -0,0 +1,78 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_CXX11_TENSOR_TENSOR_CONTRACTION_BLOCKING_H
+#define EIGEN_CXX11_TENSOR_TENSOR_CONTRACTION_BLOCKING_H
+
+#if defined(EIGEN_USE_LIBXSMM)
+#include "third_party/libxsmm/include/libxsmm.h"
+#endif
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+namespace internal {
+
+enum {
+ ShardByRow = 0,
+ ShardByCol = 1
+};
+
+
+// Default Blocking Strategy
+template<typename ResScalar, typename LhsScalar, typename RhsScalar, typename StorageIndex, int ShardingType = ShardByCol>
+class TensorContractionBlocking {
+ public:
+
+ /*
+ adding EIGEN_DEVICE_FUNC unconditionally to 'TensorContractionBlocking' constructor in `TensorContractionBlocking.h`
+ requires adding EIGEN_DEVICE_FUNC to `computeProductBlockingSizes` in `GeneralBlockPanelKernel.h`
+ which in turn, requires adding EIGEN_DEVICE_FUNC to `evaluateProductBlockingSizesHeuristic` in `GeneralBlockPanelKernel.h`
+ which in turn, requires adding EIGEN_DEVICE_FUNC to `manage_caching_sizes` in `GeneralBlockPanelKernel.h`
+ (else HIPCC will error out)
+
+ However adding EIGEN_DEVICE_FUNC to `manage_caching_sizes` in `GeneralBlockPanelKernel.h`
+ results in NVCC erroring out with the following error
+
+ ../Eigen/src/Core/products/GeneralBlockPanelKernel.h(57): error #2901:
+ dynamic initialization is not supported for function-scope static variables within a __device__/__global__ function
+ */
+
+ #if !defined(EIGEN_HIPCC)
+ EIGEN_DEVICE_FUNC
+ #endif
+ TensorContractionBlocking(StorageIndex k, StorageIndex m, StorageIndex n, StorageIndex num_threads = 1) :
+ kc_(k), mc_(m), nc_(n)
+ {
+ if (ShardingType == ShardByCol) {
+ computeProductBlockingSizes<LhsScalar, RhsScalar, 1>(kc_, mc_, nc_, num_threads);
+ }
+ else {
+ computeProductBlockingSizes<LhsScalar, RhsScalar, 1>(kc_, nc_, mc_, num_threads);
+ }
+
+ const int rhs_packet_size = internal::packet_traits<RhsScalar>::size;
+ kc_ = (rhs_packet_size <= 8 || kc_ <= rhs_packet_size) ?
+ kc_ : (kc_ / rhs_packet_size) * rhs_packet_size;
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE StorageIndex kc() const { return kc_; }
+ EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE StorageIndex mc() const { return mc_; }
+ EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE StorageIndex nc() const { return nc_; }
+
+ private:
+ StorageIndex kc_;
+ StorageIndex mc_;
+ StorageIndex nc_;
+};
+
+} // end namespace internal
+} // end namespace Eigen
+
+#endif // EIGEN_CXX11_TENSOR_TENSOR_CONTRACTION_BLOCKING_H
diff --git a/unsupported/Eigen/CXX11/src/Tensor/TensorContractionCuda.h b/unsupported/Eigen/CXX11/src/Tensor/TensorContractionCuda.h
new file mode 100644
index 0000000..3f315fe
--- /dev/null
+++ b/unsupported/Eigen/CXX11/src/Tensor/TensorContractionCuda.h
@@ -0,0 +1,6 @@
+
+#if defined(__clang__) || defined(__GNUC__)
+#warning "Deprecated header file, please either include the main Eigen/CXX11/Tensor header or the respective TensorContractionGpu.h file"
+#endif
+
+#include "TensorContractionGpu.h"
diff --git a/unsupported/Eigen/CXX11/src/Tensor/TensorContractionGpu.h b/unsupported/Eigen/CXX11/src/Tensor/TensorContractionGpu.h
new file mode 100644
index 0000000..698baab
--- /dev/null
+++ b/unsupported/Eigen/CXX11/src/Tensor/TensorContractionGpu.h
@@ -0,0 +1,1411 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2014-2015 Benoit Steiner <benoit.steiner.goog@gmail.com>
+// Copyright (C) 2015 Navdeep Jaitly <ndjaitly@google.com>
+// Copyright (C) 2014 Eric Martin <eric@ericmart.in>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_CXX11_TENSOR_TENSOR_CONTRACTION_GPU_H
+#define EIGEN_CXX11_TENSOR_TENSOR_CONTRACTION_GPU_H
+
+#if defined(EIGEN_USE_GPU) && defined(EIGEN_GPUCC)
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+template<typename Scalar, typename Index, typename LhsMapper,
+ typename RhsMapper, typename OutputMapper, bool needs_edge_check>
+__device__ EIGEN_STRONG_INLINE void
+EigenContractionKernelInternal(const LhsMapper lhs, const RhsMapper rhs,
+ const OutputMapper output, Scalar* lhs_shmem, Scalar* rhs_shmem,
+ const Index m_size, const Index n_size, const Index k_size) {
+
+ const Index m_block_idx = blockIdx.x;
+ const Index n_block_idx = blockIdx.y;
+
+ const Index base_m = 64 * m_block_idx;
+ const Index base_n = 64 * n_block_idx;
+
+ // declare and initialize 64 registers for output 8x8 block
+
+ // prefetch registers
+ Scalar lhs_pf0;
+ Scalar lhs_pf1;
+ Scalar lhs_pf2;
+ Scalar lhs_pf3;
+ Scalar lhs_pf4;
+ Scalar lhs_pf5;
+ Scalar lhs_pf6;
+ Scalar lhs_pf7;
+
+ Scalar rhs_pf0;
+ Scalar rhs_pf1;
+ Scalar rhs_pf2;
+ Scalar rhs_pf3;
+ Scalar rhs_pf4;
+ Scalar rhs_pf5;
+ Scalar rhs_pf6;
+ Scalar rhs_pf7;
+
+ // shared memory is formatted
+ // (contract idx in block, nocontract idx in block, block idx)
+ // where block idx is column major. This transposition limits the number of
+ // bank conflicts when reading the LHS. The core idea is that since the contracting
+ // index is shared by both sides, then the contracting index should be in threadIdx.x.
+
+ // On the LHS, we pad each row inside of each block with an extra element. This makes
+ // each block 8 rows of 9 elements, which is 72 elements. This gives no bank conflicts
+ // on writes and very few 2-way conflicts on reads. There is an 8x8 grid of these blocks.
+
+ // On the RHS we just add 8 padding elements to the end of each block. This gives no bank
+ // conflicts on writes and also none on reads.
+
+ // storage indices
+ const Index lhs_store_idx_base = threadIdx.y * 72 + threadIdx.x * 9 + threadIdx.z;
+ const Index rhs_store_idx_base = threadIdx.y * 72 + threadIdx.z * 8 + threadIdx.x;
+
+ const Index lhs_store_idx_0 = lhs_store_idx_base + 576 * 0;
+ const Index lhs_store_idx_1 = lhs_store_idx_base + 576 * 1;
+ const Index lhs_store_idx_2 = lhs_store_idx_base + 576 * 2;
+ const Index lhs_store_idx_3 = lhs_store_idx_base + 576 * 3;
+ const Index lhs_store_idx_4 = lhs_store_idx_base + 576 * 4;
+ const Index lhs_store_idx_5 = lhs_store_idx_base + 576 * 5;
+ const Index lhs_store_idx_6 = lhs_store_idx_base + 576 * 6;
+ const Index lhs_store_idx_7 = lhs_store_idx_base + 576 * 7;
+
+ const Index rhs_store_idx_0 = rhs_store_idx_base + 576 * 0;
+ const Index rhs_store_idx_1 = rhs_store_idx_base + 576 * 1;
+ const Index rhs_store_idx_2 = rhs_store_idx_base + 576 * 2;
+ const Index rhs_store_idx_3 = rhs_store_idx_base + 576 * 3;
+ const Index rhs_store_idx_4 = rhs_store_idx_base + 576 * 4;
+ const Index rhs_store_idx_5 = rhs_store_idx_base + 576 * 5;
+ const Index rhs_store_idx_6 = rhs_store_idx_base + 576 * 6;
+ const Index rhs_store_idx_7 = rhs_store_idx_base + 576 * 7;
+
+ // in the loading code, the following variables are important:
+ // threadIdx.x: the vertical position in an 8x8 block
+ // threadIdx.y: the vertical index of the 8x8 block in the grid
+ // threadIdx.z: the horizontal position in an 8x8 block
+ // k: the horizontal index of the 8x8 block in the grid
+ //
+ // The k parameter is implicit (it was the loop counter for a loop that went
+ // from 0 to <8, but now that loop is unrolled in the below code.
+
+ const Index load_idx_vert = threadIdx.x + 8 * threadIdx.y;
+ const Index lhs_vert = base_m + load_idx_vert;
+
+#define prefetchIntoRegisters(base_k) \
+ { \
+ lhs_pf0 = conv(0); \
+ lhs_pf1 = conv(0); \
+ lhs_pf2 = conv(0); \
+ lhs_pf3 = conv(0); \
+ lhs_pf4 = conv(0); \
+ lhs_pf5 = conv(0); \
+ lhs_pf6 = conv(0); \
+ lhs_pf7 = conv(0); \
+ \
+ rhs_pf0 = conv(0); \
+ rhs_pf1 = conv(0); \
+ rhs_pf2 = conv(0); \
+ rhs_pf3 = conv(0); \
+ rhs_pf4 = conv(0); \
+ rhs_pf5 = conv(0); \
+ rhs_pf6 = conv(0); \
+ rhs_pf7 = conv(0); \
+ \
+ if (!needs_edge_check || lhs_vert < m_size) { \
+ const Index lhs_horiz_0 = base_k + threadIdx.z + 0 * 8; \
+ const Index lhs_horiz_1 = base_k + threadIdx.z + 1 * 8; \
+ const Index lhs_horiz_2 = base_k + threadIdx.z + 2 * 8; \
+ const Index lhs_horiz_3 = base_k + threadIdx.z + 3 * 8; \
+ const Index lhs_horiz_4 = base_k + threadIdx.z + 4 * 8; \
+ const Index lhs_horiz_5 = base_k + threadIdx.z + 5 * 8; \
+ const Index lhs_horiz_6 = base_k + threadIdx.z + 6 * 8; \
+ const Index lhs_horiz_7 = base_k + threadIdx.z + 7 * 8; \
+ \
+ if (!needs_edge_check || lhs_horiz_7 < k_size) { \
+ lhs_pf0 = lhs(lhs_vert, lhs_horiz_0); \
+ lhs_pf1 = lhs(lhs_vert, lhs_horiz_1); \
+ lhs_pf2 = lhs(lhs_vert, lhs_horiz_2); \
+ lhs_pf3 = lhs(lhs_vert, lhs_horiz_3); \
+ lhs_pf4 = lhs(lhs_vert, lhs_horiz_4); \
+ lhs_pf5 = lhs(lhs_vert, lhs_horiz_5); \
+ lhs_pf6 = lhs(lhs_vert, lhs_horiz_6); \
+ lhs_pf7 = lhs(lhs_vert, lhs_horiz_7); \
+ } else if (lhs_horiz_6 < k_size) { \
+ lhs_pf0 = lhs(lhs_vert, lhs_horiz_0); \
+ lhs_pf1 = lhs(lhs_vert, lhs_horiz_1); \
+ lhs_pf2 = lhs(lhs_vert, lhs_horiz_2); \
+ lhs_pf3 = lhs(lhs_vert, lhs_horiz_3); \
+ lhs_pf4 = lhs(lhs_vert, lhs_horiz_4); \
+ lhs_pf5 = lhs(lhs_vert, lhs_horiz_5); \
+ lhs_pf6 = lhs(lhs_vert, lhs_horiz_6); \
+ } else if (lhs_horiz_5 < k_size) { \
+ lhs_pf0 = lhs(lhs_vert, lhs_horiz_0); \
+ lhs_pf1 = lhs(lhs_vert, lhs_horiz_1); \
+ lhs_pf2 = lhs(lhs_vert, lhs_horiz_2); \
+ lhs_pf3 = lhs(lhs_vert, lhs_horiz_3); \
+ lhs_pf4 = lhs(lhs_vert, lhs_horiz_4); \
+ lhs_pf5 = lhs(lhs_vert, lhs_horiz_5); \
+ } else if (lhs_horiz_4 < k_size) { \
+ lhs_pf0 = lhs(lhs_vert, lhs_horiz_0); \
+ lhs_pf1 = lhs(lhs_vert, lhs_horiz_1); \
+ lhs_pf2 = lhs(lhs_vert, lhs_horiz_2); \
+ lhs_pf3 = lhs(lhs_vert, lhs_horiz_3); \
+ lhs_pf4 = lhs(lhs_vert, lhs_horiz_4); \
+ } else if (lhs_horiz_3 < k_size) { \
+ lhs_pf0 = lhs(lhs_vert, lhs_horiz_0); \
+ lhs_pf1 = lhs(lhs_vert, lhs_horiz_1); \
+ lhs_pf2 = lhs(lhs_vert, lhs_horiz_2); \
+ lhs_pf3 = lhs(lhs_vert, lhs_horiz_3); \
+ } else if (lhs_horiz_2 < k_size) { \
+ lhs_pf0 = lhs(lhs_vert, lhs_horiz_0); \
+ lhs_pf1 = lhs(lhs_vert, lhs_horiz_1); \
+ lhs_pf2 = lhs(lhs_vert, lhs_horiz_2); \
+ } else if (lhs_horiz_1 < k_size) { \
+ lhs_pf0 = lhs(lhs_vert, lhs_horiz_0); \
+ lhs_pf1 = lhs(lhs_vert, lhs_horiz_1); \
+ } else if (lhs_horiz_0 < k_size) { \
+ lhs_pf0 = lhs(lhs_vert, lhs_horiz_0); \
+ } \
+ } \
+ \
+ const Index rhs_vert = base_k + load_idx_vert; \
+ if (!needs_edge_check || rhs_vert < k_size) { \
+ const Index rhs_horiz_0 = base_n + threadIdx.z + 0 * 8; \
+ const Index rhs_horiz_1 = base_n + threadIdx.z + 1 * 8; \
+ const Index rhs_horiz_2 = base_n + threadIdx.z + 2 * 8; \
+ const Index rhs_horiz_3 = base_n + threadIdx.z + 3 * 8; \
+ const Index rhs_horiz_4 = base_n + threadIdx.z + 4 * 8; \
+ const Index rhs_horiz_5 = base_n + threadIdx.z + 5 * 8; \
+ const Index rhs_horiz_6 = base_n + threadIdx.z + 6 * 8; \
+ const Index rhs_horiz_7 = base_n + threadIdx.z + 7 * 8; \
+ \
+ if (rhs_horiz_7 < n_size) { \
+ rhs_pf0 = rhs(rhs_vert, rhs_horiz_0); \
+ rhs_pf1 = rhs(rhs_vert, rhs_horiz_1); \
+ rhs_pf2 = rhs(rhs_vert, rhs_horiz_2); \
+ rhs_pf3 = rhs(rhs_vert, rhs_horiz_3); \
+ rhs_pf4 = rhs(rhs_vert, rhs_horiz_4); \
+ rhs_pf5 = rhs(rhs_vert, rhs_horiz_5); \
+ rhs_pf6 = rhs(rhs_vert, rhs_horiz_6); \
+ rhs_pf7 = rhs(rhs_vert, rhs_horiz_7); \
+ } else if (rhs_horiz_6 < n_size) { \
+ rhs_pf0 = rhs(rhs_vert, rhs_horiz_0); \
+ rhs_pf1 = rhs(rhs_vert, rhs_horiz_1); \
+ rhs_pf2 = rhs(rhs_vert, rhs_horiz_2); \
+ rhs_pf3 = rhs(rhs_vert, rhs_horiz_3); \
+ rhs_pf4 = rhs(rhs_vert, rhs_horiz_4); \
+ rhs_pf5 = rhs(rhs_vert, rhs_horiz_5); \
+ rhs_pf6 = rhs(rhs_vert, rhs_horiz_6); \
+ } else if (rhs_horiz_5 < n_size) { \
+ rhs_pf0 = rhs(rhs_vert, rhs_horiz_0); \
+ rhs_pf1 = rhs(rhs_vert, rhs_horiz_1); \
+ rhs_pf2 = rhs(rhs_vert, rhs_horiz_2); \
+ rhs_pf3 = rhs(rhs_vert, rhs_horiz_3); \
+ rhs_pf4 = rhs(rhs_vert, rhs_horiz_4); \
+ rhs_pf5 = rhs(rhs_vert, rhs_horiz_5); \
+ } else if (rhs_horiz_4 < n_size) { \
+ rhs_pf0 = rhs(rhs_vert, rhs_horiz_0); \
+ rhs_pf1 = rhs(rhs_vert, rhs_horiz_1); \
+ rhs_pf2 = rhs(rhs_vert, rhs_horiz_2); \
+ rhs_pf3 = rhs(rhs_vert, rhs_horiz_3); \
+ rhs_pf4 = rhs(rhs_vert, rhs_horiz_4); \
+ } else if (rhs_horiz_3 < n_size) { \
+ rhs_pf0 = rhs(rhs_vert, rhs_horiz_0); \
+ rhs_pf1 = rhs(rhs_vert, rhs_horiz_1); \
+ rhs_pf2 = rhs(rhs_vert, rhs_horiz_2); \
+ rhs_pf3 = rhs(rhs_vert, rhs_horiz_3); \
+ } else if (rhs_horiz_2 < n_size) { \
+ rhs_pf0 = rhs(rhs_vert, rhs_horiz_0); \
+ rhs_pf1 = rhs(rhs_vert, rhs_horiz_1); \
+ rhs_pf2 = rhs(rhs_vert, rhs_horiz_2); \
+ } else if (rhs_horiz_1 < n_size) { \
+ rhs_pf0 = rhs(rhs_vert, rhs_horiz_0); \
+ rhs_pf1 = rhs(rhs_vert, rhs_horiz_1); \
+ } else if (rhs_horiz_0 < n_size) { \
+ rhs_pf0 = rhs(rhs_vert, rhs_horiz_0); \
+ } \
+ } \
+ } \
+
+#define writeRegToShmem() \
+ lhs_shmem[lhs_store_idx_0] = lhs_pf0; \
+ rhs_shmem[rhs_store_idx_0] = rhs_pf0; \
+ \
+ lhs_shmem[lhs_store_idx_1] = lhs_pf1; \
+ rhs_shmem[rhs_store_idx_1] = rhs_pf1; \
+ \
+ lhs_shmem[lhs_store_idx_2] = lhs_pf2; \
+ rhs_shmem[rhs_store_idx_2] = rhs_pf2; \
+ \
+ lhs_shmem[lhs_store_idx_3] = lhs_pf3; \
+ rhs_shmem[rhs_store_idx_3] = rhs_pf3; \
+ \
+ lhs_shmem[lhs_store_idx_4] = lhs_pf4; \
+ rhs_shmem[rhs_store_idx_4] = rhs_pf4; \
+ \
+ lhs_shmem[lhs_store_idx_5] = lhs_pf5; \
+ rhs_shmem[rhs_store_idx_5] = rhs_pf5; \
+ \
+ lhs_shmem[lhs_store_idx_6] = lhs_pf6; \
+ rhs_shmem[rhs_store_idx_6] = rhs_pf6; \
+ \
+ lhs_shmem[lhs_store_idx_7] = lhs_pf7; \
+ rhs_shmem[rhs_store_idx_7] = rhs_pf7; \
+
+ // declare and initialize result array
+#define res(i, j) _res_##i##j
+#define initResultRow(i) \
+ Scalar res(i, 0) = conv(0); \
+ Scalar res(i, 1) = conv(0); \
+ Scalar res(i, 2) = conv(0); \
+ Scalar res(i, 3) = conv(0); \
+ Scalar res(i, 4) = conv(0); \
+ Scalar res(i, 5) = conv(0); \
+ Scalar res(i, 6) = conv(0); \
+ Scalar res(i, 7) = conv(0); \
+
+ internal::scalar_cast_op<int, Scalar> conv;
+ initResultRow(0);
+ initResultRow(1);
+ initResultRow(2);
+ initResultRow(3);
+ initResultRow(4);
+ initResultRow(5);
+ initResultRow(6);
+ initResultRow(7);
+#undef initResultRow
+
+ for (Index base_k = 0; base_k < k_size; base_k += 64) {
+ // wait for previous iteration to finish with shmem. Despite common sense,
+ // the code is a bit faster with this here then at bottom of loop
+ __syncthreads();
+
+ prefetchIntoRegisters(base_k);
+ writeRegToShmem();
+
+ #undef prefetchIntoRegisters
+ #undef writeRegToShmem
+
+ // wait for shared mem packing to be done before starting computation
+ __syncthreads();
+
+ // compute 8x8 matrix product by outer product. This involves packing one column
+ // of LHS and one row of RHS into registers (takes 16 registers).
+
+#define lcol(i) _lcol##i
+ Scalar lcol(0);
+ Scalar lcol(1);
+ Scalar lcol(2);
+ Scalar lcol(3);
+ Scalar lcol(4);
+ Scalar lcol(5);
+ Scalar lcol(6);
+ Scalar lcol(7);
+
+#define rrow(j) _rrow##j
+ Scalar rrow(0);
+ Scalar rrow(1);
+ Scalar rrow(2);
+ Scalar rrow(3);
+ Scalar rrow(4);
+ Scalar rrow(5);
+ Scalar rrow(6);
+ Scalar rrow(7);
+
+ // Now x corresponds to k, y to m, and z to n
+ const Scalar* lhs_block = &lhs_shmem[threadIdx.x + 9 * threadIdx.y];
+ const Scalar* rhs_block = &rhs_shmem[threadIdx.x + 8 * threadIdx.z];
+
+#define lhs_element(i, j) lhs_block[72 * ((i) + 8 * (j))]
+#define rhs_element(i, j) rhs_block[72 * ((i) + 8 * (j))]
+
+#define loadData(i, j) \
+ lcol(0) = lhs_element(0, j); \
+ rrow(0) = rhs_element(i, 0); \
+ lcol(1) = lhs_element(1, j); \
+ rrow(1) = rhs_element(i, 1); \
+ lcol(2) = lhs_element(2, j); \
+ rrow(2) = rhs_element(i, 2); \
+ lcol(3) = lhs_element(3, j); \
+ rrow(3) = rhs_element(i, 3); \
+ lcol(4) = lhs_element(4, j); \
+ rrow(4) = rhs_element(i, 4); \
+ lcol(5) = lhs_element(5, j); \
+ rrow(5) = rhs_element(i, 5); \
+ lcol(6) = lhs_element(6, j); \
+ rrow(6) = rhs_element(i, 6); \
+ lcol(7) = lhs_element(7, j); \
+ rrow(7) = rhs_element(i, 7); \
+
+#define computeCol(j) \
+ res(0, j) += lcol(0) * rrow(j); \
+ res(1, j) += lcol(1) * rrow(j); \
+ res(2, j) += lcol(2) * rrow(j); \
+ res(3, j) += lcol(3) * rrow(j); \
+ res(4, j) += lcol(4) * rrow(j); \
+ res(5, j) += lcol(5) * rrow(j); \
+ res(6, j) += lcol(6) * rrow(j); \
+ res(7, j) += lcol(7) * rrow(j); \
+
+#define computePass(i) \
+ loadData(i, i); \
+ \
+ computeCol(0); \
+ computeCol(1); \
+ computeCol(2); \
+ computeCol(3); \
+ computeCol(4); \
+ computeCol(5); \
+ computeCol(6); \
+ computeCol(7); \
+
+ computePass(0);
+ computePass(1);
+ computePass(2);
+ computePass(3);
+ computePass(4);
+ computePass(5);
+ computePass(6);
+ computePass(7);
+
+#undef lcol
+#undef rrow
+#undef lhs_element
+#undef rhs_element
+#undef loadData
+#undef computeCol
+#undef computePass
+ } // end loop over k
+
+ // we've now iterated over all of the large (ie width 64) k blocks and
+ // accumulated results in registers. At this point thread (x, y, z) contains
+ // the sum across all big k blocks of the product of little k block of index (x, y)
+ // with block of index (y, z). To compute the final output, we need to reduce
+ // the 8 threads over y by summation.
+#if defined(EIGEN_HIPCC) || (defined(EIGEN_CUDA_SDK_VER) && EIGEN_CUDA_SDK_VER < 90000)
+#define shuffleInc(i, j, mask) res(i, j) += __shfl_xor(res(i, j), mask)
+#else
+#define shuffleInc(i, j, mask) res(i, j) += __shfl_xor_sync(0xFFFFFFFF, res(i, j), mask)
+#endif
+
+#define reduceRow(i, mask) \
+ shuffleInc(i, 0, mask); \
+ shuffleInc(i, 1, mask); \
+ shuffleInc(i, 2, mask); \
+ shuffleInc(i, 3, mask); \
+ shuffleInc(i, 4, mask); \
+ shuffleInc(i, 5, mask); \
+ shuffleInc(i, 6, mask); \
+ shuffleInc(i, 7, mask); \
+
+#define reduceMatrix(mask) \
+ reduceRow(0, mask); \
+ reduceRow(1, mask); \
+ reduceRow(2, mask); \
+ reduceRow(3, mask); \
+ reduceRow(4, mask); \
+ reduceRow(5, mask); \
+ reduceRow(6, mask); \
+ reduceRow(7, mask); \
+
+ // actually perform the reduction, now each thread of index (_, y, z)
+ // contains the correct values in its registers that belong in the output
+ // block
+ reduceMatrix(1);
+ reduceMatrix(2);
+ reduceMatrix(4);
+
+#undef shuffleInc
+#undef reduceRow
+#undef reduceMatrix
+
+ // now we need to copy the 64 values into main memory. We can't split work
+ // among threads because all variables are in registers. There's 2 ways
+ // to do this:
+ // (1) have 1 thread do 64 writes from registers into global memory
+ // (2) have 1 thread do 64 writes into shared memory, and then 8 threads
+ // each do 8 writes into global memory. We can just overwrite the shared
+ // memory from the problem we just solved.
+ // (2) is slightly faster than (1) due to less branching and more ILP
+
+ // TODO: won't yield much gain, but could just use currently unused shared mem
+ // and then we won't have to sync
+ // wait for shared mem to be out of use
+ __syncthreads();
+
+#define writeResultShmem(i, j) \
+ lhs_shmem[i + 8 * threadIdx.y + 64 * threadIdx.z + 512 * j] = res(i, j); \
+
+#define writeRow(i) \
+ writeResultShmem(i, 0); \
+ writeResultShmem(i, 1); \
+ writeResultShmem(i, 2); \
+ writeResultShmem(i, 3); \
+ writeResultShmem(i, 4); \
+ writeResultShmem(i, 5); \
+ writeResultShmem(i, 6); \
+ writeResultShmem(i, 7); \
+
+ if (threadIdx.x == 0) {
+ writeRow(0);
+ writeRow(1);
+ writeRow(2);
+ writeRow(3);
+ writeRow(4);
+ writeRow(5);
+ writeRow(6);
+ writeRow(7);
+ }
+#undef writeResultShmem
+#undef writeRow
+
+ const int max_i_write = numext::mini((int)((m_size - base_m - threadIdx.y + 7) / 8), 8);
+ const int max_j_write = numext::mini((int)((n_size - base_n - threadIdx.z + 7) / 8), 8);
+
+ if (threadIdx.x < max_i_write) {
+ if (max_j_write == 8) {
+ // TODO: can i trade bank conflicts for coalesced writes?
+ Scalar val0 = lhs_shmem[threadIdx.x + 8 * threadIdx.y + 64 * threadIdx.z + 512 * 0];
+ Scalar val1 = lhs_shmem[threadIdx.x + 8 * threadIdx.y + 64 * threadIdx.z + 512 * 1];
+ Scalar val2 = lhs_shmem[threadIdx.x + 8 * threadIdx.y + 64 * threadIdx.z + 512 * 2];
+ Scalar val3 = lhs_shmem[threadIdx.x + 8 * threadIdx.y + 64 * threadIdx.z + 512 * 3];
+ Scalar val4 = lhs_shmem[threadIdx.x + 8 * threadIdx.y + 64 * threadIdx.z + 512 * 4];
+ Scalar val5 = lhs_shmem[threadIdx.x + 8 * threadIdx.y + 64 * threadIdx.z + 512 * 5];
+ Scalar val6 = lhs_shmem[threadIdx.x + 8 * threadIdx.y + 64 * threadIdx.z + 512 * 6];
+ Scalar val7 = lhs_shmem[threadIdx.x + 8 * threadIdx.y + 64 * threadIdx.z + 512 * 7];
+
+ output(base_m + threadIdx.y + 8 * threadIdx.x, base_n + threadIdx.z + 8 * 0) = val0;
+ output(base_m + threadIdx.y + 8 * threadIdx.x, base_n + threadIdx.z + 8 * 1) = val1;
+ output(base_m + threadIdx.y + 8 * threadIdx.x, base_n + threadIdx.z + 8 * 2) = val2;
+ output(base_m + threadIdx.y + 8 * threadIdx.x, base_n + threadIdx.z + 8 * 3) = val3;
+ output(base_m + threadIdx.y + 8 * threadIdx.x, base_n + threadIdx.z + 8 * 4) = val4;
+ output(base_m + threadIdx.y + 8 * threadIdx.x, base_n + threadIdx.z + 8 * 5) = val5;
+ output(base_m + threadIdx.y + 8 * threadIdx.x, base_n + threadIdx.z + 8 * 6) = val6;
+ output(base_m + threadIdx.y + 8 * threadIdx.x, base_n + threadIdx.z + 8 * 7) = val7;
+ } else {
+#pragma unroll 7
+ for (int j = 0; j < max_j_write; j++) {
+ Scalar val = lhs_shmem[threadIdx.x + 8 * threadIdx.y + 64 * threadIdx.z + 512 * j];
+ output(base_m + threadIdx.y + 8 * threadIdx.x, base_n + threadIdx.z + 8 * j) = val;
+ }
+ }
+ }
+#undef res
+}
+
+
+template<typename Scalar, typename Index, typename LhsMapper,
+ typename RhsMapper, typename OutputMapper>
+__global__ void
+#if defined(EIGEN_HIPCC)
+__launch_bounds__(512, 1)
+#else
+__launch_bounds__(512)
+#endif
+EigenContractionKernel(const LhsMapper lhs, const RhsMapper rhs,
+ const OutputMapper output,
+ const Index m_size, const Index n_size, const Index k_size) {
+ __shared__ Scalar lhs_shmem[72 * 64];
+ __shared__ Scalar rhs_shmem[72 * 64];
+
+ const Index m_block_idx = blockIdx.x;
+ const Index n_block_idx = blockIdx.y;
+
+ const Index base_m = 64 * m_block_idx;
+ const Index base_n = 64 * n_block_idx;
+
+ if (base_m + 63 < m_size && base_n + 63 < n_size) {
+ EigenContractionKernelInternal<Scalar, Index, LhsMapper, RhsMapper, OutputMapper, false>(lhs, rhs, output, lhs_shmem, rhs_shmem, m_size, n_size, k_size);
+ } else {
+ EigenContractionKernelInternal<Scalar, Index, LhsMapper, RhsMapper, OutputMapper, true>(lhs, rhs, output, lhs_shmem, rhs_shmem, m_size, n_size, k_size);
+ }
+}
+
+
+template<typename Index, typename LhsMapper,
+ typename RhsMapper, typename OutputMapper, bool CHECK_LHS_BOUNDARY,
+ bool CHECK_RHS_BOUNDARY>
+__device__ __forceinline__ void
+EigenFloatContractionKernelInternal16x16(const LhsMapper lhs, const RhsMapper rhs,
+ const OutputMapper output, float2 lhs_shmem2[][16],
+ float2 rhs_shmem2[][8], const Index m_size,
+ const Index n_size, const Index k_size,
+ const Index base_m, const Index base_n) {
+
+ // prefetch registers
+ float4 lhs_pf0, rhs_pf0;
+
+ float4 results[4];
+ for (int i=0; i < 4; i++) {
+ results[i].x = results[i].y = results[i].z = results[i].w = 0;
+ }
+
+#define prefetch_lhs(reg, row, col) \
+ if (!CHECK_LHS_BOUNDARY) { \
+ if (col < k_size) { \
+ reg =lhs.template loadPacket<float4,Unaligned>(row, col); \
+ } \
+ } else { \
+ if (col < k_size) { \
+ if (row + 3 < m_size) { \
+ reg =lhs.template loadPacket<float4,Unaligned>(row, col); \
+ } else if (row + 2 < m_size) { \
+ reg.x =lhs(row + 0, col); \
+ reg.y =lhs(row + 1, col); \
+ reg.z =lhs(row + 2, col); \
+ } else if (row + 1 < m_size) { \
+ reg.x =lhs(row + 0, col); \
+ reg.y =lhs(row + 1, col); \
+ } else if (row < m_size) { \
+ reg.x =lhs(row + 0, col); \
+ } \
+ } \
+ } \
+
+ Index lhs_vert = base_m+threadIdx.x*4;
+
+ for (Index k = 0; k < k_size; k += 16) {
+
+ lhs_pf0 = internal::pset1<float4>(0);
+ rhs_pf0 = internal::pset1<float4>(0);
+
+ Index lhs_horiz = threadIdx.y+k;
+ prefetch_lhs(lhs_pf0, lhs_vert, lhs_horiz)
+
+ Index rhs_vert = k+(threadIdx.x%4)*4;
+ Index rhs_horiz0 = (threadIdx.x>>2)+threadIdx.y*4+base_n;
+
+ if (!CHECK_RHS_BOUNDARY) {
+ if ((rhs_vert + 3) < k_size) {
+ // just CHECK_RHS_BOUNDARY
+ rhs_pf0 = rhs.template loadPacket<float4,Unaligned>(rhs_vert, rhs_horiz0);
+ } else if (rhs_vert + 2 < k_size) {
+ // just CHECK_RHS_BOUNDARY
+ rhs_pf0.x = rhs(rhs_vert, rhs_horiz0);
+ rhs_pf0.y = rhs(rhs_vert + 1, rhs_horiz0);
+ rhs_pf0.z = rhs(rhs_vert + 2, rhs_horiz0);
+ } else if (rhs_vert + 1 < k_size) {
+ rhs_pf0.x = rhs(rhs_vert, rhs_horiz0);
+ rhs_pf0.y = rhs(rhs_vert + 1, rhs_horiz0);
+ } else if (rhs_vert < k_size) {
+ rhs_pf0.x = rhs(rhs_vert, rhs_horiz0);
+ }
+ } else {
+ if (rhs_horiz0 < n_size) {
+ if ((rhs_vert + 3) < k_size) {
+ rhs_pf0 = rhs.template loadPacket<float4,Unaligned>(rhs_vert, rhs_horiz0);
+ } else if ((rhs_vert + 2) < k_size) {
+ rhs_pf0.x = rhs(rhs_vert, rhs_horiz0);
+ rhs_pf0.y = rhs(rhs_vert + 1, rhs_horiz0);
+ rhs_pf0.z = rhs(rhs_vert + 2, rhs_horiz0);
+ } else if ((rhs_vert + 1) < k_size) {
+ rhs_pf0.x = rhs(rhs_vert, rhs_horiz0);
+ rhs_pf0.y = rhs(rhs_vert + 1, rhs_horiz0);
+ } else if (rhs_vert < k_size) {
+ rhs_pf0.x = rhs(rhs_vert, rhs_horiz0);
+ }
+ }
+ }
+ float x1, x2 ;
+ // the following can be a bitwise operation..... some day.
+ if((threadIdx.x%8) < 4) {
+ x1 = rhs_pf0.y;
+ x2 = rhs_pf0.w;
+ } else {
+ x1 = rhs_pf0.x;
+ x2 = rhs_pf0.z;
+ }
+ #if defined(EIGEN_HIPCC) || (defined(EIGEN_CUDA_SDK_VER) && EIGEN_CUDA_SDK_VER < 90000)
+ x1 = __shfl_xor(x1, 4);
+ x2 = __shfl_xor(x2, 4);
+ #else
+ x1 = __shfl_xor_sync(0xFFFFFFFF, x1, 4);
+ x2 = __shfl_xor_sync(0xFFFFFFFF, x2, 4);
+ #endif
+ if((threadIdx.x%8) < 4) {
+ rhs_pf0.y = x1;
+ rhs_pf0.w = x2;
+ } else {
+ rhs_pf0.x = x1;
+ rhs_pf0.z = x2;
+ }
+
+ // We have 64 features.
+ // Row 0 -> times (0, 4, 8, 12, 1, 5, 9, 13) for features 0, 1.
+ // Row 1 -> times (0, 4, 8, 12, 1, 5, 9, 13) for features 2, 3.
+ // ...
+ // Row 31 -> times (0, 4, 8, 12, 1, 5, 9, 13) for features 62, 63
+ // Row 32 -> times (2, 6, 10, 14, 3, 7, 11, 15) for features 0, 1
+ // ...
+ rhs_shmem2[(threadIdx.x>>3)+ threadIdx.y*2][threadIdx.x%8] = make_float2(rhs_pf0.x, rhs_pf0.y);
+ rhs_shmem2[(threadIdx.x>>3)+ threadIdx.y*2+32][threadIdx.x%8] = make_float2(rhs_pf0.z, rhs_pf0.w);
+
+ // Row 0 (time 0) -> features (0, 1), (4, 5), .. (28, 29), (32, 33), .. (60, 61)
+ // Row 1 (time 1) -> features (0, 1), (4, 5), .. (28, 29), (32, 33), .. (60, 61)
+ // ...
+ // Row 15 (time 15) -> features (0, 1), (4, 5), .. (28, 29), (32, 33), .. (60, 61)
+ // Row 16 (time 0) -> features (2, 3), (6, 7), .. (30, 31), (34, 35), .. (62, 63)
+ // ...
+
+ lhs_shmem2[threadIdx.y][threadIdx.x] = make_float2(lhs_pf0.x, lhs_pf0.y);
+ lhs_shmem2[threadIdx.y+16][threadIdx.x] = make_float2(lhs_pf0.z, lhs_pf0.w);
+
+
+#define add_vals(fl1, fl2, fr1, fr2)\
+ results[0].x += fl1.x * fr1.x;\
+ results[0].y += fl1.y * fr1.x;\
+ results[0].z += fl2.x * fr1.x;\
+ results[0].w += fl2.y * fr1.x;\
+\
+ results[1].x += fl1.x * fr1.y;\
+ results[1].y += fl1.y * fr1.y;\
+ results[1].z += fl2.x * fr1.y;\
+ results[1].w += fl2.y * fr1.y;\
+\
+ results[2].x += fl1.x * fr2.x;\
+ results[2].y += fl1.y * fr2.x;\
+ results[2].z += fl2.x * fr2.x;\
+ results[2].w += fl2.y * fr2.x;\
+\
+ results[3].x += fl1.x * fr2.y;\
+ results[3].y += fl1.y * fr2.y;\
+ results[3].z += fl2.x * fr2.y;\
+ results[3].w += fl2.y * fr2.y;\
+
+ __syncthreads();
+
+ // Do the multiplies.
+ #pragma unroll
+ for (int koff = 0; koff < 16; koff ++) {
+ // 32 x threads.
+ float2 fl1 = lhs_shmem2[koff][threadIdx.x];
+ float2 fl2 = lhs_shmem2[koff + 16][threadIdx.x];
+
+ int start_feature = threadIdx.y * 4;
+ float2 fr1 = rhs_shmem2[(start_feature>>1) + 32*((koff%4)/2)][koff/4 + (koff%2)*4];
+ float2 fr2 = rhs_shmem2[(start_feature>>1) + 1 + 32*((koff%4)/2)][koff/4 + (koff%2)*4];
+
+ add_vals(fl1, fl2, fr1, fr2)
+ }
+ __syncthreads();
+ }
+
+#undef prefetch_lhs
+#undef add_vals
+
+ Index horiz_base = threadIdx.y*4+base_n;
+ if (!CHECK_LHS_BOUNDARY && !CHECK_RHS_BOUNDARY) {
+ for (int i = 0; i < 4; i++) {
+ output(lhs_vert, horiz_base + i) = results[i].x;
+ output(lhs_vert + 1, horiz_base + i) = results[i].y;
+ output(lhs_vert + 2, horiz_base + i) = results[i].z;
+ output(lhs_vert + 3, horiz_base + i) = results[i].w;
+ }
+ } else if (!CHECK_RHS_BOUNDARY) {
+ // CHECK LHS
+ if (lhs_vert + 3 < m_size) {
+ for (int i = 0; i < 4; i++) {
+ output(lhs_vert, horiz_base + i) = results[i].x;
+ output(lhs_vert + 1, horiz_base + i) = results[i].y;
+ output(lhs_vert + 2, horiz_base + i) = results[i].z;
+ output(lhs_vert + 3, horiz_base + i) = results[i].w;
+ }
+ } else if (lhs_vert + 2 < m_size) {
+ for (int i = 0; i < 4; i++) {
+ output(lhs_vert, horiz_base + i) = results[i].x;
+ output(lhs_vert + 1, horiz_base + i) = results[i].y;
+ output(lhs_vert + 2, horiz_base + i) = results[i].z;
+ }
+ } else if (lhs_vert + 1 < m_size) {
+ for (int i = 0; i < 4; i++) {
+ output(lhs_vert, horiz_base + i) = results[i].x;
+ output(lhs_vert + 1, horiz_base + i) = results[i].y;
+ }
+ } else if (lhs_vert < m_size) {
+ for (int i = 0; i < 4; i++) {
+ output(lhs_vert, horiz_base + i) = results[i].x;
+ }
+ }
+ } else if (!CHECK_LHS_BOUNDARY) {
+ // CHECK RHS
+ /*
+ int ncols_rem = fminf(n_size- horiz_base, 4);
+ for (int i = 0; i < ncols_rem; i++) {
+ output(lhs_vert, horiz_base + i) = results[i].x;
+ output(lhs_vert + 1, horiz_base + i) = results[i].y;
+ output(lhs_vert + 2, horiz_base + i) = results[i].z;
+ output(lhs_vert + 3, horiz_base + i) = results[i].w;
+ }*/
+ for (int i = 0; i < 4; i++) {
+ if (horiz_base+i < n_size) {
+ output(lhs_vert, horiz_base + i) = results[i].x;
+ output(lhs_vert + 1, horiz_base + i) = results[i].y;
+ output(lhs_vert + 2, horiz_base + i) = results[i].z;
+ output(lhs_vert + 3, horiz_base + i) = results[i].w;
+ }
+ }
+ } else {
+ // CHECK both boundaries.
+ for (int i = 0; i < 4; i++) {
+ if (horiz_base+i < n_size) {
+ if (lhs_vert < m_size)
+ output(lhs_vert, horiz_base + i) = results[i].x;
+ if (lhs_vert + 1 < m_size)
+ output(lhs_vert + 1, horiz_base + i) = results[i].y;
+ if (lhs_vert + 2 < m_size)
+ output(lhs_vert + 2, horiz_base + i) = results[i].z;
+ if (lhs_vert + 3 < m_size)
+ output(lhs_vert + 3, horiz_base + i) = results[i].w;
+ }
+ }
+ }
+}
+
+
+template<typename Index, typename LhsMapper,
+ typename RhsMapper, typename OutputMapper, bool CHECK_LHS_BOUNDARY,
+ bool CHECK_RHS_BOUNDARY>
+__device__ __forceinline__ void
+EigenFloatContractionKernelInternal(const LhsMapper lhs, const RhsMapper rhs,
+ const OutputMapper output, float2 lhs_shmem2[][32],
+ float2 rhs_shmem2[][8], const Index m_size,
+ const Index n_size, const Index k_size,
+ const Index base_m, const Index base_n) {
+
+ // prefetch registers
+ float4 lhs_pf0, lhs_pf1, lhs_pf2, lhs_pf3;
+ float4 rhs_pf0, rhs_pf1;
+
+ float4 results[8];
+ for (int i=0; i < 8; i++) {
+ results[i].x = results[i].y = results[i].z = results[i].w = 0;
+ }
+
+ Index lhs_vert = base_m+threadIdx.x*4+(threadIdx.y%4)*32;
+ for (Index k = 0; k < k_size; k += 32) {
+ lhs_pf0 = internal::pset1<float4>(0);
+ lhs_pf1 = internal::pset1<float4>(0);
+ lhs_pf2 = internal::pset1<float4>(0);
+ lhs_pf3 = internal::pset1<float4>(0);
+
+ rhs_pf0 = internal::pset1<float4>(0);
+ rhs_pf1 = internal::pset1<float4>(0);
+
+ if (!CHECK_LHS_BOUNDARY) {
+ if ((threadIdx.y/4+k+24) < k_size) {
+ lhs_pf0 =lhs.template loadPacket<float4,Unaligned>(lhs_vert, (threadIdx.y/4+k));
+ lhs_pf1 =lhs.template loadPacket<float4,Unaligned>(lhs_vert, (threadIdx.y/4+k+8));
+ lhs_pf2 =lhs.template loadPacket<float4,Unaligned>(lhs_vert, (threadIdx.y/4+k+16));
+ lhs_pf3 =lhs.template loadPacket<float4,Unaligned>(lhs_vert, (threadIdx.y/4+k+24));
+ } else if ((threadIdx.y/4+k+16) < k_size) {
+ lhs_pf0 =lhs.template loadPacket<float4,Unaligned>(lhs_vert, (threadIdx.y/4+k));
+ lhs_pf1 =lhs.template loadPacket<float4,Unaligned>(lhs_vert, (threadIdx.y/4+k+8));
+ lhs_pf2 =lhs.template loadPacket<float4,Unaligned>(lhs_vert, (threadIdx.y/4+k+16));
+ } else if ((threadIdx.y/4+k+8) < k_size) {
+ lhs_pf0 =lhs.template loadPacket<float4,Unaligned>(lhs_vert, (threadIdx.y/4+k));
+ lhs_pf1 =lhs.template loadPacket<float4,Unaligned>(lhs_vert, (threadIdx.y/4+k+8));
+ } else if ((threadIdx.y/4+k) < k_size) {
+ lhs_pf0 =lhs.template loadPacket<float4,Unaligned>(lhs_vert, (threadIdx.y/4+k));
+ }
+ } else {
+ // just CHECK_LHS_BOUNDARY
+ if (lhs_vert + 3 < m_size) {
+ if ((threadIdx.y/4+k+24) < k_size) {
+ lhs_pf0 =lhs.template loadPacket<float4,Unaligned>(lhs_vert, (threadIdx.y/4+k));
+ lhs_pf1 =lhs.template loadPacket<float4,Unaligned>(lhs_vert, (threadIdx.y/4+k+8));
+ lhs_pf2 =lhs.template loadPacket<float4,Unaligned>(lhs_vert, (threadIdx.y/4+k+16));
+ lhs_pf3 =lhs.template loadPacket<float4,Unaligned>(lhs_vert, (threadIdx.y/4+k+24));
+ } else if ((threadIdx.y/4+k+16) < k_size) {
+ lhs_pf0 =lhs.template loadPacket<float4,Unaligned>(lhs_vert, (threadIdx.y/4+k));
+ lhs_pf1 =lhs.template loadPacket<float4,Unaligned>(lhs_vert, (threadIdx.y/4+k+8));
+ lhs_pf2 =lhs.template loadPacket<float4,Unaligned>(lhs_vert, (threadIdx.y/4+k+16));
+ } else if ((threadIdx.y/4+k+8) < k_size) {
+ lhs_pf0 =lhs.template loadPacket<float4,Unaligned>(lhs_vert, (threadIdx.y/4+k));
+ lhs_pf1 =lhs.template loadPacket<float4,Unaligned>(lhs_vert, (threadIdx.y/4+k+8));
+ } else if ((threadIdx.y/4+k) < k_size) {
+ lhs_pf0 =lhs.template loadPacket<float4,Unaligned>(lhs_vert, (threadIdx.y/4+k));
+ }
+ } else if (lhs_vert + 2 < m_size) {
+ if ((threadIdx.y/4+k+24) < k_size) {
+ lhs_pf0.x =lhs(lhs_vert + 0, (threadIdx.y/4+k));
+ lhs_pf0.y =lhs(lhs_vert + 1, (threadIdx.y/4+k));
+ lhs_pf0.z =lhs(lhs_vert + 2, (threadIdx.y/4+k));
+ lhs_pf1.x =lhs(lhs_vert + 0, (threadIdx.y/4+k+8));
+ lhs_pf1.y =lhs(lhs_vert + 1, (threadIdx.y/4+k+8));
+ lhs_pf1.z =lhs(lhs_vert + 2, (threadIdx.y/4+k+8));
+ lhs_pf2.x =lhs(lhs_vert + 0, (threadIdx.y/4+k+16));
+ lhs_pf2.y =lhs(lhs_vert + 1, (threadIdx.y/4+k+16));
+ lhs_pf2.z =lhs(lhs_vert + 2, (threadIdx.y/4+k+16));
+ lhs_pf3.x =lhs(lhs_vert + 0, (threadIdx.y/4+k+24));
+ lhs_pf3.y =lhs(lhs_vert + 1, (threadIdx.y/4+k+24));
+ lhs_pf3.z =lhs(lhs_vert + 2, (threadIdx.y/4+k+24));
+ } else if ((threadIdx.y/4+k+16) < k_size) {
+ lhs_pf0.x =lhs(lhs_vert + 0, (threadIdx.y/4+k));
+ lhs_pf0.y =lhs(lhs_vert + 1, (threadIdx.y/4+k));
+ lhs_pf0.z =lhs(lhs_vert + 2, (threadIdx.y/4+k));
+ lhs_pf1.x =lhs(lhs_vert + 0, (threadIdx.y/4+k+8));
+ lhs_pf1.y =lhs(lhs_vert + 1, (threadIdx.y/4+k+8));
+ lhs_pf1.z =lhs(lhs_vert + 2, (threadIdx.y/4+k+8));
+ lhs_pf2.x =lhs(lhs_vert + 0, (threadIdx.y/4+k+16));
+ lhs_pf2.y =lhs(lhs_vert + 1, (threadIdx.y/4+k+16));
+ lhs_pf2.z =lhs(lhs_vert + 2, (threadIdx.y/4+k+16));
+ } else if ((threadIdx.y/4+k+8) < k_size) {
+ lhs_pf0.x =lhs(lhs_vert + 0, (threadIdx.y/4+k));
+ lhs_pf0.y =lhs(lhs_vert + 1, (threadIdx.y/4+k));
+ lhs_pf0.z =lhs(lhs_vert + 2, (threadIdx.y/4+k));
+ lhs_pf1.x =lhs(lhs_vert + 0, (threadIdx.y/4+k+8));
+ lhs_pf1.y =lhs(lhs_vert + 1, (threadIdx.y/4+k+8));
+ lhs_pf1.z =lhs(lhs_vert + 2, (threadIdx.y/4+k+8));
+ } else if ((threadIdx.y/4+k) < k_size) {
+ lhs_pf0.x =lhs(lhs_vert + 0, (threadIdx.y/4+k));
+ lhs_pf0.y =lhs(lhs_vert + 1, (threadIdx.y/4+k));
+ lhs_pf0.z =lhs(lhs_vert + 2, (threadIdx.y/4+k));
+ }
+ } else if (lhs_vert + 1 < m_size) {
+ if ((threadIdx.y/4+k+24) < k_size) {
+ lhs_pf0.x =lhs(lhs_vert + 0, (threadIdx.y/4+k));
+ lhs_pf0.y =lhs(lhs_vert + 1, (threadIdx.y/4+k));
+ lhs_pf1.x =lhs(lhs_vert + 0, (threadIdx.y/4+k+8));
+ lhs_pf1.y =lhs(lhs_vert + 1, (threadIdx.y/4+k+8));
+ lhs_pf2.x =lhs(lhs_vert + 0, (threadIdx.y/4+k+16));
+ lhs_pf2.y =lhs(lhs_vert + 1, (threadIdx.y/4+k+16));
+ lhs_pf3.x =lhs(lhs_vert + 0, (threadIdx.y/4+k+24));
+ lhs_pf3.y =lhs(lhs_vert + 1, (threadIdx.y/4+k+24));
+ } else if ((threadIdx.y/4+k+16) < k_size) {
+ lhs_pf0.x =lhs(lhs_vert + 0, (threadIdx.y/4+k));
+ lhs_pf0.y =lhs(lhs_vert + 1, (threadIdx.y/4+k));
+ lhs_pf1.x =lhs(lhs_vert + 0, (threadIdx.y/4+k+8));
+ lhs_pf1.y =lhs(lhs_vert + 1, (threadIdx.y/4+k+8));
+ lhs_pf2.x =lhs(lhs_vert + 0, (threadIdx.y/4+k+16));
+ lhs_pf2.y =lhs(lhs_vert + 1, (threadIdx.y/4+k+16));
+ } else if ((threadIdx.y/4+k+8) < k_size) {
+ lhs_pf0.x =lhs(lhs_vert + 0, (threadIdx.y/4+k));
+ lhs_pf0.y =lhs(lhs_vert + 1, (threadIdx.y/4+k));
+ lhs_pf1.x =lhs(lhs_vert + 0, (threadIdx.y/4+k+8));
+ lhs_pf1.y =lhs(lhs_vert + 1, (threadIdx.y/4+k+8));
+ } else if ((threadIdx.y/4+k) < k_size) {
+ lhs_pf0.x =lhs(lhs_vert + 0, (threadIdx.y/4+k));
+ lhs_pf0.y =lhs(lhs_vert + 1, (threadIdx.y/4+k));
+ }
+ } else if (lhs_vert < m_size) {
+ if ((threadIdx.y/4+k+24) < k_size) {
+ lhs_pf0.x =lhs(lhs_vert + 0, (threadIdx.y/4+k));
+ lhs_pf1.x =lhs(lhs_vert + 0, (threadIdx.y/4+k+8));
+ lhs_pf2.x =lhs(lhs_vert + 0, (threadIdx.y/4+k+16));
+ lhs_pf3.x =lhs(lhs_vert + 0, (threadIdx.y/4+k+24));
+ } else if ((threadIdx.y/4+k+16) < k_size) {
+ lhs_pf0.x =lhs(lhs_vert + 0, (threadIdx.y/4+k));
+ lhs_pf1.x =lhs(lhs_vert + 0, (threadIdx.y/4+k+8));
+ lhs_pf2.x =lhs(lhs_vert + 0, (threadIdx.y/4+k+16));
+ } else if ((threadIdx.y/4+k+8) < k_size) {
+ lhs_pf0.x =lhs(lhs_vert + 0, (threadIdx.y/4+k));
+ lhs_pf1.x =lhs(lhs_vert + 0, (threadIdx.y/4+k+8));
+ } else if ((threadIdx.y/4+k) < k_size) {
+ lhs_pf0.x =lhs(lhs_vert + 0, (threadIdx.y/4+k));
+ }
+ }
+ }
+ __syncthreads();
+ Index rhs_vert = k+threadIdx.x*4;
+ Index rhs_horiz0 = threadIdx.y*2+base_n;
+ Index rhs_horiz1 = threadIdx.y*2+1+base_n;
+ if (!CHECK_RHS_BOUNDARY) {
+ if ((rhs_vert + 3) < k_size) {
+ // just CHECK_RHS_BOUNDARY
+ rhs_pf0 = rhs.template loadPacket<float4,Unaligned>(rhs_vert, rhs_horiz0);
+ rhs_pf1 = rhs.template loadPacket<float4,Unaligned>(rhs_vert, rhs_horiz1);
+ } else if (rhs_vert + 2 < k_size) {
+ // just CHECK_RHS_BOUNDARY
+ rhs_pf0.x = rhs(rhs_vert, rhs_horiz0);
+ rhs_pf0.y = rhs(rhs_vert + 1, rhs_horiz0);
+ rhs_pf0.z = rhs(rhs_vert + 2, rhs_horiz0);
+ rhs_pf1.x = rhs(rhs_vert, rhs_horiz1);
+ rhs_pf1.y = rhs(rhs_vert + 1, rhs_horiz1);
+ rhs_pf1.z = rhs(rhs_vert + 2, rhs_horiz1);
+ } else if (rhs_vert + 1 < k_size) {
+ rhs_pf0.x = rhs(rhs_vert, rhs_horiz0);
+ rhs_pf0.y = rhs(rhs_vert + 1, rhs_horiz0);
+ rhs_pf1.x = rhs(rhs_vert, rhs_horiz1);
+ rhs_pf1.y = rhs(rhs_vert + 1, rhs_horiz1);
+ } else if (rhs_vert < k_size) {
+ rhs_pf0.x = rhs(rhs_vert, rhs_horiz0);
+ rhs_pf1.x = rhs(rhs_vert, rhs_horiz1);
+ }
+ } else {
+ if (rhs_horiz1 < n_size) {
+ if ((rhs_vert + 3) < k_size) {
+ // just CHECK_RHS_BOUNDARY
+ rhs_pf0 = rhs.template loadPacket<float4,Unaligned>(rhs_vert, rhs_horiz0);
+ rhs_pf1 = rhs.template loadPacket<float4,Unaligned>(rhs_vert, rhs_horiz1);
+ } else if (rhs_vert + 2 < k_size) {
+ // just CHECK_RHS_BOUNDARY
+ rhs_pf0.x = rhs(rhs_vert, rhs_horiz0);
+ rhs_pf0.y = rhs(rhs_vert + 1, rhs_horiz0);
+ rhs_pf0.z = rhs(rhs_vert + 2, rhs_horiz0);
+ rhs_pf1.x = rhs(rhs_vert, rhs_horiz1);
+ rhs_pf1.y = rhs(rhs_vert + 1, rhs_horiz1);
+ rhs_pf1.z = rhs(rhs_vert + 2, rhs_horiz1);
+ } else if (k+threadIdx.x*4 + 1 < k_size) {
+ rhs_pf0.x = rhs(rhs_vert, rhs_horiz0);
+ rhs_pf0.y = rhs(rhs_vert + 1, rhs_horiz0);
+ rhs_pf1.x = rhs(rhs_vert, rhs_horiz1);
+ rhs_pf1.y = rhs(rhs_vert + 1, rhs_horiz1);
+ } else if (k+threadIdx.x*4 < k_size) {
+ rhs_pf0.x = rhs(rhs_vert, rhs_horiz0);
+ rhs_pf1.x = rhs(rhs_vert, rhs_horiz1);
+ }
+ } else if (rhs_horiz0 < n_size) {
+ if ((rhs_vert + 3) < k_size) {
+ // just CHECK_RHS_BOUNDARY
+ rhs_pf0 = rhs.template loadPacket<float4,Unaligned>(rhs_vert, rhs_horiz0);
+ } else if ((rhs_vert + 2) < k_size) {
+ // just CHECK_RHS_BOUNDARY
+ rhs_pf0.x = rhs(rhs_vert, rhs_horiz0);
+ rhs_pf0.y = rhs(rhs_vert + 1, rhs_horiz0);
+ rhs_pf0.z = rhs(rhs_vert + 2, rhs_horiz0);
+ } else if ((rhs_vert + 1) < k_size) {
+ rhs_pf0.x = rhs(rhs_vert, rhs_horiz0);
+ rhs_pf0.y = rhs(rhs_vert + 1, rhs_horiz0);
+ } else if (rhs_vert < k_size) {
+ rhs_pf0.x = rhs(rhs_vert, rhs_horiz0);
+ }
+ }
+ }
+ __syncthreads();
+ // Loaded. Do computation
+ // Row 0 -> times (0, 4, 8, .. 28) for features 0, 1.
+ // Row 1 -> times (0, 4, 8, .. 28) for features 2, 3.
+ // ..
+ // Row 31 -> times (0, 4, 8, .. 28) for features 62, 63
+ rhs_shmem2[threadIdx.y][threadIdx.x] = make_float2(rhs_pf0.x, rhs_pf1.x);
+ // Row 32 -> times (1, 5, 9, .. 29) for features 0, 1.
+ // Row 33 -> times (1, 5, 9, .. 29) for features 2, 3.
+ // ..
+ rhs_shmem2[threadIdx.y+32][threadIdx.x] = make_float2(rhs_pf0.y, rhs_pf1.y);
+ // Row 64 -> times (2, 6, 10, .. 30) for features 0, 1.
+ // Row 65 -> times (2, 6, 10, .. 30) for features 2, 3.
+ rhs_shmem2[threadIdx.y+64][threadIdx.x] = make_float2(rhs_pf0.z, rhs_pf1.z);
+ // Row 96 -> times (3, 7, 11, .. 31) for features 0, 1.
+ // Row 97 -> times (3, 7, 11, .. 31) for features 2, 3.
+ rhs_shmem2[threadIdx.y+96][threadIdx.x] = make_float2(rhs_pf0.w, rhs_pf1.w);
+
+ // LHS.
+ // Row 0 (time 0) -> features (0, 1), (4, 5), .. (28, 29), (32, 33), .. (60, 61) .. (124, 125)
+ // Row 1 (time 1) -> features (0, 1), (4, 5), .. (28, 29), (32, 33), .. (60, 61) .. (124, 125)
+ // ...
+ // Row 8 (time 0) -> features (2, 3), (6, 7), .. (30, 31), (34, 35), .. (62, 63) .. (126, 127)
+ // Row 15 (time 7) -> features (2, 3), (6, 7), .. (30, 31), (34, 35), .. (62, 63) .. (126, 127)
+
+
+#define add_vals(a_feat1, a_feat2, f1, f2, f3, f4)\
+ results[0].x += a_feat1.x * f1.x;\
+ results[1].x += a_feat1.x * f1.y;\
+ results[2].x += a_feat1.x * f2.x;\
+ results[3].x += a_feat1.x * f2.y;\
+ results[4].x += a_feat1.x * f3.x;\
+ results[5].x += a_feat1.x * f3.y;\
+ results[6].x += a_feat1.x * f4.x;\
+ results[7].x += a_feat1.x * f4.y;\
+\
+ results[0].y += a_feat1.y * f1.x;\
+ results[1].y += a_feat1.y * f1.y;\
+ results[2].y += a_feat1.y * f2.x;\
+ results[3].y += a_feat1.y * f2.y;\
+ results[4].y += a_feat1.y * f3.x;\
+ results[5].y += a_feat1.y * f3.y;\
+ results[6].y += a_feat1.y * f4.x;\
+ results[7].y += a_feat1.y * f4.y;\
+\
+ results[0].z += a_feat2.x * f1.x;\
+ results[1].z += a_feat2.x * f1.y;\
+ results[2].z += a_feat2.x * f2.x;\
+ results[3].z += a_feat2.x * f2.y;\
+ results[4].z += a_feat2.x * f3.x;\
+ results[5].z += a_feat2.x * f3.y;\
+ results[6].z += a_feat2.x * f4.x;\
+ results[7].z += a_feat2.x * f4.y;\
+\
+ results[0].w += a_feat2.y * f1.x;\
+ results[1].w += a_feat2.y * f1.y;\
+ results[2].w += a_feat2.y * f2.x;\
+ results[3].w += a_feat2.y * f2.y;\
+ results[4].w += a_feat2.y * f3.x;\
+ results[5].w += a_feat2.y * f3.y;\
+ results[6].w += a_feat2.y * f4.x;\
+ results[7].w += a_feat2.y * f4.y;\
+
+ lhs_shmem2[threadIdx.y/4][threadIdx.x+(threadIdx.y%4)*8] = make_float2(lhs_pf0.x, lhs_pf0.y);
+ lhs_shmem2[threadIdx.y/4+8][threadIdx.x+(threadIdx.y%4)*8] = make_float2(lhs_pf1.x, lhs_pf1.y);
+ lhs_shmem2[threadIdx.y/4+16][threadIdx.x+(threadIdx.y%4)*8] = make_float2(lhs_pf2.x, lhs_pf2.y);
+ lhs_shmem2[threadIdx.y/4+24][threadIdx.x+(threadIdx.y%4)*8] = make_float2(lhs_pf3.x, lhs_pf3.y);
+
+ lhs_shmem2[threadIdx.y/4 + 32][threadIdx.x+(threadIdx.y%4)*8] = make_float2(lhs_pf0.z, lhs_pf0.w);
+ lhs_shmem2[threadIdx.y/4 + 40][threadIdx.x+(threadIdx.y%4)*8] = make_float2(lhs_pf1.z, lhs_pf1.w);
+ lhs_shmem2[threadIdx.y/4 + 48][threadIdx.x+(threadIdx.y%4)*8] = make_float2(lhs_pf2.z, lhs_pf2.w);
+ lhs_shmem2[threadIdx.y/4 + 56][threadIdx.x+(threadIdx.y%4)*8] = make_float2(lhs_pf3.z, lhs_pf3.w);
+
+ __syncthreads();
+
+ // Do the multiplies.
+ #pragma unroll
+ for (int koff = 0; koff < 32; koff ++) {
+ float2 a3 = lhs_shmem2[koff][threadIdx.x + (threadIdx.y % 4) * 8];
+ float2 a4 = lhs_shmem2[koff + 32][threadIdx.x + (threadIdx.y % 4) * 8];
+
+ // first feature is at (threadIdx.y/4) * 8 last is at start + 8.
+ int start_feature = (threadIdx.y / 4) * 8;
+
+ float2 br1 = rhs_shmem2[start_feature/2 + (koff % 4) * 32][koff/4];
+ float2 br2 = rhs_shmem2[start_feature/2 + 1 + (koff % 4) * 32][koff/4];
+ float2 br3 = rhs_shmem2[start_feature/2 + 2 + (koff % 4) * 32][koff/4];
+ float2 br4 = rhs_shmem2[start_feature/2 + 3 + (koff % 4) * 32][koff/4];
+
+ add_vals(a3, a4, br1, br2, br3, br4)
+ }
+ __syncthreads();
+ } // end loop over k
+
+ __syncthreads();
+ Index horiz_base = (threadIdx.y/4)*8+base_n;
+ if (!CHECK_LHS_BOUNDARY && !CHECK_RHS_BOUNDARY) {
+ for (int i = 0; i < 8; i++) {
+ output(lhs_vert, horiz_base + i) = results[i].x;
+ output(lhs_vert + 1, horiz_base + i) = results[i].y;
+ output(lhs_vert + 2, horiz_base + i) = results[i].z;
+ output(lhs_vert + 3, horiz_base + i) = results[i].w;
+ }
+ } else if (!CHECK_RHS_BOUNDARY) {
+ if (lhs_vert + 3 < m_size) {
+ for (int i = 0; i < 8; i++) {
+ output(lhs_vert, horiz_base + i) = results[i].x;
+ output(lhs_vert + 1, horiz_base + i) = results[i].y;
+ output(lhs_vert + 2, horiz_base + i) = results[i].z;
+ output(lhs_vert + 3, horiz_base + i) = results[i].w;
+ }
+ } else if (lhs_vert + 2 < m_size) {
+ for (int i = 0; i < 8; i++) {
+ output(lhs_vert, horiz_base + i) = results[i].x;
+ output(lhs_vert + 1, horiz_base + i) = results[i].y;
+ output(lhs_vert + 2, horiz_base + i) = results[i].z;
+ }
+ } else if (lhs_vert + 1 < m_size) {
+ for (int i = 0; i < 8; i++) {
+ output(lhs_vert, horiz_base + i) = results[i].x;
+ output(lhs_vert + 1, horiz_base + i) = results[i].y;
+ }
+ } else if (lhs_vert < m_size) {
+ for (int i = 0; i < 8; i++) {
+ output(lhs_vert, horiz_base + i) = results[i].x;
+ }
+ }
+ } else if (!CHECK_LHS_BOUNDARY) {
+ // CHECK BOUNDARY_B
+ for (int i = 0; i < 8; i++) {
+ if (horiz_base + i < n_size) {
+ output(lhs_vert, horiz_base + i) = results[i].x;
+ output(lhs_vert + 1, horiz_base + i) = results[i].y;
+ output(lhs_vert + 2, horiz_base + i) = results[i].z;
+ output(lhs_vert + 3, horiz_base + i) = results[i].w;
+ }
+ }
+ } else {
+ // CHECK both boundaries.
+ for (int i = 0; i < 8; i++) {
+ if (horiz_base + i < n_size) {
+ if (lhs_vert < m_size)
+ output(lhs_vert, horiz_base + i) = results[i].x;
+ if (lhs_vert + 1 < m_size)
+ output(lhs_vert + 1, horiz_base + i) = results[i].y;
+ if (lhs_vert + 2 < m_size)
+ output(lhs_vert + 2, horiz_base + i) = results[i].z;
+ if (lhs_vert + 3 < m_size)
+ output(lhs_vert + 3, horiz_base + i) = results[i].w;
+ }
+ }
+ }
+}
+
+
+template<typename Index, typename LhsMapper,
+ typename RhsMapper, typename OutputMapper>
+__global__ void
+#if defined(EIGEN_HIPCC)
+__launch_bounds__(256, 1)
+#else
+__launch_bounds__(256)
+#endif
+EigenFloatContractionKernel(const LhsMapper lhs, const RhsMapper rhs,
+ const OutputMapper output,
+ const Index m_size, const Index n_size, const Index k_size) {
+ __shared__ float2 lhs_shmem[64*32];
+ __shared__ float2 rhs_shmem[128*8];
+
+ typedef float2 LHS_MEM[64][32];
+ typedef float2 RHS_MEM[128][8];
+
+ const Index m_block_idx = blockIdx.x;
+ const Index n_block_idx = blockIdx.y;
+
+ const Index base_m = 128 * m_block_idx;
+ const Index base_n = 64 * n_block_idx;
+
+ bool check_rhs = (base_n + 63) >= n_size;
+ bool check_lhs128 = (base_m + 127) >= m_size;
+
+ if (!check_rhs) {
+ if (!check_lhs128) {
+ // >= 128 rows left
+ EigenFloatContractionKernelInternal<Index, LhsMapper, RhsMapper, OutputMapper, false, false>(
+ lhs, rhs, output, *((LHS_MEM *) lhs_shmem), *((RHS_MEM *) rhs_shmem), m_size, n_size, k_size, base_m, base_n);
+ } else {
+ EigenFloatContractionKernelInternal<Index, LhsMapper, RhsMapper, OutputMapper, true, false>(
+ lhs, rhs, output, *((LHS_MEM *) lhs_shmem), *((RHS_MEM *) rhs_shmem), m_size, n_size, k_size, base_m, base_n);
+ }
+ } else {
+ if (!check_lhs128) {
+ // >= 128 rows left
+ EigenFloatContractionKernelInternal<Index, LhsMapper, RhsMapper, OutputMapper, false, true>(
+ lhs, rhs, output, *((LHS_MEM *) lhs_shmem), *((RHS_MEM *) rhs_shmem), m_size, n_size, k_size, base_m, base_n);
+ } else {
+ EigenFloatContractionKernelInternal<Index, LhsMapper, RhsMapper, OutputMapper, true, true>(
+ lhs, rhs, output, *((LHS_MEM *) lhs_shmem), *((RHS_MEM *) rhs_shmem), m_size, n_size, k_size, base_m, base_n);
+ }
+ }
+}
+
+template<typename Index, typename LhsMapper,
+ typename RhsMapper, typename OutputMapper>
+__global__ void
+#if defined(EIGEN_HIPCC)
+__launch_bounds__(256, 1)
+#else
+__launch_bounds__(256)
+#endif
+EigenFloatContractionKernel16x16(const LhsMapper lhs, const RhsMapper rhs,
+ const OutputMapper output,
+ const Index m_size, const Index n_size, const Index k_size) {
+ __shared__ float2 lhs_shmem[32][16];
+ __shared__ float2 rhs_shmem[64][8];
+
+ const Index m_block_idx = blockIdx.x;
+ const Index n_block_idx = blockIdx.y;
+
+ const Index base_m = 64 * m_block_idx;
+ const Index base_n = 64 * n_block_idx;
+
+ if (base_m + 63 < m_size) {
+ if (base_n + 63 < n_size) {
+ EigenFloatContractionKernelInternal16x16<Index, LhsMapper, RhsMapper, OutputMapper, false, false>(lhs, rhs, output, lhs_shmem, rhs_shmem, m_size, n_size, k_size, base_m, base_n);
+ } else {
+ EigenFloatContractionKernelInternal16x16<Index, LhsMapper, RhsMapper, OutputMapper, false, true>(lhs, rhs, output, lhs_shmem, rhs_shmem, m_size, n_size, k_size, base_m, base_n);
+ }
+ } else {
+ if (base_n + 63 < n_size) {
+ EigenFloatContractionKernelInternal16x16<Index, LhsMapper, RhsMapper, OutputMapper, true, false>(lhs, rhs, output, lhs_shmem, rhs_shmem, m_size, n_size, k_size, base_m, base_n);
+ } else {
+ EigenFloatContractionKernelInternal16x16<Index, LhsMapper, RhsMapper, OutputMapper, true, true>(lhs, rhs, output, lhs_shmem, rhs_shmem, m_size, n_size, k_size, base_m, base_n);
+ }
+ }
+}
+
+
+template<typename Indices, typename LeftArgType, typename RightArgType, typename OutputKernelType>
+struct TensorEvaluator<const TensorContractionOp<Indices, LeftArgType, RightArgType, OutputKernelType>, GpuDevice> :
+ public TensorContractionEvaluatorBase<TensorEvaluator<const TensorContractionOp<Indices, LeftArgType, RightArgType, OutputKernelType>, GpuDevice> > {
+
+ typedef GpuDevice Device;
+
+ typedef TensorEvaluator<const TensorContractionOp<Indices, LeftArgType, RightArgType, OutputKernelType>, Device> Self;
+ typedef TensorContractionEvaluatorBase<Self> Base;
+
+ typedef TensorContractionOp<Indices, LeftArgType, RightArgType, OutputKernelType> XprType;
+ typedef std::remove_const_t<typename XprType::Scalar> Scalar;
+ typedef typename XprType::Index Index;
+ typedef typename XprType::CoeffReturnType CoeffReturnType;
+ typedef typename PacketType<CoeffReturnType, GpuDevice>::type PacketReturnType;
+
+ static constexpr int Layout = TensorEvaluator<LeftArgType, Device>::Layout;
+
+ // Most of the code is assuming that both input tensors are ColMajor. If the
+ // inputs are RowMajor, we will "cheat" by swapping the LHS and RHS:
+ // If we want to compute A * B = C, where A is LHS and B is RHS, the code
+ // will pretend B is LHS and A is RHS.
+ typedef std::conditional_t<Layout == static_cast<int>(ColMajor), LeftArgType, RightArgType> EvalLeftArgType;
+ typedef std::conditional_t<Layout == static_cast<int>(ColMajor), RightArgType, LeftArgType> EvalRightArgType;
+
+ static constexpr int LDims =
+ internal::array_size<typename TensorEvaluator<EvalLeftArgType, Device>::Dimensions>::value;
+ static constexpr int RDims =
+ internal::array_size<typename TensorEvaluator<EvalRightArgType, Device>::Dimensions>::value;
+ static constexpr int ContractDims = internal::array_size<Indices>::value;
+
+ typedef array<Index, LDims> left_dim_mapper_t;
+ typedef array<Index, RDims> right_dim_mapper_t;
+
+ typedef array<Index, ContractDims> contract_t;
+ typedef array<Index, LDims - ContractDims> left_nocontract_t;
+ typedef array<Index, RDims - ContractDims> right_nocontract_t;
+
+ static constexpr int NumDims = LDims + RDims - 2 * ContractDims;
+
+ typedef DSizes<Index, NumDims> Dimensions;
+
+ // typedefs needed in evalTo
+ typedef std::remove_const_t<typename EvalLeftArgType::Scalar> LhsScalar;
+ typedef std::remove_const_t<typename EvalRightArgType::Scalar> RhsScalar;
+
+ typedef TensorEvaluator<EvalLeftArgType, Device> LeftEvaluator;
+ typedef TensorEvaluator<EvalRightArgType, Device> RightEvaluator;
+
+ typedef typename LeftEvaluator::Dimensions LeftDimensions;
+ typedef typename RightEvaluator::Dimensions RightDimensions;
+
+ TensorEvaluator(const XprType& op, const Device& device) :
+ Base(op, device)
+ {
+ EIGEN_STATIC_ASSERT( (internal::is_same<OutputKernelType, const NoOpOutputKernel>::value),
+ GPU_TENSOR_CONTRACTION_DOES_NOT_SUPPORT_OUTPUT_KERNELS);
+ }
+
+ // We need to redefine this method to make nvcc happy
+ EIGEN_STRONG_INLINE bool evalSubExprsIfNeeded(Scalar* data) {
+ this->m_leftImpl.evalSubExprsIfNeeded(NULL);
+ this->m_rightImpl.evalSubExprsIfNeeded(NULL);
+ if (data) {
+ evalTo(data);
+ return false;
+ } else {
+ this->m_result = static_cast<Scalar *>(this->m_device.allocate(this->dimensions().TotalSize() * sizeof(Scalar)));
+ evalTo(this->m_result);
+ return true;
+ }
+ }
+
+ void evalTo(Scalar* buffer) const {
+ if (this->m_lhs_inner_dim_contiguous) {
+ if (this->m_rhs_inner_dim_contiguous) {
+ if (this->m_rhs_inner_dim_reordered) {
+ evalTyped<true, true, true, Unaligned>(buffer);
+ }
+ else {
+ evalTyped<true, true, false, Unaligned>(buffer);
+ }
+ }
+ else {
+ if (this->m_rhs_inner_dim_reordered) {
+ evalTyped<true, false, true, Unaligned>(buffer);
+ }
+ else {
+ evalTyped<true, false, false, Unaligned>(buffer);
+ }
+ }
+ }
+ else {
+ if (this->m_rhs_inner_dim_contiguous) {
+ if (this->m_rhs_inner_dim_reordered) {
+ evalTyped<false, true, true, Unaligned>(buffer);
+ }
+ else {
+ evalTyped<false, true, false, Unaligned>(buffer);
+ }
+ }
+ else {
+ if (this->m_rhs_inner_dim_reordered) {
+ evalTyped<false, false, true, Unaligned>(buffer);
+ }
+ else {
+ evalTyped<false, false, false, Unaligned>(buffer);
+ }
+ }
+ }
+ }
+
+ template <typename LhsScalar, typename RhsScalar, typename Index, typename LhsMapper, typename RhsMapper, typename OutputMapper> struct LaunchKernels {
+ static void Run(const LhsMapper& lhs, const RhsMapper& rhs, const OutputMapper& output, Index m, Index n, Index k, const GpuDevice& device) {
+ const Index m_blocks = (m + 63) / 64;
+ const Index n_blocks = (n + 63) / 64;
+ const dim3 num_blocks(m_blocks, n_blocks, 1);
+ const dim3 block_size(8, 8, 8);
+ LAUNCH_GPU_KERNEL((EigenContractionKernel<Scalar, Index, LhsMapper, RhsMapper, OutputMapper>), num_blocks, block_size, 0, device, lhs, rhs, output, m, n, k);
+ }
+ };
+
+ template <typename Index, typename LhsMapper, typename RhsMapper, typename OutputMapper> struct LaunchKernels<float, float, Index, LhsMapper, RhsMapper, OutputMapper> {
+ static void Run(const LhsMapper& lhs, const RhsMapper& rhs, const OutputMapper& output, Index m, Index n, Index k, const GpuDevice& device) {
+ if (m < 768 || n < 768) {
+ const Index m_blocks = (m + 63) / 64;
+ const Index n_blocks = (n + 63) / 64;
+ const dim3 num_blocks(m_blocks, n_blocks, 1);
+ const dim3 block_size(16, 16, 1);
+ LAUNCH_GPU_KERNEL((EigenFloatContractionKernel16x16<Index, LhsMapper, RhsMapper, OutputMapper>), num_blocks, block_size, 0, device, lhs, rhs, output, m, n, k);
+ } else {
+ const Index m_blocks = (m + 127) / 128;
+ const Index n_blocks = (n + 63) / 64;
+ const dim3 num_blocks(m_blocks, n_blocks, 1);
+ const dim3 block_size(8, 32, 1);
+ LAUNCH_GPU_KERNEL((EigenFloatContractionKernel<Index, LhsMapper, RhsMapper, OutputMapper>), num_blocks, block_size, 0, device, lhs, rhs, output, m, n, k);
+ }
+ }
+ };
+
+ template <bool lhs_inner_dim_contiguous, bool rhs_inner_dim_contiguous, bool rhs_inner_dim_reordered, int Alignment>
+ void evalTyped(Scalar* buffer) const {
+ // columns in left side, rows in right side
+ const Index k = this->m_k_size;
+ EIGEN_UNUSED_VARIABLE(k)
+
+ // rows in left side
+ const Index m = this->m_i_size;
+
+ // columns in right side
+ const Index n = this->m_j_size;
+
+ // zero out the result buffer (which must be of size at least m * n * sizeof(Scalar))
+ this->m_device.fill(buffer, buffer + m * n, Scalar(0));
+
+ typedef internal::TensorContractionInputMapper<LhsScalar, Index, internal::Lhs,
+ LeftEvaluator, left_nocontract_t,
+ contract_t, 4,
+ lhs_inner_dim_contiguous,
+ false, Unaligned> LhsMapper;
+
+ typedef internal::TensorContractionInputMapper<RhsScalar, Index, internal::Rhs,
+ RightEvaluator, right_nocontract_t,
+ contract_t, 4,
+ rhs_inner_dim_contiguous,
+ rhs_inner_dim_reordered, Unaligned> RhsMapper;
+
+ typedef internal::blas_data_mapper<Scalar, Index, ColMajor> OutputMapper;
+
+
+ // initialize data mappers
+ LhsMapper lhs(this->m_leftImpl, this->m_left_nocontract_strides, this->m_i_strides,
+ this->m_left_contracting_strides, this->m_k_strides);
+
+ RhsMapper rhs(this->m_rightImpl, this->m_right_nocontract_strides, this->m_j_strides,
+ this->m_right_contracting_strides, this->m_k_strides);
+
+ OutputMapper output(buffer, m);
+
+#if defined(EIGEN_USE_HIP)
+ setGpuSharedMemConfig(hipSharedMemBankSizeEightByte);
+#else
+ setGpuSharedMemConfig(cudaSharedMemBankSizeEightByte);
+#endif
+
+ LaunchKernels<LhsScalar, RhsScalar, Index, LhsMapper, RhsMapper, OutputMapper>::Run(lhs, rhs, output, m, n, k, this->m_device);
+ }
+};
+
+} // end namespace Eigen
+
+#endif // EIGEN_USE_GPU and EIGEN_GPUCC
+#endif // EIGEN_CXX11_TENSOR_TENSOR_CONTRACTION_GPU_H
diff --git a/unsupported/Eigen/CXX11/src/Tensor/TensorContractionMapper.h b/unsupported/Eigen/CXX11/src/Tensor/TensorContractionMapper.h
new file mode 100644
index 0000000..92cbaf6
--- /dev/null
+++ b/unsupported/Eigen/CXX11/src/Tensor/TensorContractionMapper.h
@@ -0,0 +1,590 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_CXX11_TENSOR_TENSOR_CONTRACTION_MAPPER_H
+#define EIGEN_CXX11_TENSOR_TENSOR_CONTRACTION_MAPPER_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+
+enum {
+ Rhs = 0,
+ Lhs = 1
+};
+
+/*
+ * Implementation of the Eigen blas_data_mapper class for tensors.
+ */
+/// The make pointer class is used by sycl in order to build the mapper class on the device. For other platform the default make pointer is used which
+/// is scalar * for CoeffLoader.
+template <typename Tensor, bool HasRawAccess, template <class> class MakePointer_ = MakePointer>
+struct CoeffLoader;
+
+template <typename Scalar, typename Index, int side, typename Tensor,
+ typename nocontract_t, typename contract_t, int packet_size,
+ bool inner_dim_contiguous, bool inner_dim_reordered, int Alignment,
+ template <class> class MakePointer_ = MakePointer>
+class BaseTensorContractionMapper;
+
+template <typename Tensor, bool HasRawAccess, template <class> class MakePointer_>
+struct CoeffLoader {
+ enum {
+ DirectOffsets = false
+ };
+
+ EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE CoeffLoader(const Tensor& tensor) : m_tensor(tensor) { }
+
+ EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE void offsetBuffer(typename Tensor::Index) {
+ eigen_assert(false && "unsupported");
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE const typename MakePointer_<const typename Tensor::Scalar>::Type
+ data() const {
+ eigen_assert(false && "unsupported");
+ return NULL;
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE typename Tensor::Scalar coeff(typename Tensor::Index index) const { return m_tensor.coeff(index); }
+
+ template<int LoadMode> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ typename Tensor::PacketReturnType packet(typename Tensor::Index index) const
+ {
+ return m_tensor.template packet<LoadMode>(index);
+ }
+
+ #ifdef EIGEN_USE_SYCL
+ // The placeholder accessors require to be bound to a command group handler for SYCL
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void bind(cl::sycl::handler &cgh) const {
+ m_tensor.bind(cgh);
+ }
+ #endif
+
+ private:
+ const Tensor m_tensor;
+};
+
+template <typename Tensor, template <class> class MakePointer_>
+struct CoeffLoader<Tensor, true, MakePointer_> {
+ enum {
+ DirectOffsets = true
+ };
+
+ EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE CoeffLoader(const Tensor& tensor) : m_data(tensor.data()) {}
+
+ EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE void offsetBuffer(typename Tensor::Index offset) {
+ m_data += offset;
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE const typename MakePointer_<const typename Tensor::Scalar>::Type
+ data() const {
+ return m_data;
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE typename Tensor::Scalar coeff(typename Tensor::Index index) const { return loadConstant(m_data+index); }
+
+ template<int LoadMode> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ typename Tensor::PacketReturnType packet(typename Tensor::Index index) const
+ {
+ return internal::ploadt_ro<typename Tensor::PacketReturnType, LoadMode>(m_data + index);
+ }
+
+ #ifdef EIGEN_USE_SYCL
+ // The placeholder accessors require to be bound to a command group handler for SYCL
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void bind(cl::sycl::handler &cgh) const {
+ m_data.bind(cgh);
+ }
+ #endif
+ private:
+ typedef typename Tensor::Scalar Scalar;
+
+ typename MakePointer_<const Scalar>::Type m_data;
+};
+
+template<typename Scalar, typename Index, int side,
+ typename Tensor,
+ typename nocontract_t, typename contract_t,
+ int packet_size, bool inner_dim_contiguous, int Alignment, template <class> class MakePointer_ = MakePointer>
+class SimpleTensorContractionMapper {
+ public:
+ EIGEN_DEVICE_FUNC
+ SimpleTensorContractionMapper(const Tensor& tensor,
+ const nocontract_t& nocontract_strides,
+ const nocontract_t& ij_strides,
+ const contract_t& contract_strides,
+ const contract_t& k_strides) :
+ m_tensor(tensor),
+ m_nocontract_strides(nocontract_strides),
+ m_ij_strides(ij_strides),
+ m_contract_strides(contract_strides),
+ m_k_strides(k_strides) { }
+
+ enum {
+ DirectOffsets = CoeffLoader<Tensor, Tensor::RawAccess, MakePointer_>::DirectOffsets
+ };
+
+ EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE void offsetBuffer(typename Tensor::Index offset) {
+ m_tensor.offsetBuffer(offset);
+ }
+
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE void prefetch(Index /*i*/) { }
+
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE Scalar operator()(Index row) const {
+ // column major assumption
+ return operator()(row, 0);
+ }
+
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE Scalar operator()(Index row, Index col) const {
+ return m_tensor.coeff(computeIndex(row, col));
+ }
+
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE Index computeIndex(Index row, Index col) const {
+ const bool left = (side == Lhs);
+ EIGEN_UNUSED_VARIABLE(left); // annoying bug in g++8.1: https://gcc.gnu.org/bugzilla/show_bug.cgi?id=85963
+ Index nocontract_val = left ? row : col;
+ Index linidx = 0;
+ EIGEN_UNROLL_LOOP
+ for (int i = static_cast<int>(array_size<nocontract_t>::value) - 1; i > 0; i--) {
+ const Index idx = nocontract_val / m_ij_strides[i];
+ linidx += idx * m_nocontract_strides[i];
+ nocontract_val -= idx * m_ij_strides[i];
+ }
+ if (array_size<typename Tensor::Dimensions>::value > array_size<contract_t>::value) {
+ if (side == Lhs && inner_dim_contiguous) {
+ eigen_assert(m_nocontract_strides[0] == 1);
+ linidx += nocontract_val;
+ } else {
+ linidx += nocontract_val * m_nocontract_strides[0];
+ }
+ }
+
+ Index contract_val = left ? col : row;
+ if(array_size<contract_t>::value > 0) {
+ EIGEN_UNROLL_LOOP
+ for (int i = static_cast<int>(array_size<contract_t>::value) - 1; i > 0; i--) {
+ const Index idx = contract_val / m_k_strides[i];
+ linidx += idx * m_contract_strides[i];
+ contract_val -= idx * m_k_strides[i];
+ }
+
+ if (side == Rhs && inner_dim_contiguous) {
+ eigen_assert(m_contract_strides[0] == 1);
+ linidx += contract_val;
+ } else {
+ linidx += contract_val * m_contract_strides[0];
+ }
+ }
+
+ return linidx;
+ }
+
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE IndexPair<Index> computeIndexPair(Index row, Index col, const Index distance) const {
+ const bool left = (side == Lhs);
+ EIGEN_UNUSED_VARIABLE(left); // annoying bug in g++8.1: https://gcc.gnu.org/bugzilla/show_bug.cgi?id=85963
+ Index nocontract_val[2] = {left ? row : col, left ? row + distance : col};
+ Index linidx[2] = {0, 0};
+ if (array_size<typename Tensor::Dimensions>::value > array_size<contract_t>::value) {
+ EIGEN_UNROLL_LOOP
+ for (int i = static_cast<int>(array_size<nocontract_t>::value) - 1; i > 0; i--) {
+ const Index idx0 = nocontract_val[0] / m_ij_strides[i];
+ const Index idx1 = nocontract_val[1] / m_ij_strides[i];
+ linidx[0] += idx0 * m_nocontract_strides[i];
+ linidx[1] += idx1 * m_nocontract_strides[i];
+ nocontract_val[0] -= idx0 * m_ij_strides[i];
+ nocontract_val[1] -= idx1 * m_ij_strides[i];
+ }
+ if (side == Lhs && inner_dim_contiguous) {
+ eigen_assert(m_nocontract_strides[0] == 1);
+ linidx[0] += nocontract_val[0];
+ linidx[1] += nocontract_val[1];
+ } else {
+ linidx[0] += nocontract_val[0] * m_nocontract_strides[0];
+ linidx[1] += nocontract_val[1] * m_nocontract_strides[0];
+ }
+ }
+
+ Index contract_val[2] = {left ? col : row, left ? col : row + distance};
+ if (array_size<contract_t>::value> 0) {
+ EIGEN_UNROLL_LOOP
+ for (int i = static_cast<int>(array_size<contract_t>::value) - 1; i > 0; i--) {
+ const Index idx0 = contract_val[0] / m_k_strides[i];
+ const Index idx1 = contract_val[1] / m_k_strides[i];
+ linidx[0] += idx0 * m_contract_strides[i];
+ linidx[1] += idx1 * m_contract_strides[i];
+ contract_val[0] -= idx0 * m_k_strides[i];
+ contract_val[1] -= idx1 * m_k_strides[i];
+ }
+
+ if (side == Rhs && inner_dim_contiguous) {
+ eigen_assert(m_contract_strides[0] == 1);
+ linidx[0] += contract_val[0];
+ linidx[1] += contract_val[1];
+ } else {
+ linidx[0] += contract_val[0] * m_contract_strides[0];
+ linidx[1] += contract_val[1] * m_contract_strides[0];
+ }
+ }
+ return IndexPair<Index>(linidx[0], linidx[1]);
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE Index firstAligned(Index size) const {
+ // Only claim alignment when we can compute the actual stride (ie when we're
+ // dealing with the lhs with inner_dim_contiguous. This is because the
+ // matrix-vector product relies on the stride when dealing with aligned inputs.
+ return (Alignment == Aligned) && (side == Lhs) && inner_dim_contiguous ? 0 : size;
+ }
+ EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE Index stride() const {
+ return ((side == Lhs) && inner_dim_contiguous && array_size<contract_t>::value > 0) ? m_contract_strides[0] : 1;
+ }
+
+ #ifdef EIGEN_USE_SYCL
+ // The placeholder accessors require to be bound to a command group handler for SYCL
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void bind(cl::sycl::handler &cgh) const {
+ m_tensor.bind(cgh);
+ }
+ #endif
+
+ const CoeffLoader<Tensor, Tensor::RawAccess, MakePointer_>& tensor() const {
+ return m_tensor;
+ }
+
+ const nocontract_t& nocontract_strides() const {
+ return m_nocontract_strides;
+ }
+ const nocontract_t& ij_strides() const { return m_ij_strides; }
+ const contract_t& contract_strides() const { return m_contract_strides; }
+ const contract_t& k_strides() const { return m_k_strides; }
+
+ protected:
+ CoeffLoader<Tensor, Tensor::RawAccess, MakePointer_> m_tensor;
+ const nocontract_t m_nocontract_strides;
+ const nocontract_t m_ij_strides;
+ const contract_t m_contract_strides;
+ const contract_t m_k_strides;
+};
+
+template<typename Scalar, typename Index, int side,
+ typename Tensor,
+ typename nocontract_t, typename contract_t,
+ int packet_size, bool inner_dim_contiguous,
+ bool inner_dim_reordered, int Alignment, template <class> class MakePointer_>
+class BaseTensorContractionMapper : public SimpleTensorContractionMapper<Scalar, Index, side, Tensor, nocontract_t, contract_t, packet_size, inner_dim_contiguous, Alignment, MakePointer_>
+{
+ public:
+ typedef SimpleTensorContractionMapper<Scalar, Index, side, Tensor, nocontract_t, contract_t, packet_size, inner_dim_contiguous, Alignment, MakePointer_> ParentMapper;
+
+ EIGEN_DEVICE_FUNC
+ BaseTensorContractionMapper(const Tensor& tensor,
+ const nocontract_t& nocontract_strides,
+ const nocontract_t& ij_strides,
+ const contract_t& contract_strides,
+ const contract_t& k_strides) :
+ ParentMapper(tensor, nocontract_strides, ij_strides, contract_strides, k_strides) { }
+
+ template <typename PacketT,int AlignmentType>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ std::enable_if_t<internal::unpacket_traits<PacketT>::size==packet_size,PacketT>
+ load(Index i, Index j) const
+ {
+ // whole method makes column major assumption
+
+ // don't need to add offsets for now (because operator handles that)
+ // current code assumes packet size must be a multiple of 2
+ EIGEN_STATIC_ASSERT(packet_size % 2 == 0, YOU_MADE_A_PROGRAMMING_MISTAKE);
+
+ if (Tensor::PacketAccess && inner_dim_contiguous && !inner_dim_reordered) {
+ const Index index = this->computeIndex(i, j);
+ eigen_assert(this->computeIndex(i+packet_size-1, j) == index + packet_size-1);
+ return this->m_tensor.template packet<AlignmentType>(index);
+ }
+
+ const IndexPair<Index> indexPair = this->computeIndexPair(i, j, packet_size - 1);
+ const Index first = indexPair.first;
+ const Index lastIdx = indexPair.second;
+
+ // We can always do optimized packet reads from left hand side right now, because
+ // the vertical matrix dimension on the left hand side is never contracting.
+ // On the right hand side we need to check if the contracting dimensions may have
+ // been shuffled first.
+ if (Tensor::PacketAccess &&
+ (side == Lhs || internal::array_size<contract_t>::value <= 1 || !inner_dim_reordered) &&
+ (lastIdx - first) == (packet_size - 1)) {
+
+ return this->m_tensor.template packet<AlignmentType>(first);
+ }
+
+ EIGEN_ALIGN_MAX Scalar data[packet_size];
+
+ data[0] = this->m_tensor.coeff(first);
+ EIGEN_UNROLL_LOOP
+ for (Index k = 1; k < packet_size - 1; k += 2) {
+ const IndexPair<Index> internal_pair = this->computeIndexPair(i + k, j, 1);
+ data[k] = this->m_tensor.coeff(internal_pair.first);
+ data[k + 1] = this->m_tensor.coeff(internal_pair.second);
+ }
+ data[packet_size - 1] = this->m_tensor.coeff(lastIdx);
+
+ return pload<PacketT>(data);
+ }
+
+ template <typename PacketT,int AlignmentType>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ std::enable_if_t<internal::unpacket_traits<PacketT>::size!=packet_size,PacketT>
+ load(Index i, Index j) const
+ {
+ const Index requested_packet_size = internal::unpacket_traits<PacketT>::size;
+ EIGEN_ALIGN_MAX Scalar data[requested_packet_size];
+
+ const IndexPair<Index> indexPair = this->computeIndexPair(i, j, requested_packet_size - 1);
+ const Index first = indexPair.first;
+ const Index lastIdx = indexPair.second;
+
+ data[0] = this->m_tensor.coeff(first);
+ for (Index k = 1; k < requested_packet_size - 1; k += 2) {
+ const IndexPair<Index> internal_pair = this->computeIndexPair(i + k, j, 1);
+ data[k] = this->m_tensor.coeff(internal_pair.first);
+ data[k + 1] = this->m_tensor.coeff(internal_pair.second);
+ }
+ data[requested_packet_size - 1] = this->m_tensor.coeff(lastIdx);
+
+ return pload<PacketT>(data);
+ }
+
+ template <typename PacketT,int AlignmentType>
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE PacketT loadPacket(Index i, Index j) const {
+ return this->load<PacketT,AlignmentType>(i,j);
+ }
+};
+
+
+template<typename Scalar, typename Index, int side,
+ typename Tensor,
+ typename nocontract_t, typename contract_t,
+ bool inner_dim_contiguous,
+ bool inner_dim_reordered, int Alignment, template <class> class MakePointer_>
+class BaseTensorContractionMapper<Scalar, Index, side, Tensor, nocontract_t, contract_t, 1, inner_dim_contiguous, inner_dim_reordered, Alignment, MakePointer_>
+ : public SimpleTensorContractionMapper<Scalar, Index, side, Tensor, nocontract_t, contract_t, 1, inner_dim_contiguous, Alignment, MakePointer_>
+{
+ public:
+ typedef SimpleTensorContractionMapper<Scalar, Index, side, Tensor, nocontract_t, contract_t, 1, inner_dim_contiguous, Alignment, MakePointer_> ParentMapper;
+
+ EIGEN_DEVICE_FUNC
+ BaseTensorContractionMapper(const Tensor& tensor,
+ const nocontract_t& nocontract_strides,
+ const nocontract_t& ij_strides,
+ const contract_t& contract_strides,
+ const contract_t& k_strides) :
+ ParentMapper(tensor, nocontract_strides, ij_strides, contract_strides, k_strides) { }
+
+ template <typename PacketT,int> EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE PacketT loadPacket(Index i, Index j) const {
+ EIGEN_ALIGN_MAX Scalar data[1];
+ data[0] = this->m_tensor.coeff(this->computeIndex(i, j));
+ return pload<PacketT>(data);
+ }
+ template <typename PacketT,int> EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE PacketT load(Index i, Index j) const {
+ EIGEN_ALIGN_MAX Scalar data[1];
+ data[0] = this->m_tensor.coeff(this->computeIndex(i, j));
+ return pload<PacketT>(data);
+ }
+};
+
+
+template<typename Scalar, typename Index, int side,
+ typename Tensor,
+ typename nocontract_t, typename contract_t,
+ int packet_size,
+ bool inner_dim_contiguous, bool inner_dim_reordered, int Alignment, template <class> class MakePointer_=MakePointer>
+class TensorContractionSubMapper {
+ public:
+
+ typedef BaseTensorContractionMapper<Scalar, Index, side, Tensor, nocontract_t, contract_t, packet_size, inner_dim_contiguous, inner_dim_reordered, Alignment, MakePointer_> ParentMapper;
+ typedef TensorContractionSubMapper<Scalar, Index, side, Tensor, nocontract_t, contract_t, packet_size, inner_dim_contiguous, inner_dim_reordered, Alignment, MakePointer_> Self;
+ typedef Self LinearMapper;
+ typedef Self SubMapper;
+
+ enum {
+ // We can use direct offsets iff the parent mapper supports then and we can compute the strides.
+ // TODO: we should also enable direct offsets for the Rhs case.
+ UseDirectOffsets = ParentMapper::DirectOffsets && (side == Lhs) && inner_dim_contiguous && (array_size<contract_t>::value > 0)
+ };
+
+ EIGEN_DEVICE_FUNC TensorContractionSubMapper(const ParentMapper& base_mapper, Index vert_offset, Index horiz_offset)
+ : m_base_mapper(base_mapper), m_vert_offset(vert_offset), m_horiz_offset(horiz_offset) {
+ // Bake the offsets into the buffer used by the base mapper whenever possible. This avoids the need to recompute
+ // this offset every time we attempt to access a coefficient.
+ if (UseDirectOffsets) {
+ Index stride = m_base_mapper.stride();
+ m_base_mapper.offsetBuffer(vert_offset + horiz_offset * stride);
+ }
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE Scalar operator()(Index i) const {
+ if (UseDirectOffsets) {
+ return m_base_mapper(i, 0);
+ }
+ return m_base_mapper(i + m_vert_offset, m_horiz_offset);
+ }
+ EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE Scalar operator()(Index i, Index j) const {
+ if (UseDirectOffsets) {
+ return m_base_mapper(i, j);
+ }
+ return m_base_mapper(i + m_vert_offset, j + m_horiz_offset);
+ }
+
+ template <typename PacketT>
+ EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE PacketT loadPacket(Index i) const {
+ if (UseDirectOffsets) {
+ return m_base_mapper.template loadPacket<PacketT,Alignment>(i, 0);
+ }
+ return m_base_mapper.template loadPacket<PacketT,Alignment>(i + m_vert_offset, m_horiz_offset);
+ }
+
+ template <typename PacketT>
+ EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE PacketT loadPacket(Index i, Index j) const {
+ if (UseDirectOffsets) {
+ return m_base_mapper.template loadPacket<PacketT,Alignment>(i, j);
+ }
+ return m_base_mapper.template loadPacket<PacketT,Alignment>(i + m_vert_offset, j + m_horiz_offset);
+ }
+
+ template <typename PacketT, int AlignmentType>
+ EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE PacketT loadPacket(Index i, Index j) const {
+ if (UseDirectOffsets) {
+ return m_base_mapper.template load<PacketT,AlignmentType>(i, j);
+ }
+ return m_base_mapper.template loadPacket<PacketT,AlignmentType>(i + m_vert_offset, j + m_horiz_offset);
+ }
+
+ template <typename PacketT>
+ EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE void storePacket(Index i, const PacketT& p) const {
+ if (UseDirectOffsets) {
+ m_base_mapper.storePacket(i, 0, p);
+ }
+ m_base_mapper.storePacket(i + m_vert_offset, m_horiz_offset, p);
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE LinearMapper getLinearMapper(Index i, Index j) const {
+ if (UseDirectOffsets) {
+ return LinearMapper(m_base_mapper, i, j);
+ }
+ return LinearMapper(m_base_mapper, i + m_vert_offset, j + m_horiz_offset);
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE SubMapper getSubMapper(Index i, Index j) const {
+ if (UseDirectOffsets) {
+ return SubMapper(m_base_mapper, i, j);
+ }
+ return SubMapper(m_base_mapper, i + m_vert_offset, j + m_horiz_offset);
+ }
+
+ template <typename PacketT, int AlignmentType>
+ EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE PacketT load(Index i) const {
+ EIGEN_STATIC_ASSERT((internal::is_same<PacketT, PacketT>::value), YOU_MADE_A_PROGRAMMING_MISTAKE);
+ const int ActualAlignment = (AlignmentType == Aligned) && (Alignment == Aligned) ? Aligned : Unaligned;
+ if (UseDirectOffsets) {
+ return m_base_mapper.template loadPacket<PacketT,ActualAlignment>(i, 0);
+ }
+ return m_base_mapper.template loadPacket<PacketT,ActualAlignment>(i + m_vert_offset, m_horiz_offset);
+ }
+
+ template <typename PacketT>
+ EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE bool aligned(Index) const {
+ return false;
+ }
+
+ #ifdef EIGEN_USE_SYCL
+ // The placeholder accessors require to be bound to a command group handler for SYCL
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void bind(cl::sycl::handler &cgh) const {
+ m_base_mapper.bind(cgh);
+ }
+ #endif
+
+ const ParentMapper& base_mapper() const { return m_base_mapper; }
+ Index vert_offset() const { return m_vert_offset; }
+ Index horiz_offset() const { return m_horiz_offset; }
+
+ private:
+ ParentMapper m_base_mapper;
+ const Index m_vert_offset;
+ const Index m_horiz_offset;
+};
+
+
+template<typename Scalar_, typename Index, int side,
+ typename Tensor,
+ typename nocontract_t, typename contract_t,
+ int packet_size,
+ bool inner_dim_contiguous, bool inner_dim_reordered, int Alignment, template <class> class MakePointer_=MakePointer>
+class TensorContractionInputMapper
+ : public BaseTensorContractionMapper<Scalar_, Index, side, Tensor, nocontract_t, contract_t, packet_size, inner_dim_contiguous, inner_dim_reordered, Alignment, MakePointer_> {
+
+ public:
+ typedef Scalar_ Scalar;
+ typedef BaseTensorContractionMapper<Scalar, Index, side, Tensor, nocontract_t, contract_t, packet_size, inner_dim_contiguous, inner_dim_reordered, Alignment, MakePointer_> Base;
+ typedef TensorContractionSubMapper<Scalar, Index, side, Tensor, nocontract_t, contract_t, packet_size, inner_dim_contiguous, inner_dim_reordered, Alignment, MakePointer_> SubMapper;
+ typedef SubMapper VectorMapper;
+ typedef SubMapper LinearMapper;
+
+ EIGEN_DEVICE_FUNC TensorContractionInputMapper(const Tensor& tensor,
+ const nocontract_t& nocontract_strides,
+ const nocontract_t& ij_strides,
+ const contract_t& contract_strides,
+ const contract_t& k_strides)
+ : Base(tensor, nocontract_strides, ij_strides, contract_strides, k_strides) { }
+
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE SubMapper getSubMapper(Index i, Index j) const {
+ return SubMapper(*this, i, j);
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE LinearMapper getLinearMapper(Index i, Index j) const {
+ return LinearMapper(*this, i, j);
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE VectorMapper getVectorMapper(Index i, Index j) const {
+ return VectorMapper(*this, i, j);
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE const CoeffLoader<Tensor, Tensor::RawAccess, MakePointer_>& get_tensor() const {
+ return Base::m_tensor;
+ }
+};
+
+
+template <typename T> struct TensorContractionInputMapperTrait;
+
+template<typename Scalar_, typename Index_, int side_,
+ typename Tensor_,
+ typename nocontract_t_, typename contract_t_,
+ int packet_size_,
+ bool inner_dim_contiguous_, bool inner_dim_reordered_, int Alignment_, template <class> class MakePointer_>
+struct TensorContractionInputMapperTrait<TensorContractionInputMapper<Scalar_, Index_, side_, Tensor_,
+ nocontract_t_, contract_t_, packet_size_, inner_dim_contiguous_,
+ inner_dim_reordered_, Alignment_, MakePointer_> > {
+
+ typedef Tensor_ XprType;
+ static const bool inner_dim_contiguous = inner_dim_contiguous_;
+ static const bool inner_dim_reordered = inner_dim_reordered_;
+ };
+
+
+} // end namespace internal
+} // end namespace Eigen
+
+#endif // EIGEN_CXX11_TENSOR_TENSOR_CONTRACTION_MAPPER_H
diff --git a/unsupported/Eigen/CXX11/src/Tensor/TensorContractionSycl.h b/unsupported/Eigen/CXX11/src/Tensor/TensorContractionSycl.h
new file mode 100644
index 0000000..c6c4077
--- /dev/null
+++ b/unsupported/Eigen/CXX11/src/Tensor/TensorContractionSycl.h
@@ -0,0 +1,1651 @@
+// This file is part of Eigen, a lightweight C++ template library for linear algebra.
+//
+// Mehdi Goli Codeplay Software Ltd.
+// Ralph Potter Codeplay Software Ltd.
+// Luke Iwanski Codeplay Software Ltd.
+// Contact: <eigen@codeplay.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla Public License v. 2.0. If a copy of the MPL was not
+// distributed with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+/*****************************************************************
+ * TensorContractionSycl.h
+ *
+ * \brief:
+ * TensorContractionSycl.h, provides various tensor contraction kernel for SYCL backend
+ *
+ *****************************************************************/
+
+#ifndef EIGEN_CXX11_TENSOR_TENSOR_CONTRACTION_SYCL_H
+#define EIGEN_CXX11_TENSOR_TENSOR_CONTRACTION_SYCL_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace TensorSycl {
+namespace internal {
+
+#ifndef EIGEN_SYCL_DISABLE_GEMV
+/*!
+ * \brief TVPanelSize, a template class used for setting the panel size required for launching General TensorVector
+ * contraction kernel on various hardware devices.
+ *
+ * \tparam Scalar: determines the element type of the tensor/vector
+ *
+ * \tparam StorageIndex determines the Index type.
+ *
+ * \tparam NCWindow: determines the number of non-contracting element to be process by each work-group
+ *
+ * \tparam CFactor: determines the number of contracting element to be process by each thread
+ *
+ * \tparam NCFactor: determines the number of non-contracting element to be process by each thread
+ */
+template <typename Scalar, typename StorageIndex, StorageIndex NCWindow, StorageIndex CFactor, StorageIndex NCFactor>
+struct TVPanelSize {
+ // LocalThreadSizeC: determines total number of thread per workgroup for the contracting dimension
+ static EIGEN_CONSTEXPR StorageIndex LocalThreadSizeC = EIGEN_SYCL_LOCAL_THREAD_DIM0;
+ // LocalThreadSizeNC: determines total number of thread per workgroup for the non-contracting dimension
+ static EIGEN_CONSTEXPR StorageIndex LocalThreadSizeNC = EIGEN_SYCL_LOCAL_THREAD_DIM1;
+ // TileSizeDimNC: determines the tile size for the non-contracting dimension
+ static EIGEN_CONSTEXPR StorageIndex TileSizeDimNC = NCWindow / NCFactor;
+ // TileSizeDimC: determines the tile size for the contracting dimension
+ static EIGEN_CONSTEXPR StorageIndex TileSizeDimC = CFactor * LocalThreadSizeNC * LocalThreadSizeC;
+ // WorkLoadPerThreadNC : determines workload per thread for loading the non-contracting dimension
+ static EIGEN_CONSTEXPR StorageIndex WorkLoadPerThreadNC = TileSizeDimNC / LocalThreadSizeNC;
+ // WorkLoadPerThreadC: determines workload per thread for loading the non-contracting dimension
+ static EIGEN_CONSTEXPR StorageIndex WorkLoadPerThreadC = TileSizeDimC / LocalThreadSizeC;
+ // BC : determines if supporting bank conflict is required
+ static EIGEN_CONSTEXPR bool BC = false;
+};
+#endif
+
+/*!
+ * \brief TTPanelSize, a template class used for setting the panel size required for launching General Tensor Tensor
+ contraction kernel on various hardware devices.
+ *
+ * \tparam Scalar: determines the element type of the tensor
+ *
+ * \tparam StorageIndex: determines the Index type.
+ *
+ * \tparam REG_SIZE_M: determines workload per thread for loading the M dimension This can be varied based on the
+ available register on a chosen device(can be controlled by EIGEN_SYCL_REG_M macro).
+ *
+ * \tparam REG_SIZE_N: determines workload per thread for loading the N dimension This can be varied based on the
+ available register on a chosen device(can be controlled by EIGEN_SYCL_REG_N macro).
+ *
+ * \tparam TSDK: determines Tile size for dimension K. The packet size is assumed to be considered
+ */
+
+template <typename Scalar, typename StorageIndex, StorageIndex REG_SIZE_M, StorageIndex REG_SIZE_N, StorageIndex TSDK>
+struct TTPanelSize {
+ // TileSizeDimK: determines Tile size for dimension K. The packet size is assumed to be considered
+ static EIGEN_CONSTEXPR StorageIndex TileSizeDimK = TSDK;
+ // WorkLoadPerThreadM : determines workload per thread for loading the M dimension This can be varied based on the
+ // available register on a chosen device(can be controlled by EIGEN_SYCL_REG_M macro//
+#ifndef EIGEN_SYCL_REG_M
+ static EIGEN_CONSTEXPR StorageIndex WorkLoadPerThreadM = REG_SIZE_M;
+#else
+ static EIGEN_CONSTEXPR StorageIndex WorkLoadPerThreadM = EIGEN_SYCL_REG_M;
+#endif
+// WorkLoadPerThreadN : determines workload per thread for loading the N dimension This can be varied based on the
+// available register on a chosen device(can be controlled by EIGEN_SYCL_REG_N macro
+#ifndef EIGEN_SYCL_REG_N
+ static EIGEN_CONSTEXPR StorageIndex WorkLoadPerThreadN = REG_SIZE_N;
+#else
+ static EIGEN_CONSTEXPR StorageIndex WorkLoadPerThreadN = EIGEN_SYCL_REG_N;
+#endif
+ // LocalThreadSizeM: determines total number of thread per workgroup for the m dimension
+ static EIGEN_CONSTEXPR StorageIndex LocalThreadSizeM = EIGEN_SYCL_LOCAL_THREAD_DIM0;
+ // LocalThreadSizeN: determines total number of thread per workgroup for the n dimension
+ static EIGEN_CONSTEXPR StorageIndex LocalThreadSizeN = EIGEN_SYCL_LOCAL_THREAD_DIM1;
+ // TileSizeDimM: determines the tile size for the m dimension
+ static EIGEN_CONSTEXPR StorageIndex TileSizeDimM = LocalThreadSizeM * WorkLoadPerThreadM;
+ // TileSizeDimN: determines the tile size for the n dimension
+ static EIGEN_CONSTEXPR StorageIndex TileSizeDimN = LocalThreadSizeN * WorkLoadPerThreadN;
+ // LoadPerThreadLhs: determines workload per thread for loading Lhs Tensor. This must be divisable by packetsize
+ static EIGEN_CONSTEXPR StorageIndex LoadPerThreadLhs =
+ ((TileSizeDimK * WorkLoadPerThreadM * WorkLoadPerThreadN) / (TileSizeDimN));
+ // LoadPerThreadRhs: determines workload per thread for loading Rhs Tensor. This must be divisable by packetsize
+ static EIGEN_CONSTEXPR StorageIndex LoadPerThreadRhs =
+ ((TileSizeDimK * WorkLoadPerThreadM * WorkLoadPerThreadN) / (TileSizeDimM));
+ // BC : determines if supporting bank conflict is required
+ static EIGEN_CONSTEXPR bool BC = true;
+ // DoubleBuffer: determines if double buffering technique should be used (This can be disabled by
+ // EIGEN_SYCL_DISABLE_DOUBLE_BUFFER macro when the device does not have sufficient local memory)
+ static EIGEN_CONSTEXPR bool DoubleBuffer =
+#ifdef EIGEN_SYCL_DISABLE_DOUBLE_BUFFER
+ false;
+#else
+ true;
+#endif
+};
+
+/* !
+ * \brief contraction_type: an enum class representing the Tensor Contraction implementation algorithm. This is used to
+ * specialize the contraction algorithm based on device support for dedicated local memory.
+ */
+enum class contraction_type { local, no_local };
+/* !
+ * \brief data_source an enum class determining the location of the data in a memory hierarchy (global, local, private).
+ */
+enum class data_source { global_mem, local_mem, private_mem };
+
+/*!
+ * \brief read, a template function used for loading the data from global
+ memory. This function is used to guarantee coalesced and vectorized load whenever possible
+ *
+ * \tparam PacketLoad: determines if the each element of this tensor block should be loaded in a packet mode
+ *
+ * \param is_coalesced_layout: determines whether or not the Tensor data in a memory can be access coalesced and
+ vectorized when possible. Coalesced memory access is a key factor in Kernel performance. When a tensor is 2d and the
+ contracting dimension is 1, it is always possible to accessed tensor data coalesced and vectorized. This is the case
+ when RHS(right hand side) Tensor is transposed or when LHS(left hand side) Tensor is not transposed.
+ *
+ * \tparam PacketType: determines the type of packet
+ *
+ * \tparam TensorMapper: determines the input tensor mapper type
+ *
+ * \tparam StorageIndex: determines the Index type
+
+ * \param tensorMapper: is the input tensor
+ *
+ * \param NCIndex: is the non-contracting dim index
+ *
+ * \param CIndex is the contracting dim index
+ *
+ * \param ld: is the leading dimension of the flattened tensor
+ */
+template <bool PacketLoad, bool is_coalesced_layout, bool, typename PacketType, typename TensorMapper,
+ typename StorageIndex>
+static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE std::enable_if_t<PacketLoad, PacketType> read(
+ const TensorMapper &tensorMapper, const StorageIndex &NCIndex, const StorageIndex &CIndex, const StorageIndex &ld) {
+ const StorageIndex row = (is_coalesced_layout) ? NCIndex : CIndex;
+ const StorageIndex col = (is_coalesced_layout) ? CIndex : NCIndex;
+ return tensorMapper.get_tensor().template packet<Unaligned>(row + (col * ld));
+}
+
+/*!
+ * \brief read, special overload of read function, when the read access is not vectorized
+ *
+ * \tparam PacketLoad: determines if the each element of this tensor block should be loaded in a packet mode
+ *
+ * \param is_coalesced_layout: determines whether or not the Tensor data in a memory can be access coalesced and
+ vectorized when possible. Coalesced memory access is a key factor in Kernel performance. When a tensor is 2d and the
+ contracting dimension is 1, it is always possible to accessed tensor data coalesced and vectorized. This is the case
+ when RHS(right hand side) Tensor is transposed or when LHS(left hand side) Tensor is not transposed.
+ *
+ * \tparam PacketType: determines the type of packet
+ *
+ * \tparam TensorMapper: determines the input tensor mapper type
+ *
+ * \tparam StorageIndex: determines the Index type
+
+ * \param tensorMapper: is the input tensor
+ *
+ * \param NCIndex: is the non-contracting dim index
+ *
+ * \param CIndex: is the contracting dim index
+ */
+template <bool PacketLoad, bool, bool IsRhs, typename PacketType, typename TensorMapper, typename StorageIndex>
+static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE std::enable_if_t<!PacketLoad, PacketType> read(
+ const TensorMapper &tensorMapper, const StorageIndex &NCIndex, const StorageIndex &CIndex, const StorageIndex &) {
+ const StorageIndex row = (IsRhs) ? CIndex : NCIndex;
+ const StorageIndex col = (IsRhs) ? NCIndex : CIndex;
+ return tensorMapper(row, col);
+}
+
+/*!
+ * \brief write, a template function used for storing the data to local memory. This function is used to guarantee
+ * coalesced and vectorized store whenever possible.
+ *
+ * \tparam StorageIndex: determines the Index type
+ *
+ * \param ld is the leading dimension of the local memory. ld is a compile time value for the local memory
+ *
+ * \tparam data_source: an enum value representing if the location of the data in a memory hierarchy.
+ *
+ * \tparam PacketType: determines the type of packet
+ *
+ * \tparam DataScalar: determines the output data type
+ *
+ * \param packet_data: the data to be written in the local memory
+ *
+ * \param ptr: a pointer to the local memory
+ *
+ * \param CIndex is the contracting dim index
+ */
+
+template <typename StorageIndex, StorageIndex ld, data_source dt, typename PacketType, typename DataScalar>
+static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ std::enable_if_t<dt != data_source::global_mem, void>
+ write(PacketType &packet_data, DataScalar ptr) {
+ EIGEN_CONSTEXPR int PacketSize = Eigen::internal::unpacket_traits<PacketType>::size;
+ EIGEN_UNROLL_LOOP
+ for (int i = 0; i < PacketSize; i++) {
+ *ptr = PacketWrapper<PacketType, PacketSize>::scalarize(i, packet_data);
+ ptr += ld;
+ }
+}
+
+/*!
+ * \brief Overloading the write function for storing the data to global memory, when vectorization enabled This function
+ * is used to guarantee coalesced and vectorized store whenever possible.
+ *
+ * \tparam data_source: an enum value representing if the location of the data in a memory hierarchy.
+ *
+ * \tparam PacketType: determines the type of packet
+ *
+ * \tparam DataScalar: determines the output data type
+ *
+ * \param packet_data: the data to be written in the local memory
+ *
+ * \param ptr: a pointer to the local memory
+ */
+
+template <data_source dt, typename PacketType, typename DataScalar>
+static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE typename std::enable_if_t<
+ Eigen::internal::unpacket_traits<PacketType>::size != 1 && dt == data_source::global_mem, void>
+write(PacketType &packet_data, DataScalar *ptr) {
+ ::Eigen::internal::pstoreu<DataScalar, PacketType>(ptr, packet_data);
+}
+
+/*!
+ * \brief Overloading the write function for storing the data to global memory, when vectorization is disabled.
+ *
+ * \tparam data_source: an enum value representing if the location of the data in a memory hierarchy.
+ *
+ * \tparam PacketType: determines the type of packet
+ *
+ * \tparam DataScalar: determines the output data type
+ *
+ * \param packet_data: the data to be written in the local memory
+ *
+ * \param ptr: a pointer to the local memory
+ */
+template <data_source dt, typename PacketType, typename DataScalar>
+static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE typename std::enable_if_t<
+ Eigen::internal::unpacket_traits<PacketType>::size == 1 && dt == data_source::global_mem, void>
+write(PacketType &packet_data, DataScalar *ptr) {
+ *ptr = packet_data;
+}
+
+/*!
+ * \brief check_boundary: is used to check the edge condition for non-internal blocks.
+ *
+ * \tparam is_internal: determines if the block is internal
+ */
+template <bool is_internal>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE bool check_boundary(bool) {
+ return true;
+}
+
+/*!
+ * \brief check_boundary: specialization of the check_boundary for non-internal blocks.
+ *
+ * \param cond: true when the data is in range. Otherwise false
+ */
+template <>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE bool check_boundary<false>(bool cond) {
+ return cond;
+}
+
+/*!
+ * \brief BlockProperties is a template class that provides different characteristic of a block of each Tensor processed
+ * by each workgroup.
+ *
+ * \tparam is_transposed: iff true, determines whether or not the block of the Tensor is transposed
+ *
+ * \tparam packet_load_: determines if the each element of this tensor block should be loaded in a packet mode
+ *
+ * \tparam PacketType: determines the type of packet
+ *
+ * \tparam OutType: determines the type of each element for this block of tensor. If packet load is true, it will be
+ * packetType; Otherwise it will be scalar Type
+ *
+ * \param elements_per_access determines the size of each element based on OutType
+ *
+ * \param is_coalesced_layout determines whether or not the Tensor data in a memory can be access coalesced and
+ * vectorized when possible. Coalesced memory access is a key factor in Kernel performance. When a tensor is 2d and the
+ * contracting dimension is 1, it is always possible to accessed tensor data coalesced and vectorized. This is the case
+ * when RHS(right hand side) Tensor is transposed or when LHS(left hand side) Tensor is not transposed.
+ *
+ * \param nc_stride determines the stride of non-contracting dimension to access the next adjustment element within the
+ * Tensor Block for each workgroup
+ *
+ * \param c_stride determines the stride of contracting dimension to access the next adjustment element within the
+ * Tensor Block for each workgroup
+ */
+template <bool is_transposed, bool is_rhs_, bool packet_load_, typename PacketType>
+struct BlockProperties {
+ static EIGEN_CONSTEXPR bool packet_load = packet_load_;
+ typedef typename Eigen::internal::unpacket_traits<PacketType>::type OutScalar;
+ static EIGEN_CONSTEXPR bool is_rhs = is_rhs_;
+ typedef std::conditional_t<packet_load, PacketType, OutScalar> OutType;
+ static EIGEN_CONSTEXPR int elements_per_access = Eigen::internal::unpacket_traits<OutType>::size;
+ static EIGEN_CONSTEXPR bool is_coalesced_layout = !(is_transposed ^ is_rhs);
+ static EIGEN_CONSTEXPR int nc_stride = (is_coalesced_layout ? elements_per_access : 1);
+ static EIGEN_CONSTEXPR int c_stride = (is_coalesced_layout ? 1 : elements_per_access);
+};
+
+/*!
+ * \brief ThreadProperties is a template class that provides each thread's properties within a workgroup. Please see
+ * the sycl-1.2.1 specification (https://www.khronos.org/registry/SYCL/specs/sycl-1.2.1.pdf) for the workgroup,
+ * work-items
+ *
+ * \tparam StorageIndex: determines the StorageIndex Type
+ *
+ * \param linearLocalThreadId: determines the linearized location of a thread within a work-group
+ *
+ * \param kGroupId: determines the logical group id in a k dimension of the flattened tensor. It will be > 1 when
+ * tall/skinny algorithm is used
+ *
+ * \param mGroupOffset: determines the logical start position of all thread within a workgroup for the m dimension of
+ * the flattened tensor.
+ *
+ * \param kGroupOffset determines the logical start position of all thread within a workgroup for the k dimension of the
+ * flattened tensor. It will be > 1 when tall/skinny algorithm is used.
+ *
+ * \param mLocalOffset: determines the logical start position of each thread within a workgroup for the m dimension of a
+ * flattened tensor. The position determines the distance of each thread within the workgroup from each other
+ * independent from their global position.
+ *
+ * \param nLocalOffset: determines the logical start position of each thread within a workgroup for the n dimension of a
+ * flattened tensor. The position determines the distance of each thread within the workgroup from each other
+ * independent from their global position.
+ *
+ * \param mGlobalOffset: determines the logical start position of each thread a thread for the m dimension on a
+ * flattened tensor
+ *
+ * \param nGlobalOffset: determines the logical start position of each thread a thread for the n dimension on a
+ * flattened tensor
+ *
+ * \param kSize : determine the number of the k elements of the flattened Tensor to be processed by each thread for the
+ * given tensor block. This is !=K dimension of Flattened Tensor when Tall/Skinny matrix is used.
+ *
+ * \param is_internal : this will determined if the thread within the work-group computes an internal block of tensor or
+ * the edge blocks. When it is internal, there is no need to check the boundaries and all the if stantement can be
+ * resolve by compiler.
+ */
+template <typename StorageIndex>
+struct ThreadProperties {
+ const StorageIndex linearLocalThreadId;
+ const StorageIndex kGroupId;
+ const StorageIndex mGroupOffset;
+ const StorageIndex nGroupOffset;
+ const StorageIndex kGroupOffset;
+ const StorageIndex mLocalOffset;
+ const StorageIndex nLocalOffset;
+ const StorageIndex mGlobalOffset;
+ const StorageIndex nGlobalOffset;
+ StorageIndex kSize;
+ const bool is_internal;
+ // this is used to adjust the last block
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE ThreadProperties(
+ const StorageIndex linearLocalThreadId_, const StorageIndex kGroupId_, const StorageIndex mGroupOffset_,
+ const StorageIndex nGroupOffset_, const StorageIndex kGroupOffset_, const StorageIndex mLocalOffset_,
+ const StorageIndex nLocalOffset_, const StorageIndex mGlobalOffset_, const StorageIndex nGlobalOffset_,
+ StorageIndex kSize_, const bool is_internal_)
+ : linearLocalThreadId(linearLocalThreadId_),
+ kGroupId(kGroupId_),
+ mGroupOffset(mGroupOffset_),
+ nGroupOffset(nGroupOffset_),
+ kGroupOffset(kGroupOffset_),
+ mLocalOffset(mLocalOffset_),
+ nLocalOffset(nLocalOffset_),
+ mGlobalOffset(mGlobalOffset_),
+ nGlobalOffset(nGlobalOffset_),
+ kSize(kSize_),
+ is_internal(is_internal_) {}
+};
+
+/*!
+ * \brief TensorContractionKernel is a template class that provides Tensor -Tensor contraction operation.
+ *
+ * \tparam OutScalar: determines the output scalar type
+ *
+ * \tparam LhsScalar: determines the left-hand-side scalar type
+ *
+ * \tparam RhsScalar: determines the right-hand-side scalar type
+ *
+ * \tparam OutAccessor: determines the sycl accessor type for out put (please see the sycl-1.2.1 specification
+ (https://www.khronos.org/registry/SYCL/specs/sycl-1.2.1.pdf) for accessor definition)
+ *
+ * \tparam LhsMapper determines the tensor contraction mapper type for left-hand-side matrix
+ *
+ * \tparam RhsMapper determines the tensor contraction mapper type for right-hand-side matrix
+ *
+ * \tparam StorageIndex: determines the StorageIndex Type
+ *
+ * \tparam Properties: determines the Contraction Panel properties
+ *
+ * \tparam TripleDim: determines the M, K, N dimensions for the flatten tensors in order to treat them as a matrix
+ *
+ * \tparam Vectorizable: determines whether or not the vectorization is enabled for the Eigen expression.
+ *
+ * \tparam input_mapper_properties : determine if the input tensors are matrix. If they are matrix, special memory
+ access is used to guarantee that always the memory access are coalesced.
+ *
+ * \tptaram IsFinal : determine if this is the final kernel. If so, the result will be written in a final output.
+ Otherwise, the result of contraction will be written iin a temporary buffer. This is the case when Tall/Skinny
+ contraction is used. So in this case, a final reduction step is required to compute final output.
+
+ * \tparam contraction_tp: it is an enum value representing whether the local memory/no local memory implementation of
+ the algorithm to be used
+ *
+ * \param scratch: local memory containing tiles of LHS and RHS tensors for each work-group
+ *
+ * \param lhs: determines the left-hand-side flattened tensor (tensor mapper)
+ *
+ * \param rhs: determines the right-hand-side flattened tensor (tensor mapper)
+ *
+ * \param out_res: determines the output tensor containing the contraction result
+ *
+ * \param groupSizeM: a logical number determining the number of work-group for m dimension
+ *
+ * \param groupSizeN: a logical number determining the number of work-group for n dimension
+ *
+ * \param numTiles: determines total number of tiles on the k dimension
+ *
+ * \param TripleDim: determines the M, K, N dimensions for the flatten tensors in order to treat them as a matrix
+ */
+template <typename OutScalar, typename LhsScalar, typename RhsScalar, typename OutAccessor, typename LhsMapper,
+ typename RhsMapper, typename StorageIndex, typename Properties, typename TripleDim, bool Vectorizable,
+ typename input_mapper_properties, bool IsFinal, contraction_type contraction_tp>
+class TensorContractionKernel {
+ public:
+ typedef typename Eigen::TensorSycl::internal::Vectorise<OutScalar, Eigen::SyclDevice, Vectorizable>::PacketReturnType
+ PacketReturnType;
+ static EIGEN_CONSTEXPR int PacketSize =
+ Eigen::TensorSycl::internal::Vectorise<OutScalar, Eigen::SyclDevice, Vectorizable>::PacketSize;
+ static EIGEN_CONSTEXPR bool is_lhs_transposed =
+ !::Eigen::internal::TensorContractionInputMapperTrait<LhsMapper>::inner_dim_contiguous;
+ static EIGEN_CONSTEXPR bool is_rhs_transposed =
+ !::Eigen::internal::TensorContractionInputMapperTrait<RhsMapper>::inner_dim_contiguous;
+
+ typedef BlockProperties<is_lhs_transposed, false, input_mapper_properties::is_lhs_matrix && Vectorizable,
+ PacketReturnType>
+ LHSBlockProperties;
+
+ typedef BlockProperties<is_rhs_transposed, true, input_mapper_properties::is_rhs_matrix && Vectorizable,
+ PacketReturnType>
+ RHSBlockProperties;
+
+ static EIGEN_CONSTEXPR StorageIndex NStride =
+ contraction_tp == contraction_type::local ? Properties::WorkLoadPerThreadN : RHSBlockProperties::nc_stride;
+
+ typedef cl::sycl::accessor<OutScalar, 1, cl::sycl::access::mode::read_write, cl::sycl::access::target::local> Scratch;
+ typedef cl::sycl::multi_ptr<OutScalar, cl::sycl::access::address_space::local_space> local_ptr;
+ typedef OutScalar * /*cl::sycl::multi_ptr<OutScalar, cl::sycl::access::address_space::private_space>*/ private_ptr;
+ typedef std::conditional_t<contraction_tp == contraction_type::local, local_ptr, private_ptr>
+ tile_ptr;
+ static EIGEN_CONSTEXPR StorageIndex LSDL = contraction_tp == contraction_type::local
+ ? Properties::TileSizeDimM + Properties::BC
+ : Properties::WorkLoadPerThreadM;
+ static EIGEN_CONSTEXPR StorageIndex LSDR = contraction_tp == contraction_type::local
+ ? Properties::TileSizeDimN + Properties::BC
+ : Properties::WorkLoadPerThreadN;
+ static EIGEN_CONSTEXPR StorageIndex LocalOffset = Properties::LocalThreadSizeM * Properties::LocalThreadSizeN;
+
+ /**
+ * \brief MemHolder this is a place holder struct for creating memory hierarchy in SYCL. Inside SYCL kernel it is not
+ * allowed to have dynamic memory allocation. While the local memory is created outside of the kernel and passed to
+ * the kernel as an accessor, the private memory can only allowed to be allocated statically. Since we are abstracting
+ * the TiledMemory for both local and private memory, the MemHolder structs is used as a helper to abstract out
+ * different type of memory needed when local/no_local memory computation is called.
+ *
+ * \tparam contraction_type: it is an enum value representing whether the local memory/no local memory implementation
+ of the algorithm to be used
+ * \tparam the private memory size
+ * \param ptr the tile memory pointer type
+ */
+ template <contraction_type, StorageIndex>
+ struct MemHolder {
+ tile_ptr ptr;
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE MemHolder(local_ptr block_start_ptr) : ptr(block_start_ptr) {}
+ };
+ /**
+ * \brief specialization of memHolder class when no local memory kernel is used.
+ */
+ template <StorageIndex MemSize>
+ struct MemHolder<contraction_type::no_local, MemSize> {
+ OutScalar ptr[MemSize] = {OutScalar{0}};
+ };
+ /**
+ * \brief TiledMemory: contains required memory pointer for loading each tile of the TensorContraction panel from
+ * global memory to local/private memory when local/no_local algorithm used.
+ *
+ * \param lhs_scratch_extract : determines the LHS tile memory. It is either private or local memory based on the
+ * selected contraction_type.
+ *
+ * \param rhs_scratch_extract : determines the RHS tile memory. It is either private or local memory based on the
+ * selected contraction_type.
+ *
+ * \param lhs_extract_index: determines the position of each thread on a local memory for lhs input. When private
+ * memory is used this is set to zero as this is not applicable in case of private memory.
+ *
+ * \param rhs_extract_index: determines the position of each thread on a local memory for rhs input. When private
+ * memory is used this is set to zero as this is not applicable in case of private memory.
+ *
+ * \param lhs_scratch_compute : determines the location to load for computation for lhs_local memory. This is the
+ * same as lhs_scratch_extract for private memory.
+ *
+ * \param rhs_scratch_compute : determines the location to load for computation for rhs_local memory. This is the
+ * same as rhs_scratch_extract for private memory.
+ */
+ struct TiledMemory {
+ MemHolder<contraction_tp, Properties::WorkLoadPerThreadM * Properties::TileSizeDimK> lhs_scratch_extract;
+ MemHolder<contraction_tp, Properties::WorkLoadPerThreadN * Properties::TileSizeDimK> rhs_scratch_extract;
+ tile_ptr lhs_scratch_ptr_compute;
+ tile_ptr rhs_scratch_ptr_compute;
+ const std::pair<StorageIndex, StorageIndex> lhs_extract_index;
+ const std::pair<StorageIndex, StorageIndex> rhs_extract_index;
+ template <contraction_type tp = contraction_tp>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ TiledMemory(const ThreadProperties<StorageIndex> &, local_ptr,
+ std::enable_if_t<tp == contraction_type::no_local> * = 0)
+ : lhs_scratch_extract{},
+ rhs_scratch_extract{},
+ lhs_scratch_ptr_compute(lhs_scratch_extract.ptr),
+ rhs_scratch_ptr_compute(rhs_scratch_extract.ptr),
+ lhs_extract_index(std::pair<StorageIndex, StorageIndex>(StorageIndex{0}, StorageIndex{0})),
+ rhs_extract_index(std::pair<StorageIndex, StorageIndex>(StorageIndex{0}, StorageIndex{0})) {}
+
+ template <contraction_type tp = contraction_tp>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ TiledMemory(const ThreadProperties<StorageIndex> &thread_properties, local_ptr block_start_ptr,
+ std::enable_if_t<tp == contraction_type::local> * = 0)
+ : lhs_scratch_extract{block_start_ptr},
+ rhs_scratch_extract{lhs_scratch_extract.ptr +
+ ((Properties::DoubleBuffer + 1) * LSDL * Properties::TileSizeDimK)},
+ lhs_scratch_ptr_compute(lhs_scratch_extract.ptr + thread_properties.mLocalOffset),
+ rhs_scratch_ptr_compute(rhs_scratch_extract.ptr + thread_properties.nLocalOffset),
+ lhs_extract_index(
+ local_id_extract<LHSBlockProperties, Properties::TileSizeDimM>(thread_properties.linearLocalThreadId)),
+ rhs_extract_index(
+ local_id_extract<RHSBlockProperties, Properties::TileSizeDimN>(thread_properties.linearLocalThreadId)) {}
+ };
+
+ Scratch scratch;
+ const LhsMapper lhs;
+ const RhsMapper rhs;
+ OutAccessor out_res;
+ const StorageIndex groupSizeM;
+ const StorageIndex groupSizeN;
+ const StorageIndex numTiles;
+ const TripleDim triple_dim;
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorContractionKernel(Scratch scratch_, const LhsMapper lhs_,
+ const RhsMapper rhs_, OutAccessor out_res_,
+ const StorageIndex groupSizeM_,
+ const StorageIndex groupSizeN_,
+ const StorageIndex numTiles_,
+ const TripleDim triple_dim_)
+ : scratch(scratch_),
+ lhs(lhs_),
+ rhs(rhs_),
+ out_res(out_res_),
+ groupSizeM(groupSizeM_),
+ groupSizeN(groupSizeN_),
+ numTiles(numTiles_),
+ triple_dim(triple_dim_) {}
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorContractionKernel(Scratch scratch_, const LhsMapper lhs_,
+ const RhsMapper rhs_, OutAccessor out_res_,
+ const StorageIndex groupSizeM_,
+ const StorageIndex numTiles_,
+ const TripleDim triple_dim_)
+ : TensorContractionKernel(scratch_, lhs_, rhs_, out_res_, groupSizeM_, 1, numTiles_, triple_dim_) {}
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void operator()(cl::sycl::nd_item<1> itemID) {
+ const StorageIndex linearLocalThreadId = itemID.get_local_id(0);
+ const StorageIndex nLocalThreadId = linearLocalThreadId / Properties::LocalThreadSizeM;
+ const StorageIndex mLocalThreadId = linearLocalThreadId % Properties::LocalThreadSizeM;
+ const StorageIndex mGroupId = itemID.get_group(0) % groupSizeM;
+ const StorageIndex tmp = itemID.get_group(0) / groupSizeM;
+ const StorageIndex nGroupId = IsFinal ? tmp : tmp % groupSizeN;
+ const StorageIndex kGroupId = IsFinal ? 0 : tmp / groupSizeN;
+ const StorageIndex mGroupOffset = mGroupId * Properties::TileSizeDimM;
+ const StorageIndex nGroupOffset = nGroupId * Properties::TileSizeDimN;
+ const StorageIndex mLocalOffset = PacketSize * mLocalThreadId;
+ const StorageIndex nLocalOffset = NStride * nLocalThreadId;
+ const StorageIndex mGlobalOffset = mGroupOffset + mLocalOffset;
+ const StorageIndex nGlobalOffset = nGroupOffset + nLocalOffset;
+
+ const StorageIndex kSizePerWG = IsFinal ? triple_dim.K : numTiles * Properties::TileSizeDimK;
+ StorageIndex kGroupOffset = kGroupId * kSizePerWG;
+ const bool is_internal = triple_dim.M - mGroupOffset >= Properties::TileSizeDimM &&
+ triple_dim.N - nGroupOffset >= Properties::TileSizeDimN &&
+ triple_dim.K - kGroupOffset >= kSizePerWG;
+ // this is used to adjust the last block
+ StorageIndex kSize = IsFinal ? triple_dim.K : std::min(kSizePerWG, triple_dim.K - kGroupOffset);
+ // This is used to find out the lats K offset so that kGroupOffset -kSize can compute the coffset for loading to
+ // tile
+ kGroupOffset += kSize;
+
+ auto thread_properties =
+ ThreadProperties<StorageIndex>(linearLocalThreadId, kGroupId, mGroupOffset, nGroupOffset, kGroupOffset,
+ mLocalOffset, nLocalOffset, mGlobalOffset, nGlobalOffset, kSize, is_internal);
+
+ auto out_ptr = out_res.get_pointer() + (IsFinal ? 0 : thread_properties.kGroupId * triple_dim.M * triple_dim.N);
+
+ (thread_properties.is_internal) ? compute_panel<true>(itemID, thread_properties, out_ptr)
+ : compute_panel<false>(itemID, thread_properties, out_ptr);
+ }
+ // The compute block computes the contraction operation private block for each thread and store the resutl in the
+ // privateRes memory of Each computation the compute block function is independent of local and no local concepts as
+ // it only compute the block on each thread's private memory space
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void compute_block_per_tile(OutScalar *lhs_block_ptr, OutScalar *rhs_block_ptr,
+ PacketReturnType *privateRes) {
+ StorageIndex idx = 0;
+ EIGEN_CONSTEXPR StorageIndex lhs_stride =
+ contraction_tp == contraction_type::local ? (PacketSize * Properties::LocalThreadSizeM) : 1;
+ EIGEN_UNROLL_LOOP
+ for (StorageIndex wLPTN = 0; wLPTN < Properties::WorkLoadPerThreadN; wLPTN++) {
+ auto rhsPacket = PacketReturnType{*(rhs_block_ptr + wLPTN)};
+ StorageIndex lhs_index = 0;
+ EIGEN_UNROLL_LOOP
+ for (StorageIndex wLPTM = 0; wLPTM < Properties::WorkLoadPerThreadM / PacketSize; wLPTM++) {
+ PacketReturnType lhsPack{};
+ Eigen::TensorSycl::internal::PacketWrapper<PacketReturnType, PacketSize>::set_packet(lhsPack,
+ lhs_block_ptr + lhs_index);
+ privateRes[idx] = ::Eigen::internal::pmadd(lhsPack, rhsPacket, privateRes[idx]);
+
+ lhs_index += lhs_stride;
+ idx++;
+ }
+ }
+ }
+ // The store function write the computed contraction operation in the private memory of each thread to the global
+ // memory. The store function is independent of local and no local concepts s that it can be abstract out in the base
+ // class.
+ template <bool is_internal_block, StorageIndex PrivateNStride, typename OutPtr>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void store(OutPtr *out_ptr, PacketReturnType *privateRes,
+ StorageIndex mGlobalOffset, StorageIndex nGlobalOffset) {
+ auto chk_bound = [&](const StorageIndex &mIndex, const StorageIndex &nIndex) EIGEN_DEVICE_FUNC {
+ return (mIndex + PacketSize - 1 < triple_dim.M && nGlobalOffset + nIndex < triple_dim.N);
+ };
+ // when local memory is not used M and N are both accessed in a coalesced way. However, when local memory is
+ // available the k*N is transposed in the local to N*K therefore, each blocks operates on blockId*
+ // WorkLoadPerThreadN slice of N
+ EIGEN_CONSTEXPR StorageIndex GlobalNStride =
+ contraction_tp == contraction_type::local ? 1 : Properties::LocalThreadSizeN;
+ EIGEN_UNROLL_LOOP
+ for (StorageIndex wLPTN = 0; wLPTN < Properties::WorkLoadPerThreadN / PrivateNStride; wLPTN++) {
+ // output leading dimension
+ StorageIndex outputLD = 0;
+ // When local memory is used the PrivateNstride is always 1 because the coalesed access on N is loaded into Local
+ // memory and extracting from local to global is the same as no transposed version. However, when local memory is
+ // not used and RHS is transposed we packetize the load for RHS.
+ EIGEN_UNROLL_LOOP
+ for (StorageIndex nId = 0; nId < PrivateNStride; nId++) {
+ StorageIndex globalRow = mGlobalOffset;
+ EIGEN_UNROLL_LOOP
+ for (StorageIndex wLPTM = 0; wLPTM < Properties::WorkLoadPerThreadM / PacketSize; wLPTM++) {
+ PacketReturnType privetOut = privateRes[wLPTM];
+ if (check_boundary<is_internal_block>(chk_bound(globalRow, nId))) {
+ // Store the final results in C. The C matrix has always M as a first StorageIndex and N as a second
+ // StorageIndex Therefore it is always coalesced layout
+ write<data_source::global_mem>(privetOut, out_ptr + outputLD + globalRow);
+ } else {
+ EIGEN_UNROLL_LOOP
+ for (StorageIndex mId = 0; mId < PacketSize; mId++) {
+ StorageIndex mOffset = globalRow + mId;
+ if (mOffset < triple_dim.M && (nGlobalOffset + nId < triple_dim.N)) {
+ out_ptr[mOffset + outputLD] =
+ Eigen::TensorSycl::internal::PacketWrapper<PacketReturnType, PacketSize>::scalarize(mId, privetOut);
+ }
+ }
+ }
+ globalRow += (PacketSize * Properties::LocalThreadSizeM);
+ }
+ outputLD += triple_dim.M;
+ privateRes += Properties::WorkLoadPerThreadM / PacketSize;
+ }
+ out_ptr += (GlobalNStride * outputLD);
+
+ nGlobalOffset += (PrivateNStride * GlobalNStride);
+ }
+ }
+ // when no local memory is used the following extract_block will be enabled
+ template <typename InputBlockProperties, bool is_internal_block, typename Input, typename PrivateReg,
+ contraction_type contract_tp = contraction_tp>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ std::enable_if_t<contract_tp == contraction_type::no_local>
+ extract_block(const Input &inpt, PrivateReg private_ptr, const std::pair<StorageIndex, StorageIndex> &,
+ const StorageIndex &ncOffset, const StorageIndex cOffset) {
+ EIGEN_CONSTEXPR StorageIndex LocalThreadSizeNC =
+ InputBlockProperties::is_rhs ? Properties::LocalThreadSizeN : Properties::LocalThreadSizeM;
+ EIGEN_CONSTEXPR StorageIndex WorkLoadPerThreadNC =
+ InputBlockProperties::is_rhs ? Properties::WorkLoadPerThreadN : Properties::WorkLoadPerThreadM;
+ const StorageIndex &NC = InputBlockProperties::is_rhs ? triple_dim.N : triple_dim.M;
+
+ auto chk_bound = [&](const StorageIndex &CIndex, const StorageIndex &NCIndex) EIGEN_DEVICE_FUNC {
+ return ((CIndex + InputBlockProperties::c_stride - 1 < triple_dim.K) &&
+ (NCIndex + InputBlockProperties::nc_stride - 1 < NC));
+ };
+ const StorageIndex ld = InputBlockProperties::is_coalesced_layout ? NC : triple_dim.K;
+ StorageIndex cIndex = cOffset;
+
+ EIGEN_UNROLL_LOOP
+ for (StorageIndex cId = 0; cId < Properties::TileSizeDimK / InputBlockProperties::c_stride; cId++) {
+ StorageIndex ncIndex = ncOffset;
+ EIGEN_UNROLL_LOOP
+ for (StorageIndex ncId = 0; ncId < WorkLoadPerThreadNC / InputBlockProperties::nc_stride; ncId++) {
+ if (check_boundary<is_internal_block>(chk_bound(cIndex, ncIndex))) {
+ auto val =
+ read<InputBlockProperties::packet_load, InputBlockProperties::is_coalesced_layout,
+ InputBlockProperties::is_rhs, typename InputBlockProperties::OutType>(inpt, ncIndex, cIndex, ld);
+
+ write<StorageIndex, (InputBlockProperties::is_coalesced_layout ? 1 : WorkLoadPerThreadNC),
+ data_source::private_mem>(val, private_ptr);
+ } else {
+ EIGEN_UNROLL_LOOP
+ for (StorageIndex i = 0; i < InputBlockProperties::elements_per_access; i++) {
+ const StorageIndex ncInd = ncIndex + (InputBlockProperties::is_coalesced_layout ? i : 0);
+ const StorageIndex cInd = cIndex + (InputBlockProperties::is_coalesced_layout ? 0 : i);
+ OutScalar val =
+ (ncInd < NC && cInd < triple_dim.K)
+ ? read<false, InputBlockProperties::is_coalesced_layout, InputBlockProperties::is_rhs, OutScalar>(
+ inpt, ncInd, cInd, ld)
+ : OutScalar(0);
+ write<StorageIndex, (InputBlockProperties::is_coalesced_layout ? 1 : WorkLoadPerThreadNC),
+ data_source::private_mem>(
+ val, private_ptr + (InputBlockProperties::is_coalesced_layout ? i : 0) +
+ ((InputBlockProperties::is_coalesced_layout ? 0 : i) * WorkLoadPerThreadNC));
+ }
+ }
+
+ // if it is lhs we have to load it packetised when the packet size is > 1, because the output is coalesced. So
+ // even if M is not accessed in a coalesced mode, we have to load packet_size number of m per thread.
+ ncIndex = (!InputBlockProperties::is_rhs && InputBlockProperties::nc_stride == 1 && PacketSize != 1)
+ ? ncOffset + (ncId + 1) % PacketSize + ((ncId + 1) / PacketSize) * LocalThreadSizeNC
+ : (ncIndex + InputBlockProperties::nc_stride * LocalThreadSizeNC);
+ private_ptr += InputBlockProperties::nc_stride;
+ }
+ // the previous for loop ( private_ptr += (ncId * nc_stride)) has already moved ptr with one WorkLoadPerThreadNC
+ private_ptr += (InputBlockProperties::c_stride - 1) * WorkLoadPerThreadNC;
+ cIndex += InputBlockProperties::c_stride;
+ }
+ }
+ template <typename InputBlockProperties, StorageIndex TileSizeDimNC>
+ static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE std::pair<StorageIndex, StorageIndex> local_id_extract(
+ const StorageIndex &linearLocalThreadId) {
+ const StorageIndex localThreadNC =
+ (InputBlockProperties::is_coalesced_layout)
+ ? linearLocalThreadId % (TileSizeDimNC / InputBlockProperties::nc_stride)
+ : linearLocalThreadId / (Properties::TileSizeDimK / InputBlockProperties::c_stride);
+ const StorageIndex localThreadC =
+ (InputBlockProperties::is_coalesced_layout)
+ ? linearLocalThreadId / (TileSizeDimNC / InputBlockProperties::nc_stride)
+ : linearLocalThreadId % (Properties::TileSizeDimK / InputBlockProperties::c_stride);
+ return std::pair<StorageIndex, StorageIndex>(localThreadNC, localThreadC);
+ }
+
+ template <bool db = Properties::DoubleBuffer, contraction_type ctp = contraction_tp>
+ static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ std::enable_if_t<db && ctp == contraction_type::local>
+ sync_mem(const cl::sycl::nd_item<1> &, bool &db_offset) noexcept {
+ db_offset = !db_offset;
+ }
+
+ template <bool db = Properties::DoubleBuffer, contraction_type ctp = contraction_tp>
+ static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ std::enable_if_t<!db && ctp == contraction_type::local>
+ sync_mem(const cl::sycl::nd_item<1> &itemID, bool &) noexcept {
+ itemID.barrier(cl::sycl::access::fence_space::local_space);
+ }
+
+ template <contraction_type ctp = contraction_tp>
+ static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ std::enable_if_t<ctp == contraction_type::no_local>
+ sync_mem(const cl::sycl::nd_item<1> &, bool &) noexcept {
+ return;
+ }
+
+ template <bool need_sync, contraction_type ctp = contraction_tp>
+ static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ std::enable_if_t<need_sync && ctp == contraction_type::no_local>
+ sync_thread(const cl::sycl::nd_item<1> &
+#ifdef EIGEN_SYCL_ARM_GPU_CACHE_OPTIMISATION
+ itemID
+#endif
+ ) noexcept {
+#ifdef EIGEN_SYCL_ARM_GPU_CACHE_OPTIMISATION
+ itemID.barrier(cl::sycl::access::fence_spacce::local_space);
+#else
+ return;
+#endif
+ }
+ template <bool need_sync, contraction_type ctp = contraction_tp>
+ static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ std::enable_if_t<need_sync && ctp == contraction_type::local>
+ sync_thread(const cl::sycl::nd_item<1> &itemID) {
+ itemID.barrier(cl::sycl::access::fence_space::local_space);
+ }
+ template <bool need_sync>
+ static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE std::enable_if_t<!need_sync> sync_thread(
+ const cl::sycl::nd_item<1> &) {
+ return;
+ }
+
+ template <bool is_internal_block>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void compute_tile_per_panel(const cl::sycl::nd_item<1> &itemID,
+ ThreadProperties<StorageIndex> &thread_properties,
+ TiledMemory &tiled_input_block,
+ PacketReturnType *privateRes, bool &db_offset) {
+ // Tiling the Rhs block from global to local memory
+ extract_block<RHSBlockProperties, is_internal_block>(
+ rhs, tiled_input_block.rhs_scratch_extract.ptr + (db_offset * Properties::TileSizeDimK * LSDR),
+ tiled_input_block.rhs_extract_index,
+ contraction_tp == contraction_type::local ? thread_properties.nGroupOffset : thread_properties.nGlobalOffset,
+ thread_properties.kGroupOffset - thread_properties.kSize);
+
+ sync_thread<contraction_tp == contraction_type::no_local>(itemID);
+
+ // Tiling the Lhs block from global to local memory
+ extract_block<LHSBlockProperties, is_internal_block>(
+ lhs, tiled_input_block.lhs_scratch_extract.ptr + (db_offset * LSDL * Properties::TileSizeDimK),
+ tiled_input_block.lhs_extract_index,
+ contraction_tp == contraction_type::local ? thread_properties.mGroupOffset : thread_properties.mGlobalOffset,
+ thread_properties.kGroupOffset - thread_properties.kSize);
+
+ // itemID.barrier(cl::sycl::access::fence_space::local_space);
+ sync_thread<contraction_tp == contraction_type::local>(itemID);
+ // switch to compute mede
+ StorageIndex lhs_offset = (db_offset * LSDL * Properties::TileSizeDimK);
+ StorageIndex rhs_offset = (db_offset * Properties::TileSizeDimK * LSDR);
+ // Loop over the values of a single tile
+ for (StorageIndex k = 0; k < Properties::TileSizeDimK; k++) {
+ compute_block_per_tile(tiled_input_block.lhs_scratch_ptr_compute + lhs_offset,
+ tiled_input_block.rhs_scratch_ptr_compute + rhs_offset, privateRes);
+ lhs_offset += LSDL;
+ rhs_offset += LSDR;
+ }
+ // computing the K index for the next tile
+ thread_properties.kSize -= Properties::TileSizeDimK;
+ sync_mem(itemID, db_offset);
+ }
+
+ // when local memory is available the following compute_panel will be enabled
+ template <bool is_internal_block, typename OutPtr>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void compute_panel(const cl::sycl::nd_item<1> &itemID,
+ ThreadProperties<StorageIndex> &thread_properties,
+ OutPtr out_ptr) {
+ auto tiled_input_block = TiledMemory{thread_properties, scratch.get_pointer()};
+ // Allocate register space
+ PacketReturnType privateRes[Properties::WorkLoadPerThreadM * Properties::WorkLoadPerThreadN / PacketSize] = {
+ PacketReturnType{0}};
+ bool db_offset = 0;
+
+ while (thread_properties.kSize >= Properties::TileSizeDimK) {
+ compute_tile_per_panel<is_internal_block>(itemID, thread_properties, tiled_input_block, privateRes, db_offset);
+ }
+ if (thread_properties.kSize > 0) {
+ compute_tile_per_panel<false>(itemID, thread_properties, tiled_input_block, privateRes, db_offset);
+ }
+
+ // Storing the final results in the output
+ store<is_internal_block,
+ contraction_tp == contraction_type::local ? static_cast<StorageIndex>(1) : RHSBlockProperties::nc_stride>(
+ out_ptr + thread_properties.nGlobalOffset * triple_dim.M, privateRes, thread_properties.mGlobalOffset,
+ thread_properties.nGlobalOffset);
+ }
+ // When local memory is available the following extract_block will be enabled
+ template <typename InputBlockProperties, bool is_internal_block, typename Input, typename Local,
+ contraction_type contract_tp = contraction_tp>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ std::enable_if_t<contract_tp == contraction_type::local>
+ extract_block(const Input &inpt, Local local_ptr, const std::pair<StorageIndex, StorageIndex>& local_index,
+ const StorageIndex &ncOffset, const StorageIndex cOffset) {
+ EIGEN_CONSTEXPR StorageIndex TileSizeDimNC =
+ InputBlockProperties::is_rhs ? Properties::TileSizeDimN : Properties::TileSizeDimM;
+ EIGEN_CONSTEXPR StorageIndex LoadPerThread =
+ InputBlockProperties::is_rhs ? Properties::LoadPerThreadRhs : Properties::LoadPerThreadLhs;
+ EIGEN_CONSTEXPR StorageIndex LSD = InputBlockProperties::is_rhs ? LSDR : LSDL;
+ static_assert(((LocalOffset % (TileSizeDimNC / InputBlockProperties::nc_stride) == 0) &&
+ (LocalOffset % (Properties::TileSizeDimK / InputBlockProperties::c_stride) == 0)),
+ " LocalOffset must be divisable by stride");
+ const StorageIndex &NC = InputBlockProperties::is_rhs ? triple_dim.N : triple_dim.M;
+ StorageIndex localThreadNC = local_index.first;
+ StorageIndex localThreadC = local_index.second;
+ auto chk_bound = [&](const StorageIndex &CIndex, const StorageIndex &NCIndex) EIGEN_DEVICE_FUNC {
+ return ((CIndex + InputBlockProperties::c_stride - 1 < triple_dim.K) &&
+ (NCIndex + InputBlockProperties::nc_stride - 1 < NC));
+ };
+ EIGEN_UNROLL_LOOP
+ for (StorageIndex lPT = 0; lPT < LoadPerThread / InputBlockProperties::elements_per_access; lPT++) {
+ const StorageIndex CIndex = cOffset + (InputBlockProperties::c_stride * localThreadC);
+ const StorageIndex NCIndex = ncOffset + (InputBlockProperties::nc_stride * localThreadNC);
+ const StorageIndex ld = InputBlockProperties::is_coalesced_layout ? NC : triple_dim.K;
+ if (check_boundary<is_internal_block>(chk_bound(CIndex, NCIndex))) {
+ auto val =
+ read<InputBlockProperties::packet_load, InputBlockProperties::is_coalesced_layout,
+ InputBlockProperties::is_rhs, typename InputBlockProperties::OutType>(inpt, NCIndex, CIndex, ld);
+ write<StorageIndex, (InputBlockProperties::is_coalesced_layout ? 1 : LSD), data_source::local_mem>(
+ val, local_ptr + (InputBlockProperties::nc_stride * localThreadNC) +
+ (InputBlockProperties::c_stride * localThreadC * LSD));
+ } else {
+ EIGEN_UNROLL_LOOP
+ for (StorageIndex i = 0; i < InputBlockProperties::elements_per_access; i++) {
+ const StorageIndex nCInd = NCIndex + (InputBlockProperties::is_coalesced_layout ? i : 0);
+ const StorageIndex cInd = CIndex + (InputBlockProperties::is_coalesced_layout ? 0 : i);
+ OutScalar val =
+ (nCInd < NC && cInd < triple_dim.K)
+ ? read<false, InputBlockProperties::is_coalesced_layout, InputBlockProperties::is_rhs, OutScalar>(
+ inpt, nCInd, cInd, ld)
+ : OutScalar(0);
+
+ write<StorageIndex, (InputBlockProperties::is_coalesced_layout ? 1 : LSD), data_source::local_mem>(
+ val, local_ptr + (InputBlockProperties::nc_stride * localThreadNC) +
+ (InputBlockProperties::is_coalesced_layout ? i : 0) +
+ ((InputBlockProperties::c_stride * localThreadC +
+ (InputBlockProperties::is_coalesced_layout ? 0 : i)) *
+ LSD));
+ }
+ }
+ localThreadNC += (InputBlockProperties::is_coalesced_layout)
+ ? LocalOffset % (TileSizeDimNC / InputBlockProperties::nc_stride)
+ : LocalOffset / (Properties::TileSizeDimK / InputBlockProperties::c_stride);
+ localThreadC += (InputBlockProperties::is_coalesced_layout)
+ ? LocalOffset / (TileSizeDimNC / InputBlockProperties::nc_stride)
+ : LocalOffset % (Properties::TileSizeDimK / InputBlockProperties::c_stride);
+ }
+ }
+};
+
+#ifndef EIGEN_SYCL_DISABLE_GEMV
+
+/*!
+ * \brief GeneralVectorTensor is a template class that provides Tensor -vector contraction operation, which is a special
+ * case of Tensor Tensor contraction.
+ *
+ * \tparam OutScalar: determines the output scalar type
+ *
+ * \tparam OutAccessor: determines the sycl accessor type for out put (please see the sycl-1.2.1 specification
+ * (https://www.khronos.org/registry/SYCL/specs/sycl-1.2.1.pdf) for accessor definition)
+ *
+ * \tparam VectorMapper: determines the tensor contraction mapper for the vector input (can be lhs or rhs)
+ *
+ * \tparam TensorMapper: determines the tensor contraction mapper for the tensor input (can be lhs or rhs)
+ *
+ * \tparam StorageIndex: determines the StorageIndex Type
+ *
+ * \tparam Properties: determines the Contraction Panel properties
+ *
+ * \tparam KFactor: determines the number of elements in K dimension in a Tile
+ *
+ * \tparam Vectorizable: determines whether or not the vectorization is enabled for the Eigen expression.
+ *
+ * \tparam is_lhs_vec: determines whether lhs is a vector or rhs is a vector
+ *
+ * \tparam IsFinal: determine if this is the final kernel. If so, the result will be written in a final output.
+ * Otherwise, the result of contraction will be written iin a temporary buffer.
+ *
+ * \param scratch: determines the local memory containing the vector block for each work-group
+ *
+ * \param vec: determines the vector input (tensor mapper)
+ *
+ * \param mat: determines the tensor input (tensor mapper)
+ *
+ * \param out_res: determines the output vector containing the contraction result
+ *
+ * \param nonContractGroupSize: a logical number determining the number of work-group for non-contracting dimension
+ *
+ * \param nonContractDim: determines the size of non contracting dimension for the flattened tensor
+ *
+ * \param contractDim: determines the size of non contracting dimension for the flattened tensor
+ *
+ */
+template <typename OutScalar, typename OutAccessor, typename VectorMapper, typename TensorMapper, typename StorageIndex,
+ typename Properties, StorageIndex KFactor, bool Vectorizable, bool is_lhs_vec, bool IsFinal>
+struct GeneralVectorTensor {
+ typedef typename Eigen::TensorSycl::internal::Vectorise<OutScalar, Eigen::SyclDevice, Vectorizable>::PacketReturnType
+ PacketReturnType;
+ static EIGEN_CONSTEXPR int PacketSize =
+ Eigen::TensorSycl::internal::Vectorise<OutScalar, Eigen::SyclDevice, Vectorizable>::PacketSize;
+ typedef cl::sycl::accessor<OutScalar, 1, cl::sycl::access::mode::read_write, cl::sycl::access::target::local> Scratch;
+
+ static EIGEN_CONSTEXPR StorageIndex OutScratchOffset =
+ KFactor * Properties::LocalThreadSizeC * Properties::LocalThreadSizeNC;
+
+ // Since the access layout for a vector can always be coalesced, when LHS is a vector, we pass false and false to make
+ // sure that the !^ is true When RHS is a vector, we pass true and true to make sure that the !^ is true.
+ typedef BlockProperties<is_lhs_vec ? false : true, is_lhs_vec ? false : true, Vectorizable, PacketReturnType>
+ VecBlockProperties;
+
+ Scratch scratch;
+ const VectorMapper vec;
+ const TensorMapper mat;
+ OutAccessor out_res;
+ const StorageIndex nonContractGroupSize;
+ const StorageIndex nonContractDim;
+ const StorageIndex contractDim;
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE GeneralVectorTensor(Scratch scratch_, const VectorMapper vec_,
+ const TensorMapper mat_, OutAccessor out_res_,
+ const StorageIndex nonContractGroupSize_,
+ const StorageIndex nonContractDim_,
+ const StorageIndex contractDim_)
+ : scratch(scratch_),
+ vec(vec_),
+ mat(mat_),
+ out_res(out_res_),
+ nonContractGroupSize(nonContractGroupSize_),
+ nonContractDim(nonContractDim_),
+ contractDim(contractDim_) {}
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void operator()(cl::sycl::nd_item<1> itemID) {
+ auto scratch_ptr = scratch.get_pointer();
+ const StorageIndex linearLocalThreadId = itemID.get_local_id(0);
+ StorageIndex nonContractId = is_lhs_vec ? linearLocalThreadId / Properties::LocalThreadSizeC
+ : linearLocalThreadId % Properties::LocalThreadSizeNC;
+ StorageIndex contractId = is_lhs_vec ? linearLocalThreadId % Properties::LocalThreadSizeC
+ : linearLocalThreadId / Properties::LocalThreadSizeNC;
+ const StorageIndex cGroupSize = itemID.get_group_range(0) / nonContractGroupSize;
+ const StorageIndex nonContractGroupId =
+ is_lhs_vec ? itemID.get_group(0) / cGroupSize : itemID.get_group(0) % nonContractGroupSize;
+ const StorageIndex contractGroupId =
+ is_lhs_vec ? itemID.get_group(0) % cGroupSize : itemID.get_group(0) / nonContractGroupSize;
+ auto out_ptr = out_res.get_pointer() + (IsFinal ? 0 : contractGroupId * nonContractDim);
+
+ const StorageIndex nonContractGroupOffset = nonContractGroupId * Properties::TileSizeDimNC;
+ const StorageIndex contractGroupOffset = contractGroupId * Properties::TileSizeDimC;
+ auto outScratchIndex = nonContractId + contractId * Properties::LocalThreadSizeNC;
+ const StorageIndex globalNonContractDimOffset = nonContractGroupOffset + nonContractId;
+ const StorageIndex globalContractDimOffset = contractGroupOffset + contractId;
+ auto local_output = scratch_ptr + OutScratchOffset;
+ const bool is_internal = nonContractDim - nonContractGroupOffset >= Properties::TileSizeDimNC &&
+ contractDim - contractGroupOffset >= Properties::TileSizeDimC;
+ is_internal
+ ? compute_panel<true>(itemID, vec, mat, local_output, out_ptr,
+#ifdef EIGEN_SYCL_LOCAL_MEM_UNSET_OR_ON
+ scratch_ptr, contractGroupOffset,
+#endif
+ nonContractGroupOffset, linearLocalThreadId, contractDim, nonContractDim, contractId,
+ nonContractId, globalContractDimOffset, globalNonContractDimOffset, outScratchIndex)
+ : compute_panel<false>(itemID, vec, mat, local_output, out_ptr,
+#ifdef EIGEN_SYCL_LOCAL_MEM_UNSET_OR_ON
+ scratch_ptr, contractGroupOffset,
+#endif
+ nonContractGroupOffset, linearLocalThreadId, contractDim, nonContractDim, contractId,
+ nonContractId, globalContractDimOffset, globalNonContractDimOffset, outScratchIndex);
+ }
+ template <bool is_internal_block, typename OutPtr>
+ static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void compute_panel(
+ const cl::sycl::nd_item<1> &itemID, const VectorMapper &vec, const TensorMapper &mat, OutScalar *local_output,
+ OutPtr out_ptr,
+#ifdef EIGEN_SYCL_LOCAL_MEM_UNSET_OR_ON
+ OutScalar *scratch_ptr, const StorageIndex contractGroupOffset,
+#endif
+ const StorageIndex nonContractGroupOffset, const StorageIndex linearLocalThreadId, StorageIndex contractDim,
+ StorageIndex nonContractDim, StorageIndex contractId, StorageIndex nonContractId,
+ StorageIndex globalContractDimOffset, StorageIndex globalNonContractDimOffset, StorageIndex outScratchIndex) {
+ OutScalar outScalar[Properties::WorkLoadPerThreadNC] = {OutScalar(0)};
+ // Reading the vector
+#ifdef EIGEN_SYCL_LOCAL_MEM_UNSET_OR_ON
+ const StorageIndex vectorOffset = contractGroupOffset + linearLocalThreadId;
+ extract_block<VecBlockProperties, is_internal_block, KFactor,
+ Properties::LocalThreadSizeNC * Properties::LocalThreadSizeC>(vec, scratch_ptr, linearLocalThreadId,
+ vectorOffset, contractDim);
+
+ itemID.barrier(cl::sycl::access::fence_space::local_space);
+ auto in_scratch_ptr = scratch_ptr + contractId;
+#endif
+
+ StorageIndex privateOffsetC = 0;
+ EIGEN_UNROLL_LOOP
+ for (StorageIndex i = 0; i < Properties::WorkLoadPerThreadC; i++) {
+ StorageIndex privateOffsetNC = 0;
+ bool contract_conds = ((globalContractDimOffset + privateOffsetC) < contractDim);
+#ifdef EIGEN_SYCL_LOCAL_MEM_UNSET_OR_ON
+ auto vecScalar = *in_scratch_ptr;
+#else
+ auto vecScalar = (check_boundary<is_internal_block>(contract_conds))
+ ? vec(is_lhs_vec ? StorageIndex(0) : globalContractDimOffset + privateOffsetC,
+ is_lhs_vec ? globalContractDimOffset + privateOffsetC : StorageIndex(0))
+ : OutScalar(0);
+#endif
+ EIGEN_UNROLL_LOOP
+ for (StorageIndex j = 0; j < Properties::WorkLoadPerThreadNC; j++) {
+ auto matScalar = (check_boundary<is_internal_block>(
+ contract_conds && ((globalNonContractDimOffset + privateOffsetNC) < nonContractDim)))
+ ? mat(is_lhs_vec ? globalContractDimOffset + privateOffsetC
+ : globalNonContractDimOffset + privateOffsetNC,
+ is_lhs_vec ? globalNonContractDimOffset + privateOffsetNC
+ : globalContractDimOffset + privateOffsetC)
+ : OutScalar(0);
+
+ outScalar[j] = cl::sycl::mad(matScalar, vecScalar, outScalar[j]);
+ privateOffsetNC += Properties::LocalThreadSizeNC;
+ }
+ privateOffsetC += Properties::LocalThreadSizeC;
+#ifdef EIGEN_SYCL_LOCAL_MEM_UNSET_OR_ON
+ in_scratch_ptr += Properties::LocalThreadSizeC;
+#endif
+ }
+
+ auto out_scratch_ptr = local_output + outScratchIndex;
+ // Each block of 16*16 element in shared memory should reduce to 16*1
+ EIGEN_UNROLL_LOOP
+ for (StorageIndex j = 0; j < Properties::WorkLoadPerThreadNC; j++) {
+ *out_scratch_ptr = outScalar[j];
+
+ out_scratch_ptr += (Properties::LocalThreadSizeNC * Properties::LocalThreadSizeC);
+ }
+ if (is_lhs_vec) {
+ nonContractId = linearLocalThreadId % Properties::LocalThreadSizeNC;
+ contractId = linearLocalThreadId / Properties::LocalThreadSizeNC;
+ outScratchIndex = nonContractId + contractId * Properties::LocalThreadSizeNC;
+ }
+
+ out_scratch_ptr = local_output + outScratchIndex;
+ EIGEN_UNROLL_LOOP
+ for (StorageIndex j = 0; j < Properties::WorkLoadPerThreadNC; j++) {
+ EIGEN_UNROLL_LOOP
+ for (StorageIndex offset = Properties::LocalThreadSizeC >> 1; offset > 0; offset >>= 1) {
+ itemID.barrier(cl::sycl::access::fence_space::local_space);
+ if (contractId < offset) {
+ StorageIndex myNeigbourId = (Properties::LocalThreadSizeNC * offset);
+ *out_scratch_ptr += out_scratch_ptr[myNeigbourId];
+ }
+ }
+ // moving to next 16 by 16 block
+ out_scratch_ptr += (Properties::LocalThreadSizeNC * Properties::LocalThreadSizeC);
+ }
+
+ if (contractId == 0) {
+ out_scratch_ptr = local_output + nonContractId;
+ StorageIndex global_final_offset = nonContractGroupOffset + nonContractId;
+ out_ptr += global_final_offset;
+ EIGEN_UNROLL_LOOP
+ for (StorageIndex j = 0; j < Properties::WorkLoadPerThreadNC; j++) {
+ if (check_boundary<is_internal_block>(global_final_offset < nonContractDim)) {
+ auto res = *out_scratch_ptr;
+
+ *out_ptr = res;
+ out_ptr += Properties::LocalThreadSizeNC;
+ }
+ // moving to next 16 by 16 block to ge the next 16 reduced elements
+ out_scratch_ptr += (Properties::LocalThreadSizeNC * Properties::LocalThreadSizeC);
+ if (!(is_internal_block)) global_final_offset += Properties::LocalThreadSizeNC;
+ }
+ }
+ }
+
+ template <typename InputBlockProperties, bool is_internal_block, int CFactor, int GroupSize, typename Input,
+ typename Local>
+ static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void extract_block(const Input &inpt, Local *local_ptr,
+ const StorageIndex &linearLocalThreadId,
+ const StorageIndex &cOffset, const StorageIndex &C) {
+ local_ptr += InputBlockProperties::c_stride * linearLocalThreadId;
+ StorageIndex cIndex = cOffset;
+ for (StorageIndex cId = 0; cId < CFactor / InputBlockProperties::c_stride; cId++) {
+ if (check_boundary<is_internal_block>(cIndex + InputBlockProperties::c_stride - 1 < C)) {
+ auto val = read<InputBlockProperties::packet_load, InputBlockProperties::is_coalesced_layout,
+ InputBlockProperties::is_rhs, typename InputBlockProperties::OutType>(inpt, StorageIndex(0),
+ cIndex, StorageIndex(1));
+ write<StorageIndex, 1, data_source::local_mem>(val, local_ptr);
+ } else {
+ EIGEN_UNROLL_LOOP
+ for (StorageIndex i = 0; i < InputBlockProperties::elements_per_access; i++) {
+ OutScalar val =
+ (cIndex + i < C)
+ ? read<false, InputBlockProperties::is_coalesced_layout, InputBlockProperties::is_rhs, OutScalar>(
+ inpt, StorageIndex(0), cIndex + i, StorageIndex(1))
+ : OutScalar(0);
+ write<StorageIndex, 1, data_source::local_mem>(val, local_ptr + i);
+ }
+ }
+ local_ptr += InputBlockProperties::c_stride * GroupSize;
+ cIndex += InputBlockProperties::c_stride * GroupSize;
+ }
+ }
+};
+#endif
+
+#ifndef EIGEN_SYCL_DISABLE_SCALAR
+
+/*!
+ * \brief GeneralScalarContraction is a template class that provides the scalar value of Tensor -Tensor contraction
+ * operation, when all the dimensions are contracting dimensions. This Kernel reduces two tensors to an scalar
+ *
+ * \tparam OutScalar: determines the output scalar type
+ *
+ * \tparam LhsScalar: determines the left-hand-side scalar type
+ *
+ * \tparam RhsScalar: determines the right-hand-side scalar type
+ *
+ * \tparam OutAccessor: determines the sycl accessor type for out put (please see the sycl-1.2.1 specification
+ * (https://www.khronos.org/registry/SYCL/specs/sycl-1.2.1.pdf) for accessor definition)
+ *
+ * \tparam LhsMapper: determines the tensor contraction mapper type for left-hand-side matrix
+ *
+ * \tparam RhsMapper: determines the tensor contraction mapper type for right-hand-side matrix
+ *
+ * \tparam StorageIndex: determines the StorageIndex Type
+ *
+ * \tparam Vectorizable: determines whether or not the vectorization is enabled for the Eigen expression.
+ *
+ * \param scratch: local memory containing tiles of LHS and RHS tensors for each work-group
+ *
+ * \param lhs: determines the left-hand-side flattened tensor (tensor mapper)
+ *
+ * \param rhs: determines the right-hand-side flattened tensor (tensor mapper)
+ *
+ * \param out_res: determines the output tensor containing the contraction result
+ *
+ * \param rng: determines the total input data size
+ */
+template <typename OutScalar, typename LhsScalar, typename RhsScalar, typename OutAccessor, typename LhsMapper,
+ typename RhsMapper, typename StorageIndex, bool Vectorizable>
+struct GeneralScalarContraction {
+ typedef cl::sycl::accessor<OutScalar, 1, cl::sycl::access::mode::read_write, cl::sycl::access::target::local> Scratch;
+ Scratch scratch;
+ const LhsMapper lhs;
+ const RhsMapper rhs;
+ OutAccessor out_res;
+ const StorageIndex rng;
+
+ EIGEN_DEVICE_FUNC
+ GeneralScalarContraction(Scratch scratch_, const LhsMapper lhs_, const RhsMapper rhs_, OutAccessor out_res_,
+ const StorageIndex rng_)
+ : scratch(scratch_), lhs(lhs_), rhs(rhs_), out_res(out_res_), rng(rng_) {}
+
+ EIGEN_DEVICE_FUNC void operator()(cl::sycl::nd_item<1> itemID) {
+ auto out_ptr = out_res.get_pointer();
+ auto scratch_ptr = scratch.get_pointer().get();
+
+ StorageIndex globalid = itemID.get_global_id(0);
+ StorageIndex localid = itemID.get_local_id(0);
+ OutScalar accumulator = OutScalar(0);
+ for (StorageIndex i = globalid; i < rng; i += itemID.get_global_range(0)) {
+ accumulator = cl::sycl::mad(lhs(0, i), rhs(i, 0), accumulator);
+ }
+ auto out_scratch_ptr = scratch_ptr + localid;
+ *out_scratch_ptr = accumulator;
+ for (StorageIndex offset = itemID.get_local_range(0) >> 1; offset > 0; offset >>= 1) {
+ itemID.barrier(cl::sycl::access::fence_space::local_space);
+ if (localid < offset) {
+ *out_scratch_ptr = (accumulator += out_scratch_ptr[offset]);
+ }
+ }
+ if (localid == 0) {
+ out_ptr[itemID.get_group(0)] = accumulator;
+ }
+ }
+};
+#endif
+
+} // namespace internal
+} // namespace TensorSycl
+
+template <typename Indices, typename LeftArgType, typename RightArgType, typename OutputKernelType>
+struct TensorEvaluator<const TensorContractionOp<Indices, LeftArgType, RightArgType, OutputKernelType>,
+ Eigen::SyclDevice>
+ : public TensorContractionEvaluatorBase<TensorEvaluator<
+ const TensorContractionOp<Indices, LeftArgType, RightArgType, OutputKernelType>, Eigen::SyclDevice>> {
+ static_assert(std::is_same<OutputKernelType, const NoOpOutputKernel>::value,
+ "SYCL tensor contraction does not support output kernels.");
+
+ typedef Eigen::SyclDevice Device;
+
+ typedef TensorEvaluator<const TensorContractionOp<Indices, LeftArgType, RightArgType, OutputKernelType>, Device> Self;
+ typedef TensorContractionEvaluatorBase<Self> Base;
+ typedef TensorContractionOp<Indices, LeftArgType, RightArgType, OutputKernelType> XprType;
+ typedef std::remove_const_t<typename XprType::Scalar> Scalar;
+ typedef typename XprType::Index StorageIndex;
+ typedef typename XprType::CoeffReturnType CoeffReturnType;
+ typedef typename PacketType<CoeffReturnType, Device>::type PacketReturnType;
+ typedef typename Base::Storage Storage;
+ typedef typename Base::EvaluatorPointerType EvaluatorPointerType;
+ struct TripleDim {
+ const StorageIndex M;
+ const StorageIndex N;
+ const StorageIndex K;
+ TripleDim(const StorageIndex M_, const StorageIndex N_, const StorageIndex K_) : M(M_), N(N_), K(K_) {}
+ };
+ enum {
+ PacketAccess = (PacketType<CoeffReturnType, Device>::size > 1),
+ BlockAccess = false,
+ };
+
+ static constexpr int Layout = TensorEvaluator<LeftArgType, Device>::Layout;
+ static constexpr int LDims = Base::LDims;
+ static constexpr int RDims = Base::RDims;
+ static constexpr int ContractDims = Base::ContractDims;
+
+ typedef array<StorageIndex, LDims> left_dim_mapper_t;
+ typedef array<StorageIndex, RDims> right_dim_mapper_t;
+
+ typedef array<StorageIndex, ContractDims> contract_t;
+ typedef array<StorageIndex, LDims - ContractDims> left_nocontract_t;
+ typedef array<StorageIndex, RDims - ContractDims> right_nocontract_t;
+
+ static constexpr int NumDims = LDims + RDims - 2 * ContractDims;
+
+ typedef DSizes<StorageIndex, NumDims> Dimensions;
+
+ typedef TensorEvaluator<typename Base::EvalLeftArgType, Device> LeftEvaluator;
+ typedef TensorEvaluator<typename Base::EvalRightArgType, Device> RightEvaluator;
+ typedef std::remove_const_t<typename LeftEvaluator::CoeffReturnType> LhsScalar;
+ typedef std::remove_const_t<typename RightEvaluator::CoeffReturnType> RhsScalar;
+
+ typedef typename LeftEvaluator::Dimensions LeftDimensions;
+ typedef typename RightEvaluator::Dimensions RightDimensions;
+
+ template <bool lhs_inner_dim_contiguous, bool rhs_inner_dim_contiguous, bool rhs_inner_dim_reordered>
+ struct input_mapper_propertis {
+ static EIGEN_CONSTEXPR bool is_lhs_matrix = (LDims == 2 && ContractDims == 1) || lhs_inner_dim_contiguous;
+ static EIGEN_CONSTEXPR bool is_rhs_matrix =
+ (RDims == 2 && ContractDims == 1) || (rhs_inner_dim_contiguous && !rhs_inner_dim_reordered);
+ };
+
+ TensorEvaluator(const XprType &op, const Device &device) : Base(op, device) {}
+
+ // We need to redefine this method to make nvcc happy
+ EIGEN_STRONG_INLINE bool evalSubExprsIfNeeded(typename Base::EvaluatorPointerType data) {
+ this->m_leftImpl.evalSubExprsIfNeeded(NULL);
+ this->m_rightImpl.evalSubExprsIfNeeded(NULL);
+ if (!data) {
+ this->m_result = this->m_device.get(
+ static_cast<Scalar *>(this->m_device.allocate_temp(this->dimensions().TotalSize() * sizeof(Scalar))));
+ data = this->m_result;
+ }
+ evalToSycl(data);
+ return (this->m_result != NULL);
+ }
+ const Eigen::SyclDevice &device() const { return this->m_device; }
+ void evalToSycl(typename Base::EvaluatorPointerType buffer) const {
+ if (this->m_lhs_inner_dim_contiguous) {
+ if (this->m_rhs_inner_dim_contiguous) {
+ if (this->m_rhs_inner_dim_reordered) {
+ evalTyped<true, true, true, Unaligned>(buffer);
+ } else {
+ evalTyped<true, true, false, Unaligned>(buffer);
+ }
+ } else {
+ if (this->m_rhs_inner_dim_reordered) {
+ evalTyped<true, false, true, Unaligned>(buffer);
+ } else {
+ evalTyped<true, false, false, Unaligned>(buffer);
+ }
+ }
+ } else {
+ if (this->m_rhs_inner_dim_contiguous) {
+ if (this->m_rhs_inner_dim_reordered) {
+ evalTyped<false, true, true, Unaligned>(buffer);
+ } else {
+ evalTyped<false, true, false, Unaligned>(buffer);
+ }
+ } else {
+ if (this->m_rhs_inner_dim_reordered) {
+ evalTyped<false, false, true, Unaligned>(buffer);
+ } else {
+ evalTyped<false, false, false, Unaligned>(buffer);
+ }
+ }
+ }
+ }
+
+ template <bool lhs_inner_dim_contiguous, bool rhs_inner_dim_contiguous, bool rhs_inner_dim_reordered, int Alignment>
+ void evalTyped(typename Base::EvaluatorPointerType buffer) const {
+ const auto triple_dim = TripleDim{this->m_i_size, this->m_j_size, this->m_k_size};
+ typedef internal::TensorContractionInputMapper<
+ LhsScalar, StorageIndex, internal::Lhs, LeftEvaluator, left_nocontract_t, contract_t,
+ PacketType<CoeffReturnType, Device>::size, lhs_inner_dim_contiguous, false, Unaligned, MakeSYCLPointer>
+ LhsMapper;
+
+ typedef internal::TensorContractionInputMapper<RhsScalar, StorageIndex, internal::Rhs, RightEvaluator,
+ right_nocontract_t, contract_t,
+ PacketType<CoeffReturnType, Device>::size, rhs_inner_dim_contiguous,
+ rhs_inner_dim_reordered, Unaligned, MakeSYCLPointer>
+ RhsMapper;
+
+ // initialize data mappers
+ LhsMapper lhs(this->m_leftImpl, this->m_left_nocontract_strides, this->m_i_strides,
+ this->m_left_contracting_strides, this->m_k_strides);
+
+ RhsMapper rhs(this->m_rightImpl, this->m_right_nocontract_strides, this->m_j_strides,
+ this->m_right_contracting_strides, this->m_k_strides);
+
+#ifndef EIGEN_SYCL_DISABLE_SCALAR
+ if (triple_dim.M == 1 && triple_dim.N == 1) {
+ launchSC(buffer, lhs, rhs, triple_dim.K);
+ } else
+#endif
+#ifndef EIGEN_SYCL_DISABLE_GEMV
+ if (triple_dim.M != 1 && triple_dim.N == 1) {
+ LaunchVT<false>(buffer, rhs, lhs, triple_dim.M, triple_dim.K);
+ } else if (triple_dim.M == 1 && triple_dim.N != 1) {
+ LaunchVT<true>(buffer, lhs, rhs, triple_dim.N, triple_dim.K);
+ } else // This is equivalent of if (m!=1 && n!=1)
+#endif
+ {
+ typedef input_mapper_propertis<lhs_inner_dim_contiguous, rhs_inner_dim_contiguous, rhs_inner_dim_reordered>
+ inpt_mapper_properties;
+#ifndef EIGEN_SYCL_DISABLE_SKINNY
+ bool skinny = false;
+ auto platform_name = this->device().getPlatformName();
+ // This is based on empirical calculation for AMD r9-nano and Fiji
+ if (platform_name.find("AMD") == 0) {
+ skinny = (triple_dim.M < triple_dim.K || triple_dim.N < triple_dim.K) &&
+ ((triple_dim.M < 1024 && triple_dim.N < 1024) ||
+ (uint64_t(triple_dim.M * triple_dim.N) < uint64_t(triple_dim.K)));
+ } else {
+ skinny = (((std::max(triple_dim.K, triple_dim.N) / std::min(triple_dim.K, triple_dim.N)) > 100) ||
+ ((std::max(triple_dim.K, triple_dim.M) / std::min(triple_dim.K, triple_dim.M)) > 100) ||
+ ((std::max(triple_dim.N, triple_dim.M) / std::min(triple_dim.N, triple_dim.M)) > 100));
+ }
+ if (skinny)
+ adjustTT<true, inpt_mapper_properties>(buffer, lhs, rhs, triple_dim);
+ else
+#endif // EIGEN_SYCL_DISABLE_SKINNY
+ adjustTT<false, inpt_mapper_properties>(buffer, lhs, rhs, triple_dim);
+ }
+ }
+
+ template <bool skinny, typename input_mapper_properties, typename LhsMapper, typename RhsMapper>
+ void EIGEN_ALWAYS_INLINE adjustTT(EvaluatorPointerType buffer, const LhsMapper &lhs, const RhsMapper &rhs,
+ const TripleDim &triple_dim) const {
+#ifdef EIGEN_SYCL_LOCAL_MEM_UNSET_OR_ON
+ if (device().has_local_memory()) {
+ typedef TensorSycl::internal::TTPanelSize<CoeffReturnType, StorageIndex, 4, 4, 16> PanelParameters;
+ launchTT<TensorSycl::internal::contraction_type::local, skinny, input_mapper_properties, PanelParameters>(
+ buffer, lhs, rhs, triple_dim);
+ }
+#endif
+#ifdef EIGEN_SYCL_LOCAL_MEM_UNSET_OR_OFF
+ if (!(device().has_local_memory())) {
+ typedef TensorSycl::internal::TTPanelSize<CoeffReturnType, StorageIndex, 4, 4, 4> PanelParameters;
+ launchTT<TensorSycl::internal::contraction_type::no_local, skinny, input_mapper_properties, PanelParameters>(
+ buffer, lhs, rhs, triple_dim);
+ }
+#endif
+ }
+
+ template <TensorSycl::internal::contraction_type ct, bool skinny, typename input_mapper_properties,
+ typename Properties, typename LhsMapper, typename RhsMapper>
+ void launchTT(EvaluatorPointerType buffer, const LhsMapper &lhs, const RhsMapper &rhs,
+ const TripleDim &triple_dim) const {
+ const StorageIndex roundUpM = Eigen::TensorSycl::internal::roundUp(triple_dim.M, Properties::TileSizeDimM);
+ const StorageIndex roundUpN = Eigen::TensorSycl::internal::roundUp(triple_dim.N, Properties::TileSizeDimN);
+ const StorageIndex groupSizeM = roundUpM / Properties::TileSizeDimM;
+ const StorageIndex groupSizeN = roundUpN / Properties::TileSizeDimN;
+
+ const StorageIndex roundUpK = Eigen::TensorSycl::internal::roundUp(triple_dim.K, Properties::TileSizeDimK);
+ StorageIndex totalTilesK = roundUpK / Properties::TileSizeDimK;
+ StorageIndex groupSizeK =
+ skinny
+ ? std::max(std::min(totalTilesK,
+ (StorageIndex)(device().getPowerOfTwo(device().getNumSyclMultiProcessors(), true) * 4) /
+ (groupSizeM * groupSizeN)),
+ StorageIndex(1))
+ : StorageIndex(1);
+
+ const StorageIndex numTilesPerGroup = Eigen::TensorSycl::internal::roundUp(totalTilesK, groupSizeK) / groupSizeK;
+
+ const StorageIndex totalGroupSize = groupSizeM * groupSizeN * groupSizeK;
+
+ const StorageIndex localRange = Properties::LocalThreadSizeM * Properties::LocalThreadSizeN;
+ const StorageIndex globalRange = totalGroupSize * localRange;
+
+ const StorageIndex scratchSize = (ct == TensorSycl::internal::contraction_type::local)
+ ? ((Properties::DoubleBuffer + 1) *
+ (Properties::TileSizeDimM + Properties::BC) * (Properties::TileSizeDimK)) +
+ ((Properties::DoubleBuffer + 1) * (Properties::TileSizeDimK) *
+ (Properties::TileSizeDimN + Properties::BC))
+ : StorageIndex(1);
+
+ auto thread_range = cl::sycl::nd_range<1>(cl::sycl::range<1>(globalRange), cl::sycl::range<1>(localRange));
+ if (groupSizeK == 1) {
+ typedef TensorSycl::internal::TensorContractionKernel<CoeffReturnType, LhsScalar, RhsScalar, EvaluatorPointerType,
+ LhsMapper, RhsMapper, StorageIndex, Properties, TripleDim,
+ PacketAccess, input_mapper_properties, true, ct>
+ ContractKernelName;
+ device().template binary_kernel_launcher<CoeffReturnType, ContractKernelName>(
+ lhs, rhs, buffer, thread_range, scratchSize, groupSizeM, groupSizeN, numTilesPerGroup, triple_dim);
+ } else {
+ typedef TensorSycl::internal::TensorContractionKernel<CoeffReturnType, LhsScalar, RhsScalar, EvaluatorPointerType,
+ LhsMapper, RhsMapper, StorageIndex, Properties, TripleDim,
+ PacketAccess, input_mapper_properties, false, ct>
+ ContractKernelName;
+ CoeffReturnType *temp_pointer = static_cast<CoeffReturnType *>(
+ device().allocate_temp(triple_dim.M * triple_dim.N * groupSizeK * sizeof(CoeffReturnType)));
+ EvaluatorPointerType tmp_global_accessor = device().get(temp_pointer);
+
+ device().template binary_kernel_launcher<CoeffReturnType, ContractKernelName>(
+ lhs, rhs, tmp_global_accessor, thread_range, scratchSize, groupSizeM, groupSizeN, numTilesPerGroup,
+ triple_dim);
+
+ typedef Eigen::internal::SumReducer<CoeffReturnType> Op;
+ auto op = Op();
+ typedef TensorSycl::internal::SecondStepPartialReduction<CoeffReturnType, StorageIndex, EvaluatorPointerType,
+ EvaluatorPointerType, Op>
+ ReductionKernel;
+
+ device().template unary_kernel_launcher<CoeffReturnType, ReductionKernel>(
+ tmp_global_accessor, buffer,
+ cl::sycl::nd_range<1>(cl::sycl::range<1>(StorageIndex(
+ Eigen::TensorSycl::internal::roundUp(triple_dim.M * triple_dim.N, localRange))),
+ cl::sycl::range<1>(localRange)),
+ StorageIndex(1), op, StorageIndex(triple_dim.M * triple_dim.N), groupSizeK);
+
+ device().deallocate_temp(temp_pointer);
+ }
+ }
+
+#ifndef EIGEN_SYCL_DISABLE_GEMV
+ template <bool is_lhs_vec, typename VectorMapper, typename TensorMapper, typename StorageIndex>
+ void EIGEN_ALWAYS_INLINE LaunchVT(EvaluatorPointerType buffer, const VectorMapper &vec, const TensorMapper &mat,
+ StorageIndex NC, StorageIndex C) const {
+ const StorageIndex nonContractDim = NC;
+ EIGEN_CONSTEXPR StorageIndex NCFactor = 1;
+ EIGEN_CONSTEXPR StorageIndex CFactor = 1;
+ EIGEN_CONSTEXPR StorageIndex NCWindow = 16;
+ typedef Eigen::TensorSycl::internal::TVPanelSize<CoeffReturnType, StorageIndex, NCWindow, CFactor, NCFactor>
+ Properties;
+ const StorageIndex roundUpC = Eigen::TensorSycl::internal::roundUp(C, Properties::TileSizeDimC);
+ const StorageIndex cNumGroups = roundUpC / (Properties::LocalThreadSizeC * Properties::WorkLoadPerThreadC);
+ const StorageIndex roundUpNC = Eigen::TensorSycl::internal::roundUp(nonContractDim, Properties::TileSizeDimNC);
+ const StorageIndex nCNumGroups = roundUpNC / (Properties::LocalThreadSizeNC * Properties::WorkLoadPerThreadNC);
+ const StorageIndex globalRange =
+ (roundUpNC / (Properties::WorkLoadPerThreadNC)) * (roundUpC / (Properties::WorkLoadPerThreadC));
+ const StorageIndex localRange = Properties::LocalThreadSizeNC * Properties::LocalThreadSizeC;
+ const StorageIndex scratchSize =
+ (Properties::WorkLoadPerThreadNC + CFactor) * Properties::LocalThreadSizeC * Properties::LocalThreadSizeNC;
+ auto thread_range = cl::sycl::nd_range<1>(cl::sycl::range<1>(globalRange), cl::sycl::range<1>(localRange));
+ if (cNumGroups > 1) {
+ typedef Eigen::TensorSycl::internal::GeneralVectorTensor<CoeffReturnType, EvaluatorPointerType, VectorMapper,
+ TensorMapper, StorageIndex, Properties, CFactor, false,
+ is_lhs_vec, false>
+ ContractKernelName;
+ CoeffReturnType *temp_pointer =
+ static_cast<CoeffReturnType *>(device().allocate_temp(nonContractDim * cNumGroups * sizeof(CoeffReturnType)));
+ EvaluatorPointerType tmp_global_accessor = device().get(temp_pointer);
+
+ device().template binary_kernel_launcher<CoeffReturnType, ContractKernelName>(
+ vec, mat, tmp_global_accessor, thread_range, scratchSize, nCNumGroups, nonContractDim, C);
+
+ typedef Eigen::internal::SumReducer<CoeffReturnType> Op;
+ typedef TensorSycl::internal::SecondStepPartialReduction<CoeffReturnType, StorageIndex, EvaluatorPointerType,
+ EvaluatorPointerType, Op>
+ ReductionKernel;
+
+ device().template unary_kernel_launcher<CoeffReturnType, ReductionKernel>(
+ tmp_global_accessor, buffer,
+ cl::sycl::nd_range<1>(cl::sycl::range<1>(Eigen::TensorSycl::internal::roundUp(nonContractDim, localRange)),
+ cl::sycl::range<1>(localRange)),
+ StorageIndex(1), Op(), nonContractDim, cNumGroups);
+
+ device().deallocate_temp(temp_pointer);
+ } else {
+ typedef Eigen::TensorSycl::internal::GeneralVectorTensor<CoeffReturnType, EvaluatorPointerType, VectorMapper,
+ TensorMapper, StorageIndex, Properties, CFactor, false,
+ is_lhs_vec, true>
+ ContractKernelName;
+ device().template binary_kernel_launcher<CoeffReturnType, ContractKernelName>(
+ vec, mat, buffer, thread_range, scratchSize, nCNumGroups, nonContractDim, C);
+ }
+ }
+#endif
+
+#ifndef EIGEN_SYCL_DISABLE_SCALAR
+ template <typename LhsMapper, typename RhsMapper>
+ EIGEN_ALWAYS_INLINE void launchSC(EvaluatorPointerType buffer, const LhsMapper &lhs, const RhsMapper &rhs,
+ StorageIndex K) const {
+ EIGEN_STATIC_ASSERT(!((EIGEN_SYCL_LOCAL_THREAD_DIM0 * EIGEN_SYCL_LOCAL_THREAD_DIM1) &
+ (EIGEN_SYCL_LOCAL_THREAD_DIM0 * EIGEN_SYCL_LOCAL_THREAD_DIM1 - 1)),
+ "The Local thread size must be a power of 2 for the reduction "
+ "operation");
+ EIGEN_CONSTEXPR StorageIndex local_range = EIGEN_SYCL_LOCAL_THREAD_DIM0 * EIGEN_SYCL_LOCAL_THREAD_DIM1;
+
+ // Here we force the code not to be more than 2-step reduction: Our empirical research shows that if each thread
+ // reduces at least 512 elementss individually, we get better performance.
+ const StorageIndex num_work_group = ((K + (512 * local_range - 1)) / (512 * local_range) > 1 ? local_range : 1);
+ const StorageIndex global_range = num_work_group * local_range;
+
+ typedef Eigen::TensorSycl::internal::GeneralScalarContraction<
+ CoeffReturnType, LhsScalar, RhsScalar, EvaluatorPointerType, LhsMapper, RhsMapper, StorageIndex, false>
+ ContractKernelName;
+ auto thread_range = cl::sycl::nd_range<1>(cl::sycl::range<1>(global_range), cl::sycl::range<1>(local_range));
+ if (num_work_group > 1) {
+ CoeffReturnType *temp_pointer =
+ static_cast<CoeffReturnType *>(device().allocate_temp(num_work_group * sizeof(CoeffReturnType)));
+ EvaluatorPointerType tmp_global_accessor = device().get(temp_pointer);
+ device().template binary_kernel_launcher<CoeffReturnType, ContractKernelName>(lhs, rhs, tmp_global_accessor,
+ thread_range, local_range, K);
+ typedef Eigen::internal::SumReducer<CoeffReturnType> Op;
+ typedef TensorSycl::internal::SecondStepFullReducer<CoeffReturnType, Op, EvaluatorPointerType,
+ EvaluatorPointerType, StorageIndex, local_range>
+ GenericRKernel;
+ device().template unary_kernel_launcher<CoeffReturnType, GenericRKernel>(
+ tmp_global_accessor, buffer,
+ cl::sycl::nd_range<1>(cl::sycl::range<1>(local_range), cl::sycl::range<1>(local_range)), local_range, Op());
+
+ device().deallocate_temp(temp_pointer);
+ } else {
+ device().template binary_kernel_launcher<CoeffReturnType, ContractKernelName>(lhs, rhs, buffer, thread_range,
+ local_range, K);
+ }
+ }
+#endif
+
+ EIGEN_STRONG_INLINE void cleanup() {
+ this->m_leftImpl.cleanup();
+ this->m_rightImpl.cleanup();
+
+ if (this->m_result) {
+ this->m_device.deallocate_temp(this->m_result);
+ this->m_result = NULL;
+ }
+ }
+ // The placeholder accessors must bound to a command group handler for SYCL
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void bind(cl::sycl::handler &cgh) const {
+ this->m_leftImpl.bind(cgh);
+ this->m_rightImpl.bind(cgh);
+ this->m_result.bind(cgh);
+ }
+};
+} // namespace Eigen
+#endif // EIGEN_CXX11_TENSOR_TENSOR_CONTRACTION_SYCL_H
diff --git a/unsupported/Eigen/CXX11/src/Tensor/TensorContractionThreadPool.h b/unsupported/Eigen/CXX11/src/Tensor/TensorContractionThreadPool.h
new file mode 100644
index 0000000..19f664c
--- /dev/null
+++ b/unsupported/Eigen/CXX11/src/Tensor/TensorContractionThreadPool.h
@@ -0,0 +1,1679 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_CXX11_TENSOR_TENSOR_CONTRACTION_THREAD_POOL_H
+#define EIGEN_CXX11_TENSOR_TENSOR_CONTRACTION_THREAD_POOL_H
+
+// evaluator for thread pool device
+#ifdef EIGEN_USE_THREADS
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+template<typename Indices, typename LeftArgType, typename RightArgType, typename OutputKernelType>
+struct TensorEvaluator<const TensorContractionOp<Indices, LeftArgType, RightArgType, OutputKernelType>, ThreadPoolDevice> :
+ public TensorContractionEvaluatorBase<TensorEvaluator<const TensorContractionOp<Indices, LeftArgType, RightArgType, OutputKernelType>, ThreadPoolDevice> > {
+
+ typedef ThreadPoolDevice Device;
+
+ typedef TensorEvaluator<const TensorContractionOp<Indices, LeftArgType, RightArgType, OutputKernelType>, Device> Self;
+ typedef TensorContractionEvaluatorBase<Self> Base;
+
+ typedef TensorContractionOp<Indices, LeftArgType, RightArgType, OutputKernelType> XprType;
+ typedef std::remove_const_t<typename XprType::Scalar> Scalar;
+ typedef typename XprType::Index Index;
+ typedef typename XprType::CoeffReturnType CoeffReturnType;
+ typedef typename PacketType<CoeffReturnType, Device>::type PacketReturnType;
+
+ static constexpr int Layout = TensorEvaluator<LeftArgType, Device>::Layout;
+
+ // Most of the code is assuming that both input tensors are ColMajor. If the
+ // inputs are RowMajor, we will "cheat" by swapping the LHS and RHS:
+ // If we want to compute A * B = C, where A is LHS and B is RHS, the code
+ // will pretend B is LHS and A is RHS.
+ typedef std::conditional_t<
+ static_cast<int>(Layout) == static_cast<int>(ColMajor), LeftArgType, RightArgType> EvalLeftArgType;
+ typedef std::conditional_t<
+ static_cast<int>(Layout) == static_cast<int>(ColMajor), RightArgType, LeftArgType> EvalRightArgType;
+
+ static constexpr int LDims =
+ internal::array_size<typename TensorEvaluator<EvalLeftArgType, Device>::Dimensions>::value;
+ static constexpr int RDims =
+ internal::array_size<typename TensorEvaluator<EvalRightArgType, Device>::Dimensions>::value;
+ static constexpr int ContractDims = internal::array_size<Indices>::value;
+
+ typedef array<Index, LDims> left_dim_mapper_t;
+ typedef array<Index, RDims> right_dim_mapper_t;
+
+ typedef array<Index, ContractDims> contract_t;
+ typedef array<Index, LDims - ContractDims> left_nocontract_t;
+ typedef array<Index, RDims - ContractDims> right_nocontract_t;
+
+ static constexpr int NumDims = LDims + RDims - 2 * ContractDims;
+
+ typedef DSizes<Index, NumDims> Dimensions;
+
+ // typedefs needed in evalTo
+ typedef std::remove_const_t<typename EvalLeftArgType::Scalar> LhsScalar;
+ typedef std::remove_const_t<typename EvalRightArgType::Scalar> RhsScalar;
+ typedef typename internal::gebp_traits<LhsScalar, RhsScalar> Traits;
+
+ typedef TensorEvaluator<EvalLeftArgType, Device> LeftEvaluator;
+ typedef TensorEvaluator<EvalRightArgType, Device> RightEvaluator;
+
+ TensorEvaluator(const XprType& op, const Device& device) :
+ Base(op, device) {}
+
+ template <int Alignment>
+ void evalProduct(Scalar* buffer) const {
+ evalProductImpl<NoCallback, Alignment>(buffer, NoCallback());
+ }
+
+ template <typename EvalToCallback, int Alignment>
+ void evalProductAsync(Scalar* buffer, EvalToCallback done) const {
+ evalProductImpl<EvalToCallback, Alignment>(buffer, std::move(done));
+ }
+
+ template <typename DoneCallback, int Alignment>
+ void evalProductImpl(Scalar* buffer, DoneCallback done) const {
+ // This function computes a lot of heuristics in multiple steps, and it
+ // also has multiple exit points. To keep it sane, readable and all in one
+ // place, sync/async execution decision is made at runtime at the very end.
+ //
+ // (1) In sync mode we allocate Context on the stack, submit computations
+ // to the device thread pool, and block on a barrier until it is
+ // completed.
+ //
+ // (2) In async mode we allocate Context on the heap, and after all tasks
+ // are finished, we call provided the done callback, and delete a
+ // context from the heap.
+ //
+ // (*) EvalParallelContext & EvalShardedByInnerDimContext owns all the state
+ // and temporary buffers, required for executing the tensor contraction.
+ // They are responsible for cleaning it up after contraction is done.
+ static const bool IsEvalInSyncMode =
+ std::is_same<DoneCallback, NoCallback>::value;
+
+ const Index m = this->m_i_size;
+ const Index n = this->m_j_size;
+ const Index k = this->m_k_size;
+ if (m == 0 || n == 0 || k == 0) return;
+
+ // Compute a set of algorithm parameters:
+ // - kernel block sizes (bm, bn, bk)
+ // - task grain sizes (number of kernels executed per task: gm, gn)
+ // - number of threads
+ // - sharding by row/column
+ // - parallel packing or first lhs then rhs
+ // and some derived parameters:
+ // - number of tasks (nm, nn, nk)
+ // - number of kernels (nm0, nn0)
+ // Unfortunately, all these parameters are tightly interdependent.
+ // So in some cases we first compute approximate values, then compute other
+ // values based on these approximations and then refine the approximations.
+
+ // There are lots of heuristics here. There is some reasoning behind them,
+ // but ultimately they are just tuned on contraction benchmarks for
+ // different input configurations, thread counts and instruction sets.
+ // So feel free to question any of them.
+
+ // Compute whether we want to shard by row or by column.
+ // This is a first approximation, it will be refined later. Since we don't
+ // know number of threads yet we use 2, because what's we are most
+ // interested in at this point is whether it makes sense to use
+ // parallelization at all or not.
+ bool shard_by_col = shardByCol(m, n, 2);
+
+ // First approximation of kernel blocking sizes.
+ // Again, we don't know number of threads yet, so we use 2.
+ Index bm, bn, bk;
+ if (shard_by_col) {
+ internal::TensorContractionBlocking<Scalar, LhsScalar, RhsScalar, Index,
+ internal::ShardByCol>
+ blocking(k, m, n, 2);
+ bm = blocking.mc();
+ bn = blocking.nc();
+ bk = blocking.kc();
+ } else {
+ internal::TensorContractionBlocking<Scalar, LhsScalar, RhsScalar, Index,
+ internal::ShardByRow>
+ blocking(k, m, n, 2);
+ bm = blocking.mc();
+ bn = blocking.nc();
+ bk = blocking.kc();
+ }
+
+ // Compute optimal number of threads.
+ // Note: we use bk instead of k here because we are interested in amount of
+ // _parallelizable_ computations, and computations are not parallelizable
+ // across k dimension.
+ const TensorOpCost cost =
+ contractionCost(m, n, bm, bn, bk, shard_by_col, false);
+ int num_threads = TensorCostModel<ThreadPoolDevice>::numThreads(
+ static_cast<double>(n) * m, cost, this->m_device.numThreads());
+ int num_threads_by_k = numThreadsInnerDim(m, n, k);
+ if (shardByInnerDim(m, n, k, num_threads, num_threads_by_k)) {
+ // We are in the scenario where it is more effective to shard by the
+ // inner dimension.
+ if (IsEvalInSyncMode) {
+ EvalShardedByInnerDimContext<DoneCallback> ctx(
+ this, num_threads_by_k, buffer, m, n, k, std::move(done));
+ ctx.template run<Alignment>();
+ } else {
+ auto* ctx = new EvalShardedByInnerDimContext<DoneCallback>(
+ this, num_threads_by_k, buffer, m, n, k, std::move(done));
+ ctx->template runAsync<Alignment>();
+ }
+
+ return;
+ }
+
+ // TODO(dvyukov): this is a stop-gap to prevent regressions while the cost
+ // model is not tuned. Remove this when the cost model is tuned.
+ if (n == 1) num_threads = 1;
+
+ if (num_threads == 1) {
+ TENSOR_CONTRACTION_DISPATCH(this->template evalProductSequential,
+ Unaligned, (buffer));
+ if (!IsEvalInSyncMode) done();
+ return;
+ }
+
+ // Now that we know number of threads, recalculate sharding and blocking.
+ shard_by_col = shardByCol(m, n, num_threads);
+ if (shard_by_col) {
+ internal::TensorContractionBlocking<Scalar, LhsScalar, RhsScalar, Index,
+ internal::ShardByCol>
+ blocking(k, m, n, num_threads);
+ bm = blocking.mc();
+ bn = blocking.nc();
+ bk = blocking.kc();
+ } else {
+ internal::TensorContractionBlocking<Scalar, LhsScalar, RhsScalar, Index,
+ internal::ShardByRow>
+ blocking(k, m, n, num_threads);
+ bm = blocking.mc();
+ bn = blocking.nc();
+ bk = blocking.kc();
+ }
+
+ // Number of kernels for each dimension.
+ Index nm0 = divup(m, bm);
+ Index nn0 = divup(n, bn);
+ Index nk = divup(k, bk);
+
+ // Calculate task grain size (number of kernels executed per task).
+ // This task size coarsening serves two purposes:
+ // 1. It reduces per-task overheads including synchronization overheads.
+ // 2. It allows to use caches better (reuse the same packed rhs in several
+ // consecutive kernels).
+ Index gm = 1;
+ Index gn = 1;
+ // If we are sharding by column, then we prefer to reduce rows first.
+ if (shard_by_col) {
+ gm = coarsenM(m, n, bm, bn, bk, gn, num_threads, shard_by_col);
+ gn = coarsenN(m, n, bm, bn, bk, gm, num_threads, shard_by_col);
+ } else {
+ gn = coarsenN(m, n, bm, bn, bk, gm, num_threads, shard_by_col);
+ gm = coarsenM(m, n, bm, bn, bk, gn, num_threads, shard_by_col);
+ }
+ // Number of tasks in each dimension.
+ Index nm = divup(nm0, gm);
+ Index nn = divup(nn0, gn);
+
+ // If there is enough concurrency in the sharding dimension, we choose not
+ // to paralellize by the other dimension, and execute all kernels in sync
+ // mode. This reduces parallelism from the nm x nn down to nn
+ // (shard_by_col==true) or nm (shard_by_col==false).
+ const Index sharding_dim_tasks = shard_by_col ? nn : nm;
+ const int num_worker_threads = this->m_device.numThreadsInPool();
+
+ // With small number of threads we want to make sure that we do not reduce
+ // parallelism too much. With large number of threads we trade maximum
+ // parallelism for better memory locality.
+ const float oversharding_factor =
+ num_worker_threads <= 4 ? 8.0 :
+ num_worker_threads <= 8 ? 4.0 :
+ num_worker_threads <= 16 ? 2.0 :
+ num_worker_threads <= 32 ? 1.0 :
+ num_worker_threads <= 64 ? 0.8 : /* num_worker_threads > 64 */ 0.6;
+
+ const bool parallelize_by_sharding_dim_only =
+ sharding_dim_tasks >= oversharding_factor * num_worker_threads;
+
+ // Last by not least, decide whether we want to issue both lhs and rhs
+ // packing in parallel; or issue lhs packing first, and then issue rhs
+ // packing when lhs packing completes (for !shard_by_col lhs and rhs are
+ // swapped). Parallel packing allows more parallelism (for both packing and
+ // kernels), while sequential packing provides better locality (once
+ // a thread finishes rhs packing it proceed to kernels with that rhs).
+ // First, we are interested in parallel packing if there are few tasks.
+ bool parallel_pack = num_threads >= nm * nn;
+ // Also do parallel packing if all data fits into L2$.
+ if (m * bk * Index(sizeof(LhsScalar)) + n * bk * Index(sizeof(RhsScalar)) <=
+ l2CacheSize() * num_threads)
+ parallel_pack = true;
+ // But don't do it if we will use each rhs only once. Locality seems to be
+ // more important in this case.
+ if ((shard_by_col ? nm : nn) == 1) parallel_pack = false;
+ // Also don't get in the way of parallelize_by_sharding_dim_only
+ // optimization.
+ if (parallelize_by_sharding_dim_only) parallel_pack = false;
+
+ // TODO(ezhulnev): With if contexpr we don't need SyncEvalParallelContext.
+ if (IsEvalInSyncMode) {
+#define CONTEXT_ARGS \
+ (this, num_threads, buffer, m, n, k, bm, bn, bk, nm, nn, nk, gm, gn, nm0, \
+ nn0, shard_by_col, parallel_pack, parallelize_by_sharding_dim_only, \
+ NoCallback()) \
+ .run()
+ TENSOR_CONTRACTION_DISPATCH(SyncEvalParallelContext, Alignment,
+ CONTEXT_ARGS);
+#undef CONTEXT_ARGS
+
+ } else {
+#define CONTEXT_ARGS \
+ (this, num_threads, buffer, m, n, k, bm, bn, bk, nm, nn, nk, gm, gn, nm0, \
+ nn0, shard_by_col, parallel_pack, parallelize_by_sharding_dim_only, \
+ std::move(done))
+ TENSOR_CONTRACTION_ASYNC_DISPATCH(EvalParallelContext, DoneCallback,
+ Alignment, CONTEXT_ARGS, run());
+#undef CONTEXT_ARGS
+ }
+ }
+
+ // ------------------------------------------------------------------------ //
+
+ // Dummy struct to represent an empty DoneCallback.
+
+ struct NoCallback {
+ void operator()() {
+ eigen_assert(false && "NoCallback should never be called");
+ }
+ };
+
+ // ------------------------------------------------------------------------ //
+
+ template <typename DoneCallback, typename Context>
+ class EvalParallelNotification;
+
+ // Synchronous evaluation notification that blocks caller thread in Wait().
+ template <typename Context>
+ class EvalParallelNotification<NoCallback, Context> {
+ public:
+ EvalParallelNotification(Context*, NoCallback) {}
+ void Notify() { done_.Notify(); }
+ void Wait() { done_.Wait(); }
+ private:
+ Eigen::Notification done_;
+ };
+
+ // Asynchronous evaluation notification that does not block in Wait().
+ template <typename DoneCallback, typename Context>
+ class EvalParallelNotification {
+ public:
+ EvalParallelNotification(Context* ctx, DoneCallback done)
+ : ctx_(ctx), done_(std::move(done)) {}
+
+ void Notify() {
+ // Make a copy of done callback, because it will be destructed when we
+ // will delete context in the next line (EvalParallelNotification is a
+ // data member of EvalParallelContext class).
+ DoneCallback done_copy = std::move(done_);
+
+ // Delete parallel evaluation context.
+ delete ctx_;
+
+ // Now safely call the done callback.
+ done_copy();
+ }
+
+ void Wait() {}
+
+ private:
+ Context* ctx_;
+ DoneCallback done_;
+ };
+
+ // Context orchestrates sync/async parallel contraction evaluation. When it is
+ // executed in asynchronous mode, it owns all the shared state that might be
+ // accessible by block packing and kernel tasks.
+
+ template <typename DoneCallback, bool lhs_inner_dim_contiguous,
+ bool rhs_inner_dim_contiguous, bool rhs_inner_dim_reordered,
+ int Alignment>
+ class EvalParallelContext {
+ public:
+ typedef internal::TensorContractionInputMapper<
+ LhsScalar, Index, internal::Lhs, LeftEvaluator, left_nocontract_t,
+ contract_t, internal::packet_traits<LhsScalar>::size,
+ lhs_inner_dim_contiguous, false, Unaligned>
+ LhsMapper;
+ typedef internal::TensorContractionInputMapper<
+ RhsScalar, Index, internal::Rhs, RightEvaluator, right_nocontract_t,
+ contract_t, internal::packet_traits<RhsScalar>::size,
+ rhs_inner_dim_contiguous, rhs_inner_dim_reordered, Unaligned>
+ RhsMapper;
+
+ typedef internal::blas_data_mapper<Scalar, Index, ColMajor> OutputMapper;
+
+ typedef internal::TensorContractionKernel<
+ Scalar, LhsScalar, RhsScalar, Index, OutputMapper, LhsMapper, RhsMapper>
+ TensorContractionKernel;
+
+ typedef typename TensorContractionKernel::LhsBlock LhsBlock;
+ typedef typename TensorContractionKernel::RhsBlock RhsBlock;
+ typedef typename TensorContractionKernel::BlockMemHandle BlockMemHandle;
+
+ EvalParallelContext(const Self* self, int num_threads, Scalar* buffer,
+ Index tm, Index tn, Index tk, Index bm, Index bn,
+ Index bk, Index nm, Index nn, Index nk, Index gm,
+ Index gn, Index nm0, Index nn0, bool shard_by_col,
+ bool parallel_pack,
+ bool parallelize_by_sharding_dim_only,
+ DoneCallback done)
+ : created_by_thread_id_(std::this_thread::get_id()),
+ done_(this, std::move(done)),
+ device_(self->m_device),
+ lhs_(self->m_leftImpl, self->m_left_nocontract_strides,
+ self->m_i_strides, self->m_left_contracting_strides,
+ self->m_k_strides),
+ rhs_(self->m_rightImpl, self->m_right_nocontract_strides,
+ self->m_j_strides, self->m_right_contracting_strides,
+ self->m_k_strides),
+ buffer_(buffer),
+ output_(buffer, tm),
+ output_kernel_(self->m_output_kernel),
+ tensor_contraction_params_(self->m_tensor_contraction_params),
+ num_threads_(num_threads),
+ shard_by_col_(shard_by_col),
+ parallel_pack_(parallel_pack),
+ parallelize_by_sharding_dim_only_(parallelize_by_sharding_dim_only),
+ m_(tm),
+ n_(tn),
+ k_(tk),
+ bm_(bm),
+ bn_(bn),
+ bk_(bk),
+ nm_(nm),
+ nn_(nn),
+ nk_(nk),
+ gm_(gm),
+ gn_(gn),
+ nm0_(nm0),
+ nn0_(nn0),
+ kernel_(m_, k_, n_, bm_, bk_, bn_),
+ num_thread_local_allocations_(0),
+ // We reserve 2X more capacity for a thread local values, than the
+ // number of threads in the pool to efficiently handle task stealing
+ // by threads that are not managed by the pool.
+ thread_local_capacity(2 * (parallelize_by_sharding_dim_only_
+ ? device_.numThreadsInPool()
+ : 0)),
+ // We will use only one of the Lhs/Rhs thread local storage depending
+ // on the shard_by_col value and we parallelize by sharding dim ONLY.
+ lhs_thread_local_blocks_(shard_by_col_ ? 0 : thread_local_capacity,
+ {*this}, {*this}),
+ rhs_thread_local_blocks_(shard_by_col_ ? thread_local_capacity : 0,
+ {*this}, {*this}) {
+ // These two options are mutually exclusive.
+ eigen_assert(!(parallel_pack && parallelize_by_sharding_dim_only));
+
+ for (Index x = 0; x < P; x++) {
+ // Normal number of notifications for k slice switch is
+ // nm_ + nn_ + nm_ * nn_. However, first P - 1 slices will receive only
+ // nm_ + nn_ notifications, because they will not receive notifications
+ // from preceding kernels.
+ state_switch_[x] =
+ x == 0
+ ? 1
+ : (parallel_pack_ ? nn_ + nm_ : (shard_by_col_ ? nn_ : nm_)) +
+ (x == P - 1 ? nm_ * nn_ : 0);
+ state_packing_ready_[x] =
+ parallel_pack_ ? 0 : (shard_by_col_ ? nm_ : nn_);
+ state_kernel_[x] = new std::atomic<uint8_t>*[nm_];
+ for (Index m = 0; m < nm_; m++) {
+ state_kernel_[x][m] = new std::atomic<uint8_t>[nn_];
+ // Kernels generally receive 3 notifications (previous kernel + 2
+ // packing), but the first slice won't get notifications from previous
+ // kernels.
+ for (Index n = 0; n < nn_; n++)
+ state_kernel_[x][m][n].store(
+ (x == 0 ? 0 : 1) + (parallel_pack_ ? 2 : 1),
+ std::memory_order_relaxed);
+ }
+ }
+
+ // Allocate memory for packed rhs/lhs matrices.
+ packed_mem_ = kernel_.allocateSlices( //
+ device_, //
+ /*num_lhs=*/nm0_, //
+ /*num_rhs=*/nn0_, //
+ /*num_slices=*/std::min<Index>(nk_, P - 1), //
+ packed_lhs_, packed_rhs_);
+
+ if (parallelize_by_sharding_dim_only_) {
+ const int num_worker_threads = device_.numThreadsInPool();
+
+ if (shard_by_col) {
+ can_use_thread_local_packed_ = new std::atomic<bool>[nn_];
+ for (int i = 0; i < nn_; ++i)
+ can_use_thread_local_packed_[i].store(true,
+ std::memory_order_relaxed);
+
+ Index num_blocks = num_worker_threads * gn_;
+ thread_local_pre_alocated_mem_ = kernel_.allocateSlices( //
+ device_, //
+ /*num_lhs=*/0, //
+ /*num_rhs=*/num_blocks, //
+ /*num_slices=*/1, //
+ /*lhs_blocks=*/nullptr, &rhs_thread_local_pre_allocated_);
+
+ } else {
+ can_use_thread_local_packed_ = new std::atomic<bool>[nm_];
+ for (int i = 0; i < nm_; ++i)
+ can_use_thread_local_packed_[i].store(true,
+ std::memory_order_relaxed);
+
+ Index num_blocks = num_worker_threads * gm_;
+ thread_local_pre_alocated_mem_ = kernel_.allocateSlices( //
+ device_, //
+ /*num_lhs=*/num_blocks, //
+ /*num_rhs=*/0, //
+ /*num_slices=*/1, &lhs_thread_local_pre_allocated_, //
+ /*rhs_blocks=*/nullptr);
+ }
+ }
+ }
+
+ ~EvalParallelContext() {
+ for (Index x = 0; x < P; x++) {
+ for (Index m = 0; m < nm_; m++) delete[] state_kernel_[x][m];
+ delete[] state_kernel_[x];
+ }
+ kernel_.deallocate(device_, packed_mem_);
+ if (parallelize_by_sharding_dim_only_) {
+ kernel_.deallocate(device_, thread_local_pre_alocated_mem_);
+ delete[] can_use_thread_local_packed_;
+ }
+ }
+
+ void run() {
+ // Kick off packing of the first slice.
+ signal_switch(0, 1);
+
+ // Wait for overall completion.
+ //
+ // If parallel evaluation is executed in async mode, this is a no-op, and
+ // Wait() will return immediately. In synchronous mode it will block the
+ // caller thread until it will receive notification from last task.
+ //
+ // In async mode, last task when completed will call done callback from
+ // the same thread, and will delete this context.
+ //
+ // TODO(dvyukov): This wait can lead to deadlock if contraction is
+ // evaluated in synchronous mode. If nthreads contractions are
+ // concurrently submitted from worker threads, this wait will block all
+ // worker threads and the system will deadlock.
+ done_.Wait();
+ }
+
+ private:
+ std::thread::id created_by_thread_id_;
+
+ // This notification is specialized on the type of DoneCallback and can be
+ // blocking or non-blocking.
+ EvalParallelNotification<DoneCallback, EvalParallelContext> done_;
+
+ const Device& device_;
+ LhsMapper lhs_;
+ RhsMapper rhs_;
+ Scalar* const buffer_;
+ OutputMapper output_;
+ OutputKernelType output_kernel_;
+ TensorContractionParams tensor_contraction_params_;
+ const int num_threads_;
+ const bool shard_by_col_;
+ const bool parallel_pack_;
+ const bool parallelize_by_sharding_dim_only_;
+ // Matrix sizes.
+ const Index m_;
+ const Index n_;
+ const Index k_;
+ // Block sizes.
+ const Index bm_;
+ const Index bn_;
+ const Index bk_;
+ // Number of tasks.
+ const Index nm_;
+ const Index nn_;
+ const Index nk_;
+ // Task grain sizes (number of kernels executed per task).
+ const Index gm_;
+ const Index gn_;
+ // Number of blocks (this is different from ni_/nn_ because of task size
+ // coarsening).
+ const Index nm0_;
+ const Index nn0_;
+ // Tensor contraction kernel.
+ TensorContractionKernel kernel_;
+
+ // Parallelization strategy.
+ //
+ // Blocks related to the same k block can run in parallel because they write
+ // to different output blocks. So we parallelize within k slices, this
+ // gives us parallelism level of m x n. Before we can start any kernels
+ // related to k-th slice, we need to issue m lhs packing tasks and n rhs
+ // packing tasks.
+ //
+ // However, there is a bottleneck when we are finishing kernels for k-th
+ // slice (at the very end there is only 1 runnable kernel). To mitigate this
+ // bottleneck we allow kernels from k-th and k+1-th slices to run in
+ // parallel. Note that (m, n, k) and (m, n, k+1) kernels write to the same
+ // output block, so they must not run in parallel.
+ //
+ // This gives us the following dependency graph.
+ // On each k slice we have m x n kernel tasks, m lhs paking tasks and n rhs
+ // packing tasks.
+ // Kernel (m, n, k) can start when:
+ // - kernel (m, n, k-1) has finished
+ // - lhs packing (m, k) has finished
+ // - rhs packing (n, k) has finished
+ // Lhs/rhs packing can start when:
+ // - all k-1 packing has finished (artificially imposed to limit amount of
+ // parallel packing)
+ //
+ // On top of that we limit runnable tasks to two consecutive k slices.
+ // This is done to limit amount of memory we need for packed lhs/rhs
+ // (for each k slice we need m*bk + n*bk memory in packed_lhs_/packed_rhs_).
+ //
+ // state_switch_ tracks when we are ready to switch to the next k slice.
+ // state_kernel_[m][n] tracks when we are ready to kick off kernel (m, n).
+ // These variable are rolling over 3 consecutive k slices: first two we are
+ // actively executing + one to track completion of kernels in the second
+ // slice.
+ static constexpr Index P = 3;
+
+ // Handle to the allocated temporary storage for Lhs/Rhs blocks.
+ BlockMemHandle packed_mem_;
+ std::vector<LhsBlock> packed_lhs_[P - 1];
+ std::vector<RhsBlock> packed_rhs_[P - 1];
+
+ // If we choose to parallelize only by the sharding dimension, each thread
+ // will have it's own "thead local" (not a c++ thread local storage) memory
+ // for packed_lhs or packed_rhs (shard_by_col = false of true). This memory
+ // can't be passed to a kernel that might execute on a different thread.
+ //
+ // In practice when we are ready to pack memory for the sharding dimension
+ // (rhs if shard_by_col==true) of the K-th slice, all kernels for K-1 slice
+ // already computed (99% of the time), and we can pack data into the thread
+ // local storage, and guarantee that all the kernels will be executed
+ // immediately in the same thread. This significantly increases L1 cache hit
+ // ratio and reduces pressure on the memory bus.
+ //
+ // It's still possible that kernel for the K-th slice will be ready before
+ // completion of the K-1 kernel, so we have to allocate "global" packed_lhs_
+ // and packed_rhs_ to allow kernels to be executed later on a thread
+ // different from the thread that was used for packing.
+
+ // Handle for pre-allocated thread local memory buffers.
+ BlockMemHandle thread_local_pre_alocated_mem_;
+
+ // Only one of these will be initialized depending on shard_by_col value
+ // (the size will be `num_worker_threads * num_grains_in_the_sharding_dim`).
+ std::vector<LhsBlock> lhs_thread_local_pre_allocated_;
+ std::vector<RhsBlock> rhs_thread_local_pre_allocated_;
+
+ // How many thread local blocks were already allocated.
+ std::atomic<int> num_thread_local_allocations_;
+ const int thread_local_capacity;
+
+ // We will use pre-allocated Lhs/Rhs blocks defined above, if the number of
+ // unique threads in a system is below or equal to the number of threads in
+ // a thread pool. We will fallback on dynamic memory allocation after that.
+
+ // ThreadLocalBlocks is a container for Lhs or Rhs thread local buffers. Its
+ // size is equal to the grain size in Lhs/Rhs sharding dimension.
+ template <typename BlockType>
+ class ThreadLocalBlocks {
+ public:
+ ThreadLocalBlocks() = default;
+
+ ThreadLocalBlocks(BlockType* base, size_t grain_size)
+ : is_pre_allocated_(true),
+ thread_local_pre_allocated_base_(base),
+ grain_size_(grain_size) {}
+
+ ThreadLocalBlocks(BlockMemHandle mem_handle,
+ std::vector<BlockType> blocks)
+ : is_pre_allocated_(false),
+ mem_handle_(std::move(mem_handle)),
+ blocks_(std::move(blocks)) {}
+
+ BlockType& block(int grain_index) {
+ eigen_assert(grain_index >= 0);
+ eigen_assert(static_cast<size_t>(grain_index) < size());
+ return is_pre_allocated_ ? thread_local_pre_allocated_base_[grain_index]
+ : blocks_[grain_index];
+ }
+
+ void Release(EvalParallelContext& ctx) const {
+ if (!is_pre_allocated_) {
+ ctx.kernel_.deallocate(ctx.device_, mem_handle_);
+ }
+ }
+
+ size_t size() const {
+ return is_pre_allocated_ ? grain_size_ : blocks_.size();
+ }
+
+ private:
+ bool is_pre_allocated_;
+
+ // Reuse pre-allocated thread local buffers.
+ BlockType* thread_local_pre_allocated_base_ = nullptr;
+ size_t grain_size_ = 0;
+
+ // These will be initialized only if `is_pre_allocated == false`.
+ BlockMemHandle mem_handle_{};
+ std::vector<BlockType> blocks_;
+ };
+
+ // ThreadLocalBlocksInitialize callable does custom thread local blocks
+ // initialization, and will reuse pre-allocated buffers if possible, or will
+ // dynamically allocate new memory.
+ //
+ // Lhs/Rhs blocks might be of the same type, so we have to pass explicitly
+ // for what side do we plan to do block allocation.
+ template <typename BlockType, bool is_rhs>
+ class ThreadLocalBlocksInitialize {
+ static constexpr bool kIsLhs =
+ !is_rhs && std::is_same<BlockType, LhsBlock>::value;
+ static const bool kIsRhs =
+ is_rhs && std::is_same<BlockType, RhsBlock>::value;
+ static_assert(kIsLhs || kIsRhs, "Unknown block type");
+
+ using Blocks = ThreadLocalBlocks<BlockType>;
+
+ public:
+ ThreadLocalBlocksInitialize(EvalParallelContext& ctx)
+ : ctx_(ctx),
+ num_worker_threads_(ctx_.device_.numThreadsInPool()) {}
+
+ void operator()(Blocks& blocks) {
+ const int n = ctx_.num_thread_local_allocations_.fetch_add(
+ 1, std::memory_order_relaxed);
+
+ if (n >= num_worker_threads_) {
+ ThreadLocalBlocksAllocator<is_rhs>::allocate(ctx_, blocks);
+ } else {
+ ThreadLocalBlocksAllocator<is_rhs>::reuse(ctx_, n, blocks);
+ }
+ }
+
+ private:
+ // NOTE(ezhulenev): Without 'if constexpr' we have to put calls to
+ // TensorContractionKernel::allocateSlices into template specializations.
+ // Also explicit specializations are not allowed at class scope in C++03,
+ // EvalCtx type parameter is just a workaround for that limitation.
+ template <bool pack_rhs, typename EvalCtx = EvalParallelContext>
+ struct ThreadLocalBlocksAllocator;
+
+ template <typename EvalCtx>
+ struct ThreadLocalBlocksAllocator</*pack_rhs=*/true, EvalCtx> {
+ static void allocate(EvalCtx& ctx, Blocks& blocks) {
+ std::vector<RhsBlock> rhs_blocks;
+ BlockMemHandle mem_handle = ctx.kernel_.allocateSlices(
+ ctx.device_,
+ /*num_lhs=*/0,
+ /*num_rhs=*/ctx.gn_,
+ /*num_slices=*/1,
+ /*lhs_blocks=*/nullptr, /*rhs_blocks=*/&rhs_blocks);
+
+ blocks = ThreadLocalBlocks<RhsBlock>(std::move(mem_handle),
+ std::move(rhs_blocks));
+ }
+
+ static void reuse(EvalCtx& ctx, int index, Blocks& blocks) {
+ RhsBlock* ptr = &ctx.rhs_thread_local_pre_allocated_[ctx.gn_ * index];
+ blocks = ThreadLocalBlocks<RhsBlock>(ptr, ctx.gn_);
+ }
+ };
+
+ template <typename EvalCtx>
+ struct ThreadLocalBlocksAllocator</*pack_rhs=*/false, EvalCtx> {
+ static void allocate(EvalCtx& ctx, Blocks& blocks) {
+ std::vector<LhsBlock> lhs_blocks;
+ BlockMemHandle mem_handle = ctx.kernel_.allocateSlices(
+ ctx.device_,
+ /*num_lhs=*/ctx.gm_,
+ /*num_rhs=*/0,
+ /*num_slices=*/1,
+ /*lhs_blocks=*/&lhs_blocks, /*rhs_blocks=*/nullptr);
+
+ blocks = ThreadLocalBlocks<LhsBlock>(std::move(mem_handle),
+ std::move(lhs_blocks));
+ }
+
+ static void reuse(EvalCtx& ctx, int index, Blocks& blocks) {
+ LhsBlock* ptr = &ctx.lhs_thread_local_pre_allocated_[ctx.gm_ * index];
+ blocks = ThreadLocalBlocks<LhsBlock>(ptr, ctx.gm_);
+ }
+ };
+
+ EvalParallelContext& ctx_;
+ const int num_worker_threads_;
+ };
+
+ template <typename BlockType>
+ class ThreadLocalBlocksRelease {
+ public:
+ using Blocks = ThreadLocalBlocks<BlockType>;
+ ThreadLocalBlocksRelease(EvalParallelContext& ctx) : ctx_(ctx) {}
+ void operator()(Blocks& blocks) { blocks.Release(ctx_); }
+
+ private:
+ EvalParallelContext& ctx_;
+ };
+
+ // ThreadLocalBlocks initialization callables.
+ using ThreadLocalLhsInit =
+ ThreadLocalBlocksInitialize<LhsBlock, /*is_rhs=*/false>;
+ using ThreadLocalRhsInit =
+ ThreadLocalBlocksInitialize<RhsBlock, /*is_rhs=*/true>;
+
+ // ThreadLocalBlocks release callables.
+ using ThreadLocalLhsRelease = ThreadLocalBlocksRelease<LhsBlock>;
+ using ThreadLocalRhsRelease = ThreadLocalBlocksRelease<RhsBlock>;
+
+ // Thread local containers for Lhs/Rhs block packs. In practice only one of
+ // them will be used, depending on the shard_by_col value.
+ Eigen::ThreadLocal<ThreadLocalBlocks<LhsBlock>, ThreadLocalLhsInit,
+ ThreadLocalLhsRelease>
+ lhs_thread_local_blocks_;
+ Eigen::ThreadLocal<ThreadLocalBlocks<RhsBlock>, ThreadLocalRhsInit,
+ ThreadLocalRhsRelease>
+ rhs_thread_local_blocks_;
+
+ // After a particular shard for Kth slice missed thread local execution
+ // opportunity (K-1 slice didn't complete kernels execution), we can no
+ // longer schedule K+1 and following slices in thread local mode, because
+ // there is no more guarantee that previous kernels were executed
+ // sequentially in the same thread (size is nn_ or nm_).
+ std::atomic<bool>* can_use_thread_local_packed_;
+
+ std::atomic<uint8_t>** state_kernel_[P];
+ // state_switch_ is frequently modified by worker threads, while other
+ // fields are read-only after constructor. Let's move it to a separate cache
+ // line to reduce cache-coherency traffic.
+ char pad_[128];
+ std::atomic<Index> state_packing_ready_[P];
+ std::atomic<Index> state_switch_[P];
+
+ LhsBlock& packed_lhs(Index m, Index k, Index m1, bool use_thread_local) {
+ if (use_thread_local) {
+ eigen_assert(!shard_by_col_);
+ ThreadLocalBlocks<LhsBlock>& blocks = lhs_thread_local_blocks_.local();
+
+ Index grain_index = m1 - m * gm_;
+ return blocks.block(internal::convert_index<int>(grain_index)); // FIXME better make ThreadLocalBlocks use Eigen::Index?
+ } else {
+ return packed_lhs_[k % (P - 1)][m1];
+ }
+ }
+
+ RhsBlock& packed_rhs(Index n, Index k, Index n1, bool use_thread_local) {
+ if (use_thread_local) {
+ eigen_assert(shard_by_col_);
+ ThreadLocalBlocks<RhsBlock>& blocks = rhs_thread_local_blocks_.local();
+
+ Index grain_index = n1 - n * gn_;
+ return blocks.block(internal::convert_index<int>(grain_index)); // FIXME better make ThreadLocalBlocks use Eigen::Index?
+ } else {
+ return packed_rhs_[k % (P - 1)][n1];
+ }
+ }
+
+ // In following two methods (pack_lhs and pack_rhs), if we know for sure
+ // that we'll be able to immediately call a kernel with packed data, and do
+ // not submit it to the thread pool, we can use thread local memory for
+ // packed data.
+ //
+ // We can only reliably check it if we are running all kernels in sync mode
+ // (parallelize only by sharding dim). If kernel for m==0 (n==0) is ready to
+ // run, it's guaranteed that all kernels with larger values of m (n) are
+ // also ready, because we execute them in the same order for all K slices.
+
+ void pack_lhs(Index m, Index k) {
+ bool use_thread_local = false;
+
+ if (parallelize_by_sharding_dim_only_ && !shard_by_col_ &&
+ can_use_thread_local_packed_[m].load(std::memory_order_relaxed)) {
+ if (state_kernel_[k % P][m][0].load(std::memory_order_relaxed) == 1) {
+ use_thread_local = true;
+ } else {
+ // If we can't guarantee that all kernels in `k` slice will be
+ // executed sequentially in current thread, it's no longer safe to use
+ // thread local memory in following slices along the k dimensions.
+ eigen_assert(k > 0);
+ can_use_thread_local_packed_[m].store(false,
+ std::memory_order_relaxed);
+ }
+ }
+
+ const Index mend = m * gm_ + gm(m);
+ for (Index m1 = m * gm_; m1 < mend; m1++)
+ kernel_.packLhs(&packed_lhs(m, k, m1, use_thread_local),
+ lhs_.getSubMapper(m1 * bm_, k * bk_), bk(k), bm(m1));
+
+ if (!parallel_pack_ && shard_by_col_) {
+ eigen_assert(!use_thread_local);
+ signal_packing(k);
+ } else {
+ signal_switch(k + 1);
+ for (Index n = nn_ - 1; n >= 0; n--) {
+ bool sync = parallelize_by_sharding_dim_only_ || n == 0;
+ signal_kernel(m, n, k, sync, use_thread_local);
+ }
+ }
+ }
+
+ void pack_rhs(Index n, Index k) {
+ bool use_thread_local = false;
+
+ if (parallelize_by_sharding_dim_only_ && shard_by_col_ &&
+ can_use_thread_local_packed_[n].load(std::memory_order_relaxed)) {
+ if (state_kernel_[k % P][0][n].load(std::memory_order_relaxed) == 1) {
+ use_thread_local = true;
+ } else {
+ // If we can't guarantee that all kernels in `k` slice will be
+ // executed sequentially in current thread, it's no longer safe to use
+ // thread local memory in following slices along the k dimensions.
+ eigen_assert(k > 0);
+ can_use_thread_local_packed_[n].store(false,
+ std::memory_order_relaxed);
+ }
+ }
+
+ const Index nend = n * gn_ + gn(n);
+ for (Index n1 = n * gn_; n1 < nend; n1++) {
+ if (!TensorContractionKernel::HasBeta && k == 0) {
+ // Zero the output memory in parallel, only if contraction kernel does
+ // not support `beta`. Otherwise we will pass beta 0.0 to the first
+ // call to the `TensorContractionKernel::invoke()`.
+ //
+ // On 10000x2x10000 mm zeroing can easily take half of time. Zero (bn
+ // x m) row. Safe to do here because all kernels that will write to
+ // this memory depend on completion of this task. Note: don't call
+ // device_.fill() here. device_.fill() blocks on thread pool
+ // worker thread, which can lead to underutilization and deadlocks.
+ std::fill_n(buffer_ + n1 * bn_ * m_, bn(n1) * m_, Scalar(0));
+ }
+ kernel_.packRhs(&packed_rhs(n, k, n1, use_thread_local),
+ rhs_.getSubMapper(k * bk_, n1 * bn_), bk(k), bn(n1));
+ }
+
+ if (parallel_pack_ || shard_by_col_) {
+ signal_switch(k + 1);
+ for (Index m = nm_ - 1; m >= 0; m--) {
+ bool sync = parallelize_by_sharding_dim_only_ || m == 0;
+ signal_kernel(m, n, k, sync, use_thread_local);
+ }
+ } else {
+ eigen_assert(!use_thread_local);
+ signal_packing(k);
+ }
+ }
+
+ void kernel(Index m, Index n, Index k, bool use_thread_local) {
+ // Note: order of iteration matters here. Iteration over m is innermost
+ // because we want to reuse the same packed rhs in consecutive tasks
+ // (rhs fits into L2$ while lhs only into L3$).
+ const Index nend = n * gn_ + gn(n);
+ const Index mend = m * gm_ + gm(m);
+
+ // NOTE: output = alpha * LHS * RHS + beta * output.
+ const Scalar alpha = Scalar(1);
+ const Scalar beta =
+ (TensorContractionKernel::HasBeta && k == 0) ? Scalar(0) : Scalar(1);
+
+ if (shard_by_col_) {
+ for (Index n1 = n * gn_; n1 < nend; n1++) {
+ for (Index m1 = m * gm_; m1 < mend; m1++) {
+ const auto output_mapper = output_.getSubMapper(m1 * bm_, n1 * bn_);
+ kernel_.invoke(
+ output_mapper,
+ packed_lhs(m, k, m1, !shard_by_col_ && use_thread_local),
+ packed_rhs(n, k, n1, shard_by_col_ && use_thread_local), bm(m1),
+ bk(k), bn(n1), alpha, beta);
+
+ // We are done with the last task for the [m1, n1] block.
+ if (k + 1 == nk_) {
+ output_kernel_(output_mapper, tensor_contraction_params_,
+ m1 * bm_, n1 * bn_, bm(m1), bn(n1));
+ }
+ }
+ }
+ } else {
+ for (Index m1 = m * gm_; m1 < mend; m1++)
+ for (Index n1 = n * gn_; n1 < nend; n1++) {
+ const auto output_mapper = output_.getSubMapper(m1 * bm_, n1 * bn_);
+ kernel_.invoke(
+ output_mapper,
+ packed_lhs(m, k, m1, !shard_by_col_ && use_thread_local),
+ packed_rhs(n, k, n1, shard_by_col_ && use_thread_local), bm(m1),
+ bk(k), bn(n1), alpha, beta);
+
+ // We are done with the last task for the [m1, n1] block.
+ if (k + 1 == nk_) {
+ output_kernel_(output_mapper, tensor_contraction_params_,
+ m1 * bm_, n1 * bn_, bm(m1), bn(n1));
+ }
+ }
+ }
+ signal_kernel(m, n, k + 1, /*sync=*/false, /*use_thread_local=*/false);
+ signal_switch(k + 2);
+ }
+
+ void signal_packing(Index k) {
+ eigen_assert(!parallel_pack_);
+ Index s = state_packing_ready_[k % P].fetch_sub(1);
+ eigen_assert(s > 0);
+ if (s != 1) return;
+ state_packing_ready_[k % P] = shard_by_col_ ? nm_ : nn_;
+ enqueue_packing(k, shard_by_col_);
+ }
+
+ void signal_kernel(Index m, Index n, Index k, bool sync,
+ bool use_thread_local) {
+ std::atomic<uint8_t>* state = &state_kernel_[k % P][m][n];
+ Index s = state->load();
+ eigen_assert(s > 0);
+ if (s != 1 && state->fetch_sub(1) != 1) {
+ eigen_assert(!use_thread_local);
+ return;
+ }
+ state->store(parallel_pack_ ? 3 : 2, std::memory_order_relaxed);
+ if (sync) {
+ kernel(m, n, k, use_thread_local);
+ } else {
+ eigen_assert(!use_thread_local);
+ device_.enqueueNoNotification(
+ [=]() { kernel(m, n, k, use_thread_local); });
+ }
+ }
+
+ void signal_switch(Index k, Index v = 1) {
+ Index s = state_switch_[k % P].fetch_sub(v);
+ eigen_assert(s >= v);
+ if (s != v) return;
+
+ // Ready to switch to the next k slice.
+ // Reset counter for the next iteration.
+ state_switch_[k % P] =
+ (parallel_pack_ ? nm_ + nn_ : (shard_by_col_ ? nn_ : nm_)) +
+ nm_ * nn_;
+ if (k < nk_) {
+ // Issue lhs/rhs packing. Their completion will in turn kick off
+ // kernels.
+ if (parallel_pack_) {
+ enqueue_packing(k, !shard_by_col_);
+ enqueue_packing(k, shard_by_col_);
+ } else if (shard_by_col_) {
+ enqueue_packing(k, false);
+ } else {
+ enqueue_packing(k, true);
+ }
+
+ // Termination handling.
+ // Because kernel completion signals k + 2 switch, we need to finish nk
+ // + 2 slices without issuing any tasks on nk + 1 slice. So here we
+ // pretend that all nk + 1 packing tasks just finish instantly; so that
+ // nk + 2 switch only waits for completion of nk kernels.
+ } else if (k == nk_) {
+ signal_switch(k + 1,
+ parallel_pack_ ? nm_ + nn_ : (shard_by_col_ ? nn_ : nm_));
+ } else {
+ done_.Notify();
+ }
+ }
+
+ // Enqueue all rhs/lhs packing for k-th slice.
+ void enqueue_packing(Index k, bool rhs) {
+ enqueue_packing_helper(0, rhs ? nn_ : nm_, k, rhs);
+ }
+
+ void enqueue_packing_helper(Index start, Index end, Index k, bool rhs) {
+ if (end - start == 1) {
+ if (rhs)
+ pack_rhs(start, k);
+ else
+ pack_lhs(start, k);
+ } else {
+ while (end - start > 1) {
+ Index mid = (start + end) / 2;
+ device_.enqueueNoNotification(
+ [=]() { enqueue_packing_helper(mid, end, k, rhs); });
+ end = mid;
+ }
+
+ // Decide if we want to run first packing task (start == 0) in
+ // async mode if we parallelize only by sharding dim:
+ // (1) pack_lhs and pack_rhs call signal_switch before completing
+ // all calls to signal_kernel, which in sync mode might lead
+ // to the execution of the first kernel of the k+1 slice, before
+ // completing a call to the last kernel of the k slice.
+ // (2) all pack tasks for sharded dim must be executed in a thread
+ // pool to get pre-allocated thead local buffers.
+ bool pack_async =
+ (start == 0) &&
+ (parallelize_by_sharding_dim_only_&& shard_by_col_ == rhs) &&
+ (k > 0 || std::this_thread::get_id() == created_by_thread_id_);
+
+ if (pack_async) {
+ device_.enqueueNoNotification(
+ [=]() { enqueue_packing_helper(start, end, k, rhs); });
+ } else {
+ enqueue_packing_helper(start, end, k, rhs);
+ }
+ }
+ }
+
+ // Block sizes with accounting for potentially incomplete last block.
+ Index bm(Index m) const { return m + 1 < nm0_ ? bm_ : m_ + bm_ - bm_ * nm0_; }
+ Index bn(Index n) const { return n + 1 < nn0_ ? bn_ : n_ + bn_ - bn_ * nn0_; }
+ Index bk(Index k) const { return k + 1 < nk_ ? bk_ : k_ + bk_ - bk_ * nk_; }
+ // Task grain sizes accounting for potentially incomplete last task.
+ Index gm(Index m) const { return m + 1 < nm_ ? gm_ : nm0_ + gm_ - gm_ * nm_; }
+ Index gn(Index n) const { return n + 1 < nn_ ? gn_ : nn0_ + gn_ - gn_ * nn_; }
+
+ EvalParallelContext(const EvalParallelContext&) = delete;
+ void operator=(const EvalParallelContext&) = delete;
+ };
+
+ template <bool lhs_inner_dim_contiguous, bool rhs_inner_dim_contiguous,
+ bool rhs_inner_dim_reordered, int Alignment>
+ using SyncEvalParallelContext =
+ EvalParallelContext<NoCallback, lhs_inner_dim_contiguous,
+ rhs_inner_dim_contiguous, rhs_inner_dim_reordered,
+ Alignment>;
+
+ // ------------------------------------------------------------------------ //
+
+ // EvalShardedByInnerDimContext orchestrates sync/async contraction
+ // evaluation, when we shard by inner dimension. When it is executed in
+ // asynchronous mode, it owns all the shared state that might be accessible by
+ // block processing tasks.
+
+ template <typename DoneCallback>
+ struct EvalShardedByInnerDimContext {
+ EvalShardedByInnerDimContext(const Self* self, int num_threads,
+ Scalar* result_buffer,
+ Index m_size, Index n_size, Index k_size,
+ DoneCallback done_callback)
+ : evaluator(self),
+ m_lhs_inner_dim_contiguous(evaluator->m_lhs_inner_dim_contiguous),
+ m_rhs_inner_dim_contiguous(evaluator->m_rhs_inner_dim_contiguous),
+ m_rhs_inner_dim_reordered(evaluator->m_rhs_inner_dim_reordered),
+ result(result_buffer),
+ m(m_size),
+ n(n_size),
+ k(k_size),
+ done(std::move(done_callback)),
+ buffer_size_bytes(m * n * sizeof(Scalar)),
+ block_size(blockSize(k, num_threads)),
+ num_blocks(divup<Index>(k, block_size)),
+ num_pending_blocks(internal::convert_index<int>(num_blocks)),
+ l0_ranges(divup<Index>(num_blocks, l0_size)),
+ l0_state(l0_ranges),
+ block_buffers(num_blocks) {
+ // Keep count of pending gemm tasks for each l0 range.
+ for (int i = 0; i < l0_ranges; ++i) {
+ const Index num_pending_tasks = actualRangeSize(l0_ranges, l0_size, i);
+ l0_state.emplace_back(internal::convert_index<int>(num_pending_tasks));
+ }
+
+ // Allocate temporary buffers for each block.
+ for (Index block_idx = 0; block_idx < num_blocks; ++block_idx) {
+ Scalar* buf = block_idx == 0
+ ? result
+ : static_cast<Scalar*>(evaluator->m_device.allocate(
+ buffer_size_bytes));
+ block_buffers.emplace_back(buf);
+ }
+ }
+
+ ~EvalShardedByInnerDimContext() {
+ for (Index i = 1; i < num_blocks; ++i) {
+ evaluator->m_device.deallocate(block_buffers[i]);
+ }
+ }
+
+ template <int Alignment>
+ void run() {
+ Barrier barrier(internal::convert_index<int>(num_blocks));
+ eval<Alignment>(barrier, 0, num_blocks);
+ barrier.Wait();
+
+ // Aggregate partial sums from l0 ranges.
+ aggregateL0Blocks<Alignment>();
+
+ // Apply output kernel.
+ applyOutputKernel();
+ }
+
+ template <int Alignment>
+ void runAsync() {
+ evalAsync<Alignment>(0, num_blocks);
+ }
+
+ private:
+ // The underlying GEMM kernel assumes that k is a multiple of
+ // the packet size and subtle breakage occurs if this is violated.
+ static const Index packet_size = internal::packet_traits<RhsScalar>::size;
+
+ const Self* evaluator; // TensorContraction evaluator
+
+ // These fields required fromTENSOR_CONTRACTION_DISPATCH macro.
+ bool m_lhs_inner_dim_contiguous;
+ bool m_rhs_inner_dim_contiguous;
+ bool m_rhs_inner_dim_reordered;
+
+ Scalar* result;
+
+ Index m;
+ Index n;
+ Index k;
+
+ DoneCallback done;
+
+ // ----------------------------------------------------------------------//
+ // Algorithm parameters.
+
+ // We will compute partial results into the buffers of this size.
+ Index buffer_size_bytes;
+
+ Index block_size;
+ Index num_blocks;
+
+ // Keep track of pending tasks when evaluate in async mode.
+ std::atomic<int> num_pending_blocks;
+
+ // We compute partial gemm results in parallel, and to get the final result
+ // we need to add them all together. For the large number of threads (>= 48)
+ // this adds a very expensive sequential step at the end.
+ //
+ // We split the [0, num_blocks) into small ranges, and when a task for the
+ // block finishes its partial gemm computation, it checks if it was the last
+ // gemm in the range, and if so, it will add all blocks of the range.
+ //
+ // After all tasks done, we need to add only these pre-aggregated blocks.
+
+ // For now we use just a single level of ranges to compute pre-aggregated
+ // partial sums, but in general we can use more layers to compute tree
+ // aggregation in parallel and reduce the size of the sequential step.
+ //
+ // TODO(ezhulenev): Add multilevel tree aggregation? Probably will make
+ // sense only if number of threads >= ~128?
+ static const Index l0_size = 4;
+ Index l0_ranges;
+
+ // Keep count of pending gemm tasks for each l0 range.
+ MaxSizeVector<std::atomic<int>> l0_state; // [0, l0_ranges)
+
+ // Buffers allocated for each temporary block computation.
+ MaxSizeVector<Scalar*> block_buffers; // [0, num_blocks)
+
+ template <int Alignment>
+ void processBlock(Index block_idx, Index begin, Index end) {
+ Scalar* buf = block_buffers[block_idx];
+
+ TENSOR_CONTRACTION_DISPATCH(
+ evaluator->template evalGemmPartialWithoutOutputKernel, Alignment,
+ (buf, begin, end,
+ /*num_threads=*/internal::convert_index<int>(num_blocks)));
+
+ // Check if it was the last task in l0 range.
+ const Index l0_index = block_idx / l0_size;
+ const int v = l0_state[l0_index].fetch_sub(1);
+ eigen_assert(v >= 1);
+
+ // If we processed the last block of the range, we can aggregate all
+ // partial results into the first block of the range.
+ if (v == 1) {
+ const Index rng_size = actualRangeSize(l0_ranges, l0_size, l0_index);
+ const Index dst_block_idx = l0_index * l0_size;
+
+ if (rng_size == l0_size) {
+ addAllToBuffer<Alignment>(
+ m * n,
+ /*src_buf0=*/block_buffers[dst_block_idx + 1],
+ /*src_buf1=*/block_buffers[dst_block_idx + 2],
+ /*src_buf2=*/block_buffers[dst_block_idx + 3],
+ /*dst_buf= */ block_buffers[dst_block_idx]);
+ } else {
+ // Aggregate blocks of potentially incomplete last range.
+ for (int i = 1; i < rng_size; ++i) {
+ addToBuffer<Alignment>(m * n,
+ /*src_buf=*/block_buffers[dst_block_idx + i],
+ /*dst_buf=*/block_buffers[dst_block_idx]);
+ }
+ }
+ }
+ }
+
+ // Aggregate partial sums from l0 ranges.
+ template <int Alignment>
+ void aggregateL0Blocks() const {
+ Index l0_index = 1;
+
+ for (; l0_index + 2 < l0_ranges; l0_index += 3) {
+ addAllToBuffer<Alignment>(
+ m * n,
+ /*src_buf0=*/block_buffers[(l0_index + 0) * l0_size],
+ /*src_buf1=*/block_buffers[(l0_index + 1) * l0_size],
+ /*src_buf2=*/block_buffers[(l0_index + 2) * l0_size],
+ /*dst_buf= */ block_buffers[0]);
+ }
+
+ for (; l0_index < l0_ranges; ++l0_index) {
+ addToBuffer<Alignment>(m * n, block_buffers[l0_index * l0_size],
+ block_buffers[0]);
+ }
+ }
+
+ void applyOutputKernel() const {
+ typedef internal::blas_data_mapper<Scalar, Index, ColMajor> OutputMapper;
+ evaluator->m_output_kernel(
+ OutputMapper(result, m), evaluator->m_tensor_contraction_params,
+ static_cast<Eigen::Index>(0), static_cast<Eigen::Index>(0), m, n);
+ }
+
+ // Compute block size with accounting for potentially incomplete last block.
+ Index actualBlockSize(Index block_idx) const {
+ return block_idx + 1 < num_blocks
+ ? block_size
+ : k + block_size - block_size * num_blocks;
+ };
+
+ // Compute range size with accounting for potentially incomplete last range.
+ Index actualRangeSize(Index num_ranges, Index range_size,
+ Index range_idx) const {
+ eigen_assert(range_idx < num_ranges);
+ return range_idx + 1 < num_ranges
+ ? range_size
+ : num_blocks + range_size - range_size * num_ranges;
+ };
+
+ template <int Alignment>
+ EIGEN_STRONG_INLINE static void addToBuffer(size_t n, const Scalar* src_buf,
+ Scalar* tgt_buf) {
+ const int output_packet_size =
+ internal::unpacket_traits<PacketReturnType>::size;
+ size_t i = 0;
+ const size_t num_packets = n / output_packet_size;
+ for (; i < output_packet_size * num_packets; i += output_packet_size) {
+ const PacketReturnType src_val =
+ internal::pload<PacketReturnType>(src_buf + i);
+ const PacketReturnType tgt_val =
+ internal::ploadt<PacketReturnType, Alignment>(tgt_buf + i);
+ const PacketReturnType sum = internal::padd(src_val, tgt_val);
+ internal::pstoret<Scalar, PacketReturnType, Alignment>(tgt_buf + i,
+ sum);
+ }
+ for (; i < n; ++i) {
+ tgt_buf[i] += src_buf[i];
+ }
+ }
+
+ template <int Alignment>
+ EIGEN_STRONG_INLINE static void addAllToBuffer(size_t n,
+ const Scalar* src_buf0,
+ const Scalar* src_buf1,
+ const Scalar* src_buf2,
+ Scalar* dst_buf) {
+ using ::Eigen::internal::padd;
+ using ::Eigen::internal::pload;
+ using ::Eigen::internal::ploadt;
+ using ::Eigen::internal::pstoret;
+
+ const int output_packet_size =
+ internal::unpacket_traits<PacketReturnType>::size;
+
+ size_t i = 0;
+ const size_t num_packets = n / output_packet_size;
+ for (; i < output_packet_size * num_packets; i += output_packet_size) {
+ const auto src_val0 = pload<PacketReturnType>(src_buf0 + i);
+ const auto src_val1 = pload<PacketReturnType>(src_buf1 + i);
+ const auto src_val2 = pload<PacketReturnType>(src_buf2 + i);
+
+ const auto dst_val = ploadt<PacketReturnType, Alignment>(dst_buf + i);
+ const auto sum =
+ padd(padd(dst_val, src_val0), padd(src_val1, src_val2));
+
+ pstoret<Scalar, PacketReturnType, Alignment>(dst_buf + i, sum);
+ }
+ for (; i < n; ++i) {
+ dst_buf[i] += src_buf0[i] + src_buf1[i] + src_buf2[i];
+ }
+ }
+
+ template <int Alignment>
+ void eval(Barrier& barrier, Index start_block_idx, Index end_block_idx) {
+ while (end_block_idx - start_block_idx > 1) {
+ Index mid_block_idx = (start_block_idx + end_block_idx) / 2;
+ evaluator->m_device.enqueueNoNotification(
+ [this, &barrier, mid_block_idx, end_block_idx]() {
+ eval<Alignment>(barrier, mid_block_idx, end_block_idx);
+ });
+ end_block_idx = mid_block_idx;
+ }
+
+ Index block_idx = start_block_idx;
+ Index block_start = block_idx * block_size;
+ Index block_end = block_start + actualBlockSize(block_idx);
+
+ processBlock<Alignment>(block_idx, block_start, block_end);
+ barrier.Notify();
+ }
+
+ template <int Alignment>
+ void evalAsync(Index start_block_idx, Index end_block_idx) {
+ while (end_block_idx - start_block_idx > 1) {
+ Index mid_block_idx = (start_block_idx + end_block_idx) / 2;
+ evaluator->m_device.enqueueNoNotification(
+ [this, mid_block_idx, end_block_idx]() {
+ evalAsync<Alignment>(mid_block_idx, end_block_idx);
+ });
+ end_block_idx = mid_block_idx;
+ }
+
+ Index block_idx = start_block_idx;
+
+ Index block_start = block_idx * block_size;
+ Index block_end = block_start + actualBlockSize(block_idx);
+
+ processBlock<Alignment>(block_idx, block_start, block_end);
+
+ int v = num_pending_blocks.fetch_sub(1);
+ eigen_assert(v >= 1);
+
+ if (v == 1) {
+ // Aggregate partial sums from l0 ranges.
+ aggregateL0Blocks<Alignment>();
+
+ // Apply output kernel.
+ applyOutputKernel();
+
+ // NOTE: If we call `done` callback before deleting this (context),
+ // it might deallocate Self* pointer captured by context, and we'll
+ // fail in destructor trying to deallocate temporary buffers.
+
+ // Move done call back from context before it will be destructed.
+ DoneCallback done_copy = std::move(done);
+
+ // We are confident that we are the last one who touches context.
+ delete this;
+
+ // Now safely call the done callback.
+ done_copy();
+ }
+ }
+
+ // Cost model doesn't capture well the cost associated with constructing
+ // tensor contraction mappers and computing loop bounds in gemm_pack_lhs
+ // and gemm_pack_rhs, so we specify minimum desired block size.
+ static Index blockSize(Index k, int num_threads) {
+ const auto round_up = [=](Index index) -> Index {
+ const Index kmultiple = packet_size <= 8 ? 8 : packet_size;
+ return divup<Index>(index, kmultiple) * kmultiple;
+ };
+
+ const Index target_block_size = round_up(divup<Index>(k, num_threads));
+ const Index desired_min_block_size = 12 * packet_size;
+
+ return numext::mini<Index>(
+ k, numext::maxi<Index>(desired_min_block_size, target_block_size));
+ }
+
+ EvalShardedByInnerDimContext(const EvalShardedByInnerDimContext&) = delete;
+ void operator=(const EvalShardedByInnerDimContext&) = delete;
+ };
+
+ // ------------------------------------------------------------------------ //
+
+ // Below are the function used by evalProductImpl heuristics, trying to select
+ // optimcal parameters for parallelization algorithm.
+
+ // Decide whether we want to shard m x n contraction by columns or by rows.
+ static bool shardByCol(Index m, Index n, Index num_threads) {
+ // Note: we are comparing both n and m against Traits::nr, it is not
+ // a mistake. We are trying to figure out how both n and m will fit into
+ // the main sharding dimension.
+
+ // Sharding by column is the default
+ // ... unless there is enough data for vectorization over rows
+ if (m / num_threads >= Traits::nr &&
+ // and not enough data for vectorization over columns
+ (n / num_threads < Traits::nr ||
+ // ... or barely enough data for vectorization over columns,
+ // but it is not evenly dividable across threads
+ (n / num_threads < 4 * Traits::nr &&
+ (n % (num_threads * Traits::nr)) != 0 &&
+ // ... and it is evenly dividable across threads for rows
+ ((m % (num_threads * Traits::nr)) == 0 ||
+ // .. or it is not evenly dividable for both dimensions but
+ // there is much more data over rows so that corner effects are
+ // mitigated.
+ (m / n >= 6)))))
+ return false;
+ // Wait, or if matrices are just substantially prolonged over the other
+ // dimension.
+ if (n / num_threads < 16 * Traits::nr && m > n * 32) return false;
+ return true;
+ }
+
+ Index coarsenM(Index m, Index n, Index bm, Index bn, Index bk, Index gn,
+ int num_threads, bool shard_by_col) const {
+ Index gm = 1;
+ Index gm1 = 1;
+ Index nm0 = divup(m, bm);
+ Index nm1 = nm0;
+ for (;;) {
+ // Find the next candidate for m grain size. It needs to result in
+ // different number of blocks. E.g. if we have 10 kernels, we want to try
+ // 5 and 10, but not 6, 7, 8 and 9.
+ while (gm1 <= nm0 && nm1 == divup(nm0, gm1)) gm1++;
+ if (gm1 > nm0) break;
+ // Check the candidate.
+ int res = checkGrain(m, n, bm, bn, bk, gm1, gn, gm, gn, num_threads,
+ shard_by_col);
+ if (res < 0) break;
+ nm1 = divup(nm0, gm1);
+ if (res == 0) continue;
+ // Commit new grain size.
+ gm = gm1;
+ }
+ return gm;
+ }
+
+ Index coarsenN(Index m, Index n, Index bm, Index bn, Index bk, Index gm,
+ int num_threads, bool shard_by_col) const {
+ Index gn = 1;
+ Index gn1 = 1;
+ Index nn0 = divup(n, bn);
+ Index nn1 = nn0;
+ for (;;) {
+ while (gn1 <= nn0 && nn1 == divup(nn0, gn1)) gn1++;
+ if (gn1 > nn0) break;
+ int res = checkGrain(m, n, bm, bn, bk, gm, gn1, gm, gn, num_threads,
+ shard_by_col);
+ if (res < 0) break;
+ nn1 = divup(nn0, gn1);
+ if (res == 0) continue;
+ gn = gn1;
+ }
+ return gn;
+ }
+
+ // checkGrain checks whether grain (gm, gn) is suitable and is better than
+ // (oldgm, oldgn).
+ int checkGrain(Index m, Index n, Index bm, Index bn, Index bk, Index gm,
+ Index gn, Index oldgm, Index oldgn, int num_threads,
+ bool shard_by_col) const {
+ const TensorOpCost cost =
+ contractionCost(bm * gm, bn * gn, bm, bn, bk, shard_by_col, true);
+ double taskSize = TensorCostModel<ThreadPoolDevice>::taskSize(
+ static_cast<double>(bm) * gm * bn * gn, cost);
+ // If the task is too small, then we agree on it regardless of anything
+ // else. Otherwise synchronization overheads will dominate.
+ if (taskSize < 1) return 1;
+ // If it is too large, then we reject it and all larger tasks.
+ if (taskSize > 2) return -1;
+ // Now we are in presumably good task size range.
+ // The main deciding factor here is parallelism. Consider that we have 12
+ // kernels and 4 threads. Grains of 2, 3 and 4 all yield good task sizes.
+ // But 2/4 yield 6/3 tasks, which gives us parallelism of 0.75 (at most 3/4
+ // of cores will be busy). While grain size 3 gives us 4 tasks, which gives
+ // us parallelism of 1 (we can load all cores).
+ Index nm0 = divup(m, bm);
+ Index nn0 = divup(n, bn);
+ Index new_tasks = divup(nm0, gm) * divup(nn0, gn);
+ double new_parallelism = static_cast<double>(new_tasks) /
+ (divup<int>(new_tasks, num_threads) * num_threads);
+ Index old_tasks = divup(nm0, oldgm) * divup(nn0, oldgn);
+ double old_parallelism = static_cast<double>(old_tasks) /
+ (divup<int>(old_tasks, num_threads) * num_threads);
+ if (new_parallelism > old_parallelism || new_parallelism == 1) return 1;
+ return 0;
+ }
+
+ TensorOpCost contractionCost(Index m, Index n, Index bm, Index bn, Index bk,
+ bool shard_by_col, bool prepacked) const {
+ const int packed_size = std::min<int>(PacketType<LhsScalar, Device>::size,
+ PacketType<RhsScalar, Device>::size);
+ const int output_packet_size = internal::unpacket_traits<PacketReturnType>::size;
+ const double kd = static_cast<double>(bk);
+ double compute_bandwidth = computeBandwidth(false, bm, bn, bk);
+ // Computations.
+ TensorOpCost cost = TensorOpCost(0, 0, kd * compute_bandwidth, true, packed_size);
+ // Output stores.
+ cost += TensorOpCost(0, sizeof(CoeffReturnType), 0, true, output_packet_size);
+ if (prepacked) {
+ // Packing and kernels are executed in different tasks. When we calculate
+ // task grain size we look only at kernel cost assuming that kernel
+ // is more expensive than packing.
+ return cost;
+ }
+ // Lhs/rhs loads + computations.
+ TensorOpCost lhsCost = this->m_leftImpl.costPerCoeff(true) * (kd / n);
+ TensorOpCost rhsCost = this->m_rightImpl.costPerCoeff(true) * (kd / m);
+ // Lhs packing memory cost does not contribute considerably to overall
+ // execution time because lhs is prefetched early and accessed sequentially.
+ if (shard_by_col)
+ lhsCost.dropMemoryCost();
+ else
+ rhsCost.dropMemoryCost();
+ return cost + lhsCost + rhsCost;
+ }
+
+ // Decide whether we want to shard m x k x n contraction over the inner
+ // (contraction) dimension (k).
+ static bool shardByInnerDim(Index m, Index n, Index k, int num_threads,
+ int num_threads_by_k) {
+ std::ptrdiff_t bufsize = m * n * sizeof(Scalar);
+ bool shard_by_k = false;
+ if (n == 1 || // If mat*vec or...
+ num_threads_by_k < 2 || // running single threaded or...
+ num_threads_by_k <
+ num_threads || // sharding by k gives less parallelism or...
+ bufsize > l3CacheSize() / num_threads_by_k || // need more buffer space
+ // than L3 cache or...
+ k / num_threads_by_k < 2 * Traits::nr) { // k per thread is tiny.
+ shard_by_k = false;
+ } else if (numext::maxi(m, n) / num_threads <
+ Traits::nr || // both other dimensions are tiny or...
+ // k per thread is not small and...
+ (k / num_threads_by_k > 8 * Traits::nr &&
+ // one of the outer dimensions is tiny or sharding by k offers
+ // more parallelism.
+ (numext::mini(m, n) < 2 * Traits::nr ||
+ num_threads_by_k > num_threads))) {
+ shard_by_k = true;
+ }
+ return shard_by_k;
+ }
+
+ TensorOpCost contractionCostPerInnerDim(Index m, Index n, Index k) const {
+ // Compute cost.
+ const int output_packet_size = internal::unpacket_traits<PacketReturnType>::size;
+ TensorOpCost cost(0, 0, (computeBandwidth(true, m, n, k) * m) * n, true, output_packet_size);
+ // Output stores.
+ cost += TensorOpCost(0, sizeof(CoeffReturnType), 0, true, output_packet_size);
+ TensorOpCost lhsCost = this->m_leftImpl.costPerCoeff(true) * m;
+ TensorOpCost rhsCost = this->m_rightImpl.costPerCoeff(true) * n;
+ // Since the inner gemm kernel is always sharded by column, the lhs
+ // load cost is negligible.
+ lhsCost.dropMemoryCost();
+ return cost + lhsCost + rhsCost;
+ }
+
+ int numThreadsInnerDim(Index m, Index n, Index k) const {
+ const int output_packet_size = internal::unpacket_traits<PacketReturnType>::size;
+ TensorOpCost cost = contractionCostPerInnerDim(m, n, k);
+ double total_parallel_cost =
+ TensorCostModel<ThreadPoolDevice>::totalCost(k, cost);
+ // Cost of reduction step accumulating the m*n per-thread buffers into the
+ // result.
+ double reduction_cost = TensorCostModel<ThreadPoolDevice>::totalCost(
+ m * n, TensorOpCost(2, 1, 1, true, output_packet_size));
+ int num_threads = 1;
+ double min_cost = total_parallel_cost;
+ double kPerThreadOverHead = 3000;
+ double kFixedOverHead = 100000;
+ for (int nt = 2; nt <= this->m_device.numThreads(); nt += 2) {
+ double sequential_cost =
+ kFixedOverHead + nt * (reduction_cost + kPerThreadOverHead);
+ double parallel_cost = total_parallel_cost / nt + sequential_cost;
+ if (parallel_cost < min_cost) {
+ num_threads = nt;
+ min_cost = parallel_cost;
+ }
+ }
+ return num_threads;
+ }
+
+ double computeBandwidth(bool shard_by_col, Index bm, Index bn,
+ Index bk) const {
+ // Peak VFMA bandwidth is 0.5. However if we have not enough data for
+ // vectorization bandwidth drops. The 4.0 and 2.0 bandwidth is determined
+ // experimentally.
+ double computeBandwidth =
+ bk == 1 ? 4.0
+ : (shard_by_col ? bn : bm) < Traits::nr ||
+ (shard_by_col ? bm : bn) < Traits::mr
+ ? 2.0
+ : 0.5;
+#ifndef EIGEN_VECTORIZE_FMA
+ // Bandwidth of all of VFMA/MULPS/ADDPS is 0.5 on latest Intel processors.
+ // However for MULPS/ADDPS we have dependent sequence of 2 such
+ // instructions,
+ // so overall bandwidth is 1.0.
+ if (computeBandwidth == 0.5) computeBandwidth = 1.0;
+#endif
+ return computeBandwidth;
+ }
+
+};
+
+} // end namespace Eigen
+
+#endif // EIGEN_USE_THREADS
+#endif // EIGEN_CXX11_TENSOR_TENSOR_CONTRACTION_THREAD_POOL_H
diff --git a/unsupported/Eigen/CXX11/src/Tensor/TensorConversion.h b/unsupported/Eigen/CXX11/src/Tensor/TensorConversion.h
new file mode 100644
index 0000000..bfb7b12
--- /dev/null
+++ b/unsupported/Eigen/CXX11/src/Tensor/TensorConversion.h
@@ -0,0 +1,458 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2015 Benoit Steiner <benoit.steiner.goog@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_CXX11_TENSOR_TENSOR_CONVERSION_H
+#define EIGEN_CXX11_TENSOR_TENSOR_CONVERSION_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+/** \class TensorConversionOp
+ * \ingroup CXX11_Tensor_Module
+ *
+ * \brief Tensor conversion class. This class makes it possible to vectorize
+ * type casting operations when the number of scalars per packet in the source
+ * and the destination type differ
+ */
+namespace internal {
+template<typename TargetType, typename XprType>
+struct traits<TensorConversionOp<TargetType, XprType> >
+{
+ // Type promotion to handle the case where the types of the lhs and the rhs are different.
+ typedef TargetType Scalar;
+ typedef typename traits<XprType>::StorageKind StorageKind;
+ typedef typename traits<XprType>::Index Index;
+ typedef typename XprType::Nested Nested;
+ typedef std::remove_reference_t<Nested> Nested_;
+ static constexpr int NumDimensions = traits<XprType>::NumDimensions;
+ static constexpr int Layout = traits<XprType>::Layout;
+ enum { Flags = 0 };
+ typedef typename TypeConversion<Scalar, typename traits<XprType>::PointerType>::type PointerType;
+};
+
+template<typename TargetType, typename XprType>
+struct eval<TensorConversionOp<TargetType, XprType>, Eigen::Dense>
+{
+ typedef const TensorConversionOp<TargetType, XprType>& type;
+};
+
+template<typename TargetType, typename XprType>
+struct nested<TensorConversionOp<TargetType, XprType>, 1, typename eval<TensorConversionOp<TargetType, XprType> >::type>
+{
+ typedef TensorConversionOp<TargetType, XprType> type;
+};
+
+} // end namespace internal
+
+
+template <typename TensorEvaluator, typename SrcPacket, typename TgtPacket, int SrcCoeffRatio, int TgtCoeffRatio>
+struct PacketConverter;
+
+template <typename TensorEvaluator, typename SrcPacket, typename TgtPacket>
+struct PacketConverter<TensorEvaluator, SrcPacket, TgtPacket, 1, 1> {
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ PacketConverter(const TensorEvaluator& impl)
+ : m_impl(impl) {}
+
+ template<int LoadMode, typename Index>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TgtPacket packet(Index index) const {
+ return internal::pcast<SrcPacket, TgtPacket>(m_impl.template packet<LoadMode>(index));
+ }
+
+ private:
+ const TensorEvaluator& m_impl;
+};
+
+
+template <typename TensorEvaluator, typename SrcPacket, typename TgtPacket>
+struct PacketConverter<TensorEvaluator, SrcPacket, TgtPacket, 2, 1> {
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ PacketConverter(const TensorEvaluator& impl)
+ : m_impl(impl) {}
+
+ template<int LoadMode, typename Index>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TgtPacket packet(Index index) const {
+ const int SrcPacketSize = internal::unpacket_traits<SrcPacket>::size;
+
+ SrcPacket src1 = m_impl.template packet<LoadMode>(index);
+ SrcPacket src2 = m_impl.template packet<LoadMode>(index + SrcPacketSize);
+ TgtPacket result = internal::pcast<SrcPacket, TgtPacket>(src1, src2);
+ return result;
+ }
+
+ private:
+ const TensorEvaluator& m_impl;
+};
+
+template <typename TensorEvaluator, typename SrcPacket, typename TgtPacket>
+struct PacketConverter<TensorEvaluator, SrcPacket, TgtPacket, 4, 1> {
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ PacketConverter(const TensorEvaluator& impl)
+ : m_impl(impl) {}
+
+ template<int LoadMode, typename Index>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TgtPacket packet(Index index) const {
+ const int SrcPacketSize = internal::unpacket_traits<SrcPacket>::size;
+
+ SrcPacket src1 = m_impl.template packet<LoadMode>(index);
+ SrcPacket src2 = m_impl.template packet<LoadMode>(index + SrcPacketSize);
+ SrcPacket src3 = m_impl.template packet<LoadMode>(index + 2 * SrcPacketSize);
+ SrcPacket src4 = m_impl.template packet<LoadMode>(index + 3 * SrcPacketSize);
+ TgtPacket result = internal::pcast<SrcPacket, TgtPacket>(src1, src2, src3, src4);
+ return result;
+ }
+
+ private:
+ const TensorEvaluator& m_impl;
+};
+
+template <typename TensorEvaluator, typename SrcPacket, typename TgtPacket>
+struct PacketConverter<TensorEvaluator, SrcPacket, TgtPacket, 8, 1> {
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ PacketConverter(const TensorEvaluator& impl)
+ : m_impl(impl) {}
+
+ template<int LoadMode, typename Index>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TgtPacket packet(Index index) const {
+ const int SrcPacketSize = internal::unpacket_traits<SrcPacket>::size;
+
+ SrcPacket src1 = m_impl.template packet<LoadMode>(index);
+ SrcPacket src2 = m_impl.template packet<LoadMode>(index + 1 * SrcPacketSize);
+ SrcPacket src3 = m_impl.template packet<LoadMode>(index + 2 * SrcPacketSize);
+ SrcPacket src4 = m_impl.template packet<LoadMode>(index + 3 * SrcPacketSize);
+ SrcPacket src5 = m_impl.template packet<LoadMode>(index + 4 * SrcPacketSize);
+ SrcPacket src6 = m_impl.template packet<LoadMode>(index + 5 * SrcPacketSize);
+ SrcPacket src7 = m_impl.template packet<LoadMode>(index + 6 * SrcPacketSize);
+ SrcPacket src8 = m_impl.template packet<LoadMode>(index + 7 * SrcPacketSize);
+ TgtPacket result = internal::pcast<SrcPacket, TgtPacket>(src1, src2, src3, src4, src5, src6, src7, src8);
+ return result;
+ }
+
+ private:
+ const TensorEvaluator& m_impl;
+};
+
+template <typename TensorEvaluator, typename SrcPacket, typename TgtPacket, int TgtCoeffRatio>
+struct PacketConverter<TensorEvaluator, SrcPacket, TgtPacket, 1, TgtCoeffRatio> {
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ PacketConverter(const TensorEvaluator& impl)
+ : m_impl(impl), m_maxIndex(impl.dimensions().TotalSize()) {}
+
+ template<int LoadMode, typename Index>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TgtPacket packet(Index index) const {
+ const int SrcPacketSize = internal::unpacket_traits<SrcPacket>::size;
+ // Only call m_impl.packet() when we have direct access to the underlying data. This
+ // ensures that we don't compute the subexpression twice. We may however load some
+ // coefficients twice, but in practice this doesn't negatively impact performance.
+ if (m_impl.data() && (index + SrcPacketSize < m_maxIndex)) {
+ // Force unaligned memory loads since we can't ensure alignment anymore
+ return internal::pcast<SrcPacket, TgtPacket>(m_impl.template packet<Unaligned>(index));
+ } else {
+ const int TgtPacketSize = internal::unpacket_traits<TgtPacket>::size;
+ typedef typename internal::unpacket_traits<SrcPacket>::type SrcType;
+ typedef typename internal::unpacket_traits<TgtPacket>::type TgtType;
+ internal::scalar_cast_op<SrcType, TgtType> converter;
+ EIGEN_ALIGN_MAX typename internal::unpacket_traits<TgtPacket>::type values[TgtPacketSize];
+ EIGEN_UNROLL_LOOP
+ for (int i = 0; i < TgtPacketSize; ++i) {
+ values[i] = converter(m_impl.coeff(index+i));
+ }
+ TgtPacket rslt = internal::pload<TgtPacket>(values);
+ return rslt;
+ }
+ }
+
+ private:
+ const TensorEvaluator& m_impl;
+ const typename TensorEvaluator::Index m_maxIndex;
+};
+
+template<typename TargetType, typename XprType>
+class TensorConversionOp : public TensorBase<TensorConversionOp<TargetType, XprType>, ReadOnlyAccessors>
+{
+ public:
+ typedef typename internal::traits<TensorConversionOp>::Scalar Scalar;
+ typedef typename internal::traits<TensorConversionOp>::StorageKind StorageKind;
+ typedef typename internal::traits<TensorConversionOp>::Index Index;
+ typedef typename internal::nested<TensorConversionOp>::type Nested;
+ typedef Scalar CoeffReturnType;
+ typedef typename NumTraits<Scalar>::Real RealScalar;
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorConversionOp(const XprType& xpr)
+ : m_xpr(xpr) {}
+
+ EIGEN_DEVICE_FUNC
+ const internal::remove_all_t<typename XprType::Nested>&
+ expression() const { return m_xpr; }
+
+ protected:
+ typename XprType::Nested m_xpr;
+};
+
+template <bool SameType, typename Eval, typename EvalPointerType> struct ConversionSubExprEval {
+ static EIGEN_STRONG_INLINE bool run(Eval& impl, EvalPointerType) {
+ impl.evalSubExprsIfNeeded(NULL);
+ return true;
+ }
+};
+
+template <typename Eval, typename EvalPointerType> struct ConversionSubExprEval<true, Eval, EvalPointerType> {
+ static EIGEN_STRONG_INLINE bool run(Eval& impl, EvalPointerType data) {
+ return impl.evalSubExprsIfNeeded(data);
+ }
+};
+
+#ifdef EIGEN_USE_THREADS
+template <bool SameType, typename Eval, typename EvalPointerType,
+ typename EvalSubExprsCallback>
+struct ConversionSubExprEvalAsync {
+ static EIGEN_STRONG_INLINE void run(Eval& impl, EvalPointerType, EvalSubExprsCallback done) {
+ impl.evalSubExprsIfNeededAsync(nullptr, std::move(done));
+ }
+};
+
+template <typename Eval, typename EvalPointerType,
+ typename EvalSubExprsCallback>
+struct ConversionSubExprEvalAsync<true, Eval, EvalPointerType,
+ EvalSubExprsCallback> {
+ static EIGEN_STRONG_INLINE void run(Eval& impl, EvalPointerType data, EvalSubExprsCallback done) {
+ impl.evalSubExprsIfNeededAsync(data, std::move(done));
+ }
+};
+#endif
+
+namespace internal {
+
+template <typename SrcType, typename TargetType, bool IsSameT>
+struct CoeffConv {
+ template <typename ArgType, typename Device>
+ static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TargetType run(const TensorEvaluator<ArgType, Device>& impl, Index index) {
+ internal::scalar_cast_op<SrcType, TargetType> converter;
+ return converter(impl.coeff(index));
+ }
+};
+
+template <typename SrcType, typename TargetType>
+struct CoeffConv<SrcType, TargetType, true> {
+ template <typename ArgType, typename Device>
+ static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TargetType run(const TensorEvaluator<ArgType, Device>& impl, Index index) {
+ return impl.coeff(index);
+ }
+};
+
+template <typename SrcPacket, typename TargetPacket, int LoadMode, bool ActuallyVectorize, bool IsSameT>
+struct PacketConv {
+ typedef typename internal::unpacket_traits<SrcPacket>::type SrcType;
+ typedef typename internal::unpacket_traits<TargetPacket>::type TargetType;
+
+ static constexpr int PacketSize = internal::unpacket_traits<TargetPacket>::size;
+
+ template <typename ArgType, typename Device>
+ static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TargetPacket run(const TensorEvaluator<ArgType, Device>& impl, Index index) {
+ internal::scalar_cast_op<SrcType, TargetType> converter;
+ EIGEN_ALIGN_MAX std::remove_const_t<TargetType> values[PacketSize];
+ EIGEN_UNROLL_LOOP
+ for (int i = 0; i < PacketSize; ++i) {
+ values[i] = converter(impl.coeff(index+i));
+ }
+ TargetPacket rslt = internal::pload<TargetPacket>(values);
+ return rslt;
+ }
+};
+
+template <typename SrcPacket, typename TargetPacket, int LoadMode, bool IsSameT>
+struct PacketConv<SrcPacket, TargetPacket, LoadMode, true, IsSameT> {
+ typedef typename internal::unpacket_traits<SrcPacket>::type SrcType;
+ typedef typename internal::unpacket_traits<TargetPacket>::type TargetType;
+
+ template <typename ArgType, typename Device>
+ static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TargetPacket run(const TensorEvaluator<ArgType, Device>& impl, Index index) {
+ const int SrcCoeffRatio = internal::type_casting_traits<SrcType, TargetType>::SrcCoeffRatio;
+ const int TgtCoeffRatio = internal::type_casting_traits<SrcType, TargetType>::TgtCoeffRatio;
+ PacketConverter<TensorEvaluator<ArgType, Device>, SrcPacket, TargetPacket,
+ SrcCoeffRatio, TgtCoeffRatio> converter(impl);
+ return converter.template packet<LoadMode>(index);
+ }
+};
+
+template <typename SrcPacket, typename TargetPacket, int LoadMode>
+struct PacketConv<SrcPacket, TargetPacket, LoadMode, /*ActuallyVectorize=*/false, /*IsSameT=*/true> {
+ typedef typename internal::unpacket_traits<TargetPacket>::type TargetType;
+ static constexpr int PacketSize = internal::unpacket_traits<TargetPacket>::size;
+
+ template <typename ArgType, typename Device>
+ static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TargetPacket run(const TensorEvaluator<ArgType, Device>& impl, Index index) {
+ EIGEN_ALIGN_MAX std::remove_const_t<TargetType> values[PacketSize];
+ for (int i = 0; i < PacketSize; ++i) values[i] = impl.coeff(index+i);
+ return internal::pload<TargetPacket>(values);
+ }
+};
+
+template <typename SrcPacket, typename TargetPacket, int LoadMode>
+struct PacketConv<SrcPacket, TargetPacket, LoadMode, /*ActuallyVectorize=*/true, /*IsSameT=*/true> {
+ template <typename ArgType, typename Device>
+ static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TargetPacket run(const TensorEvaluator<ArgType, Device>& impl, Index index) {
+ return impl.template packet<LoadMode>(index);
+ }
+};
+
+} // namespace internal
+
+// Eval as rvalue
+template<typename TargetType, typename ArgType, typename Device>
+struct TensorEvaluator<const TensorConversionOp<TargetType, ArgType>, Device>
+{
+ typedef TensorConversionOp<TargetType, ArgType> XprType;
+ typedef typename XprType::Index Index;
+ typedef typename TensorEvaluator<ArgType, Device>::Dimensions Dimensions;
+ typedef TargetType Scalar;
+ typedef TargetType CoeffReturnType;
+ typedef internal::remove_all_t<typename internal::traits<ArgType>::Scalar> SrcType;
+ typedef typename PacketType<CoeffReturnType, Device>::type PacketReturnType;
+ typedef typename PacketType<SrcType, Device>::type PacketSourceType;
+ static constexpr int PacketSize = PacketType<CoeffReturnType, Device>::size;
+ static constexpr bool IsSameType = internal::is_same<TargetType, SrcType>::value;
+ typedef StorageMemory<CoeffReturnType, Device> Storage;
+ typedef typename Storage::Type EvaluatorPointerType;
+
+ enum {
+ IsAligned = false,
+ PacketAccess =
+ #ifndef EIGEN_USE_SYCL
+ true,
+ #else
+ TensorEvaluator<ArgType, Device>::PacketAccess &
+ internal::type_casting_traits<SrcType, TargetType>::VectorizedCast,
+ #endif
+ BlockAccess = TensorEvaluator<ArgType, Device>::BlockAccess,
+ PreferBlockAccess = TensorEvaluator<ArgType, Device>::PreferBlockAccess,
+ RawAccess = false
+ };
+
+ static constexpr int Layout = TensorEvaluator<ArgType, Device>::Layout;
+ static constexpr int NumDims = internal::array_size<Dimensions>::value;
+
+ //===- Tensor block evaluation strategy (see TensorBlock.h) -------------===//
+ typedef internal::TensorBlockDescriptor<NumDims, Index> TensorBlockDesc;
+ typedef internal::TensorBlockScratchAllocator<Device> TensorBlockScratch;
+
+ typedef typename TensorEvaluator<const ArgType, Device>::TensorBlock
+ ArgTensorBlock;
+
+ struct TensorConversionOpBlockFactory {
+ template <typename ArgXprType>
+ struct XprType {
+ typedef TensorConversionOp<TargetType, const ArgXprType> type;
+ };
+
+ template <typename ArgXprType>
+ typename XprType<ArgXprType>::type expr(const ArgXprType& expr) const {
+ return typename XprType<ArgXprType>::type(expr);
+ }
+ };
+
+ typedef internal::TensorUnaryExprBlock<TensorConversionOpBlockFactory,
+ ArgTensorBlock>
+ TensorBlock;
+ //===--------------------------------------------------------------------===//
+
+ EIGEN_STRONG_INLINE TensorEvaluator(const XprType& op, const Device& device)
+ : m_impl(op.expression(), device)
+ {
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Dimensions& dimensions() const { return m_impl.dimensions(); }
+
+ EIGEN_STRONG_INLINE bool evalSubExprsIfNeeded(EvaluatorPointerType data)
+ {
+ return ConversionSubExprEval<IsSameType, TensorEvaluator<ArgType, Device>, EvaluatorPointerType>::run(m_impl, data);
+ }
+
+#ifdef EIGEN_USE_THREADS
+ template <typename EvalSubExprsCallback>
+ EIGEN_STRONG_INLINE void evalSubExprsIfNeededAsync(
+ EvaluatorPointerType data, EvalSubExprsCallback done) {
+ ConversionSubExprEvalAsync<IsSameType, TensorEvaluator<ArgType, Device>,
+ EvaluatorPointerType,
+ EvalSubExprsCallback>::run(m_impl, data, std::move(done));
+ }
+#endif
+
+ EIGEN_STRONG_INLINE void cleanup()
+ {
+ m_impl.cleanup();
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE CoeffReturnType coeff(Index index) const
+ {
+ return internal::CoeffConv<SrcType, TargetType, IsSameType>::run(m_impl,index);
+ }
+
+ template<int LoadMode>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE PacketReturnType
+ packet(Index index) const {
+ // If we are not going to do the cast, we just need to check that base
+ // TensorEvaluator has packet access. Otherwise we also need to make sure,
+ // that we have an implementation of vectorized cast.
+ const bool Vectorizable =
+ IsSameType
+ ? TensorEvaluator<ArgType, Device>::PacketAccess
+ : int(TensorEvaluator<ArgType, Device>::PacketAccess) &
+ int(internal::type_casting_traits<SrcType, TargetType>::VectorizedCast);
+
+ return internal::PacketConv<PacketSourceType, PacketReturnType, LoadMode,
+ Vectorizable, IsSameType>::run(m_impl, index);
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorOpCost
+ costPerCoeff(bool vectorized) const {
+ const double cast_cost = TensorOpCost::CastCost<SrcType, TargetType>();
+ if (vectorized) {
+ const double SrcCoeffRatio =
+ internal::type_casting_traits<SrcType, TargetType>::SrcCoeffRatio;
+ const double TgtCoeffRatio =
+ internal::type_casting_traits<SrcType, TargetType>::TgtCoeffRatio;
+ return m_impl.costPerCoeff(vectorized) * (SrcCoeffRatio / PacketSize) +
+ TensorOpCost(0, 0, TgtCoeffRatio * (cast_cost / PacketSize));
+ } else {
+ return m_impl.costPerCoeff(vectorized) + TensorOpCost(0, 0, cast_cost);
+ }
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ internal::TensorBlockResourceRequirements getResourceRequirements() const {
+ return m_impl.getResourceRequirements();
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorBlock
+ block(TensorBlockDesc& desc, TensorBlockScratch& scratch,
+ bool /*root_of_expr_ast*/ = false) const {
+ return TensorBlock(m_impl.block(desc, scratch),
+ TensorConversionOpBlockFactory());
+ }
+
+ EIGEN_DEVICE_FUNC EvaluatorPointerType data() const { return NULL; }
+
+ /// required by sycl in order to extract the sycl accessor
+ const TensorEvaluator<ArgType, Device>& impl() const { return m_impl; }
+#ifdef EIGEN_USE_SYCL
+ // binding placeholder accessors to a command group handler for SYCL
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void bind(cl::sycl::handler &cgh) const {
+ m_impl.bind(cgh);
+ }
+#endif
+
+ protected:
+ TensorEvaluator<ArgType, Device> m_impl;
+};
+
+} // end namespace Eigen
+
+#endif // EIGEN_CXX11_TENSOR_TENSOR_CONVERSION_H
diff --git a/unsupported/Eigen/CXX11/src/Tensor/TensorConvolution.h b/unsupported/Eigen/CXX11/src/Tensor/TensorConvolution.h
new file mode 100644
index 0000000..70d2129
--- /dev/null
+++ b/unsupported/Eigen/CXX11/src/Tensor/TensorConvolution.h
@@ -0,0 +1,1134 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_CXX11_TENSOR_TENSOR_CONVOLUTION_H
+#define EIGEN_CXX11_TENSOR_TENSOR_CONVOLUTION_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+/** \class TensorConvolution
+ * \ingroup CXX11_Tensor_Module
+ *
+ * \brief Tensor convolution class.
+ *
+ *
+ */
+namespace internal {
+
+template <typename Index, typename InputDims, int NumKernelDims, int Layout>
+class IndexMapper {
+ public:
+ IndexMapper(const InputDims& input_dims, const array<Index, NumKernelDims>& kernel_dims,
+ const array<Index, NumKernelDims>& indices) {
+
+ array<Index, NumDims> dimensions = input_dims;
+ for (int i = 0; i < NumKernelDims; ++i) {
+ const Index index = indices[i];
+ const Index input_dim = input_dims[index];
+ const Index kernel_dim = kernel_dims[i];
+ const Index result_dim = input_dim - kernel_dim + 1;
+ dimensions[index] = result_dim;
+ }
+
+ array<Index, NumDims> inputStrides;
+ array<Index, NumDims> outputStrides;
+ if (static_cast<int>(Layout) == static_cast<int>(ColMajor)) {
+ inputStrides[0] = 1;
+ outputStrides[0] = 1;
+ for (int i = 1; i < NumDims; ++i) {
+ inputStrides[i] = inputStrides[i-1] * input_dims[i-1];
+ outputStrides[i] = outputStrides[i-1] * dimensions[i-1];
+ }
+ } else {
+ inputStrides[NumDims - 1] = 1;
+ outputStrides[NumDims - 1] = 1;
+ for (int i = static_cast<int>(NumDims) - 2; i >= 0; --i) {
+ inputStrides[i] = inputStrides[i + 1] * input_dims[i + 1];
+ outputStrides[i] = outputStrides[i + 1] * dimensions[i + 1];
+ }
+ }
+
+ array<Index, NumDims> gpuInputDimensions;
+ array<Index, NumDims> gpuOutputDimensions;
+ array<Index, NumDims> tmp = dimensions;
+ array<Index, NumDims> ordering;
+ const size_t offset = static_cast<int>(Layout) == static_cast<int>(ColMajor)
+ ? 0
+ : NumDims - NumKernelDims;
+ for (int i = 0; i < NumKernelDims; ++i) {
+ const Index index = i + offset;
+ ordering[index] = indices[i];
+ tmp[indices[i]] = -1;
+ gpuInputDimensions[index] = input_dims[indices[i]];
+ gpuOutputDimensions[index] = dimensions[indices[i]];
+ }
+
+ int written = static_cast<int>(Layout) == static_cast<int>(ColMajor)
+ ? NumKernelDims
+ : 0;
+ for (int i = 0; i < NumDims; ++i) {
+ if (tmp[i] >= 0) {
+ ordering[written] = i;
+ gpuInputDimensions[written] = input_dims[i];
+ gpuOutputDimensions[written] = dimensions[i];
+ ++written;
+ }
+ }
+
+ for (int i = 0; i < NumDims; ++i) {
+ m_inputStrides[i] = inputStrides[ordering[i]];
+ m_outputStrides[i] = outputStrides[ordering[i]];
+ }
+
+ if (static_cast<int>(Layout) == static_cast<int>(ColMajor)) {
+ for (int i = 0; i < NumDims; ++i) {
+ if (i > NumKernelDims) {
+ m_gpuInputStrides[i] =
+ m_gpuInputStrides[i - 1] * gpuInputDimensions[i - 1];
+ m_gpuOutputStrides[i] =
+ m_gpuOutputStrides[i - 1] * gpuOutputDimensions[i - 1];
+ } else {
+ m_gpuInputStrides[i] = 1;
+ m_gpuOutputStrides[i] = 1;
+ }
+ }
+ } else {
+ for (int i = NumDims - 1; i >= 0; --i) {
+ if (static_cast<size_t>(i + 1) < offset) {
+ m_gpuInputStrides[i] =
+ m_gpuInputStrides[i + 1] * gpuInputDimensions[i + 1];
+ m_gpuOutputStrides[i] =
+ m_gpuOutputStrides[i + 1] * gpuOutputDimensions[i + 1];
+ } else {
+ m_gpuInputStrides[i] = 1;
+ m_gpuOutputStrides[i] = 1;
+ }
+ }
+ }
+ }
+
+ EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Index mapGpuInputPlaneToTensorInputOffset(Index p) const {
+ Index inputIndex = 0;
+ if (static_cast<int>(Layout) == static_cast<int>(ColMajor)) {
+ for (int d = NumDims - 1; d > NumKernelDims; --d) {
+ const Index idx = p / m_gpuInputStrides[d];
+ inputIndex += idx * m_inputStrides[d];
+ p -= idx * m_gpuInputStrides[d];
+ }
+ inputIndex += p * m_inputStrides[NumKernelDims];
+ } else {
+ std::ptrdiff_t limit = 0;
+ if (NumKernelDims < NumDims) {
+ limit = NumDims - NumKernelDims - 1;
+ }
+ for (int d = 0; d < limit; ++d) {
+ const Index idx = p / m_gpuInputStrides[d];
+ inputIndex += idx * m_inputStrides[d];
+ p -= idx * m_gpuInputStrides[d];
+ }
+ inputIndex += p * m_inputStrides[limit];
+ }
+ return inputIndex;
+ }
+
+ EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Index mapGpuOutputPlaneToTensorOutputOffset(Index p) const {
+ Index outputIndex = 0;
+ if (static_cast<int>(Layout) == static_cast<int>(ColMajor)) {
+ for (int d = NumDims - 1; d > NumKernelDims; --d) {
+ const Index idx = p / m_gpuOutputStrides[d];
+ outputIndex += idx * m_outputStrides[d];
+ p -= idx * m_gpuOutputStrides[d];
+ }
+ outputIndex += p * m_outputStrides[NumKernelDims];
+ } else {
+ std::ptrdiff_t limit = 0;
+ if (NumKernelDims < NumDims) {
+ limit = NumDims - NumKernelDims - 1;
+ }
+ for (int d = 0; d < limit; ++d) {
+ const Index idx = p / m_gpuOutputStrides[d];
+ outputIndex += idx * m_outputStrides[d];
+ p -= idx * m_gpuOutputStrides[d];
+ }
+ outputIndex += p * m_outputStrides[limit];
+ }
+ return outputIndex;
+ }
+
+ EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Index mapGpuInputKernelToTensorInputOffset(Index i) const {
+ const size_t offset = static_cast<int>(Layout) == static_cast<int>(ColMajor)
+ ? 0
+ : NumDims - NumKernelDims;
+ return i * m_inputStrides[offset];
+ }
+
+ EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Index mapGpuOutputKernelToTensorOutputOffset(Index i) const {
+ const size_t offset = static_cast<int>(Layout) == static_cast<int>(ColMajor)
+ ? 0
+ : NumDims - NumKernelDims;
+ return i * m_outputStrides[offset];
+ }
+
+ EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Index mapGpuInputKernelToTensorInputOffset(Index i, Index j) const {
+ const size_t offset = static_cast<int>(Layout) == static_cast<int>(ColMajor)
+ ? 0
+ : NumDims - NumKernelDims;
+ return i * m_inputStrides[offset] + j * m_inputStrides[offset + 1];
+ }
+
+ EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Index mapGpuOutputKernelToTensorOutputOffset(Index i, Index j) const {
+ const size_t offset = static_cast<int>(Layout) == static_cast<int>(ColMajor)
+ ? 0
+ : NumDims - NumKernelDims;
+ return i * m_outputStrides[offset] + j * m_outputStrides[offset + 1];
+ }
+
+ EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Index mapGpuInputKernelToTensorInputOffset(Index i, Index j, Index k) const {
+ const size_t offset = static_cast<int>(Layout) == static_cast<int>(ColMajor)
+ ? 0
+ : NumDims - NumKernelDims;
+ return i * m_inputStrides[offset] + j * m_inputStrides[offset + 1] +
+ k * m_inputStrides[offset + 2];
+ }
+
+ EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Index mapGpuOutputKernelToTensorOutputOffset(Index i, Index j, Index k) const {
+ const size_t offset = static_cast<int>(Layout) == static_cast<int>(ColMajor)
+ ? 0
+ : NumDims - NumKernelDims;
+ return i * m_outputStrides[offset] + j * m_outputStrides[offset + 1] +
+ k * m_outputStrides[offset + 2];
+ }
+
+ private:
+ static constexpr int NumDims = internal::array_size<InputDims>::value;
+ array<Index, NumDims> m_inputStrides;
+ array<Index, NumDims> m_outputStrides;
+ array<Index, NumDims> m_gpuInputStrides;
+ array<Index, NumDims> m_gpuOutputStrides;
+};
+
+
+
+template<typename Dimensions, typename InputXprType, typename KernelXprType>
+struct traits<TensorConvolutionOp<Dimensions, InputXprType, KernelXprType> >
+{
+ // Type promotion to handle the case where the types of the lhs and the rhs are different.
+ typedef typename promote_storage_type<typename InputXprType::Scalar,
+ typename KernelXprType::Scalar>::ret Scalar;
+ typedef typename promote_storage_type<typename traits<InputXprType>::StorageKind,
+ typename traits<KernelXprType>::StorageKind>::ret StorageKind;
+ typedef typename promote_index_type<typename traits<InputXprType>::Index,
+ typename traits<KernelXprType>::Index>::type Index;
+ typedef typename InputXprType::Nested LhsNested;
+ typedef typename KernelXprType::Nested RhsNested;
+ typedef std::remove_reference_t<LhsNested> LhsNested_;
+ typedef std::remove_reference_t<RhsNested> RhsNested_;
+ static constexpr int NumDimensions = traits<InputXprType>::NumDimensions;
+ static constexpr int Layout = traits<InputXprType>::Layout;
+ typedef std::conditional_t<Pointer_type_promotion<typename InputXprType::Scalar, Scalar>::val,
+ typename traits<InputXprType>::PointerType, typename traits<KernelXprType>::PointerType> PointerType;
+
+ enum {
+ Flags = 0
+ };
+};
+
+template<typename Dimensions, typename InputXprType, typename KernelXprType>
+struct eval<TensorConvolutionOp<Dimensions, InputXprType, KernelXprType>, Eigen::Dense>
+{
+ typedef const TensorConvolutionOp<Dimensions, InputXprType, KernelXprType>& type;
+};
+
+template<typename Dimensions, typename InputXprType, typename KernelXprType>
+struct nested<TensorConvolutionOp<Dimensions, InputXprType, KernelXprType>, 1, typename eval<TensorConvolutionOp<Dimensions, InputXprType, KernelXprType> >::type>
+{
+ typedef TensorConvolutionOp<Dimensions, InputXprType, KernelXprType> type;
+};
+
+} // end namespace internal
+
+
+
+template<typename Indices, typename InputXprType, typename KernelXprType>
+class TensorConvolutionOp : public TensorBase<TensorConvolutionOp<Indices, InputXprType, KernelXprType>, ReadOnlyAccessors>
+{
+ public:
+ typedef typename Eigen::internal::traits<TensorConvolutionOp>::Scalar Scalar;
+ typedef typename Eigen::NumTraits<Scalar>::Real RealScalar;
+ typedef typename internal::promote_storage_type<typename InputXprType::CoeffReturnType,
+ typename KernelXprType::CoeffReturnType>::ret CoeffReturnType;
+ typedef typename Eigen::internal::nested<TensorConvolutionOp>::type Nested;
+ typedef typename Eigen::internal::traits<TensorConvolutionOp>::StorageKind StorageKind;
+ typedef typename Eigen::internal::traits<TensorConvolutionOp>::Index Index;
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorConvolutionOp(const InputXprType& input, const KernelXprType& kernel, const Indices& dims)
+ : m_input_xpr(input), m_kernel_xpr(kernel), m_indices(dims) {}
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ const Indices& indices() const { return m_indices; }
+
+ /** \returns the nested expressions */
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ const internal::remove_all_t<typename InputXprType::Nested>&
+ inputExpression() const { return m_input_xpr; }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ const internal::remove_all_t<typename KernelXprType::Nested>&
+ kernelExpression() const { return m_kernel_xpr; }
+
+ protected:
+ typename InputXprType::Nested m_input_xpr;
+ typename KernelXprType::Nested m_kernel_xpr;
+ const Indices m_indices;
+};
+
+
+template<typename Indices, typename InputArgType, typename KernelArgType, typename Device>
+struct TensorEvaluator<const TensorConvolutionOp<Indices, InputArgType, KernelArgType>, Device>
+{
+ typedef TensorConvolutionOp<Indices, InputArgType, KernelArgType> XprType;
+
+ static constexpr int NumDims = internal::array_size<typename TensorEvaluator<InputArgType, Device>::Dimensions>::value;
+ static constexpr int NumKernelDims = internal::array_size<Indices>::value;
+ typedef typename XprType::Index Index;
+ typedef DSizes<Index, NumDims> Dimensions;
+
+ typedef typename XprType::Scalar Scalar;
+ typedef typename XprType::CoeffReturnType CoeffReturnType;
+ typedef typename PacketType<CoeffReturnType, Device>::type PacketReturnType;
+ static constexpr int PacketSize = PacketType<CoeffReturnType, Device>::size;
+ typedef StorageMemory<Scalar, Device> Storage;
+ typedef typename Storage::Type EvaluatorPointerType;
+
+ static constexpr int Layout = TensorEvaluator<InputArgType, Device>::Layout;
+ enum {
+ IsAligned = int(TensorEvaluator<InputArgType, Device>::IsAligned) & int(TensorEvaluator<KernelArgType, Device>::IsAligned),
+ PacketAccess = int(TensorEvaluator<InputArgType, Device>::PacketAccess) & int(TensorEvaluator<KernelArgType, Device>::PacketAccess),
+ BlockAccess = false,
+ PreferBlockAccess = false,
+ CoordAccess = false, // to be implemented
+ RawAccess = false
+ };
+
+ //===- Tensor block evaluation strategy (see TensorBlock.h) -------------===//
+ typedef internal::TensorBlockNotImplemented TensorBlock;
+ //===--------------------------------------------------------------------===//
+
+ EIGEN_STRONG_INLINE TensorEvaluator(const XprType& op, const Device& device)
+ : m_inputImpl(op.inputExpression(), device), m_kernelImpl(op.kernelExpression(), device), m_kernelArg(op.kernelExpression()), m_kernel(NULL), m_local_kernel(false), m_device(device)
+ {
+ EIGEN_STATIC_ASSERT((static_cast<int>(TensorEvaluator<InputArgType, Device>::Layout) == static_cast<int>(TensorEvaluator<KernelArgType, Device>::Layout)), YOU_MADE_A_PROGRAMMING_MISTAKE);
+
+ const typename TensorEvaluator<InputArgType, Device>::Dimensions& input_dims = m_inputImpl.dimensions();
+ const typename TensorEvaluator<KernelArgType, Device>::Dimensions& kernel_dims = m_kernelImpl.dimensions();
+
+ if (static_cast<int>(Layout) == static_cast<int>(ColMajor)) {
+ m_inputStride[0] = 1;
+ for (int i = 1; i < NumDims; ++i) {
+ m_inputStride[i] = m_inputStride[i - 1] * input_dims[i - 1];
+ }
+ } else {
+ m_inputStride[NumDims - 1] = 1;
+ for (int i = NumDims - 2; i >= 0; --i) {
+ m_inputStride[i] = m_inputStride[i + 1] * input_dims[i + 1];
+ }
+ }
+
+ m_dimensions = m_inputImpl.dimensions();
+ if (static_cast<int>(Layout) == static_cast<int>(ColMajor)) {
+ for (int i = 0; i < NumKernelDims; ++i) {
+ const Index index = op.indices()[i];
+ const Index input_dim = input_dims[index];
+ const Index kernel_dim = kernel_dims[i];
+ const Index result_dim = input_dim - kernel_dim + 1;
+ m_dimensions[index] = result_dim;
+ if (i > 0) {
+ m_kernelStride[i] = m_kernelStride[i - 1] * kernel_dims[i - 1];
+ } else {
+ m_kernelStride[0] = 1;
+ }
+ m_indexStride[i] = m_inputStride[index];
+ }
+
+ m_outputStride[0] = 1;
+ for (int i = 1; i < NumDims; ++i) {
+ m_outputStride[i] = m_outputStride[i - 1] * m_dimensions[i - 1];
+ }
+ } else {
+ for (int i = NumKernelDims - 1; i >= 0; --i) {
+ const Index index = op.indices()[i];
+ const Index input_dim = input_dims[index];
+ const Index kernel_dim = kernel_dims[i];
+ const Index result_dim = input_dim - kernel_dim + 1;
+ m_dimensions[index] = result_dim;
+ if (i < NumKernelDims - 1) {
+ m_kernelStride[i] = m_kernelStride[i + 1] * kernel_dims[i + 1];
+ } else {
+ m_kernelStride[NumKernelDims - 1] = 1;
+ }
+ m_indexStride[i] = m_inputStride[index];
+ }
+
+ m_outputStride[NumDims - 1] = 1;
+ for (int i = NumDims - 2; i >= 0; --i) {
+ m_outputStride[i] = m_outputStride[i + 1] * m_dimensions[i + 1];
+ }
+ }
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Dimensions& dimensions() const { return m_dimensions; }
+
+ EIGEN_STRONG_INLINE bool evalSubExprsIfNeeded(Scalar*) {
+ m_inputImpl.evalSubExprsIfNeeded(NULL);
+ preloadKernel();
+ return true;
+ }
+ EIGEN_STRONG_INLINE void cleanup() {
+ m_inputImpl.cleanup();
+ if (m_local_kernel) {
+ m_device.deallocate((void*)m_kernel);
+ m_local_kernel = false;
+ }
+ m_kernel = NULL;
+ }
+
+ void evalTo(typename XprType::Scalar* buffer) {
+ evalSubExprsIfNeeded(NULL);
+ for (int i = 0; i < dimensions().TotalSize(); ++i) {
+ buffer[i] += coeff(i);
+ }
+ cleanup();
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE CoeffReturnType coeff(Index index) const
+ {
+ CoeffReturnType result = CoeffReturnType(0);
+ convolve(firstInput(index), 0, NumKernelDims-1, result);
+ return result;
+ }
+
+ template<int LoadMode>
+ EIGEN_DEVICE_FUNC PacketReturnType packet(const Index index) const
+ {
+ Index indices[2] = {index, index+PacketSize-1};
+ Index startInputs[2] = {0, 0};
+ if (static_cast<int>(Layout) == static_cast<int>(ColMajor)) {
+ for (int i = NumDims - 1; i > 0; --i) {
+ const Index idx0 = indices[0] / m_outputStride[i];
+ const Index idx1 = indices[1] / m_outputStride[i];
+ startInputs[0] += idx0 * m_inputStride[i];
+ startInputs[1] += idx1 * m_inputStride[i];
+ indices[0] -= idx0 * m_outputStride[i];
+ indices[1] -= idx1 * m_outputStride[i];
+ }
+ } else {
+ for (int i = 0; i < NumDims - 1; ++i) {
+ const Index idx0 = indices[0] / m_outputStride[i];
+ const Index idx1 = indices[1] / m_outputStride[i];
+ startInputs[0] += idx0 * m_inputStride[i];
+ startInputs[1] += idx1 * m_inputStride[i];
+ indices[0] -= idx0 * m_outputStride[i];
+ indices[1] -= idx1 * m_outputStride[i];
+ }
+ }
+ startInputs[0] += indices[0];
+ startInputs[1] += indices[1];
+
+ if (startInputs[1]-startInputs[0] == PacketSize-1) {
+ PacketReturnType result = internal::pset1<PacketReturnType>(0);
+ convolvePacket(startInputs[0], 0, NumKernelDims-1, result);
+ return result;
+ } else {
+ EIGEN_ALIGN_MAX Scalar data[PacketSize];
+ data[0] = Scalar(0);
+ convolve(startInputs[0], 0, NumKernelDims-1, data[0]);
+ for (int i = 1; i < PacketSize-1; ++i) {
+ data[i] = Scalar(0);
+ convolve(firstInput(index+i), 0, NumKernelDims-1, data[i]);
+ }
+ data[PacketSize-1] = Scalar(0);
+ convolve(startInputs[1], 0, NumKernelDims-1, data[PacketSize-1]);
+ return internal::pload<PacketReturnType>(data);
+ }
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorOpCost
+ costPerCoeff(bool vectorized) const {
+ const double kernel_size = m_kernelImpl.dimensions().TotalSize();
+ // We ignore the use of fused multiply-add.
+ const double convolve_compute_cost =
+ TensorOpCost::AddCost<Scalar>() + TensorOpCost::MulCost<Scalar>();
+ const double firstIndex_compute_cost =
+ NumDims *
+ (2 * TensorOpCost::AddCost<Index>() + 2 * TensorOpCost::MulCost<Index>() +
+ TensorOpCost::DivCost<Index>());
+ return TensorOpCost(0, 0, firstIndex_compute_cost, vectorized, PacketSize) +
+ kernel_size * (m_inputImpl.costPerCoeff(vectorized) +
+ m_kernelImpl.costPerCoeff(vectorized) +
+ TensorOpCost(0, 0, convolve_compute_cost, vectorized,
+ PacketSize));
+ }
+
+ EIGEN_DEVICE_FUNC EvaluatorPointerType data() const { return NULL; }
+
+ private:
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Index firstInput(Index index) const {
+ Index startInput = 0;
+ if (static_cast<int>(Layout) == static_cast<int>(ColMajor)) {
+ for (int i = NumDims - 1; i > 0; --i) {
+ const Index idx = index / m_outputStride[i];
+ startInput += idx * m_inputStride[i];
+ index -= idx * m_outputStride[i];
+ }
+ } else {
+ for (int i = 0; i < NumDims - 1; ++i) {
+ const Index idx = index / m_outputStride[i];
+ startInput += idx * m_inputStride[i];
+ index -= idx * m_outputStride[i];
+ }
+ }
+ startInput += index;
+ return startInput;
+ }
+
+ EIGEN_DEVICE_FUNC void convolve(Index firstIndex, Index firstKernel, int DimIndex, CoeffReturnType& accum) const {
+ for (int j = 0; j < m_kernelImpl.dimensions()[DimIndex]; ++j) {
+ const Index input = firstIndex + j * m_indexStride[DimIndex];
+ const Index kernel = firstKernel + j * m_kernelStride[DimIndex];
+ if (DimIndex > 0) {
+ convolve(input, kernel, DimIndex-1, accum);
+ } else {
+ accum += m_inputImpl.coeff(input) * m_kernel[kernel];
+ }
+ }
+ }
+
+ template <typename Packet>
+ EIGEN_DEVICE_FUNC void convolvePacket(Index firstIndex, Index firstKernel, int DimIndex, Packet& accum) const {
+ for (int j = 0; j < m_kernelImpl.dimensions()[DimIndex]; ++j) {
+ const Index input = firstIndex + j * m_indexStride[DimIndex];
+ const Index kernel = firstKernel + j * m_kernelStride[DimIndex];
+ if (DimIndex > 0) {
+ convolvePacket(input, kernel, DimIndex-1, accum);
+ } else {
+ accum = internal::pmadd<Packet>(m_inputImpl.template packet<Unaligned>(input), internal::pset1<Packet>(m_kernel[kernel]), accum);
+ }
+ }
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void preloadKernel() {
+ // Don't make a local copy of the kernel unless we have to (i.e. it's an
+ // expression that needs to be evaluated)
+ const Scalar* in_place = m_kernelImpl.data();
+ if (in_place) {
+ m_kernel = in_place;
+ m_local_kernel = false;
+ } else {
+ size_t kernel_sz = m_kernelImpl.dimensions().TotalSize() * sizeof(Scalar);
+ Scalar* local = (Scalar*)m_device.allocate_temp(kernel_sz);
+ typedef TensorEvalToOp<const KernelArgType> EvalTo;
+ EvalTo evalToTmp(local, m_kernelArg);
+ const bool Vectorize = internal::IsVectorizable<Device, KernelArgType>::value;
+ internal::TensorExecutor<const EvalTo, Device, Vectorize>::run(evalToTmp, m_device);
+
+ m_kernel = local;
+ m_local_kernel = true;
+ }
+ }
+
+ array<Index, NumDims> m_inputStride;
+ array<Index, NumDims> m_outputStride;
+
+ array<Index, NumKernelDims> m_indexStride;
+ array<Index, NumKernelDims> m_kernelStride;
+ TensorEvaluator<InputArgType, Device> m_inputImpl;
+ TensorEvaluator<KernelArgType, Device> m_kernelImpl;
+ Dimensions m_dimensions;
+
+ KernelArgType m_kernelArg;
+ const Scalar* m_kernel;
+ bool m_local_kernel;
+ const Device EIGEN_DEVICE_REF m_device;
+};
+
+
+
+
+// Use an optimized implementation of the evaluation code for GPUs whenever possible.
+#if defined(EIGEN_USE_GPU) && defined(EIGEN_GPUCC)
+
+template <int StaticKernelSize>
+struct GetKernelSize {
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE int operator() (const int /*kernelSize*/) const {
+ return StaticKernelSize;
+ }
+};
+template <>
+struct GetKernelSize<Dynamic> {
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE int operator() (const int kernelSize) const {
+ return kernelSize;
+ }
+};
+
+template <typename InputEvaluator, typename Index, typename InputDims,
+ int StaticKernelSize>
+__global__ EIGEN_HIP_LAUNCH_BOUNDS_1024 void EigenConvolutionKernel1D(
+ InputEvaluator eval,
+ const internal::IndexMapper<Index, InputDims, 1, InputEvaluator::Layout>
+ indexMapper,
+ const float* __restrict kernel, const int numPlanes, const int numX,
+ const int maxX, const int kernelSize, float* buffer) {
+#if defined(EIGEN_HIPCC)
+ HIP_DYNAMIC_SHARED(float, s)
+#else
+ extern __shared__ float s[];
+#endif
+
+ const int first_x = blockIdx.x * maxX;
+ const int last_x = (first_x + maxX < numX ? first_x + maxX : numX) - 1;
+ const int num_x_input = last_x - first_x + GetKernelSize<StaticKernelSize>()(kernelSize);
+ const int num_x_output = last_x - first_x + 1;
+
+ const int first_plane = blockIdx.y * blockDim.y;
+ const int plane_stride = blockDim.y * gridDim.y;
+
+ for (int p = first_plane + threadIdx.y; p < numPlanes; p += plane_stride) {
+ // Load inputs to shared memory
+ const int plane_input_offset = indexMapper.mapGpuInputPlaneToTensorInputOffset(p);
+ const int plane_kernel_offset = threadIdx.y * num_x_input;
+ #pragma unroll
+ for (int i = threadIdx.x; i < num_x_input; i += blockDim.x) {
+ const int tensor_index = plane_input_offset + indexMapper.mapGpuInputKernelToTensorInputOffset(i+first_x);
+ s[i + plane_kernel_offset] = eval.coeff(tensor_index);
+ }
+
+ __syncthreads();
+
+ // Compute the convolution
+ const int plane_output_offset = indexMapper.mapGpuOutputPlaneToTensorOutputOffset(p);
+
+ #pragma unroll
+ for (int i = threadIdx.x; i < num_x_output; i += blockDim.x) {
+ const int kernel_offset = plane_kernel_offset + i;
+ float result = 0.0f;
+ #pragma unroll
+ for (int k = 0; k < GetKernelSize<StaticKernelSize>()(kernelSize); ++k) {
+ result += s[k + kernel_offset] * kernel[k];
+ }
+ const int tensor_index = plane_output_offset + indexMapper.mapGpuOutputKernelToTensorOutputOffset(i+first_x);
+ buffer[tensor_index] = result;
+ }
+ __syncthreads();
+ }
+};
+
+template <typename InputEvaluator, typename Index, typename InputDims,
+ int StaticKernelSizeX, int StaticKernelSizeY>
+__global__ EIGEN_HIP_LAUNCH_BOUNDS_1024 void EigenConvolutionKernel2D(
+ InputEvaluator eval,
+ const internal::IndexMapper<Index, InputDims, 2, InputEvaluator::Layout>
+ indexMapper,
+ const float* __restrict kernel, const int numPlanes, const int numX,
+ const int maxX, const int numY, const int maxY, const int kernelSizeX,
+ const int kernelSizeY, float* buffer) {
+#if defined(EIGEN_HIPCC)
+ HIP_DYNAMIC_SHARED(float, s)
+#else
+ extern __shared__ float s[];
+#endif
+
+ const int first_x = blockIdx.x * maxX;
+ const int last_x = (first_x + maxX < numX ? first_x + maxX : numX) - 1;
+ const int num_x_input = last_x - first_x + GetKernelSize<StaticKernelSizeX>()(kernelSizeX);
+ const int num_x_output = last_x - first_x + 1;
+
+ const int first_y = blockIdx.y * maxY;
+ const int last_y = (first_y + maxY < numY ? first_y + maxY : numY) - 1;
+ const int num_y_input = last_y - first_y + GetKernelSize<StaticKernelSizeY>()(kernelSizeY);
+ const int num_y_output = last_y - first_y + 1;
+
+ const int first_plane = blockIdx.z * blockDim.z;
+ const int plane_stride = blockDim.z * gridDim.z;
+
+ for (int p = first_plane + threadIdx.z; p < numPlanes; p += plane_stride) {
+
+ const int plane_input_offset = indexMapper.mapGpuInputPlaneToTensorInputOffset(p);
+ const int plane_kernel_offset = threadIdx.z * num_y_input;
+
+ // Load inputs to shared memory
+ #pragma unroll
+ for (int j = threadIdx.y; j < num_y_input; j += blockDim.y) {
+ const int input_offset = num_x_input * (j + plane_kernel_offset);
+ #pragma unroll
+ for (int i = threadIdx.x; i < num_x_input; i += blockDim.x) {
+ const int tensor_index = plane_input_offset + indexMapper.mapGpuInputKernelToTensorInputOffset(i+first_x, j+first_y);
+ s[i + input_offset] = eval.coeff(tensor_index);
+ }
+ }
+
+ __syncthreads();
+
+ // Convolution
+ const int plane_output_offset = indexMapper.mapGpuOutputPlaneToTensorOutputOffset(p);
+
+ #pragma unroll
+ for (int j = threadIdx.y; j < num_y_output; j += blockDim.y) {
+ #pragma unroll
+ for (int i = threadIdx.x; i < num_x_output; i += blockDim.x) {
+ float result = 0.0f;
+ #pragma unroll
+ for (int l = 0; l < GetKernelSize<StaticKernelSizeY>()(kernelSizeY); ++l) {
+ const int kernel_offset = kernelSizeX * l;
+ const int input_offset = i + num_x_input * (j + l + plane_kernel_offset);
+ #pragma unroll
+ for (int k = 0; k < GetKernelSize<StaticKernelSizeX>()(kernelSizeX); ++k) {
+ result += s[k + input_offset] * kernel[k + kernel_offset];
+ }
+ }
+ const int tensor_index = plane_output_offset + indexMapper.mapGpuOutputKernelToTensorOutputOffset(i+first_x, j+first_y);
+ buffer[tensor_index] = result;
+ }
+ }
+
+ __syncthreads();
+ }
+};
+
+template <typename InputEvaluator, typename Index, typename InputDims>
+__global__ EIGEN_HIP_LAUNCH_BOUNDS_1024 void EigenConvolutionKernel3D(
+ InputEvaluator eval,
+ const internal::IndexMapper<Index, InputDims, 3, InputEvaluator::Layout>
+ indexMapper,
+ const float* __restrict kernel, const size_t numPlanes, const size_t numX,
+ const size_t maxX, const size_t numY, const size_t maxY, const size_t numZ,
+ const size_t maxZ, const size_t kernelSizeX, const size_t kernelSizeY,
+ const size_t kernelSizeZ, float* buffer) {
+#if defined(EIGEN_HIPCC)
+ HIP_DYNAMIC_SHARED(float, s)
+#else
+ extern __shared__ float s[];
+#endif
+
+ // Load inputs to shared memory
+ const int first_x = blockIdx.x * maxX;
+ const int last_x = (first_x + maxX < numX ? first_x + maxX : numX) - 1;
+ const int num_x_input = last_x - first_x + kernelSizeX;
+
+ const int first_y = blockIdx.y * maxY;
+ const int last_y = (first_y + maxY < numY ? first_y + maxY : numY) - 1;
+ const int num_y_input = last_y - first_y + kernelSizeY;
+
+ const int first_z = blockIdx.z * maxZ;
+ const int last_z = (first_z + maxZ < numZ ? first_z + maxZ : numZ) - 1;
+ const int num_z_input = last_z - first_z + kernelSizeZ;
+
+ for (int p = 0; p < numPlanes; ++p) {
+
+ const int plane_input_offset = indexMapper.mapGpuInputPlaneToTensorInputOffset(p);
+ const int plane_kernel_offset = 0;
+
+ for (int k = threadIdx.z; k < num_z_input; k += blockDim.z) {
+ for (int j = threadIdx.y; j < num_y_input; j += blockDim.y) {
+ for (int i = threadIdx.x; i < num_x_input; i += blockDim.x) {
+ const int tensor_index = plane_input_offset + indexMapper.mapGpuInputKernelToTensorInputOffset(i+first_x, j+first_y, k+first_z);
+ s[i + num_x_input * (j + num_y_input * (k + plane_kernel_offset))] = eval.coeff(tensor_index);
+ }
+ }
+ }
+
+ __syncthreads();
+
+ // Convolution
+ const int num_z_output = last_z - first_z + 1;
+ const int num_y_output = last_y - first_y + 1;
+ const int num_x_output = last_x - first_x + 1;
+ const int plane_output_offset = indexMapper.mapGpuOutputPlaneToTensorOutputOffset(p);
+
+ for (int k = threadIdx.z; k < num_z_output; k += blockDim.z) {
+ for (int j = threadIdx.y; j < num_y_output; j += blockDim.y) {
+ for (int i = threadIdx.x; i < num_x_output; i += blockDim.x) {
+ float result = 0.0f;
+ for (int n = 0; n < kernelSizeZ; ++n) {
+ for (int m = 0; m < kernelSizeY; ++m) {
+ for (int l = 0; l < kernelSizeX; ++l) {
+ result += s[i + l + num_x_input * (j + m + num_y_input * (k + n + plane_kernel_offset))] * kernel[l + kernelSizeX * (m + kernelSizeY * n)];
+ }
+ }
+ }
+ const int tensor_index = plane_output_offset + indexMapper.mapGpuOutputKernelToTensorOutputOffset(i+first_x, j+first_y, k+first_z);
+ buffer[tensor_index] = result;
+ }
+ }
+ }
+ __syncthreads();
+ }
+};
+
+
+
+template<typename Indices, typename InputArgType, typename KernelArgType>
+struct TensorEvaluator<const TensorConvolutionOp<Indices, InputArgType, KernelArgType>, GpuDevice>
+{
+ typedef TensorConvolutionOp<Indices, InputArgType, KernelArgType> XprType;
+
+ static constexpr int NumDims = internal::array_size<typename TensorEvaluator<InputArgType, GpuDevice>::Dimensions>::value;
+ static constexpr int NumKernelDims = internal::array_size<Indices>::value;
+ typedef typename XprType::Index Index;
+ typedef DSizes<Index, NumDims> Dimensions;
+ typedef typename TensorEvaluator<KernelArgType, GpuDevice>::Dimensions KernelDimensions;
+
+ static constexpr int Layout = TensorEvaluator<InputArgType, GpuDevice>::Layout;
+ enum {
+ IsAligned = TensorEvaluator<InputArgType, GpuDevice>::IsAligned & TensorEvaluator<KernelArgType, GpuDevice>::IsAligned,
+ PacketAccess = false,
+ BlockAccess = false,
+ PreferBlockAccess = false,
+ CoordAccess = false, // to be implemented
+ RawAccess = false
+ };
+
+ //===- Tensor block evaluation strategy (see TensorBlock.h) -------------===//
+ typedef internal::TensorBlockNotImplemented TensorBlock;
+ //===--------------------------------------------------------------------===//
+
+ TensorEvaluator(const XprType& op, const GpuDevice& device)
+ : m_inputImpl(op.inputExpression(), device), m_kernelImpl(op.kernelExpression(), device), m_kernelArg(op.kernelExpression()), m_indices(op.indices()), m_buf(NULL), m_kernel(NULL), m_local_kernel(false), m_device(device)
+ {
+ EIGEN_STATIC_ASSERT((static_cast<int>(TensorEvaluator<InputArgType, GpuDevice>::Layout) == static_cast<int>(TensorEvaluator<KernelArgType, GpuDevice>::Layout)), YOU_MADE_A_PROGRAMMING_MISTAKE);
+
+ const typename TensorEvaluator<InputArgType, GpuDevice>::Dimensions& input_dims = m_inputImpl.dimensions();
+ const typename TensorEvaluator<KernelArgType, GpuDevice>::Dimensions& kernel_dims = m_kernelImpl.dimensions();
+
+ m_dimensions = m_inputImpl.dimensions();
+ for (int i = 0; i < NumKernelDims; ++i) {
+ const Index index = op.indices()[i];
+ const Index input_dim = input_dims[index];
+ const Index kernel_dim = kernel_dims[i];
+ const Index result_dim = input_dim - kernel_dim + 1;
+ m_dimensions[index] = result_dim;
+ }
+ }
+
+ typedef typename XprType::CoeffReturnType CoeffReturnType;
+ typedef typename PacketType<CoeffReturnType, GpuDevice>::type PacketReturnType;
+ typedef typename InputArgType::Scalar Scalar;
+ static constexpr int PacketSize = internal::unpacket_traits<PacketReturnType>::size;
+
+ EIGEN_DEVICE_FUNC const Dimensions& dimensions() const { return m_dimensions; }
+
+ EIGEN_STRONG_INLINE bool evalSubExprsIfNeeded(Scalar* data) {
+ preloadKernel();
+ m_inputImpl.evalSubExprsIfNeeded(NULL);
+ if (data) {
+ executeEval(data);
+ return false;
+ } else {
+ m_buf = (Scalar*)m_device.allocate(dimensions().TotalSize() * sizeof(Scalar));
+ executeEval(m_buf);
+ return true;
+ }
+ }
+
+ EIGEN_STRONG_INLINE void cleanup() {
+ m_inputImpl.cleanup();
+ if (m_buf) {
+ m_device.deallocate(m_buf);
+ m_buf = NULL;
+ }
+ if (m_local_kernel) {
+ m_device.deallocate((void*)m_kernel);
+ m_local_kernel = false;
+ }
+ m_kernel = NULL;
+ }
+
+ EIGEN_STRONG_INLINE void preloadKernel() {
+ // Don't make a local copy of the kernel unless we have to (i.e. it's an
+ // expression that needs to be evaluated)
+ const Scalar* in_place = m_kernelImpl.data();
+ if (in_place) {
+ m_kernel = in_place;
+ m_local_kernel = false;
+ } else {
+ size_t kernel_sz = m_kernelImpl.dimensions().TotalSize() * sizeof(Scalar);
+ Scalar* local = (Scalar*)m_device.allocate(kernel_sz);
+ typedef TensorEvalToOp<const KernelArgType> EvalTo;
+ EvalTo evalToTmp(local, m_kernelArg);
+ const bool PacketAccess = internal::IsVectorizable<GpuDevice, KernelArgType>::value;
+ internal::TensorExecutor<const EvalTo, GpuDevice, PacketAccess>::run(evalToTmp, m_device);
+
+ m_kernel = local;
+ m_local_kernel = true;
+ }
+ }
+
+ static unsigned int ceil(unsigned int num, unsigned int denom) {
+ const unsigned int rounded_toward_zero = num / denom;
+ if (num > rounded_toward_zero * denom) {
+ return rounded_toward_zero + 1;
+ }
+ return rounded_toward_zero;
+ }
+
+ void executeEval(Scalar* data) const {
+ typedef typename TensorEvaluator<InputArgType, GpuDevice>::Dimensions InputDims;
+
+ const int maxSharedMem = m_device.sharedMemPerBlock();
+ const int maxThreadsPerBlock = m_device.maxGpuThreadsPerBlock();
+ const int maxBlocksPerProcessor = m_device.maxGpuThreadsPerMultiProcessor() / maxThreadsPerBlock;
+ const int numMultiProcessors = m_device.getNumGpuMultiProcessors();
+ const int warpSize = 32;
+
+ switch (NumKernelDims) {
+ case 1: {
+ const int kernel_size = m_kernelImpl.dimensions().TotalSize();
+
+ const int numX = dimensions()[m_indices[0]];
+ const int numP = dimensions().TotalSize() / numX;
+ int maxX;
+ dim3 block_size;
+
+ const int single_stride_dim =
+ static_cast<int>(Layout) == static_cast<int>(ColMajor)
+ ? 0
+ : m_inputImpl.dimensions().rank() - 1;
+ if (m_indices[0] == single_stride_dim) {
+ // Maximum the reuse
+ const int inner_dim = ((maxSharedMem / (sizeof(Scalar)) - kernel_size + 1 + 31) / 32) * 32;
+ maxX = numext::mini<int>(inner_dim, numX);
+ const int maxP = numext::mini<int>(maxSharedMem / ((kernel_size - 1 + maxX) * sizeof(Scalar)), numP);
+ block_size.x = numext::mini(maxThreadsPerBlock, maxX);
+ block_size.y = numext::mini<int>(maxThreadsPerBlock / block_size.x, maxP);
+ }
+ else {
+ // Read as much as possible alongside the inner most dimension, that is the plane
+ const int inner_dim = maxSharedMem / ((warpSize + kernel_size) * sizeof(Scalar));
+ const int maxP = numext::mini<int>(inner_dim, numP);
+ maxX = numext::mini<int>(maxSharedMem / (inner_dim * sizeof(Scalar)) - kernel_size + 1, numX);
+
+ block_size.x = numext::mini(warpSize, maxX);
+ block_size.y = numext::mini<int>(maxThreadsPerBlock/block_size.x, maxP);
+ }
+
+ const int shared_mem = block_size.y * (maxX + kernel_size - 1) * sizeof(Scalar);
+ gpu_assert(shared_mem <= maxSharedMem);
+
+ const int num_x_blocks = ceil(numX, maxX);
+ const int blocksPerProcessor = numext::mini(maxBlocksPerProcessor, maxSharedMem / shared_mem);
+ const int num_y_blocks = ceil(numMultiProcessors * blocksPerProcessor, num_x_blocks);
+
+ dim3 num_blocks(num_x_blocks, numext::mini<int>(num_y_blocks, ceil(numP, block_size.y)));
+
+
+ //cout << "launching 1D kernel with block_size.x: " << block_size.x << " block_size.y: " << block_size.y << " num_blocks.x: " << num_blocks.x << " num_blocks.y: " << num_blocks.y << " maxX: " << maxX << " shared_mem: " << shared_mem << " in stream " << m_device.stream() << endl;
+
+ const array<Index, 1> indices(m_indices[0]);
+ const array<Index, 1> kernel_dims(m_kernelImpl.dimensions()[0]);
+ internal::IndexMapper<Index, InputDims, 1, Layout> indexMapper(
+ m_inputImpl.dimensions(), kernel_dims, indices);
+ switch(kernel_size) {
+ case 4: {
+ LAUNCH_GPU_KERNEL((EigenConvolutionKernel1D<TensorEvaluator<InputArgType, GpuDevice>, Index, InputDims, 4>), num_blocks, block_size, shared_mem, m_device, m_inputImpl, indexMapper, m_kernel, numP, numX, maxX, 4, data);
+ break;
+ }
+ case 7: {
+ LAUNCH_GPU_KERNEL((EigenConvolutionKernel1D<TensorEvaluator<InputArgType, GpuDevice>, Index, InputDims, 7>), num_blocks, block_size, shared_mem, m_device, m_inputImpl, indexMapper, m_kernel, numP, numX, maxX, 7, data);
+ break;
+ }
+ default: {
+ LAUNCH_GPU_KERNEL((EigenConvolutionKernel1D<TensorEvaluator<InputArgType, GpuDevice>, Index, InputDims, Dynamic>), num_blocks, block_size, shared_mem, m_device, m_inputImpl, indexMapper, m_kernel, numP, numX, maxX, kernel_size, data);
+ }
+ }
+ break;
+ }
+
+ case 2: {
+ const int idxX =
+ static_cast<int>(Layout) == static_cast<int>(ColMajor) ? 0 : 1;
+ const int idxY =
+ static_cast<int>(Layout) == static_cast<int>(ColMajor) ? 1 : 0;
+ const int kernel_size_x = m_kernelImpl.dimensions()[idxX];
+ const int kernel_size_y = m_kernelImpl.dimensions()[idxY];
+
+ const int numX = dimensions()[m_indices[idxX]];
+ const int numY = dimensions()[m_indices[idxY]];
+ const int numP = dimensions().TotalSize() / (numX*numY);
+
+ const float scaling_factor = sqrtf(static_cast<float>(maxSharedMem) / (sizeof(Scalar) * kernel_size_y * kernel_size_x));
+
+ // Snap maxX to warp size
+ int inner_dim = ((static_cast<int>(scaling_factor * kernel_size_x) - kernel_size_x + 1 + 32) / 32) * 32;
+ const int maxX = numext::mini<int>(inner_dim, numX);
+ const int maxY = numext::mini<int>(maxSharedMem / (sizeof(Scalar) * (maxX + kernel_size_x - 1)) - kernel_size_y + 1, numY);
+ const int maxP = numext::mini<int>(maxSharedMem / ((kernel_size_x - 1 + maxX) * (kernel_size_y - 1 + maxY) * sizeof(Scalar)), numP);
+
+ dim3 block_size;
+ block_size.x = numext::mini(1024, maxX);
+ block_size.y = numext::mini<int>(1024/block_size.x, maxY);
+ block_size.z = numext::mini<int>(1024/(block_size.x*block_size.y), maxP);
+
+ const int shared_mem = block_size.z * (maxX + kernel_size_x - 1) * (maxY + kernel_size_y - 1) * sizeof(Scalar);
+ gpu_assert(shared_mem <= maxSharedMem);
+
+ const int num_x_blocks = ceil(numX, maxX);
+ const int num_y_blocks = ceil(numY, maxY);
+ const int blocksPerProcessor = numext::mini(maxBlocksPerProcessor, maxSharedMem / shared_mem);
+ const int num_z_blocks = ceil(numMultiProcessors * blocksPerProcessor, num_x_blocks * num_y_blocks);
+
+ dim3 num_blocks(num_x_blocks, num_y_blocks, numext::mini<int>(num_z_blocks, ceil(numP, block_size.z)));
+
+
+ //cout << "launching 2D kernel with block_size.x: " << block_size.x << " block_size.y: " << block_size.y << " block_size.z: " << block_size.z << " num_blocks.x: " << num_blocks.x << " num_blocks.y: " << num_blocks.y << " num_blocks.z: " << num_blocks.z << " maxX: " << maxX << " maxY: " << maxY << " maxP: " << maxP << " shared_mem: " << shared_mem << " in stream " << m_device.stream() << endl;
+
+ const array<Index, 2> indices(m_indices[idxX], m_indices[idxY]);
+ const array<Index, 2> kernel_dims(m_kernelImpl.dimensions()[idxX],
+ m_kernelImpl.dimensions()[idxY]);
+ internal::IndexMapper<Index, InputDims, 2, Layout> indexMapper(
+ m_inputImpl.dimensions(), kernel_dims, indices);
+ switch (kernel_size_x) {
+ case 4: {
+ switch (kernel_size_y) {
+ case 7: {
+ LAUNCH_GPU_KERNEL((EigenConvolutionKernel2D<TensorEvaluator<InputArgType, GpuDevice>, Index, InputDims, 4, 7>), num_blocks, block_size, shared_mem, m_device, m_inputImpl, indexMapper, m_kernel, numP, numX, maxX, numY, maxY, 4, 7, data);
+ break;
+ }
+ default: {
+ LAUNCH_GPU_KERNEL((EigenConvolutionKernel2D<TensorEvaluator<InputArgType, GpuDevice>, Index, InputDims, 4, Dynamic>), num_blocks, block_size, shared_mem, m_device, m_inputImpl, indexMapper, m_kernel, numP, numX, maxX, numY, maxY, 4, kernel_size_y, data);
+ break;
+ }
+ }
+ break;
+ }
+ case 7: {
+ switch (kernel_size_y) {
+ case 4: {
+ LAUNCH_GPU_KERNEL((EigenConvolutionKernel2D<TensorEvaluator<InputArgType, GpuDevice>, Index, InputDims, 7, 4>), num_blocks, block_size, shared_mem, m_device, m_inputImpl, indexMapper, m_kernel, numP, numX, maxX, numY, maxY, 7, 4, data);
+ break;
+ }
+ default: {
+ LAUNCH_GPU_KERNEL((EigenConvolutionKernel2D<TensorEvaluator<InputArgType, GpuDevice>, Index, InputDims, 7, Dynamic>), num_blocks, block_size, shared_mem, m_device, m_inputImpl, indexMapper, m_kernel, numP, numX, maxX, numY, maxY, 7, kernel_size_y, data);
+ break;
+ }
+ }
+ break;
+ }
+ default: {
+ LAUNCH_GPU_KERNEL((EigenConvolutionKernel2D<TensorEvaluator<InputArgType, GpuDevice>, Index, InputDims, Dynamic, Dynamic>), num_blocks, block_size, shared_mem, m_device, m_inputImpl, indexMapper, m_kernel, numP, numX, maxX, numY, maxY, kernel_size_x, kernel_size_y, data);
+ break;
+ }
+ }
+ break;
+ }
+
+ case 3: {
+ const int idxX =
+ static_cast<int>(Layout) == static_cast<int>(ColMajor) ? 0 : 2;
+ const int idxY =
+ static_cast<int>(Layout) == static_cast<int>(ColMajor) ? 1 : 1;
+ const int idxZ =
+ static_cast<int>(Layout) == static_cast<int>(ColMajor) ? 2 : 0;
+
+ const int kernel_size_x = m_kernelImpl.dimensions()[idxX];
+ const int kernel_size_y = m_kernelImpl.dimensions()[idxY];
+ const int kernel_size_z = m_kernelImpl.dimensions()[idxZ];
+
+ const int numX = dimensions()[m_indices[idxX]];
+ const int numY = dimensions()[m_indices[idxY]];
+ const int numZ = dimensions()[m_indices[idxZ]];
+ const int numP = dimensions().TotalSize() / (numX*numY*numZ);
+
+ const int maxX = numext::mini<int>(128, numext::mini<int>(maxSharedMem / (sizeof(Scalar) * kernel_size_y * kernel_size_z) - kernel_size_x + 1, numX));
+ const int maxY = numext::mini<int>(128, numext::mini<int>(maxSharedMem / (sizeof(Scalar) * (maxX + kernel_size_x - 1) * kernel_size_z) - kernel_size_y + 1, numY));
+ const int maxZ = numext::mini<int>(128, numext::mini<int>(maxSharedMem / (sizeof(Scalar) * (maxX + kernel_size_x - 1) * (maxY + kernel_size_y - 1)) - kernel_size_z + 1, numZ));
+
+ dim3 block_size;
+ block_size.x = numext::mini(32, maxX);
+ block_size.y = numext::mini(32, maxY);
+ block_size.z = numext::mini<int>(1024/(block_size.x*block_size.y), maxZ);
+ dim3 num_blocks(ceil(numX, maxX), ceil(numY, maxY), ceil(numZ, maxZ));
+
+ const int shared_mem = (maxX + kernel_size_x - 1) * (maxY + kernel_size_y - 1) * (maxZ + kernel_size_z - 1) * sizeof(Scalar);
+ gpu_assert(shared_mem <= maxSharedMem);
+
+ //cout << "launching 3D kernel with block_size.x: " << block_size.x << " block_size.y: " << block_size.y << " block_size.z: " << block_size.z << " num_blocks.x: " << num_blocks.x << " num_blocks.y: " << num_blocks.y << " num_blocks.z: " << num_blocks.z << " shared_mem: " << shared_mem << " in stream " << m_device.stream() << endl;
+ const array<Index, 3> indices(m_indices[idxX], m_indices[idxY],
+ m_indices[idxZ]);
+ const array<Index, 3> kernel_dims(m_kernelImpl.dimensions()[idxX],
+ m_kernelImpl.dimensions()[idxY],
+ m_kernelImpl.dimensions()[idxZ]);
+ internal::IndexMapper<Index, InputDims, 3, Layout> indexMapper(
+ m_inputImpl.dimensions(), kernel_dims, indices);
+
+ LAUNCH_GPU_KERNEL((EigenConvolutionKernel3D<TensorEvaluator<InputArgType, GpuDevice>, Index, InputDims>), num_blocks, block_size, shared_mem, m_device, m_inputImpl, indexMapper, m_kernel, numP, numX, maxX, numY, maxY, numZ, maxZ, kernel_size_x, kernel_size_y, kernel_size_z, data);
+ break;
+ }
+
+ default: {
+ EIGEN_STATIC_ASSERT((NumKernelDims >= 1 && NumKernelDims <= 3), THIS_METHOD_IS_ONLY_FOR_OBJECTS_OF_A_SPECIFIC_SIZE);
+ }
+ }
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE CoeffReturnType coeff(Index index) const
+ {
+ eigen_assert(m_buf);
+ eigen_assert(index < m_dimensions.TotalSize());
+ return m_buf[index];
+ }
+
+ template<int LoadMode>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE PacketReturnType packet(const Index index) const
+ {
+ eigen_assert(m_buf);
+ eigen_assert(index < m_dimensions.TotalSize());
+ return internal::ploadt<PacketReturnType, LoadMode>(m_buf+index);
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorOpCost
+ costPerCoeff(bool vectorized) const {
+ // TODO(rmlarsen): FIXME: For now, this is just a copy of the CPU cost
+ // model.
+ const double kernel_size = m_kernelImpl.dimensions().TotalSize();
+ // We ignore the use of fused multiply-add.
+ const double convolve_compute_cost =
+ TensorOpCost::AddCost<Scalar>() + TensorOpCost::MulCost<Scalar>();
+ const double firstIndex_compute_cost =
+ NumDims *
+ (2 * TensorOpCost::AddCost<Index>() + 2 * TensorOpCost::MulCost<Index>() +
+ TensorOpCost::DivCost<Index>());
+ return TensorOpCost(0, 0, firstIndex_compute_cost, vectorized, PacketSize) +
+ kernel_size * (m_inputImpl.costPerCoeff(vectorized) +
+ m_kernelImpl.costPerCoeff(vectorized) +
+ TensorOpCost(0, 0, convolve_compute_cost, vectorized,
+ PacketSize));
+ }
+
+ private:
+ // No assignment (copies are needed by the kernels)
+ TensorEvaluator& operator = (const TensorEvaluator&);
+
+ TensorEvaluator<InputArgType, GpuDevice> m_inputImpl;
+ TensorEvaluator<KernelArgType, GpuDevice> m_kernelImpl;
+ KernelArgType m_kernelArg;
+ Indices m_indices;
+ Dimensions m_dimensions;
+ Scalar* m_buf;
+ const Scalar* m_kernel;
+ bool m_local_kernel;
+
+ const GpuDevice& m_device;
+};
+#endif
+
+
+} // end namespace Eigen
+
+#endif // EIGEN_CXX11_TENSOR_TENSOR_CONVOLUTION_H
diff --git a/unsupported/Eigen/CXX11/src/Tensor/TensorConvolutionSycl.h b/unsupported/Eigen/CXX11/src/Tensor/TensorConvolutionSycl.h
new file mode 100644
index 0000000..3cbc1ab
--- /dev/null
+++ b/unsupported/Eigen/CXX11/src/Tensor/TensorConvolutionSycl.h
@@ -0,0 +1,546 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Mehdi Goli Codeplay Software Ltd.
+// Ralph Potter Codeplay Software Ltd.
+// Luke Iwanski Codeplay Software Ltd.
+// Contact: <eigen@codeplay.com>
+// Copyright (C) 2016 Benoit Steiner <benoit.steiner.goog@gmail.com>
+
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_CXX11_TENSOR_TENSOR_CONVOLUTION_SYCL_H
+#define EIGEN_CXX11_TENSOR_TENSOR_CONVOLUTION_SYCL_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+/** \class TensorConvolution
+ * \ingroup CXX11_Tensor_Module
+ *
+ * \brief Tensor convolution class.
+ *
+ *
+ */
+
+enum class convolution_type { CONV1D, CONV2D, CONV3D };
+template <typename Evaluator, typename CoeffReturnType, typename KernelType, typename Index, typename InputDims,
+ typename Kernel_accessor, typename Buffer_accessor, convolution_type Conv_Dim>
+struct EigenConvolutionKernel;
+template <typename Evaluator, typename CoeffReturnType, typename KernelType, typename Index, typename InputDims,
+ typename Kernel_accessor, typename Buffer_accessor>
+struct EigenConvolutionKernel<Evaluator, CoeffReturnType, KernelType, Index, InputDims, Kernel_accessor,
+ Buffer_accessor, convolution_type::CONV1D> {
+ typedef cl::sycl::accessor<CoeffReturnType, 1, cl::sycl::access::mode::read_write, cl::sycl::access::target::local>
+ Local_accessor;
+ Local_accessor local_acc;
+ Evaluator device_evaluator;
+ Kernel_accessor kernel_filter;
+ Buffer_accessor buffer_acc;
+ internal::IndexMapper<Index, InputDims, 1, Evaluator::Layout> indexMapper;
+ const size_t kernelSize;
+ const cl::sycl::range<2> input_range;
+ EigenConvolutionKernel(Local_accessor local_acc_, Evaluator device_evaluator_, Kernel_accessor kernel_filter_,
+ Buffer_accessor buffer_acc_,
+ internal::IndexMapper<Index, InputDims, 1, Evaluator::Layout> indexMapper_,
+ const size_t kernelSize_, const cl::sycl::range<2> input_range_)
+ : local_acc(local_acc_),
+ device_evaluator(device_evaluator_),
+ kernel_filter(kernel_filter_),
+ buffer_acc(buffer_acc_),
+ indexMapper(indexMapper_),
+ kernelSize(kernelSize_),
+ input_range(input_range_) {}
+
+ template <typename BooleanDim2>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE bool boundary_check(const BooleanDim2 boolean_check) {
+ return (boolean_check[0] && boolean_check[1]);
+ }
+ void operator()(cl::sycl::nd_item<2> itemID) {
+ auto buffer_ptr = buffer_acc.get_pointer();
+ auto kernel_ptr = kernel_filter.get_pointer();
+ // the required row to be calculated for the for each plane in shered memory
+ const size_t num_input = (itemID.get_local_range()[0] + kernelSize - 1);
+ const size_t plane_kernel_offset = itemID.get_local_id(1) * num_input;
+ const size_t input_offset = itemID.get_group(0) * itemID.get_local_range()[0];
+ const size_t plane_tensor_offset = indexMapper.mapGpuInputPlaneToTensorInputOffset(itemID.get_global_id(1));
+ /// fill the shared memory
+ for (size_t i = itemID.get_local_id(0); i < num_input; i += itemID.get_local_range()[0]) {
+ const size_t local_index = i + plane_kernel_offset;
+ const size_t tensor_index =
+ plane_tensor_offset + indexMapper.mapGpuInputKernelToTensorInputOffset(i + input_offset);
+
+ local_acc[local_index] =
+ (((i + input_offset) < (input_range[0] + kernelSize - 1)) && itemID.get_global_id(1) < input_range[1])
+ ? device_evaluator.coeff(tensor_index)
+ : CoeffReturnType(0);
+ }
+
+ itemID.barrier(cl::sycl::access::fence_space::local_space);
+
+ // calculate the convolution // output start x
+ const size_t first_output_start = itemID.get_group(0) * (itemID.get_local_range()[0]);
+ if (boundary_check(itemID.get_global_id() < input_range)) {
+ CoeffReturnType result = static_cast<CoeffReturnType>(0);
+ const size_t index = plane_kernel_offset + itemID.get_local_id(0);
+ for (size_t k = 0; k < kernelSize; ++k) {
+ result += (local_acc[k + index] * kernel_ptr[k]);
+ }
+ const size_t tensor_index =
+ indexMapper.mapGpuOutputPlaneToTensorOutputOffset(itemID.get_global_id(1)) +
+ indexMapper.mapGpuOutputKernelToTensorOutputOffset(itemID.get_local_id(0) + first_output_start);
+ buffer_ptr[tensor_index] = result;
+ }
+ }
+};
+
+template <typename Evaluator, typename CoeffReturnType, typename KernelType, typename Index, typename InputDims,
+ typename Kernel_accessor, typename Buffer_accessor>
+struct EigenConvolutionKernel<Evaluator, CoeffReturnType, KernelType, Index, InputDims, Kernel_accessor,
+ Buffer_accessor, convolution_type::CONV2D> {
+ typedef cl::sycl::accessor<CoeffReturnType, 1, cl::sycl::access::mode::read_write, cl::sycl::access::target::local>
+ Local_accessor;
+ Local_accessor local_acc;
+ Evaluator device_evaluator;
+ Kernel_accessor kernel_filter;
+ Buffer_accessor buffer_acc;
+ internal::IndexMapper<Index, InputDims, 2, Evaluator::Layout> indexMapper;
+ const cl::sycl::range<2> kernel_size;
+ const cl::sycl::range<3> input_range;
+ EigenConvolutionKernel(Local_accessor local_acc_, Evaluator device_evaluator_, Kernel_accessor kernel_filter_,
+ Buffer_accessor buffer_acc_,
+ internal::IndexMapper<Index, InputDims, 2, Evaluator::Layout> indexMapper_,
+ const cl::sycl::range<2> kernel_size_, const cl::sycl::range<3> input_range_)
+ : local_acc(local_acc_),
+ device_evaluator(device_evaluator_),
+ kernel_filter(kernel_filter_),
+ buffer_acc(buffer_acc_),
+ indexMapper(indexMapper_),
+ kernel_size(kernel_size_),
+ input_range(input_range_) {}
+ template <typename BooleanDim3>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE bool boundary_check(const BooleanDim3 boolean_check) {
+ return (boolean_check[0] && boolean_check[1] && boolean_check[2]);
+ }
+
+ void operator()(cl::sycl::nd_item<3> itemID) {
+ auto buffer_ptr = buffer_acc.get_pointer();
+ auto kernel_ptr = kernel_filter.get_pointer();
+ // the required row to be calculated for the for each plane in shered memory
+ const auto num_input = cl::sycl::range<2>{
+ (cl::sycl::range<2>(itemID.get_local_range()[0], itemID.get_local_range()[1]) + kernel_size - 1)};
+
+ const size_t plane_input_offset = indexMapper.mapGpuInputPlaneToTensorInputOffset(itemID.get_global_id(2));
+ const size_t plane_kernel_offset = itemID.get_local_id(2) * num_input[1];
+
+ const auto input_offset = cl::sycl::range<2>{itemID.get_group(0) * itemID.get_local_range()[0],
+ itemID.get_group(1) * itemID.get_local_range()[1]};
+
+ // fill the local memory
+ bool in_range_dim2 = itemID.get_global_id(2) < input_range[2];
+ for (size_t j = itemID.get_local_id(1); j < num_input[1]; j += itemID.get_local_range()[1]) {
+ const size_t local_input_offset = num_input[0] * (j + plane_kernel_offset);
+ bool in_range_dim1 = ((j + input_offset[1]) < (input_range[1] + kernel_size[1] - 1));
+ for (size_t i = itemID.get_local_id(0); i < num_input[0]; i += itemID.get_local_range()[0]) {
+ const size_t local_index = i + local_input_offset;
+ const size_t tensor_index = plane_input_offset + indexMapper.mapGpuInputKernelToTensorInputOffset(
+ i + input_offset[0], j + input_offset[1]);
+ local_acc[local_index] = (((i + input_offset[0]) < (input_range[0] + kernel_size[0] - 1)) &&
+ in_range_dim1 && in_range_dim2)
+ ? device_evaluator.coeff(tensor_index)
+ : CoeffReturnType(0);
+ }
+ }
+
+ itemID.barrier(cl::sycl::access::fence_space::local_space);
+
+ // output offset start for each thread
+ const auto output_offset = cl::sycl::range<2>{itemID.get_group(0) * itemID.get_local_range()[0],
+ itemID.get_group(1) * itemID.get_local_range()[1]};
+
+ if (boundary_check(itemID.get_global_id() < input_range)) {
+ CoeffReturnType result = static_cast<CoeffReturnType>(0);
+
+ for (size_t j = 0; j < kernel_size[1]; j++) {
+ size_t kernel_offset = kernel_size[0] * j;
+ const size_t index =
+ (num_input[0] * (plane_kernel_offset + j + itemID.get_local_id(1))) + itemID.get_local_id(0);
+ for (size_t i = 0; i < kernel_size[0]; i++) {
+ result += (local_acc[i + index] * kernel_ptr[i + kernel_offset]);
+ }
+ }
+ const size_t tensor_index =
+ indexMapper.mapGpuOutputPlaneToTensorOutputOffset(itemID.get_global_id(2)) +
+ indexMapper.mapGpuOutputKernelToTensorOutputOffset(itemID.get_local_id(0) + output_offset[0],
+ itemID.get_local_id(1) + output_offset[1]);
+
+ buffer_ptr[tensor_index] = result;
+ }
+ }
+};
+
+template <typename Evaluator, typename CoeffReturnType, typename KernelType, typename Index, typename InputDims,
+ typename Kernel_accessor, typename Buffer_accessor>
+struct EigenConvolutionKernel<Evaluator, CoeffReturnType, KernelType, Index, InputDims, Kernel_accessor,
+ Buffer_accessor, convolution_type::CONV3D> {
+ typedef cl::sycl::accessor<CoeffReturnType, 1, cl::sycl::access::mode::read_write, cl::sycl::access::target::local>
+ Local_accessor;
+ Local_accessor local_acc;
+ Evaluator device_evaluator;
+ Kernel_accessor kernel_filter;
+ Buffer_accessor buffer_acc;
+ internal::IndexMapper<Index, InputDims, 3, Evaluator::Layout> indexMapper;
+ const cl::sycl::range<3> kernel_size;
+ const cl::sycl::range<3> input_range;
+ const size_t numP;
+
+ EigenConvolutionKernel(Local_accessor local_acc_, Evaluator device_evaluator_, Kernel_accessor kernel_filter_,
+ Buffer_accessor buffer_acc_,
+ internal::IndexMapper<Index, InputDims, 3, Evaluator::Layout> indexMapper_,
+ const cl::sycl::range<3> kernel_size_, const cl::sycl::range<3> input_range_,
+ const size_t numP_)
+ : local_acc(local_acc_),
+ device_evaluator(device_evaluator_),
+ kernel_filter(kernel_filter_),
+ buffer_acc(buffer_acc_),
+ indexMapper(indexMapper_),
+ kernel_size(kernel_size_),
+ input_range(input_range_),
+ numP(numP_) {}
+ template <typename BooleanDim3>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE bool boundary_check(const BooleanDim3 boolean_check) {
+ return (boolean_check[0] && boolean_check[1] && boolean_check[2]);
+ }
+ void operator()(cl::sycl::nd_item<3> itemID) {
+ auto buffer_ptr = buffer_acc.get_pointer();
+ auto kernel_ptr = kernel_filter.get_pointer();
+ const auto num_input = cl::sycl::range<3>{itemID.get_local_range() + kernel_size - 1};
+
+ const auto input_offset = cl::sycl::range<3>{itemID.get_group().get_id() * itemID.get_local_range()};
+
+ const auto output_offset =
+ cl::sycl::range<3>{itemID.get_group().get_id() * itemID.get_local_range() + itemID.get_local_id()};
+
+ for (size_t p = 0; p < numP; p++) {
+ /// fill the shared memory
+ const size_t plane_input_offset = indexMapper.mapGpuInputPlaneToTensorInputOffset(p);
+ for (size_t k = itemID.get_local_id(2); k < num_input[2]; k += itemID.get_local_range()[2]) {
+ size_t local_index_dim2 = num_input[0] * num_input[1] * k;
+ bool cond_k_dim = (k + input_offset[2] < (input_range[2] + kernel_size[2] - 1));
+ for (size_t j = itemID.get_local_id(1); j < num_input[1]; j += itemID.get_local_range()[1]) {
+ bool cond_j_dim = cond_k_dim && (j + input_offset[1] < (input_range[1] + kernel_size[1] - 1));
+ size_t local_index_dim1 = (num_input[0] * j) + local_index_dim2;
+ for (size_t i = itemID.get_local_id(0); i < num_input[0]; i += itemID.get_local_range()[0]) {
+ bool conds = cond_j_dim && (i + input_offset[0] < (input_range[0] + kernel_size[0] - 1));
+ const size_t local_index = local_index_dim1 + i;
+ const size_t tensor_index =
+ plane_input_offset + indexMapper.mapGpuInputKernelToTensorInputOffset(
+ i + input_offset[0], j + input_offset[1], k + input_offset[2]);
+ local_acc[local_index] = conds ? device_evaluator.coeff(tensor_index) : CoeffReturnType(0);
+ }
+ }
+ }
+ itemID.barrier(cl::sycl::access::fence_space::local_space);
+
+ // calculate the convolution
+
+ if (boundary_check(itemID.get_global_id() < input_range)) {
+ CoeffReturnType result = static_cast<CoeffReturnType>(0);
+ for (size_t k = 0; k < kernel_size[2]; k++) {
+ for (size_t j = 0; j < kernel_size[1]; j++) {
+ for (size_t i = 0; i < kernel_size[0]; i++) {
+ const size_t kernel_index = i + kernel_size[0] * (j + kernel_size[1] * k);
+ const size_t local_index =
+ ((i + itemID.get_local_id(0)) +
+ num_input[0] * ((j + itemID.get_local_id(1)) + num_input[1] * (k + itemID.get_local_id(2))));
+
+ result += (local_acc[local_index] * kernel_ptr[kernel_index]);
+ }
+ }
+ }
+ const size_t tensor_index =
+ indexMapper.mapGpuOutputPlaneToTensorOutputOffset(p) +
+ indexMapper.mapGpuOutputKernelToTensorOutputOffset(output_offset[0], output_offset[1], output_offset[2]);
+ buffer_ptr[tensor_index] = result;
+ }
+
+ itemID.barrier(cl::sycl::access::fence_space::local_space);
+ }
+ }
+};
+
+template <typename Indices, typename InputArgType, typename KernelArgType>
+struct TensorEvaluator<const TensorConvolutionOp<Indices, InputArgType, KernelArgType>, Eigen::SyclDevice> {
+ typedef TensorConvolutionOp<Indices, InputArgType, KernelArgType> XprType;
+
+ static constexpr int NumDims =
+ internal::array_size<typename TensorEvaluator<InputArgType, Eigen::SyclDevice>::Dimensions>::value;
+ static constexpr int NumKernelDims = internal::array_size<Indices>::value;
+ typedef typename XprType::Index Index;
+ typedef DSizes<Index, NumDims> Dimensions;
+ typedef typename TensorEvaluator<KernelArgType, Eigen::SyclDevice>::Dimensions KernelDimensions;
+ typedef const Eigen::SyclDevice Device;
+ typedef typename XprType::CoeffReturnType CoeffReturnType;
+ typedef typename PacketType<CoeffReturnType, Eigen::SyclDevice>::type PacketReturnType;
+ typedef typename InputArgType::Scalar Scalar;
+ static constexpr int PacketSize = PacketType<CoeffReturnType, Device>::size;
+ typedef StorageMemory<CoeffReturnType, Eigen::SyclDevice> Storage;
+ typedef typename Storage::Type EvaluatorPointerType;
+ typedef StorageMemory<const CoeffReturnType, Eigen::SyclDevice> KernelStorage;
+
+ static constexpr int Layout = TensorEvaluator<InputArgType, Eigen::SyclDevice>::Layout;
+ enum {
+ IsAligned = TensorEvaluator<InputArgType, Eigen::SyclDevice>::IsAligned &
+ TensorEvaluator<KernelArgType, Eigen::SyclDevice>::IsAligned,
+ PacketAccess = false,
+ BlockAccess = false,
+ PreferBlockAccess = false,
+ CoordAccess = false, // to be implemented
+ RawAccess = false
+ };
+
+ //===- Tensor block evaluation strategy (see TensorBlock.h) -------------===//
+ typedef internal::TensorBlockNotImplemented TensorBlock;
+ //===--------------------------------------------------------------------===//
+
+ TensorEvaluator(const XprType &op, const Eigen::SyclDevice &device)
+ : m_inputImpl(op.inputExpression(), device),
+ m_kernelArg(op.kernelExpression()),
+ m_kernelImpl(op.kernelExpression(), device),
+ m_indices(op.indices()),
+ m_buf(NULL),
+ m_kernel(NULL),
+ m_local_kernel(false),
+ m_device(device) {
+ EIGEN_STATIC_ASSERT((static_cast<int>(TensorEvaluator<InputArgType, Eigen::SyclDevice>::Layout) ==
+ static_cast<int>(TensorEvaluator<KernelArgType, Eigen::SyclDevice>::Layout)),
+ YOU_MADE_A_PROGRAMMING_MISTAKE);
+
+ const typename TensorEvaluator<InputArgType, Eigen::SyclDevice>::Dimensions &input_dims = m_inputImpl.dimensions();
+ const typename TensorEvaluator<KernelArgType, Eigen::SyclDevice>::Dimensions &kernel_dims =
+ m_kernelImpl.dimensions();
+
+ m_dimensions = m_inputImpl.dimensions();
+ for (int i = 0; i < NumKernelDims; ++i) {
+ const Index index = op.indices()[i];
+ const Index input_dim = input_dims[index];
+ const Index kernel_dim = kernel_dims[i];
+ const Index result_dim = input_dim - kernel_dim + 1;
+ m_dimensions[index] = result_dim;
+ }
+ }
+
+ EIGEN_DEVICE_FUNC const Dimensions &dimensions() const { return m_dimensions; }
+
+ EIGEN_STRONG_INLINE bool evalSubExprsIfNeeded(EvaluatorPointerType data) {
+ preloadKernel();
+ m_inputImpl.evalSubExprsIfNeeded(NULL);
+ if (data) {
+ executeEval(data);
+ return false;
+ } else {
+ m_buf = (EvaluatorPointerType)m_device.get(
+ (Scalar *)m_device.allocate_temp(dimensions().TotalSize() * sizeof(Scalar)));
+ executeEval(m_buf);
+ return true;
+ }
+ }
+
+ EIGEN_STRONG_INLINE void cleanup() {
+ m_inputImpl.cleanup();
+ if (m_buf) {
+ m_device.deallocate_temp(m_buf);
+ m_buf = NULL;
+ }
+ if (m_local_kernel) {
+ m_device.deallocate_temp(m_kernel);
+ m_local_kernel = false;
+ }
+ m_kernel = NULL;
+ }
+ /// used by sycl in order to build the sycl buffer
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Device &device() const { return m_device; }
+ /// used by sycl in order to build the sycl buffer
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE EvaluatorPointerType data() const { return m_buf; }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void preloadKernel() {
+ // Don't make a local copy of the kernel unless we have to (i.e. it's an
+ // expression that needs to be evaluated)
+ typename KernelStorage::Type in_place = m_kernelImpl.data();
+ if (in_place) {
+ m_kernel = in_place;
+ m_local_kernel = false;
+ } else {
+ ptrdiff_t kernel_sz = m_kernelImpl.dimensions().TotalSize() * sizeof(Scalar);
+ EvaluatorPointerType local = (EvaluatorPointerType)m_device.get((Scalar *)m_device.allocate_temp(kernel_sz));
+ typedef TensorEvalToOp<const KernelArgType> EvalTo;
+ EvalTo evalToTmp(m_device.get(local), m_kernelArg);
+ const bool PacketAccess = internal::IsVectorizable<Eigen::SyclDevice, KernelArgType>::value;
+ internal::TensorExecutor<const EvalTo, Eigen::SyclDevice, PacketAccess>::run(evalToTmp, m_device);
+ m_kernel = local;
+ m_local_kernel = true;
+ }
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void executeEval(EvaluatorPointerType data) const {
+ typedef TensorEvaluator<InputArgType, Eigen::SyclDevice> InputEvaluator;
+ typedef typename InputEvaluator::Dimensions InputDims;
+ switch (NumKernelDims) {
+ case 1: {
+ const size_t numX = dimensions()[m_indices[0]];
+ const size_t numP = dimensions().TotalSize() / numX;
+ const auto input_dim = std::array<size_t, 2>{numX, numP};
+ auto global_range = cl::sycl::range<2>{1, 1};
+ auto local_range = cl::sycl::range<2>{1, 1};
+ const size_t kernel_size = m_kernelImpl.dimensions().TotalSize();
+
+ m_device.parallel_for_setup(input_dim, global_range, local_range);
+ const size_t local_memory_size = (local_range[0] + kernel_size - 1) * (local_range[1]);
+ gpu_assert(static_cast<unsigned long>(local_memory_size) <= m_device.sharedMemPerBlock());
+ const array<Index, 1> indices{{m_indices[0]}};
+ const array<Index, 1> kernel_dims{{m_kernelImpl.dimensions()[0]}};
+ internal::IndexMapper<Index, InputDims, 1, Layout> indexMapper(m_inputImpl.dimensions(), kernel_dims, indices);
+
+ typedef EigenConvolutionKernel<InputEvaluator, CoeffReturnType, Scalar, Index, InputDims,
+ typename KernelStorage::Type, EvaluatorPointerType, convolution_type::CONV1D>
+ ConvKernel;
+
+ m_device.template binary_kernel_launcher<CoeffReturnType, ConvKernel>(
+ m_inputImpl, m_kernel, data, cl::sycl::nd_range<2>(global_range, local_range), local_memory_size,
+ indexMapper, kernel_size, cl::sycl::range<2>(input_dim[0], input_dim[1]));
+ break;
+ }
+
+ case 2: {
+ auto kernel_index = std::array<size_t, 2>{static_cast<int>(Layout) == static_cast<int>(ColMajor) ? 0 : 1,
+ static_cast<int>(Layout) == static_cast<int>(ColMajor) ? 1 : 0};
+ auto kernel_size = cl::sycl::range<2>{(size_t)m_kernelImpl.dimensions()[kernel_index[0]],
+ (size_t)m_kernelImpl.dimensions()[kernel_index[1]]};
+ const size_t numX = dimensions()[m_indices[kernel_index[0]]];
+ const size_t numY = dimensions()[m_indices[kernel_index[1]]];
+ const size_t numP = dimensions().TotalSize() / (numX * numY);
+ auto input_dim = std::array<size_t, 3>{numX, numY, numP};
+
+ auto global_range = cl::sycl::range<3>{1, 1, 1};
+ auto local_range = cl::sycl::range<3>{1, 1, 1};
+
+ m_device.parallel_for_setup(input_dim, global_range, local_range);
+
+ const size_t local_memory_size =
+ (local_range[0] + kernel_size[0] - 1) * (local_range[1] + kernel_size[1] - 1) * local_range[2];
+ gpu_assert(static_cast<unsigned long>(local_memory_size) <= m_device.sharedMemPerBlock());
+ const array<Index, 2> indices{{m_indices[kernel_index[0]], m_indices[kernel_index[1]]}};
+ const array<Index, 2> kernel_dims{
+ {m_kernelImpl.dimensions()[kernel_index[0]], m_kernelImpl.dimensions()[kernel_index[1]]}};
+ internal::IndexMapper<Index, InputDims, 2, Layout> indexMapper(m_inputImpl.dimensions(), kernel_dims, indices);
+ typedef EigenConvolutionKernel<InputEvaluator, CoeffReturnType, Scalar, Index, InputDims,
+ typename KernelStorage::Type, EvaluatorPointerType, convolution_type::CONV2D>
+ ConvKernel;
+ m_device.template binary_kernel_launcher<CoeffReturnType, ConvKernel>(
+ m_inputImpl, m_kernel, data, cl::sycl::nd_range<3>(global_range, local_range), local_memory_size,
+ indexMapper, kernel_size, cl::sycl::range<3>{input_dim[0], input_dim[1], input_dim[2]});
+ break;
+ }
+
+ case 3: {
+ auto kernel_index = std::array<size_t, 3>{static_cast<int>(Layout) == static_cast<int>(ColMajor) ? 0 : 2,
+ static_cast<int>(Layout) == static_cast<int>(ColMajor) ? 1 : 1,
+ static_cast<int>(Layout) == static_cast<int>(ColMajor) ? 2 : 0};
+
+ auto kernel_size = cl::sycl::range<3>{(size_t)m_kernelImpl.dimensions()[kernel_index[0]],
+ (size_t)m_kernelImpl.dimensions()[kernel_index[1]],
+ (size_t)m_kernelImpl.dimensions()[kernel_index[2]]};
+
+ const size_t numX = dimensions()[m_indices[kernel_index[0]]];
+ const size_t numY = dimensions()[m_indices[kernel_index[1]]];
+ const size_t numZ = dimensions()[m_indices[kernel_index[2]]];
+ auto input_dim = std::array<size_t, 3>{numX, numY, numZ};
+ const size_t numP = dimensions().TotalSize() / (numX * numY * numZ);
+
+ const array<Index, 3> indices{
+ {m_indices[kernel_index[0]], m_indices[kernel_index[1]], m_indices[kernel_index[2]]}};
+ const array<Index, 3> kernel_dims{{m_kernelImpl.dimensions()[kernel_index[0]],
+ m_kernelImpl.dimensions()[kernel_index[1]],
+ m_kernelImpl.dimensions()[kernel_index[2]]}};
+
+ internal::IndexMapper<Index, InputDims, 3, Layout> indexMapper(m_inputImpl.dimensions(), kernel_dims, indices);
+
+ auto global_range = cl::sycl::range<3>{1, 1, 1};
+ auto local_range = cl::sycl::range<3>{1, 1, 1};
+
+ m_device.parallel_for_setup(input_dim, global_range, local_range);
+ auto local_memory_range = (local_range + kernel_size - 1);
+ const size_t local_memory_size = local_memory_range[0] * local_memory_range[1] * local_memory_range[2];
+
+ gpu_assert(static_cast<unsigned long>(local_memory_size) <= m_device.sharedMemPerBlock());
+ typedef EigenConvolutionKernel<InputEvaluator, CoeffReturnType, Scalar, Index, InputDims,
+ typename KernelStorage::Type, EvaluatorPointerType, convolution_type::CONV3D>
+ ConvKernel;
+ m_device.template binary_kernel_launcher<CoeffReturnType, ConvKernel>(
+ m_inputImpl, m_kernel, data, cl::sycl::nd_range<3>(global_range, local_range), local_memory_size,
+ indexMapper, kernel_size, cl::sycl::range<3>(input_dim[0], input_dim[1], input_dim[2]), numP);
+ break;
+ }
+
+ default: {
+ EIGEN_STATIC_ASSERT((NumKernelDims >= 1 && NumKernelDims <= 3),
+ THIS_METHOD_IS_ONLY_FOR_OBJECTS_OF_A_SPECIFIC_SIZE);
+ }
+ }
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE CoeffReturnType coeff(Index index) const {
+ eigen_assert(m_buf != NULL);
+ eigen_assert(index < m_dimensions.TotalSize());
+ return m_buf[index];
+ }
+
+ template <int LoadMode>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE PacketReturnType packet(const Index index) const {
+ eigen_assert(m_buf != NULL);
+ eigen_assert(index < m_dimensions.TotalSize());
+ return internal::ploadt<PacketReturnType, LoadMode>(m_buf + index);
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorOpCost costPerCoeff(bool vectorized) const {
+ // TODO(rmlarsen): FIXME: For now, this is just a copy of the CPU cost
+ // model.
+ const double kernel_size = m_kernelImpl.dimensions().TotalSize();
+ // We ignore the use of fused multiply-add.
+ const double convolve_compute_cost = TensorOpCost::AddCost<Scalar>() + TensorOpCost::MulCost<Scalar>();
+ const double firstIndex_compute_cost =
+ NumDims *
+ (2 * TensorOpCost::AddCost<Index>() + 2 * TensorOpCost::MulCost<Index>() + TensorOpCost::DivCost<Index>());
+ return TensorOpCost(0, 0, firstIndex_compute_cost, vectorized, PacketSize) +
+ kernel_size * (m_inputImpl.costPerCoeff(vectorized) + m_kernelImpl.costPerCoeff(vectorized) +
+ TensorOpCost(0, 0, convolve_compute_cost, vectorized, PacketSize));
+ }
+ // binding placeholder accessors to a command group handler for SYCL
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void bind(cl::sycl::handler &cgh) const {
+ m_kernelImpl.bind(cgh);
+ m_inputImpl.bind(cgh);
+ m_buf.bind(cgh);
+ m_kernel.bind(cgh);
+ }
+
+ private:
+ // No assignment (copies are needed by the kernels)
+ TensorEvaluator &operator=(const TensorEvaluator &);
+ TensorEvaluator<InputArgType, Eigen::SyclDevice> m_inputImpl;
+ KernelArgType m_kernelArg;
+ TensorEvaluator<KernelArgType, Eigen::SyclDevice> m_kernelImpl;
+ Indices m_indices;
+ Dimensions m_dimensions;
+ EvaluatorPointerType m_buf;
+ typename KernelStorage::Type m_kernel;
+ bool m_local_kernel;
+ const Eigen::SyclDevice EIGEN_DEVICE_REF m_device;
+}; // namespace Eigen
+
+} // end namespace Eigen
+
+#endif // EIGEN_CXX11_TENSOR_TENSOR_CONVOLUTION_H
diff --git a/unsupported/Eigen/CXX11/src/Tensor/TensorCostModel.h b/unsupported/Eigen/CXX11/src/Tensor/TensorCostModel.h
new file mode 100644
index 0000000..c3f4bdd
--- /dev/null
+++ b/unsupported/Eigen/CXX11/src/Tensor/TensorCostModel.h
@@ -0,0 +1,216 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2016 Rasmus Munk Larsen <rmlarsen@google.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_CXX11_TENSOR_TENSOR_COST_MODEL_H
+#define EIGEN_CXX11_TENSOR_TENSOR_COST_MODEL_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+/** \class TensorEvaluator
+ * \ingroup CXX11_Tensor_Module
+ *
+ * \brief A cost model used to limit the number of threads used for evaluating
+ * tensor expression.
+ *
+ */
+
+// Class storing the cost of evaluating a tensor expression in terms of the
+// estimated number of operand bytes loads, bytes stored, and compute cycles.
+class TensorOpCost {
+ public:
+ // TODO(rmlarsen): Fix the scalar op costs in Eigen proper. Even a simple
+ // model based on minimal reciprocal throughput numbers from Intel or
+ // Agner Fog's tables would be better than what is there now.
+ template <typename ArgType>
+ static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE int MulCost() {
+ return internal::functor_traits<
+ internal::scalar_product_op<ArgType, ArgType> >::Cost;
+ }
+ template <typename ArgType>
+ static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE int AddCost() {
+ return internal::functor_traits<internal::scalar_sum_op<ArgType> >::Cost;
+ }
+ template <typename ArgType>
+ static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE int DivCost() {
+ return internal::functor_traits<
+ internal::scalar_quotient_op<ArgType, ArgType> >::Cost;
+ }
+ template <typename ArgType>
+ static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE int ModCost() {
+ return internal::functor_traits<internal::scalar_mod_op<ArgType> >::Cost;
+ }
+ template <typename SrcType, typename TargetType>
+ static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE int CastCost() {
+ return internal::functor_traits<
+ internal::scalar_cast_op<SrcType, TargetType> >::Cost;
+ }
+
+ EIGEN_DEVICE_FUNC
+ TensorOpCost() : bytes_loaded_(0), bytes_stored_(0), compute_cycles_(0) {}
+ EIGEN_DEVICE_FUNC
+ TensorOpCost(double bytes_loaded, double bytes_stored, double compute_cycles)
+ : bytes_loaded_(bytes_loaded),
+ bytes_stored_(bytes_stored),
+ compute_cycles_(compute_cycles) {}
+
+ EIGEN_DEVICE_FUNC
+ TensorOpCost(double bytes_loaded, double bytes_stored, double compute_cycles,
+ bool vectorized, double packet_size)
+ : bytes_loaded_(bytes_loaded),
+ bytes_stored_(bytes_stored),
+ compute_cycles_(vectorized ? compute_cycles / packet_size
+ : compute_cycles) {
+ eigen_assert(bytes_loaded >= 0 && (numext::isfinite)(bytes_loaded));
+ eigen_assert(bytes_stored >= 0 && (numext::isfinite)(bytes_stored));
+ eigen_assert(compute_cycles >= 0 && (numext::isfinite)(compute_cycles));
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE double bytes_loaded() const {
+ return bytes_loaded_;
+ }
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE double bytes_stored() const {
+ return bytes_stored_;
+ }
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE double compute_cycles() const {
+ return compute_cycles_;
+ }
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE double total_cost(
+ double load_cost, double store_cost, double compute_cost) const {
+ return load_cost * bytes_loaded_ + store_cost * bytes_stored_ +
+ compute_cost * compute_cycles_;
+ }
+
+ // Drop memory access component. Intended for cases when memory accesses are
+ // sequential or are completely masked by computations.
+ EIGEN_DEVICE_FUNC void dropMemoryCost() {
+ bytes_loaded_ = 0;
+ bytes_stored_ = 0;
+ }
+
+ // TODO(rmlarsen): Define min in terms of total cost, not elementwise.
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorOpCost cwiseMin(
+ const TensorOpCost& rhs) const {
+ double bytes_loaded = numext::mini(bytes_loaded_, rhs.bytes_loaded());
+ double bytes_stored = numext::mini(bytes_stored_, rhs.bytes_stored());
+ double compute_cycles = numext::mini(compute_cycles_, rhs.compute_cycles());
+ return TensorOpCost(bytes_loaded, bytes_stored, compute_cycles);
+ }
+
+ // TODO(rmlarsen): Define max in terms of total cost, not elementwise.
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorOpCost cwiseMax(
+ const TensorOpCost& rhs) const {
+ double bytes_loaded = numext::maxi(bytes_loaded_, rhs.bytes_loaded());
+ double bytes_stored = numext::maxi(bytes_stored_, rhs.bytes_stored());
+ double compute_cycles = numext::maxi(compute_cycles_, rhs.compute_cycles());
+ return TensorOpCost(bytes_loaded, bytes_stored, compute_cycles);
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorOpCost& operator+=(
+ const TensorOpCost& rhs) {
+ bytes_loaded_ += rhs.bytes_loaded();
+ bytes_stored_ += rhs.bytes_stored();
+ compute_cycles_ += rhs.compute_cycles();
+ return *this;
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorOpCost& operator*=(double rhs) {
+ bytes_loaded_ *= rhs;
+ bytes_stored_ *= rhs;
+ compute_cycles_ *= rhs;
+ return *this;
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE friend TensorOpCost operator+(
+ TensorOpCost lhs, const TensorOpCost& rhs) {
+ lhs += rhs;
+ return lhs;
+ }
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE friend TensorOpCost operator*(
+ TensorOpCost lhs, double rhs) {
+ lhs *= rhs;
+ return lhs;
+ }
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE friend TensorOpCost operator*(
+ double lhs, TensorOpCost rhs) {
+ rhs *= lhs;
+ return rhs;
+ }
+
+ friend std::ostream& operator<<(std::ostream& os, const TensorOpCost& tc) {
+ return os << "[bytes_loaded = " << tc.bytes_loaded()
+ << ", bytes_stored = " << tc.bytes_stored()
+ << ", compute_cycles = " << tc.compute_cycles() << "]";
+ }
+
+ private:
+ double bytes_loaded_;
+ double bytes_stored_;
+ double compute_cycles_;
+};
+
+// TODO(rmlarsen): Implement a policy that chooses an "optimal" number of theads
+// in [1:max_threads] instead of just switching multi-threading off for small
+// work units.
+template <typename Device>
+class TensorCostModel {
+ public:
+ // Scaling from Eigen compute cost to device cycles.
+ static const int kDeviceCyclesPerComputeCycle = 1;
+
+ // Costs in device cycles.
+ static const int kStartupCycles = 100000;
+ static const int kPerThreadCycles = 100000;
+ static const int kTaskSize = 40000;
+
+ // Returns the number of threads in [1:max_threads] to use for
+ // evaluating an expression with the given output size and cost per
+ // coefficient.
+ static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE int numThreads(
+ double output_size, const TensorOpCost& cost_per_coeff, int max_threads) {
+ double cost = totalCost(output_size, cost_per_coeff);
+ double threads = (cost - kStartupCycles) / kPerThreadCycles + 0.9;
+ // Make sure we don't invoke undefined behavior when we convert to an int.
+ threads = numext::mini<double>(threads, GenericNumTraits<int>::highest());
+ return numext::mini(max_threads,
+ numext::maxi<int>(1, static_cast<int>(threads)));
+ }
+
+ // taskSize assesses parallel task size.
+ // Value of 1.0 means ideal parallel task size. Values < 1.0 mean that task
+ // granularity needs to be increased to mitigate parallelization overheads.
+ static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE double taskSize(
+ double output_size, const TensorOpCost& cost_per_coeff) {
+ return totalCost(output_size, cost_per_coeff) / kTaskSize;
+ }
+
+ static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE double totalCost(
+ double output_size, const TensorOpCost& cost_per_coeff) {
+ // Cost of memory fetches from L2 cache. 64 is typical cache line size.
+ // 11 is L2 cache latency on Haswell.
+ // We don't know whether data is in L1, L2 or L3. But we are most interested
+ // in single-threaded computational time around 100us-10ms (smaller time
+ // is too small for parallelization, larger time is not interesting
+ // either because we are probably using all available threads already).
+ // And for the target time range, L2 seems to be what matters. Data set
+ // fitting into L1 is too small to take noticeable time. Data set fitting
+ // only into L3 presumably will take more than 10ms to load and process.
+ const double kLoadCycles = 1.0 / 64 * 11;
+ const double kStoreCycles = 1.0 / 64 * 11;
+ // Scaling from Eigen compute cost to device cycles.
+ return output_size *
+ cost_per_coeff.total_cost(kLoadCycles, kStoreCycles,
+ kDeviceCyclesPerComputeCycle);
+ }
+};
+
+} // namespace Eigen
+
+#endif // EIGEN_CXX11_TENSOR_TENSOR_COST_MODEL_H
diff --git a/unsupported/Eigen/CXX11/src/Tensor/TensorCustomOp.h b/unsupported/Eigen/CXX11/src/Tensor/TensorCustomOp.h
new file mode 100644
index 0000000..0634be8
--- /dev/null
+++ b/unsupported/Eigen/CXX11/src/Tensor/TensorCustomOp.h
@@ -0,0 +1,349 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_CXX11_TENSOR_TENSOR_CUSTOM_OP_H
+#define EIGEN_CXX11_TENSOR_TENSOR_CUSTOM_OP_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+/** \class TensorCustomUnaryOp
+ * \ingroup CXX11_Tensor_Module
+ *
+ * \brief Tensor custom class.
+ *
+ *
+ */
+namespace internal {
+template<typename CustomUnaryFunc, typename XprType>
+struct traits<TensorCustomUnaryOp<CustomUnaryFunc, XprType> >
+{
+ typedef typename XprType::Scalar Scalar;
+ typedef typename XprType::StorageKind StorageKind;
+ typedef typename XprType::Index Index;
+ typedef typename XprType::Nested Nested;
+ typedef std::remove_reference_t<Nested> Nested_;
+ static constexpr int NumDimensions = traits<XprType>::NumDimensions;
+ static constexpr int Layout = traits<XprType>::Layout;
+ typedef typename traits<XprType>::PointerType PointerType;
+};
+
+template<typename CustomUnaryFunc, typename XprType>
+struct eval<TensorCustomUnaryOp<CustomUnaryFunc, XprType>, Eigen::Dense>
+{
+ typedef const TensorCustomUnaryOp<CustomUnaryFunc, XprType>EIGEN_DEVICE_REF type;
+};
+
+template<typename CustomUnaryFunc, typename XprType>
+struct nested<TensorCustomUnaryOp<CustomUnaryFunc, XprType> >
+{
+ typedef TensorCustomUnaryOp<CustomUnaryFunc, XprType> type;
+};
+
+} // end namespace internal
+
+
+
+template<typename CustomUnaryFunc, typename XprType>
+class TensorCustomUnaryOp : public TensorBase<TensorCustomUnaryOp<CustomUnaryFunc, XprType>, ReadOnlyAccessors>
+{
+ public:
+ typedef typename internal::traits<TensorCustomUnaryOp>::Scalar Scalar;
+ typedef typename Eigen::NumTraits<Scalar>::Real RealScalar;
+ typedef typename XprType::CoeffReturnType CoeffReturnType;
+ typedef typename internal::nested<TensorCustomUnaryOp>::type Nested;
+ typedef typename internal::traits<TensorCustomUnaryOp>::StorageKind StorageKind;
+ typedef typename internal::traits<TensorCustomUnaryOp>::Index Index;
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorCustomUnaryOp(const XprType& expr, const CustomUnaryFunc& func)
+ : m_expr(expr), m_func(func) {}
+
+ EIGEN_DEVICE_FUNC
+ const CustomUnaryFunc& func() const { return m_func; }
+
+ EIGEN_DEVICE_FUNC
+ const internal::remove_all_t<typename XprType::Nested>&
+ expression() const { return m_expr; }
+
+ protected:
+ typename XprType::Nested m_expr;
+ const CustomUnaryFunc m_func;
+};
+
+
+// Eval as rvalue
+template<typename CustomUnaryFunc, typename XprType, typename Device>
+struct TensorEvaluator<const TensorCustomUnaryOp<CustomUnaryFunc, XprType>, Device>
+{
+ typedef TensorCustomUnaryOp<CustomUnaryFunc, XprType> ArgType;
+ typedef typename internal::traits<ArgType>::Index Index;
+ static constexpr int NumDims = internal::traits<ArgType>::NumDimensions;
+ typedef DSizes<Index, NumDims> Dimensions;
+ typedef std::remove_const_t<typename ArgType::Scalar> Scalar;
+ typedef std::remove_const_t<typename XprType::CoeffReturnType> CoeffReturnType;
+ typedef typename PacketType<CoeffReturnType, Device>::type PacketReturnType;
+ static constexpr int PacketSize = PacketType<CoeffReturnType, Device>::size;
+ typedef typename Eigen::internal::traits<XprType>::PointerType TensorPointerType;
+ typedef StorageMemory<CoeffReturnType, Device> Storage;
+ typedef typename Storage::Type EvaluatorPointerType;
+
+ static constexpr int Layout = TensorEvaluator<XprType, Device>::Layout;
+ enum {
+ IsAligned = false,
+ PacketAccess = (PacketType<CoeffReturnType, Device>::size > 1),
+ BlockAccess = false,
+ PreferBlockAccess = false,
+ CoordAccess = false, // to be implemented
+ RawAccess = false
+ };
+
+ //===- Tensor block evaluation strategy (see TensorBlock.h) -------------===//
+ typedef internal::TensorBlockNotImplemented TensorBlock;
+ //===--------------------------------------------------------------------===//
+
+ EIGEN_STRONG_INLINE TensorEvaluator(const ArgType& op, const Device& device)
+ : m_op(op), m_device(device), m_result(NULL)
+ {
+ m_dimensions = op.func().dimensions(op.expression());
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Dimensions& dimensions() const { return m_dimensions; }
+
+ EIGEN_STRONG_INLINE bool evalSubExprsIfNeeded(EvaluatorPointerType data) {
+ if (data) {
+ evalTo(data);
+ return false;
+ } else {
+ m_result = static_cast<EvaluatorPointerType>(m_device.get( (CoeffReturnType*)
+ m_device.allocate_temp(dimensions().TotalSize() * sizeof(Scalar))));
+ evalTo(m_result);
+ return true;
+ }
+ }
+
+ EIGEN_STRONG_INLINE void cleanup() {
+ if (m_result) {
+ m_device.deallocate_temp(m_result);
+ m_result = NULL;
+ }
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE CoeffReturnType coeff(Index index) const {
+ return m_result[index];
+ }
+
+ template<int LoadMode>
+ EIGEN_DEVICE_FUNC PacketReturnType packet(Index index) const {
+ return internal::ploadt<PacketReturnType, LoadMode>(m_result + index);
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorOpCost costPerCoeff(bool vectorized) const {
+ // TODO(rmlarsen): Extend CustomOp API to return its cost estimate.
+ return TensorOpCost(sizeof(CoeffReturnType), 0, 0, vectorized, PacketSize);
+ }
+
+ EIGEN_DEVICE_FUNC EvaluatorPointerType data() const { return m_result; }
+
+#ifdef EIGEN_USE_SYCL
+ // binding placeholder accessors to a command group handler for SYCL
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void bind(cl::sycl::handler &cgh) const {
+ m_result.bind(cgh);
+ }
+#endif
+
+ protected:
+ void evalTo(EvaluatorPointerType data) {
+ TensorMap<Tensor<CoeffReturnType, NumDims, Layout, Index> > result(m_device.get(data), m_dimensions);
+ m_op.func().eval(m_op.expression(), result, m_device);
+ }
+
+ Dimensions m_dimensions;
+ const ArgType m_op;
+ const Device EIGEN_DEVICE_REF m_device;
+ EvaluatorPointerType m_result;
+};
+
+
+
+/** \class TensorCustomBinaryOp
+ * \ingroup CXX11_Tensor_Module
+ *
+ * \brief Tensor custom class.
+ *
+ *
+ */
+namespace internal {
+template<typename CustomBinaryFunc, typename LhsXprType, typename RhsXprType>
+struct traits<TensorCustomBinaryOp<CustomBinaryFunc, LhsXprType, RhsXprType> >
+{
+ typedef typename internal::promote_storage_type<typename LhsXprType::Scalar,
+ typename RhsXprType::Scalar>::ret Scalar;
+ typedef typename internal::promote_storage_type<typename LhsXprType::CoeffReturnType,
+ typename RhsXprType::CoeffReturnType>::ret CoeffReturnType;
+ typedef typename promote_storage_type<typename traits<LhsXprType>::StorageKind,
+ typename traits<RhsXprType>::StorageKind>::ret StorageKind;
+ typedef typename promote_index_type<typename traits<LhsXprType>::Index,
+ typename traits<RhsXprType>::Index>::type Index;
+ typedef typename LhsXprType::Nested LhsNested;
+ typedef typename RhsXprType::Nested RhsNested;
+ typedef std::remove_reference_t<LhsNested> LhsNested_;
+ typedef std::remove_reference_t<RhsNested> RhsNested_;
+ static constexpr int NumDimensions = traits<LhsXprType>::NumDimensions;
+ static constexpr int Layout = traits<LhsXprType>::Layout;
+ typedef std::conditional_t<Pointer_type_promotion<typename LhsXprType::Scalar, Scalar>::val,
+ typename traits<LhsXprType>::PointerType, typename traits<RhsXprType>::PointerType> PointerType;
+};
+
+template<typename CustomBinaryFunc, typename LhsXprType, typename RhsXprType>
+struct eval<TensorCustomBinaryOp<CustomBinaryFunc, LhsXprType, RhsXprType>, Eigen::Dense>
+{
+ typedef const TensorCustomBinaryOp<CustomBinaryFunc, LhsXprType, RhsXprType>& type;
+};
+
+template<typename CustomBinaryFunc, typename LhsXprType, typename RhsXprType>
+struct nested<TensorCustomBinaryOp<CustomBinaryFunc, LhsXprType, RhsXprType> >
+{
+ typedef TensorCustomBinaryOp<CustomBinaryFunc, LhsXprType, RhsXprType> type;
+};
+
+} // end namespace internal
+
+
+
+template<typename CustomBinaryFunc, typename LhsXprType, typename RhsXprType>
+class TensorCustomBinaryOp : public TensorBase<TensorCustomBinaryOp<CustomBinaryFunc, LhsXprType, RhsXprType>, ReadOnlyAccessors>
+{
+ public:
+ typedef typename internal::traits<TensorCustomBinaryOp>::Scalar Scalar;
+ typedef typename Eigen::NumTraits<Scalar>::Real RealScalar;
+ typedef typename internal::traits<TensorCustomBinaryOp>::CoeffReturnType CoeffReturnType;
+ typedef typename internal::nested<TensorCustomBinaryOp>::type Nested;
+ typedef typename internal::traits<TensorCustomBinaryOp>::StorageKind StorageKind;
+ typedef typename internal::traits<TensorCustomBinaryOp>::Index Index;
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorCustomBinaryOp(const LhsXprType& lhs, const RhsXprType& rhs, const CustomBinaryFunc& func)
+
+ : m_lhs_xpr(lhs), m_rhs_xpr(rhs), m_func(func) {}
+
+ EIGEN_DEVICE_FUNC
+ const CustomBinaryFunc& func() const { return m_func; }
+
+ EIGEN_DEVICE_FUNC
+ const internal::remove_all_t<typename LhsXprType::Nested>&
+ lhsExpression() const { return m_lhs_xpr; }
+
+ EIGEN_DEVICE_FUNC
+ const internal::remove_all_t<typename RhsXprType::Nested>&
+ rhsExpression() const { return m_rhs_xpr; }
+
+ protected:
+ typename LhsXprType::Nested m_lhs_xpr;
+ typename RhsXprType::Nested m_rhs_xpr;
+ const CustomBinaryFunc m_func;
+};
+
+
+// Eval as rvalue
+template<typename CustomBinaryFunc, typename LhsXprType, typename RhsXprType, typename Device>
+struct TensorEvaluator<const TensorCustomBinaryOp<CustomBinaryFunc, LhsXprType, RhsXprType>, Device>
+{
+ typedef TensorCustomBinaryOp<CustomBinaryFunc, LhsXprType, RhsXprType> XprType;
+ typedef typename internal::traits<XprType>::Index Index;
+ static constexpr int NumDims = internal::traits<XprType>::NumDimensions;
+ typedef DSizes<Index, NumDims> Dimensions;
+ typedef typename XprType::Scalar Scalar;
+ typedef std::remove_const_t<typename XprType::CoeffReturnType> CoeffReturnType;
+ typedef typename PacketType<CoeffReturnType, Device>::type PacketReturnType;
+ static constexpr int PacketSize = PacketType<CoeffReturnType, Device>::size;
+
+ typedef typename Eigen::internal::traits<XprType>::PointerType TensorPointerType;
+ typedef StorageMemory<CoeffReturnType, Device> Storage;
+ typedef typename Storage::Type EvaluatorPointerType;
+
+ static constexpr int Layout = TensorEvaluator<LhsXprType, Device>::Layout;
+ enum {
+ IsAligned = false,
+ PacketAccess = (PacketType<CoeffReturnType, Device>::size > 1),
+ BlockAccess = false,
+ PreferBlockAccess = false,
+ CoordAccess = false, // to be implemented
+ RawAccess = false
+ };
+
+ //===- Tensor block evaluation strategy (see TensorBlock.h) -------------===//
+ typedef internal::TensorBlockNotImplemented TensorBlock;
+ //===--------------------------------------------------------------------===//
+
+ EIGEN_STRONG_INLINE TensorEvaluator(const XprType& op, const Device& device)
+ : m_op(op), m_device(device), m_result(NULL)
+ {
+ m_dimensions = op.func().dimensions(op.lhsExpression(), op.rhsExpression());
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Dimensions& dimensions() const { return m_dimensions; }
+
+ EIGEN_STRONG_INLINE bool evalSubExprsIfNeeded(EvaluatorPointerType data) {
+ if (data) {
+ evalTo(data);
+ return false;
+ } else {
+ m_result = static_cast<EvaluatorPointerType>(m_device.get( (CoeffReturnType*)
+ m_device.allocate_temp(dimensions().TotalSize() * sizeof(CoeffReturnType))));
+ evalTo(m_result);
+ return true;
+ }
+ }
+
+ EIGEN_STRONG_INLINE void cleanup() {
+ if (m_result != NULL) {
+ m_device.deallocate_temp(m_result);
+ m_result = NULL;
+ }
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE CoeffReturnType coeff(Index index) const {
+ return m_result[index];
+ }
+
+ template<int LoadMode>
+ EIGEN_DEVICE_FUNC PacketReturnType packet(Index index) const {
+ return internal::ploadt<PacketReturnType, LoadMode>(m_result + index);
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorOpCost costPerCoeff(bool vectorized) const {
+ // TODO(rmlarsen): Extend CustomOp API to return its cost estimate.
+ return TensorOpCost(sizeof(CoeffReturnType), 0, 0, vectorized, PacketSize);
+ }
+
+ EIGEN_DEVICE_FUNC EvaluatorPointerType data() const { return m_result; }
+
+#ifdef EIGEN_USE_SYCL
+ // binding placeholder accessors to a command group handler for SYCL
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void bind(cl::sycl::handler &cgh) const {
+ m_result.bind(cgh);
+ }
+#endif
+
+ protected:
+ void evalTo(EvaluatorPointerType data) {
+ TensorMap<Tensor<CoeffReturnType, NumDims, Layout> > result(m_device.get(data), m_dimensions);
+ m_op.func().eval(m_op.lhsExpression(), m_op.rhsExpression(), result, m_device);
+ }
+
+ Dimensions m_dimensions;
+ const XprType m_op;
+ const Device EIGEN_DEVICE_REF m_device;
+ EvaluatorPointerType m_result;
+};
+
+
+} // end namespace Eigen
+
+#endif // EIGEN_CXX11_TENSOR_TENSOR_CUSTOM_OP_H
diff --git a/unsupported/Eigen/CXX11/src/Tensor/TensorDevice.h b/unsupported/Eigen/CXX11/src/Tensor/TensorDevice.h
new file mode 100644
index 0000000..8148441
--- /dev/null
+++ b/unsupported/Eigen/CXX11/src/Tensor/TensorDevice.h
@@ -0,0 +1,139 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_CXX11_TENSOR_TENSOR_DEVICE_H
+#define EIGEN_CXX11_TENSOR_TENSOR_DEVICE_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+/** \class TensorDevice
+ * \ingroup CXX11_Tensor_Module
+ *
+ * \brief Pseudo expression providing an operator = that will evaluate its argument
+ * on the specified computing 'device' (GPU, thread pool, ...)
+ *
+ * Example:
+ * C.device(EIGEN_GPU) = A + B;
+ *
+ * Todo: operator *= and /=.
+ */
+
+template <typename ExpressionType, typename DeviceType> class TensorDevice {
+ public:
+ TensorDevice(const DeviceType& device, ExpressionType& expression) : m_device(device), m_expression(expression) {}
+
+ EIGEN_DEFAULT_COPY_CONSTRUCTOR(TensorDevice)
+
+ template<typename OtherDerived>
+ EIGEN_STRONG_INLINE TensorDevice& operator=(const OtherDerived& other) {
+ typedef TensorAssignOp<ExpressionType, const OtherDerived> Assign;
+ Assign assign(m_expression, other);
+ internal::TensorExecutor<const Assign, DeviceType>::run(assign, m_device);
+ return *this;
+ }
+
+ template<typename OtherDerived>
+ EIGEN_STRONG_INLINE TensorDevice& operator+=(const OtherDerived& other) {
+ typedef typename OtherDerived::Scalar Scalar;
+ typedef TensorCwiseBinaryOp<internal::scalar_sum_op<Scalar>, const ExpressionType, const OtherDerived> Sum;
+ Sum sum(m_expression, other);
+ typedef TensorAssignOp<ExpressionType, const Sum> Assign;
+ Assign assign(m_expression, sum);
+ internal::TensorExecutor<const Assign, DeviceType>::run(assign, m_device);
+ return *this;
+ }
+
+ template<typename OtherDerived>
+ EIGEN_STRONG_INLINE TensorDevice& operator-=(const OtherDerived& other) {
+ typedef typename OtherDerived::Scalar Scalar;
+ typedef TensorCwiseBinaryOp<internal::scalar_difference_op<Scalar>, const ExpressionType, const OtherDerived> Difference;
+ Difference difference(m_expression, other);
+ typedef TensorAssignOp<ExpressionType, const Difference> Assign;
+ Assign assign(m_expression, difference);
+ internal::TensorExecutor<const Assign, DeviceType>::run(assign, m_device);
+ return *this;
+ }
+
+ protected:
+ const DeviceType& m_device;
+ ExpressionType& m_expression;
+};
+
+/** \class TensorAsyncDevice
+ * \ingroup CXX11_Tensor_Module
+ *
+ * \brief Pseudo expression providing an operator = that will evaluate its
+ * argument asynchronously on the specified device. Currently only
+ * ThreadPoolDevice implements proper asynchronous execution, while the default
+ * and GPU devices just run the expression synchronously and call m_done() on
+ * completion..
+ *
+ * Example:
+ * auto done = []() { ... expression evaluation done ... };
+ * C.device(thread_pool_device, std::move(done)) = A + B;
+ */
+
+template <typename ExpressionType, typename DeviceType, typename DoneCallback>
+class TensorAsyncDevice {
+ public:
+ TensorAsyncDevice(const DeviceType& device, ExpressionType& expression,
+ DoneCallback done)
+ : m_device(device), m_expression(expression), m_done(std::move(done)) {}
+
+ template <typename OtherDerived>
+ EIGEN_STRONG_INLINE TensorAsyncDevice& operator=(const OtherDerived& other) {
+ typedef TensorAssignOp<ExpressionType, const OtherDerived> Assign;
+ typedef internal::TensorExecutor<const Assign, DeviceType> Executor;
+
+ Assign assign(m_expression, other);
+ Executor::run(assign, m_device);
+ m_done();
+
+ return *this;
+ }
+
+ protected:
+ const DeviceType& m_device;
+ ExpressionType& m_expression;
+ DoneCallback m_done;
+};
+
+
+#ifdef EIGEN_USE_THREADS
+template <typename ExpressionType, typename DoneCallback>
+class TensorAsyncDevice<ExpressionType, ThreadPoolDevice, DoneCallback> {
+ public:
+ TensorAsyncDevice(const ThreadPoolDevice& device, ExpressionType& expression,
+ DoneCallback done)
+ : m_device(device), m_expression(expression), m_done(std::move(done)) {}
+
+ template <typename OtherDerived>
+ EIGEN_STRONG_INLINE TensorAsyncDevice& operator=(const OtherDerived& other) {
+ typedef TensorAssignOp<ExpressionType, const OtherDerived> Assign;
+ typedef internal::TensorAsyncExecutor<const Assign, ThreadPoolDevice, DoneCallback> Executor;
+
+ // WARNING: After assignment 'm_done' callback will be in undefined state.
+ Assign assign(m_expression, other);
+ Executor::runAsync(assign, m_device, std::move(m_done));
+
+ return *this;
+ }
+
+ protected:
+ const ThreadPoolDevice& m_device;
+ ExpressionType& m_expression;
+ DoneCallback m_done;
+};
+#endif
+
+} // end namespace Eigen
+
+#endif // EIGEN_CXX11_TENSOR_TENSOR_DEVICE_H
diff --git a/unsupported/Eigen/CXX11/src/Tensor/TensorDeviceCuda.h b/unsupported/Eigen/CXX11/src/Tensor/TensorDeviceCuda.h
new file mode 100644
index 0000000..f779239
--- /dev/null
+++ b/unsupported/Eigen/CXX11/src/Tensor/TensorDeviceCuda.h
@@ -0,0 +1,6 @@
+
+#if defined(__clang__) || defined(__GNUC__)
+#warning "Deprecated header file, please either include the main Eigen/CXX11/Tensor header or the respective TensorDeviceGpu.h file"
+#endif
+
+#include "TensorDeviceGpu.h"
diff --git a/unsupported/Eigen/CXX11/src/Tensor/TensorDeviceDefault.h b/unsupported/Eigen/CXX11/src/Tensor/TensorDeviceDefault.h
new file mode 100644
index 0000000..d9a3d32
--- /dev/null
+++ b/unsupported/Eigen/CXX11/src/Tensor/TensorDeviceDefault.h
@@ -0,0 +1,117 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_CXX11_TENSOR_TENSOR_DEVICE_DEFAULT_H
+#define EIGEN_CXX11_TENSOR_TENSOR_DEVICE_DEFAULT_H
+
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+// Default device for the machine (typically a single cpu core)
+struct DefaultDevice {
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void* allocate(size_t num_bytes) const {
+ return internal::aligned_malloc(num_bytes);
+ }
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void deallocate(void* buffer) const {
+ internal::aligned_free(buffer);
+ }
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void* allocate_temp(size_t num_bytes) const {
+ return allocate(num_bytes);
+ }
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void deallocate_temp(void* buffer) const {
+ deallocate(buffer);
+ }
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void memcpy(void* dst, const void* src, size_t n) const {
+ ::memcpy(dst, src, n);
+ }
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void memcpyHostToDevice(void* dst, const void* src, size_t n) const {
+ memcpy(dst, src, n);
+ }
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void memcpyDeviceToHost(void* dst, const void* src, size_t n) const {
+ memcpy(dst, src, n);
+ }
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void memset(void* buffer, int c, size_t n) const {
+ ::memset(buffer, c, n);
+ }
+ template<typename T>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void fill(T* begin, T* end, const T& value) const {
+#ifdef EIGEN_GPU_COMPILE_PHASE
+ // std::fill is not a device function, so resort to simple loop.
+ for (T* it = begin; it != end; ++it) {
+ *it = value;
+ }
+#else
+ std::fill(begin, end, value);
+#endif
+ }
+ template<typename Type>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Type get(Type data) const {
+ return data;
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE size_t numThreads() const {
+#if !defined(EIGEN_GPU_COMPILE_PHASE)
+ // Running on the host CPU
+ return 1;
+#elif defined(EIGEN_HIP_DEVICE_COMPILE)
+ // Running on a HIP device
+ return 64;
+#else
+ // Running on a CUDA device
+ return 32;
+#endif
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE size_t firstLevelCacheSize() const {
+#if !defined(EIGEN_GPU_COMPILE_PHASE) && !defined(SYCL_DEVICE_ONLY)
+ // Running on the host CPU
+ return l1CacheSize();
+#elif defined(EIGEN_HIP_DEVICE_COMPILE)
+ // Running on a HIP device
+ return 48*1024; // FIXME : update this number for HIP
+#else
+ // Running on a CUDA device, return the amount of shared memory available.
+ return 48*1024;
+#endif
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE size_t lastLevelCacheSize() const {
+#if !defined(EIGEN_GPU_COMPILE_PHASE) && !defined(SYCL_DEVICE_ONLY)
+ // Running single threaded on the host CPU
+ return l3CacheSize();
+#elif defined(EIGEN_HIP_DEVICE_COMPILE)
+ // Running on a HIP device
+ return firstLevelCacheSize(); // FIXME : update this number for HIP
+#else
+ // Running on a CUDA device
+ return firstLevelCacheSize();
+#endif
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE int majorDeviceVersion() const {
+#if !defined(EIGEN_GPU_COMPILE_PHASE)
+ // Running single threaded on the host CPU
+ // Should return an enum that encodes the ISA supported by the CPU
+ return 1;
+#elif defined(EIGEN_HIP_DEVICE_COMPILE)
+ // Running on a HIP device
+ // return 1 as major for HIP
+ return 1;
+#else
+ // Running on a CUDA device
+ return EIGEN_CUDA_ARCH / 100;
+#endif
+ }
+};
+
+} // namespace Eigen
+
+#endif // EIGEN_CXX11_TENSOR_TENSOR_DEVICE_DEFAULT_H
diff --git a/unsupported/Eigen/CXX11/src/Tensor/TensorDeviceGpu.h b/unsupported/Eigen/CXX11/src/Tensor/TensorDeviceGpu.h
new file mode 100644
index 0000000..8ea1bf0
--- /dev/null
+++ b/unsupported/Eigen/CXX11/src/Tensor/TensorDeviceGpu.h
@@ -0,0 +1,442 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#if defined(EIGEN_USE_GPU) && !defined(EIGEN_CXX11_TENSOR_TENSOR_DEVICE_GPU_H)
+#define EIGEN_CXX11_TENSOR_TENSOR_DEVICE_GPU_H
+
+// This header file container defines fo gpu* macros which will resolve to
+// their equivalent hip* or cuda* versions depending on the compiler in use
+// A separate header (included at the end of this file) will undefine all
+#include "TensorGpuHipCudaDefines.h"
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+static const int kGpuScratchSize = 1024;
+
+// This defines an interface that GPUDevice can take to use
+// HIP / CUDA streams underneath.
+class StreamInterface {
+ public:
+ virtual ~StreamInterface() {}
+
+ virtual const gpuStream_t& stream() const = 0;
+ virtual const gpuDeviceProp_t& deviceProperties() const = 0;
+
+ // Allocate memory on the actual device where the computation will run
+ virtual void* allocate(size_t num_bytes) const = 0;
+ virtual void deallocate(void* buffer) const = 0;
+
+ // Return a scratchpad buffer of size 1k
+ virtual void* scratchpad() const = 0;
+
+ // Return a semaphore. The semaphore is initially initialized to 0, and
+ // each kernel using it is responsible for resetting to 0 upon completion
+ // to maintain the invariant that the semaphore is always equal to 0 upon
+ // each kernel start.
+ virtual unsigned int* semaphore() const = 0;
+};
+
+class GpuDeviceProperties {
+ public:
+ GpuDeviceProperties() :
+ initialized_(false), first_(true), device_properties_(nullptr) {}
+
+ ~GpuDeviceProperties() {
+ if (device_properties_) {
+ delete[] device_properties_;
+ }
+ }
+
+ EIGEN_STRONG_INLINE const gpuDeviceProp_t& get(int device) const {
+ return device_properties_[device];
+ }
+
+ EIGEN_STRONG_INLINE bool isInitialized() const {
+ return initialized_;
+ }
+
+ void initialize() {
+ if (!initialized_) {
+ // Attempts to ensure proper behavior in the case of multiple threads
+ // calling this function simultaneously. This would be trivial to
+ // implement if we could use std::mutex, but unfortunately mutex don't
+ // compile with nvcc, so we resort to atomics and thread fences instead.
+ // Note that if the caller uses a compiler that doesn't support c++11 we
+ // can't ensure that the initialization is thread safe.
+ if (first_.exchange(false)) {
+ // We're the first thread to reach this point.
+ int num_devices;
+ gpuError_t status = gpuGetDeviceCount(&num_devices);
+ if (status != gpuSuccess) {
+ std::cerr << "Failed to get the number of GPU devices: "
+ << gpuGetErrorString(status)
+ << std::endl;
+ gpu_assert(status == gpuSuccess);
+ }
+ device_properties_ = new gpuDeviceProp_t[num_devices];
+ for (int i = 0; i < num_devices; ++i) {
+ status = gpuGetDeviceProperties(&device_properties_[i], i);
+ if (status != gpuSuccess) {
+ std::cerr << "Failed to initialize GPU device #"
+ << i
+ << ": "
+ << gpuGetErrorString(status)
+ << std::endl;
+ gpu_assert(status == gpuSuccess);
+ }
+ }
+
+ std::atomic_thread_fence(std::memory_order_release);
+ initialized_ = true;
+ } else {
+ // Wait for the other thread to inititialize the properties.
+ while (!initialized_) {
+ std::atomic_thread_fence(std::memory_order_acquire);
+ std::this_thread::sleep_for(std::chrono::milliseconds(1000));
+ }
+ }
+ }
+ }
+
+ private:
+ volatile bool initialized_;
+ std::atomic<bool> first_;
+ gpuDeviceProp_t* device_properties_;
+};
+
+EIGEN_ALWAYS_INLINE const GpuDeviceProperties& GetGpuDeviceProperties() {
+ static GpuDeviceProperties* deviceProperties = new GpuDeviceProperties();
+ if (!deviceProperties->isInitialized()) {
+ deviceProperties->initialize();
+ }
+ return *deviceProperties;
+}
+
+EIGEN_ALWAYS_INLINE const gpuDeviceProp_t& GetGpuDeviceProperties(int device) {
+ return GetGpuDeviceProperties().get(device);
+}
+
+static const gpuStream_t default_stream = gpuStreamDefault;
+
+class GpuStreamDevice : public StreamInterface {
+ public:
+ // Use the default stream on the current device
+ GpuStreamDevice() : stream_(&default_stream), scratch_(NULL), semaphore_(NULL) {
+ gpuError_t status = gpuGetDevice(&device_);
+ if (status != gpuSuccess) {
+ std::cerr << "Failed to get the GPU devices "
+ << gpuGetErrorString(status)
+ << std::endl;
+ gpu_assert(status == gpuSuccess);
+ }
+ }
+ // Use the default stream on the specified device
+ GpuStreamDevice(int device) : stream_(&default_stream), device_(device), scratch_(NULL), semaphore_(NULL) {}
+ // Use the specified stream. Note that it's the
+ // caller responsibility to ensure that the stream can run on
+ // the specified device. If no device is specified the code
+ // assumes that the stream is associated to the current gpu device.
+ GpuStreamDevice(const gpuStream_t* stream, int device = -1)
+ : stream_(stream), device_(device), scratch_(NULL), semaphore_(NULL) {
+ if (device < 0) {
+ gpuError_t status = gpuGetDevice(&device_);
+ if (status != gpuSuccess) {
+ std::cerr << "Failed to get the GPU devices "
+ << gpuGetErrorString(status)
+ << std::endl;
+ gpu_assert(status == gpuSuccess);
+ }
+ } else {
+ int num_devices;
+ gpuError_t err = gpuGetDeviceCount(&num_devices);
+ EIGEN_UNUSED_VARIABLE(err)
+ gpu_assert(err == gpuSuccess);
+ gpu_assert(device < num_devices);
+ device_ = device;
+ }
+ }
+
+ virtual ~GpuStreamDevice() {
+ if (scratch_) {
+ deallocate(scratch_);
+ }
+ }
+
+ const gpuStream_t& stream() const { return *stream_; }
+ const gpuDeviceProp_t& deviceProperties() const {
+ return GetGpuDeviceProperties(device_);
+ }
+ virtual void* allocate(size_t num_bytes) const {
+ gpuError_t err = gpuSetDevice(device_);
+ EIGEN_UNUSED_VARIABLE(err)
+ gpu_assert(err == gpuSuccess);
+ void* result;
+ err = gpuMalloc(&result, num_bytes);
+ gpu_assert(err == gpuSuccess);
+ gpu_assert(result != NULL);
+ return result;
+ }
+ virtual void deallocate(void* buffer) const {
+ gpuError_t err = gpuSetDevice(device_);
+ EIGEN_UNUSED_VARIABLE(err)
+ gpu_assert(err == gpuSuccess);
+ gpu_assert(buffer != NULL);
+ err = gpuFree(buffer);
+ gpu_assert(err == gpuSuccess);
+ }
+
+ virtual void* scratchpad() const {
+ if (scratch_ == NULL) {
+ scratch_ = allocate(kGpuScratchSize + sizeof(unsigned int));
+ }
+ return scratch_;
+ }
+
+ virtual unsigned int* semaphore() const {
+ if (semaphore_ == NULL) {
+ char* scratch = static_cast<char*>(scratchpad()) + kGpuScratchSize;
+ semaphore_ = reinterpret_cast<unsigned int*>(scratch);
+ gpuError_t err = gpuMemsetAsync(semaphore_, 0, sizeof(unsigned int), *stream_);
+ EIGEN_UNUSED_VARIABLE(err)
+ gpu_assert(err == gpuSuccess);
+ }
+ return semaphore_;
+ }
+
+ private:
+ const gpuStream_t* stream_;
+ int device_;
+ mutable void* scratch_;
+ mutable unsigned int* semaphore_;
+};
+
+struct GpuDevice {
+ // The StreamInterface is not owned: the caller is
+ // responsible for its initialization and eventual destruction.
+ explicit GpuDevice(const StreamInterface* stream) : stream_(stream), max_blocks_(INT_MAX) {
+ eigen_assert(stream);
+ }
+ explicit GpuDevice(const StreamInterface* stream, int num_blocks) : stream_(stream), max_blocks_(num_blocks) {
+ eigen_assert(stream);
+ }
+ // TODO(bsteiner): This is an internal API, we should not expose it.
+ EIGEN_STRONG_INLINE const gpuStream_t& stream() const {
+ return stream_->stream();
+ }
+
+ EIGEN_STRONG_INLINE void* allocate(size_t num_bytes) const {
+ return stream_->allocate(num_bytes);
+ }
+
+ EIGEN_STRONG_INLINE void deallocate(void* buffer) const {
+ stream_->deallocate(buffer);
+ }
+
+ EIGEN_STRONG_INLINE void* allocate_temp(size_t num_bytes) const {
+ return stream_->allocate(num_bytes);
+ }
+
+ EIGEN_STRONG_INLINE void deallocate_temp(void* buffer) const {
+ stream_->deallocate(buffer);
+ }
+
+ template<typename Type>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Type get(Type data) const {
+ return data;
+ }
+
+ EIGEN_STRONG_INLINE void* scratchpad() const {
+ return stream_->scratchpad();
+ }
+
+ EIGEN_STRONG_INLINE unsigned int* semaphore() const {
+ return stream_->semaphore();
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void memcpy(void* dst, const void* src, size_t n) const {
+#ifndef EIGEN_GPU_COMPILE_PHASE
+ gpuError_t err = gpuMemcpyAsync(dst, src, n, gpuMemcpyDeviceToDevice,
+ stream_->stream());
+ EIGEN_UNUSED_VARIABLE(err)
+ gpu_assert(err == gpuSuccess);
+#else
+ EIGEN_UNUSED_VARIABLE(dst);
+ EIGEN_UNUSED_VARIABLE(src);
+ EIGEN_UNUSED_VARIABLE(n);
+ eigen_assert(false && "The default device should be used instead to generate kernel code");
+#endif
+ }
+
+ EIGEN_STRONG_INLINE void memcpyHostToDevice(void* dst, const void* src, size_t n) const {
+ gpuError_t err =
+ gpuMemcpyAsync(dst, src, n, gpuMemcpyHostToDevice, stream_->stream());
+ EIGEN_UNUSED_VARIABLE(err)
+ gpu_assert(err == gpuSuccess);
+ }
+
+ EIGEN_STRONG_INLINE void memcpyDeviceToHost(void* dst, const void* src, size_t n) const {
+ gpuError_t err =
+ gpuMemcpyAsync(dst, src, n, gpuMemcpyDeviceToHost, stream_->stream());
+ EIGEN_UNUSED_VARIABLE(err)
+ gpu_assert(err == gpuSuccess);
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void memset(void* buffer, int c, size_t n) const {
+#ifndef EIGEN_GPU_COMPILE_PHASE
+ gpuError_t err = gpuMemsetAsync(buffer, c, n, stream_->stream());
+ EIGEN_UNUSED_VARIABLE(err)
+ gpu_assert(err == gpuSuccess);
+#else
+ EIGEN_UNUSED_VARIABLE(buffer)
+ EIGEN_UNUSED_VARIABLE(c)
+ EIGEN_UNUSED_VARIABLE(n)
+ eigen_assert(false && "The default device should be used instead to generate kernel code");
+#endif
+ }
+
+ template<typename T>
+ EIGEN_STRONG_INLINE void fill(T* begin, T* end, const T& value) const {
+#ifndef EIGEN_GPU_COMPILE_PHASE
+ const size_t count = end - begin;
+ // Split value into bytes and run memset with stride.
+ const int value_size = sizeof(value);
+ char* buffer = (char*)begin;
+ char* value_bytes = (char*)(&value);
+ gpuError_t err;
+ EIGEN_UNUSED_VARIABLE(err)
+
+ // If all value bytes are equal, then a single memset can be much faster.
+ bool use_single_memset = true;
+ for (int i=1; i<value_size; ++i) {
+ if (value_bytes[i] != value_bytes[0]) {
+ use_single_memset = false;
+ }
+ }
+
+ if (use_single_memset) {
+ err = gpuMemsetAsync(buffer, value_bytes[0], count * sizeof(T), stream_->stream());
+ gpu_assert(err == gpuSuccess);
+ } else {
+ for (int b=0; b<value_size; ++b) {
+ err = gpuMemset2DAsync(buffer+b, value_size, value_bytes[b], 1, count, stream_->stream());
+ gpu_assert(err == gpuSuccess);
+ }
+ }
+#else
+ EIGEN_UNUSED_VARIABLE(begin)
+ EIGEN_UNUSED_VARIABLE(end)
+ EIGEN_UNUSED_VARIABLE(value)
+ eigen_assert(false && "The default device should be used instead to generate kernel code");
+#endif
+ }
+
+ EIGEN_STRONG_INLINE size_t numThreads() const {
+ // FIXME
+ return 32;
+ }
+
+ EIGEN_STRONG_INLINE size_t firstLevelCacheSize() const {
+ // FIXME
+ return 48*1024;
+ }
+
+ EIGEN_STRONG_INLINE size_t lastLevelCacheSize() const {
+ // We won't try to take advantage of the l2 cache for the time being, and
+ // there is no l3 cache on hip/cuda devices.
+ return firstLevelCacheSize();
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void synchronize() const {
+#ifndef EIGEN_GPU_COMPILE_PHASE
+ gpuError_t err = gpuStreamSynchronize(stream_->stream());
+ if (err != gpuSuccess) {
+ std::cerr << "Error detected in GPU stream: "
+ << gpuGetErrorString(err)
+ << std::endl;
+ gpu_assert(err == gpuSuccess);
+ }
+#else
+ gpu_assert(false && "The default device should be used instead to generate kernel code");
+#endif
+ }
+
+ EIGEN_STRONG_INLINE int getNumGpuMultiProcessors() const {
+ return stream_->deviceProperties().multiProcessorCount;
+ }
+ EIGEN_STRONG_INLINE int maxGpuThreadsPerBlock() const {
+ return stream_->deviceProperties().maxThreadsPerBlock;
+ }
+ EIGEN_STRONG_INLINE int maxGpuThreadsPerMultiProcessor() const {
+ return stream_->deviceProperties().maxThreadsPerMultiProcessor;
+ }
+ EIGEN_STRONG_INLINE int sharedMemPerBlock() const {
+ return stream_->deviceProperties().sharedMemPerBlock;
+ }
+ EIGEN_STRONG_INLINE int majorDeviceVersion() const {
+ return stream_->deviceProperties().major;
+ }
+ EIGEN_STRONG_INLINE int minorDeviceVersion() const {
+ return stream_->deviceProperties().minor;
+ }
+
+ EIGEN_STRONG_INLINE int maxBlocks() const {
+ return max_blocks_;
+ }
+
+ // This function checks if the GPU runtime recorded an error for the
+ // underlying stream device.
+ inline bool ok() const {
+#ifdef EIGEN_GPUCC
+ gpuError_t error = gpuStreamQuery(stream_->stream());
+ return (error == gpuSuccess) || (error == gpuErrorNotReady);
+#else
+ return false;
+#endif
+ }
+
+ private:
+ const StreamInterface* stream_;
+ int max_blocks_;
+};
+
+#if defined(EIGEN_HIPCC)
+
+#define LAUNCH_GPU_KERNEL(kernel, gridsize, blocksize, sharedmem, device, ...) \
+ hipLaunchKernelGGL(kernel, dim3(gridsize), dim3(blocksize), (sharedmem), (device).stream(), __VA_ARGS__); \
+ gpu_assert(hipGetLastError() == hipSuccess);
+
+#else
+
+#define LAUNCH_GPU_KERNEL(kernel, gridsize, blocksize, sharedmem, device, ...) \
+ (kernel) <<< (gridsize), (blocksize), (sharedmem), (device).stream() >>> (__VA_ARGS__); \
+ gpu_assert(cudaGetLastError() == cudaSuccess);
+
+#endif
+
+// FIXME: Should be device and kernel specific.
+#ifdef EIGEN_GPUCC
+static EIGEN_DEVICE_FUNC inline void setGpuSharedMemConfig(gpuSharedMemConfig config) {
+#ifndef EIGEN_GPU_COMPILE_PHASE
+ gpuError_t status = gpuDeviceSetSharedMemConfig(config);
+ EIGEN_UNUSED_VARIABLE(status)
+ gpu_assert(status == gpuSuccess);
+#else
+ EIGEN_UNUSED_VARIABLE(config)
+#endif
+}
+#endif
+
+} // end namespace Eigen
+
+// undefine all the gpu* macros we defined at the beginning of the file
+#include "TensorGpuHipCudaUndefines.h"
+
+#endif // EIGEN_CXX11_TENSOR_TENSOR_DEVICE_GPU_H
diff --git a/unsupported/Eigen/CXX11/src/Tensor/TensorDeviceSycl.h b/unsupported/Eigen/CXX11/src/Tensor/TensorDeviceSycl.h
new file mode 100644
index 0000000..84ebe38
--- /dev/null
+++ b/unsupported/Eigen/CXX11/src/Tensor/TensorDeviceSycl.h
@@ -0,0 +1,1114 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Mehdi Goli Codeplay Software Ltd.
+// Ralph Potter Codeplay Software Ltd.
+// Luke Iwanski Codeplay Software Ltd.
+// Contact: <eigen@codeplay.com>
+// Copyright (C) 2016 Benoit Steiner <benoit.steiner.goog@gmail.com>
+
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#if defined(EIGEN_USE_SYCL) && !defined(EIGEN_CXX11_TENSOR_TENSOR_DEVICE_SYCL_H)
+#define EIGEN_CXX11_TENSOR_TENSOR_DEVICE_SYCL_H
+#include <unordered_set>
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace TensorSycl {
+namespace internal {
+
+/// Cache all the device information needed
+struct SyclDeviceInfo {
+ SyclDeviceInfo(cl::sycl::queue queue)
+ : local_mem_type(
+ queue.get_device()
+ .template get_info<cl::sycl::info::device::local_mem_type>()),
+ max_work_item_sizes(
+ queue.get_device()
+ .template get_info<
+ cl::sycl::info::device::max_work_item_sizes>()),
+ max_mem_alloc_size(
+ queue.get_device()
+ .template get_info<
+ cl::sycl::info::device::max_mem_alloc_size>()),
+ max_compute_units(queue.get_device()
+ .template get_info<
+ cl::sycl::info::device::max_compute_units>()),
+ max_work_group_size(
+ queue.get_device()
+ .template get_info<
+ cl::sycl::info::device::max_work_group_size>()),
+ local_mem_size(
+ queue.get_device()
+ .template get_info<cl::sycl::info::device::local_mem_size>()),
+ platform_name(queue.get_device()
+ .get_platform()
+ .template get_info<cl::sycl::info::platform::name>()),
+ device_name(queue.get_device()
+ .template get_info<cl::sycl::info::device::name>()),
+ device_vendor(
+ queue.get_device()
+ .template get_info<cl::sycl::info::device::vendor>()) {}
+
+ cl::sycl::info::local_mem_type local_mem_type;
+ cl::sycl::id<3> max_work_item_sizes;
+ unsigned long max_mem_alloc_size;
+ unsigned long max_compute_units;
+ unsigned long max_work_group_size;
+ size_t local_mem_size;
+ std::string platform_name;
+ std::string device_name;
+ std::string device_vendor;
+};
+
+} // end namespace internal
+} // end namespace TensorSycl
+
+typedef TensorSycl::internal::buffer_data_type_t buffer_scalar_t;
+// All devices (even AMD CPU with intel OpenCL runtime) that support OpenCL and
+// can consume SPIR or SPIRV can use the Eigen SYCL backend and consequently
+// TensorFlow via the Eigen SYCL Backend.
+EIGEN_STRONG_INLINE auto get_sycl_supported_devices()
+ -> decltype(cl::sycl::device::get_devices()) {
+#ifdef EIGEN_SYCL_USE_DEFAULT_SELECTOR
+ return {cl::sycl::device(cl::sycl::default_selector())};
+#else
+ std::vector<cl::sycl::device> supported_devices;
+ auto platform_list = cl::sycl::platform::get_platforms();
+ for (const auto &platform : platform_list) {
+ auto device_list = platform.get_devices();
+ auto platform_name =
+ platform.template get_info<cl::sycl::info::platform::name>();
+ std::transform(platform_name.begin(), platform_name.end(),
+ platform_name.begin(), ::tolower);
+ for (const auto &device : device_list) {
+ auto vendor = device.template get_info<cl::sycl::info::device::vendor>();
+ std::transform(vendor.begin(), vendor.end(), vendor.begin(), ::tolower);
+ bool unsupported_condition =
+ (device.is_cpu() && platform_name.find("amd") != std::string::npos &&
+ vendor.find("apu") == std::string::npos) ||
+ (platform_name.find("experimental") != std::string::npos) ||
+ device.is_host();
+ if (!unsupported_condition) {
+ supported_devices.push_back(device);
+ }
+ }
+ }
+ return supported_devices;
+#endif
+}
+
+class QueueInterface {
+ public:
+ /// Creating device by using cl::sycl::selector or cl::sycl::device.
+ template <typename DeviceOrSelector>
+ explicit QueueInterface(
+ const DeviceOrSelector &dev_or_sel, cl::sycl::async_handler handler,
+ unsigned num_threads = std::thread::hardware_concurrency())
+ : m_queue(dev_or_sel, handler),
+#ifdef EIGEN_SYCL_USE_PROGRAM_CLASS
+ m_prog(m_queue.get_context(), get_sycl_supported_devices()),
+#endif
+ m_thread_pool(num_threads),
+ m_device_info(m_queue) {
+#ifdef EIGEN_SYCL_USE_PROGRAM_CLASS
+ m_prog.build_with_kernel_type<DeviceOrSelector>();
+ auto f = [&](cl::sycl::handler &cgh) {
+ cgh.single_task<DeviceOrSelector>(m_prog.get_kernel<DeviceOrSelector>(),
+ [=]() {})
+ };
+ EIGEN_SYCL_TRY_CATCH(m_queue.submit(f));
+#endif
+ }
+
+ template <typename DeviceOrSelector>
+ explicit QueueInterface(
+ const DeviceOrSelector &dev_or_sel,
+ unsigned num_threads = std::thread::hardware_concurrency())
+ : QueueInterface(dev_or_sel,
+ [this](cl::sycl::exception_list l) {
+ this->exception_caught_ = this->sycl_async_handler(l);
+ },
+ num_threads) {}
+
+ explicit QueueInterface(
+ const cl::sycl::queue& q, unsigned num_threads = std::thread::hardware_concurrency())
+ : m_queue(q),
+#ifdef EIGEN_SYCL_USE_PROGRAM_CLASS
+ m_prog(m_queue.get_context(), get_sycl_supported_devices()),
+#endif
+ m_thread_pool(num_threads),
+ m_device_info(m_queue) {}
+
+#ifdef EIGEN_SYCL_USE_PROGRAM_CLASS
+ EIGEN_STRONG_INLINE cl::sycl::program &program() const { return m_prog; }
+#endif
+
+ /// Attach an existing buffer to the pointer map, Eigen will not reuse it
+ EIGEN_STRONG_INLINE void *attach_buffer(
+ cl::sycl::buffer<buffer_scalar_t, 1> &buf) const {
+ std::lock_guard<std::mutex> lock(pmapper_mutex_);
+ return static_cast<void *>(pMapper.add_pointer(buf));
+ }
+
+ /// Detach previously attached buffer
+ EIGEN_STRONG_INLINE void detach_buffer(void *p) const {
+ std::lock_guard<std::mutex> lock(pmapper_mutex_);
+ TensorSycl::internal::SYCLfree<false>(p, pMapper);
+ }
+
+ /// Allocating device pointer. This pointer is actually an 8 bytes host
+ /// pointer used as key to access the sycl device buffer. The reason is that
+ /// we cannot use device buffer as a pointer as a m_data in Eigen leafNode
+ /// expressions. So we create a key pointer to be used in Eigen expression
+ /// construction. When we convert the Eigen construction into the sycl
+ /// construction we use this pointer as a key in our buffer_map and we make
+ /// sure that we dedicate only one buffer only for this pointer. The device
+ /// pointer would be deleted by calling deallocate function.
+ EIGEN_STRONG_INLINE void *allocate(size_t num_bytes) const {
+#if EIGEN_MAX_ALIGN_BYTES > 0
+ size_t align = num_bytes % EIGEN_MAX_ALIGN_BYTES;
+ if (align > 0) {
+ num_bytes += EIGEN_MAX_ALIGN_BYTES - align;
+ }
+#endif
+ std::lock_guard<std::mutex> lock(pmapper_mutex_);
+ return TensorSycl::internal::SYCLmalloc(num_bytes, pMapper);
+ }
+
+ EIGEN_STRONG_INLINE void *allocate_temp(size_t num_bytes) const {
+#if EIGEN_MAX_ALIGN_BYTES > 0
+ size_t align = num_bytes % EIGEN_MAX_ALIGN_BYTES;
+ if (align > 0) {
+ num_bytes += EIGEN_MAX_ALIGN_BYTES - align;
+ }
+#endif
+ std::lock_guard<std::mutex> lock(pmapper_mutex_);
+#ifndef EIGEN_SYCL_NO_REUSE_BUFFERS
+ if (scratch_buffers.empty()) {
+ return TensorSycl::internal::SYCLmalloc(num_bytes, pMapper);
+ ;
+ } else {
+ for (auto it = scratch_buffers.begin(); it != scratch_buffers.end();) {
+ auto buff = pMapper.get_buffer(*it);
+ if (buff.get_size() >= num_bytes) {
+ auto ptr = *it;
+ scratch_buffers.erase(it);
+ return ptr;
+ } else {
+ ++it;
+ }
+ }
+ return TensorSycl::internal::SYCLmalloc(num_bytes, pMapper);
+ }
+#else
+ return TensorSycl::internal::SYCLmalloc(num_bytes, pMapper);
+#endif
+ }
+ template <typename data_t>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorSycl::internal::RangeAccess<
+ cl::sycl::access::mode::read_write, data_t>
+ get(data_t *data) const {
+ return get_range_accessor<cl::sycl::access::mode::read_write, data_t>(data);
+ }
+ template <typename data_t>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE data_t *get(
+ TensorSycl::internal::RangeAccess<cl::sycl::access::mode::read_write,
+ data_t>
+ data) const {
+ return static_cast<data_t *>(data.get_virtual_pointer());
+ }
+
+ EIGEN_STRONG_INLINE void deallocate_temp(void *p) const {
+ std::lock_guard<std::mutex> lock(pmapper_mutex_);
+#ifndef EIGEN_SYCL_NO_REUSE_BUFFERS
+ scratch_buffers.insert(p);
+#else
+ TensorSycl::internal::SYCLfree(p, pMapper);
+#endif
+ }
+ template <cl::sycl::access::mode AcMd, typename T>
+ EIGEN_STRONG_INLINE void deallocate_temp(
+ const TensorSycl::internal::RangeAccess<AcMd, T> &p) const {
+ deallocate_temp(p.get_virtual_pointer());
+ }
+
+ /// This is used to deallocate the device pointer. p is used as a key inside
+ /// the map to find the device buffer and delete it.
+ EIGEN_STRONG_INLINE void deallocate(void *p) const {
+ std::lock_guard<std::mutex> lock(pmapper_mutex_);
+ TensorSycl::internal::SYCLfree(p, pMapper);
+ }
+
+ EIGEN_STRONG_INLINE void deallocate_all() const {
+ std::lock_guard<std::mutex> lock(pmapper_mutex_);
+ TensorSycl::internal::SYCLfreeAll(pMapper);
+#ifndef EIGEN_SYCL_NO_REUSE_BUFFERS
+ scratch_buffers.clear();
+#endif
+ }
+
+ /// The memcpyHostToDevice is used to copy the data from host to device
+ /// The destination pointer could be deleted before the copy happened which is
+ /// why a callback function is needed. By default if none is provided, the
+ /// function is blocking.
+ EIGEN_STRONG_INLINE void memcpyHostToDevice(
+ void *dst, const void *src, size_t n,
+ std::function<void()> callback) const {
+ static const auto write_mode = cl::sycl::access::mode::discard_write;
+ static const auto global_access = cl::sycl::access::target::global_buffer;
+ typedef cl::sycl::accessor<buffer_scalar_t, 1, write_mode, global_access>
+ write_accessor;
+ if (n == 0) {
+ if (callback) callback();
+ return;
+ }
+ n /= sizeof(buffer_scalar_t);
+ auto f = [&](cl::sycl::handler &cgh) {
+ write_accessor dst_acc = get_range_accessor<write_mode>(cgh, dst, n);
+ buffer_scalar_t const *ptr = static_cast<buffer_scalar_t const *>(src);
+ auto non_deleter = [](buffer_scalar_t const *) {};
+ std::shared_ptr<const buffer_scalar_t> s_ptr(ptr, non_deleter);
+ cgh.copy(s_ptr, dst_acc);
+ };
+ cl::sycl::event e;
+ EIGEN_SYCL_TRY_CATCH(e = m_queue.submit(f));
+ synchronize_and_callback(e, callback);
+ }
+
+ /// The memcpyDeviceToHost is used to copy the data from device to host.
+ /// The source pointer could be deleted before the copy happened which is
+ /// why a callback function is needed. By default if none is provided, the
+ /// function is blocking.
+ EIGEN_STRONG_INLINE void memcpyDeviceToHost(
+ void *dst, const void *src, size_t n,
+ std::function<void()> callback) const {
+ static const auto read_mode = cl::sycl::access::mode::read;
+ static const auto global_access = cl::sycl::access::target::global_buffer;
+ typedef cl::sycl::accessor<buffer_scalar_t, 1, read_mode, global_access>
+ read_accessor;
+ if (n == 0) {
+ if (callback) callback();
+ return;
+ }
+ n /= sizeof(buffer_scalar_t);
+ auto f = [&](cl::sycl::handler &cgh) {
+ read_accessor src_acc = get_range_accessor<read_mode>(cgh, src, n);
+ buffer_scalar_t *ptr = static_cast<buffer_scalar_t *>(dst);
+ auto non_deleter = [](buffer_scalar_t *) {};
+ std::shared_ptr<buffer_scalar_t> s_ptr(ptr, non_deleter);
+ cgh.copy(src_acc, s_ptr);
+ };
+ cl::sycl::event e;
+ EIGEN_SYCL_TRY_CATCH(e = m_queue.submit(f));
+ synchronize_and_callback(e, callback);
+ }
+
+ /// The memcpy function.
+ /// No callback is required here as both arguments are on the device
+ /// and SYCL can handle the dependency.
+ EIGEN_STRONG_INLINE void memcpy(void *dst, const void *src, size_t n) const {
+ static const auto read_mode = cl::sycl::access::mode::read;
+ static const auto write_mode = cl::sycl::access::mode::discard_write;
+ if (n == 0) {
+ return;
+ }
+ n /= sizeof(buffer_scalar_t);
+ auto f = [&](cl::sycl::handler &cgh) {
+ auto src_acc = get_range_accessor<read_mode>(cgh, src, n);
+ auto dst_acc = get_range_accessor<write_mode>(cgh, dst, n);
+ cgh.copy(src_acc, dst_acc);
+ };
+ cl::sycl::event e;
+ EIGEN_SYCL_TRY_CATCH(e = m_queue.submit(f));
+ async_synchronize(e);
+ }
+
+ /// the memset function.
+ /// No callback is required here as both arguments are on the device
+ /// and SYCL can handle the dependency.
+ EIGEN_STRONG_INLINE void memset(void *data, int c, size_t n) const {
+ static const auto write_mode = cl::sycl::access::mode::discard_write;
+ if (n == 0) {
+ return;
+ }
+ auto f = [&](cl::sycl::handler &cgh) {
+ // Get a typed range accesser to ensure we fill each byte, in case
+ // `buffer_scalar_t` is not (u)int8_t.
+ auto dst_acc = get_typed_range_accessor<write_mode, uint8_t>(cgh, data, n);
+ cgh.fill(dst_acc, static_cast<uint8_t>(c));
+ };
+ cl::sycl::event e;
+ EIGEN_SYCL_TRY_CATCH(e = m_queue.submit(f));
+ async_synchronize(e);
+ }
+
+ template<typename T>
+ EIGEN_STRONG_INLINE void fill(T* begin, T* end, const T& value) const {
+ static const auto write_mode = cl::sycl::access::mode::discard_write;
+ if (begin == end) {
+ return;
+ }
+ const ptrdiff_t count = end - begin;
+ auto f = [&](cl::sycl::handler &cgh) {
+ auto dst_acc = get_typed_range_accessor<write_mode, T>(cgh, begin, count);
+ cgh.fill(dst_acc, value);
+ };
+ cl::sycl::event e;
+ EIGEN_SYCL_TRY_CATCH(e = m_queue.submit(f));
+ async_synchronize(e);
+ }
+
+ /// Get a range accessor to the virtual pointer's device memory. This range
+ /// accessor will allow access to the memory from the pointer to the end of
+ /// the buffer.
+ ///
+ /// NOTE: Inside a kernel the range accessor will always be indexed from the
+ /// start of the buffer, so the offset in the accessor is only used by
+ /// methods like handler::copy and will not be available inside a kernel.
+ template <cl::sycl::access::mode AcMd, typename T>
+ EIGEN_STRONG_INLINE TensorSycl::internal::RangeAccess<AcMd, T>
+ get_range_accessor(const void *ptr) const {
+ static const auto global_access = cl::sycl::access::target::global_buffer;
+ static const auto is_place_holder = cl::sycl::access::placeholder::true_t;
+ typedef TensorSycl::internal::RangeAccess<AcMd, T> ret_type;
+ typedef const TensorSycl::internal::buffer_data_type_t *internal_ptr_t;
+
+ std::lock_guard<std::mutex> lock(pmapper_mutex_);
+
+ auto original_buffer = pMapper.get_buffer(ptr);
+ const ptrdiff_t offset = pMapper.get_offset(ptr);
+ eigen_assert(offset % sizeof(T) == 0 && "The offset must be a multiple of sizeof(T)");
+ eigen_assert(original_buffer.get_size() % sizeof(T) == 0 && "The buffer size must be a multiple of sizeof(T)");
+ const ptrdiff_t typed_offset = offset / sizeof(T);
+ eigen_assert(typed_offset >= 0);
+ const auto typed_size = original_buffer.get_size() / sizeof(T);
+ auto buffer = original_buffer.template reinterpret<
+ std::remove_const_t<T>>(
+ cl::sycl::range<1>(typed_size));
+ const ptrdiff_t size = buffer.get_count() - typed_offset;
+ eigen_assert(size >= 0);
+ typedef cl::sycl::accessor<std::remove_const_t<T>,
+ 1, AcMd, global_access, is_place_holder>
+ placeholder_accessor_t;
+ const auto start_ptr = static_cast<internal_ptr_t>(ptr) - offset;
+ return ret_type(placeholder_accessor_t(buffer, cl::sycl::range<1>(size),
+ cl::sycl::id<1>(typed_offset)),
+ static_cast<size_t>(typed_offset),
+ reinterpret_cast<std::intptr_t>(start_ptr));
+ }
+
+ /// Get a range accessor to the virtual pointer's device memory with a
+ /// specified size.
+ template <cl::sycl::access::mode AcMd, typename Index>
+ EIGEN_STRONG_INLINE cl::sycl::accessor<
+ buffer_scalar_t, 1, AcMd, cl::sycl::access::target::global_buffer>
+ get_range_accessor(cl::sycl::handler &cgh, const void *ptr,
+ const Index n_bytes) const {
+ static const auto global_access = cl::sycl::access::target::global_buffer;
+ eigen_assert(n_bytes >= 0);
+ std::lock_guard<std::mutex> lock(pmapper_mutex_);
+ auto buffer = pMapper.get_buffer(ptr);
+ const ptrdiff_t offset = pMapper.get_offset(ptr);
+ eigen_assert(offset >= 0);
+ eigen_assert(offset + n_bytes <= buffer.get_size());
+ return buffer.template get_access<AcMd, global_access>(
+ cgh, cl::sycl::range<1>(n_bytes), cl::sycl::id<1>(offset));
+ }
+
+ /// Get a range accessor to the virtual pointer's device memory with a
+ /// specified type and count.
+ template <cl::sycl::access::mode AcMd, typename T, typename Index>
+ EIGEN_STRONG_INLINE cl::sycl::accessor<
+ T, 1, AcMd, cl::sycl::access::target::global_buffer>
+ get_typed_range_accessor(cl::sycl::handler &cgh, const void *ptr,
+ const Index count) const {
+ static const auto global_access = cl::sycl::access::target::global_buffer;
+ eigen_assert(count >= 0);
+ std::lock_guard<std::mutex> lock(pmapper_mutex_);
+ auto buffer = pMapper.get_buffer(ptr);
+ const ptrdiff_t offset = pMapper.get_offset(ptr);
+ eigen_assert(offset >= 0);
+
+ // Technically we should create a subbuffer for the desired range,
+ // then reinterpret that. However, I was not able to get changes to reflect
+ // in the original buffer (only the subbuffer and reinterpretted buffer).
+ // This current implementation now has the restriction that the buffer
+ // offset and original buffer size must be a multiple of sizeof(T).
+ // Note that get_range_accessor(void*) currently has the same restriction.
+ //
+ // auto subbuffer = cl::sycl::buffer<buffer_scalar_t, 1>(buffer,
+ // cl::sycl::id<1>(offset), cl::sycl::range<1>(n_bytes));
+ eigen_assert(offset % sizeof(T) == 0 && "The offset must be a multiple of sizeof(T)");
+ eigen_assert(buffer.get_size() % sizeof(T) == 0 && "The buffer size must be a multiple of sizeof(T)");
+ const ptrdiff_t typed_offset = offset / sizeof(T);
+ const size_t typed_size = buffer.get_size() / sizeof(T);
+ auto reint = buffer.template reinterpret<
+ std::remove_const_t<T>>(
+ cl::sycl::range<1>(typed_size));
+ return reint.template get_access<AcMd, global_access>(
+ cgh, cl::sycl::range<1>(count), cl::sycl::id<1>(typed_offset));
+ }
+
+ /// Creation of sycl accessor for a buffer. This function first tries to find
+ /// the buffer in the buffer_map. If found it gets the accessor from it, if
+ /// not, the function then adds an entry by creating a sycl buffer for that
+ /// particular pointer.
+ template <cl::sycl::access::mode AcMd>
+ EIGEN_STRONG_INLINE cl::sycl::accessor<
+ buffer_scalar_t, 1, AcMd, cl::sycl::access::target::global_buffer>
+ get_sycl_accessor(cl::sycl::handler &cgh, const void *ptr) const {
+ std::lock_guard<std::mutex> lock(pmapper_mutex_);
+ return pMapper.get_buffer(ptr)
+ .template get_access<AcMd, cl::sycl::access::target::global_buffer>(
+ cgh);
+ }
+
+ EIGEN_STRONG_INLINE cl::sycl::buffer<buffer_scalar_t, 1> get_sycl_buffer(
+ const void *ptr) const {
+ std::lock_guard<std::mutex> lock(pmapper_mutex_);
+ return pMapper.get_buffer(ptr);
+ }
+
+ EIGEN_STRONG_INLINE ptrdiff_t get_offset(const void *ptr) const {
+ std::lock_guard<std::mutex> lock(pmapper_mutex_);
+ return pMapper.get_offset(ptr);
+ }
+
+ template <typename OutScalar, typename sycl_kernel, typename Lhs,
+ typename Rhs, typename OutPtr, typename Range, typename Index,
+ typename... T>
+ EIGEN_ALWAYS_INLINE void binary_kernel_launcher(const Lhs &lhs,
+ const Rhs &rhs, OutPtr outptr,
+ Range thread_range,
+ Index scratchSize,
+ T... var) const {
+ auto kernel_functor = [=](cl::sycl::handler &cgh) {
+ // binding the placeholder accessors to a commandgroup handler
+ lhs.bind(cgh);
+ rhs.bind(cgh);
+ outptr.bind(cgh);
+ typedef cl::sycl::accessor<OutScalar, 1,
+ cl::sycl::access::mode::read_write,
+ cl::sycl::access::target::local>
+ LocalAccessor;
+
+ LocalAccessor scratch(cl::sycl::range<1>(scratchSize), cgh);
+ cgh.parallel_for(
+#ifdef EIGEN_SYCL_USE_PROGRAM_CLASS
+ program().template get_kernel<sycl_kernel>(),
+#endif
+ thread_range, sycl_kernel(scratch, lhs, rhs, outptr, var...));
+ };
+ cl::sycl::event e;
+ EIGEN_SYCL_TRY_CATCH(e = m_queue.submit(kernel_functor));
+ async_synchronize(e);
+ }
+
+ template <typename OutScalar, typename sycl_kernel, typename InPtr,
+ typename OutPtr, typename Range, typename Index, typename... T>
+ EIGEN_ALWAYS_INLINE void unary_kernel_launcher(const InPtr &inptr,
+ OutPtr &outptr,
+ Range thread_range,
+ Index scratchSize,
+ T... var) const {
+ auto kernel_functor = [=](cl::sycl::handler &cgh) {
+ // binding the placeholder accessors to a commandgroup handler
+ inptr.bind(cgh);
+ outptr.bind(cgh);
+ typedef cl::sycl::accessor<OutScalar, 1,
+ cl::sycl::access::mode::read_write,
+ cl::sycl::access::target::local>
+ LocalAccessor;
+
+ LocalAccessor scratch(cl::sycl::range<1>(scratchSize), cgh);
+ cgh.parallel_for(
+#ifdef EIGEN_SYCL_USE_PROGRAM_CLASS
+ program().template get_kernel<sycl_kernel>(),
+#endif
+ thread_range, sycl_kernel(scratch, inptr, outptr, var...));
+ };
+ cl::sycl::event e;
+ EIGEN_SYCL_TRY_CATCH(e = m_queue.submit(kernel_functor));
+ async_synchronize(e);
+ }
+
+ template <typename OutScalar, typename sycl_kernel, typename InPtr,
+ typename Range, typename Index, typename... T>
+ EIGEN_ALWAYS_INLINE void nullary_kernel_launcher(const InPtr &inptr,
+ Range thread_range,
+ Index scratchSize,
+ T... var) const {
+ auto kernel_functor = [=](cl::sycl::handler &cgh) {
+ // binding the placeholder accessors to a commandgroup handler
+ inptr.bind(cgh);
+ typedef cl::sycl::accessor<OutScalar, 1,
+ cl::sycl::access::mode::read_write,
+ cl::sycl::access::target::local>
+ LocalAccessor;
+
+ LocalAccessor scratch(cl::sycl::range<1>(scratchSize), cgh);
+ cgh.parallel_for(
+#ifdef EIGEN_SYCL_USE_PROGRAM_CLASS
+ program().template get_kernel<sycl_kernel>(),
+#endif
+ thread_range, sycl_kernel(scratch, inptr, var...));
+ };
+ cl::sycl::event e;
+ EIGEN_SYCL_TRY_CATCH(e = m_queue.submit(kernel_functor));
+ async_synchronize(e);
+ }
+
+
+ EIGEN_STRONG_INLINE void synchronize() const {
+#ifdef EIGEN_EXCEPTIONS
+ m_queue.wait_and_throw();
+#else
+ m_queue.wait();
+#endif
+ }
+
+
+ EIGEN_STRONG_INLINE void async_synchronize(cl::sycl::event e) const {
+ set_latest_event(e);
+#ifndef EIGEN_SYCL_ASYNC_EXECUTION
+ synchronize();
+#endif
+ }
+
+ template <typename Index>
+ EIGEN_STRONG_INLINE void parallel_for_setup(Index n, Index &tileSize,
+ Index &rng, Index &GRange) const {
+ tileSize = static_cast<Index>(getNearestPowerOfTwoWorkGroupSize());
+ tileSize = std::min(static_cast<Index>(EIGEN_SYCL_LOCAL_THREAD_DIM0 *
+ EIGEN_SYCL_LOCAL_THREAD_DIM1),
+ static_cast<Index>(tileSize));
+ rng = n;
+ if (rng == 0) rng = static_cast<Index>(1);
+ GRange = rng;
+ if (tileSize > GRange)
+ tileSize = GRange;
+ else if (GRange > tileSize) {
+ Index xMode = static_cast<Index>(GRange % tileSize);
+ if (xMode != 0) GRange += static_cast<Index>(tileSize - xMode);
+ }
+ }
+
+ /// This is used to prepare the number of threads and also the number of
+ /// threads per block for sycl kernels
+ template <typename Index>
+ EIGEN_STRONG_INLINE void parallel_for_setup(
+ const std::array<Index, 2> &input_dim, cl::sycl::range<2> &global_range,
+ cl::sycl::range<2> &local_range) const {
+ std::array<Index, 2> input_range = input_dim;
+ Index max_workgroup_Size =
+ static_cast<Index>(getNearestPowerOfTwoWorkGroupSize());
+ max_workgroup_Size =
+ std::min(static_cast<Index>(EIGEN_SYCL_LOCAL_THREAD_DIM0 *
+ EIGEN_SYCL_LOCAL_THREAD_DIM1),
+ static_cast<Index>(max_workgroup_Size));
+ Index pow_of_2 = static_cast<Index>(std::log2(max_workgroup_Size));
+ local_range[1] =
+ static_cast<Index>(std::pow(2, static_cast<Index>(pow_of_2 / 2)));
+ input_range[1] = input_dim[1];
+ if (input_range[1] == 0) input_range[1] = static_cast<Index>(1);
+ global_range[1] = input_range[1];
+ if (local_range[1] > global_range[1])
+ local_range[1] = global_range[1];
+ else if (global_range[1] > local_range[1]) {
+ Index xMode = static_cast<Index>(global_range[1] % local_range[1]);
+ if (xMode != 0)
+ global_range[1] += static_cast<Index>(local_range[1] - xMode);
+ }
+ local_range[0] = static_cast<Index>(max_workgroup_Size / local_range[1]);
+ input_range[0] = input_dim[0];
+ if (input_range[0] == 0) input_range[0] = static_cast<Index>(1);
+ global_range[0] = input_range[0];
+ if (local_range[0] > global_range[0])
+ local_range[0] = global_range[0];
+ else if (global_range[0] > local_range[0]) {
+ Index xMode = static_cast<Index>(global_range[0] % local_range[0]);
+ if (xMode != 0)
+ global_range[0] += static_cast<Index>(local_range[0] - xMode);
+ }
+ }
+
+ /// This is used to prepare the number of threads and also the number of
+ /// threads per block for sycl kernels
+ template <typename Index>
+ EIGEN_STRONG_INLINE void parallel_for_setup(
+ const std::array<Index, 3> &input_dim, cl::sycl::range<3> &global_range,
+ cl::sycl::range<3> &local_range) const {
+ std::array<Index, 3> input_range = input_dim;
+ Index max_workgroup_Size =
+ static_cast<Index>(getNearestPowerOfTwoWorkGroupSize());
+ max_workgroup_Size =
+ std::min(static_cast<Index>(EIGEN_SYCL_LOCAL_THREAD_DIM0 *
+ EIGEN_SYCL_LOCAL_THREAD_DIM1),
+ static_cast<Index>(max_workgroup_Size));
+ Index pow_of_2 = static_cast<Index>(std::log2(max_workgroup_Size));
+ local_range[2] =
+ static_cast<Index>(std::pow(2, static_cast<Index>(pow_of_2 / 3)));
+ input_range[2] = input_dim[2];
+ if (input_range[2] == 0) input_range[1] = static_cast<Index>(1);
+ global_range[2] = input_range[2];
+ if (local_range[2] > global_range[2])
+ local_range[2] = global_range[2];
+ else if (global_range[2] > local_range[2]) {
+ Index xMode = static_cast<Index>(global_range[2] % local_range[2]);
+ if (xMode != 0)
+ global_range[2] += static_cast<Index>(local_range[2] - xMode);
+ }
+ pow_of_2 = static_cast<Index>(
+ std::log2(static_cast<Index>(max_workgroup_Size / local_range[2])));
+ local_range[1] =
+ static_cast<Index>(std::pow(2, static_cast<Index>(pow_of_2 / 2)));
+ input_range[1] = input_dim[1];
+ if (input_range[1] == 0) input_range[1] = static_cast<Index>(1);
+ global_range[1] = input_range[1];
+ if (local_range[1] > global_range[1])
+ local_range[1] = global_range[1];
+ else if (global_range[1] > local_range[1]) {
+ Index xMode = static_cast<Index>(global_range[1] % local_range[1]);
+ if (xMode != 0)
+ global_range[1] += static_cast<Index>(local_range[1] - xMode);
+ }
+ local_range[0] = static_cast<Index>(max_workgroup_Size /
+ (local_range[1] * local_range[2]));
+ input_range[0] = input_dim[0];
+ if (input_range[0] == 0) input_range[0] = static_cast<Index>(1);
+ global_range[0] = input_range[0];
+ if (local_range[0] > global_range[0])
+ local_range[0] = global_range[0];
+ else if (global_range[0] > local_range[0]) {
+ Index xMode = static_cast<Index>(global_range[0] % local_range[0]);
+ if (xMode != 0)
+ global_range[0] += static_cast<Index>(local_range[0] - xMode);
+ }
+ }
+
+ EIGEN_STRONG_INLINE bool has_local_memory() const {
+#if !defined(EIGEN_SYCL_LOCAL_MEM) && defined(EIGEN_SYCL_NO_LOCAL_MEM)
+ return false;
+#elif defined(EIGEN_SYCL_LOCAL_MEM) && !defined(EIGEN_SYCL_NO_LOCAL_MEM)
+ return true;
+#else
+ return m_device_info.local_mem_type ==
+ cl::sycl::info::local_mem_type::local;
+#endif
+ }
+
+ EIGEN_STRONG_INLINE unsigned long max_buffer_size() const {
+ return m_device_info.max_mem_alloc_size;
+ }
+
+ EIGEN_STRONG_INLINE unsigned long getNumSyclMultiProcessors() const {
+ return m_device_info.max_compute_units;
+ }
+
+ EIGEN_STRONG_INLINE unsigned long maxSyclThreadsPerBlock() const {
+ return m_device_info.max_work_group_size;
+ }
+
+ EIGEN_STRONG_INLINE cl::sycl::id<3> maxWorkItemSizes() const {
+ return m_device_info.max_work_item_sizes;
+ }
+
+ /// No need for sycl it should act the same as CPU version
+ EIGEN_STRONG_INLINE int majorDeviceVersion() const { return 1; }
+
+ EIGEN_STRONG_INLINE unsigned long maxSyclThreadsPerMultiProcessor() const {
+ // OpenCL does not have such a concept
+ return 2;
+ }
+
+ EIGEN_STRONG_INLINE size_t sharedMemPerBlock() const {
+ return m_device_info.local_mem_size;
+ }
+
+ // This function returns the nearest power of 2 Work-group size which is <=
+ // maximum device workgroup size.
+ EIGEN_STRONG_INLINE size_t getNearestPowerOfTwoWorkGroupSize() const {
+ return getPowerOfTwo(m_device_info.max_work_group_size, false);
+ }
+
+ EIGEN_STRONG_INLINE std::string getPlatformName() const {
+ return m_device_info.platform_name;
+ }
+
+ EIGEN_STRONG_INLINE std::string getDeviceName() const {
+ return m_device_info.device_name;
+ }
+
+ EIGEN_STRONG_INLINE std::string getDeviceVendor() const {
+ return m_device_info.device_vendor;
+ }
+
+ // This function returns the nearest power of 2
+ // if roundup is true returns result>=wgsize
+ // else it return result <= wgsize
+ EIGEN_STRONG_INLINE size_t getPowerOfTwo(size_t wGSize, bool roundUp) const {
+ if (roundUp) --wGSize;
+ wGSize |= (wGSize >> 1);
+ wGSize |= (wGSize >> 2);
+ wGSize |= (wGSize >> 4);
+ wGSize |= (wGSize >> 8);
+ wGSize |= (wGSize >> 16);
+#if EIGEN_ARCH_x86_64 || EIGEN_ARCH_ARM64 || EIGEN_OS_WIN64
+ wGSize |= (wGSize >> 32);
+#endif
+ return ((!roundUp) ? (wGSize - (wGSize >> 1)) : ++wGSize);
+ }
+
+ EIGEN_STRONG_INLINE cl::sycl::queue &sycl_queue() const { return m_queue; }
+
+ // This function checks if the runtime recorded an error for the
+ // underlying stream device.
+ EIGEN_STRONG_INLINE bool ok() const {
+ if (!exception_caught_) {
+ synchronize();
+ }
+ return !exception_caught_;
+ }
+
+ EIGEN_STRONG_INLINE cl::sycl::event get_latest_event() const {
+#ifdef EIGEN_SYCL_STORE_LATEST_EVENT
+ std::lock_guard<std::mutex> lock(event_mutex_);
+ return latest_events_[std::this_thread::get_id()];
+#else
+ eigen_assert(false);
+ return cl::sycl::event();
+#endif
+ }
+
+ // destructor
+ ~QueueInterface() {
+ pMapper.clear();
+#ifndef EIGEN_SYCL_NO_REUSE_BUFFERS
+ scratch_buffers.clear();
+#endif
+ }
+
+ protected:
+ EIGEN_STRONG_INLINE void set_latest_event(cl::sycl::event e) const {
+#ifdef EIGEN_SYCL_STORE_LATEST_EVENT
+ std::lock_guard<std::mutex> lock(event_mutex_);
+ latest_events_[std::this_thread::get_id()] = e;
+#else
+ EIGEN_UNUSED_VARIABLE(e);
+#endif
+ }
+
+ void synchronize_and_callback(cl::sycl::event e,
+ const std::function<void()> &callback) const {
+ set_latest_event(e);
+ if (callback) {
+ auto callback_ = [=]() {
+#ifdef EIGEN_EXCEPTIONS
+ cl::sycl::event(e).wait_and_throw();
+#else
+ cl::sycl::event(e).wait();
+#endif
+ callback();
+ };
+ m_thread_pool.Schedule(std::move(callback_));
+ } else {
+#ifdef EIGEN_EXCEPTIONS
+ m_queue.wait_and_throw();
+#else
+ m_queue.wait();
+#endif
+ }
+ }
+
+ bool sycl_async_handler(cl::sycl::exception_list exceptions) const {
+ bool exception_caught = false;
+ for (const auto &e : exceptions) {
+ if (e) {
+ exception_caught = true;
+ EIGEN_THROW_X(e);
+ }
+ }
+ return exception_caught;
+ }
+
+ /// class members:
+ bool exception_caught_ = false;
+
+ mutable std::mutex pmapper_mutex_;
+
+#ifdef EIGEN_SYCL_STORE_LATEST_EVENT
+ mutable std::mutex event_mutex_;
+ mutable std::unordered_map<std::thread::id, cl::sycl::event> latest_events_;
+#endif
+
+ /// std::map is the container used to make sure that we create only one buffer
+ /// per pointer. The lifespan of the buffer now depends on the lifespan of
+ /// SyclDevice. If a non-read-only pointer is needed to be accessed on the
+ /// host we should manually deallocate it.
+ mutable TensorSycl::internal::PointerMapper pMapper;
+#ifndef EIGEN_SYCL_NO_REUSE_BUFFERS
+ mutable std::unordered_set<void *> scratch_buffers;
+#endif
+ /// sycl queue
+ mutable cl::sycl::queue m_queue;
+#ifdef EIGEN_SYCL_USE_PROGRAM_CLASS
+ mutable cl::sycl::program m_prog;
+#endif
+
+ /// The thread pool is used to wait on events and call callbacks
+ /// asynchronously
+ mutable Eigen::ThreadPool m_thread_pool;
+
+ const TensorSycl::internal::SyclDeviceInfo m_device_info;
+};
+
+struct SyclDeviceBase {
+ /// QueueInterface is not owned. it is the caller's responsibility to destroy
+ /// it
+ const QueueInterface *m_queue_stream;
+ explicit SyclDeviceBase(const QueueInterface *queue_stream)
+ : m_queue_stream(queue_stream) {}
+ EIGEN_STRONG_INLINE const QueueInterface *queue_stream() const {
+ return m_queue_stream;
+ }
+};
+
+// Here is a sycl device struct which accept the sycl queue interface
+// as an input
+struct SyclDevice : public SyclDeviceBase {
+ explicit SyclDevice(const QueueInterface *queue_stream)
+ : SyclDeviceBase(queue_stream) {}
+
+ // this is the accessor used to construct the evaluator
+ template <cl::sycl::access::mode AcMd, typename T>
+ EIGEN_STRONG_INLINE TensorSycl::internal::RangeAccess<AcMd, T>
+ get_range_accessor(const void *ptr) const {
+ return queue_stream()->template get_range_accessor<AcMd, T>(ptr);
+ }
+
+ // get sycl accessor
+ template <cl::sycl::access::mode AcMd>
+ EIGEN_STRONG_INLINE cl::sycl::accessor<
+ buffer_scalar_t, 1, AcMd, cl::sycl::access::target::global_buffer>
+ get_sycl_accessor(cl::sycl::handler &cgh, const void *ptr) const {
+ return queue_stream()->template get_sycl_accessor<AcMd>(cgh, ptr);
+ }
+
+ /// Accessing the created sycl device buffer for the device pointer
+ EIGEN_STRONG_INLINE cl::sycl::buffer<buffer_scalar_t, 1> get_sycl_buffer(
+ const void *ptr) const {
+ return queue_stream()->get_sycl_buffer(ptr);
+ }
+
+ /// This is used to prepare the number of threads and also the number of
+ /// threads per block for sycl kernels
+ template <typename Index>
+ EIGEN_STRONG_INLINE void parallel_for_setup(Index n, Index &tileSize,
+ Index &rng, Index &GRange) const {
+ queue_stream()->parallel_for_setup(n, tileSize, rng, GRange);
+ }
+
+ /// This is used to prepare the number of threads and also the number of
+ /// threads per block for sycl kernels
+ template <typename Index>
+ EIGEN_STRONG_INLINE void parallel_for_setup(
+ const std::array<Index, 2> &input_dim, cl::sycl::range<2> &global_range,
+ cl::sycl::range<2> &local_range) const {
+ queue_stream()->parallel_for_setup(input_dim, global_range, local_range);
+ }
+
+ /// This is used to prepare the number of threads and also the number of
+ /// threads per block for sycl kernels
+ template <typename Index>
+ EIGEN_STRONG_INLINE void parallel_for_setup(
+ const std::array<Index, 3> &input_dim, cl::sycl::range<3> &global_range,
+ cl::sycl::range<3> &local_range) const {
+ queue_stream()->parallel_for_setup(input_dim, global_range, local_range);
+ }
+
+ /// allocate device memory
+ EIGEN_STRONG_INLINE void *allocate(size_t num_bytes) const {
+ return queue_stream()->allocate(num_bytes);
+ }
+
+ EIGEN_STRONG_INLINE void *allocate_temp(size_t num_bytes) const {
+ return queue_stream()->allocate_temp(num_bytes);
+ }
+
+ /// deallocate device memory
+ EIGEN_STRONG_INLINE void deallocate(void *p) const {
+ queue_stream()->deallocate(p);
+ }
+
+ EIGEN_STRONG_INLINE void deallocate_temp(void *buffer) const {
+ queue_stream()->deallocate_temp(buffer);
+ }
+ template <cl::sycl::access::mode AcMd, typename T>
+ EIGEN_STRONG_INLINE void deallocate_temp(
+ const TensorSycl::internal::RangeAccess<AcMd, T> &buffer) const {
+ queue_stream()->deallocate_temp(buffer);
+ }
+ EIGEN_STRONG_INLINE void deallocate_all() const {
+ queue_stream()->deallocate_all();
+ }
+
+ template <typename data_t>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorSycl::internal::RangeAccess<
+ cl::sycl::access::mode::read_write, data_t>
+ get(data_t *data) const {
+ return queue_stream()->get(data);
+ }
+ template <typename data_t>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE data_t *get(
+ TensorSycl::internal::RangeAccess<cl::sycl::access::mode::read_write,
+ data_t>
+ data) const {
+ return queue_stream()->get(data);
+ }
+
+ /// attach existing buffer
+ EIGEN_STRONG_INLINE void *attach_buffer(
+ cl::sycl::buffer<buffer_scalar_t, 1> &buf) const {
+ return queue_stream()->attach_buffer(buf);
+ }
+ /// detach buffer
+ EIGEN_STRONG_INLINE void detach_buffer(void *p) const {
+ queue_stream()->detach_buffer(p);
+ }
+ EIGEN_STRONG_INLINE ptrdiff_t get_offset(const void *ptr) const {
+ return queue_stream()->get_offset(ptr);
+ }
+
+ // some runtime conditions that can be applied here
+ EIGEN_STRONG_INLINE bool isDeviceSuitable() const { return true; }
+
+ /// memcpyHostToDevice
+ template <typename Index>
+ EIGEN_STRONG_INLINE void memcpyHostToDevice(
+ Index *dst, const Index *src, size_t n,
+ std::function<void()> callback = {}) const {
+ queue_stream()->memcpyHostToDevice(dst, src, n, callback);
+ }
+ /// memcpyDeviceToHost
+ template <typename Index>
+ EIGEN_STRONG_INLINE void memcpyDeviceToHost(
+ void *dst, const Index *src, size_t n,
+ std::function<void()> callback = {}) const {
+ queue_stream()->memcpyDeviceToHost(dst, src, n, callback);
+ }
+ /// the memcpy function
+ template <typename Index>
+ EIGEN_STRONG_INLINE void memcpy(void *dst, const Index *src, size_t n) const {
+ queue_stream()->memcpy(dst, src, n);
+ }
+ /// the memset function
+ EIGEN_STRONG_INLINE void memset(void *data, int c, size_t n) const {
+ queue_stream()->memset(data, c, n);
+ }
+ /// the fill function
+ template<typename T>
+ EIGEN_STRONG_INLINE void fill(T* begin, T* end, const T& value) const {
+ queue_stream()->fill(begin, end, value);
+ }
+ /// returning the sycl queue
+ EIGEN_STRONG_INLINE cl::sycl::queue &sycl_queue() const {
+ return queue_stream()->sycl_queue();
+ }
+#ifdef EIGEN_SYCL_USE_PROGRAM_CLASS
+ EIGEN_STRONG_INLINE cl::sycl::program &program() const {
+ return queue_stream()->program();
+ }
+#endif
+
+ EIGEN_STRONG_INLINE size_t firstLevelCacheSize() const { return 48 * 1024; }
+
+ EIGEN_STRONG_INLINE size_t lastLevelCacheSize() const {
+ // We won't try to take advantage of the l2 cache for the time being, and
+ // there is no l3 cache on sycl devices.
+ return firstLevelCacheSize();
+ }
+ EIGEN_STRONG_INLINE unsigned long getNumSyclMultiProcessors() const {
+ return queue_stream()->getNumSyclMultiProcessors();
+ }
+ EIGEN_STRONG_INLINE unsigned long maxSyclThreadsPerBlock() const {
+ return queue_stream()->maxSyclThreadsPerBlock();
+ }
+ EIGEN_STRONG_INLINE cl::sycl::id<3> maxWorkItemSizes() const {
+ return queue_stream()->maxWorkItemSizes();
+ }
+ EIGEN_STRONG_INLINE unsigned long maxSyclThreadsPerMultiProcessor() const {
+ // OpenCL does not have such a concept
+ return queue_stream()->maxSyclThreadsPerMultiProcessor();
+ }
+ EIGEN_STRONG_INLINE size_t sharedMemPerBlock() const {
+ return queue_stream()->sharedMemPerBlock();
+ }
+ EIGEN_STRONG_INLINE size_t getNearestPowerOfTwoWorkGroupSize() const {
+ return queue_stream()->getNearestPowerOfTwoWorkGroupSize();
+ }
+
+ EIGEN_STRONG_INLINE size_t getPowerOfTwo(size_t val, bool roundUp) const {
+ return queue_stream()->getPowerOfTwo(val, roundUp);
+ }
+ /// No need for sycl it should act the same as CPU version
+ EIGEN_STRONG_INLINE int majorDeviceVersion() const {
+ return queue_stream()->majorDeviceVersion();
+ }
+
+ EIGEN_STRONG_INLINE void synchronize() const {
+ queue_stream()->synchronize();
+ }
+ EIGEN_STRONG_INLINE void async_synchronize(
+ cl::sycl::event e = cl::sycl::event()) const {
+ queue_stream()->async_synchronize(e);
+ }
+ EIGEN_STRONG_INLINE cl::sycl::event get_latest_event() const {
+ return queue_stream()->get_latest_event();
+ }
+
+ // This function checks if the runtime recorded an error for the
+ // underlying stream device.
+ EIGEN_STRONG_INLINE bool ok() const { return queue_stream()->ok(); }
+
+ EIGEN_STRONG_INLINE bool has_local_memory() const {
+ return queue_stream()->has_local_memory();
+ }
+ EIGEN_STRONG_INLINE long max_buffer_size() const {
+ return queue_stream()->max_buffer_size();
+ }
+ EIGEN_STRONG_INLINE std::string getPlatformName() const {
+ return queue_stream()->getPlatformName();
+ }
+ EIGEN_STRONG_INLINE std::string getDeviceName() const {
+ return queue_stream()->getDeviceName();
+ }
+ EIGEN_STRONG_INLINE std::string getDeviceVendor() const {
+ return queue_stream()->getDeviceVendor();
+ }
+ template <typename OutScalar, typename KernelType, typename... T>
+ EIGEN_ALWAYS_INLINE void binary_kernel_launcher(T... var) const {
+ queue_stream()->template binary_kernel_launcher<OutScalar, KernelType>(
+ var...);
+ }
+ template <typename OutScalar, typename KernelType, typename... T>
+ EIGEN_ALWAYS_INLINE void unary_kernel_launcher(T... var) const {
+ queue_stream()->template unary_kernel_launcher<OutScalar, KernelType>(
+ var...);
+ }
+
+ template <typename OutScalar, typename KernelType, typename... T>
+ EIGEN_ALWAYS_INLINE void nullary_kernel_launcher(T... var) const {
+ queue_stream()->template nullary_kernel_launcher<OutScalar, KernelType>(
+ var...);
+ }
+};
+} // end namespace Eigen
+
+#endif // EIGEN_CXX11_TENSOR_TENSOR_DEVICE_SYCL_H
diff --git a/unsupported/Eigen/CXX11/src/Tensor/TensorDeviceThreadPool.h b/unsupported/Eigen/CXX11/src/Tensor/TensorDeviceThreadPool.h
new file mode 100644
index 0000000..a3adf61
--- /dev/null
+++ b/unsupported/Eigen/CXX11/src/Tensor/TensorDeviceThreadPool.h
@@ -0,0 +1,416 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#if defined(EIGEN_USE_THREADS) && !defined(EIGEN_CXX11_TENSOR_TENSOR_DEVICE_THREAD_POOL_H)
+#define EIGEN_CXX11_TENSOR_TENSOR_DEVICE_THREAD_POOL_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+// Runs an arbitrary function and then calls Notify() on the passed in
+// Notification.
+template <typename Function, typename... Args> struct FunctionWrapperWithNotification
+{
+ static void run(Notification* n, Function f, Args... args) {
+ f(args...);
+ if (n) {
+ n->Notify();
+ }
+ }
+};
+
+template <typename Function, typename... Args> struct FunctionWrapperWithBarrier
+{
+ static void run(Barrier* b, Function f, Args... args) {
+ f(args...);
+ if (b) {
+ b->Notify();
+ }
+ }
+};
+
+template <typename SyncType>
+static EIGEN_STRONG_INLINE void wait_until_ready(SyncType* n) {
+ if (n) {
+ n->Wait();
+ }
+}
+
+// An abstract interface to a device specific memory allocator.
+class Allocator {
+ public:
+ virtual ~Allocator() {}
+ virtual void* allocate(size_t num_bytes) const = 0;
+ virtual void deallocate(void* buffer) const = 0;
+};
+
+// Build a thread pool device on top the an existing pool of threads.
+struct ThreadPoolDevice {
+ // The ownership of the thread pool remains with the caller.
+ ThreadPoolDevice(ThreadPoolInterface* pool, int num_cores, Allocator* allocator = nullptr)
+ : pool_(pool), num_threads_(num_cores), allocator_(allocator) { }
+
+ EIGEN_STRONG_INLINE void* allocate(size_t num_bytes) const {
+ return allocator_ ? allocator_->allocate(num_bytes)
+ : internal::aligned_malloc(num_bytes);
+ }
+
+ EIGEN_STRONG_INLINE void deallocate(void* buffer) const {
+ if (allocator_) {
+ allocator_->deallocate(buffer);
+ } else {
+ internal::aligned_free(buffer);
+ }
+ }
+
+ EIGEN_STRONG_INLINE void* allocate_temp(size_t num_bytes) const {
+ return allocate(num_bytes);
+ }
+
+ EIGEN_STRONG_INLINE void deallocate_temp(void* buffer) const {
+ deallocate(buffer);
+ }
+
+ template<typename Type>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Type get(Type data) const {
+ return data;
+ }
+
+ EIGEN_STRONG_INLINE void memcpy(void* dst, const void* src, size_t n) const {
+#ifdef __ANDROID__
+ ::memcpy(dst, src, n);
+#else
+ // TODO(rmlarsen): Align blocks on cache lines.
+ // We have observed that going beyond 4 threads usually just wastes
+ // CPU cycles due to the threads competing for memory bandwidth, so we
+ // statically schedule at most 4 block copies here.
+ const size_t kMinBlockSize = 32768;
+ const size_t num_threads = CostModel::numThreads(n, TensorOpCost(1.0, 1.0, 0), 4);
+ if (n <= kMinBlockSize || num_threads < 2) {
+ ::memcpy(dst, src, n);
+ } else {
+ const char* src_ptr = static_cast<const char*>(src);
+ char* dst_ptr = static_cast<char*>(dst);
+ const size_t blocksize = (n + (num_threads - 1)) / num_threads;
+ Barrier barrier(static_cast<int>(num_threads - 1));
+ // Launch the last 3 blocks on worker threads.
+ for (size_t i = 1; i < num_threads; ++i) {
+ enqueue_with_barrier(&barrier, [n, i, src_ptr, dst_ptr, blocksize] {
+ ::memcpy(dst_ptr + i * blocksize, src_ptr + i * blocksize,
+ numext::mini(blocksize, n - (i * blocksize)));
+ });
+ }
+ // Launch the first block on the main thread.
+ ::memcpy(dst_ptr, src_ptr, blocksize);
+ barrier.Wait();
+ }
+#endif
+ }
+ EIGEN_STRONG_INLINE void memcpyHostToDevice(void* dst, const void* src, size_t n) const {
+ memcpy(dst, src, n);
+ }
+ EIGEN_STRONG_INLINE void memcpyDeviceToHost(void* dst, const void* src, size_t n) const {
+ memcpy(dst, src, n);
+ }
+
+ EIGEN_STRONG_INLINE void memset(void* buffer, int c, size_t n) const {
+ ::memset(buffer, c, n);
+ }
+
+ template<typename T>
+ EIGEN_STRONG_INLINE void fill(T* begin, T* end, const T& value) const {
+ std::fill(begin, end, value);
+ }
+
+ EIGEN_STRONG_INLINE int numThreads() const {
+ return num_threads_;
+ }
+
+ // Number of theads available in the underlying thread pool. This number can
+ // be different from the value returned by numThreads().
+ EIGEN_STRONG_INLINE int numThreadsInPool() const {
+ return pool_->NumThreads();
+ }
+
+ EIGEN_STRONG_INLINE size_t firstLevelCacheSize() const {
+ return l1CacheSize();
+ }
+
+ EIGEN_STRONG_INLINE size_t lastLevelCacheSize() const {
+ // The l3 cache size is shared between all the cores.
+ return l3CacheSize() / num_threads_;
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE int majorDeviceVersion() const {
+ // Should return an enum that encodes the ISA supported by the CPU
+ return 1;
+ }
+
+ template <class Function, class... Args>
+ EIGEN_STRONG_INLINE Notification* enqueue(Function&& f,
+ Args&&... args) const {
+ Notification* n = new Notification();
+ pool_->Schedule(
+ std::bind(&FunctionWrapperWithNotification<Function, Args...>::run, n,
+ std::move(f), args...));
+ return n;
+ }
+
+ template <class Function, class... Args>
+ EIGEN_STRONG_INLINE void enqueue_with_barrier(Barrier* b, Function&& f,
+ Args&&... args) const {
+ pool_->Schedule(
+ std::bind(&FunctionWrapperWithBarrier<Function, Args...>::run, b,
+ std::move(f), args...));
+ }
+
+ template <class Function, class... Args>
+ EIGEN_STRONG_INLINE void enqueueNoNotification(Function&& f,
+ Args&&... args) const {
+ if (sizeof...(args) > 0) {
+ pool_->Schedule(std::bind(std::move(f), args...));
+ } else {
+ pool_->Schedule(std::move(f));
+ }
+ }
+
+ // Returns a logical thread index between 0 and pool_->NumThreads() - 1 if
+ // called from one of the threads in pool_. Returns -1 otherwise.
+ EIGEN_STRONG_INLINE int currentThreadId() const {
+ return pool_->CurrentThreadId();
+ }
+
+ // WARNING: This function is synchronous and will block the calling thread.
+ //
+ // Synchronous parallelFor executes f with [0, n) arguments in parallel and
+ // waits for completion. F accepts a half-open interval [first, last). Block
+ // size is chosen based on the iteration cost and resulting parallel
+ // efficiency. If block_align is not nullptr, it is called to round up the
+ // block size.
+ void parallelFor(Index n, const TensorOpCost& cost,
+ std::function<Index(Index)> block_align,
+ std::function<void(Index, Index)> f) const {
+ if (EIGEN_PREDICT_FALSE(n <= 0)){
+ return;
+ // Compute small problems directly in the caller thread.
+ } else if (n == 1 || numThreads() == 1 ||
+ CostModel::numThreads(n, cost, static_cast<int>(numThreads())) == 1) {
+ f(0, n);
+ return;
+ }
+
+ // Compute block size and total count of blocks.
+ ParallelForBlock block = CalculateParallelForBlock(n, cost, block_align);
+
+ // Recursively divide size into halves until we reach block_size.
+ // Division code rounds mid to block_size, so we are guaranteed to get
+ // block_count leaves that do actual computations.
+ Barrier barrier(static_cast<unsigned int>(block.count));
+ std::function<void(Index, Index)> handleRange;
+ handleRange = [=, &handleRange, &barrier, &f](Index firstIdx,
+ Index lastIdx) {
+ while (lastIdx - firstIdx > block.size) {
+ // Split into halves and schedule the second half on a different thread.
+ const Index midIdx = firstIdx + divup((lastIdx - firstIdx) / 2, block.size) * block.size;
+ pool_->Schedule([=, &handleRange]() { handleRange(midIdx, lastIdx); });
+ lastIdx = midIdx;
+ }
+ // Single block or less, execute directly.
+ f(firstIdx, lastIdx);
+ barrier.Notify();
+ };
+
+ if (block.count <= numThreads()) {
+ // Avoid a thread hop by running the root of the tree and one block on the
+ // main thread.
+ handleRange(0, n);
+ } else {
+ // Execute the root in the thread pool to avoid running work on more than
+ // numThreads() threads.
+ pool_->Schedule([=, &handleRange]() { handleRange(0, n); });
+ }
+
+ barrier.Wait();
+ }
+
+ // Convenience wrapper for parallelFor that does not align blocks.
+ void parallelFor(Index n, const TensorOpCost& cost,
+ std::function<void(Index, Index)> f) const {
+ parallelFor(n, cost, nullptr, std::move(f));
+ }
+
+ // WARNING: This function is asynchronous and will not block the calling thread.
+ //
+ // Asynchronous parallelFor executes f with [0, n) arguments in parallel
+ // without waiting for completion. When the last block finished, it will call
+ // 'done' callback. F accepts a half-open interval [first, last). Block size
+ // is chosen based on the iteration cost and resulting parallel efficiency. If
+ // block_align is not nullptr, it is called to round up the block size.
+ void parallelForAsync(Index n, const TensorOpCost& cost,
+ std::function<Index(Index)> block_align,
+ std::function<void(Index, Index)> f,
+ std::function<void()> done) const {
+ // Compute small problems directly in the caller thread.
+ if (n <= 1 || numThreads() == 1 ||
+ CostModel::numThreads(n, cost, static_cast<int>(numThreads())) == 1) {
+ f(0, n);
+ done();
+ return;
+ }
+
+ // Compute block size and total count of blocks.
+ ParallelForBlock block = CalculateParallelForBlock(n, cost, block_align);
+
+ ParallelForAsyncContext* const ctx =
+ new ParallelForAsyncContext(block.count, std::move(f), std::move(done));
+
+ // Recursively divide size into halves until we reach block_size.
+ // Division code rounds mid to block_size, so we are guaranteed to get
+ // block_count leaves that do actual computations.
+ ctx->handle_range = [this, ctx, block](Index firstIdx, Index lastIdx) {
+ while (lastIdx - firstIdx > block.size) {
+ // Split into halves and schedule the second half on a different thread.
+ const Index midIdx = firstIdx + divup((lastIdx - firstIdx) / 2, block.size) * block.size;
+ pool_->Schedule(
+ [ctx, midIdx, lastIdx]() { ctx->handle_range(midIdx, lastIdx); });
+ lastIdx = midIdx;
+ }
+
+ // Single block or less, execute directly.
+ ctx->f(firstIdx, lastIdx);
+
+ // Delete async context if it was the last block.
+ if (ctx->count.fetch_sub(1) == 1) delete ctx;
+ };
+
+ if (block.count <= numThreads()) {
+ // Avoid a thread hop by running the root of the tree and one block on the
+ // main thread.
+ ctx->handle_range(0, n);
+ } else {
+ // Execute the root in the thread pool to avoid running work on more than
+ // numThreads() threads.
+ pool_->Schedule([ctx, n]() { ctx->handle_range(0, n); });
+ }
+ }
+
+ // Convenience wrapper for parallelForAsync that does not align blocks.
+ void parallelForAsync(Index n, const TensorOpCost& cost,
+ std::function<void(Index, Index)> f,
+ std::function<void()> done) const {
+ parallelForAsync(n, cost, nullptr, std::move(f), std::move(done));
+ }
+
+ // Thread pool accessor.
+ ThreadPoolInterface* getPool() const { return pool_; }
+
+ // Allocator accessor.
+ Allocator* allocator() const { return allocator_; }
+
+ private:
+ typedef TensorCostModel<ThreadPoolDevice> CostModel;
+
+ // For parallelForAsync we must keep passed in closures on the heap, and
+ // delete them only after `done` callback finished.
+ struct ParallelForAsyncContext {
+ ParallelForAsyncContext(Index block_count,
+ std::function<void(Index, Index)> block_f,
+ std::function<void()> done_callback)
+ : count(block_count),
+ f(std::move(block_f)),
+ done(std::move(done_callback)) {}
+ ~ParallelForAsyncContext() { done(); }
+
+ std::atomic<Index> count;
+ std::function<void(Index, Index)> f;
+ std::function<void()> done;
+
+ std::function<void(Index, Index)> handle_range;
+ };
+
+ struct ParallelForBlock {
+ Index size; // block size
+ Index count; // number of blocks
+ };
+
+ // Calculates block size based on (1) the iteration cost and (2) parallel
+ // efficiency. We want blocks to be not too small to mitigate parallelization
+ // overheads; not too large to mitigate tail effect and potential load
+ // imbalance and we also want number of blocks to be evenly dividable across
+ // threads.
+ ParallelForBlock CalculateParallelForBlock(
+ const Index n, const TensorOpCost& cost,
+ std::function<Index(Index)> block_align) const {
+ const double block_size_f = 1.0 / CostModel::taskSize(1, cost);
+ const Index max_oversharding_factor = 4;
+ Index block_size = numext::mini(
+ n, numext::maxi<Index>(
+ divup<Index>(n, max_oversharding_factor * numThreads()),
+ block_size_f));
+ const Index max_block_size = numext::mini(n, 2 * block_size);
+
+ if (block_align) {
+ Index new_block_size = block_align(block_size);
+ eigen_assert(new_block_size >= block_size);
+ block_size = numext::mini(n, new_block_size);
+ }
+
+ Index block_count = divup(n, block_size);
+
+ // Calculate parallel efficiency as fraction of total CPU time used for
+ // computations:
+ double max_efficiency =
+ static_cast<double>(block_count) /
+ (divup<int>(block_count, numThreads()) * numThreads());
+
+ // Now try to increase block size up to max_block_size as long as it
+ // doesn't decrease parallel efficiency.
+ for (Index prev_block_count = block_count;
+ max_efficiency < 1.0 && prev_block_count > 1;) {
+ // This is the next block size that divides size into a smaller number
+ // of blocks than the current block_size.
+ Index coarser_block_size = divup(n, prev_block_count - 1);
+ if (block_align) {
+ Index new_block_size = block_align(coarser_block_size);
+ eigen_assert(new_block_size >= coarser_block_size);
+ coarser_block_size = numext::mini(n, new_block_size);
+ }
+ if (coarser_block_size > max_block_size) {
+ break; // Reached max block size. Stop.
+ }
+ // Recalculate parallel efficiency.
+ const Index coarser_block_count = divup(n, coarser_block_size);
+ eigen_assert(coarser_block_count < prev_block_count);
+ prev_block_count = coarser_block_count;
+ const double coarser_efficiency =
+ static_cast<double>(coarser_block_count) /
+ (divup<int>(coarser_block_count, numThreads()) * numThreads());
+ if (coarser_efficiency + 0.01 >= max_efficiency) {
+ // Taking it.
+ block_size = coarser_block_size;
+ block_count = coarser_block_count;
+ if (max_efficiency < coarser_efficiency) {
+ max_efficiency = coarser_efficiency;
+ }
+ }
+ }
+
+ return {block_size, block_count};
+ }
+
+ ThreadPoolInterface* pool_;
+ int num_threads_;
+ Allocator* allocator_;
+};
+
+
+} // end namespace Eigen
+
+#endif // EIGEN_CXX11_TENSOR_TENSOR_DEVICE_THREAD_POOL_H
diff --git a/unsupported/Eigen/CXX11/src/Tensor/TensorDimensionList.h b/unsupported/Eigen/CXX11/src/Tensor/TensorDimensionList.h
new file mode 100644
index 0000000..c58838e
--- /dev/null
+++ b/unsupported/Eigen/CXX11/src/Tensor/TensorDimensionList.h
@@ -0,0 +1,143 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2015 Benoit Steiner <benoit.steiner.goog@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_CXX11_TENSOR_TENSOR_DIMENSION_LIST_H
+#define EIGEN_CXX11_TENSOR_TENSOR_DIMENSION_LIST_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+/** \internal
+ *
+ * \class TensorDimensionList
+ * \ingroup CXX11_Tensor_Module
+ *
+ * \brief Special case of tensor index list used to list all the dimensions of a tensor of rank n.
+ *
+ * \sa Tensor
+ */
+
+template <typename Index, std::size_t Rank> struct DimensionList {
+ EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
+ const Index operator[] (const Index i) const { return i; }
+};
+
+namespace internal {
+
+template<typename Index, std::size_t Rank> struct array_size<DimensionList<Index, Rank> > {
+ static const size_t value = Rank;
+};
+template<typename Index, std::size_t Rank> struct array_size<const DimensionList<Index, Rank> > {
+ static const size_t value = Rank;
+};
+
+template<DenseIndex n, typename Index, std::size_t Rank> const Index array_get(DimensionList<Index, Rank>&) {
+ return n;
+}
+template<DenseIndex n, typename Index, std::size_t Rank> const Index array_get(const DimensionList<Index, Rank>&) {
+ return n;
+}
+
+template <typename Index, std::size_t Rank>
+struct index_known_statically_impl<DimensionList<Index, Rank> > {
+ EIGEN_DEVICE_FUNC static constexpr bool run(const DenseIndex) {
+ return true;
+ }
+};
+template <typename Index, std::size_t Rank>
+struct index_known_statically_impl<const DimensionList<Index, Rank> > {
+ EIGEN_DEVICE_FUNC static constexpr bool run(const DenseIndex) {
+ return true;
+ }
+};
+
+template <typename Index, std::size_t Rank>
+struct all_indices_known_statically_impl<DimensionList<Index, Rank> > {
+ EIGEN_DEVICE_FUNC static constexpr bool run() {
+ return true;
+ }
+};
+template <typename Index, std::size_t Rank>
+struct all_indices_known_statically_impl<const DimensionList<Index, Rank> > {
+ EIGEN_DEVICE_FUNC static constexpr bool run() {
+ return true;
+ }
+};
+
+template <typename Index, std::size_t Rank>
+struct indices_statically_known_to_increase_impl<DimensionList<Index, Rank> > {
+ EIGEN_DEVICE_FUNC static constexpr bool run() {
+ return true;
+ }
+};
+template <typename Index, std::size_t Rank>
+struct indices_statically_known_to_increase_impl<const DimensionList<Index, Rank> > {
+ EIGEN_DEVICE_FUNC static constexpr bool run() {
+ return true;
+ }
+};
+
+template <typename Index, std::size_t Rank>
+struct index_statically_eq_impl<DimensionList<Index, Rank> > {
+ static constexpr bool run(const DenseIndex i, const DenseIndex value) {
+ return i == value;
+ }
+};
+template <typename Index, std::size_t Rank>
+struct index_statically_eq_impl<const DimensionList<Index, Rank> > {
+ EIGEN_DEVICE_FUNC static constexpr bool run(const DenseIndex i, const DenseIndex value) {
+ return i == value;
+ }
+};
+
+template <typename Index, std::size_t Rank>
+struct index_statically_ne_impl<DimensionList<Index, Rank> > {
+ EIGEN_DEVICE_FUNC static constexpr bool run(const DenseIndex i, const DenseIndex value) {
+ return i != value;
+ }
+};
+template <typename Index, std::size_t Rank>
+struct index_statically_ne_impl<const DimensionList<Index, Rank> > {
+ static constexpr bool run(const DenseIndex i, const DenseIndex value) {
+ return i != value;
+ }
+};
+
+template <typename Index, std::size_t Rank>
+struct index_statically_gt_impl<DimensionList<Index, Rank> > {
+ EIGEN_DEVICE_FUNC static constexpr bool run(const DenseIndex i, const DenseIndex value) {
+ return i > value;
+ }
+};
+template <typename Index, std::size_t Rank>
+struct index_statically_gt_impl<const DimensionList<Index, Rank> > {
+ EIGEN_DEVICE_FUNC static constexpr bool run(const DenseIndex i, const DenseIndex value) {
+ return i > value;
+ }
+};
+
+template <typename Index, std::size_t Rank>
+struct index_statically_lt_impl<DimensionList<Index, Rank> > {
+ EIGEN_DEVICE_FUNC static constexpr bool run(const DenseIndex i, const DenseIndex value) {
+ return i < value;
+ }
+};
+template <typename Index, std::size_t Rank>
+struct index_statically_lt_impl<const DimensionList<Index, Rank> > {
+ EIGEN_DEVICE_FUNC static constexpr bool run(const DenseIndex i, const DenseIndex value) {
+ return i < value;
+ }
+};
+
+} // end namespace internal
+} // end namespace Eigen
+
+
+#endif // EIGEN_CXX11_TENSOR_TENSOR_DIMENSION_LIST_H
diff --git a/unsupported/Eigen/CXX11/src/Tensor/TensorDimensions.h b/unsupported/Eigen/CXX11/src/Tensor/TensorDimensions.h
new file mode 100644
index 0000000..6d9e9dc
--- /dev/null
+++ b/unsupported/Eigen/CXX11/src/Tensor/TensorDimensions.h
@@ -0,0 +1,447 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_CXX11_TENSOR_TENSOR_DIMENSIONS_H
+#define EIGEN_CXX11_TENSOR_TENSOR_DIMENSIONS_H
+
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+/** \internal
+ *
+ * \class TensorDimensions
+ * \ingroup CXX11_Tensor_Module
+ *
+ * \brief Set of classes used to encode and store the dimensions of a Tensor.
+ *
+ * The Sizes class encodes as part of the type the number of dimensions and the
+ * sizes corresponding to each dimension. It uses no storage space since it is
+ * entirely known at compile time.
+ * The DSizes class is its dynamic sibling: the number of dimensions is known
+ * at compile time but the sizes are set during execution.
+ *
+ * \sa Tensor
+ */
+
+// Boilerplate code
+namespace internal {
+
+template<std::ptrdiff_t n, typename Dimension> struct dget {
+ static const std::ptrdiff_t value = get<n, Dimension>::value;
+};
+
+
+template<typename Index, std::ptrdiff_t NumIndices, std::ptrdiff_t n, bool RowMajor>
+struct fixed_size_tensor_index_linearization_helper
+{
+ template <typename Dimensions> EIGEN_DEVICE_FUNC
+ static EIGEN_STRONG_INLINE Index run(array<Index, NumIndices> const& indices,
+ const Dimensions& dimensions)
+ {
+ return array_get<RowMajor ? n - 1 : (NumIndices - n)>(indices) +
+ dget<RowMajor ? n - 1 : (NumIndices - n), Dimensions>::value *
+ fixed_size_tensor_index_linearization_helper<Index, NumIndices, n - 1, RowMajor>::run(indices, dimensions);
+ }
+};
+
+template<typename Index, std::ptrdiff_t NumIndices, bool RowMajor>
+struct fixed_size_tensor_index_linearization_helper<Index, NumIndices, 0, RowMajor>
+{
+ template <typename Dimensions> EIGEN_DEVICE_FUNC
+ static EIGEN_STRONG_INLINE Index run(array<Index, NumIndices> const&, const Dimensions&)
+ {
+ return 0;
+ }
+};
+
+template<typename Index, std::ptrdiff_t n>
+struct fixed_size_tensor_index_extraction_helper
+{
+ template <typename Dimensions> EIGEN_DEVICE_FUNC
+ static EIGEN_STRONG_INLINE Index run(const Index index,
+ const Dimensions& dimensions)
+ {
+ const Index mult = (index == n-1) ? 1 : 0;
+ return array_get<n-1>(dimensions) * mult +
+ fixed_size_tensor_index_extraction_helper<Index, n - 1>::run(index, dimensions);
+ }
+};
+
+template<typename Index>
+struct fixed_size_tensor_index_extraction_helper<Index, 0>
+{
+ template <typename Dimensions> EIGEN_DEVICE_FUNC
+ static EIGEN_STRONG_INLINE Index run(const Index,
+ const Dimensions&)
+ {
+ return 0;
+ }
+ };
+
+} // end namespace internal
+
+
+// Fixed size
+#ifndef EIGEN_EMULATE_CXX11_META_H
+template <typename std::ptrdiff_t... Indices>
+struct Sizes {
+ typedef internal::numeric_list<std::ptrdiff_t, Indices...> Base;
+ const Base t = Base();
+ static const std::ptrdiff_t total_size = internal::arg_prod(Indices...);
+ static const ptrdiff_t count = Base::count;
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE std::ptrdiff_t rank() const {
+ return Base::count;
+ }
+
+ static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE std::ptrdiff_t TotalSize() {
+ return internal::arg_prod(Indices...);
+ }
+
+ EIGEN_DEVICE_FUNC Sizes() { }
+ template <typename DenseIndex>
+ explicit EIGEN_DEVICE_FUNC Sizes(const array<DenseIndex, Base::count>& /*indices*/) {
+ // todo: add assertion
+ }
+ template <typename... DenseIndex> EIGEN_DEVICE_FUNC Sizes(DenseIndex...) { }
+ explicit EIGEN_DEVICE_FUNC Sizes(std::initializer_list<std::ptrdiff_t> /*l*/) {
+ // todo: add assertion
+ }
+
+ template <typename T> Sizes& operator = (const T& /*other*/) {
+ // add assertion failure if the size of other is different
+ return *this;
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE std::ptrdiff_t operator[] (const std::ptrdiff_t index) const {
+ return internal::fixed_size_tensor_index_extraction_helper<std::ptrdiff_t, Base::count>::run(index, t);
+ }
+
+ template <typename DenseIndex> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ ptrdiff_t IndexOfColMajor(const array<DenseIndex, Base::count>& indices) const {
+ return internal::fixed_size_tensor_index_linearization_helper<DenseIndex, Base::count, Base::count, false>::run(indices, t);
+ }
+ template <typename DenseIndex> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ ptrdiff_t IndexOfRowMajor(const array<DenseIndex, Base::count>& indices) const {
+ return internal::fixed_size_tensor_index_linearization_helper<DenseIndex, Base::count, Base::count, true>::run(indices, t);
+ }
+};
+
+namespace internal {
+template <typename std::ptrdiff_t... Indices>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE std::ptrdiff_t array_prod(const Sizes<Indices...>&) {
+ return Sizes<Indices...>::total_size;
+}
+}
+
+#else
+
+template <std::ptrdiff_t n>
+struct non_zero_size {
+ typedef internal::type2val<std::ptrdiff_t, n> type;
+};
+template <>
+struct non_zero_size<0> {
+ typedef internal::null_type type;
+};
+
+template <std::ptrdiff_t V1=0, std::ptrdiff_t V2=0, std::ptrdiff_t V3=0, std::ptrdiff_t V4=0, std::ptrdiff_t V5=0> struct Sizes {
+ typedef typename internal::make_type_list<typename non_zero_size<V1>::type, typename non_zero_size<V2>::type, typename non_zero_size<V3>::type, typename non_zero_size<V4>::type, typename non_zero_size<V5>::type >::type Base;
+ static const std::ptrdiff_t count = Base::count;
+ static const std::ptrdiff_t total_size = internal::arg_prod<Base>::value;
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE ptrdiff_t rank() const {
+ return count;
+ }
+
+ static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE ptrdiff_t TotalSize() {
+ return internal::arg_prod<Base>::value;
+ }
+
+ Sizes() { }
+ template <typename DenseIndex>
+ explicit Sizes(const array<DenseIndex, Base::count>& /*indices*/) {
+ // todo: add assertion
+ }
+
+ template <typename T> Sizes& operator = (const T& /*other*/) {
+ // add assertion failure if the size of other is different
+ return *this;
+ }
+
+ template <typename... DenseIndex> Sizes(DenseIndex... /*indices*/) { }
+ explicit Sizes(std::initializer_list<std::ptrdiff_t>) {
+ // todo: add assertion
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Index operator[] (const Index index) const {
+ switch (index) {
+ case 0:
+ return internal::get<0, Base>::value;
+ case 1:
+ return internal::get<1, Base>::value;
+ case 2:
+ return internal::get<2, Base>::value;
+ case 3:
+ return internal::get<3, Base>::value;
+ case 4:
+ return internal::get<4, Base>::value;
+ default:
+ eigen_assert(false && "index overflow");
+ return static_cast<Index>(-1);
+ }
+ }
+
+ template <typename DenseIndex> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ ptrdiff_t IndexOfColMajor(const array<DenseIndex, Base::count>& indices) const {
+ return internal::fixed_size_tensor_index_linearization_helper<DenseIndex, Base::count, Base::count, false>::run(indices, *reinterpret_cast<const Base*>(this));
+ }
+ template <typename DenseIndex> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ ptrdiff_t IndexOfRowMajor(const array<DenseIndex, Base::count>& indices) const {
+ return internal::fixed_size_tensor_index_linearization_helper<DenseIndex, Base::count, Base::count, true>::run(indices, *reinterpret_cast<const Base*>(this));
+ }
+};
+
+namespace internal {
+template <std::ptrdiff_t V1, std::ptrdiff_t V2, std::ptrdiff_t V3, std::ptrdiff_t V4, std::ptrdiff_t V5>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE std::ptrdiff_t array_prod(const Sizes<V1, V2, V3, V4, V5>&) {
+ return Sizes<V1, V2, V3, V4, V5>::total_size;
+}
+}
+
+#endif
+
+// Boilerplate
+namespace internal {
+template<typename Index, std::ptrdiff_t NumIndices, std::ptrdiff_t n, bool RowMajor>
+struct tensor_index_linearization_helper
+{
+ static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ Index run(array<Index, NumIndices> const& indices, array<Index, NumIndices> const& dimensions)
+ {
+ return array_get<RowMajor ? n : (NumIndices - n - 1)>(indices) +
+ array_get<RowMajor ? n : (NumIndices - n - 1)>(dimensions) *
+ tensor_index_linearization_helper<Index, NumIndices, n - 1, RowMajor>::run(indices, dimensions);
+ }
+};
+
+template<typename Index, std::ptrdiff_t NumIndices, bool RowMajor>
+struct tensor_index_linearization_helper<Index, NumIndices, 0, RowMajor>
+{
+ static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ Index run(array<Index, NumIndices> const& indices, array<Index, NumIndices> const&)
+ {
+ return array_get<RowMajor ? 0 : NumIndices - 1>(indices);
+ }
+};
+} // end namespace internal
+
+
+
+// Dynamic size
+template <typename DenseIndex, int NumDims>
+struct DSizes : array<DenseIndex, NumDims> {
+ typedef array<DenseIndex, NumDims> Base;
+ static const int count = NumDims;
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Index rank() const {
+ return NumDims;
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE DenseIndex TotalSize() const {
+ return (NumDims == 0) ? 1 : internal::array_prod(*static_cast<const Base*>(this));
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE DSizes() {
+ for (int i = 0 ; i < NumDims; ++i) {
+ (*this)[i] = 0;
+ }
+ }
+ EIGEN_DEVICE_FUNC explicit DSizes(const array<DenseIndex, NumDims>& a) : Base(a) { }
+
+ EIGEN_DEVICE_FUNC explicit DSizes(const DenseIndex i0) {
+ eigen_assert(NumDims == 1);
+ (*this)[0] = i0;
+ }
+
+ EIGEN_DEVICE_FUNC DSizes(const DimensionList<DenseIndex, NumDims>& a) {
+ for (int i = 0 ; i < NumDims; ++i) {
+ (*this)[i] = a[i];
+ }
+ }
+
+ // Enable DSizes index type promotion only if we are promoting to the
+ // larger type, e.g. allow to promote dimensions of type int to long.
+ template<typename OtherIndex>
+ EIGEN_DEVICE_FUNC
+ explicit DSizes(const array<OtherIndex, NumDims>& other,
+ // Default template parameters require c++11.
+ std::enable_if_t<
+ internal::is_same<
+ DenseIndex,
+ typename internal::promote_index_type<
+ DenseIndex,
+ OtherIndex
+ >::type
+ >::value, void*> = 0) {
+ for (int i = 0; i < NumDims; ++i) {
+ (*this)[i] = static_cast<DenseIndex>(other[i]);
+ }
+ }
+
+ template <typename FirstType, typename... OtherTypes>
+ EIGEN_DEVICE_FUNC
+ explicit DSizes(const Eigen::IndexList<FirstType, OtherTypes...>& dimensions) {
+ for (int i = 0; i < dimensions.count; ++i) {
+ (*this)[i] = dimensions[i];
+ }
+ }
+
+#ifndef EIGEN_EMULATE_CXX11_META_H
+ template <typename std::ptrdiff_t... Indices>
+ EIGEN_DEVICE_FUNC DSizes(const Sizes<Indices...>& a) {
+ for (int i = 0 ; i < NumDims; ++i) {
+ (*this)[i] = a[i];
+ }
+ }
+#else
+ template <std::ptrdiff_t V1, std::ptrdiff_t V2, std::ptrdiff_t V3, std::ptrdiff_t V4, std::ptrdiff_t V5>
+ EIGEN_DEVICE_FUNC DSizes(const Sizes<V1, V2, V3, V4, V5>& a) {
+ for (int i = 0 ; i < NumDims; ++i) {
+ (*this)[i] = a[i];
+ }
+ }
+#endif
+
+ template<typename... IndexTypes> EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE explicit DSizes(DenseIndex firstDimension, DenseIndex secondDimension, IndexTypes... otherDimensions) : Base({{firstDimension, secondDimension, otherDimensions...}}) {
+ EIGEN_STATIC_ASSERT(sizeof...(otherDimensions) + 2 == NumDims, YOU_MADE_A_PROGRAMMING_MISTAKE)
+ }
+
+ EIGEN_DEVICE_FUNC DSizes& operator = (const array<DenseIndex, NumDims>& other) {
+ *static_cast<Base*>(this) = other;
+ return *this;
+ }
+
+ // A constexpr would be so much better here
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE DenseIndex IndexOfColMajor(const array<DenseIndex, NumDims>& indices) const {
+ return internal::tensor_index_linearization_helper<DenseIndex, NumDims, NumDims - 1, false>::run(indices, *static_cast<const Base*>(this));
+ }
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE DenseIndex IndexOfRowMajor(const array<DenseIndex, NumDims>& indices) const {
+ return internal::tensor_index_linearization_helper<DenseIndex, NumDims, NumDims - 1, true>::run(indices, *static_cast<const Base*>(this));
+ }
+};
+
+template <typename IndexType, int NumDims>
+std::ostream& operator<<(std::ostream& os,
+ const DSizes<IndexType, NumDims>& dims) {
+ os << "[";
+ for (int i = 0; i < NumDims; ++i) {
+ if (i > 0) os << ", ";
+ os << dims[i];
+ }
+ os << "]";
+ return os;
+}
+
+// Boilerplate
+namespace internal {
+template<typename Index, std::ptrdiff_t NumIndices, std::ptrdiff_t n, bool RowMajor>
+struct tensor_vsize_index_linearization_helper
+{
+ static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ Index run(array<Index, NumIndices> const& indices, std::vector<DenseIndex> const& dimensions)
+ {
+ return array_get<RowMajor ? n : (NumIndices - n - 1)>(indices) +
+ array_get<RowMajor ? n : (NumIndices - n - 1)>(dimensions) *
+ tensor_vsize_index_linearization_helper<Index, NumIndices, n - 1, RowMajor>::run(indices, dimensions);
+ }
+};
+
+template<typename Index, std::ptrdiff_t NumIndices, bool RowMajor>
+struct tensor_vsize_index_linearization_helper<Index, NumIndices, 0, RowMajor>
+{
+ static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ Index run(array<Index, NumIndices> const& indices, std::vector<DenseIndex> const&)
+ {
+ return array_get<RowMajor ? 0 : NumIndices - 1>(indices);
+ }
+};
+} // end namespace internal
+
+
+namespace internal {
+
+template <typename DenseIndex, int NumDims> struct array_size<const DSizes<DenseIndex, NumDims> > {
+ static const ptrdiff_t value = NumDims;
+};
+template <typename DenseIndex, int NumDims> struct array_size<DSizes<DenseIndex, NumDims> > {
+ static const ptrdiff_t value = NumDims;
+};
+#ifndef EIGEN_EMULATE_CXX11_META_H
+template <typename std::ptrdiff_t... Indices> struct array_size<const Sizes<Indices...> > {
+static const std::ptrdiff_t value = Sizes<Indices...>::count;
+};
+template <typename std::ptrdiff_t... Indices> struct array_size<Sizes<Indices...> > {
+static const std::ptrdiff_t value = Sizes<Indices...>::count;
+};
+template <std::ptrdiff_t n, typename std::ptrdiff_t... Indices> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE std::ptrdiff_t array_get(const Sizes<Indices...>&) {
+ return get<n, internal::numeric_list<std::ptrdiff_t, Indices...> >::value;
+}
+template <std::ptrdiff_t n> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE std::ptrdiff_t array_get(const Sizes<>&) {
+ eigen_assert(false && "should never be called");
+ return -1;
+}
+#else
+template <std::ptrdiff_t V1, std::ptrdiff_t V2, std::ptrdiff_t V3, std::ptrdiff_t V4, std::ptrdiff_t V5> struct array_size<const Sizes<V1,V2,V3,V4,V5> > {
+ static const ptrdiff_t value = Sizes<V1,V2,V3,V4,V5>::count;
+};
+template <std::ptrdiff_t V1, std::ptrdiff_t V2, std::ptrdiff_t V3, std::ptrdiff_t V4, std::ptrdiff_t V5> struct array_size<Sizes<V1,V2,V3,V4,V5> > {
+ static const ptrdiff_t value = Sizes<V1,V2,V3,V4,V5>::count;
+};
+template <std::ptrdiff_t n, std::ptrdiff_t V1, std::ptrdiff_t V2, std::ptrdiff_t V3, std::ptrdiff_t V4, std::ptrdiff_t V5> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE std::ptrdiff_t array_get(const Sizes<V1,V2,V3,V4,V5>&) {
+ return get<n, typename Sizes<V1,V2,V3,V4,V5>::Base>::value;
+}
+
+#endif
+
+
+template <typename Dims1, typename Dims2, ptrdiff_t n, ptrdiff_t m>
+struct sizes_match_below_dim {
+ static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE bool run(Dims1&, Dims2&) {
+ return false;
+ }
+};
+template <typename Dims1, typename Dims2, ptrdiff_t n>
+struct sizes_match_below_dim<Dims1, Dims2, n, n> {
+ static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE bool run(Dims1& dims1, Dims2& dims2) {
+ return (array_get<n-1>(dims1) == array_get<n-1>(dims2)) &&
+ sizes_match_below_dim<Dims1, Dims2, n-1, n-1>::run(dims1, dims2);
+ }
+};
+template <typename Dims1, typename Dims2>
+struct sizes_match_below_dim<Dims1, Dims2, 0, 0> {
+ static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE bool run(Dims1&, Dims2&) {
+ return true;
+ }
+};
+
+} // end namespace internal
+
+
+template <typename Dims1, typename Dims2>
+EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE bool dimensions_match(Dims1 dims1, Dims2 dims2) {
+ return internal::sizes_match_below_dim<Dims1, Dims2, internal::array_size<Dims1>::value, internal::array_size<Dims2>::value>::run(dims1, dims2);
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_CXX11_TENSOR_TENSOR_DIMENSIONS_H
diff --git a/unsupported/Eigen/CXX11/src/Tensor/TensorEvalTo.h b/unsupported/Eigen/CXX11/src/Tensor/TensorEvalTo.h
new file mode 100644
index 0000000..0e9cdfe
--- /dev/null
+++ b/unsupported/Eigen/CXX11/src/Tensor/TensorEvalTo.h
@@ -0,0 +1,238 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_CXX11_TENSOR_TENSOR_EVAL_TO_H
+#define EIGEN_CXX11_TENSOR_TENSOR_EVAL_TO_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+/** \class TensorForcedEval
+ * \ingroup CXX11_Tensor_Module
+ *
+ * \brief Tensor reshaping class.
+ *
+ *
+ */
+namespace internal {
+template<typename XprType, template <class> class MakePointer_>
+struct traits<TensorEvalToOp<XprType, MakePointer_> >
+{
+ // Type promotion to handle the case where the types of the lhs and the rhs are different.
+ typedef typename XprType::Scalar Scalar;
+ typedef traits<XprType> XprTraits;
+ typedef typename XprTraits::StorageKind StorageKind;
+ typedef typename XprTraits::Index Index;
+ typedef typename XprType::Nested Nested;
+ typedef std::remove_reference_t<Nested> Nested_;
+ static constexpr int NumDimensions = XprTraits::NumDimensions;
+ static constexpr int Layout = XprTraits::Layout;
+ typedef typename MakePointer_<Scalar>::Type PointerType;
+
+ enum {
+ Flags = 0
+ };
+ template <class T>
+ struct MakePointer {
+ // Intermediate typedef to workaround MSVC issue.
+ typedef MakePointer_<T> MakePointerT;
+ typedef typename MakePointerT::Type Type;
+
+
+ };
+};
+
+template<typename XprType, template <class> class MakePointer_>
+struct eval<TensorEvalToOp<XprType, MakePointer_>, Eigen::Dense>
+{
+ typedef const TensorEvalToOp<XprType, MakePointer_>& type;
+};
+
+template<typename XprType, template <class> class MakePointer_>
+struct nested<TensorEvalToOp<XprType, MakePointer_>, 1, typename eval<TensorEvalToOp<XprType, MakePointer_> >::type>
+{
+ typedef TensorEvalToOp<XprType, MakePointer_> type;
+};
+
+} // end namespace internal
+
+
+
+
+template<typename XprType, template <class> class MakePointer_>
+class TensorEvalToOp : public TensorBase<TensorEvalToOp<XprType, MakePointer_>, ReadOnlyAccessors>
+{
+ public:
+ typedef typename Eigen::internal::traits<TensorEvalToOp>::Scalar Scalar;
+ typedef typename Eigen::NumTraits<Scalar>::Real RealScalar;
+ typedef std::remove_const_t<typename XprType::CoeffReturnType> CoeffReturnType;
+ typedef typename MakePointer_<CoeffReturnType>::Type PointerType;
+ typedef typename Eigen::internal::nested<TensorEvalToOp>::type Nested;
+ typedef typename Eigen::internal::traits<TensorEvalToOp>::StorageKind StorageKind;
+ typedef typename Eigen::internal::traits<TensorEvalToOp>::Index Index;
+
+ static constexpr int NumDims = Eigen::internal::traits<TensorEvalToOp>::NumDimensions;
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorEvalToOp(PointerType buffer, const XprType& expr)
+ : m_xpr(expr), m_buffer(buffer) {}
+
+ EIGEN_DEVICE_FUNC
+ const internal::remove_all_t<typename XprType::Nested>&
+ expression() const { return m_xpr; }
+
+ EIGEN_DEVICE_FUNC PointerType buffer() const { return m_buffer; }
+
+ protected:
+ typename XprType::Nested m_xpr;
+ PointerType m_buffer;
+};
+
+
+
+template<typename ArgType, typename Device, template <class> class MakePointer_>
+struct TensorEvaluator<const TensorEvalToOp<ArgType, MakePointer_>, Device>
+{
+ typedef TensorEvalToOp<ArgType, MakePointer_> XprType;
+ typedef typename ArgType::Scalar Scalar;
+ typedef typename TensorEvaluator<ArgType, Device>::Dimensions Dimensions;
+ typedef typename XprType::Index Index;
+ typedef std::remove_const_t<typename XprType::CoeffReturnType> CoeffReturnType;
+ typedef typename PacketType<CoeffReturnType, Device>::type PacketReturnType;
+ static constexpr int PacketSize = PacketType<CoeffReturnType, Device>::size;
+ typedef typename Eigen::internal::traits<XprType>::PointerType TensorPointerType;
+ typedef StorageMemory<CoeffReturnType, Device> Storage;
+ typedef typename Storage::Type EvaluatorPointerType;
+ enum {
+ IsAligned = TensorEvaluator<ArgType, Device>::IsAligned,
+ PacketAccess = TensorEvaluator<ArgType, Device>::PacketAccess,
+ BlockAccess = true,
+ PreferBlockAccess = false,
+ CoordAccess = false, // to be implemented
+ RawAccess = true
+ };
+
+ static constexpr int Layout = TensorEvaluator<ArgType, Device>::Layout;
+ static constexpr int NumDims = internal::traits<ArgType>::NumDimensions;
+
+ //===- Tensor block evaluation strategy (see TensorBlock.h) -------------===//
+ typedef internal::TensorBlockDescriptor<NumDims, Index> TensorBlockDesc;
+ typedef internal::TensorBlockScratchAllocator<Device> TensorBlockScratch;
+
+ typedef typename TensorEvaluator<const ArgType, Device>::TensorBlock
+ ArgTensorBlock;
+
+ typedef internal::TensorBlockAssignment<
+ CoeffReturnType, NumDims, typename ArgTensorBlock::XprType, Index>
+ TensorBlockAssignment;
+ //===--------------------------------------------------------------------===//
+
+ EIGEN_STRONG_INLINE TensorEvaluator(const XprType& op, const Device& device)
+ : m_impl(op.expression(), device), m_buffer(device.get(op.buffer())), m_expression(op.expression()){}
+
+
+ EIGEN_STRONG_INLINE ~TensorEvaluator() {
+ }
+
+
+ EIGEN_DEVICE_FUNC const Dimensions& dimensions() const { return m_impl.dimensions(); }
+
+ EIGEN_STRONG_INLINE bool evalSubExprsIfNeeded(EvaluatorPointerType scalar) {
+ EIGEN_UNUSED_VARIABLE(scalar);
+ eigen_assert(scalar == NULL);
+ return m_impl.evalSubExprsIfNeeded(m_buffer);
+ }
+
+#ifdef EIGEN_USE_THREADS
+ template <typename EvalSubExprsCallback>
+ EIGEN_STRONG_INLINE void evalSubExprsIfNeededAsync(
+ EvaluatorPointerType scalar, EvalSubExprsCallback done) {
+ EIGEN_UNUSED_VARIABLE(scalar);
+ eigen_assert(scalar == NULL);
+ m_impl.evalSubExprsIfNeededAsync(m_buffer, std::move(done));
+ }
+#endif
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void evalScalar(Index i) {
+ m_buffer[i] = m_impl.coeff(i);
+ }
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void evalPacket(Index i) {
+ internal::pstoret<CoeffReturnType, PacketReturnType, Aligned>(m_buffer + i, m_impl.template packet<TensorEvaluator<ArgType, Device>::IsAligned ? Aligned : Unaligned>(i));
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ internal::TensorBlockResourceRequirements getResourceRequirements() const {
+ return m_impl.getResourceRequirements();
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void evalBlock(
+ TensorBlockDesc& desc, TensorBlockScratch& scratch) {
+ // Add `m_buffer` as destination buffer to the block descriptor.
+ desc.template AddDestinationBuffer<Layout>(
+ /*dst_base=*/m_buffer + desc.offset(),
+ /*dst_strides=*/internal::strides<Layout>(m_impl.dimensions()));
+
+ ArgTensorBlock block =
+ m_impl.block(desc, scratch, /*root_of_expr_ast=*/true);
+
+ // If block was evaluated into a destination buffer, there is no need to do
+ // an assignment.
+ if (block.kind() != internal::TensorBlockKind::kMaterializedInOutput) {
+ TensorBlockAssignment::Run(
+ TensorBlockAssignment::target(
+ desc.dimensions(), internal::strides<Layout>(m_impl.dimensions()),
+ m_buffer, desc.offset()),
+ block.expr());
+ }
+ block.cleanup();
+ }
+
+ EIGEN_STRONG_INLINE void cleanup() {
+ m_impl.cleanup();
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE CoeffReturnType coeff(Index index) const
+ {
+ return m_buffer[index];
+ }
+
+ template<int LoadMode>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE PacketReturnType packet(Index index) const
+ {
+ return internal::ploadt<PacketReturnType, LoadMode>(m_buffer + index);
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorOpCost costPerCoeff(bool vectorized) const {
+ // We assume that evalPacket or evalScalar is called to perform the
+ // assignment and account for the cost of the write here.
+ return m_impl.costPerCoeff(vectorized) +
+ TensorOpCost(0, sizeof(CoeffReturnType), 0, vectorized, PacketSize);
+ }
+
+ EIGEN_DEVICE_FUNC EvaluatorPointerType data() const { return m_buffer; }
+ ArgType expression() const { return m_expression; }
+ #ifdef EIGEN_USE_SYCL
+ // binding placeholder accessors to a command group handler for SYCL
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void bind(cl::sycl::handler &cgh) const {
+ m_impl.bind(cgh);
+ m_buffer.bind(cgh);
+ }
+ #endif
+
+
+ private:
+ TensorEvaluator<ArgType, Device> m_impl;
+ EvaluatorPointerType m_buffer;
+ const ArgType m_expression;
+};
+
+
+} // end namespace Eigen
+
+#endif // EIGEN_CXX11_TENSOR_TENSOR_EVAL_TO_H
diff --git a/unsupported/Eigen/CXX11/src/Tensor/TensorEvaluator.h b/unsupported/Eigen/CXX11/src/Tensor/TensorEvaluator.h
new file mode 100644
index 0000000..92ad0f5
--- /dev/null
+++ b/unsupported/Eigen/CXX11/src/Tensor/TensorEvaluator.h
@@ -0,0 +1,984 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_CXX11_TENSOR_TENSOR_EVALUATOR_H
+#define EIGEN_CXX11_TENSOR_TENSOR_EVALUATOR_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+/** \class TensorEvaluator
+ * \ingroup CXX11_Tensor_Module
+ *
+ * \brief The tensor evaluator classes.
+ *
+ * These classes are responsible for the evaluation of the tensor expression.
+ *
+ * TODO: add support for more types of expressions, in particular expressions
+ * leading to lvalues (slicing, reshaping, etc...)
+ */
+
+// Generic evaluator
+template<typename Derived, typename Device>
+struct TensorEvaluator
+{
+ typedef typename Derived::Index Index;
+ typedef typename Derived::Scalar Scalar;
+ typedef typename Derived::Scalar CoeffReturnType;
+ typedef typename PacketType<CoeffReturnType, Device>::type PacketReturnType;
+ typedef typename Derived::Dimensions Dimensions;
+ typedef Derived XprType;
+ static constexpr int PacketSize = PacketType<CoeffReturnType, Device>::size;
+ typedef typename internal::traits<Derived>::template MakePointer<Scalar>::Type TensorPointerType;
+ typedef StorageMemory<Scalar, Device> Storage;
+ typedef typename Storage::Type EvaluatorPointerType;
+
+ // NumDimensions is -1 for variable dim tensors
+ static constexpr int NumCoords = internal::traits<Derived>::NumDimensions > 0 ?
+ internal::traits<Derived>::NumDimensions : 0;
+ static constexpr int Layout = Derived::Layout;
+
+ enum {
+ IsAligned = Derived::IsAligned,
+ PacketAccess = (PacketType<CoeffReturnType, Device>::size > 1),
+ BlockAccess = internal::is_arithmetic<std::remove_const_t<Scalar>>::value,
+ PreferBlockAccess = false,
+ CoordAccess = NumCoords > 0,
+ RawAccess = true
+ };
+
+ typedef std::remove_const_t<Scalar> ScalarNoConst;
+
+ //===- Tensor block evaluation strategy (see TensorBlock.h) -------------===//
+ typedef internal::TensorBlockDescriptor<NumCoords, Index> TensorBlockDesc;
+ typedef internal::TensorBlockScratchAllocator<Device> TensorBlockScratch;
+
+ typedef typename internal::TensorMaterializedBlock<ScalarNoConst, NumCoords,
+ Layout, Index>
+ TensorBlock;
+ //===--------------------------------------------------------------------===//
+
+ EIGEN_STRONG_INLINE TensorEvaluator(const Derived& m, const Device& device)
+ : m_data(device.get((const_cast<TensorPointerType>(m.data())))),
+ m_dims(m.dimensions()),
+ m_device(device)
+ { }
+
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Dimensions& dimensions() const { return m_dims; }
+
+ EIGEN_STRONG_INLINE bool evalSubExprsIfNeeded(EvaluatorPointerType dest) {
+ if (!NumTraits<std::remove_const_t<Scalar>>::RequireInitialization && dest) {
+ m_device.memcpy((void*)(m_device.get(dest)), m_device.get(m_data), m_dims.TotalSize() * sizeof(Scalar));
+ return false;
+ }
+ return true;
+ }
+
+#ifdef EIGEN_USE_THREADS
+ template <typename EvalSubExprsCallback>
+ EIGEN_STRONG_INLINE void evalSubExprsIfNeededAsync(
+ EvaluatorPointerType dest, EvalSubExprsCallback done) {
+ // TODO(ezhulenev): ThreadPoolDevice memcpy is blockign operation.
+ done(evalSubExprsIfNeeded(dest));
+ }
+#endif // EIGEN_USE_THREADS
+
+ EIGEN_STRONG_INLINE void cleanup() {}
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE CoeffReturnType coeff(Index index) const {
+ eigen_assert(m_data != NULL);
+ return m_data[index];
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE CoeffReturnType& coeffRef(Index index) {
+ eigen_assert(m_data != NULL);
+ return m_data[index];
+ }
+
+ template<int LoadMode> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ PacketReturnType packet(Index index) const
+ {
+ return internal::ploadt<PacketReturnType, LoadMode>(m_data + index);
+ }
+
+ // Return a packet starting at `index` where `umask` specifies which elements
+ // have to be loaded. Type/size of mask depends on PacketReturnType, e.g. for
+ // Packet16f, `umask` is of type uint16_t and if a bit is 1, corresponding
+ // float element will be loaded, otherwise 0 will be loaded.
+ // Function has been templatized to enable Sfinae.
+ template <typename PacketReturnTypeT> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ std::enable_if_t<internal::unpacket_traits<PacketReturnTypeT>::masked_load_available, PacketReturnTypeT>
+ partialPacket(Index index, typename internal::unpacket_traits<PacketReturnTypeT>::mask_t umask) const
+ {
+ return internal::ploadu<PacketReturnTypeT>(m_data + index, umask);
+ }
+
+ template <int StoreMode> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ void writePacket(Index index, const PacketReturnType& x)
+ {
+ return internal::pstoret<Scalar, PacketReturnType, StoreMode>(m_data + index, x);
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE CoeffReturnType coeff(const array<DenseIndex, NumCoords>& coords) const {
+ eigen_assert(m_data != NULL);
+ if (static_cast<int>(Layout) == static_cast<int>(ColMajor)) {
+ return m_data[m_dims.IndexOfColMajor(coords)];
+ } else {
+ return m_data[m_dims.IndexOfRowMajor(coords)];
+ }
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE CoeffReturnType&
+ coeffRef(const array<DenseIndex, NumCoords>& coords) {
+ eigen_assert(m_data != NULL);
+ if (static_cast<int>(Layout) == static_cast<int>(ColMajor)) {
+ return m_data[m_dims.IndexOfColMajor(coords)];
+ } else {
+ return m_data[m_dims.IndexOfRowMajor(coords)];
+ }
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorOpCost costPerCoeff(bool vectorized) const {
+ return TensorOpCost(sizeof(CoeffReturnType), 0, 0, vectorized,
+ PacketType<CoeffReturnType, Device>::size);
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ internal::TensorBlockResourceRequirements getResourceRequirements() const {
+ return internal::TensorBlockResourceRequirements::any();
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorBlock
+ block(TensorBlockDesc& desc, TensorBlockScratch& scratch,
+ bool /*root_of_expr_ast*/ = false) const {
+ eigen_assert(m_data != NULL);
+ return TensorBlock::materialize(m_data, m_dims, desc, scratch);
+ }
+
+ template<typename TensorBlock>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void writeBlock(
+ const TensorBlockDesc& desc, const TensorBlock& block) {
+ eigen_assert(m_data != NULL);
+
+ typedef typename TensorBlock::XprType TensorBlockExpr;
+ typedef internal::TensorBlockAssignment<Scalar, NumCoords, TensorBlockExpr,
+ Index>
+ TensorBlockAssign;
+
+ TensorBlockAssign::Run(
+ TensorBlockAssign::target(desc.dimensions(),
+ internal::strides<Layout>(m_dims), m_data,
+ desc.offset()),
+ block.expr());
+ }
+
+ EIGEN_DEVICE_FUNC EvaluatorPointerType data() const { return m_data; }
+
+#ifdef EIGEN_USE_SYCL
+ // binding placeholder accessors to a command group handler for SYCL
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void bind(cl::sycl::handler &cgh) const {
+ m_data.bind(cgh);
+ }
+#endif
+ protected:
+ EvaluatorPointerType m_data;
+ Dimensions m_dims;
+ const Device EIGEN_DEVICE_REF m_device;
+};
+
+namespace internal {
+template <typename T> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
+T loadConstant(const T* address) {
+ return *address;
+}
+// Use the texture cache on CUDA devices whenever possible
+#if defined(EIGEN_CUDA_ARCH) && EIGEN_CUDA_ARCH >= 350
+template <> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
+float loadConstant(const float* address) {
+ return __ldg(address);
+}
+template <> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
+double loadConstant(const double* address) {
+ return __ldg(address);
+}
+template <> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
+Eigen::half loadConstant(const Eigen::half* address) {
+ return Eigen::half(half_impl::raw_uint16_to_half(__ldg(&address->x)));
+}
+#endif
+#ifdef EIGEN_USE_SYCL
+// overload of load constant should be implemented here based on range access
+template <cl::sycl::access::mode AcMd, typename T>
+T &loadConstant(const Eigen::TensorSycl::internal::RangeAccess<AcMd, T> &address) {
+ return *address;
+}
+#endif
+} // namespace internal
+
+// Default evaluator for rvalues
+template<typename Derived, typename Device>
+struct TensorEvaluator<const Derived, Device>
+{
+ typedef typename Derived::Index Index;
+ typedef typename Derived::Scalar Scalar;
+ typedef typename Derived::Scalar CoeffReturnType;
+ typedef typename PacketType<CoeffReturnType, Device>::type PacketReturnType;
+ typedef typename Derived::Dimensions Dimensions;
+ typedef const Derived XprType;
+ typedef typename internal::traits<Derived>::template MakePointer<const Scalar>::Type TensorPointerType;
+ typedef StorageMemory<const Scalar, Device> Storage;
+ typedef typename Storage::Type EvaluatorPointerType;
+
+ typedef std::remove_const_t<Scalar> ScalarNoConst;
+
+ // NumDimensions is -1 for variable dim tensors
+ static constexpr int NumCoords = internal::traits<Derived>::NumDimensions > 0 ?
+ internal::traits<Derived>::NumDimensions : 0;
+ static constexpr int PacketSize = PacketType<CoeffReturnType, Device>::size;
+ static constexpr int Layout = Derived::Layout;
+
+ enum {
+ IsAligned = Derived::IsAligned,
+ PacketAccess = (PacketType<CoeffReturnType, Device>::size > 1),
+ BlockAccess = internal::is_arithmetic<ScalarNoConst>::value,
+ PreferBlockAccess = false,
+ CoordAccess = NumCoords > 0,
+ RawAccess = true
+ };
+
+ //===- Tensor block evaluation strategy (see TensorBlock.h) -------------===//
+ typedef internal::TensorBlockDescriptor<NumCoords, Index> TensorBlockDesc;
+ typedef internal::TensorBlockScratchAllocator<Device> TensorBlockScratch;
+
+ typedef typename internal::TensorMaterializedBlock<ScalarNoConst, NumCoords,
+ Layout, Index>
+ TensorBlock;
+ //===--------------------------------------------------------------------===//
+
+ EIGEN_STRONG_INLINE TensorEvaluator(const Derived& m, const Device& device)
+ : m_data(device.get(m.data())), m_dims(m.dimensions()), m_device(device)
+ { }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Dimensions& dimensions() const { return m_dims; }
+
+ EIGEN_STRONG_INLINE bool evalSubExprsIfNeeded(EvaluatorPointerType data) {
+ if (!NumTraits<std::remove_const_t<Scalar>>::RequireInitialization && data) {
+ m_device.memcpy((void*)(m_device.get(data)),m_device.get(m_data), m_dims.TotalSize() * sizeof(Scalar));
+ return false;
+ }
+ return true;
+ }
+
+#ifdef EIGEN_USE_THREADS
+ template <typename EvalSubExprsCallback>
+ EIGEN_STRONG_INLINE void evalSubExprsIfNeededAsync(
+ EvaluatorPointerType dest, EvalSubExprsCallback done) {
+ // TODO(ezhulenev): ThreadPoolDevice memcpy is a blockign operation.
+ done(evalSubExprsIfNeeded(dest));
+ }
+#endif // EIGEN_USE_THREADS
+
+ EIGEN_STRONG_INLINE void cleanup() { }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE CoeffReturnType coeff(Index index) const {
+ eigen_assert(m_data != NULL);
+ return internal::loadConstant(m_data+index);
+ }
+
+ template<int LoadMode> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ PacketReturnType packet(Index index) const
+ {
+ return internal::ploadt_ro<PacketReturnType, LoadMode>(m_data + index);
+ }
+
+ // Return a packet starting at `index` where `umask` specifies which elements
+ // have to be loaded. Type/size of mask depends on PacketReturnType, e.g. for
+ // Packet16f, `umask` is of type uint16_t and if a bit is 1, corresponding
+ // float element will be loaded, otherwise 0 will be loaded.
+ // Function has been templatized to enable Sfinae.
+ template <typename PacketReturnTypeT> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ std::enable_if_t<internal::unpacket_traits<PacketReturnTypeT>::masked_load_available, PacketReturnTypeT>
+ partialPacket(Index index, typename internal::unpacket_traits<PacketReturnTypeT>::mask_t umask) const
+ {
+ return internal::ploadu<PacketReturnTypeT>(m_data + index, umask);
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE CoeffReturnType coeff(const array<DenseIndex, NumCoords>& coords) const {
+ eigen_assert(m_data != NULL);
+ const Index index = (static_cast<int>(Layout) == static_cast<int>(ColMajor)) ? m_dims.IndexOfColMajor(coords)
+ : m_dims.IndexOfRowMajor(coords);
+ return internal::loadConstant(m_data+index);
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorOpCost costPerCoeff(bool vectorized) const {
+ return TensorOpCost(sizeof(CoeffReturnType), 0, 0, vectorized,
+ PacketType<CoeffReturnType, Device>::size);
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ internal::TensorBlockResourceRequirements getResourceRequirements() const {
+ return internal::TensorBlockResourceRequirements::any();
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorBlock
+ block(TensorBlockDesc& desc, TensorBlockScratch& scratch,
+ bool /*root_of_expr_ast*/ = false) const {
+ eigen_assert(m_data != NULL);
+ return TensorBlock::materialize(m_data, m_dims, desc, scratch);
+ }
+
+ EIGEN_DEVICE_FUNC EvaluatorPointerType data() const { return m_data; }
+#ifdef EIGEN_USE_SYCL
+ // binding placeholder accessors to a command group handler for SYCL
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void bind(cl::sycl::handler &cgh) const {
+ m_data.bind(cgh);
+ }
+#endif
+ protected:
+ EvaluatorPointerType m_data;
+ Dimensions m_dims;
+ const Device EIGEN_DEVICE_REF m_device;
+};
+
+
+
+
+// -------------------- CwiseNullaryOp --------------------
+
+template<typename NullaryOp, typename ArgType, typename Device>
+struct TensorEvaluator<const TensorCwiseNullaryOp<NullaryOp, ArgType>, Device>
+{
+ typedef TensorCwiseNullaryOp<NullaryOp, ArgType> XprType;
+
+ TensorEvaluator(const XprType& op, const Device& device)
+ : m_functor(op.functor()), m_argImpl(op.nestedExpression(), device), m_wrapper()
+ { }
+
+ typedef typename XprType::Index Index;
+ typedef typename XprType::Scalar Scalar;
+ typedef typename internal::traits<XprType>::Scalar CoeffReturnType;
+ typedef typename PacketType<CoeffReturnType, Device>::type PacketReturnType;
+ static constexpr int PacketSize = PacketType<CoeffReturnType, Device>::size;
+ typedef typename TensorEvaluator<ArgType, Device>::Dimensions Dimensions;
+ typedef StorageMemory<CoeffReturnType, Device> Storage;
+ typedef typename Storage::Type EvaluatorPointerType;
+
+ static constexpr int Layout = TensorEvaluator<ArgType, Device>::Layout;
+ enum {
+ IsAligned = true,
+ PacketAccess = internal::functor_traits<NullaryOp>::PacketAccess
+ #ifdef EIGEN_USE_SYCL
+ && (PacketType<CoeffReturnType, Device>::size >1)
+ #endif
+ ,
+ BlockAccess = false,
+ PreferBlockAccess = false,
+ CoordAccess = false, // to be implemented
+ RawAccess = false
+ };
+
+ //===- Tensor block evaluation strategy (see TensorBlock.h) -------------===//
+ typedef internal::TensorBlockNotImplemented TensorBlock;
+ //===--------------------------------------------------------------------===//
+
+ EIGEN_DEVICE_FUNC const Dimensions& dimensions() const { return m_argImpl.dimensions(); }
+
+ EIGEN_STRONG_INLINE bool evalSubExprsIfNeeded(EvaluatorPointerType) { return true; }
+
+#ifdef EIGEN_USE_THREADS
+ template <typename EvalSubExprsCallback>
+ EIGEN_STRONG_INLINE void evalSubExprsIfNeededAsync(
+ EvaluatorPointerType, EvalSubExprsCallback done) {
+ done(true);
+ }
+#endif // EIGEN_USE_THREADS
+
+ EIGEN_STRONG_INLINE void cleanup() { }
+
+ EIGEN_DEVICE_FUNC CoeffReturnType coeff(Index index) const
+ {
+ return m_wrapper(m_functor, index);
+ }
+
+ template<int LoadMode>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE PacketReturnType packet(Index index) const
+ {
+ return m_wrapper.template packetOp<PacketReturnType, Index>(m_functor, index);
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorOpCost
+ costPerCoeff(bool vectorized) const {
+ return TensorOpCost(sizeof(CoeffReturnType), 0, 0, vectorized,
+ PacketType<CoeffReturnType, Device>::size);
+ }
+
+ EIGEN_DEVICE_FUNC EvaluatorPointerType data() const { return NULL; }
+
+#ifdef EIGEN_USE_SYCL
+ // binding placeholder accessors to a command group handler for SYCL
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void bind(cl::sycl::handler &cgh) const {
+ m_argImpl.bind(cgh);
+ }
+#endif
+
+ private:
+ const NullaryOp m_functor;
+ TensorEvaluator<ArgType, Device> m_argImpl;
+ const internal::nullary_wrapper<CoeffReturnType,NullaryOp> m_wrapper;
+};
+
+
+
+// -------------------- CwiseUnaryOp --------------------
+
+template<typename UnaryOp, typename ArgType, typename Device>
+struct TensorEvaluator<const TensorCwiseUnaryOp<UnaryOp, ArgType>, Device>
+{
+ typedef TensorCwiseUnaryOp<UnaryOp, ArgType> XprType;
+
+ static constexpr int Layout = TensorEvaluator<ArgType, Device>::Layout;
+ enum {
+ IsAligned = TensorEvaluator<ArgType, Device>::IsAligned,
+ PacketAccess = int(TensorEvaluator<ArgType, Device>::PacketAccess) &
+ int(internal::functor_traits<UnaryOp>::PacketAccess),
+ BlockAccess = TensorEvaluator<ArgType, Device>::BlockAccess,
+ PreferBlockAccess = TensorEvaluator<ArgType, Device>::PreferBlockAccess,
+ CoordAccess = false, // to be implemented
+ RawAccess = false
+ };
+
+ TensorEvaluator(const XprType& op, const Device& device)
+ : m_device(device),
+ m_functor(op.functor()),
+ m_argImpl(op.nestedExpression(), device)
+ { }
+
+ typedef typename XprType::Index Index;
+ typedef typename XprType::Scalar Scalar;
+ typedef std::remove_const_t<Scalar> ScalarNoConst;
+ typedef typename internal::traits<XprType>::Scalar CoeffReturnType;
+ typedef typename PacketType<CoeffReturnType, Device>::type PacketReturnType;
+ static constexpr int PacketSize = PacketType<CoeffReturnType, Device>::size;
+ typedef typename TensorEvaluator<ArgType, Device>::Dimensions Dimensions;
+ typedef StorageMemory<CoeffReturnType, Device> Storage;
+ typedef typename Storage::Type EvaluatorPointerType;
+ static constexpr int NumDims = internal::array_size<Dimensions>::value;
+
+ //===- Tensor block evaluation strategy (see TensorBlock.h) -------------===//
+ typedef internal::TensorBlockDescriptor<NumDims, Index> TensorBlockDesc;
+ typedef internal::TensorBlockScratchAllocator<Device> TensorBlockScratch;
+
+ typedef typename TensorEvaluator<const ArgType, Device>::TensorBlock
+ ArgTensorBlock;
+
+ typedef internal::TensorCwiseUnaryBlock<UnaryOp, ArgTensorBlock>
+ TensorBlock;
+ //===--------------------------------------------------------------------===//
+
+ EIGEN_DEVICE_FUNC const Dimensions& dimensions() const { return m_argImpl.dimensions(); }
+
+ EIGEN_STRONG_INLINE bool evalSubExprsIfNeeded(EvaluatorPointerType) {
+ m_argImpl.evalSubExprsIfNeeded(NULL);
+ return true;
+ }
+
+#ifdef EIGEN_USE_THREADS
+ template <typename EvalSubExprsCallback>
+ EIGEN_STRONG_INLINE void evalSubExprsIfNeededAsync(
+ EvaluatorPointerType, EvalSubExprsCallback done) {
+ m_argImpl.evalSubExprsIfNeededAsync(nullptr, [done](bool) { done(true); });
+ }
+#endif // EIGEN_USE_THREADS
+
+ EIGEN_STRONG_INLINE void cleanup() {
+ m_argImpl.cleanup();
+ }
+
+ EIGEN_DEVICE_FUNC CoeffReturnType coeff(Index index) const
+ {
+ return m_functor(m_argImpl.coeff(index));
+ }
+
+ template<int LoadMode>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE PacketReturnType packet(Index index) const
+ {
+ return m_functor.packetOp(m_argImpl.template packet<LoadMode>(index));
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorOpCost costPerCoeff(bool vectorized) const {
+ const double functor_cost = internal::functor_traits<UnaryOp>::Cost;
+ return m_argImpl.costPerCoeff(vectorized) +
+ TensorOpCost(0, 0, functor_cost, vectorized, PacketSize);
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ internal::TensorBlockResourceRequirements getResourceRequirements() const {
+ static const double functor_cost = internal::functor_traits<UnaryOp>::Cost;
+ return m_argImpl.getResourceRequirements().addCostPerCoeff(
+ {0, 0, functor_cost / PacketSize});
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorBlock
+ block(TensorBlockDesc& desc, TensorBlockScratch& scratch,
+ bool /*root_of_expr_ast*/ = false) const {
+ return TensorBlock(m_argImpl.block(desc, scratch), m_functor);
+ }
+
+ EIGEN_DEVICE_FUNC EvaluatorPointerType data() const { return NULL; }
+
+#ifdef EIGEN_USE_SYCL
+ // binding placeholder accessors to a command group handler for SYCL
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void bind(cl::sycl::handler &cgh) const{
+ m_argImpl.bind(cgh);
+ }
+#endif
+
+
+ private:
+ const Device EIGEN_DEVICE_REF m_device;
+ const UnaryOp m_functor;
+ TensorEvaluator<ArgType, Device> m_argImpl;
+};
+
+
+// -------------------- CwiseBinaryOp --------------------
+
+template<typename BinaryOp, typename LeftArgType, typename RightArgType, typename Device>
+struct TensorEvaluator<const TensorCwiseBinaryOp<BinaryOp, LeftArgType, RightArgType>, Device>
+{
+ typedef TensorCwiseBinaryOp<BinaryOp, LeftArgType, RightArgType> XprType;
+
+ static constexpr int Layout = TensorEvaluator<LeftArgType, Device>::Layout;
+ enum {
+ IsAligned = int(TensorEvaluator<LeftArgType, Device>::IsAligned) &
+ int(TensorEvaluator<RightArgType, Device>::IsAligned),
+ PacketAccess = int(TensorEvaluator<LeftArgType, Device>::PacketAccess) &
+ int(TensorEvaluator<RightArgType, Device>::PacketAccess) &
+ int(internal::functor_traits<BinaryOp>::PacketAccess),
+ BlockAccess = int(TensorEvaluator<LeftArgType, Device>::BlockAccess) &
+ int(TensorEvaluator<RightArgType, Device>::BlockAccess),
+ PreferBlockAccess = int(TensorEvaluator<LeftArgType, Device>::PreferBlockAccess) |
+ int(TensorEvaluator<RightArgType, Device>::PreferBlockAccess),
+ CoordAccess = false, // to be implemented
+ RawAccess = false
+ };
+
+ TensorEvaluator(const XprType& op, const Device& device)
+ : m_device(device),
+ m_functor(op.functor()),
+ m_leftImpl(op.lhsExpression(), device),
+ m_rightImpl(op.rhsExpression(), device)
+ {
+ EIGEN_STATIC_ASSERT((static_cast<int>(TensorEvaluator<LeftArgType, Device>::Layout) == static_cast<int>(TensorEvaluator<RightArgType, Device>::Layout) || internal::traits<XprType>::NumDimensions <= 1), YOU_MADE_A_PROGRAMMING_MISTAKE);
+ eigen_assert(dimensions_match(m_leftImpl.dimensions(), m_rightImpl.dimensions()));
+ }
+
+ typedef typename XprType::Index Index;
+ typedef typename XprType::Scalar Scalar;
+ typedef typename internal::traits<XprType>::Scalar CoeffReturnType;
+ typedef typename PacketType<CoeffReturnType, Device>::type PacketReturnType;
+ static constexpr int PacketSize = PacketType<CoeffReturnType, Device>::size;
+ typedef typename TensorEvaluator<LeftArgType, Device>::Dimensions Dimensions;
+ typedef StorageMemory<CoeffReturnType, Device> Storage;
+ typedef typename Storage::Type EvaluatorPointerType;
+
+ static constexpr int NumDims = internal::array_size<
+ typename TensorEvaluator<LeftArgType, Device>::Dimensions>::value;
+
+ //===- Tensor block evaluation strategy (see TensorBlock.h) -------------===//
+ typedef internal::TensorBlockDescriptor<NumDims, Index> TensorBlockDesc;
+ typedef internal::TensorBlockScratchAllocator<Device> TensorBlockScratch;
+
+ typedef typename TensorEvaluator<const LeftArgType, Device>::TensorBlock
+ LeftTensorBlock;
+ typedef typename TensorEvaluator<const RightArgType, Device>::TensorBlock
+ RightTensorBlock;
+
+ typedef internal::TensorCwiseBinaryBlock<BinaryOp, LeftTensorBlock,
+ RightTensorBlock>
+ TensorBlock;
+ //===--------------------------------------------------------------------===//
+
+ EIGEN_DEVICE_FUNC const Dimensions& dimensions() const
+ {
+ // TODO: use right impl instead if right impl dimensions are known at compile time.
+ return m_leftImpl.dimensions();
+ }
+
+ EIGEN_STRONG_INLINE bool evalSubExprsIfNeeded(EvaluatorPointerType) {
+ m_leftImpl.evalSubExprsIfNeeded(NULL);
+ m_rightImpl.evalSubExprsIfNeeded(NULL);
+ return true;
+ }
+
+#ifdef EIGEN_USE_THREADS
+ template <typename EvalSubExprsCallback>
+ EIGEN_STRONG_INLINE void evalSubExprsIfNeededAsync(
+ EvaluatorPointerType, EvalSubExprsCallback done) {
+ // TODO(ezhulenev): Evaluate two expression in parallel?
+ m_leftImpl.evalSubExprsIfNeededAsync(nullptr, [this, done](bool) {
+ m_rightImpl.evalSubExprsIfNeededAsync(nullptr,
+ [done](bool) { done(true); });
+ });
+ }
+#endif // EIGEN_USE_THREADS
+
+ EIGEN_STRONG_INLINE void cleanup() {
+ m_leftImpl.cleanup();
+ m_rightImpl.cleanup();
+ }
+
+ EIGEN_DEVICE_FUNC CoeffReturnType coeff(Index index) const
+ {
+ return m_functor(m_leftImpl.coeff(index), m_rightImpl.coeff(index));
+ }
+ template<int LoadMode>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE PacketReturnType packet(Index index) const
+ {
+ return m_functor.packetOp(m_leftImpl.template packet<LoadMode>(index), m_rightImpl.template packet<LoadMode>(index));
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorOpCost
+ costPerCoeff(bool vectorized) const {
+ const double functor_cost = internal::functor_traits<BinaryOp>::Cost;
+ return m_leftImpl.costPerCoeff(vectorized) +
+ m_rightImpl.costPerCoeff(vectorized) +
+ TensorOpCost(0, 0, functor_cost, vectorized, PacketSize);
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ internal::TensorBlockResourceRequirements getResourceRequirements() const {
+ static const double functor_cost = internal::functor_traits<BinaryOp>::Cost;
+ return internal::TensorBlockResourceRequirements::merge(
+ m_leftImpl.getResourceRequirements(),
+ m_rightImpl.getResourceRequirements())
+ .addCostPerCoeff({0, 0, functor_cost / PacketSize});
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorBlock
+ block(TensorBlockDesc& desc, TensorBlockScratch& scratch,
+ bool /*root_of_expr_ast*/ = false) const {
+ desc.DropDestinationBuffer();
+ return TensorBlock(m_leftImpl.block(desc, scratch),
+ m_rightImpl.block(desc, scratch), m_functor);
+ }
+
+ EIGEN_DEVICE_FUNC EvaluatorPointerType data() const { return NULL; }
+
+ #ifdef EIGEN_USE_SYCL
+ // binding placeholder accessors to a command group handler for SYCL
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void bind(cl::sycl::handler &cgh) const {
+ m_leftImpl.bind(cgh);
+ m_rightImpl.bind(cgh);
+ }
+ #endif
+ private:
+ const Device EIGEN_DEVICE_REF m_device;
+ const BinaryOp m_functor;
+ TensorEvaluator<LeftArgType, Device> m_leftImpl;
+ TensorEvaluator<RightArgType, Device> m_rightImpl;
+};
+
+// -------------------- CwiseTernaryOp --------------------
+
+template<typename TernaryOp, typename Arg1Type, typename Arg2Type, typename Arg3Type, typename Device>
+struct TensorEvaluator<const TensorCwiseTernaryOp<TernaryOp, Arg1Type, Arg2Type, Arg3Type>, Device>
+{
+ typedef TensorCwiseTernaryOp<TernaryOp, Arg1Type, Arg2Type, Arg3Type> XprType;
+
+ static constexpr int Layout = TensorEvaluator<Arg1Type, Device>::Layout;
+ enum {
+ IsAligned = TensorEvaluator<Arg1Type, Device>::IsAligned & TensorEvaluator<Arg2Type, Device>::IsAligned & TensorEvaluator<Arg3Type, Device>::IsAligned,
+ PacketAccess = TensorEvaluator<Arg1Type, Device>::PacketAccess &&
+ TensorEvaluator<Arg2Type, Device>::PacketAccess &&
+ TensorEvaluator<Arg3Type, Device>::PacketAccess &&
+ internal::functor_traits<TernaryOp>::PacketAccess,
+ BlockAccess = false,
+ PreferBlockAccess = TensorEvaluator<Arg1Type, Device>::PreferBlockAccess ||
+ TensorEvaluator<Arg2Type, Device>::PreferBlockAccess ||
+ TensorEvaluator<Arg3Type, Device>::PreferBlockAccess,
+ CoordAccess = false, // to be implemented
+ RawAccess = false
+ };
+
+ TensorEvaluator(const XprType& op, const Device& device)
+ : m_functor(op.functor()),
+ m_arg1Impl(op.arg1Expression(), device),
+ m_arg2Impl(op.arg2Expression(), device),
+ m_arg3Impl(op.arg3Expression(), device)
+ {
+ EIGEN_STATIC_ASSERT((static_cast<int>(TensorEvaluator<Arg1Type, Device>::Layout) == static_cast<int>(TensorEvaluator<Arg3Type, Device>::Layout) || internal::traits<XprType>::NumDimensions <= 1), YOU_MADE_A_PROGRAMMING_MISTAKE);
+
+ EIGEN_STATIC_ASSERT((internal::is_same<typename internal::traits<Arg1Type>::StorageKind,
+ typename internal::traits<Arg2Type>::StorageKind>::value),
+ STORAGE_KIND_MUST_MATCH)
+ EIGEN_STATIC_ASSERT((internal::is_same<typename internal::traits<Arg1Type>::StorageKind,
+ typename internal::traits<Arg3Type>::StorageKind>::value),
+ STORAGE_KIND_MUST_MATCH)
+ EIGEN_STATIC_ASSERT((internal::is_same<typename internal::traits<Arg1Type>::Index,
+ typename internal::traits<Arg2Type>::Index>::value),
+ STORAGE_INDEX_MUST_MATCH)
+ EIGEN_STATIC_ASSERT((internal::is_same<typename internal::traits<Arg1Type>::Index,
+ typename internal::traits<Arg3Type>::Index>::value),
+ STORAGE_INDEX_MUST_MATCH)
+
+ eigen_assert(dimensions_match(m_arg1Impl.dimensions(), m_arg2Impl.dimensions()) && dimensions_match(m_arg1Impl.dimensions(), m_arg3Impl.dimensions()));
+ }
+
+ typedef typename XprType::Index Index;
+ typedef typename XprType::Scalar Scalar;
+ typedef typename internal::traits<XprType>::Scalar CoeffReturnType;
+ typedef typename PacketType<CoeffReturnType, Device>::type PacketReturnType;
+ static constexpr int PacketSize = PacketType<CoeffReturnType, Device>::size;
+ typedef typename TensorEvaluator<Arg1Type, Device>::Dimensions Dimensions;
+ typedef StorageMemory<CoeffReturnType, Device> Storage;
+ typedef typename Storage::Type EvaluatorPointerType;
+
+ //===- Tensor block evaluation strategy (see TensorBlock.h) -------------===//
+ typedef internal::TensorBlockNotImplemented TensorBlock;
+ //===--------------------------------------------------------------------===//
+
+ EIGEN_DEVICE_FUNC const Dimensions& dimensions() const
+ {
+ // TODO: use arg2 or arg3 dimensions if they are known at compile time.
+ return m_arg1Impl.dimensions();
+ }
+
+ EIGEN_STRONG_INLINE bool evalSubExprsIfNeeded(EvaluatorPointerType) {
+ m_arg1Impl.evalSubExprsIfNeeded(NULL);
+ m_arg2Impl.evalSubExprsIfNeeded(NULL);
+ m_arg3Impl.evalSubExprsIfNeeded(NULL);
+ return true;
+ }
+ EIGEN_STRONG_INLINE void cleanup() {
+ m_arg1Impl.cleanup();
+ m_arg2Impl.cleanup();
+ m_arg3Impl.cleanup();
+ }
+
+ EIGEN_DEVICE_FUNC CoeffReturnType coeff(Index index) const
+ {
+ return m_functor(m_arg1Impl.coeff(index), m_arg2Impl.coeff(index), m_arg3Impl.coeff(index));
+ }
+ template<int LoadMode>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE PacketReturnType packet(Index index) const
+ {
+ return m_functor.packetOp(m_arg1Impl.template packet<LoadMode>(index),
+ m_arg2Impl.template packet<LoadMode>(index),
+ m_arg3Impl.template packet<LoadMode>(index));
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorOpCost
+ costPerCoeff(bool vectorized) const {
+ const double functor_cost = internal::functor_traits<TernaryOp>::Cost;
+ return m_arg1Impl.costPerCoeff(vectorized) +
+ m_arg2Impl.costPerCoeff(vectorized) +
+ m_arg3Impl.costPerCoeff(vectorized) +
+ TensorOpCost(0, 0, functor_cost, vectorized, PacketSize);
+ }
+
+ EIGEN_DEVICE_FUNC EvaluatorPointerType data() const { return NULL; }
+
+#ifdef EIGEN_USE_SYCL
+ // binding placeholder accessors to a command group handler for SYCL
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void bind(cl::sycl::handler &cgh) const {
+ m_arg1Impl.bind(cgh);
+ m_arg2Impl.bind(cgh);
+ m_arg3Impl.bind(cgh);
+ }
+#endif
+
+ private:
+ const TernaryOp m_functor;
+ TensorEvaluator<Arg1Type, Device> m_arg1Impl;
+ TensorEvaluator<Arg2Type, Device> m_arg2Impl;
+ TensorEvaluator<Arg3Type, Device> m_arg3Impl;
+};
+
+
+// -------------------- SelectOp --------------------
+
+template<typename IfArgType, typename ThenArgType, typename ElseArgType, typename Device>
+struct TensorEvaluator<const TensorSelectOp<IfArgType, ThenArgType, ElseArgType>, Device>
+{
+ typedef TensorSelectOp<IfArgType, ThenArgType, ElseArgType> XprType;
+ typedef typename XprType::Scalar Scalar;
+
+ static constexpr int Layout = TensorEvaluator<IfArgType, Device>::Layout;
+ enum {
+ IsAligned = TensorEvaluator<ThenArgType, Device>::IsAligned &
+ TensorEvaluator<ElseArgType, Device>::IsAligned,
+ PacketAccess = TensorEvaluator<ThenArgType, Device>::PacketAccess &
+ TensorEvaluator<ElseArgType, Device>::PacketAccess &
+ PacketType<Scalar, Device>::HasBlend,
+ BlockAccess = TensorEvaluator<IfArgType, Device>::BlockAccess &&
+ TensorEvaluator<ThenArgType, Device>::BlockAccess &&
+ TensorEvaluator<ElseArgType, Device>::BlockAccess,
+ PreferBlockAccess = TensorEvaluator<IfArgType, Device>::PreferBlockAccess ||
+ TensorEvaluator<ThenArgType, Device>::PreferBlockAccess ||
+ TensorEvaluator<ElseArgType, Device>::PreferBlockAccess,
+ CoordAccess = false, // to be implemented
+ RawAccess = false
+ };
+
+ TensorEvaluator(const XprType& op, const Device& device)
+ : m_condImpl(op.ifExpression(), device),
+ m_thenImpl(op.thenExpression(), device),
+ m_elseImpl(op.elseExpression(), device)
+ {
+ EIGEN_STATIC_ASSERT((static_cast<int>(TensorEvaluator<IfArgType, Device>::Layout) == static_cast<int>(TensorEvaluator<ThenArgType, Device>::Layout)), YOU_MADE_A_PROGRAMMING_MISTAKE);
+ EIGEN_STATIC_ASSERT((static_cast<int>(TensorEvaluator<IfArgType, Device>::Layout) == static_cast<int>(TensorEvaluator<ElseArgType, Device>::Layout)), YOU_MADE_A_PROGRAMMING_MISTAKE);
+ eigen_assert(dimensions_match(m_condImpl.dimensions(), m_thenImpl.dimensions()));
+ eigen_assert(dimensions_match(m_thenImpl.dimensions(), m_elseImpl.dimensions()));
+ }
+
+ typedef typename XprType::Index Index;
+ typedef typename internal::traits<XprType>::Scalar CoeffReturnType;
+ typedef typename PacketType<CoeffReturnType, Device>::type PacketReturnType;
+ static constexpr int PacketSize = PacketType<CoeffReturnType, Device>::size;
+ typedef typename TensorEvaluator<IfArgType, Device>::Dimensions Dimensions;
+ typedef StorageMemory<CoeffReturnType, Device> Storage;
+ typedef typename Storage::Type EvaluatorPointerType;
+
+ static constexpr int NumDims = internal::array_size<Dimensions>::value;
+
+ //===- Tensor block evaluation strategy (see TensorBlock.h) -------------===//
+ typedef internal::TensorBlockDescriptor<NumDims, Index> TensorBlockDesc;
+ typedef internal::TensorBlockScratchAllocator<Device> TensorBlockScratch;
+
+ typedef typename TensorEvaluator<const IfArgType, Device>::TensorBlock
+ IfArgTensorBlock;
+ typedef typename TensorEvaluator<const ThenArgType, Device>::TensorBlock
+ ThenArgTensorBlock;
+ typedef typename TensorEvaluator<const ElseArgType, Device>::TensorBlock
+ ElseArgTensorBlock;
+
+ struct TensorSelectOpBlockFactory {
+ template <typename IfArgXprType, typename ThenArgXprType, typename ElseArgXprType>
+ struct XprType {
+ typedef TensorSelectOp<const IfArgXprType, const ThenArgXprType, const ElseArgXprType> type;
+ };
+
+ template <typename IfArgXprType, typename ThenArgXprType, typename ElseArgXprType>
+ typename XprType<IfArgXprType, ThenArgXprType, ElseArgXprType>::type expr(
+ const IfArgXprType& if_expr, const ThenArgXprType& then_expr, const ElseArgXprType& else_expr) const {
+ return typename XprType<IfArgXprType, ThenArgXprType, ElseArgXprType>::type(if_expr, then_expr, else_expr);
+ }
+ };
+
+ typedef internal::TensorTernaryExprBlock<TensorSelectOpBlockFactory,
+ IfArgTensorBlock, ThenArgTensorBlock,
+ ElseArgTensorBlock>
+ TensorBlock;
+ //===--------------------------------------------------------------------===//
+
+ EIGEN_DEVICE_FUNC const Dimensions& dimensions() const
+ {
+ // TODO: use then or else impl instead if they happen to be known at compile time.
+ return m_condImpl.dimensions();
+ }
+
+ EIGEN_STRONG_INLINE bool evalSubExprsIfNeeded(EvaluatorPointerType) {
+ m_condImpl.evalSubExprsIfNeeded(NULL);
+ m_thenImpl.evalSubExprsIfNeeded(NULL);
+ m_elseImpl.evalSubExprsIfNeeded(NULL);
+ return true;
+ }
+
+#ifdef EIGEN_USE_THREADS
+ template <typename EvalSubExprsCallback>
+ EIGEN_STRONG_INLINE void evalSubExprsIfNeededAsync(
+ EvaluatorPointerType, EvalSubExprsCallback done) {
+ m_condImpl.evalSubExprsIfNeeded(nullptr, [this, done](bool) {
+ m_thenImpl.evalSubExprsIfNeeded(nullptr, [this, done](bool) {
+ m_elseImpl.evalSubExprsIfNeeded(nullptr, [done](bool) { done(true); });
+ });
+ });
+ }
+#endif // EIGEN_USE_THREADS
+
+ EIGEN_STRONG_INLINE void cleanup() {
+ m_condImpl.cleanup();
+ m_thenImpl.cleanup();
+ m_elseImpl.cleanup();
+ }
+
+ EIGEN_DEVICE_FUNC CoeffReturnType coeff(Index index) const
+ {
+ return m_condImpl.coeff(index) ? m_thenImpl.coeff(index) : m_elseImpl.coeff(index);
+ }
+ template<int LoadMode>
+ EIGEN_DEVICE_FUNC PacketReturnType packet(Index index) const
+ {
+ internal::Selector<PacketSize> select;
+ EIGEN_UNROLL_LOOP
+ for (Index i = 0; i < PacketSize; ++i) {
+ select.select[i] = m_condImpl.coeff(index+i);
+ }
+ return internal::pblend(select,
+ m_thenImpl.template packet<LoadMode>(index),
+ m_elseImpl.template packet<LoadMode>(index));
+
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorOpCost
+ costPerCoeff(bool vectorized) const {
+ return m_condImpl.costPerCoeff(vectorized) +
+ m_thenImpl.costPerCoeff(vectorized)
+ .cwiseMax(m_elseImpl.costPerCoeff(vectorized));
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ internal::TensorBlockResourceRequirements getResourceRequirements() const {
+ auto then_req = m_thenImpl.getResourceRequirements();
+ auto else_req = m_elseImpl.getResourceRequirements();
+
+ auto merged_req =
+ internal::TensorBlockResourceRequirements::merge(then_req, else_req);
+ merged_req.cost_per_coeff =
+ then_req.cost_per_coeff.cwiseMax(else_req.cost_per_coeff);
+
+ return internal::TensorBlockResourceRequirements::merge(
+ m_condImpl.getResourceRequirements(), merged_req);
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorBlock
+ block(TensorBlockDesc& desc, TensorBlockScratch& scratch,
+ bool /*root_of_expr_ast*/ = false) const {
+ // It's unsafe to pass destination buffer to underlying expressions, because
+ // output might be aliased with one of the inputs.
+ desc.DropDestinationBuffer();
+
+ return TensorBlock(
+ m_condImpl.block(desc, scratch), m_thenImpl.block(desc, scratch),
+ m_elseImpl.block(desc, scratch), TensorSelectOpBlockFactory());
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE EvaluatorPointerType data() const { return NULL; }
+
+#ifdef EIGEN_USE_SYCL
+ // binding placeholder accessors to a command group handler for SYCL
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void bind(cl::sycl::handler &cgh) const {
+ m_condImpl.bind(cgh);
+ m_thenImpl.bind(cgh);
+ m_elseImpl.bind(cgh);
+ }
+#endif
+ private:
+ TensorEvaluator<IfArgType, Device> m_condImpl;
+ TensorEvaluator<ThenArgType, Device> m_thenImpl;
+ TensorEvaluator<ElseArgType, Device> m_elseImpl;
+};
+
+
+} // end namespace Eigen
+
+#endif // EIGEN_CXX11_TENSOR_TENSOR_EVALUATOR_H
diff --git a/unsupported/Eigen/CXX11/src/Tensor/TensorExecutor.h b/unsupported/Eigen/CXX11/src/Tensor/TensorExecutor.h
new file mode 100644
index 0000000..de9bed4
--- /dev/null
+++ b/unsupported/Eigen/CXX11/src/Tensor/TensorExecutor.h
@@ -0,0 +1,760 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_CXX11_TENSOR_TENSOR_EXECUTOR_H
+#define EIGEN_CXX11_TENSOR_TENSOR_EXECUTOR_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+/**
+ * \class TensorExecutor
+ * \ingroup CXX11_Tensor_Module
+ *
+ * \brief The tensor executor class.
+ *
+ * This class is responsible for launch the evaluation of the expression on
+ * the specified computing device.
+ *
+ * @tparam Vectorizable can use packet math (SSE/AVX/etc... registers and
+ * instructions)
+ * @tparam Tiling can use block based tensor evaluation
+ * (see TensorBlock.h)
+ */
+namespace internal {
+
+/**
+ * Evaluating TensorBroadcastingOp via coefficient of packet path is extremely
+ * expensive. If expression has at least one broadcast op in it, and it supports
+ * block based evaluation, we always prefer it, even for the small tensors. For
+ * all other tileable ops, block evaluation overhead for small tensors (fits
+ * into L1) is too large, and we fallback on vectorized evaluation.
+ */
+
+// TODO(ezhulenev): Add specializations for all other types of Tensor ops.
+
+template<typename Expression>
+struct ExpressionHasTensorBroadcastingOp {
+ enum { value = false };
+};
+
+template<typename LhsXprType, typename RhsXprType>
+struct ExpressionHasTensorBroadcastingOp<
+ const TensorAssignOp<LhsXprType, RhsXprType> > {
+ enum { value = ExpressionHasTensorBroadcastingOp<RhsXprType>::value };
+};
+
+template<typename UnaryOp, typename XprType>
+struct ExpressionHasTensorBroadcastingOp<
+ const TensorCwiseUnaryOp<UnaryOp, XprType> > {
+ enum { value = ExpressionHasTensorBroadcastingOp<XprType>::value };
+};
+
+template<typename BinaryOp, typename LhsXprType, typename RhsXprType>
+struct ExpressionHasTensorBroadcastingOp<
+ const TensorCwiseBinaryOp<BinaryOp, LhsXprType, RhsXprType> > {
+ enum {
+ value = ExpressionHasTensorBroadcastingOp<LhsXprType>::value ||
+ ExpressionHasTensorBroadcastingOp<RhsXprType>::value
+ };
+};
+
+template<typename Broadcast, typename XprType>
+struct ExpressionHasTensorBroadcastingOp<
+ const TensorBroadcastingOp<Broadcast, XprType> > {
+ enum { value = true };
+};
+
+// -------------------------------------------------------------------------- //
+
+/**
+ * Default strategy: the expression is evaluated sequentially with a single cpu
+ * thread, without vectorization and block evaluation.
+ */
+template <typename Expression, typename Device, bool Vectorizable,
+ TiledEvaluation Tiling>
+class TensorExecutor {
+ public:
+ typedef typename Expression::Index StorageIndex;
+
+ // Including `unsupported/Eigen/CXX11/Tensor` in different translation units
+ // with/without `EIGEN_USE_THREADS` or `EIGEN_USE_GPU` is a potential ODR
+ // violation. If this template is instantiated with a non-default device, it
+ // means that this header file was included without defining
+ // `EIGEN_USE_THREADS`, `EIGEN_USE_GPU` or `EIGEN_USE_SYCL`.
+ static_assert(std::is_same<Device, DefaultDevice>::value,
+ "Default executor instantiated with non-default device. "
+ "You must #define EIGEN_USE_THREADS, EIGEN_USE_GPU or "
+ "EIGEN_USE_SYCL before including Eigen headers.");
+
+ EIGEN_DEVICE_FUNC
+ static EIGEN_STRONG_INLINE void run(const Expression& expr,
+ const Device& device = Device()) {
+ TensorEvaluator<Expression, Device> evaluator(expr, device);
+ const bool needs_assign = evaluator.evalSubExprsIfNeeded(NULL);
+ if (needs_assign) {
+ const StorageIndex size = array_prod(evaluator.dimensions());
+ for (StorageIndex i = 0; i < size; ++i) {
+ evaluator.evalScalar(i);
+ }
+ }
+ evaluator.cleanup();
+ }
+};
+
+/**
+ * Default async execution strategy is not implemented. Currently it's only
+ * available for ThreadPoolDevice (see definition below).
+ */
+template <typename Expression, typename Device, typename DoneCallback,
+ bool Vectorizable, TiledEvaluation Tiling>
+class TensorAsyncExecutor {};
+
+/**
+ * Process all the data with a single cpu thread, using vectorized instructions.
+ */
+template <typename Expression>
+class TensorExecutor<Expression, DefaultDevice, /*Vectorizable=*/true,
+ /*Tiling=*/TiledEvaluation::Off> {
+ public:
+ typedef typename Expression::Index StorageIndex;
+
+ EIGEN_DEVICE_FUNC
+ static EIGEN_STRONG_INLINE void run(
+ const Expression& expr, const DefaultDevice& device = DefaultDevice()) {
+ TensorEvaluator<Expression, DefaultDevice> evaluator(expr, device);
+ const bool needs_assign = evaluator.evalSubExprsIfNeeded(NULL);
+ if (needs_assign) {
+ const StorageIndex size = array_prod(evaluator.dimensions());
+ const int PacketSize = unpacket_traits<typename TensorEvaluator<
+ Expression, DefaultDevice>::PacketReturnType>::size;
+
+ // Give compiler a strong possibility to unroll the loop. But don't insist
+ // on unrolling, because if the function is expensive compiler should not
+ // unroll the loop at the expense of inlining.
+ const StorageIndex UnrolledSize =
+ (size / (4 * PacketSize)) * 4 * PacketSize;
+ for (StorageIndex i = 0; i < UnrolledSize; i += 4 * PacketSize) {
+ for (StorageIndex j = 0; j < 4; j++) {
+ evaluator.evalPacket(i + j * PacketSize);
+ }
+ }
+ const StorageIndex VectorizedSize = (size / PacketSize) * PacketSize;
+ for (StorageIndex i = UnrolledSize; i < VectorizedSize; i += PacketSize) {
+ evaluator.evalPacket(i);
+ }
+ for (StorageIndex i = VectorizedSize; i < size; ++i) {
+ evaluator.evalScalar(i);
+ }
+ }
+ evaluator.cleanup();
+ }
+};
+
+/**
+ * Process all the data with a single cpu thread, using blocks of data. By
+ * sizing a block to fit L1 cache we get better cache performance.
+ */
+template <typename Expression, bool Vectorizable>
+class TensorExecutor<Expression, DefaultDevice, Vectorizable,
+ /*Tiling=*/TiledEvaluation::On> {
+ public:
+ typedef typename traits<Expression>::Scalar Scalar;
+ typedef std::remove_const_t<Scalar> ScalarNoConst;
+
+ typedef TensorEvaluator<Expression, DefaultDevice> Evaluator;
+ typedef typename traits<Expression>::Index StorageIndex;
+
+ static constexpr int NumDims = traits<Expression>::NumDimensions;
+
+ EIGEN_DEVICE_FUNC
+ static EIGEN_STRONG_INLINE void run(const Expression& expr,
+ const DefaultDevice& device = DefaultDevice()) {
+ typedef TensorBlockMapper<NumDims, Evaluator::Layout, StorageIndex>
+ TensorBlockMapper;
+
+ typedef internal::TensorBlockDescriptor<NumDims, StorageIndex>
+ TensorBlockDesc;
+ typedef internal::TensorBlockScratchAllocator<DefaultDevice>
+ TensorBlockScratch;
+
+ Evaluator evaluator(expr, device);
+
+ // TODO(ezhulenev): Do not use tiling for small tensors?
+ const bool needs_assign = evaluator.evalSubExprsIfNeeded(NULL);
+
+ if (needs_assign) {
+ // Query expression tree for desired block size/shape.
+ const TensorBlockResourceRequirements requirements =
+ evaluator.getResourceRequirements();
+
+ const TensorBlockMapper block_mapper(
+ typename TensorBlockDesc::Dimensions(evaluator.dimensions()),
+ requirements);
+
+ // Share scratch memory allocator between all blocks.
+ TensorBlockScratch scratch(device);
+
+ const StorageIndex total_block_count = block_mapper.blockCount();
+ for (StorageIndex i = 0; i < total_block_count; ++i) {
+ TensorBlockDesc desc = block_mapper.blockDescriptor(i);
+ evaluator.evalBlock(desc, scratch);
+ scratch.reset();
+ }
+ }
+ evaluator.cleanup();
+ }
+};
+
+/**
+ * Multicore strategy: the index space is partitioned and each partition is
+ * executed on a single core.
+ *
+ * (1) TensorExecutor will submit work to the ThreadPoolDevice managed thread
+ * pool, and will block the caller thread until all tasks are finished.
+ *
+ * (2) TensorAsyncExecutor is a non-blocking version, that will submit work to
+ * the ThreadPoolDevice managed thread pool, and will return immediately.
+ * It will call 'done' callback after all tasks are finished.
+ */
+#ifdef EIGEN_USE_THREADS
+
+template <typename TensorBlockMapper>
+struct TensorExecutorTilingContext {
+ TensorExecutorTilingContext() = default;
+ TensorExecutorTilingContext(const TensorBlockMapper& b_mapper,
+ const TensorOpCost& b_cost, size_t b_aligned_size)
+ : block_mapper(b_mapper),
+ cost(b_cost),
+ aligned_blocksize(b_aligned_size) {}
+
+ TensorBlockMapper block_mapper; // navigate through blocks
+ TensorOpCost cost; // cost of computing a single block
+ size_t aligned_blocksize; // block size after memory alignment
+};
+
+// Computes a block evaluation parameters, and allocates temporary memory buffer
+// for blocks. See TensorExecutor/TensorAsyncExecutor (Tiling=On) below.
+template <typename Evaluator, typename TensorBlockMapper, bool Vectorizable>
+TensorExecutorTilingContext<TensorBlockMapper> GetTensorExecutorTilingContext(
+ const Evaluator& evaluator) {
+ // Query expression tree for desired block size/shape.
+ TensorBlockResourceRequirements requirements =
+ evaluator.getResourceRequirements();
+
+ // Update target block size based on cost model.
+ double taskSize = TensorCostModel<ThreadPoolDevice>::taskSize(
+ 1, requirements.cost_per_coeff);
+ requirements.size = static_cast<size_t>(1.0 / taskSize);
+
+ TensorBlockMapper block_mapper(
+ typename TensorBlockMapper::Dimensions(evaluator.dimensions()),
+ requirements);
+
+ size_t block_size = block_mapper.blockTotalSize();
+ const size_t align = numext::maxi(EIGEN_MAX_ALIGN_BYTES, 1);
+ const size_t aligned_blocksize =
+ align *
+ divup<size_t>(block_size * sizeof(typename Evaluator::Scalar), align);
+
+ return {block_mapper, requirements.cost_per_coeff * block_size,
+ aligned_blocksize};
+}
+
+template <typename Evaluator, typename StorageIndex, bool Vectorizable>
+struct EvalRange {
+ static void run(Evaluator* evaluator_in, const StorageIndex firstIdx,
+ const StorageIndex lastIdx) {
+ Evaluator evaluator = *evaluator_in;
+ eigen_assert(lastIdx >= firstIdx);
+ for (StorageIndex i = firstIdx; i < lastIdx; ++i) {
+ evaluator.evalScalar(i);
+ }
+ }
+
+ static StorageIndex alignBlockSize(StorageIndex size) { return size; }
+};
+
+template <typename Evaluator, typename StorageIndex>
+struct EvalRange<Evaluator, StorageIndex, /*Vectorizable*/ true> {
+ static constexpr int PacketSize =
+ unpacket_traits<typename Evaluator::PacketReturnType>::size;
+
+ static void run(Evaluator* evaluator_in, const StorageIndex firstIdx,
+ const StorageIndex lastIdx) {
+ Evaluator evaluator = *evaluator_in;
+ eigen_assert(lastIdx >= firstIdx);
+ StorageIndex i = firstIdx;
+ if (lastIdx - firstIdx >= PacketSize) {
+ eigen_assert(firstIdx % PacketSize == 0);
+ StorageIndex last_chunk_offset = lastIdx - 4 * PacketSize;
+ // Give compiler a strong possibility to unroll the loop. But don't insist
+ // on unrolling, because if the function is expensive compiler should not
+ // unroll the loop at the expense of inlining.
+ for (; i <= last_chunk_offset; i += 4 * PacketSize) {
+ for (StorageIndex j = 0; j < 4; j++) {
+ evaluator.evalPacket(i + j * PacketSize);
+ }
+ }
+ last_chunk_offset = lastIdx - PacketSize;
+ for (; i <= last_chunk_offset; i += PacketSize) {
+ evaluator.evalPacket(i);
+ }
+ }
+ for (; i < lastIdx; ++i) {
+ evaluator.evalScalar(i);
+ }
+ }
+
+ static StorageIndex alignBlockSize(StorageIndex size) {
+ // Align block size to packet size and account for unrolling in run above.
+ if (size >= 16 * PacketSize) {
+ return (size + 4 * PacketSize - 1) & ~(4 * PacketSize - 1);
+ }
+ // Aligning to 4 * PacketSize would increase block size by more than 25%.
+ return (size + PacketSize - 1) & ~(PacketSize - 1);
+ }
+};
+
+template <typename Expression, bool Vectorizable, TiledEvaluation Tiling>
+class TensorExecutor<Expression, ThreadPoolDevice, Vectorizable, Tiling> {
+ public:
+ typedef typename Expression::Index StorageIndex;
+
+ static EIGEN_STRONG_INLINE void run(const Expression& expr,
+ const ThreadPoolDevice& device) {
+ typedef TensorEvaluator<Expression, ThreadPoolDevice> Evaluator;
+ typedef EvalRange<Evaluator, StorageIndex, Vectorizable> EvalRange;
+
+ Evaluator evaluator(expr, device);
+ const bool needs_assign = evaluator.evalSubExprsIfNeeded(nullptr);
+ if (needs_assign) {
+ const StorageIndex size = array_prod(evaluator.dimensions());
+ device.parallelFor(size, evaluator.costPerCoeff(Vectorizable),
+ EvalRange::alignBlockSize,
+ [&evaluator](StorageIndex firstIdx, StorageIndex lastIdx) {
+ EvalRange::run(&evaluator, firstIdx, lastIdx);
+ });
+ }
+ evaluator.cleanup();
+ }
+};
+
+template <typename Expression, bool Vectorizable>
+class TensorExecutor<Expression, ThreadPoolDevice, Vectorizable,
+ /*Tiling=*/TiledEvaluation::On> {
+ public:
+ typedef typename traits<Expression>::Index IndexType;
+ typedef typename traits<Expression>::Scalar Scalar;
+ typedef std::remove_const_t<Scalar> ScalarNoConst;
+
+ static constexpr int NumDims = traits<Expression>::NumDimensions;
+
+ typedef TensorEvaluator<Expression, ThreadPoolDevice> Evaluator;
+ typedef TensorBlockMapper<NumDims, Evaluator::Layout, IndexType> BlockMapper;
+ typedef TensorExecutorTilingContext<BlockMapper> TilingContext;
+
+ typedef internal::TensorBlockDescriptor<NumDims, IndexType>
+ TensorBlockDesc;
+ typedef internal::TensorBlockScratchAllocator<ThreadPoolDevice>
+ TensorBlockScratch;
+
+ static EIGEN_STRONG_INLINE void run(const Expression& expr,
+ const ThreadPoolDevice& device) {
+ Evaluator evaluator(expr, device);
+
+ const bool needs_assign = evaluator.evalSubExprsIfNeeded(nullptr);
+ if (needs_assign) {
+ const TilingContext tiling =
+ internal::GetTensorExecutorTilingContext<Evaluator, BlockMapper,
+ Vectorizable>(evaluator);
+
+ auto eval_block = [&device, &evaluator, &tiling](IndexType firstBlockIdx,
+ IndexType lastBlockIdx) {
+ TensorBlockScratch scratch(device);
+
+ for (IndexType block_idx = firstBlockIdx; block_idx < lastBlockIdx;
+ ++block_idx) {
+ TensorBlockDesc desc = tiling.block_mapper.blockDescriptor(block_idx);
+ evaluator.evalBlock(desc, scratch);
+ scratch.reset();
+ }
+ };
+
+ // Evaluate small expressions directly as a single block.
+ if (tiling.block_mapper.blockCount() == 1) {
+ TensorBlockScratch scratch(device);
+ TensorBlockDesc desc(0, tiling.block_mapper.blockDimensions());
+ evaluator.evalBlock(desc, scratch);
+ } else {
+ device.parallelFor(tiling.block_mapper.blockCount(), tiling.cost,
+ eval_block);
+ }
+ }
+ evaluator.cleanup();
+ }
+};
+
+template <typename Expression, typename DoneCallback, bool Vectorizable,
+ TiledEvaluation Tiling>
+class TensorAsyncExecutor<Expression, ThreadPoolDevice, DoneCallback,
+ Vectorizable, Tiling> {
+ public:
+ typedef typename Expression::Index StorageIndex;
+ typedef TensorEvaluator<Expression, ThreadPoolDevice> Evaluator;
+
+ static EIGEN_STRONG_INLINE void runAsync(const Expression& expr,
+ const ThreadPoolDevice& device,
+ DoneCallback done) {
+ TensorAsyncExecutorContext* const ctx =
+ new TensorAsyncExecutorContext(expr, device, std::move(done));
+
+ const auto on_eval_subexprs = [ctx, &device](bool need_assign) -> void {
+ if (!need_assign) {
+ delete ctx;
+ return;
+ }
+
+ typedef EvalRange<Evaluator, StorageIndex, Vectorizable> EvalRange;
+ const StorageIndex size = array_prod(ctx->evaluator.dimensions());
+ device.parallelForAsync(
+ size, ctx->evaluator.costPerCoeff(Vectorizable),
+ EvalRange::alignBlockSize,
+ [ctx](StorageIndex firstIdx, StorageIndex lastIdx) {
+ EvalRange::run(&ctx->evaluator, firstIdx, lastIdx);
+ },
+ [ctx]() { delete ctx; });
+ };
+
+ ctx->evaluator.evalSubExprsIfNeededAsync(nullptr, on_eval_subexprs);
+ }
+
+ private:
+ struct TensorAsyncExecutorContext {
+ TensorAsyncExecutorContext(const Expression& expr,
+ const ThreadPoolDevice& thread_pool,
+ DoneCallback done)
+ : evaluator(expr, thread_pool), on_done(std::move(done)) {}
+
+ ~TensorAsyncExecutorContext() {
+ evaluator.cleanup();
+ on_done();
+ }
+
+ Evaluator evaluator;
+
+ private:
+ DoneCallback on_done;
+ };
+};
+
+template <typename Expression, typename DoneCallback, bool Vectorizable>
+class TensorAsyncExecutor<Expression, ThreadPoolDevice, DoneCallback,
+ Vectorizable, /*Tileable*/ TiledEvaluation::On> {
+ public:
+ typedef typename traits<Expression>::Index IndexType;
+ typedef typename traits<Expression>::Scalar Scalar;
+ typedef std::remove_const_t<Scalar> ScalarNoConst;
+
+ static constexpr int NumDims = traits<Expression>::NumDimensions;
+
+ typedef TensorEvaluator<Expression, ThreadPoolDevice> Evaluator;
+ typedef TensorBlockMapper<NumDims, Evaluator::Layout, IndexType> BlockMapper;
+ typedef TensorExecutorTilingContext<BlockMapper> TilingContext;
+
+ typedef internal::TensorBlockDescriptor<NumDims, IndexType> TensorBlockDesc;
+ typedef internal::TensorBlockScratchAllocator<ThreadPoolDevice>
+ TensorBlockScratch;
+
+ static EIGEN_STRONG_INLINE void runAsync(const Expression& expr,
+ const ThreadPoolDevice& device,
+ DoneCallback done) {
+
+ TensorAsyncExecutorContext* const ctx =
+ new TensorAsyncExecutorContext(expr, device, std::move(done));
+
+ const auto on_eval_subexprs = [ctx](bool need_assign) -> void {
+ if (!need_assign) {
+ delete ctx;
+ return;
+ }
+
+ ctx->tiling = internal::GetTensorExecutorTilingContext<
+ Evaluator, BlockMapper, Vectorizable>(ctx->evaluator);
+
+ auto eval_block = [ctx](IndexType firstBlockIdx, IndexType lastBlockIdx) {
+ TensorBlockScratch scratch(ctx->device);
+
+ for (IndexType block_idx = firstBlockIdx; block_idx < lastBlockIdx;
+ ++block_idx) {
+ TensorBlockDesc desc =
+ ctx->tiling.block_mapper.blockDescriptor(block_idx);
+ ctx->evaluator.evalBlock(desc, scratch);
+ scratch.reset();
+ }
+ };
+
+ // Evaluate small expressions directly as a single block.
+ if (ctx->tiling.block_mapper.blockCount() == 1) {
+ TensorBlockScratch scratch(ctx->device);
+ TensorBlockDesc desc(0, ctx->tiling.block_mapper.blockDimensions());
+ ctx->evaluator.evalBlock(desc, scratch);
+ delete ctx;
+ } else {
+ ctx->device.parallelForAsync(ctx->tiling.block_mapper.blockCount(),
+ ctx->tiling.cost, eval_block,
+ [ctx]() { delete ctx; });
+ }
+ };
+
+ ctx->evaluator.evalSubExprsIfNeededAsync(nullptr, on_eval_subexprs);
+ }
+
+ private:
+ struct TensorAsyncExecutorContext {
+ TensorAsyncExecutorContext(const Expression& expr,
+ const ThreadPoolDevice& thread_pool,
+ DoneCallback done)
+ : device(thread_pool),
+ evaluator(expr, thread_pool),
+ on_done(std::move(done)) {}
+
+ ~TensorAsyncExecutorContext() {
+ evaluator.cleanup();
+ on_done();
+ }
+
+ const ThreadPoolDevice& device;
+ Evaluator evaluator;
+ TilingContext tiling;
+
+ private:
+ DoneCallback on_done;
+ };
+};
+
+#endif // EIGEN_USE_THREADS
+
+// GPU: the evaluation of the expression is offloaded to a GPU.
+#if defined(EIGEN_USE_GPU)
+
+template <typename Expression, bool Vectorizable, TiledEvaluation Tiling>
+class TensorExecutor<Expression, GpuDevice, Vectorizable, Tiling> {
+ public:
+ typedef typename Expression::Index StorageIndex;
+ static void run(const Expression& expr, const GpuDevice& device);
+};
+
+#if defined(EIGEN_GPUCC)
+// Returns 1 if lhs + rhs would overflow, -1 if it would underflow, otherwise 0.
+template <typename Index>
+EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE int sum_will_overflow(Index lhs,
+ Index rhs) {
+ const Index highest = NumTraits<Index>::highest();
+ const Index lowest = NumTraits<Index>::lowest();
+ if (lhs > 0 && rhs > 0) {
+ return lhs > highest - rhs ? 1 : 0;
+ } else if (lhs < 0 && rhs < 0) {
+ return lhs < lowest - rhs ? -1 : 0;
+ } else {
+ return 0;
+ }
+}
+
+// Returns lhs + rhs, saturating to the highest/lowest representable value on
+// overflow/underflow respectively.
+template <typename Index>
+EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE Index saturate_add(Index lhs, Index rhs) {
+ const Index highest = NumTraits<Index>::highest();
+ const Index lowest = NumTraits<Index>::lowest();
+ int overflow = sum_will_overflow(lhs, rhs);
+ return overflow == 1 ? highest : overflow == -1 ? lowest : lhs + rhs;
+}
+
+// A functor that adds step_size to a given index, saturating to avoid
+// overflow/underflow. If overflow/underflow is not possible, regular addition
+// is used (for efficiency).
+template <typename Index>
+struct SafeStep {
+ // lastIdx is one past the end of the possible indexes.
+ // step_size is the value that will be added to the given index when the
+ // functor is called.
+ EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE SafeStep(Index lastIdx, Index step_size)
+ : can_overflow_(sum_will_overflow(lastIdx, step_size)),
+ step_size_(step_size) {}
+
+ // Adds step_size to index, saturating on overflow (if overflow is possible).
+ EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE Index operator()(Index index) const {
+ return can_overflow_ ? saturate_add(index, step_size_) : index + step_size_;
+ }
+
+ private:
+ const bool can_overflow_;
+ const Index step_size_;
+};
+
+template <typename Evaluator, typename StorageIndex, bool Vectorizable>
+struct EigenMetaKernelEval {
+ static EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
+ void run(Evaluator& eval, StorageIndex firstIdx, StorageIndex lastIdx, StorageIndex step_size) {
+ SafeStep<StorageIndex> safe_step(lastIdx, step_size);
+ for (StorageIndex i = firstIdx; i < lastIdx; i = safe_step(i)) {
+ eval.evalScalar(i);
+ }
+ }
+};
+
+template <typename Evaluator, typename StorageIndex>
+struct EigenMetaKernelEval<Evaluator, StorageIndex, true> {
+ static EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
+ void run(Evaluator& eval, StorageIndex firstIdx, StorageIndex lastIdx, StorageIndex step_size) {
+ const StorageIndex PacketSize = unpacket_traits<typename Evaluator::PacketReturnType>::size;
+ const StorageIndex vectorized_size = (lastIdx / PacketSize) * PacketSize;
+ const StorageIndex vectorized_step_size = step_size * PacketSize;
+
+ SafeStep<StorageIndex> safe_vectorized_step(vectorized_size,
+ vectorized_step_size);
+ // Use the vector path
+ for (StorageIndex i = firstIdx * PacketSize; i < vectorized_size;
+ i = safe_vectorized_step(i)) {
+ eval.evalPacket(i);
+ }
+ SafeStep<StorageIndex> safe_step(lastIdx, step_size);
+ for (StorageIndex i = saturate_add(vectorized_size, firstIdx); i < lastIdx;
+ i = safe_step(i)) {
+ eval.evalScalar(i);
+ }
+ }
+};
+
+template <typename Evaluator, typename StorageIndex>
+__global__ void
+__launch_bounds__(1024)
+EigenMetaKernel(Evaluator eval, StorageIndex size) {
+
+ const StorageIndex first_index = blockIdx.x * blockDim.x + threadIdx.x;
+ const StorageIndex step_size = blockDim.x * gridDim.x;
+
+ const bool vectorizable = Evaluator::PacketAccess & Evaluator::IsAligned;
+ EigenMetaKernelEval<Evaluator, StorageIndex, vectorizable>::run(eval, first_index, size, step_size);
+}
+
+/*static*/
+template <typename Expression, bool Vectorizable, TiledEvaluation Tiling>
+EIGEN_STRONG_INLINE void TensorExecutor<Expression, GpuDevice, Vectorizable, Tiling>::run(
+ const Expression& expr, const GpuDevice& device) {
+ TensorEvaluator<Expression, GpuDevice> evaluator(expr, device);
+ const bool needs_assign = evaluator.evalSubExprsIfNeeded(nullptr);
+ if (needs_assign) {
+
+ const int block_size = device.maxGpuThreadsPerBlock();
+ const int max_blocks =
+ numext::mini<int64_t>(device.getNumGpuMultiProcessors() *
+ device.maxGpuThreadsPerMultiProcessor(),
+ NumTraits<StorageIndex>::highest()) /
+ block_size;
+ const StorageIndex size = array_prod(evaluator.dimensions());
+ // Create a least one block to ensure we won't crash when tensorflow calls with tensors of size 0.
+ const int num_blocks = numext::maxi<int>(numext::mini<int>(max_blocks, divup<int>(size, block_size)), 1);
+
+ LAUNCH_GPU_KERNEL(
+ (EigenMetaKernel<TensorEvaluator<Expression, GpuDevice>, StorageIndex>),
+ num_blocks, block_size, 0, device, evaluator, size);
+ }
+ evaluator.cleanup();
+}
+
+#endif // EIGEN_GPUCC
+#endif // EIGEN_USE_GPU
+
+// SYCL Executor policy
+#ifdef EIGEN_USE_SYCL
+
+template <typename Evaluator>
+struct ExecExprFunctorKernel {
+ typedef typename Evaluator::Index Index;
+ Evaluator evaluator;
+ const Index range;
+ template <typename Scratch>
+ EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE ExecExprFunctorKernel(
+ const Scratch, Evaluator evaluator_, const Index range_)
+ : evaluator(evaluator_), range(range_) {}
+
+ EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE void operator()(
+ cl::sycl::nd_item<1> itemID) {
+ compute(itemID);
+ }
+ template <bool is_vec = Evaluator::PacketAccess>
+ EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE std::enable_if_t<!is_vec>
+ compute(const cl::sycl::nd_item<1>& itemID) {
+ Index gId = static_cast<Index>(itemID.get_global_linear_id());
+ Index total_threads = itemID.get_global_range(0);
+
+ for (Index i = gId; i < range; i += total_threads) {
+ evaluator.evalScalar(i);
+ }
+ }
+ template <bool is_vec = Evaluator::PacketAccess>
+ EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE std::enable_if_t<is_vec>
+ compute(const cl::sycl::nd_item<1>& itemID) {
+ const Index vectorizedRange =
+ (range / Evaluator::PacketSize) * Evaluator::PacketSize;
+ Index gId = static_cast<Index>(itemID.get_global_linear_id());
+ const Index step = Evaluator::PacketSize * itemID.get_global_range(0);
+ const Index start = Evaluator::PacketSize * gId;
+ for (Index i = start; i < vectorizedRange; i += step) {
+ evaluator.evalPacket(i);
+ }
+ gId += vectorizedRange;
+ for (Index i = gId; i < range; i += itemID.get_global_range(0)) {
+ evaluator.evalScalar(i);
+ }
+ }
+};
+
+template <typename Expression, bool Vectorizable, TiledEvaluation Tiling>
+class TensorExecutor<Expression, Eigen::SyclDevice, Vectorizable, Tiling> {
+ public:
+ typedef typename Expression::Index Index;
+ static EIGEN_STRONG_INLINE void run(const Expression& expr,
+ const Eigen::SyclDevice& dev) {
+ typedef Eigen::TensorEvaluator<Expression, Eigen::SyclDevice> Evaluator;
+ Evaluator evaluator(expr, dev);
+ const bool needs_assign = evaluator.evalSubExprsIfNeeded(NULL);
+ if (needs_assign) {
+ Index range, GRange, tileSize;
+ Index total_size = ::Eigen::internal::array_prod(evaluator.dimensions());
+ total_size = (total_size == 0) ? 1 : total_size;
+ const int PacketSize =
+ Eigen::PacketType<typename Evaluator::CoeffReturnType,
+ Eigen::SyclDevice>::size;
+ Index vectorizable_threads = static_cast<Index>(total_size / PacketSize);
+ dev.parallel_for_setup(vectorizable_threads, tileSize, range, GRange);
+ range = total_size;
+
+ dev.template nullary_kernel_launcher<
+ typename Evaluator::CoeffReturnType,
+ ExecExprFunctorKernel<Evaluator> >(
+ evaluator,
+ cl::sycl::nd_range<1>(cl::sycl::range<1>(GRange),
+ cl::sycl::range<1>(tileSize)),
+ Index(1), range);
+ }
+ evaluator.cleanup();
+ }
+};
+
+#endif
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_CXX11_TENSOR_TENSOR_EXECUTOR_H
diff --git a/unsupported/Eigen/CXX11/src/Tensor/TensorExpr.h b/unsupported/Eigen/CXX11/src/Tensor/TensorExpr.h
new file mode 100644
index 0000000..9bed2a1
--- /dev/null
+++ b/unsupported/Eigen/CXX11/src/Tensor/TensorExpr.h
@@ -0,0 +1,390 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_CXX11_TENSOR_TENSOR_EXPR_H
+#define EIGEN_CXX11_TENSOR_TENSOR_EXPR_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+/** \class TensorExpr
+ * \ingroup CXX11_Tensor_Module
+ *
+ * \brief Tensor expression classes.
+ *
+ * The TensorCwiseNullaryOp class applies a nullary operators to an expression.
+ * This is typically used to generate constants.
+ *
+ * The TensorCwiseUnaryOp class represents an expression where a unary operator
+ * (e.g. cwiseSqrt) is applied to an expression.
+ *
+ * The TensorCwiseBinaryOp class represents an expression where a binary
+ * operator (e.g. addition) is applied to a lhs and a rhs expression.
+ *
+ */
+namespace internal {
+template<typename NullaryOp, typename XprType>
+struct traits<TensorCwiseNullaryOp<NullaryOp, XprType> >
+ : traits<XprType>
+{
+ typedef traits<XprType> XprTraits;
+ typedef typename XprType::Scalar Scalar;
+ typedef typename XprType::Nested XprTypeNested;
+ typedef std::remove_reference_t<XprTypeNested> XprTypeNested_;
+ static constexpr int NumDimensions = XprTraits::NumDimensions;
+ static constexpr int Layout = XprTraits::Layout;
+ typedef typename XprTraits::PointerType PointerType;
+ enum {
+ Flags = 0
+ };
+};
+
+} // end namespace internal
+
+
+
+template<typename NullaryOp, typename XprType>
+class TensorCwiseNullaryOp : public TensorBase<TensorCwiseNullaryOp<NullaryOp, XprType>, ReadOnlyAccessors>
+{
+ public:
+ typedef typename Eigen::internal::traits<TensorCwiseNullaryOp>::Scalar Scalar;
+ typedef typename Eigen::NumTraits<Scalar>::Real RealScalar;
+ typedef typename XprType::CoeffReturnType CoeffReturnType;
+ typedef TensorCwiseNullaryOp<NullaryOp, XprType> Nested;
+ typedef typename Eigen::internal::traits<TensorCwiseNullaryOp>::StorageKind StorageKind;
+ typedef typename Eigen::internal::traits<TensorCwiseNullaryOp>::Index Index;
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorCwiseNullaryOp(const XprType& xpr, const NullaryOp& func = NullaryOp())
+ : m_xpr(xpr), m_functor(func) {}
+
+ EIGEN_DEVICE_FUNC
+ const internal::remove_all_t<typename XprType::Nested>&
+ nestedExpression() const { return m_xpr; }
+
+ EIGEN_DEVICE_FUNC
+ const NullaryOp& functor() const { return m_functor; }
+
+ protected:
+ typename XprType::Nested m_xpr;
+ const NullaryOp m_functor;
+};
+
+
+
+namespace internal {
+template<typename UnaryOp, typename XprType>
+struct traits<TensorCwiseUnaryOp<UnaryOp, XprType> >
+ : traits<XprType>
+{
+ // TODO(phli): Add InputScalar, InputPacket. Check references to
+ // current Scalar/Packet to see if the intent is Input or Output.
+ typedef typename result_of<UnaryOp(typename XprType::Scalar)>::type Scalar;
+ typedef traits<XprType> XprTraits;
+ typedef typename XprType::Nested XprTypeNested;
+ typedef std::remove_reference_t<XprTypeNested> XprTypeNested_;
+ static constexpr int NumDimensions = XprTraits::NumDimensions;
+ static constexpr int Layout = XprTraits::Layout;
+ typedef typename TypeConversion<Scalar,
+ typename XprTraits::PointerType
+ >::type
+ PointerType;
+};
+
+template<typename UnaryOp, typename XprType>
+struct eval<TensorCwiseUnaryOp<UnaryOp, XprType>, Eigen::Dense>
+{
+ typedef const TensorCwiseUnaryOp<UnaryOp, XprType>& type;
+};
+
+template<typename UnaryOp, typename XprType>
+struct nested<TensorCwiseUnaryOp<UnaryOp, XprType>, 1, typename eval<TensorCwiseUnaryOp<UnaryOp, XprType> >::type>
+{
+ typedef TensorCwiseUnaryOp<UnaryOp, XprType> type;
+};
+
+} // end namespace internal
+
+
+
+template<typename UnaryOp, typename XprType>
+class TensorCwiseUnaryOp : public TensorBase<TensorCwiseUnaryOp<UnaryOp, XprType>, ReadOnlyAccessors>
+{
+ public:
+ // TODO(phli): Add InputScalar, InputPacket. Check references to
+ // current Scalar/Packet to see if the intent is Input or Output.
+ typedef typename Eigen::internal::traits<TensorCwiseUnaryOp>::Scalar Scalar;
+ typedef typename Eigen::NumTraits<Scalar>::Real RealScalar;
+ typedef Scalar CoeffReturnType;
+ typedef typename Eigen::internal::nested<TensorCwiseUnaryOp>::type Nested;
+ typedef typename Eigen::internal::traits<TensorCwiseUnaryOp>::StorageKind StorageKind;
+ typedef typename Eigen::internal::traits<TensorCwiseUnaryOp>::Index Index;
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorCwiseUnaryOp(const XprType& xpr, const UnaryOp& func = UnaryOp())
+ : m_xpr(xpr), m_functor(func) {}
+
+ EIGEN_DEVICE_FUNC
+ const UnaryOp& functor() const { return m_functor; }
+
+ /** \returns the nested expression */
+ EIGEN_DEVICE_FUNC
+ const internal::remove_all_t<typename XprType::Nested>&
+ nestedExpression() const { return m_xpr; }
+
+ protected:
+ typename XprType::Nested m_xpr;
+ const UnaryOp m_functor;
+};
+
+
+namespace internal {
+template<typename BinaryOp, typename LhsXprType, typename RhsXprType>
+struct traits<TensorCwiseBinaryOp<BinaryOp, LhsXprType, RhsXprType> >
+{
+ // Type promotion to handle the case where the types of the lhs and the rhs
+ // are different.
+ // TODO(phli): Add Lhs/RhsScalar, Lhs/RhsPacket. Check references to
+ // current Scalar/Packet to see if the intent is Inputs or Output.
+ typedef typename result_of<
+ BinaryOp(typename LhsXprType::Scalar,
+ typename RhsXprType::Scalar)>::type Scalar;
+ typedef traits<LhsXprType> XprTraits;
+ typedef typename promote_storage_type<
+ typename traits<LhsXprType>::StorageKind,
+ typename traits<RhsXprType>::StorageKind>::ret StorageKind;
+ typedef typename promote_index_type<
+ typename traits<LhsXprType>::Index,
+ typename traits<RhsXprType>::Index>::type Index;
+ typedef typename LhsXprType::Nested LhsNested;
+ typedef typename RhsXprType::Nested RhsNested;
+ typedef std::remove_reference_t<LhsNested> LhsNested_;
+ typedef std::remove_reference_t<RhsNested> RhsNested_;
+ static constexpr int NumDimensions = XprTraits::NumDimensions;
+ static constexpr int Layout = XprTraits::Layout;
+ typedef typename TypeConversion<Scalar,
+ std::conditional_t<Pointer_type_promotion<typename LhsXprType::Scalar, Scalar>::val,
+ typename traits<LhsXprType>::PointerType,
+ typename traits<RhsXprType>::PointerType>
+ >::type
+ PointerType;
+ enum {
+ Flags = 0
+ };
+};
+
+template<typename BinaryOp, typename LhsXprType, typename RhsXprType>
+struct eval<TensorCwiseBinaryOp<BinaryOp, LhsXprType, RhsXprType>, Eigen::Dense>
+{
+ typedef const TensorCwiseBinaryOp<BinaryOp, LhsXprType, RhsXprType>& type;
+};
+
+template<typename BinaryOp, typename LhsXprType, typename RhsXprType>
+struct nested<TensorCwiseBinaryOp<BinaryOp, LhsXprType, RhsXprType>, 1, typename eval<TensorCwiseBinaryOp<BinaryOp, LhsXprType, RhsXprType> >::type>
+{
+ typedef TensorCwiseBinaryOp<BinaryOp, LhsXprType, RhsXprType> type;
+};
+
+} // end namespace internal
+
+
+
+template<typename BinaryOp, typename LhsXprType, typename RhsXprType>
+class TensorCwiseBinaryOp : public TensorBase<TensorCwiseBinaryOp<BinaryOp, LhsXprType, RhsXprType>, ReadOnlyAccessors>
+{
+ public:
+ // TODO(phli): Add Lhs/RhsScalar, Lhs/RhsPacket. Check references to
+ // current Scalar/Packet to see if the intent is Inputs or Output.
+ typedef typename Eigen::internal::traits<TensorCwiseBinaryOp>::Scalar Scalar;
+ typedef typename Eigen::NumTraits<Scalar>::Real RealScalar;
+ typedef Scalar CoeffReturnType;
+ typedef typename Eigen::internal::nested<TensorCwiseBinaryOp>::type Nested;
+ typedef typename Eigen::internal::traits<TensorCwiseBinaryOp>::StorageKind StorageKind;
+ typedef typename Eigen::internal::traits<TensorCwiseBinaryOp>::Index Index;
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorCwiseBinaryOp(const LhsXprType& lhs, const RhsXprType& rhs, const BinaryOp& func = BinaryOp())
+ : m_lhs_xpr(lhs), m_rhs_xpr(rhs), m_functor(func) {}
+
+ EIGEN_DEVICE_FUNC
+ const BinaryOp& functor() const { return m_functor; }
+
+ /** \returns the nested expressions */
+ EIGEN_DEVICE_FUNC
+ const internal::remove_all_t<typename LhsXprType::Nested>&
+ lhsExpression() const { return m_lhs_xpr; }
+
+ EIGEN_DEVICE_FUNC
+ const internal::remove_all_t<typename RhsXprType::Nested>&
+ rhsExpression() const { return m_rhs_xpr; }
+
+ protected:
+ typename LhsXprType::Nested m_lhs_xpr;
+ typename RhsXprType::Nested m_rhs_xpr;
+ const BinaryOp m_functor;
+};
+
+
+namespace internal {
+template<typename TernaryOp, typename Arg1XprType, typename Arg2XprType, typename Arg3XprType>
+struct traits<TensorCwiseTernaryOp<TernaryOp, Arg1XprType, Arg2XprType, Arg3XprType> >
+{
+ // Type promotion to handle the case where the types of the args are different.
+ typedef typename result_of<
+ TernaryOp(typename Arg1XprType::Scalar,
+ typename Arg2XprType::Scalar,
+ typename Arg3XprType::Scalar)>::type Scalar;
+ typedef traits<Arg1XprType> XprTraits;
+ typedef typename traits<Arg1XprType>::StorageKind StorageKind;
+ typedef typename traits<Arg1XprType>::Index Index;
+ typedef typename Arg1XprType::Nested Arg1Nested;
+ typedef typename Arg2XprType::Nested Arg2Nested;
+ typedef typename Arg3XprType::Nested Arg3Nested;
+ typedef std::remove_reference_t<Arg1Nested> Arg1Nested_;
+ typedef std::remove_reference_t<Arg2Nested> Arg2Nested_;
+ typedef std::remove_reference_t<Arg3Nested> Arg3Nested_;
+ static constexpr int NumDimensions = XprTraits::NumDimensions;
+ static constexpr int Layout = XprTraits::Layout;
+ typedef typename TypeConversion<Scalar,
+ std::conditional_t<Pointer_type_promotion<typename Arg2XprType::Scalar, Scalar>::val,
+ typename traits<Arg2XprType>::PointerType,
+ typename traits<Arg3XprType>::PointerType>
+ >::type
+ PointerType;
+ enum {
+ Flags = 0
+ };
+};
+
+template<typename TernaryOp, typename Arg1XprType, typename Arg2XprType, typename Arg3XprType>
+struct eval<TensorCwiseTernaryOp<TernaryOp, Arg1XprType, Arg2XprType, Arg3XprType>, Eigen::Dense>
+{
+ typedef const TensorCwiseTernaryOp<TernaryOp, Arg1XprType, Arg2XprType, Arg3XprType>& type;
+};
+
+template<typename TernaryOp, typename Arg1XprType, typename Arg2XprType, typename Arg3XprType>
+struct nested<TensorCwiseTernaryOp<TernaryOp, Arg1XprType, Arg2XprType, Arg3XprType>, 1, typename eval<TensorCwiseTernaryOp<TernaryOp, Arg1XprType, Arg2XprType, Arg3XprType> >::type>
+{
+ typedef TensorCwiseTernaryOp<TernaryOp, Arg1XprType, Arg2XprType, Arg3XprType> type;
+};
+
+} // end namespace internal
+
+
+
+template<typename TernaryOp, typename Arg1XprType, typename Arg2XprType, typename Arg3XprType>
+class TensorCwiseTernaryOp : public TensorBase<TensorCwiseTernaryOp<TernaryOp, Arg1XprType, Arg2XprType, Arg3XprType>, ReadOnlyAccessors>
+{
+ public:
+ typedef typename Eigen::internal::traits<TensorCwiseTernaryOp>::Scalar Scalar;
+ typedef typename Eigen::NumTraits<Scalar>::Real RealScalar;
+ typedef Scalar CoeffReturnType;
+ typedef typename Eigen::internal::nested<TensorCwiseTernaryOp>::type Nested;
+ typedef typename Eigen::internal::traits<TensorCwiseTernaryOp>::StorageKind StorageKind;
+ typedef typename Eigen::internal::traits<TensorCwiseTernaryOp>::Index Index;
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorCwiseTernaryOp(const Arg1XprType& arg1, const Arg2XprType& arg2, const Arg3XprType& arg3, const TernaryOp& func = TernaryOp())
+ : m_arg1_xpr(arg1), m_arg2_xpr(arg2), m_arg3_xpr(arg3), m_functor(func) {}
+
+ EIGEN_DEVICE_FUNC
+ const TernaryOp& functor() const { return m_functor; }
+
+ /** \returns the nested expressions */
+ EIGEN_DEVICE_FUNC
+ const internal::remove_all_t<typename Arg1XprType::Nested>&
+ arg1Expression() const { return m_arg1_xpr; }
+
+ EIGEN_DEVICE_FUNC
+ const internal::remove_all_t<typename Arg2XprType::Nested>&
+ arg2Expression() const { return m_arg2_xpr; }
+
+ EIGEN_DEVICE_FUNC
+ const internal::remove_all_t<typename Arg3XprType::Nested>&
+ arg3Expression() const { return m_arg3_xpr; }
+
+ protected:
+ typename Arg1XprType::Nested m_arg1_xpr;
+ typename Arg2XprType::Nested m_arg2_xpr;
+ typename Arg3XprType::Nested m_arg3_xpr;
+ const TernaryOp m_functor;
+};
+
+
+namespace internal {
+template<typename IfXprType, typename ThenXprType, typename ElseXprType>
+struct traits<TensorSelectOp<IfXprType, ThenXprType, ElseXprType> >
+ : traits<ThenXprType>
+{
+ typedef typename traits<ThenXprType>::Scalar Scalar;
+ typedef traits<ThenXprType> XprTraits;
+ typedef typename promote_storage_type<typename traits<ThenXprType>::StorageKind,
+ typename traits<ElseXprType>::StorageKind>::ret StorageKind;
+ typedef typename promote_index_type<typename traits<ElseXprType>::Index,
+ typename traits<ThenXprType>::Index>::type Index;
+ typedef typename IfXprType::Nested IfNested;
+ typedef typename ThenXprType::Nested ThenNested;
+ typedef typename ElseXprType::Nested ElseNested;
+ static constexpr int NumDimensions = XprTraits::NumDimensions;
+ static constexpr int Layout = XprTraits::Layout;
+ typedef std::conditional_t<Pointer_type_promotion<typename ThenXprType::Scalar, Scalar>::val,
+ typename traits<ThenXprType>::PointerType,
+ typename traits<ElseXprType>::PointerType> PointerType;
+};
+
+template<typename IfXprType, typename ThenXprType, typename ElseXprType>
+struct eval<TensorSelectOp<IfXprType, ThenXprType, ElseXprType>, Eigen::Dense>
+{
+ typedef const TensorSelectOp<IfXprType, ThenXprType, ElseXprType>& type;
+};
+
+template<typename IfXprType, typename ThenXprType, typename ElseXprType>
+struct nested<TensorSelectOp<IfXprType, ThenXprType, ElseXprType>, 1, typename eval<TensorSelectOp<IfXprType, ThenXprType, ElseXprType> >::type>
+{
+ typedef TensorSelectOp<IfXprType, ThenXprType, ElseXprType> type;
+};
+
+} // end namespace internal
+
+
+template<typename IfXprType, typename ThenXprType, typename ElseXprType>
+class TensorSelectOp : public TensorBase<TensorSelectOp<IfXprType, ThenXprType, ElseXprType>, ReadOnlyAccessors>
+{
+ public:
+ typedef typename Eigen::internal::traits<TensorSelectOp>::Scalar Scalar;
+ typedef typename Eigen::NumTraits<Scalar>::Real RealScalar;
+ typedef typename internal::promote_storage_type<typename ThenXprType::CoeffReturnType,
+ typename ElseXprType::CoeffReturnType>::ret CoeffReturnType;
+ typedef typename Eigen::internal::nested<TensorSelectOp>::type Nested;
+ typedef typename Eigen::internal::traits<TensorSelectOp>::StorageKind StorageKind;
+ typedef typename Eigen::internal::traits<TensorSelectOp>::Index Index;
+
+ EIGEN_DEVICE_FUNC
+ TensorSelectOp(const IfXprType& a_condition,
+ const ThenXprType& a_then,
+ const ElseXprType& a_else)
+ : m_condition(a_condition), m_then(a_then), m_else(a_else)
+ { }
+
+ EIGEN_DEVICE_FUNC
+ const IfXprType& ifExpression() const { return m_condition; }
+
+ EIGEN_DEVICE_FUNC
+ const ThenXprType& thenExpression() const { return m_then; }
+
+ EIGEN_DEVICE_FUNC
+ const ElseXprType& elseExpression() const { return m_else; }
+
+ protected:
+ typename IfXprType::Nested m_condition;
+ typename ThenXprType::Nested m_then;
+ typename ElseXprType::Nested m_else;
+};
+
+
+} // end namespace Eigen
+
+#endif // EIGEN_CXX11_TENSOR_TENSOR_EXPR_H
diff --git a/unsupported/Eigen/CXX11/src/Tensor/TensorFFT.h b/unsupported/Eigen/CXX11/src/Tensor/TensorFFT.h
new file mode 100644
index 0000000..c744d79
--- /dev/null
+++ b/unsupported/Eigen/CXX11/src/Tensor/TensorFFT.h
@@ -0,0 +1,671 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2015 Jianwei Cui <thucjw@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_CXX11_TENSOR_TENSOR_FFT_H
+#define EIGEN_CXX11_TENSOR_TENSOR_FFT_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+/** \class TensorFFT
+ * \ingroup CXX11_Tensor_Module
+ *
+ * \brief Tensor FFT class.
+ *
+ * TODO:
+ * Vectorize the Cooley Tukey and the Bluestein algorithm
+ * Add support for multithreaded evaluation
+ * Improve the performance on GPU
+ */
+
+template <bool NeedUprade> struct MakeComplex {
+ template <typename T>
+ EIGEN_DEVICE_FUNC
+ T operator() (const T& val) const { return val; }
+};
+
+template <> struct MakeComplex<true> {
+ template <typename T>
+ EIGEN_DEVICE_FUNC
+ std::complex<T> operator() (const T& val) const { return std::complex<T>(val, 0); }
+};
+
+template <> struct MakeComplex<false> {
+ template <typename T>
+ EIGEN_DEVICE_FUNC
+ std::complex<T> operator() (const std::complex<T>& val) const { return val; }
+};
+
+template <int ResultType> struct PartOf {
+ template <typename T> T operator() (const T& val) const { return val; }
+};
+
+template <> struct PartOf<RealPart> {
+ template <typename T> T operator() (const std::complex<T>& val) const { return val.real(); }
+};
+
+template <> struct PartOf<ImagPart> {
+ template <typename T> T operator() (const std::complex<T>& val) const { return val.imag(); }
+};
+
+namespace internal {
+template <typename FFT, typename XprType, int FFTResultType, int FFTDir>
+struct traits<TensorFFTOp<FFT, XprType, FFTResultType, FFTDir> > : public traits<XprType> {
+ typedef traits<XprType> XprTraits;
+ typedef typename NumTraits<typename XprTraits::Scalar>::Real RealScalar;
+ typedef typename std::complex<RealScalar> ComplexScalar;
+ typedef typename XprTraits::Scalar InputScalar;
+ typedef std::conditional_t<FFTResultType == RealPart || FFTResultType == ImagPart, RealScalar, ComplexScalar> OutputScalar;
+ typedef typename XprTraits::StorageKind StorageKind;
+ typedef typename XprTraits::Index Index;
+ typedef typename XprType::Nested Nested;
+ typedef std::remove_reference_t<Nested> Nested_;
+ static constexpr int NumDimensions = XprTraits::NumDimensions;
+ static constexpr int Layout = XprTraits::Layout;
+ typedef typename traits<XprType>::PointerType PointerType;
+};
+
+template <typename FFT, typename XprType, int FFTResultType, int FFTDirection>
+struct eval<TensorFFTOp<FFT, XprType, FFTResultType, FFTDirection>, Eigen::Dense> {
+ typedef const TensorFFTOp<FFT, XprType, FFTResultType, FFTDirection>& type;
+};
+
+template <typename FFT, typename XprType, int FFTResultType, int FFTDirection>
+struct nested<TensorFFTOp<FFT, XprType, FFTResultType, FFTDirection>, 1, typename eval<TensorFFTOp<FFT, XprType, FFTResultType, FFTDirection> >::type> {
+ typedef TensorFFTOp<FFT, XprType, FFTResultType, FFTDirection> type;
+};
+
+} // end namespace internal
+
+template <typename FFT, typename XprType, int FFTResultType, int FFTDir>
+class TensorFFTOp : public TensorBase<TensorFFTOp<FFT, XprType, FFTResultType, FFTDir>, ReadOnlyAccessors> {
+ public:
+ typedef typename Eigen::internal::traits<TensorFFTOp>::Scalar Scalar;
+ typedef typename Eigen::NumTraits<Scalar>::Real RealScalar;
+ typedef typename std::complex<RealScalar> ComplexScalar;
+ typedef std::conditional_t<FFTResultType == RealPart || FFTResultType == ImagPart, RealScalar, ComplexScalar> OutputScalar;
+ typedef OutputScalar CoeffReturnType;
+ typedef typename Eigen::internal::nested<TensorFFTOp>::type Nested;
+ typedef typename Eigen::internal::traits<TensorFFTOp>::StorageKind StorageKind;
+ typedef typename Eigen::internal::traits<TensorFFTOp>::Index Index;
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorFFTOp(const XprType& expr, const FFT& fft)
+ : m_xpr(expr), m_fft(fft) {}
+
+ EIGEN_DEVICE_FUNC
+ const FFT& fft() const { return m_fft; }
+
+ EIGEN_DEVICE_FUNC
+ const internal::remove_all_t<typename XprType::Nested>& expression() const {
+ return m_xpr;
+ }
+
+ protected:
+ typename XprType::Nested m_xpr;
+ const FFT m_fft;
+};
+
+// Eval as rvalue
+template <typename FFT, typename ArgType, typename Device, int FFTResultType, int FFTDir>
+struct TensorEvaluator<const TensorFFTOp<FFT, ArgType, FFTResultType, FFTDir>, Device> {
+ typedef TensorFFTOp<FFT, ArgType, FFTResultType, FFTDir> XprType;
+ typedef typename XprType::Index Index;
+ static constexpr int NumDims = internal::array_size<typename TensorEvaluator<ArgType, Device>::Dimensions>::value;
+ typedef DSizes<Index, NumDims> Dimensions;
+ typedef typename XprType::Scalar Scalar;
+ typedef typename Eigen::NumTraits<Scalar>::Real RealScalar;
+ typedef typename std::complex<RealScalar> ComplexScalar;
+ typedef typename TensorEvaluator<ArgType, Device>::Dimensions InputDimensions;
+ typedef internal::traits<XprType> XprTraits;
+ typedef typename XprTraits::Scalar InputScalar;
+ typedef std::conditional_t<FFTResultType == RealPart || FFTResultType == ImagPart, RealScalar, ComplexScalar> OutputScalar;
+ typedef OutputScalar CoeffReturnType;
+ typedef typename PacketType<OutputScalar, Device>::type PacketReturnType;
+ static constexpr int PacketSize = internal::unpacket_traits<PacketReturnType>::size;
+ typedef StorageMemory<CoeffReturnType, Device> Storage;
+ typedef typename Storage::Type EvaluatorPointerType;
+
+ static constexpr int Layout = TensorEvaluator<ArgType, Device>::Layout;
+ enum {
+ IsAligned = false,
+ PacketAccess = true,
+ BlockAccess = false,
+ PreferBlockAccess = false,
+ CoordAccess = false,
+ RawAccess = false
+ };
+
+ //===- Tensor block evaluation strategy (see TensorBlock.h) -------------===//
+ typedef internal::TensorBlockNotImplemented TensorBlock;
+ //===--------------------------------------------------------------------===//
+
+ EIGEN_STRONG_INLINE TensorEvaluator(const XprType& op, const Device& device) : m_fft(op.fft()), m_impl(op.expression(), device), m_data(NULL), m_device(device) {
+ const typename TensorEvaluator<ArgType, Device>::Dimensions& input_dims = m_impl.dimensions();
+ for (int i = 0; i < NumDims; ++i) {
+ eigen_assert(input_dims[i] > 0);
+ m_dimensions[i] = input_dims[i];
+ }
+
+ if (static_cast<int>(Layout) == static_cast<int>(ColMajor)) {
+ m_strides[0] = 1;
+ for (int i = 1; i < NumDims; ++i) {
+ m_strides[i] = m_strides[i - 1] * m_dimensions[i - 1];
+ }
+ } else {
+ m_strides[NumDims - 1] = 1;
+ for (int i = NumDims - 2; i >= 0; --i) {
+ m_strides[i] = m_strides[i + 1] * m_dimensions[i + 1];
+ }
+ }
+ m_size = m_dimensions.TotalSize();
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Dimensions& dimensions() const {
+ return m_dimensions;
+ }
+
+ EIGEN_STRONG_INLINE bool evalSubExprsIfNeeded(EvaluatorPointerType data) {
+ m_impl.evalSubExprsIfNeeded(NULL);
+ if (data) {
+ evalToBuf(data);
+ return false;
+ } else {
+ m_data = (EvaluatorPointerType)m_device.get((CoeffReturnType*)(m_device.allocate_temp(sizeof(CoeffReturnType) * m_size)));
+ evalToBuf(m_data);
+ return true;
+ }
+ }
+
+ EIGEN_STRONG_INLINE void cleanup() {
+ if (m_data) {
+ m_device.deallocate(m_data);
+ m_data = NULL;
+ }
+ m_impl.cleanup();
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE CoeffReturnType coeff(Index index) const {
+ return m_data[index];
+ }
+
+ template <int LoadMode>
+ EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE PacketReturnType
+ packet(Index index) const {
+ return internal::ploadt<PacketReturnType, LoadMode>(m_data + index);
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorOpCost
+ costPerCoeff(bool vectorized) const {
+ return TensorOpCost(sizeof(CoeffReturnType), 0, 0, vectorized, PacketSize);
+ }
+
+ EIGEN_DEVICE_FUNC EvaluatorPointerType data() const { return m_data; }
+#ifdef EIGEN_USE_SYCL
+ // binding placeholder accessors to a command group handler for SYCL
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void bind(cl::sycl::handler &cgh) const {
+ m_data.bind(cgh);
+ }
+#endif
+
+ private:
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void evalToBuf(EvaluatorPointerType data) {
+ const bool write_to_out = internal::is_same<OutputScalar, ComplexScalar>::value;
+ ComplexScalar* buf = write_to_out ? (ComplexScalar*)data : (ComplexScalar*)m_device.allocate(sizeof(ComplexScalar) * m_size);
+
+ for (Index i = 0; i < m_size; ++i) {
+ buf[i] = MakeComplex<internal::is_same<InputScalar, RealScalar>::value>()(m_impl.coeff(i));
+ }
+
+ for (size_t i = 0; i < m_fft.size(); ++i) {
+ Index dim = m_fft[i];
+ eigen_assert(dim >= 0 && dim < NumDims);
+ Index line_len = m_dimensions[dim];
+ eigen_assert(line_len >= 1);
+ ComplexScalar* line_buf = (ComplexScalar*)m_device.allocate(sizeof(ComplexScalar) * line_len);
+ const bool is_power_of_two = isPowerOfTwo(line_len);
+ const Index good_composite = is_power_of_two ? 0 : findGoodComposite(line_len);
+ const Index log_len = is_power_of_two ? getLog2(line_len) : getLog2(good_composite);
+
+ ComplexScalar* a = is_power_of_two ? NULL : (ComplexScalar*)m_device.allocate(sizeof(ComplexScalar) * good_composite);
+ ComplexScalar* b = is_power_of_two ? NULL : (ComplexScalar*)m_device.allocate(sizeof(ComplexScalar) * good_composite);
+ ComplexScalar* pos_j_base_powered = is_power_of_two ? NULL : (ComplexScalar*)m_device.allocate(sizeof(ComplexScalar) * (line_len + 1));
+ if (!is_power_of_two) {
+ // Compute twiddle factors
+ // t_n = exp(sqrt(-1) * pi * n^2 / line_len)
+ // for n = 0, 1,..., line_len-1.
+ // For n > 2 we use the recurrence t_n = t_{n-1}^2 / t_{n-2} * t_1^2
+
+ // The recurrence is correct in exact arithmetic, but causes
+ // numerical issues for large transforms, especially in
+ // single-precision floating point.
+ //
+ // pos_j_base_powered[0] = ComplexScalar(1, 0);
+ // if (line_len > 1) {
+ // const ComplexScalar pos_j_base = ComplexScalar(
+ // numext::cos(M_PI / line_len), numext::sin(M_PI / line_len));
+ // pos_j_base_powered[1] = pos_j_base;
+ // if (line_len > 2) {
+ // const ComplexScalar pos_j_base_sq = pos_j_base * pos_j_base;
+ // for (int i = 2; i < line_len + 1; ++i) {
+ // pos_j_base_powered[i] = pos_j_base_powered[i - 1] *
+ // pos_j_base_powered[i - 1] /
+ // pos_j_base_powered[i - 2] *
+ // pos_j_base_sq;
+ // }
+ // }
+ // }
+ // TODO(rmlarsen): Find a way to use Eigen's vectorized sin
+ // and cosine functions here.
+ for (int j = 0; j < line_len + 1; ++j) {
+ double arg = ((EIGEN_PI * j) * j) / line_len;
+ std::complex<double> tmp(numext::cos(arg), numext::sin(arg));
+ pos_j_base_powered[j] = static_cast<ComplexScalar>(tmp);
+ }
+ }
+
+ for (Index partial_index = 0; partial_index < m_size / line_len; ++partial_index) {
+ const Index base_offset = getBaseOffsetFromIndex(partial_index, dim);
+
+ // get data into line_buf
+ const Index stride = m_strides[dim];
+ if (stride == 1) {
+ m_device.memcpy(line_buf, &buf[base_offset], line_len*sizeof(ComplexScalar));
+ } else {
+ Index offset = base_offset;
+ for (int j = 0; j < line_len; ++j, offset += stride) {
+ line_buf[j] = buf[offset];
+ }
+ }
+
+ // process the line
+ if (is_power_of_two) {
+ processDataLineCooleyTukey(line_buf, line_len, log_len);
+ }
+ else {
+ processDataLineBluestein(line_buf, line_len, good_composite, log_len, a, b, pos_j_base_powered);
+ }
+
+ // write back
+ if (FFTDir == FFT_FORWARD && stride == 1) {
+ m_device.memcpy(&buf[base_offset], line_buf, line_len*sizeof(ComplexScalar));
+ } else {
+ Index offset = base_offset;
+ const ComplexScalar div_factor = ComplexScalar(1.0 / line_len, 0);
+ for (int j = 0; j < line_len; ++j, offset += stride) {
+ buf[offset] = (FFTDir == FFT_FORWARD) ? line_buf[j] : line_buf[j] * div_factor;
+ }
+ }
+ }
+ m_device.deallocate(line_buf);
+ if (!is_power_of_two) {
+ m_device.deallocate(a);
+ m_device.deallocate(b);
+ m_device.deallocate(pos_j_base_powered);
+ }
+ }
+
+ if(!write_to_out) {
+ for (Index i = 0; i < m_size; ++i) {
+ data[i] = PartOf<FFTResultType>()(buf[i]);
+ }
+ m_device.deallocate(buf);
+ }
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE static bool isPowerOfTwo(Index x) {
+ eigen_assert(x > 0);
+ return !(x & (x - 1));
+ }
+
+ // The composite number for padding, used in Bluestein's FFT algorithm
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE static Index findGoodComposite(Index n) {
+ Index i = 2;
+ while (i < 2 * n - 1) i *= 2;
+ return i;
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE static Index getLog2(Index m) {
+ Index log2m = 0;
+ while (m >>= 1) log2m++;
+ return log2m;
+ }
+
+ // Call Cooley Tukey algorithm directly, data length must be power of 2
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void processDataLineCooleyTukey(ComplexScalar* line_buf, Index line_len, Index log_len) {
+ eigen_assert(isPowerOfTwo(line_len));
+ scramble_FFT(line_buf, line_len);
+ compute_1D_Butterfly<FFTDir>(line_buf, line_len, log_len);
+ }
+
+ // Call Bluestein's FFT algorithm, m is a good composite number greater than (2 * n - 1), used as the padding length
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void processDataLineBluestein(ComplexScalar* line_buf, Index line_len, Index good_composite, Index log_len, ComplexScalar* a, ComplexScalar* b, const ComplexScalar* pos_j_base_powered) {
+ Index n = line_len;
+ Index m = good_composite;
+ ComplexScalar* data = line_buf;
+
+ for (Index i = 0; i < n; ++i) {
+ if(FFTDir == FFT_FORWARD) {
+ a[i] = data[i] * numext::conj(pos_j_base_powered[i]);
+ }
+ else {
+ a[i] = data[i] * pos_j_base_powered[i];
+ }
+ }
+ for (Index i = n; i < m; ++i) {
+ a[i] = ComplexScalar(0, 0);
+ }
+
+ for (Index i = 0; i < n; ++i) {
+ if(FFTDir == FFT_FORWARD) {
+ b[i] = pos_j_base_powered[i];
+ }
+ else {
+ b[i] = numext::conj(pos_j_base_powered[i]);
+ }
+ }
+ for (Index i = n; i < m - n; ++i) {
+ b[i] = ComplexScalar(0, 0);
+ }
+ for (Index i = m - n; i < m; ++i) {
+ if(FFTDir == FFT_FORWARD) {
+ b[i] = pos_j_base_powered[m-i];
+ }
+ else {
+ b[i] = numext::conj(pos_j_base_powered[m-i]);
+ }
+ }
+
+ scramble_FFT(a, m);
+ compute_1D_Butterfly<FFT_FORWARD>(a, m, log_len);
+
+ scramble_FFT(b, m);
+ compute_1D_Butterfly<FFT_FORWARD>(b, m, log_len);
+
+ for (Index i = 0; i < m; ++i) {
+ a[i] *= b[i];
+ }
+
+ scramble_FFT(a, m);
+ compute_1D_Butterfly<FFT_REVERSE>(a, m, log_len);
+
+ //Do the scaling after ifft
+ for (Index i = 0; i < m; ++i) {
+ a[i] /= m;
+ }
+
+ for (Index i = 0; i < n; ++i) {
+ if(FFTDir == FFT_FORWARD) {
+ data[i] = a[i] * numext::conj(pos_j_base_powered[i]);
+ }
+ else {
+ data[i] = a[i] * pos_j_base_powered[i];
+ }
+ }
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE static void scramble_FFT(ComplexScalar* data, Index n) {
+ eigen_assert(isPowerOfTwo(n));
+ Index j = 1;
+ for (Index i = 1; i < n; ++i){
+ if (j > i) {
+ std::swap(data[j-1], data[i-1]);
+ }
+ Index m = n >> 1;
+ while (m >= 2 && j > m) {
+ j -= m;
+ m >>= 1;
+ }
+ j += m;
+ }
+ }
+
+ template <int Dir>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void butterfly_2(ComplexScalar* data) {
+ ComplexScalar tmp = data[1];
+ data[1] = data[0] - data[1];
+ data[0] += tmp;
+ }
+
+ template <int Dir>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void butterfly_4(ComplexScalar* data) {
+ ComplexScalar tmp[4];
+ tmp[0] = data[0] + data[1];
+ tmp[1] = data[0] - data[1];
+ tmp[2] = data[2] + data[3];
+ if (Dir == FFT_FORWARD) {
+ tmp[3] = ComplexScalar(0.0, -1.0) * (data[2] - data[3]);
+ } else {
+ tmp[3] = ComplexScalar(0.0, 1.0) * (data[2] - data[3]);
+ }
+ data[0] = tmp[0] + tmp[2];
+ data[1] = tmp[1] + tmp[3];
+ data[2] = tmp[0] - tmp[2];
+ data[3] = tmp[1] - tmp[3];
+ }
+
+ template <int Dir>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void butterfly_8(ComplexScalar* data) {
+ ComplexScalar tmp_1[8];
+ ComplexScalar tmp_2[8];
+
+ tmp_1[0] = data[0] + data[1];
+ tmp_1[1] = data[0] - data[1];
+ tmp_1[2] = data[2] + data[3];
+ if (Dir == FFT_FORWARD) {
+ tmp_1[3] = (data[2] - data[3]) * ComplexScalar(0, -1);
+ } else {
+ tmp_1[3] = (data[2] - data[3]) * ComplexScalar(0, 1);
+ }
+ tmp_1[4] = data[4] + data[5];
+ tmp_1[5] = data[4] - data[5];
+ tmp_1[6] = data[6] + data[7];
+ if (Dir == FFT_FORWARD) {
+ tmp_1[7] = (data[6] - data[7]) * ComplexScalar(0, -1);
+ } else {
+ tmp_1[7] = (data[6] - data[7]) * ComplexScalar(0, 1);
+ }
+ tmp_2[0] = tmp_1[0] + tmp_1[2];
+ tmp_2[1] = tmp_1[1] + tmp_1[3];
+ tmp_2[2] = tmp_1[0] - tmp_1[2];
+ tmp_2[3] = tmp_1[1] - tmp_1[3];
+ tmp_2[4] = tmp_1[4] + tmp_1[6];
+// SQRT2DIV2 = sqrt(2)/2
+#define SQRT2DIV2 0.7071067811865476
+ if (Dir == FFT_FORWARD) {
+ tmp_2[5] = (tmp_1[5] + tmp_1[7]) * ComplexScalar(SQRT2DIV2, -SQRT2DIV2);
+ tmp_2[6] = (tmp_1[4] - tmp_1[6]) * ComplexScalar(0, -1);
+ tmp_2[7] = (tmp_1[5] - tmp_1[7]) * ComplexScalar(-SQRT2DIV2, -SQRT2DIV2);
+ } else {
+ tmp_2[5] = (tmp_1[5] + tmp_1[7]) * ComplexScalar(SQRT2DIV2, SQRT2DIV2);
+ tmp_2[6] = (tmp_1[4] - tmp_1[6]) * ComplexScalar(0, 1);
+ tmp_2[7] = (tmp_1[5] - tmp_1[7]) * ComplexScalar(-SQRT2DIV2, SQRT2DIV2);
+ }
+ data[0] = tmp_2[0] + tmp_2[4];
+ data[1] = tmp_2[1] + tmp_2[5];
+ data[2] = tmp_2[2] + tmp_2[6];
+ data[3] = tmp_2[3] + tmp_2[7];
+ data[4] = tmp_2[0] - tmp_2[4];
+ data[5] = tmp_2[1] - tmp_2[5];
+ data[6] = tmp_2[2] - tmp_2[6];
+ data[7] = tmp_2[3] - tmp_2[7];
+ }
+
+ template <int Dir>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void butterfly_1D_merge(
+ ComplexScalar* data, Index n, Index n_power_of_2) {
+ // Original code:
+ // RealScalar wtemp = std::sin(M_PI/n);
+ // RealScalar wpi = -std::sin(2 * M_PI/n);
+ const RealScalar wtemp = m_sin_PI_div_n_LUT[n_power_of_2];
+ const RealScalar wpi = (Dir == FFT_FORWARD)
+ ? m_minus_sin_2_PI_div_n_LUT[n_power_of_2]
+ : -m_minus_sin_2_PI_div_n_LUT[n_power_of_2];
+
+ const ComplexScalar wp(wtemp, wpi);
+ const ComplexScalar wp_one = wp + ComplexScalar(1, 0);
+ const ComplexScalar wp_one_2 = wp_one * wp_one;
+ const ComplexScalar wp_one_3 = wp_one_2 * wp_one;
+ const ComplexScalar wp_one_4 = wp_one_3 * wp_one;
+ const Index n2 = n / 2;
+ ComplexScalar w(1.0, 0.0);
+ for (Index i = 0; i < n2; i += 4) {
+ ComplexScalar temp0(data[i + n2] * w);
+ ComplexScalar temp1(data[i + 1 + n2] * w * wp_one);
+ ComplexScalar temp2(data[i + 2 + n2] * w * wp_one_2);
+ ComplexScalar temp3(data[i + 3 + n2] * w * wp_one_3);
+ w = w * wp_one_4;
+
+ data[i + n2] = data[i] - temp0;
+ data[i] += temp0;
+
+ data[i + 1 + n2] = data[i + 1] - temp1;
+ data[i + 1] += temp1;
+
+ data[i + 2 + n2] = data[i + 2] - temp2;
+ data[i + 2] += temp2;
+
+ data[i + 3 + n2] = data[i + 3] - temp3;
+ data[i + 3] += temp3;
+ }
+ }
+
+ template <int Dir>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void compute_1D_Butterfly(
+ ComplexScalar* data, Index n, Index n_power_of_2) {
+ eigen_assert(isPowerOfTwo(n));
+ if (n > 8) {
+ compute_1D_Butterfly<Dir>(data, n / 2, n_power_of_2 - 1);
+ compute_1D_Butterfly<Dir>(data + n / 2, n / 2, n_power_of_2 - 1);
+ butterfly_1D_merge<Dir>(data, n, n_power_of_2);
+ } else if (n == 8) {
+ butterfly_8<Dir>(data);
+ } else if (n == 4) {
+ butterfly_4<Dir>(data);
+ } else if (n == 2) {
+ butterfly_2<Dir>(data);
+ }
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Index getBaseOffsetFromIndex(Index index, Index omitted_dim) const {
+ Index result = 0;
+
+ if (static_cast<int>(Layout) == static_cast<int>(ColMajor)) {
+ for (int i = NumDims - 1; i > omitted_dim; --i) {
+ const Index partial_m_stride = m_strides[i] / m_dimensions[omitted_dim];
+ const Index idx = index / partial_m_stride;
+ index -= idx * partial_m_stride;
+ result += idx * m_strides[i];
+ }
+ result += index;
+ }
+ else {
+ for (Index i = 0; i < omitted_dim; ++i) {
+ const Index partial_m_stride = m_strides[i] / m_dimensions[omitted_dim];
+ const Index idx = index / partial_m_stride;
+ index -= idx * partial_m_stride;
+ result += idx * m_strides[i];
+ }
+ result += index;
+ }
+ // Value of index_coords[omitted_dim] is not determined to this step
+ return result;
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Index getIndexFromOffset(Index base, Index omitted_dim, Index offset) const {
+ Index result = base + offset * m_strides[omitted_dim] ;
+ return result;
+ }
+
+ protected:
+ Index m_size;
+ const FFT EIGEN_DEVICE_REF m_fft;
+ Dimensions m_dimensions;
+ array<Index, NumDims> m_strides;
+ TensorEvaluator<ArgType, Device> m_impl;
+ EvaluatorPointerType m_data;
+ const Device EIGEN_DEVICE_REF m_device;
+
+ // This will support a maximum FFT size of 2^32 for each dimension
+ // m_sin_PI_div_n_LUT[i] = (-2) * std::sin(M_PI / std::pow(2,i)) ^ 2;
+ const RealScalar m_sin_PI_div_n_LUT[32] = {
+ RealScalar(0.0),
+ RealScalar(-2),
+ RealScalar(-0.999999999999999),
+ RealScalar(-0.292893218813453),
+ RealScalar(-0.0761204674887130),
+ RealScalar(-0.0192147195967696),
+ RealScalar(-0.00481527332780311),
+ RealScalar(-0.00120454379482761),
+ RealScalar(-3.01181303795779e-04),
+ RealScalar(-7.52981608554592e-05),
+ RealScalar(-1.88247173988574e-05),
+ RealScalar(-4.70619042382852e-06),
+ RealScalar(-1.17654829809007e-06),
+ RealScalar(-2.94137117780840e-07),
+ RealScalar(-7.35342821488550e-08),
+ RealScalar(-1.83835707061916e-08),
+ RealScalar(-4.59589268710903e-09),
+ RealScalar(-1.14897317243732e-09),
+ RealScalar(-2.87243293150586e-10),
+ RealScalar( -7.18108232902250e-11),
+ RealScalar(-1.79527058227174e-11),
+ RealScalar(-4.48817645568941e-12),
+ RealScalar(-1.12204411392298e-12),
+ RealScalar(-2.80511028480785e-13),
+ RealScalar(-7.01277571201985e-14),
+ RealScalar(-1.75319392800498e-14),
+ RealScalar(-4.38298482001247e-15),
+ RealScalar(-1.09574620500312e-15),
+ RealScalar(-2.73936551250781e-16),
+ RealScalar(-6.84841378126949e-17),
+ RealScalar(-1.71210344531737e-17),
+ RealScalar(-4.28025861329343e-18)
+ };
+
+ // m_minus_sin_2_PI_div_n_LUT[i] = -std::sin(2 * M_PI / std::pow(2,i));
+ const RealScalar m_minus_sin_2_PI_div_n_LUT[32] = {
+ RealScalar(0.0),
+ RealScalar(0.0),
+ RealScalar(-1.00000000000000e+00),
+ RealScalar(-7.07106781186547e-01),
+ RealScalar(-3.82683432365090e-01),
+ RealScalar(-1.95090322016128e-01),
+ RealScalar(-9.80171403295606e-02),
+ RealScalar(-4.90676743274180e-02),
+ RealScalar(-2.45412285229123e-02),
+ RealScalar(-1.22715382857199e-02),
+ RealScalar(-6.13588464915448e-03),
+ RealScalar(-3.06795676296598e-03),
+ RealScalar(-1.53398018628477e-03),
+ RealScalar(-7.66990318742704e-04),
+ RealScalar(-3.83495187571396e-04),
+ RealScalar(-1.91747597310703e-04),
+ RealScalar(-9.58737990959773e-05),
+ RealScalar(-4.79368996030669e-05),
+ RealScalar(-2.39684498084182e-05),
+ RealScalar(-1.19842249050697e-05),
+ RealScalar(-5.99211245264243e-06),
+ RealScalar(-2.99605622633466e-06),
+ RealScalar(-1.49802811316901e-06),
+ RealScalar(-7.49014056584716e-07),
+ RealScalar(-3.74507028292384e-07),
+ RealScalar(-1.87253514146195e-07),
+ RealScalar(-9.36267570730981e-08),
+ RealScalar(-4.68133785365491e-08),
+ RealScalar(-2.34066892682746e-08),
+ RealScalar(-1.17033446341373e-08),
+ RealScalar(-5.85167231706864e-09),
+ RealScalar(-2.92583615853432e-09)
+ };
+};
+
+} // end namespace Eigen
+
+#endif // EIGEN_CXX11_TENSOR_TENSOR_FFT_H
diff --git a/unsupported/Eigen/CXX11/src/Tensor/TensorFixedSize.h b/unsupported/Eigen/CXX11/src/Tensor/TensorFixedSize.h
new file mode 100644
index 0000000..08b182a
--- /dev/null
+++ b/unsupported/Eigen/CXX11/src/Tensor/TensorFixedSize.h
@@ -0,0 +1,280 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_CXX11_TENSOR_TENSOR_FIXED_SIZE_H
+#define EIGEN_CXX11_TENSOR_TENSOR_FIXED_SIZE_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+/** \class TensorFixedSize
+ * \ingroup CXX11_Tensor_Module
+ *
+ * \brief The fixed sized version of the tensor class.
+ *
+ * The fixed sized equivalent of
+ * Eigen::Tensor<float, 3> t(3, 5, 7);
+ * is
+ * Eigen::TensorFixedSize<float, Sizes<3,5,7>> t;
+ */
+
+template<typename Scalar_, typename Dimensions_, int Options_, typename IndexType>
+class TensorFixedSize : public TensorBase<TensorFixedSize<Scalar_, Dimensions_, Options_, IndexType> >
+{
+ public:
+ typedef TensorFixedSize<Scalar_, Dimensions_, Options_, IndexType> Self;
+ typedef TensorBase<TensorFixedSize<Scalar_, Dimensions_, Options_, IndexType> > Base;
+ typedef typename Eigen::internal::nested<Self>::type Nested;
+ typedef typename internal::traits<Self>::StorageKind StorageKind;
+ typedef typename internal::traits<Self>::Index Index;
+ typedef Scalar_ Scalar;
+ typedef typename NumTraits<Scalar>::Real RealScalar;
+ typedef typename Base::CoeffReturnType CoeffReturnType;
+
+ static constexpr int Options = Options_;
+ static constexpr int Layout = Options_ & RowMajor ? RowMajor : ColMajor;
+
+ enum {
+ IsAligned = bool(EIGEN_MAX_ALIGN_BYTES>0),
+ PacketAccess = (internal::packet_traits<Scalar>::size > 1),
+ BlockAccess = false,
+ PreferBlockAccess = false,
+ CoordAccess = true,
+ RawAccess = true
+ };
+
+ //===- Tensor block evaluation strategy (see TensorBlock.h) -------------===//
+ typedef internal::TensorBlockNotImplemented TensorBlock;
+ //===--------------------------------------------------------------------===//
+
+ typedef Dimensions_ Dimensions;
+ static constexpr std::size_t NumIndices = Dimensions::count;
+
+ protected:
+ TensorStorage<Scalar, Dimensions, Options> m_storage;
+
+ public:
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Index rank() const { return NumIndices; }
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Index dimension(std::size_t n) const { return m_storage.dimensions()[n]; }
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Dimensions dimensions() const { return m_storage.dimensions(); }
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Index size() const { return m_storage.size(); }
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar *data() { return m_storage.data(); }
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar *data() const { return m_storage.data(); }
+
+ // This makes EIGEN_INITIALIZE_COEFFS_IF_THAT_OPTION_IS_ENABLED
+ // work, because that uses base().coeffRef() - and we don't yet
+ // implement a similar class hierarchy
+ inline Self& base() { return *this; }
+ inline const Self& base() const { return *this; }
+
+ template<typename... IndexTypes>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar& coeff(Index firstIndex, IndexTypes... otherIndices) const
+ {
+ // The number of indices used to access a tensor coefficient must be equal to the rank of the tensor.
+ EIGEN_STATIC_ASSERT(sizeof...(otherIndices) + 1 == NumIndices, YOU_MADE_A_PROGRAMMING_MISTAKE)
+ return coeff(array<Index, NumIndices>{{firstIndex, otherIndices...}});
+ }
+
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE const Scalar& coeff(const array<Index, NumIndices>& indices) const
+ {
+ eigen_internal_assert(checkIndexRange(indices));
+ return m_storage.data()[linearizedIndex(indices)];
+ }
+
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE const Scalar& coeff(Index index) const
+ {
+ eigen_internal_assert(index >= 0 && index < size());
+ return m_storage.data()[index];
+ }
+
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE const Scalar& coeff() const
+ {
+ EIGEN_STATIC_ASSERT(NumIndices == 0, YOU_MADE_A_PROGRAMMING_MISTAKE);
+ return m_storage.data()[0];
+ }
+
+
+ template<typename... IndexTypes>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar& coeffRef(Index firstIndex, IndexTypes... otherIndices)
+ {
+ // The number of indices used to access a tensor coefficient must be equal to the rank of the tensor.
+ EIGEN_STATIC_ASSERT(sizeof...(otherIndices) + 1 == NumIndices, YOU_MADE_A_PROGRAMMING_MISTAKE)
+ return coeffRef(array<Index, NumIndices>{{firstIndex, otherIndices...}});
+ }
+
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE Scalar& coeffRef(const array<Index, NumIndices>& indices)
+ {
+ eigen_internal_assert(checkIndexRange(indices));
+ return m_storage.data()[linearizedIndex(indices)];
+ }
+
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE Scalar& coeffRef(Index index)
+ {
+ eigen_internal_assert(index >= 0 && index < size());
+ return m_storage.data()[index];
+ }
+
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE Scalar& coeffRef()
+ {
+ EIGEN_STATIC_ASSERT(NumIndices == 0, YOU_MADE_A_PROGRAMMING_MISTAKE);
+ return m_storage.data()[0];
+ }
+
+ template<typename... IndexTypes>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar& operator()(Index firstIndex, IndexTypes... otherIndices) const
+ {
+ // The number of indices used to access a tensor coefficient must be equal to the rank of the tensor.
+ EIGEN_STATIC_ASSERT(sizeof...(otherIndices) + 1 == NumIndices, YOU_MADE_A_PROGRAMMING_MISTAKE)
+ return this->operator()(array<Index, NumIndices>{{firstIndex, otherIndices...}});
+ }
+
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE const Scalar& operator()(const array<Index, NumIndices>& indices) const
+ {
+ eigen_assert(checkIndexRange(indices));
+ return coeff(indices);
+ }
+
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE const Scalar& operator()(Index index) const
+ {
+ eigen_internal_assert(index >= 0 && index < size());
+ return coeff(index);
+ }
+
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE const Scalar& operator()() const
+ {
+ EIGEN_STATIC_ASSERT(NumIndices == 0, YOU_MADE_A_PROGRAMMING_MISTAKE);
+ return coeff();
+ }
+
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE const Scalar& operator[](Index index) const
+ {
+ // The bracket operator is only for vectors, use the parenthesis operator instead.
+ EIGEN_STATIC_ASSERT(NumIndices == 1, YOU_MADE_A_PROGRAMMING_MISTAKE);
+ return coeff(index);
+ }
+
+ template<typename... IndexTypes>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar& operator()(Index firstIndex, IndexTypes... otherIndices)
+ {
+ // The number of indices used to access a tensor coefficient must be equal to the rank of the tensor.
+ EIGEN_STATIC_ASSERT(sizeof...(otherIndices) + 1 == NumIndices, YOU_MADE_A_PROGRAMMING_MISTAKE)
+ return operator()(array<Index, NumIndices>{{firstIndex, otherIndices...}});
+ }
+
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE Scalar& operator()(const array<Index, NumIndices>& indices)
+ {
+ eigen_assert(checkIndexRange(indices));
+ return coeffRef(indices);
+ }
+
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE Scalar& operator()(Index index)
+ {
+ eigen_assert(index >= 0 && index < size());
+ return coeffRef(index);
+ }
+
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE Scalar& operator()()
+ {
+ EIGEN_STATIC_ASSERT(NumIndices == 0, YOU_MADE_A_PROGRAMMING_MISTAKE);
+ return coeffRef();
+ }
+
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE Scalar& operator[](Index index)
+ {
+ // The bracket operator is only for vectors, use the parenthesis operator instead
+ EIGEN_STATIC_ASSERT(NumIndices == 1, YOU_MADE_A_PROGRAMMING_MISTAKE)
+ return coeffRef(index);
+ }
+
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE TensorFixedSize()
+ : m_storage()
+ {
+ }
+
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE TensorFixedSize(const Self& other)
+ : Base(other), m_storage(other.m_storage)
+ {
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorFixedSize(Self&& other)
+ : m_storage(other.m_storage)
+ {
+ }
+
+ template<typename OtherDerived>
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE TensorFixedSize(const TensorBase<OtherDerived, ReadOnlyAccessors>& other)
+ {
+ typedef TensorAssignOp<TensorFixedSize, const OtherDerived> Assign;
+ Assign assign(*this, other.derived());
+ internal::TensorExecutor<const Assign, DefaultDevice>::run(assign, DefaultDevice());
+ }
+ template<typename OtherDerived>
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE TensorFixedSize(const TensorBase<OtherDerived, WriteAccessors>& other)
+ {
+ typedef TensorAssignOp<TensorFixedSize, const OtherDerived> Assign;
+ Assign assign(*this, other.derived());
+ internal::TensorExecutor<const Assign, DefaultDevice>::run(assign, DefaultDevice());
+ }
+
+ // FIXME: check that the dimensions of other match the dimensions of *this.
+ // Unfortunately this isn't possible yet when the rhs is an expression.
+ EIGEN_TENSOR_INHERIT_ASSIGNMENT_EQUAL_OPERATOR(TensorFixedSize)
+
+
+ protected:
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE bool checkIndexRange(const array<Index, NumIndices>& /*indices*/) const
+ {
+ using internal::array_apply_and_reduce;
+ using internal::array_zip_and_reduce;
+ using internal::greater_equal_zero_op;
+ using internal::logical_and_op;
+ using internal::lesser_op;
+
+ return true;
+ // check whether the indices are all >= 0
+ /* array_apply_and_reduce<logical_and_op, greater_equal_zero_op>(indices) &&
+ // check whether the indices fit in the dimensions
+ array_zip_and_reduce<logical_and_op, lesser_op>(indices, m_storage.dimensions());*/
+ }
+
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE Index linearizedIndex(const array<Index, NumIndices>& indices) const
+ {
+ if (Options&RowMajor) {
+ return m_storage.dimensions().IndexOfRowMajor(indices);
+ } else {
+ return m_storage.dimensions().IndexOfColMajor(indices);
+ }
+ }
+};
+
+
+} // end namespace Eigen
+
+#endif // EIGEN_CXX11_TENSOR_TENSOR_FIXED_SIZE_H
diff --git a/unsupported/Eigen/CXX11/src/Tensor/TensorForcedEval.h b/unsupported/Eigen/CXX11/src/Tensor/TensorForcedEval.h
new file mode 100644
index 0000000..4550fca
--- /dev/null
+++ b/unsupported/Eigen/CXX11/src/Tensor/TensorForcedEval.h
@@ -0,0 +1,239 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_CXX11_TENSOR_TENSOR_FORCED_EVAL_H
+#define EIGEN_CXX11_TENSOR_TENSOR_FORCED_EVAL_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+/** \class TensorForcedEval
+ * \ingroup CXX11_Tensor_Module
+ *
+ * \brief Tensor reshaping class.
+ *
+ *
+ */
+namespace internal {
+template<typename XprType>
+struct traits<TensorForcedEvalOp<XprType> >
+{
+ // Type promotion to handle the case where the types of the lhs and the rhs are different.
+ typedef typename XprType::Scalar Scalar;
+ typedef traits<XprType> XprTraits;
+ typedef typename traits<XprType>::StorageKind StorageKind;
+ typedef typename traits<XprType>::Index Index;
+ typedef typename XprType::Nested Nested;
+ typedef std::remove_reference_t<Nested> Nested_;
+ static constexpr int NumDimensions = XprTraits::NumDimensions;
+ static constexpr int Layout = XprTraits::Layout;
+ typedef typename XprTraits::PointerType PointerType;
+
+ enum {
+ Flags = 0
+ };
+};
+
+template<typename XprType>
+struct eval<TensorForcedEvalOp<XprType>, Eigen::Dense>
+{
+ typedef const TensorForcedEvalOp<XprType>& type;
+};
+
+template<typename XprType>
+struct nested<TensorForcedEvalOp<XprType>, 1, typename eval<TensorForcedEvalOp<XprType> >::type>
+{
+ typedef TensorForcedEvalOp<XprType> type;
+};
+
+} // end namespace internal
+
+
+
+template<typename XprType>
+class TensorForcedEvalOp : public TensorBase<TensorForcedEvalOp<XprType>, ReadOnlyAccessors>
+{
+ public:
+ typedef typename Eigen::internal::traits<TensorForcedEvalOp>::Scalar Scalar;
+ typedef typename Eigen::NumTraits<Scalar>::Real RealScalar;
+ typedef std::remove_const_t<typename XprType::CoeffReturnType> CoeffReturnType;
+ typedef typename Eigen::internal::nested<TensorForcedEvalOp>::type Nested;
+ typedef typename Eigen::internal::traits<TensorForcedEvalOp>::StorageKind StorageKind;
+ typedef typename Eigen::internal::traits<TensorForcedEvalOp>::Index Index;
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorForcedEvalOp(const XprType& expr)
+ : m_xpr(expr) {}
+
+ EIGEN_DEVICE_FUNC
+ const internal::remove_all_t<typename XprType::Nested>&
+ expression() const { return m_xpr; }
+
+ protected:
+ typename XprType::Nested m_xpr;
+};
+
+namespace internal {
+template <typename Device, typename CoeffReturnType>
+struct non_integral_type_placement_new{
+ template <typename StorageType>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void operator()(Index numValues, StorageType m_buffer) {
+ // Initialize non-trivially constructible types.
+ if (!internal::is_arithmetic<CoeffReturnType>::value) {
+ for (Index i = 0; i < numValues; ++i) new (m_buffer + i) CoeffReturnType();
+ }
+}
+};
+
+// SYCL does not support non-integral types
+// having new (m_buffer + i) CoeffReturnType() causes the following compiler error for SYCL Devices
+// no matching function for call to 'operator new'
+template <typename CoeffReturnType>
+struct non_integral_type_placement_new<Eigen::SyclDevice, CoeffReturnType> {
+ template <typename StorageType>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void operator()(Index, StorageType) {
+}
+};
+} // end namespace internal
+
+template<typename ArgType_, typename Device>
+struct TensorEvaluator<const TensorForcedEvalOp<ArgType_>, Device>
+{
+ typedef const internal::remove_all_t<ArgType_> ArgType;
+ typedef TensorForcedEvalOp<ArgType> XprType;
+ typedef typename ArgType::Scalar Scalar;
+ typedef typename TensorEvaluator<ArgType, Device>::Dimensions Dimensions;
+ typedef typename XprType::Index Index;
+ typedef typename XprType::CoeffReturnType CoeffReturnType;
+ typedef typename PacketType<CoeffReturnType, Device>::type PacketReturnType;
+ static constexpr int PacketSize = PacketType<CoeffReturnType, Device>::size;
+ typedef typename Eigen::internal::traits<XprType>::PointerType TensorPointerType;
+ typedef StorageMemory<CoeffReturnType, Device> Storage;
+ typedef typename Storage::Type EvaluatorPointerType;
+
+ enum {
+ IsAligned = true,
+ PacketAccess = (PacketType<CoeffReturnType, Device>::size > 1),
+ BlockAccess = internal::is_arithmetic<CoeffReturnType>::value,
+ PreferBlockAccess = false,
+ RawAccess = true
+ };
+
+ static constexpr int Layout = TensorEvaluator<ArgType, Device>::Layout;
+ static constexpr int NumDims = internal::traits<ArgType>::NumDimensions;
+
+ //===- Tensor block evaluation strategy (see TensorBlock.h) -------------===//
+ typedef internal::TensorBlockDescriptor<NumDims, Index> TensorBlockDesc;
+ typedef internal::TensorBlockScratchAllocator<Device> TensorBlockScratch;
+
+ typedef typename internal::TensorMaterializedBlock<CoeffReturnType, NumDims,
+ Layout, Index>
+ TensorBlock;
+ //===--------------------------------------------------------------------===//
+
+ TensorEvaluator(const XprType& op, const Device& device)
+ : m_impl(op.expression(), device), m_op(op.expression()),
+ m_device(device), m_buffer(NULL)
+ { }
+
+ EIGEN_DEVICE_FUNC const Dimensions& dimensions() const { return m_impl.dimensions(); }
+
+ EIGEN_STRONG_INLINE bool evalSubExprsIfNeeded(EvaluatorPointerType) {
+ const Index numValues = internal::array_prod(m_impl.dimensions());
+ m_buffer = m_device.get((CoeffReturnType*)m_device.allocate_temp(numValues * sizeof(CoeffReturnType)));
+
+ internal::non_integral_type_placement_new<Device, CoeffReturnType>()(numValues, m_buffer);
+
+ typedef TensorEvalToOp< const std::remove_const_t<ArgType> > EvalTo;
+ EvalTo evalToTmp(m_device.get(m_buffer), m_op);
+
+ internal::TensorExecutor<
+ const EvalTo, std::remove_const_t<Device>,
+ /*Vectorizable=*/internal::IsVectorizable<Device, const ArgType>::value,
+ /*Tiling=*/internal::IsTileable<Device, const ArgType>::value>::
+ run(evalToTmp, m_device);
+
+ return true;
+ }
+
+#ifdef EIGEN_USE_THREADS
+ template <typename EvalSubExprsCallback>
+ EIGEN_STRONG_INLINE void evalSubExprsIfNeededAsync(
+ EvaluatorPointerType, EvalSubExprsCallback done) {
+ const Index numValues = internal::array_prod(m_impl.dimensions());
+ m_buffer = m_device.get((CoeffReturnType*)m_device.allocate_temp(
+ numValues * sizeof(CoeffReturnType)));
+ typedef TensorEvalToOp<const std::remove_const_t<ArgType>>
+ EvalTo;
+ EvalTo evalToTmp(m_device.get(m_buffer), m_op);
+
+ auto on_done = std::bind([](EvalSubExprsCallback done_) { done_(true); },
+ std::move(done));
+ internal::TensorAsyncExecutor<
+ const EvalTo, std::remove_const_t<Device>,
+ decltype(on_done),
+ /*Vectorizable=*/internal::IsVectorizable<Device, const ArgType>::value,
+ /*Tiling=*/internal::IsTileable<Device, const ArgType>::value>::
+ runAsync(evalToTmp, m_device, std::move(on_done));
+ }
+#endif
+
+ EIGEN_STRONG_INLINE void cleanup() {
+ m_device.deallocate_temp(m_buffer);
+ m_buffer = NULL;
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE CoeffReturnType coeff(Index index) const
+ {
+ return m_buffer[index];
+ }
+
+ template<int LoadMode>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE PacketReturnType packet(Index index) const
+ {
+ return internal::ploadt<PacketReturnType, LoadMode>(m_buffer + index);
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ internal::TensorBlockResourceRequirements getResourceRequirements() const {
+ return internal::TensorBlockResourceRequirements::any();
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorBlock
+ block(TensorBlockDesc& desc, TensorBlockScratch& scratch,
+ bool /*root_of_expr_ast*/ = false) const {
+ eigen_assert(m_buffer != NULL);
+ return TensorBlock::materialize(m_buffer, m_impl.dimensions(), desc, scratch);
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorOpCost costPerCoeff(bool vectorized) const {
+ return TensorOpCost(sizeof(CoeffReturnType), 0, 0, vectorized, PacketSize);
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ EvaluatorPointerType data() const { return m_buffer; }
+
+#ifdef EIGEN_USE_SYCL
+ // binding placeholder accessors to a command group handler for SYCL
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void bind(cl::sycl::handler &cgh) const {
+ m_buffer.bind(cgh);
+ m_impl.bind(cgh);
+ }
+#endif
+ private:
+ TensorEvaluator<ArgType, Device> m_impl;
+ const ArgType m_op;
+ const Device EIGEN_DEVICE_REF m_device;
+ EvaluatorPointerType m_buffer;
+};
+
+
+} // end namespace Eigen
+
+#endif // EIGEN_CXX11_TENSOR_TENSOR_FORCED_EVAL_H
diff --git a/unsupported/Eigen/CXX11/src/Tensor/TensorForwardDeclarations.h b/unsupported/Eigen/CXX11/src/Tensor/TensorForwardDeclarations.h
new file mode 100644
index 0000000..b52833c
--- /dev/null
+++ b/unsupported/Eigen/CXX11/src/Tensor/TensorForwardDeclarations.h
@@ -0,0 +1,193 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_CXX11_TENSOR_TENSOR_FORWARD_DECLARATIONS_H
+#define EIGEN_CXX11_TENSOR_TENSOR_FORWARD_DECLARATIONS_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+// MakePointer class is used as a container of the address space of the pointer
+// on the host and on the device. From the host side it generates the T* pointer
+// and when EIGEN_USE_SYCL is used it construct a buffer with a map_allocator to
+// T* m_data on the host. It is always called on the device.
+// Specialisation of MakePointer class for creating the sycl buffer with
+// map_allocator.
+template<typename T> struct MakePointer {
+ typedef T* Type;
+ typedef const T* ConstType;
+};
+
+template <typename T>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE T* constCast(const T* data) {
+ return const_cast<T*>(data);
+}
+
+// The StorageMemory class is a container of the device specific pointer
+// used for referring to a Pointer on TensorEvaluator class. While the TensorExpression
+// is a device-agnostic type and need MakePointer class for type conversion,
+// the TensorEvaluator class can be specialized for a device, hence it is possible
+// to construct different types of temproray storage memory in TensorEvaluator
+// for different devices by specializing the following StorageMemory class.
+template<typename T, typename device> struct StorageMemory: MakePointer <T> {};
+
+namespace internal{
+template<typename A, typename B> struct Pointer_type_promotion {
+ static const bool val=false;
+};
+template<typename A> struct Pointer_type_promotion<A, A> {
+ static const bool val = true;
+};
+template<typename A, typename B> struct TypeConversion {
+ typedef A* type;
+};
+}
+
+
+template<typename PlainObjectType, int Options_ = Unaligned, template <class> class MakePointer_ = MakePointer> class TensorMap;
+template<typename Scalar_, int NumIndices_, int Options_ = 0, typename IndexType = DenseIndex> class Tensor;
+template<typename Scalar_, typename Dimensions, int Options_ = 0, typename IndexType = DenseIndex> class TensorFixedSize;
+template<typename PlainObjectType> class TensorRef;
+template<typename Derived, int AccessLevel> class TensorBase;
+
+template<typename NullaryOp, typename PlainObjectType> class TensorCwiseNullaryOp;
+template<typename UnaryOp, typename XprType> class TensorCwiseUnaryOp;
+template<typename BinaryOp, typename LeftXprType, typename RightXprType> class TensorCwiseBinaryOp;
+template<typename TernaryOp, typename Arg1XprType, typename Arg2XprType, typename Arg3XprType> class TensorCwiseTernaryOp;
+template<typename IfXprType, typename ThenXprType, typename ElseXprType> class TensorSelectOp;
+template<typename Op, typename Dims, typename XprType, template <class> class MakePointer_ = MakePointer > class TensorReductionOp;
+template<typename XprType> class TensorIndexPairOp;
+template<typename ReduceOp, typename Dims, typename XprType> class TensorPairReducerOp;
+template<typename Axis, typename LeftXprType, typename RightXprType> class TensorConcatenationOp;
+template<typename Dimensions, typename LeftXprType, typename RightXprType, typename OutputKernelType> class TensorContractionOp;
+template<typename TargetType, typename XprType> class TensorConversionOp;
+template<typename Dimensions, typename InputXprType, typename KernelXprType> class TensorConvolutionOp;
+template<typename FFT, typename XprType, int FFTDataType, int FFTDirection> class TensorFFTOp;
+template<typename PatchDim, typename XprType> class TensorPatchOp;
+template<DenseIndex Rows, DenseIndex Cols, typename XprType> class TensorImagePatchOp;
+template<DenseIndex Planes, DenseIndex Rows, DenseIndex Cols, typename XprType> class TensorVolumePatchOp;
+template<typename Broadcast, typename XprType> class TensorBroadcastingOp;
+template<DenseIndex DimId, typename XprType> class TensorChippingOp;
+template<typename NewDimensions, typename XprType> class TensorReshapingOp;
+template<typename XprType> class TensorLayoutSwapOp;
+template<typename StartIndices, typename Sizes, typename XprType> class TensorSlicingOp;
+template<typename ReverseDimensions, typename XprType> class TensorReverseOp;
+template<typename PaddingDimensions, typename XprType> class TensorPaddingOp;
+template<typename Shuffle, typename XprType> class TensorShufflingOp;
+template<typename Strides, typename XprType> class TensorStridingOp;
+template<typename StartIndices, typename StopIndices, typename Strides, typename XprType> class TensorStridingSlicingOp;
+template<typename Strides, typename XprType> class TensorInflationOp;
+template<typename Generator, typename XprType> class TensorGeneratorOp;
+template<typename LeftXprType, typename RightXprType> class TensorAssignOp;
+template<typename Op, typename XprType> class TensorScanOp;
+template<typename Dims, typename XprType> class TensorTraceOp;
+
+template<typename CustomUnaryFunc, typename XprType> class TensorCustomUnaryOp;
+template<typename CustomBinaryFunc, typename LhsXprType, typename RhsXprType> class TensorCustomBinaryOp;
+
+template<typename XprType, template <class> class MakePointer_ = MakePointer> class TensorEvalToOp;
+template<typename XprType> class TensorForcedEvalOp;
+
+template<typename ExpressionType, typename DeviceType> class TensorDevice;
+template<typename ExpressionType, typename DeviceType, typename DoneCallback> class TensorAsyncDevice;
+template<typename Derived, typename Device> struct TensorEvaluator;
+
+struct NoOpOutputKernel;
+
+struct DefaultDevice;
+struct ThreadPoolDevice;
+struct GpuDevice;
+struct SyclDevice;
+
+#ifdef EIGEN_USE_SYCL
+
+template <typename T> struct MakeSYCLPointer {
+ typedef Eigen::TensorSycl::internal::RangeAccess<cl::sycl::access::mode::read_write, T> Type;
+};
+
+template <typename T>
+EIGEN_STRONG_INLINE const Eigen::TensorSycl::internal::RangeAccess<cl::sycl::access::mode::read_write, T>&
+constCast(const Eigen::TensorSycl::internal::RangeAccess<cl::sycl::access::mode::read_write, T>& data) {
+ return data;
+}
+
+template <typename T>
+struct StorageMemory<T, SyclDevice> : MakeSYCLPointer<T> {};
+template <typename T>
+struct StorageMemory<T, const SyclDevice> : StorageMemory<T, SyclDevice> {};
+
+namespace TensorSycl {
+namespace internal{
+template <typename Evaluator, typename Op> class GenericNondeterministicReducer;
+}
+}
+#endif
+
+
+enum FFTResultType {
+ RealPart = 0,
+ ImagPart = 1,
+ BothParts = 2
+};
+
+enum FFTDirection {
+ FFT_FORWARD = 0,
+ FFT_REVERSE = 1
+};
+
+
+namespace internal {
+
+template <typename Device, typename Expression>
+struct IsVectorizable {
+ static const bool value = TensorEvaluator<Expression, Device>::PacketAccess;
+};
+
+template <typename Expression>
+struct IsVectorizable<GpuDevice, Expression> {
+ static const bool value = TensorEvaluator<Expression, GpuDevice>::PacketAccess &&
+ TensorEvaluator<Expression, GpuDevice>::IsAligned;
+};
+
+// Tiled evaluation strategy.
+enum TiledEvaluation {
+ Off = 0, // tiled evaluation is not supported
+ On = 1, // still work in progress (see TensorBlock.h)
+};
+
+template <typename Device, typename Expression>
+struct IsTileable {
+ // Check that block evaluation is supported and it's a preferred option (at
+ // least one sub-expression has much faster block evaluation, e.g.
+ // broadcasting).
+ static constexpr bool BlockAccess =
+ TensorEvaluator<Expression, Device>::BlockAccess &&
+ TensorEvaluator<Expression, Device>::PreferBlockAccess;
+
+ static const TiledEvaluation value =
+ BlockAccess ? TiledEvaluation::On : TiledEvaluation::Off;
+};
+
+template <typename Expression, typename Device,
+ bool Vectorizable = IsVectorizable<Device, Expression>::value,
+ TiledEvaluation Tiling = IsTileable<Device, Expression>::value>
+class TensorExecutor;
+
+template <typename Expression, typename Device, typename DoneCallback,
+ bool Vectorizable = IsVectorizable<Device, Expression>::value,
+ TiledEvaluation Tiling = IsTileable<Device, Expression>::value>
+class TensorAsyncExecutor;
+
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_CXX11_TENSOR_TENSOR_FORWARD_DECLARATIONS_H
diff --git a/unsupported/Eigen/CXX11/src/Tensor/TensorFunctors.h b/unsupported/Eigen/CXX11/src/Tensor/TensorFunctors.h
new file mode 100644
index 0000000..137fe58
--- /dev/null
+++ b/unsupported/Eigen/CXX11/src/Tensor/TensorFunctors.h
@@ -0,0 +1,488 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_CXX11_TENSOR_TENSOR_FUNCTORS_H
+#define EIGEN_CXX11_TENSOR_TENSOR_FUNCTORS_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+namespace internal {
+
+
+/** \internal
+ * \brief Template functor to compute the modulo between an array and a scalar.
+ */
+template <typename Scalar>
+struct scalar_mod_op {
+ EIGEN_DEVICE_FUNC scalar_mod_op(const Scalar& divisor) : m_divisor(divisor) {}
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar operator() (const Scalar& a) const { return a % m_divisor; }
+ const Scalar m_divisor;
+};
+template <typename Scalar>
+struct functor_traits<scalar_mod_op<Scalar> >
+{ enum { Cost = scalar_div_cost<Scalar,false>::value, PacketAccess = false }; };
+
+
+/** \internal
+ * \brief Template functor to compute the modulo between 2 arrays.
+ */
+template <typename Scalar>
+struct scalar_mod2_op {
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar operator() (const Scalar& a, const Scalar& b) const { return a % b; }
+};
+template <typename Scalar>
+struct functor_traits<scalar_mod2_op<Scalar> >
+{ enum { Cost = scalar_div_cost<Scalar,false>::value, PacketAccess = false }; };
+
+template <typename Scalar>
+struct scalar_fmod_op {
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar
+ operator()(const Scalar& a, const Scalar& b) const {
+ return numext::fmod(a, b);
+ }
+};
+template <typename Scalar>
+struct functor_traits<scalar_fmod_op<Scalar> > {
+ enum { Cost = 13, // Reciprocal throughput of FPREM on Haswell.
+ PacketAccess = false };
+};
+
+template<typename Reducer, typename Device>
+struct reducer_traits {
+ enum {
+ Cost = 1,
+ PacketAccess = false,
+ IsStateful = false,
+ IsExactlyAssociative = true
+ };
+};
+
+// Standard reduction functors
+template <typename T> struct SumReducer
+{
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void reduce(const T t, T* accum) const {
+ internal::scalar_sum_op<T> sum_op;
+ *accum = sum_op(*accum, t);
+ }
+ template <typename Packet>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void reducePacket(const Packet& p, Packet* accum) const {
+ (*accum) = padd<Packet>(*accum, p);
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE T initialize() const {
+ internal::scalar_cast_op<int, T> conv;
+ return conv(0);
+ }
+ template <typename Packet>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet initializePacket() const {
+ return pset1<Packet>(initialize());
+ }
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE T finalize(const T accum) const {
+ return accum;
+ }
+ template <typename Packet>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet finalizePacket(const Packet& vaccum) const {
+ return vaccum;
+ }
+ template <typename Packet>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE T finalizeBoth(const T saccum, const Packet& vaccum) const {
+ internal::scalar_sum_op<T> sum_op;
+ return sum_op(saccum, predux(vaccum));
+ }
+};
+
+template <typename T, typename Device>
+struct reducer_traits<SumReducer<T>, Device> {
+ enum {
+ Cost = NumTraits<T>::AddCost,
+ PacketAccess = PacketType<T, Device>::HasAdd,
+ IsStateful = false,
+ IsExactlyAssociative = NumTraits<T>::IsInteger
+ };
+};
+
+template <typename T> struct MeanReducer
+{
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ MeanReducer() : scalarCount_(0), packetCount_(0) { }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void reduce(const T t, T* accum) {
+ internal::scalar_sum_op<T> sum_op;
+ *accum = sum_op(*accum, t);
+ scalarCount_++;
+ }
+ template <typename Packet>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void reducePacket(const Packet& p, Packet* accum) {
+ (*accum) = padd<Packet>(*accum, p);
+ packetCount_++;
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE T initialize() const {
+ internal::scalar_cast_op<int, T> conv;
+ return conv(0);
+ }
+ template <typename Packet>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet initializePacket() const {
+ return pset1<Packet>(initialize());
+ }
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE T finalize(const T accum) const {
+ internal::scalar_quotient_op<T> quotient_op;
+ return quotient_op(accum, T(scalarCount_));
+ }
+ template <typename Packet>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet finalizePacket(const Packet& vaccum) const {
+ return pdiv(vaccum, pset1<Packet>(T(packetCount_)));
+ }
+ template <typename Packet>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE T finalizeBoth(const T saccum, const Packet& vaccum) const {
+ internal::scalar_sum_op<T> sum_op;
+ internal::scalar_quotient_op<T> quotient_op;
+ return quotient_op(
+ sum_op(saccum, predux(vaccum)),
+ T(scalarCount_ + packetCount_ * unpacket_traits<Packet>::size));
+ }
+
+ protected:
+ DenseIndex scalarCount_;
+ DenseIndex packetCount_;
+};
+
+template <typename T, typename Device>
+struct reducer_traits<MeanReducer<T>, Device> {
+ enum {
+ Cost = NumTraits<T>::AddCost,
+ PacketAccess = PacketType<T, Device>::HasAdd &&
+ PacketType<T, Device>::HasDiv && !NumTraits<T>::IsInteger,
+ IsStateful = true,
+ IsExactlyAssociative = NumTraits<T>::IsInteger
+ };
+};
+
+
+template <typename T, bool IsMax = true, bool IsInteger = true>
+struct MinMaxBottomValue {
+ EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE T bottom_value() {
+ return Eigen::NumTraits<T>::lowest();
+ }
+};
+template <typename T>
+struct MinMaxBottomValue<T, true, false> {
+ EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE T bottom_value() {
+ return -Eigen::NumTraits<T>::infinity();
+ }
+};
+template <typename T>
+struct MinMaxBottomValue<T, false, true> {
+ EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE T bottom_value() {
+ return Eigen::NumTraits<T>::highest();
+ }
+};
+template <typename T>
+struct MinMaxBottomValue<T, false, false> {
+ EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE T bottom_value() {
+ return Eigen::NumTraits<T>::infinity();
+ }
+};
+
+
+template <typename T, int NaNPropagation=PropagateFast> struct MaxReducer
+{
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void reduce(const T t, T* accum) const {
+ scalar_max_op<T, T, NaNPropagation> op;
+ *accum = op(t, *accum);
+ }
+ template <typename Packet>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void reducePacket(const Packet& p, Packet* accum) const {
+ scalar_max_op<T, T, NaNPropagation> op;
+ (*accum) = op.packetOp(*accum, p);
+ }
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE T initialize() const {
+ return MinMaxBottomValue<T, /*IsMax=*/true, Eigen::NumTraits<T>::IsInteger>::bottom_value();
+ }
+ template <typename Packet>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet initializePacket() const {
+ return pset1<Packet>(initialize());
+ }
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE T finalize(const T accum) const {
+ return accum;
+ }
+ template <typename Packet>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet finalizePacket(const Packet& vaccum) const {
+ return vaccum;
+ }
+ template <typename Packet>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE T finalizeBoth(const T saccum, const Packet& vaccum) const {
+ scalar_max_op<T, T, NaNPropagation> op;
+ return op(saccum, op.predux(vaccum));
+ }
+};
+
+template <typename T, typename Device, int NaNPropagation>
+ struct reducer_traits<MaxReducer<T, NaNPropagation>, Device> {
+ enum {
+ Cost = NumTraits<T>::AddCost,
+ PacketAccess = PacketType<T, Device>::HasMax,
+ IsStateful = false,
+ IsExactlyAssociative = (NaNPropagation!=PropagateFast)
+ };
+};
+
+template <typename T, int NaNPropagation=PropagateFast> struct MinReducer
+{
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void reduce(const T t, T* accum) const {
+ scalar_min_op<T, T, NaNPropagation> op;
+ *accum = op(t, *accum);
+ }
+ template <typename Packet>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void reducePacket(const Packet& p, Packet* accum) const {
+ scalar_min_op<T, T, NaNPropagation> op;
+ (*accum) = op.packetOp(*accum, p);
+ }
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE T initialize() const {
+ return MinMaxBottomValue<T, /*IsMax=*/false, Eigen::NumTraits<T>::IsInteger>::bottom_value();
+ }
+ template <typename Packet>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet initializePacket() const {
+ return pset1<Packet>(initialize());
+ }
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE T finalize(const T accum) const {
+ return accum;
+ }
+ template <typename Packet>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet finalizePacket(const Packet& vaccum) const {
+ return vaccum;
+ }
+ template <typename Packet>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE T finalizeBoth(const T saccum, const Packet& vaccum) const {
+ scalar_min_op<T, T, NaNPropagation> op;
+ return op(saccum, op.predux(vaccum));
+ }
+};
+
+template <typename T, typename Device, int NaNPropagation>
+ struct reducer_traits<MinReducer<T, NaNPropagation>, Device> {
+ enum {
+ Cost = NumTraits<T>::AddCost,
+ PacketAccess = PacketType<T, Device>::HasMin,
+ IsStateful = false,
+ IsExactlyAssociative = (NaNPropagation!=PropagateFast)
+ };
+};
+
+template <typename T> struct ProdReducer
+{
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void reduce(const T t, T* accum) const {
+ internal::scalar_product_op<T> prod_op;
+ (*accum) = prod_op(*accum, t);
+ }
+ template <typename Packet>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void reducePacket(const Packet& p, Packet* accum) const {
+ (*accum) = pmul<Packet>(*accum, p);
+ }
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE T initialize() const {
+ internal::scalar_cast_op<int, T> conv;
+ return conv(1);
+ }
+ template <typename Packet>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet initializePacket() const {
+ return pset1<Packet>(initialize());
+ }
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE T finalize(const T accum) const {
+ return accum;
+ }
+ template <typename Packet>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet finalizePacket(const Packet& vaccum) const {
+ return vaccum;
+ }
+ template <typename Packet>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE T finalizeBoth(const T saccum, const Packet& vaccum) const {
+ internal::scalar_product_op<T> prod_op;
+ return prod_op(saccum, predux_mul(vaccum));
+ }
+};
+
+template <typename T, typename Device>
+struct reducer_traits<ProdReducer<T>, Device> {
+ enum {
+ Cost = NumTraits<T>::MulCost,
+ PacketAccess = PacketType<T, Device>::HasMul,
+ IsStateful = false,
+ IsExactlyAssociative = true
+ };
+};
+
+
+struct AndReducer
+{
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void reduce(bool t, bool* accum) const {
+ *accum = *accum && t;
+ }
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE bool initialize() const {
+ return true;
+ }
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE bool finalize(bool accum) const {
+ return accum;
+ }
+};
+
+template <typename Device>
+struct reducer_traits<AndReducer, Device> {
+ enum {
+ Cost = 1,
+ PacketAccess = false,
+ IsStateful = false,
+ IsExactlyAssociative = true
+ };
+};
+
+
+struct OrReducer {
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void reduce(bool t, bool* accum) const {
+ *accum = *accum || t;
+ }
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE bool initialize() const {
+ return false;
+ }
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE bool finalize(bool accum) const {
+ return accum;
+ }
+};
+
+template <typename Device>
+struct reducer_traits<OrReducer, Device> {
+ enum {
+ Cost = 1,
+ PacketAccess = false,
+ IsStateful = false,
+ IsExactlyAssociative = true
+ };
+};
+
+// Argmin/Argmax reducers. Returns the first occurrence if multiple locations
+// contain the same min/max value.
+template <typename T> struct ArgMaxPairReducer
+{
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void reduce(const T t, T* accum) const {
+ if (t.second < accum->second) {
+ return;
+ } else if (t.second > accum->second || accum->first > t.first ) {
+ *accum = t;
+ }
+ }
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE T initialize() const {
+ return T(0, NumTraits<typename T::second_type>::lowest());
+ }
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE T finalize(const T& accum) const {
+ return accum;
+ }
+};
+
+template <typename T, typename Device>
+struct reducer_traits<ArgMaxPairReducer<T>, Device> {
+ enum {
+ Cost = NumTraits<T>::AddCost,
+ PacketAccess = false,
+ IsStateful = false,
+ IsExactlyAssociative = true
+ };
+};
+
+
+template <typename T> struct ArgMinPairReducer
+{
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void reduce(const T& t, T* accum) const {
+ if (t.second > accum->second) {
+ return;
+ } else if (t.second < accum->second || accum->first > t.first) {
+ *accum = t;
+ }
+ }
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE T initialize() const {
+ return T(0, NumTraits<typename T::second_type>::highest());
+ }
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE T finalize(const T& accum) const {
+ return accum;
+ }
+};
+
+template <typename T, typename Device>
+struct reducer_traits<ArgMinPairReducer<T>, Device> {
+ enum {
+ Cost = NumTraits<T>::AddCost,
+ PacketAccess = false,
+ IsStateful = false,
+ IsExactlyAssociative = true
+ };
+};
+
+
+template <typename T, typename Index, size_t NumDims>
+class GaussianGenerator {
+ public:
+ static constexpr bool PacketAccess = false;
+
+ EIGEN_DEVICE_FUNC GaussianGenerator(const array<T, NumDims>& means,
+ const array<T, NumDims>& std_devs)
+ : m_means(means)
+ {
+ EIGEN_UNROLL_LOOP
+ for (size_t i = 0; i < NumDims; ++i) {
+ m_two_sigmas[i] = std_devs[i] * std_devs[i] * 2;
+ }
+ }
+
+ EIGEN_DEVICE_FUNC T operator()(const array<Index, NumDims>& coordinates) const {
+ T tmp = T(0);
+ EIGEN_UNROLL_LOOP
+ for (size_t i = 0; i < NumDims; ++i) {
+ T offset = coordinates[i] - m_means[i];
+ tmp += offset * offset / m_two_sigmas[i];
+ }
+ return numext::exp(-tmp);
+ }
+
+ private:
+ array<T, NumDims> m_means;
+ array<T, NumDims> m_two_sigmas;
+};
+
+template <typename T, typename Index, size_t NumDims>
+struct functor_traits<GaussianGenerator<T, Index, NumDims> > {
+ enum {
+ Cost = NumDims * (2 * NumTraits<T>::AddCost + NumTraits<T>::MulCost +
+ functor_traits<scalar_quotient_op<T, T> >::Cost) +
+ functor_traits<scalar_exp_op<T> >::Cost,
+ PacketAccess = GaussianGenerator<T, Index, NumDims>::PacketAccess
+ };
+};
+
+template <typename Scalar>
+struct scalar_clamp_op {
+ EIGEN_DEVICE_FUNC inline scalar_clamp_op(const Scalar& _min, const Scalar& _max) : m_min(_min), m_max(_max) {}
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar
+ operator()(const Scalar& x) const {
+ return numext::mini(numext::maxi(x, m_min), m_max);
+ }
+ template <typename Packet>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Packet
+ packetOp(const Packet& x) const {
+ return internal::pmin(internal::pmax(x, pset1<Packet>(m_min)), pset1<Packet>(m_max));
+ }
+ const Scalar m_min;
+ const Scalar m_max;
+};
+template<typename Scalar>
+struct functor_traits<scalar_clamp_op<Scalar> >
+{ enum { Cost = 2 * NumTraits<Scalar>::AddCost, PacketAccess = (packet_traits<Scalar>::HasMin && packet_traits<Scalar>::HasMax)}; };
+
+} // end namespace internal
+} // end namespace Eigen
+
+#endif // EIGEN_CXX11_TENSOR_TENSOR_FUNCTORS_H
diff --git a/unsupported/Eigen/CXX11/src/Tensor/TensorGenerator.h b/unsupported/Eigen/CXX11/src/Tensor/TensorGenerator.h
new file mode 100644
index 0000000..9b8469b
--- /dev/null
+++ b/unsupported/Eigen/CXX11/src/Tensor/TensorGenerator.h
@@ -0,0 +1,303 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2015 Benoit Steiner <benoit.steiner.goog@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_CXX11_TENSOR_TENSOR_GENERATOR_H
+#define EIGEN_CXX11_TENSOR_TENSOR_GENERATOR_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+/** \class TensorGeneratorOp
+ * \ingroup CXX11_Tensor_Module
+ *
+ * \brief Tensor generator class.
+ *
+ *
+ */
+namespace internal {
+template<typename Generator, typename XprType>
+struct traits<TensorGeneratorOp<Generator, XprType> > : public traits<XprType>
+{
+ typedef typename XprType::Scalar Scalar;
+ typedef traits<XprType> XprTraits;
+ typedef typename XprTraits::StorageKind StorageKind;
+ typedef typename XprTraits::Index Index;
+ typedef typename XprType::Nested Nested;
+ typedef std::remove_reference_t<Nested> Nested_;
+ static constexpr int NumDimensions = XprTraits::NumDimensions;
+ static constexpr int Layout = XprTraits::Layout;
+ typedef typename XprTraits::PointerType PointerType;
+};
+
+template<typename Generator, typename XprType>
+struct eval<TensorGeneratorOp<Generator, XprType>, Eigen::Dense>
+{
+ typedef const TensorGeneratorOp<Generator, XprType>& type;
+};
+
+template<typename Generator, typename XprType>
+struct nested<TensorGeneratorOp<Generator, XprType>, 1, typename eval<TensorGeneratorOp<Generator, XprType> >::type>
+{
+ typedef TensorGeneratorOp<Generator, XprType> type;
+};
+
+} // end namespace internal
+
+
+
+template<typename Generator, typename XprType>
+class TensorGeneratorOp : public TensorBase<TensorGeneratorOp<Generator, XprType>, ReadOnlyAccessors>
+{
+ public:
+ typedef typename Eigen::internal::traits<TensorGeneratorOp>::Scalar Scalar;
+ typedef typename Eigen::NumTraits<Scalar>::Real RealScalar;
+ typedef typename XprType::CoeffReturnType CoeffReturnType;
+ typedef typename Eigen::internal::nested<TensorGeneratorOp>::type Nested;
+ typedef typename Eigen::internal::traits<TensorGeneratorOp>::StorageKind StorageKind;
+ typedef typename Eigen::internal::traits<TensorGeneratorOp>::Index Index;
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorGeneratorOp(const XprType& expr, const Generator& generator)
+ : m_xpr(expr), m_generator(generator) {}
+
+ EIGEN_DEVICE_FUNC
+ const Generator& generator() const { return m_generator; }
+
+ EIGEN_DEVICE_FUNC
+ const internal::remove_all_t<typename XprType::Nested>&
+ expression() const { return m_xpr; }
+
+ protected:
+ typename XprType::Nested m_xpr;
+ const Generator m_generator;
+};
+
+
+// Eval as rvalue
+template<typename Generator, typename ArgType, typename Device>
+struct TensorEvaluator<const TensorGeneratorOp<Generator, ArgType>, Device>
+{
+ typedef TensorGeneratorOp<Generator, ArgType> XprType;
+ typedef typename XprType::Index Index;
+ typedef typename TensorEvaluator<ArgType, Device>::Dimensions Dimensions;
+ static constexpr int NumDims = internal::array_size<Dimensions>::value;
+ typedef typename XprType::Scalar Scalar;
+ typedef typename XprType::CoeffReturnType CoeffReturnType;
+ typedef typename PacketType<CoeffReturnType, Device>::type PacketReturnType;
+ typedef StorageMemory<CoeffReturnType, Device> Storage;
+ typedef typename Storage::Type EvaluatorPointerType;
+ static constexpr int Layout = TensorEvaluator<ArgType, Device>::Layout;
+ enum {
+ IsAligned = false,
+ PacketAccess = (PacketType<CoeffReturnType, Device>::size > 1),
+ BlockAccess = true,
+ PreferBlockAccess = true,
+ CoordAccess = false, // to be implemented
+ RawAccess = false
+ };
+
+ typedef internal::TensorIntDivisor<Index> IndexDivisor;
+
+ //===- Tensor block evaluation strategy (see TensorBlock.h) -------------===//
+ typedef internal::TensorBlockDescriptor<NumDims, Index> TensorBlockDesc;
+ typedef internal::TensorBlockScratchAllocator<Device> TensorBlockScratch;
+
+ typedef typename internal::TensorMaterializedBlock<CoeffReturnType, NumDims,
+ Layout, Index>
+ TensorBlock;
+ //===--------------------------------------------------------------------===//
+
+ EIGEN_STRONG_INLINE TensorEvaluator(const XprType& op, const Device& device)
+ : m_device(device), m_generator(op.generator())
+ {
+ TensorEvaluator<ArgType, Device> argImpl(op.expression(), device);
+ m_dimensions = argImpl.dimensions();
+
+ if (static_cast<int>(Layout) == static_cast<int>(ColMajor)) {
+ m_strides[0] = 1;
+ EIGEN_UNROLL_LOOP
+ for (int i = 1; i < NumDims; ++i) {
+ m_strides[i] = m_strides[i - 1] * m_dimensions[i - 1];
+ if (m_strides[i] != 0) m_fast_strides[i] = IndexDivisor(m_strides[i]);
+ }
+ } else {
+ m_strides[NumDims - 1] = 1;
+ EIGEN_UNROLL_LOOP
+ for (int i = NumDims - 2; i >= 0; --i) {
+ m_strides[i] = m_strides[i + 1] * m_dimensions[i + 1];
+ if (m_strides[i] != 0) m_fast_strides[i] = IndexDivisor(m_strides[i]);
+ }
+ }
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Dimensions& dimensions() const { return m_dimensions; }
+
+ EIGEN_STRONG_INLINE bool evalSubExprsIfNeeded(EvaluatorPointerType /*data*/) {
+ return true;
+ }
+ EIGEN_STRONG_INLINE void cleanup() {
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE CoeffReturnType coeff(Index index) const
+ {
+ array<Index, NumDims> coords;
+ extract_coordinates(index, coords);
+ return m_generator(coords);
+ }
+
+ template<int LoadMode>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE PacketReturnType packet(Index index) const
+ {
+ const int packetSize = PacketType<CoeffReturnType, Device>::size;
+ eigen_assert(index+packetSize-1 < dimensions().TotalSize());
+
+ EIGEN_ALIGN_MAX std::remove_const_t<CoeffReturnType> values[packetSize];
+ for (int i = 0; i < packetSize; ++i) {
+ values[i] = coeff(index+i);
+ }
+ PacketReturnType rslt = internal::pload<PacketReturnType>(values);
+ return rslt;
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ internal::TensorBlockResourceRequirements getResourceRequirements() const {
+ const size_t target_size = m_device.firstLevelCacheSize();
+ // TODO(ezhulenev): Generator should have a cost.
+ return internal::TensorBlockResourceRequirements::skewed<Scalar>(
+ target_size);
+ }
+
+ struct BlockIteratorState {
+ Index stride;
+ Index span;
+ Index size;
+ Index count;
+ };
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorBlock
+ block(TensorBlockDesc& desc, TensorBlockScratch& scratch,
+ bool /*root_of_expr_ast*/ = false) const {
+ static const bool is_col_major =
+ static_cast<int>(Layout) == static_cast<int>(ColMajor);
+
+ // Compute spatial coordinates for the first block element.
+ array<Index, NumDims> coords;
+ extract_coordinates(desc.offset(), coords);
+ array<Index, NumDims> initial_coords = coords;
+
+ // Offset in the output block buffer.
+ Index offset = 0;
+
+ // Initialize output block iterator state. Dimension in this array are
+ // always in inner_most -> outer_most order (col major layout).
+ array<BlockIteratorState, NumDims> it;
+ for (int i = 0; i < NumDims; ++i) {
+ const int dim = is_col_major ? i : NumDims - 1 - i;
+ it[i].size = desc.dimension(dim);
+ it[i].stride = i == 0 ? 1 : (it[i - 1].size * it[i - 1].stride);
+ it[i].span = it[i].stride * (it[i].size - 1);
+ it[i].count = 0;
+ }
+ eigen_assert(it[0].stride == 1);
+
+ // Prepare storage for the materialized generator result.
+ const typename TensorBlock::Storage block_storage =
+ TensorBlock::prepareStorage(desc, scratch);
+
+ CoeffReturnType* block_buffer = block_storage.data();
+
+ static const int packet_size = PacketType<CoeffReturnType, Device>::size;
+
+ static const int inner_dim = is_col_major ? 0 : NumDims - 1;
+ const Index inner_dim_size = it[0].size;
+ const Index inner_dim_vectorized = inner_dim_size - packet_size;
+
+ while (it[NumDims - 1].count < it[NumDims - 1].size) {
+ Index i = 0;
+ // Generate data for the vectorized part of the inner-most dimension.
+ for (; i <= inner_dim_vectorized; i += packet_size) {
+ for (Index j = 0; j < packet_size; ++j) {
+ array<Index, NumDims> j_coords = coords; // Break loop dependence.
+ j_coords[inner_dim] += j;
+ *(block_buffer + offset + i + j) = m_generator(j_coords);
+ }
+ coords[inner_dim] += packet_size;
+ }
+ // Finalize non-vectorized part of the inner-most dimension.
+ for (; i < inner_dim_size; ++i) {
+ *(block_buffer + offset + i) = m_generator(coords);
+ coords[inner_dim]++;
+ }
+ coords[inner_dim] = initial_coords[inner_dim];
+
+ // For the 1d tensor we need to generate only one inner-most dimension.
+ if (NumDims == 1) break;
+
+ // Update offset.
+ for (i = 1; i < NumDims; ++i) {
+ if (++it[i].count < it[i].size) {
+ offset += it[i].stride;
+ coords[is_col_major ? i : NumDims - 1 - i]++;
+ break;
+ }
+ if (i != NumDims - 1) it[i].count = 0;
+ coords[is_col_major ? i : NumDims - 1 - i] =
+ initial_coords[is_col_major ? i : NumDims - 1 - i];
+ offset -= it[i].span;
+ }
+ }
+
+ return block_storage.AsTensorMaterializedBlock();
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorOpCost
+ costPerCoeff(bool) const {
+ // TODO(rmlarsen): This is just a placeholder. Define interface to make
+ // generators return their cost.
+ return TensorOpCost(0, 0, TensorOpCost::AddCost<Scalar>() +
+ TensorOpCost::MulCost<Scalar>());
+ }
+
+ EIGEN_DEVICE_FUNC EvaluatorPointerType data() const { return NULL; }
+
+#ifdef EIGEN_USE_SYCL
+ // binding placeholder accessors to a command group handler for SYCL
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void bind(cl::sycl::handler&) const {}
+#endif
+
+ protected:
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ void extract_coordinates(Index index, array<Index, NumDims>& coords) const {
+ if (static_cast<int>(Layout) == static_cast<int>(ColMajor)) {
+ for (int i = NumDims - 1; i > 0; --i) {
+ const Index idx = index / m_fast_strides[i];
+ index -= idx * m_strides[i];
+ coords[i] = idx;
+ }
+ coords[0] = index;
+ } else {
+ for (int i = 0; i < NumDims - 1; ++i) {
+ const Index idx = index / m_fast_strides[i];
+ index -= idx * m_strides[i];
+ coords[i] = idx;
+ }
+ coords[NumDims-1] = index;
+ }
+ }
+
+ const Device EIGEN_DEVICE_REF m_device;
+ Dimensions m_dimensions;
+ array<Index, NumDims> m_strides;
+ array<IndexDivisor, NumDims> m_fast_strides;
+ Generator m_generator;
+};
+
+} // end namespace Eigen
+
+#endif // EIGEN_CXX11_TENSOR_TENSOR_GENERATOR_H
diff --git a/unsupported/Eigen/CXX11/src/Tensor/TensorGlobalFunctions.h b/unsupported/Eigen/CXX11/src/Tensor/TensorGlobalFunctions.h
new file mode 100644
index 0000000..65052a2
--- /dev/null
+++ b/unsupported/Eigen/CXX11/src/Tensor/TensorGlobalFunctions.h
@@ -0,0 +1,35 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2016 Eugene Brevdo <ebrevdo@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_CXX11_TENSOR_TENSOR_GLOBAL_FUNCTIONS_H
+#define EIGEN_CXX11_TENSOR_TENSOR_GLOBAL_FUNCTIONS_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+/** \cpp11 \returns an expression of the coefficient-wise betainc(\a x, \a a, \a b) to the given tensors.
+ *
+ * This function computes the regularized incomplete beta function (integral).
+ *
+ */
+template <typename ADerived, typename BDerived, typename XDerived>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const
+ TensorCwiseTernaryOp<internal::scalar_betainc_op<typename XDerived::Scalar>,
+ const ADerived, const BDerived, const XDerived>
+ betainc(const ADerived& a, const BDerived& b, const XDerived& x) {
+ return TensorCwiseTernaryOp<
+ internal::scalar_betainc_op<typename XDerived::Scalar>, const ADerived,
+ const BDerived, const XDerived>(
+ a, b, x, internal::scalar_betainc_op<typename XDerived::Scalar>());
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_CXX11_TENSOR_TENSOR_GLOBAL_FUNCTIONS_H
diff --git a/unsupported/Eigen/CXX11/src/Tensor/TensorGpuHipCudaDefines.h b/unsupported/Eigen/CXX11/src/Tensor/TensorGpuHipCudaDefines.h
new file mode 100644
index 0000000..ae79a1d
--- /dev/null
+++ b/unsupported/Eigen/CXX11/src/Tensor/TensorGpuHipCudaDefines.h
@@ -0,0 +1,101 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>
+// Copyright (C) 2018 Deven Desai <deven.desai.amd@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#if defined(EIGEN_USE_GPU) && !defined(EIGEN_CXX11_TENSOR_GPU_HIP_CUDA_DEFINES_H)
+#define EIGEN_CXX11_TENSOR_GPU_HIP_CUDA_DEFINES_H
+
+// Note that we are using EIGEN_USE_HIP here instead of EIGEN_HIPCC...this is by design
+// There is code in the Tensorflow codebase that will define EIGEN_USE_GPU, but
+// for some reason gets sent to the gcc/host compiler instead of the gpu/nvcc/hipcc compiler
+// When compiling such files, gcc will end up trying to pick up the CUDA headers by
+// default (see the code within "unsupported/Eigen/CXX11/Tensor" that is guarded by EIGEN_USE_GPU)
+// This will obviously not work when trying to compile tensorflow on a system with no CUDA
+// To work around this issue for HIP systems (and leave the default behaviour intact), the
+// HIP tensorflow build defines EIGEN_USE_HIP when compiling all source files, and
+// "unsupported/Eigen/CXX11/Tensor" has been updated to use HIP header when EIGEN_USE_HIP is
+// defined. In continuation of that requirement, the guard here needs to be EIGEN_USE_HIP as well
+
+#if defined(EIGEN_USE_HIP)
+
+#define gpuStream_t hipStream_t
+#define gpuDeviceProp_t hipDeviceProp_t
+#define gpuError_t hipError_t
+#define gpuSuccess hipSuccess
+#define gpuErrorNotReady hipErrorNotReady
+#define gpuGetDeviceCount hipGetDeviceCount
+#define gpuGetLastError hipGetLastError
+#define gpuPeekAtLastError hipPeekAtLastError
+#define gpuGetErrorName hipGetErrorName
+#define gpuGetErrorString hipGetErrorString
+#define gpuGetDeviceProperties hipGetDeviceProperties
+#define gpuStreamDefault hipStreamDefault
+#define gpuGetDevice hipGetDevice
+#define gpuSetDevice hipSetDevice
+#define gpuMalloc hipMalloc
+#define gpuFree hipFree
+#define gpuMemsetAsync hipMemsetAsync
+#define gpuMemset2DAsync hipMemset2DAsync
+#define gpuMemcpyAsync hipMemcpyAsync
+#define gpuMemcpyDeviceToDevice hipMemcpyDeviceToDevice
+#define gpuMemcpyDeviceToHost hipMemcpyDeviceToHost
+#define gpuMemcpyHostToDevice hipMemcpyHostToDevice
+#define gpuStreamQuery hipStreamQuery
+#define gpuSharedMemConfig hipSharedMemConfig
+#define gpuDeviceSetSharedMemConfig hipDeviceSetSharedMemConfig
+#define gpuStreamSynchronize hipStreamSynchronize
+#define gpuDeviceSynchronize hipDeviceSynchronize
+#define gpuMemcpy hipMemcpy
+
+#else
+
+#define gpuStream_t cudaStream_t
+#define gpuDeviceProp_t cudaDeviceProp
+#define gpuError_t cudaError_t
+#define gpuSuccess cudaSuccess
+#define gpuErrorNotReady cudaErrorNotReady
+#define gpuGetDeviceCount cudaGetDeviceCount
+#define gpuGetLastError cudaGetLastError
+#define gpuPeekAtLastError cudaPeekAtLastError
+#define gpuGetErrorName cudaGetErrorName
+#define gpuGetErrorString cudaGetErrorString
+#define gpuGetDeviceProperties cudaGetDeviceProperties
+#define gpuStreamDefault cudaStreamDefault
+#define gpuGetDevice cudaGetDevice
+#define gpuSetDevice cudaSetDevice
+#define gpuMalloc cudaMalloc
+#define gpuFree cudaFree
+#define gpuMemsetAsync cudaMemsetAsync
+#define gpuMemset2DAsync cudaMemset2DAsync
+#define gpuMemcpyAsync cudaMemcpyAsync
+#define gpuMemcpyDeviceToDevice cudaMemcpyDeviceToDevice
+#define gpuMemcpyDeviceToHost cudaMemcpyDeviceToHost
+#define gpuMemcpyHostToDevice cudaMemcpyHostToDevice
+#define gpuStreamQuery cudaStreamQuery
+#define gpuSharedMemConfig cudaSharedMemConfig
+#define gpuDeviceSetSharedMemConfig cudaDeviceSetSharedMemConfig
+#define gpuStreamSynchronize cudaStreamSynchronize
+#define gpuDeviceSynchronize cudaDeviceSynchronize
+#define gpuMemcpy cudaMemcpy
+
+#endif
+
+// gpu_assert can be overridden
+#ifndef gpu_assert
+
+#if defined(EIGEN_HIP_DEVICE_COMPILE)
+// HIPCC do not support the use of assert on the GPU side.
+#define gpu_assert(COND)
+#else
+#define gpu_assert(COND) eigen_assert(COND)
+#endif
+
+#endif // gpu_assert
+
+#endif // EIGEN_CXX11_TENSOR_GPU_HIP_CUDA_DEFINES_H
diff --git a/unsupported/Eigen/CXX11/src/Tensor/TensorGpuHipCudaUndefines.h b/unsupported/Eigen/CXX11/src/Tensor/TensorGpuHipCudaUndefines.h
new file mode 100644
index 0000000..e4d4bd5
--- /dev/null
+++ b/unsupported/Eigen/CXX11/src/Tensor/TensorGpuHipCudaUndefines.h
@@ -0,0 +1,45 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>
+// Copyright (C) 2018 Deven Desai <deven.desai.amd@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#if defined(EIGEN_CXX11_TENSOR_GPU_HIP_CUDA_DEFINES_H)
+
+#ifndef EIGEN_PERMANENTLY_ENABLE_GPU_HIP_CUDA_DEFINES
+
+#undef gpuStream_t
+#undef gpuDeviceProp_t
+#undef gpuError_t
+#undef gpuSuccess
+#undef gpuErrorNotReady
+#undef gpuGetDeviceCount
+#undef gpuGetErrorString
+#undef gpuGetDeviceProperties
+#undef gpuStreamDefault
+#undef gpuGetDevice
+#undef gpuSetDevice
+#undef gpuMalloc
+#undef gpuFree
+#undef gpuMemsetAsync
+#undef gpuMemset2DAsync
+#undef gpuMemcpyAsync
+#undef gpuMemcpyDeviceToDevice
+#undef gpuMemcpyDeviceToHost
+#undef gpuMemcpyHostToDevice
+#undef gpuStreamQuery
+#undef gpuSharedMemConfig
+#undef gpuDeviceSetSharedMemConfig
+#undef gpuStreamSynchronize
+#undef gpuDeviceSynchronize
+#undef gpuMemcpy
+
+#endif // EIGEN_PERMANENTLY_ENABLE_GPU_HIP_CUDA_DEFINES
+
+#undef EIGEN_CXX11_TENSOR_GPU_HIP_CUDA_DEFINES_H
+
+#endif // EIGEN_CXX11_TENSOR_GPU_HIP_CUDA_DEFINES_H
diff --git a/unsupported/Eigen/CXX11/src/Tensor/TensorIO.h b/unsupported/Eigen/CXX11/src/Tensor/TensorIO.h
new file mode 100644
index 0000000..efda741
--- /dev/null
+++ b/unsupported/Eigen/CXX11/src/Tensor/TensorIO.h
@@ -0,0 +1,374 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_CXX11_TENSOR_TENSOR_IO_H
+#define EIGEN_CXX11_TENSOR_TENSOR_IO_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+struct TensorIOFormat;
+
+namespace internal {
+template <typename Tensor, std::size_t rank>
+struct TensorPrinter;
+}
+
+struct TensorIOFormat {
+ TensorIOFormat(const std::vector<std::string>& _separator, const std::vector<std::string>& _prefix,
+ const std::vector<std::string>& _suffix, int _precision = StreamPrecision, int _flags = 0,
+ const std::string& _tenPrefix = "", const std::string& _tenSuffix = "", const char _fill = ' ')
+ : tenPrefix(_tenPrefix),
+ tenSuffix(_tenSuffix),
+ prefix(_prefix),
+ suffix(_suffix),
+ separator(_separator),
+ fill(_fill),
+ precision(_precision),
+ flags(_flags) {
+ init_spacer();
+ }
+
+ TensorIOFormat(int _precision = StreamPrecision, int _flags = 0, const std::string& _tenPrefix = "",
+ const std::string& _tenSuffix = "", const char _fill = ' ')
+ : tenPrefix(_tenPrefix), tenSuffix(_tenSuffix), fill(_fill), precision(_precision), flags(_flags) {
+ // default values of prefix, suffix and separator
+ prefix = {"", "["};
+ suffix = {"", "]"};
+ separator = {", ", "\n"};
+
+ init_spacer();
+ }
+
+ void init_spacer() {
+ if ((flags & DontAlignCols)) return;
+ spacer.resize(prefix.size());
+ spacer[0] = "";
+ int i = int(tenPrefix.length()) - 1;
+ while (i >= 0 && tenPrefix[i] != '\n') {
+ spacer[0] += ' ';
+ i--;
+ }
+
+ for (std::size_t k = 1; k < prefix.size(); k++) {
+ int j = int(prefix[k].length()) - 1;
+ while (j >= 0 && prefix[k][j] != '\n') {
+ spacer[k] += ' ';
+ j--;
+ }
+ }
+ }
+
+ static inline const TensorIOFormat Numpy() {
+ std::vector<std::string> prefix = {"", "["};
+ std::vector<std::string> suffix = {"", "]"};
+ std::vector<std::string> separator = {" ", "\n"};
+ return TensorIOFormat(separator, prefix, suffix, StreamPrecision, 0, "[", "]");
+ }
+
+ static inline const TensorIOFormat Plain() {
+ std::vector<std::string> separator = {" ", "\n", "\n", ""};
+ std::vector<std::string> prefix = {""};
+ std::vector<std::string> suffix = {""};
+ return TensorIOFormat(separator, prefix, suffix, StreamPrecision, 0, "", "", ' ');
+ }
+
+ static inline const TensorIOFormat Native() {
+ std::vector<std::string> separator = {", ", ",\n", "\n"};
+ std::vector<std::string> prefix = {"", "{"};
+ std::vector<std::string> suffix = {"", "}"};
+ return TensorIOFormat(separator, prefix, suffix, StreamPrecision, 0, "{", "}", ' ');
+ }
+
+ static inline const TensorIOFormat Legacy() {
+ TensorIOFormat LegacyFormat(StreamPrecision, 0, "", "", ' ');
+ LegacyFormat.legacy_bit = true;
+ return LegacyFormat;
+ }
+
+ std::string tenPrefix;
+ std::string tenSuffix;
+ std::vector<std::string> prefix;
+ std::vector<std::string> suffix;
+ std::vector<std::string> separator;
+ char fill;
+ int precision;
+ int flags;
+ std::vector<std::string> spacer{};
+ bool legacy_bit = false;
+};
+
+template <typename T, int Layout, int rank>
+class TensorWithFormat;
+// specialize for Layout=ColMajor, Layout=RowMajor and rank=0.
+template <typename T, int rank>
+class TensorWithFormat<T, RowMajor, rank> {
+ public:
+ TensorWithFormat(const T& tensor, const TensorIOFormat& format) : t_tensor(tensor), t_format(format) {}
+
+ friend std::ostream& operator<<(std::ostream& os, const TensorWithFormat<T, RowMajor, rank>& wf) {
+ // Evaluate the expression if needed
+ typedef TensorEvaluator<const TensorForcedEvalOp<const T>, DefaultDevice> Evaluator;
+ TensorForcedEvalOp<const T> eval = wf.t_tensor.eval();
+ Evaluator tensor(eval, DefaultDevice());
+ tensor.evalSubExprsIfNeeded(NULL);
+ internal::TensorPrinter<Evaluator, rank>::run(os, tensor, wf.t_format);
+ // Cleanup.
+ tensor.cleanup();
+ return os;
+ }
+
+ protected:
+ T t_tensor;
+ TensorIOFormat t_format;
+};
+
+template <typename T, int rank>
+class TensorWithFormat<T, ColMajor, rank> {
+ public:
+ TensorWithFormat(const T& tensor, const TensorIOFormat& format) : t_tensor(tensor), t_format(format) {}
+
+ friend std::ostream& operator<<(std::ostream& os, const TensorWithFormat<T, ColMajor, rank>& wf) {
+ // Switch to RowMajor storage and print afterwards
+ typedef typename T::Index IndexType;
+ std::array<IndexType, rank> shuffle;
+ std::array<IndexType, rank> id;
+ std::iota(id.begin(), id.end(), IndexType(0));
+ std::copy(id.begin(), id.end(), shuffle.rbegin());
+ auto tensor_row_major = wf.t_tensor.swap_layout().shuffle(shuffle);
+
+ // Evaluate the expression if needed
+ typedef TensorEvaluator<const TensorForcedEvalOp<const decltype(tensor_row_major)>, DefaultDevice> Evaluator;
+ TensorForcedEvalOp<const decltype(tensor_row_major)> eval = tensor_row_major.eval();
+ Evaluator tensor(eval, DefaultDevice());
+ tensor.evalSubExprsIfNeeded(NULL);
+ internal::TensorPrinter<Evaluator, rank>::run(os, tensor, wf.t_format);
+ // Cleanup.
+ tensor.cleanup();
+ return os;
+ }
+
+ protected:
+ T t_tensor;
+ TensorIOFormat t_format;
+};
+
+template <typename T>
+class TensorWithFormat<T, ColMajor, 0> {
+ public:
+ TensorWithFormat(const T& tensor, const TensorIOFormat& format) : t_tensor(tensor), t_format(format) {}
+
+ friend std::ostream& operator<<(std::ostream& os, const TensorWithFormat<T, ColMajor, 0>& wf) {
+ // Evaluate the expression if needed
+ typedef TensorEvaluator<const TensorForcedEvalOp<const T>, DefaultDevice> Evaluator;
+ TensorForcedEvalOp<const T> eval = wf.t_tensor.eval();
+ Evaluator tensor(eval, DefaultDevice());
+ tensor.evalSubExprsIfNeeded(NULL);
+ internal::TensorPrinter<Evaluator, 0>::run(os, tensor, wf.t_format);
+ // Cleanup.
+ tensor.cleanup();
+ return os;
+ }
+
+ protected:
+ T t_tensor;
+ TensorIOFormat t_format;
+};
+
+namespace internal {
+template <typename Tensor, std::size_t rank>
+struct TensorPrinter {
+ static void run(std::ostream& s, const Tensor& _t, const TensorIOFormat& fmt) {
+ typedef std::remove_const_t<typename Tensor::Scalar> Scalar;
+ typedef typename Tensor::Index IndexType;
+ static const int layout = Tensor::Layout;
+ // backwards compatibility case: print tensor after reshaping to matrix of size dim(0) x
+ // (dim(1)*dim(2)*...*dim(rank-1)).
+ if (fmt.legacy_bit) {
+ const IndexType total_size = internal::array_prod(_t.dimensions());
+ if (total_size > 0) {
+ const IndexType first_dim = Eigen::internal::array_get<0>(_t.dimensions());
+ Map<const Array<Scalar, Dynamic, Dynamic, layout> > matrix(_t.data(), first_dim,
+ total_size / first_dim);
+ s << matrix;
+ return;
+ }
+ }
+
+ eigen_assert(layout == RowMajor);
+ typedef std::conditional_t<is_same<Scalar, char>::value || is_same<Scalar, unsigned char>::value ||
+ is_same<Scalar, numext::int8_t>::value || is_same<Scalar, numext::uint8_t>::value,
+ int,
+ std::conditional_t<is_same<Scalar, std::complex<char> >::value ||
+ is_same<Scalar, std::complex<unsigned char> >::value ||
+ is_same<Scalar, std::complex<numext::int8_t> >::value ||
+ is_same<Scalar, std::complex<numext::uint8_t> >::value,
+ std::complex<int>, const Scalar&>> PrintType;
+
+ const IndexType total_size = array_prod(_t.dimensions());
+
+ std::streamsize explicit_precision;
+ if (fmt.precision == StreamPrecision) {
+ explicit_precision = 0;
+ } else if (fmt.precision == FullPrecision) {
+ if (NumTraits<Scalar>::IsInteger) {
+ explicit_precision = 0;
+ } else {
+ explicit_precision = significant_decimals_impl<Scalar>::run();
+ }
+ } else {
+ explicit_precision = fmt.precision;
+ }
+
+ std::streamsize old_precision = 0;
+ if (explicit_precision) old_precision = s.precision(explicit_precision);
+
+ IndexType width = 0;
+
+ bool align_cols = !(fmt.flags & DontAlignCols);
+ if (align_cols) {
+ // compute the largest width
+ for (IndexType i = 0; i < total_size; i++) {
+ std::stringstream sstr;
+ sstr.copyfmt(s);
+ sstr << static_cast<PrintType>(_t.data()[i]);
+ width = std::max<IndexType>(width, IndexType(sstr.str().length()));
+ }
+ }
+ std::streamsize old_width = s.width();
+ char old_fill_character = s.fill();
+
+ s << fmt.tenPrefix;
+ for (IndexType i = 0; i < total_size; i++) {
+ std::array<bool, rank> is_at_end{};
+ std::array<bool, rank> is_at_begin{};
+
+ // is the ith element the end of an coeff (always true), of a row, of a matrix, ...?
+ for (std::size_t k = 0; k < rank; k++) {
+ if ((i + 1) % (std::accumulate(_t.dimensions().rbegin(), _t.dimensions().rbegin() + k, 1,
+ std::multiplies<IndexType>())) ==
+ 0) {
+ is_at_end[k] = true;
+ }
+ }
+
+ // is the ith element the begin of an coeff (always true), of a row, of a matrix, ...?
+ for (std::size_t k = 0; k < rank; k++) {
+ if (i % (std::accumulate(_t.dimensions().rbegin(), _t.dimensions().rbegin() + k, 1,
+ std::multiplies<IndexType>())) ==
+ 0) {
+ is_at_begin[k] = true;
+ }
+ }
+
+ // do we have a line break?
+ bool is_at_begin_after_newline = false;
+ for (std::size_t k = 0; k < rank; k++) {
+ if (is_at_begin[k]) {
+ std::size_t separator_index = (k < fmt.separator.size()) ? k : fmt.separator.size() - 1;
+ if (fmt.separator[separator_index].find('\n') != std::string::npos) {
+ is_at_begin_after_newline = true;
+ }
+ }
+ }
+
+ bool is_at_end_before_newline = false;
+ for (std::size_t k = 0; k < rank; k++) {
+ if (is_at_end[k]) {
+ std::size_t separator_index = (k < fmt.separator.size()) ? k : fmt.separator.size() - 1;
+ if (fmt.separator[separator_index].find('\n') != std::string::npos) {
+ is_at_end_before_newline = true;
+ }
+ }
+ }
+
+ std::stringstream suffix, prefix, separator;
+ for (std::size_t k = 0; k < rank; k++) {
+ std::size_t suffix_index = (k < fmt.suffix.size()) ? k : fmt.suffix.size() - 1;
+ if (is_at_end[k]) {
+ suffix << fmt.suffix[suffix_index];
+ }
+ }
+ for (std::size_t k = 0; k < rank; k++) {
+ std::size_t separator_index = (k < fmt.separator.size()) ? k : fmt.separator.size() - 1;
+ if (is_at_end[k] &&
+ (!is_at_end_before_newline || fmt.separator[separator_index].find('\n') != std::string::npos)) {
+ separator << fmt.separator[separator_index];
+ }
+ }
+ for (std::size_t k = 0; k < rank; k++) {
+ std::size_t spacer_index = (k < fmt.spacer.size()) ? k : fmt.spacer.size() - 1;
+ if (i != 0 && is_at_begin_after_newline && (!is_at_begin[k] || k == 0)) {
+ prefix << fmt.spacer[spacer_index];
+ }
+ }
+ for (int k = rank - 1; k >= 0; k--) {
+ std::size_t prefix_index = (static_cast<std::size_t>(k) < fmt.prefix.size()) ? k : fmt.prefix.size() - 1;
+ if (is_at_begin[k]) {
+ prefix << fmt.prefix[prefix_index];
+ }
+ }
+
+ s << prefix.str();
+ if (width) {
+ s.fill(fmt.fill);
+ s.width(width);
+ s << std::right;
+ }
+ s << _t.data()[i];
+ s << suffix.str();
+ if (i < total_size - 1) {
+ s << separator.str();
+ }
+ }
+ s << fmt.tenSuffix;
+ if (explicit_precision) s.precision(old_precision);
+ if (width) {
+ s.fill(old_fill_character);
+ s.width(old_width);
+ }
+ }
+};
+
+template <typename Tensor>
+struct TensorPrinter<Tensor, 0> {
+ static void run(std::ostream& s, const Tensor& _t, const TensorIOFormat& fmt) {
+ typedef typename Tensor::Scalar Scalar;
+
+ std::streamsize explicit_precision;
+ if (fmt.precision == StreamPrecision) {
+ explicit_precision = 0;
+ } else if (fmt.precision == FullPrecision) {
+ if (NumTraits<Scalar>::IsInteger) {
+ explicit_precision = 0;
+ } else {
+ explicit_precision = significant_decimals_impl<Scalar>::run();
+ }
+ } else {
+ explicit_precision = fmt.precision;
+ }
+
+ std::streamsize old_precision = 0;
+ if (explicit_precision) old_precision = s.precision(explicit_precision);
+
+ s << fmt.tenPrefix << _t.coeff(0) << fmt.tenSuffix;
+ if (explicit_precision) s.precision(old_precision);
+ }
+};
+
+} // end namespace internal
+template <typename T>
+std::ostream& operator<<(std::ostream& s, const TensorBase<T, ReadOnlyAccessors>& t) {
+ s << t.format(TensorIOFormat::Plain());
+ return s;
+}
+} // end namespace Eigen
+
+#endif // EIGEN_CXX11_TENSOR_TENSOR_IO_H
diff --git a/unsupported/Eigen/CXX11/src/Tensor/TensorImagePatch.h b/unsupported/Eigen/CXX11/src/Tensor/TensorImagePatch.h
new file mode 100644
index 0000000..a9b281f
--- /dev/null
+++ b/unsupported/Eigen/CXX11/src/Tensor/TensorImagePatch.h
@@ -0,0 +1,604 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_CXX11_TENSOR_TENSOR_IMAGE_PATCH_H
+#define EIGEN_CXX11_TENSOR_TENSOR_IMAGE_PATCH_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+/** \class TensorImagePatch
+ * \ingroup CXX11_Tensor_Module
+ *
+ * \brief Patch extraction specialized for image processing.
+ * This assumes that the input has a least 3 dimensions ordered as follow:
+ * 1st dimension: channels (of size d)
+ * 2nd dimension: rows (of size r)
+ * 3rd dimension: columns (of size c)
+ * There can be additional dimensions such as time (for video) or batch (for
+ * bulk processing after the first 3.
+ * Calling the image patch code with patch_rows and patch_cols is equivalent
+ * to calling the regular patch extraction code with parameters d, patch_rows,
+ * patch_cols, and 1 for all the additional dimensions.
+ */
+namespace internal {
+
+template<DenseIndex Rows, DenseIndex Cols, typename XprType>
+struct traits<TensorImagePatchOp<Rows, Cols, XprType> > : public traits<XprType>
+{
+ typedef std::remove_const_t<typename XprType::Scalar> Scalar;
+ typedef traits<XprType> XprTraits;
+ typedef typename XprTraits::StorageKind StorageKind;
+ typedef typename XprTraits::Index Index;
+ typedef typename XprType::Nested Nested;
+ typedef std::remove_reference_t<Nested> Nested_;
+ static constexpr int NumDimensions = XprTraits::NumDimensions + 1;
+ static constexpr int Layout = XprTraits::Layout;
+ typedef typename XprTraits::PointerType PointerType;
+};
+
+template<DenseIndex Rows, DenseIndex Cols, typename XprType>
+struct eval<TensorImagePatchOp<Rows, Cols, XprType>, Eigen::Dense>
+{
+ typedef const TensorImagePatchOp<Rows, Cols, XprType>& type;
+};
+
+template<DenseIndex Rows, DenseIndex Cols, typename XprType>
+struct nested<TensorImagePatchOp<Rows, Cols, XprType>, 1, typename eval<TensorImagePatchOp<Rows, Cols, XprType> >::type>
+{
+ typedef TensorImagePatchOp<Rows, Cols, XprType> type;
+};
+
+template <typename Self, bool Vectorizable>
+struct ImagePatchCopyOp {
+ typedef typename Self::Index Index;
+ typedef typename Self::Scalar Scalar;
+ typedef typename Self::Impl Impl;
+ static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void Run(
+ const Self& self, const Index num_coeff_to_copy, const Index dst_index,
+ Scalar* dst_data, const Index src_index) {
+ const Impl& impl = self.impl();
+ for (Index i = 0; i < num_coeff_to_copy; ++i) {
+ dst_data[dst_index + i] = impl.coeff(src_index + i);
+ }
+ }
+};
+
+template <typename Self>
+struct ImagePatchCopyOp<Self, true> {
+ typedef typename Self::Index Index;
+ typedef typename Self::Scalar Scalar;
+ typedef typename Self::Impl Impl;
+ typedef typename packet_traits<Scalar>::type Packet;
+ static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void Run(
+ const Self& self, const Index num_coeff_to_copy, const Index dst_index,
+ Scalar* dst_data, const Index src_index) {
+ const Impl& impl = self.impl();
+ const Index packet_size = internal::unpacket_traits<Packet>::size;
+ const Index vectorized_size =
+ (num_coeff_to_copy / packet_size) * packet_size;
+ for (Index i = 0; i < vectorized_size; i += packet_size) {
+ Packet p = impl.template packet<Unaligned>(src_index + i);
+ internal::pstoret<Scalar, Packet, Unaligned>(dst_data + dst_index + i, p);
+ }
+ for (Index i = vectorized_size; i < num_coeff_to_copy; ++i) {
+ dst_data[dst_index + i] = impl.coeff(src_index + i);
+ }
+ }
+};
+
+template <typename Self>
+struct ImagePatchPaddingOp {
+ typedef typename Self::Index Index;
+ typedef typename Self::Scalar Scalar;
+ typedef typename packet_traits<Scalar>::type Packet;
+ static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void Run(
+ const Index num_coeff_to_pad, const Scalar padding_value,
+ const Index dst_index, Scalar* dst_data) {
+ const Index packet_size = internal::unpacket_traits<Packet>::size;
+ const Packet padded_packet = internal::pset1<Packet>(padding_value);
+ const Index vectorized_size =
+ (num_coeff_to_pad / packet_size) * packet_size;
+ for (Index i = 0; i < vectorized_size; i += packet_size) {
+ internal::pstoret<Scalar, Packet, Unaligned>(dst_data + dst_index + i,
+ padded_packet);
+ }
+ for (Index i = vectorized_size; i < num_coeff_to_pad; ++i) {
+ dst_data[dst_index + i] = padding_value;
+ }
+ }
+};
+
+} // end namespace internal
+
+template<DenseIndex Rows, DenseIndex Cols, typename XprType>
+class TensorImagePatchOp : public TensorBase<TensorImagePatchOp<Rows, Cols, XprType>, ReadOnlyAccessors>
+{
+ public:
+ typedef typename Eigen::internal::traits<TensorImagePatchOp>::Scalar Scalar;
+ typedef typename Eigen::NumTraits<Scalar>::Real RealScalar;
+ typedef typename XprType::CoeffReturnType CoeffReturnType;
+ typedef typename Eigen::internal::nested<TensorImagePatchOp>::type Nested;
+ typedef typename Eigen::internal::traits<TensorImagePatchOp>::StorageKind StorageKind;
+ typedef typename Eigen::internal::traits<TensorImagePatchOp>::Index Index;
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorImagePatchOp(const XprType& expr, DenseIndex patch_rows, DenseIndex patch_cols,
+ DenseIndex row_strides, DenseIndex col_strides,
+ DenseIndex in_row_strides, DenseIndex in_col_strides,
+ DenseIndex row_inflate_strides, DenseIndex col_inflate_strides,
+ PaddingType padding_type, Scalar padding_value)
+ : m_xpr(expr), m_patch_rows(patch_rows), m_patch_cols(patch_cols),
+ m_row_strides(row_strides), m_col_strides(col_strides),
+ m_in_row_strides(in_row_strides), m_in_col_strides(in_col_strides),
+ m_row_inflate_strides(row_inflate_strides), m_col_inflate_strides(col_inflate_strides),
+ m_padding_explicit(false), m_padding_top(0), m_padding_bottom(0), m_padding_left(0), m_padding_right(0),
+ m_padding_type(padding_type), m_padding_value(padding_value) {}
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorImagePatchOp(const XprType& expr, DenseIndex patch_rows, DenseIndex patch_cols,
+ DenseIndex row_strides, DenseIndex col_strides,
+ DenseIndex in_row_strides, DenseIndex in_col_strides,
+ DenseIndex row_inflate_strides, DenseIndex col_inflate_strides,
+ DenseIndex padding_top, DenseIndex padding_bottom,
+ DenseIndex padding_left, DenseIndex padding_right,
+ Scalar padding_value)
+ : m_xpr(expr), m_patch_rows(patch_rows), m_patch_cols(patch_cols),
+ m_row_strides(row_strides), m_col_strides(col_strides),
+ m_in_row_strides(in_row_strides), m_in_col_strides(in_col_strides),
+ m_row_inflate_strides(row_inflate_strides), m_col_inflate_strides(col_inflate_strides),
+ m_padding_explicit(true), m_padding_top(padding_top), m_padding_bottom(padding_bottom),
+ m_padding_left(padding_left), m_padding_right(padding_right),
+ m_padding_type(PADDING_VALID), m_padding_value(padding_value) {}
+
+
+ EIGEN_DEVICE_FUNC
+ DenseIndex patch_rows() const { return m_patch_rows; }
+ EIGEN_DEVICE_FUNC
+ DenseIndex patch_cols() const { return m_patch_cols; }
+ EIGEN_DEVICE_FUNC
+ DenseIndex row_strides() const { return m_row_strides; }
+ EIGEN_DEVICE_FUNC
+ DenseIndex col_strides() const { return m_col_strides; }
+ EIGEN_DEVICE_FUNC
+ DenseIndex in_row_strides() const { return m_in_row_strides; }
+ EIGEN_DEVICE_FUNC
+ DenseIndex in_col_strides() const { return m_in_col_strides; }
+ EIGEN_DEVICE_FUNC
+ DenseIndex row_inflate_strides() const { return m_row_inflate_strides; }
+ EIGEN_DEVICE_FUNC
+ DenseIndex col_inflate_strides() const { return m_col_inflate_strides; }
+ EIGEN_DEVICE_FUNC
+ bool padding_explicit() const { return m_padding_explicit; }
+ EIGEN_DEVICE_FUNC
+ DenseIndex padding_top() const { return m_padding_top; }
+ EIGEN_DEVICE_FUNC
+ DenseIndex padding_bottom() const { return m_padding_bottom; }
+ EIGEN_DEVICE_FUNC
+ DenseIndex padding_left() const { return m_padding_left; }
+ EIGEN_DEVICE_FUNC
+ DenseIndex padding_right() const { return m_padding_right; }
+ EIGEN_DEVICE_FUNC
+ PaddingType padding_type() const { return m_padding_type; }
+ EIGEN_DEVICE_FUNC
+ Scalar padding_value() const { return m_padding_value; }
+
+ EIGEN_DEVICE_FUNC
+ const internal::remove_all_t<typename XprType::Nested>&
+ expression() const { return m_xpr; }
+
+ protected:
+ typename XprType::Nested m_xpr;
+ const DenseIndex m_patch_rows;
+ const DenseIndex m_patch_cols;
+ const DenseIndex m_row_strides;
+ const DenseIndex m_col_strides;
+ const DenseIndex m_in_row_strides;
+ const DenseIndex m_in_col_strides;
+ const DenseIndex m_row_inflate_strides;
+ const DenseIndex m_col_inflate_strides;
+ const bool m_padding_explicit;
+ const DenseIndex m_padding_top;
+ const DenseIndex m_padding_bottom;
+ const DenseIndex m_padding_left;
+ const DenseIndex m_padding_right;
+ const PaddingType m_padding_type;
+ const Scalar m_padding_value;
+};
+
+// Eval as rvalue
+template<DenseIndex Rows, DenseIndex Cols, typename ArgType, typename Device>
+struct TensorEvaluator<const TensorImagePatchOp<Rows, Cols, ArgType>, Device>
+{
+ typedef TensorImagePatchOp<Rows, Cols, ArgType> XprType;
+ typedef typename XprType::Index Index;
+ static constexpr int NumInputDims = internal::array_size<typename TensorEvaluator<ArgType, Device>::Dimensions>::value;
+ static constexpr int NumDims = NumInputDims + 1;
+ typedef DSizes<Index, NumDims> Dimensions;
+ typedef std::remove_const_t<typename XprType::Scalar> Scalar;
+ typedef TensorEvaluator<const TensorImagePatchOp<Rows, Cols, ArgType>,
+ Device> Self;
+ typedef TensorEvaluator<ArgType, Device> Impl;
+ typedef typename XprType::CoeffReturnType CoeffReturnType;
+ typedef typename PacketType<CoeffReturnType, Device>::type PacketReturnType;
+ static constexpr int PacketSize = PacketType<CoeffReturnType, Device>::size;
+ typedef StorageMemory<CoeffReturnType, Device> Storage;
+ typedef typename Storage::Type EvaluatorPointerType;
+
+ static constexpr int Layout = TensorEvaluator<ArgType, Device>::Layout;
+ enum {
+ IsAligned = false,
+ PacketAccess = TensorEvaluator<ArgType, Device>::PacketAccess,
+ BlockAccess = false,
+ PreferBlockAccess = true,
+ CoordAccess = false,
+ RawAccess = false
+ };
+
+ //===- Tensor block evaluation strategy (see TensorBlock.h) -------------===//
+ typedef internal::TensorBlockNotImplemented TensorBlock;
+ //===--------------------------------------------------------------------===//
+
+ EIGEN_STRONG_INLINE TensorEvaluator( const XprType& op, const Device& device)
+ : m_device(device), m_impl(op.expression(), device)
+ {
+ EIGEN_STATIC_ASSERT((NumDims >= 4), YOU_MADE_A_PROGRAMMING_MISTAKE);
+
+ m_paddingValue = op.padding_value();
+
+ const typename TensorEvaluator<ArgType, Device>::Dimensions& input_dims = m_impl.dimensions();
+
+ // Caches a few variables.
+ if (static_cast<int>(Layout) == static_cast<int>(ColMajor)) {
+ m_inputDepth = input_dims[0];
+ m_inputRows = input_dims[1];
+ m_inputCols = input_dims[2];
+ } else {
+ m_inputDepth = input_dims[NumInputDims-1];
+ m_inputRows = input_dims[NumInputDims-2];
+ m_inputCols = input_dims[NumInputDims-3];
+ }
+
+ m_row_strides = op.row_strides();
+ m_col_strides = op.col_strides();
+
+ // Input strides and effective input/patch size
+ m_in_row_strides = op.in_row_strides();
+ m_in_col_strides = op.in_col_strides();
+ m_row_inflate_strides = op.row_inflate_strides();
+ m_col_inflate_strides = op.col_inflate_strides();
+ // The "effective" input rows and input cols are the input rows and cols
+ // after inflating them with zeros.
+ // For examples, a 2x3 matrix with row_inflate_strides and
+ // col_inflate_strides of 2 comes from:
+ // A B C
+ // D E F
+ //
+ // to a matrix is 3 x 5:
+ //
+ // A . B . C
+ // . . . . .
+ // D . E . F
+
+ m_input_rows_eff = (m_inputRows - 1) * m_row_inflate_strides + 1;
+ m_input_cols_eff = (m_inputCols - 1) * m_col_inflate_strides + 1;
+ m_patch_rows_eff = op.patch_rows() + (op.patch_rows() - 1) * (m_in_row_strides - 1);
+ m_patch_cols_eff = op.patch_cols() + (op.patch_cols() - 1) * (m_in_col_strides - 1);
+
+ if (op.padding_explicit()) {
+ m_outputRows = numext::ceil((m_input_rows_eff + op.padding_top() + op.padding_bottom() - m_patch_rows_eff + 1.f) / static_cast<float>(m_row_strides));
+ m_outputCols = numext::ceil((m_input_cols_eff + op.padding_left() + op.padding_right() - m_patch_cols_eff + 1.f) / static_cast<float>(m_col_strides));
+ m_rowPaddingTop = op.padding_top();
+ m_colPaddingLeft = op.padding_left();
+ } else {
+ // Computing padding from the type
+ switch (op.padding_type()) {
+ case PADDING_VALID:
+ m_outputRows = numext::ceil((m_input_rows_eff - m_patch_rows_eff + 1.f) / static_cast<float>(m_row_strides));
+ m_outputCols = numext::ceil((m_input_cols_eff - m_patch_cols_eff + 1.f) / static_cast<float>(m_col_strides));
+ // Calculate the padding
+ m_rowPaddingTop = numext::maxi<Index>(0, ((m_outputRows - 1) * m_row_strides + m_patch_rows_eff - m_input_rows_eff) / 2);
+ m_colPaddingLeft = numext::maxi<Index>(0, ((m_outputCols - 1) * m_col_strides + m_patch_cols_eff - m_input_cols_eff) / 2);
+ break;
+ case PADDING_SAME:
+ m_outputRows = numext::ceil(m_input_rows_eff / static_cast<float>(m_row_strides));
+ m_outputCols = numext::ceil(m_input_cols_eff / static_cast<float>(m_col_strides));
+ // Calculate the padding
+ m_rowPaddingTop = ((m_outputRows - 1) * m_row_strides + m_patch_rows_eff - m_input_rows_eff) / 2;
+ m_colPaddingLeft = ((m_outputCols - 1) * m_col_strides + m_patch_cols_eff - m_input_cols_eff) / 2;
+ // The padding size calculation for PADDING_SAME has been updated to
+ // be consistent with how TensorFlow extracts its paddings.
+ m_rowPaddingTop = numext::maxi<Index>(0, m_rowPaddingTop);
+ m_colPaddingLeft = numext::maxi<Index>(0, m_colPaddingLeft);
+ break;
+ default:
+ eigen_assert(false && "unexpected padding");
+ m_outputCols=0; // silence the uninitialised warning;
+ m_outputRows=0; //// silence the uninitialised warning;
+ }
+ }
+ eigen_assert(m_outputRows > 0);
+ eigen_assert(m_outputCols > 0);
+
+ // Dimensions for result of extraction.
+ if (static_cast<int>(Layout) == static_cast<int>(ColMajor)) {
+ // ColMajor
+ // 0: depth
+ // 1: patch_rows
+ // 2: patch_cols
+ // 3: number of patches
+ // 4 and beyond: anything else (such as batch).
+ m_dimensions[0] = input_dims[0];
+ m_dimensions[1] = op.patch_rows();
+ m_dimensions[2] = op.patch_cols();
+ m_dimensions[3] = m_outputRows * m_outputCols;
+ for (int i = 4; i < NumDims; ++i) {
+ m_dimensions[i] = input_dims[i-1];
+ }
+ } else {
+ // RowMajor
+ // NumDims-1: depth
+ // NumDims-2: patch_rows
+ // NumDims-3: patch_cols
+ // NumDims-4: number of patches
+ // NumDims-5 and beyond: anything else (such as batch).
+ m_dimensions[NumDims-1] = input_dims[NumInputDims-1];
+ m_dimensions[NumDims-2] = op.patch_rows();
+ m_dimensions[NumDims-3] = op.patch_cols();
+ m_dimensions[NumDims-4] = m_outputRows * m_outputCols;
+ for (int i = NumDims-5; i >= 0; --i) {
+ m_dimensions[i] = input_dims[i];
+ }
+ }
+
+ // Strides for moving the patch in various dimensions.
+ if (static_cast<int>(Layout) == static_cast<int>(ColMajor)) {
+ m_colStride = m_dimensions[1];
+ m_patchStride = m_colStride * m_dimensions[2] * m_dimensions[0];
+ m_otherStride = m_patchStride * m_dimensions[3];
+ } else {
+ m_colStride = m_dimensions[NumDims-2];
+ m_patchStride = m_colStride * m_dimensions[NumDims-3] * m_dimensions[NumDims-1];
+ m_otherStride = m_patchStride * m_dimensions[NumDims-4];
+ }
+
+ // Strides for navigating through the input tensor.
+ m_rowInputStride = m_inputDepth;
+ m_colInputStride = m_inputDepth * m_inputRows;
+ m_patchInputStride = m_inputDepth * m_inputRows * m_inputCols;
+
+ // Fast representations of different variables.
+ m_fastOtherStride = internal::TensorIntDivisor<Index>(m_otherStride);
+ m_fastPatchStride = internal::TensorIntDivisor<Index>(m_patchStride);
+ m_fastColStride = internal::TensorIntDivisor<Index>(m_colStride);
+ m_fastInflateRowStride = internal::TensorIntDivisor<Index>(m_row_inflate_strides);
+ m_fastInflateColStride = internal::TensorIntDivisor<Index>(m_col_inflate_strides);
+ m_fastInputColsEff = internal::TensorIntDivisor<Index>(m_input_cols_eff);
+
+ // Number of patches in the width dimension.
+ m_fastOutputRows = internal::TensorIntDivisor<Index>(m_outputRows);
+ if (static_cast<int>(Layout) == static_cast<int>(ColMajor)) {
+ m_fastOutputDepth = internal::TensorIntDivisor<Index>(m_dimensions[0]);
+ } else {
+ m_fastOutputDepth = internal::TensorIntDivisor<Index>(m_dimensions[NumDims-1]);
+ }
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Dimensions& dimensions() const { return m_dimensions; }
+
+ EIGEN_STRONG_INLINE bool evalSubExprsIfNeeded(EvaluatorPointerType /*data*/) {
+ m_impl.evalSubExprsIfNeeded(NULL);
+ return true;
+ }
+
+#ifdef EIGEN_USE_THREADS
+ template <typename EvalSubExprsCallback>
+ EIGEN_STRONG_INLINE void evalSubExprsIfNeededAsync(
+ EvaluatorPointerType, EvalSubExprsCallback done) {
+ m_impl.evalSubExprsIfNeededAsync(nullptr, [done](bool) { done(true); });
+ }
+#endif // EIGEN_USE_THREADS
+
+ EIGEN_STRONG_INLINE void cleanup() {
+ m_impl.cleanup();
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE CoeffReturnType coeff(Index index) const
+ {
+ // Patch index corresponding to the passed in index.
+ const Index patchIndex = index / m_fastPatchStride;
+ // Find the offset of the element wrt the location of the first element.
+ const Index patchOffset = (index - patchIndex * m_patchStride) / m_fastOutputDepth;
+
+ // Other ways to index this element.
+ const Index otherIndex = (NumDims == 4) ? 0 : index / m_fastOtherStride;
+ const Index patch2DIndex = (NumDims == 4) ? patchIndex : (index - otherIndex * m_otherStride) / m_fastPatchStride;
+
+ // Calculate col index in the input original tensor.
+ const Index colIndex = patch2DIndex / m_fastOutputRows;
+ const Index colOffset = patchOffset / m_fastColStride;
+ const Index inputCol = colIndex * m_col_strides + colOffset * m_in_col_strides - m_colPaddingLeft;
+ const Index origInputCol = (m_col_inflate_strides == 1) ? inputCol : ((inputCol >= 0) ? (inputCol / m_fastInflateColStride) : 0);
+ if (inputCol < 0 || inputCol >= m_input_cols_eff ||
+ ((m_col_inflate_strides != 1) && (inputCol != origInputCol * m_col_inflate_strides))) {
+ return Scalar(m_paddingValue);
+ }
+
+ // Calculate row index in the original input tensor.
+ const Index rowIndex = patch2DIndex - colIndex * m_outputRows;
+ const Index rowOffset = patchOffset - colOffset * m_colStride;
+ const Index inputRow = rowIndex * m_row_strides + rowOffset * m_in_row_strides - m_rowPaddingTop;
+ const Index origInputRow = (m_row_inflate_strides == 1) ? inputRow : ((inputRow >= 0) ? (inputRow / m_fastInflateRowStride) : 0);
+ if (inputRow < 0 || inputRow >= m_input_rows_eff ||
+ ((m_row_inflate_strides != 1) && (inputRow != origInputRow * m_row_inflate_strides))) {
+ return Scalar(m_paddingValue);
+ }
+
+ const int depth_index = static_cast<int>(Layout) == static_cast<int>(ColMajor) ? 0 : NumDims - 1;
+ const Index depth = index - (index / m_fastOutputDepth) * m_dimensions[depth_index];
+
+ const Index inputIndex = depth + origInputRow * m_rowInputStride + origInputCol * m_colInputStride + otherIndex * m_patchInputStride;
+ return m_impl.coeff(inputIndex);
+ }
+
+ template<int LoadMode>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE PacketReturnType packet(Index index) const
+ {
+ eigen_assert(index+PacketSize-1 < dimensions().TotalSize());
+
+ if (m_in_row_strides != 1 || m_in_col_strides != 1 || m_row_inflate_strides != 1 || m_col_inflate_strides != 1) {
+ return packetWithPossibleZero(index);
+ }
+
+ const Index indices[2] = {index, index + PacketSize - 1};
+ const Index patchIndex = indices[0] / m_fastPatchStride;
+ if (patchIndex != indices[1] / m_fastPatchStride) {
+ return packetWithPossibleZero(index);
+ }
+ const Index otherIndex = (NumDims == 4) ? 0 : indices[0] / m_fastOtherStride;
+ eigen_assert(otherIndex == indices[1] / m_fastOtherStride);
+
+ // Find the offset of the element wrt the location of the first element.
+ const Index patchOffsets[2] = {(indices[0] - patchIndex * m_patchStride) / m_fastOutputDepth,
+ (indices[1] - patchIndex * m_patchStride) / m_fastOutputDepth};
+
+ const Index patch2DIndex = (NumDims == 4) ? patchIndex : (indices[0] - otherIndex * m_otherStride) / m_fastPatchStride;
+ eigen_assert(patch2DIndex == (indices[1] - otherIndex * m_otherStride) / m_fastPatchStride);
+
+ const Index colIndex = patch2DIndex / m_fastOutputRows;
+ const Index colOffsets[2] = {patchOffsets[0] / m_fastColStride, patchOffsets[1] / m_fastColStride};
+
+ // Calculate col indices in the original input tensor.
+ const Index inputCols[2] = {colIndex * m_col_strides + colOffsets[0] -
+ m_colPaddingLeft, colIndex * m_col_strides + colOffsets[1] - m_colPaddingLeft};
+ if (inputCols[1] < 0 || inputCols[0] >= m_inputCols) {
+ return internal::pset1<PacketReturnType>(Scalar(m_paddingValue));
+ }
+
+ if (inputCols[0] == inputCols[1]) {
+ const Index rowIndex = patch2DIndex - colIndex * m_outputRows;
+ const Index rowOffsets[2] = {patchOffsets[0] - colOffsets[0]*m_colStride, patchOffsets[1] - colOffsets[1]*m_colStride};
+ eigen_assert(rowOffsets[0] <= rowOffsets[1]);
+ // Calculate col indices in the original input tensor.
+ const Index inputRows[2] = {rowIndex * m_row_strides + rowOffsets[0] -
+ m_rowPaddingTop, rowIndex * m_row_strides + rowOffsets[1] - m_rowPaddingTop};
+
+ if (inputRows[1] < 0 || inputRows[0] >= m_inputRows) {
+ return internal::pset1<PacketReturnType>(Scalar(m_paddingValue));
+ }
+
+ if (inputRows[0] >= 0 && inputRows[1] < m_inputRows) {
+ // no padding
+ const int depth_index = static_cast<int>(Layout) == static_cast<int>(ColMajor) ? 0 : NumDims - 1;
+ const Index depth = index - (index / m_fastOutputDepth) * m_dimensions[depth_index];
+ const Index inputIndex = depth + inputRows[0] * m_rowInputStride + inputCols[0] * m_colInputStride + otherIndex * m_patchInputStride;
+ return m_impl.template packet<Unaligned>(inputIndex);
+ }
+ }
+
+ return packetWithPossibleZero(index);
+ }
+
+ EIGEN_DEVICE_FUNC EvaluatorPointerType data() const { return NULL; }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const TensorEvaluator<ArgType, Device>& impl() const { return m_impl; }
+
+#ifdef EIGEN_USE_SYCL
+ // binding placeholder accessors to a command group handler for SYCL
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void bind(cl::sycl::handler &cgh) const {
+ m_impl.bind(cgh);
+ }
+#endif
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Index rowPaddingTop() const { return m_rowPaddingTop; }
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Index colPaddingLeft() const { return m_colPaddingLeft; }
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Index outputRows() const { return m_outputRows; }
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Index outputCols() const { return m_outputCols; }
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Index userRowStride() const { return m_row_strides; }
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Index userColStride() const { return m_col_strides; }
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Index userInRowStride() const { return m_in_row_strides; }
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Index userInColStride() const { return m_in_col_strides; }
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Index rowInflateStride() const { return m_row_inflate_strides; }
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Index colInflateStride() const { return m_col_inflate_strides; }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorOpCost
+ costPerCoeff(bool vectorized) const {
+ // We conservatively estimate the cost for the code path where the computed
+ // index is inside the original image and
+ // TensorEvaluator<ArgType, Device>::CoordAccess is false.
+ const double compute_cost = 3 * TensorOpCost::DivCost<Index>() +
+ 6 * TensorOpCost::MulCost<Index>() +
+ 8 * TensorOpCost::MulCost<Index>();
+ return m_impl.costPerCoeff(vectorized) +
+ TensorOpCost(0, 0, compute_cost, vectorized, PacketSize);
+ }
+
+ protected:
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE PacketReturnType packetWithPossibleZero(Index index) const
+ {
+ EIGEN_ALIGN_MAX std::remove_const_t<CoeffReturnType> values[PacketSize];
+ EIGEN_UNROLL_LOOP
+ for (int i = 0; i < PacketSize; ++i) {
+ values[i] = coeff(index+i);
+ }
+ PacketReturnType rslt = internal::pload<PacketReturnType>(values);
+ return rslt;
+ }
+
+ Dimensions m_dimensions;
+
+ Index m_otherStride;
+ Index m_patchStride;
+ Index m_colStride;
+ Index m_row_strides;
+ Index m_col_strides;
+
+ Index m_in_row_strides;
+ Index m_in_col_strides;
+ Index m_row_inflate_strides;
+ Index m_col_inflate_strides;
+
+ Index m_input_rows_eff;
+ Index m_input_cols_eff;
+ Index m_patch_rows_eff;
+ Index m_patch_cols_eff;
+
+ internal::TensorIntDivisor<Index> m_fastOtherStride;
+ internal::TensorIntDivisor<Index> m_fastPatchStride;
+ internal::TensorIntDivisor<Index> m_fastColStride;
+ internal::TensorIntDivisor<Index> m_fastInflateRowStride;
+ internal::TensorIntDivisor<Index> m_fastInflateColStride;
+ internal::TensorIntDivisor<Index> m_fastInputColsEff;
+
+ Index m_rowInputStride;
+ Index m_colInputStride;
+ Index m_patchInputStride;
+
+ Index m_inputDepth;
+ Index m_inputRows;
+ Index m_inputCols;
+
+ Index m_outputRows;
+ Index m_outputCols;
+
+ Index m_rowPaddingTop;
+ Index m_colPaddingLeft;
+
+ internal::TensorIntDivisor<Index> m_fastOutputRows;
+ internal::TensorIntDivisor<Index> m_fastOutputDepth;
+
+ Scalar m_paddingValue;
+
+ const Device EIGEN_DEVICE_REF m_device;
+ TensorEvaluator<ArgType, Device> m_impl;
+};
+
+
+} // end namespace Eigen
+
+#endif // EIGEN_CXX11_TENSOR_TENSOR_IMAGE_PATCH_H
diff --git a/unsupported/Eigen/CXX11/src/Tensor/TensorIndexList.h b/unsupported/Eigen/CXX11/src/Tensor/TensorIndexList.h
new file mode 100644
index 0000000..dc97d21
--- /dev/null
+++ b/unsupported/Eigen/CXX11/src/Tensor/TensorIndexList.h
@@ -0,0 +1,665 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_CXX11_TENSOR_TENSOR_INDEX_LIST_H
+#define EIGEN_CXX11_TENSOR_TENSOR_INDEX_LIST_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+/** \internal
+ *
+ * \class TensorIndexList
+ * \ingroup CXX11_Tensor_Module
+ *
+ * \brief Set of classes used to encode a set of Tensor dimensions/indices.
+ *
+ * The indices in the list can be known at compile time or at runtime. A mix
+ * of static and dynamic indices can also be provided if needed. The tensor
+ * code will attempt to take advantage of the indices that are known at
+ * compile time to optimize the code it generates.
+ *
+ * This functionality requires a c++11 compliant compiler. If your compiler
+ * is older you need to use arrays of indices instead.
+ *
+ * Several examples are provided in the cxx11_tensor_index_list.cpp file.
+ *
+ * \sa Tensor
+ */
+
+template <Index n>
+struct type2index {
+ static const Index value = n;
+ EIGEN_DEVICE_FUNC constexpr operator Index() const { return n; }
+ EIGEN_DEVICE_FUNC void set(Index val) {
+ eigen_assert(val == n);
+ }
+};
+
+// This can be used with IndexPairList to get compile-time constant pairs,
+// such as IndexPairList<type2indexpair<1,2>, type2indexpair<3,4>>().
+template <Index f, Index s>
+struct type2indexpair {
+ static const Index first = f;
+ static const Index second = s;
+
+ constexpr EIGEN_DEVICE_FUNC operator IndexPair<Index>() const {
+ return IndexPair<Index>(f, s);
+ }
+
+ EIGEN_DEVICE_FUNC void set(const IndexPair<Index>& val) {
+ eigen_assert(val.first == f);
+ eigen_assert(val.second == s);
+ }
+};
+
+
+template<Index n> struct NumTraits<type2index<n> >
+{
+ typedef Index Real;
+ enum {
+ IsComplex = 0,
+ RequireInitialization = false,
+ ReadCost = 1,
+ AddCost = 1,
+ MulCost = 1
+ };
+
+ EIGEN_DEVICE_FUNC static EIGEN_CONSTEXPR EIGEN_STRONG_INLINE Real epsilon() { return 0; }
+ EIGEN_DEVICE_FUNC static EIGEN_CONSTEXPR EIGEN_STRONG_INLINE Real dummy_precision() { return 0; }
+ EIGEN_DEVICE_FUNC static EIGEN_CONSTEXPR EIGEN_STRONG_INLINE Real highest() { return n; }
+ EIGEN_DEVICE_FUNC static EIGEN_CONSTEXPR EIGEN_STRONG_INLINE Real lowest() { return n; }
+};
+
+namespace internal {
+template <typename T>
+EIGEN_DEVICE_FUNC void update_value(T& val, Index new_val) {
+ val = internal::convert_index<T>(new_val);
+}
+template <Index n>
+EIGEN_DEVICE_FUNC void update_value(type2index<n>& val, Index new_val) {
+ val.set(new_val);
+}
+
+template <typename T>
+EIGEN_DEVICE_FUNC void update_value(T& val, IndexPair<Index> new_val) {
+ val = new_val;
+}
+template <Index f, Index s>
+EIGEN_DEVICE_FUNC void update_value(type2indexpair<f, s>& val, IndexPair<Index> new_val) {
+ val.set(new_val);
+}
+
+
+template <typename T>
+struct is_compile_time_constant {
+ static constexpr bool value = false;
+};
+
+template <Index idx>
+struct is_compile_time_constant<type2index<idx> > {
+ static constexpr bool value = true;
+};
+template <Index idx>
+struct is_compile_time_constant<const type2index<idx> > {
+ static constexpr bool value = true;
+};
+template <Index idx>
+struct is_compile_time_constant<type2index<idx>& > {
+ static constexpr bool value = true;
+};
+template <Index idx>
+struct is_compile_time_constant<const type2index<idx>& > {
+ static constexpr bool value = true;
+};
+
+template <Index f, Index s>
+struct is_compile_time_constant<type2indexpair<f, s> > {
+ static constexpr bool value = true;
+};
+template <Index f, Index s>
+struct is_compile_time_constant<const type2indexpair<f, s> > {
+ static constexpr bool value = true;
+};
+template <Index f, Index s>
+struct is_compile_time_constant<type2indexpair<f, s>& > {
+ static constexpr bool value = true;
+};
+template <Index f, Index s>
+struct is_compile_time_constant<const type2indexpair<f, s>& > {
+ static constexpr bool value = true;
+};
+
+
+template<typename... T>
+struct IndexTuple;
+
+template<typename T, typename... O>
+struct IndexTuple<T, O...> {
+ EIGEN_DEVICE_FUNC constexpr IndexTuple() : head(), others() { }
+ EIGEN_DEVICE_FUNC constexpr IndexTuple(const T& v, const O... o) : head(v), others(o...) { }
+
+ constexpr static int count = 1 + sizeof...(O);
+ T head;
+ IndexTuple<O...> others;
+ typedef T Head;
+ typedef IndexTuple<O...> Other;
+};
+
+template<typename T>
+ struct IndexTuple<T> {
+ EIGEN_DEVICE_FUNC constexpr IndexTuple() : head() { }
+ EIGEN_DEVICE_FUNC constexpr IndexTuple(const T& v) : head(v) { }
+
+ constexpr static int count = 1;
+ T head;
+ typedef T Head;
+};
+
+
+template<int N, typename... T>
+struct IndexTupleExtractor;
+
+template<int N, typename T, typename... O>
+struct IndexTupleExtractor<N, T, O...> {
+
+ typedef typename IndexTupleExtractor<N-1, O...>::ValType ValType;
+
+ EIGEN_DEVICE_FUNC static constexpr ValType& get_val(IndexTuple<T, O...>& val) {
+ return IndexTupleExtractor<N-1, O...>::get_val(val.others);
+ }
+
+ EIGEN_DEVICE_FUNC static constexpr const ValType& get_val(const IndexTuple<T, O...>& val) {
+ return IndexTupleExtractor<N-1, O...>::get_val(val.others);
+ }
+ template <typename V>
+ EIGEN_DEVICE_FUNC static void set_val(IndexTuple<T, O...>& val, V& new_val) {
+ IndexTupleExtractor<N-1, O...>::set_val(val.others, new_val);
+ }
+
+};
+
+template<typename T, typename... O>
+ struct IndexTupleExtractor<0, T, O...> {
+
+ typedef T ValType;
+
+ EIGEN_DEVICE_FUNC static constexpr ValType& get_val(IndexTuple<T, O...>& val) {
+ return val.head;
+ }
+ EIGEN_DEVICE_FUNC static constexpr const ValType& get_val(const IndexTuple<T, O...>& val) {
+ return val.head;
+ }
+ template <typename V>
+ EIGEN_DEVICE_FUNC static void set_val(IndexTuple<T, O...>& val, V& new_val) {
+ val.head = new_val;
+ }
+};
+
+
+
+template <int N, typename T, typename... O>
+EIGEN_DEVICE_FUNC constexpr typename IndexTupleExtractor<N, T, O...>::ValType& array_get(IndexTuple<T, O...>& tuple) {
+ return IndexTupleExtractor<N, T, O...>::get_val(tuple);
+}
+template <int N, typename T, typename... O>
+EIGEN_DEVICE_FUNC constexpr const typename IndexTupleExtractor<N, T, O...>::ValType& array_get(const IndexTuple<T, O...>& tuple) {
+ return IndexTupleExtractor<N, T, O...>::get_val(tuple);
+}
+template <typename T, typename... O>
+ struct array_size<IndexTuple<T, O...> > {
+ static const size_t value = IndexTuple<T, O...>::count;
+};
+template <typename T, typename... O>
+ struct array_size<const IndexTuple<T, O...> > {
+ static const size_t value = IndexTuple<T, O...>::count;
+};
+
+
+
+
+template <Index Idx, typename ValueT>
+struct tuple_coeff {
+ template <typename... T>
+ EIGEN_DEVICE_FUNC static constexpr ValueT get(const Index i, const IndexTuple<T...>& t) {
+ // return array_get<Idx>(t) * (i == Idx) + tuple_coeff<Idx-1>::get(i, t) * (i != Idx);
+ return (i == Idx ? array_get<Idx>(t) : tuple_coeff<Idx-1, ValueT>::get(i, t));
+ }
+ template <typename... T>
+ EIGEN_DEVICE_FUNC static void set(const Index i, IndexTuple<T...>& t, const ValueT& value) {
+ if (i == Idx) {
+ update_value(array_get<Idx>(t), value);
+ } else {
+ tuple_coeff<Idx-1, ValueT>::set(i, t, value);
+ }
+ }
+
+ template <typename... T>
+ EIGEN_DEVICE_FUNC static constexpr bool value_known_statically(const Index i, const IndexTuple<T...>& t) {
+ return ((i == Idx) && is_compile_time_constant<typename IndexTupleExtractor<Idx, T...>::ValType>::value) ||
+ tuple_coeff<Idx-1, ValueT>::value_known_statically(i, t);
+ }
+
+ template <typename... T>
+ EIGEN_DEVICE_FUNC static constexpr bool values_up_to_known_statically(const IndexTuple<T...>& t) {
+ return is_compile_time_constant<typename IndexTupleExtractor<Idx, T...>::ValType>::value &&
+ tuple_coeff<Idx-1, ValueT>::values_up_to_known_statically(t);
+ }
+
+ template <typename... T>
+ EIGEN_DEVICE_FUNC static constexpr bool values_up_to_statically_known_to_increase(const IndexTuple<T...>& t) {
+ return is_compile_time_constant<typename IndexTupleExtractor<Idx, T...>::ValType>::value &&
+ is_compile_time_constant<typename IndexTupleExtractor<Idx, T...>::ValType>::value &&
+ array_get<Idx>(t) > array_get<Idx-1>(t) &&
+ tuple_coeff<Idx-1, ValueT>::values_up_to_statically_known_to_increase(t);
+ }
+};
+
+template <typename ValueT>
+struct tuple_coeff<0, ValueT> {
+ template <typename... T>
+ EIGEN_DEVICE_FUNC static constexpr ValueT get(const Index /*i*/, const IndexTuple<T...>& t) {
+ // eigen_assert (i == 0); // gcc fails to compile assertions in constexpr
+ return array_get<0>(t)/* * (i == 0)*/;
+ }
+ template <typename... T>
+ EIGEN_DEVICE_FUNC static void set(const Index i, IndexTuple<T...>& t, const ValueT value) {
+ eigen_assert (i == 0);
+ update_value(array_get<0>(t), value);
+ }
+ template <typename... T>
+ EIGEN_DEVICE_FUNC static constexpr bool value_known_statically(const Index i, const IndexTuple<T...>&) {
+ return is_compile_time_constant<typename IndexTupleExtractor<0, T...>::ValType>::value && (i == 0);
+ }
+
+ template <typename... T>
+ EIGEN_DEVICE_FUNC static constexpr bool values_up_to_known_statically(const IndexTuple<T...>&) {
+ return is_compile_time_constant<typename IndexTupleExtractor<0, T...>::ValType>::value;
+ }
+
+ template <typename... T>
+ EIGEN_DEVICE_FUNC static constexpr bool values_up_to_statically_known_to_increase(const IndexTuple<T...>&) {
+ return true;
+ }
+};
+} // namespace internal
+
+
+
+template<typename FirstType, typename... OtherTypes>
+struct IndexList : internal::IndexTuple<FirstType, OtherTypes...> {
+ EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC constexpr Index operator[] (const Index i) const {
+ return internal::tuple_coeff<internal::array_size<internal::IndexTuple<FirstType, OtherTypes...> >::value-1, Index>::get(i, *this);
+ }
+ EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC constexpr Index get(const Index i) const {
+ return internal::tuple_coeff<internal::array_size<internal::IndexTuple<FirstType, OtherTypes...> >::value-1, Index>::get(i, *this);
+ }
+ EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC void set(const Index i, const Index value) {
+ return internal::tuple_coeff<internal::array_size<internal::IndexTuple<FirstType, OtherTypes...> >::value-1, Index>::set(i, *this, value);
+ }
+
+ EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC constexpr std::size_t size() const {
+ return 1 + sizeof...(OtherTypes);
+ };
+
+
+ EIGEN_DEVICE_FUNC constexpr IndexList(const internal::IndexTuple<FirstType, OtherTypes...>& other) : internal::IndexTuple<FirstType, OtherTypes...>(other) { }
+ EIGEN_DEVICE_FUNC constexpr IndexList(FirstType& first, OtherTypes... other) : internal::IndexTuple<FirstType, OtherTypes...>(first, other...) { }
+ EIGEN_DEVICE_FUNC constexpr IndexList() : internal::IndexTuple<FirstType, OtherTypes...>() { }
+
+ EIGEN_DEVICE_FUNC constexpr bool value_known_statically(const Index i) const {
+ return internal::tuple_coeff<internal::array_size<internal::IndexTuple<FirstType, OtherTypes...> >::value-1, Index>::value_known_statically(i, *this);
+ }
+ EIGEN_DEVICE_FUNC constexpr bool all_values_known_statically() const {
+ return internal::tuple_coeff<internal::array_size<internal::IndexTuple<FirstType, OtherTypes...> >::value-1, Index>::values_up_to_known_statically(*this);
+ }
+
+ EIGEN_DEVICE_FUNC constexpr bool values_statically_known_to_increase() const {
+ return internal::tuple_coeff<internal::array_size<internal::IndexTuple<FirstType, OtherTypes...> >::value-1, Index>::values_up_to_statically_known_to_increase(*this);
+ }
+};
+
+template <typename FirstType, typename... OtherTypes>
+std::ostream& operator<<(std::ostream& os,
+ const IndexList<FirstType, OtherTypes...>& dims) {
+ os << "[";
+ for (size_t i = 0; i < 1 + sizeof...(OtherTypes); ++i) {
+ if (i > 0) os << ", ";
+ os << dims[i];
+ }
+ os << "]";
+ return os;
+}
+
+template<typename FirstType, typename... OtherTypes>
+constexpr IndexList<FirstType, OtherTypes...> make_index_list(FirstType val1, OtherTypes... other_vals) {
+ return IndexList<FirstType, OtherTypes...>(val1, other_vals...);
+}
+
+
+template<typename FirstType, typename... OtherTypes>
+struct IndexPairList : internal::IndexTuple<FirstType, OtherTypes...> {
+ EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC constexpr IndexPair<Index> operator[] (const Index i) const {
+ return internal::tuple_coeff<internal::array_size<internal::IndexTuple<FirstType, OtherTypes...> >::value-1, IndexPair<Index>>::get(i, *this);
+ }
+ EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC void set(const Index i, const IndexPair<Index> value) {
+ return internal::tuple_coeff<internal::array_size<internal::IndexTuple<FirstType, OtherTypes...>>::value-1, IndexPair<Index> >::set(i, *this, value);
+ }
+
+ EIGEN_DEVICE_FUNC constexpr IndexPairList(const internal::IndexTuple<FirstType, OtherTypes...>& other) : internal::IndexTuple<FirstType, OtherTypes...>(other) { }
+ EIGEN_DEVICE_FUNC constexpr IndexPairList() : internal::IndexTuple<FirstType, OtherTypes...>() { }
+
+ EIGEN_DEVICE_FUNC constexpr bool value_known_statically(const Index i) const {
+ return internal::tuple_coeff<internal::array_size<internal::IndexTuple<FirstType, OtherTypes...> >::value-1, Index>::value_known_statically(i, *this);
+ }
+};
+
+namespace internal {
+
+template<typename FirstType, typename... OtherTypes>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Index array_prod(const IndexList<FirstType, OtherTypes...>& sizes) {
+ Index result = 1;
+ EIGEN_UNROLL_LOOP
+ for (size_t i = 0; i < array_size<IndexList<FirstType, OtherTypes...> >::value; ++i) {
+ result *= sizes[i];
+ }
+ return result;
+}
+
+template<typename FirstType, typename... OtherTypes> struct array_size<IndexList<FirstType, OtherTypes...> > {
+ static const size_t value = array_size<IndexTuple<FirstType, OtherTypes...> >::value;
+};
+template<typename FirstType, typename... OtherTypes> struct array_size<const IndexList<FirstType, OtherTypes...> > {
+ static const size_t value = array_size<IndexTuple<FirstType, OtherTypes...> >::value;
+};
+
+template<typename FirstType, typename... OtherTypes> struct array_size<IndexPairList<FirstType, OtherTypes...> > {
+ static const size_t value = 1 + sizeof...(OtherTypes);
+};
+template<typename FirstType, typename... OtherTypes> struct array_size<const IndexPairList<FirstType, OtherTypes...> > {
+ static const size_t value = 1 + sizeof...(OtherTypes);
+};
+
+template<Index N, typename FirstType, typename... OtherTypes> EIGEN_DEVICE_FUNC constexpr Index array_get(IndexList<FirstType, OtherTypes...>& a) {
+ return IndexTupleExtractor<N, FirstType, OtherTypes...>::get_val(a);
+}
+template<Index N, typename FirstType, typename... OtherTypes> EIGEN_DEVICE_FUNC constexpr Index array_get(const IndexList<FirstType, OtherTypes...>& a) {
+ return IndexTupleExtractor<N, FirstType, OtherTypes...>::get_val(a);
+}
+
+template <typename T>
+struct index_known_statically_impl {
+ EIGEN_DEVICE_FUNC static constexpr bool run(const Index) {
+ return false;
+ }
+};
+
+template <typename FirstType, typename... OtherTypes>
+struct index_known_statically_impl<IndexList<FirstType, OtherTypes...> > {
+ EIGEN_DEVICE_FUNC static constexpr bool run(const Index i) {
+ return IndexList<FirstType, OtherTypes...>().value_known_statically(i);
+ }
+};
+
+template <typename FirstType, typename... OtherTypes>
+struct index_known_statically_impl<const IndexList<FirstType, OtherTypes...> > {
+ EIGEN_DEVICE_FUNC static constexpr bool run(const Index i) {
+ return IndexList<FirstType, OtherTypes...>().value_known_statically(i);
+ }
+};
+
+
+template <typename T>
+struct all_indices_known_statically_impl {
+ static constexpr bool run() {
+ return false;
+ }
+};
+
+template <typename FirstType, typename... OtherTypes>
+struct all_indices_known_statically_impl<IndexList<FirstType, OtherTypes...> > {
+ EIGEN_DEVICE_FUNC static constexpr bool run() {
+ return IndexList<FirstType, OtherTypes...>().all_values_known_statically();
+ }
+};
+
+template <typename FirstType, typename... OtherTypes>
+struct all_indices_known_statically_impl<const IndexList<FirstType, OtherTypes...> > {
+ EIGEN_DEVICE_FUNC static constexpr bool run() {
+ return IndexList<FirstType, OtherTypes...>().all_values_known_statically();
+ }
+};
+
+
+template <typename T>
+struct indices_statically_known_to_increase_impl {
+ EIGEN_DEVICE_FUNC static constexpr bool run() {
+ return false;
+ }
+};
+
+template <typename FirstType, typename... OtherTypes>
+ struct indices_statically_known_to_increase_impl<IndexList<FirstType, OtherTypes...> > {
+ EIGEN_DEVICE_FUNC static constexpr bool run() {
+ return Eigen::IndexList<FirstType, OtherTypes...>().values_statically_known_to_increase();
+ }
+};
+
+template <typename FirstType, typename... OtherTypes>
+ struct indices_statically_known_to_increase_impl<const IndexList<FirstType, OtherTypes...> > {
+ EIGEN_DEVICE_FUNC static constexpr bool run() {
+ return Eigen::IndexList<FirstType, OtherTypes...>().values_statically_known_to_increase();
+ }
+};
+
+
+template <typename Tx>
+struct index_statically_eq_impl {
+ EIGEN_DEVICE_FUNC static constexpr bool run(Index, Index) {
+ return false;
+ }
+};
+
+template <typename FirstType, typename... OtherTypes>
+struct index_statically_eq_impl<IndexList<FirstType, OtherTypes...> > {
+ EIGEN_DEVICE_FUNC static constexpr bool run(const Index i, const Index value) {
+ return IndexList<FirstType, OtherTypes...>().value_known_statically(i) &&
+ (IndexList<FirstType, OtherTypes...>().get(i) == value);
+ }
+};
+
+template <typename FirstType, typename... OtherTypes>
+struct index_statically_eq_impl<const IndexList<FirstType, OtherTypes...> > {
+ EIGEN_DEVICE_FUNC static constexpr bool run(const Index i, const Index value) {
+ return IndexList<FirstType, OtherTypes...>().value_known_statically(i) &&
+ (IndexList<FirstType, OtherTypes...>().get(i) == value);
+ }
+};
+
+
+template <typename T>
+struct index_statically_ne_impl {
+ EIGEN_DEVICE_FUNC static constexpr bool run(Index, Index) {
+ return false;
+ }
+};
+
+template <typename FirstType, typename... OtherTypes>
+struct index_statically_ne_impl<IndexList<FirstType, OtherTypes...> > {
+ EIGEN_DEVICE_FUNC static constexpr bool run(const Index i, const Index value) {
+ return IndexList<FirstType, OtherTypes...>().value_known_statically(i) &&
+ (IndexList<FirstType, OtherTypes...>().get(i) != value);
+ }
+};
+
+template <typename FirstType, typename... OtherTypes>
+struct index_statically_ne_impl<const IndexList<FirstType, OtherTypes...> > {
+ EIGEN_DEVICE_FUNC static constexpr bool run(const Index i, const Index value) {
+ return IndexList<FirstType, OtherTypes...>().value_known_statically(i) &&
+ (IndexList<FirstType, OtherTypes...>().get(i) != value);
+ }
+};
+
+
+template <typename T>
+struct index_statically_gt_impl {
+ EIGEN_DEVICE_FUNC static constexpr bool run(Index, Index) {
+ return false;
+ }
+};
+
+template <typename FirstType, typename... OtherTypes>
+struct index_statically_gt_impl<IndexList<FirstType, OtherTypes...> > {
+ EIGEN_DEVICE_FUNC static constexpr bool run(const Index i, const Index value) {
+ return IndexList<FirstType, OtherTypes...>().value_known_statically(i) &&
+ (IndexList<FirstType, OtherTypes...>().get(i) > value);
+ }
+};
+
+template <typename FirstType, typename... OtherTypes>
+struct index_statically_gt_impl<const IndexList<FirstType, OtherTypes...> > {
+ EIGEN_DEVICE_FUNC static constexpr bool run(const Index i, const Index value) {
+ return IndexList<FirstType, OtherTypes...>().value_known_statically(i) &&
+ (IndexList<FirstType, OtherTypes...>().get(i) > value);
+ }
+};
+
+
+
+template <typename T>
+struct index_statically_lt_impl {
+ EIGEN_DEVICE_FUNC static constexpr bool run(Index, Index) {
+ return false;
+ }
+};
+
+template <typename FirstType, typename... OtherTypes>
+struct index_statically_lt_impl<IndexList<FirstType, OtherTypes...> > {
+ EIGEN_DEVICE_FUNC static constexpr bool run(const Index i, const Index value) {
+ return IndexList<FirstType, OtherTypes...>().value_known_statically(i) &&
+ (IndexList<FirstType, OtherTypes...>().get(i) < value);
+ }
+};
+
+template <typename FirstType, typename... OtherTypes>
+struct index_statically_lt_impl<const IndexList<FirstType, OtherTypes...> > {
+ EIGEN_DEVICE_FUNC static constexpr bool run(const Index i, const Index value) {
+ return IndexList<FirstType, OtherTypes...>().value_known_statically(i) &&
+ (IndexList<FirstType, OtherTypes...>().get(i) < value);
+ }
+};
+
+
+
+template <typename Tx>
+struct index_pair_first_statically_eq_impl {
+ EIGEN_DEVICE_FUNC static constexpr bool run(Index, Index) {
+ return false;
+ }
+};
+
+template <typename FirstType, typename... OtherTypes>
+struct index_pair_first_statically_eq_impl<IndexPairList<FirstType, OtherTypes...> > {
+ EIGEN_DEVICE_FUNC static constexpr bool run(const Index i, const Index value) {
+ return IndexPairList<FirstType, OtherTypes...>().value_known_statically(i) &&
+ (IndexPairList<FirstType, OtherTypes...>().operator[](i).first == value);
+ }
+};
+
+template <typename FirstType, typename... OtherTypes>
+struct index_pair_first_statically_eq_impl<const IndexPairList<FirstType, OtherTypes...> > {
+ EIGEN_DEVICE_FUNC static constexpr bool run(const Index i, const Index value) {
+ return IndexPairList<FirstType, OtherTypes...>().value_known_statically(i) &&
+ (IndexPairList<FirstType, OtherTypes...>().operator[](i).first == value);
+ }
+};
+
+
+
+template <typename Tx>
+struct index_pair_second_statically_eq_impl {
+ EIGEN_DEVICE_FUNC static constexpr bool run(Index, Index) {
+ return false;
+ }
+};
+
+template <typename FirstType, typename... OtherTypes>
+struct index_pair_second_statically_eq_impl<IndexPairList<FirstType, OtherTypes...> > {
+ EIGEN_DEVICE_FUNC static constexpr bool run(const Index i, const Index value) {
+ return IndexPairList<FirstType, OtherTypes...>().value_known_statically(i) &&
+ (IndexPairList<FirstType, OtherTypes...>().operator[](i).second == value);
+ }
+};
+
+template <typename FirstType, typename... OtherTypes>
+struct index_pair_second_statically_eq_impl<const IndexPairList<FirstType, OtherTypes...> > {
+ EIGEN_DEVICE_FUNC static constexpr bool run(const Index i, const Index value) {
+ return IndexPairList<FirstType, OtherTypes...>().value_known_statically(i) &&
+ (IndexPairList<FirstType, OtherTypes...>().operator[](i).second == value);
+ }
+};
+
+
+} // end namespace internal
+} // end namespace Eigen
+
+
+namespace Eigen {
+namespace internal {
+template <typename T>
+static EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR bool index_known_statically(Index i) {
+ return index_known_statically_impl<T>::run(i);
+}
+
+template <typename T>
+static EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR bool all_indices_known_statically() {
+ return all_indices_known_statically_impl<T>::run();
+}
+
+template <typename T>
+static EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR bool indices_statically_known_to_increase() {
+ return indices_statically_known_to_increase_impl<T>::run();
+}
+
+template <typename T>
+static EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR bool index_statically_eq(Index i, Index value) {
+ return index_statically_eq_impl<T>::run(i, value);
+}
+
+template <typename T>
+static EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR bool index_statically_ne(Index i, Index value) {
+ return index_statically_ne_impl<T>::run(i, value);
+}
+
+template <typename T>
+static EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR bool index_statically_gt(Index i, Index value) {
+ return index_statically_gt_impl<T>::run(i, value);
+}
+
+template <typename T>
+static EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR bool index_statically_lt(Index i, Index value) {
+ return index_statically_lt_impl<T>::run(i, value);
+}
+
+template <typename T>
+static EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR bool index_pair_first_statically_eq(Index i, Index value) {
+ return index_pair_first_statically_eq_impl<T>::run(i, value);
+}
+
+template <typename T>
+static EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR bool index_pair_second_statically_eq(Index i, Index value) {
+ return index_pair_second_statically_eq_impl<T>::run(i, value);
+}
+
+} // end namespace internal
+} // end namespace Eigen
+
+
+#endif // EIGEN_CXX11_TENSOR_TENSOR_INDEX_LIST_H
diff --git a/unsupported/Eigen/CXX11/src/Tensor/TensorInflation.h b/unsupported/Eigen/CXX11/src/Tensor/TensorInflation.h
new file mode 100644
index 0000000..8188194
--- /dev/null
+++ b/unsupported/Eigen/CXX11/src/Tensor/TensorInflation.h
@@ -0,0 +1,249 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2015 Ke Yang <yangke@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_CXX11_TENSOR_TENSOR_INFLATION_H
+#define EIGEN_CXX11_TENSOR_TENSOR_INFLATION_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+/** \class TensorInflation
+ * \ingroup CXX11_Tensor_Module
+ *
+ * \brief Tensor inflation class.
+ *
+ *
+ */
+namespace internal {
+template<typename Strides, typename XprType>
+struct traits<TensorInflationOp<Strides, XprType> > : public traits<XprType>
+{
+ typedef typename XprType::Scalar Scalar;
+ typedef traits<XprType> XprTraits;
+ typedef typename XprTraits::StorageKind StorageKind;
+ typedef typename XprTraits::Index Index;
+ typedef typename XprType::Nested Nested;
+ typedef std::remove_reference_t<Nested> Nested_;
+ static constexpr int NumDimensions = XprTraits::NumDimensions;
+ static constexpr int Layout = XprTraits::Layout;
+ typedef typename XprTraits::PointerType PointerType;
+};
+
+template<typename Strides, typename XprType>
+struct eval<TensorInflationOp<Strides, XprType>, Eigen::Dense>
+{
+ typedef const TensorInflationOp<Strides, XprType>& type;
+};
+
+template<typename Strides, typename XprType>
+struct nested<TensorInflationOp<Strides, XprType>, 1, typename eval<TensorInflationOp<Strides, XprType> >::type>
+{
+ typedef TensorInflationOp<Strides, XprType> type;
+};
+
+} // end namespace internal
+
+template<typename Strides, typename XprType>
+class TensorInflationOp : public TensorBase<TensorInflationOp<Strides, XprType>, ReadOnlyAccessors>
+{
+ public:
+ typedef typename Eigen::internal::traits<TensorInflationOp>::Scalar Scalar;
+ typedef typename Eigen::NumTraits<Scalar>::Real RealScalar;
+ typedef typename XprType::CoeffReturnType CoeffReturnType;
+ typedef typename Eigen::internal::nested<TensorInflationOp>::type Nested;
+ typedef typename Eigen::internal::traits<TensorInflationOp>::StorageKind StorageKind;
+ typedef typename Eigen::internal::traits<TensorInflationOp>::Index Index;
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorInflationOp(const XprType& expr, const Strides& strides)
+ : m_xpr(expr), m_strides(strides) {}
+
+ EIGEN_DEVICE_FUNC
+ const Strides& strides() const { return m_strides; }
+
+ EIGEN_DEVICE_FUNC
+ const internal::remove_all_t<typename XprType::Nested>&
+ expression() const { return m_xpr; }
+
+ protected:
+ typename XprType::Nested m_xpr;
+ const Strides m_strides;
+};
+
+// Eval as rvalue
+template<typename Strides, typename ArgType, typename Device>
+struct TensorEvaluator<const TensorInflationOp<Strides, ArgType>, Device>
+{
+ typedef TensorInflationOp<Strides, ArgType> XprType;
+ typedef typename XprType::Index Index;
+ static constexpr int NumDims = internal::array_size<typename TensorEvaluator<ArgType, Device>::Dimensions>::value;
+ typedef DSizes<Index, NumDims> Dimensions;
+ typedef typename XprType::Scalar Scalar;
+ typedef typename XprType::CoeffReturnType CoeffReturnType;
+ typedef typename PacketType<CoeffReturnType, Device>::type PacketReturnType;
+ static constexpr int PacketSize = PacketType<CoeffReturnType, Device>::size;
+ typedef StorageMemory<CoeffReturnType, Device> Storage;
+ typedef typename Storage::Type EvaluatorPointerType;
+
+ static constexpr int Layout = TensorEvaluator<ArgType, Device>::Layout;
+ enum {
+ IsAligned = /*TensorEvaluator<ArgType, Device>::IsAligned*/ false,
+ PacketAccess = TensorEvaluator<ArgType, Device>::PacketAccess,
+ BlockAccess = false,
+ PreferBlockAccess = false,
+ CoordAccess = false, // to be implemented
+ RawAccess = false
+ };
+
+ //===- Tensor block evaluation strategy (see TensorBlock.h) -------------===//
+ typedef internal::TensorBlockNotImplemented TensorBlock;
+ //===--------------------------------------------------------------------===//
+
+ EIGEN_STRONG_INLINE TensorEvaluator(const XprType& op, const Device& device)
+ : m_impl(op.expression(), device), m_strides(op.strides())
+ {
+ m_dimensions = m_impl.dimensions();
+ // Expand each dimension to the inflated dimension.
+ for (int i = 0; i < NumDims; ++i) {
+ m_dimensions[i] = (m_dimensions[i] - 1) * op.strides()[i] + 1;
+ }
+
+ // Remember the strides for fast division.
+ for (int i = 0; i < NumDims; ++i) {
+ m_fastStrides[i] = internal::TensorIntDivisor<Index>(m_strides[i]);
+ }
+
+ const typename TensorEvaluator<ArgType, Device>::Dimensions& input_dims = m_impl.dimensions();
+ if (static_cast<int>(Layout) == static_cast<int>(ColMajor)) {
+ m_outputStrides[0] = 1;
+ m_inputStrides[0] = 1;
+ for (int i = 1; i < NumDims; ++i) {
+ m_outputStrides[i] = m_outputStrides[i-1] * m_dimensions[i-1];
+ m_inputStrides[i] = m_inputStrides[i-1] * input_dims[i-1];
+ }
+ } else { // RowMajor
+ m_outputStrides[NumDims-1] = 1;
+ m_inputStrides[NumDims-1] = 1;
+ for (int i = NumDims - 2; i >= 0; --i) {
+ m_outputStrides[i] = m_outputStrides[i+1] * m_dimensions[i+1];
+ m_inputStrides[i] = m_inputStrides[i+1] * input_dims[i+1];
+ }
+ }
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Dimensions& dimensions() const { return m_dimensions; }
+
+ EIGEN_STRONG_INLINE bool evalSubExprsIfNeeded(EvaluatorPointerType /*data*/) {
+ m_impl.evalSubExprsIfNeeded(NULL);
+ return true;
+ }
+ EIGEN_STRONG_INLINE void cleanup() {
+ m_impl.cleanup();
+ }
+
+ // Computes the input index given the output index. Returns true if the output
+ // index doesn't fall into a hole.
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE bool getInputIndex(Index index, Index* inputIndex) const
+ {
+ eigen_assert(index < dimensions().TotalSize());
+ *inputIndex = 0;
+ if (static_cast<int>(Layout) == static_cast<int>(ColMajor)) {
+ EIGEN_UNROLL_LOOP
+ for (int i = NumDims - 1; i > 0; --i) {
+ const Index idx = index / m_outputStrides[i];
+ if (idx != idx / m_fastStrides[i] * m_strides[i]) {
+ return false;
+ }
+ *inputIndex += idx / m_strides[i] * m_inputStrides[i];
+ index -= idx * m_outputStrides[i];
+ }
+ if (index != index / m_fastStrides[0] * m_strides[0]) {
+ return false;
+ }
+ *inputIndex += index / m_strides[0];
+ return true;
+ } else {
+ EIGEN_UNROLL_LOOP
+ for (int i = 0; i < NumDims - 1; ++i) {
+ const Index idx = index / m_outputStrides[i];
+ if (idx != idx / m_fastStrides[i] * m_strides[i]) {
+ return false;
+ }
+ *inputIndex += idx / m_strides[i] * m_inputStrides[i];
+ index -= idx * m_outputStrides[i];
+ }
+ if (index != index / m_fastStrides[NumDims-1] * m_strides[NumDims-1]) {
+ return false;
+ }
+ *inputIndex += index / m_strides[NumDims - 1];
+ }
+ return true;
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE CoeffReturnType coeff(Index index) const
+ {
+ Index inputIndex = 0;
+ if (getInputIndex(index, &inputIndex)) {
+ return m_impl.coeff(inputIndex);
+ } else {
+ return Scalar(0);
+ }
+ }
+
+ // TODO(yangke): optimize this function so that we can detect and produce
+ // all-zero packets
+ template<int LoadMode>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE PacketReturnType packet(Index index) const
+ {
+ EIGEN_STATIC_ASSERT((PacketSize > 1), YOU_MADE_A_PROGRAMMING_MISTAKE)
+ eigen_assert(index+PacketSize-1 < dimensions().TotalSize());
+
+ EIGEN_ALIGN_MAX std::remove_const_t<CoeffReturnType> values[PacketSize];
+ EIGEN_UNROLL_LOOP
+ for (int i = 0; i < PacketSize; ++i) {
+ values[i] = coeff(index+i);
+ }
+ PacketReturnType rslt = internal::pload<PacketReturnType>(values);
+ return rslt;
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorOpCost costPerCoeff(bool vectorized) const {
+ const double compute_cost = NumDims * (3 * TensorOpCost::DivCost<Index>() +
+ 3 * TensorOpCost::MulCost<Index>() +
+ 2 * TensorOpCost::AddCost<Index>());
+ const double input_size = m_impl.dimensions().TotalSize();
+ const double output_size = m_dimensions.TotalSize();
+ if (output_size == 0)
+ return TensorOpCost();
+ return m_impl.costPerCoeff(vectorized) +
+ TensorOpCost(sizeof(CoeffReturnType) * input_size / output_size, 0,
+ compute_cost, vectorized, PacketSize);
+ }
+
+ EIGEN_DEVICE_FUNC EvaluatorPointerType data() const { return NULL; }
+
+#ifdef EIGEN_USE_SYCL
+ // binding placeholder accessors to a command group handler for SYCL
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void bind(cl::sycl::handler &cgh) const {
+ m_impl.bind(cgh);
+ }
+#endif
+
+ protected:
+ Dimensions m_dimensions;
+ array<Index, NumDims> m_outputStrides;
+ array<Index, NumDims> m_inputStrides;
+ TensorEvaluator<ArgType, Device> m_impl;
+ const Strides m_strides;
+ array<internal::TensorIntDivisor<Index>, NumDims> m_fastStrides;
+};
+
+} // end namespace Eigen
+
+#endif // EIGEN_CXX11_TENSOR_TENSOR_INFLATION_H
diff --git a/unsupported/Eigen/CXX11/src/Tensor/TensorInitializer.h b/unsupported/Eigen/CXX11/src/Tensor/TensorInitializer.h
new file mode 100644
index 0000000..d8d977c
--- /dev/null
+++ b/unsupported/Eigen/CXX11/src/Tensor/TensorInitializer.h
@@ -0,0 +1,80 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_CXX11_TENSOR_TENSOR_INITIALIZER_H
+#define EIGEN_CXX11_TENSOR_TENSOR_INITIALIZER_H
+
+#include <initializer_list>
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+/** \class TensorInitializer
+ * \ingroup CXX11_Tensor_Module
+ *
+ * \brief Helper template to initialize Tensors from std::initializer_lists.
+ */
+namespace internal {
+
+template <typename Derived, int N>
+struct Initializer {
+ typedef std::initializer_list<
+ typename Initializer<Derived, N - 1>::InitList> InitList;
+
+ static void run(TensorEvaluator<Derived, DefaultDevice>& tensor,
+ Eigen::array<typename traits<Derived>::Index, traits<Derived>::NumDimensions>* indices,
+ const InitList& vals) {
+ int i = 0;
+ for (const auto& v : vals) {
+ (*indices)[traits<Derived>::NumDimensions - N] = i++;
+ Initializer<Derived, N - 1>::run(tensor, indices, v);
+ }
+ }
+};
+
+template <typename Derived>
+struct Initializer<Derived, 1> {
+ typedef std::initializer_list<typename traits<Derived>::Scalar> InitList;
+
+ static void run(TensorEvaluator<Derived, DefaultDevice>& tensor,
+ Eigen::array<typename traits<Derived>::Index, traits<Derived>::NumDimensions>* indices,
+ const InitList& vals) {
+ int i = 0;
+ // There is likely a faster way to do that than iterating.
+ for (const auto& v : vals) {
+ (*indices)[traits<Derived>::NumDimensions - 1] = i++;
+ tensor.coeffRef(*indices) = v;
+ }
+ }
+};
+
+template <typename Derived>
+struct Initializer<Derived, 0> {
+ typedef typename traits<Derived>::Scalar InitList;
+
+ static void run(TensorEvaluator<Derived, DefaultDevice>& tensor,
+ Eigen::array<typename traits<Derived>::Index, traits<Derived>::NumDimensions>*,
+ const InitList& v) {
+ tensor.coeffRef(0) = v;
+ }
+};
+
+
+template <typename Derived, int N>
+void initialize_tensor(TensorEvaluator<Derived, DefaultDevice>& tensor,
+ const typename Initializer<Derived, traits<Derived>::NumDimensions>::InitList& vals) {
+ Eigen::array<typename traits<Derived>::Index, traits<Derived>::NumDimensions> indices;
+ Initializer<Derived, traits<Derived>::NumDimensions>::run(tensor, &indices, vals);
+}
+
+} // namespace internal
+} // namespace Eigen
+
+#endif // EIGEN_CXX11_TENSOR_TENSOR_INITIALIZER_H
diff --git a/unsupported/Eigen/CXX11/src/Tensor/TensorIntDiv.h b/unsupported/Eigen/CXX11/src/Tensor/TensorIntDiv.h
new file mode 100644
index 0000000..a921fea
--- /dev/null
+++ b/unsupported/Eigen/CXX11/src/Tensor/TensorIntDiv.h
@@ -0,0 +1,261 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_CXX11_TENSOR_TENSOR_INTDIV_H
+#define EIGEN_CXX11_TENSOR_TENSOR_INTDIV_H
+
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+/** \internal
+ *
+ * \class TensorIntDiv
+ * \ingroup CXX11_Tensor_Module
+ *
+ * \brief Fast integer division by a constant.
+ *
+ * See the paper from Granlund and Montgomery for explanation.
+ * (at https://doi.org/10.1145/773473.178249)
+ *
+ * \sa Tensor
+ */
+
+namespace internal {
+
+ // Note: result is undefined if val == 0
+ template <typename T>
+ EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
+ std::enable_if_t<sizeof(T)==4,int> count_leading_zeros(const T val)
+ {
+#ifdef EIGEN_GPU_COMPILE_PHASE
+ return __clz(val);
+#elif defined(SYCL_DEVICE_ONLY)
+ return cl::sycl::clz(val);
+#elif EIGEN_COMP_MSVC
+ unsigned long index;
+ _BitScanReverse(&index, val);
+ return 31 - index;
+#else
+ EIGEN_STATIC_ASSERT(sizeof(unsigned long long) == 8, YOU_MADE_A_PROGRAMMING_MISTAKE);
+ return __builtin_clz(static_cast<uint32_t>(val));
+#endif
+ }
+
+ template <typename T>
+ EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
+ std::enable_if_t<sizeof(T)==8,int> count_leading_zeros(const T val)
+ {
+#ifdef EIGEN_GPU_COMPILE_PHASE
+ return __clzll(val);
+#elif defined(SYCL_DEVICE_ONLY)
+ return static_cast<int>(cl::sycl::clz(val));
+#elif EIGEN_COMP_MSVC && EIGEN_ARCH_x86_64
+ unsigned long index;
+ _BitScanReverse64(&index, val);
+ return 63 - index;
+#elif EIGEN_COMP_MSVC
+ // MSVC's _BitScanReverse64 is not available for 32bits builds.
+ unsigned int lo = (unsigned int)(val&0xffffffff);
+ unsigned int hi = (unsigned int)((val>>32)&0xffffffff);
+ int n;
+ if(hi==0)
+ n = 32 + count_leading_zeros<unsigned int>(lo);
+ else
+ n = count_leading_zeros<unsigned int>(hi);
+ return n;
+#else
+ EIGEN_STATIC_ASSERT(sizeof(unsigned long long) == 8, YOU_MADE_A_PROGRAMMING_MISTAKE);
+ return __builtin_clzll(static_cast<uint64_t>(val));
+#endif
+ }
+
+ template <typename T>
+ struct UnsignedTraits {
+ typedef std::conditional_t<sizeof(T) == 8, uint64_t, uint32_t> type;
+ };
+
+ template <typename T>
+ struct DividerTraits {
+ typedef typename UnsignedTraits<T>::type type;
+ static constexpr int N = sizeof(T) * 8;
+ };
+
+ template <typename T>
+ EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE uint32_t muluh(const uint32_t a, const T b) {
+#if defined(EIGEN_GPU_COMPILE_PHASE)
+ return __umulhi(a, b);
+#elif defined(SYCL_DEVICE_ONLY)
+ return cl::sycl::mul_hi(a, static_cast<uint32_t>(b));
+#else
+ return (static_cast<uint64_t>(a) * b) >> 32;
+#endif
+ }
+
+ template <typename T>
+ EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE uint64_t muluh(const uint64_t a, const T b) {
+#if defined(EIGEN_GPU_COMPILE_PHASE)
+ return __umul64hi(a, b);
+#elif defined(SYCL_DEVICE_ONLY)
+ return cl::sycl::mul_hi(a, static_cast<uint64_t>(b));
+#elif EIGEN_HAS_BUILTIN_INT128
+ __uint128_t v = static_cast<__uint128_t>(a) * static_cast<__uint128_t>(b);
+ return static_cast<uint64_t>(v >> 64);
+#else
+ return (TensorUInt128<static_val<0>, uint64_t>(a) * TensorUInt128<static_val<0>, uint64_t>(b)).upper();
+#endif
+ }
+
+ template <int N, typename T>
+ struct DividerHelper {
+ static EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE uint32_t computeMultiplier(const int log_div, const T divider) {
+ EIGEN_STATIC_ASSERT(N == 32, YOU_MADE_A_PROGRAMMING_MISTAKE);
+ return static_cast<uint32_t>((static_cast<uint64_t>(1) << (N+log_div)) / divider - (static_cast<uint64_t>(1) << N) + 1);
+ }
+ };
+
+ template <typename T>
+ struct DividerHelper<64, T> {
+ static EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE uint64_t computeMultiplier(const int log_div, const T divider) {
+#if EIGEN_HAS_BUILTIN_INT128 && !defined(EIGEN_GPU_COMPILE_PHASE) && !defined(SYCL_DEVICE_ONLY)
+ return static_cast<uint64_t>((static_cast<__uint128_t>(1) << (64+log_div)) / static_cast<__uint128_t>(divider) - (static_cast<__uint128_t>(1) << 64) + 1);
+#else
+ const uint64_t shift = 1ULL << log_div;
+ TensorUInt128<uint64_t, uint64_t> result = TensorUInt128<uint64_t, static_val<0> >(shift, 0) / TensorUInt128<static_val<0>, uint64_t>(divider)
+ - TensorUInt128<static_val<1>, static_val<0> >(1, 0)
+ + TensorUInt128<static_val<0>, static_val<1> >(1);
+ return static_cast<uint64_t>(result);
+#endif
+ }
+ };
+
+template <typename T, bool div_gt_one = false>
+struct TensorIntDivisor {
+ public:
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorIntDivisor() {
+ multiplier = 0;
+ shift1 = 0;
+ shift2 = 0;
+ }
+
+ // Must have 0 < divider < 2^31. This is relaxed to
+ // 0 < divider < 2^63 when using 64-bit indices on platforms that support
+ // the __uint128_t type.
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorIntDivisor(const T divider) {
+ const int N = DividerTraits<T>::N;
+ eigen_assert(static_cast<typename UnsignedTraits<T>::type>(divider) < NumTraits<UnsignedType>::highest()/2);
+ eigen_assert(divider > 0);
+
+ // fast ln2
+ const int leading_zeros = count_leading_zeros(static_cast<UnsignedType>(divider));
+ int log_div = N - leading_zeros;
+ // if divider is a power of two then log_div is 1 more than it should be.
+ if ((static_cast<typename UnsignedTraits<T>::type>(1) << (log_div-1)) == static_cast<typename UnsignedTraits<T>::type>(divider))
+ log_div--;
+
+ multiplier = DividerHelper<N, T>::computeMultiplier(log_div, divider);
+ shift1 = log_div > 1 ? 1 : log_div;
+ shift2 = log_div > 1 ? log_div-1 : 0;
+ }
+
+ // Must have 0 <= numerator. On platforms that don't support the __uint128_t
+ // type numerator should also be less than 2^32-1.
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE T divide(const T numerator) const {
+ eigen_assert(static_cast<typename UnsignedTraits<T>::type>(numerator) < NumTraits<UnsignedType>::highest()/2);
+ //eigen_assert(numerator >= 0); // this is implicitly asserted by the line above
+
+ UnsignedType t1 = muluh(multiplier, numerator);
+ UnsignedType t = (static_cast<UnsignedType>(numerator) - t1) >> shift1;
+ return (t1 + t) >> shift2;
+ }
+
+ private:
+ typedef typename DividerTraits<T>::type UnsignedType;
+ UnsignedType multiplier;
+ int32_t shift1;
+ int32_t shift2;
+};
+
+
+// Optimized version for signed 32 bit integers.
+// Derived from Hacker's Delight.
+// Only works for divisors strictly greater than one
+template <>
+class TensorIntDivisor<int32_t, true> {
+ public:
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorIntDivisor() {
+ magic = 0;
+ shift = 0;
+ }
+ // Must have 2 <= divider
+ EIGEN_DEVICE_FUNC TensorIntDivisor(int32_t divider) {
+ eigen_assert(divider >= 2);
+ calcMagic(divider);
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE int divide(const int32_t n) const {
+#ifdef EIGEN_GPU_COMPILE_PHASE
+ return (__umulhi(magic, n) >> shift);
+#elif defined(SYCL_DEVICE_ONLY)
+ return (cl::sycl::mul_hi(magic, static_cast<uint32_t>(n)) >> shift);
+#else
+ uint64_t v = static_cast<uint64_t>(magic) * static_cast<uint64_t>(n);
+ return (static_cast<uint32_t>(v >> 32) >> shift);
+#endif
+ }
+
+private:
+ // Compute the magic numbers. See Hacker's Delight section 10 for an in
+ // depth explanation.
+ EIGEN_DEVICE_FUNC void calcMagic(int32_t d) {
+ const unsigned two31 = 0x80000000; // 2**31.
+ unsigned ad = d;
+ unsigned t = two31 + (ad >> 31);
+ unsigned anc = t - 1 - t%ad; // Absolute value of nc.
+ int p = 31; // Init. p.
+ unsigned q1 = two31/anc; // Init. q1 = 2**p/|nc|.
+ unsigned r1 = two31 - q1*anc; // Init. r1 = rem(2**p, |nc|).
+ unsigned q2 = two31/ad; // Init. q2 = 2**p/|d|.
+ unsigned r2 = two31 - q2*ad; // Init. r2 = rem(2**p, |d|).
+ unsigned delta = 0;
+ do {
+ p = p + 1;
+ q1 = 2*q1; // Update q1 = 2**p/|nc|.
+ r1 = 2*r1; // Update r1 = rem(2**p, |nc|).
+ if (r1 >= anc) { // (Must be an unsigned
+ q1 = q1 + 1; // comparison here).
+ r1 = r1 - anc;}
+ q2 = 2*q2; // Update q2 = 2**p/|d|.
+ r2 = 2*r2; // Update r2 = rem(2**p, |d|).
+ if (r2 >= ad) { // (Must be an unsigned
+ q2 = q2 + 1; // comparison here).
+ r2 = r2 - ad;}
+ delta = ad - r2;
+ } while (q1 < delta || (q1 == delta && r1 == 0));
+
+ magic = (unsigned)(q2 + 1);
+ shift = p - 32;
+ }
+
+ uint32_t magic;
+ int32_t shift;
+};
+
+
+template <typename T, bool div_gt_one>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE T operator / (const T& numerator, const TensorIntDivisor<T, div_gt_one>& divisor) {
+ return divisor.divide(numerator);
+}
+
+
+} // end namespace internal
+} // end namespace Eigen
+
+#endif // EIGEN_CXX11_TENSOR_TENSOR_INTDIV_H
diff --git a/unsupported/Eigen/CXX11/src/Tensor/TensorLayoutSwap.h b/unsupported/Eigen/CXX11/src/Tensor/TensorLayoutSwap.h
new file mode 100644
index 0000000..d12bd6d
--- /dev/null
+++ b/unsupported/Eigen/CXX11/src/Tensor/TensorLayoutSwap.h
@@ -0,0 +1,218 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_CXX11_TENSOR_TENSOR_LAYOUT_SWAP_H
+#define EIGEN_CXX11_TENSOR_TENSOR_LAYOUT_SWAP_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+/** \class TensorLayoutSwap
+ * \ingroup CXX11_Tensor_Module
+ *
+ * \brief Swap the layout from col-major to row-major, or row-major
+ * to col-major, and invert the order of the dimensions.
+ *
+ * Beware: the dimensions are reversed by this operation. If you want to
+ * preserve the ordering of the dimensions, you need to combine this
+ * operation with a shuffle.
+ *
+ * \example:
+ * Tensor<float, 2, ColMajor> input(2, 4);
+ * Tensor<float, 2, RowMajor> output = input.swap_layout();
+ * eigen_assert(output.dimension(0) == 4);
+ * eigen_assert(output.dimension(1) == 2);
+ *
+ * array<int, 2> shuffle(1, 0);
+ * output = input.swap_layout().shuffle(shuffle);
+ * eigen_assert(output.dimension(0) == 2);
+ * eigen_assert(output.dimension(1) == 4);
+ *
+ */
+namespace internal {
+template<typename XprType>
+struct traits<TensorLayoutSwapOp<XprType> > : public traits<XprType>
+{
+ typedef typename XprType::Scalar Scalar;
+ typedef traits<XprType> XprTraits;
+ typedef typename XprTraits::StorageKind StorageKind;
+ typedef typename XprTraits::Index Index;
+ typedef typename XprType::Nested Nested;
+ typedef std::remove_reference_t<Nested> Nested_;
+ static constexpr int NumDimensions = traits<XprType>::NumDimensions;
+ static constexpr int Layout = (traits<XprType>::Layout == ColMajor) ? RowMajor : ColMajor;
+ typedef typename XprTraits::PointerType PointerType;
+};
+
+template<typename XprType>
+struct eval<TensorLayoutSwapOp<XprType>, Eigen::Dense>
+{
+ typedef const TensorLayoutSwapOp<XprType>& type;
+};
+
+template<typename XprType>
+struct nested<TensorLayoutSwapOp<XprType>, 1, typename eval<TensorLayoutSwapOp<XprType> >::type>
+{
+ typedef TensorLayoutSwapOp<XprType> type;
+};
+
+} // end namespace internal
+
+
+
+template<typename XprType>
+class TensorLayoutSwapOp : public TensorBase<TensorLayoutSwapOp<XprType>, WriteAccessors>
+{
+ public:
+ typedef TensorBase<TensorLayoutSwapOp<XprType>, WriteAccessors> Base;
+ typedef typename Eigen::internal::traits<TensorLayoutSwapOp>::Scalar Scalar;
+ typedef typename Eigen::NumTraits<Scalar>::Real RealScalar;
+ typedef std::remove_const_t<typename XprType::CoeffReturnType> CoeffReturnType;
+ typedef typename Eigen::internal::nested<TensorLayoutSwapOp>::type Nested;
+ typedef typename Eigen::internal::traits<TensorLayoutSwapOp>::StorageKind StorageKind;
+ typedef typename Eigen::internal::traits<TensorLayoutSwapOp>::Index Index;
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorLayoutSwapOp(const XprType& expr)
+ : m_xpr(expr) {}
+
+ EIGEN_DEVICE_FUNC
+ const internal::remove_all_t<typename XprType::Nested>&
+ expression() const { return m_xpr; }
+
+ EIGEN_TENSOR_INHERIT_ASSIGNMENT_OPERATORS(TensorLayoutSwapOp)
+ protected:
+ typename XprType::Nested m_xpr;
+};
+
+
+// Eval as rvalue
+template<typename ArgType, typename Device>
+struct TensorEvaluator<const TensorLayoutSwapOp<ArgType>, Device>
+{
+ typedef TensorLayoutSwapOp<ArgType> XprType;
+ typedef typename XprType::Index Index;
+ static constexpr int NumDims = internal::array_size<typename TensorEvaluator<ArgType, Device>::Dimensions>::value;
+ typedef DSizes<Index, NumDims> Dimensions;
+
+ static constexpr int Layout = (TensorEvaluator<ArgType, Device>::Layout == static_cast<int>(ColMajor)) ? RowMajor : ColMajor;
+ enum {
+ IsAligned = TensorEvaluator<ArgType, Device>::IsAligned,
+ PacketAccess = TensorEvaluator<ArgType, Device>::PacketAccess,
+ BlockAccess = false,
+ PreferBlockAccess = TensorEvaluator<ArgType, Device>::PreferBlockAccess,
+ CoordAccess = false, // to be implemented
+ RawAccess = TensorEvaluator<ArgType, Device>::RawAccess
+ };
+
+ //===- Tensor block evaluation strategy (see TensorBlock.h) -------------===//
+ typedef internal::TensorBlockNotImplemented TensorBlock;
+ //===--------------------------------------------------------------------===//
+
+ EIGEN_STRONG_INLINE TensorEvaluator(const XprType& op, const Device& device)
+ : m_impl(op.expression(), device)
+ {
+ for(int i = 0; i < NumDims; ++i) {
+ m_dimensions[i] = m_impl.dimensions()[NumDims-1-i];
+ }
+ }
+
+#ifdef EIGEN_USE_SYCL
+ // binding placeholder accessors to a command group handler for SYCL
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void bind(cl::sycl::handler &cgh) const {
+ m_impl.bind(cgh);
+ }
+#endif
+
+ typedef typename XprType::Scalar Scalar;
+ typedef typename XprType::CoeffReturnType CoeffReturnType;
+ typedef typename PacketType<CoeffReturnType, Device>::type PacketReturnType;
+ typedef StorageMemory<CoeffReturnType, Device> Storage;
+ typedef typename Storage::Type EvaluatorPointerType;
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Dimensions& dimensions() const { return m_dimensions; }
+
+ EIGEN_STRONG_INLINE bool evalSubExprsIfNeeded(EvaluatorPointerType data) {
+ return m_impl.evalSubExprsIfNeeded(data);
+ }
+ EIGEN_STRONG_INLINE void cleanup() {
+ m_impl.cleanup();
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE CoeffReturnType coeff(Index index) const
+ {
+ return m_impl.coeff(index);
+ }
+
+ template<int LoadMode>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE PacketReturnType packet(Index index) const
+ {
+ return m_impl.template packet<LoadMode>(index);
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorOpCost costPerCoeff(bool vectorized) const {
+ return m_impl.costPerCoeff(vectorized);
+ }
+
+ EIGEN_DEVICE_FUNC typename Storage::Type data() const {
+ return constCast(m_impl.data());
+ }
+
+ const TensorEvaluator<ArgType, Device>& impl() const { return m_impl; }
+
+ protected:
+ TensorEvaluator<ArgType, Device> m_impl;
+ Dimensions m_dimensions;
+};
+
+
+// Eval as lvalue
+template<typename ArgType, typename Device>
+ struct TensorEvaluator<TensorLayoutSwapOp<ArgType>, Device>
+ : public TensorEvaluator<const TensorLayoutSwapOp<ArgType>, Device>
+{
+ typedef TensorEvaluator<const TensorLayoutSwapOp<ArgType>, Device> Base;
+ typedef TensorLayoutSwapOp<ArgType> XprType;
+
+ static constexpr int Layout = (TensorEvaluator<ArgType, Device>::Layout == static_cast<int>(ColMajor)) ? RowMajor : ColMajor;
+ enum {
+ IsAligned = TensorEvaluator<ArgType, Device>::IsAligned,
+ PacketAccess = TensorEvaluator<ArgType, Device>::PacketAccess,
+ BlockAccess = false,
+ PreferBlockAccess = TensorEvaluator<ArgType, Device>::PreferBlockAccess,
+ CoordAccess = false // to be implemented
+ };
+
+ //===- Tensor block evaluation strategy (see TensorBlock.h) -------------===//
+ typedef internal::TensorBlockNotImplemented TensorBlock;
+ //===--------------------------------------------------------------------===//
+
+ EIGEN_STRONG_INLINE TensorEvaluator(const XprType& op, const Device& device)
+ : Base(op, device)
+ { }
+
+ typedef typename XprType::Index Index;
+ typedef typename XprType::Scalar Scalar;
+ typedef typename XprType::CoeffReturnType CoeffReturnType;
+ typedef typename PacketType<CoeffReturnType, Device>::type PacketReturnType;
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE CoeffReturnType& coeffRef(Index index)
+ {
+ return this->m_impl.coeffRef(index);
+ }
+ template <int StoreMode> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ void writePacket(Index index, const PacketReturnType& x)
+ {
+ this->m_impl.template writePacket<StoreMode>(index, x);
+ }
+};
+
+} // end namespace Eigen
+
+#endif // EIGEN_CXX11_TENSOR_TENSOR_LAYOUT_SWAP_H
diff --git a/unsupported/Eigen/CXX11/src/Tensor/TensorMacros.h b/unsupported/Eigen/CXX11/src/Tensor/TensorMacros.h
new file mode 100644
index 0000000..7d8814a
--- /dev/null
+++ b/unsupported/Eigen/CXX11/src/Tensor/TensorMacros.h
@@ -0,0 +1,84 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2015 Benoit Steiner <benoit.steiner.goog@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_CXX11_TENSOR_TENSOR_META_MACROS_H
+#define EIGEN_CXX11_TENSOR_TENSOR_META_MACROS_H
+
+
+/** use this macro in sfinae selection in templated functions
+ *
+ * template<typename T,
+ * std::enable_if_t< isBanana<T>::value , int > = 0
+ * >
+ * void foo(){}
+ *
+ * becomes =>
+ *
+ * template<typename TopoType,
+ * SFINAE_ENABLE_IF( isBanana<T>::value )
+ * >
+ * void foo(){}
+ */
+
+#define EIGEN_SFINAE_ENABLE_IF( __condition__ ) \
+ std::enable_if_t< ( __condition__ ) , int > = 0
+
+// Define a macro to use a reference on the host but a value on the device
+#if defined(SYCL_DEVICE_ONLY)
+ #define EIGEN_DEVICE_REF
+#else
+ #define EIGEN_DEVICE_REF &
+#endif
+
+// Define a macro for catching SYCL exceptions if exceptions are enabled
+#define EIGEN_SYCL_TRY_CATCH(X) \
+ do { \
+ EIGEN_TRY {X;} \
+ EIGEN_CATCH(const cl::sycl::exception& e) { \
+ EIGEN_THROW_X(std::runtime_error("SYCL exception at " + \
+ std::string(__FILE__) + ":" + \
+ std::to_string(__LINE__) + "\n" + \
+ e.what())); \
+ } \
+ } while (false)
+
+// Define a macro if local memory flags are unset or one of them is set
+// Setting both flags is the same as unsetting them
+#if (!defined(EIGEN_SYCL_LOCAL_MEM) && !defined(EIGEN_SYCL_NO_LOCAL_MEM)) || \
+ (defined(EIGEN_SYCL_LOCAL_MEM) && defined(EIGEN_SYCL_NO_LOCAL_MEM))
+ #define EIGEN_SYCL_LOCAL_MEM_UNSET_OR_ON 1
+ #define EIGEN_SYCL_LOCAL_MEM_UNSET_OR_OFF 1
+#elif defined(EIGEN_SYCL_LOCAL_MEM) && !defined(EIGEN_SYCL_NO_LOCAL_MEM)
+ #define EIGEN_SYCL_LOCAL_MEM_UNSET_OR_ON 1
+#elif !defined(EIGEN_SYCL_LOCAL_MEM) && defined(EIGEN_SYCL_NO_LOCAL_MEM)
+ #define EIGEN_SYCL_LOCAL_MEM_UNSET_OR_OFF 1
+#endif
+
+#if EIGEN_COMP_CLANG // workaround clang bug (see http://forum.kde.org/viewtopic.php?f=74&t=102653)
+ #define EIGEN_TENSOR_INHERIT_ASSIGNMENT_EQUAL_OPERATOR(Derived) \
+ using Base::operator =; \
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& operator=(const Derived& other) { Base::operator=(other); return *this; } \
+ template <typename OtherDerived> \
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& operator=(const OtherDerived& other) { Base::operator=(other); return *this; }
+#else
+ #define EIGEN_TENSOR_INHERIT_ASSIGNMENT_EQUAL_OPERATOR(Derived) \
+ EIGEN_INHERIT_ASSIGNMENT_EQUAL_OPERATOR(Derived)
+#endif
+
+/** \internal
+ * \brief Macro to manually inherit assignment operators.
+ * This is necessary, because the implicitly defined assignment operator gets deleted when a custom operator= is defined.
+ * This also inherits template<OtherDerived> operator=(const OtherDerived&) assignments.
+ * With C++11 or later this also default-implements the copy-constructor
+ */
+#define EIGEN_TENSOR_INHERIT_ASSIGNMENT_OPERATORS(Derived) \
+ EIGEN_TENSOR_INHERIT_ASSIGNMENT_EQUAL_OPERATOR(Derived) \
+ EIGEN_DEFAULT_COPY_CONSTRUCTOR(Derived)
+
+#endif
diff --git a/unsupported/Eigen/CXX11/src/Tensor/TensorMap.h b/unsupported/Eigen/CXX11/src/Tensor/TensorMap.h
new file mode 100644
index 0000000..7a601ca
--- /dev/null
+++ b/unsupported/Eigen/CXX11/src/Tensor/TensorMap.h
@@ -0,0 +1,211 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_CXX11_TENSOR_TENSOR_MAP_H
+#define EIGEN_CXX11_TENSOR_TENSOR_MAP_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+// FIXME use proper doxygen documentation (e.g. \tparam MakePointer_)
+
+/** \class TensorMap
+ * \ingroup CXX11_Tensor_Module
+ *
+ * \brief A tensor expression mapping an existing array of data.
+ *
+ */
+/// `template <class> class MakePointer_` is added to convert the host pointer to the device pointer.
+/// It is added due to the fact that for our device compiler `T*` is not allowed.
+/// If we wanted to use the same Evaluator functions we have to convert that type to our pointer `T`.
+/// This is done through our `MakePointer_` class. By default the Type in the `MakePointer_<T>` is `T*` .
+/// Therefore, by adding the default value, we managed to convert the type and it does not break any
+/// existing code as its default value is `T*`.
+template<typename PlainObjectType, int Options_, template <class> class MakePointer_> class TensorMap : public TensorBase<TensorMap<PlainObjectType, Options_, MakePointer_> >
+{
+ public:
+ typedef TensorMap<PlainObjectType, Options_, MakePointer_> Self;
+ typedef TensorBase<TensorMap<PlainObjectType, Options_, MakePointer_> > Base;
+ #ifdef EIGEN_USE_SYCL
+ typedef std::remove_reference_t<typename Eigen::internal::nested<Self>::type> Nested;
+ #else
+ typedef typename Eigen::internal::nested<Self>::type Nested;
+ #endif
+ typedef typename internal::traits<PlainObjectType>::StorageKind StorageKind;
+ typedef typename internal::traits<PlainObjectType>::Index Index;
+ typedef typename internal::traits<PlainObjectType>::Scalar Scalar;
+ typedef typename NumTraits<Scalar>::Real RealScalar;
+ typedef typename PlainObjectType::Base::CoeffReturnType CoeffReturnType;
+
+ typedef typename MakePointer_<Scalar>::Type PointerType;
+ typedef typename MakePointer_<Scalar>::ConstType PointerConstType;
+
+ // WARN: PointerType still can be a pointer to const (const Scalar*), for
+ // example in TensorMap<Tensor<const Scalar, ...>> expression. This type of
+ // expression should be illegal, but adding this restriction is not possible
+ // in practice (see https://bitbucket.org/eigen/eigen/pull-requests/488).
+ typedef std::conditional_t<
+ bool(internal::is_lvalue<PlainObjectType>::value),
+ PointerType, // use simple pointer in lvalue expressions
+ PointerConstType // use const pointer in rvalue expressions
+ > StoragePointerType;
+
+ // If TensorMap was constructed over rvalue expression (e.g. const Tensor),
+ // we should return a reference to const from operator() (and others), even
+ // if TensorMap itself is not const.
+ typedef std::conditional_t<
+ bool(internal::is_lvalue<PlainObjectType>::value),
+ Scalar&,
+ const Scalar&
+ > StorageRefType;
+
+ static constexpr int Options = Options_;
+
+ static constexpr Index NumIndices = PlainObjectType::NumIndices;
+ typedef typename PlainObjectType::Dimensions Dimensions;
+
+ static constexpr int Layout = PlainObjectType::Layout;
+ enum {
+ IsAligned = ((int(Options_)&Aligned)==Aligned),
+ CoordAccess = true,
+ RawAccess = true
+ };
+
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE TensorMap(StoragePointerType dataPtr) : m_data(dataPtr), m_dimensions() {
+ // The number of dimensions used to construct a tensor must be equal to the rank of the tensor.
+ EIGEN_STATIC_ASSERT((0 == NumIndices || NumIndices == Dynamic), YOU_MADE_A_PROGRAMMING_MISTAKE)
+ }
+
+ template<typename... IndexTypes> EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE TensorMap(StoragePointerType dataPtr, Index firstDimension, IndexTypes... otherDimensions) : m_data(dataPtr), m_dimensions(firstDimension, otherDimensions...) {
+ // The number of dimensions used to construct a tensor must be equal to the rank of the tensor.
+ EIGEN_STATIC_ASSERT((sizeof...(otherDimensions) + 1 == NumIndices || NumIndices == Dynamic), YOU_MADE_A_PROGRAMMING_MISTAKE)
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorMap(StoragePointerType dataPtr, const array<Index, NumIndices>& dimensions)
+ : m_data(dataPtr), m_dimensions(dimensions)
+ { }
+
+ template <typename Dimensions>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorMap(StoragePointerType dataPtr, const Dimensions& dimensions)
+ : m_data(dataPtr), m_dimensions(dimensions)
+ { }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorMap(PlainObjectType& tensor)
+ : m_data(tensor.data()), m_dimensions(tensor.dimensions())
+ { }
+
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE Index rank() const { return m_dimensions.rank(); }
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE Index dimension(Index n) const { return m_dimensions[n]; }
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE const Dimensions& dimensions() const { return m_dimensions; }
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE Index size() const { return m_dimensions.TotalSize(); }
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE StoragePointerType data() { return m_data; }
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE StoragePointerType data() const { return m_data; }
+
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE StorageRefType operator()(const array<Index, NumIndices>& indices) const
+ {
+ // eigen_assert(checkIndexRange(indices));
+ if (PlainObjectType::Options&RowMajor) {
+ const Index index = m_dimensions.IndexOfRowMajor(indices);
+ return m_data[index];
+ } else {
+ const Index index = m_dimensions.IndexOfColMajor(indices);
+ return m_data[index];
+ }
+ }
+
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE StorageRefType operator()() const
+ {
+ EIGEN_STATIC_ASSERT(NumIndices == 0, YOU_MADE_A_PROGRAMMING_MISTAKE)
+ return m_data[0];
+ }
+
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE StorageRefType operator()(Index index) const
+ {
+ eigen_internal_assert(index >= 0 && index < size());
+ return m_data[index];
+ }
+
+ template<typename... IndexTypes> EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE StorageRefType operator()(Index firstIndex, Index secondIndex, IndexTypes... otherIndices) const
+ {
+ EIGEN_STATIC_ASSERT(sizeof...(otherIndices) + 2 == NumIndices, YOU_MADE_A_PROGRAMMING_MISTAKE)
+ eigen_assert(internal::all((Eigen::NumTraits<Index>::highest() >= otherIndices)...));
+ if (PlainObjectType::Options&RowMajor) {
+ const Index index = m_dimensions.IndexOfRowMajor(array<Index, NumIndices>{{firstIndex, secondIndex, otherIndices...}});
+ return m_data[index];
+ } else {
+ const Index index = m_dimensions.IndexOfColMajor(array<Index, NumIndices>{{firstIndex, secondIndex, otherIndices...}});
+ return m_data[index];
+ }
+ }
+
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE StorageRefType operator()(const array<Index, NumIndices>& indices)
+ {
+ // eigen_assert(checkIndexRange(indices));
+ if (PlainObjectType::Options&RowMajor) {
+ const Index index = m_dimensions.IndexOfRowMajor(indices);
+ return m_data[index];
+ } else {
+ const Index index = m_dimensions.IndexOfColMajor(indices);
+ return m_data[index];
+ }
+ }
+
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE StorageRefType operator()()
+ {
+ EIGEN_STATIC_ASSERT(NumIndices == 0, YOU_MADE_A_PROGRAMMING_MISTAKE)
+ return m_data[0];
+ }
+
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE StorageRefType operator()(Index index)
+ {
+ eigen_internal_assert(index >= 0 && index < size());
+ return m_data[index];
+ }
+
+ template<typename... IndexTypes> EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE StorageRefType operator()(Index firstIndex, Index secondIndex, IndexTypes... otherIndices)
+ {
+ static_assert(sizeof...(otherIndices) + 2 == NumIndices || NumIndices == Dynamic, "Number of indices used to access a tensor coefficient must be equal to the rank of the tensor.");
+ eigen_assert(internal::all((Eigen::NumTraits<Index>::highest() >= otherIndices)...));
+ const std::size_t NumDims = sizeof...(otherIndices) + 2;
+ if (PlainObjectType::Options&RowMajor) {
+ const Index index = m_dimensions.IndexOfRowMajor(array<Index, NumDims>{{firstIndex, secondIndex, otherIndices...}});
+ return m_data[index];
+ } else {
+ const Index index = m_dimensions.IndexOfColMajor(array<Index, NumDims>{{firstIndex, secondIndex, otherIndices...}});
+ return m_data[index];
+ }
+ }
+
+ EIGEN_TENSOR_INHERIT_ASSIGNMENT_OPERATORS(TensorMap)
+
+ private:
+ StoragePointerType m_data;
+ Dimensions m_dimensions;
+};
+
+} // end namespace Eigen
+
+#endif // EIGEN_CXX11_TENSOR_TENSOR_MAP_H
diff --git a/unsupported/Eigen/CXX11/src/Tensor/TensorMeta.h b/unsupported/Eigen/CXX11/src/Tensor/TensorMeta.h
new file mode 100644
index 0000000..3c9a808
--- /dev/null
+++ b/unsupported/Eigen/CXX11/src/Tensor/TensorMeta.h
@@ -0,0 +1,313 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2015 Benoit Steiner <benoit.steiner.goog@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_CXX11_TENSOR_TENSOR_META_H
+#define EIGEN_CXX11_TENSOR_TENSOR_META_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+template<bool cond> struct Cond {};
+
+template<typename T1, typename T2> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
+const T1& choose(Cond<true>, const T1& first, const T2&) {
+ return first;
+}
+
+template<typename T1, typename T2> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
+const T2& choose(Cond<false>, const T1&, const T2& second) {
+ return second;
+}
+
+
+template <typename T, typename X, typename Y>
+EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
+T divup(const X x, const Y y) {
+ // Note: This form is used because it cannot overflow.
+ return static_cast<T>(x == 0 ? 0 : (x - 1) / y + 1);
+}
+
+template <typename T>
+EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
+T divup(const T x, const T y) {
+ // Note: This form is used because it cannot overflow.
+ return static_cast<T>(x == 0 ? 0 : (x - 1) / y + 1);
+}
+
+template <size_t n> struct max_n_1 {
+ static const size_t size = n;
+};
+template <> struct max_n_1<0> {
+ static const size_t size = 1;
+};
+
+
+// Default packet types
+template <typename Scalar, typename Device>
+struct PacketType : internal::packet_traits<Scalar> {
+ typedef typename internal::packet_traits<Scalar>::type type;
+};
+
+// For CUDA packet types when using a GpuDevice
+#if defined(EIGEN_USE_GPU) && defined(EIGEN_HAS_GPU_FP16) && defined(EIGEN_GPU_COMPILE_PHASE)
+
+typedef ulonglong2 Packet4h2;
+template<>
+struct PacketType<half, GpuDevice> {
+ typedef Packet4h2 type;
+ static const int size = 8;
+ enum {
+ HasAdd = 1,
+ HasSub = 1,
+ HasMul = 1,
+ HasNegate = 1,
+ HasAbs = 1,
+ HasArg = 0,
+ HasAbs2 = 0,
+ HasMin = 1,
+ HasMax = 1,
+ HasConj = 0,
+ HasSetLinear = 0,
+ HasBlend = 0,
+
+ HasDiv = 1,
+ HasSqrt = 1,
+ HasRsqrt = 1,
+ HasExp = 1,
+ HasExpm1 = 0,
+ HasLog = 1,
+ HasLog1p = 0,
+ HasLog10 = 0,
+ HasPow = 1,
+ };
+};
+#endif
+
+#if defined(EIGEN_USE_SYCL)
+
+namespace TensorSycl {
+namespace internal {
+
+template <typename Index, Index A, Index B> struct PlusOp {
+ static constexpr Index Value = A + B;
+};
+
+template <typename Index, Index A, Index B> struct DivOp {
+ static constexpr Index Value = A / B;
+};
+
+template <typename Index, Index start, Index end, Index step,
+ template <class Indx, Indx...> class StepOp>
+struct static_for {
+ template <typename UnaryOperator>
+ static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void loop(UnaryOperator op) {
+ op(start);
+ static_for<Index, StepOp<Index, start, step>::Value, end, step,
+ StepOp>::loop(op);
+ }
+};
+template <typename Index, Index end, Index step,
+ template <class Indx, Indx...> class StepOp>
+struct static_for<Index, end, end, step, StepOp> {
+ template <typename UnaryOperator>
+ static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void loop(UnaryOperator) {}
+};
+
+template <typename OutScalar, typename Device, bool Vectorizable>
+struct Vectorise {
+ static constexpr int PacketSize = 1;
+ typedef OutScalar PacketReturnType;
+};
+
+template <typename OutScalar, typename Device>
+struct Vectorise<OutScalar, Device, true> {
+ static constexpr int PacketSize = Eigen::PacketType<OutScalar, Device>::size;
+ typedef typename Eigen::PacketType<OutScalar, Device>::type PacketReturnType;
+};
+
+static EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE Index roundUp(Index x, Index y) {
+ return ((((x) + (y)-1) / (y)) * (y));
+}
+
+} // namespace internal
+} // namespace TensorSycl
+
+template <>
+ struct PacketType<half, SyclDevice> {
+ typedef half type;
+ static const int size = 1;
+ enum {
+ HasAdd = 0,
+ HasSub = 0,
+ HasMul = 0,
+ HasNegate = 0,
+ HasAbs = 0,
+ HasArg = 0,
+ HasAbs2 = 0,
+ HasMin = 0,
+ HasMax = 0,
+ HasConj = 0,
+ HasSetLinear = 0,
+ HasBlend = 0
+ };
+};
+template <typename Scalar>
+struct PacketType<Scalar, SyclDevice> : internal::default_packet_traits {
+ typedef Scalar type;
+ typedef Scalar half;
+ enum {
+ Vectorizable = 0,
+ size = 1,
+ AlignedOnScalar = 0,
+ HasHalfPacket = 0
+ };
+ enum {
+ HasAdd = 0,
+ HasSub = 0,
+ HasMul = 0,
+ HasNegate = 0,
+ HasAbs = 0,
+ HasAbs2 = 0,
+ HasMin = 0,
+ HasMax = 0,
+ HasConj = 0,
+ HasSetLinear = 0
+ };
+
+};
+
+template <typename Scalar>
+struct PacketType<Scalar, const SyclDevice> : PacketType<Scalar, SyclDevice>{};
+
+#ifndef EIGEN_DONT_VECTORIZE_SYCL
+#define PACKET_TYPE(CVQual, Type, val, lengths, DEV)\
+template<> struct PacketType<CVQual Type, DEV> : internal::sycl_packet_traits<val, lengths> \
+{\
+ typedef typename internal::packet_traits<Type>::type type;\
+ typedef typename internal::packet_traits<Type>::half half;\
+};
+
+
+PACKET_TYPE(const, float, 1, 4, SyclDevice)
+PACKET_TYPE(, float, 1, 4, SyclDevice)
+PACKET_TYPE(const, float, 1, 4, const SyclDevice)
+PACKET_TYPE(, float, 1, 4, const SyclDevice)
+
+PACKET_TYPE(const, double, 0, 2, SyclDevice)
+PACKET_TYPE(, double, 0, 2, SyclDevice)
+PACKET_TYPE(const, double, 0, 2, const SyclDevice)
+PACKET_TYPE(, double, 0, 2, const SyclDevice)
+#undef PACKET_TYPE
+
+template<> struct PacketType<half, const SyclDevice>: PacketType<half, SyclDevice>{};
+template<> struct PacketType<const half, const SyclDevice>: PacketType<half, SyclDevice>{};
+#endif
+#endif
+
+// Pair mimics std::pair but works on e.g. nvcc.
+template <typename U, typename V> struct Pair {
+ public:
+ EIGEN_MAKE_ALIGNED_OPERATOR_NEW
+
+ U first;
+ V second;
+
+ typedef U first_type;
+ typedef V second_type;
+
+ EIGEN_CONSTEXPR EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ Pair() : first(), second() {}
+
+ EIGEN_CONSTEXPR EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ Pair(const U& f, const V& s) : first(f), second(s) {}
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ void swap(Pair& rhs) {
+ using numext::swap;
+ swap(first, rhs.first);
+ swap(second, rhs.second);
+ }
+};
+
+template <typename U, typename V>
+EIGEN_CONSTEXPR EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+bool operator==(const Pair<U, V>& x, const Pair<U, V>& y) {
+ return (x.first == y.first && x.second == y.second);
+}
+
+template <typename U, typename V>
+EIGEN_CONSTEXPR EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+bool operator!=(const Pair<U, V>& x, const Pair<U, V>& y) {
+ return !(x == y);
+}
+
+
+// Can't use std::pairs on cuda devices
+template <typename Idx> struct IndexPair {
+ EIGEN_CONSTEXPR EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE IndexPair() : first(0), second(0) {}
+ EIGEN_CONSTEXPR EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE IndexPair(Idx f, Idx s) : first(f), second(s) {}
+
+ EIGEN_DEVICE_FUNC void set(IndexPair<Idx> val) {
+ first = val.first;
+ second = val.second;
+ }
+
+ Idx first;
+ Idx second;
+};
+
+
+namespace internal {
+
+ template<typename IndexType, typename Index, Index First, Index... Is>
+ EIGEN_CONSTEXPR EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ array<Index, 1 + sizeof...(Is)> customIndices2Array(IndexType& idx, numeric_list<Index, First, Is...>) {
+ return { idx[First], idx[Is]... };
+ }
+ template<typename IndexType, typename Index>
+ EIGEN_CONSTEXPR EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ array<Index, 0> customIndices2Array(IndexType&, numeric_list<Index>) {
+ return array<Index, 0>();
+ }
+
+ /** Make an array (for index/dimensions) out of a custom index */
+ template<typename Index, std::size_t NumIndices, typename IndexType>
+ EIGEN_CONSTEXPR EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ array<Index, NumIndices> customIndices2Array(IndexType& idx) {
+ return customIndices2Array(idx, typename gen_numeric_list<Index, NumIndices>::type{});
+ }
+
+
+ template <typename B, typename D>
+ struct is_base_of
+ {
+
+ typedef char (&yes)[1];
+ typedef char (&no)[2];
+
+ template <typename BB, typename DD>
+ struct Host
+ {
+ operator BB*() const;
+ operator DD*();
+ };
+
+ template<typename T>
+ static yes check(D*, T);
+ static no check(B*, int);
+
+ static const bool value = sizeof(check(Host<B,D>(), int())) == sizeof(yes);
+ };
+
+}
+
+} // namespace Eigen
+
+#endif // EIGEN_CXX11_TENSOR_TENSOR_META_H
diff --git a/unsupported/Eigen/CXX11/src/Tensor/TensorMorphing.h b/unsupported/Eigen/CXX11/src/Tensor/TensorMorphing.h
new file mode 100644
index 0000000..0205710
--- /dev/null
+++ b/unsupported/Eigen/CXX11/src/Tensor/TensorMorphing.h
@@ -0,0 +1,1101 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_CXX11_TENSOR_TENSOR_MORPHING_H
+#define EIGEN_CXX11_TENSOR_TENSOR_MORPHING_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+/** \class TensorReshaping
+ * \ingroup CXX11_Tensor_Module
+ *
+ * \brief Tensor reshaping class.
+ *
+ *
+ */
+namespace internal {
+template<typename NewDimensions, typename XprType>
+struct traits<TensorReshapingOp<NewDimensions, XprType> > : public traits<XprType>
+{
+ typedef typename XprType::Scalar Scalar;
+ typedef traits<XprType> XprTraits;
+ typedef typename XprTraits::StorageKind StorageKind;
+ typedef typename XprTraits::Index Index;
+ typedef typename XprType::Nested Nested;
+ typedef std::remove_reference_t<Nested> Nested_;
+ static constexpr int NumDimensions = array_size<NewDimensions>::value;
+ static constexpr int Layout = XprTraits::Layout;
+ typedef typename XprTraits::PointerType PointerType;
+};
+
+template<typename NewDimensions, typename XprType>
+struct eval<TensorReshapingOp<NewDimensions, XprType>, Eigen::Dense>
+{
+ typedef const TensorReshapingOp<NewDimensions, XprType>EIGEN_DEVICE_REF type;
+};
+
+template<typename NewDimensions, typename XprType>
+struct nested<TensorReshapingOp<NewDimensions, XprType>, 1, typename eval<TensorReshapingOp<NewDimensions, XprType> >::type>
+{
+ typedef TensorReshapingOp<NewDimensions, XprType> type;
+};
+
+} // end namespace internal
+
+
+
+template<typename NewDimensions, typename XprType>
+class TensorReshapingOp : public TensorBase<TensorReshapingOp<NewDimensions, XprType>, WriteAccessors>
+{
+ public:
+ typedef TensorBase<TensorReshapingOp<NewDimensions, XprType>, WriteAccessors> Base;
+ typedef typename Eigen::internal::traits<TensorReshapingOp>::Scalar Scalar;
+ typedef std::remove_const_t<typename XprType::CoeffReturnType> CoeffReturnType;
+ typedef typename Eigen::internal::nested<TensorReshapingOp>::type Nested;
+ typedef typename Eigen::internal::traits<TensorReshapingOp>::StorageKind StorageKind;
+ typedef typename Eigen::internal::traits<TensorReshapingOp>::Index Index;
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorReshapingOp(const XprType& expr, const NewDimensions& dims)
+ : m_xpr(expr), m_dims(dims) {}
+
+ EIGEN_DEVICE_FUNC
+ const NewDimensions& dimensions() const { return m_dims; }
+
+ EIGEN_DEVICE_FUNC
+ const internal::remove_all_t<typename XprType::Nested>&
+ expression() const { return m_xpr; }
+
+ EIGEN_TENSOR_INHERIT_ASSIGNMENT_OPERATORS(TensorReshapingOp)
+
+ protected:
+ typename XprType::Nested m_xpr;
+ const NewDimensions m_dims;
+};
+
+
+// Eval as rvalue
+template<typename NewDimensions, typename ArgType, typename Device>
+struct TensorEvaluator<const TensorReshapingOp<NewDimensions, ArgType>, Device>
+{
+ typedef TensorReshapingOp<NewDimensions, ArgType> XprType;
+ typedef NewDimensions Dimensions;
+
+ typedef typename XprType::Index Index;
+ typedef typename XprType::Scalar Scalar;
+ typedef typename XprType::CoeffReturnType CoeffReturnType;
+ typedef typename PacketType<CoeffReturnType, Device>::type PacketReturnType;
+ typedef StorageMemory<CoeffReturnType, Device> Storage;
+ typedef typename Storage::Type EvaluatorPointerType;
+ typedef StorageMemory<std::remove_const_t<CoeffReturnType>, Device> ConstCastStorage;
+
+ static constexpr int NumOutputDims = internal::array_size<Dimensions>::value;
+ static constexpr int NumInputDims = internal::array_size<typename TensorEvaluator<ArgType, Device>::Dimensions>::value;
+
+ enum ReshapingKind {
+ // We do not use layout information to determine reshaping kind.
+ // Depending on the layout `N` can be inner or outer dimension.
+ OneByN = 0, // expr.reshape(1, N)
+ NByOne = 1, // expr.reshape(N, 1)
+ Runtime = 2 // Reshape dimensions are dynamic (specified at runtime).
+ };
+
+ // clang-format off
+ static const ReshapingKind kind =
+ (NumOutputDims == 2 && internal::index_statically_eq<NewDimensions>(/*index=*/0, /*value=*/1)) ? OneByN
+ : (NumOutputDims == 2 && internal::index_statically_eq<NewDimensions>(/*index=*/1, /*value=*/1)) ? NByOne
+ : Runtime;
+ // clang-format on
+
+ static constexpr int Layout = TensorEvaluator<ArgType, Device>::Layout;
+ enum {
+ IsAligned = TensorEvaluator<ArgType, Device>::IsAligned,
+ PacketAccess = TensorEvaluator<ArgType, Device>::PacketAccess,
+ // For trivial reshapes with raw access to underlying data we will provide
+ // zero overhead block access.
+ // TODO(ezhulenev): Consider adding block access without raw access?
+ BlockAccess = TensorEvaluator<ArgType, Device>::RawAccess &&
+ NumInputDims > 0 && NumOutputDims > 0,
+ PreferBlockAccess = false,
+ CoordAccess = false, // to be implemented
+ RawAccess = TensorEvaluator<ArgType, Device>::RawAccess
+ };
+
+ typedef std::remove_const_t<Scalar> ScalarNoConst;
+
+ //===- Tensor block evaluation strategy (see TensorBlock.h) -------------===//
+ typedef internal::TensorBlockDescriptor<NumOutputDims, Index> TensorBlockDesc;
+ typedef internal::TensorBlockScratchAllocator<Device> TensorBlockScratch;
+
+ typedef
+ typename internal::TensorMaterializedBlock<ScalarNoConst, NumOutputDims,
+ Layout, Index>
+ TensorBlock;
+ //===--------------------------------------------------------------------===//
+
+ EIGEN_STRONG_INLINE TensorEvaluator(const XprType& op, const Device& device)
+ : m_impl(op.expression(), device), m_dimensions(op.dimensions())
+ {
+ // The total size of the reshaped tensor must be equal to the total size
+ // of the input tensor.
+ eigen_assert(internal::array_prod(m_impl.dimensions()) == internal::array_prod(op.dimensions()));
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Dimensions& dimensions() const { return m_dimensions; }
+
+#ifdef EIGEN_USE_THREADS
+ template <typename EvalSubExprsCallback>
+ EIGEN_STRONG_INLINE void evalSubExprsIfNeededAsync(
+ EvaluatorPointerType data, EvalSubExprsCallback done) {
+ m_impl.evalSubExprsIfNeededAsync(data, std::move(done));
+ }
+#endif
+
+ EIGEN_STRONG_INLINE bool evalSubExprsIfNeeded(EvaluatorPointerType data) {
+ return m_impl.evalSubExprsIfNeeded(data);
+ }
+ EIGEN_STRONG_INLINE void cleanup() {
+ m_impl.cleanup();
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE CoeffReturnType coeff(Index index) const
+ {
+ return m_impl.coeff(index);
+ }
+
+ template<int LoadMode>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE PacketReturnType packet(Index index) const
+ {
+ return m_impl.template packet<LoadMode>(index);
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorOpCost costPerCoeff(bool vectorized) const {
+ return m_impl.costPerCoeff(vectorized);
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ internal::TensorBlockResourceRequirements getResourceRequirements() const {
+ return internal::TensorBlockResourceRequirements::any();
+ }
+
+ // required in block(OutputTensorBlock* output_block) const
+ // For C++03 compatibility this must be defined outside the method
+ struct BlockIteratorState {
+ Index stride;
+ Index span;
+ Index size;
+ Index count;
+ };
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorBlock
+ block(TensorBlockDesc& desc, TensorBlockScratch& scratch,
+ bool /*root_of_expr_ast*/ = false) const {
+ eigen_assert(m_impl.data() != NULL);
+ eigen_assert((kind == Runtime) ||
+ (kind == OneByN && desc.dimensions()[0] == 1) ||
+ (kind == NByOne && desc.dimensions()[1] == 1));
+
+ if (kind == OneByN || kind == NByOne) {
+ // We can guarantee at compile time that block is just a contiguous slice
+ // of the underlying expression memory buffer.
+ return TensorBlock(internal::TensorBlockKind::kView,
+ m_impl.data() + desc.offset(), desc.dimensions());
+ } else {
+ // This will do additional runtime checks, and in the end it might be also
+ // a view, or it might be a block materialized in the temporary buffer.
+ return TensorBlock::materialize(m_impl.data(), m_dimensions, desc,
+ scratch);
+ }
+ }
+
+ EIGEN_DEVICE_FUNC typename Storage::Type data() const {
+ return constCast(m_impl.data());
+ }
+
+ EIGEN_DEVICE_FUNC const TensorEvaluator<ArgType, Device>& impl() const { return m_impl; }
+
+ #ifdef EIGEN_USE_SYCL
+ // binding placeholder accessors to a command group handler for SYCL
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void bind(cl::sycl::handler &cgh) const {
+ m_impl.bind(cgh);
+ }
+ #endif
+ protected:
+ TensorEvaluator<ArgType, Device> m_impl;
+ NewDimensions m_dimensions;
+};
+
+
+// Eval as lvalue
+template<typename NewDimensions, typename ArgType, typename Device>
+ struct TensorEvaluator<TensorReshapingOp<NewDimensions, ArgType>, Device>
+ : public TensorEvaluator<const TensorReshapingOp<NewDimensions, ArgType>, Device>
+
+{
+ typedef TensorEvaluator<const TensorReshapingOp<NewDimensions, ArgType>, Device> Base;
+ typedef TensorReshapingOp<NewDimensions, ArgType> XprType;
+ typedef NewDimensions Dimensions;
+
+ static constexpr int Layout = TensorEvaluator<ArgType, Device>::Layout;
+ enum {
+ IsAligned = TensorEvaluator<ArgType, Device>::IsAligned,
+ PacketAccess = TensorEvaluator<ArgType, Device>::PacketAccess,
+ BlockAccess = TensorEvaluator<ArgType, Device>::RawAccess,
+ PreferBlockAccess = false,
+ CoordAccess = false, // to be implemented
+ RawAccess = TensorEvaluator<ArgType, Device>::RawAccess
+ };
+
+ EIGEN_STRONG_INLINE TensorEvaluator(const XprType& op, const Device& device)
+ : Base(op, device)
+ { }
+
+ typedef typename XprType::Index Index;
+ typedef typename XprType::Scalar Scalar;
+ typedef typename XprType::CoeffReturnType CoeffReturnType;
+ typedef typename PacketType<CoeffReturnType, Device>::type PacketReturnType;
+
+ //===- Tensor block evaluation strategy (see TensorBlock.h) -------------===//
+ typedef internal::TensorBlockDescriptor<TensorEvaluator::NumOutputDims, Index>
+ TensorBlockDesc;
+ //===--------------------------------------------------------------------===//
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE CoeffReturnType& coeffRef(Index index)
+ {
+ return this->m_impl.coeffRef(index);
+ }
+
+ template <int StoreMode> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ void writePacket(Index index, const PacketReturnType& x)
+ {
+ this->m_impl.template writePacket<StoreMode>(index, x);
+ }
+
+ template <typename TensorBlock>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void writeBlock(
+ const TensorBlockDesc& desc, const TensorBlock& block) {
+ eigen_assert(this->m_impl.data() != NULL);
+
+ typedef typename TensorBlock::XprType TensorBlockExpr;
+ typedef internal::TensorBlockAssignment<
+ Scalar, TensorEvaluator::NumOutputDims, TensorBlockExpr, Index>
+ TensorBlockAssign;
+
+ TensorBlockAssign::Run(
+ TensorBlockAssign::target(desc.dimensions(),
+ internal::strides<Layout>(this->dimensions()),
+ this->m_impl.data(), desc.offset()),
+ block.expr());
+ }
+};
+
+
+/** \class TensorSlicing
+ * \ingroup CXX11_Tensor_Module
+ *
+ * \brief Tensor slicing class.
+ *
+ *
+ */
+namespace internal {
+template<typename StartIndices, typename Sizes, typename XprType>
+struct traits<TensorSlicingOp<StartIndices, Sizes, XprType> > : public traits<XprType>
+{
+ typedef typename XprType::Scalar Scalar;
+ typedef traits<XprType> XprTraits;
+ typedef typename XprTraits::StorageKind StorageKind;
+ typedef typename XprTraits::Index Index;
+ typedef typename XprType::Nested Nested;
+ typedef std::remove_reference_t<Nested> Nested_;
+ static constexpr int NumDimensions = array_size<StartIndices>::value;
+ static constexpr int Layout = XprTraits::Layout;
+ typedef typename XprTraits::PointerType PointerType;
+};
+
+template<typename StartIndices, typename Sizes, typename XprType>
+struct eval<TensorSlicingOp<StartIndices, Sizes, XprType>, Eigen::Dense>
+{
+ typedef const TensorSlicingOp<StartIndices, Sizes, XprType>EIGEN_DEVICE_REF type;
+};
+
+template<typename StartIndices, typename Sizes, typename XprType>
+struct nested<TensorSlicingOp<StartIndices, Sizes, XprType>, 1, typename eval<TensorSlicingOp<StartIndices, Sizes, XprType> >::type>
+{
+ typedef TensorSlicingOp<StartIndices, Sizes, XprType> type;
+};
+
+} // end namespace internal
+
+
+
+template<typename StartIndices, typename Sizes, typename XprType>
+class TensorSlicingOp : public TensorBase<TensorSlicingOp<StartIndices, Sizes, XprType> >
+{
+ public:
+ typedef TensorBase<TensorSlicingOp<StartIndices, Sizes, XprType> > Base;
+ typedef typename Eigen::internal::traits<TensorSlicingOp>::Scalar Scalar;
+ typedef typename XprType::CoeffReturnType CoeffReturnType;
+ typedef typename Eigen::internal::nested<TensorSlicingOp>::type Nested;
+ typedef typename Eigen::internal::traits<TensorSlicingOp>::StorageKind StorageKind;
+ typedef typename Eigen::internal::traits<TensorSlicingOp>::Index Index;
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorSlicingOp(const XprType& expr, const StartIndices& indices, const Sizes& sizes)
+ : m_xpr(expr), m_indices(indices), m_sizes(sizes) {}
+
+ EIGEN_DEVICE_FUNC
+ const StartIndices& startIndices() const { return m_indices; }
+ EIGEN_DEVICE_FUNC
+ const Sizes& sizes() const { return m_sizes; }
+
+ EIGEN_DEVICE_FUNC
+ const internal::remove_all_t<typename XprType::Nested>&
+ expression() const { return m_xpr; }
+
+ EIGEN_TENSOR_INHERIT_ASSIGNMENT_OPERATORS(TensorSlicingOp)
+
+ protected:
+ typename XprType::Nested m_xpr;
+ const StartIndices m_indices;
+ const Sizes m_sizes;
+};
+
+
+namespace internal {
+
+// Fixme: figure out the exact threshold
+template <typename Index, typename Device, bool BlockAccess> struct MemcpyTriggerForSlicing {
+ EIGEN_DEVICE_FUNC MemcpyTriggerForSlicing(const Device& device) : threshold_(2 * device.numThreads()) { }
+ EIGEN_DEVICE_FUNC bool operator ()(Index total, Index contiguous) const {
+ const bool prefer_block_evaluation = BlockAccess && total > 32*1024;
+ return !prefer_block_evaluation && contiguous > threshold_;
+ }
+
+ private:
+ Index threshold_;
+};
+
+// It is very expensive to start the memcpy kernel on GPU: we therefore only
+// use it for large copies.
+#ifdef EIGEN_USE_GPU
+template <typename Index, bool BlockAccess> struct MemcpyTriggerForSlicing<Index, GpuDevice, BlockAccess> {
+ EIGEN_DEVICE_FUNC MemcpyTriggerForSlicing(const GpuDevice&) { }
+ EIGEN_DEVICE_FUNC bool operator ()(Index, Index contiguous) const { return contiguous > 4*1024*1024; }
+};
+#endif
+
+// It is very expensive to start the memcpy kernel on GPU: we therefore only
+// use it for large copies.
+#ifdef EIGEN_USE_SYCL
+template <typename Index, bool BlockAccess> struct MemcpyTriggerForSlicing<Index, Eigen::SyclDevice, BlockAccess> {
+ EIGEN_DEVICE_FUNC MemcpyTriggerForSlicing(const SyclDevice&) { }
+ EIGEN_DEVICE_FUNC bool operator ()(Index, Index contiguous) const { return contiguous > 4*1024*1024; }
+};
+#endif
+
+} // namespace internal
+
+// Eval as rvalue
+template<typename StartIndices, typename Sizes, typename ArgType, typename Device>
+struct TensorEvaluator<const TensorSlicingOp<StartIndices, Sizes, ArgType>, Device>
+{
+ typedef TensorSlicingOp<StartIndices, Sizes, ArgType> XprType;
+ static constexpr int NumDims = internal::array_size<Sizes>::value;
+
+ typedef typename XprType::Index Index;
+ typedef typename XprType::Scalar Scalar;
+ typedef typename XprType::CoeffReturnType CoeffReturnType;
+ typedef typename PacketType<CoeffReturnType, Device>::type PacketReturnType;
+ typedef Sizes Dimensions;
+ typedef StorageMemory<CoeffReturnType, Device> Storage;
+ typedef StorageMemory<std::remove_const_t<CoeffReturnType>, Device> ConstCastStorage;
+ typedef typename Storage::Type EvaluatorPointerType;
+
+ static constexpr int Layout = TensorEvaluator<ArgType, Device>::Layout;
+ enum {
+ // Alignment can't be guaranteed at compile time since it depends on the
+ // slice offsets and sizes.
+ IsAligned = false,
+ PacketAccess = TensorEvaluator<ArgType, Device>::PacketAccess,
+ BlockAccess = TensorEvaluator<ArgType, Device>::BlockAccess &&
+ // FIXME: Temporary workaround for bug in slicing of bool tensors.
+ !internal::is_same<std::remove_const_t<Scalar>, bool>::value,
+ PreferBlockAccess = true,
+ CoordAccess = false,
+ RawAccess = false
+ };
+
+ typedef std::remove_const_t<Scalar> ScalarNoConst;
+
+ //===- Tensor block evaluation strategy (see TensorBlock.h) -------------===//
+ typedef internal::TensorBlockDescriptor<NumDims, Index> TensorBlockDesc;
+ typedef internal::TensorBlockScratchAllocator<Device> TensorBlockScratch;
+
+ // Tensor slicing does not change the block type.
+ typedef typename TensorEvaluator<const ArgType, Device>::TensorBlock
+ TensorBlock;
+ //===--------------------------------------------------------------------===//
+
+ EIGEN_STRONG_INLINE TensorEvaluator(const XprType& op, const Device& device)
+ : m_impl(op.expression(), device), m_device(device), m_dimensions(op.sizes()), m_offsets(op.startIndices())
+ {
+ m_is_identity = true;
+ for (int i = 0; i < internal::array_size<Dimensions>::value; ++i) {
+ eigen_assert(m_impl.dimensions()[i] >=
+ op.sizes()[i] + op.startIndices()[i]);
+ if (m_impl.dimensions()[i] != op.sizes()[i] ||
+ op.startIndices()[i] != 0) {
+ m_is_identity = false;
+ }
+ }
+
+ // No strides for scalars.
+ if (NumDims == 0) return;
+
+ const typename TensorEvaluator<ArgType, Device>::Dimensions& input_dims = m_impl.dimensions();
+ const Sizes& output_dims = op.sizes();
+ if (static_cast<int>(Layout) == static_cast<int>(ColMajor)) {
+ m_inputStrides[0] = 1;
+ for (int i = 1; i < NumDims; ++i) {
+ m_inputStrides[i] = m_inputStrides[i-1] * input_dims[i-1];
+ }
+
+ // Don't initialize m_fastOutputStrides[0] since it won't ever be accessed.
+ m_outputStrides[0] = 1;
+ for (int i = 1; i < NumDims; ++i) {
+ m_outputStrides[i] = m_outputStrides[i-1] * output_dims[i-1];
+ m_fastOutputStrides[i] = internal::TensorIntDivisor<Index>(m_outputStrides[i] > 0 ? m_outputStrides[i] : 1);
+ }
+ } else {
+ m_inputStrides[NumDims-1] = 1;
+ for (int i = NumDims - 2; i >= 0; --i) {
+ m_inputStrides[i] = m_inputStrides[i+1] * input_dims[i+1];
+ }
+
+ // Don't initialize m_fastOutputStrides[NumDims-1] since it won't ever be accessed.
+ m_outputStrides[NumDims-1] = 1;
+ for (int i = NumDims - 2; i >= 0; --i) {
+ m_outputStrides[i] = m_outputStrides[i+1] * output_dims[i+1];
+ m_fastOutputStrides[i] = internal::TensorIntDivisor<Index>(m_outputStrides[i] > 0 ? m_outputStrides[i] : 1);
+ }
+ }
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Dimensions& dimensions() const { return m_dimensions; }
+
+ EIGEN_STRONG_INLINE bool evalSubExprsIfNeeded(EvaluatorPointerType data) {
+ m_impl.evalSubExprsIfNeeded(NULL);
+ if (!NumTraits<std::remove_const_t<Scalar>>::RequireInitialization
+ && data && m_impl.data()) {
+ Index contiguous_values = 1;
+ if (static_cast<int>(Layout) == static_cast<int>(ColMajor)) {
+ for (int i = 0; i < NumDims; ++i) {
+ contiguous_values *= dimensions()[i];
+ if (dimensions()[i] != m_impl.dimensions()[i]) {
+ break;
+ }
+ }
+ } else {
+ for (int i = NumDims-1; i >= 0; --i) {
+ contiguous_values *= dimensions()[i];
+ if (dimensions()[i] != m_impl.dimensions()[i]) {
+ break;
+ }
+ }
+ }
+ // Use memcpy if it's going to be faster than using the regular evaluation.
+ const internal::MemcpyTriggerForSlicing<Index, Device, BlockAccess> trigger(m_device);
+ if (trigger(internal::array_prod(dimensions()), contiguous_values)) {
+ EvaluatorPointerType src = (EvaluatorPointerType)m_impl.data();
+ for (Index i = 0; i < internal::array_prod(dimensions()); i += contiguous_values) {
+ Index offset = srcCoeff(i);
+ m_device.memcpy((void*)(m_device.get(data + i)), m_device.get(src+offset), contiguous_values * sizeof(Scalar));
+ }
+ return false;
+ }
+ }
+ return true;
+ }
+
+#ifdef EIGEN_USE_THREADS
+ template <typename EvalSubExprsCallback>
+ EIGEN_STRONG_INLINE void evalSubExprsIfNeededAsync(
+ EvaluatorPointerType /*data*/, EvalSubExprsCallback done) {
+ m_impl.evalSubExprsIfNeededAsync(nullptr, [done](bool) { done(true); });
+ }
+#endif // EIGEN_USE_THREADS
+
+ EIGEN_STRONG_INLINE void cleanup() {
+ m_impl.cleanup();
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE CoeffReturnType coeff(Index index) const
+ {
+ if (m_is_identity) {
+ return m_impl.coeff(index);
+ } else {
+ return m_impl.coeff(srcCoeff(index));
+ }
+ }
+
+ template<int LoadMode>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE PacketReturnType packet(Index index) const
+ {
+ const int packetSize = PacketType<CoeffReturnType, Device>::size;
+ EIGEN_STATIC_ASSERT((packetSize > 1), YOU_MADE_A_PROGRAMMING_MISTAKE)
+ eigen_assert(index+packetSize-1 < internal::array_prod(dimensions()));
+
+ if (m_is_identity) {
+ return m_impl.template packet<LoadMode>(index);
+ }
+
+ Index inputIndices[] = {0, 0};
+ Index indices[] = {index, index + packetSize - 1};
+ if (static_cast<int>(Layout) == static_cast<int>(ColMajor)) {
+ EIGEN_UNROLL_LOOP
+ for (int i = NumDims - 1; i > 0; --i) {
+ const Index idx0 = indices[0] / m_fastOutputStrides[i];
+ const Index idx1 = indices[1] / m_fastOutputStrides[i];
+ inputIndices[0] += (idx0 + m_offsets[i]) * m_inputStrides[i];
+ inputIndices[1] += (idx1 + m_offsets[i]) * m_inputStrides[i];
+ indices[0] -= idx0 * m_outputStrides[i];
+ indices[1] -= idx1 * m_outputStrides[i];
+ }
+ inputIndices[0] += (indices[0] + m_offsets[0]);
+ inputIndices[1] += (indices[1] + m_offsets[0]);
+ } else {
+ EIGEN_UNROLL_LOOP
+ for (int i = 0; i < NumDims - 1; ++i) {
+ const Index idx0 = indices[0] / m_fastOutputStrides[i];
+ const Index idx1 = indices[1] / m_fastOutputStrides[i];
+ inputIndices[0] += (idx0 + m_offsets[i]) * m_inputStrides[i];
+ inputIndices[1] += (idx1 + m_offsets[i]) * m_inputStrides[i];
+ indices[0] -= idx0 * m_outputStrides[i];
+ indices[1] -= idx1 * m_outputStrides[i];
+ }
+ inputIndices[0] += (indices[0] + m_offsets[NumDims-1]);
+ inputIndices[1] += (indices[1] + m_offsets[NumDims-1]);
+ }
+ if (inputIndices[1] - inputIndices[0] == packetSize - 1) {
+ PacketReturnType rslt = m_impl.template packet<Unaligned>(inputIndices[0]);
+ return rslt;
+ }
+ else {
+ EIGEN_ALIGN_MAX std::remove_const_t<CoeffReturnType> values[packetSize];
+ values[0] = m_impl.coeff(inputIndices[0]);
+ values[packetSize-1] = m_impl.coeff(inputIndices[1]);
+ EIGEN_UNROLL_LOOP
+ for (int i = 1; i < packetSize-1; ++i) {
+ values[i] = coeff(index+i);
+ }
+ PacketReturnType rslt = internal::pload<PacketReturnType>(values);
+ return rslt;
+ }
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorOpCost costPerCoeff(bool vectorized) const {
+ return m_impl.costPerCoeff(vectorized) + TensorOpCost(0, 0, m_is_identity ? 1 : NumDims);
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ internal::TensorBlockResourceRequirements getResourceRequirements() const {
+ const size_t target_size = m_device.lastLevelCacheSize();
+ return internal::TensorBlockResourceRequirements::merge(
+ internal::TensorBlockResourceRequirements::skewed<Scalar>(target_size),
+ m_impl.getResourceRequirements());
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorBlock
+ block(TensorBlockDesc& desc, TensorBlockScratch& scratch,
+ bool /*root_of_expr_ast*/ = false) const {
+ TensorBlockDesc arg_desc = desc.WithOffset(srcCoeff(desc.offset()));
+ TensorBlock block = m_impl.block(arg_desc, scratch);
+ if (!arg_desc.HasDestinationBuffer()) desc.DropDestinationBuffer();
+ return block;
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE typename Storage::Type data() const {
+ typename Storage::Type result = constCast(m_impl.data());
+ if (result) {
+ Index offset = 0;
+ if (static_cast<int>(Layout) == static_cast<int>(ColMajor)) {
+ for (int i = 0; i < NumDims; ++i) {
+ if (m_dimensions[i] != m_impl.dimensions()[i]) {
+ offset += m_offsets[i] * m_inputStrides[i];
+ for (int j = i+1; j < NumDims; ++j) {
+ if (m_dimensions[j] > 1) {
+ return NULL;
+ }
+ offset += m_offsets[j] * m_inputStrides[j];
+ }
+ break;
+ }
+ }
+ } else {
+ for (int i = NumDims - 1; i >= 0; --i) {
+ if (m_dimensions[i] != m_impl.dimensions()[i]) {
+ offset += m_offsets[i] * m_inputStrides[i];
+ for (int j = i-1; j >= 0; --j) {
+ if (m_dimensions[j] > 1) {
+ return NULL;
+ }
+ offset += m_offsets[j] * m_inputStrides[j];
+ }
+ break;
+ }
+ }
+ }
+ return result + offset;
+ }
+ return NULL;
+ }
+#ifdef EIGEN_USE_SYCL
+ // binding placeholder accessors to a command group handler for SYCL
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void bind(cl::sycl::handler &cgh) const {
+ m_impl.bind(cgh);
+ }
+#endif
+
+ protected:
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Index srcCoeff(Index index) const
+ {
+ Index inputIndex = 0;
+ if (static_cast<int>(Layout) == static_cast<int>(ColMajor)) {
+ EIGEN_UNROLL_LOOP
+ for (int i = NumDims - 1; i > 0; --i) {
+ const Index idx = index / m_fastOutputStrides[i];
+ inputIndex += (idx + m_offsets[i]) * m_inputStrides[i];
+ index -= idx * m_outputStrides[i];
+ }
+ inputIndex += (index + m_offsets[0]);
+ } else {
+ EIGEN_UNROLL_LOOP
+ for (int i = 0; i < NumDims - 1; ++i) {
+ const Index idx = index / m_fastOutputStrides[i];
+ inputIndex += (idx + m_offsets[i]) * m_inputStrides[i];
+ index -= idx * m_outputStrides[i];
+ }
+ inputIndex += (index + m_offsets[NumDims-1]);
+ }
+ return inputIndex;
+ }
+
+ array<Index, NumDims> m_outputStrides;
+ array<internal::TensorIntDivisor<Index>, NumDims> m_fastOutputStrides;
+ array<Index, NumDims> m_inputStrides;
+ TensorEvaluator<ArgType, Device> m_impl;
+ const Device EIGEN_DEVICE_REF m_device;
+ Dimensions m_dimensions;
+ bool m_is_identity;
+ const StartIndices m_offsets;
+};
+
+
+// Eval as lvalue
+template<typename StartIndices, typename Sizes, typename ArgType, typename Device>
+struct TensorEvaluator<TensorSlicingOp<StartIndices, Sizes, ArgType>, Device>
+ : public TensorEvaluator<const TensorSlicingOp<StartIndices, Sizes, ArgType>, Device>
+{
+ typedef TensorEvaluator<const TensorSlicingOp<StartIndices, Sizes, ArgType>, Device> Base;
+ typedef TensorSlicingOp<StartIndices, Sizes, ArgType> XprType;
+ static constexpr int NumDims = internal::array_size<Sizes>::value;
+
+ typedef typename XprType::Index Index;
+ typedef typename XprType::Scalar Scalar;
+ typedef typename XprType::CoeffReturnType CoeffReturnType;
+ typedef typename PacketType<CoeffReturnType, Device>::type PacketReturnType;
+ typedef Sizes Dimensions;
+
+ static constexpr int Layout = TensorEvaluator<ArgType, Device>::Layout;
+ enum {
+ IsAligned = false,
+ PacketAccess = TensorEvaluator<ArgType, Device>::PacketAccess,
+ BlockAccess = TensorEvaluator<ArgType, Device>::BlockAccess,
+ PreferBlockAccess = true,
+ CoordAccess = false,
+ RawAccess = (NumDims == 1) & TensorEvaluator<ArgType, Device>::RawAccess
+ };
+
+ typedef std::remove_const_t<Scalar> ScalarNoConst;
+
+ //===- Tensor block evaluation strategy (see TensorBlock.h) -------------===//
+ typedef internal::TensorBlockDescriptor<NumDims, Index> TensorBlockDesc;
+ typedef internal::TensorBlockScratchAllocator<Device> TensorBlockScratch;
+ //===--------------------------------------------------------------------===//
+
+ EIGEN_STRONG_INLINE TensorEvaluator(const XprType& op, const Device& device)
+ : Base(op, device)
+ { }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE CoeffReturnType& coeffRef(Index index)
+ {
+ if (this->m_is_identity) {
+ return this->m_impl.coeffRef(index);
+ } else {
+ return this->m_impl.coeffRef(this->srcCoeff(index));
+ }
+ }
+
+ template <int StoreMode> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ void writePacket(Index index, const PacketReturnType& x)
+ {
+ if (this->m_is_identity) {
+ this->m_impl.template writePacket<StoreMode>(index, x);
+ return;
+ }
+
+ const int packetSize = PacketType<CoeffReturnType, Device>::size;
+ Index inputIndices[] = {0, 0};
+ Index indices[] = {index, index + packetSize - 1};
+ if (static_cast<int>(Layout) == static_cast<int>(ColMajor)) {
+ EIGEN_UNROLL_LOOP
+ for (int i = NumDims - 1; i > 0; --i) {
+ const Index idx0 = indices[0] / this->m_fastOutputStrides[i];
+ const Index idx1 = indices[1] / this->m_fastOutputStrides[i];
+ inputIndices[0] += (idx0 + this->m_offsets[i]) * this->m_inputStrides[i];
+ inputIndices[1] += (idx1 + this->m_offsets[i]) * this->m_inputStrides[i];
+ indices[0] -= idx0 * this->m_outputStrides[i];
+ indices[1] -= idx1 * this->m_outputStrides[i];
+ }
+ inputIndices[0] += (indices[0] + this->m_offsets[0]);
+ inputIndices[1] += (indices[1] + this->m_offsets[0]);
+ } else {
+ EIGEN_UNROLL_LOOP
+ for (int i = 0; i < NumDims - 1; ++i) {
+ const Index idx0 = indices[0] / this->m_fastOutputStrides[i];
+ const Index idx1 = indices[1] / this->m_fastOutputStrides[i];
+ inputIndices[0] += (idx0 + this->m_offsets[i]) * this->m_inputStrides[i];
+ inputIndices[1] += (idx1 + this->m_offsets[i]) * this->m_inputStrides[i];
+ indices[0] -= idx0 * this->m_outputStrides[i];
+ indices[1] -= idx1 * this->m_outputStrides[i];
+ }
+ inputIndices[0] += (indices[0] + this->m_offsets[NumDims-1]);
+ inputIndices[1] += (indices[1] + this->m_offsets[NumDims-1]);
+ }
+ if (inputIndices[1] - inputIndices[0] == packetSize - 1) {
+ this->m_impl.template writePacket<StoreMode>(inputIndices[0], x);
+ }
+ else {
+ EIGEN_ALIGN_MAX CoeffReturnType values[packetSize];
+ internal::pstore<CoeffReturnType, PacketReturnType>(values, x);
+ this->m_impl.coeffRef(inputIndices[0]) = values[0];
+ this->m_impl.coeffRef(inputIndices[1]) = values[packetSize-1];
+ EIGEN_UNROLL_LOOP
+ for (int i = 1; i < packetSize-1; ++i) {
+ this->coeffRef(index+i) = values[i];
+ }
+ }
+ }
+
+ template<typename TensorBlock>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void writeBlock(
+ const TensorBlockDesc& desc, const TensorBlock& block) {
+ TensorBlockDesc arg_desc = desc.WithOffset(this->srcCoeff(desc.offset()));
+ this->m_impl.writeBlock(arg_desc, block);
+ }
+};
+
+namespace internal {
+template<typename StartIndices, typename StopIndices, typename Strides, typename XprType>
+struct traits<TensorStridingSlicingOp<StartIndices, StopIndices, Strides, XprType> > : public traits<XprType>
+{
+ typedef typename XprType::Scalar Scalar;
+ typedef traits<XprType> XprTraits;
+ typedef typename XprTraits::StorageKind StorageKind;
+ typedef typename XprTraits::Index Index;
+ typedef typename XprType::Nested Nested;
+ typedef std::remove_reference_t<Nested> Nested_;
+ static constexpr int NumDimensions = array_size<StartIndices>::value;
+ static constexpr int Layout = XprTraits::Layout;
+ typedef typename XprTraits::PointerType PointerType;
+};
+
+template<typename StartIndices, typename StopIndices, typename Strides, typename XprType>
+struct eval<TensorStridingSlicingOp<StartIndices, StopIndices, Strides, XprType>, Eigen::Dense>
+{
+ typedef const TensorStridingSlicingOp<StartIndices, StopIndices, Strides, XprType>EIGEN_DEVICE_REF type;
+};
+
+template<typename StartIndices, typename StopIndices, typename Strides, typename XprType>
+struct nested<TensorStridingSlicingOp<StartIndices, StopIndices, Strides, XprType>, 1, typename eval<TensorStridingSlicingOp<StartIndices, StopIndices, Strides, XprType> >::type>
+{
+ typedef TensorStridingSlicingOp<StartIndices, StopIndices, Strides, XprType> type;
+};
+
+} // end namespace internal
+
+
+template<typename StartIndices, typename StopIndices, typename Strides, typename XprType>
+class TensorStridingSlicingOp : public TensorBase<TensorStridingSlicingOp<StartIndices, StopIndices, Strides, XprType> >
+{
+ public:
+ typedef TensorBase<TensorStridingSlicingOp<StartIndices, StopIndices, Strides, XprType> > Base;
+ typedef typename internal::traits<TensorStridingSlicingOp>::Scalar Scalar;
+ typedef typename XprType::CoeffReturnType CoeffReturnType;
+ typedef typename internal::nested<TensorStridingSlicingOp>::type Nested;
+ typedef typename internal::traits<TensorStridingSlicingOp>::StorageKind StorageKind;
+ typedef typename internal::traits<TensorStridingSlicingOp>::Index Index;
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorStridingSlicingOp(
+ const XprType& expr, const StartIndices& startIndices,
+ const StopIndices& stopIndices, const Strides& strides)
+ : m_xpr(expr), m_startIndices(startIndices), m_stopIndices(stopIndices),
+ m_strides(strides) {}
+
+ EIGEN_DEVICE_FUNC
+ const StartIndices& startIndices() const { return m_startIndices; }
+ EIGEN_DEVICE_FUNC
+ const StartIndices& stopIndices() const { return m_stopIndices; }
+ EIGEN_DEVICE_FUNC
+ const StartIndices& strides() const { return m_strides; }
+
+ EIGEN_DEVICE_FUNC
+ const internal::remove_all_t<typename XprType::Nested>&
+ expression() const { return m_xpr; }
+
+ EIGEN_TENSOR_INHERIT_ASSIGNMENT_OPERATORS(TensorStridingSlicingOp)
+
+ protected:
+ typename XprType::Nested m_xpr;
+ const StartIndices m_startIndices;
+ const StopIndices m_stopIndices;
+ const Strides m_strides;
+};
+
+// Eval as rvalue
+template<typename StartIndices, typename StopIndices, typename Strides, typename ArgType, typename Device>
+struct TensorEvaluator<const TensorStridingSlicingOp<StartIndices, StopIndices, Strides, ArgType>, Device>
+{
+ typedef TensorStridingSlicingOp<StartIndices, StopIndices, Strides, ArgType> XprType;
+ static constexpr int NumDims = internal::array_size<Strides>::value;
+ typedef typename XprType::Index Index;
+ typedef typename XprType::Scalar Scalar;
+ typedef typename XprType::CoeffReturnType CoeffReturnType;
+ typedef typename PacketType<CoeffReturnType, Device>::type PacketReturnType;
+ typedef StorageMemory<CoeffReturnType, Device> Storage;
+ typedef typename Storage::Type EvaluatorPointerType;
+ typedef Strides Dimensions;
+
+ static constexpr int Layout = TensorEvaluator<ArgType, Device>::Layout;
+ enum {
+ // Alignment can't be guaranteed at compile time since it depends on the
+ // slice offsets and sizes.
+ IsAligned = false,
+ PacketAccess = false,
+ BlockAccess = false,
+ PreferBlockAccess = TensorEvaluator<ArgType, Device>::PreferBlockAccess,
+ RawAccess = false
+ };
+
+ //===- Tensor block evaluation strategy (see TensorBlock.h) -------------===//
+ typedef internal::TensorBlockNotImplemented TensorBlock;
+ //===--------------------------------------------------------------------===//
+
+ EIGEN_STRONG_INLINE TensorEvaluator(const XprType& op, const Device& device)
+ : m_impl(op.expression(), device),
+ m_device(device),
+ m_strides(op.strides())
+ {
+ // Handle degenerate intervals by gracefully clamping and allowing m_dimensions to be zero
+ DSizes<Index, NumDims> startIndicesClamped, stopIndicesClamped;
+ for (ptrdiff_t i = 0; i < internal::array_size<Dimensions>::value; ++i) {
+ eigen_assert(m_strides[i] != 0 && "0 stride is invalid");
+ if (m_strides[i] > 0) {
+ startIndicesClamped[i] =
+ clamp(op.startIndices()[i], 0, m_impl.dimensions()[i]);
+ stopIndicesClamped[i] =
+ clamp(op.stopIndices()[i], 0, m_impl.dimensions()[i]);
+ } else {
+ /* implies m_strides[i] < 0 by assert */
+ startIndicesClamped[i] =
+ clamp(op.startIndices()[i], -1, m_impl.dimensions()[i] - 1);
+ stopIndicesClamped[i] =
+ clamp(op.stopIndices()[i], -1, m_impl.dimensions()[i] - 1);
+ }
+ m_startIndices[i] = startIndicesClamped[i];
+ }
+
+ typedef typename TensorEvaluator<ArgType, Device>::Dimensions InputDimensions;
+ const InputDimensions& input_dims = m_impl.dimensions();
+
+ // compute output tensor shape
+ m_is_identity = true;
+ for (int i = 0; i < NumDims; i++) {
+ Index interval = stopIndicesClamped[i] - startIndicesClamped[i];
+ if (interval == 0 || ((interval < 0) != (m_strides[i] < 0))) {
+ m_dimensions[i] = 0;
+ } else {
+ m_dimensions[i] =
+ (interval / m_strides[i]) + (interval % m_strides[i] != 0 ? 1 : 0);
+ eigen_assert(m_dimensions[i] >= 0);
+ }
+ if (m_strides[i] != 1 || interval != m_impl.dimensions()[i]) {
+ m_is_identity = false;
+ }
+ }
+
+ Strides output_dims = m_dimensions;
+
+ if (static_cast<int>(Layout) == static_cast<int>(ColMajor)) {
+ m_inputStrides[0] = m_strides[0];
+ m_offsets[0] = startIndicesClamped[0];
+ Index previousDimProduct = 1;
+ for (int i = 1; i < NumDims; ++i) {
+ previousDimProduct *= input_dims[i-1];
+ m_inputStrides[i] = previousDimProduct * m_strides[i];
+ m_offsets[i] = startIndicesClamped[i] * previousDimProduct;
+ }
+
+ // Don't initialize m_fastOutputStrides[0] since it won't ever be accessed.
+ m_outputStrides[0] = 1;
+ for (int i = 1; i < NumDims; ++i) {
+ m_outputStrides[i] = m_outputStrides[i-1] * output_dims[i-1];
+ m_fastOutputStrides[i] = internal::TensorIntDivisor<Index>(m_outputStrides[i] > 0 ? m_outputStrides[i] : 1);
+ }
+ } else {
+ m_inputStrides[NumDims-1] = m_strides[NumDims-1];
+ m_offsets[NumDims-1] = startIndicesClamped[NumDims-1];
+ Index previousDimProduct = 1;
+ for (int i = NumDims - 2; i >= 0; --i) {
+ previousDimProduct *= input_dims[i+1];
+ m_inputStrides[i] = previousDimProduct * m_strides[i];
+ m_offsets[i] = startIndicesClamped[i] * previousDimProduct;
+ }
+
+ m_outputStrides[NumDims-1] = 1;
+ for (int i = NumDims - 2; i >= 0; --i) {
+ m_outputStrides[i] = m_outputStrides[i+1] * output_dims[i+1];
+ m_fastOutputStrides[i] = internal::TensorIntDivisor<Index>(m_outputStrides[i] > 0 ? m_outputStrides[i] : 1);
+ }
+ }
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Dimensions& dimensions() const { return m_dimensions; }
+
+
+ EIGEN_STRONG_INLINE bool evalSubExprsIfNeeded(EvaluatorPointerType) {
+ m_impl.evalSubExprsIfNeeded(NULL);
+ return true;
+ }
+
+ EIGEN_STRONG_INLINE void cleanup() {
+ m_impl.cleanup();
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE CoeffReturnType coeff(Index index) const
+ {
+ if (m_is_identity) {
+ return m_impl.coeff(index);
+ } else {
+ return m_impl.coeff(srcCoeff(index));
+ }
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorOpCost costPerCoeff(bool vectorized) const {
+ return m_impl.costPerCoeff(vectorized) + TensorOpCost(0, 0, m_is_identity ? 1 : NumDims);
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE typename Storage::Type data() const {
+ return NULL;
+ }
+#ifdef EIGEN_USE_SYCL
+ // binding placeholder accessors to a command group handler for SYCL
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void bind(cl::sycl::handler &cgh) const {
+ m_impl.bind(cgh);
+ }
+#endif
+ protected:
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Index srcCoeff(Index index) const
+ {
+ Index inputIndex = 0;
+ if (static_cast<int>(Layout) == static_cast<int>(ColMajor)) {
+ EIGEN_UNROLL_LOOP
+ for (int i = NumDims - 1; i >= 0; --i) {
+ const Index idx = index / m_fastOutputStrides[i];
+ inputIndex += idx * m_inputStrides[i] + m_offsets[i];
+ index -= idx * m_outputStrides[i];
+ }
+ } else {
+ EIGEN_UNROLL_LOOP
+ for (int i = 0; i < NumDims; ++i) {
+ const Index idx = index / m_fastOutputStrides[i];
+ inputIndex += idx * m_inputStrides[i] + m_offsets[i];
+ index -= idx * m_outputStrides[i];
+ }
+ }
+ return inputIndex;
+ }
+
+ static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Index clamp(Index value, Index min, Index max) {
+#ifndef SYCL_DEVICE_ONLY
+ return numext::maxi(min, numext::mini(max,value));
+#else
+ return cl::sycl::clamp(value, min, max);
+#endif
+ }
+
+ array<Index, NumDims> m_outputStrides;
+ array<internal::TensorIntDivisor<Index>, NumDims> m_fastOutputStrides;
+ array<Index, NumDims> m_inputStrides;
+ bool m_is_identity;
+ TensorEvaluator<ArgType, Device> m_impl;
+ const Device EIGEN_DEVICE_REF m_device;
+ DSizes<Index, NumDims> m_startIndices; // clamped startIndices
+ DSizes<Index, NumDims> m_dimensions;
+ DSizes<Index, NumDims> m_offsets; // offset in a flattened shape
+ const Strides m_strides;
+};
+
+// Eval as lvalue
+template<typename StartIndices, typename StopIndices, typename Strides, typename ArgType, typename Device>
+struct TensorEvaluator<TensorStridingSlicingOp<StartIndices, StopIndices, Strides, ArgType>, Device>
+ : public TensorEvaluator<const TensorStridingSlicingOp<StartIndices, StopIndices, Strides, ArgType>, Device>
+{
+ typedef TensorEvaluator<const TensorStridingSlicingOp<StartIndices, StopIndices, Strides, ArgType>, Device> Base;
+ typedef TensorStridingSlicingOp<StartIndices, StopIndices, Strides, ArgType> XprType;
+ static constexpr int NumDims = internal::array_size<Strides>::value;
+ static constexpr int Layout = TensorEvaluator<ArgType, Device>::Layout;
+
+ enum {
+ IsAligned = false,
+ PacketAccess = false,
+ BlockAccess = false,
+ PreferBlockAccess = TensorEvaluator<ArgType, Device>::PreferBlockAccess,
+ CoordAccess = TensorEvaluator<ArgType, Device>::CoordAccess,
+ RawAccess = false
+ };
+
+ //===- Tensor block evaluation strategy (see TensorBlock.h) -------------===//
+ typedef internal::TensorBlockNotImplemented TensorBlock;
+ //===--------------------------------------------------------------------===//
+
+ EIGEN_STRONG_INLINE TensorEvaluator(const XprType& op, const Device& device)
+ : Base(op, device)
+ { }
+
+ typedef typename XprType::Index Index;
+ typedef typename XprType::Scalar Scalar;
+ typedef typename XprType::CoeffReturnType CoeffReturnType;
+ typedef typename PacketType<CoeffReturnType, Device>::type PacketReturnType;
+ typedef Strides Dimensions;
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE CoeffReturnType& coeffRef(Index index)
+ {
+ if (this->m_is_identity) {
+ return this->m_impl.coeffRef(index);
+ } else {
+ return this->m_impl.coeffRef(this->srcCoeff(index));
+ }
+ }
+};
+
+
+} // end namespace Eigen
+
+#endif // EIGEN_CXX11_TENSOR_TENSOR_MORPHING_H
diff --git a/unsupported/Eigen/CXX11/src/Tensor/TensorPadding.h b/unsupported/Eigen/CXX11/src/Tensor/TensorPadding.h
new file mode 100644
index 0000000..cf348c3
--- /dev/null
+++ b/unsupported/Eigen/CXX11/src/Tensor/TensorPadding.h
@@ -0,0 +1,693 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_CXX11_TENSOR_TENSOR_PADDING_H
+#define EIGEN_CXX11_TENSOR_TENSOR_PADDING_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+/** \class TensorPadding
+ * \ingroup CXX11_Tensor_Module
+ *
+ * \brief Tensor padding class.
+ * At the moment only padding with a constant value is supported.
+ *
+ */
+namespace internal {
+template<typename PaddingDimensions, typename XprType>
+struct traits<TensorPaddingOp<PaddingDimensions, XprType> > : public traits<XprType>
+{
+ typedef typename XprType::Scalar Scalar;
+ typedef traits<XprType> XprTraits;
+ typedef typename XprTraits::StorageKind StorageKind;
+ typedef typename XprTraits::Index Index;
+ typedef typename XprType::Nested Nested;
+ typedef std::remove_reference_t<Nested> Nested_;
+ static constexpr int NumDimensions = XprTraits::NumDimensions;
+ static constexpr int Layout = XprTraits::Layout;
+ typedef typename XprTraits::PointerType PointerType;
+};
+
+template<typename PaddingDimensions, typename XprType>
+struct eval<TensorPaddingOp<PaddingDimensions, XprType>, Eigen::Dense>
+{
+ typedef const TensorPaddingOp<PaddingDimensions, XprType>& type;
+};
+
+template<typename PaddingDimensions, typename XprType>
+struct nested<TensorPaddingOp<PaddingDimensions, XprType>, 1, typename eval<TensorPaddingOp<PaddingDimensions, XprType> >::type>
+{
+ typedef TensorPaddingOp<PaddingDimensions, XprType> type;
+};
+
+} // end namespace internal
+
+
+
+template<typename PaddingDimensions, typename XprType>
+class TensorPaddingOp : public TensorBase<TensorPaddingOp<PaddingDimensions, XprType>, ReadOnlyAccessors>
+{
+ public:
+ typedef typename Eigen::internal::traits<TensorPaddingOp>::Scalar Scalar;
+ typedef typename Eigen::NumTraits<Scalar>::Real RealScalar;
+ typedef typename XprType::CoeffReturnType CoeffReturnType;
+ typedef typename Eigen::internal::nested<TensorPaddingOp>::type Nested;
+ typedef typename Eigen::internal::traits<TensorPaddingOp>::StorageKind StorageKind;
+ typedef typename Eigen::internal::traits<TensorPaddingOp>::Index Index;
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorPaddingOp(const XprType& expr, const PaddingDimensions& padding_dims, const Scalar padding_value)
+ : m_xpr(expr), m_padding_dims(padding_dims), m_padding_value(padding_value) {}
+
+ EIGEN_DEVICE_FUNC
+ const PaddingDimensions& padding() const { return m_padding_dims; }
+ EIGEN_DEVICE_FUNC
+ Scalar padding_value() const { return m_padding_value; }
+
+ EIGEN_DEVICE_FUNC
+ const internal::remove_all_t<typename XprType::Nested>&
+ expression() const { return m_xpr; }
+
+ protected:
+ typename XprType::Nested m_xpr;
+ const PaddingDimensions m_padding_dims;
+ const Scalar m_padding_value;
+};
+
+
+// Eval as rvalue
+template<typename PaddingDimensions, typename ArgType, typename Device>
+struct TensorEvaluator<const TensorPaddingOp<PaddingDimensions, ArgType>, Device>
+{
+ typedef TensorPaddingOp<PaddingDimensions, ArgType> XprType;
+ typedef typename XprType::Index Index;
+ static constexpr int NumDims = internal::array_size<PaddingDimensions>::value;
+ typedef DSizes<Index, NumDims> Dimensions;
+ typedef typename XprType::Scalar Scalar;
+ typedef typename XprType::CoeffReturnType CoeffReturnType;
+ typedef typename PacketType<CoeffReturnType, Device>::type PacketReturnType;
+ static constexpr int PacketSize = PacketType<CoeffReturnType, Device>::size;
+ typedef StorageMemory<CoeffReturnType, Device> Storage;
+ typedef typename Storage::Type EvaluatorPointerType;
+
+ static constexpr int Layout = TensorEvaluator<ArgType, Device>::Layout;
+ enum {
+ IsAligned = true,
+ PacketAccess = TensorEvaluator<ArgType, Device>::PacketAccess,
+ BlockAccess = TensorEvaluator<ArgType, Device>::RawAccess,
+ PreferBlockAccess = true,
+ CoordAccess = true,
+ RawAccess = false
+ };
+
+ typedef std::remove_const_t<Scalar> ScalarNoConst;
+
+ //===- Tensor block evaluation strategy (see TensorBlock.h) -------------===//
+ typedef internal::TensorBlockDescriptor<NumDims, Index> TensorBlockDesc;
+ typedef internal::TensorBlockScratchAllocator<Device> TensorBlockScratch;
+
+ typedef typename internal::TensorMaterializedBlock<ScalarNoConst, NumDims,
+ Layout, Index>
+ TensorBlock;
+ //===--------------------------------------------------------------------===//
+
+ EIGEN_STRONG_INLINE TensorEvaluator(const XprType& op, const Device& device)
+ : m_impl(op.expression(), device), m_padding(op.padding()), m_paddingValue(op.padding_value()), m_device(device)
+ {
+ // The padding op doesn't change the rank of the tensor. Directly padding a scalar would lead
+ // to a vector, which doesn't make sense. Instead one should reshape the scalar into a vector
+ // of 1 element first and then pad.
+ EIGEN_STATIC_ASSERT((NumDims > 0), YOU_MADE_A_PROGRAMMING_MISTAKE);
+
+ // Compute dimensions
+ m_dimensions = m_impl.dimensions();
+ for (int i = 0; i < NumDims; ++i) {
+ m_dimensions[i] += m_padding[i].first + m_padding[i].second;
+ }
+ const typename TensorEvaluator<ArgType, Device>::Dimensions& input_dims = m_impl.dimensions();
+ if (static_cast<int>(Layout) == static_cast<int>(ColMajor)) {
+ m_inputStrides[0] = 1;
+ m_outputStrides[0] = 1;
+ for (int i = 1; i < NumDims; ++i) {
+ m_inputStrides[i] = m_inputStrides[i-1] * input_dims[i-1];
+ m_outputStrides[i] = m_outputStrides[i-1] * m_dimensions[i-1];
+ }
+ m_outputStrides[NumDims] = m_outputStrides[NumDims-1] * m_dimensions[NumDims-1];
+ } else {
+ m_inputStrides[NumDims - 1] = 1;
+ m_outputStrides[NumDims] = 1;
+ for (int i = NumDims - 2; i >= 0; --i) {
+ m_inputStrides[i] = m_inputStrides[i+1] * input_dims[i+1];
+ m_outputStrides[i+1] = m_outputStrides[i+2] * m_dimensions[i+1];
+ }
+ m_outputStrides[0] = m_outputStrides[1] * m_dimensions[0];
+ }
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Dimensions& dimensions() const { return m_dimensions; }
+
+ EIGEN_STRONG_INLINE bool evalSubExprsIfNeeded(EvaluatorPointerType) {
+ m_impl.evalSubExprsIfNeeded(NULL);
+ return true;
+ }
+
+#ifdef EIGEN_USE_THREADS
+ template <typename EvalSubExprsCallback>
+ EIGEN_STRONG_INLINE void evalSubExprsIfNeededAsync(
+ EvaluatorPointerType, EvalSubExprsCallback done) {
+ m_impl.evalSubExprsIfNeededAsync(nullptr, [done](bool) { done(true); });
+ }
+#endif // EIGEN_USE_THREADS
+
+ EIGEN_STRONG_INLINE void cleanup() {
+ m_impl.cleanup();
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE CoeffReturnType coeff(Index index) const
+ {
+ eigen_assert(index < dimensions().TotalSize());
+ Index inputIndex = 0;
+ if (static_cast<int>(Layout) == static_cast<int>(ColMajor)) {
+ EIGEN_UNROLL_LOOP
+ for (int i = NumDims - 1; i > 0; --i) {
+ const Index idx = index / m_outputStrides[i];
+ if (isPaddingAtIndexForDim(idx, i)) {
+ return m_paddingValue;
+ }
+ inputIndex += (idx - m_padding[i].first) * m_inputStrides[i];
+ index -= idx * m_outputStrides[i];
+ }
+ if (isPaddingAtIndexForDim(index, 0)) {
+ return m_paddingValue;
+ }
+ inputIndex += (index - m_padding[0].first);
+ } else {
+ EIGEN_UNROLL_LOOP
+ for (int i = 0; i < NumDims - 1; ++i) {
+ const Index idx = index / m_outputStrides[i+1];
+ if (isPaddingAtIndexForDim(idx, i)) {
+ return m_paddingValue;
+ }
+ inputIndex += (idx - m_padding[i].first) * m_inputStrides[i];
+ index -= idx * m_outputStrides[i+1];
+ }
+ if (isPaddingAtIndexForDim(index, NumDims-1)) {
+ return m_paddingValue;
+ }
+ inputIndex += (index - m_padding[NumDims-1].first);
+ }
+ return m_impl.coeff(inputIndex);
+ }
+
+ template<int LoadMode>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE PacketReturnType packet(Index index) const
+ {
+ if (static_cast<int>(Layout) == static_cast<int>(ColMajor)) {
+ return packetColMajor(index);
+ }
+ return packetRowMajor(index);
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorOpCost costPerCoeff(bool vectorized) const {
+ TensorOpCost cost = m_impl.costPerCoeff(vectorized);
+ if (static_cast<int>(Layout) == static_cast<int>(ColMajor)) {
+ EIGEN_UNROLL_LOOP
+ for (int i = 0; i < NumDims; ++i)
+ updateCostPerDimension(cost, i, i == 0);
+ } else {
+ EIGEN_UNROLL_LOOP
+ for (int i = NumDims - 1; i >= 0; --i)
+ updateCostPerDimension(cost, i, i == NumDims - 1);
+ }
+ return cost;
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ internal::TensorBlockResourceRequirements getResourceRequirements() const {
+ const size_t target_size = m_device.lastLevelCacheSize();
+ return internal::TensorBlockResourceRequirements::merge(
+ internal::TensorBlockResourceRequirements::skewed<Scalar>(target_size),
+ m_impl.getResourceRequirements());
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorBlock
+ block(TensorBlockDesc& desc, TensorBlockScratch& scratch,
+ bool /*root_of_expr_ast*/ = false) const {
+ // If one of the dimensions is zero, return empty block view.
+ if (desc.size() == 0) {
+ return TensorBlock(internal::TensorBlockKind::kView, NULL,
+ desc.dimensions());
+ }
+
+ static const bool IsColMajor = Layout == static_cast<int>(ColMajor);
+ const int inner_dim_idx = IsColMajor ? 0 : NumDims - 1;
+
+ Index offset = desc.offset();
+
+ // Compute offsets in the output tensor corresponding to the desc.offset().
+ DSizes<Index, NumDims> output_offsets;
+ for (int i = NumDims - 1; i > 0; --i) {
+ const int dim = IsColMajor ? i : NumDims - i - 1;
+ const int stride_dim = IsColMajor ? dim : dim + 1;
+ output_offsets[dim] = offset / m_outputStrides[stride_dim];
+ offset -= output_offsets[dim] * m_outputStrides[stride_dim];
+ }
+ output_offsets[inner_dim_idx] = offset;
+
+ // Offsets in the input corresponding to output offsets.
+ DSizes<Index, NumDims> input_offsets = output_offsets;
+ for (int i = 0; i < NumDims; ++i) {
+ const int dim = IsColMajor ? i : NumDims - i - 1;
+ input_offsets[dim] = input_offsets[dim] - m_padding[dim].first;
+ }
+
+ // Compute offset in the input buffer (at this point it might be illegal and
+ // point outside of the input buffer, because we don't check for negative
+ // offsets, it will be autocorrected in the block iteration loop below).
+ Index input_offset = 0;
+ for (int i = 0; i < NumDims; ++i) {
+ const int dim = IsColMajor ? i : NumDims - i - 1;
+ input_offset += input_offsets[dim] * m_inputStrides[dim];
+ }
+
+ // Destination buffer and scratch buffer both indexed from 0 and have the
+ // same dimensions as the requested block (for destination buffer this
+ // property is guaranteed by `desc.destination()`).
+ Index output_offset = 0;
+ const DSizes<Index, NumDims> output_strides =
+ internal::strides<Layout>(desc.dimensions());
+
+ // NOTE(ezhulenev): We initialize bock iteration state for `NumDims - 1`
+ // dimensions, skipping innermost dimension. In theory it should be possible
+ // to squeeze matching innermost dimensions, however in practice that did
+ // not show any improvements in benchmarks. Also in practice first outer
+ // dimension usually has padding, and will prevent squeezing.
+
+ // Initialize output block iterator state. Dimension in this array are
+ // always in inner_most -> outer_most order (col major layout).
+ array<BlockIteratorState, NumDims - 1> it;
+ for (int i = 0; i < NumDims - 1; ++i) {
+ const int dim = IsColMajor ? i + 1 : NumDims - i - 2;
+ it[i].count = 0;
+ it[i].size = desc.dimension(dim);
+
+ it[i].input_stride = m_inputStrides[dim];
+ it[i].input_span = it[i].input_stride * (it[i].size - 1);
+
+ it[i].output_stride = output_strides[dim];
+ it[i].output_span = it[i].output_stride * (it[i].size - 1);
+ }
+
+ const Index input_inner_dim_size =
+ static_cast<Index>(m_impl.dimensions()[inner_dim_idx]);
+
+ // Total output size.
+ const Index output_size = desc.size();
+
+ // We will fill inner dimension of this size in the output. It might be
+ // larger than the inner dimension in the input, so we might have to pad
+ // before/after we copy values from the input inner dimension.
+ const Index output_inner_dim_size = desc.dimension(inner_dim_idx);
+
+ // How many values to fill with padding BEFORE reading from the input inner
+ // dimension.
+ const Index output_inner_pad_before_size =
+ input_offsets[inner_dim_idx] < 0
+ ? numext::mini(numext::abs(input_offsets[inner_dim_idx]),
+ output_inner_dim_size)
+ : 0;
+
+ // How many values we can actually copy from the input inner dimension.
+ const Index output_inner_copy_size = numext::mini(
+ // Want to copy from input.
+ (output_inner_dim_size - output_inner_pad_before_size),
+ // Can copy from input.
+ numext::maxi(input_inner_dim_size - (input_offsets[inner_dim_idx] +
+ output_inner_pad_before_size),
+ Index(0)));
+
+ eigen_assert(output_inner_copy_size >= 0);
+
+ // How many values to fill with padding AFTER reading from the input inner
+ // dimension.
+ const Index output_inner_pad_after_size =
+ (output_inner_dim_size - output_inner_copy_size -
+ output_inner_pad_before_size);
+
+ // Sanity check, sum of all sizes must be equal to the output size.
+ eigen_assert(output_inner_dim_size ==
+ (output_inner_pad_before_size + output_inner_copy_size +
+ output_inner_pad_after_size));
+
+ // Keep track of current coordinates and padding in the output.
+ DSizes<Index, NumDims> output_coord = output_offsets;
+ DSizes<Index, NumDims> output_padded;
+ for (int i = 0; i < NumDims; ++i) {
+ const int dim = IsColMajor ? i : NumDims - i - 1;
+ output_padded[dim] = isPaddingAtIndexForDim(output_coord[dim], dim);
+ }
+
+ typedef internal::StridedLinearBufferCopy<ScalarNoConst, Index> LinCopy;
+
+ // Prepare storage for the materialized padding result.
+ const typename TensorBlock::Storage block_storage =
+ TensorBlock::prepareStorage(desc, scratch);
+
+ // TODO(ezhulenev): Squeeze multiple non-padded inner dimensions into a
+ // single logical inner dimension.
+
+ // When possible we squeeze writes for the innermost (only if non-padded)
+ // dimension with the first padded dimension. This allows to reduce the
+ // number of calls to LinCopy and better utilize vector instructions.
+ const bool squeeze_writes =
+ NumDims > 1 &&
+ // inner dimension is not padded
+ (input_inner_dim_size == m_dimensions[inner_dim_idx]) &&
+ // and equal to the block inner dimension
+ (input_inner_dim_size == output_inner_dim_size);
+
+ const int squeeze_dim = IsColMajor ? inner_dim_idx + 1 : inner_dim_idx - 1;
+
+ // Maximum coordinate on a squeeze dimension that we can write to.
+ const Index squeeze_max_coord =
+ squeeze_writes ? numext::mini(
+ // max non-padded element in the input
+ static_cast<Index>(m_dimensions[squeeze_dim] -
+ m_padding[squeeze_dim].second),
+ // max element in the output buffer
+ static_cast<Index>(output_offsets[squeeze_dim] +
+ desc.dimension(squeeze_dim)))
+ : static_cast<Index>(0);
+
+ // Iterate copying data from `m_impl.data()` to the output buffer.
+ for (Index size = 0; size < output_size;) {
+ // Detect if we are in the padded region (exclude innermost dimension).
+ bool is_padded = false;
+ for (int j = 1; j < NumDims; ++j) {
+ const int dim = IsColMajor ? j : NumDims - j - 1;
+ is_padded = output_padded[dim];
+ if (is_padded) break;
+ }
+
+ if (is_padded) {
+ // Fill single innermost dimension with padding value.
+ size += output_inner_dim_size;
+
+ LinCopy::template Run<LinCopy::Kind::FillLinear>(
+ typename LinCopy::Dst(output_offset, 1, block_storage.data()),
+ typename LinCopy::Src(0, 0, &m_paddingValue),
+ output_inner_dim_size);
+
+
+ } else if (squeeze_writes) {
+ // Squeeze multiple reads from innermost dimensions.
+ const Index squeeze_num = squeeze_max_coord - output_coord[squeeze_dim];
+ size += output_inner_dim_size * squeeze_num;
+
+ // Copy `squeeze_num` inner dimensions from input to output.
+ LinCopy::template Run<LinCopy::Kind::Linear>(
+ typename LinCopy::Dst(output_offset, 1, block_storage.data()),
+ typename LinCopy::Src(input_offset, 1, m_impl.data()),
+ output_inner_dim_size * squeeze_num);
+
+ // Update iteration state for only `squeeze_num - 1` processed inner
+ // dimensions, because we have another iteration state update at the end
+ // of the loop that will update iteration state for the last inner
+ // processed dimension.
+ it[0].count += (squeeze_num - 1);
+ input_offset += it[0].input_stride * (squeeze_num - 1);
+ output_offset += it[0].output_stride * (squeeze_num - 1);
+ output_coord[squeeze_dim] += (squeeze_num - 1);
+
+ } else {
+ // Single read from innermost dimension.
+ size += output_inner_dim_size;
+
+ { // Fill with padding before copying from input inner dimension.
+ const Index out = output_offset;
+
+ LinCopy::template Run<LinCopy::Kind::FillLinear>(
+ typename LinCopy::Dst(out, 1, block_storage.data()),
+ typename LinCopy::Src(0, 0, &m_paddingValue),
+ output_inner_pad_before_size);
+ }
+
+ { // Copy data from input inner dimension.
+ const Index out = output_offset + output_inner_pad_before_size;
+ const Index in = input_offset + output_inner_pad_before_size;
+
+ eigen_assert(output_inner_copy_size == 0 || m_impl.data() != NULL);
+
+ LinCopy::template Run<LinCopy::Kind::Linear>(
+ typename LinCopy::Dst(out, 1, block_storage.data()),
+ typename LinCopy::Src(in, 1, m_impl.data()),
+ output_inner_copy_size);
+ }
+
+ { // Fill with padding after copying from input inner dimension.
+ const Index out = output_offset + output_inner_pad_before_size +
+ output_inner_copy_size;
+
+ LinCopy::template Run<LinCopy::Kind::FillLinear>(
+ typename LinCopy::Dst(out, 1, block_storage.data()),
+ typename LinCopy::Src(0, 0, &m_paddingValue),
+ output_inner_pad_after_size);
+ }
+ }
+
+ for (int j = 0; j < NumDims - 1; ++j) {
+ const int dim = IsColMajor ? j + 1 : NumDims - j - 2;
+
+ if (++it[j].count < it[j].size) {
+ input_offset += it[j].input_stride;
+ output_offset += it[j].output_stride;
+ output_coord[dim] += 1;
+ output_padded[dim] = isPaddingAtIndexForDim(output_coord[dim], dim);
+ break;
+ }
+ it[j].count = 0;
+ input_offset -= it[j].input_span;
+ output_offset -= it[j].output_span;
+ output_coord[dim] -= it[j].size - 1;
+ output_padded[dim] = isPaddingAtIndexForDim(output_coord[dim], dim);
+ }
+ }
+
+ return block_storage.AsTensorMaterializedBlock();
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE EvaluatorPointerType data() const { return NULL; }
+
+#ifdef EIGEN_USE_SYCL
+ // binding placeholder accessors to a command group handler for SYCL
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void bind(cl::sycl::handler &cgh) const {
+ m_impl.bind(cgh);
+ }
+#endif
+
+ private:
+ struct BlockIteratorState {
+ BlockIteratorState()
+ : count(0),
+ size(0),
+ input_stride(0),
+ input_span(0),
+ output_stride(0),
+ output_span(0) {}
+
+ Index count;
+ Index size;
+ Index input_stride;
+ Index input_span;
+ Index output_stride;
+ Index output_span;
+ };
+
+ EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE bool isPaddingAtIndexForDim(
+ Index index, int dim_index) const {
+ return (!internal::index_pair_first_statically_eq<PaddingDimensions>(dim_index, 0) &&
+ index < m_padding[dim_index].first) ||
+ (!internal::index_pair_second_statically_eq<PaddingDimensions>(dim_index, 0) &&
+ index >= m_dimensions[dim_index] - m_padding[dim_index].second);
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE bool isLeftPaddingCompileTimeZero(
+ int dim_index) const {
+ return internal::index_pair_first_statically_eq<PaddingDimensions>(dim_index, 0);
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE bool isRightPaddingCompileTimeZero(
+ int dim_index) const {
+ return internal::index_pair_second_statically_eq<PaddingDimensions>(dim_index, 0);
+ }
+
+
+ void updateCostPerDimension(TensorOpCost& cost, int i, bool first) const {
+ const double in = static_cast<double>(m_impl.dimensions()[i]);
+ const double out = in + m_padding[i].first + m_padding[i].second;
+ if (out == 0)
+ return;
+ const double reduction = in / out;
+ cost *= reduction;
+ if (first) {
+ cost += TensorOpCost(0, 0, 2 * TensorOpCost::AddCost<Index>() +
+ reduction * (1 * TensorOpCost::AddCost<Index>()));
+ } else {
+ cost += TensorOpCost(0, 0, 2 * TensorOpCost::AddCost<Index>() +
+ 2 * TensorOpCost::MulCost<Index>() +
+ reduction * (2 * TensorOpCost::MulCost<Index>() +
+ 1 * TensorOpCost::DivCost<Index>()));
+ }
+ }
+
+ protected:
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE PacketReturnType packetColMajor(Index index) const
+ {
+ eigen_assert(index+PacketSize-1 < dimensions().TotalSize());
+
+ const Index initialIndex = index;
+ Index inputIndex = 0;
+ EIGEN_UNROLL_LOOP
+ for (int i = NumDims - 1; i > 0; --i) {
+ const Index firstIdx = index;
+ const Index lastIdx = index + PacketSize - 1;
+ const Index lastPaddedLeft = m_padding[i].first * m_outputStrides[i];
+ const Index firstPaddedRight = (m_dimensions[i] - m_padding[i].second) * m_outputStrides[i];
+ const Index lastPaddedRight = m_outputStrides[i+1];
+
+ if (!isLeftPaddingCompileTimeZero(i) && lastIdx < lastPaddedLeft) {
+ // all the coefficient are in the padding zone.
+ return internal::pset1<PacketReturnType>(m_paddingValue);
+ }
+ else if (!isRightPaddingCompileTimeZero(i) && firstIdx >= firstPaddedRight && lastIdx < lastPaddedRight) {
+ // all the coefficient are in the padding zone.
+ return internal::pset1<PacketReturnType>(m_paddingValue);
+ }
+ else if ((isLeftPaddingCompileTimeZero(i) && isRightPaddingCompileTimeZero(i)) || (firstIdx >= lastPaddedLeft && lastIdx < firstPaddedRight)) {
+ // all the coefficient are between the 2 padding zones.
+ const Index idx = index / m_outputStrides[i];
+ inputIndex += (idx - m_padding[i].first) * m_inputStrides[i];
+ index -= idx * m_outputStrides[i];
+ }
+ else {
+ // Every other case
+ return packetWithPossibleZero(initialIndex);
+ }
+ }
+
+ const Index lastIdx = index + PacketSize - 1;
+ const Index firstIdx = index;
+ const Index lastPaddedLeft = m_padding[0].first;
+ const Index firstPaddedRight = (m_dimensions[0] - m_padding[0].second);
+ const Index lastPaddedRight = m_outputStrides[1];
+
+ if (!isLeftPaddingCompileTimeZero(0) && lastIdx < lastPaddedLeft) {
+ // all the coefficient are in the padding zone.
+ return internal::pset1<PacketReturnType>(m_paddingValue);
+ }
+ else if (!isRightPaddingCompileTimeZero(0) && firstIdx >= firstPaddedRight && lastIdx < lastPaddedRight) {
+ // all the coefficient are in the padding zone.
+ return internal::pset1<PacketReturnType>(m_paddingValue);
+ }
+ else if ((isLeftPaddingCompileTimeZero(0) && isRightPaddingCompileTimeZero(0)) || (firstIdx >= lastPaddedLeft && lastIdx < firstPaddedRight)) {
+ // all the coefficient are between the 2 padding zones.
+ inputIndex += (index - m_padding[0].first);
+ return m_impl.template packet<Unaligned>(inputIndex);
+ }
+ // Every other case
+ return packetWithPossibleZero(initialIndex);
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE PacketReturnType packetRowMajor(Index index) const
+ {
+ eigen_assert(index+PacketSize-1 < dimensions().TotalSize());
+
+ const Index initialIndex = index;
+ Index inputIndex = 0;
+ EIGEN_UNROLL_LOOP
+ for (int i = 0; i < NumDims - 1; ++i) {
+ const Index firstIdx = index;
+ const Index lastIdx = index + PacketSize - 1;
+ const Index lastPaddedLeft = m_padding[i].first * m_outputStrides[i+1];
+ const Index firstPaddedRight = (m_dimensions[i] - m_padding[i].second) * m_outputStrides[i+1];
+ const Index lastPaddedRight = m_outputStrides[i];
+
+ if (!isLeftPaddingCompileTimeZero(i) && lastIdx < lastPaddedLeft) {
+ // all the coefficient are in the padding zone.
+ return internal::pset1<PacketReturnType>(m_paddingValue);
+ }
+ else if (!isRightPaddingCompileTimeZero(i) && firstIdx >= firstPaddedRight && lastIdx < lastPaddedRight) {
+ // all the coefficient are in the padding zone.
+ return internal::pset1<PacketReturnType>(m_paddingValue);
+ }
+ else if ((isLeftPaddingCompileTimeZero(i) && isRightPaddingCompileTimeZero(i)) || (firstIdx >= lastPaddedLeft && lastIdx < firstPaddedRight)) {
+ // all the coefficient are between the 2 padding zones.
+ const Index idx = index / m_outputStrides[i+1];
+ inputIndex += (idx - m_padding[i].first) * m_inputStrides[i];
+ index -= idx * m_outputStrides[i+1];
+ }
+ else {
+ // Every other case
+ return packetWithPossibleZero(initialIndex);
+ }
+ }
+
+ const Index lastIdx = index + PacketSize - 1;
+ const Index firstIdx = index;
+ const Index lastPaddedLeft = m_padding[NumDims-1].first;
+ const Index firstPaddedRight = (m_dimensions[NumDims-1] - m_padding[NumDims-1].second);
+ const Index lastPaddedRight = m_outputStrides[NumDims-1];
+
+ if (!isLeftPaddingCompileTimeZero(NumDims-1) && lastIdx < lastPaddedLeft) {
+ // all the coefficient are in the padding zone.
+ return internal::pset1<PacketReturnType>(m_paddingValue);
+ }
+ else if (!isRightPaddingCompileTimeZero(NumDims-1) && firstIdx >= firstPaddedRight && lastIdx < lastPaddedRight) {
+ // all the coefficient are in the padding zone.
+ return internal::pset1<PacketReturnType>(m_paddingValue);
+ }
+ else if ((isLeftPaddingCompileTimeZero(NumDims-1) && isRightPaddingCompileTimeZero(NumDims-1)) || (firstIdx >= lastPaddedLeft && lastIdx < firstPaddedRight)) {
+ // all the coefficient are between the 2 padding zones.
+ inputIndex += (index - m_padding[NumDims-1].first);
+ return m_impl.template packet<Unaligned>(inputIndex);
+ }
+ // Every other case
+ return packetWithPossibleZero(initialIndex);
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE PacketReturnType packetWithPossibleZero(Index index) const
+ {
+ EIGEN_ALIGN_MAX std::remove_const_t<CoeffReturnType> values[PacketSize];
+ EIGEN_UNROLL_LOOP
+ for (int i = 0; i < PacketSize; ++i) {
+ values[i] = coeff(index+i);
+ }
+ PacketReturnType rslt = internal::pload<PacketReturnType>(values);
+ return rslt;
+ }
+
+ Dimensions m_dimensions;
+ array<Index, NumDims+1> m_outputStrides;
+ array<Index, NumDims> m_inputStrides;
+ TensorEvaluator<ArgType, Device> m_impl;
+ PaddingDimensions m_padding;
+
+ Scalar m_paddingValue;
+
+ const Device EIGEN_DEVICE_REF m_device;
+};
+
+
+
+
+} // end namespace Eigen
+
+#endif // EIGEN_CXX11_TENSOR_TENSOR_PADDING_H
diff --git a/unsupported/Eigen/CXX11/src/Tensor/TensorPatch.h b/unsupported/Eigen/CXX11/src/Tensor/TensorPatch.h
new file mode 100644
index 0000000..413c5c4
--- /dev/null
+++ b/unsupported/Eigen/CXX11/src/Tensor/TensorPatch.h
@@ -0,0 +1,291 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_CXX11_TENSOR_TENSOR_PATCH_H
+#define EIGEN_CXX11_TENSOR_TENSOR_PATCH_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+/** \class TensorPatch
+ * \ingroup CXX11_Tensor_Module
+ *
+ * \brief Tensor patch class.
+ *
+ *
+ */
+namespace internal {
+template<typename PatchDim, typename XprType>
+struct traits<TensorPatchOp<PatchDim, XprType> > : public traits<XprType>
+{
+ typedef typename XprType::Scalar Scalar;
+ typedef traits<XprType> XprTraits;
+ typedef typename XprTraits::StorageKind StorageKind;
+ typedef typename XprTraits::Index Index;
+ typedef typename XprType::Nested Nested;
+ typedef std::remove_reference_t<Nested> Nested_;
+ static constexpr int NumDimensions = XprTraits::NumDimensions + 1;
+ static constexpr int Layout = XprTraits::Layout;
+ typedef typename XprTraits::PointerType PointerType;
+};
+
+template<typename PatchDim, typename XprType>
+struct eval<TensorPatchOp<PatchDim, XprType>, Eigen::Dense>
+{
+ typedef const TensorPatchOp<PatchDim, XprType>& type;
+};
+
+template<typename PatchDim, typename XprType>
+struct nested<TensorPatchOp<PatchDim, XprType>, 1, typename eval<TensorPatchOp<PatchDim, XprType> >::type>
+{
+ typedef TensorPatchOp<PatchDim, XprType> type;
+};
+
+} // end namespace internal
+
+
+
+template<typename PatchDim, typename XprType>
+class TensorPatchOp : public TensorBase<TensorPatchOp<PatchDim, XprType>, ReadOnlyAccessors>
+{
+ public:
+ typedef typename Eigen::internal::traits<TensorPatchOp>::Scalar Scalar;
+ typedef typename Eigen::NumTraits<Scalar>::Real RealScalar;
+ typedef typename XprType::CoeffReturnType CoeffReturnType;
+ typedef typename Eigen::internal::nested<TensorPatchOp>::type Nested;
+ typedef typename Eigen::internal::traits<TensorPatchOp>::StorageKind StorageKind;
+ typedef typename Eigen::internal::traits<TensorPatchOp>::Index Index;
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorPatchOp(const XprType& expr, const PatchDim& patch_dims)
+ : m_xpr(expr), m_patch_dims(patch_dims) {}
+
+ EIGEN_DEVICE_FUNC
+ const PatchDim& patch_dims() const { return m_patch_dims; }
+
+ EIGEN_DEVICE_FUNC
+ const internal::remove_all_t<typename XprType::Nested>&
+ expression() const { return m_xpr; }
+
+ protected:
+ typename XprType::Nested m_xpr;
+ const PatchDim m_patch_dims;
+};
+
+
+// Eval as rvalue
+template<typename PatchDim, typename ArgType, typename Device>
+struct TensorEvaluator<const TensorPatchOp<PatchDim, ArgType>, Device>
+{
+ typedef TensorPatchOp<PatchDim, ArgType> XprType;
+ typedef typename XprType::Index Index;
+ static constexpr int NumDims = internal::array_size<typename TensorEvaluator<ArgType, Device>::Dimensions>::value + 1;
+ typedef DSizes<Index, NumDims> Dimensions;
+ typedef typename XprType::Scalar Scalar;
+ typedef typename XprType::CoeffReturnType CoeffReturnType;
+ typedef typename PacketType<CoeffReturnType, Device>::type PacketReturnType;
+ static constexpr int PacketSize = PacketType<CoeffReturnType, Device>::size;
+ typedef StorageMemory<CoeffReturnType, Device> Storage;
+ typedef typename Storage::Type EvaluatorPointerType;
+
+ static constexpr int Layout = TensorEvaluator<ArgType, Device>::Layout;
+ enum {
+ IsAligned = false,
+ PacketAccess = TensorEvaluator<ArgType, Device>::PacketAccess,
+ BlockAccess = false,
+ PreferBlockAccess = TensorEvaluator<ArgType, Device>::PreferBlockAccess,
+ CoordAccess = false,
+ RawAccess = false
+ };
+
+ //===- Tensor block evaluation strategy (see TensorBlock.h) -------------===//
+ typedef internal::TensorBlockNotImplemented TensorBlock;
+ //===--------------------------------------------------------------------===//
+
+ EIGEN_STRONG_INLINE TensorEvaluator(const XprType& op, const Device& device)
+ : m_impl(op.expression(), device)
+ {
+ Index num_patches = 1;
+ const typename TensorEvaluator<ArgType, Device>::Dimensions& input_dims = m_impl.dimensions();
+ const PatchDim& patch_dims = op.patch_dims();
+ if (static_cast<int>(Layout) == static_cast<int>(ColMajor)) {
+ for (int i = 0; i < NumDims-1; ++i) {
+ m_dimensions[i] = patch_dims[i];
+ num_patches *= (input_dims[i] - patch_dims[i] + 1);
+ }
+ m_dimensions[NumDims-1] = num_patches;
+
+ m_inputStrides[0] = 1;
+ m_patchStrides[0] = 1;
+ for (int i = 1; i < NumDims-1; ++i) {
+ m_inputStrides[i] = m_inputStrides[i-1] * input_dims[i-1];
+ m_patchStrides[i] = m_patchStrides[i-1] * (input_dims[i-1] - patch_dims[i-1] + 1);
+ }
+ m_outputStrides[0] = 1;
+ for (int i = 1; i < NumDims; ++i) {
+ m_outputStrides[i] = m_outputStrides[i-1] * m_dimensions[i-1];
+ }
+ } else {
+ for (int i = 0; i < NumDims-1; ++i) {
+ m_dimensions[i+1] = patch_dims[i];
+ num_patches *= (input_dims[i] - patch_dims[i] + 1);
+ }
+ m_dimensions[0] = num_patches;
+
+ m_inputStrides[NumDims-2] = 1;
+ m_patchStrides[NumDims-2] = 1;
+ for (int i = NumDims-3; i >= 0; --i) {
+ m_inputStrides[i] = m_inputStrides[i+1] * input_dims[i+1];
+ m_patchStrides[i] = m_patchStrides[i+1] * (input_dims[i+1] - patch_dims[i+1] + 1);
+ }
+ m_outputStrides[NumDims-1] = 1;
+ for (int i = NumDims-2; i >= 0; --i) {
+ m_outputStrides[i] = m_outputStrides[i+1] * m_dimensions[i+1];
+ }
+ }
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Dimensions& dimensions() const { return m_dimensions; }
+
+ EIGEN_STRONG_INLINE bool evalSubExprsIfNeeded(EvaluatorPointerType /*data*/) {
+ m_impl.evalSubExprsIfNeeded(NULL);
+ return true;
+ }
+
+ EIGEN_STRONG_INLINE void cleanup() {
+ m_impl.cleanup();
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE CoeffReturnType coeff(Index index) const
+ {
+ Index output_stride_index = (static_cast<int>(Layout) == static_cast<int>(ColMajor)) ? NumDims - 1 : 0;
+ // Find the location of the first element of the patch.
+ Index patchIndex = index / m_outputStrides[output_stride_index];
+ // Find the offset of the element wrt the location of the first element.
+ Index patchOffset = index - patchIndex * m_outputStrides[output_stride_index];
+ Index inputIndex = 0;
+ if (static_cast<int>(Layout) == static_cast<int>(ColMajor)) {
+ EIGEN_UNROLL_LOOP
+ for (int i = NumDims - 2; i > 0; --i) {
+ const Index patchIdx = patchIndex / m_patchStrides[i];
+ patchIndex -= patchIdx * m_patchStrides[i];
+ const Index offsetIdx = patchOffset / m_outputStrides[i];
+ patchOffset -= offsetIdx * m_outputStrides[i];
+ inputIndex += (patchIdx + offsetIdx) * m_inputStrides[i];
+ }
+ } else {
+ EIGEN_UNROLL_LOOP
+ for (int i = 0; i < NumDims - 2; ++i) {
+ const Index patchIdx = patchIndex / m_patchStrides[i];
+ patchIndex -= patchIdx * m_patchStrides[i];
+ const Index offsetIdx = patchOffset / m_outputStrides[i+1];
+ patchOffset -= offsetIdx * m_outputStrides[i+1];
+ inputIndex += (patchIdx + offsetIdx) * m_inputStrides[i];
+ }
+ }
+ inputIndex += (patchIndex + patchOffset);
+ return m_impl.coeff(inputIndex);
+ }
+
+ template<int LoadMode>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE PacketReturnType packet(Index index) const
+ {
+ eigen_assert(index+PacketSize-1 < dimensions().TotalSize());
+
+ Index output_stride_index = (static_cast<int>(Layout) == static_cast<int>(ColMajor)) ? NumDims - 1 : 0;
+ Index indices[2] = {index, index + PacketSize - 1};
+ Index patchIndices[2] = {indices[0] / m_outputStrides[output_stride_index],
+ indices[1] / m_outputStrides[output_stride_index]};
+ Index patchOffsets[2] = {indices[0] - patchIndices[0] * m_outputStrides[output_stride_index],
+ indices[1] - patchIndices[1] * m_outputStrides[output_stride_index]};
+
+ Index inputIndices[2] = {0, 0};
+ if (static_cast<int>(Layout) == static_cast<int>(ColMajor)) {
+ EIGEN_UNROLL_LOOP
+ for (int i = NumDims - 2; i > 0; --i) {
+ const Index patchIdx[2] = {patchIndices[0] / m_patchStrides[i],
+ patchIndices[1] / m_patchStrides[i]};
+ patchIndices[0] -= patchIdx[0] * m_patchStrides[i];
+ patchIndices[1] -= patchIdx[1] * m_patchStrides[i];
+
+ const Index offsetIdx[2] = {patchOffsets[0] / m_outputStrides[i],
+ patchOffsets[1] / m_outputStrides[i]};
+ patchOffsets[0] -= offsetIdx[0] * m_outputStrides[i];
+ patchOffsets[1] -= offsetIdx[1] * m_outputStrides[i];
+
+ inputIndices[0] += (patchIdx[0] + offsetIdx[0]) * m_inputStrides[i];
+ inputIndices[1] += (patchIdx[1] + offsetIdx[1]) * m_inputStrides[i];
+ }
+ } else {
+ EIGEN_UNROLL_LOOP
+ for (int i = 0; i < NumDims - 2; ++i) {
+ const Index patchIdx[2] = {patchIndices[0] / m_patchStrides[i],
+ patchIndices[1] / m_patchStrides[i]};
+ patchIndices[0] -= patchIdx[0] * m_patchStrides[i];
+ patchIndices[1] -= patchIdx[1] * m_patchStrides[i];
+
+ const Index offsetIdx[2] = {patchOffsets[0] / m_outputStrides[i+1],
+ patchOffsets[1] / m_outputStrides[i+1]};
+ patchOffsets[0] -= offsetIdx[0] * m_outputStrides[i+1];
+ patchOffsets[1] -= offsetIdx[1] * m_outputStrides[i+1];
+
+ inputIndices[0] += (patchIdx[0] + offsetIdx[0]) * m_inputStrides[i];
+ inputIndices[1] += (patchIdx[1] + offsetIdx[1]) * m_inputStrides[i];
+ }
+ }
+ inputIndices[0] += (patchIndices[0] + patchOffsets[0]);
+ inputIndices[1] += (patchIndices[1] + patchOffsets[1]);
+
+ if (inputIndices[1] - inputIndices[0] == PacketSize - 1) {
+ PacketReturnType rslt = m_impl.template packet<Unaligned>(inputIndices[0]);
+ return rslt;
+ }
+ else {
+ EIGEN_ALIGN_MAX CoeffReturnType values[PacketSize];
+ values[0] = m_impl.coeff(inputIndices[0]);
+ values[PacketSize-1] = m_impl.coeff(inputIndices[1]);
+ EIGEN_UNROLL_LOOP
+ for (int i = 1; i < PacketSize-1; ++i) {
+ values[i] = coeff(index+i);
+ }
+ PacketReturnType rslt = internal::pload<PacketReturnType>(values);
+ return rslt;
+ }
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorOpCost costPerCoeff(bool vectorized) const {
+ const double compute_cost = NumDims * (TensorOpCost::DivCost<Index>() +
+ TensorOpCost::MulCost<Index>() +
+ 2 * TensorOpCost::AddCost<Index>());
+ return m_impl.costPerCoeff(vectorized) +
+ TensorOpCost(0, 0, compute_cost, vectorized, PacketSize);
+ }
+
+ EIGEN_DEVICE_FUNC EvaluatorPointerType data() const { return NULL; }
+
+#ifdef EIGEN_USE_SYCL
+ // binding placeholder accessors to a command group handler for SYCL
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void bind(cl::sycl::handler &cgh) const {
+ m_impl.bind(cgh);
+ }
+#endif
+
+ protected:
+ Dimensions m_dimensions;
+ array<Index, NumDims> m_outputStrides;
+ array<Index, NumDims-1> m_inputStrides;
+ array<Index, NumDims-1> m_patchStrides;
+
+ TensorEvaluator<ArgType, Device> m_impl;
+
+};
+
+} // end namespace Eigen
+
+#endif // EIGEN_CXX11_TENSOR_TENSOR_PATCH_H
diff --git a/unsupported/Eigen/CXX11/src/Tensor/TensorRandom.h b/unsupported/Eigen/CXX11/src/Tensor/TensorRandom.h
new file mode 100644
index 0000000..0de4047
--- /dev/null
+++ b/unsupported/Eigen/CXX11/src/Tensor/TensorRandom.h
@@ -0,0 +1,319 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2016 Benoit Steiner <benoit.steiner.goog@gmail.com>
+// Copyright (C) 2018 Mehdi Goli <eigen@codeplay.com> Codeplay Software Ltd.
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_CXX11_TENSOR_TENSOR_RANDOM_H
+#define EIGEN_CXX11_TENSOR_TENSOR_RANDOM_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+namespace internal {
+
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE uint64_t get_random_seed() {
+#if defined(EIGEN_GPU_COMPILE_PHASE)
+ // We don't support 3d kernels since we currently only use 1 and
+ // 2d kernels.
+ gpu_assert(threadIdx.z == 0);
+ return blockIdx.x * blockDim.x + threadIdx.x
+ + gridDim.x * blockDim.x * (blockIdx.y * blockDim.y + threadIdx.y);
+#else
+ // Rely on Eigen's random implementation.
+ return random<uint64_t>();
+#endif
+}
+
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE unsigned PCG_XSH_RS_generator(uint64_t* state, uint64_t stream) {
+ // TODO: Unify with the implementation in the non blocking thread pool.
+ uint64_t current = *state;
+ // Update the internal state
+ *state = current * 6364136223846793005ULL + (stream << 1 | 1);
+ // Generate the random output (using the PCG-XSH-RS scheme)
+ return static_cast<unsigned>((current ^ (current >> 22)) >> (22 + (current >> 61)));
+}
+
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE uint64_t PCG_XSH_RS_state(uint64_t seed) {
+ seed = seed ? seed : get_random_seed();
+ return seed * 6364136223846793005ULL + 0xda3e39cb94b95bdbULL;
+}
+
+template <typename T> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+T RandomToTypeUniform(uint64_t* state, uint64_t stream) {
+ unsigned rnd = PCG_XSH_RS_generator(state, stream);
+ return static_cast<T>(rnd);
+}
+
+
+template <> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+Eigen::half RandomToTypeUniform<Eigen::half>(uint64_t* state, uint64_t stream) {
+ // Generate 10 random bits for the mantissa, merge with exponent.
+ unsigned rnd = PCG_XSH_RS_generator(state, stream);
+ const uint16_t half_bits = static_cast<uint16_t>(rnd & 0x3ffu) | (static_cast<uint16_t>(15) << 10);
+ Eigen::half result = Eigen::numext::bit_cast<Eigen::half>(half_bits);
+ // Return the final result
+ return result - Eigen::half(1.0f);
+}
+
+template <> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+Eigen::bfloat16 RandomToTypeUniform<Eigen::bfloat16>(uint64_t* state, uint64_t stream) {
+
+ // Generate 7 random bits for the mantissa, merge with exponent.
+ unsigned rnd = PCG_XSH_RS_generator(state, stream);
+ const uint16_t half_bits = static_cast<uint16_t>(rnd & 0x7fu) | (static_cast<uint16_t>(127) << 7);
+ Eigen::bfloat16 result = Eigen::numext::bit_cast<Eigen::bfloat16>(half_bits);
+ // Return the final result
+ return result - Eigen::bfloat16(1.0f);
+}
+
+template <> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+float RandomToTypeUniform<float>(uint64_t* state, uint64_t stream) {
+ typedef union {
+ uint32_t raw;
+ float fp;
+ } internal;
+ internal result;
+ // Generate 23 random bits for the mantissa mantissa
+ const unsigned rnd = PCG_XSH_RS_generator(state, stream);
+ result.raw = rnd & 0x7fffffu;
+ // Set the exponent
+ result.raw |= (static_cast<uint32_t>(127) << 23);
+ // Return the final result
+ return result.fp - 1.0f;
+}
+
+template <> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+double RandomToTypeUniform<double>(uint64_t* state, uint64_t stream) {
+ typedef union {
+ uint64_t raw;
+ double dp;
+ } internal;
+ internal result;
+ result.raw = 0;
+ // Generate 52 random bits for the mantissa
+ // First generate the upper 20 bits
+ unsigned rnd1 = PCG_XSH_RS_generator(state, stream) & 0xfffffu;
+ // The generate the lower 32 bits
+ unsigned rnd2 = PCG_XSH_RS_generator(state, stream);
+ result.raw = (static_cast<uint64_t>(rnd1) << 32) | rnd2;
+ // Set the exponent
+ result.raw |= (static_cast<uint64_t>(1023) << 52);
+ // Return the final result
+ return result.dp - 1.0;
+}
+
+template <> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+std::complex<float> RandomToTypeUniform<std::complex<float> >(uint64_t* state, uint64_t stream) {
+ return std::complex<float>(RandomToTypeUniform<float>(state, stream),
+ RandomToTypeUniform<float>(state, stream));
+}
+template <> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+std::complex<double> RandomToTypeUniform<std::complex<double> >(uint64_t* state, uint64_t stream) {
+ return std::complex<double>(RandomToTypeUniform<double>(state, stream),
+ RandomToTypeUniform<double>(state, stream));
+}
+
+template <typename T> class UniformRandomGenerator {
+ public:
+ static constexpr bool PacketAccess = true;
+
+ // Uses the given "seed" if non-zero, otherwise uses a random seed.
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE UniformRandomGenerator(
+ uint64_t seed = 0) {
+ m_state = PCG_XSH_RS_state(seed);
+ #ifdef EIGEN_USE_SYCL
+ // In SYCL it is not possible to build PCG_XSH_RS_state in one step.
+ // Therefore, we need two steps to initializate the m_state.
+ // IN SYCL, the constructor of the functor is s called on the CPU
+ // and we get the clock seed here from the CPU. However, This seed is
+ //the same for all the thread. As unlike CUDA, the thread.ID, BlockID, etc is not a global function.
+ // and only available on the Operator() function (which is called on the GPU).
+ // Thus for CUDA (((CLOCK + global_thread_id)* 6364136223846793005ULL) + 0xda3e39cb94b95bdbULL) is passed to each thread
+ // but for SYCL ((CLOCK * 6364136223846793005ULL) + 0xda3e39cb94b95bdbULL) is passed to each thread and each thread adds
+ // the (global_thread_id* 6364136223846793005ULL) for itself only once, in order to complete the construction
+ // similar to CUDA Therefore, the thread Id injection is not available at this stage.
+ //However when the operator() is called the thread ID will be available. So inside the opeator,
+ // we add the thrreadID, BlockId,... (which is equivalent of i)
+ //to the seed and construct the unique m_state per thead similar to cuda.
+ m_exec_once =false;
+ #endif
+ }
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE UniformRandomGenerator(
+ const UniformRandomGenerator& other) {
+ m_state = other.m_state;
+ #ifdef EIGEN_USE_SYCL
+ m_exec_once =other.m_exec_once;
+ #endif
+ }
+
+ template<typename Index> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ T operator()(Index i) const {
+ #ifdef EIGEN_USE_SYCL
+ if(!m_exec_once) {
+ // This is the second stage of adding thread Id to the CPU clock seed and build unique seed per thread
+ // The (i * 6364136223846793005ULL) is the remaining part of the PCG_XSH_RS_state on the GPU side
+ m_state += (i * 6364136223846793005ULL);
+ m_exec_once =true;
+ }
+ #endif
+ T result = RandomToTypeUniform<T>(&m_state, i);
+ return result;
+ }
+
+ template<typename Packet, typename Index> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ Packet packetOp(Index i) const {
+ const int packetSize = internal::unpacket_traits<Packet>::size;
+ EIGEN_ALIGN_MAX T values[packetSize];
+ #ifdef EIGEN_USE_SYCL
+ if(!m_exec_once) {
+ // This is the second stage of adding thread Id to the CPU clock seed and build unique seed per thread
+ m_state += (i * 6364136223846793005ULL);
+ m_exec_once =true;
+ }
+ #endif
+ EIGEN_UNROLL_LOOP
+ for (int j = 0; j < packetSize; ++j) {
+ values[j] = RandomToTypeUniform<T>(&m_state, i);
+ }
+ return internal::pload<Packet>(values);
+ }
+
+ private:
+ mutable uint64_t m_state;
+ #ifdef EIGEN_USE_SYCL
+ mutable bool m_exec_once;
+ #endif
+};
+
+template <typename Scalar>
+struct functor_traits<UniformRandomGenerator<Scalar> > {
+ enum {
+ // Rough estimate for floating point, multiplied by ceil(sizeof(T) / sizeof(float)).
+ Cost = 12 * NumTraits<Scalar>::AddCost *
+ ((sizeof(Scalar) + sizeof(float) - 1) / sizeof(float)),
+ PacketAccess = UniformRandomGenerator<Scalar>::PacketAccess
+ };
+};
+
+
+
+template <typename T> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+T RandomToTypeNormal(uint64_t* state, uint64_t stream) {
+ // Use the ratio of uniform method to generate numbers following a normal
+ // distribution. See for example Numerical Recipes chapter 7.3.9 for the
+ // details.
+ T u, v, q;
+ do {
+ u = RandomToTypeUniform<T>(state, stream);
+ v = T(1.7156) * (RandomToTypeUniform<T>(state, stream) - T(0.5));
+ const T x = u - T(0.449871);
+ const T y = numext::abs(v) + T(0.386595);
+ q = x*x + y * (T(0.196)*y - T(0.25472)*x);
+ } while (q > T(0.27597) &&
+ (q > T(0.27846) || v*v > T(-4) * numext::log(u) * u*u));
+
+ return v/u;
+}
+
+template <> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+std::complex<float> RandomToTypeNormal<std::complex<float> >(uint64_t* state, uint64_t stream) {
+ return std::complex<float>(RandomToTypeNormal<float>(state, stream),
+ RandomToTypeNormal<float>(state, stream));
+}
+template <> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+std::complex<double> RandomToTypeNormal<std::complex<double> >(uint64_t* state, uint64_t stream) {
+ return std::complex<double>(RandomToTypeNormal<double>(state, stream),
+ RandomToTypeNormal<double>(state, stream));
+}
+
+
+template <typename T> class NormalRandomGenerator {
+ public:
+ static constexpr bool PacketAccess = true;
+
+ // Uses the given "seed" if non-zero, otherwise uses a random seed.
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE NormalRandomGenerator(uint64_t seed = 0) {
+ m_state = PCG_XSH_RS_state(seed);
+ #ifdef EIGEN_USE_SYCL
+ // In SYCL it is not possible to build PCG_XSH_RS_state in one step.
+ // Therefore, we need two steps to initializate the m_state.
+ // IN SYCL, the constructor of the functor is s called on the CPU
+ // and we get the clock seed here from the CPU. However, This seed is
+ //the same for all the thread. As unlike CUDA, the thread.ID, BlockID, etc is not a global function.
+ // and only available on the Operator() function (which is called on the GPU).
+ // Therefore, the thread Id injection is not available at this stage. However when the operator()
+ //is called the thread ID will be available. So inside the operator,
+ // we add the thrreadID, BlockId,... (which is equivalent of i)
+ //to the seed and construct the unique m_state per thead similar to cuda.
+ m_exec_once =false;
+ #endif
+ }
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE NormalRandomGenerator(
+ const NormalRandomGenerator& other) {
+ m_state = other.m_state;
+#ifdef EIGEN_USE_SYCL
+ m_exec_once=other.m_exec_once;
+#endif
+ }
+
+ template<typename Index> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ T operator()(Index i) const {
+ #ifdef EIGEN_USE_SYCL
+ if(!m_exec_once) {
+ // This is the second stage of adding thread Id to the CPU clock seed and build unique seed per thread
+ m_state += (i * 6364136223846793005ULL);
+ m_exec_once =true;
+ }
+ #endif
+ T result = RandomToTypeNormal<T>(&m_state, i);
+ return result;
+ }
+
+ template<typename Packet, typename Index> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ Packet packetOp(Index i) const {
+ const int packetSize = internal::unpacket_traits<Packet>::size;
+ EIGEN_ALIGN_MAX T values[packetSize];
+ #ifdef EIGEN_USE_SYCL
+ if(!m_exec_once) {
+ // This is the second stage of adding thread Id to the CPU clock seed and build unique seed per thread
+ m_state += (i * 6364136223846793005ULL);
+ m_exec_once =true;
+ }
+ #endif
+ EIGEN_UNROLL_LOOP
+ for (int j = 0; j < packetSize; ++j) {
+ values[j] = RandomToTypeNormal<T>(&m_state, i);
+ }
+ return internal::pload<Packet>(values);
+ }
+
+ private:
+ mutable uint64_t m_state;
+ #ifdef EIGEN_USE_SYCL
+ mutable bool m_exec_once;
+ #endif
+};
+
+
+template <typename Scalar>
+struct functor_traits<NormalRandomGenerator<Scalar> > {
+ enum {
+ // On average, we need to generate about 3 random numbers
+ // 15 mul, 8 add, 1.5 logs
+ Cost = 3 * functor_traits<UniformRandomGenerator<Scalar> >::Cost +
+ 15 * NumTraits<Scalar>::AddCost + 8 * NumTraits<Scalar>::AddCost +
+ 3 * functor_traits<scalar_log_op<Scalar> >::Cost / 2,
+ PacketAccess = NormalRandomGenerator<Scalar>::PacketAccess
+ };
+};
+
+
+} // end namespace internal
+} // end namespace Eigen
+
+#endif // EIGEN_CXX11_TENSOR_TENSOR_RANDOM_H
diff --git a/unsupported/Eigen/CXX11/src/Tensor/TensorReduction.h b/unsupported/Eigen/CXX11/src/Tensor/TensorReduction.h
new file mode 100644
index 0000000..e62397a
--- /dev/null
+++ b/unsupported/Eigen/CXX11/src/Tensor/TensorReduction.h
@@ -0,0 +1,1039 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>
+// Copyright (C) 2016 Mehdi Goli, Codeplay Software Ltd <eigen@codeplay.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_CXX11_TENSOR_TENSOR_REDUCTION_H
+#define EIGEN_CXX11_TENSOR_TENSOR_REDUCTION_H
+
+// clang is incompatible with the CUDA syntax wrt making a kernel a class friend,
+// so we'll use a macro to make clang happy.
+#ifndef KERNEL_FRIEND
+#if defined(__clang__) && (defined(__CUDA__) || defined(__HIP__))
+#define KERNEL_FRIEND friend __global__ EIGEN_HIP_LAUNCH_BOUNDS_1024
+#else
+#define KERNEL_FRIEND friend
+#endif
+#endif
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+
+/** \class TensorReduction
+ * \ingroup CXX11_Tensor_Module
+ *
+ * \brief Tensor reduction class.
+ *
+ */
+
+namespace internal {
+ template<typename Op, typename Dims, typename XprType,template <class> class MakePointer_ >
+ struct traits<TensorReductionOp<Op, Dims, XprType, MakePointer_> >
+ : traits<XprType>
+{
+ typedef traits<XprType> XprTraits;
+ typedef typename XprTraits::Scalar Scalar;
+ typedef typename XprTraits::StorageKind StorageKind;
+ typedef typename XprTraits::Index Index;
+ typedef typename XprType::Nested Nested;
+ static constexpr int NumDimensions = XprTraits::NumDimensions - array_size<Dims>::value;
+ static constexpr int Layout = XprTraits::Layout;
+ typedef typename XprTraits::PointerType PointerType;
+
+ template <class T> struct MakePointer {
+ // Intermediate typedef to workaround MSVC issue.
+ typedef MakePointer_<T> MakePointerT;
+ typedef typename MakePointerT::Type Type;
+ };
+};
+
+template<typename Op, typename Dims, typename XprType, template <class> class MakePointer_>
+struct eval<TensorReductionOp<Op, Dims, XprType, MakePointer_>, Eigen::Dense>
+{
+ typedef const TensorReductionOp<Op, Dims, XprType, MakePointer_>& type;
+};
+
+template<typename Op, typename Dims, typename XprType, template <class> class MakePointer_>
+struct nested<TensorReductionOp<Op, Dims, XprType, MakePointer_>, 1, typename eval<TensorReductionOp<Op, Dims, XprType, MakePointer_> >::type>
+{
+ typedef TensorReductionOp<Op, Dims, XprType, MakePointer_> type;
+};
+
+
+template <typename OutputDims> struct DimInitializer {
+ template <typename InputDims, typename ReducedDims> EIGEN_DEVICE_FUNC
+ static void run(const InputDims& input_dims,
+ const array<bool, internal::array_size<InputDims>::value>& reduced,
+ OutputDims* output_dims, ReducedDims* reduced_dims) {
+ const int NumInputDims = internal::array_size<InputDims>::value;
+ int outputIndex = 0;
+ int reduceIndex = 0;
+ for (int i = 0; i < NumInputDims; ++i) {
+ if (reduced[i]) {
+ (*reduced_dims)[reduceIndex] = input_dims[i];
+ ++reduceIndex;
+ } else {
+ (*output_dims)[outputIndex] = input_dims[i];
+ ++outputIndex;
+ }
+ }
+ }
+};
+
+template <> struct DimInitializer<Sizes<> > {
+ template <typename InputDims, typename Index, size_t Rank> EIGEN_DEVICE_FUNC
+ static void run(const InputDims& input_dims, const array<bool, Rank>&,
+ Sizes<>*, array<Index, Rank>* reduced_dims) {
+ const int NumInputDims = internal::array_size<InputDims>::value;
+ for (int i = 0; i < NumInputDims; ++i) {
+ (*reduced_dims)[i] = input_dims[i];
+ }
+ }
+};
+
+
+template <typename ReducedDims, int NumTensorDims, int Layout>
+struct are_inner_most_dims {
+ static const bool value = false;
+};
+template <typename ReducedDims, int NumTensorDims, int Layout>
+struct preserve_inner_most_dims {
+ static const bool value = false;
+};
+
+template <typename ReducedDims, int NumTensorDims>
+struct are_inner_most_dims<ReducedDims, NumTensorDims, ColMajor>{
+ static const bool tmp1 = indices_statically_known_to_increase<ReducedDims>();
+ static const bool tmp2 = index_statically_eq<ReducedDims>(0, 0);
+ static const bool tmp3 = index_statically_eq<ReducedDims>(array_size<ReducedDims>::value-1, array_size<ReducedDims>::value-1);
+ static const bool value = tmp1 & tmp2 & tmp3;
+};
+template <typename ReducedDims, int NumTensorDims>
+struct are_inner_most_dims<ReducedDims, NumTensorDims, RowMajor>{
+ static const bool tmp1 = indices_statically_known_to_increase<ReducedDims>();
+ static const bool tmp2 = index_statically_eq<ReducedDims>(0, NumTensorDims - array_size<ReducedDims>::value);
+ static const bool tmp3 = index_statically_eq<ReducedDims>(array_size<ReducedDims>::value - 1, NumTensorDims - 1);
+ static const bool value = tmp1 & tmp2 & tmp3;
+
+};
+template <typename ReducedDims, int NumTensorDims>
+struct preserve_inner_most_dims<ReducedDims, NumTensorDims, ColMajor>{
+ static const bool tmp1 = indices_statically_known_to_increase<ReducedDims>();
+ static const bool tmp2 = index_statically_gt<ReducedDims>(0, 0);
+ static const bool value = tmp1 & tmp2;
+
+};
+template <typename ReducedDims, int NumTensorDims>
+struct preserve_inner_most_dims<ReducedDims, NumTensorDims, RowMajor>{
+ static const bool tmp1 = indices_statically_known_to_increase<ReducedDims>();
+ static const bool tmp2 = index_statically_lt<ReducedDims>(array_size<ReducedDims>::value - 1, NumTensorDims - 1);
+ static const bool value = tmp1 & tmp2;
+};
+
+
+template <int DimIndex, typename Self, typename Op>
+struct GenericDimReducer {
+ static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void reduce(const Self& self, typename Self::Index firstIndex, Op& reducer, typename Self::CoeffReturnType* accum) {
+ EIGEN_STATIC_ASSERT((DimIndex > 0), YOU_MADE_A_PROGRAMMING_MISTAKE);
+ for (int j = 0; j < self.m_reducedDims[DimIndex]; ++j) {
+ const typename Self::Index input = firstIndex + j * self.m_reducedStrides[DimIndex];
+ GenericDimReducer<DimIndex-1, Self, Op>::reduce(self, input, reducer, accum);
+ }
+ }
+};
+template <typename Self, typename Op>
+struct GenericDimReducer<0, Self, Op> {
+ static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void reduce(const Self& self, typename Self::Index firstIndex, Op& reducer, typename Self::CoeffReturnType* accum) {
+ for (int j = 0; j < self.m_reducedDims[0]; ++j) {
+ const typename Self::Index input = firstIndex + j * self.m_reducedStrides[0];
+ reducer.reduce(self.m_impl.coeff(input), accum);
+ }
+ }
+};
+template <typename Self, typename Op>
+struct GenericDimReducer<-1, Self, Op> {
+ static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void reduce(const Self& self, typename Self::Index index, Op& reducer, typename Self::CoeffReturnType* accum) {
+ reducer.reduce(self.m_impl.coeff(index), accum);
+ }
+};
+
+template <typename Self, typename Op, bool Vectorizable = (Self::InputPacketAccess && Self::ReducerTraits::PacketAccess),
+ bool UseTreeReduction = (!Self::ReducerTraits::IsStateful &&
+ !Self::ReducerTraits::IsExactlyAssociative &&
+ // GPU threads can quickly run out of stack space
+ // for moderately sized inputs.
+ !Self::RunningOnGPU
+ )>
+struct InnerMostDimReducer {
+ static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE typename Self::CoeffReturnType reduce(const Self& self, typename Self::Index firstIndex, typename Self::Index numValuesToReduce, Op& reducer) {
+ typename Self::CoeffReturnType accum = reducer.initialize();
+ for (typename Self::Index j = 0; j < numValuesToReduce; ++j) {
+ reducer.reduce(self.m_impl.coeff(firstIndex + j), &accum);
+ }
+ return reducer.finalize(accum);
+ }
+};
+
+template <typename Self, typename Op>
+struct InnerMostDimReducer<Self, Op, true, false> {
+ static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE typename Self::CoeffReturnType reduce(const Self& self, typename Self::Index firstIndex, typename Self::Index numValuesToReduce, Op& reducer0) {
+ using Index = typename Self::Index;
+ constexpr Index packetSize = internal::unpacket_traits<typename Self::PacketReturnType>::size;
+ Index start = 0;
+ typename Self::PacketReturnType paccum0 = reducer0.template initializePacket<typename Self::PacketReturnType>();
+ if (!Self::ReducerTraits::IsStateful && numValuesToReduce >= 4*packetSize) {
+ const Index VectorizedSize4 = (numValuesToReduce / (4*packetSize)) * (4*packetSize);
+ typename Self::PacketReturnType paccum1 = reducer0.template initializePacket<typename Self::PacketReturnType>();
+ typename Self::PacketReturnType paccum2 = reducer0.template initializePacket<typename Self::PacketReturnType>();
+ typename Self::PacketReturnType paccum3 = reducer0.template initializePacket<typename Self::PacketReturnType>();
+ const Index offset0 = firstIndex;
+ const Index offset1 = firstIndex + packetSize;
+ const Index offset2 = firstIndex + 2*packetSize;
+ const Index offset3 = firstIndex + 3*packetSize;
+ for (Index j = 0; j < VectorizedSize4; j += 4*packetSize) {
+ reducer0.reducePacket(self.m_impl.template packet<Unaligned>(offset0 + j), &paccum0);
+ reducer0.reducePacket(self.m_impl.template packet<Unaligned>(offset1 + j), &paccum1);
+ reducer0.reducePacket(self.m_impl.template packet<Unaligned>(offset2 + j), &paccum2);
+ reducer0.reducePacket(self.m_impl.template packet<Unaligned>(offset3 + j), &paccum3);
+ }
+ reducer0.reducePacket(paccum1, &paccum0);
+ reducer0.reducePacket(paccum2, &paccum0);
+ reducer0.reducePacket(paccum3, &paccum0);
+ start = VectorizedSize4;
+ }
+ if (start <= (numValuesToReduce - packetSize)) {
+ const Index VectorizedSize = (numValuesToReduce / packetSize) * packetSize;
+ for (Index j = start; j < VectorizedSize; j += packetSize) {
+ reducer0.reducePacket(self.m_impl.template packet<Unaligned>(firstIndex + j), &paccum0);
+ }
+ start = VectorizedSize;
+ }
+ typename Self::CoeffReturnType accum = reducer0.initialize();
+ for (Index j = start; j < numValuesToReduce; ++j) {
+ reducer0.reduce(self.m_impl.coeff(firstIndex + j), &accum);
+ }
+ return reducer0.finalizeBoth(accum, paccum0);
+ }
+};
+
+
+#if !defined(EIGEN_HIPCC)
+
+// The following implements tree-based reduction, which improves the accuracy
+// of sum and mean reductions, since each of the n inputs only participates in
+// O(log n) additions.
+template <typename T>
+EIGEN_DEVICE_FUNC inline Index LeafSize() { return 1024; }
+template <>
+EIGEN_DEVICE_FUNC inline Index LeafSize<half>() { return 200; }
+template <>
+EIGEN_DEVICE_FUNC inline Index LeafSize<bfloat16>() { return 128; }
+
+template <typename Self, typename Op>
+struct InnerMostDimReducer<Self, Op, false, true> {
+ static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE typename Self::CoeffReturnType
+ reduce(const Self& self, typename Self::Index firstIndex,
+ typename Self::Index numValuesToReduce, Op& reducer) {
+ const Index kLeafSize = LeafSize<typename Self::CoeffReturnType>();
+ typename Self::CoeffReturnType accum = reducer.initialize();
+ if (numValuesToReduce > kLeafSize) {
+ const typename Self::Index half = numValuesToReduce / 2;
+ // Recursively reduce the two halves.
+ reducer.reduce(reduce(self, firstIndex, half, reducer), &accum);
+ reducer.reduce(
+ reduce(self, firstIndex + half, numValuesToReduce - half, reducer),
+ &accum);
+ return reducer.finalize(accum);
+ } else {
+ return InnerMostDimReducer<Self, Op, false, false>::reduce(self, firstIndex, numValuesToReduce, reducer);
+ }
+ }
+};
+
+template <typename Self, typename Op>
+struct InnerMostDimReducer<Self, Op, true, true> {
+ static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE typename Self::CoeffReturnType
+ reduce(const Self& self, typename Self::Index firstIndex,
+ typename Self::Index numValuesToReduce, Op& reducer) {
+ const Index kLeafSize = LeafSize<typename Self::CoeffReturnType>();
+ const typename Self::Index packetSize =
+ internal::unpacket_traits<typename Self::PacketReturnType>::size;
+ typename Self::CoeffReturnType accum = reducer.initialize();
+ if (numValuesToReduce > packetSize * kLeafSize) {
+ // Make sure the split point is aligned on a packet boundary.
+ const typename Self::Index split =
+ packetSize *
+ divup(firstIndex + divup(numValuesToReduce, typename Self::Index(2)),
+ packetSize);
+ const typename Self::Index num_left =
+ numext::mini(split - firstIndex, numValuesToReduce);
+ reducer.reduce(reduce(self, firstIndex, num_left, reducer), &accum);
+ if (num_left < numValuesToReduce) {
+ reducer.reduce(
+ reduce(self, split, numValuesToReduce - num_left, reducer), &accum);
+ }
+ return reducer.finalize(accum);
+ } else {
+ return InnerMostDimReducer<Self, Op, true, false>::reduce(self, firstIndex, numValuesToReduce, reducer);
+ }
+ }
+};
+#endif
+
+template <int DimIndex, typename Self, typename Op, bool vectorizable = (Self::InputPacketAccess && Self::ReducerTraits::PacketAccess)>
+struct InnerMostDimPreserver {
+ static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void reduce(const Self&, typename Self::Index, Op&, typename Self::PacketReturnType*) {
+ eigen_assert(false && "should never be called");
+ }
+};
+
+template <int DimIndex, typename Self, typename Op>
+struct InnerMostDimPreserver<DimIndex, Self, Op, true> {
+ static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void reduce(const Self& self, typename Self::Index firstIndex, Op& reducer, typename Self::PacketReturnType* accum) {
+ EIGEN_STATIC_ASSERT((DimIndex > 0), YOU_MADE_A_PROGRAMMING_MISTAKE);
+ for (typename Self::Index j = 0; j < self.m_reducedDims[DimIndex]; ++j) {
+ const typename Self::Index input = firstIndex + j * self.m_reducedStrides[DimIndex];
+ InnerMostDimPreserver<DimIndex-1, Self, Op>::reduce(self, input, reducer, accum);
+ }
+ }
+};
+
+template <typename Self, typename Op>
+struct InnerMostDimPreserver<0, Self, Op, true> {
+ static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void reduce(const Self& self, typename Self::Index firstIndex, Op& reducer0, typename Self::PacketReturnType* accum0) {
+ using Index = typename Self::Index;
+ const Index stride = self.m_reducedStrides[0];
+ const Index size = self.m_reducedDims[0];
+ if (!Self::ReducerTraits::IsStateful && size >= 16) {
+ const Index unrolled_size4 = (size / 4) * 4;
+ typename Self::PacketReturnType accum1 = reducer0.template initializePacket<typename Self::PacketReturnType>();
+ typename Self::PacketReturnType accum2 = reducer0.template initializePacket<typename Self::PacketReturnType>();
+ typename Self::PacketReturnType accum3 = reducer0.template initializePacket<typename Self::PacketReturnType>();
+ for (Index j = 0; j < unrolled_size4; j += 4) {
+ const Index input0 = firstIndex + j * stride;
+ reducer0.reducePacket(self.m_impl.template packet<Unaligned>(input0), accum0);
+ const Index input1 = firstIndex + (j+1) * stride;
+ reducer0.reducePacket(self.m_impl.template packet<Unaligned>(input1), &accum1);
+ const Index input2 = firstIndex + (j+2) * stride;
+ reducer0.reducePacket(self.m_impl.template packet<Unaligned>(input2), &accum2);
+ const Index input3 = firstIndex + (j+3) * stride;
+ reducer0.reducePacket(self.m_impl.template packet<Unaligned>(input3), &accum3);
+ }
+ reducer0.reducePacket(accum1, accum0);
+ reducer0.reducePacket(accum2, accum0);
+ reducer0.reducePacket(accum3, accum0);
+ for (Index j = unrolled_size4; j < size; ++j) {
+ Index input = firstIndex + j * stride;
+ reducer0.reducePacket(self.m_impl.template packet<Unaligned>(input), accum0);
+ }
+ } else {
+ for (Index j = 0; j < size; ++j) {
+ Index input = firstIndex + j * stride;
+ reducer0.reducePacket(self.m_impl.template packet<Unaligned>(input), accum0);
+ }
+ }
+ }
+};
+template <typename Self, typename Op>
+struct InnerMostDimPreserver<-1, Self, Op, true> {
+ static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void reduce(const Self&, typename Self::Index, Op&, typename Self::PacketReturnType*) {
+ eigen_assert(false && "should never be called");
+ }
+};
+
+// Default full reducer
+template <typename Self, typename Op, typename Device, bool Vectorizable = (Self::InputPacketAccess && Self::ReducerTraits::PacketAccess)>
+struct FullReducer {
+ static constexpr bool HasOptimizedImplementation = false;
+
+ static EIGEN_DEVICE_FUNC void run(const Self& self, Op& reducer, const Device&, typename Self::EvaluatorPointerType output) {
+ const typename Self::Index num_coeffs = array_prod(self.m_impl.dimensions());
+ *output = InnerMostDimReducer<Self, Op, Vectorizable>::reduce(self, 0, num_coeffs, reducer);
+ }
+};
+
+
+#ifdef EIGEN_USE_THREADS
+// Multithreaded full reducers
+template <typename Self, typename Op,
+ bool Vectorizable = (Self::InputPacketAccess && Self::ReducerTraits::PacketAccess)>
+struct FullReducerShard {
+ static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void run(const Self& self, typename Self::Index firstIndex,
+ typename Self::Index numValuesToReduce, Op& reducer,
+ typename Self::CoeffReturnType* output) {
+ *output = InnerMostDimReducer<Self, Op, Vectorizable>::reduce(
+ self, firstIndex, numValuesToReduce, reducer);
+ }
+};
+
+// Multithreaded full reducer
+template <typename Self, typename Op, bool Vectorizable>
+struct FullReducer<Self, Op, ThreadPoolDevice, Vectorizable> {
+ static constexpr bool HasOptimizedImplementation = !Self::ReducerTraits::IsStateful;
+ static constexpr Index PacketSize =
+ unpacket_traits<typename Self::PacketReturnType>::size;
+
+ // launch one reducer per thread and accumulate the result.
+ static void run(const Self& self, Op& reducer, const ThreadPoolDevice& device,
+ typename Self::CoeffReturnType* output) {
+ typedef typename Self::Index Index;
+ const Index num_coeffs = array_prod(self.m_impl.dimensions());
+ if (num_coeffs == 0) {
+ *output = reducer.finalize(reducer.initialize());
+ return;
+ }
+ const TensorOpCost cost =
+ self.m_impl.costPerCoeff(Vectorizable) +
+ TensorOpCost(0, 0, internal::functor_traits<Op>::Cost, Vectorizable,
+ PacketSize);
+ const Index num_threads = TensorCostModel<ThreadPoolDevice>::numThreads(
+ num_coeffs, cost, device.numThreads());
+ if (num_threads == 1) {
+ *output =
+ InnerMostDimReducer<Self, Op, Vectorizable>::reduce(self, 0, num_coeffs, reducer);
+ return;
+ }
+ const Index blocksize = num_coeffs / num_threads;
+ const Index numblocks = blocksize > 0 ? num_coeffs / blocksize : 0;
+ eigen_assert(num_coeffs >= numblocks * blocksize);
+
+ Barrier barrier(internal::convert_index<unsigned int>(numblocks));
+ MaxSizeVector<typename Self::CoeffReturnType> shards(numblocks, reducer.initialize());
+ for (Index i = 0; i < numblocks; ++i) {
+ device.enqueue_with_barrier(&barrier, &FullReducerShard<Self, Op, Vectorizable>::run,
+ self, i * blocksize, blocksize, reducer,
+ &shards[i]);
+ }
+ typename Self::CoeffReturnType finalShard;
+ if (numblocks * blocksize < num_coeffs) {
+ finalShard = InnerMostDimReducer<Self, Op, Vectorizable>::reduce(
+ self, numblocks * blocksize, num_coeffs - numblocks * blocksize,
+ reducer);
+ } else {
+ finalShard = reducer.initialize();
+ }
+ barrier.Wait();
+
+ for (Index i = 0; i < numblocks; ++i) {
+ reducer.reduce(shards[i], &finalShard);
+ }
+ *output = reducer.finalize(finalShard);
+ }
+};
+
+#endif
+
+
+// Default inner reducer
+template <typename Self, typename Op, typename Device>
+struct InnerReducer {
+ static constexpr bool HasOptimizedImplementation = false;
+
+ EIGEN_DEVICE_FUNC static bool run(const Self&, Op&, const Device&, typename Self::CoeffReturnType*, typename Self::Index, typename Self::Index) {
+ eigen_assert(false && "Not implemented");
+ return true;
+ }
+};
+
+// Default outer reducer
+template <typename Self, typename Op, typename Device>
+struct OuterReducer {
+ static constexpr bool HasOptimizedImplementation = false;
+
+ EIGEN_DEVICE_FUNC static bool run(const Self&, Op&, const Device&, typename Self::CoeffReturnType*, typename Self::Index, typename Self::Index) {
+ eigen_assert(false && "Not implemented");
+ return true;
+ }
+};
+
+#ifdef EIGEN_USE_SYCL
+// Default Generic reducer
+template <typename Self, typename Op, typename Device>
+struct GenericReducer {
+ static constexpr bool HasOptimizedImplementation = false;
+
+ EIGEN_DEVICE_FUNC static bool run(const Self&, Op&, const Device&, typename Self::CoeffReturnType*, typename Self::Index, typename Self::Index) {
+ eigen_assert(false && "Not implemented");
+ return true;
+ }
+};
+#endif
+
+#if defined(EIGEN_USE_GPU) && (defined(EIGEN_GPUCC))
+template <int B, int N, typename S, typename R, typename I_>
+__global__ EIGEN_HIP_LAUNCH_BOUNDS_1024 void FullReductionKernel(R, const S, I_, typename S::CoeffReturnType*, unsigned int*);
+
+
+#if defined(EIGEN_HAS_GPU_FP16)
+template <typename S, typename R, typename I_>
+__global__ EIGEN_HIP_LAUNCH_BOUNDS_1024 void ReductionInitFullReduxKernelHalfFloat(R, const S, I_, internal::packet_traits<half>::type*);
+template <int B, int N, typename S, typename R, typename I_>
+__global__ EIGEN_HIP_LAUNCH_BOUNDS_1024 void FullReductionKernelHalfFloat(R, const S, I_, half*, internal::packet_traits<half>::type*);
+template <int NPT, typename S, typename R, typename I_>
+__global__ EIGEN_HIP_LAUNCH_BOUNDS_1024 void InnerReductionKernelHalfFloat(R, const S, I_, I_, half*);
+
+#endif
+
+template <int NPT, typename S, typename R, typename I_>
+__global__ EIGEN_HIP_LAUNCH_BOUNDS_1024 void InnerReductionKernel(R, const S, I_, I_, typename S::CoeffReturnType*);
+
+template <int NPT, typename S, typename R, typename I_>
+__global__ EIGEN_HIP_LAUNCH_BOUNDS_1024 void OuterReductionKernel(R, const S, I_, I_, typename S::CoeffReturnType*);
+#endif
+
+/**
+ * For SYCL, the return type of the reduction is deduced from the initialize method of the given Op.
+ * This allows the reduction to have a different type for the accumulator than the input data type.
+ * If this is the case, the functor needs to have two reduce method: one for reducing an element of the input
+ * with the accumulator and the other for reducing two accumulators.
+ * Such a reducer can be useful for instance when the accumulator is a boolean or a bitset that checks for
+ * some properties of the input.
+ */
+template <typename Op, typename CoeffReturnType>
+struct ReductionReturnType {
+#if defined(EIGEN_USE_SYCL)
+ typedef std::remove_const_t<decltype(std::declval<Op>().initialize())> type;
+#else
+ typedef std::remove_const_t<CoeffReturnType> type;
+#endif
+};
+
+} // end namespace internal
+
+
+template <typename Op, typename Dims, typename XprType, template <class> class MakePointer_>
+class TensorReductionOp : public TensorBase<TensorReductionOp<Op, Dims, XprType, MakePointer_>, ReadOnlyAccessors> {
+ public:
+ typedef typename Eigen::internal::traits<TensorReductionOp>::Scalar Scalar;
+ typedef typename Eigen::NumTraits<Scalar>::Real RealScalar;
+ typedef std::remove_const_t<typename XprType::CoeffReturnType> CoeffReturnType;
+ typedef typename Eigen::internal::nested<TensorReductionOp>::type Nested;
+ typedef typename Eigen::internal::traits<TensorReductionOp>::StorageKind StorageKind;
+ typedef typename Eigen::internal::traits<TensorReductionOp>::Index Index;
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ TensorReductionOp(const XprType& expr, const Dims& dims) : m_expr(expr), m_dims(dims)
+ { }
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ TensorReductionOp(const XprType& expr, const Dims& dims, const Op& reducer) : m_expr(expr), m_dims(dims), m_reducer(reducer)
+ { }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ const XprType& expression() const { return m_expr; }
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ const Dims& dims() const { return m_dims; }
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ const Op& reducer() const { return m_reducer; }
+
+ protected:
+ typename XprType::Nested m_expr;
+ const Dims m_dims;
+ const Op m_reducer;
+};
+
+template<typename ArgType, typename Device>
+struct TensorReductionEvaluatorBase;
+
+// Eval as rvalue
+template<typename Op, typename Dims, typename ArgType, template <class> class MakePointer_, typename Device>
+struct TensorReductionEvaluatorBase<const TensorReductionOp<Op, Dims, ArgType, MakePointer_>, Device>
+{
+ typedef internal::reducer_traits<Op, Device> ReducerTraits;
+ typedef Dims ReducedDims;
+ typedef TensorReductionOp<Op, Dims, ArgType, MakePointer_> XprType;
+ typedef typename XprType::Index Index;
+ typedef ArgType ChildType;
+ typedef typename TensorEvaluator<ArgType, Device>::Dimensions InputDimensions;
+ static constexpr int NumInputDims = internal::array_size<InputDimensions>::value;
+ static constexpr int NumReducedDims = internal::array_size<Dims>::value;
+ static constexpr int NumOutputDims = NumInputDims - NumReducedDims;
+ typedef std::conditional_t<NumOutputDims==0, Sizes<>, DSizes<Index, NumOutputDims> > Dimensions;
+ typedef typename XprType::Scalar Scalar;
+ typedef TensorReductionEvaluatorBase<const TensorReductionOp<Op, Dims, ArgType, MakePointer_>, Device> Self;
+ static constexpr bool InputPacketAccess = TensorEvaluator<ArgType, Device>::PacketAccess;
+ typedef typename internal::ReductionReturnType<Op, typename XprType::CoeffReturnType>::type CoeffReturnType;
+ typedef typename PacketType<CoeffReturnType, Device>::type PacketReturnType;
+ static constexpr Index PacketSize = PacketType<CoeffReturnType, Device>::size;
+
+ typedef typename Eigen::internal::traits<XprType>::PointerType TensorPointerType;
+ typedef StorageMemory<CoeffReturnType, Device> Storage;
+ typedef typename Storage::Type EvaluatorPointerType;
+
+ // Subset of strides of the input tensor for the non-reduced dimensions.
+ // Indexed by output dimensions.
+ static constexpr int NumPreservedStrides = max_n_1<NumOutputDims>::size;
+
+ // For full reductions
+#if defined(EIGEN_USE_GPU) && (defined(EIGEN_GPUCC))
+ static constexpr bool RunningOnGPU = internal::is_same<Device, Eigen::GpuDevice>::value;
+ static constexpr bool RunningOnSycl = false;
+#elif defined(EIGEN_USE_SYCL)
+static constexpr bool RunningOnSycl = internal::is_same<internal::remove_all_t<Device>, Eigen::SyclDevice>::value;
+static constexpr bool RunningOnGPU = false;
+#else
+ static constexpr bool RunningOnGPU = false;
+ static constexpr bool RunningOnSycl = false;
+#endif
+
+ static constexpr int Layout = TensorEvaluator<ArgType, Device>::Layout;
+ enum {
+ IsAligned = false,
+ PacketAccess = Self::InputPacketAccess && ReducerTraits::PacketAccess,
+ BlockAccess = false,
+ PreferBlockAccess = true,
+ CoordAccess = false, // to be implemented
+ RawAccess = false
+ };
+
+ typedef std::remove_const_t<Scalar> ScalarNoConst;
+
+ //===- Tensor block evaluation strategy (see TensorBlock.h) -------------===//
+ typedef internal::TensorBlockNotImplemented TensorBlock;
+ //===--------------------------------------------------------------------===//
+
+ static constexpr bool ReducingInnerMostDims = internal::are_inner_most_dims<Dims, NumInputDims, Layout>::value;
+ static constexpr bool PreservingInnerMostDims = internal::preserve_inner_most_dims<Dims, NumInputDims, Layout>::value;
+ static constexpr bool RunningFullReduction = (NumOutputDims==0);
+
+ EIGEN_STRONG_INLINE TensorReductionEvaluatorBase(const XprType& op, const Device& device)
+ : m_impl(op.expression(), device), m_reducer(op.reducer()), m_result(NULL), m_device(device)
+ {
+ EIGEN_STATIC_ASSERT((NumInputDims >= NumReducedDims), YOU_MADE_A_PROGRAMMING_MISTAKE);
+ EIGEN_STATIC_ASSERT((!ReducingInnerMostDims | !PreservingInnerMostDims | (NumReducedDims == NumInputDims)),
+ YOU_MADE_A_PROGRAMMING_MISTAKE);
+
+ // Build the bitmap indicating if an input dimension is reduced or not.
+ for (int i = 0; i < NumInputDims; ++i) {
+ m_reduced[i] = false;
+ }
+ for (int i = 0; i < NumReducedDims; ++i) {
+ eigen_assert(op.dims()[i] >= 0);
+ eigen_assert(op.dims()[i] < NumInputDims);
+ m_reduced[op.dims()[i]] = true;
+ }
+
+ const typename TensorEvaluator<ArgType, Device>::Dimensions& input_dims = m_impl.dimensions();
+ internal::DimInitializer<Dimensions>::run(input_dims, m_reduced, &m_dimensions, &m_reducedDims);
+
+ // Precompute output strides.
+ if (NumOutputDims > 0) {
+ if (static_cast<int>(Layout) == static_cast<int>(ColMajor)) {
+ m_outputStrides[0] = 1;
+ for (int i = 1; i < NumOutputDims; ++i) {
+ m_outputStrides[i] = m_outputStrides[i - 1] * m_dimensions[i - 1];
+ m_fastOutputStrides[i] = internal::TensorIntDivisor<Index>(m_outputStrides[i]);
+ }
+ } else {
+ m_outputStrides[static_cast<size_t>(NumOutputDims - 1)] = 1;
+ for (int i = NumOutputDims - 2; i >= 0; --i) {
+ m_outputStrides[i] = m_outputStrides[i + 1] * m_dimensions[i + 1];
+ m_fastOutputStrides[i] = internal::TensorIntDivisor<Index>(m_outputStrides[i]);
+ }
+ }
+ }
+
+ // Precompute input strides.
+ if (NumInputDims > 0) {
+ array<Index, NumInputDims> input_strides;
+ if (static_cast<int>(Layout) == static_cast<int>(ColMajor)) {
+ input_strides[0] = 1;
+ for (int i = 1; i < NumInputDims; ++i) {
+ input_strides[i] = input_strides[i-1] * input_dims[i-1];
+ }
+ } else {
+ input_strides.back() = 1;
+ for (int i = NumInputDims - 2; i >= 0; --i) {
+ input_strides[i] = input_strides[i + 1] * input_dims[i + 1];
+ }
+ }
+
+ int outputIndex = 0;
+ int reduceIndex = 0;
+ for (int i = 0; i < NumInputDims; ++i) {
+ if (m_reduced[i]) {
+ m_reducedStrides[reduceIndex] = input_strides[i];
+ ++reduceIndex;
+ } else {
+ m_preservedStrides[outputIndex] = input_strides[i];
+ m_output_to_input_dim_map[outputIndex] = i;
+ ++outputIndex;
+ }
+ }
+ }
+
+ // Special case for full reductions
+ if (NumOutputDims == 0) {
+ m_preservedStrides[0] = internal::array_prod(input_dims);
+ }
+
+ m_numValuesToReduce =
+ NumOutputDims == 0
+ ? internal::array_prod(input_dims)
+ : (static_cast<int>(Layout) == static_cast<int>(ColMajor))
+ ? m_preservedStrides[0]
+ : m_preservedStrides[static_cast<size_t>(NumOutputDims - 1)];
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Dimensions& dimensions() const { return m_dimensions; }
+
+ EIGEN_STRONG_INLINE
+ bool evalSubExprsIfNeededCommon(EvaluatorPointerType data) {
+ // Use the FullReducer if possible.
+ if ((RunningFullReduction && RunningOnSycl) ||(RunningFullReduction &&
+ internal::FullReducer<Self, Op, Device>::HasOptimizedImplementation &&
+ ((RunningOnGPU && (m_device.majorDeviceVersion() >= 3)) ||
+ !RunningOnGPU))) {
+ bool need_assign = false;
+ if (!data) {
+ m_result = static_cast<EvaluatorPointerType>(m_device.get((CoeffReturnType*)m_device.allocate_temp(sizeof(CoeffReturnType))));
+ data = m_result;
+ need_assign = true;
+ }
+ Op reducer(m_reducer);
+ internal::FullReducer<Self, Op, Device>::run(*this, reducer, m_device, data);
+ return need_assign;
+ }
+
+ // Attempt to use an optimized reduction.
+ else if ((RunningOnGPU && (m_device.majorDeviceVersion() >= 3)) || (RunningOnSycl)) {
+ bool reducing_inner_dims = true;
+ for (int i = 0; i < NumReducedDims; ++i) {
+ if (static_cast<int>(Layout) == static_cast<int>(ColMajor)) {
+ reducing_inner_dims &= m_reduced[i];
+ } else {
+ reducing_inner_dims &= m_reduced[NumInputDims - 1 - i];
+ }
+ }
+ if (internal::InnerReducer<Self, Op, Device>::HasOptimizedImplementation &&
+ (reducing_inner_dims || ReducingInnerMostDims)) {
+ const Index num_values_to_reduce = internal::array_prod(m_reducedDims);
+ const Index num_coeffs_to_preserve = internal::array_prod(m_dimensions);
+ if (!data) {
+ if ((num_coeffs_to_preserve < 1024 && num_values_to_reduce > num_coeffs_to_preserve && num_values_to_reduce > 128) || (RunningOnSycl)) {
+ data = static_cast<EvaluatorPointerType>(m_device.get((CoeffReturnType*)m_device.allocate_temp(sizeof(CoeffReturnType) * num_coeffs_to_preserve)));
+ m_result = data;
+ }
+ else {
+ return true;
+ }
+ }
+ Op reducer(m_reducer);
+ // For SYCL this if always return false
+ if (internal::InnerReducer<Self, Op, Device>::run(*this, reducer, m_device, data, num_values_to_reduce, num_coeffs_to_preserve)) {
+ if (m_result) {
+ m_device.deallocate_temp(m_result);
+ m_result = NULL;
+ }
+ return true;
+ } else {
+ return (m_result != NULL);
+ }
+ }
+
+ bool preserving_inner_dims = true;
+ for (int i = 0; i < NumReducedDims; ++i) {
+ if (static_cast<int>(Layout) == static_cast<int>(ColMajor)) {
+ preserving_inner_dims &= m_reduced[NumInputDims - 1 - i];
+ } else {
+ preserving_inner_dims &= m_reduced[i];
+ }
+ }
+ if (internal::OuterReducer<Self, Op, Device>::HasOptimizedImplementation &&
+ preserving_inner_dims) {
+ const Index num_values_to_reduce = internal::array_prod(m_reducedDims);
+ const Index num_coeffs_to_preserve = internal::array_prod(m_dimensions);
+ if (!data) {
+ if ((num_coeffs_to_preserve < 1024 && num_values_to_reduce > num_coeffs_to_preserve && num_values_to_reduce > 32) || (RunningOnSycl)) {
+ data = static_cast<EvaluatorPointerType>(m_device.get((CoeffReturnType*)m_device.allocate_temp(sizeof(CoeffReturnType) * num_coeffs_to_preserve)));
+ m_result = data;
+ }
+ else {
+ return true;
+ }
+ }
+ Op reducer(m_reducer);
+ // For SYCL this if always return false
+ if (internal::OuterReducer<Self, Op, Device>::run(*this, reducer, m_device, data, num_values_to_reduce, num_coeffs_to_preserve)) {
+ if (m_result) {
+ m_device.deallocate_temp(m_result);
+ m_result = NULL;
+ }
+ return true;
+ } else {
+ return (m_result != NULL);
+ }
+ }
+ #if defined(EIGEN_USE_SYCL)
+ // If there is no Optimised version for SYCL, the reduction expression
+ // must break into two subexpression and use the SYCL generic Reducer on the device.
+ if(RunningOnSycl) {
+ const Index num_values_to_reduce = internal::array_prod(m_reducedDims);
+ const Index num_coeffs_to_preserve = internal::array_prod(m_dimensions);
+ if (!data) {
+ data = static_cast<EvaluatorPointerType>(m_device.get((CoeffReturnType*)m_device.allocate_temp(sizeof(CoeffReturnType) * num_coeffs_to_preserve)));
+ m_result = data;
+ }
+ Op reducer(m_reducer);
+ internal::GenericReducer<Self, Op, Device>::run(*this, reducer, m_device, data, num_values_to_reduce, num_coeffs_to_preserve);
+ return (m_result != NULL);
+ }
+ #endif
+ }
+ return true;
+ }
+
+#ifdef EIGEN_USE_THREADS
+ template <typename EvalSubExprsCallback>
+ EIGEN_STRONG_INLINE
+ void
+ evalSubExprsIfNeededAsync(EvaluatorPointerType data,
+ EvalSubExprsCallback done) {
+ m_impl.evalSubExprsIfNeededAsync(NULL, [this, data, done](bool) {
+ done(evalSubExprsIfNeededCommon(data));
+ });
+ }
+#endif
+
+ EIGEN_STRONG_INLINE
+ bool evalSubExprsIfNeeded(EvaluatorPointerType data) {
+ m_impl.evalSubExprsIfNeeded(NULL);
+ return evalSubExprsIfNeededCommon(data);
+ }
+
+ EIGEN_STRONG_INLINE void cleanup() {
+ m_impl.cleanup();
+ if (m_result) {
+ m_device.deallocate_temp(m_result);
+ m_result = NULL;
+ }
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE CoeffReturnType coeff(Index index) const
+ {
+ if (( RunningFullReduction || RunningOnGPU) && m_result ) {
+ return *(m_result + index);
+ }
+ Op reducer(m_reducer);
+ if (ReducingInnerMostDims || RunningFullReduction) {
+ const Index num_values_to_reduce =
+ (static_cast<int>(Layout) == static_cast<int>(ColMajor)) ? m_preservedStrides[0] : m_preservedStrides[NumPreservedStrides - 1];
+ return internal::InnerMostDimReducer<Self, Op>::reduce(*this, firstInput(index),
+ num_values_to_reduce, reducer);
+ } else {
+ typename Self::CoeffReturnType accum = reducer.initialize();
+ internal::GenericDimReducer<NumReducedDims-1, Self, Op>::reduce(*this, firstInput(index), reducer, &accum);
+ return reducer.finalize(accum);
+ }
+ }
+
+ // TODO(bsteiner): provide a more efficient implementation.
+ template<int LoadMode>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE PacketReturnType packet(Index index) const
+ {
+ eigen_assert(index + PacketSize - 1 < Index(internal::array_prod(dimensions())));
+
+ if (RunningOnGPU && m_result) {
+ return internal::pload<PacketReturnType>(m_result + index);
+ }
+
+ EIGEN_ALIGN_MAX std::remove_const_t<CoeffReturnType> values[PacketSize];
+ if (ReducingInnerMostDims) {
+ const Index num_values_to_reduce =
+ (static_cast<int>(Layout) == static_cast<int>(ColMajor)) ? m_preservedStrides[0] : m_preservedStrides[NumPreservedStrides - 1];
+ const Index firstIndex = firstInput(index);
+ for (Index i = 0; i < PacketSize; ++i) {
+ Op reducer(m_reducer);
+ values[i] = internal::InnerMostDimReducer<Self, Op>::reduce(*this, firstIndex + i * num_values_to_reduce,
+ num_values_to_reduce, reducer);
+ }
+ } else if (PreservingInnerMostDims) {
+ const Index firstIndex = firstInput(index);
+ const int innermost_dim = (static_cast<int>(Layout) == static_cast<int>(ColMajor)) ? 0 : NumOutputDims - 1;
+ // TBD: extend this the the n innermost dimensions that we preserve.
+ if (((firstIndex % m_dimensions[innermost_dim]) + PacketSize - 1) < m_dimensions[innermost_dim]) {
+ Op reducer(m_reducer);
+ typename Self::PacketReturnType accum = reducer.template initializePacket<typename Self::PacketReturnType>();
+ internal::InnerMostDimPreserver<NumReducedDims-1, Self, Op>::reduce(*this, firstIndex, reducer, &accum);
+ return reducer.finalizePacket(accum);
+ } else {
+ for (int i = 0; i < PacketSize; ++i) {
+ values[i] = coeff(index + i);
+ }
+ }
+ } else {
+ for (int i = 0; i < PacketSize; ++i) {
+ values[i] = coeff(index + i);
+ }
+ }
+ PacketReturnType rslt = internal::pload<PacketReturnType>(values);
+ return rslt;
+ }
+
+ // Must be called after evalSubExprsIfNeeded().
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorOpCost costPerCoeff(bool vectorized) const {
+ if (RunningFullReduction && m_result) {
+ return TensorOpCost(sizeof(CoeffReturnType), 0, 0, vectorized, PacketSize);
+ } else {
+ const Index num_values_to_reduce = internal::array_prod(m_reducedDims);
+ const double compute_cost = num_values_to_reduce * internal::functor_traits<Op>::Cost;
+ return m_impl.costPerCoeff(vectorized) * num_values_to_reduce +
+ TensorOpCost(0, 0, compute_cost, vectorized, PacketSize);
+ }
+ }
+
+ EIGEN_DEVICE_FUNC EvaluatorPointerType data() const { return m_result; }
+ EIGEN_DEVICE_FUNC const TensorEvaluator<ArgType, Device>& impl() const { return m_impl; }
+ EIGEN_DEVICE_FUNC const Device& device() const { return m_device; }
+#ifdef EIGEN_USE_SYCL
+ // binding placeholder accessors to a command group handler for SYCL
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void bind(cl::sycl::handler &cgh) const {
+ m_impl.bind(cgh);
+ m_result.bind(cgh);
+ }
+#endif
+
+ private:
+ template <int, typename, typename> friend struct internal::GenericDimReducer;
+ template <typename, typename, bool, bool> friend struct internal::InnerMostDimReducer;
+ template <int, typename, typename, bool> friend struct internal::InnerMostDimPreserver;
+ template <typename S, typename O, typename D, bool V> friend struct internal::FullReducer;
+#ifdef EIGEN_USE_THREADS
+ template <typename S, typename O, bool V> friend struct internal::FullReducerShard;
+#endif
+#if defined(EIGEN_USE_GPU) && (defined(EIGEN_GPUCC))
+ template <int B, int N, typename S, typename R, typename I_> KERNEL_FRIEND void internal::FullReductionKernel(R, const S, I_, typename S::CoeffReturnType*, unsigned int*);
+#if defined(EIGEN_HAS_GPU_FP16)
+ template <typename S, typename R, typename I_> KERNEL_FRIEND void internal::ReductionInitFullReduxKernelHalfFloat(R, const S, I_, internal::packet_traits<Eigen::half>::type*);
+ template <int B, int N, typename S, typename R, typename I_> KERNEL_FRIEND void internal::FullReductionKernelHalfFloat(R, const S, I_, half*, internal::packet_traits<Eigen::half>::type*);
+ template <int NPT, typename S, typename R, typename I_> KERNEL_FRIEND void internal::InnerReductionKernelHalfFloat(R, const S, I_, I_, half*);
+#endif
+ template <int NPT, typename S, typename R, typename I_> KERNEL_FRIEND void internal::InnerReductionKernel(R, const S, I_, I_, typename S::CoeffReturnType*);
+
+ template <int NPT, typename S, typename R, typename I_> KERNEL_FRIEND void internal::OuterReductionKernel(R, const S, I_, I_, typename S::CoeffReturnType*);
+#endif
+
+#if defined(EIGEN_USE_SYCL)
+ template < typename Evaluator_, typename Op__> friend class TensorSycl::internal::GenericNondeterministicReducer;
+ // SYCL need the Generic reducer for the case the recution algorithm is neither inner, outer, and full reducer
+ template <typename, typename, typename> friend struct internal::GenericReducer;
+#endif
+
+
+ template <typename S, typename O, typename D> friend struct internal::InnerReducer;
+
+ struct BlockIteratorState {
+ Index input_dim;
+ Index output_size;
+ Index output_count;
+ };
+
+ // Returns the Index in the input tensor of the first value that needs to be
+ // used to compute the reduction at output index "index".
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Index firstInput(Index index) const {
+ if (ReducingInnerMostDims) {
+ if (static_cast<int>(Layout) == static_cast<int>(ColMajor)) {
+ return index * m_preservedStrides[0];
+ } else {
+ return index * m_preservedStrides[NumPreservedStrides - 1];
+ }
+ }
+ // TBD: optimize the case where we preserve the innermost dimensions.
+ Index startInput = 0;
+ if (static_cast<int>(Layout) == static_cast<int>(ColMajor)) {
+ for (int i = NumOutputDims - 1; i > 0; --i) {
+ // This is index_i in the output tensor.
+ const Index idx = index / m_outputStrides[i];
+ startInput += idx * m_preservedStrides[i];
+ index -= idx * m_outputStrides[i];
+ }
+ if (PreservingInnerMostDims) {
+ eigen_assert(m_preservedStrides[0] == 1);
+ startInput += index;
+ } else {
+ startInput += index * m_preservedStrides[0];
+ }
+ } else {
+ for (int i = 0; i < NumOutputDims - 1; ++i) {
+ // This is index_i in the output tensor.
+ const Index idx = index / m_outputStrides[i];
+ startInput += idx * m_preservedStrides[i];
+ index -= idx * m_outputStrides[i];
+ }
+ if (PreservingInnerMostDims) {
+ eigen_assert(m_preservedStrides[NumPreservedStrides - 1] == 1);
+ startInput += index;
+ } else {
+ startInput += index * m_preservedStrides[NumPreservedStrides - 1];
+ }
+ }
+ return startInput;
+ }
+
+ // Bitmap indicating if an input dimension is reduced or not.
+ array<bool, NumInputDims> m_reduced;
+ // Dimensions of the output of the operation.
+ Dimensions m_dimensions;
+ // Precomputed strides for the output tensor.
+ array<Index, NumOutputDims> m_outputStrides;
+ array<internal::TensorIntDivisor<Index>, NumOutputDims> m_fastOutputStrides;
+ array<Index, NumPreservedStrides> m_preservedStrides;
+ // Map from output to input dimension index.
+ array<Index, NumOutputDims> m_output_to_input_dim_map;
+ // How many values go into each reduction
+ Index m_numValuesToReduce;
+
+ // Subset of strides of the input tensor for the reduced dimensions.
+ // Indexed by reduced dimensions.
+ array<Index, NumReducedDims> m_reducedStrides;
+ // Size of the input dimensions that are reduced.
+ // Indexed by reduced dimensions.
+ array<Index, NumReducedDims> m_reducedDims;
+
+ // Evaluator for the input expression.
+ TensorEvaluator<ArgType, Device> m_impl;
+
+ // Operation to apply for computing the reduction.
+ Op m_reducer;
+
+ EvaluatorPointerType m_result;
+
+ const Device EIGEN_DEVICE_REF m_device;
+};
+
+template<typename Op, typename Dims, typename ArgType, template <class> class MakePointer_, typename Device>
+struct TensorEvaluator<const TensorReductionOp<Op, Dims, ArgType, MakePointer_>, Device>
+: public TensorReductionEvaluatorBase<const TensorReductionOp<Op, Dims, ArgType, MakePointer_>, Device> {
+ typedef TensorReductionEvaluatorBase<const TensorReductionOp<Op, Dims, ArgType, MakePointer_>, Device> Base;
+ EIGEN_STRONG_INLINE TensorEvaluator(const typename Base::XprType& op, const Device& device) : Base(op, device){}
+};
+
+
+template<typename Op, typename Dims, typename ArgType, template <class> class MakePointer_>
+struct TensorEvaluator<const TensorReductionOp<Op, Dims, ArgType, MakePointer_>, Eigen::SyclDevice>
+: public TensorReductionEvaluatorBase<const TensorReductionOp<Op, Dims, ArgType, MakePointer_>, Eigen::SyclDevice> {
+
+ typedef TensorReductionEvaluatorBase<const TensorReductionOp<Op, Dims, ArgType, MakePointer_>, Eigen::SyclDevice> Base;
+ EIGEN_STRONG_INLINE TensorEvaluator(const typename Base::XprType& op, const Eigen::SyclDevice& device) : Base(op, device){}
+ // The coeff function in the base the recursive method which is not an standard layout and cannot be used in the SYCL kernel
+ //Therefore the coeff function should be overridden by for SYCL kernel
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE typename Base::CoeffReturnType coeff(typename Base::Index index) const {
+ return *(this->data() + index);
+ }
+ // The packet function in the base the recursive method which is not an standard layout and cannot be used in the SYCL kernel
+ //Therefore the packet function should be overridden by for SYCL kernel
+ template<int LoadMode>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE typename Base::PacketReturnType packet(typename Base::Index index) const {
+ return internal::pload<typename Base::PacketReturnType>(this->data() + index);
+ }
+};
+
+} // end namespace Eigen
+
+#endif // EIGEN_CXX11_TENSOR_TENSOR_REDUCTION_H
diff --git a/unsupported/Eigen/CXX11/src/Tensor/TensorReductionGpu.h b/unsupported/Eigen/CXX11/src/Tensor/TensorReductionGpu.h
new file mode 100644
index 0000000..51cdf44
--- /dev/null
+++ b/unsupported/Eigen/CXX11/src/Tensor/TensorReductionGpu.h
@@ -0,0 +1,975 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_CXX11_TENSOR_TENSOR_REDUCTION_GPU_H
+#define EIGEN_CXX11_TENSOR_TENSOR_REDUCTION_GPU_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+namespace internal {
+
+
+#if defined(EIGEN_USE_GPU) && defined(EIGEN_GPUCC)
+// Full reducers for GPU, don't vectorize for now
+
+// Reducer function that enables multiple gpu thread to safely accumulate at the same
+// output address. It basically reads the current value of the output variable, and
+// attempts to update it with the new value. If in the meantime another gpu thread
+// updated the content of the output address it will try again.
+template <typename T, typename R>
+__device__ EIGEN_ALWAYS_INLINE void atomicReduce(T* output, T accum, R& reducer) {
+#if (defined(EIGEN_HIP_DEVICE_COMPILE) && defined(__HIP_ARCH_HAS_WARP_SHUFFLE__)) || (EIGEN_CUDA_ARCH >= 300)
+ if (sizeof(T) == 4)
+ {
+ unsigned int oldval = *reinterpret_cast<unsigned int*>(output);
+ unsigned int newval = oldval;
+ reducer.reduce(accum, reinterpret_cast<T*>(&newval));
+ if (newval == oldval) {
+ return;
+ }
+ unsigned int readback;
+ while ((readback = atomicCAS((unsigned int*)output, oldval, newval)) != oldval) {
+ oldval = readback;
+ newval = oldval;
+ reducer.reduce(accum, reinterpret_cast<T*>(&newval));
+ if (newval == oldval) {
+ return;
+ }
+ }
+ }
+ else if (sizeof(T) == 8) {
+ unsigned long long oldval = *reinterpret_cast<unsigned long long*>(output);
+ unsigned long long newval = oldval;
+ reducer.reduce(accum, reinterpret_cast<T*>(&newval));
+ if (newval == oldval) {
+ return;
+ }
+ unsigned long long readback;
+ while ((readback = atomicCAS((unsigned long long*)output, oldval, newval)) != oldval) {
+ oldval = readback;
+ newval = oldval;
+ reducer.reduce(accum, reinterpret_cast<T*>(&newval));
+ if (newval == oldval) {
+ return;
+ }
+ }
+ }
+ else {
+ gpu_assert(0 && "Wordsize not supported");
+ }
+#else // EIGEN_CUDA_ARCH >= 300
+ gpu_assert(0 && "Shouldn't be called on unsupported device");
+#endif // EIGEN_CUDA_ARCH >= 300
+}
+
+// We extend atomicExch to support extra data types
+template <typename Type>
+__device__ inline Type atomicExchCustom(Type* address, Type val) {
+ return atomicExch(address, val);
+}
+
+template <>
+__device__ inline double atomicExchCustom(double* address, double val) {
+ unsigned long long int* address_as_ull = reinterpret_cast<unsigned long long int*>(address);
+ return __longlong_as_double(atomicExch(address_as_ull, __double_as_longlong(val)));
+}
+
+#ifdef EIGEN_HAS_GPU_FP16
+template <typename R>
+__device__ inline void atomicReduce(half2* output, half2 accum, R& reducer) {
+ unsigned int oldval = *reinterpret_cast<unsigned int*>(output);
+ unsigned int newval = oldval;
+ reducer.reducePacket(accum, reinterpret_cast<half2*>(&newval));
+ if (newval == oldval) {
+ return;
+ }
+ unsigned int readback;
+ while ((readback = atomicCAS((unsigned int*)output, oldval, newval)) != oldval) {
+ oldval = readback;
+ newval = oldval;
+ reducer.reducePacket(accum, reinterpret_cast<half2*>(&newval));
+ if (newval == oldval) {
+ return;
+ }
+ }
+}
+#ifdef EIGEN_GPU_COMPILE_PHASE
+// reduction should be associative since reduction is not atomic in wide vector but atomic in half2 operations
+template <typename R>
+__device__ inline void atomicReduce(Packet4h2* output, Packet4h2 accum, R& reducer) {
+ half2* houtput=reinterpret_cast<half2*>(output);
+ half2* haccum=reinterpret_cast<half2*>(&accum);
+ for(int i=0;i<4;++i){
+ atomicReduce(houtput+i,*(haccum+i),reducer);
+ }
+}
+#endif // EIGEN_GPU_COMPILE_PHASE
+#endif // EIGEN_HAS_GPU_FP16
+
+template <>
+__device__ inline void atomicReduce(float* output, float accum, SumReducer<float>&) {
+#if (defined(EIGEN_HIP_DEVICE_COMPILE) && defined(__HIP_ARCH_HAS_WARP_SHUFFLE__)) || (EIGEN_CUDA_ARCH >= 300)
+ atomicAdd(output, accum);
+#else // EIGEN_CUDA_ARCH >= 300
+ gpu_assert(0 && "Shouldn't be called on unsupported device");
+#endif // EIGEN_CUDA_ARCH >= 300
+}
+
+
+template <typename CoeffType, typename Index>
+__global__ EIGEN_HIP_LAUNCH_BOUNDS_1024 void ReductionInitKernel(const CoeffType val, Index num_preserved_coeffs, CoeffType* output) {
+ const Index thread_id = blockIdx.x * blockDim.x + threadIdx.x;
+ const Index num_threads = blockDim.x * gridDim.x;
+ for (Index i = thread_id; i < num_preserved_coeffs; i += num_threads) {
+ output[i] = val;
+ }
+}
+
+
+template <int BlockSize, int NumPerThread, typename Self,
+ typename Reducer, typename Index>
+__global__ EIGEN_HIP_LAUNCH_BOUNDS_1024 void FullReductionKernel(Reducer reducer, const Self input, Index num_coeffs,
+ typename Self::CoeffReturnType* output, unsigned int* semaphore) {
+#if (defined(EIGEN_HIP_DEVICE_COMPILE) && defined(__HIP_ARCH_HAS_WARP_SHUFFLE__)) || (EIGEN_CUDA_ARCH >= 300)
+ // Initialize the output value
+ const Index first_index = blockIdx.x * BlockSize * NumPerThread + threadIdx.x;
+ if (gridDim.x == 1) {
+ if (first_index == 0) {
+ *output = reducer.initialize();
+ }
+ }
+ else {
+ if (threadIdx.x == 0) {
+ unsigned int block = atomicCAS(semaphore, 0u, 1u);
+ if (block == 0) {
+ // We're the first block to run, initialize the output value
+ atomicExchCustom(output, reducer.initialize());
+ __threadfence();
+ atomicExch(semaphore, 2u);
+ }
+ else {
+ // Wait for the first block to initialize the output value.
+ // Use atomicCAS here to ensure that the reads aren't cached
+ unsigned int val;
+ do {
+ val = atomicCAS(semaphore, 2u, 2u);
+ }
+ while (val < 2u);
+ }
+ }
+ }
+
+ __syncthreads();
+
+ eigen_assert(gridDim.x == 1 || *semaphore >= 2u);
+
+ typename Self::CoeffReturnType accum = reducer.initialize();
+ Index max_iter = numext::mini<Index>(num_coeffs - first_index, NumPerThread*BlockSize);
+ for (Index i = 0; i < max_iter; i+=BlockSize) {
+ const Index index = first_index + i;
+ eigen_assert(index < num_coeffs);
+ typename Self::CoeffReturnType val = input.m_impl.coeff(index);
+ reducer.reduce(val, &accum);
+ }
+
+#pragma unroll
+ for (int offset = warpSize/2; offset > 0; offset /= 2) {
+ #if defined(EIGEN_HIPCC)
+ // use std::is_floating_point to determine the type of reduced_val
+ // This is needed because when Type == double, hipcc will give a "call to __shfl_down is ambguous" error
+ // and list the float and int versions of __shfl_down as the candidate functions.
+ if (std::is_floating_point<typename Self::CoeffReturnType>::value) {
+ reducer.reduce(__shfl_down(static_cast<float>(accum), offset, warpSize), &accum);
+ } else {
+ reducer.reduce(__shfl_down(static_cast<int>(accum), offset, warpSize), &accum);
+ }
+ #elif defined(EIGEN_CUDA_SDK_VER) && EIGEN_CUDA_SDK_VER < 90000
+ reducer.reduce(__shfl_down(accum, offset, warpSize), &accum);
+ #else
+ reducer.reduce(__shfl_down_sync(0xFFFFFFFF, accum, offset, warpSize), &accum);
+ #endif
+ }
+
+ if ((threadIdx.x & (warpSize - 1)) == 0) {
+ atomicReduce(output, accum, reducer);
+ }
+
+ if (gridDim.x > 1 && threadIdx.x == 0) {
+ // Let the last block reset the semaphore
+ atomicInc(semaphore, gridDim.x + 1);
+#if defined(EIGEN_HIPCC)
+ __threadfence_system();
+#endif
+ }
+#else // EIGEN_CUDA_ARCH >= 300
+ gpu_assert(0 && "Shouldn't be called on unsupported device");
+#endif // EIGEN_CUDA_ARCH >= 300
+}
+
+
+#ifdef EIGEN_HAS_GPU_FP16
+template <typename Self,
+ typename Reducer, typename Index>
+__global__ EIGEN_HIP_LAUNCH_BOUNDS_1024 void ReductionInitFullReduxKernelHalfFloat(
+ Reducer reducer, const Self input, Index num_coeffs, half* scratch) {
+ eigen_assert(blockDim.x == 1);
+ eigen_assert(gridDim.x == 1);
+ typedef packet_traits<Eigen::half>::type packet_type;
+ Index packet_remainder =
+ num_coeffs % Index(unpacket_traits<packet_type>::size);
+ if (packet_remainder != 0) {
+ half2* h2scratch = reinterpret_cast<half2*>(scratch);
+ for (Index i = num_coeffs - packet_remainder; i + 2 <= num_coeffs; i += 2) {
+ *h2scratch =
+ __halves2half2(input.coeff(i), input.coeff(i + 1));
+ h2scratch++;
+ }
+ if ((num_coeffs & 1) != 0) {
+ half lastCoeff = input.coeff(num_coeffs - 1);
+ *h2scratch = __halves2half2(lastCoeff, reducer.initialize());
+ }
+ } else {
+ packet_type reduce = reducer.template initializePacket<packet_type>();
+ internal::pstoreu(scratch, reduce);
+ }
+}
+
+template <typename Self,
+ typename Reducer, typename Index>
+__global__ EIGEN_HIP_LAUNCH_BOUNDS_1024 void ReductionInitKernelHalfFloat(Reducer reducer, const Self input, Index num_coeffs, half* output) {
+ const Index thread_id = blockIdx.x * blockDim.x + threadIdx.x;
+ const Index num_threads = blockDim.x * gridDim.x;
+ typedef typename packet_traits<Eigen::half>::type PacketType;
+
+ const Index num_packets =
+ num_coeffs / Index(unpacket_traits<PacketType>::size);
+ PacketType* p_output = reinterpret_cast<PacketType*>(output);
+ for (Index i = thread_id; i < num_packets; i += num_threads) {
+ p_output[i] = reducer.template initializePacket<PacketType>();
+ }
+ Index packet_remainder =
+ num_coeffs % Index(unpacket_traits<PacketType>::size);
+ if (thread_id < packet_remainder) {
+ output[num_coeffs - packet_remainder + thread_id] = reducer.initialize();
+ }
+}
+
+template <int BlockSize, int NumPerThread, typename Self,
+ typename Reducer, typename Index>
+__global__ EIGEN_HIP_LAUNCH_BOUNDS_1024 void FullReductionKernelHalfFloat(
+ Reducer reducer, const Self input, Index num_coeffs,
+ half* output, half* scratch) {
+ typedef typename packet_traits<Eigen::half>::type PacketType;
+ const int packet_width = unpacket_traits<PacketType>::size;
+ eigen_assert(NumPerThread % packet_width == 0);
+ const Index first_index =
+ blockIdx.x * BlockSize * NumPerThread + packet_width * threadIdx.x;
+
+ // Initialize the output value if it wasn't initialized by the ReductionInitKernel
+
+ if (gridDim.x == 1) {
+ if (first_index == 0) {
+ int rem = num_coeffs % packet_width;
+ if (rem != 0) {
+ half2* p_scratch = reinterpret_cast<half2*>(scratch);
+ pstoreu(scratch, reducer.template initializePacket<PacketType>());
+ for (int i = 0; i < rem / 2; i++) {
+ *p_scratch = __halves2half2(
+ input.coeff(num_coeffs - packet_width + 2 * i),
+ input.coeff(num_coeffs - packet_width + 2 * i + 1));
+ p_scratch++;
+ }
+ if ((num_coeffs & 1) != 0) {
+ half last = input.coeff(num_coeffs - 1);
+ *p_scratch = __halves2half2(last, reducer.initialize());
+ }
+ } else {
+ PacketType reduce = reducer.template initializePacket<PacketType>();
+ pstoreu(scratch, reduce);
+ }
+ }
+ __syncthreads();
+ }
+
+ PacketType accum = reducer.template initializePacket<PacketType>();
+ const Index max_iter =
+ numext::mini<Index>((num_coeffs - first_index) / packet_width,
+ NumPerThread * BlockSize / packet_width);
+ for (Index i = 0; i < max_iter; i += BlockSize) {
+ const Index index = first_index + packet_width * i;
+ eigen_assert(index + packet_width < num_coeffs);
+ PacketType val = input.template packet<Unaligned>(index);
+ reducer.reducePacket(val, &accum);
+ }
+
+#pragma unroll
+ for (int offset = warpSize/2; offset > 0; offset /= 2) {
+ #if defined(EIGEN_HIPCC)
+ PacketType r1;
+ half2* hr = reinterpret_cast<half2*>(&r1);
+ half2* hacc = reinterpret_cast<half2*>(&accum);
+ for (int i = 0; i < packet_width / 2; i++) {
+ // FIXME : remove this workaround once we have native half/half2 support for __shfl_down
+ union { int i; half2 h; } wka_in, wka_out;
+ wka_in.h = hacc[i];
+ wka_out.i = __shfl_down(wka_in.i, offset, warpSize);
+ hr[i] = wka_out.h;
+ }
+ reducer.reducePacket(r1, &accum);
+ #elif defined(EIGEN_CUDA_SDK_VER) && EIGEN_CUDA_SDK_VER < 90000
+ PacketType r1;
+ half2* hr = reinterpret_cast<half2*>(&r1);
+ half2* hacc = reinterpret_cast<half2*>(&accum);
+ for (int i = 0; i < packet_width / 2; i++) {
+ hr[i] = __shfl_down(hacc[i], offset, warpSize);
+ }
+ reducer.reducePacket(r1, &accum);
+ #else
+ PacketType r1;
+ half2* hr = reinterpret_cast<half2*>(&r1);
+ half2* hacc = reinterpret_cast<half2*>(&accum);
+ for (int i = 0; i < packet_width / 2; i++) {
+ hr[i] = __shfl_down_sync(0xFFFFFFFF, hacc[i], (unsigned)offset, warpSize);
+ }
+ reducer.reducePacket(r1, &accum);
+
+ #endif
+ }
+
+ if ((threadIdx.x & (warpSize - 1)) == 0) {
+ atomicReduce(reinterpret_cast<PacketType*>(scratch), accum, reducer);
+ }
+
+ __syncthreads();
+ half2* rv1 = reinterpret_cast<half2*>(scratch);
+ if (packet_width > 2) {
+ reducer.reducePacket(rv1[2], rv1);
+ reducer.reducePacket(rv1[3], rv1 + 1);
+ reducer.reducePacket(rv1[1], rv1);
+ }
+ if (gridDim.x == 1) {
+ if (first_index == 0) {
+ half tmp = __low2half(*rv1);
+ reducer.reduce(__high2half(*rv1), &tmp);
+ *output = tmp;
+ }
+ }
+}
+
+template <typename Op>
+__global__ EIGEN_HIP_LAUNCH_BOUNDS_1024 void ReductionCleanupKernelHalfFloat(Op reducer, half* output, half* scratch) {
+ eigen_assert(threadIdx.x == 1);
+ typedef packet_traits<Eigen::half>::type packet_type;
+ if (unpacket_traits<packet_type>::size == 1) {
+ *output = *scratch;
+ } else {
+ half2* pscratch = reinterpret_cast<half2*>(scratch);
+ half tmp = __float2half(0.f);
+ for (int i = 0; i < unpacket_traits<packet_type>::size; i += 2) {
+ reducer.reduce(__low2half(*pscratch), &tmp);
+ reducer.reduce(__high2half(*pscratch), &tmp);
+ pscratch++;
+ }
+ *output = tmp;
+ }
+}
+
+#endif // EIGEN_HAS_GPU_FP16
+
+template <typename Self, typename Op, typename OutputType, bool PacketAccess, typename Enabled = void>
+struct FullReductionLauncher {
+ static void run(const Self&, Op&, const GpuDevice&, OutputType*, typename Self::Index) {
+ gpu_assert(false && "Should only be called on doubles, floats and half floats");
+ }
+};
+
+// Specialization for float and double
+template <typename Self, typename Op, typename OutputType, bool PacketAccess>
+struct FullReductionLauncher<
+ Self, Op, OutputType, PacketAccess,
+ std::enable_if_t<
+ internal::is_same<float, OutputType>::value ||
+ internal::is_same<double, OutputType>::value,
+ void>> {
+ static void run(const Self& self, Op& reducer, const GpuDevice& device, OutputType* output, typename Self::Index num_coeffs) {
+
+ typedef typename Self::Index Index;
+ const int block_size = 256;
+ const int num_per_thread = 128;
+ const int num_blocks = divup<int>(num_coeffs, block_size * num_per_thread);
+
+ unsigned int* semaphore = NULL;
+ if (num_blocks > 1) {
+ semaphore = device.semaphore();
+ }
+
+ LAUNCH_GPU_KERNEL((FullReductionKernel<block_size, num_per_thread, Self, Op, Index>),
+ num_blocks, block_size, 0, device, reducer, self, num_coeffs, output, semaphore);
+ }
+};
+
+#ifdef EIGEN_HAS_GPU_FP16
+template <typename Self, typename Op>
+struct FullReductionLauncher<Self, Op, Eigen::half, false> {
+ static void run(const Self&, Op&, const GpuDevice&, half*, typename Self::Index) {
+ gpu_assert(false && "Should not be called since there is no packet accessor");
+ }
+};
+
+template <typename Self, typename Op>
+struct FullReductionLauncher<Self, Op, Eigen::half, true> {
+ static void run(const Self& self, Op& reducer, const GpuDevice& device, half* output, typename Self::Index num_coeffs) {
+ typedef typename Self::Index Index;
+
+ const int block_size = 256;
+ const int num_per_thread = 128;
+ const int num_blocks = divup<int>(num_coeffs, block_size * num_per_thread);
+ half* scratch = static_cast<half*>(device.scratchpad());
+
+ if (num_blocks > 1) {
+ // We initialize the output and the scrathpad outside the reduction kernel when we can't be sure that there
+ // won't be a race conditions between multiple thread blocks.
+ LAUNCH_GPU_KERNEL((ReductionInitFullReduxKernelHalfFloat<Self, Op, Index>),
+ 1, 1, 0, device, reducer, self, num_coeffs, scratch);
+ }
+
+ LAUNCH_GPU_KERNEL((FullReductionKernelHalfFloat<block_size, num_per_thread, Self, Op, Index>),
+ num_blocks, block_size, 0, device, reducer, self, num_coeffs, output, scratch);
+
+ if (num_blocks > 1) {
+ LAUNCH_GPU_KERNEL((ReductionCleanupKernelHalfFloat<Op>),
+ 1, 1, 0, device, reducer, output, scratch);
+ }
+ }
+};
+#endif // EIGEN_HAS_GPU_FP16
+
+
+template <typename Self, typename Op, bool Vectorizable>
+struct FullReducer<Self, Op, GpuDevice, Vectorizable> {
+ // Unfortunately nvidia doesn't support well exotic types such as complex,
+ // so reduce the scope of the optimized version of the code to the simple cases
+ // of doubles, floats and half floats
+#ifdef EIGEN_HAS_GPU_FP16
+ static constexpr bool HasOptimizedImplementation = !Self::ReducerTraits::IsStateful &&
+ (internal::is_same<typename Self::CoeffReturnType, float>::value ||
+ internal::is_same<typename Self::CoeffReturnType, double>::value ||
+ (internal::is_same<typename Self::CoeffReturnType, Eigen::half>::value && reducer_traits<Op, GpuDevice>::PacketAccess));
+#else // EIGEN_HAS_GPU_FP16
+ static constexpr bool HasOptimizedImplementation = !Self::ReducerTraits::IsStateful &&
+ (internal::is_same<typename Self::CoeffReturnType, float>::value ||
+ internal::is_same<typename Self::CoeffReturnType, double>::value);
+#endif // EIGEN_HAS_GPU_FP16
+
+ template <typename OutputType>
+ static void run(const Self& self, Op& reducer, const GpuDevice& device, OutputType* output) {
+ gpu_assert(HasOptimizedImplementation && "Should only be called on doubles, floats or half floats");
+ const Index num_coeffs = array_prod(self.m_impl.dimensions());
+ // Don't crash when we're called with an input tensor of size 0.
+ if (num_coeffs == 0) {
+ return;
+ }
+
+ FullReductionLauncher<Self, Op, OutputType, reducer_traits<Op, GpuDevice>::PacketAccess>::run(self, reducer, device, output, num_coeffs);
+ }
+};
+
+
+template <int NumPerThread, typename Self,
+ typename Reducer, typename Index>
+__global__ EIGEN_HIP_LAUNCH_BOUNDS_1024 void InnerReductionKernel(Reducer reducer, const Self input, Index num_coeffs_to_reduce, Index num_preserved_coeffs,
+ typename Self::CoeffReturnType* output) {
+#if (defined(EIGEN_HIP_DEVICE_COMPILE) && defined(__HIP_ARCH_HAS_WARP_SHUFFLE__)) || (EIGEN_CUDA_ARCH >= 300)
+ typedef typename Self::CoeffReturnType Type;
+ eigen_assert(blockDim.y == 1);
+ eigen_assert(blockDim.z == 1);
+ eigen_assert(gridDim.y == 1);
+ eigen_assert(gridDim.z == 1);
+
+ const int unroll_times = 16;
+ eigen_assert(NumPerThread % unroll_times == 0);
+
+ const Index input_col_blocks = divup<Index>(num_coeffs_to_reduce, blockDim.x * NumPerThread);
+ const Index num_input_blocks = input_col_blocks * num_preserved_coeffs;
+
+ const Index num_threads = blockDim.x * gridDim.x;
+ const Index thread_id = blockIdx.x * blockDim.x + threadIdx.x;
+
+ // Initialize the output values if they weren't initialized by the ReductionInitKernel
+ if (gridDim.x == 1) {
+ for (Index i = thread_id; i < num_preserved_coeffs; i += num_threads) {
+ output[i] = reducer.initialize();
+ }
+ __syncthreads();
+ }
+
+ for (Index i = blockIdx.x; i < num_input_blocks; i += gridDim.x) {
+ const Index row = i / input_col_blocks;
+
+ if (row < num_preserved_coeffs) {
+ const Index col_block = i % input_col_blocks;
+ const Index col_begin = col_block * blockDim.x * NumPerThread + threadIdx.x;
+
+ Type reduced_val = reducer.initialize();
+
+ for (Index j = 0; j < NumPerThread; j += unroll_times) {
+ const Index last_col = col_begin + blockDim.x * (j + unroll_times - 1);
+ if (last_col >= num_coeffs_to_reduce) {
+ for (Index col = col_begin + blockDim.x * j; col < num_coeffs_to_reduce; col += blockDim.x) {
+ const Type val = input.m_impl.coeff(row * num_coeffs_to_reduce + col);
+ reducer.reduce(val, &reduced_val);
+ }
+ break;
+ } else {
+ // Faster version of the loop with no branches after unrolling.
+#pragma unroll
+ for (int k = 0; k < unroll_times; ++k) {
+ const Index col = col_begin + blockDim.x * (j + k);
+ reducer.reduce(input.m_impl.coeff(row * num_coeffs_to_reduce + col), &reduced_val);
+ }
+ }
+ }
+
+#pragma unroll
+ for (int offset = warpSize/2; offset > 0; offset /= 2) {
+ #if defined(EIGEN_HIPCC)
+ // use std::is_floating_point to determine the type of reduced_val
+ // This is needed because when Type == double, hipcc will give a "call to __shfl_down is ambguous" error
+ // and list the float and int versions of __shfl_down as the candidate functions.
+ if (std::is_floating_point<Type>::value) {
+ reducer.reduce(__shfl_down(static_cast<float>(reduced_val), offset), &reduced_val);
+ } else {
+ reducer.reduce(__shfl_down(static_cast<int>(reduced_val), offset), &reduced_val);
+ }
+ #elif defined(EIGEN_CUDA_SDK_VER) && EIGEN_CUDA_SDK_VER < 90000
+ reducer.reduce(__shfl_down(reduced_val, offset), &reduced_val);
+ #else
+ reducer.reduce(__shfl_down_sync(0xFFFFFFFF, reduced_val, offset), &reduced_val);
+ #endif
+ }
+
+ if ((threadIdx.x & (warpSize - 1)) == 0) {
+ atomicReduce(&(output[row]), reduced_val, reducer);
+ }
+ }
+ }
+#else // EIGEN_CUDA_ARCH >= 300
+ gpu_assert(0 && "Shouldn't be called on unsupported device");
+#endif // EIGEN_CUDA_ARCH >= 300
+}
+
+#ifdef EIGEN_HAS_GPU_FP16
+
+template <int NumPerThread, typename Self,
+ typename Reducer, typename Index>
+__global__ EIGEN_HIP_LAUNCH_BOUNDS_1024 void InnerReductionKernelHalfFloat(Reducer reducer, const Self input, Index num_coeffs_to_reduce, Index num_preserved_coeffs,
+ half* output) {
+ eigen_assert(blockDim.y == 1);
+ eigen_assert(blockDim.z == 1);
+ eigen_assert(gridDim.y == 1);
+ eigen_assert(gridDim.z == 1);
+
+ typedef typename packet_traits<Eigen::half>::type PacketType;
+ const int packet_width = unpacket_traits<PacketType>::size;
+ const int unroll_times = 16 / packet_width;
+ eigen_assert(NumPerThread % unroll_times == 0);
+ eigen_assert(unroll_times % 2 == 0);
+
+ const Index input_col_blocks = divup<Index>(num_coeffs_to_reduce, blockDim.x * NumPerThread * 2);
+ const Index num_input_blocks = divup<Index>(input_col_blocks * num_preserved_coeffs, 2);
+
+ const Index num_threads = blockDim.x * gridDim.x;
+ const Index thread_id = blockIdx.x * blockDim.x + threadIdx.x;
+
+ // Initialize the output values if they weren't initialized by the ReductionInitKernel
+ if (gridDim.x == 1) {
+ Index i = packet_width * thread_id;
+ for (; i + packet_width <= num_preserved_coeffs;
+ i += packet_width * num_threads) {
+ PacketType* poutput = reinterpret_cast<PacketType*>(output + i);
+ *poutput = reducer.template initializePacket<PacketType>();
+ }
+ if (i < num_preserved_coeffs) {
+ output[i] = reducer.initialize();
+ }
+ __syncthreads();
+ }
+
+ for (Index i = blockIdx.x; i < num_input_blocks; i += gridDim.x) {
+ const Index row = 2 * (i / input_col_blocks); // everybody takes 2 rows
+
+ if (row + 1 < num_preserved_coeffs) {
+ const Index col_block = i % input_col_blocks;
+ const Index col_begin =
+ packet_width * (col_block * blockDim.x * NumPerThread + threadIdx.x);
+
+ PacketType reduced_val1 = reducer.template initializePacket<PacketType>();
+ PacketType reduced_val2 = reducer.template initializePacket<PacketType>();
+
+ for (Index j = 0; j < NumPerThread; j += unroll_times) {
+ const Index last_col =
+ col_begin + blockDim.x * (j + unroll_times - 1) * packet_width;
+ if (last_col >= num_coeffs_to_reduce) {
+ Index col = col_begin + blockDim.x * j;
+ for (; col + packet_width <= num_coeffs_to_reduce;
+ col += blockDim.x) {
+ const PacketType val1 = input.m_impl.template packet<Unaligned>(
+ row * num_coeffs_to_reduce + col);
+ reducer.reducePacket(val1, &reduced_val1);
+ const PacketType val2 = input.m_impl.template packet<Unaligned>(
+ (row + 1) * num_coeffs_to_reduce + col);
+ reducer.reducePacket(val2, &reduced_val2);
+ }
+ if (col < num_coeffs_to_reduce) {
+ PacketType r1 = reducer.template initializePacket<PacketType>();
+ PacketType r2 = reducer.template initializePacket<PacketType>();
+ half2* hr1 = reinterpret_cast<half2*>(&r1);
+ half2* hr2 = reinterpret_cast<half2*>(&r2);
+ while (col + 1 < num_coeffs_to_reduce) {
+ *hr1 = __halves2half2(
+ input.m_impl.coeff(row * num_coeffs_to_reduce + col),
+ input.m_impl.coeff(row * num_coeffs_to_reduce + col + 1));
+ *hr2 = __halves2half2(
+ input.m_impl.coeff((row + 1) * num_coeffs_to_reduce + col),
+ input.m_impl.coeff((row + 1) * num_coeffs_to_reduce + col +
+ 1));
+ hr1++;
+ hr2++;
+ col += 2;
+ }
+ if (col < num_coeffs_to_reduce) {
+ // Peel;
+ const half last1 =
+ input.m_impl.coeff(row * num_coeffs_to_reduce + col);
+ *hr1 = __halves2half2(last1, reducer.initialize());
+ const half last2 =
+ input.m_impl.coeff((row + 1) * num_coeffs_to_reduce + col);
+ *hr2 = __halves2half2(last2, reducer.initialize());
+ }
+ reducer.reducePacket(r1, &reduced_val1);
+ reducer.reducePacket(r2, &reduced_val2);
+ }
+ break;
+ } else {
+ // Faster version of the loop with no branches after unrolling.
+#pragma unroll
+ for (int k = 0; k < unroll_times; ++k) {
+ const Index col = col_begin + blockDim.x * (j + k) * packet_width;
+ reducer.reducePacket(input.m_impl.template packet<Unaligned>(
+ row * num_coeffs_to_reduce + col),
+ &reduced_val1);
+ reducer.reducePacket(input.m_impl.template packet<Unaligned>(
+ (row + 1) * num_coeffs_to_reduce + col),
+ &reduced_val2);
+ }
+ }
+ }
+
+#pragma unroll
+ for (int offset = warpSize/2; offset > 0; offset /= 2) {
+ #if defined(EIGEN_HIPCC)
+ PacketType r1;
+ PacketType r2;
+ half2* hr1 = reinterpret_cast<half2*>(&r1);
+ half2* hr2 = reinterpret_cast<half2*>(&r2);
+ half2* rv1 = reinterpret_cast<half2*>(&reduced_val1);
+ half2* rv2 = reinterpret_cast<half2*>(&reduced_val2);
+ for (int i = 0; i < packet_width / 2; i++) {
+ // FIXME : remove this workaround once we have native half/half2 support for __shfl_down
+ union { int i; half2 h; } wka_in1, wka_out1;
+ wka_in1.h = rv1[i];
+ wka_out1.i = __shfl_down(wka_in1.i, offset, warpSize);
+ hr1[i] = wka_out1.h;
+
+ union { int i; half2 h; } wka_in2, wka_out2;
+ wka_in2.h = rv2[i];
+ wka_out2.i = __shfl_down(wka_in2.i, offset, warpSize);
+ hr2[i] = wka_out2.h;
+ }
+ reducer.reducePacket(r1, &reduced_val1);
+ reducer.reducePacket(r2, &reduced_val2);
+ #elif defined(EIGEN_CUDA_SDK_VER) && EIGEN_CUDA_SDK_VER < 90000
+ PacketType r1;
+ PacketType r2;
+ half2* hr1 = reinterpret_cast<half2*>(&r1);
+ half2* hr2 = reinterpret_cast<half2*>(&r2);
+ half2* rv1 = reinterpret_cast<half2*>(&reduced_val1);
+ half2* rv2 = reinterpret_cast<half2*>(&reduced_val2);
+ for (int i = 0; i < packet_width / 2; i++) {
+ hr1[i] = __shfl_down(rv1[i], offset, warpSize);
+ hr2[i] = __shfl_down(rv2[i], offset, warpSize);
+ }
+ reducer.reducePacket(r1, &reduced_val1);
+ reducer.reducePacket(r2, &reduced_val2);
+ #else
+ PacketType r1;
+ PacketType r2;
+ half2* hr1 = reinterpret_cast<half2*>(&r1);
+ half2* hr2 = reinterpret_cast<half2*>(&r2);
+ half2* rr1 = reinterpret_cast<half2*>(&reduced_val1);
+ half2* rr2 = reinterpret_cast<half2*>(&reduced_val2);
+ for (int i = 0; i < packet_width / 2; i++) {
+ hr1[i] =
+ __shfl_down_sync(0xFFFFFFFF, rr1[i], (unsigned)offset, warpSize);
+ hr2[i] =
+ __shfl_down_sync(0xFFFFFFFF, rr2[i], (unsigned)offset, warpSize);
+ }
+ reducer.reducePacket(r1, &reduced_val1);
+ reducer.reducePacket(r2, &reduced_val2);
+
+ #endif
+ }
+ half2* rv1 = reinterpret_cast<half2*>(&reduced_val1);
+ half2* rv2 = reinterpret_cast<half2*>(&reduced_val2);
+ half2 val;
+ if (packet_width > 2) {
+ reducer.reducePacket(rv1[2], rv1);
+ reducer.reducePacket(rv1[3], rv1 + 1);
+ reducer.reducePacket(rv1[1], rv1);
+ reducer.reducePacket(rv2[2], rv2);
+ reducer.reducePacket(rv2[3], rv2 + 1);
+ reducer.reducePacket(rv2[1], rv2);
+ }
+ half val1 = __low2half(*rv1);
+ reducer.reduce(__high2half(*rv1), &val1);
+ half val2 = __low2half(*rv2);
+ reducer.reduce(__high2half(*rv2), &val2);
+ val = __halves2half2(val1, val2);
+ if ((threadIdx.x & (warpSize - 1)) == 0) {
+ half* loc = output + row;
+ atomicReduce((half2*)loc, val, reducer);
+ }
+ }
+ }
+}
+
+#endif // EIGEN_HAS_GPU_FP16
+
+template <typename Self, typename Op, typename OutputType, bool PacketAccess, typename Enabled = void>
+struct InnerReductionLauncher {
+ static EIGEN_DEVICE_FUNC bool run(const Self&, Op&, const GpuDevice&, OutputType*, typename Self::Index, typename Self::Index) {
+ gpu_assert(false && "Should only be called to reduce doubles, floats and half floats on a gpu device");
+ return true;
+ }
+};
+
+// Specialization for float and double
+template <typename Self, typename Op, typename OutputType, bool PacketAccess>
+struct InnerReductionLauncher<
+ Self, Op, OutputType, PacketAccess,
+ std::enable_if_t<
+ internal::is_same<float, OutputType>::value ||
+ internal::is_same<double, OutputType>::value,
+ void>> {
+ static bool run(const Self& self, Op& reducer, const GpuDevice& device, OutputType* output, typename Self::Index num_coeffs_to_reduce, typename Self::Index num_preserved_vals) {
+ typedef typename Self::Index Index;
+
+ const Index num_coeffs = num_coeffs_to_reduce * num_preserved_vals;
+ const int block_size = 256;
+ const int num_per_thread = 128;
+ const int dyn_blocks = divup<int>(num_coeffs, block_size * num_per_thread);
+ const int max_blocks = device.getNumGpuMultiProcessors() *
+ device.maxGpuThreadsPerMultiProcessor() / block_size;
+ const int num_blocks = numext::mini<int>(max_blocks, dyn_blocks);
+
+ if (num_blocks > 1) {
+ // We initialize the outputs outside the reduction kernel when we can't be sure that there
+ // won't be a race conditions between multiple thread blocks.
+ const int dyn_blocks = divup<int>(num_preserved_vals, 1024);
+ const int max_blocks = device.getNumGpuMultiProcessors() *
+ device.maxGpuThreadsPerMultiProcessor() / 1024;
+ const int num_blocks = numext::mini<int>(max_blocks, dyn_blocks);
+ LAUNCH_GPU_KERNEL((ReductionInitKernel<OutputType, Index>),
+ num_blocks, 1024, 0, device, reducer.initialize(),
+ num_preserved_vals, output);
+ }
+
+ LAUNCH_GPU_KERNEL((InnerReductionKernel<num_per_thread, Self, Op, Index>),
+ num_blocks, block_size, 0, device, reducer, self, num_coeffs_to_reduce, num_preserved_vals, output);
+
+ return false;
+ }
+};
+
+#ifdef EIGEN_HAS_GPU_FP16
+template <typename Self, typename Op>
+struct InnerReductionLauncher<Self, Op, Eigen::half, false> {
+ static bool run(const Self&, Op&, const GpuDevice&, half*, typename Self::Index, typename Self::Index) {
+ gpu_assert(false && "Should not be called since there is no packet accessor");
+ return true;
+ }
+};
+
+template <typename Self, typename Op>
+struct InnerReductionLauncher<Self, Op, Eigen::half, true> {
+ static bool run(const Self& self, Op& reducer, const GpuDevice& device, half* output, typename Self::Index num_coeffs_to_reduce, typename Self::Index num_preserved_vals) {
+ typedef typename Self::Index Index;
+
+ if (num_preserved_vals % 2 != 0) {
+ // Not supported yet, revert to the slower code path
+ return true;
+ }
+
+ const Index num_coeffs = num_coeffs_to_reduce * num_preserved_vals;
+ const int block_size = /*256*/128;
+ const int num_per_thread = /*128*/64;
+ const int dyn_blocks = divup<int>(num_coeffs, block_size * num_per_thread);
+ const int max_blocks = device.getNumGpuMultiProcessors() *
+ device.maxGpuThreadsPerMultiProcessor() / block_size;
+ const int num_blocks = numext::mini<int>(max_blocks, dyn_blocks);
+
+ if (num_blocks > 1) {
+ // We initialize the outputs outside the reduction kernel when we can't be sure that there
+ // won't be a race conditions between multiple thread blocks.
+ LAUNCH_GPU_KERNEL((ReductionInitKernelHalfFloat<Self, Op, Index>),
+ 1, 1, 0, device, reducer, self, num_preserved_vals, output);
+ }
+
+ LAUNCH_GPU_KERNEL((InnerReductionKernelHalfFloat<num_per_thread, Self, Op, Index>),
+ num_blocks, block_size, 0, device, reducer, self, num_coeffs_to_reduce, num_preserved_vals, output);
+
+ return false;
+ }
+};
+#endif // EIGEN_HAS_GPU_FP16
+
+
+template <typename Self, typename Op>
+struct InnerReducer<Self, Op, GpuDevice> {
+ // Unfortunately nvidia doesn't support well exotic types such as complex,
+ // so reduce the scope of the optimized version of the code to the simple case
+ // of floats and half floats.
+#ifdef EIGEN_HAS_GPU_FP16
+ static constexpr bool HasOptimizedImplementation = !Self::ReducerTraits::IsStateful &&
+ (internal::is_same<typename Self::CoeffReturnType, float>::value ||
+ internal::is_same<typename Self::CoeffReturnType, double>::value ||
+ (internal::is_same<typename Self::CoeffReturnType, Eigen::half>::value && reducer_traits<Op, GpuDevice>::PacketAccess));
+#else // EIGEN_HAS_GPU_FP16
+ static constexpr bool HasOptimizedImplementation = !Self::ReducerTraits::IsStateful &&
+ (internal::is_same<typename Self::CoeffReturnType, float>::value ||
+ internal::is_same<typename Self::CoeffReturnType, double>::value);
+#endif // EIGEN_HAS_GPU_FP16
+
+ template <typename OutputType>
+ static bool run(const Self& self, Op& reducer, const GpuDevice& device, OutputType* output, typename Self::Index num_coeffs_to_reduce, typename Self::Index num_preserved_vals) {
+ gpu_assert(HasOptimizedImplementation && "Should only be called on doubles, floats or half floats");
+ const Index num_coeffs = array_prod(self.m_impl.dimensions());
+ // Don't crash when we're called with an input tensor of size 0.
+ if (num_coeffs == 0) {
+ return true;
+ }
+ // It's faster to use the usual code.
+ if (num_coeffs_to_reduce <= 128) {
+ return true;
+ }
+
+ return InnerReductionLauncher<Self, Op, OutputType, reducer_traits<Op, GpuDevice>::PacketAccess>::run(self, reducer, device, output, num_coeffs_to_reduce, num_preserved_vals);
+ }
+};
+
+template <int NumPerThread, typename Self,
+ typename Reducer, typename Index>
+__global__ EIGEN_HIP_LAUNCH_BOUNDS_1024 void OuterReductionKernel(Reducer reducer, const Self input, Index num_coeffs_to_reduce, Index num_preserved_coeffs,
+ typename Self::CoeffReturnType* output) {
+ const Index num_threads = blockDim.x * gridDim.x;
+ const Index thread_id = blockIdx.x * blockDim.x + threadIdx.x;
+ // Initialize the output values if they weren't initialized by the ReductionInitKernel
+ if (gridDim.x == 1) {
+ for (Index i = thread_id; i < num_preserved_coeffs; i += num_threads) {
+ output[i] = reducer.initialize();
+ }
+ __syncthreads();
+ }
+
+ // Do the reduction.
+ const Index max_iter = num_preserved_coeffs * divup<Index>(num_coeffs_to_reduce, NumPerThread);
+ for (Index i = thread_id; i < max_iter; i += num_threads) {
+ const Index input_col = i % num_preserved_coeffs;
+ const Index input_row = (i / num_preserved_coeffs) * NumPerThread;
+ typename Self::CoeffReturnType reduced_val = reducer.initialize();
+ const Index max_row = numext::mini(input_row + NumPerThread, num_coeffs_to_reduce);
+ for (Index j = input_row; j < max_row; j++) {
+ typename Self::CoeffReturnType val = input.m_impl.coeff(j * num_preserved_coeffs + input_col);
+ reducer.reduce(val, &reduced_val);
+ }
+ atomicReduce(&(output[input_col]), reduced_val, reducer);
+ }
+}
+
+
+template <typename Self, typename Op>
+struct OuterReducer<Self, Op, GpuDevice> {
+ // Unfortunately nvidia doesn't support well exotic types such as complex,
+ // so reduce the scope of the optimized version of the code to the simple case
+ // of floats.
+ static constexpr bool HasOptimizedImplementation = !Self::ReducerTraits::IsStateful &&
+ (internal::is_same<typename Self::CoeffReturnType, float>::value ||
+ internal::is_same<typename Self::CoeffReturnType, double>::value);
+ template <typename Device, typename OutputType>
+ static
+ #if !defined(EIGEN_HIPCC)
+ // FIXME : leaving this EIGEN_DEVICE_FUNC in, results in the following runtime error
+ // (in the cxx11_tensor_reduction_gpu test)
+ //
+ // terminate called after throwing an instance of 'std::runtime_error'
+ // what(): No device code available for function: _ZN5Eigen8internal20OuterReductionKernelIL...
+ //
+ // don't know why this happens (and why is it a runtime error instead of a compile time error)
+ //
+ // this will be fixed by HIP PR#457
+ EIGEN_DEVICE_FUNC
+ #endif
+ bool run(const Self&, Op&, const Device&, OutputType*, typename Self::Index, typename Self::Index) {
+ gpu_assert(false && "Should only be called to reduce doubles or floats on a gpu device");
+ return true;
+ }
+
+ static bool run(const Self& self, Op& reducer, const GpuDevice& device, float* output, typename Self::Index num_coeffs_to_reduce, typename Self::Index num_preserved_vals) {
+ typedef typename Self::Index Index;
+
+ // It's faster to use the usual code.
+ if (num_coeffs_to_reduce <= 32) {
+ return true;
+ }
+
+ const Index num_coeffs = num_coeffs_to_reduce * num_preserved_vals;
+ const int block_size = 256;
+ const int num_per_thread = 16;
+ const int dyn_blocks = divup<int>(num_coeffs, block_size * num_per_thread);
+ const int max_blocks = device.getNumGpuMultiProcessors() *
+ device.maxGpuThreadsPerMultiProcessor() / block_size;
+ const int num_blocks = numext::mini<int>(max_blocks, dyn_blocks);
+
+ if (num_blocks > 1) {
+ // We initialize the outputs in the reduction kernel itself when we don't have to worry
+ // about race conditions between multiple thread blocks.
+ const int dyn_blocks = divup<int>(num_preserved_vals, 1024);
+ const int max_blocks = device.getNumGpuMultiProcessors() *
+ device.maxGpuThreadsPerMultiProcessor() / 1024;
+ const int num_blocks = numext::mini<int>(max_blocks, dyn_blocks);
+ LAUNCH_GPU_KERNEL((ReductionInitKernel<float, Index>),
+ num_blocks, 1024, 0, device, reducer.initialize(),
+ num_preserved_vals, output);
+ }
+
+ LAUNCH_GPU_KERNEL((OuterReductionKernel<num_per_thread, Self, Op, Index>),
+ num_blocks, block_size, 0, device, reducer, self, num_coeffs_to_reduce, num_preserved_vals, output);
+
+ return false;
+ }
+};
+
+#endif // defined(EIGEN_USE_GPU) && defined(EIGEN_GPUCC)
+
+
+} // end namespace internal
+} // end namespace Eigen
+
+#endif // EIGEN_CXX11_TENSOR_TENSOR_REDUCTION_GPU_H
diff --git a/unsupported/Eigen/CXX11/src/Tensor/TensorReductionSycl.h b/unsupported/Eigen/CXX11/src/Tensor/TensorReductionSycl.h
new file mode 100644
index 0000000..397870f
--- /dev/null
+++ b/unsupported/Eigen/CXX11/src/Tensor/TensorReductionSycl.h
@@ -0,0 +1,583 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Mehdi Goli Codeplay Software Ltd.
+// Ralph Potter Codeplay Software Ltd.
+// Luke Iwanski Codeplay Software Ltd.
+// Contact: <eigen@codeplay.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+/*****************************************************************
+ * TensorReductionSycl.h
+ *
+ * \brief:
+ * This is the specialization of the reduction operation. Two phase reduction approach
+ * is used since the GPU does not have Global Synchronization for global memory among
+ * different work-group/thread block. To solve the problem, we need to create two kernels
+ * to reduce the data, where the first kernel reduce the data locally and each local
+ * workgroup/thread-block save the input data into global memory. In the second phase (global reduction)
+ * one work-group uses one work-group/thread-block to reduces the intermediate data into one single element.
+ * Here is an NVIDIA presentation explaining the optimized two phase reduction algorithm on GPU:
+ * https://developer.download.nvidia.com/assets/cuda/files/reduction.pdf
+ *
+ *****************************************************************/
+
+#ifndef UNSUPPORTED_EIGEN_CXX11_SRC_TENSOR_TENSOR_REDUCTION_SYCL_HPP
+#define UNSUPPORTED_EIGEN_CXX11_SRC_TENSOR_TENSOR_REDUCTION_SYCL_HPP
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+namespace TensorSycl {
+namespace internal {
+
+template <typename Op, typename CoeffReturnType, typename Index, bool Vectorizable>
+struct OpDefiner {
+ typedef typename Vectorise<CoeffReturnType, Eigen::SyclDevice, Vectorizable>::PacketReturnType PacketReturnType;
+ typedef Op type;
+ static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE type get_op(Op &op) { return op; }
+
+ static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE PacketReturnType finalise_op(const PacketReturnType &accumulator,
+ const Index &) {
+ return accumulator;
+ }
+};
+
+template <typename CoeffReturnType, typename Index>
+struct OpDefiner<Eigen::internal::MeanReducer<CoeffReturnType>, CoeffReturnType, Index, false> {
+ typedef Eigen::internal::SumReducer<CoeffReturnType> type;
+ static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE type get_op(Eigen::internal::MeanReducer<CoeffReturnType> &) {
+ return type();
+ }
+
+ static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE CoeffReturnType finalise_op(const CoeffReturnType &accumulator,
+ const Index &scale) {
+ ::Eigen::internal::scalar_quotient_op<CoeffReturnType> quotient_op;
+ return quotient_op(accumulator, CoeffReturnType(scale));
+ }
+};
+
+template <typename CoeffReturnType, typename Index>
+struct OpDefiner<Eigen::internal::MeanReducer<CoeffReturnType>, CoeffReturnType, Index, true> {
+ typedef typename Vectorise<CoeffReturnType, Eigen::SyclDevice, true>::PacketReturnType PacketReturnType;
+ typedef Eigen::internal::SumReducer<CoeffReturnType> type;
+ static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE type get_op(Eigen::internal::MeanReducer<CoeffReturnType> &) {
+ return type();
+ }
+
+ static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE PacketReturnType finalise_op(const PacketReturnType &accumulator,
+ const Index &scale) {
+ return ::Eigen::internal::pdiv(accumulator, ::Eigen::internal::pset1<PacketReturnType>(CoeffReturnType(scale)));
+ }
+};
+
+template <typename CoeffReturnType, typename OpType, typename InputAccessor, typename OutputAccessor, typename Index,
+ Index local_range>
+struct SecondStepFullReducer {
+ typedef cl::sycl::accessor<CoeffReturnType, 1, cl::sycl::access::mode::read_write, cl::sycl::access::target::local>
+ LocalAccessor;
+ typedef OpDefiner<OpType, CoeffReturnType, Index, true> OpDef;
+ typedef typename OpDef::type Op;
+ LocalAccessor scratch;
+ InputAccessor aI;
+ OutputAccessor outAcc;
+ Op op;
+ SecondStepFullReducer(LocalAccessor scratch_, InputAccessor aI_, OutputAccessor outAcc_, OpType op_)
+ : scratch(scratch_), aI(aI_), outAcc(outAcc_), op(OpDef::get_op(op_)) {}
+
+ void operator()(cl::sycl::nd_item<1> itemID) {
+ // Our empirical research shows that the best performance will be achieved
+ // when there is only one element per thread to reduce in the second step.
+ // in this step the second step reduction time is almost negligible.
+ // Hence, in the second step of reduction the input size is fixed to the
+ // local size, thus, there is only one element read per thread. The
+ // algorithm must be changed if the number of reduce per thread in the
+ // second step is greater than 1. Otherwise, the result will be wrong.
+ const Index localid = itemID.get_local_id(0);
+ auto aInPtr = aI.get_pointer() + localid;
+ auto aOutPtr = outAcc.get_pointer();
+ CoeffReturnType *scratchptr = scratch.get_pointer();
+ CoeffReturnType accumulator = *aInPtr;
+
+ scratchptr[localid] = op.finalize(accumulator);
+ for (Index offset = itemID.get_local_range(0) / 2; offset > 0; offset /= 2) {
+ itemID.barrier(cl::sycl::access::fence_space::local_space);
+ if (localid < offset) {
+ op.reduce(scratchptr[localid + offset], &accumulator);
+ scratchptr[localid] = op.finalize(accumulator);
+ }
+ }
+ if (localid == 0) *aOutPtr = op.finalize(accumulator);
+ }
+};
+
+// Full reduction first phase. In this version the vectorization is true and the reduction accept
+// any generic reducerOp e.g( max, min, sum, mean, iamax, iamin, etc ).
+template <typename Evaluator, typename OpType, typename Evaluator::Index local_range>
+class FullReductionKernelFunctor {
+ public:
+ typedef typename Evaluator::CoeffReturnType CoeffReturnType;
+ typedef typename Evaluator::Index Index;
+ typedef OpDefiner<OpType, typename Evaluator::CoeffReturnType, Index,
+ (Evaluator::ReducerTraits::PacketAccess & Evaluator::InputPacketAccess)>
+ OpDef;
+
+ typedef typename OpDef::type Op;
+ typedef typename Evaluator::EvaluatorPointerType EvaluatorPointerType;
+ typedef typename Evaluator::PacketReturnType PacketReturnType;
+ typedef std::conditional_t<(Evaluator::ReducerTraits::PacketAccess & Evaluator::InputPacketAccess),
+ PacketReturnType, CoeffReturnType> OutType;
+ typedef cl::sycl::accessor<OutType, 1, cl::sycl::access::mode::read_write, cl::sycl::access::target::local>
+ LocalAccessor;
+ LocalAccessor scratch;
+ Evaluator evaluator;
+ EvaluatorPointerType final_output;
+ Index rng;
+ Op op;
+
+ FullReductionKernelFunctor(LocalAccessor scratch_, Evaluator evaluator_, EvaluatorPointerType final_output_,
+ Index rng_, OpType op_)
+ : scratch(scratch_), evaluator(evaluator_), final_output(final_output_), rng(rng_), op(OpDef::get_op(op_)) {}
+
+ void operator()(cl::sycl::nd_item<1> itemID) { compute_reduction(itemID); }
+
+ template <bool Vect = (Evaluator::ReducerTraits::PacketAccess & Evaluator::InputPacketAccess)>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE std::enable_if_t<Vect> compute_reduction(
+ const cl::sycl::nd_item<1> &itemID) {
+ auto output_ptr = final_output.get_pointer();
+ Index VectorizedRange = (rng / Evaluator::PacketSize) * Evaluator::PacketSize;
+ Index globalid = itemID.get_global_id(0);
+ Index localid = itemID.get_local_id(0);
+ Index step = Evaluator::PacketSize * itemID.get_global_range(0);
+ Index start = Evaluator::PacketSize * globalid;
+ // vectorizable parts
+ PacketReturnType packetAccumulator = op.template initializePacket<PacketReturnType>();
+ for (Index i = start; i < VectorizedRange; i += step) {
+ op.template reducePacket<PacketReturnType>(evaluator.impl().template packet<Unaligned>(i), &packetAccumulator);
+ }
+ globalid += VectorizedRange;
+ // non vectorizable parts
+ for (Index i = globalid; i < rng; i += itemID.get_global_range(0)) {
+ op.template reducePacket<PacketReturnType>(
+ ::Eigen::TensorSycl::internal::PacketWrapper<PacketReturnType, Evaluator::PacketSize>::convert_to_packet_type(
+ evaluator.impl().coeff(i), op.initialize()),
+ &packetAccumulator);
+ }
+ scratch[localid] = packetAccumulator =
+ OpDef::finalise_op(op.template finalizePacket<PacketReturnType>(packetAccumulator), rng);
+ // reduction parts // Local size is always power of 2
+ EIGEN_UNROLL_LOOP
+ for (Index offset = local_range / 2; offset > 0; offset /= 2) {
+ itemID.barrier(cl::sycl::access::fence_space::local_space);
+ if (localid < offset) {
+ op.template reducePacket<PacketReturnType>(scratch[localid + offset], &packetAccumulator);
+ scratch[localid] = op.template finalizePacket<PacketReturnType>(packetAccumulator);
+ }
+ }
+ if (localid == 0) {
+ output_ptr[itemID.get_group(0)] =
+ op.finalizeBoth(op.initialize(), op.template finalizePacket<PacketReturnType>(packetAccumulator));
+ }
+ }
+
+ template <bool Vect = (Evaluator::ReducerTraits::PacketAccess & Evaluator::InputPacketAccess)>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE std::enable_if_t<!Vect> compute_reduction(
+ const cl::sycl::nd_item<1> &itemID) {
+ auto output_ptr = final_output.get_pointer();
+ Index globalid = itemID.get_global_id(0);
+ Index localid = itemID.get_local_id(0);
+ // vectorizable parts
+ CoeffReturnType accumulator = op.initialize();
+ // non vectorizable parts
+ for (Index i = globalid; i < rng; i += itemID.get_global_range(0)) {
+ op.reduce(evaluator.impl().coeff(i), &accumulator);
+ }
+ scratch[localid] = accumulator = OpDef::finalise_op(op.finalize(accumulator), rng);
+
+ // reduction parts. the local size is always power of 2
+ EIGEN_UNROLL_LOOP
+ for (Index offset = local_range / 2; offset > 0; offset /= 2) {
+ itemID.barrier(cl::sycl::access::fence_space::local_space);
+ if (localid < offset) {
+ op.reduce(scratch[localid + offset], &accumulator);
+ scratch[localid] = op.finalize(accumulator);
+ }
+ }
+ if (localid == 0) {
+ output_ptr[itemID.get_group(0)] = op.finalize(accumulator);
+ }
+ }
+};
+
+template <typename Evaluator, typename OpType>
+class GenericNondeterministicReducer {
+ public:
+ typedef typename Evaluator::CoeffReturnType CoeffReturnType;
+ typedef typename Evaluator::EvaluatorPointerType EvaluatorPointerType;
+ typedef typename Evaluator::Index Index;
+ typedef OpDefiner<OpType, CoeffReturnType, Index, false> OpDef;
+ typedef typename OpDef::type Op;
+ template <typename Scratch>
+ GenericNondeterministicReducer(Scratch, Evaluator evaluator_, EvaluatorPointerType output_accessor_, OpType functor_,
+ Index range_, Index num_values_to_reduce_)
+ : evaluator(evaluator_),
+ output_accessor(output_accessor_),
+ functor(OpDef::get_op(functor_)),
+ range(range_),
+ num_values_to_reduce(num_values_to_reduce_) {}
+
+ void operator()(cl::sycl::nd_item<1> itemID) {
+ auto output_accessor_ptr = output_accessor.get_pointer();
+ /// const cast added as a naive solution to solve the qualifier drop error
+ Index globalid = static_cast<Index>(itemID.get_global_linear_id());
+ if (globalid < range) {
+ CoeffReturnType accum = functor.initialize();
+ Eigen::internal::GenericDimReducer<Evaluator::NumReducedDims - 1, Evaluator, Op>::reduce(
+ evaluator, evaluator.firstInput(globalid), functor, &accum);
+ output_accessor_ptr[globalid] = OpDef::finalise_op(functor.finalize(accum), num_values_to_reduce);
+ }
+ }
+
+ private:
+ Evaluator evaluator;
+ EvaluatorPointerType output_accessor;
+ Op functor;
+ Index range;
+ Index num_values_to_reduce;
+};
+
+enum class reduction_dim { inner_most, outer_most };
+// default is preserver
+template <typename Evaluator, typename OpType, typename PannelParameters, reduction_dim rt>
+struct PartialReductionKernel {
+ typedef typename Evaluator::CoeffReturnType CoeffReturnType;
+ typedef typename Evaluator::EvaluatorPointerType EvaluatorPointerType;
+ typedef typename Evaluator::Index Index;
+ typedef OpDefiner<OpType, CoeffReturnType, Index, false> OpDef;
+ typedef typename OpDef::type Op;
+ typedef cl::sycl::accessor<CoeffReturnType, 1, cl::sycl::access::mode::read_write, cl::sycl::access::target::local>
+ ScratchAcc;
+ ScratchAcc scratch;
+ Evaluator evaluator;
+ EvaluatorPointerType output_accessor;
+ Op op;
+ const Index preserve_elements_num_groups;
+ const Index reduce_elements_num_groups;
+ const Index num_coeffs_to_preserve;
+ const Index num_coeffs_to_reduce;
+
+ PartialReductionKernel(ScratchAcc scratch_, Evaluator evaluator_, EvaluatorPointerType output_accessor_, OpType op_,
+ const Index preserve_elements_num_groups_, const Index reduce_elements_num_groups_,
+ const Index num_coeffs_to_preserve_, const Index num_coeffs_to_reduce_)
+ : scratch(scratch_),
+ evaluator(evaluator_),
+ output_accessor(output_accessor_),
+ op(OpDef::get_op(op_)),
+ preserve_elements_num_groups(preserve_elements_num_groups_),
+ reduce_elements_num_groups(reduce_elements_num_groups_),
+ num_coeffs_to_preserve(num_coeffs_to_preserve_),
+ num_coeffs_to_reduce(num_coeffs_to_reduce_) {}
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void element_wise_reduce(Index globalRId, Index globalPId,
+ CoeffReturnType &accumulator) {
+ if (globalPId >= num_coeffs_to_preserve) {
+ return;
+ }
+ Index global_offset = rt == reduction_dim::outer_most ? globalPId + (globalRId * num_coeffs_to_preserve)
+ : globalRId + (globalPId * num_coeffs_to_reduce);
+ Index localOffset = globalRId;
+
+ const Index per_thread_local_stride = PannelParameters::LocalThreadSizeR * reduce_elements_num_groups;
+ const Index per_thread_global_stride =
+ rt == reduction_dim::outer_most ? num_coeffs_to_preserve * per_thread_local_stride : per_thread_local_stride;
+ for (Index i = globalRId; i < num_coeffs_to_reduce; i += per_thread_local_stride) {
+ op.reduce(evaluator.impl().coeff(global_offset), &accumulator);
+ localOffset += per_thread_local_stride;
+ global_offset += per_thread_global_stride;
+ }
+ }
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void operator()(cl::sycl::nd_item<1> itemID) {
+ const Index linearLocalThreadId = itemID.get_local_id(0);
+ Index pLocalThreadId = rt == reduction_dim::outer_most ? linearLocalThreadId % PannelParameters::LocalThreadSizeP
+ : linearLocalThreadId / PannelParameters::LocalThreadSizeR;
+ Index rLocalThreadId = rt == reduction_dim::outer_most ? linearLocalThreadId / PannelParameters::LocalThreadSizeP
+ : linearLocalThreadId % PannelParameters::LocalThreadSizeR;
+ const Index pGroupId = rt == reduction_dim::outer_most ? itemID.get_group(0) % preserve_elements_num_groups
+ : itemID.get_group(0) / reduce_elements_num_groups;
+ const Index rGroupId = rt == reduction_dim::outer_most ? itemID.get_group(0) / preserve_elements_num_groups
+ : itemID.get_group(0) % reduce_elements_num_groups;
+
+ Index globalPId = pGroupId * PannelParameters::LocalThreadSizeP + pLocalThreadId;
+ const Index globalRId = rGroupId * PannelParameters::LocalThreadSizeR + rLocalThreadId;
+ auto scratchPtr = scratch.get_pointer().get();
+ auto outPtr =
+ output_accessor.get_pointer() + (reduce_elements_num_groups > 1 ? rGroupId * num_coeffs_to_preserve : 0);
+ CoeffReturnType accumulator = op.initialize();
+
+ element_wise_reduce(globalRId, globalPId, accumulator);
+
+ accumulator = OpDef::finalise_op(op.finalize(accumulator), num_coeffs_to_reduce);
+ scratchPtr[pLocalThreadId + rLocalThreadId * (PannelParameters::LocalThreadSizeP + PannelParameters::BC)] =
+ accumulator;
+ if (rt == reduction_dim::inner_most) {
+ pLocalThreadId = linearLocalThreadId % PannelParameters::LocalThreadSizeP;
+ rLocalThreadId = linearLocalThreadId / PannelParameters::LocalThreadSizeP;
+ globalPId = pGroupId * PannelParameters::LocalThreadSizeP + pLocalThreadId;
+ }
+
+ /* Apply the reduction operation between the current local
+ * id and the one on the other half of the vector. */
+ auto out_scratch_ptr =
+ scratchPtr + (pLocalThreadId + (rLocalThreadId * (PannelParameters::LocalThreadSizeP + PannelParameters::BC)));
+ itemID.barrier(cl::sycl::access::fence_space::local_space);
+ if (rt == reduction_dim::inner_most) {
+ accumulator = *out_scratch_ptr;
+ }
+ // The Local LocalThreadSizeR is always power of 2
+ EIGEN_UNROLL_LOOP
+ for (Index offset = PannelParameters::LocalThreadSizeR >> 1; offset > 0; offset >>= 1) {
+ if (rLocalThreadId < offset) {
+ op.reduce(out_scratch_ptr[(PannelParameters::LocalThreadSizeP + PannelParameters::BC) * offset], &accumulator);
+ // The result has already been divided for mean reducer in the
+ // previous reduction so no need to divide furthermore
+ *out_scratch_ptr = op.finalize(accumulator);
+ }
+ /* All threads collectively read from global memory into local.
+ * The barrier ensures all threads' IO is resolved before
+ * execution continues (strictly speaking, all threads within
+ * a single work-group - there is no co-ordination between
+ * work-groups, only work-items). */
+ itemID.barrier(cl::sycl::access::fence_space::local_space);
+ }
+
+ if (rLocalThreadId == 0 && (globalPId < num_coeffs_to_preserve)) {
+ outPtr[globalPId] = op.finalize(accumulator);
+ }
+ }
+};
+
+template <typename OutScalar, typename Index, typename InputAccessor, typename OutputAccessor, typename OpType>
+struct SecondStepPartialReduction {
+ typedef OpDefiner<OpType, OutScalar, Index, false> OpDef;
+ typedef typename OpDef::type Op;
+ typedef cl::sycl::accessor<OutScalar, 1, cl::sycl::access::mode::read_write, cl::sycl::access::target::local>
+ ScratchAccessor;
+ InputAccessor input_accessor;
+ OutputAccessor output_accessor;
+ Op op;
+ const Index num_coeffs_to_preserve;
+ const Index num_coeffs_to_reduce;
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE SecondStepPartialReduction(ScratchAccessor, InputAccessor input_accessor_,
+ OutputAccessor output_accessor_, OpType op_,
+ const Index num_coeffs_to_preserve_,
+ const Index num_coeffs_to_reduce_)
+ : input_accessor(input_accessor_),
+ output_accessor(output_accessor_),
+ op(OpDef::get_op(op_)),
+ num_coeffs_to_preserve(num_coeffs_to_preserve_),
+ num_coeffs_to_reduce(num_coeffs_to_reduce_) {}
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void operator()(cl::sycl::nd_item<1> itemID) {
+ const Index globalId = itemID.get_global_id(0);
+
+ if (globalId >= num_coeffs_to_preserve) return;
+
+ auto in_ptr = input_accessor.get_pointer() + globalId;
+
+ OutScalar accumulator = op.initialize();
+// num_coeffs_to_reduce is not bigger that 256
+ for (Index i = 0; i < num_coeffs_to_reduce; i++) {
+ op.reduce(*in_ptr, &accumulator);
+ in_ptr += num_coeffs_to_preserve;
+ }
+ output_accessor.get_pointer()[globalId] = op.finalize(accumulator);
+ }
+}; // namespace internal
+
+template <typename Index, Index LTP, Index LTR, bool BC_>
+struct ReductionPannel {
+ static EIGEN_CONSTEXPR Index LocalThreadSizeP = LTP;
+ static EIGEN_CONSTEXPR Index LocalThreadSizeR = LTR;
+ static EIGEN_CONSTEXPR bool BC = BC_;
+};
+
+template <typename Self, typename Op, TensorSycl::internal::reduction_dim rt>
+struct PartialReducerLauncher {
+ typedef typename Self::EvaluatorPointerType EvaluatorPointerType;
+ typedef typename Self::CoeffReturnType CoeffReturnType;
+ typedef typename Self::Storage Storage;
+ typedef typename Self::Index Index;
+ typedef ReductionPannel<typename Self::Index, EIGEN_SYCL_LOCAL_THREAD_DIM0, EIGEN_SYCL_LOCAL_THREAD_DIM1, true>
+ PannelParameters;
+
+ typedef PartialReductionKernel<Self, Op, PannelParameters, rt> SyclReducerKerneType;
+
+ static bool run(const Self &self, const Op &reducer, const Eigen::SyclDevice &dev, EvaluatorPointerType output,
+ Index num_coeffs_to_reduce, Index num_coeffs_to_preserve) {
+ Index roundUpP = roundUp(num_coeffs_to_preserve, PannelParameters::LocalThreadSizeP);
+
+ // getPowerOfTwo makes sure local range is power of 2 and <=
+ // maxSyclThreadPerBlock this will help us to avoid extra check on the
+ // kernel
+ static_assert(!((PannelParameters::LocalThreadSizeP * PannelParameters::LocalThreadSizeR) &
+ (PannelParameters::LocalThreadSizeP * PannelParameters::LocalThreadSizeR - 1)),
+ "The Local thread size must be a power of 2 for the reduction "
+ "operation");
+
+ EIGEN_CONSTEXPR Index localRange = PannelParameters::LocalThreadSizeP * PannelParameters::LocalThreadSizeR;
+ // In this step, we force the code not to be more than 2-step reduction:
+ // Our empirical research shows that if each thread reduces at least 64
+ // elemnts individually, we get better performance. However, this can change
+ // on different platforms. In this step we force the code not to be
+ // morthan step reduction: Our empirical research shows that for inner_most
+ // dim reducer, it is better to have 8 group in a reduce dimension for sizes
+ // > 1024 to achieve the best performance.
+ const Index reductionPerThread = 64;
+ Index cu = dev.getPowerOfTwo(dev.getNumSyclMultiProcessors(), true);
+ const Index pNumGroups = roundUpP / PannelParameters::LocalThreadSizeP;
+ Index rGroups = (cu + pNumGroups - 1) / pNumGroups;
+ const Index rNumGroups = num_coeffs_to_reduce > reductionPerThread * localRange ? std::min(rGroups, localRange) : 1;
+ const Index globalRange = pNumGroups * rNumGroups * localRange;
+
+ EIGEN_CONSTEXPR Index scratchSize =
+ PannelParameters::LocalThreadSizeR * (PannelParameters::LocalThreadSizeP + PannelParameters::BC);
+ auto thread_range = cl::sycl::nd_range<1>(cl::sycl::range<1>(globalRange), cl::sycl::range<1>(localRange));
+ if (rNumGroups > 1) {
+ CoeffReturnType *temp_pointer = static_cast<CoeffReturnType *>(
+ dev.allocate_temp(num_coeffs_to_preserve * rNumGroups * sizeof(CoeffReturnType)));
+ EvaluatorPointerType temp_accessor = dev.get(temp_pointer);
+ dev.template unary_kernel_launcher<CoeffReturnType, SyclReducerKerneType>(
+ self, temp_accessor, thread_range, scratchSize, reducer, pNumGroups, rNumGroups, num_coeffs_to_preserve,
+ num_coeffs_to_reduce);
+
+ typedef SecondStepPartialReduction<CoeffReturnType, Index, EvaluatorPointerType, EvaluatorPointerType, Op>
+ SecondStepPartialReductionKernel;
+
+ dev.template unary_kernel_launcher<CoeffReturnType, SecondStepPartialReductionKernel>(
+ temp_accessor, output,
+ cl::sycl::nd_range<1>(cl::sycl::range<1>(pNumGroups * localRange), cl::sycl::range<1>(localRange)), Index(1),
+ reducer, num_coeffs_to_preserve, rNumGroups);
+
+ self.device().deallocate_temp(temp_pointer);
+ } else {
+ dev.template unary_kernel_launcher<CoeffReturnType, SyclReducerKerneType>(
+ self, output, thread_range, scratchSize, reducer, pNumGroups, rNumGroups, num_coeffs_to_preserve,
+ num_coeffs_to_reduce);
+ }
+ return false;
+ }
+};
+} // namespace internal
+} // namespace TensorSycl
+
+namespace internal {
+
+template <typename Self, typename Op, bool Vectorizable>
+struct FullReducer<Self, Op, Eigen::SyclDevice, Vectorizable> {
+ typedef typename Self::CoeffReturnType CoeffReturnType;
+ typedef typename Self::EvaluatorPointerType EvaluatorPointerType;
+ static EIGEN_CONSTEXPR bool HasOptimizedImplementation = true;
+ static EIGEN_CONSTEXPR int PacketSize = Self::PacketAccess ? Self::PacketSize : 1;
+ static void run(const Self &self, Op &reducer, const Eigen::SyclDevice &dev, EvaluatorPointerType data) {
+ typedef std::conditional_t<Self::PacketAccess, typename Self::PacketReturnType, CoeffReturnType> OutType;
+ static_assert(!((EIGEN_SYCL_LOCAL_THREAD_DIM0 * EIGEN_SYCL_LOCAL_THREAD_DIM1) &
+ (EIGEN_SYCL_LOCAL_THREAD_DIM0 * EIGEN_SYCL_LOCAL_THREAD_DIM1 - 1)),
+ "The Local thread size must be a power of 2 for the reduction "
+ "operation");
+ EIGEN_CONSTEXPR Index local_range = EIGEN_SYCL_LOCAL_THREAD_DIM0 * EIGEN_SYCL_LOCAL_THREAD_DIM1;
+
+ typename Self::Index inputSize = self.impl().dimensions().TotalSize();
+ // In this step we force the code not to be more than 2-step reduction:
+ // Our empirical research shows that if each thread reduces at least 512
+ // elemnts individually, we get better performance.
+ const Index reductionPerThread = 2048;
+ // const Index num_work_group =
+ Index reductionGroup = dev.getPowerOfTwo(
+ (inputSize + (reductionPerThread * local_range - 1)) / (reductionPerThread * local_range), true);
+ const Index num_work_group = std::min(reductionGroup, local_range);
+ // 1
+ // ? local_range
+ // : 1);
+ const Index global_range = num_work_group * local_range;
+
+ auto thread_range = cl::sycl::nd_range<1>(cl::sycl::range<1>(global_range), cl::sycl::range<1>(local_range));
+ typedef TensorSycl::internal::FullReductionKernelFunctor<Self, Op, local_range> reduction_kernel_t;
+ if (num_work_group > 1) {
+ CoeffReturnType *temp_pointer =
+ static_cast<CoeffReturnType *>(dev.allocate_temp(num_work_group * sizeof(CoeffReturnType)));
+ typename Self::EvaluatorPointerType tmp_global_accessor = dev.get(temp_pointer);
+ dev.template unary_kernel_launcher<OutType, reduction_kernel_t>(self, tmp_global_accessor, thread_range,
+ local_range, inputSize, reducer);
+
+ typedef TensorSycl::internal::SecondStepFullReducer<CoeffReturnType, Op, EvaluatorPointerType,
+ EvaluatorPointerType, Index, local_range>
+ GenericRKernel;
+ dev.template unary_kernel_launcher<CoeffReturnType, GenericRKernel>(
+ tmp_global_accessor, data,
+ cl::sycl::nd_range<1>(cl::sycl::range<1>(num_work_group), cl::sycl::range<1>(num_work_group)), num_work_group,
+ reducer);
+
+ dev.deallocate_temp(temp_pointer);
+ } else {
+ dev.template unary_kernel_launcher<OutType, reduction_kernel_t>(self, data, thread_range, local_range, inputSize,
+ reducer);
+ }
+ }
+};
+// vectorizable inner_most most dim preserver
+// col reduction
+template <typename Self, typename Op>
+struct OuterReducer<Self, Op, Eigen::SyclDevice> {
+ static EIGEN_CONSTEXPR bool HasOptimizedImplementation = true;
+
+ static bool run(const Self &self, const Op &reducer, const Eigen::SyclDevice &dev,
+ typename Self::EvaluatorPointerType output, typename Self::Index num_coeffs_to_reduce,
+ typename Self::Index num_coeffs_to_preserve) {
+ return ::Eigen::TensorSycl::internal::PartialReducerLauncher<
+ Self, Op, ::Eigen::TensorSycl::internal::reduction_dim::outer_most>::run(self, reducer, dev, output,
+ num_coeffs_to_reduce,
+ num_coeffs_to_preserve);
+ }
+};
+// row reduction
+template <typename Self, typename Op>
+struct InnerReducer<Self, Op, Eigen::SyclDevice> {
+ static EIGEN_CONSTEXPR bool HasOptimizedImplementation = true;
+
+ static bool run(const Self &self, const Op &reducer, const Eigen::SyclDevice &dev,
+ typename Self::EvaluatorPointerType output, typename Self::Index num_coeffs_to_reduce,
+ typename Self::Index num_coeffs_to_preserve) {
+ return ::Eigen::TensorSycl::internal::PartialReducerLauncher<
+ Self, Op, ::Eigen::TensorSycl::internal::reduction_dim::inner_most>::run(self, reducer, dev, output,
+ num_coeffs_to_reduce,
+ num_coeffs_to_preserve);
+ }
+};
+
+// ArmgMax uses this kernel for partial reduction//
+// TODO(@mehdi.goli) come up with a better kernel
+// generic partial reduction
+template <typename Self, typename Op>
+struct GenericReducer<Self, Op, Eigen::SyclDevice> {
+ static EIGEN_CONSTEXPR bool HasOptimizedImplementation = false;
+ static bool run(const Self &self, const Op &reducer, const Eigen::SyclDevice &dev,
+ typename Self::EvaluatorPointerType output, typename Self::Index num_values_to_reduce,
+ typename Self::Index num_coeffs_to_preserve) {
+ typename Self::Index range, GRange, tileSize;
+ dev.parallel_for_setup(num_coeffs_to_preserve, tileSize, range, GRange);
+
+ dev.template unary_kernel_launcher<typename Self::CoeffReturnType,
+ TensorSycl::internal::GenericNondeterministicReducer<Self, Op>>(
+ self, output, cl::sycl::nd_range<1>(cl::sycl::range<1>(GRange), cl::sycl::range<1>(tileSize)), Index(1),
+ reducer, range, (num_values_to_reduce != 0) ? num_values_to_reduce : static_cast<Index>(1));
+ return false;
+ }
+};
+
+} // namespace internal
+} // namespace Eigen
+
+#endif // UNSUPPORTED_EIGEN_CXX11_SRC_TENSOR_TENSOR_REDUCTION_SYCL_HPP
diff --git a/unsupported/Eigen/CXX11/src/Tensor/TensorRef.h b/unsupported/Eigen/CXX11/src/Tensor/TensorRef.h
new file mode 100644
index 0000000..843cb9d
--- /dev/null
+++ b/unsupported/Eigen/CXX11/src/Tensor/TensorRef.h
@@ -0,0 +1,376 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_CXX11_TENSOR_TENSOR_REF_H
+#define EIGEN_CXX11_TENSOR_TENSOR_REF_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+
+template <typename Dimensions, typename Scalar>
+class TensorLazyBaseEvaluator {
+ public:
+ TensorLazyBaseEvaluator() : m_refcount(0) { }
+ virtual ~TensorLazyBaseEvaluator() { }
+
+ EIGEN_DEVICE_FUNC virtual const Dimensions& dimensions() const = 0;
+ EIGEN_DEVICE_FUNC virtual const Scalar* data() const = 0;
+
+ EIGEN_DEVICE_FUNC virtual const Scalar coeff(DenseIndex index) const = 0;
+ EIGEN_DEVICE_FUNC virtual Scalar& coeffRef(DenseIndex index) = 0;
+
+ void incrRefCount() { ++m_refcount; }
+ void decrRefCount() { --m_refcount; }
+ int refCount() const { return m_refcount; }
+
+ private:
+ // No copy, no assignment;
+ TensorLazyBaseEvaluator(const TensorLazyBaseEvaluator& other);
+ TensorLazyBaseEvaluator& operator = (const TensorLazyBaseEvaluator& other);
+
+ int m_refcount;
+};
+
+
+template <typename Dimensions, typename Expr, typename Device>
+class TensorLazyEvaluatorReadOnly : public TensorLazyBaseEvaluator<Dimensions, typename TensorEvaluator<Expr, Device>::Scalar> {
+ public:
+ // typedef typename TensorEvaluator<Expr, Device>::Dimensions Dimensions;
+ typedef typename TensorEvaluator<Expr, Device>::Scalar Scalar;
+ typedef StorageMemory<Scalar, Device> Storage;
+ typedef typename Storage::Type EvaluatorPointerType;
+ typedef TensorEvaluator<Expr, Device> EvalType;
+
+ TensorLazyEvaluatorReadOnly(const Expr& expr, const Device& device) : m_impl(expr, device), m_dummy(Scalar(0)) {
+ m_dims = m_impl.dimensions();
+ m_impl.evalSubExprsIfNeeded(NULL);
+ }
+ virtual ~TensorLazyEvaluatorReadOnly() {
+ m_impl.cleanup();
+ }
+
+ EIGEN_DEVICE_FUNC virtual const Dimensions& dimensions() const {
+ return m_dims;
+ }
+ EIGEN_DEVICE_FUNC virtual const Scalar* data() const {
+ return m_impl.data();
+ }
+
+ EIGEN_DEVICE_FUNC virtual const Scalar coeff(DenseIndex index) const {
+ return m_impl.coeff(index);
+ }
+ EIGEN_DEVICE_FUNC virtual Scalar& coeffRef(DenseIndex /*index*/) {
+ eigen_assert(false && "can't reference the coefficient of a rvalue");
+ return m_dummy;
+ };
+
+ protected:
+ TensorEvaluator<Expr, Device> m_impl;
+ Dimensions m_dims;
+ Scalar m_dummy;
+};
+
+template <typename Dimensions, typename Expr, typename Device>
+class TensorLazyEvaluatorWritable : public TensorLazyEvaluatorReadOnly<Dimensions, Expr, Device> {
+ public:
+ typedef TensorLazyEvaluatorReadOnly<Dimensions, Expr, Device> Base;
+ typedef typename Base::Scalar Scalar;
+ typedef StorageMemory<Scalar, Device> Storage;
+ typedef typename Storage::Type EvaluatorPointerType;
+
+ TensorLazyEvaluatorWritable(const Expr& expr, const Device& device) : Base(expr, device) {
+ }
+ virtual ~TensorLazyEvaluatorWritable() {
+ }
+
+ EIGEN_DEVICE_FUNC virtual Scalar& coeffRef(DenseIndex index) {
+ return this->m_impl.coeffRef(index);
+ }
+};
+
+template <typename Dimensions, typename Expr, typename Device>
+class TensorLazyEvaluator : public std::conditional_t<bool(internal::is_lvalue<Expr>::value),
+ TensorLazyEvaluatorWritable<Dimensions, Expr, Device>,
+ TensorLazyEvaluatorReadOnly<Dimensions, const Expr, Device> > {
+ public:
+ typedef std::conditional_t<bool(internal::is_lvalue<Expr>::value),
+ TensorLazyEvaluatorWritable<Dimensions, Expr, Device>,
+ TensorLazyEvaluatorReadOnly<Dimensions, const Expr, Device> > Base;
+ typedef typename Base::Scalar Scalar;
+
+ TensorLazyEvaluator(const Expr& expr, const Device& device) : Base(expr, device) {
+ }
+ virtual ~TensorLazyEvaluator() {
+ }
+};
+
+} // namespace internal
+
+
+/** \class TensorRef
+ * \ingroup CXX11_Tensor_Module
+ *
+ * \brief A reference to a tensor expression
+ * The expression will be evaluated lazily (as much as possible).
+ *
+ */
+template<typename PlainObjectType> class TensorRef : public TensorBase<TensorRef<PlainObjectType> >
+{
+ public:
+ typedef TensorRef<PlainObjectType> Self;
+ typedef typename PlainObjectType::Base Base;
+ typedef typename Eigen::internal::nested<Self>::type Nested;
+ typedef typename internal::traits<PlainObjectType>::StorageKind StorageKind;
+ typedef typename internal::traits<PlainObjectType>::Index Index;
+ typedef typename internal::traits<PlainObjectType>::Scalar Scalar;
+ typedef typename NumTraits<Scalar>::Real RealScalar;
+ typedef typename Base::CoeffReturnType CoeffReturnType;
+ typedef Scalar* PointerType;
+ typedef PointerType PointerArgType;
+
+ static constexpr Index NumIndices = PlainObjectType::NumIndices;
+ typedef typename PlainObjectType::Dimensions Dimensions;
+
+ static constexpr int Layout = PlainObjectType::Layout;
+ enum {
+ IsAligned = false,
+ PacketAccess = false,
+ BlockAccess = false,
+ PreferBlockAccess = false,
+ CoordAccess = false, // to be implemented
+ RawAccess = false
+ };
+
+ //===- Tensor block evaluation strategy (see TensorBlock.h) -----------===//
+ typedef internal::TensorBlockNotImplemented TensorBlock;
+ //===------------------------------------------------------------------===//
+
+ EIGEN_STRONG_INLINE TensorRef() : m_evaluator(NULL) {
+ }
+
+ template <typename Expression>
+ EIGEN_STRONG_INLINE TensorRef(const Expression& expr) : m_evaluator(new internal::TensorLazyEvaluator<Dimensions, Expression, DefaultDevice>(expr, DefaultDevice())) {
+ m_evaluator->incrRefCount();
+ }
+
+ template <typename Expression>
+ EIGEN_STRONG_INLINE TensorRef& operator = (const Expression& expr) {
+ unrefEvaluator();
+ m_evaluator = new internal::TensorLazyEvaluator<Dimensions, Expression, DefaultDevice>(expr, DefaultDevice());
+ m_evaluator->incrRefCount();
+ return *this;
+ }
+
+ ~TensorRef() {
+ unrefEvaluator();
+ }
+
+ TensorRef(const TensorRef& other) : TensorBase<TensorRef<PlainObjectType> >(other), m_evaluator(other.m_evaluator) {
+ eigen_assert(m_evaluator->refCount() > 0);
+ m_evaluator->incrRefCount();
+ }
+
+ TensorRef& operator = (const TensorRef& other) {
+ if (this != &other) {
+ unrefEvaluator();
+ m_evaluator = other.m_evaluator;
+ eigen_assert(m_evaluator->refCount() > 0);
+ m_evaluator->incrRefCount();
+ }
+ return *this;
+ }
+
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE Index rank() const { return m_evaluator->dimensions().size(); }
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE Index dimension(Index n) const { return m_evaluator->dimensions()[n]; }
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE const Dimensions& dimensions() const { return m_evaluator->dimensions(); }
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE Index size() const { return m_evaluator->dimensions().TotalSize(); }
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE const Scalar* data() const { return m_evaluator->data(); }
+
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE const Scalar operator()(Index index) const
+ {
+ return m_evaluator->coeff(index);
+ }
+
+ template<typename... IndexTypes> EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE const Scalar operator()(Index firstIndex, IndexTypes... otherIndices) const
+ {
+ const std::size_t num_indices = (sizeof...(otherIndices) + 1);
+ const array<Index, num_indices> indices{{firstIndex, otherIndices...}};
+ return coeff(indices);
+ }
+ template<typename... IndexTypes> EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE Scalar& coeffRef(Index firstIndex, IndexTypes... otherIndices)
+ {
+ const std::size_t num_indices = (sizeof...(otherIndices) + 1);
+ const array<Index, num_indices> indices{{firstIndex, otherIndices...}};
+ return coeffRef(indices);
+ }
+
+ template <std::size_t NumIndices> EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE const Scalar coeff(const array<Index, NumIndices>& indices) const
+ {
+ const Dimensions& dims = this->dimensions();
+ Index index = 0;
+ if (PlainObjectType::Options & RowMajor) {
+ index += indices[0];
+ for (size_t i = 1; i < NumIndices; ++i) {
+ index = index * dims[i] + indices[i];
+ }
+ } else {
+ index += indices[NumIndices-1];
+ for (int i = NumIndices-2; i >= 0; --i) {
+ index = index * dims[i] + indices[i];
+ }
+ }
+ return m_evaluator->coeff(index);
+ }
+ template <std::size_t NumIndices> EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE Scalar& coeffRef(const array<Index, NumIndices>& indices)
+ {
+ const Dimensions& dims = this->dimensions();
+ Index index = 0;
+ if (PlainObjectType::Options & RowMajor) {
+ index += indices[0];
+ for (size_t i = 1; i < NumIndices; ++i) {
+ index = index * dims[i] + indices[i];
+ }
+ } else {
+ index += indices[NumIndices-1];
+ for (int i = NumIndices-2; i >= 0; --i) {
+ index = index * dims[i] + indices[i];
+ }
+ }
+ return m_evaluator->coeffRef(index);
+ }
+
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE const Scalar coeff(Index index) const
+ {
+ return m_evaluator->coeff(index);
+ }
+
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE Scalar& coeffRef(Index index)
+ {
+ return m_evaluator->coeffRef(index);
+ }
+
+ private:
+ EIGEN_STRONG_INLINE void unrefEvaluator() {
+ if (m_evaluator) {
+ m_evaluator->decrRefCount();
+ if (m_evaluator->refCount() == 0) {
+ delete m_evaluator;
+ }
+ }
+ }
+
+ internal::TensorLazyBaseEvaluator<Dimensions, Scalar>* m_evaluator;
+};
+
+
+// evaluator for rvalues
+template<typename Derived, typename Device>
+struct TensorEvaluator<const TensorRef<Derived>, Device>
+{
+ typedef typename Derived::Index Index;
+ typedef typename Derived::Scalar Scalar;
+ typedef typename Derived::Scalar CoeffReturnType;
+ typedef typename PacketType<CoeffReturnType, Device>::type PacketReturnType;
+ typedef typename Derived::Dimensions Dimensions;
+ typedef StorageMemory<CoeffReturnType, Device> Storage;
+ typedef typename Storage::Type EvaluatorPointerType;
+
+ static constexpr int Layout = TensorRef<Derived>::Layout;
+ enum {
+ IsAligned = false,
+ PacketAccess = false,
+ BlockAccess = false,
+ PreferBlockAccess = false,
+ CoordAccess = false, // to be implemented
+ RawAccess = false
+ };
+
+ //===- Tensor block evaluation strategy (see TensorBlock.h) -------------===//
+ typedef internal::TensorBlockNotImplemented TensorBlock;
+ //===--------------------------------------------------------------------===//
+
+ EIGEN_STRONG_INLINE TensorEvaluator(const TensorRef<Derived>& m, const Device&)
+ : m_ref(m)
+ { }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Dimensions& dimensions() const { return m_ref.dimensions(); }
+
+ EIGEN_STRONG_INLINE bool evalSubExprsIfNeeded(EvaluatorPointerType) {
+ return true;
+ }
+
+ EIGEN_STRONG_INLINE void cleanup() { }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE CoeffReturnType coeff(Index index) const {
+ return m_ref.coeff(index);
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar& coeffRef(Index index) {
+ return m_ref.coeffRef(index);
+ }
+
+ EIGEN_DEVICE_FUNC const Scalar* data() const { return m_ref.data(); }
+
+ protected:
+ TensorRef<Derived> m_ref;
+};
+
+
+// evaluator for lvalues
+template<typename Derived, typename Device>
+struct TensorEvaluator<TensorRef<Derived>, Device> : public TensorEvaluator<const TensorRef<Derived>, Device>
+{
+ typedef typename Derived::Index Index;
+ typedef typename Derived::Scalar Scalar;
+ typedef typename Derived::Scalar CoeffReturnType;
+ typedef typename PacketType<CoeffReturnType, Device>::type PacketReturnType;
+ typedef typename Derived::Dimensions Dimensions;
+
+ typedef TensorEvaluator<const TensorRef<Derived>, Device> Base;
+
+ enum {
+ IsAligned = false,
+ PacketAccess = false,
+ BlockAccess = false,
+ PreferBlockAccess = false,
+ RawAccess = false
+ };
+
+ //===- Tensor block evaluation strategy (see TensorBlock.h) -------------===//
+ typedef internal::TensorBlockNotImplemented TensorBlock;
+ //===--------------------------------------------------------------------===//
+
+ EIGEN_STRONG_INLINE TensorEvaluator(TensorRef<Derived>& m, const Device& d) : Base(m, d)
+ { }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar& coeffRef(Index index) {
+ return this->m_ref.coeffRef(index);
+ }
+};
+
+
+
+} // end namespace Eigen
+
+#endif // EIGEN_CXX11_TENSOR_TENSOR_REF_H
diff --git a/unsupported/Eigen/CXX11/src/Tensor/TensorReverse.h b/unsupported/Eigen/CXX11/src/Tensor/TensorReverse.h
new file mode 100644
index 0000000..b5e66b3
--- /dev/null
+++ b/unsupported/Eigen/CXX11/src/Tensor/TensorReverse.h
@@ -0,0 +1,465 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2014 Navdeep Jaitly <ndjaitly@google.com>
+// Benoit Steiner <benoit.steiner.goog@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_CXX11_TENSOR_TENSOR_REVERSE_H
+#define EIGEN_CXX11_TENSOR_TENSOR_REVERSE_H
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+/** \class TensorReverse
+ * \ingroup CXX11_Tensor_Module
+ *
+ * \brief Tensor reverse elements class.
+ *
+ */
+namespace internal {
+template<typename ReverseDimensions, typename XprType>
+struct traits<TensorReverseOp<ReverseDimensions,
+ XprType> > : public traits<XprType>
+{
+ typedef typename XprType::Scalar Scalar;
+ typedef traits<XprType> XprTraits;
+ typedef typename XprTraits::StorageKind StorageKind;
+ typedef typename XprTraits::Index Index;
+ typedef typename XprType::Nested Nested;
+ typedef std::remove_reference_t<Nested> Nested_;
+ static constexpr int NumDimensions = XprTraits::NumDimensions;
+ static constexpr int Layout = XprTraits::Layout;
+ typedef typename XprTraits::PointerType PointerType;
+};
+
+template<typename ReverseDimensions, typename XprType>
+struct eval<TensorReverseOp<ReverseDimensions, XprType>, Eigen::Dense>
+{
+ typedef const TensorReverseOp<ReverseDimensions, XprType>& type;
+};
+
+template<typename ReverseDimensions, typename XprType>
+struct nested<TensorReverseOp<ReverseDimensions, XprType>, 1,
+ typename eval<TensorReverseOp<ReverseDimensions, XprType> >::type>
+{
+ typedef TensorReverseOp<ReverseDimensions, XprType> type;
+};
+
+} // end namespace internal
+
+template<typename ReverseDimensions, typename XprType>
+class TensorReverseOp : public TensorBase<TensorReverseOp<ReverseDimensions,
+ XprType>, WriteAccessors>
+{
+ public:
+ typedef TensorBase<TensorReverseOp<ReverseDimensions, XprType>, WriteAccessors>Base;
+ typedef typename Eigen::internal::traits<TensorReverseOp>::Scalar Scalar;
+ typedef typename Eigen::NumTraits<Scalar>::Real RealScalar;
+ typedef typename XprType::CoeffReturnType CoeffReturnType;
+ typedef typename Eigen::internal::nested<TensorReverseOp>::type Nested;
+ typedef typename Eigen::internal::traits<TensorReverseOp>::StorageKind
+ StorageKind;
+ typedef typename Eigen::internal::traits<TensorReverseOp>::Index Index;
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorReverseOp(
+ const XprType& expr, const ReverseDimensions& reverse_dims)
+ : m_xpr(expr), m_reverse_dims(reverse_dims) { }
+
+ EIGEN_DEVICE_FUNC
+ const ReverseDimensions& reverse() const { return m_reverse_dims; }
+
+ EIGEN_DEVICE_FUNC
+ const internal::remove_all_t<typename XprType::Nested>&
+ expression() const { return m_xpr; }
+
+ EIGEN_TENSOR_INHERIT_ASSIGNMENT_OPERATORS(TensorReverseOp)
+
+
+ protected:
+ typename XprType::Nested m_xpr;
+ const ReverseDimensions m_reverse_dims;
+};
+
+// Eval as rvalue
+template<typename ReverseDimensions, typename ArgType, typename Device>
+struct TensorEvaluator<const TensorReverseOp<ReverseDimensions, ArgType>, Device>
+{
+ typedef TensorReverseOp<ReverseDimensions, ArgType> XprType;
+ typedef typename XprType::Index Index;
+ static constexpr int NumDims = internal::array_size<ReverseDimensions>::value;
+ typedef DSizes<Index, NumDims> Dimensions;
+ typedef typename XprType::Scalar Scalar;
+ typedef typename XprType::CoeffReturnType CoeffReturnType;
+ typedef typename PacketType<CoeffReturnType, Device>::type PacketReturnType;
+ static constexpr int PacketSize = PacketType<CoeffReturnType, Device>::size;
+ typedef StorageMemory<CoeffReturnType, Device> Storage;
+ typedef typename Storage::Type EvaluatorPointerType;
+
+ static constexpr int Layout = TensorEvaluator<ArgType, Device>::Layout;
+ enum {
+ IsAligned = false,
+ PacketAccess = TensorEvaluator<ArgType, Device>::PacketAccess,
+ BlockAccess = NumDims > 0,
+ PreferBlockAccess = true,
+ CoordAccess = false, // to be implemented
+ RawAccess = false
+ };
+
+ typedef internal::TensorIntDivisor<Index> IndexDivisor;
+
+ //===- Tensor block evaluation strategy (see TensorBlock.h) -------------===//
+ typedef internal::TensorBlockDescriptor<NumDims, Index> TensorBlockDesc;
+ typedef internal::TensorBlockScratchAllocator<Device> TensorBlockScratch;
+
+ typedef typename TensorEvaluator<const ArgType, Device>::TensorBlock
+ ArgTensorBlock;
+
+ typedef typename internal::TensorMaterializedBlock<CoeffReturnType, NumDims,
+ Layout, Index>
+ TensorBlock;
+ //===--------------------------------------------------------------------===//
+
+ EIGEN_STRONG_INLINE TensorEvaluator(const XprType& op, const Device& device)
+ : m_impl(op.expression(), device),
+ m_reverse(op.reverse()),
+ m_device(device)
+ {
+ // Reversing a scalar isn't supported yet. It would be a no-op anyway.
+ EIGEN_STATIC_ASSERT((NumDims > 0), YOU_MADE_A_PROGRAMMING_MISTAKE);
+
+ // Compute strides
+ m_dimensions = m_impl.dimensions();
+ if (static_cast<int>(Layout) == static_cast<int>(ColMajor)) {
+ m_strides[0] = 1;
+ for (int i = 1; i < NumDims; ++i) {
+ m_strides[i] = m_strides[i-1] * m_dimensions[i-1];
+ if (m_strides[i] > 0) m_fastStrides[i] = IndexDivisor(m_strides[i]);
+ }
+ } else {
+ m_strides[NumDims-1] = 1;
+ for (int i = NumDims - 2; i >= 0; --i) {
+ m_strides[i] = m_strides[i+1] * m_dimensions[i+1];
+ if (m_strides[i] > 0) m_fastStrides[i] = IndexDivisor(m_strides[i]);
+ }
+ }
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ const Dimensions& dimensions() const { return m_dimensions; }
+
+ EIGEN_STRONG_INLINE bool evalSubExprsIfNeeded(EvaluatorPointerType) {
+ m_impl.evalSubExprsIfNeeded(NULL);
+ return true;
+ }
+
+#ifdef EIGEN_USE_THREADS
+ template <typename EvalSubExprsCallback>
+ EIGEN_STRONG_INLINE void evalSubExprsIfNeededAsync(
+ EvaluatorPointerType, EvalSubExprsCallback done) {
+ m_impl.evalSubExprsIfNeededAsync(nullptr, [done](bool) { done(true); });
+ }
+#endif // EIGEN_USE_THREADS
+
+ EIGEN_STRONG_INLINE void cleanup() {
+ m_impl.cleanup();
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Index reverseIndex(
+ Index index) const {
+ eigen_assert(index < dimensions().TotalSize());
+ Index inputIndex = 0;
+ if (static_cast<int>(Layout) == static_cast<int>(ColMajor)) {
+ EIGEN_UNROLL_LOOP
+ for (int i = NumDims - 1; i > 0; --i) {
+ Index idx = index / m_fastStrides[i];
+ index -= idx * m_strides[i];
+ if (m_reverse[i]) {
+ idx = m_dimensions[i] - idx - 1;
+ }
+ inputIndex += idx * m_strides[i] ;
+ }
+ if (m_reverse[0]) {
+ inputIndex += (m_dimensions[0] - index - 1);
+ } else {
+ inputIndex += index;
+ }
+ } else {
+ EIGEN_UNROLL_LOOP
+ for (int i = 0; i < NumDims - 1; ++i) {
+ Index idx = index / m_fastStrides[i];
+ index -= idx * m_strides[i];
+ if (m_reverse[i]) {
+ idx = m_dimensions[i] - idx - 1;
+ }
+ inputIndex += idx * m_strides[i] ;
+ }
+ if (m_reverse[NumDims-1]) {
+ inputIndex += (m_dimensions[NumDims-1] - index - 1);
+ } else {
+ inputIndex += index;
+ }
+ }
+ return inputIndex;
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE CoeffReturnType coeff(
+ Index index) const {
+ return m_impl.coeff(reverseIndex(index));
+ }
+
+ template<int LoadMode>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ PacketReturnType packet(Index index) const
+ {
+ eigen_assert(index+PacketSize-1 < dimensions().TotalSize());
+
+ // TODO(ndjaitly): write a better packing routine that uses
+ // local structure.
+ EIGEN_ALIGN_MAX std::remove_const_t<CoeffReturnType>
+ values[PacketSize];
+ EIGEN_UNROLL_LOOP
+ for (int i = 0; i < PacketSize; ++i) {
+ values[i] = coeff(index+i);
+ }
+ PacketReturnType rslt = internal::pload<PacketReturnType>(values);
+ return rslt;
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ internal::TensorBlockResourceRequirements getResourceRequirements() const {
+ const size_t target_size = m_device.lastLevelCacheSize();
+ // Block evaluation reads underlying memory in reverse order, and default
+ // cost model does not properly catch this in bytes stored/loaded.
+ return internal::TensorBlockResourceRequirements::skewed<Scalar>(
+ target_size)
+ .addCostPerCoeff({0, 0, 24});
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorBlock
+ block(TensorBlockDesc& desc, TensorBlockScratch& scratch,
+ bool /*root_of_expr_ast*/ = false) const {
+ // TODO(ezhulenev): If underlying tensor expression supports and prefers
+ // block evaluation we must use it. Currently we use coeff and packet
+ // access into the underlying tensor expression.
+ // static const bool useBlockAccessForArgType =
+ // TensorEvaluator<ArgType, Device>::BlockAccess &&
+ // TensorEvaluator<ArgType, Device>::PreferBlockAccess;
+
+ static const bool isColMajor =
+ static_cast<int>(Layout) == static_cast<int>(ColMajor);
+
+ static const Index inner_dim_idx = isColMajor ? 0 : NumDims - 1;
+ const bool inner_dim_reversed = m_reverse[inner_dim_idx];
+
+ // Offset in the output block.
+ Index block_offset = 0;
+
+ // Offset in the input Tensor.
+ Index input_offset = reverseIndex(desc.offset());
+
+ // Initialize output block iterator state. Dimension in this array are
+ // always in inner_most -> outer_most order (col major layout).
+ array<BlockIteratorState, NumDims> it;
+ for (int i = 0; i < NumDims; ++i) {
+ const int dim = isColMajor ? i : NumDims - 1 - i;
+ it[i].size = desc.dimension(dim);
+ it[i].count = 0;
+ it[i].reverse = m_reverse[dim];
+
+ it[i].block_stride =
+ i == 0 ? 1 : (it[i - 1].size * it[i - 1].block_stride);
+ it[i].block_span = it[i].block_stride * (it[i].size - 1);
+
+ it[i].input_stride = m_strides[dim];
+ it[i].input_span = it[i].input_stride * (it[i].size - 1);
+
+ if (it[i].reverse) {
+ it[i].input_stride = -1 * it[i].input_stride;
+ it[i].input_span = -1 * it[i].input_span;
+ }
+ }
+
+ // If multiple inner dimensions have the same reverse flag, check if we can
+ // merge them into a single virtual inner dimension.
+ int effective_inner_dim = 0;
+ for (int i = 1; i < NumDims; ++i) {
+ if (it[i].reverse != it[effective_inner_dim].reverse) break;
+ if (it[i].block_stride != it[effective_inner_dim].size) break;
+ if (it[i].block_stride != numext::abs(it[i].input_stride)) break;
+
+ it[i].size = it[effective_inner_dim].size * it[i].size;
+
+ it[i].block_stride = 1;
+ it[i].input_stride = (inner_dim_reversed ? -1 : 1);
+
+ it[i].block_span = it[i].block_stride * (it[i].size - 1);
+ it[i].input_span = it[i].input_stride * (it[i].size - 1);
+
+ effective_inner_dim = i;
+ }
+
+ eigen_assert(it[effective_inner_dim].block_stride == 1);
+ eigen_assert(it[effective_inner_dim].input_stride ==
+ (inner_dim_reversed ? -1 : 1));
+
+ const Index inner_dim_size = it[effective_inner_dim].size;
+
+ // Prepare storage for the materialized reverse result.
+ const typename TensorBlock::Storage block_storage =
+ TensorBlock::prepareStorage(desc, scratch);
+ CoeffReturnType* block_buffer = block_storage.data();
+
+ while (it[NumDims - 1].count < it[NumDims - 1].size) {
+ // Copy inner-most dimension data from reversed location in input.
+ Index dst = block_offset;
+ Index src = input_offset;
+
+ // NOTE(ezhulenev): Adding vectorized path with internal::preverse showed
+ // worse results in benchmarks than a simple coefficient loop.
+ if (inner_dim_reversed) {
+ for (Index i = 0; i < inner_dim_size; ++i) {
+ block_buffer[dst] = m_impl.coeff(src);
+ ++dst;
+ --src;
+ }
+ } else {
+ for (Index i = 0; i < inner_dim_size; ++i) {
+ block_buffer[dst] = m_impl.coeff(src);
+ ++dst;
+ ++src;
+ }
+ }
+
+ // For the 1d tensor we need to generate only one inner-most dimension.
+ if ((NumDims - effective_inner_dim) == 1) break;
+
+ // Update offset.
+ for (Index i = effective_inner_dim + 1; i < NumDims; ++i) {
+ if (++it[i].count < it[i].size) {
+ block_offset += it[i].block_stride;
+ input_offset += it[i].input_stride;
+ break;
+ }
+ if (i != NumDims - 1) it[i].count = 0;
+ block_offset -= it[i].block_span;
+ input_offset -= it[i].input_span;
+ }
+ }
+
+ return block_storage.AsTensorMaterializedBlock();
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorOpCost costPerCoeff(bool vectorized) const {
+ double compute_cost = NumDims * (2 * TensorOpCost::AddCost<Index>() +
+ 2 * TensorOpCost::MulCost<Index>() +
+ TensorOpCost::DivCost<Index>());
+ for (int i = 0; i < NumDims; ++i) {
+ if (m_reverse[i]) {
+ compute_cost += 2 * TensorOpCost::AddCost<Index>();
+ }
+ }
+ return m_impl.costPerCoeff(vectorized) +
+ TensorOpCost(0, 0, compute_cost, false /* vectorized */, PacketSize);
+ }
+
+ EIGEN_DEVICE_FUNC typename Storage::Type data() const { return NULL; }
+
+#ifdef EIGEN_USE_SYCL
+ // binding placeholder accessors to a command group handler for SYCL
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void bind(cl::sycl::handler &cgh) const {
+ m_impl.bind(cgh);
+ }
+#endif
+
+ protected:
+ Dimensions m_dimensions;
+ array<Index, NumDims> m_strides;
+ array<IndexDivisor, NumDims> m_fastStrides;
+ TensorEvaluator<ArgType, Device> m_impl;
+ ReverseDimensions m_reverse;
+ const Device EIGEN_DEVICE_REF m_device;
+
+ private:
+ struct BlockIteratorState {
+ BlockIteratorState()
+ : size(0),
+ count(0),
+ reverse(false),
+ block_stride(0),
+ block_span(0),
+ input_stride(0),
+ input_span(0) {}
+
+ Index size;
+ Index count;
+ bool reverse;
+ Index block_stride;
+ Index block_span;
+ Index input_stride;
+ Index input_span;
+ };
+};
+
+// Eval as lvalue
+
+template <typename ReverseDimensions, typename ArgType, typename Device>
+struct TensorEvaluator<TensorReverseOp<ReverseDimensions, ArgType>, Device>
+ : public TensorEvaluator<const TensorReverseOp<ReverseDimensions, ArgType>,
+ Device> {
+ typedef TensorEvaluator<const TensorReverseOp<ReverseDimensions, ArgType>,
+ Device> Base;
+ typedef TensorReverseOp<ReverseDimensions, ArgType> XprType;
+ typedef typename XprType::Index Index;
+ static constexpr int NumDims = internal::array_size<ReverseDimensions>::value;
+ typedef DSizes<Index, NumDims> Dimensions;
+
+ static constexpr int Layout = TensorEvaluator<ArgType, Device>::Layout;
+ enum {
+ IsAligned = false,
+ PacketAccess = TensorEvaluator<ArgType, Device>::PacketAccess,
+ BlockAccess = false,
+ PreferBlockAccess = false,
+ CoordAccess = false, // to be implemented
+ RawAccess = false
+ };
+ EIGEN_STRONG_INLINE TensorEvaluator(const XprType& op, const Device& device)
+ : Base(op, device) {}
+
+ typedef typename XprType::Scalar Scalar;
+ typedef typename XprType::CoeffReturnType CoeffReturnType;
+ typedef typename PacketType<CoeffReturnType, Device>::type PacketReturnType;
+ static constexpr int PacketSize = PacketType<CoeffReturnType, Device>::size;
+
+ //===- Tensor block evaluation strategy (see TensorBlock.h) -------------===//
+ typedef internal::TensorBlockNotImplemented TensorBlock;
+ //===--------------------------------------------------------------------===//
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ const Dimensions& dimensions() const { return this->m_dimensions; }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar& coeffRef(Index index) {
+ return this->m_impl.coeffRef(this->reverseIndex(index));
+ }
+
+ template <int StoreMode> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ void writePacket(Index index, const PacketReturnType& x) {
+ eigen_assert(index+PacketSize-1 < dimensions().TotalSize());
+
+ // This code is pilfered from TensorMorphing.h
+ EIGEN_ALIGN_MAX CoeffReturnType values[PacketSize];
+ internal::pstore<CoeffReturnType, PacketReturnType>(values, x);
+ EIGEN_UNROLL_LOOP
+ for (int i = 0; i < PacketSize; ++i) {
+ this->coeffRef(index+i) = values[i];
+ }
+ }
+};
+
+
+} // end namespace Eigen
+
+#endif // EIGEN_CXX11_TENSOR_TENSOR_REVERSE_H
diff --git a/unsupported/Eigen/CXX11/src/Tensor/TensorScan.h b/unsupported/Eigen/CXX11/src/Tensor/TensorScan.h
new file mode 100644
index 0000000..ed0a731
--- /dev/null
+++ b/unsupported/Eigen/CXX11/src/Tensor/TensorScan.h
@@ -0,0 +1,530 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2016 Igor Babuschkin <igor@babuschk.in>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_CXX11_TENSOR_TENSOR_SCAN_H
+#define EIGEN_CXX11_TENSOR_TENSOR_SCAN_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+
+template <typename Op, typename XprType>
+struct traits<TensorScanOp<Op, XprType> >
+ : public traits<XprType> {
+ typedef typename XprType::Scalar Scalar;
+ typedef traits<XprType> XprTraits;
+ typedef typename XprTraits::StorageKind StorageKind;
+ typedef typename XprType::Nested Nested;
+ typedef std::remove_reference_t<Nested> Nested_;
+ static constexpr int NumDimensions = XprTraits::NumDimensions;
+ static constexpr int Layout = XprTraits::Layout;
+ typedef typename XprTraits::PointerType PointerType;
+};
+
+template<typename Op, typename XprType>
+struct eval<TensorScanOp<Op, XprType>, Eigen::Dense>
+{
+ typedef const TensorScanOp<Op, XprType>& type;
+};
+
+template<typename Op, typename XprType>
+struct nested<TensorScanOp<Op, XprType>, 1,
+ typename eval<TensorScanOp<Op, XprType> >::type>
+{
+ typedef TensorScanOp<Op, XprType> type;
+};
+} // end namespace internal
+
+/** \class TensorScan
+ * \ingroup CXX11_Tensor_Module
+ *
+ * \brief Tensor scan class.
+ */
+template <typename Op, typename XprType>
+class TensorScanOp
+ : public TensorBase<TensorScanOp<Op, XprType>, ReadOnlyAccessors> {
+public:
+ typedef typename Eigen::internal::traits<TensorScanOp>::Scalar Scalar;
+ typedef typename Eigen::NumTraits<Scalar>::Real RealScalar;
+ typedef typename XprType::CoeffReturnType CoeffReturnType;
+ typedef typename Eigen::internal::nested<TensorScanOp>::type Nested;
+ typedef typename Eigen::internal::traits<TensorScanOp>::StorageKind StorageKind;
+ typedef typename Eigen::internal::traits<TensorScanOp>::Index Index;
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorScanOp(
+ const XprType& expr, const Index& axis, bool exclusive = false, const Op& op = Op())
+ : m_expr(expr), m_axis(axis), m_accumulator(op), m_exclusive(exclusive) {}
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ const Index axis() const { return m_axis; }
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ const XprType& expression() const { return m_expr; }
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ const Op accumulator() const { return m_accumulator; }
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ bool exclusive() const { return m_exclusive; }
+
+protected:
+ typename XprType::Nested m_expr;
+ const Index m_axis;
+ const Op m_accumulator;
+ const bool m_exclusive;
+};
+
+
+namespace internal {
+
+template <typename Self>
+EIGEN_STRONG_INLINE void ReduceScalar(Self& self, Index offset,
+ typename Self::CoeffReturnType* data) {
+ // Compute the scan along the axis, starting at the given offset
+ typename Self::CoeffReturnType accum = self.accumulator().initialize();
+ if (self.stride() == 1) {
+ if (self.exclusive()) {
+ for (Index curr = offset; curr < offset + self.size(); ++curr) {
+ data[curr] = self.accumulator().finalize(accum);
+ self.accumulator().reduce(self.inner().coeff(curr), &accum);
+ }
+ } else {
+ for (Index curr = offset; curr < offset + self.size(); ++curr) {
+ self.accumulator().reduce(self.inner().coeff(curr), &accum);
+ data[curr] = self.accumulator().finalize(accum);
+ }
+ }
+ } else {
+ if (self.exclusive()) {
+ for (Index idx3 = 0; idx3 < self.size(); idx3++) {
+ Index curr = offset + idx3 * self.stride();
+ data[curr] = self.accumulator().finalize(accum);
+ self.accumulator().reduce(self.inner().coeff(curr), &accum);
+ }
+ } else {
+ for (Index idx3 = 0; idx3 < self.size(); idx3++) {
+ Index curr = offset + idx3 * self.stride();
+ self.accumulator().reduce(self.inner().coeff(curr), &accum);
+ data[curr] = self.accumulator().finalize(accum);
+ }
+ }
+ }
+}
+
+template <typename Self>
+EIGEN_STRONG_INLINE void ReducePacket(Self& self, Index offset,
+ typename Self::CoeffReturnType* data) {
+ using Scalar = typename Self::CoeffReturnType;
+ using Packet = typename Self::PacketReturnType;
+ // Compute the scan along the axis, starting at the calculated offset
+ Packet accum = self.accumulator().template initializePacket<Packet>();
+ if (self.stride() == 1) {
+ if (self.exclusive()) {
+ for (Index curr = offset; curr < offset + self.size(); ++curr) {
+ internal::pstoreu<Scalar, Packet>(data + curr, self.accumulator().finalizePacket(accum));
+ self.accumulator().reducePacket(self.inner().template packet<Unaligned>(curr), &accum);
+ }
+ } else {
+ for (Index curr = offset; curr < offset + self.size(); ++curr) {
+ self.accumulator().reducePacket(self.inner().template packet<Unaligned>(curr), &accum);
+ internal::pstoreu<Scalar, Packet>(data + curr, self.accumulator().finalizePacket(accum));
+ }
+ }
+ } else {
+ if (self.exclusive()) {
+ for (Index idx3 = 0; idx3 < self.size(); idx3++) {
+ const Index curr = offset + idx3 * self.stride();
+ internal::pstoreu<Scalar, Packet>(data + curr, self.accumulator().finalizePacket(accum));
+ self.accumulator().reducePacket(self.inner().template packet<Unaligned>(curr), &accum);
+ }
+ } else {
+ for (Index idx3 = 0; idx3 < self.size(); idx3++) {
+ const Index curr = offset + idx3 * self.stride();
+ self.accumulator().reducePacket(self.inner().template packet<Unaligned>(curr), &accum);
+ internal::pstoreu<Scalar, Packet>(data + curr, self.accumulator().finalizePacket(accum));
+ }
+ }
+ }
+}
+
+template <typename Self, bool Vectorize, bool Parallel>
+struct ReduceBlock {
+ EIGEN_STRONG_INLINE void operator()(Self& self, Index idx1,
+ typename Self::CoeffReturnType* data) {
+ for (Index idx2 = 0; idx2 < self.stride(); idx2++) {
+ // Calculate the starting offset for the scan
+ Index offset = idx1 + idx2;
+ ReduceScalar(self, offset, data);
+ }
+ }
+};
+
+// Specialization for vectorized reduction.
+template <typename Self>
+struct ReduceBlock<Self, /*Vectorize=*/true, /*Parallel=*/false> {
+ EIGEN_STRONG_INLINE void operator()(Self& self, Index idx1,
+ typename Self::CoeffReturnType* data) {
+ using Packet = typename Self::PacketReturnType;
+ const int PacketSize = internal::unpacket_traits<Packet>::size;
+ Index idx2 = 0;
+ for (; idx2 + PacketSize <= self.stride(); idx2 += PacketSize) {
+ // Calculate the starting offset for the packet scan
+ Index offset = idx1 + idx2;
+ ReducePacket(self, offset, data);
+ }
+ for (; idx2 < self.stride(); idx2++) {
+ // Calculate the starting offset for the scan
+ Index offset = idx1 + idx2;
+ ReduceScalar(self, offset, data);
+ }
+ }
+};
+
+// Single-threaded CPU implementation of scan
+template <typename Self, typename Reducer, typename Device,
+ bool Vectorize =
+ (TensorEvaluator<typename Self::ChildTypeNoConst, Device>::PacketAccess &&
+ internal::reducer_traits<Reducer, Device>::PacketAccess)>
+struct ScanLauncher {
+ void operator()(Self& self, typename Self::CoeffReturnType* data) {
+ Index total_size = internal::array_prod(self.dimensions());
+
+ // We fix the index along the scan axis to 0 and perform a
+ // scan per remaining entry. The iteration is split into two nested
+ // loops to avoid an integer division by keeping track of each idx1 and
+ // idx2.
+ for (Index idx1 = 0; idx1 < total_size; idx1 += self.stride() * self.size()) {
+ ReduceBlock<Self, Vectorize, /*Parallel=*/false> block_reducer;
+ block_reducer(self, idx1, data);
+ }
+ }
+};
+
+#ifdef EIGEN_USE_THREADS
+
+// Adjust block_size to avoid false sharing of cachelines among
+// threads. Currently set to twice the cache line size on Intel and ARM
+// processors.
+EIGEN_STRONG_INLINE Index AdjustBlockSize(Index item_size, Index block_size) {
+ EIGEN_CONSTEXPR Index kBlockAlignment = 128;
+ const Index items_per_cacheline =
+ numext::maxi<Index>(1, kBlockAlignment / item_size);
+ return items_per_cacheline * divup(block_size, items_per_cacheline);
+}
+
+template <typename Self>
+struct ReduceBlock<Self, /*Vectorize=*/true, /*Parallel=*/true> {
+ EIGEN_STRONG_INLINE void operator()(Self& self, Index idx1,
+ typename Self::CoeffReturnType* data) {
+ using Scalar = typename Self::CoeffReturnType;
+ using Packet = typename Self::PacketReturnType;
+ const int PacketSize = internal::unpacket_traits<Packet>::size;
+ Index num_scalars = self.stride();
+ Index num_packets = 0;
+ if (self.stride() >= PacketSize) {
+ num_packets = self.stride() / PacketSize;
+ self.device().parallelFor(
+ num_packets,
+ TensorOpCost(PacketSize * self.size(), PacketSize * self.size(),
+ 16 * PacketSize * self.size(), true, PacketSize),
+ // Make the shard size large enough that two neighboring threads
+ // won't write to the same cacheline of `data`.
+ [=](Index blk_size) {
+ return AdjustBlockSize(PacketSize * sizeof(Scalar), blk_size);
+ },
+ [&](Index first, Index last) {
+ for (Index packet = first; packet < last; ++packet) {
+ const Index idx2 = packet * PacketSize;
+ ReducePacket(self, idx1 + idx2, data);
+ }
+ });
+ num_scalars -= num_packets * PacketSize;
+ }
+ self.device().parallelFor(
+ num_scalars, TensorOpCost(self.size(), self.size(), 16 * self.size()),
+ // Make the shard size large enough that two neighboring threads
+ // won't write to the same cacheline of `data`.
+ [=](Index blk_size) {
+ return AdjustBlockSize(sizeof(Scalar), blk_size);
+ },
+ [&](Index first, Index last) {
+ for (Index scalar = first; scalar < last; ++scalar) {
+ const Index idx2 = num_packets * PacketSize + scalar;
+ ReduceScalar(self, idx1 + idx2, data);
+ }
+ });
+ }
+};
+
+template <typename Self>
+struct ReduceBlock<Self, /*Vectorize=*/false, /*Parallel=*/true> {
+ EIGEN_STRONG_INLINE void operator()(Self& self, Index idx1,
+ typename Self::CoeffReturnType* data) {
+ using Scalar = typename Self::CoeffReturnType;
+ self.device().parallelFor(
+ self.stride(), TensorOpCost(self.size(), self.size(), 16 * self.size()),
+ // Make the shard size large enough that two neighboring threads
+ // won't write to the same cacheline of `data`.
+ [=](Index blk_size) {
+ return AdjustBlockSize(sizeof(Scalar), blk_size);
+ },
+ [&](Index first, Index last) {
+ for (Index idx2 = first; idx2 < last; ++idx2) {
+ ReduceScalar(self, idx1 + idx2, data);
+ }
+ });
+ }
+};
+
+// Specialization for multi-threaded execution.
+template <typename Self, typename Reducer, bool Vectorize>
+struct ScanLauncher<Self, Reducer, ThreadPoolDevice, Vectorize> {
+ void operator()(Self& self, typename Self::CoeffReturnType* data) {
+ using Scalar = typename Self::CoeffReturnType;
+ using Packet = typename Self::PacketReturnType;
+ const int PacketSize = internal::unpacket_traits<Packet>::size;
+ const Index total_size = internal::array_prod(self.dimensions());
+ const Index inner_block_size = self.stride() * self.size();
+ bool parallelize_by_outer_blocks = (total_size >= (self.stride() * inner_block_size));
+
+ if ((parallelize_by_outer_blocks && total_size <= 4096) ||
+ (!parallelize_by_outer_blocks && self.stride() < PacketSize)) {
+ ScanLauncher<Self, Reducer, DefaultDevice, Vectorize> launcher;
+ launcher(self, data);
+ return;
+ }
+
+ if (parallelize_by_outer_blocks) {
+ // Parallelize over outer blocks.
+ const Index num_outer_blocks = total_size / inner_block_size;
+ self.device().parallelFor(
+ num_outer_blocks,
+ TensorOpCost(inner_block_size, inner_block_size,
+ 16 * PacketSize * inner_block_size, Vectorize,
+ PacketSize),
+ [=](Index blk_size) {
+ return AdjustBlockSize(inner_block_size * sizeof(Scalar), blk_size);
+ },
+ [&](Index first, Index last) {
+ for (Index idx1 = first; idx1 < last; ++idx1) {
+ ReduceBlock<Self, Vectorize, /*Parallelize=*/false> block_reducer;
+ block_reducer(self, idx1 * inner_block_size, data);
+ }
+ });
+ } else {
+ // Parallelize over inner packets/scalars dimensions when the reduction
+ // axis is not an inner dimension.
+ ReduceBlock<Self, Vectorize, /*Parallelize=*/true> block_reducer;
+ for (Index idx1 = 0; idx1 < total_size;
+ idx1 += self.stride() * self.size()) {
+ block_reducer(self, idx1, data);
+ }
+ }
+ }
+};
+#endif // EIGEN_USE_THREADS
+
+#if defined(EIGEN_USE_GPU) && (defined(EIGEN_GPUCC))
+
+// GPU implementation of scan
+// TODO(ibab) This placeholder implementation performs multiple scans in
+// parallel, but it would be better to use a parallel scan algorithm and
+// optimize memory access.
+template <typename Self, typename Reducer>
+__global__ EIGEN_HIP_LAUNCH_BOUNDS_1024 void ScanKernel(Self self, Index total_size, typename Self::CoeffReturnType* data) {
+ // Compute offset as in the CPU version
+ Index val = threadIdx.x + blockIdx.x * blockDim.x;
+ Index offset = (val / self.stride()) * self.stride() * self.size() + val % self.stride();
+
+ if (offset + (self.size() - 1) * self.stride() < total_size) {
+ // Compute the scan along the axis, starting at the calculated offset
+ typename Self::CoeffReturnType accum = self.accumulator().initialize();
+ for (Index idx = 0; idx < self.size(); idx++) {
+ Index curr = offset + idx * self.stride();
+ if (self.exclusive()) {
+ data[curr] = self.accumulator().finalize(accum);
+ self.accumulator().reduce(self.inner().coeff(curr), &accum);
+ } else {
+ self.accumulator().reduce(self.inner().coeff(curr), &accum);
+ data[curr] = self.accumulator().finalize(accum);
+ }
+ }
+ }
+ __syncthreads();
+
+}
+
+template <typename Self, typename Reducer, bool Vectorize>
+struct ScanLauncher<Self, Reducer, GpuDevice, Vectorize> {
+ void operator()(const Self& self, typename Self::CoeffReturnType* data) {
+ Index total_size = internal::array_prod(self.dimensions());
+ Index num_blocks = (total_size / self.size() + 63) / 64;
+ Index block_size = 64;
+
+ LAUNCH_GPU_KERNEL((ScanKernel<Self, Reducer>), num_blocks, block_size, 0, self.device(), self, total_size, data);
+ }
+};
+#endif // EIGEN_USE_GPU && (EIGEN_GPUCC)
+
+} // namespace internal
+
+// Eval as rvalue
+template <typename Op, typename ArgType, typename Device>
+struct TensorEvaluator<const TensorScanOp<Op, ArgType>, Device> {
+
+ typedef TensorScanOp<Op, ArgType> XprType;
+ typedef typename XprType::Index Index;
+ typedef const ArgType ChildTypeNoConst;
+ typedef const ArgType ChildType;
+ static constexpr int NumDims = internal::array_size<typename TensorEvaluator<ArgType, Device>::Dimensions>::value;
+ typedef DSizes<Index, NumDims> Dimensions;
+ typedef std::remove_const_t<typename XprType::Scalar> Scalar;
+ typedef typename XprType::CoeffReturnType CoeffReturnType;
+ typedef typename PacketType<CoeffReturnType, Device>::type PacketReturnType;
+ typedef TensorEvaluator<const TensorScanOp<Op, ArgType>, Device> Self;
+ typedef StorageMemory<Scalar, Device> Storage;
+ typedef typename Storage::Type EvaluatorPointerType;
+
+ static constexpr int Layout = TensorEvaluator<ArgType, Device>::Layout;
+ enum {
+ IsAligned = false,
+ PacketAccess = (PacketType<CoeffReturnType, Device>::size > 1),
+ BlockAccess = false,
+ PreferBlockAccess = false,
+ CoordAccess = false,
+ RawAccess = true
+ };
+
+ //===- Tensor block evaluation strategy (see TensorBlock.h) -------------===//
+ typedef internal::TensorBlockNotImplemented TensorBlock;
+ //===--------------------------------------------------------------------===//
+
+ EIGEN_STRONG_INLINE TensorEvaluator(const XprType& op, const Device& device)
+ : m_impl(op.expression(), device),
+ m_device(device),
+ m_exclusive(op.exclusive()),
+ m_accumulator(op.accumulator()),
+ m_size(m_impl.dimensions()[op.axis()]),
+ m_stride(1), m_consume_dim(op.axis()),
+ m_output(NULL) {
+
+ // Accumulating a scalar isn't supported.
+ EIGEN_STATIC_ASSERT((NumDims > 0), YOU_MADE_A_PROGRAMMING_MISTAKE);
+ eigen_assert(op.axis() >= 0 && op.axis() < NumDims);
+
+ // Compute stride of scan axis
+ const Dimensions& dims = m_impl.dimensions();
+ if (static_cast<int>(Layout) == static_cast<int>(ColMajor)) {
+ for (int i = 0; i < op.axis(); ++i) {
+ m_stride = m_stride * dims[i];
+ }
+ } else {
+ // dims can only be indexed through unsigned integers,
+ // so let's use an unsigned type to let the compiler knows.
+ // This prevents stupid warnings: ""'*((void*)(& evaluator)+64)[18446744073709551615]' may be used uninitialized in this function"
+ unsigned int axis = internal::convert_index<unsigned int>(op.axis());
+ for (unsigned int i = NumDims - 1; i > axis; --i) {
+ m_stride = m_stride * dims[i];
+ }
+ }
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Dimensions& dimensions() const {
+ return m_impl.dimensions();
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Index& stride() const {
+ return m_stride;
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Index& consume_dim() const {
+ return m_consume_dim;
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Index& size() const {
+ return m_size;
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Op& accumulator() const {
+ return m_accumulator;
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE bool exclusive() const {
+ return m_exclusive;
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const TensorEvaluator<ArgType, Device>& inner() const {
+ return m_impl;
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Device& device() const {
+ return m_device;
+ }
+
+ EIGEN_STRONG_INLINE bool evalSubExprsIfNeeded(EvaluatorPointerType data) {
+ m_impl.evalSubExprsIfNeeded(NULL);
+ internal::ScanLauncher<Self, Op, Device> launcher;
+ if (data) {
+ launcher(*this, data);
+ return false;
+ }
+
+ const Index total_size = internal::array_prod(dimensions());
+ m_output = static_cast<EvaluatorPointerType>(m_device.get((Scalar*) m_device.allocate_temp(total_size * sizeof(Scalar))));
+ launcher(*this, m_output);
+ return true;
+ }
+
+ template<int LoadMode>
+ EIGEN_DEVICE_FUNC PacketReturnType packet(Index index) const {
+ return internal::ploadt<PacketReturnType, LoadMode>(m_output + index);
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE EvaluatorPointerType data() const
+ {
+ return m_output;
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE CoeffReturnType coeff(Index index) const
+ {
+ return m_output[index];
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorOpCost costPerCoeff(bool) const {
+ return TensorOpCost(sizeof(CoeffReturnType), 0, 0);
+ }
+
+ EIGEN_STRONG_INLINE void cleanup() {
+ if (m_output) {
+ m_device.deallocate_temp(m_output);
+ m_output = NULL;
+ }
+ m_impl.cleanup();
+ }
+
+#ifdef EIGEN_USE_SYCL
+ // binding placeholder accessors to a command group handler for SYCL
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void bind(cl::sycl::handler &cgh) const {
+ m_impl.bind(cgh);
+ m_output.bind(cgh);
+ }
+#endif
+protected:
+ TensorEvaluator<ArgType, Device> m_impl;
+ const Device EIGEN_DEVICE_REF m_device;
+ const bool m_exclusive;
+ Op m_accumulator;
+ const Index m_size;
+ Index m_stride;
+ Index m_consume_dim;
+ EvaluatorPointerType m_output;
+};
+
+} // end namespace Eigen
+
+#endif // EIGEN_CXX11_TENSOR_TENSOR_SCAN_H
diff --git a/unsupported/Eigen/CXX11/src/Tensor/TensorScanSycl.h b/unsupported/Eigen/CXX11/src/Tensor/TensorScanSycl.h
new file mode 100644
index 0000000..636fb7d
--- /dev/null
+++ b/unsupported/Eigen/CXX11/src/Tensor/TensorScanSycl.h
@@ -0,0 +1,515 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Mehdi Goli Codeplay Software Ltd.
+// Ralph Potter Codeplay Software Ltd.
+// Luke Iwanski Codeplay Software Ltd.
+// Contact: <eigen@codeplay.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+/*****************************************************************
+ * TensorScanSycl.h
+ *
+ * \brief:
+ * Tensor Scan Sycl implement the extend version of
+ * "Efficient parallel scan algorithms for GPUs." .for Tensor operations.
+ * The algorithm requires up to 3 stage (consequently 3 kernels) depending on
+ * the size of the tensor. In the first kernel (ScanKernelFunctor), each
+ * threads within the work-group individually reduces the allocated elements per
+ * thread in order to reduces the total number of blocks. In the next step all
+ * thread within the work-group will reduce the associated blocks into the
+ * temporary buffers. In the next kernel(ScanBlockKernelFunctor), the temporary
+ * buffer is given as an input and all the threads within a work-group scan and
+ * reduces the boundaries between the blocks (generated from the previous
+ * kernel). and write the data on the temporary buffer. If the second kernel is
+ * required, the third and final kernel (ScanAdjustmentKernelFunctor) will
+ * adjust the final result into the output buffer.
+ * The original algorithm for the parallel prefix sum can be found here:
+ *
+ * Sengupta, Shubhabrata, Mark Harris, and Michael Garland. "Efficient parallel
+ * scan algorithms for GPUs." NVIDIA, Santa Clara, CA, Tech. Rep. NVR-2008-003
+ *1, no. 1 (2008): 1-17.
+ *****************************************************************/
+
+#ifndef UNSUPPORTED_EIGEN_CXX11_SRC_TENSOR_TENSOR_SYCL_SYCL_HPP
+#define UNSUPPORTED_EIGEN_CXX11_SRC_TENSOR_TENSOR_SYCL_SYCL_HPP
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+namespace TensorSycl {
+namespace internal {
+
+#ifndef EIGEN_SYCL_MAX_GLOBAL_RANGE
+#define EIGEN_SYCL_MAX_GLOBAL_RANGE (EIGEN_SYCL_LOCAL_THREAD_DIM0 * EIGEN_SYCL_LOCAL_THREAD_DIM1 * 4)
+#endif
+
+template <typename index_t>
+struct ScanParameters {
+ // must be power of 2
+ static EIGEN_CONSTEXPR index_t ScanPerThread = 8;
+ const index_t total_size;
+ const index_t non_scan_size;
+ const index_t scan_size;
+ const index_t non_scan_stride;
+ const index_t scan_stride;
+ const index_t panel_threads;
+ const index_t group_threads;
+ const index_t block_threads;
+ const index_t elements_per_group;
+ const index_t elements_per_block;
+ const index_t loop_range;
+
+ ScanParameters(index_t total_size_, index_t non_scan_size_, index_t scan_size_, index_t non_scan_stride_,
+ index_t scan_stride_, index_t panel_threads_, index_t group_threads_, index_t block_threads_,
+ index_t elements_per_group_, index_t elements_per_block_, index_t loop_range_)
+ : total_size(total_size_),
+ non_scan_size(non_scan_size_),
+ scan_size(scan_size_),
+ non_scan_stride(non_scan_stride_),
+ scan_stride(scan_stride_),
+ panel_threads(panel_threads_),
+ group_threads(group_threads_),
+ block_threads(block_threads_),
+ elements_per_group(elements_per_group_),
+ elements_per_block(elements_per_block_),
+ loop_range(loop_range_) {}
+};
+
+enum class scan_step { first, second };
+template <typename Evaluator, typename CoeffReturnType, typename OutAccessor, typename Op, typename Index,
+ scan_step stp>
+struct ScanKernelFunctor {
+ typedef cl::sycl::accessor<CoeffReturnType, 1, cl::sycl::access::mode::read_write, cl::sycl::access::target::local>
+ LocalAccessor;
+ static EIGEN_CONSTEXPR int PacketSize = ScanParameters<Index>::ScanPerThread / 2;
+
+ LocalAccessor scratch;
+ Evaluator dev_eval;
+ OutAccessor out_accessor;
+ OutAccessor temp_accessor;
+ const ScanParameters<Index> scanParameters;
+ Op accumulator;
+ const bool inclusive;
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE ScanKernelFunctor(LocalAccessor scratch_, const Evaluator dev_eval_,
+ OutAccessor out_accessor_, OutAccessor temp_accessor_,
+ const ScanParameters<Index> scanParameters_, Op accumulator_,
+ const bool inclusive_)
+ : scratch(scratch_),
+ dev_eval(dev_eval_),
+ out_accessor(out_accessor_),
+ temp_accessor(temp_accessor_),
+ scanParameters(scanParameters_),
+ accumulator(accumulator_),
+ inclusive(inclusive_) {}
+
+ template <scan_step sst = stp, typename Input>
+ std::enable_if_t<sst == scan_step::first, CoeffReturnType> EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE
+ read(const Input &inpt, Index global_id) {
+ return inpt.coeff(global_id);
+ }
+
+ template <scan_step sst = stp, typename Input>
+ std::enable_if_t<sst != scan_step::first, CoeffReturnType> EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE
+ read(const Input &inpt, Index global_id) {
+ return inpt[global_id];
+ }
+
+ template <scan_step sst = stp, typename InclusiveOp>
+ std::enable_if_t<sst == scan_step::first> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ first_step_inclusive_Operation(InclusiveOp inclusive_op) {
+ inclusive_op();
+ }
+
+ template <scan_step sst = stp, typename InclusiveOp>
+ std::enable_if_t<sst != scan_step::first> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ first_step_inclusive_Operation(InclusiveOp) {}
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void operator()(cl::sycl::nd_item<1> itemID) {
+ auto out_ptr = out_accessor.get_pointer();
+ auto tmp_ptr = temp_accessor.get_pointer();
+ auto scratch_ptr = scratch.get_pointer().get();
+
+ for (Index loop_offset = 0; loop_offset < scanParameters.loop_range; loop_offset++) {
+ Index data_offset = (itemID.get_global_id(0) + (itemID.get_global_range(0) * loop_offset));
+ Index tmp = data_offset % scanParameters.panel_threads;
+ const Index panel_id = data_offset / scanParameters.panel_threads;
+ const Index group_id = tmp / scanParameters.group_threads;
+ tmp = tmp % scanParameters.group_threads;
+ const Index block_id = tmp / scanParameters.block_threads;
+ const Index local_id = tmp % scanParameters.block_threads;
+ // we put one element per packet in scratch_mem
+ const Index scratch_stride = scanParameters.elements_per_block / PacketSize;
+ const Index scratch_offset = (itemID.get_local_id(0) / scanParameters.block_threads) * scratch_stride;
+ CoeffReturnType private_scan[ScanParameters<Index>::ScanPerThread];
+ CoeffReturnType inclusive_scan;
+ // the actual panel size is scan_size * non_scan_size.
+ // elements_per_panel is roundup to power of 2 for binary tree
+ const Index panel_offset = panel_id * scanParameters.scan_size * scanParameters.non_scan_size;
+ const Index group_offset = group_id * scanParameters.non_scan_stride;
+ // This will be effective when the size is bigger than elements_per_block
+ const Index block_offset = block_id * scanParameters.elements_per_block * scanParameters.scan_stride;
+ const Index thread_offset = (ScanParameters<Index>::ScanPerThread * local_id * scanParameters.scan_stride);
+ const Index global_offset = panel_offset + group_offset + block_offset + thread_offset;
+ Index next_elements = 0;
+ EIGEN_UNROLL_LOOP
+ for (int i = 0; i < ScanParameters<Index>::ScanPerThread; i++) {
+ Index global_id = global_offset + next_elements;
+ private_scan[i] = ((((block_id * scanParameters.elements_per_block) +
+ (ScanParameters<Index>::ScanPerThread * local_id) + i) < scanParameters.scan_size) &&
+ (global_id < scanParameters.total_size))
+ ? read(dev_eval, global_id)
+ : accumulator.initialize();
+ next_elements += scanParameters.scan_stride;
+ }
+ first_step_inclusive_Operation([&]() EIGEN_DEVICE_FUNC {
+ if (inclusive) {
+ inclusive_scan = private_scan[ScanParameters<Index>::ScanPerThread - 1];
+ }
+ });
+ // This for loop must be 2
+ EIGEN_UNROLL_LOOP
+ for (int packetIndex = 0; packetIndex < ScanParameters<Index>::ScanPerThread; packetIndex += PacketSize) {
+ Index private_offset = 1;
+ // build sum in place up the tree
+ EIGEN_UNROLL_LOOP
+ for (Index d = PacketSize >> 1; d > 0; d >>= 1) {
+ EIGEN_UNROLL_LOOP
+ for (Index l = 0; l < d; l++) {
+ Index ai = private_offset * (2 * l + 1) - 1 + packetIndex;
+ Index bi = private_offset * (2 * l + 2) - 1 + packetIndex;
+ CoeffReturnType accum = accumulator.initialize();
+ accumulator.reduce(private_scan[ai], &accum);
+ accumulator.reduce(private_scan[bi], &accum);
+ private_scan[bi] = accumulator.finalize(accum);
+ }
+ private_offset *= 2;
+ }
+ scratch_ptr[2 * local_id + (packetIndex / PacketSize) + scratch_offset] =
+ private_scan[PacketSize - 1 + packetIndex];
+ private_scan[PacketSize - 1 + packetIndex] = accumulator.initialize();
+ // traverse down tree & build scan
+ EIGEN_UNROLL_LOOP
+ for (Index d = 1; d < PacketSize; d *= 2) {
+ private_offset >>= 1;
+ EIGEN_UNROLL_LOOP
+ for (Index l = 0; l < d; l++) {
+ Index ai = private_offset * (2 * l + 1) - 1 + packetIndex;
+ Index bi = private_offset * (2 * l + 2) - 1 + packetIndex;
+ CoeffReturnType accum = accumulator.initialize();
+ accumulator.reduce(private_scan[ai], &accum);
+ accumulator.reduce(private_scan[bi], &accum);
+ private_scan[ai] = private_scan[bi];
+ private_scan[bi] = accumulator.finalize(accum);
+ }
+ }
+ }
+
+ Index offset = 1;
+ // build sum in place up the tree
+ for (Index d = scratch_stride >> 1; d > 0; d >>= 1) {
+ // Synchronise
+ itemID.barrier(cl::sycl::access::fence_space::local_space);
+ if (local_id < d) {
+ Index ai = offset * (2 * local_id + 1) - 1 + scratch_offset;
+ Index bi = offset * (2 * local_id + 2) - 1 + scratch_offset;
+ CoeffReturnType accum = accumulator.initialize();
+ accumulator.reduce(scratch_ptr[ai], &accum);
+ accumulator.reduce(scratch_ptr[bi], &accum);
+ scratch_ptr[bi] = accumulator.finalize(accum);
+ }
+ offset *= 2;
+ }
+ // Synchronise
+ itemID.barrier(cl::sycl::access::fence_space::local_space);
+ // next step optimisation
+ if (local_id == 0) {
+ if (((scanParameters.elements_per_group / scanParameters.elements_per_block) > 1)) {
+ const Index temp_id = panel_id * (scanParameters.elements_per_group / scanParameters.elements_per_block) *
+ scanParameters.non_scan_size +
+ group_id * (scanParameters.elements_per_group / scanParameters.elements_per_block) +
+ block_id;
+ tmp_ptr[temp_id] = scratch_ptr[scratch_stride - 1 + scratch_offset];
+ }
+ // clear the last element
+ scratch_ptr[scratch_stride - 1 + scratch_offset] = accumulator.initialize();
+ }
+ // traverse down tree & build scan
+ for (Index d = 1; d < scratch_stride; d *= 2) {
+ offset >>= 1;
+ // Synchronise
+ itemID.barrier(cl::sycl::access::fence_space::local_space);
+ if (local_id < d) {
+ Index ai = offset * (2 * local_id + 1) - 1 + scratch_offset;
+ Index bi = offset * (2 * local_id + 2) - 1 + scratch_offset;
+ CoeffReturnType accum = accumulator.initialize();
+ accumulator.reduce(scratch_ptr[ai], &accum);
+ accumulator.reduce(scratch_ptr[bi], &accum);
+ scratch_ptr[ai] = scratch_ptr[bi];
+ scratch_ptr[bi] = accumulator.finalize(accum);
+ }
+ }
+ // Synchronise
+ itemID.barrier(cl::sycl::access::fence_space::local_space);
+ // This for loop must be 2
+ EIGEN_UNROLL_LOOP
+ for (int packetIndex = 0; packetIndex < ScanParameters<Index>::ScanPerThread; packetIndex += PacketSize) {
+ EIGEN_UNROLL_LOOP
+ for (Index i = 0; i < PacketSize; i++) {
+ CoeffReturnType accum = private_scan[packetIndex + i];
+ accumulator.reduce(scratch_ptr[2 * local_id + (packetIndex / PacketSize) + scratch_offset], &accum);
+ private_scan[packetIndex + i] = accumulator.finalize(accum);
+ }
+ }
+ first_step_inclusive_Operation([&]() EIGEN_DEVICE_FUNC {
+ if (inclusive) {
+ accumulator.reduce(private_scan[ScanParameters<Index>::ScanPerThread - 1], &inclusive_scan);
+ private_scan[0] = accumulator.finalize(inclusive_scan);
+ }
+ });
+ next_elements = 0;
+ // right the first set of private param
+ EIGEN_UNROLL_LOOP
+ for (Index i = 0; i < ScanParameters<Index>::ScanPerThread; i++) {
+ Index global_id = global_offset + next_elements;
+ if ((((block_id * scanParameters.elements_per_block) + (ScanParameters<Index>::ScanPerThread * local_id) + i) <
+ scanParameters.scan_size) &&
+ (global_id < scanParameters.total_size)) {
+ Index private_id = (i * !inclusive) + (((i + 1) % ScanParameters<Index>::ScanPerThread) * (inclusive));
+ out_ptr[global_id] = private_scan[private_id];
+ }
+ next_elements += scanParameters.scan_stride;
+ }
+ } // end for loop
+ }
+};
+
+template <typename CoeffReturnType, typename InAccessor, typename OutAccessor, typename Op, typename Index>
+struct ScanAdjustmentKernelFunctor {
+ typedef cl::sycl::accessor<CoeffReturnType, 1, cl::sycl::access::mode::read_write, cl::sycl::access::target::local>
+ LocalAccessor;
+ static EIGEN_CONSTEXPR int PacketSize = ScanParameters<Index>::ScanPerThread / 2;
+ InAccessor in_accessor;
+ OutAccessor out_accessor;
+ const ScanParameters<Index> scanParameters;
+ Op accumulator;
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE ScanAdjustmentKernelFunctor(LocalAccessor, InAccessor in_accessor_,
+ OutAccessor out_accessor_,
+ const ScanParameters<Index> scanParameters_,
+ Op accumulator_)
+ : in_accessor(in_accessor_),
+ out_accessor(out_accessor_),
+ scanParameters(scanParameters_),
+ accumulator(accumulator_) {}
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void operator()(cl::sycl::nd_item<1> itemID) {
+ auto in_ptr = in_accessor.get_pointer();
+ auto out_ptr = out_accessor.get_pointer();
+
+ for (Index loop_offset = 0; loop_offset < scanParameters.loop_range; loop_offset++) {
+ Index data_offset = (itemID.get_global_id(0) + (itemID.get_global_range(0) * loop_offset));
+ Index tmp = data_offset % scanParameters.panel_threads;
+ const Index panel_id = data_offset / scanParameters.panel_threads;
+ const Index group_id = tmp / scanParameters.group_threads;
+ tmp = tmp % scanParameters.group_threads;
+ const Index block_id = tmp / scanParameters.block_threads;
+ const Index local_id = tmp % scanParameters.block_threads;
+
+ // the actual panel size is scan_size * non_scan_size.
+ // elements_per_panel is roundup to power of 2 for binary tree
+ const Index panel_offset = panel_id * scanParameters.scan_size * scanParameters.non_scan_size;
+ const Index group_offset = group_id * scanParameters.non_scan_stride;
+ // This will be effective when the size is bigger than elements_per_block
+ const Index block_offset = block_id * scanParameters.elements_per_block * scanParameters.scan_stride;
+ const Index thread_offset = ScanParameters<Index>::ScanPerThread * local_id * scanParameters.scan_stride;
+
+ const Index global_offset = panel_offset + group_offset + block_offset + thread_offset;
+ const Index block_size = scanParameters.elements_per_group / scanParameters.elements_per_block;
+ const Index in_id = (panel_id * block_size * scanParameters.non_scan_size) + (group_id * block_size) + block_id;
+ CoeffReturnType adjust_val = in_ptr[in_id];
+
+ Index next_elements = 0;
+ EIGEN_UNROLL_LOOP
+ for (Index i = 0; i < ScanParameters<Index>::ScanPerThread; i++) {
+ Index global_id = global_offset + next_elements;
+ if ((((block_id * scanParameters.elements_per_block) + (ScanParameters<Index>::ScanPerThread * local_id) + i) <
+ scanParameters.scan_size) &&
+ (global_id < scanParameters.total_size)) {
+ CoeffReturnType accum = adjust_val;
+ accumulator.reduce(out_ptr[global_id], &accum);
+ out_ptr[global_id] = accumulator.finalize(accum);
+ }
+ next_elements += scanParameters.scan_stride;
+ }
+ }
+ }
+};
+
+template <typename Index>
+struct ScanInfo {
+ const Index &total_size;
+ const Index &scan_size;
+ const Index &panel_size;
+ const Index &non_scan_size;
+ const Index &scan_stride;
+ const Index &non_scan_stride;
+
+ Index max_elements_per_block;
+ Index block_size;
+ Index panel_threads;
+ Index group_threads;
+ Index block_threads;
+ Index elements_per_group;
+ Index elements_per_block;
+ Index loop_range;
+ Index global_range;
+ Index local_range;
+ const Eigen::SyclDevice &dev;
+ EIGEN_STRONG_INLINE ScanInfo(const Index &total_size_, const Index &scan_size_, const Index &panel_size_,
+ const Index &non_scan_size_, const Index &scan_stride_, const Index &non_scan_stride_,
+ const Eigen::SyclDevice &dev_)
+ : total_size(total_size_),
+ scan_size(scan_size_),
+ panel_size(panel_size_),
+ non_scan_size(non_scan_size_),
+ scan_stride(scan_stride_),
+ non_scan_stride(non_scan_stride_),
+ dev(dev_) {
+ // must be power of 2
+ local_range = std::min(Index(dev.getNearestPowerOfTwoWorkGroupSize()),
+ Index(EIGEN_SYCL_LOCAL_THREAD_DIM0 * EIGEN_SYCL_LOCAL_THREAD_DIM1));
+
+ max_elements_per_block = local_range * ScanParameters<Index>::ScanPerThread;
+
+ elements_per_group =
+ dev.getPowerOfTwo(Index(roundUp(Index(scan_size), ScanParameters<Index>::ScanPerThread)), true);
+ const Index elements_per_panel = elements_per_group * non_scan_size;
+ elements_per_block = std::min(Index(elements_per_group), Index(max_elements_per_block));
+ panel_threads = elements_per_panel / ScanParameters<Index>::ScanPerThread;
+ group_threads = elements_per_group / ScanParameters<Index>::ScanPerThread;
+ block_threads = elements_per_block / ScanParameters<Index>::ScanPerThread;
+ block_size = elements_per_group / elements_per_block;
+#ifdef EIGEN_SYCL_MAX_GLOBAL_RANGE
+ const Index max_threads = std::min(Index(panel_threads * panel_size), Index(EIGEN_SYCL_MAX_GLOBAL_RANGE));
+#else
+ const Index max_threads = panel_threads * panel_size;
+#endif
+ global_range = roundUp(max_threads, local_range);
+ loop_range = Index(
+ std::ceil(double(elements_per_panel * panel_size) / (global_range * ScanParameters<Index>::ScanPerThread)));
+ }
+ inline ScanParameters<Index> get_scan_parameter() {
+ return ScanParameters<Index>(total_size, non_scan_size, scan_size, non_scan_stride, scan_stride, panel_threads,
+ group_threads, block_threads, elements_per_group, elements_per_block, loop_range);
+ }
+ inline cl::sycl::nd_range<1> get_thread_range() {
+ return cl::sycl::nd_range<1>(cl::sycl::range<1>(global_range), cl::sycl::range<1>(local_range));
+ }
+};
+
+template <typename EvaluatorPointerType, typename CoeffReturnType, typename Reducer, typename Index>
+struct SYCLAdjustBlockOffset {
+ EIGEN_STRONG_INLINE static void adjust_scan_block_offset(EvaluatorPointerType in_ptr, EvaluatorPointerType out_ptr,
+ Reducer &accumulator, const Index total_size,
+ const Index scan_size, const Index panel_size,
+ const Index non_scan_size, const Index scan_stride,
+ const Index non_scan_stride, const Eigen::SyclDevice &dev) {
+ auto scan_info =
+ ScanInfo<Index>(total_size, scan_size, panel_size, non_scan_size, scan_stride, non_scan_stride, dev);
+
+ typedef ScanAdjustmentKernelFunctor<CoeffReturnType, EvaluatorPointerType, EvaluatorPointerType, Reducer, Index>
+ AdjustFuctor;
+ dev.template unary_kernel_launcher<CoeffReturnType, AdjustFuctor>(in_ptr, out_ptr, scan_info.get_thread_range(),
+ scan_info.max_elements_per_block,
+ scan_info.get_scan_parameter(), accumulator);
+ }
+};
+
+template <typename CoeffReturnType, scan_step stp>
+struct ScanLauncher_impl {
+ template <typename Input, typename EvaluatorPointerType, typename Reducer, typename Index>
+ EIGEN_STRONG_INLINE static void scan_block(Input in_ptr, EvaluatorPointerType out_ptr, Reducer &accumulator,
+ const Index total_size, const Index scan_size, const Index panel_size,
+ const Index non_scan_size, const Index scan_stride,
+ const Index non_scan_stride, const bool inclusive,
+ const Eigen::SyclDevice &dev) {
+ auto scan_info =
+ ScanInfo<Index>(total_size, scan_size, panel_size, non_scan_size, scan_stride, non_scan_stride, dev);
+ const Index temp_pointer_size = scan_info.block_size * non_scan_size * panel_size;
+ const Index scratch_size = scan_info.max_elements_per_block / (ScanParameters<Index>::ScanPerThread / 2);
+ CoeffReturnType *temp_pointer =
+ static_cast<CoeffReturnType *>(dev.allocate_temp(temp_pointer_size * sizeof(CoeffReturnType)));
+ EvaluatorPointerType tmp_global_accessor = dev.get(temp_pointer);
+
+ typedef ScanKernelFunctor<Input, CoeffReturnType, EvaluatorPointerType, Reducer, Index, stp> ScanFunctor;
+ dev.template binary_kernel_launcher<CoeffReturnType, ScanFunctor>(
+ in_ptr, out_ptr, tmp_global_accessor, scan_info.get_thread_range(), scratch_size,
+ scan_info.get_scan_parameter(), accumulator, inclusive);
+
+ if (scan_info.block_size > 1) {
+ ScanLauncher_impl<CoeffReturnType, scan_step::second>::scan_block(
+ tmp_global_accessor, tmp_global_accessor, accumulator, temp_pointer_size, scan_info.block_size, panel_size,
+ non_scan_size, Index(1), scan_info.block_size, false, dev);
+
+ SYCLAdjustBlockOffset<EvaluatorPointerType, CoeffReturnType, Reducer, Index>::adjust_scan_block_offset(
+ tmp_global_accessor, out_ptr, accumulator, total_size, scan_size, panel_size, non_scan_size, scan_stride,
+ non_scan_stride, dev);
+ }
+ dev.deallocate_temp(temp_pointer);
+ }
+};
+
+} // namespace internal
+} // namespace TensorSycl
+namespace internal {
+template <typename Self, typename Reducer, bool vectorize>
+struct ScanLauncher<Self, Reducer, Eigen::SyclDevice, vectorize> {
+ typedef typename Self::Index Index;
+ typedef typename Self::CoeffReturnType CoeffReturnType;
+ typedef typename Self::Storage Storage;
+ typedef typename Self::EvaluatorPointerType EvaluatorPointerType;
+ void operator()(Self &self, EvaluatorPointerType data) {
+ const Index total_size = internal::array_prod(self.dimensions());
+ const Index scan_size = self.size();
+ const Index scan_stride = self.stride();
+ // this is the scan op (can be sum or ...)
+ auto accumulator = self.accumulator();
+ auto inclusive = !self.exclusive();
+ auto consume_dim = self.consume_dim();
+ auto dev = self.device();
+
+ auto dims = self.inner().dimensions();
+
+ Index non_scan_size = 1;
+ Index panel_size = 1;
+ if (static_cast<int>(Self::Layout) == static_cast<int>(ColMajor)) {
+ for (int i = 0; i < consume_dim; i++) {
+ non_scan_size *= dims[i];
+ }
+ for (int i = consume_dim + 1; i < Self::NumDims; i++) {
+ panel_size *= dims[i];
+ }
+ } else {
+ for (int i = Self::NumDims - 1; i > consume_dim; i--) {
+ non_scan_size *= dims[i];
+ }
+ for (int i = consume_dim - 1; i >= 0; i--) {
+ panel_size *= dims[i];
+ }
+ }
+ const Index non_scan_stride = (scan_stride > 1) ? 1 : scan_size;
+ auto eval_impl = self.inner();
+ TensorSycl::internal::ScanLauncher_impl<CoeffReturnType, TensorSycl::internal::scan_step::first>::scan_block(
+ eval_impl, data, accumulator, total_size, scan_size, panel_size, non_scan_size, scan_stride, non_scan_stride,
+ inclusive, dev);
+ }
+};
+} // namespace internal
+} // namespace Eigen
+
+#endif // UNSUPPORTED_EIGEN_CXX11_SRC_TENSOR_TENSOR_SYCL_SYCL_HPP
diff --git a/unsupported/Eigen/CXX11/src/Tensor/TensorShuffling.h b/unsupported/Eigen/CXX11/src/Tensor/TensorShuffling.h
new file mode 100644
index 0000000..977263a
--- /dev/null
+++ b/unsupported/Eigen/CXX11/src/Tensor/TensorShuffling.h
@@ -0,0 +1,470 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_CXX11_TENSOR_TENSOR_SHUFFLING_H
+#define EIGEN_CXX11_TENSOR_TENSOR_SHUFFLING_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+/** \class TensorShuffling
+ * \ingroup CXX11_Tensor_Module
+ *
+ * \brief Tensor shuffling class.
+ *
+ *
+ */
+namespace internal {
+template<typename Shuffle, typename XprType>
+struct traits<TensorShufflingOp<Shuffle, XprType> > : public traits<XprType>
+{
+ typedef typename XprType::Scalar Scalar;
+ typedef traits<XprType> XprTraits;
+ typedef typename XprTraits::StorageKind StorageKind;
+ typedef typename XprTraits::Index Index;
+ typedef typename XprType::Nested Nested;
+ typedef std::remove_reference_t<Nested> Nested_;
+ static constexpr int NumDimensions = XprTraits::NumDimensions;
+ static constexpr int Layout = XprTraits::Layout;
+ typedef typename XprTraits::PointerType PointerType;
+};
+
+template<typename Shuffle, typename XprType>
+struct eval<TensorShufflingOp<Shuffle, XprType>, Eigen::Dense>
+{
+ typedef const TensorShufflingOp<Shuffle, XprType>& type;
+};
+
+template<typename Shuffle, typename XprType>
+struct nested<TensorShufflingOp<Shuffle, XprType>, 1, typename eval<TensorShufflingOp<Shuffle, XprType> >::type>
+{
+ typedef TensorShufflingOp<Shuffle, XprType> type;
+};
+
+} // end namespace internal
+
+
+
+template<typename Shuffle, typename XprType>
+class TensorShufflingOp : public TensorBase<TensorShufflingOp<Shuffle, XprType> >
+{
+ public:
+ typedef TensorBase<TensorShufflingOp<Shuffle, XprType> > Base;
+ typedef typename Eigen::internal::traits<TensorShufflingOp>::Scalar Scalar;
+ typedef typename Eigen::NumTraits<Scalar>::Real RealScalar;
+ typedef typename XprType::CoeffReturnType CoeffReturnType;
+ typedef typename Eigen::internal::nested<TensorShufflingOp>::type Nested;
+ typedef typename Eigen::internal::traits<TensorShufflingOp>::StorageKind StorageKind;
+ typedef typename Eigen::internal::traits<TensorShufflingOp>::Index Index;
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorShufflingOp(const XprType& expr, const Shuffle& shfl)
+ : m_xpr(expr), m_shuffle(shfl) {}
+
+ EIGEN_DEVICE_FUNC
+ const Shuffle& shufflePermutation() const { return m_shuffle; }
+
+ EIGEN_DEVICE_FUNC
+ const internal::remove_all_t<typename XprType::Nested>&
+ expression() const { return m_xpr; }
+
+ EIGEN_TENSOR_INHERIT_ASSIGNMENT_OPERATORS(TensorShufflingOp)
+
+
+ protected:
+ typename XprType::Nested m_xpr;
+ const Shuffle m_shuffle;
+};
+
+
+// Eval as rvalue
+template<typename Shuffle, typename ArgType, typename Device>
+struct TensorEvaluator<const TensorShufflingOp<Shuffle, ArgType>, Device>
+{
+ typedef TensorEvaluator<const TensorShufflingOp<Shuffle, ArgType>, Device> Self;
+ typedef TensorShufflingOp<Shuffle, ArgType> XprType;
+ typedef typename XprType::Index Index;
+ static constexpr int NumDims = internal::array_size<typename TensorEvaluator<ArgType, Device>::Dimensions>::value;
+ typedef DSizes<Index, NumDims> Dimensions;
+ typedef typename XprType::Scalar Scalar;
+ typedef typename XprType::CoeffReturnType CoeffReturnType;
+ typedef typename PacketType<CoeffReturnType, Device>::type PacketReturnType;
+ static constexpr int PacketSize = PacketType<CoeffReturnType, Device>::size;
+ typedef StorageMemory<CoeffReturnType, Device> Storage;
+ typedef typename Storage::Type EvaluatorPointerType;
+
+ static constexpr int Layout = TensorEvaluator<ArgType, Device>::Layout;
+ enum {
+ IsAligned = false,
+ PacketAccess = (PacketType<CoeffReturnType, Device>::size > 1),
+ BlockAccess = TensorEvaluator<ArgType, Device>::RawAccess,
+ PreferBlockAccess = true,
+ CoordAccess = false, // to be implemented
+ RawAccess = false
+ };
+
+ typedef std::remove_const_t<Scalar> ScalarNoConst;
+
+ //===- Tensor block evaluation strategy (see TensorBlock.h) -------------===//
+ typedef internal::TensorBlockDescriptor<NumDims, Index> TensorBlockDesc;
+ typedef internal::TensorBlockScratchAllocator<Device> TensorBlockScratch;
+
+ typedef typename internal::TensorMaterializedBlock<ScalarNoConst, NumDims,
+ Layout, Index>
+ TensorBlock;
+ //===--------------------------------------------------------------------===//
+
+ EIGEN_STRONG_INLINE TensorEvaluator(const XprType& op, const Device& device)
+ : m_device(device),
+ m_impl(op.expression(), device)
+ {
+ const typename TensorEvaluator<ArgType, Device>::Dimensions& input_dims = m_impl.dimensions();
+ const Shuffle& shuffle = op.shufflePermutation();
+ m_is_identity = true;
+ for (int i = 0; i < NumDims; ++i) {
+ m_shuffle[i] = static_cast<int>(shuffle[i]);
+ m_dimensions[i] = input_dims[shuffle[i]];
+ m_inverseShuffle[shuffle[i]] = i;
+ if (m_is_identity && shuffle[i] != i) {
+ m_is_identity = false;
+ }
+ }
+
+ if (static_cast<int>(Layout) == static_cast<int>(ColMajor)) {
+ m_unshuffledInputStrides[0] = 1;
+ m_outputStrides[0] = 1;
+
+ for (int i = 1; i < NumDims; ++i) {
+ m_unshuffledInputStrides[i] =
+ m_unshuffledInputStrides[i - 1] * input_dims[i - 1];
+ m_outputStrides[i] = m_outputStrides[i - 1] * m_dimensions[i - 1];
+ m_fastOutputStrides[i] = internal::TensorIntDivisor<Index>(
+ m_outputStrides[i] > 0 ? m_outputStrides[i] : Index(1));
+ }
+ } else {
+ m_unshuffledInputStrides[NumDims - 1] = 1;
+ m_outputStrides[NumDims - 1] = 1;
+ for (int i = NumDims - 2; i >= 0; --i) {
+ m_unshuffledInputStrides[i] =
+ m_unshuffledInputStrides[i + 1] * input_dims[i + 1];
+ m_outputStrides[i] = m_outputStrides[i + 1] * m_dimensions[i + 1];
+ m_fastOutputStrides[i] = internal::TensorIntDivisor<Index>(
+ m_outputStrides[i] > 0 ? m_outputStrides[i] : Index(1));
+ }
+ }
+
+ for (int i = 0; i < NumDims; ++i) {
+ m_inputStrides[i] = m_unshuffledInputStrides[shuffle[i]];
+ }
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Dimensions& dimensions() const { return m_dimensions; }
+
+ EIGEN_STRONG_INLINE bool evalSubExprsIfNeeded(EvaluatorPointerType /*data*/) {
+ m_impl.evalSubExprsIfNeeded(NULL);
+ return true;
+ }
+
+#ifdef EIGEN_USE_THREADS
+ template <typename EvalSubExprsCallback>
+ EIGEN_STRONG_INLINE void evalSubExprsIfNeededAsync(
+ EvaluatorPointerType, EvalSubExprsCallback done) {
+ m_impl.evalSubExprsIfNeededAsync(nullptr, [done](bool) { done(true); });
+ }
+#endif // EIGEN_USE_THREADS
+
+ EIGEN_STRONG_INLINE void cleanup() {
+ m_impl.cleanup();
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE CoeffReturnType coeff(Index index) const
+ {
+ if (m_is_identity) {
+ return m_impl.coeff(index);
+ } else {
+ return m_impl.coeff(srcCoeff(index));
+ }
+ }
+
+ template <int LoadMode, typename Self, bool ImplPacketAccess>
+ struct PacketLoader {
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ static PacketReturnType Run(const Self& self, Index index) {
+ EIGEN_ALIGN_MAX std::remove_const_t<CoeffReturnType> values[PacketSize];
+ EIGEN_UNROLL_LOOP
+ for (int i = 0; i < PacketSize; ++i) {
+ values[i] = self.coeff(index + i);
+ }
+ PacketReturnType rslt = internal::pload<PacketReturnType>(values);
+ return rslt;
+ }
+ };
+
+ template<int LoadMode, typename Self>
+ struct PacketLoader<LoadMode, Self, true> {
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ static PacketReturnType Run(const Self& self, Index index) {
+ if (self.m_is_identity) {
+ return self.m_impl.template packet<LoadMode>(index);
+ } else {
+ EIGEN_ALIGN_MAX std::remove_const_t<CoeffReturnType> values[PacketSize];
+ EIGEN_UNROLL_LOOP
+ for (int i = 0; i < PacketSize; ++i) {
+ values[i] = self.coeff(index + i);
+ }
+ PacketReturnType rslt = internal::pload<PacketReturnType>(values);
+ return rslt;
+ }
+ }
+ };
+
+ template<int LoadMode>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE PacketReturnType packet(Index index) const
+ {
+ eigen_assert(index + PacketSize - 1 < dimensions().TotalSize());
+ return PacketLoader<LoadMode, Self, TensorEvaluator<ArgType, Device>::PacketAccess>::Run(*this, index);
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ internal::TensorBlockResourceRequirements getResourceRequirements() const {
+ static const int inner_dim =
+ Layout == static_cast<int>(ColMajor) ? 0 : NumDims - 1;
+
+ const size_t target_size = m_device.firstLevelCacheSize();
+ const bool inner_dim_shuffled = m_shuffle[inner_dim] != inner_dim;
+
+ // Shuffled inner dimensions leads to a random memory access, which is not
+ // captured by default cost model bytes loaded/stored. We add this cost
+ // explicitly. The number of cycles picked based on the benchmarks.
+ // TODO(ezhulenev): This number was picked based on a very questionable
+ // benchmarks, add benchmarks that are representative of real workloads.
+ using BlockRequirements = internal::TensorBlockResourceRequirements;
+ if (inner_dim_shuffled) {
+ return BlockRequirements::uniform<Scalar>(target_size)
+ .addCostPerCoeff({0, 0, NumDims * 28});
+ } else {
+ return BlockRequirements::skewed<Scalar>(target_size);
+ }
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorBlock
+ block(TensorBlockDesc& desc, TensorBlockScratch& scratch,
+ bool root_of_expr_ast = false) const {
+ eigen_assert(m_impl.data() != NULL);
+
+ typedef internal::TensorBlockIO<ScalarNoConst, Index, NumDims, Layout>
+ TensorBlockIO;
+ typedef typename TensorBlockIO::Dst TensorBlockIODst;
+ typedef typename TensorBlockIO::Src TensorBlockIOSrc;
+
+ const typename TensorBlock::Storage block_storage =
+ TensorBlock::prepareStorage(
+ desc, scratch, /*allow_strided_storage=*/root_of_expr_ast);
+
+ typename TensorBlockIO::Dimensions input_strides(m_unshuffledInputStrides);
+ TensorBlockIOSrc src(input_strides, m_impl.data(), srcCoeff(desc.offset()));
+
+ TensorBlockIODst dst(block_storage.dimensions(), block_storage.strides(),
+ block_storage.data());
+
+ typename TensorBlockIO::DimensionsMap dst_to_src_dim_map(m_shuffle);
+ TensorBlockIO::Copy(dst, src, dst_to_src_dim_map);
+
+ return block_storage.AsTensorMaterializedBlock();
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorOpCost costPerCoeff(bool vectorized) const {
+ const double compute_cost = m_is_identity ? TensorOpCost::AddCost<Index>() :
+ NumDims * (2 * TensorOpCost::AddCost<Index>() +
+ 2 * TensorOpCost::MulCost<Index>() +
+ TensorOpCost::DivCost<Index>());
+ return m_impl.costPerCoeff(vectorized) +
+ TensorOpCost(0, 0, compute_cost, m_is_identity /* vectorized */, PacketSize);
+ }
+
+ EIGEN_DEVICE_FUNC typename Storage::Type data() const { return NULL; }
+
+#ifdef EIGEN_USE_SYCL
+ // binding placeholder accessors to a command group handler for SYCL
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void bind(cl::sycl::handler &cgh) const {
+ m_impl.bind(cgh);
+ }
+#endif
+ protected:
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Index GetBlockOutputIndex(
+ Index input_index,
+ const DSizes<Index, NumDims>& input_block_strides,
+ const DSizes<Index, NumDims>& output_block_strides,
+ const DSizes<internal::TensorIntDivisor<Index>, NumDims>& fast_input_block_strides) const {
+ Index output_index = 0;
+ if (static_cast<int>(Layout) == static_cast<int>(ColMajor)) {
+ for (int i = NumDims - 1; i > 0; --i) {
+ const Index idx = input_index / fast_input_block_strides[i];
+ output_index += idx * output_block_strides[m_inverseShuffle[i]];
+ input_index -= idx * input_block_strides[i];
+ }
+ return output_index + input_index *
+ output_block_strides[m_inverseShuffle[0]];
+ } else {
+ for (int i = 0; i < NumDims - 1; ++i) {
+ const Index idx = input_index / fast_input_block_strides[i];
+ output_index += idx * output_block_strides[m_inverseShuffle[i]];
+ input_index -= idx * input_block_strides[i];
+ }
+ return output_index + input_index *
+ output_block_strides[m_inverseShuffle[NumDims - 1]];
+ }
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Index srcCoeff(Index index) const {
+ Index inputIndex = 0;
+ if (static_cast<int>(Layout) == static_cast<int>(ColMajor)) {
+ for (int i = NumDims - 1; i > 0; --i) {
+ const Index idx = index / m_fastOutputStrides[i];
+ inputIndex += idx * m_inputStrides[i];
+ index -= idx * m_outputStrides[i];
+ }
+ return inputIndex + index * m_inputStrides[0];
+ } else {
+ for (int i = 0; i < NumDims - 1; ++i) {
+ const Index idx = index / m_fastOutputStrides[i];
+ inputIndex += idx * m_inputStrides[i];
+ index -= idx * m_outputStrides[i];
+ }
+ return inputIndex + index * m_inputStrides[NumDims - 1];
+ }
+ }
+
+ Dimensions m_dimensions;
+ bool m_is_identity;
+ array<int, NumDims> m_shuffle;
+ array<Index, NumDims> m_inverseShuffle; // TODO(ezhulenev): Make it int type.
+ array<Index, NumDims> m_outputStrides;
+ array<internal::TensorIntDivisor<Index>, NumDims> m_fastOutputStrides;
+ array<Index, NumDims> m_inputStrides;
+ array<Index, NumDims> m_unshuffledInputStrides;
+
+ const Device EIGEN_DEVICE_REF m_device;
+ TensorEvaluator<ArgType, Device> m_impl;
+};
+
+
+// Eval as lvalue
+template<typename Shuffle, typename ArgType, typename Device>
+struct TensorEvaluator<TensorShufflingOp<Shuffle, ArgType>, Device>
+ : public TensorEvaluator<const TensorShufflingOp<Shuffle, ArgType>, Device>
+{
+ typedef TensorEvaluator<const TensorShufflingOp<Shuffle, ArgType>, Device> Base;
+
+ typedef TensorShufflingOp<Shuffle, ArgType> XprType;
+ typedef typename XprType::Index Index;
+ static constexpr int NumDims = internal::array_size<typename TensorEvaluator<ArgType, Device>::Dimensions>::value;
+ typedef DSizes<Index, NumDims> Dimensions;
+ typedef typename XprType::Scalar Scalar;
+ typedef typename XprType::CoeffReturnType CoeffReturnType;
+ typedef typename PacketType<CoeffReturnType, Device>::type PacketReturnType;
+ static constexpr int PacketSize = PacketType<CoeffReturnType, Device>::size;
+ static constexpr int Layout = TensorEvaluator<ArgType, Device>::Layout;
+
+ enum {
+ IsAligned = false,
+ PacketAccess = (PacketType<CoeffReturnType, Device>::size > 1),
+ BlockAccess = TensorEvaluator<ArgType, Device>::RawAccess,
+ PreferBlockAccess = true,
+ RawAccess = false
+ };
+
+ typedef std::remove_const_t<Scalar> ScalarNoConst;
+
+ //===- Tensor block evaluation strategy (see TensorBlock.h) -------------===//
+ typedef internal::TensorBlockDescriptor<NumDims, Index> TensorBlockDesc;
+ //===--------------------------------------------------------------------===//
+
+ EIGEN_STRONG_INLINE TensorEvaluator(const XprType& op, const Device& device)
+ : Base(op, device)
+ { }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE CoeffReturnType& coeffRef(Index index)
+ {
+ return this->m_impl.coeffRef(this->srcCoeff(index));
+ }
+
+ template <int StoreMode> EIGEN_STRONG_INLINE
+ void writePacket(Index index, const PacketReturnType& x)
+ {
+ EIGEN_ALIGN_MAX std::remove_const_t<CoeffReturnType> values[PacketSize];
+ internal::pstore<CoeffReturnType, PacketReturnType>(values, x);
+ EIGEN_UNROLL_LOOP
+ for (int i = 0; i < PacketSize; ++i) {
+ this->coeffRef(index+i) = values[i];
+ }
+ }
+
+ template <typename TensorBlock>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void writeBlock(
+ const TensorBlockDesc& desc, const TensorBlock& block) {
+ eigen_assert(this->m_impl.data() != NULL);
+
+ typedef internal::TensorBlockIO<ScalarNoConst, Index, NumDims, Layout>
+ TensorBlockIO;
+ typedef typename TensorBlockIO::Dst TensorBlockIODst;
+ typedef typename TensorBlockIO::Src TensorBlockIOSrc;
+
+ const Scalar* block_buffer = block.data();
+
+ // TODO(ezhulenev): TensorBlockIO should be able to read from any Eigen
+ // expression with coefficient and packet access as `src`.
+ void* mem = NULL;
+ if (block_buffer == NULL) {
+ mem = this->m_device.allocate(desc.size() * sizeof(Scalar));
+ ScalarNoConst* buf = static_cast<ScalarNoConst*>(mem);
+
+ typedef internal::TensorBlockAssignment<
+ ScalarNoConst, NumDims, typename TensorBlock::XprType, Index>
+ TensorBlockAssignment;
+
+ TensorBlockAssignment::Run(
+ TensorBlockAssignment::target(
+ desc.dimensions(), internal::strides<Layout>(desc.dimensions()),
+ buf),
+ block.expr());
+
+ block_buffer = buf;
+ }
+
+ // Read from block.
+ TensorBlockIOSrc src(internal::strides<Layout>(desc.dimensions()),
+ block_buffer);
+
+ // Write to the output buffer.
+ typename TensorBlockIO::Dimensions output_strides(
+ this->m_unshuffledInputStrides);
+ typename TensorBlockIO::Dimensions output_dimensions;
+ for (int i = 0; i < NumDims; ++i) {
+ output_dimensions[this->m_shuffle[i]] = desc.dimension(i);
+ }
+ TensorBlockIODst dst(output_dimensions, output_strides, this->m_impl.data(),
+ this->srcCoeff(desc.offset()));
+
+ // Reorder dimensions according to the shuffle.
+ typename TensorBlockIO::DimensionsMap dst_to_src_dim_map;
+ for (int i = 0; i < NumDims; ++i) {
+ dst_to_src_dim_map[i] = static_cast<int>(this->m_inverseShuffle[i]);
+ }
+ TensorBlockIO::Copy(dst, src, dst_to_src_dim_map);
+
+ // Deallocate temporary buffer used for the block materialization.
+ if (mem != NULL) this->m_device.deallocate(mem);
+ }
+};
+
+
+} // end namespace Eigen
+
+#endif // EIGEN_CXX11_TENSOR_TENSOR_SHUFFLING_H
diff --git a/unsupported/Eigen/CXX11/src/Tensor/TensorStorage.h b/unsupported/Eigen/CXX11/src/Tensor/TensorStorage.h
new file mode 100644
index 0000000..f9bb8f6
--- /dev/null
+++ b/unsupported/Eigen/CXX11/src/Tensor/TensorStorage.h
@@ -0,0 +1,156 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2013 Christian Seiler <christian@iwakd.de>
+// Copyright (C) 2014-2015 Benoit Steiner <benoit.steiner.goog@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_CXX11_TENSOR_TENSORSTORAGE_H
+#define EIGEN_CXX11_TENSOR_TENSORSTORAGE_H
+
+#ifdef EIGEN_TENSOR_STORAGE_CTOR_PLUGIN
+ #define EIGEN_INTERNAL_TENSOR_STORAGE_CTOR_PLUGIN EIGEN_TENSOR_STORAGE_CTOR_PLUGIN;
+#else
+ #define EIGEN_INTERNAL_TENSOR_STORAGE_CTOR_PLUGIN
+#endif
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+/** \internal
+ *
+ * \class TensorStorage
+ * \ingroup CXX11_Tensor_Module
+ *
+ * \brief Stores the data of a tensor
+ *
+ * This class stores the data of fixed-size, dynamic-size or mixed tensors
+ * in a way as compact as possible.
+ *
+ * \sa Tensor
+ */
+template<typename T, typename Dimensions, int Options> class TensorStorage;
+
+
+// Pure fixed-size storage
+template<typename T, typename FixedDimensions, int Options_>
+class TensorStorage
+{
+ private:
+ static constexpr std::size_t Size = FixedDimensions::total_size;
+
+ // Allocate an array of size at least one to prevent compiler warnings.
+ static constexpr std::size_t MinSize = max_n_1<Size>::size;
+ EIGEN_ALIGN_MAX T m_data[MinSize];
+
+ public:
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE TensorStorage() {
+ }
+
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE T *data() { return m_data; }
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE const T *data() const { return m_data; }
+
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE const FixedDimensions dimensions() const { return FixedDimensions(); }
+
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE DenseIndex size() const { return Size; }
+};
+
+
+// pure dynamic
+template<typename T, typename IndexType, int NumIndices_, int Options_>
+class TensorStorage<T, DSizes<IndexType, NumIndices_>, Options_>
+{
+ public:
+ typedef IndexType Index;
+ typedef DSizes<IndexType, NumIndices_> Dimensions;
+ typedef TensorStorage<T, DSizes<IndexType, NumIndices_>, Options_> Self;
+
+ EIGEN_DEVICE_FUNC TensorStorage() : m_data(0), m_dimensions() {
+ if (NumIndices_ == 0) {
+ m_data = internal::conditional_aligned_new_auto<T,(Options_&DontAlign)==0>(1);
+ }
+ }
+ EIGEN_DEVICE_FUNC TensorStorage(internal::constructor_without_unaligned_array_assert)
+ : m_data(0), m_dimensions(internal::template repeat<NumIndices_, Index>(0)) {}
+ EIGEN_DEVICE_FUNC TensorStorage(Index size, const array<Index, NumIndices_>& dimensions)
+ : m_data(internal::conditional_aligned_new_auto<T,(Options_&DontAlign)==0>(size)), m_dimensions(dimensions)
+ { EIGEN_INTERNAL_TENSOR_STORAGE_CTOR_PLUGIN }
+
+ template <typename... DenseIndex>
+ EIGEN_DEVICE_FUNC TensorStorage(DenseIndex... indices) : m_dimensions(indices...) {
+ m_data = internal::conditional_aligned_new_auto<T,(Options_&DontAlign)==0>(internal::array_prod(m_dimensions));
+ }
+
+ EIGEN_DEVICE_FUNC TensorStorage(const Self& other)
+ : m_data(internal::conditional_aligned_new_auto<T,(Options_&DontAlign)==0>(internal::array_prod(other.m_dimensions)))
+ , m_dimensions(other.m_dimensions)
+ {
+ internal::smart_copy(other.m_data, other.m_data+internal::array_prod(other.m_dimensions), m_data);
+ }
+ EIGEN_DEVICE_FUNC Self& operator=(const Self& other)
+ {
+ if (this != &other) {
+ Self tmp(other);
+ this->swap(tmp);
+ }
+ return *this;
+ }
+
+ EIGEN_DEVICE_FUNC TensorStorage(Self&& other) : TensorStorage()
+ {
+ *this = std::move(other);
+ }
+
+ EIGEN_DEVICE_FUNC Self& operator=(Self&& other)
+ {
+ numext::swap(m_data, other.m_data);
+ numext::swap(m_dimensions, other.m_dimensions);
+ return *this;
+ }
+
+ EIGEN_DEVICE_FUNC ~TensorStorage() { internal::conditional_aligned_delete_auto<T,(Options_&DontAlign)==0>(m_data, internal::array_prod(m_dimensions)); }
+ EIGEN_DEVICE_FUNC void swap(Self& other)
+ { numext::swap(m_data,other.m_data); numext::swap(m_dimensions,other.m_dimensions); }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Dimensions& dimensions() const {return m_dimensions;}
+
+ EIGEN_DEVICE_FUNC void resize(Index size, const array<Index, NumIndices_>& nbDimensions)
+ {
+ const Index currentSz = internal::array_prod(m_dimensions);
+ if(size != currentSz)
+ {
+ internal::conditional_aligned_delete_auto<T,(Options_&DontAlign)==0>(m_data, currentSz);
+ if (size)
+ m_data = internal::conditional_aligned_new_auto<T,(Options_&DontAlign)==0>(size);
+ else if (NumIndices_ == 0) {
+ m_data = internal::conditional_aligned_new_auto<T,(Options_&DontAlign)==0>(1);
+ }
+ else
+ m_data = 0;
+ EIGEN_INTERNAL_DENSE_STORAGE_CTOR_PLUGIN({})
+ }
+ m_dimensions = nbDimensions;
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE T *data() { return m_data; }
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const T *data() const { return m_data; }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Index size() const { return m_dimensions.TotalSize(); }
+
+ private:
+ T *m_data;
+ Dimensions m_dimensions;
+};
+
+} // end namespace Eigen
+
+#endif // EIGEN_CXX11_TENSOR_TENSORSTORAGE_H
diff --git a/unsupported/Eigen/CXX11/src/Tensor/TensorStriding.h b/unsupported/Eigen/CXX11/src/Tensor/TensorStriding.h
new file mode 100644
index 0000000..609afe3
--- /dev/null
+++ b/unsupported/Eigen/CXX11/src/Tensor/TensorStriding.h
@@ -0,0 +1,348 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_CXX11_TENSOR_TENSOR_STRIDING_H
+#define EIGEN_CXX11_TENSOR_TENSOR_STRIDING_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+/** \class TensorStriding
+ * \ingroup CXX11_Tensor_Module
+ *
+ * \brief Tensor striding class.
+ *
+ *
+ */
+namespace internal {
+template<typename Strides, typename XprType>
+struct traits<TensorStridingOp<Strides, XprType> > : public traits<XprType>
+{
+ typedef typename XprType::Scalar Scalar;
+ typedef traits<XprType> XprTraits;
+ typedef typename XprTraits::StorageKind StorageKind;
+ typedef typename XprTraits::Index Index;
+ typedef typename XprType::Nested Nested;
+ typedef std::remove_reference_t<Nested> Nested_;
+ static constexpr int NumDimensions = XprTraits::NumDimensions;
+ static constexpr int Layout = XprTraits::Layout;
+ typedef typename XprTraits::PointerType PointerType;
+};
+
+template<typename Strides, typename XprType>
+struct eval<TensorStridingOp<Strides, XprType>, Eigen::Dense>
+{
+ typedef const TensorStridingOp<Strides, XprType>EIGEN_DEVICE_REF type;
+};
+
+template<typename Strides, typename XprType>
+struct nested<TensorStridingOp<Strides, XprType>, 1, typename eval<TensorStridingOp<Strides, XprType> >::type>
+{
+ typedef TensorStridingOp<Strides, XprType> type;
+};
+
+} // end namespace internal
+
+
+
+template<typename Strides, typename XprType>
+class TensorStridingOp : public TensorBase<TensorStridingOp<Strides, XprType> >
+{
+ public:
+ typedef TensorBase<TensorStridingOp<Strides, XprType> > Base;
+ typedef typename Eigen::internal::traits<TensorStridingOp>::Scalar Scalar;
+ typedef typename Eigen::NumTraits<Scalar>::Real RealScalar;
+ typedef typename XprType::CoeffReturnType CoeffReturnType;
+ typedef typename Eigen::internal::nested<TensorStridingOp>::type Nested;
+ typedef typename Eigen::internal::traits<TensorStridingOp>::StorageKind StorageKind;
+ typedef typename Eigen::internal::traits<TensorStridingOp>::Index Index;
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorStridingOp(const XprType& expr, const Strides& dims)
+ : m_xpr(expr), m_dims(dims) {}
+
+ EIGEN_DEVICE_FUNC
+ const Strides& strides() const { return m_dims; }
+
+ EIGEN_DEVICE_FUNC
+ const internal::remove_all_t<typename XprType::Nested>&
+ expression() const { return m_xpr; }
+
+ EIGEN_TENSOR_INHERIT_ASSIGNMENT_OPERATORS(TensorStridingOp)
+
+ protected:
+ typename XprType::Nested m_xpr;
+ const Strides m_dims;
+};
+
+
+// Eval as rvalue
+template<typename Strides, typename ArgType, typename Device>
+struct TensorEvaluator<const TensorStridingOp<Strides, ArgType>, Device>
+{
+ typedef TensorStridingOp<Strides, ArgType> XprType;
+ typedef typename XprType::Index Index;
+ static constexpr int NumDims = internal::array_size<typename TensorEvaluator<ArgType, Device>::Dimensions>::value;
+ typedef DSizes<Index, NumDims> Dimensions;
+ typedef typename XprType::Scalar Scalar;
+ typedef typename XprType::CoeffReturnType CoeffReturnType;
+ typedef typename PacketType<CoeffReturnType, Device>::type PacketReturnType;
+ static constexpr int PacketSize = PacketType<CoeffReturnType, Device>::size;
+ typedef StorageMemory<CoeffReturnType, Device> Storage;
+ typedef typename Storage::Type EvaluatorPointerType;
+
+ static constexpr int Layout = TensorEvaluator<ArgType, Device>::Layout;
+ enum {
+ IsAligned = /*TensorEvaluator<ArgType, Device>::IsAligned*/false,
+ PacketAccess = TensorEvaluator<ArgType, Device>::PacketAccess,
+ BlockAccess = false,
+ PreferBlockAccess = TensorEvaluator<ArgType, Device>::PreferBlockAccess,
+ CoordAccess = false, // to be implemented
+ RawAccess = false
+ };
+
+ //===- Tensor block evaluation strategy (see TensorBlock.h) -------------===//
+ typedef internal::TensorBlockNotImplemented TensorBlock;
+ //===--------------------------------------------------------------------===//
+
+ EIGEN_STRONG_INLINE TensorEvaluator(const XprType& op, const Device& device)
+ : m_impl(op.expression(), device)
+ {
+ m_dimensions = m_impl.dimensions();
+ for (int i = 0; i < NumDims; ++i) {
+ m_dimensions[i] =Eigen::numext::ceil(static_cast<float>(m_dimensions[i]) / op.strides()[i]);
+ }
+
+ const typename TensorEvaluator<ArgType, Device>::Dimensions& input_dims = m_impl.dimensions();
+ if (static_cast<int>(Layout) == static_cast<int>(ColMajor)) {
+ m_outputStrides[0] = 1;
+ m_inputStrides[0] = 1;
+ for (int i = 1; i < NumDims; ++i) {
+ m_outputStrides[i] = m_outputStrides[i-1] * m_dimensions[i-1];
+ m_inputStrides[i] = m_inputStrides[i-1] * input_dims[i-1];
+ m_inputStrides[i-1] *= op.strides()[i-1];
+ }
+ m_inputStrides[NumDims-1] *= op.strides()[NumDims-1];
+ } else { // RowMajor
+ m_outputStrides[NumDims-1] = 1;
+ m_inputStrides[NumDims-1] = 1;
+ for (int i = NumDims - 2; i >= 0; --i) {
+ m_outputStrides[i] = m_outputStrides[i+1] * m_dimensions[i+1];
+ m_inputStrides[i] = m_inputStrides[i+1] * input_dims[i+1];
+ m_inputStrides[i+1] *= op.strides()[i+1];
+ }
+ m_inputStrides[0] *= op.strides()[0];
+ }
+ }
+
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Dimensions& dimensions() const { return m_dimensions; }
+
+ EIGEN_STRONG_INLINE bool evalSubExprsIfNeeded(EvaluatorPointerType/*data*/) {
+ m_impl.evalSubExprsIfNeeded(NULL);
+ return true;
+ }
+ EIGEN_STRONG_INLINE void cleanup() {
+ m_impl.cleanup();
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE CoeffReturnType coeff(Index index) const
+ {
+ return m_impl.coeff(srcCoeff(index));
+ }
+
+ template<int LoadMode>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE PacketReturnType packet(Index index) const
+ {
+ EIGEN_STATIC_ASSERT((PacketSize > 1), YOU_MADE_A_PROGRAMMING_MISTAKE)
+ eigen_assert(index+PacketSize-1 < dimensions().TotalSize());
+
+ Index inputIndices[] = {0, 0};
+ Index indices[] = {index, index + PacketSize - 1};
+ if (static_cast<int>(Layout) == static_cast<int>(ColMajor)) {
+ EIGEN_UNROLL_LOOP
+ for (int i = NumDims - 1; i > 0; --i) {
+ const Index idx0 = indices[0] / m_outputStrides[i];
+ const Index idx1 = indices[1] / m_outputStrides[i];
+ inputIndices[0] += idx0 * m_inputStrides[i];
+ inputIndices[1] += idx1 * m_inputStrides[i];
+ indices[0] -= idx0 * m_outputStrides[i];
+ indices[1] -= idx1 * m_outputStrides[i];
+ }
+ inputIndices[0] += indices[0] * m_inputStrides[0];
+ inputIndices[1] += indices[1] * m_inputStrides[0];
+ } else { // RowMajor
+ EIGEN_UNROLL_LOOP
+ for (int i = 0; i < NumDims - 1; ++i) {
+ const Index idx0 = indices[0] / m_outputStrides[i];
+ const Index idx1 = indices[1] / m_outputStrides[i];
+ inputIndices[0] += idx0 * m_inputStrides[i];
+ inputIndices[1] += idx1 * m_inputStrides[i];
+ indices[0] -= idx0 * m_outputStrides[i];
+ indices[1] -= idx1 * m_outputStrides[i];
+ }
+ inputIndices[0] += indices[0] * m_inputStrides[NumDims-1];
+ inputIndices[1] += indices[1] * m_inputStrides[NumDims-1];
+ }
+ if (inputIndices[1] - inputIndices[0] == PacketSize - 1) {
+ PacketReturnType rslt = m_impl.template packet<Unaligned>(inputIndices[0]);
+ return rslt;
+ }
+ else {
+ EIGEN_ALIGN_MAX std::remove_const_t<CoeffReturnType> values[PacketSize];
+ values[0] = m_impl.coeff(inputIndices[0]);
+ values[PacketSize-1] = m_impl.coeff(inputIndices[1]);
+ EIGEN_UNROLL_LOOP
+ for (int i = 1; i < PacketSize-1; ++i) {
+ values[i] = coeff(index+i);
+ }
+ PacketReturnType rslt = internal::pload<PacketReturnType>(values);
+ return rslt;
+ }
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorOpCost costPerCoeff(bool vectorized) const {
+ double compute_cost = (NumDims - 1) * (TensorOpCost::AddCost<Index>() +
+ TensorOpCost::MulCost<Index>() +
+ TensorOpCost::DivCost<Index>()) +
+ TensorOpCost::MulCost<Index>();
+ if (vectorized) {
+ compute_cost *= 2; // packet() computes two indices
+ }
+ const int innerDim = (static_cast<int>(Layout) == static_cast<int>(ColMajor)) ? 0 : (NumDims - 1);
+ return m_impl.costPerCoeff(vectorized && m_inputStrides[innerDim] == 1) +
+ // Computation is not vectorized per se, but it is done once per packet.
+ TensorOpCost(0, 0, compute_cost, vectorized, PacketSize);
+ }
+
+ EIGEN_DEVICE_FUNC typename Storage::Type data() const { return NULL; }
+
+#ifdef EIGEN_USE_SYCL
+ // binding placeholder accessors to a command group handler for SYCL
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void bind(cl::sycl::handler &cgh) const {
+ m_impl.bind(cgh);
+ }
+#endif
+ protected:
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Index srcCoeff(Index index) const
+ {
+ Index inputIndex = 0;
+ if (static_cast<int>(Layout) == static_cast<int>(ColMajor)) {
+ EIGEN_UNROLL_LOOP
+ for (int i = NumDims - 1; i > 0; --i) {
+ const Index idx = index / m_outputStrides[i];
+ inputIndex += idx * m_inputStrides[i];
+ index -= idx * m_outputStrides[i];
+ }
+ inputIndex += index * m_inputStrides[0];
+ } else { // RowMajor
+ EIGEN_UNROLL_LOOP
+ for (int i = 0; i < NumDims - 1; ++i) {
+ const Index idx = index / m_outputStrides[i];
+ inputIndex += idx * m_inputStrides[i];
+ index -= idx * m_outputStrides[i];
+ }
+ inputIndex += index * m_inputStrides[NumDims-1];
+ }
+ return inputIndex;
+ }
+
+ Dimensions m_dimensions;
+ array<Index, NumDims> m_outputStrides;
+ array<Index, NumDims> m_inputStrides;
+ TensorEvaluator<ArgType, Device> m_impl;
+};
+
+// Eval as lvalue
+template<typename Strides, typename ArgType, typename Device>
+struct TensorEvaluator<TensorStridingOp<Strides, ArgType>, Device>
+ : public TensorEvaluator<const TensorStridingOp<Strides, ArgType>, Device>
+{
+ typedef TensorStridingOp<Strides, ArgType> XprType;
+ typedef TensorEvaluator<const XprType, Device> Base;
+ // typedef typename XprType::Index Index;
+ static constexpr int NumDims = internal::array_size<typename TensorEvaluator<ArgType, Device>::Dimensions>::value;
+ // typedef DSizes<Index, NumDims> Dimensions;
+
+ static constexpr int Layout = TensorEvaluator<ArgType, Device>::Layout;
+ enum {
+ IsAligned = /*TensorEvaluator<ArgType, Device>::IsAligned*/false,
+ PacketAccess = TensorEvaluator<ArgType, Device>::PacketAccess,
+ PreferBlockAccess = false,
+ CoordAccess = false, // to be implemented
+ RawAccess = false
+ };
+
+ EIGEN_STRONG_INLINE TensorEvaluator(const XprType& op, const Device& device)
+ : Base(op, device) { }
+
+ typedef typename XprType::Index Index;
+ typedef typename XprType::Scalar Scalar;
+ typedef typename XprType::CoeffReturnType CoeffReturnType;
+ typedef typename PacketType<CoeffReturnType, Device>::type PacketReturnType;
+ static constexpr int PacketSize = PacketType<CoeffReturnType, Device>::size;
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar& coeffRef(Index index)
+ {
+ return this->m_impl.coeffRef(this->srcCoeff(index));
+ }
+
+ template <int StoreMode> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ void writePacket(Index index, const PacketReturnType& x)
+ {
+ EIGEN_STATIC_ASSERT((PacketSize > 1), YOU_MADE_A_PROGRAMMING_MISTAKE)
+ eigen_assert(index+PacketSize-1 < this->dimensions().TotalSize());
+
+ Index inputIndices[] = {0, 0};
+ Index indices[] = {index, index + PacketSize - 1};
+ if (static_cast<int>(Layout) == static_cast<int>(ColMajor)) {
+ EIGEN_UNROLL_LOOP
+ for (int i = NumDims - 1; i > 0; --i) {
+ const Index idx0 = indices[0] / this->m_outputStrides[i];
+ const Index idx1 = indices[1] / this->m_outputStrides[i];
+ inputIndices[0] += idx0 * this->m_inputStrides[i];
+ inputIndices[1] += idx1 * this->m_inputStrides[i];
+ indices[0] -= idx0 * this->m_outputStrides[i];
+ indices[1] -= idx1 * this->m_outputStrides[i];
+ }
+ inputIndices[0] += indices[0] * this->m_inputStrides[0];
+ inputIndices[1] += indices[1] * this->m_inputStrides[0];
+ } else { // RowMajor
+ EIGEN_UNROLL_LOOP
+ for (int i = 0; i < NumDims - 1; ++i) {
+ const Index idx0 = indices[0] / this->m_outputStrides[i];
+ const Index idx1 = indices[1] / this->m_outputStrides[i];
+ inputIndices[0] += idx0 * this->m_inputStrides[i];
+ inputIndices[1] += idx1 * this->m_inputStrides[i];
+ indices[0] -= idx0 * this->m_outputStrides[i];
+ indices[1] -= idx1 * this->m_outputStrides[i];
+ }
+ inputIndices[0] += indices[0] * this->m_inputStrides[NumDims-1];
+ inputIndices[1] += indices[1] * this->m_inputStrides[NumDims-1];
+ }
+ if (inputIndices[1] - inputIndices[0] == PacketSize - 1) {
+ this->m_impl.template writePacket<Unaligned>(inputIndices[0], x);
+ }
+ else {
+ EIGEN_ALIGN_MAX Scalar values[PacketSize];
+ internal::pstore<Scalar, PacketReturnType>(values, x);
+ this->m_impl.coeffRef(inputIndices[0]) = values[0];
+ this->m_impl.coeffRef(inputIndices[1]) = values[PacketSize-1];
+ EIGEN_UNROLL_LOOP
+ for (int i = 1; i < PacketSize-1; ++i) {
+ this->coeffRef(index+i) = values[i];
+ }
+ }
+ }
+};
+
+
+} // end namespace Eigen
+
+#endif // EIGEN_CXX11_TENSOR_TENSOR_STRIDING_H
diff --git a/unsupported/Eigen/CXX11/src/Tensor/TensorTrace.h b/unsupported/Eigen/CXX11/src/Tensor/TensorTrace.h
new file mode 100644
index 0000000..d682202
--- /dev/null
+++ b/unsupported/Eigen/CXX11/src/Tensor/TensorTrace.h
@@ -0,0 +1,304 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2017 Gagan Goel <gagan.nith@gmail.com>
+// Copyright (C) 2017 Benoit Steiner <benoit.steiner.goog@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_CXX11_TENSOR_TENSOR_TRACE_H
+#define EIGEN_CXX11_TENSOR_TENSOR_TRACE_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+/** \class TensorTrace
+ * \ingroup CXX11_Tensor_Module
+ *
+ * \brief Tensor Trace class.
+ *
+ *
+ */
+
+namespace internal {
+template<typename Dims, typename XprType>
+struct traits<TensorTraceOp<Dims, XprType> > : public traits<XprType>
+{
+ typedef typename XprType::Scalar Scalar;
+ typedef traits<XprType> XprTraits;
+ typedef typename XprTraits::StorageKind StorageKind;
+ typedef typename XprTraits::Index Index;
+ typedef typename XprType::Nested Nested;
+ typedef std::remove_reference_t<Nested> Nested_;
+ static constexpr int NumDimensions = XprTraits::NumDimensions - array_size<Dims>::value;
+ static constexpr int Layout = XprTraits::Layout;
+};
+
+template<typename Dims, typename XprType>
+struct eval<TensorTraceOp<Dims, XprType>, Eigen::Dense>
+{
+ typedef const TensorTraceOp<Dims, XprType>& type;
+};
+
+template<typename Dims, typename XprType>
+struct nested<TensorTraceOp<Dims, XprType>, 1, typename eval<TensorTraceOp<Dims, XprType> >::type>
+{
+ typedef TensorTraceOp<Dims, XprType> type;
+};
+
+} // end namespace internal
+
+
+template<typename Dims, typename XprType>
+class TensorTraceOp : public TensorBase<TensorTraceOp<Dims, XprType> >
+{
+ public:
+ typedef typename Eigen::internal::traits<TensorTraceOp>::Scalar Scalar;
+ typedef typename Eigen::NumTraits<Scalar>::Real RealScalar;
+ typedef typename XprType::CoeffReturnType CoeffReturnType;
+ typedef typename Eigen::internal::nested<TensorTraceOp>::type Nested;
+ typedef typename Eigen::internal::traits<TensorTraceOp>::StorageKind StorageKind;
+ typedef typename Eigen::internal::traits<TensorTraceOp>::Index Index;
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorTraceOp(const XprType& expr, const Dims& dims)
+ : m_xpr(expr), m_dims(dims) {
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ const Dims& dims() const { return m_dims; }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ const internal::remove_all_t<typename XprType::Nested>& expression() const { return m_xpr; }
+
+ protected:
+ typename XprType::Nested m_xpr;
+ const Dims m_dims;
+};
+
+
+// Eval as rvalue
+template<typename Dims, typename ArgType, typename Device>
+struct TensorEvaluator<const TensorTraceOp<Dims, ArgType>, Device>
+{
+ typedef TensorTraceOp<Dims, ArgType> XprType;
+ static constexpr int NumInputDims = internal::array_size<typename TensorEvaluator<ArgType, Device>::Dimensions>::value;
+ static constexpr int NumReducedDims = internal::array_size<Dims>::value;
+ static constexpr int NumOutputDims = NumInputDims - NumReducedDims;
+ typedef typename XprType::Index Index;
+ typedef DSizes<Index, NumOutputDims> Dimensions;
+ typedef typename XprType::Scalar Scalar;
+ typedef typename XprType::CoeffReturnType CoeffReturnType;
+ typedef typename PacketType<CoeffReturnType, Device>::type PacketReturnType;
+ static constexpr int PacketSize = internal::unpacket_traits<PacketReturnType>::size;
+ typedef StorageMemory<CoeffReturnType, Device> Storage;
+ typedef typename Storage::Type EvaluatorPointerType;
+
+ static constexpr int Layout = TensorEvaluator<ArgType, Device>::Layout;
+ enum {
+ IsAligned = false,
+ PacketAccess = TensorEvaluator<ArgType, Device>::PacketAccess,
+ BlockAccess = false,
+ PreferBlockAccess = TensorEvaluator<ArgType, Device>::PreferBlockAccess,
+ CoordAccess = false,
+ RawAccess = false
+ };
+
+ //===- Tensor block evaluation strategy (see TensorBlock.h) -------------===//
+ typedef internal::TensorBlockNotImplemented TensorBlock;
+ //===--------------------------------------------------------------------===//
+
+ EIGEN_STRONG_INLINE TensorEvaluator(const XprType& op, const Device& device)
+ : m_impl(op.expression(), device), m_traceDim(1), m_device(device)
+ {
+
+ EIGEN_STATIC_ASSERT((NumOutputDims >= 0), YOU_MADE_A_PROGRAMMING_MISTAKE);
+ EIGEN_STATIC_ASSERT((NumReducedDims >= 2) || ((NumReducedDims == 0) && (NumInputDims == 0)), YOU_MADE_A_PROGRAMMING_MISTAKE);
+
+ for (int i = 0; i < NumInputDims; ++i) {
+ m_reduced[i] = false;
+ }
+
+ const Dims& op_dims = op.dims();
+ for (int i = 0; i < NumReducedDims; ++i) {
+ eigen_assert(op_dims[i] >= 0);
+ eigen_assert(op_dims[i] < NumInputDims);
+ m_reduced[op_dims[i]] = true;
+ }
+
+ // All the dimensions should be distinct to compute the trace
+ int num_distinct_reduce_dims = 0;
+ for (int i = 0; i < NumInputDims; ++i) {
+ if (m_reduced[i]) {
+ ++num_distinct_reduce_dims;
+ }
+ }
+
+ EIGEN_ONLY_USED_FOR_DEBUG(num_distinct_reduce_dims);
+ eigen_assert(num_distinct_reduce_dims == NumReducedDims);
+
+ // Compute the dimensions of the result.
+ const typename TensorEvaluator<ArgType, Device>::Dimensions& input_dims = m_impl.dimensions();
+
+ int output_index = 0;
+ int reduced_index = 0;
+ for (int i = 0; i < NumInputDims; ++i) {
+ if (m_reduced[i]) {
+ m_reducedDims[reduced_index] = input_dims[i];
+ if (reduced_index > 0) {
+ // All the trace dimensions must have the same size
+ eigen_assert(m_reducedDims[0] == m_reducedDims[reduced_index]);
+ }
+ ++reduced_index;
+ }
+ else {
+ m_dimensions[output_index] = input_dims[i];
+ ++output_index;
+ }
+ }
+
+ if (NumReducedDims != 0) {
+ m_traceDim = m_reducedDims[0];
+ }
+
+ // Compute the output strides
+ if (NumOutputDims > 0) {
+ if (static_cast<int>(Layout) == static_cast<int>(ColMajor)) {
+ m_outputStrides[0] = 1;
+ for (int i = 1; i < NumOutputDims; ++i) {
+ m_outputStrides[i] = m_outputStrides[i - 1] * m_dimensions[i - 1];
+ }
+ }
+ else {
+ m_outputStrides.back() = 1;
+ for (int i = NumOutputDims - 2; i >= 0; --i) {
+ m_outputStrides[i] = m_outputStrides[i + 1] * m_dimensions[i + 1];
+ }
+ }
+ }
+
+ // Compute the input strides
+ if (NumInputDims > 0) {
+ array<Index, NumInputDims> input_strides;
+ if (static_cast<int>(Layout) == static_cast<int>(ColMajor)) {
+ input_strides[0] = 1;
+ for (int i = 1; i < NumInputDims; ++i) {
+ input_strides[i] = input_strides[i - 1] * input_dims[i - 1];
+ }
+ }
+ else {
+ input_strides.back() = 1;
+ for (int i = NumInputDims - 2; i >= 0; --i) {
+ input_strides[i] = input_strides[i + 1] * input_dims[i + 1];
+ }
+ }
+
+ output_index = 0;
+ reduced_index = 0;
+ for (int i = 0; i < NumInputDims; ++i) {
+ if(m_reduced[i]) {
+ m_reducedStrides[reduced_index] = input_strides[i];
+ ++reduced_index;
+ }
+ else {
+ m_preservedStrides[output_index] = input_strides[i];
+ ++output_index;
+ }
+ }
+ }
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Dimensions& dimensions() const {
+ return m_dimensions;
+ }
+
+ EIGEN_STRONG_INLINE bool evalSubExprsIfNeeded(EvaluatorPointerType /*data*/) {
+ m_impl.evalSubExprsIfNeeded(NULL);
+ return true;
+ }
+
+ EIGEN_STRONG_INLINE void cleanup() {
+ m_impl.cleanup();
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE CoeffReturnType coeff(Index index) const
+ {
+ // Initialize the result
+ CoeffReturnType result = internal::cast<int, CoeffReturnType>(0);
+ Index index_stride = 0;
+ for (int i = 0; i < NumReducedDims; ++i) {
+ index_stride += m_reducedStrides[i];
+ }
+
+ // If trace is requested along all dimensions, starting index would be 0
+ Index cur_index = 0;
+ if (NumOutputDims != 0)
+ cur_index = firstInput(index);
+ for (Index i = 0; i < m_traceDim; ++i) {
+ result += m_impl.coeff(cur_index);
+ cur_index += index_stride;
+ }
+
+ return result;
+ }
+
+ template<int LoadMode>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE PacketReturnType packet(Index index) const {
+ eigen_assert(index + PacketSize - 1 < dimensions().TotalSize());
+
+ EIGEN_ALIGN_MAX std::remove_const_t<CoeffReturnType> values[PacketSize];
+ for (int i = 0; i < PacketSize; ++i) {
+ values[i] = coeff(index + i);
+ }
+ PacketReturnType result = internal::ploadt<PacketReturnType, LoadMode>(values);
+ return result;
+ }
+
+#ifdef EIGEN_USE_SYCL
+ // binding placeholder accessors to a command group handler for SYCL
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void bind(cl::sycl::handler &cgh) const {
+ m_impl.bind(cgh);
+ }
+#endif
+
+ protected:
+ // Given the output index, finds the first index in the input tensor used to compute the trace
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Index firstInput(Index index) const {
+ Index startInput = 0;
+ if (static_cast<int>(Layout) == static_cast<int>(ColMajor)) {
+ for (int i = NumOutputDims - 1; i > 0; --i) {
+ const Index idx = index / m_outputStrides[i];
+ startInput += idx * m_preservedStrides[i];
+ index -= idx * m_outputStrides[i];
+ }
+ startInput += index * m_preservedStrides[0];
+ }
+ else {
+ for (int i = 0; i < NumOutputDims - 1; ++i) {
+ const Index idx = index / m_outputStrides[i];
+ startInput += idx * m_preservedStrides[i];
+ index -= idx * m_outputStrides[i];
+ }
+ startInput += index * m_preservedStrides[NumOutputDims - 1];
+ }
+ return startInput;
+ }
+
+ Dimensions m_dimensions;
+ TensorEvaluator<ArgType, Device> m_impl;
+ // Initialize the size of the trace dimension
+ Index m_traceDim;
+ const Device EIGEN_DEVICE_REF m_device;
+ array<bool, NumInputDims> m_reduced;
+ array<Index, NumReducedDims> m_reducedDims;
+ array<Index, NumOutputDims> m_outputStrides;
+ array<Index, NumReducedDims> m_reducedStrides;
+ array<Index, NumOutputDims> m_preservedStrides;
+};
+
+
+} // End namespace Eigen
+
+#endif // EIGEN_CXX11_TENSOR_TENSOR_TRACE_H
diff --git a/unsupported/Eigen/CXX11/src/Tensor/TensorTraits.h b/unsupported/Eigen/CXX11/src/Tensor/TensorTraits.h
new file mode 100644
index 0000000..8c705ec
--- /dev/null
+++ b/unsupported/Eigen/CXX11/src/Tensor/TensorTraits.h
@@ -0,0 +1,266 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_CXX11_TENSOR_TENSOR_TRAITS_H
+#define EIGEN_CXX11_TENSOR_TENSOR_TRAITS_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+namespace internal {
+
+
+template<typename Scalar, int Options>
+class compute_tensor_flags
+{
+ enum {
+ is_dynamic_size_storage = 1,
+
+ is_aligned =
+ (
+ ((Options&DontAlign)==0) && (
+#if EIGEN_MAX_STATIC_ALIGN_BYTES>0
+ (!is_dynamic_size_storage)
+#else
+ 0
+#endif
+ |
+#if EIGEN_MAX_ALIGN_BYTES>0
+ is_dynamic_size_storage
+#else
+ 0
+#endif
+ )
+ ),
+ packet_access_bit = packet_traits<Scalar>::Vectorizable && is_aligned ? PacketAccessBit : 0
+ };
+
+ public:
+ enum { ret = packet_access_bit };
+};
+
+
+template<typename Scalar_, int NumIndices_, int Options_, typename IndexType_>
+struct traits<Tensor<Scalar_, NumIndices_, Options_, IndexType_> >
+{
+ typedef Scalar_ Scalar;
+ typedef Dense StorageKind;
+ typedef IndexType_ Index;
+ static constexpr int NumDimensions = NumIndices_;
+ static constexpr int Layout = Options_ & RowMajor ? RowMajor : ColMajor;
+ enum {
+ Options = Options_,
+ Flags = compute_tensor_flags<Scalar_, Options_>::ret | (is_const<Scalar_>::value ? 0 : LvalueBit)
+ };
+ template <typename T> struct MakePointer {
+ typedef T* Type;
+ };
+ typedef typename MakePointer<Scalar>::Type PointerType;
+};
+
+
+template<typename Scalar_, typename Dimensions, int Options_, typename IndexType_>
+struct traits<TensorFixedSize<Scalar_, Dimensions, Options_, IndexType_> >
+{
+ typedef Scalar_ Scalar;
+ typedef Dense StorageKind;
+ typedef IndexType_ Index;
+ static constexpr int NumDimensions = array_size<Dimensions>::value;
+ static constexpr int Layout = Options_ & RowMajor ? RowMajor : ColMajor;
+ enum {
+ Options = Options_,
+ Flags = compute_tensor_flags<Scalar_, Options_>::ret | (is_const<Scalar_>::value ? 0: LvalueBit)
+ };
+ template <typename T> struct MakePointer {
+ typedef T* Type;
+ };
+ typedef typename MakePointer<Scalar>::Type PointerType;
+};
+
+
+template<typename PlainObjectType, int Options_, template <class> class MakePointer_>
+struct traits<TensorMap<PlainObjectType, Options_, MakePointer_> >
+ : public traits<PlainObjectType>
+{
+ typedef traits<PlainObjectType> BaseTraits;
+ typedef typename BaseTraits::Scalar Scalar;
+ typedef typename BaseTraits::StorageKind StorageKind;
+ typedef typename BaseTraits::Index Index;
+ static constexpr int NumDimensions = BaseTraits::NumDimensions;
+ static constexpr int Layout = BaseTraits::Layout;
+ enum {
+ Options = Options_,
+ Flags = BaseTraits::Flags
+ };
+ template <class T> struct MakePointer {
+ // Intermediate typedef to workaround MSVC issue.
+ typedef MakePointer_<T> MakePointerT;
+ typedef typename MakePointerT::Type Type;
+ };
+ typedef typename MakePointer<Scalar>::Type PointerType;
+};
+
+template<typename PlainObjectType>
+struct traits<TensorRef<PlainObjectType> >
+ : public traits<PlainObjectType>
+{
+ typedef traits<PlainObjectType> BaseTraits;
+ typedef typename BaseTraits::Scalar Scalar;
+ typedef typename BaseTraits::StorageKind StorageKind;
+ typedef typename BaseTraits::Index Index;
+ static constexpr int NumDimensions = BaseTraits::NumDimensions;
+ static constexpr int Layout = BaseTraits::Layout;
+ enum {
+ Options = BaseTraits::Options,
+ Flags = BaseTraits::Flags
+ };
+ typedef typename BaseTraits::PointerType PointerType;
+};
+
+
+template<typename Scalar_, int NumIndices_, int Options, typename IndexType_>
+struct eval<Tensor<Scalar_, NumIndices_, Options, IndexType_>, Eigen::Dense>
+{
+ typedef const Tensor<Scalar_, NumIndices_, Options, IndexType_>EIGEN_DEVICE_REF type;
+};
+
+template<typename Scalar_, int NumIndices_, int Options, typename IndexType_>
+struct eval<const Tensor<Scalar_, NumIndices_, Options, IndexType_>, Eigen::Dense>
+{
+ typedef const Tensor<Scalar_, NumIndices_, Options, IndexType_>EIGEN_DEVICE_REF type;
+};
+
+template<typename Scalar_, typename Dimensions, int Options, typename IndexType_>
+struct eval<TensorFixedSize<Scalar_, Dimensions, Options, IndexType_>, Eigen::Dense>
+{
+ typedef const TensorFixedSize<Scalar_, Dimensions, Options, IndexType_>EIGEN_DEVICE_REF type;
+};
+
+template<typename Scalar_, typename Dimensions, int Options, typename IndexType_>
+struct eval<const TensorFixedSize<Scalar_, Dimensions, Options, IndexType_>, Eigen::Dense>
+{
+ typedef const TensorFixedSize<Scalar_, Dimensions, Options, IndexType_>EIGEN_DEVICE_REF type;
+};
+
+template<typename PlainObjectType, int Options, template <class> class MakePointer>
+struct eval<TensorMap<PlainObjectType, Options, MakePointer>, Eigen::Dense>
+{
+ typedef const TensorMap<PlainObjectType, Options, MakePointer>EIGEN_DEVICE_REF type;
+};
+
+template<typename PlainObjectType, int Options, template <class> class MakePointer>
+struct eval<const TensorMap<PlainObjectType, Options, MakePointer>, Eigen::Dense>
+{
+ typedef const TensorMap<PlainObjectType, Options, MakePointer>EIGEN_DEVICE_REF type;
+};
+
+template<typename PlainObjectType>
+struct eval<TensorRef<PlainObjectType>, Eigen::Dense>
+{
+ typedef const TensorRef<PlainObjectType>EIGEN_DEVICE_REF type;
+};
+
+template<typename PlainObjectType>
+struct eval<const TensorRef<PlainObjectType>, Eigen::Dense>
+{
+ typedef const TensorRef<PlainObjectType>EIGEN_DEVICE_REF type;
+};
+
+// TODO nested<> does not exist anymore in Eigen/Core, and it thus has to be removed in favor of ref_selector.
+template<typename T, int n=1, typename PlainObject = void> struct nested
+{
+ typedef typename ref_selector<T>::type type;
+};
+
+template <typename Scalar_, int NumIndices_, int Options_, typename IndexType_>
+struct nested<Tensor<Scalar_, NumIndices_, Options_, IndexType_> >
+{
+ typedef const Tensor<Scalar_, NumIndices_, Options_, IndexType_>EIGEN_DEVICE_REF type;
+};
+
+template <typename Scalar_, int NumIndices_, int Options_, typename IndexType_>
+struct nested<const Tensor<Scalar_, NumIndices_, Options_, IndexType_> >
+{
+ typedef const Tensor<Scalar_, NumIndices_, Options_, IndexType_>EIGEN_DEVICE_REF type;
+};
+
+template <typename Scalar_, typename Dimensions, int Options, typename IndexType_>
+struct nested<TensorFixedSize<Scalar_, Dimensions, Options, IndexType_> >
+{
+ typedef const TensorFixedSize<Scalar_, Dimensions, Options, IndexType_>EIGEN_DEVICE_REF type;
+};
+
+template <typename Scalar_, typename Dimensions, int Options, typename IndexType_>
+struct nested<const TensorFixedSize<Scalar_, Dimensions, Options, IndexType_> >
+{
+ typedef const TensorFixedSize<Scalar_, Dimensions, Options, IndexType_>EIGEN_DEVICE_REF type;
+};
+
+
+template <typename PlainObjectType>
+struct nested<TensorRef<PlainObjectType> >
+{
+ typedef const TensorRef<PlainObjectType>EIGEN_DEVICE_REF type;
+};
+
+template <typename PlainObjectType>
+struct nested<const TensorRef<PlainObjectType> >
+{
+ typedef const TensorRef<PlainObjectType>EIGEN_DEVICE_REF type;
+};
+
+} // end namespace internal
+
+// Convolutional layers take in an input tensor of shape (D, R, C, B), or (D, C,
+// R, B), and convolve it with a set of filters, which can also be presented as
+// a tensor (D, K, K, M), where M is the number of filters, K is the filter
+// size, and each 3-dimensional tensor of size (D, K, K) is a filter. For
+// simplicity we assume that we always use square filters (which is usually the
+// case in images), hence the two Ks in the tensor dimension. It also takes in
+// a few additional parameters:
+// Stride (S): The convolution stride is the offset between locations where we
+// apply the filters. A larger stride means that the output will be
+// spatially smaller.
+// Padding (P): The padding we apply to the input tensor along the R and C
+// dimensions. This is usually used to make sure that the spatial
+// dimensions of the output matches our intention.
+//
+// Two types of padding are often used:
+// SAME: The pad value is computed so that the output will have size
+// R/S and C/S.
+// VALID: no padding is carried out.
+// When we do padding, the padded values at the padded locations are usually
+// zero.
+//
+// The output dimensions for convolution, when given all the parameters above,
+// are as follows:
+// When Padding = SAME: the output size is (B, R', C', M), where
+// R' = ceil(float(R) / float(S))
+// C' = ceil(float(C) / float(S))
+// where ceil is the ceiling function. The input tensor is padded with 0 as
+// needed. The number of padded rows and columns are computed as:
+// Pr = ((R' - 1) * S + K - R) / 2
+// Pc = ((C' - 1) * S + K - C) / 2
+// when the stride is 1, we have the simplified case R'=R, C'=C, Pr=Pc=(K-1)/2.
+// This is where SAME comes from - the output has the same size as the input has.
+// When Padding = VALID: the output size is computed as
+// R' = ceil(float(R - K + 1) / float(S))
+// C' = ceil(float(C - K + 1) / float(S))
+// and the number of padded rows and columns are computed in the same way as in
+// the SAME case.
+// When the stride is 1, we have the simplified case R'=R-K+1, C'=C-K+1, Pr=0,
+// Pc=0.
+enum PaddingType {
+ PADDING_VALID = 1,
+ PADDING_SAME = 2
+};
+
+} // end namespace Eigen
+
+#endif // EIGEN_CXX11_TENSOR_TENSOR_TRAITS_H
diff --git a/unsupported/Eigen/CXX11/src/Tensor/TensorUInt128.h b/unsupported/Eigen/CXX11/src/Tensor/TensorUInt128.h
new file mode 100644
index 0000000..37be364
--- /dev/null
+++ b/unsupported/Eigen/CXX11/src/Tensor/TensorUInt128.h
@@ -0,0 +1,251 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2015 Benoit Steiner <benoit.steiner.goog@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_CXX11_TENSOR_TENSOR_UINT128_H
+#define EIGEN_CXX11_TENSOR_TENSOR_UINT128_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+namespace internal {
+
+
+template <uint64_t n>
+struct static_val {
+ static const uint64_t value = n;
+ EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE operator uint64_t() const { return n; }
+
+ EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE static_val() { }
+
+ template <typename T>
+ EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE static_val(const T& v) {
+ EIGEN_UNUSED_VARIABLE(v);
+ eigen_assert(v == n);
+ }
+};
+
+
+template <typename HIGH = uint64_t, typename LOW = uint64_t>
+struct TensorUInt128
+{
+ HIGH high;
+ LOW low;
+
+ template<typename OTHER_HIGH, typename OTHER_LOW>
+ EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
+ TensorUInt128(const TensorUInt128<OTHER_HIGH, OTHER_LOW>& other) : high(other.high), low(other.low) {
+ EIGEN_STATIC_ASSERT(sizeof(OTHER_HIGH) <= sizeof(HIGH), YOU_MADE_A_PROGRAMMING_MISTAKE);
+ EIGEN_STATIC_ASSERT(sizeof(OTHER_LOW) <= sizeof(LOW), YOU_MADE_A_PROGRAMMING_MISTAKE);
+ }
+
+ template<typename OTHER_HIGH, typename OTHER_LOW>
+ EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
+ TensorUInt128& operator = (const TensorUInt128<OTHER_HIGH, OTHER_LOW>& other) {
+ EIGEN_STATIC_ASSERT(sizeof(OTHER_HIGH) <= sizeof(HIGH), YOU_MADE_A_PROGRAMMING_MISTAKE);
+ EIGEN_STATIC_ASSERT(sizeof(OTHER_LOW) <= sizeof(LOW), YOU_MADE_A_PROGRAMMING_MISTAKE);
+ high = other.high;
+ low = other.low;
+ return *this;
+ }
+
+ template<typename T>
+ EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
+ explicit TensorUInt128(const T& x) : high(0), low(x) {
+ eigen_assert((static_cast<std::conditional_t<sizeof(T) == 8, uint64_t, uint32_t>>(x) <= NumTraits<uint64_t>::highest()));
+ eigen_assert(x >= 0);
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
+ TensorUInt128(HIGH y, LOW x) : high(y), low(x) { }
+
+ EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE operator LOW() const {
+ return low;
+ }
+ EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE LOW lower() const {
+ return low;
+ }
+ EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE HIGH upper() const {
+ return high;
+ }
+};
+
+
+template <typename HL, typename LL, typename HR, typename LR>
+EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
+bool operator == (const TensorUInt128<HL, LL>& lhs, const TensorUInt128<HR, LR>& rhs)
+{
+ return (lhs.high == rhs.high) && (lhs.low == rhs.low);
+}
+
+template <typename HL, typename LL, typename HR, typename LR>
+EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
+bool operator != (const TensorUInt128<HL, LL>& lhs, const TensorUInt128<HR, LR>& rhs)
+{
+ return (lhs.high != rhs.high) || (lhs.low != rhs.low);
+}
+
+template <typename HL, typename LL, typename HR, typename LR>
+EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
+bool operator >= (const TensorUInt128<HL, LL>& lhs, const TensorUInt128<HR, LR>& rhs)
+{
+ if (lhs.high != rhs.high) {
+ return lhs.high > rhs.high;
+ }
+ return lhs.low >= rhs.low;
+}
+
+template <typename HL, typename LL, typename HR, typename LR>
+EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
+bool operator < (const TensorUInt128<HL, LL>& lhs, const TensorUInt128<HR, LR>& rhs)
+{
+ if (lhs.high != rhs.high) {
+ return lhs.high < rhs.high;
+ }
+ return lhs.low < rhs.low;
+}
+
+template <typename HL, typename LL, typename HR, typename LR>
+EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
+TensorUInt128<uint64_t, uint64_t> operator + (const TensorUInt128<HL, LL>& lhs, const TensorUInt128<HR, LR>& rhs)
+{
+ TensorUInt128<uint64_t, uint64_t> result(lhs.high + rhs.high, lhs.low + rhs.low);
+ if (result.low < rhs.low) {
+ result.high += 1;
+ }
+ return result;
+}
+
+template <typename HL, typename LL, typename HR, typename LR>
+EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
+TensorUInt128<uint64_t, uint64_t> operator - (const TensorUInt128<HL, LL>& lhs, const TensorUInt128<HR, LR>& rhs)
+{
+ TensorUInt128<uint64_t, uint64_t> result(lhs.high - rhs.high, lhs.low - rhs.low);
+ if (result.low > lhs.low) {
+ result.high -= 1;
+ }
+ return result;
+}
+
+
+template <typename HL, typename LL, typename HR, typename LR>
+static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+TensorUInt128<uint64_t, uint64_t> operator * (const TensorUInt128<HL, LL>& lhs, const TensorUInt128<HR, LR>& rhs)
+{
+ // Split each 128-bit integer into 4 32-bit integers, and then do the
+ // multiplications by hand as follow:
+ // lhs a b c d
+ // rhs e f g h
+ // -----------
+ // ah bh ch dh
+ // bg cg dg
+ // cf df
+ // de
+ // The result is stored in 2 64bit integers, high and low.
+
+ const uint64_t LOW = 0x00000000FFFFFFFFLL;
+ const uint64_t HIGH = 0xFFFFFFFF00000000LL;
+
+ uint64_t d = lhs.low & LOW;
+ uint64_t c = (lhs.low & HIGH) >> 32LL;
+ uint64_t b = lhs.high & LOW;
+ uint64_t a = (lhs.high & HIGH) >> 32LL;
+
+ uint64_t h = rhs.low & LOW;
+ uint64_t g = (rhs.low & HIGH) >> 32LL;
+ uint64_t f = rhs.high & LOW;
+ uint64_t e = (rhs.high & HIGH) >> 32LL;
+
+ // Compute the low 32 bits of low
+ uint64_t acc = d * h;
+ uint64_t low = acc & LOW;
+ // Compute the high 32 bits of low. Add a carry every time we wrap around
+ acc >>= 32LL;
+ uint64_t carry = 0;
+ uint64_t acc2 = acc + c * h;
+ if (acc2 < acc) {
+ carry++;
+ }
+ acc = acc2 + d * g;
+ if (acc < acc2) {
+ carry++;
+ }
+ low |= (acc << 32LL);
+
+ // Carry forward the high bits of acc to initiate the computation of the
+ // low 32 bits of high
+ acc2 = (acc >> 32LL) | (carry << 32LL);
+ carry = 0;
+
+ acc = acc2 + b * h;
+ if (acc < acc2) {
+ carry++;
+ }
+ acc2 = acc + c * g;
+ if (acc2 < acc) {
+ carry++;
+ }
+ acc = acc2 + d * f;
+ if (acc < acc2) {
+ carry++;
+ }
+ uint64_t high = acc & LOW;
+
+ // Start to compute the high 32 bits of high.
+ acc2 = (acc >> 32LL) | (carry << 32LL);
+
+ acc = acc2 + a * h;
+ acc2 = acc + b * g;
+ acc = acc2 + c * f;
+ acc2 = acc + d * e;
+ high |= (acc2 << 32LL);
+
+ return TensorUInt128<uint64_t, uint64_t>(high, low);
+}
+
+template <typename HL, typename LL, typename HR, typename LR>
+static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+TensorUInt128<uint64_t, uint64_t> operator / (const TensorUInt128<HL, LL>& lhs, const TensorUInt128<HR, LR>& rhs)
+{
+ if (rhs == TensorUInt128<static_val<0>, static_val<1> >(1)) {
+ return TensorUInt128<uint64_t, uint64_t>(lhs.high, lhs.low);
+ } else if (lhs < rhs) {
+ return TensorUInt128<uint64_t, uint64_t>(0);
+ } else {
+ // calculate the biggest power of 2 times rhs that's less than or equal to lhs
+ TensorUInt128<uint64_t, uint64_t> power2(1);
+ TensorUInt128<uint64_t, uint64_t> d(rhs);
+ TensorUInt128<uint64_t, uint64_t> tmp(lhs - d);
+ while (lhs >= d) {
+ tmp = tmp - d;
+ d = d + d;
+ power2 = power2 + power2;
+ }
+
+ tmp = TensorUInt128<uint64_t, uint64_t>(lhs.high, lhs.low);
+ TensorUInt128<uint64_t, uint64_t> result(0);
+ while (power2 != TensorUInt128<static_val<0>, static_val<0> >(0)) {
+ if (tmp >= d) {
+ tmp = tmp - d;
+ result = result + power2;
+ }
+ // Shift right
+ power2 = TensorUInt128<uint64_t, uint64_t>(power2.high >> 1, (power2.low >> 1) | (power2.high << 63));
+ d = TensorUInt128<uint64_t, uint64_t>(d.high >> 1, (d.low >> 1) | (d.high << 63));
+ }
+
+ return result;
+ }
+}
+
+
+} // namespace internal
+} // namespace Eigen
+
+
+#endif // EIGEN_CXX11_TENSOR_TENSOR_UINT128_H
diff --git a/unsupported/Eigen/CXX11/src/Tensor/TensorVolumePatch.h b/unsupported/Eigen/CXX11/src/Tensor/TensorVolumePatch.h
new file mode 100644
index 0000000..3523a94
--- /dev/null
+++ b/unsupported/Eigen/CXX11/src/Tensor/TensorVolumePatch.h
@@ -0,0 +1,630 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+
+#ifndef EIGEN_CXX11_TENSOR_TENSOR_VOLUME_PATCH_H
+#define EIGEN_CXX11_TENSOR_TENSOR_VOLUME_PATCH_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+/** \class TensorVolumePatch
+ * \ingroup CXX11_Tensor_Module
+ *
+ * \brief Patch extraction specialized for processing of volumetric data.
+ * This assumes that the input has a least 4 dimensions ordered as follows:
+ * - channels
+ * - planes
+ * - rows
+ * - columns
+ * - (optional) additional dimensions such as time or batch size.
+ * Calling the volume patch code with patch_planes, patch_rows, and patch_cols
+ * is equivalent to calling the regular patch extraction code with parameters
+ * d, patch_planes, patch_rows, patch_cols, and 1 for all the additional
+ * dimensions.
+ */
+namespace internal {
+
+template<DenseIndex Planes, DenseIndex Rows, DenseIndex Cols, typename XprType>
+struct traits<TensorVolumePatchOp<Planes, Rows, Cols, XprType> > : public traits<XprType>
+{
+ typedef std::remove_const_t<typename XprType::Scalar> Scalar;
+ typedef traits<XprType> XprTraits;
+ typedef typename XprTraits::StorageKind StorageKind;
+ typedef typename XprTraits::Index Index;
+ typedef typename XprType::Nested Nested;
+ typedef std::remove_reference_t<Nested> Nested_;
+ static constexpr int NumDimensions = XprTraits::NumDimensions + 1;
+ static constexpr int Layout = XprTraits::Layout;
+ typedef typename XprTraits::PointerType PointerType;
+
+};
+
+template<DenseIndex Planes, DenseIndex Rows, DenseIndex Cols, typename XprType>
+struct eval<TensorVolumePatchOp<Planes, Rows, Cols, XprType>, Eigen::Dense>
+{
+ typedef const TensorVolumePatchOp<Planes, Rows, Cols, XprType>& type;
+};
+
+template<DenseIndex Planes, DenseIndex Rows, DenseIndex Cols, typename XprType>
+struct nested<TensorVolumePatchOp<Planes, Rows, Cols, XprType>, 1, typename eval<TensorVolumePatchOp<Planes, Rows, Cols, XprType> >::type>
+{
+ typedef TensorVolumePatchOp<Planes, Rows, Cols, XprType> type;
+};
+
+} // end namespace internal
+
+template<DenseIndex Planes, DenseIndex Rows, DenseIndex Cols, typename XprType>
+class TensorVolumePatchOp : public TensorBase<TensorVolumePatchOp<Planes, Rows, Cols, XprType>, ReadOnlyAccessors>
+{
+ public:
+ typedef typename Eigen::internal::traits<TensorVolumePatchOp>::Scalar Scalar;
+ typedef typename Eigen::NumTraits<Scalar>::Real RealScalar;
+ typedef typename XprType::CoeffReturnType CoeffReturnType;
+ typedef typename Eigen::internal::nested<TensorVolumePatchOp>::type Nested;
+ typedef typename Eigen::internal::traits<TensorVolumePatchOp>::StorageKind StorageKind;
+ typedef typename Eigen::internal::traits<TensorVolumePatchOp>::Index Index;
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorVolumePatchOp(const XprType& expr, DenseIndex patch_planes, DenseIndex patch_rows, DenseIndex patch_cols,
+ DenseIndex plane_strides, DenseIndex row_strides, DenseIndex col_strides,
+ DenseIndex in_plane_strides, DenseIndex in_row_strides, DenseIndex in_col_strides,
+ DenseIndex plane_inflate_strides, DenseIndex row_inflate_strides, DenseIndex col_inflate_strides,
+ PaddingType padding_type, Scalar padding_value)
+ : m_xpr(expr), m_patch_planes(patch_planes), m_patch_rows(patch_rows), m_patch_cols(patch_cols),
+ m_plane_strides(plane_strides), m_row_strides(row_strides), m_col_strides(col_strides),
+ m_in_plane_strides(in_plane_strides), m_in_row_strides(in_row_strides), m_in_col_strides(in_col_strides),
+ m_plane_inflate_strides(plane_inflate_strides), m_row_inflate_strides(row_inflate_strides), m_col_inflate_strides(col_inflate_strides),
+ m_padding_explicit(false), m_padding_top_z(0), m_padding_bottom_z(0), m_padding_top(0), m_padding_bottom(0), m_padding_left(0), m_padding_right(0),
+ m_padding_type(padding_type), m_padding_value(padding_value) {}
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorVolumePatchOp(const XprType& expr, DenseIndex patch_planes, DenseIndex patch_rows, DenseIndex patch_cols,
+ DenseIndex plane_strides, DenseIndex row_strides, DenseIndex col_strides,
+ DenseIndex in_plane_strides, DenseIndex in_row_strides, DenseIndex in_col_strides,
+ DenseIndex plane_inflate_strides, DenseIndex row_inflate_strides, DenseIndex col_inflate_strides,
+ DenseIndex padding_top_z, DenseIndex padding_bottom_z,
+ DenseIndex padding_top, DenseIndex padding_bottom,
+ DenseIndex padding_left, DenseIndex padding_right,
+ Scalar padding_value)
+ : m_xpr(expr), m_patch_planes(patch_planes), m_patch_rows(patch_rows), m_patch_cols(patch_cols),
+ m_plane_strides(plane_strides), m_row_strides(row_strides), m_col_strides(col_strides),
+ m_in_plane_strides(in_plane_strides), m_in_row_strides(in_row_strides), m_in_col_strides(in_col_strides),
+ m_plane_inflate_strides(plane_inflate_strides), m_row_inflate_strides(row_inflate_strides), m_col_inflate_strides(col_inflate_strides),
+ m_padding_explicit(true), m_padding_top_z(padding_top_z), m_padding_bottom_z(padding_bottom_z), m_padding_top(padding_top), m_padding_bottom(padding_bottom),
+ m_padding_left(padding_left), m_padding_right(padding_right),
+ m_padding_type(PADDING_VALID), m_padding_value(padding_value) {}
+
+ EIGEN_DEVICE_FUNC
+ DenseIndex patch_planes() const { return m_patch_planes; }
+ EIGEN_DEVICE_FUNC
+ DenseIndex patch_rows() const { return m_patch_rows; }
+ EIGEN_DEVICE_FUNC
+ DenseIndex patch_cols() const { return m_patch_cols; }
+ EIGEN_DEVICE_FUNC
+ DenseIndex plane_strides() const { return m_plane_strides; }
+ EIGEN_DEVICE_FUNC
+ DenseIndex row_strides() const { return m_row_strides; }
+ EIGEN_DEVICE_FUNC
+ DenseIndex col_strides() const { return m_col_strides; }
+ EIGEN_DEVICE_FUNC
+ DenseIndex in_plane_strides() const { return m_in_plane_strides; }
+ EIGEN_DEVICE_FUNC
+ DenseIndex in_row_strides() const { return m_in_row_strides; }
+ EIGEN_DEVICE_FUNC
+ DenseIndex in_col_strides() const { return m_in_col_strides; }
+ EIGEN_DEVICE_FUNC
+ DenseIndex plane_inflate_strides() const { return m_plane_inflate_strides; }
+ EIGEN_DEVICE_FUNC
+ DenseIndex row_inflate_strides() const { return m_row_inflate_strides; }
+ EIGEN_DEVICE_FUNC
+ DenseIndex col_inflate_strides() const { return m_col_inflate_strides; }
+ EIGEN_DEVICE_FUNC
+ bool padding_explicit() const { return m_padding_explicit; }
+ EIGEN_DEVICE_FUNC
+ DenseIndex padding_top_z() const { return m_padding_top_z; }
+ EIGEN_DEVICE_FUNC
+ DenseIndex padding_bottom_z() const { return m_padding_bottom_z; }
+ EIGEN_DEVICE_FUNC
+ DenseIndex padding_top() const { return m_padding_top; }
+ EIGEN_DEVICE_FUNC
+ DenseIndex padding_bottom() const { return m_padding_bottom; }
+ EIGEN_DEVICE_FUNC
+ DenseIndex padding_left() const { return m_padding_left; }
+ EIGEN_DEVICE_FUNC
+ DenseIndex padding_right() const { return m_padding_right; }
+ EIGEN_DEVICE_FUNC
+ PaddingType padding_type() const { return m_padding_type; }
+ EIGEN_DEVICE_FUNC
+ Scalar padding_value() const { return m_padding_value; }
+
+ EIGEN_DEVICE_FUNC
+ const internal::remove_all_t<typename XprType::Nested>&
+ expression() const { return m_xpr; }
+
+ protected:
+ typename XprType::Nested m_xpr;
+ const DenseIndex m_patch_planes;
+ const DenseIndex m_patch_rows;
+ const DenseIndex m_patch_cols;
+ const DenseIndex m_plane_strides;
+ const DenseIndex m_row_strides;
+ const DenseIndex m_col_strides;
+ const DenseIndex m_in_plane_strides;
+ const DenseIndex m_in_row_strides;
+ const DenseIndex m_in_col_strides;
+ const DenseIndex m_plane_inflate_strides;
+ const DenseIndex m_row_inflate_strides;
+ const DenseIndex m_col_inflate_strides;
+ const bool m_padding_explicit;
+ const DenseIndex m_padding_top_z;
+ const DenseIndex m_padding_bottom_z;
+ const DenseIndex m_padding_top;
+ const DenseIndex m_padding_bottom;
+ const DenseIndex m_padding_left;
+ const DenseIndex m_padding_right;
+ const PaddingType m_padding_type;
+ const Scalar m_padding_value;
+};
+
+
+// Eval as rvalue
+template<DenseIndex Planes, DenseIndex Rows, DenseIndex Cols, typename ArgType, typename Device>
+struct TensorEvaluator<const TensorVolumePatchOp<Planes, Rows, Cols, ArgType>, Device>
+{
+ typedef TensorVolumePatchOp<Planes, Rows, Cols, ArgType> XprType;
+ typedef typename XprType::Index Index;
+ static constexpr int NumInputDims = internal::array_size<typename TensorEvaluator<ArgType, Device>::Dimensions>::value;
+ static constexpr int NumDims = NumInputDims + 1;
+ typedef DSizes<Index, NumDims> Dimensions;
+ typedef std::remove_const_t<typename XprType::Scalar> Scalar;
+ typedef typename XprType::CoeffReturnType CoeffReturnType;
+ typedef typename PacketType<CoeffReturnType, Device>::type PacketReturnType;
+ static constexpr int PacketSize = PacketType<CoeffReturnType, Device>::size;
+ typedef StorageMemory<CoeffReturnType, Device> Storage;
+ typedef typename Storage::Type EvaluatorPointerType;
+
+ static constexpr int Layout = TensorEvaluator<ArgType, Device>::Layout;
+ enum {
+ IsAligned = false,
+ PacketAccess = TensorEvaluator<ArgType, Device>::PacketAccess,
+ BlockAccess = false,
+ PreferBlockAccess = TensorEvaluator<ArgType, Device>::PreferBlockAccess,
+ CoordAccess = false,
+ RawAccess = false
+ };
+
+ //===- Tensor block evaluation strategy (see TensorBlock.h) -------------===//
+ typedef internal::TensorBlockNotImplemented TensorBlock;
+ //===--------------------------------------------------------------------===//
+
+ EIGEN_STRONG_INLINE TensorEvaluator(const XprType& op, const Device& device) :
+ m_impl(op.expression(), device)
+ {
+ EIGEN_STATIC_ASSERT((NumDims >= 5), YOU_MADE_A_PROGRAMMING_MISTAKE);
+
+ m_paddingValue = op.padding_value();
+
+ const typename TensorEvaluator<ArgType, Device>::Dimensions& input_dims = m_impl.dimensions();
+
+ // Cache a few variables.
+ if (static_cast<int>(Layout) == static_cast<int>(ColMajor)) {
+ m_inputDepth = input_dims[0];
+ m_inputPlanes = input_dims[1];
+ m_inputRows = input_dims[2];
+ m_inputCols = input_dims[3];
+ } else {
+ m_inputDepth = input_dims[NumInputDims-1];
+ m_inputPlanes = input_dims[NumInputDims-2];
+ m_inputRows = input_dims[NumInputDims-3];
+ m_inputCols = input_dims[NumInputDims-4];
+ }
+
+ m_plane_strides = op.plane_strides();
+ m_row_strides = op.row_strides();
+ m_col_strides = op.col_strides();
+
+ // Input strides and effective input/patch size
+ m_in_plane_strides = op.in_plane_strides();
+ m_in_row_strides = op.in_row_strides();
+ m_in_col_strides = op.in_col_strides();
+ m_plane_inflate_strides = op.plane_inflate_strides();
+ m_row_inflate_strides = op.row_inflate_strides();
+ m_col_inflate_strides = op.col_inflate_strides();
+
+ // The "effective" spatial size after inflating data with zeros.
+ m_input_planes_eff = (m_inputPlanes - 1) * m_plane_inflate_strides + 1;
+ m_input_rows_eff = (m_inputRows - 1) * m_row_inflate_strides + 1;
+ m_input_cols_eff = (m_inputCols - 1) * m_col_inflate_strides + 1;
+ m_patch_planes_eff = op.patch_planes() + (op.patch_planes() - 1) * (m_in_plane_strides - 1);
+ m_patch_rows_eff = op.patch_rows() + (op.patch_rows() - 1) * (m_in_row_strides - 1);
+ m_patch_cols_eff = op.patch_cols() + (op.patch_cols() - 1) * (m_in_col_strides - 1);
+
+ if (op.padding_explicit()) {
+ m_outputPlanes = numext::ceil((m_input_planes_eff + op.padding_top_z() + op.padding_bottom_z() - m_patch_planes_eff + 1.f) / static_cast<float>(m_plane_strides));
+ m_outputRows = numext::ceil((m_input_rows_eff + op.padding_top() + op.padding_bottom() - m_patch_rows_eff + 1.f) / static_cast<float>(m_row_strides));
+ m_outputCols = numext::ceil((m_input_cols_eff + op.padding_left() + op.padding_right() - m_patch_cols_eff + 1.f) / static_cast<float>(m_col_strides));
+ m_planePaddingTop = op.padding_top_z();
+ m_rowPaddingTop = op.padding_top();
+ m_colPaddingLeft = op.padding_left();
+ } else {
+ // Computing padding from the type
+ switch (op.padding_type()) {
+ case PADDING_VALID:
+ m_outputPlanes = numext::ceil((m_input_planes_eff - m_patch_planes_eff + 1.f) / static_cast<float>(m_plane_strides));
+ m_outputRows = numext::ceil((m_input_rows_eff - m_patch_rows_eff + 1.f) / static_cast<float>(m_row_strides));
+ m_outputCols = numext::ceil((m_input_cols_eff - m_patch_cols_eff + 1.f) / static_cast<float>(m_col_strides));
+ m_planePaddingTop = 0;
+ m_rowPaddingTop = 0;
+ m_colPaddingLeft = 0;
+ break;
+ case PADDING_SAME: {
+ m_outputPlanes = numext::ceil(m_input_planes_eff / static_cast<float>(m_plane_strides));
+ m_outputRows = numext::ceil(m_input_rows_eff / static_cast<float>(m_row_strides));
+ m_outputCols = numext::ceil(m_input_cols_eff / static_cast<float>(m_col_strides));
+ const Index dz = (m_outputPlanes - 1) * m_plane_strides + m_patch_planes_eff - m_input_planes_eff;
+ const Index dy = (m_outputRows - 1) * m_row_strides + m_patch_rows_eff - m_input_rows_eff;
+ const Index dx = (m_outputCols - 1) * m_col_strides + m_patch_cols_eff - m_input_cols_eff;
+ m_planePaddingTop = dz / 2;
+ m_rowPaddingTop = dy / 2;
+ m_colPaddingLeft = dx / 2;
+ break;
+ }
+ default:
+ eigen_assert(false && "unexpected padding");
+ }
+ }
+ eigen_assert(m_outputRows > 0);
+ eigen_assert(m_outputCols > 0);
+ eigen_assert(m_outputPlanes > 0);
+
+ // Dimensions for result of extraction.
+ if (static_cast<int>(Layout) == static_cast<int>(ColMajor)) {
+ // ColMajor
+ // 0: depth
+ // 1: patch_planes
+ // 2: patch_rows
+ // 3: patch_cols
+ // 4: number of patches
+ // 5 and beyond: anything else (such as batch).
+ m_dimensions[0] = input_dims[0];
+ m_dimensions[1] = op.patch_planes();
+ m_dimensions[2] = op.patch_rows();
+ m_dimensions[3] = op.patch_cols();
+ m_dimensions[4] = m_outputPlanes * m_outputRows * m_outputCols;
+ for (int i = 5; i < NumDims; ++i) {
+ m_dimensions[i] = input_dims[i-1];
+ }
+ } else {
+ // RowMajor
+ // NumDims-1: depth
+ // NumDims-2: patch_planes
+ // NumDims-3: patch_rows
+ // NumDims-4: patch_cols
+ // NumDims-5: number of patches
+ // NumDims-6 and beyond: anything else (such as batch).
+ m_dimensions[NumDims-1] = input_dims[NumInputDims-1];
+ m_dimensions[NumDims-2] = op.patch_planes();
+ m_dimensions[NumDims-3] = op.patch_rows();
+ m_dimensions[NumDims-4] = op.patch_cols();
+ m_dimensions[NumDims-5] = m_outputPlanes * m_outputRows * m_outputCols;
+ for (int i = NumDims-6; i >= 0; --i) {
+ m_dimensions[i] = input_dims[i];
+ }
+ }
+
+ // Strides for the output tensor.
+ if (static_cast<int>(Layout) == static_cast<int>(ColMajor)) {
+ m_rowStride = m_dimensions[1];
+ m_colStride = m_dimensions[2] * m_rowStride;
+ m_patchStride = m_colStride * m_dimensions[3] * m_dimensions[0];
+ m_otherStride = m_patchStride * m_dimensions[4];
+ } else {
+ m_rowStride = m_dimensions[NumDims-2];
+ m_colStride = m_dimensions[NumDims-3] * m_rowStride;
+ m_patchStride = m_colStride * m_dimensions[NumDims-4] * m_dimensions[NumDims-1];
+ m_otherStride = m_patchStride * m_dimensions[NumDims-5];
+ }
+
+ // Strides for navigating through the input tensor.
+ m_planeInputStride = m_inputDepth;
+ m_rowInputStride = m_inputDepth * m_inputPlanes;
+ m_colInputStride = m_inputDepth * m_inputRows * m_inputPlanes;
+ m_otherInputStride = m_inputDepth * m_inputRows * m_inputCols * m_inputPlanes;
+
+ m_outputPlanesRows = m_outputPlanes * m_outputRows;
+
+ // Fast representations of different variables.
+ m_fastOtherStride = internal::TensorIntDivisor<Index>(m_otherStride);
+
+ m_fastPatchStride = internal::TensorIntDivisor<Index>(m_patchStride);
+ m_fastColStride = internal::TensorIntDivisor<Index>(m_colStride);
+ m_fastRowStride = internal::TensorIntDivisor<Index>(m_rowStride);
+ m_fastInputRowStride = internal::TensorIntDivisor<Index>(m_row_inflate_strides);
+ m_fastInputColStride = internal::TensorIntDivisor<Index>(m_col_inflate_strides);
+ m_fastInputPlaneStride = internal::TensorIntDivisor<Index>(m_plane_inflate_strides);
+ m_fastInputColsEff = internal::TensorIntDivisor<Index>(m_input_cols_eff);
+ m_fastOutputPlanes = internal::TensorIntDivisor<Index>(m_outputPlanes);
+ m_fastOutputPlanesRows = internal::TensorIntDivisor<Index>(m_outputPlanesRows);
+
+ if (static_cast<int>(Layout) == static_cast<int>(ColMajor)) {
+ m_fastOutputDepth = internal::TensorIntDivisor<Index>(m_dimensions[0]);
+ } else {
+ m_fastOutputDepth = internal::TensorIntDivisor<Index>(m_dimensions[NumDims-1]);
+ }
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Dimensions& dimensions() const { return m_dimensions; }
+
+ EIGEN_STRONG_INLINE bool evalSubExprsIfNeeded(EvaluatorPointerType /*data*/) {
+ m_impl.evalSubExprsIfNeeded(NULL);
+ return true;
+ }
+
+ EIGEN_STRONG_INLINE void cleanup() {
+ m_impl.cleanup();
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE CoeffReturnType coeff(Index index) const
+ {
+ // Patch index corresponding to the passed in index.
+ const Index patchIndex = index / m_fastPatchStride;
+
+ // Spatial offset within the patch. This has to be translated into 3D
+ // coordinates within the patch.
+ const Index patchOffset = (index - patchIndex * m_patchStride) / m_fastOutputDepth;
+
+ // Batch, etc.
+ const Index otherIndex = (NumDims == 5) ? 0 : index / m_fastOtherStride;
+ const Index patch3DIndex = (NumDims == 5) ? patchIndex : (index - otherIndex * m_otherStride) / m_fastPatchStride;
+
+ // Calculate column index in the input original tensor.
+ const Index colIndex = patch3DIndex / m_fastOutputPlanesRows;
+ const Index colOffset = patchOffset / m_fastColStride;
+ const Index inputCol = colIndex * m_col_strides + colOffset * m_in_col_strides - m_colPaddingLeft;
+ const Index origInputCol = (m_col_inflate_strides == 1) ? inputCol : ((inputCol >= 0) ? (inputCol / m_fastInputColStride) : 0);
+ if (inputCol < 0 || inputCol >= m_input_cols_eff ||
+ ((m_col_inflate_strides != 1) && (inputCol != origInputCol * m_col_inflate_strides))) {
+ return Scalar(m_paddingValue);
+ }
+
+ // Calculate row index in the original input tensor.
+ const Index rowIndex = (patch3DIndex - colIndex * m_outputPlanesRows) / m_fastOutputPlanes;
+ const Index rowOffset = (patchOffset - colOffset * m_colStride) / m_fastRowStride;
+ const Index inputRow = rowIndex * m_row_strides + rowOffset * m_in_row_strides - m_rowPaddingTop;
+ const Index origInputRow = (m_row_inflate_strides == 1) ? inputRow : ((inputRow >= 0) ? (inputRow / m_fastInputRowStride) : 0);
+ if (inputRow < 0 || inputRow >= m_input_rows_eff ||
+ ((m_row_inflate_strides != 1) && (inputRow != origInputRow * m_row_inflate_strides))) {
+ return Scalar(m_paddingValue);
+ }
+
+ // Calculate plane index in the original input tensor.
+ const Index planeIndex = (patch3DIndex - m_outputPlanes * (colIndex * m_outputRows + rowIndex));
+ const Index planeOffset = patchOffset - colOffset * m_colStride - rowOffset * m_rowStride;
+ const Index inputPlane = planeIndex * m_plane_strides + planeOffset * m_in_plane_strides - m_planePaddingTop;
+ const Index origInputPlane = (m_plane_inflate_strides == 1) ? inputPlane : ((inputPlane >= 0) ? (inputPlane / m_fastInputPlaneStride) : 0);
+ if (inputPlane < 0 || inputPlane >= m_input_planes_eff ||
+ ((m_plane_inflate_strides != 1) && (inputPlane != origInputPlane * m_plane_inflate_strides))) {
+ return Scalar(m_paddingValue);
+ }
+
+ const int depth_index = static_cast<int>(Layout) == static_cast<int>(ColMajor) ? 0 : NumDims - 1;
+ const Index depth = index - (index / m_fastOutputDepth) * m_dimensions[depth_index];
+
+ const Index inputIndex = depth +
+ origInputRow * m_rowInputStride +
+ origInputCol * m_colInputStride +
+ origInputPlane * m_planeInputStride +
+ otherIndex * m_otherInputStride;
+
+ return m_impl.coeff(inputIndex);
+ }
+
+ template<int LoadMode>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE PacketReturnType packet(Index index) const
+ {
+ eigen_assert(index+PacketSize-1 < dimensions().TotalSize());
+
+ if (m_in_row_strides != 1 || m_in_col_strides != 1 || m_row_inflate_strides != 1 || m_col_inflate_strides != 1 ||
+ m_in_plane_strides != 1 || m_plane_inflate_strides != 1) {
+ return packetWithPossibleZero(index);
+ }
+
+ const Index indices[2] = {index, index + PacketSize - 1};
+ const Index patchIndex = indices[0] / m_fastPatchStride;
+ if (patchIndex != indices[1] / m_fastPatchStride) {
+ return packetWithPossibleZero(index);
+ }
+ const Index otherIndex = (NumDims == 5) ? 0 : indices[0] / m_fastOtherStride;
+ eigen_assert(otherIndex == indices[1] / m_fastOtherStride);
+
+ // Find the offset of the element wrt the location of the first element.
+ const Index patchOffsets[2] = {(indices[0] - patchIndex * m_patchStride) / m_fastOutputDepth,
+ (indices[1] - patchIndex * m_patchStride) / m_fastOutputDepth};
+
+ const Index patch3DIndex = (NumDims == 5) ? patchIndex : (indices[0] - otherIndex * m_otherStride) / m_fastPatchStride;
+ eigen_assert(patch3DIndex == (indices[1] - otherIndex * m_otherStride) / m_fastPatchStride);
+
+ const Index colIndex = patch3DIndex / m_fastOutputPlanesRows;
+ const Index colOffsets[2] = {
+ patchOffsets[0] / m_fastColStride,
+ patchOffsets[1] / m_fastColStride};
+
+ // Calculate col indices in the original input tensor.
+ const Index inputCols[2] = {
+ colIndex * m_col_strides + colOffsets[0] - m_colPaddingLeft,
+ colIndex * m_col_strides + colOffsets[1] - m_colPaddingLeft};
+ if (inputCols[1] < 0 || inputCols[0] >= m_inputCols) {
+ return internal::pset1<PacketReturnType>(Scalar(m_paddingValue));
+ }
+
+ if (inputCols[0] != inputCols[1]) {
+ return packetWithPossibleZero(index);
+ }
+
+ const Index rowIndex = (patch3DIndex - colIndex * m_outputPlanesRows) / m_fastOutputPlanes;
+ const Index rowOffsets[2] = {
+ (patchOffsets[0] - colOffsets[0] * m_colStride) / m_fastRowStride,
+ (patchOffsets[1] - colOffsets[1] * m_colStride) / m_fastRowStride};
+ eigen_assert(rowOffsets[0] <= rowOffsets[1]);
+ // Calculate col indices in the original input tensor.
+ const Index inputRows[2] = {
+ rowIndex * m_row_strides + rowOffsets[0] - m_rowPaddingTop,
+ rowIndex * m_row_strides + rowOffsets[1] - m_rowPaddingTop};
+
+ if (inputRows[1] < 0 || inputRows[0] >= m_inputRows) {
+ return internal::pset1<PacketReturnType>(Scalar(m_paddingValue));
+ }
+
+ if (inputRows[0] != inputRows[1]) {
+ return packetWithPossibleZero(index);
+ }
+
+ const Index planeIndex = (patch3DIndex - m_outputPlanes * (colIndex * m_outputRows + rowIndex));
+ const Index planeOffsets[2] = {
+ patchOffsets[0] - colOffsets[0] * m_colStride - rowOffsets[0] * m_rowStride,
+ patchOffsets[1] - colOffsets[1] * m_colStride - rowOffsets[1] * m_rowStride};
+ eigen_assert(planeOffsets[0] <= planeOffsets[1]);
+ const Index inputPlanes[2] = {
+ planeIndex * m_plane_strides + planeOffsets[0] - m_planePaddingTop,
+ planeIndex * m_plane_strides + planeOffsets[1] - m_planePaddingTop};
+
+ if (inputPlanes[1] < 0 || inputPlanes[0] >= m_inputPlanes) {
+ return internal::pset1<PacketReturnType>(Scalar(m_paddingValue));
+ }
+
+ if (inputPlanes[0] >= 0 && inputPlanes[1] < m_inputPlanes) {
+ // no padding
+ const int depth_index = static_cast<int>(Layout) == static_cast<int>(ColMajor) ? 0 : NumDims - 1;
+ const Index depth = index - (index / m_fastOutputDepth) * m_dimensions[depth_index];
+ const Index inputIndex = depth +
+ inputRows[0] * m_rowInputStride +
+ inputCols[0] * m_colInputStride +
+ m_planeInputStride * inputPlanes[0] +
+ otherIndex * m_otherInputStride;
+ return m_impl.template packet<Unaligned>(inputIndex);
+ }
+
+ return packetWithPossibleZero(index);
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorOpCost
+ costPerCoeff(bool vectorized) const {
+ const double compute_cost =
+ 10 * TensorOpCost::DivCost<Index>() + 21 * TensorOpCost::MulCost<Index>() +
+ 8 * TensorOpCost::AddCost<Index>();
+ return TensorOpCost(0, 0, compute_cost, vectorized, PacketSize);
+ }
+
+ EIGEN_DEVICE_FUNC EvaluatorPointerType data() const { return NULL; }
+
+ const TensorEvaluator<ArgType, Device>& impl() const { return m_impl; }
+
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Index planePaddingTop() const { return m_planePaddingTop; }
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Index rowPaddingTop() const { return m_rowPaddingTop; }
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Index colPaddingLeft() const { return m_colPaddingLeft; }
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Index outputPlanes() const { return m_outputPlanes; }
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Index outputRows() const { return m_outputRows; }
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Index outputCols() const { return m_outputCols; }
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Index userPlaneStride() const { return m_plane_strides; }
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Index userRowStride() const { return m_row_strides; }
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Index userColStride() const { return m_col_strides; }
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Index userInPlaneStride() const { return m_in_plane_strides; }
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Index userInRowStride() const { return m_in_row_strides; }
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Index userInColStride() const { return m_in_col_strides; }
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Index planeInflateStride() const { return m_plane_inflate_strides; }
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Index rowInflateStride() const { return m_row_inflate_strides; }
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Index colInflateStride() const { return m_col_inflate_strides; }
+
+#ifdef EIGEN_USE_SYCL
+ // binding placeholder accessors to a command group handler for SYCL
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void bind(cl::sycl::handler &cgh) const {
+ m_impl.bind(cgh);
+ }
+#endif
+ protected:
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE PacketReturnType packetWithPossibleZero(Index index) const
+ {
+ EIGEN_ALIGN_MAX std::remove_const_t<CoeffReturnType> values[PacketSize];
+ EIGEN_UNROLL_LOOP
+ for (int i = 0; i < PacketSize; ++i) {
+ values[i] = coeff(index+i);
+ }
+ PacketReturnType rslt = internal::pload<PacketReturnType>(values);
+ return rslt;
+ }
+
+ Dimensions m_dimensions;
+
+ // Parameters passed to the constructor.
+ Index m_plane_strides;
+ Index m_row_strides;
+ Index m_col_strides;
+
+ Index m_outputPlanes;
+ Index m_outputRows;
+ Index m_outputCols;
+
+ Index m_planePaddingTop;
+ Index m_rowPaddingTop;
+ Index m_colPaddingLeft;
+
+ Index m_in_plane_strides;
+ Index m_in_row_strides;
+ Index m_in_col_strides;
+
+ Index m_plane_inflate_strides;
+ Index m_row_inflate_strides;
+ Index m_col_inflate_strides;
+
+ // Cached input size.
+ Index m_inputDepth;
+ Index m_inputPlanes;
+ Index m_inputRows;
+ Index m_inputCols;
+
+ // Other cached variables.
+ Index m_outputPlanesRows;
+
+ // Effective input/patch post-inflation size.
+ Index m_input_planes_eff;
+ Index m_input_rows_eff;
+ Index m_input_cols_eff;
+ Index m_patch_planes_eff;
+ Index m_patch_rows_eff;
+ Index m_patch_cols_eff;
+
+ // Strides for the output tensor.
+ Index m_otherStride;
+ Index m_patchStride;
+ Index m_rowStride;
+ Index m_colStride;
+
+ // Strides for the input tensor.
+ Index m_planeInputStride;
+ Index m_rowInputStride;
+ Index m_colInputStride;
+ Index m_otherInputStride;
+
+ internal::TensorIntDivisor<Index> m_fastOtherStride;
+ internal::TensorIntDivisor<Index> m_fastPatchStride;
+ internal::TensorIntDivisor<Index> m_fastColStride;
+ internal::TensorIntDivisor<Index> m_fastRowStride;
+ internal::TensorIntDivisor<Index> m_fastInputPlaneStride;
+ internal::TensorIntDivisor<Index> m_fastInputRowStride;
+ internal::TensorIntDivisor<Index> m_fastInputColStride;
+ internal::TensorIntDivisor<Index> m_fastInputColsEff;
+ internal::TensorIntDivisor<Index> m_fastOutputPlanesRows;
+ internal::TensorIntDivisor<Index> m_fastOutputPlanes;
+ internal::TensorIntDivisor<Index> m_fastOutputDepth;
+
+ Scalar m_paddingValue;
+
+ TensorEvaluator<ArgType, Device> m_impl;
+
+
+};
+
+
+} // end namespace Eigen
+
+#endif // EIGEN_CXX11_TENSOR_TENSOR_VOLUME_PATCH_H
diff --git a/unsupported/Eigen/CXX11/src/TensorSymmetry/DynamicSymmetry.h b/unsupported/Eigen/CXX11/src/TensorSymmetry/DynamicSymmetry.h
new file mode 100644
index 0000000..200f588
--- /dev/null
+++ b/unsupported/Eigen/CXX11/src/TensorSymmetry/DynamicSymmetry.h
@@ -0,0 +1,295 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2013 Christian Seiler <christian@iwakd.de>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_CXX11_TENSORSYMMETRY_DYNAMICSYMMETRY_H
+#define EIGEN_CXX11_TENSORSYMMETRY_DYNAMICSYMMETRY_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+class DynamicSGroup
+{
+ public:
+ inline explicit DynamicSGroup() : m_numIndices(1), m_elements(), m_generators(), m_globalFlags(0) { m_elements.push_back(ge(Generator(0, 0, 0))); }
+ inline DynamicSGroup(const DynamicSGroup& o) : m_numIndices(o.m_numIndices), m_elements(o.m_elements), m_generators(o.m_generators), m_globalFlags(o.m_globalFlags) { }
+ inline DynamicSGroup(DynamicSGroup&& o) : m_numIndices(o.m_numIndices), m_elements(), m_generators(o.m_generators), m_globalFlags(o.m_globalFlags) { std::swap(m_elements, o.m_elements); }
+ inline DynamicSGroup& operator=(const DynamicSGroup& o) { m_numIndices = o.m_numIndices; m_elements = o.m_elements; m_generators = o.m_generators; m_globalFlags = o.m_globalFlags; return *this; }
+ inline DynamicSGroup& operator=(DynamicSGroup&& o) { m_numIndices = o.m_numIndices; std::swap(m_elements, o.m_elements); m_generators = o.m_generators; m_globalFlags = o.m_globalFlags; return *this; }
+
+ void add(int one, int two, int flags = 0);
+
+ template<typename Gen_>
+ inline void add(Gen_) { add(Gen_::One, Gen_::Two, Gen_::Flags); }
+ inline void addSymmetry(int one, int two) { add(one, two, 0); }
+ inline void addAntiSymmetry(int one, int two) { add(one, two, NegationFlag); }
+ inline void addHermiticity(int one, int two) { add(one, two, ConjugationFlag); }
+ inline void addAntiHermiticity(int one, int two) { add(one, two, NegationFlag | ConjugationFlag); }
+
+ template<typename Op, typename RV, typename Index, std::size_t N, typename... Args>
+ inline RV apply(const std::array<Index, N>& idx, RV initial, Args&&... args) const
+ {
+ eigen_assert(N >= m_numIndices && "Can only apply symmetry group to objects that have at least the required amount of indices.");
+ for (std::size_t i = 0; i < size(); i++)
+ initial = Op::run(h_permute(i, idx, typename internal::gen_numeric_list<int, N>::type()), m_elements[i].flags, initial, std::forward<Args>(args)...);
+ return initial;
+ }
+
+ template<typename Op, typename RV, typename Index, typename... Args>
+ inline RV apply(const std::vector<Index>& idx, RV initial, Args&&... args) const
+ {
+ eigen_assert(idx.size() >= m_numIndices && "Can only apply symmetry group to objects that have at least the required amount of indices.");
+ for (std::size_t i = 0; i < size(); i++)
+ initial = Op::run(h_permute(i, idx), m_elements[i].flags, initial, std::forward<Args>(args)...);
+ return initial;
+ }
+
+ inline int globalFlags() const { return m_globalFlags; }
+ inline std::size_t size() const { return m_elements.size(); }
+
+ template<typename Tensor_, typename... IndexTypes>
+ inline internal::tensor_symmetry_value_setter<Tensor_, DynamicSGroup> operator()(Tensor_& tensor, typename Tensor_::Index firstIndex, IndexTypes... otherIndices) const
+ {
+ static_assert(sizeof...(otherIndices) + 1 == Tensor_::NumIndices, "Number of indices used to access a tensor coefficient must be equal to the rank of the tensor.");
+ return operator()(tensor, std::array<typename Tensor_::Index, Tensor_::NumIndices>{{firstIndex, otherIndices...}});
+ }
+
+ template<typename Tensor_>
+ inline internal::tensor_symmetry_value_setter<Tensor_, DynamicSGroup> operator()(Tensor_& tensor, std::array<typename Tensor_::Index, Tensor_::NumIndices> const& indices) const
+ {
+ return internal::tensor_symmetry_value_setter<Tensor_, DynamicSGroup>(tensor, *this, indices);
+ }
+ private:
+ struct GroupElement {
+ std::vector<int> representation;
+ int flags;
+ bool isId() const
+ {
+ for (std::size_t i = 0; i < representation.size(); i++)
+ if (i != (size_t)representation[i])
+ return false;
+ return true;
+ }
+ };
+ struct Generator {
+ int one;
+ int two;
+ int flags;
+ constexpr inline Generator(int one_, int two_, int flags_) : one(one_), two(two_), flags(flags_) {}
+ };
+
+ std::size_t m_numIndices;
+ std::vector<GroupElement> m_elements;
+ std::vector<Generator> m_generators;
+ int m_globalFlags;
+
+ template<typename Index, std::size_t N, int... n>
+ inline std::array<Index, N> h_permute(std::size_t which, const std::array<Index, N>& idx, internal::numeric_list<int, n...>) const
+ {
+ return std::array<Index, N>{{ idx[n >= m_numIndices ? n : m_elements[which].representation[n]]... }};
+ }
+
+ template<typename Index>
+ inline std::vector<Index> h_permute(std::size_t which, std::vector<Index> idx) const
+ {
+ std::vector<Index> result;
+ result.reserve(idx.size());
+ for (auto k : m_elements[which].representation)
+ result.push_back(idx[k]);
+ for (std::size_t i = m_numIndices; i < idx.size(); i++)
+ result.push_back(idx[i]);
+ return result;
+ }
+
+ inline GroupElement ge(Generator const& g) const
+ {
+ GroupElement result;
+ result.representation.reserve(m_numIndices);
+ result.flags = g.flags;
+ for (std::size_t k = 0; k < m_numIndices; k++) {
+ if (k == (std::size_t)g.one)
+ result.representation.push_back(g.two);
+ else if (k == (std::size_t)g.two)
+ result.representation.push_back(g.one);
+ else
+ result.representation.push_back(int(k));
+ }
+ return result;
+ }
+
+ GroupElement mul(GroupElement, GroupElement) const;
+ inline GroupElement mul(Generator g1, GroupElement g2) const
+ {
+ return mul(ge(g1), g2);
+ }
+
+ inline GroupElement mul(GroupElement g1, Generator g2) const
+ {
+ return mul(g1, ge(g2));
+ }
+
+ inline GroupElement mul(Generator g1, Generator g2) const
+ {
+ return mul(ge(g1), ge(g2));
+ }
+
+ inline int findElement(GroupElement e) const
+ {
+ for (auto ee : m_elements) {
+ if (ee.representation == e.representation)
+ return ee.flags ^ e.flags;
+ }
+ return -1;
+ }
+
+ void updateGlobalFlags(int flagDiffOfSameGenerator);
+};
+
+// dynamic symmetry group that auto-adds the template parameters in the constructor
+template<typename... Gen>
+class DynamicSGroupFromTemplateArgs : public DynamicSGroup
+{
+ public:
+ inline DynamicSGroupFromTemplateArgs() : DynamicSGroup()
+ {
+ add_all(internal::type_list<Gen...>());
+ }
+ inline DynamicSGroupFromTemplateArgs(DynamicSGroupFromTemplateArgs const& other) : DynamicSGroup(other) { }
+ inline DynamicSGroupFromTemplateArgs(DynamicSGroupFromTemplateArgs&& other) : DynamicSGroup(other) { }
+ inline DynamicSGroupFromTemplateArgs<Gen...>& operator=(const DynamicSGroupFromTemplateArgs<Gen...>& o) { DynamicSGroup::operator=(o); return *this; }
+ inline DynamicSGroupFromTemplateArgs<Gen...>& operator=(DynamicSGroupFromTemplateArgs<Gen...>&& o) { DynamicSGroup::operator=(o); return *this; }
+
+ private:
+ template<typename Gen1, typename... GenNext>
+ inline void add_all(internal::type_list<Gen1, GenNext...>)
+ {
+ add(Gen1());
+ add_all(internal::type_list<GenNext...>());
+ }
+
+ inline void add_all(internal::type_list<>)
+ {
+ }
+};
+
+inline DynamicSGroup::GroupElement DynamicSGroup::mul(GroupElement g1, GroupElement g2) const
+{
+ eigen_internal_assert(g1.representation.size() == m_numIndices);
+ eigen_internal_assert(g2.representation.size() == m_numIndices);
+
+ GroupElement result;
+ result.representation.reserve(m_numIndices);
+ for (std::size_t i = 0; i < m_numIndices; i++) {
+ int v = g2.representation[g1.representation[i]];
+ eigen_assert(v >= 0);
+ result.representation.push_back(v);
+ }
+ result.flags = g1.flags ^ g2.flags;
+ return result;
+}
+
+inline void DynamicSGroup::add(int one, int two, int flags)
+{
+ eigen_assert(one >= 0);
+ eigen_assert(two >= 0);
+ eigen_assert(one != two);
+
+ if ((std::size_t)one >= m_numIndices || (std::size_t)two >= m_numIndices) {
+ std::size_t newNumIndices = (one > two) ? one : two + 1;
+ for (auto& gelem : m_elements) {
+ gelem.representation.reserve(newNumIndices);
+ for (std::size_t i = m_numIndices; i < newNumIndices; i++)
+ gelem.representation.push_back(i);
+ }
+ m_numIndices = newNumIndices;
+ }
+
+ Generator g{one, two, flags};
+ GroupElement e = ge(g);
+
+ /* special case for first generator */
+ if (m_elements.size() == 1) {
+ while (!e.isId()) {
+ m_elements.push_back(e);
+ e = mul(e, g);
+ }
+
+ if (e.flags > 0)
+ updateGlobalFlags(e.flags);
+
+ // only add in case we didn't have identity
+ if (m_elements.size() > 1)
+ m_generators.push_back(g);
+ return;
+ }
+
+ int p = findElement(e);
+ if (p >= 0) {
+ updateGlobalFlags(p);
+ return;
+ }
+
+ std::size_t coset_order = m_elements.size();
+ m_elements.push_back(e);
+ for (std::size_t i = 1; i < coset_order; i++)
+ m_elements.push_back(mul(m_elements[i], e));
+ m_generators.push_back(g);
+
+ std::size_t coset_rep = coset_order;
+ do {
+ for (auto g : m_generators) {
+ e = mul(m_elements[coset_rep], g);
+ p = findElement(e);
+ if (p < 0) {
+ // element not yet in group
+ m_elements.push_back(e);
+ for (std::size_t i = 1; i < coset_order; i++)
+ m_elements.push_back(mul(m_elements[i], e));
+ } else if (p > 0) {
+ updateGlobalFlags(p);
+ }
+ }
+ coset_rep += coset_order;
+ } while (coset_rep < m_elements.size());
+}
+
+inline void DynamicSGroup::updateGlobalFlags(int flagDiffOfSameGenerator)
+{
+ switch (flagDiffOfSameGenerator) {
+ case 0:
+ default:
+ // nothing happened
+ break;
+ case NegationFlag:
+ // every element is it's own negative => whole tensor is zero
+ m_globalFlags |= GlobalZeroFlag;
+ break;
+ case ConjugationFlag:
+ // every element is it's own conjugate => whole tensor is real
+ m_globalFlags |= GlobalRealFlag;
+ break;
+ case (NegationFlag | ConjugationFlag):
+ // every element is it's own negative conjugate => whole tensor is imaginary
+ m_globalFlags |= GlobalImagFlag;
+ break;
+ /* NOTE:
+ * since GlobalZeroFlag == GlobalRealFlag | GlobalImagFlag, if one generator
+ * causes the tensor to be real and the next one to be imaginary, this will
+ * trivially give the correct result
+ */
+ }
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_CXX11_TENSORSYMMETRY_DYNAMICSYMMETRY_H
+
+/*
+ * kate: space-indent on; indent-width 2; mixedindent off; indent-mode cstyle;
+ */
diff --git a/unsupported/Eigen/CXX11/src/TensorSymmetry/InternalHeaderCheck.h b/unsupported/Eigen/CXX11/src/TensorSymmetry/InternalHeaderCheck.h
new file mode 100644
index 0000000..b0affe6
--- /dev/null
+++ b/unsupported/Eigen/CXX11/src/TensorSymmetry/InternalHeaderCheck.h
@@ -0,0 +1,3 @@
+#ifndef EIGEN_CXX11_TENSORSYMMETRY_MODULE_H
+#error "Please include unsupported/Eigen/CXX11/TensorSymmetry instead of including headers inside the src directory directly."
+#endif
diff --git a/unsupported/Eigen/CXX11/src/TensorSymmetry/StaticSymmetry.h b/unsupported/Eigen/CXX11/src/TensorSymmetry/StaticSymmetry.h
new file mode 100644
index 0000000..e87403a
--- /dev/null
+++ b/unsupported/Eigen/CXX11/src/TensorSymmetry/StaticSymmetry.h
@@ -0,0 +1,238 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2013 Christian Seiler <christian@iwakd.de>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_CXX11_TENSORSYMMETRY_STATICSYMMETRY_H
+#define EIGEN_CXX11_TENSORSYMMETRY_STATICSYMMETRY_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+
+template<typename list> struct tensor_static_symgroup_permutate;
+
+template<int... nn>
+struct tensor_static_symgroup_permutate<numeric_list<int, nn...>>
+{
+ constexpr static std::size_t N = sizeof...(nn);
+
+ template<typename T>
+ constexpr static inline std::array<T, N> run(const std::array<T, N>& indices)
+ {
+ return {{indices[nn]...}};
+ }
+};
+
+template<typename indices_, int flags_>
+struct tensor_static_symgroup_element
+{
+ typedef indices_ indices;
+ constexpr static int flags = flags_;
+};
+
+template<typename Gen, int N>
+struct tensor_static_symgroup_element_ctor
+{
+ typedef tensor_static_symgroup_element<
+ typename gen_numeric_list_swapped_pair<int, N, Gen::One, Gen::Two>::type,
+ Gen::Flags
+ > type;
+};
+
+template<int N>
+struct tensor_static_symgroup_identity_ctor
+{
+ typedef tensor_static_symgroup_element<
+ typename gen_numeric_list<int, N>::type,
+ 0
+ > type;
+};
+
+template<typename iib>
+struct tensor_static_symgroup_multiply_helper
+{
+ template<int... iia>
+ constexpr static inline numeric_list<int, get<iia, iib>::value...> helper(numeric_list<int, iia...>) {
+ return numeric_list<int, get<iia, iib>::value...>();
+ }
+};
+
+template<typename A, typename B>
+struct tensor_static_symgroup_multiply
+{
+ private:
+ typedef typename A::indices iia;
+ typedef typename B::indices iib;
+ constexpr static int ffa = A::flags;
+ constexpr static int ffb = B::flags;
+
+ public:
+ static_assert(iia::count == iib::count, "Cannot multiply symmetry elements with different number of indices.");
+
+ typedef tensor_static_symgroup_element<
+ decltype(tensor_static_symgroup_multiply_helper<iib>::helper(iia())),
+ ffa ^ ffb
+ > type;
+};
+
+template<typename A, typename B>
+struct tensor_static_symgroup_equality
+{
+ typedef typename A::indices iia;
+ typedef typename B::indices iib;
+ constexpr static int ffa = A::flags;
+ constexpr static int ffb = B::flags;
+ static_assert(iia::count == iib::count, "Cannot compare symmetry elements with different number of indices.");
+
+ constexpr static bool value = is_same<iia, iib>::value;
+
+ private:
+ /* this should be zero if they are identical, or else the tensor
+ * will be forced to be pure real, pure imaginary or even pure zero
+ */
+ constexpr static int flags_cmp_ = ffa ^ ffb;
+
+ /* either they are not equal, then we don't care whether the flags
+ * match, or they are equal, and then we have to check
+ */
+ constexpr static bool is_zero = value && flags_cmp_ == NegationFlag;
+ constexpr static bool is_real = value && flags_cmp_ == ConjugationFlag;
+ constexpr static bool is_imag = value && flags_cmp_ == (NegationFlag | ConjugationFlag);
+
+ public:
+ constexpr static int global_flags =
+ (is_real ? GlobalRealFlag : 0) |
+ (is_imag ? GlobalImagFlag : 0) |
+ (is_zero ? GlobalZeroFlag : 0);
+};
+
+template<std::size_t NumIndices, typename... Gen>
+struct tensor_static_symgroup
+{
+ typedef StaticSGroup<Gen...> type;
+ constexpr static std::size_t size = type::static_size;
+};
+
+template<typename Index, std::size_t N, int... ii, int... jj>
+constexpr static inline std::array<Index, N> tensor_static_symgroup_index_permute(std::array<Index, N> idx, internal::numeric_list<int, ii...>, internal::numeric_list<int, jj...>)
+{
+ return {{ idx[ii]..., idx[jj]... }};
+}
+
+template<typename Index, int... ii>
+static inline std::vector<Index> tensor_static_symgroup_index_permute(std::vector<Index> idx, internal::numeric_list<int, ii...>)
+{
+ std::vector<Index> result{{ idx[ii]... }};
+ std::size_t target_size = idx.size();
+ for (std::size_t i = result.size(); i < target_size; i++)
+ result.push_back(idx[i]);
+ return result;
+}
+
+template<typename T> struct tensor_static_symgroup_do_apply;
+
+template<typename first, typename... next>
+struct tensor_static_symgroup_do_apply<internal::type_list<first, next...>>
+{
+ template<typename Op, typename RV, std::size_t SGNumIndices, typename Index, std::size_t NumIndices, typename... Args>
+ static inline RV run(const std::array<Index, NumIndices>& idx, RV initial, Args&&... args)
+ {
+ static_assert(NumIndices >= SGNumIndices, "Can only apply symmetry group to objects that have at least the required amount of indices.");
+ typedef typename internal::gen_numeric_list<int, NumIndices - SGNumIndices, SGNumIndices>::type remaining_indices;
+ initial = Op::run(tensor_static_symgroup_index_permute(idx, typename first::indices(), remaining_indices()), first::flags, initial, std::forward<Args>(args)...);
+ return tensor_static_symgroup_do_apply<internal::type_list<next...>>::template run<Op, RV, SGNumIndices>(idx, initial, args...);
+ }
+
+ template<typename Op, typename RV, std::size_t SGNumIndices, typename Index, typename... Args>
+ static inline RV run(const std::vector<Index>& idx, RV initial, Args&&... args)
+ {
+ eigen_assert(idx.size() >= SGNumIndices && "Can only apply symmetry group to objects that have at least the required amount of indices.");
+ initial = Op::run(tensor_static_symgroup_index_permute(idx, typename first::indices()), first::flags, initial, std::forward<Args>(args)...);
+ return tensor_static_symgroup_do_apply<internal::type_list<next...>>::template run<Op, RV, SGNumIndices>(idx, initial, args...);
+ }
+};
+
+template<EIGEN_TPL_PP_SPEC_HACK_DEF(typename, empty)>
+struct tensor_static_symgroup_do_apply<internal::type_list<EIGEN_TPL_PP_SPEC_HACK_USE(empty)>>
+{
+ template<typename Op, typename RV, std::size_t SGNumIndices, typename Index, std::size_t NumIndices, typename... Args>
+ static inline RV run(const std::array<Index, NumIndices>&, RV initial, Args&&...)
+ {
+ // do nothing
+ return initial;
+ }
+
+ template<typename Op, typename RV, std::size_t SGNumIndices, typename Index, typename... Args>
+ static inline RV run(const std::vector<Index>&, RV initial, Args&&...)
+ {
+ // do nothing
+ return initial;
+ }
+};
+
+} // end namespace internal
+
+template<typename... Gen>
+class StaticSGroup
+{
+ constexpr static std::size_t NumIndices = internal::tensor_symmetry_num_indices<Gen...>::value;
+ typedef internal::group_theory::enumerate_group_elements<
+ internal::tensor_static_symgroup_multiply,
+ internal::tensor_static_symgroup_equality,
+ typename internal::tensor_static_symgroup_identity_ctor<NumIndices>::type,
+ internal::type_list<typename internal::tensor_static_symgroup_element_ctor<Gen, NumIndices>::type...>
+ > group_elements;
+ typedef typename group_elements::type ge;
+ public:
+ constexpr inline StaticSGroup() {}
+ constexpr inline StaticSGroup(const StaticSGroup<Gen...>&) {}
+ constexpr inline StaticSGroup(StaticSGroup<Gen...>&&) {}
+
+ template<typename Op, typename RV, typename Index, std::size_t N, typename... Args>
+ static inline RV apply(const std::array<Index, N>& idx, RV initial, Args&&... args)
+ {
+ return internal::tensor_static_symgroup_do_apply<ge>::template run<Op, RV, NumIndices>(idx, initial, args...);
+ }
+
+ template<typename Op, typename RV, typename Index, typename... Args>
+ static inline RV apply(const std::vector<Index>& idx, RV initial, Args&&... args)
+ {
+ eigen_assert(idx.size() == NumIndices);
+ return internal::tensor_static_symgroup_do_apply<ge>::template run<Op, RV, NumIndices>(idx, initial, args...);
+ }
+
+ constexpr static std::size_t static_size = ge::count;
+
+ constexpr static inline std::size_t size() {
+ return ge::count;
+ }
+ constexpr static inline int globalFlags() { return group_elements::global_flags; }
+
+ template<typename Tensor_, typename... IndexTypes>
+ inline internal::tensor_symmetry_value_setter<Tensor_, StaticSGroup<Gen...>> operator()(Tensor_& tensor, typename Tensor_::Index firstIndex, IndexTypes... otherIndices) const
+ {
+ static_assert(sizeof...(otherIndices) + 1 == Tensor_::NumIndices, "Number of indices used to access a tensor coefficient must be equal to the rank of the tensor.");
+ return operator()(tensor, std::array<typename Tensor_::Index, Tensor_::NumIndices>{{firstIndex, otherIndices...}});
+ }
+
+ template<typename Tensor_>
+ inline internal::tensor_symmetry_value_setter<Tensor_, StaticSGroup<Gen...>> operator()(Tensor_& tensor, std::array<typename Tensor_::Index, Tensor_::NumIndices> const& indices) const
+ {
+ return internal::tensor_symmetry_value_setter<Tensor_, StaticSGroup<Gen...>>(tensor, *this, indices);
+ }
+};
+
+} // end namespace Eigen
+
+#endif // EIGEN_CXX11_TENSORSYMMETRY_STATICSYMMETRY_H
+
+/*
+ * kate: space-indent on; indent-width 2; mixedindent off; indent-mode cstyle;
+ */
diff --git a/unsupported/Eigen/CXX11/src/TensorSymmetry/Symmetry.h b/unsupported/Eigen/CXX11/src/TensorSymmetry/Symmetry.h
new file mode 100644
index 0000000..a95f79c
--- /dev/null
+++ b/unsupported/Eigen/CXX11/src/TensorSymmetry/Symmetry.h
@@ -0,0 +1,340 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2013 Christian Seiler <christian@iwakd.de>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_CXX11_TENSORSYMMETRY_SYMMETRY_H
+#define EIGEN_CXX11_TENSORSYMMETRY_SYMMETRY_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+enum {
+ NegationFlag = 0x01,
+ ConjugationFlag = 0x02
+};
+
+enum {
+ GlobalRealFlag = 0x01,
+ GlobalImagFlag = 0x02,
+ GlobalZeroFlag = 0x03
+};
+
+namespace internal {
+
+template<std::size_t NumIndices, typename... Sym> struct tensor_symmetry_pre_analysis;
+template<std::size_t NumIndices, typename... Sym> struct tensor_static_symgroup;
+template<bool instantiate, std::size_t NumIndices, typename... Sym> struct tensor_static_symgroup_if;
+template<typename Tensor_> struct tensor_symmetry_calculate_flags;
+template<typename Tensor_> struct tensor_symmetry_assign_value;
+template<typename... Sym> struct tensor_symmetry_num_indices;
+
+} // end namespace internal
+
+template<int One_, int Two_>
+struct Symmetry
+{
+ static_assert(One_ != Two_, "Symmetries must cover distinct indices.");
+ constexpr static int One = One_;
+ constexpr static int Two = Two_;
+ constexpr static int Flags = 0;
+};
+
+template<int One_, int Two_>
+struct AntiSymmetry
+{
+ static_assert(One_ != Two_, "Symmetries must cover distinct indices.");
+ constexpr static int One = One_;
+ constexpr static int Two = Two_;
+ constexpr static int Flags = NegationFlag;
+};
+
+template<int One_, int Two_>
+struct Hermiticity
+{
+ static_assert(One_ != Two_, "Symmetries must cover distinct indices.");
+ constexpr static int One = One_;
+ constexpr static int Two = Two_;
+ constexpr static int Flags = ConjugationFlag;
+};
+
+template<int One_, int Two_>
+struct AntiHermiticity
+{
+ static_assert(One_ != Two_, "Symmetries must cover distinct indices.");
+ constexpr static int One = One_;
+ constexpr static int Two = Two_;
+ constexpr static int Flags = ConjugationFlag | NegationFlag;
+};
+
+/** \class DynamicSGroup
+ * \ingroup TensorSymmetry_Module
+ *
+ * \brief Dynamic symmetry group
+ *
+ * The %DynamicSGroup class represents a symmetry group that need not be known at
+ * compile time. It is useful if one wants to support arbitrary run-time defineable
+ * symmetries for tensors, but it is also instantiated if a symmetry group is defined
+ * at compile time that would be either too large for the compiler to reasonably
+ * generate (using templates to calculate this at compile time is very inefficient)
+ * or that the compiler could generate the group but that it wouldn't make sense to
+ * unroll the loop for setting coefficients anymore.
+ */
+class DynamicSGroup;
+
+/** \internal
+ *
+ * \class DynamicSGroupFromTemplateArgs
+ * \ingroup TensorSymmetry_Module
+ *
+ * \brief Dynamic symmetry group, initialized from template arguments
+ *
+ * This class is a child class of DynamicSGroup. It uses the template arguments
+ * specified to initialize itself.
+ */
+template<typename... Gen>
+class DynamicSGroupFromTemplateArgs;
+
+/** \class StaticSGroup
+ * \ingroup TensorSymmetry_Module
+ *
+ * \brief Static symmetry group
+ *
+ * This class represents a symmetry group that is known and resolved completely
+ * at compile time. Ideally, no run-time penalty is incurred compared to the
+ * manual unrolling of the symmetry.
+ *
+ * <b><i>CAUTION:</i></b>
+ *
+ * Do not use this class directly for large symmetry groups. The compiler
+ * may run into a limit, or segfault or in the very least will take a very,
+ * very, very long time to compile the code. Use the SGroup class instead
+ * if you want a static group. That class contains logic that will
+ * automatically select the DynamicSGroup class instead if the symmetry
+ * group becomes too large. (In that case, unrolling may not even be
+ * beneficial.)
+ */
+template<typename... Gen>
+class StaticSGroup;
+
+/** \class SGroup
+ * \ingroup TensorSymmetry_Module
+ *
+ * \brief Symmetry group, initialized from template arguments
+ *
+ * This class represents a symmetry group whose generators are already
+ * known at compile time. It may or may not be resolved at compile time,
+ * depending on the estimated size of the group.
+ *
+ * \sa StaticSGroup
+ * \sa DynamicSGroup
+ */
+template<typename... Gen>
+class SGroup : public internal::tensor_symmetry_pre_analysis<internal::tensor_symmetry_num_indices<Gen...>::value, Gen...>::root_type
+{
+ public:
+ constexpr static std::size_t NumIndices = internal::tensor_symmetry_num_indices<Gen...>::value;
+ typedef typename internal::tensor_symmetry_pre_analysis<NumIndices, Gen...>::root_type Base;
+
+ // make standard constructors + assignment operators public
+ inline SGroup() : Base() { }
+ inline SGroup(const SGroup<Gen...>& other) : Base(other) { }
+ inline SGroup(SGroup<Gen...>&& other) : Base(other) { }
+ inline SGroup<Gen...>& operator=(const SGroup<Gen...>& other) { Base::operator=(other); return *this; }
+ inline SGroup<Gen...>& operator=(SGroup<Gen...>&& other) { Base::operator=(other); return *this; }
+
+ // all else is defined in the base class
+};
+
+namespace internal {
+
+template<typename... Sym> struct tensor_symmetry_num_indices
+{
+ constexpr static std::size_t value = 1;
+};
+
+template<int One_, int Two_, typename... Sym> struct tensor_symmetry_num_indices<Symmetry<One_, Two_>, Sym...>
+{
+private:
+ constexpr static std::size_t One = static_cast<std::size_t>(One_);
+ constexpr static std::size_t Two = static_cast<std::size_t>(Two_);
+ constexpr static std::size_t Three = tensor_symmetry_num_indices<Sym...>::value;
+
+ // don't use std::max, since it's not constexpr until C++14...
+ constexpr static std::size_t maxOneTwoPlusOne = ((One > Two) ? One : Two) + 1;
+public:
+ constexpr static std::size_t value = (maxOneTwoPlusOne > Three) ? maxOneTwoPlusOne : Three;
+};
+
+template<int One_, int Two_, typename... Sym> struct tensor_symmetry_num_indices<AntiSymmetry<One_, Two_>, Sym...>
+ : public tensor_symmetry_num_indices<Symmetry<One_, Two_>, Sym...> {};
+template<int One_, int Two_, typename... Sym> struct tensor_symmetry_num_indices<Hermiticity<One_, Two_>, Sym...>
+ : public tensor_symmetry_num_indices<Symmetry<One_, Two_>, Sym...> {};
+template<int One_, int Two_, typename... Sym> struct tensor_symmetry_num_indices<AntiHermiticity<One_, Two_>, Sym...>
+ : public tensor_symmetry_num_indices<Symmetry<One_, Two_>, Sym...> {};
+
+/** \internal
+ *
+ * \class tensor_symmetry_pre_analysis
+ * \ingroup TensorSymmetry_Module
+ *
+ * \brief Pre-select whether to use a static or dynamic symmetry group
+ *
+ * When a symmetry group could in principle be determined at compile time,
+ * this template implements the logic whether to actually do that or whether
+ * to rather defer that to runtime.
+ *
+ * The logic is as follows:
+ * <dl>
+ * <dt><b>No generators (trivial symmetry):</b></dt>
+ * <dd>Use a trivial static group. Ideally, this has no performance impact
+ * compared to not using symmetry at all. In practice, this might not
+ * be the case.</dd>
+ * <dt><b>More than 4 generators:</b></dt>
+ * <dd>Calculate the group at run time, it is likely far too large for the
+ * compiler to be able to properly generate it in a realistic time.</dd>
+ * <dt><b>Up to and including 4 generators:</b></dt>
+ * <dd>Actually enumerate all group elements, but then check how many there
+ * are. If there are more than 16, it is unlikely that unrolling the
+ * loop (as is done in the static compile-time case) is sensible, so
+ * use a dynamic group instead. If there are at most 16 elements, actually
+ * use that static group. Note that the largest group with 4 generators
+ * still compiles with reasonable resources.</dd>
+ * </dl>
+ *
+ * Note: Example compile time performance with g++-4.6 on an Intenl Core i5-3470
+ * with 16 GiB RAM (all generators non-redundant and the subgroups don't
+ * factorize):
+ *
+ * # Generators -O0 -ggdb -O2
+ * -------------------------------------------------------------------
+ * 1 0.5 s / 250 MiB 0.45s / 230 MiB
+ * 2 0.5 s / 260 MiB 0.5 s / 250 MiB
+ * 3 0.65s / 310 MiB 0.62s / 310 MiB
+ * 4 2.2 s / 860 MiB 1.7 s / 770 MiB
+ * 5 130 s / 13000 MiB 120 s / 11000 MiB
+ *
+ * It is clear that everything is still very efficient up to 4 generators, then
+ * the memory and CPU requirements become unreasonable. Thus we only instantiate
+ * the template group theory logic if the number of generators supplied is 4 or
+ * lower, otherwise this will be forced to be done during runtime, where the
+ * algorithm is reasonably fast.
+ */
+template<std::size_t NumIndices>
+struct tensor_symmetry_pre_analysis<NumIndices>
+{
+ typedef StaticSGroup<> root_type;
+};
+
+template<std::size_t NumIndices, typename Gen_, typename... Gens_>
+struct tensor_symmetry_pre_analysis<NumIndices, Gen_, Gens_...>
+{
+ constexpr static std::size_t max_static_generators = 4;
+ constexpr static std::size_t max_static_elements = 16;
+ typedef tensor_static_symgroup_if<(sizeof...(Gens_) + 1 <= max_static_generators), NumIndices, Gen_, Gens_...> helper;
+ constexpr static std::size_t possible_size = helper::size;
+
+ typedef std::conditional_t<
+ possible_size == 0 || possible_size >= max_static_elements,
+ DynamicSGroupFromTemplateArgs<Gen_, Gens_...>,
+ typename helper::type
+ > root_type;
+};
+
+template<bool instantiate, std::size_t NumIndices, typename... Gens>
+struct tensor_static_symgroup_if
+{
+ constexpr static std::size_t size = 0;
+ typedef void type;
+};
+
+template<std::size_t NumIndices, typename... Gens>
+struct tensor_static_symgroup_if<true, NumIndices, Gens...> : tensor_static_symgroup<NumIndices, Gens...> {};
+
+template<typename Tensor_>
+struct tensor_symmetry_assign_value
+{
+ typedef typename Tensor_::Index Index;
+ typedef typename Tensor_::Scalar Scalar;
+ constexpr static std::size_t NumIndices = Tensor_::NumIndices;
+
+ static inline int run(const std::array<Index, NumIndices>& transformed_indices, int transformation_flags, int dummy, Tensor_& tensor, const Scalar& value_)
+ {
+ Scalar value(value_);
+ if (transformation_flags & ConjugationFlag)
+ value = numext::conj(value);
+ if (transformation_flags & NegationFlag)
+ value = -value;
+ tensor.coeffRef(transformed_indices) = value;
+ return dummy;
+ }
+};
+
+template<typename Tensor_>
+struct tensor_symmetry_calculate_flags
+{
+ typedef typename Tensor_::Index Index;
+ constexpr static std::size_t NumIndices = Tensor_::NumIndices;
+
+ static inline int run(const std::array<Index, NumIndices>& transformed_indices, int transform_flags, int current_flags, const std::array<Index, NumIndices>& orig_indices)
+ {
+ if (transformed_indices == orig_indices) {
+ if (transform_flags & (ConjugationFlag | NegationFlag))
+ return current_flags | GlobalImagFlag; // anti-hermitian diagonal
+ else if (transform_flags & ConjugationFlag)
+ return current_flags | GlobalRealFlag; // hermitian diagonal
+ else if (transform_flags & NegationFlag)
+ return current_flags | GlobalZeroFlag; // anti-symmetric diagonal
+ }
+ return current_flags;
+ }
+};
+
+template<typename Tensor_, typename Symmetry_, int Flags = 0>
+class tensor_symmetry_value_setter
+{
+ public:
+ typedef typename Tensor_::Index Index;
+ typedef typename Tensor_::Scalar Scalar;
+ constexpr static std::size_t NumIndices = Tensor_::NumIndices;
+
+ inline tensor_symmetry_value_setter(Tensor_& tensor, Symmetry_ const& symmetry, std::array<Index, NumIndices> const& indices)
+ : m_tensor(tensor), m_symmetry(symmetry), m_indices(indices) { }
+
+ inline tensor_symmetry_value_setter<Tensor_, Symmetry_, Flags>& operator=(Scalar const& value)
+ {
+ doAssign(value);
+ return *this;
+ }
+ private:
+ Tensor_& m_tensor;
+ Symmetry_ m_symmetry;
+ std::array<Index, NumIndices> m_indices;
+
+ inline void doAssign(Scalar const& value)
+ {
+ #ifdef EIGEN_TENSOR_SYMMETRY_CHECK_VALUES
+ int value_flags = m_symmetry.template apply<internal::tensor_symmetry_calculate_flags<Tensor_>, int>(m_indices, m_symmetry.globalFlags(), m_indices);
+ if (value_flags & GlobalRealFlag)
+ eigen_assert(numext::imag(value) == 0);
+ if (value_flags & GlobalImagFlag)
+ eigen_assert(numext::real(value) == 0);
+ #endif
+ m_symmetry.template apply<internal::tensor_symmetry_assign_value<Tensor_>, int>(m_indices, 0, m_tensor, value);
+ }
+};
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_CXX11_TENSORSYMMETRY_SYMMETRY_H
+
+/*
+ * kate: space-indent on; indent-width 2; mixedindent off; indent-mode cstyle;
+ */
diff --git a/unsupported/Eigen/CXX11/src/TensorSymmetry/util/TemplateGroupTheory.h b/unsupported/Eigen/CXX11/src/TensorSymmetry/util/TemplateGroupTheory.h
new file mode 100644
index 0000000..c27d1ed
--- /dev/null
+++ b/unsupported/Eigen/CXX11/src/TensorSymmetry/util/TemplateGroupTheory.h
@@ -0,0 +1,671 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2013 Christian Seiler <christian@iwakd.de>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_CXX11_TENSORSYMMETRY_TEMPLATEGROUPTHEORY_H
+#define EIGEN_CXX11_TENSORSYMMETRY_TEMPLATEGROUPTHEORY_H
+
+#include "../InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+
+namespace group_theory {
+
+/** \internal
+ * \file CXX11/src/TensorSymmetry/util/TemplateGroupTheory.h
+ * This file contains C++ templates that implement group theory algorithms.
+ *
+ * The algorithms allow for a compile-time analysis of finite groups.
+ *
+ * Currently only Dimino's algorithm is implemented, which returns a list
+ * of all elements in a group given a set of (possibly redundant) generators.
+ * (One could also do that with the so-called orbital algorithm, but that
+ * is much more expensive and usually has no advantages.)
+ */
+
+/**********************************************************************
+ * "Ok kid, here is where it gets complicated."
+ * - Amelia Pond in the "Doctor Who" episode
+ * "The Big Bang"
+ *
+ * Dimino's algorithm
+ * ==================
+ *
+ * The following is Dimino's algorithm in sequential form:
+ *
+ * Input: identity element, list of generators, equality check,
+ * multiplication operation
+ * Output: list of group elements
+ *
+ * 1. add identity element
+ * 2. remove identities from list of generators
+ * 3. add all powers of first generator that aren't the
+ * identity element
+ * 4. go through all remaining generators:
+ * a. if generator is already in the list of elements
+ * -> do nothing
+ * b. otherwise
+ * i. remember current # of elements
+ * (i.e. the size of the current subgroup)
+ * ii. add all current elements (which includes
+ * the identity) each multiplied from right
+ * with the current generator to the group
+ * iii. add all remaining cosets that are generated
+ * by products of the new generator with itself
+ * and all other generators seen so far
+ *
+ * In functional form, this is implemented as a long set of recursive
+ * templates that have a complicated relationship.
+ *
+ * The main interface for Dimino's algorithm is the template
+ * enumerate_group_elements. All lists are implemented as variadic
+ * type_list<typename...> and numeric_list<typename = int, int...>
+ * templates.
+ *
+ * 'Calling' templates is usually done via typedefs.
+ *
+ * This algorithm is an extended version of the basic version. The
+ * extension consists in the fact that each group element has a set
+ * of flags associated with it. Multiplication of two group elements
+ * with each other results in a group element whose flags are the
+ * XOR of the flags of the previous elements. Each time the algorithm
+ * notices that a group element it just calculated is already in the
+ * list of current elements, the flags of both will be compared and
+ * added to the so-called 'global flags' of the group.
+ *
+ * The rationale behind this extension is that this allows not only
+ * for the description of symmetries between tensor indices, but
+ * also allows for the description of hermiticity, antisymmetry and
+ * antihermiticity. Negation and conjugation each are specific bit
+ * in the flags value and if two different ways to reach a group
+ * element lead to two different flags, this poses a constraint on
+ * the allowed values of the resulting tensor. For example, if a
+ * group element is reach both with and without the conjugation
+ * flags, it is clear that the resulting tensor has to be real.
+ *
+ * Note that this flag mechanism is quite generic and may have other
+ * uses beyond tensor properties.
+ *
+ * IMPORTANT:
+ * This algorithm assumes the group to be finite. If you try to
+ * run it with a group that's infinite, the algorithm will only
+ * terminate once you hit a compiler limit (max template depth).
+ * Also note that trying to use this implementation to create a
+ * very large group will probably either make you hit the same
+ * limit, cause the compiler to segfault or at the very least
+ * take a *really* long time (hours, days, weeks - sic!) to
+ * compile. It is not recommended to plug in more than 4
+ * generators, unless they are independent of each other.
+ */
+
+/** \internal
+ *
+ * \class strip_identities
+ * \ingroup CXX11_TensorSymmetry_Module
+ *
+ * \brief Cleanse a list of group elements of the identity element
+ *
+ * This template is used to make a first pass through all initial
+ * generators of Dimino's algorithm and remove the identity
+ * elements.
+ *
+ * \sa enumerate_group_elements
+ */
+template<template<typename, typename> class Equality, typename id, typename L> struct strip_identities;
+
+template<
+ template<typename, typename> class Equality,
+ typename id,
+ typename t,
+ typename... ts
+>
+struct strip_identities<Equality, id, type_list<t, ts...>>
+{
+ typedef std::conditional_t<
+ Equality<id, t>::value,
+ typename strip_identities<Equality, id, type_list<ts...>>::type,
+ typename concat<type_list<t>, typename strip_identities<Equality, id, type_list<ts...>>::type>::type
+ > type;
+ constexpr static int global_flags = Equality<id, t>::global_flags | strip_identities<Equality, id, type_list<ts...>>::global_flags;
+};
+
+template<
+ template<typename, typename> class Equality,
+ typename id
+ EIGEN_TPL_PP_SPEC_HACK_DEFC(typename, ts)
+>
+struct strip_identities<Equality, id, type_list<EIGEN_TPL_PP_SPEC_HACK_USE(ts)>>
+{
+ typedef type_list<> type;
+ constexpr static int global_flags = 0;
+};
+
+/** \internal
+ *
+ * \class dimino_first_step_elements_helper
+ * \ingroup CXX11_TensorSymmetry_Module
+ *
+ * \brief Recursive template that adds powers of the first generator to the list of group elements
+ *
+ * This template calls itself recursively to add powers of the first
+ * generator to the list of group elements. It stops if it reaches
+ * the identity element again.
+ *
+ * \sa enumerate_group_elements, dimino_first_step_elements
+ */
+template<
+ template<typename, typename> class Multiply,
+ template<typename, typename> class Equality,
+ typename id,
+ typename g,
+ typename current_element,
+ typename elements,
+ bool dont_add_current_element // = false
+>
+struct dimino_first_step_elements_helper
+#ifndef EIGEN_PARSED_BY_DOXYGEN
+ : // recursive inheritance is too difficult for Doxygen
+ public dimino_first_step_elements_helper<
+ Multiply,
+ Equality,
+ id,
+ g,
+ typename Multiply<current_element, g>::type,
+ typename concat<elements, type_list<current_element>>::type,
+ Equality<typename Multiply<current_element, g>::type, id>::value
+ > {};
+
+template<
+ template<typename, typename> class Multiply,
+ template<typename, typename> class Equality,
+ typename id,
+ typename g,
+ typename current_element,
+ typename elements
+>
+struct dimino_first_step_elements_helper<Multiply, Equality, id, g, current_element, elements, true>
+#endif // EIGEN_PARSED_BY_DOXYGEN
+{
+ typedef elements type;
+ constexpr static int global_flags = Equality<current_element, id>::global_flags;
+};
+
+/** \internal
+ *
+ * \class dimino_first_step_elements
+ * \ingroup CXX11_TensorSymmetry_Module
+ *
+ * \brief Add all powers of the first generator to the list of group elements
+ *
+ * This template takes the first non-identity generator and generates the initial
+ * list of elements which consists of all powers of that generator. For a group
+ * with just one generated, it would be enumerated after this.
+ *
+ * \sa enumerate_group_elements
+ */
+template<
+ template<typename, typename> class Multiply,
+ template<typename, typename> class Equality,
+ typename id,
+ typename generators
+>
+struct dimino_first_step_elements
+{
+ typedef typename get<0, generators>::type first_generator;
+ typedef typename skip<1, generators>::type next_generators;
+ typedef type_list<first_generator> generators_done;
+
+ typedef dimino_first_step_elements_helper<
+ Multiply,
+ Equality,
+ id,
+ first_generator,
+ first_generator,
+ type_list<id>,
+ false
+ > helper;
+ typedef typename helper::type type;
+ constexpr static int global_flags = helper::global_flags;
+};
+
+/** \internal
+ *
+ * \class dimino_get_coset_elements
+ * \ingroup CXX11_TensorSymmetry_Module
+ *
+ * \brief Generate all elements of a specific coset
+ *
+ * This template generates all the elements of a specific coset by
+ * multiplying all elements in the given subgroup with the new
+ * coset representative. Note that the first element of the
+ * subgroup is always the identity element, so the first element of
+ * the result of this template is going to be the coset
+ * representative itself.
+ *
+ * Note that this template accepts an additional boolean parameter
+ * that specifies whether to actually generate the coset (true) or
+ * just return an empty list (false).
+ *
+ * \sa enumerate_group_elements, dimino_add_cosets_for_rep
+ */
+template<
+ template<typename, typename> class Multiply,
+ typename sub_group_elements,
+ typename new_coset_rep,
+ bool generate_coset // = true
+>
+struct dimino_get_coset_elements
+{
+ typedef typename apply_op_from_right<Multiply, new_coset_rep, sub_group_elements>::type type;
+};
+
+template<
+ template<typename, typename> class Multiply,
+ typename sub_group_elements,
+ typename new_coset_rep
+>
+struct dimino_get_coset_elements<Multiply, sub_group_elements, new_coset_rep, false>
+{
+ typedef type_list<> type;
+};
+
+/** \internal
+ *
+ * \class dimino_add_cosets_for_rep
+ * \ingroup CXX11_TensorSymmetry_Module
+ *
+ * \brief Recursive template for adding coset spaces
+ *
+ * This template multiplies the coset representative with a generator
+ * from the list of previous generators. If the new element is not in
+ * the group already, it adds the corresponding coset. Finally it
+ * proceeds to call itself with the next generator from the list.
+ *
+ * \sa enumerate_group_elements, dimino_add_all_coset_spaces
+ */
+template<
+ template<typename, typename> class Multiply,
+ template<typename, typename> class Equality,
+ typename id,
+ typename sub_group_elements,
+ typename elements,
+ typename generators,
+ typename rep_element,
+ int sub_group_size
+>
+struct dimino_add_cosets_for_rep;
+
+template<
+ template<typename, typename> class Multiply,
+ template<typename, typename> class Equality,
+ typename id,
+ typename sub_group_elements,
+ typename elements,
+ typename g,
+ typename... gs,
+ typename rep_element,
+ int sub_group_size
+>
+struct dimino_add_cosets_for_rep<Multiply, Equality, id, sub_group_elements, elements, type_list<g, gs...>, rep_element, sub_group_size>
+{
+ typedef typename Multiply<rep_element, g>::type new_coset_rep;
+ typedef contained_in_list_gf<Equality, new_coset_rep, elements> _cil;
+ constexpr static bool add_coset = !_cil::value;
+
+ typedef typename dimino_get_coset_elements<
+ Multiply,
+ sub_group_elements,
+ new_coset_rep,
+ add_coset
+ >::type coset_elements;
+
+ typedef dimino_add_cosets_for_rep<
+ Multiply,
+ Equality,
+ id,
+ sub_group_elements,
+ typename concat<elements, coset_elements>::type,
+ type_list<gs...>,
+ rep_element,
+ sub_group_size
+ > _helper;
+
+ typedef typename _helper::type type;
+ constexpr static int global_flags = _cil::global_flags | _helper::global_flags;
+
+ /* Note that we don't have to update global flags here, since
+ * we will only add these elements if they are not part of
+ * the group already. But that only happens if the coset rep
+ * is not already in the group, so the check for the coset rep
+ * will catch this.
+ */
+};
+
+template<
+ template<typename, typename> class Multiply,
+ template<typename, typename> class Equality,
+ typename id,
+ typename sub_group_elements,
+ typename elements
+ EIGEN_TPL_PP_SPEC_HACK_DEFC(typename, empty),
+ typename rep_element,
+ int sub_group_size
+>
+struct dimino_add_cosets_for_rep<Multiply, Equality, id, sub_group_elements, elements, type_list<EIGEN_TPL_PP_SPEC_HACK_USE(empty)>, rep_element, sub_group_size>
+{
+ typedef elements type;
+ constexpr static int global_flags = 0;
+};
+
+/** \internal
+ *
+ * \class dimino_add_all_coset_spaces
+ * \ingroup CXX11_TensorSymmetry_Module
+ *
+ * \brief Recursive template for adding all coset spaces for a new generator
+ *
+ * This template tries to go through the list of generators (with
+ * the help of the dimino_add_cosets_for_rep template) as long as
+ * it still finds elements that are not part of the group and add
+ * the corresponding cosets.
+ *
+ * \sa enumerate_group_elements, dimino_add_cosets_for_rep
+ */
+template<
+ template<typename, typename> class Multiply,
+ template<typename, typename> class Equality,
+ typename id,
+ typename sub_group_elements,
+ typename elements,
+ typename generators,
+ int sub_group_size,
+ int rep_pos,
+ bool stop_condition // = false
+>
+struct dimino_add_all_coset_spaces
+{
+ typedef typename get<rep_pos, elements>::type rep_element;
+ typedef dimino_add_cosets_for_rep<
+ Multiply,
+ Equality,
+ id,
+ sub_group_elements,
+ elements,
+ generators,
+ rep_element,
+ sub_group_elements::count
+ > _ac4r;
+ typedef typename _ac4r::type new_elements;
+
+ constexpr static int new_rep_pos = rep_pos + sub_group_elements::count;
+ constexpr static bool new_stop_condition = new_rep_pos >= new_elements::count;
+
+ typedef dimino_add_all_coset_spaces<
+ Multiply,
+ Equality,
+ id,
+ sub_group_elements,
+ new_elements,
+ generators,
+ sub_group_size,
+ new_rep_pos,
+ new_stop_condition
+ > _helper;
+
+ typedef typename _helper::type type;
+ constexpr static int global_flags = _helper::global_flags | _ac4r::global_flags;
+};
+
+template<
+ template<typename, typename> class Multiply,
+ template<typename, typename> class Equality,
+ typename id,
+ typename sub_group_elements,
+ typename elements,
+ typename generators,
+ int sub_group_size,
+ int rep_pos
+>
+struct dimino_add_all_coset_spaces<Multiply, Equality, id, sub_group_elements, elements, generators, sub_group_size, rep_pos, true>
+{
+ typedef elements type;
+ constexpr static int global_flags = 0;
+};
+
+/** \internal
+ *
+ * \class dimino_add_generator
+ * \ingroup CXX11_TensorSymmetry_Module
+ *
+ * \brief Enlarge the group by adding a new generator.
+ *
+ * It accepts a boolean parameter that determines if the generator is redundant,
+ * i.e. was already seen in the group. In that case, it reduces to a no-op.
+ *
+ * \sa enumerate_group_elements, dimino_add_all_coset_spaces
+ */
+template<
+ template<typename, typename> class Multiply,
+ template<typename, typename> class Equality,
+ typename id,
+ typename elements,
+ typename generators_done,
+ typename current_generator,
+ bool redundant // = false
+>
+struct dimino_add_generator
+{
+ /* this template is only called if the generator is not redundant
+ * => all elements of the group multiplied with the new generator
+ * are going to be new elements of the most trivial coset space
+ */
+ typedef typename apply_op_from_right<Multiply, current_generator, elements>::type multiplied_elements;
+ typedef typename concat<elements, multiplied_elements>::type new_elements;
+
+ constexpr static int rep_pos = elements::count;
+
+ typedef dimino_add_all_coset_spaces<
+ Multiply,
+ Equality,
+ id,
+ elements, // elements of previous subgroup
+ new_elements,
+ typename concat<generators_done, type_list<current_generator>>::type,
+ elements::count, // size of previous subgroup
+ rep_pos,
+ false // don't stop (because rep_pos >= new_elements::count is always false at this point)
+ > _helper;
+ typedef typename _helper::type type;
+ constexpr static int global_flags = _helper::global_flags;
+};
+
+template<
+ template<typename, typename> class Multiply,
+ template<typename, typename> class Equality,
+ typename id,
+ typename elements,
+ typename generators_done,
+ typename current_generator
+>
+struct dimino_add_generator<Multiply, Equality, id, elements, generators_done, current_generator, true>
+{
+ // redundant case
+ typedef elements type;
+ constexpr static int global_flags = 0;
+};
+
+/** \internal
+ *
+ * \class dimino_add_remaining_generators
+ * \ingroup CXX11_TensorSymmetry_Module
+ *
+ * \brief Recursive template that adds all remaining generators to a group
+ *
+ * Loop through the list of generators that remain and successively
+ * add them to the group.
+ *
+ * \sa enumerate_group_elements, dimino_add_generator
+ */
+template<
+ template<typename, typename> class Multiply,
+ template<typename, typename> class Equality,
+ typename id,
+ typename generators_done,
+ typename remaining_generators,
+ typename elements
+>
+struct dimino_add_remaining_generators
+{
+ typedef typename get<0, remaining_generators>::type first_generator;
+ typedef typename skip<1, remaining_generators>::type next_generators;
+
+ typedef contained_in_list_gf<Equality, first_generator, elements> _cil;
+
+ typedef dimino_add_generator<
+ Multiply,
+ Equality,
+ id,
+ elements,
+ generators_done,
+ first_generator,
+ _cil::value
+ > _helper;
+
+ typedef typename _helper::type new_elements;
+
+ typedef dimino_add_remaining_generators<
+ Multiply,
+ Equality,
+ id,
+ typename concat<generators_done, type_list<first_generator>>::type,
+ next_generators,
+ new_elements
+ > _next_iter;
+
+ typedef typename _next_iter::type type;
+ constexpr static int global_flags =
+ _cil::global_flags |
+ _helper::global_flags |
+ _next_iter::global_flags;
+};
+
+template<
+ template<typename, typename> class Multiply,
+ template<typename, typename> class Equality,
+ typename id,
+ typename generators_done,
+ typename elements
+>
+struct dimino_add_remaining_generators<Multiply, Equality, id, generators_done, type_list<>, elements>
+{
+ typedef elements type;
+ constexpr static int global_flags = 0;
+};
+
+/** \internal
+ *
+ * \class enumerate_group_elements_noid
+ * \ingroup CXX11_TensorSymmetry_Module
+ *
+ * \brief Helper template that implements group element enumeration
+ *
+ * This is a helper template that implements the actual enumeration
+ * of group elements. This has been split so that the list of
+ * generators can be cleansed of the identity element before
+ * performing the actual operation.
+ *
+ * \sa enumerate_group_elements
+ */
+template<
+ template<typename, typename> class Multiply,
+ template<typename, typename> class Equality,
+ typename id,
+ typename generators,
+ int initial_global_flags = 0
+>
+struct enumerate_group_elements_noid
+{
+ typedef dimino_first_step_elements<Multiply, Equality, id, generators> first_step;
+ typedef typename first_step::type first_step_elements;
+
+ typedef dimino_add_remaining_generators<
+ Multiply,
+ Equality,
+ id,
+ typename first_step::generators_done,
+ typename first_step::next_generators, // remaining_generators
+ typename first_step::type // first_step elements
+ > _helper;
+
+ typedef typename _helper::type type;
+ constexpr static int global_flags =
+ initial_global_flags |
+ first_step::global_flags |
+ _helper::global_flags;
+};
+
+// in case when no generators are specified
+template<
+ template<typename, typename> class Multiply,
+ template<typename, typename> class Equality,
+ typename id,
+ int initial_global_flags
+>
+struct enumerate_group_elements_noid<Multiply, Equality, id, type_list<>, initial_global_flags>
+{
+ typedef type_list<id> type;
+ constexpr static int global_flags = initial_global_flags;
+};
+
+/** \internal
+ *
+ * \class enumerate_group_elements
+ * \ingroup CXX11_TensorSymmetry_Module
+ *
+ * \brief Enumerate all elements in a finite group
+ *
+ * This template enumerates all elements in a finite group. It accepts
+ * the following template parameters:
+ *
+ * \tparam Multiply The multiplication operation that multiplies two group elements
+ * with each other.
+ * \tparam Equality The equality check operation that checks if two group elements
+ * are equal to another.
+ * \tparam id The identity element
+ * \tparam Generators_ A list of (possibly redundant) generators of the group
+ */
+template<
+ template<typename, typename> class Multiply,
+ template<typename, typename> class Equality,
+ typename id,
+ typename Generators_
+>
+struct enumerate_group_elements
+ : public enumerate_group_elements_noid<
+ Multiply,
+ Equality,
+ id,
+ typename strip_identities<Equality, id, Generators_>::type,
+ strip_identities<Equality, id, Generators_>::global_flags
+ >
+{
+};
+
+} // end namespace group_theory
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_CXX11_TENSORSYMMETRY_TEMPLATEGROUPTHEORY_H
+
+/*
+ * kate: space-indent on; indent-width 2; mixedindent off; indent-mode cstyle;
+ */
diff --git a/unsupported/Eigen/CXX11/src/ThreadPool/Barrier.h b/unsupported/Eigen/CXX11/src/ThreadPool/Barrier.h
new file mode 100644
index 0000000..df58d87
--- /dev/null
+++ b/unsupported/Eigen/CXX11/src/ThreadPool/Barrier.h
@@ -0,0 +1,69 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2018 Rasmus Munk Larsen <rmlarsen@google.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+// Barrier is an object that allows one or more threads to wait until
+// Notify has been called a specified number of times.
+
+#ifndef EIGEN_CXX11_THREADPOOL_BARRIER_H
+#define EIGEN_CXX11_THREADPOOL_BARRIER_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+class Barrier {
+ public:
+ Barrier(unsigned int count) : state_(count << 1), notified_(false) {
+ eigen_plain_assert(((count << 1) >> 1) == count);
+ }
+ ~Barrier() { eigen_plain_assert((state_ >> 1) == 0); }
+
+ void Notify() {
+ unsigned int v = state_.fetch_sub(2, std::memory_order_acq_rel) - 2;
+ if (v != 1) {
+ // Clear the lowest bit (waiter flag) and check that the original state
+ // value was not zero. If it was zero, it means that notify was called
+ // more times than the original count.
+ eigen_plain_assert(((v + 2) & ~1) != 0);
+ return; // either count has not dropped to 0, or waiter is not waiting
+ }
+ EIGEN_MUTEX_LOCK l(mu_);
+ eigen_plain_assert(!notified_);
+ notified_ = true;
+ cv_.notify_all();
+ }
+
+ void Wait() {
+ unsigned int v = state_.fetch_or(1, std::memory_order_acq_rel);
+ if ((v >> 1) == 0) return;
+ EIGEN_MUTEX_LOCK l(mu_);
+ while (!notified_) {
+ cv_.wait(l);
+ }
+ }
+
+ private:
+ EIGEN_MUTEX mu_;
+ EIGEN_CONDVAR cv_;
+ std::atomic<unsigned int> state_; // low bit is waiter flag
+ bool notified_;
+};
+
+// Notification is an object that allows a user to to wait for another
+// thread to signal a notification that an event has occurred.
+//
+// Multiple threads can wait on the same Notification object,
+// but only one caller must call Notify() on the object.
+struct Notification : Barrier {
+ Notification() : Barrier(1){};
+};
+
+} // namespace Eigen
+
+#endif // EIGEN_CXX11_THREADPOOL_BARRIER_H
diff --git a/unsupported/Eigen/CXX11/src/ThreadPool/EventCount.h b/unsupported/Eigen/CXX11/src/ThreadPool/EventCount.h
new file mode 100644
index 0000000..034637c
--- /dev/null
+++ b/unsupported/Eigen/CXX11/src/ThreadPool/EventCount.h
@@ -0,0 +1,251 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2016 Dmitry Vyukov <dvyukov@google.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_CXX11_THREADPOOL_EVENTCOUNT_H
+#define EIGEN_CXX11_THREADPOOL_EVENTCOUNT_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+// EventCount allows to wait for arbitrary predicates in non-blocking
+// algorithms. Think of condition variable, but wait predicate does not need to
+// be protected by a mutex. Usage:
+// Waiting thread does:
+//
+// if (predicate)
+// return act();
+// EventCount::Waiter& w = waiters[my_index];
+// ec.Prewait(&w);
+// if (predicate) {
+// ec.CancelWait(&w);
+// return act();
+// }
+// ec.CommitWait(&w);
+//
+// Notifying thread does:
+//
+// predicate = true;
+// ec.Notify(true);
+//
+// Notify is cheap if there are no waiting threads. Prewait/CommitWait are not
+// cheap, but they are executed only if the preceding predicate check has
+// failed.
+//
+// Algorithm outline:
+// There are two main variables: predicate (managed by user) and state_.
+// Operation closely resembles Dekker mutual algorithm:
+// https://en.wikipedia.org/wiki/Dekker%27s_algorithm
+// Waiting thread sets state_ then checks predicate, Notifying thread sets
+// predicate then checks state_. Due to seq_cst fences in between these
+// operations it is guaranteed than either waiter will see predicate change
+// and won't block, or notifying thread will see state_ change and will unblock
+// the waiter, or both. But it can't happen that both threads don't see each
+// other changes, which would lead to deadlock.
+class EventCount {
+ public:
+ class Waiter;
+
+ EventCount(MaxSizeVector<Waiter>& waiters)
+ : state_(kStackMask), waiters_(waiters) {
+ eigen_plain_assert(waiters.size() < (1 << kWaiterBits) - 1);
+ }
+
+ ~EventCount() {
+ // Ensure there are no waiters.
+ eigen_plain_assert(state_.load() == kStackMask);
+ }
+
+ // Prewait prepares for waiting.
+ // After calling Prewait, the thread must re-check the wait predicate
+ // and then call either CancelWait or CommitWait.
+ void Prewait() {
+ uint64_t state = state_.load(std::memory_order_relaxed);
+ for (;;) {
+ CheckState(state);
+ uint64_t newstate = state + kWaiterInc;
+ CheckState(newstate);
+ if (state_.compare_exchange_weak(state, newstate,
+ std::memory_order_seq_cst))
+ return;
+ }
+ }
+
+ // CommitWait commits waiting after Prewait.
+ void CommitWait(Waiter* w) {
+ eigen_plain_assert((w->epoch & ~kEpochMask) == 0);
+ w->state = Waiter::kNotSignaled;
+ const uint64_t me = (w - &waiters_[0]) | w->epoch;
+ uint64_t state = state_.load(std::memory_order_seq_cst);
+ for (;;) {
+ CheckState(state, true);
+ uint64_t newstate;
+ if ((state & kSignalMask) != 0) {
+ // Consume the signal and return immediately.
+ newstate = state - kWaiterInc - kSignalInc;
+ } else {
+ // Remove this thread from pre-wait counter and add to the waiter stack.
+ newstate = ((state & kWaiterMask) - kWaiterInc) | me;
+ w->next.store(state & (kStackMask | kEpochMask),
+ std::memory_order_relaxed);
+ }
+ CheckState(newstate);
+ if (state_.compare_exchange_weak(state, newstate,
+ std::memory_order_acq_rel)) {
+ if ((state & kSignalMask) == 0) {
+ w->epoch += kEpochInc;
+ Park(w);
+ }
+ return;
+ }
+ }
+ }
+
+ // CancelWait cancels effects of the previous Prewait call.
+ void CancelWait() {
+ uint64_t state = state_.load(std::memory_order_relaxed);
+ for (;;) {
+ CheckState(state, true);
+ uint64_t newstate = state - kWaiterInc;
+ // We don't know if the thread was also notified or not,
+ // so we should not consume a signal unconditionally.
+ // Only if number of waiters is equal to number of signals,
+ // we know that the thread was notified and we must take away the signal.
+ if (((state & kWaiterMask) >> kWaiterShift) ==
+ ((state & kSignalMask) >> kSignalShift))
+ newstate -= kSignalInc;
+ CheckState(newstate);
+ if (state_.compare_exchange_weak(state, newstate,
+ std::memory_order_acq_rel))
+ return;
+ }
+ }
+
+ // Notify wakes one or all waiting threads.
+ // Must be called after changing the associated wait predicate.
+ void Notify(bool notifyAll) {
+ std::atomic_thread_fence(std::memory_order_seq_cst);
+ uint64_t state = state_.load(std::memory_order_acquire);
+ for (;;) {
+ CheckState(state);
+ const uint64_t waiters = (state & kWaiterMask) >> kWaiterShift;
+ const uint64_t signals = (state & kSignalMask) >> kSignalShift;
+ // Easy case: no waiters.
+ if ((state & kStackMask) == kStackMask && waiters == signals) return;
+ uint64_t newstate;
+ if (notifyAll) {
+ // Empty wait stack and set signal to number of pre-wait threads.
+ newstate =
+ (state & kWaiterMask) | (waiters << kSignalShift) | kStackMask;
+ } else if (signals < waiters) {
+ // There is a thread in pre-wait state, unblock it.
+ newstate = state + kSignalInc;
+ } else {
+ // Pop a waiter from list and unpark it.
+ Waiter* w = &waiters_[state & kStackMask];
+ uint64_t next = w->next.load(std::memory_order_relaxed);
+ newstate = (state & (kWaiterMask | kSignalMask)) | next;
+ }
+ CheckState(newstate);
+ if (state_.compare_exchange_weak(state, newstate,
+ std::memory_order_acq_rel)) {
+ if (!notifyAll && (signals < waiters))
+ return; // unblocked pre-wait thread
+ if ((state & kStackMask) == kStackMask) return;
+ Waiter* w = &waiters_[state & kStackMask];
+ if (!notifyAll) w->next.store(kStackMask, std::memory_order_relaxed);
+ Unpark(w);
+ return;
+ }
+ }
+ }
+
+ class Waiter {
+ friend class EventCount;
+ // Align to 128 byte boundary to prevent false sharing with other Waiter
+ // objects in the same vector.
+ EIGEN_ALIGN_TO_BOUNDARY(128) std::atomic<uint64_t> next;
+ EIGEN_MUTEX mu;
+ EIGEN_CONDVAR cv;
+ uint64_t epoch = 0;
+ unsigned state = kNotSignaled;
+ enum {
+ kNotSignaled,
+ kWaiting,
+ kSignaled,
+ };
+ };
+
+ private:
+ // State_ layout:
+ // - low kWaiterBits is a stack of waiters committed wait
+ // (indexes in waiters_ array are used as stack elements,
+ // kStackMask means empty stack).
+ // - next kWaiterBits is count of waiters in prewait state.
+ // - next kWaiterBits is count of pending signals.
+ // - remaining bits are ABA counter for the stack.
+ // (stored in Waiter node and incremented on push).
+ static const uint64_t kWaiterBits = 14;
+ static const uint64_t kStackMask = (1ull << kWaiterBits) - 1;
+ static const uint64_t kWaiterShift = kWaiterBits;
+ static const uint64_t kWaiterMask = ((1ull << kWaiterBits) - 1)
+ << kWaiterShift;
+ static const uint64_t kWaiterInc = 1ull << kWaiterShift;
+ static const uint64_t kSignalShift = 2 * kWaiterBits;
+ static const uint64_t kSignalMask = ((1ull << kWaiterBits) - 1)
+ << kSignalShift;
+ static const uint64_t kSignalInc = 1ull << kSignalShift;
+ static const uint64_t kEpochShift = 3 * kWaiterBits;
+ static const uint64_t kEpochBits = 64 - kEpochShift;
+ static const uint64_t kEpochMask = ((1ull << kEpochBits) - 1) << kEpochShift;
+ static const uint64_t kEpochInc = 1ull << kEpochShift;
+ std::atomic<uint64_t> state_;
+ MaxSizeVector<Waiter>& waiters_;
+
+ static void CheckState(uint64_t state, bool waiter = false) {
+ static_assert(kEpochBits >= 20, "not enough bits to prevent ABA problem");
+ const uint64_t waiters = (state & kWaiterMask) >> kWaiterShift;
+ const uint64_t signals = (state & kSignalMask) >> kSignalShift;
+ eigen_plain_assert(waiters >= signals);
+ eigen_plain_assert(waiters < (1 << kWaiterBits) - 1);
+ eigen_plain_assert(!waiter || waiters > 0);
+ (void)waiters;
+ (void)signals;
+ }
+
+ void Park(Waiter* w) {
+ EIGEN_MUTEX_LOCK lock(w->mu);
+ while (w->state != Waiter::kSignaled) {
+ w->state = Waiter::kWaiting;
+ w->cv.wait(lock);
+ }
+ }
+
+ void Unpark(Waiter* w) {
+ for (Waiter* next; w; w = next) {
+ uint64_t wnext = w->next.load(std::memory_order_relaxed) & kStackMask;
+ next = wnext == kStackMask ? nullptr : &waiters_[wnext];
+ unsigned state;
+ {
+ EIGEN_MUTEX_LOCK lock(w->mu);
+ state = w->state;
+ w->state = Waiter::kSignaled;
+ }
+ // Avoid notifying if it wasn't waiting.
+ if (state == Waiter::kWaiting) w->cv.notify_one();
+ }
+ }
+
+ EventCount(const EventCount&) = delete;
+ void operator=(const EventCount&) = delete;
+};
+
+} // namespace Eigen
+
+#endif // EIGEN_CXX11_THREADPOOL_EVENTCOUNT_H
diff --git a/unsupported/Eigen/CXX11/src/ThreadPool/InternalHeaderCheck.h b/unsupported/Eigen/CXX11/src/ThreadPool/InternalHeaderCheck.h
new file mode 100644
index 0000000..82a89a9
--- /dev/null
+++ b/unsupported/Eigen/CXX11/src/ThreadPool/InternalHeaderCheck.h
@@ -0,0 +1,3 @@
+#ifndef EIGEN_CXX11_THREADPOOL_MODULE_H
+#error "Please include unsupported/Eigen/CXX11/ThreadPool instead of including headers inside the src directory directly."
+#endif
diff --git a/unsupported/Eigen/CXX11/src/ThreadPool/NonBlockingThreadPool.h b/unsupported/Eigen/CXX11/src/ThreadPool/NonBlockingThreadPool.h
new file mode 100644
index 0000000..40f2f3f
--- /dev/null
+++ b/unsupported/Eigen/CXX11/src/ThreadPool/NonBlockingThreadPool.h
@@ -0,0 +1,488 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2016 Dmitry Vyukov <dvyukov@google.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_CXX11_THREADPOOL_NONBLOCKING_THREAD_POOL_H
+#define EIGEN_CXX11_THREADPOOL_NONBLOCKING_THREAD_POOL_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+template <typename Environment>
+class ThreadPoolTempl : public Eigen::ThreadPoolInterface {
+ public:
+ typedef typename Environment::Task Task;
+ typedef RunQueue<Task, 1024> Queue;
+
+ ThreadPoolTempl(int num_threads, Environment env = Environment())
+ : ThreadPoolTempl(num_threads, true, env) {}
+
+ ThreadPoolTempl(int num_threads, bool allow_spinning,
+ Environment env = Environment())
+ : env_(env),
+ num_threads_(num_threads),
+ allow_spinning_(allow_spinning),
+ thread_data_(num_threads),
+ all_coprimes_(num_threads),
+ waiters_(num_threads),
+ global_steal_partition_(EncodePartition(0, num_threads_)),
+ blocked_(0),
+ spinning_(0),
+ done_(false),
+ cancelled_(false),
+ ec_(waiters_) {
+ waiters_.resize(num_threads_);
+ // Calculate coprimes of all numbers [1, num_threads].
+ // Coprimes are used for random walks over all threads in Steal
+ // and NonEmptyQueueIndex. Iteration is based on the fact that if we take
+ // a random starting thread index t and calculate num_threads - 1 subsequent
+ // indices as (t + coprime) % num_threads, we will cover all threads without
+ // repetitions (effectively getting a presudo-random permutation of thread
+ // indices).
+ eigen_plain_assert(num_threads_ < kMaxThreads);
+ for (int i = 1; i <= num_threads_; ++i) {
+ all_coprimes_.emplace_back(i);
+ ComputeCoprimes(i, &all_coprimes_.back());
+ }
+#ifndef EIGEN_THREAD_LOCAL
+ init_barrier_.reset(new Barrier(num_threads_));
+#endif
+ thread_data_.resize(num_threads_);
+ for (int i = 0; i < num_threads_; i++) {
+ SetStealPartition(i, EncodePartition(0, num_threads_));
+ thread_data_[i].thread.reset(
+ env_.CreateThread([this, i]() { WorkerLoop(i); }));
+ }
+#ifndef EIGEN_THREAD_LOCAL
+ // Wait for workers to initialize per_thread_map_. Otherwise we might race
+ // with them in Schedule or CurrentThreadId.
+ init_barrier_->Wait();
+#endif
+ }
+
+ ~ThreadPoolTempl() {
+ done_ = true;
+
+ // Now if all threads block without work, they will start exiting.
+ // But note that threads can continue to work arbitrary long,
+ // block, submit new work, unblock and otherwise live full life.
+ if (!cancelled_) {
+ ec_.Notify(true);
+ } else {
+ // Since we were cancelled, there might be entries in the queues.
+ // Empty them to prevent their destructor from asserting.
+ for (size_t i = 0; i < thread_data_.size(); i++) {
+ thread_data_[i].queue.Flush();
+ }
+ }
+ // Join threads explicitly (by destroying) to avoid destruction order within
+ // this class.
+ for (size_t i = 0; i < thread_data_.size(); ++i)
+ thread_data_[i].thread.reset();
+ }
+
+ void SetStealPartitions(const std::vector<std::pair<unsigned, unsigned>>& partitions) {
+ eigen_plain_assert(partitions.size() == static_cast<std::size_t>(num_threads_));
+
+ // Pass this information to each thread queue.
+ for (int i = 0; i < num_threads_; i++) {
+ const auto& pair = partitions[i];
+ unsigned start = pair.first, end = pair.second;
+ AssertBounds(start, end);
+ unsigned val = EncodePartition(start, end);
+ SetStealPartition(i, val);
+ }
+ }
+
+ void Schedule(std::function<void()> fn) EIGEN_OVERRIDE {
+ ScheduleWithHint(std::move(fn), 0, num_threads_);
+ }
+
+ void ScheduleWithHint(std::function<void()> fn, int start,
+ int limit) override {
+ Task t = env_.CreateTask(std::move(fn));
+ PerThread* pt = GetPerThread();
+ if (pt->pool == this) {
+ // Worker thread of this pool, push onto the thread's queue.
+ Queue& q = thread_data_[pt->thread_id].queue;
+ t = q.PushFront(std::move(t));
+ } else {
+ // A free-standing thread (or worker of another pool), push onto a random
+ // queue.
+ eigen_plain_assert(start < limit);
+ eigen_plain_assert(limit <= num_threads_);
+ int num_queues = limit - start;
+ int rnd = Rand(&pt->rand) % num_queues;
+ eigen_plain_assert(start + rnd < limit);
+ Queue& q = thread_data_[start + rnd].queue;
+ t = q.PushBack(std::move(t));
+ }
+ // Note: below we touch this after making w available to worker threads.
+ // Strictly speaking, this can lead to a racy-use-after-free. Consider that
+ // Schedule is called from a thread that is neither main thread nor a worker
+ // thread of this pool. Then, execution of w directly or indirectly
+ // completes overall computations, which in turn leads to destruction of
+ // this. We expect that such scenario is prevented by program, that is,
+ // this is kept alive while any threads can potentially be in Schedule.
+ if (!t.f) {
+ ec_.Notify(false);
+ } else {
+ env_.ExecuteTask(t); // Push failed, execute directly.
+ }
+ }
+
+ void Cancel() EIGEN_OVERRIDE {
+ cancelled_ = true;
+ done_ = true;
+
+ // Let each thread know it's been cancelled.
+#ifdef EIGEN_THREAD_ENV_SUPPORTS_CANCELLATION
+ for (size_t i = 0; i < thread_data_.size(); i++) {
+ thread_data_[i].thread->OnCancel();
+ }
+#endif
+
+ // Wake up the threads without work to let them exit on their own.
+ ec_.Notify(true);
+ }
+
+ int NumThreads() const EIGEN_FINAL { return num_threads_; }
+
+ int CurrentThreadId() const EIGEN_FINAL {
+ const PerThread* pt = const_cast<ThreadPoolTempl*>(this)->GetPerThread();
+ if (pt->pool == this) {
+ return pt->thread_id;
+ } else {
+ return -1;
+ }
+ }
+
+ private:
+ // Create a single atomic<int> that encodes start and limit information for
+ // each thread.
+ // We expect num_threads_ < 65536, so we can store them in a single
+ // std::atomic<unsigned>.
+ // Exposed publicly as static functions so that external callers can reuse
+ // this encode/decode logic for maintaining their own thread-safe copies of
+ // scheduling and steal domain(s).
+ static const int kMaxPartitionBits = 16;
+ static const int kMaxThreads = 1 << kMaxPartitionBits;
+
+ inline unsigned EncodePartition(unsigned start, unsigned limit) {
+ return (start << kMaxPartitionBits) | limit;
+ }
+
+ inline void DecodePartition(unsigned val, unsigned* start, unsigned* limit) {
+ *limit = val & (kMaxThreads - 1);
+ val >>= kMaxPartitionBits;
+ *start = val;
+ }
+
+ void AssertBounds(int start, int end) {
+ eigen_plain_assert(start >= 0);
+ eigen_plain_assert(start < end); // non-zero sized partition
+ eigen_plain_assert(end <= num_threads_);
+ }
+
+ inline void SetStealPartition(size_t i, unsigned val) {
+ thread_data_[i].steal_partition.store(val, std::memory_order_relaxed);
+ }
+
+ inline unsigned GetStealPartition(int i) {
+ return thread_data_[i].steal_partition.load(std::memory_order_relaxed);
+ }
+
+ void ComputeCoprimes(int N, MaxSizeVector<unsigned>* coprimes) {
+ for (int i = 1; i <= N; i++) {
+ unsigned a = i;
+ unsigned b = N;
+ // If GCD(a, b) == 1, then a and b are coprimes.
+ while (b != 0) {
+ unsigned tmp = a;
+ a = b;
+ b = tmp % b;
+ }
+ if (a == 1) {
+ coprimes->push_back(i);
+ }
+ }
+ }
+
+ typedef typename Environment::EnvThread Thread;
+
+ struct PerThread {
+ constexpr PerThread() : pool(NULL), rand(0), thread_id(-1) {}
+ ThreadPoolTempl* pool; // Parent pool, or null for normal threads.
+ uint64_t rand; // Random generator state.
+ int thread_id; // Worker thread index in pool.
+#ifndef EIGEN_THREAD_LOCAL
+ // Prevent false sharing.
+ char pad_[128];
+#endif
+ };
+
+ struct ThreadData {
+ constexpr ThreadData() : thread(), steal_partition(0), queue() {}
+ std::unique_ptr<Thread> thread;
+ std::atomic<unsigned> steal_partition;
+ Queue queue;
+ };
+
+ Environment env_;
+ const int num_threads_;
+ const bool allow_spinning_;
+ MaxSizeVector<ThreadData> thread_data_;
+ MaxSizeVector<MaxSizeVector<unsigned>> all_coprimes_;
+ MaxSizeVector<EventCount::Waiter> waiters_;
+ unsigned global_steal_partition_;
+ std::atomic<unsigned> blocked_;
+ std::atomic<bool> spinning_;
+ std::atomic<bool> done_;
+ std::atomic<bool> cancelled_;
+ EventCount ec_;
+#ifndef EIGEN_THREAD_LOCAL
+ std::unique_ptr<Barrier> init_barrier_;
+ EIGEN_MUTEX per_thread_map_mutex_; // Protects per_thread_map_.
+ std::unordered_map<uint64_t, std::unique_ptr<PerThread>> per_thread_map_;
+#endif
+
+ // Main worker thread loop.
+ void WorkerLoop(int thread_id) {
+#ifndef EIGEN_THREAD_LOCAL
+ std::unique_ptr<PerThread> new_pt(new PerThread());
+ per_thread_map_mutex_.lock();
+ bool insertOK = per_thread_map_.emplace(GlobalThreadIdHash(), std::move(new_pt)).second;
+ eigen_plain_assert(insertOK);
+ EIGEN_UNUSED_VARIABLE(insertOK);
+ per_thread_map_mutex_.unlock();
+ init_barrier_->Notify();
+ init_barrier_->Wait();
+#endif
+ PerThread* pt = GetPerThread();
+ pt->pool = this;
+ pt->rand = GlobalThreadIdHash();
+ pt->thread_id = thread_id;
+ Queue& q = thread_data_[thread_id].queue;
+ EventCount::Waiter* waiter = &waiters_[thread_id];
+ // TODO(dvyukov,rmlarsen): The time spent in NonEmptyQueueIndex() is
+ // proportional to num_threads_ and we assume that new work is scheduled at
+ // a constant rate, so we set spin_count to 5000 / num_threads_. The
+ // constant was picked based on a fair dice roll, tune it.
+ const int spin_count =
+ allow_spinning_ && num_threads_ > 0 ? 5000 / num_threads_ : 0;
+ if (num_threads_ == 1) {
+ // For num_threads_ == 1 there is no point in going through the expensive
+ // steal loop. Moreover, since NonEmptyQueueIndex() calls PopBack() on the
+ // victim queues it might reverse the order in which ops are executed
+ // compared to the order in which they are scheduled, which tends to be
+ // counter-productive for the types of I/O workloads the single thread
+ // pools tend to be used for.
+ while (!cancelled_) {
+ Task t = q.PopFront();
+ for (int i = 0; i < spin_count && !t.f; i++) {
+ if (!cancelled_.load(std::memory_order_relaxed)) {
+ t = q.PopFront();
+ }
+ }
+ if (!t.f) {
+ if (!WaitForWork(waiter, &t)) {
+ return;
+ }
+ }
+ if (t.f) {
+ env_.ExecuteTask(t);
+ }
+ }
+ } else {
+ while (!cancelled_) {
+ Task t = q.PopFront();
+ if (!t.f) {
+ t = LocalSteal();
+ if (!t.f) {
+ t = GlobalSteal();
+ if (!t.f) {
+ // Leave one thread spinning. This reduces latency.
+ if (allow_spinning_ && !spinning_ && !spinning_.exchange(true)) {
+ for (int i = 0; i < spin_count && !t.f; i++) {
+ if (!cancelled_.load(std::memory_order_relaxed)) {
+ t = GlobalSteal();
+ } else {
+ return;
+ }
+ }
+ spinning_ = false;
+ }
+ if (!t.f) {
+ if (!WaitForWork(waiter, &t)) {
+ return;
+ }
+ }
+ }
+ }
+ }
+ if (t.f) {
+ env_.ExecuteTask(t);
+ }
+ }
+ }
+ }
+
+ // Steal tries to steal work from other worker threads in the range [start,
+ // limit) in best-effort manner.
+ Task Steal(unsigned start, unsigned limit) {
+ PerThread* pt = GetPerThread();
+ const size_t size = limit - start;
+ unsigned r = Rand(&pt->rand);
+ // Reduce r into [0, size) range, this utilizes trick from
+ // https://lemire.me/blog/2016/06/27/a-fast-alternative-to-the-modulo-reduction/
+ eigen_plain_assert(all_coprimes_[size - 1].size() < (1<<30));
+ unsigned victim = ((uint64_t)r * (uint64_t)size) >> 32;
+ unsigned index = ((uint64_t) all_coprimes_[size - 1].size() * (uint64_t)r) >> 32;
+ unsigned inc = all_coprimes_[size - 1][index];
+
+ for (unsigned i = 0; i < size; i++) {
+ eigen_plain_assert(start + victim < limit);
+ Task t = thread_data_[start + victim].queue.PopBack();
+ if (t.f) {
+ return t;
+ }
+ victim += inc;
+ if (victim >= size) {
+ victim -= size;
+ }
+ }
+ return Task();
+ }
+
+ // Steals work within threads belonging to the partition.
+ Task LocalSteal() {
+ PerThread* pt = GetPerThread();
+ unsigned partition = GetStealPartition(pt->thread_id);
+ // If thread steal partition is the same as global partition, there is no
+ // need to go through the steal loop twice.
+ if (global_steal_partition_ == partition) return Task();
+ unsigned start, limit;
+ DecodePartition(partition, &start, &limit);
+ AssertBounds(start, limit);
+
+ return Steal(start, limit);
+ }
+
+ // Steals work from any other thread in the pool.
+ Task GlobalSteal() {
+ return Steal(0, num_threads_);
+ }
+
+
+ // WaitForWork blocks until new work is available (returns true), or if it is
+ // time to exit (returns false). Can optionally return a task to execute in t
+ // (in such case t.f != nullptr on return).
+ bool WaitForWork(EventCount::Waiter* waiter, Task* t) {
+ eigen_plain_assert(!t->f);
+ // We already did best-effort emptiness check in Steal, so prepare for
+ // blocking.
+ ec_.Prewait();
+ // Now do a reliable emptiness check.
+ int victim = NonEmptyQueueIndex();
+ if (victim != -1) {
+ ec_.CancelWait();
+ if (cancelled_) {
+ return false;
+ } else {
+ *t = thread_data_[victim].queue.PopBack();
+ return true;
+ }
+ }
+ // Number of blocked threads is used as termination condition.
+ // If we are shutting down and all worker threads blocked without work,
+ // that's we are done.
+ blocked_++;
+ // TODO is blocked_ required to be unsigned?
+ if (done_ && blocked_ == static_cast<unsigned>(num_threads_)) {
+ ec_.CancelWait();
+ // Almost done, but need to re-check queues.
+ // Consider that all queues are empty and all worker threads are preempted
+ // right after incrementing blocked_ above. Now a free-standing thread
+ // submits work and calls destructor (which sets done_). If we don't
+ // re-check queues, we will exit leaving the work unexecuted.
+ if (NonEmptyQueueIndex() != -1) {
+ // Note: we must not pop from queues before we decrement blocked_,
+ // otherwise the following scenario is possible. Consider that instead
+ // of checking for emptiness we popped the only element from queues.
+ // Now other worker threads can start exiting, which is bad if the
+ // work item submits other work. So we just check emptiness here,
+ // which ensures that all worker threads exit at the same time.
+ blocked_--;
+ return true;
+ }
+ // Reached stable termination state.
+ ec_.Notify(true);
+ return false;
+ }
+ ec_.CommitWait(waiter);
+ blocked_--;
+ return true;
+ }
+
+ int NonEmptyQueueIndex() {
+ PerThread* pt = GetPerThread();
+ // We intentionally design NonEmptyQueueIndex to steal work from
+ // anywhere in the queue so threads don't block in WaitForWork() forever
+ // when all threads in their partition go to sleep. Steal is still local.
+ const size_t size = thread_data_.size();
+ unsigned r = Rand(&pt->rand);
+ unsigned inc = all_coprimes_[size - 1][r % all_coprimes_[size - 1].size()];
+ unsigned victim = r % size;
+ for (unsigned i = 0; i < size; i++) {
+ if (!thread_data_[victim].queue.Empty()) {
+ return victim;
+ }
+ victim += inc;
+ if (victim >= size) {
+ victim -= size;
+ }
+ }
+ return -1;
+ }
+
+ static EIGEN_STRONG_INLINE uint64_t GlobalThreadIdHash() {
+ return std::hash<std::thread::id>()(std::this_thread::get_id());
+ }
+
+ EIGEN_STRONG_INLINE PerThread* GetPerThread() {
+#ifndef EIGEN_THREAD_LOCAL
+ static PerThread dummy;
+ auto it = per_thread_map_.find(GlobalThreadIdHash());
+ if (it == per_thread_map_.end()) {
+ return &dummy;
+ } else {
+ return it->second.get();
+ }
+#else
+ EIGEN_THREAD_LOCAL PerThread per_thread_;
+ PerThread* pt = &per_thread_;
+ return pt;
+#endif
+ }
+
+ static EIGEN_STRONG_INLINE unsigned Rand(uint64_t* state) {
+ uint64_t current = *state;
+ // Update the internal state
+ *state = current * 6364136223846793005ULL + 0xda3e39cb94b95bdbULL;
+ // Generate the random output (using the PCG-XSH-RS scheme)
+ return static_cast<unsigned>((current ^ (current >> 22)) >>
+ (22 + (current >> 61)));
+ }
+};
+
+typedef ThreadPoolTempl<StlThreadEnvironment> ThreadPool;
+
+} // namespace Eigen
+
+#endif // EIGEN_CXX11_THREADPOOL_NONBLOCKING_THREAD_POOL_H
diff --git a/unsupported/Eigen/CXX11/src/ThreadPool/RunQueue.h b/unsupported/Eigen/CXX11/src/ThreadPool/RunQueue.h
new file mode 100644
index 0000000..2005fb2
--- /dev/null
+++ b/unsupported/Eigen/CXX11/src/ThreadPool/RunQueue.h
@@ -0,0 +1,238 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2016 Dmitry Vyukov <dvyukov@google.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_CXX11_THREADPOOL_RUNQUEUE_H
+#define EIGEN_CXX11_THREADPOOL_RUNQUEUE_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+// RunQueue is a fixed-size, partially non-blocking deque or Work items.
+// Operations on front of the queue must be done by a single thread (owner),
+// operations on back of the queue can be done by multiple threads concurrently.
+//
+// Algorithm outline:
+// All remote threads operating on the queue back are serialized by a mutex.
+// This ensures that at most two threads access state: owner and one remote
+// thread (Size aside). The algorithm ensures that the occupied region of the
+// underlying array is logically continuous (can wraparound, but no stray
+// occupied elements). Owner operates on one end of this region, remote thread
+// operates on the other end. Synchronization between these threads
+// (potential consumption of the last element and take up of the last empty
+// element) happens by means of state variable in each element. States are:
+// empty, busy (in process of insertion of removal) and ready. Threads claim
+// elements (empty->busy and ready->busy transitions) by means of a CAS
+// operation. The finishing transition (busy->empty and busy->ready) are done
+// with plain store as the element is exclusively owned by the current thread.
+//
+// Note: we could permit only pointers as elements, then we would not need
+// separate state variable as null/non-null pointer value would serve as state,
+// but that would require malloc/free per operation for large, complex values
+// (and this is designed to store std::function<()>).
+template <typename Work, unsigned kSize>
+class RunQueue {
+ public:
+ RunQueue() : front_(0), back_(0) {
+ // require power-of-two for fast masking
+ eigen_plain_assert((kSize & (kSize - 1)) == 0);
+ eigen_plain_assert(kSize > 2); // why would you do this?
+ eigen_plain_assert(kSize <= (64 << 10)); // leave enough space for counter
+ for (unsigned i = 0; i < kSize; i++)
+ array_[i].state.store(kEmpty, std::memory_order_relaxed);
+ }
+
+ ~RunQueue() { eigen_plain_assert(Size() == 0); }
+
+ // PushFront inserts w at the beginning of the queue.
+ // If queue is full returns w, otherwise returns default-constructed Work.
+ Work PushFront(Work w) {
+ unsigned front = front_.load(std::memory_order_relaxed);
+ Elem* e = &array_[front & kMask];
+ uint8_t s = e->state.load(std::memory_order_relaxed);
+ if (s != kEmpty ||
+ !e->state.compare_exchange_strong(s, kBusy, std::memory_order_acquire))
+ return w;
+ front_.store(front + 1 + (kSize << 1), std::memory_order_relaxed);
+ e->w = std::move(w);
+ e->state.store(kReady, std::memory_order_release);
+ return Work();
+ }
+
+ // PopFront removes and returns the first element in the queue.
+ // If the queue was empty returns default-constructed Work.
+ Work PopFront() {
+ unsigned front = front_.load(std::memory_order_relaxed);
+ Elem* e = &array_[(front - 1) & kMask];
+ uint8_t s = e->state.load(std::memory_order_relaxed);
+ if (s != kReady ||
+ !e->state.compare_exchange_strong(s, kBusy, std::memory_order_acquire))
+ return Work();
+ Work w = std::move(e->w);
+ e->state.store(kEmpty, std::memory_order_release);
+ front = ((front - 1) & kMask2) | (front & ~kMask2);
+ front_.store(front, std::memory_order_relaxed);
+ return w;
+ }
+
+ // PushBack adds w at the end of the queue.
+ // If queue is full returns w, otherwise returns default-constructed Work.
+ Work PushBack(Work w) {
+ EIGEN_MUTEX_LOCK lock(mutex_);
+ unsigned back = back_.load(std::memory_order_relaxed);
+ Elem* e = &array_[(back - 1) & kMask];
+ uint8_t s = e->state.load(std::memory_order_relaxed);
+ if (s != kEmpty ||
+ !e->state.compare_exchange_strong(s, kBusy, std::memory_order_acquire))
+ return w;
+ back = ((back - 1) & kMask2) | (back & ~kMask2);
+ back_.store(back, std::memory_order_relaxed);
+ e->w = std::move(w);
+ e->state.store(kReady, std::memory_order_release);
+ return Work();
+ }
+
+ // PopBack removes and returns the last elements in the queue.
+ Work PopBack() {
+ if (Empty()) return Work();
+ EIGEN_MUTEX_LOCK lock(mutex_);
+ unsigned back = back_.load(std::memory_order_relaxed);
+ Elem* e = &array_[back & kMask];
+ uint8_t s = e->state.load(std::memory_order_relaxed);
+ if (s != kReady ||
+ !e->state.compare_exchange_strong(s, kBusy, std::memory_order_acquire))
+ return Work();
+ Work w = std::move(e->w);
+ e->state.store(kEmpty, std::memory_order_release);
+ back_.store(back + 1 + (kSize << 1), std::memory_order_relaxed);
+ return w;
+ }
+
+ // PopBackHalf removes and returns half last elements in the queue.
+ // Returns number of elements removed.
+ unsigned PopBackHalf(std::vector<Work>* result) {
+ if (Empty()) return 0;
+ EIGEN_MUTEX_LOCK lock(mutex_);
+ unsigned back = back_.load(std::memory_order_relaxed);
+ unsigned size = Size();
+ unsigned mid = back;
+ if (size > 1) mid = back + (size - 1) / 2;
+ unsigned n = 0;
+ unsigned start = 0;
+ for (; static_cast<int>(mid - back) >= 0; mid--) {
+ Elem* e = &array_[mid & kMask];
+ uint8_t s = e->state.load(std::memory_order_relaxed);
+ if (n == 0) {
+ if (s != kReady || !e->state.compare_exchange_strong(
+ s, kBusy, std::memory_order_acquire))
+ continue;
+ start = mid;
+ } else {
+ // Note: no need to store temporal kBusy, we exclusively own these
+ // elements.
+ eigen_plain_assert(s == kReady);
+ }
+ result->push_back(std::move(e->w));
+ e->state.store(kEmpty, std::memory_order_release);
+ n++;
+ }
+ if (n != 0)
+ back_.store(start + 1 + (kSize << 1), std::memory_order_relaxed);
+ return n;
+ }
+
+ // Size returns current queue size.
+ // Can be called by any thread at any time.
+ unsigned Size() const { return SizeOrNotEmpty<true>(); }
+
+ // Empty tests whether container is empty.
+ // Can be called by any thread at any time.
+ bool Empty() const { return SizeOrNotEmpty<false>() == 0; }
+
+ // Delete all the elements from the queue.
+ void Flush() {
+ while (!Empty()) {
+ PopFront();
+ }
+ }
+
+ private:
+ static const unsigned kMask = kSize - 1;
+ static const unsigned kMask2 = (kSize << 1) - 1;
+ struct Elem {
+ std::atomic<uint8_t> state;
+ Work w;
+ };
+ enum {
+ kEmpty,
+ kBusy,
+ kReady,
+ };
+ EIGEN_MUTEX mutex_;
+ // Low log(kSize) + 1 bits in front_ and back_ contain rolling index of
+ // front/back, respectively. The remaining bits contain modification counters
+ // that are incremented on Push operations. This allows us to (1) distinguish
+ // between empty and full conditions (if we would use log(kSize) bits for
+ // position, these conditions would be indistinguishable); (2) obtain
+ // consistent snapshot of front_/back_ for Size operation using the
+ // modification counters.
+ std::atomic<unsigned> front_;
+ std::atomic<unsigned> back_;
+ Elem array_[kSize];
+
+ // SizeOrNotEmpty returns current queue size; if NeedSizeEstimate is false,
+ // only whether the size is 0 is guaranteed to be correct.
+ // Can be called by any thread at any time.
+ template<bool NeedSizeEstimate>
+ unsigned SizeOrNotEmpty() const {
+ // Emptiness plays critical role in thread pool blocking. So we go to great
+ // effort to not produce false positives (claim non-empty queue as empty).
+ unsigned front = front_.load(std::memory_order_acquire);
+ for (;;) {
+ // Capture a consistent snapshot of front/tail.
+ unsigned back = back_.load(std::memory_order_acquire);
+ unsigned front1 = front_.load(std::memory_order_relaxed);
+ if (front != front1) {
+ front = front1;
+ std::atomic_thread_fence(std::memory_order_acquire);
+ continue;
+ }
+ if (NeedSizeEstimate) {
+ return CalculateSize(front, back);
+ } else {
+ // This value will be 0 if the queue is empty, and undefined otherwise.
+ unsigned maybe_zero = ((front ^ back) & kMask2);
+ // Queue size estimate must agree with maybe zero check on the queue
+ // empty/non-empty state.
+ eigen_assert((CalculateSize(front, back) == 0) == (maybe_zero == 0));
+ return maybe_zero;
+ }
+ }
+ }
+
+ EIGEN_ALWAYS_INLINE
+ unsigned CalculateSize(unsigned front, unsigned back) const {
+ int size = (front & kMask2) - (back & kMask2);
+ // Fix overflow.
+ if (size < 0) size += 2 * kSize;
+ // Order of modification in push/pop is crafted to make the queue look
+ // larger than it is during concurrent modifications. E.g. push can
+ // increment size before the corresponding pop has decremented it.
+ // So the computed size can be up to kSize + 1, fix it.
+ if (size > static_cast<int>(kSize)) size = kSize;
+ return static_cast<unsigned>(size);
+ }
+
+ RunQueue(const RunQueue&) = delete;
+ void operator=(const RunQueue&) = delete;
+};
+
+} // namespace Eigen
+
+#endif // EIGEN_CXX11_THREADPOOL_RUNQUEUE_H
diff --git a/unsupported/Eigen/CXX11/src/ThreadPool/ThreadCancel.h b/unsupported/Eigen/CXX11/src/ThreadPool/ThreadCancel.h
new file mode 100644
index 0000000..a05685f
--- /dev/null
+++ b/unsupported/Eigen/CXX11/src/ThreadPool/ThreadCancel.h
@@ -0,0 +1,23 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2016 Benoit Steiner <benoit.steiner.goog@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_CXX11_THREADPOOL_THREAD_CANCEL_H
+#define EIGEN_CXX11_THREADPOOL_THREAD_CANCEL_H
+
+// Try to come up with a portable way to cancel a thread
+#if EIGEN_OS_GNULINUX
+ #define EIGEN_THREAD_CANCEL(t) \
+ pthread_cancel(t.native_handle());
+ #define EIGEN_SUPPORTS_THREAD_CANCELLATION 1
+#else
+#define EIGEN_THREAD_CANCEL(t)
+#endif
+
+
+#endif // EIGEN_CXX11_THREADPOOL_THREAD_CANCEL_H
diff --git a/unsupported/Eigen/CXX11/src/ThreadPool/ThreadEnvironment.h b/unsupported/Eigen/CXX11/src/ThreadPool/ThreadEnvironment.h
new file mode 100644
index 0000000..02ec366
--- /dev/null
+++ b/unsupported/Eigen/CXX11/src/ThreadPool/ThreadEnvironment.h
@@ -0,0 +1,42 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_CXX11_THREADPOOL_THREAD_ENVIRONMENT_H
+#define EIGEN_CXX11_THREADPOOL_THREAD_ENVIRONMENT_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+struct StlThreadEnvironment {
+ struct Task {
+ std::function<void()> f;
+ };
+
+ // EnvThread constructor must start the thread,
+ // destructor must join the thread.
+ class EnvThread {
+ public:
+ EnvThread(std::function<void()> f) : thr_(std::move(f)) {}
+ ~EnvThread() { thr_.join(); }
+ // This function is called when the threadpool is cancelled.
+ void OnCancel() { }
+
+ private:
+ std::thread thr_;
+ };
+
+ EnvThread* CreateThread(std::function<void()> f) { return new EnvThread(std::move(f)); }
+ Task CreateTask(std::function<void()> f) { return Task{std::move(f)}; }
+ void ExecuteTask(const Task& t) { t.f(); }
+};
+
+} // namespace Eigen
+
+#endif // EIGEN_CXX11_THREADPOOL_THREAD_ENVIRONMENT_H
diff --git a/unsupported/Eigen/CXX11/src/ThreadPool/ThreadLocal.h b/unsupported/Eigen/CXX11/src/ThreadPool/ThreadLocal.h
new file mode 100644
index 0000000..4545119
--- /dev/null
+++ b/unsupported/Eigen/CXX11/src/ThreadPool/ThreadLocal.h
@@ -0,0 +1,300 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2016 Benoit Steiner <benoit.steiner.goog@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_CXX11_THREADPOOL_THREAD_LOCAL_H
+#define EIGEN_CXX11_THREADPOOL_THREAD_LOCAL_H
+
+#ifdef EIGEN_AVOID_THREAD_LOCAL
+
+#ifdef EIGEN_THREAD_LOCAL
+#undef EIGEN_THREAD_LOCAL
+#endif
+
+#else
+
+#if ((EIGEN_COMP_GNUC) || __has_feature(cxx_thread_local) || EIGEN_COMP_MSVC )
+#define EIGEN_THREAD_LOCAL static thread_local
+#endif
+
+// Disable TLS for Apple and Android builds with older toolchains.
+#if defined(__APPLE__)
+// Included for TARGET_OS_IPHONE, __IPHONE_OS_VERSION_MIN_REQUIRED,
+// __IPHONE_8_0.
+#include <Availability.h>
+#include <TargetConditionals.h>
+#endif
+// Checks whether C++11's `thread_local` storage duration specifier is
+// supported.
+#if defined(__apple_build_version__) && \
+ ((__apple_build_version__ < 8000042) || \
+ (TARGET_OS_IPHONE && __IPHONE_OS_VERSION_MIN_REQUIRED < __IPHONE_9_0))
+// Notes: Xcode's clang did not support `thread_local` until version
+// 8, and even then not for all iOS < 9.0.
+#undef EIGEN_THREAD_LOCAL
+
+#elif defined(__ANDROID__) && EIGEN_COMP_CLANG
+// There are platforms for which TLS should not be used even though the compiler
+// makes it seem like it's supported (Android NDK < r12b for example).
+// This is primarily because of linker problems and toolchain misconfiguration:
+// TLS isn't supported until NDK r12b per
+// https://developer.android.com/ndk/downloads/revision_history.html
+// Since NDK r16, `__NDK_MAJOR__` and `__NDK_MINOR__` are defined in
+// <android/ndk-version.h>. For NDK < r16, users should define these macros,
+// e.g. `-D__NDK_MAJOR__=11 -D__NKD_MINOR__=0` for NDK r11.
+#if __has_include(<android/ndk-version.h>)
+#include <android/ndk-version.h>
+#endif // __has_include(<android/ndk-version.h>)
+#if defined(__ANDROID__) && defined(__clang__) && defined(__NDK_MAJOR__) && \
+ defined(__NDK_MINOR__) && \
+ ((__NDK_MAJOR__ < 12) || ((__NDK_MAJOR__ == 12) && (__NDK_MINOR__ < 1)))
+#undef EIGEN_THREAD_LOCAL
+#endif
+#endif // defined(__ANDROID__) && defined(__clang__)
+
+#endif // EIGEN_AVOID_THREAD_LOCAL
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+template <typename T>
+struct ThreadLocalNoOpInitialize {
+ void operator()(T&) const {}
+};
+
+template <typename T>
+struct ThreadLocalNoOpRelease {
+ void operator()(T&) const {}
+};
+
+} // namespace internal
+
+// Thread local container for elements of type T, that does not use thread local
+// storage. As long as the number of unique threads accessing this storage
+// is smaller than `capacity_`, it is lock-free and wait-free. Otherwise it will
+// use a mutex for synchronization.
+//
+// Type `T` has to be default constructible, and by default each thread will get
+// a default constructed value. It is possible to specify custom `initialize`
+// callable, that will be called lazily from each thread accessing this object,
+// and will be passed a default initialized object of type `T`. Also it's
+// possible to pass a custom `release` callable, that will be invoked before
+// calling ~T().
+//
+// Example:
+//
+// struct Counter {
+// int value = 0;
+// }
+//
+// Eigen::ThreadLocal<Counter> counter(10);
+//
+// // Each thread will have access to it's own counter object.
+// Counter& cnt = counter.local();
+// cnt++;
+//
+// WARNING: Eigen::ThreadLocal uses the OS-specific value returned by
+// std::this_thread::get_id() to identify threads. This value is not guaranteed
+// to be unique except for the life of the thread. A newly created thread may
+// get an OS-specific ID equal to that of an already destroyed thread.
+//
+// Somewhat similar to TBB thread local storage, with similar restrictions:
+// https://www.threadingbuildingblocks.org/docs/help/reference/thread_local_storage/enumerable_thread_specific_cls.html
+//
+template <typename T,
+ typename Initialize = internal::ThreadLocalNoOpInitialize<T>,
+ typename Release = internal::ThreadLocalNoOpRelease<T>>
+class ThreadLocal {
+ // We preallocate default constructed elements in MaxSizedVector.
+ static_assert(std::is_default_constructible<T>::value,
+ "ThreadLocal data type must be default constructible");
+
+ public:
+ explicit ThreadLocal(int capacity)
+ : ThreadLocal(capacity, internal::ThreadLocalNoOpInitialize<T>(),
+ internal::ThreadLocalNoOpRelease<T>()) {}
+
+ ThreadLocal(int capacity, Initialize initialize)
+ : ThreadLocal(capacity, std::move(initialize),
+ internal::ThreadLocalNoOpRelease<T>()) {}
+
+ ThreadLocal(int capacity, Initialize initialize, Release release)
+ : initialize_(std::move(initialize)),
+ release_(std::move(release)),
+ capacity_(capacity),
+ data_(capacity_),
+ ptr_(capacity_),
+ filled_records_(0) {
+ eigen_assert(capacity_ >= 0);
+ data_.resize(capacity_);
+ for (int i = 0; i < capacity_; ++i) {
+ ptr_.emplace_back(nullptr);
+ }
+ }
+
+ T& local() {
+ std::thread::id this_thread = std::this_thread::get_id();
+ if (capacity_ == 0) return SpilledLocal(this_thread);
+
+ std::size_t h = std::hash<std::thread::id>()(this_thread);
+ const int start_idx = h % capacity_;
+
+ // NOTE: From the definition of `std::this_thread::get_id()` it is
+ // guaranteed that we never can have concurrent insertions with the same key
+ // to our hash-map like data structure. If we didn't find an element during
+ // the initial traversal, it's guaranteed that no one else could have
+ // inserted it while we are in this function. This allows to massively
+ // simplify out lock-free insert-only hash map.
+
+ // Check if we already have an element for `this_thread`.
+ int idx = start_idx;
+ while (ptr_[idx].load() != nullptr) {
+ ThreadIdAndValue& record = *(ptr_[idx].load());
+ if (record.thread_id == this_thread) return record.value;
+
+ idx += 1;
+ if (idx >= capacity_) idx -= capacity_;
+ if (idx == start_idx) break;
+ }
+
+ // If we are here, it means that we found an insertion point in lookup
+ // table at `idx`, or we did a full traversal and table is full.
+
+ // If lock-free storage is full, fallback on mutex.
+ if (filled_records_.load() >= capacity_) return SpilledLocal(this_thread);
+
+ // We double check that we still have space to insert an element into a lock
+ // free storage. If old value in `filled_records_` is larger than the
+ // records capacity, it means that some other thread added an element while
+ // we were traversing lookup table.
+ int insertion_index =
+ filled_records_.fetch_add(1, std::memory_order_relaxed);
+ if (insertion_index >= capacity_) return SpilledLocal(this_thread);
+
+ // At this point it's guaranteed that we can access to
+ // data_[insertion_index_] without a data race.
+ data_[insertion_index].thread_id = this_thread;
+ initialize_(data_[insertion_index].value);
+
+ // That's the pointer we'll put into the lookup table.
+ ThreadIdAndValue* inserted = &data_[insertion_index];
+
+ // We'll use nullptr pointer to ThreadIdAndValue in a compare-and-swap loop.
+ ThreadIdAndValue* empty = nullptr;
+
+ // Now we have to find an insertion point into the lookup table. We start
+ // from the `idx` that was identified as an insertion point above, it's
+ // guaranteed that we will have an empty record somewhere in a lookup table
+ // (because we created a record in the `data_`).
+ const int insertion_idx = idx;
+
+ do {
+ // Always start search from the original insertion candidate.
+ idx = insertion_idx;
+ while (ptr_[idx].load() != nullptr) {
+ idx += 1;
+ if (idx >= capacity_) idx -= capacity_;
+ // If we did a full loop, it means that we don't have any free entries
+ // in the lookup table, and this means that something is terribly wrong.
+ eigen_assert(idx != insertion_idx);
+ }
+ // Atomic CAS of the pointer guarantees that any other thread, that will
+ // follow this pointer will see all the mutations in the `data_`.
+ } while (!ptr_[idx].compare_exchange_weak(empty, inserted));
+
+ return inserted->value;
+ }
+
+ // WARN: It's not thread safe to call it concurrently with `local()`.
+ void ForEach(std::function<void(std::thread::id, T&)> f) {
+ // Reading directly from `data_` is unsafe, because only CAS to the
+ // record in `ptr_` makes all changes visible to other threads.
+ for (auto& ptr : ptr_) {
+ ThreadIdAndValue* record = ptr.load();
+ if (record == nullptr) continue;
+ f(record->thread_id, record->value);
+ }
+
+ // We did not spill into the map based storage.
+ if (filled_records_.load(std::memory_order_relaxed) < capacity_) return;
+
+ // Adds a happens before edge from the last call to SpilledLocal().
+ EIGEN_MUTEX_LOCK lock(mu_);
+ for (auto& kv : per_thread_map_) {
+ f(kv.first, kv.second);
+ }
+ }
+
+ // WARN: It's not thread safe to call it concurrently with `local()`.
+ ~ThreadLocal() {
+ // Reading directly from `data_` is unsafe, because only CAS to the record
+ // in `ptr_` makes all changes visible to other threads.
+ for (auto& ptr : ptr_) {
+ ThreadIdAndValue* record = ptr.load();
+ if (record == nullptr) continue;
+ release_(record->value);
+ }
+
+ // We did not spill into the map based storage.
+ if (filled_records_.load(std::memory_order_relaxed) < capacity_) return;
+
+ // Adds a happens before edge from the last call to SpilledLocal().
+ EIGEN_MUTEX_LOCK lock(mu_);
+ for (auto& kv : per_thread_map_) {
+ release_(kv.second);
+ }
+ }
+
+ private:
+ struct ThreadIdAndValue {
+ std::thread::id thread_id;
+ T value;
+ };
+
+ // Use unordered map guarded by a mutex when lock free storage is full.
+ T& SpilledLocal(std::thread::id this_thread) {
+ EIGEN_MUTEX_LOCK lock(mu_);
+
+ auto it = per_thread_map_.find(this_thread);
+ if (it == per_thread_map_.end()) {
+ auto result = per_thread_map_.emplace(this_thread, T());
+ eigen_assert(result.second);
+ initialize_((*result.first).second);
+ return (*result.first).second;
+ } else {
+ return it->second;
+ }
+ }
+
+ Initialize initialize_;
+ Release release_;
+ const int capacity_;
+
+ // Storage that backs lock-free lookup table `ptr_`. Records stored in this
+ // storage contiguously starting from index 0.
+ MaxSizeVector<ThreadIdAndValue> data_;
+
+ // Atomic pointers to the data stored in `data_`. Used as a lookup table for
+ // linear probing hash map (https://en.wikipedia.org/wiki/Linear_probing).
+ MaxSizeVector<std::atomic<ThreadIdAndValue*>> ptr_;
+
+ // Number of records stored in the `data_`.
+ std::atomic<int> filled_records_;
+
+ // We fallback on per thread map if lock-free storage is full. In practice
+ // this should never happen, if `capacity_` is a reasonable estimate of the
+ // number of threads running in a system.
+ EIGEN_MUTEX mu_; // Protects per_thread_map_.
+ std::unordered_map<std::thread::id, T> per_thread_map_;
+};
+
+} // namespace Eigen
+
+#endif // EIGEN_CXX11_THREADPOOL_THREAD_LOCAL_H
diff --git a/unsupported/Eigen/CXX11/src/ThreadPool/ThreadPoolInterface.h b/unsupported/Eigen/CXX11/src/ThreadPool/ThreadPoolInterface.h
new file mode 100644
index 0000000..e6750a9
--- /dev/null
+++ b/unsupported/Eigen/CXX11/src/ThreadPool/ThreadPoolInterface.h
@@ -0,0 +1,50 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_CXX11_THREADPOOL_THREAD_POOL_INTERFACE_H
+#define EIGEN_CXX11_THREADPOOL_THREAD_POOL_INTERFACE_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+// This defines an interface that ThreadPoolDevice can take to use
+// custom thread pools underneath.
+class ThreadPoolInterface {
+ public:
+ // Submits a closure to be run by a thread in the pool.
+ virtual void Schedule(std::function<void()> fn) = 0;
+
+ // Submits a closure to be run by threads in the range [start, end) in the
+ // pool.
+ virtual void ScheduleWithHint(std::function<void()> fn, int /*start*/,
+ int /*end*/) {
+ // Just defer to Schedule in case sub-classes aren't interested in
+ // overriding this functionality.
+ Schedule(fn);
+ }
+
+ // If implemented, stop processing the closures that have been enqueued.
+ // Currently running closures may still be processed.
+ // If not implemented, does nothing.
+ virtual void Cancel() {}
+
+ // Returns the number of threads in the pool.
+ virtual int NumThreads() const = 0;
+
+ // Returns a logical thread index between 0 and NumThreads() - 1 if called
+ // from one of the threads in the pool. Returns -1 otherwise.
+ virtual int CurrentThreadId() const = 0;
+
+ virtual ~ThreadPoolInterface() {}
+};
+
+} // namespace Eigen
+
+#endif // EIGEN_CXX11_THREADPOOL_THREAD_POOL_INTERFACE_H
diff --git a/unsupported/Eigen/CXX11/src/ThreadPool/ThreadYield.h b/unsupported/Eigen/CXX11/src/ThreadPool/ThreadYield.h
new file mode 100644
index 0000000..f556ff6
--- /dev/null
+++ b/unsupported/Eigen/CXX11/src/ThreadPool/ThreadYield.h
@@ -0,0 +1,16 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2016 Benoit Steiner <benoit.steiner.goog@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_CXX11_THREADPOOL_THREAD_YIELD_H
+#define EIGEN_CXX11_THREADPOOL_THREAD_YIELD_H
+
+// Try to come up with a portable way to yield
+#define EIGEN_THREAD_YIELD() std::this_thread::yield()
+
+#endif // EIGEN_CXX11_THREADPOOL_THREAD_YIELD_H
diff --git a/unsupported/Eigen/CXX11/src/util/CXX11Meta.h b/unsupported/Eigen/CXX11/src/util/CXX11Meta.h
new file mode 100644
index 0000000..bcf847e
--- /dev/null
+++ b/unsupported/Eigen/CXX11/src/util/CXX11Meta.h
@@ -0,0 +1,539 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2013 Christian Seiler <christian@iwakd.de>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_CXX11META_H
+#define EIGEN_CXX11META_H
+
+#include <vector>
+#include "EmulateArray.h"
+
+#include "CXX11Workarounds.h"
+
+namespace Eigen {
+
+namespace internal {
+
+/** \internal
+ * \file CXX11/util/CXX11Meta.h
+ * This file contains generic metaprogramming classes which are not specifically related to Eigen.
+ * This file expands upon Core/util/Meta.h and adds support for C++11 specific features.
+ */
+
+template<typename... tt>
+struct type_list { constexpr static int count = sizeof...(tt); };
+
+template<typename t, typename... tt>
+struct type_list<t, tt...> { constexpr static int count = sizeof...(tt) + 1; typedef t first_type; };
+
+template<typename T, T... nn>
+struct numeric_list { constexpr static std::size_t count = sizeof...(nn); };
+
+template<typename T, T n, T... nn>
+struct numeric_list<T, n, nn...> { static constexpr std::size_t count = sizeof...(nn) + 1;
+ static constexpr T first_value = n; };
+
+#ifndef EIGEN_PARSED_BY_DOXYGEN
+/* numeric list constructors
+ *
+ * equivalencies:
+ * constructor result
+ * typename gen_numeric_list<int, 5>::type numeric_list<int, 0,1,2,3,4>
+ * typename gen_numeric_list_reversed<int, 5>::type numeric_list<int, 4,3,2,1,0>
+ * typename gen_numeric_list_swapped_pair<int, 5,1,2>::type numeric_list<int, 0,2,1,3,4>
+ * typename gen_numeric_list_repeated<int, 0, 5>::type numeric_list<int, 0,0,0,0,0>
+ */
+
+template<typename T, std::size_t n, T start = 0, T... ii> struct gen_numeric_list : gen_numeric_list<T, n-1, start, start + n-1, ii...> {};
+template<typename T, T start, T... ii> struct gen_numeric_list<T, 0, start, ii...> { typedef numeric_list<T, ii...> type; };
+
+template<typename T, std::size_t n, T start = 0, T... ii> struct gen_numeric_list_reversed : gen_numeric_list_reversed<T, n-1, start, ii..., start + n-1> {};
+template<typename T, T start, T... ii> struct gen_numeric_list_reversed<T, 0, start, ii...> { typedef numeric_list<T, ii...> type; };
+
+template<typename T, std::size_t n, T a, T b, T start = 0, T... ii> struct gen_numeric_list_swapped_pair : gen_numeric_list_swapped_pair<T, n-1, a, b, start, (start + n-1) == a ? b : ((start + n-1) == b ? a : (start + n-1)), ii...> {};
+template<typename T, T a, T b, T start, T... ii> struct gen_numeric_list_swapped_pair<T, 0, a, b, start, ii...> { typedef numeric_list<T, ii...> type; };
+
+template<typename T, std::size_t n, T V, T... nn> struct gen_numeric_list_repeated : gen_numeric_list_repeated<T, n-1, V, V, nn...> {};
+template<typename T, T V, T... nn> struct gen_numeric_list_repeated<T, 0, V, nn...> { typedef numeric_list<T, nn...> type; };
+
+/* list manipulation: concatenate */
+
+template<class a, class b> struct concat;
+
+template<typename... as, typename... bs> struct concat<type_list<as...>, type_list<bs...>> { typedef type_list<as..., bs...> type; };
+template<typename T, T... as, T... bs> struct concat<numeric_list<T, as...>, numeric_list<T, bs...> > { typedef numeric_list<T, as..., bs...> type; };
+
+template<typename... p> struct mconcat;
+template<typename a> struct mconcat<a> { typedef a type; };
+template<typename a, typename b> struct mconcat<a, b> : concat<a, b> {};
+template<typename a, typename b, typename... cs> struct mconcat<a, b, cs...> : concat<a, typename mconcat<b, cs...>::type> {};
+
+/* list manipulation: extract slices */
+
+template<int n, typename x> struct take;
+template<int n, typename a, typename... as> struct take<n, type_list<a, as...>> : concat<type_list<a>, typename take<n-1, type_list<as...>>::type> {};
+template<int n> struct take<n, type_list<>> { typedef type_list<> type; };
+template<typename a, typename... as> struct take<0, type_list<a, as...>> { typedef type_list<> type; };
+template<> struct take<0, type_list<>> { typedef type_list<> type; };
+
+template<typename T, int n, T a, T... as> struct take<n, numeric_list<T, a, as...>> : concat<numeric_list<T, a>, typename take<n-1, numeric_list<T, as...>>::type> {};
+// XXX The following breaks in gcc-11, and is invalid anyways.
+// template<typename T, int n> struct take<n, numeric_list<T>> { typedef numeric_list<T> type; };
+template<typename T, T a, T... as> struct take<0, numeric_list<T, a, as...>> { typedef numeric_list<T> type; };
+template<typename T> struct take<0, numeric_list<T>> { typedef numeric_list<T> type; };
+
+template<typename T, int n, T... ii> struct h_skip_helper_numeric;
+template<typename T, int n, T i, T... ii> struct h_skip_helper_numeric<T, n, i, ii...> : h_skip_helper_numeric<T, n-1, ii...> {};
+template<typename T, T i, T... ii> struct h_skip_helper_numeric<T, 0, i, ii...> { typedef numeric_list<T, i, ii...> type; };
+template<typename T, int n> struct h_skip_helper_numeric<T, n> { typedef numeric_list<T> type; };
+template<typename T> struct h_skip_helper_numeric<T, 0> { typedef numeric_list<T> type; };
+
+template<int n, typename... tt> struct h_skip_helper_type;
+template<int n, typename t, typename... tt> struct h_skip_helper_type<n, t, tt...> : h_skip_helper_type<n-1, tt...> {};
+template<typename t, typename... tt> struct h_skip_helper_type<0, t, tt...> { typedef type_list<t, tt...> type; };
+template<int n> struct h_skip_helper_type<n> { typedef type_list<> type; };
+template<> struct h_skip_helper_type<0> { typedef type_list<> type; };
+#endif //not EIGEN_PARSED_BY_DOXYGEN
+
+template<int n>
+struct h_skip {
+ template<typename T, T... ii>
+ constexpr static EIGEN_STRONG_INLINE typename h_skip_helper_numeric<T, n, ii...>::type helper(numeric_list<T, ii...>) { return typename h_skip_helper_numeric<T, n, ii...>::type(); }
+ template<typename... tt>
+ constexpr static EIGEN_STRONG_INLINE typename h_skip_helper_type<n, tt...>::type helper(type_list<tt...>) { return typename h_skip_helper_type<n, tt...>::type(); }
+};
+
+template<int n, typename a> struct skip { typedef decltype(h_skip<n>::helper(a())) type; };
+
+template<int start, int count, typename a> struct slice : take<count, typename skip<start, a>::type> {};
+
+/* list manipulation: retrieve single element from list */
+
+template<int n, typename x> struct get;
+
+template<int n, typename a, typename... as> struct get<n, type_list<a, as...>> : get<n-1, type_list<as...>> {};
+template<typename a, typename... as> struct get<0, type_list<a, as...>> { typedef a type; };
+
+template<typename T, int n, T a, T... as> struct get<n, numeric_list<T, a, as...>> : get<n-1, numeric_list<T, as...>> {};
+template<typename T, T a, T... as> struct get<0, numeric_list<T, a, as...>> { constexpr static T value = a; };
+
+template<std::size_t n, typename T, T a, T... as> constexpr T array_get(const numeric_list<T, a, as...>&) {
+ return get<(int)n, numeric_list<T, a, as...>>::value;
+}
+
+/* always get type, regardless of dummy; good for parameter pack expansion */
+
+template<typename T, T dummy, typename t> struct id_numeric { typedef t type; };
+template<typename dummy, typename t> struct id_type { typedef t type; };
+
+/* equality checking, flagged version */
+
+template<typename a, typename b> struct is_same_gf : is_same<a, b> { constexpr static int global_flags = 0; };
+
+/* apply_op to list */
+
+template<
+ bool from_left, // false
+ template<typename, typename> class op,
+ typename additional_param,
+ typename... values
+>
+struct h_apply_op_helper { typedef type_list<typename op<values, additional_param>::type...> type; };
+template<
+ template<typename, typename> class op,
+ typename additional_param,
+ typename... values
+>
+struct h_apply_op_helper<true, op, additional_param, values...> { typedef type_list<typename op<additional_param, values>::type...> type; };
+
+template<
+ bool from_left,
+ template<typename, typename> class op,
+ typename additional_param
+>
+struct h_apply_op
+{
+ template<typename... values>
+ constexpr static typename h_apply_op_helper<from_left, op, additional_param, values...>::type helper(type_list<values...>)
+ { return typename h_apply_op_helper<from_left, op, additional_param, values...>::type(); }
+};
+
+template<
+ template<typename, typename> class op,
+ typename additional_param,
+ typename a
+>
+struct apply_op_from_left { typedef decltype(h_apply_op<true, op, additional_param>::helper(a())) type; };
+
+template<
+ template<typename, typename> class op,
+ typename additional_param,
+ typename a
+>
+struct apply_op_from_right { typedef decltype(h_apply_op<false, op, additional_param>::helper(a())) type; };
+
+/* see if an element is in a list */
+
+template<
+ template<typename, typename> class test,
+ typename check_against,
+ typename h_list,
+ bool last_check_positive = false
+>
+struct contained_in_list;
+
+template<
+ template<typename, typename> class test,
+ typename check_against,
+ typename h_list
+>
+struct contained_in_list<test, check_against, h_list, true>
+{
+ constexpr static bool value = true;
+};
+
+template<
+ template<typename, typename> class test,
+ typename check_against,
+ typename a,
+ typename... as
+>
+struct contained_in_list<test, check_against, type_list<a, as...>, false> : contained_in_list<test, check_against, type_list<as...>, test<check_against, a>::value> {};
+
+template<
+ template<typename, typename> class test,
+ typename check_against
+ EIGEN_TPL_PP_SPEC_HACK_DEFC(typename, empty)
+>
+struct contained_in_list<test, check_against, type_list<EIGEN_TPL_PP_SPEC_HACK_USE(empty)>, false> { constexpr static bool value = false; };
+
+/* see if an element is in a list and check for global flags */
+
+template<
+ template<typename, typename> class test,
+ typename check_against,
+ typename h_list,
+ int default_flags = 0,
+ bool last_check_positive = false,
+ int last_check_flags = default_flags
+>
+struct contained_in_list_gf;
+
+template<
+ template<typename, typename> class test,
+ typename check_against,
+ typename h_list,
+ int default_flags,
+ int last_check_flags
+>
+struct contained_in_list_gf<test, check_against, h_list, default_flags, true, last_check_flags>
+{
+ constexpr static bool value = true;
+ constexpr static int global_flags = last_check_flags;
+};
+
+template<
+ template<typename, typename> class test,
+ typename check_against,
+ typename a,
+ typename... as,
+ int default_flags,
+ int last_check_flags
+>
+struct contained_in_list_gf<test, check_against, type_list<a, as...>, default_flags, false, last_check_flags> : contained_in_list_gf<test, check_against, type_list<as...>, default_flags, test<check_against, a>::value, test<check_against, a>::global_flags> {};
+
+template<
+ template<typename, typename> class test,
+ typename check_against
+ EIGEN_TPL_PP_SPEC_HACK_DEFC(typename, empty),
+ int default_flags,
+ int last_check_flags
+>
+struct contained_in_list_gf<test, check_against, type_list<EIGEN_TPL_PP_SPEC_HACK_USE(empty)>, default_flags, false, last_check_flags> { constexpr static bool value = false; constexpr static int global_flags = default_flags; };
+
+/* generic reductions */
+
+template<
+ typename Reducer,
+ typename... Ts
+> struct reduce;
+
+template<
+ typename Reducer
+> struct reduce<Reducer>
+{
+ EIGEN_DEVICE_FUNC constexpr static EIGEN_STRONG_INLINE int run() { return Reducer::Identity; }
+};
+
+template<
+ typename Reducer,
+ typename A
+> struct reduce<Reducer, A>
+{
+ EIGEN_DEVICE_FUNC constexpr static EIGEN_STRONG_INLINE A run(A a) { return a; }
+};
+
+template<
+ typename Reducer,
+ typename A,
+ typename... Ts
+> struct reduce<Reducer, A, Ts...>
+{
+ EIGEN_DEVICE_FUNC constexpr static EIGEN_STRONG_INLINE auto run(A a, Ts... ts) -> decltype(Reducer::run(a, reduce<Reducer, Ts...>::run(ts...))) {
+ return Reducer::run(a, reduce<Reducer, Ts...>::run(ts...));
+ }
+};
+
+/* generic binary operations */
+
+struct sum_op {
+ template<typename A, typename B> EIGEN_DEVICE_FUNC constexpr static EIGEN_STRONG_INLINE auto run(A a, B b) -> decltype(a + b) { return a + b; }
+ static constexpr int Identity = 0;
+};
+struct product_op {
+ template<typename A, typename B> EIGEN_DEVICE_FUNC constexpr static EIGEN_STRONG_INLINE auto run(A a, B b) -> decltype(a * b) { return a * b; }
+ static constexpr int Identity = 1;
+};
+
+struct logical_and_op { template<typename A, typename B> constexpr static EIGEN_STRONG_INLINE auto run(A a, B b) -> decltype(a && b) { return a && b; } };
+struct logical_or_op { template<typename A, typename B> constexpr static EIGEN_STRONG_INLINE auto run(A a, B b) -> decltype(a || b) { return a || b; } };
+
+struct equal_op { template<typename A, typename B> constexpr static EIGEN_STRONG_INLINE auto run(A a, B b) -> decltype(a == b) { return a == b; } };
+struct not_equal_op { template<typename A, typename B> constexpr static EIGEN_STRONG_INLINE auto run(A a, B b) -> decltype(a != b) { return a != b; } };
+struct lesser_op { template<typename A, typename B> constexpr static EIGEN_STRONG_INLINE auto run(A a, B b) -> decltype(a < b) { return a < b; } };
+struct lesser_equal_op { template<typename A, typename B> constexpr static EIGEN_STRONG_INLINE auto run(A a, B b) -> decltype(a <= b) { return a <= b; } };
+struct greater_op { template<typename A, typename B> constexpr static EIGEN_STRONG_INLINE auto run(A a, B b) -> decltype(a > b) { return a > b; } };
+struct greater_equal_op { template<typename A, typename B> constexpr static EIGEN_STRONG_INLINE auto run(A a, B b) -> decltype(a >= b) { return a >= b; } };
+
+/* generic unary operations */
+
+struct not_op { template<typename A> constexpr static EIGEN_STRONG_INLINE auto run(A a) -> decltype(!a) { return !a; } };
+struct negation_op { template<typename A> constexpr static EIGEN_STRONG_INLINE auto run(A a) -> decltype(-a) { return -a; } };
+struct greater_equal_zero_op { template<typename A> constexpr static EIGEN_STRONG_INLINE auto run(A a) -> decltype(a >= 0) { return a >= 0; } };
+
+
+/* reductions for lists */
+
+// using auto -> return value spec makes ICC 13.0 and 13.1 crash here, so we have to hack it
+// together in front... (13.0 doesn't work with array_prod/array_reduce/... anyway, but 13.1
+// does...
+template<typename... Ts>
+EIGEN_DEVICE_FUNC constexpr EIGEN_STRONG_INLINE decltype(reduce<product_op, Ts...>::run((*((Ts*)0))...)) arg_prod(Ts... ts)
+{
+ return reduce<product_op, Ts...>::run(ts...);
+}
+
+template<typename... Ts>
+constexpr EIGEN_STRONG_INLINE decltype(reduce<sum_op, Ts...>::run((*((Ts*)0))...)) arg_sum(Ts... ts)
+{
+ return reduce<sum_op, Ts...>::run(ts...);
+}
+
+/* reverse arrays */
+
+template<typename Array, int... n>
+constexpr EIGEN_STRONG_INLINE Array h_array_reverse(Array arr, numeric_list<int, n...>)
+{
+ return {{array_get<sizeof...(n) - n - 1>(arr)...}};
+}
+
+template<typename T, std::size_t N>
+constexpr EIGEN_STRONG_INLINE array<T, N> array_reverse(array<T, N> arr)
+{
+ return h_array_reverse(arr, typename gen_numeric_list<int, N>::type());
+}
+
+
+/* generic array reductions */
+
+// can't reuse standard reduce() interface above because Intel's Compiler
+// *really* doesn't like it, so we just reimplement the stuff
+// (start from N - 1 and work down to 0 because specialization for
+// n == N - 1 also doesn't work in Intel's compiler, so it goes into
+// an infinite loop)
+template<typename Reducer, typename T, std::size_t N, std::size_t n = N - 1>
+struct h_array_reduce {
+ EIGEN_DEVICE_FUNC constexpr static EIGEN_STRONG_INLINE auto run(array<T, N> arr, T identity) -> decltype(Reducer::run(h_array_reduce<Reducer, T, N, n - 1>::run(arr, identity), array_get<n>(arr)))
+ {
+ return Reducer::run(h_array_reduce<Reducer, T, N, n - 1>::run(arr, identity), array_get<n>(arr));
+ }
+};
+
+template<typename Reducer, typename T, std::size_t N>
+struct h_array_reduce<Reducer, T, N, 0>
+{
+ EIGEN_DEVICE_FUNC constexpr static EIGEN_STRONG_INLINE T run(const array<T, N>& arr, T)
+ {
+ return array_get<0>(arr);
+ }
+};
+
+template<typename Reducer, typename T>
+struct h_array_reduce<Reducer, T, 0>
+{
+ EIGEN_DEVICE_FUNC constexpr static EIGEN_STRONG_INLINE T run(const array<T, 0>&, T identity)
+ {
+ return identity;
+ }
+};
+
+template<typename Reducer, typename T, std::size_t N>
+EIGEN_DEVICE_FUNC constexpr EIGEN_STRONG_INLINE auto array_reduce(const array<T, N>& arr, T identity) -> decltype(h_array_reduce<Reducer, T, N>::run(arr, identity))
+{
+ return h_array_reduce<Reducer, T, N>::run(arr, identity);
+}
+
+/* standard array reductions */
+
+template<typename T, std::size_t N>
+EIGEN_DEVICE_FUNC constexpr EIGEN_STRONG_INLINE auto array_sum(const array<T, N>& arr) -> decltype(array_reduce<sum_op, T, N>(arr, static_cast<T>(0)))
+{
+ return array_reduce<sum_op, T, N>(arr, static_cast<T>(0));
+}
+
+template<typename T, std::size_t N>
+EIGEN_DEVICE_FUNC constexpr EIGEN_STRONG_INLINE auto array_prod(const array<T, N>& arr) -> decltype(array_reduce<product_op, T, N>(arr, static_cast<T>(1)))
+{
+ return array_reduce<product_op, T, N>(arr, static_cast<T>(1));
+}
+
+template<typename t>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE t array_prod(const std::vector<t>& a) {
+ eigen_assert(a.size() > 0);
+ t prod = 1;
+ for (size_t i = 0; i < a.size(); ++i) { prod *= a[i]; }
+ return prod;
+}
+
+/* zip an array */
+
+template<typename Op, typename A, typename B, std::size_t N, int... n>
+constexpr EIGEN_STRONG_INLINE array<decltype(Op::run(A(), B())),N> h_array_zip(array<A, N> a, array<B, N> b, numeric_list<int, n...>)
+{
+ return array<decltype(Op::run(A(), B())),N>{{ Op::run(array_get<n>(a), array_get<n>(b))... }};
+}
+
+template<typename Op, typename A, typename B, std::size_t N>
+constexpr EIGEN_STRONG_INLINE array<decltype(Op::run(A(), B())),N> array_zip(array<A, N> a, array<B, N> b)
+{
+ return h_array_zip<Op>(a, b, typename gen_numeric_list<int, N>::type());
+}
+
+/* zip an array and reduce the result */
+
+template<typename Reducer, typename Op, typename A, typename B, std::size_t N, int... n>
+constexpr EIGEN_STRONG_INLINE auto h_array_zip_and_reduce(array<A, N> a, array<B, N> b, numeric_list<int, n...>) -> decltype(reduce<Reducer, typename id_numeric<int,n,decltype(Op::run(A(), B()))>::type...>::run(Op::run(array_get<n>(a), array_get<n>(b))...))
+{
+ return reduce<Reducer, typename id_numeric<int,n,decltype(Op::run(A(), B()))>::type...>::run(Op::run(array_get<n>(a), array_get<n>(b))...);
+}
+
+template<typename Reducer, typename Op, typename A, typename B, std::size_t N>
+constexpr EIGEN_STRONG_INLINE auto array_zip_and_reduce(array<A, N> a, array<B, N> b) -> decltype(h_array_zip_and_reduce<Reducer, Op, A, B, N>(a, b, typename gen_numeric_list<int, N>::type()))
+{
+ return h_array_zip_and_reduce<Reducer, Op, A, B, N>(a, b, typename gen_numeric_list<int, N>::type());
+}
+
+/* apply stuff to an array */
+
+template<typename Op, typename A, std::size_t N, int... n>
+constexpr EIGEN_STRONG_INLINE array<decltype(Op::run(A())),N> h_array_apply(array<A, N> a, numeric_list<int, n...>)
+{
+ return array<decltype(Op::run(A())),N>{{ Op::run(array_get<n>(a))... }};
+}
+
+template<typename Op, typename A, std::size_t N>
+constexpr EIGEN_STRONG_INLINE array<decltype(Op::run(A())),N> array_apply(array<A, N> a)
+{
+ return h_array_apply<Op>(a, typename gen_numeric_list<int, N>::type());
+}
+
+/* apply stuff to an array and reduce */
+
+template<typename Reducer, typename Op, typename A, std::size_t N, int... n>
+constexpr EIGEN_STRONG_INLINE auto h_array_apply_and_reduce(array<A, N> arr, numeric_list<int, n...>) -> decltype(reduce<Reducer, typename id_numeric<int,n,decltype(Op::run(A()))>::type...>::run(Op::run(array_get<n>(arr))...))
+{
+ return reduce<Reducer, typename id_numeric<int,n,decltype(Op::run(A()))>::type...>::run(Op::run(array_get<n>(arr))...);
+}
+
+template<typename Reducer, typename Op, typename A, std::size_t N>
+constexpr EIGEN_STRONG_INLINE auto array_apply_and_reduce(array<A, N> a) -> decltype(h_array_apply_and_reduce<Reducer, Op, A, N>(a, typename gen_numeric_list<int, N>::type()))
+{
+ return h_array_apply_and_reduce<Reducer, Op, A, N>(a, typename gen_numeric_list<int, N>::type());
+}
+
+/* repeat a value n times (and make an array out of it
+ * usage:
+ * array<int, 16> = repeat<16>(42);
+ */
+
+template<int n>
+struct h_repeat
+{
+ template<typename t, int... ii>
+ constexpr static EIGEN_STRONG_INLINE array<t, n> run(t v, numeric_list<int, ii...>)
+ {
+ return {{ typename id_numeric<int, ii, t>::type(v)... }};
+ }
+};
+
+template<int n, typename t>
+constexpr array<t, n> repeat(t v) { return h_repeat<n>::run(v, typename gen_numeric_list<int, n>::type()); }
+
+/* instantiate a class by a C-style array */
+template<class InstType, typename ArrType, std::size_t N, bool Reverse, typename... Ps>
+struct h_instantiate_by_c_array;
+
+template<class InstType, typename ArrType, std::size_t N, typename... Ps>
+struct h_instantiate_by_c_array<InstType, ArrType, N, false, Ps...>
+{
+ static InstType run(ArrType* arr, Ps... args)
+ {
+ return h_instantiate_by_c_array<InstType, ArrType, N - 1, false, Ps..., ArrType>::run(arr + 1, args..., arr[0]);
+ }
+};
+
+template<class InstType, typename ArrType, std::size_t N, typename... Ps>
+struct h_instantiate_by_c_array<InstType, ArrType, N, true, Ps...>
+{
+ static InstType run(ArrType* arr, Ps... args)
+ {
+ return h_instantiate_by_c_array<InstType, ArrType, N - 1, false, ArrType, Ps...>::run(arr + 1, arr[0], args...);
+ }
+};
+
+template<class InstType, typename ArrType, typename... Ps>
+struct h_instantiate_by_c_array<InstType, ArrType, 0, false, Ps...>
+{
+ static InstType run(ArrType* arr, Ps... args)
+ {
+ (void)arr;
+ return InstType(args...);
+ }
+};
+
+template<class InstType, typename ArrType, typename... Ps>
+struct h_instantiate_by_c_array<InstType, ArrType, 0, true, Ps...>
+{
+ static InstType run(ArrType* arr, Ps... args)
+ {
+ (void)arr;
+ return InstType(args...);
+ }
+};
+
+template<class InstType, typename ArrType, std::size_t N, bool Reverse = false>
+InstType instantiate_by_c_array(ArrType* arr)
+{
+ return h_instantiate_by_c_array<InstType, ArrType, N, Reverse>::run(arr);
+}
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_CXX11META_H
diff --git a/unsupported/Eigen/CXX11/src/util/CXX11Workarounds.h b/unsupported/Eigen/CXX11/src/util/CXX11Workarounds.h
new file mode 100644
index 0000000..386e390
--- /dev/null
+++ b/unsupported/Eigen/CXX11/src/util/CXX11Workarounds.h
@@ -0,0 +1,76 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2013 Christian Seiler <christian@iwakd.de>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_CXX11WORKAROUNDS_H
+#define EIGEN_CXX11WORKAROUNDS_H
+
+/* COMPATIBILITY CHECKS
+ * (so users of compilers that are too old get some realistic error messages)
+ */
+#if defined(__INTEL_COMPILER) && (__INTEL_COMPILER < 1310)
+#error Intel Compiler only supports required C++ features since version 13.1.
+// note that most stuff in principle works with 13.0 but when combining
+// some features, at some point 13.0 will just fail with an internal assertion
+#elif defined(__GNUC__) && !defined(__clang__) && !defined(__INTEL_COMPILER) && (__GNUC__ < 4 || (__GNUC__ == 4 && __GNUC_MINOR__ < 6))
+// G++ < 4.6 by default will continue processing the source files - even if we use #error to make
+// it error out. For this reason, we use the pragma to make sure G++ aborts at the first error
+// it sees. Unfortunately, that is still not our #error directive, but at least the output is
+// short enough the user has a chance to see that the compiler version is not sufficient for
+// the funky template mojo we use.
+#pragma GCC diagnostic error "-Wfatal-errors"
+#error GNU C++ Compiler (g++) only supports required C++ features since version 4.6.
+#endif
+
+namespace Eigen {
+
+namespace internal {
+
+/* std::get is only constexpr in C++14, not yet in C++11
+ */
+
+
+template<std::size_t I_, class T> constexpr inline T& array_get(std::vector<T>& a) { return a[I_]; }
+template<std::size_t I_, class T> constexpr inline T&& array_get(std::vector<T>&& a) { return a[I_]; }
+template<std::size_t I_, class T> constexpr inline T const& array_get(std::vector<T> const& a) { return a[I_]; }
+
+/* Suppose you have a template of the form
+ * template<typename T> struct X;
+ * And you want to specialize it in such a way:
+ * template<typename S1, typename... SN> struct X<Foo<S1, SN...>> { ::: };
+ * template<> struct X<Foo<>> { ::: };
+ * This will work in Intel's compiler 13.0, but only to some extent in g++ 4.6, since
+ * g++ can only match templates called with parameter packs if the number of template
+ * arguments is not a fixed size (so inside the first specialization, referencing
+ * X<Foo<Sn...>> will fail in g++). On the other hand, g++ will accept the following:
+ * template<typename S...> struct X<Foo<S...>> { ::: }:
+ * as an additional (!) specialization, which will then only match the empty case.
+ * But Intel's compiler 13.0 won't accept that, it will only accept the empty syntax,
+ * so we have to create a workaround for this.
+ */
+#if defined(__GNUC__) && !defined(__INTEL_COMPILER)
+#define EIGEN_TPL_PP_SPEC_HACK_DEF(mt, n) mt... n
+#define EIGEN_TPL_PP_SPEC_HACK_DEFC(mt, n) , EIGEN_TPL_PP_SPEC_HACK_DEF(mt, n)
+#define EIGEN_TPL_PP_SPEC_HACK_USE(n) n...
+#define EIGEN_TPL_PP_SPEC_HACK_USEC(n) , n...
+#else
+#define EIGEN_TPL_PP_SPEC_HACK_DEF(mt, n)
+#define EIGEN_TPL_PP_SPEC_HACK_DEFC(mt, n)
+#define EIGEN_TPL_PP_SPEC_HACK_USE(n)
+#define EIGEN_TPL_PP_SPEC_HACK_USEC(n)
+#endif
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_CXX11WORKAROUNDS_H
+
+/*
+ * kate: space-indent on; indent-width 2; mixedindent off; indent-mode cstyle;
+ */
diff --git a/unsupported/Eigen/CXX11/src/util/EmulateArray.h b/unsupported/Eigen/CXX11/src/util/EmulateArray.h
new file mode 100644
index 0000000..a4b1d0c
--- /dev/null
+++ b/unsupported/Eigen/CXX11/src/util/EmulateArray.h
@@ -0,0 +1,286 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_EMULATE_ARRAY_H
+#define EIGEN_EMULATE_ARRAY_H
+
+// CUDA doesn't support the STL containers, so we use our own instead.
+#if defined(EIGEN_GPUCC) || defined(EIGEN_AVOID_STL_ARRAY)
+
+namespace Eigen {
+template <typename T, size_t n> class array {
+
+ public:
+ typedef T value_type;
+ typedef T* iterator;
+ typedef const T* const_iterator;
+
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE iterator begin() { return values; }
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE const_iterator begin() const { return values; }
+
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE iterator end() { return values + n; }
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE const_iterator end() const { return values + n; }
+
+
+#if !defined(EIGEN_GPUCC)
+ typedef std::reverse_iterator<iterator> reverse_iterator;
+ typedef std::reverse_iterator<const_iterator> const_reverse_iterator;
+
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE reverse_iterator rbegin() { return reverse_iterator(end());}
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE const_reverse_iterator rbegin() const { return const_reverse_iterator(end()); }
+
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE reverse_iterator rend() { return reverse_iterator(begin()); }
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE const_reverse_iterator rend() const { return const_reverse_iterator(begin()); }
+#endif
+
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE T& operator[] (size_t index) { eigen_internal_assert(index < size()); return values[index]; }
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE const T& operator[] (size_t index) const { eigen_internal_assert(index < size()); return values[index]; }
+
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE T& at(size_t index) { eigen_assert(index < size()); return values[index]; }
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE const T& at(size_t index) const { eigen_assert(index < size()); return values[index]; }
+
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE T& front() { return values[0]; }
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE const T& front() const { return values[0]; }
+
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE T& back() { return values[n-1]; }
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE const T& back() const { return values[n-1]; }
+
+
+ EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
+ static std::size_t size() { return n; }
+
+ T values[n];
+
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE array() { }
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE array(const T& v) {
+ EIGEN_STATIC_ASSERT(n==1, YOU_MADE_A_PROGRAMMING_MISTAKE)
+ values[0] = v;
+ }
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE array(const T& v1, const T& v2) {
+ EIGEN_STATIC_ASSERT(n==2, YOU_MADE_A_PROGRAMMING_MISTAKE)
+ values[0] = v1;
+ values[1] = v2;
+ }
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE array(const T& v1, const T& v2, const T& v3) {
+ EIGEN_STATIC_ASSERT(n==3, YOU_MADE_A_PROGRAMMING_MISTAKE)
+ values[0] = v1;
+ values[1] = v2;
+ values[2] = v3;
+ }
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE array(const T& v1, const T& v2, const T& v3,
+ const T& v4) {
+ EIGEN_STATIC_ASSERT(n==4, YOU_MADE_A_PROGRAMMING_MISTAKE)
+ values[0] = v1;
+ values[1] = v2;
+ values[2] = v3;
+ values[3] = v4;
+ }
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE array(const T& v1, const T& v2, const T& v3, const T& v4,
+ const T& v5) {
+ EIGEN_STATIC_ASSERT(n==5, YOU_MADE_A_PROGRAMMING_MISTAKE)
+ values[0] = v1;
+ values[1] = v2;
+ values[2] = v3;
+ values[3] = v4;
+ values[4] = v5;
+ }
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE array(const T& v1, const T& v2, const T& v3, const T& v4,
+ const T& v5, const T& v6) {
+ EIGEN_STATIC_ASSERT(n==6, YOU_MADE_A_PROGRAMMING_MISTAKE)
+ values[0] = v1;
+ values[1] = v2;
+ values[2] = v3;
+ values[3] = v4;
+ values[4] = v5;
+ values[5] = v6;
+ }
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE array(const T& v1, const T& v2, const T& v3, const T& v4,
+ const T& v5, const T& v6, const T& v7) {
+ EIGEN_STATIC_ASSERT(n==7, YOU_MADE_A_PROGRAMMING_MISTAKE)
+ values[0] = v1;
+ values[1] = v2;
+ values[2] = v3;
+ values[3] = v4;
+ values[4] = v5;
+ values[5] = v6;
+ values[6] = v7;
+ }
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE array(
+ const T& v1, const T& v2, const T& v3, const T& v4,
+ const T& v5, const T& v6, const T& v7, const T& v8) {
+ EIGEN_STATIC_ASSERT(n==8, YOU_MADE_A_PROGRAMMING_MISTAKE)
+ values[0] = v1;
+ values[1] = v2;
+ values[2] = v3;
+ values[3] = v4;
+ values[4] = v5;
+ values[5] = v6;
+ values[6] = v7;
+ values[7] = v8;
+ }
+
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE array(std::initializer_list<T> l) {
+ eigen_assert(l.size() == n);
+ internal::smart_copy(l.begin(), l.end(), values);
+ }
+};
+
+
+// Specialize array for zero size
+template <typename T> class array<T, 0> {
+ public:
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE T& operator[] (size_t) {
+ eigen_assert(false && "Can't index a zero size array");
+ return dummy;
+ }
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE const T& operator[] (size_t) const {
+ eigen_assert(false && "Can't index a zero size array");
+ return dummy;
+ }
+
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE T& front() {
+ eigen_assert(false && "Can't index a zero size array");
+ return dummy;
+ }
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE const T& front() const {
+ eigen_assert(false && "Can't index a zero size array");
+ return dummy;
+ }
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE T& back() {
+ eigen_assert(false && "Can't index a zero size array");
+ return dummy;
+ }
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE const T& back() const {
+ eigen_assert(false && "Can't index a zero size array");
+ return dummy;
+ }
+
+ static EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE std::size_t size() { return 0; }
+
+ EIGEN_DEVICE_FUNC
+ EIGEN_STRONG_INLINE array() : dummy() { }
+
+ EIGEN_DEVICE_FUNC array(std::initializer_list<T> l) : dummy() {
+ EIGEN_UNUSED_VARIABLE(l);
+ eigen_assert(l.size() == 0);
+ }
+
+ private:
+ T dummy;
+};
+
+// Comparison operator
+// Todo: implement !=, <, <=, >, and >=
+template<class T, std::size_t N>
+EIGEN_DEVICE_FUNC bool operator==(const array<T,N>& lhs, const array<T,N>& rhs) {
+ for (std::size_t i = 0; i < N; ++i) {
+ if (lhs[i] != rhs[i]) {
+ return false;
+ }
+ }
+ return true;
+}
+
+
+namespace internal {
+template<std::size_t I_, class T, std::size_t N>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE T& array_get(array<T,N>& a) {
+ return a[I_];
+}
+template<std::size_t I_, class T, std::size_t N>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const T& array_get(const array<T,N>& a) {
+ return a[I_];
+}
+
+template<class T, std::size_t N> struct array_size<array<T,N> > {
+ enum { value = N };
+};
+template<class T, std::size_t N> struct array_size<array<T,N>& > {
+ enum { value = N };
+};
+template<class T, std::size_t N> struct array_size<const array<T,N> > {
+ enum { value = N };
+};
+template<class T, std::size_t N> struct array_size<const array<T,N>& > {
+ enum { value = N };
+};
+
+} // end namespace internal
+} // end namespace Eigen
+
+#else
+
+// The compiler supports c++11, and we're not targeting cuda: use std::array as Eigen::array
+#include <array>
+
+namespace Eigen {
+
+template <typename T, std::size_t N> using array = std::array<T, N>;
+
+namespace internal {
+/* std::get is only constexpr in C++14, not yet in C++11
+ * - libstdc++ from version 4.7 onwards has it nevertheless,
+ * so use that
+ * - libstdc++ older versions: use _M_instance directly
+ * - libc++ all versions so far: use __elems_ directly
+ * - all other libs: use std::get to be portable, but
+ * this may not be constexpr
+ */
+#if defined(__GLIBCXX__) && __GLIBCXX__ < 20120322
+#define STD_GET_ARR_HACK a._M_instance[I_]
+#elif defined(_LIBCPP_VERSION)
+#define STD_GET_ARR_HACK a.__elems_[I_]
+#else
+#define STD_GET_ARR_HACK std::template get<I_, T, N>(a)
+#endif
+
+template<std::size_t I_, class T, std::size_t N> constexpr inline T& array_get(std::array<T,N>& a) { return (T&) STD_GET_ARR_HACK; }
+template<std::size_t I_, class T, std::size_t N> constexpr inline T&& array_get(std::array<T,N>&& a) { return (T&&) STD_GET_ARR_HACK; }
+template<std::size_t I_, class T, std::size_t N> constexpr inline T const& array_get(std::array<T,N> const& a) { return (T const&) STD_GET_ARR_HACK; }
+
+#undef STD_GET_ARR_HACK
+
+} // end namespace internal
+} // end namespace Eigen
+
+#endif
+
+#endif // EIGEN_EMULATE_ARRAY_H
diff --git a/unsupported/Eigen/CXX11/src/util/MaxSizeVector.h b/unsupported/Eigen/CXX11/src/util/MaxSizeVector.h
new file mode 100644
index 0000000..ca0e3d1
--- /dev/null
+++ b/unsupported/Eigen/CXX11/src/util/MaxSizeVector.h
@@ -0,0 +1,158 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_FIXEDSIZEVECTOR_H
+#define EIGEN_FIXEDSIZEVECTOR_H
+
+namespace Eigen {
+
+/** \class MaxSizeVector
+ * \ingroup Core
+ *
+ * \brief The MaxSizeVector class.
+ *
+ * The %MaxSizeVector provides a subset of std::vector functionality.
+ *
+ * The goal is to provide basic std::vector operations when using
+ * std::vector is not an option (e.g. on GPU or when compiling using
+ * FMA/AVX, as this can cause either compilation failures or illegal
+ * instruction failures).
+ *
+ * Beware: The constructors are not API compatible with these of
+ * std::vector.
+ */
+template <typename T>
+class MaxSizeVector {
+ static const size_t alignment = internal::plain_enum_max(EIGEN_ALIGNOF(T), sizeof(void*));
+ public:
+ // Construct a new MaxSizeVector, reserve n elements.
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ explicit MaxSizeVector(size_t n)
+ : reserve_(n), size_(0),
+ data_(static_cast<T*>(internal::handmade_aligned_malloc(n * sizeof(T), alignment))) {
+ }
+
+ // Construct a new MaxSizeVector, reserve and resize to n.
+ // Copy the init value to all elements.
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ MaxSizeVector(size_t n, const T& init)
+ : reserve_(n), size_(n),
+ data_(static_cast<T*>(internal::handmade_aligned_malloc(n * sizeof(T), alignment))) {
+ size_t i = 0;
+ EIGEN_TRY
+ {
+ for(; i < size_; ++i) { new (&data_[i]) T(init); }
+ }
+ EIGEN_CATCH(...)
+ {
+ // Construction failed, destruct in reverse order:
+ for(; (i+1) > 0; --i) { data_[i-1].~T(); }
+ internal::handmade_aligned_free(data_);
+ EIGEN_THROW;
+ }
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ ~MaxSizeVector() {
+ for (size_t i = size_; i > 0; --i) {
+ data_[i-1].~T();
+ }
+ internal::handmade_aligned_free(data_);
+ }
+
+ void resize(size_t n) {
+ eigen_assert(n <= reserve_);
+ for (; size_ < n; ++size_) {
+ new (&data_[size_]) T;
+ }
+ for (; size_ > n; --size_) {
+ data_[size_-1].~T();
+ }
+ eigen_assert(size_ == n);
+ }
+
+ // Append new elements (up to reserved size).
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ void push_back(const T& t) {
+ eigen_assert(size_ < reserve_);
+ new (&data_[size_++]) T(t);
+ }
+
+ // For C++03 compatibility this only takes one argument
+ template<class X>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ void emplace_back(const X& x) {
+ eigen_assert(size_ < reserve_);
+ new (&data_[size_++]) T(x);
+ }
+
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ const T& operator[] (size_t i) const {
+ eigen_assert(i < size_);
+ return data_[i];
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ T& operator[] (size_t i) {
+ eigen_assert(i < size_);
+ return data_[i];
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ T& back() {
+ eigen_assert(size_ > 0);
+ return data_[size_ - 1];
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ const T& back() const {
+ eigen_assert(size_ > 0);
+ return data_[size_ - 1];
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ void pop_back() {
+ eigen_assert(size_ > 0);
+ data_[--size_].~T();
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ size_t size() const { return size_; }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ bool empty() const { return size_ == 0; }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ T* data() { return data_; }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ const T* data() const { return data_; }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ T* begin() { return data_; }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ T* end() { return data_ + size_; }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ const T* begin() const { return data_; }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+ const T* end() const { return data_ + size_; }
+
+ private:
+ size_t reserve_;
+ size_t size_;
+ T* data_;
+};
+
+} // namespace Eigen
+
+#endif // EIGEN_FIXEDSIZEVECTOR_H
diff --git a/unsupported/Eigen/EulerAngles b/unsupported/Eigen/EulerAngles
new file mode 100644
index 0000000..f8f1c5d
--- /dev/null
+++ b/unsupported/Eigen/EulerAngles
@@ -0,0 +1,43 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2015 Tal Hadad <tal_hd@hotmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_EULERANGLES_MODULE_H
+#define EIGEN_EULERANGLES_MODULE_H
+
+
+#include "../../Eigen/Core"
+#include "../../Eigen/Geometry"
+
+#include "../../Eigen/src/Core/util/DisableStupidWarnings.h"
+
+namespace Eigen {
+
+/**
+ * \defgroup EulerAngles_Module EulerAngles module
+ * \brief This module provides generic euler angles rotation.
+ *
+ * Euler angles are a way to represent 3D rotation.
+ *
+ * In order to use this module in your code, include this header:
+ * \code
+ * #include <unsupported/Eigen/EulerAngles>
+ * \endcode
+ *
+ * See \ref EulerAngles for more information.
+ *
+ */
+
+}
+
+#include "src/EulerAngles/EulerSystem.h"
+#include "src/EulerAngles/EulerAngles.h"
+
+#include "../../Eigen/src/Core/util/ReenableStupidWarnings.h"
+
+#endif // EIGEN_EULERANGLES_MODULE_H
diff --git a/unsupported/Eigen/FFT b/unsupported/Eigen/FFT
new file mode 100644
index 0000000..b929e84
--- /dev/null
+++ b/unsupported/Eigen/FFT
@@ -0,0 +1,434 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009 Mark Borgerding mark a borgerding net
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_FFT_MODULE_H
+#define EIGEN_FFT_MODULE_H
+
+#include <complex>
+#include <vector>
+#include <map>
+#include "../../Eigen/Core"
+
+
+/**
+ * \defgroup FFT_Module Fast Fourier Transform module
+ *
+ * \code
+ * #include <unsupported/Eigen/FFT>
+ * \endcode
+ *
+ * This module provides Fast Fourier transformation, with a configurable backend
+ * implementation.
+ *
+ * The default implementation is based on kissfft. It is a small, free, and
+ * reasonably efficient default.
+ *
+ * There are currently four implementation backend:
+ *
+ * - kissfft(https://github.com/mborgerding/kissfft) : Simple and not so fast, BSD-3-Clause.
+ * It is a mixed-radix Fast Fourier Transform based up on the principle, "Keep It Simple, Stupid."
+ * Notice that:kissfft fails to handle "atypically-sized" inputs(i.e., sizes with large factors),a workaround is using fftw or pocketfft.
+ * - fftw (http://www.fftw.org) : faster, GPL -- incompatible with Eigen in LGPL form, bigger code size.
+ * - MKL (https://www.intel.com/content/www/us/en/developer/tools/oneapi/onemkl-download.html) : fastest, free -- may be incompatible with Eigen in GPL form.
+ * - pocketfft (https://gitlab.mpcdf.mpg.de/mtr/pocketfft) : faster than kissfft, BSD 3-clause.
+ * It is a heavily modified implementation of FFTPack, with the following advantages:
+ * 1.strictly C++11 compliant
+ * 2.more accurate twiddle factor computation
+ * 3.very fast plan generation
+ * 4.worst case complexity for transform sizes with large prime factors is N*log(N), because Bluestein's algorithm is used for these cases
+ *
+ * \section FFTDesign Design
+ *
+ * The following design decisions were made concerning scaling and
+ * half-spectrum for real FFT.
+ *
+ * The intent is to facilitate generic programming and ease migrating code
+ * from Matlab/octave.
+ * We think the default behavior of Eigen/FFT should favor correctness and
+ * generality over speed. Of course, the caller should be able to "opt-out" from this
+ * behavior and get the speed increase if they want it.
+ *
+ * 1) %Scaling:
+ * Other libraries (FFTW,IMKL,KISSFFT) do not perform scaling, so there
+ * is a constant gain incurred after the forward&inverse transforms , so
+ * IFFT(FFT(x)) = Kx; this is done to avoid a vector-by-value multiply.
+ * The downside is that algorithms that worked correctly in Matlab/octave
+ * don't behave the same way once implemented in C++.
+ *
+ * How Eigen/FFT differs: invertible scaling is performed so IFFT( FFT(x) ) = x.
+ *
+ * 2) Real FFT half-spectrum
+ * Other libraries use only half the frequency spectrum (plus one extra
+ * sample for the Nyquist bin) for a real FFT, the other half is the
+ * conjugate-symmetric of the first half. This saves them a copy and some
+ * memory. The downside is the caller needs to have special logic for the
+ * number of bins in complex vs real.
+ *
+ * How Eigen/FFT differs: The full spectrum is returned from the forward
+ * transform. This facilitates generic template programming by obviating
+ * separate specializations for real vs complex. On the inverse
+ * transform, only half the spectrum is actually used if the output type is real.
+ */
+
+
+#include "../../Eigen/src/Core/util/DisableStupidWarnings.h"
+
+#ifdef EIGEN_FFTW_DEFAULT
+// FFTW: faster, GPL -- incompatible with Eigen in LGPL form, bigger code size
+# include <fftw3.h>
+# include "src/FFT/ei_fftw_impl.h"
+ namespace Eigen {
+ //template <typename T> typedef struct internal::fftw_impl default_fft_impl; this does not work
+ template <typename T> struct default_fft_impl : public internal::fftw_impl<T> {};
+ }
+#elif defined EIGEN_MKL_DEFAULT
+// intel Math Kernel Library: fastest, free -- may be incompatible with Eigen in GPL form
+# include "src/FFT/ei_imklfft_impl.h"
+ namespace Eigen {
+ template <typename T> struct default_fft_impl : public internal::imklfft::imklfft_impl<T> {};
+ }
+#elif defined EIGEN_POCKETFFT_DEFAULT
+// internal::pocketfft_impl: a heavily modified implementation of FFTPack, with many advantages.
+# include<pocketfft_hdronly.h>
+# include"src/FFT/ei_pocketfft_impl.h"
+ namespace Eigen {
+ template <typename T>
+ struct default_fft_impl : public internal::pocketfft_impl<T> {};
+ }
+#else
+// internal::kissfft_impl: small, free, reasonably efficient default, derived from kissfft
+# include "src/FFT/ei_kissfft_impl.h"
+ namespace Eigen {
+ template <typename T>
+ struct default_fft_impl : public internal::kissfft_impl<T> {};
+ }
+#endif
+
+namespace Eigen {
+
+
+//
+template<typename T_SrcMat,typename T_FftIfc> struct fft_fwd_proxy;
+template<typename T_SrcMat,typename T_FftIfc> struct fft_inv_proxy;
+
+namespace internal {
+template<typename T_SrcMat,typename T_FftIfc>
+struct traits< fft_fwd_proxy<T_SrcMat,T_FftIfc> >
+{
+ typedef typename T_SrcMat::PlainObject ReturnType;
+};
+template<typename T_SrcMat,typename T_FftIfc>
+struct traits< fft_inv_proxy<T_SrcMat,T_FftIfc> >
+{
+ typedef typename T_SrcMat::PlainObject ReturnType;
+};
+}
+
+template<typename T_SrcMat,typename T_FftIfc>
+struct fft_fwd_proxy
+ : public ReturnByValue<fft_fwd_proxy<T_SrcMat,T_FftIfc> >
+{
+ typedef DenseIndex Index;
+
+ fft_fwd_proxy(const T_SrcMat& src,T_FftIfc & fft, Index nfft) : m_src(src),m_ifc(fft), m_nfft(nfft) {}
+
+ template<typename T_DestMat> void evalTo(T_DestMat& dst) const;
+
+ Index rows() const { return m_src.rows(); }
+ Index cols() const { return m_src.cols(); }
+protected:
+ const T_SrcMat & m_src;
+ T_FftIfc & m_ifc;
+ Index m_nfft;
+};
+
+template<typename T_SrcMat,typename T_FftIfc>
+struct fft_inv_proxy
+ : public ReturnByValue<fft_inv_proxy<T_SrcMat,T_FftIfc> >
+{
+ typedef DenseIndex Index;
+
+ fft_inv_proxy(const T_SrcMat& src,T_FftIfc & fft, Index nfft) : m_src(src),m_ifc(fft), m_nfft(nfft) {}
+
+ template<typename T_DestMat> void evalTo(T_DestMat& dst) const;
+
+ Index rows() const { return m_src.rows(); }
+ Index cols() const { return m_src.cols(); }
+protected:
+ const T_SrcMat & m_src;
+ T_FftIfc & m_ifc;
+ Index m_nfft;
+};
+
+
+template <typename T_Scalar,
+ typename T_Impl=default_fft_impl<T_Scalar> >
+class FFT
+{
+ public:
+ typedef T_Impl impl_type;
+ typedef DenseIndex Index;
+ typedef typename impl_type::Scalar Scalar;
+ typedef typename impl_type::Complex Complex;
+
+ enum Flag {
+ Default=0, // goof proof
+ Unscaled=1,
+ HalfSpectrum=2,
+ // SomeOtherSpeedOptimization=4
+ Speedy=32767
+ };
+
+ FFT( const impl_type & impl=impl_type() , Flag flags=Default ) :m_impl(impl),m_flag(flags) { }
+
+ inline
+ bool HasFlag(Flag f) const { return (m_flag & (int)f) == f;}
+
+ inline
+ void SetFlag(Flag f) { m_flag |= (int)f;}
+
+ inline
+ void ClearFlag(Flag f) { m_flag &= (~(int)f);}
+
+ inline
+ void fwd( Complex * dst, const Scalar * src, Index nfft)
+ {
+ m_impl.fwd(dst,src,static_cast<int>(nfft));
+ if ( HasFlag(HalfSpectrum) == false)
+ ReflectSpectrum(dst,nfft);
+ }
+
+ inline
+ void fwd( Complex * dst, const Complex * src, Index nfft)
+ {
+ m_impl.fwd(dst,src,static_cast<int>(nfft));
+ }
+
+#if defined EIGEN_FFTW_DEFAULT || defined EIGEN_POCKETFFT_DEFAULT || defined EIGEN_MKL_DEFAULT
+ inline
+ void fwd2(Complex * dst, const Complex * src, int n0,int n1)
+ {
+ m_impl.fwd2(dst,src,n0,n1);
+ }
+#endif
+
+ template <typename Input_>
+ inline
+ void fwd( std::vector<Complex> & dst, const std::vector<Input_> & src)
+ {
+ if ( NumTraits<Input_>::IsComplex == 0 && HasFlag(HalfSpectrum) )
+ dst.resize( (src.size()>>1)+1); // half the bins + Nyquist bin
+ else
+ dst.resize(src.size());
+ fwd(&dst[0],&src[0],src.size());
+ }
+
+ template<typename InputDerived, typename ComplexDerived>
+ inline
+ void fwd( MatrixBase<ComplexDerived> & dst, const MatrixBase<InputDerived> & src, Index nfft=-1)
+ {
+ typedef typename ComplexDerived::Scalar dst_type;
+ typedef typename InputDerived::Scalar src_type;
+ EIGEN_STATIC_ASSERT_VECTOR_ONLY(InputDerived)
+ EIGEN_STATIC_ASSERT_VECTOR_ONLY(ComplexDerived)
+ EIGEN_STATIC_ASSERT_SAME_VECTOR_SIZE(ComplexDerived,InputDerived) // size at compile-time
+ EIGEN_STATIC_ASSERT((internal::is_same<dst_type, Complex>::value),
+ YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY)
+ EIGEN_STATIC_ASSERT(int(InputDerived::Flags)&int(ComplexDerived::Flags)&DirectAccessBit,
+ THIS_METHOD_IS_ONLY_FOR_EXPRESSIONS_WITH_DIRECT_MEMORY_ACCESS_SUCH_AS_MAP_OR_PLAIN_MATRICES)
+
+ if (nfft<1)
+ nfft = src.size();
+
+ if ( NumTraits< src_type >::IsComplex == 0 && HasFlag(HalfSpectrum) )
+ dst.derived().resize( (nfft>>1)+1);
+ else
+ dst.derived().resize(nfft);
+
+ if ( src.innerStride() != 1 || src.size() < nfft ) {
+ Matrix<src_type,1,Dynamic> tmp;
+ if (src.size()<nfft) {
+ tmp.setZero(nfft);
+ tmp.block(0,0,src.size(),1 ) = src;
+ }else{
+ tmp = src;
+ }
+ fwd( &dst[0],&tmp[0],nfft );
+ }else{
+ fwd( &dst[0],&src[0],nfft );
+ }
+ }
+
+ template<typename InputDerived>
+ inline
+ fft_fwd_proxy< MatrixBase<InputDerived>, FFT<T_Scalar,T_Impl> >
+ fwd( const MatrixBase<InputDerived> & src, Index nfft=-1)
+ {
+ return fft_fwd_proxy< MatrixBase<InputDerived> ,FFT<T_Scalar,T_Impl> >( src, *this,nfft );
+ }
+
+ template<typename InputDerived>
+ inline
+ fft_inv_proxy< MatrixBase<InputDerived>, FFT<T_Scalar,T_Impl> >
+ inv( const MatrixBase<InputDerived> & src, Index nfft=-1)
+ {
+ return fft_inv_proxy< MatrixBase<InputDerived> ,FFT<T_Scalar,T_Impl> >( src, *this,nfft );
+ }
+
+ inline
+ void inv( Complex * dst, const Complex * src, Index nfft)
+ {
+ m_impl.inv( dst,src,static_cast<int>(nfft) );
+ if ( HasFlag( Unscaled ) == false)
+ scale(dst,Scalar(1./nfft),nfft); // scale the time series
+ }
+
+ inline
+ void inv( Scalar * dst, const Complex * src, Index nfft)
+ {
+ m_impl.inv( dst,src,static_cast<int>(nfft) );
+ if ( HasFlag( Unscaled ) == false)
+ scale(dst,Scalar(1./nfft),nfft); // scale the time series
+ }
+
+ template<typename OutputDerived, typename ComplexDerived>
+ inline
+ void inv( MatrixBase<OutputDerived> & dst, const MatrixBase<ComplexDerived> & src, Index nfft=-1)
+ {
+ typedef typename ComplexDerived::Scalar src_type;
+ typedef typename ComplexDerived::RealScalar real_type;
+ typedef typename OutputDerived::Scalar dst_type;
+ const bool realfft= (NumTraits<dst_type>::IsComplex == 0);
+ EIGEN_STATIC_ASSERT_VECTOR_ONLY(OutputDerived)
+ EIGEN_STATIC_ASSERT_VECTOR_ONLY(ComplexDerived)
+ EIGEN_STATIC_ASSERT_SAME_VECTOR_SIZE(ComplexDerived,OutputDerived) // size at compile-time
+ EIGEN_STATIC_ASSERT((internal::is_same<src_type, Complex>::value),
+ YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY)
+ EIGEN_STATIC_ASSERT(int(OutputDerived::Flags)&int(ComplexDerived::Flags)&DirectAccessBit,
+ THIS_METHOD_IS_ONLY_FOR_EXPRESSIONS_WITH_DIRECT_MEMORY_ACCESS_SUCH_AS_MAP_OR_PLAIN_MATRICES)
+
+ if (nfft<1) { //automatic FFT size determination
+ if ( realfft && HasFlag(HalfSpectrum) )
+ nfft = 2*(src.size()-1); //assume even fft size
+ else
+ nfft = src.size();
+ }
+ dst.derived().resize( nfft );
+
+ // check for nfft that does not fit the input data size
+ Index resize_input= ( realfft && HasFlag(HalfSpectrum) )
+ ? ( (nfft/2+1) - src.size() )
+ : ( nfft - src.size() );
+
+ if ( src.innerStride() != 1 || resize_input ) {
+ // if the vector is strided, then we need to copy it to a packed temporary
+ Matrix<src_type,1,Dynamic> tmp;
+ if ( resize_input ) {
+ size_t ncopy = (std::min)(src.size(),src.size() + resize_input);
+ tmp.setZero(src.size() + resize_input);
+ if ( realfft && HasFlag(HalfSpectrum) ) {
+ // pad at the Nyquist bin
+ tmp.head(ncopy) = src.head(ncopy);
+ tmp(ncopy-1) = real(tmp(ncopy-1)); // enforce real-only Nyquist bin
+ }else{
+ size_t nhead,ntail;
+ nhead = 1+ncopy/2-1; // range [0:pi)
+ ntail = ncopy/2-1; // range (-pi:0)
+ tmp.head(nhead) = src.head(nhead);
+ tmp.tail(ntail) = src.tail(ntail);
+ if (resize_input<0) { //shrinking -- create the Nyquist bin as the average of the two bins that fold into it
+ tmp(nhead) = ( src(nfft/2) + src( src.size() - nfft/2 ) )*real_type(.5);
+ }else{ // expanding -- split the old Nyquist bin into two halves
+ tmp(nhead) = src(nhead) * real_type(.5);
+ tmp(tmp.size()-nhead) = tmp(nhead);
+ }
+ }
+ }else{
+ tmp = src;
+ }
+ inv( &dst[0],&tmp[0], nfft);
+ }else{
+ inv( &dst[0],&src[0], nfft);
+ }
+ }
+
+ template <typename Output_>
+ inline
+ void inv( std::vector<Output_> & dst, const std::vector<Complex> & src,Index nfft=-1)
+ {
+ if (nfft<1)
+ nfft = ( NumTraits<Output_>::IsComplex == 0 && HasFlag(HalfSpectrum) ) ? 2*(src.size()-1) : src.size();
+ dst.resize( nfft );
+ inv( &dst[0],&src[0],nfft);
+ }
+
+
+#if defined EIGEN_FFTW_DEFAULT || defined EIGEN_POCKETFFT_DEFAULT || defined EIGEN_MKL_DEFAULT
+ inline
+ void inv2(Complex * dst, const Complex * src, int n0,int n1)
+ {
+ m_impl.inv2(dst,src,n0,n1);
+ if ( HasFlag( Unscaled ) == false)
+ scale(dst,1./(n0*n1),n0*n1);
+ }
+#endif
+
+
+ inline
+ impl_type & impl() {return m_impl;}
+ private:
+
+ template <typename T_Data>
+ inline
+ void scale(T_Data * x,Scalar s,Index nx)
+ {
+#if 1
+ for (int k=0;k<nx;++k)
+ *x++ *= s;
+#else
+ if ( ((ptrdiff_t)x) & 15 )
+ Matrix<T_Data, Dynamic, 1>::Map(x,nx) *= s;
+ else
+ Matrix<T_Data, Dynamic, 1>::MapAligned(x,nx) *= s;
+ //Matrix<T_Data, Dynamic, Dynamic>::Map(x,nx) * s;
+#endif
+ }
+
+ inline
+ void ReflectSpectrum(Complex * freq, Index nfft)
+ {
+ // create the implicit right-half spectrum (conjugate-mirror of the left-half)
+ Index nhbins=(nfft>>1)+1;
+ for (Index k=nhbins;k < nfft; ++k )
+ freq[k] = conj(freq[nfft-k]);
+ }
+
+ impl_type m_impl;
+ int m_flag;
+};
+
+template<typename T_SrcMat,typename T_FftIfc>
+template<typename T_DestMat> inline
+void fft_fwd_proxy<T_SrcMat,T_FftIfc>::evalTo(T_DestMat& dst) const
+{
+ m_ifc.fwd( dst, m_src, m_nfft);
+}
+
+template<typename T_SrcMat,typename T_FftIfc>
+template<typename T_DestMat> inline
+void fft_inv_proxy<T_SrcMat,T_FftIfc>::evalTo(T_DestMat& dst) const
+{
+ m_ifc.inv( dst, m_src, m_nfft);
+}
+
+}
+
+#include "../../Eigen/src/Core/util/ReenableStupidWarnings.h"
+
+#endif
diff --git a/unsupported/Eigen/IterativeSolvers b/unsupported/Eigen/IterativeSolvers
new file mode 100644
index 0000000..a22d2a3
--- /dev/null
+++ b/unsupported/Eigen/IterativeSolvers
@@ -0,0 +1,93 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2009 Gael Guennebaud <g.gael@free.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_ITERATIVE_SOLVERS_MODULE_H
+#define EIGEN_ITERATIVE_SOLVERS_MODULE_H
+
+#include "../../Eigen/Sparse"
+#include "../../Eigen/Jacobi"
+#include "../../Eigen/Householder"
+
+
+/**
+ * \defgroup IterativeLinearSolvers_Module Iterative Solvers module
+ * This module aims to provide various iterative linear and non linear solver algorithms.
+ * It currently provides:
+ * - a constrained conjugate gradient
+ * - a Householder GMRES implementation
+ * - an IDR(s) implementation
+ * - a BiCGSTAB(L) implementation
+ * - a DGMRES implementation
+ * - a MINRES implementation
+ * - a IDRSTABL implementation
+ *
+ * Choosing the best solver for solving \c A \c x = \c b depends a lot on the preconditioner chosen as well as the properties of \c A. The following flowchart might help you.
+ * \dot width=50%
+ * digraph g {
+* node [ fontname=Arial, fontsize=11];
+* edge [ fontname=Helvetica, fontsize=10 ];
+* A1[label="hermitian",shape="box"];
+* A2[label="positive definite",shape="box"];
+* CG[shape="plaintext"];
+* A3[label="ill conditioned",shape="box"];
+* A4[label="good preconditioner",shape="box"];
+* A5[label="flexible preconditioner",shape="box"];
+* A6[label="strongly indefinite",shape="box"];
+* A8[label="large imaginary eigenvalue",shape="box"];
+* A7[label="large imaginary eigenvalue",shape="box"];
+*
+* SYMMLQ[shape="plaintext"];
+* MINRES[shape="plaintext"];
+* GCR[shape="plaintext"];
+* GMRES[shape="plaintext"];
+* IDRSTABL[shape="plaintext"];
+* IDRS[shape="plaintext"];
+* BICGSTABL[shape="plaintext"];
+* BICGSTAB[shape="plaintext"];
+*
+* A1 -> A2 [label="yes"];
+* A2 -> CG [label="yes"];
+* A2 -> A3 [label="no"];
+* A3 -> SYMMLQ [label="yes"];
+* A3 -> MINRES [label="no"];
+*
+* A1 -> A4 [label="no"];
+* A4 -> A5 [label="yes"];
+* A5 -> GCR [label="yes"];
+* A5 -> GMRES [label="no"];
+*
+* A4 -> A6 [label="no"];
+* A6 -> A8 [label="yes"];
+* A6 -> A7 [label="no"];
+* A7 -> BICGSTABL [label="yes"];
+* A7 -> BICGSTAB [label="no"];
+* A8 -> IDRSTABL [label="yes"];
+* A8 -> IDRS [label="no"];
+* }
+ * \enddot
+ * \code
+ * #include <unsupported/Eigen/IterativeSolvers>
+ * \endcode
+ */
+
+
+#include "../../Eigen/src/Core/util/DisableStupidWarnings.h"
+
+#include "src/IterativeSolvers/IncompleteLU.h"
+#include "src/IterativeSolvers/GMRES.h"
+#include "src/IterativeSolvers/DGMRES.h"
+#include "src/IterativeSolvers/MINRES.h"
+#include "src/IterativeSolvers/IDRS.h"
+#include "src/IterativeSolvers/BiCGSTABL.h"
+#include "src/IterativeSolvers/IDRSTABL.h"
+
+#include "../../Eigen/src/Core/util/ReenableStupidWarnings.h"
+
+
+#endif // EIGEN_ITERATIVE_SOLVERS_MODULE_H
diff --git a/unsupported/Eigen/KroneckerProduct b/unsupported/Eigen/KroneckerProduct
new file mode 100644
index 0000000..9643ae2
--- /dev/null
+++ b/unsupported/Eigen/KroneckerProduct
@@ -0,0 +1,33 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_KRONECKER_PRODUCT_MODULE_H
+#define EIGEN_KRONECKER_PRODUCT_MODULE_H
+
+#include "../../Eigen/Core"
+#include "../../Eigen/SparseCore"
+
+namespace Eigen {
+
+/**
+ * \defgroup KroneckerProduct_Module KroneckerProduct module
+ *
+ * This module contains an experimental Kronecker product implementation.
+ *
+ * \code
+ * #include <Eigen/KroneckerProduct>
+ * \endcode
+ */
+
+} // namespace Eigen
+
+#include "src/KroneckerProduct/KroneckerTensorProduct.h"
+
+#include "../../Eigen/src/Core/util/ReenableStupidWarnings.h"
+
+#endif // EIGEN_KRONECKER_PRODUCT_MODULE_H
diff --git a/unsupported/Eigen/LevenbergMarquardt b/unsupported/Eigen/LevenbergMarquardt
new file mode 100644
index 0000000..b5ace56
--- /dev/null
+++ b/unsupported/Eigen/LevenbergMarquardt
@@ -0,0 +1,49 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009 Thomas Capricelli <orzel@freehackers.org>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_LEVENBERGMARQUARDT_MODULE_H
+#define EIGEN_LEVENBERGMARQUARDT_MODULE_H
+
+// #include <vector>
+
+#include "../../Eigen/Core"
+#include "../../Eigen/Jacobi"
+#include "../../Eigen/QR"
+#include "NumericalDiff"
+
+#include "../../Eigen/SparseQR"
+
+/**
+ * \defgroup LevenbergMarquardt_Module Levenberg-Marquardt module
+ *
+ * \code
+ * #include </Eigen/LevenbergMarquardt>
+ * \endcode
+ *
+ *
+ */
+
+#include "../../Eigen/SparseCore"
+
+#include "../../Eigen/src/Core/util/DisableStupidWarnings.h"
+
+#ifndef EIGEN_PARSED_BY_DOXYGEN
+
+#include "src/LevenbergMarquardt/LMqrsolv.h"
+#include "src/LevenbergMarquardt/LMcovar.h"
+#include "src/LevenbergMarquardt/LMpar.h"
+
+#endif
+
+#include "src/LevenbergMarquardt/LevenbergMarquardt.h"
+#include "src/LevenbergMarquardt/LMonestep.h"
+
+#include "../../Eigen/src/Core/util/ReenableStupidWarnings.h"
+
+#endif // EIGEN_LEVENBERGMARQUARDT_MODULE_H
diff --git a/unsupported/Eigen/MPRealSupport b/unsupported/Eigen/MPRealSupport
new file mode 100644
index 0000000..c4ea4ec
--- /dev/null
+++ b/unsupported/Eigen/MPRealSupport
@@ -0,0 +1,213 @@
+// This file is part of a joint effort between Eigen, a lightweight C++ template library
+// for linear algebra, and MPFR C++, a C++ interface to MPFR library (http://www.holoborodko.com/pavel/)
+//
+// Copyright (C) 2010-2012 Pavel Holoborodko <pavel@holoborodko.com>
+// Copyright (C) 2010 Konstantin Holoborodko <konstantin@holoborodko.com>
+// Copyright (C) 2010 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_MPREALSUPPORT_MODULE_H
+#define EIGEN_MPREALSUPPORT_MODULE_H
+
+#include "../../Eigen/Core"
+#include <mpreal.h>
+
+namespace Eigen {
+
+/**
+ * \defgroup MPRealSupport_Module MPFRC++ Support module
+ * \code
+ * #include <Eigen/MPRealSupport>
+ * \endcode
+ *
+ * This module provides support for multi precision floating point numbers
+ * via the <a href="http://www.holoborodko.com/pavel/mpfr">MPFR C++</a>
+ * library which itself is built upon <a href="http://www.mpfr.org/">MPFR</a>/<a href="http://gmplib.org/">GMP</a>.
+ *
+ * \warning MPFR C++ is licensed under the GPL.
+ *
+ * You can find a copy of MPFR C++ that is known to be compatible in the unsupported/test/mpreal folder.
+ *
+ * Here is an example:
+ *
+\code
+#include <iostream>
+#include <Eigen/MPRealSupport>
+#include <Eigen/LU>
+using namespace mpfr;
+using namespace Eigen;
+int main()
+{
+ // set precision to 256 bits (double has only 53 bits)
+ mpreal::set_default_prec(256);
+ // Declare matrix and vector types with multi-precision scalar type
+ typedef Matrix<mpreal,Dynamic,Dynamic> MatrixXmp;
+ typedef Matrix<mpreal,Dynamic,1> VectorXmp;
+
+ MatrixXmp A = MatrixXmp::Random(100,100);
+ VectorXmp b = VectorXmp::Random(100);
+
+ // Solve Ax=b using LU
+ VectorXmp x = A.lu().solve(b);
+ std::cout << "relative error: " << (A*x - b).norm() / b.norm() << std::endl;
+ return 0;
+}
+\endcode
+ *
+ */
+
+ template<> struct NumTraits<mpfr::mpreal>
+ : GenericNumTraits<mpfr::mpreal>
+ {
+ enum {
+ IsInteger = 0,
+ IsSigned = 1,
+ IsComplex = 0,
+ RequireInitialization = 1,
+ ReadCost = HugeCost,
+ AddCost = HugeCost,
+ MulCost = HugeCost
+ };
+
+ typedef mpfr::mpreal Real;
+ typedef mpfr::mpreal NonInteger;
+
+ static inline Real highest (long Precision = mpfr::mpreal::get_default_prec()) { return mpfr::maxval(Precision); }
+ static inline Real lowest (long Precision = mpfr::mpreal::get_default_prec()) { return -mpfr::maxval(Precision); }
+
+ // Constants
+ static inline Real Pi (long Precision = mpfr::mpreal::get_default_prec()) { return mpfr::const_pi(Precision); }
+ static inline Real Euler (long Precision = mpfr::mpreal::get_default_prec()) { return mpfr::const_euler(Precision); }
+ static inline Real Log2 (long Precision = mpfr::mpreal::get_default_prec()) { return mpfr::const_log2(Precision); }
+ static inline Real Catalan (long Precision = mpfr::mpreal::get_default_prec()) { return mpfr::const_catalan(Precision); }
+
+ static inline Real epsilon (long Precision = mpfr::mpreal::get_default_prec()) { return mpfr::machine_epsilon(Precision); }
+ static inline Real epsilon (const Real& x) { return mpfr::machine_epsilon(x); }
+
+#ifdef MPREAL_HAVE_DYNAMIC_STD_NUMERIC_LIMITS
+ static inline int digits10 (long Precision = mpfr::mpreal::get_default_prec()) { return std::numeric_limits<Real>::digits10(Precision); }
+ static inline int digits10 (const Real& x) { return std::numeric_limits<Real>::digits10(x); }
+
+ static inline int digits () { return std::numeric_limits<Real>::digits(); }
+ static inline int digits (const Real& x) { return std::numeric_limits<Real>::digits(x); }
+#endif
+
+ static inline Real dummy_precision()
+ {
+ mpfr_prec_t weak_prec = ((mpfr::mpreal::get_default_prec()-1) * 90) / 100;
+ return mpfr::machine_epsilon(weak_prec);
+ }
+ };
+
+ namespace internal {
+
+ template<> inline mpfr::mpreal random<mpfr::mpreal>()
+ {
+ return mpfr::random();
+ }
+
+ template<> inline mpfr::mpreal random<mpfr::mpreal>(const mpfr::mpreal& a, const mpfr::mpreal& b)
+ {
+ return a + (b-a) * random<mpfr::mpreal>();
+ }
+
+ inline bool isMuchSmallerThan(const mpfr::mpreal& a, const mpfr::mpreal& b, const mpfr::mpreal& eps)
+ {
+ return mpfr::abs(a) <= mpfr::abs(b) * eps;
+ }
+
+ inline bool isApprox(const mpfr::mpreal& a, const mpfr::mpreal& b, const mpfr::mpreal& eps)
+ {
+ return mpfr::isEqualFuzzy(a,b,eps);
+ }
+
+ inline bool isApproxOrLessThan(const mpfr::mpreal& a, const mpfr::mpreal& b, const mpfr::mpreal& eps)
+ {
+ return a <= b || mpfr::isEqualFuzzy(a,b,eps);
+ }
+
+ template<> inline long double cast<mpfr::mpreal,long double>(const mpfr::mpreal& x)
+ { return x.toLDouble(); }
+
+ template<> inline double cast<mpfr::mpreal,double>(const mpfr::mpreal& x)
+ { return x.toDouble(); }
+
+ template<> inline long cast<mpfr::mpreal,long>(const mpfr::mpreal& x)
+ { return x.toLong(); }
+
+ template<> inline int cast<mpfr::mpreal,int>(const mpfr::mpreal& x)
+ { return int(x.toLong()); }
+
+ // Specialize GEBP kernel and traits for mpreal (no need for peeling, nor complicated stuff)
+ // This also permits to directly call mpfr's routines and avoid many temporaries produced by mpreal
+ template<>
+ class gebp_traits<mpfr::mpreal, mpfr::mpreal, false, false>
+ {
+ public:
+ typedef mpfr::mpreal ResScalar;
+ enum {
+ Vectorizable = false,
+ LhsPacketSize = 1,
+ RhsPacketSize = 1,
+ ResPacketSize = 1,
+ NumberOfRegisters = 1,
+ nr = 1,
+ mr = 1,
+ LhsProgress = 1,
+ RhsProgress = 1
+ };
+ typedef ResScalar LhsPacket;
+ typedef ResScalar RhsPacket;
+ typedef ResScalar ResPacket;
+ typedef LhsPacket LhsPacket4Packing;
+
+ };
+
+
+
+ template<typename Index, typename DataMapper, bool ConjugateLhs, bool ConjugateRhs>
+ struct gebp_kernel<mpfr::mpreal,mpfr::mpreal,Index,DataMapper,1,1,ConjugateLhs,ConjugateRhs>
+ {
+ typedef mpfr::mpreal mpreal;
+
+ EIGEN_DONT_INLINE
+ void operator()(const DataMapper& res, const mpreal* blockA, const mpreal* blockB,
+ Index rows, Index depth, Index cols, const mpreal& alpha,
+ Index strideA=-1, Index strideB=-1, Index offsetA=0, Index offsetB=0)
+ {
+ if(rows==0 || cols==0 || depth==0)
+ return;
+
+ mpreal acc1(0,mpfr_get_prec(blockA[0].mpfr_srcptr())),
+ tmp (0,mpfr_get_prec(blockA[0].mpfr_srcptr()));
+
+ if(strideA==-1) strideA = depth;
+ if(strideB==-1) strideB = depth;
+
+ for(Index i=0; i<rows; ++i)
+ {
+ for(Index j=0; j<cols; ++j)
+ {
+ const mpreal *A = blockA + i*strideA + offsetA;
+ const mpreal *B = blockB + j*strideB + offsetB;
+
+ acc1 = 0;
+ for(Index k=0; k<depth; k++)
+ {
+ mpfr_mul(tmp.mpfr_ptr(), A[k].mpfr_srcptr(), B[k].mpfr_srcptr(), mpreal::get_default_rnd());
+ mpfr_add(acc1.mpfr_ptr(), acc1.mpfr_ptr(), tmp.mpfr_ptr(), mpreal::get_default_rnd());
+ }
+
+ mpfr_mul(acc1.mpfr_ptr(), acc1.mpfr_srcptr(), alpha.mpfr_srcptr(), mpreal::get_default_rnd());
+ mpfr_add(res(i,j).mpfr_ptr(), res(i,j).mpfr_srcptr(), acc1.mpfr_srcptr(), mpreal::get_default_rnd());
+ }
+ }
+ }
+ };
+ } // end namespace internal
+}
+
+#endif // EIGEN_MPREALSUPPORT_MODULE_H
diff --git a/unsupported/Eigen/MatrixFunctions b/unsupported/Eigen/MatrixFunctions
new file mode 100644
index 0000000..dddedb4
--- /dev/null
+++ b/unsupported/Eigen/MatrixFunctions
@@ -0,0 +1,503 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009 Jitse Niesen <jitse@maths.leeds.ac.uk>
+// Copyright (C) 2012 Chen-Pang He <jdh8@ms63.hinet.net>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_MATRIX_FUNCTIONS_MODULE_H
+#define EIGEN_MATRIX_FUNCTIONS_MODULE_H
+
+#include <cfloat>
+#include <list>
+
+#include "../../Eigen/Core"
+#include "../../Eigen/LU"
+#include "../../Eigen/Eigenvalues"
+
+/**
+ * \defgroup MatrixFunctions_Module Matrix functions module
+ * \brief This module aims to provide various methods for the computation of
+ * matrix functions.
+ *
+ * To use this module, add
+ * \code
+ * #include <unsupported/Eigen/MatrixFunctions>
+ * \endcode
+ * at the start of your source file.
+ *
+ * This module defines the following MatrixBase methods.
+ * - \ref matrixbase_cos "MatrixBase::cos()", for computing the matrix cosine
+ * - \ref matrixbase_cosh "MatrixBase::cosh()", for computing the matrix hyperbolic cosine
+ * - \ref matrixbase_exp "MatrixBase::exp()", for computing the matrix exponential
+ * - \ref matrixbase_log "MatrixBase::log()", for computing the matrix logarithm
+ * - \ref matrixbase_pow "MatrixBase::pow()", for computing the matrix power
+ * - \ref matrixbase_matrixfunction "MatrixBase::matrixFunction()", for computing general matrix functions
+ * - \ref matrixbase_sin "MatrixBase::sin()", for computing the matrix sine
+ * - \ref matrixbase_sinh "MatrixBase::sinh()", for computing the matrix hyperbolic sine
+ * - \ref matrixbase_sqrt "MatrixBase::sqrt()", for computing the matrix square root
+ *
+ * These methods are the main entry points to this module.
+ *
+ * %Matrix functions are defined as follows. Suppose that \f$ f \f$
+ * is an entire function (that is, a function on the complex plane
+ * that is everywhere complex differentiable). Then its Taylor
+ * series
+ * \f[ f(0) + f'(0) x + \frac{f''(0)}{2} x^2 + \frac{f'''(0)}{3!} x^3 + \cdots \f]
+ * converges to \f$ f(x) \f$. In this case, we can define the matrix
+ * function by the same series:
+ * \f[ f(M) = f(0) + f'(0) M + \frac{f''(0)}{2} M^2 + \frac{f'''(0)}{3!} M^3 + \cdots \f]
+ *
+ */
+
+#include "../../Eigen/src/Core/util/DisableStupidWarnings.h"
+
+#include "src/MatrixFunctions/MatrixExponential.h"
+#include "src/MatrixFunctions/MatrixFunction.h"
+#include "src/MatrixFunctions/MatrixSquareRoot.h"
+#include "src/MatrixFunctions/MatrixLogarithm.h"
+#include "src/MatrixFunctions/MatrixPower.h"
+
+#include "../../Eigen/src/Core/util/ReenableStupidWarnings.h"
+
+
+/**
+\page matrixbaseextra_page
+\ingroup MatrixFunctions_Module
+
+\section matrixbaseextra MatrixBase methods defined in the MatrixFunctions module
+
+The remainder of the page documents the following MatrixBase methods
+which are defined in the MatrixFunctions module.
+
+
+
+\subsection matrixbase_cos MatrixBase::cos()
+
+Compute the matrix cosine.
+
+\code
+const MatrixFunctionReturnValue<Derived> MatrixBase<Derived>::cos() const
+\endcode
+
+\param[in] M a square matrix.
+\returns expression representing \f$ \cos(M) \f$.
+
+This function computes the matrix cosine. Use ArrayBase::cos() for computing the entry-wise cosine.
+
+The implementation calls \ref matrixbase_matrixfunction "matrixFunction()" with StdStemFunctions::cos().
+
+\sa \ref matrixbase_sin "sin()" for an example.
+
+
+
+\subsection matrixbase_cosh MatrixBase::cosh()
+
+Compute the matrix hyberbolic cosine.
+
+\code
+const MatrixFunctionReturnValue<Derived> MatrixBase<Derived>::cosh() const
+\endcode
+
+\param[in] M a square matrix.
+\returns expression representing \f$ \cosh(M) \f$
+
+This function calls \ref matrixbase_matrixfunction "matrixFunction()" with StdStemFunctions::cosh().
+
+\sa \ref matrixbase_sinh "sinh()" for an example.
+
+
+
+\subsection matrixbase_exp MatrixBase::exp()
+
+Compute the matrix exponential.
+
+\code
+const MatrixExponentialReturnValue<Derived> MatrixBase<Derived>::exp() const
+\endcode
+
+\param[in] M matrix whose exponential is to be computed.
+\returns expression representing the matrix exponential of \p M.
+
+The matrix exponential of \f$ M \f$ is defined by
+\f[ \exp(M) = \sum_{k=0}^\infty \frac{M^k}{k!}. \f]
+The matrix exponential can be used to solve linear ordinary
+differential equations: the solution of \f$ y' = My \f$ with the
+initial condition \f$ y(0) = y_0 \f$ is given by
+\f$ y(t) = \exp(M) y_0 \f$.
+
+The matrix exponential is different from applying the exp function to all the entries in the matrix.
+Use ArrayBase::exp() if you want to do the latter.
+
+The cost of the computation is approximately \f$ 20 n^3 \f$ for
+matrices of size \f$ n \f$. The number 20 depends weakly on the
+norm of the matrix.
+
+The matrix exponential is computed using the scaling-and-squaring
+method combined with Padé approximation. The matrix is first
+rescaled, then the exponential of the reduced matrix is computed
+approximant, and then the rescaling is undone by repeated
+squaring. The degree of the Padé approximant is chosen such
+that the approximation error is less than the round-off
+error. However, errors may accumulate during the squaring phase.
+
+Details of the algorithm can be found in: Nicholas J. Higham, "The
+scaling and squaring method for the matrix exponential revisited,"
+<em>SIAM J. %Matrix Anal. Applic.</em>, <b>26</b>:1179–1193,
+2005.
+
+Example: The following program checks that
+\f[ \exp \left[ \begin{array}{ccc}
+ 0 & \frac14\pi & 0 \\
+ -\frac14\pi & 0 & 0 \\
+ 0 & 0 & 0
+ \end{array} \right] = \left[ \begin{array}{ccc}
+ \frac12\sqrt2 & -\frac12\sqrt2 & 0 \\
+ \frac12\sqrt2 & \frac12\sqrt2 & 0 \\
+ 0 & 0 & 1
+ \end{array} \right]. \f]
+This corresponds to a rotation of \f$ \frac14\pi \f$ radians around
+the z-axis.
+
+\include MatrixExponential.cpp
+Output: \verbinclude MatrixExponential.out
+
+\note \p M has to be a matrix of \c float, \c double, `long double`
+\c complex<float>, \c complex<double>, or `complex<long double>` .
+
+
+\subsection matrixbase_log MatrixBase::log()
+
+Compute the matrix logarithm.
+
+\code
+const MatrixLogarithmReturnValue<Derived> MatrixBase<Derived>::log() const
+\endcode
+
+\param[in] M invertible matrix whose logarithm is to be computed.
+\returns expression representing the matrix logarithm root of \p M.
+
+The matrix logarithm of \f$ M \f$ is a matrix \f$ X \f$ such that
+\f$ \exp(X) = M \f$ where exp denotes the matrix exponential. As for
+the scalar logarithm, the equation \f$ \exp(X) = M \f$ may have
+multiple solutions; this function returns a matrix whose eigenvalues
+have imaginary part in the interval \f$ (-\pi,\pi] \f$.
+
+The matrix logarithm is different from applying the log function to all the entries in the matrix.
+Use ArrayBase::log() if you want to do the latter.
+
+In the real case, the matrix \f$ M \f$ should be invertible and
+it should have no eigenvalues which are real and negative (pairs of
+complex conjugate eigenvalues are allowed). In the complex case, it
+only needs to be invertible.
+
+This function computes the matrix logarithm using the Schur-Parlett
+algorithm as implemented by MatrixBase::matrixFunction(). The
+logarithm of an atomic block is computed by MatrixLogarithmAtomic,
+which uses direct computation for 1-by-1 and 2-by-2 blocks and an
+inverse scaling-and-squaring algorithm for bigger blocks, with the
+square roots computed by MatrixBase::sqrt().
+
+Details of the algorithm can be found in Section 11.6.2 of:
+Nicholas J. Higham,
+<em>Functions of Matrices: Theory and Computation</em>,
+SIAM 2008. ISBN 978-0-898716-46-7.
+
+Example: The following program checks that
+\f[ \log \left[ \begin{array}{ccc}
+ \frac12\sqrt2 & -\frac12\sqrt2 & 0 \\
+ \frac12\sqrt2 & \frac12\sqrt2 & 0 \\
+ 0 & 0 & 1
+ \end{array} \right] = \left[ \begin{array}{ccc}
+ 0 & \frac14\pi & 0 \\
+ -\frac14\pi & 0 & 0 \\
+ 0 & 0 & 0
+ \end{array} \right]. \f]
+This corresponds to a rotation of \f$ \frac14\pi \f$ radians around
+the z-axis. This is the inverse of the example used in the
+documentation of \ref matrixbase_exp "exp()".
+
+\include MatrixLogarithm.cpp
+Output: \verbinclude MatrixLogarithm.out
+
+\note \p M has to be a matrix of \c float, \c double, `long
+double`, \c complex<float>, \c complex<double>, or `complex<long double>`.
+
+\sa MatrixBase::exp(), MatrixBase::matrixFunction(),
+ class MatrixLogarithmAtomic, MatrixBase::sqrt().
+
+
+\subsection matrixbase_pow MatrixBase::pow()
+
+Compute the matrix raised to arbitrary real power.
+
+\code
+const MatrixPowerReturnValue<Derived> MatrixBase<Derived>::pow(RealScalar p) const
+\endcode
+
+\param[in] M base of the matrix power, should be a square matrix.
+\param[in] p exponent of the matrix power.
+
+The matrix power \f$ M^p \f$ is defined as \f$ \exp(p \log(M)) \f$,
+where exp denotes the matrix exponential, and log denotes the matrix
+logarithm. This is different from raising all the entries in the matrix
+to the p-th power. Use ArrayBase::pow() if you want to do the latter.
+
+If \p p is complex, the scalar type of \p M should be the type of \p
+p . \f$ M^p \f$ simply evaluates into \f$ \exp(p \log(M)) \f$.
+Therefore, the matrix \f$ M \f$ should meet the conditions to be an
+argument of matrix logarithm.
+
+If \p p is real, it is casted into the real scalar type of \p M. Then
+this function computes the matrix power using the Schur-Padé
+algorithm as implemented by class MatrixPower. The exponent is split
+into integral part and fractional part, where the fractional part is
+in the interval \f$ (-1, 1) \f$. The main diagonal and the first
+super-diagonal is directly computed.
+
+If \p M is singular with a semisimple zero eigenvalue and \p p is
+positive, the Schur factor \f$ T \f$ is reordered with Givens
+rotations, i.e.
+
+\f[ T = \left[ \begin{array}{cc}
+ T_1 & T_2 \\
+ 0 & 0
+ \end{array} \right] \f]
+
+where \f$ T_1 \f$ is invertible. Then \f$ T^p \f$ is given by
+
+\f[ T^p = \left[ \begin{array}{cc}
+ T_1^p & T_1^{-1} T_1^p T_2 \\
+ 0 & 0
+ \end{array}. \right] \f]
+
+\warning Fractional power of a matrix with a non-semisimple zero
+eigenvalue is not well-defined. We introduce an assertion failure
+against inaccurate result, e.g. \code
+#include <unsupported/Eigen/MatrixFunctions>
+#include <iostream>
+
+int main()
+{
+ Eigen::Matrix4d A;
+ A << 0, 0, 2, 3,
+ 0, 0, 4, 5,
+ 0, 0, 6, 7,
+ 0, 0, 8, 9;
+ std::cout << A.pow(0.37) << std::endl;
+
+ // The 1 makes eigenvalue 0 non-semisimple.
+ A.coeffRef(0, 1) = 1;
+
+ // This fails if EIGEN_NO_DEBUG is undefined.
+ std::cout << A.pow(0.37) << std::endl;
+
+ return 0;
+}
+\endcode
+
+Details of the algorithm can be found in: Nicholas J. Higham and
+Lijing Lin, "A Schur-Padé algorithm for fractional powers of a
+matrix," <em>SIAM J. %Matrix Anal. Applic.</em>,
+<b>32(3)</b>:1056–1078, 2011.
+
+Example: The following program checks that
+\f[ \left[ \begin{array}{ccc}
+ \cos1 & -\sin1 & 0 \\
+ \sin1 & \cos1 & 0 \\
+ 0 & 0 & 1
+ \end{array} \right]^{\frac14\pi} = \left[ \begin{array}{ccc}
+ \frac12\sqrt2 & -\frac12\sqrt2 & 0 \\
+ \frac12\sqrt2 & \frac12\sqrt2 & 0 \\
+ 0 & 0 & 1
+ \end{array} \right]. \f]
+This corresponds to \f$ \frac14\pi \f$ rotations of 1 radian around
+the z-axis.
+
+\include MatrixPower.cpp
+Output: \verbinclude MatrixPower.out
+
+MatrixBase::pow() is user-friendly. However, there are some
+circumstances under which you should use class MatrixPower directly.
+MatrixPower can save the result of Schur decomposition, so it's
+better for computing various powers for the same matrix.
+
+Example:
+\include MatrixPower_optimal.cpp
+Output: \verbinclude MatrixPower_optimal.out
+
+\note \p M has to be a matrix of \c float, \c double, `long
+double`, \c complex<float>, \c complex<double>, or
+\c complex<long double> .
+
+\sa MatrixBase::exp(), MatrixBase::log(), class MatrixPower.
+
+
+\subsection matrixbase_matrixfunction MatrixBase::matrixFunction()
+
+Compute a matrix function.
+
+\code
+const MatrixFunctionReturnValue<Derived> MatrixBase<Derived>::matrixFunction(typename internal::stem_function<typename internal::traits<Derived>::Scalar>::type f) const
+\endcode
+
+\param[in] M argument of matrix function, should be a square matrix.
+\param[in] f an entire function; \c f(x,n) should compute the n-th
+derivative of f at x.
+\returns expression representing \p f applied to \p M.
+
+Suppose that \p M is a matrix whose entries have type \c Scalar.
+Then, the second argument, \p f, should be a function with prototype
+\code
+ComplexScalar f(ComplexScalar, int)
+\endcode
+where \c ComplexScalar = \c std::complex<Scalar> if \c Scalar is
+real (e.g., \c float or \c double) and \c ComplexScalar =
+\c Scalar if \c Scalar is complex. The return value of \c f(x,n)
+should be \f$ f^{(n)}(x) \f$, the n-th derivative of f at x.
+
+This routine uses the algorithm described in:
+Philip Davies and Nicholas J. Higham,
+"A Schur-Parlett algorithm for computing matrix functions",
+<em>SIAM J. %Matrix Anal. Applic.</em>, <b>25</b>:464–485, 2003.
+
+The actual work is done by the MatrixFunction class.
+
+Example: The following program checks that
+\f[ \exp \left[ \begin{array}{ccc}
+ 0 & \frac14\pi & 0 \\
+ -\frac14\pi & 0 & 0 \\
+ 0 & 0 & 0
+ \end{array} \right] = \left[ \begin{array}{ccc}
+ \frac12\sqrt2 & -\frac12\sqrt2 & 0 \\
+ \frac12\sqrt2 & \frac12\sqrt2 & 0 \\
+ 0 & 0 & 1
+ \end{array} \right]. \f]
+This corresponds to a rotation of \f$ \frac14\pi \f$ radians around
+the z-axis. This is the same example as used in the documentation
+of \ref matrixbase_exp "exp()".
+
+\include MatrixFunction.cpp
+Output: \verbinclude MatrixFunction.out
+
+Note that the function \c expfn is defined for complex numbers
+\c x, even though the matrix \c A is over the reals. Instead of
+\c expfn, we could also have used StdStemFunctions::exp:
+\code
+A.matrixFunction(StdStemFunctions<std::complex<double> >::exp, &B);
+\endcode
+
+
+
+\subsection matrixbase_sin MatrixBase::sin()
+
+Compute the matrix sine.
+
+\code
+const MatrixFunctionReturnValue<Derived> MatrixBase<Derived>::sin() const
+\endcode
+
+\param[in] M a square matrix.
+\returns expression representing \f$ \sin(M) \f$.
+
+This function computes the matrix sine. Use ArrayBase::sin() for computing the entry-wise sine.
+
+The implementation calls \ref matrixbase_matrixfunction "matrixFunction()" with StdStemFunctions::sin().
+
+Example: \include MatrixSine.cpp
+Output: \verbinclude MatrixSine.out
+
+
+
+\subsection matrixbase_sinh MatrixBase::sinh()
+
+Compute the matrix hyperbolic sine.
+
+\code
+MatrixFunctionReturnValue<Derived> MatrixBase<Derived>::sinh() const
+\endcode
+
+\param[in] M a square matrix.
+\returns expression representing \f$ \sinh(M) \f$
+
+This function calls \ref matrixbase_matrixfunction "matrixFunction()" with StdStemFunctions::sinh().
+
+Example: \include MatrixSinh.cpp
+Output: \verbinclude MatrixSinh.out
+
+
+\subsection matrixbase_sqrt MatrixBase::sqrt()
+
+Compute the matrix square root.
+
+\code
+const MatrixSquareRootReturnValue<Derived> MatrixBase<Derived>::sqrt() const
+\endcode
+
+\param[in] M invertible matrix whose square root is to be computed.
+\returns expression representing the matrix square root of \p M.
+
+The matrix square root of \f$ M \f$ is the matrix \f$ M^{1/2} \f$
+whose square is the original matrix; so if \f$ S = M^{1/2} \f$ then
+\f$ S^2 = M \f$. This is different from taking the square root of all
+the entries in the matrix; use ArrayBase::sqrt() if you want to do the
+latter.
+
+In the <b>real case</b>, the matrix \f$ M \f$ should be invertible and
+it should have no eigenvalues which are real and negative (pairs of
+complex conjugate eigenvalues are allowed). In that case, the matrix
+has a square root which is also real, and this is the square root
+computed by this function.
+
+The matrix square root is computed by first reducing the matrix to
+quasi-triangular form with the real Schur decomposition. The square
+root of the quasi-triangular matrix can then be computed directly. The
+cost is approximately \f$ 25 n^3 \f$ real flops for the real Schur
+decomposition and \f$ 3\frac13 n^3 \f$ real flops for the remainder
+(though the computation time in practice is likely more than this
+indicates).
+
+Details of the algorithm can be found in: Nicholas J. Highan,
+"Computing real square roots of a real matrix", <em>Linear Algebra
+Appl.</em>, 88/89:405–430, 1987.
+
+If the matrix is <b>positive-definite symmetric</b>, then the square
+root is also positive-definite symmetric. In this case, it is best to
+use SelfAdjointEigenSolver::operatorSqrt() to compute it.
+
+In the <b>complex case</b>, the matrix \f$ M \f$ should be invertible;
+this is a restriction of the algorithm. The square root computed by
+this algorithm is the one whose eigenvalues have an argument in the
+interval \f$ (-\frac12\pi, \frac12\pi] \f$. This is the usual branch
+cut.
+
+The computation is the same as in the real case, except that the
+complex Schur decomposition is used to reduce the matrix to a
+triangular matrix. The theoretical cost is the same. Details are in:
+Åke Björck and Sven Hammarling, "A Schur method for the
+square root of a matrix", <em>Linear Algebra Appl.</em>,
+52/53:127–140, 1983.
+
+Example: The following program checks that the square root of
+\f[ \left[ \begin{array}{cc}
+ \cos(\frac13\pi) & -\sin(\frac13\pi) \\
+ \sin(\frac13\pi) & \cos(\frac13\pi)
+ \end{array} \right], \f]
+corresponding to a rotation over 60 degrees, is a rotation over 30 degrees:
+\f[ \left[ \begin{array}{cc}
+ \cos(\frac16\pi) & -\sin(\frac16\pi) \\
+ \sin(\frac16\pi) & \cos(\frac16\pi)
+ \end{array} \right]. \f]
+
+\include MatrixSquareRoot.cpp
+Output: \verbinclude MatrixSquareRoot.out
+
+\sa class RealSchur, class ComplexSchur, class MatrixSquareRoot,
+ SelfAdjointEigenSolver::operatorSqrt().
+
+*/
+
+#endif // EIGEN_MATRIX_FUNCTIONS_MODULE_H
diff --git a/unsupported/Eigen/MoreVectorization b/unsupported/Eigen/MoreVectorization
new file mode 100644
index 0000000..7662b47
--- /dev/null
+++ b/unsupported/Eigen/MoreVectorization
@@ -0,0 +1,24 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_MOREVECTORIZATION_MODULE_H
+#define EIGEN_MOREVECTORIZATION_MODULE_H
+
+#include "../../Eigen/Core"
+
+namespace Eigen {
+
+/**
+ * \defgroup MoreVectorization More vectorization module
+ */
+
+}
+
+#include "src/MoreVectorization/MathFunctions.h"
+
+#endif // EIGEN_MOREVECTORIZATION_MODULE_H
diff --git a/unsupported/Eigen/NNLS b/unsupported/Eigen/NNLS
new file mode 100644
index 0000000..2804508
--- /dev/null
+++ b/unsupported/Eigen/NNLS
@@ -0,0 +1,388 @@
+/* Non-Negagive Least Squares Algorithm for Eigen.
+ *
+ * Copyright (C) 2021 Essex Edwards, <essex.edwards@gmail.com>
+ * Copyright (C) 2013 Hannes Matuschek, hannes.matuschek at uni-potsdam.de
+ *
+ * This Source Code Form is subject to the terms of the Mozilla
+ * Public License v. 2.0. If a copy of the MPL was not distributed
+ * with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+ */
+
+/** \defgroup nnls Non-Negative Least Squares (NNLS) Module
+ * This module provides a single class @c Eigen::NNLS implementing the NNLS algorithm.
+ * The algorithm is described in "SOLVING LEAST SQUARES PROBLEMS", by Charles L. Lawson and
+ * Richard J. Hanson, Prentice-Hall, 1974 and solves optimization problems of the form
+ *
+ * \f[ \min \left\Vert Ax-b\right\Vert_2^2\quad s.t.\, x\ge 0\,.\f]
+ *
+ * The algorithm solves the constrained least-squares problem above by iteratively improving
+ * an estimate of which constraints are active (elements of \f$x\f$ equal to zero)
+ * and which constraints are inactive (elements of \f$x\f$ greater than zero).
+ * Each iteration, an unconstrained linear least-squares problem solves for the
+ * components of \f$x\f$ in the (estimated) inactive set and the sets are updated.
+ * The unconstrained problem minimizes \f$\left\Vert A^Nx^N-b\right\Vert_2^2\f$,
+ * where \f$A^N\f$ is a matrix formed by selecting all columns of A which are
+ * in the inactive set \f$N\f$.
+ *
+ */
+
+#ifndef EIGEN_NNLS_H
+#define EIGEN_NNLS_H
+
+#include "../../Eigen/Core"
+#include "../../Eigen/QR"
+
+#include <limits>
+
+namespace Eigen {
+
+/** \ingroup nnls
+ * \class NNLS
+ * \brief Implementation of the Non-Negative Least Squares (NNLS) algorithm.
+ * \tparam MatrixType The type of the system matrix \f$A\f$.
+ *
+ * This class implements the NNLS algorithm as described in "SOLVING LEAST SQUARES PROBLEMS",
+ * Charles L. Lawson and Richard J. Hanson, Prentice-Hall, 1974. This algorithm solves a least
+ * squares problem iteratively and ensures that the solution is non-negative. I.e.
+ *
+ * \f[ \min \left\Vert Ax-b\right\Vert_2^2\quad s.t.\, x\ge 0 \f]
+ *
+ * The algorithm solves the constrained least-squares problem above by iteratively improving
+ * an estimate of which constraints are active (elements of \f$x\f$ equal to zero)
+ * and which constraints are inactive (elements of \f$x\f$ greater than zero).
+ * Each iteration, an unconstrained linear least-squares problem solves for the
+ * components of \f$x\f$ in the (estimated) inactive set and the sets are updated.
+ * The unconstrained problem minimizes \f$\left\Vert A^Nx^N-b\right\Vert_2^2\f$,
+ * where \f$A^N\f$ is a matrix formed by selecting all columns of A which are
+ * in the inactive set \f$N\f$.
+ *
+ * See <a href="https://en.wikipedia.org/wiki/Non-negative_least_squares">the
+ * wikipedia page on non-negative least squares</a> for more background information.
+ *
+ * \note Please note that it is possible to construct an NNLS problem for which the
+ * algorithm does not converge. In practice these cases are extremely rare.
+ */
+template <class MatrixType_>
+class NNLS {
+ public:
+ typedef MatrixType_ MatrixType;
+
+ enum {
+ RowsAtCompileTime = MatrixType::RowsAtCompileTime,
+ ColsAtCompileTime = MatrixType::ColsAtCompileTime,
+ Options = MatrixType::Options,
+ MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime,
+ MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime
+ };
+
+ typedef typename MatrixType::Scalar Scalar;
+ typedef typename MatrixType::RealScalar RealScalar;
+ typedef typename MatrixType::Index Index;
+
+ /** Type of a row vector of the system matrix \f$A\f$. */
+ typedef Matrix<Scalar, ColsAtCompileTime, 1> SolutionVectorType;
+ /** Type of a column vector of the system matrix \f$A\f$. */
+ typedef Matrix<Scalar, RowsAtCompileTime, 1> RhsVectorType;
+ typedef Matrix<Index, ColsAtCompileTime, 1> IndicesType;
+
+ /** */
+ NNLS();
+
+ /** \brief Constructs a NNLS sovler and initializes it with the given system matrix @c A.
+ * \param A Specifies the system matrix.
+ * \param max_iter Specifies the maximum number of iterations to solve the system.
+ * \param tol Specifies the precision of the optimum.
+ * This is an absolute tolerance on the gradient of the Lagrangian, \f$A^T(Ax-b)-\lambda\f$
+ * (with Lagrange multipliers \f$\lambda\f$).
+ */
+ NNLS(const MatrixType &A, Index max_iter = -1, Scalar tol = NumTraits<Scalar>::dummy_precision());
+
+ /** Initializes the solver with the matrix \a A for further solving NNLS problems.
+ *
+ * This function mostly initializes/computes the preconditioner. In the future
+ * we might, for instance, implement column reordering for faster matrix vector products.
+ */
+ template <typename MatrixDerived>
+ NNLS<MatrixType> &compute(const EigenBase<MatrixDerived> &A);
+
+ /** \brief Solves the NNLS problem.
+ *
+ * The dimension of @c b must be equal to the number of rows of @c A, given to the constructor.
+ *
+ * \returns The approximate solution vector \f$ x \f$. Use info() to determine if the solve was a success or not.
+ * \sa info()
+ */
+ const SolutionVectorType &solve(const RhsVectorType &b);
+
+ /** \brief Returns the solution if a problem was solved.
+ * If not, an uninitialized vector may be returned. */
+ const SolutionVectorType &x() const { return x_; }
+
+ /** \returns the tolerance threshold used by the stopping criteria.
+ * \sa setTolerance()
+ */
+ Scalar tolerance() const { return tolerance_; }
+
+ /** Sets the tolerance threshold used by the stopping criteria.
+ *
+ * This is an absolute tolerance on the gradient of the Lagrangian, \f$A^T(Ax-b)-\lambda\f$
+ * (with Lagrange multipliers \f$\lambda\f$).
+ */
+ NNLS<MatrixType> &setTolerance(const Scalar &tolerance) {
+ tolerance_ = tolerance;
+ return *this;
+ }
+
+ /** \returns the max number of iterations.
+ * It is either the value set by setMaxIterations or, by default, twice the number of columns of the matrix.
+ */
+ Index maxIterations() const { return max_iter_ < 0 ? 2 * A_.cols() : max_iter_; }
+
+ /** Sets the max number of iterations.
+ * Default is twice the number of columns of the matrix.
+ * The algorithm requires at least k iterations to produce a solution vector with k non-zero entries.
+ */
+ NNLS<MatrixType> &setMaxIterations(Index maxIters) {
+ max_iter_ = maxIters;
+ return *this;
+ }
+
+ /** \returns the number of iterations (least-squares solves) performed during the last solve */
+ Index iterations() const { return iterations_; }
+
+ /** \returns Success if the iterations converged, and an error values otherwise. */
+ ComputationInfo info() const { return info_; }
+
+ private:
+ /** \internal Adds the given index @c idx to the inactive set N and updates the QR decomposition of \f$A^N\f$. */
+ void moveToInactiveSet_(Index idx);
+
+ /** \internal Removes the given index idx from the inactive set N and updates the QR decomposition of \f$A^N\f$. */
+ void moveToActiveSet_(Index idx);
+
+ /** \internal Solves the least-squares problem \f$\left\Vert y-A^Nx\right\Vert_2^2\f$. */
+ void solveInactiveSet_(const RhsVectorType &b);
+
+ private:
+ typedef Matrix<Scalar, ColsAtCompileTime, ColsAtCompileTime> MatrixAtAType;
+
+ /** \internal Holds the maximum number of iterations for the NNLS algorithm.
+ * @c -1 means to use the default value. */
+ Index max_iter_;
+ /** \internal Holds the number of iterations. */
+ Index iterations_;
+ /** \internal Holds success/fail of the last solve. */
+ ComputationInfo info_;
+ /** \internal Size of the inactive set. */
+ Index numInactive_;
+ /** \internal Accuracy of the algorithm w.r.t the optimality of the solution (gradient). */
+ Scalar tolerance_;
+ /** \internal The system matrix, a copy of the one given to the constructor. */
+ MatrixType A_;
+ /** \internal Precomputed product \f$A^TA\f$. */
+ MatrixAtAType AtA_;
+ /** \internal Will hold the solution. */
+ SolutionVectorType x_;
+ /** \internal Will hold the current gradient.\f$A^Tb - A^TAx\f$ */
+ SolutionVectorType gradient_;
+ /** \internal Will hold the partial solution. */
+ SolutionVectorType y_;
+ /** \internal Precomputed product \f$A^Tb\f$. */
+ SolutionVectorType Atb_;
+ /** \internal Holds the current permutation partitioning the active and inactive sets.
+ * The first @c numInactive_ elements form the inactive set and the rest the active set. */
+ IndicesType index_sets_;
+ /** \internal QR decomposition to solve the (inactive) sub system (together with @c qrCoeffs_). */
+ MatrixType QR_;
+ /** \internal QR decomposition to solve the (inactive) sub system (together with @c QR_). */
+ SolutionVectorType qrCoeffs_;
+ /** \internal Some workspace for QR decomposition. */
+ SolutionVectorType tempSolutionVector_;
+ RhsVectorType tempRhsVector_;
+};
+
+/* ********************************************************************************************
+ * Implementation
+ * ******************************************************************************************** */
+
+template <typename MatrixType>
+NNLS<MatrixType>::NNLS()
+ : max_iter_(-1),
+ iterations_(0),
+ info_(ComputationInfo::InvalidInput),
+ numInactive_(0),
+ tolerance_(NumTraits<Scalar>::dummy_precision()) {}
+
+template <typename MatrixType>
+NNLS<MatrixType>::NNLS(const MatrixType &A, Index max_iter, Scalar tol) : max_iter_(max_iter), tolerance_(tol) {
+ compute(A);
+}
+
+template <typename MatrixType>
+template <typename MatrixDerived>
+NNLS<MatrixType> &NNLS<MatrixType>::compute(const EigenBase<MatrixDerived> &A) {
+ // Ensure Scalar type is real. The non-negativity constraint doesn't obviously extend to complex numbers.
+ EIGEN_STATIC_ASSERT(!NumTraits<Scalar>::IsComplex, NUMERIC_TYPE_MUST_BE_REAL);
+
+ // max_iter_: unchanged
+ iterations_ = 0;
+ info_ = ComputationInfo::Success;
+ numInactive_ = 0;
+ // tolerance: unchanged
+ A_ = A.derived();
+ AtA_.noalias() = A_.transpose() * A_;
+ x_.resize(A_.cols());
+ gradient_.resize(A_.cols());
+ y_.resize(A_.cols());
+ Atb_.resize(A_.cols());
+ index_sets_.resize(A_.cols());
+ QR_.resize(A_.rows(), A_.cols());
+ qrCoeffs_.resize(A_.cols());
+ tempSolutionVector_.resize(A_.cols());
+ tempRhsVector_.resize(A_.rows());
+
+ return *this;
+}
+
+template <typename MatrixType>
+const typename NNLS<MatrixType>::SolutionVectorType &NNLS<MatrixType>::solve(const RhsVectorType &b) {
+ // Initialize solver
+ iterations_ = 0;
+ info_ = ComputationInfo::NumericalIssue;
+ x_.setZero();
+
+ index_sets_ = IndicesType::LinSpaced(A_.cols(), 0, A_.cols() - 1); // Identity permutation.
+ numInactive_ = 0;
+
+ // Precompute A^T*b
+ Atb_.noalias() = A_.transpose() * b;
+
+ const Index maxIterations = this->maxIterations();
+
+ // OUTER LOOP
+ while (true) {
+ // Early exit if all variables are inactive, which breaks 'maxCoeff' below.
+ if (A_.cols() == numInactive_) {
+ info_ = ComputationInfo::Success;
+ return x_;
+ }
+
+ // Find the maximum element of the gradient in the active set.
+ // If it is small or negative, then we have converged.
+ // Else, we move that variable to the inactive set.
+ gradient_.noalias() = Atb_ - AtA_ * x_;
+
+ const Index numActive = A_.cols() - numInactive_;
+ Index argmaxGradient = -1;
+ const Scalar maxGradient = gradient_(index_sets_.tail(numActive)).maxCoeff(&argmaxGradient);
+ argmaxGradient += numInactive_; // beacause tail() skipped the first numInactive_ elements
+
+ if (maxGradient < tolerance_) {
+ info_ = ComputationInfo::Success;
+ return x_;
+ }
+
+ moveToInactiveSet_(argmaxGradient);
+
+ // INNER LOOP
+ while (true) {
+ // Check if max. number of iterations is reached
+ if (iterations_ >= maxIterations) {
+ info_ = ComputationInfo::NoConvergence;
+ return x_;
+ }
+
+ // Solve least-squares problem in inactive set only,
+ // this step is rather trivial as moveToInactiveSet_ & moveToActiveSet_
+ // updates the QR decomposition of inactive columns A^N.
+ // solveInactiveSet_ puts the solution in y_
+ solveInactiveSet_(b);
+ ++iterations_; // The solve is expensive, so that is what we count as an iteration.
+
+ // Check feasability...
+ bool feasible = true;
+ Scalar alpha = NumTraits<Scalar>::highest();
+ Index infeasibleIdx = -1; // Which variable became infeasible first.
+ for (Index i = 0; i < numInactive_; i++) {
+ Index idx = index_sets_[i];
+ if (y_(idx) < 0) {
+ // t should always be in [0,1].
+ Scalar t = -x_(idx) / (y_(idx) - x_(idx));
+ if (alpha > t) {
+ alpha = t;
+ infeasibleIdx = i;
+ feasible = false;
+ }
+ }
+ }
+ eigen_assert(feasible || 0 <= infeasibleIdx);
+
+ // If solution is feasible, exit to outer loop
+ if (feasible) {
+ x_ = y_;
+ break;
+ }
+
+ // Infeasible solution -> interpolate to feasible one
+ for (Index i = 0; i < numInactive_; i++) {
+ Index idx = index_sets_[i];
+ x_(idx) += alpha * (y_(idx) - x_(idx));
+ }
+
+ // Remove these indices from the inactive set and update QR decomposition
+ moveToActiveSet_(infeasibleIdx);
+ }
+ }
+}
+
+template <typename MatrixType>
+void NNLS<MatrixType>::moveToInactiveSet_(Index idx) {
+ // Update permutation matrix:
+ std::swap(index_sets_(idx), index_sets_(numInactive_));
+ numInactive_++;
+
+ // Perform rank-1 update of the QR decomposition stored in QR_ & qrCoeff_
+ internal::householder_qr_inplace_update(QR_, qrCoeffs_, A_.col(index_sets_(numInactive_ - 1)), numInactive_ - 1,
+ tempSolutionVector_.data());
+}
+
+template <typename MatrixType>
+void NNLS<MatrixType>::moveToActiveSet_(Index idx) {
+ // swap index with last inactive one & reduce number of inactive columns
+ std::swap(index_sets_(idx), index_sets_(numInactive_ - 1));
+ numInactive_--;
+ // Update QR decomposition starting from the removed index up to the end [idx, ..., numInactive_]
+ for (Index i = idx; i < numInactive_; i++) {
+ Index col = index_sets_(i);
+ internal::householder_qr_inplace_update(QR_, qrCoeffs_, A_.col(col), i, tempSolutionVector_.data());
+ }
+}
+
+template <typename MatrixType>
+void NNLS<MatrixType>::solveInactiveSet_(const RhsVectorType &b) {
+ eigen_assert(numInactive_ > 0);
+
+ tempRhsVector_ = b;
+
+ // tmpRHS(0:numInactive_-1) := Q'*b
+ // tmpRHS(numInactive_:end) := useless stuff we would rather not compute at all.
+ tempRhsVector_.applyOnTheLeft(
+ householderSequence(QR_.leftCols(numInactive_), qrCoeffs_.head(numInactive_)).transpose());
+
+ // tempSol(0:numInactive_-1) := inv(R) * Q' * b
+ // = the least-squares solution for the inactive variables.
+ tempSolutionVector_.head(numInactive_) = //
+ QR_.topLeftCorner(numInactive_, numInactive_) //
+ .template triangularView<Upper>() //
+ .solve(tempRhsVector_.head(numInactive_)); //
+
+ // tempSol(numInactive_:end) := 0 = the value for the constrained variables.
+ tempSolutionVector_.tail(y_.size() - numInactive_).setZero();
+
+ // Back permute into original column order of A
+ y_.noalias() = index_sets_.asPermutation() * tempSolutionVector_.head(y_.size());
+}
+
+} // namespace Eigen
+
+#endif // EIGEN_NNLS_H
diff --git a/unsupported/Eigen/NonLinearOptimization b/unsupported/Eigen/NonLinearOptimization
new file mode 100644
index 0000000..6bf566e
--- /dev/null
+++ b/unsupported/Eigen/NonLinearOptimization
@@ -0,0 +1,140 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009 Thomas Capricelli <orzel@freehackers.org>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_NONLINEAROPTIMIZATION_MODULE_H
+#define EIGEN_NONLINEAROPTIMIZATION_MODULE_H
+
+#include <vector>
+
+#include "../../Eigen/Core"
+#include "../../Eigen/Jacobi"
+#include "../../Eigen/QR"
+#include "NumericalDiff"
+
+/**
+ * \defgroup NonLinearOptimization_Module Non linear optimization module
+ *
+ * \code
+ * #include <unsupported/Eigen/NonLinearOptimization>
+ * \endcode
+ *
+ * This module provides implementation of two important algorithms in non linear
+ * optimization. In both cases, we consider a system of non linear functions. Of
+ * course, this should work, and even work very well if those functions are
+ * actually linear. But if this is so, you should probably better use other
+ * methods more fitted to this special case.
+ *
+ * One algorithm allows to find a least-squares solution of such a system
+ * (Levenberg-Marquardt algorithm) and the second one is used to find
+ * a zero for the system (Powell hybrid "dogleg" method).
+ *
+ * This code is a port of minpack (http://en.wikipedia.org/wiki/MINPACK).
+ * Minpack is a very famous, old, robust and well renowned package, written in
+ * fortran. Those implementations have been carefully tuned, tested, and used
+ * for several decades.
+ *
+ * The original fortran code was automatically translated using f2c (http://en.wikipedia.org/wiki/F2c) in C,
+ * then c++, and then cleaned by several different authors.
+ * The last one of those cleanings being our starting point :
+ * http://devernay.free.fr/hacks/cminpack.html
+ *
+ * Finally, we ported this code to Eigen, creating classes and API
+ * coherent with Eigen. When possible, we switched to Eigen
+ * implementation, such as most linear algebra (vectors, matrices, stable norms).
+ *
+ * Doing so, we were very careful to check the tests we setup at the very
+ * beginning, which ensure that the same results are found.
+ *
+ * \section Tests Tests
+ *
+ * The tests are placed in the file unsupported/test/NonLinear.cpp.
+ *
+ * There are two kinds of tests : those that come from examples bundled with cminpack.
+ * They guaranty we get the same results as the original algorithms (value for 'x',
+ * for the number of evaluations of the function, and for the number of evaluations
+ * of the Jacobian if ever).
+ *
+ * Other tests were added by myself at the very beginning of the
+ * process and check the results for Levenberg-Marquardt using the reference data
+ * on http://www.itl.nist.gov/div898/strd/nls/nls_main.shtml. Since then i've
+ * carefully checked that the same results were obtained when modifying the
+ * code. Please note that we do not always get the exact same decimals as they do,
+ * but this is ok : they use 128bits float, and we do the tests using the C type 'double',
+ * which is 64 bits on most platforms (x86 and amd64, at least).
+ * I've performed those tests on several other implementations of Levenberg-Marquardt, and
+ * (c)minpack performs VERY well compared to those, both in accuracy and speed.
+ *
+ * The documentation for running the tests is on the wiki
+ * http://eigen.tuxfamily.org/index.php?title=Tests
+ *
+ * \section API API: overview of methods
+ *
+ * Both algorithms needs a functor computing the Jacobian. It can be computed by
+ * hand, using auto-differentiation (see \ref AutoDiff_Module), or using numerical
+ * differences (see \ref NumericalDiff_Module). For instance:
+ *\code
+ * MyFunc func;
+ * NumericalDiff<MyFunc> func_with_num_diff(func);
+ * LevenbergMarquardt<NumericalDiff<MyFunc> > lm(func_with_num_diff);
+ * \endcode
+ * For HybridNonLinearSolver, the method solveNumericalDiff() does the above wrapping for
+ * you.
+ *
+ * The methods LevenbergMarquardt.lmder1()/lmdif1()/lmstr1() and
+ * HybridNonLinearSolver.hybrj1()/hybrd1() are specific methods from the original
+ * minpack package that you probably should NOT use until you are porting a code that
+ * was previously using minpack. They just define a 'simple' API with default values
+ * for some parameters.
+ *
+ * All algorithms are provided using two APIs :
+ * - one where the user inits the algorithm, and uses '*OneStep()' as much as he wants :
+ * this way the caller have control over the steps
+ * - one where the user just calls a method (optimize() or solve()) which will
+ * handle the loop: init + loop until a stop condition is met. Those are provided for
+ * convenience.
+ *
+ * As an example, the method LevenbergMarquardt::minimize() is
+ * implemented as follow:
+ * \code
+ * Status LevenbergMarquardt<FunctorType,Scalar>::minimize(FVectorType &x, const int mode)
+ * {
+ * Status status = minimizeInit(x, mode);
+ * do {
+ * status = minimizeOneStep(x, mode);
+ * } while (status==Running);
+ * return status;
+ * }
+ * \endcode
+ *
+ * \section examples Examples
+ *
+ * The easiest way to understand how to use this module is by looking at the many examples in the file
+ * unsupported/test/NonLinearOptimization.cpp.
+ */
+
+#ifndef EIGEN_PARSED_BY_DOXYGEN
+
+#include "src/NonLinearOptimization/qrsolv.h"
+#include "src/NonLinearOptimization/r1updt.h"
+#include "src/NonLinearOptimization/r1mpyq.h"
+#include "src/NonLinearOptimization/rwupdt.h"
+#include "src/NonLinearOptimization/fdjac1.h"
+#include "src/NonLinearOptimization/lmpar.h"
+#include "src/NonLinearOptimization/dogleg.h"
+#include "src/NonLinearOptimization/covar.h"
+
+#include "src/NonLinearOptimization/chkder.h"
+
+#endif
+
+#include "src/NonLinearOptimization/HybridNonLinearSolver.h"
+#include "src/NonLinearOptimization/LevenbergMarquardt.h"
+
+
+#endif // EIGEN_NONLINEAROPTIMIZATION_MODULE_H
diff --git a/unsupported/Eigen/NumericalDiff b/unsupported/Eigen/NumericalDiff
new file mode 100644
index 0000000..9d6270a
--- /dev/null
+++ b/unsupported/Eigen/NumericalDiff
@@ -0,0 +1,56 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009 Thomas Capricelli <orzel@freehackers.org>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_NUMERICALDIFF_MODULE_H
+#define EIGEN_NUMERICALDIFF_MODULE_H
+
+#include "../../Eigen/Core"
+
+namespace Eigen {
+
+/**
+ * \defgroup NumericalDiff_Module Numerical differentiation module
+ *
+ * \code
+ * #include <unsupported/Eigen/NumericalDiff>
+ * \endcode
+ *
+ * See http://en.wikipedia.org/wiki/Numerical_differentiation
+ *
+ * Warning : this should NOT be confused with automatic differentiation, which
+ * is a different method and has its own module in Eigen : \ref
+ * AutoDiff_Module.
+ *
+ * Currently only "Forward" and "Central" schemes are implemented. Those
+ * are basic methods, and there exist some more elaborated way of
+ * computing such approximates. They are implemented using both
+ * proprietary and free software, and usually requires linking to an
+ * external library. It is very easy for you to write a functor
+ * using such software, and the purpose is quite orthogonal to what we
+ * want to achieve with Eigen.
+ *
+ * This is why we will not provide wrappers for every great numerical
+ * differentiation software that exist, but should rather stick with those
+ * basic ones, that still are useful for testing.
+ *
+ * Also, the \ref NonLinearOptimization_Module needs this in order to
+ * provide full features compatibility with the original (c)minpack
+ * package.
+ *
+ */
+}
+
+//@{
+
+#include "src/NumericalDiff/NumericalDiff.h"
+
+//@}
+
+
+#endif // EIGEN_NUMERICALDIFF_MODULE_H
diff --git a/unsupported/Eigen/OpenGLSupport b/unsupported/Eigen/OpenGLSupport
new file mode 100644
index 0000000..2468333
--- /dev/null
+++ b/unsupported/Eigen/OpenGLSupport
@@ -0,0 +1,322 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2010 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_OPENGL_MODULE_H
+#define EIGEN_OPENGL_MODULE_H
+
+#include "../../Eigen/Geometry"
+
+#if defined(__APPLE_CC__)
+ #include <OpenGL/gl.h>
+#else
+ #include <GL/gl.h>
+#endif
+
+namespace Eigen {
+
+/**
+ * \defgroup OpenGLSUpport_Module OpenGL Support module
+ *
+ * This module provides wrapper functions for a couple of OpenGL functions
+ * which simplify the way to pass Eigen's object to openGL.
+ * Here is an example:
+ *
+ * \code
+ * // You need to add path_to_eigen/unsupported to your include path.
+ * #include <Eigen/OpenGLSupport>
+ * // ...
+ * Vector3f x, y;
+ * Matrix3f rot;
+ *
+ * glVertex(y + x * rot);
+ *
+ * Quaternion q;
+ * glRotate(q);
+ *
+ * // ...
+ * \endcode
+ *
+ */
+//@{
+
+#define EIGEN_GL_FUNC_DECLARATION(FUNC) \
+namespace internal { \
+ template< typename XprType, \
+ typename Scalar = typename XprType::Scalar, \
+ int Rows = XprType::RowsAtCompileTime, \
+ int Cols = XprType::ColsAtCompileTime, \
+ bool IsGLCompatible = bool(internal::evaluator<XprType>::Flags&LinearAccessBit) \
+ && bool(XprType::Flags&DirectAccessBit) \
+ && (XprType::IsVectorAtCompileTime || (XprType::Flags&RowMajorBit)==0)> \
+ struct EIGEN_CAT(EIGEN_CAT(gl_,FUNC),_impl); \
+ \
+ template<typename XprType, typename Scalar, int Rows, int Cols> \
+ struct EIGEN_CAT(EIGEN_CAT(gl_,FUNC),_impl)<XprType,Scalar,Rows,Cols,false> { \
+ inline static void run(const XprType& p) { \
+ EIGEN_CAT(EIGEN_CAT(gl_,FUNC),_impl)<typename plain_matrix_type_column_major<XprType>::type>::run(p); } \
+ }; \
+} \
+ \
+template<typename Derived> inline void FUNC(const Eigen::DenseBase<Derived>& p) { \
+ EIGEN_CAT(EIGEN_CAT(internal::gl_,FUNC),_impl)<Derived>::run(p.derived()); \
+}
+
+
+#define EIGEN_GL_FUNC_SPECIALIZATION_MAT(FUNC,SCALAR,ROWS,COLS,SUFFIX) \
+namespace internal { \
+ template< typename XprType> struct EIGEN_CAT(EIGEN_CAT(gl_,FUNC),_impl)<XprType, SCALAR, ROWS, COLS, true> { \
+ inline static void run(const XprType& p) { FUNC##SUFFIX(p.data()); } \
+ }; \
+}
+
+
+#define EIGEN_GL_FUNC_SPECIALIZATION_VEC(FUNC,SCALAR,SIZE,SUFFIX) \
+namespace internal { \
+ template< typename XprType> struct EIGEN_CAT(EIGEN_CAT(gl_,FUNC),_impl)<XprType, SCALAR, SIZE, 1, true> { \
+ inline static void run(const XprType& p) { FUNC##SUFFIX(p.data()); } \
+ }; \
+ template< typename XprType> struct EIGEN_CAT(EIGEN_CAT(gl_,FUNC),_impl)<XprType, SCALAR, 1, SIZE, true> { \
+ inline static void run(const XprType& p) { FUNC##SUFFIX(p.data()); } \
+ }; \
+}
+
+
+EIGEN_GL_FUNC_DECLARATION (glVertex)
+EIGEN_GL_FUNC_SPECIALIZATION_VEC(glVertex,int, 2,2iv)
+EIGEN_GL_FUNC_SPECIALIZATION_VEC(glVertex,short, 2,2sv)
+EIGEN_GL_FUNC_SPECIALIZATION_VEC(glVertex,float, 2,2fv)
+EIGEN_GL_FUNC_SPECIALIZATION_VEC(glVertex,double, 2,2dv)
+EIGEN_GL_FUNC_SPECIALIZATION_VEC(glVertex,int, 3,3iv)
+EIGEN_GL_FUNC_SPECIALIZATION_VEC(glVertex,short, 3,3sv)
+EIGEN_GL_FUNC_SPECIALIZATION_VEC(glVertex,float, 3,3fv)
+EIGEN_GL_FUNC_SPECIALIZATION_VEC(glVertex,double, 3,3dv)
+EIGEN_GL_FUNC_SPECIALIZATION_VEC(glVertex,int, 4,4iv)
+EIGEN_GL_FUNC_SPECIALIZATION_VEC(glVertex,short, 4,4sv)
+EIGEN_GL_FUNC_SPECIALIZATION_VEC(glVertex,float, 4,4fv)
+EIGEN_GL_FUNC_SPECIALIZATION_VEC(glVertex,double, 4,4dv)
+
+EIGEN_GL_FUNC_DECLARATION (glTexCoord)
+EIGEN_GL_FUNC_SPECIALIZATION_VEC(glTexCoord,int, 2,2iv)
+EIGEN_GL_FUNC_SPECIALIZATION_VEC(glTexCoord,short, 2,2sv)
+EIGEN_GL_FUNC_SPECIALIZATION_VEC(glTexCoord,float, 2,2fv)
+EIGEN_GL_FUNC_SPECIALIZATION_VEC(glTexCoord,double, 2,2dv)
+EIGEN_GL_FUNC_SPECIALIZATION_VEC(glTexCoord,int, 3,3iv)
+EIGEN_GL_FUNC_SPECIALIZATION_VEC(glTexCoord,short, 3,3sv)
+EIGEN_GL_FUNC_SPECIALIZATION_VEC(glTexCoord,float, 3,3fv)
+EIGEN_GL_FUNC_SPECIALIZATION_VEC(glTexCoord,double, 3,3dv)
+EIGEN_GL_FUNC_SPECIALIZATION_VEC(glTexCoord,int, 4,4iv)
+EIGEN_GL_FUNC_SPECIALIZATION_VEC(glTexCoord,short, 4,4sv)
+EIGEN_GL_FUNC_SPECIALIZATION_VEC(glTexCoord,float, 4,4fv)
+EIGEN_GL_FUNC_SPECIALIZATION_VEC(glTexCoord,double, 4,4dv)
+
+EIGEN_GL_FUNC_DECLARATION (glColor)
+EIGEN_GL_FUNC_SPECIALIZATION_VEC(glColor,int, 2,2iv)
+EIGEN_GL_FUNC_SPECIALIZATION_VEC(glColor,short, 2,2sv)
+EIGEN_GL_FUNC_SPECIALIZATION_VEC(glColor,float, 2,2fv)
+EIGEN_GL_FUNC_SPECIALIZATION_VEC(glColor,double, 2,2dv)
+EIGEN_GL_FUNC_SPECIALIZATION_VEC(glColor,int, 3,3iv)
+EIGEN_GL_FUNC_SPECIALIZATION_VEC(glColor,short, 3,3sv)
+EIGEN_GL_FUNC_SPECIALIZATION_VEC(glColor,float, 3,3fv)
+EIGEN_GL_FUNC_SPECIALIZATION_VEC(glColor,double, 3,3dv)
+EIGEN_GL_FUNC_SPECIALIZATION_VEC(glColor,int, 4,4iv)
+EIGEN_GL_FUNC_SPECIALIZATION_VEC(glColor,short, 4,4sv)
+EIGEN_GL_FUNC_SPECIALIZATION_VEC(glColor,float, 4,4fv)
+EIGEN_GL_FUNC_SPECIALIZATION_VEC(glColor,double, 4,4dv)
+
+EIGEN_GL_FUNC_DECLARATION (glNormal)
+EIGEN_GL_FUNC_SPECIALIZATION_VEC(glNormal,int, 3,3iv)
+EIGEN_GL_FUNC_SPECIALIZATION_VEC(glNormal,short, 3,3sv)
+EIGEN_GL_FUNC_SPECIALIZATION_VEC(glNormal,float, 3,3fv)
+EIGEN_GL_FUNC_SPECIALIZATION_VEC(glNormal,double, 3,3dv)
+
+inline void glScale2fv(const float* v) { glScalef(v[0], v[1], 1.f); }
+inline void glScale2dv(const double* v) { glScaled(v[0], v[1], 1.0); }
+inline void glScale3fv(const float* v) { glScalef(v[0], v[1], v[2]); }
+inline void glScale3dv(const double* v) { glScaled(v[0], v[1], v[2]); }
+
+EIGEN_GL_FUNC_DECLARATION (glScale)
+EIGEN_GL_FUNC_SPECIALIZATION_VEC(glScale,float, 2,2fv)
+EIGEN_GL_FUNC_SPECIALIZATION_VEC(glScale,double, 2,2dv)
+EIGEN_GL_FUNC_SPECIALIZATION_VEC(glScale,float, 3,3fv)
+EIGEN_GL_FUNC_SPECIALIZATION_VEC(glScale,double, 3,3dv)
+
+template<typename Scalar> void glScale(const UniformScaling<Scalar>& s) { glScale(Matrix<Scalar,3,1>::Constant(s.factor())); }
+
+inline void glTranslate2fv(const float* v) { glTranslatef(v[0], v[1], 0.f); }
+inline void glTranslate2dv(const double* v) { glTranslated(v[0], v[1], 0.0); }
+inline void glTranslate3fv(const float* v) { glTranslatef(v[0], v[1], v[2]); }
+inline void glTranslate3dv(const double* v) { glTranslated(v[0], v[1], v[2]); }
+
+EIGEN_GL_FUNC_DECLARATION (glTranslate)
+EIGEN_GL_FUNC_SPECIALIZATION_VEC(glTranslate,float, 2,2fv)
+EIGEN_GL_FUNC_SPECIALIZATION_VEC(glTranslate,double, 2,2dv)
+EIGEN_GL_FUNC_SPECIALIZATION_VEC(glTranslate,float, 3,3fv)
+EIGEN_GL_FUNC_SPECIALIZATION_VEC(glTranslate,double, 3,3dv)
+
+template<typename Scalar> void glTranslate(const Translation<Scalar,2>& t) { glTranslate(t.vector()); }
+template<typename Scalar> void glTranslate(const Translation<Scalar,3>& t) { glTranslate(t.vector()); }
+
+EIGEN_GL_FUNC_DECLARATION (glMultMatrix)
+EIGEN_GL_FUNC_SPECIALIZATION_MAT(glMultMatrix,float, 4,4,f)
+EIGEN_GL_FUNC_SPECIALIZATION_MAT(glMultMatrix,double, 4,4,d)
+
+template<typename Scalar> void glMultMatrix(const Transform<Scalar,3,Affine>& t) { glMultMatrix(t.matrix()); }
+template<typename Scalar> void glMultMatrix(const Transform<Scalar,3,Projective>& t) { glMultMatrix(t.matrix()); }
+template<typename Scalar> void glMultMatrix(const Transform<Scalar,3,AffineCompact>& t) { glMultMatrix(Transform<Scalar,3,Affine>(t).matrix()); }
+
+EIGEN_GL_FUNC_DECLARATION (glLoadMatrix)
+EIGEN_GL_FUNC_SPECIALIZATION_MAT(glLoadMatrix,float, 4,4,f)
+EIGEN_GL_FUNC_SPECIALIZATION_MAT(glLoadMatrix,double, 4,4,d)
+
+template<typename Scalar> void glLoadMatrix(const Transform<Scalar,3,Affine>& t) { glLoadMatrix(t.matrix()); }
+template<typename Scalar> void glLoadMatrix(const Transform<Scalar,3,Projective>& t) { glLoadMatrix(t.matrix()); }
+template<typename Scalar> void glLoadMatrix(const Transform<Scalar,3,AffineCompact>& t) { glLoadMatrix(Transform<Scalar,3,Affine>(t).matrix()); }
+
+inline void glRotate(const Rotation2D<float>& rot)
+{
+ glRotatef(rot.angle()*180.f/float(EIGEN_PI), 0.f, 0.f, 1.f);
+}
+inline void glRotate(const Rotation2D<double>& rot)
+{
+ glRotated(rot.angle()*180.0/double(EIGEN_PI), 0.0, 0.0, 1.0);
+}
+
+template<typename Derived> void glRotate(const RotationBase<Derived,3>& rot)
+{
+ Transform<typename Derived::Scalar,3,Projective> tr(rot);
+ glMultMatrix(tr.matrix());
+}
+
+#define EIGEN_GL_MAKE_CONST_const const
+#define EIGEN_GL_MAKE_CONST__
+#define EIGEN_GL_EVAL(X) X
+
+#define EIGEN_GL_FUNC1_DECLARATION(FUNC,ARG1,CONST) \
+namespace internal { \
+ template< typename XprType, \
+ typename Scalar = typename XprType::Scalar, \
+ int Rows = XprType::RowsAtCompileTime, \
+ int Cols = XprType::ColsAtCompileTime, \
+ bool IsGLCompatible = bool(internal::evaluator<XprType>::Flags&LinearAccessBit) \
+ && bool(XprType::Flags&DirectAccessBit) \
+ && (XprType::IsVectorAtCompileTime || (XprType::Flags&RowMajorBit)==0)> \
+ struct EIGEN_CAT(EIGEN_CAT(gl_,FUNC),_impl); \
+ \
+ template<typename XprType, typename Scalar, int Rows, int Cols> \
+ struct EIGEN_CAT(EIGEN_CAT(gl_,FUNC),_impl)<XprType,Scalar,Rows,Cols,false> { \
+ inline static void run(ARG1 a,EIGEN_GL_EVAL(EIGEN_GL_MAKE_CONST_##CONST) XprType& p) { \
+ EIGEN_CAT(EIGEN_CAT(gl_,FUNC),_impl)<typename plain_matrix_type_column_major<XprType>::type>::run(a,p); } \
+ }; \
+} \
+ \
+template<typename Derived> inline void FUNC(ARG1 a,EIGEN_GL_EVAL(EIGEN_GL_MAKE_CONST_##CONST) Eigen::DenseBase<Derived>& p) { \
+ EIGEN_CAT(EIGEN_CAT(internal::gl_,FUNC),_impl)<Derived>::run(a,p.derived()); \
+}
+
+
+#define EIGEN_GL_FUNC1_SPECIALIZATION_MAT(FUNC,ARG1,CONST,SCALAR,ROWS,COLS,SUFFIX) \
+namespace internal { \
+ template< typename XprType> struct EIGEN_CAT(EIGEN_CAT(gl_,FUNC),_impl)<XprType, SCALAR, ROWS, COLS, true> { \
+ inline static void run(ARG1 a, EIGEN_GL_EVAL(EIGEN_GL_MAKE_CONST_##CONST) XprType& p) { FUNC##SUFFIX(a,p.data()); } \
+ }; \
+}
+
+
+#define EIGEN_GL_FUNC1_SPECIALIZATION_VEC(FUNC,ARG1,CONST,SCALAR,SIZE,SUFFIX) \
+namespace internal { \
+ template< typename XprType> struct EIGEN_CAT(EIGEN_CAT(gl_,FUNC),_impl)<XprType, SCALAR, SIZE, 1, true> { \
+ inline static void run(ARG1 a, EIGEN_GL_EVAL(EIGEN_GL_MAKE_CONST_##CONST) XprType& p) { FUNC##SUFFIX(a,p.data()); } \
+ }; \
+ template< typename XprType> struct EIGEN_CAT(EIGEN_CAT(gl_,FUNC),_impl)<XprType, SCALAR, 1, SIZE, true> { \
+ inline static void run(ARG1 a, EIGEN_GL_EVAL(EIGEN_GL_MAKE_CONST_##CONST) XprType& p) { FUNC##SUFFIX(a,p.data()); } \
+ }; \
+}
+
+EIGEN_GL_FUNC1_DECLARATION (glGet,GLenum,_)
+EIGEN_GL_FUNC1_SPECIALIZATION_MAT(glGet,GLenum,_,float, 4,4,Floatv)
+EIGEN_GL_FUNC1_SPECIALIZATION_MAT(glGet,GLenum,_,double, 4,4,Doublev)
+
+// glUniform API
+
+#ifdef GL_VERSION_2_0
+
+inline void glUniform2fv_ei (GLint loc, const float* v) { glUniform2fv(loc,1,v); }
+inline void glUniform2iv_ei (GLint loc, const int* v) { glUniform2iv(loc,1,v); }
+
+inline void glUniform3fv_ei (GLint loc, const float* v) { glUniform3fv(loc,1,v); }
+inline void glUniform3iv_ei (GLint loc, const int* v) { glUniform3iv(loc,1,v); }
+
+inline void glUniform4fv_ei (GLint loc, const float* v) { glUniform4fv(loc,1,v); }
+inline void glUniform4iv_ei (GLint loc, const int* v) { glUniform4iv(loc,1,v); }
+
+inline void glUniformMatrix2fv_ei (GLint loc, const float* v) { glUniformMatrix2fv(loc,1,false,v); }
+inline void glUniformMatrix3fv_ei (GLint loc, const float* v) { glUniformMatrix3fv(loc,1,false,v); }
+inline void glUniformMatrix4fv_ei (GLint loc, const float* v) { glUniformMatrix4fv(loc,1,false,v); }
+
+
+EIGEN_GL_FUNC1_DECLARATION (glUniform,GLint,const)
+EIGEN_GL_FUNC1_SPECIALIZATION_VEC(glUniform,GLint,const,float, 2,2fv_ei)
+EIGEN_GL_FUNC1_SPECIALIZATION_VEC(glUniform,GLint,const,int, 2,2iv_ei)
+EIGEN_GL_FUNC1_SPECIALIZATION_VEC(glUniform,GLint,const,float, 3,3fv_ei)
+EIGEN_GL_FUNC1_SPECIALIZATION_VEC(glUniform,GLint,const,int, 3,3iv_ei)
+EIGEN_GL_FUNC1_SPECIALIZATION_VEC(glUniform,GLint,const,float, 4,4fv_ei)
+EIGEN_GL_FUNC1_SPECIALIZATION_VEC(glUniform,GLint,const,int, 4,4iv_ei)
+
+EIGEN_GL_FUNC1_SPECIALIZATION_MAT(glUniform,GLint,const,float, 2,2,Matrix2fv_ei)
+EIGEN_GL_FUNC1_SPECIALIZATION_MAT(glUniform,GLint,const,float, 3,3,Matrix3fv_ei)
+EIGEN_GL_FUNC1_SPECIALIZATION_MAT(glUniform,GLint,const,float, 4,4,Matrix4fv_ei)
+
+#endif
+
+#ifdef GL_VERSION_2_1
+
+inline void glUniformMatrix2x3fv_ei(GLint loc, const float* v) { glUniformMatrix2x3fv(loc,1,false,v); }
+inline void glUniformMatrix3x2fv_ei(GLint loc, const float* v) { glUniformMatrix3x2fv(loc,1,false,v); }
+inline void glUniformMatrix2x4fv_ei(GLint loc, const float* v) { glUniformMatrix2x4fv(loc,1,false,v); }
+inline void glUniformMatrix4x2fv_ei(GLint loc, const float* v) { glUniformMatrix4x2fv(loc,1,false,v); }
+inline void glUniformMatrix3x4fv_ei(GLint loc, const float* v) { glUniformMatrix3x4fv(loc,1,false,v); }
+inline void glUniformMatrix4x3fv_ei(GLint loc, const float* v) { glUniformMatrix4x3fv(loc,1,false,v); }
+
+EIGEN_GL_FUNC1_SPECIALIZATION_MAT(glUniform,GLint,const,float, 2,3,Matrix2x3fv_ei)
+EIGEN_GL_FUNC1_SPECIALIZATION_MAT(glUniform,GLint,const,float, 3,2,Matrix3x2fv_ei)
+EIGEN_GL_FUNC1_SPECIALIZATION_MAT(glUniform,GLint,const,float, 2,4,Matrix2x4fv_ei)
+EIGEN_GL_FUNC1_SPECIALIZATION_MAT(glUniform,GLint,const,float, 4,2,Matrix4x2fv_ei)
+EIGEN_GL_FUNC1_SPECIALIZATION_MAT(glUniform,GLint,const,float, 3,4,Matrix3x4fv_ei)
+EIGEN_GL_FUNC1_SPECIALIZATION_MAT(glUniform,GLint,const,float, 4,3,Matrix4x3fv_ei)
+
+#endif
+
+#ifdef GL_VERSION_3_0
+
+inline void glUniform2uiv_ei (GLint loc, const unsigned int* v) { glUniform2uiv(loc,1,v); }
+inline void glUniform3uiv_ei (GLint loc, const unsigned int* v) { glUniform3uiv(loc,1,v); }
+inline void glUniform4uiv_ei (GLint loc, const unsigned int* v) { glUniform4uiv(loc,1,v); }
+
+EIGEN_GL_FUNC1_SPECIALIZATION_VEC(glUniform,GLint,const,unsigned int, 2,2uiv_ei)
+EIGEN_GL_FUNC1_SPECIALIZATION_VEC(glUniform,GLint,const,unsigned int, 3,3uiv_ei)
+EIGEN_GL_FUNC1_SPECIALIZATION_VEC(glUniform,GLint,const,unsigned int, 4,4uiv_ei)
+
+#endif
+
+#ifdef GL_ARB_gpu_shader_fp64
+inline void glUniform2dv_ei (GLint loc, const double* v) { glUniform2dv(loc,1,v); }
+inline void glUniform3dv_ei (GLint loc, const double* v) { glUniform3dv(loc,1,v); }
+inline void glUniform4dv_ei (GLint loc, const double* v) { glUniform4dv(loc,1,v); }
+
+EIGEN_GL_FUNC1_SPECIALIZATION_VEC(glUniform,GLint,const,double, 2,2dv_ei)
+EIGEN_GL_FUNC1_SPECIALIZATION_VEC(glUniform,GLint,const,double, 3,3dv_ei)
+EIGEN_GL_FUNC1_SPECIALIZATION_VEC(glUniform,GLint,const,double, 4,4dv_ei)
+#endif
+
+
+//@}
+
+}
+
+#endif // EIGEN_OPENGL_MODULE_H
diff --git a/unsupported/Eigen/Polynomials b/unsupported/Eigen/Polynomials
new file mode 100644
index 0000000..32ce2a2
--- /dev/null
+++ b/unsupported/Eigen/Polynomials
@@ -0,0 +1,137 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_POLYNOMIALS_MODULE_H
+#define EIGEN_POLYNOMIALS_MODULE_H
+
+#include "../../Eigen/Core"
+
+#include "../../Eigen/Eigenvalues"
+
+#include "../../Eigen/src/Core/util/DisableStupidWarnings.h"
+
+// Note that EIGEN_HIDE_HEAVY_CODE has to be defined per module
+#if (defined EIGEN_EXTERN_INSTANTIATIONS) && (EIGEN_EXTERN_INSTANTIATIONS>=2)
+ #ifndef EIGEN_HIDE_HEAVY_CODE
+ #define EIGEN_HIDE_HEAVY_CODE
+ #endif
+#elif defined EIGEN_HIDE_HEAVY_CODE
+ #undef EIGEN_HIDE_HEAVY_CODE
+#endif
+
+/**
+ * \defgroup Polynomials_Module Polynomials module
+ * \brief This module provides a QR based polynomial solver.
+ *
+ * To use this module, add
+ * \code
+ * #include <unsupported/Eigen/Polynomials>
+ * \endcode
+ * at the start of your source file.
+ */
+
+#include "src/Polynomials/PolynomialUtils.h"
+#include "src/Polynomials/Companion.h"
+#include "src/Polynomials/PolynomialSolver.h"
+
+/**
+ \page polynomials Polynomials defines functions for dealing with polynomials
+ and a QR based polynomial solver.
+ \ingroup Polynomials_Module
+
+ The remainder of the page documents first the functions for evaluating, computing
+ polynomials, computing estimates about polynomials and next the QR based polynomial
+ solver.
+
+ \section polynomialUtils convenient functions to deal with polynomials
+ \subsection roots_to_monicPolynomial
+ The function
+ \code
+ void roots_to_monicPolynomial( const RootVector& rv, Polynomial& poly )
+ \endcode
+ computes the coefficients \f$ a_i \f$ of
+
+ \f$ p(x) = a_0 + a_{1}x + ... + a_{n-1}x^{n-1} + x^n \f$
+
+ where \f$ p \f$ is known through its roots i.e. \f$ p(x) = (x-r_1)(x-r_2)...(x-r_n) \f$.
+
+ \subsection poly_eval
+ The function
+ \code
+ T poly_eval( const Polynomials& poly, const T& x )
+ \endcode
+ evaluates a polynomial at a given point using stabilized Hörner method.
+
+ The following code: first computes the coefficients in the monomial basis of the monic polynomial that has the provided roots;
+ then, it evaluates the computed polynomial, using a stabilized Hörner method.
+
+ \include PolynomialUtils1.cpp
+ Output: \verbinclude PolynomialUtils1.out
+
+ \subsection Cauchy bounds
+ The function
+ \code
+ Real cauchy_max_bound( const Polynomial& poly )
+ \endcode
+ provides a maximum bound (the Cauchy one: \f$C(p)\f$) for the absolute value of a root of the given polynomial i.e.
+ \f$ \forall r_i \f$ root of \f$ p(x) = \sum_{k=0}^d a_k x^k \f$,
+ \f$ |r_i| \le C(p) = \sum_{k=0}^{d} \left | \frac{a_k}{a_d} \right | \f$
+ The leading coefficient \f$ p \f$: should be non zero \f$a_d \neq 0\f$.
+
+
+ The function
+ \code
+ Real cauchy_min_bound( const Polynomial& poly )
+ \endcode
+ provides a minimum bound (the Cauchy one: \f$c(p)\f$) for the absolute value of a non zero root of the given polynomial i.e.
+ \f$ \forall r_i \neq 0 \f$ root of \f$ p(x) = \sum_{k=0}^d a_k x^k \f$,
+ \f$ |r_i| \ge c(p) = \left( \sum_{k=0}^{d} \left | \frac{a_k}{a_0} \right | \right)^{-1} \f$
+
+
+
+
+ \section QR polynomial solver class
+ Computes the complex roots of a polynomial by computing the eigenvalues of the associated companion matrix with the QR algorithm.
+
+ The roots of \f$ p(x) = a_0 + a_1 x + a_2 x^2 + a_{3} x^3 + x^4 \f$ are the eigenvalues of
+ \f$
+ \left [
+ \begin{array}{cccc}
+ 0 & 0 & 0 & a_0 \\
+ 1 & 0 & 0 & a_1 \\
+ 0 & 1 & 0 & a_2 \\
+ 0 & 0 & 1 & a_3
+ \end{array} \right ]
+ \f$
+
+ However, the QR algorithm is not guaranteed to converge when there are several eigenvalues with same modulus.
+
+ Therefore the current polynomial solver is guaranteed to provide a correct result only when the complex roots \f$r_1,r_2,...,r_d\f$ have distinct moduli i.e.
+
+ \f$ \forall i,j \in [1;d],~ \| r_i \| \neq \| r_j \| \f$.
+
+ With 32bit (float) floating types this problem shows up frequently.
+ However, almost always, correct accuracy is reached even in these cases for 64bit
+ (double) floating types and small polynomial degree (<20).
+
+ \include PolynomialSolver1.cpp
+
+ In the above example:
+
+ -# a simple use of the polynomial solver is shown;
+ -# the accuracy problem with the QR algorithm is presented: a polynomial with almost conjugate roots is provided to the solver.
+ Those roots have almost same module therefore the QR algorithm failed to converge: the accuracy
+ of the last root is bad;
+ -# a simple way to circumvent the problem is shown: use doubles instead of floats.
+
+ Output: \verbinclude PolynomialSolver1.out
+*/
+
+#include "../../Eigen/src/Core/util/ReenableStupidWarnings.h"
+
+#endif // EIGEN_POLYNOMIALS_MODULE_H
diff --git a/unsupported/Eigen/Skyline b/unsupported/Eigen/Skyline
new file mode 100644
index 0000000..ebdf143
--- /dev/null
+++ b/unsupported/Eigen/Skyline
@@ -0,0 +1,39 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_SKYLINE_MODULE_H
+#define EIGEN_SKYLINE_MODULE_H
+
+
+#include "../../Eigen/Core"
+
+#include "../../Eigen/src/Core/util/DisableStupidWarnings.h"
+
+#include <map>
+#include <cstdlib>
+#include <cstring>
+#include <algorithm>
+
+/**
+ * \defgroup Skyline_Module Skyline module
+ *
+ *
+ *
+ *
+ */
+
+#include "src/Skyline/SkylineUtil.h"
+#include "src/Skyline/SkylineMatrixBase.h"
+#include "src/Skyline/SkylineStorage.h"
+#include "src/Skyline/SkylineMatrix.h"
+#include "src/Skyline/SkylineInplaceLU.h"
+#include "src/Skyline/SkylineProduct.h"
+
+#include "../../Eigen/src/Core/util/ReenableStupidWarnings.h"
+
+#endif // EIGEN_SKYLINE_MODULE_H
diff --git a/unsupported/Eigen/SparseExtra b/unsupported/Eigen/SparseExtra
new file mode 100644
index 0000000..f4920de
--- /dev/null
+++ b/unsupported/Eigen/SparseExtra
@@ -0,0 +1,57 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2009 Gael Guennebaud <g.gael@free.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_SPARSE_EXTRA_MODULE_H
+#define EIGEN_SPARSE_EXTRA_MODULE_H
+
+#include "../../Eigen/Sparse"
+
+#include "../../Eigen/src/Core/util/DisableStupidWarnings.h"
+
+#include <vector>
+#include <map>
+#include <unordered_map>
+#include <cstdlib>
+#include <cstring>
+#include <algorithm>
+#include <fstream>
+#include <sstream>
+
+#ifdef EIGEN_GOOGLEHASH_SUPPORT
+ #include <google/dense_hash_map>
+ #include <google/sparse_hash_map>
+#endif
+
+/**
+ * \defgroup SparseExtra_Module SparseExtra module
+ *
+ * This module contains some experimental features extending the sparse module:
+ * - A RandomSetter which is a wrapper object allowing to set/update a sparse matrix with random access.
+ * - A SparseInverse which calculates a sparse subset of the inverse of a sparse matrix corresponding to nonzeros of the input
+ * - MatrixMarket format(https://math.nist.gov/MatrixMarket/formats.html) readers and writers for sparse and dense matrices.
+ *
+ * \code
+ * #include <unsupported/Eigen/SparseExtra>
+ * \endcode
+ */
+
+
+#include "src/SparseExtra/RandomSetter.h"
+#include "src/SparseExtra/SparseInverse.h"
+
+#include "src/SparseExtra/MarketIO.h"
+
+#if !defined(_WIN32)
+#include <dirent.h>
+#include "src/SparseExtra/MatrixMarketIterator.h"
+#endif
+
+#include "../../Eigen/src/Core/util/ReenableStupidWarnings.h"
+
+#endif // EIGEN_SPARSE_EXTRA_MODULE_H
diff --git a/unsupported/Eigen/SpecialFunctions b/unsupported/Eigen/SpecialFunctions
new file mode 100644
index 0000000..41a3631
--- /dev/null
+++ b/unsupported/Eigen/SpecialFunctions
@@ -0,0 +1,103 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2016 Gael Guennebaud <g.gael@free.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_SPECIALFUNCTIONS_MODULE_H
+#define EIGEN_SPECIALFUNCTIONS_MODULE_H
+
+#include <math.h>
+
+#include "../../Eigen/Core"
+
+#include "../../Eigen/src/Core/util/DisableStupidWarnings.h"
+
+namespace Eigen {
+
+/**
+ * \defgroup SpecialFunctions_Module Special math functions module
+ *
+ * This module features additional coefficient-wise math functions available
+ * within the numext:: namespace for the scalar version, and as method and/or free
+ * functions of Array. Those include:
+ *
+ * - erf
+ * - erfc
+ * - lgamma
+ * - igamma
+ * - igamma_der_a
+ * - gamma_sample_der_alpha
+ * - igammac
+ * - digamma
+ * - ndtri
+ * - polygamma
+ * - zeta
+ * - betainc
+ *
+ * Bessel Functions
+ * - bessel_i0
+ * - bessel_i0e
+ * - bessel_i1
+ * - bessel_i1e
+ * - bessel_j0
+ * - bessel_j1
+ * - bessel_k0
+ * - bessel_k0e
+ * - bessel_k1
+ * - bessel_k1e
+ * - bessel_y0
+ * - bessel_y1
+ *
+ * \code
+ * #include <unsupported/Eigen/SpecialFunctions>
+ * \endcode
+ */
+//@{
+
+}
+
+#include "src/SpecialFunctions/BesselFunctionsImpl.h"
+#include "src/SpecialFunctions/BesselFunctionsBFloat16.h"
+#include "src/SpecialFunctions/BesselFunctionsHalf.h"
+#include "src/SpecialFunctions/BesselFunctionsPacketMath.h"
+#include "src/SpecialFunctions/BesselFunctionsFunctors.h"
+#include "src/SpecialFunctions/BesselFunctionsArrayAPI.h"
+#include "src/SpecialFunctions/SpecialFunctionsImpl.h"
+#if defined(EIGEN_HIPCC)
+#include "src/SpecialFunctions/HipVectorCompatibility.h"
+#endif
+#include "src/SpecialFunctions/SpecialFunctionsBFloat16.h"
+#include "src/SpecialFunctions/SpecialFunctionsHalf.h"
+#include "src/SpecialFunctions/SpecialFunctionsPacketMath.h"
+#include "src/SpecialFunctions/SpecialFunctionsFunctors.h"
+#include "src/SpecialFunctions/SpecialFunctionsArrayAPI.h"
+
+#if defined EIGEN_VECTORIZE_AVX512
+ #include "src/SpecialFunctions/arch/AVX/BesselFunctions.h"
+ #include "src/SpecialFunctions/arch/AVX/SpecialFunctions.h"
+ #include "src/SpecialFunctions/arch/AVX512/BesselFunctions.h"
+ #include "src/SpecialFunctions/arch/AVX512/SpecialFunctions.h"
+#elif defined EIGEN_VECTORIZE_AVX
+ #include "src/SpecialFunctions/arch/AVX/BesselFunctions.h"
+ #include "src/SpecialFunctions/arch/AVX/SpecialFunctions.h"
+#elif defined EIGEN_VECTORIZE_NEON
+ #include "src/SpecialFunctions/arch/NEON/BesselFunctions.h"
+ #include "src/SpecialFunctions/arch/NEON/SpecialFunctions.h"
+#endif
+
+#if defined EIGEN_VECTORIZE_GPU
+ #include "src/SpecialFunctions/arch/GPU/SpecialFunctions.h"
+#endif
+
+namespace Eigen {
+//@}
+}
+
+
+#include "../../Eigen/src/Core/util/ReenableStupidWarnings.h"
+
+#endif // EIGEN_SPECIALFUNCTIONS_MODULE_H
diff --git a/unsupported/Eigen/Splines b/unsupported/Eigen/Splines
new file mode 100644
index 0000000..2ca5813
--- /dev/null
+++ b/unsupported/Eigen/Splines
@@ -0,0 +1,35 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 20010-2011 Hauke Heibel <hauke.heibel@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_SPLINES_MODULE_H
+#define EIGEN_SPLINES_MODULE_H
+
+namespace Eigen
+{
+/**
+ * \defgroup Splines_Module Spline and spline fitting module
+ *
+ * This module provides a simple multi-dimensional spline class while
+ * offering most basic functionality to fit a spline to point sets.
+ *
+ * \code
+ * #include <unsupported/Eigen/Splines>
+ * \endcode
+ */
+}
+
+#include "../../Eigen/src/Core/util/DisableStupidWarnings.h"
+
+#include "src/Splines/SplineFwd.h"
+#include "src/Splines/Spline.h"
+#include "src/Splines/SplineFitting.h"
+
+#include "../../Eigen/src/Core/util/ReenableStupidWarnings.h"
+
+#endif // EIGEN_SPLINES_MODULE_H
diff --git a/unsupported/Eigen/src/AutoDiff/AutoDiffJacobian.h b/unsupported/Eigen/src/AutoDiff/AutoDiffJacobian.h
new file mode 100644
index 0000000..6ef6bf4
--- /dev/null
+++ b/unsupported/Eigen/src/AutoDiff/AutoDiffJacobian.h
@@ -0,0 +1,89 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_AUTODIFF_JACOBIAN_H
+#define EIGEN_AUTODIFF_JACOBIAN_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen
+{
+
+template<typename Functor> class AutoDiffJacobian : public Functor
+{
+public:
+ AutoDiffJacobian() : Functor() {}
+ AutoDiffJacobian(const Functor& f) : Functor(f) {}
+
+ // forward constructors
+ template<typename... T>
+ AutoDiffJacobian(const T& ...Values) : Functor(Values...) {}
+
+ typedef typename Functor::InputType InputType;
+ typedef typename Functor::ValueType ValueType;
+ typedef typename ValueType::Scalar Scalar;
+
+ enum {
+ InputsAtCompileTime = InputType::RowsAtCompileTime,
+ ValuesAtCompileTime = ValueType::RowsAtCompileTime
+ };
+
+ typedef Matrix<Scalar, ValuesAtCompileTime, InputsAtCompileTime> JacobianType;
+ typedef typename JacobianType::Index Index;
+
+ typedef Matrix<Scalar, InputsAtCompileTime, 1> DerivativeType;
+ typedef AutoDiffScalar<DerivativeType> ActiveScalar;
+
+ typedef Matrix<ActiveScalar, InputsAtCompileTime, 1> ActiveInput;
+ typedef Matrix<ActiveScalar, ValuesAtCompileTime, 1> ActiveValue;
+
+ // Some compilers don't accept variadic parameters after a default parameter,
+ // i.e., we can't just write _jac=0 but we need to overload operator():
+ EIGEN_STRONG_INLINE
+ void operator() (const InputType& x, ValueType* v) const
+ {
+ this->operator()(x, v, 0);
+ }
+ template<typename... ParamsType>
+ void operator() (const InputType& x, ValueType* v, JacobianType* _jac,
+ const ParamsType&... Params) const
+ {
+ eigen_assert(v!=0);
+
+ if (!_jac)
+ {
+ Functor::operator()(x, v, Params...);
+ return;
+ }
+
+ JacobianType& jac = *_jac;
+
+ ActiveInput ax = x.template cast<ActiveScalar>();
+ ActiveValue av(jac.rows());
+
+ if(InputsAtCompileTime==Dynamic)
+ for (Index j=0; j<jac.rows(); j++)
+ av[j].derivatives().resize(x.rows());
+
+ for (Index i=0; i<jac.cols(); i++)
+ ax[i].derivatives() = DerivativeType::Unit(x.rows(),i);
+
+ Functor::operator()(ax, &av, Params...);
+
+ for (Index i=0; i<jac.rows(); i++)
+ {
+ (*v)[i] = av[i].value();
+ jac.row(i) = av[i].derivatives();
+ }
+ }
+};
+
+}
+
+#endif // EIGEN_AUTODIFF_JACOBIAN_H
diff --git a/unsupported/Eigen/src/AutoDiff/AutoDiffScalar.h b/unsupported/Eigen/src/AutoDiff/AutoDiffScalar.h
new file mode 100644
index 0000000..97222d1
--- /dev/null
+++ b/unsupported/Eigen/src/AutoDiff/AutoDiffScalar.h
@@ -0,0 +1,749 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_AUTODIFF_SCALAR_H
+#define EIGEN_AUTODIFF_SCALAR_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+
+template<typename A, typename B>
+struct make_coherent_impl {
+ static void run(A&, B&) {}
+};
+
+// resize a to match b is a.size()==0, and conversely.
+template<typename A, typename B>
+void make_coherent(const A& a, const B&b)
+{
+ make_coherent_impl<A,B>::run(a.const_cast_derived(), b.const_cast_derived());
+}
+
+template<typename DerivativeType, bool Enable> struct auto_diff_special_op;
+
+} // end namespace internal
+
+template<typename DerivativeType> class AutoDiffScalar;
+
+template<typename NewDerType>
+inline AutoDiffScalar<NewDerType> MakeAutoDiffScalar(const typename NewDerType::Scalar& value, const NewDerType &der) {
+ return AutoDiffScalar<NewDerType>(value,der);
+}
+
+/** \class AutoDiffScalar
+ * \brief A scalar type replacement with automatic differentiation capability
+ *
+ * \param DerivativeType the vector type used to store/represent the derivatives. The base scalar type
+ * as well as the number of derivatives to compute are determined from this type.
+ * Typical choices include, e.g., \c Vector4f for 4 derivatives, or \c VectorXf
+ * if the number of derivatives is not known at compile time, and/or, the number
+ * of derivatives is large.
+ * Note that DerivativeType can also be a reference (e.g., \c VectorXf&) to wrap a
+ * existing vector into an AutoDiffScalar.
+ * Finally, DerivativeType can also be any Eigen compatible expression.
+ *
+ * This class represents a scalar value while tracking its respective derivatives using Eigen's expression
+ * template mechanism.
+ *
+ * It supports the following list of global math function:
+ * - std::abs, std::sqrt, std::pow, std::exp, std::log, std::sin, std::cos,
+ * - internal::abs, internal::sqrt, numext::pow, internal::exp, internal::log, internal::sin, internal::cos,
+ * - internal::conj, internal::real, internal::imag, numext::abs2.
+ *
+ * AutoDiffScalar can be used as the scalar type of an Eigen::Matrix object. However,
+ * in that case, the expression template mechanism only occurs at the top Matrix level,
+ * while derivatives are computed right away.
+ *
+ */
+
+template<typename DerivativeType>
+class AutoDiffScalar
+ : public internal::auto_diff_special_op
+ <DerivativeType, !internal::is_same<typename internal::traits<internal::remove_all_t<DerivativeType>>::Scalar,
+ typename NumTraits<typename internal::traits<internal::remove_all_t<DerivativeType>>::Scalar>::Real>::value>
+{
+ public:
+ typedef internal::auto_diff_special_op
+ <DerivativeType, !internal::is_same<typename internal::traits<internal::remove_all_t<DerivativeType>>::Scalar,
+ typename NumTraits<typename internal::traits<internal::remove_all_t<DerivativeType>>::Scalar>::Real>::value> Base;
+ typedef internal::remove_all_t<DerivativeType> DerType;
+ typedef typename internal::traits<DerType>::Scalar Scalar;
+ typedef typename NumTraits<Scalar>::Real Real;
+
+ using Base::operator+;
+ using Base::operator*;
+
+ /** Default constructor without any initialization. */
+ AutoDiffScalar() {}
+
+ /** Constructs an active scalar from its \a value,
+ and initializes the \a nbDer derivatives such that it corresponds to the \a derNumber -th variable */
+ AutoDiffScalar(const Scalar& value, int nbDer, int derNumber)
+ : m_value(value), m_derivatives(DerType::Zero(nbDer))
+ {
+ m_derivatives.coeffRef(derNumber) = Scalar(1);
+ }
+
+ /** Conversion from a scalar constant to an active scalar.
+ * The derivatives are set to zero. */
+ /*explicit*/ AutoDiffScalar(const Real& value)
+ : m_value(value)
+ {
+ if(m_derivatives.size()>0)
+ m_derivatives.setZero();
+ }
+
+ /** Constructs an active scalar from its \a value and derivatives \a der */
+ AutoDiffScalar(const Scalar& value, const DerType& der)
+ : m_value(value), m_derivatives(der)
+ {}
+
+ template<typename OtherDerType>
+ AutoDiffScalar(const AutoDiffScalar<OtherDerType>& other
+#ifndef EIGEN_PARSED_BY_DOXYGEN
+ , std::enable_if_t<
+ internal::is_same<Scalar, typename internal::traits<internal::remove_all_t<OtherDerType>>::Scalar>::value
+ && internal::is_convertible<OtherDerType,DerType>::value , void*> = 0
+#endif
+ )
+ : m_value(other.value()), m_derivatives(other.derivatives())
+ {}
+
+ friend std::ostream & operator << (std::ostream & s, const AutoDiffScalar& a)
+ {
+ return s << a.value();
+ }
+
+ AutoDiffScalar(const AutoDiffScalar& other)
+ : m_value(other.value()), m_derivatives(other.derivatives())
+ {}
+
+ template<typename OtherDerType>
+ inline AutoDiffScalar& operator=(const AutoDiffScalar<OtherDerType>& other)
+ {
+ m_value = other.value();
+ m_derivatives = other.derivatives();
+ return *this;
+ }
+
+ inline AutoDiffScalar& operator=(const AutoDiffScalar& other)
+ {
+ m_value = other.value();
+ m_derivatives = other.derivatives();
+ return *this;
+ }
+
+ inline AutoDiffScalar& operator=(const Scalar& other)
+ {
+ m_value = other;
+ if(m_derivatives.size()>0)
+ m_derivatives.setZero();
+ return *this;
+ }
+
+// inline operator const Scalar& () const { return m_value; }
+// inline operator Scalar& () { return m_value; }
+
+ inline const Scalar& value() const { return m_value; }
+ inline Scalar& value() { return m_value; }
+
+ inline const DerType& derivatives() const { return m_derivatives; }
+ inline DerType& derivatives() { return m_derivatives; }
+
+ inline bool operator< (const Scalar& other) const { return m_value < other; }
+ inline bool operator<=(const Scalar& other) const { return m_value <= other; }
+ inline bool operator> (const Scalar& other) const { return m_value > other; }
+ inline bool operator>=(const Scalar& other) const { return m_value >= other; }
+ inline bool operator==(const Scalar& other) const { return m_value == other; }
+ inline bool operator!=(const Scalar& other) const { return m_value != other; }
+
+ friend inline bool operator< (const Scalar& a, const AutoDiffScalar& b) { return a < b.value(); }
+ friend inline bool operator<=(const Scalar& a, const AutoDiffScalar& b) { return a <= b.value(); }
+ friend inline bool operator> (const Scalar& a, const AutoDiffScalar& b) { return a > b.value(); }
+ friend inline bool operator>=(const Scalar& a, const AutoDiffScalar& b) { return a >= b.value(); }
+ friend inline bool operator==(const Scalar& a, const AutoDiffScalar& b) { return a == b.value(); }
+ friend inline bool operator!=(const Scalar& a, const AutoDiffScalar& b) { return a != b.value(); }
+
+ template<typename OtherDerType> inline bool operator< (const AutoDiffScalar<OtherDerType>& b) const { return m_value < b.value(); }
+ template<typename OtherDerType> inline bool operator<=(const AutoDiffScalar<OtherDerType>& b) const { return m_value <= b.value(); }
+ template<typename OtherDerType> inline bool operator> (const AutoDiffScalar<OtherDerType>& b) const { return m_value > b.value(); }
+ template<typename OtherDerType> inline bool operator>=(const AutoDiffScalar<OtherDerType>& b) const { return m_value >= b.value(); }
+ template<typename OtherDerType> inline bool operator==(const AutoDiffScalar<OtherDerType>& b) const { return m_value == b.value(); }
+ template<typename OtherDerType> inline bool operator!=(const AutoDiffScalar<OtherDerType>& b) const { return m_value != b.value(); }
+
+ inline AutoDiffScalar<DerType&> operator+(const Scalar& other) const
+ {
+ return AutoDiffScalar<DerType&>(m_value + other, m_derivatives);
+ }
+
+ friend inline AutoDiffScalar<DerType&> operator+(const Scalar& a, const AutoDiffScalar& b)
+ {
+ return AutoDiffScalar<DerType&>(a + b.value(), b.derivatives());
+ }
+
+// inline const AutoDiffScalar<DerType&> operator+(const Real& other) const
+// {
+// return AutoDiffScalar<DerType&>(m_value + other, m_derivatives);
+// }
+
+// friend inline const AutoDiffScalar<DerType&> operator+(const Real& a, const AutoDiffScalar& b)
+// {
+// return AutoDiffScalar<DerType&>(a + b.value(), b.derivatives());
+// }
+
+ inline AutoDiffScalar& operator+=(const Scalar& other)
+ {
+ value() += other;
+ return *this;
+ }
+
+ template<typename OtherDerType>
+ inline AutoDiffScalar<CwiseBinaryOp<internal::scalar_sum_op<Scalar>,const DerType,const internal::remove_all_t<OtherDerType>> >
+ operator+(const AutoDiffScalar<OtherDerType>& other) const
+ {
+ internal::make_coherent(m_derivatives, other.derivatives());
+ return AutoDiffScalar<CwiseBinaryOp<internal::scalar_sum_op<Scalar>,const DerType,const internal::remove_all_t<OtherDerType>> >(
+ m_value + other.value(),
+ m_derivatives + other.derivatives());
+ }
+
+ template<typename OtherDerType>
+ inline AutoDiffScalar&
+ operator+=(const AutoDiffScalar<OtherDerType>& other)
+ {
+ (*this) = (*this) + other;
+ return *this;
+ }
+
+ inline AutoDiffScalar<DerType&> operator-(const Scalar& b) const
+ {
+ return AutoDiffScalar<DerType&>(m_value - b, m_derivatives);
+ }
+
+ friend inline AutoDiffScalar<CwiseUnaryOp<internal::scalar_opposite_op<Scalar>, const DerType> >
+ operator-(const Scalar& a, const AutoDiffScalar& b)
+ {
+ return AutoDiffScalar<CwiseUnaryOp<internal::scalar_opposite_op<Scalar>, const DerType> >
+ (a - b.value(), -b.derivatives());
+ }
+
+ inline AutoDiffScalar& operator-=(const Scalar& other)
+ {
+ value() -= other;
+ return *this;
+ }
+
+ template<typename OtherDerType>
+ inline AutoDiffScalar<CwiseBinaryOp<internal::scalar_difference_op<Scalar>, const DerType,const internal::remove_all_t<OtherDerType>> >
+ operator-(const AutoDiffScalar<OtherDerType>& other) const
+ {
+ internal::make_coherent(m_derivatives, other.derivatives());
+ return AutoDiffScalar<CwiseBinaryOp<internal::scalar_difference_op<Scalar>, const DerType,const internal::remove_all_t<OtherDerType>> >(
+ m_value - other.value(),
+ m_derivatives - other.derivatives());
+ }
+
+ template<typename OtherDerType>
+ inline AutoDiffScalar&
+ operator-=(const AutoDiffScalar<OtherDerType>& other)
+ {
+ *this = *this - other;
+ return *this;
+ }
+
+ inline AutoDiffScalar<CwiseUnaryOp<internal::scalar_opposite_op<Scalar>, const DerType> >
+ operator-() const
+ {
+ return AutoDiffScalar<CwiseUnaryOp<internal::scalar_opposite_op<Scalar>, const DerType> >(
+ -m_value,
+ -m_derivatives);
+ }
+
+ inline AutoDiffScalar<EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(DerType,Scalar,product) >
+ operator*(const Scalar& other) const
+ {
+ return MakeAutoDiffScalar(m_value * other, m_derivatives * other);
+ }
+
+ friend inline AutoDiffScalar<EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(DerType,Scalar,product) >
+ operator*(const Scalar& other, const AutoDiffScalar& a)
+ {
+ return MakeAutoDiffScalar(a.value() * other, a.derivatives() * other);
+ }
+
+// inline const AutoDiffScalar<typename CwiseUnaryOp<internal::scalar_multiple_op<Real>, DerType>::Type >
+// operator*(const Real& other) const
+// {
+// return AutoDiffScalar<typename CwiseUnaryOp<internal::scalar_multiple_op<Real>, DerType>::Type >(
+// m_value * other,
+// (m_derivatives * other));
+// }
+//
+// friend inline const AutoDiffScalar<typename CwiseUnaryOp<internal::scalar_multiple_op<Real>, DerType>::Type >
+// operator*(const Real& other, const AutoDiffScalar& a)
+// {
+// return AutoDiffScalar<typename CwiseUnaryOp<internal::scalar_multiple_op<Real>, DerType>::Type >(
+// a.value() * other,
+// a.derivatives() * other);
+// }
+
+ inline AutoDiffScalar<EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(DerType,Scalar,product) >
+ operator/(const Scalar& other) const
+ {
+ return MakeAutoDiffScalar(m_value / other, (m_derivatives * (Scalar(1)/other)));
+ }
+
+ friend inline AutoDiffScalar<EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(DerType,Scalar,product) >
+ operator/(const Scalar& other, const AutoDiffScalar& a)
+ {
+ return MakeAutoDiffScalar(other / a.value(), a.derivatives() * (Scalar(-other) / (a.value()*a.value())));
+ }
+
+// inline const AutoDiffScalar<typename CwiseUnaryOp<internal::scalar_multiple_op<Real>, DerType>::Type >
+// operator/(const Real& other) const
+// {
+// return AutoDiffScalar<typename CwiseUnaryOp<internal::scalar_multiple_op<Real>, DerType>::Type >(
+// m_value / other,
+// (m_derivatives * (Real(1)/other)));
+// }
+//
+// friend inline const AutoDiffScalar<typename CwiseUnaryOp<internal::scalar_multiple_op<Real>, DerType>::Type >
+// operator/(const Real& other, const AutoDiffScalar& a)
+// {
+// return AutoDiffScalar<typename CwiseUnaryOp<internal::scalar_multiple_op<Real>, DerType>::Type >(
+// other / a.value(),
+// a.derivatives() * (-Real(1)/other));
+// }
+
+ template<typename OtherDerType>
+ inline AutoDiffScalar<EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(
+ CwiseBinaryOp<internal::scalar_difference_op<Scalar> EIGEN_COMMA
+ const EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(DerType,Scalar,product) EIGEN_COMMA
+ const EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(internal::remove_all_t<OtherDerType>,Scalar,product) >,Scalar,product) >
+ operator/(const AutoDiffScalar<OtherDerType>& other) const
+ {
+ internal::make_coherent(m_derivatives, other.derivatives());
+ return MakeAutoDiffScalar(
+ m_value / other.value(),
+ ((m_derivatives * other.value()) - (other.derivatives() * m_value))
+ * (Scalar(1)/(other.value()*other.value())));
+ }
+
+ template<typename OtherDerType>
+ inline AutoDiffScalar<CwiseBinaryOp<internal::scalar_sum_op<Scalar>,
+ const EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(DerType,Scalar,product),
+ const EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(internal::remove_all_t<OtherDerType>,Scalar,product) > >
+ operator*(const AutoDiffScalar<OtherDerType>& other) const
+ {
+ internal::make_coherent(m_derivatives, other.derivatives());
+ return MakeAutoDiffScalar(
+ m_value * other.value(),
+ (m_derivatives * other.value()) + (other.derivatives() * m_value));
+ }
+
+ inline AutoDiffScalar& operator*=(const Scalar& other)
+ {
+ *this = *this * other;
+ return *this;
+ }
+
+ template<typename OtherDerType>
+ inline AutoDiffScalar& operator*=(const AutoDiffScalar<OtherDerType>& other)
+ {
+ *this = *this * other;
+ return *this;
+ }
+
+ inline AutoDiffScalar& operator/=(const Scalar& other)
+ {
+ *this = *this / other;
+ return *this;
+ }
+
+ template<typename OtherDerType>
+ inline AutoDiffScalar& operator/=(const AutoDiffScalar<OtherDerType>& other)
+ {
+ *this = *this / other;
+ return *this;
+ }
+
+ protected:
+ Scalar m_value;
+ DerType m_derivatives;
+
+};
+
+namespace internal {
+
+template<typename DerivativeType>
+struct auto_diff_special_op<DerivativeType, true>
+// : auto_diff_scalar_op<DerivativeType, typename NumTraits<Scalar>::Real,
+// is_same<Scalar,typename NumTraits<Scalar>::Real>::value>
+{
+ typedef remove_all_t<DerivativeType> DerType;
+ typedef typename traits<DerType>::Scalar Scalar;
+ typedef typename NumTraits<Scalar>::Real Real;
+
+// typedef auto_diff_scalar_op<DerivativeType, typename NumTraits<Scalar>::Real,
+// is_same<Scalar,typename NumTraits<Scalar>::Real>::value> Base;
+
+// using Base::operator+;
+// using Base::operator+=;
+// using Base::operator-;
+// using Base::operator-=;
+// using Base::operator*;
+// using Base::operator*=;
+
+ const AutoDiffScalar<DerivativeType>& derived() const { return *static_cast<const AutoDiffScalar<DerivativeType>*>(this); }
+ AutoDiffScalar<DerivativeType>& derived() { return *static_cast<AutoDiffScalar<DerivativeType>*>(this); }
+
+
+ inline AutoDiffScalar<DerType&> operator+(const Real& other) const
+ {
+ return AutoDiffScalar<DerType&>(derived().value() + other, derived().derivatives());
+ }
+
+ friend inline AutoDiffScalar<DerType&> operator+(const Real& a, const AutoDiffScalar<DerivativeType>& b)
+ {
+ return AutoDiffScalar<DerType&>(a + b.value(), b.derivatives());
+ }
+
+ inline AutoDiffScalar<DerivativeType>& operator+=(const Real& other)
+ {
+ derived().value() += other;
+ return derived();
+ }
+
+
+ inline AutoDiffScalar<typename CwiseUnaryOp<bind2nd_op<scalar_product_op<Scalar,Real> >, DerType>::Type >
+ operator*(const Real& other) const
+ {
+ return AutoDiffScalar<typename CwiseUnaryOp<bind2nd_op<scalar_product_op<Scalar,Real> >, DerType>::Type >(
+ derived().value() * other,
+ derived().derivatives() * other);
+ }
+
+ friend inline AutoDiffScalar<typename CwiseUnaryOp<bind1st_op<scalar_product_op<Real,Scalar> >, DerType>::Type >
+ operator*(const Real& other, const AutoDiffScalar<DerivativeType>& a)
+ {
+ return AutoDiffScalar<typename CwiseUnaryOp<bind1st_op<scalar_product_op<Real,Scalar> >, DerType>::Type >(
+ a.value() * other,
+ a.derivatives() * other);
+ }
+
+ inline AutoDiffScalar<DerivativeType>& operator*=(const Scalar& other)
+ {
+ *this = *this * other;
+ return derived();
+ }
+};
+
+template<typename DerivativeType>
+struct auto_diff_special_op<DerivativeType, false>
+{
+ void operator*() const;
+ void operator-() const;
+ void operator+() const;
+};
+
+template<typename BinOp, typename A, typename B, typename RefType>
+void make_coherent_expression(CwiseBinaryOp<BinOp,A,B> xpr, const RefType &ref)
+{
+ make_coherent(xpr.const_cast_derived().lhs(), ref);
+ make_coherent(xpr.const_cast_derived().rhs(), ref);
+}
+
+template<typename UnaryOp, typename A, typename RefType>
+void make_coherent_expression(const CwiseUnaryOp<UnaryOp,A> &xpr, const RefType &ref)
+{
+ make_coherent(xpr.nestedExpression().const_cast_derived(), ref);
+}
+
+// needed for compilation only
+template<typename UnaryOp, typename A, typename RefType>
+void make_coherent_expression(const CwiseNullaryOp<UnaryOp,A> &, const RefType &)
+{}
+
+template<typename A_Scalar, int A_Rows, int A_Cols, int A_Options, int A_MaxRows, int A_MaxCols, typename B>
+struct make_coherent_impl<Matrix<A_Scalar, A_Rows, A_Cols, A_Options, A_MaxRows, A_MaxCols>, B> {
+ typedef Matrix<A_Scalar, A_Rows, A_Cols, A_Options, A_MaxRows, A_MaxCols> A;
+ static void run(A& a, B& b) {
+ if((A_Rows==Dynamic || A_Cols==Dynamic) && (a.size()==0))
+ {
+ a.resize(b.size());
+ a.setZero();
+ }
+ else if (B::SizeAtCompileTime==Dynamic && a.size()!=0 && b.size()==0)
+ {
+ make_coherent_expression(b,a);
+ }
+ }
+};
+
+template<typename A, typename B_Scalar, int B_Rows, int B_Cols, int B_Options, int B_MaxRows, int B_MaxCols>
+struct make_coherent_impl<A, Matrix<B_Scalar, B_Rows, B_Cols, B_Options, B_MaxRows, B_MaxCols> > {
+ typedef Matrix<B_Scalar, B_Rows, B_Cols, B_Options, B_MaxRows, B_MaxCols> B;
+ static void run(A& a, B& b) {
+ if((B_Rows==Dynamic || B_Cols==Dynamic) && (b.size()==0))
+ {
+ b.resize(a.size());
+ b.setZero();
+ }
+ else if (A::SizeAtCompileTime==Dynamic && b.size()!=0 && a.size()==0)
+ {
+ make_coherent_expression(a,b);
+ }
+ }
+};
+
+template<typename A_Scalar, int A_Rows, int A_Cols, int A_Options, int A_MaxRows, int A_MaxCols,
+ typename B_Scalar, int B_Rows, int B_Cols, int B_Options, int B_MaxRows, int B_MaxCols>
+struct make_coherent_impl<Matrix<A_Scalar, A_Rows, A_Cols, A_Options, A_MaxRows, A_MaxCols>,
+ Matrix<B_Scalar, B_Rows, B_Cols, B_Options, B_MaxRows, B_MaxCols> > {
+ typedef Matrix<A_Scalar, A_Rows, A_Cols, A_Options, A_MaxRows, A_MaxCols> A;
+ typedef Matrix<B_Scalar, B_Rows, B_Cols, B_Options, B_MaxRows, B_MaxCols> B;
+ static void run(A& a, B& b) {
+ if((A_Rows==Dynamic || A_Cols==Dynamic) && (a.size()==0))
+ {
+ a.resize(b.size());
+ a.setZero();
+ }
+ else if((B_Rows==Dynamic || B_Cols==Dynamic) && (b.size()==0))
+ {
+ b.resize(a.size());
+ b.setZero();
+ }
+ }
+};
+
+} // end namespace internal
+
+template<typename DerType, typename BinOp>
+struct ScalarBinaryOpTraits<AutoDiffScalar<DerType>,typename DerType::Scalar,BinOp>
+{
+ typedef AutoDiffScalar<DerType> ReturnType;
+};
+
+template<typename DerType, typename BinOp>
+struct ScalarBinaryOpTraits<typename DerType::Scalar,AutoDiffScalar<DerType>, BinOp>
+{
+ typedef AutoDiffScalar<DerType> ReturnType;
+};
+
+
+// The following is an attempt to let Eigen's known about expression template, but that's more tricky!
+
+// template<typename DerType, typename BinOp>
+// struct ScalarBinaryOpTraits<AutoDiffScalar<DerType>,AutoDiffScalar<DerType>, BinOp>
+// {
+// enum { Defined = 1 };
+// typedef AutoDiffScalar<typename DerType::PlainObject> ReturnType;
+// };
+//
+// template<typename DerType1,typename DerType2, typename BinOp>
+// struct ScalarBinaryOpTraits<AutoDiffScalar<DerType1>,AutoDiffScalar<DerType2>, BinOp>
+// {
+// enum { Defined = 1 };//internal::is_same<typename DerType1::Scalar,typename DerType2::Scalar>::value };
+// typedef AutoDiffScalar<typename DerType1::PlainObject> ReturnType;
+// };
+
+#define EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY(FUNC,CODE) \
+ template<typename DerType> \
+ inline Eigen::AutoDiffScalar< \
+ EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(Eigen::internal::remove_all_t<DerType>, typename Eigen::internal::traits<Eigen::internal::remove_all_t<DerType>>::Scalar, product) > \
+ FUNC(const Eigen::AutoDiffScalar<DerType>& x) { \
+ using namespace Eigen; \
+ typedef typename Eigen::internal::traits<Eigen::internal::remove_all_t<DerType>>::Scalar Scalar; \
+ EIGEN_UNUSED_VARIABLE(sizeof(Scalar)); \
+ CODE; \
+ }
+
+template<typename DerType>
+struct CleanedUpDerType {
+ typedef AutoDiffScalar<typename Eigen::internal::remove_all_t<DerType>::PlainObject> type;
+};
+
+template<typename DerType>
+inline const AutoDiffScalar<DerType>& conj(const AutoDiffScalar<DerType>& x) { return x; }
+template<typename DerType>
+inline const AutoDiffScalar<DerType>& real(const AutoDiffScalar<DerType>& x) { return x; }
+template<typename DerType>
+inline typename DerType::Scalar imag(const AutoDiffScalar<DerType>&) { return 0.; }
+template<typename DerType, typename T>
+inline typename CleanedUpDerType<DerType>::type (min)(const AutoDiffScalar<DerType>& x, const T& y) {
+ typedef typename CleanedUpDerType<DerType>::type ADS;
+ return (x <= y ? ADS(x) : ADS(y));
+}
+template<typename DerType, typename T>
+inline typename CleanedUpDerType<DerType>::type (max)(const AutoDiffScalar<DerType>& x, const T& y) {
+ typedef typename CleanedUpDerType<DerType>::type ADS;
+ return (x >= y ? ADS(x) : ADS(y));
+}
+template<typename DerType, typename T>
+inline typename CleanedUpDerType<DerType>::type (min)(const T& x, const AutoDiffScalar<DerType>& y) {
+ typedef typename CleanedUpDerType<DerType>::type ADS;
+ return (x < y ? ADS(x) : ADS(y));
+}
+template<typename DerType, typename T>
+inline typename CleanedUpDerType<DerType>::type (max)(const T& x, const AutoDiffScalar<DerType>& y) {
+ typedef typename CleanedUpDerType<DerType>::type ADS;
+ return (x > y ? ADS(x) : ADS(y));
+}
+template<typename DerType>
+inline typename CleanedUpDerType<DerType>::type (min)(const AutoDiffScalar<DerType>& x, const AutoDiffScalar<DerType>& y) {
+ return (x.value() < y.value() ? x : y);
+}
+template<typename DerType>
+inline typename CleanedUpDerType<DerType>::type (max)(const AutoDiffScalar<DerType>& x, const AutoDiffScalar<DerType>& y) {
+ return (x.value() >= y.value() ? x : y);
+}
+
+
+EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY(abs,
+ using std::abs;
+ return Eigen::MakeAutoDiffScalar(abs(x.value()), x.derivatives() * (x.value()<0 ? -1 : 1) );)
+
+EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY(abs2,
+ using numext::abs2;
+ return Eigen::MakeAutoDiffScalar(abs2(x.value()), x.derivatives() * (Scalar(2)*x.value()));)
+
+EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY(sqrt,
+ using std::sqrt;
+ Scalar sqrtx = sqrt(x.value());
+ return Eigen::MakeAutoDiffScalar(sqrtx,x.derivatives() * (Scalar(0.5) / sqrtx));)
+
+EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY(cos,
+ using std::cos;
+ using std::sin;
+ return Eigen::MakeAutoDiffScalar(cos(x.value()), x.derivatives() * (-sin(x.value())));)
+
+EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY(sin,
+ using std::sin;
+ using std::cos;
+ return Eigen::MakeAutoDiffScalar(sin(x.value()),x.derivatives() * cos(x.value()));)
+
+EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY(exp,
+ using std::exp;
+ Scalar expx = exp(x.value());
+ return Eigen::MakeAutoDiffScalar(expx,x.derivatives() * expx);)
+
+EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY(log,
+ using std::log;
+ return Eigen::MakeAutoDiffScalar(log(x.value()),x.derivatives() * (Scalar(1)/x.value()));)
+
+template<typename DerType>
+inline Eigen::AutoDiffScalar<
+EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(internal::remove_all_t<DerType>, typename internal::traits<internal::remove_all_t<DerType>>::Scalar,product) >
+pow(const Eigen::AutoDiffScalar<DerType> &x, const typename internal::traits<internal::remove_all_t<DerType>>::Scalar &y)
+{
+ using namespace Eigen;
+ using std::pow;
+ return Eigen::MakeAutoDiffScalar(pow(x.value(),y), x.derivatives() * (y * pow(x.value(),y-1)));
+}
+
+
+template<typename DerTypeA,typename DerTypeB>
+inline AutoDiffScalar<Matrix<typename internal::traits<internal::remove_all_t<DerTypeA>>::Scalar,Dynamic,1> >
+atan2(const AutoDiffScalar<DerTypeA>& a, const AutoDiffScalar<DerTypeB>& b)
+{
+ using std::atan2;
+ typedef typename internal::traits<internal::remove_all_t<DerTypeA>>::Scalar Scalar;
+ typedef AutoDiffScalar<Matrix<Scalar,Dynamic,1> > PlainADS;
+ PlainADS ret;
+ ret.value() = atan2(a.value(), b.value());
+
+ Scalar squared_hypot = a.value() * a.value() + b.value() * b.value();
+
+ // if (squared_hypot==0) the derivation is undefined and the following results in a NaN:
+ ret.derivatives() = (a.derivatives() * b.value() - a.value() * b.derivatives()) / squared_hypot;
+
+ return ret;
+}
+
+EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY(tan,
+ using std::tan;
+ using std::cos;
+ return Eigen::MakeAutoDiffScalar(tan(x.value()),x.derivatives() * (Scalar(1)/numext::abs2(cos(x.value()))));)
+
+EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY(asin,
+ using std::sqrt;
+ using std::asin;
+ return Eigen::MakeAutoDiffScalar(asin(x.value()),x.derivatives() * (Scalar(1)/sqrt(1-numext::abs2(x.value()))));)
+
+EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY(acos,
+ using std::sqrt;
+ using std::acos;
+ return Eigen::MakeAutoDiffScalar(acos(x.value()),x.derivatives() * (Scalar(-1)/sqrt(1-numext::abs2(x.value()))));)
+
+EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY(tanh,
+ using std::cosh;
+ using std::tanh;
+ return Eigen::MakeAutoDiffScalar(tanh(x.value()),x.derivatives() * (Scalar(1)/numext::abs2(cosh(x.value()))));)
+
+EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY(sinh,
+ using std::sinh;
+ using std::cosh;
+ return Eigen::MakeAutoDiffScalar(sinh(x.value()),x.derivatives() * cosh(x.value()));)
+
+EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY(cosh,
+ using std::sinh;
+ using std::cosh;
+ return Eigen::MakeAutoDiffScalar(cosh(x.value()),x.derivatives() * sinh(x.value()));)
+
+#undef EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY
+
+template<typename DerType> struct NumTraits<AutoDiffScalar<DerType> >
+ : NumTraits< typename NumTraits<typename internal::remove_all_t<DerType>::Scalar>::Real >
+{
+ typedef internal::remove_all_t<DerType> DerTypeCleaned;
+ typedef AutoDiffScalar<Matrix<typename NumTraits<typename DerTypeCleaned::Scalar>::Real,DerTypeCleaned::RowsAtCompileTime,DerTypeCleaned::ColsAtCompileTime,
+ 0, DerTypeCleaned::MaxRowsAtCompileTime, DerTypeCleaned::MaxColsAtCompileTime> > Real;
+ typedef AutoDiffScalar<DerType> NonInteger;
+ typedef AutoDiffScalar<DerType> Nested;
+ typedef typename NumTraits<typename DerTypeCleaned::Scalar>::Literal Literal;
+ enum{
+ RequireInitialization = 1
+ };
+};
+
+namespace internal {
+template<typename DerivativeType>
+struct is_identically_zero_impl<AutoDiffScalar<DerivativeType>> {
+ static inline bool run(const AutoDiffScalar<DerivativeType>& s)
+ {
+ const DerivativeType& derivatives = s.derivatives();
+ for(int i=0; i<derivatives.size(); ++i)
+ {
+ if(!numext::is_exactly_zero(derivatives[i]))
+ {
+ return false;
+ }
+ }
+ return numext::is_exactly_zero(s.value());
+ }
+};
+}
+}
+
+namespace std {
+
+template <typename T>
+class numeric_limits<Eigen::AutoDiffScalar<T> >
+ : public numeric_limits<typename T::Scalar> {};
+
+template <typename T>
+class numeric_limits<Eigen::AutoDiffScalar<T&> >
+ : public numeric_limits<typename T::Scalar> {};
+
+} // namespace std
+
+#endif // EIGEN_AUTODIFF_SCALAR_H
diff --git a/unsupported/Eigen/src/AutoDiff/AutoDiffVector.h b/unsupported/Eigen/src/AutoDiff/AutoDiffVector.h
new file mode 100644
index 0000000..c544422
--- /dev/null
+++ b/unsupported/Eigen/src/AutoDiff/AutoDiffVector.h
@@ -0,0 +1,222 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_AUTODIFF_VECTOR_H
+#define EIGEN_AUTODIFF_VECTOR_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+/* \class AutoDiffScalar
+ * \brief A scalar type replacement with automatic differentation capability
+ *
+ * \param DerType the vector type used to store/represent the derivatives (e.g. Vector3f)
+ *
+ * This class represents a scalar value while tracking its respective derivatives.
+ *
+ * It supports the following list of global math function:
+ * - std::abs, std::sqrt, std::pow, std::exp, std::log, std::sin, std::cos,
+ * - internal::abs, internal::sqrt, numext::pow, internal::exp, internal::log, internal::sin, internal::cos,
+ * - internal::conj, internal::real, internal::imag, numext::abs2.
+ *
+ * AutoDiffScalar can be used as the scalar type of an Eigen::Matrix object. However,
+ * in that case, the expression template mechanism only occurs at the top Matrix level,
+ * while derivatives are computed right away.
+ *
+ */
+template<typename ValueType, typename JacobianType>
+class AutoDiffVector
+{
+ public:
+ //typedef typename internal::traits<ValueType>::Scalar Scalar;
+ typedef typename internal::traits<ValueType>::Scalar BaseScalar;
+ typedef AutoDiffScalar<Matrix<BaseScalar,JacobianType::RowsAtCompileTime,1> > ActiveScalar;
+ typedef ActiveScalar Scalar;
+ typedef AutoDiffScalar<typename JacobianType::ColXpr> CoeffType;
+ typedef typename JacobianType::Index Index;
+
+ inline AutoDiffVector() {}
+
+ inline AutoDiffVector(const ValueType& values)
+ : m_values(values)
+ {
+ m_jacobian.setZero();
+ }
+
+
+ CoeffType operator[] (Index i) { return CoeffType(m_values[i], m_jacobian.col(i)); }
+ const CoeffType operator[] (Index i) const { return CoeffType(m_values[i], m_jacobian.col(i)); }
+
+ CoeffType operator() (Index i) { return CoeffType(m_values[i], m_jacobian.col(i)); }
+ const CoeffType operator() (Index i) const { return CoeffType(m_values[i], m_jacobian.col(i)); }
+
+ CoeffType coeffRef(Index i) { return CoeffType(m_values[i], m_jacobian.col(i)); }
+ const CoeffType coeffRef(Index i) const { return CoeffType(m_values[i], m_jacobian.col(i)); }
+
+ Index size() const { return m_values.size(); }
+
+ // FIXME here we could return an expression of the sum
+ Scalar sum() const { /*std::cerr << "sum \n\n";*/ /*std::cerr << m_jacobian.rowwise().sum() << "\n\n";*/ return Scalar(m_values.sum(), m_jacobian.rowwise().sum()); }
+
+
+ inline AutoDiffVector(const ValueType& values, const JacobianType& jac)
+ : m_values(values), m_jacobian(jac)
+ {}
+
+ template<typename OtherValueType, typename OtherJacobianType>
+ inline AutoDiffVector(const AutoDiffVector<OtherValueType, OtherJacobianType>& other)
+ : m_values(other.values()), m_jacobian(other.jacobian())
+ {}
+
+ inline AutoDiffVector(const AutoDiffVector& other)
+ : m_values(other.values()), m_jacobian(other.jacobian())
+ {}
+
+ template<typename OtherValueType, typename OtherJacobianType>
+ inline AutoDiffVector& operator=(const AutoDiffVector<OtherValueType, OtherJacobianType>& other)
+ {
+ m_values = other.values();
+ m_jacobian = other.jacobian();
+ return *this;
+ }
+
+ inline AutoDiffVector& operator=(const AutoDiffVector& other)
+ {
+ m_values = other.values();
+ m_jacobian = other.jacobian();
+ return *this;
+ }
+
+ inline const ValueType& values() const { return m_values; }
+ inline ValueType& values() { return m_values; }
+
+ inline const JacobianType& jacobian() const { return m_jacobian; }
+ inline JacobianType& jacobian() { return m_jacobian; }
+
+ template<typename OtherValueType,typename OtherJacobianType>
+ inline const AutoDiffVector<
+ typename MakeCwiseBinaryOp<internal::scalar_sum_op<BaseScalar>,ValueType,OtherValueType>::Type,
+ typename MakeCwiseBinaryOp<internal::scalar_sum_op<BaseScalar>,JacobianType,OtherJacobianType>::Type >
+ operator+(const AutoDiffVector<OtherValueType,OtherJacobianType>& other) const
+ {
+ return AutoDiffVector<
+ typename MakeCwiseBinaryOp<internal::scalar_sum_op<BaseScalar>,ValueType,OtherValueType>::Type,
+ typename MakeCwiseBinaryOp<internal::scalar_sum_op<BaseScalar>,JacobianType,OtherJacobianType>::Type >(
+ m_values + other.values(),
+ m_jacobian + other.jacobian());
+ }
+
+ template<typename OtherValueType, typename OtherJacobianType>
+ inline AutoDiffVector&
+ operator+=(const AutoDiffVector<OtherValueType,OtherJacobianType>& other)
+ {
+ m_values += other.values();
+ m_jacobian += other.jacobian();
+ return *this;
+ }
+
+ template<typename OtherValueType,typename OtherJacobianType>
+ inline const AutoDiffVector<
+ typename MakeCwiseBinaryOp<internal::scalar_difference_op<Scalar>,ValueType,OtherValueType>::Type,
+ typename MakeCwiseBinaryOp<internal::scalar_difference_op<Scalar>,JacobianType,OtherJacobianType>::Type >
+ operator-(const AutoDiffVector<OtherValueType,OtherJacobianType>& other) const
+ {
+ return AutoDiffVector<
+ typename MakeCwiseBinaryOp<internal::scalar_difference_op<Scalar>,ValueType,OtherValueType>::Type,
+ typename MakeCwiseBinaryOp<internal::scalar_difference_op<Scalar>,JacobianType,OtherJacobianType>::Type >(
+ m_values - other.values(),
+ m_jacobian - other.jacobian());
+ }
+
+ template<typename OtherValueType, typename OtherJacobianType>
+ inline AutoDiffVector&
+ operator-=(const AutoDiffVector<OtherValueType,OtherJacobianType>& other)
+ {
+ m_values -= other.values();
+ m_jacobian -= other.jacobian();
+ return *this;
+ }
+
+ inline const AutoDiffVector<
+ typename MakeCwiseUnaryOp<internal::scalar_opposite_op<Scalar>, ValueType>::Type,
+ typename MakeCwiseUnaryOp<internal::scalar_opposite_op<Scalar>, JacobianType>::Type >
+ operator-() const
+ {
+ return AutoDiffVector<
+ typename MakeCwiseUnaryOp<internal::scalar_opposite_op<Scalar>, ValueType>::Type,
+ typename MakeCwiseUnaryOp<internal::scalar_opposite_op<Scalar>, JacobianType>::Type >(
+ -m_values,
+ -m_jacobian);
+ }
+
+ inline const AutoDiffVector<
+ typename MakeCwiseUnaryOp<internal::scalar_multiple_op<Scalar>, ValueType>::Type,
+ typename MakeCwiseUnaryOp<internal::scalar_multiple_op<Scalar>, JacobianType>::Type>
+ operator*(const BaseScalar& other) const
+ {
+ return AutoDiffVector<
+ typename MakeCwiseUnaryOp<internal::scalar_multiple_op<Scalar>, ValueType>::Type,
+ typename MakeCwiseUnaryOp<internal::scalar_multiple_op<Scalar>, JacobianType>::Type >(
+ m_values * other,
+ m_jacobian * other);
+ }
+
+ friend inline const AutoDiffVector<
+ typename MakeCwiseUnaryOp<internal::scalar_multiple_op<Scalar>, ValueType>::Type,
+ typename MakeCwiseUnaryOp<internal::scalar_multiple_op<Scalar>, JacobianType>::Type >
+ operator*(const Scalar& other, const AutoDiffVector& v)
+ {
+ return AutoDiffVector<
+ typename MakeCwiseUnaryOp<internal::scalar_multiple_op<Scalar>, ValueType>::Type,
+ typename MakeCwiseUnaryOp<internal::scalar_multiple_op<Scalar>, JacobianType>::Type >(
+ v.values() * other,
+ v.jacobian() * other);
+ }
+
+// template<typename OtherValueType,typename OtherJacobianType>
+// inline const AutoDiffVector<
+// CwiseBinaryOp<internal::scalar_multiple_op<Scalar>, ValueType, OtherValueType>
+// CwiseBinaryOp<internal::scalar_sum_op<Scalar>,
+// CwiseUnaryOp<internal::scalar_multiple_op<Scalar>, JacobianType>,
+// CwiseUnaryOp<internal::scalar_multiple_op<Scalar>, OtherJacobianType> > >
+// operator*(const AutoDiffVector<OtherValueType,OtherJacobianType>& other) const
+// {
+// return AutoDiffVector<
+// CwiseBinaryOp<internal::scalar_multiple_op<Scalar>, ValueType, OtherValueType>
+// CwiseBinaryOp<internal::scalar_sum_op<Scalar>,
+// CwiseUnaryOp<internal::scalar_multiple_op<Scalar>, JacobianType>,
+// CwiseUnaryOp<internal::scalar_multiple_op<Scalar>, OtherJacobianType> > >(
+// m_values.cwise() * other.values(),
+// (m_jacobian * other.values()) + (m_values * other.jacobian()));
+// }
+
+ inline AutoDiffVector& operator*=(const Scalar& other)
+ {
+ m_values *= other;
+ m_jacobian *= other;
+ return *this;
+ }
+
+ template<typename OtherValueType,typename OtherJacobianType>
+ inline AutoDiffVector& operator*=(const AutoDiffVector<OtherValueType,OtherJacobianType>& other)
+ {
+ *this = *this * other;
+ return *this;
+ }
+
+ protected:
+ ValueType m_values;
+ JacobianType m_jacobian;
+
+};
+
+}
+
+#endif // EIGEN_AUTODIFF_VECTOR_H
diff --git a/unsupported/Eigen/src/AutoDiff/InternalHeaderCheck.h b/unsupported/Eigen/src/AutoDiff/InternalHeaderCheck.h
new file mode 100644
index 0000000..1584337
--- /dev/null
+++ b/unsupported/Eigen/src/AutoDiff/InternalHeaderCheck.h
@@ -0,0 +1,3 @@
+#ifndef EIGEN_AUTODIFF_MODULE_H
+#error "Please include unsupported/Eigen/AutoDiff instead of including headers inside the src directory directly."
+#endif
diff --git a/unsupported/Eigen/src/BVH/BVAlgorithms.h b/unsupported/Eigen/src/BVH/BVAlgorithms.h
new file mode 100644
index 0000000..7c83a5f
--- /dev/null
+++ b/unsupported/Eigen/src/BVH/BVAlgorithms.h
@@ -0,0 +1,295 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009 Ilya Baran <ibaran@mit.edu>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_BVALGORITHMS_H
+#define EIGEN_BVALGORITHMS_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+
+#ifndef EIGEN_PARSED_BY_DOXYGEN
+template<typename BVH, typename Intersector>
+bool intersect_helper(const BVH &tree, Intersector &intersector, typename BVH::Index root)
+{
+ typedef typename BVH::Index Index;
+ typedef typename BVH::VolumeIterator VolIter;
+ typedef typename BVH::ObjectIterator ObjIter;
+
+ VolIter vBegin = VolIter(), vEnd = VolIter();
+ ObjIter oBegin = ObjIter(), oEnd = ObjIter();
+
+ std::vector<Index> todo(1, root);
+
+ while(!todo.empty()) {
+ tree.getChildren(todo.back(), vBegin, vEnd, oBegin, oEnd);
+ todo.pop_back();
+
+ for(; vBegin != vEnd; ++vBegin) //go through child volumes
+ if(intersector.intersectVolume(tree.getVolume(*vBegin)))
+ todo.push_back(*vBegin);
+
+ for(; oBegin != oEnd; ++oBegin) //go through child objects
+ if(intersector.intersectObject(*oBegin))
+ return true; //intersector said to stop query
+ }
+ return false;
+}
+#endif //not EIGEN_PARSED_BY_DOXYGEN
+
+template<typename Volume1, typename Object1, typename Object2, typename Intersector>
+struct intersector_helper1
+{
+ intersector_helper1(const Object2 &inStored, Intersector &in) : stored(inStored), intersector(in) {}
+ bool intersectVolume(const Volume1 &vol) { return intersector.intersectVolumeObject(vol, stored); }
+ bool intersectObject(const Object1 &obj) { return intersector.intersectObjectObject(obj, stored); }
+ Object2 stored;
+ Intersector &intersector;
+private:
+ intersector_helper1& operator=(const intersector_helper1&);
+};
+
+template<typename Volume2, typename Object2, typename Object1, typename Intersector>
+struct intersector_helper2
+{
+ intersector_helper2(const Object1 &inStored, Intersector &in) : stored(inStored), intersector(in) {}
+ bool intersectVolume(const Volume2 &vol) { return intersector.intersectObjectVolume(stored, vol); }
+ bool intersectObject(const Object2 &obj) { return intersector.intersectObjectObject(stored, obj); }
+ Object1 stored;
+ Intersector &intersector;
+private:
+ intersector_helper2& operator=(const intersector_helper2&);
+};
+
+} // end namespace internal
+
+/** Given a BVH, runs the query encapsulated by \a intersector.
+ * The Intersector type must provide the following members: \code
+ bool intersectVolume(const BVH::Volume &volume) //returns true if volume intersects the query
+ bool intersectObject(const BVH::Object &object) //returns true if the search should terminate immediately
+ \endcode
+ */
+template<typename BVH, typename Intersector>
+void BVIntersect(const BVH &tree, Intersector &intersector)
+{
+ internal::intersect_helper(tree, intersector, tree.getRootIndex());
+}
+
+/** Given two BVH's, runs the query on their Cartesian product encapsulated by \a intersector.
+ * The Intersector type must provide the following members: \code
+ bool intersectVolumeVolume(const BVH1::Volume &v1, const BVH2::Volume &v2) //returns true if product of volumes intersects the query
+ bool intersectVolumeObject(const BVH1::Volume &v1, const BVH2::Object &o2) //returns true if the volume-object product intersects the query
+ bool intersectObjectVolume(const BVH1::Object &o1, const BVH2::Volume &v2) //returns true if the volume-object product intersects the query
+ bool intersectObjectObject(const BVH1::Object &o1, const BVH2::Object &o2) //returns true if the search should terminate immediately
+ \endcode
+ */
+template<typename BVH1, typename BVH2, typename Intersector>
+void BVIntersect(const BVH1 &tree1, const BVH2 &tree2, Intersector &intersector) //TODO: tandem descent when it makes sense
+{
+ typedef typename BVH1::Index Index1;
+ typedef typename BVH2::Index Index2;
+ typedef internal::intersector_helper1<typename BVH1::Volume, typename BVH1::Object, typename BVH2::Object, Intersector> Helper1;
+ typedef internal::intersector_helper2<typename BVH2::Volume, typename BVH2::Object, typename BVH1::Object, Intersector> Helper2;
+ typedef typename BVH1::VolumeIterator VolIter1;
+ typedef typename BVH1::ObjectIterator ObjIter1;
+ typedef typename BVH2::VolumeIterator VolIter2;
+ typedef typename BVH2::ObjectIterator ObjIter2;
+
+ VolIter1 vBegin1 = VolIter1(), vEnd1 = VolIter1();
+ ObjIter1 oBegin1 = ObjIter1(), oEnd1 = ObjIter1();
+ VolIter2 vBegin2 = VolIter2(), vEnd2 = VolIter2(), vCur2 = VolIter2();
+ ObjIter2 oBegin2 = ObjIter2(), oEnd2 = ObjIter2(), oCur2 = ObjIter2();
+
+ std::vector<std::pair<Index1, Index2> > todo(1, std::make_pair(tree1.getRootIndex(), tree2.getRootIndex()));
+
+ while(!todo.empty()) {
+ tree1.getChildren(todo.back().first, vBegin1, vEnd1, oBegin1, oEnd1);
+ tree2.getChildren(todo.back().second, vBegin2, vEnd2, oBegin2, oEnd2);
+ todo.pop_back();
+
+ for(; vBegin1 != vEnd1; ++vBegin1) { //go through child volumes of first tree
+ const typename BVH1::Volume &vol1 = tree1.getVolume(*vBegin1);
+ for(vCur2 = vBegin2; vCur2 != vEnd2; ++vCur2) { //go through child volumes of second tree
+ if(intersector.intersectVolumeVolume(vol1, tree2.getVolume(*vCur2)))
+ todo.push_back(std::make_pair(*vBegin1, *vCur2));
+ }
+
+ for(oCur2 = oBegin2; oCur2 != oEnd2; ++oCur2) {//go through child objects of second tree
+ Helper1 helper(*oCur2, intersector);
+ if(internal::intersect_helper(tree1, helper, *vBegin1))
+ return; //intersector said to stop query
+ }
+ }
+
+ for(; oBegin1 != oEnd1; ++oBegin1) { //go through child objects of first tree
+ for(vCur2 = vBegin2; vCur2 != vEnd2; ++vCur2) { //go through child volumes of second tree
+ Helper2 helper(*oBegin1, intersector);
+ if(internal::intersect_helper(tree2, helper, *vCur2))
+ return; //intersector said to stop query
+ }
+
+ for(oCur2 = oBegin2; oCur2 != oEnd2; ++oCur2) {//go through child objects of second tree
+ if(intersector.intersectObjectObject(*oBegin1, *oCur2))
+ return; //intersector said to stop query
+ }
+ }
+ }
+}
+
+namespace internal {
+
+#ifndef EIGEN_PARSED_BY_DOXYGEN
+template<typename BVH, typename Minimizer>
+typename Minimizer::Scalar minimize_helper(const BVH &tree, Minimizer &minimizer, typename BVH::Index root, typename Minimizer::Scalar minimum)
+{
+ typedef typename Minimizer::Scalar Scalar;
+ typedef typename BVH::Index Index;
+ typedef std::pair<Scalar, Index> QueueElement; //first element is priority
+ typedef typename BVH::VolumeIterator VolIter;
+ typedef typename BVH::ObjectIterator ObjIter;
+
+ VolIter vBegin = VolIter(), vEnd = VolIter();
+ ObjIter oBegin = ObjIter(), oEnd = ObjIter();
+ std::priority_queue<QueueElement, std::vector<QueueElement>, std::greater<QueueElement> > todo; //smallest is at the top
+
+ todo.push(std::make_pair(Scalar(), root));
+
+ while(!todo.empty()) {
+ tree.getChildren(todo.top().second, vBegin, vEnd, oBegin, oEnd);
+ todo.pop();
+
+ for(; oBegin != oEnd; ++oBegin) //go through child objects
+ minimum = (std::min)(minimum, minimizer.minimumOnObject(*oBegin));
+
+ for(; vBegin != vEnd; ++vBegin) { //go through child volumes
+ Scalar val = minimizer.minimumOnVolume(tree.getVolume(*vBegin));
+ if(val < minimum)
+ todo.push(std::make_pair(val, *vBegin));
+ }
+ }
+
+ return minimum;
+}
+#endif //not EIGEN_PARSED_BY_DOXYGEN
+
+
+template<typename Volume1, typename Object1, typename Object2, typename Minimizer>
+struct minimizer_helper1
+{
+ typedef typename Minimizer::Scalar Scalar;
+ minimizer_helper1(const Object2 &inStored, Minimizer &m) : stored(inStored), minimizer(m) {}
+ Scalar minimumOnVolume(const Volume1 &vol) { return minimizer.minimumOnVolumeObject(vol, stored); }
+ Scalar minimumOnObject(const Object1 &obj) { return minimizer.minimumOnObjectObject(obj, stored); }
+ Object2 stored;
+ Minimizer &minimizer;
+private:
+ minimizer_helper1& operator=(const minimizer_helper1&);
+};
+
+template<typename Volume2, typename Object2, typename Object1, typename Minimizer>
+struct minimizer_helper2
+{
+ typedef typename Minimizer::Scalar Scalar;
+ minimizer_helper2(const Object1 &inStored, Minimizer &m) : stored(inStored), minimizer(m) {}
+ Scalar minimumOnVolume(const Volume2 &vol) { return minimizer.minimumOnObjectVolume(stored, vol); }
+ Scalar minimumOnObject(const Object2 &obj) { return minimizer.minimumOnObjectObject(stored, obj); }
+ Object1 stored;
+ Minimizer &minimizer;
+private:
+ minimizer_helper2& operator=(const minimizer_helper2&);
+};
+
+} // end namespace internal
+
+/** Given a BVH, runs the query encapsulated by \a minimizer.
+ * \returns the minimum value.
+ * The Minimizer type must provide the following members: \code
+ typedef Scalar //the numeric type of what is being minimized--not necessarily the Scalar type of the BVH (if it has one)
+ Scalar minimumOnVolume(const BVH::Volume &volume)
+ Scalar minimumOnObject(const BVH::Object &object)
+ \endcode
+ */
+template<typename BVH, typename Minimizer>
+typename Minimizer::Scalar BVMinimize(const BVH &tree, Minimizer &minimizer)
+{
+ return internal::minimize_helper(tree, minimizer, tree.getRootIndex(), (std::numeric_limits<typename Minimizer::Scalar>::max)());
+}
+
+/** Given two BVH's, runs the query on their cartesian product encapsulated by \a minimizer.
+ * \returns the minimum value.
+ * The Minimizer type must provide the following members: \code
+ typedef Scalar //the numeric type of what is being minimized--not necessarily the Scalar type of the BVH (if it has one)
+ Scalar minimumOnVolumeVolume(const BVH1::Volume &v1, const BVH2::Volume &v2)
+ Scalar minimumOnVolumeObject(const BVH1::Volume &v1, const BVH2::Object &o2)
+ Scalar minimumOnObjectVolume(const BVH1::Object &o1, const BVH2::Volume &v2)
+ Scalar minimumOnObjectObject(const BVH1::Object &o1, const BVH2::Object &o2)
+ \endcode
+ */
+template<typename BVH1, typename BVH2, typename Minimizer>
+typename Minimizer::Scalar BVMinimize(const BVH1 &tree1, const BVH2 &tree2, Minimizer &minimizer)
+{
+ typedef typename Minimizer::Scalar Scalar;
+ typedef typename BVH1::Index Index1;
+ typedef typename BVH2::Index Index2;
+ typedef internal::minimizer_helper1<typename BVH1::Volume, typename BVH1::Object, typename BVH2::Object, Minimizer> Helper1;
+ typedef internal::minimizer_helper2<typename BVH2::Volume, typename BVH2::Object, typename BVH1::Object, Minimizer> Helper2;
+ typedef std::pair<Scalar, std::pair<Index1, Index2> > QueueElement; //first element is priority
+ typedef typename BVH1::VolumeIterator VolIter1;
+ typedef typename BVH1::ObjectIterator ObjIter1;
+ typedef typename BVH2::VolumeIterator VolIter2;
+ typedef typename BVH2::ObjectIterator ObjIter2;
+
+ VolIter1 vBegin1 = VolIter1(), vEnd1 = VolIter1();
+ ObjIter1 oBegin1 = ObjIter1(), oEnd1 = ObjIter1();
+ VolIter2 vBegin2 = VolIter2(), vEnd2 = VolIter2(), vCur2 = VolIter2();
+ ObjIter2 oBegin2 = ObjIter2(), oEnd2 = ObjIter2(), oCur2 = ObjIter2();
+ std::priority_queue<QueueElement, std::vector<QueueElement>, std::greater<QueueElement> > todo; //smallest is at the top
+
+ Scalar minimum = (std::numeric_limits<Scalar>::max)();
+ todo.push(std::make_pair(Scalar(), std::make_pair(tree1.getRootIndex(), tree2.getRootIndex())));
+
+ while(!todo.empty()) {
+ tree1.getChildren(todo.top().second.first, vBegin1, vEnd1, oBegin1, oEnd1);
+ tree2.getChildren(todo.top().second.second, vBegin2, vEnd2, oBegin2, oEnd2);
+ todo.pop();
+
+ for(; oBegin1 != oEnd1; ++oBegin1) { //go through child objects of first tree
+ for(oCur2 = oBegin2; oCur2 != oEnd2; ++oCur2) {//go through child objects of second tree
+ minimum = (std::min)(minimum, minimizer.minimumOnObjectObject(*oBegin1, *oCur2));
+ }
+
+ for(vCur2 = vBegin2; vCur2 != vEnd2; ++vCur2) { //go through child volumes of second tree
+ Helper2 helper(*oBegin1, minimizer);
+ minimum = (std::min)(minimum, internal::minimize_helper(tree2, helper, *vCur2, minimum));
+ }
+ }
+
+ for(; vBegin1 != vEnd1; ++vBegin1) { //go through child volumes of first tree
+ const typename BVH1::Volume &vol1 = tree1.getVolume(*vBegin1);
+
+ for(oCur2 = oBegin2; oCur2 != oEnd2; ++oCur2) {//go through child objects of second tree
+ Helper1 helper(*oCur2, minimizer);
+ minimum = (std::min)(minimum, internal::minimize_helper(tree1, helper, *vBegin1, minimum));
+ }
+
+ for(vCur2 = vBegin2; vCur2 != vEnd2; ++vCur2) { //go through child volumes of second tree
+ Scalar val = minimizer.minimumOnVolumeVolume(vol1, tree2.getVolume(*vCur2));
+ if(val < minimum)
+ todo.push(std::make_pair(val, std::make_pair(*vBegin1, *vCur2)));
+ }
+ }
+ }
+ return minimum;
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_BVALGORITHMS_H
diff --git a/unsupported/Eigen/src/BVH/InternalHeaderCheck.h b/unsupported/Eigen/src/BVH/InternalHeaderCheck.h
new file mode 100644
index 0000000..7aade9b
--- /dev/null
+++ b/unsupported/Eigen/src/BVH/InternalHeaderCheck.h
@@ -0,0 +1,3 @@
+#ifndef EIGEN_BVH_MODULE_H
+#error "Please include unsupported/Eigen/BVH instead of including headers inside the src directory directly."
+#endif
diff --git a/unsupported/Eigen/src/BVH/KdBVH.h b/unsupported/Eigen/src/BVH/KdBVH.h
new file mode 100644
index 0000000..e7d6684
--- /dev/null
+++ b/unsupported/Eigen/src/BVH/KdBVH.h
@@ -0,0 +1,225 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009 Ilya Baran <ibaran@mit.edu>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef KDBVH_H_INCLUDED
+#define KDBVH_H_INCLUDED
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+
+//internal pair class for the BVH--used instead of std::pair because of alignment
+template<typename Scalar, int Dim>
+struct vector_int_pair
+{
+EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE(Scalar, Dim)
+ typedef Matrix<Scalar, Dim, 1> VectorType;
+
+ vector_int_pair(const VectorType &v, int i) : first(v), second(i) {}
+
+ VectorType first;
+ int second;
+};
+
+//these templates help the tree initializer get the bounding boxes either from a provided
+//iterator range or using bounding_box in a unified way
+template<typename ObjectList, typename VolumeList, typename BoxIter>
+struct get_boxes_helper {
+ void operator()(const ObjectList &objects, BoxIter boxBegin, BoxIter boxEnd, VolumeList &outBoxes)
+ {
+ outBoxes.insert(outBoxes.end(), boxBegin, boxEnd);
+ eigen_assert(outBoxes.size() == objects.size());
+ EIGEN_ONLY_USED_FOR_DEBUG(objects);
+ }
+};
+
+template<typename ObjectList, typename VolumeList>
+struct get_boxes_helper<ObjectList, VolumeList, int> {
+ void operator()(const ObjectList &objects, int, int, VolumeList &outBoxes)
+ {
+ outBoxes.reserve(objects.size());
+ for(int i = 0; i < (int)objects.size(); ++i)
+ outBoxes.push_back(bounding_box(objects[i]));
+ }
+};
+
+} // end namespace internal
+
+
+/** \class KdBVH
+ * \brief A simple bounding volume hierarchy based on AlignedBox
+ *
+ * \param Scalar_ The underlying scalar type of the bounding boxes
+ * \param Dim_ The dimension of the space in which the hierarchy lives
+ * \param _Object The object type that lives in the hierarchy. It must have value semantics. Either bounding_box(_Object) must
+ * be defined and return an AlignedBox<Scalar_, Dim_> or bounding boxes must be provided to the tree initializer.
+ *
+ * This class provides a simple (as opposed to optimized) implementation of a bounding volume hierarchy analogous to a Kd-tree.
+ * Given a sequence of objects, it computes their bounding boxes, constructs a Kd-tree of their centers
+ * and builds a BVH with the structure of that Kd-tree. When the elements of the tree are too expensive to be copied around,
+ * it is useful for _Object to be a pointer.
+ */
+template<typename Scalar_, int Dim_, typename _Object> class KdBVH
+{
+public:
+ enum { Dim = Dim_ };
+ typedef _Object Object;
+ typedef std::vector<Object, aligned_allocator<Object> > ObjectList;
+ typedef Scalar_ Scalar;
+ typedef AlignedBox<Scalar, Dim> Volume;
+ typedef std::vector<Volume, aligned_allocator<Volume> > VolumeList;
+ typedef int Index;
+ typedef const int *VolumeIterator; //the iterators are just pointers into the tree's vectors
+ typedef const Object *ObjectIterator;
+
+ KdBVH() {}
+
+ /** Given an iterator range over \a Object references, constructs the BVH. Requires that bounding_box(Object) return a Volume. */
+ template<typename Iter> KdBVH(Iter begin, Iter end) { init(begin, end, 0, 0); } //int is recognized by init as not being an iterator type
+
+ /** Given an iterator range over \a Object references and an iterator range over their bounding boxes, constructs the BVH */
+ template<typename OIter, typename BIter> KdBVH(OIter begin, OIter end, BIter boxBegin, BIter boxEnd) { init(begin, end, boxBegin, boxEnd); }
+
+ /** Given an iterator range over \a Object references, constructs the BVH, overwriting whatever is in there currently.
+ * Requires that bounding_box(Object) return a Volume. */
+ template<typename Iter> void init(Iter begin, Iter end) { init(begin, end, 0, 0); }
+
+ /** Given an iterator range over \a Object references and an iterator range over their bounding boxes,
+ * constructs the BVH, overwriting whatever is in there currently. */
+ template<typename OIter, typename BIter> void init(OIter begin, OIter end, BIter boxBegin, BIter boxEnd)
+ {
+ objects.clear();
+ boxes.clear();
+ children.clear();
+
+ objects.insert(objects.end(), begin, end);
+ int n = static_cast<int>(objects.size());
+
+ if(n < 2)
+ return; //if we have at most one object, we don't need any internal nodes
+
+ VolumeList objBoxes;
+ VIPairList objCenters;
+
+ //compute the bounding boxes depending on BIter type
+ internal::get_boxes_helper<ObjectList, VolumeList, BIter>()(objects, boxBegin, boxEnd, objBoxes);
+
+ objCenters.reserve(n);
+ boxes.reserve(n - 1);
+ children.reserve(2 * n - 2);
+
+ for(int i = 0; i < n; ++i)
+ objCenters.push_back(VIPair(objBoxes[i].center(), i));
+
+ build(objCenters, 0, n, objBoxes, 0); //the recursive part of the algorithm
+
+ ObjectList tmp(n);
+ tmp.swap(objects);
+ for(int i = 0; i < n; ++i)
+ objects[i] = tmp[objCenters[i].second];
+ }
+
+ /** \returns the index of the root of the hierarchy */
+ inline Index getRootIndex() const { return (int)boxes.size() - 1; }
+
+ /** Given an \a index of a node, on exit, \a outVBegin and \a outVEnd range over the indices of the volume children of the node
+ * and \a outOBegin and \a outOEnd range over the object children of the node */
+ EIGEN_STRONG_INLINE void getChildren(Index index, VolumeIterator &outVBegin, VolumeIterator &outVEnd,
+ ObjectIterator &outOBegin, ObjectIterator &outOEnd) const
+ { //inlining this function should open lots of optimization opportunities to the compiler
+ if(index < 0) {
+ outVBegin = outVEnd;
+ if(!objects.empty())
+ outOBegin = &(objects[0]);
+ outOEnd = outOBegin + objects.size(); //output all objects--necessary when the tree has only one object
+ return;
+ }
+
+ int numBoxes = static_cast<int>(boxes.size());
+
+ int idx = index * 2;
+ if(children[idx + 1] < numBoxes) { //second index is always bigger
+ outVBegin = &(children[idx]);
+ outVEnd = outVBegin + 2;
+ outOBegin = outOEnd;
+ }
+ else if(children[idx] >= numBoxes) { //if both children are objects
+ outVBegin = outVEnd;
+ outOBegin = &(objects[children[idx] - numBoxes]);
+ outOEnd = outOBegin + 2;
+ } else { //if the first child is a volume and the second is an object
+ outVBegin = &(children[idx]);
+ outVEnd = outVBegin + 1;
+ outOBegin = &(objects[children[idx + 1] - numBoxes]);
+ outOEnd = outOBegin + 1;
+ }
+ }
+
+ /** \returns the bounding box of the node at \a index */
+ inline const Volume &getVolume(Index index) const
+ {
+ return boxes[index];
+ }
+
+private:
+ typedef internal::vector_int_pair<Scalar, Dim> VIPair;
+ typedef std::vector<VIPair, aligned_allocator<VIPair> > VIPairList;
+ typedef Matrix<Scalar, Dim, 1> VectorType;
+ struct VectorComparator //compares vectors, or more specifically, VIPairs along a particular dimension
+ {
+ VectorComparator(int inDim) : dim(inDim) {}
+ inline bool operator()(const VIPair &v1, const VIPair &v2) const { return v1.first[dim] < v2.first[dim]; }
+ int dim;
+ };
+
+ //Build the part of the tree between objects[from] and objects[to] (not including objects[to]).
+ //This routine partitions the objCenters in [from, to) along the dimension dim, recursively constructs
+ //the two halves, and adds their parent node. TODO: a cache-friendlier layout
+ void build(VIPairList &objCenters, int from, int to, const VolumeList &objBoxes, int dim)
+ {
+ eigen_assert(to - from > 1);
+ if(to - from == 2) {
+ boxes.push_back(objBoxes[objCenters[from].second].merged(objBoxes[objCenters[from + 1].second]));
+ children.push_back(from + (int)objects.size() - 1); //there are objects.size() - 1 tree nodes
+ children.push_back(from + (int)objects.size());
+ }
+ else if(to - from == 3) {
+ int mid = from + 2;
+ std::nth_element(objCenters.begin() + from, objCenters.begin() + mid,
+ objCenters.begin() + to, VectorComparator(dim)); //partition
+ build(objCenters, from, mid, objBoxes, (dim + 1) % Dim);
+ int idx1 = (int)boxes.size() - 1;
+ boxes.push_back(boxes[idx1].merged(objBoxes[objCenters[mid].second]));
+ children.push_back(idx1);
+ children.push_back(mid + (int)objects.size() - 1);
+ }
+ else {
+ int mid = from + (to - from) / 2;
+ nth_element(objCenters.begin() + from, objCenters.begin() + mid,
+ objCenters.begin() + to, VectorComparator(dim)); //partition
+ build(objCenters, from, mid, objBoxes, (dim + 1) % Dim);
+ int idx1 = (int)boxes.size() - 1;
+ build(objCenters, mid, to, objBoxes, (dim + 1) % Dim);
+ int idx2 = (int)boxes.size() - 1;
+ boxes.push_back(boxes[idx1].merged(boxes[idx2]));
+ children.push_back(idx1);
+ children.push_back(idx2);
+ }
+ }
+
+ std::vector<int> children; //children of x are children[2x] and children[2x+1], indices bigger than boxes.size() index into objects.
+ VolumeList boxes;
+ ObjectList objects;
+};
+
+} // end namespace Eigen
+
+#endif //KDBVH_H_INCLUDED
diff --git a/unsupported/Eigen/src/Eigenvalues/ArpackSelfAdjointEigenSolver.h b/unsupported/Eigen/src/Eigenvalues/ArpackSelfAdjointEigenSolver.h
new file mode 100644
index 0000000..b74449f
--- /dev/null
+++ b/unsupported/Eigen/src/Eigenvalues/ArpackSelfAdjointEigenSolver.h
@@ -0,0 +1,792 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2012 David Harmon <dharmon@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_ARPACKGENERALIZEDSELFADJOINTEIGENSOLVER_H
+#define EIGEN_ARPACKGENERALIZEDSELFADJOINTEIGENSOLVER_H
+
+#include "../../../../Eigen/Dense"
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+ template<typename Scalar, typename RealScalar> struct arpack_wrapper;
+ template<typename MatrixSolver, typename MatrixType, typename Scalar, bool BisSPD> struct OP;
+}
+
+
+
+template<typename MatrixType, typename MatrixSolver=SimplicialLLT<MatrixType>, bool BisSPD=false>
+class ArpackGeneralizedSelfAdjointEigenSolver
+{
+public:
+ //typedef typename MatrixSolver::MatrixType MatrixType;
+
+ /** \brief Scalar type for matrices of type \p MatrixType. */
+ typedef typename MatrixType::Scalar Scalar;
+ typedef typename MatrixType::Index Index;
+
+ /** \brief Real scalar type for \p MatrixType.
+ *
+ * This is just \c Scalar if #Scalar is real (e.g., \c float or
+ * \c Scalar), and the type of the real part of \c Scalar if #Scalar is
+ * complex.
+ */
+ typedef typename NumTraits<Scalar>::Real RealScalar;
+
+ /** \brief Type for vector of eigenvalues as returned by eigenvalues().
+ *
+ * This is a column vector with entries of type #RealScalar.
+ * The length of the vector is the size of \p nbrEigenvalues.
+ */
+ typedef typename internal::plain_col_type<MatrixType, RealScalar>::type RealVectorType;
+
+ /** \brief Default constructor.
+ *
+ * The default constructor is for cases in which the user intends to
+ * perform decompositions via compute().
+ *
+ */
+ ArpackGeneralizedSelfAdjointEigenSolver()
+ : m_eivec(),
+ m_eivalues(),
+ m_isInitialized(false),
+ m_eigenvectorsOk(false),
+ m_nbrConverged(0),
+ m_nbrIterations(0)
+ { }
+
+ /** \brief Constructor; computes generalized eigenvalues of given matrix with respect to another matrix.
+ *
+ * \param[in] A Self-adjoint matrix whose eigenvalues / eigenvectors will
+ * computed. By default, the upper triangular part is used, but can be changed
+ * through the template parameter.
+ * \param[in] B Self-adjoint matrix for the generalized eigenvalue problem.
+ * \param[in] nbrEigenvalues The number of eigenvalues / eigenvectors to compute.
+ * Must be less than the size of the input matrix, or an error is returned.
+ * \param[in] eigs_sigma String containing either "LM", "SM", "LA", or "SA", with
+ * respective meanings to find the largest magnitude , smallest magnitude,
+ * largest algebraic, or smallest algebraic eigenvalues. Alternatively, this
+ * value can contain floating point value in string form, in which case the
+ * eigenvalues closest to this value will be found.
+ * \param[in] options Can be #ComputeEigenvectors (default) or #EigenvaluesOnly.
+ * \param[in] tol What tolerance to find the eigenvalues to. Default is 0, which
+ * means machine precision.
+ *
+ * This constructor calls compute(const MatrixType&, const MatrixType&, Index, string, int, RealScalar)
+ * to compute the eigenvalues of the matrix \p A with respect to \p B. The eigenvectors are computed if
+ * \p options equals #ComputeEigenvectors.
+ *
+ */
+ ArpackGeneralizedSelfAdjointEigenSolver(const MatrixType& A, const MatrixType& B,
+ Index nbrEigenvalues, std::string eigs_sigma="LM",
+ int options=ComputeEigenvectors, RealScalar tol=0.0)
+ : m_eivec(),
+ m_eivalues(),
+ m_isInitialized(false),
+ m_eigenvectorsOk(false),
+ m_nbrConverged(0),
+ m_nbrIterations(0)
+ {
+ compute(A, B, nbrEigenvalues, eigs_sigma, options, tol);
+ }
+
+ /** \brief Constructor; computes eigenvalues of given matrix.
+ *
+ * \param[in] A Self-adjoint matrix whose eigenvalues / eigenvectors will
+ * computed. By default, the upper triangular part is used, but can be changed
+ * through the template parameter.
+ * \param[in] nbrEigenvalues The number of eigenvalues / eigenvectors to compute.
+ * Must be less than the size of the input matrix, or an error is returned.
+ * \param[in] eigs_sigma String containing either "LM", "SM", "LA", or "SA", with
+ * respective meanings to find the largest magnitude , smallest magnitude,
+ * largest algebraic, or smallest algebraic eigenvalues. Alternatively, this
+ * value can contain floating point value in string form, in which case the
+ * eigenvalues closest to this value will be found.
+ * \param[in] options Can be #ComputeEigenvectors (default) or #EigenvaluesOnly.
+ * \param[in] tol What tolerance to find the eigenvalues to. Default is 0, which
+ * means machine precision.
+ *
+ * This constructor calls compute(const MatrixType&, Index, string, int, RealScalar)
+ * to compute the eigenvalues of the matrix \p A. The eigenvectors are computed if
+ * \p options equals #ComputeEigenvectors.
+ *
+ */
+
+ ArpackGeneralizedSelfAdjointEigenSolver(const MatrixType& A,
+ Index nbrEigenvalues, std::string eigs_sigma="LM",
+ int options=ComputeEigenvectors, RealScalar tol=0.0)
+ : m_eivec(),
+ m_eivalues(),
+ m_isInitialized(false),
+ m_eigenvectorsOk(false),
+ m_nbrConverged(0),
+ m_nbrIterations(0)
+ {
+ compute(A, nbrEigenvalues, eigs_sigma, options, tol);
+ }
+
+
+ /** \brief Computes generalized eigenvalues / eigenvectors of given matrix using the external ARPACK library.
+ *
+ * \param[in] A Selfadjoint matrix whose eigendecomposition is to be computed.
+ * \param[in] B Selfadjoint matrix for generalized eigenvalues.
+ * \param[in] nbrEigenvalues The number of eigenvalues / eigenvectors to compute.
+ * Must be less than the size of the input matrix, or an error is returned.
+ * \param[in] eigs_sigma String containing either "LM", "SM", "LA", or "SA", with
+ * respective meanings to find the largest magnitude , smallest magnitude,
+ * largest algebraic, or smallest algebraic eigenvalues. Alternatively, this
+ * value can contain floating point value in string form, in which case the
+ * eigenvalues closest to this value will be found.
+ * \param[in] options Can be #ComputeEigenvectors (default) or #EigenvaluesOnly.
+ * \param[in] tol What tolerance to find the eigenvalues to. Default is 0, which
+ * means machine precision.
+ *
+ * \returns Reference to \c *this
+ *
+ * This function computes the generalized eigenvalues of \p A with respect to \p B using ARPACK. The eigenvalues()
+ * function can be used to retrieve them. If \p options equals #ComputeEigenvectors,
+ * then the eigenvectors are also computed and can be retrieved by
+ * calling eigenvectors().
+ *
+ */
+ ArpackGeneralizedSelfAdjointEigenSolver& compute(const MatrixType& A, const MatrixType& B,
+ Index nbrEigenvalues, std::string eigs_sigma="LM",
+ int options=ComputeEigenvectors, RealScalar tol=0.0);
+
+ /** \brief Computes eigenvalues / eigenvectors of given matrix using the external ARPACK library.
+ *
+ * \param[in] A Selfadjoint matrix whose eigendecomposition is to be computed.
+ * \param[in] nbrEigenvalues The number of eigenvalues / eigenvectors to compute.
+ * Must be less than the size of the input matrix, or an error is returned.
+ * \param[in] eigs_sigma String containing either "LM", "SM", "LA", or "SA", with
+ * respective meanings to find the largest magnitude , smallest magnitude,
+ * largest algebraic, or smallest algebraic eigenvalues. Alternatively, this
+ * value can contain floating point value in string form, in which case the
+ * eigenvalues closest to this value will be found.
+ * \param[in] options Can be #ComputeEigenvectors (default) or #EigenvaluesOnly.
+ * \param[in] tol What tolerance to find the eigenvalues to. Default is 0, which
+ * means machine precision.
+ *
+ * \returns Reference to \c *this
+ *
+ * This function computes the eigenvalues of \p A using ARPACK. The eigenvalues()
+ * function can be used to retrieve them. If \p options equals #ComputeEigenvectors,
+ * then the eigenvectors are also computed and can be retrieved by
+ * calling eigenvectors().
+ *
+ */
+ ArpackGeneralizedSelfAdjointEigenSolver& compute(const MatrixType& A,
+ Index nbrEigenvalues, std::string eigs_sigma="LM",
+ int options=ComputeEigenvectors, RealScalar tol=0.0);
+
+
+ /** \brief Returns the eigenvectors of given matrix.
+ *
+ * \returns A const reference to the matrix whose columns are the eigenvectors.
+ *
+ * \pre The eigenvectors have been computed before.
+ *
+ * Column \f$ k \f$ of the returned matrix is an eigenvector corresponding
+ * to eigenvalue number \f$ k \f$ as returned by eigenvalues(). The
+ * eigenvectors are normalized to have (Euclidean) norm equal to one. If
+ * this object was used to solve the eigenproblem for the selfadjoint
+ * matrix \f$ A \f$, then the matrix returned by this function is the
+ * matrix \f$ V \f$ in the eigendecomposition \f$ A V = D V \f$.
+ * For the generalized eigenproblem, the matrix returned is the solution \f$ A V = D B V \f$
+ *
+ * Example: \include SelfAdjointEigenSolver_eigenvectors.cpp
+ * Output: \verbinclude SelfAdjointEigenSolver_eigenvectors.out
+ *
+ * \sa eigenvalues()
+ */
+ const Matrix<Scalar, Dynamic, Dynamic>& eigenvectors() const
+ {
+ eigen_assert(m_isInitialized && "ArpackGeneralizedSelfAdjointEigenSolver is not initialized.");
+ eigen_assert(m_eigenvectorsOk && "The eigenvectors have not been computed together with the eigenvalues.");
+ return m_eivec;
+ }
+
+ /** \brief Returns the eigenvalues of given matrix.
+ *
+ * \returns A const reference to the column vector containing the eigenvalues.
+ *
+ * \pre The eigenvalues have been computed before.
+ *
+ * The eigenvalues are repeated according to their algebraic multiplicity,
+ * so there are as many eigenvalues as rows in the matrix. The eigenvalues
+ * are sorted in increasing order.
+ *
+ * Example: \include SelfAdjointEigenSolver_eigenvalues.cpp
+ * Output: \verbinclude SelfAdjointEigenSolver_eigenvalues.out
+ *
+ * \sa eigenvectors(), MatrixBase::eigenvalues()
+ */
+ const Matrix<Scalar, Dynamic, 1>& eigenvalues() const
+ {
+ eigen_assert(m_isInitialized && "ArpackGeneralizedSelfAdjointEigenSolver is not initialized.");
+ return m_eivalues;
+ }
+
+ /** \brief Computes the positive-definite square root of the matrix.
+ *
+ * \returns the positive-definite square root of the matrix
+ *
+ * \pre The eigenvalues and eigenvectors of a positive-definite matrix
+ * have been computed before.
+ *
+ * The square root of a positive-definite matrix \f$ A \f$ is the
+ * positive-definite matrix whose square equals \f$ A \f$. This function
+ * uses the eigendecomposition \f$ A = V D V^{-1} \f$ to compute the
+ * square root as \f$ A^{1/2} = V D^{1/2} V^{-1} \f$.
+ *
+ * Example: \include SelfAdjointEigenSolver_operatorSqrt.cpp
+ * Output: \verbinclude SelfAdjointEigenSolver_operatorSqrt.out
+ *
+ * \sa operatorInverseSqrt(),
+ * \ref MatrixFunctions_Module "MatrixFunctions Module"
+ */
+ Matrix<Scalar, Dynamic, Dynamic> operatorSqrt() const
+ {
+ eigen_assert(m_isInitialized && "SelfAdjointEigenSolver is not initialized.");
+ eigen_assert(m_eigenvectorsOk && "The eigenvectors have not been computed together with the eigenvalues.");
+ return m_eivec * m_eivalues.cwiseSqrt().asDiagonal() * m_eivec.adjoint();
+ }
+
+ /** \brief Computes the inverse square root of the matrix.
+ *
+ * \returns the inverse positive-definite square root of the matrix
+ *
+ * \pre The eigenvalues and eigenvectors of a positive-definite matrix
+ * have been computed before.
+ *
+ * This function uses the eigendecomposition \f$ A = V D V^{-1} \f$ to
+ * compute the inverse square root as \f$ V D^{-1/2} V^{-1} \f$. This is
+ * cheaper than first computing the square root with operatorSqrt() and
+ * then its inverse with MatrixBase::inverse().
+ *
+ * Example: \include SelfAdjointEigenSolver_operatorInverseSqrt.cpp
+ * Output: \verbinclude SelfAdjointEigenSolver_operatorInverseSqrt.out
+ *
+ * \sa operatorSqrt(), MatrixBase::inverse(),
+ * \ref MatrixFunctions_Module "MatrixFunctions Module"
+ */
+ Matrix<Scalar, Dynamic, Dynamic> operatorInverseSqrt() const
+ {
+ eigen_assert(m_isInitialized && "SelfAdjointEigenSolver is not initialized.");
+ eigen_assert(m_eigenvectorsOk && "The eigenvectors have not been computed together with the eigenvalues.");
+ return m_eivec * m_eivalues.cwiseInverse().cwiseSqrt().asDiagonal() * m_eivec.adjoint();
+ }
+
+ /** \brief Reports whether previous computation was successful.
+ *
+ * \returns \c Success if computation was successful, \c NoConvergence otherwise.
+ */
+ ComputationInfo info() const
+ {
+ eigen_assert(m_isInitialized && "ArpackGeneralizedSelfAdjointEigenSolver is not initialized.");
+ return m_info;
+ }
+
+ size_t getNbrConvergedEigenValues() const
+ { return m_nbrConverged; }
+
+ size_t getNbrIterations() const
+ { return m_nbrIterations; }
+
+protected:
+ Matrix<Scalar, Dynamic, Dynamic> m_eivec;
+ Matrix<Scalar, Dynamic, 1> m_eivalues;
+ ComputationInfo m_info;
+ bool m_isInitialized;
+ bool m_eigenvectorsOk;
+
+ size_t m_nbrConverged;
+ size_t m_nbrIterations;
+};
+
+
+
+
+
+template<typename MatrixType, typename MatrixSolver, bool BisSPD>
+ArpackGeneralizedSelfAdjointEigenSolver<MatrixType, MatrixSolver, BisSPD>&
+ ArpackGeneralizedSelfAdjointEigenSolver<MatrixType, MatrixSolver, BisSPD>
+::compute(const MatrixType& A, Index nbrEigenvalues,
+ std::string eigs_sigma, int options, RealScalar tol)
+{
+ MatrixType B(0,0);
+ compute(A, B, nbrEigenvalues, eigs_sigma, options, tol);
+
+ return *this;
+}
+
+
+template<typename MatrixType, typename MatrixSolver, bool BisSPD>
+ArpackGeneralizedSelfAdjointEigenSolver<MatrixType, MatrixSolver, BisSPD>&
+ ArpackGeneralizedSelfAdjointEigenSolver<MatrixType, MatrixSolver, BisSPD>
+::compute(const MatrixType& A, const MatrixType& B, Index nbrEigenvalues,
+ std::string eigs_sigma, int options, RealScalar tol)
+{
+ eigen_assert(A.cols() == A.rows());
+ eigen_assert(B.cols() == B.rows());
+ eigen_assert(B.rows() == 0 || A.cols() == B.rows());
+ eigen_assert((options &~ (EigVecMask | GenEigMask)) == 0
+ && (options & EigVecMask) != EigVecMask
+ && "invalid option parameter");
+
+ bool isBempty = (B.rows() == 0) || (B.cols() == 0);
+
+ // For clarity, all parameters match their ARPACK name
+ //
+ // Always 0 on the first call
+ //
+ int ido = 0;
+
+ int n = (int)A.cols();
+
+ // User options: "LA", "SA", "SM", "LM", "BE"
+ //
+ char whch[3] = "LM";
+
+ // Specifies the shift if iparam[6] = { 3, 4, 5 }, not used if iparam[6] = { 1, 2 }
+ //
+ RealScalar sigma = 0.0;
+
+ if (eigs_sigma.length() >= 2 && isalpha(eigs_sigma[0]) && isalpha(eigs_sigma[1]))
+ {
+ eigs_sigma[0] = toupper(eigs_sigma[0]);
+ eigs_sigma[1] = toupper(eigs_sigma[1]);
+
+ // In the following special case we're going to invert the problem, since solving
+ // for larger magnitude is much much faster
+ // i.e., if 'SM' is specified, we're going to really use 'LM', the default
+ //
+ if (eigs_sigma.substr(0,2) != "SM")
+ {
+ whch[0] = eigs_sigma[0];
+ whch[1] = eigs_sigma[1];
+ }
+ }
+ else
+ {
+ eigen_assert(false && "Specifying clustered eigenvalues is not yet supported!");
+
+ // If it's not scalar values, then the user may be explicitly
+ // specifying the sigma value to cluster the evs around
+ //
+ sigma = atof(eigs_sigma.c_str());
+
+ // If atof fails, it returns 0.0, which is a fine default
+ //
+ }
+
+ // "I" means normal eigenvalue problem, "G" means generalized
+ //
+ char bmat[2] = "I";
+ if (eigs_sigma.substr(0,2) == "SM" || !(isalpha(eigs_sigma[0]) && isalpha(eigs_sigma[1])) || (!isBempty && !BisSPD))
+ bmat[0] = 'G';
+
+ // Now we determine the mode to use
+ //
+ int mode = (bmat[0] == 'G') + 1;
+ if (eigs_sigma.substr(0,2) == "SM" || !(isalpha(eigs_sigma[0]) && isalpha(eigs_sigma[1])))
+ {
+ // We're going to use shift-and-invert mode, and basically find
+ // the largest eigenvalues of the inverse operator
+ //
+ mode = 3;
+ }
+
+ // The user-specified number of eigenvalues/vectors to compute
+ //
+ int nev = (int)nbrEigenvalues;
+
+ // Allocate space for ARPACK to store the residual
+ //
+ Scalar *resid = new Scalar[n];
+
+ // Number of Lanczos vectors, must satisfy nev < ncv <= n
+ // Note that this indicates that nev != n, and we cannot compute
+ // all eigenvalues of a mtrix
+ //
+ int ncv = std::min(std::max(2*nev, 20), n);
+
+ // The working n x ncv matrix, also store the final eigenvectors (if computed)
+ //
+ Scalar *v = new Scalar[n*ncv];
+ int ldv = n;
+
+ // Working space
+ //
+ Scalar *workd = new Scalar[3*n];
+ int lworkl = ncv*ncv+8*ncv; // Must be at least this length
+ Scalar *workl = new Scalar[lworkl];
+
+ int *iparam= new int[11];
+ iparam[0] = 1; // 1 means we let ARPACK perform the shifts, 0 means we'd have to do it
+ iparam[2] = std::max(300, (int)std::ceil(2*n/std::max(ncv,1)));
+ iparam[6] = mode; // The mode, 1 is standard ev problem, 2 for generalized ev, 3 for shift-and-invert
+
+ // Used during reverse communicate to notify where arrays start
+ //
+ int *ipntr = new int[11];
+
+ // Error codes are returned in here, initial value of 0 indicates a random initial
+ // residual vector is used, any other values means resid contains the initial residual
+ // vector, possibly from a previous run
+ //
+ int info = 0;
+
+ Scalar scale = 1.0;
+ //if (!isBempty)
+ //{
+ //Scalar scale = B.norm() / std::sqrt(n);
+ //scale = std::pow(2, std::floor(std::log(scale+1)));
+ ////M /= scale;
+ //for (size_t i=0; i<(size_t)B.outerSize(); i++)
+ // for (typename MatrixType::InnerIterator it(B, i); it; ++it)
+ // it.valueRef() /= scale;
+ //}
+
+ MatrixSolver OP;
+ if (mode == 1 || mode == 2)
+ {
+ if (!isBempty)
+ OP.compute(B);
+ }
+ else if (mode == 3)
+ {
+ if (sigma == 0.0)
+ {
+ OP.compute(A);
+ }
+ else
+ {
+ // Note: We will never enter here because sigma must be 0.0
+ //
+ if (isBempty)
+ {
+ MatrixType AminusSigmaB(A);
+ for (Index i=0; i<A.rows(); ++i)
+ AminusSigmaB.coeffRef(i,i) -= sigma;
+
+ OP.compute(AminusSigmaB);
+ }
+ else
+ {
+ MatrixType AminusSigmaB = A - sigma * B;
+ OP.compute(AminusSigmaB);
+ }
+ }
+ }
+
+ if (!(mode == 1 && isBempty) && !(mode == 2 && isBempty) && OP.info() != Success)
+ std::cout << "Error factoring matrix" << std::endl;
+
+ do
+ {
+ internal::arpack_wrapper<Scalar, RealScalar>::saupd(&ido, bmat, &n, whch, &nev, &tol, resid,
+ &ncv, v, &ldv, iparam, ipntr, workd, workl,
+ &lworkl, &info);
+
+ if (ido == -1 || ido == 1)
+ {
+ Scalar *in = workd + ipntr[0] - 1;
+ Scalar *out = workd + ipntr[1] - 1;
+
+ if (ido == 1 && mode != 2)
+ {
+ Scalar *out2 = workd + ipntr[2] - 1;
+ if (isBempty || mode == 1)
+ Matrix<Scalar, Dynamic, 1>::Map(out2, n) = Matrix<Scalar, Dynamic, 1>::Map(in, n);
+ else
+ Matrix<Scalar, Dynamic, 1>::Map(out2, n) = B * Matrix<Scalar, Dynamic, 1>::Map(in, n);
+
+ in = workd + ipntr[2] - 1;
+ }
+
+ if (mode == 1)
+ {
+ if (isBempty)
+ {
+ // OP = A
+ //
+ Matrix<Scalar, Dynamic, 1>::Map(out, n) = A * Matrix<Scalar, Dynamic, 1>::Map(in, n);
+ }
+ else
+ {
+ // OP = L^{-1}AL^{-T}
+ //
+ internal::OP<MatrixSolver, MatrixType, Scalar, BisSPD>::applyOP(OP, A, n, in, out);
+ }
+ }
+ else if (mode == 2)
+ {
+ if (ido == 1)
+ Matrix<Scalar, Dynamic, 1>::Map(in, n) = A * Matrix<Scalar, Dynamic, 1>::Map(in, n);
+
+ // OP = B^{-1} A
+ //
+ Matrix<Scalar, Dynamic, 1>::Map(out, n) = OP.solve(Matrix<Scalar, Dynamic, 1>::Map(in, n));
+ }
+ else if (mode == 3)
+ {
+ // OP = (A-\sigmaB)B (\sigma could be 0, and B could be I)
+ // The B * in is already computed and stored at in if ido == 1
+ //
+ if (ido == 1 || isBempty)
+ Matrix<Scalar, Dynamic, 1>::Map(out, n) = OP.solve(Matrix<Scalar, Dynamic, 1>::Map(in, n));
+ else
+ Matrix<Scalar, Dynamic, 1>::Map(out, n) = OP.solve(B * Matrix<Scalar, Dynamic, 1>::Map(in, n));
+ }
+ }
+ else if (ido == 2)
+ {
+ Scalar *in = workd + ipntr[0] - 1;
+ Scalar *out = workd + ipntr[1] - 1;
+
+ if (isBempty || mode == 1)
+ Matrix<Scalar, Dynamic, 1>::Map(out, n) = Matrix<Scalar, Dynamic, 1>::Map(in, n);
+ else
+ Matrix<Scalar, Dynamic, 1>::Map(out, n) = B * Matrix<Scalar, Dynamic, 1>::Map(in, n);
+ }
+ } while (ido != 99);
+
+ if (info == 1)
+ m_info = NoConvergence;
+ else if (info == 3)
+ m_info = NumericalIssue;
+ else if (info < 0)
+ m_info = InvalidInput;
+ else if (info != 0)
+ eigen_assert(false && "Unknown ARPACK return value!");
+ else
+ {
+ // Do we compute eigenvectors or not?
+ //
+ int rvec = (options & ComputeEigenvectors) == ComputeEigenvectors;
+
+ // "A" means "All", use "S" to choose specific eigenvalues (not yet supported in ARPACK))
+ //
+ char howmny[2] = "A";
+
+ // if howmny == "S", specifies the eigenvalues to compute (not implemented in ARPACK)
+ //
+ int *select = new int[ncv];
+
+ // Final eigenvalues
+ //
+ m_eivalues.resize(nev, 1);
+
+ internal::arpack_wrapper<Scalar, RealScalar>::seupd(&rvec, howmny, select, m_eivalues.data(), v, &ldv,
+ &sigma, bmat, &n, whch, &nev, &tol, resid, &ncv,
+ v, &ldv, iparam, ipntr, workd, workl, &lworkl, &info);
+
+ if (info == -14)
+ m_info = NoConvergence;
+ else if (info != 0)
+ m_info = InvalidInput;
+ else
+ {
+ if (rvec)
+ {
+ m_eivec.resize(A.rows(), nev);
+ for (int i=0; i<nev; i++)
+ for (int j=0; j<n; j++)
+ m_eivec(j,i) = v[i*n+j] / scale;
+
+ if (mode == 1 && !isBempty && BisSPD)
+ internal::OP<MatrixSolver, MatrixType, Scalar, BisSPD>::project(OP, n, nev, m_eivec.data());
+
+ m_eigenvectorsOk = true;
+ }
+
+ m_nbrIterations = iparam[2];
+ m_nbrConverged = iparam[4];
+
+ m_info = Success;
+ }
+
+ delete[] select;
+ }
+
+ delete[] v;
+ delete[] iparam;
+ delete[] ipntr;
+ delete[] workd;
+ delete[] workl;
+ delete[] resid;
+
+ m_isInitialized = true;
+
+ return *this;
+}
+
+
+// Single precision
+//
+extern "C" void ssaupd_(int *ido, char *bmat, int *n, char *which,
+ int *nev, float *tol, float *resid, int *ncv,
+ float *v, int *ldv, int *iparam, int *ipntr,
+ float *workd, float *workl, int *lworkl,
+ int *info);
+
+extern "C" void sseupd_(int *rvec, char *All, int *select, float *d,
+ float *z, int *ldz, float *sigma,
+ char *bmat, int *n, char *which, int *nev,
+ float *tol, float *resid, int *ncv, float *v,
+ int *ldv, int *iparam, int *ipntr, float *workd,
+ float *workl, int *lworkl, int *ierr);
+
+// Double precision
+//
+extern "C" void dsaupd_(int *ido, char *bmat, int *n, char *which,
+ int *nev, double *tol, double *resid, int *ncv,
+ double *v, int *ldv, int *iparam, int *ipntr,
+ double *workd, double *workl, int *lworkl,
+ int *info);
+
+extern "C" void dseupd_(int *rvec, char *All, int *select, double *d,
+ double *z, int *ldz, double *sigma,
+ char *bmat, int *n, char *which, int *nev,
+ double *tol, double *resid, int *ncv, double *v,
+ int *ldv, int *iparam, int *ipntr, double *workd,
+ double *workl, int *lworkl, int *ierr);
+
+
+namespace internal {
+
+template<typename Scalar, typename RealScalar> struct arpack_wrapper
+{
+ static inline void saupd(int *ido, char *bmat, int *n, char *which,
+ int *nev, RealScalar *tol, Scalar *resid, int *ncv,
+ Scalar *v, int *ldv, int *iparam, int *ipntr,
+ Scalar *workd, Scalar *workl, int *lworkl, int *info)
+ {
+ EIGEN_STATIC_ASSERT(!NumTraits<Scalar>::IsComplex, NUMERIC_TYPE_MUST_BE_REAL)
+ }
+
+ static inline void seupd(int *rvec, char *All, int *select, Scalar *d,
+ Scalar *z, int *ldz, RealScalar *sigma,
+ char *bmat, int *n, char *which, int *nev,
+ RealScalar *tol, Scalar *resid, int *ncv, Scalar *v,
+ int *ldv, int *iparam, int *ipntr, Scalar *workd,
+ Scalar *workl, int *lworkl, int *ierr)
+ {
+ EIGEN_STATIC_ASSERT(!NumTraits<Scalar>::IsComplex, NUMERIC_TYPE_MUST_BE_REAL)
+ }
+};
+
+template <> struct arpack_wrapper<float, float>
+{
+ static inline void saupd(int *ido, char *bmat, int *n, char *which,
+ int *nev, float *tol, float *resid, int *ncv,
+ float *v, int *ldv, int *iparam, int *ipntr,
+ float *workd, float *workl, int *lworkl, int *info)
+ {
+ ssaupd_(ido, bmat, n, which, nev, tol, resid, ncv, v, ldv, iparam, ipntr, workd, workl, lworkl, info);
+ }
+
+ static inline void seupd(int *rvec, char *All, int *select, float *d,
+ float *z, int *ldz, float *sigma,
+ char *bmat, int *n, char *which, int *nev,
+ float *tol, float *resid, int *ncv, float *v,
+ int *ldv, int *iparam, int *ipntr, float *workd,
+ float *workl, int *lworkl, int *ierr)
+ {
+ sseupd_(rvec, All, select, d, z, ldz, sigma, bmat, n, which, nev, tol, resid, ncv, v, ldv, iparam, ipntr,
+ workd, workl, lworkl, ierr);
+ }
+};
+
+template <> struct arpack_wrapper<double, double>
+{
+ static inline void saupd(int *ido, char *bmat, int *n, char *which,
+ int *nev, double *tol, double *resid, int *ncv,
+ double *v, int *ldv, int *iparam, int *ipntr,
+ double *workd, double *workl, int *lworkl, int *info)
+ {
+ dsaupd_(ido, bmat, n, which, nev, tol, resid, ncv, v, ldv, iparam, ipntr, workd, workl, lworkl, info);
+ }
+
+ static inline void seupd(int *rvec, char *All, int *select, double *d,
+ double *z, int *ldz, double *sigma,
+ char *bmat, int *n, char *which, int *nev,
+ double *tol, double *resid, int *ncv, double *v,
+ int *ldv, int *iparam, int *ipntr, double *workd,
+ double *workl, int *lworkl, int *ierr)
+ {
+ dseupd_(rvec, All, select, d, v, ldv, sigma, bmat, n, which, nev, tol, resid, ncv, v, ldv, iparam, ipntr,
+ workd, workl, lworkl, ierr);
+ }
+};
+
+
+template<typename MatrixSolver, typename MatrixType, typename Scalar, bool BisSPD>
+struct OP
+{
+ static inline void applyOP(MatrixSolver &OP, const MatrixType &A, int n, Scalar *in, Scalar *out);
+ static inline void project(MatrixSolver &OP, int n, int k, Scalar *vecs);
+};
+
+template<typename MatrixSolver, typename MatrixType, typename Scalar>
+struct OP<MatrixSolver, MatrixType, Scalar, true>
+{
+ static inline void applyOP(MatrixSolver &OP, const MatrixType &A, int n, Scalar *in, Scalar *out)
+{
+ // OP = L^{-1} A L^{-T} (B = LL^T)
+ //
+ // First solve L^T out = in
+ //
+ Matrix<Scalar, Dynamic, 1>::Map(out, n) = OP.matrixU().solve(Matrix<Scalar, Dynamic, 1>::Map(in, n));
+ Matrix<Scalar, Dynamic, 1>::Map(out, n) = OP.permutationPinv() * Matrix<Scalar, Dynamic, 1>::Map(out, n);
+
+ // Then compute out = A out
+ //
+ Matrix<Scalar, Dynamic, 1>::Map(out, n) = A * Matrix<Scalar, Dynamic, 1>::Map(out, n);
+
+ // Then solve L out = out
+ //
+ Matrix<Scalar, Dynamic, 1>::Map(out, n) = OP.permutationP() * Matrix<Scalar, Dynamic, 1>::Map(out, n);
+ Matrix<Scalar, Dynamic, 1>::Map(out, n) = OP.matrixL().solve(Matrix<Scalar, Dynamic, 1>::Map(out, n));
+}
+
+ static inline void project(MatrixSolver &OP, int n, int k, Scalar *vecs)
+{
+ // Solve L^T out = in
+ //
+ Matrix<Scalar, Dynamic, Dynamic>::Map(vecs, n, k) = OP.matrixU().solve(Matrix<Scalar, Dynamic, Dynamic>::Map(vecs, n, k));
+ Matrix<Scalar, Dynamic, Dynamic>::Map(vecs, n, k) = OP.permutationPinv() * Matrix<Scalar, Dynamic, Dynamic>::Map(vecs, n, k);
+}
+
+};
+
+template<typename MatrixSolver, typename MatrixType, typename Scalar>
+struct OP<MatrixSolver, MatrixType, Scalar, false>
+{
+ static inline void applyOP(MatrixSolver &OP, const MatrixType &A, int n, Scalar *in, Scalar *out)
+{
+ eigen_assert(false && "Should never be in here...");
+}
+
+ static inline void project(MatrixSolver &OP, int n, int k, Scalar *vecs)
+{
+ eigen_assert(false && "Should never be in here...");
+}
+
+};
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_ARPACKSELFADJOINTEIGENSOLVER_H
+
diff --git a/unsupported/Eigen/src/Eigenvalues/InternalHeaderCheck.h b/unsupported/Eigen/src/Eigenvalues/InternalHeaderCheck.h
new file mode 100644
index 0000000..c00cb57
--- /dev/null
+++ b/unsupported/Eigen/src/Eigenvalues/InternalHeaderCheck.h
@@ -0,0 +1,3 @@
+#ifndef EIGEN_EIGENVALUES_MODULE_H
+#error "Please include unsupported/Eigen/Eigenvalues instead of including headers inside the src directory directly."
+#endif
diff --git a/unsupported/Eigen/src/EulerAngles/CMakeLists.txt b/unsupported/Eigen/src/EulerAngles/CMakeLists.txt
new file mode 100644
index 0000000..22088eb
--- /dev/null
+++ b/unsupported/Eigen/src/EulerAngles/CMakeLists.txt
@@ -0,0 +1,6 @@
+file(GLOB Eigen_EulerAngles_SRCS "*.h")
+
+install(FILES
+ ${Eigen_EulerAngles_SRCS}
+ DESTINATION ${INCLUDE_INSTALL_DIR}/unsupported/Eigen/src/EulerAngles COMPONENT Devel
+ )
diff --git a/unsupported/Eigen/src/EulerAngles/EulerAngles.h b/unsupported/Eigen/src/EulerAngles/EulerAngles.h
new file mode 100644
index 0000000..252be42
--- /dev/null
+++ b/unsupported/Eigen/src/EulerAngles/EulerAngles.h
@@ -0,0 +1,357 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2015 Tal Hadad <tal_hd@hotmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_EULERANGLESCLASS_H// TODO: Fix previous "EIGEN_EULERANGLES_H" definition?
+#define EIGEN_EULERANGLESCLASS_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen
+{
+ /** \class EulerAngles
+ *
+ * \ingroup EulerAngles_Module
+ *
+ * \brief Represents a rotation in a 3 dimensional space as three Euler angles.
+ *
+ * Euler rotation is a set of three rotation of three angles over three fixed axes, defined by the EulerSystem given as a template parameter.
+ *
+ * Here is how intrinsic Euler angles works:
+ * - first, rotate the axes system over the alpha axis in angle alpha
+ * - then, rotate the axes system over the beta axis(which was rotated in the first stage) in angle beta
+ * - then, rotate the axes system over the gamma axis(which was rotated in the two stages above) in angle gamma
+ *
+ * \note This class support only intrinsic Euler angles for simplicity,
+ * see EulerSystem how to easily overcome this for extrinsic systems.
+ *
+ * ### Rotation representation and conversions ###
+ *
+ * It has been proved(see Wikipedia link below) that every rotation can be represented
+ * by Euler angles, but there is no single representation (e.g. unlike rotation matrices).
+ * Therefore, you can convert from Eigen rotation and to them
+ * (including rotation matrices, which is not called "rotations" by Eigen design).
+ *
+ * Euler angles usually used for:
+ * - convenient human representation of rotation, especially in interactive GUI.
+ * - gimbal systems and robotics
+ * - efficient encoding(i.e. 3 floats only) of rotation for network protocols.
+ *
+ * However, Euler angles are slow comparing to quaternion or matrices,
+ * because their unnatural math definition, although it's simple for human.
+ * To overcome this, this class provide easy movement from the math friendly representation
+ * to the human friendly representation, and vise-versa.
+ *
+ * All the user need to do is a safe simple C++ type conversion,
+ * and this class take care for the math.
+ * Additionally, some axes related computation is done in compile time.
+ *
+ * #### Euler angles ranges in conversions ####
+ * Rotations representation as EulerAngles are not single (unlike matrices),
+ * and even have infinite EulerAngles representations.<BR>
+ * For example, add or subtract 2*PI from either angle of EulerAngles
+ * and you'll get the same rotation.
+ * This is the general reason for infinite representation,
+ * but it's not the only general reason for not having a single representation.
+ *
+ * When converting rotation to EulerAngles, this class convert it to specific ranges
+ * When converting some rotation to EulerAngles, the rules for ranges are as follow:
+ * - If the rotation we converting from is an EulerAngles
+ * (even when it represented as RotationBase explicitly), angles ranges are __undefined__.
+ * - otherwise, alpha and gamma angles will be in the range [-PI, PI].<BR>
+ * As for Beta angle:
+ * - If the system is Tait-Bryan, the beta angle will be in the range [-PI/2, PI/2].
+ * - otherwise:
+ * - If the beta axis is positive, the beta angle will be in the range [0, PI]
+ * - If the beta axis is negative, the beta angle will be in the range [-PI, 0]
+ *
+ * \sa EulerAngles(const MatrixBase<Derived>&)
+ * \sa EulerAngles(const RotationBase<Derived, 3>&)
+ *
+ * ### Convenient user typedefs ###
+ *
+ * Convenient typedefs for EulerAngles exist for float and double scalar,
+ * in a form of EulerAngles{A}{B}{C}{scalar},
+ * e.g. \ref EulerAnglesXYZd, \ref EulerAnglesZYZf.
+ *
+ * Only for positive axes{+x,+y,+z} Euler systems are have convenient typedef.
+ * If you need negative axes{-x,-y,-z}, it is recommended to create you own typedef with
+ * a word that represent what you need.
+ *
+ * ### Example ###
+ *
+ * \include EulerAngles.cpp
+ * Output: \verbinclude EulerAngles.out
+ *
+ * ### Additional reading ###
+ *
+ * If you're want to get more idea about how Euler system work in Eigen see EulerSystem.
+ *
+ * More information about Euler angles: https://en.wikipedia.org/wiki/Euler_angles
+ *
+ * \tparam Scalar_ the scalar type, i.e. the type of the angles.
+ *
+ * \tparam _System the EulerSystem to use, which represents the axes of rotation.
+ */
+ template <typename Scalar_, class _System>
+ class EulerAngles : public RotationBase<EulerAngles<Scalar_, _System>, 3>
+ {
+ public:
+ typedef RotationBase<EulerAngles<Scalar_, _System>, 3> Base;
+
+ /** the scalar type of the angles */
+ typedef Scalar_ Scalar;
+ typedef typename NumTraits<Scalar>::Real RealScalar;
+
+ /** the EulerSystem to use, which represents the axes of rotation. */
+ typedef _System System;
+
+ typedef Matrix<Scalar,3,3> Matrix3; /*!< the equivalent rotation matrix type */
+ typedef Matrix<Scalar,3,1> Vector3; /*!< the equivalent 3 dimension vector type */
+ typedef Quaternion<Scalar> QuaternionType; /*!< the equivalent quaternion type */
+ typedef AngleAxis<Scalar> AngleAxisType; /*!< the equivalent angle-axis type */
+
+ /** \returns the axis vector of the first (alpha) rotation */
+ static Vector3 AlphaAxisVector() {
+ const Vector3& u = Vector3::Unit(System::AlphaAxisAbs - 1);
+ return System::IsAlphaOpposite ? -u : u;
+ }
+
+ /** \returns the axis vector of the second (beta) rotation */
+ static Vector3 BetaAxisVector() {
+ const Vector3& u = Vector3::Unit(System::BetaAxisAbs - 1);
+ return System::IsBetaOpposite ? -u : u;
+ }
+
+ /** \returns the axis vector of the third (gamma) rotation */
+ static Vector3 GammaAxisVector() {
+ const Vector3& u = Vector3::Unit(System::GammaAxisAbs - 1);
+ return System::IsGammaOpposite ? -u : u;
+ }
+
+ private:
+ Vector3 m_angles;
+
+ public:
+ /** Default constructor without initialization. */
+ EulerAngles() {}
+ /** Constructs and initialize an EulerAngles (\p alpha, \p beta, \p gamma). */
+ EulerAngles(const Scalar& alpha, const Scalar& beta, const Scalar& gamma) :
+ m_angles(alpha, beta, gamma) {}
+
+ // TODO: Test this constructor
+ /** Constructs and initialize an EulerAngles from the array data {alpha, beta, gamma} */
+ explicit EulerAngles(const Scalar* data) : m_angles(data) {}
+
+ /** Constructs and initializes an EulerAngles from either:
+ * - a 3x3 rotation matrix expression(i.e. pure orthogonal matrix with determinant of +1),
+ * - a 3D vector expression representing Euler angles.
+ *
+ * \note If \p other is a 3x3 rotation matrix, the angles range rules will be as follow:<BR>
+ * Alpha and gamma angles will be in the range [-PI, PI].<BR>
+ * As for Beta angle:
+ * - If the system is Tait-Bryan, the beta angle will be in the range [-PI/2, PI/2].
+ * - otherwise:
+ * - If the beta axis is positive, the beta angle will be in the range [0, PI]
+ * - If the beta axis is negative, the beta angle will be in the range [-PI, 0]
+ */
+ template<typename Derived>
+ explicit EulerAngles(const MatrixBase<Derived>& other) { *this = other; }
+
+ /** Constructs and initialize Euler angles from a rotation \p rot.
+ *
+ * \note If \p rot is an EulerAngles (even when it represented as RotationBase explicitly),
+ * angles ranges are __undefined__.
+ * Otherwise, alpha and gamma angles will be in the range [-PI, PI].<BR>
+ * As for Beta angle:
+ * - If the system is Tait-Bryan, the beta angle will be in the range [-PI/2, PI/2].
+ * - otherwise:
+ * - If the beta axis is positive, the beta angle will be in the range [0, PI]
+ * - If the beta axis is negative, the beta angle will be in the range [-PI, 0]
+ */
+ template<typename Derived>
+ EulerAngles(const RotationBase<Derived, 3>& rot) { System::CalcEulerAngles(*this, rot.toRotationMatrix()); }
+
+ /*EulerAngles(const QuaternionType& q)
+ {
+ // TODO: Implement it in a faster way for quaternions
+ // According to http://www.euclideanspace.com/maths/geometry/rotations/conversions/quaternionToEuler/
+ // we can compute only the needed matrix cells and then convert to euler angles. (see ZYX example below)
+ // Currently we compute all matrix cells from quaternion.
+
+ // Special case only for ZYX
+ //Scalar y2 = q.y() * q.y();
+ //m_angles[0] = std::atan2(2*(q.w()*q.z() + q.x()*q.y()), (1 - 2*(y2 + q.z()*q.z())));
+ //m_angles[1] = std::asin( 2*(q.w()*q.y() - q.z()*q.x()));
+ //m_angles[2] = std::atan2(2*(q.w()*q.x() + q.y()*q.z()), (1 - 2*(q.x()*q.x() + y2)));
+ }*/
+
+ /** \returns The angle values stored in a vector (alpha, beta, gamma). */
+ const Vector3& angles() const { return m_angles; }
+ /** \returns A read-write reference to the angle values stored in a vector (alpha, beta, gamma). */
+ Vector3& angles() { return m_angles; }
+
+ /** \returns The value of the first angle. */
+ Scalar alpha() const { return m_angles[0]; }
+ /** \returns A read-write reference to the angle of the first angle. */
+ Scalar& alpha() { return m_angles[0]; }
+
+ /** \returns The value of the second angle. */
+ Scalar beta() const { return m_angles[1]; }
+ /** \returns A read-write reference to the angle of the second angle. */
+ Scalar& beta() { return m_angles[1]; }
+
+ /** \returns The value of the third angle. */
+ Scalar gamma() const { return m_angles[2]; }
+ /** \returns A read-write reference to the angle of the third angle. */
+ Scalar& gamma() { return m_angles[2]; }
+
+ /** \returns The Euler angles rotation inverse (which is as same as the negative),
+ * (-alpha, -beta, -gamma).
+ */
+ EulerAngles inverse() const
+ {
+ EulerAngles res;
+ res.m_angles = -m_angles;
+ return res;
+ }
+
+ /** \returns The Euler angles rotation negative (which is as same as the inverse),
+ * (-alpha, -beta, -gamma).
+ */
+ EulerAngles operator -() const
+ {
+ return inverse();
+ }
+
+ /** Set \c *this from either:
+ * - a 3x3 rotation matrix expression(i.e. pure orthogonal matrix with determinant of +1),
+ * - a 3D vector expression representing Euler angles.
+ *
+ * See EulerAngles(const MatrixBase<Derived, 3>&) for more information about
+ * angles ranges output.
+ */
+ template<class Derived>
+ EulerAngles& operator=(const MatrixBase<Derived>& other)
+ {
+ EIGEN_STATIC_ASSERT((internal::is_same<Scalar, typename Derived::Scalar>::value),
+ YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY)
+
+ internal::eulerangles_assign_impl<System, Derived>::run(*this, other.derived());
+ return *this;
+ }
+
+ // TODO: Assign and construct from another EulerAngles (with different system)
+
+ /** Set \c *this from a rotation.
+ *
+ * See EulerAngles(const RotationBase<Derived, 3>&) for more information about
+ * angles ranges output.
+ */
+ template<typename Derived>
+ EulerAngles& operator=(const RotationBase<Derived, 3>& rot) {
+ System::CalcEulerAngles(*this, rot.toRotationMatrix());
+ return *this;
+ }
+
+ /** \returns \c true if \c *this is approximately equal to \a other, within the precision
+ * determined by \a prec.
+ *
+ * \sa MatrixBase::isApprox() */
+ bool isApprox(const EulerAngles& other,
+ const RealScalar& prec = NumTraits<Scalar>::dummy_precision()) const
+ { return angles().isApprox(other.angles(), prec); }
+
+ /** \returns an equivalent 3x3 rotation matrix. */
+ Matrix3 toRotationMatrix() const
+ {
+ // TODO: Calc it faster
+ return static_cast<QuaternionType>(*this).toRotationMatrix();
+ }
+
+ /** Convert the Euler angles to quaternion. */
+ operator QuaternionType() const
+ {
+ return
+ AngleAxisType(alpha(), AlphaAxisVector()) *
+ AngleAxisType(beta(), BetaAxisVector()) *
+ AngleAxisType(gamma(), GammaAxisVector());
+ }
+
+ friend std::ostream& operator<<(std::ostream& s, const EulerAngles<Scalar, System>& eulerAngles)
+ {
+ s << eulerAngles.angles().transpose();
+ return s;
+ }
+
+ /** \returns \c *this with scalar type casted to \a NewScalarType */
+ template <typename NewScalarType>
+ EulerAngles<NewScalarType, System> cast() const
+ {
+ EulerAngles<NewScalarType, System> e;
+ e.angles() = angles().template cast<NewScalarType>();
+ return e;
+ }
+ };
+
+#define EIGEN_EULER_ANGLES_SINGLE_TYPEDEF(AXES, SCALAR_TYPE, SCALAR_POSTFIX) \
+ /** \ingroup EulerAngles_Module */ \
+ typedef EulerAngles<SCALAR_TYPE, EulerSystem##AXES> EulerAngles##AXES##SCALAR_POSTFIX;
+
+#define EIGEN_EULER_ANGLES_TYPEDEFS(SCALAR_TYPE, SCALAR_POSTFIX) \
+ EIGEN_EULER_ANGLES_SINGLE_TYPEDEF(XYZ, SCALAR_TYPE, SCALAR_POSTFIX) \
+ EIGEN_EULER_ANGLES_SINGLE_TYPEDEF(XYX, SCALAR_TYPE, SCALAR_POSTFIX) \
+ EIGEN_EULER_ANGLES_SINGLE_TYPEDEF(XZY, SCALAR_TYPE, SCALAR_POSTFIX) \
+ EIGEN_EULER_ANGLES_SINGLE_TYPEDEF(XZX, SCALAR_TYPE, SCALAR_POSTFIX) \
+ \
+ EIGEN_EULER_ANGLES_SINGLE_TYPEDEF(YZX, SCALAR_TYPE, SCALAR_POSTFIX) \
+ EIGEN_EULER_ANGLES_SINGLE_TYPEDEF(YZY, SCALAR_TYPE, SCALAR_POSTFIX) \
+ EIGEN_EULER_ANGLES_SINGLE_TYPEDEF(YXZ, SCALAR_TYPE, SCALAR_POSTFIX) \
+ EIGEN_EULER_ANGLES_SINGLE_TYPEDEF(YXY, SCALAR_TYPE, SCALAR_POSTFIX) \
+ \
+ EIGEN_EULER_ANGLES_SINGLE_TYPEDEF(ZXY, SCALAR_TYPE, SCALAR_POSTFIX) \
+ EIGEN_EULER_ANGLES_SINGLE_TYPEDEF(ZXZ, SCALAR_TYPE, SCALAR_POSTFIX) \
+ EIGEN_EULER_ANGLES_SINGLE_TYPEDEF(ZYX, SCALAR_TYPE, SCALAR_POSTFIX) \
+ EIGEN_EULER_ANGLES_SINGLE_TYPEDEF(ZYZ, SCALAR_TYPE, SCALAR_POSTFIX)
+
+EIGEN_EULER_ANGLES_TYPEDEFS(float, f)
+EIGEN_EULER_ANGLES_TYPEDEFS(double, d)
+
+ namespace internal
+ {
+ template<typename Scalar_, class _System>
+ struct traits<EulerAngles<Scalar_, _System> >
+ {
+ typedef Scalar_ Scalar;
+ };
+
+ // set from a rotation matrix
+ template<class System, class Other>
+ struct eulerangles_assign_impl<System,Other,3,3>
+ {
+ typedef typename Other::Scalar Scalar;
+ static void run(EulerAngles<Scalar, System>& e, const Other& m)
+ {
+ System::CalcEulerAngles(e, m);
+ }
+ };
+
+ // set from a vector of Euler angles
+ template<class System, class Other>
+ struct eulerangles_assign_impl<System,Other,3,1>
+ {
+ typedef typename Other::Scalar Scalar;
+ static void run(EulerAngles<Scalar, System>& e, const Other& vec)
+ {
+ e.angles() = vec;
+ }
+ };
+ }
+}
+
+#endif // EIGEN_EULERANGLESCLASS_H
diff --git a/unsupported/Eigen/src/EulerAngles/EulerSystem.h b/unsupported/Eigen/src/EulerAngles/EulerSystem.h
new file mode 100644
index 0000000..278f9bf
--- /dev/null
+++ b/unsupported/Eigen/src/EulerAngles/EulerSystem.h
@@ -0,0 +1,307 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2015 Tal Hadad <tal_hd@hotmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_EULERSYSTEM_H
+#define EIGEN_EULERSYSTEM_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen
+{
+ // Forward declarations
+ template <typename Scalar_, class _System>
+ class EulerAngles;
+
+ namespace internal
+ {
+ // TODO: Add this trait to the Eigen internal API?
+ template <int Num, bool IsPositive = (Num > 0)>
+ struct Abs
+ {
+ enum { value = Num };
+ };
+
+ template <int Num>
+ struct Abs<Num, false>
+ {
+ enum { value = -Num };
+ };
+
+ template <int Axis>
+ struct IsValidAxis
+ {
+ enum { value = Axis != 0 && Abs<Axis>::value <= 3 };
+ };
+
+ template<typename System,
+ typename Other,
+ int OtherRows=Other::RowsAtCompileTime,
+ int OtherCols=Other::ColsAtCompileTime>
+ struct eulerangles_assign_impl;
+ }
+
+ #define EIGEN_EULER_ANGLES_CLASS_STATIC_ASSERT(COND,MSG) typedef char static_assertion_##MSG[(COND)?1:-1]
+
+ /** \brief Representation of a fixed signed rotation axis for EulerSystem.
+ *
+ * \ingroup EulerAngles_Module
+ *
+ * Values here represent:
+ * - The axis of the rotation: X, Y or Z.
+ * - The sign (i.e. direction of the rotation along the axis): positive(+) or negative(-)
+ *
+ * Therefore, this could express all the axes {+X,+Y,+Z,-X,-Y,-Z}
+ *
+ * For positive axis, use +EULER_{axis}, and for negative axis use -EULER_{axis}.
+ */
+ enum EulerAxis
+ {
+ EULER_X = 1, /*!< the X axis */
+ EULER_Y = 2, /*!< the Y axis */
+ EULER_Z = 3 /*!< the Z axis */
+ };
+
+ /** \class EulerSystem
+ *
+ * \ingroup EulerAngles_Module
+ *
+ * \brief Represents a fixed Euler rotation system.
+ *
+ * This meta-class goal is to represent the Euler system in compilation time, for EulerAngles.
+ *
+ * You can use this class to get two things:
+ * - Build an Euler system, and then pass it as a template parameter to EulerAngles.
+ * - Query some compile time data about an Euler system. (e.g. Whether it's Tait-Bryan)
+ *
+ * Euler rotation is a set of three rotation on fixed axes. (see \ref EulerAngles)
+ * This meta-class store constantly those signed axes. (see \ref EulerAxis)
+ *
+ * ### Types of Euler systems ###
+ *
+ * All and only valid 3 dimension Euler rotation over standard
+ * signed axes{+X,+Y,+Z,-X,-Y,-Z} are supported:
+ * - all axes X, Y, Z in each valid order (see below what order is valid)
+ * - rotation over the axis is supported both over the positive and negative directions.
+ * - both Tait-Bryan and proper/classic Euler angles (i.e. the opposite).
+ *
+ * Since EulerSystem support both positive and negative directions,
+ * you may call this rotation distinction in other names:
+ * - _right handed_ or _left handed_
+ * - _counterclockwise_ or _clockwise_
+ *
+ * Notice all axed combination are valid, and would trigger a static assertion.
+ * Same unsigned axes can't be neighbors, e.g. {X,X,Y} is invalid.
+ * This yield two and only two classes:
+ * - _Tait-Bryan_ - all unsigned axes are distinct, e.g. {X,Y,Z}
+ * - _proper/classic Euler angles_ - The first and the third unsigned axes is equal,
+ * and the second is different, e.g. {X,Y,X}
+ *
+ * ### Intrinsic vs extrinsic Euler systems ###
+ *
+ * Only intrinsic Euler systems are supported for simplicity.
+ * If you want to use extrinsic Euler systems,
+ * just use the equal intrinsic opposite order for axes and angles.
+ * I.e axes (A,B,C) becomes (C,B,A), and angles (a,b,c) becomes (c,b,a).
+ *
+ * ### Convenient user typedefs ###
+ *
+ * Convenient typedefs for EulerSystem exist (only for positive axes Euler systems),
+ * in a form of EulerSystem{A}{B}{C}, e.g. \ref EulerSystemXYZ.
+ *
+ * ### Additional reading ###
+ *
+ * More information about Euler angles: https://en.wikipedia.org/wiki/Euler_angles
+ *
+ * \tparam _AlphaAxis the first fixed EulerAxis
+ *
+ * \tparam _BetaAxis the second fixed EulerAxis
+ *
+ * \tparam _GammaAxis the third fixed EulerAxis
+ */
+ template <int _AlphaAxis, int _BetaAxis, int _GammaAxis>
+ class EulerSystem
+ {
+ public:
+ // It's defined this way and not as enum, because I think
+ // that enum is not guerantee to support negative numbers
+
+ /** The first rotation axis */
+ static constexpr int AlphaAxis = _AlphaAxis;
+
+ /** The second rotation axis */
+ static constexpr int BetaAxis = _BetaAxis;
+
+ /** The third rotation axis */
+ static constexpr int GammaAxis = _GammaAxis;
+
+ enum
+ {
+ AlphaAxisAbs = internal::Abs<AlphaAxis>::value, /*!< the first rotation axis unsigned */
+ BetaAxisAbs = internal::Abs<BetaAxis>::value, /*!< the second rotation axis unsigned */
+ GammaAxisAbs = internal::Abs<GammaAxis>::value, /*!< the third rotation axis unsigned */
+
+ IsAlphaOpposite = (AlphaAxis < 0) ? 1 : 0, /*!< whether alpha axis is negative */
+ IsBetaOpposite = (BetaAxis < 0) ? 1 : 0, /*!< whether beta axis is negative */
+ IsGammaOpposite = (GammaAxis < 0) ? 1 : 0, /*!< whether gamma axis is negative */
+
+ // Parity is even if alpha axis X is followed by beta axis Y, or Y is followed
+ // by Z, or Z is followed by X; otherwise it is odd.
+ IsOdd = ((AlphaAxisAbs)%3 == (BetaAxisAbs - 1)%3) ? 0 : 1, /*!< whether the Euler system is odd */
+ IsEven = IsOdd ? 0 : 1, /*!< whether the Euler system is even */
+
+ IsTaitBryan = ((unsigned)AlphaAxisAbs != (unsigned)GammaAxisAbs) ? 1 : 0 /*!< whether the Euler system is Tait-Bryan */
+ };
+
+ private:
+
+ EIGEN_EULER_ANGLES_CLASS_STATIC_ASSERT(internal::IsValidAxis<AlphaAxis>::value,
+ ALPHA_AXIS_IS_INVALID);
+
+ EIGEN_EULER_ANGLES_CLASS_STATIC_ASSERT(internal::IsValidAxis<BetaAxis>::value,
+ BETA_AXIS_IS_INVALID);
+
+ EIGEN_EULER_ANGLES_CLASS_STATIC_ASSERT(internal::IsValidAxis<GammaAxis>::value,
+ GAMMA_AXIS_IS_INVALID);
+
+ EIGEN_EULER_ANGLES_CLASS_STATIC_ASSERT((unsigned)AlphaAxisAbs != (unsigned)BetaAxisAbs,
+ ALPHA_AXIS_CANT_BE_EQUAL_TO_BETA_AXIS);
+
+ EIGEN_EULER_ANGLES_CLASS_STATIC_ASSERT((unsigned)BetaAxisAbs != (unsigned)GammaAxisAbs,
+ BETA_AXIS_CANT_BE_EQUAL_TO_GAMMA_AXIS);
+
+ static const int
+ // I, J, K are the pivot indexes permutation for the rotation matrix, that match this Euler system.
+ // They are used in this class converters.
+ // They are always different from each other, and their possible values are: 0, 1, or 2.
+ I_ = AlphaAxisAbs - 1,
+ J_ = (AlphaAxisAbs - 1 + 1 + IsOdd)%3,
+ K_ = (AlphaAxisAbs - 1 + 2 - IsOdd)%3
+ ;
+
+ // TODO: Get @mat parameter in form that avoids double evaluation.
+ template <typename Derived>
+ static void CalcEulerAngles_imp(Matrix<typename MatrixBase<Derived>::Scalar, 3, 1>& res, const MatrixBase<Derived>& mat, internal::true_type /*isTaitBryan*/)
+ {
+ using std::atan2;
+ using std::sqrt;
+
+ typedef typename Derived::Scalar Scalar;
+
+ const Scalar plusMinus = IsEven? 1 : -1;
+ const Scalar minusPlus = IsOdd? 1 : -1;
+
+ const Scalar Rsum = sqrt((mat(I_,I_) * mat(I_,I_) + mat(I_,J_) * mat(I_,J_) + mat(J_,K_) * mat(J_,K_) + mat(K_,K_) * mat(K_,K_))/2);
+ res[1] = atan2(plusMinus * mat(I_,K_), Rsum);
+
+ // There is a singularity when cos(beta) == 0
+ if(Rsum > 4 * NumTraits<Scalar>::epsilon()) {// cos(beta) != 0
+ res[0] = atan2(minusPlus * mat(J_, K_), mat(K_, K_));
+ res[2] = atan2(minusPlus * mat(I_, J_), mat(I_, I_));
+ }
+ else if(plusMinus * mat(I_, K_) > 0) {// cos(beta) == 0 and sin(beta) == 1
+ Scalar spos = mat(J_, I_) + plusMinus * mat(K_, J_); // 2*sin(alpha + plusMinus * gamma
+ Scalar cpos = mat(J_, J_) + minusPlus * mat(K_, I_); // 2*cos(alpha + plusMinus * gamma)
+ Scalar alphaPlusMinusGamma = atan2(spos, cpos);
+ res[0] = alphaPlusMinusGamma;
+ res[2] = 0;
+ }
+ else {// cos(beta) == 0 and sin(beta) == -1
+ Scalar sneg = plusMinus * (mat(K_, J_) + minusPlus * mat(J_, I_)); // 2*sin(alpha + minusPlus*gamma)
+ Scalar cneg = mat(J_, J_) + plusMinus * mat(K_, I_); // 2*cos(alpha + minusPlus*gamma)
+ Scalar alphaMinusPlusBeta = atan2(sneg, cneg);
+ res[0] = alphaMinusPlusBeta;
+ res[2] = 0;
+ }
+ }
+
+ template <typename Derived>
+ static void CalcEulerAngles_imp(Matrix<typename MatrixBase<Derived>::Scalar,3,1>& res,
+ const MatrixBase<Derived>& mat, internal::false_type /*isTaitBryan*/)
+ {
+ using std::atan2;
+ using std::sqrt;
+
+ typedef typename Derived::Scalar Scalar;
+
+ const Scalar plusMinus = IsEven? 1 : -1;
+ const Scalar minusPlus = IsOdd? 1 : -1;
+
+ const Scalar Rsum = sqrt((mat(I_, J_) * mat(I_, J_) + mat(I_, K_) * mat(I_, K_) + mat(J_, I_) * mat(J_, I_) + mat(K_, I_) * mat(K_, I_)) / 2);
+
+ res[1] = atan2(Rsum, mat(I_, I_));
+
+ // There is a singularity when sin(beta) == 0
+ if(Rsum > 4 * NumTraits<Scalar>::epsilon()) {// sin(beta) != 0
+ res[0] = atan2(mat(J_, I_), minusPlus * mat(K_, I_));
+ res[2] = atan2(mat(I_, J_), plusMinus * mat(I_, K_));
+ }
+ else if(mat(I_, I_) > 0) {// sin(beta) == 0 and cos(beta) == 1
+ Scalar spos = plusMinus * mat(K_, J_) + minusPlus * mat(J_, K_); // 2*sin(alpha + gamma)
+ Scalar cpos = mat(J_, J_) + mat(K_, K_); // 2*cos(alpha + gamma)
+ res[0] = atan2(spos, cpos);
+ res[2] = 0;
+ }
+ else {// sin(beta) == 0 and cos(beta) == -1
+ Scalar sneg = plusMinus * mat(K_, J_) + plusMinus * mat(J_, K_); // 2*sin(alpha - gamma)
+ Scalar cneg = mat(J_, J_) - mat(K_, K_); // 2*cos(alpha - gamma)
+ res[0] = atan2(sneg, cneg);
+ res[2] = 0;
+ }
+ }
+
+ template<typename Scalar>
+ static void CalcEulerAngles(
+ EulerAngles<Scalar, EulerSystem>& res,
+ const typename EulerAngles<Scalar, EulerSystem>::Matrix3& mat)
+ {
+ CalcEulerAngles_imp(
+ res.angles(), mat,
+ std::conditional_t<IsTaitBryan, internal::true_type, internal::false_type>());
+
+ if (IsAlphaOpposite)
+ res.alpha() = -res.alpha();
+
+ if (IsBetaOpposite)
+ res.beta() = -res.beta();
+
+ if (IsGammaOpposite)
+ res.gamma() = -res.gamma();
+ }
+
+ template <typename Scalar_, class _System>
+ friend class Eigen::EulerAngles;
+
+ template<typename System,
+ typename Other,
+ int OtherRows,
+ int OtherCols>
+ friend struct internal::eulerangles_assign_impl;
+ };
+
+#define EIGEN_EULER_SYSTEM_TYPEDEF(A, B, C) \
+ /** \ingroup EulerAngles_Module */ \
+ typedef EulerSystem<EULER_##A, EULER_##B, EULER_##C> EulerSystem##A##B##C;
+
+ EIGEN_EULER_SYSTEM_TYPEDEF(X,Y,Z)
+ EIGEN_EULER_SYSTEM_TYPEDEF(X,Y,X)
+ EIGEN_EULER_SYSTEM_TYPEDEF(X,Z,Y)
+ EIGEN_EULER_SYSTEM_TYPEDEF(X,Z,X)
+
+ EIGEN_EULER_SYSTEM_TYPEDEF(Y,Z,X)
+ EIGEN_EULER_SYSTEM_TYPEDEF(Y,Z,Y)
+ EIGEN_EULER_SYSTEM_TYPEDEF(Y,X,Z)
+ EIGEN_EULER_SYSTEM_TYPEDEF(Y,X,Y)
+
+ EIGEN_EULER_SYSTEM_TYPEDEF(Z,X,Y)
+ EIGEN_EULER_SYSTEM_TYPEDEF(Z,X,Z)
+ EIGEN_EULER_SYSTEM_TYPEDEF(Z,Y,X)
+ EIGEN_EULER_SYSTEM_TYPEDEF(Z,Y,Z)
+}
+
+#endif // EIGEN_EULERSYSTEM_H
diff --git a/unsupported/Eigen/src/EulerAngles/InternalHeaderCheck.h b/unsupported/Eigen/src/EulerAngles/InternalHeaderCheck.h
new file mode 100644
index 0000000..0c00a30
--- /dev/null
+++ b/unsupported/Eigen/src/EulerAngles/InternalHeaderCheck.h
@@ -0,0 +1,3 @@
+#ifndef EIGEN_EULERANGLES_MODULE_H
+#error "Please include unsupported/Eigen/EulerAngles instead of including headers inside the src directory directly."
+#endif
diff --git a/unsupported/Eigen/src/FFT/InternalHeaderCheck.h b/unsupported/Eigen/src/FFT/InternalHeaderCheck.h
new file mode 100644
index 0000000..801e245
--- /dev/null
+++ b/unsupported/Eigen/src/FFT/InternalHeaderCheck.h
@@ -0,0 +1,3 @@
+#ifndef EIGEN_FFT_MODULE_H
+#error "Please include unsupported/Eigen/FFT instead of including headers inside the src directory directly."
+#endif
diff --git a/unsupported/Eigen/src/FFT/ei_fftw_impl.h b/unsupported/Eigen/src/FFT/ei_fftw_impl.h
new file mode 100644
index 0000000..f188027
--- /dev/null
+++ b/unsupported/Eigen/src/FFT/ei_fftw_impl.h
@@ -0,0 +1,263 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009 Mark Borgerding mark a borgerding net
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+
+ // FFTW uses non-const arguments
+ // so we must use ugly const_cast calls for all the args it uses
+ //
+ // This should be safe as long as
+ // 1. we use FFTW_ESTIMATE for all our planning
+ // see the FFTW docs section 4.3.2 "Planner Flags"
+ // 2. fftw_complex is compatible with std::complex
+ // This assumes std::complex<T> layout is array of size 2 with real,imag
+ template <typename T>
+ inline
+ T * fftw_cast(const T* p)
+ {
+ return const_cast<T*>( p);
+ }
+
+ inline
+ fftw_complex * fftw_cast( const std::complex<double> * p)
+ {
+ return const_cast<fftw_complex*>( reinterpret_cast<const fftw_complex*>(p) );
+ }
+
+ inline
+ fftwf_complex * fftw_cast( const std::complex<float> * p)
+ {
+ return const_cast<fftwf_complex*>( reinterpret_cast<const fftwf_complex*>(p) );
+ }
+
+ inline
+ fftwl_complex * fftw_cast( const std::complex<long double> * p)
+ {
+ return const_cast<fftwl_complex*>( reinterpret_cast<const fftwl_complex*>(p) );
+ }
+
+ template <typename T>
+ struct fftw_plan {};
+
+ template <>
+ struct fftw_plan<float>
+ {
+ typedef float scalar_type;
+ typedef fftwf_complex complex_type;
+ fftwf_plan m_plan;
+ fftw_plan() :m_plan(NULL) {}
+ ~fftw_plan() {if (m_plan) fftwf_destroy_plan(m_plan);}
+
+ inline
+ void fwd(complex_type * dst,complex_type * src,int nfft) {
+ if (m_plan==NULL) m_plan = fftwf_plan_dft_1d(nfft,src,dst, FFTW_FORWARD, FFTW_ESTIMATE|FFTW_PRESERVE_INPUT);
+ fftwf_execute_dft( m_plan, src,dst);
+ }
+ inline
+ void inv(complex_type * dst,complex_type * src,int nfft) {
+ if (m_plan==NULL) m_plan = fftwf_plan_dft_1d(nfft,src,dst, FFTW_BACKWARD , FFTW_ESTIMATE|FFTW_PRESERVE_INPUT);
+ fftwf_execute_dft( m_plan, src,dst);
+ }
+ inline
+ void fwd(complex_type * dst,scalar_type * src,int nfft) {
+ if (m_plan==NULL) m_plan = fftwf_plan_dft_r2c_1d(nfft,src,dst,FFTW_ESTIMATE|FFTW_PRESERVE_INPUT);
+ fftwf_execute_dft_r2c( m_plan,src,dst);
+ }
+ inline
+ void inv(scalar_type * dst,complex_type * src,int nfft) {
+ if (m_plan==NULL)
+ m_plan = fftwf_plan_dft_c2r_1d(nfft,src,dst,FFTW_ESTIMATE|FFTW_PRESERVE_INPUT);
+ fftwf_execute_dft_c2r( m_plan, src,dst);
+ }
+
+ inline
+ void fwd2( complex_type * dst,complex_type * src,int n0,int n1) {
+ if (m_plan==NULL) m_plan = fftwf_plan_dft_2d(n0,n1,src,dst,FFTW_FORWARD,FFTW_ESTIMATE|FFTW_PRESERVE_INPUT);
+ fftwf_execute_dft( m_plan, src,dst);
+ }
+ inline
+ void inv2( complex_type * dst,complex_type * src,int n0,int n1) {
+ if (m_plan==NULL) m_plan = fftwf_plan_dft_2d(n0,n1,src,dst,FFTW_BACKWARD,FFTW_ESTIMATE|FFTW_PRESERVE_INPUT);
+ fftwf_execute_dft( m_plan, src,dst);
+ }
+
+ };
+ template <>
+ struct fftw_plan<double>
+ {
+ typedef double scalar_type;
+ typedef fftw_complex complex_type;
+ ::fftw_plan m_plan;
+ fftw_plan() :m_plan(NULL) {}
+ ~fftw_plan() {if (m_plan) fftw_destroy_plan(m_plan);}
+
+ inline
+ void fwd(complex_type * dst,complex_type * src,int nfft) {
+ if (m_plan==NULL) m_plan = fftw_plan_dft_1d(nfft,src,dst, FFTW_FORWARD, FFTW_ESTIMATE|FFTW_PRESERVE_INPUT);
+ fftw_execute_dft( m_plan, src,dst);
+ }
+ inline
+ void inv(complex_type * dst,complex_type * src,int nfft) {
+ if (m_plan==NULL) m_plan = fftw_plan_dft_1d(nfft,src,dst, FFTW_BACKWARD , FFTW_ESTIMATE|FFTW_PRESERVE_INPUT);
+ fftw_execute_dft( m_plan, src,dst);
+ }
+ inline
+ void fwd(complex_type * dst,scalar_type * src,int nfft) {
+ if (m_plan==NULL) m_plan = fftw_plan_dft_r2c_1d(nfft,src,dst,FFTW_ESTIMATE|FFTW_PRESERVE_INPUT);
+ fftw_execute_dft_r2c( m_plan,src,dst);
+ }
+ inline
+ void inv(scalar_type * dst,complex_type * src,int nfft) {
+ if (m_plan==NULL)
+ m_plan = fftw_plan_dft_c2r_1d(nfft,src,dst,FFTW_ESTIMATE|FFTW_PRESERVE_INPUT);
+ fftw_execute_dft_c2r( m_plan, src,dst);
+ }
+ inline
+ void fwd2( complex_type * dst,complex_type * src,int n0,int n1) {
+ if (m_plan==NULL) m_plan = fftw_plan_dft_2d(n0,n1,src,dst,FFTW_FORWARD,FFTW_ESTIMATE|FFTW_PRESERVE_INPUT);
+ fftw_execute_dft( m_plan, src,dst);
+ }
+ inline
+ void inv2( complex_type * dst,complex_type * src,int n0,int n1) {
+ if (m_plan==NULL) m_plan = fftw_plan_dft_2d(n0,n1,src,dst,FFTW_BACKWARD,FFTW_ESTIMATE|FFTW_PRESERVE_INPUT);
+ fftw_execute_dft( m_plan, src,dst);
+ }
+ };
+ template <>
+ struct fftw_plan<long double>
+ {
+ typedef long double scalar_type;
+ typedef fftwl_complex complex_type;
+ fftwl_plan m_plan;
+ fftw_plan() :m_plan(NULL) {}
+ ~fftw_plan() {if (m_plan) fftwl_destroy_plan(m_plan);}
+
+ inline
+ void fwd(complex_type * dst,complex_type * src,int nfft) {
+ if (m_plan==NULL) m_plan = fftwl_plan_dft_1d(nfft,src,dst, FFTW_FORWARD, FFTW_ESTIMATE|FFTW_PRESERVE_INPUT);
+ fftwl_execute_dft( m_plan, src,dst);
+ }
+ inline
+ void inv(complex_type * dst,complex_type * src,int nfft) {
+ if (m_plan==NULL) m_plan = fftwl_plan_dft_1d(nfft,src,dst, FFTW_BACKWARD , FFTW_ESTIMATE|FFTW_PRESERVE_INPUT);
+ fftwl_execute_dft( m_plan, src,dst);
+ }
+ inline
+ void fwd(complex_type * dst,scalar_type * src,int nfft) {
+ if (m_plan==NULL) m_plan = fftwl_plan_dft_r2c_1d(nfft,src,dst,FFTW_ESTIMATE|FFTW_PRESERVE_INPUT);
+ fftwl_execute_dft_r2c( m_plan,src,dst);
+ }
+ inline
+ void inv(scalar_type * dst,complex_type * src,int nfft) {
+ if (m_plan==NULL)
+ m_plan = fftwl_plan_dft_c2r_1d(nfft,src,dst,FFTW_ESTIMATE|FFTW_PRESERVE_INPUT);
+ fftwl_execute_dft_c2r( m_plan, src,dst);
+ }
+ inline
+ void fwd2( complex_type * dst,complex_type * src,int n0,int n1) {
+ if (m_plan==NULL) m_plan = fftwl_plan_dft_2d(n0,n1,src,dst,FFTW_FORWARD,FFTW_ESTIMATE|FFTW_PRESERVE_INPUT);
+ fftwl_execute_dft( m_plan, src,dst);
+ }
+ inline
+ void inv2( complex_type * dst,complex_type * src,int n0,int n1) {
+ if (m_plan==NULL) m_plan = fftwl_plan_dft_2d(n0,n1,src,dst,FFTW_BACKWARD,FFTW_ESTIMATE|FFTW_PRESERVE_INPUT);
+ fftwl_execute_dft( m_plan, src,dst);
+ }
+ };
+
+ template <typename Scalar_>
+ struct fftw_impl
+ {
+ typedef Scalar_ Scalar;
+ typedef std::complex<Scalar> Complex;
+
+ inline
+ void clear()
+ {
+ m_plans.clear();
+ }
+
+ // complex-to-complex forward FFT
+ inline
+ void fwd( Complex * dst,const Complex *src,int nfft)
+ {
+ get_plan(nfft,false,dst,src).fwd(fftw_cast(dst), fftw_cast(src),nfft );
+ }
+
+ // real-to-complex forward FFT
+ inline
+ void fwd( Complex * dst,const Scalar * src,int nfft)
+ {
+ get_plan(nfft,false,dst,src).fwd(fftw_cast(dst), fftw_cast(src) ,nfft);
+ }
+
+ // 2-d complex-to-complex
+ inline
+ void fwd2(Complex * dst, const Complex * src, int n0,int n1)
+ {
+ get_plan(n0,n1,false,dst,src).fwd2(fftw_cast(dst), fftw_cast(src) ,n0,n1);
+ }
+
+ // inverse complex-to-complex
+ inline
+ void inv(Complex * dst,const Complex *src,int nfft)
+ {
+ get_plan(nfft,true,dst,src).inv(fftw_cast(dst), fftw_cast(src),nfft );
+ }
+
+ // half-complex to scalar
+ inline
+ void inv( Scalar * dst,const Complex * src,int nfft)
+ {
+ get_plan(nfft,true,dst,src).inv(fftw_cast(dst), fftw_cast(src),nfft );
+ }
+
+ // 2-d complex-to-complex
+ inline
+ void inv2(Complex * dst, const Complex * src, int n0,int n1)
+ {
+ get_plan(n0,n1,true,dst,src).inv2(fftw_cast(dst), fftw_cast(src) ,n0,n1);
+ }
+
+
+ protected:
+ typedef fftw_plan<Scalar> PlanData;
+
+ typedef Eigen::numext::int64_t int64_t;
+
+ typedef std::map<int64_t,PlanData> PlanMap;
+
+ PlanMap m_plans;
+
+ inline
+ PlanData & get_plan(int nfft,bool inverse,void * dst,const void * src)
+ {
+ bool inplace = (dst==src);
+ bool aligned = ( (reinterpret_cast<size_t>(src)&15) | (reinterpret_cast<size_t>(dst)&15) ) == 0;
+ int64_t key = ( (nfft<<3 ) | (inverse<<2) | (inplace<<1) | aligned ) << 1;
+ return m_plans[key];
+ }
+
+ inline
+ PlanData & get_plan(int n0,int n1,bool inverse,void * dst,const void * src)
+ {
+ bool inplace = (dst==src);
+ bool aligned = ( (reinterpret_cast<size_t>(src)&15) | (reinterpret_cast<size_t>(dst)&15) ) == 0;
+ int64_t key = ( ( (((int64_t)n0) << 30)|(n1<<3 ) | (inverse<<2) | (inplace<<1) | aligned ) << 1 ) + 1;
+ return m_plans[key];
+ }
+ };
+
+} // end namespace internal
+
+} // end namespace Eigen
diff --git a/unsupported/Eigen/src/FFT/ei_imklfft_impl.h b/unsupported/Eigen/src/FFT/ei_imklfft_impl.h
new file mode 100644
index 0000000..186a66c
--- /dev/null
+++ b/unsupported/Eigen/src/FFT/ei_imklfft_impl.h
@@ -0,0 +1,288 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include <mkl_dfti.h>
+
+#include "./InternalHeaderCheck.h"
+
+#include <complex>
+
+namespace Eigen {
+namespace internal {
+namespace imklfft {
+
+#define RUN_OR_ASSERT(EXPR, ERROR_MSG) \
+ { \
+ MKL_LONG status = (EXPR); \
+ eigen_assert(status == DFTI_NO_ERROR && (ERROR_MSG)); \
+ };
+
+inline MKL_Complex16* complex_cast(const std::complex<double>* p) {
+ return const_cast<MKL_Complex16*>(reinterpret_cast<const MKL_Complex16*>(p));
+}
+
+inline MKL_Complex8* complex_cast(const std::complex<float>* p) {
+ return const_cast<MKL_Complex8*>(reinterpret_cast<const MKL_Complex8*>(p));
+}
+
+/*
+ * Parameters:
+ * precision: enum, Precision of the transform: DFTI_SINGLE or DFTI_DOUBLE.
+ * forward_domain: enum, Forward domain of the transform: DFTI_COMPLEX or
+ * DFTI_REAL. dimension: MKL_LONG Dimension of the transform. sizes: MKL_LONG if
+ * dimension = 1.Length of the transform for a one-dimensional transform. sizes:
+ * Array of type MKL_LONG otherwise. Lengths of each dimension for a
+ * multi-dimensional transform.
+ */
+inline void configure_descriptor(DFTI_DESCRIPTOR_HANDLE* handl,
+ enum DFTI_CONFIG_VALUE precision,
+ enum DFTI_CONFIG_VALUE forward_domain,
+ MKL_LONG dimension, MKL_LONG* sizes) {
+ eigen_assert(dimension == 1 ||
+ dimension == 2 &&
+ "Transformation dimension must be less than 3.");
+
+ if (dimension == 1) {
+ RUN_OR_ASSERT(DftiCreateDescriptor(handl, precision, forward_domain,
+ dimension, *sizes),
+ "DftiCreateDescriptor failed.")
+ if (forward_domain == DFTI_REAL) {
+ // Set CCE storage
+ RUN_OR_ASSERT(DftiSetValue(*handl, DFTI_CONJUGATE_EVEN_STORAGE,
+ DFTI_COMPLEX_COMPLEX),
+ "DftiSetValue failed.")
+ }
+ } else {
+ RUN_OR_ASSERT(
+ DftiCreateDescriptor(handl, precision, DFTI_COMPLEX, dimension, sizes),
+ "DftiCreateDescriptor failed.")
+ }
+
+ RUN_OR_ASSERT(DftiSetValue(*handl, DFTI_PLACEMENT, DFTI_NOT_INPLACE),
+ "DftiSetValue failed.")
+ RUN_OR_ASSERT(DftiCommitDescriptor(*handl), "DftiCommitDescriptor failed.")
+}
+
+template <typename T>
+struct plan {};
+
+template <>
+struct plan<float> {
+ typedef float scalar_type;
+ typedef MKL_Complex8 complex_type;
+
+ DFTI_DESCRIPTOR_HANDLE m_plan;
+
+ plan() : m_plan(0) {}
+ ~plan() {
+ if (m_plan) DftiFreeDescriptor(&m_plan);
+ };
+
+ enum DFTI_CONFIG_VALUE precision = DFTI_SINGLE;
+
+ inline void forward(complex_type* dst, complex_type* src, MKL_LONG nfft) {
+ if (m_plan == 0) {
+ configure_descriptor(&m_plan, precision, DFTI_COMPLEX, 1, &nfft);
+ }
+ RUN_OR_ASSERT(DftiComputeForward(m_plan, src, dst),
+ "DftiComputeForward failed.")
+ }
+
+ inline void inverse(complex_type* dst, complex_type* src, MKL_LONG nfft) {
+ if (m_plan == 0) {
+ configure_descriptor(&m_plan, precision, DFTI_COMPLEX, 1, &nfft);
+ }
+ RUN_OR_ASSERT(DftiComputeBackward(m_plan, src, dst),
+ "DftiComputeBackward failed.")
+ }
+
+ inline void forward(complex_type* dst, scalar_type* src, MKL_LONG nfft) {
+ if (m_plan == 0) {
+ configure_descriptor(&m_plan, precision, DFTI_REAL, 1, &nfft);
+ }
+ RUN_OR_ASSERT(DftiComputeForward(m_plan, src, dst),
+ "DftiComputeForward failed.")
+ }
+
+ inline void inverse(scalar_type* dst, complex_type* src, MKL_LONG nfft) {
+ if (m_plan == 0) {
+ configure_descriptor(&m_plan, precision, DFTI_REAL, 1, &nfft);
+ }
+ RUN_OR_ASSERT(DftiComputeBackward(m_plan, src, dst),
+ "DftiComputeBackward failed.")
+ }
+
+ inline void forward2(complex_type* dst, complex_type* src, int n0, int n1) {
+ if (m_plan == 0) {
+ MKL_LONG sizes[2] = {n0, n1};
+ configure_descriptor(&m_plan, precision, DFTI_COMPLEX, 2, sizes);
+ }
+ RUN_OR_ASSERT(DftiComputeForward(m_plan, src, dst),
+ "DftiComputeForward failed.")
+ }
+
+ inline void inverse2(complex_type* dst, complex_type* src, int n0, int n1) {
+ if (m_plan == 0) {
+ MKL_LONG sizes[2] = {n0, n1};
+ configure_descriptor(&m_plan, precision, DFTI_COMPLEX, 2, sizes);
+ }
+ RUN_OR_ASSERT(DftiComputeBackward(m_plan, src, dst),
+ "DftiComputeBackward failed.")
+ }
+};
+
+template <>
+struct plan<double> {
+ typedef double scalar_type;
+ typedef MKL_Complex16 complex_type;
+
+ DFTI_DESCRIPTOR_HANDLE m_plan;
+
+ plan() : m_plan(0) {}
+ ~plan() {
+ if (m_plan) DftiFreeDescriptor(&m_plan);
+ };
+
+ enum DFTI_CONFIG_VALUE precision = DFTI_DOUBLE;
+
+ inline void forward(complex_type* dst, complex_type* src, MKL_LONG nfft) {
+ if (m_plan == 0) {
+ configure_descriptor(&m_plan, precision, DFTI_COMPLEX, 1, &nfft);
+ }
+ RUN_OR_ASSERT(DftiComputeForward(m_plan, src, dst),
+ "DftiComputeForward failed.")
+ }
+
+ inline void inverse(complex_type* dst, complex_type* src, MKL_LONG nfft) {
+ if (m_plan == 0) {
+ configure_descriptor(&m_plan, precision, DFTI_COMPLEX, 1, &nfft);
+ }
+ RUN_OR_ASSERT(DftiComputeBackward(m_plan, src, dst),
+ "DftiComputeBackward failed.")
+ }
+
+ inline void forward(complex_type* dst, scalar_type* src, MKL_LONG nfft) {
+ if (m_plan == 0) {
+ configure_descriptor(&m_plan, precision, DFTI_REAL, 1, &nfft);
+ }
+ RUN_OR_ASSERT(DftiComputeForward(m_plan, src, dst),
+ "DftiComputeForward failed.")
+ }
+
+ inline void inverse(scalar_type* dst, complex_type* src, MKL_LONG nfft) {
+ if (m_plan == 0) {
+ configure_descriptor(&m_plan, precision, DFTI_REAL, 1, &nfft);
+ }
+ RUN_OR_ASSERT(DftiComputeBackward(m_plan, src, dst),
+ "DftiComputeBackward failed.")
+ }
+
+ inline void forward2(complex_type* dst, complex_type* src, int n0, int n1) {
+ if (m_plan == 0) {
+ MKL_LONG sizes[2] = {n0, n1};
+ configure_descriptor(&m_plan, precision, DFTI_COMPLEX, 2, sizes);
+ }
+ RUN_OR_ASSERT(DftiComputeForward(m_plan, src, dst),
+ "DftiComputeForward failed.")
+ }
+
+ inline void inverse2(complex_type* dst, complex_type* src, int n0, int n1) {
+ if (m_plan == 0) {
+ MKL_LONG sizes[2] = {n0, n1};
+ configure_descriptor(&m_plan, precision, DFTI_COMPLEX, 2, sizes);
+ }
+ RUN_OR_ASSERT(DftiComputeBackward(m_plan, src, dst),
+ "DftiComputeBackward failed.")
+ }
+};
+
+template <typename Scalar_>
+struct imklfft_impl {
+ typedef Scalar_ Scalar;
+ typedef std::complex<Scalar> Complex;
+
+ inline void clear() { m_plans.clear(); }
+
+ // complex-to-complex forward FFT
+ inline void fwd(Complex* dst, const Complex* src, int nfft) {
+ MKL_LONG size = nfft;
+ get_plan(nfft, dst, src)
+ .forward(complex_cast(dst), complex_cast(src), size);
+ }
+
+ // real-to-complex forward FFT
+ inline void fwd(Complex* dst, const Scalar* src, int nfft) {
+ MKL_LONG size = nfft;
+ get_plan(nfft, dst, src)
+ .forward(complex_cast(dst), const_cast<Scalar*>(src), nfft);
+ }
+
+ // 2-d complex-to-complex
+ inline void fwd2(Complex* dst, const Complex* src, int n0, int n1) {
+ get_plan(n0, n1, dst, src)
+ .forward2(complex_cast(dst), complex_cast(src), n0, n1);
+ }
+
+ // inverse complex-to-complex
+ inline void inv(Complex* dst, const Complex* src, int nfft) {
+ MKL_LONG size = nfft;
+ get_plan(nfft, dst, src)
+ .inverse(complex_cast(dst), complex_cast(src), nfft);
+ }
+
+ // half-complex to scalar
+ inline void inv(Scalar* dst, const Complex* src, int nfft) {
+ MKL_LONG size = nfft;
+ get_plan(nfft, dst, src)
+ .inverse(const_cast<Scalar*>(dst), complex_cast(src), nfft);
+ }
+
+ // 2-d complex-to-complex
+ inline void inv2(Complex* dst, const Complex* src, int n0, int n1) {
+ get_plan(n0, n1, dst, src)
+ .inverse2(complex_cast(dst), complex_cast(src), n0, n1);
+ }
+
+ private:
+ std::map<int64_t, plan<Scalar>> m_plans;
+
+ inline plan<Scalar>& get_plan(int nfft, void* dst,
+ const void* src) {
+ int inplace = dst == src ? 1 : 0;
+ int aligned = ((reinterpret_cast<size_t>(src) & 15) |
+ (reinterpret_cast<size_t>(dst) & 15)) == 0
+ ? 1
+ : 0;
+ int64_t key = ((nfft << 2) | (inplace << 1) | aligned)
+ << 1;
+
+ // Create element if key does not exist.
+ return m_plans[key];
+ }
+
+ inline plan<Scalar>& get_plan(int n0, int n1, void* dst,
+ const void* src) {
+ int inplace = (dst == src) ? 1 : 0;
+ int aligned = ((reinterpret_cast<size_t>(src) & 15) |
+ (reinterpret_cast<size_t>(dst) & 15)) == 0
+ ? 1
+ : 0;
+ int64_t key = (((((int64_t)n0) << 31) | (n1 << 2) |
+ (inplace << 1) | aligned)
+ << 1) +
+ 1;
+
+ // Create element if key does not exist.
+ return m_plans[key];
+ }
+};
+
+#undef RUN_OR_ASSERT
+
+} // namespace imklfft
+} // namespace internal
+} // namespace Eigen
diff --git a/unsupported/Eigen/src/FFT/ei_kissfft_impl.h b/unsupported/Eigen/src/FFT/ei_kissfft_impl.h
new file mode 100644
index 0000000..90e6690
--- /dev/null
+++ b/unsupported/Eigen/src/FFT/ei_kissfft_impl.h
@@ -0,0 +1,451 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009 Mark Borgerding mark a borgerding net
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+
+ // This FFT implementation was derived from kissfft http:sourceforge.net/projects/kissfft
+ // Copyright 2003-2009 Mark Borgerding
+
+template <typename Scalar_>
+struct kiss_cpx_fft
+{
+ typedef Scalar_ Scalar;
+ typedef std::complex<Scalar> Complex;
+ std::vector<Complex> m_twiddles;
+ std::vector<int> m_stageRadix;
+ std::vector<int> m_stageRemainder;
+ std::vector<Complex> m_scratchBuf;
+ bool m_inverse;
+
+ inline void make_twiddles(int nfft, bool inverse)
+ {
+ using numext::sin;
+ using numext::cos;
+ m_inverse = inverse;
+ m_twiddles.resize(nfft);
+ double phinc = 0.25 * double(EIGEN_PI) / nfft;
+ Scalar flip = inverse ? Scalar(1) : Scalar(-1);
+ m_twiddles[0] = Complex(Scalar(1), Scalar(0));
+ if ((nfft&1)==0)
+ m_twiddles[nfft/2] = Complex(Scalar(-1), Scalar(0));
+ int i=1;
+ for (;i*8<nfft;++i)
+ {
+ Scalar c = Scalar(cos(i*8*phinc));
+ Scalar s = Scalar(sin(i*8*phinc));
+ m_twiddles[i] = Complex(c, s*flip);
+ m_twiddles[nfft-i] = Complex(c, -s*flip);
+ }
+ for (;i*4<nfft;++i)
+ {
+ Scalar c = Scalar(cos((2*nfft-8*i)*phinc));
+ Scalar s = Scalar(sin((2*nfft-8*i)*phinc));
+ m_twiddles[i] = Complex(s, c*flip);
+ m_twiddles[nfft-i] = Complex(s, -c*flip);
+ }
+ for (;i*8<3*nfft;++i)
+ {
+ Scalar c = Scalar(cos((8*i-2*nfft)*phinc));
+ Scalar s = Scalar(sin((8*i-2*nfft)*phinc));
+ m_twiddles[i] = Complex(-s, c*flip);
+ m_twiddles[nfft-i] = Complex(-s, -c*flip);
+ }
+ for (;i*2<nfft;++i)
+ {
+ Scalar c = Scalar(cos((4*nfft-8*i)*phinc));
+ Scalar s = Scalar(sin((4*nfft-8*i)*phinc));
+ m_twiddles[i] = Complex(-c, s*flip);
+ m_twiddles[nfft-i] = Complex(-c, -s*flip);
+ }
+ }
+
+ void factorize(int nfft)
+ {
+ //start factoring out 4's, then 2's, then 3,5,7,9,...
+ int n= nfft;
+ int p=4;
+ do {
+ while (n % p) {
+ switch (p) {
+ case 4: p = 2; break;
+ case 2: p = 3; break;
+ default: p += 2; break;
+ }
+ if (p*p>n)
+ p=n;// impossible to have a factor > sqrt(n)
+ }
+ n /= p;
+ m_stageRadix.push_back(p);
+ m_stageRemainder.push_back(n);
+ if ( p > 5 )
+ m_scratchBuf.resize(p); // scratchbuf will be needed in bfly_generic
+ }while(n>1);
+ }
+
+ template <typename Src_>
+ inline
+ void work( int stage,Complex * xout, const Src_ * xin, size_t fstride,size_t in_stride)
+ {
+ int p = m_stageRadix[stage];
+ int m = m_stageRemainder[stage];
+ Complex * Fout_beg = xout;
+ Complex * Fout_end = xout + p*m;
+
+ if (m>1) {
+ do{
+ // recursive call:
+ // DFT of size m*p performed by doing
+ // p instances of smaller DFTs of size m,
+ // each one takes a decimated version of the input
+ work(stage+1, xout , xin, fstride*p,in_stride);
+ xin += fstride*in_stride;
+ }while( (xout += m) != Fout_end );
+ }else{
+ do{
+ *xout = *xin;
+ xin += fstride*in_stride;
+ }while(++xout != Fout_end );
+ }
+ xout=Fout_beg;
+
+ // recombine the p smaller DFTs
+ switch (p) {
+ case 2: bfly2(xout,fstride,m); break;
+ case 3: bfly3(xout,fstride,m); break;
+ case 4: bfly4(xout,fstride,m); break;
+ case 5: bfly5(xout,fstride,m); break;
+ default: bfly_generic(xout,fstride,m,p); break;
+ }
+ }
+
+ inline
+ void bfly2( Complex * Fout, const size_t fstride, int m)
+ {
+ for (int k=0;k<m;++k) {
+ Complex t = Fout[m+k] * m_twiddles[k*fstride];
+ Fout[m+k] = Fout[k] - t;
+ Fout[k] += t;
+ }
+ }
+
+ inline
+ void bfly4( Complex * Fout, const size_t fstride, const size_t m)
+ {
+ Complex scratch[6];
+ int negative_if_inverse = m_inverse * -2 +1;
+ for (size_t k=0;k<m;++k) {
+ scratch[0] = Fout[k+m] * m_twiddles[k*fstride];
+ scratch[1] = Fout[k+2*m] * m_twiddles[k*fstride*2];
+ scratch[2] = Fout[k+3*m] * m_twiddles[k*fstride*3];
+ scratch[5] = Fout[k] - scratch[1];
+
+ Fout[k] += scratch[1];
+ scratch[3] = scratch[0] + scratch[2];
+ scratch[4] = scratch[0] - scratch[2];
+ scratch[4] = Complex( scratch[4].imag()*negative_if_inverse , -scratch[4].real()* negative_if_inverse );
+
+ Fout[k+2*m] = Fout[k] - scratch[3];
+ Fout[k] += scratch[3];
+ Fout[k+m] = scratch[5] + scratch[4];
+ Fout[k+3*m] = scratch[5] - scratch[4];
+ }
+ }
+
+ inline
+ void bfly3( Complex * Fout, const size_t fstride, const size_t m)
+ {
+ size_t k=m;
+ const size_t m2 = 2*m;
+ Complex *tw1,*tw2;
+ Complex scratch[5];
+ Complex epi3;
+ epi3 = m_twiddles[fstride*m];
+
+ tw1=tw2=&m_twiddles[0];
+
+ do{
+ scratch[1]=Fout[m] * *tw1;
+ scratch[2]=Fout[m2] * *tw2;
+
+ scratch[3]=scratch[1]+scratch[2];
+ scratch[0]=scratch[1]-scratch[2];
+ tw1 += fstride;
+ tw2 += fstride*2;
+ Fout[m] = Complex( Fout->real() - Scalar(.5)*scratch[3].real() , Fout->imag() - Scalar(.5)*scratch[3].imag() );
+ scratch[0] *= epi3.imag();
+ *Fout += scratch[3];
+ Fout[m2] = Complex( Fout[m].real() + scratch[0].imag() , Fout[m].imag() - scratch[0].real() );
+ Fout[m] += Complex( -scratch[0].imag(),scratch[0].real() );
+ ++Fout;
+ }while(--k);
+ }
+
+ inline
+ void bfly5( Complex * Fout, const size_t fstride, const size_t m)
+ {
+ Complex *Fout0,*Fout1,*Fout2,*Fout3,*Fout4;
+ size_t u;
+ Complex scratch[13];
+ Complex * twiddles = &m_twiddles[0];
+ Complex *tw;
+ Complex ya,yb;
+ ya = twiddles[fstride*m];
+ yb = twiddles[fstride*2*m];
+
+ Fout0=Fout;
+ Fout1=Fout0+m;
+ Fout2=Fout0+2*m;
+ Fout3=Fout0+3*m;
+ Fout4=Fout0+4*m;
+
+ tw=twiddles;
+ for ( u=0; u<m; ++u ) {
+ scratch[0] = *Fout0;
+
+ scratch[1] = *Fout1 * tw[u*fstride];
+ scratch[2] = *Fout2 * tw[2*u*fstride];
+ scratch[3] = *Fout3 * tw[3*u*fstride];
+ scratch[4] = *Fout4 * tw[4*u*fstride];
+
+ scratch[7] = scratch[1] + scratch[4];
+ scratch[10] = scratch[1] - scratch[4];
+ scratch[8] = scratch[2] + scratch[3];
+ scratch[9] = scratch[2] - scratch[3];
+
+ *Fout0 += scratch[7];
+ *Fout0 += scratch[8];
+
+ scratch[5] = scratch[0] + Complex(
+ (scratch[7].real()*ya.real() ) + (scratch[8].real() *yb.real() ),
+ (scratch[7].imag()*ya.real()) + (scratch[8].imag()*yb.real())
+ );
+
+ scratch[6] = Complex(
+ (scratch[10].imag()*ya.imag()) + (scratch[9].imag()*yb.imag()),
+ -(scratch[10].real()*ya.imag()) - (scratch[9].real()*yb.imag())
+ );
+
+ *Fout1 = scratch[5] - scratch[6];
+ *Fout4 = scratch[5] + scratch[6];
+
+ scratch[11] = scratch[0] +
+ Complex(
+ (scratch[7].real()*yb.real()) + (scratch[8].real()*ya.real()),
+ (scratch[7].imag()*yb.real()) + (scratch[8].imag()*ya.real())
+ );
+
+ scratch[12] = Complex(
+ -(scratch[10].imag()*yb.imag()) + (scratch[9].imag()*ya.imag()),
+ (scratch[10].real()*yb.imag()) - (scratch[9].real()*ya.imag())
+ );
+
+ *Fout2=scratch[11]+scratch[12];
+ *Fout3=scratch[11]-scratch[12];
+
+ ++Fout0;++Fout1;++Fout2;++Fout3;++Fout4;
+ }
+ }
+
+ /* perform the butterfly for one stage of a mixed radix FFT */
+ inline
+ void bfly_generic(
+ Complex * Fout,
+ const size_t fstride,
+ int m,
+ int p
+ )
+ {
+ int u,k,q1,q;
+ Complex * twiddles = &m_twiddles[0];
+ Complex t;
+ int Norig = static_cast<int>(m_twiddles.size());
+ Complex * scratchbuf = &m_scratchBuf[0];
+
+ for ( u=0; u<m; ++u ) {
+ k=u;
+ for ( q1=0 ; q1<p ; ++q1 ) {
+ scratchbuf[q1] = Fout[ k ];
+ k += m;
+ }
+
+ k=u;
+ for ( q1=0 ; q1<p ; ++q1 ) {
+ int twidx=0;
+ Fout[ k ] = scratchbuf[0];
+ for (q=1;q<p;++q ) {
+ twidx += static_cast<int>(fstride) * k;
+ if (twidx>=Norig) twidx-=Norig;
+ t=scratchbuf[q] * twiddles[twidx];
+ Fout[ k ] += t;
+ }
+ k += m;
+ }
+ }
+ }
+};
+
+template <typename Scalar_>
+struct kissfft_impl
+{
+ typedef Scalar_ Scalar;
+ typedef std::complex<Scalar> Complex;
+
+ void clear()
+ {
+ m_plans.clear();
+ m_realTwiddles.clear();
+ }
+
+ inline
+ void fwd( Complex * dst,const Complex *src,int nfft)
+ {
+ get_plan(nfft,false).work(0, dst, src, 1,1);
+ }
+
+ inline
+ void fwd2( Complex * dst,const Complex *src,int n0,int n1)
+ {
+ EIGEN_UNUSED_VARIABLE(dst);
+ EIGEN_UNUSED_VARIABLE(src);
+ EIGEN_UNUSED_VARIABLE(n0);
+ EIGEN_UNUSED_VARIABLE(n1);
+ }
+
+ inline
+ void inv2( Complex * dst,const Complex *src,int n0,int n1)
+ {
+ EIGEN_UNUSED_VARIABLE(dst);
+ EIGEN_UNUSED_VARIABLE(src);
+ EIGEN_UNUSED_VARIABLE(n0);
+ EIGEN_UNUSED_VARIABLE(n1);
+ }
+
+ // real-to-complex forward FFT
+ // perform two FFTs of src even and src odd
+ // then twiddle to recombine them into the half-spectrum format
+ // then fill in the conjugate symmetric half
+ inline
+ void fwd( Complex * dst,const Scalar * src,int nfft)
+ {
+ if ( nfft&3 ) {
+ // use generic mode for odd
+ m_tmpBuf1.resize(nfft);
+ get_plan(nfft,false).work(0, &m_tmpBuf1[0], src, 1,1);
+ std::copy(m_tmpBuf1.begin(),m_tmpBuf1.begin()+(nfft>>1)+1,dst );
+ }else{
+ int ncfft = nfft>>1;
+ int ncfft2 = nfft>>2;
+ Complex * rtw = real_twiddles(ncfft2);
+
+ // use optimized mode for even real
+ fwd( dst, reinterpret_cast<const Complex*> (src), ncfft);
+ Complex dc(dst[0].real() + dst[0].imag());
+ Complex nyquist(dst[0].real() - dst[0].imag());
+ int k;
+ for ( k=1;k <= ncfft2 ; ++k ) {
+ Complex fpk = dst[k];
+ Complex fpnk = conj(dst[ncfft-k]);
+ Complex f1k = fpk + fpnk;
+ Complex f2k = fpk - fpnk;
+ Complex tw= f2k * rtw[k-1];
+ dst[k] = (f1k + tw) * Scalar(.5);
+ dst[ncfft-k] = conj(f1k -tw)*Scalar(.5);
+ }
+ dst[0] = dc;
+ dst[ncfft] = nyquist;
+ }
+ }
+
+ // inverse complex-to-complex
+ inline
+ void inv(Complex * dst,const Complex *src,int nfft)
+ {
+ get_plan(nfft,true).work(0, dst, src, 1,1);
+ }
+
+ // half-complex to scalar
+ inline
+ void inv( Scalar * dst,const Complex * src,int nfft)
+ {
+ if (nfft&3) {
+ m_tmpBuf1.resize(nfft);
+ m_tmpBuf2.resize(nfft);
+ std::copy(src,src+(nfft>>1)+1,m_tmpBuf1.begin() );
+ for (int k=1;k<(nfft>>1)+1;++k)
+ m_tmpBuf1[nfft-k] = conj(m_tmpBuf1[k]);
+ inv(&m_tmpBuf2[0],&m_tmpBuf1[0],nfft);
+ for (int k=0;k<nfft;++k)
+ dst[k] = m_tmpBuf2[k].real();
+ }else{
+ // optimized version for multiple of 4
+ int ncfft = nfft>>1;
+ int ncfft2 = nfft>>2;
+ Complex * rtw = real_twiddles(ncfft2);
+ m_tmpBuf1.resize(ncfft);
+ m_tmpBuf1[0] = Complex( src[0].real() + src[ncfft].real(), src[0].real() - src[ncfft].real() );
+ for (int k = 1; k <= ncfft / 2; ++k) {
+ Complex fk = src[k];
+ Complex fnkc = conj(src[ncfft-k]);
+ Complex fek = fk + fnkc;
+ Complex tmp = fk - fnkc;
+ Complex fok = tmp * conj(rtw[k-1]);
+ m_tmpBuf1[k] = fek + fok;
+ m_tmpBuf1[ncfft-k] = conj(fek - fok);
+ }
+ get_plan(ncfft,true).work(0, reinterpret_cast<Complex*>(dst), &m_tmpBuf1[0], 1,1);
+ }
+ }
+
+ protected:
+ typedef kiss_cpx_fft<Scalar> PlanData;
+ typedef std::map<int,PlanData> PlanMap;
+
+ PlanMap m_plans;
+ std::map<int, std::vector<Complex> > m_realTwiddles;
+ std::vector<Complex> m_tmpBuf1;
+ std::vector<Complex> m_tmpBuf2;
+
+ inline
+ int PlanKey(int nfft, bool isinverse) const { return (nfft<<1) | int(isinverse); }
+
+ inline
+ PlanData & get_plan(int nfft, bool inverse)
+ {
+ // TODO look for PlanKey(nfft, ! inverse) and conjugate the twiddles
+ PlanData & pd = m_plans[ PlanKey(nfft,inverse) ];
+ if ( pd.m_twiddles.size() == 0 ) {
+ pd.make_twiddles(nfft,inverse);
+ pd.factorize(nfft);
+ }
+ return pd;
+ }
+
+ inline
+ Complex * real_twiddles(int ncfft2)
+ {
+ using std::acos;
+ std::vector<Complex> & twidref = m_realTwiddles[ncfft2];// creates new if not there
+ if ( (int)twidref.size() != ncfft2 ) {
+ twidref.resize(ncfft2);
+ int ncfft= ncfft2<<1;
+ Scalar pi = acos( Scalar(-1) );
+ for (int k=1;k<=ncfft2;++k)
+ twidref[k-1] = exp( Complex(0,-pi * (Scalar(k) / ncfft + Scalar(.5)) ) );
+ }
+ return &twidref[0];
+ }
+};
+
+} // end namespace internal
+
+} // end namespace Eigen
diff --git a/unsupported/Eigen/src/FFT/ei_pocketfft_impl.h b/unsupported/Eigen/src/FFT/ei_pocketfft_impl.h
new file mode 100644
index 0000000..f2da890
--- /dev/null
+++ b/unsupported/Eigen/src/FFT/ei_pocketfft_impl.h
@@ -0,0 +1,69 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+using namespace pocketfft;
+using namespace pocketfft::detail;
+
+namespace Eigen {
+
+namespace internal {
+
+template<typename _Scalar>
+struct pocketfft_impl
+{
+ typedef _Scalar Scalar;
+ typedef std::complex<Scalar> Complex;
+
+ inline void clear() {}
+
+ inline void fwd(Complex* dst, const Scalar* src, int nfft){
+ const shape_t shape_{ static_cast<size_t>(nfft) };
+ const shape_t axes_{ 0 };
+ const stride_t stride_in{ sizeof(Scalar) };
+ const stride_t stride_out{ sizeof(Complex) };
+ r2c(shape_, stride_in, stride_out, axes_, FORWARD, src, dst, static_cast<Scalar>(1));
+ }
+
+ inline void fwd(Complex* dst, const Complex* src, int nfft){
+ const shape_t shape_{ static_cast<size_t>(nfft) };
+ const shape_t axes_{ 0 };
+ const stride_t stride_{ sizeof(Complex) };
+ c2c(shape_, stride_, stride_, axes_, FORWARD, src, dst, static_cast<Scalar>(1));
+ }
+
+ inline void inv(Scalar* dst, const Complex* src, int nfft){
+ const shape_t shape_{ static_cast<size_t>(nfft) };
+ const shape_t axes_{ 0 };
+ const stride_t stride_in{ sizeof(Complex) };
+ const stride_t stride_out{ sizeof(Scalar) };
+ c2r(shape_, stride_in, stride_out, axes_, BACKWARD, src, dst, static_cast<Scalar>(1));
+ }
+
+ inline void inv(Complex* dst, const Complex* src, int nfft){
+ const shape_t shape_{ static_cast<size_t>(nfft) };
+ const shape_t axes_{ 0 };
+ const stride_t stride_{ sizeof(Complex) };
+ c2c(shape_, stride_, stride_, axes_, BACKWARD, src, dst, static_cast<Scalar>(1));
+ }
+
+ inline void fwd2(Complex* dst, const Complex* src, int nfft0, int nfft1){
+ const shape_t shape_{ static_cast<size_t>(nfft0), static_cast<size_t>(nfft1) };
+ const shape_t axes_{ 0, 1 };
+ const stride_t stride_{ static_cast<ptrdiff_t>(sizeof(Complex)*nfft1), static_cast<ptrdiff_t>(sizeof(Complex)) };
+ c2c(shape_, stride_, stride_, axes_, FORWARD, src, dst, static_cast<Scalar>(1));
+ }
+
+ inline void inv2(Complex* dst, const Complex* src, int nfft0, int nfft1){
+ const shape_t shape_{ static_cast<size_t>(nfft0), static_cast<size_t>(nfft1) };
+ const shape_t axes_{ 0, 1 };
+ const stride_t stride_{ static_cast<ptrdiff_t>(sizeof(Complex)*nfft1), static_cast<ptrdiff_t>(sizeof(Complex)) };
+ c2c(shape_, stride_, stride_, axes_, BACKWARD, src, dst, static_cast<Scalar>(1));
+ }
+};
+
+} // namespace internal
+} // namespace Eigen
diff --git a/unsupported/Eigen/src/IterativeSolvers/BiCGSTABL.h b/unsupported/Eigen/src/IterativeSolvers/BiCGSTABL.h
new file mode 100644
index 0000000..141d705
--- /dev/null
+++ b/unsupported/Eigen/src/IterativeSolvers/BiCGSTABL.h
@@ -0,0 +1,339 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2020 Chris Schoutrop <c.e.m.schoutrop@tue.nl>
+// Copyright (C) 2020 Jens Wehner <j.wehner@esciencecenter.nl>
+// Copyright (C) 2020 Jan van Dijk <j.v.dijk@tue.nl>
+// Copyright (C) 2020 Adithya Vijaykumar
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+/*
+
+ This implementation of BiCGStab(L) is based on the papers
+ General algorithm:
+ 1. G.L.G. Sleijpen, D.R. Fokkema. (1993). BiCGstab(l) for linear equations
+ involving unsymmetric matrices with complex spectrum. Electronic Transactions
+ on Numerical Analysis. Polynomial step update:
+ 2. G.L.G. Sleijpen, M.B. Van Gijzen. (2010) Exploiting BiCGstab(l)
+ strategies to induce dimension reduction SIAM Journal on Scientific Computing.
+ 3. Fokkema, Diederik R. Enhanced implementation of BiCGstab (l) for
+ solving linear systems of equations. Universiteit Utrecht. Mathematisch
+ Instituut, 1996
+ 4. Sleijpen, G. L., & van der Vorst, H. A. (1996). Reliable updated
+ residuals in hybrid Bi-CG methods. Computing, 56(2), 141-163.
+*/
+
+#ifndef EIGEN_BICGSTABL_H
+#define EIGEN_BICGSTABL_H
+
+namespace Eigen {
+
+namespace internal {
+/** \internal Low-level bi conjugate gradient stabilized algorithm with L
+ additional residual minimization steps \param mat The matrix A \param rhs The
+ right hand side vector b \param x On input and initial solution, on output
+ the computed solution. \param precond A preconditioner being able to
+ efficiently solve for an approximation of Ax=b (regardless of b) \param iters
+ On input the max number of iteration, on output the number of performed
+ iterations. \param tol_error On input the tolerance error, on output an
+ estimation of the relative error. \param L On input Number of additional
+ GMRES steps to take. If L is too large (~20) instabilities occur. \return
+ false in the case of numerical issue, for example a break down of BiCGSTABL.
+*/
+template <typename MatrixType, typename Rhs, typename Dest, typename Preconditioner>
+bool bicgstabl(const MatrixType &mat, const Rhs &rhs, Dest &x, const Preconditioner &precond, Index &iters,
+ typename Dest::RealScalar &tol_error, Index L) {
+ using numext::abs;
+ using numext::sqrt;
+ typedef typename Dest::RealScalar RealScalar;
+ typedef typename Dest::Scalar Scalar;
+ const Index N = rhs.size();
+ L = L < x.rows() ? L : x.rows();
+
+ Index k = 0;
+
+ const RealScalar tol = tol_error;
+ const Index maxIters = iters;
+
+ typedef Matrix<Scalar, Dynamic, 1> VectorType;
+ typedef Matrix<Scalar, Dynamic, Dynamic, ColMajor> DenseMatrixType;
+
+ DenseMatrixType rHat(N, L + 1);
+ DenseMatrixType uHat(N, L + 1);
+
+ // We start with an initial guess x_0 and let us set r_0 as (residual
+ // calculated from x_0)
+ VectorType x0 = x;
+ rHat.col(0) = rhs - mat * x0; // r_0
+
+ x.setZero(); // This will contain the updates to the solution.
+ // rShadow is arbritary, but must never be orthogonal to any residual.
+ VectorType rShadow = VectorType::Random(N);
+
+ VectorType x_prime = x;
+
+ // Redundant: x is already set to 0
+ // x.setZero();
+ VectorType b_prime = rHat.col(0);
+
+ // Other vectors and scalars initialization
+ Scalar rho0 = 1.0;
+ Scalar alpha = 0.0;
+ Scalar omega = 1.0;
+
+ uHat.col(0).setZero();
+
+ bool bicg_convergence = false;
+
+ const RealScalar normb = rhs.stableNorm();
+ if (internal::isApprox(normb, RealScalar(0))) {
+ x.setZero();
+ iters = 0;
+ return true;
+ }
+ RealScalar normr = rHat.col(0).stableNorm();
+ RealScalar Mx = normr;
+ RealScalar Mr = normr;
+
+ // Keep track of the solution with the lowest residual
+ RealScalar normr_min = normr;
+ VectorType x_min = x_prime + x;
+
+ // Criterion for when to apply the group-wise update, conform ref 3.
+ const RealScalar delta = 0.01;
+
+ bool compute_res = false;
+ bool update_app = false;
+
+ while (normr > tol * normb && k < maxIters) {
+ rho0 *= -omega;
+
+ for (Index j = 0; j < L; ++j) {
+ const Scalar rho1 = rShadow.dot(rHat.col(j));
+
+ if (!(numext::isfinite)(rho1) || rho0 == RealScalar(0.0)) {
+ // We cannot continue computing, return the best solution found.
+ x += x_prime;
+
+ // Check if x is better than the best stored solution thus far.
+ normr = (rhs - mat * (precond.solve(x) + x0)).stableNorm();
+
+ if (normr > normr_min || !(numext::isfinite)(normr)) {
+ // x_min is a better solution than x, return x_min
+ x = x_min;
+ normr = normr_min;
+ }
+ tol_error = normr / normb;
+ iters = k;
+ // x contains the updates to x0, add those back to obtain the solution
+ x = precond.solve(x);
+ x += x0;
+ return (normr < tol * normb);
+ }
+
+ const Scalar beta = alpha * (rho1 / rho0);
+ rho0 = rho1;
+ // Update search directions
+ uHat.leftCols(j + 1) = rHat.leftCols(j + 1) - beta * uHat.leftCols(j + 1);
+ uHat.col(j + 1) = mat * precond.solve(uHat.col(j));
+ const Scalar sigma = rShadow.dot(uHat.col(j + 1));
+ alpha = rho1 / sigma;
+ // Update residuals
+ rHat.leftCols(j + 1) -= alpha * uHat.middleCols(1, j + 1);
+ rHat.col(j + 1) = mat * precond.solve(rHat.col(j));
+ // Complete BiCG iteration by updating x
+ x += alpha * uHat.col(0);
+ normr = rHat.col(0).stableNorm();
+ // Check for early exit
+ if (normr < tol * normb) {
+ /*
+ Convergence was achieved during BiCG step.
+ Without this check BiCGStab(L) fails for trivial matrices, such as
+ when the preconditioner already is the inverse, or the input matrix is
+ identity.
+ */
+ bicg_convergence = true;
+ break;
+ } else if (normr < normr_min) {
+ // We found an x with lower residual, keep this one.
+ x_min = x + x_prime;
+ normr_min = normr;
+ }
+ }
+ if (!bicg_convergence) {
+ /*
+ The polynomial/minimize residual step.
+
+ QR Householder method for argmin is more stable than (modified)
+ Gram-Schmidt, in the sense that there is less loss of orthogonality. It
+ is more accurate than solving the normal equations, since the normal
+ equations scale with condition number squared.
+ */
+ const VectorType gamma = rHat.rightCols(L).householderQr().solve(rHat.col(0));
+ x += rHat.leftCols(L) * gamma;
+ rHat.col(0) -= rHat.rightCols(L) * gamma;
+ uHat.col(0) -= uHat.rightCols(L) * gamma;
+ normr = rHat.col(0).stableNorm();
+ omega = gamma(L - 1);
+ }
+ if (normr < normr_min) {
+ // We found an x with lower residual, keep this one.
+ x_min = x + x_prime;
+ normr_min = normr;
+ }
+
+ k++;
+
+ /*
+ Reliable update part
+
+ The recursively computed residual can deviate from the actual residual
+ after several iterations. However, computing the residual from the
+ definition costs extra MVs and should not be done at each iteration. The
+ reliable update strategy computes the true residual from the definition:
+ r=b-A*x at strategic intervals. Furthermore a "group wise update" strategy
+ is used to combine updates, which improves accuracy.
+ */
+
+ // Maximum norm of residuals since last update of x.
+ Mx = numext::maxi(Mx, normr);
+ // Maximum norm of residuals since last computation of the true residual.
+ Mr = numext::maxi(Mr, normr);
+
+ if (normr < delta * normb && normb <= Mx) {
+ update_app = true;
+ }
+
+ if (update_app || (normr < delta * Mr && normb <= Mr)) {
+ compute_res = true;
+ }
+
+ if (bicg_convergence) {
+ update_app = true;
+ compute_res = true;
+ bicg_convergence = false;
+ }
+
+ if (compute_res) {
+ // Explicitly compute residual from the definition
+
+ // This is equivalent to the shifted version of rhs - mat *
+ // (precond.solve(x)+x0)
+ rHat.col(0) = b_prime - mat * precond.solve(x);
+ normr = rHat.col(0).stableNorm();
+ Mr = normr;
+
+ if (update_app) {
+ // After the group wise update, the original problem is translated to a
+ // shifted one.
+ x_prime += x;
+ x.setZero();
+ b_prime = rHat.col(0);
+ Mx = normr;
+ }
+ }
+ if (normr < normr_min) {
+ // We found an x with lower residual, keep this one.
+ x_min = x + x_prime;
+ normr_min = normr;
+ }
+
+ compute_res = false;
+ update_app = false;
+ }
+
+ // Convert internal variable to the true solution vector x
+ x += x_prime;
+
+ normr = (rhs - mat * (precond.solve(x) + x0)).stableNorm();
+ if (normr > normr_min || !(numext::isfinite)(normr)) {
+ // x_min is a better solution than x, return x_min
+ x = x_min;
+ normr = normr_min;
+ }
+ tol_error = normr / normb;
+ iters = k;
+
+ // x contains the updates to x0, add those back to obtain the solution
+ x = precond.solve(x);
+ x += x0;
+ return true;
+}
+
+} // namespace internal
+
+template <typename MatrixType_, typename Preconditioner_ = DiagonalPreconditioner<typename MatrixType_::Scalar>>
+class BiCGSTABL;
+
+namespace internal {
+
+template <typename MatrixType_, typename Preconditioner_>
+struct traits<Eigen::BiCGSTABL<MatrixType_, Preconditioner_>> {
+ typedef MatrixType_ MatrixType;
+ typedef Preconditioner_ Preconditioner;
+};
+
+} // namespace internal
+
+template <typename MatrixType_, typename Preconditioner_>
+class BiCGSTABL : public IterativeSolverBase<BiCGSTABL<MatrixType_, Preconditioner_>> {
+ typedef IterativeSolverBase<BiCGSTABL> Base;
+ using Base::m_error;
+ using Base::m_info;
+ using Base::m_isInitialized;
+ using Base::m_iterations;
+ using Base::matrix;
+ Index m_L;
+
+ public:
+ typedef MatrixType_ MatrixType;
+ typedef typename MatrixType::Scalar Scalar;
+ typedef typename MatrixType::RealScalar RealScalar;
+ typedef Preconditioner_ Preconditioner;
+
+ /** Default constructor. */
+ BiCGSTABL() : m_L(2) {}
+
+ /**
+ Initialize the solver with matrix \a A for further \c Ax=b solving.
+
+ This constructor is a shortcut for the default constructor followed
+ by a call to compute().
+
+ \warning this class stores a reference to the matrix A as well as some
+ precomputed values that depend on it. Therefore, if \a A is changed
+ this class becomes invalid. Call compute() to update it with the new
+ matrix A, or modify a copy of A.
+ */
+ template <typename MatrixDerived>
+ explicit BiCGSTABL(const EigenBase<MatrixDerived> &A) : Base(A.derived()), m_L(2) {}
+
+ /** \internal */
+ /** Loops over the number of columns of b and does the following:
+ 1. sets the tolerence and maxIterations
+ 2. Calls the function that has the core solver routine
+ */
+ template <typename Rhs, typename Dest>
+ void _solve_vector_with_guess_impl(const Rhs &b, Dest &x) const {
+ m_iterations = Base::maxIterations();
+
+ m_error = Base::m_tolerance;
+
+ bool ret = internal::bicgstabl(matrix(), b, x, Base::m_preconditioner, m_iterations, m_error, m_L);
+ m_info = (!ret) ? NumericalIssue : m_error <= Base::m_tolerance ? Success : NoConvergence;
+ }
+
+ /** Sets the parameter L, indicating how many minimize residual steps are
+ * used. Default: 2 */
+ void setL(Index L) {
+ eigen_assert(L >= 1 && "L needs to be positive");
+ m_L = L;
+ }
+};
+
+} // namespace Eigen
+
+#endif /* EIGEN_BICGSTABL_H */
diff --git a/unsupported/Eigen/src/IterativeSolvers/DGMRES.h b/unsupported/Eigen/src/IterativeSolvers/DGMRES.h
new file mode 100644
index 0000000..0387ef3
--- /dev/null
+++ b/unsupported/Eigen/src/IterativeSolvers/DGMRES.h
@@ -0,0 +1,513 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2012 Désiré Nuentsa-Wakam <desire.nuentsa_wakam@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_DGMRES_H
+#define EIGEN_DGMRES_H
+
+#include "../../../../Eigen/Eigenvalues"
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+template< typename MatrixType_,
+ typename Preconditioner_ = DiagonalPreconditioner<typename MatrixType_::Scalar> >
+class DGMRES;
+
+namespace internal {
+
+template< typename MatrixType_, typename Preconditioner_>
+struct traits<DGMRES<MatrixType_,Preconditioner_> >
+{
+ typedef MatrixType_ MatrixType;
+ typedef Preconditioner_ Preconditioner;
+};
+
+/** \brief Computes a permutation vector to have a sorted sequence
+ * \param vec The vector to reorder.
+ * \param perm gives the sorted sequence on output. Must be initialized with 0..n-1
+ * \param ncut Put the ncut smallest elements at the end of the vector
+ * WARNING This is an expensive sort, so should be used only
+ * for small size vectors
+ * TODO Use modified QuickSplit or std::nth_element to get the smallest values
+ */
+template <typename VectorType, typename IndexType>
+void sortWithPermutation (VectorType& vec, IndexType& perm, typename IndexType::Scalar& ncut)
+{
+ eigen_assert(vec.size() == perm.size());
+ bool flag;
+ for (Index k = 0; k < ncut; k++)
+ {
+ flag = false;
+ for (Index j = 0; j < vec.size()-1; j++)
+ {
+ if ( vec(perm(j)) < vec(perm(j+1)) )
+ {
+ std::swap(perm(j),perm(j+1));
+ flag = true;
+ }
+ if (!flag) break; // The vector is in sorted order
+ }
+ }
+}
+
+}
+/**
+ * \ingroup IterativeLinearSolvers_Module
+ * \brief A Restarted GMRES with deflation.
+ * This class implements a modification of the GMRES solver for
+ * sparse linear systems. The basis is built with modified
+ * Gram-Schmidt. At each restart, a few approximated eigenvectors
+ * corresponding to the smallest eigenvalues are used to build a
+ * preconditioner for the next cycle. This preconditioner
+ * for deflation can be combined with any other preconditioner,
+ * the IncompleteLUT for instance. The preconditioner is applied
+ * at right of the matrix and the combination is multiplicative.
+ *
+ * \tparam MatrixType_ the type of the sparse matrix A, can be a dense or a sparse matrix.
+ * \tparam Preconditioner_ the type of the preconditioner. Default is DiagonalPreconditioner
+ * Typical usage :
+ * \code
+ * SparseMatrix<double> A;
+ * VectorXd x, b;
+ * //Fill A and b ...
+ * DGMRES<SparseMatrix<double> > solver;
+ * solver.set_restart(30); // Set restarting value
+ * solver.setEigenv(1); // Set the number of eigenvalues to deflate
+ * solver.compute(A);
+ * x = solver.solve(b);
+ * \endcode
+ *
+ * DGMRES can also be used in a matrix-free context, see the following \link MatrixfreeSolverExample example \endlink.
+ *
+ * References :
+ * [1] D. NUENTSA WAKAM and F. PACULL, Memory Efficient Hybrid
+ * Algebraic Solvers for Linear Systems Arising from Compressible
+ * Flows, Computers and Fluids, In Press,
+ * https://doi.org/10.1016/j.compfluid.2012.03.023
+ * [2] K. Burrage and J. Erhel, On the performance of various
+ * adaptive preconditioned GMRES strategies, 5(1998), 101-121.
+ * [3] J. Erhel, K. Burrage and B. Pohl, Restarted GMRES
+ * preconditioned by deflation,J. Computational and Applied
+ * Mathematics, 69(1996), 303-318.
+
+ *
+ */
+template< typename MatrixType_, typename Preconditioner_>
+class DGMRES : public IterativeSolverBase<DGMRES<MatrixType_,Preconditioner_> >
+{
+ typedef IterativeSolverBase<DGMRES> Base;
+ using Base::matrix;
+ using Base::m_error;
+ using Base::m_iterations;
+ using Base::m_info;
+ using Base::m_isInitialized;
+ using Base::m_tolerance;
+ public:
+ using Base::_solve_impl;
+ using Base::_solve_with_guess_impl;
+ typedef MatrixType_ MatrixType;
+ typedef typename MatrixType::Scalar Scalar;
+ typedef typename MatrixType::StorageIndex StorageIndex;
+ typedef typename MatrixType::RealScalar RealScalar;
+ typedef Preconditioner_ Preconditioner;
+ typedef Matrix<Scalar,Dynamic,Dynamic> DenseMatrix;
+ typedef Matrix<RealScalar,Dynamic,Dynamic> DenseRealMatrix;
+ typedef Matrix<Scalar,Dynamic,1> DenseVector;
+ typedef Matrix<RealScalar,Dynamic,1> DenseRealVector;
+ typedef Matrix<std::complex<RealScalar>, Dynamic, 1> ComplexVector;
+
+
+ /** Default constructor. */
+ DGMRES() : Base(),m_restart(30),m_neig(0),m_r(0),m_maxNeig(5),m_isDeflAllocated(false),m_isDeflInitialized(false) {}
+
+ /** Initialize the solver with matrix \a A for further \c Ax=b solving.
+ *
+ * This constructor is a shortcut for the default constructor followed
+ * by a call to compute().
+ *
+ * \warning this class stores a reference to the matrix A as well as some
+ * precomputed values that depend on it. Therefore, if \a A is changed
+ * this class becomes invalid. Call compute() to update it with the new
+ * matrix A, or modify a copy of A.
+ */
+ template<typename MatrixDerived>
+ explicit DGMRES(const EigenBase<MatrixDerived>& A) : Base(A.derived()), m_restart(30),m_neig(0),m_r(0),m_maxNeig(5),m_isDeflAllocated(false),m_isDeflInitialized(false) {}
+
+ ~DGMRES() {}
+
+ /** \internal */
+ template<typename Rhs,typename Dest>
+ void _solve_vector_with_guess_impl(const Rhs& b, Dest& x) const
+ {
+ EIGEN_STATIC_ASSERT(Rhs::ColsAtCompileTime==1 || Dest::ColsAtCompileTime==1, YOU_TRIED_CALLING_A_VECTOR_METHOD_ON_A_MATRIX);
+
+ m_iterations = Base::maxIterations();
+ m_error = Base::m_tolerance;
+
+ dgmres(matrix(), b, x, Base::m_preconditioner);
+ }
+
+ /**
+ * Get the restart value
+ */
+ Index restart() { return m_restart; }
+
+ /**
+ * Set the restart value (default is 30)
+ */
+ void set_restart(const Index restart) { m_restart=restart; }
+
+ /**
+ * Set the number of eigenvalues to deflate at each restart
+ */
+ void setEigenv(const Index neig)
+ {
+ m_neig = neig;
+ if (neig+1 > m_maxNeig) m_maxNeig = neig+1; // To allow for complex conjugates
+ }
+
+ /**
+ * Get the size of the deflation subspace size
+ */
+ Index deflSize() {return m_r; }
+
+ /**
+ * Set the maximum size of the deflation subspace
+ */
+ void setMaxEigenv(const Index maxNeig) { m_maxNeig = maxNeig; }
+
+ protected:
+ // DGMRES algorithm
+ template<typename Rhs, typename Dest>
+ void dgmres(const MatrixType& mat,const Rhs& rhs, Dest& x, const Preconditioner& precond) const;
+ // Perform one cycle of GMRES
+ template<typename Dest>
+ Index dgmresCycle(const MatrixType& mat, const Preconditioner& precond, Dest& x, DenseVector& r0, RealScalar& beta, const RealScalar& normRhs, Index& nbIts) const;
+ // Compute data to use for deflation
+ Index dgmresComputeDeflationData(const MatrixType& mat, const Preconditioner& precond, const Index& it, StorageIndex& neig) const;
+ // Apply deflation to a vector
+ template<typename RhsType, typename DestType>
+ Index dgmresApplyDeflation(const RhsType& In, DestType& Out) const;
+ ComplexVector schurValues(const ComplexSchur<DenseMatrix>& schurofH) const;
+ ComplexVector schurValues(const RealSchur<DenseMatrix>& schurofH) const;
+ // Init data for deflation
+ void dgmresInitDeflation(Index& rows) const;
+ mutable DenseMatrix m_V; // Krylov basis vectors
+ mutable DenseMatrix m_H; // Hessenberg matrix
+ mutable DenseMatrix m_Hes; // Initial hessenberg matrix without Givens rotations applied
+ mutable Index m_restart; // Maximum size of the Krylov subspace
+ mutable DenseMatrix m_U; // Vectors that form the basis of the invariant subspace
+ mutable DenseMatrix m_MU; // matrix operator applied to m_U (for next cycles)
+ mutable DenseMatrix m_T; /* T=U^T*M^{-1}*A*U */
+ mutable PartialPivLU<DenseMatrix> m_luT; // LU factorization of m_T
+ mutable StorageIndex m_neig; //Number of eigenvalues to extract at each restart
+ mutable Index m_r; // Current number of deflated eigenvalues, size of m_U
+ mutable Index m_maxNeig; // Maximum number of eigenvalues to deflate
+ mutable RealScalar m_lambdaN; //Modulus of the largest eigenvalue of A
+ mutable bool m_isDeflAllocated;
+ mutable bool m_isDeflInitialized;
+
+ //Adaptive strategy
+ mutable RealScalar m_smv; // Smaller multiple of the remaining number of steps allowed
+ mutable bool m_force; // Force the use of deflation at each restart
+
+};
+/**
+ * \brief Perform several cycles of restarted GMRES with modified Gram Schmidt,
+ *
+ * A right preconditioner is used combined with deflation.
+ *
+ */
+template< typename MatrixType_, typename Preconditioner_>
+template<typename Rhs, typename Dest>
+void DGMRES<MatrixType_, Preconditioner_>::dgmres(const MatrixType& mat,const Rhs& rhs, Dest& x,
+ const Preconditioner& precond) const
+{
+ const RealScalar considerAsZero = (std::numeric_limits<RealScalar>::min)();
+
+ RealScalar normRhs = rhs.norm();
+ if(normRhs <= considerAsZero)
+ {
+ x.setZero();
+ m_error = 0;
+ return;
+ }
+
+ //Initialization
+ m_isDeflInitialized = false;
+ Index n = mat.rows();
+ DenseVector r0(n);
+ Index nbIts = 0;
+ m_H.resize(m_restart+1, m_restart);
+ m_Hes.resize(m_restart, m_restart);
+ m_V.resize(n,m_restart+1);
+ //Initial residual vector and initial norm
+ if(x.squaredNorm()==0)
+ x = precond.solve(rhs);
+ r0 = rhs - mat * x;
+ RealScalar beta = r0.norm();
+
+ m_error = beta/normRhs;
+ if(m_error < m_tolerance)
+ m_info = Success;
+ else
+ m_info = NoConvergence;
+
+ // Iterative process
+ while (nbIts < m_iterations && m_info == NoConvergence)
+ {
+ dgmresCycle(mat, precond, x, r0, beta, normRhs, nbIts);
+
+ // Compute the new residual vector for the restart
+ if (nbIts < m_iterations && m_info == NoConvergence) {
+ r0 = rhs - mat * x;
+ beta = r0.norm();
+ }
+ }
+}
+
+/**
+ * \brief Perform one restart cycle of DGMRES
+ * \param mat The coefficient matrix
+ * \param precond The preconditioner
+ * \param x the new approximated solution
+ * \param r0 The initial residual vector
+ * \param beta The norm of the residual computed so far
+ * \param normRhs The norm of the right hand side vector
+ * \param nbIts The number of iterations
+ */
+template< typename MatrixType_, typename Preconditioner_>
+template<typename Dest>
+Index DGMRES<MatrixType_, Preconditioner_>::dgmresCycle(const MatrixType& mat, const Preconditioner& precond, Dest& x, DenseVector& r0, RealScalar& beta, const RealScalar& normRhs, Index& nbIts) const
+{
+ //Initialization
+ DenseVector g(m_restart+1); // Right hand side of the least square problem
+ g.setZero();
+ g(0) = Scalar(beta);
+ m_V.col(0) = r0/beta;
+ m_info = NoConvergence;
+ std::vector<JacobiRotation<Scalar> >gr(m_restart); // Givens rotations
+ Index it = 0; // Number of inner iterations
+ Index n = mat.rows();
+ DenseVector tv1(n), tv2(n); //Temporary vectors
+ while (m_info == NoConvergence && it < m_restart && nbIts < m_iterations)
+ {
+ // Apply preconditioner(s) at right
+ if (m_isDeflInitialized )
+ {
+ dgmresApplyDeflation(m_V.col(it), tv1); // Deflation
+ tv2 = precond.solve(tv1);
+ }
+ else
+ {
+ tv2 = precond.solve(m_V.col(it)); // User's selected preconditioner
+ }
+ tv1 = mat * tv2;
+
+ // Orthogonalize it with the previous basis in the basis using modified Gram-Schmidt
+ Scalar coef;
+ for (Index i = 0; i <= it; ++i)
+ {
+ coef = tv1.dot(m_V.col(i));
+ tv1 = tv1 - coef * m_V.col(i);
+ m_H(i,it) = coef;
+ m_Hes(i,it) = coef;
+ }
+ // Normalize the vector
+ coef = tv1.norm();
+ m_V.col(it+1) = tv1/coef;
+ m_H(it+1, it) = coef;
+// m_Hes(it+1,it) = coef;
+
+ // FIXME Check for happy breakdown
+
+ // Update Hessenberg matrix with Givens rotations
+ for (Index i = 1; i <= it; ++i)
+ {
+ m_H.col(it).applyOnTheLeft(i-1,i,gr[i-1].adjoint());
+ }
+ // Compute the new plane rotation
+ gr[it].makeGivens(m_H(it, it), m_H(it+1,it));
+ // Apply the new rotation
+ m_H.col(it).applyOnTheLeft(it,it+1,gr[it].adjoint());
+ g.applyOnTheLeft(it,it+1, gr[it].adjoint());
+
+ beta = std::abs(g(it+1));
+ m_error = beta/normRhs;
+ // std::cerr << nbIts << " Relative Residual Norm " << m_error << std::endl;
+ it++; nbIts++;
+
+ if (m_error < m_tolerance)
+ {
+ // The method has converged
+ m_info = Success;
+ break;
+ }
+ }
+
+ // Compute the new coefficients by solving the least square problem
+// it++;
+ //FIXME Check first if the matrix is singular ... zero diagonal
+ DenseVector nrs(m_restart);
+ nrs = m_H.topLeftCorner(it,it).template triangularView<Upper>().solve(g.head(it));
+
+ // Form the new solution
+ if (m_isDeflInitialized)
+ {
+ tv1 = m_V.leftCols(it) * nrs;
+ dgmresApplyDeflation(tv1, tv2);
+ x = x + precond.solve(tv2);
+ }
+ else
+ x = x + precond.solve(m_V.leftCols(it) * nrs);
+
+ // Go for a new cycle and compute data for deflation
+ if(nbIts < m_iterations && m_info == NoConvergence && m_neig > 0 && (m_r+m_neig) < m_maxNeig)
+ dgmresComputeDeflationData(mat, precond, it, m_neig);
+ return 0;
+
+}
+
+
+template< typename MatrixType_, typename Preconditioner_>
+void DGMRES<MatrixType_, Preconditioner_>::dgmresInitDeflation(Index& rows) const
+{
+ m_U.resize(rows, m_maxNeig);
+ m_MU.resize(rows, m_maxNeig);
+ m_T.resize(m_maxNeig, m_maxNeig);
+ m_lambdaN = 0.0;
+ m_isDeflAllocated = true;
+}
+
+template< typename MatrixType_, typename Preconditioner_>
+inline typename DGMRES<MatrixType_, Preconditioner_>::ComplexVector DGMRES<MatrixType_, Preconditioner_>::schurValues(const ComplexSchur<DenseMatrix>& schurofH) const
+{
+ return schurofH.matrixT().diagonal();
+}
+
+template< typename MatrixType_, typename Preconditioner_>
+inline typename DGMRES<MatrixType_, Preconditioner_>::ComplexVector DGMRES<MatrixType_, Preconditioner_>::schurValues(const RealSchur<DenseMatrix>& schurofH) const
+{
+ const DenseMatrix& T = schurofH.matrixT();
+ Index it = T.rows();
+ ComplexVector eig(it);
+ Index j = 0;
+ while (j < it-1)
+ {
+ if (T(j+1,j) ==Scalar(0))
+ {
+ eig(j) = std::complex<RealScalar>(T(j,j),RealScalar(0));
+ j++;
+ }
+ else
+ {
+ eig(j) = std::complex<RealScalar>(T(j,j),T(j+1,j));
+ eig(j+1) = std::complex<RealScalar>(T(j,j+1),T(j+1,j+1));
+ j++;
+ }
+ }
+ if (j < it-1) eig(j) = std::complex<RealScalar>(T(j,j),RealScalar(0));
+ return eig;
+}
+
+template< typename MatrixType_, typename Preconditioner_>
+Index DGMRES<MatrixType_, Preconditioner_>::dgmresComputeDeflationData(const MatrixType& mat, const Preconditioner& precond, const Index& it, StorageIndex& neig) const
+{
+ // First, find the Schur form of the Hessenberg matrix H
+ std::conditional_t<NumTraits<Scalar>::IsComplex, ComplexSchur<DenseMatrix>, RealSchur<DenseMatrix> > schurofH;
+ bool computeU = true;
+ DenseMatrix matrixQ(it,it);
+ matrixQ.setIdentity();
+ schurofH.computeFromHessenberg(m_Hes.topLeftCorner(it,it), matrixQ, computeU);
+
+ ComplexVector eig(it);
+ Matrix<StorageIndex,Dynamic,1>perm(it);
+ eig = this->schurValues(schurofH);
+
+ // Reorder the absolute values of Schur values
+ DenseRealVector modulEig(it);
+ for (Index j=0; j<it; ++j) modulEig(j) = std::abs(eig(j));
+ perm.setLinSpaced(it,0,internal::convert_index<StorageIndex>(it-1));
+ internal::sortWithPermutation(modulEig, perm, neig);
+
+ if (!m_lambdaN)
+ {
+ m_lambdaN = (std::max)(modulEig.maxCoeff(), m_lambdaN);
+ }
+ //Count the real number of extracted eigenvalues (with complex conjugates)
+ Index nbrEig = 0;
+ while (nbrEig < neig)
+ {
+ if(eig(perm(it-nbrEig-1)).imag() == RealScalar(0)) nbrEig++;
+ else nbrEig += 2;
+ }
+ // Extract the Schur vectors corresponding to the smallest Ritz values
+ DenseMatrix Sr(it, nbrEig);
+ Sr.setZero();
+ for (Index j = 0; j < nbrEig; j++)
+ {
+ Sr.col(j) = schurofH.matrixU().col(perm(it-j-1));
+ }
+
+ // Form the Schur vectors of the initial matrix using the Krylov basis
+ DenseMatrix X;
+ X = m_V.leftCols(it) * Sr;
+ if (m_r)
+ {
+ // Orthogonalize X against m_U using modified Gram-Schmidt
+ for (Index j = 0; j < nbrEig; j++)
+ for (Index k =0; k < m_r; k++)
+ X.col(j) = X.col(j) - (m_U.col(k).dot(X.col(j)))*m_U.col(k);
+ }
+
+ // Compute m_MX = A * M^-1 * X
+ Index m = m_V.rows();
+ if (!m_isDeflAllocated)
+ dgmresInitDeflation(m);
+ DenseMatrix MX(m, nbrEig);
+ DenseVector tv1(m);
+ for (Index j = 0; j < nbrEig; j++)
+ {
+ tv1 = mat * X.col(j);
+ MX.col(j) = precond.solve(tv1);
+ }
+
+ //Update m_T = [U'MU U'MX; X'MU X'MX]
+ m_T.block(m_r, m_r, nbrEig, nbrEig) = X.transpose() * MX;
+ if(m_r)
+ {
+ m_T.block(0, m_r, m_r, nbrEig) = m_U.leftCols(m_r).transpose() * MX;
+ m_T.block(m_r, 0, nbrEig, m_r) = X.transpose() * m_MU.leftCols(m_r);
+ }
+
+ // Save X into m_U and m_MX in m_MU
+ for (Index j = 0; j < nbrEig; j++) m_U.col(m_r+j) = X.col(j);
+ for (Index j = 0; j < nbrEig; j++) m_MU.col(m_r+j) = MX.col(j);
+ // Increase the size of the invariant subspace
+ m_r += nbrEig;
+
+ // Factorize m_T into m_luT
+ m_luT.compute(m_T.topLeftCorner(m_r, m_r));
+
+ //FIXME CHeck if the factorization was correctly done (nonsingular matrix)
+ m_isDeflInitialized = true;
+ return 0;
+}
+template<typename MatrixType_, typename Preconditioner_>
+template<typename RhsType, typename DestType>
+Index DGMRES<MatrixType_, Preconditioner_>::dgmresApplyDeflation(const RhsType &x, DestType &y) const
+{
+ DenseVector x1 = m_U.leftCols(m_r).transpose() * x;
+ y = x + m_U.leftCols(m_r) * ( m_lambdaN * m_luT.solve(x1) - x1);
+ return 0;
+}
+
+} // end namespace Eigen
+#endif
diff --git a/unsupported/Eigen/src/IterativeSolvers/GMRES.h b/unsupported/Eigen/src/IterativeSolvers/GMRES.h
new file mode 100644
index 0000000..741d9fe
--- /dev/null
+++ b/unsupported/Eigen/src/IterativeSolvers/GMRES.h
@@ -0,0 +1,337 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2011 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2012, 2014 Kolja Brix <brix@igpm.rwth-aaachen.de>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_GMRES_H
+#define EIGEN_GMRES_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+
+/**
+* Generalized Minimal Residual Algorithm based on the
+* Arnoldi algorithm implemented with Householder reflections.
+*
+* Parameters:
+* \param mat matrix of linear system of equations
+* \param rhs right hand side vector of linear system of equations
+* \param x on input: initial guess, on output: solution
+* \param precond preconditioner used
+* \param iters on input: maximum number of iterations to perform
+* on output: number of iterations performed
+* \param restart number of iterations for a restart
+* \param tol_error on input: relative residual tolerance
+* on output: residuum achieved
+*
+* \sa IterativeMethods::bicgstab()
+*
+*
+* For references, please see:
+*
+* Saad, Y. and Schultz, M. H.
+* GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems.
+* SIAM J.Sci.Stat.Comp. 7, 1986, pp. 856 - 869.
+*
+* Saad, Y.
+* Iterative Methods for Sparse Linear Systems.
+* Society for Industrial and Applied Mathematics, Philadelphia, 2003.
+*
+* Walker, H. F.
+* Implementations of the GMRES method.
+* Comput.Phys.Comm. 53, 1989, pp. 311 - 320.
+*
+* Walker, H. F.
+* Implementation of the GMRES Method using Householder Transformations.
+* SIAM J.Sci.Stat.Comp. 9, 1988, pp. 152 - 163.
+*
+*/
+template<typename MatrixType, typename Rhs, typename Dest, typename Preconditioner>
+bool gmres(const MatrixType & mat, const Rhs & rhs, Dest & x, const Preconditioner & precond,
+ Index &iters, const Index &restart, typename Dest::RealScalar & tol_error) {
+
+ using std::sqrt;
+ using std::abs;
+
+ typedef typename Dest::RealScalar RealScalar;
+ typedef typename Dest::Scalar Scalar;
+ typedef Matrix < Scalar, Dynamic, 1 > VectorType;
+ typedef Matrix < Scalar, Dynamic, Dynamic, ColMajor> FMatrixType;
+
+ const RealScalar considerAsZero = (std::numeric_limits<RealScalar>::min)();
+
+ if(rhs.norm() <= considerAsZero)
+ {
+ x.setZero();
+ tol_error = 0;
+ return true;
+ }
+
+ RealScalar tol = tol_error;
+ const Index maxIters = iters;
+ iters = 0;
+
+ const Index m = mat.rows();
+
+ // residual and preconditioned residual
+ VectorType p0 = rhs - mat*x;
+ VectorType r0 = precond.solve(p0);
+
+ const RealScalar r0Norm = r0.norm();
+
+ // is initial guess already good enough?
+ if(r0Norm == 0)
+ {
+ tol_error = 0;
+ return true;
+ }
+
+ // storage for Hessenberg matrix and Householder data
+ FMatrixType H = FMatrixType::Zero(m, restart + 1);
+ VectorType w = VectorType::Zero(restart + 1);
+ VectorType tau = VectorType::Zero(restart + 1);
+
+ // storage for Jacobi rotations
+ std::vector < JacobiRotation < Scalar > > G(restart);
+
+ // storage for temporaries
+ VectorType t(m), v(m), workspace(m), x_new(m);
+
+ // generate first Householder vector
+ Ref<VectorType> H0_tail = H.col(0).tail(m - 1);
+ RealScalar beta;
+ r0.makeHouseholder(H0_tail, tau.coeffRef(0), beta);
+ w(0) = Scalar(beta);
+
+ for (Index k = 1; k <= restart; ++k)
+ {
+ ++iters;
+
+ v = VectorType::Unit(m, k - 1);
+
+ // apply Householder reflections H_{1} ... H_{k-1} to v
+ // TODO: use a HouseholderSequence
+ for (Index i = k - 1; i >= 0; --i) {
+ v.tail(m - i).applyHouseholderOnTheLeft(H.col(i).tail(m - i - 1), tau.coeffRef(i), workspace.data());
+ }
+
+ // apply matrix M to v: v = mat * v;
+ t.noalias() = mat * v;
+ v = precond.solve(t);
+
+ // apply Householder reflections H_{k-1} ... H_{1} to v
+ // TODO: use a HouseholderSequence
+ for (Index i = 0; i < k; ++i) {
+ v.tail(m - i).applyHouseholderOnTheLeft(H.col(i).tail(m - i - 1), tau.coeffRef(i), workspace.data());
+ }
+
+ if (v.tail(m - k).norm() != 0.0)
+ {
+ if (k <= restart)
+ {
+ // generate new Householder vector
+ Ref<VectorType> Hk_tail = H.col(k).tail(m - k - 1);
+ v.tail(m - k).makeHouseholder(Hk_tail, tau.coeffRef(k), beta);
+
+ // apply Householder reflection H_{k} to v
+ v.tail(m - k).applyHouseholderOnTheLeft(Hk_tail, tau.coeffRef(k), workspace.data());
+ }
+ }
+
+ if (k > 1)
+ {
+ for (Index i = 0; i < k - 1; ++i)
+ {
+ // apply old Givens rotations to v
+ v.applyOnTheLeft(i, i + 1, G[i].adjoint());
+ }
+ }
+
+ if (k<m && v(k) != (Scalar) 0)
+ {
+ // determine next Givens rotation
+ G[k - 1].makeGivens(v(k - 1), v(k));
+
+ // apply Givens rotation to v and w
+ v.applyOnTheLeft(k - 1, k, G[k - 1].adjoint());
+ w.applyOnTheLeft(k - 1, k, G[k - 1].adjoint());
+ }
+
+ // insert coefficients into upper matrix triangle
+ H.col(k-1).head(k) = v.head(k);
+
+ tol_error = abs(w(k)) / r0Norm;
+ bool stop = (k==m || tol_error < tol || iters == maxIters);
+
+ if (stop || k == restart)
+ {
+ // solve upper triangular system
+ Ref<VectorType> y = w.head(k);
+ H.topLeftCorner(k, k).template triangularView <Upper>().solveInPlace(y);
+
+ // use Horner-like scheme to calculate solution vector
+ x_new.setZero();
+ for (Index i = k - 1; i >= 0; --i)
+ {
+ x_new(i) += y(i);
+ // apply Householder reflection H_{i} to x_new
+ x_new.tail(m - i).applyHouseholderOnTheLeft(H.col(i).tail(m - i - 1), tau.coeffRef(i), workspace.data());
+ }
+
+ x += x_new;
+
+ if(stop)
+ {
+ return true;
+ }
+ else
+ {
+ k=0;
+
+ // reset data for restart
+ p0.noalias() = rhs - mat*x;
+ r0 = precond.solve(p0);
+
+ // clear Hessenberg matrix and Householder data
+ H.setZero();
+ w.setZero();
+ tau.setZero();
+
+ // generate first Householder vector
+ r0.makeHouseholder(H0_tail, tau.coeffRef(0), beta);
+ w(0) = Scalar(beta);
+ }
+ }
+ }
+
+ return false;
+
+}
+
+}
+
+template< typename MatrixType_,
+ typename Preconditioner_ = DiagonalPreconditioner<typename MatrixType_::Scalar> >
+class GMRES;
+
+namespace internal {
+
+template< typename MatrixType_, typename Preconditioner_>
+struct traits<GMRES<MatrixType_,Preconditioner_> >
+{
+ typedef MatrixType_ MatrixType;
+ typedef Preconditioner_ Preconditioner;
+};
+
+}
+
+/** \ingroup IterativeLinearSolvers_Module
+ * \brief A GMRES solver for sparse square problems
+ *
+ * This class allows to solve for A.x = b sparse linear problems using a generalized minimal
+ * residual method. The vectors x and b can be either dense or sparse.
+ *
+ * \tparam MatrixType_ the type of the sparse matrix A, can be a dense or a sparse matrix.
+ * \tparam Preconditioner_ the type of the preconditioner. Default is DiagonalPreconditioner
+ *
+ * The maximal number of iterations and tolerance value can be controlled via the setMaxIterations()
+ * and setTolerance() methods. The defaults are the size of the problem for the maximal number of iterations
+ * and NumTraits<Scalar>::epsilon() for the tolerance.
+ *
+ * This class can be used as the direct solver classes. Here is a typical usage example:
+ * \code
+ * int n = 10000;
+ * VectorXd x(n), b(n);
+ * SparseMatrix<double> A(n,n);
+ * // fill A and b
+ * GMRES<SparseMatrix<double> > solver(A);
+ * x = solver.solve(b);
+ * std::cout << "#iterations: " << solver.iterations() << std::endl;
+ * std::cout << "estimated error: " << solver.error() << std::endl;
+ * // update b, and solve again
+ * x = solver.solve(b);
+ * \endcode
+ *
+ * By default the iterations start with x=0 as an initial guess of the solution.
+ * One can control the start using the solveWithGuess() method.
+ *
+ * GMRES can also be used in a matrix-free context, see the following \link MatrixfreeSolverExample example \endlink.
+ *
+ * \sa class SimplicialCholesky, DiagonalPreconditioner, IdentityPreconditioner
+ */
+template< typename MatrixType_, typename Preconditioner_>
+class GMRES : public IterativeSolverBase<GMRES<MatrixType_,Preconditioner_> >
+{
+ typedef IterativeSolverBase<GMRES> Base;
+ using Base::matrix;
+ using Base::m_error;
+ using Base::m_iterations;
+ using Base::m_info;
+ using Base::m_isInitialized;
+
+private:
+ Index m_restart;
+
+public:
+ using Base::_solve_impl;
+ typedef MatrixType_ MatrixType;
+ typedef typename MatrixType::Scalar Scalar;
+ typedef typename MatrixType::RealScalar RealScalar;
+ typedef Preconditioner_ Preconditioner;
+
+public:
+
+ /** Default constructor. */
+ GMRES() : Base(), m_restart(30) {}
+
+ /** Initialize the solver with matrix \a A for further \c Ax=b solving.
+ *
+ * This constructor is a shortcut for the default constructor followed
+ * by a call to compute().
+ *
+ * \warning this class stores a reference to the matrix A as well as some
+ * precomputed values that depend on it. Therefore, if \a A is changed
+ * this class becomes invalid. Call compute() to update it with the new
+ * matrix A, or modify a copy of A.
+ */
+ template<typename MatrixDerived>
+ explicit GMRES(const EigenBase<MatrixDerived>& A) : Base(A.derived()), m_restart(30) {}
+
+ ~GMRES() {}
+
+ /** Get the number of iterations after that a restart is performed.
+ */
+ Index get_restart() { return m_restart; }
+
+ /** Set the number of iterations after that a restart is performed.
+ * \param restart number of iterations for a restarti, default is 30.
+ */
+ void set_restart(const Index restart) { m_restart=restart; }
+
+ /** \internal */
+ template<typename Rhs,typename Dest>
+ void _solve_vector_with_guess_impl(const Rhs& b, Dest& x) const
+ {
+ m_iterations = Base::maxIterations();
+ m_error = Base::m_tolerance;
+ bool ret = internal::gmres(matrix(), b, x, Base::m_preconditioner, m_iterations, m_restart, m_error);
+ m_info = (!ret) ? NumericalIssue
+ : m_error <= Base::m_tolerance ? Success
+ : NoConvergence;
+ }
+
+protected:
+
+};
+
+} // end namespace Eigen
+
+#endif // EIGEN_GMRES_H
diff --git a/unsupported/Eigen/src/IterativeSolvers/IDRS.h b/unsupported/Eigen/src/IterativeSolvers/IDRS.h
new file mode 100644
index 0000000..2c7d7b0
--- /dev/null
+++ b/unsupported/Eigen/src/IterativeSolvers/IDRS.h
@@ -0,0 +1,397 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2020 Chris Schoutrop <c.e.m.schoutrop@tue.nl>
+// Copyright (C) 2020 Jens Wehner <j.wehner@esciencecenter.nl>
+// Copyright (C) 2020 Jan van Dijk <j.v.dijk@tue.nl>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_IDRS_H
+#define EIGEN_IDRS_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+/** \internal Low-level Induced Dimension Reduction algorithm
+ \param A The matrix A
+ \param b The right hand side vector b
+ \param x On input and initial solution, on output the computed solution.
+ \param precond A preconditioner being able to efficiently solve for an
+ approximation of Ax=b (regardless of b)
+ \param iter On input the max number of iteration, on output the number of performed iterations.
+ \param relres On input the tolerance error, on output an estimation of the relative error.
+ \param S On input Number of the dimension of the shadow space.
+ \param smoothing switches residual smoothing on.
+ \param angle small omega lead to faster convergence at the expense of numerical stability
+ \param replacement switches on a residual replacement strategy to increase accuracy of residual at the
+ expense of more Mat*vec products \return false in the case of numerical issue, for example a break down of IDRS.
+*/
+template <typename Vector, typename RealScalar>
+typename Vector::Scalar omega(const Vector& t, const Vector& s, RealScalar angle) {
+ using numext::abs;
+ typedef typename Vector::Scalar Scalar;
+ const RealScalar ns = s.stableNorm();
+ const RealScalar nt = t.stableNorm();
+ const Scalar ts = t.dot(s);
+ const RealScalar rho = abs(ts / (nt * ns));
+
+ if (rho < angle) {
+ if (ts == Scalar(0)) {
+ return Scalar(0);
+ }
+ // Original relation for om is given by
+ // om = om * angle / rho;
+ // To alleviate potential (near) division by zero this can be rewritten as
+ // om = angle * (ns / nt) * (ts / abs(ts)) = angle * (ns / nt) * sgn(ts)
+ return angle * (ns / nt) * (ts / abs(ts));
+ }
+ return ts / (nt * nt);
+}
+
+template <typename MatrixType, typename Rhs, typename Dest, typename Preconditioner>
+bool idrs(const MatrixType& A, const Rhs& b, Dest& x, const Preconditioner& precond, Index& iter,
+ typename Dest::RealScalar& relres, Index S, bool smoothing, typename Dest::RealScalar angle,
+ bool replacement) {
+ typedef typename Dest::RealScalar RealScalar;
+ typedef typename Dest::Scalar Scalar;
+ typedef Matrix<Scalar, Dynamic, 1> VectorType;
+ typedef Matrix<Scalar, Dynamic, Dynamic, ColMajor> DenseMatrixType;
+ const Index N = b.size();
+ S = S < x.rows() ? S : x.rows();
+ const RealScalar tol = relres;
+ const Index maxit = iter;
+
+ Index replacements = 0;
+ bool trueres = false;
+
+ FullPivLU<DenseMatrixType> lu_solver;
+
+ DenseMatrixType P;
+ {
+ HouseholderQR<DenseMatrixType> qr(DenseMatrixType::Random(N, S));
+ P = (qr.householderQ() * DenseMatrixType::Identity(N, S));
+ }
+
+ const RealScalar normb = b.stableNorm();
+
+ if (internal::isApprox(normb, RealScalar(0))) {
+ // Solution is the zero vector
+ x.setZero();
+ iter = 0;
+ relres = 0;
+ return true;
+ }
+ // from http://homepage.tudelft.nl/1w5b5/IDRS/manual.pdf
+ // A peak in the residual is considered dangerously high if‖ri‖/‖b‖> C(tol/epsilon).
+ // With epsilon the
+ // relative machine precision. The factor tol/epsilon corresponds to the size of a
+ // finite precision number that is so large that the absolute round-off error in
+ // this number, when propagated through the process, makes it impossible to
+ // achieve the required accuracy.The factor C accounts for the accumulation of
+ // round-off errors. This parameter has beenset to 10−3.
+ // mp is epsilon/C
+ // 10^3 * eps is very conservative, so normally no residual replacements will take place.
+ // It only happens if things go very wrong. Too many restarts may ruin the convergence.
+ const RealScalar mp = RealScalar(1e3) * NumTraits<Scalar>::epsilon();
+
+ // Compute initial residual
+ const RealScalar tolb = tol * normb; // Relative tolerance
+ VectorType r = b - A * x;
+
+ VectorType x_s, r_s;
+
+ if (smoothing) {
+ x_s = x;
+ r_s = r;
+ }
+
+ RealScalar normr = r.stableNorm();
+
+ if (normr <= tolb) {
+ // Initial guess is a good enough solution
+ iter = 0;
+ relres = normr / normb;
+ return true;
+ }
+
+ DenseMatrixType G = DenseMatrixType::Zero(N, S);
+ DenseMatrixType U = DenseMatrixType::Zero(N, S);
+ DenseMatrixType M = DenseMatrixType::Identity(S, S);
+ VectorType t(N), v(N);
+ Scalar om = 1.;
+
+ // Main iteration loop, guild G-spaces:
+ iter = 0;
+
+ while (normr > tolb && iter < maxit) {
+ // New right hand size for small system:
+ VectorType f = (r.adjoint() * P).adjoint();
+
+ for (Index k = 0; k < S; ++k) {
+ // Solve small system and make v orthogonal to P:
+ // c = M(k:s,k:s)\f(k:s);
+ lu_solver.compute(M.block(k, k, S - k, S - k));
+ VectorType c = lu_solver.solve(f.segment(k, S - k));
+ // v = r - G(:,k:s)*c;
+ v = r - G.rightCols(S - k) * c;
+ // Preconditioning
+ v = precond.solve(v);
+
+ // Compute new U(:,k) and G(:,k), G(:,k) is in space G_j
+ U.col(k) = U.rightCols(S - k) * c + om * v;
+ G.col(k) = A * U.col(k);
+
+ // Bi-Orthogonalise the new basis vectors:
+ for (Index i = 0; i < k - 1; ++i) {
+ // alpha = ( P(:,i)'*G(:,k) )/M(i,i);
+ Scalar alpha = P.col(i).dot(G.col(k)) / M(i, i);
+ G.col(k) = G.col(k) - alpha * G.col(i);
+ U.col(k) = U.col(k) - alpha * U.col(i);
+ }
+
+ // New column of M = P'*G (first k-1 entries are zero)
+ // M(k:s,k) = (G(:,k)'*P(:,k:s))';
+ M.block(k, k, S - k, 1) = (G.col(k).adjoint() * P.rightCols(S - k)).adjoint();
+
+ if (internal::isApprox(M(k, k), Scalar(0))) {
+ return false;
+ }
+
+ // Make r orthogonal to q_i, i = 0..k-1
+ Scalar beta = f(k) / M(k, k);
+ r = r - beta * G.col(k);
+ x = x + beta * U.col(k);
+ normr = r.stableNorm();
+
+ if (replacement && normr > tolb / mp) {
+ trueres = true;
+ }
+
+ // Smoothing:
+ if (smoothing) {
+ t = r_s - r;
+ // gamma is a Scalar, but the conversion is not allowed
+ Scalar gamma = t.dot(r_s) / t.stableNorm();
+ r_s = r_s - gamma * t;
+ x_s = x_s - gamma * (x_s - x);
+ normr = r_s.stableNorm();
+ }
+
+ if (normr < tolb || iter == maxit) {
+ break;
+ }
+
+ // New f = P'*r (first k components are zero)
+ if (k < S - 1) {
+ f.segment(k + 1, S - (k + 1)) = f.segment(k + 1, S - (k + 1)) - beta * M.block(k + 1, k, S - (k + 1), 1);
+ }
+ } // end for
+
+ if (normr < tolb || iter == maxit) {
+ break;
+ }
+
+ // Now we have sufficient vectors in G_j to compute residual in G_j+1
+ // Note: r is already perpendicular to P so v = r
+ // Preconditioning
+ v = r;
+ v = precond.solve(v);
+
+ // Matrix-vector multiplication:
+ t = A * v;
+
+ // Computation of a new omega
+ om = internal::omega(t, r, angle);
+
+ if (om == RealScalar(0.0)) {
+ return false;
+ }
+
+ r = r - om * t;
+ x = x + om * v;
+ normr = r.stableNorm();
+
+ if (replacement && normr > tolb / mp) {
+ trueres = true;
+ }
+
+ // Residual replacement?
+ if (trueres && normr < normb) {
+ r = b - A * x;
+ trueres = false;
+ replacements++;
+ }
+
+ // Smoothing:
+ if (smoothing) {
+ t = r_s - r;
+ Scalar gamma = t.dot(r_s) / t.stableNorm();
+ r_s = r_s - gamma * t;
+ x_s = x_s - gamma * (x_s - x);
+ normr = r_s.stableNorm();
+ }
+
+ iter++;
+
+ } // end while
+
+ if (smoothing) {
+ x = x_s;
+ }
+ relres = normr / normb;
+ return true;
+}
+
+} // namespace internal
+
+template <typename MatrixType_, typename Preconditioner_ = DiagonalPreconditioner<typename MatrixType_::Scalar> >
+class IDRS;
+
+namespace internal {
+
+template <typename MatrixType_, typename Preconditioner_>
+struct traits<Eigen::IDRS<MatrixType_, Preconditioner_> > {
+ typedef MatrixType_ MatrixType;
+ typedef Preconditioner_ Preconditioner;
+};
+
+} // namespace internal
+
+/** \ingroup IterativeLinearSolvers_Module
+ * \brief The Induced Dimension Reduction method (IDR(s)) is a short-recurrences Krylov method for sparse square
+ * problems.
+ *
+ * This class allows to solve for A.x = b sparse linear problems. The vectors x and b can be either dense or sparse.
+ * he Induced Dimension Reduction method, IDR(), is a robust and efficient short-recurrence Krylov subspace method for
+ * solving large nonsymmetric systems of linear equations.
+ *
+ * For indefinite systems IDR(S) outperforms both BiCGStab and BiCGStab(L). Additionally, IDR(S) can handle matrices
+ * with complex eigenvalues more efficiently than BiCGStab.
+ *
+ * Many problems that do not converge for BiCGSTAB converge for IDR(s) (for larger values of s). And if both methods
+ * converge the convergence for IDR(s) is typically much faster for difficult systems (for example indefinite problems).
+ *
+ * IDR(s) is a limited memory finite termination method. In exact arithmetic it converges in at most N+N/s iterations,
+ * with N the system size. It uses a fixed number of 4+3s vector. In comparison, BiCGSTAB terminates in 2N iterations
+ * and uses 7 vectors. GMRES terminates in at most N iterations, and uses I+3 vectors, with I the number of iterations.
+ * Restarting GMRES limits the memory consumption, but destroys the finite termination property.
+ *
+ * \tparam MatrixType_ the type of the sparse matrix A, can be a dense or a sparse matrix.
+ * \tparam Preconditioner_ the type of the preconditioner. Default is DiagonalPreconditioner
+ *
+ * \implsparsesolverconcept
+ *
+ * The maximal number of iterations and tolerance value can be controlled via the setMaxIterations()
+ * and setTolerance() methods. The defaults are the size of the problem for the maximal number of iterations
+ * and NumTraits<Scalar>::epsilon() for the tolerance.
+ *
+ * The tolerance corresponds to the relative residual error: |Ax-b|/|b|
+ *
+ * \b Performance: when using sparse matrices, best performance is achied for a row-major sparse matrix format.
+ * Moreover, in this case multi-threading can be exploited if the user code is compiled with OpenMP enabled.
+ * See \ref TopicMultiThreading for details.
+ *
+ * By default the iterations start with x=0 as an initial guess of the solution.
+ * One can control the start using the solveWithGuess() method.
+ *
+ * IDR(s) can also be used in a matrix-free context, see the following \link MatrixfreeSolverExample example \endlink.
+ *
+ * \sa class SimplicialCholesky, DiagonalPreconditioner, IdentityPreconditioner
+ */
+template <typename MatrixType_, typename Preconditioner_>
+class IDRS : public IterativeSolverBase<IDRS<MatrixType_, Preconditioner_> > {
+ public:
+ typedef MatrixType_ MatrixType;
+ typedef typename MatrixType::Scalar Scalar;
+ typedef typename MatrixType::RealScalar RealScalar;
+ typedef Preconditioner_ Preconditioner;
+
+ private:
+ typedef IterativeSolverBase<IDRS> Base;
+ using Base::m_error;
+ using Base::m_info;
+ using Base::m_isInitialized;
+ using Base::m_iterations;
+ using Base::matrix;
+ Index m_S;
+ bool m_smoothing;
+ RealScalar m_angle;
+ bool m_residual;
+
+ public:
+ /** Default constructor. */
+ IDRS() : m_S(4), m_smoothing(false), m_angle(RealScalar(0.7)), m_residual(false) {}
+
+ /** Initialize the solver with matrix \a A for further \c Ax=b solving.
+
+ This constructor is a shortcut for the default constructor followed
+ by a call to compute().
+
+ \warning this class stores a reference to the matrix A as well as some
+ precomputed values that depend on it. Therefore, if \a A is changed
+ this class becomes invalid. Call compute() to update it with the new
+ matrix A, or modify a copy of A.
+ */
+ template <typename MatrixDerived>
+ explicit IDRS(const EigenBase<MatrixDerived>& A)
+ : Base(A.derived()), m_S(4), m_smoothing(false), m_angle(RealScalar(0.7)), m_residual(false) {}
+
+ /** \internal */
+ /** Loops over the number of columns of b and does the following:
+ 1. sets the tolerance and maxIterations
+ 2. Calls the function that has the core solver routine
+ */
+ template <typename Rhs, typename Dest>
+ void _solve_vector_with_guess_impl(const Rhs& b, Dest& x) const {
+ m_iterations = Base::maxIterations();
+ m_error = Base::m_tolerance;
+
+ bool ret = internal::idrs(matrix(), b, x, Base::m_preconditioner, m_iterations, m_error, m_S, m_smoothing, m_angle,
+ m_residual);
+
+ m_info = (!ret) ? NumericalIssue : m_error <= Base::m_tolerance ? Success : NoConvergence;
+ }
+
+ /** Sets the parameter S, indicating the dimension of the shadow space. Default is 4*/
+ void setS(Index S) {
+ if (S < 1) {
+ S = 4;
+ }
+
+ m_S = S;
+ }
+
+ /** Switches off and on smoothing.
+ Residual smoothing results in monotonically decreasing residual norms at
+ the expense of two extra vectors of storage and a few extra vector
+ operations. Although monotonic decrease of the residual norms is a
+ desirable property, the rate of convergence of the unsmoothed process and
+ the smoothed process is basically the same. Default is off */
+ void setSmoothing(bool smoothing) { m_smoothing = smoothing; }
+
+ /** The angle must be a real scalar. In IDR(s), a value for the
+ iteration parameter omega must be chosen in every s+1th step. The most
+ natural choice is to select a value to minimize the norm of the next residual.
+ This corresponds to the parameter omega = 0. In practice, this may lead to
+ values of omega that are so small that the other iteration parameters
+ cannot be computed with sufficient accuracy. In such cases it is better to
+ increase the value of omega sufficiently such that a compromise is reached
+ between accurate computations and reduction of the residual norm. The
+ parameter angle =0.7 (”maintaining the convergence strategy”)
+ results in such a compromise. */
+ void setAngle(RealScalar angle) { m_angle = angle; }
+
+ /** The parameter replace is a logical that determines whether a
+ residual replacement strategy is employed to increase the accuracy of the
+ solution. */
+ void setResidualUpdate(bool update) { m_residual = update; }
+};
+
+} // namespace Eigen
+
+#endif /* EIGEN_IDRS_H */
diff --git a/unsupported/Eigen/src/IterativeSolvers/IDRSTABL.h b/unsupported/Eigen/src/IterativeSolvers/IDRSTABL.h
new file mode 100644
index 0000000..712c171
--- /dev/null
+++ b/unsupported/Eigen/src/IterativeSolvers/IDRSTABL.h
@@ -0,0 +1,476 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2020 Chris Schoutrop <c.e.m.schoutrop@tue.nl>
+// Copyright (C) 2020 Mischa Senders <m.j.senders@student.tue.nl>
+// Copyright (C) 2020 Lex Kuijpers <l.kuijpers@student.tue.nl>
+// Copyright (C) 2020 Jens Wehner <j.wehner@esciencecenter.nl>
+// Copyright (C) 2020 Jan van Dijk <j.v.dijk@tue.nl>
+// Copyright (C) 2020 Adithya Vijaykumar
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+/*
+
+The IDR(S)Stab(L) method is a combination of IDR(S) and BiCGStab(L)
+
+This implementation of IDRSTABL is based on
+1. Aihara, K., Abe, K., & Ishiwata, E. (2014). A variant of IDRstab with
+reliable update strategies for solving sparse linear systems. Journal of
+Computational and Applied Mathematics, 259, 244-258.
+ doi:10.1016/j.cam.2013.08.028
+ 2. Aihara, K., Abe, K., & Ishiwata, E. (2015). Preconditioned
+IDRSTABL Algorithms for Solving Nonsymmetric Linear Systems. International
+Journal of Applied Mathematics, 45(3).
+ 3. Saad, Y. (2003). Iterative Methods for Sparse Linear Systems:
+Second Edition. Philadelphia, PA: SIAM.
+ 4. Sonneveld, P., & Van Gijzen, M. B. (2009). IDR(s): A Family
+of Simple and Fast Algorithms for Solving Large Nonsymmetric Systems of Linear
+Equations. SIAM Journal on Scientific Computing, 31(2), 1035-1062.
+ doi:10.1137/070685804
+ 5. Sonneveld, P. (2012). On the convergence behavior of IDR (s)
+and related methods. SIAM Journal on Scientific Computing, 34(5), A2576-A2598.
+
+ Right-preconditioning based on Ref. 3 is implemented here.
+*/
+
+#ifndef EIGEN_IDRSTABL_H
+#define EIGEN_IDRSTABL_H
+
+namespace Eigen {
+
+namespace internal {
+
+template <typename MatrixType, typename Rhs, typename Dest, typename Preconditioner>
+bool idrstabl(const MatrixType &mat, const Rhs &rhs, Dest &x, const Preconditioner &precond, Index &iters,
+ typename Dest::RealScalar &tol_error, Index L, Index S) {
+ /*
+ Setup and type definitions.
+ */
+ using numext::abs;
+ using numext::sqrt;
+ typedef typename Dest::Scalar Scalar;
+ typedef typename Dest::RealScalar RealScalar;
+ typedef Matrix<Scalar, Dynamic, 1> VectorType;
+ typedef Matrix<Scalar, Dynamic, Dynamic, ColMajor> DenseMatrixType;
+
+ const Index N = x.rows();
+
+ Index k = 0; // Iteration counter
+ const Index maxIters = iters;
+
+ const RealScalar rhs_norm = rhs.stableNorm();
+ const RealScalar tol = tol_error * rhs_norm;
+
+ if (rhs_norm == 0) {
+ /*
+ If b==0, then the exact solution is x=0.
+ rhs_norm is needed for other calculations anyways, this exit is a freebie.
+ */
+ x.setZero();
+ tol_error = 0.0;
+ return true;
+ }
+ // Construct decomposition objects beforehand.
+ FullPivLU<DenseMatrixType> lu_solver;
+
+ if (S >= N || L >= N) {
+ /*
+ The matrix is very small, or the choice of L and S is very poor
+ in that case solving directly will be best.
+ */
+ lu_solver.compute(DenseMatrixType(mat));
+ x = lu_solver.solve(rhs);
+ tol_error = (rhs - mat * x).stableNorm() / rhs_norm;
+ return true;
+ }
+
+ // Define maximum sizes to prevent any reallocation later on.
+ DenseMatrixType u(N, L + 1);
+ DenseMatrixType r(N, L + 1);
+
+ DenseMatrixType V(N * (L + 1), S);
+
+ VectorType alpha(S);
+ VectorType gamma(L);
+ VectorType update(N);
+
+ /*
+ Main IDRSTABL algorithm
+ */
+ // Set up the initial residual
+ VectorType x0 = x;
+ r.col(0) = rhs - mat * x;
+ x.setZero(); // The final solution will be x0+x
+
+ tol_error = r.col(0).stableNorm();
+
+ // FOM = Full orthogonalisation method
+ DenseMatrixType h_FOM = DenseMatrixType::Zero(S, S - 1);
+
+ // Construct an initial U matrix of size N x S
+ DenseMatrixType U(N * (L + 1), S);
+ for (Index col_index = 0; col_index < S; ++col_index) {
+ // Arnoldi-like process to generate a set of orthogonal vectors spanning
+ // {u,A*u,A*A*u,...,A^(S-1)*u}. This construction can be combined with the
+ // Full Orthogonalization Method (FOM) from Ref.3 to provide a possible
+ // early exit with no additional MV.
+ if (col_index != 0) {
+ /*
+ Modified Gram-Schmidt strategy:
+ */
+ VectorType w = mat * precond.solve(u.col(0));
+ for (Index i = 0; i < col_index; ++i) {
+ auto v = U.col(i).head(N);
+ h_FOM(i, col_index - 1) = v.dot(w);
+ w -= h_FOM(i, col_index - 1) * v;
+ }
+ u.col(0) = w;
+ h_FOM(col_index, col_index - 1) = u.col(0).stableNorm();
+
+ if (abs(h_FOM(col_index, col_index - 1)) != RealScalar(0)) {
+ /*
+ This only happens if u is NOT exactly zero. In case it is exactly zero
+ it would imply that that this u has no component in the direction of the
+ current residual.
+
+ By then setting u to zero it will not contribute any further (as it
+ should). Whereas attempting to normalize results in division by zero.
+
+ Such cases occur if:
+ 1. The basis of dimension <S is sufficient to exactly solve the linear
+ system. I.e. the current residual is in span{r,Ar,...A^{m-1}r}, where
+ (m-1)<=S.
+ 2. Two vectors vectors generated from r, Ar,... are (numerically)
+ parallel.
+
+ In case 1, the exact solution to the system can be obtained from the
+ "Full Orthogonalization Method" (Algorithm 6.4 in the book of Saad),
+ without any additional MV.
+
+ Contrary to what one would suspect, the comparison with ==0.0 for
+ floating-point types is intended here. Any arbritary non-zero u is fine
+ to continue, however if u contains either NaN or Inf the algorithm will
+ break down.
+ */
+ u.col(0) /= h_FOM(col_index, col_index - 1);
+ }
+ } else {
+ u.col(0) = r.col(0);
+ u.col(0).normalize();
+ }
+
+ U.col(col_index).head(N) = u.col(0);
+ }
+
+ if (S > 1) {
+ // Check for early FOM exit.
+ Scalar beta = r.col(0).stableNorm();
+ VectorType e1 = VectorType::Zero(S - 1);
+ e1(0) = beta;
+ lu_solver.compute(h_FOM.topLeftCorner(S - 1, S - 1));
+ VectorType y = lu_solver.solve(e1);
+ VectorType x2 = x + U.topLeftCorner(N, S - 1) * y;
+
+ // Using proposition 6.7 in Saad, one MV can be saved to calculate the
+ // residual
+ RealScalar FOM_residual = (h_FOM(S - 1, S - 2) * y(S - 2) * U.col(S - 1).head(N)).stableNorm();
+
+ if (FOM_residual < tol) {
+ // Exit, the FOM algorithm was already accurate enough
+ iters = k;
+ // Convert back to the unpreconditioned solution
+ x = precond.solve(x2);
+ // x contains the updates to x0, add those back to obtain the solution
+ x += x0;
+ tol_error = FOM_residual / rhs_norm;
+ return true;
+ }
+ }
+
+ /*
+ Select an initial (N x S) matrix R0.
+ 1. Generate random R0, orthonormalize the result.
+ 2. This results in R0, however to save memory and compute we only need the
+ adjoint of R0. This is given by the matrix R_T.\ Additionally, the matrix
+ (mat.adjoint()*R_tilde).adjoint()=R_tilde.adjoint()*mat by the
+ anti-distributivity property of the adjoint. This results in AR_T, which is
+ constant if R_T does not have to be regenerated and can be precomputed.
+ Based on reference 4, this has zero probability in exact arithmetic.
+ */
+
+ // Original IDRSTABL and Kensuke choose S random vectors:
+ const HouseholderQR<DenseMatrixType> qr(DenseMatrixType::Random(N, S));
+ DenseMatrixType R_T = (qr.householderQ() * DenseMatrixType::Identity(N, S)).adjoint();
+ DenseMatrixType AR_T = DenseMatrixType(R_T * mat);
+
+ // Pre-allocate sigma.
+ DenseMatrixType sigma(S, S);
+
+ bool reset_while = false; // Should the while loop be reset for some reason?
+
+ while (k < maxIters) {
+ for (Index j = 1; j <= L; ++j) {
+ /*
+ The IDR Step
+ */
+ // Construction of the sigma-matrix, and the decomposition of sigma.
+ for (Index i = 0; i < S; ++i) {
+ sigma.col(i).noalias() = AR_T * precond.solve(U.block(N * (j - 1), i, N, 1));
+ }
+
+ lu_solver.compute(sigma);
+ // Obtain the update coefficients alpha
+ if (j == 1) {
+ // alpha=inverse(sigma)*(R_T*r_0);
+ alpha.noalias() = lu_solver.solve(R_T * r.col(0));
+ } else {
+ // alpha=inverse(sigma)*(AR_T*r_{j-2})
+ alpha.noalias() = lu_solver.solve(AR_T * precond.solve(r.col(j - 2)));
+ }
+
+ // Obtain new solution and residual from this update
+ update.noalias() = U.topRows(N) * alpha;
+ r.col(0) -= mat * precond.solve(update);
+ x += update;
+
+ for (Index i = 1; i <= j - 2; ++i) {
+ // This only affects the case L>2
+ r.col(i) -= U.block(N * (i + 1), 0, N, S) * alpha;
+ }
+ if (j > 1) {
+ // r=[r;A*r_{j-2}]
+ r.col(j - 1).noalias() = mat * precond.solve(r.col(j - 2));
+ }
+ tol_error = r.col(0).stableNorm();
+
+ if (tol_error < tol) {
+ // If at this point the algorithm has converged, exit.
+ reset_while = true;
+ break;
+ }
+
+ bool break_normalization = false;
+ for (Index q = 1; q <= S; ++q) {
+ if (q == 1) {
+ // u = r;
+ u.leftCols(j + 1) = r.leftCols(j + 1);
+ } else {
+ // u=[u_1;u_2;...;u_j]
+ u.leftCols(j) = u.middleCols(1, j);
+ }
+
+ // Obtain the update coefficients beta implicitly
+ // beta=lu_sigma.solve(AR_T * u.block(N * (j - 1), 0, N, 1)
+ u.reshaped().head(u.rows() * j) -= U.topRows(N * j) * lu_solver.solve(AR_T * precond.solve(u.col(j - 1)));
+
+ // u=[u;Au_{j-1}]
+ u.col(j).noalias() = mat * precond.solve(u.col(j - 1));
+
+ // Orthonormalize u_j to the columns of V_j(:,1:q-1)
+ if (q > 1) {
+ /*
+ Modified Gram-Schmidt-like procedure to make u orthogonal to the
+ columns of V from Ref. 1.
+
+ The vector mu from Ref. 1 is obtained implicitly:
+ mu=V.block(N * j, 0, N, q - 1).adjoint() * u.block(N * j, 0, N, 1).
+ */
+ for (Index i = 0; i <= q - 2; ++i) {
+ auto v = V.col(i).segment(N * j, N);
+ Scalar h = v.squaredNorm();
+ h = v.dot(u.col(j)) / h;
+ u.reshaped().head(u.rows() * (j + 1)) -= h * V.block(0, i, N * (j + 1), 1);
+ }
+ }
+ // Normalize u and assign to a column of V
+ Scalar normalization_constant = u.col(j).stableNorm();
+ // If u is exactly zero, this will lead to a NaN. Small, non-zero u is
+ // fine.
+ if (normalization_constant == RealScalar(0.0)) {
+ break_normalization = true;
+ break;
+ } else {
+ u.leftCols(j + 1) /= normalization_constant;
+ }
+
+ V.block(0, q - 1, N * (j + 1), 1).noalias() = u.reshaped().head(u.rows() * (j + 1));
+ }
+
+ if (break_normalization == false) {
+ U = V;
+ }
+ }
+ if (reset_while) {
+ break;
+ }
+
+ // r=[r;mat*r_{L-1}]
+ r.col(L).noalias() = mat * precond.solve(r.col(L - 1));
+
+ /*
+ The polynomial step
+ */
+ ColPivHouseholderQR<DenseMatrixType> qr_solver(r.rightCols(L));
+ gamma.noalias() = qr_solver.solve(r.col(0));
+
+ // Update solution and residual using the "minimized residual coefficients"
+ update.noalias() = r.leftCols(L) * gamma;
+ x += update;
+ r.col(0) -= mat * precond.solve(update);
+
+ // Update iteration info
+ ++k;
+ tol_error = r.col(0).stableNorm();
+
+ if (tol_error < tol) {
+ // Slightly early exit by moving the criterion before the update of U,
+ // after the main while loop the result of that calculation would not be
+ // needed.
+ break;
+ }
+
+ /*
+ U=U0-sum(gamma_j*U_j)
+ Consider the first iteration. Then U only contains U0, so at the start of
+ the while-loop U should be U0. Therefore only the first N rows of U have to
+ be updated.
+ */
+ for (Index i = 1; i <= L; ++i) {
+ U.topRows(N) -= U.block(N * i, 0, N, S) * gamma(i - 1);
+ }
+ }
+
+ /*
+ Exit after the while loop terminated.
+ */
+ iters = k;
+ // Convert back to the unpreconditioned solution
+ x = precond.solve(x);
+ // x contains the updates to x0, add those back to obtain the solution
+ x += x0;
+ tol_error = tol_error / rhs_norm;
+ return true;
+}
+
+} // namespace internal
+
+template <typename MatrixType_, typename Preconditioner_ = DiagonalPreconditioner<typename MatrixType_::Scalar>>
+class IDRSTABL;
+
+namespace internal {
+
+template <typename MatrixType_, typename Preconditioner_>
+struct traits<IDRSTABL<MatrixType_, Preconditioner_>> {
+ typedef MatrixType_ MatrixType;
+ typedef Preconditioner_ Preconditioner;
+};
+
+} // namespace internal
+
+/** \ingroup IterativeLinearSolvers_Module
+ * \brief The IDR(s)STAB(l) is a combination of IDR(s) and BiCGSTAB(l). It is a
+ * short-recurrences Krylov method for sparse square problems. It can outperform
+ * both IDR(s) and BiCGSTAB(l). IDR(s)STAB(l) generally closely follows the
+ * optimal GMRES convergence in terms of the number of Matrix-Vector products.
+ * However, without the increasing cost per iteration of GMRES. IDR(s)STAB(l) is
+ * suitable for both indefinite systems and systems with complex eigenvalues.
+ *
+ * This class allows solving for A.x = b sparse linear problems. The vectors x
+ * and b can be either dense or sparse.
+ *
+ * \tparam MatrixType_ the type of the sparse matrix A, can be a dense or a
+ * sparse matrix. \tparam Preconditioner_ the type of the preconditioner.
+ * Default is DiagonalPreconditioner
+ *
+ * \implsparsesolverconcept
+ *
+ * The maximum number of iterations and tolerance value can be controlled via
+ * the setMaxIterations() and setTolerance() methods. The defaults are the size
+ * of the problem for the maximum number of iterations and
+ * NumTraits<Scalar>::epsilon() for the tolerance.
+ *
+ * The tolerance is the maximum relative residual error: |Ax-b|/|b| for which
+ * the linear system is considered solved.
+ *
+ * \b Performance: When using sparse matrices, best performance is achieved for
+ * a row-major sparse matrix format. Moreover, in this case multi-threading can
+ * be exploited if the user code is compiled with OpenMP enabled. See \ref
+ * TopicMultiThreading for details.
+ *
+ * By default the iterations start with x=0 as an initial guess of the solution.
+ * One can control the start using the solveWithGuess() method.
+ *
+ * IDR(s)STAB(l) can also be used in a matrix-free context, see the following
+ * \link MatrixfreeSolverExample example \endlink.
+ *
+ * \sa class SimplicialCholesky, DiagonalPreconditioner, IdentityPreconditioner
+ */
+
+template <typename MatrixType_, typename Preconditioner_>
+class IDRSTABL : public IterativeSolverBase<IDRSTABL<MatrixType_, Preconditioner_>> {
+ typedef IterativeSolverBase<IDRSTABL> Base;
+ using Base::m_error;
+ using Base::m_info;
+ using Base::m_isInitialized;
+ using Base::m_iterations;
+ using Base::matrix;
+ Index m_L;
+ Index m_S;
+
+ public:
+ typedef MatrixType_ MatrixType;
+ typedef typename MatrixType::Scalar Scalar;
+ typedef typename MatrixType::RealScalar RealScalar;
+ typedef Preconditioner_ Preconditioner;
+
+ public:
+ /** Default constructor. */
+ IDRSTABL() : m_L(2), m_S(4) {}
+
+ /** Initialize the solver with matrix \a A for further \c Ax=b solving.
+
+ This constructor is a shortcut for the default constructor followed
+ by a call to compute().
+
+ \warning this class stores a reference to the matrix A as well as some
+ precomputed values that depend on it. Therefore, if \a A is changed
+ this class becomes invalid. Call compute() to update it with the new
+ matrix A, or modify a copy of A.
+ */
+ template <typename MatrixDerived>
+ explicit IDRSTABL(const EigenBase<MatrixDerived> &A) : Base(A.derived()), m_L(2), m_S(4) {}
+
+ /** \internal */
+ /** Loops over the number of columns of b and does the following:
+ 1. sets the tolerance and maxIterations
+ 2. Calls the function that has the core solver
+ routine
+ */
+ template <typename Rhs, typename Dest>
+ void _solve_vector_with_guess_impl(const Rhs &b, Dest &x) const {
+ m_iterations = Base::maxIterations();
+ m_error = Base::m_tolerance;
+ bool ret = internal::idrstabl(matrix(), b, x, Base::m_preconditioner, m_iterations, m_error, m_L, m_S);
+
+ m_info = (!ret) ? NumericalIssue : m_error <= 10 * Base::m_tolerance ? Success : NoConvergence;
+ }
+
+ /** Sets the parameter L, indicating the amount of minimize residual steps are
+ * used. */
+ void setL(Index L) {
+ eigen_assert(L >= 1 && "L needs to be positive");
+ m_L = L;
+ }
+ /** Sets the parameter S, indicating the dimension of the shadow residual
+ * space.. */
+ void setS(Index S) {
+ eigen_assert(S >= 1 && "S needs to be positive");
+ m_S = S;
+ }
+};
+
+} // namespace Eigen
+
+#endif /* EIGEN_IDRSTABL_H */
diff --git a/unsupported/Eigen/src/IterativeSolvers/IncompleteLU.h b/unsupported/Eigen/src/IterativeSolvers/IncompleteLU.h
new file mode 100644
index 0000000..3bf564c
--- /dev/null
+++ b/unsupported/Eigen/src/IterativeSolvers/IncompleteLU.h
@@ -0,0 +1,92 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2011 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_INCOMPLETE_LU_H
+#define EIGEN_INCOMPLETE_LU_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+template <typename Scalar_>
+class IncompleteLU : public SparseSolverBase<IncompleteLU<Scalar_> >
+{
+ protected:
+ typedef SparseSolverBase<IncompleteLU<Scalar_> > Base;
+ using Base::m_isInitialized;
+
+ typedef Scalar_ Scalar;
+ typedef Matrix<Scalar,Dynamic,1> Vector;
+ typedef typename Vector::Index Index;
+ typedef SparseMatrix<Scalar,RowMajor> FactorType;
+
+ public:
+ typedef Matrix<Scalar,Dynamic,Dynamic> MatrixType;
+
+ IncompleteLU() {}
+
+ template<typename MatrixType>
+ IncompleteLU(const MatrixType& mat)
+ {
+ compute(mat);
+ }
+
+ Index rows() const { return m_lu.rows(); }
+ Index cols() const { return m_lu.cols(); }
+
+ template<typename MatrixType>
+ IncompleteLU& compute(const MatrixType& mat)
+ {
+ m_lu = mat;
+ int size = mat.cols();
+ Vector diag(size);
+ for(int i=0; i<size; ++i)
+ {
+ typename FactorType::InnerIterator k_it(m_lu,i);
+ for(; k_it && k_it.index()<i; ++k_it)
+ {
+ int k = k_it.index();
+ k_it.valueRef() /= diag(k);
+
+ typename FactorType::InnerIterator j_it(k_it);
+ typename FactorType::InnerIterator kj_it(m_lu, k);
+ while(kj_it && kj_it.index()<=k) ++kj_it;
+ for(++j_it; j_it; )
+ {
+ if(kj_it.index()==j_it.index())
+ {
+ j_it.valueRef() -= k_it.value() * kj_it.value();
+ ++j_it;
+ ++kj_it;
+ }
+ else if(kj_it.index()<j_it.index()) ++kj_it;
+ else ++j_it;
+ }
+ }
+ if(k_it && k_it.index()==i) diag(i) = k_it.value();
+ else diag(i) = 1;
+ }
+ m_isInitialized = true;
+ return *this;
+ }
+
+ template<typename Rhs, typename Dest>
+ void _solve_impl(const Rhs& b, Dest& x) const
+ {
+ x = m_lu.template triangularView<UnitLower>().solve(b);
+ x = m_lu.template triangularView<Upper>().solve(x);
+ }
+
+ protected:
+ FactorType m_lu;
+};
+
+} // end namespace Eigen
+
+#endif // EIGEN_INCOMPLETE_LU_H
diff --git a/unsupported/Eigen/src/IterativeSolvers/InternalHeaderCheck.h b/unsupported/Eigen/src/IterativeSolvers/InternalHeaderCheck.h
new file mode 100644
index 0000000..679c7fa
--- /dev/null
+++ b/unsupported/Eigen/src/IterativeSolvers/InternalHeaderCheck.h
@@ -0,0 +1,3 @@
+#ifndef EIGEN_ITERATIVE_SOLVERS_MODULE_H
+#error "Please include unsupported/Eigen/IterativeSolvers instead of including headers inside the src directory directly."
+#endif
diff --git a/unsupported/Eigen/src/IterativeSolvers/MINRES.h b/unsupported/Eigen/src/IterativeSolvers/MINRES.h
new file mode 100644
index 0000000..2282777
--- /dev/null
+++ b/unsupported/Eigen/src/IterativeSolvers/MINRES.h
@@ -0,0 +1,269 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2012 Giacomo Po <gpo@ucla.edu>
+// Copyright (C) 2011-2014 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2018 David Hyde <dabh@stanford.edu>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+
+#ifndef EIGEN_MINRES_H
+#define EIGEN_MINRES_H
+
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+ namespace internal {
+
+ /** \internal Low-level MINRES algorithm
+ * \param mat The matrix A
+ * \param rhs The right hand side vector b
+ * \param x On input and initial solution, on output the computed solution.
+ * \param precond A right preconditioner being able to efficiently solve for an
+ * approximation of Ax=b (regardless of b)
+ * \param iters On input the max number of iteration, on output the number of performed iterations.
+ * \param tol_error On input the tolerance error, on output an estimation of the relative error.
+ */
+ template<typename MatrixType, typename Rhs, typename Dest, typename Preconditioner>
+ EIGEN_DONT_INLINE
+ void minres(const MatrixType& mat, const Rhs& rhs, Dest& x,
+ const Preconditioner& precond, Index& iters,
+ typename Dest::RealScalar& tol_error)
+ {
+ using std::sqrt;
+ typedef typename Dest::RealScalar RealScalar;
+ typedef typename Dest::Scalar Scalar;
+ typedef Matrix<Scalar,Dynamic,1> VectorType;
+
+ // Check for zero rhs
+ const RealScalar rhsNorm2(rhs.squaredNorm());
+ if(rhsNorm2 == 0)
+ {
+ x.setZero();
+ iters = 0;
+ tol_error = 0;
+ return;
+ }
+
+ // initialize
+ const Index maxIters(iters); // initialize maxIters to iters
+ const Index N(mat.cols()); // the size of the matrix
+ const RealScalar threshold2(tol_error*tol_error*rhsNorm2); // convergence threshold (compared to residualNorm2)
+
+ // Initialize preconditioned Lanczos
+ VectorType v_old(N); // will be initialized inside loop
+ VectorType v( VectorType::Zero(N) ); //initialize v
+ VectorType v_new(rhs-mat*x); //initialize v_new
+ RealScalar residualNorm2(v_new.squaredNorm());
+ VectorType w(N); // will be initialized inside loop
+ VectorType w_new(precond.solve(v_new)); // initialize w_new
+// RealScalar beta; // will be initialized inside loop
+ RealScalar beta_new2(v_new.dot(w_new));
+ eigen_assert(beta_new2 >= 0.0 && "PRECONDITIONER IS NOT POSITIVE DEFINITE");
+ RealScalar beta_new(sqrt(beta_new2));
+ const RealScalar beta_one(beta_new);
+ // Initialize other variables
+ RealScalar c(1.0); // the cosine of the Givens rotation
+ RealScalar c_old(1.0);
+ RealScalar s(0.0); // the sine of the Givens rotation
+ RealScalar s_old(0.0); // the sine of the Givens rotation
+ VectorType p_oold(N); // will be initialized in loop
+ VectorType p_old(VectorType::Zero(N)); // initialize p_old=0
+ VectorType p(p_old); // initialize p=0
+ RealScalar eta(1.0);
+
+ iters = 0; // reset iters
+ while ( iters < maxIters )
+ {
+ // Preconditioned Lanczos
+ /* Note that there are 4 variants on the Lanczos algorithm. These are
+ * described in Paige, C. C. (1972). Computational variants of
+ * the Lanczos method for the eigenproblem. IMA Journal of Applied
+ * Mathematics, 10(3), 373-381. The current implementation corresponds
+ * to the case A(2,7) in the paper. It also corresponds to
+ * algorithm 6.14 in Y. Saad, Iterative Methods for Sparse Linear
+ * Systems, 2003 p.173. For the preconditioned version see
+ * A. Greenbaum, Iterative Methods for Solving Linear Systems, SIAM (1987).
+ */
+ const RealScalar beta(beta_new);
+ v_old = v; // update: at first time step, this makes v_old = 0 so value of beta doesn't matter
+ v_new /= beta_new; // overwrite v_new for next iteration
+ w_new /= beta_new; // overwrite w_new for next iteration
+ v = v_new; // update
+ w = w_new; // update
+ v_new.noalias() = mat*w - beta*v_old; // compute v_new
+ const RealScalar alpha = v_new.dot(w);
+ v_new -= alpha*v; // overwrite v_new
+ w_new = precond.solve(v_new); // overwrite w_new
+ beta_new2 = v_new.dot(w_new); // compute beta_new
+ eigen_assert(beta_new2 >= 0.0 && "PRECONDITIONER IS NOT POSITIVE DEFINITE");
+ beta_new = sqrt(beta_new2); // compute beta_new
+
+ // Givens rotation
+ const RealScalar r2 =s*alpha+c*c_old*beta; // s, s_old, c and c_old are still from previous iteration
+ const RealScalar r3 =s_old*beta; // s, s_old, c and c_old are still from previous iteration
+ const RealScalar r1_hat=c*alpha-c_old*s*beta;
+ const RealScalar r1 =sqrt( std::pow(r1_hat,2) + std::pow(beta_new,2) );
+ c_old = c; // store for next iteration
+ s_old = s; // store for next iteration
+ c=r1_hat/r1; // new cosine
+ s=beta_new/r1; // new sine
+
+ // Update solution
+ p_oold = p_old;
+ p_old = p;
+ p.noalias()=(w-r2*p_old-r3*p_oold) /r1; // IS NOALIAS REQUIRED?
+ x += beta_one*c*eta*p;
+
+ /* Update the squared residual. Note that this is the estimated residual.
+ The real residual |Ax-b|^2 may be slightly larger */
+ residualNorm2 *= s*s;
+
+ if ( residualNorm2 < threshold2)
+ {
+ break;
+ }
+
+ eta=-s*eta; // update eta
+ iters++; // increment iteration number (for output purposes)
+ }
+
+ /* Compute error. Note that this is the estimated error. The real
+ error |Ax-b|/|b| may be slightly larger */
+ tol_error = std::sqrt(residualNorm2 / rhsNorm2);
+ }
+
+ }
+
+ template< typename MatrixType_, int UpLo_=Lower,
+ typename Preconditioner_ = IdentityPreconditioner>
+ class MINRES;
+
+ namespace internal {
+
+ template< typename MatrixType_, int UpLo_, typename Preconditioner_>
+ struct traits<MINRES<MatrixType_,UpLo_,Preconditioner_> >
+ {
+ typedef MatrixType_ MatrixType;
+ typedef Preconditioner_ Preconditioner;
+ };
+
+ }
+
+ /** \ingroup IterativeLinearSolvers_Module
+ * \brief A minimal residual solver for sparse symmetric problems
+ *
+ * This class allows to solve for A.x = b sparse linear problems using the MINRES algorithm
+ * of Paige and Saunders (1975). The sparse matrix A must be symmetric (possibly indefinite).
+ * The vectors x and b can be either dense or sparse.
+ *
+ * \tparam MatrixType_ the type of the sparse matrix A, can be a dense or a sparse matrix.
+ * \tparam UpLo_ the triangular part that will be used for the computations. It can be Lower,
+ * Upper, or Lower|Upper in which the full matrix entries will be considered. Default is Lower.
+ * \tparam Preconditioner_ the type of the preconditioner. Default is DiagonalPreconditioner
+ *
+ * The maximal number of iterations and tolerance value can be controlled via the setMaxIterations()
+ * and setTolerance() methods. The defaults are the size of the problem for the maximal number of iterations
+ * and NumTraits<Scalar>::epsilon() for the tolerance.
+ *
+ * This class can be used as the direct solver classes. Here is a typical usage example:
+ * \code
+ * int n = 10000;
+ * VectorXd x(n), b(n);
+ * SparseMatrix<double> A(n,n);
+ * // fill A and b
+ * MINRES<SparseMatrix<double> > mr;
+ * mr.compute(A);
+ * x = mr.solve(b);
+ * std::cout << "#iterations: " << mr.iterations() << std::endl;
+ * std::cout << "estimated error: " << mr.error() << std::endl;
+ * // update b, and solve again
+ * x = mr.solve(b);
+ * \endcode
+ *
+ * By default the iterations start with x=0 as an initial guess of the solution.
+ * One can control the start using the solveWithGuess() method.
+ *
+ * MINRES can also be used in a matrix-free context, see the following \link MatrixfreeSolverExample example \endlink.
+ *
+ * \sa class ConjugateGradient, BiCGSTAB, SimplicialCholesky, DiagonalPreconditioner, IdentityPreconditioner
+ */
+ template< typename MatrixType_, int UpLo_, typename Preconditioner_>
+ class MINRES : public IterativeSolverBase<MINRES<MatrixType_,UpLo_,Preconditioner_> >
+ {
+
+ typedef IterativeSolverBase<MINRES> Base;
+ using Base::matrix;
+ using Base::m_error;
+ using Base::m_iterations;
+ using Base::m_info;
+ using Base::m_isInitialized;
+ public:
+ using Base::_solve_impl;
+ typedef MatrixType_ MatrixType;
+ typedef typename MatrixType::Scalar Scalar;
+ typedef typename MatrixType::RealScalar RealScalar;
+ typedef Preconditioner_ Preconditioner;
+
+ enum {UpLo = UpLo_};
+
+ public:
+
+ /** Default constructor. */
+ MINRES() : Base() {}
+
+ /** Initialize the solver with matrix \a A for further \c Ax=b solving.
+ *
+ * This constructor is a shortcut for the default constructor followed
+ * by a call to compute().
+ *
+ * \warning this class stores a reference to the matrix A as well as some
+ * precomputed values that depend on it. Therefore, if \a A is changed
+ * this class becomes invalid. Call compute() to update it with the new
+ * matrix A, or modify a copy of A.
+ */
+ template<typename MatrixDerived>
+ explicit MINRES(const EigenBase<MatrixDerived>& A) : Base(A.derived()) {}
+
+ /** Destructor. */
+ ~MINRES(){}
+
+ /** \internal */
+ template<typename Rhs,typename Dest>
+ void _solve_vector_with_guess_impl(const Rhs& b, Dest& x) const
+ {
+ typedef typename Base::MatrixWrapper MatrixWrapper;
+ typedef typename Base::ActualMatrixType ActualMatrixType;
+ enum {
+ TransposeInput = (!MatrixWrapper::MatrixFree)
+ && (UpLo==(Lower|Upper))
+ && (!MatrixType::IsRowMajor)
+ && (!NumTraits<Scalar>::IsComplex)
+ };
+ typedef std::conditional_t<TransposeInput,Transpose<const ActualMatrixType>, ActualMatrixType const&> RowMajorWrapper;
+ EIGEN_STATIC_ASSERT(internal::check_implication(MatrixWrapper::MatrixFree, UpLo==(Lower|Upper)),MATRIX_FREE_CONJUGATE_GRADIENT_IS_COMPATIBLE_WITH_UPPER_UNION_LOWER_MODE_ONLY);
+ typedef std::conditional_t<UpLo==(Lower|Upper),
+ RowMajorWrapper,
+ typename MatrixWrapper::template ConstSelfAdjointViewReturnType<UpLo>::Type
+ > SelfAdjointWrapper;
+
+ m_iterations = Base::maxIterations();
+ m_error = Base::m_tolerance;
+ RowMajorWrapper row_mat(matrix());
+ internal::minres(SelfAdjointWrapper(row_mat), b, x,
+ Base::m_preconditioner, m_iterations, m_error);
+ m_info = m_error <= Base::m_tolerance ? Success : NoConvergence;
+ }
+
+ protected:
+
+ };
+
+} // end namespace Eigen
+
+#endif // EIGEN_MINRES_H
diff --git a/unsupported/Eigen/src/IterativeSolvers/Scaling.h b/unsupported/Eigen/src/IterativeSolvers/Scaling.h
new file mode 100644
index 0000000..9400e81
--- /dev/null
+++ b/unsupported/Eigen/src/IterativeSolvers/Scaling.h
@@ -0,0 +1,195 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2012 Desire NUENTSA WAKAM <desire.nuentsa_wakam@inria.fr
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_ITERSCALING_H
+#define EIGEN_ITERSCALING_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+/**
+ * \ingroup IterativeSolvers_Module
+ * \brief iterative scaling algorithm to equilibrate rows and column norms in matrices
+ *
+ * This class can be used as a preprocessing tool to accelerate the convergence of iterative methods
+ *
+ * This feature is useful to limit the pivoting amount during LU/ILU factorization
+ * The scaling strategy as presented here preserves the symmetry of the problem
+ * NOTE It is assumed that the matrix does not have empty row or column,
+ *
+ * Example with key steps
+ * \code
+ * VectorXd x(n), b(n);
+ * SparseMatrix<double> A;
+ * // fill A and b;
+ * IterScaling<SparseMatrix<double> > scal;
+ * // Compute the left and right scaling vectors. The matrix is equilibrated at output
+ * scal.computeRef(A);
+ * // Scale the right hand side
+ * b = scal.LeftScaling().cwiseProduct(b);
+ * // Now, solve the equilibrated linear system with any available solver
+ *
+ * // Scale back the computed solution
+ * x = scal.RightScaling().cwiseProduct(x);
+ * \endcode
+ *
+ * \tparam MatrixType_ the type of the matrix. It should be a real square sparsematrix
+ *
+ * References : D. Ruiz and B. Ucar, A Symmetry Preserving Algorithm for Matrix Scaling, INRIA Research report RR-7552
+ *
+ * \sa \ref IncompleteLUT
+ */
+template<typename MatrixType_>
+class IterScaling
+{
+ public:
+ typedef MatrixType_ MatrixType;
+ typedef typename MatrixType::Scalar Scalar;
+ typedef typename MatrixType::Index Index;
+
+ public:
+ IterScaling() { init(); }
+
+ IterScaling(const MatrixType& matrix)
+ {
+ init();
+ compute(matrix);
+ }
+
+ ~IterScaling() { }
+
+ /**
+ * Compute the left and right diagonal matrices to scale the input matrix @p mat
+ *
+ * FIXME This algorithm will be modified such that the diagonal elements are permuted on the diagonal.
+ *
+ * \sa LeftScaling() RightScaling()
+ */
+ void compute (const MatrixType& mat)
+ {
+ using std::abs;
+ int m = mat.rows();
+ int n = mat.cols();
+ eigen_assert((m>0 && m == n) && "Please give a non - empty matrix");
+ m_left.resize(m);
+ m_right.resize(n);
+ m_left.setOnes();
+ m_right.setOnes();
+ m_matrix = mat;
+ VectorXd Dr, Dc, DrRes, DcRes; // Temporary Left and right scaling vectors
+ Dr.resize(m); Dc.resize(n);
+ DrRes.resize(m); DcRes.resize(n);
+ double EpsRow = 1.0, EpsCol = 1.0;
+ int its = 0;
+ do
+ { // Iterate until the infinite norm of each row and column is approximately 1
+ // Get the maximum value in each row and column
+ Dr.setZero(); Dc.setZero();
+ for (int k=0; k<m_matrix.outerSize(); ++k)
+ {
+ for (typename MatrixType::InnerIterator it(m_matrix, k); it; ++it)
+ {
+ if ( Dr(it.row()) < abs(it.value()) )
+ Dr(it.row()) = abs(it.value());
+
+ if ( Dc(it.col()) < abs(it.value()) )
+ Dc(it.col()) = abs(it.value());
+ }
+ }
+ for (int i = 0; i < m; ++i)
+ {
+ Dr(i) = std::sqrt(Dr(i));
+ }
+ for (int i = 0; i < n; ++i)
+ {
+ Dc(i) = std::sqrt(Dc(i));
+ }
+ // Save the scaling factors
+ for (int i = 0; i < m; ++i)
+ {
+ m_left(i) /= Dr(i);
+ }
+ for (int i = 0; i < n; ++i)
+ {
+ m_right(i) /= Dc(i);
+ }
+ // Scale the rows and the columns of the matrix
+ DrRes.setZero(); DcRes.setZero();
+ for (int k=0; k<m_matrix.outerSize(); ++k)
+ {
+ for (typename MatrixType::InnerIterator it(m_matrix, k); it; ++it)
+ {
+ it.valueRef() = it.value()/( Dr(it.row()) * Dc(it.col()) );
+ // Accumulate the norms of the row and column vectors
+ if ( DrRes(it.row()) < abs(it.value()) )
+ DrRes(it.row()) = abs(it.value());
+
+ if ( DcRes(it.col()) < abs(it.value()) )
+ DcRes(it.col()) = abs(it.value());
+ }
+ }
+ DrRes.array() = (1-DrRes.array()).abs();
+ EpsRow = DrRes.maxCoeff();
+ DcRes.array() = (1-DcRes.array()).abs();
+ EpsCol = DcRes.maxCoeff();
+ its++;
+ }while ( (EpsRow >m_tol || EpsCol > m_tol) && (its < m_maxits) );
+ m_isInitialized = true;
+ }
+ /** Compute the left and right vectors to scale the vectors
+ * the input matrix is scaled with the computed vectors at output
+ *
+ * \sa compute()
+ */
+ void computeRef (MatrixType& mat)
+ {
+ compute (mat);
+ mat = m_matrix;
+ }
+ /** Get the vector to scale the rows of the matrix
+ */
+ VectorXd& LeftScaling()
+ {
+ return m_left;
+ }
+
+ /** Get the vector to scale the columns of the matrix
+ */
+ VectorXd& RightScaling()
+ {
+ return m_right;
+ }
+
+ /** Set the tolerance for the convergence of the iterative scaling algorithm
+ */
+ void setTolerance(double tol)
+ {
+ m_tol = tol;
+ }
+
+ protected:
+
+ void init()
+ {
+ m_tol = 1e-10;
+ m_maxits = 5;
+ m_isInitialized = false;
+ }
+
+ MatrixType m_matrix;
+ mutable ComputationInfo m_info;
+ bool m_isInitialized;
+ VectorXd m_left; // Left scaling vector
+ VectorXd m_right; // m_right scaling vector
+ double m_tol;
+ int m_maxits; // Maximum number of iterations allowed
+};
+}
+#endif
diff --git a/unsupported/Eigen/src/KroneckerProduct/InternalHeaderCheck.h b/unsupported/Eigen/src/KroneckerProduct/InternalHeaderCheck.h
new file mode 100644
index 0000000..3db2edc
--- /dev/null
+++ b/unsupported/Eigen/src/KroneckerProduct/InternalHeaderCheck.h
@@ -0,0 +1,3 @@
+#ifndef EIGEN_KRONECKER_PRODUCT_MODULE_H
+#error "Please include unsupported/Eigen/KroneckerProduct instead of including headers inside the src directory directly."
+#endif
diff --git a/unsupported/Eigen/src/KroneckerProduct/KroneckerTensorProduct.h b/unsupported/Eigen/src/KroneckerProduct/KroneckerTensorProduct.h
new file mode 100644
index 0000000..01a75ef
--- /dev/null
+++ b/unsupported/Eigen/src/KroneckerProduct/KroneckerTensorProduct.h
@@ -0,0 +1,307 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2011 Kolja Brix <brix@igpm.rwth-aachen.de>
+// Copyright (C) 2011 Andreas Platen <andiplaten@gmx.de>
+// Copyright (C) 2012 Chen-Pang He <jdh8@ms63.hinet.net>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef KRONECKER_TENSOR_PRODUCT_H
+#define KRONECKER_TENSOR_PRODUCT_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+/*!
+ * \ingroup KroneckerProduct_Module
+ *
+ * \brief The base class of dense and sparse Kronecker product.
+ *
+ * \tparam Derived is the derived type.
+ */
+template<typename Derived>
+class KroneckerProductBase : public ReturnByValue<Derived>
+{
+ private:
+ typedef typename internal::traits<Derived> Traits;
+ typedef typename Traits::Scalar Scalar;
+
+ protected:
+ typedef typename Traits::Lhs Lhs;
+ typedef typename Traits::Rhs Rhs;
+
+ public:
+ /*! \brief Constructor. */
+ KroneckerProductBase(const Lhs& A, const Rhs& B)
+ : m_A(A), m_B(B)
+ {}
+
+ inline Index rows() const { return m_A.rows() * m_B.rows(); }
+ inline Index cols() const { return m_A.cols() * m_B.cols(); }
+
+ /*!
+ * This overrides ReturnByValue::coeff because this function is
+ * efficient enough.
+ */
+ Scalar coeff(Index row, Index col) const
+ {
+ return m_A.coeff(row / m_B.rows(), col / m_B.cols()) *
+ m_B.coeff(row % m_B.rows(), col % m_B.cols());
+ }
+
+ /*!
+ * This overrides ReturnByValue::coeff because this function is
+ * efficient enough.
+ */
+ Scalar coeff(Index i) const
+ {
+ EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived);
+ return m_A.coeff(i / m_A.size()) * m_B.coeff(i % m_A.size());
+ }
+
+ protected:
+ typename Lhs::Nested m_A;
+ typename Rhs::Nested m_B;
+};
+
+/*!
+ * \ingroup KroneckerProduct_Module
+ *
+ * \brief Kronecker tensor product helper class for dense matrices
+ *
+ * This class is the return value of kroneckerProduct(MatrixBase,
+ * MatrixBase). Use the function rather than construct this class
+ * directly to avoid specifying template prarameters.
+ *
+ * \tparam Lhs Type of the left-hand side, a matrix expression.
+ * \tparam Rhs Type of the rignt-hand side, a matrix expression.
+ */
+template<typename Lhs, typename Rhs>
+class KroneckerProduct : public KroneckerProductBase<KroneckerProduct<Lhs,Rhs> >
+{
+ private:
+ typedef KroneckerProductBase<KroneckerProduct> Base;
+ using Base::m_A;
+ using Base::m_B;
+
+ public:
+ /*! \brief Constructor. */
+ KroneckerProduct(const Lhs& A, const Rhs& B)
+ : Base(A, B)
+ {}
+
+ /*! \brief Evaluate the Kronecker tensor product. */
+ template<typename Dest> void evalTo(Dest& dst) const;
+};
+
+/*!
+ * \ingroup KroneckerProduct_Module
+ *
+ * \brief Kronecker tensor product helper class for sparse matrices
+ *
+ * If at least one of the operands is a sparse matrix expression,
+ * then this class is returned and evaluates into a sparse matrix.
+ *
+ * This class is the return value of kroneckerProduct(EigenBase,
+ * EigenBase). Use the function rather than construct this class
+ * directly to avoid specifying template prarameters.
+ *
+ * \tparam Lhs Type of the left-hand side, a matrix expression.
+ * \tparam Rhs Type of the rignt-hand side, a matrix expression.
+ */
+template<typename Lhs, typename Rhs>
+class KroneckerProductSparse : public KroneckerProductBase<KroneckerProductSparse<Lhs,Rhs> >
+{
+ private:
+ typedef KroneckerProductBase<KroneckerProductSparse> Base;
+ using Base::m_A;
+ using Base::m_B;
+
+ public:
+ /*! \brief Constructor. */
+ KroneckerProductSparse(const Lhs& A, const Rhs& B)
+ : Base(A, B)
+ {}
+
+ /*! \brief Evaluate the Kronecker tensor product. */
+ template<typename Dest> void evalTo(Dest& dst) const;
+};
+
+template<typename Lhs, typename Rhs>
+template<typename Dest>
+void KroneckerProduct<Lhs,Rhs>::evalTo(Dest& dst) const
+{
+ const int BlockRows = Rhs::RowsAtCompileTime,
+ BlockCols = Rhs::ColsAtCompileTime;
+ const Index Br = m_B.rows(),
+ Bc = m_B.cols();
+ for (Index i=0; i < m_A.rows(); ++i)
+ for (Index j=0; j < m_A.cols(); ++j)
+ Block<Dest,BlockRows,BlockCols>(dst,i*Br,j*Bc,Br,Bc) = m_A.coeff(i,j) * m_B;
+}
+
+template<typename Lhs, typename Rhs>
+template<typename Dest>
+void KroneckerProductSparse<Lhs,Rhs>::evalTo(Dest& dst) const
+{
+ Index Br = m_B.rows(), Bc = m_B.cols();
+ dst.resize(this->rows(), this->cols());
+ dst.resizeNonZeros(0);
+
+ // 1 - evaluate the operands if needed:
+ typedef typename internal::nested_eval<Lhs,Dynamic>::type Lhs1;
+ typedef internal::remove_all_t<Lhs1> Lhs1Cleaned;
+ const Lhs1 lhs1(m_A);
+ typedef typename internal::nested_eval<Rhs,Dynamic>::type Rhs1;
+ typedef internal::remove_all_t<Rhs1> Rhs1Cleaned;
+ const Rhs1 rhs1(m_B);
+
+ // 2 - construct respective iterators
+ typedef Eigen::InnerIterator<Lhs1Cleaned> LhsInnerIterator;
+ typedef Eigen::InnerIterator<Rhs1Cleaned> RhsInnerIterator;
+
+ // compute number of non-zeros per innervectors of dst
+ {
+ // TODO VectorXi is not necessarily big enough!
+ VectorXi nnzA = VectorXi::Zero(Dest::IsRowMajor ? m_A.rows() : m_A.cols());
+ for (Index kA=0; kA < m_A.outerSize(); ++kA)
+ for (LhsInnerIterator itA(lhs1,kA); itA; ++itA)
+ nnzA(Dest::IsRowMajor ? itA.row() : itA.col())++;
+
+ VectorXi nnzB = VectorXi::Zero(Dest::IsRowMajor ? m_B.rows() : m_B.cols());
+ for (Index kB=0; kB < m_B.outerSize(); ++kB)
+ for (RhsInnerIterator itB(rhs1,kB); itB; ++itB)
+ nnzB(Dest::IsRowMajor ? itB.row() : itB.col())++;
+
+ Matrix<int,Dynamic,Dynamic,ColMajor> nnzAB = nnzB * nnzA.transpose();
+ dst.reserve(VectorXi::Map(nnzAB.data(), nnzAB.size()));
+ }
+
+ for (Index kA=0; kA < m_A.outerSize(); ++kA)
+ {
+ for (Index kB=0; kB < m_B.outerSize(); ++kB)
+ {
+ for (LhsInnerIterator itA(lhs1,kA); itA; ++itA)
+ {
+ for (RhsInnerIterator itB(rhs1,kB); itB; ++itB)
+ {
+ Index i = itA.row() * Br + itB.row(),
+ j = itA.col() * Bc + itB.col();
+ dst.insert(i,j) = itA.value() * itB.value();
+ }
+ }
+ }
+ }
+}
+
+namespace internal {
+
+template<typename Lhs_, typename Rhs_>
+struct traits<KroneckerProduct<Lhs_,Rhs_> >
+{
+ typedef remove_all_t<Lhs_> Lhs;
+ typedef remove_all_t<Rhs_> Rhs;
+ typedef typename ScalarBinaryOpTraits<typename Lhs::Scalar, typename Rhs::Scalar>::ReturnType Scalar;
+ typedef typename promote_index_type<typename Lhs::StorageIndex, typename Rhs::StorageIndex>::type StorageIndex;
+
+ enum {
+ Rows = size_at_compile_time(traits<Lhs>::RowsAtCompileTime, traits<Rhs>::RowsAtCompileTime),
+ Cols = size_at_compile_time(traits<Lhs>::ColsAtCompileTime, traits<Rhs>::ColsAtCompileTime),
+ MaxRows = size_at_compile_time(traits<Lhs>::MaxRowsAtCompileTime, traits<Rhs>::MaxRowsAtCompileTime),
+ MaxCols = size_at_compile_time(traits<Lhs>::MaxColsAtCompileTime, traits<Rhs>::MaxColsAtCompileTime)
+ };
+
+ typedef Matrix<Scalar,Rows,Cols> ReturnType;
+};
+
+template<typename Lhs_, typename Rhs_>
+struct traits<KroneckerProductSparse<Lhs_,Rhs_> >
+{
+ typedef MatrixXpr XprKind;
+ typedef remove_all_t<Lhs_> Lhs;
+ typedef remove_all_t<Rhs_> Rhs;
+ typedef typename ScalarBinaryOpTraits<typename Lhs::Scalar, typename Rhs::Scalar>::ReturnType Scalar;
+ typedef typename cwise_promote_storage_type<typename traits<Lhs>::StorageKind, typename traits<Rhs>::StorageKind, scalar_product_op<typename Lhs::Scalar, typename Rhs::Scalar> >::ret StorageKind;
+ typedef typename promote_index_type<typename Lhs::StorageIndex, typename Rhs::StorageIndex>::type StorageIndex;
+
+ enum {
+ LhsFlags = Lhs::Flags,
+ RhsFlags = Rhs::Flags,
+
+ RowsAtCompileTime = size_at_compile_time(traits<Lhs>::RowsAtCompileTime, traits<Rhs>::RowsAtCompileTime),
+ ColsAtCompileTime = size_at_compile_time(traits<Lhs>::ColsAtCompileTime, traits<Rhs>::ColsAtCompileTime),
+ MaxRowsAtCompileTime = size_at_compile_time(traits<Lhs>::MaxRowsAtCompileTime, traits<Rhs>::MaxRowsAtCompileTime),
+ MaxColsAtCompileTime = size_at_compile_time(traits<Lhs>::MaxColsAtCompileTime, traits<Rhs>::MaxColsAtCompileTime),
+
+ EvalToRowMajor = (int(LhsFlags) & int(RhsFlags) & RowMajorBit),
+ RemovedBits = ~(EvalToRowMajor ? 0 : RowMajorBit),
+
+ Flags = ((int(LhsFlags) | int(RhsFlags)) & HereditaryBits & RemovedBits)
+ | EvalBeforeNestingBit,
+ CoeffReadCost = HugeCost
+ };
+
+ typedef SparseMatrix<Scalar, 0, StorageIndex> ReturnType;
+};
+
+} // end namespace internal
+
+/*!
+ * \ingroup KroneckerProduct_Module
+ *
+ * Computes Kronecker tensor product of two dense matrices
+ *
+ * \warning If you want to replace a matrix by its Kronecker product
+ * with some matrix, do \b NOT do this:
+ * \code
+ * A = kroneckerProduct(A,B); // bug!!! caused by aliasing effect
+ * \endcode
+ * instead, use eval() to work around this:
+ * \code
+ * A = kroneckerProduct(A,B).eval();
+ * \endcode
+ *
+ * \param a Dense matrix a
+ * \param b Dense matrix b
+ * \return Kronecker tensor product of a and b
+ */
+template<typename A, typename B>
+KroneckerProduct<A,B> kroneckerProduct(const MatrixBase<A>& a, const MatrixBase<B>& b)
+{
+ return KroneckerProduct<A, B>(a.derived(), b.derived());
+}
+
+/*!
+ * \ingroup KroneckerProduct_Module
+ *
+ * Computes Kronecker tensor product of two matrices, at least one of
+ * which is sparse
+ *
+ * \warning If you want to replace a matrix by its Kronecker product
+ * with some matrix, do \b NOT do this:
+ * \code
+ * A = kroneckerProduct(A,B); // bug!!! caused by aliasing effect
+ * \endcode
+ * instead, use eval() to work around this:
+ * \code
+ * A = kroneckerProduct(A,B).eval();
+ * \endcode
+ *
+ * \param a Dense/sparse matrix a
+ * \param b Dense/sparse matrix b
+ * \return Kronecker tensor product of a and b, stored in a sparse
+ * matrix
+ */
+template<typename A, typename B>
+KroneckerProductSparse<A,B> kroneckerProduct(const EigenBase<A>& a, const EigenBase<B>& b)
+{
+ return KroneckerProductSparse<A,B>(a.derived(), b.derived());
+}
+
+} // end namespace Eigen
+
+#endif // KRONECKER_TENSOR_PRODUCT_H
diff --git a/unsupported/Eigen/src/LevenbergMarquardt/CopyrightMINPACK.txt b/unsupported/Eigen/src/LevenbergMarquardt/CopyrightMINPACK.txt
new file mode 100644
index 0000000..ae7984d
--- /dev/null
+++ b/unsupported/Eigen/src/LevenbergMarquardt/CopyrightMINPACK.txt
@@ -0,0 +1,52 @@
+Minpack Copyright Notice (1999) University of Chicago. All rights reserved
+
+Redistribution and use in source and binary forms, with or
+without modification, are permitted provided that the
+following conditions are met:
+
+1. Redistributions of source code must retain the above
+copyright notice, this list of conditions and the following
+disclaimer.
+
+2. Redistributions in binary form must reproduce the above
+copyright notice, this list of conditions and the following
+disclaimer in the documentation and/or other materials
+provided with the distribution.
+
+3. The end-user documentation included with the
+redistribution, if any, must include the following
+acknowledgment:
+
+ "This product includes software developed by the
+ University of Chicago, as Operator of Argonne National
+ Laboratory.
+
+Alternately, this acknowledgment may appear in the software
+itself, if and wherever such third-party acknowledgments
+normally appear.
+
+4. WARRANTY DISCLAIMER. THE SOFTWARE IS SUPPLIED "AS IS"
+WITHOUT WARRANTY OF ANY KIND. THE COPYRIGHT HOLDER, THE
+UNITED STATES, THE UNITED STATES DEPARTMENT OF ENERGY, AND
+THEIR EMPLOYEES: (1) DISCLAIM ANY WARRANTIES, EXPRESS OR
+IMPLIED, INCLUDING BUT NOT LIMITED TO ANY IMPLIED WARRANTIES
+OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE, TITLE
+OR NON-INFRINGEMENT, (2) DO NOT ASSUME ANY LEGAL LIABILITY
+OR RESPONSIBILITY FOR THE ACCURACY, COMPLETENESS, OR
+USEFULNESS OF THE SOFTWARE, (3) DO NOT REPRESENT THAT USE OF
+THE SOFTWARE WOULD NOT INFRINGE PRIVATELY OWNED RIGHTS, (4)
+DO NOT WARRANT THAT THE SOFTWARE WILL FUNCTION
+UNINTERRUPTED, THAT IT IS ERROR-FREE OR THAT ANY ERRORS WILL
+BE CORRECTED.
+
+5. LIMITATION OF LIABILITY. IN NO EVENT WILL THE COPYRIGHT
+HOLDER, THE UNITED STATES, THE UNITED STATES DEPARTMENT OF
+ENERGY, OR THEIR EMPLOYEES: BE LIABLE FOR ANY INDIRECT,
+INCIDENTAL, CONSEQUENTIAL, SPECIAL OR PUNITIVE DAMAGES OF
+ANY KIND OR NATURE, INCLUDING BUT NOT LIMITED TO LOSS OF
+PROFITS OR LOSS OF DATA, FOR ANY REASON WHATSOEVER, WHETHER
+SUCH LIABILITY IS ASSERTED ON THE BASIS OF CONTRACT, TORT
+(INCLUDING NEGLIGENCE OR STRICT LIABILITY), OR OTHERWISE,
+EVEN IF ANY OF SAID PARTIES HAS BEEN WARNED OF THE
+POSSIBILITY OF SUCH LOSS OR DAMAGES.
+
diff --git a/unsupported/Eigen/src/LevenbergMarquardt/InternalHeaderCheck.h b/unsupported/Eigen/src/LevenbergMarquardt/InternalHeaderCheck.h
new file mode 100644
index 0000000..bc76f4e
--- /dev/null
+++ b/unsupported/Eigen/src/LevenbergMarquardt/InternalHeaderCheck.h
@@ -0,0 +1,3 @@
+#ifndef EIGEN_LEVENBERGMARQUARDT_MODULE_H
+#error "Please include unsupported/Eigen/LevenbergMarquardt instead of including headers inside the src directory directly."
+#endif
diff --git a/unsupported/Eigen/src/LevenbergMarquardt/LMcovar.h b/unsupported/Eigen/src/LevenbergMarquardt/LMcovar.h
new file mode 100644
index 0000000..344c22e
--- /dev/null
+++ b/unsupported/Eigen/src/LevenbergMarquardt/LMcovar.h
@@ -0,0 +1,86 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// This code initially comes from MINPACK whose original authors are:
+// Copyright Jorge More - Argonne National Laboratory
+// Copyright Burt Garbow - Argonne National Laboratory
+// Copyright Ken Hillstrom - Argonne National Laboratory
+//
+// This Source Code Form is subject to the terms of the Minpack license
+// (a BSD-like license) described in the campaigned CopyrightMINPACK.txt file.
+
+#ifndef EIGEN_LMCOVAR_H
+#define EIGEN_LMCOVAR_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+
+template <typename Scalar>
+void covar(
+ Matrix< Scalar, Dynamic, Dynamic > &r,
+ const VectorXi& ipvt,
+ Scalar tol = std::sqrt(NumTraits<Scalar>::epsilon()) )
+{
+ using std::abs;
+ /* Local variables */
+ Index i, j, k, l, ii, jj;
+ bool sing;
+ Scalar temp;
+
+ /* Function Body */
+ const Index n = r.cols();
+ const Scalar tolr = tol * abs(r(0,0));
+ Matrix< Scalar, Dynamic, 1 > wa(n);
+ eigen_assert(ipvt.size()==n);
+
+ /* form the inverse of r in the full upper triangle of r. */
+ l = -1;
+ for (k = 0; k < n; ++k)
+ if (abs(r(k,k)) > tolr) {
+ r(k,k) = 1. / r(k,k);
+ for (j = 0; j <= k-1; ++j) {
+ temp = r(k,k) * r(j,k);
+ r(j,k) = 0.;
+ r.col(k).head(j+1) -= r.col(j).head(j+1) * temp;
+ }
+ l = k;
+ }
+
+ /* form the full upper triangle of the inverse of (r transpose)*r */
+ /* in the full upper triangle of r. */
+ for (k = 0; k <= l; ++k) {
+ for (j = 0; j <= k-1; ++j)
+ r.col(j).head(j+1) += r.col(k).head(j+1) * r(j,k);
+ r.col(k).head(k+1) *= r(k,k);
+ }
+
+ /* form the full lower triangle of the covariance matrix */
+ /* in the strict lower triangle of r and in wa. */
+ for (j = 0; j < n; ++j) {
+ jj = ipvt[j];
+ sing = j > l;
+ for (i = 0; i <= j; ++i) {
+ if (sing)
+ r(i,j) = 0.;
+ ii = ipvt[i];
+ if (ii > jj)
+ r(ii,jj) = r(i,j);
+ if (ii < jj)
+ r(jj,ii) = r(i,j);
+ }
+ wa[jj] = r(j,j);
+ }
+
+ /* symmetrize the covariance matrix in r. */
+ r.topLeftCorner(n,n).template triangularView<StrictlyUpper>() = r.topLeftCorner(n,n).transpose();
+ r.diagonal() = wa;
+}
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_LMCOVAR_H
diff --git a/unsupported/Eigen/src/LevenbergMarquardt/LMonestep.h b/unsupported/Eigen/src/LevenbergMarquardt/LMonestep.h
new file mode 100644
index 0000000..92cb6f6
--- /dev/null
+++ b/unsupported/Eigen/src/LevenbergMarquardt/LMonestep.h
@@ -0,0 +1,204 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009 Thomas Capricelli <orzel@freehackers.org>
+//
+// This code initially comes from MINPACK whose original authors are:
+// Copyright Jorge More - Argonne National Laboratory
+// Copyright Burt Garbow - Argonne National Laboratory
+// Copyright Ken Hillstrom - Argonne National Laboratory
+//
+// This Source Code Form is subject to the terms of the Minpack license
+// (a BSD-like license) described in the campaigned CopyrightMINPACK.txt file.
+
+#ifndef EIGEN_LMONESTEP_H
+#define EIGEN_LMONESTEP_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+template<typename FunctorType>
+LevenbergMarquardtSpace::Status
+LevenbergMarquardt<FunctorType>::minimizeOneStep(FVectorType &x)
+{
+ using std::abs;
+ using std::sqrt;
+ RealScalar temp, temp1,temp2;
+ RealScalar ratio;
+ RealScalar pnorm, xnorm, fnorm1, actred, dirder, prered;
+ eigen_assert(x.size()==n); // check the caller is not cheating us
+
+ temp = 0.0; xnorm = 0.0;
+ /* calculate the jacobian matrix. */
+ Index df_ret = m_functor.df(x, m_fjac);
+ if (df_ret<0)
+ return LevenbergMarquardtSpace::UserAsked;
+ if (df_ret>0)
+ // numerical diff, we evaluated the function df_ret times
+ m_nfev += df_ret;
+ else m_njev++;
+
+ /* compute the qr factorization of the jacobian. */
+ for (int j = 0; j < x.size(); ++j)
+ m_wa2(j) = m_fjac.col(j).blueNorm();
+ QRSolver qrfac(m_fjac);
+ if(qrfac.info() != Success) {
+ m_info = NumericalIssue;
+ return LevenbergMarquardtSpace::ImproperInputParameters;
+ }
+ // Make a copy of the first factor with the associated permutation
+ m_rfactor = qrfac.matrixR();
+ m_permutation = (qrfac.colsPermutation());
+
+ /* on the first iteration and if external scaling is not used, scale according */
+ /* to the norms of the columns of the initial jacobian. */
+ if (m_iter == 1) {
+ if (!m_useExternalScaling)
+ for (Index j = 0; j < n; ++j)
+ m_diag[j] = (m_wa2[j]==0.)? 1. : m_wa2[j];
+
+ /* on the first iteration, calculate the norm of the scaled x */
+ /* and initialize the step bound m_delta. */
+ xnorm = m_diag.cwiseProduct(x).stableNorm();
+ m_delta = m_factor * xnorm;
+ if (m_delta == 0.)
+ m_delta = m_factor;
+ }
+
+ /* form (q transpose)*m_fvec and store the first n components in */
+ /* m_qtf. */
+ m_wa4 = m_fvec;
+ m_wa4 = qrfac.matrixQ().adjoint() * m_fvec;
+ m_qtf = m_wa4.head(n);
+
+ /* compute the norm of the scaled gradient. */
+ m_gnorm = 0.;
+ if (m_fnorm != 0.)
+ for (Index j = 0; j < n; ++j)
+ if (m_wa2[m_permutation.indices()[j]] != 0.)
+ m_gnorm = (std::max)(m_gnorm, abs( m_rfactor.col(j).head(j+1).dot(m_qtf.head(j+1)/m_fnorm) / m_wa2[m_permutation.indices()[j]]));
+
+ /* test for convergence of the gradient norm. */
+ if (m_gnorm <= m_gtol) {
+ m_info = Success;
+ return LevenbergMarquardtSpace::CosinusTooSmall;
+ }
+
+ /* rescale if necessary. */
+ if (!m_useExternalScaling)
+ m_diag = m_diag.cwiseMax(m_wa2);
+
+ do {
+ /* determine the levenberg-marquardt parameter. */
+ internal::lmpar2(qrfac, m_diag, m_qtf, m_delta, m_par, m_wa1);
+
+ /* store the direction p and x + p. calculate the norm of p. */
+ m_wa1 = -m_wa1;
+ m_wa2 = x + m_wa1;
+ pnorm = m_diag.cwiseProduct(m_wa1).stableNorm();
+
+ /* on the first iteration, adjust the initial step bound. */
+ if (m_iter == 1)
+ m_delta = (std::min)(m_delta,pnorm);
+
+ /* evaluate the function at x + p and calculate its norm. */
+ if ( m_functor(m_wa2, m_wa4) < 0)
+ return LevenbergMarquardtSpace::UserAsked;
+ ++m_nfev;
+ fnorm1 = m_wa4.stableNorm();
+
+ /* compute the scaled actual reduction. */
+ actred = -1.;
+ if (Scalar(.1) * fnorm1 < m_fnorm)
+ actred = 1. - numext::abs2(fnorm1 / m_fnorm);
+
+ /* compute the scaled predicted reduction and */
+ /* the scaled directional derivative. */
+ m_wa3 = m_rfactor.template triangularView<Upper>() * (m_permutation.inverse() *m_wa1);
+ temp1 = numext::abs2(m_wa3.stableNorm() / m_fnorm);
+ temp2 = numext::abs2(sqrt(m_par) * pnorm / m_fnorm);
+ prered = temp1 + temp2 / Scalar(.5);
+ dirder = -(temp1 + temp2);
+
+ /* compute the ratio of the actual to the predicted */
+ /* reduction. */
+ ratio = 0.;
+ if (prered != 0.)
+ ratio = actred / prered;
+
+ /* update the step bound. */
+ if (ratio <= Scalar(.25)) {
+ if (actred >= 0.)
+ temp = RealScalar(.5);
+ if (actred < 0.)
+ temp = RealScalar(.5) * dirder / (dirder + RealScalar(.5) * actred);
+ if (RealScalar(.1) * fnorm1 >= m_fnorm || temp < RealScalar(.1))
+ temp = Scalar(.1);
+ /* Computing MIN */
+ m_delta = temp * (std::min)(m_delta, pnorm / RealScalar(.1));
+ m_par /= temp;
+ } else if (!(m_par != 0. && ratio < RealScalar(.75))) {
+ m_delta = pnorm / RealScalar(.5);
+ m_par = RealScalar(.5) * m_par;
+ }
+
+ /* test for successful iteration. */
+ if (ratio >= RealScalar(1e-4)) {
+ /* successful iteration. update x, m_fvec, and their norms. */
+ x = m_wa2;
+ m_wa2 = m_diag.cwiseProduct(x);
+ m_fvec = m_wa4;
+ xnorm = m_wa2.stableNorm();
+ m_fnorm = fnorm1;
+ ++m_iter;
+ }
+
+ /* tests for convergence. */
+ if (abs(actred) <= m_ftol && prered <= m_ftol && Scalar(.5) * ratio <= 1. && m_delta <= m_xtol * xnorm)
+ {
+ m_info = Success;
+ return LevenbergMarquardtSpace::RelativeErrorAndReductionTooSmall;
+ }
+ if (abs(actred) <= m_ftol && prered <= m_ftol && Scalar(.5) * ratio <= 1.)
+ {
+ m_info = Success;
+ return LevenbergMarquardtSpace::RelativeReductionTooSmall;
+ }
+ if (m_delta <= m_xtol * xnorm)
+ {
+ m_info = Success;
+ return LevenbergMarquardtSpace::RelativeErrorTooSmall;
+ }
+
+ /* tests for termination and stringent tolerances. */
+ if (m_nfev >= m_maxfev)
+ {
+ m_info = NoConvergence;
+ return LevenbergMarquardtSpace::TooManyFunctionEvaluation;
+ }
+ if (abs(actred) <= NumTraits<Scalar>::epsilon() && prered <= NumTraits<Scalar>::epsilon() && Scalar(.5) * ratio <= 1.)
+ {
+ m_info = Success;
+ return LevenbergMarquardtSpace::FtolTooSmall;
+ }
+ if (m_delta <= NumTraits<Scalar>::epsilon() * xnorm)
+ {
+ m_info = Success;
+ return LevenbergMarquardtSpace::XtolTooSmall;
+ }
+ if (m_gnorm <= NumTraits<Scalar>::epsilon())
+ {
+ m_info = Success;
+ return LevenbergMarquardtSpace::GtolTooSmall;
+ }
+
+ } while (ratio < Scalar(1e-4));
+
+ return LevenbergMarquardtSpace::Running;
+}
+
+
+} // end namespace Eigen
+
+#endif // EIGEN_LMONESTEP_H
diff --git a/unsupported/Eigen/src/LevenbergMarquardt/LMpar.h b/unsupported/Eigen/src/LevenbergMarquardt/LMpar.h
new file mode 100644
index 0000000..74acc9a
--- /dev/null
+++ b/unsupported/Eigen/src/LevenbergMarquardt/LMpar.h
@@ -0,0 +1,162 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// This code initially comes from MINPACK whose original authors are:
+// Copyright Jorge More - Argonne National Laboratory
+// Copyright Burt Garbow - Argonne National Laboratory
+// Copyright Ken Hillstrom - Argonne National Laboratory
+//
+// This Source Code Form is subject to the terms of the Minpack license
+// (a BSD-like license) described in the campaigned CopyrightMINPACK.txt file.
+
+#ifndef EIGEN_LMPAR_H
+#define EIGEN_LMPAR_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+
+ template <typename QRSolver, typename VectorType>
+ void lmpar2(
+ const QRSolver &qr,
+ const VectorType &diag,
+ const VectorType &qtb,
+ typename VectorType::Scalar m_delta,
+ typename VectorType::Scalar &par,
+ VectorType &x)
+
+ {
+ using std::sqrt;
+ using std::abs;
+ typedef typename QRSolver::MatrixType MatrixType;
+ typedef typename QRSolver::Scalar Scalar;
+// typedef typename QRSolver::StorageIndex StorageIndex;
+
+ /* Local variables */
+ Index j;
+ Scalar fp;
+ Scalar parc, parl;
+ Index iter;
+ Scalar temp, paru;
+ Scalar gnorm;
+ Scalar dxnorm;
+
+ // Make a copy of the triangular factor.
+ // This copy is modified during call the qrsolv
+ MatrixType s;
+ s = qr.matrixR();
+
+ /* Function Body */
+ const Scalar dwarf = (std::numeric_limits<Scalar>::min)();
+ const Index n = qr.matrixR().cols();
+ eigen_assert(n==diag.size());
+ eigen_assert(n==qtb.size());
+
+ VectorType wa1, wa2;
+
+ /* compute and store in x the gauss-newton direction. if the */
+ /* jacobian is rank-deficient, obtain a least squares solution. */
+
+ // const Index rank = qr.nonzeroPivots(); // exactly double(0.)
+ const Index rank = qr.rank(); // use a threshold
+ wa1 = qtb;
+ wa1.tail(n-rank).setZero();
+ //FIXME There is no solve in place for sparse triangularView
+ wa1.head(rank) = s.topLeftCorner(rank,rank).template triangularView<Upper>().solve(qtb.head(rank));
+
+ x = qr.colsPermutation()*wa1;
+
+ /* initialize the iteration counter. */
+ /* evaluate the function at the origin, and test */
+ /* for acceptance of the gauss-newton direction. */
+ iter = 0;
+ wa2 = diag.cwiseProduct(x);
+ dxnorm = wa2.blueNorm();
+ fp = dxnorm - m_delta;
+ if (fp <= Scalar(0.1) * m_delta) {
+ par = 0;
+ return;
+ }
+
+ /* if the jacobian is not rank deficient, the newton */
+ /* step provides a lower bound, parl, for the zero of */
+ /* the function. otherwise set this bound to zero. */
+ parl = 0.;
+ if (rank==n) {
+ wa1 = qr.colsPermutation().inverse() * diag.cwiseProduct(wa2)/dxnorm;
+ s.topLeftCorner(n,n).transpose().template triangularView<Lower>().solveInPlace(wa1);
+ temp = wa1.blueNorm();
+ parl = fp / m_delta / temp / temp;
+ }
+
+ /* calculate an upper bound, paru, for the zero of the function. */
+ for (j = 0; j < n; ++j)
+ wa1[j] = s.col(j).head(j+1).dot(qtb.head(j+1)) / diag[qr.colsPermutation().indices()(j)];
+
+ gnorm = wa1.stableNorm();
+ paru = gnorm / m_delta;
+ if (paru == 0.)
+ paru = dwarf / (std::min)(m_delta,Scalar(0.1));
+
+ /* if the input par lies outside of the interval (parl,paru), */
+ /* set par to the closer endpoint. */
+ par = (std::max)(par,parl);
+ par = (std::min)(par,paru);
+ if (par == 0.)
+ par = gnorm / dxnorm;
+
+ /* beginning of an iteration. */
+ while (true) {
+ ++iter;
+
+ /* evaluate the function at the current value of par. */
+ if (par == 0.)
+ par = (std::max)(dwarf,Scalar(.001) * paru); /* Computing MAX */
+ wa1 = sqrt(par)* diag;
+
+ VectorType sdiag(n);
+ lmqrsolv(s, qr.colsPermutation(), wa1, qtb, x, sdiag);
+
+ wa2 = diag.cwiseProduct(x);
+ dxnorm = wa2.blueNorm();
+ temp = fp;
+ fp = dxnorm - m_delta;
+
+ /* if the function is small enough, accept the current value */
+ /* of par. also test for the exceptional cases where parl */
+ /* is zero or the number of iterations has reached 10. */
+ if (abs(fp) <= Scalar(0.1) * m_delta || (parl == 0. && fp <= temp && temp < 0.) || iter == 10)
+ break;
+
+ /* compute the newton correction. */
+ wa1 = qr.colsPermutation().inverse() * diag.cwiseProduct(wa2/dxnorm);
+ // we could almost use this here, but the diagonal is outside qr, in sdiag[]
+ for (j = 0; j < n; ++j) {
+ wa1[j] /= sdiag[j];
+ temp = wa1[j];
+ for (Index i = j+1; i < n; ++i)
+ wa1[i] -= s.coeff(i,j) * temp;
+ }
+ temp = wa1.blueNorm();
+ parc = fp / m_delta / temp / temp;
+
+ /* depending on the sign of the function, update parl or paru. */
+ if (fp > 0.)
+ parl = (std::max)(parl,par);
+ if (fp < 0.)
+ paru = (std::min)(paru,par);
+
+ /* compute an improved estimate for par. */
+ par = (std::max)(parl,par+parc);
+ }
+ if (iter == 0)
+ par = 0.;
+ return;
+ }
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_LMPAR_H
diff --git a/unsupported/Eigen/src/LevenbergMarquardt/LMqrsolv.h b/unsupported/Eigen/src/LevenbergMarquardt/LMqrsolv.h
new file mode 100644
index 0000000..385b7b5
--- /dev/null
+++ b/unsupported/Eigen/src/LevenbergMarquardt/LMqrsolv.h
@@ -0,0 +1,190 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009 Thomas Capricelli <orzel@freehackers.org>
+// Copyright (C) 2012 Desire Nuentsa <desire.nuentsa_wakam@inria.fr>
+//
+// This code initially comes from MINPACK whose original authors are:
+// Copyright Jorge More - Argonne National Laboratory
+// Copyright Burt Garbow - Argonne National Laboratory
+// Copyright Ken Hillstrom - Argonne National Laboratory
+//
+// This Source Code Form is subject to the terms of the Minpack license
+// (a BSD-like license) described in the campaigned CopyrightMINPACK.txt file.
+
+#ifndef EIGEN_LMQRSOLV_H
+#define EIGEN_LMQRSOLV_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+
+template <typename Scalar,int Rows, int Cols, typename PermIndex>
+void lmqrsolv(
+ Matrix<Scalar,Rows,Cols> &s,
+ const PermutationMatrix<Dynamic,Dynamic,PermIndex> &iPerm,
+ const Matrix<Scalar,Dynamic,1> &diag,
+ const Matrix<Scalar,Dynamic,1> &qtb,
+ Matrix<Scalar,Dynamic,1> &x,
+ Matrix<Scalar,Dynamic,1> &sdiag)
+{
+ /* Local variables */
+ Index i, j, k;
+ Scalar temp;
+ Index n = s.cols();
+ Matrix<Scalar,Dynamic,1> wa(n);
+ JacobiRotation<Scalar> givens;
+
+ /* Function Body */
+ // the following will only change the lower triangular part of s, including
+ // the diagonal, though the diagonal is restored afterward
+
+ /* copy r and (q transpose)*b to preserve input and initialize s. */
+ /* in particular, save the diagonal elements of r in x. */
+ x = s.diagonal();
+ wa = qtb;
+
+
+ s.topLeftCorner(n,n).template triangularView<StrictlyLower>() = s.topLeftCorner(n,n).transpose();
+ /* eliminate the diagonal matrix d using a givens rotation. */
+ for (j = 0; j < n; ++j) {
+
+ /* prepare the row of d to be eliminated, locating the */
+ /* diagonal element using p from the qr factorization. */
+ const PermIndex l = iPerm.indices()(j);
+ if (diag[l] == 0.)
+ break;
+ sdiag.tail(n-j).setZero();
+ sdiag[j] = diag[l];
+
+ /* the transformations to eliminate the row of d */
+ /* modify only a single element of (q transpose)*b */
+ /* beyond the first n, which is initially zero. */
+ Scalar qtbpj = 0.;
+ for (k = j; k < n; ++k) {
+ /* determine a givens rotation which eliminates the */
+ /* appropriate element in the current row of d. */
+ givens.makeGivens(-s(k,k), sdiag[k]);
+
+ /* compute the modified diagonal element of r and */
+ /* the modified element of ((q transpose)*b,0). */
+ s(k,k) = givens.c() * s(k,k) + givens.s() * sdiag[k];
+ temp = givens.c() * wa[k] + givens.s() * qtbpj;
+ qtbpj = -givens.s() * wa[k] + givens.c() * qtbpj;
+ wa[k] = temp;
+
+ /* accumulate the transformation in the row of s. */
+ for (i = k+1; i<n; ++i) {
+ temp = givens.c() * s(i,k) + givens.s() * sdiag[i];
+ sdiag[i] = -givens.s() * s(i,k) + givens.c() * sdiag[i];
+ s(i,k) = temp;
+ }
+ }
+ }
+
+ /* solve the triangular system for z. if the system is */
+ /* singular, then obtain a least squares solution. */
+ Index nsing;
+ for(nsing=0; nsing<n && sdiag[nsing]!=0; nsing++) {}
+
+ wa.tail(n-nsing).setZero();
+ s.topLeftCorner(nsing, nsing).transpose().template triangularView<Upper>().solveInPlace(wa.head(nsing));
+
+ // restore
+ sdiag = s.diagonal();
+ s.diagonal() = x;
+
+ /* permute the components of z back to components of x. */
+ x = iPerm * wa;
+}
+
+template <typename Scalar, int Options_, typename Index>
+void lmqrsolv(
+ SparseMatrix<Scalar,Options_,Index> &s,
+ const PermutationMatrix<Dynamic,Dynamic> &iPerm,
+ const Matrix<Scalar,Dynamic,1> &diag,
+ const Matrix<Scalar,Dynamic,1> &qtb,
+ Matrix<Scalar,Dynamic,1> &x,
+ Matrix<Scalar,Dynamic,1> &sdiag)
+{
+ /* Local variables */
+ typedef SparseMatrix<Scalar,RowMajor,Index> FactorType;
+ Index i, j, k, l;
+ Scalar temp;
+ Index n = s.cols();
+ Matrix<Scalar,Dynamic,1> wa(n);
+ JacobiRotation<Scalar> givens;
+
+ /* Function Body */
+ // the following will only change the lower triangular part of s, including
+ // the diagonal, though the diagonal is restored afterward
+
+ /* copy r and (q transpose)*b to preserve input and initialize R. */
+ wa = qtb;
+ FactorType R(s);
+ // Eliminate the diagonal matrix d using a givens rotation
+ for (j = 0; j < n; ++j)
+ {
+ // Prepare the row of d to be eliminated, locating the
+ // diagonal element using p from the qr factorization
+ l = iPerm.indices()(j);
+ if (diag(l) == Scalar(0))
+ break;
+ sdiag.tail(n-j).setZero();
+ sdiag[j] = diag[l];
+ // the transformations to eliminate the row of d
+ // modify only a single element of (q transpose)*b
+ // beyond the first n, which is initially zero.
+
+ Scalar qtbpj = 0;
+ // Browse the nonzero elements of row j of the upper triangular s
+ for (k = j; k < n; ++k)
+ {
+ typename FactorType::InnerIterator itk(R,k);
+ for (; itk; ++itk){
+ if (itk.index() < k) continue;
+ else break;
+ }
+ //At this point, we have the diagonal element R(k,k)
+ // Determine a givens rotation which eliminates
+ // the appropriate element in the current row of d
+ givens.makeGivens(-itk.value(), sdiag(k));
+
+ // Compute the modified diagonal element of r and
+ // the modified element of ((q transpose)*b,0).
+ itk.valueRef() = givens.c() * itk.value() + givens.s() * sdiag(k);
+ temp = givens.c() * wa(k) + givens.s() * qtbpj;
+ qtbpj = -givens.s() * wa(k) + givens.c() * qtbpj;
+ wa(k) = temp;
+
+ // Accumulate the transformation in the remaining k row/column of R
+ for (++itk; itk; ++itk)
+ {
+ i = itk.index();
+ temp = givens.c() * itk.value() + givens.s() * sdiag(i);
+ sdiag(i) = -givens.s() * itk.value() + givens.c() * sdiag(i);
+ itk.valueRef() = temp;
+ }
+ }
+ }
+
+ // Solve the triangular system for z. If the system is
+ // singular, then obtain a least squares solution
+ Index nsing;
+ for(nsing = 0; nsing<n && sdiag(nsing) !=0; nsing++) {}
+
+ wa.tail(n-nsing).setZero();
+// x = wa;
+ wa.head(nsing) = R.topLeftCorner(nsing,nsing).template triangularView<Upper>().solve/*InPlace*/(wa.head(nsing));
+
+ sdiag = R.diagonal();
+ // Permute the components of z back to components of x
+ x = iPerm * wa;
+}
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_LMQRSOLV_H
diff --git a/unsupported/Eigen/src/LevenbergMarquardt/LevenbergMarquardt.h b/unsupported/Eigen/src/LevenbergMarquardt/LevenbergMarquardt.h
new file mode 100644
index 0000000..f823ae0
--- /dev/null
+++ b/unsupported/Eigen/src/LevenbergMarquardt/LevenbergMarquardt.h
@@ -0,0 +1,398 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009 Thomas Capricelli <orzel@freehackers.org>
+// Copyright (C) 2012 Desire Nuentsa <desire.nuentsa_wakam@inria.fr>
+//
+// The algorithm of this class initially comes from MINPACK whose original authors are:
+// Copyright Jorge More - Argonne National Laboratory
+// Copyright Burt Garbow - Argonne National Laboratory
+// Copyright Ken Hillstrom - Argonne National Laboratory
+//
+// This Source Code Form is subject to the terms of the Minpack license
+// (a BSD-like license) described in the campaigned CopyrightMINPACK.txt file.
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_LEVENBERGMARQUARDT_H
+#define EIGEN_LEVENBERGMARQUARDT_H
+
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+namespace LevenbergMarquardtSpace {
+ enum Status {
+ NotStarted = -2,
+ Running = -1,
+ ImproperInputParameters = 0,
+ RelativeReductionTooSmall = 1,
+ RelativeErrorTooSmall = 2,
+ RelativeErrorAndReductionTooSmall = 3,
+ CosinusTooSmall = 4,
+ TooManyFunctionEvaluation = 5,
+ FtolTooSmall = 6,
+ XtolTooSmall = 7,
+ GtolTooSmall = 8,
+ UserAsked = 9
+ };
+}
+
+template <typename Scalar_, int NX=Dynamic, int NY=Dynamic>
+struct DenseFunctor
+{
+ typedef Scalar_ Scalar;
+ enum {
+ InputsAtCompileTime = NX,
+ ValuesAtCompileTime = NY
+ };
+ typedef Matrix<Scalar,InputsAtCompileTime,1> InputType;
+ typedef Matrix<Scalar,ValuesAtCompileTime,1> ValueType;
+ typedef Matrix<Scalar,ValuesAtCompileTime,InputsAtCompileTime> JacobianType;
+ typedef ColPivHouseholderQR<JacobianType> QRSolver;
+ const int m_inputs, m_values;
+
+ DenseFunctor() : m_inputs(InputsAtCompileTime), m_values(ValuesAtCompileTime) {}
+ DenseFunctor(int inputs, int values) : m_inputs(inputs), m_values(values) {}
+
+ int inputs() const { return m_inputs; }
+ int values() const { return m_values; }
+
+ //int operator()(const InputType &x, ValueType& fvec) { }
+ // should be defined in derived classes
+
+ //int df(const InputType &x, JacobianType& fjac) { }
+ // should be defined in derived classes
+};
+
+template <typename Scalar_, typename Index_>
+struct SparseFunctor
+{
+ typedef Scalar_ Scalar;
+ typedef Index_ Index;
+ typedef Matrix<Scalar,Dynamic,1> InputType;
+ typedef Matrix<Scalar,Dynamic,1> ValueType;
+ typedef SparseMatrix<Scalar, ColMajor, Index> JacobianType;
+ typedef SparseQR<JacobianType, COLAMDOrdering<int> > QRSolver;
+ enum {
+ InputsAtCompileTime = Dynamic,
+ ValuesAtCompileTime = Dynamic
+ };
+
+ SparseFunctor(int inputs, int values) : m_inputs(inputs), m_values(values) {}
+
+ int inputs() const { return m_inputs; }
+ int values() const { return m_values; }
+
+ const int m_inputs, m_values;
+ //int operator()(const InputType &x, ValueType& fvec) { }
+ // to be defined in the functor
+
+ //int df(const InputType &x, JacobianType& fjac) { }
+ // to be defined in the functor if no automatic differentiation
+
+};
+namespace internal {
+template <typename QRSolver, typename VectorType>
+void lmpar2(const QRSolver &qr, const VectorType &diag, const VectorType &qtb,
+ typename VectorType::Scalar m_delta, typename VectorType::Scalar &par,
+ VectorType &x);
+ }
+/**
+ * \ingroup NonLinearOptimization_Module
+ * \brief Performs non linear optimization over a non-linear function,
+ * using a variant of the Levenberg Marquardt algorithm.
+ *
+ * Check wikipedia for more information.
+ * http://en.wikipedia.org/wiki/Levenberg%E2%80%93Marquardt_algorithm
+ */
+template<typename FunctorType_>
+class LevenbergMarquardt : internal::no_assignment_operator
+{
+ public:
+ typedef FunctorType_ FunctorType;
+ typedef typename FunctorType::QRSolver QRSolver;
+ typedef typename FunctorType::JacobianType JacobianType;
+ typedef typename JacobianType::Scalar Scalar;
+ typedef typename JacobianType::RealScalar RealScalar;
+ typedef typename QRSolver::StorageIndex PermIndex;
+ typedef Matrix<Scalar,Dynamic,1> FVectorType;
+ typedef PermutationMatrix<Dynamic,Dynamic,int> PermutationType;
+ public:
+ LevenbergMarquardt(FunctorType& functor)
+ : m_functor(functor),m_nfev(0),m_njev(0),m_fnorm(0.0),m_gnorm(0),
+ m_isInitialized(false),m_info(InvalidInput)
+ {
+ resetParameters();
+ m_useExternalScaling=false;
+ }
+
+ LevenbergMarquardtSpace::Status minimize(FVectorType &x);
+ LevenbergMarquardtSpace::Status minimizeInit(FVectorType &x);
+ LevenbergMarquardtSpace::Status minimizeOneStep(FVectorType &x);
+ LevenbergMarquardtSpace::Status lmder1(
+ FVectorType &x,
+ const Scalar tol = std::sqrt(NumTraits<Scalar>::epsilon())
+ );
+ static LevenbergMarquardtSpace::Status lmdif1(
+ FunctorType &functor,
+ FVectorType &x,
+ Index *nfev,
+ const Scalar tol = std::sqrt(NumTraits<Scalar>::epsilon())
+ );
+
+ /** Sets the default parameters */
+ void resetParameters()
+ {
+ using std::sqrt;
+
+ m_factor = 100.;
+ m_maxfev = 400;
+ m_ftol = sqrt(NumTraits<RealScalar>::epsilon());
+ m_xtol = sqrt(NumTraits<RealScalar>::epsilon());
+ m_gtol = 0. ;
+ m_epsfcn = 0. ;
+ }
+
+ /** Sets the tolerance for the norm of the solution vector*/
+ void setXtol(RealScalar xtol) { m_xtol = xtol; }
+
+ /** Sets the tolerance for the norm of the vector function*/
+ void setFtol(RealScalar ftol) { m_ftol = ftol; }
+
+ /** Sets the tolerance for the norm of the gradient of the error vector*/
+ void setGtol(RealScalar gtol) { m_gtol = gtol; }
+
+ /** Sets the step bound for the diagonal shift */
+ void setFactor(RealScalar factor) { m_factor = factor; }
+
+ /** Sets the error precision */
+ void setEpsilon (RealScalar epsfcn) { m_epsfcn = epsfcn; }
+
+ /** Sets the maximum number of function evaluation */
+ void setMaxfev(Index maxfev) {m_maxfev = maxfev; }
+
+ /** Use an external Scaling. If set to true, pass a nonzero diagonal to diag() */
+ void setExternalScaling(bool value) {m_useExternalScaling = value; }
+
+ /** \returns the tolerance for the norm of the solution vector */
+ RealScalar xtol() const {return m_xtol; }
+
+ /** \returns the tolerance for the norm of the vector function */
+ RealScalar ftol() const {return m_ftol; }
+
+ /** \returns the tolerance for the norm of the gradient of the error vector */
+ RealScalar gtol() const {return m_gtol; }
+
+ /** \returns the step bound for the diagonal shift */
+ RealScalar factor() const {return m_factor; }
+
+ /** \returns the error precision */
+ RealScalar epsilon() const {return m_epsfcn; }
+
+ /** \returns the maximum number of function evaluation */
+ Index maxfev() const {return m_maxfev; }
+
+ /** \returns a reference to the diagonal of the jacobian */
+ FVectorType& diag() {return m_diag; }
+
+ /** \returns the number of iterations performed */
+ Index iterations() { return m_iter; }
+
+ /** \returns the number of functions evaluation */
+ Index nfev() { return m_nfev; }
+
+ /** \returns the number of jacobian evaluation */
+ Index njev() { return m_njev; }
+
+ /** \returns the norm of current vector function */
+ RealScalar fnorm() {return m_fnorm; }
+
+ /** \returns the norm of the gradient of the error */
+ RealScalar gnorm() {return m_gnorm; }
+
+ /** \returns the LevenbergMarquardt parameter */
+ RealScalar lm_param(void) { return m_par; }
+
+ /** \returns a reference to the current vector function
+ */
+ FVectorType& fvec() {return m_fvec; }
+
+ /** \returns a reference to the matrix where the current Jacobian matrix is stored
+ */
+ JacobianType& jacobian() {return m_fjac; }
+
+ /** \returns a reference to the triangular matrix R from the QR of the jacobian matrix.
+ * \sa jacobian()
+ */
+ JacobianType& matrixR() {return m_rfactor; }
+
+ /** the permutation used in the QR factorization
+ */
+ PermutationType permutation() {return m_permutation; }
+
+ /**
+ * \brief Reports whether the minimization was successful
+ * \returns \c Success if the minimization was successful,
+ * \c NumericalIssue if a numerical problem arises during the
+ * minimization process, for example during the QR factorization
+ * \c NoConvergence if the minimization did not converge after
+ * the maximum number of function evaluation allowed
+ * \c InvalidInput if the input matrix is invalid
+ */
+ ComputationInfo info() const
+ {
+
+ return m_info;
+ }
+ private:
+ JacobianType m_fjac;
+ JacobianType m_rfactor; // The triangular matrix R from the QR of the jacobian matrix m_fjac
+ FunctorType &m_functor;
+ FVectorType m_fvec, m_qtf, m_diag;
+ Index n;
+ Index m;
+ Index m_nfev;
+ Index m_njev;
+ RealScalar m_fnorm; // Norm of the current vector function
+ RealScalar m_gnorm; //Norm of the gradient of the error
+ RealScalar m_factor; //
+ Index m_maxfev; // Maximum number of function evaluation
+ RealScalar m_ftol; //Tolerance in the norm of the vector function
+ RealScalar m_xtol; //
+ RealScalar m_gtol; //tolerance of the norm of the error gradient
+ RealScalar m_epsfcn; //
+ Index m_iter; // Number of iterations performed
+ RealScalar m_delta;
+ bool m_useExternalScaling;
+ PermutationType m_permutation;
+ FVectorType m_wa1, m_wa2, m_wa3, m_wa4; //Temporary vectors
+ RealScalar m_par;
+ bool m_isInitialized; // Check whether the minimization step has been called
+ ComputationInfo m_info;
+};
+
+template<typename FunctorType>
+LevenbergMarquardtSpace::Status
+LevenbergMarquardt<FunctorType>::minimize(FVectorType &x)
+{
+ LevenbergMarquardtSpace::Status status = minimizeInit(x);
+ if (status==LevenbergMarquardtSpace::ImproperInputParameters) {
+ m_isInitialized = true;
+ return status;
+ }
+ do {
+// std::cout << " uv " << x.transpose() << "\n";
+ status = minimizeOneStep(x);
+ } while (status==LevenbergMarquardtSpace::Running);
+ m_isInitialized = true;
+ return status;
+}
+
+template<typename FunctorType>
+LevenbergMarquardtSpace::Status
+LevenbergMarquardt<FunctorType>::minimizeInit(FVectorType &x)
+{
+ n = x.size();
+ m = m_functor.values();
+
+ m_wa1.resize(n); m_wa2.resize(n); m_wa3.resize(n);
+ m_wa4.resize(m);
+ m_fvec.resize(m);
+ //FIXME Sparse Case : Allocate space for the jacobian
+ m_fjac.resize(m, n);
+// m_fjac.reserve(VectorXi::Constant(n,5)); // FIXME Find a better alternative
+ if (!m_useExternalScaling)
+ m_diag.resize(n);
+ eigen_assert( (!m_useExternalScaling || m_diag.size()==n) && "When m_useExternalScaling is set, the caller must provide a valid 'm_diag'");
+ m_qtf.resize(n);
+
+ /* Function Body */
+ m_nfev = 0;
+ m_njev = 0;
+
+ /* check the input parameters for errors. */
+ if (n <= 0 || m < n || m_ftol < 0. || m_xtol < 0. || m_gtol < 0. || m_maxfev <= 0 || m_factor <= 0.){
+ m_info = InvalidInput;
+ return LevenbergMarquardtSpace::ImproperInputParameters;
+ }
+
+ if (m_useExternalScaling)
+ for (Index j = 0; j < n; ++j)
+ if (m_diag[j] <= 0.)
+ {
+ m_info = InvalidInput;
+ return LevenbergMarquardtSpace::ImproperInputParameters;
+ }
+
+ /* evaluate the function at the starting point */
+ /* and calculate its norm. */
+ m_nfev = 1;
+ if ( m_functor(x, m_fvec) < 0)
+ return LevenbergMarquardtSpace::UserAsked;
+ m_fnorm = m_fvec.stableNorm();
+
+ /* initialize levenberg-marquardt parameter and iteration counter. */
+ m_par = 0.;
+ m_iter = 1;
+
+ return LevenbergMarquardtSpace::NotStarted;
+}
+
+template<typename FunctorType>
+LevenbergMarquardtSpace::Status
+LevenbergMarquardt<FunctorType>::lmder1(
+ FVectorType &x,
+ const Scalar tol
+ )
+{
+ n = x.size();
+ m = m_functor.values();
+
+ /* check the input parameters for errors. */
+ if (n <= 0 || m < n || tol < 0.)
+ return LevenbergMarquardtSpace::ImproperInputParameters;
+
+ resetParameters();
+ m_ftol = tol;
+ m_xtol = tol;
+ m_maxfev = 100*(n+1);
+
+ return minimize(x);
+}
+
+
+template<typename FunctorType>
+LevenbergMarquardtSpace::Status
+LevenbergMarquardt<FunctorType>::lmdif1(
+ FunctorType &functor,
+ FVectorType &x,
+ Index *nfev,
+ const Scalar tol
+ )
+{
+ Index n = x.size();
+ Index m = functor.values();
+
+ /* check the input parameters for errors. */
+ if (n <= 0 || m < n || tol < 0.)
+ return LevenbergMarquardtSpace::ImproperInputParameters;
+
+ NumericalDiff<FunctorType> numDiff(functor);
+ // embedded LevenbergMarquardt
+ LevenbergMarquardt<NumericalDiff<FunctorType> > lm(numDiff);
+ lm.setFtol(tol);
+ lm.setXtol(tol);
+ lm.setMaxfev(200*(n+1));
+
+ LevenbergMarquardtSpace::Status info = LevenbergMarquardtSpace::Status(lm.minimize(x));
+ if (nfev)
+ * nfev = lm.nfev();
+ return info;
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_LEVENBERGMARQUARDT_H
diff --git a/unsupported/Eigen/src/MatrixFunctions/InternalHeaderCheck.h b/unsupported/Eigen/src/MatrixFunctions/InternalHeaderCheck.h
new file mode 100644
index 0000000..b737f3c
--- /dev/null
+++ b/unsupported/Eigen/src/MatrixFunctions/InternalHeaderCheck.h
@@ -0,0 +1,3 @@
+#ifndef EIGEN_MATRIX_FUNCTIONS_MODULE_H
+#error "Please include unsupported/Eigen/MatrixFunctions instead of including headers inside the src directory directly."
+#endif
diff --git a/unsupported/Eigen/src/MatrixFunctions/MatrixExponential.h b/unsupported/Eigen/src/MatrixFunctions/MatrixExponential.h
new file mode 100644
index 0000000..ab6284a
--- /dev/null
+++ b/unsupported/Eigen/src/MatrixFunctions/MatrixExponential.h
@@ -0,0 +1,443 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009, 2010, 2013 Jitse Niesen <jitse@maths.leeds.ac.uk>
+// Copyright (C) 2011, 2013 Chen-Pang He <jdh8@ms63.hinet.net>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_MATRIX_EXPONENTIAL
+#define EIGEN_MATRIX_EXPONENTIAL
+
+#include "StemFunction.h"
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+namespace internal {
+
+/** \brief Scaling operator.
+ *
+ * This struct is used by CwiseUnaryOp to scale a matrix by \f$ 2^{-s} \f$.
+ */
+template <typename RealScalar>
+struct MatrixExponentialScalingOp
+{
+ /** \brief Constructor.
+ *
+ * \param[in] squarings The integer \f$ s \f$ in this document.
+ */
+ MatrixExponentialScalingOp(int squarings) : m_squarings(squarings) { }
+
+
+ /** \brief Scale a matrix coefficient.
+ *
+ * \param[in,out] x The scalar to be scaled, becoming \f$ 2^{-s} x \f$.
+ */
+ inline const RealScalar operator() (const RealScalar& x) const
+ {
+ using std::ldexp;
+ return ldexp(x, -m_squarings);
+ }
+
+ typedef std::complex<RealScalar> ComplexScalar;
+
+ /** \brief Scale a matrix coefficient.
+ *
+ * \param[in,out] x The scalar to be scaled, becoming \f$ 2^{-s} x \f$.
+ */
+ inline const ComplexScalar operator() (const ComplexScalar& x) const
+ {
+ using std::ldexp;
+ return ComplexScalar(ldexp(x.real(), -m_squarings), ldexp(x.imag(), -m_squarings));
+ }
+
+ private:
+ int m_squarings;
+};
+
+/** \brief Compute the (3,3)-Padé approximant to the exponential.
+ *
+ * After exit, \f$ (V+U)(V-U)^{-1} \f$ is the Padé
+ * approximant of \f$ \exp(A) \f$ around \f$ A = 0 \f$.
+ */
+template <typename MatA, typename MatU, typename MatV>
+void matrix_exp_pade3(const MatA& A, MatU& U, MatV& V)
+{
+ typedef typename MatA::PlainObject MatrixType;
+ typedef typename NumTraits<typename traits<MatA>::Scalar>::Real RealScalar;
+ const RealScalar b[] = {120.L, 60.L, 12.L, 1.L};
+ const MatrixType A2 = A * A;
+ const MatrixType tmp = b[3] * A2 + b[1] * MatrixType::Identity(A.rows(), A.cols());
+ U.noalias() = A * tmp;
+ V = b[2] * A2 + b[0] * MatrixType::Identity(A.rows(), A.cols());
+}
+
+/** \brief Compute the (5,5)-Padé approximant to the exponential.
+ *
+ * After exit, \f$ (V+U)(V-U)^{-1} \f$ is the Padé
+ * approximant of \f$ \exp(A) \f$ around \f$ A = 0 \f$.
+ */
+template <typename MatA, typename MatU, typename MatV>
+void matrix_exp_pade5(const MatA& A, MatU& U, MatV& V)
+{
+ typedef typename MatA::PlainObject MatrixType;
+ typedef typename NumTraits<typename traits<MatrixType>::Scalar>::Real RealScalar;
+ const RealScalar b[] = {30240.L, 15120.L, 3360.L, 420.L, 30.L, 1.L};
+ const MatrixType A2 = A * A;
+ const MatrixType A4 = A2 * A2;
+ const MatrixType tmp = b[5] * A4 + b[3] * A2 + b[1] * MatrixType::Identity(A.rows(), A.cols());
+ U.noalias() = A * tmp;
+ V = b[4] * A4 + b[2] * A2 + b[0] * MatrixType::Identity(A.rows(), A.cols());
+}
+
+/** \brief Compute the (7,7)-Padé approximant to the exponential.
+ *
+ * After exit, \f$ (V+U)(V-U)^{-1} \f$ is the Padé
+ * approximant of \f$ \exp(A) \f$ around \f$ A = 0 \f$.
+ */
+template <typename MatA, typename MatU, typename MatV>
+void matrix_exp_pade7(const MatA& A, MatU& U, MatV& V)
+{
+ typedef typename MatA::PlainObject MatrixType;
+ typedef typename NumTraits<typename traits<MatrixType>::Scalar>::Real RealScalar;
+ const RealScalar b[] = {17297280.L, 8648640.L, 1995840.L, 277200.L, 25200.L, 1512.L, 56.L, 1.L};
+ const MatrixType A2 = A * A;
+ const MatrixType A4 = A2 * A2;
+ const MatrixType A6 = A4 * A2;
+ const MatrixType tmp = b[7] * A6 + b[5] * A4 + b[3] * A2
+ + b[1] * MatrixType::Identity(A.rows(), A.cols());
+ U.noalias() = A * tmp;
+ V = b[6] * A6 + b[4] * A4 + b[2] * A2 + b[0] * MatrixType::Identity(A.rows(), A.cols());
+
+}
+
+/** \brief Compute the (9,9)-Padé approximant to the exponential.
+ *
+ * After exit, \f$ (V+U)(V-U)^{-1} \f$ is the Padé
+ * approximant of \f$ \exp(A) \f$ around \f$ A = 0 \f$.
+ */
+template <typename MatA, typename MatU, typename MatV>
+void matrix_exp_pade9(const MatA& A, MatU& U, MatV& V)
+{
+ typedef typename MatA::PlainObject MatrixType;
+ typedef typename NumTraits<typename traits<MatrixType>::Scalar>::Real RealScalar;
+ const RealScalar b[] = {17643225600.L, 8821612800.L, 2075673600.L, 302702400.L, 30270240.L,
+ 2162160.L, 110880.L, 3960.L, 90.L, 1.L};
+ const MatrixType A2 = A * A;
+ const MatrixType A4 = A2 * A2;
+ const MatrixType A6 = A4 * A2;
+ const MatrixType A8 = A6 * A2;
+ const MatrixType tmp = b[9] * A8 + b[7] * A6 + b[5] * A4 + b[3] * A2
+ + b[1] * MatrixType::Identity(A.rows(), A.cols());
+ U.noalias() = A * tmp;
+ V = b[8] * A8 + b[6] * A6 + b[4] * A4 + b[2] * A2 + b[0] * MatrixType::Identity(A.rows(), A.cols());
+}
+
+/** \brief Compute the (13,13)-Padé approximant to the exponential.
+ *
+ * After exit, \f$ (V+U)(V-U)^{-1} \f$ is the Padé
+ * approximant of \f$ \exp(A) \f$ around \f$ A = 0 \f$.
+ */
+template <typename MatA, typename MatU, typename MatV>
+void matrix_exp_pade13(const MatA& A, MatU& U, MatV& V)
+{
+ typedef typename MatA::PlainObject MatrixType;
+ typedef typename NumTraits<typename traits<MatrixType>::Scalar>::Real RealScalar;
+ const RealScalar b[] = {64764752532480000.L, 32382376266240000.L, 7771770303897600.L,
+ 1187353796428800.L, 129060195264000.L, 10559470521600.L, 670442572800.L,
+ 33522128640.L, 1323241920.L, 40840800.L, 960960.L, 16380.L, 182.L, 1.L};
+ const MatrixType A2 = A * A;
+ const MatrixType A4 = A2 * A2;
+ const MatrixType A6 = A4 * A2;
+ V = b[13] * A6 + b[11] * A4 + b[9] * A2; // used for temporary storage
+ MatrixType tmp = A6 * V;
+ tmp += b[7] * A6 + b[5] * A4 + b[3] * A2 + b[1] * MatrixType::Identity(A.rows(), A.cols());
+ U.noalias() = A * tmp;
+ tmp = b[12] * A6 + b[10] * A4 + b[8] * A2;
+ V.noalias() = A6 * tmp;
+ V += b[6] * A6 + b[4] * A4 + b[2] * A2 + b[0] * MatrixType::Identity(A.rows(), A.cols());
+}
+
+/** \brief Compute the (17,17)-Padé approximant to the exponential.
+ *
+ * After exit, \f$ (V+U)(V-U)^{-1} \f$ is the Padé
+ * approximant of \f$ \exp(A) \f$ around \f$ A = 0 \f$.
+ *
+ * This function activates only if your long double is double-double or quadruple.
+ */
+#if LDBL_MANT_DIG > 64
+template <typename MatA, typename MatU, typename MatV>
+void matrix_exp_pade17(const MatA& A, MatU& U, MatV& V)
+{
+ typedef typename MatA::PlainObject MatrixType;
+ typedef typename NumTraits<typename traits<MatrixType>::Scalar>::Real RealScalar;
+ const RealScalar b[] = {830034394580628357120000.L, 415017197290314178560000.L,
+ 100610229646136770560000.L, 15720348382208870400000.L,
+ 1774878043152614400000.L, 153822763739893248000.L, 10608466464820224000.L,
+ 595373117923584000.L, 27563570274240000.L, 1060137318240000.L,
+ 33924394183680.L, 899510451840.L, 19554575040.L, 341863200.L, 4651200.L,
+ 46512.L, 306.L, 1.L};
+ const MatrixType A2 = A * A;
+ const MatrixType A4 = A2 * A2;
+ const MatrixType A6 = A4 * A2;
+ const MatrixType A8 = A4 * A4;
+ V = b[17] * A8 + b[15] * A6 + b[13] * A4 + b[11] * A2; // used for temporary storage
+ MatrixType tmp = A8 * V;
+ tmp += b[9] * A8 + b[7] * A6 + b[5] * A4 + b[3] * A2
+ + b[1] * MatrixType::Identity(A.rows(), A.cols());
+ U.noalias() = A * tmp;
+ tmp = b[16] * A8 + b[14] * A6 + b[12] * A4 + b[10] * A2;
+ V.noalias() = tmp * A8;
+ V += b[8] * A8 + b[6] * A6 + b[4] * A4 + b[2] * A2
+ + b[0] * MatrixType::Identity(A.rows(), A.cols());
+}
+#endif
+
+template <typename MatrixType, typename RealScalar = typename NumTraits<typename traits<MatrixType>::Scalar>::Real>
+struct matrix_exp_computeUV
+{
+ /** \brief Compute Padé approximant to the exponential.
+ *
+ * Computes \c U, \c V and \c squarings such that \f$ (V+U)(V-U)^{-1} \f$ is a Padé
+ * approximant of \f$ \exp(2^{-\mbox{squarings}}M) \f$ around \f$ M = 0 \f$, where \f$ M \f$
+ * denotes the matrix \c arg. The degree of the Padé approximant and the value of squarings
+ * are chosen such that the approximation error is no more than the round-off error.
+ */
+ static void run(const MatrixType& arg, MatrixType& U, MatrixType& V, int& squarings);
+};
+
+template <typename MatrixType>
+struct matrix_exp_computeUV<MatrixType, float>
+{
+ template <typename ArgType>
+ static void run(const ArgType& arg, MatrixType& U, MatrixType& V, int& squarings)
+ {
+ using std::frexp;
+ using std::pow;
+ const float l1norm = arg.cwiseAbs().colwise().sum().maxCoeff();
+ squarings = 0;
+ if (l1norm < 4.258730016922831e-001f) {
+ matrix_exp_pade3(arg, U, V);
+ } else if (l1norm < 1.880152677804762e+000f) {
+ matrix_exp_pade5(arg, U, V);
+ } else {
+ const float maxnorm = 3.925724783138660f;
+ frexp(l1norm / maxnorm, &squarings);
+ if (squarings < 0) squarings = 0;
+ MatrixType A = arg.unaryExpr(MatrixExponentialScalingOp<float>(squarings));
+ matrix_exp_pade7(A, U, V);
+ }
+ }
+};
+
+template <typename MatrixType>
+struct matrix_exp_computeUV<MatrixType, double>
+{
+ typedef typename NumTraits<typename traits<MatrixType>::Scalar>::Real RealScalar;
+ template <typename ArgType>
+ static void run(const ArgType& arg, MatrixType& U, MatrixType& V, int& squarings)
+ {
+ using std::frexp;
+ using std::pow;
+ const RealScalar l1norm = arg.cwiseAbs().colwise().sum().maxCoeff();
+ squarings = 0;
+ if (l1norm < 1.495585217958292e-002) {
+ matrix_exp_pade3(arg, U, V);
+ } else if (l1norm < 2.539398330063230e-001) {
+ matrix_exp_pade5(arg, U, V);
+ } else if (l1norm < 9.504178996162932e-001) {
+ matrix_exp_pade7(arg, U, V);
+ } else if (l1norm < 2.097847961257068e+000) {
+ matrix_exp_pade9(arg, U, V);
+ } else {
+ const RealScalar maxnorm = 5.371920351148152;
+ frexp(l1norm / maxnorm, &squarings);
+ if (squarings < 0) squarings = 0;
+ MatrixType A = arg.unaryExpr(MatrixExponentialScalingOp<RealScalar>(squarings));
+ matrix_exp_pade13(A, U, V);
+ }
+ }
+};
+
+template <typename MatrixType>
+struct matrix_exp_computeUV<MatrixType, long double>
+{
+ template <typename ArgType>
+ static void run(const ArgType& arg, MatrixType& U, MatrixType& V, int& squarings)
+ {
+#if LDBL_MANT_DIG == 53 // double precision
+ matrix_exp_computeUV<MatrixType, double>::run(arg, U, V, squarings);
+
+#else
+
+ using std::frexp;
+ using std::pow;
+ const long double l1norm = arg.cwiseAbs().colwise().sum().maxCoeff();
+ squarings = 0;
+
+#if LDBL_MANT_DIG <= 64 // extended precision
+
+ if (l1norm < 4.1968497232266989671e-003L) {
+ matrix_exp_pade3(arg, U, V);
+ } else if (l1norm < 1.1848116734693823091e-001L) {
+ matrix_exp_pade5(arg, U, V);
+ } else if (l1norm < 5.5170388480686700274e-001L) {
+ matrix_exp_pade7(arg, U, V);
+ } else if (l1norm < 1.3759868875587845383e+000L) {
+ matrix_exp_pade9(arg, U, V);
+ } else {
+ const long double maxnorm = 4.0246098906697353063L;
+ frexp(l1norm / maxnorm, &squarings);
+ if (squarings < 0) squarings = 0;
+ MatrixType A = arg.unaryExpr(MatrixExponentialScalingOp<long double>(squarings));
+ matrix_exp_pade13(A, U, V);
+ }
+
+#elif LDBL_MANT_DIG <= 106 // double-double
+
+ if (l1norm < 3.2787892205607026992947488108213e-005L) {
+ matrix_exp_pade3(arg, U, V);
+ } else if (l1norm < 6.4467025060072760084130906076332e-003L) {
+ matrix_exp_pade5(arg, U, V);
+ } else if (l1norm < 6.8988028496595374751374122881143e-002L) {
+ matrix_exp_pade7(arg, U, V);
+ } else if (l1norm < 2.7339737518502231741495857201670e-001L) {
+ matrix_exp_pade9(arg, U, V);
+ } else if (l1norm < 1.3203382096514474905666448850278e+000L) {
+ matrix_exp_pade13(arg, U, V);
+ } else {
+ const long double maxnorm = 3.2579440895405400856599663723517L;
+ frexp(l1norm / maxnorm, &squarings);
+ if (squarings < 0) squarings = 0;
+ MatrixType A = arg.unaryExpr(MatrixExponentialScalingOp<long double>(squarings));
+ matrix_exp_pade17(A, U, V);
+ }
+
+#elif LDBL_MANT_DIG <= 113 // quadruple precision
+
+ if (l1norm < 1.639394610288918690547467954466970e-005L) {
+ matrix_exp_pade3(arg, U, V);
+ } else if (l1norm < 4.253237712165275566025884344433009e-003L) {
+ matrix_exp_pade5(arg, U, V);
+ } else if (l1norm < 5.125804063165764409885122032933142e-002L) {
+ matrix_exp_pade7(arg, U, V);
+ } else if (l1norm < 2.170000765161155195453205651889853e-001L) {
+ matrix_exp_pade9(arg, U, V);
+ } else if (l1norm < 1.125358383453143065081397882891878e+000L) {
+ matrix_exp_pade13(arg, U, V);
+ } else {
+ const long double maxnorm = 2.884233277829519311757165057717815L;
+ frexp(l1norm / maxnorm, &squarings);
+ if (squarings < 0) squarings = 0;
+ MatrixType A = arg.unaryExpr(MatrixExponentialScalingOp<long double>(squarings));
+ matrix_exp_pade17(A, U, V);
+ }
+
+#else
+
+ // this case should be handled in compute()
+ eigen_assert(false && "Bug in MatrixExponential");
+
+#endif
+#endif // LDBL_MANT_DIG
+ }
+};
+
+template<typename T> struct is_exp_known_type : false_type {};
+template<> struct is_exp_known_type<float> : true_type {};
+template<> struct is_exp_known_type<double> : true_type {};
+#if LDBL_MANT_DIG <= 113
+template<> struct is_exp_known_type<long double> : true_type {};
+#endif
+
+template <typename ArgType, typename ResultType>
+void matrix_exp_compute(const ArgType& arg, ResultType &result, true_type) // natively supported scalar type
+{
+ typedef typename ArgType::PlainObject MatrixType;
+ MatrixType U, V;
+ int squarings;
+ matrix_exp_computeUV<MatrixType>::run(arg, U, V, squarings); // Pade approximant is (U+V) / (-U+V)
+ MatrixType numer = U + V;
+ MatrixType denom = -U + V;
+ result = denom.partialPivLu().solve(numer);
+ for (int i=0; i<squarings; i++)
+ result *= result; // undo scaling by repeated squaring
+}
+
+
+/* Computes the matrix exponential
+ *
+ * \param arg argument of matrix exponential (should be plain object)
+ * \param result variable in which result will be stored
+ */
+template <typename ArgType, typename ResultType>
+void matrix_exp_compute(const ArgType& arg, ResultType &result, false_type) // default
+{
+ typedef typename ArgType::PlainObject MatrixType;
+ typedef typename traits<MatrixType>::Scalar Scalar;
+ typedef typename NumTraits<Scalar>::Real RealScalar;
+ typedef typename std::complex<RealScalar> ComplexScalar;
+ result = arg.matrixFunction(internal::stem_function_exp<ComplexScalar>);
+}
+
+} // end namespace Eigen::internal
+
+/** \ingroup MatrixFunctions_Module
+ *
+ * \brief Proxy for the matrix exponential of some matrix (expression).
+ *
+ * \tparam Derived Type of the argument to the matrix exponential.
+ *
+ * This class holds the argument to the matrix exponential until it is assigned or evaluated for
+ * some other reason (so the argument should not be changed in the meantime). It is the return type
+ * of MatrixBase::exp() and most of the time this is the only way it is used.
+ */
+template<typename Derived> struct MatrixExponentialReturnValue
+: public ReturnByValue<MatrixExponentialReturnValue<Derived> >
+{
+ public:
+ /** \brief Constructor.
+ *
+ * \param src %Matrix (expression) forming the argument of the matrix exponential.
+ */
+ MatrixExponentialReturnValue(const Derived& src) : m_src(src) { }
+
+ /** \brief Compute the matrix exponential.
+ *
+ * \param result the matrix exponential of \p src in the constructor.
+ */
+ template <typename ResultType>
+ inline void evalTo(ResultType& result) const
+ {
+ const typename internal::nested_eval<Derived, 10>::type tmp(m_src);
+ internal::matrix_exp_compute(tmp, result, internal::is_exp_known_type<typename Derived::RealScalar>());
+ }
+
+ Index rows() const { return m_src.rows(); }
+ Index cols() const { return m_src.cols(); }
+
+ protected:
+ const typename internal::ref_selector<Derived>::type m_src;
+};
+
+namespace internal {
+template<typename Derived>
+struct traits<MatrixExponentialReturnValue<Derived> >
+{
+ typedef typename Derived::PlainObject ReturnType;
+};
+}
+
+template <typename Derived>
+const MatrixExponentialReturnValue<Derived> MatrixBase<Derived>::exp() const
+{
+ eigen_assert(rows() == cols());
+ return MatrixExponentialReturnValue<Derived>(derived());
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_MATRIX_EXPONENTIAL
diff --git a/unsupported/Eigen/src/MatrixFunctions/MatrixFunction.h b/unsupported/Eigen/src/MatrixFunctions/MatrixFunction.h
new file mode 100644
index 0000000..8076bf5
--- /dev/null
+++ b/unsupported/Eigen/src/MatrixFunctions/MatrixFunction.h
@@ -0,0 +1,571 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009-2011, 2013 Jitse Niesen <jitse@maths.leeds.ac.uk>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_MATRIX_FUNCTION_H
+#define EIGEN_MATRIX_FUNCTION_H
+
+#include "StemFunction.h"
+
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+
+/** \brief Maximum distance allowed between eigenvalues to be considered "close". */
+static const float matrix_function_separation = 0.1f;
+
+/** \ingroup MatrixFunctions_Module
+ * \class MatrixFunctionAtomic
+ * \brief Helper class for computing matrix functions of atomic matrices.
+ *
+ * Here, an atomic matrix is a triangular matrix whose diagonal entries are close to each other.
+ */
+template <typename MatrixType>
+class MatrixFunctionAtomic
+{
+ public:
+
+ typedef typename MatrixType::Scalar Scalar;
+ typedef typename stem_function<Scalar>::type StemFunction;
+
+ /** \brief Constructor
+ * \param[in] f matrix function to compute.
+ */
+ MatrixFunctionAtomic(StemFunction f) : m_f(f) { }
+
+ /** \brief Compute matrix function of atomic matrix
+ * \param[in] A argument of matrix function, should be upper triangular and atomic
+ * \returns f(A), the matrix function evaluated at the given matrix
+ */
+ MatrixType compute(const MatrixType& A);
+
+ private:
+ StemFunction* m_f;
+};
+
+template <typename MatrixType>
+typename NumTraits<typename MatrixType::Scalar>::Real matrix_function_compute_mu(const MatrixType& A)
+{
+ typedef typename plain_col_type<MatrixType>::type VectorType;
+ Index rows = A.rows();
+ const MatrixType N = MatrixType::Identity(rows, rows) - A;
+ VectorType e = VectorType::Ones(rows);
+ N.template triangularView<Upper>().solveInPlace(e);
+ return e.cwiseAbs().maxCoeff();
+}
+
+template <typename MatrixType>
+MatrixType MatrixFunctionAtomic<MatrixType>::compute(const MatrixType& A)
+{
+ // TODO: Use that A is upper triangular
+ typedef typename NumTraits<Scalar>::Real RealScalar;
+ Index rows = A.rows();
+ Scalar avgEival = A.trace() / Scalar(RealScalar(rows));
+ MatrixType Ashifted = A - avgEival * MatrixType::Identity(rows, rows);
+ RealScalar mu = matrix_function_compute_mu(Ashifted);
+ MatrixType F = m_f(avgEival, 0) * MatrixType::Identity(rows, rows);
+ MatrixType P = Ashifted;
+ MatrixType Fincr;
+ for (Index s = 1; double(s) < 1.1 * double(rows) + 10.0; s++) { // upper limit is fairly arbitrary
+ Fincr = m_f(avgEival, static_cast<int>(s)) * P;
+ F += Fincr;
+ P = Scalar(RealScalar(1)/RealScalar(s + 1)) * P * Ashifted;
+
+ // test whether Taylor series converged
+ const RealScalar F_norm = F.cwiseAbs().rowwise().sum().maxCoeff();
+ const RealScalar Fincr_norm = Fincr.cwiseAbs().rowwise().sum().maxCoeff();
+ if (Fincr_norm < NumTraits<Scalar>::epsilon() * F_norm) {
+ RealScalar delta = 0;
+ RealScalar rfactorial = 1;
+ for (Index r = 0; r < rows; r++) {
+ RealScalar mx = 0;
+ for (Index i = 0; i < rows; i++)
+ mx = (std::max)(mx, std::abs(m_f(Ashifted(i, i) + avgEival, static_cast<int>(s+r))));
+ if (r != 0)
+ rfactorial *= RealScalar(r);
+ delta = (std::max)(delta, mx / rfactorial);
+ }
+ const RealScalar P_norm = P.cwiseAbs().rowwise().sum().maxCoeff();
+ if (mu * delta * P_norm < NumTraits<Scalar>::epsilon() * F_norm) // series converged
+ break;
+ }
+ }
+ return F;
+}
+
+/** \brief Find cluster in \p clusters containing some value
+ * \param[in] key Value to find
+ * \returns Iterator to cluster containing \p key, or \c clusters.end() if no cluster in \p m_clusters
+ * contains \p key.
+ */
+template <typename Index, typename ListOfClusters>
+typename ListOfClusters::iterator matrix_function_find_cluster(Index key, ListOfClusters& clusters)
+{
+ typename std::list<Index>::iterator j;
+ for (typename ListOfClusters::iterator i = clusters.begin(); i != clusters.end(); ++i) {
+ j = std::find(i->begin(), i->end(), key);
+ if (j != i->end())
+ return i;
+ }
+ return clusters.end();
+}
+
+/** \brief Partition eigenvalues in clusters of ei'vals close to each other
+ *
+ * \param[in] eivals Eigenvalues
+ * \param[out] clusters Resulting partition of eigenvalues
+ *
+ * The partition satisfies the following two properties:
+ * # Any eigenvalue in a certain cluster is at most matrix_function_separation() away from another eigenvalue
+ * in the same cluster.
+ * # The distance between two eigenvalues in different clusters is more than matrix_function_separation().
+ * The implementation follows Algorithm 4.1 in the paper of Davies and Higham.
+ */
+template <typename EivalsType, typename Cluster>
+void matrix_function_partition_eigenvalues(const EivalsType& eivals, std::list<Cluster>& clusters)
+{
+ typedef typename EivalsType::RealScalar RealScalar;
+ for (Index i=0; i<eivals.rows(); ++i) {
+ // Find cluster containing i-th ei'val, adding a new cluster if necessary
+ typename std::list<Cluster>::iterator qi = matrix_function_find_cluster(i, clusters);
+ if (qi == clusters.end()) {
+ Cluster l;
+ l.push_back(i);
+ clusters.push_back(l);
+ qi = clusters.end();
+ --qi;
+ }
+
+ // Look for other element to add to the set
+ for (Index j=i+1; j<eivals.rows(); ++j) {
+ if (abs(eivals(j) - eivals(i)) <= RealScalar(matrix_function_separation)
+ && std::find(qi->begin(), qi->end(), j) == qi->end()) {
+ typename std::list<Cluster>::iterator qj = matrix_function_find_cluster(j, clusters);
+ if (qj == clusters.end()) {
+ qi->push_back(j);
+ } else {
+ qi->insert(qi->end(), qj->begin(), qj->end());
+ clusters.erase(qj);
+ }
+ }
+ }
+ }
+}
+
+/** \brief Compute size of each cluster given a partitioning */
+template <typename ListOfClusters, typename Index>
+void matrix_function_compute_cluster_size(const ListOfClusters& clusters, Matrix<Index, Dynamic, 1>& clusterSize)
+{
+ const Index numClusters = static_cast<Index>(clusters.size());
+ clusterSize.setZero(numClusters);
+ Index clusterIndex = 0;
+ for (typename ListOfClusters::const_iterator cluster = clusters.begin(); cluster != clusters.end(); ++cluster) {
+ clusterSize[clusterIndex] = cluster->size();
+ ++clusterIndex;
+ }
+}
+
+/** \brief Compute start of each block using clusterSize */
+template <typename VectorType>
+void matrix_function_compute_block_start(const VectorType& clusterSize, VectorType& blockStart)
+{
+ blockStart.resize(clusterSize.rows());
+ blockStart(0) = 0;
+ for (Index i = 1; i < clusterSize.rows(); i++) {
+ blockStart(i) = blockStart(i-1) + clusterSize(i-1);
+ }
+}
+
+/** \brief Compute mapping of eigenvalue indices to cluster indices */
+template <typename EivalsType, typename ListOfClusters, typename VectorType>
+void matrix_function_compute_map(const EivalsType& eivals, const ListOfClusters& clusters, VectorType& eivalToCluster)
+{
+ eivalToCluster.resize(eivals.rows());
+ Index clusterIndex = 0;
+ for (typename ListOfClusters::const_iterator cluster = clusters.begin(); cluster != clusters.end(); ++cluster) {
+ for (Index i = 0; i < eivals.rows(); ++i) {
+ if (std::find(cluster->begin(), cluster->end(), i) != cluster->end()) {
+ eivalToCluster[i] = clusterIndex;
+ }
+ }
+ ++clusterIndex;
+ }
+}
+
+/** \brief Compute permutation which groups ei'vals in same cluster together */
+template <typename DynVectorType, typename VectorType>
+void matrix_function_compute_permutation(const DynVectorType& blockStart, const DynVectorType& eivalToCluster, VectorType& permutation)
+{
+ DynVectorType indexNextEntry = blockStart;
+ permutation.resize(eivalToCluster.rows());
+ for (Index i = 0; i < eivalToCluster.rows(); i++) {
+ Index cluster = eivalToCluster[i];
+ permutation[i] = indexNextEntry[cluster];
+ ++indexNextEntry[cluster];
+ }
+}
+
+/** \brief Permute Schur decomposition in U and T according to permutation */
+template <typename VectorType, typename MatrixType>
+void matrix_function_permute_schur(VectorType& permutation, MatrixType& U, MatrixType& T)
+{
+ for (Index i = 0; i < permutation.rows() - 1; i++) {
+ Index j;
+ for (j = i; j < permutation.rows(); j++) {
+ if (permutation(j) == i) break;
+ }
+ eigen_assert(permutation(j) == i);
+ for (Index k = j-1; k >= i; k--) {
+ JacobiRotation<typename MatrixType::Scalar> rotation;
+ rotation.makeGivens(T(k, k+1), T(k+1, k+1) - T(k, k));
+ T.applyOnTheLeft(k, k+1, rotation.adjoint());
+ T.applyOnTheRight(k, k+1, rotation);
+ U.applyOnTheRight(k, k+1, rotation);
+ std::swap(permutation.coeffRef(k), permutation.coeffRef(k+1));
+ }
+ }
+}
+
+/** \brief Compute block diagonal part of matrix function.
+ *
+ * This routine computes the matrix function applied to the block diagonal part of \p T (which should be
+ * upper triangular), with the blocking given by \p blockStart and \p clusterSize. The matrix function of
+ * each diagonal block is computed by \p atomic. The off-diagonal parts of \p fT are set to zero.
+ */
+template <typename MatrixType, typename AtomicType, typename VectorType>
+void matrix_function_compute_block_atomic(const MatrixType& T, AtomicType& atomic, const VectorType& blockStart, const VectorType& clusterSize, MatrixType& fT)
+{
+ fT.setZero(T.rows(), T.cols());
+ for (Index i = 0; i < clusterSize.rows(); ++i) {
+ fT.block(blockStart(i), blockStart(i), clusterSize(i), clusterSize(i))
+ = atomic.compute(T.block(blockStart(i), blockStart(i), clusterSize(i), clusterSize(i)));
+ }
+}
+
+/** \brief Solve a triangular Sylvester equation AX + XB = C
+ *
+ * \param[in] A the matrix A; should be square and upper triangular
+ * \param[in] B the matrix B; should be square and upper triangular
+ * \param[in] C the matrix C; should have correct size.
+ *
+ * \returns the solution X.
+ *
+ * If A is m-by-m and B is n-by-n, then both C and X are m-by-n. The (i,j)-th component of the Sylvester
+ * equation is
+ * \f[
+ * \sum_{k=i}^m A_{ik} X_{kj} + \sum_{k=1}^j X_{ik} B_{kj} = C_{ij}.
+ * \f]
+ * This can be re-arranged to yield:
+ * \f[
+ * X_{ij} = \frac{1}{A_{ii} + B_{jj}} \Bigl( C_{ij}
+ * - \sum_{k=i+1}^m A_{ik} X_{kj} - \sum_{k=1}^{j-1} X_{ik} B_{kj} \Bigr).
+ * \f]
+ * It is assumed that A and B are such that the numerator is never zero (otherwise the Sylvester equation
+ * does not have a unique solution). In that case, these equations can be evaluated in the order
+ * \f$ i=m,\ldots,1 \f$ and \f$ j=1,\ldots,n \f$.
+ */
+template <typename MatrixType>
+MatrixType matrix_function_solve_triangular_sylvester(const MatrixType& A, const MatrixType& B, const MatrixType& C)
+{
+ eigen_assert(A.rows() == A.cols());
+ eigen_assert(A.isUpperTriangular());
+ eigen_assert(B.rows() == B.cols());
+ eigen_assert(B.isUpperTriangular());
+ eigen_assert(C.rows() == A.rows());
+ eigen_assert(C.cols() == B.rows());
+
+ typedef typename MatrixType::Scalar Scalar;
+
+ Index m = A.rows();
+ Index n = B.rows();
+ MatrixType X(m, n);
+
+ for (Index i = m - 1; i >= 0; --i) {
+ for (Index j = 0; j < n; ++j) {
+
+ // Compute AX = \sum_{k=i+1}^m A_{ik} X_{kj}
+ Scalar AX;
+ if (i == m - 1) {
+ AX = 0;
+ } else {
+ Matrix<Scalar,1,1> AXmatrix = A.row(i).tail(m-1-i) * X.col(j).tail(m-1-i);
+ AX = AXmatrix(0,0);
+ }
+
+ // Compute XB = \sum_{k=1}^{j-1} X_{ik} B_{kj}
+ Scalar XB;
+ if (j == 0) {
+ XB = 0;
+ } else {
+ Matrix<Scalar,1,1> XBmatrix = X.row(i).head(j) * B.col(j).head(j);
+ XB = XBmatrix(0,0);
+ }
+
+ X(i,j) = (C(i,j) - AX - XB) / (A(i,i) + B(j,j));
+ }
+ }
+ return X;
+}
+
+/** \brief Compute part of matrix function above block diagonal.
+ *
+ * This routine completes the computation of \p fT, denoting a matrix function applied to the triangular
+ * matrix \p T. It assumes that the block diagonal part of \p fT has already been computed. The part below
+ * the diagonal is zero, because \p T is upper triangular.
+ */
+template <typename MatrixType, typename VectorType>
+void matrix_function_compute_above_diagonal(const MatrixType& T, const VectorType& blockStart, const VectorType& clusterSize, MatrixType& fT)
+{
+ typedef internal::traits<MatrixType> Traits;
+ typedef typename MatrixType::Scalar Scalar;
+ static const int Options = MatrixType::Options;
+ typedef Matrix<Scalar, Dynamic, Dynamic, Options, Traits::RowsAtCompileTime, Traits::ColsAtCompileTime> DynMatrixType;
+
+ for (Index k = 1; k < clusterSize.rows(); k++) {
+ for (Index i = 0; i < clusterSize.rows() - k; i++) {
+ // compute (i, i+k) block
+ DynMatrixType A = T.block(blockStart(i), blockStart(i), clusterSize(i), clusterSize(i));
+ DynMatrixType B = -T.block(blockStart(i+k), blockStart(i+k), clusterSize(i+k), clusterSize(i+k));
+ DynMatrixType C = fT.block(blockStart(i), blockStart(i), clusterSize(i), clusterSize(i))
+ * T.block(blockStart(i), blockStart(i+k), clusterSize(i), clusterSize(i+k));
+ C -= T.block(blockStart(i), blockStart(i+k), clusterSize(i), clusterSize(i+k))
+ * fT.block(blockStart(i+k), blockStart(i+k), clusterSize(i+k), clusterSize(i+k));
+ for (Index m = i + 1; m < i + k; m++) {
+ C += fT.block(blockStart(i), blockStart(m), clusterSize(i), clusterSize(m))
+ * T.block(blockStart(m), blockStart(i+k), clusterSize(m), clusterSize(i+k));
+ C -= T.block(blockStart(i), blockStart(m), clusterSize(i), clusterSize(m))
+ * fT.block(blockStart(m), blockStart(i+k), clusterSize(m), clusterSize(i+k));
+ }
+ fT.block(blockStart(i), blockStart(i+k), clusterSize(i), clusterSize(i+k))
+ = matrix_function_solve_triangular_sylvester(A, B, C);
+ }
+ }
+}
+
+/** \ingroup MatrixFunctions_Module
+ * \brief Class for computing matrix functions.
+ * \tparam MatrixType type of the argument of the matrix function,
+ * expected to be an instantiation of the Matrix class template.
+ * \tparam AtomicType type for computing matrix function of atomic blocks.
+ * \tparam IsComplex used internally to select correct specialization.
+ *
+ * This class implements the Schur-Parlett algorithm for computing matrix functions. The spectrum of the
+ * matrix is divided in clustered of eigenvalues that lies close together. This class delegates the
+ * computation of the matrix function on every block corresponding to these clusters to an object of type
+ * \p AtomicType and uses these results to compute the matrix function of the whole matrix. The class
+ * \p AtomicType should have a \p compute() member function for computing the matrix function of a block.
+ *
+ * \sa class MatrixFunctionAtomic, class MatrixLogarithmAtomic
+ */
+template <typename MatrixType, int IsComplex = NumTraits<typename internal::traits<MatrixType>::Scalar>::IsComplex>
+struct matrix_function_compute
+{
+ /** \brief Compute the matrix function.
+ *
+ * \param[in] A argument of matrix function, should be a square matrix.
+ * \param[in] atomic class for computing matrix function of atomic blocks.
+ * \param[out] result the function \p f applied to \p A, as
+ * specified in the constructor.
+ *
+ * See MatrixBase::matrixFunction() for details on how this computation
+ * is implemented.
+ */
+ template <typename AtomicType, typename ResultType>
+ static void run(const MatrixType& A, AtomicType& atomic, ResultType &result);
+};
+
+/** \internal \ingroup MatrixFunctions_Module
+ * \brief Partial specialization of MatrixFunction for real matrices
+ *
+ * This converts the real matrix to a complex matrix, compute the matrix function of that matrix, and then
+ * converts the result back to a real matrix.
+ */
+template <typename MatrixType>
+struct matrix_function_compute<MatrixType, 0>
+{
+ template <typename MatA, typename AtomicType, typename ResultType>
+ static void run(const MatA& A, AtomicType& atomic, ResultType &result)
+ {
+ typedef internal::traits<MatrixType> Traits;
+ typedef typename Traits::Scalar Scalar;
+ static const int Rows = Traits::RowsAtCompileTime, Cols = Traits::ColsAtCompileTime;
+ static const int MaxRows = Traits::MaxRowsAtCompileTime, MaxCols = Traits::MaxColsAtCompileTime;
+
+ typedef std::complex<Scalar> ComplexScalar;
+ typedef Matrix<ComplexScalar, Rows, Cols, 0, MaxRows, MaxCols> ComplexMatrix;
+
+ ComplexMatrix CA = A.template cast<ComplexScalar>();
+ ComplexMatrix Cresult;
+ matrix_function_compute<ComplexMatrix>::run(CA, atomic, Cresult);
+ result = Cresult.real();
+ }
+};
+
+/** \internal \ingroup MatrixFunctions_Module
+ * \brief Partial specialization of MatrixFunction for complex matrices
+ */
+template <typename MatrixType>
+struct matrix_function_compute<MatrixType, 1>
+{
+ template <typename MatA, typename AtomicType, typename ResultType>
+ static void run(const MatA& A, AtomicType& atomic, ResultType &result)
+ {
+ typedef internal::traits<MatrixType> Traits;
+
+ // compute Schur decomposition of A
+ const ComplexSchur<MatrixType> schurOfA(A);
+ eigen_assert(schurOfA.info()==Success);
+ MatrixType T = schurOfA.matrixT();
+ MatrixType U = schurOfA.matrixU();
+
+ // partition eigenvalues into clusters of ei'vals "close" to each other
+ std::list<std::list<Index> > clusters;
+ matrix_function_partition_eigenvalues(T.diagonal(), clusters);
+
+ // compute size of each cluster
+ Matrix<Index, Dynamic, 1> clusterSize;
+ matrix_function_compute_cluster_size(clusters, clusterSize);
+
+ // blockStart[i] is row index at which block corresponding to i-th cluster starts
+ Matrix<Index, Dynamic, 1> blockStart;
+ matrix_function_compute_block_start(clusterSize, blockStart);
+
+ // compute map so that eivalToCluster[i] = j means that i-th ei'val is in j-th cluster
+ Matrix<Index, Dynamic, 1> eivalToCluster;
+ matrix_function_compute_map(T.diagonal(), clusters, eivalToCluster);
+
+ // compute permutation which groups ei'vals in same cluster together
+ Matrix<Index, Traits::RowsAtCompileTime, 1> permutation;
+ matrix_function_compute_permutation(blockStart, eivalToCluster, permutation);
+
+ // permute Schur decomposition
+ matrix_function_permute_schur(permutation, U, T);
+
+ // compute result
+ MatrixType fT; // matrix function applied to T
+ matrix_function_compute_block_atomic(T, atomic, blockStart, clusterSize, fT);
+ matrix_function_compute_above_diagonal(T, blockStart, clusterSize, fT);
+ result = U * (fT.template triangularView<Upper>() * U.adjoint());
+ }
+};
+
+} // end of namespace internal
+
+/** \ingroup MatrixFunctions_Module
+ *
+ * \brief Proxy for the matrix function of some matrix (expression).
+ *
+ * \tparam Derived Type of the argument to the matrix function.
+ *
+ * This class holds the argument to the matrix function until it is assigned or evaluated for some other
+ * reason (so the argument should not be changed in the meantime). It is the return type of
+ * matrixBase::matrixFunction() and related functions and most of the time this is the only way it is used.
+ */
+template<typename Derived> class MatrixFunctionReturnValue
+: public ReturnByValue<MatrixFunctionReturnValue<Derived> >
+{
+ public:
+ typedef typename Derived::Scalar Scalar;
+ typedef typename internal::stem_function<Scalar>::type StemFunction;
+
+ protected:
+ typedef typename internal::ref_selector<Derived>::type DerivedNested;
+
+ public:
+
+ /** \brief Constructor.
+ *
+ * \param[in] A %Matrix (expression) forming the argument of the matrix function.
+ * \param[in] f Stem function for matrix function under consideration.
+ */
+ MatrixFunctionReturnValue(const Derived& A, StemFunction f) : m_A(A), m_f(f) { }
+
+ /** \brief Compute the matrix function.
+ *
+ * \param[out] result \p f applied to \p A, where \p f and \p A are as in the constructor.
+ */
+ template <typename ResultType>
+ inline void evalTo(ResultType& result) const
+ {
+ typedef typename internal::nested_eval<Derived, 10>::type NestedEvalType;
+ typedef internal::remove_all_t<NestedEvalType> NestedEvalTypeClean;
+ typedef internal::traits<NestedEvalTypeClean> Traits;
+ typedef std::complex<typename NumTraits<Scalar>::Real> ComplexScalar;
+ typedef Matrix<ComplexScalar, Dynamic, Dynamic, 0, Traits::RowsAtCompileTime, Traits::ColsAtCompileTime> DynMatrixType;
+
+ typedef internal::MatrixFunctionAtomic<DynMatrixType> AtomicType;
+ AtomicType atomic(m_f);
+
+ internal::matrix_function_compute<typename NestedEvalTypeClean::PlainObject>::run(m_A, atomic, result);
+ }
+
+ Index rows() const { return m_A.rows(); }
+ Index cols() const { return m_A.cols(); }
+
+ private:
+ const DerivedNested m_A;
+ StemFunction *m_f;
+};
+
+namespace internal {
+template<typename Derived>
+struct traits<MatrixFunctionReturnValue<Derived> >
+{
+ typedef typename Derived::PlainObject ReturnType;
+};
+}
+
+
+/********** MatrixBase methods **********/
+
+
+template <typename Derived>
+const MatrixFunctionReturnValue<Derived> MatrixBase<Derived>::matrixFunction(typename internal::stem_function<typename internal::traits<Derived>::Scalar>::type f) const
+{
+ eigen_assert(rows() == cols());
+ return MatrixFunctionReturnValue<Derived>(derived(), f);
+}
+
+template <typename Derived>
+const MatrixFunctionReturnValue<Derived> MatrixBase<Derived>::sin() const
+{
+ eigen_assert(rows() == cols());
+ typedef typename internal::stem_function<Scalar>::ComplexScalar ComplexScalar;
+ return MatrixFunctionReturnValue<Derived>(derived(), internal::stem_function_sin<ComplexScalar>);
+}
+
+template <typename Derived>
+const MatrixFunctionReturnValue<Derived> MatrixBase<Derived>::cos() const
+{
+ eigen_assert(rows() == cols());
+ typedef typename internal::stem_function<Scalar>::ComplexScalar ComplexScalar;
+ return MatrixFunctionReturnValue<Derived>(derived(), internal::stem_function_cos<ComplexScalar>);
+}
+
+template <typename Derived>
+const MatrixFunctionReturnValue<Derived> MatrixBase<Derived>::sinh() const
+{
+ eigen_assert(rows() == cols());
+ typedef typename internal::stem_function<Scalar>::ComplexScalar ComplexScalar;
+ return MatrixFunctionReturnValue<Derived>(derived(), internal::stem_function_sinh<ComplexScalar>);
+}
+
+template <typename Derived>
+const MatrixFunctionReturnValue<Derived> MatrixBase<Derived>::cosh() const
+{
+ eigen_assert(rows() == cols());
+ typedef typename internal::stem_function<Scalar>::ComplexScalar ComplexScalar;
+ return MatrixFunctionReturnValue<Derived>(derived(), internal::stem_function_cosh<ComplexScalar>);
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_MATRIX_FUNCTION_H
diff --git a/unsupported/Eigen/src/MatrixFunctions/MatrixLogarithm.h b/unsupported/Eigen/src/MatrixFunctions/MatrixLogarithm.h
new file mode 100644
index 0000000..2036fe4
--- /dev/null
+++ b/unsupported/Eigen/src/MatrixFunctions/MatrixLogarithm.h
@@ -0,0 +1,375 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2011, 2013 Jitse Niesen <jitse@maths.leeds.ac.uk>
+// Copyright (C) 2011 Chen-Pang He <jdh8@ms63.hinet.net>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_MATRIX_LOGARITHM
+#define EIGEN_MATRIX_LOGARITHM
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+
+template <typename Scalar>
+struct matrix_log_min_pade_degree
+{
+ static const int value = 3;
+};
+
+template <typename Scalar>
+struct matrix_log_max_pade_degree
+{
+ typedef typename NumTraits<Scalar>::Real RealScalar;
+ static const int value = std::numeric_limits<RealScalar>::digits<= 24? 5: // single precision
+ std::numeric_limits<RealScalar>::digits<= 53? 7: // double precision
+ std::numeric_limits<RealScalar>::digits<= 64? 8: // extended precision
+ std::numeric_limits<RealScalar>::digits<=106? 10: // double-double
+ 11; // quadruple precision
+};
+
+/** \brief Compute logarithm of 2x2 triangular matrix. */
+template <typename MatrixType>
+void matrix_log_compute_2x2(const MatrixType& A, MatrixType& result)
+{
+ typedef typename MatrixType::Scalar Scalar;
+ typedef typename MatrixType::RealScalar RealScalar;
+ using std::abs;
+ using std::ceil;
+ using std::imag;
+ using std::log;
+
+ Scalar logA00 = log(A(0,0));
+ Scalar logA11 = log(A(1,1));
+
+ result(0,0) = logA00;
+ result(1,0) = Scalar(0);
+ result(1,1) = logA11;
+
+ Scalar y = A(1,1) - A(0,0);
+ if (y==Scalar(0))
+ {
+ result(0,1) = A(0,1) / A(0,0);
+ }
+ else if ((abs(A(0,0)) < RealScalar(0.5)*abs(A(1,1))) || (abs(A(0,0)) > 2*abs(A(1,1))))
+ {
+ result(0,1) = A(0,1) * (logA11 - logA00) / y;
+ }
+ else
+ {
+ // computation in previous branch is inaccurate if A(1,1) \approx A(0,0)
+ RealScalar unwindingNumber = ceil((imag(logA11 - logA00) - RealScalar(EIGEN_PI)) / RealScalar(2*EIGEN_PI));
+ result(0,1) = A(0,1) * (numext::log1p(y/A(0,0)) + Scalar(0,RealScalar(2*EIGEN_PI)*unwindingNumber)) / y;
+ }
+}
+
+/* \brief Get suitable degree for Pade approximation. (specialized for RealScalar = float) */
+inline int matrix_log_get_pade_degree(float normTminusI)
+{
+ const float maxNormForPade[] = { 2.5111573934555054e-1 /* degree = 3 */ , 4.0535837411880493e-1,
+ 5.3149729967117310e-1 };
+ const int minPadeDegree = matrix_log_min_pade_degree<float>::value;
+ const int maxPadeDegree = matrix_log_max_pade_degree<float>::value;
+ int degree = minPadeDegree;
+ for (; degree <= maxPadeDegree; ++degree)
+ if (normTminusI <= maxNormForPade[degree - minPadeDegree])
+ break;
+ return degree;
+}
+
+/* \brief Get suitable degree for Pade approximation. (specialized for RealScalar = double) */
+inline int matrix_log_get_pade_degree(double normTminusI)
+{
+ const double maxNormForPade[] = { 1.6206284795015624e-2 /* degree = 3 */ , 5.3873532631381171e-2,
+ 1.1352802267628681e-1, 1.8662860613541288e-1, 2.642960831111435e-1 };
+ const int minPadeDegree = matrix_log_min_pade_degree<double>::value;
+ const int maxPadeDegree = matrix_log_max_pade_degree<double>::value;
+ int degree = minPadeDegree;
+ for (; degree <= maxPadeDegree; ++degree)
+ if (normTminusI <= maxNormForPade[degree - minPadeDegree])
+ break;
+ return degree;
+}
+
+/* \brief Get suitable degree for Pade approximation. (specialized for RealScalar = long double) */
+inline int matrix_log_get_pade_degree(long double normTminusI)
+{
+#if LDBL_MANT_DIG == 53 // double precision
+ const long double maxNormForPade[] = { 1.6206284795015624e-2L /* degree = 3 */ , 5.3873532631381171e-2L,
+ 1.1352802267628681e-1L, 1.8662860613541288e-1L, 2.642960831111435e-1L };
+#elif LDBL_MANT_DIG <= 64 // extended precision
+ const long double maxNormForPade[] = { 5.48256690357782863103e-3L /* degree = 3 */, 2.34559162387971167321e-2L,
+ 5.84603923897347449857e-2L, 1.08486423756725170223e-1L, 1.68385767881294446649e-1L,
+ 2.32777776523703892094e-1L };
+#elif LDBL_MANT_DIG <= 106 // double-double
+ const long double maxNormForPade[] = { 8.58970550342939562202529664318890e-5L /* degree = 3 */,
+ 9.34074328446359654039446552677759e-4L, 4.26117194647672175773064114582860e-3L,
+ 1.21546224740281848743149666560464e-2L, 2.61100544998339436713088248557444e-2L,
+ 4.66170074627052749243018566390567e-2L, 7.32585144444135027565872014932387e-2L,
+ 1.05026503471351080481093652651105e-1L };
+#else // quadruple precision
+ const long double maxNormForPade[] = { 4.7419931187193005048501568167858103e-5L /* degree = 3 */,
+ 5.8853168473544560470387769480192666e-4L, 2.9216120366601315391789493628113520e-3L,
+ 8.8415758124319434347116734705174308e-3L, 1.9850836029449446668518049562565291e-2L,
+ 3.6688019729653446926585242192447447e-2L, 5.9290962294020186998954055264528393e-2L,
+ 8.6998436081634343903250580992127677e-2L, 1.1880960220216759245467951592883642e-1L };
+#endif
+ const int minPadeDegree = matrix_log_min_pade_degree<long double>::value;
+ const int maxPadeDegree = matrix_log_max_pade_degree<long double>::value;
+ int degree = minPadeDegree;
+ for (; degree <= maxPadeDegree; ++degree)
+ if (normTminusI <= maxNormForPade[degree - minPadeDegree])
+ break;
+ return degree;
+}
+
+/* \brief Compute Pade approximation to matrix logarithm */
+template <typename MatrixType>
+void matrix_log_compute_pade(MatrixType& result, const MatrixType& T, int degree)
+{
+ typedef typename NumTraits<typename MatrixType::Scalar>::Real RealScalar;
+ const int minPadeDegree = 3;
+ const int maxPadeDegree = 11;
+ eigen_assert(degree >= minPadeDegree && degree <= maxPadeDegree);
+ // FIXME this creates float-conversion-warnings if these are enabled.
+ // Either manually convert each value, or disable the warning locally
+ const RealScalar nodes[][maxPadeDegree] = {
+ { 0.1127016653792583114820734600217600L, 0.5000000000000000000000000000000000L, // degree 3
+ 0.8872983346207416885179265399782400L },
+ { 0.0694318442029737123880267555535953L, 0.3300094782075718675986671204483777L, // degree 4
+ 0.6699905217924281324013328795516223L, 0.9305681557970262876119732444464048L },
+ { 0.0469100770306680036011865608503035L, 0.2307653449471584544818427896498956L, // degree 5
+ 0.5000000000000000000000000000000000L, 0.7692346550528415455181572103501044L,
+ 0.9530899229693319963988134391496965L },
+ { 0.0337652428984239860938492227530027L, 0.1693953067668677431693002024900473L, // degree 6
+ 0.3806904069584015456847491391596440L, 0.6193095930415984543152508608403560L,
+ 0.8306046932331322568306997975099527L, 0.9662347571015760139061507772469973L },
+ { 0.0254460438286207377369051579760744L, 0.1292344072003027800680676133596058L, // degree 7
+ 0.2970774243113014165466967939615193L, 0.5000000000000000000000000000000000L,
+ 0.7029225756886985834533032060384807L, 0.8707655927996972199319323866403942L,
+ 0.9745539561713792622630948420239256L },
+ { 0.0198550717512318841582195657152635L, 0.1016667612931866302042230317620848L, // degree 8
+ 0.2372337950418355070911304754053768L, 0.4082826787521750975302619288199080L,
+ 0.5917173212478249024697380711800920L, 0.7627662049581644929088695245946232L,
+ 0.8983332387068133697957769682379152L, 0.9801449282487681158417804342847365L },
+ { 0.0159198802461869550822118985481636L, 0.0819844463366821028502851059651326L, // degree 9
+ 0.1933142836497048013456489803292629L, 0.3378732882980955354807309926783317L,
+ 0.5000000000000000000000000000000000L, 0.6621267117019044645192690073216683L,
+ 0.8066857163502951986543510196707371L, 0.9180155536633178971497148940348674L,
+ 0.9840801197538130449177881014518364L },
+ { 0.0130467357414141399610179939577740L, 0.0674683166555077446339516557882535L, // degree 10
+ 0.1602952158504877968828363174425632L, 0.2833023029353764046003670284171079L,
+ 0.4255628305091843945575869994351400L, 0.5744371694908156054424130005648600L,
+ 0.7166976970646235953996329715828921L, 0.8397047841495122031171636825574368L,
+ 0.9325316833444922553660483442117465L, 0.9869532642585858600389820060422260L },
+ { 0.0108856709269715035980309994385713L, 0.0564687001159523504624211153480364L, // degree 11
+ 0.1349239972129753379532918739844233L, 0.2404519353965940920371371652706952L,
+ 0.3652284220238275138342340072995692L, 0.5000000000000000000000000000000000L,
+ 0.6347715779761724861657659927004308L, 0.7595480646034059079628628347293048L,
+ 0.8650760027870246620467081260155767L, 0.9435312998840476495375788846519636L,
+ 0.9891143290730284964019690005614287L } };
+
+ const RealScalar weights[][maxPadeDegree] = {
+ { 0.2777777777777777777777777777777778L, 0.4444444444444444444444444444444444L, // degree 3
+ 0.2777777777777777777777777777777778L },
+ { 0.1739274225687269286865319746109997L, 0.3260725774312730713134680253890003L, // degree 4
+ 0.3260725774312730713134680253890003L, 0.1739274225687269286865319746109997L },
+ { 0.1184634425280945437571320203599587L, 0.2393143352496832340206457574178191L, // degree 5
+ 0.2844444444444444444444444444444444L, 0.2393143352496832340206457574178191L,
+ 0.1184634425280945437571320203599587L },
+ { 0.0856622461895851725201480710863665L, 0.1803807865240693037849167569188581L, // degree 6
+ 0.2339569672863455236949351719947755L, 0.2339569672863455236949351719947755L,
+ 0.1803807865240693037849167569188581L, 0.0856622461895851725201480710863665L },
+ { 0.0647424830844348466353057163395410L, 0.1398526957446383339507338857118898L, // degree 7
+ 0.1909150252525594724751848877444876L, 0.2089795918367346938775510204081633L,
+ 0.1909150252525594724751848877444876L, 0.1398526957446383339507338857118898L,
+ 0.0647424830844348466353057163395410L },
+ { 0.0506142681451881295762656771549811L, 0.1111905172266872352721779972131204L, // degree 8
+ 0.1568533229389436436689811009933007L, 0.1813418916891809914825752246385978L,
+ 0.1813418916891809914825752246385978L, 0.1568533229389436436689811009933007L,
+ 0.1111905172266872352721779972131204L, 0.0506142681451881295762656771549811L },
+ { 0.0406371941807872059859460790552618L, 0.0903240803474287020292360156214564L, // degree 9
+ 0.1303053482014677311593714347093164L, 0.1561735385200014200343152032922218L,
+ 0.1651196775006298815822625346434870L, 0.1561735385200014200343152032922218L,
+ 0.1303053482014677311593714347093164L, 0.0903240803474287020292360156214564L,
+ 0.0406371941807872059859460790552618L },
+ { 0.0333356721543440687967844049466659L, 0.0747256745752902965728881698288487L, // degree 10
+ 0.1095431812579910219977674671140816L, 0.1346333596549981775456134607847347L,
+ 0.1477621123573764350869464973256692L, 0.1477621123573764350869464973256692L,
+ 0.1346333596549981775456134607847347L, 0.1095431812579910219977674671140816L,
+ 0.0747256745752902965728881698288487L, 0.0333356721543440687967844049466659L },
+ { 0.0278342835580868332413768602212743L, 0.0627901847324523123173471496119701L, // degree 11
+ 0.0931451054638671257130488207158280L, 0.1165968822959952399592618524215876L,
+ 0.1314022722551233310903444349452546L, 0.1364625433889503153572417641681711L,
+ 0.1314022722551233310903444349452546L, 0.1165968822959952399592618524215876L,
+ 0.0931451054638671257130488207158280L, 0.0627901847324523123173471496119701L,
+ 0.0278342835580868332413768602212743L } };
+
+ MatrixType TminusI = T - MatrixType::Identity(T.rows(), T.rows());
+ result.setZero(T.rows(), T.rows());
+ for (int k = 0; k < degree; ++k) {
+ RealScalar weight = weights[degree-minPadeDegree][k];
+ RealScalar node = nodes[degree-minPadeDegree][k];
+ result += weight * (MatrixType::Identity(T.rows(), T.rows()) + node * TminusI)
+ .template triangularView<Upper>().solve(TminusI);
+ }
+}
+
+/** \brief Compute logarithm of triangular matrices with size > 2.
+ * \details This uses a inverse scale-and-square algorithm. */
+template <typename MatrixType>
+void matrix_log_compute_big(const MatrixType& A, MatrixType& result)
+{
+ typedef typename MatrixType::Scalar Scalar;
+ typedef typename NumTraits<Scalar>::Real RealScalar;
+ using std::pow;
+
+ int numberOfSquareRoots = 0;
+ int numberOfExtraSquareRoots = 0;
+ int degree;
+ MatrixType T = A, sqrtT;
+
+ const int maxPadeDegree = matrix_log_max_pade_degree<Scalar>::value;
+ const RealScalar maxNormForPade = RealScalar(
+ maxPadeDegree<= 5? 5.3149729967117310e-1L: // single precision
+ maxPadeDegree<= 7? 2.6429608311114350e-1L: // double precision
+ maxPadeDegree<= 8? 2.32777776523703892094e-1L: // extended precision
+ maxPadeDegree<=10? 1.05026503471351080481093652651105e-1L: // double-double
+ 1.1880960220216759245467951592883642e-1L); // quadruple precision
+
+ while (true) {
+ RealScalar normTminusI = (T - MatrixType::Identity(T.rows(), T.rows())).cwiseAbs().colwise().sum().maxCoeff();
+ if (normTminusI < maxNormForPade) {
+ degree = matrix_log_get_pade_degree(normTminusI);
+ int degree2 = matrix_log_get_pade_degree(normTminusI / RealScalar(2));
+ if ((degree - degree2 <= 1) || (numberOfExtraSquareRoots == 1))
+ break;
+ ++numberOfExtraSquareRoots;
+ }
+ matrix_sqrt_triangular(T, sqrtT);
+ T = sqrtT.template triangularView<Upper>();
+ ++numberOfSquareRoots;
+ }
+
+ matrix_log_compute_pade(result, T, degree);
+ result *= pow(RealScalar(2), RealScalar(numberOfSquareRoots)); // TODO replace by bitshift if possible
+}
+
+/** \ingroup MatrixFunctions_Module
+ * \class MatrixLogarithmAtomic
+ * \brief Helper class for computing matrix logarithm of atomic matrices.
+ *
+ * Here, an atomic matrix is a triangular matrix whose diagonal entries are close to each other.
+ *
+ * \sa class MatrixFunctionAtomic, MatrixBase::log()
+ */
+template <typename MatrixType>
+class MatrixLogarithmAtomic
+{
+public:
+ /** \brief Compute matrix logarithm of atomic matrix
+ * \param[in] A argument of matrix logarithm, should be upper triangular and atomic
+ * \returns The logarithm of \p A.
+ */
+ MatrixType compute(const MatrixType& A);
+};
+
+template <typename MatrixType>
+MatrixType MatrixLogarithmAtomic<MatrixType>::compute(const MatrixType& A)
+{
+ using std::log;
+ MatrixType result(A.rows(), A.rows());
+ if (A.rows() == 1)
+ result(0,0) = log(A(0,0));
+ else if (A.rows() == 2)
+ matrix_log_compute_2x2(A, result);
+ else
+ matrix_log_compute_big(A, result);
+ return result;
+}
+
+} // end of namespace internal
+
+/** \ingroup MatrixFunctions_Module
+ *
+ * \brief Proxy for the matrix logarithm of some matrix (expression).
+ *
+ * \tparam Derived Type of the argument to the matrix function.
+ *
+ * This class holds the argument to the matrix function until it is
+ * assigned or evaluated for some other reason (so the argument
+ * should not be changed in the meantime). It is the return type of
+ * MatrixBase::log() and most of the time this is the only way it
+ * is used.
+ */
+template<typename Derived> class MatrixLogarithmReturnValue
+: public ReturnByValue<MatrixLogarithmReturnValue<Derived> >
+{
+public:
+ typedef typename Derived::Scalar Scalar;
+ typedef typename Derived::Index Index;
+
+protected:
+ typedef typename internal::ref_selector<Derived>::type DerivedNested;
+
+public:
+
+ /** \brief Constructor.
+ *
+ * \param[in] A %Matrix (expression) forming the argument of the matrix logarithm.
+ */
+ explicit MatrixLogarithmReturnValue(const Derived& A) : m_A(A) { }
+
+ /** \brief Compute the matrix logarithm.
+ *
+ * \param[out] result Logarithm of \c A, where \c A is as specified in the constructor.
+ */
+ template <typename ResultType>
+ inline void evalTo(ResultType& result) const
+ {
+ typedef typename internal::nested_eval<Derived, 10>::type DerivedEvalType;
+ typedef internal::remove_all_t<DerivedEvalType> DerivedEvalTypeClean;
+ typedef internal::traits<DerivedEvalTypeClean> Traits;
+ typedef std::complex<typename NumTraits<Scalar>::Real> ComplexScalar;
+ typedef Matrix<ComplexScalar, Dynamic, Dynamic, 0, Traits::RowsAtCompileTime, Traits::ColsAtCompileTime> DynMatrixType;
+ typedef internal::MatrixLogarithmAtomic<DynMatrixType> AtomicType;
+ AtomicType atomic;
+
+ internal::matrix_function_compute<typename DerivedEvalTypeClean::PlainObject>::run(m_A, atomic, result);
+ }
+
+ Index rows() const { return m_A.rows(); }
+ Index cols() const { return m_A.cols(); }
+
+private:
+ const DerivedNested m_A;
+};
+
+namespace internal {
+ template<typename Derived>
+ struct traits<MatrixLogarithmReturnValue<Derived> >
+ {
+ typedef typename Derived::PlainObject ReturnType;
+ };
+}
+
+
+/********** MatrixBase method **********/
+
+
+template <typename Derived>
+const MatrixLogarithmReturnValue<Derived> MatrixBase<Derived>::log() const
+{
+ eigen_assert(rows() == cols());
+ return MatrixLogarithmReturnValue<Derived>(derived());
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_MATRIX_LOGARITHM
diff --git a/unsupported/Eigen/src/MatrixFunctions/MatrixPower.h b/unsupported/Eigen/src/MatrixFunctions/MatrixPower.h
new file mode 100644
index 0000000..4eb8651
--- /dev/null
+++ b/unsupported/Eigen/src/MatrixFunctions/MatrixPower.h
@@ -0,0 +1,707 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2012, 2013 Chen-Pang He <jdh8@ms63.hinet.net>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_MATRIX_POWER
+#define EIGEN_MATRIX_POWER
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+template<typename MatrixType> class MatrixPower;
+
+/**
+ * \ingroup MatrixFunctions_Module
+ *
+ * \brief Proxy for the matrix power of some matrix.
+ *
+ * \tparam MatrixType type of the base, a matrix.
+ *
+ * This class holds the arguments to the matrix power until it is
+ * assigned or evaluated for some other reason (so the argument
+ * should not be changed in the meantime). It is the return type of
+ * MatrixPower::operator() and related functions and most of the
+ * time this is the only way it is used.
+ */
+/* TODO This class is only used by MatrixPower, so it should be nested
+ * into MatrixPower, like MatrixPower::ReturnValue. However, my
+ * compiler complained about unused template parameter in the
+ * following declaration in namespace internal.
+ *
+ * template<typename MatrixType>
+ * struct traits<MatrixPower<MatrixType>::ReturnValue>;
+ */
+template<typename MatrixType>
+class MatrixPowerParenthesesReturnValue : public ReturnByValue< MatrixPowerParenthesesReturnValue<MatrixType> >
+{
+ public:
+ typedef typename MatrixType::RealScalar RealScalar;
+
+ /**
+ * \brief Constructor.
+ *
+ * \param[in] pow %MatrixPower storing the base.
+ * \param[in] p scalar, the exponent of the matrix power.
+ */
+ MatrixPowerParenthesesReturnValue(MatrixPower<MatrixType>& pow, RealScalar p) : m_pow(pow), m_p(p)
+ { }
+
+ /**
+ * \brief Compute the matrix power.
+ *
+ * \param[out] result
+ */
+ template<typename ResultType>
+ inline void evalTo(ResultType& result) const
+ { m_pow.compute(result, m_p); }
+
+ Index rows() const { return m_pow.rows(); }
+ Index cols() const { return m_pow.cols(); }
+
+ private:
+ MatrixPower<MatrixType>& m_pow;
+ const RealScalar m_p;
+};
+
+/**
+ * \ingroup MatrixFunctions_Module
+ *
+ * \brief Class for computing matrix powers.
+ *
+ * \tparam MatrixType type of the base, expected to be an instantiation
+ * of the Matrix class template.
+ *
+ * This class is capable of computing triangular real/complex matrices
+ * raised to a power in the interval \f$ (-1, 1) \f$.
+ *
+ * \note Currently this class is only used by MatrixPower. One may
+ * insist that this be nested into MatrixPower. This class is here to
+ * facilitate future development of triangular matrix functions.
+ */
+template<typename MatrixType>
+class MatrixPowerAtomic : internal::noncopyable
+{
+ private:
+ enum {
+ RowsAtCompileTime = MatrixType::RowsAtCompileTime,
+ MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime
+ };
+ typedef typename MatrixType::Scalar Scalar;
+ typedef typename MatrixType::RealScalar RealScalar;
+ typedef std::complex<RealScalar> ComplexScalar;
+ typedef Block<MatrixType,Dynamic,Dynamic> ResultType;
+
+ const MatrixType& m_A;
+ RealScalar m_p;
+
+ void computePade(int degree, const MatrixType& IminusT, ResultType& res) const;
+ void compute2x2(ResultType& res, RealScalar p) const;
+ void computeBig(ResultType& res) const;
+ static int getPadeDegree(float normIminusT);
+ static int getPadeDegree(double normIminusT);
+ static int getPadeDegree(long double normIminusT);
+ static ComplexScalar computeSuperDiag(const ComplexScalar&, const ComplexScalar&, RealScalar p);
+ static RealScalar computeSuperDiag(RealScalar, RealScalar, RealScalar p);
+
+ public:
+ /**
+ * \brief Constructor.
+ *
+ * \param[in] T the base of the matrix power.
+ * \param[in] p the exponent of the matrix power, should be in
+ * \f$ (-1, 1) \f$.
+ *
+ * The class stores a reference to T, so it should not be changed
+ * (or destroyed) before evaluation. Only the upper triangular
+ * part of T is read.
+ */
+ MatrixPowerAtomic(const MatrixType& T, RealScalar p);
+
+ /**
+ * \brief Compute the matrix power.
+ *
+ * \param[out] res \f$ A^p \f$ where A and p are specified in the
+ * constructor.
+ */
+ void compute(ResultType& res) const;
+};
+
+template<typename MatrixType>
+MatrixPowerAtomic<MatrixType>::MatrixPowerAtomic(const MatrixType& T, RealScalar p) :
+ m_A(T), m_p(p)
+{
+ eigen_assert(T.rows() == T.cols());
+ eigen_assert(p > -1 && p < 1);
+}
+
+template<typename MatrixType>
+void MatrixPowerAtomic<MatrixType>::compute(ResultType& res) const
+{
+ using std::pow;
+ switch (m_A.rows()) {
+ case 0:
+ break;
+ case 1:
+ res(0,0) = pow(m_A(0,0), m_p);
+ break;
+ case 2:
+ compute2x2(res, m_p);
+ break;
+ default:
+ computeBig(res);
+ }
+}
+
+template<typename MatrixType>
+void MatrixPowerAtomic<MatrixType>::computePade(int degree, const MatrixType& IminusT, ResultType& res) const
+{
+ int i = 2*degree;
+ res = (m_p-RealScalar(degree)) / RealScalar(2*i-2) * IminusT;
+
+ for (--i; i; --i) {
+ res = (MatrixType::Identity(IminusT.rows(), IminusT.cols()) + res).template triangularView<Upper>()
+ .solve((i==1 ? -m_p : i&1 ? (-m_p-RealScalar(i/2))/RealScalar(2*i) : (m_p-RealScalar(i/2))/RealScalar(2*i-2)) * IminusT).eval();
+ }
+ res += MatrixType::Identity(IminusT.rows(), IminusT.cols());
+}
+
+// This function assumes that res has the correct size (see bug 614)
+template<typename MatrixType>
+void MatrixPowerAtomic<MatrixType>::compute2x2(ResultType& res, RealScalar p) const
+{
+ using std::abs;
+ using std::pow;
+ res.coeffRef(0,0) = pow(m_A.coeff(0,0), p);
+
+ for (Index i=1; i < m_A.cols(); ++i) {
+ res.coeffRef(i,i) = pow(m_A.coeff(i,i), p);
+ if (m_A.coeff(i-1,i-1) == m_A.coeff(i,i))
+ res.coeffRef(i-1,i) = p * pow(m_A.coeff(i,i), p-1);
+ else if (2*abs(m_A.coeff(i-1,i-1)) < abs(m_A.coeff(i,i)) || 2*abs(m_A.coeff(i,i)) < abs(m_A.coeff(i-1,i-1)))
+ res.coeffRef(i-1,i) = (res.coeff(i,i)-res.coeff(i-1,i-1)) / (m_A.coeff(i,i)-m_A.coeff(i-1,i-1));
+ else
+ res.coeffRef(i-1,i) = computeSuperDiag(m_A.coeff(i,i), m_A.coeff(i-1,i-1), p);
+ res.coeffRef(i-1,i) *= m_A.coeff(i-1,i);
+ }
+}
+
+template<typename MatrixType>
+void MatrixPowerAtomic<MatrixType>::computeBig(ResultType& res) const
+{
+ using std::ldexp;
+ const int digits = std::numeric_limits<RealScalar>::digits;
+ const RealScalar maxNormForPade = RealScalar(
+ digits <= 24? 4.3386528e-1L // single precision
+ : digits <= 53? 2.789358995219730e-1L // double precision
+ : digits <= 64? 2.4471944416607995472e-1L // extended precision
+ : digits <= 106? 1.1016843812851143391275867258512e-1L // double-double
+ : 9.134603732914548552537150753385375e-2L); // quadruple precision
+ MatrixType IminusT, sqrtT, T = m_A.template triangularView<Upper>();
+ RealScalar normIminusT;
+ int degree, degree2, numberOfSquareRoots = 0;
+ bool hasExtraSquareRoot = false;
+
+ for (Index i=0; i < m_A.cols(); ++i)
+ eigen_assert(m_A(i,i) != RealScalar(0));
+
+ while (true) {
+ IminusT = MatrixType::Identity(m_A.rows(), m_A.cols()) - T;
+ normIminusT = IminusT.cwiseAbs().colwise().sum().maxCoeff();
+ if (normIminusT < maxNormForPade) {
+ degree = getPadeDegree(normIminusT);
+ degree2 = getPadeDegree(normIminusT/2);
+ if (degree - degree2 <= 1 || hasExtraSquareRoot)
+ break;
+ hasExtraSquareRoot = true;
+ }
+ matrix_sqrt_triangular(T, sqrtT);
+ T = sqrtT.template triangularView<Upper>();
+ ++numberOfSquareRoots;
+ }
+ computePade(degree, IminusT, res);
+
+ for (; numberOfSquareRoots; --numberOfSquareRoots) {
+ compute2x2(res, ldexp(m_p, -numberOfSquareRoots));
+ res = res.template triangularView<Upper>() * res;
+ }
+ compute2x2(res, m_p);
+}
+
+template<typename MatrixType>
+inline int MatrixPowerAtomic<MatrixType>::getPadeDegree(float normIminusT)
+{
+ const float maxNormForPade[] = { 2.8064004e-1f /* degree = 3 */ , 4.3386528e-1f };
+ int degree = 3;
+ for (; degree <= 4; ++degree)
+ if (normIminusT <= maxNormForPade[degree - 3])
+ break;
+ return degree;
+}
+
+template<typename MatrixType>
+inline int MatrixPowerAtomic<MatrixType>::getPadeDegree(double normIminusT)
+{
+ const double maxNormForPade[] = { 1.884160592658218e-2 /* degree = 3 */ , 6.038881904059573e-2, 1.239917516308172e-1,
+ 1.999045567181744e-1, 2.789358995219730e-1 };
+ int degree = 3;
+ for (; degree <= 7; ++degree)
+ if (normIminusT <= maxNormForPade[degree - 3])
+ break;
+ return degree;
+}
+
+template<typename MatrixType>
+inline int MatrixPowerAtomic<MatrixType>::getPadeDegree(long double normIminusT)
+{
+#if LDBL_MANT_DIG == 53
+ const int maxPadeDegree = 7;
+ const double maxNormForPade[] = { 1.884160592658218e-2L /* degree = 3 */ , 6.038881904059573e-2L, 1.239917516308172e-1L,
+ 1.999045567181744e-1L, 2.789358995219730e-1L };
+#elif LDBL_MANT_DIG <= 64
+ const int maxPadeDegree = 8;
+ const long double maxNormForPade[] = { 6.3854693117491799460e-3L /* degree = 3 */ , 2.6394893435456973676e-2L,
+ 6.4216043030404063729e-2L, 1.1701165502926694307e-1L, 1.7904284231268670284e-1L, 2.4471944416607995472e-1L };
+#elif LDBL_MANT_DIG <= 106
+ const int maxPadeDegree = 10;
+ const double maxNormForPade[] = { 1.0007161601787493236741409687186e-4L /* degree = 3 */ ,
+ 1.0007161601787493236741409687186e-3L, 4.7069769360887572939882574746264e-3L, 1.3220386624169159689406653101695e-2L,
+ 2.8063482381631737920612944054906e-2L, 4.9625993951953473052385361085058e-2L, 7.7367040706027886224557538328171e-2L,
+ 1.1016843812851143391275867258512e-1L };
+#else
+ const int maxPadeDegree = 10;
+ const double maxNormForPade[] = { 5.524506147036624377378713555116378e-5L /* degree = 3 */ ,
+ 6.640600568157479679823602193345995e-4L, 3.227716520106894279249709728084626e-3L,
+ 9.619593944683432960546978734646284e-3L, 2.134595382433742403911124458161147e-2L,
+ 3.908166513900489428442993794761185e-2L, 6.266780814639442865832535460550138e-2L,
+ 9.134603732914548552537150753385375e-2L };
+#endif
+ int degree = 3;
+ for (; degree <= maxPadeDegree; ++degree)
+ if (normIminusT <= maxNormForPade[degree - 3])
+ break;
+ return degree;
+}
+
+template<typename MatrixType>
+inline typename MatrixPowerAtomic<MatrixType>::ComplexScalar
+MatrixPowerAtomic<MatrixType>::computeSuperDiag(const ComplexScalar& curr, const ComplexScalar& prev, RealScalar p)
+{
+ using std::ceil;
+ using std::exp;
+ using std::log;
+ using std::sinh;
+
+ ComplexScalar logCurr = log(curr);
+ ComplexScalar logPrev = log(prev);
+ RealScalar unwindingNumber = ceil((numext::imag(logCurr - logPrev) - RealScalar(EIGEN_PI)) / RealScalar(2*EIGEN_PI));
+ ComplexScalar w = numext::log1p((curr-prev)/prev)/RealScalar(2) + ComplexScalar(0, RealScalar(EIGEN_PI)*unwindingNumber);
+ return RealScalar(2) * exp(RealScalar(0.5) * p * (logCurr + logPrev)) * sinh(p * w) / (curr - prev);
+}
+
+template<typename MatrixType>
+inline typename MatrixPowerAtomic<MatrixType>::RealScalar
+MatrixPowerAtomic<MatrixType>::computeSuperDiag(RealScalar curr, RealScalar prev, RealScalar p)
+{
+ using std::exp;
+ using std::log;
+ using std::sinh;
+
+ RealScalar w = numext::log1p((curr-prev)/prev)/RealScalar(2);
+ return 2 * exp(p * (log(curr) + log(prev)) / 2) * sinh(p * w) / (curr - prev);
+}
+
+/**
+ * \ingroup MatrixFunctions_Module
+ *
+ * \brief Class for computing matrix powers.
+ *
+ * \tparam MatrixType type of the base, expected to be an instantiation
+ * of the Matrix class template.
+ *
+ * This class is capable of computing real/complex matrices raised to
+ * an arbitrary real power. Meanwhile, it saves the result of Schur
+ * decomposition if an non-integral power has even been calculated.
+ * Therefore, if you want to compute multiple (>= 2) matrix powers
+ * for the same matrix, using the class directly is more efficient than
+ * calling MatrixBase::pow().
+ *
+ * Example:
+ * \include MatrixPower_optimal.cpp
+ * Output: \verbinclude MatrixPower_optimal.out
+ */
+template<typename MatrixType>
+class MatrixPower : internal::noncopyable
+{
+ private:
+ typedef typename MatrixType::Scalar Scalar;
+ typedef typename MatrixType::RealScalar RealScalar;
+
+ public:
+ /**
+ * \brief Constructor.
+ *
+ * \param[in] A the base of the matrix power.
+ *
+ * The class stores a reference to A, so it should not be changed
+ * (or destroyed) before evaluation.
+ */
+ explicit MatrixPower(const MatrixType& A) :
+ m_A(A),
+ m_conditionNumber(0),
+ m_rank(A.cols()),
+ m_nulls(0)
+ { eigen_assert(A.rows() == A.cols()); }
+
+ /**
+ * \brief Returns the matrix power.
+ *
+ * \param[in] p exponent, a real scalar.
+ * \return The expression \f$ A^p \f$, where A is specified in the
+ * constructor.
+ */
+ const MatrixPowerParenthesesReturnValue<MatrixType> operator()(RealScalar p)
+ { return MatrixPowerParenthesesReturnValue<MatrixType>(*this, p); }
+
+ /**
+ * \brief Compute the matrix power.
+ *
+ * \param[in] p exponent, a real scalar.
+ * \param[out] res \f$ A^p \f$ where A is specified in the
+ * constructor.
+ */
+ template<typename ResultType>
+ void compute(ResultType& res, RealScalar p);
+
+ Index rows() const { return m_A.rows(); }
+ Index cols() const { return m_A.cols(); }
+
+ private:
+ typedef std::complex<RealScalar> ComplexScalar;
+ typedef Matrix<ComplexScalar, Dynamic, Dynamic, 0,
+ MatrixType::RowsAtCompileTime, MatrixType::ColsAtCompileTime> ComplexMatrix;
+
+ /** \brief Reference to the base of matrix power. */
+ typename MatrixType::Nested m_A;
+
+ /** \brief Temporary storage. */
+ MatrixType m_tmp;
+
+ /** \brief Store the result of Schur decomposition. */
+ ComplexMatrix m_T, m_U;
+
+ /** \brief Store fractional power of m_T. */
+ ComplexMatrix m_fT;
+
+ /**
+ * \brief Condition number of m_A.
+ *
+ * It is initialized as 0 to avoid performing unnecessary Schur
+ * decomposition, which is the bottleneck.
+ */
+ RealScalar m_conditionNumber;
+
+ /** \brief Rank of m_A. */
+ Index m_rank;
+
+ /** \brief Rank deficiency of m_A. */
+ Index m_nulls;
+
+ /**
+ * \brief Split p into integral part and fractional part.
+ *
+ * \param[in] p The exponent.
+ * \param[out] p The fractional part ranging in \f$ (-1, 1) \f$.
+ * \param[out] intpart The integral part.
+ *
+ * Only if the fractional part is nonzero, it calls initialize().
+ */
+ void split(RealScalar& p, RealScalar& intpart);
+
+ /** \brief Perform Schur decomposition for fractional power. */
+ void initialize();
+
+ template<typename ResultType>
+ void computeIntPower(ResultType& res, RealScalar p);
+
+ template<typename ResultType>
+ void computeFracPower(ResultType& res, RealScalar p);
+
+ template<int Rows, int Cols, int Options, int MaxRows, int MaxCols>
+ static void revertSchur(
+ Matrix<ComplexScalar, Rows, Cols, Options, MaxRows, MaxCols>& res,
+ const ComplexMatrix& T,
+ const ComplexMatrix& U);
+
+ template<int Rows, int Cols, int Options, int MaxRows, int MaxCols>
+ static void revertSchur(
+ Matrix<RealScalar, Rows, Cols, Options, MaxRows, MaxCols>& res,
+ const ComplexMatrix& T,
+ const ComplexMatrix& U);
+};
+
+template<typename MatrixType>
+template<typename ResultType>
+void MatrixPower<MatrixType>::compute(ResultType& res, RealScalar p)
+{
+ using std::pow;
+ switch (cols()) {
+ case 0:
+ break;
+ case 1:
+ res(0,0) = pow(m_A.coeff(0,0), p);
+ break;
+ default:
+ RealScalar intpart;
+ split(p, intpart);
+
+ res = MatrixType::Identity(rows(), cols());
+ computeIntPower(res, intpart);
+ if (p) computeFracPower(res, p);
+ }
+}
+
+template<typename MatrixType>
+void MatrixPower<MatrixType>::split(RealScalar& p, RealScalar& intpart)
+{
+ using std::floor;
+ using std::pow;
+
+ intpart = floor(p);
+ p -= intpart;
+
+ // Perform Schur decomposition if it is not yet performed and the power is
+ // not an integer.
+ if (!m_conditionNumber && p)
+ initialize();
+
+ // Choose the more stable of intpart = floor(p) and intpart = ceil(p).
+ if (p > RealScalar(0.5) && p > (1-p) * pow(m_conditionNumber, p)) {
+ --p;
+ ++intpart;
+ }
+}
+
+template<typename MatrixType>
+void MatrixPower<MatrixType>::initialize()
+{
+ const ComplexSchur<MatrixType> schurOfA(m_A);
+ JacobiRotation<ComplexScalar> rot;
+ ComplexScalar eigenvalue;
+
+ m_fT.resizeLike(m_A);
+ m_T = schurOfA.matrixT();
+ m_U = schurOfA.matrixU();
+ m_conditionNumber = m_T.diagonal().array().abs().maxCoeff() / m_T.diagonal().array().abs().minCoeff();
+
+ // Move zero eigenvalues to the bottom right corner.
+ for (Index i = cols()-1; i>=0; --i) {
+ if (m_rank <= 2)
+ return;
+ if (m_T.coeff(i,i) == RealScalar(0)) {
+ for (Index j=i+1; j < m_rank; ++j) {
+ eigenvalue = m_T.coeff(j,j);
+ rot.makeGivens(m_T.coeff(j-1,j), eigenvalue);
+ m_T.applyOnTheRight(j-1, j, rot);
+ m_T.applyOnTheLeft(j-1, j, rot.adjoint());
+ m_T.coeffRef(j-1,j-1) = eigenvalue;
+ m_T.coeffRef(j,j) = RealScalar(0);
+ m_U.applyOnTheRight(j-1, j, rot);
+ }
+ --m_rank;
+ }
+ }
+
+ m_nulls = rows() - m_rank;
+ if (m_nulls) {
+ eigen_assert(m_T.bottomRightCorner(m_nulls, m_nulls).isZero()
+ && "Base of matrix power should be invertible or with a semisimple zero eigenvalue.");
+ m_fT.bottomRows(m_nulls).fill(RealScalar(0));
+ }
+}
+
+template<typename MatrixType>
+template<typename ResultType>
+void MatrixPower<MatrixType>::computeIntPower(ResultType& res, RealScalar p)
+{
+ using std::abs;
+ using std::fmod;
+ RealScalar pp = abs(p);
+
+ if (p<0)
+ m_tmp = m_A.inverse();
+ else
+ m_tmp = m_A;
+
+ while (true) {
+ if (fmod(pp, 2) >= 1)
+ res = m_tmp * res;
+ pp /= 2;
+ if (pp < 1)
+ break;
+ m_tmp *= m_tmp;
+ }
+}
+
+template<typename MatrixType>
+template<typename ResultType>
+void MatrixPower<MatrixType>::computeFracPower(ResultType& res, RealScalar p)
+{
+ Block<ComplexMatrix,Dynamic,Dynamic> blockTp(m_fT, 0, 0, m_rank, m_rank);
+ eigen_assert(m_conditionNumber);
+ eigen_assert(m_rank + m_nulls == rows());
+
+ MatrixPowerAtomic<ComplexMatrix>(m_T.topLeftCorner(m_rank, m_rank), p).compute(blockTp);
+ if (m_nulls) {
+ m_fT.topRightCorner(m_rank, m_nulls) = m_T.topLeftCorner(m_rank, m_rank).template triangularView<Upper>()
+ .solve(blockTp * m_T.topRightCorner(m_rank, m_nulls));
+ }
+ revertSchur(m_tmp, m_fT, m_U);
+ res = m_tmp * res;
+}
+
+template<typename MatrixType>
+template<int Rows, int Cols, int Options, int MaxRows, int MaxCols>
+inline void MatrixPower<MatrixType>::revertSchur(
+ Matrix<ComplexScalar, Rows, Cols, Options, MaxRows, MaxCols>& res,
+ const ComplexMatrix& T,
+ const ComplexMatrix& U)
+{ res.noalias() = U * (T.template triangularView<Upper>() * U.adjoint()); }
+
+template<typename MatrixType>
+template<int Rows, int Cols, int Options, int MaxRows, int MaxCols>
+inline void MatrixPower<MatrixType>::revertSchur(
+ Matrix<RealScalar, Rows, Cols, Options, MaxRows, MaxCols>& res,
+ const ComplexMatrix& T,
+ const ComplexMatrix& U)
+{ res.noalias() = (U * (T.template triangularView<Upper>() * U.adjoint())).real(); }
+
+/**
+ * \ingroup MatrixFunctions_Module
+ *
+ * \brief Proxy for the matrix power of some matrix (expression).
+ *
+ * \tparam Derived type of the base, a matrix (expression).
+ *
+ * This class holds the arguments to the matrix power until it is
+ * assigned or evaluated for some other reason (so the argument
+ * should not be changed in the meantime). It is the return type of
+ * MatrixBase::pow() and related functions and most of the
+ * time this is the only way it is used.
+ */
+template<typename Derived>
+class MatrixPowerReturnValue : public ReturnByValue< MatrixPowerReturnValue<Derived> >
+{
+ public:
+ typedef typename Derived::PlainObject PlainObject;
+ typedef typename Derived::RealScalar RealScalar;
+
+ /**
+ * \brief Constructor.
+ *
+ * \param[in] A %Matrix (expression), the base of the matrix power.
+ * \param[in] p real scalar, the exponent of the matrix power.
+ */
+ MatrixPowerReturnValue(const Derived& A, RealScalar p) : m_A(A), m_p(p)
+ { }
+
+ /**
+ * \brief Compute the matrix power.
+ *
+ * \param[out] result \f$ A^p \f$ where \p A and \p p are as in the
+ * constructor.
+ */
+ template<typename ResultType>
+ inline void evalTo(ResultType& result) const
+ { MatrixPower<PlainObject>(m_A.eval()).compute(result, m_p); }
+
+ Index rows() const { return m_A.rows(); }
+ Index cols() const { return m_A.cols(); }
+
+ private:
+ const Derived& m_A;
+ const RealScalar m_p;
+};
+
+/**
+ * \ingroup MatrixFunctions_Module
+ *
+ * \brief Proxy for the matrix power of some matrix (expression).
+ *
+ * \tparam Derived type of the base, a matrix (expression).
+ *
+ * This class holds the arguments to the matrix power until it is
+ * assigned or evaluated for some other reason (so the argument
+ * should not be changed in the meantime). It is the return type of
+ * MatrixBase::pow() and related functions and most of the
+ * time this is the only way it is used.
+ */
+template<typename Derived>
+class MatrixComplexPowerReturnValue : public ReturnByValue< MatrixComplexPowerReturnValue<Derived> >
+{
+ public:
+ typedef typename Derived::PlainObject PlainObject;
+ typedef typename std::complex<typename Derived::RealScalar> ComplexScalar;
+
+ /**
+ * \brief Constructor.
+ *
+ * \param[in] A %Matrix (expression), the base of the matrix power.
+ * \param[in] p complex scalar, the exponent of the matrix power.
+ */
+ MatrixComplexPowerReturnValue(const Derived& A, const ComplexScalar& p) : m_A(A), m_p(p)
+ { }
+
+ /**
+ * \brief Compute the matrix power.
+ *
+ * Because \p p is complex, \f$ A^p \f$ is simply evaluated as \f$
+ * \exp(p \log(A)) \f$.
+ *
+ * \param[out] result \f$ A^p \f$ where \p A and \p p are as in the
+ * constructor.
+ */
+ template<typename ResultType>
+ inline void evalTo(ResultType& result) const
+ { result = (m_p * m_A.log()).exp(); }
+
+ Index rows() const { return m_A.rows(); }
+ Index cols() const { return m_A.cols(); }
+
+ private:
+ const Derived& m_A;
+ const ComplexScalar m_p;
+};
+
+namespace internal {
+
+template<typename MatrixPowerType>
+struct traits< MatrixPowerParenthesesReturnValue<MatrixPowerType> >
+{ typedef typename MatrixPowerType::PlainObject ReturnType; };
+
+template<typename Derived>
+struct traits< MatrixPowerReturnValue<Derived> >
+{ typedef typename Derived::PlainObject ReturnType; };
+
+template<typename Derived>
+struct traits< MatrixComplexPowerReturnValue<Derived> >
+{ typedef typename Derived::PlainObject ReturnType; };
+
+}
+
+template<typename Derived>
+const MatrixPowerReturnValue<Derived> MatrixBase<Derived>::pow(const RealScalar& p) const
+{ return MatrixPowerReturnValue<Derived>(derived(), p); }
+
+template<typename Derived>
+const MatrixComplexPowerReturnValue<Derived> MatrixBase<Derived>::pow(const std::complex<RealScalar>& p) const
+{ return MatrixComplexPowerReturnValue<Derived>(derived(), p); }
+
+} // namespace Eigen
+
+#endif // EIGEN_MATRIX_POWER
diff --git a/unsupported/Eigen/src/MatrixFunctions/MatrixSquareRoot.h b/unsupported/Eigen/src/MatrixFunctions/MatrixSquareRoot.h
new file mode 100644
index 0000000..6c58cae
--- /dev/null
+++ b/unsupported/Eigen/src/MatrixFunctions/MatrixSquareRoot.h
@@ -0,0 +1,370 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2011, 2013 Jitse Niesen <jitse@maths.leeds.ac.uk>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_MATRIX_SQUARE_ROOT
+#define EIGEN_MATRIX_SQUARE_ROOT
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+
+// pre: T.block(i,i,2,2) has complex conjugate eigenvalues
+// post: sqrtT.block(i,i,2,2) is square root of T.block(i,i,2,2)
+template <typename MatrixType, typename ResultType>
+void matrix_sqrt_quasi_triangular_2x2_diagonal_block(const MatrixType& T, Index i, ResultType& sqrtT)
+{
+ // TODO: This case (2-by-2 blocks with complex conjugate eigenvalues) is probably hidden somewhere
+ // in EigenSolver. If we expose it, we could call it directly from here.
+ typedef typename traits<MatrixType>::Scalar Scalar;
+ Matrix<Scalar,2,2> block = T.template block<2,2>(i,i);
+ EigenSolver<Matrix<Scalar,2,2> > es(block);
+ sqrtT.template block<2,2>(i,i)
+ = (es.eigenvectors() * es.eigenvalues().cwiseSqrt().asDiagonal() * es.eigenvectors().inverse()).real();
+}
+
+// pre: block structure of T is such that (i,j) is a 1x1 block,
+// all blocks of sqrtT to left of and below (i,j) are correct
+// post: sqrtT(i,j) has the correct value
+template <typename MatrixType, typename ResultType>
+void matrix_sqrt_quasi_triangular_1x1_off_diagonal_block(const MatrixType& T, Index i, Index j, ResultType& sqrtT)
+{
+ typedef typename traits<MatrixType>::Scalar Scalar;
+ Scalar tmp = (sqrtT.row(i).segment(i+1,j-i-1) * sqrtT.col(j).segment(i+1,j-i-1)).value();
+ sqrtT.coeffRef(i,j) = (T.coeff(i,j) - tmp) / (sqrtT.coeff(i,i) + sqrtT.coeff(j,j));
+}
+
+// similar to compute1x1offDiagonalBlock()
+template <typename MatrixType, typename ResultType>
+void matrix_sqrt_quasi_triangular_1x2_off_diagonal_block(const MatrixType& T, Index i, Index j, ResultType& sqrtT)
+{
+ typedef typename traits<MatrixType>::Scalar Scalar;
+ Matrix<Scalar,1,2> rhs = T.template block<1,2>(i,j);
+ if (j-i > 1)
+ rhs -= sqrtT.block(i, i+1, 1, j-i-1) * sqrtT.block(i+1, j, j-i-1, 2);
+ Matrix<Scalar,2,2> A = sqrtT.coeff(i,i) * Matrix<Scalar,2,2>::Identity();
+ A += sqrtT.template block<2,2>(j,j).transpose();
+ sqrtT.template block<1,2>(i,j).transpose() = A.fullPivLu().solve(rhs.transpose());
+}
+
+// similar to compute1x1offDiagonalBlock()
+template <typename MatrixType, typename ResultType>
+void matrix_sqrt_quasi_triangular_2x1_off_diagonal_block(const MatrixType& T, Index i, Index j, ResultType& sqrtT)
+{
+ typedef typename traits<MatrixType>::Scalar Scalar;
+ Matrix<Scalar,2,1> rhs = T.template block<2,1>(i,j);
+ if (j-i > 2)
+ rhs -= sqrtT.block(i, i+2, 2, j-i-2) * sqrtT.block(i+2, j, j-i-2, 1);
+ Matrix<Scalar,2,2> A = sqrtT.coeff(j,j) * Matrix<Scalar,2,2>::Identity();
+ A += sqrtT.template block<2,2>(i,i);
+ sqrtT.template block<2,1>(i,j) = A.fullPivLu().solve(rhs);
+}
+
+// solves the equation A X + X B = C where all matrices are 2-by-2
+template <typename MatrixType>
+void matrix_sqrt_quasi_triangular_solve_auxiliary_equation(MatrixType& X, const MatrixType& A, const MatrixType& B, const MatrixType& C)
+{
+ typedef typename traits<MatrixType>::Scalar Scalar;
+ Matrix<Scalar,4,4> coeffMatrix = Matrix<Scalar,4,4>::Zero();
+ coeffMatrix.coeffRef(0,0) = A.coeff(0,0) + B.coeff(0,0);
+ coeffMatrix.coeffRef(1,1) = A.coeff(0,0) + B.coeff(1,1);
+ coeffMatrix.coeffRef(2,2) = A.coeff(1,1) + B.coeff(0,0);
+ coeffMatrix.coeffRef(3,3) = A.coeff(1,1) + B.coeff(1,1);
+ coeffMatrix.coeffRef(0,1) = B.coeff(1,0);
+ coeffMatrix.coeffRef(0,2) = A.coeff(0,1);
+ coeffMatrix.coeffRef(1,0) = B.coeff(0,1);
+ coeffMatrix.coeffRef(1,3) = A.coeff(0,1);
+ coeffMatrix.coeffRef(2,0) = A.coeff(1,0);
+ coeffMatrix.coeffRef(2,3) = B.coeff(1,0);
+ coeffMatrix.coeffRef(3,1) = A.coeff(1,0);
+ coeffMatrix.coeffRef(3,2) = B.coeff(0,1);
+
+ Matrix<Scalar,4,1> rhs;
+ rhs.coeffRef(0) = C.coeff(0,0);
+ rhs.coeffRef(1) = C.coeff(0,1);
+ rhs.coeffRef(2) = C.coeff(1,0);
+ rhs.coeffRef(3) = C.coeff(1,1);
+
+ Matrix<Scalar,4,1> result;
+ result = coeffMatrix.fullPivLu().solve(rhs);
+
+ X.coeffRef(0,0) = result.coeff(0);
+ X.coeffRef(0,1) = result.coeff(1);
+ X.coeffRef(1,0) = result.coeff(2);
+ X.coeffRef(1,1) = result.coeff(3);
+}
+
+// similar to compute1x1offDiagonalBlock()
+template <typename MatrixType, typename ResultType>
+void matrix_sqrt_quasi_triangular_2x2_off_diagonal_block(const MatrixType& T, Index i, Index j, ResultType& sqrtT)
+{
+ typedef typename traits<MatrixType>::Scalar Scalar;
+ Matrix<Scalar,2,2> A = sqrtT.template block<2,2>(i,i);
+ Matrix<Scalar,2,2> B = sqrtT.template block<2,2>(j,j);
+ Matrix<Scalar,2,2> C = T.template block<2,2>(i,j);
+ if (j-i > 2)
+ C -= sqrtT.block(i, i+2, 2, j-i-2) * sqrtT.block(i+2, j, j-i-2, 2);
+ Matrix<Scalar,2,2> X;
+ matrix_sqrt_quasi_triangular_solve_auxiliary_equation(X, A, B, C);
+ sqrtT.template block<2,2>(i,j) = X;
+}
+
+// pre: T is quasi-upper-triangular and sqrtT is a zero matrix of the same size
+// post: the diagonal blocks of sqrtT are the square roots of the diagonal blocks of T
+template <typename MatrixType, typename ResultType>
+void matrix_sqrt_quasi_triangular_diagonal(const MatrixType& T, ResultType& sqrtT)
+{
+ using std::sqrt;
+ const Index size = T.rows();
+ for (Index i = 0; i < size; i++) {
+ if (i == size - 1 || T.coeff(i+1, i) == 0) {
+ eigen_assert(T(i,i) >= 0);
+ sqrtT.coeffRef(i,i) = sqrt(T.coeff(i,i));
+ }
+ else {
+ matrix_sqrt_quasi_triangular_2x2_diagonal_block(T, i, sqrtT);
+ ++i;
+ }
+ }
+}
+
+// pre: T is quasi-upper-triangular and diagonal blocks of sqrtT are square root of diagonal blocks of T.
+// post: sqrtT is the square root of T.
+template <typename MatrixType, typename ResultType>
+void matrix_sqrt_quasi_triangular_off_diagonal(const MatrixType& T, ResultType& sqrtT)
+{
+ const Index size = T.rows();
+ for (Index j = 1; j < size; j++) {
+ if (T.coeff(j, j-1) != 0) // if T(j-1:j, j-1:j) is a 2-by-2 block
+ continue;
+ for (Index i = j-1; i >= 0; i--) {
+ if (i > 0 && T.coeff(i, i-1) != 0) // if T(i-1:i, i-1:i) is a 2-by-2 block
+ continue;
+ bool iBlockIs2x2 = (i < size - 1) && (T.coeff(i+1, i) != 0);
+ bool jBlockIs2x2 = (j < size - 1) && (T.coeff(j+1, j) != 0);
+ if (iBlockIs2x2 && jBlockIs2x2)
+ matrix_sqrt_quasi_triangular_2x2_off_diagonal_block(T, i, j, sqrtT);
+ else if (iBlockIs2x2 && !jBlockIs2x2)
+ matrix_sqrt_quasi_triangular_2x1_off_diagonal_block(T, i, j, sqrtT);
+ else if (!iBlockIs2x2 && jBlockIs2x2)
+ matrix_sqrt_quasi_triangular_1x2_off_diagonal_block(T, i, j, sqrtT);
+ else if (!iBlockIs2x2 && !jBlockIs2x2)
+ matrix_sqrt_quasi_triangular_1x1_off_diagonal_block(T, i, j, sqrtT);
+ }
+ }
+}
+
+} // end of namespace internal
+
+/** \ingroup MatrixFunctions_Module
+ * \brief Compute matrix square root of quasi-triangular matrix.
+ *
+ * \tparam MatrixType type of \p arg, the argument of matrix square root,
+ * expected to be an instantiation of the Matrix class template.
+ * \tparam ResultType type of \p result, where result is to be stored.
+ * \param[in] arg argument of matrix square root.
+ * \param[out] result matrix square root of upper Hessenberg part of \p arg.
+ *
+ * This function computes the square root of the upper quasi-triangular matrix stored in the upper
+ * Hessenberg part of \p arg. Only the upper Hessenberg part of \p result is updated, the rest is
+ * not touched. See MatrixBase::sqrt() for details on how this computation is implemented.
+ *
+ * \sa MatrixSquareRoot, MatrixSquareRootQuasiTriangular
+ */
+template <typename MatrixType, typename ResultType>
+void matrix_sqrt_quasi_triangular(const MatrixType &arg, ResultType &result)
+{
+ eigen_assert(arg.rows() == arg.cols());
+ result.resize(arg.rows(), arg.cols());
+ internal::matrix_sqrt_quasi_triangular_diagonal(arg, result);
+ internal::matrix_sqrt_quasi_triangular_off_diagonal(arg, result);
+}
+
+
+/** \ingroup MatrixFunctions_Module
+ * \brief Compute matrix square root of triangular matrix.
+ *
+ * \tparam MatrixType type of \p arg, the argument of matrix square root,
+ * expected to be an instantiation of the Matrix class template.
+ * \tparam ResultType type of \p result, where result is to be stored.
+ * \param[in] arg argument of matrix square root.
+ * \param[out] result matrix square root of upper triangular part of \p arg.
+ *
+ * Only the upper triangular part (including the diagonal) of \p result is updated, the rest is not
+ * touched. See MatrixBase::sqrt() for details on how this computation is implemented.
+ *
+ * \sa MatrixSquareRoot, MatrixSquareRootQuasiTriangular
+ */
+template <typename MatrixType, typename ResultType>
+void matrix_sqrt_triangular(const MatrixType &arg, ResultType &result)
+{
+ using std::sqrt;
+ typedef typename MatrixType::Scalar Scalar;
+
+ eigen_assert(arg.rows() == arg.cols());
+
+ // Compute square root of arg and store it in upper triangular part of result
+ // This uses that the square root of triangular matrices can be computed directly.
+ result.resize(arg.rows(), arg.cols());
+ for (Index i = 0; i < arg.rows(); i++) {
+ result.coeffRef(i,i) = sqrt(arg.coeff(i,i));
+ }
+ for (Index j = 1; j < arg.cols(); j++) {
+ for (Index i = j-1; i >= 0; i--) {
+ // if i = j-1, then segment has length 0 so tmp = 0
+ Scalar tmp = (result.row(i).segment(i+1,j-i-1) * result.col(j).segment(i+1,j-i-1)).value();
+ // denominator may be zero if original matrix is singular
+ result.coeffRef(i,j) = (arg.coeff(i,j) - tmp) / (result.coeff(i,i) + result.coeff(j,j));
+ }
+ }
+}
+
+
+namespace internal {
+
+/** \ingroup MatrixFunctions_Module
+ * \brief Helper struct for computing matrix square roots of general matrices.
+ * \tparam MatrixType type of the argument of the matrix square root,
+ * expected to be an instantiation of the Matrix class template.
+ *
+ * \sa MatrixSquareRootTriangular, MatrixSquareRootQuasiTriangular, MatrixBase::sqrt()
+ */
+template <typename MatrixType, int IsComplex = NumTraits<typename internal::traits<MatrixType>::Scalar>::IsComplex>
+struct matrix_sqrt_compute
+{
+ /** \brief Compute the matrix square root
+ *
+ * \param[in] arg matrix whose square root is to be computed.
+ * \param[out] result square root of \p arg.
+ *
+ * See MatrixBase::sqrt() for details on how this computation is implemented.
+ */
+ template <typename ResultType> static void run(const MatrixType &arg, ResultType &result);
+};
+
+
+// ********** Partial specialization for real matrices **********
+
+template <typename MatrixType>
+struct matrix_sqrt_compute<MatrixType, 0>
+{
+ typedef typename MatrixType::PlainObject PlainType;
+ template <typename ResultType>
+ static void run(const MatrixType &arg, ResultType &result)
+ {
+ eigen_assert(arg.rows() == arg.cols());
+
+ // Compute Schur decomposition of arg
+ const RealSchur<PlainType> schurOfA(arg);
+ const PlainType& T = schurOfA.matrixT();
+ const PlainType& U = schurOfA.matrixU();
+
+ // Compute square root of T
+ PlainType sqrtT = PlainType::Zero(arg.rows(), arg.cols());
+ matrix_sqrt_quasi_triangular(T, sqrtT);
+
+ // Compute square root of arg
+ result = U * sqrtT * U.adjoint();
+ }
+};
+
+
+// ********** Partial specialization for complex matrices **********
+
+template <typename MatrixType>
+struct matrix_sqrt_compute<MatrixType, 1>
+{
+ typedef typename MatrixType::PlainObject PlainType;
+ template <typename ResultType>
+ static void run(const MatrixType &arg, ResultType &result)
+ {
+ eigen_assert(arg.rows() == arg.cols());
+
+ // Compute Schur decomposition of arg
+ const ComplexSchur<PlainType> schurOfA(arg);
+ const PlainType& T = schurOfA.matrixT();
+ const PlainType& U = schurOfA.matrixU();
+
+ // Compute square root of T
+ PlainType sqrtT;
+ matrix_sqrt_triangular(T, sqrtT);
+
+ // Compute square root of arg
+ result = U * (sqrtT.template triangularView<Upper>() * U.adjoint());
+ }
+};
+
+} // end namespace internal
+
+/** \ingroup MatrixFunctions_Module
+ *
+ * \brief Proxy for the matrix square root of some matrix (expression).
+ *
+ * \tparam Derived Type of the argument to the matrix square root.
+ *
+ * This class holds the argument to the matrix square root until it
+ * is assigned or evaluated for some other reason (so the argument
+ * should not be changed in the meantime). It is the return type of
+ * MatrixBase::sqrt() and most of the time this is the only way it is
+ * used.
+ */
+template<typename Derived> class MatrixSquareRootReturnValue
+: public ReturnByValue<MatrixSquareRootReturnValue<Derived> >
+{
+ protected:
+ typedef typename internal::ref_selector<Derived>::type DerivedNested;
+
+ public:
+ /** \brief Constructor.
+ *
+ * \param[in] src %Matrix (expression) forming the argument of the
+ * matrix square root.
+ */
+ explicit MatrixSquareRootReturnValue(const Derived& src) : m_src(src) { }
+
+ /** \brief Compute the matrix square root.
+ *
+ * \param[out] result the matrix square root of \p src in the
+ * constructor.
+ */
+ template <typename ResultType>
+ inline void evalTo(ResultType& result) const
+ {
+ typedef typename internal::nested_eval<Derived, 10>::type DerivedEvalType;
+ typedef internal::remove_all_t<DerivedEvalType> DerivedEvalTypeClean;
+ DerivedEvalType tmp(m_src);
+ internal::matrix_sqrt_compute<DerivedEvalTypeClean>::run(tmp, result);
+ }
+
+ Index rows() const { return m_src.rows(); }
+ Index cols() const { return m_src.cols(); }
+
+ protected:
+ const DerivedNested m_src;
+};
+
+namespace internal {
+template<typename Derived>
+struct traits<MatrixSquareRootReturnValue<Derived> >
+{
+ typedef typename Derived::PlainObject ReturnType;
+};
+}
+
+template <typename Derived>
+const MatrixSquareRootReturnValue<Derived> MatrixBase<Derived>::sqrt() const
+{
+ eigen_assert(rows() == cols());
+ return MatrixSquareRootReturnValue<Derived>(derived());
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_MATRIX_FUNCTION
diff --git a/unsupported/Eigen/src/MatrixFunctions/StemFunction.h b/unsupported/Eigen/src/MatrixFunctions/StemFunction.h
new file mode 100644
index 0000000..25a3ef2
--- /dev/null
+++ b/unsupported/Eigen/src/MatrixFunctions/StemFunction.h
@@ -0,0 +1,119 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2010, 2013 Jitse Niesen <jitse@maths.leeds.ac.uk>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_STEM_FUNCTION
+#define EIGEN_STEM_FUNCTION
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+
+/** \brief The exponential function (and its derivatives). */
+template <typename Scalar>
+Scalar stem_function_exp(Scalar x, int)
+{
+ using std::exp;
+ return exp(x);
+}
+
+/** \brief Cosine (and its derivatives). */
+template <typename Scalar>
+Scalar stem_function_cos(Scalar x, int n)
+{
+ using std::cos;
+ using std::sin;
+ Scalar res;
+
+ switch (n % 4) {
+ case 0:
+ res = std::cos(x);
+ break;
+ case 1:
+ res = -std::sin(x);
+ break;
+ case 2:
+ res = -std::cos(x);
+ break;
+ case 3:
+ res = std::sin(x);
+ break;
+ }
+ return res;
+}
+
+/** \brief Sine (and its derivatives). */
+template <typename Scalar>
+Scalar stem_function_sin(Scalar x, int n)
+{
+ using std::cos;
+ using std::sin;
+ Scalar res;
+
+ switch (n % 4) {
+ case 0:
+ res = std::sin(x);
+ break;
+ case 1:
+ res = std::cos(x);
+ break;
+ case 2:
+ res = -std::sin(x);
+ break;
+ case 3:
+ res = -std::cos(x);
+ break;
+ }
+ return res;
+}
+
+/** \brief Hyperbolic cosine (and its derivatives). */
+template <typename Scalar>
+Scalar stem_function_cosh(Scalar x, int n)
+{
+ using std::cosh;
+ using std::sinh;
+ Scalar res;
+
+ switch (n % 2) {
+ case 0:
+ res = std::cosh(x);
+ break;
+ case 1:
+ res = std::sinh(x);
+ break;
+ }
+ return res;
+}
+
+/** \brief Hyperbolic sine (and its derivatives). */
+template <typename Scalar>
+Scalar stem_function_sinh(Scalar x, int n)
+{
+ using std::cosh;
+ using std::sinh;
+ Scalar res;
+
+ switch (n % 2) {
+ case 0:
+ res = std::sinh(x);
+ break;
+ case 1:
+ res = std::cosh(x);
+ break;
+ }
+ return res;
+}
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_STEM_FUNCTION
diff --git a/unsupported/Eigen/src/MoreVectorization/InternalHeaderCheck.h b/unsupported/Eigen/src/MoreVectorization/InternalHeaderCheck.h
new file mode 100644
index 0000000..3c294b3
--- /dev/null
+++ b/unsupported/Eigen/src/MoreVectorization/InternalHeaderCheck.h
@@ -0,0 +1,3 @@
+#ifndef EIGEN_MOREVECTORIZATION_MODULE_H
+#error "Please include unsupported/Eigen/MoreVectorization instead of including headers inside the src directory directly."
+#endif
diff --git a/unsupported/Eigen/src/MoreVectorization/MathFunctions.h b/unsupported/Eigen/src/MoreVectorization/MathFunctions.h
new file mode 100644
index 0000000..9084298
--- /dev/null
+++ b/unsupported/Eigen/src/MoreVectorization/MathFunctions.h
@@ -0,0 +1,97 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009 Rohit Garg <rpg.314@gmail.com>
+// Copyright (C) 2009 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_MOREVECTORIZATION_MATHFUNCTIONS_H
+#define EIGEN_MOREVECTORIZATION_MATHFUNCTIONS_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+
+/** \internal \returns the arcsin of \a a (coeff-wise) */
+template<typename Packet> inline static Packet pasin(Packet a) { return std::asin(a); }
+
+#ifdef EIGEN_VECTORIZE_SSE
+
+template<> EIGEN_DONT_INLINE Packet4f pasin(Packet4f x)
+{
+ EIGEN_DECLARE_CONST_Packet4f(half, 0.5);
+ EIGEN_DECLARE_CONST_Packet4f(minus_half, -0.5);
+ EIGEN_DECLARE_CONST_Packet4f(3half, 1.5);
+
+ EIGEN_DECLARE_CONST_Packet4f_FROM_INT(sign_mask, 0x80000000);
+
+ EIGEN_DECLARE_CONST_Packet4f(pi, 3.141592654);
+ EIGEN_DECLARE_CONST_Packet4f(pi_over_2, 3.141592654*0.5);
+
+ EIGEN_DECLARE_CONST_Packet4f(asin1, 4.2163199048E-2);
+ EIGEN_DECLARE_CONST_Packet4f(asin2, 2.4181311049E-2);
+ EIGEN_DECLARE_CONST_Packet4f(asin3, 4.5470025998E-2);
+ EIGEN_DECLARE_CONST_Packet4f(asin4, 7.4953002686E-2);
+ EIGEN_DECLARE_CONST_Packet4f(asin5, 1.6666752422E-1);
+
+ Packet4f a = pabs(x);//got the absolute value
+
+ Packet4f sign_bit= _mm_and_ps(x, p4f_sign_mask);//extracted the sign bit
+
+ Packet4f z1,z2;//will need them during computation
+
+
+//will compute the two branches for asin
+//so first compare with half
+
+ Packet4f branch_mask= _mm_cmpgt_ps(a, p4f_half);//this is to select which branch to take
+//both will be taken, and finally results will be merged
+//the branch for values >0.5
+
+ {
+//the core series expansion
+ z1=pmadd(p4f_minus_half,a,p4f_half);
+ Packet4f x1=psqrt(z1);
+ Packet4f s1=pmadd(p4f_asin1, z1, p4f_asin2);
+ Packet4f s2=pmadd(s1, z1, p4f_asin3);
+ Packet4f s3=pmadd(s2,z1, p4f_asin4);
+ Packet4f s4=pmadd(s3,z1, p4f_asin5);
+ Packet4f temp=pmul(s4,z1);//not really a madd but a mul by z so that the next term can be a madd
+ z1=pmadd(temp,x1,x1);
+ z1=padd(z1,z1);
+ z1=psub(p4f_pi_over_2,z1);
+ }
+
+ {
+//the core series expansion
+ Packet4f x2=a;
+ z2=pmul(x2,x2);
+ Packet4f s1=pmadd(p4f_asin1, z2, p4f_asin2);
+ Packet4f s2=pmadd(s1, z2, p4f_asin3);
+ Packet4f s3=pmadd(s2,z2, p4f_asin4);
+ Packet4f s4=pmadd(s3,z2, p4f_asin5);
+ Packet4f temp=pmul(s4,z2);//not really a madd but a mul by z so that the next term can be a madd
+ z2=pmadd(temp,x2,x2);
+ }
+
+/* select the correct result from the two branch evaluations */
+ z1 = _mm_and_ps(branch_mask, z1);
+ z2 = _mm_andnot_ps(branch_mask, z2);
+ Packet4f z = _mm_or_ps(z1,z2);
+
+/* update the sign */
+ return _mm_xor_ps(z, sign_bit);
+}
+
+#endif // EIGEN_VECTORIZE_SSE
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_MOREVECTORIZATION_MATHFUNCTIONS_H
diff --git a/unsupported/Eigen/src/NonLinearOptimization/HybridNonLinearSolver.h b/unsupported/Eigen/src/NonLinearOptimization/HybridNonLinearSolver.h
new file mode 100644
index 0000000..4c38426
--- /dev/null
+++ b/unsupported/Eigen/src/NonLinearOptimization/HybridNonLinearSolver.h
@@ -0,0 +1,603 @@
+// -*- coding: utf-8
+// vim: set fileencoding=utf-8
+
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009 Thomas Capricelli <orzel@freehackers.org>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_HYBRIDNONLINEARSOLVER_H
+#define EIGEN_HYBRIDNONLINEARSOLVER_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace HybridNonLinearSolverSpace {
+ enum Status {
+ Running = -1,
+ ImproperInputParameters = 0,
+ RelativeErrorTooSmall = 1,
+ TooManyFunctionEvaluation = 2,
+ TolTooSmall = 3,
+ NotMakingProgressJacobian = 4,
+ NotMakingProgressIterations = 5,
+ UserAsked = 6
+ };
+}
+
+/**
+ * \ingroup NonLinearOptimization_Module
+ * \brief Finds a zero of a system of n
+ * nonlinear functions in n variables by a modification of the Powell
+ * hybrid method ("dogleg").
+ *
+ * The user must provide a subroutine which calculates the
+ * functions. The Jacobian is either provided by the user, or approximated
+ * using a forward-difference method.
+ *
+ */
+template<typename FunctorType, typename Scalar=double>
+class HybridNonLinearSolver
+{
+public:
+ typedef DenseIndex Index;
+
+ HybridNonLinearSolver(FunctorType &_functor)
+ : functor(_functor) { nfev=njev=iter = 0; fnorm= 0.; useExternalScaling=false;}
+
+ struct Parameters {
+ Parameters()
+ : factor(Scalar(100.))
+ , maxfev(1000)
+ , xtol(numext::sqrt(NumTraits<Scalar>::epsilon()))
+ , nb_of_subdiagonals(-1)
+ , nb_of_superdiagonals(-1)
+ , epsfcn(Scalar(0.)) {}
+ Scalar factor;
+ Index maxfev; // maximum number of function evaluation
+ Scalar xtol;
+ Index nb_of_subdiagonals;
+ Index nb_of_superdiagonals;
+ Scalar epsfcn;
+ };
+ typedef Matrix< Scalar, Dynamic, 1 > FVectorType;
+ typedef Matrix< Scalar, Dynamic, Dynamic > JacobianType;
+ /* TODO: if eigen provides a triangular storage, use it here */
+ typedef Matrix< Scalar, Dynamic, Dynamic > UpperTriangularType;
+
+ HybridNonLinearSolverSpace::Status hybrj1(
+ FVectorType &x,
+ const Scalar tol = numext::sqrt(NumTraits<Scalar>::epsilon())
+ );
+
+ HybridNonLinearSolverSpace::Status solveInit(FVectorType &x);
+ HybridNonLinearSolverSpace::Status solveOneStep(FVectorType &x);
+ HybridNonLinearSolverSpace::Status solve(FVectorType &x);
+
+ HybridNonLinearSolverSpace::Status hybrd1(
+ FVectorType &x,
+ const Scalar tol = numext::sqrt(NumTraits<Scalar>::epsilon())
+ );
+
+ HybridNonLinearSolverSpace::Status solveNumericalDiffInit(FVectorType &x);
+ HybridNonLinearSolverSpace::Status solveNumericalDiffOneStep(FVectorType &x);
+ HybridNonLinearSolverSpace::Status solveNumericalDiff(FVectorType &x);
+
+ void resetParameters(void) { parameters = Parameters(); }
+ Parameters parameters;
+ FVectorType fvec, qtf, diag;
+ JacobianType fjac;
+ UpperTriangularType R;
+ Index nfev;
+ Index njev;
+ Index iter;
+ Scalar fnorm;
+ bool useExternalScaling;
+private:
+ FunctorType &functor;
+ Index n;
+ Scalar sum;
+ bool sing;
+ Scalar temp;
+ Scalar delta;
+ bool jeval;
+ Index ncsuc;
+ Scalar ratio;
+ Scalar pnorm, xnorm, fnorm1;
+ Index nslow1, nslow2;
+ Index ncfail;
+ Scalar actred, prered;
+ FVectorType wa1, wa2, wa3, wa4;
+
+ HybridNonLinearSolver& operator=(const HybridNonLinearSolver&);
+};
+
+
+
+template<typename FunctorType, typename Scalar>
+HybridNonLinearSolverSpace::Status
+HybridNonLinearSolver<FunctorType,Scalar>::hybrj1(
+ FVectorType &x,
+ const Scalar tol
+ )
+{
+ n = x.size();
+
+ /* check the input parameters for errors. */
+ if (n <= 0 || tol < 0.)
+ return HybridNonLinearSolverSpace::ImproperInputParameters;
+
+ resetParameters();
+ parameters.maxfev = 100*(n+1);
+ parameters.xtol = tol;
+ diag.setConstant(n, 1.);
+ useExternalScaling = true;
+ return solve(x);
+}
+
+template<typename FunctorType, typename Scalar>
+HybridNonLinearSolverSpace::Status
+HybridNonLinearSolver<FunctorType,Scalar>::solveInit(FVectorType &x)
+{
+ n = x.size();
+
+ wa1.resize(n); wa2.resize(n); wa3.resize(n); wa4.resize(n);
+ fvec.resize(n);
+ qtf.resize(n);
+ fjac.resize(n, n);
+ if (!useExternalScaling)
+ diag.resize(n);
+ eigen_assert( (!useExternalScaling || diag.size()==n) && "When useExternalScaling is set, the caller must provide a valid 'diag'");
+
+ /* Function Body */
+ nfev = 0;
+ njev = 0;
+
+ /* check the input parameters for errors. */
+ if (n <= 0 || parameters.xtol < 0. || parameters.maxfev <= 0 || parameters.factor <= 0. )
+ return HybridNonLinearSolverSpace::ImproperInputParameters;
+ if (useExternalScaling)
+ for (Index j = 0; j < n; ++j)
+ if (diag[j] <= 0.)
+ return HybridNonLinearSolverSpace::ImproperInputParameters;
+
+ /* evaluate the function at the starting point */
+ /* and calculate its norm. */
+ nfev = 1;
+ if ( functor(x, fvec) < 0)
+ return HybridNonLinearSolverSpace::UserAsked;
+ fnorm = fvec.stableNorm();
+
+ /* initialize iteration counter and monitors. */
+ iter = 1;
+ ncsuc = 0;
+ ncfail = 0;
+ nslow1 = 0;
+ nslow2 = 0;
+
+ return HybridNonLinearSolverSpace::Running;
+}
+
+template<typename FunctorType, typename Scalar>
+HybridNonLinearSolverSpace::Status
+HybridNonLinearSolver<FunctorType,Scalar>::solveOneStep(FVectorType &x)
+{
+ using std::abs;
+
+ eigen_assert(x.size()==n); // check the caller is not cheating us
+
+ Index j;
+ std::vector<JacobiRotation<Scalar> > v_givens(n), w_givens(n);
+
+ jeval = true;
+
+ /* calculate the jacobian matrix. */
+ if ( functor.df(x, fjac) < 0)
+ return HybridNonLinearSolverSpace::UserAsked;
+ ++njev;
+
+ wa2 = fjac.colwise().blueNorm();
+
+ /* on the first iteration and if external scaling is not used, scale according */
+ /* to the norms of the columns of the initial jacobian. */
+ if (iter == 1) {
+ if (!useExternalScaling)
+ for (j = 0; j < n; ++j)
+ diag[j] = (wa2[j]==0.) ? 1. : wa2[j];
+
+ /* on the first iteration, calculate the norm of the scaled x */
+ /* and initialize the step bound delta. */
+ xnorm = diag.cwiseProduct(x).stableNorm();
+ delta = parameters.factor * xnorm;
+ if (delta == 0.)
+ delta = parameters.factor;
+ }
+
+ /* compute the qr factorization of the jacobian. */
+ HouseholderQR<JacobianType> qrfac(fjac); // no pivoting:
+
+ /* copy the triangular factor of the qr factorization into r. */
+ R = qrfac.matrixQR();
+
+ /* accumulate the orthogonal factor in fjac. */
+ fjac = qrfac.householderQ();
+
+ /* form (q transpose)*fvec and store in qtf. */
+ qtf = fjac.transpose() * fvec;
+
+ /* rescale if necessary. */
+ if (!useExternalScaling)
+ diag = diag.cwiseMax(wa2);
+
+ while (true) {
+ /* determine the direction p. */
+ internal::dogleg<Scalar>(R, diag, qtf, delta, wa1);
+
+ /* store the direction p and x + p. calculate the norm of p. */
+ wa1 = -wa1;
+ wa2 = x + wa1;
+ pnorm = diag.cwiseProduct(wa1).stableNorm();
+
+ /* on the first iteration, adjust the initial step bound. */
+ if (iter == 1)
+ delta = (std::min)(delta,pnorm);
+
+ /* evaluate the function at x + p and calculate its norm. */
+ if ( functor(wa2, wa4) < 0)
+ return HybridNonLinearSolverSpace::UserAsked;
+ ++nfev;
+ fnorm1 = wa4.stableNorm();
+
+ /* compute the scaled actual reduction. */
+ actred = -1.;
+ if (fnorm1 < fnorm) /* Computing 2nd power */
+ actred = 1. - numext::abs2(fnorm1 / fnorm);
+
+ /* compute the scaled predicted reduction. */
+ wa3 = R.template triangularView<Upper>()*wa1 + qtf;
+ temp = wa3.stableNorm();
+ prered = 0.;
+ if (temp < fnorm) /* Computing 2nd power */
+ prered = 1. - numext::abs2(temp / fnorm);
+
+ /* compute the ratio of the actual to the predicted reduction. */
+ ratio = 0.;
+ if (prered > 0.)
+ ratio = actred / prered;
+
+ /* update the step bound. */
+ if (ratio < Scalar(.1)) {
+ ncsuc = 0;
+ ++ncfail;
+ delta = Scalar(.5) * delta;
+ } else {
+ ncfail = 0;
+ ++ncsuc;
+ if (ratio >= Scalar(.5) || ncsuc > 1)
+ delta = (std::max)(delta, pnorm / Scalar(.5));
+ if (abs(ratio - 1.) <= Scalar(.1)) {
+ delta = pnorm / Scalar(.5);
+ }
+ }
+
+ /* test for successful iteration. */
+ if (ratio >= Scalar(1e-4)) {
+ /* successful iteration. update x, fvec, and their norms. */
+ x = wa2;
+ wa2 = diag.cwiseProduct(x);
+ fvec = wa4;
+ xnorm = wa2.stableNorm();
+ fnorm = fnorm1;
+ ++iter;
+ }
+
+ /* determine the progress of the iteration. */
+ ++nslow1;
+ if (actred >= Scalar(.001))
+ nslow1 = 0;
+ if (jeval)
+ ++nslow2;
+ if (actred >= Scalar(.1))
+ nslow2 = 0;
+
+ /* test for convergence. */
+ if (delta <= parameters.xtol * xnorm || fnorm == 0.)
+ return HybridNonLinearSolverSpace::RelativeErrorTooSmall;
+
+ /* tests for termination and stringent tolerances. */
+ if (nfev >= parameters.maxfev)
+ return HybridNonLinearSolverSpace::TooManyFunctionEvaluation;
+ if (Scalar(.1) * (std::max)(Scalar(.1) * delta, pnorm) <= NumTraits<Scalar>::epsilon() * xnorm)
+ return HybridNonLinearSolverSpace::TolTooSmall;
+ if (nslow2 == 5)
+ return HybridNonLinearSolverSpace::NotMakingProgressJacobian;
+ if (nslow1 == 10)
+ return HybridNonLinearSolverSpace::NotMakingProgressIterations;
+
+ /* criterion for recalculating jacobian. */
+ if (ncfail == 2)
+ break; // leave inner loop and go for the next outer loop iteration
+
+ /* calculate the rank one modification to the jacobian */
+ /* and update qtf if necessary. */
+ wa1 = diag.cwiseProduct( diag.cwiseProduct(wa1)/pnorm );
+ wa2 = fjac.transpose() * wa4;
+ if (ratio >= Scalar(1e-4))
+ qtf = wa2;
+ wa2 = (wa2-wa3)/pnorm;
+
+ /* compute the qr factorization of the updated jacobian. */
+ internal::r1updt<Scalar>(R, wa1, v_givens, w_givens, wa2, wa3, &sing);
+ internal::r1mpyq<Scalar>(n, n, fjac.data(), v_givens, w_givens);
+ internal::r1mpyq<Scalar>(1, n, qtf.data(), v_givens, w_givens);
+
+ jeval = false;
+ }
+ return HybridNonLinearSolverSpace::Running;
+}
+
+template<typename FunctorType, typename Scalar>
+HybridNonLinearSolverSpace::Status
+HybridNonLinearSolver<FunctorType,Scalar>::solve(FVectorType &x)
+{
+ HybridNonLinearSolverSpace::Status status = solveInit(x);
+ if (status==HybridNonLinearSolverSpace::ImproperInputParameters)
+ return status;
+ while (status==HybridNonLinearSolverSpace::Running)
+ status = solveOneStep(x);
+ return status;
+}
+
+
+
+template<typename FunctorType, typename Scalar>
+HybridNonLinearSolverSpace::Status
+HybridNonLinearSolver<FunctorType,Scalar>::hybrd1(
+ FVectorType &x,
+ const Scalar tol
+ )
+{
+ n = x.size();
+
+ /* check the input parameters for errors. */
+ if (n <= 0 || tol < 0.)
+ return HybridNonLinearSolverSpace::ImproperInputParameters;
+
+ resetParameters();
+ parameters.maxfev = 200*(n+1);
+ parameters.xtol = tol;
+
+ diag.setConstant(n, 1.);
+ useExternalScaling = true;
+ return solveNumericalDiff(x);
+}
+
+template<typename FunctorType, typename Scalar>
+HybridNonLinearSolverSpace::Status
+HybridNonLinearSolver<FunctorType,Scalar>::solveNumericalDiffInit(FVectorType &x)
+{
+ n = x.size();
+
+ if (parameters.nb_of_subdiagonals<0) parameters.nb_of_subdiagonals= n-1;
+ if (parameters.nb_of_superdiagonals<0) parameters.nb_of_superdiagonals= n-1;
+
+ wa1.resize(n); wa2.resize(n); wa3.resize(n); wa4.resize(n);
+ qtf.resize(n);
+ fjac.resize(n, n);
+ fvec.resize(n);
+ if (!useExternalScaling)
+ diag.resize(n);
+ eigen_assert( (!useExternalScaling || diag.size()==n) && "When useExternalScaling is set, the caller must provide a valid 'diag'");
+
+ /* Function Body */
+ nfev = 0;
+ njev = 0;
+
+ /* check the input parameters for errors. */
+ if (n <= 0 || parameters.xtol < 0. || parameters.maxfev <= 0 || parameters.nb_of_subdiagonals< 0 || parameters.nb_of_superdiagonals< 0 || parameters.factor <= 0. )
+ return HybridNonLinearSolverSpace::ImproperInputParameters;
+ if (useExternalScaling)
+ for (Index j = 0; j < n; ++j)
+ if (diag[j] <= 0.)
+ return HybridNonLinearSolverSpace::ImproperInputParameters;
+
+ /* evaluate the function at the starting point */
+ /* and calculate its norm. */
+ nfev = 1;
+ if ( functor(x, fvec) < 0)
+ return HybridNonLinearSolverSpace::UserAsked;
+ fnorm = fvec.stableNorm();
+
+ /* initialize iteration counter and monitors. */
+ iter = 1;
+ ncsuc = 0;
+ ncfail = 0;
+ nslow1 = 0;
+ nslow2 = 0;
+
+ return HybridNonLinearSolverSpace::Running;
+}
+
+template<typename FunctorType, typename Scalar>
+HybridNonLinearSolverSpace::Status
+HybridNonLinearSolver<FunctorType,Scalar>::solveNumericalDiffOneStep(FVectorType &x)
+{
+ using std::sqrt;
+ using std::abs;
+
+ eigen_assert(x.size()==n); // check the caller is not cheating us
+
+ Index j;
+ std::vector<JacobiRotation<Scalar> > v_givens(n), w_givens(n);
+
+ jeval = true;
+ if (parameters.nb_of_subdiagonals<0) parameters.nb_of_subdiagonals= n-1;
+ if (parameters.nb_of_superdiagonals<0) parameters.nb_of_superdiagonals= n-1;
+
+ /* calculate the jacobian matrix. */
+ if (internal::fdjac1(functor, x, fvec, fjac, parameters.nb_of_subdiagonals, parameters.nb_of_superdiagonals, parameters.epsfcn) <0)
+ return HybridNonLinearSolverSpace::UserAsked;
+ nfev += (std::min)(parameters.nb_of_subdiagonals+parameters.nb_of_superdiagonals+ 1, n);
+
+ wa2 = fjac.colwise().blueNorm();
+
+ /* on the first iteration and if external scaling is not used, scale according */
+ /* to the norms of the columns of the initial jacobian. */
+ if (iter == 1) {
+ if (!useExternalScaling)
+ for (j = 0; j < n; ++j)
+ diag[j] = (wa2[j]==0.) ? 1. : wa2[j];
+
+ /* on the first iteration, calculate the norm of the scaled x */
+ /* and initialize the step bound delta. */
+ xnorm = diag.cwiseProduct(x).stableNorm();
+ delta = parameters.factor * xnorm;
+ if (delta == 0.)
+ delta = parameters.factor;
+ }
+
+ /* compute the qr factorization of the jacobian. */
+ HouseholderQR<JacobianType> qrfac(fjac); // no pivoting:
+
+ /* copy the triangular factor of the qr factorization into r. */
+ R = qrfac.matrixQR();
+
+ /* accumulate the orthogonal factor in fjac. */
+ fjac = qrfac.householderQ();
+
+ /* form (q transpose)*fvec and store in qtf. */
+ qtf = fjac.transpose() * fvec;
+
+ /* rescale if necessary. */
+ if (!useExternalScaling)
+ diag = diag.cwiseMax(wa2);
+
+ while (true) {
+ /* determine the direction p. */
+ internal::dogleg<Scalar>(R, diag, qtf, delta, wa1);
+
+ /* store the direction p and x + p. calculate the norm of p. */
+ wa1 = -wa1;
+ wa2 = x + wa1;
+ pnorm = diag.cwiseProduct(wa1).stableNorm();
+
+ /* on the first iteration, adjust the initial step bound. */
+ if (iter == 1)
+ delta = (std::min)(delta,pnorm);
+
+ /* evaluate the function at x + p and calculate its norm. */
+ if ( functor(wa2, wa4) < 0)
+ return HybridNonLinearSolverSpace::UserAsked;
+ ++nfev;
+ fnorm1 = wa4.stableNorm();
+
+ /* compute the scaled actual reduction. */
+ actred = -1.;
+ if (fnorm1 < fnorm) /* Computing 2nd power */
+ actred = 1. - numext::abs2(fnorm1 / fnorm);
+
+ /* compute the scaled predicted reduction. */
+ wa3 = R.template triangularView<Upper>()*wa1 + qtf;
+ temp = wa3.stableNorm();
+ prered = 0.;
+ if (temp < fnorm) /* Computing 2nd power */
+ prered = 1. - numext::abs2(temp / fnorm);
+
+ /* compute the ratio of the actual to the predicted reduction. */
+ ratio = 0.;
+ if (prered > 0.)
+ ratio = actred / prered;
+
+ /* update the step bound. */
+ if (ratio < Scalar(.1)) {
+ ncsuc = 0;
+ ++ncfail;
+ delta = Scalar(.5) * delta;
+ } else {
+ ncfail = 0;
+ ++ncsuc;
+ if (ratio >= Scalar(.5) || ncsuc > 1)
+ delta = (std::max)(delta, pnorm / Scalar(.5));
+ if (abs(ratio - 1.) <= Scalar(.1)) {
+ delta = pnorm / Scalar(.5);
+ }
+ }
+
+ /* test for successful iteration. */
+ if (ratio >= Scalar(1e-4)) {
+ /* successful iteration. update x, fvec, and their norms. */
+ x = wa2;
+ wa2 = diag.cwiseProduct(x);
+ fvec = wa4;
+ xnorm = wa2.stableNorm();
+ fnorm = fnorm1;
+ ++iter;
+ }
+
+ /* determine the progress of the iteration. */
+ ++nslow1;
+ if (actred >= Scalar(.001))
+ nslow1 = 0;
+ if (jeval)
+ ++nslow2;
+ if (actred >= Scalar(.1))
+ nslow2 = 0;
+
+ /* test for convergence. */
+ if (delta <= parameters.xtol * xnorm || fnorm == 0.)
+ return HybridNonLinearSolverSpace::RelativeErrorTooSmall;
+
+ /* tests for termination and stringent tolerances. */
+ if (nfev >= parameters.maxfev)
+ return HybridNonLinearSolverSpace::TooManyFunctionEvaluation;
+ if (Scalar(.1) * (std::max)(Scalar(.1) * delta, pnorm) <= NumTraits<Scalar>::epsilon() * xnorm)
+ return HybridNonLinearSolverSpace::TolTooSmall;
+ if (nslow2 == 5)
+ return HybridNonLinearSolverSpace::NotMakingProgressJacobian;
+ if (nslow1 == 10)
+ return HybridNonLinearSolverSpace::NotMakingProgressIterations;
+
+ /* criterion for recalculating jacobian. */
+ if (ncfail == 2)
+ break; // leave inner loop and go for the next outer loop iteration
+
+ /* calculate the rank one modification to the jacobian */
+ /* and update qtf if necessary. */
+ wa1 = diag.cwiseProduct( diag.cwiseProduct(wa1)/pnorm );
+ wa2 = fjac.transpose() * wa4;
+ if (ratio >= Scalar(1e-4))
+ qtf = wa2;
+ wa2 = (wa2-wa3)/pnorm;
+
+ /* compute the qr factorization of the updated jacobian. */
+ internal::r1updt<Scalar>(R, wa1, v_givens, w_givens, wa2, wa3, &sing);
+ internal::r1mpyq<Scalar>(n, n, fjac.data(), v_givens, w_givens);
+ internal::r1mpyq<Scalar>(1, n, qtf.data(), v_givens, w_givens);
+
+ jeval = false;
+ }
+ return HybridNonLinearSolverSpace::Running;
+}
+
+template<typename FunctorType, typename Scalar>
+HybridNonLinearSolverSpace::Status
+HybridNonLinearSolver<FunctorType,Scalar>::solveNumericalDiff(FVectorType &x)
+{
+ HybridNonLinearSolverSpace::Status status = solveNumericalDiffInit(x);
+ if (status==HybridNonLinearSolverSpace::ImproperInputParameters)
+ return status;
+ while (status==HybridNonLinearSolverSpace::Running)
+ status = solveNumericalDiffOneStep(x);
+ return status;
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_HYBRIDNONLINEARSOLVER_H
+
+//vim: ai ts=4 sts=4 et sw=4
diff --git a/unsupported/Eigen/src/NonLinearOptimization/InternalHeaderCheck.h b/unsupported/Eigen/src/NonLinearOptimization/InternalHeaderCheck.h
new file mode 100644
index 0000000..5b2276c
--- /dev/null
+++ b/unsupported/Eigen/src/NonLinearOptimization/InternalHeaderCheck.h
@@ -0,0 +1,3 @@
+#ifndef EIGEN_NONLINEAROPTIMIZATION_MODULE_H
+#error "Please include unsupported/Eigen/NonLinearOptimization instead of including headers inside the src directory directly."
+#endif
diff --git a/unsupported/Eigen/src/NonLinearOptimization/LevenbergMarquardt.h b/unsupported/Eigen/src/NonLinearOptimization/LevenbergMarquardt.h
new file mode 100644
index 0000000..a176c25
--- /dev/null
+++ b/unsupported/Eigen/src/NonLinearOptimization/LevenbergMarquardt.h
@@ -0,0 +1,659 @@
+// -*- coding: utf-8
+// vim: set fileencoding=utf-8
+
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009 Thomas Capricelli <orzel@freehackers.org>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_LEVENBERGMARQUARDT__H
+#define EIGEN_LEVENBERGMARQUARDT__H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace LevenbergMarquardtSpace {
+ enum Status {
+ NotStarted = -2,
+ Running = -1,
+ ImproperInputParameters = 0,
+ RelativeReductionTooSmall = 1,
+ RelativeErrorTooSmall = 2,
+ RelativeErrorAndReductionTooSmall = 3,
+ CosinusTooSmall = 4,
+ TooManyFunctionEvaluation = 5,
+ FtolTooSmall = 6,
+ XtolTooSmall = 7,
+ GtolTooSmall = 8,
+ UserAsked = 9
+ };
+}
+
+
+
+/**
+ * \ingroup NonLinearOptimization_Module
+ * \brief Performs non linear optimization over a non-linear function,
+ * using a variant of the Levenberg Marquardt algorithm.
+ *
+ * Check wikipedia for more information.
+ * http://en.wikipedia.org/wiki/Levenberg%E2%80%93Marquardt_algorithm
+ */
+template<typename FunctorType, typename Scalar=double>
+class LevenbergMarquardt
+{
+ static Scalar sqrt_epsilon()
+ {
+ using std::sqrt;
+ return sqrt(NumTraits<Scalar>::epsilon());
+ }
+
+public:
+ LevenbergMarquardt(FunctorType &_functor)
+ : functor(_functor) { nfev = njev = iter = 0; fnorm = gnorm = 0.; useExternalScaling=false; }
+
+ typedef DenseIndex Index;
+
+ struct Parameters {
+ Parameters()
+ : factor(Scalar(100.))
+ , maxfev(400)
+ , ftol(sqrt_epsilon())
+ , xtol(sqrt_epsilon())
+ , gtol(Scalar(0.))
+ , epsfcn(Scalar(0.)) {}
+ Scalar factor;
+ Index maxfev; // maximum number of function evaluation
+ Scalar ftol;
+ Scalar xtol;
+ Scalar gtol;
+ Scalar epsfcn;
+ };
+
+ typedef Matrix< Scalar, Dynamic, 1 > FVectorType;
+ typedef Matrix< Scalar, Dynamic, Dynamic > JacobianType;
+
+ LevenbergMarquardtSpace::Status lmder1(
+ FVectorType &x,
+ const Scalar tol = sqrt_epsilon()
+ );
+
+ LevenbergMarquardtSpace::Status minimize(FVectorType &x);
+ LevenbergMarquardtSpace::Status minimizeInit(FVectorType &x);
+ LevenbergMarquardtSpace::Status minimizeOneStep(FVectorType &x);
+
+ static LevenbergMarquardtSpace::Status lmdif1(
+ FunctorType &functor,
+ FVectorType &x,
+ Index *nfev,
+ const Scalar tol = sqrt_epsilon()
+ );
+
+ LevenbergMarquardtSpace::Status lmstr1(
+ FVectorType &x,
+ const Scalar tol = sqrt_epsilon()
+ );
+
+ LevenbergMarquardtSpace::Status minimizeOptimumStorage(FVectorType &x);
+ LevenbergMarquardtSpace::Status minimizeOptimumStorageInit(FVectorType &x);
+ LevenbergMarquardtSpace::Status minimizeOptimumStorageOneStep(FVectorType &x);
+
+ void resetParameters(void) { parameters = Parameters(); }
+
+ Parameters parameters;
+ FVectorType fvec, qtf, diag;
+ JacobianType fjac;
+ PermutationMatrix<Dynamic,Dynamic> permutation;
+ Index nfev;
+ Index njev;
+ Index iter;
+ Scalar fnorm, gnorm;
+ bool useExternalScaling;
+
+ Scalar lm_param(void) { return par; }
+private:
+
+ FunctorType &functor;
+ Index n;
+ Index m;
+ FVectorType wa1, wa2, wa3, wa4;
+
+ Scalar par, sum;
+ Scalar temp, temp1, temp2;
+ Scalar delta;
+ Scalar ratio;
+ Scalar pnorm, xnorm, fnorm1, actred, dirder, prered;
+
+ LevenbergMarquardt& operator=(const LevenbergMarquardt&);
+};
+
+template<typename FunctorType, typename Scalar>
+LevenbergMarquardtSpace::Status
+LevenbergMarquardt<FunctorType,Scalar>::lmder1(
+ FVectorType &x,
+ const Scalar tol
+ )
+{
+ n = x.size();
+ m = functor.values();
+
+ /* check the input parameters for errors. */
+ if (n <= 0 || m < n || tol < 0.)
+ return LevenbergMarquardtSpace::ImproperInputParameters;
+
+ resetParameters();
+ parameters.ftol = tol;
+ parameters.xtol = tol;
+ parameters.maxfev = 100*(n+1);
+
+ return minimize(x);
+}
+
+
+template<typename FunctorType, typename Scalar>
+LevenbergMarquardtSpace::Status
+LevenbergMarquardt<FunctorType,Scalar>::minimize(FVectorType &x)
+{
+ LevenbergMarquardtSpace::Status status = minimizeInit(x);
+ if (status==LevenbergMarquardtSpace::ImproperInputParameters)
+ return status;
+ do {
+ status = minimizeOneStep(x);
+ } while (status==LevenbergMarquardtSpace::Running);
+ return status;
+}
+
+template<typename FunctorType, typename Scalar>
+LevenbergMarquardtSpace::Status
+LevenbergMarquardt<FunctorType,Scalar>::minimizeInit(FVectorType &x)
+{
+ n = x.size();
+ m = functor.values();
+
+ wa1.resize(n); wa2.resize(n); wa3.resize(n);
+ wa4.resize(m);
+ fvec.resize(m);
+ fjac.resize(m, n);
+ if (!useExternalScaling)
+ diag.resize(n);
+ eigen_assert( (!useExternalScaling || diag.size()==n) && "When useExternalScaling is set, the caller must provide a valid 'diag'");
+ qtf.resize(n);
+
+ /* Function Body */
+ nfev = 0;
+ njev = 0;
+
+ /* check the input parameters for errors. */
+ if (n <= 0 || m < n || parameters.ftol < 0. || parameters.xtol < 0. || parameters.gtol < 0. || parameters.maxfev <= 0 || parameters.factor <= 0.)
+ return LevenbergMarquardtSpace::ImproperInputParameters;
+
+ if (useExternalScaling)
+ for (Index j = 0; j < n; ++j)
+ if (diag[j] <= 0.)
+ return LevenbergMarquardtSpace::ImproperInputParameters;
+
+ /* evaluate the function at the starting point */
+ /* and calculate its norm. */
+ nfev = 1;
+ if ( functor(x, fvec) < 0)
+ return LevenbergMarquardtSpace::UserAsked;
+ fnorm = fvec.stableNorm();
+
+ /* initialize levenberg-marquardt parameter and iteration counter. */
+ par = 0.;
+ iter = 1;
+
+ return LevenbergMarquardtSpace::NotStarted;
+}
+
+template<typename FunctorType, typename Scalar>
+LevenbergMarquardtSpace::Status
+LevenbergMarquardt<FunctorType,Scalar>::minimizeOneStep(FVectorType &x)
+{
+ using std::abs;
+ using std::sqrt;
+
+ eigen_assert(x.size()==n); // check the caller is not cheating us
+
+ /* calculate the jacobian matrix. */
+ Index df_ret = functor.df(x, fjac);
+ if (df_ret<0)
+ return LevenbergMarquardtSpace::UserAsked;
+ if (df_ret>0)
+ // numerical diff, we evaluated the function df_ret times
+ nfev += df_ret;
+ else njev++;
+
+ /* compute the qr factorization of the jacobian. */
+ wa2 = fjac.colwise().blueNorm();
+ ColPivHouseholderQR<JacobianType> qrfac(fjac);
+ fjac = qrfac.matrixQR();
+ permutation = qrfac.colsPermutation();
+
+ /* on the first iteration and if external scaling is not used, scale according */
+ /* to the norms of the columns of the initial jacobian. */
+ if (iter == 1) {
+ if (!useExternalScaling)
+ for (Index j = 0; j < n; ++j)
+ diag[j] = (wa2[j]==0.)? 1. : wa2[j];
+
+ /* on the first iteration, calculate the norm of the scaled x */
+ /* and initialize the step bound delta. */
+ xnorm = diag.cwiseProduct(x).stableNorm();
+ delta = parameters.factor * xnorm;
+ if (delta == 0.)
+ delta = parameters.factor;
+ }
+
+ /* form (q transpose)*fvec and store the first n components in */
+ /* qtf. */
+ wa4 = fvec;
+ wa4.applyOnTheLeft(qrfac.householderQ().adjoint());
+ qtf = wa4.head(n);
+
+ /* compute the norm of the scaled gradient. */
+ gnorm = 0.;
+ if (fnorm != 0.)
+ for (Index j = 0; j < n; ++j)
+ if (wa2[permutation.indices()[j]] != 0.)
+ gnorm = (std::max)(gnorm, abs( fjac.col(j).head(j+1).dot(qtf.head(j+1)/fnorm) / wa2[permutation.indices()[j]]));
+
+ /* test for convergence of the gradient norm. */
+ if (gnorm <= parameters.gtol)
+ return LevenbergMarquardtSpace::CosinusTooSmall;
+
+ /* rescale if necessary. */
+ if (!useExternalScaling)
+ diag = diag.cwiseMax(wa2);
+
+ do {
+
+ /* determine the levenberg-marquardt parameter. */
+ internal::lmpar2<Scalar>(qrfac, diag, qtf, delta, par, wa1);
+
+ /* store the direction p and x + p. calculate the norm of p. */
+ wa1 = -wa1;
+ wa2 = x + wa1;
+ pnorm = diag.cwiseProduct(wa1).stableNorm();
+
+ /* on the first iteration, adjust the initial step bound. */
+ if (iter == 1)
+ delta = (std::min)(delta,pnorm);
+
+ /* evaluate the function at x + p and calculate its norm. */
+ if ( functor(wa2, wa4) < 0)
+ return LevenbergMarquardtSpace::UserAsked;
+ ++nfev;
+ fnorm1 = wa4.stableNorm();
+
+ /* compute the scaled actual reduction. */
+ actred = -1.;
+ if (Scalar(.1) * fnorm1 < fnorm)
+ actred = 1. - numext::abs2(fnorm1 / fnorm);
+
+ /* compute the scaled predicted reduction and */
+ /* the scaled directional derivative. */
+ wa3 = fjac.template triangularView<Upper>() * (qrfac.colsPermutation().inverse() *wa1);
+ temp1 = numext::abs2(wa3.stableNorm() / fnorm);
+ temp2 = numext::abs2(sqrt(par) * pnorm / fnorm);
+ prered = temp1 + temp2 / Scalar(.5);
+ dirder = -(temp1 + temp2);
+
+ /* compute the ratio of the actual to the predicted */
+ /* reduction. */
+ ratio = 0.;
+ if (prered != 0.)
+ ratio = actred / prered;
+
+ /* update the step bound. */
+ if (ratio <= Scalar(.25)) {
+ if (actred >= 0.)
+ temp = Scalar(.5);
+ if (actred < 0.)
+ temp = Scalar(.5) * dirder / (dirder + Scalar(.5) * actred);
+ if (Scalar(.1) * fnorm1 >= fnorm || temp < Scalar(.1))
+ temp = Scalar(.1);
+ /* Computing MIN */
+ delta = temp * (std::min)(delta, pnorm / Scalar(.1));
+ par /= temp;
+ } else if (!(par != 0. && ratio < Scalar(.75))) {
+ delta = pnorm / Scalar(.5);
+ par = Scalar(.5) * par;
+ }
+
+ /* test for successful iteration. */
+ if (ratio >= Scalar(1e-4)) {
+ /* successful iteration. update x, fvec, and their norms. */
+ x = wa2;
+ wa2 = diag.cwiseProduct(x);
+ fvec = wa4;
+ xnorm = wa2.stableNorm();
+ fnorm = fnorm1;
+ ++iter;
+ }
+
+ /* tests for convergence. */
+ if (abs(actred) <= parameters.ftol && prered <= parameters.ftol && Scalar(.5) * ratio <= 1. && delta <= parameters.xtol * xnorm)
+ return LevenbergMarquardtSpace::RelativeErrorAndReductionTooSmall;
+ if (abs(actred) <= parameters.ftol && prered <= parameters.ftol && Scalar(.5) * ratio <= 1.)
+ return LevenbergMarquardtSpace::RelativeReductionTooSmall;
+ if (delta <= parameters.xtol * xnorm)
+ return LevenbergMarquardtSpace::RelativeErrorTooSmall;
+
+ /* tests for termination and stringent tolerances. */
+ if (nfev >= parameters.maxfev)
+ return LevenbergMarquardtSpace::TooManyFunctionEvaluation;
+ if (abs(actred) <= NumTraits<Scalar>::epsilon() && prered <= NumTraits<Scalar>::epsilon() && Scalar(.5) * ratio <= 1.)
+ return LevenbergMarquardtSpace::FtolTooSmall;
+ if (delta <= NumTraits<Scalar>::epsilon() * xnorm)
+ return LevenbergMarquardtSpace::XtolTooSmall;
+ if (gnorm <= NumTraits<Scalar>::epsilon())
+ return LevenbergMarquardtSpace::GtolTooSmall;
+
+ } while (ratio < Scalar(1e-4));
+
+ return LevenbergMarquardtSpace::Running;
+}
+
+template<typename FunctorType, typename Scalar>
+LevenbergMarquardtSpace::Status
+LevenbergMarquardt<FunctorType,Scalar>::lmstr1(
+ FVectorType &x,
+ const Scalar tol
+ )
+{
+ n = x.size();
+ m = functor.values();
+
+ /* check the input parameters for errors. */
+ if (n <= 0 || m < n || tol < 0.)
+ return LevenbergMarquardtSpace::ImproperInputParameters;
+
+ resetParameters();
+ parameters.ftol = tol;
+ parameters.xtol = tol;
+ parameters.maxfev = 100*(n+1);
+
+ return minimizeOptimumStorage(x);
+}
+
+template<typename FunctorType, typename Scalar>
+LevenbergMarquardtSpace::Status
+LevenbergMarquardt<FunctorType,Scalar>::minimizeOptimumStorageInit(FVectorType &x)
+{
+ n = x.size();
+ m = functor.values();
+
+ wa1.resize(n); wa2.resize(n); wa3.resize(n);
+ wa4.resize(m);
+ fvec.resize(m);
+ // Only R is stored in fjac. Q is only used to compute 'qtf', which is
+ // Q.transpose()*rhs. qtf will be updated using givens rotation,
+ // instead of storing them in Q.
+ // The purpose it to only use a nxn matrix, instead of mxn here, so
+ // that we can handle cases where m>>n :
+ fjac.resize(n, n);
+ if (!useExternalScaling)
+ diag.resize(n);
+ eigen_assert( (!useExternalScaling || diag.size()==n) && "When useExternalScaling is set, the caller must provide a valid 'diag'");
+ qtf.resize(n);
+
+ /* Function Body */
+ nfev = 0;
+ njev = 0;
+
+ /* check the input parameters for errors. */
+ if (n <= 0 || m < n || parameters.ftol < 0. || parameters.xtol < 0. || parameters.gtol < 0. || parameters.maxfev <= 0 || parameters.factor <= 0.)
+ return LevenbergMarquardtSpace::ImproperInputParameters;
+
+ if (useExternalScaling)
+ for (Index j = 0; j < n; ++j)
+ if (diag[j] <= 0.)
+ return LevenbergMarquardtSpace::ImproperInputParameters;
+
+ /* evaluate the function at the starting point */
+ /* and calculate its norm. */
+ nfev = 1;
+ if ( functor(x, fvec) < 0)
+ return LevenbergMarquardtSpace::UserAsked;
+ fnorm = fvec.stableNorm();
+
+ /* initialize levenberg-marquardt parameter and iteration counter. */
+ par = 0.;
+ iter = 1;
+
+ return LevenbergMarquardtSpace::NotStarted;
+}
+
+
+template<typename FunctorType, typename Scalar>
+LevenbergMarquardtSpace::Status
+LevenbergMarquardt<FunctorType,Scalar>::minimizeOptimumStorageOneStep(FVectorType &x)
+{
+ using std::abs;
+ using std::sqrt;
+
+ eigen_assert(x.size()==n); // check the caller is not cheating us
+
+ Index i, j;
+ bool sing;
+
+ /* compute the qr factorization of the jacobian matrix */
+ /* calculated one row at a time, while simultaneously */
+ /* forming (q transpose)*fvec and storing the first */
+ /* n components in qtf. */
+ qtf.fill(0.);
+ fjac.fill(0.);
+ Index rownb = 2;
+ for (i = 0; i < m; ++i) {
+ if (functor.df(x, wa3, rownb) < 0) return LevenbergMarquardtSpace::UserAsked;
+ internal::rwupdt<Scalar>(fjac, wa3, qtf, fvec[i]);
+ ++rownb;
+ }
+ ++njev;
+
+ /* if the jacobian is rank deficient, call qrfac to */
+ /* reorder its columns and update the components of qtf. */
+ sing = false;
+ for (j = 0; j < n; ++j) {
+ if (fjac(j,j) == 0.)
+ sing = true;
+ wa2[j] = fjac.col(j).head(j).stableNorm();
+ }
+ permutation.setIdentity(n);
+ if (sing) {
+ wa2 = fjac.colwise().blueNorm();
+ // TODO We have no unit test covering this code path, do not modify
+ // until it is carefully tested
+ ColPivHouseholderQR<JacobianType> qrfac(fjac);
+ fjac = qrfac.matrixQR();
+ wa1 = fjac.diagonal();
+ fjac.diagonal() = qrfac.hCoeffs();
+ permutation = qrfac.colsPermutation();
+ // TODO : avoid this:
+ for(Index ii=0; ii< fjac.cols(); ii++) fjac.col(ii).segment(ii+1, fjac.rows()-ii-1) *= fjac(ii,ii); // rescale vectors
+
+ for (j = 0; j < n; ++j) {
+ if (fjac(j,j) != 0.) {
+ sum = 0.;
+ for (i = j; i < n; ++i)
+ sum += fjac(i,j) * qtf[i];
+ temp = -sum / fjac(j,j);
+ for (i = j; i < n; ++i)
+ qtf[i] += fjac(i,j) * temp;
+ }
+ fjac(j,j) = wa1[j];
+ }
+ }
+
+ /* on the first iteration and if external scaling is not used, scale according */
+ /* to the norms of the columns of the initial jacobian. */
+ if (iter == 1) {
+ if (!useExternalScaling)
+ for (j = 0; j < n; ++j)
+ diag[j] = (wa2[j]==0.)? 1. : wa2[j];
+
+ /* on the first iteration, calculate the norm of the scaled x */
+ /* and initialize the step bound delta. */
+ xnorm = diag.cwiseProduct(x).stableNorm();
+ delta = parameters.factor * xnorm;
+ if (delta == 0.)
+ delta = parameters.factor;
+ }
+
+ /* compute the norm of the scaled gradient. */
+ gnorm = 0.;
+ if (fnorm != 0.)
+ for (j = 0; j < n; ++j)
+ if (wa2[permutation.indices()[j]] != 0.)
+ gnorm = (std::max)(gnorm, abs( fjac.col(j).head(j+1).dot(qtf.head(j+1)/fnorm) / wa2[permutation.indices()[j]]));
+
+ /* test for convergence of the gradient norm. */
+ if (gnorm <= parameters.gtol)
+ return LevenbergMarquardtSpace::CosinusTooSmall;
+
+ /* rescale if necessary. */
+ if (!useExternalScaling)
+ diag = diag.cwiseMax(wa2);
+
+ do {
+
+ /* determine the levenberg-marquardt parameter. */
+ internal::lmpar<Scalar>(fjac, permutation.indices(), diag, qtf, delta, par, wa1);
+
+ /* store the direction p and x + p. calculate the norm of p. */
+ wa1 = -wa1;
+ wa2 = x + wa1;
+ pnorm = diag.cwiseProduct(wa1).stableNorm();
+
+ /* on the first iteration, adjust the initial step bound. */
+ if (iter == 1)
+ delta = (std::min)(delta,pnorm);
+
+ /* evaluate the function at x + p and calculate its norm. */
+ if ( functor(wa2, wa4) < 0)
+ return LevenbergMarquardtSpace::UserAsked;
+ ++nfev;
+ fnorm1 = wa4.stableNorm();
+
+ /* compute the scaled actual reduction. */
+ actred = -1.;
+ if (Scalar(.1) * fnorm1 < fnorm)
+ actred = 1. - numext::abs2(fnorm1 / fnorm);
+
+ /* compute the scaled predicted reduction and */
+ /* the scaled directional derivative. */
+ wa3 = fjac.topLeftCorner(n,n).template triangularView<Upper>() * (permutation.inverse() * wa1);
+ temp1 = numext::abs2(wa3.stableNorm() / fnorm);
+ temp2 = numext::abs2(sqrt(par) * pnorm / fnorm);
+ prered = temp1 + temp2 / Scalar(.5);
+ dirder = -(temp1 + temp2);
+
+ /* compute the ratio of the actual to the predicted */
+ /* reduction. */
+ ratio = 0.;
+ if (prered != 0.)
+ ratio = actred / prered;
+
+ /* update the step bound. */
+ if (ratio <= Scalar(.25)) {
+ if (actred >= 0.)
+ temp = Scalar(.5);
+ if (actred < 0.)
+ temp = Scalar(.5) * dirder / (dirder + Scalar(.5) * actred);
+ if (Scalar(.1) * fnorm1 >= fnorm || temp < Scalar(.1))
+ temp = Scalar(.1);
+ /* Computing MIN */
+ delta = temp * (std::min)(delta, pnorm / Scalar(.1));
+ par /= temp;
+ } else if (!(par != 0. && ratio < Scalar(.75))) {
+ delta = pnorm / Scalar(.5);
+ par = Scalar(.5) * par;
+ }
+
+ /* test for successful iteration. */
+ if (ratio >= Scalar(1e-4)) {
+ /* successful iteration. update x, fvec, and their norms. */
+ x = wa2;
+ wa2 = diag.cwiseProduct(x);
+ fvec = wa4;
+ xnorm = wa2.stableNorm();
+ fnorm = fnorm1;
+ ++iter;
+ }
+
+ /* tests for convergence. */
+ if (abs(actred) <= parameters.ftol && prered <= parameters.ftol && Scalar(.5) * ratio <= 1. && delta <= parameters.xtol * xnorm)
+ return LevenbergMarquardtSpace::RelativeErrorAndReductionTooSmall;
+ if (abs(actred) <= parameters.ftol && prered <= parameters.ftol && Scalar(.5) * ratio <= 1.)
+ return LevenbergMarquardtSpace::RelativeReductionTooSmall;
+ if (delta <= parameters.xtol * xnorm)
+ return LevenbergMarquardtSpace::RelativeErrorTooSmall;
+
+ /* tests for termination and stringent tolerances. */
+ if (nfev >= parameters.maxfev)
+ return LevenbergMarquardtSpace::TooManyFunctionEvaluation;
+ if (abs(actred) <= NumTraits<Scalar>::epsilon() && prered <= NumTraits<Scalar>::epsilon() && Scalar(.5) * ratio <= 1.)
+ return LevenbergMarquardtSpace::FtolTooSmall;
+ if (delta <= NumTraits<Scalar>::epsilon() * xnorm)
+ return LevenbergMarquardtSpace::XtolTooSmall;
+ if (gnorm <= NumTraits<Scalar>::epsilon())
+ return LevenbergMarquardtSpace::GtolTooSmall;
+
+ } while (ratio < Scalar(1e-4));
+
+ return LevenbergMarquardtSpace::Running;
+}
+
+template<typename FunctorType, typename Scalar>
+LevenbergMarquardtSpace::Status
+LevenbergMarquardt<FunctorType,Scalar>::minimizeOptimumStorage(FVectorType &x)
+{
+ LevenbergMarquardtSpace::Status status = minimizeOptimumStorageInit(x);
+ if (status==LevenbergMarquardtSpace::ImproperInputParameters)
+ return status;
+ do {
+ status = minimizeOptimumStorageOneStep(x);
+ } while (status==LevenbergMarquardtSpace::Running);
+ return status;
+}
+
+template<typename FunctorType, typename Scalar>
+LevenbergMarquardtSpace::Status
+LevenbergMarquardt<FunctorType,Scalar>::lmdif1(
+ FunctorType &functor,
+ FVectorType &x,
+ Index *nfev,
+ const Scalar tol
+ )
+{
+ Index n = x.size();
+ Index m = functor.values();
+
+ /* check the input parameters for errors. */
+ if (n <= 0 || m < n || tol < 0.)
+ return LevenbergMarquardtSpace::ImproperInputParameters;
+
+ NumericalDiff<FunctorType> numDiff(functor);
+ // embedded LevenbergMarquardt
+ LevenbergMarquardt<NumericalDiff<FunctorType>, Scalar > lm(numDiff);
+ lm.parameters.ftol = tol;
+ lm.parameters.xtol = tol;
+ lm.parameters.maxfev = 200*(n+1);
+
+ LevenbergMarquardtSpace::Status info = LevenbergMarquardtSpace::Status(lm.minimize(x));
+ if (nfev)
+ * nfev = lm.nfev;
+ return info;
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_LEVENBERGMARQUARDT__H
+
+//vim: ai ts=4 sts=4 et sw=4
diff --git a/unsupported/Eigen/src/NonLinearOptimization/chkder.h b/unsupported/Eigen/src/NonLinearOptimization/chkder.h
new file mode 100644
index 0000000..d0974a0
--- /dev/null
+++ b/unsupported/Eigen/src/NonLinearOptimization/chkder.h
@@ -0,0 +1,68 @@
+#define chkder_log10e 0.43429448190325182765
+#define chkder_factor 100.
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+
+template<typename Scalar>
+void chkder(
+ const Matrix< Scalar, Dynamic, 1 > &x,
+ const Matrix< Scalar, Dynamic, 1 > &fvec,
+ const Matrix< Scalar, Dynamic, Dynamic > &fjac,
+ Matrix< Scalar, Dynamic, 1 > &xp,
+ const Matrix< Scalar, Dynamic, 1 > &fvecp,
+ int mode,
+ Matrix< Scalar, Dynamic, 1 > &err
+ )
+{
+ using std::sqrt;
+ using std::abs;
+ using std::log;
+
+ typedef DenseIndex Index;
+
+ const Scalar eps = sqrt(NumTraits<Scalar>::epsilon());
+ const Scalar epsf = chkder_factor * NumTraits<Scalar>::epsilon();
+ const Scalar epslog = chkder_log10e * log(eps);
+ Scalar temp;
+
+ const Index m = fvec.size(), n = x.size();
+
+ if (mode != 2) {
+ /* mode = 1. */
+ xp.resize(n);
+ for (Index j = 0; j < n; ++j) {
+ temp = eps * abs(x[j]);
+ if (temp == 0.)
+ temp = eps;
+ xp[j] = x[j] + temp;
+ }
+ }
+ else {
+ /* mode = 2. */
+ err.setZero(m);
+ for (Index j = 0; j < n; ++j) {
+ temp = abs(x[j]);
+ if (temp == 0.)
+ temp = 1.;
+ err += temp * fjac.col(j);
+ }
+ for (Index i = 0; i < m; ++i) {
+ temp = 1.;
+ if (fvec[i] != 0. && fvecp[i] != 0. && abs(fvecp[i] - fvec[i]) >= epsf * abs(fvec[i]))
+ temp = eps * abs((fvecp[i] - fvec[i]) / eps - err[i]) / (abs(fvec[i]) + abs(fvecp[i]));
+ err[i] = 1.;
+ if (temp > NumTraits<Scalar>::epsilon() && temp < eps)
+ err[i] = (chkder_log10e * log(temp) - epslog) / epslog;
+ if (temp >= eps)
+ err[i] = 0.;
+ }
+ }
+}
+
+} // end namespace internal
+
+} // end namespace Eigen
diff --git a/unsupported/Eigen/src/NonLinearOptimization/covar.h b/unsupported/Eigen/src/NonLinearOptimization/covar.h
new file mode 100644
index 0000000..181c4f3
--- /dev/null
+++ b/unsupported/Eigen/src/NonLinearOptimization/covar.h
@@ -0,0 +1,72 @@
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+
+template <typename Scalar>
+void covar(
+ Matrix< Scalar, Dynamic, Dynamic > &r,
+ const VectorXi &ipvt,
+ Scalar tol = std::sqrt(NumTraits<Scalar>::epsilon()) )
+{
+ using std::abs;
+ typedef DenseIndex Index;
+
+ /* Local variables */
+ Index i, j, k, l, ii, jj;
+ bool sing;
+ Scalar temp;
+
+ /* Function Body */
+ const Index n = r.cols();
+ const Scalar tolr = tol * abs(r(0,0));
+ Matrix< Scalar, Dynamic, 1 > wa(n);
+ eigen_assert(ipvt.size()==n);
+
+ /* form the inverse of r in the full upper triangle of r. */
+ l = -1;
+ for (k = 0; k < n; ++k)
+ if (abs(r(k,k)) > tolr) {
+ r(k,k) = 1. / r(k,k);
+ for (j = 0; j <= k-1; ++j) {
+ temp = r(k,k) * r(j,k);
+ r(j,k) = 0.;
+ r.col(k).head(j+1) -= r.col(j).head(j+1) * temp;
+ }
+ l = k;
+ }
+
+ /* form the full upper triangle of the inverse of (r transpose)*r */
+ /* in the full upper triangle of r. */
+ for (k = 0; k <= l; ++k) {
+ for (j = 0; j <= k-1; ++j)
+ r.col(j).head(j+1) += r.col(k).head(j+1) * r(j,k);
+ r.col(k).head(k+1) *= r(k,k);
+ }
+
+ /* form the full lower triangle of the covariance matrix */
+ /* in the strict lower triangle of r and in wa. */
+ for (j = 0; j < n; ++j) {
+ jj = ipvt[j];
+ sing = j > l;
+ for (i = 0; i <= j; ++i) {
+ if (sing)
+ r(i,j) = 0.;
+ ii = ipvt[i];
+ if (ii > jj)
+ r(ii,jj) = r(i,j);
+ if (ii < jj)
+ r(jj,ii) = r(i,j);
+ }
+ wa[jj] = r(j,j);
+ }
+
+ /* symmetrize the covariance matrix in r. */
+ r.topLeftCorner(n,n).template triangularView<StrictlyUpper>() = r.topLeftCorner(n,n).transpose();
+ r.diagonal() = wa;
+}
+
+} // end namespace internal
+
+} // end namespace Eigen
diff --git a/unsupported/Eigen/src/NonLinearOptimization/dogleg.h b/unsupported/Eigen/src/NonLinearOptimization/dogleg.h
new file mode 100644
index 0000000..7c170a2
--- /dev/null
+++ b/unsupported/Eigen/src/NonLinearOptimization/dogleg.h
@@ -0,0 +1,109 @@
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+
+template <typename Scalar>
+void dogleg(
+ const Matrix< Scalar, Dynamic, Dynamic > &qrfac,
+ const Matrix< Scalar, Dynamic, 1 > &diag,
+ const Matrix< Scalar, Dynamic, 1 > &qtb,
+ Scalar delta,
+ Matrix< Scalar, Dynamic, 1 > &x)
+{
+ using std::abs;
+ using std::sqrt;
+
+ typedef DenseIndex Index;
+
+ /* Local variables */
+ Index i, j;
+ Scalar sum, temp, alpha, bnorm;
+ Scalar gnorm, qnorm;
+ Scalar sgnorm;
+
+ /* Function Body */
+ const Scalar epsmch = NumTraits<Scalar>::epsilon();
+ const Index n = qrfac.cols();
+ eigen_assert(n==qtb.size());
+ eigen_assert(n==x.size());
+ eigen_assert(n==diag.size());
+ Matrix< Scalar, Dynamic, 1 > wa1(n), wa2(n);
+
+ /* first, calculate the gauss-newton direction. */
+ for (j = n-1; j >=0; --j) {
+ temp = qrfac(j,j);
+ if (temp == 0.) {
+ temp = epsmch * qrfac.col(j).head(j+1).maxCoeff();
+ if (temp == 0.)
+ temp = epsmch;
+ }
+ if (j==n-1)
+ x[j] = qtb[j] / temp;
+ else
+ x[j] = (qtb[j] - qrfac.row(j).tail(n-j-1).dot(x.tail(n-j-1))) / temp;
+ }
+
+ /* test whether the gauss-newton direction is acceptable. */
+ qnorm = diag.cwiseProduct(x).stableNorm();
+ if (qnorm <= delta)
+ return;
+
+ // TODO : this path is not tested by Eigen unit tests
+
+ /* the gauss-newton direction is not acceptable. */
+ /* next, calculate the scaled gradient direction. */
+
+ wa1.fill(0.);
+ for (j = 0; j < n; ++j) {
+ wa1.tail(n-j) += qrfac.row(j).tail(n-j) * qtb[j];
+ wa1[j] /= diag[j];
+ }
+
+ /* calculate the norm of the scaled gradient and test for */
+ /* the special case in which the scaled gradient is zero. */
+ gnorm = wa1.stableNorm();
+ sgnorm = 0.;
+ alpha = delta / qnorm;
+ if (gnorm == 0.)
+ goto algo_end;
+
+ /* calculate the point along the scaled gradient */
+ /* at which the quadratic is minimized. */
+ wa1.array() /= (diag*gnorm).array();
+ // TODO : once unit tests cover this part,:
+ // wa2 = qrfac.template triangularView<Upper>() * wa1;
+ for (j = 0; j < n; ++j) {
+ sum = 0.;
+ for (i = j; i < n; ++i) {
+ sum += qrfac(j,i) * wa1[i];
+ }
+ wa2[j] = sum;
+ }
+ temp = wa2.stableNorm();
+ sgnorm = gnorm / temp / temp;
+
+ /* test whether the scaled gradient direction is acceptable. */
+ alpha = 0.;
+ if (sgnorm >= delta)
+ goto algo_end;
+
+ /* the scaled gradient direction is not acceptable. */
+ /* finally, calculate the point along the dogleg */
+ /* at which the quadratic is minimized. */
+ bnorm = qtb.stableNorm();
+ temp = bnorm / gnorm * (bnorm / qnorm) * (sgnorm / delta);
+ temp = temp - delta / qnorm * numext::abs2(sgnorm / delta) + sqrt(numext::abs2(temp - delta / qnorm) + (1.-numext::abs2(delta / qnorm)) * (1.-numext::abs2(sgnorm / delta)));
+ alpha = delta / qnorm * (1. - numext::abs2(sgnorm / delta)) / temp;
+algo_end:
+
+ /* form appropriate convex combination of the gauss-newton */
+ /* direction and the scaled gradient direction. */
+ temp = (1.-alpha) * (std::min)(sgnorm,delta);
+ x = temp * wa1 + alpha * x;
+}
+
+} // end namespace internal
+
+} // end namespace Eigen
diff --git a/unsupported/Eigen/src/NonLinearOptimization/fdjac1.h b/unsupported/Eigen/src/NonLinearOptimization/fdjac1.h
new file mode 100644
index 0000000..317b157
--- /dev/null
+++ b/unsupported/Eigen/src/NonLinearOptimization/fdjac1.h
@@ -0,0 +1,81 @@
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+
+template<typename FunctorType, typename Scalar>
+DenseIndex fdjac1(
+ const FunctorType &Functor,
+ Matrix< Scalar, Dynamic, 1 > &x,
+ Matrix< Scalar, Dynamic, 1 > &fvec,
+ Matrix< Scalar, Dynamic, Dynamic > &fjac,
+ DenseIndex ml, DenseIndex mu,
+ Scalar epsfcn)
+{
+ using std::sqrt;
+ using std::abs;
+
+ typedef DenseIndex Index;
+
+ /* Local variables */
+ Scalar h;
+ Index j, k;
+ Scalar eps, temp;
+ Index msum;
+ int iflag;
+ Index start, length;
+
+ /* Function Body */
+ const Scalar epsmch = NumTraits<Scalar>::epsilon();
+ const Index n = x.size();
+ eigen_assert(fvec.size()==n);
+ Matrix< Scalar, Dynamic, 1 > wa1(n);
+ Matrix< Scalar, Dynamic, 1 > wa2(n);
+
+ eps = sqrt((std::max)(epsfcn,epsmch));
+ msum = ml + mu + 1;
+ if (msum >= n) {
+ /* computation of dense approximate jacobian. */
+ for (j = 0; j < n; ++j) {
+ temp = x[j];
+ h = eps * abs(temp);
+ if (h == 0.)
+ h = eps;
+ x[j] = temp + h;
+ iflag = Functor(x, wa1);
+ if (iflag < 0)
+ return iflag;
+ x[j] = temp;
+ fjac.col(j) = (wa1-fvec)/h;
+ }
+
+ }else {
+ /* computation of banded approximate jacobian. */
+ for (k = 0; k < msum; ++k) {
+ for (j = k; (msum<0) ? (j>n): (j<n); j += msum) {
+ wa2[j] = x[j];
+ h = eps * abs(wa2[j]);
+ if (h == 0.) h = eps;
+ x[j] = wa2[j] + h;
+ }
+ iflag = Functor(x, wa1);
+ if (iflag < 0)
+ return iflag;
+ for (j = k; (msum<0) ? (j>n): (j<n); j += msum) {
+ x[j] = wa2[j];
+ h = eps * abs(wa2[j]);
+ if (h == 0.) h = eps;
+ fjac.col(j).setZero();
+ start = std::max<Index>(0,j-mu);
+ length = (std::min)(n-1, j+ml) - start + 1;
+ fjac.col(j).segment(start, length) = ( wa1.segment(start, length)-fvec.segment(start, length))/h;
+ }
+ }
+ }
+ return 0;
+}
+
+} // end namespace internal
+
+} // end namespace Eigen
diff --git a/unsupported/Eigen/src/NonLinearOptimization/lmpar.h b/unsupported/Eigen/src/NonLinearOptimization/lmpar.h
new file mode 100644
index 0000000..64af0fd
--- /dev/null
+++ b/unsupported/Eigen/src/NonLinearOptimization/lmpar.h
@@ -0,0 +1,300 @@
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+
+template <typename Scalar>
+void lmpar(
+ Matrix< Scalar, Dynamic, Dynamic > &r,
+ const VectorXi &ipvt,
+ const Matrix< Scalar, Dynamic, 1 > &diag,
+ const Matrix< Scalar, Dynamic, 1 > &qtb,
+ Scalar delta,
+ Scalar &par,
+ Matrix< Scalar, Dynamic, 1 > &x)
+{
+ using std::abs;
+ using std::sqrt;
+ typedef DenseIndex Index;
+
+ /* Local variables */
+ Index i, j, l;
+ Scalar fp;
+ Scalar parc, parl;
+ Index iter;
+ Scalar temp, paru;
+ Scalar gnorm;
+ Scalar dxnorm;
+
+
+ /* Function Body */
+ const Scalar dwarf = (std::numeric_limits<Scalar>::min)();
+ const Index n = r.cols();
+ eigen_assert(n==diag.size());
+ eigen_assert(n==qtb.size());
+ eigen_assert(n==x.size());
+
+ Matrix< Scalar, Dynamic, 1 > wa1, wa2;
+
+ /* compute and store in x the gauss-newton direction. if the */
+ /* jacobian is rank-deficient, obtain a least squares solution. */
+ Index nsing = n-1;
+ wa1 = qtb;
+ for (j = 0; j < n; ++j) {
+ if (r(j,j) == 0. && nsing == n-1)
+ nsing = j - 1;
+ if (nsing < n-1)
+ wa1[j] = 0.;
+ }
+ for (j = nsing; j>=0; --j) {
+ wa1[j] /= r(j,j);
+ temp = wa1[j];
+ for (i = 0; i < j ; ++i)
+ wa1[i] -= r(i,j) * temp;
+ }
+
+ for (j = 0; j < n; ++j)
+ x[ipvt[j]] = wa1[j];
+
+ /* initialize the iteration counter. */
+ /* evaluate the function at the origin, and test */
+ /* for acceptance of the gauss-newton direction. */
+ iter = 0;
+ wa2 = diag.cwiseProduct(x);
+ dxnorm = wa2.blueNorm();
+ fp = dxnorm - delta;
+ if (fp <= Scalar(0.1) * delta) {
+ par = 0;
+ return;
+ }
+
+ /* if the jacobian is not rank deficient, the newton */
+ /* step provides a lower bound, parl, for the zero of */
+ /* the function. otherwise set this bound to zero. */
+ parl = 0.;
+ if (nsing >= n-1) {
+ for (j = 0; j < n; ++j) {
+ l = ipvt[j];
+ wa1[j] = diag[l] * (wa2[l] / dxnorm);
+ }
+ // it's actually a triangularView.solveInplace(), though in a weird
+ // way:
+ for (j = 0; j < n; ++j) {
+ Scalar sum = 0.;
+ for (i = 0; i < j; ++i)
+ sum += r(i,j) * wa1[i];
+ wa1[j] = (wa1[j] - sum) / r(j,j);
+ }
+ temp = wa1.blueNorm();
+ parl = fp / delta / temp / temp;
+ }
+
+ /* calculate an upper bound, paru, for the zero of the function. */
+ for (j = 0; j < n; ++j)
+ wa1[j] = r.col(j).head(j+1).dot(qtb.head(j+1)) / diag[ipvt[j]];
+
+ gnorm = wa1.stableNorm();
+ paru = gnorm / delta;
+ if (paru == 0.)
+ paru = dwarf / (std::min)(delta,Scalar(0.1));
+
+ /* if the input par lies outside of the interval (parl,paru), */
+ /* set par to the closer endpoint. */
+ par = (std::max)(par,parl);
+ par = (std::min)(par,paru);
+ if (par == 0.)
+ par = gnorm / dxnorm;
+
+ /* beginning of an iteration. */
+ while (true) {
+ ++iter;
+
+ /* evaluate the function at the current value of par. */
+ if (par == 0.)
+ par = (std::max)(dwarf,Scalar(.001) * paru); /* Computing MAX */
+ wa1 = sqrt(par)* diag;
+
+ Matrix< Scalar, Dynamic, 1 > sdiag(n);
+ qrsolv<Scalar>(r, ipvt, wa1, qtb, x, sdiag);
+
+ wa2 = diag.cwiseProduct(x);
+ dxnorm = wa2.blueNorm();
+ temp = fp;
+ fp = dxnorm - delta;
+
+ /* if the function is small enough, accept the current value */
+ /* of par. also test for the exceptional cases where parl */
+ /* is zero or the number of iterations has reached 10. */
+ if (abs(fp) <= Scalar(0.1) * delta || (parl == 0. && fp <= temp && temp < 0.) || iter == 10)
+ break;
+
+ /* compute the newton correction. */
+ for (j = 0; j < n; ++j) {
+ l = ipvt[j];
+ wa1[j] = diag[l] * (wa2[l] / dxnorm);
+ }
+ for (j = 0; j < n; ++j) {
+ wa1[j] /= sdiag[j];
+ temp = wa1[j];
+ for (i = j+1; i < n; ++i)
+ wa1[i] -= r(i,j) * temp;
+ }
+ temp = wa1.blueNorm();
+ parc = fp / delta / temp / temp;
+
+ /* depending on the sign of the function, update parl or paru. */
+ if (fp > 0.)
+ parl = (std::max)(parl,par);
+ if (fp < 0.)
+ paru = (std::min)(paru,par);
+
+ /* compute an improved estimate for par. */
+ /* Computing MAX */
+ par = (std::max)(parl,par+parc);
+
+ /* end of an iteration. */
+ }
+
+ /* termination. */
+ if (iter == 0)
+ par = 0.;
+ return;
+}
+
+template <typename Scalar>
+void lmpar2(
+ const ColPivHouseholderQR<Matrix< Scalar, Dynamic, Dynamic> > &qr,
+ const Matrix< Scalar, Dynamic, 1 > &diag,
+ const Matrix< Scalar, Dynamic, 1 > &qtb,
+ Scalar delta,
+ Scalar &par,
+ Matrix< Scalar, Dynamic, 1 > &x)
+
+{
+ using std::sqrt;
+ using std::abs;
+ typedef DenseIndex Index;
+
+ /* Local variables */
+ Index j;
+ Scalar fp;
+ Scalar parc, parl;
+ Index iter;
+ Scalar temp, paru;
+ Scalar gnorm;
+ Scalar dxnorm;
+
+
+ /* Function Body */
+ const Scalar dwarf = (std::numeric_limits<Scalar>::min)();
+ const Index n = qr.matrixQR().cols();
+ eigen_assert(n==diag.size());
+ eigen_assert(n==qtb.size());
+
+ Matrix< Scalar, Dynamic, 1 > wa1, wa2;
+
+ /* compute and store in x the gauss-newton direction. if the */
+ /* jacobian is rank-deficient, obtain a least squares solution. */
+
+// const Index rank = qr.nonzeroPivots(); // exactly double(0.)
+ const Index rank = qr.rank(); // use a threshold
+ wa1 = qtb;
+ wa1.tail(n-rank).setZero();
+ qr.matrixQR().topLeftCorner(rank, rank).template triangularView<Upper>().solveInPlace(wa1.head(rank));
+
+ x = qr.colsPermutation()*wa1;
+
+ /* initialize the iteration counter. */
+ /* evaluate the function at the origin, and test */
+ /* for acceptance of the gauss-newton direction. */
+ iter = 0;
+ wa2 = diag.cwiseProduct(x);
+ dxnorm = wa2.blueNorm();
+ fp = dxnorm - delta;
+ if (fp <= Scalar(0.1) * delta) {
+ par = 0;
+ return;
+ }
+
+ /* if the jacobian is not rank deficient, the newton */
+ /* step provides a lower bound, parl, for the zero of */
+ /* the function. otherwise set this bound to zero. */
+ parl = 0.;
+ if (rank==n) {
+ wa1 = qr.colsPermutation().inverse() * diag.cwiseProduct(wa2)/dxnorm;
+ qr.matrixQR().topLeftCorner(n, n).transpose().template triangularView<Lower>().solveInPlace(wa1);
+ temp = wa1.blueNorm();
+ parl = fp / delta / temp / temp;
+ }
+
+ /* calculate an upper bound, paru, for the zero of the function. */
+ for (j = 0; j < n; ++j)
+ wa1[j] = qr.matrixQR().col(j).head(j+1).dot(qtb.head(j+1)) / diag[qr.colsPermutation().indices()(j)];
+
+ gnorm = wa1.stableNorm();
+ paru = gnorm / delta;
+ if (paru == 0.)
+ paru = dwarf / (std::min)(delta,Scalar(0.1));
+
+ /* if the input par lies outside of the interval (parl,paru), */
+ /* set par to the closer endpoint. */
+ par = (std::max)(par,parl);
+ par = (std::min)(par,paru);
+ if (par == 0.)
+ par = gnorm / dxnorm;
+
+ /* beginning of an iteration. */
+ Matrix< Scalar, Dynamic, Dynamic > s = qr.matrixQR();
+ while (true) {
+ ++iter;
+
+ /* evaluate the function at the current value of par. */
+ if (par == 0.)
+ par = (std::max)(dwarf,Scalar(.001) * paru); /* Computing MAX */
+ wa1 = sqrt(par)* diag;
+
+ Matrix< Scalar, Dynamic, 1 > sdiag(n);
+ qrsolv<Scalar>(s, qr.colsPermutation().indices(), wa1, qtb, x, sdiag);
+
+ wa2 = diag.cwiseProduct(x);
+ dxnorm = wa2.blueNorm();
+ temp = fp;
+ fp = dxnorm - delta;
+
+ /* if the function is small enough, accept the current value */
+ /* of par. also test for the exceptional cases where parl */
+ /* is zero or the number of iterations has reached 10. */
+ if (abs(fp) <= Scalar(0.1) * delta || (parl == 0. && fp <= temp && temp < 0.) || iter == 10)
+ break;
+
+ /* compute the newton correction. */
+ wa1 = qr.colsPermutation().inverse() * diag.cwiseProduct(wa2/dxnorm);
+ // we could almost use this here, but the diagonal is outside qr, in sdiag[]
+ // qr.matrixQR().topLeftCorner(n, n).transpose().template triangularView<Lower>().solveInPlace(wa1);
+ for (j = 0; j < n; ++j) {
+ wa1[j] /= sdiag[j];
+ temp = wa1[j];
+ for (Index i = j+1; i < n; ++i)
+ wa1[i] -= s(i,j) * temp;
+ }
+ temp = wa1.blueNorm();
+ parc = fp / delta / temp / temp;
+
+ /* depending on the sign of the function, update parl or paru. */
+ if (fp > 0.)
+ parl = (std::max)(parl,par);
+ if (fp < 0.)
+ paru = (std::min)(paru,par);
+
+ /* compute an improved estimate for par. */
+ par = (std::max)(parl,par+parc);
+ }
+ if (iter == 0)
+ par = 0.;
+ return;
+}
+
+} // end namespace internal
+
+} // end namespace Eigen
diff --git a/unsupported/Eigen/src/NonLinearOptimization/qrsolv.h b/unsupported/Eigen/src/NonLinearOptimization/qrsolv.h
new file mode 100644
index 0000000..1cdcd4e
--- /dev/null
+++ b/unsupported/Eigen/src/NonLinearOptimization/qrsolv.h
@@ -0,0 +1,93 @@
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+
+// TODO : once qrsolv2 is removed, use ColPivHouseholderQR or PermutationMatrix instead of ipvt
+template <typename Scalar>
+void qrsolv(
+ Matrix< Scalar, Dynamic, Dynamic > &s,
+ // TODO : use a PermutationMatrix once lmpar is no more:
+ const VectorXi &ipvt,
+ const Matrix< Scalar, Dynamic, 1 > &diag,
+ const Matrix< Scalar, Dynamic, 1 > &qtb,
+ Matrix< Scalar, Dynamic, 1 > &x,
+ Matrix< Scalar, Dynamic, 1 > &sdiag)
+
+{
+ typedef DenseIndex Index;
+
+ /* Local variables */
+ Index i, j, k, l;
+ Scalar temp;
+ Index n = s.cols();
+ Matrix< Scalar, Dynamic, 1 > wa(n);
+ JacobiRotation<Scalar> givens;
+
+ /* Function Body */
+ // the following will only change the lower triangular part of s, including
+ // the diagonal, though the diagonal is restored afterward
+
+ /* copy r and (q transpose)*b to preserve input and initialize s. */
+ /* in particular, save the diagonal elements of r in x. */
+ x = s.diagonal();
+ wa = qtb;
+
+ s.topLeftCorner(n,n).template triangularView<StrictlyLower>() = s.topLeftCorner(n,n).transpose();
+
+ /* eliminate the diagonal matrix d using a givens rotation. */
+ for (j = 0; j < n; ++j) {
+
+ /* prepare the row of d to be eliminated, locating the */
+ /* diagonal element using p from the qr factorization. */
+ l = ipvt[j];
+ if (diag[l] == 0.)
+ break;
+ sdiag.tail(n-j).setZero();
+ sdiag[j] = diag[l];
+
+ /* the transformations to eliminate the row of d */
+ /* modify only a single element of (q transpose)*b */
+ /* beyond the first n, which is initially zero. */
+ Scalar qtbpj = 0.;
+ for (k = j; k < n; ++k) {
+ /* determine a givens rotation which eliminates the */
+ /* appropriate element in the current row of d. */
+ givens.makeGivens(-s(k,k), sdiag[k]);
+
+ /* compute the modified diagonal element of r and */
+ /* the modified element of ((q transpose)*b,0). */
+ s(k,k) = givens.c() * s(k,k) + givens.s() * sdiag[k];
+ temp = givens.c() * wa[k] + givens.s() * qtbpj;
+ qtbpj = -givens.s() * wa[k] + givens.c() * qtbpj;
+ wa[k] = temp;
+
+ /* accumulate the transformation in the row of s. */
+ for (i = k+1; i<n; ++i) {
+ temp = givens.c() * s(i,k) + givens.s() * sdiag[i];
+ sdiag[i] = -givens.s() * s(i,k) + givens.c() * sdiag[i];
+ s(i,k) = temp;
+ }
+ }
+ }
+
+ /* solve the triangular system for z. if the system is */
+ /* singular, then obtain a least squares solution. */
+ Index nsing;
+ for(nsing=0; nsing<n && sdiag[nsing]!=0; nsing++) {}
+
+ wa.tail(n-nsing).setZero();
+ s.topLeftCorner(nsing, nsing).transpose().template triangularView<Upper>().solveInPlace(wa.head(nsing));
+
+ // restore
+ sdiag = s.diagonal();
+ s.diagonal() = x;
+
+ /* permute the components of z back to components of x. */
+ for (j = 0; j < n; ++j) x[ipvt[j]] = wa[j];
+}
+
+} // end namespace internal
+
+} // end namespace Eigen
diff --git a/unsupported/Eigen/src/NonLinearOptimization/r1mpyq.h b/unsupported/Eigen/src/NonLinearOptimization/r1mpyq.h
new file mode 100644
index 0000000..37ef258
--- /dev/null
+++ b/unsupported/Eigen/src/NonLinearOptimization/r1mpyq.h
@@ -0,0 +1,32 @@
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+
+// TODO : move this to GivensQR once there's such a thing in Eigen
+
+template <typename Scalar>
+void r1mpyq(DenseIndex m, DenseIndex n, Scalar *a, const std::vector<JacobiRotation<Scalar> > &v_givens, const std::vector<JacobiRotation<Scalar> > &w_givens)
+{
+ typedef DenseIndex Index;
+
+ /* apply the first set of givens rotations to a. */
+ for (Index j = n-2; j>=0; --j)
+ for (Index i = 0; i<m; ++i) {
+ Scalar temp = v_givens[j].c() * a[i+m*j] - v_givens[j].s() * a[i+m*(n-1)];
+ a[i+m*(n-1)] = v_givens[j].s() * a[i+m*j] + v_givens[j].c() * a[i+m*(n-1)];
+ a[i+m*j] = temp;
+ }
+ /* apply the second set of givens rotations to a. */
+ for (Index j = 0; j<n-1; ++j)
+ for (Index i = 0; i<m; ++i) {
+ Scalar temp = w_givens[j].c() * a[i+m*j] + w_givens[j].s() * a[i+m*(n-1)];
+ a[i+m*(n-1)] = -w_givens[j].s() * a[i+m*j] + w_givens[j].c() * a[i+m*(n-1)];
+ a[i+m*j] = temp;
+ }
+}
+
+} // end namespace internal
+
+} // end namespace Eigen
diff --git a/unsupported/Eigen/src/NonLinearOptimization/r1updt.h b/unsupported/Eigen/src/NonLinearOptimization/r1updt.h
new file mode 100644
index 0000000..7b3a599
--- /dev/null
+++ b/unsupported/Eigen/src/NonLinearOptimization/r1updt.h
@@ -0,0 +1,101 @@
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+
+template <typename Scalar>
+void r1updt(
+ Matrix< Scalar, Dynamic, Dynamic > &s,
+ const Matrix< Scalar, Dynamic, 1> &u,
+ std::vector<JacobiRotation<Scalar> > &v_givens,
+ std::vector<JacobiRotation<Scalar> > &w_givens,
+ Matrix< Scalar, Dynamic, 1> &v,
+ Matrix< Scalar, Dynamic, 1> &w,
+ bool *sing)
+{
+ typedef DenseIndex Index;
+ const JacobiRotation<Scalar> IdentityRotation = JacobiRotation<Scalar>(1,0);
+
+ /* Local variables */
+ const Index m = s.rows();
+ const Index n = s.cols();
+ Index i, j=1;
+ Scalar temp;
+ JacobiRotation<Scalar> givens;
+
+ // r1updt had a broader usecase, but we don't use it here. And, more
+ // importantly, we can not test it.
+ eigen_assert(m==n);
+ eigen_assert(u.size()==m);
+ eigen_assert(v.size()==n);
+ eigen_assert(w.size()==n);
+
+ /* move the nontrivial part of the last column of s into w. */
+ w[n-1] = s(n-1,n-1);
+
+ /* rotate the vector v into a multiple of the n-th unit vector */
+ /* in such a way that a spike is introduced into w. */
+ for (j=n-2; j>=0; --j) {
+ w[j] = 0.;
+ if (v[j] != 0.) {
+ /* determine a givens rotation which eliminates the */
+ /* j-th element of v. */
+ givens.makeGivens(-v[n-1], v[j]);
+
+ /* apply the transformation to v and store the information */
+ /* necessary to recover the givens rotation. */
+ v[n-1] = givens.s() * v[j] + givens.c() * v[n-1];
+ v_givens[j] = givens;
+
+ /* apply the transformation to s and extend the spike in w. */
+ for (i = j; i < m; ++i) {
+ temp = givens.c() * s(j,i) - givens.s() * w[i];
+ w[i] = givens.s() * s(j,i) + givens.c() * w[i];
+ s(j,i) = temp;
+ }
+ } else
+ v_givens[j] = IdentityRotation;
+ }
+
+ /* add the spike from the rank 1 update to w. */
+ w += v[n-1] * u;
+
+ /* eliminate the spike. */
+ *sing = false;
+ for (j = 0; j < n-1; ++j) {
+ if (w[j] != 0.) {
+ /* determine a givens rotation which eliminates the */
+ /* j-th element of the spike. */
+ givens.makeGivens(-s(j,j), w[j]);
+
+ /* apply the transformation to s and reduce the spike in w. */
+ for (i = j; i < m; ++i) {
+ temp = givens.c() * s(j,i) + givens.s() * w[i];
+ w[i] = -givens.s() * s(j,i) + givens.c() * w[i];
+ s(j,i) = temp;
+ }
+
+ /* store the information necessary to recover the */
+ /* givens rotation. */
+ w_givens[j] = givens;
+ } else
+ v_givens[j] = IdentityRotation;
+
+ /* test for zero diagonal elements in the output s. */
+ if (s(j,j) == 0.) {
+ *sing = true;
+ }
+ }
+ /* move w back into the last column of the output s. */
+ s(n-1,n-1) = w[n-1];
+
+ if (s(j,j) == 0.) {
+ *sing = true;
+ }
+ return;
+}
+
+} // end namespace internal
+
+} // end namespace Eigen
diff --git a/unsupported/Eigen/src/NonLinearOptimization/rwupdt.h b/unsupported/Eigen/src/NonLinearOptimization/rwupdt.h
new file mode 100644
index 0000000..f9ca504
--- /dev/null
+++ b/unsupported/Eigen/src/NonLinearOptimization/rwupdt.h
@@ -0,0 +1,51 @@
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+
+template <typename Scalar>
+void rwupdt(
+ Matrix< Scalar, Dynamic, Dynamic > &r,
+ const Matrix< Scalar, Dynamic, 1> &w,
+ Matrix< Scalar, Dynamic, 1> &b,
+ Scalar alpha)
+{
+ typedef DenseIndex Index;
+
+ const Index n = r.cols();
+ eigen_assert(r.rows()>=n);
+ std::vector<JacobiRotation<Scalar> > givens(n);
+
+ /* Local variables */
+ Scalar temp, rowj;
+
+ /* Function Body */
+ for (Index j = 0; j < n; ++j) {
+ rowj = w[j];
+
+ /* apply the previous transformations to */
+ /* r(i,j), i=0,1,...,j-1, and to w(j). */
+ for (Index i = 0; i < j; ++i) {
+ temp = givens[i].c() * r(i,j) + givens[i].s() * rowj;
+ rowj = -givens[i].s() * r(i,j) + givens[i].c() * rowj;
+ r(i,j) = temp;
+ }
+
+ /* determine a givens rotation which eliminates w(j). */
+ givens[j].makeGivens(-r(j,j), rowj);
+
+ if (rowj == 0.)
+ continue; // givens[j] is identity
+
+ /* apply the current transformation to r(j,j), b(j), and alpha. */
+ r(j,j) = givens[j].c() * r(j,j) + givens[j].s() * rowj;
+ temp = givens[j].c() * b[j] + givens[j].s() * alpha;
+ alpha = -givens[j].s() * b[j] + givens[j].c() * alpha;
+ b[j] = temp;
+ }
+}
+
+} // end namespace internal
+
+} // end namespace Eigen
diff --git a/unsupported/Eigen/src/NumericalDiff/InternalHeaderCheck.h b/unsupported/Eigen/src/NumericalDiff/InternalHeaderCheck.h
new file mode 100644
index 0000000..8c513d2
--- /dev/null
+++ b/unsupported/Eigen/src/NumericalDiff/InternalHeaderCheck.h
@@ -0,0 +1,3 @@
+#ifndef EIGEN_NUMERICALDIFF_MODULE_H
+#error "Please include unsupported/Eigen/NumericalDiff instead of including headers inside the src directory directly."
+#endif
diff --git a/unsupported/Eigen/src/NumericalDiff/NumericalDiff.h b/unsupported/Eigen/src/NumericalDiff/NumericalDiff.h
new file mode 100644
index 0000000..daa4210
--- /dev/null
+++ b/unsupported/Eigen/src/NumericalDiff/NumericalDiff.h
@@ -0,0 +1,132 @@
+// -*- coding: utf-8
+// vim: set fileencoding=utf-8
+
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009 Thomas Capricelli <orzel@freehackers.org>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_NUMERICAL_DIFF_H
+#define EIGEN_NUMERICAL_DIFF_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+enum NumericalDiffMode {
+ Forward,
+ Central
+};
+
+
+/**
+ * This class allows you to add a method df() to your functor, which will
+ * use numerical differentiation to compute an approximate of the
+ * derivative for the functor. Of course, if you have an analytical form
+ * for the derivative, you should rather implement df() by yourself.
+ *
+ * More information on
+ * http://en.wikipedia.org/wiki/Numerical_differentiation
+ *
+ * Currently only "Forward" and "Central" scheme are implemented.
+ */
+template<typename Functor_, NumericalDiffMode mode=Forward>
+class NumericalDiff : public Functor_
+{
+public:
+ typedef Functor_ Functor;
+ typedef typename Functor::Scalar Scalar;
+ typedef typename Functor::InputType InputType;
+ typedef typename Functor::ValueType ValueType;
+ typedef typename Functor::JacobianType JacobianType;
+
+ NumericalDiff(Scalar _epsfcn=0.) : Functor(), epsfcn(_epsfcn) {}
+ NumericalDiff(const Functor& f, Scalar _epsfcn=0.) : Functor(f), epsfcn(_epsfcn) {}
+
+ // forward constructors
+ template<typename T0>
+ NumericalDiff(const T0& a0) : Functor(a0), epsfcn(0) {}
+ template<typename T0, typename T1>
+ NumericalDiff(const T0& a0, const T1& a1) : Functor(a0, a1), epsfcn(0) {}
+ template<typename T0, typename T1, typename T2>
+ NumericalDiff(const T0& a0, const T1& a1, const T2& a2) : Functor(a0, a1, a2), epsfcn(0) {}
+
+ enum {
+ InputsAtCompileTime = Functor::InputsAtCompileTime,
+ ValuesAtCompileTime = Functor::ValuesAtCompileTime
+ };
+
+ /**
+ * return the number of evaluation of functor
+ */
+ int df(const InputType& _x, JacobianType &jac) const
+ {
+ using std::sqrt;
+ using std::abs;
+ /* Local variables */
+ Scalar h;
+ int nfev=0;
+ const typename InputType::Index n = _x.size();
+ const Scalar eps = sqrt(((std::max)(epsfcn,NumTraits<Scalar>::epsilon() )));
+ ValueType val1, val2;
+ InputType x = _x;
+ // TODO : we should do this only if the size is not already known
+ val1.resize(Functor::values());
+ val2.resize(Functor::values());
+
+ // initialization
+ switch(mode) {
+ case Forward:
+ // compute f(x)
+ Functor::operator()(x, val1); nfev++;
+ break;
+ case Central:
+ // do nothing
+ break;
+ default:
+ eigen_assert(false);
+ };
+
+ // Function Body
+ for (int j = 0; j < n; ++j) {
+ h = eps * abs(x[j]);
+ if (h == 0.) {
+ h = eps;
+ }
+ switch(mode) {
+ case Forward:
+ x[j] += h;
+ Functor::operator()(x, val2);
+ nfev++;
+ x[j] = _x[j];
+ jac.col(j) = (val2-val1)/h;
+ break;
+ case Central:
+ x[j] += h;
+ Functor::operator()(x, val2); nfev++;
+ x[j] -= 2*h;
+ Functor::operator()(x, val1); nfev++;
+ x[j] = _x[j];
+ jac.col(j) = (val2-val1)/(2*h);
+ break;
+ default:
+ eigen_assert(false);
+ };
+ }
+ return nfev;
+ }
+private:
+ Scalar epsfcn;
+
+ NumericalDiff& operator=(const NumericalDiff&);
+};
+
+} // end namespace Eigen
+
+//vim: ai ts=4 sts=4 et sw=4
+#endif // EIGEN_NUMERICAL_DIFF_H
+
diff --git a/unsupported/Eigen/src/Polynomials/Companion.h b/unsupported/Eigen/src/Polynomials/Companion.h
new file mode 100644
index 0000000..23c281a
--- /dev/null
+++ b/unsupported/Eigen/src/Polynomials/Companion.h
@@ -0,0 +1,282 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2010 Manuel Yguel <manuel.yguel@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_COMPANION_H
+#define EIGEN_COMPANION_H
+
+// This file requires the user to include
+// * Eigen/Core
+// * Eigen/src/PolynomialSolver.h
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+
+#ifndef EIGEN_PARSED_BY_DOXYGEN
+
+template<int Size>
+struct decrement_if_fixed_size
+{
+ enum {
+ ret = (Size == Dynamic) ? Dynamic : Size-1 };
+};
+
+#endif
+
+template< typename Scalar_, int Deg_ >
+class companion
+{
+ public:
+ EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE(Scalar_,Deg_==Dynamic ? Dynamic : Deg_)
+
+ enum {
+ Deg = Deg_,
+ Deg_1=decrement_if_fixed_size<Deg>::ret
+ };
+
+ typedef Scalar_ Scalar;
+ typedef typename NumTraits<Scalar>::Real RealScalar;
+ typedef Matrix<Scalar, Deg, 1> RightColumn;
+ //typedef DiagonalMatrix< Scalar, Deg_1, Deg_1 > BottomLeftDiagonal;
+ typedef Matrix<Scalar, Deg_1, 1> BottomLeftDiagonal;
+
+ typedef Matrix<Scalar, Deg, Deg> DenseCompanionMatrixType;
+ typedef Matrix< Scalar, Deg_, Deg_1 > LeftBlock;
+ typedef Matrix< Scalar, Deg_1, Deg_1 > BottomLeftBlock;
+ typedef Matrix< Scalar, 1, Deg_1 > LeftBlockFirstRow;
+
+ typedef DenseIndex Index;
+
+ public:
+ EIGEN_STRONG_INLINE const Scalar_ operator()(Index row, Index col ) const
+ {
+ if( m_bl_diag.rows() > col )
+ {
+ if( 0 < row ){ return m_bl_diag[col]; }
+ else{ return 0; }
+ }
+ else{ return m_monic[row]; }
+ }
+
+ public:
+ template<typename VectorType>
+ void setPolynomial( const VectorType& poly )
+ {
+ const Index deg = poly.size()-1;
+ m_monic = -poly.head(deg)/poly[deg];
+ m_bl_diag.setOnes(deg-1);
+ }
+
+ template<typename VectorType>
+ companion( const VectorType& poly ){
+ setPolynomial( poly ); }
+
+ public:
+ DenseCompanionMatrixType denseMatrix() const
+ {
+ const Index deg = m_monic.size();
+ const Index deg_1 = deg-1;
+ DenseCompanionMatrixType companMat(deg,deg);
+ companMat <<
+ ( LeftBlock(deg,deg_1)
+ << LeftBlockFirstRow::Zero(1,deg_1),
+ BottomLeftBlock::Identity(deg-1,deg-1)*m_bl_diag.asDiagonal() ).finished()
+ , m_monic;
+ return companMat;
+ }
+
+
+
+ protected:
+ /** Helper function for the balancing algorithm.
+ * \returns true if the row and the column, having colNorm and rowNorm
+ * as norms, are balanced, false otherwise.
+ * colB and rowB are respectively the multipliers for
+ * the column and the row in order to balance them.
+ * */
+ bool balanced( RealScalar colNorm, RealScalar rowNorm,
+ bool& isBalanced, RealScalar& colB, RealScalar& rowB );
+
+ /** Helper function for the balancing algorithm.
+ * \returns true if the row and the column, having colNorm and rowNorm
+ * as norms, are balanced, false otherwise.
+ * colB and rowB are respectively the multipliers for
+ * the column and the row in order to balance them.
+ * */
+ bool balancedR( RealScalar colNorm, RealScalar rowNorm,
+ bool& isBalanced, RealScalar& colB, RealScalar& rowB );
+
+ public:
+ /**
+ * Balancing algorithm from B. N. PARLETT and C. REINSCH (1969)
+ * "Balancing a matrix for calculation of eigenvalues and eigenvectors"
+ * adapted to the case of companion matrices.
+ * A matrix with non zero row and non zero column is balanced
+ * for a certain norm if the i-th row and the i-th column
+ * have same norm for all i.
+ */
+ void balance();
+
+ protected:
+ RightColumn m_monic;
+ BottomLeftDiagonal m_bl_diag;
+};
+
+
+
+template< typename Scalar_, int Deg_ >
+inline
+bool companion<Scalar_,Deg_>::balanced( RealScalar colNorm, RealScalar rowNorm,
+ bool& isBalanced, RealScalar& colB, RealScalar& rowB )
+{
+ if( RealScalar(0) == colNorm || RealScalar(0) == rowNorm
+ || !(numext::isfinite)(colNorm) || !(numext::isfinite)(rowNorm)){
+ return true;
+ }
+ else
+ {
+ //To find the balancing coefficients, if the radix is 2,
+ //one finds \f$ \sigma \f$ such that
+ // \f$ 2^{2\sigma-1} < rowNorm / colNorm \le 2^{2\sigma+1} \f$
+ // then the balancing coefficient for the row is \f$ 1/2^{\sigma} \f$
+ // and the balancing coefficient for the column is \f$ 2^{\sigma} \f$
+ const RealScalar radix = RealScalar(2);
+ const RealScalar radix2 = RealScalar(4);
+
+ rowB = rowNorm / radix;
+ colB = RealScalar(1);
+ const RealScalar s = colNorm + rowNorm;
+
+ // Find sigma s.t. rowNorm / 2 <= 2^(2*sigma) * colNorm
+ RealScalar scout = colNorm;
+ while (scout < rowB)
+ {
+ colB *= radix;
+ scout *= radix2;
+ }
+
+ // We now have an upper-bound for sigma, try to lower it.
+ // Find sigma s.t. 2^(2*sigma) * colNorm / 2 < rowNorm
+ scout = colNorm * (colB / radix) * colB; // Avoid overflow.
+ while (scout >= rowNorm)
+ {
+ colB /= radix;
+ scout /= radix2;
+ }
+
+ // This line is used to avoid insubstantial balancing.
+ if ((rowNorm + radix * scout) < RealScalar(0.95) * s * colB)
+ {
+ isBalanced = false;
+ rowB = RealScalar(1) / colB;
+ return false;
+ }
+ else
+ {
+ return true;
+ }
+ }
+}
+
+template< typename Scalar_, int Deg_ >
+inline
+bool companion<Scalar_,Deg_>::balancedR( RealScalar colNorm, RealScalar rowNorm,
+ bool& isBalanced, RealScalar& colB, RealScalar& rowB )
+{
+ if( RealScalar(0) == colNorm || RealScalar(0) == rowNorm ){ return true; }
+ else
+ {
+ /**
+ * Set the norm of the column and the row to the geometric mean
+ * of the row and column norm
+ */
+ const RealScalar q = colNorm/rowNorm;
+ if( !isApprox( q, Scalar_(1) ) )
+ {
+ rowB = sqrt( colNorm/rowNorm );
+ colB = RealScalar(1)/rowB;
+
+ isBalanced = false;
+ return false;
+ }
+ else{
+ return true; }
+ }
+}
+
+
+template< typename Scalar_, int Deg_ >
+void companion<Scalar_,Deg_>::balance()
+{
+ using std::abs;
+ EIGEN_STATIC_ASSERT( Deg == Dynamic || 1 < Deg, YOU_MADE_A_PROGRAMMING_MISTAKE );
+ const Index deg = m_monic.size();
+ const Index deg_1 = deg-1;
+
+ bool hasConverged=false;
+ while( !hasConverged )
+ {
+ hasConverged = true;
+ RealScalar colNorm,rowNorm;
+ RealScalar colB,rowB;
+
+ //First row, first column excluding the diagonal
+ //==============================================
+ colNorm = abs(m_bl_diag[0]);
+ rowNorm = abs(m_monic[0]);
+
+ //Compute balancing of the row and the column
+ if( !balanced( colNorm, rowNorm, hasConverged, colB, rowB ) )
+ {
+ m_bl_diag[0] *= colB;
+ m_monic[0] *= rowB;
+ }
+
+ //Middle rows and columns excluding the diagonal
+ //==============================================
+ for( Index i=1; i<deg_1; ++i )
+ {
+ // column norm, excluding the diagonal
+ colNorm = abs(m_bl_diag[i]);
+
+ // row norm, excluding the diagonal
+ rowNorm = abs(m_bl_diag[i-1]) + abs(m_monic[i]);
+
+ //Compute balancing of the row and the column
+ if( !balanced( colNorm, rowNorm, hasConverged, colB, rowB ) )
+ {
+ m_bl_diag[i] *= colB;
+ m_bl_diag[i-1] *= rowB;
+ m_monic[i] *= rowB;
+ }
+ }
+
+ //Last row, last column excluding the diagonal
+ //============================================
+ const Index ebl = m_bl_diag.size()-1;
+ VectorBlock<RightColumn,Deg_1> headMonic( m_monic, 0, deg_1 );
+ colNorm = headMonic.array().abs().sum();
+ rowNorm = abs( m_bl_diag[ebl] );
+
+ //Compute balancing of the row and the column
+ if( !balanced( colNorm, rowNorm, hasConverged, colB, rowB ) )
+ {
+ headMonic *= colB;
+ m_bl_diag[ebl] *= rowB;
+ }
+ }
+}
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_COMPANION_H
diff --git a/unsupported/Eigen/src/Polynomials/InternalHeaderCheck.h b/unsupported/Eigen/src/Polynomials/InternalHeaderCheck.h
new file mode 100644
index 0000000..b3aa50c
--- /dev/null
+++ b/unsupported/Eigen/src/Polynomials/InternalHeaderCheck.h
@@ -0,0 +1,3 @@
+#ifndef EIGEN_POLYNOMIALS_MODULE_H
+#error "Please include unsupported/Eigen/Polynomials instead of including headers inside the src directory directly."
+#endif
diff --git a/unsupported/Eigen/src/Polynomials/PolynomialSolver.h b/unsupported/Eigen/src/Polynomials/PolynomialSolver.h
new file mode 100644
index 0000000..64cab12
--- /dev/null
+++ b/unsupported/Eigen/src/Polynomials/PolynomialSolver.h
@@ -0,0 +1,430 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2010 Manuel Yguel <manuel.yguel@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_POLYNOMIAL_SOLVER_H
+#define EIGEN_POLYNOMIAL_SOLVER_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+/** \ingroup Polynomials_Module
+ * \class PolynomialSolverBase.
+ *
+ * \brief Defined to be inherited by polynomial solvers: it provides
+ * convenient methods such as
+ * - real roots,
+ * - greatest, smallest complex roots,
+ * - real roots with greatest, smallest absolute real value,
+ * - greatest, smallest real roots.
+ *
+ * It stores the set of roots as a vector of complexes.
+ *
+ */
+template< typename Scalar_, int Deg_ >
+class PolynomialSolverBase
+{
+ public:
+ EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE(Scalar_,Deg_==Dynamic ? Dynamic : Deg_)
+
+ typedef Scalar_ Scalar;
+ typedef typename NumTraits<Scalar>::Real RealScalar;
+ typedef std::complex<RealScalar> RootType;
+ typedef Matrix<RootType,Deg_,1> RootsType;
+
+ typedef DenseIndex Index;
+
+ protected:
+ template< typename OtherPolynomial >
+ inline void setPolynomial( const OtherPolynomial& poly ){
+ m_roots.resize(poly.size()-1); }
+
+ public:
+ template< typename OtherPolynomial >
+ inline PolynomialSolverBase( const OtherPolynomial& poly ){
+ setPolynomial( poly() ); }
+
+ inline PolynomialSolverBase(){}
+
+ public:
+ /** \returns the complex roots of the polynomial */
+ inline const RootsType& roots() const { return m_roots; }
+
+ public:
+ /** Clear and fills the back insertion sequence with the real roots of the polynomial
+ * i.e. the real part of the complex roots that have an imaginary part which
+ * absolute value is smaller than absImaginaryThreshold.
+ * absImaginaryThreshold takes the dummy_precision associated
+ * with the Scalar_ template parameter of the PolynomialSolver class as the default value.
+ *
+ * \param[out] bi_seq : the back insertion sequence (stl concept)
+ * \param[in] absImaginaryThreshold : the maximum bound of the imaginary part of a complex
+ * number that is considered as real.
+ * */
+ template<typename Stl_back_insertion_sequence>
+ inline void realRoots( Stl_back_insertion_sequence& bi_seq,
+ const RealScalar& absImaginaryThreshold = NumTraits<Scalar>::dummy_precision() ) const
+ {
+ using std::abs;
+ bi_seq.clear();
+ for(Index i=0; i<m_roots.size(); ++i )
+ {
+ if( abs( m_roots[i].imag() ) < absImaginaryThreshold ){
+ bi_seq.push_back( m_roots[i].real() ); }
+ }
+ }
+
+ protected:
+ template<typename squaredNormBinaryPredicate>
+ inline const RootType& selectComplexRoot_withRespectToNorm( squaredNormBinaryPredicate& pred ) const
+ {
+ Index res=0;
+ RealScalar norm2 = numext::abs2( m_roots[0] );
+ for( Index i=1; i<m_roots.size(); ++i )
+ {
+ const RealScalar currNorm2 = numext::abs2( m_roots[i] );
+ if( pred( currNorm2, norm2 ) ){
+ res=i; norm2=currNorm2; }
+ }
+ return m_roots[res];
+ }
+
+ public:
+ /**
+ * \returns the complex root with greatest norm.
+ */
+ inline const RootType& greatestRoot() const
+ {
+ std::greater<RealScalar> greater;
+ return selectComplexRoot_withRespectToNorm( greater );
+ }
+
+ /**
+ * \returns the complex root with smallest norm.
+ */
+ inline const RootType& smallestRoot() const
+ {
+ std::less<RealScalar> less;
+ return selectComplexRoot_withRespectToNorm( less );
+ }
+
+ protected:
+ template<typename squaredRealPartBinaryPredicate>
+ inline const RealScalar& selectRealRoot_withRespectToAbsRealPart(
+ squaredRealPartBinaryPredicate& pred,
+ bool& hasArealRoot,
+ const RealScalar& absImaginaryThreshold = NumTraits<Scalar>::dummy_precision() ) const
+ {
+ using std::abs;
+ hasArealRoot = false;
+ Index res=0;
+ RealScalar abs2(0);
+
+ for( Index i=0; i<m_roots.size(); ++i )
+ {
+ if( abs( m_roots[i].imag() ) <= absImaginaryThreshold )
+ {
+ if( !hasArealRoot )
+ {
+ hasArealRoot = true;
+ res = i;
+ abs2 = m_roots[i].real() * m_roots[i].real();
+ }
+ else
+ {
+ const RealScalar currAbs2 = m_roots[i].real() * m_roots[i].real();
+ if( pred( currAbs2, abs2 ) )
+ {
+ abs2 = currAbs2;
+ res = i;
+ }
+ }
+ }
+ else if(!hasArealRoot)
+ {
+ if( abs( m_roots[i].imag() ) < abs( m_roots[res].imag() ) ){
+ res = i;}
+ }
+ }
+ return numext::real_ref(m_roots[res]);
+ }
+
+
+ template<typename RealPartBinaryPredicate>
+ inline const RealScalar& selectRealRoot_withRespectToRealPart(
+ RealPartBinaryPredicate& pred,
+ bool& hasArealRoot,
+ const RealScalar& absImaginaryThreshold = NumTraits<Scalar>::dummy_precision() ) const
+ {
+ using std::abs;
+ hasArealRoot = false;
+ Index res=0;
+ RealScalar val(0);
+
+ for( Index i=0; i<m_roots.size(); ++i )
+ {
+ if( abs( m_roots[i].imag() ) <= absImaginaryThreshold )
+ {
+ if( !hasArealRoot )
+ {
+ hasArealRoot = true;
+ res = i;
+ val = m_roots[i].real();
+ }
+ else
+ {
+ const RealScalar curr = m_roots[i].real();
+ if( pred( curr, val ) )
+ {
+ val = curr;
+ res = i;
+ }
+ }
+ }
+ else
+ {
+ if( abs( m_roots[i].imag() ) < abs( m_roots[res].imag() ) ){
+ res = i; }
+ }
+ }
+ return numext::real_ref(m_roots[res]);
+ }
+
+ public:
+ /**
+ * \returns a real root with greatest absolute magnitude.
+ * A real root is defined as the real part of a complex root with absolute imaginary
+ * part smallest than absImaginaryThreshold.
+ * absImaginaryThreshold takes the dummy_precision associated
+ * with the Scalar_ template parameter of the PolynomialSolver class as the default value.
+ * If no real root is found the boolean hasArealRoot is set to false and the real part of
+ * the root with smallest absolute imaginary part is returned instead.
+ *
+ * \param[out] hasArealRoot : boolean true if a real root is found according to the
+ * absImaginaryThreshold criterion, false otherwise.
+ * \param[in] absImaginaryThreshold : threshold on the absolute imaginary part to decide
+ * whether or not a root is real.
+ */
+ inline const RealScalar& absGreatestRealRoot(
+ bool& hasArealRoot,
+ const RealScalar& absImaginaryThreshold = NumTraits<Scalar>::dummy_precision() ) const
+ {
+ std::greater<RealScalar> greater;
+ return selectRealRoot_withRespectToAbsRealPart( greater, hasArealRoot, absImaginaryThreshold );
+ }
+
+
+ /**
+ * \returns a real root with smallest absolute magnitude.
+ * A real root is defined as the real part of a complex root with absolute imaginary
+ * part smallest than absImaginaryThreshold.
+ * absImaginaryThreshold takes the dummy_precision associated
+ * with the Scalar_ template parameter of the PolynomialSolver class as the default value.
+ * If no real root is found the boolean hasArealRoot is set to false and the real part of
+ * the root with smallest absolute imaginary part is returned instead.
+ *
+ * \param[out] hasArealRoot : boolean true if a real root is found according to the
+ * absImaginaryThreshold criterion, false otherwise.
+ * \param[in] absImaginaryThreshold : threshold on the absolute imaginary part to decide
+ * whether or not a root is real.
+ */
+ inline const RealScalar& absSmallestRealRoot(
+ bool& hasArealRoot,
+ const RealScalar& absImaginaryThreshold = NumTraits<Scalar>::dummy_precision() ) const
+ {
+ std::less<RealScalar> less;
+ return selectRealRoot_withRespectToAbsRealPart( less, hasArealRoot, absImaginaryThreshold );
+ }
+
+
+ /**
+ * \returns the real root with greatest value.
+ * A real root is defined as the real part of a complex root with absolute imaginary
+ * part smallest than absImaginaryThreshold.
+ * absImaginaryThreshold takes the dummy_precision associated
+ * with the Scalar_ template parameter of the PolynomialSolver class as the default value.
+ * If no real root is found the boolean hasArealRoot is set to false and the real part of
+ * the root with smallest absolute imaginary part is returned instead.
+ *
+ * \param[out] hasArealRoot : boolean true if a real root is found according to the
+ * absImaginaryThreshold criterion, false otherwise.
+ * \param[in] absImaginaryThreshold : threshold on the absolute imaginary part to decide
+ * whether or not a root is real.
+ */
+ inline const RealScalar& greatestRealRoot(
+ bool& hasArealRoot,
+ const RealScalar& absImaginaryThreshold = NumTraits<Scalar>::dummy_precision() ) const
+ {
+ std::greater<RealScalar> greater;
+ return selectRealRoot_withRespectToRealPart( greater, hasArealRoot, absImaginaryThreshold );
+ }
+
+
+ /**
+ * \returns the real root with smallest value.
+ * A real root is defined as the real part of a complex root with absolute imaginary
+ * part smallest than absImaginaryThreshold.
+ * absImaginaryThreshold takes the dummy_precision associated
+ * with the Scalar_ template parameter of the PolynomialSolver class as the default value.
+ * If no real root is found the boolean hasArealRoot is set to false and the real part of
+ * the root with smallest absolute imaginary part is returned instead.
+ *
+ * \param[out] hasArealRoot : boolean true if a real root is found according to the
+ * absImaginaryThreshold criterion, false otherwise.
+ * \param[in] absImaginaryThreshold : threshold on the absolute imaginary part to decide
+ * whether or not a root is real.
+ */
+ inline const RealScalar& smallestRealRoot(
+ bool& hasArealRoot,
+ const RealScalar& absImaginaryThreshold = NumTraits<Scalar>::dummy_precision() ) const
+ {
+ std::less<RealScalar> less;
+ return selectRealRoot_withRespectToRealPart( less, hasArealRoot, absImaginaryThreshold );
+ }
+
+ protected:
+ RootsType m_roots;
+};
+
+#define EIGEN_POLYNOMIAL_SOLVER_BASE_INHERITED_TYPES( BASE ) \
+ typedef typename BASE::Scalar Scalar; \
+ typedef typename BASE::RealScalar RealScalar; \
+ typedef typename BASE::RootType RootType; \
+ typedef typename BASE::RootsType RootsType;
+
+
+
+/** \ingroup Polynomials_Module
+ *
+ * \class PolynomialSolver
+ *
+ * \brief A polynomial solver
+ *
+ * Computes the complex roots of a real polynomial.
+ *
+ * \param Scalar_ the scalar type, i.e., the type of the polynomial coefficients
+ * \param Deg_ the degree of the polynomial, can be a compile time value or Dynamic.
+ * Notice that the number of polynomial coefficients is Deg_+1.
+ *
+ * This class implements a polynomial solver and provides convenient methods such as
+ * - real roots,
+ * - greatest, smallest complex roots,
+ * - real roots with greatest, smallest absolute real value.
+ * - greatest, smallest real roots.
+ *
+ * WARNING: this polynomial solver is experimental, part of the unsupported Eigen modules.
+ *
+ *
+ * Currently a QR algorithm is used to compute the eigenvalues of the companion matrix of
+ * the polynomial to compute its roots.
+ * This supposes that the complex moduli of the roots are all distinct: e.g. there should
+ * be no multiple roots or conjugate roots for instance.
+ * With 32bit (float) floating types this problem shows up frequently.
+ * However, almost always, correct accuracy is reached even in these cases for 64bit
+ * (double) floating types and small polynomial degree (<20).
+ */
+template<typename Scalar_, int Deg_>
+class PolynomialSolver : public PolynomialSolverBase<Scalar_,Deg_>
+{
+ public:
+ EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE(Scalar_,Deg_==Dynamic ? Dynamic : Deg_)
+
+ typedef PolynomialSolverBase<Scalar_,Deg_> PS_Base;
+ EIGEN_POLYNOMIAL_SOLVER_BASE_INHERITED_TYPES( PS_Base )
+
+ typedef Matrix<Scalar,Deg_,Deg_> CompanionMatrixType;
+ typedef std::conditional_t<NumTraits<Scalar>::IsComplex,
+ ComplexEigenSolver<CompanionMatrixType>,
+ EigenSolver<CompanionMatrixType> > EigenSolverType;
+ typedef std::conditional_t<NumTraits<Scalar>::IsComplex, Scalar, std::complex<Scalar> > ComplexScalar;
+
+ public:
+ /** Computes the complex roots of a new polynomial. */
+ template< typename OtherPolynomial >
+ void compute( const OtherPolynomial& poly )
+ {
+ eigen_assert( Scalar(0) != poly[poly.size()-1] );
+ eigen_assert( poly.size() > 1 );
+ if(poly.size() > 2 )
+ {
+ internal::companion<Scalar,Deg_> companion( poly );
+ companion.balance();
+ m_eigenSolver.compute( companion.denseMatrix() );
+ m_roots = m_eigenSolver.eigenvalues();
+ // cleanup noise in imaginary part of real roots:
+ // if the imaginary part is rather small compared to the real part
+ // and that cancelling the imaginary part yield a smaller evaluation,
+ // then it's safe to keep the real part only.
+ RealScalar coarse_prec = RealScalar(std::pow(4,poly.size()+1))*NumTraits<RealScalar>::epsilon();
+ for(Index i = 0; i<m_roots.size(); ++i)
+ {
+ if( internal::isMuchSmallerThan(numext::abs(numext::imag(m_roots[i])),
+ numext::abs(numext::real(m_roots[i])),
+ coarse_prec) )
+ {
+ ComplexScalar as_real_root = ComplexScalar(numext::real(m_roots[i]));
+ if( numext::abs(poly_eval(poly, as_real_root))
+ <= numext::abs(poly_eval(poly, m_roots[i])))
+ {
+ m_roots[i] = as_real_root;
+ }
+ }
+ }
+ }
+ else if(poly.size () == 2)
+ {
+ m_roots.resize(1);
+ m_roots[0] = -poly[0]/poly[1];
+ }
+ }
+
+ public:
+ template< typename OtherPolynomial >
+ inline PolynomialSolver( const OtherPolynomial& poly ){
+ compute( poly ); }
+
+ inline PolynomialSolver(){}
+
+ protected:
+ using PS_Base::m_roots;
+ EigenSolverType m_eigenSolver;
+};
+
+
+template< typename Scalar_ >
+class PolynomialSolver<Scalar_,1> : public PolynomialSolverBase<Scalar_,1>
+{
+ public:
+ typedef PolynomialSolverBase<Scalar_,1> PS_Base;
+ EIGEN_POLYNOMIAL_SOLVER_BASE_INHERITED_TYPES( PS_Base )
+
+ public:
+ /** Computes the complex roots of a new polynomial. */
+ template< typename OtherPolynomial >
+ void compute( const OtherPolynomial& poly )
+ {
+ eigen_assert( poly.size() == 2 );
+ eigen_assert( Scalar(0) != poly[1] );
+ m_roots[0] = -poly[0]/poly[1];
+ }
+
+ public:
+ template< typename OtherPolynomial >
+ inline PolynomialSolver( const OtherPolynomial& poly ){
+ compute( poly ); }
+
+ inline PolynomialSolver(){}
+
+ protected:
+ using PS_Base::m_roots;
+};
+
+} // end namespace Eigen
+
+#endif // EIGEN_POLYNOMIAL_SOLVER_H
diff --git a/unsupported/Eigen/src/Polynomials/PolynomialUtils.h b/unsupported/Eigen/src/Polynomials/PolynomialUtils.h
new file mode 100644
index 0000000..6af8613
--- /dev/null
+++ b/unsupported/Eigen/src/Polynomials/PolynomialUtils.h
@@ -0,0 +1,145 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2010 Manuel Yguel <manuel.yguel@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_POLYNOMIAL_UTILS_H
+#define EIGEN_POLYNOMIAL_UTILS_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+/** \ingroup Polynomials_Module
+ * \returns the evaluation of the polynomial at x using Horner algorithm.
+ *
+ * \param[in] poly : the vector of coefficients of the polynomial ordered
+ * by degrees i.e. poly[i] is the coefficient of degree i of the polynomial
+ * e.g. \f$ 1 + 3x^2 \f$ is stored as a vector \f$ [ 1, 0, 3 ] \f$.
+ * \param[in] x : the value to evaluate the polynomial at.
+ *
+ * \note for stability:
+ * \f$ |x| \le 1 \f$
+ */
+template <typename Polynomials, typename T>
+inline
+T poly_eval_horner( const Polynomials& poly, const T& x )
+{
+ T val=poly[poly.size()-1];
+ for(DenseIndex i=poly.size()-2; i>=0; --i ){
+ val = val*x + poly[i]; }
+ return val;
+}
+
+/** \ingroup Polynomials_Module
+ * \returns the evaluation of the polynomial at x using stabilized Horner algorithm.
+ *
+ * \param[in] poly : the vector of coefficients of the polynomial ordered
+ * by degrees i.e. poly[i] is the coefficient of degree i of the polynomial
+ * e.g. \f$ 1 + 3x^2 \f$ is stored as a vector \f$ [ 1, 0, 3 ] \f$.
+ * \param[in] x : the value to evaluate the polynomial at.
+ */
+template <typename Polynomials, typename T>
+inline
+T poly_eval( const Polynomials& poly, const T& x )
+{
+ typedef typename NumTraits<T>::Real Real;
+
+ if( numext::abs2( x ) <= Real(1) ){
+ return poly_eval_horner( poly, x ); }
+ else
+ {
+ T val=poly[0];
+ T inv_x = T(1)/x;
+ for( DenseIndex i=1; i<poly.size(); ++i ){
+ val = val*inv_x + poly[i]; }
+
+ return numext::pow(x,(T)(poly.size()-1)) * val;
+ }
+}
+
+/** \ingroup Polynomials_Module
+ * \returns a maximum bound for the absolute value of any root of the polynomial.
+ *
+ * \param[in] poly : the vector of coefficients of the polynomial ordered
+ * by degrees i.e. poly[i] is the coefficient of degree i of the polynomial
+ * e.g. \f$ 1 + 3x^2 \f$ is stored as a vector \f$ [ 1, 0, 3 ] \f$.
+ *
+ * \pre
+ * the leading coefficient of the input polynomial poly must be non zero
+ */
+template <typename Polynomial>
+inline
+typename NumTraits<typename Polynomial::Scalar>::Real cauchy_max_bound( const Polynomial& poly )
+{
+ using std::abs;
+ typedef typename Polynomial::Scalar Scalar;
+ typedef typename NumTraits<Scalar>::Real Real;
+
+ eigen_assert( Scalar(0) != poly[poly.size()-1] );
+ const Scalar inv_leading_coeff = Scalar(1)/poly[poly.size()-1];
+ Real cb(0);
+
+ for( DenseIndex i=0; i<poly.size()-1; ++i ){
+ cb += abs(poly[i]*inv_leading_coeff); }
+ return cb + Real(1);
+}
+
+/** \ingroup Polynomials_Module
+ * \returns a minimum bound for the absolute value of any non zero root of the polynomial.
+ * \param[in] poly : the vector of coefficients of the polynomial ordered
+ * by degrees i.e. poly[i] is the coefficient of degree i of the polynomial
+ * e.g. \f$ 1 + 3x^2 \f$ is stored as a vector \f$ [ 1, 0, 3 ] \f$.
+ */
+template <typename Polynomial>
+inline
+typename NumTraits<typename Polynomial::Scalar>::Real cauchy_min_bound( const Polynomial& poly )
+{
+ using std::abs;
+ typedef typename Polynomial::Scalar Scalar;
+ typedef typename NumTraits<Scalar>::Real Real;
+
+ DenseIndex i=0;
+ while( i<poly.size()-1 && Scalar(0) == poly(i) ){ ++i; }
+ if( poly.size()-1 == i ){
+ return Real(1); }
+
+ const Scalar inv_min_coeff = Scalar(1)/poly[i];
+ Real cb(1);
+ for( DenseIndex j=i+1; j<poly.size(); ++j ){
+ cb += abs(poly[j]*inv_min_coeff); }
+ return Real(1)/cb;
+}
+
+/** \ingroup Polynomials_Module
+ * Given the roots of a polynomial compute the coefficients in the
+ * monomial basis of the monic polynomial with same roots and minimal degree.
+ * If RootVector is a vector of complexes, Polynomial should also be a vector
+ * of complexes.
+ * \param[in] rv : a vector containing the roots of a polynomial.
+ * \param[out] poly : the vector of coefficients of the polynomial ordered
+ * by degrees i.e. poly[i] is the coefficient of degree i of the polynomial
+ * e.g. \f$ 3 + x^2 \f$ is stored as a vector \f$ [ 3, 0, 1 ] \f$.
+ */
+template <typename RootVector, typename Polynomial>
+void roots_to_monicPolynomial( const RootVector& rv, Polynomial& poly )
+{
+
+ typedef typename Polynomial::Scalar Scalar;
+
+ poly.setZero( rv.size()+1 );
+ poly[0] = -rv[0]; poly[1] = Scalar(1);
+ for( DenseIndex i=1; i< rv.size(); ++i )
+ {
+ for( DenseIndex j=i+1; j>0; --j ){ poly[j] = poly[j-1] - rv[i]*poly[j]; }
+ poly[0] = -rv[i]*poly[0];
+ }
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_POLYNOMIAL_UTILS_H
diff --git a/unsupported/Eigen/src/Skyline/InternalHeaderCheck.h b/unsupported/Eigen/src/Skyline/InternalHeaderCheck.h
new file mode 100644
index 0000000..bddf0b0
--- /dev/null
+++ b/unsupported/Eigen/src/Skyline/InternalHeaderCheck.h
@@ -0,0 +1,3 @@
+#ifndef EIGEN_SKYLINE_MODULE_H
+#error "Please include unsupported/Eigen/Skyline instead of including headers inside the src directory directly."
+#endif
diff --git a/unsupported/Eigen/src/Skyline/SkylineInplaceLU.h b/unsupported/Eigen/src/Skyline/SkylineInplaceLU.h
new file mode 100644
index 0000000..ef90438
--- /dev/null
+++ b/unsupported/Eigen/src/Skyline/SkylineInplaceLU.h
@@ -0,0 +1,354 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008 Guillaume Saupin <guillaume.saupin@cea.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_SKYLINEINPLACELU_H
+#define EIGEN_SKYLINEINPLACELU_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+/** \ingroup Skyline_Module
+ *
+ * \class SkylineInplaceLU
+ *
+ * \brief Inplace LU decomposition of a skyline matrix and associated features
+ *
+ * \param MatrixType the type of the matrix of which we are computing the LU factorization
+ *
+ */
+template<typename MatrixType>
+class SkylineInplaceLU {
+protected:
+ typedef typename MatrixType::Scalar Scalar;
+ typedef typename MatrixType::Index Index;
+
+ typedef typename NumTraits<typename MatrixType::Scalar>::Real RealScalar;
+
+public:
+
+ /** Creates a LU object and compute the respective factorization of \a matrix using
+ * flags \a flags. */
+ SkylineInplaceLU(MatrixType& matrix, int flags = 0)
+ : /*m_matrix(matrix.rows(), matrix.cols()),*/ m_flags(flags), m_status(0), m_lu(matrix) {
+ m_precision = RealScalar(0.1) * Eigen::dummy_precision<RealScalar > ();
+ m_lu.IsRowMajor ? computeRowMajor() : compute();
+ }
+
+ /** Sets the relative threshold value used to prune zero coefficients during the decomposition.
+ *
+ * Setting a value greater than zero speeds up computation, and yields to an incomplete
+ * factorization with fewer non zero coefficients. Such approximate factors are especially
+ * useful to initialize an iterative solver.
+ *
+ * Note that the exact meaning of this parameter might depends on the actual
+ * backend. Moreover, not all backends support this feature.
+ *
+ * \sa precision() */
+ void setPrecision(RealScalar v) {
+ m_precision = v;
+ }
+
+ /** \returns the current precision.
+ *
+ * \sa setPrecision() */
+ RealScalar precision() const {
+ return m_precision;
+ }
+
+ /** Sets the flags. Possible values are:
+ * - CompleteFactorization
+ * - IncompleteFactorization
+ * - MemoryEfficient
+ * - one of the ordering methods
+ * - etc...
+ *
+ * \sa flags() */
+ void setFlags(int f) {
+ m_flags = f;
+ }
+
+ /** \returns the current flags */
+ int flags() const {
+ return m_flags;
+ }
+
+ void setOrderingMethod(int m) {
+ m_flags = m;
+ }
+
+ int orderingMethod() const {
+ return m_flags;
+ }
+
+ /** Computes/re-computes the LU factorization */
+ void compute();
+ void computeRowMajor();
+
+ /** \returns the lower triangular matrix L */
+ //inline const MatrixType& matrixL() const { return m_matrixL; }
+
+ /** \returns the upper triangular matrix U */
+ //inline const MatrixType& matrixU() const { return m_matrixU; }
+
+ template<typename BDerived, typename XDerived>
+ bool solve(const MatrixBase<BDerived> &b, MatrixBase<XDerived>* x,
+ const int transposed = 0) const;
+
+ /** \returns true if the factorization succeeded */
+ inline bool succeeded(void) const {
+ return m_succeeded;
+ }
+
+protected:
+ RealScalar m_precision;
+ int m_flags;
+ mutable int m_status;
+ bool m_succeeded;
+ MatrixType& m_lu;
+};
+
+/** Computes / recomputes the in place LU decomposition of the SkylineInplaceLU.
+ * using the default algorithm.
+ */
+template<typename MatrixType>
+//template<typename Scalar_>
+void SkylineInplaceLU<MatrixType>::compute() {
+ const size_t rows = m_lu.rows();
+ const size_t cols = m_lu.cols();
+
+ eigen_assert(rows == cols && "We do not (yet) support rectangular LU.");
+ eigen_assert(!m_lu.IsRowMajor && "LU decomposition does not work with rowMajor Storage");
+
+ for (Index row = 0; row < rows; row++) {
+ const double pivot = m_lu.coeffDiag(row);
+
+ //Lower matrix Columns update
+ const Index& col = row;
+ for (typename MatrixType::InnerLowerIterator lIt(m_lu, col); lIt; ++lIt) {
+ lIt.valueRef() /= pivot;
+ }
+
+ //Upper matrix update -> contiguous memory access
+ typename MatrixType::InnerLowerIterator lIt(m_lu, col);
+ for (Index rrow = row + 1; rrow < m_lu.rows(); rrow++) {
+ typename MatrixType::InnerUpperIterator uItPivot(m_lu, row);
+ typename MatrixType::InnerUpperIterator uIt(m_lu, rrow);
+ const double coef = lIt.value();
+
+ uItPivot += (rrow - row - 1);
+
+ //update upper part -> contiguous memory access
+ for (++uItPivot; uIt && uItPivot;) {
+ uIt.valueRef() -= uItPivot.value() * coef;
+
+ ++uIt;
+ ++uItPivot;
+ }
+ ++lIt;
+ }
+
+ //Upper matrix update -> non contiguous memory access
+ typename MatrixType::InnerLowerIterator lIt3(m_lu, col);
+ for (Index rrow = row + 1; rrow < m_lu.rows(); rrow++) {
+ typename MatrixType::InnerUpperIterator uItPivot(m_lu, row);
+ const double coef = lIt3.value();
+
+ //update lower part -> non contiguous memory access
+ for (Index i = 0; i < rrow - row - 1; i++) {
+ m_lu.coeffRefLower(rrow, row + i + 1) -= uItPivot.value() * coef;
+ ++uItPivot;
+ }
+ ++lIt3;
+ }
+ //update diag -> contiguous
+ typename MatrixType::InnerLowerIterator lIt2(m_lu, col);
+ for (Index rrow = row + 1; rrow < m_lu.rows(); rrow++) {
+
+ typename MatrixType::InnerUpperIterator uItPivot(m_lu, row);
+ typename MatrixType::InnerUpperIterator uIt(m_lu, rrow);
+ const double coef = lIt2.value();
+
+ uItPivot += (rrow - row - 1);
+ m_lu.coeffRefDiag(rrow) -= uItPivot.value() * coef;
+ ++lIt2;
+ }
+ }
+}
+
+template<typename MatrixType>
+void SkylineInplaceLU<MatrixType>::computeRowMajor() {
+ const size_t rows = m_lu.rows();
+ const size_t cols = m_lu.cols();
+
+ eigen_assert(rows == cols && "We do not (yet) support rectangular LU.");
+ eigen_assert(m_lu.IsRowMajor && "You're trying to apply rowMajor decomposition on a ColMajor matrix !");
+
+ for (Index row = 0; row < rows; row++) {
+ typename MatrixType::InnerLowerIterator llIt(m_lu, row);
+
+
+ for (Index col = llIt.col(); col < row; col++) {
+ if (m_lu.coeffExistLower(row, col)) {
+ const double diag = m_lu.coeffDiag(col);
+
+ typename MatrixType::InnerLowerIterator lIt(m_lu, row);
+ typename MatrixType::InnerUpperIterator uIt(m_lu, col);
+
+
+ const Index offset = lIt.col() - uIt.row();
+
+
+ Index stop = offset > 0 ? col - lIt.col() : col - uIt.row();
+
+ //#define VECTORIZE
+#ifdef VECTORIZE
+ Map<VectorXd > rowVal(lIt.valuePtr() + (offset > 0 ? 0 : -offset), stop);
+ Map<VectorXd > colVal(uIt.valuePtr() + (offset > 0 ? offset : 0), stop);
+
+
+ Scalar newCoeff = m_lu.coeffLower(row, col) - rowVal.dot(colVal);
+#else
+ if (offset > 0) //Skip zero value of lIt
+ uIt += offset;
+ else //Skip zero values of uIt
+ lIt += -offset;
+ Scalar newCoeff = m_lu.coeffLower(row, col);
+
+ for (Index k = 0; k < stop; ++k) {
+ const Scalar tmp = newCoeff;
+ newCoeff = tmp - lIt.value() * uIt.value();
+ ++lIt;
+ ++uIt;
+ }
+#endif
+
+ m_lu.coeffRefLower(row, col) = newCoeff / diag;
+ }
+ }
+
+ //Upper matrix update
+ const Index col = row;
+ typename MatrixType::InnerUpperIterator uuIt(m_lu, col);
+ for (Index rrow = uuIt.row(); rrow < col; rrow++) {
+
+ typename MatrixType::InnerLowerIterator lIt(m_lu, rrow);
+ typename MatrixType::InnerUpperIterator uIt(m_lu, col);
+ const Index offset = lIt.col() - uIt.row();
+
+ Index stop = offset > 0 ? rrow - lIt.col() : rrow - uIt.row();
+
+#ifdef VECTORIZE
+ Map<VectorXd > rowVal(lIt.valuePtr() + (offset > 0 ? 0 : -offset), stop);
+ Map<VectorXd > colVal(uIt.valuePtr() + (offset > 0 ? offset : 0), stop);
+
+ Scalar newCoeff = m_lu.coeffUpper(rrow, col) - rowVal.dot(colVal);
+#else
+ if (offset > 0) //Skip zero value of lIt
+ uIt += offset;
+ else //Skip zero values of uIt
+ lIt += -offset;
+ Scalar newCoeff = m_lu.coeffUpper(rrow, col);
+ for (Index k = 0; k < stop; ++k) {
+ const Scalar tmp = newCoeff;
+ newCoeff = tmp - lIt.value() * uIt.value();
+
+ ++lIt;
+ ++uIt;
+ }
+#endif
+ m_lu.coeffRefUpper(rrow, col) = newCoeff;
+ }
+
+
+ //Diag matrix update
+ typename MatrixType::InnerLowerIterator lIt(m_lu, row);
+ typename MatrixType::InnerUpperIterator uIt(m_lu, row);
+
+ const Index offset = lIt.col() - uIt.row();
+
+
+ Index stop = offset > 0 ? lIt.size() : uIt.size();
+#ifdef VECTORIZE
+ Map<VectorXd > rowVal(lIt.valuePtr() + (offset > 0 ? 0 : -offset), stop);
+ Map<VectorXd > colVal(uIt.valuePtr() + (offset > 0 ? offset : 0), stop);
+ Scalar newCoeff = m_lu.coeffDiag(row) - rowVal.dot(colVal);
+#else
+ if (offset > 0) //Skip zero value of lIt
+ uIt += offset;
+ else //Skip zero values of uIt
+ lIt += -offset;
+ Scalar newCoeff = m_lu.coeffDiag(row);
+ for (Index k = 0; k < stop; ++k) {
+ const Scalar tmp = newCoeff;
+ newCoeff = tmp - lIt.value() * uIt.value();
+ ++lIt;
+ ++uIt;
+ }
+#endif
+ m_lu.coeffRefDiag(row) = newCoeff;
+ }
+}
+
+/** Computes *x = U^-1 L^-1 b
+ *
+ * If \a transpose is set to SvTranspose or SvAdjoint, the solution
+ * of the transposed/adjoint system is computed instead.
+ *
+ * Not all backends implement the solution of the transposed or
+ * adjoint system.
+ */
+template<typename MatrixType>
+template<typename BDerived, typename XDerived>
+bool SkylineInplaceLU<MatrixType>::solve(const MatrixBase<BDerived> &b, MatrixBase<XDerived>* x, const int transposed) const {
+ const size_t rows = m_lu.rows();
+ const size_t cols = m_lu.cols();
+
+
+ for (Index row = 0; row < rows; row++) {
+ x->coeffRef(row) = b.coeff(row);
+ Scalar newVal = x->coeff(row);
+ typename MatrixType::InnerLowerIterator lIt(m_lu, row);
+
+ Index col = lIt.col();
+ while (lIt.col() < row) {
+
+ newVal -= x->coeff(col++) * lIt.value();
+ ++lIt;
+ }
+
+ x->coeffRef(row) = newVal;
+ }
+
+
+ for (Index col = rows - 1; col > 0; col--) {
+ x->coeffRef(col) = x->coeff(col) / m_lu.coeffDiag(col);
+
+ const Scalar x_col = x->coeff(col);
+
+ typename MatrixType::InnerUpperIterator uIt(m_lu, col);
+ uIt += uIt.size()-1;
+
+
+ while (uIt) {
+ x->coeffRef(uIt.row()) -= x_col * uIt.value();
+ //TODO : introduce --operator
+ uIt += -1;
+ }
+
+
+ }
+ x->coeffRef(0) = x->coeff(0) / m_lu.coeffDiag(0);
+
+ return true;
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_SKYLINEINPLACELU_H
diff --git a/unsupported/Eigen/src/Skyline/SkylineMatrix.h b/unsupported/Eigen/src/Skyline/SkylineMatrix.h
new file mode 100644
index 0000000..887bf83
--- /dev/null
+++ b/unsupported/Eigen/src/Skyline/SkylineMatrix.h
@@ -0,0 +1,864 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2009 Guillaume Saupin <guillaume.saupin@cea.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_SKYLINEMATRIX_H
+#define EIGEN_SKYLINEMATRIX_H
+
+#include "SkylineStorage.h"
+#include "SkylineMatrixBase.h"
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+/** \ingroup Skyline_Module
+ *
+ * \class SkylineMatrix
+ *
+ * \brief The main skyline matrix class
+ *
+ * This class implements a skyline matrix using the very uncommon storage
+ * scheme.
+ *
+ * \param Scalar_ the scalar type, i.e. the type of the coefficients
+ * \param Options_ Union of bit flags controlling the storage scheme. Currently the only possibility
+ * is RowMajor. The default is 0 which means column-major.
+ *
+ *
+ */
+namespace internal {
+template<typename Scalar_, int Options_>
+struct traits<SkylineMatrix<Scalar_, Options_> > {
+ typedef Scalar_ Scalar;
+ typedef Sparse StorageKind;
+
+ enum {
+ RowsAtCompileTime = Dynamic,
+ ColsAtCompileTime = Dynamic,
+ MaxRowsAtCompileTime = Dynamic,
+ MaxColsAtCompileTime = Dynamic,
+ Flags = SkylineBit | Options_,
+ CoeffReadCost = NumTraits<Scalar>::ReadCost,
+ };
+};
+}
+
+template<typename Scalar_, int Options_>
+class SkylineMatrix
+: public SkylineMatrixBase<SkylineMatrix<Scalar_, Options_> > {
+public:
+ EIGEN_SKYLINE_GENERIC_PUBLIC_INTERFACE(SkylineMatrix)
+ EIGEN_SKYLINE_INHERIT_ASSIGNMENT_OPERATOR(SkylineMatrix, +=)
+ EIGEN_SKYLINE_INHERIT_ASSIGNMENT_OPERATOR(SkylineMatrix, -=)
+
+ using Base::IsRowMajor;
+
+protected:
+
+ typedef SkylineMatrix<Scalar, (Flags&~RowMajorBit) | (IsRowMajor ? RowMajorBit : 0) > TransposedSkylineMatrix;
+
+ Index m_outerSize;
+ Index m_innerSize;
+
+public:
+ Index* m_colStartIndex;
+ Index* m_rowStartIndex;
+ SkylineStorage<Scalar> m_data;
+
+public:
+
+ inline Index rows() const {
+ return IsRowMajor ? m_outerSize : m_innerSize;
+ }
+
+ inline Index cols() const {
+ return IsRowMajor ? m_innerSize : m_outerSize;
+ }
+
+ inline Index innerSize() const {
+ return m_innerSize;
+ }
+
+ inline Index outerSize() const {
+ return m_outerSize;
+ }
+
+ inline Index upperNonZeros() const {
+ return m_data.upperSize();
+ }
+
+ inline Index lowerNonZeros() const {
+ return m_data.lowerSize();
+ }
+
+ inline Index upperNonZeros(Index j) const {
+ return m_colStartIndex[j + 1] - m_colStartIndex[j];
+ }
+
+ inline Index lowerNonZeros(Index j) const {
+ return m_rowStartIndex[j + 1] - m_rowStartIndex[j];
+ }
+
+ inline const Scalar* _diagPtr() const {
+ return &m_data.diag(0);
+ }
+
+ inline Scalar* _diagPtr() {
+ return &m_data.diag(0);
+ }
+
+ inline const Scalar* _upperPtr() const {
+ return &m_data.upper(0);
+ }
+
+ inline Scalar* _upperPtr() {
+ return &m_data.upper(0);
+ }
+
+ inline const Scalar* _lowerPtr() const {
+ return &m_data.lower(0);
+ }
+
+ inline Scalar* _lowerPtr() {
+ return &m_data.lower(0);
+ }
+
+ inline const Index* _upperProfilePtr() const {
+ return &m_data.upperProfile(0);
+ }
+
+ inline Index* _upperProfilePtr() {
+ return &m_data.upperProfile(0);
+ }
+
+ inline const Index* _lowerProfilePtr() const {
+ return &m_data.lowerProfile(0);
+ }
+
+ inline Index* _lowerProfilePtr() {
+ return &m_data.lowerProfile(0);
+ }
+
+ inline Scalar coeff(Index row, Index col) const {
+ const Index outer = IsRowMajor ? row : col;
+ const Index inner = IsRowMajor ? col : row;
+
+ eigen_assert(outer < outerSize());
+ eigen_assert(inner < innerSize());
+
+ if (outer == inner)
+ return this->m_data.diag(outer);
+
+ if (IsRowMajor) {
+ if (inner > outer) //upper matrix
+ {
+ const Index minOuterIndex = inner - m_data.upperProfile(inner);
+ if (outer >= minOuterIndex)
+ return this->m_data.upper(m_colStartIndex[inner] + outer - (inner - m_data.upperProfile(inner)));
+ else
+ return Scalar(0);
+ }
+ if (inner < outer) //lower matrix
+ {
+ const Index minInnerIndex = outer - m_data.lowerProfile(outer);
+ if (inner >= minInnerIndex)
+ return this->m_data.lower(m_rowStartIndex[outer] + inner - (outer - m_data.lowerProfile(outer)));
+ else
+ return Scalar(0);
+ }
+ return m_data.upper(m_colStartIndex[inner] + outer - inner);
+ } else {
+ if (outer > inner) //upper matrix
+ {
+ const Index maxOuterIndex = inner + m_data.upperProfile(inner);
+ if (outer <= maxOuterIndex)
+ return this->m_data.upper(m_colStartIndex[inner] + (outer - inner));
+ else
+ return Scalar(0);
+ }
+ if (outer < inner) //lower matrix
+ {
+ const Index maxInnerIndex = outer + m_data.lowerProfile(outer);
+
+ if (inner <= maxInnerIndex)
+ return this->m_data.lower(m_rowStartIndex[outer] + (inner - outer));
+ else
+ return Scalar(0);
+ }
+ }
+ }
+
+ inline Scalar& coeffRef(Index row, Index col) {
+ const Index outer = IsRowMajor ? row : col;
+ const Index inner = IsRowMajor ? col : row;
+
+ eigen_assert(outer < outerSize());
+ eigen_assert(inner < innerSize());
+
+ if (outer == inner)
+ return this->m_data.diag(outer);
+
+ if (IsRowMajor) {
+ if (col > row) //upper matrix
+ {
+ const Index minOuterIndex = inner - m_data.upperProfile(inner);
+ eigen_assert(outer >= minOuterIndex && "You tried to access a coeff that does not exist in the storage");
+ return this->m_data.upper(m_colStartIndex[inner] + outer - (inner - m_data.upperProfile(inner)));
+ }
+ if (col < row) //lower matrix
+ {
+ const Index minInnerIndex = outer - m_data.lowerProfile(outer);
+ eigen_assert(inner >= minInnerIndex && "You tried to access a coeff that does not exist in the storage");
+ return this->m_data.lower(m_rowStartIndex[outer] + inner - (outer - m_data.lowerProfile(outer)));
+ }
+ } else {
+ if (outer > inner) //upper matrix
+ {
+ const Index maxOuterIndex = inner + m_data.upperProfile(inner);
+ eigen_assert(outer <= maxOuterIndex && "You tried to access a coeff that does not exist in the storage");
+ return this->m_data.upper(m_colStartIndex[inner] + (outer - inner));
+ }
+ if (outer < inner) //lower matrix
+ {
+ const Index maxInnerIndex = outer + m_data.lowerProfile(outer);
+ eigen_assert(inner <= maxInnerIndex && "You tried to access a coeff that does not exist in the storage");
+ return this->m_data.lower(m_rowStartIndex[outer] + (inner - outer));
+ }
+ }
+ }
+
+ inline Scalar coeffDiag(Index idx) const {
+ eigen_assert(idx < outerSize());
+ eigen_assert(idx < innerSize());
+ return this->m_data.diag(idx);
+ }
+
+ inline Scalar coeffLower(Index row, Index col) const {
+ const Index outer = IsRowMajor ? row : col;
+ const Index inner = IsRowMajor ? col : row;
+
+ eigen_assert(outer < outerSize());
+ eigen_assert(inner < innerSize());
+ eigen_assert(inner != outer);
+
+ if (IsRowMajor) {
+ const Index minInnerIndex = outer - m_data.lowerProfile(outer);
+ if (inner >= minInnerIndex)
+ return this->m_data.lower(m_rowStartIndex[outer] + inner - (outer - m_data.lowerProfile(outer)));
+ else
+ return Scalar(0);
+
+ } else {
+ const Index maxInnerIndex = outer + m_data.lowerProfile(outer);
+ if (inner <= maxInnerIndex)
+ return this->m_data.lower(m_rowStartIndex[outer] + (inner - outer));
+ else
+ return Scalar(0);
+ }
+ }
+
+ inline Scalar coeffUpper(Index row, Index col) const {
+ const Index outer = IsRowMajor ? row : col;
+ const Index inner = IsRowMajor ? col : row;
+
+ eigen_assert(outer < outerSize());
+ eigen_assert(inner < innerSize());
+ eigen_assert(inner != outer);
+
+ if (IsRowMajor) {
+ const Index minOuterIndex = inner - m_data.upperProfile(inner);
+ if (outer >= minOuterIndex)
+ return this->m_data.upper(m_colStartIndex[inner] + outer - (inner - m_data.upperProfile(inner)));
+ else
+ return Scalar(0);
+ } else {
+ const Index maxOuterIndex = inner + m_data.upperProfile(inner);
+ if (outer <= maxOuterIndex)
+ return this->m_data.upper(m_colStartIndex[inner] + (outer - inner));
+ else
+ return Scalar(0);
+ }
+ }
+
+ inline Scalar& coeffRefDiag(Index idx) {
+ eigen_assert(idx < outerSize());
+ eigen_assert(idx < innerSize());
+ return this->m_data.diag(idx);
+ }
+
+ inline Scalar& coeffRefLower(Index row, Index col) {
+ const Index outer = IsRowMajor ? row : col;
+ const Index inner = IsRowMajor ? col : row;
+
+ eigen_assert(outer < outerSize());
+ eigen_assert(inner < innerSize());
+ eigen_assert(inner != outer);
+
+ if (IsRowMajor) {
+ const Index minInnerIndex = outer - m_data.lowerProfile(outer);
+ eigen_assert(inner >= minInnerIndex && "You tried to access a coeff that does not exist in the storage");
+ return this->m_data.lower(m_rowStartIndex[outer] + inner - (outer - m_data.lowerProfile(outer)));
+ } else {
+ const Index maxInnerIndex = outer + m_data.lowerProfile(outer);
+ eigen_assert(inner <= maxInnerIndex && "You tried to access a coeff that does not exist in the storage");
+ return this->m_data.lower(m_rowStartIndex[outer] + (inner - outer));
+ }
+ }
+
+ inline bool coeffExistLower(Index row, Index col) {
+ const Index outer = IsRowMajor ? row : col;
+ const Index inner = IsRowMajor ? col : row;
+
+ eigen_assert(outer < outerSize());
+ eigen_assert(inner < innerSize());
+ eigen_assert(inner != outer);
+
+ if (IsRowMajor) {
+ const Index minInnerIndex = outer - m_data.lowerProfile(outer);
+ return inner >= minInnerIndex;
+ } else {
+ const Index maxInnerIndex = outer + m_data.lowerProfile(outer);
+ return inner <= maxInnerIndex;
+ }
+ }
+
+ inline Scalar& coeffRefUpper(Index row, Index col) {
+ const Index outer = IsRowMajor ? row : col;
+ const Index inner = IsRowMajor ? col : row;
+
+ eigen_assert(outer < outerSize());
+ eigen_assert(inner < innerSize());
+ eigen_assert(inner != outer);
+
+ if (IsRowMajor) {
+ const Index minOuterIndex = inner - m_data.upperProfile(inner);
+ eigen_assert(outer >= minOuterIndex && "You tried to access a coeff that does not exist in the storage");
+ return this->m_data.upper(m_colStartIndex[inner] + outer - (inner - m_data.upperProfile(inner)));
+ } else {
+ const Index maxOuterIndex = inner + m_data.upperProfile(inner);
+ eigen_assert(outer <= maxOuterIndex && "You tried to access a coeff that does not exist in the storage");
+ return this->m_data.upper(m_colStartIndex[inner] + (outer - inner));
+ }
+ }
+
+ inline bool coeffExistUpper(Index row, Index col) {
+ const Index outer = IsRowMajor ? row : col;
+ const Index inner = IsRowMajor ? col : row;
+
+ eigen_assert(outer < outerSize());
+ eigen_assert(inner < innerSize());
+ eigen_assert(inner != outer);
+
+ if (IsRowMajor) {
+ const Index minOuterIndex = inner - m_data.upperProfile(inner);
+ return outer >= minOuterIndex;
+ } else {
+ const Index maxOuterIndex = inner + m_data.upperProfile(inner);
+ return outer <= maxOuterIndex;
+ }
+ }
+
+
+protected:
+
+public:
+ class InnerUpperIterator;
+ class InnerLowerIterator;
+
+ class OuterUpperIterator;
+ class OuterLowerIterator;
+
+ /** Removes all non zeros */
+ inline void setZero() {
+ m_data.clear();
+ std::fill_n(m_colStartIndex, m_outerSize + 1, Index(0));
+ std::fill_n(m_rowStartIndex, m_outerSize + 1, Index(0));
+ }
+
+ /** \returns the number of non zero coefficients */
+ inline Index nonZeros() const {
+ return m_data.diagSize() + m_data.upperSize() + m_data.lowerSize();
+ }
+
+ /** Preallocates \a reserveSize non zeros */
+ inline void reserve(Index reserveSize, Index reserveUpperSize, Index reserveLowerSize) {
+ m_data.reserve(reserveSize, reserveUpperSize, reserveLowerSize);
+ }
+
+ /** \returns a reference to a novel non zero coefficient with coordinates \a row x \a col.
+
+ *
+ * \warning This function can be extremely slow if the non zero coefficients
+ * are not inserted in a coherent order.
+ *
+ * After an insertion session, you should call the finalize() function.
+ */
+ EIGEN_DONT_INLINE Scalar & insert(Index row, Index col) {
+ const Index outer = IsRowMajor ? row : col;
+ const Index inner = IsRowMajor ? col : row;
+
+ eigen_assert(outer < outerSize());
+ eigen_assert(inner < innerSize());
+
+ if (outer == inner)
+ return m_data.diag(col);
+
+ if (IsRowMajor) {
+ if (outer < inner) //upper matrix
+ {
+ Index minOuterIndex = 0;
+ minOuterIndex = inner - m_data.upperProfile(inner);
+
+ if (outer < minOuterIndex) //The value does not yet exist
+ {
+ const Index previousProfile = m_data.upperProfile(inner);
+
+ m_data.upperProfile(inner) = inner - outer;
+
+
+ const Index bandIncrement = m_data.upperProfile(inner) - previousProfile;
+ //shift data stored after this new one
+ const Index stop = m_colStartIndex[cols()];
+ const Index start = m_colStartIndex[inner];
+
+
+ for (Index innerIdx = stop; innerIdx >= start; innerIdx--) {
+ m_data.upper(innerIdx + bandIncrement) = m_data.upper(innerIdx);
+ }
+
+ for (Index innerIdx = cols(); innerIdx > inner; innerIdx--) {
+ m_colStartIndex[innerIdx] += bandIncrement;
+ }
+
+ //zeros new data
+ std::fill_n(this->_upperPtr() + start, bandIncrement - 1, Scalar(0));
+
+ return m_data.upper(m_colStartIndex[inner]);
+ } else {
+ return m_data.upper(m_colStartIndex[inner] + outer - (inner - m_data.upperProfile(inner)));
+ }
+ }
+
+ if (outer > inner) //lower matrix
+ {
+ const Index minInnerIndex = outer - m_data.lowerProfile(outer);
+ if (inner < minInnerIndex) //The value does not yet exist
+ {
+ const Index previousProfile = m_data.lowerProfile(outer);
+ m_data.lowerProfile(outer) = outer - inner;
+
+ const Index bandIncrement = m_data.lowerProfile(outer) - previousProfile;
+ //shift data stored after this new one
+ const Index stop = m_rowStartIndex[rows()];
+ const Index start = m_rowStartIndex[outer];
+
+
+ for (Index innerIdx = stop; innerIdx >= start; innerIdx--) {
+ m_data.lower(innerIdx + bandIncrement) = m_data.lower(innerIdx);
+ }
+
+ for (Index innerIdx = rows(); innerIdx > outer; innerIdx--) {
+ m_rowStartIndex[innerIdx] += bandIncrement;
+ }
+
+ //zeros new data
+ std::fill_n(this->_lowerPtr() + start, bandIncrement - 1, Scalar(0));
+ return m_data.lower(m_rowStartIndex[outer]);
+ } else {
+ return m_data.lower(m_rowStartIndex[outer] + inner - (outer - m_data.lowerProfile(outer)));
+ }
+ }
+ } else {
+ if (outer > inner) //upper matrix
+ {
+ const Index maxOuterIndex = inner + m_data.upperProfile(inner);
+ if (outer > maxOuterIndex) //The value does not yet exist
+ {
+ const Index previousProfile = m_data.upperProfile(inner);
+ m_data.upperProfile(inner) = outer - inner;
+
+ const Index bandIncrement = m_data.upperProfile(inner) - previousProfile;
+ //shift data stored after this new one
+ const Index stop = m_rowStartIndex[rows()];
+ const Index start = m_rowStartIndex[inner + 1];
+
+ for (Index innerIdx = stop; innerIdx >= start; innerIdx--) {
+ m_data.upper(innerIdx + bandIncrement) = m_data.upper(innerIdx);
+ }
+
+ for (Index innerIdx = inner + 1; innerIdx < outerSize() + 1; innerIdx++) {
+ m_rowStartIndex[innerIdx] += bandIncrement;
+ }
+ std::fill_n(this->_upperPtr() + m_rowStartIndex[inner] + previousProfile + 1, bandIncrement - 1, Scalar(0));
+ return m_data.upper(m_rowStartIndex[inner] + m_data.upperProfile(inner));
+ } else {
+ return m_data.upper(m_rowStartIndex[inner] + (outer - inner));
+ }
+ }
+
+ if (outer < inner) //lower matrix
+ {
+ const Index maxInnerIndex = outer + m_data.lowerProfile(outer);
+ if (inner > maxInnerIndex) //The value does not yet exist
+ {
+ const Index previousProfile = m_data.lowerProfile(outer);
+ m_data.lowerProfile(outer) = inner - outer;
+
+ const Index bandIncrement = m_data.lowerProfile(outer) - previousProfile;
+ //shift data stored after this new one
+ const Index stop = m_colStartIndex[cols()];
+ const Index start = m_colStartIndex[outer + 1];
+
+ for (Index innerIdx = stop; innerIdx >= start; innerIdx--) {
+ m_data.lower(innerIdx + bandIncrement) = m_data.lower(innerIdx);
+ }
+
+ for (Index innerIdx = outer + 1; innerIdx < outerSize() + 1; innerIdx++) {
+ m_colStartIndex[innerIdx] += bandIncrement;
+ }
+ std::fill_n(this->_lowerPtr() + m_colStartIndex[outer] + previousProfile + 1, bandIncrement - 1, Scalar(0));
+ return m_data.lower(m_colStartIndex[outer] + m_data.lowerProfile(outer));
+ } else {
+ return m_data.lower(m_colStartIndex[outer] + (inner - outer));
+ }
+ }
+ }
+ }
+
+ /** Must be called after inserting a set of non zero entries.
+ */
+ inline void finalize() {
+ if (IsRowMajor) {
+ if (rows() > cols())
+ m_data.resize(cols(), cols(), rows(), m_colStartIndex[cols()] + 1, m_rowStartIndex[rows()] + 1);
+ else
+ m_data.resize(rows(), cols(), rows(), m_colStartIndex[cols()] + 1, m_rowStartIndex[rows()] + 1);
+
+ // eigen_assert(rows() == cols() && "memory reorganisatrion only works with suare matrix");
+ //
+ // Scalar* newArray = new Scalar[m_colStartIndex[cols()] + 1 + m_rowStartIndex[rows()] + 1];
+ // Index dataIdx = 0;
+ // for (Index row = 0; row < rows(); row++) {
+ //
+ // const Index nbLowerElts = m_rowStartIndex[row + 1] - m_rowStartIndex[row];
+ // // std::cout << "nbLowerElts" << nbLowerElts << std::endl;
+ // memcpy(newArray + dataIdx, m_data.m_lower + m_rowStartIndex[row], nbLowerElts * sizeof (Scalar));
+ // m_rowStartIndex[row] = dataIdx;
+ // dataIdx += nbLowerElts;
+ //
+ // const Index nbUpperElts = m_colStartIndex[row + 1] - m_colStartIndex[row];
+ // memcpy(newArray + dataIdx, m_data.m_upper + m_colStartIndex[row], nbUpperElts * sizeof (Scalar));
+ // m_colStartIndex[row] = dataIdx;
+ // dataIdx += nbUpperElts;
+ //
+ //
+ // }
+ // //todo : don't access m_data profile directly : add an accessor from SkylineMatrix
+ // m_rowStartIndex[rows()] = m_rowStartIndex[rows()-1] + m_data.lowerProfile(rows()-1);
+ // m_colStartIndex[cols()] = m_colStartIndex[cols()-1] + m_data.upperProfile(cols()-1);
+ //
+ // delete[] m_data.m_lower;
+ // delete[] m_data.m_upper;
+ //
+ // m_data.m_lower = newArray;
+ // m_data.m_upper = newArray;
+ } else {
+ if (rows() > cols())
+ m_data.resize(cols(), rows(), cols(), m_rowStartIndex[cols()] + 1, m_colStartIndex[cols()] + 1);
+ else
+ m_data.resize(rows(), rows(), cols(), m_rowStartIndex[rows()] + 1, m_colStartIndex[rows()] + 1);
+ }
+ }
+
+ inline void squeeze() {
+ finalize();
+ m_data.squeeze();
+ }
+
+ void prune(Scalar reference, RealScalar epsilon = dummy_precision<RealScalar > ()) {
+ //TODO
+ }
+
+ /** Resizes the matrix to a \a rows x \a cols matrix and initializes it to zero
+ * \sa resizeNonZeros(Index), reserve(), setZero()
+ */
+ void resize(size_t rows, size_t cols) {
+ const Index diagSize = rows > cols ? cols : rows;
+ m_innerSize = IsRowMajor ? cols : rows;
+
+ eigen_assert(rows == cols && "Skyline matrix must be square matrix");
+
+ if (diagSize % 2) { // diagSize is odd
+ const Index k = (diagSize - 1) / 2;
+
+ m_data.resize(diagSize, IsRowMajor ? cols : rows, IsRowMajor ? rows : cols,
+ 2 * k * k + k + 1,
+ 2 * k * k + k + 1);
+
+ } else // diagSize is even
+ {
+ const Index k = diagSize / 2;
+ m_data.resize(diagSize, IsRowMajor ? cols : rows, IsRowMajor ? rows : cols,
+ 2 * k * k - k + 1,
+ 2 * k * k - k + 1);
+ }
+
+ if (m_colStartIndex && m_rowStartIndex) {
+ delete[] m_colStartIndex;
+ delete[] m_rowStartIndex;
+ }
+ m_colStartIndex = new Index [cols + 1];
+ m_rowStartIndex = new Index [rows + 1];
+ m_outerSize = diagSize;
+
+ m_data.reset();
+ m_data.clear();
+
+ m_outerSize = diagSize;
+ std::fill_n(m_colStartIndex, cols + 1, Index(0));
+ std::fill_n(m_rowStartIndex, rows + 1, Index(0));
+ }
+
+ void resizeNonZeros(Index size) {
+ m_data.resize(size);
+ }
+
+ inline SkylineMatrix()
+ : m_outerSize(-1), m_innerSize(0), m_colStartIndex(0), m_rowStartIndex(0) {
+ resize(0, 0);
+ }
+
+ inline SkylineMatrix(size_t rows, size_t cols)
+ : m_outerSize(0), m_innerSize(0), m_colStartIndex(0), m_rowStartIndex(0) {
+ resize(rows, cols);
+ }
+
+ template<typename OtherDerived>
+ inline SkylineMatrix(const SkylineMatrixBase<OtherDerived>& other)
+ : m_outerSize(0), m_innerSize(0), m_colStartIndex(0), m_rowStartIndex(0) {
+ *this = other.derived();
+ }
+
+ inline SkylineMatrix(const SkylineMatrix & other)
+ : Base(), m_outerSize(0), m_innerSize(0), m_colStartIndex(0), m_rowStartIndex(0) {
+ *this = other.derived();
+ }
+
+ inline void swap(SkylineMatrix & other) {
+ //EIGEN_DBG_SKYLINE(std::cout << "SkylineMatrix:: swap\n");
+ std::swap(m_colStartIndex, other.m_colStartIndex);
+ std::swap(m_rowStartIndex, other.m_rowStartIndex);
+ std::swap(m_innerSize, other.m_innerSize);
+ std::swap(m_outerSize, other.m_outerSize);
+ m_data.swap(other.m_data);
+ }
+
+ inline SkylineMatrix & operator=(const SkylineMatrix & other) {
+ std::cout << "SkylineMatrix& operator=(const SkylineMatrix& other)\n";
+ if (other.isRValue()) {
+ swap(other.const_cast_derived());
+ } else {
+ resize(other.rows(), other.cols());
+ memcpy(m_colStartIndex, other.m_colStartIndex, (m_outerSize + 1) * sizeof (Index));
+ memcpy(m_rowStartIndex, other.m_rowStartIndex, (m_outerSize + 1) * sizeof (Index));
+ m_data = other.m_data;
+ }
+ return *this;
+ }
+
+ template<typename OtherDerived>
+ inline SkylineMatrix & operator=(const SkylineMatrixBase<OtherDerived>& other) {
+ const bool needToTranspose = (Flags & RowMajorBit) != (OtherDerived::Flags & RowMajorBit);
+ if (needToTranspose) {
+ // TODO
+ // return *this;
+ } else {
+ // there is no special optimization
+ return SkylineMatrixBase<SkylineMatrix>::operator=(other.derived());
+ }
+ }
+
+ friend std::ostream & operator <<(std::ostream & s, const SkylineMatrix & m) {
+
+ EIGEN_DBG_SKYLINE(
+ std::cout << "upper elements : " << std::endl;
+ for (Index i = 0; i < m.m_data.upperSize(); i++)
+ std::cout << m.m_data.upper(i) << "\t";
+ std::cout << std::endl;
+ std::cout << "upper profile : " << std::endl;
+ for (Index i = 0; i < m.m_data.upperProfileSize(); i++)
+ std::cout << m.m_data.upperProfile(i) << "\t";
+ std::cout << std::endl;
+ std::cout << "lower startIdx : " << std::endl;
+ for (Index i = 0; i < m.m_data.upperProfileSize(); i++)
+ std::cout << (IsRowMajor ? m.m_colStartIndex[i] : m.m_rowStartIndex[i]) << "\t";
+ std::cout << std::endl;
+
+
+ std::cout << "lower elements : " << std::endl;
+ for (Index i = 0; i < m.m_data.lowerSize(); i++)
+ std::cout << m.m_data.lower(i) << "\t";
+ std::cout << std::endl;
+ std::cout << "lower profile : " << std::endl;
+ for (Index i = 0; i < m.m_data.lowerProfileSize(); i++)
+ std::cout << m.m_data.lowerProfile(i) << "\t";
+ std::cout << std::endl;
+ std::cout << "lower startIdx : " << std::endl;
+ for (Index i = 0; i < m.m_data.lowerProfileSize(); i++)
+ std::cout << (IsRowMajor ? m.m_rowStartIndex[i] : m.m_colStartIndex[i]) << "\t";
+ std::cout << std::endl;
+ );
+ for (Index rowIdx = 0; rowIdx < m.rows(); rowIdx++) {
+ for (Index colIdx = 0; colIdx < m.cols(); colIdx++) {
+ s << m.coeff(rowIdx, colIdx) << "\t";
+ }
+ s << std::endl;
+ }
+ return s;
+ }
+
+ /** Destructor */
+ inline ~SkylineMatrix() {
+ delete[] m_colStartIndex;
+ delete[] m_rowStartIndex;
+ }
+
+ /** Overloaded for performance */
+ Scalar sum() const;
+};
+
+template<typename Scalar, int Options_>
+class SkylineMatrix<Scalar, Options_>::InnerUpperIterator {
+public:
+
+ InnerUpperIterator(const SkylineMatrix& mat, Index outer)
+ : m_matrix(mat), m_outer(outer),
+ m_id(Options_ == RowMajor ? mat.m_colStartIndex[outer] : mat.m_rowStartIndex[outer] + 1),
+ m_start(m_id),
+ m_end(Options_ == RowMajor ? mat.m_colStartIndex[outer + 1] : mat.m_rowStartIndex[outer + 1] + 1) {
+ }
+
+ inline InnerUpperIterator & operator++() {
+ m_id++;
+ return *this;
+ }
+
+ inline InnerUpperIterator & operator+=(Index shift) {
+ m_id += shift;
+ return *this;
+ }
+
+ inline Scalar value() const {
+ return m_matrix.m_data.upper(m_id);
+ }
+
+ inline Scalar* valuePtr() {
+ return const_cast<Scalar*> (&(m_matrix.m_data.upper(m_id)));
+ }
+
+ inline Scalar& valueRef() {
+ return const_cast<Scalar&> (m_matrix.m_data.upper(m_id));
+ }
+
+ inline Index index() const {
+ return IsRowMajor ? m_outer - m_matrix.m_data.upperProfile(m_outer) + (m_id - m_start) :
+ m_outer + (m_id - m_start) + 1;
+ }
+
+ inline Index row() const {
+ return IsRowMajor ? index() : m_outer;
+ }
+
+ inline Index col() const {
+ return IsRowMajor ? m_outer : index();
+ }
+
+ inline size_t size() const {
+ return m_matrix.m_data.upperProfile(m_outer);
+ }
+
+ inline operator bool() const {
+ return (m_id < m_end) && (m_id >= m_start);
+ }
+
+protected:
+ const SkylineMatrix& m_matrix;
+ const Index m_outer;
+ Index m_id;
+ const Index m_start;
+ const Index m_end;
+};
+
+template<typename Scalar, int Options_>
+class SkylineMatrix<Scalar, Options_>::InnerLowerIterator {
+public:
+
+ InnerLowerIterator(const SkylineMatrix& mat, Index outer)
+ : m_matrix(mat),
+ m_outer(outer),
+ m_id(Options_ == RowMajor ? mat.m_rowStartIndex[outer] : mat.m_colStartIndex[outer] + 1),
+ m_start(m_id),
+ m_end(Options_ == RowMajor ? mat.m_rowStartIndex[outer + 1] : mat.m_colStartIndex[outer + 1] + 1) {
+ }
+
+ inline InnerLowerIterator & operator++() {
+ m_id++;
+ return *this;
+ }
+
+ inline InnerLowerIterator & operator+=(Index shift) {
+ m_id += shift;
+ return *this;
+ }
+
+ inline Scalar value() const {
+ return m_matrix.m_data.lower(m_id);
+ }
+
+ inline Scalar* valuePtr() {
+ return const_cast<Scalar*> (&(m_matrix.m_data.lower(m_id)));
+ }
+
+ inline Scalar& valueRef() {
+ return const_cast<Scalar&> (m_matrix.m_data.lower(m_id));
+ }
+
+ inline Index index() const {
+ return IsRowMajor ? m_outer - m_matrix.m_data.lowerProfile(m_outer) + (m_id - m_start) :
+ m_outer + (m_id - m_start) + 1;
+ ;
+ }
+
+ inline Index row() const {
+ return IsRowMajor ? m_outer : index();
+ }
+
+ inline Index col() const {
+ return IsRowMajor ? index() : m_outer;
+ }
+
+ inline size_t size() const {
+ return m_matrix.m_data.lowerProfile(m_outer);
+ }
+
+ inline operator bool() const {
+ return (m_id < m_end) && (m_id >= m_start);
+ }
+
+protected:
+ const SkylineMatrix& m_matrix;
+ const Index m_outer;
+ Index m_id;
+ const Index m_start;
+ const Index m_end;
+};
+
+} // end namespace Eigen
+
+#endif // EIGEN_SKYLINEMATRIX_H
diff --git a/unsupported/Eigen/src/Skyline/SkylineMatrixBase.h b/unsupported/Eigen/src/Skyline/SkylineMatrixBase.h
new file mode 100644
index 0000000..86fd10d
--- /dev/null
+++ b/unsupported/Eigen/src/Skyline/SkylineMatrixBase.h
@@ -0,0 +1,213 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2009 Guillaume Saupin <guillaume.saupin@cea.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_SKYLINEMATRIXBASE_H
+#define EIGEN_SKYLINEMATRIXBASE_H
+
+#include "SkylineUtil.h"
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+/** \ingroup Skyline_Module
+ *
+ * \class SkylineMatrixBase
+ *
+ * \brief Base class of any skyline matrices or skyline expressions
+ *
+ * \param Derived
+ *
+ */
+template<typename Derived> class SkylineMatrixBase : public EigenBase<Derived> {
+public:
+
+ typedef typename internal::traits<Derived>::Scalar Scalar;
+ typedef typename internal::traits<Derived>::StorageKind StorageKind;
+ typedef typename internal::index<StorageKind>::type Index;
+
+ enum {
+ RowsAtCompileTime = internal::traits<Derived>::RowsAtCompileTime,
+ /**< The number of rows at compile-time. This is just a copy of the value provided
+ * by the \a Derived type. If a value is not known at compile-time,
+ * it is set to the \a Dynamic constant.
+ * \sa MatrixBase::rows(), MatrixBase::cols(), ColsAtCompileTime, SizeAtCompileTime */
+
+ ColsAtCompileTime = internal::traits<Derived>::ColsAtCompileTime,
+ /**< The number of columns at compile-time. This is just a copy of the value provided
+ * by the \a Derived type. If a value is not known at compile-time,
+ * it is set to the \a Dynamic constant.
+ * \sa MatrixBase::rows(), MatrixBase::cols(), RowsAtCompileTime, SizeAtCompileTime */
+
+
+ SizeAtCompileTime = (internal::size_of_xpr_at_compile_time<Derived>::ret),
+ /**< This is equal to the number of coefficients, i.e. the number of
+ * rows times the number of columns, or to \a Dynamic if this is not
+ * known at compile-time. \sa RowsAtCompileTime, ColsAtCompileTime */
+
+ MaxRowsAtCompileTime = RowsAtCompileTime,
+ MaxColsAtCompileTime = ColsAtCompileTime,
+
+ MaxSizeAtCompileTime = (internal::size_at_compile_time(MaxRowsAtCompileTime,
+ MaxColsAtCompileTime)),
+
+ IsVectorAtCompileTime = RowsAtCompileTime == 1 || ColsAtCompileTime == 1,
+ /**< This is set to true if either the number of rows or the number of
+ * columns is known at compile-time to be equal to 1. Indeed, in that case,
+ * we are dealing with a column-vector (if there is only one column) or with
+ * a row-vector (if there is only one row). */
+
+ Flags = internal::traits<Derived>::Flags,
+ /**< This stores expression \ref flags flags which may or may not be inherited by new expressions
+ * constructed from this one. See the \ref flags "list of flags".
+ */
+
+ CoeffReadCost = internal::traits<Derived>::CoeffReadCost,
+ /**< This is a rough measure of how expensive it is to read one coefficient from
+ * this expression.
+ */
+
+ IsRowMajor = Flags & RowMajorBit ? 1 : 0
+ };
+
+#ifndef EIGEN_PARSED_BY_DOXYGEN
+ /** This is the "real scalar" type; if the \a Scalar type is already real numbers
+ * (e.g. int, float or double) then \a RealScalar is just the same as \a Scalar. If
+ * \a Scalar is \a std::complex<T> then RealScalar is \a T.
+ *
+ * \sa class NumTraits
+ */
+ typedef typename NumTraits<Scalar>::Real RealScalar;
+
+ /** type of the equivalent square matrix */
+ typedef Matrix<Scalar, internal::max_size_prefer_dynamic(RowsAtCompileTime, ColsAtCompileTime),
+ internal::max_size_prefer_dynamic(RowsAtCompileTime, ColsAtCompileTime) > SquareMatrixType;
+
+ inline const Derived& derived() const {
+ return *static_cast<const Derived*> (this);
+ }
+
+ inline Derived& derived() {
+ return *static_cast<Derived*> (this);
+ }
+
+ inline Derived& const_cast_derived() const {
+ return *static_cast<Derived*> (const_cast<SkylineMatrixBase*> (this));
+ }
+#endif // not EIGEN_PARSED_BY_DOXYGEN
+
+ /** \returns the number of rows. \sa cols(), RowsAtCompileTime */
+ inline EIGEN_CONSTEXPR Index rows() const EIGEN_NOEXCEPT {
+ return derived().rows();
+ }
+
+ /** \returns the number of columns. \sa rows(), ColsAtCompileTime*/
+ inline EIGEN_CONSTEXPR Index cols() const EIGEN_NOEXCEPT {
+ return derived().cols();
+ }
+
+ /** \returns the number of coefficients, which is \a rows()*cols().
+ * \sa rows(), cols(), SizeAtCompileTime. */
+ inline EIGEN_CONSTEXPR Index size() const EIGEN_NOEXCEPT {
+ return rows() * cols();
+ }
+
+ /** \returns the number of nonzero coefficients which is in practice the number
+ * of stored coefficients. */
+ inline Index nonZeros() const {
+ return derived().nonZeros();
+ }
+
+ /** \returns the size of the storage major dimension,
+ * i.e., the number of columns for a columns major matrix, and the number of rows otherwise */
+ Index outerSize() const {
+ return (int(Flags) & RowMajorBit) ? this->rows() : this->cols();
+ }
+
+ /** \returns the size of the inner dimension according to the storage order,
+ * i.e., the number of rows for a columns major matrix, and the number of cols otherwise */
+ Index innerSize() const {
+ return (int(Flags) & RowMajorBit) ? this->cols() : this->rows();
+ }
+
+ bool isRValue() const {
+ return m_isRValue;
+ }
+
+ Derived& markAsRValue() {
+ m_isRValue = true;
+ return derived();
+ }
+
+ SkylineMatrixBase() : m_isRValue(false) {
+ /* TODO check flags */
+ }
+
+ inline Derived & operator=(const Derived& other) {
+ this->operator=<Derived > (other);
+ return derived();
+ }
+
+ template<typename OtherDerived>
+ inline void assignGeneric(const OtherDerived& other) {
+ derived().resize(other.rows(), other.cols());
+ for (Index row = 0; row < rows(); row++)
+ for (Index col = 0; col < cols(); col++) {
+ if (other.coeff(row, col) != Scalar(0))
+ derived().insert(row, col) = other.coeff(row, col);
+ }
+ derived().finalize();
+ }
+
+ template<typename OtherDerived>
+ inline Derived & operator=(const SkylineMatrixBase<OtherDerived>& other) {
+ //TODO
+ }
+
+ template<typename Lhs, typename Rhs>
+ inline Derived & operator=(const SkylineProduct<Lhs, Rhs, SkylineTimeSkylineProduct>& product);
+
+ friend std::ostream & operator <<(std::ostream & s, const SkylineMatrixBase& m) {
+ s << m.derived();
+ return s;
+ }
+
+ template<typename OtherDerived>
+ const typename SkylineProductReturnType<Derived, OtherDerived>::Type
+ operator*(const MatrixBase<OtherDerived> &other) const;
+
+ /** \internal use operator= */
+ template<typename DenseDerived>
+ void evalTo(MatrixBase<DenseDerived>& dst) const {
+ dst.setZero();
+ for (Index i = 0; i < rows(); i++)
+ for (Index j = 0; j < rows(); j++)
+ dst(i, j) = derived().coeff(i, j);
+ }
+
+ Matrix<Scalar, RowsAtCompileTime, ColsAtCompileTime> toDense() const {
+ return derived();
+ }
+
+ /** \returns the matrix or vector obtained by evaluating this expression.
+ *
+ * Notice that in the case of a plain matrix or vector (not an expression) this function just returns
+ * a const reference, in order to avoid a useless copy.
+ */
+ EIGEN_STRONG_INLINE const typename internal::eval<Derived, IsSkyline>::type eval() const {
+ return typename internal::eval<Derived>::type(derived());
+ }
+
+protected:
+ bool m_isRValue;
+};
+
+} // end namespace Eigen
+
+#endif // EIGEN_SKYLINEMATRIXBASE_H
diff --git a/unsupported/Eigen/src/Skyline/SkylineProduct.h b/unsupported/Eigen/src/Skyline/SkylineProduct.h
new file mode 100644
index 0000000..03f4269
--- /dev/null
+++ b/unsupported/Eigen/src/Skyline/SkylineProduct.h
@@ -0,0 +1,297 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2009 Guillaume Saupin <guillaume.saupin@cea.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_SKYLINEPRODUCT_H
+#define EIGEN_SKYLINEPRODUCT_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+template<typename Lhs, typename Rhs, int ProductMode>
+struct SkylineProductReturnType {
+ typedef const typename internal::nested_eval<Lhs, Rhs::RowsAtCompileTime>::type LhsNested;
+ typedef const typename internal::nested_eval<Rhs, Lhs::RowsAtCompileTime>::type RhsNested;
+
+ typedef SkylineProduct<LhsNested, RhsNested, ProductMode> Type;
+};
+
+template<typename LhsNested, typename RhsNested, int ProductMode>
+struct internal::traits<SkylineProduct<LhsNested, RhsNested, ProductMode> > {
+ // clean the nested types:
+ typedef internal::remove_all_t<LhsNested> LhsNested_;
+ typedef internal::remove_all_t<RhsNested> RhsNested_;
+ typedef typename LhsNested_::Scalar Scalar;
+
+ enum {
+ LhsCoeffReadCost = LhsNested_::CoeffReadCost,
+ RhsCoeffReadCost = RhsNested_::CoeffReadCost,
+ LhsFlags = LhsNested_::Flags,
+ RhsFlags = RhsNested_::Flags,
+
+ RowsAtCompileTime = LhsNested_::RowsAtCompileTime,
+ ColsAtCompileTime = RhsNested_::ColsAtCompileTime,
+ InnerSize = internal::min_size_prefer_fixed(LhsNested_::ColsAtCompileTime, RhsNested_::RowsAtCompileTime),
+
+ MaxRowsAtCompileTime = LhsNested_::MaxRowsAtCompileTime,
+ MaxColsAtCompileTime = RhsNested_::MaxColsAtCompileTime,
+
+ EvalToRowMajor = (RhsFlags & LhsFlags & RowMajorBit),
+ ResultIsSkyline = ProductMode == SkylineTimeSkylineProduct,
+
+ RemovedBits = ~((EvalToRowMajor ? 0 : RowMajorBit) | (ResultIsSkyline ? 0 : SkylineBit)),
+
+ Flags = (int(LhsFlags | RhsFlags) & HereditaryBits & RemovedBits)
+ | EvalBeforeAssigningBit
+ | EvalBeforeNestingBit,
+
+ CoeffReadCost = HugeCost
+ };
+
+ typedef std::conditional_t<ResultIsSkyline,
+ SkylineMatrixBase<SkylineProduct<LhsNested, RhsNested, ProductMode> >,
+ MatrixBase<SkylineProduct<LhsNested, RhsNested, ProductMode> > > Base;
+};
+
+namespace internal {
+template<typename LhsNested, typename RhsNested, int ProductMode>
+class SkylineProduct : no_assignment_operator,
+public traits<SkylineProduct<LhsNested, RhsNested, ProductMode> >::Base {
+public:
+
+ EIGEN_GENERIC_PUBLIC_INTERFACE(SkylineProduct)
+
+private:
+
+ typedef typename traits<SkylineProduct>::LhsNested_ LhsNested_;
+ typedef typename traits<SkylineProduct>::RhsNested_ RhsNested_;
+
+public:
+
+ template<typename Lhs, typename Rhs>
+ EIGEN_STRONG_INLINE SkylineProduct(const Lhs& lhs, const Rhs& rhs)
+ : m_lhs(lhs), m_rhs(rhs) {
+ eigen_assert(lhs.cols() == rhs.rows());
+
+ enum {
+ ProductIsValid = LhsNested_::ColsAtCompileTime == Dynamic
+ || RhsNested_::RowsAtCompileTime == Dynamic
+ || int(LhsNested_::ColsAtCompileTime) == int(RhsNested_::RowsAtCompileTime),
+ AreVectors = LhsNested_::IsVectorAtCompileTime && RhsNested_::IsVectorAtCompileTime,
+ SameSizes = EIGEN_PREDICATE_SAME_MATRIX_SIZE(LhsNested_, RhsNested_)
+ };
+ // note to the lost user:
+ // * for a dot product use: v1.dot(v2)
+ // * for a coeff-wise product use: v1.cwise()*v2
+ EIGEN_STATIC_ASSERT(ProductIsValid || !(AreVectors && SameSizes),
+ INVALID_VECTOR_VECTOR_PRODUCT__IF_YOU_WANTED_A_DOT_OR_COEFF_WISE_PRODUCT_YOU_MUST_USE_THE_EXPLICIT_FUNCTIONS)
+ EIGEN_STATIC_ASSERT(ProductIsValid || !(SameSizes && !AreVectors),
+ INVALID_MATRIX_PRODUCT__IF_YOU_WANTED_A_COEFF_WISE_PRODUCT_YOU_MUST_USE_THE_EXPLICIT_FUNCTION)
+ EIGEN_STATIC_ASSERT(ProductIsValid || SameSizes, INVALID_MATRIX_PRODUCT)
+ }
+
+ EIGEN_STRONG_INLINE Index rows() const {
+ return m_lhs.rows();
+ }
+
+ EIGEN_STRONG_INLINE Index cols() const {
+ return m_rhs.cols();
+ }
+
+ EIGEN_STRONG_INLINE const LhsNested_& lhs() const {
+ return m_lhs;
+ }
+
+ EIGEN_STRONG_INLINE const RhsNested_& rhs() const {
+ return m_rhs;
+ }
+
+protected:
+ LhsNested m_lhs;
+ RhsNested m_rhs;
+};
+
+// dense = skyline * dense
+// Note that here we force no inlining and separate the setZero() because GCC messes up otherwise
+
+template<typename Lhs, typename Rhs, typename Dest>
+EIGEN_DONT_INLINE void skyline_row_major_time_dense_product(const Lhs& lhs, const Rhs& rhs, Dest& dst) {
+ typedef remove_all_t<Lhs> Lhs_;
+ typedef remove_all_t<Rhs> Rhs_;
+ typedef typename traits<Lhs>::Scalar Scalar;
+
+ enum {
+ LhsIsRowMajor = (Lhs_::Flags & RowMajorBit) == RowMajorBit,
+ LhsIsSelfAdjoint = (Lhs_::Flags & SelfAdjointBit) == SelfAdjointBit,
+ ProcessFirstHalf = LhsIsSelfAdjoint
+ && (((Lhs_::Flags & (UpperTriangularBit | LowerTriangularBit)) == 0)
+ || ((Lhs_::Flags & UpperTriangularBit) && !LhsIsRowMajor)
+ || ((Lhs_::Flags & LowerTriangularBit) && LhsIsRowMajor)),
+ ProcessSecondHalf = LhsIsSelfAdjoint && (!ProcessFirstHalf)
+ };
+
+ //Use matrix diagonal part <- Improvement : use inner iterator on dense matrix.
+ for (Index col = 0; col < rhs.cols(); col++) {
+ for (Index row = 0; row < lhs.rows(); row++) {
+ dst(row, col) = lhs.coeffDiag(row) * rhs(row, col);
+ }
+ }
+ //Use matrix lower triangular part
+ for (Index row = 0; row < lhs.rows(); row++) {
+ typename Lhs_::InnerLowerIterator lIt(lhs, row);
+ const Index stop = lIt.col() + lIt.size();
+ for (Index col = 0; col < rhs.cols(); col++) {
+
+ Index k = lIt.col();
+ Scalar tmp = 0;
+ while (k < stop) {
+ tmp +=
+ lIt.value() *
+ rhs(k++, col);
+ ++lIt;
+ }
+ dst(row, col) += tmp;
+ lIt += -lIt.size();
+ }
+
+ }
+
+ //Use matrix upper triangular part
+ for (Index lhscol = 0; lhscol < lhs.cols(); lhscol++) {
+ typename Lhs_::InnerUpperIterator uIt(lhs, lhscol);
+ const Index stop = uIt.size() + uIt.row();
+ for (Index rhscol = 0; rhscol < rhs.cols(); rhscol++) {
+
+
+ const Scalar rhsCoeff = rhs.coeff(lhscol, rhscol);
+ Index k = uIt.row();
+ while (k < stop) {
+ dst(k++, rhscol) +=
+ uIt.value() *
+ rhsCoeff;
+ ++uIt;
+ }
+ uIt += -uIt.size();
+ }
+ }
+
+}
+
+template<typename Lhs, typename Rhs, typename Dest>
+EIGEN_DONT_INLINE void skyline_col_major_time_dense_product(const Lhs& lhs, const Rhs& rhs, Dest& dst) {
+ typedef remove_all_t<Lhs> Lhs_;
+ typedef remove_all_t<Rhs> Rhs_;
+ typedef typename traits<Lhs>::Scalar Scalar;
+
+ enum {
+ LhsIsRowMajor = (Lhs_::Flags & RowMajorBit) == RowMajorBit,
+ LhsIsSelfAdjoint = (Lhs_::Flags & SelfAdjointBit) == SelfAdjointBit,
+ ProcessFirstHalf = LhsIsSelfAdjoint
+ && (((Lhs_::Flags & (UpperTriangularBit | LowerTriangularBit)) == 0)
+ || ((Lhs_::Flags & UpperTriangularBit) && !LhsIsRowMajor)
+ || ((Lhs_::Flags & LowerTriangularBit) && LhsIsRowMajor)),
+ ProcessSecondHalf = LhsIsSelfAdjoint && (!ProcessFirstHalf)
+ };
+
+ //Use matrix diagonal part <- Improvement : use inner iterator on dense matrix.
+ for (Index col = 0; col < rhs.cols(); col++) {
+ for (Index row = 0; row < lhs.rows(); row++) {
+ dst(row, col) = lhs.coeffDiag(row) * rhs(row, col);
+ }
+ }
+
+ //Use matrix upper triangular part
+ for (Index row = 0; row < lhs.rows(); row++) {
+ typename Lhs_::InnerUpperIterator uIt(lhs, row);
+ const Index stop = uIt.col() + uIt.size();
+ for (Index col = 0; col < rhs.cols(); col++) {
+
+ Index k = uIt.col();
+ Scalar tmp = 0;
+ while (k < stop) {
+ tmp +=
+ uIt.value() *
+ rhs(k++, col);
+ ++uIt;
+ }
+
+
+ dst(row, col) += tmp;
+ uIt += -uIt.size();
+ }
+ }
+
+ //Use matrix lower triangular part
+ for (Index lhscol = 0; lhscol < lhs.cols(); lhscol++) {
+ typename Lhs_::InnerLowerIterator lIt(lhs, lhscol);
+ const Index stop = lIt.size() + lIt.row();
+ for (Index rhscol = 0; rhscol < rhs.cols(); rhscol++) {
+
+ const Scalar rhsCoeff = rhs.coeff(lhscol, rhscol);
+ Index k = lIt.row();
+ while (k < stop) {
+ dst(k++, rhscol) +=
+ lIt.value() *
+ rhsCoeff;
+ ++lIt;
+ }
+ lIt += -lIt.size();
+ }
+ }
+
+}
+
+template<typename Lhs, typename Rhs, typename ResultType,
+ int LhsStorageOrder = traits<Lhs>::Flags&RowMajorBit>
+ struct skyline_product_selector;
+
+template<typename Lhs, typename Rhs, typename ResultType>
+struct skyline_product_selector<Lhs, Rhs, ResultType, RowMajor> {
+ typedef typename traits<remove_all_t<Lhs>>::Scalar Scalar;
+
+ static void run(const Lhs& lhs, const Rhs& rhs, ResultType & res) {
+ skyline_row_major_time_dense_product<Lhs, Rhs, ResultType > (lhs, rhs, res);
+ }
+};
+
+template<typename Lhs, typename Rhs, typename ResultType>
+struct skyline_product_selector<Lhs, Rhs, ResultType, ColMajor> {
+ typedef typename traits<remove_all_t<Lhs>>::Scalar Scalar;
+
+ static void run(const Lhs& lhs, const Rhs& rhs, ResultType & res) {
+ skyline_col_major_time_dense_product<Lhs, Rhs, ResultType > (lhs, rhs, res);
+ }
+};
+
+} // end namespace internal
+
+// template<typename Derived>
+// template<typename Lhs, typename Rhs >
+// Derived & MatrixBase<Derived>::lazyAssign(const SkylineProduct<Lhs, Rhs, SkylineTimeDenseProduct>& product) {
+// typedef internal::remove_all_t<Lhs> Lhs_;
+// internal::skyline_product_selector<internal::remove_all_t<Lhs>,
+// internal::remove_all_t<Rhs>,
+// Derived>::run(product.lhs(), product.rhs(), derived());
+//
+// return derived();
+// }
+
+// skyline * dense
+
+template<typename Derived>
+template<typename OtherDerived >
+EIGEN_STRONG_INLINE const typename SkylineProductReturnType<Derived, OtherDerived>::Type
+SkylineMatrixBase<Derived>::operator*(const MatrixBase<OtherDerived> &other) const {
+
+ return typename SkylineProductReturnType<Derived, OtherDerived>::Type(derived(), other.derived());
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_SKYLINEPRODUCT_H
diff --git a/unsupported/Eigen/src/Skyline/SkylineStorage.h b/unsupported/Eigen/src/Skyline/SkylineStorage.h
new file mode 100644
index 0000000..73b15a6
--- /dev/null
+++ b/unsupported/Eigen/src/Skyline/SkylineStorage.h
@@ -0,0 +1,261 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2009 Guillaume Saupin <guillaume.saupin@cea.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_SKYLINE_STORAGE_H
+#define EIGEN_SKYLINE_STORAGE_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+/** Stores a skyline set of values in three structures :
+ * The diagonal elements
+ * The upper elements
+ * The lower elements
+ *
+ */
+template<typename Scalar>
+class SkylineStorage {
+ typedef typename NumTraits<Scalar>::Real RealScalar;
+ typedef SparseIndex Index;
+public:
+
+ SkylineStorage()
+ : m_diag(0),
+ m_lower(0),
+ m_upper(0),
+ m_lowerProfile(0),
+ m_upperProfile(0),
+ m_diagSize(0),
+ m_upperSize(0),
+ m_lowerSize(0),
+ m_upperProfileSize(0),
+ m_lowerProfileSize(0),
+ m_allocatedSize(0) {
+ }
+
+ SkylineStorage(const SkylineStorage& other)
+ : m_diag(0),
+ m_lower(0),
+ m_upper(0),
+ m_lowerProfile(0),
+ m_upperProfile(0),
+ m_diagSize(0),
+ m_upperSize(0),
+ m_lowerSize(0),
+ m_upperProfileSize(0),
+ m_lowerProfileSize(0),
+ m_allocatedSize(0) {
+ *this = other;
+ }
+
+ SkylineStorage & operator=(const SkylineStorage& other) {
+ resize(other.diagSize(), other.m_upperProfileSize, other.m_lowerProfileSize, other.upperSize(), other.lowerSize());
+ memcpy(m_diag, other.m_diag, m_diagSize * sizeof (Scalar));
+ memcpy(m_upper, other.m_upper, other.upperSize() * sizeof (Scalar));
+ memcpy(m_lower, other.m_lower, other.lowerSize() * sizeof (Scalar));
+ memcpy(m_upperProfile, other.m_upperProfile, m_upperProfileSize * sizeof (Index));
+ memcpy(m_lowerProfile, other.m_lowerProfile, m_lowerProfileSize * sizeof (Index));
+ return *this;
+ }
+
+ void swap(SkylineStorage& other) {
+ std::swap(m_diag, other.m_diag);
+ std::swap(m_upper, other.m_upper);
+ std::swap(m_lower, other.m_lower);
+ std::swap(m_upperProfile, other.m_upperProfile);
+ std::swap(m_lowerProfile, other.m_lowerProfile);
+ std::swap(m_diagSize, other.m_diagSize);
+ std::swap(m_upperSize, other.m_upperSize);
+ std::swap(m_lowerSize, other.m_lowerSize);
+ std::swap(m_allocatedSize, other.m_allocatedSize);
+ }
+
+ ~SkylineStorage() {
+ delete[] m_diag;
+ delete[] m_upper;
+ if (m_upper != m_lower)
+ delete[] m_lower;
+ delete[] m_upperProfile;
+ delete[] m_lowerProfile;
+ }
+
+ void reserve(Index size, Index upperProfileSize, Index lowerProfileSize, Index upperSize, Index lowerSize) {
+ Index newAllocatedSize = size + upperSize + lowerSize;
+ if (newAllocatedSize > m_allocatedSize)
+ reallocate(size, upperProfileSize, lowerProfileSize, upperSize, lowerSize);
+ }
+
+ void squeeze() {
+ if (m_allocatedSize > m_diagSize + m_upperSize + m_lowerSize)
+ reallocate(m_diagSize, m_upperProfileSize, m_lowerProfileSize, m_upperSize, m_lowerSize);
+ }
+
+ void resize(Index diagSize, Index upperProfileSize, Index lowerProfileSize, Index upperSize, Index lowerSize, float reserveSizeFactor = 0) {
+ if (m_allocatedSize < diagSize + upperSize + lowerSize)
+ reallocate(diagSize, upperProfileSize, lowerProfileSize, upperSize + Index(reserveSizeFactor * upperSize), lowerSize + Index(reserveSizeFactor * lowerSize));
+ m_diagSize = diagSize;
+ m_upperSize = upperSize;
+ m_lowerSize = lowerSize;
+ m_upperProfileSize = upperProfileSize;
+ m_lowerProfileSize = lowerProfileSize;
+ }
+
+ inline Index diagSize() const {
+ return m_diagSize;
+ }
+
+ inline Index upperSize() const {
+ return m_upperSize;
+ }
+
+ inline Index lowerSize() const {
+ return m_lowerSize;
+ }
+
+ inline Index upperProfileSize() const {
+ return m_upperProfileSize;
+ }
+
+ inline Index lowerProfileSize() const {
+ return m_lowerProfileSize;
+ }
+
+ inline Index allocatedSize() const {
+ return m_allocatedSize;
+ }
+
+ inline void clear() {
+ m_diagSize = 0;
+ }
+
+ inline Scalar& diag(Index i) {
+ return m_diag[i];
+ }
+
+ inline const Scalar& diag(Index i) const {
+ return m_diag[i];
+ }
+
+ inline Scalar& upper(Index i) {
+ return m_upper[i];
+ }
+
+ inline const Scalar& upper(Index i) const {
+ return m_upper[i];
+ }
+
+ inline Scalar& lower(Index i) {
+ return m_lower[i];
+ }
+
+ inline const Scalar& lower(Index i) const {
+ return m_lower[i];
+ }
+
+ inline Index& upperProfile(Index i) {
+ return m_upperProfile[i];
+ }
+
+ inline const Index& upperProfile(Index i) const {
+ return m_upperProfile[i];
+ }
+
+ inline Index& lowerProfile(Index i) {
+ return m_lowerProfile[i];
+ }
+
+ inline const Index& lowerProfile(Index i) const {
+ return m_lowerProfile[i];
+ }
+
+ static SkylineStorage Map(Index* upperProfile, Index* lowerProfile, Scalar* diag, Scalar* upper, Scalar* lower, Index size, Index upperSize, Index lowerSize) {
+ SkylineStorage res;
+ res.m_upperProfile = upperProfile;
+ res.m_lowerProfile = lowerProfile;
+ res.m_diag = diag;
+ res.m_upper = upper;
+ res.m_lower = lower;
+ res.m_allocatedSize = res.m_diagSize = size;
+ res.m_upperSize = upperSize;
+ res.m_lowerSize = lowerSize;
+ return res;
+ }
+
+ inline void reset() {
+ std::fill_n(m_diag, m_diagSize, Scalar(0));
+ std::fill_n(m_upper, m_upperSize, Scalar(0));
+ std::fill_n(m_lower, m_lowerSize, Scalar(0));
+ std::fill_n(m_upperProfile, m_diagSize, Index(0));
+ std::fill_n(m_lowerProfile, m_diagSize, Index(0));
+ }
+
+ void prune(Scalar reference, RealScalar epsilon = dummy_precision<RealScalar>()) {
+ //TODO
+ }
+
+protected:
+
+ inline void reallocate(Index diagSize, Index upperProfileSize, Index lowerProfileSize, Index upperSize, Index lowerSize) {
+
+ Scalar* diag = new Scalar[diagSize];
+ Scalar* upper = new Scalar[upperSize];
+ Scalar* lower = new Scalar[lowerSize];
+ Index* upperProfile = new Index[upperProfileSize];
+ Index* lowerProfile = new Index[lowerProfileSize];
+
+ Index copyDiagSize = (std::min)(diagSize, m_diagSize);
+ Index copyUpperSize = (std::min)(upperSize, m_upperSize);
+ Index copyLowerSize = (std::min)(lowerSize, m_lowerSize);
+ Index copyUpperProfileSize = (std::min)(upperProfileSize, m_upperProfileSize);
+ Index copyLowerProfileSize = (std::min)(lowerProfileSize, m_lowerProfileSize);
+
+ // copy
+ memcpy(diag, m_diag, copyDiagSize * sizeof (Scalar));
+ memcpy(upper, m_upper, copyUpperSize * sizeof (Scalar));
+ memcpy(lower, m_lower, copyLowerSize * sizeof (Scalar));
+ memcpy(upperProfile, m_upperProfile, copyUpperProfileSize * sizeof (Index));
+ memcpy(lowerProfile, m_lowerProfile, copyLowerProfileSize * sizeof (Index));
+
+
+
+ // delete old stuff
+ delete[] m_diag;
+ delete[] m_upper;
+ delete[] m_lower;
+ delete[] m_upperProfile;
+ delete[] m_lowerProfile;
+ m_diag = diag;
+ m_upper = upper;
+ m_lower = lower;
+ m_upperProfile = upperProfile;
+ m_lowerProfile = lowerProfile;
+ m_allocatedSize = diagSize + upperSize + lowerSize;
+ m_upperSize = upperSize;
+ m_lowerSize = lowerSize;
+ }
+
+public:
+ Scalar* m_diag;
+ Scalar* m_upper;
+ Scalar* m_lower;
+ Index* m_upperProfile;
+ Index* m_lowerProfile;
+ Index m_diagSize;
+ Index m_upperSize;
+ Index m_lowerSize;
+ Index m_upperProfileSize;
+ Index m_lowerProfileSize;
+ Index m_allocatedSize;
+
+};
+
+} // end namespace Eigen
+
+#endif // EIGEN_SKYLINE_STORAGE_H
diff --git a/unsupported/Eigen/src/Skyline/SkylineUtil.h b/unsupported/Eigen/src/Skyline/SkylineUtil.h
new file mode 100644
index 0000000..47fb4e3
--- /dev/null
+++ b/unsupported/Eigen/src/Skyline/SkylineUtil.h
@@ -0,0 +1,91 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009 Guillaume Saupin <guillaume.saupin@cea.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_SKYLINEUTIL_H
+#define EIGEN_SKYLINEUTIL_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+#ifdef NDEBUG
+#define EIGEN_DBG_SKYLINE(X)
+#else
+#define EIGEN_DBG_SKYLINE(X) X
+#endif
+
+const unsigned int SkylineBit = 0x1200;
+template<typename Lhs, typename Rhs, int ProductMode> class SkylineProduct;
+enum AdditionalProductEvaluationMode {SkylineTimeDenseProduct, SkylineTimeSkylineProduct, DenseTimeSkylineProduct};
+enum {IsSkyline = SkylineBit};
+
+
+#define EIGEN_SKYLINE_INHERIT_ASSIGNMENT_OPERATOR(Derived, Op) \
+template<typename OtherDerived> \
+EIGEN_STRONG_INLINE Derived& operator Op(const Eigen::SkylineMatrixBase<OtherDerived>& other) \
+{ \
+ return Base::operator Op(other.derived()); \
+} \
+EIGEN_STRONG_INLINE Derived& operator Op(const Derived& other) \
+{ \
+ return Base::operator Op(other); \
+}
+
+#define EIGEN_SKYLINE_INHERIT_SCALAR_ASSIGNMENT_OPERATOR(Derived, Op) \
+template<typename Other> \
+EIGEN_STRONG_INLINE Derived& operator Op(const Other& scalar) \
+{ \
+ return Base::operator Op(scalar); \
+}
+
+#define EIGEN_SKYLINE_INHERIT_ASSIGNMENT_OPERATORS(Derived) \
+ EIGEN_SKYLINE_INHERIT_ASSIGNMENT_OPERATOR(Derived, =) \
+ EIGEN_SKYLINE_INHERIT_ASSIGNMENT_OPERATOR(Derived, +=) \
+ EIGEN_SKYLINE_INHERIT_ASSIGNMENT_OPERATOR(Derived, -=) \
+ EIGEN_SKYLINE_INHERIT_SCALAR_ASSIGNMENT_OPERATOR(Derived, *=) \
+ EIGEN_SKYLINE_INHERIT_SCALAR_ASSIGNMENT_OPERATOR(Derived, /=)
+
+#define EIGEN_SKYLINE_GENERIC_PUBLIC_INTERFACE_(Derived, BaseClass) \
+ typedef BaseClass Base; \
+ typedef typename Eigen::internal::traits<Derived>::Scalar Scalar; \
+ typedef typename Eigen::NumTraits<Scalar>::Real RealScalar; \
+ typedef typename Eigen::internal::traits<Derived>::StorageKind StorageKind; \
+ typedef typename Eigen::internal::index<StorageKind>::type Index; \
+ enum { Flags = Eigen::internal::traits<Derived>::Flags, };
+
+#define EIGEN_SKYLINE_GENERIC_PUBLIC_INTERFACE(Derived) \
+ EIGEN_SKYLINE_GENERIC_PUBLIC_INTERFACE_(Derived, Eigen::SkylineMatrixBase<Derived>)
+
+template<typename Derived> class SkylineMatrixBase;
+template<typename Scalar_, int Flags_ = 0> class SkylineMatrix;
+template<typename Scalar_, int Flags_ = 0> class DynamicSkylineMatrix;
+template<typename Scalar_, int Flags_ = 0> class SkylineVector;
+template<typename Scalar_, int Flags_ = 0> class MappedSkylineMatrix;
+
+namespace internal {
+
+template<typename Lhs, typename Rhs> struct skyline_product_mode;
+template<typename Lhs, typename Rhs, int ProductMode = skyline_product_mode<Lhs,Rhs>::value> struct SkylineProductReturnType;
+
+template<typename T> class eval<T,IsSkyline>
+{
+ typedef typename traits<T>::Scalar Scalar_;
+ enum {
+ Flags_ = traits<T>::Flags
+ };
+
+ public:
+ typedef SkylineMatrix<Scalar_, Flags_> type;
+};
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_SKYLINEUTIL_H
diff --git a/unsupported/Eigen/src/SparseExtra/BlockSparseMatrix.h b/unsupported/Eigen/src/SparseExtra/BlockSparseMatrix.h
new file mode 100644
index 0000000..853fbb0
--- /dev/null
+++ b/unsupported/Eigen/src/SparseExtra/BlockSparseMatrix.h
@@ -0,0 +1,1081 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2013 Desire Nuentsa <desire.nuentsa_wakam@inria.fr>
+// Copyright (C) 2013 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_SPARSEBLOCKMATRIX_H
+#define EIGEN_SPARSEBLOCKMATRIX_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+/** \ingroup SparseCore_Module
+ *
+ * \class BlockSparseMatrix
+ *
+ * \brief A versatile sparse matrix representation where each element is a block
+ *
+ * This class provides routines to manipulate block sparse matrices stored in a
+ * BSR-like representation. There are two main types :
+ *
+ * 1. All blocks have the same number of rows and columns, called block size
+ * in the following. In this case, if this block size is known at compile time,
+ * it can be given as a template parameter like
+ * \code
+ * BlockSparseMatrix<Scalar, 3, ColMajor> bmat(b_rows, b_cols);
+ * \endcode
+ * Here, bmat is a b_rows x b_cols block sparse matrix
+ * where each coefficient is a 3x3 dense matrix.
+ * If the block size is fixed but will be given at runtime,
+ * \code
+ * BlockSparseMatrix<Scalar, Dynamic, ColMajor> bmat(b_rows, b_cols);
+ * bmat.setBlockSize(block_size);
+ * \endcode
+ *
+ * 2. The second case is for variable-block sparse matrices.
+ * Here each block has its own dimensions. The only restriction is that all the blocks
+ * in a row (resp. a column) should have the same number of rows (resp. of columns).
+ * It is thus required in this case to describe the layout of the matrix by calling
+ * setBlockLayout(rowBlocks, colBlocks).
+ *
+ * In any of the previous case, the matrix can be filled by calling setFromTriplets().
+ * A regular sparse matrix can be converted to a block sparse matrix and vice versa.
+ * It is obviously required to describe the block layout beforehand by calling either
+ * setBlockSize() for fixed-size blocks or setBlockLayout for variable-size blocks.
+ *
+ * \tparam Scalar_ The Scalar type
+ * \tparam _BlockAtCompileTime The block layout option. It takes the following values
+ * Dynamic : block size known at runtime
+ * a numeric number : fixed-size block known at compile time
+ */
+template<typename Scalar_, int _BlockAtCompileTime=Dynamic, int Options_=ColMajor, typename StorageIndex_=int> class BlockSparseMatrix;
+
+template<typename BlockSparseMatrixT> class BlockSparseMatrixView;
+
+namespace internal {
+template<typename Scalar_, int _BlockAtCompileTime, int Options_, typename Index_>
+struct traits<BlockSparseMatrix<Scalar_,_BlockAtCompileTime,Options_, Index_> >
+{
+ typedef Scalar_ Scalar;
+ typedef Index_ Index;
+ typedef Sparse StorageKind; // FIXME Where is it used ??
+ typedef MatrixXpr XprKind;
+ enum {
+ RowsAtCompileTime = Dynamic,
+ ColsAtCompileTime = Dynamic,
+ MaxRowsAtCompileTime = Dynamic,
+ MaxColsAtCompileTime = Dynamic,
+ BlockSize = _BlockAtCompileTime,
+ Flags = Options_ | NestByRefBit | LvalueBit,
+ CoeffReadCost = NumTraits<Scalar>::ReadCost,
+ SupportedAccessPatterns = InnerRandomAccessPattern
+ };
+};
+template<typename BlockSparseMatrixT>
+struct traits<BlockSparseMatrixView<BlockSparseMatrixT> >
+{
+ typedef Ref<Matrix<typename BlockSparseMatrixT::Scalar, BlockSparseMatrixT::BlockSize, BlockSparseMatrixT::BlockSize> > Scalar;
+ typedef Ref<Matrix<typename BlockSparseMatrixT::RealScalar, BlockSparseMatrixT::BlockSize, BlockSparseMatrixT::BlockSize> > RealScalar;
+
+};
+
+// Function object to sort a triplet list
+template<typename Iterator, bool IsColMajor>
+struct TripletComp
+{
+ typedef typename Iterator::value_type Triplet;
+ bool operator()(const Triplet& a, const Triplet& b)
+ { if(IsColMajor)
+ return ((a.col() == b.col() && a.row() < b.row()) || (a.col() < b.col()));
+ else
+ return ((a.row() == b.row() && a.col() < b.col()) || (a.row() < b.row()));
+ }
+};
+} // end namespace internal
+
+
+/* Proxy to view the block sparse matrix as a regular sparse matrix */
+template<typename BlockSparseMatrixT>
+class BlockSparseMatrixView : public SparseMatrixBase<BlockSparseMatrixT>
+{
+ public:
+ typedef Ref<typename BlockSparseMatrixT::BlockScalar> Scalar;
+ typedef Ref<typename BlockSparseMatrixT::BlockRealScalar> RealScalar;
+ typedef typename BlockSparseMatrixT::Index Index;
+ typedef BlockSparseMatrixT Nested;
+ enum {
+ Flags = BlockSparseMatrixT::Options,
+ Options = BlockSparseMatrixT::Options,
+ RowsAtCompileTime = BlockSparseMatrixT::RowsAtCompileTime,
+ ColsAtCompileTime = BlockSparseMatrixT::ColsAtCompileTime,
+ MaxColsAtCompileTime = BlockSparseMatrixT::MaxColsAtCompileTime,
+ MaxRowsAtCompileTime = BlockSparseMatrixT::MaxRowsAtCompileTime
+ };
+ public:
+ BlockSparseMatrixView(const BlockSparseMatrixT& spblockmat)
+ : m_spblockmat(spblockmat)
+ {}
+
+ Index outerSize() const
+ {
+ return (Flags&RowMajorBit) == 1 ? this->rows() : this->cols();
+ }
+ Index cols() const
+ {
+ return m_spblockmat.blockCols();
+ }
+ Index rows() const
+ {
+ return m_spblockmat.blockRows();
+ }
+ Scalar coeff(Index row, Index col)
+ {
+ return m_spblockmat.coeff(row, col);
+ }
+ Scalar coeffRef(Index row, Index col)
+ {
+ return m_spblockmat.coeffRef(row, col);
+ }
+ // Wrapper to iterate over all blocks
+ class InnerIterator : public BlockSparseMatrixT::BlockInnerIterator
+ {
+ public:
+ InnerIterator(const BlockSparseMatrixView& mat, Index outer)
+ : BlockSparseMatrixT::BlockInnerIterator(mat.m_spblockmat, outer)
+ {}
+
+ };
+
+ protected:
+ const BlockSparseMatrixT& m_spblockmat;
+};
+
+// Proxy to view a regular vector as a block vector
+template<typename BlockSparseMatrixT, typename VectorType>
+class BlockVectorView
+{
+ public:
+ enum {
+ BlockSize = BlockSparseMatrixT::BlockSize,
+ ColsAtCompileTime = VectorType::ColsAtCompileTime,
+ RowsAtCompileTime = VectorType::RowsAtCompileTime,
+ Flags = VectorType::Flags
+ };
+ typedef Ref<const Matrix<typename BlockSparseMatrixT::Scalar, (RowsAtCompileTime==1)? 1 : BlockSize, (ColsAtCompileTime==1)? 1 : BlockSize> >Scalar;
+ typedef typename BlockSparseMatrixT::Index Index;
+ public:
+ BlockVectorView(const BlockSparseMatrixT& spblockmat, const VectorType& vec)
+ : m_spblockmat(spblockmat),m_vec(vec)
+ { }
+ inline Index cols() const
+ {
+ return m_vec.cols();
+ }
+ inline Index size() const
+ {
+ return m_spblockmat.blockRows();
+ }
+ inline Scalar coeff(Index bi) const
+ {
+ Index startRow = m_spblockmat.blockRowsIndex(bi);
+ Index rowSize = m_spblockmat.blockRowsIndex(bi+1) - startRow;
+ return m_vec.middleRows(startRow, rowSize);
+ }
+ inline Scalar coeff(Index bi, Index j) const
+ {
+ Index startRow = m_spblockmat.blockRowsIndex(bi);
+ Index rowSize = m_spblockmat.blockRowsIndex(bi+1) - startRow;
+ return m_vec.block(startRow, j, rowSize, 1);
+ }
+ protected:
+ const BlockSparseMatrixT& m_spblockmat;
+ const VectorType& m_vec;
+};
+
+template<typename VectorType, typename Index> class BlockVectorReturn;
+
+
+// Proxy to view a regular vector as a block vector
+template<typename BlockSparseMatrixT, typename VectorType>
+class BlockVectorReturn
+{
+ public:
+ enum {
+ ColsAtCompileTime = VectorType::ColsAtCompileTime,
+ RowsAtCompileTime = VectorType::RowsAtCompileTime,
+ Flags = VectorType::Flags
+ };
+ typedef Ref<Matrix<typename VectorType::Scalar, RowsAtCompileTime, ColsAtCompileTime> > Scalar;
+ typedef typename BlockSparseMatrixT::Index Index;
+ public:
+ BlockVectorReturn(const BlockSparseMatrixT& spblockmat, VectorType& vec)
+ : m_spblockmat(spblockmat),m_vec(vec)
+ { }
+ inline Index size() const
+ {
+ return m_spblockmat.blockRows();
+ }
+ inline Scalar coeffRef(Index bi)
+ {
+ Index startRow = m_spblockmat.blockRowsIndex(bi);
+ Index rowSize = m_spblockmat.blockRowsIndex(bi+1) - startRow;
+ return m_vec.middleRows(startRow, rowSize);
+ }
+ inline Scalar coeffRef(Index bi, Index j)
+ {
+ Index startRow = m_spblockmat.blockRowsIndex(bi);
+ Index rowSize = m_spblockmat.blockRowsIndex(bi+1) - startRow;
+ return m_vec.block(startRow, j, rowSize, 1);
+ }
+
+ protected:
+ const BlockSparseMatrixT& m_spblockmat;
+ VectorType& m_vec;
+};
+
+// Block version of the sparse dense product
+template<typename Lhs, typename Rhs>
+class BlockSparseTimeDenseProduct;
+
+namespace internal {
+
+template<typename BlockSparseMatrixT, typename VecType>
+struct traits<BlockSparseTimeDenseProduct<BlockSparseMatrixT, VecType> >
+{
+ typedef Dense StorageKind;
+ typedef MatrixXpr XprKind;
+ typedef typename BlockSparseMatrixT::Scalar Scalar;
+ typedef typename BlockSparseMatrixT::Index Index;
+ enum {
+ RowsAtCompileTime = Dynamic,
+ ColsAtCompileTime = Dynamic,
+ MaxRowsAtCompileTime = Dynamic,
+ MaxColsAtCompileTime = Dynamic,
+ Flags = 0,
+ CoeffReadCost = internal::traits<BlockSparseMatrixT>::CoeffReadCost
+ };
+};
+} // end namespace internal
+
+template<typename Lhs, typename Rhs>
+class BlockSparseTimeDenseProduct
+ : public ProductBase<BlockSparseTimeDenseProduct<Lhs,Rhs>, Lhs, Rhs>
+{
+ public:
+ EIGEN_PRODUCT_PUBLIC_INTERFACE(BlockSparseTimeDenseProduct)
+
+ BlockSparseTimeDenseProduct(const Lhs& lhs, const Rhs& rhs) : Base(lhs,rhs)
+ {}
+
+ template<typename Dest> void scaleAndAddTo(Dest& dest, const typename Rhs::Scalar& alpha) const
+ {
+ BlockVectorReturn<Lhs,Dest> tmpDest(m_lhs, dest);
+ internal::sparse_time_dense_product( BlockSparseMatrixView<Lhs>(m_lhs), BlockVectorView<Lhs, Rhs>(m_lhs, m_rhs), tmpDest, alpha);
+ }
+
+ private:
+ BlockSparseTimeDenseProduct& operator=(const BlockSparseTimeDenseProduct&);
+};
+
+template<typename Scalar_, int _BlockAtCompileTime, int Options_, typename StorageIndex_>
+class BlockSparseMatrix : public SparseMatrixBase<BlockSparseMatrix<Scalar_,_BlockAtCompileTime, Options_,StorageIndex_> >
+{
+ public:
+ typedef Scalar_ Scalar;
+ typedef typename NumTraits<Scalar>::Real RealScalar;
+ typedef StorageIndex_ StorageIndex;
+ typedef typename internal::ref_selector<BlockSparseMatrix<Scalar_, _BlockAtCompileTime, Options_, StorageIndex_> >::type Nested;
+
+ enum {
+ Options = Options_,
+ Flags = Options,
+ BlockSize=_BlockAtCompileTime,
+ RowsAtCompileTime = Dynamic,
+ ColsAtCompileTime = Dynamic,
+ MaxRowsAtCompileTime = Dynamic,
+ MaxColsAtCompileTime = Dynamic,
+ IsVectorAtCompileTime = 0,
+ IsColMajor = Flags&RowMajorBit ? 0 : 1
+ };
+ typedef Matrix<Scalar, _BlockAtCompileTime, _BlockAtCompileTime,IsColMajor ? ColMajor : RowMajor> BlockScalar;
+ typedef Matrix<RealScalar, _BlockAtCompileTime, _BlockAtCompileTime,IsColMajor ? ColMajor : RowMajor> BlockRealScalar;
+ typedef std::conditional_t<_BlockAtCompileTime==Dynamic, Scalar, BlockScalar> BlockScalarReturnType;
+ typedef BlockSparseMatrix<Scalar, BlockSize, IsColMajor ? ColMajor : RowMajor, StorageIndex> PlainObject;
+ public:
+ // Default constructor
+ BlockSparseMatrix()
+ : m_innerBSize(0),m_outerBSize(0),m_innerOffset(0),m_outerOffset(0),
+ m_nonzerosblocks(0),m_values(0),m_blockPtr(0),m_indices(0),
+ m_outerIndex(0),m_blockSize(BlockSize)
+ { }
+
+
+ /**
+ * \brief Construct and resize
+ *
+ */
+ BlockSparseMatrix(Index brow, Index bcol)
+ : m_innerBSize(IsColMajor ? brow : bcol),
+ m_outerBSize(IsColMajor ? bcol : brow),
+ m_innerOffset(0),m_outerOffset(0),m_nonzerosblocks(0),
+ m_values(0),m_blockPtr(0),m_indices(0),
+ m_outerIndex(0),m_blockSize(BlockSize)
+ { }
+
+ /**
+ * \brief Copy-constructor
+ */
+ BlockSparseMatrix(const BlockSparseMatrix& other)
+ : m_innerBSize(other.m_innerBSize),m_outerBSize(other.m_outerBSize),
+ m_nonzerosblocks(other.m_nonzerosblocks),m_nonzeros(other.m_nonzeros),
+ m_blockPtr(0),m_blockSize(other.m_blockSize)
+ {
+ // should we allow copying between variable-size blocks and fixed-size blocks ??
+ eigen_assert(m_blockSize == BlockSize && " CAN NOT COPY BETWEEN FIXED-SIZE AND VARIABLE-SIZE BLOCKS");
+
+ std::copy(other.m_innerOffset, other.m_innerOffset+m_innerBSize+1, m_innerOffset);
+ std::copy(other.m_outerOffset, other.m_outerOffset+m_outerBSize+1, m_outerOffset);
+ std::copy(other.m_values, other.m_values+m_nonzeros, m_values);
+
+ if(m_blockSize != Dynamic)
+ std::copy(other.m_blockPtr, other.m_blockPtr+m_nonzerosblocks, m_blockPtr);
+
+ std::copy(other.m_indices, other.m_indices+m_nonzerosblocks, m_indices);
+ std::copy(other.m_outerIndex, other.m_outerIndex+m_outerBSize, m_outerIndex);
+ }
+
+ friend void swap(BlockSparseMatrix& first, BlockSparseMatrix& second)
+ {
+ std::swap(first.m_innerBSize, second.m_innerBSize);
+ std::swap(first.m_outerBSize, second.m_outerBSize);
+ std::swap(first.m_innerOffset, second.m_innerOffset);
+ std::swap(first.m_outerOffset, second.m_outerOffset);
+ std::swap(first.m_nonzerosblocks, second.m_nonzerosblocks);
+ std::swap(first.m_nonzeros, second.m_nonzeros);
+ std::swap(first.m_values, second.m_values);
+ std::swap(first.m_blockPtr, second.m_blockPtr);
+ std::swap(first.m_indices, second.m_indices);
+ std::swap(first.m_outerIndex, second.m_outerIndex);
+ std::swap(first.m_BlockSize, second.m_blockSize);
+ }
+
+ BlockSparseMatrix& operator=(BlockSparseMatrix other)
+ {
+ //Copy-and-swap paradigm ... avoid leaked data if thrown
+ swap(*this, other);
+ return *this;
+ }
+
+ // Destructor
+ ~BlockSparseMatrix()
+ {
+ delete[] m_outerIndex;
+ delete[] m_innerOffset;
+ delete[] m_outerOffset;
+ delete[] m_indices;
+ delete[] m_blockPtr;
+ delete[] m_values;
+ }
+
+
+ /**
+ * \brief Constructor from a sparse matrix
+ *
+ */
+ template<typename MatrixType>
+ inline BlockSparseMatrix(const MatrixType& spmat) : m_blockSize(BlockSize)
+ {
+ EIGEN_STATIC_ASSERT((m_blockSize != Dynamic), THIS_METHOD_IS_ONLY_FOR_FIXED_SIZE);
+
+ *this = spmat;
+ }
+
+ /**
+ * \brief Assignment from a sparse matrix with the same storage order
+ *
+ * Convert from a sparse matrix to block sparse matrix.
+ * \warning Before calling this function, tt is necessary to call
+ * either setBlockLayout() (matrices with variable-size blocks)
+ * or setBlockSize() (for fixed-size blocks).
+ */
+ template<typename MatrixType>
+ inline BlockSparseMatrix& operator=(const MatrixType& spmat)
+ {
+ eigen_assert((m_innerBSize != 0 && m_outerBSize != 0)
+ && "Trying to assign to a zero-size matrix, call resize() first");
+ eigen_assert(((MatrixType::Options&RowMajorBit) != IsColMajor) && "Wrong storage order");
+ typedef SparseMatrix<bool,MatrixType::Options,typename MatrixType::Index> MatrixPatternType;
+ MatrixPatternType blockPattern(blockRows(), blockCols());
+ m_nonzeros = 0;
+
+ // First, compute the number of nonzero blocks and their locations
+ for(StorageIndex bj = 0; bj < m_outerBSize; ++bj)
+ {
+ // Browse each outer block and compute the structure
+ std::vector<bool> nzblocksFlag(m_innerBSize,false); // Record the existing blocks
+ blockPattern.startVec(bj);
+ for(StorageIndex j = blockOuterIndex(bj); j < blockOuterIndex(bj+1); ++j)
+ {
+ typename MatrixType::InnerIterator it_spmat(spmat, j);
+ for(; it_spmat; ++it_spmat)
+ {
+ StorageIndex bi = innerToBlock(it_spmat.index()); // Index of the current nonzero block
+ if(!nzblocksFlag[bi])
+ {
+ // Save the index of this nonzero block
+ nzblocksFlag[bi] = true;
+ blockPattern.insertBackByOuterInnerUnordered(bj, bi) = true;
+ // Compute the total number of nonzeros (including explicit zeros in blocks)
+ m_nonzeros += blockOuterSize(bj) * blockInnerSize(bi);
+ }
+ }
+ } // end current outer block
+ }
+ blockPattern.finalize();
+
+ // Allocate the internal arrays
+ setBlockStructure(blockPattern);
+
+ for(StorageIndex nz = 0; nz < m_nonzeros; ++nz) m_values[nz] = Scalar(0);
+ for(StorageIndex bj = 0; bj < m_outerBSize; ++bj)
+ {
+ // Now copy the values
+ for(StorageIndex j = blockOuterIndex(bj); j < blockOuterIndex(bj+1); ++j)
+ {
+ // Browse the outer block column by column (for column-major matrices)
+ typename MatrixType::InnerIterator it_spmat(spmat, j);
+ for(; it_spmat; ++it_spmat)
+ {
+ StorageIndex idx = 0; // Position of this block in the column block
+ StorageIndex bi = innerToBlock(it_spmat.index()); // Index of the current nonzero block
+ // Go to the inner block where this element belongs to
+ while(bi > m_indices[m_outerIndex[bj]+idx]) ++idx; // Not expensive for ordered blocks
+ StorageIndex idxVal;// Get the right position in the array of values for this element
+ if(m_blockSize == Dynamic)
+ {
+ // Offset from all blocks before ...
+ idxVal = m_blockPtr[m_outerIndex[bj]+idx];
+ // ... and offset inside the block
+ idxVal += (j - blockOuterIndex(bj)) * blockOuterSize(bj) + it_spmat.index() - m_innerOffset[bi];
+ }
+ else
+ {
+ // All blocks before
+ idxVal = (m_outerIndex[bj] + idx) * m_blockSize * m_blockSize;
+ // inside the block
+ idxVal += (j - blockOuterIndex(bj)) * m_blockSize + (it_spmat.index()%m_blockSize);
+ }
+ // Insert the value
+ m_values[idxVal] = it_spmat.value();
+ } // end of this column
+ } // end of this block
+ } // end of this outer block
+
+ return *this;
+ }
+
+ /**
+ * \brief Set the nonzero block pattern of the matrix
+ *
+ * Given a sparse matrix describing the nonzero block pattern,
+ * this function prepares the internal pointers for values.
+ * After calling this function, any *nonzero* block (bi, bj) can be set
+ * with a simple call to coeffRef(bi,bj).
+ *
+ *
+ * \warning Before calling this function, tt is necessary to call
+ * either setBlockLayout() (matrices with variable-size blocks)
+ * or setBlockSize() (for fixed-size blocks).
+ *
+ * \param blockPattern Sparse matrix of boolean elements describing the block structure
+ *
+ * \sa setBlockLayout() \sa setBlockSize()
+ */
+ template<typename MatrixType>
+ void setBlockStructure(const MatrixType& blockPattern)
+ {
+ resize(blockPattern.rows(), blockPattern.cols());
+ reserve(blockPattern.nonZeros());
+
+ // Browse the block pattern and set up the various pointers
+ m_outerIndex[0] = 0;
+ if(m_blockSize == Dynamic) m_blockPtr[0] = 0;
+ for(StorageIndex nz = 0; nz < m_nonzeros; ++nz) m_values[nz] = Scalar(0);
+ for(StorageIndex bj = 0; bj < m_outerBSize; ++bj)
+ {
+ //Browse each outer block
+
+ //First, copy and save the indices of nonzero blocks
+ //FIXME : find a way to avoid this ...
+ std::vector<int> nzBlockIdx;
+ typename MatrixType::InnerIterator it(blockPattern, bj);
+ for(; it; ++it)
+ {
+ nzBlockIdx.push_back(it.index());
+ }
+ std::sort(nzBlockIdx.begin(), nzBlockIdx.end());
+
+ // Now, fill block indices and (eventually) pointers to blocks
+ for(StorageIndex idx = 0; idx < nzBlockIdx.size(); ++idx)
+ {
+ StorageIndex offset = m_outerIndex[bj]+idx; // offset in m_indices
+ m_indices[offset] = nzBlockIdx[idx];
+ if(m_blockSize == Dynamic)
+ m_blockPtr[offset] = m_blockPtr[offset-1] + blockInnerSize(nzBlockIdx[idx]) * blockOuterSize(bj);
+ // There is no blockPtr for fixed-size blocks... not needed !???
+ }
+ // Save the pointer to the next outer block
+ m_outerIndex[bj+1] = m_outerIndex[bj] + nzBlockIdx.size();
+ }
+ }
+
+ /**
+ * \brief Set the number of rows and columns blocks
+ */
+ inline void resize(Index brow, Index bcol)
+ {
+ m_innerBSize = IsColMajor ? brow : bcol;
+ m_outerBSize = IsColMajor ? bcol : brow;
+ }
+
+ /**
+ * \brief set the block size at runtime for fixed-size block layout
+ *
+ * Call this only for fixed-size blocks
+ */
+ inline void setBlockSize(Index blockSize)
+ {
+ m_blockSize = blockSize;
+ }
+
+ /**
+ * \brief Set the row and column block layouts,
+ *
+ * This function set the size of each row and column block.
+ * So this function should be used only for blocks with variable size.
+ * \param rowBlocks : Number of rows per row block
+ * \param colBlocks : Number of columns per column block
+ * \sa resize(), setBlockSize()
+ */
+ inline void setBlockLayout(const VectorXi& rowBlocks, const VectorXi& colBlocks)
+ {
+ const VectorXi& innerBlocks = IsColMajor ? rowBlocks : colBlocks;
+ const VectorXi& outerBlocks = IsColMajor ? colBlocks : rowBlocks;
+ eigen_assert(m_innerBSize == innerBlocks.size() && "CHECK THE NUMBER OF ROW OR COLUMN BLOCKS");
+ eigen_assert(m_outerBSize == outerBlocks.size() && "CHECK THE NUMBER OF ROW OR COLUMN BLOCKS");
+ m_outerBSize = outerBlocks.size();
+ // starting index of blocks... cumulative sums
+ m_innerOffset = new StorageIndex[m_innerBSize+1];
+ m_outerOffset = new StorageIndex[m_outerBSize+1];
+ m_innerOffset[0] = 0;
+ m_outerOffset[0] = 0;
+ std::partial_sum(&innerBlocks[0], &innerBlocks[m_innerBSize-1]+1, &m_innerOffset[1]);
+ std::partial_sum(&outerBlocks[0], &outerBlocks[m_outerBSize-1]+1, &m_outerOffset[1]);
+
+ // Compute the total number of nonzeros
+ m_nonzeros = 0;
+ for(StorageIndex bj = 0; bj < m_outerBSize; ++bj)
+ for(StorageIndex bi = 0; bi < m_innerBSize; ++bi)
+ m_nonzeros += outerBlocks[bj] * innerBlocks[bi];
+
+ }
+
+ /**
+ * \brief Allocate the internal array of pointers to blocks and their inner indices
+ *
+ * \note For fixed-size blocks, call setBlockSize() to set the block.
+ * And For variable-size blocks, call setBlockLayout() before using this function
+ *
+ * \param nonzerosblocks Number of nonzero blocks. The total number of nonzeros is
+ * is computed in setBlockLayout() for variable-size blocks
+ * \sa setBlockSize()
+ */
+ inline void reserve(const Index nonzerosblocks)
+ {
+ eigen_assert((m_innerBSize != 0 && m_outerBSize != 0) &&
+ "TRYING TO RESERVE ZERO-SIZE MATRICES, CALL resize() first");
+
+ //FIXME Should free if already allocated
+ m_outerIndex = new StorageIndex[m_outerBSize+1];
+
+ m_nonzerosblocks = nonzerosblocks;
+ if(m_blockSize != Dynamic)
+ {
+ m_nonzeros = nonzerosblocks * (m_blockSize * m_blockSize);
+ m_blockPtr = 0;
+ }
+ else
+ {
+ // m_nonzeros is already computed in setBlockLayout()
+ m_blockPtr = new StorageIndex[m_nonzerosblocks+1];
+ }
+ m_indices = new StorageIndex[m_nonzerosblocks+1];
+ m_values = new Scalar[m_nonzeros];
+ }
+
+
+ /**
+ * \brief Fill values in a matrix from a triplet list.
+ *
+ * Each triplet item has a block stored in an Eigen dense matrix.
+ * The InputIterator class should provide the functions row(), col() and value()
+ *
+ * \note For fixed-size blocks, call setBlockSize() before this function.
+ *
+ * FIXME Do not accept duplicates
+ */
+ template<typename InputIterator>
+ void setFromTriplets(const InputIterator& begin, const InputIterator& end)
+ {
+ eigen_assert((m_innerBSize!=0 && m_outerBSize !=0) && "ZERO BLOCKS, PLEASE CALL resize() before");
+
+ /* First, sort the triplet list
+ * FIXME This can be unnecessarily expensive since only the inner indices have to be sorted
+ * The best approach is like in SparseMatrix::setFromTriplets()
+ */
+ internal::TripletComp<InputIterator, IsColMajor> tripletcomp;
+ std::sort(begin, end, tripletcomp);
+
+ /* Count the number of rows and column blocks,
+ * and the number of nonzero blocks per outer dimension
+ */
+ VectorXi rowBlocks(m_innerBSize); // Size of each block row
+ VectorXi colBlocks(m_outerBSize); // Size of each block column
+ rowBlocks.setZero(); colBlocks.setZero();
+ VectorXi nzblock_outer(m_outerBSize); // Number of nz blocks per outer vector
+ VectorXi nz_outer(m_outerBSize); // Number of nz per outer vector...for variable-size blocks
+ nzblock_outer.setZero();
+ nz_outer.setZero();
+ for(InputIterator it(begin); it !=end; ++it)
+ {
+ eigen_assert(it->row() >= 0 && it->row() < this->blockRows() && it->col() >= 0 && it->col() < this->blockCols());
+ eigen_assert((it->value().rows() == it->value().cols() && (it->value().rows() == m_blockSize))
+ || (m_blockSize == Dynamic));
+
+ if(m_blockSize == Dynamic)
+ {
+ eigen_assert((rowBlocks[it->row()] == 0 || rowBlocks[it->row()] == it->value().rows()) &&
+ "NON CORRESPONDING SIZES FOR ROW BLOCKS");
+ eigen_assert((colBlocks[it->col()] == 0 || colBlocks[it->col()] == it->value().cols()) &&
+ "NON CORRESPONDING SIZES FOR COLUMN BLOCKS");
+ rowBlocks[it->row()] =it->value().rows();
+ colBlocks[it->col()] = it->value().cols();
+ }
+ nz_outer(IsColMajor ? it->col() : it->row()) += it->value().rows() * it->value().cols();
+ nzblock_outer(IsColMajor ? it->col() : it->row())++;
+ }
+ // Allocate member arrays
+ if(m_blockSize == Dynamic) setBlockLayout(rowBlocks, colBlocks);
+ StorageIndex nzblocks = nzblock_outer.sum();
+ reserve(nzblocks);
+
+ // Temporary markers
+ VectorXi block_id(m_outerBSize); // To be used as a block marker during insertion
+
+ // Setup outer index pointers and markers
+ m_outerIndex[0] = 0;
+ if (m_blockSize == Dynamic) m_blockPtr[0] = 0;
+ for(StorageIndex bj = 0; bj < m_outerBSize; ++bj)
+ {
+ m_outerIndex[bj+1] = m_outerIndex[bj] + nzblock_outer(bj);
+ block_id(bj) = m_outerIndex[bj];
+ if(m_blockSize==Dynamic)
+ {
+ m_blockPtr[m_outerIndex[bj+1]] = m_blockPtr[m_outerIndex[bj]] + nz_outer(bj);
+ }
+ }
+
+ // Fill the matrix
+ for(InputIterator it(begin); it!=end; ++it)
+ {
+ StorageIndex outer = IsColMajor ? it->col() : it->row();
+ StorageIndex inner = IsColMajor ? it->row() : it->col();
+ m_indices[block_id(outer)] = inner;
+ StorageIndex block_size = it->value().rows()*it->value().cols();
+ StorageIndex nz_marker = blockPtr(block_id[outer]);
+ memcpy(&(m_values[nz_marker]), it->value().data(), block_size * sizeof(Scalar));
+ if(m_blockSize == Dynamic)
+ {
+ m_blockPtr[block_id(outer)+1] = m_blockPtr[block_id(outer)] + block_size;
+ }
+ block_id(outer)++;
+ }
+
+ // An alternative when the outer indices are sorted...no need to use an array of markers
+// for(Index bcol = 0; bcol < m_outerBSize; ++bcol)
+// {
+// Index id = 0, id_nz = 0, id_nzblock = 0;
+// for(InputIterator it(begin); it!=end; ++it)
+// {
+// while (id<bcol) // one pass should do the job unless there are empty columns
+// {
+// id++;
+// m_outerIndex[id+1]=m_outerIndex[id];
+// }
+// m_outerIndex[id+1] += 1;
+// m_indices[id_nzblock]=brow;
+// Index block_size = it->value().rows()*it->value().cols();
+// m_blockPtr[id_nzblock+1] = m_blockPtr[id_nzblock] + block_size;
+// id_nzblock++;
+// memcpy(&(m_values[id_nz]),it->value().data(), block_size*sizeof(Scalar));
+// id_nz += block_size;
+// }
+// while(id < m_outerBSize-1) // Empty columns at the end
+// {
+// id++;
+// m_outerIndex[id+1]=m_outerIndex[id];
+// }
+// }
+ }
+
+
+ /**
+ * \returns the number of rows
+ */
+ inline Index rows() const
+ {
+// return blockRows();
+ return (IsColMajor ? innerSize() : outerSize());
+ }
+
+ /**
+ * \returns the number of cols
+ */
+ inline Index cols() const
+ {
+// return blockCols();
+ return (IsColMajor ? outerSize() : innerSize());
+ }
+
+ inline Index innerSize() const
+ {
+ if(m_blockSize == Dynamic) return m_innerOffset[m_innerBSize];
+ else return (m_innerBSize * m_blockSize) ;
+ }
+
+ inline Index outerSize() const
+ {
+ if(m_blockSize == Dynamic) return m_outerOffset[m_outerBSize];
+ else return (m_outerBSize * m_blockSize) ;
+ }
+ /** \returns the number of rows grouped by blocks */
+ inline Index blockRows() const
+ {
+ return (IsColMajor ? m_innerBSize : m_outerBSize);
+ }
+ /** \returns the number of columns grouped by blocks */
+ inline Index blockCols() const
+ {
+ return (IsColMajor ? m_outerBSize : m_innerBSize);
+ }
+
+ inline Index outerBlocks() const { return m_outerBSize; }
+ inline Index innerBlocks() const { return m_innerBSize; }
+
+ /** \returns the block index where outer belongs to */
+ inline Index outerToBlock(Index outer) const
+ {
+ eigen_assert(outer < outerSize() && "OUTER INDEX OUT OF BOUNDS");
+
+ if(m_blockSize != Dynamic)
+ return (outer / m_blockSize); // Integer division
+
+ StorageIndex b_outer = 0;
+ while(m_outerOffset[b_outer] <= outer) ++b_outer;
+ return b_outer - 1;
+ }
+ /** \returns the block index where inner belongs to */
+ inline Index innerToBlock(Index inner) const
+ {
+ eigen_assert(inner < innerSize() && "OUTER INDEX OUT OF BOUNDS");
+
+ if(m_blockSize != Dynamic)
+ return (inner / m_blockSize); // Integer division
+
+ StorageIndex b_inner = 0;
+ while(m_innerOffset[b_inner] <= inner) ++b_inner;
+ return b_inner - 1;
+ }
+
+ /**
+ *\returns a reference to the (i,j) block as an Eigen Dense Matrix
+ */
+ Ref<BlockScalar> coeffRef(Index brow, Index bcol)
+ {
+ eigen_assert(brow < blockRows() && "BLOCK ROW INDEX OUT OF BOUNDS");
+ eigen_assert(bcol < blockCols() && "BLOCK nzblocksFlagCOLUMN OUT OF BOUNDS");
+
+ StorageIndex rsize = IsColMajor ? blockInnerSize(brow): blockOuterSize(bcol);
+ StorageIndex csize = IsColMajor ? blockOuterSize(bcol) : blockInnerSize(brow);
+ StorageIndex inner = IsColMajor ? brow : bcol;
+ StorageIndex outer = IsColMajor ? bcol : brow;
+ StorageIndex offset = m_outerIndex[outer];
+ while(offset < m_outerIndex[outer+1] && m_indices[offset] != inner)
+ offset++;
+ if(m_indices[offset] == inner)
+ {
+ return Map<BlockScalar>(&(m_values[blockPtr(offset)]), rsize, csize);
+ }
+ else
+ {
+ //FIXME the block does not exist, Insert it !!!!!!!!!
+ eigen_assert("DYNAMIC INSERTION IS NOT YET SUPPORTED");
+ }
+ }
+
+ /**
+ * \returns the value of the (i,j) block as an Eigen Dense Matrix
+ */
+ Map<const BlockScalar> coeff(Index brow, Index bcol) const
+ {
+ eigen_assert(brow < blockRows() && "BLOCK ROW INDEX OUT OF BOUNDS");
+ eigen_assert(bcol < blockCols() && "BLOCK COLUMN OUT OF BOUNDS");
+
+ StorageIndex rsize = IsColMajor ? blockInnerSize(brow): blockOuterSize(bcol);
+ StorageIndex csize = IsColMajor ? blockOuterSize(bcol) : blockInnerSize(brow);
+ StorageIndex inner = IsColMajor ? brow : bcol;
+ StorageIndex outer = IsColMajor ? bcol : brow;
+ StorageIndex offset = m_outerIndex[outer];
+ while(offset < m_outerIndex[outer+1] && m_indices[offset] != inner) offset++;
+ if(m_indices[offset] == inner)
+ {
+ return Map<const BlockScalar> (&(m_values[blockPtr(offset)]), rsize, csize);
+ }
+ else
+// return BlockScalar::Zero(rsize, csize);
+ eigen_assert("NOT YET SUPPORTED");
+ }
+
+ // Block Matrix times vector product
+ template<typename VecType>
+ BlockSparseTimeDenseProduct<BlockSparseMatrix, VecType> operator*(const VecType& lhs) const
+ {
+ return BlockSparseTimeDenseProduct<BlockSparseMatrix, VecType>(*this, lhs);
+ }
+
+ /** \returns the number of nonzero blocks */
+ inline Index nonZerosBlocks() const { return m_nonzerosblocks; }
+ /** \returns the total number of nonzero elements, including eventual explicit zeros in blocks */
+ inline Index nonZeros() const { return m_nonzeros; }
+
+ inline BlockScalarReturnType *valuePtr() {return static_cast<BlockScalarReturnType *>(m_values);}
+// inline Scalar *valuePtr(){ return m_values; }
+ inline StorageIndex *innerIndexPtr() {return m_indices; }
+ inline const StorageIndex *innerIndexPtr() const {return m_indices; }
+ inline StorageIndex *outerIndexPtr() {return m_outerIndex; }
+ inline const StorageIndex* outerIndexPtr() const {return m_outerIndex; }
+
+ /** \brief for compatibility purposes with the SparseMatrix class */
+ inline bool isCompressed() const {return true;}
+ /**
+ * \returns the starting index of the bi row block
+ */
+ inline Index blockRowsIndex(Index bi) const
+ {
+ return IsColMajor ? blockInnerIndex(bi) : blockOuterIndex(bi);
+ }
+
+ /**
+ * \returns the starting index of the bj col block
+ */
+ inline Index blockColsIndex(Index bj) const
+ {
+ return IsColMajor ? blockOuterIndex(bj) : blockInnerIndex(bj);
+ }
+
+ inline Index blockOuterIndex(Index bj) const
+ {
+ return (m_blockSize == Dynamic) ? m_outerOffset[bj] : (bj * m_blockSize);
+ }
+ inline Index blockInnerIndex(Index bi) const
+ {
+ return (m_blockSize == Dynamic) ? m_innerOffset[bi] : (bi * m_blockSize);
+ }
+
+ // Not needed ???
+ inline Index blockInnerSize(Index bi) const
+ {
+ return (m_blockSize == Dynamic) ? (m_innerOffset[bi+1] - m_innerOffset[bi]) : m_blockSize;
+ }
+ inline Index blockOuterSize(Index bj) const
+ {
+ return (m_blockSize == Dynamic) ? (m_outerOffset[bj+1]- m_outerOffset[bj]) : m_blockSize;
+ }
+
+ /**
+ * \brief Browse the matrix by outer index
+ */
+ class InnerIterator; // Browse column by column
+
+ /**
+ * \brief Browse the matrix by block outer index
+ */
+ class BlockInnerIterator; // Browse block by block
+
+ friend std::ostream & operator << (std::ostream & s, const BlockSparseMatrix& m)
+ {
+ for (StorageIndex j = 0; j < m.outerBlocks(); ++j)
+ {
+ BlockInnerIterator itb(m, j);
+ for(; itb; ++itb)
+ {
+ s << "("<<itb.row() << ", " << itb.col() << ")\n";
+ s << itb.value() <<"\n";
+ }
+ }
+ s << std::endl;
+ return s;
+ }
+
+ /**
+ * \returns the starting position of the block \p id in the array of values
+ */
+ Index blockPtr(Index id) const
+ {
+ if(m_blockSize == Dynamic) return m_blockPtr[id];
+ else return id * m_blockSize * m_blockSize;
+ //return blockDynIdx(id, std::conditional_t<(BlockSize==Dynamic), internal::true_type, internal::false_type>());
+ }
+
+
+ protected:
+// inline Index blockDynIdx(Index id, internal::true_type) const
+// {
+// return m_blockPtr[id];
+// }
+// inline Index blockDynIdx(Index id, internal::false_type) const
+// {
+// return id * BlockSize * BlockSize;
+// }
+
+ // To be implemented
+ // Insert a block at a particular location... need to make a room for that
+ Map<BlockScalar> insert(Index brow, Index bcol);
+
+ Index m_innerBSize; // Number of block rows
+ Index m_outerBSize; // Number of block columns
+ StorageIndex *m_innerOffset; // Starting index of each inner block (size m_innerBSize+1)
+ StorageIndex *m_outerOffset; // Starting index of each outer block (size m_outerBSize+1)
+ Index m_nonzerosblocks; // Total nonzeros blocks (lower than m_innerBSize x m_outerBSize)
+ Index m_nonzeros; // Total nonzeros elements
+ Scalar *m_values; //Values stored block column after block column (size m_nonzeros)
+ StorageIndex *m_blockPtr; // Pointer to the beginning of each block in m_values, size m_nonzeroblocks ... null for fixed-size blocks
+ StorageIndex *m_indices; //Inner block indices, size m_nonzerosblocks ... OK
+ StorageIndex *m_outerIndex; // Starting pointer of each block column in m_indices (size m_outerBSize)... OK
+ Index m_blockSize; // Size of a block for fixed-size blocks, otherwise -1
+};
+
+template<typename Scalar_, int _BlockAtCompileTime, int Options_, typename StorageIndex_>
+class BlockSparseMatrix<Scalar_, _BlockAtCompileTime, Options_, StorageIndex_>::BlockInnerIterator
+{
+ public:
+
+ enum{
+ Flags = Options_
+ };
+
+ BlockInnerIterator(const BlockSparseMatrix& mat, const Index outer)
+ : m_mat(mat),m_outer(outer),
+ m_id(mat.m_outerIndex[outer]),
+ m_end(mat.m_outerIndex[outer+1])
+ {
+ }
+
+ inline BlockInnerIterator& operator++() {m_id++; return *this; }
+
+ inline const Map<const BlockScalar> value() const
+ {
+ return Map<const BlockScalar>(&(m_mat.m_values[m_mat.blockPtr(m_id)]),
+ rows(),cols());
+ }
+ inline Map<BlockScalar> valueRef()
+ {
+ return Map<BlockScalar>(&(m_mat.m_values[m_mat.blockPtr(m_id)]),
+ rows(),cols());
+ }
+ // Block inner index
+ inline Index index() const {return m_mat.m_indices[m_id]; }
+ inline Index outer() const { return m_outer; }
+ // block row index
+ inline Index row() const {return index(); }
+ // block column index
+ inline Index col() const {return outer(); }
+ // FIXME Number of rows in the current block
+ inline Index rows() const { return (m_mat.m_blockSize==Dynamic) ? (m_mat.m_innerOffset[index()+1] - m_mat.m_innerOffset[index()]) : m_mat.m_blockSize; }
+ // Number of columns in the current block ...
+ inline Index cols() const { return (m_mat.m_blockSize==Dynamic) ? (m_mat.m_outerOffset[m_outer+1]-m_mat.m_outerOffset[m_outer]) : m_mat.m_blockSize;}
+ inline operator bool() const { return (m_id < m_end); }
+
+ protected:
+ const BlockSparseMatrix<Scalar_, _BlockAtCompileTime, Options_, StorageIndex>& m_mat;
+ const Index m_outer;
+ Index m_id;
+ Index m_end;
+};
+
+template<typename Scalar_, int _BlockAtCompileTime, int Options_, typename StorageIndex_>
+class BlockSparseMatrix<Scalar_, _BlockAtCompileTime, Options_, StorageIndex_>::InnerIterator
+{
+ public:
+ InnerIterator(const BlockSparseMatrix& mat, Index outer)
+ : m_mat(mat),m_outerB(mat.outerToBlock(outer)),m_outer(outer),
+ itb(mat, mat.outerToBlock(outer)),
+ m_offset(outer - mat.blockOuterIndex(m_outerB))
+ {
+ if (itb)
+ {
+ m_id = m_mat.blockInnerIndex(itb.index());
+ m_start = m_id;
+ m_end = m_mat.blockInnerIndex(itb.index()+1);
+ }
+ }
+ inline InnerIterator& operator++()
+ {
+ m_id++;
+ if (m_id >= m_end)
+ {
+ ++itb;
+ if (itb)
+ {
+ m_id = m_mat.blockInnerIndex(itb.index());
+ m_start = m_id;
+ m_end = m_mat.blockInnerIndex(itb.index()+1);
+ }
+ }
+ return *this;
+ }
+ inline const Scalar& value() const
+ {
+ return itb.value().coeff(m_id - m_start, m_offset);
+ }
+ inline Scalar& valueRef()
+ {
+ return itb.valueRef().coeff(m_id - m_start, m_offset);
+ }
+ inline Index index() const { return m_id; }
+ inline Index outer() const {return m_outer; }
+ inline Index col() const {return outer(); }
+ inline Index row() const { return index();}
+ inline operator bool() const
+ {
+ return itb;
+ }
+ protected:
+ const BlockSparseMatrix& m_mat;
+ const Index m_outer;
+ const Index m_outerB;
+ BlockInnerIterator itb; // Iterator through the blocks
+ const Index m_offset; // Position of this column in the block
+ Index m_start; // starting inner index of this block
+ Index m_id; // current inner index in the block
+ Index m_end; // starting inner index of the next block
+
+};
+} // end namespace Eigen
+
+#endif // EIGEN_SPARSEBLOCKMATRIX_H
diff --git a/unsupported/Eigen/src/SparseExtra/InternalHeaderCheck.h b/unsupported/Eigen/src/SparseExtra/InternalHeaderCheck.h
new file mode 100644
index 0000000..0e55251
--- /dev/null
+++ b/unsupported/Eigen/src/SparseExtra/InternalHeaderCheck.h
@@ -0,0 +1,3 @@
+#ifndef EIGEN_SPARSE_EXTRA_MODULE_H
+#error "Please include unsupported/Eigen/SparseExtra instead of including headers inside the src directory directly."
+#endif
diff --git a/unsupported/Eigen/src/SparseExtra/MarketIO.h b/unsupported/Eigen/src/SparseExtra/MarketIO.h
new file mode 100644
index 0000000..cf5828e
--- /dev/null
+++ b/unsupported/Eigen/src/SparseExtra/MarketIO.h
@@ -0,0 +1,384 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2011 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2012 Desire NUENTSA WAKAM <desire.nuentsa_wakam@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_SPARSE_MARKET_IO_H
+#define EIGEN_SPARSE_MARKET_IO_H
+
+#include <iostream>
+#include <vector>
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal
+{
+ template <typename Scalar, typename StorageIndex>
+ inline void GetMarketLine (const char* line, StorageIndex& i, StorageIndex& j, Scalar& value)
+ {
+ std::stringstream sline(line);
+ sline >> i >> j >> value;
+ }
+
+ template<> inline void GetMarketLine (const char* line, int& i, int& j, float& value)
+ { std::sscanf(line, "%d %d %g", &i, &j, &value); }
+
+ template<> inline void GetMarketLine (const char* line, int& i, int& j, double& value)
+ { std::sscanf(line, "%d %d %lg", &i, &j, &value); }
+
+ template<> inline void GetMarketLine (const char* line, int& i, int& j, std::complex<float>& value)
+ { std::sscanf(line, "%d %d %g %g", &i, &j, &numext::real_ref(value), &numext::imag_ref(value)); }
+
+ template<> inline void GetMarketLine (const char* line, int& i, int& j, std::complex<double>& value)
+ { std::sscanf(line, "%d %d %lg %lg", &i, &j, &numext::real_ref(value), &numext::imag_ref(value)); }
+
+ template <typename Scalar, typename StorageIndex>
+ inline void GetMarketLine (const char* line, StorageIndex& i, StorageIndex& j, std::complex<Scalar>& value)
+ {
+ std::stringstream sline(line);
+ Scalar valR, valI;
+ sline >> i >> j >> valR >> valI;
+ value = std::complex<Scalar>(valR,valI);
+ }
+
+ template <typename RealScalar>
+ inline void GetDenseElt (const std::string& line, RealScalar& val)
+ {
+ std::istringstream newline(line);
+ newline >> val;
+ }
+
+ template <typename RealScalar>
+ inline void GetDenseElt (const std::string& line, std::complex<RealScalar>& val)
+ {
+ RealScalar valR, valI;
+ std::istringstream newline(line);
+ newline >> valR >> valI;
+ val = std::complex<RealScalar>(valR, valI);
+ }
+
+ template<typename Scalar>
+ inline void putMarketHeader(std::string& header,int sym)
+ {
+ header= "%%MatrixMarket matrix coordinate ";
+ if(internal::is_same<Scalar, std::complex<float> >::value || internal::is_same<Scalar, std::complex<double> >::value)
+ {
+ header += " complex";
+ if(sym == Symmetric) header += " symmetric";
+ else if (sym == SelfAdjoint) header += " Hermitian";
+ else header += " general";
+ }
+ else
+ {
+ header += " real";
+ if(sym == Symmetric) header += " symmetric";
+ else header += " general";
+ }
+ }
+
+ template<typename Scalar, typename StorageIndex>
+ inline void PutMatrixElt(Scalar value, StorageIndex row, StorageIndex col, std::ofstream& out)
+ {
+ out << row << " "<< col << " " << value << "\n";
+ }
+ template<typename Scalar, typename StorageIndex>
+ inline void PutMatrixElt(std::complex<Scalar> value, StorageIndex row, StorageIndex col, std::ofstream& out)
+ {
+ out << row << " " << col << " " << value.real() << " " << value.imag() << "\n";
+ }
+
+
+ template<typename Scalar>
+ inline void putDenseElt(Scalar value, std::ofstream& out)
+ {
+ out << value << "\n";
+ }
+ template<typename Scalar>
+ inline void putDenseElt(std::complex<Scalar> value, std::ofstream& out)
+ {
+ out << value.real() << " " << value.imag()<< "\n";
+ }
+
+} // end namespace internal
+
+
+/**
+ * \ingroup SparseExtra_Module
+ * @brief Reads the header of a matrixmarket file and determines the properties of a matrix
+ *
+ * @param filename of the file
+ * @param sym if the matrix is hermitian,symmetric or none of the latter (sym=0)
+ * @param iscomplex if the matrix has complex or real coefficients
+ * @param isdense if the matrix is dense or sparse
+ * @return true if the file was found
+ */
+inline bool getMarketHeader(const std::string& filename, int& sym, bool& iscomplex, bool& isdense)
+{
+ sym = 0;
+ iscomplex = false;
+ isdense = false;
+ std::ifstream in(filename.c_str(),std::ios::in);
+ if(!in)
+ return false;
+
+ std::string line;
+ // The matrix header is always the first line in the file
+ std::getline(in, line); eigen_assert(in.good());
+
+ std::stringstream fmtline(line);
+ std::string substr[5];
+ fmtline>> substr[0] >> substr[1] >> substr[2] >> substr[3] >> substr[4];
+ if(substr[2].compare("array") == 0) isdense = true;
+ if(substr[3].compare("complex") == 0) iscomplex = true;
+ if(substr[4].compare("symmetric") == 0) sym = Symmetric;
+ else if (substr[4].compare("Hermitian") == 0) sym = SelfAdjoint;
+
+ return true;
+}
+/**
+ * \ingroup SparseExtra_Module
+ * @brief Loads a sparse matrix from a matrixmarket format file.
+ *
+ * @tparam SparseMatrixType to read into, symmetries are not supported
+ * @param mat SparseMatrix to read into, current values are overwritten
+ * @param filename to parse matrix from
+ * @return returns true if file exists. Returns false if the parsing did not succeed.
+ */
+template<typename SparseMatrixType>
+bool loadMarket(SparseMatrixType& mat, const std::string& filename)
+{
+ typedef typename SparseMatrixType::Scalar Scalar;
+ typedef typename SparseMatrixType::StorageIndex StorageIndex;
+ std::ifstream input(filename.c_str(),std::ios::in);
+ if(!input)
+ return false;
+
+ char rdbuffer[4096];
+ input.rdbuf()->pubsetbuf(rdbuffer, 4096);
+
+ const int maxBuffersize = 2048;
+ char buffer[maxBuffersize];
+
+ bool readsizes = false;
+
+ typedef Triplet<Scalar,StorageIndex> T;
+ std::vector<T> elements;
+
+ Index M(-1), N(-1), NNZ(-1);
+ Index count = 0;
+ while(input.getline(buffer, maxBuffersize))
+ {
+ // skip comments
+ //NOTE An appropriate test should be done on the header to get the symmetry
+ if(buffer[0]=='%')
+ continue;
+
+ if(!readsizes)
+ {
+ std::stringstream line(buffer);
+ line >> M >> N >> NNZ;
+ if(M > 0 && N > 0)
+ {
+ readsizes = true;
+ mat.resize(M,N);
+ mat.reserve(NNZ);
+ }
+ }
+ else
+ {
+ StorageIndex i(-1), j(-1);
+ Scalar value;
+ internal::GetMarketLine(buffer, i, j, value);
+
+ i--;
+ j--;
+ if(i>=0 && j>=0 && i<M && j<N)
+ {
+ ++count;
+ elements.push_back(T(i,j,value));
+ }
+ else
+ {
+ std::cerr << "Invalid read: " << i << "," << j << "\n";
+ return false;
+ }
+ }
+ }
+
+ mat.setFromTriplets(elements.begin(), elements.end());
+ if(count!=NNZ){
+ std::cerr << count << "!=" << NNZ << "\n";
+ return false;
+ }
+ input.close();
+ return true;
+}
+
+
+/**
+ * \ingroup SparseExtra_Module
+ * @brief Loads a dense Matrix or Vector from a matrixmarket file. If a statically sized matrix has to be parsed and the file contains the wrong dimensions it is undefined behaviour.
+ *
+ * @tparam DenseMatrixType to read into
+ * @param mat DenseMatrix to read into, current values are overwritten, symmetries are not supported
+ * @param filename to parse matrix from
+ * @return true if parsing was successful. Returns false if the parsing did not succeed.
+ */
+template<typename DenseType>
+bool loadMarketDense(DenseType& mat, const std::string& filename)
+{
+ typedef typename DenseType::Scalar Scalar;
+ std::ifstream in(filename.c_str(), std::ios::in);
+ if(!in)
+ return false;
+
+ std::string line;
+ Index rows(0), cols(0);
+ do
+ { // Skip comments
+ std::getline(in, line); eigen_assert(in.good());
+ } while (line[0] == '%');
+ std::istringstream newline(line);
+ newline >> rows >> cols;
+
+ bool sizes_not_positive=(rows<1 || cols<1);
+ bool wrong_input_rows = (DenseType::MaxRowsAtCompileTime != Dynamic && rows > DenseType::MaxRowsAtCompileTime) ||
+ (DenseType::RowsAtCompileTime!=Dynamic && rows!=DenseType::RowsAtCompileTime);
+ bool wrong_input_cols = (DenseType::MaxColsAtCompileTime != Dynamic && cols > DenseType::MaxColsAtCompileTime) ||
+ (DenseType::ColsAtCompileTime!=Dynamic && cols!=DenseType::ColsAtCompileTime);
+
+ if(sizes_not_positive || wrong_input_rows || wrong_input_cols){
+ if(sizes_not_positive){
+ std::cerr<< "non-positive row or column size in file" << filename << "\n";
+ }else{
+ std::cerr<< "Input matrix can not be resized to"<<rows<<" x "<<cols<< "as given in " << filename << "\n";
+ }
+ in.close();
+ return false;
+ }
+
+ mat.resize(rows,cols);
+ Index row = 0;
+ Index col = 0;
+ Index n=0;
+ Scalar value;
+ while ( std::getline(in, line) && (row < rows) && (col < cols)){
+ internal::GetDenseElt(line, value);
+ //matrixmarket format is column major
+ mat(row,col) = value;
+ row++;
+ if(row==rows){
+ row=0;
+ col++;
+ }
+ n++;
+ }
+ in.close();
+ if (n!=mat.size()){
+ std::cerr<< "Unable to read all elements from file " << filename << "\n";
+ return false;
+ }
+ return true;
+}
+/**
+ * \ingroup SparseExtra_Module
+ * @brief Same functionality as loadMarketDense, deprecated
+ */
+template<typename VectorType>
+bool loadMarketVector(VectorType& vec, const std::string& filename)
+{
+ return loadMarketDense(vec, filename);
+}
+
+/**
+ * \ingroup SparseExtra_Module
+ * @brief writes a sparse Matrix to a marketmarket format file
+ *
+ * @tparam SparseMatrixType to write to file
+ * @param mat matrix to write to file
+ * @param filename filename to write to
+ * @param sym at the moment no symmetry operations are supported
+ * @return true if writing succeeded
+ */
+template<typename SparseMatrixType>
+bool saveMarket(const SparseMatrixType& mat, const std::string& filename, int sym = 0)
+{
+ typedef typename SparseMatrixType::Scalar Scalar;
+ typedef typename SparseMatrixType::RealScalar RealScalar;
+ std::ofstream out(filename.c_str(),std::ios::out);
+ if(!out)
+ return false;
+
+ out.flags(std::ios_base::scientific);
+ out.precision(std::numeric_limits<RealScalar>::digits10 + 2);
+ std::string header;
+ internal::putMarketHeader<Scalar>(header, sym);
+ out << header << std::endl;
+ out << mat.rows() << " " << mat.cols() << " " << mat.nonZeros() << "\n";
+ int count = 0;
+ for(int j=0; j<mat.outerSize(); ++j)
+ for(typename SparseMatrixType::InnerIterator it(mat,j); it; ++it)
+ {
+ ++ count;
+ internal::PutMatrixElt(it.value(), it.row()+1, it.col()+1, out);
+ }
+ out.close();
+ return true;
+}
+
+
+/**
+ * \ingroup SparseExtra_Module
+ * @brief writes a dense Matrix or vector to a marketmarket format file
+ *
+ * @tparam DenseMatrixType to write to file
+ * @param mat matrix to write to file
+ * @param filename filename to write to
+ * @return true if writing succeeded
+ */
+
+template<typename DenseType>
+bool saveMarketDense (const DenseType& mat, const std::string& filename)
+{
+ typedef typename DenseType::Scalar Scalar;
+ typedef typename DenseType::RealScalar RealScalar;
+ std::ofstream out(filename.c_str(),std::ios::out);
+ if(!out)
+ return false;
+
+ out.flags(std::ios_base::scientific);
+ out.precision(std::numeric_limits<RealScalar>::digits10 + 2);
+ if(internal::is_same<Scalar, std::complex<float> >::value || internal::is_same<Scalar, std::complex<double> >::value)
+ out << "%%MatrixMarket matrix array complex general\n";
+ else
+ out << "%%MatrixMarket matrix array real general\n";
+ out << mat.rows() << " "<< mat.cols() << "\n";
+ for (Index i=0; i < mat.cols(); i++){
+ for (Index j=0; j < mat.rows(); j++){
+ internal::putDenseElt(mat(j,i), out);
+ }
+ }
+ out.close();
+ return true;
+}
+
+/**
+ * \ingroup SparseExtra_Module
+ * @brief Same functionality as saveMarketDense, deprecated
+ */
+template<typename VectorType>
+bool saveMarketVector (const VectorType& vec, const std::string& filename)
+{
+ return saveMarketDense(vec, filename);
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_SPARSE_MARKET_IO_H
diff --git a/unsupported/Eigen/src/SparseExtra/MatrixMarketIterator.h b/unsupported/Eigen/src/SparseExtra/MatrixMarketIterator.h
new file mode 100644
index 0000000..12e4cb4
--- /dev/null
+++ b/unsupported/Eigen/src/SparseExtra/MatrixMarketIterator.h
@@ -0,0 +1,249 @@
+
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2012 Desire NUENTSA WAKAM <desire.nuentsa_wakam@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_BROWSE_MATRICES_H
+#define EIGEN_BROWSE_MATRICES_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+enum {
+ SPD = 0x100,
+ NonSymmetric = 0x0
+};
+
+/**
+ * @brief Iterator to browse matrices from a specified folder
+ *
+ * This is used to load all the matrices from a folder.
+ * The matrices should be in Matrix Market format
+ * It is assumed that the matrices are named as matname.mtx
+ * and matname_SPD.mtx if the matrix is Symmetric and positive definite (or Hermitian)
+ * The right hand side vectors are loaded as well, if they exist.
+ * They should be named as matname_b.mtx.
+ * Note that the right hand side for a SPD matrix is named as matname_SPD_b.mtx
+ *
+ * Sometimes a reference solution is available. In this case, it should be named as matname_x.mtx
+ *
+ * Sample code
+ * \code
+ *
+ * \endcode
+ *
+ * \tparam Scalar The scalar type
+ */
+template <typename Scalar>
+class MatrixMarketIterator
+{
+ typedef typename NumTraits<Scalar>::Real RealScalar;
+ public:
+ typedef Matrix<Scalar,Dynamic,1> VectorType;
+ typedef SparseMatrix<Scalar,ColMajor> MatrixType;
+
+ public:
+ MatrixMarketIterator(const std::string &folder)
+ : m_sym(0), m_isvalid(false), m_matIsLoaded(false), m_hasRhs(false), m_hasrefX(false), m_folder(folder)
+ {
+ m_folder_id = opendir(folder.c_str());
+ if(m_folder_id)
+ Getnextvalidmatrix();
+ }
+
+ ~MatrixMarketIterator()
+ {
+ if (m_folder_id) closedir(m_folder_id);
+ }
+
+ inline MatrixMarketIterator& operator++()
+ {
+ m_matIsLoaded = false;
+ m_hasrefX = false;
+ m_hasRhs = false;
+ Getnextvalidmatrix();
+ return *this;
+ }
+ inline operator bool() const { return m_isvalid;}
+
+ /** Return the sparse matrix corresponding to the current file */
+ inline MatrixType& matrix()
+ {
+ // Read the matrix
+ if (m_matIsLoaded) return m_mat;
+
+ std::string matrix_file = m_folder + "/" + m_matname + ".mtx";
+ if ( !loadMarket(m_mat, matrix_file))
+ {
+ std::cerr << "Warning loadMarket failed when loading \"" << matrix_file << "\"" << std::endl;
+ m_matIsLoaded = false;
+ return m_mat;
+ }
+ m_matIsLoaded = true;
+
+ if (m_sym != NonSymmetric)
+ {
+ // Check whether we need to restore a full matrix:
+ RealScalar diag_norm = m_mat.diagonal().norm();
+ RealScalar lower_norm = m_mat.template triangularView<Lower>().norm();
+ RealScalar upper_norm = m_mat.template triangularView<Upper>().norm();
+ if(lower_norm>diag_norm && upper_norm==diag_norm)
+ {
+ // only the lower part is stored
+ MatrixType tmp(m_mat);
+ m_mat = tmp.template selfadjointView<Lower>();
+ }
+ else if(upper_norm>diag_norm && lower_norm==diag_norm)
+ {
+ // only the upper part is stored
+ MatrixType tmp(m_mat);
+ m_mat = tmp.template selfadjointView<Upper>();
+ }
+ }
+ return m_mat;
+ }
+
+ /** Return the right hand side corresponding to the current matrix.
+ * If the rhs file is not provided, a random rhs is generated
+ */
+ inline VectorType& rhs()
+ {
+ // Get the right hand side
+ if (m_hasRhs) return m_rhs;
+
+ std::string rhs_file;
+ rhs_file = m_folder + "/" + m_matname + "_b.mtx"; // The pattern is matname_b.mtx
+ m_hasRhs = Fileexists(rhs_file);
+ if (m_hasRhs)
+ {
+ m_rhs.resize(m_mat.cols());
+ m_hasRhs = loadMarketVector(m_rhs, rhs_file);
+ }
+ if (!m_hasRhs)
+ {
+ // Generate a random right hand side
+ if (!m_matIsLoaded) this->matrix();
+ m_refX.resize(m_mat.cols());
+ m_refX.setRandom();
+ m_rhs = m_mat * m_refX;
+ m_hasrefX = true;
+ m_hasRhs = true;
+ }
+ return m_rhs;
+ }
+
+ /** Return a reference solution
+ * If it is not provided and if the right hand side is not available
+ * then refX is randomly generated such that A*refX = b
+ * where A and b are the matrix and the rhs.
+ * Note that when a rhs is provided, refX is not available
+ */
+ inline VectorType& refX()
+ {
+ // Check if a reference solution is provided
+ if (m_hasrefX) return m_refX;
+
+ std::string lhs_file;
+ lhs_file = m_folder + "/" + m_matname + "_x.mtx";
+ m_hasrefX = Fileexists(lhs_file);
+ if (m_hasrefX)
+ {
+ m_refX.resize(m_mat.cols());
+ m_hasrefX = loadMarketVector(m_refX, lhs_file);
+ }
+ else
+ m_refX.resize(0);
+ return m_refX;
+ }
+
+ inline std::string& matname() { return m_matname; }
+
+ inline int sym() { return m_sym; }
+
+ bool hasRhs() {return m_hasRhs; }
+ bool hasrefX() {return m_hasrefX; }
+ bool isFolderValid() { return bool(m_folder_id); }
+
+ protected:
+
+ inline bool Fileexists(std::string file)
+ {
+ std::ifstream file_id(file.c_str());
+ if (!file_id.good() )
+ {
+ return false;
+ }
+ else
+ {
+ file_id.close();
+ return true;
+ }
+ }
+
+ void Getnextvalidmatrix( )
+ {
+ m_isvalid = false;
+ // Here, we return with the next valid matrix in the folder
+ while ( (m_curs_id = readdir(m_folder_id)) != NULL) {
+ m_isvalid = false;
+ std::string curfile;
+ curfile = m_folder + "/" + m_curs_id->d_name;
+ // Discard if it is a folder
+ if (m_curs_id->d_type == DT_DIR) continue; //FIXME This may not be available on non BSD systems
+// struct stat st_buf;
+// stat (curfile.c_str(), &st_buf);
+// if (S_ISDIR(st_buf.st_mode)) continue;
+
+ // Determine from the header if it is a matrix or a right hand side
+ bool isvector,iscomplex=false;
+ if(!getMarketHeader(curfile,m_sym,iscomplex,isvector)) continue;
+ if(isvector) continue;
+ if (!iscomplex)
+ {
+ if(internal::is_same<Scalar, std::complex<float> >::value || internal::is_same<Scalar, std::complex<double> >::value)
+ continue;
+ }
+ if (iscomplex)
+ {
+ if(internal::is_same<Scalar, float>::value || internal::is_same<Scalar, double>::value)
+ continue;
+ }
+
+
+ // Get the matrix name
+ std::string filename = m_curs_id->d_name;
+ m_matname = filename.substr(0, filename.length()-4);
+
+ // Find if the matrix is SPD
+ size_t found = m_matname.find("SPD");
+ if( (found!=std::string::npos) && (m_sym != NonSymmetric) )
+ m_sym = SPD;
+
+ m_isvalid = true;
+ break;
+ }
+ }
+ int m_sym; // Symmetry of the matrix
+ MatrixType m_mat; // Current matrix
+ VectorType m_rhs; // Current vector
+ VectorType m_refX; // The reference solution, if exists
+ std::string m_matname; // Matrix Name
+ bool m_isvalid;
+ bool m_matIsLoaded; // Determine if the matrix has already been loaded from the file
+ bool m_hasRhs; // The right hand side exists
+ bool m_hasrefX; // A reference solution is provided
+ std::string m_folder;
+ DIR * m_folder_id;
+ struct dirent *m_curs_id;
+
+};
+
+} // end namespace Eigen
+
+#endif
diff --git a/unsupported/Eigen/src/SparseExtra/RandomSetter.h b/unsupported/Eigen/src/SparseExtra/RandomSetter.h
new file mode 100644
index 0000000..9476ee3
--- /dev/null
+++ b/unsupported/Eigen/src/SparseExtra/RandomSetter.h
@@ -0,0 +1,335 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_RANDOMSETTER_H
+#define EIGEN_RANDOMSETTER_H
+
+#if defined(EIGEN_GOOGLEHASH_SUPPORT)
+// Ensure the ::google namespace exists, required for checking existence of
+// ::google::dense_hash_map and ::google::sparse_hash_map.
+namespace google {}
+#endif
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+/** Represents a std::map
+ *
+ * \see RandomSetter
+ */
+template<typename Scalar> struct StdMapTraits
+{
+ typedef int KeyType;
+ typedef std::map<KeyType,Scalar> Type;
+ enum {
+ IsSorted = 1
+ };
+
+ static void setInvalidKey(Type&, const KeyType&) {}
+};
+
+
+/** Represents a std::unordered_map
+ * \see RandomSetter
+ */
+template<typename Scalar> struct StdUnorderedMapTraits
+{
+ typedef int KeyType;
+ typedef std::unordered_map<KeyType,Scalar> Type;
+ enum {
+ IsSorted = 0
+ };
+
+ static void setInvalidKey(Type&, const KeyType&) {}
+};
+
+#if defined(EIGEN_GOOGLEHASH_SUPPORT)
+
+namespace google {
+
+// Namespace work-around, since sometimes dense_hash_map and sparse_hash_map
+// are in the global namespace, and other times they are under ::google.
+using namespace ::google;
+
+template<typename KeyType, typename Scalar>
+struct DenseHashMap {
+ typedef dense_hash_map<KeyType, Scalar> type;
+};
+
+template<typename KeyType, typename Scalar>
+struct SparseHashMap {
+ typedef sparse_hash_map<KeyType, Scalar> type;
+};
+
+} // namespace google
+
+/** Represents a google::dense_hash_map
+ *
+ * \see RandomSetter
+ */
+template<typename Scalar> struct GoogleDenseHashMapTraits
+{
+ typedef int KeyType;
+ typedef typename google::DenseHashMap<KeyType,Scalar>::type Type;
+ enum {
+ IsSorted = 0
+ };
+
+ static void setInvalidKey(Type& map, const KeyType& k)
+ { map.set_empty_key(k); }
+};
+
+/** Represents a google::sparse_hash_map
+ *
+ * \see RandomSetter
+ */
+template<typename Scalar> struct GoogleSparseHashMapTraits
+{
+ typedef int KeyType;
+ typedef typename google::SparseHashMap<KeyType,Scalar>::type Type;
+ enum {
+ IsSorted = 0
+ };
+
+ static void setInvalidKey(Type&, const KeyType&) {}
+};
+#endif
+
+/** \class RandomSetter
+ * \ingroup SparseExtra_Module
+ * \brief The RandomSetter is a wrapper object allowing to set/update a sparse matrix with random access
+ *
+ * \tparam SparseMatrixType the type of the sparse matrix we are updating
+ * \tparam MapTraits a traits class representing the map implementation used for the temporary sparse storage.
+ * Its default value depends on the system.
+ * \tparam OuterPacketBits defines the number of rows (or columns) manage by a single map object
+ * as a power of two exponent.
+ *
+ * This class temporarily represents a sparse matrix object using a generic map implementation allowing for
+ * efficient random access. The conversion from the compressed representation to a hash_map object is performed
+ * in the RandomSetter constructor, while the sparse matrix is updated back at destruction time. This strategy
+ * suggest the use of nested blocks as in this example:
+ *
+ * \code
+ * SparseMatrix<double> m(rows,cols);
+ * {
+ * RandomSetter<SparseMatrix<double> > w(m);
+ * // don't use m but w instead with read/write random access to the coefficients:
+ * for(;;)
+ * w(rand(),rand()) = rand;
+ * }
+ * // when w is deleted, the data are copied back to m
+ * // and m is ready to use.
+ * \endcode
+ *
+ * Since hash_map objects are not fully sorted, representing a full matrix as a single hash_map would
+ * involve a big and costly sort to update the compressed matrix back. To overcome this issue, a RandomSetter
+ * use multiple hash_map, each representing 2^OuterPacketBits columns or rows according to the storage order.
+ * To reach optimal performance, this value should be adjusted according to the average number of nonzeros
+ * per rows/columns.
+ *
+ * The possible values for the template parameter MapTraits are:
+ * - \b StdMapTraits: corresponds to std::map. (does not perform very well)
+ * - \b StdUnorderedMapTraits: corresponds to std::unordered_map
+ * - \b GoogleDenseHashMapTraits: corresponds to google::dense_hash_map (best efficiency, reasonable memory consumption)
+ * - \b GoogleSparseHashMapTraits: corresponds to google::sparse_hash_map (best memory consumption, relatively good performance)
+ *
+ * The default map implementation depends on the availability, and the preferred order is:
+ * GoogleSparseHashMapTraits, StdUnorderedMapTraits, and finally StdMapTraits.
+ *
+ * For performance and memory consumption reasons it is highly recommended to use one of
+ * Google's hash_map implementations. To enable the support for them, you must define
+ * EIGEN_GOOGLEHASH_SUPPORT. This will include both <google/dense_hash_map> and
+ * <google/sparse_hash_map> for you.
+ *
+ * \see https://github.com/sparsehash/sparsehash
+ */
+template<typename SparseMatrixType,
+ template <typename T> class MapTraits =
+#if defined(EIGEN_GOOGLEHASH_SUPPORT)
+ GoogleDenseHashMapTraits
+#else
+ StdUnorderedMapTraits
+#endif
+ ,int OuterPacketBits = 6>
+class RandomSetter
+{
+ typedef typename SparseMatrixType::Scalar Scalar;
+ typedef typename SparseMatrixType::StorageIndex StorageIndex;
+
+ struct ScalarWrapper
+ {
+ ScalarWrapper() : value(0) {}
+ Scalar value;
+ };
+ typedef typename MapTraits<ScalarWrapper>::KeyType KeyType;
+ typedef typename MapTraits<ScalarWrapper>::Type HashMapType;
+ static constexpr int OuterPacketMask = (1 << OuterPacketBits) - 1;
+ enum {
+ SwapStorage = 1 - MapTraits<ScalarWrapper>::IsSorted,
+ TargetRowMajor = (SparseMatrixType::Flags & RowMajorBit) ? 1 : 0,
+ SetterRowMajor = SwapStorage ? 1-TargetRowMajor : TargetRowMajor
+ };
+
+ public:
+
+ /** Constructs a random setter object from the sparse matrix \a target
+ *
+ * Note that the initial value of \a target are imported. If you want to re-set
+ * a sparse matrix from scratch, then you must set it to zero first using the
+ * setZero() function.
+ */
+ inline RandomSetter(SparseMatrixType& target)
+ : mp_target(&target)
+ {
+ const Index outerSize = SwapStorage ? target.innerSize() : target.outerSize();
+ const Index innerSize = SwapStorage ? target.outerSize() : target.innerSize();
+ m_outerPackets = outerSize >> OuterPacketBits;
+ if (outerSize&OuterPacketMask)
+ m_outerPackets += 1;
+ m_hashmaps = new HashMapType[m_outerPackets];
+ // compute number of bits needed to store inner indices
+ Index aux = innerSize - 1;
+ m_keyBitsOffset = 0;
+ while (aux)
+ {
+ ++m_keyBitsOffset;
+ aux = aux >> 1;
+ }
+ KeyType ik = (1<<(OuterPacketBits+m_keyBitsOffset));
+ for (Index k=0; k<m_outerPackets; ++k)
+ MapTraits<ScalarWrapper>::setInvalidKey(m_hashmaps[k],ik);
+
+ // insert current coeffs
+ for (Index j=0; j<mp_target->outerSize(); ++j)
+ for (typename SparseMatrixType::InnerIterator it(*mp_target,j); it; ++it)
+ (*this)(TargetRowMajor?j:it.index(), TargetRowMajor?it.index():j) = it.value();
+ }
+
+ /** Destructor updating back the sparse matrix target */
+ ~RandomSetter()
+ {
+ KeyType keyBitsMask = (1<<m_keyBitsOffset)-1;
+ if (!SwapStorage) // also means the map is sorted
+ {
+ mp_target->setZero();
+ mp_target->makeCompressed();
+ mp_target->reserve(nonZeros());
+ Index prevOuter = -1;
+ for (Index k=0; k<m_outerPackets; ++k)
+ {
+ const Index outerOffset = (1<<OuterPacketBits) * k;
+ typename HashMapType::iterator end = m_hashmaps[k].end();
+ for (typename HashMapType::iterator it = m_hashmaps[k].begin(); it!=end; ++it)
+ {
+ const Index outer = (it->first >> m_keyBitsOffset) + outerOffset;
+ const Index inner = it->first & keyBitsMask;
+ if (prevOuter!=outer)
+ {
+ for (Index j=prevOuter+1;j<=outer;++j)
+ mp_target->startVec(j);
+ prevOuter = outer;
+ }
+ mp_target->insertBackByOuterInner(outer, inner) = it->second.value;
+ }
+ }
+ mp_target->finalize();
+ }
+ else
+ {
+ VectorXi positions(mp_target->outerSize());
+ positions.setZero();
+ // pass 1
+ for (Index k=0; k<m_outerPackets; ++k)
+ {
+ typename HashMapType::iterator end = m_hashmaps[k].end();
+ for (typename HashMapType::iterator it = m_hashmaps[k].begin(); it!=end; ++it)
+ {
+ const Index outer = it->first & keyBitsMask;
+ ++positions[outer];
+ }
+ }
+ // prefix sum
+ StorageIndex count = 0;
+ for (Index j=0; j<mp_target->outerSize(); ++j)
+ {
+ StorageIndex tmp = positions[j];
+ mp_target->outerIndexPtr()[j] = count;
+ positions[j] = count;
+ count += tmp;
+ }
+ mp_target->makeCompressed();
+ mp_target->outerIndexPtr()[mp_target->outerSize()] = count;
+ mp_target->resizeNonZeros(count);
+ // pass 2
+ for (Index k=0; k<m_outerPackets; ++k)
+ {
+ const Index outerOffset = (1<<OuterPacketBits) * k;
+ typename HashMapType::iterator end = m_hashmaps[k].end();
+ for (typename HashMapType::iterator it = m_hashmaps[k].begin(); it!=end; ++it)
+ {
+ const Index inner = (it->first >> m_keyBitsOffset) + outerOffset;
+ const Index outer = it->first & keyBitsMask;
+ // sorted insertion
+ // Note that we have to deal with at most 2^OuterPacketBits unsorted coefficients,
+ // moreover those 2^OuterPacketBits coeffs are likely to be sparse, an so only a
+ // small fraction of them have to be sorted, whence the following simple procedure:
+ Index posStart = mp_target->outerIndexPtr()[outer];
+ Index i = (positions[outer]++) - 1;
+ while ( (i >= posStart) && (mp_target->innerIndexPtr()[i] > inner) )
+ {
+ mp_target->valuePtr()[i+1] = mp_target->valuePtr()[i];
+ mp_target->innerIndexPtr()[i+1] = mp_target->innerIndexPtr()[i];
+ --i;
+ }
+ mp_target->innerIndexPtr()[i+1] = internal::convert_index<StorageIndex>(inner);
+ mp_target->valuePtr()[i+1] = it->second.value;
+ }
+ }
+ }
+ delete[] m_hashmaps;
+ }
+
+ /** \returns a reference to the coefficient at given coordinates \a row, \a col */
+ Scalar& operator() (Index row, Index col)
+ {
+ const Index outer = SetterRowMajor ? row : col;
+ const Index inner = SetterRowMajor ? col : row;
+ const Index outerMajor = outer >> OuterPacketBits; // index of the packet/map
+ const Index outerMinor = outer & OuterPacketMask; // index of the inner vector in the packet
+ const KeyType key = internal::convert_index<KeyType>((outerMinor<<m_keyBitsOffset) | inner);
+ return m_hashmaps[outerMajor][key].value;
+ }
+
+ /** \returns the number of non zero coefficients
+ *
+ * \note According to the underlying map/hash_map implementation,
+ * this function might be quite expensive.
+ */
+ Index nonZeros() const
+ {
+ Index nz = 0;
+ for (Index k=0; k<m_outerPackets; ++k)
+ nz += static_cast<Index>(m_hashmaps[k].size());
+ return nz;
+ }
+
+
+ protected:
+
+ HashMapType* m_hashmaps;
+ SparseMatrixType* mp_target;
+ Index m_outerPackets;
+ unsigned char m_keyBitsOffset;
+};
+
+} // end namespace Eigen
+
+#endif // EIGEN_RANDOMSETTER_H
diff --git a/unsupported/Eigen/src/SparseExtra/SparseInverse.h b/unsupported/Eigen/src/SparseExtra/SparseInverse.h
new file mode 100644
index 0000000..c8a4920
--- /dev/null
+++ b/unsupported/Eigen/src/SparseExtra/SparseInverse.h
@@ -0,0 +1,231 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2022 Julian Kent <jkflying@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_SPARSEINVERSE_H
+#define EIGEN_SPARSEINVERSE_H
+
+#include "./InternalHeaderCheck.h"
+
+#include "../../../../Eigen/Sparse"
+#include "../../../../Eigen/SparseLU"
+
+namespace Eigen {
+
+/**
+ * @brief Kahan algorithm based accumulator
+ *
+ * The Kahan sum algorithm guarantees to bound the error from floating point
+ * accumulation to a fixed value, regardless of the number of accumulations
+ * performed. Naive accumulation accumulates errors O(N), and pairwise O(logN).
+ * However pairwise also requires O(logN) memory while Kahan summation requires
+ * O(1) memory, but 4x the operations / latency.
+ *
+ * NB! Do not enable associative math optimizations, they may cause the Kahan
+ * summation to be optimized out leaving you with naive summation again.
+ *
+ */
+template <typename Scalar>
+class KahanSum {
+ // Straighforward Kahan summation for accurate accumulation of a sum of numbers
+ Scalar _sum{};
+ Scalar _correction{};
+
+ public:
+ Scalar value() { return _sum; }
+
+ void operator+=(Scalar increment) {
+ const Scalar correctedIncrement = increment + _correction;
+ const Scalar previousSum = _sum;
+ _sum += correctedIncrement;
+ _correction = correctedIncrement - (_sum - previousSum);
+ }
+};
+template <typename Scalar, Index Width = 16>
+class FABSum {
+ // https://epubs.siam.org/doi/pdf/10.1137/19M1257780
+ // Fast and Accurate Blocked Summation
+ // Uses naive summation for the fast sum, and Kahan summation for the accurate sum
+ // Theoretically SIMD sum could be changed to a tree sum which would improve accuracy
+ // over naive summation
+ KahanSum<Scalar> _totalSum;
+ Matrix<Scalar, Width, 1> _block;
+ Index _blockUsed{};
+
+ public:
+ Scalar value() { return _block.topRows(_blockUsed).sum() + _totalSum.value(); }
+
+ void operator+=(Scalar increment) {
+ _block(_blockUsed++, 0) = increment;
+ if (_blockUsed == Width) {
+ _totalSum += _block.sum();
+ _blockUsed = 0;
+ }
+ }
+};
+
+/**
+ * @brief computes an accurate dot product on two sparse vectors
+ *
+ * Uses an accurate summation algorithm for the accumulator in order to
+ * compute an accurate dot product for two sparse vectors.
+ *
+ */
+template <typename Derived, typename OtherDerived>
+typename Derived::Scalar accurateDot(const SparseMatrixBase<Derived>& A, const SparseMatrixBase<OtherDerived>& other) {
+ typedef typename Derived::Scalar Scalar;
+ EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
+ EIGEN_STATIC_ASSERT_VECTOR_ONLY(OtherDerived)
+ EIGEN_STATIC_ASSERT_SAME_VECTOR_SIZE(Derived, OtherDerived)
+ static_assert(internal::is_same<Scalar, typename OtherDerived::Scalar>::value, "mismatched types");
+
+ internal::evaluator<Derived> thisEval(A.derived());
+ typename Derived::ReverseInnerIterator i(thisEval, 0);
+
+ internal::evaluator<OtherDerived> otherEval(other.derived());
+ typename OtherDerived::ReverseInnerIterator j(otherEval, 0);
+
+ FABSum<Scalar> res;
+ while (i && j) {
+ if (i.index() == j.index()) {
+ res += numext::conj(i.value()) * j.value();
+ --i;
+ --j;
+ } else if (i.index() > j.index())
+ --i;
+ else
+ --j;
+ }
+ return res.value();
+}
+
+/**
+ * @brief calculate sparse subset of inverse of sparse matrix
+ *
+ * This class returns a sparse subset of the inverse of the input matrix.
+ * The nonzeros correspond to the nonzeros of the input, plus any additional
+ * elements required due to fill-in of the internal LU factorization. This is
+ * is minimized via a applying a fill-reducing permutation as part of the LU
+ * factorization.
+ *
+ * If there are specific entries of the input matrix which you need inverse
+ * values for, which are zero for the input, you need to insert entries into
+ * the input sparse matrix for them to be calculated.
+ *
+ * Due to the sensitive nature of matrix inversion, particularly on large
+ * matrices which are made possible via sparsity, high accuracy dot products
+ * based on Kahan summation are used to reduce numerical error. If you still
+ * encounter numerical errors you may with to equilibrate your matrix before
+ * calculating the inverse, as well as making sure it is actually full rank.
+ */
+template <typename Scalar>
+class SparseInverse {
+ public:
+ typedef SparseMatrix<Scalar, ColMajor> MatrixType;
+ typedef SparseMatrix<Scalar, RowMajor> RowMatrixType;
+
+ SparseInverse() {}
+
+ /**
+ * @brief This Constructor is for if you already have a factored SparseLU and would like to use it to calculate a
+ * sparse inverse.
+ *
+ * Just call this constructor with your already factored SparseLU class and you can directly call the .inverse()
+ * method to get the result.
+ */
+ SparseInverse(const SparseLU<MatrixType>& slu) { _result = computeInverse(slu); }
+
+ /**
+ * @brief Calculate the sparse inverse from a given sparse input
+ */
+ SparseInverse& compute(const SparseMatrix<Scalar>& A) {
+ SparseLU<MatrixType> slu;
+ slu.compute(A);
+ _result = computeInverse(slu);
+ return *this;
+ }
+
+ /**
+ * @brief return the already-calculated sparse inverse, or a 0x0 matrix if it could not be computed
+ */
+ const MatrixType& inverse() const { return _result; }
+
+ /**
+ * @brief Internal function to calculate the sparse inverse in a functional way
+ * @return A sparse inverse representation, or, if the decomposition didn't complete, a 0x0 matrix.
+ */
+ static MatrixType computeInverse(const SparseLU<MatrixType>& slu) {
+ if (slu.info() != Success) {
+ return MatrixType(0, 0);
+ }
+
+ // Extract from SparseLU and decompose into L, inverse D and U terms
+ Matrix<Scalar, Dynamic, 1> invD;
+ RowMatrixType Upper;
+ {
+ RowMatrixType DU = slu.matrixU().toSparse();
+ invD = DU.diagonal().cwiseInverse();
+ Upper = (invD.asDiagonal() * DU).template triangularView<StrictlyUpper>();
+ }
+ MatrixType Lower = slu.matrixL().toSparse().template triangularView<StrictlyLower>();
+
+ // Compute the inverse and reapply the permutation matrix from the LU decomposition
+ return slu.colsPermutation().transpose() * computeInverse(Upper, invD, Lower) * slu.rowsPermutation();
+ }
+
+ /**
+ * @brief Internal function to calculate the inverse from strictly upper, diagonal and strictly lower components
+ */
+ static MatrixType computeInverse(const RowMatrixType& Upper, const Matrix<Scalar, Dynamic, 1>& inverseDiagonal,
+ const MatrixType& Lower) {
+ // Calculate the 'minimal set', which is the nonzeros of (L+U).transpose()
+ // It could be zeroed, but we will overwrite all non-zeros anyways.
+ MatrixType colInv = Lower.transpose().template triangularView<UnitUpper>();
+ colInv += Upper.transpose();
+
+ // We also need rowmajor representation in order to do efficient row-wise dot products
+ RowMatrixType rowInv = Upper.transpose().template triangularView<UnitLower>();
+ rowInv += Lower.transpose();
+
+ // Use the Takahashi algorithm to build the supporting elements of the inverse
+ // upwards and to the left, from the bottom right element, 1 col/row at a time
+ for (Index recurseLevel = Upper.cols() - 1; recurseLevel >= 0; recurseLevel--) {
+ const auto& col = Lower.col(recurseLevel);
+ const auto& row = Upper.row(recurseLevel);
+
+ // Calculate the inverse values for the nonzeros in this column
+ typename MatrixType::ReverseInnerIterator colIter(colInv, recurseLevel);
+ for (; recurseLevel < colIter.index(); --colIter) {
+ const Scalar element = -accurateDot(col, rowInv.row(colIter.index()));
+ colIter.valueRef() = element;
+ rowInv.coeffRef(colIter.index(), recurseLevel) = element;
+ }
+
+ // Calculate the inverse values for the nonzeros in this row
+ typename RowMatrixType::ReverseInnerIterator rowIter(rowInv, recurseLevel);
+ for (; recurseLevel < rowIter.index(); --rowIter) {
+ const Scalar element = -accurateDot(row, colInv.col(rowIter.index()));
+ rowIter.valueRef() = element;
+ colInv.coeffRef(recurseLevel, rowIter.index()) = element;
+ }
+
+ // And finally the diagonal, which corresponds to both row and col iterator now
+ const Scalar diag = inverseDiagonal(recurseLevel) - accurateDot(row, colInv.col(recurseLevel));
+ rowIter.valueRef() = diag;
+ colIter.valueRef() = diag;
+ }
+
+ return colInv;
+ }
+
+ private:
+ MatrixType _result;
+};
+
+} // namespace Eigen
+#endif
diff --git a/unsupported/Eigen/src/SpecialFunctions/BesselFunctionsArrayAPI.h b/unsupported/Eigen/src/SpecialFunctions/BesselFunctionsArrayAPI.h
new file mode 100644
index 0000000..7fa85e2
--- /dev/null
+++ b/unsupported/Eigen/src/SpecialFunctions/BesselFunctionsArrayAPI.h
@@ -0,0 +1,288 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2016 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+
+#ifndef EIGEN_BESSELFUNCTIONS_ARRAYAPI_H
+#define EIGEN_BESSELFUNCTIONS_ARRAYAPI_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+/** \returns an expression of the coefficient-wise i0(\a x) to the given
+ * arrays.
+ *
+ * It returns the modified Bessel function of the first kind of order zero.
+ *
+ * \param x is the argument
+ *
+ * \note This function supports only float and double scalar types. To support
+ * other scalar types, the user has to provide implementations of i0(T) for
+ * any scalar type T to be supported.
+ *
+ * \sa ArrayBase::bessel_i0()
+ */
+template <typename Derived>
+EIGEN_STRONG_INLINE const Eigen::CwiseUnaryOp<
+ Eigen::internal::scalar_bessel_i0_op<typename Derived::Scalar>, const Derived>
+bessel_i0(const Eigen::ArrayBase<Derived>& x) {
+ return Eigen::CwiseUnaryOp<
+ Eigen::internal::scalar_bessel_i0_op<typename Derived::Scalar>,
+ const Derived>(x.derived());
+}
+
+/** \returns an expression of the coefficient-wise i0e(\a x) to the given
+ * arrays.
+ *
+ * It returns the exponentially scaled modified Bessel
+ * function of the first kind of order zero.
+ *
+ * \param x is the argument
+ *
+ * \note This function supports only float and double scalar types. To support
+ * other scalar types, the user has to provide implementations of i0e(T) for
+ * any scalar type T to be supported.
+ *
+ * \sa ArrayBase::bessel_i0e()
+ */
+template <typename Derived>
+EIGEN_STRONG_INLINE const Eigen::CwiseUnaryOp<
+ Eigen::internal::scalar_bessel_i0e_op<typename Derived::Scalar>, const Derived>
+bessel_i0e(const Eigen::ArrayBase<Derived>& x) {
+ return Eigen::CwiseUnaryOp<
+ Eigen::internal::scalar_bessel_i0e_op<typename Derived::Scalar>,
+ const Derived>(x.derived());
+}
+
+/** \returns an expression of the coefficient-wise i1(\a x) to the given
+ * arrays.
+ *
+ * It returns the modified Bessel function of the first kind of order one.
+ *
+ * \param x is the argument
+ *
+ * \note This function supports only float and double scalar types. To support
+ * other scalar types, the user has to provide implementations of i1(T) for
+ * any scalar type T to be supported.
+ *
+ * \sa ArrayBase::bessel_i1()
+ */
+template <typename Derived>
+EIGEN_STRONG_INLINE const Eigen::CwiseUnaryOp<
+ Eigen::internal::scalar_bessel_i1_op<typename Derived::Scalar>, const Derived>
+bessel_i1(const Eigen::ArrayBase<Derived>& x) {
+ return Eigen::CwiseUnaryOp<
+ Eigen::internal::scalar_bessel_i1_op<typename Derived::Scalar>,
+ const Derived>(x.derived());
+}
+
+/** \returns an expression of the coefficient-wise i1e(\a x) to the given
+ * arrays.
+ *
+ * It returns the exponentially scaled modified Bessel
+ * function of the first kind of order one.
+ *
+ * \param x is the argument
+ *
+ * \note This function supports only float and double scalar types. To support
+ * other scalar types, the user has to provide implementations of i1e(T) for
+ * any scalar type T to be supported.
+ *
+ * \sa ArrayBase::bessel_i1e()
+ */
+template <typename Derived>
+EIGEN_STRONG_INLINE const Eigen::CwiseUnaryOp<
+ Eigen::internal::scalar_bessel_i1e_op<typename Derived::Scalar>, const Derived>
+bessel_i1e(const Eigen::ArrayBase<Derived>& x) {
+ return Eigen::CwiseUnaryOp<
+ Eigen::internal::scalar_bessel_i1e_op<typename Derived::Scalar>,
+ const Derived>(x.derived());
+}
+
+/** \returns an expression of the coefficient-wise k0(\a x) to the given
+ * arrays.
+ *
+ * It returns the modified Bessel function of the second kind of order zero.
+ *
+ * \param x is the argument
+ *
+ * \note This function supports only float and double scalar types. To support
+ * other scalar types, the user has to provide implementations of k0(T) for
+ * any scalar type T to be supported.
+ *
+ * \sa ArrayBase::bessel_k0()
+ */
+template <typename Derived>
+EIGEN_STRONG_INLINE const Eigen::CwiseUnaryOp<
+ Eigen::internal::scalar_bessel_k0_op<typename Derived::Scalar>, const Derived>
+bessel_k0(const Eigen::ArrayBase<Derived>& x) {
+ return Eigen::CwiseUnaryOp<
+ Eigen::internal::scalar_bessel_k0_op<typename Derived::Scalar>,
+ const Derived>(x.derived());
+}
+
+/** \returns an expression of the coefficient-wise k0e(\a x) to the given
+ * arrays.
+ *
+ * It returns the exponentially scaled modified Bessel
+ * function of the second kind of order zero.
+ *
+ * \param x is the argument
+ *
+ * \note This function supports only float and double scalar types. To support
+ * other scalar types, the user has to provide implementations of k0e(T) for
+ * any scalar type T to be supported.
+ *
+ * \sa ArrayBase::bessel_k0e()
+ */
+template <typename Derived>
+EIGEN_STRONG_INLINE const Eigen::CwiseUnaryOp<
+ Eigen::internal::scalar_bessel_k0e_op<typename Derived::Scalar>, const Derived>
+bessel_k0e(const Eigen::ArrayBase<Derived>& x) {
+ return Eigen::CwiseUnaryOp<
+ Eigen::internal::scalar_bessel_k0e_op<typename Derived::Scalar>,
+ const Derived>(x.derived());
+}
+
+/** \returns an expression of the coefficient-wise k1(\a x) to the given
+ * arrays.
+ *
+ * It returns the modified Bessel function of the second kind of order one.
+ *
+ * \param x is the argument
+ *
+ * \note This function supports only float and double scalar types. To support
+ * other scalar types, the user has to provide implementations of k1(T) for
+ * any scalar type T to be supported.
+ *
+ * \sa ArrayBase::bessel_k1()
+ */
+template <typename Derived>
+EIGEN_STRONG_INLINE const Eigen::CwiseUnaryOp<
+ Eigen::internal::scalar_bessel_k1_op<typename Derived::Scalar>, const Derived>
+bessel_k1(const Eigen::ArrayBase<Derived>& x) {
+ return Eigen::CwiseUnaryOp<
+ Eigen::internal::scalar_bessel_k1_op<typename Derived::Scalar>,
+ const Derived>(x.derived());
+}
+
+/** \returns an expression of the coefficient-wise k1e(\a x) to the given
+ * arrays.
+ *
+ * It returns the exponentially scaled modified Bessel
+ * function of the second kind of order one.
+ *
+ * \param x is the argument
+ *
+ * \note This function supports only float and double scalar types. To support
+ * other scalar types, the user has to provide implementations of k1e(T) for
+ * any scalar type T to be supported.
+ *
+ * \sa ArrayBase::bessel_k1e()
+ */
+template <typename Derived>
+EIGEN_STRONG_INLINE const Eigen::CwiseUnaryOp<
+ Eigen::internal::scalar_bessel_k1e_op<typename Derived::Scalar>, const Derived>
+bessel_k1e(const Eigen::ArrayBase<Derived>& x) {
+ return Eigen::CwiseUnaryOp<
+ Eigen::internal::scalar_bessel_k1e_op<typename Derived::Scalar>,
+ const Derived>(x.derived());
+}
+
+/** \returns an expression of the coefficient-wise j0(\a x) to the given
+ * arrays.
+ *
+ * It returns the Bessel function of the first kind of order zero.
+ *
+ * \param x is the argument
+ *
+ * \note This function supports only float and double scalar types. To support
+ * other scalar types, the user has to provide implementations of j0(T) for
+ * any scalar type T to be supported.
+ *
+ * \sa ArrayBase::bessel_j0()
+ */
+template <typename Derived>
+EIGEN_STRONG_INLINE const Eigen::CwiseUnaryOp<
+ Eigen::internal::scalar_bessel_j0_op<typename Derived::Scalar>, const Derived>
+bessel_j0(const Eigen::ArrayBase<Derived>& x) {
+ return Eigen::CwiseUnaryOp<
+ Eigen::internal::scalar_bessel_j0_op<typename Derived::Scalar>,
+ const Derived>(x.derived());
+}
+
+/** \returns an expression of the coefficient-wise y0(\a x) to the given
+ * arrays.
+ *
+ * It returns the Bessel function of the second kind of order zero.
+ *
+ * \param x is the argument
+ *
+ * \note This function supports only float and double scalar types. To support
+ * other scalar types, the user has to provide implementations of y0(T) for
+ * any scalar type T to be supported.
+ *
+ * \sa ArrayBase::bessel_y0()
+ */
+template <typename Derived>
+EIGEN_STRONG_INLINE const Eigen::CwiseUnaryOp<
+ Eigen::internal::scalar_bessel_y0_op<typename Derived::Scalar>, const Derived>
+bessel_y0(const Eigen::ArrayBase<Derived>& x) {
+ return Eigen::CwiseUnaryOp<
+ Eigen::internal::scalar_bessel_y0_op<typename Derived::Scalar>,
+ const Derived>(x.derived());
+}
+
+/** \returns an expression of the coefficient-wise j1(\a x) to the given
+ * arrays.
+ *
+ * It returns the modified Bessel function of the first kind of order one.
+ *
+ * \param x is the argument
+ *
+ * \note This function supports only float and double scalar types. To support
+ * other scalar types, the user has to provide implementations of j1(T) for
+ * any scalar type T to be supported.
+ *
+ * \sa ArrayBase::bessel_j1()
+ */
+template <typename Derived>
+EIGEN_STRONG_INLINE const Eigen::CwiseUnaryOp<
+ Eigen::internal::scalar_bessel_j1_op<typename Derived::Scalar>, const Derived>
+bessel_j1(const Eigen::ArrayBase<Derived>& x) {
+ return Eigen::CwiseUnaryOp<
+ Eigen::internal::scalar_bessel_j1_op<typename Derived::Scalar>,
+ const Derived>(x.derived());
+}
+
+/** \returns an expression of the coefficient-wise y1(\a x) to the given
+ * arrays.
+ *
+ * It returns the Bessel function of the second kind of order one.
+ *
+ * \param x is the argument
+ *
+ * \note This function supports only float and double scalar types. To support
+ * other scalar types, the user has to provide implementations of y1(T) for
+ * any scalar type T to be supported.
+ *
+ * \sa ArrayBase::bessel_y1()
+ */
+template <typename Derived>
+EIGEN_STRONG_INLINE const Eigen::CwiseUnaryOp<
+ Eigen::internal::scalar_bessel_y1_op<typename Derived::Scalar>, const Derived>
+bessel_y1(const Eigen::ArrayBase<Derived>& x) {
+ return Eigen::CwiseUnaryOp<
+ Eigen::internal::scalar_bessel_y1_op<typename Derived::Scalar>,
+ const Derived>(x.derived());
+}
+
+} // end namespace Eigen
+
+#endif // EIGEN_BESSELFUNCTIONS_ARRAYAPI_H
diff --git a/unsupported/Eigen/src/SpecialFunctions/BesselFunctionsBFloat16.h b/unsupported/Eigen/src/SpecialFunctions/BesselFunctionsBFloat16.h
new file mode 100644
index 0000000..c016004
--- /dev/null
+++ b/unsupported/Eigen/src/SpecialFunctions/BesselFunctionsBFloat16.h
@@ -0,0 +1,70 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_BESSELFUNCTIONS_BFLOAT16_H
+#define EIGEN_BESSELFUNCTIONS_BFLOAT16_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+namespace numext {
+
+#if EIGEN_HAS_C99_MATH
+template <>
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::bfloat16 bessel_i0(const Eigen::bfloat16& x) {
+ return Eigen::bfloat16(Eigen::numext::bessel_i0(static_cast<float>(x)));
+}
+template <>
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::bfloat16 bessel_i0e(const Eigen::bfloat16& x) {
+ return Eigen::bfloat16(Eigen::numext::bessel_i0e(static_cast<float>(x)));
+}
+template <>
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::bfloat16 bessel_i1(const Eigen::bfloat16& x) {
+ return Eigen::bfloat16(Eigen::numext::bessel_i1(static_cast<float>(x)));
+}
+template <>
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::bfloat16 bessel_i1e(const Eigen::bfloat16& x) {
+ return Eigen::bfloat16(Eigen::numext::bessel_i1e(static_cast<float>(x)));
+}
+template <>
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::bfloat16 bessel_j0(const Eigen::bfloat16& x) {
+ return Eigen::bfloat16(Eigen::numext::bessel_j0(static_cast<float>(x)));
+}
+template <>
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::bfloat16 bessel_j1(const Eigen::bfloat16& x) {
+ return Eigen::bfloat16(Eigen::numext::bessel_j1(static_cast<float>(x)));
+}
+template <>
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::bfloat16 bessel_y0(const Eigen::bfloat16& x) {
+ return Eigen::bfloat16(Eigen::numext::bessel_y0(static_cast<float>(x)));
+}
+template <>
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::bfloat16 bessel_y1(const Eigen::bfloat16& x) {
+ return Eigen::bfloat16(Eigen::numext::bessel_y1(static_cast<float>(x)));
+}
+template <>
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::bfloat16 bessel_k0(const Eigen::bfloat16& x) {
+ return Eigen::bfloat16(Eigen::numext::bessel_k0(static_cast<float>(x)));
+}
+template <>
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::bfloat16 bessel_k0e(const Eigen::bfloat16& x) {
+ return Eigen::bfloat16(Eigen::numext::bessel_k0e(static_cast<float>(x)));
+}
+template <>
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::bfloat16 bessel_k1(const Eigen::bfloat16& x) {
+ return Eigen::bfloat16(Eigen::numext::bessel_k1(static_cast<float>(x)));
+}
+template <>
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::bfloat16 bessel_k1e(const Eigen::bfloat16& x) {
+ return Eigen::bfloat16(Eigen::numext::bessel_k1e(static_cast<float>(x)));
+}
+#endif
+
+} // end namespace numext
+} // end namespace Eigen
+
+#endif // EIGEN_BESSELFUNCTIONS_BFLOAT16_H
diff --git a/unsupported/Eigen/src/SpecialFunctions/BesselFunctionsFunctors.h b/unsupported/Eigen/src/SpecialFunctions/BesselFunctionsFunctors.h
new file mode 100644
index 0000000..2d6b386
--- /dev/null
+++ b/unsupported/Eigen/src/SpecialFunctions/BesselFunctionsFunctors.h
@@ -0,0 +1,347 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2016 Eugene Brevdo <ebrevdo@gmail.com>
+// Copyright (C) 2016 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_BESSELFUNCTIONS_FUNCTORS_H
+#define EIGEN_BESSELFUNCTIONS_FUNCTORS_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+
+/** \internal
+ * \brief Template functor to compute the modified Bessel function of the first
+ * kind of order zero.
+ * \sa class CwiseUnaryOp, Cwise::bessel_i0()
+ */
+template <typename Scalar>
+struct scalar_bessel_i0_op {
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar operator()(const Scalar& x) const {
+ using numext::bessel_i0;
+ return bessel_i0(x);
+ }
+ typedef typename packet_traits<Scalar>::type Packet;
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet packetOp(const Packet& x) const {
+ return internal::pbessel_i0(x);
+ }
+};
+template <typename Scalar>
+struct functor_traits<scalar_bessel_i0_op<Scalar> > {
+ enum {
+ // On average, a Chebyshev polynomial of order N=20 is computed.
+ // The cost is N multiplications and 2N additions. We also add
+ // the cost of an additional exp over i0e.
+ Cost = 28 * NumTraits<Scalar>::MulCost + 48 * NumTraits<Scalar>::AddCost,
+ PacketAccess = packet_traits<Scalar>::HasBessel
+ };
+};
+
+/** \internal
+ * \brief Template functor to compute the exponentially scaled modified Bessel
+ * function of the first kind of order zero
+ * \sa class CwiseUnaryOp, Cwise::bessel_i0e()
+ */
+template <typename Scalar>
+struct scalar_bessel_i0e_op {
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar operator()(const Scalar& x) const {
+ using numext::bessel_i0e;
+ return bessel_i0e(x);
+ }
+ typedef typename packet_traits<Scalar>::type Packet;
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet packetOp(const Packet& x) const {
+ return internal::pbessel_i0e(x);
+ }
+};
+template <typename Scalar>
+struct functor_traits<scalar_bessel_i0e_op<Scalar> > {
+ enum {
+ // On average, a Chebyshev polynomial of order N=20 is computed.
+ // The cost is N multiplications and 2N additions.
+ Cost = 20 * NumTraits<Scalar>::MulCost + 40 * NumTraits<Scalar>::AddCost,
+ PacketAccess = packet_traits<Scalar>::HasBessel
+ };
+};
+
+/** \internal
+ * \brief Template functor to compute the modified Bessel function of the first
+ * kind of order one
+ * \sa class CwiseUnaryOp, Cwise::bessel_i1()
+ */
+template <typename Scalar>
+struct scalar_bessel_i1_op {
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar operator()(const Scalar& x) const {
+ using numext::bessel_i1;
+ return bessel_i1(x);
+ }
+ typedef typename packet_traits<Scalar>::type Packet;
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet packetOp(const Packet& x) const {
+ return internal::pbessel_i1(x);
+ }
+};
+template <typename Scalar>
+struct functor_traits<scalar_bessel_i1_op<Scalar> > {
+ enum {
+ // On average, a Chebyshev polynomial of order N=20 is computed.
+ // The cost is N multiplications and 2N additions. We also add
+ // the cost of an additional exp over i1e.
+ Cost = 28 * NumTraits<Scalar>::MulCost + 48 * NumTraits<Scalar>::AddCost,
+ PacketAccess = packet_traits<Scalar>::HasBessel
+ };
+};
+
+/** \internal
+ * \brief Template functor to compute the exponentially scaled modified Bessel
+ * function of the first kind of order zero
+ * \sa class CwiseUnaryOp, Cwise::bessel_i1e()
+ */
+template <typename Scalar>
+struct scalar_bessel_i1e_op {
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar operator()(const Scalar& x) const {
+ using numext::bessel_i1e;
+ return bessel_i1e(x);
+ }
+ typedef typename packet_traits<Scalar>::type Packet;
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet packetOp(const Packet& x) const {
+ return internal::pbessel_i1e(x);
+ }
+};
+template <typename Scalar>
+struct functor_traits<scalar_bessel_i1e_op<Scalar> > {
+ enum {
+ // On average, a Chebyshev polynomial of order N=20 is computed.
+ // The cost is N multiplications and 2N additions.
+ Cost = 20 * NumTraits<Scalar>::MulCost + 40 * NumTraits<Scalar>::AddCost,
+ PacketAccess = packet_traits<Scalar>::HasBessel
+ };
+};
+
+/** \internal
+ * \brief Template functor to compute the Bessel function of the second kind of
+ * order zero
+ * \sa class CwiseUnaryOp, Cwise::bessel_j0()
+ */
+template <typename Scalar>
+struct scalar_bessel_j0_op {
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar operator()(const Scalar& x) const {
+ using numext::bessel_j0;
+ return bessel_j0(x);
+ }
+ typedef typename packet_traits<Scalar>::type Packet;
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet packetOp(const Packet& x) const {
+ return internal::pbessel_j0(x);
+ }
+};
+template <typename Scalar>
+struct functor_traits<scalar_bessel_j0_op<Scalar> > {
+ enum {
+ // 6 polynomial of order ~N=8 is computed.
+ // The cost is N multiplications and N additions each, along with a
+ // sine, cosine and rsqrt cost.
+ Cost = 63 * NumTraits<Scalar>::MulCost + 48 * NumTraits<Scalar>::AddCost,
+ PacketAccess = packet_traits<Scalar>::HasBessel
+ };
+};
+
+/** \internal
+ * \brief Template functor to compute the Bessel function of the second kind of
+ * order zero
+ * \sa class CwiseUnaryOp, Cwise::bessel_y0()
+ */
+template <typename Scalar>
+struct scalar_bessel_y0_op {
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar operator()(const Scalar& x) const {
+ using numext::bessel_y0;
+ return bessel_y0(x);
+ }
+ typedef typename packet_traits<Scalar>::type Packet;
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet packetOp(const Packet& x) const {
+ return internal::pbessel_y0(x);
+ }
+};
+template <typename Scalar>
+struct functor_traits<scalar_bessel_y0_op<Scalar> > {
+ enum {
+ // 6 polynomial of order ~N=8 is computed.
+ // The cost is N multiplications and N additions each, along with a
+ // sine, cosine, rsqrt and j0 cost.
+ Cost = 126 * NumTraits<Scalar>::MulCost + 96 * NumTraits<Scalar>::AddCost,
+ PacketAccess = packet_traits<Scalar>::HasBessel
+ };
+};
+
+/** \internal
+ * \brief Template functor to compute the Bessel function of the first kind of
+ * order one
+ * \sa class CwiseUnaryOp, Cwise::bessel_j1()
+ */
+template <typename Scalar>
+struct scalar_bessel_j1_op {
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar operator()(const Scalar& x) const {
+ using numext::bessel_j1;
+ return bessel_j1(x);
+ }
+ typedef typename packet_traits<Scalar>::type Packet;
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet packetOp(const Packet& x) const {
+ return internal::pbessel_j1(x);
+ }
+};
+template <typename Scalar>
+struct functor_traits<scalar_bessel_j1_op<Scalar> > {
+ enum {
+ // 6 polynomial of order ~N=8 is computed.
+ // The cost is N multiplications and N additions each, along with a
+ // sine, cosine and rsqrt cost.
+ Cost = 63 * NumTraits<Scalar>::MulCost + 48 * NumTraits<Scalar>::AddCost,
+ PacketAccess = packet_traits<Scalar>::HasBessel
+ };
+};
+
+/** \internal
+ * \brief Template functor to compute the Bessel function of the second kind of
+ * order one
+ * \sa class CwiseUnaryOp, Cwise::bessel_j1e()
+ */
+template <typename Scalar>
+struct scalar_bessel_y1_op {
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar operator()(const Scalar& x) const {
+ using numext::bessel_y1;
+ return bessel_y1(x);
+ }
+ typedef typename packet_traits<Scalar>::type Packet;
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet packetOp(const Packet& x) const {
+ return internal::pbessel_y1(x);
+ }
+};
+template <typename Scalar>
+struct functor_traits<scalar_bessel_y1_op<Scalar> > {
+ enum {
+ // 6 polynomial of order ~N=8 is computed.
+ // The cost is N multiplications and N additions each, along with a
+ // sine, cosine, rsqrt and j1 cost.
+ Cost = 126 * NumTraits<Scalar>::MulCost + 96 * NumTraits<Scalar>::AddCost,
+ PacketAccess = packet_traits<Scalar>::HasBessel
+ };
+};
+
+/** \internal
+ * \brief Template functor to compute the modified Bessel function of the second
+ * kind of order zero
+ * \sa class CwiseUnaryOp, Cwise::bessel_k0()
+ */
+template <typename Scalar>
+struct scalar_bessel_k0_op {
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar operator()(const Scalar& x) const {
+ using numext::bessel_k0;
+ return bessel_k0(x);
+ }
+ typedef typename packet_traits<Scalar>::type Packet;
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet packetOp(const Packet& x) const {
+ return internal::pbessel_k0(x);
+ }
+};
+template <typename Scalar>
+struct functor_traits<scalar_bessel_k0_op<Scalar> > {
+ enum {
+ // On average, a Chebyshev polynomial of order N=10 is computed.
+ // The cost is N multiplications and 2N additions. In addition we compute
+ // i0, a log, exp and prsqrt and sin and cos.
+ Cost = 68 * NumTraits<Scalar>::MulCost + 88 * NumTraits<Scalar>::AddCost,
+ PacketAccess = packet_traits<Scalar>::HasBessel
+ };
+};
+
+/** \internal
+ * \brief Template functor to compute the exponentially scaled modified Bessel
+ * function of the second kind of order zero
+ * \sa class CwiseUnaryOp, Cwise::bessel_k0e()
+ */
+template <typename Scalar>
+struct scalar_bessel_k0e_op {
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar operator()(const Scalar& x) const {
+ using numext::bessel_k0e;
+ return bessel_k0e(x);
+ }
+ typedef typename packet_traits<Scalar>::type Packet;
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet packetOp(const Packet& x) const {
+ return internal::pbessel_k0e(x);
+ }
+};
+template <typename Scalar>
+struct functor_traits<scalar_bessel_k0e_op<Scalar> > {
+ enum {
+ // On average, a Chebyshev polynomial of order N=10 is computed.
+ // The cost is N multiplications and 2N additions. In addition we compute
+ // i0, a log, exp and prsqrt and sin and cos.
+ Cost = 68 * NumTraits<Scalar>::MulCost + 88 * NumTraits<Scalar>::AddCost,
+ PacketAccess = packet_traits<Scalar>::HasBessel
+ };
+};
+
+/** \internal
+ * \brief Template functor to compute the modified Bessel function of the
+ * second kind of order one
+ * \sa class CwiseUnaryOp, Cwise::bessel_k1()
+ */
+template <typename Scalar>
+struct scalar_bessel_k1_op {
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar operator()(const Scalar& x) const {
+ using numext::bessel_k1;
+ return bessel_k1(x);
+ }
+ typedef typename packet_traits<Scalar>::type Packet;
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet packetOp(const Packet& x) const {
+ return internal::pbessel_k1(x);
+ }
+};
+template <typename Scalar>
+struct functor_traits<scalar_bessel_k1_op<Scalar> > {
+ enum {
+ // On average, a Chebyshev polynomial of order N=10 is computed.
+ // The cost is N multiplications and 2N additions. In addition we compute
+ // i1, a log, exp and prsqrt and sin and cos.
+ Cost = 68 * NumTraits<Scalar>::MulCost + 88 * NumTraits<Scalar>::AddCost,
+ PacketAccess = packet_traits<Scalar>::HasBessel
+ };
+};
+
+/** \internal
+ * \brief Template functor to compute the exponentially scaled modified Bessel
+ * function of the second kind of order one
+ * \sa class CwiseUnaryOp, Cwise::bessel_k1e()
+ */
+template <typename Scalar>
+struct scalar_bessel_k1e_op {
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar operator()(const Scalar& x) const {
+ using numext::bessel_k1e;
+ return bessel_k1e(x);
+ }
+ typedef typename packet_traits<Scalar>::type Packet;
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet packetOp(const Packet& x) const {
+ return internal::pbessel_k1e(x);
+ }
+};
+template <typename Scalar>
+struct functor_traits<scalar_bessel_k1e_op<Scalar> > {
+ enum {
+ // On average, a Chebyshev polynomial of order N=10 is computed.
+ // The cost is N multiplications and 2N additions. In addition we compute
+ // i1, a log, exp and prsqrt and sin and cos.
+ Cost = 68 * NumTraits<Scalar>::MulCost + 88 * NumTraits<Scalar>::AddCost,
+ PacketAccess = packet_traits<Scalar>::HasBessel
+ };
+};
+
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_BESSELFUNCTIONS_FUNCTORS_H
diff --git a/unsupported/Eigen/src/SpecialFunctions/BesselFunctionsHalf.h b/unsupported/Eigen/src/SpecialFunctions/BesselFunctionsHalf.h
new file mode 100644
index 0000000..4d50503
--- /dev/null
+++ b/unsupported/Eigen/src/SpecialFunctions/BesselFunctionsHalf.h
@@ -0,0 +1,68 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_BESSELFUNCTIONS_HALF_H
+#define EIGEN_BESSELFUNCTIONS_HALF_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+namespace numext {
+
+#if EIGEN_HAS_C99_MATH
+template <>
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half bessel_i0(const Eigen::half& x) {
+ return Eigen::half(Eigen::numext::bessel_i0(static_cast<float>(x)));
+}
+template <>
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half bessel_i0e(const Eigen::half& x) {
+ return Eigen::half(Eigen::numext::bessel_i0e(static_cast<float>(x)));
+}
+template <>
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half bessel_i1(const Eigen::half& x) {
+ return Eigen::half(Eigen::numext::bessel_i1(static_cast<float>(x)));
+}
+template <>
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half bessel_i1e(const Eigen::half& x) {
+ return Eigen::half(Eigen::numext::bessel_i1e(static_cast<float>(x)));
+}
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half bessel_j0(const Eigen::half& x) {
+ return Eigen::half(Eigen::numext::bessel_j0(static_cast<float>(x)));
+}
+template <>
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half bessel_j1(const Eigen::half& x) {
+ return Eigen::half(Eigen::numext::bessel_j1(static_cast<float>(x)));
+}
+template <>
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half bessel_y0(const Eigen::half& x) {
+ return Eigen::half(Eigen::numext::bessel_y0(static_cast<float>(x)));
+}
+template <>
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half bessel_y1(const Eigen::half& x) {
+ return Eigen::half(Eigen::numext::bessel_y1(static_cast<float>(x)));
+}
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half bessel_k0(const Eigen::half& x) {
+ return Eigen::half(Eigen::numext::bessel_k0(static_cast<float>(x)));
+}
+template <>
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half bessel_k0e(const Eigen::half& x) {
+ return Eigen::half(Eigen::numext::bessel_k0e(static_cast<float>(x)));
+}
+template <>
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half bessel_k1(const Eigen::half& x) {
+ return Eigen::half(Eigen::numext::bessel_k1(static_cast<float>(x)));
+}
+template <>
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half bessel_k1e(const Eigen::half& x) {
+ return Eigen::half(Eigen::numext::bessel_k1e(static_cast<float>(x)));
+}
+#endif
+
+} // end namespace numext
+} // end namespace Eigen
+
+#endif // EIGEN_BESSELFUNCTIONS_HALF_H
diff --git a/unsupported/Eigen/src/SpecialFunctions/BesselFunctionsImpl.h b/unsupported/Eigen/src/SpecialFunctions/BesselFunctionsImpl.h
new file mode 100644
index 0000000..b600079
--- /dev/null
+++ b/unsupported/Eigen/src/SpecialFunctions/BesselFunctionsImpl.h
@@ -0,0 +1,1961 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2015 Eugene Brevdo <ebrevdo@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_BESSEL_FUNCTIONS_H
+#define EIGEN_BESSEL_FUNCTIONS_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+namespace internal {
+
+// Parts of this code are based on the Cephes Math Library.
+//
+// Cephes Math Library Release 2.8: June, 2000
+// Copyright 1984, 1987, 1992, 2000 by Stephen L. Moshier
+//
+// Permission has been kindly provided by the original author
+// to incorporate the Cephes software into the Eigen codebase:
+//
+// From: Stephen Moshier
+// To: Eugene Brevdo
+// Subject: Re: Permission to wrap several cephes functions in Eigen
+//
+// Hello Eugene,
+//
+// Thank you for writing.
+//
+// If your licensing is similar to BSD, the formal way that has been
+// handled is simply to add a statement to the effect that you are incorporating
+// the Cephes software by permission of the author.
+//
+// Good luck with your project,
+// Steve
+
+
+/****************************************************************************
+ * Implementation of Bessel function, based on Cephes *
+ ****************************************************************************/
+
+template <typename Scalar>
+struct bessel_i0e_retval {
+ typedef Scalar type;
+};
+
+template <typename T, typename ScalarType = typename unpacket_traits<T>::type>
+struct generic_i0e {
+ EIGEN_STATIC_ASSERT((internal::is_same<T, T>::value == false),
+ THIS_TYPE_IS_NOT_SUPPORTED)
+
+ EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE T run(const T&) {
+ return ScalarType(0);
+ }
+};
+
+template <typename T>
+struct generic_i0e<T, float> {
+ EIGEN_DEVICE_FUNC
+ static EIGEN_STRONG_INLINE T run(const T& x) {
+ /* i0ef.c
+ *
+ * Modified Bessel function of order zero,
+ * exponentially scaled
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float x, y, i0ef();
+ *
+ * y = i0ef( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns exponentially scaled modified Bessel function
+ * of order zero of the argument.
+ *
+ * The function is defined as i0e(x) = exp(-|x|) j0( ix ).
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE 0,30 100000 3.7e-7 7.0e-8
+ * See i0f().
+ *
+ */
+
+ const float A[] = {-1.30002500998624804212E-8f, 6.04699502254191894932E-8f,
+ -2.67079385394061173391E-7f, 1.11738753912010371815E-6f,
+ -4.41673835845875056359E-6f, 1.64484480707288970893E-5f,
+ -5.75419501008210370398E-5f, 1.88502885095841655729E-4f,
+ -5.76375574538582365885E-4f, 1.63947561694133579842E-3f,
+ -4.32430999505057594430E-3f, 1.05464603945949983183E-2f,
+ -2.37374148058994688156E-2f, 4.93052842396707084878E-2f,
+ -9.49010970480476444210E-2f, 1.71620901522208775349E-1f,
+ -3.04682672343198398683E-1f, 6.76795274409476084995E-1f};
+
+ const float B[] = {3.39623202570838634515E-9f, 2.26666899049817806459E-8f,
+ 2.04891858946906374183E-7f, 2.89137052083475648297E-6f,
+ 6.88975834691682398426E-5f, 3.36911647825569408990E-3f,
+ 8.04490411014108831608E-1f};
+ T y = pabs(x);
+ T y_le_eight = internal::pchebevl<T, 18>::run(
+ pmadd(pset1<T>(0.5f), y, pset1<T>(-2.0f)), A);
+ T y_gt_eight = pmul(
+ internal::pchebevl<T, 7>::run(
+ psub(pdiv(pset1<T>(32.0f), y), pset1<T>(2.0f)), B),
+ prsqrt(y));
+ // TODO: Perhaps instead check whether all packet elements are in
+ // [-8, 8] and evaluate a branch based off of that. It's possible
+ // in practice most elements are in this region.
+ return pselect(pcmp_le(y, pset1<T>(8.0f)), y_le_eight, y_gt_eight);
+ }
+};
+
+template <typename T>
+struct generic_i0e<T, double> {
+ EIGEN_DEVICE_FUNC
+ static EIGEN_STRONG_INLINE T run(const T& x) {
+ /* i0e.c
+ *
+ * Modified Bessel function of order zero,
+ * exponentially scaled
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, i0e();
+ *
+ * y = i0e( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns exponentially scaled modified Bessel function
+ * of order zero of the argument.
+ *
+ * The function is defined as i0e(x) = exp(-|x|) j0( ix ).
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE 0,30 30000 5.4e-16 1.2e-16
+ * See i0().
+ *
+ */
+
+ const double A[] = {-4.41534164647933937950E-18, 3.33079451882223809783E-17,
+ -2.43127984654795469359E-16, 1.71539128555513303061E-15,
+ -1.16853328779934516808E-14, 7.67618549860493561688E-14,
+ -4.85644678311192946090E-13, 2.95505266312963983461E-12,
+ -1.72682629144155570723E-11, 9.67580903537323691224E-11,
+ -5.18979560163526290666E-10, 2.65982372468238665035E-9,
+ -1.30002500998624804212E-8, 6.04699502254191894932E-8,
+ -2.67079385394061173391E-7, 1.11738753912010371815E-6,
+ -4.41673835845875056359E-6, 1.64484480707288970893E-5,
+ -5.75419501008210370398E-5, 1.88502885095841655729E-4,
+ -5.76375574538582365885E-4, 1.63947561694133579842E-3,
+ -4.32430999505057594430E-3, 1.05464603945949983183E-2,
+ -2.37374148058994688156E-2, 4.93052842396707084878E-2,
+ -9.49010970480476444210E-2, 1.71620901522208775349E-1,
+ -3.04682672343198398683E-1, 6.76795274409476084995E-1};
+ const double B[] = {
+ -7.23318048787475395456E-18, -4.83050448594418207126E-18,
+ 4.46562142029675999901E-17, 3.46122286769746109310E-17,
+ -2.82762398051658348494E-16, -3.42548561967721913462E-16,
+ 1.77256013305652638360E-15, 3.81168066935262242075E-15,
+ -9.55484669882830764870E-15, -4.15056934728722208663E-14,
+ 1.54008621752140982691E-14, 3.85277838274214270114E-13,
+ 7.18012445138366623367E-13, -1.79417853150680611778E-12,
+ -1.32158118404477131188E-11, -3.14991652796324136454E-11,
+ 1.18891471078464383424E-11, 4.94060238822496958910E-10,
+ 3.39623202570838634515E-9, 2.26666899049817806459E-8,
+ 2.04891858946906374183E-7, 2.89137052083475648297E-6,
+ 6.88975834691682398426E-5, 3.36911647825569408990E-3,
+ 8.04490411014108831608E-1};
+ T y = pabs(x);
+ T y_le_eight = internal::pchebevl<T, 30>::run(
+ pmadd(pset1<T>(0.5), y, pset1<T>(-2.0)), A);
+ T y_gt_eight = pmul(
+ internal::pchebevl<T, 25>::run(
+ psub(pdiv(pset1<T>(32.0), y), pset1<T>(2.0)), B),
+ prsqrt(y));
+ // TODO: Perhaps instead check whether all packet elements are in
+ // [-8, 8] and evaluate a branch based off of that. It's possible
+ // in practice most elements are in this region.
+ return pselect(pcmp_le(y, pset1<T>(8.0)), y_le_eight, y_gt_eight);
+ }
+};
+
+template <typename T>
+struct bessel_i0e_impl {
+ EIGEN_DEVICE_FUNC
+ static EIGEN_STRONG_INLINE T run(const T x) {
+ return generic_i0e<T>::run(x);
+ }
+};
+
+template <typename Scalar>
+struct bessel_i0_retval {
+ typedef Scalar type;
+};
+
+template <typename T, typename ScalarType = typename unpacket_traits<T>::type>
+struct generic_i0 {
+ EIGEN_DEVICE_FUNC
+ static EIGEN_STRONG_INLINE T run(const T& x) {
+ return pmul(
+ pexp(pabs(x)),
+ generic_i0e<T, ScalarType>::run(x));
+ }
+};
+
+template <typename T>
+struct bessel_i0_impl {
+ EIGEN_DEVICE_FUNC
+ static EIGEN_STRONG_INLINE T run(const T x) {
+ return generic_i0<T>::run(x);
+ }
+};
+
+template <typename Scalar>
+struct bessel_i1e_retval {
+ typedef Scalar type;
+};
+
+template <typename T, typename ScalarType = typename unpacket_traits<T>::type >
+struct generic_i1e {
+ EIGEN_STATIC_ASSERT((internal::is_same<T, T>::value == false),
+ THIS_TYPE_IS_NOT_SUPPORTED)
+
+ EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE T run(const T&) {
+ return ScalarType(0);
+ }
+};
+
+template <typename T>
+struct generic_i1e<T, float> {
+ EIGEN_DEVICE_FUNC
+ static EIGEN_STRONG_INLINE T run(const T& x) {
+ /* i1ef.c
+ *
+ * Modified Bessel function of order one,
+ * exponentially scaled
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float x, y, i1ef();
+ *
+ * y = i1ef( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns exponentially scaled modified Bessel function
+ * of order one of the argument.
+ *
+ * The function is defined as i1(x) = -i exp(-|x|) j1( ix ).
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE 0, 30 30000 1.5e-6 1.5e-7
+ * See i1().
+ *
+ */
+ const float A[] = {9.38153738649577178388E-9f, -4.44505912879632808065E-8f,
+ 2.00329475355213526229E-7f, -8.56872026469545474066E-7f,
+ 3.47025130813767847674E-6f, -1.32731636560394358279E-5f,
+ 4.78156510755005422638E-5f, -1.61760815825896745588E-4f,
+ 5.12285956168575772895E-4f, -1.51357245063125314899E-3f,
+ 4.15642294431288815669E-3f, -1.05640848946261981558E-2f,
+ 2.47264490306265168283E-2f, -5.29459812080949914269E-2f,
+ 1.02643658689847095384E-1f, -1.76416518357834055153E-1f,
+ 2.52587186443633654823E-1f};
+
+ const float B[] = {-3.83538038596423702205E-9f, -2.63146884688951950684E-8f,
+ -2.51223623787020892529E-7f, -3.88256480887769039346E-6f,
+ -1.10588938762623716291E-4f, -9.76109749136146840777E-3f,
+ 7.78576235018280120474E-1f};
+
+
+ T y = pabs(x);
+ T y_le_eight = pmul(y, internal::pchebevl<T, 17>::run(
+ pmadd(pset1<T>(0.5f), y, pset1<T>(-2.0f)), A));
+ T y_gt_eight = pmul(
+ internal::pchebevl<T, 7>::run(
+ psub(pdiv(pset1<T>(32.0f), y),
+ pset1<T>(2.0f)), B),
+ prsqrt(y));
+ // TODO: Perhaps instead check whether all packet elements are in
+ // [-8, 8] and evaluate a branch based off of that. It's possible
+ // in practice most elements are in this region.
+ y = pselect(pcmp_le(y, pset1<T>(8.0f)), y_le_eight, y_gt_eight);
+ return pselect(pcmp_lt(x, pset1<T>(0.0f)), pnegate(y), y);
+ }
+};
+
+template <typename T>
+struct generic_i1e<T, double> {
+ EIGEN_DEVICE_FUNC
+ static EIGEN_STRONG_INLINE T run(const T& x) {
+ /* i1e.c
+ *
+ * Modified Bessel function of order one,
+ * exponentially scaled
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, i1e();
+ *
+ * y = i1e( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns exponentially scaled modified Bessel function
+ * of order one of the argument.
+ *
+ * The function is defined as i1(x) = -i exp(-|x|) j1( ix ).
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE 0, 30 30000 2.0e-15 2.0e-16
+ * See i1().
+ *
+ */
+ const double A[] = {2.77791411276104639959E-18, -2.11142121435816608115E-17,
+ 1.55363195773620046921E-16, -1.10559694773538630805E-15,
+ 7.60068429473540693410E-15, -5.04218550472791168711E-14,
+ 3.22379336594557470981E-13, -1.98397439776494371520E-12,
+ 1.17361862988909016308E-11, -6.66348972350202774223E-11,
+ 3.62559028155211703701E-10, -1.88724975172282928790E-9,
+ 9.38153738649577178388E-9, -4.44505912879632808065E-8,
+ 2.00329475355213526229E-7, -8.56872026469545474066E-7,
+ 3.47025130813767847674E-6, -1.32731636560394358279E-5,
+ 4.78156510755005422638E-5, -1.61760815825896745588E-4,
+ 5.12285956168575772895E-4, -1.51357245063125314899E-3,
+ 4.15642294431288815669E-3, -1.05640848946261981558E-2,
+ 2.47264490306265168283E-2, -5.29459812080949914269E-2,
+ 1.02643658689847095384E-1, -1.76416518357834055153E-1,
+ 2.52587186443633654823E-1};
+ const double B[] = {
+ 7.51729631084210481353E-18, 4.41434832307170791151E-18,
+ -4.65030536848935832153E-17, -3.20952592199342395980E-17,
+ 2.96262899764595013876E-16, 3.30820231092092828324E-16,
+ -1.88035477551078244854E-15, -3.81440307243700780478E-15,
+ 1.04202769841288027642E-14, 4.27244001671195135429E-14,
+ -2.10154184277266431302E-14, -4.08355111109219731823E-13,
+ -7.19855177624590851209E-13, 2.03562854414708950722E-12,
+ 1.41258074366137813316E-11, 3.25260358301548823856E-11,
+ -1.89749581235054123450E-11, -5.58974346219658380687E-10,
+ -3.83538038596423702205E-9, -2.63146884688951950684E-8,
+ -2.51223623787020892529E-7, -3.88256480887769039346E-6,
+ -1.10588938762623716291E-4, -9.76109749136146840777E-3,
+ 7.78576235018280120474E-1};
+ T y = pabs(x);
+ T y_le_eight = pmul(y, internal::pchebevl<T, 29>::run(
+ pmadd(pset1<T>(0.5), y, pset1<T>(-2.0)), A));
+ T y_gt_eight = pmul(
+ internal::pchebevl<T, 25>::run(
+ psub(pdiv(pset1<T>(32.0), y),
+ pset1<T>(2.0)), B),
+ prsqrt(y));
+ // TODO: Perhaps instead check whether all packet elements are in
+ // [-8, 8] and evaluate a branch based off of that. It's possible
+ // in practice most elements are in this region.
+ y = pselect(pcmp_le(y, pset1<T>(8.0)), y_le_eight, y_gt_eight);
+ return pselect(pcmp_lt(x, pset1<T>(0.0)), pnegate(y), y);
+ }
+};
+
+template <typename T>
+struct bessel_i1e_impl {
+ EIGEN_DEVICE_FUNC
+ static EIGEN_STRONG_INLINE T run(const T x) {
+ return generic_i1e<T>::run(x);
+ }
+};
+
+template <typename T>
+struct bessel_i1_retval {
+ typedef T type;
+};
+
+template <typename T, typename ScalarType = typename unpacket_traits<T>::type>
+struct generic_i1 {
+ EIGEN_DEVICE_FUNC
+ static EIGEN_STRONG_INLINE T run(const T& x) {
+ return pmul(
+ pexp(pabs(x)),
+ generic_i1e<T, ScalarType>::run(x));
+ }
+};
+
+template <typename T>
+struct bessel_i1_impl {
+ EIGEN_DEVICE_FUNC
+ static EIGEN_STRONG_INLINE T run(const T x) {
+ return generic_i1<T>::run(x);
+ }
+};
+
+template <typename T>
+struct bessel_k0e_retval {
+ typedef T type;
+};
+
+template <typename T, typename ScalarType = typename unpacket_traits<T>::type>
+struct generic_k0e {
+ EIGEN_STATIC_ASSERT((internal::is_same<T, T>::value == false),
+ THIS_TYPE_IS_NOT_SUPPORTED)
+
+ EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE T run(const T&) {
+ return ScalarType(0);
+ }
+};
+
+template <typename T>
+struct generic_k0e<T, float> {
+ EIGEN_DEVICE_FUNC
+ static EIGEN_STRONG_INLINE T run(const T& x) {
+ /* k0ef.c
+ * Modified Bessel function, third kind, order zero,
+ * exponentially scaled
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float x, y, k0ef();
+ *
+ * y = k0ef( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns exponentially scaled modified Bessel function
+ * of the third kind of order zero of the argument.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE 0, 30 30000 8.1e-7 7.8e-8
+ * See k0().
+ *
+ */
+
+ const float A[] = {1.90451637722020886025E-9f, 2.53479107902614945675E-7f,
+ 2.28621210311945178607E-5f, 1.26461541144692592338E-3f,
+ 3.59799365153615016266E-2f, 3.44289899924628486886E-1f,
+ -5.35327393233902768720E-1f};
+
+ const float B[] = {-1.69753450938905987466E-9f, 8.57403401741422608519E-9f,
+ -4.66048989768794782956E-8f, 2.76681363944501510342E-7f,
+ -1.83175552271911948767E-6f, 1.39498137188764993662E-5f,
+ -1.28495495816278026384E-4f, 1.56988388573005337491E-3f,
+ -3.14481013119645005427E-2f, 2.44030308206595545468E0f};
+ const T MAXNUM = pset1<T>(NumTraits<float>::infinity());
+ const T two = pset1<T>(2.0);
+ T x_le_two = internal::pchebevl<T, 7>::run(
+ pmadd(x, x, pset1<T>(-2.0)), A);
+ x_le_two = pmadd(
+ generic_i0<T, float>::run(x), pnegate(
+ plog(pmul(pset1<T>(0.5), x))), x_le_two);
+ x_le_two = pmul(pexp(x), x_le_two);
+ T x_gt_two = pmul(
+ internal::pchebevl<T, 10>::run(
+ psub(pdiv(pset1<T>(8.0), x), two), B),
+ prsqrt(x));
+ return pselect(
+ pcmp_le(x, pset1<T>(0.0)),
+ MAXNUM,
+ pselect(pcmp_le(x, two), x_le_two, x_gt_two));
+ }
+};
+
+template <typename T>
+struct generic_k0e<T, double> {
+ EIGEN_DEVICE_FUNC
+ static EIGEN_STRONG_INLINE T run(const T& x) {
+ /* k0e.c
+ * Modified Bessel function, third kind, order zero,
+ * exponentially scaled
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, k0e();
+ *
+ * y = k0e( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns exponentially scaled modified Bessel function
+ * of the third kind of order zero of the argument.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE 0, 30 30000 1.4e-15 1.4e-16
+ * See k0().
+ *
+ */
+
+ const double A[] = {
+ 1.37446543561352307156E-16,
+ 4.25981614279661018399E-14,
+ 1.03496952576338420167E-11,
+ 1.90451637722020886025E-9,
+ 2.53479107902614945675E-7,
+ 2.28621210311945178607E-5,
+ 1.26461541144692592338E-3,
+ 3.59799365153615016266E-2,
+ 3.44289899924628486886E-1,
+ -5.35327393233902768720E-1};
+ const double B[] = {
+ 5.30043377268626276149E-18, -1.64758043015242134646E-17,
+ 5.21039150503902756861E-17, -1.67823109680541210385E-16,
+ 5.51205597852431940784E-16, -1.84859337734377901440E-15,
+ 6.34007647740507060557E-15, -2.22751332699166985548E-14,
+ 8.03289077536357521100E-14, -2.98009692317273043925E-13,
+ 1.14034058820847496303E-12, -4.51459788337394416547E-12,
+ 1.85594911495471785253E-11, -7.95748924447710747776E-11,
+ 3.57739728140030116597E-10, -1.69753450938905987466E-9,
+ 8.57403401741422608519E-9, -4.66048989768794782956E-8,
+ 2.76681363944501510342E-7, -1.83175552271911948767E-6,
+ 1.39498137188764993662E-5, -1.28495495816278026384E-4,
+ 1.56988388573005337491E-3, -3.14481013119645005427E-2,
+ 2.44030308206595545468E0
+ };
+ const T MAXNUM = pset1<T>(NumTraits<double>::infinity());
+ const T two = pset1<T>(2.0);
+ T x_le_two = internal::pchebevl<T, 10>::run(
+ pmadd(x, x, pset1<T>(-2.0)), A);
+ x_le_two = pmadd(
+ generic_i0<T, double>::run(x), pmul(
+ pset1<T>(-1.0), plog(pmul(pset1<T>(0.5), x))), x_le_two);
+ x_le_two = pmul(pexp(x), x_le_two);
+ x_le_two = pselect(pcmp_le(x, pset1<T>(0.0)), MAXNUM, x_le_two);
+ T x_gt_two = pmul(
+ internal::pchebevl<T, 25>::run(
+ psub(pdiv(pset1<T>(8.0), x), two), B),
+ prsqrt(x));
+ return pselect(pcmp_le(x, two), x_le_two, x_gt_two);
+ }
+};
+
+template <typename T>
+struct bessel_k0e_impl {
+ EIGEN_DEVICE_FUNC
+ static EIGEN_STRONG_INLINE T run(const T x) {
+ return generic_k0e<T>::run(x);
+ }
+};
+
+template <typename T>
+struct bessel_k0_retval {
+ typedef T type;
+};
+
+template <typename T, typename ScalarType = typename unpacket_traits<T>::type>
+struct generic_k0 {
+ EIGEN_STATIC_ASSERT((internal::is_same<T, T>::value == false),
+ THIS_TYPE_IS_NOT_SUPPORTED)
+
+ EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE T run(const T&) {
+ return ScalarType(0);
+ }
+};
+
+template <typename T>
+struct generic_k0<T, float> {
+ EIGEN_DEVICE_FUNC
+ static EIGEN_STRONG_INLINE T run(const T& x) {
+ /* k0f.c
+ * Modified Bessel function, third kind, order zero
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float x, y, k0f();
+ *
+ * y = k0f( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns modified Bessel function of the third kind
+ * of order zero of the argument.
+ *
+ * The range is partitioned into the two intervals [0,8] and
+ * (8, infinity). Chebyshev polynomial expansions are employed
+ * in each interval.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Tested at 2000 random points between 0 and 8. Peak absolute
+ * error (relative when K0 > 1) was 1.46e-14; rms, 4.26e-15.
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE 0, 30 30000 7.8e-7 8.5e-8
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * K0 domain x <= 0 MAXNUM
+ *
+ */
+
+ const float A[] = {1.90451637722020886025E-9f, 2.53479107902614945675E-7f,
+ 2.28621210311945178607E-5f, 1.26461541144692592338E-3f,
+ 3.59799365153615016266E-2f, 3.44289899924628486886E-1f,
+ -5.35327393233902768720E-1f};
+
+ const float B[] = {-1.69753450938905987466E-9f, 8.57403401741422608519E-9f,
+ -4.66048989768794782956E-8f, 2.76681363944501510342E-7f,
+ -1.83175552271911948767E-6f, 1.39498137188764993662E-5f,
+ -1.28495495816278026384E-4f, 1.56988388573005337491E-3f,
+ -3.14481013119645005427E-2f, 2.44030308206595545468E0f};
+ const T MAXNUM = pset1<T>(NumTraits<float>::infinity());
+ const T two = pset1<T>(2.0);
+ T x_le_two = internal::pchebevl<T, 7>::run(
+ pmadd(x, x, pset1<T>(-2.0)), A);
+ x_le_two = pmadd(
+ generic_i0<T, float>::run(x), pnegate(
+ plog(pmul(pset1<T>(0.5), x))), x_le_two);
+ x_le_two = pselect(pcmp_le(x, pset1<T>(0.0)), MAXNUM, x_le_two);
+ T x_gt_two = pmul(
+ pmul(
+ pexp(pnegate(x)),
+ internal::pchebevl<T, 10>::run(
+ psub(pdiv(pset1<T>(8.0), x), two), B)),
+ prsqrt(x));
+ return pselect(pcmp_le(x, two), x_le_two, x_gt_two);
+ }
+};
+
+template <typename T>
+struct generic_k0<T, double> {
+ EIGEN_DEVICE_FUNC
+ static EIGEN_STRONG_INLINE T run(const T& x) {
+ /*
+ *
+ * Modified Bessel function, third kind, order zero,
+ * exponentially scaled
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, k0();
+ *
+ * y = k0( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns exponentially scaled modified Bessel function
+ * of the third kind of order zero of the argument.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE 0, 30 30000 1.4e-15 1.4e-16
+ * See k0().
+ *
+ */
+ const double A[] = {
+ 1.37446543561352307156E-16,
+ 4.25981614279661018399E-14,
+ 1.03496952576338420167E-11,
+ 1.90451637722020886025E-9,
+ 2.53479107902614945675E-7,
+ 2.28621210311945178607E-5,
+ 1.26461541144692592338E-3,
+ 3.59799365153615016266E-2,
+ 3.44289899924628486886E-1,
+ -5.35327393233902768720E-1};
+ const double B[] = {
+ 5.30043377268626276149E-18, -1.64758043015242134646E-17,
+ 5.21039150503902756861E-17, -1.67823109680541210385E-16,
+ 5.51205597852431940784E-16, -1.84859337734377901440E-15,
+ 6.34007647740507060557E-15, -2.22751332699166985548E-14,
+ 8.03289077536357521100E-14, -2.98009692317273043925E-13,
+ 1.14034058820847496303E-12, -4.51459788337394416547E-12,
+ 1.85594911495471785253E-11, -7.95748924447710747776E-11,
+ 3.57739728140030116597E-10, -1.69753450938905987466E-9,
+ 8.57403401741422608519E-9, -4.66048989768794782956E-8,
+ 2.76681363944501510342E-7, -1.83175552271911948767E-6,
+ 1.39498137188764993662E-5, -1.28495495816278026384E-4,
+ 1.56988388573005337491E-3, -3.14481013119645005427E-2,
+ 2.44030308206595545468E0
+ };
+ const T MAXNUM = pset1<T>(NumTraits<double>::infinity());
+ const T two = pset1<T>(2.0);
+ T x_le_two = internal::pchebevl<T, 10>::run(
+ pmadd(x, x, pset1<T>(-2.0)), A);
+ x_le_two = pmadd(
+ generic_i0<T, double>::run(x), pnegate(
+ plog(pmul(pset1<T>(0.5), x))), x_le_two);
+ x_le_two = pselect(pcmp_le(x, pset1<T>(0.0)), MAXNUM, x_le_two);
+ T x_gt_two = pmul(
+ pmul(
+ pexp(-x),
+ internal::pchebevl<T, 25>::run(
+ psub(pdiv(pset1<T>(8.0), x), two), B)),
+ prsqrt(x));
+ return pselect(pcmp_le(x, two), x_le_two, x_gt_two);
+ }
+};
+
+template <typename T>
+struct bessel_k0_impl {
+ EIGEN_DEVICE_FUNC
+ static EIGEN_STRONG_INLINE T run(const T x) {
+ return generic_k0<T>::run(x);
+ }
+};
+
+template <typename T>
+struct bessel_k1e_retval {
+ typedef T type;
+};
+
+template <typename T, typename ScalarType = typename unpacket_traits<T>::type>
+struct generic_k1e {
+ EIGEN_STATIC_ASSERT((internal::is_same<T, T>::value == false),
+ THIS_TYPE_IS_NOT_SUPPORTED)
+
+ EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE T run(const T&) {
+ return ScalarType(0);
+ }
+};
+
+template <typename T>
+struct generic_k1e<T, float> {
+ EIGEN_DEVICE_FUNC
+ static EIGEN_STRONG_INLINE T run(const T& x) {
+ /* k1ef.c
+ *
+ * Modified Bessel function, third kind, order one,
+ * exponentially scaled
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float x, y, k1ef();
+ *
+ * y = k1ef( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns exponentially scaled modified Bessel function
+ * of the third kind of order one of the argument:
+ *
+ * k1e(x) = exp(x) * k1(x).
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE 0, 30 30000 4.9e-7 6.7e-8
+ * See k1().
+ *
+ */
+
+ const float A[] = {-2.21338763073472585583E-8f, -2.43340614156596823496E-6f,
+ -1.73028895751305206302E-4f, -6.97572385963986435018E-3f,
+ -1.22611180822657148235E-1f, -3.53155960776544875667E-1f,
+ 1.52530022733894777053E0f};
+ const float B[] = {2.01504975519703286596E-9f, -1.03457624656780970260E-8f,
+ 5.74108412545004946722E-8f, -3.50196060308781257119E-7f,
+ 2.40648494783721712015E-6f, -1.93619797416608296024E-5f,
+ 1.95215518471351631108E-4f, -2.85781685962277938680E-3f,
+ 1.03923736576817238437E-1f, 2.72062619048444266945E0f};
+ const T MAXNUM = pset1<T>(NumTraits<float>::infinity());
+ const T two = pset1<T>(2.0);
+ T x_le_two = pdiv(internal::pchebevl<T, 7>::run(
+ pmadd(x, x, pset1<T>(-2.0)), A), x);
+ x_le_two = pmadd(
+ generic_i1<T, float>::run(x), plog(pmul(pset1<T>(0.5), x)), x_le_two);
+ x_le_two = pmul(x_le_two, pexp(x));
+ x_le_two = pselect(pcmp_le(x, pset1<T>(0.0)), MAXNUM, x_le_two);
+ T x_gt_two = pmul(
+ internal::pchebevl<T, 10>::run(
+ psub(pdiv(pset1<T>(8.0), x), two), B),
+ prsqrt(x));
+ return pselect(pcmp_le(x, two), x_le_two, x_gt_two);
+ }
+};
+
+template <typename T>
+struct generic_k1e<T, double> {
+ EIGEN_DEVICE_FUNC
+ static EIGEN_STRONG_INLINE T run(const T& x) {
+ /* k1e.c
+ *
+ * Modified Bessel function, third kind, order one,
+ * exponentially scaled
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, k1e();
+ *
+ * y = k1e( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns exponentially scaled modified Bessel function
+ * of the third kind of order one of the argument:
+ *
+ * k1e(x) = exp(x) * k1(x).
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE 0, 30 30000 7.8e-16 1.2e-16
+ * See k1().
+ *
+ */
+ const double A[] = {-7.02386347938628759343E-18, -2.42744985051936593393E-15,
+ -6.66690169419932900609E-13, -1.41148839263352776110E-10,
+ -2.21338763073472585583E-8, -2.43340614156596823496E-6,
+ -1.73028895751305206302E-4, -6.97572385963986435018E-3,
+ -1.22611180822657148235E-1, -3.53155960776544875667E-1,
+ 1.52530022733894777053E0};
+ const double B[] = {-5.75674448366501715755E-18, 1.79405087314755922667E-17,
+ -5.68946255844285935196E-17, 1.83809354436663880070E-16,
+ -6.05704724837331885336E-16, 2.03870316562433424052E-15,
+ -7.01983709041831346144E-15, 2.47715442448130437068E-14,
+ -8.97670518232499435011E-14, 3.34841966607842919884E-13,
+ -1.28917396095102890680E-12, 5.13963967348173025100E-12,
+ -2.12996783842756842877E-11, 9.21831518760500529508E-11,
+ -4.19035475934189648750E-10, 2.01504975519703286596E-9,
+ -1.03457624656780970260E-8, 5.74108412545004946722E-8,
+ -3.50196060308781257119E-7, 2.40648494783721712015E-6,
+ -1.93619797416608296024E-5, 1.95215518471351631108E-4,
+ -2.85781685962277938680E-3, 1.03923736576817238437E-1,
+ 2.72062619048444266945E0};
+ const T MAXNUM = pset1<T>(NumTraits<double>::infinity());
+ const T two = pset1<T>(2.0);
+ T x_le_two = pdiv(internal::pchebevl<T, 11>::run(
+ pmadd(x, x, pset1<T>(-2.0)), A), x);
+ x_le_two = pmadd(
+ generic_i1<T, double>::run(x), plog(pmul(pset1<T>(0.5), x)), x_le_two);
+ x_le_two = pmul(x_le_two, pexp(x));
+ x_le_two = pselect(pcmp_le(x, pset1<T>(0.0)), MAXNUM, x_le_two);
+ T x_gt_two = pmul(
+ internal::pchebevl<T, 25>::run(
+ psub(pdiv(pset1<T>(8.0), x), two), B),
+ prsqrt(x));
+ return pselect(pcmp_le(x, two), x_le_two, x_gt_two);
+ }
+};
+
+template <typename T>
+struct bessel_k1e_impl {
+ EIGEN_DEVICE_FUNC
+ static EIGEN_STRONG_INLINE T run(const T x) {
+ return generic_k1e<T>::run(x);
+ }
+};
+
+template <typename T>
+struct bessel_k1_retval {
+ typedef T type;
+};
+
+template <typename T, typename ScalarType = typename unpacket_traits<T>::type>
+struct generic_k1 {
+ EIGEN_STATIC_ASSERT((internal::is_same<T, T>::value == false),
+ THIS_TYPE_IS_NOT_SUPPORTED)
+
+ EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE T run(const T&) {
+ return ScalarType(0);
+ }
+};
+
+template <typename T>
+struct generic_k1<T, float> {
+ EIGEN_DEVICE_FUNC
+ static EIGEN_STRONG_INLINE T run(const T& x) {
+ /* k1f.c
+ * Modified Bessel function, third kind, order one
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float x, y, k1f();
+ *
+ * y = k1f( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Computes the modified Bessel function of the third kind
+ * of order one of the argument.
+ *
+ * The range is partitioned into the two intervals [0,2] and
+ * (2, infinity). Chebyshev polynomial expansions are employed
+ * in each interval.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE 0, 30 30000 4.6e-7 7.6e-8
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * k1 domain x <= 0 MAXNUM
+ *
+ */
+
+ const float A[] = {-2.21338763073472585583E-8f, -2.43340614156596823496E-6f,
+ -1.73028895751305206302E-4f, -6.97572385963986435018E-3f,
+ -1.22611180822657148235E-1f, -3.53155960776544875667E-1f,
+ 1.52530022733894777053E0f};
+ const float B[] = {2.01504975519703286596E-9f, -1.03457624656780970260E-8f,
+ 5.74108412545004946722E-8f, -3.50196060308781257119E-7f,
+ 2.40648494783721712015E-6f, -1.93619797416608296024E-5f,
+ 1.95215518471351631108E-4f, -2.85781685962277938680E-3f,
+ 1.03923736576817238437E-1f, 2.72062619048444266945E0f};
+ const T MAXNUM = pset1<T>(NumTraits<float>::infinity());
+ const T two = pset1<T>(2.0);
+ T x_le_two = pdiv(internal::pchebevl<T, 7>::run(
+ pmadd(x, x, pset1<T>(-2.0)), A), x);
+ x_le_two = pmadd(
+ generic_i1<T, float>::run(x), plog(pmul(pset1<T>(0.5), x)), x_le_two);
+ x_le_two = pselect(pcmp_le(x, pset1<T>(0.0)), MAXNUM, x_le_two);
+ T x_gt_two = pmul(
+ pexp(pnegate(x)),
+ pmul(
+ internal::pchebevl<T, 10>::run(
+ psub(pdiv(pset1<T>(8.0), x), two), B),
+ prsqrt(x)));
+ return pselect(pcmp_le(x, two), x_le_two, x_gt_two);
+ }
+};
+
+template <typename T>
+struct generic_k1<T, double> {
+ EIGEN_DEVICE_FUNC
+ static EIGEN_STRONG_INLINE T run(const T& x) {
+ /* k1.c
+ * Modified Bessel function, third kind, order one
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float x, y, k1f();
+ *
+ * y = k1f( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Computes the modified Bessel function of the third kind
+ * of order one of the argument.
+ *
+ * The range is partitioned into the two intervals [0,2] and
+ * (2, infinity). Chebyshev polynomial expansions are employed
+ * in each interval.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE 0, 30 30000 4.6e-7 7.6e-8
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * k1 domain x <= 0 MAXNUM
+ *
+ */
+ const double A[] = {-7.02386347938628759343E-18, -2.42744985051936593393E-15,
+ -6.66690169419932900609E-13, -1.41148839263352776110E-10,
+ -2.21338763073472585583E-8, -2.43340614156596823496E-6,
+ -1.73028895751305206302E-4, -6.97572385963986435018E-3,
+ -1.22611180822657148235E-1, -3.53155960776544875667E-1,
+ 1.52530022733894777053E0};
+ const double B[] = {-5.75674448366501715755E-18, 1.79405087314755922667E-17,
+ -5.68946255844285935196E-17, 1.83809354436663880070E-16,
+ -6.05704724837331885336E-16, 2.03870316562433424052E-15,
+ -7.01983709041831346144E-15, 2.47715442448130437068E-14,
+ -8.97670518232499435011E-14, 3.34841966607842919884E-13,
+ -1.28917396095102890680E-12, 5.13963967348173025100E-12,
+ -2.12996783842756842877E-11, 9.21831518760500529508E-11,
+ -4.19035475934189648750E-10, 2.01504975519703286596E-9,
+ -1.03457624656780970260E-8, 5.74108412545004946722E-8,
+ -3.50196060308781257119E-7, 2.40648494783721712015E-6,
+ -1.93619797416608296024E-5, 1.95215518471351631108E-4,
+ -2.85781685962277938680E-3, 1.03923736576817238437E-1,
+ 2.72062619048444266945E0};
+ const T MAXNUM = pset1<T>(NumTraits<double>::infinity());
+ const T two = pset1<T>(2.0);
+ T x_le_two = pdiv(internal::pchebevl<T, 11>::run(
+ pmadd(x, x, pset1<T>(-2.0)), A), x);
+ x_le_two = pmadd(
+ generic_i1<T, double>::run(x), plog(pmul(pset1<T>(0.5), x)), x_le_two);
+ x_le_two = pselect(pcmp_le(x, pset1<T>(0.0)), MAXNUM, x_le_two);
+ T x_gt_two = pmul(
+ pexp(-x),
+ pmul(
+ internal::pchebevl<T, 25>::run(
+ psub(pdiv(pset1<T>(8.0), x), two), B),
+ prsqrt(x)));
+ return pselect(pcmp_le(x, two), x_le_two, x_gt_two);
+ }
+};
+
+template <typename T>
+struct bessel_k1_impl {
+ EIGEN_DEVICE_FUNC
+ static EIGEN_STRONG_INLINE T run(const T x) {
+ return generic_k1<T>::run(x);
+ }
+};
+
+template <typename T>
+struct bessel_j0_retval {
+ typedef T type;
+};
+
+template <typename T, typename ScalarType = typename unpacket_traits<T>::type>
+struct generic_j0 {
+ EIGEN_STATIC_ASSERT((internal::is_same<T, T>::value == false),
+ THIS_TYPE_IS_NOT_SUPPORTED)
+
+ EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE T run(const T&) {
+ return ScalarType(0);
+ }
+};
+
+template <typename T>
+struct generic_j0<T, float> {
+ EIGEN_DEVICE_FUNC
+ static EIGEN_STRONG_INLINE T run(const T& x) {
+ /* j0f.c
+ * Bessel function of order zero
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float x, y, j0f();
+ *
+ * y = j0f( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns Bessel function of order zero of the argument.
+ *
+ * The domain is divided into the intervals [0, 2] and
+ * (2, infinity). In the first interval the following polynomial
+ * approximation is used:
+ *
+ *
+ * 2 2 2
+ * (w - r ) (w - r ) (w - r ) P(w)
+ * 1 2 3
+ *
+ * 2
+ * where w = x and the three r's are zeros of the function.
+ *
+ * In the second interval, the modulus and phase are approximated
+ * by polynomials of the form Modulus(x) = sqrt(1/x) Q(1/x)
+ * and Phase(x) = x + 1/x R(1/x^2) - pi/4. The function is
+ *
+ * j0(x) = Modulus(x) cos( Phase(x) ).
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Absolute error:
+ * arithmetic domain # trials peak rms
+ * IEEE 0, 2 100000 1.3e-7 3.6e-8
+ * IEEE 2, 32 100000 1.9e-7 5.4e-8
+ *
+ */
+
+ const float JP[] = {-6.068350350393235E-008f, 6.388945720783375E-006f,
+ -3.969646342510940E-004f, 1.332913422519003E-002f,
+ -1.729150680240724E-001f};
+ const float MO[] = {-6.838999669318810E-002f, 1.864949361379502E-001f,
+ -2.145007480346739E-001f, 1.197549369473540E-001f,
+ -3.560281861530129E-003f, -4.969382655296620E-002f,
+ -3.355424622293709E-006f, 7.978845717621440E-001f};
+ const float PH[] = {3.242077816988247E+001f, -3.630592630518434E+001f,
+ 1.756221482109099E+001f, -4.974978466280903E+000f,
+ 1.001973420681837E+000f, -1.939906941791308E-001f,
+ 6.490598792654666E-002f, -1.249992184872738E-001f};
+ const T DR1 = pset1<T>(5.78318596294678452118f);
+ const T NEG_PIO4F = pset1<T>(-0.7853981633974483096f); /* -pi / 4 */
+ T y = pabs(x);
+ T z = pmul(y, y);
+ T y_le_two = pselect(
+ pcmp_lt(y, pset1<T>(1.0e-3f)),
+ pmadd(z, pset1<T>(-0.25f), pset1<T>(1.0f)),
+ pmul(psub(z, DR1), internal::ppolevl<T, 4>::run(z, JP)));
+ T q = pdiv(pset1<T>(1.0f), y);
+ T w = prsqrt(y);
+ T p = pmul(w, internal::ppolevl<T, 7>::run(q, MO));
+ w = pmul(q, q);
+ T yn = pmadd(q, internal::ppolevl<T, 7>::run(w, PH), NEG_PIO4F);
+ T y_gt_two = pmul(p, pcos(padd(yn, y)));
+ return pselect(pcmp_le(y, pset1<T>(2.0)), y_le_two, y_gt_two);
+ }
+};
+
+template <typename T>
+struct generic_j0<T, double> {
+ EIGEN_DEVICE_FUNC
+ static EIGEN_STRONG_INLINE T run(const T& x) {
+ /* j0.c
+ * Bessel function of order zero
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, j0();
+ *
+ * y = j0( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns Bessel function of order zero of the argument.
+ *
+ * The domain is divided into the intervals [0, 5] and
+ * (5, infinity). In the first interval the following rational
+ * approximation is used:
+ *
+ *
+ * 2 2
+ * (w - r ) (w - r ) P (w) / Q (w)
+ * 1 2 3 8
+ *
+ * 2
+ * where w = x and the two r's are zeros of the function.
+ *
+ * In the second interval, the Hankel asymptotic expansion
+ * is employed with two rational functions of degree 6/6
+ * and 7/7.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Absolute error:
+ * arithmetic domain # trials peak rms
+ * DEC 0, 30 10000 4.4e-17 6.3e-18
+ * IEEE 0, 30 60000 4.2e-16 1.1e-16
+ *
+ */
+ const double PP[] = {7.96936729297347051624E-4, 8.28352392107440799803E-2,
+ 1.23953371646414299388E0, 5.44725003058768775090E0,
+ 8.74716500199817011941E0, 5.30324038235394892183E0,
+ 9.99999999999999997821E-1};
+ const double PQ[] = {9.24408810558863637013E-4, 8.56288474354474431428E-2,
+ 1.25352743901058953537E0, 5.47097740330417105182E0,
+ 8.76190883237069594232E0, 5.30605288235394617618E0,
+ 1.00000000000000000218E0};
+ const double QP[] = {-1.13663838898469149931E-2, -1.28252718670509318512E0,
+ -1.95539544257735972385E1, -9.32060152123768231369E1,
+ -1.77681167980488050595E2, -1.47077505154951170175E2,
+ -5.14105326766599330220E1, -6.05014350600728481186E0};
+ const double QQ[] = {1.00000000000000000000E0, 6.43178256118178023184E1,
+ 8.56430025976980587198E2, 3.88240183605401609683E3,
+ 7.24046774195652478189E3, 5.93072701187316984827E3,
+ 2.06209331660327847417E3, 2.42005740240291393179E2};
+ const double RP[] = {-4.79443220978201773821E9, 1.95617491946556577543E12,
+ -2.49248344360967716204E14, 9.70862251047306323952E15};
+ const double RQ[] = {1.00000000000000000000E0, 4.99563147152651017219E2,
+ 1.73785401676374683123E5, 4.84409658339962045305E7,
+ 1.11855537045356834862E10, 2.11277520115489217587E12,
+ 3.10518229857422583814E14, 3.18121955943204943306E16,
+ 1.71086294081043136091E18};
+ const T DR1 = pset1<T>(5.78318596294678452118E0);
+ const T DR2 = pset1<T>(3.04712623436620863991E1);
+ const T SQ2OPI = pset1<T>(7.9788456080286535587989E-1); /* sqrt(2 / pi) */
+ const T NEG_PIO4 = pset1<T>(-0.7853981633974483096); /* pi / 4 */
+
+ T y = pabs(x);
+ T z = pmul(y, y);
+ T y_le_five = pselect(
+ pcmp_lt(y, pset1<T>(1.0e-5)),
+ pmadd(z, pset1<T>(-0.25), pset1<T>(1.0)),
+ pmul(pmul(psub(z, DR1), psub(z, DR2)),
+ pdiv(internal::ppolevl<T, 3>::run(z, RP),
+ internal::ppolevl<T, 8>::run(z, RQ))));
+ T s = pdiv(pset1<T>(25.0), z);
+ T p = pdiv(
+ internal::ppolevl<T, 6>::run(s, PP),
+ internal::ppolevl<T, 6>::run(s, PQ));
+ T q = pdiv(
+ internal::ppolevl<T, 7>::run(s, QP),
+ internal::ppolevl<T, 7>::run(s, QQ));
+ T yn = padd(y, NEG_PIO4);
+ T w = pdiv(pset1<T>(-5.0), y);
+ p = pmadd(p, pcos(yn), pmul(w, pmul(q, psin(yn))));
+ T y_gt_five = pmul(p, pmul(SQ2OPI, prsqrt(y)));
+ return pselect(pcmp_le(y, pset1<T>(5.0)), y_le_five, y_gt_five);
+ }
+};
+
+template <typename T>
+struct bessel_j0_impl {
+ EIGEN_DEVICE_FUNC
+ static EIGEN_STRONG_INLINE T run(const T x) {
+ return generic_j0<T>::run(x);
+ }
+};
+
+template <typename T>
+struct bessel_y0_retval {
+ typedef T type;
+};
+
+template <typename T, typename ScalarType = typename unpacket_traits<T>::type>
+struct generic_y0 {
+ EIGEN_STATIC_ASSERT((internal::is_same<T, T>::value == false),
+ THIS_TYPE_IS_NOT_SUPPORTED)
+
+ EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE T run(const T&) {
+ return ScalarType(0);
+ }
+};
+
+template <typename T>
+struct generic_y0<T, float> {
+ EIGEN_DEVICE_FUNC
+ static EIGEN_STRONG_INLINE T run(const T& x) {
+ /* j0f.c
+ * Bessel function of the second kind, order zero
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float x, y, y0f();
+ *
+ * y = y0f( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns Bessel function of the second kind, of order
+ * zero, of the argument.
+ *
+ * The domain is divided into the intervals [0, 2] and
+ * (2, infinity). In the first interval a rational approximation
+ * R(x) is employed to compute
+ *
+ * 2 2 2
+ * y0(x) = (w - r ) (w - r ) (w - r ) R(x) + 2/pi ln(x) j0(x).
+ * 1 2 3
+ *
+ * Thus a call to j0() is required. The three zeros are removed
+ * from R(x) to improve its numerical stability.
+ *
+ * In the second interval, the modulus and phase are approximated
+ * by polynomials of the form Modulus(x) = sqrt(1/x) Q(1/x)
+ * and Phase(x) = x + 1/x S(1/x^2) - pi/4. Then the function is
+ *
+ * y0(x) = Modulus(x) sin( Phase(x) ).
+ *
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Absolute error, when y0(x) < 1; else relative error:
+ *
+ * arithmetic domain # trials peak rms
+ * IEEE 0, 2 100000 2.4e-7 3.4e-8
+ * IEEE 2, 32 100000 1.8e-7 5.3e-8
+ *
+ */
+
+ const float YP[] = {9.454583683980369E-008f, -9.413212653797057E-006f,
+ 5.344486707214273E-004f, -1.584289289821316E-002f,
+ 1.707584643733568E-001f};
+ const float MO[] = {-6.838999669318810E-002f, 1.864949361379502E-001f,
+ -2.145007480346739E-001f, 1.197549369473540E-001f,
+ -3.560281861530129E-003f, -4.969382655296620E-002f,
+ -3.355424622293709E-006f, 7.978845717621440E-001f};
+ const float PH[] = {3.242077816988247E+001f, -3.630592630518434E+001f,
+ 1.756221482109099E+001f, -4.974978466280903E+000f,
+ 1.001973420681837E+000f, -1.939906941791308E-001f,
+ 6.490598792654666E-002f, -1.249992184872738E-001f};
+ const T YZ1 = pset1<T>(0.43221455686510834878f);
+ const T TWOOPI = pset1<T>(0.636619772367581343075535f); /* 2 / pi */
+ const T NEG_PIO4F = pset1<T>(-0.7853981633974483096f); /* -pi / 4 */
+ const T NEG_MAXNUM = pset1<T>(-NumTraits<float>::infinity());
+ T z = pmul(x, x);
+ T x_le_two = pmul(TWOOPI, pmul(plog(x), generic_j0<T, float>::run(x)));
+ x_le_two = pmadd(
+ psub(z, YZ1), internal::ppolevl<T, 4>::run(z, YP), x_le_two);
+ x_le_two = pselect(pcmp_le(x, pset1<T>(0.0)), NEG_MAXNUM, x_le_two);
+ T q = pdiv(pset1<T>(1.0), x);
+ T w = prsqrt(x);
+ T p = pmul(w, internal::ppolevl<T, 7>::run(q, MO));
+ T u = pmul(q, q);
+ T xn = pmadd(q, internal::ppolevl<T, 7>::run(u, PH), NEG_PIO4F);
+ T x_gt_two = pmul(p, psin(padd(xn, x)));
+ return pselect(pcmp_le(x, pset1<T>(2.0)), x_le_two, x_gt_two);
+ }
+};
+
+template <typename T>
+struct generic_y0<T, double> {
+ EIGEN_DEVICE_FUNC
+ static EIGEN_STRONG_INLINE T run(const T& x) {
+ /* j0.c
+ * Bessel function of the second kind, order zero
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, y0();
+ *
+ * y = y0( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns Bessel function of the second kind, of order
+ * zero, of the argument.
+ *
+ * The domain is divided into the intervals [0, 5] and
+ * (5, infinity). In the first interval a rational approximation
+ * R(x) is employed to compute
+ * y0(x) = R(x) + 2 * log(x) * j0(x) / PI.
+ * Thus a call to j0() is required.
+ *
+ * In the second interval, the Hankel asymptotic expansion
+ * is employed with two rational functions of degree 6/6
+ * and 7/7.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Absolute error, when y0(x) < 1; else relative error:
+ *
+ * arithmetic domain # trials peak rms
+ * DEC 0, 30 9400 7.0e-17 7.9e-18
+ * IEEE 0, 30 30000 1.3e-15 1.6e-16
+ *
+ */
+ const double PP[] = {7.96936729297347051624E-4, 8.28352392107440799803E-2,
+ 1.23953371646414299388E0, 5.44725003058768775090E0,
+ 8.74716500199817011941E0, 5.30324038235394892183E0,
+ 9.99999999999999997821E-1};
+ const double PQ[] = {9.24408810558863637013E-4, 8.56288474354474431428E-2,
+ 1.25352743901058953537E0, 5.47097740330417105182E0,
+ 8.76190883237069594232E0, 5.30605288235394617618E0,
+ 1.00000000000000000218E0};
+ const double QP[] = {-1.13663838898469149931E-2, -1.28252718670509318512E0,
+ -1.95539544257735972385E1, -9.32060152123768231369E1,
+ -1.77681167980488050595E2, -1.47077505154951170175E2,
+ -5.14105326766599330220E1, -6.05014350600728481186E0};
+ const double QQ[] = {1.00000000000000000000E0, 6.43178256118178023184E1,
+ 8.56430025976980587198E2, 3.88240183605401609683E3,
+ 7.24046774195652478189E3, 5.93072701187316984827E3,
+ 2.06209331660327847417E3, 2.42005740240291393179E2};
+ const double YP[] = {1.55924367855235737965E4, -1.46639295903971606143E7,
+ 5.43526477051876500413E9, -9.82136065717911466409E11,
+ 8.75906394395366999549E13, -3.46628303384729719441E15,
+ 4.42733268572569800351E16, -1.84950800436986690637E16};
+ const double YQ[] = {1.00000000000000000000E0, 1.04128353664259848412E3,
+ 6.26107330137134956842E5, 2.68919633393814121987E8,
+ 8.64002487103935000337E10, 2.02979612750105546709E13,
+ 3.17157752842975028269E15, 2.50596256172653059228E17};
+ const T SQ2OPI = pset1<T>(7.9788456080286535587989E-1); /* sqrt(2 / pi) */
+ const T TWOOPI = pset1<T>(0.636619772367581343075535); /* 2 / pi */
+ const T NEG_PIO4 = pset1<T>(-0.7853981633974483096); /* -pi / 4 */
+ const T NEG_MAXNUM = pset1<T>(-NumTraits<double>::infinity());
+
+ T z = pmul(x, x);
+ T x_le_five = pdiv(internal::ppolevl<T, 7>::run(z, YP),
+ internal::ppolevl<T, 7>::run(z, YQ));
+ x_le_five = pmadd(
+ pmul(TWOOPI, plog(x)), generic_j0<T, double>::run(x), x_le_five);
+ x_le_five = pselect(pcmp_le(x, pset1<T>(0.0)), NEG_MAXNUM, x_le_five);
+ T s = pdiv(pset1<T>(25.0), z);
+ T p = pdiv(
+ internal::ppolevl<T, 6>::run(s, PP),
+ internal::ppolevl<T, 6>::run(s, PQ));
+ T q = pdiv(
+ internal::ppolevl<T, 7>::run(s, QP),
+ internal::ppolevl<T, 7>::run(s, QQ));
+ T xn = padd(x, NEG_PIO4);
+ T w = pdiv(pset1<T>(5.0), x);
+ p = pmadd(p, psin(xn), pmul(w, pmul(q, pcos(xn))));
+ T x_gt_five = pmul(p, pmul(SQ2OPI, prsqrt(x)));
+ return pselect(pcmp_le(x, pset1<T>(5.0)), x_le_five, x_gt_five);
+ }
+};
+
+template <typename T>
+struct bessel_y0_impl {
+ EIGEN_DEVICE_FUNC
+ static EIGEN_STRONG_INLINE T run(const T x) {
+ return generic_y0<T>::run(x);
+ }
+};
+
+template <typename T>
+struct bessel_j1_retval {
+ typedef T type;
+};
+
+template <typename T, typename ScalarType = typename unpacket_traits<T>::type>
+struct generic_j1 {
+ EIGEN_STATIC_ASSERT((internal::is_same<T, T>::value == false),
+ THIS_TYPE_IS_NOT_SUPPORTED)
+
+ EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE T run(const T&) {
+ return ScalarType(0);
+ }
+};
+
+template <typename T>
+struct generic_j1<T, float> {
+ EIGEN_DEVICE_FUNC
+ static EIGEN_STRONG_INLINE T run(const T& x) {
+ /* j1f.c
+ * Bessel function of order one
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float x, y, j1f();
+ *
+ * y = j1f( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns Bessel function of order one of the argument.
+ *
+ * The domain is divided into the intervals [0, 2] and
+ * (2, infinity). In the first interval a polynomial approximation
+ * 2
+ * (w - r ) x P(w)
+ * 1
+ * 2
+ * is used, where w = x and r is the first zero of the function.
+ *
+ * In the second interval, the modulus and phase are approximated
+ * by polynomials of the form Modulus(x) = sqrt(1/x) Q(1/x)
+ * and Phase(x) = x + 1/x R(1/x^2) - 3pi/4. The function is
+ *
+ * j0(x) = Modulus(x) cos( Phase(x) ).
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Absolute error:
+ * arithmetic domain # trials peak rms
+ * IEEE 0, 2 100000 1.2e-7 2.5e-8
+ * IEEE 2, 32 100000 2.0e-7 5.3e-8
+ *
+ *
+ */
+
+ const float JP[] = {-4.878788132172128E-009f, 6.009061827883699E-007f,
+ -4.541343896997497E-005f, 1.937383947804541E-003f,
+ -3.405537384615824E-002f};
+ const float MO1[] = {6.913942741265801E-002f, -2.284801500053359E-001f,
+ 3.138238455499697E-001f, -2.102302420403875E-001f,
+ 5.435364690523026E-003f, 1.493389585089498E-001f,
+ 4.976029650847191E-006f, 7.978845453073848E-001f};
+ const float PH1[] = {-4.497014141919556E+001f, 5.073465654089319E+001f,
+ -2.485774108720340E+001f, 7.222973196770240E+000f,
+ -1.544842782180211E+000f, 3.503787691653334E-001f,
+ -1.637986776941202E-001f, 3.749989509080821E-001f};
+ const T Z1 = pset1<T>(1.46819706421238932572E1f);
+ const T NEG_THPIO4F = pset1<T>(-2.35619449019234492885f); /* -3*pi/4 */
+
+ T y = pabs(x);
+ T z = pmul(y, y);
+ T y_le_two = pmul(
+ psub(z, Z1),
+ pmul(x, internal::ppolevl<T, 4>::run(z, JP)));
+ T q = pdiv(pset1<T>(1.0f), y);
+ T w = prsqrt(y);
+ T p = pmul(w, internal::ppolevl<T, 7>::run(q, MO1));
+ w = pmul(q, q);
+ T yn = pmadd(q, internal::ppolevl<T, 7>::run(w, PH1), NEG_THPIO4F);
+ T y_gt_two = pmul(p, pcos(padd(yn, y)));
+ // j1 is an odd function. This implementation differs from cephes to
+ // take this fact in to account. Cephes returns -j1(x) for y > 2 range.
+ y_gt_two = pselect(
+ pcmp_lt(x, pset1<T>(0.0f)), pnegate(y_gt_two), y_gt_two);
+ return pselect(pcmp_le(y, pset1<T>(2.0f)), y_le_two, y_gt_two);
+ }
+};
+
+template <typename T>
+struct generic_j1<T, double> {
+ EIGEN_DEVICE_FUNC
+ static EIGEN_STRONG_INLINE T run(const T& x) {
+ /* j1.c
+ * Bessel function of order one
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, j1();
+ *
+ * y = j1( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns Bessel function of order one of the argument.
+ *
+ * The domain is divided into the intervals [0, 8] and
+ * (8, infinity). In the first interval a 24 term Chebyshev
+ * expansion is used. In the second, the asymptotic
+ * trigonometric representation is employed using two
+ * rational functions of degree 5/5.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Absolute error:
+ * arithmetic domain # trials peak rms
+ * DEC 0, 30 10000 4.0e-17 1.1e-17
+ * IEEE 0, 30 30000 2.6e-16 1.1e-16
+ *
+ */
+ const double PP[] = {7.62125616208173112003E-4, 7.31397056940917570436E-2,
+ 1.12719608129684925192E0, 5.11207951146807644818E0,
+ 8.42404590141772420927E0, 5.21451598682361504063E0,
+ 1.00000000000000000254E0};
+ const double PQ[] = {5.71323128072548699714E-4, 6.88455908754495404082E-2,
+ 1.10514232634061696926E0, 5.07386386128601488557E0,
+ 8.39985554327604159757E0, 5.20982848682361821619E0,
+ 9.99999999999999997461E-1};
+ const double QP[] = {5.10862594750176621635E-2, 4.98213872951233449420E0,
+ 7.58238284132545283818E1, 3.66779609360150777800E2,
+ 7.10856304998926107277E2, 5.97489612400613639965E2,
+ 2.11688757100572135698E2, 2.52070205858023719784E1};
+ const double QQ[] = {1.00000000000000000000E0, 7.42373277035675149943E1,
+ 1.05644886038262816351E3, 4.98641058337653607651E3,
+ 9.56231892404756170795E3, 7.99704160447350683650E3,
+ 2.82619278517639096600E3, 3.36093607810698293419E2};
+ const double RP[] = {-8.99971225705559398224E8, 4.52228297998194034323E11,
+ -7.27494245221818276015E13, 3.68295732863852883286E15};
+ const double RQ[] = {1.00000000000000000000E0, 6.20836478118054335476E2,
+ 2.56987256757748830383E5, 8.35146791431949253037E7,
+ 2.21511595479792499675E10, 4.74914122079991414898E12,
+ 7.84369607876235854894E14, 8.95222336184627338078E16,
+ 5.32278620332680085395E18};
+ const T Z1 = pset1<T>(1.46819706421238932572E1);
+ const T Z2 = pset1<T>(4.92184563216946036703E1);
+ const T NEG_THPIO4 = pset1<T>(-2.35619449019234492885); /* -3*pi/4 */
+ const T SQ2OPI = pset1<T>(7.9788456080286535587989E-1); /* sqrt(2 / pi) */
+ T y = pabs(x);
+ T z = pmul(y, y);
+ T y_le_five = pdiv(internal::ppolevl<T, 3>::run(z, RP),
+ internal::ppolevl<T, 8>::run(z, RQ));
+ y_le_five = pmul(pmul(pmul(y_le_five, x), psub(z, Z1)), psub(z, Z2));
+ T s = pdiv(pset1<T>(25.0), z);
+ T p = pdiv(
+ internal::ppolevl<T, 6>::run(s, PP),
+ internal::ppolevl<T, 6>::run(s, PQ));
+ T q = pdiv(
+ internal::ppolevl<T, 7>::run(s, QP),
+ internal::ppolevl<T, 7>::run(s, QQ));
+ T yn = padd(y, NEG_THPIO4);
+ T w = pdiv(pset1<T>(-5.0), y);
+ p = pmadd(p, pcos(yn), pmul(w, pmul(q, psin(yn))));
+ T y_gt_five = pmul(p, pmul(SQ2OPI, prsqrt(y)));
+ // j1 is an odd function. This implementation differs from cephes to
+ // take this fact in to account. Cephes returns -j1(x) for y > 5 range.
+ y_gt_five = pselect(
+ pcmp_lt(x, pset1<T>(0.0)), pnegate(y_gt_five), y_gt_five);
+ return pselect(pcmp_le(y, pset1<T>(5.0)), y_le_five, y_gt_five);
+ }
+};
+
+template <typename T>
+struct bessel_j1_impl {
+ EIGEN_DEVICE_FUNC
+ static EIGEN_STRONG_INLINE T run(const T x) {
+ return generic_j1<T>::run(x);
+ }
+};
+
+template <typename T>
+struct bessel_y1_retval {
+ typedef T type;
+};
+
+template <typename T, typename ScalarType = typename unpacket_traits<T>::type>
+struct generic_y1 {
+ EIGEN_STATIC_ASSERT((internal::is_same<T, T>::value == false),
+ THIS_TYPE_IS_NOT_SUPPORTED)
+
+ EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE T run(const T&) {
+ return ScalarType(0);
+ }
+};
+
+template <typename T>
+struct generic_y1<T, float> {
+ EIGEN_DEVICE_FUNC
+ static EIGEN_STRONG_INLINE T run(const T& x) {
+ /* j1f.c
+ * Bessel function of second kind of order one
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, y1();
+ *
+ * y = y1( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns Bessel function of the second kind of order one
+ * of the argument.
+ *
+ * The domain is divided into the intervals [0, 2] and
+ * (2, infinity). In the first interval a rational approximation
+ * R(x) is employed to compute
+ *
+ * 2
+ * y0(x) = (w - r ) x R(x^2) + 2/pi (ln(x) j1(x) - 1/x) .
+ * 1
+ *
+ * Thus a call to j1() is required.
+ *
+ * In the second interval, the modulus and phase are approximated
+ * by polynomials of the form Modulus(x) = sqrt(1/x) Q(1/x)
+ * and Phase(x) = x + 1/x S(1/x^2) - 3pi/4. Then the function is
+ *
+ * y0(x) = Modulus(x) sin( Phase(x) ).
+ *
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Absolute error:
+ * arithmetic domain # trials peak rms
+ * IEEE 0, 2 100000 2.2e-7 4.6e-8
+ * IEEE 2, 32 100000 1.9e-7 5.3e-8
+ *
+ * (error criterion relative when |y1| > 1).
+ *
+ */
+
+ const float YP[] = {8.061978323326852E-009f, -9.496460629917016E-007f,
+ 6.719543806674249E-005f, -2.641785726447862E-003f,
+ 4.202369946500099E-002f};
+ const float MO1[] = {6.913942741265801E-002f, -2.284801500053359E-001f,
+ 3.138238455499697E-001f, -2.102302420403875E-001f,
+ 5.435364690523026E-003f, 1.493389585089498E-001f,
+ 4.976029650847191E-006f, 7.978845453073848E-001f};
+ const float PH1[] = {-4.497014141919556E+001f, 5.073465654089319E+001f,
+ -2.485774108720340E+001f, 7.222973196770240E+000f,
+ -1.544842782180211E+000f, 3.503787691653334E-001f,
+ -1.637986776941202E-001f, 3.749989509080821E-001f};
+ const T YO1 = pset1<T>(4.66539330185668857532f);
+ const T NEG_THPIO4F = pset1<T>(-2.35619449019234492885f); /* -3*pi/4 */
+ const T TWOOPI = pset1<T>(0.636619772367581343075535f); /* 2/pi */
+ const T NEG_MAXNUM = pset1<T>(-NumTraits<float>::infinity());
+
+ T z = pmul(x, x);
+ T x_le_two = pmul(psub(z, YO1), internal::ppolevl<T, 4>::run(z, YP));
+ x_le_two = pmadd(
+ x_le_two, x,
+ pmul(TWOOPI, pmadd(
+ generic_j1<T, float>::run(x), plog(x),
+ pdiv(pset1<T>(-1.0f), x))));
+ x_le_two = pselect(pcmp_lt(x, pset1<T>(0.0f)), NEG_MAXNUM, x_le_two);
+
+ T q = pdiv(pset1<T>(1.0), x);
+ T w = prsqrt(x);
+ T p = pmul(w, internal::ppolevl<T, 7>::run(q, MO1));
+ w = pmul(q, q);
+ T xn = pmadd(q, internal::ppolevl<T, 7>::run(w, PH1), NEG_THPIO4F);
+ T x_gt_two = pmul(p, psin(padd(xn, x)));
+ return pselect(pcmp_le(x, pset1<T>(2.0)), x_le_two, x_gt_two);
+ }
+};
+
+template <typename T>
+struct generic_y1<T, double> {
+ EIGEN_DEVICE_FUNC
+ static EIGEN_STRONG_INLINE T run(const T& x) {
+ /* j1.c
+ * Bessel function of second kind of order one
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, y1();
+ *
+ * y = y1( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns Bessel function of the second kind of order one
+ * of the argument.
+ *
+ * The domain is divided into the intervals [0, 8] and
+ * (8, infinity). In the first interval a 25 term Chebyshev
+ * expansion is used, and a call to j1() is required.
+ * In the second, the asymptotic trigonometric representation
+ * is employed using two rational functions of degree 5/5.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Absolute error:
+ * arithmetic domain # trials peak rms
+ * DEC 0, 30 10000 8.6e-17 1.3e-17
+ * IEEE 0, 30 30000 1.0e-15 1.3e-16
+ *
+ * (error criterion relative when |y1| > 1).
+ *
+ */
+ const double PP[] = {7.62125616208173112003E-4, 7.31397056940917570436E-2,
+ 1.12719608129684925192E0, 5.11207951146807644818E0,
+ 8.42404590141772420927E0, 5.21451598682361504063E0,
+ 1.00000000000000000254E0};
+ const double PQ[] = {5.71323128072548699714E-4, 6.88455908754495404082E-2,
+ 1.10514232634061696926E0, 5.07386386128601488557E0,
+ 8.39985554327604159757E0, 5.20982848682361821619E0,
+ 9.99999999999999997461E-1};
+ const double QP[] = {5.10862594750176621635E-2, 4.98213872951233449420E0,
+ 7.58238284132545283818E1, 3.66779609360150777800E2,
+ 7.10856304998926107277E2, 5.97489612400613639965E2,
+ 2.11688757100572135698E2, 2.52070205858023719784E1};
+ const double QQ[] = {1.00000000000000000000E0, 7.42373277035675149943E1,
+ 1.05644886038262816351E3, 4.98641058337653607651E3,
+ 9.56231892404756170795E3, 7.99704160447350683650E3,
+ 2.82619278517639096600E3, 3.36093607810698293419E2};
+ const double YP[] = {1.26320474790178026440E9, -6.47355876379160291031E11,
+ 1.14509511541823727583E14, -8.12770255501325109621E15,
+ 2.02439475713594898196E17, -7.78877196265950026825E17};
+ const double YQ[] = {1.00000000000000000000E0, 5.94301592346128195359E2,
+ 2.35564092943068577943E5, 7.34811944459721705660E7,
+ 1.87601316108706159478E10, 3.88231277496238566008E12,
+ 6.20557727146953693363E14, 6.87141087355300489866E16,
+ 3.97270608116560655612E18};
+ const T SQ2OPI = pset1<T>(.79788456080286535588);
+ const T NEG_THPIO4 = pset1<T>(-2.35619449019234492885); /* -3*pi/4 */
+ const T TWOOPI = pset1<T>(0.636619772367581343075535); /* 2/pi */
+ const T NEG_MAXNUM = pset1<T>(-NumTraits<double>::infinity());
+
+ T z = pmul(x, x);
+ T x_le_five = pdiv(internal::ppolevl<T, 5>::run(z, YP),
+ internal::ppolevl<T, 8>::run(z, YQ));
+ x_le_five = pmadd(
+ x_le_five, x, pmul(
+ TWOOPI, pmadd(generic_j1<T, double>::run(x), plog(x),
+ pdiv(pset1<T>(-1.0), x))));
+
+ x_le_five = pselect(pcmp_le(x, pset1<T>(0.0)), NEG_MAXNUM, x_le_five);
+ T s = pdiv(pset1<T>(25.0), z);
+ T p = pdiv(
+ internal::ppolevl<T, 6>::run(s, PP),
+ internal::ppolevl<T, 6>::run(s, PQ));
+ T q = pdiv(
+ internal::ppolevl<T, 7>::run(s, QP),
+ internal::ppolevl<T, 7>::run(s, QQ));
+ T xn = padd(x, NEG_THPIO4);
+ T w = pdiv(pset1<T>(5.0), x);
+ p = pmadd(p, psin(xn), pmul(w, pmul(q, pcos(xn))));
+ T x_gt_five = pmul(p, pmul(SQ2OPI, prsqrt(x)));
+ return pselect(pcmp_le(x, pset1<T>(5.0)), x_le_five, x_gt_five);
+ }
+};
+
+template <typename T>
+struct bessel_y1_impl {
+ EIGEN_DEVICE_FUNC
+ static EIGEN_STRONG_INLINE T run(const T x) {
+ return generic_y1<T>::run(x);
+ }
+};
+
+} // end namespace internal
+
+namespace numext {
+
+template <typename Scalar>
+EIGEN_DEVICE_FUNC inline EIGEN_MATHFUNC_RETVAL(bessel_i0, Scalar)
+ bessel_i0(const Scalar& x) {
+ return EIGEN_MATHFUNC_IMPL(bessel_i0, Scalar)::run(x);
+}
+
+template <typename Scalar>
+EIGEN_DEVICE_FUNC inline EIGEN_MATHFUNC_RETVAL(bessel_i0e, Scalar)
+ bessel_i0e(const Scalar& x) {
+ return EIGEN_MATHFUNC_IMPL(bessel_i0e, Scalar)::run(x);
+}
+
+template <typename Scalar>
+EIGEN_DEVICE_FUNC inline EIGEN_MATHFUNC_RETVAL(bessel_i1, Scalar)
+ bessel_i1(const Scalar& x) {
+ return EIGEN_MATHFUNC_IMPL(bessel_i1, Scalar)::run(x);
+}
+
+template <typename Scalar>
+EIGEN_DEVICE_FUNC inline EIGEN_MATHFUNC_RETVAL(bessel_i1e, Scalar)
+ bessel_i1e(const Scalar& x) {
+ return EIGEN_MATHFUNC_IMPL(bessel_i1e, Scalar)::run(x);
+}
+
+template <typename Scalar>
+EIGEN_DEVICE_FUNC inline EIGEN_MATHFUNC_RETVAL(bessel_k0, Scalar)
+ bessel_k0(const Scalar& x) {
+ return EIGEN_MATHFUNC_IMPL(bessel_k0, Scalar)::run(x);
+}
+
+template <typename Scalar>
+EIGEN_DEVICE_FUNC inline EIGEN_MATHFUNC_RETVAL(bessel_k0e, Scalar)
+ bessel_k0e(const Scalar& x) {
+ return EIGEN_MATHFUNC_IMPL(bessel_k0e, Scalar)::run(x);
+}
+
+template <typename Scalar>
+EIGEN_DEVICE_FUNC inline EIGEN_MATHFUNC_RETVAL(bessel_k1, Scalar)
+ bessel_k1(const Scalar& x) {
+ return EIGEN_MATHFUNC_IMPL(bessel_k1, Scalar)::run(x);
+}
+
+template <typename Scalar>
+EIGEN_DEVICE_FUNC inline EIGEN_MATHFUNC_RETVAL(bessel_k1e, Scalar)
+ bessel_k1e(const Scalar& x) {
+ return EIGEN_MATHFUNC_IMPL(bessel_k1e, Scalar)::run(x);
+}
+
+template <typename Scalar>
+EIGEN_DEVICE_FUNC inline EIGEN_MATHFUNC_RETVAL(bessel_j0, Scalar)
+ bessel_j0(const Scalar& x) {
+ return EIGEN_MATHFUNC_IMPL(bessel_j0, Scalar)::run(x);
+}
+
+template <typename Scalar>
+EIGEN_DEVICE_FUNC inline EIGEN_MATHFUNC_RETVAL(bessel_y0, Scalar)
+ bessel_y0(const Scalar& x) {
+ return EIGEN_MATHFUNC_IMPL(bessel_y0, Scalar)::run(x);
+}
+
+template <typename Scalar>
+EIGEN_DEVICE_FUNC inline EIGEN_MATHFUNC_RETVAL(bessel_j1, Scalar)
+ bessel_j1(const Scalar& x) {
+ return EIGEN_MATHFUNC_IMPL(bessel_j1, Scalar)::run(x);
+}
+
+template <typename Scalar>
+EIGEN_DEVICE_FUNC inline EIGEN_MATHFUNC_RETVAL(bessel_y1, Scalar)
+ bessel_y1(const Scalar& x) {
+ return EIGEN_MATHFUNC_IMPL(bessel_y1, Scalar)::run(x);
+}
+
+} // end namespace numext
+
+} // end namespace Eigen
+
+#endif // EIGEN_BESSEL_FUNCTIONS_H
diff --git a/unsupported/Eigen/src/SpecialFunctions/BesselFunctionsPacketMath.h b/unsupported/Eigen/src/SpecialFunctions/BesselFunctionsPacketMath.h
new file mode 100644
index 0000000..ac8c57b
--- /dev/null
+++ b/unsupported/Eigen/src/SpecialFunctions/BesselFunctionsPacketMath.h
@@ -0,0 +1,120 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2016 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_BESSELFUNCTIONS_PACKETMATH_H
+#define EIGEN_BESSELFUNCTIONS_PACKETMATH_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+
+/** \internal \returns the exponentially scaled modified Bessel function of
+ * order zero i0(\a a) (coeff-wise) */
+template <typename Packet>
+EIGEN_DEVICE_FUNC EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+Packet pbessel_i0(const Packet& x) {
+ return numext::bessel_i0(x);
+}
+
+/** \internal \returns the exponentially scaled modified Bessel function of
+ * order zero i0e(\a a) (coeff-wise) */
+template <typename Packet>
+EIGEN_DEVICE_FUNC EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+Packet pbessel_i0e(const Packet& x) {
+ return numext::bessel_i0e(x);
+}
+
+/** \internal \returns the exponentially scaled modified Bessel function of
+ * order one i1(\a a) (coeff-wise) */
+template <typename Packet>
+EIGEN_DEVICE_FUNC EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+Packet pbessel_i1(const Packet& x) {
+ return numext::bessel_i1(x);
+}
+
+/** \internal \returns the exponentially scaled modified Bessel function of
+ * order one i1e(\a a) (coeff-wise) */
+template <typename Packet>
+EIGEN_DEVICE_FUNC EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+Packet pbessel_i1e(const Packet& x) {
+ return numext::bessel_i1e(x);
+}
+
+/** \internal \returns the exponentially scaled modified Bessel function of
+ * order zero j0(\a a) (coeff-wise) */
+template <typename Packet>
+EIGEN_DEVICE_FUNC EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+Packet pbessel_j0(const Packet& x) {
+ return numext::bessel_j0(x);
+}
+
+/** \internal \returns the exponentially scaled modified Bessel function of
+ * order zero j1(\a a) (coeff-wise) */
+template <typename Packet>
+EIGEN_DEVICE_FUNC EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+Packet pbessel_j1(const Packet& x) {
+ return numext::bessel_j1(x);
+}
+
+/** \internal \returns the exponentially scaled modified Bessel function of
+ * order one y0(\a a) (coeff-wise) */
+template <typename Packet>
+EIGEN_DEVICE_FUNC EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+Packet pbessel_y0(const Packet& x) {
+ return numext::bessel_y0(x);
+}
+
+/** \internal \returns the exponentially scaled modified Bessel function of
+ * order one y1(\a a) (coeff-wise) */
+template <typename Packet>
+EIGEN_DEVICE_FUNC EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+Packet pbessel_y1(const Packet& x) {
+ return numext::bessel_y1(x);
+}
+
+/** \internal \returns the exponentially scaled modified Bessel function of
+ * order zero k0(\a a) (coeff-wise) */
+template <typename Packet>
+EIGEN_DEVICE_FUNC EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+Packet pbessel_k0(const Packet& x) {
+ return numext::bessel_k0(x);
+}
+
+/** \internal \returns the exponentially scaled modified Bessel function of
+ * order zero k0e(\a a) (coeff-wise) */
+template <typename Packet>
+EIGEN_DEVICE_FUNC EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+Packet pbessel_k0e(const Packet& x) {
+ return numext::bessel_k0e(x);
+}
+
+/** \internal \returns the exponentially scaled modified Bessel function of
+ * order one k1e(\a a) (coeff-wise) */
+template <typename Packet>
+EIGEN_DEVICE_FUNC EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+Packet pbessel_k1(const Packet& x) {
+ return numext::bessel_k1(x);
+}
+
+/** \internal \returns the exponentially scaled modified Bessel function of
+ * order one k1e(\a a) (coeff-wise) */
+template <typename Packet>
+EIGEN_DEVICE_FUNC EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+Packet pbessel_k1e(const Packet& x) {
+ return numext::bessel_k1e(x);
+}
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_BESSELFUNCTIONS_PACKETMATH_H
+
diff --git a/unsupported/Eigen/src/SpecialFunctions/HipVectorCompatibility.h b/unsupported/Eigen/src/SpecialFunctions/HipVectorCompatibility.h
new file mode 100644
index 0000000..bc6f912
--- /dev/null
+++ b/unsupported/Eigen/src/SpecialFunctions/HipVectorCompatibility.h
@@ -0,0 +1,69 @@
+#ifndef HIP_VECTOR_COMPATIBILITY_H
+#define HIP_VECTOR_COMPATIBILITY_H
+
+namespace hip_impl {
+ template <typename, typename, unsigned int> struct Scalar_accessor;
+} // end namespace hip_impl
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+namespace internal {
+
+#define HIP_SCALAR_ACCESSOR_BUILDER(NAME) \
+template <typename T, typename U, unsigned int n> \
+struct NAME <hip_impl::Scalar_accessor<T, U, n>> : NAME <T> {};
+
+#define HIP_SCALAR_ACCESSOR_BUILDER_RETVAL(NAME) \
+template <typename T, typename U, unsigned int n> \
+struct NAME##_impl <hip_impl::Scalar_accessor<T, U, n>> : NAME##_impl <T> {}; \
+template <typename T, typename U, unsigned int n> \
+struct NAME##_retval <hip_impl::Scalar_accessor<T, U, n>> : NAME##_retval <T> {};
+
+#define HIP_SCALAR_ACCESSOR_BUILDER_IGAMMA(NAME) \
+template <typename T, typename U, unsigned int n, IgammaComputationMode mode> \
+struct NAME <hip_impl::Scalar_accessor<T, U, n>, mode> : NAME <T, mode> {};
+
+#if EIGEN_HAS_C99_MATH
+HIP_SCALAR_ACCESSOR_BUILDER(betainc_helper)
+HIP_SCALAR_ACCESSOR_BUILDER(incbeta_cfe)
+
+HIP_SCALAR_ACCESSOR_BUILDER_RETVAL(erf)
+HIP_SCALAR_ACCESSOR_BUILDER_RETVAL(erfc)
+HIP_SCALAR_ACCESSOR_BUILDER_RETVAL(igammac)
+HIP_SCALAR_ACCESSOR_BUILDER_RETVAL(lgamma)
+HIP_SCALAR_ACCESSOR_BUILDER_RETVAL(ndtri)
+HIP_SCALAR_ACCESSOR_BUILDER_RETVAL(polygamma)
+
+HIP_SCALAR_ACCESSOR_BUILDER_IGAMMA(igamma_generic_impl)
+#endif
+
+HIP_SCALAR_ACCESSOR_BUILDER(digamma_impl_maybe_poly)
+HIP_SCALAR_ACCESSOR_BUILDER(zeta_impl_series)
+
+HIP_SCALAR_ACCESSOR_BUILDER_RETVAL(bessel_i0)
+HIP_SCALAR_ACCESSOR_BUILDER_RETVAL(bessel_i0e)
+HIP_SCALAR_ACCESSOR_BUILDER_RETVAL(bessel_i1)
+HIP_SCALAR_ACCESSOR_BUILDER_RETVAL(bessel_i1e)
+HIP_SCALAR_ACCESSOR_BUILDER_RETVAL(bessel_j0)
+HIP_SCALAR_ACCESSOR_BUILDER_RETVAL(bessel_j1)
+HIP_SCALAR_ACCESSOR_BUILDER_RETVAL(bessel_k0)
+HIP_SCALAR_ACCESSOR_BUILDER_RETVAL(bessel_k0e)
+HIP_SCALAR_ACCESSOR_BUILDER_RETVAL(bessel_k1)
+HIP_SCALAR_ACCESSOR_BUILDER_RETVAL(bessel_k1e)
+HIP_SCALAR_ACCESSOR_BUILDER_RETVAL(bessel_y0)
+HIP_SCALAR_ACCESSOR_BUILDER_RETVAL(bessel_y1)
+HIP_SCALAR_ACCESSOR_BUILDER_RETVAL(betainc)
+HIP_SCALAR_ACCESSOR_BUILDER_RETVAL(digamma)
+HIP_SCALAR_ACCESSOR_BUILDER_RETVAL(gamma_sample_der_alpha)
+HIP_SCALAR_ACCESSOR_BUILDER_RETVAL(igamma_der_a)
+HIP_SCALAR_ACCESSOR_BUILDER_RETVAL(igamma)
+HIP_SCALAR_ACCESSOR_BUILDER_RETVAL(zeta)
+
+HIP_SCALAR_ACCESSOR_BUILDER_IGAMMA(igamma_series_impl)
+HIP_SCALAR_ACCESSOR_BUILDER_IGAMMA(igammac_cf_impl)
+
+} // end namespace internal
+} // end namespace Eigen
+
+#endif // HIP_VECTOR_COMPATIBILITY_H
diff --git a/unsupported/Eigen/src/SpecialFunctions/InternalHeaderCheck.h b/unsupported/Eigen/src/SpecialFunctions/InternalHeaderCheck.h
new file mode 100644
index 0000000..c80ebd8
--- /dev/null
+++ b/unsupported/Eigen/src/SpecialFunctions/InternalHeaderCheck.h
@@ -0,0 +1,3 @@
+#ifndef EIGEN_SPECIALFUNCTIONS_MODULE_H
+#error "Please include unsupported/Eigen/SpecialFunctions instead of including headers inside the src directory directly."
+#endif
diff --git a/unsupported/Eigen/src/SpecialFunctions/SpecialFunctionsArrayAPI.h b/unsupported/Eigen/src/SpecialFunctions/SpecialFunctionsArrayAPI.h
new file mode 100644
index 0000000..4429333
--- /dev/null
+++ b/unsupported/Eigen/src/SpecialFunctions/SpecialFunctionsArrayAPI.h
@@ -0,0 +1,169 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2016 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+
+#ifndef EIGEN_SPECIALFUNCTIONS_ARRAYAPI_H
+#define EIGEN_SPECIALFUNCTIONS_ARRAYAPI_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+/** \cpp11 \returns an expression of the coefficient-wise igamma(\a a, \a x) to the given arrays.
+ *
+ * This function computes the coefficient-wise incomplete gamma function.
+ *
+ * \note This function supports only float and double scalar types in c++11 mode. To support other scalar types,
+ * or float/double in non c++11 mode, the user has to provide implementations of igammac(T,T) for any scalar
+ * type T to be supported.
+ *
+ * \sa Eigen::igammac(), Eigen::lgamma()
+ */
+template<typename Derived,typename ExponentDerived>
+EIGEN_STRONG_INLINE const Eigen::CwiseBinaryOp<Eigen::internal::scalar_igamma_op<typename Derived::Scalar>, const Derived, const ExponentDerived>
+igamma(const Eigen::ArrayBase<Derived>& a, const Eigen::ArrayBase<ExponentDerived>& x)
+{
+ return Eigen::CwiseBinaryOp<Eigen::internal::scalar_igamma_op<typename Derived::Scalar>, const Derived, const ExponentDerived>(
+ a.derived(),
+ x.derived()
+ );
+}
+
+/** \cpp11 \returns an expression of the coefficient-wise igamma_der_a(\a a, \a x) to the given arrays.
+ *
+ * This function computes the coefficient-wise derivative of the incomplete
+ * gamma function with respect to the parameter a.
+ *
+ * \note This function supports only float and double scalar types in c++11
+ * mode. To support other scalar types,
+ * or float/double in non c++11 mode, the user has to provide implementations
+ * of igamma_der_a(T,T) for any scalar
+ * type T to be supported.
+ *
+ * \sa Eigen::igamma(), Eigen::lgamma()
+ */
+template <typename Derived, typename ExponentDerived>
+EIGEN_STRONG_INLINE const Eigen::CwiseBinaryOp<Eigen::internal::scalar_igamma_der_a_op<typename Derived::Scalar>, const Derived, const ExponentDerived>
+igamma_der_a(const Eigen::ArrayBase<Derived>& a, const Eigen::ArrayBase<ExponentDerived>& x) {
+ return Eigen::CwiseBinaryOp<Eigen::internal::scalar_igamma_der_a_op<typename Derived::Scalar>, const Derived, const ExponentDerived>(
+ a.derived(),
+ x.derived());
+}
+
+/** \cpp11 \returns an expression of the coefficient-wise gamma_sample_der_alpha(\a alpha, \a sample) to the given arrays.
+ *
+ * This function computes the coefficient-wise derivative of the sample
+ * of a Gamma(alpha, 1) random variable with respect to the parameter alpha.
+ *
+ * \note This function supports only float and double scalar types in c++11
+ * mode. To support other scalar types,
+ * or float/double in non c++11 mode, the user has to provide implementations
+ * of gamma_sample_der_alpha(T,T) for any scalar
+ * type T to be supported.
+ *
+ * \sa Eigen::igamma(), Eigen::lgamma()
+ */
+template <typename AlphaDerived, typename SampleDerived>
+EIGEN_STRONG_INLINE const Eigen::CwiseBinaryOp<Eigen::internal::scalar_gamma_sample_der_alpha_op<typename AlphaDerived::Scalar>, const AlphaDerived, const SampleDerived>
+gamma_sample_der_alpha(const Eigen::ArrayBase<AlphaDerived>& alpha, const Eigen::ArrayBase<SampleDerived>& sample) {
+ return Eigen::CwiseBinaryOp<Eigen::internal::scalar_gamma_sample_der_alpha_op<typename AlphaDerived::Scalar>, const AlphaDerived, const SampleDerived>(
+ alpha.derived(),
+ sample.derived());
+}
+
+/** \cpp11 \returns an expression of the coefficient-wise igammac(\a a, \a x) to the given arrays.
+ *
+ * This function computes the coefficient-wise complementary incomplete gamma function.
+ *
+ * \note This function supports only float and double scalar types in c++11 mode. To support other scalar types,
+ * or float/double in non c++11 mode, the user has to provide implementations of igammac(T,T) for any scalar
+ * type T to be supported.
+ *
+ * \sa Eigen::igamma(), Eigen::lgamma()
+ */
+template<typename Derived,typename ExponentDerived>
+EIGEN_STRONG_INLINE const Eigen::CwiseBinaryOp<Eigen::internal::scalar_igammac_op<typename Derived::Scalar>, const Derived, const ExponentDerived>
+igammac(const Eigen::ArrayBase<Derived>& a, const Eigen::ArrayBase<ExponentDerived>& x)
+{
+ return Eigen::CwiseBinaryOp<Eigen::internal::scalar_igammac_op<typename Derived::Scalar>, const Derived, const ExponentDerived>(
+ a.derived(),
+ x.derived()
+ );
+}
+
+/** \cpp11 \returns an expression of the coefficient-wise polygamma(\a n, \a x) to the given arrays.
+ *
+ * It returns the \a n -th derivative of the digamma(psi) evaluated at \c x.
+ *
+ * \note This function supports only float and double scalar types in c++11 mode. To support other scalar types,
+ * or float/double in non c++11 mode, the user has to provide implementations of polygamma(T,T) for any scalar
+ * type T to be supported.
+ *
+ * \sa Eigen::digamma()
+ */
+// * \warning Be careful with the order of the parameters: x.polygamma(n) is equivalent to polygamma(n,x)
+// * \sa ArrayBase::polygamma()
+template<typename DerivedN,typename DerivedX>
+EIGEN_STRONG_INLINE const Eigen::CwiseBinaryOp<Eigen::internal::scalar_polygamma_op<typename DerivedX::Scalar>, const DerivedN, const DerivedX>
+polygamma(const Eigen::ArrayBase<DerivedN>& n, const Eigen::ArrayBase<DerivedX>& x)
+{
+ return Eigen::CwiseBinaryOp<Eigen::internal::scalar_polygamma_op<typename DerivedX::Scalar>, const DerivedN, const DerivedX>(
+ n.derived(),
+ x.derived()
+ );
+}
+
+/** \cpp11 \returns an expression of the coefficient-wise betainc(\a x, \a a, \a b) to the given arrays.
+ *
+ * This function computes the regularized incomplete beta function (integral).
+ *
+ * \note This function supports only float and double scalar types in c++11 mode. To support other scalar types,
+ * or float/double in non c++11 mode, the user has to provide implementations of betainc(T,T,T) for any scalar
+ * type T to be supported.
+ *
+ * \sa Eigen::betainc(), Eigen::lgamma()
+ */
+template<typename ArgADerived, typename ArgBDerived, typename ArgXDerived>
+EIGEN_STRONG_INLINE const Eigen::CwiseTernaryOp<Eigen::internal::scalar_betainc_op<typename ArgXDerived::Scalar>, const ArgADerived, const ArgBDerived, const ArgXDerived>
+betainc(const Eigen::ArrayBase<ArgADerived>& a, const Eigen::ArrayBase<ArgBDerived>& b, const Eigen::ArrayBase<ArgXDerived>& x)
+{
+ return Eigen::CwiseTernaryOp<Eigen::internal::scalar_betainc_op<typename ArgXDerived::Scalar>, const ArgADerived, const ArgBDerived, const ArgXDerived>(
+ a.derived(),
+ b.derived(),
+ x.derived()
+ );
+}
+
+
+/** \returns an expression of the coefficient-wise zeta(\a x, \a q) to the given arrays.
+ *
+ * It returns the Riemann zeta function of two arguments \a x and \a q:
+ *
+ * \param x is the exponent, it must be > 1
+ * \param q is the shift, it must be > 0
+ *
+ * \note This function supports only float and double scalar types. To support other scalar types, the user has
+ * to provide implementations of zeta(T,T) for any scalar type T to be supported.
+ *
+ * \sa ArrayBase::zeta()
+ */
+template<typename DerivedX,typename DerivedQ>
+EIGEN_STRONG_INLINE const Eigen::CwiseBinaryOp<Eigen::internal::scalar_zeta_op<typename DerivedX::Scalar>, const DerivedX, const DerivedQ>
+zeta(const Eigen::ArrayBase<DerivedX>& x, const Eigen::ArrayBase<DerivedQ>& q)
+{
+ return Eigen::CwiseBinaryOp<Eigen::internal::scalar_zeta_op<typename DerivedX::Scalar>, const DerivedX, const DerivedQ>(
+ x.derived(),
+ q.derived()
+ );
+}
+
+
+} // end namespace Eigen
+
+#endif // EIGEN_SPECIALFUNCTIONS_ARRAYAPI_H
diff --git a/unsupported/Eigen/src/SpecialFunctions/SpecialFunctionsBFloat16.h b/unsupported/Eigen/src/SpecialFunctions/SpecialFunctionsBFloat16.h
new file mode 100644
index 0000000..56e0b95
--- /dev/null
+++ b/unsupported/Eigen/src/SpecialFunctions/SpecialFunctionsBFloat16.h
@@ -0,0 +1,60 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_SPECIALFUNCTIONS_BFLOAT16_H
+#define EIGEN_SPECIALFUNCTIONS_BFLOAT16_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+namespace numext {
+
+#if EIGEN_HAS_C99_MATH
+template<> EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::bfloat16 lgamma(const Eigen::bfloat16& a) {
+ return Eigen::bfloat16(Eigen::numext::lgamma(static_cast<float>(a)));
+}
+template<> EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::bfloat16 digamma(const Eigen::bfloat16& a) {
+ return Eigen::bfloat16(Eigen::numext::digamma(static_cast<float>(a)));
+}
+template<> EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::bfloat16 zeta(const Eigen::bfloat16& x, const Eigen::bfloat16& q) {
+ return Eigen::bfloat16(Eigen::numext::zeta(static_cast<float>(x), static_cast<float>(q)));
+}
+template<> EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::bfloat16 polygamma(const Eigen::bfloat16& n, const Eigen::bfloat16& x) {
+ return Eigen::bfloat16(Eigen::numext::polygamma(static_cast<float>(n), static_cast<float>(x)));
+}
+template<> EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::bfloat16 erf(const Eigen::bfloat16& a) {
+ return Eigen::bfloat16(Eigen::numext::erf(static_cast<float>(a)));
+}
+template<> EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::bfloat16 erfc(const Eigen::bfloat16& a) {
+ return Eigen::bfloat16(Eigen::numext::erfc(static_cast<float>(a)));
+}
+template<> EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::bfloat16 ndtri(const Eigen::bfloat16& a) {
+ return Eigen::bfloat16(Eigen::numext::ndtri(static_cast<float>(a)));
+}
+template<> EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::bfloat16 igamma(const Eigen::bfloat16& a, const Eigen::bfloat16& x) {
+ return Eigen::bfloat16(Eigen::numext::igamma(static_cast<float>(a), static_cast<float>(x)));
+}
+template <>
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::bfloat16 igamma_der_a(const Eigen::bfloat16& a, const Eigen::bfloat16& x) {
+ return Eigen::bfloat16(Eigen::numext::igamma_der_a(static_cast<float>(a), static_cast<float>(x)));
+}
+template <>
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::bfloat16 gamma_sample_der_alpha(const Eigen::bfloat16& alpha, const Eigen::bfloat16& sample) {
+ return Eigen::bfloat16(Eigen::numext::gamma_sample_der_alpha(static_cast<float>(alpha), static_cast<float>(sample)));
+}
+template<> EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::bfloat16 igammac(const Eigen::bfloat16& a, const Eigen::bfloat16& x) {
+ return Eigen::bfloat16(Eigen::numext::igammac(static_cast<float>(a), static_cast<float>(x)));
+}
+template<> EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::bfloat16 betainc(const Eigen::bfloat16& a, const Eigen::bfloat16& b, const Eigen::bfloat16& x) {
+ return Eigen::bfloat16(Eigen::numext::betainc(static_cast<float>(a), static_cast<float>(b), static_cast<float>(x)));
+}
+#endif
+
+} // end namespace numext
+} // end namespace Eigen
+
+#endif // EIGEN_SPECIALFUNCTIONS_BFLOAT16_H
diff --git a/unsupported/Eigen/src/SpecialFunctions/SpecialFunctionsFunctors.h b/unsupported/Eigen/src/SpecialFunctions/SpecialFunctionsFunctors.h
new file mode 100644
index 0000000..0955c43
--- /dev/null
+++ b/unsupported/Eigen/src/SpecialFunctions/SpecialFunctionsFunctors.h
@@ -0,0 +1,320 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2016 Eugene Brevdo <ebrevdo@gmail.com>
+// Copyright (C) 2016 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_SPECIALFUNCTIONS_FUNCTORS_H
+#define EIGEN_SPECIALFUNCTIONS_FUNCTORS_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+
+
+/** \internal
+ * \brief Template functor to compute the incomplete gamma function igamma(a, x)
+ *
+ * \sa class CwiseBinaryOp, Cwise::igamma
+ */
+template<typename Scalar> struct scalar_igamma_op : binary_op_base<Scalar,Scalar>
+{
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar operator() (const Scalar& a, const Scalar& x) const {
+ using numext::igamma; return igamma(a, x);
+ }
+ template<typename Packet>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Packet packetOp(const Packet& a, const Packet& x) const {
+ return internal::pigamma(a, x);
+ }
+};
+template<typename Scalar>
+struct functor_traits<scalar_igamma_op<Scalar> > {
+ enum {
+ // Guesstimate
+ Cost = 20 * NumTraits<Scalar>::MulCost + 10 * NumTraits<Scalar>::AddCost,
+ PacketAccess = packet_traits<Scalar>::HasIGamma
+ };
+};
+
+/** \internal
+ * \brief Template functor to compute the derivative of the incomplete gamma
+ * function igamma_der_a(a, x)
+ *
+ * \sa class CwiseBinaryOp, Cwise::igamma_der_a
+ */
+template <typename Scalar>
+struct scalar_igamma_der_a_op {
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar operator()(const Scalar& a, const Scalar& x) const {
+ using numext::igamma_der_a;
+ return igamma_der_a(a, x);
+ }
+ template <typename Packet>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Packet packetOp(const Packet& a, const Packet& x) const {
+ return internal::pigamma_der_a(a, x);
+ }
+};
+template <typename Scalar>
+struct functor_traits<scalar_igamma_der_a_op<Scalar> > {
+ enum {
+ // 2x the cost of igamma
+ Cost = 40 * NumTraits<Scalar>::MulCost + 20 * NumTraits<Scalar>::AddCost,
+ PacketAccess = packet_traits<Scalar>::HasIGammaDerA
+ };
+};
+
+/** \internal
+ * \brief Template functor to compute the derivative of the sample
+ * of a Gamma(alpha, 1) random variable with respect to the parameter alpha
+ * gamma_sample_der_alpha(alpha, sample)
+ *
+ * \sa class CwiseBinaryOp, Cwise::gamma_sample_der_alpha
+ */
+template <typename Scalar>
+struct scalar_gamma_sample_der_alpha_op {
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar operator()(const Scalar& alpha, const Scalar& sample) const {
+ using numext::gamma_sample_der_alpha;
+ return gamma_sample_der_alpha(alpha, sample);
+ }
+ template <typename Packet>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Packet packetOp(const Packet& alpha, const Packet& sample) const {
+ return internal::pgamma_sample_der_alpha(alpha, sample);
+ }
+};
+template <typename Scalar>
+struct functor_traits<scalar_gamma_sample_der_alpha_op<Scalar> > {
+ enum {
+ // 2x the cost of igamma, minus the lgamma cost (the lgamma cancels out)
+ Cost = 30 * NumTraits<Scalar>::MulCost + 15 * NumTraits<Scalar>::AddCost,
+ PacketAccess = packet_traits<Scalar>::HasGammaSampleDerAlpha
+ };
+};
+
+/** \internal
+ * \brief Template functor to compute the complementary incomplete gamma function igammac(a, x)
+ *
+ * \sa class CwiseBinaryOp, Cwise::igammac
+ */
+template<typename Scalar> struct scalar_igammac_op : binary_op_base<Scalar,Scalar>
+{
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar operator() (const Scalar& a, const Scalar& x) const {
+ using numext::igammac; return igammac(a, x);
+ }
+ template<typename Packet>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Packet packetOp(const Packet& a, const Packet& x) const
+ {
+ return internal::pigammac(a, x);
+ }
+};
+template<typename Scalar>
+struct functor_traits<scalar_igammac_op<Scalar> > {
+ enum {
+ // Guesstimate
+ Cost = 20 * NumTraits<Scalar>::MulCost + 10 * NumTraits<Scalar>::AddCost,
+ PacketAccess = packet_traits<Scalar>::HasIGammac
+ };
+};
+
+
+/** \internal
+ * \brief Template functor to compute the incomplete beta integral betainc(a, b, x)
+ *
+ */
+template<typename Scalar> struct scalar_betainc_op {
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar operator() (const Scalar& x, const Scalar& a, const Scalar& b) const {
+ using numext::betainc; return betainc(x, a, b);
+ }
+ template<typename Packet>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Packet packetOp(const Packet& x, const Packet& a, const Packet& b) const
+ {
+ return internal::pbetainc(x, a, b);
+ }
+};
+template<typename Scalar>
+struct functor_traits<scalar_betainc_op<Scalar> > {
+ enum {
+ // Guesstimate
+ Cost = 400 * NumTraits<Scalar>::MulCost + 400 * NumTraits<Scalar>::AddCost,
+ PacketAccess = packet_traits<Scalar>::HasBetaInc
+ };
+};
+
+
+/** \internal
+ * \brief Template functor to compute the natural log of the absolute
+ * value of Gamma of a scalar
+ * \sa class CwiseUnaryOp, Cwise::lgamma()
+ */
+template<typename Scalar> struct scalar_lgamma_op {
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar operator() (const Scalar& a) const {
+ using numext::lgamma; return lgamma(a);
+ }
+ typedef typename packet_traits<Scalar>::type Packet;
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet packetOp(const Packet& a) const { return internal::plgamma(a); }
+};
+template<typename Scalar>
+struct functor_traits<scalar_lgamma_op<Scalar> >
+{
+ enum {
+ // Guesstimate
+ Cost = 10 * NumTraits<Scalar>::MulCost + 5 * NumTraits<Scalar>::AddCost,
+ PacketAccess = packet_traits<Scalar>::HasLGamma
+ };
+};
+
+/** \internal
+ * \brief Template functor to compute psi, the derivative of lgamma of a scalar.
+ * \sa class CwiseUnaryOp, Cwise::digamma()
+ */
+template<typename Scalar> struct scalar_digamma_op {
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar operator() (const Scalar& a) const {
+ using numext::digamma; return digamma(a);
+ }
+ typedef typename packet_traits<Scalar>::type Packet;
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet packetOp(const Packet& a) const { return internal::pdigamma(a); }
+};
+template<typename Scalar>
+struct functor_traits<scalar_digamma_op<Scalar> >
+{
+ enum {
+ // Guesstimate
+ Cost = 10 * NumTraits<Scalar>::MulCost + 5 * NumTraits<Scalar>::AddCost,
+ PacketAccess = packet_traits<Scalar>::HasDiGamma
+ };
+};
+
+/** \internal
+ * \brief Template functor to compute the Riemann Zeta function of two arguments.
+ * \sa class CwiseUnaryOp, Cwise::zeta()
+ */
+template<typename Scalar> struct scalar_zeta_op {
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar operator() (const Scalar& x, const Scalar& q) const {
+ using numext::zeta; return zeta(x, q);
+ }
+ typedef typename packet_traits<Scalar>::type Packet;
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet packetOp(const Packet& x, const Packet& q) const { return internal::pzeta(x, q); }
+};
+template<typename Scalar>
+struct functor_traits<scalar_zeta_op<Scalar> >
+{
+ enum {
+ // Guesstimate
+ Cost = 10 * NumTraits<Scalar>::MulCost + 5 * NumTraits<Scalar>::AddCost,
+ PacketAccess = packet_traits<Scalar>::HasZeta
+ };
+};
+
+/** \internal
+ * \brief Template functor to compute the polygamma function.
+ * \sa class CwiseUnaryOp, Cwise::polygamma()
+ */
+template<typename Scalar> struct scalar_polygamma_op {
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar operator() (const Scalar& n, const Scalar& x) const {
+ using numext::polygamma; return polygamma(n, x);
+ }
+ typedef typename packet_traits<Scalar>::type Packet;
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet packetOp(const Packet& n, const Packet& x) const { return internal::ppolygamma(n, x); }
+};
+template<typename Scalar>
+struct functor_traits<scalar_polygamma_op<Scalar> >
+{
+ enum {
+ // Guesstimate
+ Cost = 10 * NumTraits<Scalar>::MulCost + 5 * NumTraits<Scalar>::AddCost,
+ PacketAccess = packet_traits<Scalar>::HasPolygamma
+ };
+};
+
+/** \internal
+ * \brief Template functor to compute the error function of a scalar
+ * \sa class CwiseUnaryOp, ArrayBase::erf()
+ */
+template<typename Scalar> struct scalar_erf_op {
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar
+ operator()(const Scalar& a) const {
+ return numext::erf(a);
+ }
+ template <typename Packet>
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet packetOp(const Packet& x) const {
+ return perf(x);
+ }
+};
+template <typename Scalar>
+struct functor_traits<scalar_erf_op<Scalar> > {
+ enum {
+ PacketAccess = packet_traits<Scalar>::HasErf,
+ Cost =
+ (PacketAccess
+#ifdef EIGEN_VECTORIZE_FMA
+ // TODO(rmlarsen): Move the FMA cost model to a central location.
+ // Haswell can issue 2 add/mul/madd per cycle.
+ // 10 pmadd, 2 pmul, 1 div, 2 other
+ ? (2 * NumTraits<Scalar>::AddCost +
+ 7 * NumTraits<Scalar>::MulCost +
+ scalar_div_cost<Scalar, packet_traits<Scalar>::HasDiv>::value)
+#else
+ ? (12 * NumTraits<Scalar>::AddCost +
+ 12 * NumTraits<Scalar>::MulCost +
+ scalar_div_cost<Scalar, packet_traits<Scalar>::HasDiv>::value)
+#endif
+ // Assume for simplicity that this is as expensive as an exp().
+ : (functor_traits<scalar_exp_op<Scalar> >::Cost))
+ };
+};
+
+/** \internal
+ * \brief Template functor to compute the Complementary Error Function
+ * of a scalar
+ * \sa class CwiseUnaryOp, Cwise::erfc()
+ */
+template<typename Scalar> struct scalar_erfc_op {
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar operator() (const Scalar& a) const {
+ using numext::erfc; return erfc(a);
+ }
+ typedef typename packet_traits<Scalar>::type Packet;
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet packetOp(const Packet& a) const { return internal::perfc(a); }
+};
+template<typename Scalar>
+struct functor_traits<scalar_erfc_op<Scalar> >
+{
+ enum {
+ // Guesstimate
+ Cost = 10 * NumTraits<Scalar>::MulCost + 5 * NumTraits<Scalar>::AddCost,
+ PacketAccess = packet_traits<Scalar>::HasErfc
+ };
+};
+
+/** \internal
+ * \brief Template functor to compute the Inverse of the normal distribution
+ * function of a scalar
+ * \sa class CwiseUnaryOp, Cwise::ndtri()
+ */
+template<typename Scalar> struct scalar_ndtri_op {
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar operator() (const Scalar& a) const {
+ using numext::ndtri; return ndtri(a);
+ }
+ typedef typename packet_traits<Scalar>::type Packet;
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet packetOp(const Packet& a) const { return internal::pndtri(a); }
+};
+template<typename Scalar>
+struct functor_traits<scalar_ndtri_op<Scalar> >
+{
+ enum {
+ // On average, We are evaluating rational functions with degree N=9 in the
+ // numerator and denominator. This results in 2*N additions and 2*N
+ // multiplications.
+ Cost = 18 * NumTraits<Scalar>::MulCost + 18 * NumTraits<Scalar>::AddCost,
+ PacketAccess = packet_traits<Scalar>::HasNdtri
+ };
+};
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_SPECIALFUNCTIONS_FUNCTORS_H
diff --git a/unsupported/Eigen/src/SpecialFunctions/SpecialFunctionsHalf.h b/unsupported/Eigen/src/SpecialFunctions/SpecialFunctionsHalf.h
new file mode 100644
index 0000000..4b8a35f
--- /dev/null
+++ b/unsupported/Eigen/src/SpecialFunctions/SpecialFunctionsHalf.h
@@ -0,0 +1,60 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_SPECIALFUNCTIONS_HALF_H
+#define EIGEN_SPECIALFUNCTIONS_HALF_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+namespace numext {
+
+#if EIGEN_HAS_C99_MATH
+template<> EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half lgamma(const Eigen::half& a) {
+ return Eigen::half(Eigen::numext::lgamma(static_cast<float>(a)));
+}
+template<> EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half digamma(const Eigen::half& a) {
+ return Eigen::half(Eigen::numext::digamma(static_cast<float>(a)));
+}
+template<> EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half zeta(const Eigen::half& x, const Eigen::half& q) {
+ return Eigen::half(Eigen::numext::zeta(static_cast<float>(x), static_cast<float>(q)));
+}
+template<> EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half polygamma(const Eigen::half& n, const Eigen::half& x) {
+ return Eigen::half(Eigen::numext::polygamma(static_cast<float>(n), static_cast<float>(x)));
+}
+template<> EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half erf(const Eigen::half& a) {
+ return Eigen::half(Eigen::numext::erf(static_cast<float>(a)));
+}
+template<> EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half erfc(const Eigen::half& a) {
+ return Eigen::half(Eigen::numext::erfc(static_cast<float>(a)));
+}
+template<> EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half ndtri(const Eigen::half& a) {
+ return Eigen::half(Eigen::numext::ndtri(static_cast<float>(a)));
+}
+template<> EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half igamma(const Eigen::half& a, const Eigen::half& x) {
+ return Eigen::half(Eigen::numext::igamma(static_cast<float>(a), static_cast<float>(x)));
+}
+template <>
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half igamma_der_a(const Eigen::half& a, const Eigen::half& x) {
+ return Eigen::half(Eigen::numext::igamma_der_a(static_cast<float>(a), static_cast<float>(x)));
+}
+template <>
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half gamma_sample_der_alpha(const Eigen::half& alpha, const Eigen::half& sample) {
+ return Eigen::half(Eigen::numext::gamma_sample_der_alpha(static_cast<float>(alpha), static_cast<float>(sample)));
+}
+template<> EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half igammac(const Eigen::half& a, const Eigen::half& x) {
+ return Eigen::half(Eigen::numext::igammac(static_cast<float>(a), static_cast<float>(x)));
+}
+template<> EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half betainc(const Eigen::half& a, const Eigen::half& b, const Eigen::half& x) {
+ return Eigen::half(Eigen::numext::betainc(static_cast<float>(a), static_cast<float>(b), static_cast<float>(x)));
+}
+#endif
+
+} // end namespace numext
+} // end namespace Eigen
+
+#endif // EIGEN_SPECIALFUNCTIONS_HALF_H
diff --git a/unsupported/Eigen/src/SpecialFunctions/SpecialFunctionsImpl.h b/unsupported/Eigen/src/SpecialFunctions/SpecialFunctionsImpl.h
new file mode 100644
index 0000000..d85729d
--- /dev/null
+++ b/unsupported/Eigen/src/SpecialFunctions/SpecialFunctionsImpl.h
@@ -0,0 +1,2053 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2015 Eugene Brevdo <ebrevdo@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_SPECIAL_FUNCTIONS_H
+#define EIGEN_SPECIAL_FUNCTIONS_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+namespace internal {
+
+// Parts of this code are based on the Cephes Math Library.
+//
+// Cephes Math Library Release 2.8: June, 2000
+// Copyright 1984, 1987, 1992, 2000 by Stephen L. Moshier
+//
+// Permission has been kindly provided by the original author
+// to incorporate the Cephes software into the Eigen codebase:
+//
+// From: Stephen Moshier
+// To: Eugene Brevdo
+// Subject: Re: Permission to wrap several cephes functions in Eigen
+//
+// Hello Eugene,
+//
+// Thank you for writing.
+//
+// If your licensing is similar to BSD, the formal way that has been
+// handled is simply to add a statement to the effect that you are incorporating
+// the Cephes software by permission of the author.
+//
+// Good luck with your project,
+// Steve
+
+
+/****************************************************************************
+ * Implementation of lgamma, requires C++11/C99 *
+ ****************************************************************************/
+
+template <typename Scalar>
+struct lgamma_impl {
+ EIGEN_STATIC_ASSERT((internal::is_same<Scalar, Scalar>::value == false),
+ THIS_TYPE_IS_NOT_SUPPORTED)
+
+ EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE Scalar run(const Scalar) {
+ return Scalar(0);
+ }
+};
+
+template <typename Scalar>
+struct lgamma_retval {
+ typedef Scalar type;
+};
+
+#if EIGEN_HAS_C99_MATH
+// Since glibc 2.19
+#if defined(__GLIBC__) && ((__GLIBC__>=2 && __GLIBC_MINOR__ >= 19) || __GLIBC__>2) \
+ && (defined(_DEFAULT_SOURCE) || defined(_BSD_SOURCE) || defined(_SVID_SOURCE))
+#define EIGEN_HAS_LGAMMA_R
+#endif
+
+// Glibc versions before 2.19
+#if defined(__GLIBC__) && ((__GLIBC__==2 && __GLIBC_MINOR__ < 19) || __GLIBC__<2) \
+ && (defined(_BSD_SOURCE) || defined(_SVID_SOURCE))
+#define EIGEN_HAS_LGAMMA_R
+#endif
+
+template <>
+struct lgamma_impl<float> {
+ EIGEN_DEVICE_FUNC
+ static EIGEN_STRONG_INLINE float run(float x) {
+#if !defined(EIGEN_GPU_COMPILE_PHASE) && defined (EIGEN_HAS_LGAMMA_R) && !defined(__APPLE__)
+ int dummy;
+ return ::lgammaf_r(x, &dummy);
+#elif defined(SYCL_DEVICE_ONLY)
+ return cl::sycl::lgamma(x);
+#else
+ return ::lgammaf(x);
+#endif
+ }
+};
+
+template <>
+struct lgamma_impl<double> {
+ EIGEN_DEVICE_FUNC
+ static EIGEN_STRONG_INLINE double run(double x) {
+#if !defined(EIGEN_GPU_COMPILE_PHASE) && defined(EIGEN_HAS_LGAMMA_R) && !defined(__APPLE__)
+ int dummy;
+ return ::lgamma_r(x, &dummy);
+#elif defined(SYCL_DEVICE_ONLY)
+ return cl::sycl::lgamma(x);
+#else
+ return ::lgamma(x);
+#endif
+ }
+};
+
+#undef EIGEN_HAS_LGAMMA_R
+#endif
+
+/****************************************************************************
+ * Implementation of digamma (psi), based on Cephes *
+ ****************************************************************************/
+
+template <typename Scalar>
+struct digamma_retval {
+ typedef Scalar type;
+};
+
+/*
+ *
+ * Polynomial evaluation helper for the Psi (digamma) function.
+ *
+ * digamma_impl_maybe_poly::run(s) evaluates the asymptotic Psi expansion for
+ * input Scalar s, assuming s is above 10.0.
+ *
+ * If s is above a certain threshold for the given Scalar type, zero
+ * is returned. Otherwise the polynomial is evaluated with enough
+ * coefficients for results matching Scalar machine precision.
+ *
+ *
+ */
+template <typename Scalar>
+struct digamma_impl_maybe_poly {
+ EIGEN_STATIC_ASSERT((internal::is_same<Scalar, Scalar>::value == false),
+ THIS_TYPE_IS_NOT_SUPPORTED)
+
+ EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE Scalar run(const Scalar) {
+ return Scalar(0);
+ }
+};
+
+
+template <>
+struct digamma_impl_maybe_poly<float> {
+ EIGEN_DEVICE_FUNC
+ static EIGEN_STRONG_INLINE float run(const float s) {
+ const float A[] = {
+ -4.16666666666666666667E-3f,
+ 3.96825396825396825397E-3f,
+ -8.33333333333333333333E-3f,
+ 8.33333333333333333333E-2f
+ };
+
+ float z;
+ if (s < 1.0e8f) {
+ z = 1.0f / (s * s);
+ return z * internal::ppolevl<float, 3>::run(z, A);
+ } else return 0.0f;
+ }
+};
+
+template <>
+struct digamma_impl_maybe_poly<double> {
+ EIGEN_DEVICE_FUNC
+ static EIGEN_STRONG_INLINE double run(const double s) {
+ const double A[] = {
+ 8.33333333333333333333E-2,
+ -2.10927960927960927961E-2,
+ 7.57575757575757575758E-3,
+ -4.16666666666666666667E-3,
+ 3.96825396825396825397E-3,
+ -8.33333333333333333333E-3,
+ 8.33333333333333333333E-2
+ };
+
+ double z;
+ if (s < 1.0e17) {
+ z = 1.0 / (s * s);
+ return z * internal::ppolevl<double, 6>::run(z, A);
+ }
+ else return 0.0;
+ }
+};
+
+template <typename Scalar>
+struct digamma_impl {
+ EIGEN_DEVICE_FUNC
+ static Scalar run(Scalar x) {
+ /*
+ *
+ * Psi (digamma) function (modified for Eigen)
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, psi();
+ *
+ * y = psi( x );
+ *
+ *
+ * DESCRIPTION:
+ *
+ * d -
+ * psi(x) = -- ln | (x)
+ * dx
+ *
+ * is the logarithmic derivative of the gamma function.
+ * For integer x,
+ * n-1
+ * -
+ * psi(n) = -EUL + > 1/k.
+ * -
+ * k=1
+ *
+ * If x is negative, it is transformed to a positive argument by the
+ * reflection formula psi(1-x) = psi(x) + pi cot(pi x).
+ * For general positive x, the argument is made greater than 10
+ * using the recurrence psi(x+1) = psi(x) + 1/x.
+ * Then the following asymptotic expansion is applied:
+ *
+ * inf. B
+ * - 2k
+ * psi(x) = log(x) - 1/2x - > -------
+ * - 2k
+ * k=1 2k x
+ *
+ * where the B2k are Bernoulli numbers.
+ *
+ * ACCURACY (float):
+ * Relative error (except absolute when |psi| < 1):
+ * arithmetic domain # trials peak rms
+ * IEEE 0,30 30000 1.3e-15 1.4e-16
+ * IEEE -30,0 40000 1.5e-15 2.2e-16
+ *
+ * ACCURACY (double):
+ * Absolute error, relative when |psi| > 1 :
+ * arithmetic domain # trials peak rms
+ * IEEE -33,0 30000 8.2e-7 1.2e-7
+ * IEEE 0,33 100000 7.3e-7 7.7e-8
+ *
+ * ERROR MESSAGES:
+ * message condition value returned
+ * psi singularity x integer <=0 INFINITY
+ */
+
+ Scalar p, q, nz, s, w, y;
+ bool negative = false;
+
+ const Scalar nan = NumTraits<Scalar>::quiet_NaN();
+ const Scalar m_pi = Scalar(EIGEN_PI);
+
+ const Scalar zero = Scalar(0);
+ const Scalar one = Scalar(1);
+ const Scalar half = Scalar(0.5);
+ nz = zero;
+
+ if (x <= zero) {
+ negative = true;
+ q = x;
+ p = numext::floor(q);
+ if (p == q) {
+ return nan;
+ }
+ /* Remove the zeros of tan(m_pi x)
+ * by subtracting the nearest integer from x
+ */
+ nz = q - p;
+ if (nz != half) {
+ if (nz > half) {
+ p += one;
+ nz = q - p;
+ }
+ nz = m_pi / numext::tan(m_pi * nz);
+ }
+ else {
+ nz = zero;
+ }
+ x = one - x;
+ }
+
+ /* use the recurrence psi(x+1) = psi(x) + 1/x. */
+ s = x;
+ w = zero;
+ while (s < Scalar(10)) {
+ w += one / s;
+ s += one;
+ }
+
+ y = digamma_impl_maybe_poly<Scalar>::run(s);
+
+ y = numext::log(s) - (half / s) - y - w;
+
+ return (negative) ? y - nz : y;
+ }
+};
+
+/****************************************************************************
+ * Implementation of erf, requires C++11/C99 *
+ ****************************************************************************/
+
+/** \internal \returns the error function of \a a (coeff-wise)
+ Doesn't do anything fancy, just a 13/8-degree rational interpolant which
+ is accurate up to a couple of ulp in the range [-4, 4], outside of which
+ fl(erf(x)) = +/-1.
+
+ This implementation works on both scalars and Ts.
+*/
+template <typename T>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE T generic_fast_erf_float(const T& a_x) {
+ // Clamp the inputs to the range [-4, 4] since anything outside
+ // this range is +/-1.0f in single-precision.
+ const T plus_4 = pset1<T>(4.f);
+ const T minus_4 = pset1<T>(-4.f);
+ const T x = pmax(pmin(a_x, plus_4), minus_4);
+ // The monomial coefficients of the numerator polynomial (odd).
+ const T alpha_1 = pset1<T>(-1.60960333262415e-02f);
+ const T alpha_3 = pset1<T>(-2.95459980854025e-03f);
+ const T alpha_5 = pset1<T>(-7.34990630326855e-04f);
+ const T alpha_7 = pset1<T>(-5.69250639462346e-05f);
+ const T alpha_9 = pset1<T>(-2.10102402082508e-06f);
+ const T alpha_11 = pset1<T>(2.77068142495902e-08f);
+ const T alpha_13 = pset1<T>(-2.72614225801306e-10f);
+
+ // The monomial coefficients of the denominator polynomial (even).
+ const T beta_0 = pset1<T>(-1.42647390514189e-02f);
+ const T beta_2 = pset1<T>(-7.37332916720468e-03f);
+ const T beta_4 = pset1<T>(-1.68282697438203e-03f);
+ const T beta_6 = pset1<T>(-2.13374055278905e-04f);
+ const T beta_8 = pset1<T>(-1.45660718464996e-05f);
+
+ // Since the polynomials are odd/even, we need x^2.
+ const T x2 = pmul(x, x);
+
+ // Evaluate the numerator polynomial p.
+ T p = pmadd(x2, alpha_13, alpha_11);
+ p = pmadd(x2, p, alpha_9);
+ p = pmadd(x2, p, alpha_7);
+ p = pmadd(x2, p, alpha_5);
+ p = pmadd(x2, p, alpha_3);
+ p = pmadd(x2, p, alpha_1);
+ p = pmul(x, p);
+
+ // Evaluate the denominator polynomial p.
+ T q = pmadd(x2, beta_8, beta_6);
+ q = pmadd(x2, q, beta_4);
+ q = pmadd(x2, q, beta_2);
+ q = pmadd(x2, q, beta_0);
+
+ // Divide the numerator by the denominator.
+ return pdiv(p, q);
+}
+
+template <typename T>
+struct erf_impl {
+ EIGEN_DEVICE_FUNC
+ static EIGEN_STRONG_INLINE T run(const T& x) {
+ return generic_fast_erf_float(x);
+ }
+};
+
+template <typename Scalar>
+struct erf_retval {
+ typedef Scalar type;
+};
+
+#if EIGEN_HAS_C99_MATH
+template <>
+struct erf_impl<float> {
+ EIGEN_DEVICE_FUNC
+ static EIGEN_STRONG_INLINE float run(float x) {
+#if defined(SYCL_DEVICE_ONLY)
+ return cl::sycl::erf(x);
+#else
+ return generic_fast_erf_float(x);
+#endif
+ }
+};
+
+template <>
+struct erf_impl<double> {
+ EIGEN_DEVICE_FUNC
+ static EIGEN_STRONG_INLINE double run(double x) {
+#if defined(SYCL_DEVICE_ONLY)
+ return cl::sycl::erf(x);
+#else
+ return ::erf(x);
+#endif
+ }
+};
+#endif // EIGEN_HAS_C99_MATH
+
+/***************************************************************************
+* Implementation of erfc, requires C++11/C99 *
+****************************************************************************/
+
+template <typename Scalar>
+struct erfc_impl {
+ EIGEN_STATIC_ASSERT((internal::is_same<Scalar, Scalar>::value == false),
+ THIS_TYPE_IS_NOT_SUPPORTED)
+
+ EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE Scalar run(const Scalar) {
+ return Scalar(0);
+ }
+};
+
+template <typename Scalar>
+struct erfc_retval {
+ typedef Scalar type;
+};
+
+#if EIGEN_HAS_C99_MATH
+template <>
+struct erfc_impl<float> {
+ EIGEN_DEVICE_FUNC
+ static EIGEN_STRONG_INLINE float run(const float x) {
+#if defined(SYCL_DEVICE_ONLY)
+ return cl::sycl::erfc(x);
+#else
+ return ::erfcf(x);
+#endif
+ }
+};
+
+template <>
+struct erfc_impl<double> {
+ EIGEN_DEVICE_FUNC
+ static EIGEN_STRONG_INLINE double run(const double x) {
+#if defined(SYCL_DEVICE_ONLY)
+ return cl::sycl::erfc(x);
+#else
+ return ::erfc(x);
+#endif
+ }
+};
+#endif // EIGEN_HAS_C99_MATH
+
+
+/***************************************************************************
+* Implementation of ndtri. *
+****************************************************************************/
+
+/* Inverse of Normal distribution function (modified for Eigen).
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, ndtri();
+ *
+ * x = ndtri( y );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the argument, x, for which the area under the
+ * Gaussian probability density function (integrated from
+ * minus infinity to x) is equal to y.
+ *
+ *
+ * For small arguments 0 < y < exp(-2), the program computes
+ * z = sqrt( -2.0 * log(y) ); then the approximation is
+ * x = z - log(z)/z - (1/z) P(1/z) / Q(1/z).
+ * There are two rational functions P/Q, one for 0 < y < exp(-32)
+ * and the other for y up to exp(-2). For larger arguments,
+ * w = y - 0.5, and x/sqrt(2pi) = w + w**3 R(w**2)/S(w**2)).
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * DEC 0.125, 1 5500 9.5e-17 2.1e-17
+ * DEC 6e-39, 0.135 3500 5.7e-17 1.3e-17
+ * IEEE 0.125, 1 20000 7.2e-16 1.3e-16
+ * IEEE 3e-308, 0.135 50000 4.6e-16 9.8e-17
+ *
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * ndtri domain x <= 0 -MAXNUM
+ * ndtri domain x >= 1 MAXNUM
+ *
+ */
+ /*
+ Cephes Math Library Release 2.2: June, 1992
+ Copyright 1985, 1987, 1992 by Stephen L. Moshier
+ Direct inquiries to 30 Frost Street, Cambridge, MA 02140
+ */
+
+
+// TODO: Add a cheaper approximation for float.
+
+
+template<typename T>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE T flipsign(
+ const T& should_flipsign, const T& x) {
+ typedef typename unpacket_traits<T>::type Scalar;
+ const T sign_mask = pset1<T>(Scalar(-0.0));
+ T sign_bit = pand<T>(should_flipsign, sign_mask);
+ return pxor<T>(sign_bit, x);
+}
+
+template<>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE double flipsign<double>(
+ const double& should_flipsign, const double& x) {
+ return should_flipsign == 0 ? x : -x;
+}
+
+template<>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE float flipsign<float>(
+ const float& should_flipsign, const float& x) {
+ return should_flipsign == 0 ? x : -x;
+}
+
+// We split this computation in to two so that in the scalar path
+// only one branch is evaluated (due to our template specialization of pselect
+// being an if statement.)
+
+template <typename T, typename ScalarType>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE T generic_ndtri_gt_exp_neg_two(const T& b) {
+ const ScalarType p0[] = {
+ ScalarType(-5.99633501014107895267e1),
+ ScalarType(9.80010754185999661536e1),
+ ScalarType(-5.66762857469070293439e1),
+ ScalarType(1.39312609387279679503e1),
+ ScalarType(-1.23916583867381258016e0)
+ };
+ const ScalarType q0[] = {
+ ScalarType(1.0),
+ ScalarType(1.95448858338141759834e0),
+ ScalarType(4.67627912898881538453e0),
+ ScalarType(8.63602421390890590575e1),
+ ScalarType(-2.25462687854119370527e2),
+ ScalarType(2.00260212380060660359e2),
+ ScalarType(-8.20372256168333339912e1),
+ ScalarType(1.59056225126211695515e1),
+ ScalarType(-1.18331621121330003142e0)
+ };
+ const T sqrt2pi = pset1<T>(ScalarType(2.50662827463100050242e0));
+ const T half = pset1<T>(ScalarType(0.5));
+ T c, c2, ndtri_gt_exp_neg_two;
+
+ c = psub(b, half);
+ c2 = pmul(c, c);
+ ndtri_gt_exp_neg_two = pmadd(c, pmul(
+ c2, pdiv(
+ internal::ppolevl<T, 4>::run(c2, p0),
+ internal::ppolevl<T, 8>::run(c2, q0))), c);
+ return pmul(ndtri_gt_exp_neg_two, sqrt2pi);
+}
+
+template <typename T, typename ScalarType>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE T generic_ndtri_lt_exp_neg_two(
+ const T& b, const T& should_flipsign) {
+ /* Approximation for interval z = sqrt(-2 log a ) between 2 and 8
+ * i.e., a between exp(-2) = .135 and exp(-32) = 1.27e-14.
+ */
+ const ScalarType p1[] = {
+ ScalarType(4.05544892305962419923e0),
+ ScalarType(3.15251094599893866154e1),
+ ScalarType(5.71628192246421288162e1),
+ ScalarType(4.40805073893200834700e1),
+ ScalarType(1.46849561928858024014e1),
+ ScalarType(2.18663306850790267539e0),
+ ScalarType(-1.40256079171354495875e-1),
+ ScalarType(-3.50424626827848203418e-2),
+ ScalarType(-8.57456785154685413611e-4)
+ };
+ const ScalarType q1[] = {
+ ScalarType(1.0),
+ ScalarType(1.57799883256466749731e1),
+ ScalarType(4.53907635128879210584e1),
+ ScalarType(4.13172038254672030440e1),
+ ScalarType(1.50425385692907503408e1),
+ ScalarType(2.50464946208309415979e0),
+ ScalarType(-1.42182922854787788574e-1),
+ ScalarType(-3.80806407691578277194e-2),
+ ScalarType(-9.33259480895457427372e-4)
+ };
+ /* Approximation for interval z = sqrt(-2 log a ) between 8 and 64
+ * i.e., a between exp(-32) = 1.27e-14 and exp(-2048) = 3.67e-890.
+ */
+ const ScalarType p2[] = {
+ ScalarType(3.23774891776946035970e0),
+ ScalarType(6.91522889068984211695e0),
+ ScalarType(3.93881025292474443415e0),
+ ScalarType(1.33303460815807542389e0),
+ ScalarType(2.01485389549179081538e-1),
+ ScalarType(1.23716634817820021358e-2),
+ ScalarType(3.01581553508235416007e-4),
+ ScalarType(2.65806974686737550832e-6),
+ ScalarType(6.23974539184983293730e-9)
+ };
+ const ScalarType q2[] = {
+ ScalarType(1.0),
+ ScalarType(6.02427039364742014255e0),
+ ScalarType(3.67983563856160859403e0),
+ ScalarType(1.37702099489081330271e0),
+ ScalarType(2.16236993594496635890e-1),
+ ScalarType(1.34204006088543189037e-2),
+ ScalarType(3.28014464682127739104e-4),
+ ScalarType(2.89247864745380683936e-6),
+ ScalarType(6.79019408009981274425e-9)
+ };
+ const T eight = pset1<T>(ScalarType(8.0));
+ const T neg_two = pset1<T>(ScalarType(-2));
+ T x, x0, x1, z;
+
+ x = psqrt(pmul(neg_two, plog(b)));
+ x0 = psub(x, pdiv(plog(x), x));
+ z = preciprocal(x);
+ x1 = pmul(
+ z, pselect(
+ pcmp_lt(x, eight),
+ pdiv(internal::ppolevl<T, 8>::run(z, p1),
+ internal::ppolevl<T, 8>::run(z, q1)),
+ pdiv(internal::ppolevl<T, 8>::run(z, p2),
+ internal::ppolevl<T, 8>::run(z, q2))));
+ return flipsign(should_flipsign, psub(x0, x1));
+}
+
+template <typename T, typename ScalarType>
+EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
+T generic_ndtri(const T& a) {
+ const T maxnum = pset1<T>(NumTraits<ScalarType>::infinity());
+ const T neg_maxnum = pset1<T>(-NumTraits<ScalarType>::infinity());
+
+ const T zero = pset1<T>(ScalarType(0));
+ const T one = pset1<T>(ScalarType(1));
+ // exp(-2)
+ const T exp_neg_two = pset1<T>(ScalarType(0.13533528323661269189));
+ T b, ndtri, should_flipsign;
+
+ should_flipsign = pcmp_le(a, psub(one, exp_neg_two));
+ b = pselect(should_flipsign, a, psub(one, a));
+
+ ndtri = pselect(
+ pcmp_lt(exp_neg_two, b),
+ generic_ndtri_gt_exp_neg_two<T, ScalarType>(b),
+ generic_ndtri_lt_exp_neg_two<T, ScalarType>(b, should_flipsign));
+
+ return pselect(
+ pcmp_le(a, zero), neg_maxnum,
+ pselect(pcmp_le(one, a), maxnum, ndtri));
+}
+
+template <typename Scalar>
+struct ndtri_retval {
+ typedef Scalar type;
+};
+
+#if !EIGEN_HAS_C99_MATH
+
+template <typename Scalar>
+struct ndtri_impl {
+ EIGEN_STATIC_ASSERT((internal::is_same<Scalar, Scalar>::value == false),
+ THIS_TYPE_IS_NOT_SUPPORTED)
+
+ EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE Scalar run(const Scalar) {
+ return Scalar(0);
+ }
+};
+
+# else
+
+template <typename Scalar>
+struct ndtri_impl {
+ EIGEN_DEVICE_FUNC
+ static EIGEN_STRONG_INLINE Scalar run(const Scalar x) {
+ return generic_ndtri<Scalar, Scalar>(x);
+ }
+};
+
+#endif // EIGEN_HAS_C99_MATH
+
+
+/**************************************************************************************************************
+ * Implementation of igammac (complemented incomplete gamma integral), based on Cephes but requires C++11/C99 *
+ **************************************************************************************************************/
+
+template <typename Scalar>
+struct igammac_retval {
+ typedef Scalar type;
+};
+
+// NOTE: cephes_helper is also used to implement zeta
+template <typename Scalar>
+struct cephes_helper {
+ EIGEN_DEVICE_FUNC
+ static EIGEN_STRONG_INLINE Scalar machep() { eigen_assert(false && "machep not supported for this type"); return 0.0; }
+ EIGEN_DEVICE_FUNC
+ static EIGEN_STRONG_INLINE Scalar big() { eigen_assert(false && "big not supported for this type"); return 0.0; }
+ EIGEN_DEVICE_FUNC
+ static EIGEN_STRONG_INLINE Scalar biginv() { eigen_assert(false && "biginv not supported for this type"); return 0.0; }
+};
+
+template <>
+struct cephes_helper<float> {
+ EIGEN_DEVICE_FUNC
+ static EIGEN_STRONG_INLINE float machep() {
+ return NumTraits<float>::epsilon() / 2; // 1.0 - machep == 1.0
+ }
+ EIGEN_DEVICE_FUNC
+ static EIGEN_STRONG_INLINE float big() {
+ // use epsneg (1.0 - epsneg == 1.0)
+ return 1.0f / (NumTraits<float>::epsilon() / 2);
+ }
+ EIGEN_DEVICE_FUNC
+ static EIGEN_STRONG_INLINE float biginv() {
+ // epsneg
+ return machep();
+ }
+};
+
+template <>
+struct cephes_helper<double> {
+ EIGEN_DEVICE_FUNC
+ static EIGEN_STRONG_INLINE double machep() {
+ return NumTraits<double>::epsilon() / 2; // 1.0 - machep == 1.0
+ }
+ EIGEN_DEVICE_FUNC
+ static EIGEN_STRONG_INLINE double big() {
+ return 1.0 / NumTraits<double>::epsilon();
+ }
+ EIGEN_DEVICE_FUNC
+ static EIGEN_STRONG_INLINE double biginv() {
+ // inverse of eps
+ return NumTraits<double>::epsilon();
+ }
+};
+
+enum IgammaComputationMode { VALUE, DERIVATIVE, SAMPLE_DERIVATIVE };
+
+template <typename Scalar>
+EIGEN_DEVICE_FUNC
+static EIGEN_STRONG_INLINE Scalar main_igamma_term(Scalar a, Scalar x) {
+ /* Compute x**a * exp(-x) / gamma(a) */
+ Scalar logax = a * numext::log(x) - x - lgamma_impl<Scalar>::run(a);
+ if (logax < -numext::log(NumTraits<Scalar>::highest()) ||
+ // Assuming x and a aren't Nan.
+ (numext::isnan)(logax)) {
+ return Scalar(0);
+ }
+ return numext::exp(logax);
+}
+
+template <typename Scalar, IgammaComputationMode mode>
+EIGEN_DEVICE_FUNC
+int igamma_num_iterations() {
+ /* Returns the maximum number of internal iterations for igamma computation.
+ */
+ if (mode == VALUE) {
+ return 2000;
+ }
+
+ if (internal::is_same<Scalar, float>::value) {
+ return 200;
+ } else if (internal::is_same<Scalar, double>::value) {
+ return 500;
+ } else {
+ return 2000;
+ }
+}
+
+template <typename Scalar, IgammaComputationMode mode>
+struct igammac_cf_impl {
+ /* Computes igamc(a, x) or derivative (depending on the mode)
+ * using the continued fraction expansion of the complementary
+ * incomplete Gamma function.
+ *
+ * Preconditions:
+ * a > 0
+ * x >= 1
+ * x >= a
+ */
+ EIGEN_DEVICE_FUNC
+ static Scalar run(Scalar a, Scalar x) {
+ const Scalar zero = 0;
+ const Scalar one = 1;
+ const Scalar two = 2;
+ const Scalar machep = cephes_helper<Scalar>::machep();
+ const Scalar big = cephes_helper<Scalar>::big();
+ const Scalar biginv = cephes_helper<Scalar>::biginv();
+
+ if ((numext::isinf)(x)) {
+ return zero;
+ }
+
+ Scalar ax = main_igamma_term<Scalar>(a, x);
+ // This is independent of mode. If this value is zero,
+ // then the function value is zero. If the function value is zero,
+ // then we are in a neighborhood where the function value evaluates to zero,
+ // so the derivative is zero.
+ if (ax == zero) {
+ return zero;
+ }
+
+ // continued fraction
+ Scalar y = one - a;
+ Scalar z = x + y + one;
+ Scalar c = zero;
+ Scalar pkm2 = one;
+ Scalar qkm2 = x;
+ Scalar pkm1 = x + one;
+ Scalar qkm1 = z * x;
+ Scalar ans = pkm1 / qkm1;
+
+ Scalar dpkm2_da = zero;
+ Scalar dqkm2_da = zero;
+ Scalar dpkm1_da = zero;
+ Scalar dqkm1_da = -x;
+ Scalar dans_da = (dpkm1_da - ans * dqkm1_da) / qkm1;
+
+ for (int i = 0; i < igamma_num_iterations<Scalar, mode>(); i++) {
+ c += one;
+ y += one;
+ z += two;
+
+ Scalar yc = y * c;
+ Scalar pk = pkm1 * z - pkm2 * yc;
+ Scalar qk = qkm1 * z - qkm2 * yc;
+
+ Scalar dpk_da = dpkm1_da * z - pkm1 - dpkm2_da * yc + pkm2 * c;
+ Scalar dqk_da = dqkm1_da * z - qkm1 - dqkm2_da * yc + qkm2 * c;
+
+ if (qk != zero) {
+ Scalar ans_prev = ans;
+ ans = pk / qk;
+
+ Scalar dans_da_prev = dans_da;
+ dans_da = (dpk_da - ans * dqk_da) / qk;
+
+ if (mode == VALUE) {
+ if (numext::abs(ans_prev - ans) <= machep * numext::abs(ans)) {
+ break;
+ }
+ } else {
+ if (numext::abs(dans_da - dans_da_prev) <= machep) {
+ break;
+ }
+ }
+ }
+
+ pkm2 = pkm1;
+ pkm1 = pk;
+ qkm2 = qkm1;
+ qkm1 = qk;
+
+ dpkm2_da = dpkm1_da;
+ dpkm1_da = dpk_da;
+ dqkm2_da = dqkm1_da;
+ dqkm1_da = dqk_da;
+
+ if (numext::abs(pk) > big) {
+ pkm2 *= biginv;
+ pkm1 *= biginv;
+ qkm2 *= biginv;
+ qkm1 *= biginv;
+
+ dpkm2_da *= biginv;
+ dpkm1_da *= biginv;
+ dqkm2_da *= biginv;
+ dqkm1_da *= biginv;
+ }
+ }
+
+ /* Compute x**a * exp(-x) / gamma(a) */
+ Scalar dlogax_da = numext::log(x) - digamma_impl<Scalar>::run(a);
+ Scalar dax_da = ax * dlogax_da;
+
+ switch (mode) {
+ case VALUE:
+ return ans * ax;
+ case DERIVATIVE:
+ return ans * dax_da + dans_da * ax;
+ case SAMPLE_DERIVATIVE:
+ default: // this is needed to suppress clang warning
+ return -(dans_da + ans * dlogax_da) * x;
+ }
+ }
+};
+
+template <typename Scalar, IgammaComputationMode mode>
+struct igamma_series_impl {
+ /* Computes igam(a, x) or its derivative (depending on the mode)
+ * using the series expansion of the incomplete Gamma function.
+ *
+ * Preconditions:
+ * x > 0
+ * a > 0
+ * !(x > 1 && x > a)
+ */
+ EIGEN_DEVICE_FUNC
+ static Scalar run(Scalar a, Scalar x) {
+ const Scalar zero = 0;
+ const Scalar one = 1;
+ const Scalar machep = cephes_helper<Scalar>::machep();
+
+ Scalar ax = main_igamma_term<Scalar>(a, x);
+
+ // This is independent of mode. If this value is zero,
+ // then the function value is zero. If the function value is zero,
+ // then we are in a neighborhood where the function value evaluates to zero,
+ // so the derivative is zero.
+ if (ax == zero) {
+ return zero;
+ }
+
+ ax /= a;
+
+ /* power series */
+ Scalar r = a;
+ Scalar c = one;
+ Scalar ans = one;
+
+ Scalar dc_da = zero;
+ Scalar dans_da = zero;
+
+ for (int i = 0; i < igamma_num_iterations<Scalar, mode>(); i++) {
+ r += one;
+ Scalar term = x / r;
+ Scalar dterm_da = -x / (r * r);
+ dc_da = term * dc_da + dterm_da * c;
+ dans_da += dc_da;
+ c *= term;
+ ans += c;
+
+ if (mode == VALUE) {
+ if (c <= machep * ans) {
+ break;
+ }
+ } else {
+ if (numext::abs(dc_da) <= machep * numext::abs(dans_da)) {
+ break;
+ }
+ }
+ }
+
+ Scalar dlogax_da = numext::log(x) - digamma_impl<Scalar>::run(a + one);
+ Scalar dax_da = ax * dlogax_da;
+
+ switch (mode) {
+ case VALUE:
+ return ans * ax;
+ case DERIVATIVE:
+ return ans * dax_da + dans_da * ax;
+ case SAMPLE_DERIVATIVE:
+ default: // this is needed to suppress clang warning
+ return -(dans_da + ans * dlogax_da) * x / a;
+ }
+ }
+};
+
+#if !EIGEN_HAS_C99_MATH
+
+template <typename Scalar>
+struct igammac_impl {
+ EIGEN_STATIC_ASSERT((internal::is_same<Scalar, Scalar>::value == false),
+ THIS_TYPE_IS_NOT_SUPPORTED)
+
+ EIGEN_DEVICE_FUNC static Scalar run(Scalar a, Scalar x) {
+ return Scalar(0);
+ }
+};
+
+#else
+
+template <typename Scalar>
+struct igammac_impl {
+ EIGEN_DEVICE_FUNC
+ static Scalar run(Scalar a, Scalar x) {
+ /* igamc()
+ *
+ * Incomplete gamma integral (modified for Eigen)
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double a, x, y, igamc();
+ *
+ * y = igamc( a, x );
+ *
+ * DESCRIPTION:
+ *
+ * The function is defined by
+ *
+ *
+ * igamc(a,x) = 1 - igam(a,x)
+ *
+ * inf.
+ * -
+ * 1 | | -t a-1
+ * = ----- | e t dt.
+ * - | |
+ * | (a) -
+ * x
+ *
+ *
+ * In this implementation both arguments must be positive.
+ * The integral is evaluated by either a power series or
+ * continued fraction expansion, depending on the relative
+ * values of a and x.
+ *
+ * ACCURACY (float):
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE 0,30 30000 7.8e-6 5.9e-7
+ *
+ *
+ * ACCURACY (double):
+ *
+ * Tested at random a, x.
+ * a x Relative error:
+ * arithmetic domain domain # trials peak rms
+ * IEEE 0.5,100 0,100 200000 1.9e-14 1.7e-15
+ * IEEE 0.01,0.5 0,100 200000 1.4e-13 1.6e-15
+ *
+ */
+ /*
+ Cephes Math Library Release 2.2: June, 1992
+ Copyright 1985, 1987, 1992 by Stephen L. Moshier
+ Direct inquiries to 30 Frost Street, Cambridge, MA 02140
+ */
+ const Scalar zero = 0;
+ const Scalar one = 1;
+ const Scalar nan = NumTraits<Scalar>::quiet_NaN();
+
+ if ((x < zero) || (a <= zero)) {
+ // domain error
+ return nan;
+ }
+
+ if ((numext::isnan)(a) || (numext::isnan)(x)) { // propagate nans
+ return nan;
+ }
+
+ if ((x < one) || (x < a)) {
+ return (one - igamma_series_impl<Scalar, VALUE>::run(a, x));
+ }
+
+ return igammac_cf_impl<Scalar, VALUE>::run(a, x);
+ }
+};
+
+#endif // EIGEN_HAS_C99_MATH
+
+/************************************************************************************************
+ * Implementation of igamma (incomplete gamma integral), based on Cephes but requires C++11/C99 *
+ ************************************************************************************************/
+
+#if !EIGEN_HAS_C99_MATH
+
+template <typename Scalar, IgammaComputationMode mode>
+struct igamma_generic_impl {
+ EIGEN_STATIC_ASSERT((internal::is_same<Scalar, Scalar>::value == false),
+ THIS_TYPE_IS_NOT_SUPPORTED)
+
+ EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE Scalar run(Scalar a, Scalar x) {
+ return Scalar(0);
+ }
+};
+
+#else
+
+template <typename Scalar, IgammaComputationMode mode>
+struct igamma_generic_impl {
+ EIGEN_DEVICE_FUNC
+ static Scalar run(Scalar a, Scalar x) {
+ /* Depending on the mode, returns
+ * - VALUE: incomplete Gamma function igamma(a, x)
+ * - DERIVATIVE: derivative of incomplete Gamma function d/da igamma(a, x)
+ * - SAMPLE_DERIVATIVE: implicit derivative of a Gamma random variable
+ * x ~ Gamma(x | a, 1), dx/da = -1 / Gamma(x | a, 1) * d igamma(a, x) / dx
+ *
+ * Derivatives are implemented by forward-mode differentiation.
+ */
+ const Scalar zero = 0;
+ const Scalar one = 1;
+ const Scalar nan = NumTraits<Scalar>::quiet_NaN();
+
+ if (x == zero) return zero;
+
+ if ((x < zero) || (a <= zero)) { // domain error
+ return nan;
+ }
+
+ if ((numext::isnan)(a) || (numext::isnan)(x)) { // propagate nans
+ return nan;
+ }
+
+ if ((x > one) && (x > a)) {
+ Scalar ret = igammac_cf_impl<Scalar, mode>::run(a, x);
+ if (mode == VALUE) {
+ return one - ret;
+ } else {
+ return -ret;
+ }
+ }
+
+ return igamma_series_impl<Scalar, mode>::run(a, x);
+ }
+};
+
+#endif // EIGEN_HAS_C99_MATH
+
+template <typename Scalar>
+struct igamma_retval {
+ typedef Scalar type;
+};
+
+template <typename Scalar>
+struct igamma_impl : igamma_generic_impl<Scalar, VALUE> {
+ /* igam()
+ * Incomplete gamma integral.
+ *
+ * The CDF of Gamma(a, 1) random variable at the point x.
+ *
+ * Accuracy estimation. For each a in [10^-2, 10^-1...10^3] we sample
+ * 50 Gamma random variables x ~ Gamma(x | a, 1), a total of 300 points.
+ * The ground truth is computed by mpmath. Mean absolute error:
+ * float: 1.26713e-05
+ * double: 2.33606e-12
+ *
+ * Cephes documentation below.
+ *
+ * SYNOPSIS:
+ *
+ * double a, x, y, igam();
+ *
+ * y = igam( a, x );
+ *
+ * DESCRIPTION:
+ *
+ * The function is defined by
+ *
+ * x
+ * -
+ * 1 | | -t a-1
+ * igam(a,x) = ----- | e t dt.
+ * - | |
+ * | (a) -
+ * 0
+ *
+ *
+ * In this implementation both arguments must be positive.
+ * The integral is evaluated by either a power series or
+ * continued fraction expansion, depending on the relative
+ * values of a and x.
+ *
+ * ACCURACY (double):
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE 0,30 200000 3.6e-14 2.9e-15
+ * IEEE 0,100 300000 9.9e-14 1.5e-14
+ *
+ *
+ * ACCURACY (float):
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE 0,30 20000 7.8e-6 5.9e-7
+ *
+ */
+ /*
+ Cephes Math Library Release 2.2: June, 1992
+ Copyright 1985, 1987, 1992 by Stephen L. Moshier
+ Direct inquiries to 30 Frost Street, Cambridge, MA 02140
+ */
+
+ /* left tail of incomplete gamma function:
+ *
+ * inf. k
+ * a -x - x
+ * x e > ----------
+ * - -
+ * k=0 | (a+k+1)
+ *
+ */
+};
+
+template <typename Scalar>
+struct igamma_der_a_retval : igamma_retval<Scalar> {};
+
+template <typename Scalar>
+struct igamma_der_a_impl : igamma_generic_impl<Scalar, DERIVATIVE> {
+ /* Derivative of the incomplete Gamma function with respect to a.
+ *
+ * Computes d/da igamma(a, x) by forward differentiation of the igamma code.
+ *
+ * Accuracy estimation. For each a in [10^-2, 10^-1...10^3] we sample
+ * 50 Gamma random variables x ~ Gamma(x | a, 1), a total of 300 points.
+ * The ground truth is computed by mpmath. Mean absolute error:
+ * float: 6.17992e-07
+ * double: 4.60453e-12
+ *
+ * Reference:
+ * R. Moore. "Algorithm AS 187: Derivatives of the incomplete gamma
+ * integral". Journal of the Royal Statistical Society. 1982
+ */
+};
+
+template <typename Scalar>
+struct gamma_sample_der_alpha_retval : igamma_retval<Scalar> {};
+
+template <typename Scalar>
+struct gamma_sample_der_alpha_impl
+ : igamma_generic_impl<Scalar, SAMPLE_DERIVATIVE> {
+ /* Derivative of a Gamma random variable sample with respect to alpha.
+ *
+ * Consider a sample of a Gamma random variable with the concentration
+ * parameter alpha: sample ~ Gamma(alpha, 1). The reparameterization
+ * derivative that we want to compute is dsample / dalpha =
+ * d igammainv(alpha, u) / dalpha, where u = igamma(alpha, sample).
+ * However, this formula is numerically unstable and expensive, so instead
+ * we use implicit differentiation:
+ *
+ * igamma(alpha, sample) = u, where u ~ Uniform(0, 1).
+ * Apply d / dalpha to both sides:
+ * d igamma(alpha, sample) / dalpha
+ * + d igamma(alpha, sample) / dsample * dsample/dalpha = 0
+ * d igamma(alpha, sample) / dalpha
+ * + Gamma(sample | alpha, 1) dsample / dalpha = 0
+ * dsample/dalpha = - (d igamma(alpha, sample) / dalpha)
+ * / Gamma(sample | alpha, 1)
+ *
+ * Here Gamma(sample | alpha, 1) is the PDF of the Gamma distribution
+ * (note that the derivative of the CDF w.r.t. sample is the PDF).
+ * See the reference below for more details.
+ *
+ * The derivative of igamma(alpha, sample) is computed by forward
+ * differentiation of the igamma code. Division by the Gamma PDF is performed
+ * in the same code, increasing the accuracy and speed due to cancellation
+ * of some terms.
+ *
+ * Accuracy estimation. For each alpha in [10^-2, 10^-1...10^3] we sample
+ * 50 Gamma random variables sample ~ Gamma(sample | alpha, 1), a total of 300
+ * points. The ground truth is computed by mpmath. Mean absolute error:
+ * float: 2.1686e-06
+ * double: 1.4774e-12
+ *
+ * Reference:
+ * M. Figurnov, S. Mohamed, A. Mnih "Implicit Reparameterization Gradients".
+ * 2018
+ */
+};
+
+/*****************************************************************************
+ * Implementation of Riemann zeta function of two arguments, based on Cephes *
+ *****************************************************************************/
+
+template <typename Scalar>
+struct zeta_retval {
+ typedef Scalar type;
+};
+
+template <typename Scalar>
+struct zeta_impl_series {
+ EIGEN_STATIC_ASSERT((internal::is_same<Scalar, Scalar>::value == false),
+ THIS_TYPE_IS_NOT_SUPPORTED)
+
+ EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE Scalar run(const Scalar) {
+ return Scalar(0);
+ }
+};
+
+template <>
+struct zeta_impl_series<float> {
+ EIGEN_DEVICE_FUNC
+ static EIGEN_STRONG_INLINE bool run(float& a, float& b, float& s, const float x, const float machep) {
+ int i = 0;
+ while(i < 9)
+ {
+ i += 1;
+ a += 1.0f;
+ b = numext::pow( a, -x );
+ s += b;
+ if( numext::abs(b/s) < machep )
+ return true;
+ }
+
+ //Return whether we are done
+ return false;
+ }
+};
+
+template <>
+struct zeta_impl_series<double> {
+ EIGEN_DEVICE_FUNC
+ static EIGEN_STRONG_INLINE bool run(double& a, double& b, double& s, const double x, const double machep) {
+ int i = 0;
+ while( (i < 9) || (a <= 9.0) )
+ {
+ i += 1;
+ a += 1.0;
+ b = numext::pow( a, -x );
+ s += b;
+ if( numext::abs(b/s) < machep )
+ return true;
+ }
+
+ //Return whether we are done
+ return false;
+ }
+};
+
+template <typename Scalar>
+struct zeta_impl {
+ EIGEN_DEVICE_FUNC
+ static Scalar run(Scalar x, Scalar q) {
+ /* zeta.c
+ *
+ * Riemann zeta function of two arguments
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, q, y, zeta();
+ *
+ * y = zeta( x, q );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ *
+ *
+ * inf.
+ * - -x
+ * zeta(x,q) = > (k+q)
+ * -
+ * k=0
+ *
+ * where x > 1 and q is not a negative integer or zero.
+ * The Euler-Maclaurin summation formula is used to obtain
+ * the expansion
+ *
+ * n
+ * - -x
+ * zeta(x,q) = > (k+q)
+ * -
+ * k=1
+ *
+ * 1-x inf. B x(x+1)...(x+2j)
+ * (n+q) 1 - 2j
+ * + --------- - ------- + > --------------------
+ * x-1 x - x+2j+1
+ * 2(n+q) j=1 (2j)! (n+q)
+ *
+ * where the B2j are Bernoulli numbers. Note that (see zetac.c)
+ * zeta(x,1) = zetac(x) + 1.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error for single precision:
+ * arithmetic domain # trials peak rms
+ * IEEE 0,25 10000 6.9e-7 1.0e-7
+ *
+ * Large arguments may produce underflow in powf(), in which
+ * case the results are inaccurate.
+ *
+ * REFERENCE:
+ *
+ * Gradshteyn, I. S., and I. M. Ryzhik, Tables of Integrals,
+ * Series, and Products, p. 1073; Academic Press, 1980.
+ *
+ */
+
+ int i;
+ Scalar p, r, a, b, k, s, t, w;
+
+ const Scalar A[] = {
+ Scalar(12.0),
+ Scalar(-720.0),
+ Scalar(30240.0),
+ Scalar(-1209600.0),
+ Scalar(47900160.0),
+ Scalar(-1.8924375803183791606e9), /*1.307674368e12/691*/
+ Scalar(7.47242496e10),
+ Scalar(-2.950130727918164224e12), /*1.067062284288e16/3617*/
+ Scalar(1.1646782814350067249e14), /*5.109094217170944e18/43867*/
+ Scalar(-4.5979787224074726105e15), /*8.028576626982912e20/174611*/
+ Scalar(1.8152105401943546773e17), /*1.5511210043330985984e23/854513*/
+ Scalar(-7.1661652561756670113e18) /*1.6938241367317436694528e27/236364091*/
+ };
+
+ const Scalar maxnum = NumTraits<Scalar>::infinity();
+ const Scalar zero = Scalar(0.0), half = Scalar(0.5), one = Scalar(1.0);
+ const Scalar machep = cephes_helper<Scalar>::machep();
+ const Scalar nan = NumTraits<Scalar>::quiet_NaN();
+
+ if( x == one )
+ return maxnum;
+
+ if( x < one )
+ {
+ return nan;
+ }
+
+ if( q <= zero )
+ {
+ if(q == numext::floor(q))
+ {
+ if (x == numext::floor(x) && long(x) % 2 == 0) {
+ return maxnum;
+ }
+ else {
+ return nan;
+ }
+ }
+ p = x;
+ r = numext::floor(p);
+ if (p != r)
+ return nan;
+ }
+
+ /* Permit negative q but continue sum until n+q > +9 .
+ * This case should be handled by a reflection formula.
+ * If q<0 and x is an integer, there is a relation to
+ * the polygamma function.
+ */
+ s = numext::pow( q, -x );
+ a = q;
+ b = zero;
+ // Run the summation in a helper function that is specific to the floating precision
+ if (zeta_impl_series<Scalar>::run(a, b, s, x, machep)) {
+ return s;
+ }
+
+ // If b is zero, then the tail sum will also end up being zero.
+ // Exiting early here can prevent NaNs for some large inputs, where
+ // the tail sum computed below has term `a` which can overflow to `inf`.
+ if (numext::equal_strict(b, zero)) {
+ return s;
+ }
+
+ w = a;
+ s += b*w/(x-one);
+ s -= half * b;
+ a = one;
+ k = zero;
+
+ for( i=0; i<12; i++ )
+ {
+ a *= x + k;
+ b /= w;
+ t = a*b/A[i];
+ s = s + t;
+ t = numext::abs(t/s);
+ if( t < machep ) {
+ break;
+ }
+ k += one;
+ a *= x + k;
+ b /= w;
+ k += one;
+ }
+ return s;
+ }
+};
+
+/****************************************************************************
+ * Implementation of polygamma function, requires C++11/C99 *
+ ****************************************************************************/
+
+template <typename Scalar>
+struct polygamma_retval {
+ typedef Scalar type;
+};
+
+#if !EIGEN_HAS_C99_MATH
+
+template <typename Scalar>
+struct polygamma_impl {
+ EIGEN_STATIC_ASSERT((internal::is_same<Scalar, Scalar>::value == false),
+ THIS_TYPE_IS_NOT_SUPPORTED)
+
+ EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE Scalar run(Scalar n, Scalar x) {
+ return Scalar(0);
+ }
+};
+
+#else
+
+template <typename Scalar>
+struct polygamma_impl {
+ EIGEN_DEVICE_FUNC
+ static Scalar run(Scalar n, Scalar x) {
+ Scalar zero = 0.0, one = 1.0;
+ Scalar nplus = n + one;
+ const Scalar nan = NumTraits<Scalar>::quiet_NaN();
+
+ // Check that n is a non-negative integer
+ if (numext::floor(n) != n || n < zero) {
+ return nan;
+ }
+ // Just return the digamma function for n = 0
+ else if (n == zero) {
+ return digamma_impl<Scalar>::run(x);
+ }
+ // Use the same implementation as scipy
+ else {
+ Scalar factorial = numext::exp(lgamma_impl<Scalar>::run(nplus));
+ return numext::pow(-one, nplus) * factorial * zeta_impl<Scalar>::run(nplus, x);
+ }
+ }
+};
+
+#endif // EIGEN_HAS_C99_MATH
+
+/************************************************************************************************
+ * Implementation of betainc (incomplete beta integral), based on Cephes but requires C++11/C99 *
+ ************************************************************************************************/
+
+template <typename Scalar>
+struct betainc_retval {
+ typedef Scalar type;
+};
+
+#if !EIGEN_HAS_C99_MATH
+
+template <typename Scalar>
+struct betainc_impl {
+ EIGEN_STATIC_ASSERT((internal::is_same<Scalar, Scalar>::value == false),
+ THIS_TYPE_IS_NOT_SUPPORTED)
+
+ EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE Scalar run(Scalar a, Scalar b, Scalar x) {
+ return Scalar(0);
+ }
+};
+
+#else
+
+template <typename Scalar>
+struct betainc_impl {
+ EIGEN_STATIC_ASSERT((internal::is_same<Scalar, Scalar>::value == false),
+ THIS_TYPE_IS_NOT_SUPPORTED)
+
+ EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE Scalar run(Scalar, Scalar, Scalar) {
+ /* betaincf.c
+ *
+ * Incomplete beta integral
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float a, b, x, y, betaincf();
+ *
+ * y = betaincf( a, b, x );
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns incomplete beta integral of the arguments, evaluated
+ * from zero to x. The function is defined as
+ *
+ * x
+ * - -
+ * | (a+b) | | a-1 b-1
+ * ----------- | t (1-t) dt.
+ * - - | |
+ * | (a) | (b) -
+ * 0
+ *
+ * The domain of definition is 0 <= x <= 1. In this
+ * implementation a and b are restricted to positive values.
+ * The integral from x to 1 may be obtained by the symmetry
+ * relation
+ *
+ * 1 - betainc( a, b, x ) = betainc( b, a, 1-x ).
+ *
+ * The integral is evaluated by a continued fraction expansion.
+ * If a < 1, the function calls itself recursively after a
+ * transformation to increase a to a+1.
+ *
+ * ACCURACY (float):
+ *
+ * Tested at random points (a,b,x) with a and b in the indicated
+ * interval and x between 0 and 1.
+ *
+ * arithmetic domain # trials peak rms
+ * Relative error:
+ * IEEE 0,30 10000 3.7e-5 5.1e-6
+ * IEEE 0,100 10000 1.7e-4 2.5e-5
+ * The useful domain for relative error is limited by underflow
+ * of the single precision exponential function.
+ * Absolute error:
+ * IEEE 0,30 100000 2.2e-5 9.6e-7
+ * IEEE 0,100 10000 6.5e-5 3.7e-6
+ *
+ * Larger errors may occur for extreme ratios of a and b.
+ *
+ * ACCURACY (double):
+ * arithmetic domain # trials peak rms
+ * IEEE 0,5 10000 6.9e-15 4.5e-16
+ * IEEE 0,85 250000 2.2e-13 1.7e-14
+ * IEEE 0,1000 30000 5.3e-12 6.3e-13
+ * IEEE 0,10000 250000 9.3e-11 7.1e-12
+ * IEEE 0,100000 10000 8.7e-10 4.8e-11
+ * Outputs smaller than the IEEE gradual underflow threshold
+ * were excluded from these statistics.
+ *
+ * ERROR MESSAGES:
+ * message condition value returned
+ * incbet domain x<0, x>1 nan
+ * incbet underflow nan
+ */
+ return Scalar(0);
+ }
+};
+
+/* Continued fraction expansion #1 for incomplete beta integral (small_branch = True)
+ * Continued fraction expansion #2 for incomplete beta integral (small_branch = False)
+ */
+template <typename Scalar>
+struct incbeta_cfe {
+ EIGEN_STATIC_ASSERT((internal::is_same<Scalar, float>::value ||
+ internal::is_same<Scalar, double>::value),
+ THIS_TYPE_IS_NOT_SUPPORTED)
+
+ EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE Scalar run(Scalar a, Scalar b, Scalar x, bool small_branch) {
+ const Scalar big = cephes_helper<Scalar>::big();
+ const Scalar machep = cephes_helper<Scalar>::machep();
+ const Scalar biginv = cephes_helper<Scalar>::biginv();
+
+ const Scalar zero = 0;
+ const Scalar one = 1;
+ const Scalar two = 2;
+
+ Scalar xk, pk, pkm1, pkm2, qk, qkm1, qkm2;
+ Scalar k1, k2, k3, k4, k5, k6, k7, k8, k26update;
+ Scalar ans;
+ int n;
+
+ const int num_iters = (internal::is_same<Scalar, float>::value) ? 100 : 300;
+ const Scalar thresh =
+ (internal::is_same<Scalar, float>::value) ? machep : Scalar(3) * machep;
+ Scalar r = (internal::is_same<Scalar, float>::value) ? zero : one;
+
+ if (small_branch) {
+ k1 = a;
+ k2 = a + b;
+ k3 = a;
+ k4 = a + one;
+ k5 = one;
+ k6 = b - one;
+ k7 = k4;
+ k8 = a + two;
+ k26update = one;
+ } else {
+ k1 = a;
+ k2 = b - one;
+ k3 = a;
+ k4 = a + one;
+ k5 = one;
+ k6 = a + b;
+ k7 = a + one;
+ k8 = a + two;
+ k26update = -one;
+ x = x / (one - x);
+ }
+
+ pkm2 = zero;
+ qkm2 = one;
+ pkm1 = one;
+ qkm1 = one;
+ ans = one;
+ n = 0;
+
+ do {
+ xk = -(x * k1 * k2) / (k3 * k4);
+ pk = pkm1 + pkm2 * xk;
+ qk = qkm1 + qkm2 * xk;
+ pkm2 = pkm1;
+ pkm1 = pk;
+ qkm2 = qkm1;
+ qkm1 = qk;
+
+ xk = (x * k5 * k6) / (k7 * k8);
+ pk = pkm1 + pkm2 * xk;
+ qk = qkm1 + qkm2 * xk;
+ pkm2 = pkm1;
+ pkm1 = pk;
+ qkm2 = qkm1;
+ qkm1 = qk;
+
+ if (qk != zero) {
+ r = pk / qk;
+ if (numext::abs(ans - r) < numext::abs(r) * thresh) {
+ return r;
+ }
+ ans = r;
+ }
+
+ k1 += one;
+ k2 += k26update;
+ k3 += two;
+ k4 += two;
+ k5 += one;
+ k6 -= k26update;
+ k7 += two;
+ k8 += two;
+
+ if ((numext::abs(qk) + numext::abs(pk)) > big) {
+ pkm2 *= biginv;
+ pkm1 *= biginv;
+ qkm2 *= biginv;
+ qkm1 *= biginv;
+ }
+ if ((numext::abs(qk) < biginv) || (numext::abs(pk) < biginv)) {
+ pkm2 *= big;
+ pkm1 *= big;
+ qkm2 *= big;
+ qkm1 *= big;
+ }
+ } while (++n < num_iters);
+
+ return ans;
+ }
+};
+
+/* Helper functions depending on the Scalar type */
+template <typename Scalar>
+struct betainc_helper {};
+
+template <>
+struct betainc_helper<float> {
+ /* Core implementation, assumes a large (> 1.0) */
+ EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE float incbsa(float aa, float bb,
+ float xx) {
+ float ans, a, b, t, x, onemx;
+ bool reversed_a_b = false;
+
+ onemx = 1.0f - xx;
+
+ /* see if x is greater than the mean */
+ if (xx > (aa / (aa + bb))) {
+ reversed_a_b = true;
+ a = bb;
+ b = aa;
+ t = xx;
+ x = onemx;
+ } else {
+ a = aa;
+ b = bb;
+ t = onemx;
+ x = xx;
+ }
+
+ /* Choose expansion for optimal convergence */
+ if (b > 10.0f) {
+ if (numext::abs(b * x / a) < 0.3f) {
+ t = betainc_helper<float>::incbps(a, b, x);
+ if (reversed_a_b) t = 1.0f - t;
+ return t;
+ }
+ }
+
+ ans = x * (a + b - 2.0f) / (a - 1.0f);
+ if (ans < 1.0f) {
+ ans = incbeta_cfe<float>::run(a, b, x, true /* small_branch */);
+ t = b * numext::log(t);
+ } else {
+ ans = incbeta_cfe<float>::run(a, b, x, false /* small_branch */);
+ t = (b - 1.0f) * numext::log(t);
+ }
+
+ t += a * numext::log(x) + lgamma_impl<float>::run(a + b) -
+ lgamma_impl<float>::run(a) - lgamma_impl<float>::run(b);
+ t += numext::log(ans / a);
+ t = numext::exp(t);
+
+ if (reversed_a_b) t = 1.0f - t;
+ return t;
+ }
+
+ EIGEN_DEVICE_FUNC
+ static EIGEN_STRONG_INLINE float incbps(float a, float b, float x) {
+ float t, u, y, s;
+ const float machep = cephes_helper<float>::machep();
+
+ y = a * numext::log(x) + (b - 1.0f) * numext::log1p(-x) - numext::log(a);
+ y -= lgamma_impl<float>::run(a) + lgamma_impl<float>::run(b);
+ y += lgamma_impl<float>::run(a + b);
+
+ t = x / (1.0f - x);
+ s = 0.0f;
+ u = 1.0f;
+ do {
+ b -= 1.0f;
+ if (b == 0.0f) {
+ break;
+ }
+ a += 1.0f;
+ u *= t * b / a;
+ s += u;
+ } while (numext::abs(u) > machep);
+
+ return numext::exp(y) * (1.0f + s);
+ }
+};
+
+template <>
+struct betainc_impl<float> {
+ EIGEN_DEVICE_FUNC
+ static float run(float a, float b, float x) {
+ const float nan = NumTraits<float>::quiet_NaN();
+ float ans, t;
+
+ if (a <= 0.0f) return nan;
+ if (b <= 0.0f) return nan;
+ if ((x <= 0.0f) || (x >= 1.0f)) {
+ if (x == 0.0f) return 0.0f;
+ if (x == 1.0f) return 1.0f;
+ // mtherr("betaincf", DOMAIN);
+ return nan;
+ }
+
+ /* transformation for small aa */
+ if (a <= 1.0f) {
+ ans = betainc_helper<float>::incbsa(a + 1.0f, b, x);
+ t = a * numext::log(x) + b * numext::log1p(-x) +
+ lgamma_impl<float>::run(a + b) - lgamma_impl<float>::run(a + 1.0f) -
+ lgamma_impl<float>::run(b);
+ return (ans + numext::exp(t));
+ } else {
+ return betainc_helper<float>::incbsa(a, b, x);
+ }
+ }
+};
+
+template <>
+struct betainc_helper<double> {
+ EIGEN_DEVICE_FUNC
+ static EIGEN_STRONG_INLINE double incbps(double a, double b, double x) {
+ const double machep = cephes_helper<double>::machep();
+
+ double s, t, u, v, n, t1, z, ai;
+
+ ai = 1.0 / a;
+ u = (1.0 - b) * x;
+ v = u / (a + 1.0);
+ t1 = v;
+ t = u;
+ n = 2.0;
+ s = 0.0;
+ z = machep * ai;
+ while (numext::abs(v) > z) {
+ u = (n - b) * x / n;
+ t *= u;
+ v = t / (a + n);
+ s += v;
+ n += 1.0;
+ }
+ s += t1;
+ s += ai;
+
+ u = a * numext::log(x);
+ // TODO: gamma() is not directly implemented in Eigen.
+ /*
+ if ((a + b) < maxgam && numext::abs(u) < maxlog) {
+ t = gamma(a + b) / (gamma(a) * gamma(b));
+ s = s * t * pow(x, a);
+ }
+ */
+ t = lgamma_impl<double>::run(a + b) - lgamma_impl<double>::run(a) -
+ lgamma_impl<double>::run(b) + u + numext::log(s);
+ return s = numext::exp(t);
+ }
+};
+
+template <>
+struct betainc_impl<double> {
+ EIGEN_DEVICE_FUNC
+ static double run(double aa, double bb, double xx) {
+ const double nan = NumTraits<double>::quiet_NaN();
+ const double machep = cephes_helper<double>::machep();
+ // const double maxgam = 171.624376956302725;
+
+ double a, b, t, x, xc, w, y;
+ bool reversed_a_b = false;
+
+ if (aa <= 0.0 || bb <= 0.0) {
+ return nan; // goto domerr;
+ }
+
+ if ((xx <= 0.0) || (xx >= 1.0)) {
+ if (xx == 0.0) return (0.0);
+ if (xx == 1.0) return (1.0);
+ // mtherr("incbet", DOMAIN);
+ return nan;
+ }
+
+ if ((bb * xx) <= 1.0 && xx <= 0.95) {
+ return betainc_helper<double>::incbps(aa, bb, xx);
+ }
+
+ w = 1.0 - xx;
+
+ /* Reverse a and b if x is greater than the mean. */
+ if (xx > (aa / (aa + bb))) {
+ reversed_a_b = true;
+ a = bb;
+ b = aa;
+ xc = xx;
+ x = w;
+ } else {
+ a = aa;
+ b = bb;
+ xc = w;
+ x = xx;
+ }
+
+ if (reversed_a_b && (b * x) <= 1.0 && x <= 0.95) {
+ t = betainc_helper<double>::incbps(a, b, x);
+ if (t <= machep) {
+ t = 1.0 - machep;
+ } else {
+ t = 1.0 - t;
+ }
+ return t;
+ }
+
+ /* Choose expansion for better convergence. */
+ y = x * (a + b - 2.0) - (a - 1.0);
+ if (y < 0.0) {
+ w = incbeta_cfe<double>::run(a, b, x, true /* small_branch */);
+ } else {
+ w = incbeta_cfe<double>::run(a, b, x, false /* small_branch */) / xc;
+ }
+
+ /* Multiply w by the factor
+ a b _ _ _
+ x (1-x) | (a+b) / ( a | (a) | (b) ) . */
+
+ y = a * numext::log(x);
+ t = b * numext::log(xc);
+ // TODO: gamma is not directly implemented in Eigen.
+ /*
+ if ((a + b) < maxgam && numext::abs(y) < maxlog && numext::abs(t) < maxlog)
+ {
+ t = pow(xc, b);
+ t *= pow(x, a);
+ t /= a;
+ t *= w;
+ t *= gamma(a + b) / (gamma(a) * gamma(b));
+ } else {
+ */
+ /* Resort to logarithms. */
+ y += t + lgamma_impl<double>::run(a + b) - lgamma_impl<double>::run(a) -
+ lgamma_impl<double>::run(b);
+ y += numext::log(w / a);
+ t = numext::exp(y);
+
+ /* } */
+ // done:
+
+ if (reversed_a_b) {
+ if (t <= machep) {
+ t = 1.0 - machep;
+ } else {
+ t = 1.0 - t;
+ }
+ }
+ return t;
+ }
+};
+
+#endif // EIGEN_HAS_C99_MATH
+
+} // end namespace internal
+
+namespace numext {
+
+template <typename Scalar>
+EIGEN_DEVICE_FUNC inline EIGEN_MATHFUNC_RETVAL(lgamma, Scalar)
+ lgamma(const Scalar& x) {
+ return EIGEN_MATHFUNC_IMPL(lgamma, Scalar)::run(x);
+}
+
+template <typename Scalar>
+EIGEN_DEVICE_FUNC inline EIGEN_MATHFUNC_RETVAL(digamma, Scalar)
+ digamma(const Scalar& x) {
+ return EIGEN_MATHFUNC_IMPL(digamma, Scalar)::run(x);
+}
+
+template <typename Scalar>
+EIGEN_DEVICE_FUNC inline EIGEN_MATHFUNC_RETVAL(zeta, Scalar)
+zeta(const Scalar& x, const Scalar& q) {
+ return EIGEN_MATHFUNC_IMPL(zeta, Scalar)::run(x, q);
+}
+
+template <typename Scalar>
+EIGEN_DEVICE_FUNC inline EIGEN_MATHFUNC_RETVAL(polygamma, Scalar)
+polygamma(const Scalar& n, const Scalar& x) {
+ return EIGEN_MATHFUNC_IMPL(polygamma, Scalar)::run(n, x);
+}
+
+template <typename Scalar>
+EIGEN_DEVICE_FUNC inline EIGEN_MATHFUNC_RETVAL(erf, Scalar)
+ erf(const Scalar& x) {
+ return EIGEN_MATHFUNC_IMPL(erf, Scalar)::run(x);
+}
+
+template <typename Scalar>
+EIGEN_DEVICE_FUNC inline EIGEN_MATHFUNC_RETVAL(erfc, Scalar)
+ erfc(const Scalar& x) {
+ return EIGEN_MATHFUNC_IMPL(erfc, Scalar)::run(x);
+}
+
+template <typename Scalar>
+EIGEN_DEVICE_FUNC inline EIGEN_MATHFUNC_RETVAL(ndtri, Scalar)
+ ndtri(const Scalar& x) {
+ return EIGEN_MATHFUNC_IMPL(ndtri, Scalar)::run(x);
+}
+
+template <typename Scalar>
+EIGEN_DEVICE_FUNC inline EIGEN_MATHFUNC_RETVAL(igamma, Scalar)
+ igamma(const Scalar& a, const Scalar& x) {
+ return EIGEN_MATHFUNC_IMPL(igamma, Scalar)::run(a, x);
+}
+
+template <typename Scalar>
+EIGEN_DEVICE_FUNC inline EIGEN_MATHFUNC_RETVAL(igamma_der_a, Scalar)
+ igamma_der_a(const Scalar& a, const Scalar& x) {
+ return EIGEN_MATHFUNC_IMPL(igamma_der_a, Scalar)::run(a, x);
+}
+
+template <typename Scalar>
+EIGEN_DEVICE_FUNC inline EIGEN_MATHFUNC_RETVAL(gamma_sample_der_alpha, Scalar)
+ gamma_sample_der_alpha(const Scalar& a, const Scalar& x) {
+ return EIGEN_MATHFUNC_IMPL(gamma_sample_der_alpha, Scalar)::run(a, x);
+}
+
+template <typename Scalar>
+EIGEN_DEVICE_FUNC inline EIGEN_MATHFUNC_RETVAL(igammac, Scalar)
+ igammac(const Scalar& a, const Scalar& x) {
+ return EIGEN_MATHFUNC_IMPL(igammac, Scalar)::run(a, x);
+}
+
+template <typename Scalar>
+EIGEN_DEVICE_FUNC inline EIGEN_MATHFUNC_RETVAL(betainc, Scalar)
+ betainc(const Scalar& a, const Scalar& b, const Scalar& x) {
+ return EIGEN_MATHFUNC_IMPL(betainc, Scalar)::run(a, b, x);
+}
+
+} // end namespace numext
+} // end namespace Eigen
+
+#endif // EIGEN_SPECIAL_FUNCTIONS_H
diff --git a/unsupported/Eigen/src/SpecialFunctions/SpecialFunctionsPacketMath.h b/unsupported/Eigen/src/SpecialFunctions/SpecialFunctionsPacketMath.h
new file mode 100644
index 0000000..651457f
--- /dev/null
+++ b/unsupported/Eigen/src/SpecialFunctions/SpecialFunctionsPacketMath.h
@@ -0,0 +1,81 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2016 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_SPECIALFUNCTIONS_PACKETMATH_H
+#define EIGEN_SPECIALFUNCTIONS_PACKETMATH_H
+
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+
+/** \internal \returns the ln(|gamma(\a a)|) (coeff-wise) */
+template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+Packet plgamma(const Packet& a) { using numext::lgamma; return lgamma(a); }
+
+/** \internal \returns the derivative of lgamma, psi(\a a) (coeff-wise) */
+template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+Packet pdigamma(const Packet& a) { using numext::digamma; return digamma(a); }
+
+/** \internal \returns the zeta function of two arguments (coeff-wise) */
+template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+Packet pzeta(const Packet& x, const Packet& q) { using numext::zeta; return zeta(x, q); }
+
+/** \internal \returns the polygamma function (coeff-wise) */
+template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+Packet ppolygamma(const Packet& n, const Packet& x) { using numext::polygamma; return polygamma(n, x); }
+
+/** \internal \returns the erf(\a a) (coeff-wise) */
+template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+Packet perf(const Packet& a) { using numext::erf; return erf(a); }
+
+/** \internal \returns the erfc(\a a) (coeff-wise) */
+template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+Packet perfc(const Packet& a) { using numext::erfc; return erfc(a); }
+
+/** \internal \returns the ndtri(\a a) (coeff-wise) */
+template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+Packet pndtri(const Packet& a) {
+ typedef typename unpacket_traits<Packet>::type ScalarType;
+ using internal::generic_ndtri; return generic_ndtri<Packet, ScalarType>(a);
+}
+
+/** \internal \returns the incomplete gamma function igamma(\a a, \a x) */
+template<typename Packet> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+Packet pigamma(const Packet& a, const Packet& x) { using numext::igamma; return igamma(a, x); }
+
+/** \internal \returns the derivative of the incomplete gamma function
+ * igamma_der_a(\a a, \a x) */
+template <typename Packet>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet pigamma_der_a(const Packet& a, const Packet& x) {
+ using numext::igamma_der_a; return igamma_der_a(a, x);
+}
+
+/** \internal \returns compute the derivative of the sample
+ * of Gamma(alpha, 1) random variable with respect to the parameter a
+ * gamma_sample_der_alpha(\a alpha, \a sample) */
+template <typename Packet>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet pgamma_sample_der_alpha(const Packet& alpha, const Packet& sample) {
+ using numext::gamma_sample_der_alpha; return gamma_sample_der_alpha(alpha, sample);
+}
+
+/** \internal \returns the complementary incomplete gamma function igammac(\a a, \a x) */
+template<typename Packet> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+Packet pigammac(const Packet& a, const Packet& x) { using numext::igammac; return igammac(a, x); }
+
+/** \internal \returns the complementary incomplete gamma function betainc(\a a, \a b, \a x) */
+template<typename Packet> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+Packet pbetainc(const Packet& a, const Packet& b,const Packet& x) { using numext::betainc; return betainc(a, b, x); }
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_SPECIALFUNCTIONS_PACKETMATH_H
diff --git a/unsupported/Eigen/src/SpecialFunctions/arch/AVX/BesselFunctions.h b/unsupported/Eigen/src/SpecialFunctions/arch/AVX/BesselFunctions.h
new file mode 100644
index 0000000..2d76692
--- /dev/null
+++ b/unsupported/Eigen/src/SpecialFunctions/arch/AVX/BesselFunctions.h
@@ -0,0 +1,46 @@
+#ifndef EIGEN_AVX_BESSELFUNCTIONS_H
+#define EIGEN_AVX_BESSELFUNCTIONS_H
+
+namespace Eigen {
+namespace internal {
+
+F16_PACKET_FUNCTION(Packet8f, Packet8h, pbessel_i0)
+BF16_PACKET_FUNCTION(Packet8f, Packet8bf, pbessel_i0)
+
+F16_PACKET_FUNCTION(Packet8f, Packet8h, pbessel_i0e)
+BF16_PACKET_FUNCTION(Packet8f, Packet8bf, pbessel_i0e)
+
+F16_PACKET_FUNCTION(Packet8f, Packet8h, pbessel_i1)
+BF16_PACKET_FUNCTION(Packet8f, Packet8bf, pbessel_i1)
+
+F16_PACKET_FUNCTION(Packet8f, Packet8h, pbessel_i1e)
+BF16_PACKET_FUNCTION(Packet8f, Packet8bf, pbessel_i1e)
+
+F16_PACKET_FUNCTION(Packet8f, Packet8h, pbessel_j0)
+BF16_PACKET_FUNCTION(Packet8f, Packet8bf, pbessel_j0)
+
+F16_PACKET_FUNCTION(Packet8f, Packet8h, pbessel_j1)
+BF16_PACKET_FUNCTION(Packet8f, Packet8bf, pbessel_j1)
+
+F16_PACKET_FUNCTION(Packet8f, Packet8h, pbessel_k0)
+BF16_PACKET_FUNCTION(Packet8f, Packet8bf, pbessel_k0)
+
+F16_PACKET_FUNCTION(Packet8f, Packet8h, pbessel_k0e)
+BF16_PACKET_FUNCTION(Packet8f, Packet8bf, pbessel_k0e)
+
+F16_PACKET_FUNCTION(Packet8f, Packet8h, pbessel_k1)
+BF16_PACKET_FUNCTION(Packet8f, Packet8bf, pbessel_k1)
+
+F16_PACKET_FUNCTION(Packet8f, Packet8h, pbessel_k1e)
+BF16_PACKET_FUNCTION(Packet8f, Packet8bf, pbessel_k1e)
+
+F16_PACKET_FUNCTION(Packet8f, Packet8h, pbessel_y0)
+BF16_PACKET_FUNCTION(Packet8f, Packet8bf, pbessel_y0)
+
+F16_PACKET_FUNCTION(Packet8f, Packet8h, pbessel_y1)
+BF16_PACKET_FUNCTION(Packet8f, Packet8bf, pbessel_y1)
+
+} // namespace internal
+} // namespace Eigen
+
+#endif // EIGEN_AVX_BESSELFUNCTIONS_H
diff --git a/unsupported/Eigen/src/SpecialFunctions/arch/AVX/SpecialFunctions.h b/unsupported/Eigen/src/SpecialFunctions/arch/AVX/SpecialFunctions.h
new file mode 100644
index 0000000..35e62a8
--- /dev/null
+++ b/unsupported/Eigen/src/SpecialFunctions/arch/AVX/SpecialFunctions.h
@@ -0,0 +1,16 @@
+#ifndef EIGEN_AVX_SPECIALFUNCTIONS_H
+#define EIGEN_AVX_SPECIALFUNCTIONS_H
+
+namespace Eigen {
+namespace internal {
+
+F16_PACKET_FUNCTION(Packet8f, Packet8h, perf)
+BF16_PACKET_FUNCTION(Packet8f, Packet8bf, perf)
+
+F16_PACKET_FUNCTION(Packet8f, Packet8h, pndtri)
+BF16_PACKET_FUNCTION(Packet8f, Packet8bf, pndtri)
+
+} // namespace internal
+} // namespace Eigen
+
+#endif // EIGEN_AVX_SPECIAL_FUNCTIONS_H
diff --git a/unsupported/Eigen/src/SpecialFunctions/arch/AVX512/BesselFunctions.h b/unsupported/Eigen/src/SpecialFunctions/arch/AVX512/BesselFunctions.h
new file mode 100644
index 0000000..909b08e
--- /dev/null
+++ b/unsupported/Eigen/src/SpecialFunctions/arch/AVX512/BesselFunctions.h
@@ -0,0 +1,51 @@
+#ifndef EIGEN_AVX512_BESSELFUNCTIONS_H
+#define EIGEN_AVX512_BESSELFUNCTIONS_H
+
+namespace Eigen {
+namespace internal {
+
+// Bessel functions only available for some compilers.
+#if EIGEN_HAS_AVX512_MATH
+
+F16_PACKET_FUNCTION(Packet16f, Packet16h, pbessel_i0)
+BF16_PACKET_FUNCTION(Packet16f, Packet16bf, pbessel_i0)
+
+F16_PACKET_FUNCTION(Packet16f, Packet16h, pbessel_i0e)
+BF16_PACKET_FUNCTION(Packet16f, Packet16bf, pbessel_i0e)
+
+F16_PACKET_FUNCTION(Packet16f, Packet16h, pbessel_i1)
+BF16_PACKET_FUNCTION(Packet16f, Packet16bf, pbessel_i1)
+
+F16_PACKET_FUNCTION(Packet16f, Packet16h, pbessel_i1e)
+BF16_PACKET_FUNCTION(Packet16f, Packet16bf, pbessel_i1e)
+
+F16_PACKET_FUNCTION(Packet16f, Packet16h, pbessel_j0)
+BF16_PACKET_FUNCTION(Packet16f, Packet16bf, pbessel_j0)
+
+F16_PACKET_FUNCTION(Packet16f, Packet16h, pbessel_j1)
+BF16_PACKET_FUNCTION(Packet16f, Packet16bf, pbessel_j1)
+
+F16_PACKET_FUNCTION(Packet16f, Packet16h, pbessel_k0)
+BF16_PACKET_FUNCTION(Packet16f, Packet16bf, pbessel_k0)
+
+F16_PACKET_FUNCTION(Packet16f, Packet16h, pbessel_k0e)
+BF16_PACKET_FUNCTION(Packet16f, Packet16bf, pbessel_k0e)
+
+F16_PACKET_FUNCTION(Packet16f, Packet16h, pbessel_k1)
+BF16_PACKET_FUNCTION(Packet16f, Packet16bf, pbessel_k1)
+
+F16_PACKET_FUNCTION(Packet16f, Packet16h, pbessel_k1e)
+BF16_PACKET_FUNCTION(Packet16f, Packet16bf, pbessel_k1e)
+
+F16_PACKET_FUNCTION(Packet16f, Packet16h, pbessel_y0)
+BF16_PACKET_FUNCTION(Packet16f, Packet16bf, pbessel_y0)
+
+F16_PACKET_FUNCTION(Packet16f, Packet16h, pbessel_y1)
+BF16_PACKET_FUNCTION(Packet16f, Packet16bf, pbessel_y1)
+
+#endif
+
+} // namespace internal
+} // namespace Eigen
+
+#endif // EIGEN_AVX512_BESSELFUNCTIONS_H
diff --git a/unsupported/Eigen/src/SpecialFunctions/arch/AVX512/SpecialFunctions.h b/unsupported/Eigen/src/SpecialFunctions/arch/AVX512/SpecialFunctions.h
new file mode 100644
index 0000000..79878f2
--- /dev/null
+++ b/unsupported/Eigen/src/SpecialFunctions/arch/AVX512/SpecialFunctions.h
@@ -0,0 +1,16 @@
+#ifndef EIGEN_AVX512_SPECIALFUNCTIONS_H
+#define EIGEN_AVX512_SPECIALFUNCTIONS_H
+
+namespace Eigen {
+namespace internal {
+
+F16_PACKET_FUNCTION(Packet16f, Packet16h, perf)
+BF16_PACKET_FUNCTION(Packet16f, Packet16bf, perf)
+
+F16_PACKET_FUNCTION(Packet16f, Packet16h, pndtri)
+BF16_PACKET_FUNCTION(Packet16f, Packet16bf, pndtri)
+
+} // namespace internal
+} // namespace Eigen
+
+#endif // EIGEN_AVX512_SPECIAL_FUNCTIONS_H
diff --git a/unsupported/Eigen/src/SpecialFunctions/arch/GPU/SpecialFunctions.h b/unsupported/Eigen/src/SpecialFunctions/arch/GPU/SpecialFunctions.h
new file mode 100644
index 0000000..dd3bf4d
--- /dev/null
+++ b/unsupported/Eigen/src/SpecialFunctions/arch/GPU/SpecialFunctions.h
@@ -0,0 +1,369 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_GPU_SPECIALFUNCTIONS_H
+#define EIGEN_GPU_SPECIALFUNCTIONS_H
+
+namespace Eigen {
+
+namespace internal {
+
+// Make sure this is only available when targeting a GPU: we don't want to
+// introduce conflicts between these packet_traits definitions and the ones
+// we'll use on the host side (SSE, AVX, ...)
+#if defined(EIGEN_GPUCC) && defined(EIGEN_USE_GPU)
+
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+float4 plgamma<float4>(const float4& a)
+{
+ return make_float4(lgammaf(a.x), lgammaf(a.y), lgammaf(a.z), lgammaf(a.w));
+}
+
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+double2 plgamma<double2>(const double2& a)
+{
+ using numext::lgamma;
+ return make_double2(lgamma(a.x), lgamma(a.y));
+}
+
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+float4 pdigamma<float4>(const float4& a)
+{
+ using numext::digamma;
+ return make_float4(digamma(a.x), digamma(a.y), digamma(a.z), digamma(a.w));
+}
+
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+double2 pdigamma<double2>(const double2& a)
+{
+ using numext::digamma;
+ return make_double2(digamma(a.x), digamma(a.y));
+}
+
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+float4 pzeta<float4>(const float4& x, const float4& q)
+{
+ using numext::zeta;
+ return make_float4(zeta(x.x, q.x), zeta(x.y, q.y), zeta(x.z, q.z), zeta(x.w, q.w));
+}
+
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+double2 pzeta<double2>(const double2& x, const double2& q)
+{
+ using numext::zeta;
+ return make_double2(zeta(x.x, q.x), zeta(x.y, q.y));
+}
+
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+float4 ppolygamma<float4>(const float4& n, const float4& x)
+{
+ using numext::polygamma;
+ return make_float4(polygamma(n.x, x.x), polygamma(n.y, x.y), polygamma(n.z, x.z), polygamma(n.w, x.w));
+}
+
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+double2 ppolygamma<double2>(const double2& n, const double2& x)
+{
+ using numext::polygamma;
+ return make_double2(polygamma(n.x, x.x), polygamma(n.y, x.y));
+}
+
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+float4 perf<float4>(const float4& a)
+{
+ return make_float4(erff(a.x), erff(a.y), erff(a.z), erff(a.w));
+}
+
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+double2 perf<double2>(const double2& a)
+{
+ using numext::erf;
+ return make_double2(erf(a.x), erf(a.y));
+}
+
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+float4 perfc<float4>(const float4& a)
+{
+ using numext::erfc;
+ return make_float4(erfc(a.x), erfc(a.y), erfc(a.z), erfc(a.w));
+}
+
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+double2 perfc<double2>(const double2& a)
+{
+ using numext::erfc;
+ return make_double2(erfc(a.x), erfc(a.y));
+}
+
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+float4 pndtri<float4>(const float4& a)
+{
+ using numext::ndtri;
+ return make_float4(ndtri(a.x), ndtri(a.y), ndtri(a.z), ndtri(a.w));
+}
+
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+double2 pndtri<double2>(const double2& a)
+{
+ using numext::ndtri;
+ return make_double2(ndtri(a.x), ndtri(a.y));
+}
+
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+float4 pigamma<float4>(const float4& a, const float4& x)
+{
+ using numext::igamma;
+ return make_float4(
+ igamma(a.x, x.x),
+ igamma(a.y, x.y),
+ igamma(a.z, x.z),
+ igamma(a.w, x.w));
+}
+
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+double2 pigamma<double2>(const double2& a, const double2& x)
+{
+ using numext::igamma;
+ return make_double2(igamma(a.x, x.x), igamma(a.y, x.y));
+}
+
+template <>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE float4 pigamma_der_a<float4>(
+ const float4& a, const float4& x) {
+ using numext::igamma_der_a;
+ return make_float4(igamma_der_a(a.x, x.x), igamma_der_a(a.y, x.y),
+ igamma_der_a(a.z, x.z), igamma_der_a(a.w, x.w));
+}
+
+template <>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE double2
+pigamma_der_a<double2>(const double2& a, const double2& x) {
+ using numext::igamma_der_a;
+ return make_double2(igamma_der_a(a.x, x.x), igamma_der_a(a.y, x.y));
+}
+
+template <>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE float4 pgamma_sample_der_alpha<float4>(
+ const float4& alpha, const float4& sample) {
+ using numext::gamma_sample_der_alpha;
+ return make_float4(
+ gamma_sample_der_alpha(alpha.x, sample.x),
+ gamma_sample_der_alpha(alpha.y, sample.y),
+ gamma_sample_der_alpha(alpha.z, sample.z),
+ gamma_sample_der_alpha(alpha.w, sample.w));
+}
+
+template <>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE double2
+pgamma_sample_der_alpha<double2>(const double2& alpha, const double2& sample) {
+ using numext::gamma_sample_der_alpha;
+ return make_double2(
+ gamma_sample_der_alpha(alpha.x, sample.x),
+ gamma_sample_der_alpha(alpha.y, sample.y));
+}
+
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+float4 pigammac<float4>(const float4& a, const float4& x)
+{
+ using numext::igammac;
+ return make_float4(
+ igammac(a.x, x.x),
+ igammac(a.y, x.y),
+ igammac(a.z, x.z),
+ igammac(a.w, x.w));
+}
+
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+double2 pigammac<double2>(const double2& a, const double2& x)
+{
+ using numext::igammac;
+ return make_double2(igammac(a.x, x.x), igammac(a.y, x.y));
+}
+
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+float4 pbetainc<float4>(const float4& a, const float4& b, const float4& x)
+{
+ using numext::betainc;
+ return make_float4(
+ betainc(a.x, b.x, x.x),
+ betainc(a.y, b.y, x.y),
+ betainc(a.z, b.z, x.z),
+ betainc(a.w, b.w, x.w));
+}
+
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+double2 pbetainc<double2>(const double2& a, const double2& b, const double2& x)
+{
+ using numext::betainc;
+ return make_double2(betainc(a.x, b.x, x.x), betainc(a.y, b.y, x.y));
+}
+
+template <>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE float4 pbessel_i0e<float4>(const float4& x) {
+ using numext::bessel_i0e;
+ return make_float4(bessel_i0e(x.x), bessel_i0e(x.y), bessel_i0e(x.z), bessel_i0e(x.w));
+}
+
+template <>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE double2
+pbessel_i0e<double2>(const double2& x) {
+ using numext::bessel_i0e;
+ return make_double2(bessel_i0e(x.x), bessel_i0e(x.y));
+}
+
+template <>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE float4 pbessel_i0<float4>(const float4& x) {
+ using numext::bessel_i0;
+ return make_float4(bessel_i0(x.x), bessel_i0(x.y), bessel_i0(x.z), bessel_i0(x.w));
+}
+
+template <>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE double2
+pbessel_i0<double2>(const double2& x) {
+ using numext::bessel_i0;
+ return make_double2(bessel_i0(x.x), bessel_i0(x.y));
+}
+
+template <>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE float4 pbessel_i1e<float4>(const float4& x) {
+ using numext::bessel_i1e;
+ return make_float4(bessel_i1e(x.x), bessel_i1e(x.y), bessel_i1e(x.z), bessel_i1e(x.w));
+}
+
+template <>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE double2
+pbessel_i1e<double2>(const double2& x) {
+ using numext::bessel_i1e;
+ return make_double2(bessel_i1e(x.x), bessel_i1e(x.y));
+}
+
+template <>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE float4 pbessel_i1<float4>(const float4& x) {
+ using numext::bessel_i1;
+ return make_float4(bessel_i1(x.x), bessel_i1(x.y), bessel_i1(x.z), bessel_i1(x.w));
+}
+
+template <>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE double2
+pbessel_i1<double2>(const double2& x) {
+ using numext::bessel_i1;
+ return make_double2(bessel_i1(x.x), bessel_i1(x.y));
+}
+
+template <>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE float4 pbessel_k0e<float4>(const float4& x) {
+ using numext::bessel_k0e;
+ return make_float4(bessel_k0e(x.x), bessel_k0e(x.y), bessel_k0e(x.z), bessel_k0e(x.w));
+}
+
+template <>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE double2
+pbessel_k0e<double2>(const double2& x) {
+ using numext::bessel_k0e;
+ return make_double2(bessel_k0e(x.x), bessel_k0e(x.y));
+}
+
+template <>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE float4 pbessel_k0<float4>(const float4& x) {
+ using numext::bessel_k0;
+ return make_float4(bessel_k0(x.x), bessel_k0(x.y), bessel_k0(x.z), bessel_k0(x.w));
+}
+
+template <>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE double2
+pbessel_k0<double2>(const double2& x) {
+ using numext::bessel_k0;
+ return make_double2(bessel_k0(x.x), bessel_k0(x.y));
+}
+
+template <>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE float4 pbessel_k1e<float4>(const float4& x) {
+ using numext::bessel_k1e;
+ return make_float4(bessel_k1e(x.x), bessel_k1e(x.y), bessel_k1e(x.z), bessel_k1e(x.w));
+}
+
+template <>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE double2
+pbessel_k1e<double2>(const double2& x) {
+ using numext::bessel_k1e;
+ return make_double2(bessel_k1e(x.x), bessel_k1e(x.y));
+}
+
+template <>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE float4 pbessel_k1<float4>(const float4& x) {
+ using numext::bessel_k1;
+ return make_float4(bessel_k1(x.x), bessel_k1(x.y), bessel_k1(x.z), bessel_k1(x.w));
+}
+
+template <>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE double2
+pbessel_k1<double2>(const double2& x) {
+ using numext::bessel_k1;
+ return make_double2(bessel_k1(x.x), bessel_k1(x.y));
+}
+
+template <>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE float4 pbessel_j0<float4>(const float4& x) {
+ using numext::bessel_j0;
+ return make_float4(bessel_j0(x.x), bessel_j0(x.y), bessel_j0(x.z), bessel_j0(x.w));
+}
+
+template <>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE double2
+pbessel_j0<double2>(const double2& x) {
+ using numext::bessel_j0;
+ return make_double2(bessel_j0(x.x), bessel_j0(x.y));
+}
+
+template <>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE float4 pbessel_j1<float4>(const float4& x) {
+ using numext::bessel_j1;
+ return make_float4(bessel_j1(x.x), bessel_j1(x.y), bessel_j1(x.z), bessel_j1(x.w));
+}
+
+template <>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE double2
+pbessel_j1<double2>(const double2& x) {
+ using numext::bessel_j1;
+ return make_double2(bessel_j1(x.x), bessel_j1(x.y));
+}
+
+template <>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE float4 pbessel_y0<float4>(const float4& x) {
+ using numext::bessel_y0;
+ return make_float4(bessel_y0(x.x), bessel_y0(x.y), bessel_y0(x.z), bessel_y0(x.w));
+}
+
+template <>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE double2
+pbessel_y0<double2>(const double2& x) {
+ using numext::bessel_y0;
+ return make_double2(bessel_y0(x.x), bessel_y0(x.y));
+}
+
+template <>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE float4 pbessel_y1<float4>(const float4& x) {
+ using numext::bessel_y1;
+ return make_float4(bessel_y1(x.x), bessel_y1(x.y), bessel_y1(x.z), bessel_y1(x.w));
+}
+
+template <>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE double2
+pbessel_y1<double2>(const double2& x) {
+ using numext::bessel_y1;
+ return make_double2(bessel_y1(x.x), bessel_y1(x.y));
+}
+
+#endif
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_GPU_SPECIALFUNCTIONS_H
diff --git a/unsupported/Eigen/src/SpecialFunctions/arch/NEON/BesselFunctions.h b/unsupported/Eigen/src/SpecialFunctions/arch/NEON/BesselFunctions.h
new file mode 100644
index 0000000..67433b0
--- /dev/null
+++ b/unsupported/Eigen/src/SpecialFunctions/arch/NEON/BesselFunctions.h
@@ -0,0 +1,54 @@
+#ifndef EIGEN_NEON_BESSELFUNCTIONS_H
+#define EIGEN_NEON_BESSELFUNCTIONS_H
+
+namespace Eigen {
+namespace internal {
+
+#if EIGEN_HAS_ARM64_FP16_VECTOR_ARITHMETIC
+
+#define NEON_HALF_TO_FLOAT_FUNCTIONS(METHOD) \
+template <> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE \
+Packet8hf METHOD<Packet8hf>(const Packet8hf& x) { \
+ const Packet4f lo = METHOD<Packet4f>(vcvt_f32_f16(vget_low_f16(x))); \
+ const Packet4f hi = METHOD<Packet4f>(vcvt_f32_f16(vget_high_f16(x))); \
+ return vcombine_f16(vcvt_f16_f32(lo), vcvt_f16_f32(hi)); \
+} \
+ \
+template <> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE \
+Packet4hf METHOD<Packet4hf>(const Packet4hf& x) { \
+ return vcvt_f16_f32(METHOD<Packet4f>(vcvt_f32_f16(x))); \
+}
+
+NEON_HALF_TO_FLOAT_FUNCTIONS(pbessel_i0)
+NEON_HALF_TO_FLOAT_FUNCTIONS(pbessel_i0e)
+NEON_HALF_TO_FLOAT_FUNCTIONS(pbessel_i1)
+NEON_HALF_TO_FLOAT_FUNCTIONS(pbessel_i1e)
+NEON_HALF_TO_FLOAT_FUNCTIONS(pbessel_j0)
+NEON_HALF_TO_FLOAT_FUNCTIONS(pbessel_j1)
+NEON_HALF_TO_FLOAT_FUNCTIONS(pbessel_k0)
+NEON_HALF_TO_FLOAT_FUNCTIONS(pbessel_k0e)
+NEON_HALF_TO_FLOAT_FUNCTIONS(pbessel_k1)
+NEON_HALF_TO_FLOAT_FUNCTIONS(pbessel_k1e)
+NEON_HALF_TO_FLOAT_FUNCTIONS(pbessel_y0)
+NEON_HALF_TO_FLOAT_FUNCTIONS(pbessel_y1)
+
+#undef NEON_HALF_TO_FLOAT_FUNCTIONS
+#endif
+
+BF16_PACKET_FUNCTION(Packet4f, Packet4bf, pbessel_i0)
+BF16_PACKET_FUNCTION(Packet4f, Packet4bf, pbessel_i0e)
+BF16_PACKET_FUNCTION(Packet4f, Packet4bf, pbessel_i1)
+BF16_PACKET_FUNCTION(Packet4f, Packet4bf, pbessel_i1e)
+BF16_PACKET_FUNCTION(Packet4f, Packet4bf, pbessel_j0)
+BF16_PACKET_FUNCTION(Packet4f, Packet4bf, pbessel_j1)
+BF16_PACKET_FUNCTION(Packet4f, Packet4bf, pbessel_k0)
+BF16_PACKET_FUNCTION(Packet4f, Packet4bf, pbessel_k0e)
+BF16_PACKET_FUNCTION(Packet4f, Packet4bf, pbessel_k1)
+BF16_PACKET_FUNCTION(Packet4f, Packet4bf, pbessel_k1e)
+BF16_PACKET_FUNCTION(Packet4f, Packet4bf, pbessel_y0)
+BF16_PACKET_FUNCTION(Packet4f, Packet4bf, pbessel_y1)
+
+} // namespace internal
+} // namespace Eigen
+
+#endif // EIGEN_NEON_BESSELFUNCTIONS_H
diff --git a/unsupported/Eigen/src/SpecialFunctions/arch/NEON/SpecialFunctions.h b/unsupported/Eigen/src/SpecialFunctions/arch/NEON/SpecialFunctions.h
new file mode 100644
index 0000000..ec92951
--- /dev/null
+++ b/unsupported/Eigen/src/SpecialFunctions/arch/NEON/SpecialFunctions.h
@@ -0,0 +1,34 @@
+#ifndef EIGEN_NEON_SPECIALFUNCTIONS_H
+#define EIGEN_NEON_SPECIALFUNCTIONS_H
+
+namespace Eigen {
+namespace internal {
+
+#if EIGEN_HAS_ARM64_FP16_VECTOR_ARITHMETIC
+
+#define NEON_HALF_TO_FLOAT_FUNCTIONS(METHOD) \
+template <> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE \
+Packet8hf METHOD<Packet8hf>(const Packet8hf& x) { \
+ const Packet4f lo = METHOD<Packet4f>(vcvt_f32_f16(vget_low_f16(x))); \
+ const Packet4f hi = METHOD<Packet4f>(vcvt_f32_f16(vget_high_f16(x))); \
+ return vcombine_f16(vcvt_f16_f32(lo), vcvt_f16_f32(hi)); \
+} \
+ \
+template <> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE \
+Packet4hf METHOD<Packet4hf>(const Packet4hf& x) { \
+ return vcvt_f16_f32(METHOD<Packet4f>(vcvt_f32_f16(x))); \
+}
+
+NEON_HALF_TO_FLOAT_FUNCTIONS(perf)
+NEON_HALF_TO_FLOAT_FUNCTIONS(pndtri)
+
+#undef NEON_HALF_TO_FLOAT_FUNCTIONS
+#endif
+
+BF16_PACKET_FUNCTION(Packet4f, Packet4bf, perf)
+BF16_PACKET_FUNCTION(Packet4f, Packet4bf, pndtri)
+
+} // namespace internal
+} // namespace Eigen
+
+#endif // EIGEN_NEON_SPECIALFUNCTIONS_H
diff --git a/unsupported/Eigen/src/Splines/InternalHeaderCheck.h b/unsupported/Eigen/src/Splines/InternalHeaderCheck.h
new file mode 100644
index 0000000..4a6087e
--- /dev/null
+++ b/unsupported/Eigen/src/Splines/InternalHeaderCheck.h
@@ -0,0 +1,3 @@
+#ifndef EIGEN_SPLINES_MODULE_H
+#error "Please include unsupported/Eigen/Splines instead of including headers inside the src directory directly."
+#endif
diff --git a/unsupported/Eigen/src/Splines/Spline.h b/unsupported/Eigen/src/Splines/Spline.h
new file mode 100644
index 0000000..ce786ee
--- /dev/null
+++ b/unsupported/Eigen/src/Splines/Spline.h
@@ -0,0 +1,509 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 20010-2011 Hauke Heibel <hauke.heibel@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_SPLINE_H
+#define EIGEN_SPLINE_H
+
+#include "./InternalHeaderCheck.h"
+
+#include "SplineFwd.h"
+
+namespace Eigen
+{
+ /**
+ * \ingroup Splines_Module
+ * \class Spline
+ * \brief A class representing multi-dimensional spline curves.
+ *
+ * The class represents B-splines with non-uniform knot vectors. Each control
+ * point of the B-spline is associated with a basis function
+ * \f{align*}
+ * C(u) & = \sum_{i=0}^{n}N_{i,p}(u)P_i
+ * \f}
+ *
+ * \tparam Scalar_ The underlying data type (typically float or double)
+ * \tparam Dim_ The curve dimension (e.g. 2 or 3)
+ * \tparam Degree_ Per default set to Dynamic; could be set to the actual desired
+ * degree for optimization purposes (would result in stack allocation
+ * of several temporary variables).
+ **/
+ template <typename Scalar_, int Dim_, int Degree_>
+ class Spline
+ {
+ public:
+ typedef Scalar_ Scalar; /*!< The spline curve's scalar type. */
+ enum { Dimension = Dim_ /*!< The spline curve's dimension. */ };
+ enum { Degree = Degree_ /*!< The spline curve's degree. */ };
+
+ /** \brief The point type the spline is representing. */
+ typedef typename SplineTraits<Spline>::PointType PointType;
+
+ /** \brief The data type used to store knot vectors. */
+ typedef typename SplineTraits<Spline>::KnotVectorType KnotVectorType;
+
+ /** \brief The data type used to store parameter vectors. */
+ typedef typename SplineTraits<Spline>::ParameterVectorType ParameterVectorType;
+
+ /** \brief The data type used to store non-zero basis functions. */
+ typedef typename SplineTraits<Spline>::BasisVectorType BasisVectorType;
+
+ /** \brief The data type used to store the values of the basis function derivatives. */
+ typedef typename SplineTraits<Spline>::BasisDerivativeType BasisDerivativeType;
+
+ /** \brief The data type representing the spline's control points. */
+ typedef typename SplineTraits<Spline>::ControlPointVectorType ControlPointVectorType;
+
+ /**
+ * \brief Creates a (constant) zero spline.
+ * For Splines with dynamic degree, the resulting degree will be 0.
+ **/
+ Spline()
+ : m_knots(1, (Degree==Dynamic ? 2 : 2*Degree+2))
+ , m_ctrls(ControlPointVectorType::Zero(Dimension,(Degree==Dynamic ? 1 : Degree+1)))
+ {
+ // in theory this code can go to the initializer list but it will get pretty
+ // much unreadable ...
+ enum { MinDegree = (Degree==Dynamic ? 0 : Degree) };
+ m_knots.template segment<MinDegree+1>(0) = Array<Scalar,1,MinDegree+1>::Zero();
+ m_knots.template segment<MinDegree+1>(MinDegree+1) = Array<Scalar,1,MinDegree+1>::Ones();
+ }
+
+ /**
+ * \brief Creates a spline from a knot vector and control points.
+ * \param knots The spline's knot vector.
+ * \param ctrls The spline's control point vector.
+ **/
+ template <typename OtherVectorType, typename OtherArrayType>
+ Spline(const OtherVectorType& knots, const OtherArrayType& ctrls) : m_knots(knots), m_ctrls(ctrls) {}
+
+ /**
+ * \brief Copy constructor for splines.
+ * \param spline The input spline.
+ **/
+ template <int OtherDegree>
+ Spline(const Spline<Scalar, Dimension, OtherDegree>& spline) :
+ m_knots(spline.knots()), m_ctrls(spline.ctrls()) {}
+
+ /**
+ * \brief Returns the knots of the underlying spline.
+ **/
+ const KnotVectorType& knots() const { return m_knots; }
+
+ /**
+ * \brief Returns the ctrls of the underlying spline.
+ **/
+ const ControlPointVectorType& ctrls() const { return m_ctrls; }
+
+ /**
+ * \brief Returns the spline value at a given site \f$u\f$.
+ *
+ * The function returns
+ * \f{align*}
+ * C(u) & = \sum_{i=0}^{n}N_{i,p}P_i
+ * \f}
+ *
+ * \param u Parameter \f$u \in [0;1]\f$ at which the spline is evaluated.
+ * \return The spline value at the given location \f$u\f$.
+ **/
+ PointType operator()(Scalar u) const;
+
+ /**
+ * \brief Evaluation of spline derivatives of up-to given order.
+ *
+ * The function returns
+ * \f{align*}
+ * \frac{d^i}{du^i}C(u) & = \sum_{i=0}^{n} \frac{d^i}{du^i} N_{i,p}(u)P_i
+ * \f}
+ * for i ranging between 0 and order.
+ *
+ * \param u Parameter \f$u \in [0;1]\f$ at which the spline derivative is evaluated.
+ * \param order The order up to which the derivatives are computed.
+ **/
+ typename SplineTraits<Spline>::DerivativeType
+ derivatives(Scalar u, DenseIndex order) const;
+
+ /**
+ * \copydoc Spline::derivatives
+ * Using the template version of this function is more efficieent since
+ * temporary objects are allocated on the stack whenever this is possible.
+ **/
+ template <int DerivativeOrder>
+ typename SplineTraits<Spline,DerivativeOrder>::DerivativeType
+ derivatives(Scalar u, DenseIndex order = DerivativeOrder) const;
+
+ /**
+ * \brief Computes the non-zero basis functions at the given site.
+ *
+ * Splines have local support and a point from their image is defined
+ * by exactly \f$p+1\f$ control points \f$P_i\f$ where \f$p\f$ is the
+ * spline degree.
+ *
+ * This function computes the \f$p+1\f$ non-zero basis function values
+ * for a given parameter value \f$u\f$. It returns
+ * \f{align*}{
+ * N_{i,p}(u), \hdots, N_{i+p+1,p}(u)
+ * \f}
+ *
+ * \param u Parameter \f$u \in [0;1]\f$ at which the non-zero basis functions
+ * are computed.
+ **/
+ typename SplineTraits<Spline>::BasisVectorType
+ basisFunctions(Scalar u) const;
+
+ /**
+ * \brief Computes the non-zero spline basis function derivatives up to given order.
+ *
+ * The function computes
+ * \f{align*}{
+ * \frac{d^i}{du^i} N_{i,p}(u), \hdots, \frac{d^i}{du^i} N_{i+p+1,p}(u)
+ * \f}
+ * with i ranging from 0 up to the specified order.
+ *
+ * \param u Parameter \f$u \in [0;1]\f$ at which the non-zero basis function
+ * derivatives are computed.
+ * \param order The order up to which the basis function derivatives are computes.
+ **/
+ typename SplineTraits<Spline>::BasisDerivativeType
+ basisFunctionDerivatives(Scalar u, DenseIndex order) const;
+
+ /**
+ * \copydoc Spline::basisFunctionDerivatives
+ * Using the template version of this function is more efficieent since
+ * temporary objects are allocated on the stack whenever this is possible.
+ **/
+ template <int DerivativeOrder>
+ typename SplineTraits<Spline,DerivativeOrder>::BasisDerivativeType
+ basisFunctionDerivatives(Scalar u, DenseIndex order = DerivativeOrder) const;
+
+ /**
+ * \brief Returns the spline degree.
+ **/
+ DenseIndex degree() const;
+
+ /**
+ * \brief Returns the span within the knot vector in which u is falling.
+ * \param u The site for which the span is determined.
+ **/
+ DenseIndex span(Scalar u) const;
+
+ /**
+ * \brief Computes the span within the provided knot vector in which u is falling.
+ **/
+ static DenseIndex Span(typename SplineTraits<Spline>::Scalar u, DenseIndex degree, const typename SplineTraits<Spline>::KnotVectorType& knots);
+
+ /**
+ * \brief Returns the spline's non-zero basis functions.
+ *
+ * The function computes and returns
+ * \f{align*}{
+ * N_{i,p}(u), \hdots, N_{i+p+1,p}(u)
+ * \f}
+ *
+ * \param u The site at which the basis functions are computed.
+ * \param degree The degree of the underlying spline.
+ * \param knots The underlying spline's knot vector.
+ **/
+ static BasisVectorType BasisFunctions(Scalar u, DenseIndex degree, const KnotVectorType& knots);
+
+ /**
+ * \copydoc Spline::basisFunctionDerivatives
+ * \param degree The degree of the underlying spline
+ * \param knots The underlying spline's knot vector.
+ **/
+ static BasisDerivativeType BasisFunctionDerivatives(
+ const Scalar u, const DenseIndex order, const DenseIndex degree, const KnotVectorType& knots);
+
+ private:
+ KnotVectorType m_knots; /*!< Knot vector. */
+ ControlPointVectorType m_ctrls; /*!< Control points. */
+
+ template <typename DerivativeType>
+ static void BasisFunctionDerivativesImpl(
+ const typename Spline<Scalar_, Dim_, Degree_>::Scalar u,
+ const DenseIndex order,
+ const DenseIndex p,
+ const typename Spline<Scalar_, Dim_, Degree_>::KnotVectorType& U,
+ DerivativeType& N_);
+ };
+
+ template <typename Scalar_, int Dim_, int Degree_>
+ DenseIndex Spline<Scalar_, Dim_, Degree_>::Span(
+ typename SplineTraits< Spline<Scalar_, Dim_, Degree_> >::Scalar u,
+ DenseIndex degree,
+ const typename SplineTraits< Spline<Scalar_, Dim_, Degree_> >::KnotVectorType& knots)
+ {
+ // Piegl & Tiller, "The NURBS Book", A2.1 (p. 68)
+ if (u <= knots(0)) return degree;
+ const Scalar* pos = std::upper_bound(knots.data()+degree-1, knots.data()+knots.size()-degree-1, u);
+ return static_cast<DenseIndex>( std::distance(knots.data(), pos) - 1 );
+ }
+
+ template <typename Scalar_, int Dim_, int Degree_>
+ typename Spline<Scalar_, Dim_, Degree_>::BasisVectorType
+ Spline<Scalar_, Dim_, Degree_>::BasisFunctions(
+ typename Spline<Scalar_, Dim_, Degree_>::Scalar u,
+ DenseIndex degree,
+ const typename Spline<Scalar_, Dim_, Degree_>::KnotVectorType& knots)
+ {
+ const DenseIndex p = degree;
+ const DenseIndex i = Spline::Span(u, degree, knots);
+
+ const KnotVectorType& U = knots;
+
+ BasisVectorType left(p+1); left(0) = Scalar(0);
+ BasisVectorType right(p+1); right(0) = Scalar(0);
+
+ VectorBlock<BasisVectorType,Degree>(left,1,p) = u - VectorBlock<const KnotVectorType,Degree>(U,i+1-p,p).reverse();
+ VectorBlock<BasisVectorType,Degree>(right,1,p) = VectorBlock<const KnotVectorType,Degree>(U,i+1,p) - u;
+
+ BasisVectorType N(1,p+1);
+ N(0) = Scalar(1);
+ for (DenseIndex j=1; j<=p; ++j)
+ {
+ Scalar saved = Scalar(0);
+ for (DenseIndex r=0; r<j; r++)
+ {
+ const Scalar tmp = N(r)/(right(r+1)+left(j-r));
+ N[r] = saved + right(r+1)*tmp;
+ saved = left(j-r)*tmp;
+ }
+ N(j) = saved;
+ }
+ return N;
+ }
+
+ template <typename Scalar_, int Dim_, int Degree_>
+ DenseIndex Spline<Scalar_, Dim_, Degree_>::degree() const
+ {
+ if (Degree_ == Dynamic)
+ return m_knots.size() - m_ctrls.cols() - 1;
+ else
+ return Degree_;
+ }
+
+ template <typename Scalar_, int Dim_, int Degree_>
+ DenseIndex Spline<Scalar_, Dim_, Degree_>::span(Scalar u) const
+ {
+ return Spline::Span(u, degree(), knots());
+ }
+
+ template <typename Scalar_, int Dim_, int Degree_>
+ typename Spline<Scalar_, Dim_, Degree_>::PointType Spline<Scalar_, Dim_, Degree_>::operator()(Scalar u) const
+ {
+ enum { Order = SplineTraits<Spline>::OrderAtCompileTime };
+
+ const DenseIndex span = this->span(u);
+ const DenseIndex p = degree();
+ const BasisVectorType basis_funcs = basisFunctions(u);
+
+ const Replicate<BasisVectorType,Dimension,1> ctrl_weights(basis_funcs);
+ const Block<const ControlPointVectorType,Dimension,Order> ctrl_pts(ctrls(),0,span-p,Dimension,p+1);
+ return (ctrl_weights * ctrl_pts).rowwise().sum();
+ }
+
+ /* --------------------------------------------------------------------------------------------- */
+
+ template <typename SplineType, typename DerivativeType>
+ void derivativesImpl(const SplineType& spline, typename SplineType::Scalar u, DenseIndex order, DerivativeType& der)
+ {
+ enum { Dimension = SplineTraits<SplineType>::Dimension };
+ enum { Order = SplineTraits<SplineType>::OrderAtCompileTime };
+ enum { DerivativeOrder = DerivativeType::ColsAtCompileTime };
+
+ typedef typename SplineTraits<SplineType>::ControlPointVectorType ControlPointVectorType;
+ typedef typename SplineTraits<SplineType,DerivativeOrder>::BasisDerivativeType BasisDerivativeType;
+ typedef typename BasisDerivativeType::ConstRowXpr BasisDerivativeRowXpr;
+
+ const DenseIndex p = spline.degree();
+ const DenseIndex span = spline.span(u);
+
+ const DenseIndex n = (std::min)(p, order);
+
+ der.resize(Dimension,n+1);
+
+ // Retrieve the basis function derivatives up to the desired order...
+ const BasisDerivativeType basis_func_ders = spline.template basisFunctionDerivatives<DerivativeOrder>(u, n+1);
+
+ // ... and perform the linear combinations of the control points.
+ for (DenseIndex der_order=0; der_order<n+1; ++der_order)
+ {
+ const Replicate<BasisDerivativeRowXpr,Dimension,1> ctrl_weights( basis_func_ders.row(der_order) );
+ const Block<const ControlPointVectorType,Dimension,Order> ctrl_pts(spline.ctrls(),0,span-p,Dimension,p+1);
+ der.col(der_order) = (ctrl_weights * ctrl_pts).rowwise().sum();
+ }
+ }
+
+ template <typename Scalar_, int Dim_, int Degree_>
+ typename SplineTraits< Spline<Scalar_, Dim_, Degree_> >::DerivativeType
+ Spline<Scalar_, Dim_, Degree_>::derivatives(Scalar u, DenseIndex order) const
+ {
+ typename SplineTraits< Spline >::DerivativeType res;
+ derivativesImpl(*this, u, order, res);
+ return res;
+ }
+
+ template <typename Scalar_, int Dim_, int Degree_>
+ template <int DerivativeOrder>
+ typename SplineTraits< Spline<Scalar_, Dim_, Degree_>, DerivativeOrder >::DerivativeType
+ Spline<Scalar_, Dim_, Degree_>::derivatives(Scalar u, DenseIndex order) const
+ {
+ typename SplineTraits< Spline, DerivativeOrder >::DerivativeType res;
+ derivativesImpl(*this, u, order, res);
+ return res;
+ }
+
+ template <typename Scalar_, int Dim_, int Degree_>
+ typename SplineTraits< Spline<Scalar_, Dim_, Degree_> >::BasisVectorType
+ Spline<Scalar_, Dim_, Degree_>::basisFunctions(Scalar u) const
+ {
+ return Spline::BasisFunctions(u, degree(), knots());
+ }
+
+ /* --------------------------------------------------------------------------------------------- */
+
+
+ template <typename Scalar_, int Dim_, int Degree_>
+ template <typename DerivativeType>
+ void Spline<Scalar_, Dim_, Degree_>::BasisFunctionDerivativesImpl(
+ const typename Spline<Scalar_, Dim_, Degree_>::Scalar u,
+ const DenseIndex order,
+ const DenseIndex p,
+ const typename Spline<Scalar_, Dim_, Degree_>::KnotVectorType& U,
+ DerivativeType& N_)
+ {
+ typedef Spline<Scalar_, Dim_, Degree_> SplineType;
+ enum { Order = SplineTraits<SplineType>::OrderAtCompileTime };
+
+ const DenseIndex span = SplineType::Span(u, p, U);
+
+ const DenseIndex n = (std::min)(p, order);
+
+ N_.resize(n+1, p+1);
+
+ BasisVectorType left = BasisVectorType::Zero(p+1);
+ BasisVectorType right = BasisVectorType::Zero(p+1);
+
+ Matrix<Scalar,Order,Order> ndu(p+1,p+1);
+
+ Scalar saved, temp; // FIXME These were double instead of Scalar. Was there a reason for that?
+
+ ndu(0,0) = 1.0;
+
+ DenseIndex j;
+ for (j=1; j<=p; ++j)
+ {
+ left[j] = u-U[span+1-j];
+ right[j] = U[span+j]-u;
+ saved = 0.0;
+
+ for (DenseIndex r=0; r<j; ++r)
+ {
+ /* Lower triangle */
+ ndu(j,r) = right[r+1]+left[j-r];
+ temp = ndu(r,j-1)/ndu(j,r);
+ /* Upper triangle */
+ ndu(r,j) = static_cast<Scalar>(saved+right[r+1] * temp);
+ saved = left[j-r] * temp;
+ }
+
+ ndu(j,j) = static_cast<Scalar>(saved);
+ }
+
+ for (j = p; j>=0; --j)
+ N_(0,j) = ndu(j,p);
+
+ // Compute the derivatives
+ DerivativeType a(n+1,p+1);
+ DenseIndex r=0;
+ for (; r<=p; ++r)
+ {
+ DenseIndex s1,s2;
+ s1 = 0; s2 = 1; // alternate rows in array a
+ a(0,0) = 1.0;
+
+ // Compute the k-th derivative
+ for (DenseIndex k=1; k<=static_cast<DenseIndex>(n); ++k)
+ {
+ Scalar d = 0.0;
+ DenseIndex rk,pk,j1,j2;
+ rk = r-k; pk = p-k;
+
+ if (r>=k)
+ {
+ a(s2,0) = a(s1,0)/ndu(pk+1,rk);
+ d = a(s2,0)*ndu(rk,pk);
+ }
+
+ if (rk>=-1) j1 = 1;
+ else j1 = -rk;
+
+ if (r-1 <= pk) j2 = k-1;
+ else j2 = p-r;
+
+ for (j=j1; j<=j2; ++j)
+ {
+ a(s2,j) = (a(s1,j)-a(s1,j-1))/ndu(pk+1,rk+j);
+ d += a(s2,j)*ndu(rk+j,pk);
+ }
+
+ if (r<=pk)
+ {
+ a(s2,k) = -a(s1,k-1)/ndu(pk+1,r);
+ d += a(s2,k)*ndu(r,pk);
+ }
+
+ N_(k,r) = static_cast<Scalar>(d);
+ j = s1; s1 = s2; s2 = j; // Switch rows
+ }
+ }
+
+ /* Multiply through by the correct factors */
+ /* (Eq. [2.9]) */
+ r = p;
+ for (DenseIndex k=1; k<=static_cast<DenseIndex>(n); ++k)
+ {
+ for (j=p; j>=0; --j) N_(k,j) *= r;
+ r *= p-k;
+ }
+ }
+
+ template <typename Scalar_, int Dim_, int Degree_>
+ typename SplineTraits< Spline<Scalar_, Dim_, Degree_> >::BasisDerivativeType
+ Spline<Scalar_, Dim_, Degree_>::basisFunctionDerivatives(Scalar u, DenseIndex order) const
+ {
+ typename SplineTraits<Spline<Scalar_, Dim_, Degree_> >::BasisDerivativeType der;
+ BasisFunctionDerivativesImpl(u, order, degree(), knots(), der);
+ return der;
+ }
+
+ template <typename Scalar_, int Dim_, int Degree_>
+ template <int DerivativeOrder>
+ typename SplineTraits< Spline<Scalar_, Dim_, Degree_>, DerivativeOrder >::BasisDerivativeType
+ Spline<Scalar_, Dim_, Degree_>::basisFunctionDerivatives(Scalar u, DenseIndex order) const
+ {
+ typename SplineTraits< Spline<Scalar_, Dim_, Degree_>, DerivativeOrder >::BasisDerivativeType der;
+ BasisFunctionDerivativesImpl(u, order, degree(), knots(), der);
+ return der;
+ }
+
+ template <typename Scalar_, int Dim_, int Degree_>
+ typename SplineTraits<Spline<Scalar_, Dim_, Degree_> >::BasisDerivativeType
+ Spline<Scalar_, Dim_, Degree_>::BasisFunctionDerivatives(
+ const typename Spline<Scalar_, Dim_, Degree_>::Scalar u,
+ const DenseIndex order,
+ const DenseIndex degree,
+ const typename Spline<Scalar_, Dim_, Degree_>::KnotVectorType& knots)
+ {
+ typename SplineTraits<Spline>::BasisDerivativeType der;
+ BasisFunctionDerivativesImpl(u, order, degree, knots, der);
+ return der;
+ }
+}
+
+#endif // EIGEN_SPLINE_H
diff --git a/unsupported/Eigen/src/Splines/SplineFitting.h b/unsupported/Eigen/src/Splines/SplineFitting.h
new file mode 100644
index 0000000..fe70658
--- /dev/null
+++ b/unsupported/Eigen/src/Splines/SplineFitting.h
@@ -0,0 +1,434 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 20010-2011 Hauke Heibel <hauke.heibel@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_SPLINE_FITTING_H
+#define EIGEN_SPLINE_FITTING_H
+
+#include <algorithm>
+#include <functional>
+#include <numeric>
+#include <vector>
+
+#include "./InternalHeaderCheck.h"
+
+#include "SplineFwd.h"
+
+#include "../../../../Eigen/LU"
+#include "../../../../Eigen/QR"
+
+
+namespace Eigen
+{
+ /**
+ * \brief Computes knot averages.
+ * \ingroup Splines_Module
+ *
+ * The knots are computed as
+ * \f{align*}
+ * u_0 & = \hdots = u_p = 0 \\
+ * u_{m-p} & = \hdots = u_{m} = 1 \\
+ * u_{j+p} & = \frac{1}{p}\sum_{i=j}^{j+p-1}\bar{u}_i \quad\quad j=1,\hdots,n-p
+ * \f}
+ * where \f$p\f$ is the degree and \f$m+1\f$ the number knots
+ * of the desired interpolating spline.
+ *
+ * \param[in] parameters The input parameters. During interpolation one for each data point.
+ * \param[in] degree The spline degree which is used during the interpolation.
+ * \param[out] knots The output knot vector.
+ *
+ * \sa Les Piegl and Wayne Tiller, The NURBS book (2nd ed.), 1997, 9.2.1 Global Curve Interpolation to Point Data
+ **/
+ template <typename KnotVectorType>
+ void KnotAveraging(const KnotVectorType& parameters, DenseIndex degree, KnotVectorType& knots)
+ {
+ knots.resize(parameters.size()+degree+1);
+
+ for (DenseIndex j=1; j<parameters.size()-degree; ++j)
+ knots(j+degree) = parameters.segment(j,degree).mean();
+
+ knots.segment(0,degree+1) = KnotVectorType::Zero(degree+1);
+ knots.segment(knots.size()-degree-1,degree+1) = KnotVectorType::Ones(degree+1);
+ }
+
+ /**
+ * \brief Computes knot averages when derivative constraints are present.
+ * Note that this is a technical interpretation of the referenced article
+ * since the algorithm contained therein is incorrect as written.
+ * \ingroup Splines_Module
+ *
+ * \param[in] parameters The parameters at which the interpolation B-Spline
+ * will intersect the given interpolation points. The parameters
+ * are assumed to be a non-decreasing sequence.
+ * \param[in] degree The degree of the interpolating B-Spline. This must be
+ * greater than zero.
+ * \param[in] derivativeIndices The indices corresponding to parameters at
+ * which there are derivative constraints. The indices are assumed
+ * to be a non-decreasing sequence.
+ * \param[out] knots The calculated knot vector. These will be returned as a
+ * non-decreasing sequence
+ *
+ * \sa Les A. Piegl, Khairan Rajab, Volha Smarodzinana. 2008.
+ * Curve interpolation with directional constraints for engineering design.
+ * Engineering with Computers
+ **/
+ template <typename KnotVectorType, typename ParameterVectorType, typename IndexArray>
+ void KnotAveragingWithDerivatives(const ParameterVectorType& parameters,
+ const unsigned int degree,
+ const IndexArray& derivativeIndices,
+ KnotVectorType& knots)
+ {
+ typedef typename ParameterVectorType::Scalar Scalar;
+
+ DenseIndex numParameters = parameters.size();
+ DenseIndex numDerivatives = derivativeIndices.size();
+
+ if (numDerivatives < 1)
+ {
+ KnotAveraging(parameters, degree, knots);
+ return;
+ }
+
+ DenseIndex startIndex;
+ DenseIndex endIndex;
+
+ DenseIndex numInternalDerivatives = numDerivatives;
+
+ if (derivativeIndices[0] == 0)
+ {
+ startIndex = 0;
+ --numInternalDerivatives;
+ }
+ else
+ {
+ startIndex = 1;
+ }
+ if (derivativeIndices[numDerivatives - 1] == numParameters - 1)
+ {
+ endIndex = numParameters - degree;
+ --numInternalDerivatives;
+ }
+ else
+ {
+ endIndex = numParameters - degree - 1;
+ }
+
+ // There are (endIndex - startIndex + 1) knots obtained from the averaging
+ // and 2 for the first and last parameters.
+ DenseIndex numAverageKnots = endIndex - startIndex + 3;
+ KnotVectorType averageKnots(numAverageKnots);
+ averageKnots[0] = parameters[0];
+
+ int newKnotIndex = 0;
+ for (DenseIndex i = startIndex; i <= endIndex; ++i)
+ averageKnots[++newKnotIndex] = parameters.segment(i, degree).mean();
+ averageKnots[++newKnotIndex] = parameters[numParameters - 1];
+
+ newKnotIndex = -1;
+
+ ParameterVectorType temporaryParameters(numParameters + 1);
+ KnotVectorType derivativeKnots(numInternalDerivatives);
+ for (DenseIndex i = 0; i < numAverageKnots - 1; ++i)
+ {
+ temporaryParameters[0] = averageKnots[i];
+ ParameterVectorType parameterIndices(numParameters);
+ int temporaryParameterIndex = 1;
+ for (DenseIndex j = 0; j < numParameters; ++j)
+ {
+ Scalar parameter = parameters[j];
+ if (parameter >= averageKnots[i] && parameter < averageKnots[i + 1])
+ {
+ parameterIndices[temporaryParameterIndex] = j;
+ temporaryParameters[temporaryParameterIndex++] = parameter;
+ }
+ }
+ temporaryParameters[temporaryParameterIndex] = averageKnots[i + 1];
+
+ for (int j = 0; j <= temporaryParameterIndex - 2; ++j)
+ {
+ for (DenseIndex k = 0; k < derivativeIndices.size(); ++k)
+ {
+ if (parameterIndices[j + 1] == derivativeIndices[k]
+ && parameterIndices[j + 1] != 0
+ && parameterIndices[j + 1] != numParameters - 1)
+ {
+ derivativeKnots[++newKnotIndex] = temporaryParameters.segment(j, 3).mean();
+ break;
+ }
+ }
+ }
+ }
+
+ KnotVectorType temporaryKnots(averageKnots.size() + derivativeKnots.size());
+
+ std::merge(averageKnots.data(), averageKnots.data() + averageKnots.size(),
+ derivativeKnots.data(), derivativeKnots.data() + derivativeKnots.size(),
+ temporaryKnots.data());
+
+ // Number of knots (one for each point and derivative) plus spline order.
+ DenseIndex numKnots = numParameters + numDerivatives + degree + 1;
+ knots.resize(numKnots);
+
+ knots.head(degree).fill(temporaryKnots[0]);
+ knots.tail(degree).fill(temporaryKnots.template tail<1>()[0]);
+ knots.segment(degree, temporaryKnots.size()) = temporaryKnots;
+ }
+
+ /**
+ * \brief Computes chord length parameters which are required for spline interpolation.
+ * \ingroup Splines_Module
+ *
+ * \param[in] pts The data points to which a spline should be fit.
+ * \param[out] chord_lengths The resulting chord length vector.
+ *
+ * \sa Les Piegl and Wayne Tiller, The NURBS book (2nd ed.), 1997, 9.2.1 Global Curve Interpolation to Point Data
+ **/
+ template <typename PointArrayType, typename KnotVectorType>
+ void ChordLengths(const PointArrayType& pts, KnotVectorType& chord_lengths)
+ {
+ typedef typename KnotVectorType::Scalar Scalar;
+
+ const DenseIndex n = pts.cols();
+
+ // 1. compute the column-wise norms
+ chord_lengths.resize(pts.cols());
+ chord_lengths[0] = 0;
+ chord_lengths.rightCols(n-1) = (pts.array().leftCols(n-1) - pts.array().rightCols(n-1)).matrix().colwise().norm();
+
+ // 2. compute the partial sums
+ std::partial_sum(chord_lengths.data(), chord_lengths.data()+n, chord_lengths.data());
+
+ // 3. normalize the data
+ chord_lengths /= chord_lengths(n-1);
+ chord_lengths(n-1) = Scalar(1);
+ }
+
+ /**
+ * \brief Spline fitting methods.
+ * \ingroup Splines_Module
+ **/
+ template <typename SplineType>
+ struct SplineFitting
+ {
+ typedef typename SplineType::KnotVectorType KnotVectorType;
+ typedef typename SplineType::ParameterVectorType ParameterVectorType;
+
+ /**
+ * \brief Fits an interpolating Spline to the given data points.
+ *
+ * \param pts The points for which an interpolating spline will be computed.
+ * \param degree The degree of the interpolating spline.
+ *
+ * \returns A spline interpolating the initially provided points.
+ **/
+ template <typename PointArrayType>
+ static SplineType Interpolate(const PointArrayType& pts, DenseIndex degree);
+
+ /**
+ * \brief Fits an interpolating Spline to the given data points.
+ *
+ * \param pts The points for which an interpolating spline will be computed.
+ * \param degree The degree of the interpolating spline.
+ * \param knot_parameters The knot parameters for the interpolation.
+ *
+ * \returns A spline interpolating the initially provided points.
+ **/
+ template <typename PointArrayType>
+ static SplineType Interpolate(const PointArrayType& pts, DenseIndex degree, const KnotVectorType& knot_parameters);
+
+ /**
+ * \brief Fits an interpolating spline to the given data points and
+ * derivatives.
+ *
+ * \param points The points for which an interpolating spline will be computed.
+ * \param derivatives The desired derivatives of the interpolating spline at interpolation
+ * points.
+ * \param derivativeIndices An array indicating which point each derivative belongs to. This
+ * must be the same size as @a derivatives.
+ * \param degree The degree of the interpolating spline.
+ *
+ * \returns A spline interpolating @a points with @a derivatives at those points.
+ *
+ * \sa Les A. Piegl, Khairan Rajab, Volha Smarodzinana. 2008.
+ * Curve interpolation with directional constraints for engineering design.
+ * Engineering with Computers
+ **/
+ template <typename PointArrayType, typename IndexArray>
+ static SplineType InterpolateWithDerivatives(const PointArrayType& points,
+ const PointArrayType& derivatives,
+ const IndexArray& derivativeIndices,
+ const unsigned int degree);
+
+ /**
+ * \brief Fits an interpolating spline to the given data points and derivatives.
+ *
+ * \param points The points for which an interpolating spline will be computed.
+ * \param derivatives The desired derivatives of the interpolating spline at interpolation points.
+ * \param derivativeIndices An array indicating which point each derivative belongs to. This
+ * must be the same size as @a derivatives.
+ * \param degree The degree of the interpolating spline.
+ * \param parameters The parameters corresponding to the interpolation points.
+ *
+ * \returns A spline interpolating @a points with @a derivatives at those points.
+ *
+ * \sa Les A. Piegl, Khairan Rajab, Volha Smarodzinana. 2008.
+ * Curve interpolation with directional constraints for engineering design.
+ * Engineering with Computers
+ */
+ template <typename PointArrayType, typename IndexArray>
+ static SplineType InterpolateWithDerivatives(const PointArrayType& points,
+ const PointArrayType& derivatives,
+ const IndexArray& derivativeIndices,
+ const unsigned int degree,
+ const ParameterVectorType& parameters);
+ };
+
+ template <typename SplineType>
+ template <typename PointArrayType>
+ SplineType SplineFitting<SplineType>::Interpolate(const PointArrayType& pts, DenseIndex degree, const KnotVectorType& knot_parameters)
+ {
+ typedef typename SplineType::KnotVectorType::Scalar Scalar;
+ typedef typename SplineType::ControlPointVectorType ControlPointVectorType;
+
+ typedef Matrix<Scalar,Dynamic,Dynamic> MatrixType;
+
+ KnotVectorType knots;
+ KnotAveraging(knot_parameters, degree, knots);
+
+ DenseIndex n = pts.cols();
+ MatrixType A = MatrixType::Zero(n,n);
+ for (DenseIndex i=1; i<n-1; ++i)
+ {
+ const DenseIndex span = SplineType::Span(knot_parameters[i], degree, knots);
+
+ // The segment call should somehow be told the spline order at compile time.
+ A.row(i).segment(span-degree, degree+1) = SplineType::BasisFunctions(knot_parameters[i], degree, knots);
+ }
+ A(0,0) = 1.0;
+ A(n-1,n-1) = 1.0;
+
+ HouseholderQR<MatrixType> qr(A);
+
+ // Here, we are creating a temporary due to an Eigen issue.
+ ControlPointVectorType ctrls = qr.solve(MatrixType(pts.transpose())).transpose();
+
+ return SplineType(knots, ctrls);
+ }
+
+ template <typename SplineType>
+ template <typename PointArrayType>
+ SplineType SplineFitting<SplineType>::Interpolate(const PointArrayType& pts, DenseIndex degree)
+ {
+ KnotVectorType chord_lengths; // knot parameters
+ ChordLengths(pts, chord_lengths);
+ return Interpolate(pts, degree, chord_lengths);
+ }
+
+ template <typename SplineType>
+ template <typename PointArrayType, typename IndexArray>
+ SplineType
+ SplineFitting<SplineType>::InterpolateWithDerivatives(const PointArrayType& points,
+ const PointArrayType& derivatives,
+ const IndexArray& derivativeIndices,
+ const unsigned int degree,
+ const ParameterVectorType& parameters)
+ {
+ typedef typename SplineType::KnotVectorType::Scalar Scalar;
+ typedef typename SplineType::ControlPointVectorType ControlPointVectorType;
+
+ typedef Matrix<Scalar, Dynamic, Dynamic> MatrixType;
+
+ const DenseIndex n = points.cols() + derivatives.cols();
+
+ KnotVectorType knots;
+
+ KnotAveragingWithDerivatives(parameters, degree, derivativeIndices, knots);
+
+ // fill matrix
+ MatrixType A = MatrixType::Zero(n, n);
+
+ // Use these dimensions for quicker populating, then transpose for solving.
+ MatrixType b(points.rows(), n);
+
+ DenseIndex startRow;
+ DenseIndex derivativeStart;
+
+ // End derivatives.
+ if (derivativeIndices[0] == 0)
+ {
+ A.template block<1, 2>(1, 0) << -1, 1;
+
+ Scalar y = (knots(degree + 1) - knots(0)) / degree;
+ b.col(1) = y*derivatives.col(0);
+
+ startRow = 2;
+ derivativeStart = 1;
+ }
+ else
+ {
+ startRow = 1;
+ derivativeStart = 0;
+ }
+ if (derivativeIndices[derivatives.cols() - 1] == points.cols() - 1)
+ {
+ A.template block<1, 2>(n - 2, n - 2) << -1, 1;
+
+ Scalar y = (knots(knots.size() - 1) - knots(knots.size() - (degree + 2))) / degree;
+ b.col(b.cols() - 2) = y*derivatives.col(derivatives.cols() - 1);
+ }
+
+ DenseIndex row = startRow;
+ DenseIndex derivativeIndex = derivativeStart;
+ for (DenseIndex i = 1; i < parameters.size() - 1; ++i)
+ {
+ const DenseIndex span = SplineType::Span(parameters[i], degree, knots);
+
+ if (derivativeIndex < derivativeIndices.size() && derivativeIndices[derivativeIndex] == i)
+ {
+ A.block(row, span - degree, 2, degree + 1)
+ = SplineType::BasisFunctionDerivatives(parameters[i], 1, degree, knots);
+
+ b.col(row++) = points.col(i);
+ b.col(row++) = derivatives.col(derivativeIndex++);
+ }
+ else
+ {
+ A.row(row).segment(span - degree, degree + 1)
+ = SplineType::BasisFunctions(parameters[i], degree, knots);
+ b.col(row++) = points.col(i);
+ }
+ }
+ b.col(0) = points.col(0);
+ b.col(b.cols() - 1) = points.col(points.cols() - 1);
+ A(0,0) = 1;
+ A(n - 1, n - 1) = 1;
+
+ // Solve
+ FullPivLU<MatrixType> lu(A);
+ ControlPointVectorType controlPoints = lu.solve(MatrixType(b.transpose())).transpose();
+
+ SplineType spline(knots, controlPoints);
+
+ return spline;
+ }
+
+ template <typename SplineType>
+ template <typename PointArrayType, typename IndexArray>
+ SplineType
+ SplineFitting<SplineType>::InterpolateWithDerivatives(const PointArrayType& points,
+ const PointArrayType& derivatives,
+ const IndexArray& derivativeIndices,
+ const unsigned int degree)
+ {
+ ParameterVectorType parameters;
+ ChordLengths(points, parameters);
+ return InterpolateWithDerivatives(points, derivatives, derivativeIndices, degree, parameters);
+ }
+}
+
+#endif // EIGEN_SPLINE_FITTING_H
diff --git a/unsupported/Eigen/src/Splines/SplineFwd.h b/unsupported/Eigen/src/Splines/SplineFwd.h
new file mode 100644
index 0000000..2cc0977
--- /dev/null
+++ b/unsupported/Eigen/src/Splines/SplineFwd.h
@@ -0,0 +1,94 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 20010-2011 Hauke Heibel <hauke.heibel@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_SPLINES_FWD_H
+#define EIGEN_SPLINES_FWD_H
+
+#include "./InternalHeaderCheck.h"
+#include "../../../../Eigen/Core"
+
+namespace Eigen
+{
+ template <typename Scalar, int Dim, int Degree = Dynamic> class Spline;
+
+ template < typename SplineType, int DerivativeOrder = Dynamic > struct SplineTraits {};
+
+ /**
+ * \ingroup Splines_Module
+ * \brief Compile-time attributes of the Spline class for Dynamic degree.
+ **/
+ template <typename Scalar_, int Dim_, int Degree_>
+ struct SplineTraits< Spline<Scalar_, Dim_, Degree_>, Dynamic >
+ {
+ typedef Scalar_ Scalar; /*!< The spline curve's scalar type. */
+ enum { Dimension = Dim_ /*!< The spline curve's dimension. */ };
+ enum { Degree = Degree_ /*!< The spline curve's degree. */ };
+
+ enum { OrderAtCompileTime = Degree_==Dynamic ? Dynamic : Degree_+1 /*!< The spline curve's order at compile-time. */ };
+ enum { NumOfDerivativesAtCompileTime = OrderAtCompileTime /*!< The number of derivatives defined for the current spline. */ };
+
+ enum { DerivativeMemoryLayout = Dimension==1 ? RowMajor : ColMajor /*!< The derivative type's memory layout. */ };
+
+ /** \brief The data type used to store non-zero basis functions. */
+ typedef Array<Scalar,1,OrderAtCompileTime> BasisVectorType;
+
+ /** \brief The data type used to store the values of the basis function derivatives. */
+ typedef Array<Scalar,Dynamic,Dynamic,RowMajor,NumOfDerivativesAtCompileTime,OrderAtCompileTime> BasisDerivativeType;
+
+ /** \brief The data type used to store the spline's derivative values. */
+ typedef Array<Scalar,Dimension,Dynamic,DerivativeMemoryLayout,Dimension,NumOfDerivativesAtCompileTime> DerivativeType;
+
+ /** \brief The point type the spline is representing. */
+ typedef Array<Scalar,Dimension,1> PointType;
+
+ /** \brief The data type used to store knot vectors. */
+ typedef Array<Scalar,1,Dynamic> KnotVectorType;
+
+ /** \brief The data type used to store parameter vectors. */
+ typedef Array<Scalar,1,Dynamic> ParameterVectorType;
+
+ /** \brief The data type representing the spline's control points. */
+ typedef Array<Scalar,Dimension,Dynamic> ControlPointVectorType;
+ };
+
+ /**
+ * \ingroup Splines_Module
+ * \brief Compile-time attributes of the Spline class for fixed degree.
+ *
+ * The traits class inherits all attributes from the SplineTraits of Dynamic degree.
+ **/
+ template < typename Scalar_, int Dim_, int Degree_, int _DerivativeOrder >
+ struct SplineTraits< Spline<Scalar_, Dim_, Degree_>, _DerivativeOrder > : public SplineTraits< Spline<Scalar_, Dim_, Degree_> >
+ {
+ enum { OrderAtCompileTime = Degree_==Dynamic ? Dynamic : Degree_+1 /*!< The spline curve's order at compile-time. */ };
+ enum { NumOfDerivativesAtCompileTime = _DerivativeOrder==Dynamic ? Dynamic : _DerivativeOrder+1 /*!< The number of derivatives defined for the current spline. */ };
+
+ enum { DerivativeMemoryLayout = Dim_==1 ? RowMajor : ColMajor /*!< The derivative type's memory layout. */ };
+
+ /** \brief The data type used to store the values of the basis function derivatives. */
+ typedef Array<Scalar_,Dynamic,Dynamic,RowMajor,NumOfDerivativesAtCompileTime,OrderAtCompileTime> BasisDerivativeType;
+
+ /** \brief The data type used to store the spline's derivative values. */
+ typedef Array<Scalar_,Dim_,Dynamic,DerivativeMemoryLayout,Dim_,NumOfDerivativesAtCompileTime> DerivativeType;
+ };
+
+ /** \brief 2D float B-spline with dynamic degree. */
+ typedef Spline<float,2> Spline2f;
+
+ /** \brief 3D float B-spline with dynamic degree. */
+ typedef Spline<float,3> Spline3f;
+
+ /** \brief 2D double B-spline with dynamic degree. */
+ typedef Spline<double,2> Spline2d;
+
+ /** \brief 3D double B-spline with dynamic degree. */
+ typedef Spline<double,3> Spline3d;
+}
+
+#endif // EIGEN_SPLINES_FWD_H
diff --git a/unsupported/README.txt b/unsupported/README.txt
new file mode 100644
index 0000000..70793bf
--- /dev/null
+++ b/unsupported/README.txt
@@ -0,0 +1,50 @@
+This directory contains contributions from various users.
+They are provided "as is", without any support. Nevertheless,
+most of them are subject to be included in Eigen in the future.
+
+In order to use an unsupported module you have to do either:
+
+ - add the path_to_eigen/unsupported directory to your include path and do:
+ #include <Eigen/ModuleHeader>
+
+ - or directly do:
+ #include <unsupported/Eigen/ModuleHeader>
+
+
+If you are interested in contributing to one of them, or have other stuff
+you would like to share, feel free to contact us:
+http://eigen.tuxfamily.org/index.php?title=Main_Page#Mailing_list
+
+Any kind of contributions are much appreciated, even very preliminary ones.
+However, it:
+ - must rely on Eigen,
+ - must be highly related to math,
+ - should have some general purpose in the sense that it could
+ potentially become an official Eigen module (or be merged into another one).
+
+In doubt feel free to contact us. For instance, if your addons is very too specific
+but it shows an interesting way of using Eigen, then it could be a nice demo.
+
+
+This directory is organized as follow:
+
+unsupported/Eigen/ModuleHeader1
+unsupported/Eigen/ModuleHeader2
+unsupported/Eigen/...
+unsupported/Eigen/src/Module1/SourceFile1.h
+unsupported/Eigen/src/Module1/SourceFile2.h
+unsupported/Eigen/src/Module1/...
+unsupported/Eigen/src/Module2/SourceFile1.h
+unsupported/Eigen/src/Module2/SourceFile2.h
+unsupported/Eigen/src/Module2/...
+unsupported/Eigen/src/...
+unsupported/doc/snippets/.cpp <- code snippets for the doc
+unsupported/doc/examples/.cpp <- examples for the doc
+unsupported/doc/TutorialModule1.dox
+unsupported/doc/TutorialModule2.dox
+unsupported/doc/...
+unsupported/test/.cpp <- unit test files
+
+The documentation is generated at the same time than the main Eigen documentation.
+The .html files are generated in: build_dir/doc/html/unsupported/
+
diff --git a/unsupported/bench/bench_svd.cpp b/unsupported/bench/bench_svd.cpp
new file mode 100644
index 0000000..e7028a2
--- /dev/null
+++ b/unsupported/bench/bench_svd.cpp
@@ -0,0 +1,123 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2013 Gauthier Brun <brun.gauthier@gmail.com>
+// Copyright (C) 2013 Nicolas Carre <nicolas.carre@ensimag.fr>
+// Copyright (C) 2013 Jean Ceccato <jean.ceccato@ensimag.fr>
+// Copyright (C) 2013 Pierre Zoppitelli <pierre.zoppitelli@ensimag.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/
+
+// Bench to compare the efficiency of SVD algorithms
+
+#include <iostream>
+#include <bench/BenchTimer.h>
+#include <unsupported/Eigen/SVD>
+
+
+using namespace Eigen;
+using namespace std;
+
+// number of computations of each algorithm before the print of the time
+#ifndef REPEAT
+#define REPEAT 10
+#endif
+
+// number of tests of the same type
+#ifndef NUMBER_SAMPLE
+#define NUMBER_SAMPLE 2
+#endif
+
+template<typename MatrixType>
+void bench_svd(const MatrixType& a = MatrixType())
+{
+ MatrixType m = MatrixType::Random(a.rows(), a.cols());
+ BenchTimer timerJacobi;
+ BenchTimer timerBDC;
+ timerJacobi.reset();
+ timerBDC.reset();
+
+ cout << " Only compute Singular Values" <<endl;
+ for (int k=1; k<=NUMBER_SAMPLE; ++k)
+ {
+ timerBDC.start();
+ for (int i=0; i<REPEAT; ++i)
+ {
+ BDCSVD<MatrixType> bdc_matrix(m);
+ }
+ timerBDC.stop();
+
+ timerJacobi.start();
+ for (int i=0; i<REPEAT; ++i)
+ {
+ JacobiSVD<MatrixType> jacobi_matrix(m);
+ }
+ timerJacobi.stop();
+
+
+ cout << "Sample " << k << " : " << REPEAT << " computations : Jacobi : " << fixed << timerJacobi.value() << "s ";
+ cout << " || " << " BDC : " << timerBDC.value() << "s " <<endl <<endl;
+
+ if (timerBDC.value() >= timerJacobi.value())
+ cout << "KO : BDC is " << timerJacobi.value() / timerBDC.value() << " times faster than Jacobi" <<endl;
+ else
+ cout << "OK : BDC is " << timerJacobi.value() / timerBDC.value() << " times faster than Jacobi" <<endl;
+
+ }
+ cout << " =================" <<endl;
+ std::cout<< std::endl;
+ timerJacobi.reset();
+ timerBDC.reset();
+ cout << " Computes rotation matrix" <<endl;
+ for (int k=1; k<=NUMBER_SAMPLE; ++k)
+ {
+ timerBDC.start();
+ for (int i=0; i<REPEAT; ++i)
+ {
+ BDCSVD<MatrixType> bdc_matrix(m, ComputeFullU|ComputeFullV);
+ }
+ timerBDC.stop();
+
+ timerJacobi.start();
+ for (int i=0; i<REPEAT; ++i)
+ {
+ JacobiSVD<MatrixType> jacobi_matrix(m, ComputeFullU|ComputeFullV);
+ }
+ timerJacobi.stop();
+
+
+ cout << "Sample " << k << " : " << REPEAT << " computations : Jacobi : " << fixed << timerJacobi.value() << "s ";
+ cout << " || " << " BDC : " << timerBDC.value() << "s " <<endl <<endl;
+
+ if (timerBDC.value() >= timerJacobi.value())
+ cout << "KO : BDC is " << timerJacobi.value() / timerBDC.value() << " times faster than Jacobi" <<endl;
+ else
+ cout << "OK : BDC is " << timerJacobi.value() / timerBDC.value() << " times faster than Jacobi" <<endl;
+
+ }
+ std::cout<< std::endl;
+}
+
+
+
+int main(int argc, char* argv[])
+{
+ std::cout<< std::endl;
+
+ std::cout<<"On a (Dynamic, Dynamic) (6, 6) Matrix" <<std::endl;
+ bench_svd<Matrix<double,Dynamic,Dynamic> >(Matrix<double,Dynamic,Dynamic>(6, 6));
+
+ std::cout<<"On a (Dynamic, Dynamic) (32, 32) Matrix" <<std::endl;
+ bench_svd<Matrix<double,Dynamic,Dynamic> >(Matrix<double,Dynamic,Dynamic>(32, 32));
+
+ //std::cout<<"On a (Dynamic, Dynamic) (128, 128) Matrix" <<std::endl;
+ //bench_svd<Matrix<double,Dynamic,Dynamic> >(Matrix<double,Dynamic,Dynamic>(128, 128));
+
+ std::cout<<"On a (Dynamic, Dynamic) (160, 160) Matrix" <<std::endl;
+ bench_svd<Matrix<double,Dynamic,Dynamic> >(Matrix<double,Dynamic,Dynamic>(160, 160));
+
+ std::cout<< "--------------------------------------------------------------------"<< std::endl;
+
+}
diff --git a/unsupported/doc/CMakeLists.txt b/unsupported/doc/CMakeLists.txt
new file mode 100644
index 0000000..9e9ab98
--- /dev/null
+++ b/unsupported/doc/CMakeLists.txt
@@ -0,0 +1,4 @@
+set_directory_properties(PROPERTIES EXCLUDE_FROM_ALL TRUE)
+
+add_subdirectory(examples)
+add_subdirectory(snippets)
diff --git a/unsupported/doc/Overview.dox b/unsupported/doc/Overview.dox
new file mode 100644
index 0000000..bae51dc
--- /dev/null
+++ b/unsupported/doc/Overview.dox
@@ -0,0 +1,31 @@
+/// \brief Namespace containing all symbols from the %Eigen library.
+namespace Eigen {
+
+/** \mainpage %Eigen's unsupported modules
+
+This is the API documentation for %Eigen's unsupported modules.
+
+These modules are contributions from various users. They are provided "as is", without any support.
+
+Click on the \e Modules tab at the top of this page to get a list of all unsupported modules.
+
+Don't miss the <a href="../index.html">official Eigen documentation</a>.
+
+ \subpage SYCL_EIGEN "SYCL backend for Eigen"
+
+*/
+
+/*
+
+\defgroup Unsupported_modules Unsupported modules
+
+The unsupported modules are contributions from various users. They are
+provided "as is", without any support. Nevertheless, some of them are
+subject to be included in %Eigen in the future.
+
+*/
+
+/// \internal \brief Namespace containing low-level routines from the %Eigen library.
+namespace internal {}
+}
+
diff --git a/unsupported/doc/SYCL.dox b/unsupported/doc/SYCL.dox
new file mode 100644
index 0000000..2295adf
--- /dev/null
+++ b/unsupported/doc/SYCL.dox
@@ -0,0 +1,9 @@
+/** \page SYCL_EIGEN Eigen SYCL Backend
+
+Useful information for Eigen SYCL Backend:
+
+- <a href="https://developer.codeplay.com/computecppce/latest/getting-started-with-eigen">Getting Started with Eigen</a>
+
+- <a href="https://developer.codeplay.com/computecppce/latest/options-for-building-eigen-sycl">Options for Building Eigen SYCL</a>
+
+*/
diff --git a/unsupported/doc/eigendoxy_layout.xml.in b/unsupported/doc/eigendoxy_layout.xml.in
new file mode 100644
index 0000000..c93621e
--- /dev/null
+++ b/unsupported/doc/eigendoxy_layout.xml.in
@@ -0,0 +1,177 @@
+<?xml version="1.0"?>
+<doxygenlayout version="1.0">
+ <!-- Navigation index tabs for HTML output -->
+ <navindex>
+ <tab type="user" url="index.html" title="Overview" />
+ <tab type="modules" visible="yes" title="Unsupported Modules" intro=""/>
+<!-- <tab type="mainpage" visible="yes" title=""/> -->
+ <tab type="classlist" visible="yes" title="" intro=""/>
+<!-- <tab type="classmembers" visible="yes" title="" intro=""/> -->
+ </navindex>
+
+ <!-- Layout definition for a class page -->
+ <class>
+ <briefdescription visible="no"/>
+ <includes visible="$SHOW_INCLUDE_FILES"/>
+ <detaileddescription title=""/>
+ <inheritancegraph visible="$CLASS_GRAPH"/>
+ <collaborationgraph visible="$COLLABORATION_GRAPH"/>
+ <allmemberslink visible="yes"/>
+ <memberdecl>
+ <nestedclasses visible="yes" title=""/>
+ <publictypes title=""/>
+ <publicslots title=""/>
+ <signals title=""/>
+ <publicmethods title=""/>
+ <publicstaticmethods title=""/>
+ <publicattributes title=""/>
+ <publicstaticattributes title=""/>
+ <protectedtypes title=""/>
+ <protectedslots title=""/>
+ <protectedmethods title=""/>
+ <protectedstaticmethods title=""/>
+ <protectedattributes title=""/>
+ <protectedstaticattributes title=""/>
+ <packagetypes title=""/>
+ <packagemethods title=""/>
+ <packagestaticmethods title=""/>
+ <packageattributes title=""/>
+ <packagestaticattributes title=""/>
+ <properties title=""/>
+ <events title=""/>
+ <privatetypes title=""/>
+ <privateslots title=""/>
+ <privatemethods title=""/>
+ <privatestaticmethods title=""/>
+ <privateattributes title=""/>
+ <privatestaticattributes title=""/>
+ <friends title=""/>
+ <related title="" subtitle=""/>
+ <membergroups visible="yes"/>
+ </memberdecl>
+
+ <memberdef>
+ <inlineclasses title=""/>
+ <typedefs title=""/>
+ <enums title=""/>
+ <constructors title=""/>
+ <functions title=""/>
+ <related title=""/>
+ <variables title=""/>
+ <properties title=""/>
+ <events title=""/>
+ </memberdef>
+ <usedfiles visible="$SHOW_USED_FILES"/>
+ <authorsection visible="yes"/>
+ </class>
+
+ <!-- Layout definition for a namespace page -->
+ <namespace>
+ <briefdescription visible="yes"/>
+ <memberdecl>
+ <nestednamespaces visible="yes" title=""/>
+ <classes visible="yes" title=""/>
+ <typedefs title=""/>
+ <enums title=""/>
+ <functions title=""/>
+ <variables title=""/>
+ <membergroups visible="yes"/>
+ </memberdecl>
+ <detaileddescription title=""/>
+ <memberdef>
+ <inlineclasses title=""/>
+ <typedefs title=""/>
+ <enums title=""/>
+ <functions title=""/>
+ <variables title=""/>
+ </memberdef>
+ <authorsection visible="yes"/>
+ </namespace>
+
+ <!-- Layout definition for a file page -->
+ <file>
+ <briefdescription visible="yes"/>
+ <includes visible="$SHOW_INCLUDE_FILES"/>
+ <includegraph visible="$INCLUDE_GRAPH"/>
+ <includedbygraph visible="$INCLUDED_BY_GRAPH"/>
+ <sourcelink visible="yes"/>
+ <memberdecl>
+ <classes visible="yes" title=""/>
+ <namespaces visible="yes" title=""/>
+ <defines title=""/>
+ <typedefs title=""/>
+ <enums title=""/>
+ <functions title=""/>
+ <variables title=""/>
+ <membergroups visible="yes"/>
+ </memberdecl>
+ <detaileddescription title=""/>
+ <memberdef>
+ <inlineclasses title=""/>
+ <defines title=""/>
+ <typedefs title=""/>
+ <enums title=""/>
+ <functions title=""/>
+ <variables title=""/>
+ </memberdef>
+ <authorsection/>
+ </file>
+
+ <!-- Layout definition for a group page -->
+ <group>
+ <briefdescription visible="no"/>
+ <detaileddescription title=""/>
+ <groupgraph visible="$GROUP_GRAPHS"/>
+ <memberdecl>
+ <nestedgroups visible="yes" title=""/>
+ <dirs visible="yes" title=""/>
+ <files visible="yes" title=""/>
+ <namespaces visible="yes" title=""/>
+ <classes visible="yes" title=""/>
+ <defines title=""/>
+ <typedefs title=""/>
+ <enums title=""/>
+ <enumvalues title=""/>
+ <functions title=""/>
+ <variables title=""/>
+ <signals title=""/>
+ <publicslots title=""/>
+ <protectedslots title=""/>
+ <privateslots title=""/>
+ <events title=""/>
+ <properties title=""/>
+ <friends title=""/>
+ <membergroups visible="yes"/>
+ </memberdecl>
+
+ <memberdef>
+ <pagedocs/>
+ <inlineclasses title=""/>
+ <defines title=""/>
+ <typedefs title=""/>
+ <enums title=""/>
+ <enumvalues title=""/>
+ <functions title=""/>
+ <variables title=""/>
+ <signals title=""/>
+ <publicslots title=""/>
+ <protectedslots title=""/>
+ <privateslots title=""/>
+ <events title=""/>
+ <properties title=""/>
+ <friends title=""/>
+ </memberdef>
+ <authorsection visible="yes"/>
+ </group>
+
+ <!-- Layout definition for a directory page -->
+ <directory>
+ <briefdescription visible="yes"/>
+ <directorygraph visible="yes"/>
+ <memberdecl>
+ <dirs visible="yes"/>
+ <files visible="yes"/>
+ </memberdecl>
+ <detaileddescription title=""/>
+ </directory>
+</doxygenlayout>
diff --git a/unsupported/doc/examples/BVH_Example.cpp b/unsupported/doc/examples/BVH_Example.cpp
new file mode 100644
index 0000000..afb0c94
--- /dev/null
+++ b/unsupported/doc/examples/BVH_Example.cpp
@@ -0,0 +1,50 @@
+#include <Eigen/StdVector>
+#include <unsupported/Eigen/BVH>
+#include <iostream>
+
+using namespace Eigen;
+typedef AlignedBox<double, 2> Box2d;
+
+namespace Eigen {
+ Box2d bounding_box(const Vector2d &v) { return Box2d(v, v); } //compute the bounding box of a single point
+}
+
+struct PointPointMinimizer //how to compute squared distances between points and rectangles
+{
+ PointPointMinimizer() : calls(0) {}
+ typedef double Scalar;
+
+ double minimumOnVolumeVolume(const Box2d &r1, const Box2d &r2) { ++calls; return r1.squaredExteriorDistance(r2); }
+ double minimumOnVolumeObject(const Box2d &r, const Vector2d &v) { ++calls; return r.squaredExteriorDistance(v); }
+ double minimumOnObjectVolume(const Vector2d &v, const Box2d &r) { ++calls; return r.squaredExteriorDistance(v); }
+ double minimumOnObjectObject(const Vector2d &v1, const Vector2d &v2) { ++calls; return (v1 - v2).squaredNorm(); }
+
+ int calls;
+};
+
+int main()
+{
+ typedef std::vector<Vector2d, aligned_allocator<Vector2d> > StdVectorOfVector2d;
+ StdVectorOfVector2d redPoints, bluePoints;
+ for(int i = 0; i < 100; ++i) { //initialize random set of red points and blue points
+ redPoints.push_back(Vector2d::Random());
+ bluePoints.push_back(Vector2d::Random());
+ }
+
+ PointPointMinimizer minimizer;
+ double minDistSq = std::numeric_limits<double>::max();
+
+ //brute force to find closest red-blue pair
+ for(int i = 0; i < (int)redPoints.size(); ++i)
+ for(int j = 0; j < (int)bluePoints.size(); ++j)
+ minDistSq = std::min(minDistSq, minimizer.minimumOnObjectObject(redPoints[i], bluePoints[j]));
+ std::cout << "Brute force distance = " << sqrt(minDistSq) << ", calls = " << minimizer.calls << std::endl;
+
+ //using BVH to find closest red-blue pair
+ minimizer.calls = 0;
+ KdBVH<double, 2, Vector2d> redTree(redPoints.begin(), redPoints.end()), blueTree(bluePoints.begin(), bluePoints.end()); //construct the trees
+ minDistSq = BVMinimize(redTree, blueTree, minimizer); //actual BVH minimization call
+ std::cout << "BVH distance = " << sqrt(minDistSq) << ", calls = " << minimizer.calls << std::endl;
+
+ return 0;
+}
diff --git a/unsupported/doc/examples/CMakeLists.txt b/unsupported/doc/examples/CMakeLists.txt
new file mode 100644
index 0000000..7bb6773
--- /dev/null
+++ b/unsupported/doc/examples/CMakeLists.txt
@@ -0,0 +1,24 @@
+file(GLOB examples_SRCS "*.cpp")
+
+add_custom_target(unsupported_examples)
+
+include_directories(../../../unsupported ../../../unsupported/test)
+
+foreach(example_src ${examples_SRCS})
+ get_filename_component(example ${example_src} NAME_WE)
+ add_executable(example_${example} ${example_src})
+ if(EIGEN_STANDARD_LIBRARIES_TO_LINK_TO)
+ target_link_libraries(example_${example} ${EIGEN_STANDARD_LIBRARIES_TO_LINK_TO})
+ endif()
+ add_custom_command(
+ TARGET example_${example}
+ POST_BUILD
+ COMMAND example_${example}
+ ARGS >${CMAKE_CURRENT_BINARY_DIR}/${example}.out
+ )
+ add_dependencies(unsupported_examples example_${example})
+endforeach(example_src)
+
+if(EIGEN_TEST_SYCL)
+ add_subdirectory(SYCL)
+endif(EIGEN_TEST_SYCL)
diff --git a/unsupported/doc/examples/EulerAngles.cpp b/unsupported/doc/examples/EulerAngles.cpp
new file mode 100644
index 0000000..3f8ca8c
--- /dev/null
+++ b/unsupported/doc/examples/EulerAngles.cpp
@@ -0,0 +1,46 @@
+#include <unsupported/Eigen/EulerAngles>
+#include <iostream>
+
+using namespace Eigen;
+
+int main()
+{
+ // A common Euler system by many armies around the world,
+ // where the first one is the azimuth(the angle from the north -
+ // the same angle that is show in compass)
+ // and the second one is elevation(the angle from the horizon)
+ // and the third one is roll(the angle between the horizontal body
+ // direction and the plane ground surface)
+ // Keep remembering we're using radian angles here!
+ typedef EulerSystem<-EULER_Z, EULER_Y, EULER_X> MyArmySystem;
+ typedef EulerAngles<double, MyArmySystem> MyArmyAngles;
+
+ MyArmyAngles vehicleAngles(
+ 3.14/*PI*/ / 2, /* heading to east, notice that this angle is counter-clockwise */
+ -0.3, /* going down from a mountain */
+ 0.1); /* slightly rolled to the right */
+
+ // Some Euler angles representation that our plane use.
+ EulerAnglesZYZd planeAngles(0.78474, 0.5271, -0.513794);
+
+ MyArmyAngles planeAnglesInMyArmyAngles(planeAngles);
+
+ std::cout << "vehicle angles(MyArmy): " << vehicleAngles << std::endl;
+ std::cout << "plane angles(ZYZ): " << planeAngles << std::endl;
+ std::cout << "plane angles(MyArmy): " << planeAnglesInMyArmyAngles << std::endl;
+
+ // Now lets rotate the plane a little bit
+ std::cout << "==========================================================\n";
+ std::cout << "rotating plane now!\n";
+ std::cout << "==========================================================\n";
+
+ Quaterniond planeRotated = AngleAxisd(-0.342, Vector3d::UnitY()) * planeAngles;
+
+ planeAngles = planeRotated;
+ planeAnglesInMyArmyAngles = planeRotated;
+
+ std::cout << "new plane angles(ZYZ): " << planeAngles << std::endl;
+ std::cout << "new plane angles(MyArmy): " << planeAnglesInMyArmyAngles << std::endl;
+
+ return 0;
+}
diff --git a/unsupported/doc/examples/FFT.cpp b/unsupported/doc/examples/FFT.cpp
new file mode 100644
index 0000000..85e8a02
--- /dev/null
+++ b/unsupported/doc/examples/FFT.cpp
@@ -0,0 +1,118 @@
+// To use the simple FFT implementation
+// g++ -o demofft -I.. -Wall -O3 FFT.cpp
+
+// To use the FFTW implementation
+// g++ -o demofft -I.. -DUSE_FFTW -Wall -O3 FFT.cpp -lfftw3 -lfftw3f -lfftw3l
+
+#ifdef USE_FFTW
+#include <fftw3.h>
+#endif
+
+#include <vector>
+#include <complex>
+#include <algorithm>
+#include <iterator>
+#include <iostream>
+#include <Eigen/Core>
+#include <unsupported/Eigen/FFT>
+
+using namespace std;
+using namespace Eigen;
+
+template <typename T>
+T mag2(T a)
+{
+ return a*a;
+}
+template <typename T>
+T mag2(std::complex<T> a)
+{
+ return norm(a);
+}
+
+template <typename T>
+T mag2(const std::vector<T> & vec)
+{
+ T out=0;
+ for (size_t k=0;k<vec.size();++k)
+ out += mag2(vec[k]);
+ return out;
+}
+
+template <typename T>
+T mag2(const std::vector<std::complex<T> > & vec)
+{
+ T out=0;
+ for (size_t k=0;k<vec.size();++k)
+ out += mag2(vec[k]);
+ return out;
+}
+
+template <typename T>
+vector<T> operator-(const vector<T> & a,const vector<T> & b )
+{
+ vector<T> c(a);
+ for (size_t k=0;k<b.size();++k)
+ c[k] -= b[k];
+ return c;
+}
+
+template <typename T>
+void RandomFill(std::vector<T> & vec)
+{
+ for (size_t k=0;k<vec.size();++k)
+ vec[k] = T( rand() )/T(RAND_MAX) - T(.5);
+}
+
+template <typename T>
+void RandomFill(std::vector<std::complex<T> > & vec)
+{
+ for (size_t k=0;k<vec.size();++k)
+ vec[k] = std::complex<T> ( T( rand() )/T(RAND_MAX) - T(.5), T( rand() )/T(RAND_MAX) - T(.5));
+}
+
+template <typename T_time,typename T_freq>
+void fwd_inv(size_t nfft)
+{
+ typedef typename NumTraits<T_freq>::Real Scalar;
+ vector<T_time> timebuf(nfft);
+ RandomFill(timebuf);
+
+ vector<T_freq> freqbuf;
+ static FFT<Scalar> fft;
+ fft.fwd(freqbuf,timebuf);
+
+ vector<T_time> timebuf2;
+ fft.inv(timebuf2,freqbuf);
+
+ T_time rmse = mag2(timebuf - timebuf2) / mag2(timebuf);
+ cout << "roundtrip rmse: " << rmse << endl;
+}
+
+template <typename T_scalar>
+void two_demos(int nfft)
+{
+ cout << " scalar ";
+ fwd_inv<T_scalar,std::complex<T_scalar> >(nfft);
+ cout << " complex ";
+ fwd_inv<std::complex<T_scalar>,std::complex<T_scalar> >(nfft);
+}
+
+void demo_all_types(int nfft)
+{
+ cout << "nfft=" << nfft << endl;
+ cout << " float" << endl;
+ two_demos<float>(nfft);
+ cout << " double" << endl;
+ two_demos<double>(nfft);
+ cout << " long double" << endl;
+ two_demos<long double>(nfft);
+}
+
+int main()
+{
+ demo_all_types( 2*3*4*5*7 );
+ demo_all_types( 2*9*16*25 );
+ demo_all_types( 1024 );
+ return 0;
+}
diff --git a/unsupported/doc/examples/MatrixExponential.cpp b/unsupported/doc/examples/MatrixExponential.cpp
new file mode 100644
index 0000000..ebd3b96
--- /dev/null
+++ b/unsupported/doc/examples/MatrixExponential.cpp
@@ -0,0 +1,16 @@
+#include <unsupported/Eigen/MatrixFunctions>
+#include <iostream>
+
+using namespace Eigen;
+
+int main()
+{
+ const double pi = std::acos(-1.0);
+
+ MatrixXd A(3,3);
+ A << 0, -pi/4, 0,
+ pi/4, 0, 0,
+ 0, 0, 0;
+ std::cout << "The matrix A is:\n" << A << "\n\n";
+ std::cout << "The matrix exponential of A is:\n" << A.exp() << "\n\n";
+}
diff --git a/unsupported/doc/examples/MatrixFunction.cpp b/unsupported/doc/examples/MatrixFunction.cpp
new file mode 100644
index 0000000..a4172e4
--- /dev/null
+++ b/unsupported/doc/examples/MatrixFunction.cpp
@@ -0,0 +1,23 @@
+#include <unsupported/Eigen/MatrixFunctions>
+#include <iostream>
+
+using namespace Eigen;
+
+std::complex<double> expfn(std::complex<double> x, int)
+{
+ return std::exp(x);
+}
+
+int main()
+{
+ const double pi = std::acos(-1.0);
+
+ MatrixXd A(3,3);
+ A << 0, -pi/4, 0,
+ pi/4, 0, 0,
+ 0, 0, 0;
+
+ std::cout << "The matrix A is:\n" << A << "\n\n";
+ std::cout << "The matrix exponential of A is:\n"
+ << A.matrixFunction(expfn) << "\n\n";
+}
diff --git a/unsupported/doc/examples/MatrixLogarithm.cpp b/unsupported/doc/examples/MatrixLogarithm.cpp
new file mode 100644
index 0000000..8c5d970
--- /dev/null
+++ b/unsupported/doc/examples/MatrixLogarithm.cpp
@@ -0,0 +1,15 @@
+#include <unsupported/Eigen/MatrixFunctions>
+#include <iostream>
+
+using namespace Eigen;
+
+int main()
+{
+ using std::sqrt;
+ MatrixXd A(3,3);
+ A << 0.5*sqrt(2), -0.5*sqrt(2), 0,
+ 0.5*sqrt(2), 0.5*sqrt(2), 0,
+ 0, 0, 1;
+ std::cout << "The matrix A is:\n" << A << "\n\n";
+ std::cout << "The matrix logarithm of A is:\n" << A.log() << "\n";
+}
diff --git a/unsupported/doc/examples/MatrixPower.cpp b/unsupported/doc/examples/MatrixPower.cpp
new file mode 100644
index 0000000..2224524
--- /dev/null
+++ b/unsupported/doc/examples/MatrixPower.cpp
@@ -0,0 +1,16 @@
+#include <unsupported/Eigen/MatrixFunctions>
+#include <iostream>
+
+using namespace Eigen;
+
+int main()
+{
+ const double pi = std::acos(-1.0);
+ Matrix3d A;
+ A << cos(1), -sin(1), 0,
+ sin(1), cos(1), 0,
+ 0 , 0 , 1;
+ std::cout << "The matrix A is:\n" << A << "\n\n"
+ "The matrix power A^(pi/4) is:\n" << A.pow(pi/4) << std::endl;
+ return 0;
+}
diff --git a/unsupported/doc/examples/MatrixPower_optimal.cpp b/unsupported/doc/examples/MatrixPower_optimal.cpp
new file mode 100644
index 0000000..86470ba
--- /dev/null
+++ b/unsupported/doc/examples/MatrixPower_optimal.cpp
@@ -0,0 +1,17 @@
+#include <unsupported/Eigen/MatrixFunctions>
+#include <iostream>
+
+using namespace Eigen;
+
+int main()
+{
+ Matrix4cd A = Matrix4cd::Random();
+ MatrixPower<Matrix4cd> Apow(A);
+
+ std::cout << "The matrix A is:\n" << A << "\n\n"
+ "A^3.1 is:\n" << Apow(3.1) << "\n\n"
+ "A^3.3 is:\n" << Apow(3.3) << "\n\n"
+ "A^3.7 is:\n" << Apow(3.7) << "\n\n"
+ "A^3.9 is:\n" << Apow(3.9) << std::endl;
+ return 0;
+}
diff --git a/unsupported/doc/examples/MatrixSine.cpp b/unsupported/doc/examples/MatrixSine.cpp
new file mode 100644
index 0000000..9eea9a0
--- /dev/null
+++ b/unsupported/doc/examples/MatrixSine.cpp
@@ -0,0 +1,20 @@
+#include <unsupported/Eigen/MatrixFunctions>
+#include <iostream>
+
+using namespace Eigen;
+
+int main()
+{
+ MatrixXd A = MatrixXd::Random(3,3);
+ std::cout << "A = \n" << A << "\n\n";
+
+ MatrixXd sinA = A.sin();
+ std::cout << "sin(A) = \n" << sinA << "\n\n";
+
+ MatrixXd cosA = A.cos();
+ std::cout << "cos(A) = \n" << cosA << "\n\n";
+
+ // The matrix functions satisfy sin^2(A) + cos^2(A) = I,
+ // like the scalar functions.
+ std::cout << "sin^2(A) + cos^2(A) = \n" << sinA*sinA + cosA*cosA << "\n\n";
+}
diff --git a/unsupported/doc/examples/MatrixSinh.cpp b/unsupported/doc/examples/MatrixSinh.cpp
new file mode 100644
index 0000000..f771867
--- /dev/null
+++ b/unsupported/doc/examples/MatrixSinh.cpp
@@ -0,0 +1,20 @@
+#include <unsupported/Eigen/MatrixFunctions>
+#include <iostream>
+
+using namespace Eigen;
+
+int main()
+{
+ MatrixXf A = MatrixXf::Random(3,3);
+ std::cout << "A = \n" << A << "\n\n";
+
+ MatrixXf sinhA = A.sinh();
+ std::cout << "sinh(A) = \n" << sinhA << "\n\n";
+
+ MatrixXf coshA = A.cosh();
+ std::cout << "cosh(A) = \n" << coshA << "\n\n";
+
+ // The matrix functions satisfy cosh^2(A) - sinh^2(A) = I,
+ // like the scalar functions.
+ std::cout << "cosh^2(A) - sinh^2(A) = \n" << coshA*coshA - sinhA*sinhA << "\n\n";
+}
diff --git a/unsupported/doc/examples/MatrixSquareRoot.cpp b/unsupported/doc/examples/MatrixSquareRoot.cpp
new file mode 100644
index 0000000..88e7557
--- /dev/null
+++ b/unsupported/doc/examples/MatrixSquareRoot.cpp
@@ -0,0 +1,16 @@
+#include <unsupported/Eigen/MatrixFunctions>
+#include <iostream>
+
+using namespace Eigen;
+
+int main()
+{
+ const double pi = std::acos(-1.0);
+
+ MatrixXd A(2,2);
+ A << cos(pi/3), -sin(pi/3),
+ sin(pi/3), cos(pi/3);
+ std::cout << "The matrix A is:\n" << A << "\n\n";
+ std::cout << "The matrix square root of A is:\n" << A.sqrt() << "\n\n";
+ std::cout << "The square of the last matrix is:\n" << A.sqrt() * A.sqrt() << "\n";
+}
diff --git a/unsupported/doc/examples/PolynomialSolver1.cpp b/unsupported/doc/examples/PolynomialSolver1.cpp
new file mode 100644
index 0000000..cd777a4
--- /dev/null
+++ b/unsupported/doc/examples/PolynomialSolver1.cpp
@@ -0,0 +1,53 @@
+#include <unsupported/Eigen/Polynomials>
+#include <vector>
+#include <iostream>
+
+using namespace Eigen;
+using namespace std;
+
+int main()
+{
+ typedef Matrix<double,5,1> Vector5d;
+
+ Vector5d roots = Vector5d::Random();
+ cout << "Roots: " << roots.transpose() << endl;
+ Eigen::Matrix<double,6,1> polynomial;
+ roots_to_monicPolynomial( roots, polynomial );
+
+ PolynomialSolver<double,5> psolve( polynomial );
+ cout << "Complex roots: " << psolve.roots().transpose() << endl;
+
+ std::vector<double> realRoots;
+ psolve.realRoots( realRoots );
+ Map<Vector5d> mapRR( &realRoots[0] );
+ cout << "Real roots: " << mapRR.transpose() << endl;
+
+ cout << endl;
+ cout << "Illustration of the convergence problem with the QR algorithm: " << endl;
+ cout << "---------------------------------------------------------------" << endl;
+ Eigen::Matrix<float,7,1> hardCase_polynomial;
+ hardCase_polynomial <<
+ -0.957, 0.9219, 0.3516, 0.9453, -0.4023, -0.5508, -0.03125;
+ cout << "Hard case polynomial defined by floats: " << hardCase_polynomial.transpose() << endl;
+ PolynomialSolver<float,6> psolvef( hardCase_polynomial );
+ cout << "Complex roots: " << psolvef.roots().transpose() << endl;
+ Eigen::Matrix<float,6,1> evals;
+ for( int i=0; i<6; ++i ){ evals[i] = std::abs( poly_eval( hardCase_polynomial, psolvef.roots()[i] ) ); }
+ cout << "Norms of the evaluations of the polynomial at the roots: " << evals.transpose() << endl << endl;
+
+ cout << "Using double's almost always solves the problem for small degrees: " << endl;
+ cout << "-------------------------------------------------------------------" << endl;
+ PolynomialSolver<double,6> psolve6d( hardCase_polynomial.cast<double>() );
+ cout << "Complex roots: " << psolve6d.roots().transpose() << endl;
+ for( int i=0; i<6; ++i )
+ {
+ std::complex<float> castedRoot( psolve6d.roots()[i].real(), psolve6d.roots()[i].imag() );
+ evals[i] = std::abs( poly_eval( hardCase_polynomial, castedRoot ) );
+ }
+ cout << "Norms of the evaluations of the polynomial at the roots: " << evals.transpose() << endl << endl;
+
+ cout.precision(10);
+ cout << "The last root in float then in double: " << psolvef.roots()[5] << "\t" << psolve6d.roots()[5] << endl;
+ std::complex<float> castedRoot( psolve6d.roots()[5].real(), psolve6d.roots()[5].imag() );
+ cout << "Norm of the difference: " << std::abs( psolvef.roots()[5] - castedRoot ) << endl;
+}
diff --git a/unsupported/doc/examples/PolynomialUtils1.cpp b/unsupported/doc/examples/PolynomialUtils1.cpp
new file mode 100644
index 0000000..dbfe520
--- /dev/null
+++ b/unsupported/doc/examples/PolynomialUtils1.cpp
@@ -0,0 +1,20 @@
+#include <unsupported/Eigen/Polynomials>
+#include <iostream>
+
+using namespace Eigen;
+using namespace std;
+
+int main()
+{
+ Vector4d roots = Vector4d::Random();
+ cout << "Roots: " << roots.transpose() << endl;
+ Eigen::Matrix<double,5,1> polynomial;
+ roots_to_monicPolynomial( roots, polynomial );
+ cout << "Polynomial: ";
+ for( int i=0; i<4; ++i ){ cout << polynomial[i] << ".x^" << i << "+ "; }
+ cout << polynomial[4] << ".x^4" << endl;
+ Vector4d evaluation;
+ for( int i=0; i<4; ++i ){
+ evaluation[i] = poly_eval( polynomial, roots[i] ); }
+ cout << "Evaluation of the polynomial at the roots: " << evaluation.transpose();
+}
diff --git a/unsupported/doc/examples/SYCL/CMakeLists.txt b/unsupported/doc/examples/SYCL/CMakeLists.txt
new file mode 100644
index 0000000..8ee96f5
--- /dev/null
+++ b/unsupported/doc/examples/SYCL/CMakeLists.txt
@@ -0,0 +1,32 @@
+FILE(GLOB examples_SRCS "*.cpp")
+
+set(EIGEN_SYCL ON)
+list(APPEND CMAKE_EXE_LINKER_FLAGS -pthread)
+if(EIGEN_SYCL_TRISYCL)
+ set(CMAKE_CXX_STANDARD 17)
+else(EIGEN_SYCL_TRISYCL)
+ if(MSVC)
+ list(APPEND COMPUTECPP_USER_FLAGS -DWIN32)
+ else()
+ list(APPEND COMPUTECPP_USER_FLAGS -Wall)
+ endif()
+ # The following flags are not supported by Clang and can cause warnings
+ # if used with -Werror so they are removed here.
+ if(COMPUTECPP_USE_COMPILER_DRIVER)
+ set(CMAKE_CXX_COMPILER ${ComputeCpp_DEVICE_COMPILER_EXECUTABLE})
+ string(REPLACE "-Wlogical-op" "" CMAKE_CXX_FLAGS ${CMAKE_CXX_FLAGS})
+ string(REPLACE "-Wno-psabi" "" CMAKE_CXX_FLAGS ${CMAKE_CXX_FLAGS})
+ endif()
+ list(APPEND COMPUTECPP_USER_FLAGS
+ -DEIGEN_NO_ASSERTION_CHECKING=1
+ -no-serial-memop
+ -Xclang
+ -cl-mad-enable)
+endif(EIGEN_SYCL_TRISYCL)
+
+FOREACH(example_src ${examples_SRCS})
+ GET_FILENAME_COMPONENT(example ${example_src} NAME_WE)
+ ei_add_test_internal(${example} example_${example})
+ ADD_DEPENDENCIES(unsupported_examples example_${example})
+ENDFOREACH(example_src)
+set(EIGEN_SYCL OFF)
diff --git a/unsupported/doc/examples/SYCL/CwiseMul.cpp b/unsupported/doc/examples/SYCL/CwiseMul.cpp
new file mode 100644
index 0000000..a7c3314
--- /dev/null
+++ b/unsupported/doc/examples/SYCL/CwiseMul.cpp
@@ -0,0 +1,63 @@
+#include <iostream>
+#define EIGEN_USE_SYCL
+#include <unsupported/Eigen/CXX11/Tensor>
+
+using Eigen::array;
+using Eigen::SyclDevice;
+using Eigen::Tensor;
+using Eigen::TensorMap;
+
+int main()
+{
+ using DataType = float;
+ using IndexType = int64_t;
+ constexpr auto DataLayout = Eigen::RowMajor;
+
+ auto devices = Eigen::get_sycl_supported_devices();
+ const auto device_selector = *devices.begin();
+ Eigen::QueueInterface queueInterface(device_selector);
+ auto sycl_device = Eigen::SyclDevice(&queueInterface);
+
+ // create the tensors to be used in the operation
+ IndexType sizeDim1 = 3;
+ IndexType sizeDim2 = 3;
+ IndexType sizeDim3 = 3;
+ array<IndexType, 3> tensorRange = {{sizeDim1, sizeDim2, sizeDim3}};
+
+ // initialize the tensors with the data we want manipulate to
+ Tensor<DataType, 3,DataLayout, IndexType> in1(tensorRange);
+ Tensor<DataType, 3,DataLayout, IndexType> in2(tensorRange);
+ Tensor<DataType, 3,DataLayout, IndexType> out(tensorRange);
+
+ // set up some random data in the tensors to be multiplied
+ in1 = in1.random();
+ in2 = in2.random();
+
+ // allocate memory for the tensors
+ DataType * gpu_in1_data = static_cast<DataType*>(sycl_device.allocate(in1.size()*sizeof(DataType)));
+ DataType * gpu_in2_data = static_cast<DataType*>(sycl_device.allocate(in2.size()*sizeof(DataType)));
+ DataType * gpu_out_data = static_cast<DataType*>(sycl_device.allocate(out.size()*sizeof(DataType)));
+
+ //
+ TensorMap<Tensor<DataType, 3, DataLayout, IndexType>> gpu_in1(gpu_in1_data, tensorRange);
+ TensorMap<Tensor<DataType, 3, DataLayout, IndexType>> gpu_in2(gpu_in2_data, tensorRange);
+ TensorMap<Tensor<DataType, 3, DataLayout, IndexType>> gpu_out(gpu_out_data, tensorRange);
+
+ // copy the memory to the device and do the c=a*b calculation
+ sycl_device.memcpyHostToDevice(gpu_in1_data, in1.data(),(in1.size())*sizeof(DataType));
+ sycl_device.memcpyHostToDevice(gpu_in2_data, in2.data(),(in2.size())*sizeof(DataType));
+ gpu_out.device(sycl_device) = gpu_in1 * gpu_in2;
+ sycl_device.memcpyDeviceToHost(out.data(), gpu_out_data,(out.size())*sizeof(DataType));
+ sycl_device.synchronize();
+
+ // print out the results
+ for (IndexType i = 0; i < sizeDim1; ++i) {
+ for (IndexType j = 0; j < sizeDim2; ++j) {
+ for (IndexType k = 0; k < sizeDim3; ++k) {
+ std::cout << "device_out" << "(" << i << ", " << j << ", " << k << ") : " << out(i,j,k)
+ << " vs host_out" << "(" << i << ", " << j << ", " << k << ") : " << in1(i,j,k) * in2(i,j,k) << "\n";
+ }
+ }
+ }
+ printf("c=a*b Done\n");
+}
diff --git a/unsupported/doc/snippets/CMakeLists.txt b/unsupported/doc/snippets/CMakeLists.txt
new file mode 100644
index 0000000..adf95a8
--- /dev/null
+++ b/unsupported/doc/snippets/CMakeLists.txt
@@ -0,0 +1,26 @@
+file(GLOB snippets_SRCS "*.cpp")
+
+add_custom_target(unsupported_snippets)
+
+foreach(snippet_src ${snippets_SRCS})
+ get_filename_component(snippet ${snippet_src} NAME_WE)
+ set(compile_snippet_target compile_${snippet})
+ set(compile_snippet_src ${compile_snippet_target}.cpp)
+ file(READ ${snippet_src} snippet_source_code)
+ configure_file(${PROJECT_SOURCE_DIR}/doc/snippets/compile_snippet.cpp.in
+ ${CMAKE_CURRENT_BINARY_DIR}/${compile_snippet_src})
+ add_executable(${compile_snippet_target}
+ ${CMAKE_CURRENT_BINARY_DIR}/${compile_snippet_src})
+ if(EIGEN_STANDARD_LIBRARIES_TO_LINK_TO)
+ target_link_libraries(${compile_snippet_target} ${EIGEN_STANDARD_LIBRARIES_TO_LINK_TO})
+ endif()
+ add_custom_command(
+ TARGET ${compile_snippet_target}
+ POST_BUILD
+ COMMAND ${compile_snippet_target}
+ ARGS >${CMAKE_CURRENT_BINARY_DIR}/${snippet}.out
+ )
+ add_dependencies(unsupported_snippets ${compile_snippet_target})
+ set_source_files_properties(${CMAKE_CURRENT_BINARY_DIR}/${compile_snippet_src}
+ PROPERTIES OBJECT_DEPENDS ${snippet_src})
+endforeach(snippet_src)
diff --git a/unsupported/test/BVH.cpp b/unsupported/test/BVH.cpp
new file mode 100644
index 0000000..d8c39d5
--- /dev/null
+++ b/unsupported/test/BVH.cpp
@@ -0,0 +1,222 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009 Ilya Baran <ibaran@mit.edu>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "main.h"
+#include <Eigen/StdVector>
+#include <Eigen/Geometry>
+#include <unsupported/Eigen/BVH>
+
+namespace Eigen {
+
+template<typename Scalar, int Dim> AlignedBox<Scalar, Dim> bounding_box(const Matrix<Scalar, Dim, 1> &v) { return AlignedBox<Scalar, Dim>(v); }
+
+}
+
+
+template<int Dim>
+struct Ball
+{
+EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE(double, Dim)
+
+ typedef Matrix<double, Dim, 1> VectorType;
+
+ Ball() {}
+ Ball(const VectorType &c, double r) : center(c), radius(r) {}
+
+ VectorType center;
+ double radius;
+};
+template<int Dim> AlignedBox<double, Dim> bounding_box(const Ball<Dim> &b)
+{ return AlignedBox<double, Dim>(b.center.array() - b.radius, b.center.array() + b.radius); }
+
+inline double SQR(double x) { return x * x; }
+
+template<int Dim>
+struct BallPointStuff //this class provides functions to be both an intersector and a minimizer, both for a ball and a point and for two trees
+{
+ typedef double Scalar;
+ typedef Matrix<double, Dim, 1> VectorType;
+ typedef Ball<Dim> BallType;
+ typedef AlignedBox<double, Dim> BoxType;
+
+ BallPointStuff() : calls(0), count(0) {}
+ BallPointStuff(const VectorType &inP) : p(inP), calls(0), count(0) {}
+
+
+ bool intersectVolume(const BoxType &r) { ++calls; return r.contains(p); }
+ bool intersectObject(const BallType &b) {
+ ++calls;
+ if((b.center - p).squaredNorm() < SQR(b.radius))
+ ++count;
+ return false; //continue
+ }
+
+ bool intersectVolumeVolume(const BoxType &r1, const BoxType &r2) { ++calls; return !(r1.intersection(r2)).isNull(); }
+ bool intersectVolumeObject(const BoxType &r, const BallType &b) { ++calls; return r.squaredExteriorDistance(b.center) < SQR(b.radius); }
+ bool intersectObjectVolume(const BallType &b, const BoxType &r) { ++calls; return r.squaredExteriorDistance(b.center) < SQR(b.radius); }
+ bool intersectObjectObject(const BallType &b1, const BallType &b2){
+ ++calls;
+ if((b1.center - b2.center).norm() < b1.radius + b2.radius)
+ ++count;
+ return false;
+ }
+ bool intersectVolumeObject(const BoxType &r, const VectorType &v) { ++calls; return r.contains(v); }
+ bool intersectObjectObject(const BallType &b, const VectorType &v){
+ ++calls;
+ if((b.center - v).squaredNorm() < SQR(b.radius))
+ ++count;
+ return false;
+ }
+
+ double minimumOnVolume(const BoxType &r) { ++calls; return r.squaredExteriorDistance(p); }
+ double minimumOnObject(const BallType &b) { ++calls; return (std::max)(0., (b.center - p).squaredNorm() - SQR(b.radius)); }
+ double minimumOnVolumeVolume(const BoxType &r1, const BoxType &r2) { ++calls; return r1.squaredExteriorDistance(r2); }
+ double minimumOnVolumeObject(const BoxType &r, const BallType &b) { ++calls; return SQR((std::max)(0., r.exteriorDistance(b.center) - b.radius)); }
+ double minimumOnObjectVolume(const BallType &b, const BoxType &r) { ++calls; return SQR((std::max)(0., r.exteriorDistance(b.center) - b.radius)); }
+ double minimumOnObjectObject(const BallType &b1, const BallType &b2){ ++calls; return SQR((std::max)(0., (b1.center - b2.center).norm() - b1.radius - b2.radius)); }
+ double minimumOnVolumeObject(const BoxType &r, const VectorType &v) { ++calls; return r.squaredExteriorDistance(v); }
+ double minimumOnObjectObject(const BallType &b, const VectorType &v){ ++calls; return SQR((std::max)(0., (b.center - v).norm() - b.radius)); }
+
+ VectorType p;
+ int calls;
+ int count;
+};
+
+
+template<int Dim>
+struct TreeTest
+{
+ typedef Matrix<double, Dim, 1> VectorType;
+ typedef std::vector<VectorType, aligned_allocator<VectorType> > VectorTypeList;
+ typedef Ball<Dim> BallType;
+ typedef std::vector<BallType, aligned_allocator<BallType> > BallTypeList;
+ typedef AlignedBox<double, Dim> BoxType;
+
+ void testIntersect1()
+ {
+ BallTypeList b;
+ for(int i = 0; i < 500; ++i) {
+ b.push_back(BallType(VectorType::Random(), 0.5 * internal::random(0., 1.)));
+ }
+ KdBVH<double, Dim, BallType> tree(b.begin(), b.end());
+
+ VectorType pt = VectorType::Random();
+ BallPointStuff<Dim> i1(pt), i2(pt);
+
+ for(int i = 0; i < (int)b.size(); ++i)
+ i1.intersectObject(b[i]);
+
+ BVIntersect(tree, i2);
+
+ VERIFY(i1.count == i2.count);
+ }
+
+ void testMinimize1()
+ {
+ BallTypeList b;
+ for(int i = 0; i < 500; ++i) {
+ b.push_back(BallType(VectorType::Random(), 0.01 * internal::random(0., 1.)));
+ }
+ KdBVH<double, Dim, BallType> tree(b.begin(), b.end());
+
+ VectorType pt = VectorType::Random();
+ BallPointStuff<Dim> i1(pt), i2(pt);
+
+ double m1 = (std::numeric_limits<double>::max)(), m2 = m1;
+
+ for(int i = 0; i < (int)b.size(); ++i)
+ m1 = (std::min)(m1, i1.minimumOnObject(b[i]));
+
+ m2 = BVMinimize(tree, i2);
+
+ VERIFY_IS_APPROX(m1, m2);
+ }
+
+ void testIntersect2()
+ {
+ BallTypeList b;
+ VectorTypeList v;
+
+ for(int i = 0; i < 50; ++i) {
+ b.push_back(BallType(VectorType::Random(), 0.5 * internal::random(0., 1.)));
+ for(int j = 0; j < 3; ++j)
+ v.push_back(VectorType::Random());
+ }
+
+ KdBVH<double, Dim, BallType> tree(b.begin(), b.end());
+ KdBVH<double, Dim, VectorType> vTree(v.begin(), v.end());
+
+ BallPointStuff<Dim> i1, i2;
+
+ for(int i = 0; i < (int)b.size(); ++i)
+ for(int j = 0; j < (int)v.size(); ++j)
+ i1.intersectObjectObject(b[i], v[j]);
+
+ BVIntersect(tree, vTree, i2);
+
+ VERIFY(i1.count == i2.count);
+ }
+
+ void testMinimize2()
+ {
+ BallTypeList b;
+ VectorTypeList v;
+
+ for(int i = 0; i < 50; ++i) {
+ b.push_back(BallType(VectorType::Random(), 1e-7 + 1e-6 * internal::random(0., 1.)));
+ for(int j = 0; j < 3; ++j)
+ v.push_back(VectorType::Random());
+ }
+
+ KdBVH<double, Dim, BallType> tree(b.begin(), b.end());
+ KdBVH<double, Dim, VectorType> vTree(v.begin(), v.end());
+
+ BallPointStuff<Dim> i1, i2;
+
+ double m1 = (std::numeric_limits<double>::max)(), m2 = m1;
+
+ for(int i = 0; i < (int)b.size(); ++i)
+ for(int j = 0; j < (int)v.size(); ++j)
+ m1 = (std::min)(m1, i1.minimumOnObjectObject(b[i], v[j]));
+
+ m2 = BVMinimize(tree, vTree, i2);
+
+ VERIFY_IS_APPROX(m1, m2);
+ }
+};
+
+
+EIGEN_DECLARE_TEST(BVH)
+{
+ for(int i = 0; i < g_repeat; i++) {
+#ifdef EIGEN_TEST_PART_1
+ TreeTest<2> test2;
+ CALL_SUBTEST(test2.testIntersect1());
+ CALL_SUBTEST(test2.testMinimize1());
+ CALL_SUBTEST(test2.testIntersect2());
+ CALL_SUBTEST(test2.testMinimize2());
+#endif
+
+#ifdef EIGEN_TEST_PART_2
+ TreeTest<3> test3;
+ CALL_SUBTEST(test3.testIntersect1());
+ CALL_SUBTEST(test3.testMinimize1());
+ CALL_SUBTEST(test3.testIntersect2());
+ CALL_SUBTEST(test3.testMinimize2());
+#endif
+
+#ifdef EIGEN_TEST_PART_3
+ TreeTest<4> test4;
+ CALL_SUBTEST(test4.testIntersect1());
+ CALL_SUBTEST(test4.testMinimize1());
+ CALL_SUBTEST(test4.testIntersect2());
+ CALL_SUBTEST(test4.testMinimize2());
+#endif
+ }
+}
diff --git a/unsupported/test/CMakeLists.txt b/unsupported/test/CMakeLists.txt
new file mode 100644
index 0000000..21d8c5e
--- /dev/null
+++ b/unsupported/test/CMakeLists.txt
@@ -0,0 +1,412 @@
+# The file split_test_helper.h was generated at first run,
+# it is now included in test/
+if(EXISTS ${CMAKE_CURRENT_BINARY_DIR}/split_test_helper.h)
+ file(REMOVE ${CMAKE_CURRENT_BINARY_DIR}/split_test_helper.h)
+endif()
+
+set_property(GLOBAL PROPERTY EIGEN_CURRENT_SUBPROJECT "Unsupported")
+add_custom_target(BuildUnsupported)
+
+include_directories(../../test ../../unsupported ../../Eigen
+ ${CMAKE_CURRENT_BINARY_DIR}/../../test)
+
+find_package (Threads)
+
+find_package(GoogleHash)
+if(GoogleHash_FOUND)
+ add_definitions("-DEIGEN_GOOGLEHASH_SUPPORT")
+ include_directories(${GOOGLEHASH_INCLUDES})
+ ei_add_property(EIGEN_TESTED_BACKENDS "GoogleHash, ")
+else()
+ ei_add_property(EIGEN_MISSING_BACKENDS "GoogleHash, ")
+endif()
+
+
+find_package(Adolc)
+if(Adolc_FOUND)
+ include_directories(${ADOLC_INCLUDES})
+ ei_add_property(EIGEN_TESTED_BACKENDS "Adolc, ")
+ ei_add_test(forward_adolc "" ${ADOLC_LIBRARIES})
+else()
+ ei_add_property(EIGEN_MISSING_BACKENDS "Adolc, ")
+endif()
+
+# this test seems to never have been successful on x87, so is considered to contain a FP-related bug.
+# see thread: "non-linear optimization test summary"
+ei_add_test(NonLinearOptimization)
+
+ei_add_test(NumericalDiff)
+ei_add_test(autodiff_scalar)
+ei_add_test(autodiff)
+
+ei_add_test(BVH)
+
+ei_add_test(matrix_exponential)
+ei_add_test(matrix_function)
+ei_add_test(matrix_power)
+ei_add_test(matrix_square_root)
+ei_add_test(alignedvector3)
+
+ei_add_test(FFT)
+
+ei_add_test(EulerAngles)
+
+find_package(MPREAL)
+if(MPREAL_FOUND)
+ ei_add_property(EIGEN_TESTED_BACKENDS "MPFR C++, ")
+ include_directories(${MPREAL_INCLUDES})
+ ei_add_test(mpreal_support "" "${MPREAL_LIBRARIES}" )
+else()
+ ei_add_property(EIGEN_MISSING_BACKENDS "MPFR C++, ")
+endif()
+
+ei_add_test(NNLS)
+
+ei_add_test(sparse_extra "" "")
+
+find_package(FFTW)
+if(FFTW_FOUND)
+ ei_add_property(EIGEN_TESTED_BACKENDS "fftw, ")
+ include_directories( ${FFTW_INCLUDES} )
+ if(FFTWL_LIB)
+ ei_add_test(FFTW "-DEIGEN_FFTW_DEFAULT -DEIGEN_HAS_FFTWL" "${FFTW_LIBRARIES}" )
+ else()
+ ei_add_test(FFTW "-DEIGEN_FFTW_DEFAULT" "${FFTW_LIBRARIES}" )
+ endif()
+else()
+ ei_add_property(EIGEN_MISSING_BACKENDS "fftw, ")
+endif()
+
+find_path(POCKETFFT pocketfft_hdronly.h)
+if(POCKETFFT)
+ if(EIGEN_TEST_CXX11)
+ ei_add_property(EIGEN_TESTED_BACKENDS "pocketfft, ")
+ include_directories( ${POCKETFFT} )
+ ei_add_test(pocketfft "-pthread" "${CMAKE_THREAD_LIBS_INIT}" "-DEIGEN_POCKETFFT_DEFAULT" )
+ endif()
+else()
+ ei_add_property(EIGEN_MISSING_BACKENDS "pocketfft, ")
+endif()
+
+option(EIGEN_TEST_OPENGL "Enable OpenGL support in unit tests" OFF)
+if(EIGEN_TEST_OPENGL)
+ find_package(OpenGL)
+ find_package(GLUT)
+ find_package(GLEW)
+ if(OPENGL_FOUND AND GLUT_FOUND AND GLEW_FOUND)
+ include_directories(${OPENGL_INCLUDE_DIR} ${GLUT_INCLUDE_DIR} ${GLEW_INCLUDE_DIRS})
+ ei_add_property(EIGEN_TESTED_BACKENDS "OpenGL, ")
+ set(EIGEN_GL_LIB ${GLUT_LIBRARIES} ${GLEW_LIBRARIES} ${OPENGL_LIBRARIES})
+ ei_add_test(openglsupport "" "${EIGEN_GL_LIB}" )
+ else()
+ ei_add_property(EIGEN_MISSING_BACKENDS "OpenGL, ")
+ endif()
+else()
+ ei_add_property(EIGEN_MISSING_BACKENDS "OpenGL, ")
+endif()
+
+ei_add_test(polynomialsolver)
+ei_add_test(polynomialutils)
+ei_add_test(splines)
+ei_add_test(gmres)
+ei_add_test(dgmres)
+ei_add_test(minres)
+ei_add_test(idrs)
+ei_add_test(bicgstabl)
+ei_add_test(idrstabl)
+ei_add_test(levenberg_marquardt)
+ei_add_test(kronecker_product)
+ei_add_test(bessel_functions)
+ei_add_test(special_functions)
+ei_add_test(special_packetmath "-DEIGEN_FAST_MATH=1")
+
+if(EIGEN_TEST_SYCL)
+ set(EIGEN_SYCL ON)
+ # Forward CMake options as preprocessor definitions
+ if(EIGEN_SYCL_USE_DEFAULT_SELECTOR)
+ add_definitions(-DEIGEN_SYCL_USE_DEFAULT_SELECTOR=${EIGEN_SYCL_USE_DEFAULT_SELECTOR})
+ endif()
+ if(EIGEN_SYCL_NO_LOCAL_MEM)
+ add_definitions(-DEIGEN_SYCL_NO_LOCAL_MEM=${EIGEN_SYCL_NO_LOCAL_MEM})
+ endif()
+ if(EIGEN_SYCL_LOCAL_MEM)
+ add_definitions(-DEIGEN_SYCL_LOCAL_MEM=${EIGEN_SYCL_LOCAL_MEM})
+ endif()
+ if(EIGEN_SYCL_MAX_GLOBAL_RANGE)
+ add_definitions(-DEIGEN_SYCL_MAX_GLOBAL_RANGE=${EIGEN_SYCL_MAX_GLOBAL_RANGE})
+ endif()
+ if(EIGEN_SYCL_LOCAL_THREAD_DIM0)
+ add_definitions(-DEIGEN_SYCL_LOCAL_THREAD_DIM0=${EIGEN_SYCL_LOCAL_THREAD_DIM0})
+ endif()
+ if(EIGEN_SYCL_LOCAL_THREAD_DIM1)
+ add_definitions(-DEIGEN_SYCL_LOCAL_THREAD_DIM1=${EIGEN_SYCL_LOCAL_THREAD_DIM1})
+ endif()
+ if(EIGEN_SYCL_REG_M)
+ add_definitions(-DEIGEN_SYCL_REG_M=${EIGEN_SYCL_REG_M})
+ endif()
+ if(EIGEN_SYCL_REG_N)
+ add_definitions(-DEIGEN_SYCL_REG_N=${EIGEN_SYCL_REG_N})
+ endif()
+ if(EIGEN_SYCL_USE_PROGRAM_CLASS)
+ add_definitions(-DEIGEN_SYCL_USE_PROGRAM_CLASS=${EIGEN_SYCL_USE_PROGRAM_CLASS})
+ endif()
+ if(EIGEN_SYCL_ASYNC_EXECUTION)
+ add_definitions(-DEIGEN_SYCL_ASYNC_EXECUTION=${EIGEN_SYCL_ASYNC_EXECUTION})
+ endif()
+ if(EIGEN_SYCL_DISABLE_SKINNY)
+ add_definitions(-DEIGEN_SYCL_DISABLE_SKINNY=${EIGEN_SYCL_DISABLE_SKINNY})
+ endif()
+ if(EIGEN_SYCL_DISABLE_DOUBLE_BUFFER)
+ add_definitions(-DEIGEN_SYCL_DISABLE_DOUBLE_BUFFER=${EIGEN_SYCL_DISABLE_DOUBLE_BUFFER})
+ endif()
+ if(EIGEN_SYCL_DISABLE_RANK1)
+ add_definitions(-DEIGEN_SYCL_DISABLE_RANK1=${EIGEN_SYCL_DISABLE_RANK1})
+ endif()
+ if(EIGEN_SYCL_DISABLE_SCALAR)
+ add_definitions(-DEIGEN_SYCL_DISABLE_SCALAR=${EIGEN_SYCL_DISABLE_SCALAR})
+ endif()
+ if(EIGEN_SYCL_DISABLE_GEMV)
+ add_definitions(-DEIGEN_SYCL_DISABLE_GEMV=${EIGEN_SYCL_DISABLE_GEMV})
+ endif()
+ if(EIGEN_SYCL_DISABLE_ARM_GPU_CACHE_OPTIMISATION)
+ add_definitions(-DEIGEN_SYCL_DISABLE_ARM_GPU_CACHE_OPTIMISATION=${EIGEN_SYCL_DISABLE_ARM_GPU_CACHE_OPTIMISATION})
+ endif()
+
+ if(EIGEN_SYCL_TRISYCL)
+ # triSYCL now requires c++17.
+ set(CMAKE_CXX_STANDARD 17)
+ else()
+ if(MSVC)
+ list(APPEND COMPUTECPP_USER_FLAGS -DWIN32)
+ else()
+ list(APPEND COMPUTECPP_USER_FLAGS -Wall)
+ endif()
+ # The following flags are not supported by Clang and can cause warnings
+ # if used with -Werror so they are removed here.
+ if(COMPUTECPP_USE_COMPILER_DRIVER)
+ set(CMAKE_CXX_COMPILER ${ComputeCpp_DEVICE_COMPILER_EXECUTABLE})
+ string(REPLACE "-Wlogical-op" "" CMAKE_CXX_FLAGS ${CMAKE_CXX_FLAGS})
+ string(REPLACE "-Wno-psabi" "" CMAKE_CXX_FLAGS ${CMAKE_CXX_FLAGS})
+ endif()
+ list(APPEND COMPUTECPP_USER_FLAGS
+ -DEIGEN_NO_ASSERTION_CHECKING=1
+ -no-serial-memop
+ -Xclang
+ -cl-mad-enable)
+ endif()
+
+ ei_add_test(cxx11_tensor_sycl)
+ ei_add_test(cxx11_tensor_image_op_sycl)
+ ei_add_test(cxx11_tensor_math_sycl)
+ ei_add_test(cxx11_tensor_forced_eval_sycl)
+ ei_add_test(cxx11_tensor_broadcast_sycl)
+ ei_add_test(cxx11_tensor_device_sycl)
+ ei_add_test(cxx11_tensor_reduction_sycl)
+ ei_add_test(cxx11_tensor_morphing_sycl)
+ ei_add_test(cxx11_tensor_shuffling_sycl)
+ ei_add_test(cxx11_tensor_padding_sycl)
+ ei_add_test(cxx11_tensor_builtins_sycl)
+ ei_add_test(cxx11_tensor_contract_sycl)
+ ei_add_test(cxx11_tensor_concatenation_sycl)
+ ei_add_test(cxx11_tensor_reverse_sycl)
+ ei_add_test(cxx11_tensor_convolution_sycl)
+ ei_add_test(cxx11_tensor_striding_sycl)
+ ei_add_test(cxx11_tensor_chipping_sycl)
+ ei_add_test(cxx11_tensor_layout_swap_sycl)
+ ei_add_test(cxx11_tensor_inflation_sycl)
+ ei_add_test(cxx11_tensor_random_sycl)
+ ei_add_test(cxx11_tensor_generator_sycl)
+ ei_add_test(cxx11_tensor_patch_sycl)
+ ei_add_test(cxx11_tensor_image_patch_sycl)
+ ei_add_test(cxx11_tensor_volume_patch_sycl)
+ ei_add_test(cxx11_tensor_argmax_sycl)
+ ei_add_test(cxx11_tensor_custom_op_sycl)
+ ei_add_test(cxx11_tensor_scan_sycl)
+ set(EIGEN_SYCL OFF)
+endif()
+
+ei_add_test(cxx11_eventcount "-pthread" "${CMAKE_THREAD_LIBS_INIT}")
+ei_add_test(cxx11_runqueue "-pthread" "${CMAKE_THREAD_LIBS_INIT}")
+ei_add_test(cxx11_non_blocking_thread_pool "-pthread" "${CMAKE_THREAD_LIBS_INIT}")
+
+ei_add_test(cxx11_meta)
+ei_add_test(cxx11_maxsizevector)
+ei_add_test(cxx11_tensor_argmax)
+ei_add_test(cxx11_tensor_assign)
+ei_add_test(cxx11_tensor_block_access)
+ei_add_test(cxx11_tensor_block_eval)
+ei_add_test(cxx11_tensor_block_io)
+ei_add_test(cxx11_tensor_broadcasting)
+ei_add_test(cxx11_tensor_casts)
+ei_add_test(cxx11_tensor_chipping)
+ei_add_test(cxx11_tensor_comparisons)
+ei_add_test(cxx11_tensor_concatenation)
+ei_add_test(cxx11_tensor_const)
+ei_add_test(cxx11_tensor_contraction)
+ei_add_test(cxx11_tensor_convolution)
+ei_add_test(cxx11_tensor_custom_index)
+ei_add_test(cxx11_tensor_custom_op)
+ei_add_test(cxx11_tensor_dimension)
+ei_add_test(cxx11_tensor_empty)
+ei_add_test(cxx11_tensor_executor "-pthread" "${CMAKE_THREAD_LIBS_INIT}")
+ei_add_test(cxx11_tensor_expr)
+ei_add_test(cxx11_tensor_fft)
+ei_add_test(cxx11_tensor_fixed_size)
+ei_add_test(cxx11_tensor_forced_eval)
+ei_add_test(cxx11_tensor_generator)
+ei_add_test(cxx11_tensor_ifft)
+ei_add_test(cxx11_tensor_image_patch)
+ei_add_test(cxx11_tensor_index_list)
+ei_add_test(cxx11_tensor_inflation)
+ei_add_test(cxx11_tensor_intdiv)
+ei_add_test(cxx11_tensor_io)
+ei_add_test(cxx11_tensor_layout_swap)
+ei_add_test(cxx11_tensor_lvalue)
+ei_add_test(cxx11_tensor_map)
+ei_add_test(cxx11_tensor_math)
+ei_add_test(cxx11_tensor_mixed_indices)
+ei_add_test(cxx11_tensor_morphing)
+ei_add_test(cxx11_tensor_move)
+ei_add_test(cxx11_tensor_notification "-pthread" "${CMAKE_THREAD_LIBS_INIT}")
+ei_add_test(cxx11_tensor_of_complex)
+ei_add_test(cxx11_tensor_of_const_values)
+ei_add_test(cxx11_tensor_of_strings)
+ei_add_test(cxx11_tensor_padding)
+ei_add_test(cxx11_tensor_patch)
+ei_add_test(cxx11_tensor_random)
+ei_add_test(cxx11_tensor_reduction)
+ei_add_test(cxx11_tensor_ref)
+ei_add_test(cxx11_tensor_roundings)
+ei_add_test(cxx11_tensor_scan)
+ei_add_test(cxx11_tensor_shuffling)
+ei_add_test(cxx11_tensor_simple)
+ei_add_test(cxx11_tensor_striding)
+ei_add_test(cxx11_tensor_sugar)
+ei_add_test(cxx11_tensor_thread_local "-pthread" "${CMAKE_THREAD_LIBS_INIT}")
+ei_add_test(cxx11_tensor_thread_pool "-pthread" "${CMAKE_THREAD_LIBS_INIT}")
+ei_add_test(cxx11_tensor_trace)
+ei_add_test(cxx11_tensor_volume_patch)
+# ei_add_test(cxx11_tensor_symmetry)
+if("${CMAKE_SIZEOF_VOID_P}" EQUAL "8" AND NOT CMAKE_CXX_COMPILER_ID STREQUAL "MSVC")
+ # This test requires __uint128_t which is only available on 64bit systems
+ ei_add_test(cxx11_tensor_uint128)
+endif()
+
+find_package(CUDA 9.0)
+if(CUDA_FOUND AND EIGEN_TEST_CUDA)
+ # Make sure to compile without the -pedantic, -Wundef, -Wnon-virtual-dtor
+ # and -fno-check-new flags since they trigger thousands of compilation warnings
+ # in the CUDA runtime
+ string(REPLACE "-pedantic" "" CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS}")
+ string(REPLACE "-Wundef" "" CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS}")
+ string(REPLACE "-Wnon-virtual-dtor" "" CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS}")
+ string(REPLACE "-fno-check-new" "" CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS}")
+
+ if(EIGEN_TEST_CUDA_CLANG)
+ string(APPEND CMAKE_CXX_FLAGS " --cuda-path=${CUDA_TOOLKIT_ROOT_DIR}")
+ foreach(ARCH IN LISTS EIGEN_CUDA_COMPUTE_ARCH)
+ string(APPEND CMAKE_CXX_FLAGS " --cuda-gpu-arch=sm_${ARCH}")
+ endforeach()
+ string(APPEND CMAKE_CXX_FLAGS " ${EIGEN_CUDA_CXX_FLAGS}")
+ else()
+ set(CUDA_PROPAGATE_HOST_FLAGS OFF)
+ set(NVCC_ARCH_FLAGS)
+ # Define an -arch=sm_<arch>, otherwise if GPU does not exactly match one of
+ # those in the arch list for -gencode, the kernels will fail to run with
+ # cudaErrorNoKernelImageForDevice
+ # This can happen with newer cards (e.g. sm_75) and compiling with older
+ # versions of nvcc (e.g. 9.2) that do not support their specific arch.
+ list(LENGTH EIGEN_CUDA_COMPUTE_ARCH EIGEN_CUDA_COMPUTE_ARCH_SIZE)
+ if(EIGEN_CUDA_COMPUTE_ARCH_SIZE)
+ list(GET EIGEN_CUDA_COMPUTE_ARCH 0 EIGEN_CUDA_COMPUTE_DEFAULT)
+ set(NVCC_ARCH_FLAGS " -arch=sm_${EIGEN_CUDA_COMPUTE_DEFAULT}")
+ endif()
+ foreach(ARCH IN LISTS EIGEN_CUDA_COMPUTE_ARCH)
+ string(APPEND NVCC_ARCH_FLAGS " -gencode arch=compute_${ARCH},code=sm_${ARCH}")
+ endforeach()
+ set(CUDA_NVCC_FLAGS "--expt-relaxed-constexpr -Xcudafe \"--display_error_number\" ${NVCC_ARCH_FLAGS} ${CUDA_NVCC_FLAGS} ${EIGEN_CUDA_CXX_FLAGS}")
+ cuda_include_directories("${CMAKE_CURRENT_BINARY_DIR}" "${CUDA_TOOLKIT_ROOT_DIR}/include")
+ endif()
+
+ set(EIGEN_ADD_TEST_FILENAME_EXTENSION "cu")
+
+ ei_add_test(cxx11_tensor_complex_gpu)
+ ei_add_test(cxx11_tensor_complex_cwise_ops_gpu)
+ ei_add_test(cxx11_tensor_reduction_gpu)
+ ei_add_test(cxx11_tensor_argmax_gpu)
+ ei_add_test(cxx11_tensor_cast_float16_gpu)
+ ei_add_test(cxx11_tensor_scan_gpu)
+
+ set(EIGEN_CUDA_OLDEST_COMPUTE_ARCH 9999)
+ foreach(ARCH IN LISTS EIGEN_CUDA_COMPUTE_ARCH)
+ if(${ARCH} LESS ${EIGEN_CUDA_OLDEST_COMPUTE_ARCH})
+ set(EIGEN_CUDA_OLDEST_COMPUTE_ARCH ${ARCH})
+ endif()
+ endforeach()
+
+ # Contractions require arch 3.0 or higher
+ if (${EIGEN_CUDA_OLDEST_COMPUTE_ARCH} GREATER 29)
+ ei_add_test(cxx11_tensor_device)
+ ei_add_test(cxx11_tensor_gpu)
+ ei_add_test(cxx11_tensor_contract_gpu)
+ ei_add_test(cxx11_tensor_of_float16_gpu)
+ endif()
+
+ # The random number generation code requires arch 3.5 or greater.
+ if (${EIGEN_CUDA_OLDEST_COMPUTE_ARCH} GREATER 34)
+ ei_add_test(cxx11_tensor_random_gpu)
+ endif()
+
+ unset(EIGEN_ADD_TEST_FILENAME_EXTENSION)
+endif()
+
+# Add HIP specific tests
+if (EIGEN_TEST_HIP)
+
+ set(HIP_PATH "/opt/rocm/hip" CACHE STRING "Path to the HIP installation.")
+
+ if (EXISTS ${HIP_PATH})
+ list(APPEND CMAKE_MODULE_PATH ${HIP_PATH}/cmake)
+
+ find_package(HIP REQUIRED)
+ if (HIP_FOUND)
+ execute_process(COMMAND ${HIP_PATH}/bin/hipconfig --platform OUTPUT_VARIABLE HIP_PLATFORM)
+
+ if ((${HIP_PLATFORM} STREQUAL "hcc") OR (${HIP_PLATFORM} STREQUAL "amd"))
+ include_directories(${CMAKE_CURRENT_BINARY_DIR})
+ include_directories(${HIP_PATH}/include)
+
+ set(EIGEN_ADD_TEST_FILENAME_EXTENSION "cu")
+ #
+ # complex datatype is not yet supported by HIP
+ # so leaving out those tests for now
+ #
+ # ei_add_test(cxx11_tensor_complex_gpu)
+ # ei_add_test(cxx11_tensor_complex_cwise_ops_gpu)
+ #
+ ei_add_test(cxx11_tensor_reduction_gpu)
+ ei_add_test(cxx11_tensor_argmax_gpu)
+ ei_add_test(cxx11_tensor_cast_float16_gpu)
+ ei_add_test(cxx11_tensor_scan_gpu)
+ ei_add_test(cxx11_tensor_device)
+
+ ei_add_test(cxx11_tensor_gpu)
+ ei_add_test(cxx11_tensor_contract_gpu)
+ ei_add_test(cxx11_tensor_of_float16_gpu)
+ ei_add_test(cxx11_tensor_of_bfloat16_gpu)
+ ei_add_test(cxx11_tensor_random_gpu)
+
+ unset(EIGEN_ADD_TEST_FILENAME_EXTENSION)
+
+ elseif ((${HIP_PLATFORM} STREQUAL "nvcc") OR (${HIP_PLATFORM} STREQUAL "nvidia"))
+ message(FATAL_ERROR "HIP_PLATFORM = nvcc is not supported within Eigen")
+ else ()
+ message(FATAL_ERROR "Unknown HIP_PLATFORM = ${HIP_PLATFORM}")
+ endif()
+ endif()
+ else ()
+ message(FATAL_ERROR "EIGEN_TEST_HIP is ON, but the specified HIP_PATH (${HIP_PATH}) does not exist")
+ endif()
+
+endif()
+
diff --git a/unsupported/test/EulerAngles.cpp b/unsupported/test/EulerAngles.cpp
new file mode 100644
index 0000000..0955795
--- /dev/null
+++ b/unsupported/test/EulerAngles.cpp
@@ -0,0 +1,296 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2015 Tal Hadad <tal_hd@hotmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "main.h"
+
+#include <unsupported/Eigen/EulerAngles>
+
+using namespace Eigen;
+
+// Unfortunately, we need to specialize it in order to work. (We could add it in main.h test framework)
+template <typename Scalar, class System>
+bool verifyIsApprox(const Eigen::EulerAngles<Scalar, System>& a, const Eigen::EulerAngles<Scalar, System>& b)
+{
+ return verifyIsApprox(a.angles(), b.angles());
+}
+
+// Verify that x is in the approxed range [a, b]
+#define VERIFY_APPROXED_RANGE(a, x, b) \
+ do { \
+ VERIFY_IS_APPROX_OR_LESS_THAN(a, x); \
+ VERIFY_IS_APPROX_OR_LESS_THAN(x, b); \
+ } while(0)
+
+const char X = EULER_X;
+const char Y = EULER_Y;
+const char Z = EULER_Z;
+
+template<typename Scalar, class EulerSystem>
+void verify_euler(const EulerAngles<Scalar, EulerSystem>& e)
+{
+ typedef EulerAngles<Scalar, EulerSystem> EulerAnglesType;
+ typedef Matrix<Scalar,3,3> Matrix3;
+ typedef Matrix<Scalar,3,1> Vector3;
+ typedef Quaternion<Scalar> QuaternionType;
+ typedef AngleAxis<Scalar> AngleAxisType;
+
+ const Scalar ONE = Scalar(1);
+ const Scalar HALF_PI = Scalar(EIGEN_PI / 2);
+ const Scalar PI = Scalar(EIGEN_PI);
+
+ // It's very important calc the acceptable precision depending on the distance from the pole.
+ const Scalar longitudeRadius = std::abs(
+ EulerSystem::IsTaitBryan ?
+ std::cos(e.beta()) :
+ std::sin(e.beta())
+ );
+ Scalar precision = test_precision<Scalar>() / longitudeRadius;
+
+ Scalar betaRangeStart, betaRangeEnd;
+ if (EulerSystem::IsTaitBryan)
+ {
+ betaRangeStart = -HALF_PI;
+ betaRangeEnd = HALF_PI;
+ }
+ else
+ {
+ if (!EulerSystem::IsBetaOpposite)
+ {
+ betaRangeStart = 0;
+ betaRangeEnd = PI;
+ }
+ else
+ {
+ betaRangeStart = -PI;
+ betaRangeEnd = 0;
+ }
+ }
+
+ const Vector3 I_ = EulerAnglesType::AlphaAxisVector();
+ const Vector3 J_ = EulerAnglesType::BetaAxisVector();
+ const Vector3 K_ = EulerAnglesType::GammaAxisVector();
+
+ // Is approx checks
+ VERIFY(e.isApprox(e));
+ VERIFY_IS_APPROX(e, e);
+ VERIFY_IS_NOT_APPROX(e, EulerAnglesType(e.alpha() + ONE, e.beta() + ONE, e.gamma() + ONE));
+
+ const Matrix3 m(e);
+ VERIFY_IS_APPROX(Scalar(m.determinant()), ONE);
+
+ EulerAnglesType ebis(m);
+
+ // When no roll(acting like polar representation), we have the best precision.
+ // One of those cases is when the Euler angles are on the pole, and because it's singular case,
+ // the computation returns no roll.
+ if (ebis.beta() == 0)
+ precision = test_precision<Scalar>();
+
+ // Check that eabis in range
+ VERIFY_APPROXED_RANGE(-PI, ebis.alpha(), PI);
+ VERIFY_APPROXED_RANGE(betaRangeStart, ebis.beta(), betaRangeEnd);
+ VERIFY_APPROXED_RANGE(-PI, ebis.gamma(), PI);
+
+ const Matrix3 mbis(AngleAxisType(ebis.alpha(), I_) * AngleAxisType(ebis.beta(), J_) * AngleAxisType(ebis.gamma(), K_));
+ VERIFY_IS_APPROX(Scalar(mbis.determinant()), ONE);
+ VERIFY_IS_APPROX(mbis, ebis.toRotationMatrix());
+ /*std::cout << "===================\n" <<
+ "e: " << e << std::endl <<
+ "eabis: " << eabis.transpose() << std::endl <<
+ "m: " << m << std::endl <<
+ "mbis: " << mbis << std::endl <<
+ "X: " << (m * Vector3::UnitX()).transpose() << std::endl <<
+ "X: " << (mbis * Vector3::UnitX()).transpose() << std::endl;*/
+ VERIFY(m.isApprox(mbis, precision));
+
+ // Test if ea and eabis are the same
+ // Need to check both singular and non-singular cases
+ // There are two singular cases.
+ // 1. When I==K and sin(ea(1)) == 0
+ // 2. When I!=K and cos(ea(1)) == 0
+
+ // TODO: Make this test work well, and use range saturation function.
+ /*// If I==K, and ea[1]==0, then there no unique solution.
+ // The remark apply in the case where I!=K, and |ea[1]| is close to +-pi/2.
+ if( (i!=k || ea[1]!=0) && (i==k || !internal::isApprox(abs(ea[1]),Scalar(EIGEN_PI/2),test_precision<Scalar>())) )
+ VERIFY_IS_APPROX(ea, eabis);*/
+
+ // Quaternions
+ const QuaternionType q(e);
+ ebis = q;
+ const QuaternionType qbis(ebis);
+ VERIFY(internal::isApprox<Scalar>(std::abs(q.dot(qbis)), ONE, precision));
+ //VERIFY_IS_APPROX(eabis, eabis2);// Verify that the euler angles are still the same
+
+ // A suggestion for simple product test when will be supported.
+ /*EulerAnglesType e2(PI/2, PI/2, PI/2);
+ Matrix3 m2(e2);
+ VERIFY_IS_APPROX(e*e2, m*m2);*/
+}
+
+template<signed char A, signed char B, signed char C, typename Scalar>
+void verify_euler_vec(const Matrix<Scalar,3,1>& ea)
+{
+ verify_euler(EulerAngles<Scalar, EulerSystem<A, B, C> >(ea[0], ea[1], ea[2]));
+}
+
+template<signed char A, signed char B, signed char C, typename Scalar>
+void verify_euler_all_neg(const Matrix<Scalar,3,1>& ea)
+{
+ verify_euler_vec<+A,+B,+C>(ea);
+ verify_euler_vec<+A,+B,-C>(ea);
+ verify_euler_vec<+A,-B,+C>(ea);
+ verify_euler_vec<+A,-B,-C>(ea);
+
+ verify_euler_vec<-A,+B,+C>(ea);
+ verify_euler_vec<-A,+B,-C>(ea);
+ verify_euler_vec<-A,-B,+C>(ea);
+ verify_euler_vec<-A,-B,-C>(ea);
+}
+
+template<typename Scalar> void check_all_var(const Matrix<Scalar,3,1>& ea)
+{
+ verify_euler_all_neg<X,Y,Z>(ea);
+ verify_euler_all_neg<X,Y,X>(ea);
+ verify_euler_all_neg<X,Z,Y>(ea);
+ verify_euler_all_neg<X,Z,X>(ea);
+
+ verify_euler_all_neg<Y,Z,X>(ea);
+ verify_euler_all_neg<Y,Z,Y>(ea);
+ verify_euler_all_neg<Y,X,Z>(ea);
+ verify_euler_all_neg<Y,X,Y>(ea);
+
+ verify_euler_all_neg<Z,X,Y>(ea);
+ verify_euler_all_neg<Z,X,Z>(ea);
+ verify_euler_all_neg<Z,Y,X>(ea);
+ verify_euler_all_neg<Z,Y,Z>(ea);
+}
+
+template<typename Scalar> void check_singular_cases(const Scalar& singularBeta)
+{
+ typedef Matrix<Scalar,3,1> Vector3;
+ const Scalar PI = Scalar(EIGEN_PI);
+
+ for (Scalar epsilon = NumTraits<Scalar>::epsilon(); epsilon < 1; epsilon *= Scalar(1.2))
+ {
+ check_all_var(Vector3(PI/4, singularBeta, PI/3));
+ check_all_var(Vector3(PI/4, singularBeta - epsilon, PI/3));
+ check_all_var(Vector3(PI/4, singularBeta - Scalar(1.5)*epsilon, PI/3));
+ check_all_var(Vector3(PI/4, singularBeta - 2*epsilon, PI/3));
+ check_all_var(Vector3(PI*Scalar(0.8), singularBeta - epsilon, Scalar(0.9)*PI));
+ check_all_var(Vector3(PI*Scalar(-0.9), singularBeta + epsilon, PI*Scalar(0.3)));
+ check_all_var(Vector3(PI*Scalar(-0.6), singularBeta + Scalar(1.5)*epsilon, PI*Scalar(0.3)));
+ check_all_var(Vector3(PI*Scalar(-0.5), singularBeta + 2*epsilon, PI*Scalar(0.4)));
+ check_all_var(Vector3(PI*Scalar(0.9), singularBeta + epsilon, Scalar(0.8)*PI));
+ }
+
+ // This one for sanity, it had a problem with near pole cases in float scalar.
+ check_all_var(Vector3(PI*Scalar(0.8), singularBeta - Scalar(1E-6), Scalar(0.9)*PI));
+}
+
+template<typename Scalar> void eulerangles_manual()
+{
+ typedef Matrix<Scalar,3,1> Vector3;
+ typedef Matrix<Scalar,Dynamic,1> VectorX;
+ const Vector3 Zero = Vector3::Zero();
+ const Scalar PI = Scalar(EIGEN_PI);
+
+ check_all_var(Zero);
+
+ // singular cases
+ check_singular_cases(PI/2);
+ check_singular_cases(-PI/2);
+
+ check_singular_cases(Scalar(0));
+ check_singular_cases(Scalar(-0));
+
+ check_singular_cases(PI);
+ check_singular_cases(-PI);
+
+ // non-singular cases
+ VectorX alpha = VectorX::LinSpaced(20, Scalar(-0.99) * PI, PI);
+ VectorX beta = VectorX::LinSpaced(20, Scalar(-0.49) * PI, Scalar(0.49) * PI);
+ VectorX gamma = VectorX::LinSpaced(20, Scalar(-0.99) * PI, PI);
+ for (int i = 0; i < alpha.size(); ++i) {
+ for (int j = 0; j < beta.size(); ++j) {
+ for (int k = 0; k < gamma.size(); ++k) {
+ check_all_var(Vector3(alpha(i), beta(j), gamma(k)));
+ }
+ }
+ }
+}
+
+template<typename Scalar> void eulerangles_rand()
+{
+ typedef Matrix<Scalar,3,3> Matrix3;
+ typedef Matrix<Scalar,3,1> Vector3;
+ typedef Array<Scalar,3,1> Array3;
+ typedef Quaternion<Scalar> Quaternionx;
+ typedef AngleAxis<Scalar> AngleAxisType;
+
+ Scalar a = internal::random<Scalar>(-Scalar(EIGEN_PI), Scalar(EIGEN_PI));
+ Quaternionx q1;
+ q1 = AngleAxisType(a, Vector3::Random().normalized());
+ Matrix3 m;
+ m = q1;
+
+ Vector3 ea = m.eulerAngles(0,1,2);
+ check_all_var(ea);
+ ea = m.eulerAngles(0,1,0);
+ check_all_var(ea);
+
+ // Check with purely random Quaternion:
+ q1.coeffs() = Quaternionx::Coefficients::Random().normalized();
+ m = q1;
+ ea = m.eulerAngles(0,1,2);
+ check_all_var(ea);
+ ea = m.eulerAngles(0,1,0);
+ check_all_var(ea);
+
+ // Check with random angles in range [0:pi]x[-pi:pi]x[-pi:pi].
+ ea = (Array3::Random() + Array3(1,0,0))*Scalar(EIGEN_PI)*Array3(0.5,1,1);
+ check_all_var(ea);
+
+ ea[2] = ea[0] = internal::random<Scalar>(0,Scalar(EIGEN_PI));
+ check_all_var(ea);
+
+ ea[0] = ea[1] = internal::random<Scalar>(0,Scalar(EIGEN_PI));
+ check_all_var(ea);
+
+ ea[1] = 0;
+ check_all_var(ea);
+
+ ea.head(2).setZero();
+ check_all_var(ea);
+
+ ea.setZero();
+ check_all_var(ea);
+}
+
+EIGEN_DECLARE_TEST(EulerAngles)
+{
+ // Simple cast test
+ EulerAnglesXYZd onesEd(1, 1, 1);
+ EulerAnglesXYZf onesEf = onesEd.cast<float>();
+ VERIFY_IS_APPROX(onesEd, onesEf.cast<double>());
+
+ // Simple Construction from Vector3 test
+ VERIFY_IS_APPROX(onesEd, EulerAnglesXYZd(Vector3d::Ones()));
+
+ CALL_SUBTEST_1( eulerangles_manual<float>() );
+ CALL_SUBTEST_2( eulerangles_manual<double>() );
+
+ for(int i = 0; i < g_repeat; i++) {
+ CALL_SUBTEST_3( eulerangles_rand<float>() );
+ CALL_SUBTEST_4( eulerangles_rand<double>() );
+ }
+
+ // TODO: Add tests for auto diff
+ // TODO: Add tests for complex numbers
+}
diff --git a/unsupported/test/FFT.cpp b/unsupported/test/FFT.cpp
new file mode 100644
index 0000000..f85461c
--- /dev/null
+++ b/unsupported/test/FFT.cpp
@@ -0,0 +1,2 @@
+#define EIGEN_FFT_DEFAULT 1
+#include "fft_test_shared.h"
diff --git a/unsupported/test/FFTW.cpp b/unsupported/test/FFTW.cpp
new file mode 100644
index 0000000..d69867c
--- /dev/null
+++ b/unsupported/test/FFTW.cpp
@@ -0,0 +1,2 @@
+#define EIGEN_FFTW_DEFAULT 1
+#include "fft_test_shared.h"
diff --git a/unsupported/test/NNLS.cpp b/unsupported/test/NNLS.cpp
new file mode 100644
index 0000000..d65920b
--- /dev/null
+++ b/unsupported/test/NNLS.cpp
@@ -0,0 +1,472 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) Essex Edwards <essex.edwards@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#define EIGEN_RUNTIME_NO_MALLOC
+
+#include "main.h"
+#include <unsupported/Eigen/NNLS>
+
+/// Check that 'x' solves the NNLS optimization problem `min ||A*x-b|| s.t. 0 <= x`.
+/// The \p tolerance parameter is the absolute tolerance on the gradient, A'*(A*x-b).
+template <typename MatrixType, typename VectorB, typename VectorX, typename Scalar>
+static void verify_nnls_optimality(const MatrixType &A, const VectorB &b, const VectorX &x, const Scalar tolerance) {
+ // The NNLS optimality conditions are:
+ //
+ // * 0 = A'*A*x - A'*b - lambda
+ // * 0 <= x[i] \forall i
+ // * 0 <= lambda[i] \forall i
+ // * 0 = x[i]*lambda[i] \forall i
+ //
+ // we don't know lambda, but by assuming the first optimality condition is true,
+ // we can derive it and then check the others conditions.
+ const VectorX lambda = A.transpose() * (A * x - b);
+
+ // NNLS solutions are EXACTLY not negative.
+ VERIFY_LE(0, x.minCoeff());
+
+ // Exact lambda would be non-negative, but computed lambda might leak a little
+ VERIFY_LE(-tolerance, lambda.minCoeff());
+
+ // x[i]*lambda[i] == 0 <~~> (x[i]==0) || (lambda[i] is small)
+ VERIFY(((x.array() == Scalar(0)) || (lambda.array() <= tolerance)).all());
+}
+
+template <typename MatrixType, typename VectorB, typename VectorX>
+static void test_nnls_known_solution(const MatrixType &A, const VectorB &b, const VectorX &x_expected) {
+ using Scalar = typename MatrixType::Scalar;
+
+ using std::sqrt;
+ const Scalar tolerance = sqrt(Eigen::GenericNumTraits<Scalar>::epsilon());
+ Index max_iter = 5 * A.cols(); // A heuristic guess.
+ NNLS<MatrixType> nnls(A, max_iter, tolerance);
+ const VectorX x = nnls.solve(b);
+
+ VERIFY_IS_EQUAL(nnls.info(), ComputationInfo::Success);
+ VERIFY_IS_APPROX(x, x_expected);
+ verify_nnls_optimality(A, b, x, tolerance);
+}
+
+template <typename MatrixType>
+static void test_nnls_random_problem() {
+ //
+ // SETUP
+ //
+
+ Index cols = MatrixType::ColsAtCompileTime;
+ if (cols == Dynamic) cols = internal::random<Index>(1, EIGEN_TEST_MAX_SIZE);
+ Index rows = MatrixType::RowsAtCompileTime;
+ if (rows == Dynamic) rows = internal::random<Index>(cols, EIGEN_TEST_MAX_SIZE);
+ VERIFY_LE(cols, rows); // To have a unique LS solution: cols <= rows.
+
+ // Make some sort of random test problem from a wide range of scales and condition numbers.
+ using std::pow;
+ using Scalar = typename MatrixType::Scalar;
+ const Scalar sqrtConditionNumber = pow(Scalar(10), internal::random<Scalar>(Scalar(0), Scalar(2)));
+ const Scalar scaleA = pow(Scalar(10), internal::random<Scalar>(Scalar(-3), Scalar(3)));
+ const Scalar minSingularValue = scaleA / sqrtConditionNumber;
+ const Scalar maxSingularValue = scaleA * sqrtConditionNumber;
+ MatrixType A(rows, cols);
+ generateRandomMatrixSvs(setupRangeSvs<Matrix<Scalar, Dynamic, 1>>(cols, minSingularValue, maxSingularValue), rows,
+ cols, A);
+
+ // Make a random RHS also with a random scaling.
+ using VectorB = decltype(A.col(0).eval());
+ const Scalar scaleB = pow(Scalar(10), internal::random<Scalar>(Scalar(-3), Scalar(3)));
+ const VectorB b = scaleB * VectorB::Random(A.rows());
+
+ //
+ // ACT
+ //
+
+ using Scalar = typename MatrixType::Scalar;
+ using std::sqrt;
+ const Scalar tolerance =
+ sqrt(Eigen::GenericNumTraits<Scalar>::epsilon()) * b.cwiseAbs().maxCoeff() * A.cwiseAbs().maxCoeff();
+ Index max_iter = 5 * A.cols(); // A heuristic guess.
+ NNLS<MatrixType> nnls(A, max_iter, tolerance);
+ const typename NNLS<MatrixType>::SolutionVectorType &x = nnls.solve(b);
+
+ //
+ // VERIFY
+ //
+
+ // In fact, NNLS can fail on some problems, but they are rare in practice.
+ VERIFY_IS_EQUAL(nnls.info(), ComputationInfo::Success);
+ verify_nnls_optimality(A, b, x, tolerance);
+}
+
+static void test_nnls_handles_zero_rhs() {
+ //
+ // SETUP
+ //
+ const Index cols = internal::random<Index>(1, EIGEN_TEST_MAX_SIZE);
+ const Index rows = internal::random<Index>(cols, EIGEN_TEST_MAX_SIZE);
+ const MatrixXd A = MatrixXd::Random(rows, cols);
+ const VectorXd b = VectorXd::Zero(rows);
+
+ //
+ // ACT
+ //
+ NNLS<MatrixXd> nnls(A);
+ const VectorXd x = nnls.solve(b);
+
+ //
+ // VERIFY
+ //
+ VERIFY_IS_EQUAL(nnls.info(), ComputationInfo::Success);
+ VERIFY_LE(nnls.iterations(), 1); // 0 or 1 would be be fine for an edge case like this.
+ VERIFY_IS_EQUAL(x, VectorXd::Zero(cols));
+}
+
+static void test_nnls_handles_Mx0_matrix() {
+ //
+ // SETUP
+ //
+ const Index rows = internal::random<Index>(1, EIGEN_TEST_MAX_SIZE);
+ const MatrixXd A(rows, 0);
+ const VectorXd b = VectorXd::Random(rows);
+
+ //
+ // ACT
+ //
+ NNLS<MatrixXd> nnls(A);
+ const VectorXd x = nnls.solve(b);
+
+ //
+ // VERIFY
+ //
+ VERIFY_IS_EQUAL(nnls.info(), ComputationInfo::Success);
+ VERIFY_LE(nnls.iterations(), 0);
+ VERIFY_IS_EQUAL(x.size(), 0);
+}
+
+static void test_nnls_handles_0x0_matrix() {
+ //
+ // SETUP
+ //
+ const MatrixXd A(0, 0);
+ const VectorXd b(0);
+
+ //
+ // ACT
+ //
+ NNLS<MatrixXd> nnls(A);
+ const VectorXd x = nnls.solve(b);
+
+ //
+ // VERIFY
+ //
+ VERIFY_IS_EQUAL(nnls.info(), ComputationInfo::Success);
+ VERIFY_LE(nnls.iterations(), 0);
+ VERIFY_IS_EQUAL(x.size(), 0);
+}
+
+static void test_nnls_handles_dependent_columns() {
+ //
+ // SETUP
+ //
+ const Index rank = internal::random<Index>(1, EIGEN_TEST_MAX_SIZE / 2);
+ const Index cols = 2 * rank;
+ const Index rows = internal::random<Index>(cols, EIGEN_TEST_MAX_SIZE);
+ const MatrixXd A = MatrixXd::Random(rows, rank) * MatrixXd::Random(rank, cols);
+ const VectorXd b = VectorXd::Random(rows);
+
+ //
+ // ACT
+ //
+ const double tolerance = 1e-8;
+ NNLS<MatrixXd> nnls(A);
+ const VectorXd &x = nnls.solve(b);
+
+ //
+ // VERIFY
+ //
+ // What should happen when the input 'A' has dependent columns?
+ // We might still succeed. Or we might not converge.
+ // Either outcome is fine. If Success is indicated,
+ // then 'x' must actually be a solution vector.
+
+ if (nnls.info() == ComputationInfo::Success) {
+ verify_nnls_optimality(A, b, x, tolerance);
+ }
+}
+
+static void test_nnls_handles_wide_matrix() {
+ //
+ // SETUP
+ //
+ const Index cols = internal::random<Index>(2, EIGEN_TEST_MAX_SIZE);
+ const Index rows = internal::random<Index>(2, cols - 1);
+ const MatrixXd A = MatrixXd::Random(rows, cols);
+ const VectorXd b = VectorXd::Random(rows);
+
+ //
+ // ACT
+ //
+ const double tolerance = 1e-8;
+ NNLS<MatrixXd> nnls(A);
+ const VectorXd &x = nnls.solve(b);
+
+ //
+ // VERIFY
+ //
+ // What should happen when the input 'A' is wide?
+ // The unconstrained least-squares problem has infinitely many solutions.
+ // Subject the the non-negativity constraints,
+ // the solution might actually be unique (e.g. it is [0,0,..,0]).
+ // So, NNLS might succeed or it might fail.
+ // Either outcome is fine. If Success is indicated,
+ // then 'x' must actually be a solution vector.
+
+ if (nnls.info() == ComputationInfo::Success) {
+ verify_nnls_optimality(A, b, x, tolerance);
+ }
+}
+
+// 4x2 problem, unconstrained solution positive
+static void test_nnls_known_1() {
+ Matrix<double, 4, 2> A(4, 2);
+ Matrix<double, 4, 1> b(4);
+ Matrix<double, 2, 1> x(2);
+ A << 1, 1, 2, 4, 3, 9, 4, 16;
+ b << 0.6, 2.2, 4.8, 8.4;
+ x << 0.1, 0.5;
+
+ return test_nnls_known_solution(A, b, x);
+}
+
+// 4x3 problem, unconstrained solution positive
+static void test_nnls_known_2() {
+ Matrix<double, 4, 3> A(4, 3);
+ Matrix<double, 4, 1> b(4);
+ Matrix<double, 3, 1> x(3);
+
+ A << 1, 1, 1, 2, 4, 8, 3, 9, 27, 4, 16, 64;
+ b << 0.73, 3.24, 8.31, 16.72;
+ x << 0.1, 0.5, 0.13;
+
+ test_nnls_known_solution(A, b, x);
+}
+
+// Simple 4x4 problem, unconstrained solution non-negative
+static void test_nnls_known_3() {
+ Matrix<double, 4, 4> A(4, 4);
+ Matrix<double, 4, 1> b(4);
+ Matrix<double, 4, 1> x(4);
+
+ A << 1, 1, 1, 1, 2, 4, 8, 16, 3, 9, 27, 81, 4, 16, 64, 256;
+ b << 0.73, 3.24, 8.31, 16.72;
+ x << 0.1, 0.5, 0.13, 0;
+
+ test_nnls_known_solution(A, b, x);
+}
+
+// Simple 4x3 problem, unconstrained solution non-negative
+static void test_nnls_known_4() {
+ Matrix<double, 4, 3> A(4, 3);
+ Matrix<double, 4, 1> b(4);
+ Matrix<double, 3, 1> x(3);
+
+ A << 1, 1, 1, 2, 4, 8, 3, 9, 27, 4, 16, 64;
+ b << 0.23, 1.24, 3.81, 8.72;
+ x << 0.1, 0, 0.13;
+
+ test_nnls_known_solution(A, b, x);
+}
+
+// Simple 4x3 problem, unconstrained solution indefinite
+static void test_nnls_known_5() {
+ Matrix<double, 4, 3> A(4, 3);
+ Matrix<double, 4, 1> b(4);
+ Matrix<double, 3, 1> x(3);
+
+ A << 1, 1, 1, 2, 4, 8, 3, 9, 27, 4, 16, 64;
+ b << 0.13, 0.84, 2.91, 7.12;
+ // Solution obtained by original nnls() implementation in Fortran
+ x << 0.0, 0.0, 0.1106544;
+
+ test_nnls_known_solution(A, b, x);
+}
+
+static void test_nnls_small_reference_problems() {
+ test_nnls_known_1();
+ test_nnls_known_2();
+ test_nnls_known_3();
+ test_nnls_known_4();
+ test_nnls_known_5();
+}
+
+static void test_nnls_with_half_precision() {
+ // The random matrix generation tools don't work with `half`,
+ // so here's a simpler setup mostly just to check that NNLS compiles & runs with custom scalar types.
+
+ using Mat = Matrix<half, 8, 2>;
+ using VecB = Matrix<half, 8, 1>;
+ using VecX = Matrix<half, 2, 1>;
+ Mat A = Mat::Random(); // full-column rank with high probability.
+ VecB b = VecB::Random();
+
+ NNLS<Mat> nnls(A, 20, half(1e-2f));
+ const VecX x = nnls.solve(b);
+
+ VERIFY_IS_EQUAL(nnls.info(), ComputationInfo::Success);
+ verify_nnls_optimality(A, b, x, half(1e-1));
+}
+
+static void test_nnls_special_case_solves_in_zero_iterations() {
+ // The particular NNLS algorithm that is implemented starts with all variables
+ // in the active set.
+ // This test builds a system where all constraints are active at the solution,
+ // so that initial guess is already correct.
+ //
+ // If the implementation changes to another algorithm that does not have this property,
+ // then this test will need to change (e.g. starting from all constraints inactive,
+ // or using ADMM, or an interior point solver).
+
+ const Index n = 10;
+ const Index m = 3 * n;
+ const VectorXd b = VectorXd::Random(m);
+ // With high probability, this is full column rank, which we need for uniqueness.
+ MatrixXd A = MatrixXd::Random(m, n);
+ // Make every column of `A` such that adding it to the active set only /increases/ the objective,
+ // this ensuring the NNLS solution is all zeros.
+ const VectorXd alignment = -(A.transpose() * b).cwiseSign();
+ A = A * alignment.asDiagonal();
+
+ NNLS<MatrixXd> nnls(A);
+ nnls.solve(b);
+
+ VERIFY_IS_EQUAL(nnls.info(), ComputationInfo::Success);
+ VERIFY(nnls.iterations() == 0);
+}
+
+static void test_nnls_special_case_solves_in_n_iterations() {
+ // The particular NNLS algorithm that is implemented starts with all variables
+ // in the active set and then adds one variable to the inactive set each iteration.
+ // This test builds a system where all variables are inactive at the solution,
+ // so it should take 'n' iterations to get there.
+ //
+ // If the implementation changes to another algorithm that does not have this property,
+ // then this test will need to change (e.g. starting from all constraints inactive,
+ // or using ADMM, or an interior point solver).
+
+ const Index n = 10;
+ const Index m = 3 * n;
+ // With high probability, this is full column rank, which we need for uniqueness.
+ const MatrixXd A = MatrixXd::Random(m, n);
+ const VectorXd x = VectorXd::Random(n).cwiseAbs().array() + 1; // all positive.
+ const VectorXd b = A * x;
+
+ NNLS<MatrixXd> nnls(A);
+ nnls.solve(b);
+
+ VERIFY_IS_EQUAL(nnls.info(), ComputationInfo::Success);
+ VERIFY(nnls.iterations() == n);
+}
+
+static void test_nnls_returns_NoConvergence_when_maxIterations_is_too_low() {
+ // Using the special case that takes `n` iterations,
+ // from `test_nnls_special_case_solves_in_n_iterations`,
+ // we can set max iterations too low and that should cause the solve to fail.
+
+ const Index n = 10;
+ const Index m = 3 * n;
+ // With high probability, this is full column rank, which we need for uniqueness.
+ const MatrixXd A = MatrixXd::Random(m, n);
+ const VectorXd x = VectorXd::Random(n).cwiseAbs().array() + 1; // all positive.
+ const VectorXd b = A * x;
+
+ NNLS<MatrixXd> nnls(A);
+ const Index max_iters = n - 1;
+ nnls.setMaxIterations(max_iters);
+ nnls.solve(b);
+
+ VERIFY_IS_EQUAL(nnls.info(), ComputationInfo::NoConvergence);
+ VERIFY(nnls.iterations() == max_iters);
+}
+
+static void test_nnls_default_maxIterations_is_twice_column_count() {
+ const Index cols = internal::random<Index>(1, EIGEN_TEST_MAX_SIZE);
+ const Index rows = internal::random<Index>(cols, EIGEN_TEST_MAX_SIZE);
+ const MatrixXd A = MatrixXd::Random(rows, cols);
+
+ NNLS<MatrixXd> nnls(A);
+
+ VERIFY_IS_EQUAL(nnls.maxIterations(), 2 * cols);
+}
+
+static void test_nnls_does_not_allocate_during_solve() {
+ const Index cols = internal::random<Index>(1, EIGEN_TEST_MAX_SIZE);
+ const Index rows = internal::random<Index>(cols, EIGEN_TEST_MAX_SIZE);
+ const MatrixXd A = MatrixXd::Random(rows, cols);
+ const VectorXd b = VectorXd::Random(rows);
+
+ NNLS<MatrixXd> nnls(A);
+
+ internal::set_is_malloc_allowed(false);
+ nnls.solve(b);
+ internal::set_is_malloc_allowed(true);
+}
+
+static void test_nnls_repeated_calls_to_compute_and_solve() {
+ const Index cols2 = internal::random<Index>(1, EIGEN_TEST_MAX_SIZE);
+ const Index rows2 = internal::random<Index>(cols2, EIGEN_TEST_MAX_SIZE);
+ const MatrixXd A2 = MatrixXd::Random(rows2, cols2);
+ const VectorXd b2 = VectorXd::Random(rows2);
+
+ NNLS<MatrixXd> nnls;
+
+ for (int i = 0; i < 4; ++i) {
+ const Index cols = internal::random<Index>(1, EIGEN_TEST_MAX_SIZE);
+ const Index rows = internal::random<Index>(cols, EIGEN_TEST_MAX_SIZE);
+ const MatrixXd A = MatrixXd::Random(rows, cols);
+
+ nnls.compute(A);
+ VERIFY_IS_EQUAL(nnls.info(), ComputationInfo::Success);
+
+ for (int j = 0; j < 3; ++j) {
+ const VectorXd b = VectorXd::Random(rows);
+ const VectorXd x = nnls.solve(b);
+ VERIFY_IS_EQUAL(nnls.info(), ComputationInfo::Success);
+ verify_nnls_optimality(A, b, x, 1e-4);
+ }
+ }
+}
+
+EIGEN_DECLARE_TEST(NNLS) {
+ // Small matrices with known solutions:
+ CALL_SUBTEST_1(test_nnls_small_reference_problems());
+ CALL_SUBTEST_1(test_nnls_handles_Mx0_matrix());
+ CALL_SUBTEST_1(test_nnls_handles_0x0_matrix());
+
+ for (int i = 0; i < g_repeat; i++) {
+ // Essential NNLS properties, across different types.
+ CALL_SUBTEST_2(test_nnls_random_problem<MatrixXf>());
+ CALL_SUBTEST_3(test_nnls_random_problem<MatrixXd>());
+ using MatFixed = Matrix<double, 12, 5>;
+ CALL_SUBTEST_4(test_nnls_random_problem<MatFixed>());
+ CALL_SUBTEST_5(test_nnls_with_half_precision());
+
+ // Robustness tests:
+ CALL_SUBTEST_6(test_nnls_handles_zero_rhs());
+ CALL_SUBTEST_6(test_nnls_handles_dependent_columns());
+ CALL_SUBTEST_6(test_nnls_handles_wide_matrix());
+
+ // Properties specific to the implementation,
+ // not NNLS in general.
+ CALL_SUBTEST_7(test_nnls_special_case_solves_in_zero_iterations());
+ CALL_SUBTEST_7(test_nnls_special_case_solves_in_n_iterations());
+ CALL_SUBTEST_7(test_nnls_returns_NoConvergence_when_maxIterations_is_too_low());
+ CALL_SUBTEST_7(test_nnls_default_maxIterations_is_twice_column_count());
+ CALL_SUBTEST_8(test_nnls_repeated_calls_to_compute_and_solve());
+
+ // This test fails. It hits allocations in HouseholderSequence.h
+ // test_nnls_does_not_allocate_during_solve();
+ }
+}
diff --git a/unsupported/test/NonLinearOptimization.cpp b/unsupported/test/NonLinearOptimization.cpp
new file mode 100644
index 0000000..aaa96ec
--- /dev/null
+++ b/unsupported/test/NonLinearOptimization.cpp
@@ -0,0 +1,1883 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009 Thomas Capricelli <orzel@freehackers.org>
+
+#include <stdio.h>
+
+#include "main.h"
+#include <unsupported/Eigen/NonLinearOptimization>
+
+// This disables some useless Warnings on MSVC.
+// It is intended to be done for this test only.
+#include <Eigen/src/Core/util/DisableStupidWarnings.h>
+
+// tolerance for checking number of iterations
+#define LM_EVAL_COUNT_TOL 2
+
+#define LM_CHECK_N_ITERS(SOLVER,NFEV,NJEV) { \
+ VERIFY(SOLVER.nfev <= NFEV * LM_EVAL_COUNT_TOL); \
+ VERIFY(SOLVER.njev <= NJEV * LM_EVAL_COUNT_TOL); \
+ }
+
+int fcn_chkder(const VectorXd &x, VectorXd &fvec, MatrixXd &fjac, int iflag)
+{
+ /* subroutine fcn for chkder example. */
+
+ int i;
+ assert(15 == fvec.size());
+ assert(3 == x.size());
+ double tmp1, tmp2, tmp3, tmp4;
+ static const double y[15]={1.4e-1, 1.8e-1, 2.2e-1, 2.5e-1, 2.9e-1, 3.2e-1, 3.5e-1,
+ 3.9e-1, 3.7e-1, 5.8e-1, 7.3e-1, 9.6e-1, 1.34, 2.1, 4.39};
+
+
+ if (iflag == 0)
+ return 0;
+
+ if (iflag != 2)
+ for (i=0; i<15; i++) {
+ tmp1 = i+1;
+ tmp2 = 16-i-1;
+ tmp3 = tmp1;
+ if (i >= 8) tmp3 = tmp2;
+ fvec[i] = y[i] - (x[0] + tmp1/(x[1]*tmp2 + x[2]*tmp3));
+ }
+ else {
+ for (i = 0; i < 15; i++) {
+ tmp1 = i+1;
+ tmp2 = 16-i-1;
+
+ /* error introduced into next statement for illustration. */
+ /* corrected statement should read tmp3 = tmp1 . */
+
+ tmp3 = tmp2;
+ if (i >= 8) tmp3 = tmp2;
+ tmp4 = (x[1]*tmp2 + x[2]*tmp3); tmp4=tmp4*tmp4;
+ fjac(i,0) = -1.;
+ fjac(i,1) = tmp1*tmp2/tmp4;
+ fjac(i,2) = tmp1*tmp3/tmp4;
+ }
+ }
+ return 0;
+}
+
+
+void testChkder()
+{
+ const int m=15, n=3;
+ VectorXd x(n), fvec(m), xp, fvecp(m), err;
+ MatrixXd fjac(m,n);
+ VectorXi ipvt;
+
+ /* the following values should be suitable for */
+ /* checking the jacobian matrix. */
+ x << 9.2e-1, 1.3e-1, 5.4e-1;
+
+ internal::chkder(x, fvec, fjac, xp, fvecp, 1, err);
+ fcn_chkder(x, fvec, fjac, 1);
+ fcn_chkder(x, fvec, fjac, 2);
+ fcn_chkder(xp, fvecp, fjac, 1);
+ internal::chkder(x, fvec, fjac, xp, fvecp, 2, err);
+
+ fvecp -= fvec;
+
+ // check those
+ VectorXd fvec_ref(m), fvecp_ref(m), err_ref(m);
+ fvec_ref <<
+ -1.181606, -1.429655, -1.606344,
+ -1.745269, -1.840654, -1.921586,
+ -1.984141, -2.022537, -2.468977,
+ -2.827562, -3.473582, -4.437612,
+ -6.047662, -9.267761, -18.91806;
+ fvecp_ref <<
+ -7.724666e-09, -3.432406e-09, -2.034843e-10,
+ 2.313685e-09, 4.331078e-09, 5.984096e-09,
+ 7.363281e-09, 8.53147e-09, 1.488591e-08,
+ 2.33585e-08, 3.522012e-08, 5.301255e-08,
+ 8.26666e-08, 1.419747e-07, 3.19899e-07;
+ err_ref <<
+ 0.1141397, 0.09943516, 0.09674474,
+ 0.09980447, 0.1073116, 0.1220445,
+ 0.1526814, 1, 1,
+ 1, 1, 1,
+ 1, 1, 1;
+
+ VERIFY_IS_APPROX(fvec, fvec_ref);
+ VERIFY_IS_APPROX(fvecp, fvecp_ref);
+ VERIFY_IS_APPROX(err, err_ref);
+}
+
+// Generic functor
+template<typename Scalar_, int NX=Dynamic, int NY=Dynamic>
+struct Functor
+{
+ typedef Scalar_ Scalar;
+ enum {
+ InputsAtCompileTime = NX,
+ ValuesAtCompileTime = NY
+ };
+ typedef Matrix<Scalar,InputsAtCompileTime,1> InputType;
+ typedef Matrix<Scalar,ValuesAtCompileTime,1> ValueType;
+ typedef Matrix<Scalar,ValuesAtCompileTime,InputsAtCompileTime> JacobianType;
+
+ const int m_inputs, m_values;
+
+ Functor() : m_inputs(InputsAtCompileTime), m_values(ValuesAtCompileTime) {}
+ Functor(int inputs, int values) : m_inputs(inputs), m_values(values) {}
+
+ int inputs() const { return m_inputs; }
+ int values() const { return m_values; }
+
+ // you should define that in the subclass :
+// void operator() (const InputType& x, ValueType* v, JacobianType* _j=0) const;
+};
+
+struct lmder_functor : Functor<double>
+{
+ lmder_functor(void): Functor<double>(3,15) {}
+ int operator()(const VectorXd &x, VectorXd &fvec) const
+ {
+ double tmp1, tmp2, tmp3;
+ static const double y[15] = {1.4e-1, 1.8e-1, 2.2e-1, 2.5e-1, 2.9e-1, 3.2e-1, 3.5e-1,
+ 3.9e-1, 3.7e-1, 5.8e-1, 7.3e-1, 9.6e-1, 1.34, 2.1, 4.39};
+
+ for (int i = 0; i < values(); i++)
+ {
+ tmp1 = i+1;
+ tmp2 = 16 - i - 1;
+ tmp3 = (i>=8)? tmp2 : tmp1;
+ fvec[i] = y[i] - (x[0] + tmp1/(x[1]*tmp2 + x[2]*tmp3));
+ }
+ return 0;
+ }
+
+ int df(const VectorXd &x, MatrixXd &fjac) const
+ {
+ double tmp1, tmp2, tmp3, tmp4;
+ for (int i = 0; i < values(); i++)
+ {
+ tmp1 = i+1;
+ tmp2 = 16 - i - 1;
+ tmp3 = (i>=8)? tmp2 : tmp1;
+ tmp4 = (x[1]*tmp2 + x[2]*tmp3); tmp4 = tmp4*tmp4;
+ fjac(i,0) = -1;
+ fjac(i,1) = tmp1*tmp2/tmp4;
+ fjac(i,2) = tmp1*tmp3/tmp4;
+ }
+ return 0;
+ }
+};
+
+void testLmder1()
+{
+ int n=3, info;
+
+ VectorXd x;
+
+ /* the following starting values provide a rough fit. */
+ x.setConstant(n, 1.);
+
+ // do the computation
+ lmder_functor functor;
+ LevenbergMarquardt<lmder_functor> lm(functor);
+ info = lm.lmder1(x);
+ EIGEN_UNUSED_VARIABLE(info)
+
+ // check return value
+ // VERIFY_IS_EQUAL(info, 1);
+ LM_CHECK_N_ITERS(lm, 6, 5);
+
+ // check norm
+ VERIFY_IS_APPROX(lm.fvec.blueNorm(), 0.09063596);
+
+ // check x
+ VectorXd x_ref(n);
+ x_ref << 0.08241058, 1.133037, 2.343695;
+ VERIFY_IS_APPROX(x, x_ref);
+}
+
+void testLmder()
+{
+ const int m=15, n=3;
+ int info;
+ double fnorm, covfac;
+ VectorXd x;
+
+ /* the following starting values provide a rough fit. */
+ x.setConstant(n, 1.);
+
+ // do the computation
+ lmder_functor functor;
+ LevenbergMarquardt<lmder_functor> lm(functor);
+ info = lm.minimize(x);
+ EIGEN_UNUSED_VARIABLE(info)
+
+ // check return values
+ // VERIFY_IS_EQUAL(info, 1);
+ LM_CHECK_N_ITERS(lm, 6, 5);
+
+ // check norm
+ fnorm = lm.fvec.blueNorm();
+ VERIFY_IS_APPROX(fnorm, 0.09063596);
+
+ // check x
+ VectorXd x_ref(n);
+ x_ref << 0.08241058, 1.133037, 2.343695;
+ VERIFY_IS_APPROX(x, x_ref);
+
+ // check covariance
+ covfac = fnorm*fnorm/(m-n);
+ internal::covar(lm.fjac, lm.permutation.indices()); // TODO : move this as a function of lm
+
+ MatrixXd cov_ref(n,n);
+ cov_ref <<
+ 0.0001531202, 0.002869941, -0.002656662,
+ 0.002869941, 0.09480935, -0.09098995,
+ -0.002656662, -0.09098995, 0.08778727;
+
+// std::cout << fjac*covfac << std::endl;
+
+ MatrixXd cov;
+ cov = covfac*lm.fjac.topLeftCorner<n,n>();
+ VERIFY_IS_APPROX( cov, cov_ref);
+ // TODO: why isn't this allowed ? :
+ // VERIFY_IS_APPROX( covfac*fjac.topLeftCorner<n,n>() , cov_ref);
+}
+
+struct hybrj_functor : Functor<double>
+{
+ hybrj_functor(void) : Functor<double>(9,9) {}
+
+ int operator()(const VectorXd &x, VectorXd &fvec)
+ {
+ double temp, temp1, temp2;
+ const VectorXd::Index n = x.size();
+ assert(fvec.size()==n);
+ for (VectorXd::Index k = 0; k < n; k++)
+ {
+ temp = (3. - 2.*x[k])*x[k];
+ temp1 = 0.;
+ if (k) temp1 = x[k-1];
+ temp2 = 0.;
+ if (k != n-1) temp2 = x[k+1];
+ fvec[k] = temp - temp1 - 2.*temp2 + 1.;
+ }
+ return 0;
+ }
+ int df(const VectorXd &x, MatrixXd &fjac)
+ {
+ const VectorXd::Index n = x.size();
+ assert(fjac.rows()==n);
+ assert(fjac.cols()==n);
+ for (VectorXd::Index k = 0; k < n; k++)
+ {
+ for (VectorXd::Index j = 0; j < n; j++)
+ fjac(k,j) = 0.;
+ fjac(k,k) = 3.- 4.*x[k];
+ if (k) fjac(k,k-1) = -1.;
+ if (k != n-1) fjac(k,k+1) = -2.;
+ }
+ return 0;
+ }
+};
+
+
+void testHybrj1()
+{
+ const int n=9;
+ int info;
+ VectorXd x(n);
+
+ /* the following starting values provide a rough fit. */
+ x.setConstant(n, -1.);
+
+ // do the computation
+ hybrj_functor functor;
+ HybridNonLinearSolver<hybrj_functor> solver(functor);
+ info = solver.hybrj1(x);
+ EIGEN_UNUSED_VARIABLE(info)
+
+ // check return value
+ // VERIFY_IS_EQUAL(info, 1);
+ LM_CHECK_N_ITERS(solver, 11, 1);
+
+ // check norm
+ VERIFY_IS_APPROX(solver.fvec.blueNorm(), 1.192636e-08);
+
+
+// check x
+ VectorXd x_ref(n);
+ x_ref <<
+ -0.5706545, -0.6816283, -0.7017325,
+ -0.7042129, -0.701369, -0.6918656,
+ -0.665792, -0.5960342, -0.4164121;
+ VERIFY_IS_APPROX(x, x_ref);
+}
+
+void testHybrj()
+{
+ const int n=9;
+ int info;
+ VectorXd x(n);
+
+ /* the following starting values provide a rough fit. */
+ x.setConstant(n, -1.);
+
+
+ // do the computation
+ hybrj_functor functor;
+ HybridNonLinearSolver<hybrj_functor> solver(functor);
+ solver.diag.setConstant(n, 1.);
+ solver.useExternalScaling = true;
+ info = solver.solve(x);
+ EIGEN_UNUSED_VARIABLE(info)
+
+ // check return value
+ // VERIFY_IS_EQUAL(info, 1);
+ LM_CHECK_N_ITERS(solver, 11, 1);
+
+ // check norm
+ VERIFY_IS_APPROX(solver.fvec.blueNorm(), 1.192636e-08);
+
+
+// check x
+ VectorXd x_ref(n);
+ x_ref <<
+ -0.5706545, -0.6816283, -0.7017325,
+ -0.7042129, -0.701369, -0.6918656,
+ -0.665792, -0.5960342, -0.4164121;
+ VERIFY_IS_APPROX(x, x_ref);
+
+}
+
+struct hybrd_functor : Functor<double>
+{
+ hybrd_functor(void) : Functor<double>(9,9) {}
+ int operator()(const VectorXd &x, VectorXd &fvec) const
+ {
+ double temp, temp1, temp2;
+ const VectorXd::Index n = x.size();
+
+ assert(fvec.size()==n);
+ for (VectorXd::Index k=0; k < n; k++)
+ {
+ temp = (3. - 2.*x[k])*x[k];
+ temp1 = 0.;
+ if (k) temp1 = x[k-1];
+ temp2 = 0.;
+ if (k != n-1) temp2 = x[k+1];
+ fvec[k] = temp - temp1 - 2.*temp2 + 1.;
+ }
+ return 0;
+ }
+};
+
+void testHybrd1()
+{
+ int n=9, info;
+ VectorXd x(n);
+
+ /* the following starting values provide a rough solution. */
+ x.setConstant(n, -1.);
+
+ // do the computation
+ hybrd_functor functor;
+ HybridNonLinearSolver<hybrd_functor> solver(functor);
+ info = solver.hybrd1(x);
+ EIGEN_UNUSED_VARIABLE(info)
+
+ // check return value
+ // VERIFY_IS_EQUAL(info, 1);
+ VERIFY(solver.nfev <= 20*LM_EVAL_COUNT_TOL);
+
+ // check norm
+ VERIFY_IS_APPROX(solver.fvec.blueNorm(), 1.192636e-08);
+
+ // check x
+ VectorXd x_ref(n);
+ x_ref << -0.5706545, -0.6816283, -0.7017325, -0.7042129, -0.701369, -0.6918656, -0.665792, -0.5960342, -0.4164121;
+ VERIFY_IS_APPROX(x, x_ref);
+}
+
+void testHybrd()
+{
+ const int n=9;
+ int info;
+ VectorXd x;
+
+ /* the following starting values provide a rough fit. */
+ x.setConstant(n, -1.);
+
+ // do the computation
+ hybrd_functor functor;
+ HybridNonLinearSolver<hybrd_functor> solver(functor);
+ solver.parameters.nb_of_subdiagonals = 1;
+ solver.parameters.nb_of_superdiagonals = 1;
+ solver.diag.setConstant(n, 1.);
+ solver.useExternalScaling = true;
+ info = solver.solveNumericalDiff(x);
+ EIGEN_UNUSED_VARIABLE(info)
+
+ // check return value
+ // VERIFY_IS_EQUAL(info, 1);
+ VERIFY(solver.nfev <= 14*LM_EVAL_COUNT_TOL);
+
+ // check norm
+ VERIFY_IS_APPROX(solver.fvec.blueNorm(), 1.192636e-08);
+
+ // check x
+ VectorXd x_ref(n);
+ x_ref <<
+ -0.5706545, -0.6816283, -0.7017325,
+ -0.7042129, -0.701369, -0.6918656,
+ -0.665792, -0.5960342, -0.4164121;
+ VERIFY_IS_APPROX(x, x_ref);
+}
+
+struct lmstr_functor : Functor<double>
+{
+ lmstr_functor(void) : Functor<double>(3,15) {}
+ int operator()(const VectorXd &x, VectorXd &fvec)
+ {
+ /* subroutine fcn for lmstr1 example. */
+ double tmp1, tmp2, tmp3;
+ static const double y[15]={1.4e-1, 1.8e-1, 2.2e-1, 2.5e-1, 2.9e-1, 3.2e-1, 3.5e-1,
+ 3.9e-1, 3.7e-1, 5.8e-1, 7.3e-1, 9.6e-1, 1.34, 2.1, 4.39};
+
+ assert(15==fvec.size());
+ assert(3==x.size());
+
+ for (int i=0; i<15; i++)
+ {
+ tmp1 = i+1;
+ tmp2 = 16 - i - 1;
+ tmp3 = (i>=8)? tmp2 : tmp1;
+ fvec[i] = y[i] - (x[0] + tmp1/(x[1]*tmp2 + x[2]*tmp3));
+ }
+ return 0;
+ }
+ int df(const VectorXd &x, VectorXd &jac_row, VectorXd::Index rownb)
+ {
+ assert(x.size()==3);
+ assert(jac_row.size()==x.size());
+ double tmp1, tmp2, tmp3, tmp4;
+
+ VectorXd::Index i = rownb-2;
+ tmp1 = i+1;
+ tmp2 = 16 - i - 1;
+ tmp3 = (i>=8)? tmp2 : tmp1;
+ tmp4 = (x[1]*tmp2 + x[2]*tmp3); tmp4 = tmp4*tmp4;
+ jac_row[0] = -1;
+ jac_row[1] = tmp1*tmp2/tmp4;
+ jac_row[2] = tmp1*tmp3/tmp4;
+ return 0;
+ }
+};
+
+void testLmstr1()
+{
+ const int n=3;
+ int info;
+
+ VectorXd x(n);
+
+ /* the following starting values provide a rough fit. */
+ x.setConstant(n, 1.);
+
+ // do the computation
+ lmstr_functor functor;
+ LevenbergMarquardt<lmstr_functor> lm(functor);
+ info = lm.lmstr1(x);
+ EIGEN_UNUSED_VARIABLE(info)
+
+ // check return value
+ // VERIFY_IS_EQUAL(info, 1);
+ LM_CHECK_N_ITERS(lm, 6, 5);
+
+ // check norm
+ VERIFY_IS_APPROX(lm.fvec.blueNorm(), 0.09063596);
+
+ // check x
+ VectorXd x_ref(n);
+ x_ref << 0.08241058, 1.133037, 2.343695 ;
+ VERIFY_IS_APPROX(x, x_ref);
+}
+
+void testLmstr()
+{
+ const int n=3;
+ int info;
+ double fnorm;
+ VectorXd x(n);
+
+ /* the following starting values provide a rough fit. */
+ x.setConstant(n, 1.);
+
+ // do the computation
+ lmstr_functor functor;
+ LevenbergMarquardt<lmstr_functor> lm(functor);
+ info = lm.minimizeOptimumStorage(x);
+ EIGEN_UNUSED_VARIABLE(info)
+
+ // check return values
+ // VERIFY_IS_EQUAL(info, 1);
+ LM_CHECK_N_ITERS(lm, 6, 5);
+
+ // check norm
+ fnorm = lm.fvec.blueNorm();
+ VERIFY_IS_APPROX(fnorm, 0.09063596);
+
+ // check x
+ VectorXd x_ref(n);
+ x_ref << 0.08241058, 1.133037, 2.343695;
+ VERIFY_IS_APPROX(x, x_ref);
+
+}
+
+struct lmdif_functor : Functor<double>
+{
+ lmdif_functor(void) : Functor<double>(3,15) {}
+ int operator()(const VectorXd &x, VectorXd &fvec) const
+ {
+ int i;
+ double tmp1,tmp2,tmp3;
+ static const double y[15]={1.4e-1,1.8e-1,2.2e-1,2.5e-1,2.9e-1,3.2e-1,3.5e-1,3.9e-1,
+ 3.7e-1,5.8e-1,7.3e-1,9.6e-1,1.34e0,2.1e0,4.39e0};
+
+ assert(x.size()==3);
+ assert(fvec.size()==15);
+ for (i=0; i<15; i++)
+ {
+ tmp1 = i+1;
+ tmp2 = 15 - i;
+ tmp3 = tmp1;
+
+ if (i >= 8) tmp3 = tmp2;
+ fvec[i] = y[i] - (x[0] + tmp1/(x[1]*tmp2 + x[2]*tmp3));
+ }
+ return 0;
+ }
+};
+
+void testLmdif1()
+{
+ const int n=3;
+ int info;
+
+ VectorXd x(n), fvec(15);
+
+ /* the following starting values provide a rough fit. */
+ x.setConstant(n, 1.);
+
+ // do the computation
+ lmdif_functor functor;
+ DenseIndex nfev = -1; // initialize to avoid maybe-uninitialized warning
+ info = LevenbergMarquardt<lmdif_functor>::lmdif1(functor, x, &nfev);
+ EIGEN_UNUSED_VARIABLE(info)
+
+ // check return value
+ // VERIFY_IS_EQUAL(info, 1);
+ VERIFY( nfev <= 26*LM_EVAL_COUNT_TOL);
+
+ // check norm
+ functor(x, fvec);
+ VERIFY_IS_APPROX(fvec.blueNorm(), 0.09063596);
+
+ // check x
+ VectorXd x_ref(n);
+ x_ref << 0.0824106, 1.1330366, 2.3436947;
+ VERIFY_IS_APPROX(x, x_ref);
+
+}
+
+void testLmdif()
+{
+ const int m=15, n=3;
+ int info;
+ double fnorm, covfac;
+ VectorXd x(n);
+
+ /* the following starting values provide a rough fit. */
+ x.setConstant(n, 1.);
+
+ // do the computation
+ lmdif_functor functor;
+ NumericalDiff<lmdif_functor> numDiff(functor);
+ LevenbergMarquardt<NumericalDiff<lmdif_functor> > lm(numDiff);
+ info = lm.minimize(x);
+ EIGEN_UNUSED_VARIABLE(info)
+
+ // check return values
+ // VERIFY_IS_EQUAL(info, 1);
+ VERIFY(lm.nfev <= 26*LM_EVAL_COUNT_TOL);
+
+ // check norm
+ fnorm = lm.fvec.blueNorm();
+ VERIFY_IS_APPROX(fnorm, 0.09063596);
+
+ // check x
+ VectorXd x_ref(n);
+ x_ref << 0.08241058, 1.133037, 2.343695;
+ VERIFY_IS_APPROX(x, x_ref);
+
+ // check covariance
+ covfac = fnorm*fnorm/(m-n);
+ internal::covar(lm.fjac, lm.permutation.indices()); // TODO : move this as a function of lm
+
+ MatrixXd cov_ref(n,n);
+ cov_ref <<
+ 0.0001531202, 0.002869942, -0.002656662,
+ 0.002869942, 0.09480937, -0.09098997,
+ -0.002656662, -0.09098997, 0.08778729;
+
+// std::cout << fjac*covfac << std::endl;
+
+ MatrixXd cov;
+ cov = covfac*lm.fjac.topLeftCorner<n,n>();
+ VERIFY_IS_APPROX( cov, cov_ref);
+ // TODO: why isn't this allowed ? :
+ // VERIFY_IS_APPROX( covfac*fjac.topLeftCorner<n,n>() , cov_ref);
+}
+
+struct chwirut2_functor : Functor<double>
+{
+ chwirut2_functor(void) : Functor<double>(3,54) {}
+ static const double m_x[54];
+ static const double m_y[54];
+ int operator()(const VectorXd &b, VectorXd &fvec)
+ {
+ int i;
+
+ assert(b.size()==3);
+ assert(fvec.size()==54);
+ for(i=0; i<54; i++) {
+ double x = m_x[i];
+ fvec[i] = exp(-b[0]*x)/(b[1]+b[2]*x) - m_y[i];
+ }
+ return 0;
+ }
+ int df(const VectorXd &b, MatrixXd &fjac)
+ {
+ assert(b.size()==3);
+ assert(fjac.rows()==54);
+ assert(fjac.cols()==3);
+ for(int i=0; i<54; i++) {
+ double x = m_x[i];
+ double factor = 1./(b[1]+b[2]*x);
+ double e = exp(-b[0]*x);
+ fjac(i,0) = -x*e*factor;
+ fjac(i,1) = -e*factor*factor;
+ fjac(i,2) = -x*e*factor*factor;
+ }
+ return 0;
+ }
+};
+const double chwirut2_functor::m_x[54] = { 0.500E0, 1.000E0, 1.750E0, 3.750E0, 5.750E0, 0.875E0, 2.250E0, 3.250E0, 5.250E0, 0.750E0, 1.750E0, 2.750E0, 4.750E0, 0.625E0, 1.250E0, 2.250E0, 4.250E0, .500E0, 3.000E0, .750E0, 3.000E0, 1.500E0, 6.000E0, 3.000E0, 6.000E0, 1.500E0, 3.000E0, .500E0, 2.000E0, 4.000E0, .750E0, 2.000E0, 5.000E0, .750E0, 2.250E0, 3.750E0, 5.750E0, 3.000E0, .750E0, 2.500E0, 4.000E0, .750E0, 2.500E0, 4.000E0, .750E0, 2.500E0, 4.000E0, .500E0, 6.000E0, 3.000E0, .500E0, 2.750E0, .500E0, 1.750E0};
+const double chwirut2_functor::m_y[54] = { 92.9000E0 ,57.1000E0 ,31.0500E0 ,11.5875E0 ,8.0250E0 ,63.6000E0 ,21.4000E0 ,14.2500E0 ,8.4750E0 ,63.8000E0 ,26.8000E0 ,16.4625E0 ,7.1250E0 ,67.3000E0 ,41.0000E0 ,21.1500E0 ,8.1750E0 ,81.5000E0 ,13.1200E0 ,59.9000E0 ,14.6200E0 ,32.9000E0 ,5.4400E0 ,12.5600E0 ,5.4400E0 ,32.0000E0 ,13.9500E0 ,75.8000E0 ,20.0000E0 ,10.4200E0 ,59.5000E0 ,21.6700E0 ,8.5500E0 ,62.0000E0 ,20.2000E0 ,7.7600E0 ,3.7500E0 ,11.8100E0 ,54.7000E0 ,23.7000E0 ,11.5500E0 ,61.3000E0 ,17.7000E0 ,8.7400E0 ,59.2000E0 ,16.3000E0 ,8.6200E0 ,81.0000E0 ,4.8700E0 ,14.6200E0 ,81.7000E0 ,17.1700E0 ,81.3000E0 ,28.9000E0 };
+
+// http://www.itl.nist.gov/div898/strd/nls/data/chwirut2.shtml
+void testNistChwirut2(void)
+{
+ const int n=3;
+ int info;
+
+ VectorXd x(n);
+
+ /*
+ * First try
+ */
+ x<< 0.1, 0.01, 0.02;
+ // do the computation
+ chwirut2_functor functor;
+ LevenbergMarquardt<chwirut2_functor> lm(functor);
+ info = lm.minimize(x);
+ EIGEN_UNUSED_VARIABLE(info)
+
+ // check return value
+ // VERIFY_IS_EQUAL(info, 1);
+ LM_CHECK_N_ITERS(lm, 10, 8);
+ // check norm^2
+ VERIFY_IS_APPROX(lm.fvec.squaredNorm(), 5.1304802941E+02);
+ // check x
+ VERIFY_IS_APPROX(x[0], 1.6657666537E-01);
+ VERIFY_IS_APPROX(x[1], 5.1653291286E-03);
+ VERIFY_IS_APPROX(x[2], 1.2150007096E-02);
+
+ /*
+ * Second try
+ */
+ x<< 0.15, 0.008, 0.010;
+ // do the computation
+ lm.resetParameters();
+ lm.parameters.ftol = 1.E6*NumTraits<double>::epsilon();
+ lm.parameters.xtol = 1.E6*NumTraits<double>::epsilon();
+ info = lm.minimize(x);
+ EIGEN_UNUSED_VARIABLE(info)
+
+ // check return value
+ // VERIFY_IS_EQUAL(info, 1);
+ LM_CHECK_N_ITERS(lm, 7, 6);
+ // check norm^2
+ VERIFY_IS_APPROX(lm.fvec.squaredNorm(), 5.1304802941E+02);
+ // check x
+ VERIFY_IS_APPROX(x[0], 1.6657666537E-01);
+ VERIFY_IS_APPROX(x[1], 5.1653291286E-03);
+ VERIFY_IS_APPROX(x[2], 1.2150007096E-02);
+}
+
+
+struct misra1a_functor : Functor<double>
+{
+ misra1a_functor(void) : Functor<double>(2,14) {}
+ static const double m_x[14];
+ static const double m_y[14];
+ int operator()(const VectorXd &b, VectorXd &fvec)
+ {
+ assert(b.size()==2);
+ assert(fvec.size()==14);
+ for(int i=0; i<14; i++) {
+ fvec[i] = b[0]*(1.-exp(-b[1]*m_x[i])) - m_y[i] ;
+ }
+ return 0;
+ }
+ int df(const VectorXd &b, MatrixXd &fjac)
+ {
+ assert(b.size()==2);
+ assert(fjac.rows()==14);
+ assert(fjac.cols()==2);
+ for(int i=0; i<14; i++) {
+ fjac(i,0) = (1.-exp(-b[1]*m_x[i]));
+ fjac(i,1) = (b[0]*m_x[i]*exp(-b[1]*m_x[i]));
+ }
+ return 0;
+ }
+};
+const double misra1a_functor::m_x[14] = { 77.6E0, 114.9E0, 141.1E0, 190.8E0, 239.9E0, 289.0E0, 332.8E0, 378.4E0, 434.8E0, 477.3E0, 536.8E0, 593.1E0, 689.1E0, 760.0E0};
+const double misra1a_functor::m_y[14] = { 10.07E0, 14.73E0, 17.94E0, 23.93E0, 29.61E0, 35.18E0, 40.02E0, 44.82E0, 50.76E0, 55.05E0, 61.01E0, 66.40E0, 75.47E0, 81.78E0};
+
+// http://www.itl.nist.gov/div898/strd/nls/data/misra1a.shtml
+void testNistMisra1a(void)
+{
+ const int n=2;
+ int info;
+
+ VectorXd x(n);
+
+ /*
+ * First try
+ */
+ x<< 500., 0.0001;
+ // do the computation
+ misra1a_functor functor;
+ LevenbergMarquardt<misra1a_functor> lm(functor);
+ info = lm.minimize(x);
+ EIGEN_UNUSED_VARIABLE(info)
+
+ // check return value
+ // VERIFY_IS_EQUAL(info, 1);
+ LM_CHECK_N_ITERS(lm, 19, 15);
+ // check norm^2
+ VERIFY_IS_APPROX(lm.fvec.squaredNorm(), 1.2455138894E-01);
+ // check x
+ VERIFY_IS_APPROX(x[0], 2.3894212918E+02);
+ VERIFY_IS_APPROX(x[1], 5.5015643181E-04);
+
+ /*
+ * Second try
+ */
+ x<< 250., 0.0005;
+ // do the computation
+ info = lm.minimize(x);
+ EIGEN_UNUSED_VARIABLE(info)
+
+ // check return value
+ // VERIFY_IS_EQUAL(info, 1);
+ LM_CHECK_N_ITERS(lm, 5, 4);
+ // check norm^2
+ VERIFY_IS_APPROX(lm.fvec.squaredNorm(), 1.2455138894E-01);
+ // check x
+ VERIFY_IS_APPROX(x[0], 2.3894212918E+02);
+ VERIFY_IS_APPROX(x[1], 5.5015643181E-04);
+}
+
+struct hahn1_functor : Functor<double>
+{
+ hahn1_functor(void) : Functor<double>(7,236) {}
+ static const double m_x[236];
+ int operator()(const VectorXd &b, VectorXd &fvec)
+ {
+ static const double m_y[236] = { .591E0 , 1.547E0 , 2.902E0 , 2.894E0 , 4.703E0 , 6.307E0 , 7.03E0 , 7.898E0 , 9.470E0 , 9.484E0 , 10.072E0 , 10.163E0 , 11.615E0 , 12.005E0 , 12.478E0 , 12.982E0 , 12.970E0 , 13.926E0 , 14.452E0 , 14.404E0 , 15.190E0 , 15.550E0 , 15.528E0 , 15.499E0 , 16.131E0 , 16.438E0 , 16.387E0 , 16.549E0 , 16.872E0 , 16.830E0 , 16.926E0 , 16.907E0 , 16.966E0 , 17.060E0 , 17.122E0 , 17.311E0 , 17.355E0 , 17.668E0 , 17.767E0 , 17.803E0 , 17.765E0 , 17.768E0 , 17.736E0 , 17.858E0 , 17.877E0 , 17.912E0 , 18.046E0 , 18.085E0 , 18.291E0 , 18.357E0 , 18.426E0 , 18.584E0 , 18.610E0 , 18.870E0 , 18.795E0 , 19.111E0 , .367E0 , .796E0 , 0.892E0 , 1.903E0 , 2.150E0 , 3.697E0 , 5.870E0 , 6.421E0 , 7.422E0 , 9.944E0 , 11.023E0 , 11.87E0 , 12.786E0 , 14.067E0 , 13.974E0 , 14.462E0 , 14.464E0 , 15.381E0 , 15.483E0 , 15.59E0 , 16.075E0 , 16.347E0 , 16.181E0 , 16.915E0 , 17.003E0 , 16.978E0 , 17.756E0 , 17.808E0 , 17.868E0 , 18.481E0 , 18.486E0 , 19.090E0 , 16.062E0 , 16.337E0 , 16.345E0 ,
+ 16.388E0 , 17.159E0 , 17.116E0 , 17.164E0 , 17.123E0 , 17.979E0 , 17.974E0 , 18.007E0 , 17.993E0 , 18.523E0 , 18.669E0 , 18.617E0 , 19.371E0 , 19.330E0 , 0.080E0 , 0.248E0 , 1.089E0 , 1.418E0 , 2.278E0 , 3.624E0 , 4.574E0 , 5.556E0 , 7.267E0 , 7.695E0 , 9.136E0 , 9.959E0 , 9.957E0 , 11.600E0 , 13.138E0 , 13.564E0 , 13.871E0 , 13.994E0 , 14.947E0 , 15.473E0 , 15.379E0 , 15.455E0 , 15.908E0 , 16.114E0 , 17.071E0 , 17.135E0 , 17.282E0 , 17.368E0 , 17.483E0 , 17.764E0 , 18.185E0 , 18.271E0 , 18.236E0 , 18.237E0 , 18.523E0 , 18.627E0 , 18.665E0 , 19.086E0 , 0.214E0 , 0.943E0 , 1.429E0 , 2.241E0 , 2.951E0 , 3.782E0 , 4.757E0 , 5.602E0 , 7.169E0 , 8.920E0 , 10.055E0 , 12.035E0 , 12.861E0 , 13.436E0 , 14.167E0 , 14.755E0 , 15.168E0 , 15.651E0 , 15.746E0 , 16.216E0 , 16.445E0 , 16.965E0 , 17.121E0 , 17.206E0 , 17.250E0 , 17.339E0 , 17.793E0 , 18.123E0 , 18.49E0 , 18.566E0 , 18.645E0 , 18.706E0 , 18.924E0 , 19.1E0 , 0.375E0 , 0.471E0 , 1.504E0 , 2.204E0 , 2.813E0 , 4.765E0 , 9.835E0 , 10.040E0 , 11.946E0 , 12.596E0 ,
+13.303E0 , 13.922E0 , 14.440E0 , 14.951E0 , 15.627E0 , 15.639E0 , 15.814E0 , 16.315E0 , 16.334E0 , 16.430E0 , 16.423E0 , 17.024E0 , 17.009E0 , 17.165E0 , 17.134E0 , 17.349E0 , 17.576E0 , 17.848E0 , 18.090E0 , 18.276E0 , 18.404E0 , 18.519E0 , 19.133E0 , 19.074E0 , 19.239E0 , 19.280E0 , 19.101E0 , 19.398E0 , 19.252E0 , 19.89E0 , 20.007E0 , 19.929E0 , 19.268E0 , 19.324E0 , 20.049E0 , 20.107E0 , 20.062E0 , 20.065E0 , 19.286E0 , 19.972E0 , 20.088E0 , 20.743E0 , 20.83E0 , 20.935E0 , 21.035E0 , 20.93E0 , 21.074E0 , 21.085E0 , 20.935E0 };
+
+ // int called=0; printf("call hahn1_functor with iflag=%d, called=%d\n", iflag, called); if (iflag==1) called++;
+
+ assert(b.size()==7);
+ assert(fvec.size()==236);
+ for(int i=0; i<236; i++) {
+ double x=m_x[i], xx=x*x, xxx=xx*x;
+ fvec[i] = (b[0]+b[1]*x+b[2]*xx+b[3]*xxx) / (1.+b[4]*x+b[5]*xx+b[6]*xxx) - m_y[i];
+ }
+ return 0;
+ }
+
+ int df(const VectorXd &b, MatrixXd &fjac)
+ {
+ assert(b.size()==7);
+ assert(fjac.rows()==236);
+ assert(fjac.cols()==7);
+ for(int i=0; i<236; i++) {
+ double x=m_x[i], xx=x*x, xxx=xx*x;
+ double fact = 1./(1.+b[4]*x+b[5]*xx+b[6]*xxx);
+ fjac(i,0) = 1.*fact;
+ fjac(i,1) = x*fact;
+ fjac(i,2) = xx*fact;
+ fjac(i,3) = xxx*fact;
+ fact = - (b[0]+b[1]*x+b[2]*xx+b[3]*xxx) * fact * fact;
+ fjac(i,4) = x*fact;
+ fjac(i,5) = xx*fact;
+ fjac(i,6) = xxx*fact;
+ }
+ return 0;
+ }
+};
+const double hahn1_functor::m_x[236] = { 24.41E0 , 34.82E0 , 44.09E0 , 45.07E0 , 54.98E0 , 65.51E0 , 70.53E0 , 75.70E0 , 89.57E0 , 91.14E0 , 96.40E0 , 97.19E0 , 114.26E0 , 120.25E0 , 127.08E0 , 133.55E0 , 133.61E0 , 158.67E0 , 172.74E0 , 171.31E0 , 202.14E0 , 220.55E0 , 221.05E0 , 221.39E0 , 250.99E0 , 268.99E0 , 271.80E0 , 271.97E0 , 321.31E0 , 321.69E0 , 330.14E0 , 333.03E0 , 333.47E0 , 340.77E0 , 345.65E0 , 373.11E0 , 373.79E0 , 411.82E0 , 419.51E0 , 421.59E0 , 422.02E0 , 422.47E0 , 422.61E0 , 441.75E0 , 447.41E0 , 448.7E0 , 472.89E0 , 476.69E0 , 522.47E0 , 522.62E0 , 524.43E0 , 546.75E0 , 549.53E0 , 575.29E0 , 576.00E0 , 625.55E0 , 20.15E0 , 28.78E0 , 29.57E0 , 37.41E0 , 39.12E0 , 50.24E0 , 61.38E0 , 66.25E0 , 73.42E0 , 95.52E0 , 107.32E0 , 122.04E0 , 134.03E0 , 163.19E0 , 163.48E0 , 175.70E0 , 179.86E0 , 211.27E0 , 217.78E0 , 219.14E0 , 262.52E0 , 268.01E0 , 268.62E0 , 336.25E0 , 337.23E0 , 339.33E0 , 427.38E0 , 428.58E0 , 432.68E0 , 528.99E0 , 531.08E0 , 628.34E0 , 253.24E0 , 273.13E0 , 273.66E0 ,
+282.10E0 , 346.62E0 , 347.19E0 , 348.78E0 , 351.18E0 , 450.10E0 , 450.35E0 , 451.92E0 , 455.56E0 , 552.22E0 , 553.56E0 , 555.74E0 , 652.59E0 , 656.20E0 , 14.13E0 , 20.41E0 , 31.30E0 , 33.84E0 , 39.70E0 , 48.83E0 , 54.50E0 , 60.41E0 , 72.77E0 , 75.25E0 , 86.84E0 , 94.88E0 , 96.40E0 , 117.37E0 , 139.08E0 , 147.73E0 , 158.63E0 , 161.84E0 , 192.11E0 , 206.76E0 , 209.07E0 , 213.32E0 , 226.44E0 , 237.12E0 , 330.90E0 , 358.72E0 , 370.77E0 , 372.72E0 , 396.24E0 , 416.59E0 , 484.02E0 , 495.47E0 , 514.78E0 , 515.65E0 , 519.47E0 , 544.47E0 , 560.11E0 , 620.77E0 , 18.97E0 , 28.93E0 , 33.91E0 , 40.03E0 , 44.66E0 , 49.87E0 , 55.16E0 , 60.90E0 , 72.08E0 , 85.15E0 , 97.06E0 , 119.63E0 , 133.27E0 , 143.84E0 , 161.91E0 , 180.67E0 , 198.44E0 , 226.86E0 , 229.65E0 , 258.27E0 , 273.77E0 , 339.15E0 , 350.13E0 , 362.75E0 , 371.03E0 , 393.32E0 , 448.53E0 , 473.78E0 , 511.12E0 , 524.70E0 , 548.75E0 , 551.64E0 , 574.02E0 , 623.86E0 , 21.46E0 , 24.33E0 , 33.43E0 , 39.22E0 , 44.18E0 , 55.02E0 , 94.33E0 , 96.44E0 , 118.82E0 , 128.48E0 ,
+141.94E0 , 156.92E0 , 171.65E0 , 190.00E0 , 223.26E0 , 223.88E0 , 231.50E0 , 265.05E0 , 269.44E0 , 271.78E0 , 273.46E0 , 334.61E0 , 339.79E0 , 349.52E0 , 358.18E0 , 377.98E0 , 394.77E0 , 429.66E0 , 468.22E0 , 487.27E0 , 519.54E0 , 523.03E0 , 612.99E0 , 638.59E0 , 641.36E0 , 622.05E0 , 631.50E0 , 663.97E0 , 646.9E0 , 748.29E0 , 749.21E0 , 750.14E0 , 647.04E0 , 646.89E0 , 746.9E0 , 748.43E0 , 747.35E0 , 749.27E0 , 647.61E0 , 747.78E0 , 750.51E0 , 851.37E0 , 845.97E0 , 847.54E0 , 849.93E0 , 851.61E0 , 849.75E0 , 850.98E0 , 848.23E0};
+
+// http://www.itl.nist.gov/div898/strd/nls/data/hahn1.shtml
+void testNistHahn1(void)
+{
+ const int n=7;
+ int info;
+
+ VectorXd x(n);
+
+ /*
+ * First try
+ */
+ x<< 10., -1., .05, -.00001, -.05, .001, -.000001;
+ // do the computation
+ hahn1_functor functor;
+ LevenbergMarquardt<hahn1_functor> lm(functor);
+ info = lm.minimize(x);
+ EIGEN_UNUSED_VARIABLE(info)
+
+ // check return value
+ // VERIFY_IS_EQUAL(info, 1);
+ LM_CHECK_N_ITERS(lm, 11, 10);
+ // check norm^2
+ VERIFY_IS_APPROX(lm.fvec.squaredNorm(), 1.5324382854E+00);
+ // check x
+ VERIFY_IS_APPROX(x[0], 1.0776351733E+00);
+ VERIFY_IS_APPROX(x[1],-1.2269296921E-01);
+ VERIFY_IS_APPROX(x[2], 4.0863750610E-03);
+ VERIFY_IS_APPROX(x[3],-1.426264e-06); // shoulde be : -1.4262662514E-06
+ VERIFY_IS_APPROX(x[4],-5.7609940901E-03);
+ VERIFY_IS_APPROX(x[5], 2.4053735503E-04);
+ VERIFY_IS_APPROX(x[6],-1.2314450199E-07);
+
+ /*
+ * Second try
+ */
+ x<< .1, -.1, .005, -.000001, -.005, .0001, -.0000001;
+ // do the computation
+ info = lm.minimize(x);
+ EIGEN_UNUSED_VARIABLE(info)
+
+ // check return value
+ // VERIFY_IS_EQUAL(info, 1);
+ LM_CHECK_N_ITERS(lm, 11, 10);
+ // check norm^2
+ VERIFY_IS_APPROX(lm.fvec.squaredNorm(), 1.5324382854E+00);
+ // check x
+ VERIFY_IS_APPROX(x[0], 1.077640); // should be : 1.0776351733E+00
+ VERIFY_IS_APPROX(x[1], -0.1226933); // should be : -1.2269296921E-01
+ VERIFY_IS_APPROX(x[2], 0.004086383); // should be : 4.0863750610E-03
+ VERIFY_IS_APPROX(x[3], -1.426277e-06); // shoulde be : -1.4262662514E-06
+ VERIFY_IS_APPROX(x[4],-5.7609940901E-03);
+ VERIFY_IS_APPROX(x[5], 0.00024053772); // should be : 2.4053735503E-04
+ VERIFY_IS_APPROX(x[6], -1.231450e-07); // should be : -1.2314450199E-07
+
+}
+
+struct misra1d_functor : Functor<double>
+{
+ misra1d_functor(void) : Functor<double>(2,14) {}
+ static const double x[14];
+ static const double y[14];
+ int operator()(const VectorXd &b, VectorXd &fvec)
+ {
+ assert(b.size()==2);
+ assert(fvec.size()==14);
+ for(int i=0; i<14; i++) {
+ fvec[i] = b[0]*b[1]*x[i]/(1.+b[1]*x[i]) - y[i];
+ }
+ return 0;
+ }
+ int df(const VectorXd &b, MatrixXd &fjac)
+ {
+ assert(b.size()==2);
+ assert(fjac.rows()==14);
+ assert(fjac.cols()==2);
+ for(int i=0; i<14; i++) {
+ double den = 1.+b[1]*x[i];
+ fjac(i,0) = b[1]*x[i] / den;
+ fjac(i,1) = b[0]*x[i]*(den-b[1]*x[i])/den/den;
+ }
+ return 0;
+ }
+};
+const double misra1d_functor::x[14] = { 77.6E0, 114.9E0, 141.1E0, 190.8E0, 239.9E0, 289.0E0, 332.8E0, 378.4E0, 434.8E0, 477.3E0, 536.8E0, 593.1E0, 689.1E0, 760.0E0};
+const double misra1d_functor::y[14] = { 10.07E0, 14.73E0, 17.94E0, 23.93E0, 29.61E0, 35.18E0, 40.02E0, 44.82E0, 50.76E0, 55.05E0, 61.01E0, 66.40E0, 75.47E0, 81.78E0};
+
+// http://www.itl.nist.gov/div898/strd/nls/data/misra1d.shtml
+void testNistMisra1d(void)
+{
+ const int n=2;
+ int info;
+
+ VectorXd x(n);
+
+ /*
+ * First try
+ */
+ x<< 500., 0.0001;
+ // do the computation
+ misra1d_functor functor;
+ LevenbergMarquardt<misra1d_functor> lm(functor);
+ info = lm.minimize(x);
+ EIGEN_UNUSED_VARIABLE(info)
+
+ // check return value
+ // VERIFY_IS_EQUAL(info, 3);
+ LM_CHECK_N_ITERS(lm, 9, 7);
+ // check norm^2
+ VERIFY_IS_APPROX(lm.fvec.squaredNorm(), 5.6419295283E-02);
+ // check x
+ VERIFY_IS_APPROX(x[0], 4.3736970754E+02);
+ VERIFY_IS_APPROX(x[1], 3.0227324449E-04);
+
+ /*
+ * Second try
+ */
+ x<< 450., 0.0003;
+ // do the computation
+ info = lm.minimize(x);
+ EIGEN_UNUSED_VARIABLE(info)
+
+ // check return value
+ // VERIFY_IS_EQUAL(info, 1);
+ LM_CHECK_N_ITERS(lm, 4, 3);
+ // check norm^2
+ VERIFY_IS_APPROX(lm.fvec.squaredNorm(), 5.6419295283E-02);
+ // check x
+ VERIFY_IS_APPROX(x[0], 4.3736970754E+02);
+ VERIFY_IS_APPROX(x[1], 3.0227324449E-04);
+}
+
+
+struct lanczos1_functor : Functor<double>
+{
+ lanczos1_functor(void) : Functor<double>(6,24) {}
+ static const double x[24];
+ static const double y[24];
+ int operator()(const VectorXd &b, VectorXd &fvec)
+ {
+ assert(b.size()==6);
+ assert(fvec.size()==24);
+ for(int i=0; i<24; i++)
+ fvec[i] = b[0]*exp(-b[1]*x[i]) + b[2]*exp(-b[3]*x[i]) + b[4]*exp(-b[5]*x[i]) - y[i];
+ return 0;
+ }
+ int df(const VectorXd &b, MatrixXd &fjac)
+ {
+ assert(b.size()==6);
+ assert(fjac.rows()==24);
+ assert(fjac.cols()==6);
+ for(int i=0; i<24; i++) {
+ fjac(i,0) = exp(-b[1]*x[i]);
+ fjac(i,1) = -b[0]*x[i]*exp(-b[1]*x[i]);
+ fjac(i,2) = exp(-b[3]*x[i]);
+ fjac(i,3) = -b[2]*x[i]*exp(-b[3]*x[i]);
+ fjac(i,4) = exp(-b[5]*x[i]);
+ fjac(i,5) = -b[4]*x[i]*exp(-b[5]*x[i]);
+ }
+ return 0;
+ }
+};
+const double lanczos1_functor::x[24] = { 0.000000000000E+00, 5.000000000000E-02, 1.000000000000E-01, 1.500000000000E-01, 2.000000000000E-01, 2.500000000000E-01, 3.000000000000E-01, 3.500000000000E-01, 4.000000000000E-01, 4.500000000000E-01, 5.000000000000E-01, 5.500000000000E-01, 6.000000000000E-01, 6.500000000000E-01, 7.000000000000E-01, 7.500000000000E-01, 8.000000000000E-01, 8.500000000000E-01, 9.000000000000E-01, 9.500000000000E-01, 1.000000000000E+00, 1.050000000000E+00, 1.100000000000E+00, 1.150000000000E+00 };
+const double lanczos1_functor::y[24] = { 2.513400000000E+00 ,2.044333373291E+00 ,1.668404436564E+00 ,1.366418021208E+00 ,1.123232487372E+00 ,9.268897180037E-01 ,7.679338563728E-01 ,6.388775523106E-01 ,5.337835317402E-01 ,4.479363617347E-01 ,3.775847884350E-01 ,3.197393199326E-01 ,2.720130773746E-01 ,2.324965529032E-01 ,1.996589546065E-01 ,1.722704126914E-01 ,1.493405660168E-01 ,1.300700206922E-01 ,1.138119324644E-01 ,1.000415587559E-01 ,8.833209084540E-02 ,7.833544019350E-02 ,6.976693743449E-02 ,6.239312536719E-02 };
+
+// http://www.itl.nist.gov/div898/strd/nls/data/lanczos1.shtml
+void testNistLanczos1(void)
+{
+ const int n=6;
+ int info;
+
+ VectorXd x(n);
+
+ /*
+ * First try
+ */
+ x<< 1.2, 0.3, 5.6, 5.5, 6.5, 7.6;
+ // do the computation
+ lanczos1_functor functor;
+ LevenbergMarquardt<lanczos1_functor> lm(functor);
+ info = lm.minimize(x);
+ EIGEN_UNUSED_VARIABLE(info)
+
+ // check return value
+ // VERIFY_IS_EQUAL(info, 2);
+ LM_CHECK_N_ITERS(lm, 79, 72);
+ // check norm^2
+ // std::cout.precision(30);
+ // std::cout << lm.fvec.squaredNorm() << "\n";
+ VERIFY(lm.fvec.squaredNorm() <= 1.4307867721E-25);
+ // check x
+ VERIFY_IS_APPROX(x[0], 9.5100000027E-02);
+ VERIFY_IS_APPROX(x[1], 1.0000000001E+00);
+ VERIFY_IS_APPROX(x[2], 8.6070000013E-01);
+ VERIFY_IS_APPROX(x[3], 3.0000000002E+00);
+ VERIFY_IS_APPROX(x[4], 1.5575999998E+00);
+ VERIFY_IS_APPROX(x[5], 5.0000000001E+00);
+
+ /*
+ * Second try
+ */
+ x<< 0.5, 0.7, 3.6, 4.2, 4., 6.3;
+ // do the computation
+ info = lm.minimize(x);
+ EIGEN_UNUSED_VARIABLE(info)
+
+ // check return value
+ // VERIFY_IS_EQUAL(info, 2);
+ LM_CHECK_N_ITERS(lm, 9, 8);
+ // check norm^2
+ VERIFY(lm.fvec.squaredNorm() <= 1.4307867721E-25);
+ // check x
+ VERIFY_IS_APPROX(x[0], 9.5100000027E-02);
+ VERIFY_IS_APPROX(x[1], 1.0000000001E+00);
+ VERIFY_IS_APPROX(x[2], 8.6070000013E-01);
+ VERIFY_IS_APPROX(x[3], 3.0000000002E+00);
+ VERIFY_IS_APPROX(x[4], 1.5575999998E+00);
+ VERIFY_IS_APPROX(x[5], 5.0000000001E+00);
+
+}
+
+struct rat42_functor : Functor<double>
+{
+ rat42_functor(void) : Functor<double>(3,9) {}
+ static const double x[9];
+ static const double y[9];
+ int operator()(const VectorXd &b, VectorXd &fvec)
+ {
+ assert(b.size()==3);
+ assert(fvec.size()==9);
+ for(int i=0; i<9; i++) {
+ fvec[i] = b[0] / (1.+exp(b[1]-b[2]*x[i])) - y[i];
+ }
+ return 0;
+ }
+
+ int df(const VectorXd &b, MatrixXd &fjac)
+ {
+ assert(b.size()==3);
+ assert(fjac.rows()==9);
+ assert(fjac.cols()==3);
+ for(int i=0; i<9; i++) {
+ double e = exp(b[1]-b[2]*x[i]);
+ fjac(i,0) = 1./(1.+e);
+ fjac(i,1) = -b[0]*e/(1.+e)/(1.+e);
+ fjac(i,2) = +b[0]*e*x[i]/(1.+e)/(1.+e);
+ }
+ return 0;
+ }
+};
+const double rat42_functor::x[9] = { 9.000E0, 14.000E0, 21.000E0, 28.000E0, 42.000E0, 57.000E0, 63.000E0, 70.000E0, 79.000E0 };
+const double rat42_functor::y[9] = { 8.930E0 ,10.800E0 ,18.590E0 ,22.330E0 ,39.350E0 ,56.110E0 ,61.730E0 ,64.620E0 ,67.080E0 };
+
+// http://www.itl.nist.gov/div898/strd/nls/data/ratkowsky2.shtml
+void testNistRat42(void)
+{
+ const int n=3;
+ int info;
+
+ VectorXd x(n);
+
+ /*
+ * First try
+ */
+ x<< 100., 1., 0.1;
+ // do the computation
+ rat42_functor functor;
+ LevenbergMarquardt<rat42_functor> lm(functor);
+ info = lm.minimize(x);
+ EIGEN_UNUSED_VARIABLE(info)
+
+ // check return value
+ // VERIFY_IS_EQUAL(info, 1);
+ LM_CHECK_N_ITERS(lm, 10, 8);
+ // check norm^2
+ VERIFY_IS_APPROX(lm.fvec.squaredNorm(), 8.0565229338E+00);
+ // check x
+ VERIFY_IS_APPROX(x[0], 7.2462237576E+01);
+ VERIFY_IS_APPROX(x[1], 2.6180768402E+00);
+ VERIFY_IS_APPROX(x[2], 6.7359200066E-02);
+
+ /*
+ * Second try
+ */
+ x<< 75., 2.5, 0.07;
+ // do the computation
+ info = lm.minimize(x);
+ EIGEN_UNUSED_VARIABLE(info)
+
+ // check return value
+ // VERIFY_IS_EQUAL(info, 1);
+ LM_CHECK_N_ITERS(lm, 6, 5);
+ // check norm^2
+ VERIFY_IS_APPROX(lm.fvec.squaredNorm(), 8.0565229338E+00);
+ // check x
+ VERIFY_IS_APPROX(x[0], 7.2462237576E+01);
+ VERIFY_IS_APPROX(x[1], 2.6180768402E+00);
+ VERIFY_IS_APPROX(x[2], 6.7359200066E-02);
+}
+
+struct MGH10_functor : Functor<double>
+{
+ MGH10_functor(void) : Functor<double>(3,16) {}
+ static const double x[16];
+ static const double y[16];
+ int operator()(const VectorXd &b, VectorXd &fvec)
+ {
+ assert(b.size()==3);
+ assert(fvec.size()==16);
+ for(int i=0; i<16; i++)
+ fvec[i] = b[0] * exp(b[1]/(x[i]+b[2])) - y[i];
+ return 0;
+ }
+ int df(const VectorXd &b, MatrixXd &fjac)
+ {
+ assert(b.size()==3);
+ assert(fjac.rows()==16);
+ assert(fjac.cols()==3);
+ for(int i=0; i<16; i++) {
+ double factor = 1./(x[i]+b[2]);
+ double e = exp(b[1]*factor);
+ fjac(i,0) = e;
+ fjac(i,1) = b[0]*factor*e;
+ fjac(i,2) = -b[1]*b[0]*factor*factor*e;
+ }
+ return 0;
+ }
+};
+const double MGH10_functor::x[16] = { 5.000000E+01, 5.500000E+01, 6.000000E+01, 6.500000E+01, 7.000000E+01, 7.500000E+01, 8.000000E+01, 8.500000E+01, 9.000000E+01, 9.500000E+01, 1.000000E+02, 1.050000E+02, 1.100000E+02, 1.150000E+02, 1.200000E+02, 1.250000E+02 };
+const double MGH10_functor::y[16] = { 3.478000E+04, 2.861000E+04, 2.365000E+04, 1.963000E+04, 1.637000E+04, 1.372000E+04, 1.154000E+04, 9.744000E+03, 8.261000E+03, 7.030000E+03, 6.005000E+03, 5.147000E+03, 4.427000E+03, 3.820000E+03, 3.307000E+03, 2.872000E+03 };
+
+// http://www.itl.nist.gov/div898/strd/nls/data/mgh10.shtml
+void testNistMGH10(void)
+{
+ const int n=3;
+ int info;
+
+ VectorXd x(n);
+
+ /*
+ * First try
+ */
+ x<< 2., 400000., 25000.;
+ // do the computation
+ MGH10_functor functor;
+ LevenbergMarquardt<MGH10_functor> lm(functor);
+ info = lm.minimize(x);
+ EIGEN_UNUSED_VARIABLE(info)
+
+ // check return value
+ // VERIFY_IS_EQUAL(info, 2);
+ LM_CHECK_N_ITERS(lm, 284, 249);
+ // check norm^2
+ VERIFY_IS_APPROX(lm.fvec.squaredNorm(), 8.7945855171E+01);
+ // check x
+ VERIFY_IS_APPROX(x[0], 5.6096364710E-03);
+ VERIFY_IS_APPROX(x[1], 6.1813463463E+03);
+ VERIFY_IS_APPROX(x[2], 3.4522363462E+02);
+
+ /*
+ * Second try
+ */
+ x<< 0.02, 4000., 250.;
+ // do the computation
+ info = lm.minimize(x);
+ EIGEN_UNUSED_VARIABLE(info)
+
+ // check return value
+ // VERIFY_IS_EQUAL(info, 3);
+ LM_CHECK_N_ITERS(lm, 126, 116);
+ // check norm^2
+ VERIFY_IS_APPROX(lm.fvec.squaredNorm(), 8.7945855171E+01);
+ // check x
+ VERIFY_IS_APPROX(x[0], 5.6096364710E-03);
+ VERIFY_IS_APPROX(x[1], 6.1813463463E+03);
+ VERIFY_IS_APPROX(x[2], 3.4522363462E+02);
+}
+
+
+struct BoxBOD_functor : Functor<double>
+{
+ BoxBOD_functor(void) : Functor<double>(2,6) {}
+ static const double x[6];
+ int operator()(const VectorXd &b, VectorXd &fvec)
+ {
+ static const double y[6] = { 109., 149., 149., 191., 213., 224. };
+ assert(b.size()==2);
+ assert(fvec.size()==6);
+ for(int i=0; i<6; i++)
+ fvec[i] = b[0]*(1.-exp(-b[1]*x[i])) - y[i];
+ return 0;
+ }
+ int df(const VectorXd &b, MatrixXd &fjac)
+ {
+ assert(b.size()==2);
+ assert(fjac.rows()==6);
+ assert(fjac.cols()==2);
+ for(int i=0; i<6; i++) {
+ double e = exp(-b[1]*x[i]);
+ fjac(i,0) = 1.-e;
+ fjac(i,1) = b[0]*x[i]*e;
+ }
+ return 0;
+ }
+};
+const double BoxBOD_functor::x[6] = { 1., 2., 3., 5., 7., 10. };
+
+// http://www.itl.nist.gov/div898/strd/nls/data/boxbod.shtml
+void testNistBoxBOD(void)
+{
+ const int n=2;
+ int info;
+
+ VectorXd x(n);
+
+ /*
+ * First try
+ */
+ x<< 1., 1.;
+ // do the computation
+ BoxBOD_functor functor;
+ LevenbergMarquardt<BoxBOD_functor> lm(functor);
+ lm.parameters.ftol = 1.E6*NumTraits<double>::epsilon();
+ lm.parameters.xtol = 1.E6*NumTraits<double>::epsilon();
+ lm.parameters.factor = 10.;
+ info = lm.minimize(x);
+ EIGEN_UNUSED_VARIABLE(info)
+
+ // check return value
+ // VERIFY_IS_EQUAL(info, 1);
+ LM_CHECK_N_ITERS(lm, 31, 25);
+ // check norm^2
+ VERIFY_IS_APPROX(lm.fvec.squaredNorm(), 1.1680088766E+03);
+ // check x
+ VERIFY_IS_APPROX(x[0], 2.1380940889E+02);
+ VERIFY_IS_APPROX(x[1], 5.4723748542E-01);
+
+ /*
+ * Second try
+ */
+ x<< 100., 0.75;
+ // do the computation
+ lm.resetParameters();
+ lm.parameters.ftol = NumTraits<double>::epsilon();
+ lm.parameters.xtol = NumTraits<double>::epsilon();
+ info = lm.minimize(x);
+ EIGEN_UNUSED_VARIABLE(info)
+
+ // check return value
+ // VERIFY_IS_EQUAL(info, 1);
+ LM_CHECK_N_ITERS(lm, 20, 14);
+ // check norm^2
+ VERIFY_IS_APPROX(lm.fvec.squaredNorm(), 1.1680088766E+03);
+ // check x
+ VERIFY_IS_APPROX(x[0], 2.1380940889E+02);
+ VERIFY_IS_APPROX(x[1], 5.4723748542E-01);
+}
+
+struct MGH17_functor : Functor<double>
+{
+ MGH17_functor(void) : Functor<double>(5,33) {}
+ static const double x[33];
+ static const double y[33];
+ int operator()(const VectorXd &b, VectorXd &fvec)
+ {
+ assert(b.size()==5);
+ assert(fvec.size()==33);
+ for(int i=0; i<33; i++)
+ fvec[i] = b[0] + b[1]*exp(-b[3]*x[i]) + b[2]*exp(-b[4]*x[i]) - y[i];
+ return 0;
+ }
+ int df(const VectorXd &b, MatrixXd &fjac)
+ {
+ assert(b.size()==5);
+ assert(fjac.rows()==33);
+ assert(fjac.cols()==5);
+ for(int i=0; i<33; i++) {
+ fjac(i,0) = 1.;
+ fjac(i,1) = exp(-b[3]*x[i]);
+ fjac(i,2) = exp(-b[4]*x[i]);
+ fjac(i,3) = -x[i]*b[1]*exp(-b[3]*x[i]);
+ fjac(i,4) = -x[i]*b[2]*exp(-b[4]*x[i]);
+ }
+ return 0;
+ }
+};
+const double MGH17_functor::x[33] = { 0.000000E+00, 1.000000E+01, 2.000000E+01, 3.000000E+01, 4.000000E+01, 5.000000E+01, 6.000000E+01, 7.000000E+01, 8.000000E+01, 9.000000E+01, 1.000000E+02, 1.100000E+02, 1.200000E+02, 1.300000E+02, 1.400000E+02, 1.500000E+02, 1.600000E+02, 1.700000E+02, 1.800000E+02, 1.900000E+02, 2.000000E+02, 2.100000E+02, 2.200000E+02, 2.300000E+02, 2.400000E+02, 2.500000E+02, 2.600000E+02, 2.700000E+02, 2.800000E+02, 2.900000E+02, 3.000000E+02, 3.100000E+02, 3.200000E+02 };
+const double MGH17_functor::y[33] = { 8.440000E-01, 9.080000E-01, 9.320000E-01, 9.360000E-01, 9.250000E-01, 9.080000E-01, 8.810000E-01, 8.500000E-01, 8.180000E-01, 7.840000E-01, 7.510000E-01, 7.180000E-01, 6.850000E-01, 6.580000E-01, 6.280000E-01, 6.030000E-01, 5.800000E-01, 5.580000E-01, 5.380000E-01, 5.220000E-01, 5.060000E-01, 4.900000E-01, 4.780000E-01, 4.670000E-01, 4.570000E-01, 4.480000E-01, 4.380000E-01, 4.310000E-01, 4.240000E-01, 4.200000E-01, 4.140000E-01, 4.110000E-01, 4.060000E-01 };
+
+// http://www.itl.nist.gov/div898/strd/nls/data/mgh17.shtml
+void testNistMGH17(void)
+{
+ const int n=5;
+ int info;
+
+ VectorXd x(n);
+
+ /*
+ * First try
+ */
+ x<< 50., 150., -100., 1., 2.;
+ // do the computation
+ MGH17_functor functor;
+ LevenbergMarquardt<MGH17_functor> lm(functor);
+ lm.parameters.ftol = NumTraits<double>::epsilon();
+ lm.parameters.xtol = NumTraits<double>::epsilon();
+ lm.parameters.maxfev = 1000;
+ info = lm.minimize(x);
+ EIGEN_UNUSED_VARIABLE(info)
+
+ // check norm^2
+ VERIFY_IS_APPROX(lm.fvec.squaredNorm(), 5.4648946975E-05);
+ // check x
+ VERIFY_IS_APPROX(x[0], 3.7541005211E-01);
+ VERIFY_IS_APPROX(x[1], 1.9358469127E+00);
+ VERIFY_IS_APPROX(x[2], -1.4646871366E+00);
+ VERIFY_IS_APPROX(x[3], 1.2867534640E-02);
+ VERIFY_IS_APPROX(x[4], 2.2122699662E-02);
+
+ // check return value
+ // VERIFY_IS_EQUAL(info, 2);
+ LM_CHECK_N_ITERS(lm, 602, 545);
+
+ /*
+ * Second try
+ */
+ x<< 0.5 ,1.5 ,-1 ,0.01 ,0.02;
+ // do the computation
+ lm.resetParameters();
+ info = lm.minimize(x);
+ EIGEN_UNUSED_VARIABLE(info)
+
+ // check return value
+ // VERIFY_IS_EQUAL(info, 1);
+ LM_CHECK_N_ITERS(lm, 18, 15);
+ // check norm^2
+ VERIFY_IS_APPROX(lm.fvec.squaredNorm(), 5.4648946975E-05);
+ // check x
+ VERIFY_IS_APPROX(x[0], 3.7541005211E-01);
+ VERIFY_IS_APPROX(x[1], 1.9358469127E+00);
+ VERIFY_IS_APPROX(x[2], -1.4646871366E+00);
+ VERIFY_IS_APPROX(x[3], 1.2867534640E-02);
+ VERIFY_IS_APPROX(x[4], 2.2122699662E-02);
+}
+
+struct MGH09_functor : Functor<double>
+{
+ MGH09_functor(void) : Functor<double>(4,11) {}
+ static const double _x[11];
+ static const double y[11];
+ int operator()(const VectorXd &b, VectorXd &fvec)
+ {
+ assert(b.size()==4);
+ assert(fvec.size()==11);
+ for(int i=0; i<11; i++) {
+ double x = _x[i], xx=x*x;
+ fvec[i] = b[0]*(xx+x*b[1])/(xx+x*b[2]+b[3]) - y[i];
+ }
+ return 0;
+ }
+ int df(const VectorXd &b, MatrixXd &fjac)
+ {
+ assert(b.size()==4);
+ assert(fjac.rows()==11);
+ assert(fjac.cols()==4);
+ for(int i=0; i<11; i++) {
+ double x = _x[i], xx=x*x;
+ double factor = 1./(xx+x*b[2]+b[3]);
+ fjac(i,0) = (xx+x*b[1]) * factor;
+ fjac(i,1) = b[0]*x* factor;
+ fjac(i,2) = - b[0]*(xx+x*b[1]) * x * factor * factor;
+ fjac(i,3) = - b[0]*(xx+x*b[1]) * factor * factor;
+ }
+ return 0;
+ }
+};
+const double MGH09_functor::_x[11] = { 4., 2., 1., 5.E-1 , 2.5E-01, 1.670000E-01, 1.250000E-01, 1.E-01, 8.330000E-02, 7.140000E-02, 6.250000E-02 };
+const double MGH09_functor::y[11] = { 1.957000E-01, 1.947000E-01, 1.735000E-01, 1.600000E-01, 8.440000E-02, 6.270000E-02, 4.560000E-02, 3.420000E-02, 3.230000E-02, 2.350000E-02, 2.460000E-02 };
+
+// http://www.itl.nist.gov/div898/strd/nls/data/mgh09.shtml
+void testNistMGH09(void)
+{
+ const int n=4;
+ int info;
+
+ VectorXd x(n);
+
+ /*
+ * First try
+ */
+ x<< 25., 39, 41.5, 39.;
+ // do the computation
+ MGH09_functor functor;
+ LevenbergMarquardt<MGH09_functor> lm(functor);
+ lm.parameters.maxfev = 1000;
+ info = lm.minimize(x);
+ EIGEN_UNUSED_VARIABLE(info)
+
+ // check return value
+ // VERIFY_IS_EQUAL(info, 1);
+ LM_CHECK_N_ITERS(lm, 490, 376);
+ // check norm^2
+ VERIFY_IS_APPROX(lm.fvec.squaredNorm(), 3.0750560385E-04);
+ // check x
+ VERIFY_IS_APPROX(x[0], 0.1928077089); // should be 1.9280693458E-01
+ VERIFY_IS_APPROX(x[1], 0.19126423573); // should be 1.9128232873E-01
+ VERIFY_IS_APPROX(x[2], 0.12305309914); // should be 1.2305650693E-01
+ VERIFY_IS_APPROX(x[3], 0.13605395375); // should be 1.3606233068E-01
+
+ /*
+ * Second try
+ */
+ x<< 0.25, 0.39, 0.415, 0.39;
+ // do the computation
+ lm.resetParameters();
+ info = lm.minimize(x);
+ EIGEN_UNUSED_VARIABLE(info)
+
+ // check return value
+ // VERIFY_IS_EQUAL(info, 1);
+ LM_CHECK_N_ITERS(lm, 18, 16);
+ // check norm^2
+ VERIFY_IS_APPROX(lm.fvec.squaredNorm(), 3.0750560385E-04);
+ // check x
+ VERIFY_IS_APPROX(x[0], 0.19280781); // should be 1.9280693458E-01
+ VERIFY_IS_APPROX(x[1], 0.19126265); // should be 1.9128232873E-01
+ VERIFY_IS_APPROX(x[2], 0.12305280); // should be 1.2305650693E-01
+ VERIFY_IS_APPROX(x[3], 0.13605322); // should be 1.3606233068E-01
+}
+
+
+
+struct Bennett5_functor : Functor<double>
+{
+ Bennett5_functor(void) : Functor<double>(3,154) {}
+ static const double x[154];
+ static const double y[154];
+ int operator()(const VectorXd &b, VectorXd &fvec)
+ {
+ assert(b.size()==3);
+ assert(fvec.size()==154);
+ for(int i=0; i<154; i++)
+ fvec[i] = b[0]* pow(b[1]+x[i],-1./b[2]) - y[i];
+ return 0;
+ }
+ int df(const VectorXd &b, MatrixXd &fjac)
+ {
+ assert(b.size()==3);
+ assert(fjac.rows()==154);
+ assert(fjac.cols()==3);
+ for(int i=0; i<154; i++) {
+ double e = pow(b[1]+x[i],-1./b[2]);
+ fjac(i,0) = e;
+ fjac(i,1) = - b[0]*e/b[2]/(b[1]+x[i]);
+ fjac(i,2) = b[0]*e*log(b[1]+x[i])/b[2]/b[2];
+ }
+ return 0;
+ }
+};
+const double Bennett5_functor::x[154] = { 7.447168E0, 8.102586E0, 8.452547E0, 8.711278E0, 8.916774E0, 9.087155E0, 9.232590E0, 9.359535E0, 9.472166E0, 9.573384E0, 9.665293E0, 9.749461E0, 9.827092E0, 9.899128E0, 9.966321E0, 10.029280E0, 10.088510E0, 10.144430E0, 10.197380E0, 10.247670E0, 10.295560E0, 10.341250E0, 10.384950E0, 10.426820E0, 10.467000E0, 10.505640E0, 10.542830E0, 10.578690E0, 10.613310E0, 10.646780E0, 10.679150E0, 10.710520E0, 10.740920E0, 10.770440E0, 10.799100E0, 10.826970E0, 10.854080E0, 10.880470E0, 10.906190E0, 10.931260E0, 10.955720E0, 10.979590E0, 11.002910E0, 11.025700E0, 11.047980E0, 11.069770E0, 11.091100E0, 11.111980E0, 11.132440E0, 11.152480E0, 11.172130E0, 11.191410E0, 11.210310E0, 11.228870E0, 11.247090E0, 11.264980E0, 11.282560E0, 11.299840E0, 11.316820E0, 11.333520E0, 11.349940E0, 11.366100E0, 11.382000E0, 11.397660E0, 11.413070E0, 11.428240E0, 11.443200E0, 11.457930E0, 11.472440E0, 11.486750E0, 11.500860E0, 11.514770E0, 11.528490E0, 11.542020E0, 11.555380E0, 11.568550E0,
+11.581560E0, 11.594420E0, 11.607121E0, 11.619640E0, 11.632000E0, 11.644210E0, 11.656280E0, 11.668200E0, 11.679980E0, 11.691620E0, 11.703130E0, 11.714510E0, 11.725760E0, 11.736880E0, 11.747890E0, 11.758780E0, 11.769550E0, 11.780200E0, 11.790730E0, 11.801160E0, 11.811480E0, 11.821700E0, 11.831810E0, 11.841820E0, 11.851730E0, 11.861550E0, 11.871270E0, 11.880890E0, 11.890420E0, 11.899870E0, 11.909220E0, 11.918490E0, 11.927680E0, 11.936780E0, 11.945790E0, 11.954730E0, 11.963590E0, 11.972370E0, 11.981070E0, 11.989700E0, 11.998260E0, 12.006740E0, 12.015150E0, 12.023490E0, 12.031760E0, 12.039970E0, 12.048100E0, 12.056170E0, 12.064180E0, 12.072120E0, 12.080010E0, 12.087820E0, 12.095580E0, 12.103280E0, 12.110920E0, 12.118500E0, 12.126030E0, 12.133500E0, 12.140910E0, 12.148270E0, 12.155570E0, 12.162830E0, 12.170030E0, 12.177170E0, 12.184270E0, 12.191320E0, 12.198320E0, 12.205270E0, 12.212170E0, 12.219030E0, 12.225840E0, 12.232600E0, 12.239320E0, 12.245990E0, 12.252620E0, 12.259200E0, 12.265750E0, 12.272240E0 };
+const double Bennett5_functor::y[154] = { -34.834702E0 ,-34.393200E0 ,-34.152901E0 ,-33.979099E0 ,-33.845901E0 ,-33.732899E0 ,-33.640301E0 ,-33.559200E0 ,-33.486801E0 ,-33.423100E0 ,-33.365101E0 ,-33.313000E0 ,-33.260899E0 ,-33.217400E0 ,-33.176899E0 ,-33.139198E0 ,-33.101601E0 ,-33.066799E0 ,-33.035000E0 ,-33.003101E0 ,-32.971298E0 ,-32.942299E0 ,-32.916302E0 ,-32.890202E0 ,-32.864101E0 ,-32.841000E0 ,-32.817799E0 ,-32.797501E0 ,-32.774300E0 ,-32.757000E0 ,-32.733799E0 ,-32.716400E0 ,-32.699100E0 ,-32.678799E0 ,-32.661400E0 ,-32.644001E0 ,-32.626701E0 ,-32.612202E0 ,-32.597698E0 ,-32.583199E0 ,-32.568699E0 ,-32.554298E0 ,-32.539799E0 ,-32.525299E0 ,-32.510799E0 ,-32.499199E0 ,-32.487598E0 ,-32.473202E0 ,-32.461601E0 ,-32.435501E0 ,-32.435501E0 ,-32.426800E0 ,-32.412300E0 ,-32.400799E0 ,-32.392101E0 ,-32.380501E0 ,-32.366001E0 ,-32.357300E0 ,-32.348598E0 ,-32.339901E0 ,-32.328400E0 ,-32.319698E0 ,-32.311001E0 ,-32.299400E0 ,-32.290699E0 ,-32.282001E0 ,-32.273300E0 ,-32.264599E0 ,-32.256001E0 ,-32.247299E0
+,-32.238602E0 ,-32.229900E0 ,-32.224098E0 ,-32.215401E0 ,-32.203800E0 ,-32.198002E0 ,-32.189400E0 ,-32.183601E0 ,-32.174900E0 ,-32.169102E0 ,-32.163300E0 ,-32.154598E0 ,-32.145901E0 ,-32.140099E0 ,-32.131401E0 ,-32.125599E0 ,-32.119801E0 ,-32.111198E0 ,-32.105400E0 ,-32.096699E0 ,-32.090900E0 ,-32.088001E0 ,-32.079300E0 ,-32.073502E0 ,-32.067699E0 ,-32.061901E0 ,-32.056099E0 ,-32.050301E0 ,-32.044498E0 ,-32.038799E0 ,-32.033001E0 ,-32.027199E0 ,-32.024300E0 ,-32.018501E0 ,-32.012699E0 ,-32.004002E0 ,-32.001099E0 ,-31.995300E0 ,-31.989500E0 ,-31.983700E0 ,-31.977900E0 ,-31.972099E0 ,-31.969299E0 ,-31.963501E0 ,-31.957701E0 ,-31.951900E0 ,-31.946100E0 ,-31.940300E0 ,-31.937401E0 ,-31.931601E0 ,-31.925800E0 ,-31.922899E0 ,-31.917101E0 ,-31.911301E0 ,-31.908400E0 ,-31.902599E0 ,-31.896900E0 ,-31.893999E0 ,-31.888201E0 ,-31.885300E0 ,-31.882401E0 ,-31.876600E0 ,-31.873699E0 ,-31.867901E0 ,-31.862101E0 ,-31.859200E0 ,-31.856300E0 ,-31.850500E0 ,-31.844700E0 ,-31.841801E0 ,-31.838900E0 ,-31.833099E0 ,-31.830200E0 ,
+-31.827299E0 ,-31.821600E0 ,-31.818701E0 ,-31.812901E0 ,-31.809999E0 ,-31.807100E0 ,-31.801300E0 ,-31.798401E0 ,-31.795500E0 ,-31.789700E0 ,-31.786800E0 };
+
+// http://www.itl.nist.gov/div898/strd/nls/data/bennett5.shtml
+void testNistBennett5(void)
+{
+ const int n=3;
+ int info;
+
+ VectorXd x(n);
+
+ /*
+ * First try
+ */
+ x<< -2000., 50., 0.8;
+ // do the computation
+ Bennett5_functor functor;
+ LevenbergMarquardt<Bennett5_functor> lm(functor);
+ lm.parameters.maxfev = 1000;
+ info = lm.minimize(x);
+ EIGEN_UNUSED_VARIABLE(info)
+
+ // check return value
+ // VERIFY_IS_EQUAL(info, 1);
+ LM_CHECK_N_ITERS(lm, 758, 744);
+ // check norm^2
+ VERIFY_IS_APPROX(lm.fvec.squaredNorm(), 5.2404744073E-04);
+ // check x
+ VERIFY_IS_APPROX(x[0], -2.5235058043E+03);
+ VERIFY_IS_APPROX(x[1], 4.6736564644E+01);
+ VERIFY_IS_APPROX(x[2], 9.3218483193E-01);
+ /*
+ * Second try
+ */
+ x<< -1500., 45., 0.85;
+ // do the computation
+ lm.resetParameters();
+ info = lm.minimize(x);
+ EIGEN_UNUSED_VARIABLE(info)
+
+ // check return value
+ // VERIFY_IS_EQUAL(info, 1);
+ LM_CHECK_N_ITERS(lm, 203, 192);
+ // check norm^2
+ VERIFY_IS_APPROX(lm.fvec.squaredNorm(), 5.2404744073E-04);
+ // check x
+ VERIFY_IS_APPROX(x[0], -2523.3007865); // should be -2.5235058043E+03
+ VERIFY_IS_APPROX(x[1], 46.735705771); // should be 4.6736564644E+01);
+ VERIFY_IS_APPROX(x[2], 0.93219881891); // should be 9.3218483193E-01);
+}
+
+struct thurber_functor : Functor<double>
+{
+ thurber_functor(void) : Functor<double>(7,37) {}
+ static const double _x[37];
+ static const double _y[37];
+ int operator()(const VectorXd &b, VectorXd &fvec)
+ {
+ // int called=0; printf("call hahn1_functor with iflag=%d, called=%d\n", iflag, called); if (iflag==1) called++;
+ assert(b.size()==7);
+ assert(fvec.size()==37);
+ for(int i=0; i<37; i++) {
+ double x=_x[i], xx=x*x, xxx=xx*x;
+ fvec[i] = (b[0]+b[1]*x+b[2]*xx+b[3]*xxx) / (1.+b[4]*x+b[5]*xx+b[6]*xxx) - _y[i];
+ }
+ return 0;
+ }
+ int df(const VectorXd &b, MatrixXd &fjac)
+ {
+ assert(b.size()==7);
+ assert(fjac.rows()==37);
+ assert(fjac.cols()==7);
+ for(int i=0; i<37; i++) {
+ double x=_x[i], xx=x*x, xxx=xx*x;
+ double fact = 1./(1.+b[4]*x+b[5]*xx+b[6]*xxx);
+ fjac(i,0) = 1.*fact;
+ fjac(i,1) = x*fact;
+ fjac(i,2) = xx*fact;
+ fjac(i,3) = xxx*fact;
+ fact = - (b[0]+b[1]*x+b[2]*xx+b[3]*xxx) * fact * fact;
+ fjac(i,4) = x*fact;
+ fjac(i,5) = xx*fact;
+ fjac(i,6) = xxx*fact;
+ }
+ return 0;
+ }
+};
+const double thurber_functor::_x[37] = { -3.067E0, -2.981E0, -2.921E0, -2.912E0, -2.840E0, -2.797E0, -2.702E0, -2.699E0, -2.633E0, -2.481E0, -2.363E0, -2.322E0, -1.501E0, -1.460E0, -1.274E0, -1.212E0, -1.100E0, -1.046E0, -0.915E0, -0.714E0, -0.566E0, -0.545E0, -0.400E0, -0.309E0, -0.109E0, -0.103E0, 0.010E0, 0.119E0, 0.377E0, 0.790E0, 0.963E0, 1.006E0, 1.115E0, 1.572E0, 1.841E0, 2.047E0, 2.200E0 };
+const double thurber_functor::_y[37] = { 80.574E0, 84.248E0, 87.264E0, 87.195E0, 89.076E0, 89.608E0, 89.868E0, 90.101E0, 92.405E0, 95.854E0, 100.696E0, 101.060E0, 401.672E0, 390.724E0, 567.534E0, 635.316E0, 733.054E0, 759.087E0, 894.206E0, 990.785E0, 1090.109E0, 1080.914E0, 1122.643E0, 1178.351E0, 1260.531E0, 1273.514E0, 1288.339E0, 1327.543E0, 1353.863E0, 1414.509E0, 1425.208E0, 1421.384E0, 1442.962E0, 1464.350E0, 1468.705E0, 1447.894E0, 1457.628E0};
+
+// http://www.itl.nist.gov/div898/strd/nls/data/thurber.shtml
+void testNistThurber(void)
+{
+ const int n=7;
+ int info;
+
+ VectorXd x(n);
+
+ /*
+ * First try
+ */
+ x<< 1000 ,1000 ,400 ,40 ,0.7,0.3,0.0 ;
+ // do the computation
+ thurber_functor functor;
+ LevenbergMarquardt<thurber_functor> lm(functor);
+ lm.parameters.ftol = 1.E4*NumTraits<double>::epsilon();
+ lm.parameters.xtol = 1.E4*NumTraits<double>::epsilon();
+ info = lm.minimize(x);
+ EIGEN_UNUSED_VARIABLE(info)
+
+ // check return value
+ // VERIFY_IS_EQUAL(info, 1);
+ LM_CHECK_N_ITERS(lm, 39,36);
+ // check norm^2
+ VERIFY_IS_APPROX(lm.fvec.squaredNorm(), 5.6427082397E+03);
+ // check x
+ VERIFY_IS_APPROX(x[0], 1.2881396800E+03);
+ VERIFY_IS_APPROX(x[1], 1.4910792535E+03);
+ VERIFY_IS_APPROX(x[2], 5.8323836877E+02);
+ VERIFY_IS_APPROX(x[3], 7.5416644291E+01);
+ VERIFY_IS_APPROX(x[4], 9.6629502864E-01);
+ VERIFY_IS_APPROX(x[5], 3.9797285797E-01);
+ VERIFY_IS_APPROX(x[6], 4.9727297349E-02);
+
+ /*
+ * Second try
+ */
+ x<< 1300 ,1500 ,500 ,75 ,1 ,0.4 ,0.05 ;
+ // do the computation
+ lm.resetParameters();
+ lm.parameters.ftol = 1.E4*NumTraits<double>::epsilon();
+ lm.parameters.xtol = 1.E4*NumTraits<double>::epsilon();
+ info = lm.minimize(x);
+ EIGEN_UNUSED_VARIABLE(info)
+
+ // check return value
+ // VERIFY_IS_EQUAL(info, 1);
+ LM_CHECK_N_ITERS(lm, 29, 28);
+ // check norm^2
+ VERIFY_IS_APPROX(lm.fvec.squaredNorm(), 5.6427082397E+03);
+ // check x
+ VERIFY_IS_APPROX(x[0], 1.2881396800E+03);
+ VERIFY_IS_APPROX(x[1], 1.4910792535E+03);
+ VERIFY_IS_APPROX(x[2], 5.8323836877E+02);
+ VERIFY_IS_APPROX(x[3], 7.5416644291E+01);
+ VERIFY_IS_APPROX(x[4], 9.6629502864E-01);
+ VERIFY_IS_APPROX(x[5], 3.9797285797E-01);
+ VERIFY_IS_APPROX(x[6], 4.9727297349E-02);
+}
+
+struct rat43_functor : Functor<double>
+{
+ rat43_functor(void) : Functor<double>(4,15) {}
+ static const double x[15];
+ static const double y[15];
+ int operator()(const VectorXd &b, VectorXd &fvec)
+ {
+ assert(b.size()==4);
+ assert(fvec.size()==15);
+ for(int i=0; i<15; i++)
+ fvec[i] = b[0] * pow(1.+exp(b[1]-b[2]*x[i]),-1./b[3]) - y[i];
+ return 0;
+ }
+ int df(const VectorXd &b, MatrixXd &fjac)
+ {
+ assert(b.size()==4);
+ assert(fjac.rows()==15);
+ assert(fjac.cols()==4);
+ for(int i=0; i<15; i++) {
+ double e = exp(b[1]-b[2]*x[i]);
+ double power = -1./b[3];
+ fjac(i,0) = pow(1.+e, power);
+ fjac(i,1) = power*b[0]*e*pow(1.+e, power-1.);
+ fjac(i,2) = -power*b[0]*e*x[i]*pow(1.+e, power-1.);
+ fjac(i,3) = b[0]*power*power*log(1.+e)*pow(1.+e, power);
+ }
+ return 0;
+ }
+};
+const double rat43_functor::x[15] = { 1., 2., 3., 4., 5., 6., 7., 8., 9., 10., 11., 12., 13., 14., 15. };
+const double rat43_functor::y[15] = { 16.08, 33.83, 65.80, 97.20, 191.55, 326.20, 386.87, 520.53, 590.03, 651.92, 724.93, 699.56, 689.96, 637.56, 717.41 };
+
+// http://www.itl.nist.gov/div898/strd/nls/data/ratkowsky3.shtml
+void testNistRat43(void)
+{
+ const int n=4;
+ int info;
+
+ VectorXd x(n);
+
+ /*
+ * First try
+ */
+ x<< 100., 10., 1., 1.;
+ // do the computation
+ rat43_functor functor;
+ LevenbergMarquardt<rat43_functor> lm(functor);
+ lm.parameters.ftol = 1.E6*NumTraits<double>::epsilon();
+ lm.parameters.xtol = 1.E6*NumTraits<double>::epsilon();
+ info = lm.minimize(x);
+ EIGEN_UNUSED_VARIABLE(info)
+
+ // check return value
+ // VERIFY_IS_EQUAL(info, 1);
+ LM_CHECK_N_ITERS(lm, 27, 20);
+ // check norm^2
+ VERIFY_IS_APPROX(lm.fvec.squaredNorm(), 8.7864049080E+03);
+ // check x
+ VERIFY_IS_APPROX(x[0], 6.9964151270E+02);
+ VERIFY_IS_APPROX(x[1], 5.2771253025E+00);
+ VERIFY_IS_APPROX(x[2], 7.5962938329E-01);
+ VERIFY_IS_APPROX(x[3], 1.2792483859E+00);
+
+ /*
+ * Second try
+ */
+ x<< 700., 5., 0.75, 1.3;
+ // do the computation
+ lm.resetParameters();
+ lm.parameters.ftol = 1.E5*NumTraits<double>::epsilon();
+ lm.parameters.xtol = 1.E5*NumTraits<double>::epsilon();
+ info = lm.minimize(x);
+ EIGEN_UNUSED_VARIABLE(info)
+
+ // check return value
+ // VERIFY_IS_EQUAL(info, 1);
+ LM_CHECK_N_ITERS(lm, 9, 8);
+ // check norm^2
+ VERIFY_IS_APPROX(lm.fvec.squaredNorm(), 8.7864049080E+03);
+ // check x
+ VERIFY_IS_APPROX(x[0], 6.9964151270E+02);
+ VERIFY_IS_APPROX(x[1], 5.2771253025E+00);
+ VERIFY_IS_APPROX(x[2], 7.5962938329E-01);
+ VERIFY_IS_APPROX(x[3], 1.2792483859E+00);
+}
+
+
+
+struct eckerle4_functor : Functor<double>
+{
+ eckerle4_functor(void) : Functor<double>(3,35) {}
+ static const double x[35];
+ static const double y[35];
+ int operator()(const VectorXd &b, VectorXd &fvec)
+ {
+ assert(b.size()==3);
+ assert(fvec.size()==35);
+ for(int i=0; i<35; i++)
+ fvec[i] = b[0]/b[1] * exp(-0.5*(x[i]-b[2])*(x[i]-b[2])/(b[1]*b[1])) - y[i];
+ return 0;
+ }
+ int df(const VectorXd &b, MatrixXd &fjac)
+ {
+ assert(b.size()==3);
+ assert(fjac.rows()==35);
+ assert(fjac.cols()==3);
+ for(int i=0; i<35; i++) {
+ double b12 = b[1]*b[1];
+ double e = exp(-0.5*(x[i]-b[2])*(x[i]-b[2])/b12);
+ fjac(i,0) = e / b[1];
+ fjac(i,1) = ((x[i]-b[2])*(x[i]-b[2])/b12-1.) * b[0]*e/b12;
+ fjac(i,2) = (x[i]-b[2])*e*b[0]/b[1]/b12;
+ }
+ return 0;
+ }
+};
+const double eckerle4_functor::x[35] = { 400.0, 405.0, 410.0, 415.0, 420.0, 425.0, 430.0, 435.0, 436.5, 438.0, 439.5, 441.0, 442.5, 444.0, 445.5, 447.0, 448.5, 450.0, 451.5, 453.0, 454.5, 456.0, 457.5, 459.0, 460.5, 462.0, 463.5, 465.0, 470.0, 475.0, 480.0, 485.0, 490.0, 495.0, 500.0};
+const double eckerle4_functor::y[35] = { 0.0001575, 0.0001699, 0.0002350, 0.0003102, 0.0004917, 0.0008710, 0.0017418, 0.0046400, 0.0065895, 0.0097302, 0.0149002, 0.0237310, 0.0401683, 0.0712559, 0.1264458, 0.2073413, 0.2902366, 0.3445623, 0.3698049, 0.3668534, 0.3106727, 0.2078154, 0.1164354, 0.0616764, 0.0337200, 0.0194023, 0.0117831, 0.0074357, 0.0022732, 0.0008800, 0.0004579, 0.0002345, 0.0001586, 0.0001143, 0.0000710 };
+
+// http://www.itl.nist.gov/div898/strd/nls/data/eckerle4.shtml
+void testNistEckerle4(void)
+{
+ const int n=3;
+ int info;
+
+ VectorXd x(n);
+
+ /*
+ * First try
+ */
+ x<< 1., 10., 500.;
+ // do the computation
+ eckerle4_functor functor;
+ LevenbergMarquardt<eckerle4_functor> lm(functor);
+ info = lm.minimize(x);
+ EIGEN_UNUSED_VARIABLE(info)
+
+ // check return value
+ // VERIFY_IS_EQUAL(info, 1);
+ LM_CHECK_N_ITERS(lm, 18, 15);
+ // check norm^2
+ VERIFY_IS_APPROX(lm.fvec.squaredNorm(), 1.4635887487E-03);
+ // check x
+ VERIFY_IS_APPROX(x[0], 1.5543827178);
+ VERIFY_IS_APPROX(x[1], 4.0888321754);
+ VERIFY_IS_APPROX(x[2], 4.5154121844E+02);
+
+ /*
+ * Second try
+ */
+ x<< 1.5, 5., 450.;
+ // do the computation
+ info = lm.minimize(x);
+ EIGEN_UNUSED_VARIABLE(info)
+
+ // check return value
+ // VERIFY_IS_EQUAL(info, 1);
+ LM_CHECK_N_ITERS(lm, 7, 6);
+ // check norm^2
+ VERIFY_IS_APPROX(lm.fvec.squaredNorm(), 1.4635887487E-03);
+ // check x
+ VERIFY_IS_APPROX(x[0], 1.5543827178);
+ VERIFY_IS_APPROX(x[1], 4.0888321754);
+ VERIFY_IS_APPROX(x[2], 4.5154121844E+02);
+}
+
+EIGEN_DECLARE_TEST(NonLinearOptimization)
+{
+ // Tests using the examples provided by (c)minpack
+ CALL_SUBTEST/*_1*/(testChkder());
+ CALL_SUBTEST/*_1*/(testLmder1());
+ CALL_SUBTEST/*_1*/(testLmder());
+ CALL_SUBTEST/*_2*/(testHybrj1());
+ CALL_SUBTEST/*_2*/(testHybrj());
+ CALL_SUBTEST/*_2*/(testHybrd1());
+ CALL_SUBTEST/*_2*/(testHybrd());
+ CALL_SUBTEST/*_3*/(testLmstr1());
+ CALL_SUBTEST/*_3*/(testLmstr());
+ CALL_SUBTEST/*_3*/(testLmdif1());
+ CALL_SUBTEST/*_3*/(testLmdif());
+
+ // NIST tests, level of difficulty = "Lower"
+ CALL_SUBTEST/*_4*/(testNistMisra1a());
+ CALL_SUBTEST/*_4*/(testNistChwirut2());
+
+ // NIST tests, level of difficulty = "Average"
+ CALL_SUBTEST/*_5*/(testNistHahn1());
+ CALL_SUBTEST/*_6*/(testNistMisra1d());
+ CALL_SUBTEST/*_7*/(testNistMGH17());
+ CALL_SUBTEST/*_8*/(testNistLanczos1());
+
+// // NIST tests, level of difficulty = "Higher"
+ CALL_SUBTEST/*_9*/(testNistRat42());
+// CALL_SUBTEST/*_10*/(testNistMGH10());
+ CALL_SUBTEST/*_11*/(testNistBoxBOD());
+// CALL_SUBTEST/*_12*/(testNistMGH09());
+ CALL_SUBTEST/*_13*/(testNistBennett5());
+ CALL_SUBTEST/*_14*/(testNistThurber());
+ CALL_SUBTEST/*_15*/(testNistRat43());
+ CALL_SUBTEST/*_16*/(testNistEckerle4());
+}
+
+/*
+ * Can be useful for debugging...
+ printf("info, nfev : %d, %d\n", info, lm.nfev);
+ printf("info, nfev, njev : %d, %d, %d\n", info, solver.nfev, solver.njev);
+ printf("info, nfev : %d, %d\n", info, solver.nfev);
+ printf("x[0] : %.32g\n", x[0]);
+ printf("x[1] : %.32g\n", x[1]);
+ printf("x[2] : %.32g\n", x[2]);
+ printf("x[3] : %.32g\n", x[3]);
+ printf("fvec.blueNorm() : %.32g\n", solver.fvec.blueNorm());
+ printf("fvec.blueNorm() : %.32g\n", lm.fvec.blueNorm());
+
+ printf("info, nfev, njev : %d, %d, %d\n", info, lm.nfev, lm.njev);
+ printf("fvec.squaredNorm() : %.13g\n", lm.fvec.squaredNorm());
+ std::cout << x << std::endl;
+ std::cout.precision(9);
+ std::cout << x[0] << std::endl;
+ std::cout << x[1] << std::endl;
+ std::cout << x[2] << std::endl;
+ std::cout << x[3] << std::endl;
+*/
+
diff --git a/unsupported/test/NumericalDiff.cpp b/unsupported/test/NumericalDiff.cpp
new file mode 100644
index 0000000..96e7f19
--- /dev/null
+++ b/unsupported/test/NumericalDiff.cpp
@@ -0,0 +1,114 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009 Thomas Capricelli <orzel@freehackers.org>
+
+#include <stdio.h>
+
+#include "main.h"
+#include <unsupported/Eigen/NumericalDiff>
+
+// Generic functor
+template<typename Scalar_, int NX=Dynamic, int NY=Dynamic>
+struct Functor
+{
+ typedef Scalar_ Scalar;
+ enum {
+ InputsAtCompileTime = NX,
+ ValuesAtCompileTime = NY
+ };
+ typedef Matrix<Scalar,InputsAtCompileTime,1> InputType;
+ typedef Matrix<Scalar,ValuesAtCompileTime,1> ValueType;
+ typedef Matrix<Scalar,ValuesAtCompileTime,InputsAtCompileTime> JacobianType;
+
+ int m_inputs, m_values;
+
+ Functor() : m_inputs(InputsAtCompileTime), m_values(ValuesAtCompileTime) {}
+ Functor(int inputs_, int values_) : m_inputs(inputs_), m_values(values_) {}
+
+ int inputs() const { return m_inputs; }
+ int values() const { return m_values; }
+
+};
+
+struct my_functor : Functor<double>
+{
+ my_functor(void): Functor<double>(3,15) {}
+ int operator()(const VectorXd &x, VectorXd &fvec) const
+ {
+ double tmp1, tmp2, tmp3;
+ double y[15] = {1.4e-1, 1.8e-1, 2.2e-1, 2.5e-1, 2.9e-1, 3.2e-1, 3.5e-1,
+ 3.9e-1, 3.7e-1, 5.8e-1, 7.3e-1, 9.6e-1, 1.34, 2.1, 4.39};
+
+ for (int i = 0; i < values(); i++)
+ {
+ tmp1 = i+1;
+ tmp2 = 16 - i - 1;
+ tmp3 = (i>=8)? tmp2 : tmp1;
+ fvec[i] = y[i] - (x[0] + tmp1/(x[1]*tmp2 + x[2]*tmp3));
+ }
+ return 0;
+ }
+
+ int actual_df(const VectorXd &x, MatrixXd &fjac) const
+ {
+ double tmp1, tmp2, tmp3, tmp4;
+ for (int i = 0; i < values(); i++)
+ {
+ tmp1 = i+1;
+ tmp2 = 16 - i - 1;
+ tmp3 = (i>=8)? tmp2 : tmp1;
+ tmp4 = (x[1]*tmp2 + x[2]*tmp3); tmp4 = tmp4*tmp4;
+ fjac(i,0) = -1;
+ fjac(i,1) = tmp1*tmp2/tmp4;
+ fjac(i,2) = tmp1*tmp3/tmp4;
+ }
+ return 0;
+ }
+};
+
+void test_forward()
+{
+ VectorXd x(3);
+ MatrixXd jac(15,3);
+ MatrixXd actual_jac(15,3);
+ my_functor functor;
+
+ x << 0.082, 1.13, 2.35;
+
+ // real one
+ functor.actual_df(x, actual_jac);
+// std::cout << actual_jac << std::endl << std::endl;
+
+ // using NumericalDiff
+ NumericalDiff<my_functor> numDiff(functor);
+ numDiff.df(x, jac);
+// std::cout << jac << std::endl;
+
+ VERIFY_IS_APPROX(jac, actual_jac);
+}
+
+void test_central()
+{
+ VectorXd x(3);
+ MatrixXd jac(15,3);
+ MatrixXd actual_jac(15,3);
+ my_functor functor;
+
+ x << 0.082, 1.13, 2.35;
+
+ // real one
+ functor.actual_df(x, actual_jac);
+
+ // using NumericalDiff
+ NumericalDiff<my_functor,Central> numDiff(functor);
+ numDiff.df(x, jac);
+
+ VERIFY_IS_APPROX(jac, actual_jac);
+}
+
+EIGEN_DECLARE_TEST(NumericalDiff)
+{
+ CALL_SUBTEST(test_forward());
+ CALL_SUBTEST(test_central());
+}
diff --git a/unsupported/test/alignedvector3.cpp b/unsupported/test/alignedvector3.cpp
new file mode 100644
index 0000000..1fc6d62
--- /dev/null
+++ b/unsupported/test/alignedvector3.cpp
@@ -0,0 +1,89 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009 Gael Guennebaud <g.gael@free.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#define EIGEN_NO_STATIC_ASSERT
+
+#include "main.h"
+#include <unsupported/Eigen/AlignedVector3>
+
+namespace Eigen {
+
+template<typename T,typename Derived>
+T test_relative_error(const AlignedVector3<T> &a, const MatrixBase<Derived> &b)
+{
+ return test_relative_error(a.coeffs().template head<3>(), b);
+}
+
+}
+
+template<typename Scalar>
+void alignedvector3()
+{
+ Scalar s1 = internal::random<Scalar>();
+ Scalar s2 = internal::random<Scalar>();
+ typedef Matrix<Scalar,3,1> RefType;
+ typedef Matrix<Scalar,3,3> Mat33;
+ typedef AlignedVector3<Scalar> FastType;
+ RefType r1(RefType::Random()), r2(RefType::Random()), r3(RefType::Random()),
+ r4(RefType::Random()), r5(RefType::Random());
+ FastType f1(r1), f2(r2), f3(r3), f4(r4), f5(r5);
+ Mat33 m1(Mat33::Random());
+
+ VERIFY_IS_APPROX(f1,r1);
+ VERIFY_IS_APPROX(f4,r4);
+
+ VERIFY_IS_APPROX(f4+f1,r4+r1);
+ VERIFY_IS_APPROX(f4-f1,r4-r1);
+ VERIFY_IS_APPROX(f4+f1-f2,r4+r1-r2);
+ VERIFY_IS_APPROX(f4+=f3,r4+=r3);
+ VERIFY_IS_APPROX(f4-=f5,r4-=r5);
+ VERIFY_IS_APPROX(f4-=f5+f1,r4-=r5+r1);
+ VERIFY_IS_APPROX(f5+f1-s1*f2,r5+r1-s1*r2);
+ VERIFY_IS_APPROX(f5+f1/s2-s1*f2,r5+r1/s2-s1*r2);
+
+ VERIFY_IS_APPROX(m1*f4,m1*r4);
+ VERIFY_IS_APPROX(f4.transpose()*m1,r4.transpose()*m1);
+
+ VERIFY_IS_APPROX(f2.dot(f3),r2.dot(r3));
+ VERIFY_IS_APPROX(f2.cross(f3),r2.cross(r3));
+ VERIFY_IS_APPROX(f2.norm(),r2.norm());
+
+ VERIFY_IS_APPROX(f2.normalized(),r2.normalized());
+
+ VERIFY_IS_APPROX((f2+f1).normalized(),(r2+r1).normalized());
+
+ f2.normalize();
+ r2.normalize();
+ VERIFY_IS_APPROX(f2,r2);
+
+ {
+ FastType f6 = RefType::Zero();
+ FastType f7 = FastType::Zero();
+ VERIFY_IS_APPROX(f6,f7);
+ f6 = r4+r1;
+ VERIFY_IS_APPROX(f6,r4+r1);
+ f6 -= Scalar(2)*r4;
+ VERIFY_IS_APPROX(f6,r1-r4);
+ }
+
+ FastType f8, f9(0,0,0);
+ VERIFY_IS_APPROX(f9-f1,-f1);
+
+ std::stringstream ss1, ss2;
+ ss1 << f1;
+ ss2 << r1;
+ VERIFY(ss1.str()==ss2.str());
+}
+
+EIGEN_DECLARE_TEST(alignedvector3)
+{
+ for(int i = 0; i < g_repeat; i++) {
+ CALL_SUBTEST( alignedvector3<float>() );
+ }
+}
diff --git a/unsupported/test/autodiff.cpp b/unsupported/test/autodiff.cpp
new file mode 100644
index 0000000..0addf2c
--- /dev/null
+++ b/unsupported/test/autodiff.cpp
@@ -0,0 +1,383 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009 Gael Guennebaud <g.gael@free.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "main.h"
+#include <unsupported/Eigen/AutoDiff>
+
+template<typename Scalar>
+EIGEN_DONT_INLINE Scalar foo(const Scalar& x, const Scalar& y)
+{
+ using namespace std;
+// return x+std::sin(y);
+ EIGEN_ASM_COMMENT("mybegin");
+ // pow(float, int) promotes to pow(double, double)
+ return x*2 - 1 + static_cast<Scalar>(pow(1+x,2)) + 2*sqrt(y*y+0) - 4 * sin(0+x) + 2 * cos(y+0) - exp(Scalar(-0.5)*x*x+0);
+ //return x+2*y*x;//x*2 -std::pow(x,2);//(2*y/x);// - y*2;
+ EIGEN_ASM_COMMENT("myend");
+}
+
+template<typename Vector>
+EIGEN_DONT_INLINE typename Vector::Scalar foo(const Vector& p)
+{
+ typedef typename Vector::Scalar Scalar;
+ return (p-Vector(Scalar(-1),Scalar(1.))).norm() + (p.array() * p.array()).sum() + p.dot(p);
+}
+
+template<typename Scalar_, int NX=Dynamic, int NY=Dynamic>
+struct TestFunc1
+{
+ typedef Scalar_ Scalar;
+ enum {
+ InputsAtCompileTime = NX,
+ ValuesAtCompileTime = NY
+ };
+ typedef Matrix<Scalar,InputsAtCompileTime,1> InputType;
+ typedef Matrix<Scalar,ValuesAtCompileTime,1> ValueType;
+ typedef Matrix<Scalar,ValuesAtCompileTime,InputsAtCompileTime> JacobianType;
+
+ int m_inputs, m_values;
+
+ TestFunc1() : m_inputs(InputsAtCompileTime), m_values(ValuesAtCompileTime) {}
+ TestFunc1(int inputs_, int values_) : m_inputs(inputs_), m_values(values_) {}
+
+ int inputs() const { return m_inputs; }
+ int values() const { return m_values; }
+
+ template<typename T>
+ void operator() (const Matrix<T,InputsAtCompileTime,1>& x, Matrix<T,ValuesAtCompileTime,1>* _v) const
+ {
+ Matrix<T,ValuesAtCompileTime,1>& v = *_v;
+
+ v[0] = 2 * x[0] * x[0] + x[0] * x[1];
+ v[1] = 3 * x[1] * x[0] + 0.5 * x[1] * x[1];
+ if(inputs()>2)
+ {
+ v[0] += 0.5 * x[2];
+ v[1] += x[2];
+ }
+ if(values()>2)
+ {
+ v[2] = 3 * x[1] * x[0] * x[0];
+ }
+ if (inputs()>2 && values()>2)
+ v[2] *= x[2];
+ }
+
+ void operator() (const InputType& x, ValueType* v, JacobianType* _j) const
+ {
+ (*this)(x, v);
+
+ if(_j)
+ {
+ JacobianType& j = *_j;
+
+ j(0,0) = 4 * x[0] + x[1];
+ j(1,0) = 3 * x[1];
+
+ j(0,1) = x[0];
+ j(1,1) = 3 * x[0] + 2 * 0.5 * x[1];
+
+ if (inputs()>2)
+ {
+ j(0,2) = 0.5;
+ j(1,2) = 1;
+ }
+ if(values()>2)
+ {
+ j(2,0) = 3 * x[1] * 2 * x[0];
+ j(2,1) = 3 * x[0] * x[0];
+ }
+ if (inputs()>2 && values()>2)
+ {
+ j(2,0) *= x[2];
+ j(2,1) *= x[2];
+
+ j(2,2) = 3 * x[1] * x[0] * x[0];
+ j(2,2) = 3 * x[1] * x[0] * x[0];
+ }
+ }
+ }
+};
+
+
+/* Test functor for the C++11 features. */
+template <typename Scalar>
+struct integratorFunctor
+{
+ typedef Matrix<Scalar, 2, 1> InputType;
+ typedef Matrix<Scalar, 2, 1> ValueType;
+
+ /*
+ * Implementation starts here.
+ */
+ integratorFunctor(const Scalar gain) : _gain(gain) {}
+ integratorFunctor(const integratorFunctor& f) : _gain(f._gain) {}
+ const Scalar _gain;
+
+ template <typename T1, typename T2>
+ void operator() (const T1 &input, T2 *output, const Scalar dt) const
+ {
+ T2 &o = *output;
+
+ /* Integrator to test the AD. */
+ o[0] = input[0] + input[1] * dt * _gain;
+ o[1] = input[1] * _gain;
+ }
+
+ /* Only needed for the test */
+ template <typename T1, typename T2, typename T3>
+ void operator() (const T1 &input, T2 *output, T3 *jacobian, const Scalar dt) const
+ {
+ T2 &o = *output;
+
+ /* Integrator to test the AD. */
+ o[0] = input[0] + input[1] * dt * _gain;
+ o[1] = input[1] * _gain;
+
+ if (jacobian)
+ {
+ T3 &j = *jacobian;
+
+ j(0, 0) = 1;
+ j(0, 1) = dt * _gain;
+ j(1, 0) = 0;
+ j(1, 1) = _gain;
+ }
+ }
+
+};
+
+template<typename Func> void forward_jacobian_cpp11(const Func& f)
+{
+ typedef typename Func::ValueType::Scalar Scalar;
+ typedef typename Func::ValueType ValueType;
+ typedef typename Func::InputType InputType;
+ typedef typename AutoDiffJacobian<Func>::JacobianType JacobianType;
+
+ InputType x = InputType::Random(InputType::RowsAtCompileTime);
+ ValueType y, yref;
+ JacobianType j, jref;
+
+ const Scalar dt = internal::random<double>();
+
+ jref.setZero();
+ yref.setZero();
+ f(x, &yref, &jref, dt);
+
+ //std::cerr << "y, yref, jref: " << "\n";
+ //std::cerr << y.transpose() << "\n\n";
+ //std::cerr << yref << "\n\n";
+ //std::cerr << jref << "\n\n";
+
+ AutoDiffJacobian<Func> autoj(f);
+ autoj(x, &y, &j, dt);
+
+ //std::cerr << "y j (via autodiff): " << "\n";
+ //std::cerr << y.transpose() << "\n\n";
+ //std::cerr << j << "\n\n";
+
+ VERIFY_IS_APPROX(y, yref);
+ VERIFY_IS_APPROX(j, jref);
+}
+
+template<typename Func> void forward_jacobian(const Func& f)
+{
+ typename Func::InputType x = Func::InputType::Random(f.inputs());
+ typename Func::ValueType y(f.values()), yref(f.values());
+ typename Func::JacobianType j(f.values(),f.inputs()), jref(f.values(),f.inputs());
+
+ jref.setZero();
+ yref.setZero();
+ f(x,&yref,&jref);
+// std::cerr << y.transpose() << "\n\n";;
+// std::cerr << j << "\n\n";;
+
+ j.setZero();
+ y.setZero();
+ AutoDiffJacobian<Func> autoj(f);
+ autoj(x, &y, &j);
+// std::cerr << y.transpose() << "\n\n";;
+// std::cerr << j << "\n\n";;
+
+ VERIFY_IS_APPROX(y, yref);
+ VERIFY_IS_APPROX(j, jref);
+}
+
+// TODO also check actual derivatives!
+template <int>
+void test_autodiff_scalar()
+{
+ Vector2f p = Vector2f::Random();
+ typedef AutoDiffScalar<Vector2f> AD;
+ AD ax(p.x(),Vector2f::UnitX());
+ AD ay(p.y(),Vector2f::UnitY());
+ AD res = foo<AD>(ax,ay);
+ VERIFY_IS_APPROX(res.value(), foo(p.x(),p.y()));
+}
+
+
+// TODO also check actual derivatives!
+template <int>
+void test_autodiff_vector()
+{
+ Vector2f p = Vector2f::Random();
+ typedef AutoDiffScalar<Vector2f> AD;
+ typedef Matrix<AD,2,1> VectorAD;
+ VectorAD ap = p.cast<AD>();
+ ap.x().derivatives() = Vector2f::UnitX();
+ ap.y().derivatives() = Vector2f::UnitY();
+
+ AD res = foo<VectorAD>(ap);
+ VERIFY_IS_APPROX(res.value(), foo(p));
+}
+
+template <int>
+void test_autodiff_jacobian()
+{
+ CALL_SUBTEST(( forward_jacobian(TestFunc1<double,2,2>()) ));
+ CALL_SUBTEST(( forward_jacobian(TestFunc1<double,2,3>()) ));
+ CALL_SUBTEST(( forward_jacobian(TestFunc1<double,3,2>()) ));
+ CALL_SUBTEST(( forward_jacobian(TestFunc1<double,3,3>()) ));
+ CALL_SUBTEST(( forward_jacobian(TestFunc1<double>(3,3)) ));
+ CALL_SUBTEST(( forward_jacobian_cpp11(integratorFunctor<double>(10)) ));
+}
+
+
+template <int>
+void test_autodiff_hessian()
+{
+ typedef AutoDiffScalar<VectorXd> AD;
+ typedef Matrix<AD,Eigen::Dynamic,1> VectorAD;
+ typedef AutoDiffScalar<VectorAD> ADD;
+ typedef Matrix<ADD,Eigen::Dynamic,1> VectorADD;
+ VectorADD x(2);
+ double s1 = internal::random<double>(), s2 = internal::random<double>(), s3 = internal::random<double>(), s4 = internal::random<double>();
+ x(0).value()=s1;
+ x(1).value()=s2;
+
+ //set unit vectors for the derivative directions (partial derivatives of the input vector)
+ x(0).derivatives().resize(2);
+ x(0).derivatives().setZero();
+ x(0).derivatives()(0)= 1;
+ x(1).derivatives().resize(2);
+ x(1).derivatives().setZero();
+ x(1).derivatives()(1)=1;
+
+ //repeat partial derivatives for the inner AutoDiffScalar
+ x(0).value().derivatives() = VectorXd::Unit(2,0);
+ x(1).value().derivatives() = VectorXd::Unit(2,1);
+
+ //set the hessian matrix to zero
+ for(int idx=0; idx<2; idx++) {
+ x(0).derivatives()(idx).derivatives() = VectorXd::Zero(2);
+ x(1).derivatives()(idx).derivatives() = VectorXd::Zero(2);
+ }
+
+ ADD y = sin(AD(s3)*x(0) + AD(s4)*x(1));
+
+ VERIFY_IS_APPROX(y.value().derivatives()(0), y.derivatives()(0).value());
+ VERIFY_IS_APPROX(y.value().derivatives()(1), y.derivatives()(1).value());
+ VERIFY_IS_APPROX(y.value().derivatives()(0), s3*std::cos(s1*s3+s2*s4));
+ VERIFY_IS_APPROX(y.value().derivatives()(1), s4*std::cos(s1*s3+s2*s4));
+ VERIFY_IS_APPROX(y.derivatives()(0).derivatives(), -std::sin(s1*s3+s2*s4)*Vector2d(s3*s3,s4*s3));
+ VERIFY_IS_APPROX(y.derivatives()(1).derivatives(), -std::sin(s1*s3+s2*s4)*Vector2d(s3*s4,s4*s4));
+
+ ADD z = x(0)*x(1);
+ VERIFY_IS_APPROX(z.derivatives()(0).derivatives(), Vector2d(0,1));
+ VERIFY_IS_APPROX(z.derivatives()(1).derivatives(), Vector2d(1,0));
+}
+
+double bug_1222() {
+ typedef Eigen::AutoDiffScalar<Eigen::Vector3d> AD;
+ const double _cv1_3 = 1.0;
+ const AD chi_3 = 1.0;
+ // this line did not work, because operator+ returns ADS<DerType&>, which then cannot be converted to ADS<DerType>
+ const AD denom = chi_3 + _cv1_3;
+ return denom.value();
+}
+
+#ifdef EIGEN_TEST_PART_5
+
+double bug_1223() {
+ using std::min;
+ typedef Eigen::AutoDiffScalar<Eigen::Vector3d> AD;
+
+ const double _cv1_3 = 1.0;
+ const AD chi_3 = 1.0;
+ const AD denom = 1.0;
+
+ // failed because implementation of min attempts to construct ADS<DerType&> via constructor AutoDiffScalar(const Real& value)
+ // without initializing m_derivatives (which is a reference in this case)
+ #define EIGEN_TEST_SPACE
+ const AD t = min EIGEN_TEST_SPACE (denom / chi_3, 1.0);
+
+ const AD t2 = min EIGEN_TEST_SPACE (denom / (chi_3 * _cv1_3), 1.0);
+
+ return t.value() + t2.value();
+}
+
+// regression test for some compilation issues with specializations of ScalarBinaryOpTraits
+void bug_1260() {
+ Matrix4d A = Matrix4d::Ones();
+ Vector4d v = Vector4d::Ones();
+ A*v;
+}
+
+// check a compilation issue with numext::max
+double bug_1261() {
+ typedef AutoDiffScalar<Matrix2d> AD;
+ typedef Matrix<AD,2,1> VectorAD;
+
+ VectorAD v(0.,0.);
+ const AD maxVal = v.maxCoeff();
+ const AD minVal = v.minCoeff();
+ return maxVal.value() + minVal.value();
+}
+
+double bug_1264() {
+ typedef AutoDiffScalar<Vector2d> AD;
+ const AD s = 0.;
+ const Matrix<AD, 3, 1> v1(0.,0.,0.);
+ const Matrix<AD, 3, 1> v2 = (s + 3.0) * v1;
+ return v2(0).value();
+}
+
+// check with expressions on constants
+double bug_1281() {
+ int n = 2;
+ typedef AutoDiffScalar<VectorXd> AD;
+ const AD c = 1.;
+ AD x0(2,n,0);
+ AD y1 = (AD(c)+AD(c))*x0;
+ y1 = x0 * (AD(c)+AD(c));
+ AD y2 = (-AD(c))+x0;
+ y2 = x0+(-AD(c));
+ AD y3 = (AD(c)*(-AD(c))+AD(c))*x0;
+ y3 = x0 * (AD(c)*(-AD(c))+AD(c));
+ return (y1+y2+y3).value();
+}
+
+#endif
+
+EIGEN_DECLARE_TEST(autodiff)
+{
+ for(int i = 0; i < g_repeat; i++) {
+ CALL_SUBTEST_1( test_autodiff_scalar<1>() );
+ CALL_SUBTEST_2( test_autodiff_vector<1>() );
+ CALL_SUBTEST_3( test_autodiff_jacobian<1>() );
+ CALL_SUBTEST_4( test_autodiff_hessian<1>() );
+ }
+
+ CALL_SUBTEST_5( bug_1222() );
+ CALL_SUBTEST_5( bug_1223() );
+ CALL_SUBTEST_5( bug_1260() );
+ CALL_SUBTEST_5( bug_1261() );
+ CALL_SUBTEST_5( bug_1281() );
+}
+
diff --git a/unsupported/test/autodiff_scalar.cpp b/unsupported/test/autodiff_scalar.cpp
new file mode 100644
index 0000000..1dbf585
--- /dev/null
+++ b/unsupported/test/autodiff_scalar.cpp
@@ -0,0 +1,99 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2013 Christoph Hertzberg <chtz@informatik.uni-bremen.de>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "main.h"
+#include <unsupported/Eigen/AutoDiff>
+
+/*
+ * In this file scalar derivations are tested for correctness.
+ * TODO add more tests!
+ */
+
+template<typename Scalar> void check_atan2()
+{
+ typedef Matrix<Scalar, 1, 1> Deriv1;
+ typedef AutoDiffScalar<Deriv1> AD;
+
+ AD x(internal::random<Scalar>(-3.0, 3.0), Deriv1::UnitX());
+
+ using std::exp;
+ Scalar r = exp(internal::random<Scalar>(-10, 10));
+
+ AD s = sin(x), c = cos(x);
+ AD res = atan2(r*s, r*c);
+
+ VERIFY_IS_APPROX(res.value(), x.value());
+ VERIFY_IS_APPROX(res.derivatives(), x.derivatives());
+
+ res = atan2(r*s+0, r*c+0);
+ VERIFY_IS_APPROX(res.value(), x.value());
+ VERIFY_IS_APPROX(res.derivatives(), x.derivatives());
+}
+
+template<typename Scalar> void check_hyperbolic_functions()
+{
+ using std::sinh;
+ using std::cosh;
+ using std::tanh;
+ typedef Matrix<Scalar, 1, 1> Deriv1;
+ typedef AutoDiffScalar<Deriv1> AD;
+ Deriv1 p = Deriv1::Random();
+ AD val(p.x(),Deriv1::UnitX());
+
+ Scalar cosh_px = std::cosh(p.x());
+ AD res1 = tanh(val);
+ VERIFY_IS_APPROX(res1.value(), std::tanh(p.x()));
+ VERIFY_IS_APPROX(res1.derivatives().x(), Scalar(1.0) / (cosh_px * cosh_px));
+
+ AD res2 = sinh(val);
+ VERIFY_IS_APPROX(res2.value(), std::sinh(p.x()));
+ VERIFY_IS_APPROX(res2.derivatives().x(), cosh_px);
+
+ AD res3 = cosh(val);
+ VERIFY_IS_APPROX(res3.value(), cosh_px);
+ VERIFY_IS_APPROX(res3.derivatives().x(), std::sinh(p.x()));
+
+ // Check constant values.
+ const Scalar sample_point = Scalar(1) / Scalar(3);
+ val = AD(sample_point,Deriv1::UnitX());
+ res1 = tanh(val);
+ VERIFY_IS_APPROX(res1.derivatives().x(), Scalar(0.896629559604914));
+
+ res2 = sinh(val);
+ VERIFY_IS_APPROX(res2.derivatives().x(), Scalar(1.056071867829939));
+
+ res3 = cosh(val);
+ VERIFY_IS_APPROX(res3.derivatives().x(), Scalar(0.339540557256150));
+}
+
+template <typename Scalar>
+void check_limits_specialization()
+{
+ typedef Eigen::Matrix<Scalar, 1, 1> Deriv;
+ typedef Eigen::AutoDiffScalar<Deriv> AD;
+
+ typedef std::numeric_limits<AD> A;
+ typedef std::numeric_limits<Scalar> B;
+
+ // workaround "unused typedef" warning:
+ VERIFY(!bool(internal::is_same<B, A>::value));
+
+ VERIFY(bool(std::is_base_of<B, A>::value));
+}
+
+EIGEN_DECLARE_TEST(autodiff_scalar)
+{
+ for(int i = 0; i < g_repeat; i++) {
+ CALL_SUBTEST_1( check_atan2<float>() );
+ CALL_SUBTEST_2( check_atan2<double>() );
+ CALL_SUBTEST_3( check_hyperbolic_functions<float>() );
+ CALL_SUBTEST_4( check_hyperbolic_functions<double>() );
+ CALL_SUBTEST_5( check_limits_specialization<double>());
+ }
+}
diff --git a/unsupported/test/bessel_functions.cpp b/unsupported/test/bessel_functions.cpp
new file mode 100644
index 0000000..06765bf
--- /dev/null
+++ b/unsupported/test/bessel_functions.cpp
@@ -0,0 +1,370 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2016 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "main.h"
+#include "../Eigen/SpecialFunctions"
+
+template<typename X, typename Y>
+void verify_component_wise(const X& x, const Y& y)
+{
+ for(Index i=0; i<x.size(); ++i)
+ {
+ if((numext::isfinite)(y(i))) {
+ VERIFY_IS_APPROX( x(i), y(i) );
+ }
+ else if((numext::isnan)(y(i)))
+ VERIFY((numext::isnan)(x(i)));
+ else
+ VERIFY_IS_EQUAL( x(i), y(i) );
+ }
+}
+
+template<typename ArrayType> void array_bessel_functions()
+{
+ // Test Bessel function i0. Reference results obtained with SciPy.
+ {
+ ArrayType x(21);
+ ArrayType expected(21);
+ ArrayType res(21);
+
+ x << -20.0, -18.0, -16.0, -14.0, -12.0, -10.0, -8.0, -6.0, -4.0, -2.0, 0.0,
+ 2.0, 4.0, 6.0, 8.0, 10.0, 12.0, 14.0, 16.0, 18.0, 20.0;
+
+ expected << 4.35582826e+07, 6.21841242e+06, 8.93446228e+05, 1.29418563e+05,
+ 1.89489253e+04, 2.81571663e+03, 4.27564116e+02, 6.72344070e+01,
+ 1.13019220e+01, 2.27958530e+00, 1.00000000e+00, 2.27958530e+00,
+ 1.13019220e+01, 6.72344070e+01, 4.27564116e+02, 2.81571663e+03,
+ 1.89489253e+04, 1.29418563e+05, 8.93446228e+05, 6.21841242e+06,
+ 4.35582826e+07;
+
+ CALL_SUBTEST(res = bessel_i0(x);
+ verify_component_wise(res, expected););
+ }
+
+ // Test Bessel function i0e. Reference results obtained with SciPy.
+ {
+ ArrayType x(21);
+ ArrayType expected(21);
+ ArrayType res(21);
+
+ x << -20.0, -18.0, -16.0, -14.0, -12.0, -10.0, -8.0, -6.0, -4.0, -2.0, 0.0,
+ 2.0, 4.0, 6.0, 8.0, 10.0, 12.0, 14.0, 16.0, 18.0, 20.0;
+
+ expected << 0.0897803118848, 0.0947062952128, 0.100544127361,
+ 0.107615251671, 0.116426221213, 0.127833337163, 0.143431781857,
+ 0.16665743264, 0.207001921224, 0.308508322554, 1.0, 0.308508322554,
+ 0.207001921224, 0.16665743264, 0.143431781857, 0.127833337163,
+ 0.116426221213, 0.107615251671, 0.100544127361, 0.0947062952128,
+ 0.0897803118848;
+
+ CALL_SUBTEST(res = bessel_i0e(x);
+ verify_component_wise(res, expected););
+ }
+
+ // Test Bessel function i1. Reference results obtained with SciPy.
+ {
+ ArrayType x(21);
+ ArrayType expected(21);
+ ArrayType res(21);
+
+ x << -20.0, -18.0, -16.0, -14.0, -12.0, -10.0, -8.0, -6.0, -4.0, -2.0, 0.0,
+ 2.0, 4.0, 6.0, 8.0, 10.0, 12.0, 14.0, 16.0, 18.0, 20.0;
+
+ expected << -4.24549734e+07, -6.04313324e+06, -8.65059436e+05, -1.24707259e+05,
+ -1.81413488e+04, -2.67098830e+03, -3.99873137e+02, -6.13419368e+01,
+ -9.75946515e+00, -1.59063685e+00, 0.00000000e+00, 1.59063685e+00,
+ 9.75946515e+00, 6.13419368e+01, 3.99873137e+02, 2.67098830e+03,
+ 1.81413488e+04, 1.24707259e+05, 8.65059436e+05, 6.04313324e+06,
+ 4.24549734e+07;
+
+ CALL_SUBTEST(res = bessel_i1(x);
+ verify_component_wise(res, expected););
+ }
+
+ // Test Bessel function i1e. Reference results obtained with SciPy.
+ {
+ ArrayType x(21);
+ ArrayType expected(21);
+ ArrayType res(21);
+
+ x << -20.0, -18.0, -16.0, -14.0, -12.0, -10.0, -8.0, -6.0, -4.0, -2.0, 0.0,
+ 2.0, 4.0, 6.0, 8.0, 10.0, 12.0, 14.0, 16.0, 18.0, 20.0;
+
+ expected << -0.0875062221833, -0.092036796872, -0.0973496147565,
+ -0.103697667463, -0.11146429929, -0.121262681384, -0.134142493293,
+ -0.152051459309, -0.178750839502, -0.215269289249, 0.0, 0.215269289249,
+ 0.178750839502, 0.152051459309, 0.134142493293, 0.121262681384,
+ 0.11146429929, 0.103697667463, 0.0973496147565, 0.092036796872,
+ 0.0875062221833;
+
+ CALL_SUBTEST(res = bessel_i1e(x);
+ verify_component_wise(res, expected););
+ }
+
+ // Test Bessel function j0. Reference results obtained with SciPy.
+ {
+ ArrayType x(77);
+ ArrayType expected(77);
+ ArrayType res(77);
+
+ x << -38., -37., -36., -35., -34., -33., -32., -31., -30.,
+ -29., -28., -27., -26., -25., -24., -23., -22., -21., -20., -19.,
+ -18., -17., -16., -15., -14., -13., -12., -11., -10., -9., -8.,
+ -7., -6., -5., -4., -3., -2., -1., 0., 1., 2., 3.,
+ 4., 5., 6., 7., 8., 9., 10., 11., 12., 13., 14.,
+ 15., 16., 17., 18., 19., 20., 21., 22., 23., 24., 25.,
+ 26., 27., 28., 29., 30., 31., 32., 33., 34., 35., 36.,
+ 37., 38.;
+
+ expected << 0.11433274, 0.01086237, -0.10556738,
+ -0.12684568, -0.03042119, 0.09727067, 0.13807901, 0.05120815,
+ -0.08636798, -0.14784876, -0.07315701, 0.07274192, 0.15599932,
+ 0.09626678, -0.05623027, -0.16241278, -0.12065148, 0.03657907,
+ 0.16702466, 0.14662944, -0.01335581, -0.16985425, -0.17489907,
+ -0.01422447, 0.17107348, 0.2069261 , 0.04768931, -0.1711903 ,
+ -0.24593576, -0.09033361, 0.17165081, 0.30007927, 0.15064526,
+ -0.17759677, -0.39714981, -0.26005195, 0.22389078, 0.76519769,
+ 1. , 0.76519769, 0.22389078, -0.26005195, -0.39714981,
+ -0.17759677, 0.15064526, 0.30007927, 0.17165081, -0.09033361,
+ -0.24593576, -0.1711903 , 0.04768931, 0.2069261 , 0.17107348,
+ -0.01422447, -0.17489907, -0.16985425, -0.01335581, 0.14662944,
+ 0.16702466, 0.03657907, -0.12065148, -0.16241278, -0.05623027,
+ 0.09626678, 0.15599932, 0.07274192, -0.07315701, -0.14784876,
+ -0.08636798, 0.05120815, 0.13807901, 0.09727067, -0.03042119,
+ -0.12684568, -0.10556738, 0.01086237, 0.11433274;
+
+ CALL_SUBTEST(res = bessel_j0(x);
+ verify_component_wise(res, expected););
+ }
+
+ // Test Bessel function j1. Reference results obtained with SciPy.
+ {
+ ArrayType x(81);
+ ArrayType expected(81);
+ ArrayType res(81);
+
+ x << -40., -39., -38., -37., -36., -35., -34., -33., -32., -31., -30.,
+ -29., -28., -27., -26., -25., -24., -23., -22., -21., -20., -19.,
+ -18., -17., -16., -15., -14., -13., -12., -11., -10., -9., -8.,
+ -7., -6., -5., -4., -3., -2., -1., 0., 1., 2., 3.,
+ 4., 5., 6., 7., 8., 9., 10., 11., 12., 13., 14.,
+ 15., 16., 17., 18., 19., 20., 21., 22., 23., 24., 25.,
+ 26., 27., 28., 29., 30., 31., 32., 33., 34., 35., 36.,
+ 37., 38., 39., 40.;
+
+ expected << -0.12603832, -0.0640561 , 0.05916189, 0.13058004, 0.08232981,
+ -0.04399094, -0.13297118, -0.10061965, 0.02658903, 0.13302432,
+ 0.11875106, -0.0069342 , -0.13055149, -0.13658472, -0.01504573,
+ 0.12535025, 0.15403807, 0.03951932, -0.11717779, -0.17112027,
+ -0.06683312, 0.10570143, 0.18799489, 0.09766849, -0.09039718,
+ -0.20510404, -0.13337515, 0.07031805, 0.2234471 , 0.1767853 ,
+ -0.04347275, -0.24531179, -0.23463635, 0.00468282, 0.27668386,
+ 0.32757914, 0.06604333, -0.33905896, -0.57672481, -0.44005059,
+ 0. , 0.44005059, 0.57672481, 0.33905896, -0.06604333,
+ -0.32757914, -0.27668386, -0.00468282, 0.23463635, 0.24531179,
+ 0.04347275, -0.1767853 , -0.2234471 , -0.07031805, 0.13337515,
+ 0.20510404, 0.09039718, -0.09766849, -0.18799489, -0.10570143,
+ 0.06683312, 0.17112027, 0.11717779, -0.03951932, -0.15403807,
+ -0.12535025, 0.01504573, 0.13658472, 0.13055149, 0.0069342 ,
+ -0.11875106, -0.13302432, -0.02658903, 0.10061965, 0.13297118,
+ 0.04399094, -0.08232981, -0.13058004, -0.05916189, 0.0640561 ,
+ 0.12603832;
+
+ CALL_SUBTEST(res = bessel_j1(x);
+ verify_component_wise(res, expected););
+ }
+ // Test Bessel function k0e. Reference results obtained with SciPy.
+ {
+ ArrayType x(42);
+ ArrayType expected(42);
+ ArrayType res(42);
+
+ x << 0.25, 0.5, 1., 2., 3., 4., 5., 6., 7., 8., 9., 10., 11., 12.,
+ 13., 14., 15., 16., 17., 18., 19., 20., 21., 22., 23., 24., 25.,
+ 26., 27., 28., 29., 30., 31., 32., 33., 34., 35., 36., 37., 38.,
+ 39., 40.;
+
+ expected << 1.97933385, 1.52410939, 1.14446308, 0.84156822,
+ 0.6977616 , 0.60929767, 0.54780756, 0.50186313, 0.4658451 ,
+ 0.43662302, 0.41229555, 0.39163193, 0.3737955 , 0.35819488,
+ 0.34439865, 0.33208364, 0.32100235, 0.31096159, 0.30180802,
+ 0.29341821, 0.28569149, 0.27854488, 0.2719092 , 0.26572635,
+ 0.25994703, 0.25452917, 0.2494366 , 0.24463801, 0.24010616,
+ 0.23581722, 0.23175022, 0.22788667, 0.22421014, 0.22070602,
+ 0.21736123, 0.21416406, 0.21110397, 0.20817141, 0.20535778,
+ 0.20265524, 0.20005668, 0.19755558;
+
+ CALL_SUBTEST(res = bessel_k0e(x);
+ verify_component_wise(res, expected););
+ }
+
+ // Test Bessel function k0. Reference results obtained with SciPy.
+ {
+ ArrayType x(42);
+ ArrayType expected(42);
+ ArrayType res(42);
+
+ x << 0.25, 0.5, 1., 2., 3., 4., 5., 6., 7., 8., 9., 10., 11., 12.,
+ 13., 14., 15., 16., 17., 18., 19., 20., 21., 22., 23., 24., 25.,
+ 26., 27., 28., 29., 30., 31., 32., 33., 34., 35., 36., 37., 38.,
+ 39., 40.;
+
+ expected << 1.54150675, 0.92441907, 4.21024438e-01, 1.13893873e-01,
+ 3.47395044e-02, 1.11596761e-02, 3.69109833e-03, 1.24399433e-03,
+ 4.24795742e-04, 1.46470705e-04, 5.08813130e-05, 1.77800623e-05,
+ 6.24302055e-06, 2.20082540e-06, 7.78454386e-07, 2.76137082e-07,
+ 9.81953648e-08, 3.49941166e-08, 1.24946640e-08, 4.46875334e-09,
+ 1.60067129e-09, 5.74123782e-10, 2.06176797e-10, 7.41235161e-11,
+ 2.66754511e-11, 9.60881878e-12, 3.46416156e-12, 1.24987740e-12,
+ 4.51286453e-13, 1.63053459e-13, 5.89495073e-14, 2.13247750e-14,
+ 7.71838266e-15, 2.79505752e-15, 1.01266123e-15, 3.67057597e-16,
+ 1.33103515e-16, 4.82858338e-17, 1.75232770e-17, 6.36161716e-18,
+ 2.31029936e-18, 8.39286110e-19;
+
+ CALL_SUBTEST(res = bessel_k0(x);
+ verify_component_wise(res, expected););
+ }
+
+ // Test Bessel function k0e. Reference results obtained with SciPy.
+ {
+ ArrayType x(42);
+ ArrayType expected(42);
+ ArrayType res(42);
+
+ x << 0.25, 0.5, 1., 2., 3., 4., 5., 6., 7., 8., 9., 10., 11., 12.,
+ 13., 14., 15., 16., 17., 18., 19., 20., 21., 22., 23., 24., 25.,
+ 26., 27., 28., 29., 30., 31., 32., 33., 34., 35., 36., 37., 38.,
+ 39., 40.;
+
+ expected << 1.97933385, 1.52410939, 1.14446308, 0.84156822,
+ 0.6977616 , 0.60929767, 0.54780756, 0.50186313,
+ 0.4658451 , 0.43662302, 0.41229555, 0.39163193,
+ 0.3737955 , 0.35819488, 0.34439865, 0.33208364,
+ 0.32100235, 0.31096159, 0.30180802, 0.29341821,
+ 0.28569149, 0.27854488, 0.2719092 , 0.26572635,
+ 0.25994703, 0.25452917, 0.2494366 , 0.24463801,
+ 0.24010616, 0.23581722, 0.23175022, 0.22788667,
+ 0.22421014, 0.22070602, 0.21736123, 0.21416406,
+ 0.21110397, 0.20817141, 0.20535778, 0.20265524,
+ 0.20005668, 0.19755558;
+
+ CALL_SUBTEST(res = bessel_k0e(x);
+ verify_component_wise(res, expected););
+ }
+
+ // Test Bessel function k1. Reference results obtained with SciPy.
+ {
+ ArrayType x(42);
+ ArrayType expected(42);
+ ArrayType res(42);
+
+ x << 0.25, 0.5, 1., 2., 3., 4., 5., 6., 7., 8., 9., 10., 11., 12.,
+ 13., 14., 15., 16., 17., 18., 19., 20., 21., 22., 23., 24., 25.,
+ 26., 27., 28., 29., 30., 31., 32., 33., 34., 35., 36., 37., 38.,
+ 39., 40.;
+
+ expected << 3.74702597, 1.65644112, 6.01907230e-01, 1.39865882e-01,
+ 4.01564311e-02, 1.24834989e-02, 4.04461345e-03, 1.34391972e-03,
+ 4.54182487e-04, 1.55369212e-04, 5.36370164e-05, 1.86487735e-05,
+ 6.52086067e-06, 2.29075746e-06, 8.07858841e-07, 2.85834365e-07,
+ 1.01417294e-07, 3.60715712e-08, 1.28570417e-08, 4.59124963e-09,
+ 1.64226697e-09, 5.88305797e-10, 2.11029922e-10, 7.57898116e-11,
+ 2.72493059e-11, 9.80699893e-12, 3.53277807e-12, 1.27369078e-12,
+ 4.59568940e-13, 1.65940011e-13, 5.99574032e-14, 2.16773200e-14,
+ 7.84189960e-15, 2.83839927e-15, 1.02789171e-15, 3.72416929e-16,
+ 1.34991783e-16, 4.89519373e-17, 1.77585196e-17, 6.44478588e-18,
+ 2.33973340e-18, 8.49713195e-19;
+
+ CALL_SUBTEST(res = bessel_k1(x);
+ verify_component_wise(res, expected););
+ }
+
+ // Test Bessel function k1e. Reference results obtained with SciPy.
+ {
+ ArrayType x(42);
+ ArrayType expected(42);
+ ArrayType res(42);
+
+ x << 0.25, 0.5, 1., 2., 3., 4., 5., 6., 7., 8., 9., 10., 11., 12.,
+ 13., 14., 15., 16., 17., 18., 19., 20., 21., 22., 23., 24., 25.,
+ 26., 27., 28., 29., 30., 31., 32., 33., 34., 35., 36., 37., 38.,
+ 39., 40.;
+
+ expected << 4.81127659, 2.73100971, 1.63615349, 1.03347685,
+ 0.80656348, 0.68157595, 0.60027386, 0.54217591,
+ 0.49807158, 0.46314909, 0.43462525, 0.41076657,
+ 0.39043094, 0.37283175, 0.35740757, 0.34374563,
+ 0.33153489, 0.32053597, 0.31056123, 0.30146131,
+ 0.29311559, 0.2854255 , 0.27830958, 0.27169987,
+ 0.26553913, 0.25977879, 0.25437733, 0.249299 ,
+ 0.24451285, 0.23999191, 0.2357126 , 0.23165413,
+ 0.22779816, 0.22412841, 0.22063036, 0.21729103,
+ 0.21409878, 0.21104314, 0.20811462, 0.20530466,
+ 0.20260547, 0.20000997;
+
+ CALL_SUBTEST(res = bessel_k1e(x);
+ verify_component_wise(res, expected););
+ }
+
+ // Test Bessel function y0. Reference results obtained with SciPy.
+ {
+ ArrayType x(42);
+ ArrayType expected(42);
+ ArrayType res(42);
+
+ x << 0.25, 0.5, 1., 2., 3., 4., 5., 6., 7., 8., 9., 10., 11., 12.,
+ 13., 14., 15., 16., 17., 18., 19., 20., 21., 22., 23., 24., 25.,
+ 26., 27., 28., 29., 30., 31., 32., 33., 34., 35., 36., 37., 38.,
+ 39., 40.;
+
+ expected << -0.93157302, -0.44451873, 0.08825696, 0.51037567, 0.37685001,
+ -0.01694074, -0.30851763, -0.28819468, -0.02594974, 0.22352149,
+ 0.2499367 , 0.05567117, -0.16884732, -0.22523731, -0.07820786,
+ 0.12719257, 0.2054643 , 0.095811 , -0.0926372 , -0.18755216,
+ -0.10951969, 0.0626406 , 0.17020176, 0.1198876 , -0.03598179,
+ -0.15283403, -0.12724943, 0.01204463, 0.13521498, 0.13183647,
+ 0.00948116, -0.11729573, -0.13383266, -0.02874248, 0.09913483,
+ 0.13340405, 0.04579799, -0.08085609, -0.13071488, -0.06066076,
+ 0.06262353, 0.12593642;
+
+ CALL_SUBTEST(res = bessel_y0(x);
+ verify_component_wise(res, expected););
+ }
+
+ // Test Bessel function y1. Reference results obtained with SciPy.
+ {
+ ArrayType x(42);
+ ArrayType expected(42);
+ ArrayType res(42);
+
+ x << 0.25, 0.5, 1., 2., 3., 4., 5., 6., 7., 8., 9., 10., 11., 12.,
+ 13., 14., 15., 16., 17., 18., 19., 20., 21., 22., 23., 24., 25.,
+ 26., 27., 28., 29., 30., 31., 32., 33., 34., 35., 36., 37., 38.,
+ 39., 40.;
+
+ expected << -2.70410523, -1.47147239, -0.78121282, -0.10703243,
+ 0.32467442, 0.39792571, 0.14786314, -0.17501034, -0.30266724,
+ -0.15806046, 0.10431458, 0.24901542, 0.16370554, -0.05709922,
+ -0.21008141, -0.16664484, 0.02107363, 0.17797517, 0.16720504,
+ 0.00815513, -0.14956011, -0.16551161, -0.03253926, 0.12340586,
+ 0.1616692 , 0.05305978, -0.09882996, -0.15579655, -0.07025124,
+ 0.07552213, 0.14803412, 0.08442557, -0.05337283, -0.13854483,
+ -0.09578012, 0.03238588, 0.12751273, 0.10445477, -0.01262946,
+ -0.11514066, -0.11056411, -0.00579351;
+
+ CALL_SUBTEST(res = bessel_y1(x);
+ verify_component_wise(res, expected););
+ }
+}
+
+EIGEN_DECLARE_TEST(bessel_functions)
+{
+ CALL_SUBTEST_1(array_bessel_functions<ArrayXf>());
+ CALL_SUBTEST_2(array_bessel_functions<ArrayXd>());
+}
diff --git a/unsupported/test/bicgstabl.cpp b/unsupported/test/bicgstabl.cpp
new file mode 100644
index 0000000..302848c
--- /dev/null
+++ b/unsupported/test/bicgstabl.cpp
@@ -0,0 +1,31 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2011 Gael Guennebaud <g.gael@free.fr>
+// Copyright (C) 2012 Kolja Brix <brix@igpm.rwth-aaachen.de>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "../../test/sparse_solver.h"
+#include <Eigen/IterativeSolvers>
+
+template<typename T> void test_bicgstabl_T()
+{
+ BiCGSTABL<SparseMatrix<T>, DiagonalPreconditioner<T> > bicgstabl_colmajor_diag;
+ BiCGSTABL<SparseMatrix<T>, IncompleteLUT<T> > bicgstabl_colmajor_ilut;
+
+ //This does not change the tolerance of the test, only the tolerance of the solver.
+ bicgstabl_colmajor_diag.setTolerance(NumTraits<T>::epsilon()*20);
+ bicgstabl_colmajor_ilut.setTolerance(NumTraits<T>::epsilon()*20);
+
+ CALL_SUBTEST( check_sparse_square_solving(bicgstabl_colmajor_diag) );
+ CALL_SUBTEST( check_sparse_square_solving(bicgstabl_colmajor_ilut) );
+}
+
+EIGEN_DECLARE_TEST(bicgstabl)
+{
+ CALL_SUBTEST_1(test_bicgstabl_T<double>());
+ CALL_SUBTEST_2(test_bicgstabl_T<std::complex<double> >());
+}
diff --git a/unsupported/test/cxx11_eventcount.cpp b/unsupported/test/cxx11_eventcount.cpp
new file mode 100644
index 0000000..7bf4e96
--- /dev/null
+++ b/unsupported/test/cxx11_eventcount.cpp
@@ -0,0 +1,142 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2016 Dmitry Vyukov <dvyukov@google.com>
+// Copyright (C) 2016 Benoit Steiner <benoit.steiner.goog@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#define EIGEN_USE_THREADS
+#include "main.h"
+#include <Eigen/CXX11/ThreadPool>
+
+// Visual studio doesn't implement a rand_r() function since its
+// implementation of rand() is already thread safe
+int rand_reentrant(unsigned int* s) {
+#ifdef EIGEN_COMP_MSVC_STRICT
+ EIGEN_UNUSED_VARIABLE(s);
+ return rand();
+#else
+ return rand_r(s);
+#endif
+}
+
+static void test_basic_eventcount()
+{
+ MaxSizeVector<EventCount::Waiter> waiters(1);
+ waiters.resize(1);
+ EventCount ec(waiters);
+ EventCount::Waiter& w = waiters[0];
+ ec.Notify(false);
+ ec.Prewait();
+ ec.Notify(true);
+ ec.CommitWait(&w);
+ ec.Prewait();
+ ec.CancelWait();
+}
+
+// Fake bounded counter-based queue.
+struct TestQueue {
+ std::atomic<int> val_;
+ static const int kQueueSize = 10;
+
+ TestQueue() : val_() {}
+
+ ~TestQueue() { VERIFY_IS_EQUAL(val_.load(), 0); }
+
+ bool Push() {
+ int val = val_.load(std::memory_order_relaxed);
+ for (;;) {
+ VERIFY_GE(val, 0);
+ VERIFY_LE(val, kQueueSize);
+ if (val == kQueueSize) return false;
+ if (val_.compare_exchange_weak(val, val + 1, std::memory_order_relaxed))
+ return true;
+ }
+ }
+
+ bool Pop() {
+ int val = val_.load(std::memory_order_relaxed);
+ for (;;) {
+ VERIFY_GE(val, 0);
+ VERIFY_LE(val, kQueueSize);
+ if (val == 0) return false;
+ if (val_.compare_exchange_weak(val, val - 1, std::memory_order_relaxed))
+ return true;
+ }
+ }
+
+ bool Empty() { return val_.load(std::memory_order_relaxed) == 0; }
+};
+
+const int TestQueue::kQueueSize;
+
+// A number of producers send messages to a set of consumers using a set of
+// fake queues. Ensure that it does not crash, consumers don't deadlock and
+// number of blocked and unblocked threads match.
+static void test_stress_eventcount()
+{
+ const int kThreads = std::thread::hardware_concurrency();
+ static const int kEvents = 1 << 16;
+ static const int kQueues = 10;
+
+ MaxSizeVector<EventCount::Waiter> waiters(kThreads);
+ waiters.resize(kThreads);
+ EventCount ec(waiters);
+ TestQueue queues[kQueues];
+
+ std::vector<std::unique_ptr<std::thread>> producers;
+ for (int i = 0; i < kThreads; i++) {
+ producers.emplace_back(new std::thread([&ec, &queues]() {
+ unsigned int rnd = static_cast<unsigned int>(std::hash<std::thread::id>()(std::this_thread::get_id()));
+ for (int j = 0; j < kEvents; j++) {
+ unsigned idx = rand_reentrant(&rnd) % kQueues;
+ if (queues[idx].Push()) {
+ ec.Notify(false);
+ continue;
+ }
+ EIGEN_THREAD_YIELD();
+ j--;
+ }
+ }));
+ }
+
+ std::vector<std::unique_ptr<std::thread>> consumers;
+ for (int i = 0; i < kThreads; i++) {
+ consumers.emplace_back(new std::thread([&ec, &queues, &waiters, i]() {
+ EventCount::Waiter& w = waiters[i];
+ unsigned int rnd = static_cast<unsigned int>(std::hash<std::thread::id>()(std::this_thread::get_id()));
+ for (int j = 0; j < kEvents; j++) {
+ unsigned idx = rand_reentrant(&rnd) % kQueues;
+ if (queues[idx].Pop()) continue;
+ j--;
+ ec.Prewait();
+ bool empty = true;
+ for (int q = 0; q < kQueues; q++) {
+ if (!queues[q].Empty()) {
+ empty = false;
+ break;
+ }
+ }
+ if (!empty) {
+ ec.CancelWait();
+ continue;
+ }
+ ec.CommitWait(&w);
+ }
+ }));
+ }
+
+ for (int i = 0; i < kThreads; i++) {
+ producers[i]->join();
+ consumers[i]->join();
+ }
+}
+
+EIGEN_DECLARE_TEST(cxx11_eventcount)
+{
+ CALL_SUBTEST(test_basic_eventcount());
+ CALL_SUBTEST(test_stress_eventcount());
+}
diff --git a/unsupported/test/cxx11_maxsizevector.cpp b/unsupported/test/cxx11_maxsizevector.cpp
new file mode 100644
index 0000000..46b689a
--- /dev/null
+++ b/unsupported/test/cxx11_maxsizevector.cpp
@@ -0,0 +1,77 @@
+#include "main.h"
+
+#include <exception> // std::exception
+
+#include <unsupported/Eigen/CXX11/Tensor>
+
+struct Foo
+{
+ static Index object_count;
+ static Index object_limit;
+ EIGEN_ALIGN_TO_BOUNDARY(128) int dummy;
+
+ Foo(int x=0) : dummy(x)
+ {
+#ifdef EIGEN_EXCEPTIONS
+ // TODO: Is this the correct way to handle this?
+ if (Foo::object_count > Foo::object_limit) { std::cout << "\nThrow!\n"; throw Foo::Fail(); }
+#endif
+ std::cout << '+';
+ ++Foo::object_count;
+ eigen_assert((internal::UIntPtr(this) & (127)) == 0);
+ }
+ Foo(const Foo&)
+ {
+ std::cout << 'c';
+ ++Foo::object_count;
+ eigen_assert((internal::UIntPtr(this) & (127)) == 0);
+ }
+
+ ~Foo()
+ {
+ std::cout << '~';
+ --Foo::object_count;
+ }
+
+ class Fail : public std::exception {};
+};
+
+Index Foo::object_count = 0;
+Index Foo::object_limit = 0;
+
+
+
+EIGEN_DECLARE_TEST(cxx11_maxsizevector)
+{
+ typedef MaxSizeVector<Foo> VectorX;
+ Foo::object_count = 0;
+ for(int r = 0; r < g_repeat; r++) {
+ Index rows = internal::random<Index>(3,30);
+ Foo::object_limit = internal::random<Index>(0, rows - 2);
+ std::cout << "object_limit = " << Foo::object_limit << std::endl;
+ bool exception_raised = false;
+#ifdef EIGEN_EXCEPTIONS
+ try
+ {
+#endif
+ std::cout << "\nVectorX m(" << rows << ");\n";
+ VectorX vect(rows);
+ for(int i=0; i<rows; ++i)
+ vect.push_back(Foo());
+#ifdef EIGEN_EXCEPTIONS
+ VERIFY(false); // not reached if exceptions are enabled
+ }
+ catch (const Foo::Fail&) { exception_raised = true; }
+ VERIFY(exception_raised);
+#endif
+ VERIFY_IS_EQUAL(Index(0), Foo::object_count);
+
+ {
+ Foo::object_limit = rows+1;
+ VectorX vect2(rows, Foo());
+ VERIFY_IS_EQUAL(Foo::object_count, rows);
+ }
+ VERIFY_IS_EQUAL(Index(0), Foo::object_count);
+ std::cout << '\n';
+ }
+}
diff --git a/unsupported/test/cxx11_meta.cpp b/unsupported/test/cxx11_meta.cpp
new file mode 100644
index 0000000..510e110
--- /dev/null
+++ b/unsupported/test/cxx11_meta.cpp
@@ -0,0 +1,357 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2013 Christian Seiler <christian@iwakd.de>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "main.h"
+
+#include <array>
+#include <Eigen/CXX11/src/util/CXX11Meta.h>
+
+using Eigen::internal::is_same;
+using Eigen::internal::type_list;
+using Eigen::internal::numeric_list;
+using Eigen::internal::gen_numeric_list;
+using Eigen::internal::gen_numeric_list_reversed;
+using Eigen::internal::gen_numeric_list_swapped_pair;
+using Eigen::internal::gen_numeric_list_repeated;
+using Eigen::internal::concat;
+using Eigen::internal::mconcat;
+using Eigen::internal::take;
+using Eigen::internal::skip;
+using Eigen::internal::slice;
+using Eigen::internal::get;
+using Eigen::internal::id_numeric;
+using Eigen::internal::id_type;
+using Eigen::internal::is_same_gf;
+using Eigen::internal::apply_op_from_left;
+using Eigen::internal::apply_op_from_right;
+using Eigen::internal::contained_in_list;
+using Eigen::internal::contained_in_list_gf;
+using Eigen::internal::arg_prod;
+using Eigen::internal::arg_sum;
+using Eigen::internal::sum_op;
+using Eigen::internal::product_op;
+using Eigen::internal::array_reverse;
+using Eigen::internal::array_sum;
+using Eigen::internal::array_prod;
+using Eigen::internal::array_reduce;
+using Eigen::internal::array_zip;
+using Eigen::internal::array_zip_and_reduce;
+using Eigen::internal::array_apply;
+using Eigen::internal::array_apply_and_reduce;
+using Eigen::internal::repeat;
+using Eigen::internal::instantiate_by_c_array;
+
+struct dummy_a {};
+struct dummy_b {};
+struct dummy_c {};
+struct dummy_d {};
+struct dummy_e {};
+
+// dummy operation for testing apply
+template<typename A, typename B> struct dummy_op;
+template<> struct dummy_op<dummy_a, dummy_b> { typedef dummy_c type; };
+template<> struct dummy_op<dummy_b, dummy_a> { typedef dummy_d type; };
+template<> struct dummy_op<dummy_b, dummy_c> { typedef dummy_a type; };
+template<> struct dummy_op<dummy_c, dummy_b> { typedef dummy_d type; };
+template<> struct dummy_op<dummy_c, dummy_a> { typedef dummy_b type; };
+template<> struct dummy_op<dummy_a, dummy_c> { typedef dummy_d type; };
+template<> struct dummy_op<dummy_a, dummy_a> { typedef dummy_e type; };
+template<> struct dummy_op<dummy_b, dummy_b> { typedef dummy_e type; };
+template<> struct dummy_op<dummy_c, dummy_c> { typedef dummy_e type; };
+
+template<typename A, typename B> struct dummy_test { constexpr static bool value = false; constexpr static int global_flags = 0; };
+template<> struct dummy_test<dummy_a, dummy_a> { constexpr static bool value = true; constexpr static int global_flags = 1; };
+template<> struct dummy_test<dummy_b, dummy_b> { constexpr static bool value = true; constexpr static int global_flags = 2; };
+template<> struct dummy_test<dummy_c, dummy_c> { constexpr static bool value = true; constexpr static int global_flags = 4; };
+
+struct times2_op { template<typename A> static A run(A v) { return v * 2; } };
+
+struct dummy_inst
+{
+ int c;
+
+ dummy_inst() : c(0) {}
+ explicit dummy_inst(int) : c(1) {}
+ dummy_inst(int, int) : c(2) {}
+ dummy_inst(int, int, int) : c(3) {}
+ dummy_inst(int, int, int, int) : c(4) {}
+ dummy_inst(int, int, int, int, int) : c(5) {}
+};
+
+static void test_gen_numeric_list()
+{
+ VERIFY((is_same<typename gen_numeric_list<int, 0>::type, numeric_list<int>>::value));
+ VERIFY((is_same<typename gen_numeric_list<int, 1>::type, numeric_list<int, 0>>::value));
+ VERIFY((is_same<typename gen_numeric_list<int, 2>::type, numeric_list<int, 0, 1>>::value));
+ VERIFY((is_same<typename gen_numeric_list<int, 5>::type, numeric_list<int, 0, 1, 2, 3, 4>>::value));
+ VERIFY((is_same<typename gen_numeric_list<int, 10>::type, numeric_list<int, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9>>::value));
+
+ VERIFY((is_same<typename gen_numeric_list<int, 0, 42>::type, numeric_list<int>>::value));
+ VERIFY((is_same<typename gen_numeric_list<int, 1, 42>::type, numeric_list<int, 42>>::value));
+ VERIFY((is_same<typename gen_numeric_list<int, 2, 42>::type, numeric_list<int, 42, 43>>::value));
+ VERIFY((is_same<typename gen_numeric_list<int, 5, 42>::type, numeric_list<int, 42, 43, 44, 45, 46>>::value));
+ VERIFY((is_same<typename gen_numeric_list<int, 10, 42>::type, numeric_list<int, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51>>::value));
+
+ VERIFY((is_same<typename gen_numeric_list_reversed<int, 0>::type, numeric_list<int>>::value));
+ VERIFY((is_same<typename gen_numeric_list_reversed<int, 1>::type, numeric_list<int, 0>>::value));
+ VERIFY((is_same<typename gen_numeric_list_reversed<int, 2>::type, numeric_list<int, 1, 0>>::value));
+ VERIFY((is_same<typename gen_numeric_list_reversed<int, 5>::type, numeric_list<int, 4, 3, 2, 1, 0>>::value));
+ VERIFY((is_same<typename gen_numeric_list_reversed<int, 10>::type, numeric_list<int, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0>>::value));
+
+ VERIFY((is_same<typename gen_numeric_list_reversed<int, 0, 42>::type, numeric_list<int>>::value));
+ VERIFY((is_same<typename gen_numeric_list_reversed<int, 1, 42>::type, numeric_list<int, 42>>::value));
+ VERIFY((is_same<typename gen_numeric_list_reversed<int, 2, 42>::type, numeric_list<int, 43, 42>>::value));
+ VERIFY((is_same<typename gen_numeric_list_reversed<int, 5, 42>::type, numeric_list<int, 46, 45, 44, 43, 42>>::value));
+ VERIFY((is_same<typename gen_numeric_list_reversed<int, 10, 42>::type, numeric_list<int, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42>>::value));
+
+ VERIFY((is_same<typename gen_numeric_list_swapped_pair<int, 0, 2, 3>::type, numeric_list<int>>::value));
+ VERIFY((is_same<typename gen_numeric_list_swapped_pair<int, 1, 2, 3>::type, numeric_list<int, 0>>::value));
+ VERIFY((is_same<typename gen_numeric_list_swapped_pair<int, 2, 2, 3>::type, numeric_list<int, 0, 1>>::value));
+ VERIFY((is_same<typename gen_numeric_list_swapped_pair<int, 5, 2, 3>::type, numeric_list<int, 0, 1, 3, 2, 4>>::value));
+ VERIFY((is_same<typename gen_numeric_list_swapped_pair<int, 10, 2, 3>::type, numeric_list<int, 0, 1, 3, 2, 4, 5, 6, 7, 8, 9>>::value));
+
+ VERIFY((is_same<typename gen_numeric_list_swapped_pair<int, 0, 44, 45, 42>::type, numeric_list<int>>::value));
+ VERIFY((is_same<typename gen_numeric_list_swapped_pair<int, 1, 44, 45, 42>::type, numeric_list<int, 42>>::value));
+ VERIFY((is_same<typename gen_numeric_list_swapped_pair<int, 2, 44, 45, 42>::type, numeric_list<int, 42, 43>>::value));
+ VERIFY((is_same<typename gen_numeric_list_swapped_pair<int, 5, 44, 45, 42>::type, numeric_list<int, 42, 43, 45, 44, 46>>::value));
+ VERIFY((is_same<typename gen_numeric_list_swapped_pair<int, 10, 44, 45, 42>::type, numeric_list<int, 42, 43, 45, 44, 46, 47, 48, 49, 50, 51>>::value));
+
+ VERIFY((is_same<typename gen_numeric_list_repeated<int, 0, 0>::type, numeric_list<int>>::value));
+ VERIFY((is_same<typename gen_numeric_list_repeated<int, 1, 0>::type, numeric_list<int, 0>>::value));
+ VERIFY((is_same<typename gen_numeric_list_repeated<int, 2, 0>::type, numeric_list<int, 0, 0>>::value));
+ VERIFY((is_same<typename gen_numeric_list_repeated<int, 5, 0>::type, numeric_list<int, 0, 0, 0, 0, 0>>::value));
+ VERIFY((is_same<typename gen_numeric_list_repeated<int, 10, 0>::type, numeric_list<int, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0>>::value));
+}
+
+static void test_concat()
+{
+ VERIFY((is_same<typename concat<type_list<dummy_a, dummy_a>, type_list<>>::type, type_list<dummy_a, dummy_a>>::value));
+ VERIFY((is_same<typename concat<type_list<>, type_list<dummy_a, dummy_a>>::type, type_list<dummy_a, dummy_a>>::value));
+ VERIFY((is_same<typename concat<type_list<dummy_a, dummy_a>, type_list<dummy_a, dummy_a>>::type, type_list<dummy_a, dummy_a, dummy_a, dummy_a>>::value));
+ VERIFY((is_same<typename concat<type_list<dummy_a, dummy_a>, type_list<dummy_b, dummy_c>>::type, type_list<dummy_a, dummy_a, dummy_b, dummy_c>>::value));
+ VERIFY((is_same<typename concat<type_list<dummy_a>, type_list<dummy_b, dummy_c>>::type, type_list<dummy_a, dummy_b, dummy_c>>::value));
+
+ VERIFY((is_same<typename concat<numeric_list<int, 0, 0>, numeric_list<int>>::type, numeric_list<int, 0, 0>>::value));
+ VERIFY((is_same<typename concat<numeric_list<int>, numeric_list<int, 0, 0>>::type, numeric_list<int, 0, 0>>::value));
+ VERIFY((is_same<typename concat<numeric_list<int, 0, 0>, numeric_list<int, 0, 0>>::type, numeric_list<int, 0, 0, 0, 0>>::value));
+ VERIFY((is_same<typename concat<numeric_list<int, 0, 0>, numeric_list<int, 1, 2>>::type, numeric_list<int, 0, 0, 1, 2>>::value));
+ VERIFY((is_same<typename concat<numeric_list<int, 0>, numeric_list<int, 1, 2>>::type, numeric_list<int, 0, 1, 2>>::value));
+
+ VERIFY((is_same<typename mconcat<type_list<dummy_a>>::type, type_list<dummy_a>>::value));
+ VERIFY((is_same<typename mconcat<type_list<dummy_a>, type_list<dummy_b>>::type, type_list<dummy_a, dummy_b>>::value));
+ VERIFY((is_same<typename mconcat<type_list<dummy_a>, type_list<dummy_b>, type_list<dummy_c>>::type, type_list<dummy_a, dummy_b, dummy_c>>::value));
+ VERIFY((is_same<typename mconcat<type_list<dummy_a>, type_list<dummy_b, dummy_c>>::type, type_list<dummy_a, dummy_b, dummy_c>>::value));
+ VERIFY((is_same<typename mconcat<type_list<dummy_a, dummy_b>, type_list<dummy_c>>::type, type_list<dummy_a, dummy_b, dummy_c>>::value));
+
+ VERIFY((is_same<typename mconcat<numeric_list<int, 0>>::type, numeric_list<int, 0>>::value));
+ VERIFY((is_same<typename mconcat<numeric_list<int, 0>, numeric_list<int, 1>>::type, numeric_list<int, 0, 1>>::value));
+ VERIFY((is_same<typename mconcat<numeric_list<int, 0>, numeric_list<int, 1>, numeric_list<int, 2>>::type, numeric_list<int, 0, 1, 2>>::value));
+ VERIFY((is_same<typename mconcat<numeric_list<int, 0>, numeric_list<int, 1, 2>>::type, numeric_list<int, 0, 1, 2>>::value));
+ VERIFY((is_same<typename mconcat<numeric_list<int, 0, 1>, numeric_list<int, 2>>::type, numeric_list<int, 0, 1, 2>>::value));
+}
+
+static void test_slice()
+{
+ typedef type_list<dummy_a, dummy_a, dummy_b, dummy_b, dummy_c, dummy_c> tl;
+ typedef numeric_list<int, 0, 1, 2, 3, 4, 5> il;
+
+ VERIFY((is_same<typename take<0, tl>::type, type_list<>>::value));
+ VERIFY((is_same<typename take<1, tl>::type, type_list<dummy_a>>::value));
+ VERIFY((is_same<typename take<2, tl>::type, type_list<dummy_a, dummy_a>>::value));
+ VERIFY((is_same<typename take<3, tl>::type, type_list<dummy_a, dummy_a, dummy_b>>::value));
+ VERIFY((is_same<typename take<4, tl>::type, type_list<dummy_a, dummy_a, dummy_b, dummy_b>>::value));
+ VERIFY((is_same<typename take<5, tl>::type, type_list<dummy_a, dummy_a, dummy_b, dummy_b, dummy_c>>::value));
+ VERIFY((is_same<typename take<6, tl>::type, type_list<dummy_a, dummy_a, dummy_b, dummy_b, dummy_c, dummy_c>>::value));
+
+ VERIFY((is_same<typename take<0, il>::type, numeric_list<int>>::value));
+ VERIFY((is_same<typename take<1, il>::type, numeric_list<int, 0>>::value));
+ VERIFY((is_same<typename take<2, il>::type, numeric_list<int, 0, 1>>::value));
+ VERIFY((is_same<typename take<3, il>::type, numeric_list<int, 0, 1, 2>>::value));
+ VERIFY((is_same<typename take<4, il>::type, numeric_list<int, 0, 1, 2, 3>>::value));
+ VERIFY((is_same<typename take<5, il>::type, numeric_list<int, 0, 1, 2, 3, 4>>::value));
+ VERIFY((is_same<typename take<6, il>::type, numeric_list<int, 0, 1, 2, 3, 4, 5>>::value));
+
+ VERIFY((is_same<typename skip<0, tl>::type, type_list<dummy_a, dummy_a, dummy_b, dummy_b, dummy_c, dummy_c>>::value));
+ VERIFY((is_same<typename skip<1, tl>::type, type_list<dummy_a, dummy_b, dummy_b, dummy_c, dummy_c>>::value));
+ VERIFY((is_same<typename skip<2, tl>::type, type_list<dummy_b, dummy_b, dummy_c, dummy_c>>::value));
+ VERIFY((is_same<typename skip<3, tl>::type, type_list<dummy_b, dummy_c, dummy_c>>::value));
+ VERIFY((is_same<typename skip<4, tl>::type, type_list<dummy_c, dummy_c>>::value));
+ VERIFY((is_same<typename skip<5, tl>::type, type_list<dummy_c>>::value));
+ VERIFY((is_same<typename skip<6, tl>::type, type_list<>>::value));
+
+ VERIFY((is_same<typename skip<0, il>::type, numeric_list<int, 0, 1, 2, 3, 4, 5>>::value));
+ VERIFY((is_same<typename skip<1, il>::type, numeric_list<int, 1, 2, 3, 4, 5>>::value));
+ VERIFY((is_same<typename skip<2, il>::type, numeric_list<int, 2, 3, 4, 5>>::value));
+ VERIFY((is_same<typename skip<3, il>::type, numeric_list<int, 3, 4, 5>>::value));
+ VERIFY((is_same<typename skip<4, il>::type, numeric_list<int, 4, 5>>::value));
+ VERIFY((is_same<typename skip<5, il>::type, numeric_list<int, 5>>::value));
+ VERIFY((is_same<typename skip<6, il>::type, numeric_list<int>>::value));
+
+ VERIFY((is_same<typename slice<0, 3, tl>::type, typename take<3, tl>::type>::value));
+ VERIFY((is_same<typename slice<0, 3, il>::type, typename take<3, il>::type>::value));
+ VERIFY((is_same<typename slice<1, 3, tl>::type, type_list<dummy_a, dummy_b, dummy_b>>::value));
+ VERIFY((is_same<typename slice<1, 3, il>::type, numeric_list<int, 1, 2, 3>>::value));
+}
+
+static void test_get()
+{
+ typedef type_list<dummy_a, dummy_a, dummy_b, dummy_b, dummy_c, dummy_c> tl;
+ typedef numeric_list<int, 4, 8, 15, 16, 23, 42> il;
+
+ VERIFY((is_same<typename get<0, tl>::type, dummy_a>::value));
+ VERIFY((is_same<typename get<1, tl>::type, dummy_a>::value));
+ VERIFY((is_same<typename get<2, tl>::type, dummy_b>::value));
+ VERIFY((is_same<typename get<3, tl>::type, dummy_b>::value));
+ VERIFY((is_same<typename get<4, tl>::type, dummy_c>::value));
+ VERIFY((is_same<typename get<5, tl>::type, dummy_c>::value));
+
+ VERIFY_IS_EQUAL(((int)get<0, il>::value), 4);
+ VERIFY_IS_EQUAL(((int)get<1, il>::value), 8);
+ VERIFY_IS_EQUAL(((int)get<2, il>::value), 15);
+ VERIFY_IS_EQUAL(((int)get<3, il>::value), 16);
+ VERIFY_IS_EQUAL(((int)get<4, il>::value), 23);
+ VERIFY_IS_EQUAL(((int)get<5, il>::value), 42);
+}
+
+static void test_id_helper(dummy_a a, dummy_a b, dummy_a c)
+{
+ (void)a;
+ (void)b;
+ (void)c;
+}
+
+template<int... ii>
+static void test_id_numeric()
+{
+ test_id_helper(typename id_numeric<int, ii, dummy_a>::type()...);
+}
+
+template<typename... tt>
+static void test_id_type()
+{
+ test_id_helper(typename id_type<tt, dummy_a>::type()...);
+}
+
+static void test_id()
+{
+ // don't call VERIFY here, just assume it works if it compiles
+ // (otherwise it will complain that it can't find the function)
+ test_id_numeric<1, 4, 6>();
+ test_id_type<dummy_a, dummy_b, dummy_c>();
+}
+
+static void test_is_same_gf()
+{
+ VERIFY((!is_same_gf<dummy_a, dummy_b>::value));
+ VERIFY((!!is_same_gf<dummy_a, dummy_a>::value));
+ VERIFY_IS_EQUAL((!!is_same_gf<dummy_a, dummy_b>::global_flags), false);
+ VERIFY_IS_EQUAL((!!is_same_gf<dummy_a, dummy_a>::global_flags), false);
+}
+
+static void test_apply_op()
+{
+ typedef type_list<dummy_a, dummy_b, dummy_c> tl;
+ VERIFY((!!is_same<typename apply_op_from_left<dummy_op, dummy_a, tl>::type, type_list<dummy_e, dummy_c, dummy_d>>::value));
+ VERIFY((!!is_same<typename apply_op_from_right<dummy_op, dummy_a, tl>::type, type_list<dummy_e, dummy_d, dummy_b>>::value));
+}
+
+static void test_contained_in_list()
+{
+ typedef type_list<dummy_a, dummy_b, dummy_c> tl;
+
+ VERIFY((!!contained_in_list<is_same, dummy_a, tl>::value));
+ VERIFY((!!contained_in_list<is_same, dummy_b, tl>::value));
+ VERIFY((!!contained_in_list<is_same, dummy_c, tl>::value));
+ VERIFY((!contained_in_list<is_same, dummy_d, tl>::value));
+ VERIFY((!contained_in_list<is_same, dummy_e, tl>::value));
+
+ VERIFY((!!contained_in_list_gf<dummy_test, dummy_a, tl>::value));
+ VERIFY((!!contained_in_list_gf<dummy_test, dummy_b, tl>::value));
+ VERIFY((!!contained_in_list_gf<dummy_test, dummy_c, tl>::value));
+ VERIFY((!contained_in_list_gf<dummy_test, dummy_d, tl>::value));
+ VERIFY((!contained_in_list_gf<dummy_test, dummy_e, tl>::value));
+
+ VERIFY_IS_EQUAL(((int)contained_in_list_gf<dummy_test, dummy_a, tl>::global_flags), 1);
+ VERIFY_IS_EQUAL(((int)contained_in_list_gf<dummy_test, dummy_b, tl>::global_flags), 2);
+ VERIFY_IS_EQUAL(((int)contained_in_list_gf<dummy_test, dummy_c, tl>::global_flags), 4);
+ VERIFY_IS_EQUAL(((int)contained_in_list_gf<dummy_test, dummy_d, tl>::global_flags), 0);
+ VERIFY_IS_EQUAL(((int)contained_in_list_gf<dummy_test, dummy_e, tl>::global_flags), 0);
+}
+
+static void test_arg_reductions()
+{
+ VERIFY_IS_EQUAL(arg_sum(1,2,3,4), 10);
+ VERIFY_IS_EQUAL(arg_prod(1,2,3,4), 24);
+ VERIFY_IS_APPROX(arg_sum(0.5, 2, 5), 7.5);
+ VERIFY_IS_APPROX(arg_prod(0.5, 2, 5), 5.0);
+}
+
+static void test_array_reverse_and_reduce()
+{
+ array<int, 6> a{{4, 8, 15, 16, 23, 42}};
+ array<int, 6> b{{42, 23, 16, 15, 8, 4}};
+
+ // there is no operator<< for std::array, so VERIFY_IS_EQUAL will
+ // not compile
+ VERIFY((array_reverse(a) == b));
+ VERIFY((array_reverse(b) == a));
+ VERIFY_IS_EQUAL((array_sum(a)), 108);
+ VERIFY_IS_EQUAL((array_sum(b)), 108);
+ VERIFY_IS_EQUAL((array_prod(a)), 7418880);
+ VERIFY_IS_EQUAL((array_prod(b)), 7418880);
+}
+
+static void test_array_zip_and_apply()
+{
+ array<int, 6> a{{4, 8, 15, 16, 23, 42}};
+ array<int, 6> b{{0, 1, 2, 3, 4, 5}};
+ array<int, 6> c{{4, 9, 17, 19, 27, 47}};
+ array<int, 6> d{{0, 8, 30, 48, 92, 210}};
+ array<int, 6> e{{0, 2, 4, 6, 8, 10}};
+
+ VERIFY((array_zip<sum_op>(a, b) == c));
+ VERIFY((array_zip<product_op>(a, b) == d));
+ VERIFY((array_apply<times2_op>(b) == e));
+ VERIFY_IS_EQUAL((array_apply_and_reduce<sum_op, times2_op>(a)), 216);
+ VERIFY_IS_EQUAL((array_apply_and_reduce<sum_op, times2_op>(b)), 30);
+ VERIFY_IS_EQUAL((array_zip_and_reduce<product_op, sum_op>(a, b)), 14755932);
+ VERIFY_IS_EQUAL((array_zip_and_reduce<sum_op, product_op>(a, b)), 388);
+}
+
+static void test_array_misc()
+{
+ array<int, 3> a3{{1, 1, 1}};
+ array<int, 6> a6{{2, 2, 2, 2, 2, 2}};
+ VERIFY((repeat<3, int>(1) == a3));
+ VERIFY((repeat<6, int>(2) == a6));
+
+ int data[5] = { 0, 1, 2, 3, 4 };
+ VERIFY_IS_EQUAL((instantiate_by_c_array<dummy_inst, int, 0>(data).c), 0);
+ VERIFY_IS_EQUAL((instantiate_by_c_array<dummy_inst, int, 1>(data).c), 1);
+ VERIFY_IS_EQUAL((instantiate_by_c_array<dummy_inst, int, 2>(data).c), 2);
+ VERIFY_IS_EQUAL((instantiate_by_c_array<dummy_inst, int, 3>(data).c), 3);
+ VERIFY_IS_EQUAL((instantiate_by_c_array<dummy_inst, int, 4>(data).c), 4);
+ VERIFY_IS_EQUAL((instantiate_by_c_array<dummy_inst, int, 5>(data).c), 5);
+}
+
+EIGEN_DECLARE_TEST(cxx11_meta)
+{
+ CALL_SUBTEST(test_gen_numeric_list());
+ CALL_SUBTEST(test_concat());
+ CALL_SUBTEST(test_slice());
+ CALL_SUBTEST(test_get());
+ CALL_SUBTEST(test_id());
+ CALL_SUBTEST(test_is_same_gf());
+ CALL_SUBTEST(test_apply_op());
+ CALL_SUBTEST(test_contained_in_list());
+ CALL_SUBTEST(test_arg_reductions());
+ CALL_SUBTEST(test_array_reverse_and_reduce());
+ CALL_SUBTEST(test_array_zip_and_apply());
+ CALL_SUBTEST(test_array_misc());
+}
diff --git a/unsupported/test/cxx11_non_blocking_thread_pool.cpp b/unsupported/test/cxx11_non_blocking_thread_pool.cpp
new file mode 100644
index 0000000..993ee17
--- /dev/null
+++ b/unsupported/test/cxx11_non_blocking_thread_pool.cpp
@@ -0,0 +1,180 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2016 Dmitry Vyukov <dvyukov@google.com>
+// Copyright (C) 2016 Benoit Steiner <benoit.steiner.goog@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#define EIGEN_USE_THREADS
+#include "main.h"
+#include "Eigen/CXX11/ThreadPool"
+#include "Eigen/CXX11/Tensor"
+
+static void test_create_destroy_empty_pool()
+{
+ // Just create and destroy the pool. This will wind up and tear down worker
+ // threads. Ensure there are no issues in that logic.
+ for (int i = 0; i < 16; ++i) {
+ ThreadPool tp(i);
+ }
+}
+
+
+static void test_parallelism(bool allow_spinning)
+{
+ // Test we never-ever fail to match available tasks with idle threads.
+ const int kThreads = 16; // code below expects that this is a multiple of 4
+ ThreadPool tp(kThreads, allow_spinning);
+ VERIFY_IS_EQUAL(tp.NumThreads(), kThreads);
+ VERIFY_IS_EQUAL(tp.CurrentThreadId(), -1);
+ for (int iter = 0; iter < 100; ++iter) {
+ std::atomic<int> running(0);
+ std::atomic<int> done(0);
+ std::atomic<int> phase(0);
+ // Schedule kThreads tasks and ensure that they all are running.
+ for (int i = 0; i < kThreads; ++i) {
+ tp.Schedule([&]() {
+ const int thread_id = tp.CurrentThreadId();
+ VERIFY_GE(thread_id, 0);
+ VERIFY_LE(thread_id, kThreads - 1);
+ running++;
+ while (phase < 1) {
+ }
+ done++;
+ });
+ }
+ while (running != kThreads) {
+ }
+ running = 0;
+ phase = 1;
+ // Now, while the previous tasks exit, schedule another kThreads tasks and
+ // ensure that they are running.
+ for (int i = 0; i < kThreads; ++i) {
+ tp.Schedule([&, i]() {
+ running++;
+ while (phase < 2) {
+ }
+ // When all tasks are running, half of tasks exit, quarter of tasks
+ // continue running and quarter of tasks schedule another 2 tasks each.
+ // Concurrently main thread schedules another quarter of tasks.
+ // This gives us another kThreads tasks and we ensure that they all
+ // are running.
+ if (i < kThreads / 2) {
+ } else if (i < 3 * kThreads / 4) {
+ running++;
+ while (phase < 3) {
+ }
+ done++;
+ } else {
+ for (int j = 0; j < 2; ++j) {
+ tp.Schedule([&]() {
+ running++;
+ while (phase < 3) {
+ }
+ done++;
+ });
+ }
+ }
+ done++;
+ });
+ }
+ while (running != kThreads) {
+ }
+ running = 0;
+ phase = 2;
+ for (int i = 0; i < kThreads / 4; ++i) {
+ tp.Schedule([&]() {
+ running++;
+ while (phase < 3) {
+ }
+ done++;
+ });
+ }
+ while (running != kThreads) {
+ }
+ phase = 3;
+ while (done != 3 * kThreads) {
+ }
+ }
+}
+
+
+static void test_cancel()
+{
+ ThreadPool tp(2);
+
+ // Schedule a large number of closure that each sleeps for one second. This
+ // will keep the thread pool busy for much longer than the default test timeout.
+ for (int i = 0; i < 1000; ++i) {
+ tp.Schedule([]() {
+ std::this_thread::sleep_for(std::chrono::milliseconds(2000));
+ });
+ }
+
+ // Cancel the processing of all the closures that are still pending.
+ tp.Cancel();
+}
+
+static void test_pool_partitions() {
+ const int kThreads = 2;
+ ThreadPool tp(kThreads);
+
+ // Assign each thread to its own partition, so that stealing other work only
+ // occurs globally when a thread is idle.
+ std::vector<std::pair<unsigned, unsigned>> steal_partitions(kThreads);
+ for (int i = 0; i < kThreads; ++i) {
+ steal_partitions[i] = std::make_pair(i, i + 1);
+ }
+ tp.SetStealPartitions(steal_partitions);
+
+ std::atomic<int> running(0);
+ std::atomic<int> done(0);
+ std::atomic<int> phase(0);
+
+ // Schedule kThreads tasks and ensure that they all are running.
+ for (int i = 0; i < kThreads; ++i) {
+ tp.Schedule([&]() {
+ const int thread_id = tp.CurrentThreadId();
+ VERIFY_GE(thread_id, 0);
+ VERIFY_LE(thread_id, kThreads - 1);
+ ++running;
+ while (phase < 1) {
+ }
+ ++done;
+ });
+ }
+ while (running != kThreads) {
+ }
+ // Schedule each closure to only run on thread 'i' and verify that it does.
+ for (int i = 0; i < kThreads; ++i) {
+ tp.ScheduleWithHint(
+ [&, i]() {
+ ++running;
+ const int thread_id = tp.CurrentThreadId();
+ VERIFY_IS_EQUAL(thread_id, i);
+ while (phase < 2) {
+ }
+ ++done;
+ },
+ i, i + 1);
+ }
+ running = 0;
+ phase = 1;
+ while (running != kThreads) {
+ }
+ running = 0;
+ phase = 2;
+}
+
+
+EIGEN_DECLARE_TEST(cxx11_non_blocking_thread_pool)
+{
+ CALL_SUBTEST(test_create_destroy_empty_pool());
+ CALL_SUBTEST(test_parallelism(true));
+ CALL_SUBTEST(test_parallelism(false));
+ CALL_SUBTEST(test_cancel());
+ CALL_SUBTEST(test_pool_partitions());
+}
diff --git a/unsupported/test/cxx11_runqueue.cpp b/unsupported/test/cxx11_runqueue.cpp
new file mode 100644
index 0000000..8fc5a30
--- /dev/null
+++ b/unsupported/test/cxx11_runqueue.cpp
@@ -0,0 +1,235 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2016 Dmitry Vyukov <dvyukov@google.com>
+// Copyright (C) 2016 Benoit Steiner <benoit.steiner.goog@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#define EIGEN_USE_THREADS
+#include <cstdlib>
+#include "main.h"
+#include <Eigen/CXX11/ThreadPool>
+
+
+// Visual studio doesn't implement a rand_r() function since its
+// implementation of rand() is already thread safe
+int rand_reentrant(unsigned int* s) {
+#ifdef EIGEN_COMP_MSVC_STRICT
+ EIGEN_UNUSED_VARIABLE(s);
+ return rand();
+#else
+ return rand_r(s);
+#endif
+}
+
+void test_basic_runqueue()
+{
+ RunQueue<int, 4> q;
+ // Check empty state.
+ VERIFY(q.Empty());
+ VERIFY_IS_EQUAL(0u, q.Size());
+ VERIFY_IS_EQUAL(0, q.PopFront());
+ std::vector<int> stolen;
+ VERIFY_IS_EQUAL(0u, q.PopBackHalf(&stolen));
+ VERIFY_IS_EQUAL(0u, stolen.size());
+ // Push one front, pop one front.
+ VERIFY_IS_EQUAL(0, q.PushFront(1));
+ VERIFY_IS_EQUAL(1u, q.Size());
+ VERIFY_IS_EQUAL(1, q.PopFront());
+ VERIFY_IS_EQUAL(0u, q.Size());
+ // Push front to overflow.
+ VERIFY_IS_EQUAL(0, q.PushFront(2));
+ VERIFY_IS_EQUAL(1u, q.Size());
+ VERIFY_IS_EQUAL(0, q.PushFront(3));
+ VERIFY_IS_EQUAL(2u, q.Size());
+ VERIFY_IS_EQUAL(0, q.PushFront(4));
+ VERIFY_IS_EQUAL(3u, q.Size());
+ VERIFY_IS_EQUAL(0, q.PushFront(5));
+ VERIFY_IS_EQUAL(4u, q.Size());
+ VERIFY_IS_EQUAL(6, q.PushFront(6));
+ VERIFY_IS_EQUAL(4u, q.Size());
+ VERIFY_IS_EQUAL(5, q.PopFront());
+ VERIFY_IS_EQUAL(3u, q.Size());
+ VERIFY_IS_EQUAL(4, q.PopFront());
+ VERIFY_IS_EQUAL(2u, q.Size());
+ VERIFY_IS_EQUAL(3, q.PopFront());
+ VERIFY_IS_EQUAL(1u, q.Size());
+ VERIFY_IS_EQUAL(2, q.PopFront());
+ VERIFY_IS_EQUAL(0u, q.Size());
+ VERIFY_IS_EQUAL(0, q.PopFront());
+ // Push one back, pop one back.
+ VERIFY_IS_EQUAL(0, q.PushBack(7));
+ VERIFY_IS_EQUAL(1u, q.Size());
+ VERIFY_IS_EQUAL(1u, q.PopBackHalf(&stolen));
+ VERIFY_IS_EQUAL(1u, stolen.size());
+ VERIFY_IS_EQUAL(7, stolen[0]);
+ VERIFY_IS_EQUAL(0u, q.Size());
+ stolen.clear();
+ // Push back to overflow.
+ VERIFY_IS_EQUAL(0, q.PushBack(8));
+ VERIFY_IS_EQUAL(1u, q.Size());
+ VERIFY_IS_EQUAL(0, q.PushBack(9));
+ VERIFY_IS_EQUAL(2u, q.Size());
+ VERIFY_IS_EQUAL(0, q.PushBack(10));
+ VERIFY_IS_EQUAL(3u, q.Size());
+ VERIFY_IS_EQUAL(0, q.PushBack(11));
+ VERIFY_IS_EQUAL(4u, q.Size());
+ VERIFY_IS_EQUAL(12, q.PushBack(12));
+ VERIFY_IS_EQUAL(4u, q.Size());
+ // Pop back in halves.
+ VERIFY_IS_EQUAL(2u, q.PopBackHalf(&stolen));
+ VERIFY_IS_EQUAL(2u, stolen.size());
+ VERIFY_IS_EQUAL(10, stolen[0]);
+ VERIFY_IS_EQUAL(11, stolen[1]);
+ VERIFY_IS_EQUAL(2u, q.Size());
+ stolen.clear();
+ VERIFY_IS_EQUAL(1u, q.PopBackHalf(&stolen));
+ VERIFY_IS_EQUAL(1u, stolen.size());
+ VERIFY_IS_EQUAL(9, stolen[0]);
+ VERIFY_IS_EQUAL(1u, q.Size());
+ stolen.clear();
+ VERIFY_IS_EQUAL(1u, q.PopBackHalf(&stolen));
+ VERIFY_IS_EQUAL(1u, stolen.size());
+ VERIFY_IS_EQUAL(8, stolen[0]);
+ stolen.clear();
+ VERIFY_IS_EQUAL(0u, q.PopBackHalf(&stolen));
+ VERIFY_IS_EQUAL(0u, stolen.size());
+ // Empty again.
+ VERIFY(q.Empty());
+ VERIFY_IS_EQUAL(0u, q.Size());
+ VERIFY_IS_EQUAL(0, q.PushFront(1));
+ VERIFY_IS_EQUAL(0, q.PushFront(2));
+ VERIFY_IS_EQUAL(0, q.PushFront(3));
+ VERIFY_IS_EQUAL(1, q.PopBack());
+ VERIFY_IS_EQUAL(2, q.PopBack());
+ VERIFY_IS_EQUAL(3, q.PopBack());
+ VERIFY(q.Empty());
+ VERIFY_IS_EQUAL(0u, q.Size());
+}
+
+// Empty tests that the queue is not claimed to be empty when is is in fact not.
+// Emptiness property is crucial part of thread pool blocking scheme,
+// so we go to great effort to ensure this property. We create a queue with
+// 1 element and then push 1 element (either front or back at random) and pop
+// 1 element (either front or back at random). So queue always contains at least
+// 1 element, but otherwise changes chaotically. Another thread constantly tests
+// that the queue is not claimed to be empty.
+void test_empty_runqueue()
+{
+ RunQueue<int, 4> q;
+ q.PushFront(1);
+ std::atomic<bool> done(false);
+ std::thread mutator([&q, &done]() {
+ unsigned rnd = 0;
+ std::vector<int> stolen;
+ for (int i = 0; i < 1 << 18; i++) {
+ if (rand_reentrant(&rnd) % 2)
+ VERIFY_IS_EQUAL(0, q.PushFront(1));
+ else
+ VERIFY_IS_EQUAL(0, q.PushBack(1));
+ if (rand_reentrant(&rnd) % 2)
+ VERIFY_IS_EQUAL(1, q.PopFront());
+ else {
+ for (;;) {
+ if (q.PopBackHalf(&stolen) == 1) {
+ stolen.clear();
+ break;
+ }
+ VERIFY_IS_EQUAL(0u, stolen.size());
+ }
+ }
+ }
+ done = true;
+ });
+ while (!done) {
+ VERIFY(!q.Empty());
+ int size = q.Size();
+ VERIFY_GE(size, 1);
+ VERIFY_LE(size, 2);
+ }
+ VERIFY_IS_EQUAL(1, q.PopFront());
+ mutator.join();
+}
+
+// Stress is a chaotic random test.
+// One thread (owner) calls PushFront/PopFront, other threads call PushBack/
+// PopBack. Ensure that we don't crash, deadlock, and all sanity checks pass.
+void test_stress_runqueue()
+{
+ static const int kEvents = 1 << 18;
+ RunQueue<int, 8> q;
+ std::atomic<int> total(0);
+ std::vector<std::unique_ptr<std::thread>> threads;
+ threads.emplace_back(new std::thread([&q, &total]() {
+ int sum = 0;
+ int pushed = 1;
+ int popped = 1;
+ while (pushed < kEvents || popped < kEvents) {
+ if (pushed < kEvents) {
+ if (q.PushFront(pushed) == 0) {
+ sum += pushed;
+ pushed++;
+ }
+ }
+ if (popped < kEvents) {
+ int v = q.PopFront();
+ if (v != 0) {
+ sum -= v;
+ popped++;
+ }
+ }
+ }
+ total += sum;
+ }));
+ for (int i = 0; i < 2; i++) {
+ threads.emplace_back(new std::thread([&q, &total]() {
+ int sum = 0;
+ for (int j = 1; j < kEvents; j++) {
+ if (q.PushBack(j) == 0) {
+ sum += j;
+ continue;
+ }
+ EIGEN_THREAD_YIELD();
+ j--;
+ }
+ total += sum;
+ }));
+ threads.emplace_back(new std::thread([&q, &total]() {
+ int sum = 0;
+ std::vector<int> stolen;
+ for (int j = 1; j < kEvents;) {
+ if (q.PopBackHalf(&stolen) == 0) {
+ EIGEN_THREAD_YIELD();
+ continue;
+ }
+ while (stolen.size() && j < kEvents) {
+ int v = stolen.back();
+ stolen.pop_back();
+ VERIFY_IS_NOT_EQUAL(v, 0);
+ sum += v;
+ j++;
+ }
+ }
+ while (stolen.size()) {
+ int v = stolen.back();
+ stolen.pop_back();
+ VERIFY_IS_NOT_EQUAL(v, 0);
+ while ((v = q.PushBack(v)) != 0) EIGEN_THREAD_YIELD();
+ }
+ total -= sum;
+ }));
+ }
+ for (size_t i = 0; i < threads.size(); i++) threads[i]->join();
+ VERIFY(q.Empty());
+ VERIFY(total.load() == 0);
+}
+
+EIGEN_DECLARE_TEST(cxx11_runqueue)
+{
+ CALL_SUBTEST_1(test_basic_runqueue());
+ CALL_SUBTEST_2(test_empty_runqueue());
+ CALL_SUBTEST_3(test_stress_runqueue());
+}
diff --git a/unsupported/test/cxx11_tensor_argmax.cpp b/unsupported/test/cxx11_tensor_argmax.cpp
new file mode 100644
index 0000000..8be622b
--- /dev/null
+++ b/unsupported/test/cxx11_tensor_argmax.cpp
@@ -0,0 +1,294 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2015 Eugene Brevdo <ebrevdo@google.com>
+// Benoit Steiner <benoit.steiner.goog@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "main.h"
+
+#include <Eigen/CXX11/Tensor>
+
+using Eigen::Tensor;
+using Eigen::array;
+using Eigen::Pair;
+
+template <int DataLayout>
+static void test_simple_index_pairs()
+{
+ Tensor<float, 4, DataLayout> tensor(2,3,5,7);
+ tensor.setRandom();
+ tensor = (tensor + tensor.constant(0.5)).log();
+
+ Tensor<Pair<DenseIndex, float>, 4, DataLayout> index_pairs(2,3,5,7);
+ index_pairs = tensor.index_pairs();
+
+ for (DenseIndex n = 0; n < 2*3*5*7; ++n) {
+ const Pair<DenseIndex, float>& v = index_pairs.coeff(n);
+ VERIFY_IS_EQUAL(v.first, n);
+ VERIFY_IS_EQUAL(v.second, tensor.coeff(n));
+ }
+}
+
+template <int DataLayout>
+static void test_index_pairs_dim()
+{
+ Tensor<float, 4, DataLayout> tensor(2,3,5,7);
+ tensor.setRandom();
+ tensor = (tensor + tensor.constant(0.5)).log();
+
+ Tensor<Pair<DenseIndex, float>, 4, DataLayout> index_pairs(2,3,5,7);
+
+ index_pairs = tensor.index_pairs();
+
+ for (Eigen::DenseIndex n = 0; n < tensor.size(); ++n) {
+ const Pair<DenseIndex, float>& v = index_pairs(n); //(i, j, k, l);
+ VERIFY_IS_EQUAL(v.first, n);
+ VERIFY_IS_EQUAL(v.second, tensor(n));
+ }
+}
+
+template <int DataLayout>
+static void test_argmax_pair_reducer()
+{
+ Tensor<float, 4, DataLayout> tensor(2,3,5,7);
+ tensor.setRandom();
+ tensor = (tensor + tensor.constant(0.5)).log();
+
+ Tensor<Pair<DenseIndex, float>, 4, DataLayout> index_pairs(2,3,5,7);
+ index_pairs = tensor.index_pairs();
+
+ Tensor<Pair<DenseIndex, float>, 0, DataLayout> reduced;
+ DimensionList<DenseIndex, 4> dims;
+ reduced = index_pairs.reduce(
+ dims, internal::ArgMaxPairReducer<Pair<DenseIndex, float> >());
+
+ Tensor<float, 0, DataLayout> maxi = tensor.maximum();
+
+ VERIFY_IS_EQUAL(maxi(), reduced(0).second);
+
+ array<DenseIndex, 3> reduce_dims;
+ for (int d = 0; d < 3; ++d) reduce_dims[d] = d;
+ Tensor<Pair<DenseIndex, float>, 1, DataLayout> reduced_by_dims(7);
+ reduced_by_dims = index_pairs.reduce(
+ reduce_dims, internal::ArgMaxPairReducer<Pair<DenseIndex, float> >());
+
+ Tensor<float, 1, DataLayout> max_by_dims = tensor.maximum(reduce_dims);
+
+ for (int l = 0; l < 7; ++l) {
+ VERIFY_IS_EQUAL(max_by_dims(l), reduced_by_dims(l).second);
+ }
+}
+
+template <int DataLayout>
+static void test_argmin_pair_reducer()
+{
+ Tensor<float, 4, DataLayout> tensor(2,3,5,7);
+ tensor.setRandom();
+ tensor = (tensor + tensor.constant(0.5)).log();
+
+ Tensor<Pair<DenseIndex, float>, 4, DataLayout> index_pairs(2,3,5,7);
+ index_pairs = tensor.index_pairs();
+
+ Tensor<Pair<DenseIndex, float>, 0, DataLayout> reduced;
+ DimensionList<DenseIndex, 4> dims;
+ reduced = index_pairs.reduce(
+ dims, internal::ArgMinPairReducer<Pair<DenseIndex, float> >());
+
+ Tensor<float, 0, DataLayout> mini = tensor.minimum();
+
+ VERIFY_IS_EQUAL(mini(), reduced(0).second);
+
+ array<DenseIndex, 3> reduce_dims;
+ for (int d = 0; d < 3; ++d) reduce_dims[d] = d;
+ Tensor<Pair<DenseIndex, float>, 1, DataLayout> reduced_by_dims(7);
+ reduced_by_dims = index_pairs.reduce(
+ reduce_dims, internal::ArgMinPairReducer<Pair<DenseIndex, float> >());
+
+ Tensor<float, 1, DataLayout> min_by_dims = tensor.minimum(reduce_dims);
+
+ for (int l = 0; l < 7; ++l) {
+ VERIFY_IS_EQUAL(min_by_dims(l), reduced_by_dims(l).second);
+ }
+}
+
+template <int DataLayout>
+static void test_simple_argmax()
+{
+ Tensor<float, 4, DataLayout> tensor(2,3,5,7);
+ tensor.setRandom();
+ tensor = (tensor + tensor.constant(0.5)).log();
+ tensor(0,0,0,0) = 10.0;
+
+ Tensor<DenseIndex, 0, DataLayout> tensor_argmax;
+
+ tensor_argmax = tensor.argmax();
+
+ VERIFY_IS_EQUAL(tensor_argmax(0), 0);
+
+ tensor(1,2,4,6) = 20.0;
+
+ tensor_argmax = tensor.argmax();
+
+ VERIFY_IS_EQUAL(tensor_argmax(0), 2*3*5*7 - 1);
+}
+
+template <int DataLayout>
+static void test_simple_argmin()
+{
+ Tensor<float, 4, DataLayout> tensor(2,3,5,7);
+ tensor.setRandom();
+ tensor = (tensor + tensor.constant(0.5)).log();
+ tensor(0,0,0,0) = -10.0;
+
+ Tensor<DenseIndex, 0, DataLayout> tensor_argmin;
+
+ tensor_argmin = tensor.argmin();
+
+ VERIFY_IS_EQUAL(tensor_argmin(0), 0);
+
+ tensor(1,2,4,6) = -20.0;
+
+ tensor_argmin = tensor.argmin();
+
+ VERIFY_IS_EQUAL(tensor_argmin(0), 2*3*5*7 - 1);
+}
+
+template <int DataLayout>
+static void test_argmax_dim()
+{
+ Tensor<float, 4, DataLayout> tensor(2,3,5,7);
+ std::vector<int> dims {2, 3, 5, 7};
+
+ for (int dim = 0; dim < 4; ++dim) {
+ tensor.setRandom();
+ tensor = (tensor + tensor.constant(0.5)).log();
+
+ Tensor<DenseIndex, 3, DataLayout> tensor_argmax;
+ array<DenseIndex, 4> ix;
+ for (int i = 0; i < 2; ++i) {
+ for (int j = 0; j < 3; ++j) {
+ for (int k = 0; k < 5; ++k) {
+ for (int l = 0; l < 7; ++l) {
+ ix[0] = i; ix[1] = j; ix[2] = k; ix[3] = l;
+ if (ix[dim] != 0) continue;
+ // suppose dim == 1, then for all i, k, l, set tensor(i, 0, k, l) = 10.0
+ tensor(ix) = 10.0;
+ }
+ }
+ }
+ }
+
+ tensor_argmax = tensor.argmax(dim);
+
+ VERIFY_IS_EQUAL(tensor_argmax.size(),
+ ptrdiff_t(2*3*5*7 / tensor.dimension(dim)));
+ for (ptrdiff_t n = 0; n < tensor_argmax.size(); ++n) {
+ // Expect max to be in the first index of the reduced dimension
+ VERIFY_IS_EQUAL(tensor_argmax.data()[n], 0);
+ }
+
+ for (int i = 0; i < 2; ++i) {
+ for (int j = 0; j < 3; ++j) {
+ for (int k = 0; k < 5; ++k) {
+ for (int l = 0; l < 7; ++l) {
+ ix[0] = i; ix[1] = j; ix[2] = k; ix[3] = l;
+ if (ix[dim] != tensor.dimension(dim) - 1) continue;
+ // suppose dim == 1, then for all i, k, l, set tensor(i, 2, k, l) = 20.0
+ tensor(ix) = 20.0;
+ }
+ }
+ }
+ }
+
+ tensor_argmax = tensor.argmax(dim);
+
+ VERIFY_IS_EQUAL(tensor_argmax.size(),
+ ptrdiff_t(2*3*5*7 / tensor.dimension(dim)));
+ for (ptrdiff_t n = 0; n < tensor_argmax.size(); ++n) {
+ // Expect max to be in the last index of the reduced dimension
+ VERIFY_IS_EQUAL(tensor_argmax.data()[n], tensor.dimension(dim) - 1);
+ }
+ }
+}
+
+template <int DataLayout>
+static void test_argmin_dim()
+{
+ Tensor<float, 4, DataLayout> tensor(2,3,5,7);
+ std::vector<int> dims {2, 3, 5, 7};
+
+ for (int dim = 0; dim < 4; ++dim) {
+ tensor.setRandom();
+ tensor = (tensor + tensor.constant(0.5)).log();
+
+ Tensor<DenseIndex, 3, DataLayout> tensor_argmin;
+ array<DenseIndex, 4> ix;
+ for (int i = 0; i < 2; ++i) {
+ for (int j = 0; j < 3; ++j) {
+ for (int k = 0; k < 5; ++k) {
+ for (int l = 0; l < 7; ++l) {
+ ix[0] = i; ix[1] = j; ix[2] = k; ix[3] = l;
+ if (ix[dim] != 0) continue;
+ // suppose dim == 1, then for all i, k, l, set tensor(i, 0, k, l) = -10.0
+ tensor(ix) = -10.0;
+ }
+ }
+ }
+ }
+
+ tensor_argmin = tensor.argmin(dim);
+
+ VERIFY_IS_EQUAL(tensor_argmin.size(),
+ ptrdiff_t(2*3*5*7 / tensor.dimension(dim)));
+ for (ptrdiff_t n = 0; n < tensor_argmin.size(); ++n) {
+ // Expect min to be in the first index of the reduced dimension
+ VERIFY_IS_EQUAL(tensor_argmin.data()[n], 0);
+ }
+
+ for (int i = 0; i < 2; ++i) {
+ for (int j = 0; j < 3; ++j) {
+ for (int k = 0; k < 5; ++k) {
+ for (int l = 0; l < 7; ++l) {
+ ix[0] = i; ix[1] = j; ix[2] = k; ix[3] = l;
+ if (ix[dim] != tensor.dimension(dim) - 1) continue;
+ // suppose dim == 1, then for all i, k, l, set tensor(i, 2, k, l) = -20.0
+ tensor(ix) = -20.0;
+ }
+ }
+ }
+ }
+
+ tensor_argmin = tensor.argmin(dim);
+
+ VERIFY_IS_EQUAL(tensor_argmin.size(),
+ ptrdiff_t(2*3*5*7 / tensor.dimension(dim)));
+ for (ptrdiff_t n = 0; n < tensor_argmin.size(); ++n) {
+ // Expect min to be in the last index of the reduced dimension
+ VERIFY_IS_EQUAL(tensor_argmin.data()[n], tensor.dimension(dim) - 1);
+ }
+ }
+}
+
+EIGEN_DECLARE_TEST(cxx11_tensor_argmax)
+{
+ CALL_SUBTEST(test_simple_index_pairs<RowMajor>());
+ CALL_SUBTEST(test_simple_index_pairs<ColMajor>());
+ CALL_SUBTEST(test_index_pairs_dim<RowMajor>());
+ CALL_SUBTEST(test_index_pairs_dim<ColMajor>());
+ CALL_SUBTEST(test_argmax_pair_reducer<RowMajor>());
+ CALL_SUBTEST(test_argmax_pair_reducer<ColMajor>());
+ CALL_SUBTEST(test_argmin_pair_reducer<RowMajor>());
+ CALL_SUBTEST(test_argmin_pair_reducer<ColMajor>());
+ CALL_SUBTEST(test_simple_argmax<RowMajor>());
+ CALL_SUBTEST(test_simple_argmax<ColMajor>());
+ CALL_SUBTEST(test_simple_argmin<RowMajor>());
+ CALL_SUBTEST(test_simple_argmin<ColMajor>());
+ CALL_SUBTEST(test_argmax_dim<RowMajor>());
+ CALL_SUBTEST(test_argmax_dim<ColMajor>());
+ CALL_SUBTEST(test_argmin_dim<RowMajor>());
+ CALL_SUBTEST(test_argmin_dim<ColMajor>());
+}
diff --git a/unsupported/test/cxx11_tensor_argmax_gpu.cu b/unsupported/test/cxx11_tensor_argmax_gpu.cu
new file mode 100644
index 0000000..79f4066
--- /dev/null
+++ b/unsupported/test/cxx11_tensor_argmax_gpu.cu
@@ -0,0 +1,253 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+
+#define EIGEN_TEST_NO_LONGDOUBLE
+
+#define EIGEN_USE_GPU
+
+#include "main.h"
+#include <unsupported/Eigen/CXX11/Tensor>
+
+#include <unsupported/Eigen/CXX11/src/Tensor/TensorGpuHipCudaDefines.h>
+
+using Eigen::Tensor;
+
+template <int Layout>
+void test_gpu_simple_argmax()
+{
+ Tensor<double, 3, Layout> in(Eigen::array<DenseIndex, 3>(72,53,97));
+ Tensor<DenseIndex, 1, Layout> out_max(Eigen::array<DenseIndex, 1>(1));
+ Tensor<DenseIndex, 1, Layout> out_min(Eigen::array<DenseIndex, 1>(1));
+ in.setRandom();
+ in *= in.constant(100.0);
+ in(0, 0, 0) = -1000.0;
+ in(71, 52, 96) = 1000.0;
+
+ std::size_t in_bytes = in.size() * sizeof(double);
+ std::size_t out_bytes = out_max.size() * sizeof(DenseIndex);
+
+ double* d_in;
+ DenseIndex* d_out_max;
+ DenseIndex* d_out_min;
+ gpuMalloc((void**)(&d_in), in_bytes);
+ gpuMalloc((void**)(&d_out_max), out_bytes);
+ gpuMalloc((void**)(&d_out_min), out_bytes);
+
+ gpuMemcpy(d_in, in.data(), in_bytes, gpuMemcpyHostToDevice);
+
+ Eigen::GpuStreamDevice stream;
+ Eigen::GpuDevice gpu_device(&stream);
+
+ Eigen::TensorMap<Eigen::Tensor<double, 3, Layout>, Aligned > gpu_in(d_in, Eigen::array<DenseIndex, 3>(72,53,97));
+ Eigen::TensorMap<Eigen::Tensor<DenseIndex, 1, Layout>, Aligned > gpu_out_max(d_out_max, Eigen::array<DenseIndex, 1>(1));
+ Eigen::TensorMap<Eigen::Tensor<DenseIndex, 1, Layout>, Aligned > gpu_out_min(d_out_min, Eigen::array<DenseIndex, 1>(1));
+
+ gpu_out_max.device(gpu_device) = gpu_in.argmax();
+ gpu_out_min.device(gpu_device) = gpu_in.argmin();
+
+ assert(gpuMemcpyAsync(out_max.data(), d_out_max, out_bytes, gpuMemcpyDeviceToHost, gpu_device.stream()) == gpuSuccess);
+ assert(gpuMemcpyAsync(out_min.data(), d_out_min, out_bytes, gpuMemcpyDeviceToHost, gpu_device.stream()) == gpuSuccess);
+ assert(gpuStreamSynchronize(gpu_device.stream()) == gpuSuccess);
+
+ VERIFY_IS_EQUAL(out_max(Eigen::array<DenseIndex, 1>(0)), 72*53*97 - 1);
+ VERIFY_IS_EQUAL(out_min(Eigen::array<DenseIndex, 1>(0)), 0);
+
+ gpuFree(d_in);
+ gpuFree(d_out_max);
+ gpuFree(d_out_min);
+}
+
+template <int DataLayout>
+void test_gpu_argmax_dim()
+{
+ Tensor<float, 4, DataLayout> tensor(2,3,5,7);
+ std::vector<int> dims;
+ dims.push_back(2); dims.push_back(3); dims.push_back(5); dims.push_back(7);
+
+ for (int dim = 0; dim < 4; ++dim) {
+ tensor.setRandom();
+ tensor = (tensor + tensor.constant(0.5)).log();
+
+ array<DenseIndex, 3> out_shape;
+ for (int d = 0; d < 3; ++d) out_shape[d] = (d < dim) ? dims[d] : dims[d+1];
+
+ Tensor<DenseIndex, 3, DataLayout> tensor_arg(out_shape);
+
+ array<DenseIndex, 4> ix;
+ for (int i = 0; i < 2; ++i) {
+ for (int j = 0; j < 3; ++j) {
+ for (int k = 0; k < 5; ++k) {
+ for (int l = 0; l < 7; ++l) {
+ ix[0] = i; ix[1] = j; ix[2] = k; ix[3] = l;
+ if (ix[dim] != 0) continue;
+ // suppose dim == 1, then for all i, k, l, set tensor(i, 0, k, l) = 10.0
+ tensor(ix) = 10.0;
+ }
+ }
+ }
+ }
+
+ std::size_t in_bytes = tensor.size() * sizeof(float);
+ std::size_t out_bytes = tensor_arg.size() * sizeof(DenseIndex);
+
+ float* d_in;
+ DenseIndex* d_out;
+ gpuMalloc((void**)(&d_in), in_bytes);
+ gpuMalloc((void**)(&d_out), out_bytes);
+
+ gpuMemcpy(d_in, tensor.data(), in_bytes, gpuMemcpyHostToDevice);
+
+ Eigen::GpuStreamDevice stream;
+ Eigen::GpuDevice gpu_device(&stream);
+
+ Eigen::TensorMap<Eigen::Tensor<float, 4, DataLayout>, Aligned > gpu_in(d_in, Eigen::array<DenseIndex, 4>(2, 3, 5, 7));
+ Eigen::TensorMap<Eigen::Tensor<DenseIndex, 3, DataLayout>, Aligned > gpu_out(d_out, out_shape);
+
+ gpu_out.device(gpu_device) = gpu_in.argmax(dim);
+
+ assert(gpuMemcpyAsync(tensor_arg.data(), d_out, out_bytes, gpuMemcpyDeviceToHost, gpu_device.stream()) == gpuSuccess);
+ assert(gpuStreamSynchronize(gpu_device.stream()) == gpuSuccess);
+
+ VERIFY_IS_EQUAL(tensor_arg.size(),
+ size_t(2*3*5*7 / tensor.dimension(dim)));
+
+ for (DenseIndex n = 0; n < tensor_arg.size(); ++n) {
+ // Expect max to be in the first index of the reduced dimension
+ VERIFY_IS_EQUAL(tensor_arg.data()[n], 0);
+ }
+
+ for (int i = 0; i < 2; ++i) {
+ for (int j = 0; j < 3; ++j) {
+ for (int k = 0; k < 5; ++k) {
+ for (int l = 0; l < 7; ++l) {
+ ix[0] = i; ix[1] = j; ix[2] = k; ix[3] = l;
+ if (ix[dim] != tensor.dimension(dim) - 1) continue;
+ // suppose dim == 1, then for all i, k, l, set tensor(i, 2, k, l) = 20.0
+ tensor(ix) = 20.0;
+ }
+ }
+ }
+ }
+
+ gpuMemcpy(d_in, tensor.data(), in_bytes, gpuMemcpyHostToDevice);
+
+ gpu_out.device(gpu_device) = gpu_in.argmax(dim);
+
+ assert(gpuMemcpyAsync(tensor_arg.data(), d_out, out_bytes, gpuMemcpyDeviceToHost, gpu_device.stream()) == gpuSuccess);
+ assert(gpuStreamSynchronize(gpu_device.stream()) == gpuSuccess);
+
+ for (DenseIndex n = 0; n < tensor_arg.size(); ++n) {
+ // Expect max to be in the last index of the reduced dimension
+ VERIFY_IS_EQUAL(tensor_arg.data()[n], tensor.dimension(dim) - 1);
+ }
+
+ gpuFree(d_in);
+ gpuFree(d_out);
+ }
+}
+
+template <int DataLayout>
+void test_gpu_argmin_dim()
+{
+ Tensor<float, 4, DataLayout> tensor(2,3,5,7);
+ std::vector<int> dims;
+ dims.push_back(2); dims.push_back(3); dims.push_back(5); dims.push_back(7);
+
+ for (int dim = 0; dim < 4; ++dim) {
+ tensor.setRandom();
+ tensor = (tensor + tensor.constant(0.5)).log();
+
+ array<DenseIndex, 3> out_shape;
+ for (int d = 0; d < 3; ++d) out_shape[d] = (d < dim) ? dims[d] : dims[d+1];
+
+ Tensor<DenseIndex, 3, DataLayout> tensor_arg(out_shape);
+
+ array<DenseIndex, 4> ix;
+ for (int i = 0; i < 2; ++i) {
+ for (int j = 0; j < 3; ++j) {
+ for (int k = 0; k < 5; ++k) {
+ for (int l = 0; l < 7; ++l) {
+ ix[0] = i; ix[1] = j; ix[2] = k; ix[3] = l;
+ if (ix[dim] != 0) continue;
+ // suppose dim == 1, then for all i, k, l, set tensor(i, 0, k, l) = 10.0
+ tensor(ix) = -10.0;
+ }
+ }
+ }
+ }
+
+ std::size_t in_bytes = tensor.size() * sizeof(float);
+ std::size_t out_bytes = tensor_arg.size() * sizeof(DenseIndex);
+
+ float* d_in;
+ DenseIndex* d_out;
+ gpuMalloc((void**)(&d_in), in_bytes);
+ gpuMalloc((void**)(&d_out), out_bytes);
+
+ gpuMemcpy(d_in, tensor.data(), in_bytes, gpuMemcpyHostToDevice);
+
+ Eigen::GpuStreamDevice stream;
+ Eigen::GpuDevice gpu_device(&stream);
+
+ Eigen::TensorMap<Eigen::Tensor<float, 4, DataLayout>, Aligned > gpu_in(d_in, Eigen::array<DenseIndex, 4>(2, 3, 5, 7));
+ Eigen::TensorMap<Eigen::Tensor<DenseIndex, 3, DataLayout>, Aligned > gpu_out(d_out, out_shape);
+
+ gpu_out.device(gpu_device) = gpu_in.argmin(dim);
+
+ assert(gpuMemcpyAsync(tensor_arg.data(), d_out, out_bytes, gpuMemcpyDeviceToHost, gpu_device.stream()) == gpuSuccess);
+ assert(gpuStreamSynchronize(gpu_device.stream()) == gpuSuccess);
+
+ VERIFY_IS_EQUAL(tensor_arg.size(),
+ 2*3*5*7 / tensor.dimension(dim));
+
+ for (DenseIndex n = 0; n < tensor_arg.size(); ++n) {
+ // Expect min to be in the first index of the reduced dimension
+ VERIFY_IS_EQUAL(tensor_arg.data()[n], 0);
+ }
+
+ for (int i = 0; i < 2; ++i) {
+ for (int j = 0; j < 3; ++j) {
+ for (int k = 0; k < 5; ++k) {
+ for (int l = 0; l < 7; ++l) {
+ ix[0] = i; ix[1] = j; ix[2] = k; ix[3] = l;
+ if (ix[dim] != tensor.dimension(dim) - 1) continue;
+ // suppose dim == 1, then for all i, k, l, set tensor(i, 2, k, l) = 20.0
+ tensor(ix) = -20.0;
+ }
+ }
+ }
+ }
+
+ gpuMemcpy(d_in, tensor.data(), in_bytes, gpuMemcpyHostToDevice);
+
+ gpu_out.device(gpu_device) = gpu_in.argmin(dim);
+
+ assert(gpuMemcpyAsync(tensor_arg.data(), d_out, out_bytes, gpuMemcpyDeviceToHost, gpu_device.stream()) == gpuSuccess);
+ assert(gpuStreamSynchronize(gpu_device.stream()) == gpuSuccess);
+
+ for (DenseIndex n = 0; n < tensor_arg.size(); ++n) {
+ // Expect max to be in the last index of the reduced dimension
+ VERIFY_IS_EQUAL(tensor_arg.data()[n], tensor.dimension(dim) - 1);
+ }
+
+ gpuFree(d_in);
+ gpuFree(d_out);
+ }
+}
+
+EIGEN_DECLARE_TEST(cxx11_tensor_argmax_gpu)
+{
+ CALL_SUBTEST_1(test_gpu_simple_argmax<RowMajor>());
+ CALL_SUBTEST_1(test_gpu_simple_argmax<ColMajor>());
+ CALL_SUBTEST_2(test_gpu_argmax_dim<RowMajor>());
+ CALL_SUBTEST_2(test_gpu_argmax_dim<ColMajor>());
+ CALL_SUBTEST_3(test_gpu_argmin_dim<RowMajor>());
+ CALL_SUBTEST_3(test_gpu_argmin_dim<ColMajor>());
+}
diff --git a/unsupported/test/cxx11_tensor_argmax_sycl.cpp b/unsupported/test/cxx11_tensor_argmax_sycl.cpp
new file mode 100644
index 0000000..41ea3cf
--- /dev/null
+++ b/unsupported/test/cxx11_tensor_argmax_sycl.cpp
@@ -0,0 +1,257 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2016
+// Mehdi Goli Codeplay Software Ltd.
+// Ralph Potter Codeplay Software Ltd.
+// Luke Iwanski Codeplay Software Ltd.
+// Contact: <eigen@codeplay.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#define EIGEN_TEST_NO_LONGDOUBLE
+#define EIGEN_TEST_NO_COMPLEX
+
+#define EIGEN_DEFAULT_DENSE_INDEX_TYPE int64_t
+#define EIGEN_USE_SYCL
+
+#include "main.h"
+
+#include <unsupported/Eigen/CXX11/Tensor>
+
+using Eigen::array;
+using Eigen::SyclDevice;
+using Eigen::Tensor;
+using Eigen::TensorMap;
+
+template <typename DataType, int Layout, typename DenseIndex>
+static void test_sycl_simple_argmax(const Eigen::SyclDevice& sycl_device) {
+ Tensor<DataType, 3, Layout, DenseIndex> in(Eigen::array<DenseIndex, 3>{{2, 2, 2}});
+ Tensor<DenseIndex, 0, Layout, DenseIndex> out_max;
+ Tensor<DenseIndex, 0, Layout, DenseIndex> out_min;
+ in.setRandom();
+ in *= in.constant(100.0);
+ in(0, 0, 0) = -1000.0;
+ in(1, 1, 1) = 1000.0;
+
+ std::size_t in_bytes = in.size() * sizeof(DataType);
+ std::size_t out_bytes = out_max.size() * sizeof(DenseIndex);
+
+ DataType* d_in = static_cast<DataType*>(sycl_device.allocate(in_bytes));
+ DenseIndex* d_out_max = static_cast<DenseIndex*>(sycl_device.allocate(out_bytes));
+ DenseIndex* d_out_min = static_cast<DenseIndex*>(sycl_device.allocate(out_bytes));
+
+ Eigen::TensorMap<Eigen::Tensor<DataType, 3, Layout, DenseIndex> > gpu_in(d_in,
+ Eigen::array<DenseIndex, 3>{{2, 2, 2}});
+ Eigen::TensorMap<Eigen::Tensor<DenseIndex, 0, Layout, DenseIndex> > gpu_out_max(d_out_max);
+ Eigen::TensorMap<Eigen::Tensor<DenseIndex, 0, Layout, DenseIndex> > gpu_out_min(d_out_min);
+ sycl_device.memcpyHostToDevice(d_in, in.data(), in_bytes);
+
+ gpu_out_max.device(sycl_device) = gpu_in.argmax();
+ gpu_out_min.device(sycl_device) = gpu_in.argmin();
+
+ sycl_device.memcpyDeviceToHost(out_max.data(), d_out_max, out_bytes);
+ sycl_device.memcpyDeviceToHost(out_min.data(), d_out_min, out_bytes);
+
+ VERIFY_IS_EQUAL(out_max(), 2 * 2 * 2 - 1);
+ VERIFY_IS_EQUAL(out_min(), 0);
+
+ sycl_device.deallocate(d_in);
+ sycl_device.deallocate(d_out_max);
+ sycl_device.deallocate(d_out_min);
+}
+
+template <typename DataType, int DataLayout, typename DenseIndex>
+static void test_sycl_argmax_dim(const Eigen::SyclDevice& sycl_device) {
+ DenseIndex sizeDim0 = 9;
+ DenseIndex sizeDim1 = 3;
+ DenseIndex sizeDim2 = 5;
+ DenseIndex sizeDim3 = 7;
+ Tensor<DataType, 4, DataLayout, DenseIndex> tensor(sizeDim0, sizeDim1, sizeDim2, sizeDim3);
+
+ std::vector<DenseIndex> dims;
+ dims.push_back(sizeDim0);
+ dims.push_back(sizeDim1);
+ dims.push_back(sizeDim2);
+ dims.push_back(sizeDim3);
+ for (DenseIndex dim = 0; dim < 4; ++dim) {
+ array<DenseIndex, 3> out_shape;
+ for (DenseIndex d = 0; d < 3; ++d) out_shape[d] = (d < dim) ? dims[d] : dims[d + 1];
+
+ Tensor<DenseIndex, 3, DataLayout, DenseIndex> tensor_arg(out_shape);
+
+ array<DenseIndex, 4> ix;
+ for (DenseIndex i = 0; i < sizeDim0; ++i) {
+ for (DenseIndex j = 0; j < sizeDim1; ++j) {
+ for (DenseIndex k = 0; k < sizeDim2; ++k) {
+ for (DenseIndex l = 0; l < sizeDim3; ++l) {
+ ix[0] = i;
+ ix[1] = j;
+ ix[2] = k;
+ ix[3] = l;
+ // suppose dim == 1, then for all i, k, l, set tensor(i, 0, k, l)
+ // = 10.0
+ tensor(ix) = (ix[dim] != 0) ? -1.0 : 10.0;
+ }
+ }
+ }
+ }
+
+ std::size_t in_bytes = tensor.size() * sizeof(DataType);
+ std::size_t out_bytes = tensor_arg.size() * sizeof(DenseIndex);
+
+ DataType* d_in = static_cast<DataType*>(sycl_device.allocate(in_bytes));
+ DenseIndex* d_out = static_cast<DenseIndex*>(sycl_device.allocate(out_bytes));
+
+ Eigen::TensorMap<Eigen::Tensor<DataType, 4, DataLayout, DenseIndex> > gpu_in(
+ d_in, Eigen::array<DenseIndex, 4>{{sizeDim0, sizeDim1, sizeDim2, sizeDim3}});
+ Eigen::TensorMap<Eigen::Tensor<DenseIndex, 3, DataLayout, DenseIndex> > gpu_out(d_out, out_shape);
+
+ sycl_device.memcpyHostToDevice(d_in, tensor.data(), in_bytes);
+ gpu_out.device(sycl_device) = gpu_in.argmax(dim);
+ sycl_device.memcpyDeviceToHost(tensor_arg.data(), d_out, out_bytes);
+
+ VERIFY_IS_EQUAL(static_cast<size_t>(tensor_arg.size()),
+ size_t(sizeDim0 * sizeDim1 * sizeDim2 * sizeDim3 / tensor.dimension(dim)));
+
+ for (DenseIndex n = 0; n < tensor_arg.size(); ++n) {
+ // Expect max to be in the first index of the reduced dimension
+ VERIFY_IS_EQUAL(tensor_arg.data()[n], 0);
+ }
+
+ sycl_device.synchronize();
+
+ for (DenseIndex i = 0; i < sizeDim0; ++i) {
+ for (DenseIndex j = 0; j < sizeDim1; ++j) {
+ for (DenseIndex k = 0; k < sizeDim2; ++k) {
+ for (DenseIndex l = 0; l < sizeDim3; ++l) {
+ ix[0] = i;
+ ix[1] = j;
+ ix[2] = k;
+ ix[3] = l;
+ // suppose dim == 1, then for all i, k, l, set tensor(i, 2, k, l) = 20.0
+ tensor(ix) = (ix[dim] != tensor.dimension(dim) - 1) ? -1.0 : 20.0;
+ }
+ }
+ }
+ }
+
+ sycl_device.memcpyHostToDevice(d_in, tensor.data(), in_bytes);
+ gpu_out.device(sycl_device) = gpu_in.argmax(dim);
+ sycl_device.memcpyDeviceToHost(tensor_arg.data(), d_out, out_bytes);
+
+ for (DenseIndex n = 0; n < tensor_arg.size(); ++n) {
+ // Expect max to be in the last index of the reduced dimension
+ VERIFY_IS_EQUAL(tensor_arg.data()[n], tensor.dimension(dim) - 1);
+ }
+ sycl_device.deallocate(d_in);
+ sycl_device.deallocate(d_out);
+ }
+}
+
+template <typename DataType, int DataLayout, typename DenseIndex>
+static void test_sycl_argmin_dim(const Eigen::SyclDevice& sycl_device) {
+ DenseIndex sizeDim0 = 9;
+ DenseIndex sizeDim1 = 3;
+ DenseIndex sizeDim2 = 5;
+ DenseIndex sizeDim3 = 7;
+ Tensor<DataType, 4, DataLayout, DenseIndex> tensor(sizeDim0, sizeDim1, sizeDim2, sizeDim3);
+
+ std::vector<DenseIndex> dims;
+ dims.push_back(sizeDim0);
+ dims.push_back(sizeDim1);
+ dims.push_back(sizeDim2);
+ dims.push_back(sizeDim3);
+ for (DenseIndex dim = 0; dim < 4; ++dim) {
+ array<DenseIndex, 3> out_shape;
+ for (DenseIndex d = 0; d < 3; ++d) out_shape[d] = (d < dim) ? dims[d] : dims[d + 1];
+
+ Tensor<DenseIndex, 3, DataLayout, DenseIndex> tensor_arg(out_shape);
+
+ array<DenseIndex, 4> ix;
+ for (DenseIndex i = 0; i < sizeDim0; ++i) {
+ for (DenseIndex j = 0; j < sizeDim1; ++j) {
+ for (DenseIndex k = 0; k < sizeDim2; ++k) {
+ for (DenseIndex l = 0; l < sizeDim3; ++l) {
+ ix[0] = i;
+ ix[1] = j;
+ ix[2] = k;
+ ix[3] = l;
+ // suppose dim == 1, then for all i, k, l, set tensor(i, 0, k, l) = -10.0
+ tensor(ix) = (ix[dim] != 0) ? 1.0 : -10.0;
+ }
+ }
+ }
+ }
+
+ std::size_t in_bytes = tensor.size() * sizeof(DataType);
+ std::size_t out_bytes = tensor_arg.size() * sizeof(DenseIndex);
+
+ DataType* d_in = static_cast<DataType*>(sycl_device.allocate(in_bytes));
+ DenseIndex* d_out = static_cast<DenseIndex*>(sycl_device.allocate(out_bytes));
+
+ Eigen::TensorMap<Eigen::Tensor<DataType, 4, DataLayout, DenseIndex> > gpu_in(
+ d_in, Eigen::array<DenseIndex, 4>{{sizeDim0, sizeDim1, sizeDim2, sizeDim3}});
+ Eigen::TensorMap<Eigen::Tensor<DenseIndex, 3, DataLayout, DenseIndex> > gpu_out(d_out, out_shape);
+
+ sycl_device.memcpyHostToDevice(d_in, tensor.data(), in_bytes);
+ gpu_out.device(sycl_device) = gpu_in.argmin(dim);
+ sycl_device.memcpyDeviceToHost(tensor_arg.data(), d_out, out_bytes);
+
+ VERIFY_IS_EQUAL(static_cast<size_t>(tensor_arg.size()),
+ size_t(sizeDim0 * sizeDim1 * sizeDim2 * sizeDim3 / tensor.dimension(dim)));
+
+ for (DenseIndex n = 0; n < tensor_arg.size(); ++n) {
+ // Expect max to be in the first index of the reduced dimension
+ VERIFY_IS_EQUAL(tensor_arg.data()[n], 0);
+ }
+
+ sycl_device.synchronize();
+
+ for (DenseIndex i = 0; i < sizeDim0; ++i) {
+ for (DenseIndex j = 0; j < sizeDim1; ++j) {
+ for (DenseIndex k = 0; k < sizeDim2; ++k) {
+ for (DenseIndex l = 0; l < sizeDim3; ++l) {
+ ix[0] = i;
+ ix[1] = j;
+ ix[2] = k;
+ ix[3] = l;
+ // suppose dim == 1, then for all i, k, l, set tensor(i, 2, k, l) = -20.0
+ tensor(ix) = (ix[dim] != tensor.dimension(dim) - 1) ? 1.0 : -20.0;
+ }
+ }
+ }
+ }
+
+ sycl_device.memcpyHostToDevice(d_in, tensor.data(), in_bytes);
+ gpu_out.device(sycl_device) = gpu_in.argmin(dim);
+ sycl_device.memcpyDeviceToHost(tensor_arg.data(), d_out, out_bytes);
+
+ for (DenseIndex n = 0; n < tensor_arg.size(); ++n) {
+ // Expect max to be in the last index of the reduced dimension
+ VERIFY_IS_EQUAL(tensor_arg.data()[n], tensor.dimension(dim) - 1);
+ }
+ sycl_device.deallocate(d_in);
+ sycl_device.deallocate(d_out);
+ }
+}
+
+template <typename DataType, typename Device_Selector>
+void sycl_argmax_test_per_device(const Device_Selector& d) {
+ QueueInterface queueInterface(d);
+ auto sycl_device = Eigen::SyclDevice(&queueInterface);
+ test_sycl_simple_argmax<DataType, RowMajor, int64_t>(sycl_device);
+ test_sycl_simple_argmax<DataType, ColMajor, int64_t>(sycl_device);
+ test_sycl_argmax_dim<DataType, ColMajor, int64_t>(sycl_device);
+ test_sycl_argmax_dim<DataType, RowMajor, int64_t>(sycl_device);
+ test_sycl_argmin_dim<DataType, ColMajor, int64_t>(sycl_device);
+ test_sycl_argmin_dim<DataType, RowMajor, int64_t>(sycl_device);
+}
+
+EIGEN_DECLARE_TEST(cxx11_tensor_argmax_sycl) {
+ for (const auto& device : Eigen::get_sycl_supported_devices()) {
+ CALL_SUBTEST(sycl_argmax_test_per_device<float>(device));
+ }
+}
diff --git a/unsupported/test/cxx11_tensor_assign.cpp b/unsupported/test/cxx11_tensor_assign.cpp
new file mode 100644
index 0000000..015865e
--- /dev/null
+++ b/unsupported/test/cxx11_tensor_assign.cpp
@@ -0,0 +1,362 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "main.h"
+
+#include <Eigen/CXX11/Tensor>
+
+using Eigen::Tensor;
+using Eigen::RowMajor;
+
+static void test_1d()
+{
+ Tensor<int, 1> vec1(6);
+ Tensor<int, 1, RowMajor> vec2(6);
+ vec1(0) = 4; vec2(0) = 0;
+ vec1(1) = 8; vec2(1) = 1;
+ vec1(2) = 15; vec2(2) = 2;
+ vec1(3) = 16; vec2(3) = 3;
+ vec1(4) = 23; vec2(4) = 4;
+ vec1(5) = 42; vec2(5) = 5;
+
+ int col_major[6] = {0};
+ int row_major[6] = {0};
+ TensorMap<Tensor<int, 1> > vec3(col_major, 6);
+ TensorMap<Tensor<int, 1, RowMajor> > vec4(row_major, 6);
+
+ vec3 = vec1;
+ vec4 = vec2;
+
+ VERIFY_IS_EQUAL(vec3(0), 4);
+ VERIFY_IS_EQUAL(vec3(1), 8);
+ VERIFY_IS_EQUAL(vec3(2), 15);
+ VERIFY_IS_EQUAL(vec3(3), 16);
+ VERIFY_IS_EQUAL(vec3(4), 23);
+ VERIFY_IS_EQUAL(vec3(5), 42);
+
+ VERIFY_IS_EQUAL(vec4(0), 0);
+ VERIFY_IS_EQUAL(vec4(1), 1);
+ VERIFY_IS_EQUAL(vec4(2), 2);
+ VERIFY_IS_EQUAL(vec4(3), 3);
+ VERIFY_IS_EQUAL(vec4(4), 4);
+ VERIFY_IS_EQUAL(vec4(5), 5);
+
+ vec1.setZero();
+ vec2.setZero();
+ vec1 = vec3;
+ vec2 = vec4;
+
+ VERIFY_IS_EQUAL(vec1(0), 4);
+ VERIFY_IS_EQUAL(vec1(1), 8);
+ VERIFY_IS_EQUAL(vec1(2), 15);
+ VERIFY_IS_EQUAL(vec1(3), 16);
+ VERIFY_IS_EQUAL(vec1(4), 23);
+ VERIFY_IS_EQUAL(vec1(5), 42);
+
+ VERIFY_IS_EQUAL(vec2(0), 0);
+ VERIFY_IS_EQUAL(vec2(1), 1);
+ VERIFY_IS_EQUAL(vec2(2), 2);
+ VERIFY_IS_EQUAL(vec2(3), 3);
+ VERIFY_IS_EQUAL(vec2(4), 4);
+ VERIFY_IS_EQUAL(vec2(5), 5);
+}
+
+static void test_2d()
+{
+ Tensor<int, 2> mat1(2,3);
+ Tensor<int, 2, RowMajor> mat2(2,3);
+
+ mat1(0,0) = 0;
+ mat1(0,1) = 1;
+ mat1(0,2) = 2;
+ mat1(1,0) = 3;
+ mat1(1,1) = 4;
+ mat1(1,2) = 5;
+
+ mat2(0,0) = 0;
+ mat2(0,1) = 1;
+ mat2(0,2) = 2;
+ mat2(1,0) = 3;
+ mat2(1,1) = 4;
+ mat2(1,2) = 5;
+
+ int col_major[6] = {0};
+ int row_major[6] = {0};
+ TensorMap<Tensor<int, 2> > mat3(row_major, 2, 3);
+ TensorMap<Tensor<int, 2, RowMajor> > mat4(col_major, 2, 3);
+
+ mat3 = mat1;
+ mat4 = mat2;
+
+ VERIFY_IS_EQUAL(mat3(0,0), 0);
+ VERIFY_IS_EQUAL(mat3(0,1), 1);
+ VERIFY_IS_EQUAL(mat3(0,2), 2);
+ VERIFY_IS_EQUAL(mat3(1,0), 3);
+ VERIFY_IS_EQUAL(mat3(1,1), 4);
+ VERIFY_IS_EQUAL(mat3(1,2), 5);
+
+ VERIFY_IS_EQUAL(mat4(0,0), 0);
+ VERIFY_IS_EQUAL(mat4(0,1), 1);
+ VERIFY_IS_EQUAL(mat4(0,2), 2);
+ VERIFY_IS_EQUAL(mat4(1,0), 3);
+ VERIFY_IS_EQUAL(mat4(1,1), 4);
+ VERIFY_IS_EQUAL(mat4(1,2), 5);
+
+ mat1.setZero();
+ mat2.setZero();
+ mat1 = mat3;
+ mat2 = mat4;
+
+ VERIFY_IS_EQUAL(mat1(0,0), 0);
+ VERIFY_IS_EQUAL(mat1(0,1), 1);
+ VERIFY_IS_EQUAL(mat1(0,2), 2);
+ VERIFY_IS_EQUAL(mat1(1,0), 3);
+ VERIFY_IS_EQUAL(mat1(1,1), 4);
+ VERIFY_IS_EQUAL(mat1(1,2), 5);
+
+ VERIFY_IS_EQUAL(mat2(0,0), 0);
+ VERIFY_IS_EQUAL(mat2(0,1), 1);
+ VERIFY_IS_EQUAL(mat2(0,2), 2);
+ VERIFY_IS_EQUAL(mat2(1,0), 3);
+ VERIFY_IS_EQUAL(mat2(1,1), 4);
+ VERIFY_IS_EQUAL(mat2(1,2), 5);
+}
+
+static void test_3d()
+{
+ Tensor<int, 3> mat1(2,3,7);
+ Tensor<int, 3, RowMajor> mat2(2,3,7);
+
+ int val = 0;
+ for (int i = 0; i < 2; ++i) {
+ for (int j = 0; j < 3; ++j) {
+ for (int k = 0; k < 7; ++k) {
+ mat1(i,j,k) = val;
+ mat2(i,j,k) = val;
+ val++;
+ }
+ }
+ }
+
+ int col_major[2*3*7] = {0};
+ int row_major[2*3*7] = {0};
+ TensorMap<Tensor<int, 3> > mat3(col_major, 2, 3, 7);
+ TensorMap<Tensor<int, 3, RowMajor> > mat4(row_major, 2, 3, 7);
+
+ mat3 = mat1;
+ mat4 = mat2;
+
+ val = 0;
+ for (int i = 0; i < 2; ++i) {
+ for (int j = 0; j < 3; ++j) {
+ for (int k = 0; k < 7; ++k) {
+ VERIFY_IS_EQUAL(mat3(i,j,k), val);
+ VERIFY_IS_EQUAL(mat4(i,j,k), val);
+ val++;
+ }
+ }
+ }
+
+ mat1.setZero();
+ mat2.setZero();
+ mat1 = mat3;
+ mat2 = mat4;
+
+ val = 0;
+ for (int i = 0; i < 2; ++i) {
+ for (int j = 0; j < 3; ++j) {
+ for (int k = 0; k < 7; ++k) {
+ VERIFY_IS_EQUAL(mat1(i,j,k), val);
+ VERIFY_IS_EQUAL(mat2(i,j,k), val);
+ val++;
+ }
+ }
+ }
+}
+
+static void test_same_type()
+{
+ Tensor<int, 1> orig_tensor(5);
+ Tensor<int, 1> dest_tensor(5);
+ orig_tensor.setRandom();
+ dest_tensor.setRandom();
+ int* orig_data = orig_tensor.data();
+ int* dest_data = dest_tensor.data();
+ dest_tensor = orig_tensor;
+ VERIFY_IS_EQUAL(orig_tensor.data(), orig_data);
+ VERIFY_IS_EQUAL(dest_tensor.data(), dest_data);
+ for (int i = 0; i < 5; ++i) {
+ VERIFY_IS_EQUAL(dest_tensor(i), orig_tensor(i));
+ }
+
+ TensorFixedSize<int, Sizes<5> > orig_array;
+ TensorFixedSize<int, Sizes<5> > dest_array;
+ orig_array.setRandom();
+ dest_array.setRandom();
+ orig_data = orig_array.data();
+ dest_data = dest_array.data();
+ dest_array = orig_array;
+ VERIFY_IS_EQUAL(orig_array.data(), orig_data);
+ VERIFY_IS_EQUAL(dest_array.data(), dest_data);
+ for (int i = 0; i < 5; ++i) {
+ VERIFY_IS_EQUAL(dest_array(i), orig_array(i));
+ }
+
+ int orig[5] = {1, 2, 3, 4, 5};
+ int dest[5] = {6, 7, 8, 9, 10};
+ TensorMap<Tensor<int, 1> > orig_map(orig, 5);
+ TensorMap<Tensor<int, 1> > dest_map(dest, 5);
+ orig_data = orig_map.data();
+ dest_data = dest_map.data();
+ dest_map = orig_map;
+ VERIFY_IS_EQUAL(orig_map.data(), orig_data);
+ VERIFY_IS_EQUAL(dest_map.data(), dest_data);
+ for (int i = 0; i < 5; ++i) {
+ VERIFY_IS_EQUAL(dest[i], i+1);
+ }
+}
+
+static void test_auto_resize()
+{
+ Tensor<int, 1> tensor1;
+ Tensor<int, 1> tensor2(3);
+ Tensor<int, 1> tensor3(5);
+ Tensor<int, 1> tensor4(7);
+
+ Tensor<int, 1> new_tensor(5);
+ new_tensor.setRandom();
+
+ tensor1 = tensor2 = tensor3 = tensor4 = new_tensor;
+
+ VERIFY_IS_EQUAL(tensor1.dimension(0), new_tensor.dimension(0));
+ VERIFY_IS_EQUAL(tensor2.dimension(0), new_tensor.dimension(0));
+ VERIFY_IS_EQUAL(tensor3.dimension(0), new_tensor.dimension(0));
+ VERIFY_IS_EQUAL(tensor4.dimension(0), new_tensor.dimension(0));
+ for (int i = 0; i < new_tensor.dimension(0); ++i) {
+ VERIFY_IS_EQUAL(tensor1(i), new_tensor(i));
+ VERIFY_IS_EQUAL(tensor2(i), new_tensor(i));
+ VERIFY_IS_EQUAL(tensor3(i), new_tensor(i));
+ VERIFY_IS_EQUAL(tensor4(i), new_tensor(i));
+ }
+}
+
+
+static void test_compound_assign()
+{
+ Tensor<int, 1> start_tensor(10);
+ Tensor<int, 1> offset_tensor(10);
+ start_tensor.setRandom();
+ offset_tensor.setRandom();
+
+ Tensor<int, 1> tensor = start_tensor;
+ tensor += offset_tensor;
+ for (int i = 0; i < 10; ++i) {
+ VERIFY_IS_EQUAL(tensor(i), start_tensor(i) + offset_tensor(i));
+ }
+
+ tensor = start_tensor;
+ tensor -= offset_tensor;
+ for (int i = 0; i < 10; ++i) {
+ VERIFY_IS_EQUAL(tensor(i), start_tensor(i) - offset_tensor(i));
+ }
+
+ tensor = start_tensor;
+ tensor *= offset_tensor;
+ for (int i = 0; i < 10; ++i) {
+ VERIFY_IS_EQUAL(tensor(i), start_tensor(i) * offset_tensor(i));
+ }
+
+ tensor = start_tensor;
+ tensor /= offset_tensor;
+ for (int i = 0; i < 10; ++i) {
+ VERIFY_IS_EQUAL(tensor(i), start_tensor(i) / offset_tensor(i));
+ }
+}
+
+static void test_std_initializers_tensor() {
+ Tensor<int, 1> a(3);
+ a.setValues({0, 1, 2});
+ VERIFY_IS_EQUAL(a(0), 0);
+ VERIFY_IS_EQUAL(a(1), 1);
+ VERIFY_IS_EQUAL(a(2), 2);
+
+ // It fills the top-left slice.
+ a.setValues({10, 20});
+ VERIFY_IS_EQUAL(a(0), 10);
+ VERIFY_IS_EQUAL(a(1), 20);
+ VERIFY_IS_EQUAL(a(2), 2);
+
+ // Chaining.
+ Tensor<int, 1> a2(3);
+ a2 = a.setValues({100, 200, 300});
+ VERIFY_IS_EQUAL(a(0), 100);
+ VERIFY_IS_EQUAL(a(1), 200);
+ VERIFY_IS_EQUAL(a(2), 300);
+ VERIFY_IS_EQUAL(a2(0), 100);
+ VERIFY_IS_EQUAL(a2(1), 200);
+ VERIFY_IS_EQUAL(a2(2), 300);
+
+ Tensor<int, 2> b(2, 3);
+ b.setValues({{0, 1, 2}, {3, 4, 5}});
+ VERIFY_IS_EQUAL(b(0, 0), 0);
+ VERIFY_IS_EQUAL(b(0, 1), 1);
+ VERIFY_IS_EQUAL(b(0, 2), 2);
+ VERIFY_IS_EQUAL(b(1, 0), 3);
+ VERIFY_IS_EQUAL(b(1, 1), 4);
+ VERIFY_IS_EQUAL(b(1, 2), 5);
+
+ // It fills the top-left slice.
+ b.setValues({{10, 20}, {30}});
+ VERIFY_IS_EQUAL(b(0, 0), 10);
+ VERIFY_IS_EQUAL(b(0, 1), 20);
+ VERIFY_IS_EQUAL(b(0, 2), 2);
+ VERIFY_IS_EQUAL(b(1, 0), 30);
+ VERIFY_IS_EQUAL(b(1, 1), 4);
+ VERIFY_IS_EQUAL(b(1, 2), 5);
+
+ Eigen::Tensor<int, 3> c(3, 2, 4);
+ c.setValues({{{0, 1, 2, 3}, {4, 5, 6, 7}},
+ {{10, 11, 12, 13}, {14, 15, 16, 17}},
+ {{20, 21, 22, 23}, {24, 25, 26, 27}}});
+ VERIFY_IS_EQUAL(c(0, 0, 0), 0);
+ VERIFY_IS_EQUAL(c(0, 0, 1), 1);
+ VERIFY_IS_EQUAL(c(0, 0, 2), 2);
+ VERIFY_IS_EQUAL(c(0, 0, 3), 3);
+ VERIFY_IS_EQUAL(c(0, 1, 0), 4);
+ VERIFY_IS_EQUAL(c(0, 1, 1), 5);
+ VERIFY_IS_EQUAL(c(0, 1, 2), 6);
+ VERIFY_IS_EQUAL(c(0, 1, 3), 7);
+ VERIFY_IS_EQUAL(c(1, 0, 0), 10);
+ VERIFY_IS_EQUAL(c(1, 0, 1), 11);
+ VERIFY_IS_EQUAL(c(1, 0, 2), 12);
+ VERIFY_IS_EQUAL(c(1, 0, 3), 13);
+ VERIFY_IS_EQUAL(c(1, 1, 0), 14);
+ VERIFY_IS_EQUAL(c(1, 1, 1), 15);
+ VERIFY_IS_EQUAL(c(1, 1, 2), 16);
+ VERIFY_IS_EQUAL(c(1, 1, 3), 17);
+ VERIFY_IS_EQUAL(c(2, 0, 0), 20);
+ VERIFY_IS_EQUAL(c(2, 0, 1), 21);
+ VERIFY_IS_EQUAL(c(2, 0, 2), 22);
+ VERIFY_IS_EQUAL(c(2, 0, 3), 23);
+ VERIFY_IS_EQUAL(c(2, 1, 0), 24);
+ VERIFY_IS_EQUAL(c(2, 1, 1), 25);
+ VERIFY_IS_EQUAL(c(2, 1, 2), 26);
+ VERIFY_IS_EQUAL(c(2, 1, 3), 27);
+}
+
+EIGEN_DECLARE_TEST(cxx11_tensor_assign)
+{
+ CALL_SUBTEST(test_1d());
+ CALL_SUBTEST(test_2d());
+ CALL_SUBTEST(test_3d());
+ CALL_SUBTEST(test_same_type());
+ CALL_SUBTEST(test_auto_resize());
+ CALL_SUBTEST(test_compound_assign());
+ CALL_SUBTEST(test_std_initializers_tensor());
+}
diff --git a/unsupported/test/cxx11_tensor_block_access.cpp b/unsupported/test/cxx11_tensor_block_access.cpp
new file mode 100644
index 0000000..5fb12e0
--- /dev/null
+++ b/unsupported/test/cxx11_tensor_block_access.cpp
@@ -0,0 +1,576 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2018 Andy Davis <andydavis@google.com>
+// Copyright (C) 2018 Eugene Zhulenev <ezhulenev@google.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "main.h"
+
+#include <algorithm>
+#include <set>
+
+#include <Eigen/CXX11/Tensor>
+
+using Eigen::Tensor;
+using Eigen::Index;
+using Eigen::RowMajor;
+using Eigen::ColMajor;
+using Eigen::internal::TensorBlockShapeType;
+
+static TensorOpCost zeroCost() { return {0, 0, 0}; }
+
+template<typename T>
+static const T& choose(int layout, const T& col, const T& row) {
+ return layout == ColMajor ? col : row;
+}
+
+static TensorBlockShapeType RandomShape() {
+ return internal::random<bool>()
+ ? TensorBlockShapeType::kUniformAllDims
+ : TensorBlockShapeType::kSkewedInnerDims;
+}
+
+template <int NumDims>
+static size_t RandomTargetSize(const DSizes<Index, NumDims>& dims) {
+ return internal::random<size_t>(1, dims.TotalSize());
+}
+
+template <int NumDims>
+static DSizes<Index, NumDims> RandomDims() {
+ array<Index, NumDims> dims;
+ for (int i = 0; i < NumDims; ++i) {
+ dims[i] = internal::random<int>(1, 20);
+ }
+ return DSizes<Index, NumDims>(dims);
+}
+
+template <typename T>
+static T* GenerateRandomData(const Index& size) {
+ T* data = new T[size];
+ for (int i = 0; i < size; ++i) {
+ data[i] = internal::random<T>();
+ }
+ return data;
+}
+
+template <int NumDims>
+static void Debug(DSizes<Index, NumDims> dims) {
+ for (int i = 0; i < NumDims; ++i) {
+ std::cout << dims[i] << "; ";
+ }
+ std::cout << std::endl;
+}
+
+template <int Layout>
+static void test_block_mapper_sanity()
+{
+ typedef internal::TensorBlockMapper<2, Layout> TensorBlockMapper;
+
+ DSizes<Index, 2> tensor_dims(100, 100);
+
+ // Test uniform blocks.
+ TensorBlockMapper uniform_block_mapper(
+ tensor_dims, {TensorBlockShapeType::kUniformAllDims, 100, zeroCost()});
+
+ VERIFY_IS_EQUAL(uniform_block_mapper.blockCount(), 100);
+ VERIFY_IS_EQUAL(uniform_block_mapper.blockTotalSize(), 100);
+
+ // 10x10 blocks
+ auto uniform_b0 = uniform_block_mapper.blockDescriptor(0);
+ VERIFY_IS_EQUAL(uniform_b0.dimensions().at(0), 10);
+ VERIFY_IS_EQUAL(uniform_b0.dimensions().at(1), 10);
+
+ // Test skewed to inner dims blocks.
+ TensorBlockMapper skewed_block_mapper(
+ tensor_dims, {TensorBlockShapeType::kSkewedInnerDims, 100, zeroCost()});
+
+ VERIFY_IS_EQUAL(skewed_block_mapper.blockCount(), 100);
+ VERIFY_IS_EQUAL(skewed_block_mapper.blockTotalSize(), 100);
+
+ // 1x100 (100x1) rows/cols depending on a tensor layout.
+ auto skewed_b0 = skewed_block_mapper.blockDescriptor(0);
+ VERIFY_IS_EQUAL(skewed_b0.dimensions().at(0), choose(Layout, 100, 1));
+ VERIFY_IS_EQUAL(skewed_b0.dimensions().at(1), choose(Layout, 1, 100));
+}
+
+// Given a TensorBlock "visit" every element accessible though it, and a keep an
+// index in the visited set. Verify that every coeff accessed only once.
+template<int NumDims, int Layout>
+static void UpdateCoeffSet(
+ const DSizes<Index, NumDims>& tensor_strides,
+ const internal::TensorBlockDescriptor<NumDims>& block,
+ Index first_coeff_index, int dim_index, std::set<Index>* visited_coeffs) {
+ const DSizes<Index, NumDims>& block_sizes = block.dimensions();
+
+ for (int i = 0; i < block_sizes[dim_index]; ++i) {
+ if (tensor_strides[dim_index] == 1) {
+ typedef std::pair<std::set<Index>::iterator, bool> ReturnType;
+ ReturnType inserted = visited_coeffs->insert(first_coeff_index + i);
+ VERIFY_IS_EQUAL(inserted.second, true);
+ } else {
+ int next_dim_index = dim_index + choose(Layout, -1, 1);
+ UpdateCoeffSet<NumDims, Layout>(tensor_strides, block, first_coeff_index,
+ next_dim_index, visited_coeffs);
+ first_coeff_index += tensor_strides[dim_index];
+ }
+ }
+}
+
+template <typename T, int NumDims, int Layout>
+static void test_block_mapper_maps_every_element() {
+ typedef internal::TensorBlockMapper<NumDims, Layout> TensorBlockMapper;
+
+ DSizes<Index, NumDims> dims = RandomDims<NumDims>();
+ DSizes<Index, NumDims> strides = internal::strides<Layout>(dims);
+
+ // Keep track of elements indices available via block access.
+ std::set<Index> coeff_set;
+
+ // Try different combinations of block types and sizes.
+ TensorBlockMapper block_mapper(
+ dims, {RandomShape(), RandomTargetSize(dims), zeroCost()});
+
+ for (int i = 0; i < block_mapper.blockCount(); ++i) {
+ auto block = block_mapper.blockDescriptor(i);
+ UpdateCoeffSet<NumDims, Layout>(strides, block, block.offset(),
+ choose(Layout, NumDims - 1, 0),
+ &coeff_set);
+ }
+
+ // Verify that every coefficient in the original Tensor is accessible through
+ // TensorBlock only once.
+ Index total_coeffs = dims.TotalSize();
+ VERIFY_IS_EQUAL(Index(coeff_set.size()), total_coeffs);
+ VERIFY_IS_EQUAL(*coeff_set.begin(), 0);
+ VERIFY_IS_EQUAL(*coeff_set.rbegin(), total_coeffs - 1);
+}
+
+template <int Layout, int NumDims>
+static Index GetInputIndex(Index output_index,
+ const array<Index, NumDims>& output_to_input_dim_map,
+ const array<Index, NumDims>& input_strides,
+ const array<Index, NumDims>& output_strides) {
+ int input_index = 0;
+ if (Layout == ColMajor) {
+ for (int i = NumDims - 1; i > 0; --i) {
+ const Index idx = output_index / output_strides[i];
+ input_index += idx * input_strides[output_to_input_dim_map[i]];
+ output_index -= idx * output_strides[i];
+ }
+ return input_index +
+ output_index * input_strides[output_to_input_dim_map[0]];
+ } else {
+ for (int i = 0; i < NumDims - 1; ++i) {
+ const Index idx = output_index / output_strides[i];
+ input_index += idx * input_strides[output_to_input_dim_map[i]];
+ output_index -= idx * output_strides[i];
+ }
+ return input_index +
+ output_index * input_strides[output_to_input_dim_map[NumDims - 1]];
+ }
+}
+
+template <int Layout, int NumDims>
+static array<Index, NumDims> ComputeStrides(
+ const array<Index, NumDims>& sizes) {
+ array<Index, NumDims> strides;
+ if (Layout == ColMajor) {
+ strides[0] = 1;
+ for (int i = 1; i < NumDims; ++i) {
+ strides[i] = strides[i - 1] * sizes[i - 1];
+ }
+ } else {
+ strides[NumDims - 1] = 1;
+ for (int i = NumDims - 2; i >= 0; --i) {
+ strides[i] = strides[i + 1] * sizes[i + 1];
+ }
+ }
+ return strides;
+}
+
+template<typename Scalar, typename StorageIndex, int Dim>
+class EqualityChecker
+{
+ const Scalar* input_data;
+ const DSizes<StorageIndex, Dim> &input_dims, &input_strides, &output_dims, &output_strides;
+ void check_recursive(const Scalar* input, const Scalar* output, int depth=0) const
+ {
+ if(depth==Dim)
+ {
+ VERIFY_IS_EQUAL(*input, *output);
+ return;
+ }
+
+ for(int i=0; i<output_dims[depth]; ++i)
+ {
+ check_recursive(input + i % input_dims[depth] * input_strides[depth], output + i*output_strides[depth], depth+1);
+ }
+ }
+public:
+ EqualityChecker(const Scalar* input_data_,
+ const DSizes<StorageIndex, Dim> &input_dims_, const DSizes<StorageIndex, Dim> &input_strides_,
+ const DSizes<StorageIndex, Dim> &output_dims_, const DSizes<StorageIndex, Dim> &output_strides_)
+ : input_data(input_data_)
+ , input_dims(input_dims_), input_strides(input_strides_)
+ , output_dims(output_dims_), output_strides(output_strides_)
+ {}
+
+ void operator()(const Scalar* output_data) const
+ {
+ check_recursive(input_data, output_data);
+ }
+};
+
+template <int Layout>
+static void test_uniform_block_shape()
+{
+ typedef internal::TensorBlockDescriptor<5> TensorBlock;
+ typedef internal::TensorBlockMapper<5, Layout> TensorBlockMapper;
+
+ {
+ // Test shape 'UniformAllDims' with uniform 'max_coeff count'.
+ DSizes<Index, 5> dims(11, 5, 6, 17, 7);
+ const Index max_coeff_count = 5 * 5 * 5 * 5 * 5;
+ TensorBlockMapper block_mapper(dims, {TensorBlockShapeType::kUniformAllDims,
+ max_coeff_count, zeroCost()});
+ TensorBlock block = block_mapper.blockDescriptor(0);
+ for (int i = 0; i < 5; ++i) {
+ VERIFY_IS_EQUAL(5, block.dimensions()[i]);
+ }
+ VERIFY(block.dimensions().TotalSize() <= max_coeff_count);
+ }
+
+ // Test shape 'UniformAllDims' with larger 'max_coeff count' which spills
+ // partially into first inner-most dimension.
+ if (Layout == ColMajor) {
+ DSizes<Index, 5> dims(11, 5, 6, 17, 7);
+ const Index max_coeff_count = 7 * 5 * 5 * 5 * 5;
+ TensorBlockMapper block_mapper(dims, {TensorBlockShapeType::kUniformAllDims,
+ max_coeff_count, zeroCost()});
+ TensorBlock block = block_mapper.blockDescriptor(0);
+ VERIFY_IS_EQUAL(7, block.dimensions()[0]);
+ for (int i = 1; i < 5; ++i) {
+ VERIFY_IS_EQUAL(5, block.dimensions()[i]);
+ }
+ VERIFY(block.dimensions().TotalSize() <= max_coeff_count);
+ } else {
+ DSizes<Index, 5> dims(11, 5, 6, 17, 7);
+ const Index max_coeff_count = 5 * 5 * 5 * 5 * 6;
+ TensorBlockMapper block_mapper(dims, {TensorBlockShapeType::kUniformAllDims,
+ max_coeff_count, zeroCost()});
+ TensorBlock block = block_mapper.blockDescriptor(0);
+ VERIFY_IS_EQUAL(6, block.dimensions()[4]);
+ for (int i = 3; i >= 0; --i) {
+ VERIFY_IS_EQUAL(5, block.dimensions()[i]);
+ }
+ VERIFY(block.dimensions().TotalSize() <= max_coeff_count);
+ }
+
+ // Test shape 'UniformAllDims' with larger 'max_coeff count' which spills
+ // fully into first inner-most dimension.
+ if (Layout == ColMajor) {
+ DSizes<Index, 5> dims(11, 5, 6, 17, 7);
+ const Index max_coeff_count = 11 * 5 * 5 * 5 * 5;
+ TensorBlockMapper block_mapper(dims, {TensorBlockShapeType::kUniformAllDims,
+ max_coeff_count, zeroCost()});
+ TensorBlock block = block_mapper.blockDescriptor(0);
+ VERIFY_IS_EQUAL(11, block.dimensions()[0]);
+ for (int i = 1; i < 5; ++i) {
+ VERIFY_IS_EQUAL(5, block.dimensions()[i]);
+ }
+ VERIFY(block.dimensions().TotalSize() <= max_coeff_count);
+ } else {
+ DSizes<Index, 5> dims(11, 5, 6, 17, 7);
+ const Index max_coeff_count = 5 * 5 * 5 * 5 * 7;
+ TensorBlockMapper block_mapper(dims, {TensorBlockShapeType::kUniformAllDims,
+ max_coeff_count, zeroCost()});
+ TensorBlock block = block_mapper.blockDescriptor(0);
+ VERIFY_IS_EQUAL(7, block.dimensions()[4]);
+ for (int i = 3; i >= 0; --i) {
+ VERIFY_IS_EQUAL(5, block.dimensions()[i]);
+ }
+ VERIFY(block.dimensions().TotalSize() <= max_coeff_count);
+ }
+
+ // Test shape 'UniformAllDims' with larger 'max_coeff count' which spills
+ // fully into first few inner-most dimensions.
+ if (Layout == ColMajor) {
+ DSizes<Index, 5> dims(7, 5, 6, 17, 7);
+ const Index max_coeff_count = 7 * 5 * 6 * 7 * 5;
+ TensorBlockMapper block_mapper(dims, {TensorBlockShapeType::kUniformAllDims,
+ max_coeff_count, zeroCost()});
+ TensorBlock block = block_mapper.blockDescriptor(0);
+ VERIFY_IS_EQUAL(7, block.dimensions()[0]);
+ VERIFY_IS_EQUAL(5, block.dimensions()[1]);
+ VERIFY_IS_EQUAL(6, block.dimensions()[2]);
+ VERIFY_IS_EQUAL(7, block.dimensions()[3]);
+ VERIFY_IS_EQUAL(5, block.dimensions()[4]);
+ VERIFY(block.dimensions().TotalSize() <= max_coeff_count);
+ } else {
+ DSizes<Index, 5> dims(7, 5, 6, 9, 7);
+ const Index max_coeff_count = 5 * 5 * 5 * 6 * 7;
+ TensorBlockMapper block_mapper(dims, {TensorBlockShapeType::kUniformAllDims,
+ max_coeff_count, zeroCost()});
+ TensorBlock block = block_mapper.blockDescriptor(0);
+ VERIFY_IS_EQUAL(7, block.dimensions()[4]);
+ VERIFY_IS_EQUAL(6, block.dimensions()[3]);
+ VERIFY_IS_EQUAL(5, block.dimensions()[2]);
+ VERIFY_IS_EQUAL(5, block.dimensions()[1]);
+ VERIFY_IS_EQUAL(5, block.dimensions()[0]);
+ VERIFY(block.dimensions().TotalSize() <= max_coeff_count);
+ }
+
+ // Test shape 'UniformAllDims' with full allocation to all dims.
+ if (Layout == ColMajor) {
+ DSizes<Index, 5> dims(7, 5, 6, 17, 7);
+ const Index max_coeff_count = 7 * 5 * 6 * 17 * 7;
+ TensorBlockMapper block_mapper(dims, {TensorBlockShapeType::kUniformAllDims,
+ max_coeff_count, zeroCost()});
+ TensorBlock block = block_mapper.blockDescriptor(0);
+ VERIFY_IS_EQUAL(7, block.dimensions()[0]);
+ VERIFY_IS_EQUAL(5, block.dimensions()[1]);
+ VERIFY_IS_EQUAL(6, block.dimensions()[2]);
+ VERIFY_IS_EQUAL(17, block.dimensions()[3]);
+ VERIFY_IS_EQUAL(7, block.dimensions()[4]);
+ VERIFY(block.dimensions().TotalSize() <= max_coeff_count);
+ } else {
+ DSizes<Index, 5> dims(7, 5, 6, 9, 7);
+ const Index max_coeff_count = 7 * 5 * 6 * 9 * 7;
+ TensorBlockMapper block_mapper(dims, {TensorBlockShapeType::kUniformAllDims,
+ max_coeff_count, zeroCost()});
+ TensorBlock block = block_mapper.blockDescriptor(0);
+ VERIFY_IS_EQUAL(7, block.dimensions()[4]);
+ VERIFY_IS_EQUAL(9, block.dimensions()[3]);
+ VERIFY_IS_EQUAL(6, block.dimensions()[2]);
+ VERIFY_IS_EQUAL(5, block.dimensions()[1]);
+ VERIFY_IS_EQUAL(7, block.dimensions()[0]);
+ VERIFY(block.dimensions().TotalSize() <= max_coeff_count);
+ }
+}
+
+template <int Layout>
+static void test_skewed_inner_dim_block_shape()
+{
+ typedef internal::TensorBlockDescriptor<5> TensorBlock;
+ typedef internal::TensorBlockMapper<5, Layout> TensorBlockMapper;
+
+ // Test shape 'SkewedInnerDims' with partial allocation to inner-most dim.
+ if (Layout == ColMajor) {
+ DSizes<Index, 5> dims(11, 5, 6, 17, 7);
+ const Index max_coeff_count = 10 * 1 * 1 * 1 * 1;
+ TensorBlockMapper block_mapper(
+ dims,
+ {TensorBlockShapeType::kSkewedInnerDims, max_coeff_count, zeroCost()});
+ TensorBlock block = block_mapper.blockDescriptor(0);
+ VERIFY_IS_EQUAL(10, block.dimensions()[0]);
+ for (int i = 1; i < 5; ++i) {
+ VERIFY_IS_EQUAL(1, block.dimensions()[i]);
+ }
+ VERIFY(block.dimensions().TotalSize() <= max_coeff_count);
+ } else {
+ DSizes<Index, 5> dims(11, 5, 6, 17, 7);
+ const Index max_coeff_count = 1 * 1 * 1 * 1 * 6;
+ TensorBlockMapper block_mapper(
+ dims,
+ {TensorBlockShapeType::kSkewedInnerDims, max_coeff_count, zeroCost()});
+ TensorBlock block = block_mapper.blockDescriptor(0);
+ VERIFY_IS_EQUAL(6, block.dimensions()[4]);
+ for (int i = 3; i >= 0; --i) {
+ VERIFY_IS_EQUAL(1, block.dimensions()[i]);
+ }
+ VERIFY(block.dimensions().TotalSize() <= max_coeff_count);
+ }
+
+ // Test shape 'SkewedInnerDims' with full allocation to inner-most dim.
+ if (Layout == ColMajor) {
+ DSizes<Index, 5> dims(11, 5, 6, 17, 7);
+ const Index max_coeff_count = 11 * 1 * 1 * 1 * 1;
+ TensorBlockMapper block_mapper(
+ dims,
+ {TensorBlockShapeType::kSkewedInnerDims, max_coeff_count, zeroCost()});
+ TensorBlock block = block_mapper.blockDescriptor(0);
+ VERIFY_IS_EQUAL(11, block.dimensions()[0]);
+ for (int i = 1; i < 5; ++i) {
+ VERIFY_IS_EQUAL(1, block.dimensions()[i]);
+ }
+ VERIFY(block.dimensions().TotalSize() <= max_coeff_count);
+ } else {
+ DSizes<Index, 5> dims(11, 5, 6, 17, 7);
+ const Index max_coeff_count = 1 * 1 * 1 * 1 * 7;
+ TensorBlockMapper block_mapper(
+ dims,
+ {TensorBlockShapeType::kSkewedInnerDims, max_coeff_count, zeroCost()});
+ TensorBlock block = block_mapper.blockDescriptor(0);
+ VERIFY_IS_EQUAL(7, block.dimensions()[4]);
+ for (int i = 3; i >= 0; --i) {
+ VERIFY_IS_EQUAL(1, block.dimensions()[i]);
+ }
+ VERIFY(block.dimensions().TotalSize() <= max_coeff_count);
+ }
+
+ // Test shape 'SkewedInnerDims' with full allocation to inner-most dim,
+ // and partial allocation to second inner-dim.
+ if (Layout == ColMajor) {
+ DSizes<Index, 5> dims(11, 5, 6, 17, 7);
+ const Index max_coeff_count = 11 * 3 * 1 * 1 * 1;
+ TensorBlockMapper block_mapper(
+ dims,
+ {TensorBlockShapeType::kSkewedInnerDims, max_coeff_count, zeroCost()});
+ TensorBlock block = block_mapper.blockDescriptor(0);
+ VERIFY_IS_EQUAL(11, block.dimensions()[0]);
+ VERIFY_IS_EQUAL(3, block.dimensions()[1]);
+ for (int i = 2; i < 5; ++i) {
+ VERIFY_IS_EQUAL(1, block.dimensions()[i]);
+ }
+ VERIFY(block.dimensions().TotalSize() <= max_coeff_count);
+ } else {
+ DSizes<Index, 5> dims(11, 5, 6, 17, 7);
+ const Index max_coeff_count = 1 * 1 * 1 * 15 * 7;
+ TensorBlockMapper block_mapper(
+ dims,
+ {TensorBlockShapeType::kSkewedInnerDims, max_coeff_count, zeroCost()});
+ TensorBlock block = block_mapper.blockDescriptor(0);
+ VERIFY_IS_EQUAL(7, block.dimensions()[4]);
+ VERIFY_IS_EQUAL(15, block.dimensions()[3]);
+ for (int i = 2; i >= 0; --i) {
+ VERIFY_IS_EQUAL(1, block.dimensions()[i]);
+ }
+ VERIFY(block.dimensions().TotalSize() <= max_coeff_count);
+ }
+
+ // Test shape 'SkewedInnerDims' with full allocation to inner-most dim,
+ // and partial allocation to third inner-dim.
+ if (Layout == ColMajor) {
+ DSizes<Index, 5> dims(11, 5, 6, 17, 7);
+ const Index max_coeff_count = 11 * 5 * 5 * 1 * 1;
+ TensorBlockMapper block_mapper(
+ dims,
+ {TensorBlockShapeType::kSkewedInnerDims, max_coeff_count, zeroCost()});
+ TensorBlock block = block_mapper.blockDescriptor(0);
+ VERIFY_IS_EQUAL(11, block.dimensions()[0]);
+ VERIFY_IS_EQUAL(5, block.dimensions()[1]);
+ VERIFY_IS_EQUAL(5, block.dimensions()[2]);
+ for (int i = 3; i < 5; ++i) {
+ VERIFY_IS_EQUAL(1, block.dimensions()[i]);
+ }
+ VERIFY(block.dimensions().TotalSize() <= max_coeff_count);
+ } else {
+ DSizes<Index, 5> dims(11, 5, 6, 17, 7);
+ const Index max_coeff_count = 1 * 1 * 5 * 17 * 7;
+ TensorBlockMapper block_mapper(
+ dims,
+ {TensorBlockShapeType::kSkewedInnerDims, max_coeff_count, zeroCost()});
+ TensorBlock block = block_mapper.blockDescriptor(0);
+ VERIFY_IS_EQUAL(7, block.dimensions()[4]);
+ VERIFY_IS_EQUAL(17, block.dimensions()[3]);
+ VERIFY_IS_EQUAL(5, block.dimensions()[2]);
+ for (int i = 1; i >= 0; --i) {
+ VERIFY_IS_EQUAL(1, block.dimensions()[i]);
+ }
+ VERIFY(block.dimensions().TotalSize() <= max_coeff_count);
+ }
+
+ // Test shape 'SkewedInnerDims' with full allocation to all dims.
+ if (Layout == ColMajor) {
+ DSizes<Index, 5> dims(11, 5, 6, 17, 7);
+ const Index max_coeff_count = 11 * 5 * 6 * 17 * 7;
+ TensorBlockMapper block_mapper(
+ dims,
+ {TensorBlockShapeType::kSkewedInnerDims, max_coeff_count, zeroCost()});
+ TensorBlock block = block_mapper.blockDescriptor(0);
+ VERIFY_IS_EQUAL(11, block.dimensions()[0]);
+ VERIFY_IS_EQUAL(5, block.dimensions()[1]);
+ VERIFY_IS_EQUAL(6, block.dimensions()[2]);
+ VERIFY_IS_EQUAL(17, block.dimensions()[3]);
+ VERIFY_IS_EQUAL(7, block.dimensions()[4]);
+ VERIFY(block.dimensions().TotalSize() <= max_coeff_count);
+ } else {
+ DSizes<Index, 5> dims(11, 5, 6, 17, 7);
+ const Index max_coeff_count = 11 * 5 * 6 * 17 * 7;
+ TensorBlockMapper block_mapper(
+ dims,
+ {TensorBlockShapeType::kSkewedInnerDims, max_coeff_count, zeroCost()});
+ TensorBlock block = block_mapper.blockDescriptor(0);
+ VERIFY_IS_EQUAL(7, block.dimensions()[4]);
+ VERIFY_IS_EQUAL(17, block.dimensions()[3]);
+ VERIFY_IS_EQUAL(6, block.dimensions()[2]);
+ VERIFY_IS_EQUAL(5, block.dimensions()[1]);
+ VERIFY_IS_EQUAL(11, block.dimensions()[0]);
+ VERIFY(block.dimensions().TotalSize() <= max_coeff_count);
+ }
+}
+
+template <int Layout>
+static void test_empty_dims(const internal::TensorBlockShapeType block_shape)
+{
+ // Test blocking of tensors with zero dimensions:
+ // - we must not crash on asserts and divisions by zero
+ // - we must not return block with zero dimensions
+ // (recipe for overflows/underflows, divisions by zero and NaNs later)
+ // - total block count must be zero
+ {
+ typedef internal::TensorBlockMapper<1, Layout> TensorBlockMapper;
+
+ DSizes<Index, 1> dims(0);
+ for (size_t max_coeff_count = 0; max_coeff_count < 2; ++max_coeff_count) {
+ TensorBlockMapper block_mapper(
+ dims, {block_shape, max_coeff_count, zeroCost()});
+ VERIFY_IS_EQUAL(block_mapper.blockCount(), 0);
+ VERIFY(block_mapper.blockTotalSize() >= 1);
+ }
+ }
+
+ {
+ typedef internal::TensorBlockMapper<2, Layout> TensorBlockMapper;
+
+ for (int dim1 = 0; dim1 < 3; ++dim1) {
+ for (int dim2 = 0; dim2 < 3; ++dim2) {
+ DSizes<Index, 2> dims(dim1, dim2);
+ for (size_t max_coeff_count = 0; max_coeff_count < 2; ++max_coeff_count) {
+ TensorBlockMapper block_mapper(
+ dims, {block_shape, max_coeff_count, zeroCost()});
+ if (dim1 * dim2 == 0) {
+ VERIFY_IS_EQUAL(block_mapper.blockCount(), 0);
+ }
+ VERIFY(block_mapper.blockTotalSize() >= 1);
+ }
+ }
+ }
+ }
+}
+
+#define TEST_LAYOUTS(NAME) \
+ CALL_SUBTEST(NAME<ColMajor>()); \
+ CALL_SUBTEST(NAME<RowMajor>())
+
+#define TEST_LAYOUTS_AND_DIMS(TYPE, NAME) \
+ CALL_SUBTEST((NAME<TYPE, 1, ColMajor>())); \
+ CALL_SUBTEST((NAME<TYPE, 1, RowMajor>())); \
+ CALL_SUBTEST((NAME<TYPE, 2, ColMajor>())); \
+ CALL_SUBTEST((NAME<TYPE, 2, RowMajor>())); \
+ CALL_SUBTEST((NAME<TYPE, 3, ColMajor>())); \
+ CALL_SUBTEST((NAME<TYPE, 3, RowMajor>())); \
+ CALL_SUBTEST((NAME<TYPE, 4, ColMajor>())); \
+ CALL_SUBTEST((NAME<TYPE, 4, RowMajor>())); \
+ CALL_SUBTEST((NAME<TYPE, 5, ColMajor>())); \
+ CALL_SUBTEST((NAME<TYPE, 5, RowMajor>()))
+
+#define TEST_LAYOUTS_WITH_ARG(NAME, ARG) \
+ CALL_SUBTEST(NAME<ColMajor>(ARG)); \
+ CALL_SUBTEST(NAME<RowMajor>(ARG))
+
+EIGEN_DECLARE_TEST(cxx11_tensor_block_access) {
+ TEST_LAYOUTS(test_block_mapper_sanity);
+ TEST_LAYOUTS_AND_DIMS(float, test_block_mapper_maps_every_element);
+ TEST_LAYOUTS(test_uniform_block_shape);
+ TEST_LAYOUTS(test_skewed_inner_dim_block_shape);
+ TEST_LAYOUTS_WITH_ARG(test_empty_dims, TensorBlockShapeType::kUniformAllDims);
+ TEST_LAYOUTS_WITH_ARG(test_empty_dims, TensorBlockShapeType::kSkewedInnerDims);
+}
+
+#undef TEST_LAYOUTS
+#undef TEST_LAYOUTS_WITH_ARG
diff --git a/unsupported/test/cxx11_tensor_block_eval.cpp b/unsupported/test/cxx11_tensor_block_eval.cpp
new file mode 100644
index 0000000..d66a63e
--- /dev/null
+++ b/unsupported/test/cxx11_tensor_block_eval.cpp
@@ -0,0 +1,858 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+// clang-format off
+#include "main.h"
+#include <Eigen/CXX11/Tensor>
+// clang-format on
+
+using Eigen::internal::TensorBlockDescriptor;
+using Eigen::internal::TensorExecutor;
+
+// -------------------------------------------------------------------------- //
+// Utility functions to generate random tensors, blocks, and evaluate them.
+
+template <int NumDims>
+static DSizes<Index, NumDims> RandomDims(Index min, Index max) {
+ DSizes<Index, NumDims> dims;
+ for (int i = 0; i < NumDims; ++i) {
+ dims[i] = internal::random<Index>(min, max);
+ }
+ return DSizes<Index, NumDims>(dims);
+}
+
+// Block offsets and extents allows to construct a TensorSlicingOp corresponding
+// to a TensorBlockDescriptor.
+template <int NumDims>
+struct TensorBlockParams {
+ DSizes<Index, NumDims> offsets;
+ DSizes<Index, NumDims> sizes;
+ TensorBlockDescriptor<NumDims, Index> desc;
+};
+
+template <int Layout, int NumDims>
+static TensorBlockParams<NumDims> RandomBlock(DSizes<Index, NumDims> dims,
+ Index min, Index max) {
+ // Choose random offsets and sizes along all tensor dimensions.
+ DSizes<Index, NumDims> offsets(RandomDims<NumDims>(min, max));
+ DSizes<Index, NumDims> sizes(RandomDims<NumDims>(min, max));
+
+ // Make sure that offset + size do not overflow dims.
+ for (int i = 0; i < NumDims; ++i) {
+ offsets[i] = numext::mini(dims[i] - 1, offsets[i]);
+ sizes[i] = numext::mini(sizes[i], dims[i] - offsets[i]);
+ }
+
+ Index offset = 0;
+ DSizes<Index, NumDims> strides = Eigen::internal::strides<Layout>(dims);
+ for (int i = 0; i < NumDims; ++i) {
+ offset += strides[i] * offsets[i];
+ }
+
+ return {offsets, sizes, TensorBlockDescriptor<NumDims, Index>(offset, sizes)};
+}
+
+// Generate block with block sizes skewed towards inner dimensions. This type of
+// block is required for evaluating broadcast expressions.
+template <int Layout, int NumDims>
+static TensorBlockParams<NumDims> SkewedInnerBlock(
+ DSizes<Index, NumDims> dims) {
+ using BlockMapper = internal::TensorBlockMapper<NumDims, Layout, Index>;
+ BlockMapper block_mapper(dims,
+ {internal::TensorBlockShapeType::kSkewedInnerDims,
+ internal::random<size_t>(1, dims.TotalSize()),
+ {0, 0, 0}});
+
+ Index total_blocks = block_mapper.blockCount();
+ Index block_index = internal::random<Index>(0, total_blocks - 1);
+ auto block = block_mapper.blockDescriptor(block_index);
+ DSizes<Index, NumDims> sizes = block.dimensions();
+
+ auto strides = internal::strides<Layout>(dims);
+ DSizes<Index, NumDims> offsets;
+
+ // Compute offsets for the first block coefficient.
+ Index index = block.offset();
+ if (static_cast<int>(Layout) == static_cast<int>(ColMajor)) {
+ for (int i = NumDims - 1; i > 0; --i) {
+ const Index idx = index / strides[i];
+ index -= idx * strides[i];
+ offsets[i] = idx;
+ }
+ if (NumDims > 0) offsets[0] = index;
+ } else {
+ for (int i = 0; i < NumDims - 1; ++i) {
+ const Index idx = index / strides[i];
+ index -= idx * strides[i];
+ offsets[i] = idx;
+ }
+ if (NumDims > 0) offsets[NumDims - 1] = index;
+ }
+
+ return {offsets, sizes, block};
+}
+
+template <int NumDims>
+static TensorBlockParams<NumDims> FixedSizeBlock(DSizes<Index, NumDims> dims) {
+ DSizes<Index, NumDims> offsets;
+ for (int i = 0; i < NumDims; ++i) offsets[i] = 0;
+
+ return {offsets, dims, TensorBlockDescriptor<NumDims, Index>(0, dims)};
+}
+
+inline Eigen::IndexList<Index, Eigen::type2index<1>> NByOne(Index n) {
+ Eigen::IndexList<Index, Eigen::type2index<1>> ret;
+ ret.set(0, n);
+ return ret;
+}
+inline Eigen::IndexList<Eigen::type2index<1>, Index> OneByM(Index m) {
+ Eigen::IndexList<Eigen::type2index<1>, Index> ret;
+ ret.set(1, m);
+ return ret;
+}
+
+// -------------------------------------------------------------------------- //
+// Verify that block expression evaluation produces the same result as a
+// TensorSliceOp (reading a tensor block is same to taking a tensor slice).
+
+template <typename T, int NumDims, int Layout, typename Expression,
+ typename GenBlockParams>
+static void VerifyBlockEvaluator(Expression expr, GenBlockParams gen_block) {
+ using Device = DefaultDevice;
+ auto d = Device();
+
+ // Scratch memory allocator for block evaluation.
+ typedef internal::TensorBlockScratchAllocator<Device> TensorBlockScratch;
+ TensorBlockScratch scratch(d);
+
+ // TensorEvaluator is needed to produce tensor blocks of the expression.
+ auto eval = TensorEvaluator<const decltype(expr), Device>(expr, d);
+ eval.evalSubExprsIfNeeded(nullptr);
+
+ // Choose a random offsets, sizes and TensorBlockDescriptor.
+ TensorBlockParams<NumDims> block_params = gen_block();
+
+ // Evaluate TensorBlock expression into a tensor.
+ Tensor<T, NumDims, Layout> block(block_params.desc.dimensions());
+
+ // Dimensions for the potential destination buffer.
+ DSizes<Index, NumDims> dst_dims;
+ if (internal::random<bool>()) {
+ dst_dims = block_params.desc.dimensions();
+ } else {
+ for (int i = 0; i < NumDims; ++i) {
+ Index extent = internal::random<Index>(0, 5);
+ dst_dims[i] = block_params.desc.dimension(i) + extent;
+ }
+ }
+
+ // Maybe use this tensor as a block desc destination.
+ Tensor<T, NumDims, Layout> dst(dst_dims);
+ dst.setZero();
+ if (internal::random<bool>()) {
+ block_params.desc.template AddDestinationBuffer<Layout>(
+ dst.data(), internal::strides<Layout>(dst.dimensions()));
+ }
+
+ const bool root_of_expr = internal::random<bool>();
+ auto tensor_block = eval.block(block_params.desc, scratch, root_of_expr);
+
+ if (tensor_block.kind() == internal::TensorBlockKind::kMaterializedInOutput) {
+ // Copy data from destination buffer.
+ if (dimensions_match(dst.dimensions(), block.dimensions())) {
+ block = dst;
+ } else {
+ DSizes<Index, NumDims> offsets;
+ for (int i = 0; i < NumDims; ++i) offsets[i] = 0;
+ block = dst.slice(offsets, block.dimensions());
+ }
+
+ } else {
+ // Assign to block from expression.
+ auto b_expr = tensor_block.expr();
+
+ // We explicitly disable vectorization and tiling, to run a simple coefficient
+ // wise assignment loop, because it's very simple and should be correct.
+ using BlockAssign = TensorAssignOp<decltype(block), const decltype(b_expr)>;
+ using BlockExecutor = TensorExecutor<const BlockAssign, Device, false,
+ internal::TiledEvaluation::Off>;
+ BlockExecutor::run(BlockAssign(block, b_expr), d);
+ }
+
+ // Cleanup temporary buffers owned by a tensor block.
+ tensor_block.cleanup();
+
+ // Compute a Tensor slice corresponding to a Tensor block.
+ Tensor<T, NumDims, Layout> slice(block_params.desc.dimensions());
+ auto s_expr = expr.slice(block_params.offsets, block_params.sizes);
+
+ // Explicitly use coefficient assignment to evaluate slice expression.
+ using SliceAssign = TensorAssignOp<decltype(slice), const decltype(s_expr)>;
+ using SliceExecutor = TensorExecutor<const SliceAssign, Device, false,
+ internal::TiledEvaluation::Off>;
+ SliceExecutor::run(SliceAssign(slice, s_expr), d);
+
+ // Tensor block and tensor slice must be the same.
+ for (Index i = 0; i < block.dimensions().TotalSize(); ++i) {
+ VERIFY_IS_EQUAL(block.coeff(i), slice.coeff(i));
+ }
+}
+
+// -------------------------------------------------------------------------- //
+
+template <typename T, int NumDims, int Layout>
+static void test_eval_tensor_block() {
+ DSizes<Index, NumDims> dims = RandomDims<NumDims>(10, 20);
+ Tensor<T, NumDims, Layout> input(dims);
+ input.setRandom();
+
+ // Identity tensor expression transformation.
+ VerifyBlockEvaluator<T, NumDims, Layout>(
+ input, [&dims]() { return RandomBlock<Layout>(dims, 1, 10); });
+}
+
+template <typename T, int NumDims, int Layout>
+static void test_eval_tensor_unary_expr_block() {
+ DSizes<Index, NumDims> dims = RandomDims<NumDims>(10, 20);
+ Tensor<T, NumDims, Layout> input(dims);
+ input.setRandom();
+
+ VerifyBlockEvaluator<T, NumDims, Layout>(
+ input.abs(), [&dims]() { return RandomBlock<Layout>(dims, 1, 10); });
+}
+
+template <typename T, int NumDims, int Layout>
+static void test_eval_tensor_binary_expr_block() {
+ DSizes<Index, NumDims> dims = RandomDims<NumDims>(10, 20);
+ Tensor<T, NumDims, Layout> lhs(dims), rhs(dims);
+ lhs.setRandom();
+ rhs.setRandom();
+
+ VerifyBlockEvaluator<T, NumDims, Layout>(
+ lhs * rhs, [&dims]() { return RandomBlock<Layout>(dims, 1, 10); });
+}
+
+template <typename T, int NumDims, int Layout>
+static void test_eval_tensor_binary_with_unary_expr_block() {
+ DSizes<Index, NumDims> dims = RandomDims<NumDims>(10, 20);
+ Tensor<T, NumDims, Layout> lhs(dims), rhs(dims);
+ lhs.setRandom();
+ rhs.setRandom();
+
+ VerifyBlockEvaluator<T, NumDims, Layout>(
+ (lhs.abs() + rhs.abs()).sqrt(),
+ [&dims]() { return RandomBlock<Layout>(dims, 1, 10); });
+}
+
+template <typename T, int NumDims, int Layout>
+static void test_eval_tensor_broadcast() {
+ DSizes<Index, NumDims> dims = RandomDims<NumDims>(1, 10);
+ Tensor<T, NumDims, Layout> input(dims);
+ input.setRandom();
+
+ DSizes<Index, NumDims> bcast = RandomDims<NumDims>(1, 5);
+
+ DSizes<Index, NumDims> bcasted_dims;
+ for (int i = 0; i < NumDims; ++i) bcasted_dims[i] = dims[i] * bcast[i];
+
+ VerifyBlockEvaluator<T, NumDims, Layout>(
+ input.broadcast(bcast),
+ [&bcasted_dims]() { return SkewedInnerBlock<Layout>(bcasted_dims); });
+
+ VerifyBlockEvaluator<T, NumDims, Layout>(
+ input.broadcast(bcast),
+ [&bcasted_dims]() { return RandomBlock<Layout>(bcasted_dims, 5, 10); });
+
+ VerifyBlockEvaluator<T, NumDims, Layout>(
+ input.broadcast(bcast),
+ [&bcasted_dims]() { return FixedSizeBlock(bcasted_dims); });
+
+ // Check that desc.destination() memory is not shared between two broadcast
+ // materializations.
+ VerifyBlockEvaluator<T, NumDims, Layout>(
+ input.broadcast(bcast) * input.abs().broadcast(bcast),
+ [&bcasted_dims]() { return SkewedInnerBlock<Layout>(bcasted_dims); });
+}
+
+template <typename T, int NumDims, int Layout>
+static void test_eval_tensor_reshape() {
+ DSizes<Index, NumDims> dims = RandomDims<NumDims>(1, 10);
+
+ DSizes<Index, NumDims> shuffled = dims;
+ std::shuffle(&shuffled[0], &shuffled[NumDims - 1], std::mt19937(g_seed));
+
+ Tensor<T, NumDims, Layout> input(dims);
+ input.setRandom();
+
+ VerifyBlockEvaluator<T, NumDims, Layout>(
+ input.reshape(shuffled),
+ [&shuffled]() { return RandomBlock<Layout>(shuffled, 1, 10); });
+
+ VerifyBlockEvaluator<T, NumDims, Layout>(
+ input.reshape(shuffled),
+ [&shuffled]() { return SkewedInnerBlock<Layout>(shuffled); });
+}
+
+template <typename T, int NumDims, int Layout>
+static void test_eval_tensor_cast() {
+ DSizes<Index, NumDims> dims = RandomDims<NumDims>(10, 20);
+ Tensor<T, NumDims, Layout> input(dims);
+ input.setRandom();
+
+ VerifyBlockEvaluator<T, NumDims, Layout>(
+ input.template cast<int>().template cast<T>(),
+ [&dims]() { return RandomBlock<Layout>(dims, 1, 10); });
+}
+
+template <typename T, int NumDims, int Layout>
+static void test_eval_tensor_select() {
+ DSizes<Index, NumDims> dims = RandomDims<NumDims>(10, 20);
+ Tensor<T, NumDims, Layout> lhs(dims);
+ Tensor<T, NumDims, Layout> rhs(dims);
+ Tensor<bool, NumDims, Layout> cond(dims);
+ lhs.setRandom();
+ rhs.setRandom();
+ cond.setRandom();
+
+ VerifyBlockEvaluator<T, NumDims, Layout>(cond.select(lhs, rhs), [&dims]() {
+ return RandomBlock<Layout>(dims, 1, 20);
+ });
+}
+
+template <typename T, int NumDims, int Layout>
+static void test_eval_tensor_padding() {
+ const int inner_dim = Layout == static_cast<int>(ColMajor) ? 0 : NumDims - 1;
+
+ DSizes<Index, NumDims> dims = RandomDims<NumDims>(10, 20);
+ Tensor<T, NumDims, Layout> input(dims);
+ input.setRandom();
+
+ DSizes<Index, NumDims> pad_before = RandomDims<NumDims>(0, 4);
+ DSizes<Index, NumDims> pad_after = RandomDims<NumDims>(0, 4);
+ array<std::pair<Index, Index>, NumDims> paddings;
+ for (int i = 0; i < NumDims; ++i) {
+ paddings[i] = std::make_pair(pad_before[i], pad_after[i]);
+ }
+
+ // Test squeezing reads from inner dim.
+ if (internal::random<bool>()) {
+ pad_before[inner_dim] = 0;
+ pad_after[inner_dim] = 0;
+ paddings[inner_dim] = std::make_pair(0, 0);
+ }
+
+ DSizes<Index, NumDims> padded_dims;
+ for (int i = 0; i < NumDims; ++i) {
+ padded_dims[i] = dims[i] + pad_before[i] + pad_after[i];
+ }
+
+ VerifyBlockEvaluator<T, NumDims, Layout>(
+ input.pad(paddings),
+ [&padded_dims]() { return FixedSizeBlock(padded_dims); });
+
+ VerifyBlockEvaluator<T, NumDims, Layout>(
+ input.pad(paddings),
+ [&padded_dims]() { return RandomBlock<Layout>(padded_dims, 1, 10); });
+
+ VerifyBlockEvaluator<T, NumDims, Layout>(
+ input.pad(paddings),
+ [&padded_dims]() { return SkewedInnerBlock<Layout>(padded_dims); });
+}
+
+template <typename T, int NumDims, int Layout>
+static void test_eval_tensor_chipping() {
+ DSizes<Index, NumDims> dims = RandomDims<NumDims>(10, 20);
+ Tensor<T, NumDims, Layout> input(dims);
+ input.setRandom();
+
+ Index chip_dim = internal::random<int>(0, NumDims - 1);
+ Index chip_offset = internal::random<Index>(0, dims[chip_dim] - 2);
+
+ DSizes<Index, NumDims - 1> chipped_dims;
+ for (Index i = 0; i < chip_dim; ++i) {
+ chipped_dims[i] = dims[i];
+ }
+ for (Index i = chip_dim + 1; i < NumDims; ++i) {
+ chipped_dims[i - 1] = dims[i];
+ }
+
+ // Block buffer forwarding.
+ VerifyBlockEvaluator<T, NumDims - 1, Layout>(
+ input.chip(chip_offset, chip_dim),
+ [&chipped_dims]() { return FixedSizeBlock(chipped_dims); });
+
+ VerifyBlockEvaluator<T, NumDims - 1, Layout>(
+ input.chip(chip_offset, chip_dim),
+ [&chipped_dims]() { return RandomBlock<Layout>(chipped_dims, 1, 10); });
+
+ // Block expression assignment.
+ VerifyBlockEvaluator<T, NumDims - 1, Layout>(
+ input.abs().chip(chip_offset, chip_dim),
+ [&chipped_dims]() { return FixedSizeBlock(chipped_dims); });
+
+ VerifyBlockEvaluator<T, NumDims - 1, Layout>(
+ input.abs().chip(chip_offset, chip_dim),
+ [&chipped_dims]() { return RandomBlock<Layout>(chipped_dims, 1, 10); });
+}
+
+
+template<typename T, int NumDims>
+struct SimpleTensorGenerator {
+ T operator()(const array<Index, NumDims>& coords) const {
+ T result = static_cast<T>(0);
+ for (int i = 0; i < NumDims; ++i) {
+ result += static_cast<T>((i + 1) * coords[i]);
+ }
+ return result;
+ }
+};
+
+// Boolean specialization to avoid -Wint-in-bool-context warnings on GCC.
+template<int NumDims>
+struct SimpleTensorGenerator<bool, NumDims> {
+ bool operator()(const array<Index, NumDims>& coords) const {
+ bool result = false;
+ for (int i = 0; i < NumDims; ++i) {
+ result ^= coords[i];
+ }
+ return result;
+ }
+};
+
+
+template <typename T, int NumDims, int Layout>
+static void test_eval_tensor_generator() {
+ DSizes<Index, NumDims> dims = RandomDims<NumDims>(10, 20);
+ Tensor<T, NumDims, Layout> input(dims);
+ input.setRandom();
+
+ auto generator = SimpleTensorGenerator<T, NumDims>();
+
+ VerifyBlockEvaluator<T, NumDims, Layout>(
+ input.generate(generator), [&dims]() { return FixedSizeBlock(dims); });
+
+ VerifyBlockEvaluator<T, NumDims, Layout>(
+ input.generate(generator),
+ [&dims]() { return RandomBlock<Layout>(dims, 1, 10); });
+}
+
+template <typename T, int NumDims, int Layout>
+static void test_eval_tensor_reverse() {
+ DSizes<Index, NumDims> dims = RandomDims<NumDims>(10, 20);
+ Tensor<T, NumDims, Layout> input(dims);
+ input.setRandom();
+
+ // Randomly reverse dimensions.
+ Eigen::DSizes<bool, NumDims> reverse;
+ for (int i = 0; i < NumDims; ++i) reverse[i] = internal::random<bool>();
+
+ VerifyBlockEvaluator<T, NumDims, Layout>(
+ input.reverse(reverse), [&dims]() { return FixedSizeBlock(dims); });
+
+ VerifyBlockEvaluator<T, NumDims, Layout>(input.reverse(reverse), [&dims]() {
+ return RandomBlock<Layout>(dims, 1, 10);
+ });
+}
+
+template <typename T, int NumDims, int Layout>
+static void test_eval_tensor_slice() {
+ DSizes<Index, NumDims> dims = RandomDims<NumDims>(10, 20);
+ Tensor<T, NumDims, Layout> input(dims);
+ input.setRandom();
+
+ // Pick a random slice of an input tensor.
+ DSizes<Index, NumDims> slice_start = RandomDims<NumDims>(5, 10);
+ DSizes<Index, NumDims> slice_size = RandomDims<NumDims>(5, 10);
+
+ // Make sure that slice start + size do not overflow tensor dims.
+ for (int i = 0; i < NumDims; ++i) {
+ slice_start[i] = numext::mini(dims[i] - 1, slice_start[i]);
+ slice_size[i] = numext::mini(slice_size[i], dims[i] - slice_start[i]);
+ }
+
+ VerifyBlockEvaluator<T, NumDims, Layout>(
+ input.slice(slice_start, slice_size),
+ [&slice_size]() { return FixedSizeBlock(slice_size); });
+
+ VerifyBlockEvaluator<T, NumDims, Layout>(
+ input.slice(slice_start, slice_size),
+ [&slice_size]() { return RandomBlock<Layout>(slice_size, 1, 10); });
+}
+
+template <typename T, int NumDims, int Layout>
+static void test_eval_tensor_shuffle() {
+ DSizes<Index, NumDims> dims = RandomDims<NumDims>(5, 15);
+ Tensor<T, NumDims, Layout> input(dims);
+ input.setRandom();
+
+ DSizes<Index, NumDims> shuffle;
+ for (int i = 0; i < NumDims; ++i) shuffle[i] = i;
+
+ do {
+ DSizes<Index, NumDims> shuffled_dims;
+ for (int i = 0; i < NumDims; ++i) shuffled_dims[i] = dims[shuffle[i]];
+
+ VerifyBlockEvaluator<T, NumDims, Layout>(
+ input.shuffle(shuffle),
+ [&shuffled_dims]() { return FixedSizeBlock(shuffled_dims); });
+
+ VerifyBlockEvaluator<T, NumDims, Layout>(
+ input.shuffle(shuffle), [&shuffled_dims]() {
+ return RandomBlock<Layout>(shuffled_dims, 1, 5);
+ });
+
+ break;
+
+ } while (std::next_permutation(&shuffle[0], &shuffle[0] + NumDims));
+}
+
+template <typename T, int Layout>
+static void test_eval_tensor_reshape_with_bcast() {
+ Index dim = internal::random<Index>(1, 100);
+
+ Tensor<T, 2, Layout> lhs(1, dim);
+ Tensor<T, 2, Layout> rhs(dim, 1);
+ lhs.setRandom();
+ rhs.setRandom();
+
+ auto reshapeLhs = NByOne(dim);
+ auto reshapeRhs = OneByM(dim);
+
+ auto bcastLhs = OneByM(dim);
+ auto bcastRhs = NByOne(dim);
+
+ DSizes<Index, 2> dims(dim, dim);
+
+ VerifyBlockEvaluator<T, 2, Layout>(
+ lhs.reshape(reshapeLhs).broadcast(bcastLhs) *
+ rhs.reshape(reshapeRhs).broadcast(bcastRhs),
+ [dims]() { return SkewedInnerBlock<Layout, 2>(dims); });
+}
+
+template <typename T, int Layout>
+static void test_eval_tensor_forced_eval() {
+ Index dim = internal::random<Index>(1, 100);
+
+ Tensor<T, 2, Layout> lhs(dim, 1);
+ Tensor<T, 2, Layout> rhs(1, dim);
+ lhs.setRandom();
+ rhs.setRandom();
+
+ auto bcastLhs = OneByM(dim);
+ auto bcastRhs = NByOne(dim);
+
+ DSizes<Index, 2> dims(dim, dim);
+
+ VerifyBlockEvaluator<T, 2, Layout>(
+ (lhs.broadcast(bcastLhs) * rhs.broadcast(bcastRhs)).eval().reshape(dims),
+ [dims]() { return SkewedInnerBlock<Layout, 2>(dims); });
+
+ VerifyBlockEvaluator<T, 2, Layout>(
+ (lhs.broadcast(bcastLhs) * rhs.broadcast(bcastRhs)).eval().reshape(dims),
+ [dims]() { return RandomBlock<Layout, 2>(dims, 1, 50); });
+}
+
+template <typename T, int Layout>
+static void test_eval_tensor_chipping_of_bcast() {
+ if (Layout != static_cast<int>(RowMajor)) return;
+
+ Index dim0 = internal::random<Index>(1, 10);
+ Index dim1 = internal::random<Index>(1, 10);
+ Index dim2 = internal::random<Index>(1, 10);
+
+ Tensor<T, 3, Layout> input(1, dim1, dim2);
+ input.setRandom();
+
+ Eigen::array<Index, 3> bcast = {{dim0, 1, 1}};
+ DSizes<Index, 2> chipped_dims(dim0, dim2);
+
+ VerifyBlockEvaluator<T, 2, Layout>(
+ input.broadcast(bcast).chip(0, 1),
+ [chipped_dims]() { return FixedSizeBlock(chipped_dims); });
+
+ VerifyBlockEvaluator<T, 2, Layout>(
+ input.broadcast(bcast).chip(0, 1),
+ [chipped_dims]() { return SkewedInnerBlock<Layout, 2>(chipped_dims); });
+
+ VerifyBlockEvaluator<T, 2, Layout>(
+ input.broadcast(bcast).chip(0, 1),
+ [chipped_dims]() { return RandomBlock<Layout, 2>(chipped_dims, 1, 5); });
+}
+
+// -------------------------------------------------------------------------- //
+// Verify that assigning block to a Tensor expression produces the same result
+// as an assignment to TensorSliceOp (writing a block is is identical to
+// assigning one tensor to a slice of another tensor).
+
+template <typename T, int NumDims, int Layout, int NumExprDims = NumDims,
+ typename Expression, typename GenBlockParams>
+static void VerifyBlockAssignment(Tensor<T, NumDims, Layout>& tensor,
+ Expression expr, GenBlockParams gen_block) {
+ using Device = DefaultDevice;
+ auto d = Device();
+
+ // We use tensor evaluator as a target for block and slice assignments.
+ auto eval = TensorEvaluator<decltype(expr), Device>(expr, d);
+
+ // Generate a random block, or choose a block that fits in full expression.
+ TensorBlockParams<NumExprDims> block_params = gen_block();
+
+ // Generate random data of the selected block size.
+ Tensor<T, NumExprDims, Layout> block(block_params.desc.dimensions());
+ block.setRandom();
+
+ // ************************************************************************ //
+ // (1) Assignment from a block.
+
+ // Construct a materialize block from a random generated block tensor.
+ internal::TensorMaterializedBlock<T, NumExprDims, Layout> blk(
+ internal::TensorBlockKind::kView, block.data(), block.dimensions());
+
+ // Reset all underlying tensor values to zero.
+ tensor.setZero();
+
+ // Use evaluator to write block into a tensor.
+ eval.writeBlock(block_params.desc, blk);
+
+ // Make a copy of the result after assignment.
+ Tensor<T, NumDims, Layout> block_assigned = tensor;
+
+ // ************************************************************************ //
+ // (2) Assignment to a slice
+
+ // Reset all underlying tensor values to zero.
+ tensor.setZero();
+
+ // Assign block to a slice of original expression
+ auto s_expr = expr.slice(block_params.offsets, block_params.sizes);
+
+ // Explicitly use coefficient assignment to evaluate slice expression.
+ using SliceAssign = TensorAssignOp<decltype(s_expr), const decltype(block)>;
+ using SliceExecutor = TensorExecutor<const SliceAssign, Device, false,
+ internal::TiledEvaluation::Off>;
+ SliceExecutor::run(SliceAssign(s_expr, block), d);
+
+ // Make a copy of the result after assignment.
+ Tensor<T, NumDims, Layout> slice_assigned = tensor;
+
+ for (Index i = 0; i < tensor.dimensions().TotalSize(); ++i) {
+ VERIFY_IS_EQUAL(block_assigned.coeff(i), slice_assigned.coeff(i));
+ }
+}
+
+// -------------------------------------------------------------------------- //
+
+template <typename T, int NumDims, int Layout>
+static void test_assign_to_tensor() {
+ DSizes<Index, NumDims> dims = RandomDims<NumDims>(10, 20);
+ Tensor<T, NumDims, Layout> tensor(dims);
+
+ TensorMap<Tensor<T, NumDims, Layout>> map(tensor.data(), dims);
+
+ VerifyBlockAssignment<T, NumDims, Layout>(
+ tensor, map, [&dims]() { return RandomBlock<Layout>(dims, 10, 20); });
+ VerifyBlockAssignment<T, NumDims, Layout>(
+ tensor, map, [&dims]() { return FixedSizeBlock(dims); });
+}
+
+template <typename T, int NumDims, int Layout>
+static void test_assign_to_tensor_reshape() {
+ DSizes<Index, NumDims> dims = RandomDims<NumDims>(10, 20);
+ Tensor<T, NumDims, Layout> tensor(dims);
+
+ TensorMap<Tensor<T, NumDims, Layout>> map(tensor.data(), dims);
+
+ DSizes<Index, NumDims> shuffled = dims;
+ std::shuffle(&shuffled[0], &shuffled[NumDims - 1], std::mt19937(g_seed));
+
+ VerifyBlockAssignment<T, NumDims, Layout>(
+ tensor, map.reshape(shuffled),
+ [&shuffled]() { return RandomBlock<Layout>(shuffled, 1, 10); });
+
+ VerifyBlockAssignment<T, NumDims, Layout>(
+ tensor, map.reshape(shuffled),
+ [&shuffled]() { return SkewedInnerBlock<Layout>(shuffled); });
+
+ VerifyBlockAssignment<T, NumDims, Layout>(
+ tensor, map.reshape(shuffled),
+ [&shuffled]() { return FixedSizeBlock(shuffled); });
+}
+
+template <typename T, int NumDims, int Layout>
+static void test_assign_to_tensor_chipping() {
+ DSizes<Index, NumDims> dims = RandomDims<NumDims>(10, 20);
+ Tensor<T, NumDims, Layout> tensor(dims);
+
+ Index chip_dim = internal::random<int>(0, NumDims - 1);
+ Index chip_offset = internal::random<Index>(0, dims[chip_dim] - 2);
+
+ DSizes<Index, NumDims - 1> chipped_dims;
+ for (Index i = 0; i < chip_dim; ++i) {
+ chipped_dims[i] = dims[i];
+ }
+ for (Index i = chip_dim + 1; i < NumDims; ++i) {
+ chipped_dims[i - 1] = dims[i];
+ }
+
+ TensorMap<Tensor<T, NumDims, Layout>> map(tensor.data(), dims);
+
+ VerifyBlockAssignment<T, NumDims, Layout, NumDims - 1>(
+ tensor, map.chip(chip_offset, chip_dim),
+ [&chipped_dims]() { return RandomBlock<Layout>(chipped_dims, 1, 10); });
+
+ VerifyBlockAssignment<T, NumDims, Layout, NumDims - 1>(
+ tensor, map.chip(chip_offset, chip_dim),
+ [&chipped_dims]() { return SkewedInnerBlock<Layout>(chipped_dims); });
+
+ VerifyBlockAssignment<T, NumDims, Layout, NumDims - 1>(
+ tensor, map.chip(chip_offset, chip_dim),
+ [&chipped_dims]() { return FixedSizeBlock(chipped_dims); });
+}
+
+template <typename T, int NumDims, int Layout>
+static void test_assign_to_tensor_slice() {
+ DSizes<Index, NumDims> dims = RandomDims<NumDims>(10, 20);
+ Tensor<T, NumDims, Layout> tensor(dims);
+
+ // Pick a random slice of tensor.
+ DSizes<Index, NumDims> slice_start = RandomDims<NumDims>(5, 10);
+ DSizes<Index, NumDims> slice_size = RandomDims<NumDims>(5, 10);
+
+ // Make sure that slice start + size do not overflow tensor dims.
+ for (int i = 0; i < NumDims; ++i) {
+ slice_start[i] = numext::mini(dims[i] - 1, slice_start[i]);
+ slice_size[i] = numext::mini(slice_size[i], dims[i] - slice_start[i]);
+ }
+
+ TensorMap<Tensor<T, NumDims, Layout>> map(tensor.data(), dims);
+
+ VerifyBlockAssignment<T, NumDims, Layout>(
+ tensor, map.slice(slice_start, slice_size),
+ [&slice_size]() { return RandomBlock<Layout>(slice_size, 1, 10); });
+
+ VerifyBlockAssignment<T, NumDims, Layout>(
+ tensor, map.slice(slice_start, slice_size),
+ [&slice_size]() { return SkewedInnerBlock<Layout>(slice_size); });
+
+ VerifyBlockAssignment<T, NumDims, Layout>(
+ tensor, map.slice(slice_start, slice_size),
+ [&slice_size]() { return FixedSizeBlock(slice_size); });
+}
+
+template <typename T, int NumDims, int Layout>
+static void test_assign_to_tensor_shuffle() {
+ DSizes<Index, NumDims> dims = RandomDims<NumDims>(5, 15);
+ Tensor<T, NumDims, Layout> tensor(dims);
+
+ DSizes<Index, NumDims> shuffle;
+ for (int i = 0; i < NumDims; ++i) shuffle[i] = i;
+
+ TensorMap<Tensor<T, NumDims, Layout>> map(tensor.data(), dims);
+
+ do {
+ DSizes<Index, NumDims> shuffled_dims;
+ for (int i = 0; i < NumDims; ++i) shuffled_dims[i] = dims[shuffle[i]];
+
+ VerifyBlockAssignment<T, NumDims, Layout>(
+ tensor, map.shuffle(shuffle),
+ [&shuffled_dims]() { return FixedSizeBlock(shuffled_dims); });
+
+ VerifyBlockAssignment<T, NumDims, Layout>(
+ tensor, map.shuffle(shuffle), [&shuffled_dims]() {
+ return RandomBlock<Layout>(shuffled_dims, 1, 5);
+ });
+
+ } while (std::next_permutation(&shuffle[0], &shuffle[0] + NumDims));
+}
+
+// -------------------------------------------------------------------------- //
+
+#define CALL_SUBTEST_PART(PART) \
+ CALL_SUBTEST_##PART
+
+#define CALL_SUBTESTS_DIMS_LAYOUTS_TYPES(PART, NAME) \
+ CALL_SUBTEST_PART(PART)((NAME<float, 1, RowMajor>())); \
+ CALL_SUBTEST_PART(PART)((NAME<float, 2, RowMajor>())); \
+ CALL_SUBTEST_PART(PART)((NAME<float, 3, RowMajor>())); \
+ CALL_SUBTEST_PART(PART)((NAME<float, 4, RowMajor>())); \
+ CALL_SUBTEST_PART(PART)((NAME<float, 5, RowMajor>())); \
+ CALL_SUBTEST_PART(PART)((NAME<float, 1, ColMajor>())); \
+ CALL_SUBTEST_PART(PART)((NAME<float, 2, ColMajor>())); \
+ CALL_SUBTEST_PART(PART)((NAME<float, 4, ColMajor>())); \
+ CALL_SUBTEST_PART(PART)((NAME<float, 4, ColMajor>())); \
+ CALL_SUBTEST_PART(PART)((NAME<float, 5, ColMajor>())); \
+ CALL_SUBTEST_PART(PART)((NAME<int, 1, RowMajor>())); \
+ CALL_SUBTEST_PART(PART)((NAME<int, 2, RowMajor>())); \
+ CALL_SUBTEST_PART(PART)((NAME<int, 3, RowMajor>())); \
+ CALL_SUBTEST_PART(PART)((NAME<int, 4, RowMajor>())); \
+ CALL_SUBTEST_PART(PART)((NAME<int, 5, RowMajor>())); \
+ CALL_SUBTEST_PART(PART)((NAME<int, 1, ColMajor>())); \
+ CALL_SUBTEST_PART(PART)((NAME<int, 2, ColMajor>())); \
+ CALL_SUBTEST_PART(PART)((NAME<int, 4, ColMajor>())); \
+ CALL_SUBTEST_PART(PART)((NAME<int, 4, ColMajor>())); \
+ CALL_SUBTEST_PART(PART)((NAME<int, 5, ColMajor>())); \
+ CALL_SUBTEST_PART(PART)((NAME<bool, 1, RowMajor>())); \
+ CALL_SUBTEST_PART(PART)((NAME<bool, 2, RowMajor>())); \
+ CALL_SUBTEST_PART(PART)((NAME<bool, 3, RowMajor>())); \
+ CALL_SUBTEST_PART(PART)((NAME<bool, 4, RowMajor>())); \
+ CALL_SUBTEST_PART(PART)((NAME<bool, 5, RowMajor>())); \
+ CALL_SUBTEST_PART(PART)((NAME<bool, 1, ColMajor>())); \
+ CALL_SUBTEST_PART(PART)((NAME<bool, 2, ColMajor>())); \
+ CALL_SUBTEST_PART(PART)((NAME<bool, 4, ColMajor>())); \
+ CALL_SUBTEST_PART(PART)((NAME<bool, 4, ColMajor>())); \
+ CALL_SUBTEST_PART(PART)((NAME<bool, 5, ColMajor>()))
+
+#define CALL_SUBTESTS_DIMS_LAYOUTS(PART, NAME) \
+ CALL_SUBTEST_PART(PART)((NAME<float, 1, RowMajor>())); \
+ CALL_SUBTEST_PART(PART)((NAME<float, 2, RowMajor>())); \
+ CALL_SUBTEST_PART(PART)((NAME<float, 3, RowMajor>())); \
+ CALL_SUBTEST_PART(PART)((NAME<float, 4, RowMajor>())); \
+ CALL_SUBTEST_PART(PART)((NAME<float, 5, RowMajor>())); \
+ CALL_SUBTEST_PART(PART)((NAME<float, 1, ColMajor>())); \
+ CALL_SUBTEST_PART(PART)((NAME<float, 2, ColMajor>())); \
+ CALL_SUBTEST_PART(PART)((NAME<float, 4, ColMajor>())); \
+ CALL_SUBTEST_PART(PART)((NAME<float, 4, ColMajor>())); \
+ CALL_SUBTEST_PART(PART)((NAME<float, 5, ColMajor>()))
+
+#define CALL_SUBTESTS_LAYOUTS_TYPES(PART, NAME) \
+ CALL_SUBTEST_PART(PART)((NAME<float, RowMajor>())); \
+ CALL_SUBTEST_PART(PART)((NAME<float, ColMajor>())); \
+ CALL_SUBTEST_PART(PART)((NAME<bool, RowMajor>())); \
+ CALL_SUBTEST_PART(PART)((NAME<bool, ColMajor>()))
+
+EIGEN_DECLARE_TEST(cxx11_tensor_block_eval) {
+ // clang-format off
+ CALL_SUBTESTS_DIMS_LAYOUTS_TYPES(1, test_eval_tensor_block);
+ CALL_SUBTESTS_DIMS_LAYOUTS_TYPES(1, test_eval_tensor_binary_expr_block);
+ CALL_SUBTESTS_DIMS_LAYOUTS(1, test_eval_tensor_unary_expr_block);
+ CALL_SUBTESTS_DIMS_LAYOUTS(2, test_eval_tensor_binary_with_unary_expr_block);
+ CALL_SUBTESTS_DIMS_LAYOUTS_TYPES(2, test_eval_tensor_broadcast);
+ CALL_SUBTESTS_DIMS_LAYOUTS_TYPES(2, test_eval_tensor_reshape);
+ CALL_SUBTESTS_DIMS_LAYOUTS_TYPES(3, test_eval_tensor_cast);
+ CALL_SUBTESTS_DIMS_LAYOUTS_TYPES(3, test_eval_tensor_select);
+ CALL_SUBTESTS_DIMS_LAYOUTS_TYPES(3, test_eval_tensor_padding);
+ CALL_SUBTESTS_DIMS_LAYOUTS_TYPES(4, test_eval_tensor_chipping);
+ CALL_SUBTESTS_DIMS_LAYOUTS_TYPES(4, test_eval_tensor_generator);
+ CALL_SUBTESTS_DIMS_LAYOUTS_TYPES(4, test_eval_tensor_reverse);
+ CALL_SUBTESTS_DIMS_LAYOUTS_TYPES(5, test_eval_tensor_slice);
+ CALL_SUBTESTS_DIMS_LAYOUTS_TYPES(5, test_eval_tensor_shuffle);
+
+ CALL_SUBTESTS_LAYOUTS_TYPES(6, test_eval_tensor_reshape_with_bcast);
+ CALL_SUBTESTS_LAYOUTS_TYPES(6, test_eval_tensor_forced_eval);
+ CALL_SUBTESTS_LAYOUTS_TYPES(6, test_eval_tensor_chipping_of_bcast);
+
+ CALL_SUBTESTS_DIMS_LAYOUTS_TYPES(7, test_assign_to_tensor);
+ CALL_SUBTESTS_DIMS_LAYOUTS_TYPES(7, test_assign_to_tensor_reshape);
+ CALL_SUBTESTS_DIMS_LAYOUTS_TYPES(7, test_assign_to_tensor_chipping);
+ CALL_SUBTESTS_DIMS_LAYOUTS_TYPES(8, test_assign_to_tensor_slice);
+ CALL_SUBTESTS_DIMS_LAYOUTS_TYPES(8, test_assign_to_tensor_shuffle);
+
+ // Force CMake to split this test.
+ // EIGEN_SUFFIXES;1;2;3;4;5;6;7;8
+
+ // clang-format on
+}
diff --git a/unsupported/test/cxx11_tensor_block_io.cpp b/unsupported/test/cxx11_tensor_block_io.cpp
new file mode 100644
index 0000000..52f7dde
--- /dev/null
+++ b/unsupported/test/cxx11_tensor_block_io.cpp
@@ -0,0 +1,445 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+// clang-format off
+#include "main.h"
+#include <Eigen/CXX11/Tensor>
+// clang-format on
+
+// -------------------------------------------------------------------------- //
+// A set of tests for TensorBlockIO: copying data between tensor blocks.
+
+template <int NumDims>
+static DSizes<Index, NumDims> RandomDims(Index min, Index max) {
+ DSizes<Index, NumDims> dims;
+ for (int i = 0; i < NumDims; ++i) {
+ dims[i] = internal::random<Index>(min, max);
+ }
+ return DSizes<Index, NumDims>(dims);
+}
+
+static internal::TensorBlockShapeType RandomBlockShape() {
+ return internal::random<bool>()
+ ? internal::TensorBlockShapeType::kUniformAllDims
+ : internal::TensorBlockShapeType::kSkewedInnerDims;
+}
+
+template <int NumDims>
+static size_t RandomTargetBlockSize(const DSizes<Index, NumDims>& dims) {
+ return internal::random<size_t>(1, dims.TotalSize());
+}
+
+template <int Layout, int NumDims>
+static Index GetInputIndex(Index output_index,
+ const array<Index, NumDims>& output_to_input_dim_map,
+ const array<Index, NumDims>& input_strides,
+ const array<Index, NumDims>& output_strides) {
+ int input_index = 0;
+ if (Layout == ColMajor) {
+ for (int i = NumDims - 1; i > 0; --i) {
+ const Index idx = output_index / output_strides[i];
+ input_index += idx * input_strides[output_to_input_dim_map[i]];
+ output_index -= idx * output_strides[i];
+ }
+ return input_index +
+ output_index * input_strides[output_to_input_dim_map[0]];
+ } else {
+ for (int i = 0; i < NumDims - 1; ++i) {
+ const Index idx = output_index / output_strides[i];
+ input_index += idx * input_strides[output_to_input_dim_map[i]];
+ output_index -= idx * output_strides[i];
+ }
+ return input_index +
+ output_index * input_strides[output_to_input_dim_map[NumDims - 1]];
+ }
+}
+
+template <typename T, int NumDims, int Layout>
+static void test_block_io_copy_data_from_source_to_target() {
+ using TensorBlockIO = internal::TensorBlockIO<T, Index, NumDims, Layout>;
+ using IODst = typename TensorBlockIO::Dst;
+ using IOSrc = typename TensorBlockIO::Src;
+
+ // Generate a random input Tensor.
+ DSizes<Index, NumDims> dims = RandomDims<NumDims>(1, 30);
+ Tensor<T, NumDims, Layout> input(dims);
+ input.setRandom();
+
+ // Write data to an output Tensor.
+ Tensor<T, NumDims, Layout> output(dims);
+
+ // Construct a tensor block mapper.
+ using TensorBlockMapper =
+ internal::TensorBlockMapper<NumDims, Layout, Index>;
+ TensorBlockMapper block_mapper(
+ dims, {RandomBlockShape(), RandomTargetBlockSize(dims), {0, 0, 0}});
+
+ // We will copy data from input to output through this buffer.
+ Tensor<T, NumDims, Layout> block(block_mapper.blockDimensions());
+
+ // Precompute strides for TensorBlockIO::Copy.
+ auto input_strides = internal::strides<Layout>(dims);
+ auto output_strides = internal::strides<Layout>(dims);
+
+ const T* input_data = input.data();
+ T* output_data = output.data();
+ T* block_data = block.data();
+
+ for (int i = 0; i < block_mapper.blockCount(); ++i) {
+ auto desc = block_mapper.blockDescriptor(i);
+
+ auto blk_dims = desc.dimensions();
+ auto blk_strides = internal::strides<Layout>(blk_dims);
+
+ {
+ // Read from input into a block buffer.
+ IODst dst(blk_dims, blk_strides, block_data, 0);
+ IOSrc src(input_strides, input_data, desc.offset());
+
+ TensorBlockIO::Copy(dst, src);
+ }
+
+ {
+ // Write from block buffer to output.
+ IODst dst(blk_dims, output_strides, output_data, desc.offset());
+ IOSrc src(blk_strides, block_data, 0);
+
+ TensorBlockIO::Copy(dst, src);
+ }
+ }
+
+ for (int i = 0; i < dims.TotalSize(); ++i) {
+ VERIFY_IS_EQUAL(input_data[i], output_data[i]);
+ }
+}
+
+template <typename T, int NumDims, int Layout>
+static void test_block_io_copy_using_reordered_dimensions() {
+ // Generate a random input Tensor.
+ DSizes<Index, NumDims> dims = RandomDims<NumDims>(1, 30);
+ Tensor<T, NumDims, Layout> input(dims);
+ input.setRandom();
+
+ // Create a random dimension re-ordering/shuffle.
+ std::vector<int> shuffle;
+
+ for (int i = 0; i < NumDims; ++i) shuffle.push_back(i);
+ std::shuffle(shuffle.begin(), shuffle.end(), std::mt19937(g_seed));
+
+ DSizes<Index, NumDims> output_tensor_dims;
+ DSizes<Index, NumDims> input_to_output_dim_map;
+ DSizes<Index, NumDims> output_to_input_dim_map;
+ for (Index i = 0; i < NumDims; ++i) {
+ output_tensor_dims[shuffle[i]] = dims[i];
+ input_to_output_dim_map[i] = shuffle[i];
+ output_to_input_dim_map[shuffle[i]] = i;
+ }
+
+ // Write data to an output Tensor.
+ Tensor<T, NumDims, Layout> output(output_tensor_dims);
+
+ // Construct a tensor block mapper.
+ // NOTE: Tensor block mapper works with shuffled dimensions.
+ using TensorBlockMapper =
+ internal::TensorBlockMapper<NumDims, Layout, Index>;
+ TensorBlockMapper block_mapper(output_tensor_dims,
+ {RandomBlockShape(),
+ RandomTargetBlockSize(output_tensor_dims),
+ {0, 0, 0}});
+
+ // We will copy data from input to output through this buffer.
+ Tensor<T, NumDims, Layout> block(block_mapper.blockDimensions());
+
+ // Precompute strides for TensorBlockIO::Copy.
+ auto input_strides = internal::strides<Layout>(dims);
+ auto output_strides = internal::strides<Layout>(output_tensor_dims);
+
+ const T* input_data = input.data();
+ T* output_data = output.data();
+ T* block_data = block.data();
+
+ for (Index i = 0; i < block_mapper.blockCount(); ++i) {
+ auto desc = block_mapper.blockDescriptor(i);
+
+ const Index first_coeff_index = GetInputIndex<Layout, NumDims>(
+ desc.offset(), output_to_input_dim_map, input_strides,
+ output_strides);
+
+ // NOTE: Block dimensions are in the same order as output dimensions.
+
+ using TensorBlockIO = internal::TensorBlockIO<T, Index, NumDims, Layout>;
+ using IODst = typename TensorBlockIO::Dst;
+ using IOSrc = typename TensorBlockIO::Src;
+
+ auto blk_dims = desc.dimensions();
+ auto blk_strides = internal::strides<Layout>(blk_dims);
+
+ {
+ // Read from input into a block buffer.
+ IODst dst(blk_dims, blk_strides, block_data, 0);
+ IOSrc src(input_strides, input_data, first_coeff_index);
+
+ // TODO(ezhulenev): Remove when fully switched to TensorBlock.
+ DSizes<int, NumDims> dim_map;
+ for (int j = 0; j < NumDims; ++j)
+ dim_map[j] = static_cast<int>(output_to_input_dim_map[j]);
+ TensorBlockIO::Copy(dst, src, /*dst_to_src_dim_map=*/dim_map);
+ }
+
+ {
+ // We need to convert block dimensions from output to input order.
+ auto dst_dims = blk_dims;
+ for (int out_dim = 0; out_dim < NumDims; ++out_dim) {
+ dst_dims[output_to_input_dim_map[out_dim]] = blk_dims[out_dim];
+ }
+
+ // Write from block buffer to output.
+ IODst dst(dst_dims, input_strides, output_data, first_coeff_index);
+ IOSrc src(blk_strides, block_data, 0);
+
+ // TODO(ezhulenev): Remove when fully switched to TensorBlock.
+ DSizes<int, NumDims> dim_map;
+ for (int j = 0; j < NumDims; ++j)
+ dim_map[j] = static_cast<int>(input_to_output_dim_map[j]);
+ TensorBlockIO::Copy(dst, src, /*dst_to_src_dim_map=*/dim_map);
+ }
+ }
+
+ for (Index i = 0; i < dims.TotalSize(); ++i) {
+ VERIFY_IS_EQUAL(input_data[i], output_data[i]);
+ }
+}
+
+// This is the special case for reading data with reordering, when dimensions
+// before/after reordering are the same. Squeezing reads along inner dimensions
+// in this case is illegal, because we reorder innermost dimension.
+template <int Layout>
+static void test_block_io_copy_using_reordered_dimensions_do_not_squeeze() {
+ DSizes<Index, 3> tensor_dims(7, 9, 7);
+ DSizes<Index, 3> block_dims = tensor_dims;
+
+ DSizes<int, 3> block_to_tensor_dim;
+ block_to_tensor_dim[0] = 2;
+ block_to_tensor_dim[1] = 1;
+ block_to_tensor_dim[2] = 0;
+
+ auto tensor_strides = internal::strides<Layout>(tensor_dims);
+ auto block_strides = internal::strides<Layout>(block_dims);
+
+ Tensor<float, 3, Layout> block(block_dims);
+ Tensor<float, 3, Layout> tensor(tensor_dims);
+ tensor.setRandom();
+
+ float* tensor_data = tensor.data();
+ float* block_data = block.data();
+
+ using TensorBlockIO = internal::TensorBlockIO<float, Index, 3, Layout>;
+ using IODst = typename TensorBlockIO::Dst;
+ using IOSrc = typename TensorBlockIO::Src;
+
+ // Read from a tensor into a block.
+ IODst dst(block_dims, block_strides, block_data, 0);
+ IOSrc src(tensor_strides, tensor_data, 0);
+
+ TensorBlockIO::Copy(dst, src, /*dst_to_src_dim_map=*/block_to_tensor_dim);
+
+ TensorMap<Tensor<float, 3, Layout> > block_tensor(block_data, block_dims);
+ TensorMap<Tensor<float, 3, Layout> > tensor_tensor(tensor_data, tensor_dims);
+
+ for (Index d0 = 0; d0 < tensor_dims[0]; ++d0) {
+ for (Index d1 = 0; d1 < tensor_dims[1]; ++d1) {
+ for (Index d2 = 0; d2 < tensor_dims[2]; ++d2) {
+ float block_value = block_tensor(d2, d1, d0);
+ float tensor_value = tensor_tensor(d0, d1, d2);
+ VERIFY_IS_EQUAL(block_value, tensor_value);
+ }
+ }
+ }
+}
+
+// This is the special case for reading data with reordering, when dimensions
+// before/after reordering are the same. Squeezing reads in this case is allowed
+// because we reorder outer dimensions.
+template <int Layout>
+static void test_block_io_copy_using_reordered_dimensions_squeeze() {
+ DSizes<Index, 4> tensor_dims(7, 5, 9, 9);
+ DSizes<Index, 4> block_dims = tensor_dims;
+
+ DSizes<int, 4> block_to_tensor_dim;
+ block_to_tensor_dim[0] = 0;
+ block_to_tensor_dim[1] = 1;
+ block_to_tensor_dim[2] = 3;
+ block_to_tensor_dim[3] = 2;
+
+ auto tensor_strides = internal::strides<Layout>(tensor_dims);
+ auto block_strides = internal::strides<Layout>(block_dims);
+
+ Tensor<float, 4, Layout> block(block_dims);
+ Tensor<float, 4, Layout> tensor(tensor_dims);
+ tensor.setRandom();
+
+ float* tensor_data = tensor.data();
+ float* block_data = block.data();
+
+ using TensorBlockIO = internal::TensorBlockIO<float, Index, 4, Layout>;
+ using IODst = typename TensorBlockIO::Dst;
+ using IOSrc = typename TensorBlockIO::Src;
+
+ // Read from a tensor into a block.
+ IODst dst(block_dims, block_strides, block_data, 0);
+ IOSrc src(tensor_strides, tensor_data, 0);
+
+ TensorBlockIO::Copy(dst, src, /*dst_to_src_dim_map=*/block_to_tensor_dim);
+
+ TensorMap<Tensor<float, 4, Layout> > block_tensor(block_data, block_dims);
+ TensorMap<Tensor<float, 4, Layout> > tensor_tensor(tensor_data, tensor_dims);
+
+ for (Index d0 = 0; d0 < tensor_dims[0]; ++d0) {
+ for (Index d1 = 0; d1 < tensor_dims[1]; ++d1) {
+ for (Index d2 = 0; d2 < tensor_dims[2]; ++d2) {
+ for (Index d3 = 0; d3 < tensor_dims[3]; ++d3) {
+ float block_value = block_tensor(d0, d1, d3, d2);
+ float tensor_value = tensor_tensor(d0, d1, d2, d3);
+ VERIFY_IS_EQUAL(block_value, tensor_value);
+ }
+ }
+ }
+ }
+}
+
+template <int Layout>
+static void test_block_io_zero_stride() {
+ DSizes<Index, 5> rnd_dims = RandomDims<5>(1, 30);
+
+ DSizes<Index, 5> input_tensor_dims = rnd_dims;
+ input_tensor_dims[0] = 1;
+ input_tensor_dims[2] = 1;
+ input_tensor_dims[4] = 1;
+
+ Tensor<float, 5, Layout> input(input_tensor_dims);
+ input.setRandom();
+
+ DSizes<Index, 5> output_tensor_dims = rnd_dims;
+
+ auto input_tensor_strides = internal::strides<Layout>(input_tensor_dims);
+ auto output_tensor_strides = internal::strides<Layout>(output_tensor_dims);
+
+ auto input_tensor_strides_with_zeros = input_tensor_strides;
+ input_tensor_strides_with_zeros[0] = 0;
+ input_tensor_strides_with_zeros[2] = 0;
+ input_tensor_strides_with_zeros[4] = 0;
+
+ Tensor<float, 5, Layout> output(output_tensor_dims);
+ output.setRandom();
+
+ using TensorBlockIO = internal::TensorBlockIO<float, Index, 5, Layout>;
+ using IODst = typename TensorBlockIO::Dst;
+ using IOSrc = typename TensorBlockIO::Src;
+
+ // Write data from input to output with broadcasting in dims [0, 2, 4].
+ IODst dst(output_tensor_dims, output_tensor_strides, output.data(), 0);
+ IOSrc src(input_tensor_strides_with_zeros, input.data(), 0);
+ TensorBlockIO::Copy(dst, src);
+
+ for (int i = 0; i < output_tensor_dims[0]; ++i) {
+ for (int j = 0; j < output_tensor_dims[1]; ++j) {
+ for (int k = 0; k < output_tensor_dims[2]; ++k) {
+ for (int l = 0; l < output_tensor_dims[3]; ++l) {
+ for (int m = 0; m < output_tensor_dims[4]; ++m) {
+ float input_value = input(0, j, 0, l, 0);
+ float output_value = output(i, j, k, l, m);
+ VERIFY_IS_EQUAL(input_value, output_value);
+ }
+ }
+ }
+ }
+ }
+}
+
+template <int Layout>
+static void test_block_io_squeeze_ones() {
+ using TensorBlockIO = internal::TensorBlockIO<float, Index, 5, Layout>;
+ using IODst = typename TensorBlockIO::Dst;
+ using IOSrc = typename TensorBlockIO::Src;
+
+ // Total size > 1.
+ {
+ DSizes<Index, 5> block_sizes(1, 2, 1, 2, 1);
+ auto strides = internal::strides<Layout>(block_sizes);
+
+ // Create a random input tensor.
+ Tensor<float, 5> input(block_sizes);
+ input.setRandom();
+
+ Tensor<float, 5> output(block_sizes);
+
+ IODst dst(block_sizes, strides, output.data(), 0);
+ IOSrc src(strides, input.data());
+ TensorBlockIO::Copy(dst, src);
+
+ for (Index i = 0; i < block_sizes.TotalSize(); ++i) {
+ VERIFY_IS_EQUAL(output.data()[i], input.data()[i]);
+ }
+ }
+
+ // Total size == 1.
+ {
+ DSizes<Index, 5> block_sizes(1, 1, 1, 1, 1);
+ auto strides = internal::strides<Layout>(block_sizes);
+
+ // Create a random input tensor.
+ Tensor<float, 5> input(block_sizes);
+ input.setRandom();
+
+ Tensor<float, 5> output(block_sizes);
+
+ IODst dst(block_sizes, strides, output.data(), 0);
+ IOSrc src(strides, input.data());
+ TensorBlockIO::Copy(dst, src);
+
+ for (Index i = 0; i < block_sizes.TotalSize(); ++i) {
+ VERIFY_IS_EQUAL(output.data()[i], input.data()[i]);
+ }
+ }
+}
+
+#define CALL_SUBTESTS(NAME) \
+ CALL_SUBTEST((NAME<float, 1, RowMajor>())); \
+ CALL_SUBTEST((NAME<float, 2, RowMajor>())); \
+ CALL_SUBTEST((NAME<float, 4, RowMajor>())); \
+ CALL_SUBTEST((NAME<float, 5, RowMajor>())); \
+ CALL_SUBTEST((NAME<float, 1, ColMajor>())); \
+ CALL_SUBTEST((NAME<float, 2, ColMajor>())); \
+ CALL_SUBTEST((NAME<float, 4, ColMajor>())); \
+ CALL_SUBTEST((NAME<float, 5, ColMajor>())); \
+ CALL_SUBTEST((NAME<bool, 1, RowMajor>())); \
+ CALL_SUBTEST((NAME<bool, 2, RowMajor>())); \
+ CALL_SUBTEST((NAME<bool, 4, RowMajor>())); \
+ CALL_SUBTEST((NAME<bool, 5, RowMajor>())); \
+ CALL_SUBTEST((NAME<bool, 1, ColMajor>())); \
+ CALL_SUBTEST((NAME<bool, 2, ColMajor>())); \
+ CALL_SUBTEST((NAME<bool, 4, ColMajor>())); \
+ CALL_SUBTEST((NAME<bool, 5, ColMajor>()))
+
+EIGEN_DECLARE_TEST(cxx11_tensor_block_io) {
+ // clang-format off
+ CALL_SUBTESTS(test_block_io_copy_data_from_source_to_target);
+ CALL_SUBTESTS(test_block_io_copy_using_reordered_dimensions);
+
+ CALL_SUBTEST(test_block_io_copy_using_reordered_dimensions_do_not_squeeze<RowMajor>());
+ CALL_SUBTEST(test_block_io_copy_using_reordered_dimensions_do_not_squeeze<ColMajor>());
+
+ CALL_SUBTEST(test_block_io_copy_using_reordered_dimensions_squeeze<RowMajor>());
+ CALL_SUBTEST(test_block_io_copy_using_reordered_dimensions_squeeze<ColMajor>());
+
+ CALL_SUBTEST(test_block_io_zero_stride<RowMajor>());
+ CALL_SUBTEST(test_block_io_zero_stride<ColMajor>());
+
+ CALL_SUBTEST(test_block_io_squeeze_ones<RowMajor>());
+ CALL_SUBTEST(test_block_io_squeeze_ones<ColMajor>());
+ // clang-format on
+}
diff --git a/unsupported/test/cxx11_tensor_broadcast_sycl.cpp b/unsupported/test/cxx11_tensor_broadcast_sycl.cpp
new file mode 100644
index 0000000..20f84b8
--- /dev/null
+++ b/unsupported/test/cxx11_tensor_broadcast_sycl.cpp
@@ -0,0 +1,144 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2016
+// Mehdi Goli Codeplay Software Ltd.
+// Ralph Potter Codeplay Software Ltd.
+// Luke Iwanski Codeplay Software Ltd.
+// Contact: <eigen@codeplay.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#define EIGEN_TEST_NO_LONGDOUBLE
+#define EIGEN_TEST_NO_COMPLEX
+
+#define EIGEN_DEFAULT_DENSE_INDEX_TYPE int64_t
+#define EIGEN_USE_SYCL
+
+#include "main.h"
+#include <unsupported/Eigen/CXX11/Tensor>
+
+using Eigen::array;
+using Eigen::SyclDevice;
+using Eigen::Tensor;
+using Eigen::TensorMap;
+
+template <typename DataType, int DataLayout, typename IndexType>
+static void test_broadcast_sycl_fixed(const Eigen::SyclDevice &sycl_device){
+
+ // BROADCAST test:
+ IndexType inDim1=2;
+ IndexType inDim2=3;
+ IndexType inDim3=5;
+ IndexType inDim4=7;
+ IndexType bDim1=2;
+ IndexType bDim2=3;
+ IndexType bDim3=1;
+ IndexType bDim4=4;
+ array<IndexType, 4> in_range = {{inDim1, inDim2, inDim3, inDim4}};
+ array<IndexType, 4> broadcasts = {{bDim1, bDim2, bDim3, bDim4}};
+ array<IndexType, 4> out_range; // = in_range * broadcasts
+ for (size_t i = 0; i < out_range.size(); ++i)
+ out_range[i] = in_range[i] * broadcasts[i];
+
+ Tensor<DataType, 4, DataLayout, IndexType> input(in_range);
+ Tensor<DataType, 4, DataLayout, IndexType> out(out_range);
+
+ for (size_t i = 0; i < in_range.size(); ++i)
+ VERIFY_IS_EQUAL(out.dimension(i), out_range[i]);
+
+
+ for (IndexType i = 0; i < input.size(); ++i)
+ input(i) = static_cast<DataType>(i);
+
+ DataType * gpu_in_data = static_cast<DataType*>(sycl_device.allocate(input.dimensions().TotalSize()*sizeof(DataType)));
+ DataType * gpu_out_data = static_cast<DataType*>(sycl_device.allocate(out.dimensions().TotalSize()*sizeof(DataType)));
+
+ TensorMap<TensorFixedSize<DataType, Sizes<2, 3, 5, 7>, DataLayout, IndexType>> gpu_in(gpu_in_data, in_range);
+ TensorMap<Tensor<DataType, 4, DataLayout, IndexType>> gpu_out(gpu_out_data, out_range);
+ sycl_device.memcpyHostToDevice(gpu_in_data, input.data(),(input.dimensions().TotalSize())*sizeof(DataType));
+ gpu_out.device(sycl_device) = gpu_in.broadcast(broadcasts);
+ sycl_device.memcpyDeviceToHost(out.data(), gpu_out_data,(out.dimensions().TotalSize())*sizeof(DataType));
+
+ for (IndexType i = 0; i < inDim1*bDim1; ++i) {
+ for (IndexType j = 0; j < inDim2*bDim2; ++j) {
+ for (IndexType k = 0; k < inDim3*bDim3; ++k) {
+ for (IndexType l = 0; l < inDim4*bDim4; ++l) {
+ VERIFY_IS_APPROX(input(i%2,j%3,k%5,l%7), out(i,j,k,l));
+ }
+ }
+ }
+ }
+ printf("Broadcast Test with fixed size Passed\n");
+ sycl_device.deallocate(gpu_in_data);
+ sycl_device.deallocate(gpu_out_data);
+}
+
+template <typename DataType, int DataLayout, typename IndexType>
+static void test_broadcast_sycl(const Eigen::SyclDevice &sycl_device){
+
+ // BROADCAST test:
+ IndexType inDim1=2;
+ IndexType inDim2=3;
+ IndexType inDim3=5;
+ IndexType inDim4=7;
+ IndexType bDim1=2;
+ IndexType bDim2=3;
+ IndexType bDim3=1;
+ IndexType bDim4=4;
+ array<IndexType, 4> in_range = {{inDim1, inDim2, inDim3, inDim4}};
+ array<IndexType, 4> broadcasts = {{bDim1, bDim2, bDim3, bDim4}};
+ array<IndexType, 4> out_range; // = in_range * broadcasts
+ for (size_t i = 0; i < out_range.size(); ++i)
+ out_range[i] = in_range[i] * broadcasts[i];
+
+ Tensor<DataType, 4, DataLayout, IndexType> input(in_range);
+ Tensor<DataType, 4, DataLayout, IndexType> out(out_range);
+
+ for (size_t i = 0; i < in_range.size(); ++i)
+ VERIFY_IS_EQUAL(out.dimension(i), out_range[i]);
+
+
+ for (IndexType i = 0; i < input.size(); ++i)
+ input(i) = static_cast<DataType>(i);
+
+ DataType * gpu_in_data = static_cast<DataType*>(sycl_device.allocate(input.dimensions().TotalSize()*sizeof(DataType)));
+ DataType * gpu_out_data = static_cast<DataType*>(sycl_device.allocate(out.dimensions().TotalSize()*sizeof(DataType)));
+
+ TensorMap<Tensor<DataType, 4, DataLayout, IndexType>> gpu_in(gpu_in_data, in_range);
+ TensorMap<Tensor<DataType, 4, DataLayout, IndexType>> gpu_out(gpu_out_data, out_range);
+ sycl_device.memcpyHostToDevice(gpu_in_data, input.data(),(input.dimensions().TotalSize())*sizeof(DataType));
+ gpu_out.device(sycl_device) = gpu_in.broadcast(broadcasts);
+ sycl_device.memcpyDeviceToHost(out.data(), gpu_out_data,(out.dimensions().TotalSize())*sizeof(DataType));
+
+ for (IndexType i = 0; i < inDim1*bDim1; ++i) {
+ for (IndexType j = 0; j < inDim2*bDim2; ++j) {
+ for (IndexType k = 0; k < inDim3*bDim3; ++k) {
+ for (IndexType l = 0; l < inDim4*bDim4; ++l) {
+ VERIFY_IS_APPROX(input(i%inDim1,j%inDim2,k%inDim3,l%inDim4), out(i,j,k,l));
+ }
+ }
+ }
+ }
+ printf("Broadcast Test Passed\n");
+ sycl_device.deallocate(gpu_in_data);
+ sycl_device.deallocate(gpu_out_data);
+}
+
+template<typename DataType> void sycl_broadcast_test_per_device(const cl::sycl::device& d){
+ std::cout << "Running on " << d.template get_info<cl::sycl::info::device::name>() << std::endl;
+ QueueInterface queueInterface(d);
+ auto sycl_device = Eigen::SyclDevice(&queueInterface);
+ test_broadcast_sycl<DataType, RowMajor, int64_t>(sycl_device);
+ test_broadcast_sycl<DataType, ColMajor, int64_t>(sycl_device);
+ test_broadcast_sycl_fixed<DataType, RowMajor, int64_t>(sycl_device);
+ test_broadcast_sycl_fixed<DataType, ColMajor, int64_t>(sycl_device);
+}
+
+EIGEN_DECLARE_TEST(cxx11_tensor_broadcast_sycl) {
+ for (const auto& device :Eigen::get_sycl_supported_devices()) {
+ CALL_SUBTEST(sycl_broadcast_test_per_device<float>(device));
+ }
+}
diff --git a/unsupported/test/cxx11_tensor_broadcasting.cpp b/unsupported/test/cxx11_tensor_broadcasting.cpp
new file mode 100644
index 0000000..2da35e4
--- /dev/null
+++ b/unsupported/test/cxx11_tensor_broadcasting.cpp
@@ -0,0 +1,325 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "main.h"
+
+#include <Eigen/CXX11/Tensor>
+
+using Eigen::Tensor;
+
+template <int DataLayout>
+static void test_simple_broadcasting()
+{
+ Tensor<float, 4, DataLayout> tensor(2,3,5,7);
+ tensor.setRandom();
+ array<ptrdiff_t, 4> broadcasts;
+ broadcasts[0] = 1;
+ broadcasts[1] = 1;
+ broadcasts[2] = 1;
+ broadcasts[3] = 1;
+
+ Tensor<float, 4, DataLayout> no_broadcast;
+ no_broadcast = tensor.broadcast(broadcasts);
+
+ VERIFY_IS_EQUAL(no_broadcast.dimension(0), 2);
+ VERIFY_IS_EQUAL(no_broadcast.dimension(1), 3);
+ VERIFY_IS_EQUAL(no_broadcast.dimension(2), 5);
+ VERIFY_IS_EQUAL(no_broadcast.dimension(3), 7);
+
+ for (int i = 0; i < 2; ++i) {
+ for (int j = 0; j < 3; ++j) {
+ for (int k = 0; k < 5; ++k) {
+ for (int l = 0; l < 7; ++l) {
+ VERIFY_IS_EQUAL(tensor(i,j,k,l), no_broadcast(i,j,k,l));
+ }
+ }
+ }
+ }
+
+ broadcasts[0] = 2;
+ broadcasts[1] = 3;
+ broadcasts[2] = 1;
+ broadcasts[3] = 4;
+ Tensor<float, 4, DataLayout> broadcast;
+ broadcast = tensor.broadcast(broadcasts);
+
+ VERIFY_IS_EQUAL(broadcast.dimension(0), 4);
+ VERIFY_IS_EQUAL(broadcast.dimension(1), 9);
+ VERIFY_IS_EQUAL(broadcast.dimension(2), 5);
+ VERIFY_IS_EQUAL(broadcast.dimension(3), 28);
+
+ for (int i = 0; i < 4; ++i) {
+ for (int j = 0; j < 9; ++j) {
+ for (int k = 0; k < 5; ++k) {
+ for (int l = 0; l < 28; ++l) {
+ VERIFY_IS_EQUAL(tensor(i%2,j%3,k%5,l%7), broadcast(i,j,k,l));
+ }
+ }
+ }
+ }
+}
+
+
+template <int DataLayout>
+static void test_vectorized_broadcasting()
+{
+ Tensor<float, 3, DataLayout> tensor(8,3,5);
+ tensor.setRandom();
+ array<ptrdiff_t, 3> broadcasts;
+ broadcasts[0] = 2;
+ broadcasts[1] = 3;
+ broadcasts[2] = 4;
+
+ Tensor<float, 3, DataLayout> broadcast;
+ broadcast = tensor.broadcast(broadcasts);
+
+ VERIFY_IS_EQUAL(broadcast.dimension(0), 16);
+ VERIFY_IS_EQUAL(broadcast.dimension(1), 9);
+ VERIFY_IS_EQUAL(broadcast.dimension(2), 20);
+
+ for (int i = 0; i < 16; ++i) {
+ for (int j = 0; j < 9; ++j) {
+ for (int k = 0; k < 20; ++k) {
+ VERIFY_IS_EQUAL(tensor(i%8,j%3,k%5), broadcast(i,j,k));
+ }
+ }
+ }
+
+ tensor.resize(11,3,5);
+
+ tensor.setRandom();
+ broadcast = tensor.broadcast(broadcasts);
+
+ VERIFY_IS_EQUAL(broadcast.dimension(0), 22);
+ VERIFY_IS_EQUAL(broadcast.dimension(1), 9);
+ VERIFY_IS_EQUAL(broadcast.dimension(2), 20);
+
+ for (int i = 0; i < 22; ++i) {
+ for (int j = 0; j < 9; ++j) {
+ for (int k = 0; k < 20; ++k) {
+ VERIFY_IS_EQUAL(tensor(i%11,j%3,k%5), broadcast(i,j,k));
+ }
+ }
+ }
+}
+
+
+template <int DataLayout>
+static void test_static_broadcasting()
+{
+ Tensor<float, 3, DataLayout> tensor(8,3,5);
+ tensor.setRandom();
+
+ Eigen::IndexList<Eigen::type2index<2>, Eigen::type2index<3>, Eigen::type2index<4>> broadcasts;
+ Tensor<float, 3, DataLayout> broadcast;
+ broadcast = tensor.broadcast(broadcasts);
+
+ VERIFY_IS_EQUAL(broadcast.dimension(0), 16);
+ VERIFY_IS_EQUAL(broadcast.dimension(1), 9);
+ VERIFY_IS_EQUAL(broadcast.dimension(2), 20);
+
+ for (int i = 0; i < 16; ++i) {
+ for (int j = 0; j < 9; ++j) {
+ for (int k = 0; k < 20; ++k) {
+ VERIFY_IS_EQUAL(tensor(i%8,j%3,k%5), broadcast(i,j,k));
+ }
+ }
+ }
+
+ tensor.resize(11,3,5);
+
+ tensor.setRandom();
+ broadcast = tensor.broadcast(broadcasts);
+
+ VERIFY_IS_EQUAL(broadcast.dimension(0), 22);
+ VERIFY_IS_EQUAL(broadcast.dimension(1), 9);
+ VERIFY_IS_EQUAL(broadcast.dimension(2), 20);
+
+ for (int i = 0; i < 22; ++i) {
+ for (int j = 0; j < 9; ++j) {
+ for (int k = 0; k < 20; ++k) {
+ VERIFY_IS_EQUAL(tensor(i%11,j%3,k%5), broadcast(i,j,k));
+ }
+ }
+ }
+}
+
+
+template <int DataLayout>
+static void test_fixed_size_broadcasting()
+{
+ // Need to add a [] operator to the Size class for this to work
+#if 0
+ Tensor<float, 1, DataLayout> t1(10);
+ t1.setRandom();
+ TensorFixedSize<float, Sizes<1>, DataLayout> t2;
+ t2 = t2.constant(20.0f);
+
+ Tensor<float, 1, DataLayout> t3 = t1 + t2.broadcast(Eigen::array<int, 1>{{10}});
+ for (int i = 0; i < 10; ++i) {
+ VERIFY_IS_APPROX(t3(i), t1(i) + t2(0));
+ }
+
+ TensorMap<TensorFixedSize<float, Sizes<1>, DataLayout> > t4(t2.data(), {{1}});
+ Tensor<float, 1, DataLayout> t5 = t1 + t4.broadcast(Eigen::array<int, 1>{{10}});
+ for (int i = 0; i < 10; ++i) {
+ VERIFY_IS_APPROX(t5(i), t1(i) + t2(0));
+ }
+#endif
+}
+
+template <int DataLayout>
+static void test_simple_broadcasting_one_by_n()
+{
+ Tensor<float, 4, DataLayout> tensor(1,13,5,7);
+ tensor.setRandom();
+ array<ptrdiff_t, 4> broadcasts;
+ broadcasts[0] = 9;
+ broadcasts[1] = 1;
+ broadcasts[2] = 1;
+ broadcasts[3] = 1;
+ Tensor<float, 4, DataLayout> broadcast;
+ broadcast = tensor.broadcast(broadcasts);
+
+ VERIFY_IS_EQUAL(broadcast.dimension(0), 9);
+ VERIFY_IS_EQUAL(broadcast.dimension(1), 13);
+ VERIFY_IS_EQUAL(broadcast.dimension(2), 5);
+ VERIFY_IS_EQUAL(broadcast.dimension(3), 7);
+
+ for (int i = 0; i < 9; ++i) {
+ for (int j = 0; j < 13; ++j) {
+ for (int k = 0; k < 5; ++k) {
+ for (int l = 0; l < 7; ++l) {
+ VERIFY_IS_EQUAL(tensor(i%1,j%13,k%5,l%7), broadcast(i,j,k,l));
+ }
+ }
+ }
+ }
+}
+
+template <int DataLayout>
+static void test_simple_broadcasting_n_by_one()
+{
+ Tensor<float, 4, DataLayout> tensor(7,3,5,1);
+ tensor.setRandom();
+ array<ptrdiff_t, 4> broadcasts;
+ broadcasts[0] = 1;
+ broadcasts[1] = 1;
+ broadcasts[2] = 1;
+ broadcasts[3] = 19;
+ Tensor<float, 4, DataLayout> broadcast;
+ broadcast = tensor.broadcast(broadcasts);
+
+ VERIFY_IS_EQUAL(broadcast.dimension(0), 7);
+ VERIFY_IS_EQUAL(broadcast.dimension(1), 3);
+ VERIFY_IS_EQUAL(broadcast.dimension(2), 5);
+ VERIFY_IS_EQUAL(broadcast.dimension(3), 19);
+
+ for (int i = 0; i < 7; ++i) {
+ for (int j = 0; j < 3; ++j) {
+ for (int k = 0; k < 5; ++k) {
+ for (int l = 0; l < 19; ++l) {
+ VERIFY_IS_EQUAL(tensor(i%7,j%3,k%5,l%1), broadcast(i,j,k,l));
+ }
+ }
+ }
+ }
+}
+
+template <int DataLayout>
+static void test_size_one_broadcasting()
+{
+ Tensor<float, 1, DataLayout> tensor(1);
+ tensor.setRandom();
+ array<ptrdiff_t, 1> broadcasts = {64};
+ Tensor<float, 1, DataLayout> broadcast;
+ broadcast = tensor.broadcast(broadcasts);
+
+ VERIFY_IS_EQUAL(broadcast.dimension(0), broadcasts[0]);
+
+ for (int i = 0; i < broadcasts[0]; ++i) {
+ VERIFY_IS_EQUAL(tensor(0), broadcast(i));
+ }
+}
+
+template <int DataLayout>
+static void test_simple_broadcasting_one_by_n_by_one_1d()
+{
+ Tensor<float, 3, DataLayout> tensor(1,7,1);
+ tensor.setRandom();
+ array<ptrdiff_t, 3> broadcasts;
+ broadcasts[0] = 5;
+ broadcasts[1] = 1;
+ broadcasts[2] = 13;
+ Tensor<float, 3, DataLayout> broadcasted;
+ broadcasted = tensor.broadcast(broadcasts);
+
+ VERIFY_IS_EQUAL(broadcasted.dimension(0), 5);
+ VERIFY_IS_EQUAL(broadcasted.dimension(1), 7);
+ VERIFY_IS_EQUAL(broadcasted.dimension(2), 13);
+
+ for (int i = 0; i < 5; ++i) {
+ for (int j = 0; j < 7; ++j) {
+ for (int k = 0; k < 13; ++k) {
+ VERIFY_IS_EQUAL(tensor(0,j%7,0), broadcasted(i,j,k));
+ }
+ }
+ }
+}
+
+template <int DataLayout>
+static void test_simple_broadcasting_one_by_n_by_one_2d()
+{
+ Tensor<float, 4, DataLayout> tensor(1,7,13,1);
+ tensor.setRandom();
+ array<ptrdiff_t, 4> broadcasts;
+ broadcasts[0] = 5;
+ broadcasts[1] = 1;
+ broadcasts[2] = 1;
+ broadcasts[3] = 19;
+ Tensor<float, 4, DataLayout> broadcast;
+ broadcast = tensor.broadcast(broadcasts);
+
+ VERIFY_IS_EQUAL(broadcast.dimension(0), 5);
+ VERIFY_IS_EQUAL(broadcast.dimension(1), 7);
+ VERIFY_IS_EQUAL(broadcast.dimension(2), 13);
+ VERIFY_IS_EQUAL(broadcast.dimension(3), 19);
+
+ for (int i = 0; i < 5; ++i) {
+ for (int j = 0; j < 7; ++j) {
+ for (int k = 0; k < 13; ++k) {
+ for (int l = 0; l < 19; ++l) {
+ VERIFY_IS_EQUAL(tensor(0,j%7,k%13,0), broadcast(i,j,k,l));
+ }
+ }
+ }
+ }
+}
+
+EIGEN_DECLARE_TEST(cxx11_tensor_broadcasting)
+{
+ CALL_SUBTEST(test_simple_broadcasting<ColMajor>());
+ CALL_SUBTEST(test_simple_broadcasting<RowMajor>());
+ CALL_SUBTEST(test_vectorized_broadcasting<ColMajor>());
+ CALL_SUBTEST(test_vectorized_broadcasting<RowMajor>());
+ CALL_SUBTEST(test_static_broadcasting<ColMajor>());
+ CALL_SUBTEST(test_static_broadcasting<RowMajor>());
+ CALL_SUBTEST(test_fixed_size_broadcasting<ColMajor>());
+ CALL_SUBTEST(test_fixed_size_broadcasting<RowMajor>());
+ CALL_SUBTEST(test_simple_broadcasting_one_by_n<RowMajor>());
+ CALL_SUBTEST(test_simple_broadcasting_n_by_one<RowMajor>());
+ CALL_SUBTEST(test_simple_broadcasting_one_by_n<ColMajor>());
+ CALL_SUBTEST(test_simple_broadcasting_n_by_one<ColMajor>());
+ CALL_SUBTEST(test_simple_broadcasting_one_by_n_by_one_1d<ColMajor>());
+ CALL_SUBTEST(test_simple_broadcasting_one_by_n_by_one_2d<ColMajor>());
+ CALL_SUBTEST(test_simple_broadcasting_one_by_n_by_one_1d<RowMajor>());
+ CALL_SUBTEST(test_simple_broadcasting_one_by_n_by_one_2d<RowMajor>());
+ CALL_SUBTEST(test_size_one_broadcasting<ColMajor>());
+ CALL_SUBTEST(test_size_one_broadcasting<RowMajor>());
+}
diff --git a/unsupported/test/cxx11_tensor_builtins_sycl.cpp b/unsupported/test/cxx11_tensor_builtins_sycl.cpp
new file mode 100644
index 0000000..27a8254
--- /dev/null
+++ b/unsupported/test/cxx11_tensor_builtins_sycl.cpp
@@ -0,0 +1,355 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2016
+// Mehdi Goli Codeplay Software Ltd.
+// Ralph Potter Codeplay Software Ltd.
+// Luke Iwanski Codeplay Software Ltd.
+// Contact: <eigen@codeplay.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#define EIGEN_TEST_NO_LONGDOUBLE
+#define EIGEN_TEST_NO_COMPLEX
+
+#define EIGEN_DEFAULT_DENSE_INDEX_TYPE int64_t
+#define EIGEN_USE_SYCL
+
+#include "main.h"
+#include <unsupported/Eigen/CXX11/Tensor>
+
+using Eigen::array;
+using Eigen::SyclDevice;
+using Eigen::Tensor;
+using Eigen::TensorMap;
+
+// Functions used to compare the TensorMap implementation on the device with
+// the equivalent on the host
+namespace cl {
+namespace sycl {
+template <typename T> T abs(T x) { return cl::sycl::fabs(x); }
+template <typename T> T square(T x) { return x * x; }
+template <typename T> T cube(T x) { return x * x * x; }
+template <typename T> T inverse(T x) { return T(1) / x; }
+template <typename T> T cwiseMax(T x, T y) { return cl::sycl::max(x, y); }
+template <typename T> T cwiseMin(T x, T y) { return cl::sycl::min(x, y); }
+}
+}
+
+struct EqualAssignment {
+ template <typename Lhs, typename Rhs>
+ void operator()(Lhs& lhs, const Rhs& rhs) { lhs = rhs; }
+};
+
+struct PlusEqualAssignment {
+ template <typename Lhs, typename Rhs>
+ void operator()(Lhs& lhs, const Rhs& rhs) { lhs += rhs; }
+};
+
+template <typename DataType, int DataLayout,
+ typename Assignment, typename Operator>
+void test_unary_builtins_for_scalar(const Eigen::SyclDevice& sycl_device,
+ const array<int64_t, 3>& tensor_range) {
+ Operator op;
+ Assignment asgn;
+ {
+ /* Assignment(out, Operator(in)) */
+ Tensor<DataType, 3, DataLayout, int64_t> in(tensor_range);
+ Tensor<DataType, 3, DataLayout, int64_t> out(tensor_range);
+ in = in.random() + DataType(0.01);
+ out = out.random() + DataType(0.01);
+ Tensor<DataType, 3, DataLayout, int64_t> reference(out);
+ DataType *gpu_data = static_cast<DataType *>(
+ sycl_device.allocate(in.size() * sizeof(DataType)));
+ DataType *gpu_data_out = static_cast<DataType *>(
+ sycl_device.allocate(out.size() * sizeof(DataType)));
+ TensorMap<Tensor<DataType, 3, DataLayout, int64_t>> gpu(gpu_data, tensor_range);
+ TensorMap<Tensor<DataType, 3, DataLayout, int64_t>> gpu_out(gpu_data_out, tensor_range);
+ sycl_device.memcpyHostToDevice(gpu_data, in.data(),
+ (in.size()) * sizeof(DataType));
+ sycl_device.memcpyHostToDevice(gpu_data_out, out.data(),
+ (out.size()) * sizeof(DataType));
+ auto device_expr = gpu_out.device(sycl_device);
+ asgn(device_expr, op(gpu));
+ sycl_device.memcpyDeviceToHost(out.data(), gpu_data_out,
+ (out.size()) * sizeof(DataType));
+ for (int64_t i = 0; i < out.size(); ++i) {
+ DataType ver = reference(i);
+ asgn(ver, op(in(i)));
+ VERIFY_IS_APPROX(out(i), ver);
+ }
+ sycl_device.deallocate(gpu_data);
+ sycl_device.deallocate(gpu_data_out);
+ }
+ {
+ /* Assignment(out, Operator(out)) */
+ Tensor<DataType, 3, DataLayout, int64_t> out(tensor_range);
+ // Offset with 1 to avoid tiny output (< 1e-6) as they can easily fail.
+ out = out.random() + DataType(1);
+ Tensor<DataType, 3, DataLayout, int64_t> reference(out);
+ DataType *gpu_data_out = static_cast<DataType *>(
+ sycl_device.allocate(out.size() * sizeof(DataType)));
+ TensorMap<Tensor<DataType, 3, DataLayout, int64_t>> gpu_out(gpu_data_out, tensor_range);
+ sycl_device.memcpyHostToDevice(gpu_data_out, out.data(),
+ (out.size()) * sizeof(DataType));
+ auto device_expr = gpu_out.device(sycl_device);
+ asgn(device_expr, op(gpu_out));
+ sycl_device.memcpyDeviceToHost(out.data(), gpu_data_out,
+ (out.size()) * sizeof(DataType));
+ for (int64_t i = 0; i < out.size(); ++i) {
+ DataType ver = reference(i);
+ asgn(ver, op(reference(i)));
+ VERIFY_IS_APPROX(out(i), ver);
+ }
+ sycl_device.deallocate(gpu_data_out);
+ }
+}
+
+#define DECLARE_UNARY_STRUCT(FUNC) \
+ struct op_##FUNC { \
+ template <typename T> \
+ auto operator()(const T& x) -> decltype(cl::sycl::FUNC(x)) { \
+ return cl::sycl::FUNC(x); \
+ } \
+ template <typename T> \
+ auto operator()(const TensorMap<T>& x) -> decltype(x.FUNC()) { \
+ return x.FUNC(); \
+ } \
+ };
+
+DECLARE_UNARY_STRUCT(abs)
+DECLARE_UNARY_STRUCT(sqrt)
+DECLARE_UNARY_STRUCT(rsqrt)
+DECLARE_UNARY_STRUCT(square)
+DECLARE_UNARY_STRUCT(cube)
+DECLARE_UNARY_STRUCT(inverse)
+DECLARE_UNARY_STRUCT(tanh)
+DECLARE_UNARY_STRUCT(exp)
+DECLARE_UNARY_STRUCT(expm1)
+DECLARE_UNARY_STRUCT(log)
+DECLARE_UNARY_STRUCT(ceil)
+DECLARE_UNARY_STRUCT(floor)
+DECLARE_UNARY_STRUCT(round)
+DECLARE_UNARY_STRUCT(log1p)
+DECLARE_UNARY_STRUCT(sign)
+DECLARE_UNARY_STRUCT(isnan)
+DECLARE_UNARY_STRUCT(isfinite)
+DECLARE_UNARY_STRUCT(isinf)
+
+template <typename DataType, int DataLayout, typename Assignment>
+void test_unary_builtins_for_assignement(const Eigen::SyclDevice& sycl_device,
+ const array<int64_t, 3>& tensor_range) {
+#define RUN_UNARY_TEST(FUNC) \
+ test_unary_builtins_for_scalar<DataType, DataLayout, Assignment, \
+ op_##FUNC>(sycl_device, tensor_range)
+ RUN_UNARY_TEST(abs);
+ RUN_UNARY_TEST(sqrt);
+ RUN_UNARY_TEST(rsqrt);
+ RUN_UNARY_TEST(square);
+ RUN_UNARY_TEST(cube);
+ RUN_UNARY_TEST(inverse);
+ RUN_UNARY_TEST(tanh);
+ RUN_UNARY_TEST(exp);
+ RUN_UNARY_TEST(expm1);
+ RUN_UNARY_TEST(log);
+ RUN_UNARY_TEST(ceil);
+ RUN_UNARY_TEST(floor);
+ RUN_UNARY_TEST(round);
+ RUN_UNARY_TEST(log1p);
+ RUN_UNARY_TEST(sign);
+}
+
+template <typename DataType, int DataLayout, typename Operator>
+void test_unary_builtins_return_bool(const Eigen::SyclDevice& sycl_device,
+ const array<int64_t, 3>& tensor_range) {
+ /* out = op(in) */
+ Operator op;
+ Tensor<DataType, 3, DataLayout, int64_t> in(tensor_range);
+ Tensor<bool, 3, DataLayout, int64_t> out(tensor_range);
+ in = in.random() + DataType(0.01);
+ DataType *gpu_data = static_cast<DataType *>(
+ sycl_device.allocate(in.size() * sizeof(DataType)));
+ bool *gpu_data_out =
+ static_cast<bool *>(sycl_device.allocate(out.size() * sizeof(bool)));
+ TensorMap<Tensor<DataType, 3, DataLayout, int64_t>> gpu(gpu_data, tensor_range);
+ TensorMap<Tensor<bool, 3, DataLayout, int64_t>> gpu_out(gpu_data_out, tensor_range);
+ sycl_device.memcpyHostToDevice(gpu_data, in.data(),
+ (in.size()) * sizeof(DataType));
+ gpu_out.device(sycl_device) = op(gpu);
+ sycl_device.memcpyDeviceToHost(out.data(), gpu_data_out,
+ (out.size()) * sizeof(bool));
+ for (int64_t i = 0; i < out.size(); ++i) {
+ VERIFY_IS_EQUAL(out(i), op(in(i)));
+ }
+ sycl_device.deallocate(gpu_data);
+ sycl_device.deallocate(gpu_data_out);
+}
+
+template <typename DataType, int DataLayout>
+void test_unary_builtins(const Eigen::SyclDevice& sycl_device,
+ const array<int64_t, 3>& tensor_range) {
+ test_unary_builtins_for_assignement<DataType, DataLayout,
+ PlusEqualAssignment>(sycl_device, tensor_range);
+ test_unary_builtins_for_assignement<DataType, DataLayout,
+ EqualAssignment>(sycl_device, tensor_range);
+ test_unary_builtins_return_bool<DataType, DataLayout,
+ op_isnan>(sycl_device, tensor_range);
+ test_unary_builtins_return_bool<DataType, DataLayout,
+ op_isfinite>(sycl_device, tensor_range);
+ test_unary_builtins_return_bool<DataType, DataLayout,
+ op_isinf>(sycl_device, tensor_range);
+}
+
+template <typename DataType>
+static void test_builtin_unary_sycl(const Eigen::SyclDevice &sycl_device) {
+ int64_t sizeDim1 = 10;
+ int64_t sizeDim2 = 10;
+ int64_t sizeDim3 = 10;
+ array<int64_t, 3> tensor_range = {{sizeDim1, sizeDim2, sizeDim3}};
+
+ test_unary_builtins<DataType, RowMajor>(sycl_device, tensor_range);
+ test_unary_builtins<DataType, ColMajor>(sycl_device, tensor_range);
+}
+
+template <typename DataType, int DataLayout, typename Operator>
+void test_binary_builtins_func(const Eigen::SyclDevice& sycl_device,
+ const array<int64_t, 3>& tensor_range) {
+ /* out = op(in_1, in_2) */
+ Operator op;
+ Tensor<DataType, 3, DataLayout, int64_t> in_1(tensor_range);
+ Tensor<DataType, 3, DataLayout, int64_t> in_2(tensor_range);
+ Tensor<DataType, 3, DataLayout, int64_t> out(tensor_range);
+ in_1 = in_1.random() + DataType(0.01);
+ in_2 = in_2.random() + DataType(0.01);
+ Tensor<DataType, 3, DataLayout, int64_t> reference(out);
+ DataType *gpu_data_1 = static_cast<DataType *>(
+ sycl_device.allocate(in_1.size() * sizeof(DataType)));
+ DataType *gpu_data_2 = static_cast<DataType *>(
+ sycl_device.allocate(in_2.size() * sizeof(DataType)));
+ DataType *gpu_data_out = static_cast<DataType *>(
+ sycl_device.allocate(out.size() * sizeof(DataType)));
+ TensorMap<Tensor<DataType, 3, DataLayout, int64_t>> gpu_1(gpu_data_1, tensor_range);
+ TensorMap<Tensor<DataType, 3, DataLayout, int64_t>> gpu_2(gpu_data_2, tensor_range);
+ TensorMap<Tensor<DataType, 3, DataLayout, int64_t>> gpu_out(gpu_data_out, tensor_range);
+ sycl_device.memcpyHostToDevice(gpu_data_1, in_1.data(),
+ (in_1.size()) * sizeof(DataType));
+ sycl_device.memcpyHostToDevice(gpu_data_2, in_2.data(),
+ (in_2.size()) * sizeof(DataType));
+ gpu_out.device(sycl_device) = op(gpu_1, gpu_2);
+ sycl_device.memcpyDeviceToHost(out.data(), gpu_data_out,
+ (out.size()) * sizeof(DataType));
+ for (int64_t i = 0; i < out.size(); ++i) {
+ VERIFY_IS_APPROX(out(i), op(in_1(i), in_2(i)));
+ }
+ sycl_device.deallocate(gpu_data_1);
+ sycl_device.deallocate(gpu_data_2);
+ sycl_device.deallocate(gpu_data_out);
+}
+
+template <typename DataType, int DataLayout, typename Operator>
+void test_binary_builtins_fixed_arg2(const Eigen::SyclDevice& sycl_device,
+ const array<int64_t, 3>& tensor_range) {
+ /* out = op(in_1, 2) */
+ Operator op;
+ const DataType arg2(2);
+ Tensor<DataType, 3, DataLayout, int64_t> in_1(tensor_range);
+ Tensor<DataType, 3, DataLayout, int64_t> out(tensor_range);
+ in_1 = in_1.random();
+ Tensor<DataType, 3, DataLayout, int64_t> reference(out);
+ DataType *gpu_data_1 = static_cast<DataType *>(
+ sycl_device.allocate(in_1.size() * sizeof(DataType)));
+ DataType *gpu_data_out = static_cast<DataType *>(
+ sycl_device.allocate(out.size() * sizeof(DataType)));
+ TensorMap<Tensor<DataType, 3, DataLayout, int64_t>> gpu_1(gpu_data_1, tensor_range);
+ TensorMap<Tensor<DataType, 3, DataLayout, int64_t>> gpu_out(gpu_data_out, tensor_range);
+ sycl_device.memcpyHostToDevice(gpu_data_1, in_1.data(),
+ (in_1.size()) * sizeof(DataType));
+ gpu_out.device(sycl_device) = op(gpu_1, arg2);
+ sycl_device.memcpyDeviceToHost(out.data(), gpu_data_out,
+ (out.size()) * sizeof(DataType));
+ for (int64_t i = 0; i < out.size(); ++i) {
+ VERIFY_IS_APPROX(out(i), op(in_1(i), arg2));
+ }
+ sycl_device.deallocate(gpu_data_1);
+ sycl_device.deallocate(gpu_data_out);
+}
+
+#define DECLARE_BINARY_STRUCT(FUNC) \
+ struct op_##FUNC { \
+ template <typename T1, typename T2> \
+ auto operator()(const T1& x, const T2& y) -> decltype(cl::sycl::FUNC(x, y)) { \
+ return cl::sycl::FUNC(x, y); \
+ } \
+ template <typename T1, typename T2> \
+ auto operator()(const TensorMap<T1>& x, const TensorMap<T2>& y) -> decltype(x.FUNC(y)) { \
+ return x.FUNC(y); \
+ } \
+ };
+
+DECLARE_BINARY_STRUCT(cwiseMax)
+DECLARE_BINARY_STRUCT(cwiseMin)
+
+#define DECLARE_BINARY_STRUCT_OP(NAME, OPERATOR) \
+ struct op_##NAME { \
+ template <typename T1, typename T2> \
+ auto operator()(const T1& x, const T2& y) -> decltype(x OPERATOR y) { \
+ return x OPERATOR y; \
+ } \
+ };
+
+DECLARE_BINARY_STRUCT_OP(plus, +)
+DECLARE_BINARY_STRUCT_OP(minus, -)
+DECLARE_BINARY_STRUCT_OP(times, *)
+DECLARE_BINARY_STRUCT_OP(divide, /)
+DECLARE_BINARY_STRUCT_OP(modulo, %)
+
+template <typename DataType, int DataLayout>
+void test_binary_builtins(const Eigen::SyclDevice& sycl_device,
+ const array<int64_t, 3>& tensor_range) {
+ test_binary_builtins_func<DataType, DataLayout,
+ op_cwiseMax>(sycl_device, tensor_range);
+ test_binary_builtins_func<DataType, DataLayout,
+ op_cwiseMin>(sycl_device, tensor_range);
+ test_binary_builtins_func<DataType, DataLayout,
+ op_plus>(sycl_device, tensor_range);
+ test_binary_builtins_func<DataType, DataLayout,
+ op_minus>(sycl_device, tensor_range);
+ test_binary_builtins_func<DataType, DataLayout,
+ op_times>(sycl_device, tensor_range);
+ test_binary_builtins_func<DataType, DataLayout,
+ op_divide>(sycl_device, tensor_range);
+}
+
+template <typename DataType>
+static void test_floating_builtin_binary_sycl(const Eigen::SyclDevice &sycl_device) {
+ int64_t sizeDim1 = 10;
+ int64_t sizeDim2 = 10;
+ int64_t sizeDim3 = 10;
+ array<int64_t, 3> tensor_range = {{sizeDim1, sizeDim2, sizeDim3}};
+ test_binary_builtins<DataType, RowMajor>(sycl_device, tensor_range);
+ test_binary_builtins<DataType, ColMajor>(sycl_device, tensor_range);
+}
+
+template <typename DataType>
+static void test_integer_builtin_binary_sycl(const Eigen::SyclDevice &sycl_device) {
+ int64_t sizeDim1 = 10;
+ int64_t sizeDim2 = 10;
+ int64_t sizeDim3 = 10;
+ array<int64_t, 3> tensor_range = {{sizeDim1, sizeDim2, sizeDim3}};
+ test_binary_builtins_fixed_arg2<DataType, RowMajor,
+ op_modulo>(sycl_device, tensor_range);
+ test_binary_builtins_fixed_arg2<DataType, ColMajor,
+ op_modulo>(sycl_device, tensor_range);
+}
+
+EIGEN_DECLARE_TEST(cxx11_tensor_builtins_sycl) {
+ for (const auto& device :Eigen::get_sycl_supported_devices()) {
+ QueueInterface queueInterface(device);
+ Eigen::SyclDevice sycl_device(&queueInterface);
+ CALL_SUBTEST_1(test_builtin_unary_sycl<float>(sycl_device));
+ CALL_SUBTEST_2(test_floating_builtin_binary_sycl<float>(sycl_device));
+ CALL_SUBTEST_3(test_integer_builtin_binary_sycl<int>(sycl_device));
+ }
+}
diff --git a/unsupported/test/cxx11_tensor_cast_float16_gpu.cu b/unsupported/test/cxx11_tensor_cast_float16_gpu.cu
new file mode 100644
index 0000000..97923d1
--- /dev/null
+++ b/unsupported/test/cxx11_tensor_cast_float16_gpu.cu
@@ -0,0 +1,79 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2016 Benoit Steiner <benoit.steiner.goog@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#define EIGEN_TEST_NO_LONGDOUBLE
+#define EIGEN_TEST_NO_COMPLEX
+
+#define EIGEN_DEFAULT_DENSE_INDEX_TYPE int
+#define EIGEN_USE_GPU
+
+#include "main.h"
+#include <unsupported/Eigen/CXX11/Tensor>
+
+using Eigen::Tensor;
+
+void test_gpu_conversion() {
+ Eigen::GpuStreamDevice stream;
+ Eigen::GpuDevice gpu_device(&stream);
+ int num_elem = 101;
+
+ Tensor<float, 1> floats(num_elem);
+ floats.setRandom();
+
+ float* d_float = (float*)gpu_device.allocate(num_elem * sizeof(float));
+ Eigen::half* d_half = (Eigen::half*)gpu_device.allocate(num_elem * sizeof(Eigen::half));
+ float* d_conv = (float*)gpu_device.allocate(num_elem * sizeof(float));
+
+ Eigen::TensorMap<Eigen::Tensor<float, 1>, Eigen::Aligned> gpu_float(
+ d_float, num_elem);
+ Eigen::TensorMap<Eigen::Tensor<Eigen::half, 1>, Eigen::Aligned> gpu_half(
+ d_half, num_elem);
+ Eigen::TensorMap<Eigen::Tensor<float, 1>, Eigen::Aligned> gpu_conv(
+ d_conv, num_elem);
+
+ gpu_device.memcpyHostToDevice(d_float, floats.data(), num_elem*sizeof(float));
+
+ gpu_half.device(gpu_device) = gpu_float.cast<Eigen::half>();
+ gpu_conv.device(gpu_device) = gpu_half.cast<float>();
+
+ Tensor<float, 1> initial(num_elem);
+ Tensor<float, 1> final(num_elem);
+ gpu_device.memcpyDeviceToHost(initial.data(), d_float, num_elem*sizeof(float));
+ gpu_device.memcpyDeviceToHost(final.data(), d_conv, num_elem*sizeof(float));
+ gpu_device.synchronize();
+
+ for (int i = 0; i < num_elem; ++i) {
+ VERIFY_IS_APPROX(initial(i), final(i));
+ }
+
+ gpu_device.deallocate(d_float);
+ gpu_device.deallocate(d_half);
+ gpu_device.deallocate(d_conv);
+}
+
+
+void test_fallback_conversion() {
+ int num_elem = 101;
+ Tensor<float, 1> floats(num_elem);
+ floats.setRandom();
+
+ Eigen::Tensor<Eigen::half, 1> halfs = floats.cast<Eigen::half>();
+ Eigen::Tensor<float, 1> conv = halfs.cast<float>();
+
+ for (int i = 0; i < num_elem; ++i) {
+ VERIFY_IS_APPROX(floats(i), conv(i));
+ }
+}
+
+
+EIGEN_DECLARE_TEST(cxx11_tensor_cast_float16_gpu)
+{
+ CALL_SUBTEST(test_gpu_conversion());
+ CALL_SUBTEST(test_fallback_conversion());
+}
diff --git a/unsupported/test/cxx11_tensor_casts.cpp b/unsupported/test/cxx11_tensor_casts.cpp
new file mode 100644
index 0000000..7b67738
--- /dev/null
+++ b/unsupported/test/cxx11_tensor_casts.cpp
@@ -0,0 +1,186 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "main.h"
+#include "random_without_cast_overflow.h"
+
+#include <Eigen/CXX11/Tensor>
+
+using Eigen::Tensor;
+using Eigen::array;
+
+static void test_simple_cast()
+{
+ Tensor<float, 2> ftensor(20,30);
+ ftensor = ftensor.random() * 100.f;
+ Tensor<char, 2> chartensor(20,30);
+ chartensor.setRandom();
+ Tensor<std::complex<float>, 2> cplextensor(20,30);
+ cplextensor.setRandom();
+
+ chartensor = ftensor.cast<char>();
+ cplextensor = ftensor.cast<std::complex<float> >();
+
+ for (int i = 0; i < 20; ++i) {
+ for (int j = 0; j < 30; ++j) {
+ VERIFY_IS_EQUAL(chartensor(i,j), static_cast<char>(ftensor(i,j)));
+ VERIFY_IS_EQUAL(cplextensor(i,j), static_cast<std::complex<float> >(ftensor(i,j)));
+ }
+ }
+}
+
+
+static void test_vectorized_cast()
+{
+ Tensor<int, 2> itensor(20,30);
+ itensor = itensor.random() / 1000;
+ Tensor<float, 2> ftensor(20,30);
+ ftensor.setRandom();
+ Tensor<double, 2> dtensor(20,30);
+ dtensor.setRandom();
+
+ ftensor = itensor.cast<float>();
+ dtensor = itensor.cast<double>();
+
+ for (int i = 0; i < 20; ++i) {
+ for (int j = 0; j < 30; ++j) {
+ VERIFY_IS_EQUAL(itensor(i,j), static_cast<int>(ftensor(i,j)));
+ VERIFY_IS_EQUAL(dtensor(i,j), static_cast<double>(ftensor(i,j)));
+ }
+ }
+}
+
+
+static void test_float_to_int_cast()
+{
+ Tensor<float, 2> ftensor(20,30);
+ ftensor = ftensor.random() * 1000.0f;
+ Tensor<double, 2> dtensor(20,30);
+ dtensor = dtensor.random() * 1000.0;
+
+ Tensor<int, 2> i1tensor = ftensor.cast<int>();
+ Tensor<int, 2> i2tensor = dtensor.cast<int>();
+
+ for (int i = 0; i < 20; ++i) {
+ for (int j = 0; j < 30; ++j) {
+ VERIFY_IS_EQUAL(i1tensor(i,j), static_cast<int>(ftensor(i,j)));
+ VERIFY_IS_EQUAL(i2tensor(i,j), static_cast<int>(dtensor(i,j)));
+ }
+ }
+}
+
+
+static void test_big_to_small_type_cast()
+{
+ Tensor<double, 2> dtensor(20, 30);
+ dtensor.setRandom();
+ Tensor<float, 2> ftensor(20, 30);
+ ftensor = dtensor.cast<float>();
+
+ for (int i = 0; i < 20; ++i) {
+ for (int j = 0; j < 30; ++j) {
+ VERIFY_IS_APPROX(dtensor(i,j), static_cast<double>(ftensor(i,j)));
+ }
+ }
+}
+
+
+static void test_small_to_big_type_cast()
+{
+ Tensor<float, 2> ftensor(20, 30);
+ ftensor.setRandom();
+ Tensor<double, 2> dtensor(20, 30);
+ dtensor = ftensor.cast<double>();
+
+ for (int i = 0; i < 20; ++i) {
+ for (int j = 0; j < 30; ++j) {
+ VERIFY_IS_APPROX(dtensor(i,j), static_cast<double>(ftensor(i,j)));
+ }
+ }
+}
+
+template <typename FromType, typename ToType>
+static void test_type_cast() {
+ Tensor<FromType, 2> ftensor(100, 200);
+ // Generate random values for a valid cast.
+ for (int i = 0; i < 100; ++i) {
+ for (int j = 0; j < 200; ++j) {
+ ftensor(i, j) = internal::random_without_cast_overflow<FromType,ToType>::value();
+ }
+ }
+
+ Tensor<ToType, 2> ttensor(100, 200);
+ ttensor = ftensor.template cast<ToType>();
+
+ for (int i = 0; i < 100; ++i) {
+ for (int j = 0; j < 200; ++j) {
+ const ToType ref = internal::cast<FromType,ToType>(ftensor(i, j));
+ VERIFY_IS_APPROX(ttensor(i, j), ref);
+ }
+ }
+}
+
+template<typename Scalar, typename EnableIf = void>
+struct test_cast_runner {
+ static void run() {
+ test_type_cast<Scalar, bool>();
+ test_type_cast<Scalar, int8_t>();
+ test_type_cast<Scalar, int16_t>();
+ test_type_cast<Scalar, int32_t>();
+ test_type_cast<Scalar, int64_t>();
+ test_type_cast<Scalar, uint8_t>();
+ test_type_cast<Scalar, uint16_t>();
+ test_type_cast<Scalar, uint32_t>();
+ test_type_cast<Scalar, uint64_t>();
+ test_type_cast<Scalar, half>();
+ test_type_cast<Scalar, bfloat16>();
+ test_type_cast<Scalar, float>();
+ test_type_cast<Scalar, double>();
+ test_type_cast<Scalar, std::complex<float>>();
+ test_type_cast<Scalar, std::complex<double>>();
+ }
+};
+
+// Only certain types allow cast from std::complex<>.
+template<typename Scalar>
+struct test_cast_runner<Scalar, std::enable_if_t<NumTraits<Scalar>::IsComplex>> {
+ static void run() {
+ test_type_cast<Scalar, half>();
+ test_type_cast<Scalar, bfloat16>();
+ test_type_cast<Scalar, std::complex<float>>();
+ test_type_cast<Scalar, std::complex<double>>();
+ }
+};
+
+
+EIGEN_DECLARE_TEST(cxx11_tensor_casts)
+{
+ CALL_SUBTEST(test_simple_cast());
+ CALL_SUBTEST(test_vectorized_cast());
+ CALL_SUBTEST(test_float_to_int_cast());
+ CALL_SUBTEST(test_big_to_small_type_cast());
+ CALL_SUBTEST(test_small_to_big_type_cast());
+
+ CALL_SUBTEST(test_cast_runner<bool>::run());
+ CALL_SUBTEST(test_cast_runner<int8_t>::run());
+ CALL_SUBTEST(test_cast_runner<int16_t>::run());
+ CALL_SUBTEST(test_cast_runner<int32_t>::run());
+ CALL_SUBTEST(test_cast_runner<int64_t>::run());
+ CALL_SUBTEST(test_cast_runner<uint8_t>::run());
+ CALL_SUBTEST(test_cast_runner<uint16_t>::run());
+ CALL_SUBTEST(test_cast_runner<uint32_t>::run());
+ CALL_SUBTEST(test_cast_runner<uint64_t>::run());
+ CALL_SUBTEST(test_cast_runner<half>::run());
+ CALL_SUBTEST(test_cast_runner<bfloat16>::run());
+ CALL_SUBTEST(test_cast_runner<float>::run());
+ CALL_SUBTEST(test_cast_runner<double>::run());
+ CALL_SUBTEST(test_cast_runner<std::complex<float>>::run());
+ CALL_SUBTEST(test_cast_runner<std::complex<double>>::run());
+
+}
diff --git a/unsupported/test/cxx11_tensor_chipping.cpp b/unsupported/test/cxx11_tensor_chipping.cpp
new file mode 100644
index 0000000..9222744
--- /dev/null
+++ b/unsupported/test/cxx11_tensor_chipping.cpp
@@ -0,0 +1,425 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "main.h"
+
+#include <Eigen/CXX11/Tensor>
+
+using Eigen::Tensor;
+
+template<int DataLayout>
+static void test_simple_chip()
+{
+ Tensor<float, 5, DataLayout> tensor(2,3,5,7,11);
+ tensor.setRandom();
+
+ Tensor<float, 4, DataLayout> chip1;
+ chip1 = tensor.template chip<0>(1);
+
+ VERIFY_IS_EQUAL(chip1.dimension(0), 3);
+ VERIFY_IS_EQUAL(chip1.dimension(1), 5);
+ VERIFY_IS_EQUAL(chip1.dimension(2), 7);
+ VERIFY_IS_EQUAL(chip1.dimension(3), 11);
+
+ for (int i = 0; i < 3; ++i) {
+ for (int j = 0; j < 5; ++j) {
+ for (int k = 0; k < 7; ++k) {
+ for (int l = 0; l < 11; ++l) {
+ VERIFY_IS_EQUAL(chip1(i,j,k,l), tensor(1,i,j,k,l));
+ }
+ }
+ }
+ }
+
+ Tensor<float, 4, DataLayout> chip2 = tensor.template chip<1>(1);
+ VERIFY_IS_EQUAL(chip2.dimension(0), 2);
+ VERIFY_IS_EQUAL(chip2.dimension(1), 5);
+ VERIFY_IS_EQUAL(chip2.dimension(2), 7);
+ VERIFY_IS_EQUAL(chip2.dimension(3), 11);
+ for (int i = 0; i < 2; ++i) {
+ for (int j = 0; j < 5; ++j) {
+ for (int k = 0; k < 7; ++k) {
+ for (int l = 0; l < 11; ++l) {
+ VERIFY_IS_EQUAL(chip2(i,j,k,l), tensor(i,1,j,k,l));
+ }
+ }
+ }
+ }
+
+ Tensor<float, 4, DataLayout> chip3 = tensor.template chip<2>(2);
+ VERIFY_IS_EQUAL(chip3.dimension(0), 2);
+ VERIFY_IS_EQUAL(chip3.dimension(1), 3);
+ VERIFY_IS_EQUAL(chip3.dimension(2), 7);
+ VERIFY_IS_EQUAL(chip3.dimension(3), 11);
+ for (int i = 0; i < 2; ++i) {
+ for (int j = 0; j < 3; ++j) {
+ for (int k = 0; k < 7; ++k) {
+ for (int l = 0; l < 11; ++l) {
+ VERIFY_IS_EQUAL(chip3(i,j,k,l), tensor(i,j,2,k,l));
+ }
+ }
+ }
+ }
+
+ Tensor<float, 4, DataLayout> chip4(tensor.template chip<3>(5));
+ VERIFY_IS_EQUAL(chip4.dimension(0), 2);
+ VERIFY_IS_EQUAL(chip4.dimension(1), 3);
+ VERIFY_IS_EQUAL(chip4.dimension(2), 5);
+ VERIFY_IS_EQUAL(chip4.dimension(3), 11);
+ for (int i = 0; i < 2; ++i) {
+ for (int j = 0; j < 3; ++j) {
+ for (int k = 0; k < 5; ++k) {
+ for (int l = 0; l < 11; ++l) {
+ VERIFY_IS_EQUAL(chip4(i,j,k,l), tensor(i,j,k,5,l));
+ }
+ }
+ }
+ }
+
+ Tensor<float, 4, DataLayout> chip5(tensor.template chip<4>(7));
+ VERIFY_IS_EQUAL(chip5.dimension(0), 2);
+ VERIFY_IS_EQUAL(chip5.dimension(1), 3);
+ VERIFY_IS_EQUAL(chip5.dimension(2), 5);
+ VERIFY_IS_EQUAL(chip5.dimension(3), 7);
+ for (int i = 0; i < 2; ++i) {
+ for (int j = 0; j < 3; ++j) {
+ for (int k = 0; k < 5; ++k) {
+ for (int l = 0; l < 7; ++l) {
+ VERIFY_IS_EQUAL(chip5(i,j,k,l), tensor(i,j,k,l,7));
+ }
+ }
+ }
+ }
+}
+
+template<int DataLayout>
+static void test_dynamic_chip()
+{
+ Tensor<float, 5, DataLayout> tensor(2,3,5,7,11);
+ tensor.setRandom();
+
+ Tensor<float, 4, DataLayout> chip1;
+ chip1 = tensor.chip(1, 0);
+ VERIFY_IS_EQUAL(chip1.dimension(0), 3);
+ VERIFY_IS_EQUAL(chip1.dimension(1), 5);
+ VERIFY_IS_EQUAL(chip1.dimension(2), 7);
+ VERIFY_IS_EQUAL(chip1.dimension(3), 11);
+ for (int i = 0; i < 3; ++i) {
+ for (int j = 0; j < 5; ++j) {
+ for (int k = 0; k < 7; ++k) {
+ for (int l = 0; l < 11; ++l) {
+ VERIFY_IS_EQUAL(chip1(i,j,k,l), tensor(1,i,j,k,l));
+ }
+ }
+ }
+ }
+
+ Tensor<float, 4, DataLayout> chip2 = tensor.chip(1, 1);
+ VERIFY_IS_EQUAL(chip2.dimension(0), 2);
+ VERIFY_IS_EQUAL(chip2.dimension(1), 5);
+ VERIFY_IS_EQUAL(chip2.dimension(2), 7);
+ VERIFY_IS_EQUAL(chip2.dimension(3), 11);
+ for (int i = 0; i < 2; ++i) {
+ for (int j = 0; j < 5; ++j) {
+ for (int k = 0; k < 7; ++k) {
+ for (int l = 0; l < 11; ++l) {
+ VERIFY_IS_EQUAL(chip2(i,j,k,l), tensor(i,1,j,k,l));
+ }
+ }
+ }
+ }
+
+ Tensor<float, 4, DataLayout> chip3 = tensor.chip(2, 2);
+ VERIFY_IS_EQUAL(chip3.dimension(0), 2);
+ VERIFY_IS_EQUAL(chip3.dimension(1), 3);
+ VERIFY_IS_EQUAL(chip3.dimension(2), 7);
+ VERIFY_IS_EQUAL(chip3.dimension(3), 11);
+ for (int i = 0; i < 2; ++i) {
+ for (int j = 0; j < 3; ++j) {
+ for (int k = 0; k < 7; ++k) {
+ for (int l = 0; l < 11; ++l) {
+ VERIFY_IS_EQUAL(chip3(i,j,k,l), tensor(i,j,2,k,l));
+ }
+ }
+ }
+ }
+
+ Tensor<float, 4, DataLayout> chip4(tensor.chip(5, 3));
+ VERIFY_IS_EQUAL(chip4.dimension(0), 2);
+ VERIFY_IS_EQUAL(chip4.dimension(1), 3);
+ VERIFY_IS_EQUAL(chip4.dimension(2), 5);
+ VERIFY_IS_EQUAL(chip4.dimension(3), 11);
+ for (int i = 0; i < 2; ++i) {
+ for (int j = 0; j < 3; ++j) {
+ for (int k = 0; k < 5; ++k) {
+ for (int l = 0; l < 11; ++l) {
+ VERIFY_IS_EQUAL(chip4(i,j,k,l), tensor(i,j,k,5,l));
+ }
+ }
+ }
+ }
+
+ Tensor<float, 4, DataLayout> chip5(tensor.chip(7, 4));
+ VERIFY_IS_EQUAL(chip5.dimension(0), 2);
+ VERIFY_IS_EQUAL(chip5.dimension(1), 3);
+ VERIFY_IS_EQUAL(chip5.dimension(2), 5);
+ VERIFY_IS_EQUAL(chip5.dimension(3), 7);
+ for (int i = 0; i < 2; ++i) {
+ for (int j = 0; j < 3; ++j) {
+ for (int k = 0; k < 5; ++k) {
+ for (int l = 0; l < 7; ++l) {
+ VERIFY_IS_EQUAL(chip5(i,j,k,l), tensor(i,j,k,l,7));
+ }
+ }
+ }
+ }
+}
+
+template<int DataLayout>
+static void test_chip_in_expr() {
+ Tensor<float, 5, DataLayout> input1(2,3,5,7,11);
+ input1.setRandom();
+ Tensor<float, 4, DataLayout> input2(3,5,7,11);
+ input2.setRandom();
+
+ Tensor<float, 4, DataLayout> result = input1.template chip<0>(0) + input2;
+ for (int i = 0; i < 3; ++i) {
+ for (int j = 0; j < 5; ++j) {
+ for (int k = 0; k < 7; ++k) {
+ for (int l = 0; l < 11; ++l) {
+ float expected = input1(0,i,j,k,l) + input2(i,j,k,l);
+ VERIFY_IS_EQUAL(result(i,j,k,l), expected);
+ }
+ }
+ }
+ }
+
+ Tensor<float, 3, DataLayout> input3(3,7,11);
+ input3.setRandom();
+ Tensor<float, 3, DataLayout> result2 = input1.template chip<0>(0).template chip<1>(2) + input3;
+ for (int i = 0; i < 3; ++i) {
+ for (int j = 0; j < 7; ++j) {
+ for (int k = 0; k < 11; ++k) {
+ float expected = input1(0,i,2,j,k) + input3(i,j,k);
+ VERIFY_IS_EQUAL(result2(i,j,k), expected);
+ }
+ }
+ }
+}
+
+template<int DataLayout>
+static void test_chip_as_lvalue()
+{
+ Tensor<float, 5, DataLayout> input1(2,3,5,7,11);
+ input1.setRandom();
+
+ Tensor<float, 4, DataLayout> input2(3,5,7,11);
+ input2.setRandom();
+ Tensor<float, 5, DataLayout> tensor = input1;
+ tensor.template chip<0>(1) = input2;
+ for (int i = 0; i < 2; ++i) {
+ for (int j = 0; j < 3; ++j) {
+ for (int k = 0; k < 5; ++k) {
+ for (int l = 0; l < 7; ++l) {
+ for (int m = 0; m < 11; ++m) {
+ if (i != 1) {
+ VERIFY_IS_EQUAL(tensor(i,j,k,l,m), input1(i,j,k,l,m));
+ } else {
+ VERIFY_IS_EQUAL(tensor(i,j,k,l,m), input2(j,k,l,m));
+ }
+ }
+ }
+ }
+ }
+ }
+
+ Tensor<float, 4, DataLayout> input3(2,5,7,11);
+ input3.setRandom();
+ tensor = input1;
+ tensor.template chip<1>(1) = input3;
+ for (int i = 0; i < 2; ++i) {
+ for (int j = 0; j < 3; ++j) {
+ for (int k = 0; k < 5; ++k) {
+ for (int l = 0; l < 7; ++l) {
+ for (int m = 0; m < 11; ++m) {
+ if (j != 1) {
+ VERIFY_IS_EQUAL(tensor(i,j,k,l,m), input1(i,j,k,l,m));
+ } else {
+ VERIFY_IS_EQUAL(tensor(i,j,k,l,m), input3(i,k,l,m));
+ }
+ }
+ }
+ }
+ }
+ }
+
+ Tensor<float, 4, DataLayout> input4(2,3,7,11);
+ input4.setRandom();
+ tensor = input1;
+ tensor.template chip<2>(3) = input4;
+ for (int i = 0; i < 2; ++i) {
+ for (int j = 0; j < 3; ++j) {
+ for (int k = 0; k < 5; ++k) {
+ for (int l = 0; l < 7; ++l) {
+ for (int m = 0; m < 11; ++m) {
+ if (k != 3) {
+ VERIFY_IS_EQUAL(tensor(i,j,k,l,m), input1(i,j,k,l,m));
+ } else {
+ VERIFY_IS_EQUAL(tensor(i,j,k,l,m), input4(i,j,l,m));
+ }
+ }
+ }
+ }
+ }
+ }
+
+ Tensor<float, 4, DataLayout> input5(2,3,5,11);
+ input5.setRandom();
+ tensor = input1;
+ tensor.template chip<3>(4) = input5;
+ for (int i = 0; i < 2; ++i) {
+ for (int j = 0; j < 3; ++j) {
+ for (int k = 0; k < 5; ++k) {
+ for (int l = 0; l < 7; ++l) {
+ for (int m = 0; m < 11; ++m) {
+ if (l != 4) {
+ VERIFY_IS_EQUAL(tensor(i,j,k,l,m), input1(i,j,k,l,m));
+ } else {
+ VERIFY_IS_EQUAL(tensor(i,j,k,l,m), input5(i,j,k,m));
+ }
+ }
+ }
+ }
+ }
+ }
+
+ Tensor<float, 4, DataLayout> input6(2,3,5,7);
+ input6.setRandom();
+ tensor = input1;
+ tensor.template chip<4>(5) = input6;
+ for (int i = 0; i < 2; ++i) {
+ for (int j = 0; j < 3; ++j) {
+ for (int k = 0; k < 5; ++k) {
+ for (int l = 0; l < 7; ++l) {
+ for (int m = 0; m < 11; ++m) {
+ if (m != 5) {
+ VERIFY_IS_EQUAL(tensor(i,j,k,l,m), input1(i,j,k,l,m));
+ } else {
+ VERIFY_IS_EQUAL(tensor(i,j,k,l,m), input6(i,j,k,l));
+ }
+ }
+ }
+ }
+ }
+ }
+
+ Tensor<float, 5, DataLayout> input7(2,3,5,7,11);
+ input7.setRandom();
+ tensor = input1;
+ tensor.chip(0, 0) = input7.chip(0, 0);
+ for (int i = 0; i < 2; ++i) {
+ for (int j = 0; j < 3; ++j) {
+ for (int k = 0; k < 5; ++k) {
+ for (int l = 0; l < 7; ++l) {
+ for (int m = 0; m < 11; ++m) {
+ if (i != 0) {
+ VERIFY_IS_EQUAL(tensor(i,j,k,l,m), input1(i,j,k,l,m));
+ } else {
+ VERIFY_IS_EQUAL(tensor(i,j,k,l,m), input7(i,j,k,l,m));
+ }
+ }
+ }
+ }
+ }
+ }
+}
+
+static void test_chip_raw_data_col_major()
+{
+ Tensor<float, 5, ColMajor> tensor(2,3,5,7,11);
+ tensor.setRandom();
+
+ typedef TensorEvaluator<decltype(tensor.chip<4>(3)), DefaultDevice> Evaluator4;
+ auto chip = Evaluator4(tensor.chip<4>(3), DefaultDevice());
+ for (int i = 0; i < 2; ++i) {
+ for (int j = 0; j < 3; ++j) {
+ for (int k = 0; k < 5; ++k) {
+ for (int l = 0; l < 7; ++l) {
+ int chip_index = i + 2 * (j + 3 * (k + 5 * l));
+ VERIFY_IS_EQUAL(chip.data()[chip_index], tensor(i,j,k,l,3));
+ }
+ }
+ }
+ }
+
+ typedef TensorEvaluator<decltype(tensor.chip<0>(0)), DefaultDevice> Evaluator0;
+ auto chip0 = Evaluator0(tensor.chip<0>(0), DefaultDevice());
+ VERIFY_IS_EQUAL(chip0.data(), static_cast<float*>(0));
+
+ typedef TensorEvaluator<decltype(tensor.chip<1>(0)), DefaultDevice> Evaluator1;
+ auto chip1 = Evaluator1(tensor.chip<1>(0), DefaultDevice());
+ VERIFY_IS_EQUAL(chip1.data(), static_cast<float*>(0));
+
+ typedef TensorEvaluator<decltype(tensor.chip<2>(0)), DefaultDevice> Evaluator2;
+ auto chip2 = Evaluator2(tensor.chip<2>(0), DefaultDevice());
+ VERIFY_IS_EQUAL(chip2.data(), static_cast<float*>(0));
+
+ typedef TensorEvaluator<decltype(tensor.chip<3>(0)), DefaultDevice> Evaluator3;
+ auto chip3 = Evaluator3(tensor.chip<3>(0), DefaultDevice());
+ VERIFY_IS_EQUAL(chip3.data(), static_cast<float*>(0));
+}
+
+static void test_chip_raw_data_row_major()
+{
+ Tensor<float, 5, RowMajor> tensor(11,7,5,3,2);
+ tensor.setRandom();
+
+ typedef TensorEvaluator<decltype(tensor.chip<0>(3)), DefaultDevice> Evaluator0;
+ auto chip = Evaluator0(tensor.chip<0>(3), DefaultDevice());
+ for (int i = 0; i < 7; ++i) {
+ for (int j = 0; j < 5; ++j) {
+ for (int k = 0; k < 3; ++k) {
+ for (int l = 0; l < 2; ++l) {
+ int chip_index = l + 2 * (k + 3 * (j + 5 * i));
+ VERIFY_IS_EQUAL(chip.data()[chip_index], tensor(3,i,j,k,l));
+ }
+ }
+ }
+ }
+
+ typedef TensorEvaluator<decltype(tensor.chip<1>(0)), DefaultDevice> Evaluator1;
+ auto chip1 = Evaluator1(tensor.chip<1>(0), DefaultDevice());
+ VERIFY_IS_EQUAL(chip1.data(), static_cast<float*>(0));
+
+ typedef TensorEvaluator<decltype(tensor.chip<2>(0)), DefaultDevice> Evaluator2;
+ auto chip2 = Evaluator2(tensor.chip<2>(0), DefaultDevice());
+ VERIFY_IS_EQUAL(chip2.data(), static_cast<float*>(0));
+
+ typedef TensorEvaluator<decltype(tensor.chip<3>(0)), DefaultDevice> Evaluator3;
+ auto chip3 = Evaluator3(tensor.chip<3>(0), DefaultDevice());
+ VERIFY_IS_EQUAL(chip3.data(), static_cast<float*>(0));
+
+ typedef TensorEvaluator<decltype(tensor.chip<4>(0)), DefaultDevice> Evaluator4;
+ auto chip4 = Evaluator4(tensor.chip<4>(0), DefaultDevice());
+ VERIFY_IS_EQUAL(chip4.data(), static_cast<float*>(0));
+}
+
+EIGEN_DECLARE_TEST(cxx11_tensor_chipping)
+{
+ CALL_SUBTEST(test_simple_chip<ColMajor>());
+ CALL_SUBTEST(test_simple_chip<RowMajor>());
+ CALL_SUBTEST(test_dynamic_chip<ColMajor>());
+ CALL_SUBTEST(test_dynamic_chip<RowMajor>());
+ CALL_SUBTEST(test_chip_in_expr<ColMajor>());
+ CALL_SUBTEST(test_chip_in_expr<RowMajor>());
+ CALL_SUBTEST(test_chip_as_lvalue<ColMajor>());
+ CALL_SUBTEST(test_chip_as_lvalue<RowMajor>());
+ CALL_SUBTEST(test_chip_raw_data_col_major());
+ CALL_SUBTEST(test_chip_raw_data_row_major());
+}
diff --git a/unsupported/test/cxx11_tensor_chipping_sycl.cpp b/unsupported/test/cxx11_tensor_chipping_sycl.cpp
new file mode 100644
index 0000000..1e70931
--- /dev/null
+++ b/unsupported/test/cxx11_tensor_chipping_sycl.cpp
@@ -0,0 +1,623 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2016
+// Mehdi Goli Codeplay Software Ltd.
+// Ralph Potter Codeplay Software Ltd.
+// Luke Iwanski Codeplay Software Ltd.
+// Contact: <eigen@codeplay.com>
+// Benoit Steiner <benoit.steiner.goog@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+
+#define EIGEN_TEST_NO_LONGDOUBLE
+#define EIGEN_TEST_NO_COMPLEX
+
+#define EIGEN_DEFAULT_DENSE_INDEX_TYPE int64_t
+#define EIGEN_USE_SYCL
+
+#include "main.h"
+
+#include <Eigen/CXX11/Tensor>
+
+using Eigen::Tensor;
+
+template <typename DataType, int DataLayout, typename IndexType>
+static void test_static_chip_sycl(const Eigen::SyclDevice& sycl_device)
+{
+ IndexType sizeDim1 = 2;
+ IndexType sizeDim2 = 3;
+ IndexType sizeDim3 = 5;
+ IndexType sizeDim4 = 7;
+ IndexType sizeDim5 = 11;
+
+ array<IndexType, 5> tensorRange = {{sizeDim1, sizeDim2, sizeDim3, sizeDim4, sizeDim5}};
+ array<IndexType, 4> chip1TensorRange = {{sizeDim2, sizeDim3, sizeDim4, sizeDim5}};
+
+ Tensor<DataType, 5, DataLayout,IndexType> tensor(tensorRange);
+ Tensor<DataType, 4, DataLayout,IndexType> chip1(chip1TensorRange);
+
+ tensor.setRandom();
+
+ const size_t tensorBuffSize =tensor.size()*sizeof(DataType);
+ const size_t chip1TensorBuffSize =chip1.size()*sizeof(DataType);
+ DataType* gpu_data_tensor = static_cast<DataType*>(sycl_device.allocate(tensorBuffSize));
+ DataType* gpu_data_chip1 = static_cast<DataType*>(sycl_device.allocate(chip1TensorBuffSize));
+
+ TensorMap<Tensor<DataType, 5, DataLayout,IndexType>> gpu_tensor(gpu_data_tensor, tensorRange);
+ TensorMap<Tensor<DataType, 4, DataLayout,IndexType>> gpu_chip1(gpu_data_chip1, chip1TensorRange);
+
+ sycl_device.memcpyHostToDevice(gpu_data_tensor, tensor.data(), tensorBuffSize);
+ gpu_chip1.device(sycl_device)=gpu_tensor.template chip<0l>(1l);
+ sycl_device.memcpyDeviceToHost(chip1.data(), gpu_data_chip1, chip1TensorBuffSize);
+
+ VERIFY_IS_EQUAL(chip1.dimension(0), sizeDim2);
+ VERIFY_IS_EQUAL(chip1.dimension(1), sizeDim3);
+ VERIFY_IS_EQUAL(chip1.dimension(2), sizeDim4);
+ VERIFY_IS_EQUAL(chip1.dimension(3), sizeDim5);
+
+ for (IndexType i = 0; i < sizeDim2; ++i) {
+ for (IndexType j = 0; j < sizeDim3; ++j) {
+ for (IndexType k = 0; k < sizeDim4; ++k) {
+ for (IndexType l = 0; l < sizeDim5; ++l) {
+ VERIFY_IS_EQUAL(chip1(i,j,k,l), tensor(1l,i,j,k,l));
+ }
+ }
+ }
+ }
+
+ array<IndexType, 4> chip2TensorRange = {{sizeDim1, sizeDim3, sizeDim4, sizeDim5}};
+ Tensor<DataType, 4, DataLayout,IndexType> chip2(chip2TensorRange);
+ const size_t chip2TensorBuffSize =chip2.size()*sizeof(DataType);
+ DataType* gpu_data_chip2 = static_cast<DataType*>(sycl_device.allocate(chip2TensorBuffSize));
+ TensorMap<Tensor<DataType, 4, DataLayout,IndexType>> gpu_chip2(gpu_data_chip2, chip2TensorRange);
+
+ gpu_chip2.device(sycl_device)=gpu_tensor.template chip<1l>(1l);
+ sycl_device.memcpyDeviceToHost(chip2.data(), gpu_data_chip2, chip2TensorBuffSize);
+
+ VERIFY_IS_EQUAL(chip2.dimension(0), sizeDim1);
+ VERIFY_IS_EQUAL(chip2.dimension(1), sizeDim3);
+ VERIFY_IS_EQUAL(chip2.dimension(2), sizeDim4);
+ VERIFY_IS_EQUAL(chip2.dimension(3), sizeDim5);
+
+ for (IndexType i = 0; i < sizeDim1; ++i) {
+ for (IndexType j = 0; j < sizeDim3; ++j) {
+ for (IndexType k = 0; k < sizeDim4; ++k) {
+ for (IndexType l = 0; l < sizeDim5; ++l) {
+ VERIFY_IS_EQUAL(chip2(i,j,k,l), tensor(i,1l,j,k,l));
+ }
+ }
+ }
+ }
+
+ array<IndexType, 4> chip3TensorRange = {{sizeDim1, sizeDim2, sizeDim4, sizeDim5}};
+ Tensor<DataType, 4, DataLayout,IndexType> chip3(chip3TensorRange);
+ const size_t chip3TensorBuffSize =chip3.size()*sizeof(DataType);
+ DataType* gpu_data_chip3 = static_cast<DataType*>(sycl_device.allocate(chip3TensorBuffSize));
+ TensorMap<Tensor<DataType, 4, DataLayout,IndexType>> gpu_chip3(gpu_data_chip3, chip3TensorRange);
+
+ gpu_chip3.device(sycl_device)=gpu_tensor.template chip<2l>(2l);
+ sycl_device.memcpyDeviceToHost(chip3.data(), gpu_data_chip3, chip3TensorBuffSize);
+
+ VERIFY_IS_EQUAL(chip3.dimension(0), sizeDim1);
+ VERIFY_IS_EQUAL(chip3.dimension(1), sizeDim2);
+ VERIFY_IS_EQUAL(chip3.dimension(2), sizeDim4);
+ VERIFY_IS_EQUAL(chip3.dimension(3), sizeDim5);
+
+ for (IndexType i = 0; i < sizeDim1; ++i) {
+ for (IndexType j = 0; j < sizeDim2; ++j) {
+ for (IndexType k = 0; k < sizeDim4; ++k) {
+ for (IndexType l = 0; l < sizeDim5; ++l) {
+ VERIFY_IS_EQUAL(chip3(i,j,k,l), tensor(i,j,2l,k,l));
+ }
+ }
+ }
+ }
+
+ array<IndexType, 4> chip4TensorRange = {{sizeDim1, sizeDim2, sizeDim3, sizeDim5}};
+ Tensor<DataType, 4, DataLayout,IndexType> chip4(chip4TensorRange);
+ const size_t chip4TensorBuffSize =chip4.size()*sizeof(DataType);
+ DataType* gpu_data_chip4 = static_cast<DataType*>(sycl_device.allocate(chip4TensorBuffSize));
+ TensorMap<Tensor<DataType, 4, DataLayout,IndexType>> gpu_chip4(gpu_data_chip4, chip4TensorRange);
+
+ gpu_chip4.device(sycl_device)=gpu_tensor.template chip<3l>(5l);
+ sycl_device.memcpyDeviceToHost(chip4.data(), gpu_data_chip4, chip4TensorBuffSize);
+
+ VERIFY_IS_EQUAL(chip4.dimension(0), sizeDim1);
+ VERIFY_IS_EQUAL(chip4.dimension(1), sizeDim2);
+ VERIFY_IS_EQUAL(chip4.dimension(2), sizeDim3);
+ VERIFY_IS_EQUAL(chip4.dimension(3), sizeDim5);
+
+ for (IndexType i = 0; i < sizeDim1; ++i) {
+ for (IndexType j = 0; j < sizeDim2; ++j) {
+ for (IndexType k = 0; k < sizeDim3; ++k) {
+ for (IndexType l = 0; l < sizeDim5; ++l) {
+ VERIFY_IS_EQUAL(chip4(i,j,k,l), tensor(i,j,k,5l,l));
+ }
+ }
+ }
+ }
+
+
+ array<IndexType, 4> chip5TensorRange = {{sizeDim1, sizeDim2, sizeDim3, sizeDim4}};
+ Tensor<DataType, 4, DataLayout,IndexType> chip5(chip5TensorRange);
+ const size_t chip5TensorBuffSize =chip5.size()*sizeof(DataType);
+ DataType* gpu_data_chip5 = static_cast<DataType*>(sycl_device.allocate(chip5TensorBuffSize));
+ TensorMap<Tensor<DataType, 4, DataLayout,IndexType>> gpu_chip5(gpu_data_chip5, chip5TensorRange);
+
+ gpu_chip5.device(sycl_device)=gpu_tensor.template chip<4l>(7l);
+ sycl_device.memcpyDeviceToHost(chip5.data(), gpu_data_chip5, chip5TensorBuffSize);
+
+ VERIFY_IS_EQUAL(chip5.dimension(0), sizeDim1);
+ VERIFY_IS_EQUAL(chip5.dimension(1), sizeDim2);
+ VERIFY_IS_EQUAL(chip5.dimension(2), sizeDim3);
+ VERIFY_IS_EQUAL(chip5.dimension(3), sizeDim4);
+
+ for (IndexType i = 0; i < sizeDim1; ++i) {
+ for (IndexType j = 0; j < sizeDim2; ++j) {
+ for (IndexType k = 0; k < sizeDim3; ++k) {
+ for (IndexType l = 0; l < sizeDim4; ++l) {
+ VERIFY_IS_EQUAL(chip5(i,j,k,l), tensor(i,j,k,l,7l));
+ }
+ }
+ }
+ }
+
+ sycl_device.deallocate(gpu_data_tensor);
+ sycl_device.deallocate(gpu_data_chip1);
+ sycl_device.deallocate(gpu_data_chip2);
+ sycl_device.deallocate(gpu_data_chip3);
+ sycl_device.deallocate(gpu_data_chip4);
+ sycl_device.deallocate(gpu_data_chip5);
+}
+
+template <typename DataType, int DataLayout, typename IndexType>
+static void test_dynamic_chip_sycl(const Eigen::SyclDevice& sycl_device)
+{
+ IndexType sizeDim1 = 2;
+ IndexType sizeDim2 = 3;
+ IndexType sizeDim3 = 5;
+ IndexType sizeDim4 = 7;
+ IndexType sizeDim5 = 11;
+
+ array<IndexType, 5> tensorRange = {{sizeDim1, sizeDim2, sizeDim3, sizeDim4, sizeDim5}};
+ array<IndexType, 4> chip1TensorRange = {{sizeDim2, sizeDim3, sizeDim4, sizeDim5}};
+
+ Tensor<DataType, 5, DataLayout,IndexType> tensor(tensorRange);
+ Tensor<DataType, 4, DataLayout,IndexType> chip1(chip1TensorRange);
+
+ tensor.setRandom();
+
+ const size_t tensorBuffSize =tensor.size()*sizeof(DataType);
+ const size_t chip1TensorBuffSize =chip1.size()*sizeof(DataType);
+ DataType* gpu_data_tensor = static_cast<DataType*>(sycl_device.allocate(tensorBuffSize));
+ DataType* gpu_data_chip1 = static_cast<DataType*>(sycl_device.allocate(chip1TensorBuffSize));
+
+ TensorMap<Tensor<DataType, 5, DataLayout,IndexType>> gpu_tensor(gpu_data_tensor, tensorRange);
+ TensorMap<Tensor<DataType, 4, DataLayout,IndexType>> gpu_chip1(gpu_data_chip1, chip1TensorRange);
+
+ sycl_device.memcpyHostToDevice(gpu_data_tensor, tensor.data(), tensorBuffSize);
+ gpu_chip1.device(sycl_device)=gpu_tensor.chip(1l,0l);
+ sycl_device.memcpyDeviceToHost(chip1.data(), gpu_data_chip1, chip1TensorBuffSize);
+
+ VERIFY_IS_EQUAL(chip1.dimension(0), sizeDim2);
+ VERIFY_IS_EQUAL(chip1.dimension(1), sizeDim3);
+ VERIFY_IS_EQUAL(chip1.dimension(2), sizeDim4);
+ VERIFY_IS_EQUAL(chip1.dimension(3), sizeDim5);
+
+ for (IndexType i = 0; i < sizeDim2; ++i) {
+ for (IndexType j = 0; j < sizeDim3; ++j) {
+ for (IndexType k = 0; k < sizeDim4; ++k) {
+ for (IndexType l = 0; l < sizeDim5; ++l) {
+ VERIFY_IS_EQUAL(chip1(i,j,k,l), tensor(1l,i,j,k,l));
+ }
+ }
+ }
+ }
+
+ array<IndexType, 4> chip2TensorRange = {{sizeDim1, sizeDim3, sizeDim4, sizeDim5}};
+ Tensor<DataType, 4, DataLayout,IndexType> chip2(chip2TensorRange);
+ const size_t chip2TensorBuffSize =chip2.size()*sizeof(DataType);
+ DataType* gpu_data_chip2 = static_cast<DataType*>(sycl_device.allocate(chip2TensorBuffSize));
+ TensorMap<Tensor<DataType, 4, DataLayout,IndexType>> gpu_chip2(gpu_data_chip2, chip2TensorRange);
+
+ gpu_chip2.device(sycl_device)=gpu_tensor.chip(1l,1l);
+ sycl_device.memcpyDeviceToHost(chip2.data(), gpu_data_chip2, chip2TensorBuffSize);
+
+ VERIFY_IS_EQUAL(chip2.dimension(0), sizeDim1);
+ VERIFY_IS_EQUAL(chip2.dimension(1), sizeDim3);
+ VERIFY_IS_EQUAL(chip2.dimension(2), sizeDim4);
+ VERIFY_IS_EQUAL(chip2.dimension(3), sizeDim5);
+
+ for (IndexType i = 0; i < sizeDim1; ++i) {
+ for (IndexType j = 0; j < sizeDim3; ++j) {
+ for (IndexType k = 0; k < sizeDim4; ++k) {
+ for (IndexType l = 0; l < sizeDim5; ++l) {
+ VERIFY_IS_EQUAL(chip2(i,j,k,l), tensor(i,1l,j,k,l));
+ }
+ }
+ }
+ }
+
+ array<IndexType, 4> chip3TensorRange = {{sizeDim1, sizeDim2, sizeDim4, sizeDim5}};
+ Tensor<DataType, 4, DataLayout,IndexType> chip3(chip3TensorRange);
+ const size_t chip3TensorBuffSize =chip3.size()*sizeof(DataType);
+ DataType* gpu_data_chip3 = static_cast<DataType*>(sycl_device.allocate(chip3TensorBuffSize));
+ TensorMap<Tensor<DataType, 4, DataLayout,IndexType>> gpu_chip3(gpu_data_chip3, chip3TensorRange);
+
+ gpu_chip3.device(sycl_device)=gpu_tensor.chip(2l,2l);
+ sycl_device.memcpyDeviceToHost(chip3.data(), gpu_data_chip3, chip3TensorBuffSize);
+
+ VERIFY_IS_EQUAL(chip3.dimension(0), sizeDim1);
+ VERIFY_IS_EQUAL(chip3.dimension(1), sizeDim2);
+ VERIFY_IS_EQUAL(chip3.dimension(2), sizeDim4);
+ VERIFY_IS_EQUAL(chip3.dimension(3), sizeDim5);
+
+ for (IndexType i = 0; i < sizeDim1; ++i) {
+ for (IndexType j = 0; j < sizeDim2; ++j) {
+ for (IndexType k = 0; k < sizeDim4; ++k) {
+ for (IndexType l = 0; l < sizeDim5; ++l) {
+ VERIFY_IS_EQUAL(chip3(i,j,k,l), tensor(i,j,2l,k,l));
+ }
+ }
+ }
+ }
+
+ array<IndexType, 4> chip4TensorRange = {{sizeDim1, sizeDim2, sizeDim3, sizeDim5}};
+ Tensor<DataType, 4, DataLayout,IndexType> chip4(chip4TensorRange);
+ const size_t chip4TensorBuffSize =chip4.size()*sizeof(DataType);
+ DataType* gpu_data_chip4 = static_cast<DataType*>(sycl_device.allocate(chip4TensorBuffSize));
+ TensorMap<Tensor<DataType, 4, DataLayout,IndexType>> gpu_chip4(gpu_data_chip4, chip4TensorRange);
+
+ gpu_chip4.device(sycl_device)=gpu_tensor.chip(5l,3l);
+ sycl_device.memcpyDeviceToHost(chip4.data(), gpu_data_chip4, chip4TensorBuffSize);
+
+ VERIFY_IS_EQUAL(chip4.dimension(0), sizeDim1);
+ VERIFY_IS_EQUAL(chip4.dimension(1), sizeDim2);
+ VERIFY_IS_EQUAL(chip4.dimension(2), sizeDim3);
+ VERIFY_IS_EQUAL(chip4.dimension(3), sizeDim5);
+
+ for (IndexType i = 0; i < sizeDim1; ++i) {
+ for (IndexType j = 0; j < sizeDim2; ++j) {
+ for (IndexType k = 0; k < sizeDim3; ++k) {
+ for (IndexType l = 0; l < sizeDim5; ++l) {
+ VERIFY_IS_EQUAL(chip4(i,j,k,l), tensor(i,j,k,5l,l));
+ }
+ }
+ }
+ }
+
+
+ array<IndexType, 4> chip5TensorRange = {{sizeDim1, sizeDim2, sizeDim3, sizeDim4}};
+ Tensor<DataType, 4, DataLayout,IndexType> chip5(chip5TensorRange);
+ const size_t chip5TensorBuffSize =chip5.size()*sizeof(DataType);
+ DataType* gpu_data_chip5 = static_cast<DataType*>(sycl_device.allocate(chip5TensorBuffSize));
+ TensorMap<Tensor<DataType, 4, DataLayout,IndexType>> gpu_chip5(gpu_data_chip5, chip5TensorRange);
+
+ gpu_chip5.device(sycl_device)=gpu_tensor.chip(7l,4l);
+ sycl_device.memcpyDeviceToHost(chip5.data(), gpu_data_chip5, chip5TensorBuffSize);
+
+ VERIFY_IS_EQUAL(chip5.dimension(0), sizeDim1);
+ VERIFY_IS_EQUAL(chip5.dimension(1), sizeDim2);
+ VERIFY_IS_EQUAL(chip5.dimension(2), sizeDim3);
+ VERIFY_IS_EQUAL(chip5.dimension(3), sizeDim4);
+
+ for (IndexType i = 0; i < sizeDim1; ++i) {
+ for (IndexType j = 0; j < sizeDim2; ++j) {
+ for (IndexType k = 0; k < sizeDim3; ++k) {
+ for (IndexType l = 0; l < sizeDim4; ++l) {
+ VERIFY_IS_EQUAL(chip5(i,j,k,l), tensor(i,j,k,l,7l));
+ }
+ }
+ }
+ }
+ sycl_device.deallocate(gpu_data_tensor);
+ sycl_device.deallocate(gpu_data_chip1);
+ sycl_device.deallocate(gpu_data_chip2);
+ sycl_device.deallocate(gpu_data_chip3);
+ sycl_device.deallocate(gpu_data_chip4);
+ sycl_device.deallocate(gpu_data_chip5);
+}
+
+template <typename DataType, int DataLayout, typename IndexType>
+static void test_chip_in_expr(const Eigen::SyclDevice& sycl_device) {
+
+ IndexType sizeDim1 = 2;
+ IndexType sizeDim2 = 3;
+ IndexType sizeDim3 = 5;
+ IndexType sizeDim4 = 7;
+ IndexType sizeDim5 = 11;
+
+ array<IndexType, 5> tensorRange = {{sizeDim1, sizeDim2, sizeDim3, sizeDim4, sizeDim5}};
+ array<IndexType, 4> chip1TensorRange = {{sizeDim2, sizeDim3, sizeDim4, sizeDim5}};
+
+ Tensor<DataType, 5, DataLayout,IndexType> tensor(tensorRange);
+
+ Tensor<DataType, 4, DataLayout,IndexType> chip1(chip1TensorRange);
+ Tensor<DataType, 4, DataLayout,IndexType> tensor1(chip1TensorRange);
+ tensor.setRandom();
+ tensor1.setRandom();
+
+ const size_t tensorBuffSize =tensor.size()*sizeof(DataType);
+ const size_t chip1TensorBuffSize =chip1.size()*sizeof(DataType);
+ DataType* gpu_data_tensor = static_cast<DataType*>(sycl_device.allocate(tensorBuffSize));
+ DataType* gpu_data_chip1 = static_cast<DataType*>(sycl_device.allocate(chip1TensorBuffSize));
+ DataType* gpu_data_tensor1 = static_cast<DataType*>(sycl_device.allocate(chip1TensorBuffSize));
+
+ TensorMap<Tensor<DataType, 5, DataLayout,IndexType>> gpu_tensor(gpu_data_tensor, tensorRange);
+ TensorMap<Tensor<DataType, 4, DataLayout,IndexType>> gpu_chip1(gpu_data_chip1, chip1TensorRange);
+ TensorMap<Tensor<DataType, 4, DataLayout,IndexType>> gpu_tensor1(gpu_data_tensor1, chip1TensorRange);
+
+
+ sycl_device.memcpyHostToDevice(gpu_data_tensor, tensor.data(), tensorBuffSize);
+ sycl_device.memcpyHostToDevice(gpu_data_tensor1, tensor1.data(), chip1TensorBuffSize);
+ gpu_chip1.device(sycl_device)=gpu_tensor.template chip<0l>(0l) + gpu_tensor1;
+ sycl_device.memcpyDeviceToHost(chip1.data(), gpu_data_chip1, chip1TensorBuffSize);
+
+ for (int i = 0; i < sizeDim2; ++i) {
+ for (int j = 0; j < sizeDim3; ++j) {
+ for (int k = 0; k < sizeDim4; ++k) {
+ for (int l = 0; l < sizeDim5; ++l) {
+ float expected = tensor(0l,i,j,k,l) + tensor1(i,j,k,l);
+ VERIFY_IS_EQUAL(chip1(i,j,k,l), expected);
+ }
+ }
+ }
+ }
+
+ array<IndexType, 3> chip2TensorRange = {{sizeDim2, sizeDim4, sizeDim5}};
+ Tensor<DataType, 3, DataLayout,IndexType> tensor2(chip2TensorRange);
+ Tensor<DataType, 3, DataLayout,IndexType> chip2(chip2TensorRange);
+ tensor2.setRandom();
+ const size_t chip2TensorBuffSize =tensor2.size()*sizeof(DataType);
+ DataType* gpu_data_tensor2 = static_cast<DataType*>(sycl_device.allocate(chip2TensorBuffSize));
+ DataType* gpu_data_chip2 = static_cast<DataType*>(sycl_device.allocate(chip2TensorBuffSize));
+ TensorMap<Tensor<DataType, 3, DataLayout,IndexType>> gpu_tensor2(gpu_data_tensor2, chip2TensorRange);
+ TensorMap<Tensor<DataType, 3, DataLayout,IndexType>> gpu_chip2(gpu_data_chip2, chip2TensorRange);
+
+ sycl_device.memcpyHostToDevice(gpu_data_tensor2, tensor2.data(), chip2TensorBuffSize);
+ gpu_chip2.device(sycl_device)=gpu_tensor.template chip<0l>(0l).template chip<1l>(2l) + gpu_tensor2;
+ sycl_device.memcpyDeviceToHost(chip2.data(), gpu_data_chip2, chip2TensorBuffSize);
+
+ for (int i = 0; i < sizeDim2; ++i) {
+ for (int j = 0; j < sizeDim4; ++j) {
+ for (int k = 0; k < sizeDim5; ++k) {
+ float expected = tensor(0l,i,2l,j,k) + tensor2(i,j,k);
+ VERIFY_IS_EQUAL(chip2(i,j,k), expected);
+ }
+ }
+ }
+ sycl_device.deallocate(gpu_data_tensor);
+ sycl_device.deallocate(gpu_data_tensor1);
+ sycl_device.deallocate(gpu_data_chip1);
+ sycl_device.deallocate(gpu_data_tensor2);
+ sycl_device.deallocate(gpu_data_chip2);
+}
+
+template <typename DataType, int DataLayout, typename IndexType>
+static void test_chip_as_lvalue_sycl(const Eigen::SyclDevice& sycl_device)
+{
+
+ IndexType sizeDim1 = 2;
+ IndexType sizeDim2 = 3;
+ IndexType sizeDim3 = 5;
+ IndexType sizeDim4 = 7;
+ IndexType sizeDim5 = 11;
+
+ array<IndexType, 5> tensorRange = {{sizeDim1, sizeDim2, sizeDim3, sizeDim4, sizeDim5}};
+ array<IndexType, 4> input2TensorRange = {{sizeDim2, sizeDim3, sizeDim4, sizeDim5}};
+
+ Tensor<DataType, 5, DataLayout,IndexType> tensor(tensorRange);
+ Tensor<DataType, 5, DataLayout,IndexType> input1(tensorRange);
+ Tensor<DataType, 4, DataLayout,IndexType> input2(input2TensorRange);
+ input1.setRandom();
+ input2.setRandom();
+
+
+ const size_t tensorBuffSize =tensor.size()*sizeof(DataType);
+ const size_t input2TensorBuffSize =input2.size()*sizeof(DataType);
+ std::cout << tensorBuffSize << " , "<< input2TensorBuffSize << std::endl;
+ DataType* gpu_data_tensor = static_cast<DataType*>(sycl_device.allocate(tensorBuffSize));
+ DataType* gpu_data_input1 = static_cast<DataType*>(sycl_device.allocate(tensorBuffSize));
+ DataType* gpu_data_input2 = static_cast<DataType*>(sycl_device.allocate(input2TensorBuffSize));
+
+ TensorMap<Tensor<DataType, 5, DataLayout,IndexType>> gpu_tensor(gpu_data_tensor, tensorRange);
+ TensorMap<Tensor<DataType, 5, DataLayout,IndexType>> gpu_input1(gpu_data_input1, tensorRange);
+ TensorMap<Tensor<DataType, 4, DataLayout,IndexType>> gpu_input2(gpu_data_input2, input2TensorRange);
+
+ sycl_device.memcpyHostToDevice(gpu_data_input1, input1.data(), tensorBuffSize);
+ gpu_tensor.device(sycl_device)=gpu_input1;
+ sycl_device.memcpyHostToDevice(gpu_data_input2, input2.data(), input2TensorBuffSize);
+ gpu_tensor.template chip<0l>(1l).device(sycl_device)=gpu_input2;
+ sycl_device.memcpyDeviceToHost(tensor.data(), gpu_data_tensor, tensorBuffSize);
+
+ for (int i = 0; i < sizeDim1; ++i) {
+ for (int j = 0; j < sizeDim2; ++j) {
+ for (int k = 0; k < sizeDim3; ++k) {
+ for (int l = 0; l < sizeDim4; ++l) {
+ for (int m = 0; m < sizeDim5; ++m) {
+ if (i != 1) {
+ VERIFY_IS_EQUAL(tensor(i,j,k,l,m), input1(i,j,k,l,m));
+ } else {
+ VERIFY_IS_EQUAL(tensor(i,j,k,l,m), input2(j,k,l,m));
+ }
+ }
+ }
+ }
+ }
+ }
+
+ gpu_tensor.device(sycl_device)=gpu_input1;
+ array<IndexType, 4> input3TensorRange = {{sizeDim1, sizeDim3, sizeDim4, sizeDim5}};
+ Tensor<DataType, 4, DataLayout,IndexType> input3(input3TensorRange);
+ input3.setRandom();
+
+ const size_t input3TensorBuffSize =input3.size()*sizeof(DataType);
+ DataType* gpu_data_input3 = static_cast<DataType*>(sycl_device.allocate(input3TensorBuffSize));
+ TensorMap<Tensor<DataType, 4, DataLayout,IndexType>> gpu_input3(gpu_data_input3, input3TensorRange);
+
+ sycl_device.memcpyHostToDevice(gpu_data_input3, input3.data(), input3TensorBuffSize);
+ gpu_tensor.template chip<1l>(1l).device(sycl_device)=gpu_input3;
+ sycl_device.memcpyDeviceToHost(tensor.data(), gpu_data_tensor, tensorBuffSize);
+
+ for (int i = 0; i < sizeDim1; ++i) {
+ for (int j = 0; j < sizeDim2; ++j) {
+ for (int k = 0; k <sizeDim3; ++k) {
+ for (int l = 0; l < sizeDim4; ++l) {
+ for (int m = 0; m < sizeDim5; ++m) {
+ if (j != 1) {
+ VERIFY_IS_EQUAL(tensor(i,j,k,l,m), input1(i,j,k,l,m));
+ } else {
+ VERIFY_IS_EQUAL(tensor(i,j,k,l,m), input3(i,k,l,m));
+ }
+ }
+ }
+ }
+ }
+ }
+
+ gpu_tensor.device(sycl_device)=gpu_input1;
+ array<IndexType, 4> input4TensorRange = {{sizeDim1, sizeDim2, sizeDim4, sizeDim5}};
+ Tensor<DataType, 4, DataLayout,IndexType> input4(input4TensorRange);
+ input4.setRandom();
+
+ const size_t input4TensorBuffSize =input4.size()*sizeof(DataType);
+ DataType* gpu_data_input4 = static_cast<DataType*>(sycl_device.allocate(input4TensorBuffSize));
+ TensorMap<Tensor<DataType, 4, DataLayout,IndexType>> gpu_input4(gpu_data_input4, input4TensorRange);
+
+ sycl_device.memcpyHostToDevice(gpu_data_input4, input4.data(), input4TensorBuffSize);
+ gpu_tensor.template chip<2l>(3l).device(sycl_device)=gpu_input4;
+ sycl_device.memcpyDeviceToHost(tensor.data(), gpu_data_tensor, tensorBuffSize);
+
+ for (int i = 0; i < sizeDim1; ++i) {
+ for (int j = 0; j < sizeDim2; ++j) {
+ for (int k = 0; k <sizeDim3; ++k) {
+ for (int l = 0; l < sizeDim4; ++l) {
+ for (int m = 0; m < sizeDim5; ++m) {
+ if (k != 3) {
+ VERIFY_IS_EQUAL(tensor(i,j,k,l,m), input1(i,j,k,l,m));
+ } else {
+ VERIFY_IS_EQUAL(tensor(i,j,k,l,m), input4(i,j,l,m));
+ }
+ }
+ }
+ }
+ }
+ }
+
+ gpu_tensor.device(sycl_device)=gpu_input1;
+ array<IndexType, 4> input5TensorRange = {{sizeDim1, sizeDim2, sizeDim3, sizeDim5}};
+ Tensor<DataType, 4, DataLayout,IndexType> input5(input5TensorRange);
+ input5.setRandom();
+
+ const size_t input5TensorBuffSize =input5.size()*sizeof(DataType);
+ DataType* gpu_data_input5 = static_cast<DataType*>(sycl_device.allocate(input5TensorBuffSize));
+ TensorMap<Tensor<DataType, 4, DataLayout,IndexType>> gpu_input5(gpu_data_input5, input5TensorRange);
+
+ sycl_device.memcpyHostToDevice(gpu_data_input5, input5.data(), input5TensorBuffSize);
+ gpu_tensor.template chip<3l>(4l).device(sycl_device)=gpu_input5;
+ sycl_device.memcpyDeviceToHost(tensor.data(), gpu_data_tensor, tensorBuffSize);
+
+ for (int i = 0; i < sizeDim1; ++i) {
+ for (int j = 0; j < sizeDim2; ++j) {
+ for (int k = 0; k <sizeDim3; ++k) {
+ for (int l = 0; l < sizeDim4; ++l) {
+ for (int m = 0; m < sizeDim5; ++m) {
+ if (l != 4) {
+ VERIFY_IS_EQUAL(tensor(i,j,k,l,m), input1(i,j,k,l,m));
+ } else {
+ VERIFY_IS_EQUAL(tensor(i,j,k,l,m), input5(i,j,k,m));
+ }
+ }
+ }
+ }
+ }
+ }
+ gpu_tensor.device(sycl_device)=gpu_input1;
+ array<IndexType, 4> input6TensorRange = {{sizeDim1, sizeDim2, sizeDim3, sizeDim4}};
+ Tensor<DataType, 4, DataLayout,IndexType> input6(input6TensorRange);
+ input6.setRandom();
+
+ const size_t input6TensorBuffSize =input6.size()*sizeof(DataType);
+ DataType* gpu_data_input6 = static_cast<DataType*>(sycl_device.allocate(input6TensorBuffSize));
+ TensorMap<Tensor<DataType, 4, DataLayout,IndexType>> gpu_input6(gpu_data_input6, input6TensorRange);
+
+ sycl_device.memcpyHostToDevice(gpu_data_input6, input6.data(), input6TensorBuffSize);
+ gpu_tensor.template chip<4l>(5l).device(sycl_device)=gpu_input6;
+ sycl_device.memcpyDeviceToHost(tensor.data(), gpu_data_tensor, tensorBuffSize);
+
+ for (int i = 0; i < sizeDim1; ++i) {
+ for (int j = 0; j < sizeDim2; ++j) {
+ for (int k = 0; k <sizeDim3; ++k) {
+ for (int l = 0; l < sizeDim4; ++l) {
+ for (int m = 0; m < sizeDim5; ++m) {
+ if (m != 5) {
+ VERIFY_IS_EQUAL(tensor(i,j,k,l,m), input1(i,j,k,l,m));
+ } else {
+ VERIFY_IS_EQUAL(tensor(i,j,k,l,m), input6(i,j,k,l));
+ }
+ }
+ }
+ }
+ }
+ }
+
+
+ gpu_tensor.device(sycl_device)=gpu_input1;
+ Tensor<DataType, 5, DataLayout,IndexType> input7(tensorRange);
+ input7.setRandom();
+
+ DataType* gpu_data_input7 = static_cast<DataType*>(sycl_device.allocate(tensorBuffSize));
+ TensorMap<Tensor<DataType, 5, DataLayout,IndexType>> gpu_input7(gpu_data_input7, tensorRange);
+
+ sycl_device.memcpyHostToDevice(gpu_data_input7, input7.data(), tensorBuffSize);
+ gpu_tensor.chip(0l,0l).device(sycl_device)=gpu_input7.chip(0l,0l);
+ sycl_device.memcpyDeviceToHost(tensor.data(), gpu_data_tensor, tensorBuffSize);
+
+ for (int i = 0; i < sizeDim1; ++i) {
+ for (int j = 0; j < sizeDim2; ++j) {
+ for (int k = 0; k <sizeDim3; ++k) {
+ for (int l = 0; l < sizeDim4; ++l) {
+ for (int m = 0; m < sizeDim5; ++m) {
+ if (i != 0) {
+ VERIFY_IS_EQUAL(tensor(i,j,k,l,m), input1(i,j,k,l,m));
+ } else {
+ VERIFY_IS_EQUAL(tensor(i,j,k,l,m), input7(i,j,k,l,m));
+ }
+ }
+ }
+ }
+ }
+ }
+ sycl_device.deallocate(gpu_data_tensor);
+ sycl_device.deallocate(gpu_data_input1);
+ sycl_device.deallocate(gpu_data_input2);
+ sycl_device.deallocate(gpu_data_input3);
+ sycl_device.deallocate(gpu_data_input4);
+ sycl_device.deallocate(gpu_data_input5);
+ sycl_device.deallocate(gpu_data_input6);
+ sycl_device.deallocate(gpu_data_input7);
+
+}
+
+template<typename DataType, typename dev_Selector> void sycl_chipping_test_per_device(dev_Selector s){
+ QueueInterface queueInterface(s);
+ auto sycl_device = Eigen::SyclDevice(&queueInterface);
+ /* test_static_chip_sycl<DataType, RowMajor, int64_t>(sycl_device);
+ test_static_chip_sycl<DataType, ColMajor, int64_t>(sycl_device);
+ test_dynamic_chip_sycl<DataType, RowMajor, int64_t>(sycl_device);
+ test_dynamic_chip_sycl<DataType, ColMajor, int64_t>(sycl_device);
+ test_chip_in_expr<DataType, RowMajor, int64_t>(sycl_device);
+ test_chip_in_expr<DataType, ColMajor, int64_t>(sycl_device);*/
+ test_chip_as_lvalue_sycl<DataType, RowMajor, int64_t>(sycl_device);
+ // test_chip_as_lvalue_sycl<DataType, ColMajor, int64_t>(sycl_device);
+}
+EIGEN_DECLARE_TEST(cxx11_tensor_chipping_sycl)
+{
+ for (const auto& device :Eigen::get_sycl_supported_devices()) {
+ CALL_SUBTEST(sycl_chipping_test_per_device<float>(device));
+ }
+}
diff --git a/unsupported/test/cxx11_tensor_comparisons.cpp b/unsupported/test/cxx11_tensor_comparisons.cpp
new file mode 100644
index 0000000..1a18e07
--- /dev/null
+++ b/unsupported/test/cxx11_tensor_comparisons.cpp
@@ -0,0 +1,84 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "main.h"
+
+#include <Eigen/CXX11/Tensor>
+
+using Eigen::Tensor;
+using Eigen::RowMajor;
+
+static void test_orderings()
+{
+ Tensor<float, 3> mat1(2,3,7);
+ Tensor<float, 3> mat2(2,3,7);
+ Tensor<bool, 3> lt(2,3,7);
+ Tensor<bool, 3> le(2,3,7);
+ Tensor<bool, 3> gt(2,3,7);
+ Tensor<bool, 3> ge(2,3,7);
+
+ mat1.setRandom();
+ mat2.setRandom();
+
+ lt = mat1 < mat2;
+ le = mat1 <= mat2;
+ gt = mat1 > mat2;
+ ge = mat1 >= mat2;
+
+ for (int i = 0; i < 2; ++i) {
+ for (int j = 0; j < 3; ++j) {
+ for (int k = 0; k < 7; ++k) {
+ VERIFY_IS_EQUAL(lt(i,j,k), mat1(i,j,k) < mat2(i,j,k));
+ VERIFY_IS_EQUAL(le(i,j,k), mat1(i,j,k) <= mat2(i,j,k));
+ VERIFY_IS_EQUAL(gt(i,j,k), mat1(i,j,k) > mat2(i,j,k));
+ VERIFY_IS_EQUAL(ge(i,j,k), mat1(i,j,k) >= mat2(i,j,k));
+ }
+ }
+ }
+}
+
+
+static void test_equality()
+{
+ Tensor<float, 3> mat1(2,3,7);
+ Tensor<float, 3> mat2(2,3,7);
+
+ mat1.setRandom();
+ mat2.setRandom();
+ for (int i = 0; i < 2; ++i) {
+ for (int j = 0; j < 3; ++j) {
+ for (int k = 0; k < 7; ++k) {
+ if (internal::random<bool>()) {
+ mat2(i,j,k) = mat1(i,j,k);
+ }
+ }
+ }
+ }
+
+ Tensor<bool, 3> eq(2,3,7);
+ Tensor<bool, 3> ne(2,3,7);
+ eq = (mat1 == mat2);
+ ne = (mat1 != mat2);
+
+ for (int i = 0; i < 2; ++i) {
+ for (int j = 0; j < 3; ++j) {
+ for (int k = 0; k < 7; ++k) {
+ VERIFY_IS_EQUAL(eq(i,j,k), mat1(i,j,k) == mat2(i,j,k));
+ VERIFY_IS_EQUAL(ne(i,j,k), mat1(i,j,k) != mat2(i,j,k));
+ }
+ }
+ }
+}
+
+
+EIGEN_DECLARE_TEST(cxx11_tensor_comparisons)
+{
+ CALL_SUBTEST(test_orderings());
+ CALL_SUBTEST(test_equality());
+}
diff --git a/unsupported/test/cxx11_tensor_complex_cwise_ops_gpu.cu b/unsupported/test/cxx11_tensor_complex_cwise_ops_gpu.cu
new file mode 100644
index 0000000..99447b2
--- /dev/null
+++ b/unsupported/test/cxx11_tensor_complex_cwise_ops_gpu.cu
@@ -0,0 +1,102 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2016 Benoit Steiner <benoit.steiner.goog@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#define EIGEN_TEST_NO_LONGDOUBLE
+
+#define EIGEN_USE_GPU
+
+#include "main.h"
+#include <unsupported/Eigen/CXX11/Tensor>
+
+using Eigen::Tensor;
+
+template<typename T>
+void test_cuda_complex_cwise_ops() {
+ const int kNumItems = 2;
+ std::size_t complex_bytes = kNumItems * sizeof(std::complex<T>);
+
+ std::complex<T>* d_in1;
+ std::complex<T>* d_in2;
+ std::complex<T>* d_out;
+ cudaMalloc((void**)(&d_in1), complex_bytes);
+ cudaMalloc((void**)(&d_in2), complex_bytes);
+ cudaMalloc((void**)(&d_out), complex_bytes);
+
+ Eigen::GpuStreamDevice stream;
+ Eigen::GpuDevice gpu_device(&stream);
+
+ Eigen::TensorMap<Eigen::Tensor<std::complex<T>, 1, 0, int>, Eigen::Aligned> gpu_in1(
+ d_in1, kNumItems);
+ Eigen::TensorMap<Eigen::Tensor<std::complex<T>, 1, 0, int>, Eigen::Aligned> gpu_in2(
+ d_in2, kNumItems);
+ Eigen::TensorMap<Eigen::Tensor<std::complex<T>, 1, 0, int>, Eigen::Aligned> gpu_out(
+ d_out, kNumItems);
+
+ const std::complex<T> a(3.14f, 2.7f);
+ const std::complex<T> b(-10.6f, 1.4f);
+
+ gpu_in1.device(gpu_device) = gpu_in1.constant(a);
+ gpu_in2.device(gpu_device) = gpu_in2.constant(b);
+
+ enum CwiseOp {
+ Add = 0,
+ Sub,
+ Mul,
+ Div,
+ Neg,
+ NbOps
+ };
+
+ Tensor<std::complex<T>, 1, 0, int> actual(kNumItems);
+ for (int op = Add; op < NbOps; op++) {
+ std::complex<T> expected;
+ switch (static_cast<CwiseOp>(op)) {
+ case Add:
+ gpu_out.device(gpu_device) = gpu_in1 + gpu_in2;
+ expected = a + b;
+ break;
+ case Sub:
+ gpu_out.device(gpu_device) = gpu_in1 - gpu_in2;
+ expected = a - b;
+ break;
+ case Mul:
+ gpu_out.device(gpu_device) = gpu_in1 * gpu_in2;
+ expected = a * b;
+ break;
+ case Div:
+ gpu_out.device(gpu_device) = gpu_in1 / gpu_in2;
+ expected = a / b;
+ break;
+ case Neg:
+ gpu_out.device(gpu_device) = -gpu_in1;
+ expected = -a;
+ break;
+ case NbOps:
+ break;
+ }
+ assert(cudaMemcpyAsync(actual.data(), d_out, complex_bytes, cudaMemcpyDeviceToHost,
+ gpu_device.stream()) == cudaSuccess);
+ assert(cudaStreamSynchronize(gpu_device.stream()) == cudaSuccess);
+
+ for (int i = 0; i < kNumItems; ++i) {
+ VERIFY_IS_APPROX(actual(i), expected);
+ }
+ }
+
+ cudaFree(d_in1);
+ cudaFree(d_in2);
+ cudaFree(d_out);
+}
+
+
+EIGEN_DECLARE_TEST(test_cxx11_tensor_complex_cwise_ops)
+{
+ CALL_SUBTEST(test_cuda_complex_cwise_ops<float>());
+ CALL_SUBTEST(test_cuda_complex_cwise_ops<double>());
+}
diff --git a/unsupported/test/cxx11_tensor_complex_gpu.cu b/unsupported/test/cxx11_tensor_complex_gpu.cu
new file mode 100644
index 0000000..f8b8ae7
--- /dev/null
+++ b/unsupported/test/cxx11_tensor_complex_gpu.cu
@@ -0,0 +1,186 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2016 Benoit Steiner <benoit.steiner.goog@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#define EIGEN_TEST_NO_LONGDOUBLE
+
+#define EIGEN_USE_GPU
+
+#include "main.h"
+#include <unsupported/Eigen/CXX11/Tensor>
+
+using Eigen::Tensor;
+
+void test_cuda_nullary() {
+ Tensor<std::complex<float>, 1, 0, int> in1(2);
+ Tensor<std::complex<float>, 1, 0, int> in2(2);
+ in1.setRandom();
+ in2.setRandom();
+
+ std::size_t float_bytes = in1.size() * sizeof(float);
+ std::size_t complex_bytes = in1.size() * sizeof(std::complex<float>);
+
+ std::complex<float>* d_in1;
+ std::complex<float>* d_in2;
+ float* d_out2;
+ cudaMalloc((void**)(&d_in1), complex_bytes);
+ cudaMalloc((void**)(&d_in2), complex_bytes);
+ cudaMalloc((void**)(&d_out2), float_bytes);
+ cudaMemcpy(d_in1, in1.data(), complex_bytes, cudaMemcpyHostToDevice);
+ cudaMemcpy(d_in2, in2.data(), complex_bytes, cudaMemcpyHostToDevice);
+
+ Eigen::GpuStreamDevice stream;
+ Eigen::GpuDevice gpu_device(&stream);
+
+ Eigen::TensorMap<Eigen::Tensor<std::complex<float>, 1, 0, int>, Eigen::Aligned> gpu_in1(
+ d_in1, 2);
+ Eigen::TensorMap<Eigen::Tensor<std::complex<float>, 1, 0, int>, Eigen::Aligned> gpu_in2(
+ d_in2, 2);
+ Eigen::TensorMap<Eigen::Tensor<float, 1, 0, int>, Eigen::Aligned> gpu_out2(
+ d_out2, 2);
+
+ gpu_in1.device(gpu_device) = gpu_in1.constant(std::complex<float>(3.14f, 2.7f));
+ gpu_out2.device(gpu_device) = gpu_in2.abs();
+
+ Tensor<std::complex<float>, 1, 0, int> new1(2);
+ Tensor<float, 1, 0, int> new2(2);
+
+ assert(cudaMemcpyAsync(new1.data(), d_in1, complex_bytes, cudaMemcpyDeviceToHost,
+ gpu_device.stream()) == cudaSuccess);
+ assert(cudaMemcpyAsync(new2.data(), d_out2, float_bytes, cudaMemcpyDeviceToHost,
+ gpu_device.stream()) == cudaSuccess);
+
+ assert(cudaStreamSynchronize(gpu_device.stream()) == cudaSuccess);
+
+ for (int i = 0; i < 2; ++i) {
+ VERIFY_IS_APPROX(new1(i), std::complex<float>(3.14f, 2.7f));
+ VERIFY_IS_APPROX(new2(i), std::abs(in2(i)));
+ }
+
+ cudaFree(d_in1);
+ cudaFree(d_in2);
+ cudaFree(d_out2);
+}
+
+
+static void test_cuda_sum_reductions() {
+
+ Eigen::GpuStreamDevice stream;
+ Eigen::GpuDevice gpu_device(&stream);
+
+ const int num_rows = internal::random<int>(1024, 5*1024);
+ const int num_cols = internal::random<int>(1024, 5*1024);
+
+ Tensor<std::complex<float>, 2> in(num_rows, num_cols);
+ in.setRandom();
+
+ Tensor<std::complex<float>, 0> full_redux;
+ full_redux = in.sum();
+
+ std::size_t in_bytes = in.size() * sizeof(std::complex<float>);
+ std::size_t out_bytes = full_redux.size() * sizeof(std::complex<float>);
+ std::complex<float>* gpu_in_ptr = static_cast<std::complex<float>*>(gpu_device.allocate(in_bytes));
+ std::complex<float>* gpu_out_ptr = static_cast<std::complex<float>*>(gpu_device.allocate(out_bytes));
+ gpu_device.memcpyHostToDevice(gpu_in_ptr, in.data(), in_bytes);
+
+ TensorMap<Tensor<std::complex<float>, 2> > in_gpu(gpu_in_ptr, num_rows, num_cols);
+ TensorMap<Tensor<std::complex<float>, 0> > out_gpu(gpu_out_ptr);
+
+ out_gpu.device(gpu_device) = in_gpu.sum();
+
+ Tensor<std::complex<float>, 0> full_redux_gpu;
+ gpu_device.memcpyDeviceToHost(full_redux_gpu.data(), gpu_out_ptr, out_bytes);
+ gpu_device.synchronize();
+
+ // Check that the CPU and GPU reductions return the same result.
+ VERIFY_IS_APPROX(full_redux(), full_redux_gpu());
+
+ gpu_device.deallocate(gpu_in_ptr);
+ gpu_device.deallocate(gpu_out_ptr);
+}
+
+static void test_cuda_mean_reductions() {
+
+ Eigen::GpuStreamDevice stream;
+ Eigen::GpuDevice gpu_device(&stream);
+
+ const int num_rows = internal::random<int>(1024, 5*1024);
+ const int num_cols = internal::random<int>(1024, 5*1024);
+
+ Tensor<std::complex<float>, 2> in(num_rows, num_cols);
+ in.setRandom();
+
+ Tensor<std::complex<float>, 0> full_redux;
+ full_redux = in.mean();
+
+ std::size_t in_bytes = in.size() * sizeof(std::complex<float>);
+ std::size_t out_bytes = full_redux.size() * sizeof(std::complex<float>);
+ std::complex<float>* gpu_in_ptr = static_cast<std::complex<float>*>(gpu_device.allocate(in_bytes));
+ std::complex<float>* gpu_out_ptr = static_cast<std::complex<float>*>(gpu_device.allocate(out_bytes));
+ gpu_device.memcpyHostToDevice(gpu_in_ptr, in.data(), in_bytes);
+
+ TensorMap<Tensor<std::complex<float>, 2> > in_gpu(gpu_in_ptr, num_rows, num_cols);
+ TensorMap<Tensor<std::complex<float>, 0> > out_gpu(gpu_out_ptr);
+
+ out_gpu.device(gpu_device) = in_gpu.mean();
+
+ Tensor<std::complex<float>, 0> full_redux_gpu;
+ gpu_device.memcpyDeviceToHost(full_redux_gpu.data(), gpu_out_ptr, out_bytes);
+ gpu_device.synchronize();
+
+ // Check that the CPU and GPU reductions return the same result.
+ VERIFY_IS_APPROX(full_redux(), full_redux_gpu());
+
+ gpu_device.deallocate(gpu_in_ptr);
+ gpu_device.deallocate(gpu_out_ptr);
+}
+
+static void test_cuda_product_reductions() {
+
+ Eigen::GpuStreamDevice stream;
+ Eigen::GpuDevice gpu_device(&stream);
+
+ const int num_rows = internal::random<int>(1024, 5*1024);
+ const int num_cols = internal::random<int>(1024, 5*1024);
+
+ Tensor<std::complex<float>, 2> in(num_rows, num_cols);
+ in.setRandom();
+
+ Tensor<std::complex<float>, 0> full_redux;
+ full_redux = in.prod();
+
+ std::size_t in_bytes = in.size() * sizeof(std::complex<float>);
+ std::size_t out_bytes = full_redux.size() * sizeof(std::complex<float>);
+ std::complex<float>* gpu_in_ptr = static_cast<std::complex<float>*>(gpu_device.allocate(in_bytes));
+ std::complex<float>* gpu_out_ptr = static_cast<std::complex<float>*>(gpu_device.allocate(out_bytes));
+ gpu_device.memcpyHostToDevice(gpu_in_ptr, in.data(), in_bytes);
+
+ TensorMap<Tensor<std::complex<float>, 2> > in_gpu(gpu_in_ptr, num_rows, num_cols);
+ TensorMap<Tensor<std::complex<float>, 0> > out_gpu(gpu_out_ptr);
+
+ out_gpu.device(gpu_device) = in_gpu.prod();
+
+ Tensor<std::complex<float>, 0> full_redux_gpu;
+ gpu_device.memcpyDeviceToHost(full_redux_gpu.data(), gpu_out_ptr, out_bytes);
+ gpu_device.synchronize();
+
+ // Check that the CPU and GPU reductions return the same result.
+ VERIFY_IS_APPROX(full_redux(), full_redux_gpu());
+
+ gpu_device.deallocate(gpu_in_ptr);
+ gpu_device.deallocate(gpu_out_ptr);
+}
+
+
+EIGEN_DECLARE_TEST(test_cxx11_tensor_complex)
+{
+ CALL_SUBTEST(test_cuda_nullary());
+ CALL_SUBTEST(test_cuda_sum_reductions());
+ CALL_SUBTEST(test_cuda_mean_reductions());
+ CALL_SUBTEST(test_cuda_product_reductions());
+}
diff --git a/unsupported/test/cxx11_tensor_concatenation.cpp b/unsupported/test/cxx11_tensor_concatenation.cpp
new file mode 100644
index 0000000..bb9418d
--- /dev/null
+++ b/unsupported/test/cxx11_tensor_concatenation.cpp
@@ -0,0 +1,143 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "main.h"
+
+#include <Eigen/CXX11/Tensor>
+
+using Eigen::Tensor;
+
+template<int DataLayout>
+static void test_dimension_failures()
+{
+ Tensor<int, 3, DataLayout> left(2, 3, 1);
+ Tensor<int, 3, DataLayout> right(3, 3, 1);
+ left.setRandom();
+ right.setRandom();
+
+ // Okay; other dimensions are equal.
+ Tensor<int, 3, DataLayout> concatenation = left.concatenate(right, 0);
+
+ // Dimension mismatches.
+ VERIFY_RAISES_ASSERT(concatenation = left.concatenate(right, 1));
+ VERIFY_RAISES_ASSERT(concatenation = left.concatenate(right, 2));
+
+ // Axis > NumDims or < 0.
+ VERIFY_RAISES_ASSERT(concatenation = left.concatenate(right, 3));
+ VERIFY_RAISES_ASSERT(concatenation = left.concatenate(right, -1));
+}
+
+template<int DataLayout>
+static void test_static_dimension_failure()
+{
+ Tensor<int, 2, DataLayout> left(2, 3);
+ Tensor<int, 3, DataLayout> right(2, 3, 1);
+
+#ifdef CXX11_TENSOR_CONCATENATION_STATIC_DIMENSION_FAILURE
+ // Technically compatible, but we static assert that the inputs have same
+ // NumDims.
+ Tensor<int, 3, DataLayout> concatenation = left.concatenate(right, 0);
+#endif
+
+ // This can be worked around in this case.
+ Tensor<int, 3, DataLayout> concatenation = left
+ .reshape(Tensor<int, 3>::Dimensions(2, 3, 1))
+ .concatenate(right, 0);
+ Tensor<int, 2, DataLayout> alternative = left
+ // Clang compiler break with {{{}}} with an ambiguous error on copy constructor
+ // the variadic DSize constructor added for #ifndef EIGEN_EMULATE_CXX11_META_H.
+ // Solution:
+ // either the code should change to
+ // Tensor<int, 2>::Dimensions{{2, 3}}
+ // or Tensor<int, 2>::Dimensions{Tensor<int, 2>::Dimensions{{2, 3}}}
+ .concatenate(right.reshape(Tensor<int, 2>::Dimensions(2, 3)), 0);
+}
+
+template<int DataLayout>
+static void test_simple_concatenation()
+{
+ Tensor<int, 3, DataLayout> left(2, 3, 1);
+ Tensor<int, 3, DataLayout> right(2, 3, 1);
+ left.setRandom();
+ right.setRandom();
+
+ Tensor<int, 3, DataLayout> concatenation = left.concatenate(right, 0);
+ VERIFY_IS_EQUAL(concatenation.dimension(0), 4);
+ VERIFY_IS_EQUAL(concatenation.dimension(1), 3);
+ VERIFY_IS_EQUAL(concatenation.dimension(2), 1);
+ for (int j = 0; j < 3; ++j) {
+ for (int i = 0; i < 2; ++i) {
+ VERIFY_IS_EQUAL(concatenation(i, j, 0), left(i, j, 0));
+ }
+ for (int i = 2; i < 4; ++i) {
+ VERIFY_IS_EQUAL(concatenation(i, j, 0), right(i - 2, j, 0));
+ }
+ }
+
+ concatenation = left.concatenate(right, 1);
+ VERIFY_IS_EQUAL(concatenation.dimension(0), 2);
+ VERIFY_IS_EQUAL(concatenation.dimension(1), 6);
+ VERIFY_IS_EQUAL(concatenation.dimension(2), 1);
+ for (int i = 0; i < 2; ++i) {
+ for (int j = 0; j < 3; ++j) {
+ VERIFY_IS_EQUAL(concatenation(i, j, 0), left(i, j, 0));
+ }
+ for (int j = 3; j < 6; ++j) {
+ VERIFY_IS_EQUAL(concatenation(i, j, 0), right(i, j - 3, 0));
+ }
+ }
+
+ concatenation = left.concatenate(right, 2);
+ VERIFY_IS_EQUAL(concatenation.dimension(0), 2);
+ VERIFY_IS_EQUAL(concatenation.dimension(1), 3);
+ VERIFY_IS_EQUAL(concatenation.dimension(2), 2);
+ for (int i = 0; i < 2; ++i) {
+ for (int j = 0; j < 3; ++j) {
+ VERIFY_IS_EQUAL(concatenation(i, j, 0), left(i, j, 0));
+ VERIFY_IS_EQUAL(concatenation(i, j, 1), right(i, j, 0));
+ }
+ }
+}
+
+
+// TODO(phli): Add test once we have a real vectorized implementation.
+// static void test_vectorized_concatenation() {}
+
+static void test_concatenation_as_lvalue()
+{
+ Tensor<int, 2> t1(2, 3);
+ Tensor<int, 2> t2(2, 3);
+ t1.setRandom();
+ t2.setRandom();
+
+ Tensor<int, 2> result(4, 3);
+ result.setRandom();
+ t1.concatenate(t2, 0) = result;
+
+ for (int i = 0; i < 2; ++i) {
+ for (int j = 0; j < 3; ++j) {
+ VERIFY_IS_EQUAL(t1(i, j), result(i, j));
+ VERIFY_IS_EQUAL(t2(i, j), result(i+2, j));
+ }
+ }
+}
+
+
+EIGEN_DECLARE_TEST(cxx11_tensor_concatenation)
+{
+ CALL_SUBTEST(test_dimension_failures<ColMajor>());
+ CALL_SUBTEST(test_dimension_failures<RowMajor>());
+ CALL_SUBTEST(test_static_dimension_failure<ColMajor>());
+ CALL_SUBTEST(test_static_dimension_failure<RowMajor>());
+ CALL_SUBTEST(test_simple_concatenation<ColMajor>());
+ CALL_SUBTEST(test_simple_concatenation<RowMajor>());
+ // CALL_SUBTEST(test_vectorized_concatenation());
+ CALL_SUBTEST(test_concatenation_as_lvalue());
+
+}
diff --git a/unsupported/test/cxx11_tensor_concatenation_sycl.cpp b/unsupported/test/cxx11_tensor_concatenation_sycl.cpp
new file mode 100644
index 0000000..765991b
--- /dev/null
+++ b/unsupported/test/cxx11_tensor_concatenation_sycl.cpp
@@ -0,0 +1,180 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2016
+// Mehdi Goli Codeplay Software Ltd.
+// Ralph Potter Codeplay Software Ltd.
+// Luke Iwanski Codeplay Software Ltd.
+// Contact: <eigen@codeplay.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#define EIGEN_TEST_NO_LONGDOUBLE
+#define EIGEN_TEST_NO_COMPLEX
+
+#define EIGEN_DEFAULT_DENSE_INDEX_TYPE int64_t
+#define EIGEN_USE_SYCL
+
+#include "main.h"
+#include <unsupported/Eigen/CXX11/Tensor>
+
+using Eigen::Tensor;
+
+template<typename DataType, int DataLayout, typename IndexType>
+static void test_simple_concatenation(const Eigen::SyclDevice& sycl_device)
+{
+ IndexType leftDim1 = 2;
+ IndexType leftDim2 = 3;
+ IndexType leftDim3 = 1;
+ Eigen::array<IndexType, 3> leftRange = {{leftDim1, leftDim2, leftDim3}};
+ IndexType rightDim1 = 2;
+ IndexType rightDim2 = 3;
+ IndexType rightDim3 = 1;
+ Eigen::array<IndexType, 3> rightRange = {{rightDim1, rightDim2, rightDim3}};
+
+ //IndexType concatDim1 = 3;
+// IndexType concatDim2 = 3;
+// IndexType concatDim3 = 1;
+ //Eigen::array<IndexType, 3> concatRange = {{concatDim1, concatDim2, concatDim3}};
+
+ Tensor<DataType, 3, DataLayout, IndexType> left(leftRange);
+ Tensor<DataType, 3, DataLayout, IndexType> right(rightRange);
+ left.setRandom();
+ right.setRandom();
+
+ DataType * gpu_in1_data = static_cast<DataType*>(sycl_device.allocate(left.dimensions().TotalSize()*sizeof(DataType)));
+ DataType * gpu_in2_data = static_cast<DataType*>(sycl_device.allocate(right.dimensions().TotalSize()*sizeof(DataType)));
+
+ Eigen::TensorMap<Eigen::Tensor<DataType, 3, DataLayout, IndexType>> gpu_in1(gpu_in1_data, leftRange);
+ Eigen::TensorMap<Eigen::Tensor<DataType, 3, DataLayout, IndexType>> gpu_in2(gpu_in2_data, rightRange);
+ sycl_device.memcpyHostToDevice(gpu_in1_data, left.data(),(left.dimensions().TotalSize())*sizeof(DataType));
+ sycl_device.memcpyHostToDevice(gpu_in2_data, right.data(),(right.dimensions().TotalSize())*sizeof(DataType));
+ ///
+ Tensor<DataType, 3, DataLayout, IndexType> concatenation1(leftDim1+rightDim1, leftDim2, leftDim3);
+ DataType * gpu_out_data1 = static_cast<DataType*>(sycl_device.allocate(concatenation1.dimensions().TotalSize()*sizeof(DataType)));
+ Eigen::TensorMap<Eigen::Tensor<DataType, 3, DataLayout, IndexType>> gpu_out1(gpu_out_data1, concatenation1.dimensions());
+
+ //concatenation = left.concatenate(right, 0);
+ gpu_out1.device(sycl_device) =gpu_in1.concatenate(gpu_in2, 0);
+ sycl_device.memcpyDeviceToHost(concatenation1.data(), gpu_out_data1,(concatenation1.dimensions().TotalSize())*sizeof(DataType));
+
+ VERIFY_IS_EQUAL(concatenation1.dimension(0), 4);
+ VERIFY_IS_EQUAL(concatenation1.dimension(1), 3);
+ VERIFY_IS_EQUAL(concatenation1.dimension(2), 1);
+ for (IndexType j = 0; j < 3; ++j) {
+ for (IndexType i = 0; i < 2; ++i) {
+ VERIFY_IS_EQUAL(concatenation1(i, j, 0), left(i, j, 0));
+ }
+ for (IndexType i = 2; i < 4; ++i) {
+ VERIFY_IS_EQUAL(concatenation1(i, j, 0), right(i - 2, j, 0));
+ }
+ }
+
+ sycl_device.deallocate(gpu_out_data1);
+ Tensor<DataType, 3, DataLayout, IndexType> concatenation2(leftDim1, leftDim2 +rightDim2, leftDim3);
+ DataType * gpu_out_data2 = static_cast<DataType*>(sycl_device.allocate(concatenation2.dimensions().TotalSize()*sizeof(DataType)));
+ Eigen::TensorMap<Eigen::Tensor<DataType, 3, DataLayout, IndexType>> gpu_out2(gpu_out_data2, concatenation2.dimensions());
+ gpu_out2.device(sycl_device) =gpu_in1.concatenate(gpu_in2, 1);
+ sycl_device.memcpyDeviceToHost(concatenation2.data(), gpu_out_data2,(concatenation2.dimensions().TotalSize())*sizeof(DataType));
+
+ //concatenation = left.concatenate(right, 1);
+ VERIFY_IS_EQUAL(concatenation2.dimension(0), 2);
+ VERIFY_IS_EQUAL(concatenation2.dimension(1), 6);
+ VERIFY_IS_EQUAL(concatenation2.dimension(2), 1);
+ for (IndexType i = 0; i < 2; ++i) {
+ for (IndexType j = 0; j < 3; ++j) {
+ VERIFY_IS_EQUAL(concatenation2(i, j, 0), left(i, j, 0));
+ }
+ for (IndexType j = 3; j < 6; ++j) {
+ VERIFY_IS_EQUAL(concatenation2(i, j, 0), right(i, j - 3, 0));
+ }
+ }
+ sycl_device.deallocate(gpu_out_data2);
+ Tensor<DataType, 3, DataLayout, IndexType> concatenation3(leftDim1, leftDim2, leftDim3+rightDim3);
+ DataType * gpu_out_data3 = static_cast<DataType*>(sycl_device.allocate(concatenation3.dimensions().TotalSize()*sizeof(DataType)));
+ Eigen::TensorMap<Eigen::Tensor<DataType, 3, DataLayout, IndexType>> gpu_out3(gpu_out_data3, concatenation3.dimensions());
+ gpu_out3.device(sycl_device) =gpu_in1.concatenate(gpu_in2, 2);
+ sycl_device.memcpyDeviceToHost(concatenation3.data(), gpu_out_data3,(concatenation3.dimensions().TotalSize())*sizeof(DataType));
+
+ //concatenation = left.concatenate(right, 2);
+ VERIFY_IS_EQUAL(concatenation3.dimension(0), 2);
+ VERIFY_IS_EQUAL(concatenation3.dimension(1), 3);
+ VERIFY_IS_EQUAL(concatenation3.dimension(2), 2);
+ for (IndexType i = 0; i < 2; ++i) {
+ for (IndexType j = 0; j < 3; ++j) {
+ VERIFY_IS_EQUAL(concatenation3(i, j, 0), left(i, j, 0));
+ VERIFY_IS_EQUAL(concatenation3(i, j, 1), right(i, j, 0));
+ }
+ }
+ sycl_device.deallocate(gpu_out_data3);
+ sycl_device.deallocate(gpu_in1_data);
+ sycl_device.deallocate(gpu_in2_data);
+}
+template<typename DataType, int DataLayout, typename IndexType>
+static void test_concatenation_as_lvalue(const Eigen::SyclDevice& sycl_device)
+{
+
+ IndexType leftDim1 = 2;
+ IndexType leftDim2 = 3;
+ Eigen::array<IndexType, 2> leftRange = {{leftDim1, leftDim2}};
+
+ IndexType rightDim1 = 2;
+ IndexType rightDim2 = 3;
+ Eigen::array<IndexType, 2> rightRange = {{rightDim1, rightDim2}};
+
+ IndexType concatDim1 = 4;
+ IndexType concatDim2 = 3;
+ Eigen::array<IndexType, 2> resRange = {{concatDim1, concatDim2}};
+
+ Tensor<DataType, 2, DataLayout, IndexType> left(leftRange);
+ Tensor<DataType, 2, DataLayout, IndexType> right(rightRange);
+ Tensor<DataType, 2, DataLayout, IndexType> result(resRange);
+
+ left.setRandom();
+ right.setRandom();
+ result.setRandom();
+
+ DataType * gpu_in1_data = static_cast<DataType*>(sycl_device.allocate(left.dimensions().TotalSize()*sizeof(DataType)));
+ DataType * gpu_in2_data = static_cast<DataType*>(sycl_device.allocate(right.dimensions().TotalSize()*sizeof(DataType)));
+ DataType * gpu_out_data = static_cast<DataType*>(sycl_device.allocate(result.dimensions().TotalSize()*sizeof(DataType)));
+
+
+ Eigen::TensorMap<Eigen::Tensor<DataType, 2, DataLayout, IndexType>> gpu_in1(gpu_in1_data, leftRange);
+ Eigen::TensorMap<Eigen::Tensor<DataType, 2, DataLayout, IndexType>> gpu_in2(gpu_in2_data, rightRange);
+ Eigen::TensorMap<Eigen::Tensor<DataType, 2, DataLayout, IndexType>> gpu_out(gpu_out_data, resRange);
+
+ sycl_device.memcpyHostToDevice(gpu_in1_data, left.data(),(left.dimensions().TotalSize())*sizeof(DataType));
+ sycl_device.memcpyHostToDevice(gpu_in2_data, right.data(),(right.dimensions().TotalSize())*sizeof(DataType));
+ sycl_device.memcpyHostToDevice(gpu_out_data, result.data(),(result.dimensions().TotalSize())*sizeof(DataType));
+
+// t1.concatenate(t2, 0) = result;
+ gpu_in1.concatenate(gpu_in2, 0).device(sycl_device) =gpu_out;
+ sycl_device.memcpyDeviceToHost(left.data(), gpu_in1_data,(left.dimensions().TotalSize())*sizeof(DataType));
+ sycl_device.memcpyDeviceToHost(right.data(), gpu_in2_data,(right.dimensions().TotalSize())*sizeof(DataType));
+
+ for (IndexType i = 0; i < 2; ++i) {
+ for (IndexType j = 0; j < 3; ++j) {
+ VERIFY_IS_EQUAL(left(i, j), result(i, j));
+ VERIFY_IS_EQUAL(right(i, j), result(i+2, j));
+ }
+ }
+ sycl_device.deallocate(gpu_in1_data);
+ sycl_device.deallocate(gpu_in2_data);
+ sycl_device.deallocate(gpu_out_data);
+}
+
+
+template <typename DataType, typename Dev_selector> void tensorConcat_perDevice(Dev_selector s){
+ QueueInterface queueInterface(s);
+ auto sycl_device = Eigen::SyclDevice(&queueInterface);
+ test_simple_concatenation<DataType, RowMajor, int64_t>(sycl_device);
+ test_simple_concatenation<DataType, ColMajor, int64_t>(sycl_device);
+ test_concatenation_as_lvalue<DataType, ColMajor, int64_t>(sycl_device);
+}
+EIGEN_DECLARE_TEST(cxx11_tensor_concatenation_sycl) {
+ for (const auto& device :Eigen::get_sycl_supported_devices()) {
+ CALL_SUBTEST(tensorConcat_perDevice<float>(device));
+ }
+}
diff --git a/unsupported/test/cxx11_tensor_const.cpp b/unsupported/test/cxx11_tensor_const.cpp
new file mode 100644
index 0000000..9d806ee
--- /dev/null
+++ b/unsupported/test/cxx11_tensor_const.cpp
@@ -0,0 +1,62 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "main.h"
+
+#include <Eigen/CXX11/Tensor>
+using Eigen::Tensor;
+
+
+static void test_simple_assign()
+{
+ Tensor<int, 3> random(2,3,7);
+ random.setRandom();
+
+ TensorMap<Tensor<const int, 3> > constant(random.data(), 2, 3, 7);
+ Tensor<int, 3> result(2,3,7);
+ result = constant;
+
+ for (int i = 0; i < 2; ++i) {
+ for (int j = 0; j < 3; ++j) {
+ for (int k = 0; k < 7; ++k) {
+ VERIFY_IS_EQUAL((result(i,j,k)), random(i,j,k));
+ }
+ }
+ }
+}
+
+
+static void test_assign_of_const_tensor()
+{
+ Tensor<int, 3> random(2,3,7);
+ random.setRandom();
+
+ TensorMap<Tensor<const int, 3> > constant1(random.data(), 2, 3, 7);
+ TensorMap<const Tensor<int, 3> > constant2(random.data(), 2, 3, 7);
+ const TensorMap<Tensor<int, 3> > constant3(random.data(), 2, 3, 7);
+
+ Tensor<int, 2> result1 = constant1.chip(0, 2);
+ Tensor<int, 2> result2 = constant2.chip(0, 2);
+ Tensor<int, 2> result3 = constant3.chip(0, 2);
+
+ for (int i = 0; i < 2; ++i) {
+ for (int j = 0; j < 3; ++j) {
+ VERIFY_IS_EQUAL((result1(i,j)), random(i,j,0));
+ VERIFY_IS_EQUAL((result2(i,j)), random(i,j,0));
+ VERIFY_IS_EQUAL((result3(i,j)), random(i,j,0));
+ }
+ }
+}
+
+
+EIGEN_DECLARE_TEST(cxx11_tensor_const)
+{
+ CALL_SUBTEST(test_simple_assign());
+ CALL_SUBTEST(test_assign_of_const_tensor());
+}
diff --git a/unsupported/test/cxx11_tensor_contract_gpu.cu b/unsupported/test/cxx11_tensor_contract_gpu.cu
new file mode 100644
index 0000000..5abf213
--- /dev/null
+++ b/unsupported/test/cxx11_tensor_contract_gpu.cu
@@ -0,0 +1,234 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>
+// Copyright (C) 2014 Navdeep Jaitly <ndjaitly@google.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#define EIGEN_TEST_NO_LONGDOUBLE
+#define EIGEN_TEST_NO_COMPLEX
+
+#define EIGEN_DEFAULT_DENSE_INDEX_TYPE int
+#define EIGEN_USE_GPU
+
+#include "main.h"
+#include <unsupported/Eigen/CXX11/Tensor>
+
+#include <unsupported/Eigen/CXX11/src/Tensor/TensorGpuHipCudaDefines.h>
+
+using Eigen::Tensor;
+typedef Tensor<float, 1>::DimensionPair DimPair;
+
+template<int DataLayout>
+void test_gpu_contraction(int m_size, int k_size, int n_size)
+{
+ Tensor<float, 2, DataLayout> t_left(m_size, k_size);
+ Tensor<float, 2, DataLayout> t_right(k_size, n_size);
+ Tensor<float, 2, DataLayout> t_result(m_size, n_size);
+ Tensor<float, 2, DataLayout> t_result_gpu(m_size, n_size);
+ Eigen::array<DimPair, 1> dims(DimPair(1, 0));
+
+ t_left.setRandom();
+ t_right.setRandom();
+
+ std::size_t t_left_bytes = t_left.size() * sizeof(float);
+ std::size_t t_right_bytes = t_right.size() * sizeof(float);
+ std::size_t t_result_bytes = t_result.size() * sizeof(float);
+
+ float* d_t_left;
+ float* d_t_right;
+ float* d_t_result;
+
+ gpuMalloc((void**)(&d_t_left), t_left_bytes);
+ gpuMalloc((void**)(&d_t_right), t_right_bytes);
+ gpuMalloc((void**)(&d_t_result), t_result_bytes);
+
+ gpuMemcpy(d_t_left, t_left.data(), t_left_bytes, gpuMemcpyHostToDevice);
+ gpuMemcpy(d_t_right, t_right.data(), t_right_bytes, gpuMemcpyHostToDevice);
+
+ Eigen::GpuStreamDevice stream;
+ Eigen::GpuDevice gpu_device(&stream);
+
+ Eigen::TensorMap<Eigen::Tensor<float, 2, DataLayout> >
+ gpu_t_left(d_t_left, Eigen::array<int, 2>(m_size, k_size));
+ Eigen::TensorMap<Eigen::Tensor<float, 2, DataLayout> >
+ gpu_t_right(d_t_right, Eigen::array<int, 2>(k_size, n_size));
+ Eigen::TensorMap<Eigen::Tensor<float, 2, DataLayout> >
+ gpu_t_result(d_t_result, Eigen::array<int, 2>(m_size, n_size));
+
+
+ gpu_t_result.device(gpu_device) = gpu_t_left.contract(gpu_t_right, dims);
+ t_result = t_left.contract(t_right, dims);
+
+ gpuMemcpy(t_result_gpu.data(), d_t_result, t_result_bytes, gpuMemcpyDeviceToHost);
+ for (DenseIndex i = 0; i < t_result.size(); i++) {
+ if (fabs(t_result(i) - t_result_gpu(i)) < 1e-4f) {
+ continue;
+ }
+ if (Eigen::internal::isApprox(t_result(i), t_result_gpu(i), 1e-4f)) {
+ continue;
+ }
+ std::cout << "mismatch detected at index " << i << ": " << t_result(i)
+ << " vs " << t_result_gpu(i) << std::endl;
+ assert(false);
+ }
+
+ gpuFree((void*)d_t_left);
+ gpuFree((void*)d_t_right);
+ gpuFree((void*)d_t_result);
+}
+
+
+template<int DataLayout>
+void test_scalar(int m_size, int k_size, int n_size)
+{
+ std::cout << "Testing for (" << m_size << "," << k_size << "," << n_size << ")" << std::endl;
+ // with these dimensions, the output has 300 * 140 elements, which is
+ // more than 30 * 1024, which is the number of threads in blocks on
+ // a 15 SM GK110 GPU
+ Tensor<float, 2, DataLayout> t_left(m_size, k_size);
+ Tensor<float, 2, DataLayout> t_right(k_size, n_size);
+ Tensor<float, 0, DataLayout> t_result;
+ Tensor<float, 0, DataLayout> t_result_gpu;
+ Eigen::array<DimPair, 2> dims(DimPair(0, 0), DimPair(1, 1));
+
+ t_left.setRandom();
+ t_right.setRandom();
+
+ std::size_t t_left_bytes = t_left.size() * sizeof(float);
+ std::size_t t_right_bytes = t_right.size() * sizeof(float);
+ std::size_t t_result_bytes = sizeof(float);
+
+ float* d_t_left;
+ float* d_t_right;
+ float* d_t_result;
+
+ gpuMalloc((void**)(&d_t_left), t_left_bytes);
+ gpuMalloc((void**)(&d_t_right), t_right_bytes);
+ gpuMalloc((void**)(&d_t_result), t_result_bytes);
+
+ gpuMemcpy(d_t_left, t_left.data(), t_left_bytes, gpuMemcpyHostToDevice);
+ gpuMemcpy(d_t_right, t_right.data(), t_right_bytes, gpuMemcpyHostToDevice);
+
+ Eigen::GpuStreamDevice stream;
+ Eigen::GpuDevice gpu_device(&stream);
+
+ Eigen::TensorMap<Eigen::Tensor<float, 2, DataLayout> >
+ gpu_t_left(d_t_left, m_size, k_size);
+ Eigen::TensorMap<Eigen::Tensor<float, 2, DataLayout> >
+ gpu_t_right(d_t_right, k_size, n_size);
+ Eigen::TensorMap<Eigen::Tensor<float, 0, DataLayout> >
+ gpu_t_result(d_t_result);
+
+ gpu_t_result.device(gpu_device) = gpu_t_left.contract(gpu_t_right, dims);
+ t_result = t_left.contract(t_right, dims);
+
+ gpuMemcpy(t_result_gpu.data(), d_t_result, t_result_bytes, gpuMemcpyDeviceToHost);
+ if (fabs(t_result() - t_result_gpu()) > 1e-4f &&
+ !Eigen::internal::isApprox(t_result(), t_result_gpu(), 1e-4f)) {
+ std::cout << "mismatch detected: " << t_result()
+ << " vs " << t_result_gpu() << std::endl;
+ assert(false);
+ }
+
+ gpuFree((void*)d_t_left);
+ gpuFree((void*)d_t_right);
+ gpuFree((void*)d_t_result);
+}
+
+
+template<int DataLayout>
+void test_gpu_contraction_m() {
+ for (int k = 32; k < 256; k++) {
+ test_gpu_contraction<ColMajor>(k, 128, 128);
+ test_gpu_contraction<RowMajor>(k, 128, 128);
+ }
+}
+
+template<int DataLayout>
+void test_gpu_contraction_k() {
+ for (int k = 32; k < 256; k++) {
+ test_gpu_contraction<ColMajor>(128, k, 128);
+ test_gpu_contraction<RowMajor>(128, k, 128);
+ }
+}
+
+template<int DataLayout>
+void test_gpu_contraction_n() {
+ for (int k = 32; k < 256; k++) {
+ test_gpu_contraction<ColMajor>(128, 128, k);
+ test_gpu_contraction<RowMajor>(128, 128, k);
+ }
+}
+
+
+template<int DataLayout>
+void test_gpu_contraction_sizes() {
+ int m_sizes[3][5] = {{ 31, 39, 63, 64, 65},
+ {127, 129, 255, 257 , 511},
+ {512, 513, 1023, 1024, 1025}};
+
+ int n_sizes[3][5] = {{ 31, 39, 63, 64, 65},
+ {127, 129, 255, 257, 511},
+ {512, 513, 1023, 1024, 1025}};
+
+ int k_sizes[3][6] = {{ 31, 39, 63, 64, 65, 95},
+ { 96, 127, 129, 255, 257, 511},
+ {512, 513, 725, 1023, 1024, 1025}};
+
+ // Some selection of specific cases.
+ // - m changes rows each iteration
+ // - n changes rows each 3 iterations
+ // - k changes rows each 9 iterations
+ // - within a row, advance once column each iteration
+ const int m_cols = 5;
+ const int n_cols = 5;
+ const int k_cols = 6;
+ int m_offset = 0;
+ int n_offset = 1;
+ int k_offset = 2;
+ for (int i = 0; i < 3; ++i) {
+ for (int j = 0; j < 3; ++j) {
+ for (int l = 0; l < 3; ++l) {
+ int m = m_sizes[l][m_offset];
+ int n = n_sizes[j][n_offset];
+ int k = k_sizes[i][k_offset];
+ test_gpu_contraction<DataLayout>(m, n, k);
+ n_offset = (n_offset + 1) % n_cols;
+ k_offset = (k_offset + 1) % k_cols;
+ }
+ m_offset = (m_offset + 1) % m_cols;
+ if (j < 2) {
+ n_offset = (n_offset + n_cols - 3) % n_cols; // Rewind 3.
+ }
+ }
+ k_offset = (k_offset + 2 * k_cols - 9) % k_cols; // Rewind 9.
+ }
+}
+
+EIGEN_DECLARE_TEST(cxx11_tensor_contract_gpu)
+{
+ CALL_SUBTEST_1(test_gpu_contraction<ColMajor>(128, 128, 128));
+ CALL_SUBTEST_1(test_gpu_contraction<RowMajor>(128, 128, 128));
+
+ CALL_SUBTEST_1(test_scalar<ColMajor>(128, 128, 128));
+ CALL_SUBTEST_1(test_scalar<RowMajor>(128, 128, 128));
+
+ CALL_SUBTEST_2(test_gpu_contraction_m<ColMajor>());
+ CALL_SUBTEST_3(test_gpu_contraction_m<RowMajor>());
+
+ CALL_SUBTEST_4(test_gpu_contraction_k<ColMajor>());
+ CALL_SUBTEST_5(test_gpu_contraction_k<RowMajor>());
+
+ CALL_SUBTEST_6(test_gpu_contraction_n<ColMajor>());
+ CALL_SUBTEST_7(test_gpu_contraction_n<RowMajor>());
+
+#if !defined(EIGEN_USE_HIP)
+// disable these subtests for HIP
+ CALL_SUBTEST_8(test_gpu_contraction_sizes<ColMajor>());
+ CALL_SUBTEST_9(test_gpu_contraction_sizes<RowMajor>());
+#endif
+}
diff --git a/unsupported/test/cxx11_tensor_contract_sycl.cpp b/unsupported/test/cxx11_tensor_contract_sycl.cpp
new file mode 100644
index 0000000..fbcc293
--- /dev/null
+++ b/unsupported/test/cxx11_tensor_contract_sycl.cpp
@@ -0,0 +1,1026 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2016
+// Mehdi Goli Codeplay Software Ltd.
+// Ralph Potter Codeplay Software Ltd.
+// Luke Iwanski Codeplay Software Ltd.
+// Contact: <eigen@codeplay.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#define EIGEN_TEST_NO_LONGDOUBLE
+#define EIGEN_TEST_NO_COMPLEX
+
+#define EIGEN_DEFAULT_DENSE_INDEX_TYPE int64_t
+#define EIGEN_USE_SYCL
+
+#include <algorithm>
+#include <chrono>
+#include <ctime>
+#include <iostream>
+
+#include "main.h"
+
+#include <unsupported/Eigen/CXX11/Tensor>
+
+using Eigen::array;
+using Eigen::SyclDevice;
+using Eigen::Tensor;
+using Eigen::TensorMap;
+
+template <int DataLayout, typename DataType, typename IndexType,
+ typename Device>
+void static test_sycl_contraction(const Device &sycl_device, IndexType m_size,
+ IndexType k_size, IndexType n_size) {
+ typedef typename Tensor<DataType, 1, DataLayout, IndexType>::DimensionPair
+ DimPair;
+ static const DataType error_threshold = DataType(1e-4);
+ // with these dimensions, the output has 300 * 140 elements, which is
+ // more than 30 * 1024, which is the number of threads in blocks on
+ // a 15 SM GK110 GPU
+ Tensor<DataType, 2, DataLayout, IndexType> t_left(m_size, k_size);
+ Tensor<DataType, 2, DataLayout, IndexType> t_right(k_size, n_size);
+ Tensor<DataType, 2, DataLayout, IndexType> t_result(m_size, n_size);
+ Tensor<DataType, 2, DataLayout, IndexType> t_result_gpu(m_size, n_size);
+ Eigen::array<DimPair, 1> dims = {{DimPair(1, 0)}};
+ Eigen::array<IndexType, 2> left_dims = {{m_size, k_size}};
+ Eigen::array<IndexType, 2> right_dims = {{k_size, n_size}};
+ Eigen::array<IndexType, 2> result_dims = {{m_size, n_size}};
+
+ t_left.setRandom();
+ t_right.setRandom();
+
+ std::size_t t_left_bytes = t_left.size() * sizeof(DataType);
+ std::size_t t_right_bytes = t_right.size() * sizeof(DataType);
+ std::size_t t_result_bytes = t_result.size() * sizeof(DataType);
+
+ DataType *d_t_left =
+ static_cast<DataType *>(sycl_device.allocate(t_left_bytes));
+ DataType *d_t_right =
+ static_cast<DataType *>(sycl_device.allocate(t_right_bytes));
+ DataType *d_t_result =
+ static_cast<DataType *>(sycl_device.allocate(t_result_bytes));
+
+ Eigen::TensorMap<Eigen::Tensor<DataType, 2, DataLayout, IndexType>>
+ gpu_t_left(d_t_left, left_dims);
+ Eigen::TensorMap<Eigen::Tensor<DataType, 2, DataLayout, IndexType>>
+ gpu_t_right(d_t_right, right_dims);
+ Eigen::TensorMap<Eigen::Tensor<DataType, 2, DataLayout, IndexType>>
+ gpu_t_result(d_t_result, result_dims);
+
+ sycl_device.memcpyHostToDevice(d_t_left, t_left.data(), t_left_bytes);
+ sycl_device.memcpyHostToDevice(d_t_right, t_right.data(), t_right_bytes);
+
+ gpu_t_result.device(sycl_device) = gpu_t_left.contract(gpu_t_right, dims);
+ sycl_device.memcpyDeviceToHost(t_result_gpu.data(), d_t_result,
+ t_result_bytes);
+
+ t_result = t_left.contract(t_right, dims);
+
+ for (IndexType i = 0; i < t_result.size(); i++) {
+ if (static_cast<DataType>(std::fabs(static_cast<DataType>(
+ t_result(i) - t_result_gpu(i)))) < error_threshold) {
+ continue;
+ }
+ if (Eigen::internal::isApprox(t_result(i), t_result_gpu(i),
+ error_threshold)) {
+ continue;
+ }
+
+ std::cout << "M : " << m_size << ", N : " << n_size << ", K : " << k_size
+ << ", mismatch detected at IndexType " << i << ": " << t_result(i)
+ << " vs " << t_result_gpu(i) << std::endl;
+ VERIFY_IS_APPROX(t_result_gpu(i), t_result(i));
+ }
+ sycl_device.deallocate(d_t_left);
+ sycl_device.deallocate(d_t_right);
+ sycl_device.deallocate(d_t_result);
+}
+
+template <int DataLayout, typename DataType, typename IndexType,
+ typename Device>
+void test_sycl_contraction_m(const Device &sycl_device) {
+ for (IndexType k = 32; k < 256; k++) {
+ test_sycl_contraction<DataLayout, DataType, IndexType>(sycl_device, k, 128,
+ 128);
+ }
+}
+
+template <int DataLayout, typename DataType, typename IndexType,
+ typename Device>
+void test_sycl_contraction_k(const Device &sycl_device) {
+ for (IndexType k = 32; k < 256; k++) {
+ test_sycl_contraction<DataLayout, DataType, IndexType>(sycl_device, 128, k,
+ 128);
+ }
+}
+
+template <int DataLayout, typename DataType, typename IndexType,
+ typename Device>
+void test_sycl_contraction_n(const Device &sycl_device) {
+ for (IndexType k = 32; k < 256; k++) {
+ test_sycl_contraction<DataLayout, DataType, IndexType>(sycl_device, 128,
+ 128, k);
+ }
+}
+
+template <int DataLayout, typename DataType, typename IndexType,
+ typename Device>
+void test_sycl_contraction_sizes(const Device &sycl_device) {
+ IndexType m_sizes[] = {31, 39, 63, 64, 65, 127, 129, 255,
+ 257, 511, 512, 513, 1023, 1024, 1025};
+
+ IndexType n_sizes[] = {31, 39, 63, 64, 65, 127, 129, 255,
+ 257, 511, 512, 513, 1023, 1024, 1025};
+
+ IndexType k_sizes[] = {31, 39, 63, 64, 65, 95, 96, 127, 129,
+ 255, 257, 511, 512, 513, 1023, 1024, 1025};
+
+ for (IndexType i = 0; i < 15; i++) {
+ for (IndexType j = 0; j < 15; j++) {
+ for (IndexType k = 0; k < 17; k++) {
+ test_sycl_contraction<DataLayout, DataType, IndexType>(
+ sycl_device, m_sizes[i], n_sizes[j], k_sizes[k]);
+ }
+ }
+ }
+}
+
+template <int DataLayout, typename DataType, typename IndexType,
+ typename Device>
+void static test_no_out_of_bounds(const Device &sycl_device, IndexType m_size,
+ IndexType k_size, IndexType n_size) {
+ typedef typename Tensor<DataType, 1, DataLayout, IndexType>::DimensionPair
+ DimPair;
+ static const DataType error_threshold = DataType(1e-4);
+ Tensor<DataType, 2, DataLayout, IndexType> t_left(m_size, k_size);
+ Tensor<DataType, 2, DataLayout, IndexType> t_right(k_size, n_size);
+ Tensor<DataType, 2, DataLayout, IndexType> t_result(m_size, n_size);
+
+ Eigen::array<DimPair, 1> dims = {{DimPair(1, 0)}};
+ Eigen::array<IndexType, 2> left_dims = {{m_size, k_size}};
+ Eigen::array<IndexType, 2> right_dims = {{k_size, n_size}};
+ Eigen::array<IndexType, 2> result_dims = {{m_size, n_size}};
+
+ t_left.setRandom();
+ t_right.setRandom();
+
+ // Allocate buffers twice as big to check for invalid read and write
+ auto padded_left_size = 2 * t_left.size();
+ auto padded_right_size = 2 * t_right.size();
+ auto padded_result_size = 2 * t_result.size();
+
+ std::size_t t_left_bytes = padded_left_size * sizeof(DataType);
+ std::size_t t_right_bytes = padded_right_size * sizeof(DataType);
+ std::size_t t_result_bytes = padded_result_size * sizeof(DataType);
+
+ DataType *d_t_left =
+ static_cast<DataType *>(sycl_device.allocate(t_left_bytes));
+ DataType *d_t_right =
+ static_cast<DataType *>(sycl_device.allocate(t_right_bytes));
+ DataType *d_t_result =
+ static_cast<DataType *>(sycl_device.allocate(t_result_bytes));
+
+ // TensorMaps are still of the same size than the Tensors
+ Eigen::TensorMap<Eigen::Tensor<DataType, 2, DataLayout, IndexType>>
+ gpu_t_left(d_t_left, left_dims);
+ Eigen::TensorMap<Eigen::Tensor<DataType, 2, DataLayout, IndexType>>
+ gpu_t_right(d_t_right, right_dims);
+ Eigen::TensorMap<Eigen::Tensor<DataType, 2, DataLayout, IndexType>>
+ gpu_t_result(d_t_result, result_dims);
+
+ // Write nan after the actual buffer to propagate nans everywhere in case of
+ // invalid reads
+ DataType nan = std::numeric_limits<DataType>::quiet_NaN();
+ auto host_left_data = new DataType[padded_left_size];
+ std::copy_n(t_left.data(), t_left.size(), host_left_data);
+ std::fill_n(host_left_data + t_left.size(), t_left.size(), nan);
+ auto host_right_data = new DataType[padded_right_size];
+ std::copy_n(t_right.data(), t_right.size(), host_right_data);
+ std::fill_n(host_right_data + t_right.size(), t_right.size(), nan);
+ auto host_result_data = new DataType[padded_result_size];
+ std::fill_n(host_result_data, padded_result_size, nan);
+
+ sycl_device.memcpyHostToDevice(d_t_left, host_left_data, t_left_bytes);
+ sycl_device.memcpyHostToDevice(d_t_right, host_right_data, t_right_bytes);
+ sycl_device.memcpyHostToDevice(d_t_result, host_result_data, t_result_bytes);
+
+ gpu_t_result.device(sycl_device) = gpu_t_left.contract(gpu_t_right, dims);
+ sycl_device.memcpyDeviceToHost(host_result_data, d_t_result, t_result_bytes);
+
+ t_result = t_left.contract(t_right, dims);
+
+ for (IndexType i = 0; i < t_result.size(); i++) {
+ if (static_cast<DataType>(std::fabs(static_cast<DataType>(
+ t_result(i) - host_result_data[i]))) < error_threshold) {
+ continue;
+ }
+ if (Eigen::internal::isApprox(t_result(i), host_result_data[i],
+ error_threshold)) {
+ continue;
+ }
+ if (std::isnan(host_result_data[i])) {
+ std::cout << "M : " << m_size << ", N : " << n_size << ", K : " << k_size
+ << ", invalid read detected at IndexType " << i << ": "
+ << t_result(i) << " vs " << host_result_data[i] << std::endl;
+ } else {
+ std::cout << "M : " << m_size << ", N : " << n_size << ", K : " << k_size
+ << ", mismatch detected at IndexType " << i << ": "
+ << t_result(i) << " vs " << host_result_data[i] << std::endl;
+ }
+ VERIFY_IS_APPROX(host_result_data[i], t_result(i));
+ }
+ // Make sure that the rest of the result is still nans
+ for (IndexType i = t_result.size(); i < padded_result_size; i++) {
+ if (std::isnan(host_result_data[i])) {
+ continue;
+ }
+ std::cout << "M : " << m_size << ", N : " << n_size << ", K : " << k_size
+ << ", invalid write detected at IndexType " << i << ": "
+ << host_result_data[i] << std::endl;
+ VERIFY_IS_APPROX(host_result_data[i], t_result(i));
+ }
+ sycl_device.deallocate(d_t_left);
+ sycl_device.deallocate(d_t_right);
+ sycl_device.deallocate(d_t_result);
+
+ delete[] host_left_data;
+ delete[] host_right_data;
+ delete[] host_result_data;
+}
+
+template <int DataLayout, typename DataType, typename IndexType,
+ typename Device>
+void test_scalar(const Device &sycl_device, IndexType m_size, IndexType k_size,
+ IndexType n_size) {
+ // std::cout << "Testing for (" << m_size << "," << k_size << "," << n_size <<
+ // ")" << std::endl;
+ // with these dimensions, the output has 300 * 140 elements, which is
+ // more than 30 * 1024, which is the number of threads in blocks on
+ // a 15 SM GK110 GPU
+ typedef typename Tensor<DataType, 1, DataLayout, IndexType>::DimensionPair
+ DimPair;
+ static const DataType error_threshold = DataType(1e-4);
+ Tensor<DataType, 2, DataLayout, IndexType> t_left(m_size, k_size);
+ Tensor<DataType, 2, DataLayout, IndexType> t_right(k_size, n_size);
+ Tensor<DataType, 0, DataLayout, IndexType> t_result;
+ Tensor<DataType, 0, DataLayout, IndexType> t_result_gpu;
+ Eigen::array<DimPair, 2> dims = {{DimPair(0, 0), DimPair(1, 1)}};
+ Eigen::array<IndexType, 2> left_dims = {{m_size, k_size}};
+ Eigen::array<IndexType, 2> right_dims = {{k_size, n_size}};
+ t_left.setRandom();
+ t_right.setRandom();
+
+ std::size_t t_left_bytes = t_left.size() * sizeof(DataType);
+ std::size_t t_right_bytes = t_right.size() * sizeof(DataType);
+ std::size_t t_result_bytes = sizeof(DataType);
+
+ DataType *d_t_left =
+ static_cast<DataType *>(sycl_device.allocate(t_left_bytes));
+ DataType *d_t_right =
+ static_cast<DataType *>(sycl_device.allocate(t_right_bytes));
+ DataType *d_t_result =
+ static_cast<DataType *>(sycl_device.allocate(t_result_bytes));
+
+ Eigen::TensorMap<Eigen::Tensor<DataType, 2, DataLayout, IndexType>>
+ gpu_t_left(d_t_left, left_dims);
+ Eigen::TensorMap<Eigen::Tensor<DataType, 2, DataLayout, IndexType>>
+ gpu_t_right(d_t_right, right_dims);
+ Eigen::TensorMap<Eigen::Tensor<DataType, 0, DataLayout, IndexType>>
+ gpu_t_result(d_t_result);
+
+ sycl_device.memcpyHostToDevice(d_t_left, t_left.data(), t_left_bytes);
+ sycl_device.memcpyHostToDevice(d_t_right, t_right.data(), t_right_bytes);
+
+ gpu_t_result.device(sycl_device) = gpu_t_left.contract(gpu_t_right, dims);
+ sycl_device.memcpyDeviceToHost(t_result_gpu.data(), d_t_result,
+ t_result_bytes);
+
+ t_result = t_left.contract(t_right, dims);
+
+ if (static_cast<DataType>(std::fabs(static_cast<DataType>(
+ t_result() - t_result_gpu()))) > error_threshold &&
+ !Eigen::internal::isApprox(t_result(), t_result_gpu(), error_threshold)) {
+ std::cout << "K: " << k_size << ", N: " << n_size << ", M: " << m_size
+ << " : mismatch detected: " << t_result() << " vs "
+ << t_result_gpu() << std::endl;
+ VERIFY_IS_APPROX(t_result_gpu(), t_result());
+ }
+
+ sycl_device.deallocate(d_t_left);
+ sycl_device.deallocate(d_t_right);
+ sycl_device.deallocate(d_t_result);
+}
+
+template <int DataLayout, typename DataType, typename IndexType,
+ typename Device>
+void contraction_batch(const Device &sycl_device, IndexType m_size,
+ IndexType k_size, IndexType n_size, IndexType m_batch,
+ IndexType start, IndexType limit) {
+ typedef typename Tensor<DataType, 1, DataLayout, IndexType>::DimensionPair
+ DimPair;
+ static const DataType error_threshold = DataType(1e-4);
+ typedef Eigen::array<IndexType, 3> TensorDim;
+ typedef Eigen::Tensor<DataType, 3, DataLayout, IndexType> TensorType;
+ TensorDim left_dims = {{m_batch, k_size, m_size}};
+ TensorDim right_dims = {{m_batch, n_size, k_size}};
+ TensorDim res_dims = {{m_batch, m_size, n_size}};
+ Eigen::array<DimPair, 1> contract_pairs = {{DimPair(0, 1)}};
+
+ TensorType t_left(left_dims);
+ TensorType t_right(right_dims);
+ TensorType t_result_gpu(res_dims);
+ TensorType t_result(res_dims);
+
+ t_left.setRandom();
+ t_right.setRandom();
+
+ std::size_t t_left_bytes = t_left.size() * sizeof(DataType);
+ std::size_t t_right_bytes = t_right.size() * sizeof(DataType);
+ std::size_t t_result_bytes = t_result.size() * sizeof(DataType);
+
+ DataType *d_t_left =
+ static_cast<DataType *>(sycl_device.allocate(t_left_bytes));
+ DataType *d_t_right =
+ static_cast<DataType *>(sycl_device.allocate(t_right_bytes));
+ DataType *d_t_result =
+ static_cast<DataType *>(sycl_device.allocate(t_result_bytes));
+
+ Eigen::TensorMap<TensorType> gpu_t_left(d_t_left, left_dims);
+ Eigen::TensorMap<TensorType> gpu_t_right(d_t_right, right_dims);
+ Eigen::TensorMap<TensorType> gpu_t_result(d_t_result, res_dims);
+
+ sycl_device.memcpyHostToDevice(d_t_left, t_left.data(), t_left_bytes);
+ sycl_device.memcpyHostToDevice(d_t_right, t_right.data(), t_right_bytes);
+ for (int i = start; i < limit; ++i) {
+ auto x = gpu_t_left.template chip<0>(i);
+ auto y = gpu_t_right.template chip<0>(i);
+ auto z = gpu_t_result.template chip<0>(i);
+ z.device(sycl_device) = x.contract(y, contract_pairs);
+ }
+ sycl_device.memcpyDeviceToHost(t_result_gpu.data(), d_t_result,
+ t_result_bytes);
+
+ for (int i = start; i < limit; ++i) {
+ auto x = t_left.template chip<0>(i);
+ auto y = t_right.template chip<0>(i);
+ auto z = t_result.template chip<0>(i);
+ z = x.contract(y, contract_pairs);
+ }
+
+ for (IndexType i = 0; i < t_result.size(); i++) {
+ if (static_cast<DataType>(std::fabs(static_cast<DataType>(
+ t_result(i) - t_result_gpu(i)))) < error_threshold) {
+ continue;
+ }
+ if (Eigen::internal::isApprox(t_result(i), t_result_gpu(i),
+ error_threshold)) {
+ continue;
+ }
+ std::cout << "mismatch detected at IndexType " << i << ": " << t_result(i)
+ << " vs " << t_result_gpu(i) << std::endl;
+ VERIFY_IS_APPROX(t_result_gpu(i), t_result(i));
+ }
+ sycl_device.deallocate(d_t_left);
+ sycl_device.deallocate(d_t_right);
+ sycl_device.deallocate(d_t_result);
+}
+
+template <int DataLayout, typename DataType, typename IndexType,
+ typename Device>
+void contraction_rhs_transposed(const Device &sycl_device, IndexType m_size,
+ IndexType k_size, IndexType n_size) {
+ typedef typename Tensor<DataType, 1, DataLayout, IndexType>::DimensionPair
+ DimPair;
+ static const DataType error_threshold = DataType(1e-4);
+ Eigen::array<IndexType, 2> left_dims = {{m_size, k_size}};
+ Eigen::array<IndexType, 2> right_dims = {{n_size, k_size}};
+ Eigen::array<IndexType, 2> res_dims = {{m_size, n_size}};
+ Eigen::array<DimPair, 1> dims = {{DimPair(1, 1)}};
+
+ Tensor<DataType, 2, DataLayout, IndexType> t_left(left_dims);
+ Tensor<DataType, 2, DataLayout, IndexType> t_right(right_dims);
+ Tensor<DataType, 2, DataLayout, IndexType> t_result_gpu(res_dims);
+ Tensor<DataType, 2, DataLayout, IndexType> t_result(res_dims);
+
+ t_left.setRandom();
+ t_right.setRandom();
+
+ std::size_t t_left_bytes = t_left.size() * sizeof(DataType);
+ std::size_t t_right_bytes = t_right.size() * sizeof(DataType);
+ std::size_t t_result_bytes = t_result.size() * sizeof(DataType);
+
+ DataType *d_t_left =
+ static_cast<DataType *>(sycl_device.allocate(t_left_bytes));
+ DataType *d_t_right =
+ static_cast<DataType *>(sycl_device.allocate(t_right_bytes));
+ DataType *d_t_result =
+ static_cast<DataType *>(sycl_device.allocate(t_result_bytes));
+
+ Eigen::TensorMap<Eigen::Tensor<DataType, 2, DataLayout, IndexType>>
+ gpu_t_left(d_t_left, left_dims);
+ Eigen::TensorMap<Eigen::Tensor<DataType, 2, DataLayout, IndexType>>
+ gpu_t_right(d_t_right, right_dims);
+ Eigen::TensorMap<Eigen::Tensor<DataType, 2, DataLayout, IndexType>>
+ gpu_t_result(d_t_result, res_dims);
+
+ sycl_device.memcpyHostToDevice(d_t_left, t_left.data(), t_left_bytes);
+ sycl_device.memcpyHostToDevice(d_t_right, t_right.data(), t_right_bytes);
+
+ gpu_t_result.device(sycl_device) = gpu_t_left.contract(gpu_t_right, dims);
+ sycl_device.memcpyDeviceToHost(t_result_gpu.data(), d_t_result,
+ t_result_bytes);
+
+ t_result = t_left.contract(t_right, dims);
+
+ for (IndexType j = 0; j < m_size; j++) {
+ for (IndexType i = 0; i < n_size; i++) {
+ if (static_cast<DataType>(std::fabs(static_cast<DataType>(
+ t_result(j, i) - t_result_gpu(j, i)))) < error_threshold) {
+ continue;
+ }
+ if (Eigen::internal::isApprox(t_result(j, i), t_result_gpu(j, i),
+ error_threshold)) {
+ continue;
+ }
+ std::cout << "M : " << m_size << ", N : " << n_size << ", K : " << k_size
+ << ", mismatch detected at IndexType m: " << j << " n: " << i
+ << " CPU : " << t_result(j, i)
+ << " vs SYCL:" << t_result_gpu(j, i) << std::endl;
+ VERIFY_IS_APPROX(t_result_gpu(j, i), t_result(j, i));
+ }
+ }
+ sycl_device.deallocate(d_t_left);
+ sycl_device.deallocate(d_t_right);
+ sycl_device.deallocate(d_t_result);
+}
+
+template <int DataLayout, typename DataType, typename IndexType,
+ typename Device>
+void contraction_lhs_transposed(const Device &sycl_device, IndexType m_size,
+ IndexType k_size, IndexType n_size) {
+ typedef typename Tensor<DataType, 1, DataLayout, IndexType>::DimensionPair
+ DimPair;
+ static const DataType error_threshold = DataType(1e-4);
+ Eigen::array<IndexType, 2> left_dims = {{k_size, m_size}};
+ Eigen::array<IndexType, 2> right_dims = {{k_size, n_size}};
+ Eigen::array<IndexType, 2> res_dims = {{m_size, n_size}};
+ Eigen::array<DimPair, 1> dims = {{DimPair(0, 0)}};
+
+ Tensor<DataType, 2, DataLayout, IndexType> t_left(left_dims);
+ Tensor<DataType, 2, DataLayout, IndexType> t_right(right_dims);
+ Tensor<DataType, 2, DataLayout, IndexType> t_result_gpu(res_dims);
+ Tensor<DataType, 2, DataLayout, IndexType> t_result(res_dims);
+
+ t_left.setRandom();
+ t_right.setRandom();
+
+ std::size_t t_left_bytes = t_left.size() * sizeof(DataType);
+ std::size_t t_right_bytes = t_right.size() * sizeof(DataType);
+ std::size_t t_result_bytes = t_result.size() * sizeof(DataType);
+
+ DataType *d_t_left =
+ static_cast<DataType *>(sycl_device.allocate(t_left_bytes));
+ DataType *d_t_right =
+ static_cast<DataType *>(sycl_device.allocate(t_right_bytes));
+ DataType *d_t_result =
+ static_cast<DataType *>(sycl_device.allocate(t_result_bytes));
+
+ Eigen::TensorMap<Eigen::Tensor<DataType, 2, DataLayout, IndexType>>
+ gpu_t_left(d_t_left, left_dims);
+ Eigen::TensorMap<Eigen::Tensor<DataType, 2, DataLayout, IndexType>>
+ gpu_t_right(d_t_right, right_dims);
+ Eigen::TensorMap<Eigen::Tensor<DataType, 2, DataLayout, IndexType>>
+ gpu_t_result(d_t_result, res_dims);
+
+ sycl_device.memcpyHostToDevice(d_t_left, t_left.data(), t_left_bytes);
+ sycl_device.memcpyHostToDevice(d_t_right, t_right.data(), t_right_bytes);
+
+ gpu_t_result.device(sycl_device) = gpu_t_left.contract(gpu_t_right, dims);
+ sycl_device.memcpyDeviceToHost(t_result_gpu.data(), d_t_result,
+ t_result_bytes);
+
+ t_result = t_left.contract(t_right, dims);
+
+ for (IndexType i = 0; i < t_result.size(); i++) {
+ if (static_cast<DataType>(std::fabs(static_cast<DataType>(
+ t_result(i) - t_result_gpu(i)))) < error_threshold) {
+ continue;
+ }
+ if (Eigen::internal::isApprox(t_result(i), t_result_gpu(i),
+ error_threshold)) {
+ continue;
+ }
+ std::cout << "M : " << m_size << ", N : " << n_size << ", K : " << k_size
+ << ", mismatch detected at IndexType " << i << ": " << t_result(i)
+ << " vs " << t_result_gpu(i) << std::endl;
+ VERIFY_IS_APPROX(t_result_gpu(i), t_result(i));
+ }
+ sycl_device.deallocate(d_t_left);
+ sycl_device.deallocate(d_t_right);
+ sycl_device.deallocate(d_t_result);
+}
+
+template <int DataLayout, typename DataType, typename IndexType,
+ typename Device>
+void contraction_both_transposed(const Device &sycl_device, IndexType m_size,
+ IndexType k_size, IndexType n_size) {
+ typedef typename Tensor<DataType, 1, DataLayout, IndexType>::DimensionPair
+ DimPair;
+ static const DataType error_threshold = DataType(1e-4);
+ Eigen::array<IndexType, 2> left_dims = {{k_size, m_size}};
+ Eigen::array<IndexType, 2> right_dims = {{n_size, k_size}};
+ Eigen::array<IndexType, 2> res_dims = {{m_size, n_size}};
+ Eigen::array<DimPair, 1> dims = {{DimPair(0, 1)}};
+
+ Tensor<DataType, 2, DataLayout, IndexType> t_left(left_dims);
+ Tensor<DataType, 2, DataLayout, IndexType> t_right(right_dims);
+ Tensor<DataType, 2, DataLayout, IndexType> t_result_gpu(res_dims);
+ Tensor<DataType, 2, DataLayout, IndexType> t_result(res_dims);
+
+ t_left.setRandom();
+ t_right.setRandom();
+
+ std::size_t t_left_bytes = t_left.size() * sizeof(DataType);
+ std::size_t t_right_bytes = t_right.size() * sizeof(DataType);
+ std::size_t t_result_bytes = t_result.size() * sizeof(DataType);
+
+ DataType *d_t_left =
+ static_cast<DataType *>(sycl_device.allocate(t_left_bytes));
+ DataType *d_t_right =
+ static_cast<DataType *>(sycl_device.allocate(t_right_bytes));
+ DataType *d_t_result =
+ static_cast<DataType *>(sycl_device.allocate(t_result_bytes));
+
+ Eigen::TensorMap<Eigen::Tensor<DataType, 2, DataLayout, IndexType>>
+ gpu_t_left(d_t_left, left_dims);
+ Eigen::TensorMap<Eigen::Tensor<DataType, 2, DataLayout, IndexType>>
+ gpu_t_right(d_t_right, right_dims);
+ Eigen::TensorMap<Eigen::Tensor<DataType, 2, DataLayout, IndexType>>
+ gpu_t_result(d_t_result, res_dims);
+
+ sycl_device.memcpyHostToDevice(d_t_left, t_left.data(), t_left_bytes);
+ sycl_device.memcpyHostToDevice(d_t_right, t_right.data(), t_right_bytes);
+
+ gpu_t_result.device(sycl_device) = gpu_t_left.contract(gpu_t_right, dims);
+ sycl_device.memcpyDeviceToHost(t_result_gpu.data(), d_t_result,
+ t_result_bytes);
+
+ t_result = t_left.contract(t_right, dims);
+
+ for (IndexType i = 0; i < t_result.size(); i++) {
+ if (static_cast<DataType>(std::fabs(static_cast<DataType>(
+ t_result(i) - t_result_gpu(i)))) < error_threshold) {
+ continue;
+ }
+ if (Eigen::internal::isApprox(t_result(i), t_result_gpu(i),
+ error_threshold)) {
+ continue;
+ }
+ std::cout << "M : " << m_size << ", N : " << n_size << ", K : " << k_size
+ << ", mismatch detected at IndexType " << i << ": " << t_result(i)
+ << " vs " << t_result_gpu(i) << std::endl;
+
+ VERIFY_IS_APPROX(t_result_gpu(i), t_result(i));
+ }
+ sycl_device.deallocate(d_t_left);
+ sycl_device.deallocate(d_t_right);
+ sycl_device.deallocate(d_t_result);
+}
+
+template <typename Dev>
+void inline tensorOutofBound(const Dev &sycl_device) {
+ typedef float DataType;
+ typedef int64_t IndexType;
+ std::chrono::time_point<std::chrono::system_clock> start, end;
+ start = std::chrono::system_clock::now();
+ // Test out of bound for Tensor-Tensor
+ test_no_out_of_bounds<RowMajor, DataType, IndexType>(sycl_device, 10, 1024,
+ 1024);
+ test_no_out_of_bounds<RowMajor, DataType, IndexType>(sycl_device, 1024, 1024,
+ 4096);
+ test_no_out_of_bounds<RowMajor, DataType, IndexType>(sycl_device, 4096, 1024,
+ 2048);
+ test_no_out_of_bounds<ColMajor, DataType, IndexType>(sycl_device, 784, 2048,
+ 1024);
+ test_no_out_of_bounds<ColMajor, DataType, IndexType>(sycl_device, 2048, 1024,
+ 784);
+ test_no_out_of_bounds<RowMajor, DataType, IndexType>(sycl_device, 10, 1024,
+ 10);
+ test_no_out_of_bounds<RowMajor, DataType, IndexType>(sycl_device, 513, 4096,
+ 513);
+ test_no_out_of_bounds<RowMajor, DataType, IndexType>(sycl_device, 783, 1024,
+ 783);
+ test_no_out_of_bounds<ColMajor, DataType, IndexType>(sycl_device, 784, 2048,
+ 784);
+ test_no_out_of_bounds<ColMajor, DataType, IndexType>(sycl_device, 11, 1024,
+ 11);
+ end = std::chrono::system_clock::now();
+ std::chrono::duration<double> elapsed_seconds = end - start;
+ std::time_t end_time = std::chrono::system_clock::to_time_t(end);
+ std::cout << "tensor out of bound tests finished computation at "
+ << std::ctime(&end_time)
+ << "elapsed time: " << elapsed_seconds.count() << "s\n";
+}
+
+template <typename Dev>
+void inline tensorTensor(const Dev &sycl_device) {
+ typedef float DataType;
+ typedef int64_t IndexType;
+ std::chrono::time_point<std::chrono::system_clock> start, end;
+ start = std::chrono::system_clock::now();
+ // Tensor Tensor Contraction
+ test_sycl_contraction<ColMajor, DataType, IndexType>(sycl_device, 128, 128,
+ 128);
+ test_sycl_contraction<RowMajor, DataType, IndexType>(sycl_device, 128, 128,
+ 128);
+ end = std::chrono::system_clock::now();
+ std::chrono::duration<double> elapsed_seconds = end - start;
+ std::time_t end_time = std::chrono::system_clock::to_time_t(end);
+ std::cout << "tensor tensor tests finished computation at "
+ << std::ctime(&end_time)
+ << "elapsed time: " << elapsed_seconds.count() << "s\n";
+}
+
+template <typename Dev>
+void inline tensorTensor_m(const Dev &sycl_device) {
+ typedef float DataType;
+ typedef int64_t IndexType;
+ std::chrono::time_point<std::chrono::system_clock> start, end;
+ start = std::chrono::system_clock::now();
+ // Tensor Tensor Contraction
+ test_sycl_contraction_m<ColMajor, DataType, IndexType>(sycl_device);
+ test_sycl_contraction_m<RowMajor, DataType, IndexType>(sycl_device);
+
+ end = std::chrono::system_clock::now();
+ std::chrono::duration<double> elapsed_seconds = end - start;
+ std::time_t end_time = std::chrono::system_clock::to_time_t(end);
+ std::cout << "tensor tensor tests finished computation at "
+ << std::ctime(&end_time)
+ << "elapsed time: " << elapsed_seconds.count() << "s\n";
+}
+
+template <typename Dev>
+void inline tensorTensor_n(const Dev &sycl_device) {
+ typedef float DataType;
+ typedef int64_t IndexType;
+ std::chrono::time_point<std::chrono::system_clock> start, end;
+ start = std::chrono::system_clock::now();
+ // Tensor Tensor Contraction
+ test_sycl_contraction_n<ColMajor, DataType, IndexType>(sycl_device);
+ test_sycl_contraction_n<RowMajor, DataType, IndexType>(sycl_device);
+
+ end = std::chrono::system_clock::now();
+ std::chrono::duration<double> elapsed_seconds = end - start;
+ std::time_t end_time = std::chrono::system_clock::to_time_t(end);
+ std::cout << "tensor tensor tests finished computation at "
+ << std::ctime(&end_time)
+ << "elapsed time: " << elapsed_seconds.count() << "s\n";
+}
+
+template <typename Dev>
+void inline tensorTensor_k(const Dev &sycl_device) {
+ typedef float DataType;
+ typedef int64_t IndexType;
+ std::chrono::time_point<std::chrono::system_clock> start, end;
+ start = std::chrono::system_clock::now();
+ test_sycl_contraction_k<ColMajor, DataType, IndexType>(sycl_device);
+ test_sycl_contraction_k<RowMajor, DataType, IndexType>(sycl_device);
+
+ end = std::chrono::system_clock::now();
+ std::chrono::duration<double> elapsed_seconds = end - start;
+ std::time_t end_time = std::chrono::system_clock::to_time_t(end);
+ std::cout << "tensor tensor tests finished computation at "
+ << std::ctime(&end_time)
+ << "elapsed time: " << elapsed_seconds.count() << "s\n";
+}
+
+template <typename Dev>
+void inline tensorTensor_sizes(const Dev &sycl_device) {
+ typedef float DataType;
+ typedef int64_t IndexType;
+ std::chrono::time_point<std::chrono::system_clock> start, end;
+ start = std::chrono::system_clock::now();
+ // Tensor Tensor Contraction
+ test_sycl_contraction_sizes<ColMajor, DataType, IndexType>(sycl_device);
+ test_sycl_contraction_sizes<RowMajor, DataType, IndexType>(sycl_device);
+
+ end = std::chrono::system_clock::now();
+ std::chrono::duration<double> elapsed_seconds = end - start;
+ std::time_t end_time = std::chrono::system_clock::to_time_t(end);
+ std::cout << "tensor tensor tests finished computation at "
+ << std::ctime(&end_time)
+ << "elapsed time: " << elapsed_seconds.count() << "s\n";
+}
+template <typename Dev>
+void inline vectorVector(const Dev &sycl_device) {
+ typedef float DataType;
+ typedef int64_t IndexType;
+ std::chrono::time_point<std::chrono::system_clock> start, end;
+ start = std::chrono::system_clock::now();
+ // VECTOR-VECTOR
+ test_sycl_contraction<ColMajor, DataType, IndexType>(sycl_device, 1025, 1,
+ 1025);
+ test_sycl_contraction<RowMajor, DataType, IndexType>(sycl_device, 1025, 1,
+ 1025);
+ test_sycl_contraction<ColMajor, DataType, IndexType>(sycl_device, 1024, 1,
+ 1024);
+ test_sycl_contraction<RowMajor, DataType, IndexType>(sycl_device, 1024, 1,
+ 1024);
+ test_sycl_contraction<ColMajor, DataType, IndexType>(sycl_device, 1023, 1,
+ 1023);
+ test_sycl_contraction<RowMajor, DataType, IndexType>(sycl_device, 1023, 1,
+ 1023);
+
+ end = std::chrono::system_clock::now();
+ std::chrono::duration<double> elapsed_seconds = end - start;
+ std::time_t end_time = std::chrono::system_clock::to_time_t(end);
+ std::cout << "contracted tensor tests finished computation at "
+ << std::ctime(&end_time)
+ << "elapsed time: " << elapsed_seconds.count() << "s\n";
+}
+
+template <typename Dev>
+void inline vectorTensor(const Dev &sycl_device) {
+ typedef float DataType;
+ typedef int64_t IndexType;
+ std::chrono::time_point<std::chrono::system_clock> start, end;
+ start = std::chrono::system_clock::now();
+ // Vector-Tensor
+ test_sycl_contraction<ColMajor, DataType, IndexType>(sycl_device, 1, 1025,
+ 1025);
+ test_sycl_contraction<RowMajor, DataType, IndexType>(sycl_device, 1, 1025,
+ 1025);
+ test_sycl_contraction<ColMajor, DataType, IndexType>(sycl_device, 1, 1024,
+ 1024);
+ test_sycl_contraction<RowMajor, DataType, IndexType>(sycl_device, 1, 1024,
+ 1024);
+ test_sycl_contraction<ColMajor, DataType, IndexType>(sycl_device, 1, 1023,
+ 1023);
+ test_sycl_contraction<RowMajor, DataType, IndexType>(sycl_device, 1, 1023,
+ 1023);
+
+ test_sycl_contraction<ColMajor, DataType, IndexType>(sycl_device, 1, 4097,
+ 4097);
+ test_sycl_contraction<RowMajor, DataType, IndexType>(sycl_device, 1, 4097,
+ 4097);
+ test_sycl_contraction<ColMajor, DataType, IndexType>(sycl_device, 1, 4096,
+ 4096);
+ test_sycl_contraction<RowMajor, DataType, IndexType>(sycl_device, 1, 4096,
+ 4096);
+ test_sycl_contraction<ColMajor, DataType, IndexType>(sycl_device, 1, 4095,
+ 4095);
+ test_sycl_contraction<RowMajor, DataType, IndexType>(sycl_device, 1, 4095,
+ 4095);
+ test_sycl_contraction<ColMajor, DataType, IndexType>(sycl_device, 1, 802816,
+ 32);
+
+ end = std::chrono::system_clock::now();
+ std::chrono::duration<double> elapsed_seconds = end - start;
+ std::time_t end_time = std::chrono::system_clock::to_time_t(end);
+ std::cout << "finished computation at " << std::ctime(&end_time)
+ << "elapsed time: " << elapsed_seconds.count() << "s\n";
+}
+
+template <typename Dev>
+void inline tensorVector(const Dev &sycl_device) {
+ typedef float DataType;
+ typedef int64_t IndexType;
+ std::chrono::time_point<std::chrono::system_clock> start, end;
+ start = std::chrono::system_clock::now();
+ // Matrix-Vector
+ test_sycl_contraction<ColMajor, DataType, IndexType>(sycl_device, 1025, 1025,
+ 1);
+ test_sycl_contraction<RowMajor, DataType, IndexType>(sycl_device, 1125, 1025,
+ 1);
+ test_sycl_contraction<ColMajor, DataType, IndexType>(sycl_device, 1224, 1024,
+ 1);
+ test_sycl_contraction<RowMajor, DataType, IndexType>(sycl_device, 1024, 1024,
+ 1);
+ test_sycl_contraction<ColMajor, DataType, IndexType>(sycl_device, 1023, 1023,
+ 1);
+ test_sycl_contraction<RowMajor, DataType, IndexType>(sycl_device, 1023, 1023,
+ 1);
+ test_sycl_contraction<ColMajor, DataType, IndexType>(sycl_device, 4097, 4197,
+ 1);
+ test_sycl_contraction<RowMajor, DataType, IndexType>(sycl_device, 4097, 4097,
+ 1);
+ test_sycl_contraction<ColMajor, DataType, IndexType>(sycl_device, 4096, 4096,
+ 1);
+ test_sycl_contraction<RowMajor, DataType, IndexType>(sycl_device, 4096, 8196,
+ 1);
+ test_sycl_contraction<ColMajor, DataType, IndexType>(sycl_device, 4095, 4095,
+ 1);
+ test_sycl_contraction<RowMajor, DataType, IndexType>(sycl_device, 4095, 4095,
+ 1);
+// If the GEMV disabled it will creates one kernel to calculate the contraction.
+// Therefore the acumuation of float number will overflow the precision
+// threshold for float and cause the test to fail. While it the GMV multiple
+// kernel will be created and each one run the overflow of accumutation breaks
+// among the kernels.
+#ifndef EIGEN_SYCL_DISABLE_GEMV
+ test_sycl_contraction<ColMajor, DataType, IndexType>(sycl_device, 32, 802032,
+ 1);
+#endif
+
+ end = std::chrono::system_clock::now();
+ std::chrono::duration<double> elapsed_seconds = end - start;
+ std::time_t end_time = std::chrono::system_clock::to_time_t(end);
+ std::cout << "finished computation at " << std::ctime(&end_time)
+ << "elapsed time: " << elapsed_seconds.count() << "s\n";
+}
+
+template <typename Dev>
+void inline tensorScalar(const Dev &sycl_device) {
+ typedef float DataType;
+ typedef int64_t IndexType;
+ std::chrono::time_point<std::chrono::system_clock> start, end;
+ start = std::chrono::system_clock::now();
+ // SCALAR Contraction
+ test_scalar<ColMajor, DataType, IndexType>(sycl_device, 127, 127, 127);
+ test_scalar<RowMajor, DataType, IndexType>(sycl_device, 127, 127, 127);
+ test_scalar<ColMajor, DataType, IndexType>(sycl_device, 128, 128, 128);
+ test_scalar<RowMajor, DataType, IndexType>(sycl_device, 128, 128, 128);
+ test_scalar<ColMajor, DataType, IndexType>(sycl_device, 129, 129, 129);
+ test_scalar<RowMajor, DataType, IndexType>(sycl_device, 129, 129, 129);
+
+ end = std::chrono::system_clock::now();
+ std::chrono::duration<double> elapsed_seconds = end - start;
+ std::time_t end_time = std::chrono::system_clock::to_time_t(end);
+ std::cout << "finished computation at " << std::ctime(&end_time)
+ << "elapsed time: " << elapsed_seconds.count() << "s\n";
+}
+
+template <typename Dev>
+void inline skinnyTensor_row(const Dev &sycl_device) {
+ typedef float DataType;
+ typedef int64_t IndexType;
+ std::chrono::time_point<std::chrono::system_clock> start, end;
+ start = std::chrono::system_clock::now();
+ // Tensor Tensor Contraction
+ test_sycl_contraction<RowMajor, DataType, IndexType>(sycl_device, 16, 4, 16);
+ test_sycl_contraction<RowMajor, DataType, IndexType>(sycl_device, 257, 131073,
+ 257);
+ test_sycl_contraction<RowMajor, DataType, IndexType>(sycl_device, 256, 131072,
+ 256);
+ test_sycl_contraction<RowMajor, DataType, IndexType>(sycl_device, 16, 131073,
+ 16);
+ test_sycl_contraction<RowMajor, DataType, IndexType>(sycl_device, 17, 131072,
+ 17);
+ end = std::chrono::system_clock::now();
+ std::chrono::duration<double> elapsed_seconds = end - start;
+ std::time_t end_time = std::chrono::system_clock::to_time_t(end);
+ std::cout << "finished computation at " << std::ctime(&end_time)
+ << "elapsed time: " << elapsed_seconds.count() << "s\n";
+}
+
+template <typename Dev>
+void inline skinnyTensor_col(const Dev &sycl_device) {
+ typedef float DataType;
+ typedef int64_t IndexType;
+ std::chrono::time_point<std::chrono::system_clock> start, end;
+ start = std::chrono::system_clock::now();
+ // Tensor Tensor Contraction
+ test_sycl_contraction<ColMajor, DataType, IndexType>(sycl_device, 16, 4, 16);
+ test_sycl_contraction<ColMajor, DataType, IndexType>(sycl_device, 257, 131073,
+ 257);
+ test_sycl_contraction<ColMajor, DataType, IndexType>(sycl_device, 256, 131072,
+ 256);
+ test_sycl_contraction<ColMajor, DataType, IndexType>(sycl_device, 16, 131073,
+ 16);
+ test_sycl_contraction<ColMajor, DataType, IndexType>(sycl_device, 17, 131072,
+ 17);
+ end = std::chrono::system_clock::now();
+ std::chrono::duration<double> elapsed_seconds = end - start;
+ std::time_t end_time = std::chrono::system_clock::to_time_t(end);
+ std::cout << "finished computation at " << std::ctime(&end_time)
+ << "elapsed time: " << elapsed_seconds.count() << "s\n";
+}
+
+template <typename Dev>
+void inline tensor_contraction_batch_per_device(const Dev &sycl_device) {
+ typedef float DataType;
+ typedef int64_t IndexType;
+ std::chrono::time_point<std::chrono::system_clock> start, end;
+ start = std::chrono::system_clock::now();
+
+ contraction_batch<RowMajor, DataType, IndexType>(sycl_device, 64, 75, 30, 4,
+ 0, 4);
+ contraction_batch<ColMajor, DataType, IndexType>(sycl_device, 64, 75, 30, 4,
+ 0, 4);
+ end = std::chrono::system_clock::now();
+ std::chrono::duration<double> elapsed_seconds = end - start;
+ std::time_t end_time = std::chrono::system_clock::to_time_t(end);
+ std::cout << "finished computation at " << std::ctime(&end_time)
+ << "elapsed time: " << elapsed_seconds.count() << "s\n";
+}
+
+template <typename Dev>
+void inline tensor_contraction_lhs_transposed_per_device(
+ const Dev &sycl_device) {
+ typedef float DataType;
+ typedef int64_t IndexType;
+ std::chrono::time_point<std::chrono::system_clock> start, end;
+ start = std::chrono::system_clock::now();
+
+ contraction_lhs_transposed<RowMajor, DataType, IndexType>(sycl_device, 8, 4,
+ 8);
+ contraction_lhs_transposed<RowMajor, DataType, IndexType>(sycl_device, 32, 8,
+ 32);
+ contraction_lhs_transposed<RowMajor, DataType, IndexType>(sycl_device, 64, 16,
+ 64);
+ contraction_lhs_transposed<RowMajor, DataType, IndexType>(sycl_device, 784,
+ 2048, 1024);
+ contraction_lhs_transposed<RowMajor, DataType, IndexType>(sycl_device, 1024,
+ 10, 1024);
+ contraction_lhs_transposed<RowMajor, DataType, IndexType>(sycl_device, 4096,
+ 1024, 1024);
+ contraction_lhs_transposed<RowMajor, DataType, IndexType>(sycl_device, 2048,
+ 4096, 1024);
+ end = std::chrono::system_clock::now();
+ std::chrono::duration<double> elapsed_seconds = end - start;
+ std::time_t end_time = std::chrono::system_clock::to_time_t(end);
+ std::cout << "finished computation at " << std::ctime(&end_time)
+ << "elapsed time: " << elapsed_seconds.count() << "s\n";
+}
+
+template <typename Dev>
+void inline tensor_contraction_rhs_transposed_per_device(
+ const Dev &sycl_device) {
+ typedef float DataType;
+ typedef int64_t IndexType;
+ std::chrono::time_point<std::chrono::system_clock> start, end;
+ start = std::chrono::system_clock::now();
+
+ contraction_rhs_transposed<RowMajor, DataType, IndexType>(sycl_device, 16, 4,
+ 16);
+ contraction_rhs_transposed<RowMajor, DataType, IndexType>(sycl_device, 17, 5,
+ 17);
+ contraction_rhs_transposed<RowMajor, DataType, IndexType>(sycl_device, 32, 8,
+ 32);
+ contraction_rhs_transposed<RowMajor, DataType, IndexType>(sycl_device, 64, 16,
+ 64);
+ contraction_rhs_transposed<RowMajor, DataType, IndexType>(sycl_device, 10,
+ 1024, 1024);
+ contraction_rhs_transposed<RowMajor, DataType, IndexType>(sycl_device, 1024,
+ 1024, 4096);
+ contraction_rhs_transposed<RowMajor, DataType, IndexType>(sycl_device, 4096,
+ 1024, 2048);
+ contraction_rhs_transposed<RowMajor, DataType, IndexType>(sycl_device, 2048,
+ 1024, 784);
+ end = std::chrono::system_clock::now();
+ std::chrono::duration<double> elapsed_seconds = end - start;
+ std::time_t end_time = std::chrono::system_clock::to_time_t(end);
+ std::cout << "finished computation at " << std::ctime(&end_time)
+ << "elapsed time: " << elapsed_seconds.count() << "s\n";
+}
+
+template <typename Dev>
+void inline tensor_contraction_both_transposed_per_device(
+ const Dev &sycl_device) {
+ typedef float DataType;
+ typedef int64_t IndexType;
+ std::chrono::time_point<std::chrono::system_clock> start, end;
+ start = std::chrono::system_clock::now();
+
+ contraction_both_transposed<RowMajor, DataType, IndexType>(sycl_device, 17, 5,
+ 17);
+ contraction_both_transposed<RowMajor, DataType, IndexType>(sycl_device, 32, 8,
+ 32);
+ contraction_both_transposed<RowMajor, DataType, IndexType>(sycl_device, 64,
+ 16, 64);
+ end = std::chrono::system_clock::now();
+ std::chrono::duration<double> elapsed_seconds = end - start;
+ std::time_t end_time = std::chrono::system_clock::to_time_t(end);
+ std::cout << "finished computation at " << std::ctime(&end_time)
+ << "elapsed time: " << elapsed_seconds.count() << "s\n";
+}
+
+EIGEN_DECLARE_TEST(cxx11_tensor_contract_sycl) {
+ for (const auto &device : Eigen::get_sycl_supported_devices()) {
+ std::cout << "Running on "
+ << device.template get_info<cl::sycl::info::device::name>()
+ << std::endl;
+ QueueInterface queueInterface(device);
+ auto sycl_device = Eigen::SyclDevice(&queueInterface);
+ CALL_SUBTEST_1(tensorOutofBound(sycl_device));
+ CALL_SUBTEST_2(tensorTensor(sycl_device));
+ CALL_SUBTEST_2(tensorTensor_m(sycl_device));
+ CALL_SUBTEST_2(tensorTensor_n(sycl_device));
+ CALL_SUBTEST_2(tensorTensor_k(sycl_device));
+ CALL_SUBTEST_2(tensorTensor_sizes(sycl_device));
+ CALL_SUBTEST_3(vectorVector(sycl_device));
+ CALL_SUBTEST_4(vectorTensor(sycl_device));
+ CALL_SUBTEST_5(tensorVector(sycl_device));
+ CALL_SUBTEST_6(tensorScalar(sycl_device));
+ CALL_SUBTEST_7(skinnyTensor_row(sycl_device));
+ CALL_SUBTEST_7(skinnyTensor_col(sycl_device));
+ CALL_SUBTEST_8(tensor_contraction_batch_per_device(sycl_device));
+ CALL_SUBTEST_9(tensor_contraction_lhs_transposed_per_device(sycl_device));
+ CALL_SUBTEST_10(tensor_contraction_rhs_transposed_per_device(sycl_device));
+ CALL_SUBTEST_11(tensor_contraction_both_transposed_per_device(sycl_device));
+ }
+}
diff --git a/unsupported/test/cxx11_tensor_contraction.cpp b/unsupported/test/cxx11_tensor_contraction.cpp
new file mode 100644
index 0000000..3b5c6a1
--- /dev/null
+++ b/unsupported/test/cxx11_tensor_contraction.cpp
@@ -0,0 +1,601 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "main.h"
+
+#include <Eigen/CXX11/Tensor>
+
+using Eigen::DefaultDevice;
+using Eigen::Tensor;
+
+typedef Tensor<float, 1>::DimensionPair DimPair;
+
+template<int DataLayout>
+static void test_evals()
+{
+ Tensor<float, 2, DataLayout> mat1(2, 3);
+ Tensor<float, 2, DataLayout> mat2(2, 3);
+ Tensor<float, 2, DataLayout> mat3(3, 2);
+
+ mat1.setRandom();
+ mat2.setRandom();
+ mat3.setRandom();
+
+ Tensor<float, 2, DataLayout> mat4(3,3);
+ mat4.setZero();
+ Eigen::array<DimPair, 1> dims3 = {{DimPair(0, 0)}};
+ typedef TensorEvaluator<decltype(mat1.contract(mat2, dims3)), DefaultDevice> Evaluator;
+ Evaluator eval(mat1.contract(mat2, dims3), DefaultDevice());
+ eval.evalTo(mat4.data());
+ EIGEN_STATIC_ASSERT(Evaluator::NumDims==2ul, YOU_MADE_A_PROGRAMMING_MISTAKE);
+ VERIFY_IS_EQUAL(eval.dimensions()[0], 3);
+ VERIFY_IS_EQUAL(eval.dimensions()[1], 3);
+
+ VERIFY_IS_APPROX(mat4(0,0), mat1(0,0)*mat2(0,0) + mat1(1,0)*mat2(1,0));
+ VERIFY_IS_APPROX(mat4(0,1), mat1(0,0)*mat2(0,1) + mat1(1,0)*mat2(1,1));
+ VERIFY_IS_APPROX(mat4(0,2), mat1(0,0)*mat2(0,2) + mat1(1,0)*mat2(1,2));
+ VERIFY_IS_APPROX(mat4(1,0), mat1(0,1)*mat2(0,0) + mat1(1,1)*mat2(1,0));
+ VERIFY_IS_APPROX(mat4(1,1), mat1(0,1)*mat2(0,1) + mat1(1,1)*mat2(1,1));
+ VERIFY_IS_APPROX(mat4(1,2), mat1(0,1)*mat2(0,2) + mat1(1,1)*mat2(1,2));
+ VERIFY_IS_APPROX(mat4(2,0), mat1(0,2)*mat2(0,0) + mat1(1,2)*mat2(1,0));
+ VERIFY_IS_APPROX(mat4(2,1), mat1(0,2)*mat2(0,1) + mat1(1,2)*mat2(1,1));
+ VERIFY_IS_APPROX(mat4(2,2), mat1(0,2)*mat2(0,2) + mat1(1,2)*mat2(1,2));
+
+ Tensor<float, 2, DataLayout> mat5(2,2);
+ mat5.setZero();
+ Eigen::array<DimPair, 1> dims4 = {{DimPair(1, 1)}};
+ typedef TensorEvaluator<decltype(mat1.contract(mat2, dims4)), DefaultDevice> Evaluator2;
+ Evaluator2 eval2(mat1.contract(mat2, dims4), DefaultDevice());
+ eval2.evalTo(mat5.data());
+ EIGEN_STATIC_ASSERT(Evaluator2::NumDims==2ul, YOU_MADE_A_PROGRAMMING_MISTAKE);
+ VERIFY_IS_EQUAL(eval2.dimensions()[0], 2);
+ VERIFY_IS_EQUAL(eval2.dimensions()[1], 2);
+
+ VERIFY_IS_APPROX(mat5(0,0), mat1(0,0)*mat2(0,0) + mat1(0,1)*mat2(0,1) + mat1(0,2)*mat2(0,2));
+ VERIFY_IS_APPROX(mat5(0,1), mat1(0,0)*mat2(1,0) + mat1(0,1)*mat2(1,1) + mat1(0,2)*mat2(1,2));
+ VERIFY_IS_APPROX(mat5(1,0), mat1(1,0)*mat2(0,0) + mat1(1,1)*mat2(0,1) + mat1(1,2)*mat2(0,2));
+ VERIFY_IS_APPROX(mat5(1,1), mat1(1,0)*mat2(1,0) + mat1(1,1)*mat2(1,1) + mat1(1,2)*mat2(1,2));
+
+ Tensor<float, 2, DataLayout> mat6(2,2);
+ mat6.setZero();
+ Eigen::array<DimPair, 1> dims6 = {{DimPair(1, 0)}};
+ typedef TensorEvaluator<decltype(mat1.contract(mat3, dims6)), DefaultDevice> Evaluator3;
+ Evaluator3 eval3(mat1.contract(mat3, dims6), DefaultDevice());
+ eval3.evalTo(mat6.data());
+ EIGEN_STATIC_ASSERT(Evaluator3::NumDims==2ul, YOU_MADE_A_PROGRAMMING_MISTAKE);
+ VERIFY_IS_EQUAL(eval3.dimensions()[0], 2);
+ VERIFY_IS_EQUAL(eval3.dimensions()[1], 2);
+
+ VERIFY_IS_APPROX(mat6(0,0), mat1(0,0)*mat3(0,0) + mat1(0,1)*mat3(1,0) + mat1(0,2)*mat3(2,0));
+ VERIFY_IS_APPROX(mat6(0,1), mat1(0,0)*mat3(0,1) + mat1(0,1)*mat3(1,1) + mat1(0,2)*mat3(2,1));
+ VERIFY_IS_APPROX(mat6(1,0), mat1(1,0)*mat3(0,0) + mat1(1,1)*mat3(1,0) + mat1(1,2)*mat3(2,0));
+ VERIFY_IS_APPROX(mat6(1,1), mat1(1,0)*mat3(0,1) + mat1(1,1)*mat3(1,1) + mat1(1,2)*mat3(2,1));
+}
+
+template<int DataLayout>
+static void test_scalar()
+{
+ Tensor<float, 1, DataLayout> vec1({6});
+ Tensor<float, 1, DataLayout> vec2({6});
+
+ vec1.setRandom();
+ vec2.setRandom();
+
+ Eigen::array<DimPair, 1> dims = {{DimPair(0, 0)}};
+ Tensor<float, 0, DataLayout> scalar = vec1.contract(vec2, dims);
+
+ float expected = 0.0f;
+ for (int i = 0; i < 6; ++i) {
+ expected += vec1(i) * vec2(i);
+ }
+ VERIFY_IS_APPROX(scalar(), expected);
+}
+
+template<int DataLayout>
+static void test_multidims()
+{
+ Tensor<float, 3, DataLayout> mat1(2, 2, 2);
+ Tensor<float, 4, DataLayout> mat2(2, 2, 2, 2);
+
+ mat1.setRandom();
+ mat2.setRandom();
+
+ Tensor<float, 3, DataLayout> mat3(2, 2, 2);
+ mat3.setZero();
+ Eigen::array<DimPair, 2> dims = {{DimPair(1, 2), DimPair(2, 3)}};
+ typedef TensorEvaluator<decltype(mat1.contract(mat2, dims)), DefaultDevice> Evaluator;
+ Evaluator eval(mat1.contract(mat2, dims), DefaultDevice());
+ eval.evalTo(mat3.data());
+ EIGEN_STATIC_ASSERT(Evaluator::NumDims==3ul, YOU_MADE_A_PROGRAMMING_MISTAKE);
+ VERIFY_IS_EQUAL(eval.dimensions()[0], 2);
+ VERIFY_IS_EQUAL(eval.dimensions()[1], 2);
+ VERIFY_IS_EQUAL(eval.dimensions()[2], 2);
+
+ VERIFY_IS_APPROX(mat3(0,0,0), mat1(0,0,0)*mat2(0,0,0,0) + mat1(0,1,0)*mat2(0,0,1,0) +
+ mat1(0,0,1)*mat2(0,0,0,1) + mat1(0,1,1)*mat2(0,0,1,1));
+ VERIFY_IS_APPROX(mat3(0,0,1), mat1(0,0,0)*mat2(0,1,0,0) + mat1(0,1,0)*mat2(0,1,1,0) +
+ mat1(0,0,1)*mat2(0,1,0,1) + mat1(0,1,1)*mat2(0,1,1,1));
+ VERIFY_IS_APPROX(mat3(0,1,0), mat1(0,0,0)*mat2(1,0,0,0) + mat1(0,1,0)*mat2(1,0,1,0) +
+ mat1(0,0,1)*mat2(1,0,0,1) + mat1(0,1,1)*mat2(1,0,1,1));
+ VERIFY_IS_APPROX(mat3(0,1,1), mat1(0,0,0)*mat2(1,1,0,0) + mat1(0,1,0)*mat2(1,1,1,0) +
+ mat1(0,0,1)*mat2(1,1,0,1) + mat1(0,1,1)*mat2(1,1,1,1));
+ VERIFY_IS_APPROX(mat3(1,0,0), mat1(1,0,0)*mat2(0,0,0,0) + mat1(1,1,0)*mat2(0,0,1,0) +
+ mat1(1,0,1)*mat2(0,0,0,1) + mat1(1,1,1)*mat2(0,0,1,1));
+ VERIFY_IS_APPROX(mat3(1,0,1), mat1(1,0,0)*mat2(0,1,0,0) + mat1(1,1,0)*mat2(0,1,1,0) +
+ mat1(1,0,1)*mat2(0,1,0,1) + mat1(1,1,1)*mat2(0,1,1,1));
+ VERIFY_IS_APPROX(mat3(1,1,0), mat1(1,0,0)*mat2(1,0,0,0) + mat1(1,1,0)*mat2(1,0,1,0) +
+ mat1(1,0,1)*mat2(1,0,0,1) + mat1(1,1,1)*mat2(1,0,1,1));
+ VERIFY_IS_APPROX(mat3(1,1,1), mat1(1,0,0)*mat2(1,1,0,0) + mat1(1,1,0)*mat2(1,1,1,0) +
+ mat1(1,0,1)*mat2(1,1,0,1) + mat1(1,1,1)*mat2(1,1,1,1));
+
+ Tensor<float, 2, DataLayout> mat4(2, 2);
+ Tensor<float, 3, DataLayout> mat5(2, 2, 2);
+
+ mat4.setRandom();
+ mat5.setRandom();
+
+ Tensor<float, 1, DataLayout> mat6(2);
+ mat6.setZero();
+ Eigen::array<DimPair, 2> dims2({{DimPair(0, 1), DimPair(1, 0)}});
+ typedef TensorEvaluator<decltype(mat4.contract(mat5, dims2)), DefaultDevice> Evaluator2;
+ Evaluator2 eval2(mat4.contract(mat5, dims2), DefaultDevice());
+ eval2.evalTo(mat6.data());
+ EIGEN_STATIC_ASSERT(Evaluator2::NumDims==1ul, YOU_MADE_A_PROGRAMMING_MISTAKE);
+ VERIFY_IS_EQUAL(eval2.dimensions()[0], 2);
+
+ VERIFY_IS_APPROX(mat6(0), mat4(0,0)*mat5(0,0,0) + mat4(1,0)*mat5(0,1,0) +
+ mat4(0,1)*mat5(1,0,0) + mat4(1,1)*mat5(1,1,0));
+ VERIFY_IS_APPROX(mat6(1), mat4(0,0)*mat5(0,0,1) + mat4(1,0)*mat5(0,1,1) +
+ mat4(0,1)*mat5(1,0,1) + mat4(1,1)*mat5(1,1,1));
+}
+
+template<int DataLayout>
+static void test_holes() {
+ Tensor<float, 4, DataLayout> t1(2, 5, 7, 3);
+ Tensor<float, 5, DataLayout> t2(2, 7, 11, 13, 3);
+ t1.setRandom();
+ t2.setRandom();
+
+ Eigen::array<DimPair, 2> dims = {{DimPair(0, 0), DimPair(3, 4)}};
+ Tensor<float, 5, DataLayout> result = t1.contract(t2, dims);
+ VERIFY_IS_EQUAL(result.dimension(0), 5);
+ VERIFY_IS_EQUAL(result.dimension(1), 7);
+ VERIFY_IS_EQUAL(result.dimension(2), 7);
+ VERIFY_IS_EQUAL(result.dimension(3), 11);
+ VERIFY_IS_EQUAL(result.dimension(4), 13);
+
+ for (int i = 0; i < 5; ++i) {
+ for (int j = 0; j < 5; ++j) {
+ for (int k = 0; k < 5; ++k) {
+ for (int l = 0; l < 5; ++l) {
+ for (int m = 0; m < 5; ++m) {
+ VERIFY_IS_APPROX(result(i, j, k, l, m),
+ t1(0, i, j, 0) * t2(0, k, l, m, 0) +
+ t1(1, i, j, 0) * t2(1, k, l, m, 0) +
+ t1(0, i, j, 1) * t2(0, k, l, m, 1) +
+ t1(1, i, j, 1) * t2(1, k, l, m, 1) +
+ t1(0, i, j, 2) * t2(0, k, l, m, 2) +
+ t1(1, i, j, 2) * t2(1, k, l, m, 2));
+ }
+ }
+ }
+ }
+ }
+}
+
+template<int DataLayout>
+static void test_full_redux()
+{
+ Tensor<float, 2, DataLayout> t1(2, 2);
+ Tensor<float, 3, DataLayout> t2(2, 2, 2);
+ t1.setRandom();
+ t2.setRandom();
+
+ Eigen::array<DimPair, 2> dims = {{DimPair(0, 0), DimPair(1, 1)}};
+ Tensor<float, 1, DataLayout> result = t1.contract(t2, dims);
+ VERIFY_IS_EQUAL(result.dimension(0), 2);
+ VERIFY_IS_APPROX(result(0), t1(0, 0) * t2(0, 0, 0) + t1(1, 0) * t2(1, 0, 0)
+ + t1(0, 1) * t2(0, 1, 0) + t1(1, 1) * t2(1, 1, 0));
+ VERIFY_IS_APPROX(result(1), t1(0, 0) * t2(0, 0, 1) + t1(1, 0) * t2(1, 0, 1)
+ + t1(0, 1) * t2(0, 1, 1) + t1(1, 1) * t2(1, 1, 1));
+
+ dims[0] = DimPair(1, 0);
+ dims[1] = DimPair(2, 1);
+ result = t2.contract(t1, dims);
+ VERIFY_IS_EQUAL(result.dimension(0), 2);
+ VERIFY_IS_APPROX(result(0), t1(0, 0) * t2(0, 0, 0) + t1(1, 0) * t2(0, 1, 0)
+ + t1(0, 1) * t2(0, 0, 1) + t1(1, 1) * t2(0, 1, 1));
+ VERIFY_IS_APPROX(result(1), t1(0, 0) * t2(1, 0, 0) + t1(1, 0) * t2(1, 1, 0)
+ + t1(0, 1) * t2(1, 0, 1) + t1(1, 1) * t2(1, 1, 1));
+}
+
+template<int DataLayout>
+static void test_contraction_of_contraction()
+{
+ Tensor<float, 2, DataLayout> t1(2, 2);
+ Tensor<float, 2, DataLayout> t2(2, 2);
+ Tensor<float, 2, DataLayout> t3(2, 2);
+ Tensor<float, 2, DataLayout> t4(2, 2);
+ t1.setRandom();
+ t2.setRandom();
+ t3.setRandom();
+ t4.setRandom();
+
+ Eigen::array<DimPair, 1> dims = {{DimPair(1, 0)}};
+ auto contract1 = t1.contract(t2, dims);
+ auto diff = t3 - contract1;
+ auto contract2 = t1.contract(t4, dims);
+ Tensor<float, 2, DataLayout> result = contract2.contract(diff, dims);
+
+ VERIFY_IS_EQUAL(result.dimension(0), 2);
+ VERIFY_IS_EQUAL(result.dimension(1), 2);
+
+ Eigen::Map<Eigen::Matrix<float, Dynamic, Dynamic, DataLayout>>
+ m1(t1.data(), 2, 2), m2(t2.data(), 2, 2), m3(t3.data(), 2, 2),
+ m4(t4.data(), 2, 2);
+ Eigen::Matrix<float, Dynamic, Dynamic, DataLayout>
+ expected = (m1 * m4) * (m3 - m1 * m2);
+
+ VERIFY_IS_APPROX(result(0, 0), expected(0, 0));
+ VERIFY_IS_APPROX(result(0, 1), expected(0, 1));
+ VERIFY_IS_APPROX(result(1, 0), expected(1, 0));
+ VERIFY_IS_APPROX(result(1, 1), expected(1, 1));
+}
+
+template<int DataLayout>
+static void test_expr()
+{
+ Tensor<float, 2, DataLayout> mat1(2, 3);
+ Tensor<float, 2, DataLayout> mat2(3, 2);
+ mat1.setRandom();
+ mat2.setRandom();
+
+ Tensor<float, 2, DataLayout> mat3(2,2);
+
+ Eigen::array<DimPair, 1> dims = {{DimPair(1, 0)}};
+ mat3 = mat1.contract(mat2, dims);
+
+ VERIFY_IS_APPROX(mat3(0,0), mat1(0,0)*mat2(0,0) + mat1(0,1)*mat2(1,0) + mat1(0,2)*mat2(2,0));
+ VERIFY_IS_APPROX(mat3(0,1), mat1(0,0)*mat2(0,1) + mat1(0,1)*mat2(1,1) + mat1(0,2)*mat2(2,1));
+ VERIFY_IS_APPROX(mat3(1,0), mat1(1,0)*mat2(0,0) + mat1(1,1)*mat2(1,0) + mat1(1,2)*mat2(2,0));
+ VERIFY_IS_APPROX(mat3(1,1), mat1(1,0)*mat2(0,1) + mat1(1,1)*mat2(1,1) + mat1(1,2)*mat2(2,1));
+}
+
+template<int DataLayout>
+static void test_out_of_order_contraction()
+{
+ Tensor<float, 3, DataLayout> mat1(2, 2, 2);
+ Tensor<float, 3, DataLayout> mat2(2, 2, 2);
+
+ mat1.setRandom();
+ mat2.setRandom();
+
+ Tensor<float, 2, DataLayout> mat3(2, 2);
+
+ Eigen::array<DimPair, 2> dims = {{DimPair(2, 0), DimPair(0, 2)}};
+ mat3 = mat1.contract(mat2, dims);
+
+ VERIFY_IS_APPROX(mat3(0, 0),
+ mat1(0,0,0)*mat2(0,0,0) + mat1(1,0,0)*mat2(0,0,1) +
+ mat1(0,0,1)*mat2(1,0,0) + mat1(1,0,1)*mat2(1,0,1));
+ VERIFY_IS_APPROX(mat3(1, 0),
+ mat1(0,1,0)*mat2(0,0,0) + mat1(1,1,0)*mat2(0,0,1) +
+ mat1(0,1,1)*mat2(1,0,0) + mat1(1,1,1)*mat2(1,0,1));
+ VERIFY_IS_APPROX(mat3(0, 1),
+ mat1(0,0,0)*mat2(0,1,0) + mat1(1,0,0)*mat2(0,1,1) +
+ mat1(0,0,1)*mat2(1,1,0) + mat1(1,0,1)*mat2(1,1,1));
+ VERIFY_IS_APPROX(mat3(1, 1),
+ mat1(0,1,0)*mat2(0,1,0) + mat1(1,1,0)*mat2(0,1,1) +
+ mat1(0,1,1)*mat2(1,1,0) + mat1(1,1,1)*mat2(1,1,1));
+
+ Eigen::array<DimPair, 2> dims2 = {{DimPair(0, 2), DimPair(2, 0)}};
+ mat3 = mat1.contract(mat2, dims2);
+
+ VERIFY_IS_APPROX(mat3(0, 0),
+ mat1(0,0,0)*mat2(0,0,0) + mat1(1,0,0)*mat2(0,0,1) +
+ mat1(0,0,1)*mat2(1,0,0) + mat1(1,0,1)*mat2(1,0,1));
+ VERIFY_IS_APPROX(mat3(1, 0),
+ mat1(0,1,0)*mat2(0,0,0) + mat1(1,1,0)*mat2(0,0,1) +
+ mat1(0,1,1)*mat2(1,0,0) + mat1(1,1,1)*mat2(1,0,1));
+ VERIFY_IS_APPROX(mat3(0, 1),
+ mat1(0,0,0)*mat2(0,1,0) + mat1(1,0,0)*mat2(0,1,1) +
+ mat1(0,0,1)*mat2(1,1,0) + mat1(1,0,1)*mat2(1,1,1));
+ VERIFY_IS_APPROX(mat3(1, 1),
+ mat1(0,1,0)*mat2(0,1,0) + mat1(1,1,0)*mat2(0,1,1) +
+ mat1(0,1,1)*mat2(1,1,0) + mat1(1,1,1)*mat2(1,1,1));
+
+}
+
+template<int DataLayout>
+static void test_consistency()
+{
+ // this does something like testing (A*B)^T = (B^T * A^T)
+
+ Tensor<float, 3, DataLayout> mat1(4, 3, 5);
+ Tensor<float, 5, DataLayout> mat2(3, 2, 1, 5, 4);
+ mat1.setRandom();
+ mat2.setRandom();
+
+ Tensor<float, 4, DataLayout> mat3(5, 2, 1, 5);
+ Tensor<float, 4, DataLayout> mat4(2, 1, 5, 5);
+
+ // contract on dimensions of size 4 and 3
+ Eigen::array<DimPair, 2> dims1 = {{DimPair(0, 4), DimPair(1, 0)}};
+ Eigen::array<DimPair, 2> dims2 = {{DimPair(4, 0), DimPair(0, 1)}};
+
+ mat3 = mat1.contract(mat2, dims1);
+ mat4 = mat2.contract(mat1, dims2);
+
+ // check that these are equal except for ordering of dimensions
+ if (DataLayout == ColMajor) {
+ for (size_t i = 0; i < 5; i++) {
+ for (size_t j = 0; j < 10; j++) {
+ VERIFY_IS_APPROX(mat3.data()[i + 5 * j], mat4.data()[j + 10 * i]);
+ }
+ }
+ } else {
+ // Row major
+ for (size_t i = 0; i < 5; i++) {
+ for (size_t j = 0; j < 10; j++) {
+ VERIFY_IS_APPROX(mat3.data()[10 * i + j], mat4.data()[i + 5 * j]);
+ }
+ }
+ }
+}
+
+template<int DataLayout>
+static void test_large_contraction()
+{
+ Tensor<float, 4, DataLayout> t_left(30, 50, 8, 31);
+ Tensor<float, 5, DataLayout> t_right(8, 31, 7, 20, 10);
+ Tensor<float, 5, DataLayout> t_result(30, 50, 7, 20, 10);
+
+ t_left.setRandom();
+ t_right.setRandom();
+
+ // Add a little offset so that the results won't be close to zero.
+ t_left += t_left.constant(1.0f);
+ t_right += t_right.constant(1.0f);
+
+ typedef Map<Eigen::Matrix<float, Dynamic, Dynamic, DataLayout>> MapXf;
+ MapXf m_left(t_left.data(), 1500, 248);
+ MapXf m_right(t_right.data(), 248, 1400);
+ Eigen::Matrix<float, Dynamic, Dynamic, DataLayout> m_result(1500, 1400);
+
+ // this contraction should be equivalent to a single matrix multiplication
+ Eigen::array<DimPair, 2> dims = {{DimPair(2, 0), DimPair(3, 1)}};
+
+ // compute results by separate methods
+ t_result = t_left.contract(t_right, dims);
+ m_result = m_left * m_right;
+
+ for (int i = 0; i < t_result.dimensions().TotalSize(); i++) {
+ VERIFY(&t_result.data()[i] != &m_result.data()[i]);
+ VERIFY_IS_APPROX(t_result.data()[i], m_result.data()[i]);
+ }
+}
+
+template<int DataLayout>
+static void test_matrix_vector()
+{
+ Tensor<float, 2, DataLayout> t_left(30, 50);
+ Tensor<float, 1, DataLayout> t_right(50);
+ Tensor<float, 1, DataLayout> t_result(30);
+
+ t_left.setRandom();
+ t_right.setRandom();
+
+ typedef Map<Eigen::Matrix<float, Dynamic, Dynamic, DataLayout>> MapXf;
+ MapXf m_left(t_left.data(), 30, 50);
+ MapXf m_right(t_right.data(), 50, 1);
+ Eigen::Matrix<float, Dynamic, Dynamic, DataLayout> m_result(30, 1);
+
+ // this contraction should be equivalent to a single matrix multiplication
+ Eigen::array<DimPair, 1> dims{{DimPair(1, 0)}};
+
+ // compute results by separate methods
+ t_result = t_left.contract(t_right, dims);
+ m_result = m_left * m_right;
+
+ for (int i = 0; i < t_result.dimensions().TotalSize(); i++) {
+ VERIFY(internal::isApprox(t_result(i), m_result(i, 0), 1));
+ }
+}
+
+
+template<int DataLayout>
+static void test_tensor_vector()
+{
+ Tensor<float, 3, DataLayout> t_left(7, 13, 17);
+ Tensor<float, 2, DataLayout> t_right(1, 7);
+
+ t_left.setRandom();
+ t_right.setRandom();
+
+ typedef typename Tensor<float, 1, DataLayout>::DimensionPair DimensionPair;
+ Eigen::array<DimensionPair, 1> dim_pair01{{{0, 1}}};
+ Tensor<float, 3, DataLayout> t_result = t_left.contract(t_right, dim_pair01);
+
+ typedef Map<Eigen::Matrix<float, Dynamic, Dynamic, DataLayout>> MapXf;
+ MapXf m_left(t_left.data(), 7, 13*17);
+ MapXf m_right(t_right.data(), 1, 7);
+ Eigen::Matrix<float, Dynamic, Dynamic, DataLayout> m_result = m_left.transpose() * m_right.transpose();
+
+ for (int i = 0; i < t_result.dimensions().TotalSize(); i++) {
+ VERIFY(internal::isApprox(t_result(i), m_result(i, 0), 1));
+ }
+}
+
+
+template<int DataLayout>
+static void test_small_blocking_factors()
+{
+ Tensor<float, 4, DataLayout> t_left(30, 5, 3, 31);
+ Tensor<float, 5, DataLayout> t_right(3, 31, 7, 20, 1);
+ t_left.setRandom();
+ t_right.setRandom();
+
+ // Add a little offset so that the results won't be close to zero.
+ t_left += t_left.constant(1.0f);
+ t_right += t_right.constant(1.0f);
+
+ // Force the cache sizes, which results in smaller blocking factors.
+ Eigen::setCpuCacheSizes(896, 1920, 2944);
+
+ // this contraction should be equivalent to a single matrix multiplication
+ Eigen::array<DimPair, 2> dims = {{DimPair(2, 0), DimPair(3, 1)}};
+ Tensor<float, 5, DataLayout> t_result;
+ t_result = t_left.contract(t_right, dims);
+
+ // compute result using a simple eigen matrix product
+ Map<Eigen::Matrix<float, Dynamic, Dynamic, DataLayout>> m_left(t_left.data(), 150, 93);
+ Map<Eigen::Matrix<float, Dynamic, Dynamic, DataLayout>> m_right(t_right.data(), 93, 140);
+ Eigen::Matrix<float, Dynamic, Dynamic, DataLayout> m_result = m_left * m_right;
+
+ for (int i = 0; i < t_result.dimensions().TotalSize(); i++) {
+ VERIFY_IS_APPROX(t_result.data()[i], m_result.data()[i]);
+ }
+}
+
+template<int DataLayout>
+static void test_tensor_product()
+{
+ Tensor<float, 2, DataLayout> mat1(2, 3);
+ Tensor<float, 2, DataLayout> mat2(4, 1);
+ mat1.setRandom();
+ mat2.setRandom();
+
+ Eigen::array<DimPair, 0> dims;
+ Tensor<float, 4, DataLayout> result = mat1.contract(mat2, dims);
+
+ VERIFY_IS_EQUAL(result.dimension(0), 2);
+ VERIFY_IS_EQUAL(result.dimension(1), 3);
+ VERIFY_IS_EQUAL(result.dimension(2), 4);
+ VERIFY_IS_EQUAL(result.dimension(3), 1);
+ for (int i = 0; i < result.dimension(0); ++i) {
+ for (int j = 0; j < result.dimension(1); ++j) {
+ for (int k = 0; k < result.dimension(2); ++k) {
+ for (int l = 0; l < result.dimension(3); ++l) {
+ VERIFY_IS_APPROX(result(i, j, k, l), mat1(i, j) * mat2(k, l) );
+ }
+ }
+ }
+ }
+}
+
+
+template<int DataLayout>
+static void test_const_inputs()
+{
+ Tensor<float, 2, DataLayout> in1(2, 3);
+ Tensor<float, 2, DataLayout> in2(3, 2);
+ in1.setRandom();
+ in2.setRandom();
+
+ TensorMap<Tensor<const float, 2, DataLayout> > mat1(in1.data(), 2, 3);
+ TensorMap<Tensor<const float, 2, DataLayout> > mat2(in2.data(), 3, 2);
+ Tensor<float, 2, DataLayout> mat3(2,2);
+
+ Eigen::array<DimPair, 1> dims = {{DimPair(1, 0)}};
+ mat3 = mat1.contract(mat2, dims);
+
+ VERIFY_IS_APPROX(mat3(0,0), mat1(0,0)*mat2(0,0) + mat1(0,1)*mat2(1,0) + mat1(0,2)*mat2(2,0));
+ VERIFY_IS_APPROX(mat3(0,1), mat1(0,0)*mat2(0,1) + mat1(0,1)*mat2(1,1) + mat1(0,2)*mat2(2,1));
+ VERIFY_IS_APPROX(mat3(1,0), mat1(1,0)*mat2(0,0) + mat1(1,1)*mat2(1,0) + mat1(1,2)*mat2(2,0));
+ VERIFY_IS_APPROX(mat3(1,1), mat1(1,0)*mat2(0,1) + mat1(1,1)*mat2(1,1) + mat1(1,2)*mat2(2,1));
+}
+
+// Apply Sqrt to all output elements.
+struct SqrtOutputKernel {
+ template <typename Index, typename Scalar>
+ EIGEN_ALWAYS_INLINE void operator()(
+ const internal::blas_data_mapper<Scalar, Index, ColMajor>& output_mapper,
+ const TensorContractionParams&, Index, Index, Index num_rows,
+ Index num_cols) const {
+ for (int i = 0; i < num_rows; ++i) {
+ for (int j = 0; j < num_cols; ++j) {
+ output_mapper(i, j) = std::sqrt(output_mapper(i, j));
+ }
+ }
+ }
+};
+
+template <int DataLayout>
+static void test_large_contraction_with_output_kernel() {
+ Tensor<float, 4, DataLayout> t_left(30, 50, 8, 31);
+ Tensor<float, 5, DataLayout> t_right(8, 31, 7, 20, 10);
+ Tensor<float, 5, DataLayout> t_result(30, 50, 7, 20, 10);
+
+ t_left.setRandom();
+ t_right.setRandom();
+ // Put trash in mat4 to verify contraction clears output memory.
+ t_result.setRandom();
+
+ // Add a little offset so that the results won't be close to zero.
+ t_left += t_left.constant(1.0f);
+ t_right += t_right.constant(1.0f);
+
+ typedef Map<Eigen::Matrix<float, Dynamic, Dynamic, DataLayout>> MapXf;
+ MapXf m_left(t_left.data(), 1500, 248);
+ MapXf m_right(t_right.data(), 248, 1400);
+ Eigen::Matrix<float, Dynamic, Dynamic, DataLayout> m_result(1500, 1400);
+
+ // this contraction should be equivalent to a single matrix multiplication
+ Eigen::array<DimPair, 2> dims({{DimPair(2, 0), DimPair(3, 1)}});
+
+ // compute results by separate methods
+ t_result = t_left.contract(t_right, dims, SqrtOutputKernel());
+
+ m_result = m_left * m_right;
+
+ for (std::ptrdiff_t i = 0; i < t_result.dimensions().TotalSize(); i++) {
+ VERIFY(&t_result.data()[i] != &m_result.data()[i]);
+ VERIFY_IS_APPROX(t_result.data()[i], std::sqrt(m_result.data()[i]));
+ }
+}
+
+EIGEN_DECLARE_TEST(cxx11_tensor_contraction)
+{
+ CALL_SUBTEST_1(test_evals<ColMajor>());
+ CALL_SUBTEST_1(test_evals<RowMajor>());
+ CALL_SUBTEST_1(test_scalar<ColMajor>());
+ CALL_SUBTEST_1(test_scalar<RowMajor>());
+ CALL_SUBTEST_2(test_multidims<ColMajor>());
+ CALL_SUBTEST_2(test_multidims<RowMajor>());
+ CALL_SUBTEST_2(test_holes<ColMajor>());
+ CALL_SUBTEST_2(test_holes<RowMajor>());
+ CALL_SUBTEST_3(test_full_redux<ColMajor>());
+ CALL_SUBTEST_3(test_full_redux<RowMajor>());
+ CALL_SUBTEST_3(test_contraction_of_contraction<ColMajor>());
+ CALL_SUBTEST_3(test_contraction_of_contraction<RowMajor>());
+ CALL_SUBTEST_4(test_expr<ColMajor>());
+ CALL_SUBTEST_4(test_expr<RowMajor>());
+ CALL_SUBTEST_4(test_out_of_order_contraction<ColMajor>());
+ CALL_SUBTEST_4(test_out_of_order_contraction<RowMajor>());
+ CALL_SUBTEST_5(test_consistency<ColMajor>());
+ CALL_SUBTEST_5(test_consistency<RowMajor>());
+ CALL_SUBTEST_5(test_large_contraction<ColMajor>());
+ CALL_SUBTEST_5(test_large_contraction<RowMajor>());
+ CALL_SUBTEST_6(test_matrix_vector<ColMajor>());
+ CALL_SUBTEST_6(test_matrix_vector<RowMajor>());
+ CALL_SUBTEST_6(test_tensor_vector<ColMajor>());
+ CALL_SUBTEST_6(test_tensor_vector<RowMajor>());
+ CALL_SUBTEST_7(test_small_blocking_factors<ColMajor>());
+ CALL_SUBTEST_7(test_small_blocking_factors<RowMajor>());
+ CALL_SUBTEST_7(test_tensor_product<ColMajor>());
+ CALL_SUBTEST_7(test_tensor_product<RowMajor>());
+ CALL_SUBTEST_8(test_const_inputs<ColMajor>());
+ CALL_SUBTEST_8(test_const_inputs<RowMajor>());
+ CALL_SUBTEST_8(test_large_contraction_with_output_kernel<ColMajor>());
+ CALL_SUBTEST_8(test_large_contraction_with_output_kernel<RowMajor>());
+
+ // Force CMake to split this test.
+ // EIGEN_SUFFIXES;1;2;3;4;5;6;7;8
+
+}
diff --git a/unsupported/test/cxx11_tensor_convolution.cpp b/unsupported/test/cxx11_tensor_convolution.cpp
new file mode 100644
index 0000000..c3688f6
--- /dev/null
+++ b/unsupported/test/cxx11_tensor_convolution.cpp
@@ -0,0 +1,150 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "main.h"
+
+#include <Eigen/CXX11/Tensor>
+
+using Eigen::Tensor;
+using Eigen::DefaultDevice;
+
+template <int DataLayout>
+static void test_evals()
+{
+ Tensor<float, 2, DataLayout> input(3, 3);
+ Tensor<float, 1, DataLayout> kernel(2);
+
+ input.setRandom();
+ kernel.setRandom();
+
+ Tensor<float, 2, DataLayout> result(2,3);
+ result.setZero();
+ Eigen::array<Tensor<float, 2>::Index, 1> dims3;
+ dims3[0] = 0;
+
+ typedef TensorEvaluator<decltype(input.convolve(kernel, dims3)), DefaultDevice> Evaluator;
+ Evaluator eval(input.convolve(kernel, dims3), DefaultDevice());
+ eval.evalTo(result.data());
+ EIGEN_STATIC_ASSERT(Evaluator::NumDims==2ul, YOU_MADE_A_PROGRAMMING_MISTAKE);
+ VERIFY_IS_EQUAL(eval.dimensions()[0], 2);
+ VERIFY_IS_EQUAL(eval.dimensions()[1], 3);
+
+ VERIFY_IS_APPROX(result(0,0), input(0,0)*kernel(0) + input(1,0)*kernel(1)); // index 0
+ VERIFY_IS_APPROX(result(0,1), input(0,1)*kernel(0) + input(1,1)*kernel(1)); // index 2
+ VERIFY_IS_APPROX(result(0,2), input(0,2)*kernel(0) + input(1,2)*kernel(1)); // index 4
+ VERIFY_IS_APPROX(result(1,0), input(1,0)*kernel(0) + input(2,0)*kernel(1)); // index 1
+ VERIFY_IS_APPROX(result(1,1), input(1,1)*kernel(0) + input(2,1)*kernel(1)); // index 3
+ VERIFY_IS_APPROX(result(1,2), input(1,2)*kernel(0) + input(2,2)*kernel(1)); // index 5
+}
+
+template <int DataLayout>
+static void test_expr()
+{
+ Tensor<float, 2, DataLayout> input(3, 3);
+ Tensor<float, 2, DataLayout> kernel(2, 2);
+ input.setRandom();
+ kernel.setRandom();
+
+ Tensor<float, 2, DataLayout> result(2,2);
+ Eigen::array<ptrdiff_t, 2> dims;
+ dims[0] = 0;
+ dims[1] = 1;
+ result = input.convolve(kernel, dims);
+
+ VERIFY_IS_APPROX(result(0,0), input(0,0)*kernel(0,0) + input(0,1)*kernel(0,1) +
+ input(1,0)*kernel(1,0) + input(1,1)*kernel(1,1));
+ VERIFY_IS_APPROX(result(0,1), input(0,1)*kernel(0,0) + input(0,2)*kernel(0,1) +
+ input(1,1)*kernel(1,0) + input(1,2)*kernel(1,1));
+ VERIFY_IS_APPROX(result(1,0), input(1,0)*kernel(0,0) + input(1,1)*kernel(0,1) +
+ input(2,0)*kernel(1,0) + input(2,1)*kernel(1,1));
+ VERIFY_IS_APPROX(result(1,1), input(1,1)*kernel(0,0) + input(1,2)*kernel(0,1) +
+ input(2,1)*kernel(1,0) + input(2,2)*kernel(1,1));
+}
+
+template <int DataLayout>
+static void test_modes() {
+ Tensor<float, 1, DataLayout> input(3);
+ Tensor<float, 1, DataLayout> kernel(3);
+ input(0) = 1.0f;
+ input(1) = 2.0f;
+ input(2) = 3.0f;
+ kernel(0) = 0.5f;
+ kernel(1) = 1.0f;
+ kernel(2) = 0.0f;
+
+ Eigen::array<ptrdiff_t, 1> dims;
+ dims[0] = 0;
+ Eigen::array<std::pair<ptrdiff_t, ptrdiff_t>, 1> padding;
+
+ // Emulate VALID mode (as defined in
+ // http://docs.scipy.org/doc/numpy/reference/generated/numpy.convolve.html).
+ padding[0] = std::make_pair(0, 0);
+ Tensor<float, 1, DataLayout> valid(1);
+ valid = input.pad(padding).convolve(kernel, dims);
+ VERIFY_IS_EQUAL(valid.dimension(0), 1);
+ VERIFY_IS_APPROX(valid(0), 2.5f);
+
+ // Emulate SAME mode (as defined in
+ // http://docs.scipy.org/doc/numpy/reference/generated/numpy.convolve.html).
+ padding[0] = std::make_pair(1, 1);
+ Tensor<float, 1, DataLayout> same(3);
+ same = input.pad(padding).convolve(kernel, dims);
+ VERIFY_IS_EQUAL(same.dimension(0), 3);
+ VERIFY_IS_APPROX(same(0), 1.0f);
+ VERIFY_IS_APPROX(same(1), 2.5f);
+ VERIFY_IS_APPROX(same(2), 4.0f);
+
+ // Emulate FULL mode (as defined in
+ // http://docs.scipy.org/doc/numpy/reference/generated/numpy.convolve.html).
+ padding[0] = std::make_pair(2, 2);
+ Tensor<float, 1, DataLayout> full(5);
+ full = input.pad(padding).convolve(kernel, dims);
+ VERIFY_IS_EQUAL(full.dimension(0), 5);
+ VERIFY_IS_APPROX(full(0), 0.0f);
+ VERIFY_IS_APPROX(full(1), 1.0f);
+ VERIFY_IS_APPROX(full(2), 2.5f);
+ VERIFY_IS_APPROX(full(3), 4.0f);
+ VERIFY_IS_APPROX(full(4), 1.5f);
+}
+
+template <int DataLayout>
+static void test_strides() {
+ Tensor<float, 1, DataLayout> input(13);
+ Tensor<float, 1, DataLayout> kernel(3);
+ input.setRandom();
+ kernel.setRandom();
+
+ Eigen::array<ptrdiff_t, 1> dims;
+ dims[0] = 0;
+ Eigen::array<ptrdiff_t, 1> stride_of_3;
+ stride_of_3[0] = 3;
+ Eigen::array<ptrdiff_t, 1> stride_of_2;
+ stride_of_2[0] = 2;
+
+ Tensor<float, 1, DataLayout> result;
+ result = input.stride(stride_of_3).convolve(kernel, dims).stride(stride_of_2);
+
+ VERIFY_IS_EQUAL(result.dimension(0), 2);
+ VERIFY_IS_APPROX(result(0), (input(0)*kernel(0) + input(3)*kernel(1) +
+ input(6)*kernel(2)));
+ VERIFY_IS_APPROX(result(1), (input(6)*kernel(0) + input(9)*kernel(1) +
+ input(12)*kernel(2)));
+}
+
+EIGEN_DECLARE_TEST(cxx11_tensor_convolution)
+{
+ CALL_SUBTEST(test_evals<ColMajor>());
+ CALL_SUBTEST(test_evals<RowMajor>());
+ CALL_SUBTEST(test_expr<ColMajor>());
+ CALL_SUBTEST(test_expr<RowMajor>());
+ CALL_SUBTEST(test_modes<ColMajor>());
+ CALL_SUBTEST(test_modes<RowMajor>());
+ CALL_SUBTEST(test_strides<ColMajor>());
+ CALL_SUBTEST(test_strides<RowMajor>());
+}
diff --git a/unsupported/test/cxx11_tensor_convolution_sycl.cpp b/unsupported/test/cxx11_tensor_convolution_sycl.cpp
new file mode 100644
index 0000000..3954c8a
--- /dev/null
+++ b/unsupported/test/cxx11_tensor_convolution_sycl.cpp
@@ -0,0 +1,469 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2016
+// Mehdi Goli Codeplay Software Ltd.
+// Ralph Potter Codeplay Software Ltd.
+// Luke Iwanski Codeplay Software Ltd.
+// Contact: <eigen@codeplay.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#define EIGEN_TEST_NO_LONGDOUBLE
+#define EIGEN_TEST_NO_COMPLEX
+
+#define EIGEN_DEFAULT_DENSE_INDEX_TYPE int64_t
+#define EIGEN_USE_SYCL
+
+#include <iostream>
+#include <chrono>
+#include <ctime>
+
+#include "main.h"
+#include <unsupported/Eigen/CXX11/Tensor>
+#include <iomanip>
+
+using Eigen::array;
+using Eigen::SyclDevice;
+using Eigen::Tensor;
+using Eigen::TensorMap;
+static const float error_threshold =1e-4f;
+
+
+template <typename DataType, int DataLayout, typename IndexType>
+static void test_larg_expr1D(const Eigen::SyclDevice& sycl_device)
+{
+ IndexType indim0 =53;
+ IndexType indim1= 55;
+ IndexType indim2= 51;
+ IndexType outdim0=50;
+ IndexType outdim1=55;
+ IndexType outdim2=51;
+ Eigen::array<IndexType, 3> input_dims = {{indim0, indim1, indim2}};
+ Eigen::array<IndexType, 1> kernel_dims = {{4}};
+ Eigen::array<IndexType, 3> result_dims = {{outdim0, outdim1, outdim2}};
+
+ Tensor<DataType, 3, DataLayout, IndexType> input(input_dims);
+ Tensor<DataType, 1, DataLayout,IndexType> kernel(kernel_dims);
+ Tensor<DataType, 3, DataLayout,IndexType> result(result_dims);
+ Tensor<DataType, 3, DataLayout,IndexType> result_host(result_dims);
+
+ Eigen::array<IndexType, 1> dims3{{0}};
+
+ input.setRandom();
+ kernel.setRandom();
+ result.setZero();
+ result_host.setZero();
+
+ std::size_t input_bytes = input.size() * sizeof(DataType);
+ std::size_t kernel_bytes = kernel.size() * sizeof(DataType);
+ std::size_t result_bytes = result.size() * sizeof(DataType);
+
+ DataType * d_input = static_cast<DataType*>(sycl_device.allocate(input_bytes));
+ DataType * d_kernel = static_cast<DataType*>(sycl_device.allocate(kernel_bytes));
+ DataType * d_result = static_cast<DataType*>(sycl_device.allocate(result_bytes));
+
+ Eigen::TensorMap<Eigen::Tensor<DataType, 3, DataLayout, IndexType> > gpu_input(d_input, input_dims);
+ Eigen::TensorMap<Eigen::Tensor<DataType, 1, DataLayout, IndexType> > gpu_kernel(d_kernel, kernel_dims);
+ Eigen::TensorMap<Eigen::Tensor<DataType, 3, DataLayout, IndexType> > gpu_result(d_result, result_dims);
+ sycl_device.memcpyHostToDevice(d_input, input.data(), input_bytes);
+ sycl_device.memcpyHostToDevice(d_kernel, kernel.data(), kernel_bytes);
+
+ gpu_result.device(sycl_device)=gpu_input.convolve(gpu_kernel, dims3);
+ sycl_device.memcpyDeviceToHost(result.data(), d_result, result_bytes);
+
+ result_host=input.convolve(kernel, dims3);
+
+for(IndexType i=0; i< outdim0; i++ ){
+ for(IndexType j=0; j< outdim1; j++ ){
+ for(IndexType k=0; k< outdim2; k++ ){
+ if (!(Eigen::internal::isApprox(result(i,j,k), result_host(i,j,k), error_threshold))) {
+ std::cout <<std::setprecision(16)<< "mismatch detected at index ( "<< i << " , " << j << ", " << k << " ) " << " \t " << result(i,j,k) << " vs "<< result_host(i,j,k) << std::endl;
+ assert(false);
+ }
+ }
+ }
+}
+ sycl_device.deallocate(d_input);
+ sycl_device.deallocate(d_kernel);
+ sycl_device.deallocate(d_result);
+
+}
+
+
+template <typename DataType, int DataLayout, typename IndexType>
+static void test_larg_expr2D(const Eigen::SyclDevice& sycl_device)
+{
+ IndexType indim0 =53;
+ IndexType indim1= 55;
+ IndexType indim2= 51;
+ IndexType outdim0=50;
+ IndexType outdim1=51;
+ IndexType outdim2=51;
+ Eigen::array<IndexType, 3> input_dims = {{indim0, indim1, indim2}};
+ Eigen::array<IndexType, 2> kernel_dims = {{4,5}};
+ Eigen::array<IndexType, 3> result_dims = {{outdim0, outdim1, outdim2}};
+
+ Tensor<DataType, 3, DataLayout, IndexType> input(input_dims);
+ Tensor<DataType, 2, DataLayout,IndexType> kernel(kernel_dims);
+ Tensor<DataType, 3, DataLayout,IndexType> result(result_dims);
+ Tensor<DataType, 3, DataLayout,IndexType> result_host(result_dims);
+
+ Eigen::array<IndexType, 2> dims3{{0,1}};
+
+ input.setRandom();
+ kernel.setRandom();
+ result.setZero();
+ result_host.setZero();
+
+ std::size_t input_bytes = input.size() * sizeof(DataType);
+ std::size_t kernel_bytes = kernel.size() * sizeof(DataType);
+ std::size_t result_bytes = result.size() * sizeof(DataType);
+
+ DataType * d_input = static_cast<DataType*>(sycl_device.allocate(input_bytes));
+ DataType * d_kernel = static_cast<DataType*>(sycl_device.allocate(kernel_bytes));
+ DataType * d_result = static_cast<DataType*>(sycl_device.allocate(result_bytes));
+
+ Eigen::TensorMap<Eigen::Tensor<DataType, 3, DataLayout, IndexType> > gpu_input(d_input, input_dims);
+ Eigen::TensorMap<Eigen::Tensor<DataType, 2, DataLayout, IndexType> > gpu_kernel(d_kernel, kernel_dims);
+ Eigen::TensorMap<Eigen::Tensor<DataType, 3, DataLayout, IndexType> > gpu_result(d_result, result_dims);
+ sycl_device.memcpyHostToDevice(d_input, input.data(), input_bytes);
+ sycl_device.memcpyHostToDevice(d_kernel, kernel.data(), kernel_bytes);
+
+ gpu_result.device(sycl_device)=gpu_input.convolve(gpu_kernel, dims3);
+ sycl_device.memcpyDeviceToHost(result.data(), d_result, result_bytes);
+
+ result_host=input.convolve(kernel, dims3);
+
+for(IndexType i=0; i< outdim0; i++ ){
+ for(IndexType j=0; j< outdim1; j++ ){
+ for(IndexType k=0; k< outdim2; k++ ){
+ if (!(Eigen::internal::isApprox(result(i,j,k), result_host(i,j,k), error_threshold))) {
+ std::cout <<std::setprecision(16)<< "mismatch detected at index ( "<< i << " , " << j << ", " << k << " ) " << " \t " << result(i,j,k) << " vs "<< result_host(i,j,k) << std::endl;
+ assert(false);
+ }
+ }
+ }
+}
+ sycl_device.deallocate(d_input);
+ sycl_device.deallocate(d_kernel);
+ sycl_device.deallocate(d_result);
+
+}
+
+
+template <typename DataType, int DataLayout, typename IndexType>
+static void test_larg_expr3D(const Eigen::SyclDevice& sycl_device)
+{
+ IndexType indim0 =53;
+ IndexType indim1= 55;
+ IndexType indim2= 51;
+ IndexType outdim0=50;
+ IndexType outdim1=51;
+ IndexType outdim2=49;
+ Eigen::array<IndexType, 3> input_dims = {{indim0, indim1, indim2}};
+ Eigen::array<IndexType, 3> kernel_dims = {{4,5,3}};
+ Eigen::array<IndexType, 3> result_dims = {{outdim0, outdim1, outdim2}};
+
+ Tensor<DataType, 3, DataLayout, IndexType> input(input_dims);
+ Tensor<DataType, 3, DataLayout,IndexType> kernel(kernel_dims);
+ Tensor<DataType, 3, DataLayout,IndexType> result(result_dims);
+ Tensor<DataType, 3, DataLayout,IndexType> result_host(result_dims);
+
+ Eigen::array<IndexType, 3> dims3{{0,1,2}};
+
+ input.setRandom();
+ kernel.setRandom();
+ result.setZero();
+ result_host.setZero();
+
+ std::size_t input_bytes = input.size() * sizeof(DataType);
+ std::size_t kernel_bytes = kernel.size() * sizeof(DataType);
+ std::size_t result_bytes = result.size() * sizeof(DataType);
+
+ DataType * d_input = static_cast<DataType*>(sycl_device.allocate(input_bytes));
+ DataType * d_kernel = static_cast<DataType*>(sycl_device.allocate(kernel_bytes));
+ DataType * d_result = static_cast<DataType*>(sycl_device.allocate(result_bytes));
+
+ Eigen::TensorMap<Eigen::Tensor<DataType, 3, DataLayout, IndexType> > gpu_input(d_input, input_dims);
+ Eigen::TensorMap<Eigen::Tensor<DataType, 3, DataLayout, IndexType> > gpu_kernel(d_kernel, kernel_dims);
+ Eigen::TensorMap<Eigen::Tensor<DataType, 3, DataLayout, IndexType> > gpu_result(d_result, result_dims);
+ sycl_device.memcpyHostToDevice(d_input, input.data(), input_bytes);
+ sycl_device.memcpyHostToDevice(d_kernel, kernel.data(), kernel_bytes);
+
+ gpu_result.device(sycl_device)=gpu_input.convolve(gpu_kernel, dims3);
+ sycl_device.memcpyDeviceToHost(result.data(), d_result, result_bytes);
+
+ result_host=input.convolve(kernel, dims3);
+
+for(IndexType i=0; i< outdim0; i++ ){
+ for(IndexType j=0; j< outdim1; j++ ){
+ for(IndexType k=0; k< outdim2; k++ ){
+ if (!(Eigen::internal::isApprox(result(i,j,k), result_host(i,j,k), error_threshold))) {
+ std::cout <<std::setprecision(16)<< "mismatch detected at index ( "<< i << " , " << j << ", " << k << " ) " << " \t " << result(i,j,k) << " vs "<< result_host(i,j,k) << std::endl;
+ assert(false);
+ }
+ }
+ }
+}
+ sycl_device.deallocate(d_input);
+ sycl_device.deallocate(d_kernel);
+ sycl_device.deallocate(d_result);
+
+}
+
+
+template <typename DataType, int DataLayout, typename IndexType>
+static void test_evals(const Eigen::SyclDevice& sycl_device)
+{
+ Eigen::array<IndexType, 2> input_dims = {{3, 3}};
+ Eigen::array<IndexType, 1> kernel_dims = {{2}};
+ Eigen::array<IndexType, 2> result_dims = {{2, 3}};
+
+ Tensor<DataType, 2, DataLayout, IndexType> input(input_dims);
+ Tensor<DataType, 1, DataLayout,IndexType> kernel(kernel_dims);
+ Tensor<DataType, 2, DataLayout,IndexType> result(result_dims);
+
+ Eigen::array<IndexType, 1> dims3{{0}};
+
+ input.setRandom();
+ kernel.setRandom();
+ result.setZero();
+
+ std::size_t input_bytes = input.size() * sizeof(DataType);
+ std::size_t kernel_bytes = kernel.size() * sizeof(DataType);
+ std::size_t result_bytes = result.size() * sizeof(DataType);
+
+ DataType * d_input = static_cast<DataType*>(sycl_device.allocate(input_bytes));
+ DataType * d_kernel = static_cast<DataType*>(sycl_device.allocate(kernel_bytes));
+ DataType * d_result = static_cast<DataType*>(sycl_device.allocate(result_bytes));
+
+ Eigen::TensorMap<Eigen::Tensor<DataType, 2, DataLayout, IndexType> > gpu_input(d_input, input_dims);
+ Eigen::TensorMap<Eigen::Tensor<DataType, 1, DataLayout, IndexType> > gpu_kernel(d_kernel, kernel_dims);
+ Eigen::TensorMap<Eigen::Tensor<DataType, 2, DataLayout, IndexType> > gpu_result(d_result, result_dims);
+ sycl_device.memcpyHostToDevice(d_input, input.data(), input_bytes);
+ sycl_device.memcpyHostToDevice(d_kernel, kernel.data(), kernel_bytes);
+
+ gpu_result.device(sycl_device)=gpu_input.convolve(gpu_kernel, dims3);
+ sycl_device.memcpyDeviceToHost(result.data(), d_result, result_bytes);
+
+ VERIFY_IS_APPROX(result(0,0), input(0,0)*kernel(0) + input(1,0)*kernel(1)); // index 0
+ VERIFY_IS_APPROX(result(0,1), input(0,1)*kernel(0) + input(1,1)*kernel(1)); // index 2
+ VERIFY_IS_APPROX(result(0,2), input(0,2)*kernel(0) + input(1,2)*kernel(1)); // index 4
+ VERIFY_IS_APPROX(result(1,0), input(1,0)*kernel(0) + input(2,0)*kernel(1)); // index 1
+ VERIFY_IS_APPROX(result(1,1), input(1,1)*kernel(0) + input(2,1)*kernel(1)); // index 3
+ VERIFY_IS_APPROX(result(1,2), input(1,2)*kernel(0) + input(2,2)*kernel(1)); // index 5
+
+ sycl_device.deallocate(d_input);
+ sycl_device.deallocate(d_kernel);
+ sycl_device.deallocate(d_result);
+}
+
+template <typename DataType, int DataLayout, typename IndexType>
+static void test_expr(const Eigen::SyclDevice& sycl_device)
+{
+ Eigen::array<IndexType, 2> input_dims = {{3, 3}};
+ Eigen::array<IndexType, 2> kernel_dims = {{2, 2}};
+ Eigen::array<IndexType, 2> result_dims = {{2, 2}};
+
+ Tensor<DataType, 2, DataLayout, IndexType> input(input_dims);
+ Tensor<DataType, 2, DataLayout, IndexType> kernel(kernel_dims);
+ Tensor<DataType, 2, DataLayout, IndexType> result(result_dims);
+
+ input.setRandom();
+ kernel.setRandom();
+ Eigen::array<IndexType, 2> dims;
+ dims[0] = 0;
+ dims[1] = 1;
+
+ std::size_t input_bytes = input.size() * sizeof(DataType);
+ std::size_t kernel_bytes = kernel.size() * sizeof(DataType);
+ std::size_t result_bytes = result.size() * sizeof(DataType);
+
+ DataType * d_input = static_cast<DataType*>(sycl_device.allocate(input_bytes));
+ DataType * d_kernel = static_cast<DataType*>(sycl_device.allocate(kernel_bytes));
+ DataType * d_result = static_cast<DataType*>(sycl_device.allocate(result_bytes));
+
+ Eigen::TensorMap<Eigen::Tensor<DataType, 2, DataLayout,IndexType> > gpu_input(d_input, input_dims);
+ Eigen::TensorMap<Eigen::Tensor<DataType, 2, DataLayout,IndexType> > gpu_kernel(d_kernel, kernel_dims);
+ Eigen::TensorMap<Eigen::Tensor<DataType, 2, DataLayout,IndexType> > gpu_result(d_result, result_dims);
+ sycl_device.memcpyHostToDevice(d_input, input.data(), input_bytes);
+ sycl_device.memcpyHostToDevice(d_kernel, kernel.data(), kernel_bytes);
+
+ gpu_result.device(sycl_device)=gpu_input.convolve(gpu_kernel, dims);
+ sycl_device.memcpyDeviceToHost(result.data(), d_result, result_bytes);
+
+ VERIFY_IS_APPROX(result(0,0), input(0,0)*kernel(0,0) + input(0,1)*kernel(0,1) +
+ input(1,0)*kernel(1,0) + input(1,1)*kernel(1,1));
+ VERIFY_IS_APPROX(result(0,1), input(0,1)*kernel(0,0) + input(0,2)*kernel(0,1) +
+ input(1,1)*kernel(1,0) + input(1,2)*kernel(1,1));
+ VERIFY_IS_APPROX(result(1,0), input(1,0)*kernel(0,0) + input(1,1)*kernel(0,1) +
+ input(2,0)*kernel(1,0) + input(2,1)*kernel(1,1));
+ VERIFY_IS_APPROX(result(1,1), input(1,1)*kernel(0,0) + input(1,2)*kernel(0,1) +
+ input(2,1)*kernel(1,0) + input(2,2)*kernel(1,1));
+
+ sycl_device.deallocate(d_input);
+ sycl_device.deallocate(d_kernel);
+ sycl_device.deallocate(d_result);
+}
+
+
+template <typename DataType, int DataLayout, typename IndexType>
+static void test_modes(const Eigen::SyclDevice& sycl_device){
+
+Eigen::array<IndexType, 1> input_dims = {{3}};
+Eigen::array<IndexType, 1> kernel_dims = {{3}};
+
+Tensor<DataType, 1, DataLayout, IndexType> input(input_dims);
+Tensor<DataType, 1, DataLayout, IndexType> kernel(kernel_dims);
+
+input.setRandom();
+kernel.setRandom();
+Eigen::array<IndexType, 1> dims;
+dims[0] = 0;
+
+ input(0) = 1.0f;
+ input(1) = 2.0f;
+ input(2) = 3.0f;
+ kernel(0) = 0.5f;
+ kernel(1) = 1.0f;
+ kernel(2) = 0.0f;
+
+ Eigen::array<std::pair<IndexType, IndexType>, 1> padding;
+
+ // Emulate VALID mode (as defined in
+ // http://docs.scipy.org/doc/numpy/reference/generated/numpy.convolve.html).
+ padding[0] = std::make_pair(0, 0);
+ Tensor<DataType, 1, DataLayout, IndexType> valid(1);
+
+ std::size_t input_bytes = input.size() * sizeof(DataType);
+ std::size_t kernel_bytes = kernel.size() * sizeof(DataType);
+ std::size_t valid_bytes = valid.size() * sizeof(DataType);
+
+ DataType * d_input = static_cast<DataType*>(sycl_device.allocate(input_bytes));
+ DataType * d_kernel = static_cast<DataType*>(sycl_device.allocate(kernel_bytes));
+ DataType * d_valid = static_cast<DataType*>(sycl_device.allocate(valid_bytes));
+
+ Eigen::TensorMap<Eigen::Tensor<DataType, 1, DataLayout,IndexType> > gpu_input(d_input, input_dims);
+ Eigen::TensorMap<Eigen::Tensor<DataType, 1, DataLayout,IndexType> > gpu_kernel(d_kernel, kernel_dims);
+ Eigen::TensorMap<Eigen::Tensor<DataType, 1, DataLayout,IndexType> > gpu_valid(d_valid, valid.dimensions());
+ sycl_device.memcpyHostToDevice(d_input, input.data(), input_bytes);
+ sycl_device.memcpyHostToDevice(d_kernel, kernel.data(), kernel_bytes);
+
+ gpu_valid.device(sycl_device)=gpu_input.pad(padding).convolve(gpu_kernel, dims);
+ sycl_device.memcpyDeviceToHost(valid.data(), d_valid, valid_bytes);
+
+ VERIFY_IS_EQUAL(valid.dimension(0), 1);
+ VERIFY_IS_APPROX(valid(0), 2.5f);
+
+ // Emulate SAME mode (as defined in
+ // http://docs.scipy.org/doc/numpy/reference/generated/numpy.convolve.html).
+ padding[0] = std::make_pair(1, 1);
+ Tensor<DataType, 1, DataLayout, IndexType> same(3);
+ std::size_t same_bytes = same.size() * sizeof(DataType);
+ DataType * d_same = static_cast<DataType*>(sycl_device.allocate(same_bytes));
+ Eigen::TensorMap<Eigen::Tensor<DataType, 1, DataLayout,IndexType> > gpu_same(d_same, same.dimensions());
+ gpu_same.device(sycl_device)=gpu_input.pad(padding).convolve(gpu_kernel, dims);
+ sycl_device.memcpyDeviceToHost(same.data(), d_same, same_bytes);
+
+ VERIFY_IS_EQUAL(same.dimension(0), 3);
+ VERIFY_IS_APPROX(same(0), 1.0f);
+ VERIFY_IS_APPROX(same(1), 2.5f);
+ VERIFY_IS_APPROX(same(2), 4.0f);
+
+ // Emulate FULL mode (as defined in
+ // http://docs.scipy.org/doc/numpy/reference/generated/numpy.convolve.html).
+ padding[0] = std::make_pair(2, 2);
+
+ Tensor<DataType, 1, DataLayout, IndexType> full(5);
+ std::size_t full_bytes = full.size() * sizeof(DataType);
+ DataType * d_full = static_cast<DataType*>(sycl_device.allocate(full_bytes));
+ Eigen::TensorMap<Eigen::Tensor<DataType, 1, DataLayout,IndexType> > gpu_full(d_full, full.dimensions());
+ gpu_full.device(sycl_device)=gpu_input.pad(padding).convolve(gpu_kernel, dims);
+ sycl_device.memcpyDeviceToHost(full.data(), d_full, full_bytes);
+
+ VERIFY_IS_EQUAL(full.dimension(0), 5);
+ VERIFY_IS_APPROX(full(0), 0.0f);
+ VERIFY_IS_APPROX(full(1), 1.0f);
+ VERIFY_IS_APPROX(full(2), 2.5f);
+ VERIFY_IS_APPROX(full(3), 4.0f);
+ VERIFY_IS_APPROX(full(4), 1.5f);
+
+ sycl_device.deallocate(d_input);
+ sycl_device.deallocate(d_kernel);
+ sycl_device.deallocate(d_valid);
+ sycl_device.deallocate(d_same);
+ sycl_device.deallocate(d_full);
+
+}
+
+template <typename DataType, int DataLayout, typename IndexType>
+static void test_strides(const Eigen::SyclDevice& sycl_device){
+
+ Eigen::array<IndexType, 1> input_dims = {{13}};
+ Eigen::array<IndexType, 1> kernel_dims = {{3}};
+
+ Tensor<DataType, 1, DataLayout, IndexType> input(input_dims);
+ Tensor<DataType, 1, DataLayout, IndexType> kernel(kernel_dims);
+ Tensor<DataType, 1, DataLayout, IndexType> result(2);
+
+ input.setRandom();
+ kernel.setRandom();
+ Eigen::array<IndexType, 1> dims;
+ dims[0] = 0;
+
+ Eigen::array<IndexType, 1> stride_of_3;
+ stride_of_3[0] = 3;
+ Eigen::array<IndexType, 1> stride_of_2;
+ stride_of_2[0] = 2;
+
+ std::size_t input_bytes = input.size() * sizeof(DataType);
+ std::size_t kernel_bytes = kernel.size() * sizeof(DataType);
+ std::size_t result_bytes = result.size() * sizeof(DataType);
+
+ DataType * d_input = static_cast<DataType*>(sycl_device.allocate(input_bytes));
+ DataType * d_kernel = static_cast<DataType*>(sycl_device.allocate(kernel_bytes));
+ DataType * d_result = static_cast<DataType*>(sycl_device.allocate(result_bytes));
+
+ Eigen::TensorMap<Eigen::Tensor<DataType, 1, DataLayout,IndexType> > gpu_input(d_input, input_dims);
+ Eigen::TensorMap<Eigen::Tensor<DataType, 1, DataLayout,IndexType> > gpu_kernel(d_kernel, kernel_dims);
+ Eigen::TensorMap<Eigen::Tensor<DataType, 1, DataLayout,IndexType> > gpu_result(d_result, result.dimensions());
+ sycl_device.memcpyHostToDevice(d_input, input.data(), input_bytes);
+ sycl_device.memcpyHostToDevice(d_kernel, kernel.data(), kernel_bytes);
+
+ gpu_result.device(sycl_device)=gpu_input.stride(stride_of_3).convolve(gpu_kernel, dims).stride(stride_of_2);
+ sycl_device.memcpyDeviceToHost(result.data(), d_result, result_bytes);
+
+ VERIFY_IS_EQUAL(result.dimension(0), 2);
+ VERIFY_IS_APPROX(result(0), (input(0)*kernel(0) + input(3)*kernel(1) +
+ input(6)*kernel(2)));
+ VERIFY_IS_APPROX(result(1), (input(6)*kernel(0) + input(9)*kernel(1) +
+ input(12)*kernel(2)));
+}
+
+template <typename Dev_selector> void tensorConvolutionPerDevice(Dev_selector& s){
+ QueueInterface queueInterface(s);
+ auto sycl_device=Eigen::SyclDevice(&queueInterface);
+ test_larg_expr1D<float, RowMajor, int64_t>(sycl_device);
+ test_larg_expr1D<float, ColMajor, int64_t>(sycl_device);
+ test_larg_expr2D<float, RowMajor, int64_t>(sycl_device);
+ test_larg_expr2D<float, ColMajor, int64_t>(sycl_device);
+ test_larg_expr3D<float, RowMajor, int64_t>(sycl_device);
+ test_larg_expr3D<float, ColMajor, int64_t>(sycl_device);
+ test_evals<float, ColMajor, int64_t>(sycl_device);
+ test_evals<float, RowMajor, int64_t>(sycl_device);
+ test_expr<float, ColMajor, int64_t>(sycl_device);
+ test_expr<float, RowMajor, int64_t>(sycl_device);
+ test_modes<float, ColMajor, int64_t>(sycl_device);
+ test_modes<float, RowMajor, int64_t>(sycl_device);
+ test_strides<float, ColMajor, int64_t>(sycl_device);
+ test_strides<float, RowMajor, int64_t>(sycl_device);
+}
+
+EIGEN_DECLARE_TEST(cxx11_tensor_convolution_sycl) {
+ for (const auto& device :Eigen::get_sycl_supported_devices()) {
+ CALL_SUBTEST(tensorConvolutionPerDevice(device));
+ }
+}
diff --git a/unsupported/test/cxx11_tensor_custom_index.cpp b/unsupported/test/cxx11_tensor_custom_index.cpp
new file mode 100644
index 0000000..38ce05b
--- /dev/null
+++ b/unsupported/test/cxx11_tensor_custom_index.cpp
@@ -0,0 +1,92 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2015 Benoit Steiner <benoit.steiner.goog@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "main.h"
+#include <limits>
+#include <map>
+
+#include <Eigen/Dense>
+#include <Eigen/CXX11/Tensor>
+
+using Eigen::Tensor;
+
+
+template <int DataLayout>
+static void test_map_as_index()
+{
+ Tensor<float, 4, DataLayout> tensor(2, 3, 5, 7);
+ tensor.setRandom();
+
+ using NormalIndex = DSizes<ptrdiff_t, 4>;
+ using CustomIndex = std::map<ptrdiff_t, ptrdiff_t>;
+ CustomIndex coeffC;
+ coeffC[0] = 1;
+ coeffC[1] = 2;
+ coeffC[2] = 4;
+ coeffC[3] = 1;
+ NormalIndex coeff(1,2,4,1);
+
+ VERIFY_IS_EQUAL(tensor.coeff(coeffC), tensor.coeff(coeff));
+ VERIFY_IS_EQUAL(tensor.coeffRef(coeffC), tensor.coeffRef(coeff));
+}
+
+
+template <int DataLayout>
+static void test_matrix_as_index()
+{
+ Tensor<float, 4, DataLayout> tensor(2, 3, 5, 7);
+ tensor.setRandom();
+
+ using NormalIndex = DSizes<ptrdiff_t, 4>;
+ using CustomIndex = Matrix<unsigned int, 4, 1>;
+ CustomIndex coeffC(1,2,4,1);
+ NormalIndex coeff(1,2,4,1);
+
+ VERIFY_IS_EQUAL(tensor.coeff(coeffC), tensor.coeff(coeff));
+ VERIFY_IS_EQUAL(tensor.coeffRef(coeffC), tensor.coeffRef(coeff));
+}
+
+
+template <int DataLayout>
+static void test_varlist_as_index()
+{
+ Tensor<float, 4, DataLayout> tensor(2, 3, 5, 7);
+ tensor.setRandom();
+
+ DSizes<ptrdiff_t, 4> coeff(1,2,4,1);
+
+ VERIFY_IS_EQUAL(tensor.coeff({1,2,4,1}), tensor.coeff(coeff));
+ VERIFY_IS_EQUAL(tensor.coeffRef({1,2,4,1}), tensor.coeffRef(coeff));
+}
+
+
+template <int DataLayout>
+static void test_sizes_as_index()
+{
+ Tensor<float, 4, DataLayout> tensor(2, 3, 5, 7);
+ tensor.setRandom();
+
+ DSizes<ptrdiff_t, 4> coeff(1,2,4,1);
+ Sizes<1,2,4,1> coeffC;
+
+ VERIFY_IS_EQUAL(tensor.coeff(coeffC), tensor.coeff(coeff));
+ VERIFY_IS_EQUAL(tensor.coeffRef(coeffC), tensor.coeffRef(coeff));
+}
+
+
+EIGEN_DECLARE_TEST(cxx11_tensor_custom_index) {
+ test_map_as_index<ColMajor>();
+ test_map_as_index<RowMajor>();
+ test_matrix_as_index<ColMajor>();
+ test_matrix_as_index<RowMajor>();
+ test_varlist_as_index<ColMajor>();
+ test_varlist_as_index<RowMajor>();
+ test_sizes_as_index<ColMajor>();
+ test_sizes_as_index<RowMajor>();
+}
diff --git a/unsupported/test/cxx11_tensor_custom_op.cpp b/unsupported/test/cxx11_tensor_custom_op.cpp
new file mode 100644
index 0000000..875ea57
--- /dev/null
+++ b/unsupported/test/cxx11_tensor_custom_op.cpp
@@ -0,0 +1,111 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "main.h"
+
+#include <Eigen/CXX11/Tensor>
+
+using Eigen::Tensor;
+
+
+struct InsertZeros {
+ DSizes<DenseIndex, 2> dimensions(const Tensor<float, 2>& input) const {
+ DSizes<DenseIndex, 2> result;
+ result[0] = input.dimension(0) * 2;
+ result[1] = input.dimension(1) * 2;
+ return result;
+ }
+
+ template <typename Output, typename Device>
+ void eval(const Tensor<float, 2>& input, Output& output, const Device& device) const
+ {
+ array<DenseIndex, 2> strides;
+ strides[0] = 2;
+ strides[1] = 2;
+ output.stride(strides).device(device) = input;
+
+ Eigen::DSizes<DenseIndex, 2> offsets(1,1);
+ Eigen::DSizes<DenseIndex, 2> extents(output.dimension(0)-1, output.dimension(1)-1);
+ output.slice(offsets, extents).stride(strides).device(device) = input.constant(0.0f);
+ }
+};
+
+static void test_custom_unary_op()
+{
+ Tensor<float, 2> tensor(3,5);
+ tensor.setRandom();
+
+ Tensor<float, 2> result = tensor.customOp(InsertZeros());
+ VERIFY_IS_EQUAL(result.dimension(0), 6);
+ VERIFY_IS_EQUAL(result.dimension(1), 10);
+
+ for (int i = 0; i < 6; i+=2) {
+ for (int j = 0; j < 10; j+=2) {
+ VERIFY_IS_EQUAL(result(i, j), tensor(i/2, j/2));
+ }
+ }
+ for (int i = 1; i < 6; i+=2) {
+ for (int j = 1; j < 10; j+=2) {
+ VERIFY_IS_EQUAL(result(i, j), 0);
+ }
+ }
+}
+
+
+struct BatchMatMul {
+ DSizes<DenseIndex, 3> dimensions(const Tensor<float, 3>& input1, const Tensor<float, 3>& input2) const {
+ DSizes<DenseIndex, 3> result;
+ result[0] = input1.dimension(0);
+ result[1] = input2.dimension(1);
+ result[2] = input2.dimension(2);
+ return result;
+ }
+
+ template <typename Output, typename Device>
+ void eval(const Tensor<float, 3>& input1, const Tensor<float, 3>& input2,
+ Output& output, const Device& device) const
+ {
+ typedef Tensor<float, 3>::DimensionPair DimPair;
+ array<DimPair, 1> dims;
+ dims[0] = DimPair(1, 0);
+ for (int i = 0; i < output.dimension(2); ++i) {
+ output.template chip<2>(i).device(device) = input1.chip<2>(i).contract(input2.chip<2>(i), dims);
+ }
+ }
+};
+
+
+static void test_custom_binary_op()
+{
+ Tensor<float, 3> tensor1(2,3,5);
+ tensor1.setRandom();
+ Tensor<float, 3> tensor2(3,7,5);
+ tensor2.setRandom();
+
+ Tensor<float, 3> result = tensor1.customOp(tensor2, BatchMatMul());
+ for (int i = 0; i < 5; ++i) {
+ typedef Tensor<float, 3>::DimensionPair DimPair;
+ array<DimPair, 1> dims;
+ dims[0] = DimPair(1, 0);
+ Tensor<float, 2> reference = tensor1.chip<2>(i).contract(tensor2.chip<2>(i), dims);
+ TensorRef<Tensor<float, 2> > val = result.chip<2>(i);
+ for (int j = 0; j < 2; ++j) {
+ for (int k = 0; k < 7; ++k) {
+ VERIFY_IS_APPROX(val(j, k), reference(j, k));
+ }
+ }
+ }
+}
+
+
+EIGEN_DECLARE_TEST(cxx11_tensor_custom_op)
+{
+ CALL_SUBTEST(test_custom_unary_op());
+ CALL_SUBTEST(test_custom_binary_op());
+}
diff --git a/unsupported/test/cxx11_tensor_custom_op_sycl.cpp b/unsupported/test/cxx11_tensor_custom_op_sycl.cpp
new file mode 100644
index 0000000..d947ead
--- /dev/null
+++ b/unsupported/test/cxx11_tensor_custom_op_sycl.cpp
@@ -0,0 +1,170 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2016
+// Mehdi Goli Codeplay Software Ltd.
+// Ralph Potter Codeplay Software Ltd.
+// Luke Iwanski Codeplay Software Ltd.
+// Contact: <eigen@codeplay.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#define EIGEN_TEST_NO_LONGDOUBLE
+#define EIGEN_TEST_NO_COMPLEX
+
+#define EIGEN_DEFAULT_DENSE_INDEX_TYPE int64_t
+#define EIGEN_USE_SYCL
+
+#include "main.h"
+#include <unsupported/Eigen/CXX11/Tensor>
+
+using Eigen::Tensor;
+template<typename TensorType>
+struct InsertZeros {
+ DSizes<DenseIndex, 2> dimensions(const TensorType& input) const {
+ DSizes<DenseIndex, 2> result;
+ result[0] = input.dimension(0) * 2;
+ result[1] = input.dimension(1) * 2;
+ return result;
+ }
+
+ template <typename Output, typename Device>
+ void eval(const TensorType& input, Output& output, const Device& device) const
+ {
+ array<DenseIndex, 2> strides;
+ strides[0] = 2;
+ strides[1] = 2;
+ output.stride(strides).device(device) = input;
+
+ Eigen::DSizes<DenseIndex, 2> offsets(1,1);
+ Eigen::DSizes<DenseIndex, 2> extents(output.dimension(0)-1, output.dimension(1)-1);
+ output.slice(offsets, extents).stride(strides).device(device) = input.constant(0.0f);
+ }
+};
+
+template<typename DataType, int DataLayout, typename IndexType>
+static void test_custom_unary_op_sycl(const Eigen::SyclDevice &sycl_device)
+{
+ IndexType sizeDim1 = 3;
+ IndexType sizeDim2 = 5;
+ Eigen::array<IndexType, 2> tensorRange = {{sizeDim1, sizeDim2}};
+ Eigen::array<IndexType, 2> tensorResultRange = {{6, 10}};
+
+ Eigen::Tensor<DataType, 2, DataLayout, IndexType> in1(tensorRange);
+ Eigen::Tensor<DataType, 2, DataLayout, IndexType> out(tensorResultRange);
+
+ DataType * gpu_in1_data = static_cast<DataType*>(sycl_device.allocate(in1.dimensions().TotalSize()*sizeof(DataType)));
+ DataType * gpu_out_data = static_cast<DataType*>(sycl_device.allocate(out.dimensions().TotalSize()*sizeof(DataType)));
+
+ typedef Eigen::TensorMap<Eigen::Tensor<DataType, 2, DataLayout, IndexType> > TensorType;
+ TensorType gpu_in1(gpu_in1_data, tensorRange);
+ TensorType gpu_out(gpu_out_data, tensorResultRange);
+
+ in1.setRandom();
+ sycl_device.memcpyHostToDevice(gpu_in1_data, in1.data(),(in1.dimensions().TotalSize())*sizeof(DataType));
+ gpu_out.device(sycl_device) = gpu_in1.customOp(InsertZeros<TensorType>());
+ sycl_device.memcpyDeviceToHost(out.data(), gpu_out_data,(out.dimensions().TotalSize())*sizeof(DataType));
+
+ VERIFY_IS_EQUAL(out.dimension(0), 6);
+ VERIFY_IS_EQUAL(out.dimension(1), 10);
+
+ for (int i = 0; i < 6; i+=2) {
+ for (int j = 0; j < 10; j+=2) {
+ VERIFY_IS_EQUAL(out(i, j), in1(i/2, j/2));
+ }
+ }
+ for (int i = 1; i < 6; i+=2) {
+ for (int j = 1; j < 10; j+=2) {
+ VERIFY_IS_EQUAL(out(i, j), 0);
+ }
+ }
+ sycl_device.deallocate(gpu_in1_data);
+sycl_device.deallocate(gpu_out_data);
+}
+
+template<typename TensorType>
+struct BatchMatMul {
+ DSizes<DenseIndex, 3> dimensions(const TensorType& input1, const TensorType& input2) const {
+ DSizes<DenseIndex, 3> result;
+ result[0] = input1.dimension(0);
+ result[1] = input2.dimension(1);
+ result[2] = input2.dimension(2);
+ return result;
+ }
+
+ template <typename Output, typename Device>
+ void eval(const TensorType& input1, const TensorType& input2,
+ Output& output, const Device& device) const
+ {
+ typedef typename TensorType::DimensionPair DimPair;
+ array<DimPair, 1> dims;
+ dims[0] = DimPair(1, 0);
+ for (int64_t i = 0; i < output.dimension(2); ++i) {
+ output.template chip<2>(i).device(device) = input1.template chip<2>(i).contract(input2.template chip<2>(i), dims);
+ }
+ }
+};
+
+template<typename DataType, int DataLayout, typename IndexType>
+static void test_custom_binary_op_sycl(const Eigen::SyclDevice &sycl_device)
+{
+
+ Eigen::array<IndexType, 3> tensorRange1 = {{2, 3, 5}};
+ Eigen::array<IndexType, 3> tensorRange2 = {{3,7,5}};
+ Eigen::array<IndexType, 3> tensorResultRange = {{2, 7, 5}};
+
+ Eigen::Tensor<DataType, 3, DataLayout, IndexType> in1(tensorRange1);
+ Eigen::Tensor<DataType, 3, DataLayout, IndexType> in2(tensorRange2);
+ Eigen::Tensor<DataType, 3, DataLayout, IndexType> out(tensorResultRange);
+
+ DataType * gpu_in1_data = static_cast<DataType*>(sycl_device.allocate(in1.dimensions().TotalSize()*sizeof(DataType)));
+ DataType * gpu_in2_data = static_cast<DataType*>(sycl_device.allocate(in2.dimensions().TotalSize()*sizeof(DataType)));
+ DataType * gpu_out_data = static_cast<DataType*>(sycl_device.allocate(out.dimensions().TotalSize()*sizeof(DataType)));
+
+ typedef Eigen::TensorMap<Eigen::Tensor<DataType, 3, DataLayout, IndexType> > TensorType;
+ TensorType gpu_in1(gpu_in1_data, tensorRange1);
+ TensorType gpu_in2(gpu_in2_data, tensorRange2);
+ TensorType gpu_out(gpu_out_data, tensorResultRange);
+
+ in1.setRandom();
+ in2.setRandom();
+
+ sycl_device.memcpyHostToDevice(gpu_in1_data, in1.data(),(in1.dimensions().TotalSize())*sizeof(DataType));
+ sycl_device.memcpyHostToDevice(gpu_in2_data, in2.data(),(in2.dimensions().TotalSize())*sizeof(DataType));
+
+ gpu_out.device(sycl_device) = gpu_in1.customOp(gpu_in2, BatchMatMul<TensorType>());
+ sycl_device.memcpyDeviceToHost(out.data(), gpu_out_data,(out.dimensions().TotalSize())*sizeof(DataType));
+
+ for (IndexType i = 0; i < 5; ++i) {
+ typedef typename Eigen::Tensor<DataType, 3, DataLayout, IndexType>::DimensionPair DimPair;
+ array<DimPair, 1> dims;
+ dims[0] = DimPair(1, 0);
+ Eigen::Tensor<DataType, 2, DataLayout, IndexType> reference = in1.template chip<2>(i).contract(in2.template chip<2>(i), dims);
+ TensorRef<Eigen::Tensor<DataType, 2, DataLayout, IndexType> > val = out.template chip<2>(i);
+ for (IndexType j = 0; j < 2; ++j) {
+ for (IndexType k = 0; k < 7; ++k) {
+ VERIFY_IS_APPROX(val(j, k), reference(j, k));
+ }
+ }
+ }
+ sycl_device.deallocate(gpu_in1_data);
+ sycl_device.deallocate(gpu_in2_data);
+ sycl_device.deallocate(gpu_out_data);
+}
+
+template <typename DataType, typename Dev_selector> void custom_op_perDevice(Dev_selector s){
+ QueueInterface queueInterface(s);
+ auto sycl_device = Eigen::SyclDevice(&queueInterface);
+ test_custom_unary_op_sycl<DataType, RowMajor, int64_t>(sycl_device);
+ test_custom_unary_op_sycl<DataType, ColMajor, int64_t>(sycl_device);
+ test_custom_binary_op_sycl<DataType, ColMajor, int64_t>(sycl_device);
+ test_custom_binary_op_sycl<DataType, RowMajor, int64_t>(sycl_device);
+
+}
+EIGEN_DECLARE_TEST(cxx11_tensor_custom_op_sycl) {
+ for (const auto& device :Eigen::get_sycl_supported_devices()) {
+ CALL_SUBTEST(custom_op_perDevice<float>(device));
+ }
+}
diff --git a/unsupported/test/cxx11_tensor_device.cu b/unsupported/test/cxx11_tensor_device.cu
new file mode 100644
index 0000000..58cfc01
--- /dev/null
+++ b/unsupported/test/cxx11_tensor_device.cu
@@ -0,0 +1,440 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#define EIGEN_TEST_NO_LONGDOUBLE
+#define EIGEN_TEST_NO_COMPLEX
+
+#define EIGEN_DEFAULT_DENSE_INDEX_TYPE int
+#define EIGEN_USE_GPU
+
+#include "main.h"
+#include "OffByOneScalar.h"
+#include <unsupported/Eigen/CXX11/Tensor>
+
+#include <unsupported/Eigen/CXX11/src/Tensor/TensorGpuHipCudaDefines.h>
+
+using Eigen::Tensor;
+using Eigen::RowMajor;
+
+// Context for evaluation on cpu
+struct CPUContext {
+ CPUContext(const Eigen::Tensor<float, 3>& in1, Eigen::Tensor<float, 3>& in2, Eigen::Tensor<float, 3>& out) : in1_(in1), in2_(in2), out_(out), kernel_1d_(2), kernel_2d_(2,2), kernel_3d_(2,2,2) {
+ kernel_1d_(0) = 3.14f;
+ kernel_1d_(1) = 2.7f;
+
+ kernel_2d_(0,0) = 3.14f;
+ kernel_2d_(1,0) = 2.7f;
+ kernel_2d_(0,1) = 0.2f;
+ kernel_2d_(1,1) = 7.0f;
+
+ kernel_3d_(0,0,0) = 3.14f;
+ kernel_3d_(0,1,0) = 2.7f;
+ kernel_3d_(0,0,1) = 0.2f;
+ kernel_3d_(0,1,1) = 7.0f;
+ kernel_3d_(1,0,0) = -1.0f;
+ kernel_3d_(1,1,0) = -0.3f;
+ kernel_3d_(1,0,1) = -0.7f;
+ kernel_3d_(1,1,1) = -0.5f;
+ }
+
+ const Eigen::DefaultDevice& device() const { return cpu_device_; }
+
+ const Eigen::Tensor<float, 3>& in1() const { return in1_; }
+ const Eigen::Tensor<float, 3>& in2() const { return in2_; }
+ Eigen::Tensor<float, 3>& out() { return out_; }
+ const Eigen::Tensor<float, 1>& kernel1d() const { return kernel_1d_; }
+ const Eigen::Tensor<float, 2>& kernel2d() const { return kernel_2d_; }
+ const Eigen::Tensor<float, 3>& kernel3d() const { return kernel_3d_; }
+
+ private:
+ const Eigen::Tensor<float, 3>& in1_;
+ const Eigen::Tensor<float, 3>& in2_;
+ Eigen::Tensor<float, 3>& out_;
+
+ Eigen::Tensor<float, 1> kernel_1d_;
+ Eigen::Tensor<float, 2> kernel_2d_;
+ Eigen::Tensor<float, 3> kernel_3d_;
+
+ Eigen::DefaultDevice cpu_device_;
+};
+
+
+// Context for evaluation on GPU
+struct GPUContext {
+ GPUContext(const Eigen::TensorMap<Eigen::Tensor<float, 3> >& in1, Eigen::TensorMap<Eigen::Tensor<float, 3> >& in2, Eigen::TensorMap<Eigen::Tensor<float, 3> >& out) : in1_(in1), in2_(in2), out_(out), gpu_device_(&stream_) {
+ assert(gpuMalloc((void**)(&kernel_1d_), 2*sizeof(float)) == gpuSuccess);
+ float kernel_1d_val[] = {3.14f, 2.7f};
+ assert(gpuMemcpy(kernel_1d_, kernel_1d_val, 2*sizeof(float), gpuMemcpyHostToDevice) == gpuSuccess);
+
+ assert(gpuMalloc((void**)(&kernel_2d_), 4*sizeof(float)) == gpuSuccess);
+ float kernel_2d_val[] = {3.14f, 2.7f, 0.2f, 7.0f};
+ assert(gpuMemcpy(kernel_2d_, kernel_2d_val, 4*sizeof(float), gpuMemcpyHostToDevice) == gpuSuccess);
+
+ assert(gpuMalloc((void**)(&kernel_3d_), 8*sizeof(float)) == gpuSuccess);
+ float kernel_3d_val[] = {3.14f, -1.0f, 2.7f, -0.3f, 0.2f, -0.7f, 7.0f, -0.5f};
+ assert(gpuMemcpy(kernel_3d_, kernel_3d_val, 8*sizeof(float), gpuMemcpyHostToDevice) == gpuSuccess);
+ }
+ ~GPUContext() {
+ assert(gpuFree(kernel_1d_) == gpuSuccess);
+ assert(gpuFree(kernel_2d_) == gpuSuccess);
+ assert(gpuFree(kernel_3d_) == gpuSuccess);
+ }
+
+ const Eigen::GpuDevice& device() const { return gpu_device_; }
+
+ const Eigen::TensorMap<Eigen::Tensor<float, 3> >& in1() const { return in1_; }
+ const Eigen::TensorMap<Eigen::Tensor<float, 3> >& in2() const { return in2_; }
+ Eigen::TensorMap<Eigen::Tensor<float, 3> >& out() { return out_; }
+ Eigen::TensorMap<Eigen::Tensor<float, 1> > kernel1d() const { return Eigen::TensorMap<Eigen::Tensor<float, 1> >(kernel_1d_, 2); }
+ Eigen::TensorMap<Eigen::Tensor<float, 2> > kernel2d() const { return Eigen::TensorMap<Eigen::Tensor<float, 2> >(kernel_2d_, 2, 2); }
+ Eigen::TensorMap<Eigen::Tensor<float, 3> > kernel3d() const { return Eigen::TensorMap<Eigen::Tensor<float, 3> >(kernel_3d_, 2, 2, 2); }
+
+ private:
+ const Eigen::TensorMap<Eigen::Tensor<float, 3> >& in1_;
+ const Eigen::TensorMap<Eigen::Tensor<float, 3> >& in2_;
+ Eigen::TensorMap<Eigen::Tensor<float, 3> >& out_;
+
+ float* kernel_1d_;
+ float* kernel_2d_;
+ float* kernel_3d_;
+
+ Eigen::GpuStreamDevice stream_;
+ Eigen::GpuDevice gpu_device_;
+};
+
+
+// The actual expression to evaluate
+template <typename Context>
+void test_contextual_eval(Context* context)
+{
+ context->out().device(context->device()) = context->in1() + context->in2() * 3.14f + context->in1().constant(2.718f);
+}
+
+template <typename Context>
+void test_forced_contextual_eval(Context* context)
+{
+ context->out().device(context->device()) = (context->in1() + context->in2()).eval() * 3.14f + context->in1().constant(2.718f);
+}
+
+template <typename Context>
+void test_compound_assignment(Context* context)
+{
+ context->out().device(context->device()) = context->in1().constant(2.718f);
+ context->out().device(context->device()) += context->in1() + context->in2() * 3.14f;
+}
+
+
+template <typename Context>
+void test_contraction(Context* context)
+{
+ Eigen::array<std::pair<int, int>, 2> dims;
+ dims[0] = std::make_pair(1, 1);
+ dims[1] = std::make_pair(2, 2);
+
+ Eigen::array<int, 2> shape(40, 50*70);
+
+ Eigen::DSizes<int, 2> indices(0,0);
+ Eigen::DSizes<int, 2> sizes(40,40);
+
+ context->out().reshape(shape).slice(indices, sizes).device(context->device()) = context->in1().contract(context->in2(), dims);
+}
+
+
+template <typename Context>
+void test_1d_convolution(Context* context)
+{
+ Eigen::DSizes<int, 3> indices(0,0,0);
+ Eigen::DSizes<int, 3> sizes(40,49,70);
+
+ Eigen::array<int, 1> dims(1);
+ context->out().slice(indices, sizes).device(context->device()) = context->in1().convolve(context->kernel1d(), dims);
+}
+
+template <typename Context>
+void test_2d_convolution(Context* context)
+{
+ Eigen::DSizes<int, 3> indices(0,0,0);
+ Eigen::DSizes<int, 3> sizes(40,49,69);
+
+ Eigen::array<int, 2> dims(1,2);
+ context->out().slice(indices, sizes).device(context->device()) = context->in1().convolve(context->kernel2d(), dims);
+}
+
+template <typename Context>
+void test_3d_convolution(Context* context)
+{
+ Eigen::DSizes<int, 3> indices(0,0,0);
+ Eigen::DSizes<int, 3> sizes(39,49,69);
+
+ Eigen::array<int, 3> dims(0,1,2);
+ context->out().slice(indices, sizes).device(context->device()) = context->in1().convolve(context->kernel3d(), dims);
+}
+
+// Helper method to synchronize device.
+template<typename Device>
+void synchronize(Device& device) { /*nothing*/ }
+template<>
+void synchronize(Eigen::GpuDevice& device) {
+ device.synchronize();
+}
+
+template <typename DataType, typename TensorDevice>
+void test_device_memory(const TensorDevice& device) {
+ int count = 100;
+ Eigen::array<int, 1> tensorRange = {{count}};
+ Eigen::Tensor<DataType, 1> host(tensorRange);
+ Eigen::Tensor<DataType, 1> expected(tensorRange);
+ DataType* device_data = static_cast<DataType*>(device.allocate(count * sizeof(DataType)));
+
+ // memset
+ const char byte_value = static_cast<char>(0xAB);
+ device.memset(device_data, byte_value, count * sizeof(DataType));
+ device.memcpyDeviceToHost(host.data(), device_data, count * sizeof(DataType));
+ synchronize(device);
+ memset(expected.data(), byte_value, count * sizeof(DataType));
+ for (size_t i=0; i<count; i++) {
+ VERIFY_IS_EQUAL(host(i), expected(i));
+ }
+
+ // fill
+ DataType fill_value = DataType(7);
+ std::fill_n(expected.data(), count, fill_value);
+ device.fill(device_data, device_data + count, fill_value);
+ device.memcpyDeviceToHost(host.data(), device_data, count * sizeof(DataType));
+ synchronize(device);
+ for (int i=0; i<count; i++) {
+ VERIFY_IS_EQUAL(host(i), expected(i));
+ }
+
+ device.deallocate(device_data);
+}
+
+void test_cpu() {
+ Eigen::Tensor<float, 3> in1(40,50,70);
+ Eigen::Tensor<float, 3> in2(40,50,70);
+ Eigen::Tensor<float, 3> out(40,50,70);
+
+ in1 = in1.random() + in1.constant(10.0f);
+ in2 = in2.random() + in2.constant(10.0f);
+
+ CPUContext context(in1, in2, out);
+ test_contextual_eval(&context);
+ for (int i = 0; i < 40; ++i) {
+ for (int j = 0; j < 50; ++j) {
+ for (int k = 0; k < 70; ++k) {
+ VERIFY_IS_APPROX(out(i,j,k), in1(i,j,k) + in2(i,j,k) * 3.14f + 2.718f);
+ }
+ }
+ }
+
+ test_forced_contextual_eval(&context);
+ for (int i = 0; i < 40; ++i) {
+ for (int j = 0; j < 50; ++j) {
+ for (int k = 0; k < 70; ++k) {
+ VERIFY_IS_APPROX(out(i,j,k), (in1(i,j,k) + in2(i,j,k)) * 3.14f + 2.718f);
+ }
+ }
+ }
+
+ test_compound_assignment(&context);
+ for (int i = 0; i < 40; ++i) {
+ for (int j = 0; j < 50; ++j) {
+ for (int k = 0; k < 70; ++k) {
+ VERIFY_IS_APPROX(out(i,j,k), in1(i,j,k) + in2(i,j,k) * 3.14f + 2.718f);
+ }
+ }
+ }
+
+ test_contraction(&context);
+ for (int i = 0; i < 40; ++i) {
+ for (int j = 0; j < 40; ++j) {
+ const float result = out(i,j,0);
+ float expected = 0;
+ for (int k = 0; k < 50; ++k) {
+ for (int l = 0; l < 70; ++l) {
+ expected += in1(i, k, l) * in2(j, k, l);
+ }
+ }
+ VERIFY_IS_APPROX(expected, result);
+ }
+ }
+
+ test_1d_convolution(&context);
+ for (int i = 0; i < 40; ++i) {
+ for (int j = 0; j < 49; ++j) {
+ for (int k = 0; k < 70; ++k) {
+ VERIFY_IS_APPROX(out(i,j,k), (in1(i,j,k) * 3.14f + in1(i,j+1,k) * 2.7f));
+ }
+ }
+ }
+
+ test_2d_convolution(&context);
+ for (int i = 0; i < 40; ++i) {
+ for (int j = 0; j < 49; ++j) {
+ for (int k = 0; k < 69; ++k) {
+ const float result = out(i,j,k);
+ const float expected = (in1(i,j,k) * 3.14f + in1(i,j+1,k) * 2.7f) +
+ (in1(i,j,k+1) * 0.2f + in1(i,j+1,k+1) * 7.0f);
+ if (fabs(expected) < 1e-4f && fabs(result) < 1e-4f) {
+ continue;
+ }
+ VERIFY_IS_APPROX(expected, result);
+ }
+ }
+ }
+
+ test_3d_convolution(&context);
+ for (int i = 0; i < 39; ++i) {
+ for (int j = 0; j < 49; ++j) {
+ for (int k = 0; k < 69; ++k) {
+ const float result = out(i,j,k);
+ const float expected = (in1(i,j,k) * 3.14f + in1(i,j+1,k) * 2.7f +
+ in1(i,j,k+1) * 0.2f + in1(i,j+1,k+1) * 7.0f) +
+ (in1(i+1,j,k) * -1.0f + in1(i+1,j+1,k) * -0.3f +
+ in1(i+1,j,k+1) * -0.7f + in1(i+1,j+1,k+1) * -0.5f);
+ if (fabs(expected) < 1e-4f && fabs(result) < 1e-4f) {
+ continue;
+ }
+ VERIFY_IS_APPROX(expected, result);
+ }
+ }
+ }
+
+ test_device_memory<float>(context.device());
+ test_device_memory<OffByOneScalar<int>>(context.device());
+}
+
+void test_gpu() {
+ Eigen::Tensor<float, 3> in1(40,50,70);
+ Eigen::Tensor<float, 3> in2(40,50,70);
+ Eigen::Tensor<float, 3> out(40,50,70);
+ in1 = in1.random() + in1.constant(10.0f);
+ in2 = in2.random() + in2.constant(10.0f);
+
+ std::size_t in1_bytes = in1.size() * sizeof(float);
+ std::size_t in2_bytes = in2.size() * sizeof(float);
+ std::size_t out_bytes = out.size() * sizeof(float);
+
+ float* d_in1;
+ float* d_in2;
+ float* d_out;
+ gpuMalloc((void**)(&d_in1), in1_bytes);
+ gpuMalloc((void**)(&d_in2), in2_bytes);
+ gpuMalloc((void**)(&d_out), out_bytes);
+
+ gpuMemcpy(d_in1, in1.data(), in1_bytes, gpuMemcpyHostToDevice);
+ gpuMemcpy(d_in2, in2.data(), in2_bytes, gpuMemcpyHostToDevice);
+
+ Eigen::TensorMap<Eigen::Tensor<float, 3> > gpu_in1(d_in1, 40,50,70);
+ Eigen::TensorMap<Eigen::Tensor<float, 3> > gpu_in2(d_in2, 40,50,70);
+ Eigen::TensorMap<Eigen::Tensor<float, 3> > gpu_out(d_out, 40,50,70);
+
+ GPUContext context(gpu_in1, gpu_in2, gpu_out);
+ test_contextual_eval(&context);
+ assert(gpuMemcpy(out.data(), d_out, out_bytes, gpuMemcpyDeviceToHost) == gpuSuccess);
+ for (int i = 0; i < 40; ++i) {
+ for (int j = 0; j < 50; ++j) {
+ for (int k = 0; k < 70; ++k) {
+ VERIFY_IS_APPROX(out(i,j,k), in1(i,j,k) + in2(i,j,k) * 3.14f + 2.718f);
+ }
+ }
+ }
+
+ test_forced_contextual_eval(&context);
+ assert(gpuMemcpy(out.data(), d_out, out_bytes, gpuMemcpyDeviceToHost) == gpuSuccess);
+ for (int i = 0; i < 40; ++i) {
+ for (int j = 0; j < 50; ++j) {
+ for (int k = 0; k < 70; ++k) {
+ VERIFY_IS_APPROX(out(i,j,k), (in1(i,j,k) + in2(i,j,k)) * 3.14f + 2.718f);
+ }
+ }
+ }
+
+ test_compound_assignment(&context);
+ assert(gpuMemcpy(out.data(), d_out, out_bytes, gpuMemcpyDeviceToHost) == gpuSuccess);
+ for (int i = 0; i < 40; ++i) {
+ for (int j = 0; j < 50; ++j) {
+ for (int k = 0; k < 70; ++k) {
+ VERIFY_IS_APPROX(out(i,j,k), in1(i,j,k) + in2(i,j,k) * 3.14f + 2.718f);
+ }
+ }
+ }
+
+ test_contraction(&context);
+ assert(gpuMemcpy(out.data(), d_out, out_bytes, gpuMemcpyDeviceToHost) == gpuSuccess);
+ for (int i = 0; i < 40; ++i) {
+ for (int j = 0; j < 40; ++j) {
+ const float result = out(i,j,0);
+ float expected = 0;
+ for (int k = 0; k < 50; ++k) {
+ for (int l = 0; l < 70; ++l) {
+ expected += in1(i, k, l) * in2(j, k, l);
+ }
+ }
+ VERIFY_IS_APPROX(expected, result);
+ }
+ }
+
+ test_1d_convolution(&context);
+ assert(gpuMemcpyAsync(out.data(), d_out, out_bytes, gpuMemcpyDeviceToHost, context.device().stream()) == gpuSuccess);
+ assert(gpuStreamSynchronize(context.device().stream()) == gpuSuccess);
+ for (int i = 0; i < 40; ++i) {
+ for (int j = 0; j < 49; ++j) {
+ for (int k = 0; k < 70; ++k) {
+ VERIFY_IS_APPROX(out(i,j,k), (in1(i,j,k) * 3.14f + in1(i,j+1,k) * 2.7f));
+ }
+ }
+ }
+
+ test_2d_convolution(&context);
+ assert(gpuMemcpyAsync(out.data(), d_out, out_bytes, gpuMemcpyDeviceToHost, context.device().stream()) == gpuSuccess);
+ assert(gpuStreamSynchronize(context.device().stream()) == gpuSuccess);
+ for (int i = 0; i < 40; ++i) {
+ for (int j = 0; j < 49; ++j) {
+ for (int k = 0; k < 69; ++k) {
+ const float result = out(i,j,k);
+ const float expected = (in1(i,j,k) * 3.14f + in1(i,j+1,k) * 2.7f +
+ in1(i,j,k+1) * 0.2f + in1(i,j+1,k+1) * 7.0f);
+ VERIFY_IS_APPROX(expected, result);
+ }
+ }
+ }
+
+#if !defined(EIGEN_USE_HIP)
+// disable this test on the HIP platform
+// 3D tensor convolutions seem to hang on the HIP platform
+
+ test_3d_convolution(&context);
+ assert(gpuMemcpyAsync(out.data(), d_out, out_bytes, gpuMemcpyDeviceToHost, context.device().stream()) == gpuSuccess);
+ assert(gpuStreamSynchronize(context.device().stream()) == gpuSuccess);
+ for (int i = 0; i < 39; ++i) {
+ for (int j = 0; j < 49; ++j) {
+ for (int k = 0; k < 69; ++k) {
+ const float result = out(i,j,k);
+ const float expected = (in1(i,j,k) * 3.14f + in1(i,j+1,k) * 2.7f +
+ in1(i,j,k+1) * 0.2f + in1(i,j+1,k+1) * 7.0f +
+ in1(i+1,j,k) * -1.0f + in1(i+1,j+1,k) * -0.3f +
+ in1(i+1,j,k+1) * -0.7f + in1(i+1,j+1,k+1) * -0.5f);
+ VERIFY_IS_APPROX(expected, result);
+ }
+ }
+ }
+
+#endif
+
+ test_device_memory<float>(context.device());
+ test_device_memory<OffByOneScalar<int>>(context.device());
+}
+
+
+EIGEN_DECLARE_TEST(cxx11_tensor_device)
+{
+ CALL_SUBTEST_1(test_cpu());
+ CALL_SUBTEST_2(test_gpu());
+}
diff --git a/unsupported/test/cxx11_tensor_device_sycl.cpp b/unsupported/test/cxx11_tensor_device_sycl.cpp
new file mode 100644
index 0000000..d7ff38d
--- /dev/null
+++ b/unsupported/test/cxx11_tensor_device_sycl.cpp
@@ -0,0 +1,114 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2016
+// Mehdi Goli Codeplay Software Ltd.
+// Ralph Potter Codeplay Software Ltd.
+// Luke Iwanski Codeplay Software Ltd.
+// Contact: <eigen@codeplay.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#define EIGEN_TEST_NO_LONGDOUBLE
+#define EIGEN_TEST_NO_COMPLEX
+
+#define EIGEN_DEFAULT_DENSE_INDEX_TYPE int64_t
+#define EIGEN_USE_SYCL
+
+#include "main.h"
+#include "OffByOneScalar.h"
+#include <unsupported/Eigen/CXX11/Tensor>
+#include <stdint.h>
+#include <iostream>
+
+template <typename DataType, int DataLayout, typename IndexType>
+void test_device_memory(const Eigen::SyclDevice &sycl_device) {
+ IndexType sizeDim1 = 100;
+ array<IndexType, 1> tensorRange = {{sizeDim1}};
+ Tensor<DataType, 1, DataLayout,IndexType> in(tensorRange);
+ Tensor<DataType, 1, DataLayout,IndexType> in1(tensorRange);
+ DataType* gpu_in_data = static_cast<DataType*>(sycl_device.allocate(in.size()*sizeof(DataType)));
+
+ // memset
+ memset(in1.data(), 1, in1.size() * sizeof(DataType));
+ sycl_device.memset(gpu_in_data, 1, in.size()*sizeof(DataType));
+ sycl_device.memcpyDeviceToHost(in.data(), gpu_in_data, in.size()*sizeof(DataType));
+ for (IndexType i=0; i<in.size(); i++) {
+ VERIFY_IS_EQUAL(in(i), in1(i));
+ }
+
+ // fill
+ DataType value = DataType(7);
+ std::fill_n(in1.data(), in1.size(), value);
+ sycl_device.fill(gpu_in_data, gpu_in_data + in.size(), value);
+ sycl_device.memcpyDeviceToHost(in.data(), gpu_in_data, in.size()*sizeof(DataType));
+ for (IndexType i=0; i<in.size(); i++) {
+ VERIFY_IS_EQUAL(in(i), in1(i));
+ }
+
+ sycl_device.deallocate(gpu_in_data);
+}
+
+template <typename DataType, int DataLayout, typename IndexType>
+void test_device_exceptions(const Eigen::SyclDevice &sycl_device) {
+ VERIFY(sycl_device.ok());
+ IndexType sizeDim1 = 100;
+ array<IndexType, 1> tensorDims = {{sizeDim1}};
+ DataType* gpu_data = static_cast<DataType*>(sycl_device.allocate(sizeDim1*sizeof(DataType)));
+ sycl_device.memset(gpu_data, 1, sizeDim1*sizeof(DataType));
+
+ TensorMap<Tensor<DataType, 1, DataLayout,IndexType>> in(gpu_data, tensorDims);
+ TensorMap<Tensor<DataType, 1, DataLayout,IndexType>> out(gpu_data, tensorDims);
+ out.device(sycl_device) = in / in.constant(0);
+
+ sycl_device.synchronize();
+ VERIFY(!sycl_device.ok());
+ sycl_device.deallocate(gpu_data);
+}
+
+template<typename DataType, int DataLayout, typename IndexType>
+void test_device_attach_buffer(const Eigen::SyclDevice &sycl_device) {
+ IndexType sizeDim1 = 100;
+
+ array<IndexType, 1> tensorRange = {{sizeDim1}};
+ Tensor<DataType, 1, DataLayout, IndexType> in(tensorRange);
+
+ cl::sycl::buffer<buffer_scalar_t, 1> buffer(cl::sycl::range<1>(sizeDim1 * sizeof(DataType)));
+ DataType* gpu_in_data = static_cast<DataType*>(sycl_device.attach_buffer(buffer));
+
+ // fill
+ DataType value = DataType(7);
+ std::fill_n(in.data(), in.size(), value);
+ sycl_device.fill(gpu_in_data, gpu_in_data + in.size(), value);
+
+ // Check that buffer is filled with the correct value.
+ auto reint = buffer.reinterpret<DataType>(cl::sycl::range<1>(sizeDim1));
+ auto access = reint.template get_access<cl::sycl::access::mode::read>();
+ for (IndexType i=0; i<in.size(); i++) {
+ VERIFY_IS_EQUAL(in(i), access[i]);
+ }
+
+ sycl_device.detach_buffer(gpu_in_data);
+}
+
+template<typename DataType> void sycl_device_test_per_device(const cl::sycl::device& d){
+ std::cout << "Running on " << d.template get_info<cl::sycl::info::device::name>() << std::endl;
+ QueueInterface queueInterface(d);
+ auto sycl_device = Eigen::SyclDevice(&queueInterface);
+ test_device_memory<DataType, RowMajor, int64_t>(sycl_device);
+ test_device_memory<DataType, ColMajor, int64_t>(sycl_device);
+ /// this test throw an exception. enable it if you want to see the exception
+ //test_device_exceptions<DataType, RowMajor>(sycl_device);
+ /// this test throw an exception. enable it if you want to see the exception
+ //test_device_exceptions<DataType, ColMajor>(sycl_device);
+ test_device_attach_buffer<DataType, ColMajor, int64_t>(sycl_device);
+}
+
+EIGEN_DECLARE_TEST(cxx11_tensor_device_sycl) {
+ for (const auto& device :Eigen::get_sycl_supported_devices()) {
+ CALL_SUBTEST(sycl_device_test_per_device<float>(device));
+ CALL_SUBTEST(sycl_device_test_per_device<OffByOneScalar<int>>(device));
+ }
+}
diff --git a/unsupported/test/cxx11_tensor_dimension.cpp b/unsupported/test/cxx11_tensor_dimension.cpp
new file mode 100644
index 0000000..ee416e1
--- /dev/null
+++ b/unsupported/test/cxx11_tensor_dimension.cpp
@@ -0,0 +1,88 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "main.h"
+
+#include <Eigen/CXX11/Tensor>
+
+using Eigen::Tensor;
+
+
+static void test_dynamic_size()
+{
+ Eigen::DSizes<int, 3> dimensions(2,3,7);
+
+ VERIFY_IS_EQUAL((int)Eigen::internal::array_get<0>(dimensions), 2);
+ VERIFY_IS_EQUAL((int)Eigen::internal::array_get<1>(dimensions), 3);
+ VERIFY_IS_EQUAL((int)Eigen::internal::array_get<2>(dimensions), 7);
+ VERIFY_IS_EQUAL((int)dimensions.TotalSize(), 2*3*7);
+ VERIFY_IS_EQUAL((int)dimensions[0], 2);
+ VERIFY_IS_EQUAL((int)dimensions[1], 3);
+ VERIFY_IS_EQUAL((int)dimensions[2], 7);
+}
+
+static void test_fixed_size()
+{
+ Eigen::Sizes<2,3,7> dimensions;
+
+ VERIFY_IS_EQUAL((int)Eigen::internal::array_get<0>(dimensions), 2);
+ VERIFY_IS_EQUAL((int)Eigen::internal::array_get<1>(dimensions), 3);
+ VERIFY_IS_EQUAL((int)Eigen::internal::array_get<2>(dimensions), 7);
+ VERIFY_IS_EQUAL((int)dimensions.TotalSize(), 2*3*7);
+}
+
+static void test_match()
+{
+ Eigen::DSizes<unsigned int, 3> dyn((unsigned int)2,(unsigned int)3,(unsigned int)7);
+ Eigen::Sizes<2,3,7> stat;
+ VERIFY_IS_EQUAL(Eigen::dimensions_match(dyn, stat), true);
+
+ Eigen::DSizes<int, 3> dyn1(2,3,7);
+ Eigen::DSizes<int, 2> dyn2(2,3);
+ VERIFY_IS_EQUAL(Eigen::dimensions_match(dyn1, dyn2), false);
+}
+
+static void test_rank_zero()
+{
+ Eigen::Sizes<> scalar;
+ VERIFY_IS_EQUAL((int)scalar.TotalSize(), 1);
+ VERIFY_IS_EQUAL((int)scalar.rank(), 0);
+ VERIFY_IS_EQUAL((int)internal::array_prod(scalar), 1);
+
+ Eigen::DSizes<ptrdiff_t, 0> dscalar;
+ VERIFY_IS_EQUAL((int)dscalar.TotalSize(), 1);
+ VERIFY_IS_EQUAL((int)dscalar.rank(), 0);
+}
+
+static void test_index_type_promotion() {
+ Eigen::DSizes<int, 3> src0(1, 2, 3);
+ Eigen::array<int, 3> src1;
+ src1[0] = 4;
+ src1[1] = 5;
+ src1[2] = 6;
+
+ Eigen::DSizes<long, 3> dst0(src0);
+ Eigen::DSizes<long, 3> dst1(src1);
+
+ VERIFY_IS_EQUAL(dst0[0], 1L);
+ VERIFY_IS_EQUAL(dst0[1], 2L);
+ VERIFY_IS_EQUAL(dst0[2], 3L);
+ VERIFY_IS_EQUAL(dst1[0], 4L);
+ VERIFY_IS_EQUAL(dst1[1], 5L);
+ VERIFY_IS_EQUAL(dst1[2], 6L);
+}
+
+EIGEN_DECLARE_TEST(cxx11_tensor_dimension)
+{
+ CALL_SUBTEST(test_dynamic_size());
+ CALL_SUBTEST(test_fixed_size());
+ CALL_SUBTEST(test_match());
+ CALL_SUBTEST(test_rank_zero());
+ CALL_SUBTEST(test_index_type_promotion());
+}
diff --git a/unsupported/test/cxx11_tensor_empty.cpp b/unsupported/test/cxx11_tensor_empty.cpp
new file mode 100644
index 0000000..fd889c4
--- /dev/null
+++ b/unsupported/test/cxx11_tensor_empty.cpp
@@ -0,0 +1,40 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2015 Benoit Steiner <benoit.steiner.goog@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "main.h"
+
+#include <Eigen/CXX11/Tensor>
+
+
+static void test_empty_tensor()
+{
+ Tensor<float, 2> source;
+ Tensor<float, 2> tgt1 = source;
+ Tensor<float, 2> tgt2(source);
+ Tensor<float, 2> tgt3;
+ tgt3 = tgt1;
+ tgt3 = tgt2;
+}
+
+static void test_empty_fixed_size_tensor()
+{
+ TensorFixedSize<float, Sizes<0> > source;
+ TensorFixedSize<float, Sizes<0> > tgt1 = source;
+ TensorFixedSize<float, Sizes<0> > tgt2(source);
+ TensorFixedSize<float, Sizes<0> > tgt3;
+ tgt3 = tgt1;
+ tgt3 = tgt2;
+}
+
+
+EIGEN_DECLARE_TEST(cxx11_tensor_empty)
+{
+ CALL_SUBTEST(test_empty_tensor());
+ CALL_SUBTEST(test_empty_fixed_size_tensor());
+}
diff --git a/unsupported/test/cxx11_tensor_executor.cpp b/unsupported/test/cxx11_tensor_executor.cpp
new file mode 100644
index 0000000..d0103dc
--- /dev/null
+++ b/unsupported/test/cxx11_tensor_executor.cpp
@@ -0,0 +1,730 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2018 Eugene Zhulenev <ezhulenev@google.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#define EIGEN_USE_THREADS
+
+#include "main.h"
+
+#include <Eigen/CXX11/Tensor>
+
+using Eigen::Tensor;
+using Eigen::RowMajor;
+using Eigen::ColMajor;
+using Eigen::internal::TiledEvaluation;
+
+// A set of tests to verify that different TensorExecutor strategies yields the
+// same results for all the ops, supporting tiled evaluation.
+
+// Default assignment that does no use block evaluation or vectorization.
+// We assume that default coefficient evaluation is well tested and correct.
+template <typename Dst, typename Expr>
+static void DefaultAssign(Dst& dst, Expr expr) {
+ using Assign = Eigen::TensorAssignOp<Dst, const Expr>;
+ using Executor =
+ Eigen::internal::TensorExecutor<const Assign, DefaultDevice,
+ /*Vectorizable=*/false,
+ /*Tiling=*/TiledEvaluation::Off>;
+
+ Executor::run(Assign(dst, expr), DefaultDevice());
+}
+
+// Assignment with specified device and tiling strategy.
+template <bool Vectorizable, TiledEvaluation Tiling, typename Device,
+ typename Dst, typename Expr>
+static void DeviceAssign(Device& d, Dst& dst, Expr expr) {
+ using Assign = Eigen::TensorAssignOp<Dst, const Expr>;
+ using Executor = Eigen::internal::TensorExecutor<const Assign, Device,
+ Vectorizable, Tiling>;
+
+ Executor::run(Assign(dst, expr), d);
+}
+
+template <int NumDims>
+static array<Index, NumDims> RandomDims(int min_dim = 1, int max_dim = 20) {
+ array<Index, NumDims> dims;
+ for (int i = 0; i < NumDims; ++i) {
+ dims[i] = internal::random<int>(min_dim, max_dim);
+ }
+ return dims;
+}
+
+template <typename T, int NumDims, typename Device, bool Vectorizable,
+ TiledEvaluation Tiling, int Layout>
+static void test_execute_unary_expr(Device d)
+{
+ static constexpr int Options = 0 | Layout;
+
+ // Pick a large enough tensor size to bypass small tensor block evaluation
+ // optimization.
+ auto dims = RandomDims<NumDims>(50 / NumDims, 100 / NumDims);
+
+ Tensor<T, NumDims, Options, Index> src(dims);
+ Tensor<T, NumDims, Options, Index> dst(dims);
+
+ src.setRandom();
+ const auto expr = src.square();
+
+ using Assign = TensorAssignOp<decltype(dst), const decltype(expr)>;
+ using Executor =
+ internal::TensorExecutor<const Assign, Device, Vectorizable, Tiling>;
+
+ Executor::run(Assign(dst, expr), d);
+
+ for (Index i = 0; i < dst.dimensions().TotalSize(); ++i) {
+ T square = src.coeff(i) * src.coeff(i);
+ VERIFY_IS_EQUAL(square, dst.coeff(i));
+ }
+}
+
+template <typename T, int NumDims, typename Device, bool Vectorizable,
+ TiledEvaluation Tiling, int Layout>
+static void test_execute_binary_expr(Device d)
+{
+ static constexpr int Options = 0 | Layout;
+
+ // Pick a large enough tensor size to bypass small tensor block evaluation
+ // optimization.
+ auto dims = RandomDims<NumDims>(50 / NumDims, 100 / NumDims);
+
+ Tensor<T, NumDims, Options, Index> lhs(dims);
+ Tensor<T, NumDims, Options, Index> rhs(dims);
+ Tensor<T, NumDims, Options, Index> dst(dims);
+
+ lhs.setRandom();
+ rhs.setRandom();
+
+ const auto expr = lhs + rhs;
+
+ using Assign = TensorAssignOp<decltype(dst), const decltype(expr)>;
+ using Executor =
+ internal::TensorExecutor<const Assign, Device, Vectorizable, Tiling>;
+
+ Executor::run(Assign(dst, expr), d);
+
+ for (Index i = 0; i < dst.dimensions().TotalSize(); ++i) {
+ T sum = lhs.coeff(i) + rhs.coeff(i);
+ VERIFY_IS_EQUAL(sum, dst.coeff(i));
+ }
+}
+
+template <typename T, int NumDims, typename Device, bool Vectorizable,
+ TiledEvaluation Tiling, int Layout>
+static void test_execute_broadcasting(Device d)
+{
+ static constexpr int Options = 0 | Layout;
+
+ auto dims = RandomDims<NumDims>(1, 10);
+ Tensor<T, NumDims, Options, Index> src(dims);
+ src.setRandom();
+
+ const auto broadcasts = RandomDims<NumDims>(1, 7);
+ const auto expr = src.broadcast(broadcasts);
+
+ // We assume that broadcasting on a default device is tested and correct, so
+ // we can rely on it to verify correctness of tensor executor and tiling.
+ Tensor<T, NumDims, Options, Index> golden;
+ golden = expr;
+
+ // Now do the broadcasting using configured tensor executor.
+ Tensor<T, NumDims, Options, Index> dst(golden.dimensions());
+
+ using Assign = TensorAssignOp<decltype(dst), const decltype(expr)>;
+ using Executor =
+ internal::TensorExecutor<const Assign, Device, Vectorizable, Tiling>;
+
+ Executor::run(Assign(dst, expr), d);
+
+ for (Index i = 0; i < dst.dimensions().TotalSize(); ++i) {
+ VERIFY_IS_EQUAL(dst.coeff(i), golden.coeff(i));
+ }
+}
+
+template <typename T, int NumDims, typename Device, bool Vectorizable,
+ TiledEvaluation Tiling, int Layout>
+static void test_execute_chipping_rvalue(Device d)
+{
+ auto dims = RandomDims<NumDims>(1, 10);
+ Tensor<T, NumDims, Layout, Index> src(dims);
+ src.setRandom();
+
+#define TEST_CHIPPING(CHIP_DIM) \
+ if (NumDims > (CHIP_DIM)) { \
+ const auto offset = internal::random<Index>(0, dims[(CHIP_DIM)] - 1); \
+ const auto expr = src.template chip<(CHIP_DIM)>(offset); \
+ \
+ Tensor<T, NumDims - 1, Layout, Index> golden; \
+ golden = expr; \
+ \
+ Tensor<T, NumDims - 1, Layout, Index> dst(golden.dimensions()); \
+ \
+ using Assign = TensorAssignOp<decltype(dst), const decltype(expr)>; \
+ using Executor = internal::TensorExecutor<const Assign, Device, \
+ Vectorizable, Tiling>; \
+ \
+ Executor::run(Assign(dst, expr), d); \
+ \
+ for (Index i = 0; i < dst.dimensions().TotalSize(); ++i) { \
+ VERIFY_IS_EQUAL(dst.coeff(i), golden.coeff(i)); \
+ } \
+ }
+
+ TEST_CHIPPING(0)
+ TEST_CHIPPING(1)
+ TEST_CHIPPING(2)
+ TEST_CHIPPING(3)
+ TEST_CHIPPING(4)
+ TEST_CHIPPING(5)
+
+#undef TEST_CHIPPING
+}
+
+template <typename T, int NumDims, typename Device, bool Vectorizable,
+ TiledEvaluation Tiling, int Layout>
+static void test_execute_chipping_lvalue(Device d)
+{
+ auto dims = RandomDims<NumDims>(1, 10);
+
+#define TEST_CHIPPING(CHIP_DIM) \
+ if (NumDims > (CHIP_DIM)) { \
+ /* Generate random data that we'll assign to the chipped tensor dim. */ \
+ array<Index, NumDims - 1> src_dims; \
+ for (int i = 0; i < NumDims - 1; ++i) { \
+ int dim = i < (CHIP_DIM) ? i : i + 1; \
+ src_dims[i] = dims[dim]; \
+ } \
+ \
+ Tensor<T, NumDims - 1, Layout, Index> src(src_dims); \
+ src.setRandom(); \
+ \
+ const auto offset = internal::random<Index>(0, dims[(CHIP_DIM)] - 1); \
+ \
+ Tensor<T, NumDims, Layout, Index> random(dims); \
+ random.setZero(); \
+ \
+ Tensor<T, NumDims, Layout, Index> golden(dims); \
+ golden = random; \
+ golden.template chip<(CHIP_DIM)>(offset) = src; \
+ \
+ Tensor<T, NumDims, Layout, Index> dst(dims); \
+ dst = random; \
+ auto expr = dst.template chip<(CHIP_DIM)>(offset); \
+ \
+ using Assign = TensorAssignOp<decltype(expr), const decltype(src)>; \
+ using Executor = internal::TensorExecutor<const Assign, Device, \
+ Vectorizable, Tiling>; \
+ \
+ Executor::run(Assign(expr, src), d); \
+ \
+ for (Index i = 0; i < dst.dimensions().TotalSize(); ++i) { \
+ VERIFY_IS_EQUAL(dst.coeff(i), golden.coeff(i)); \
+ } \
+ }
+
+ TEST_CHIPPING(0)
+ TEST_CHIPPING(1)
+ TEST_CHIPPING(2)
+ TEST_CHIPPING(3)
+ TEST_CHIPPING(4)
+ TEST_CHIPPING(5)
+
+#undef TEST_CHIPPING
+}
+
+template <typename T, int NumDims, typename Device, bool Vectorizable,
+ TiledEvaluation Tiling, int Layout>
+static void test_execute_shuffle_rvalue(Device d)
+{
+ static constexpr int Options = 0 | Layout;
+
+ auto dims = RandomDims<NumDims>(1, 10);
+ Tensor<T, NumDims, Options, Index> src(dims);
+ src.setRandom();
+
+ DSizes<Index, NumDims> shuffle;
+ for (int i = 0; i < NumDims; ++i) shuffle[i] = i;
+
+ // Test all possible shuffle permutations.
+ do {
+ DSizes<Index, NumDims> shuffled_dims;
+ for (int i = 0; i < NumDims; ++i) {
+ shuffled_dims[i] = dims[shuffle[i]];
+ }
+
+ const auto expr = src.shuffle(shuffle);
+
+ // We assume that shuffling on a default device is tested and correct, so
+ // we can rely on it to verify correctness of tensor executor and tiling.
+ Tensor<T, NumDims, Options, Index> golden(shuffled_dims);
+ DefaultAssign(golden, expr);
+
+ // Now do the shuffling using configured tensor executor.
+ Tensor<T, NumDims, Options, Index> dst(shuffled_dims);
+ DeviceAssign<Vectorizable, Tiling>(d, dst, expr);
+
+ for (Index i = 0; i < dst.dimensions().TotalSize(); ++i) {
+ VERIFY_IS_EQUAL(dst.coeff(i), golden.coeff(i));
+ }
+
+ } while (std::next_permutation(&shuffle[0], &shuffle[0] + NumDims));
+}
+
+template <typename T, int NumDims, typename Device, bool Vectorizable,
+ TiledEvaluation Tiling, int Layout>
+static void test_execute_shuffle_lvalue(Device d)
+{
+ static constexpr int Options = 0 | Layout;
+
+ auto dims = RandomDims<NumDims>(5, 10);
+ Tensor<T, NumDims, Options, Index> src(dims);
+ src.setRandom();
+
+ DSizes<Index, NumDims> shuffle;
+ for (int i = 0; i < NumDims; ++i) shuffle[i] = i;
+
+ // Test all possible shuffle permutations.
+ do {
+ DSizes<Index, NumDims> shuffled_dims;
+ for (int i = 0; i < NumDims; ++i) shuffled_dims[shuffle[i]] = dims[i];
+
+ // We assume that shuffling on a default device is tested and correct, so
+ // we can rely on it to verify correctness of tensor executor and tiling.
+ Tensor<T, NumDims, Options, Index> golden(shuffled_dims);
+ auto golden_shuffle = golden.shuffle(shuffle);
+ DefaultAssign(golden_shuffle, src);
+
+ // Now do the shuffling using configured tensor executor.
+ Tensor<T, NumDims, Options, Index> dst(shuffled_dims);
+ auto dst_shuffle = dst.shuffle(shuffle);
+ DeviceAssign<Vectorizable, Tiling>(d, dst_shuffle, src);
+
+ for (Index i = 0; i < dst.dimensions().TotalSize(); ++i) {
+ VERIFY_IS_EQUAL(dst.coeff(i), golden.coeff(i));
+ }
+
+ } while (std::next_permutation(&shuffle[0], &shuffle[0] + NumDims));
+}
+
+template <typename T, int NumDims, typename Device, bool Vectorizable,
+ TiledEvaluation Tiling, int Layout>
+static void test_execute_reshape(Device d)
+{
+ static_assert(NumDims >= 2, "NumDims must be greater or equal than 2");
+
+ static constexpr int ReshapedDims = NumDims - 1;
+ static constexpr int Options = 0 | Layout;
+
+ auto dims = RandomDims<NumDims>(5, 10);
+ Tensor<T, NumDims, Options, Index> src(dims);
+ src.setRandom();
+
+ // Multiple 0th dimension and then shuffle.
+ std::vector<Index> shuffle;
+ for (int i = 0; i < ReshapedDims; ++i) shuffle.push_back(i);
+ std::shuffle(shuffle.begin(), shuffle.end(), std::mt19937());
+
+ DSizes<Index, ReshapedDims> reshaped_dims;
+ reshaped_dims[shuffle[0]] = dims[0] * dims[1];
+ for (int i = 1; i < ReshapedDims; ++i) reshaped_dims[shuffle[i]] = dims[i + 1];
+
+ Tensor<T, ReshapedDims, Options, Index> golden = src.reshape(reshaped_dims);
+
+ // Now reshape using configured tensor executor.
+ Tensor<T, ReshapedDims, Options, Index> dst(golden.dimensions());
+
+ auto expr = src.reshape(reshaped_dims);
+
+ using Assign = TensorAssignOp<decltype(dst), const decltype(expr)>;
+ using Executor =
+ internal::TensorExecutor<const Assign, Device, Vectorizable, Tiling>;
+
+ Executor::run(Assign(dst, expr), d);
+
+ for (Index i = 0; i < dst.dimensions().TotalSize(); ++i) {
+ VERIFY_IS_EQUAL(dst.coeff(i), golden.coeff(i));
+ }
+}
+
+template <typename T, int NumDims, typename Device, bool Vectorizable,
+ TiledEvaluation Tiling, int Layout>
+static void test_execute_slice_rvalue(Device d)
+{
+ static_assert(NumDims >= 2, "NumDims must be greater or equal than 2");
+ static constexpr int Options = 0 | Layout;
+
+ auto dims = RandomDims<NumDims>(5, 10);
+ Tensor<T, NumDims, Options, Index> src(dims);
+ src.setRandom();
+
+ // Pick a random slice of src tensor.
+ auto slice_start = DSizes<Index, NumDims>(RandomDims<NumDims>());
+ auto slice_size = DSizes<Index, NumDims>(RandomDims<NumDims>());
+
+ // Make sure that slice start + size do not overflow tensor dims.
+ for (int i = 0; i < NumDims; ++i) {
+ slice_start[i] = numext::mini(dims[i] - 1, slice_start[i]);
+ slice_size[i] = numext::mini(slice_size[i], dims[i] - slice_start[i]);
+ }
+
+ Tensor<T, NumDims, Options, Index> golden =
+ src.slice(slice_start, slice_size);
+
+ // Now reshape using configured tensor executor.
+ Tensor<T, NumDims, Options, Index> dst(golden.dimensions());
+
+ auto expr = src.slice(slice_start, slice_size);
+
+ using Assign = TensorAssignOp<decltype(dst), const decltype(expr)>;
+ using Executor =
+ internal::TensorExecutor<const Assign, Device, Vectorizable, Tiling>;
+
+ Executor::run(Assign(dst, expr), d);
+
+ for (Index i = 0; i < dst.dimensions().TotalSize(); ++i) {
+ VERIFY_IS_EQUAL(dst.coeff(i), golden.coeff(i));
+ }
+}
+
+template <typename T, int NumDims, typename Device, bool Vectorizable,
+ TiledEvaluation Tiling, int Layout>
+static void test_execute_slice_lvalue(Device d)
+{
+ static_assert(NumDims >= 2, "NumDims must be greater or equal than 2");
+ static constexpr int Options = 0 | Layout;
+
+ auto dims = RandomDims<NumDims>(5, 10);
+ Tensor<T, NumDims, Options, Index> src(dims);
+ src.setRandom();
+
+ // Pick a random slice of src tensor.
+ auto slice_start = DSizes<Index, NumDims>(RandomDims<NumDims>(1, 10));
+ auto slice_size = DSizes<Index, NumDims>(RandomDims<NumDims>(1, 10));
+
+ // Make sure that slice start + size do not overflow tensor dims.
+ for (int i = 0; i < NumDims; ++i) {
+ slice_start[i] = numext::mini(dims[i] - 1, slice_start[i]);
+ slice_size[i] = numext::mini(slice_size[i], dims[i] - slice_start[i]);
+ }
+
+ Tensor<T, NumDims, Options, Index> slice(slice_size);
+ slice.setRandom();
+
+ // Assign a slice using default executor.
+ Tensor<T, NumDims, Options, Index> golden = src;
+ golden.slice(slice_start, slice_size) = slice;
+
+ // And using configured execution strategy.
+ Tensor<T, NumDims, Options, Index> dst = src;
+ auto expr = dst.slice(slice_start, slice_size);
+
+ using Assign = TensorAssignOp<decltype(expr), const decltype(slice)>;
+ using Executor =
+ internal::TensorExecutor<const Assign, Device, Vectorizable, Tiling>;
+
+ Executor::run(Assign(expr, slice), d);
+
+ for (Index i = 0; i < dst.dimensions().TotalSize(); ++i) {
+ VERIFY_IS_EQUAL(dst.coeff(i), golden.coeff(i));
+ }
+}
+
+template <typename T, int NumDims, typename Device, bool Vectorizable,
+ TiledEvaluation Tiling, int Layout>
+static void test_execute_broadcasting_of_forced_eval(Device d)
+{
+ static constexpr int Options = 0 | Layout;
+
+ auto dims = RandomDims<NumDims>(1, 10);
+ Tensor<T, NumDims, Options, Index> src(dims);
+ src.setRandom();
+
+ const auto broadcasts = RandomDims<NumDims>(1, 7);
+ const auto expr = src.square().eval().broadcast(broadcasts);
+
+ // We assume that broadcasting on a default device is tested and correct, so
+ // we can rely on it to verify correctness of tensor executor and tiling.
+ Tensor<T, NumDims, Options, Index> golden;
+ golden = expr;
+
+ // Now do the broadcasting using configured tensor executor.
+ Tensor<T, NumDims, Options, Index> dst(golden.dimensions());
+
+ using Assign = TensorAssignOp<decltype(dst), const decltype(expr)>;
+ using Executor =
+ internal::TensorExecutor<const Assign, Device, Vectorizable, Tiling>;
+
+ Executor::run(Assign(dst, expr), d);
+
+ for (Index i = 0; i < dst.dimensions().TotalSize(); ++i) {
+ VERIFY_IS_EQUAL(dst.coeff(i), golden.coeff(i));
+ }
+}
+
+template<typename T, int NumDims>
+struct DummyGenerator {
+ EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
+ T operator()(const array <Index, NumDims>& dims) const {
+ T result = static_cast<T>(0);
+ for (int i = 0; i < NumDims; ++i) {
+ result += static_cast<T>((i + 1) * dims[i]);
+ }
+ return result;
+ }
+};
+
+template <typename T, int NumDims, typename Device, bool Vectorizable,
+ TiledEvaluation Tiling, int Layout>
+static void test_execute_generator_op(Device d)
+{
+ static constexpr int Options = 0 | Layout;
+
+ auto dims = RandomDims<NumDims>(20, 30);
+ Tensor<T, NumDims, Options, Index> src(dims);
+ src.setRandom();
+
+ const auto expr = src.generate(DummyGenerator<T, NumDims>());
+
+ // We assume that generator on a default device is tested and correct, so
+ // we can rely on it to verify correctness of tensor executor and tiling.
+ Tensor<T, NumDims, Options, Index> golden;
+ golden = expr;
+
+ // Now do the broadcasting using configured tensor executor.
+ Tensor<T, NumDims, Options, Index> dst(golden.dimensions());
+
+ using Assign = TensorAssignOp<decltype(dst), const decltype(expr)>;
+ using Executor =
+ internal::TensorExecutor<const Assign, Device, Vectorizable, Tiling>;
+
+ Executor::run(Assign(dst, expr), d);
+
+ for (Index i = 0; i < dst.dimensions().TotalSize(); ++i) {
+ VERIFY_IS_EQUAL(dst.coeff(i), golden.coeff(i));
+ }
+}
+
+template <typename T, int NumDims, typename Device, bool Vectorizable,
+ TiledEvaluation Tiling, int Layout>
+static void test_execute_reverse_rvalue(Device d)
+{
+ static constexpr int Options = 0 | Layout;
+
+ auto dims = RandomDims<NumDims>(1, numext::pow(1000000.0, 1.0 / NumDims));
+ Tensor <T, NumDims, Options, Index> src(dims);
+ src.setRandom();
+
+ // Reverse half of the dimensions.
+ Eigen::array<bool, NumDims> reverse;
+ for (int i = 0; i < NumDims; ++i) reverse[i] = internal::random<bool>();
+
+ const auto expr = src.reverse(reverse);
+
+ // We assume that reversing on a default device is tested and correct, so
+ // we can rely on it to verify correctness of tensor executor and tiling.
+ Tensor <T, NumDims, Options, Index> golden;
+ golden = expr;
+
+ // Now do the reversing using configured tensor executor.
+ Tensor <T, NumDims, Options, Index> dst(golden.dimensions());
+
+ using Assign = TensorAssignOp<decltype(dst), const decltype(expr)>;
+ using Executor =
+ internal::TensorExecutor<const Assign, Device, Vectorizable, Tiling>;
+
+ Executor::run(Assign(dst, expr), d);
+
+ for (Index i = 0; i < dst.dimensions().TotalSize(); ++i) {
+ VERIFY_IS_EQUAL(dst.coeff(i), golden.coeff(i));
+ }
+}
+
+template <typename T, int NumDims, typename Device, bool Vectorizable,
+ TiledEvaluation Tiling, int Layout>
+static void test_async_execute_unary_expr(Device d)
+{
+ static constexpr int Options = 0 | Layout;
+
+ // Pick a large enough tensor size to bypass small tensor block evaluation
+ // optimization.
+ auto dims = RandomDims<NumDims>(50 / NumDims, 100 / NumDims);
+
+ Tensor<T, NumDims, Options, Index> src(dims);
+ Tensor<T, NumDims, Options, Index> dst(dims);
+
+ src.setRandom();
+ const auto expr = src.square();
+
+ Eigen::Barrier done(1);
+ auto on_done = [&done]() { done.Notify(); };
+
+ using Assign = TensorAssignOp<decltype(dst), const decltype(expr)>;
+ using DoneCallback = decltype(on_done);
+ using Executor = internal::TensorAsyncExecutor<const Assign, Device, DoneCallback,
+ Vectorizable, Tiling>;
+
+ Executor::runAsync(Assign(dst, expr), d, on_done);
+ done.Wait();
+
+ for (Index i = 0; i < dst.dimensions().TotalSize(); ++i) {
+ T square = src.coeff(i) * src.coeff(i);
+ VERIFY_IS_EQUAL(square, dst.coeff(i));
+ }
+}
+
+template <typename T, int NumDims, typename Device, bool Vectorizable,
+ TiledEvaluation Tiling, int Layout>
+static void test_async_execute_binary_expr(Device d)
+{
+ static constexpr int Options = 0 | Layout;
+
+ // Pick a large enough tensor size to bypass small tensor block evaluation
+ // optimization.
+ auto dims = RandomDims<NumDims>(50 / NumDims, 100 / NumDims);
+
+ Tensor<T, NumDims, Options, Index> lhs(dims);
+ Tensor<T, NumDims, Options, Index> rhs(dims);
+ Tensor<T, NumDims, Options, Index> dst(dims);
+
+ lhs.setRandom();
+ rhs.setRandom();
+
+ const auto expr = lhs + rhs;
+
+ Eigen::Barrier done(1);
+ auto on_done = [&done]() { done.Notify(); };
+
+ using Assign = TensorAssignOp<decltype(dst), const decltype(expr)>;
+ using DoneCallback = decltype(on_done);
+ using Executor = internal::TensorAsyncExecutor<const Assign, Device, DoneCallback,
+ Vectorizable, Tiling>;
+
+ Executor::runAsync(Assign(dst, expr), d, on_done);
+ done.Wait();
+
+ for (Index i = 0; i < dst.dimensions().TotalSize(); ++i) {
+ T sum = lhs.coeff(i) + rhs.coeff(i);
+ VERIFY_IS_EQUAL(sum, dst.coeff(i));
+ }
+}
+
+#ifndef EIGEN_DONT_VECTORIZE
+#define EIGEN_DONT_VECTORIZE 0
+#endif
+#define VECTORIZABLE(T, VAL) !EIGEN_DONT_VECTORIZE && Eigen::internal::packet_traits<T>::Vectorizable && VAL
+
+#define CALL_SUBTEST_PART(PART) \
+ CALL_SUBTEST_##PART
+
+#define CALL_SUBTEST_COMBINATIONS(PART, NAME, T, NUM_DIMS) \
+ CALL_SUBTEST_PART(PART)((NAME<T, NUM_DIMS, DefaultDevice, false, TiledEvaluation::Off, ColMajor>(default_device))); \
+ CALL_SUBTEST_PART(PART)((NAME<T, NUM_DIMS, DefaultDevice, false, TiledEvaluation::On, ColMajor>(default_device))); \
+ CALL_SUBTEST_PART(PART)((NAME<T, NUM_DIMS, DefaultDevice, VECTORIZABLE(T, true), TiledEvaluation::Off, ColMajor>(default_device))); \
+ CALL_SUBTEST_PART(PART)((NAME<T, NUM_DIMS, DefaultDevice, VECTORIZABLE(T, true), TiledEvaluation::On, ColMajor>(default_device))); \
+ CALL_SUBTEST_PART(PART)((NAME<T, NUM_DIMS, DefaultDevice, false, TiledEvaluation::Off, RowMajor>(default_device))); \
+ CALL_SUBTEST_PART(PART)((NAME<T, NUM_DIMS, DefaultDevice, false, TiledEvaluation::On, RowMajor>(default_device))); \
+ CALL_SUBTEST_PART(PART)((NAME<T, NUM_DIMS, DefaultDevice, VECTORIZABLE(T, true), TiledEvaluation::Off, RowMajor>(default_device))); \
+ CALL_SUBTEST_PART(PART)((NAME<T, NUM_DIMS, DefaultDevice, VECTORIZABLE(T, true), TiledEvaluation::On, RowMajor>(default_device))); \
+ CALL_SUBTEST_PART(PART)((NAME<T, NUM_DIMS, ThreadPoolDevice, false, TiledEvaluation::Off, ColMajor>(tp_device))); \
+ CALL_SUBTEST_PART(PART)((NAME<T, NUM_DIMS, ThreadPoolDevice, false, TiledEvaluation::On, ColMajor>(tp_device))); \
+ CALL_SUBTEST_PART(PART)((NAME<T, NUM_DIMS, ThreadPoolDevice, VECTORIZABLE(T, true), TiledEvaluation::Off, ColMajor>(tp_device))); \
+ CALL_SUBTEST_PART(PART)((NAME<T, NUM_DIMS, ThreadPoolDevice, VECTORIZABLE(T, true), TiledEvaluation::On, ColMajor>(tp_device))); \
+ CALL_SUBTEST_PART(PART)((NAME<T, NUM_DIMS, ThreadPoolDevice, false, TiledEvaluation::Off, RowMajor>(tp_device))); \
+ CALL_SUBTEST_PART(PART)((NAME<T, NUM_DIMS, ThreadPoolDevice, false, TiledEvaluation::On, RowMajor>(tp_device))); \
+ CALL_SUBTEST_PART(PART)((NAME<T, NUM_DIMS, ThreadPoolDevice, VECTORIZABLE(T, true), TiledEvaluation::Off, RowMajor>(tp_device))); \
+ CALL_SUBTEST_PART(PART)((NAME<T, NUM_DIMS, ThreadPoolDevice, VECTORIZABLE(T, true), TiledEvaluation::On, RowMajor>(tp_device)))
+
+// NOTE: Currently only ThreadPoolDevice supports async expression evaluation.
+#define CALL_ASYNC_SUBTEST_COMBINATIONS(PART, NAME, T, NUM_DIMS) \
+ CALL_SUBTEST_PART(PART)((NAME<T, NUM_DIMS, ThreadPoolDevice, false, TiledEvaluation::Off, ColMajor>(tp_device))); \
+ CALL_SUBTEST_PART(PART)((NAME<T, NUM_DIMS, ThreadPoolDevice, false, TiledEvaluation::On, ColMajor>(tp_device))); \
+ CALL_SUBTEST_PART(PART)((NAME<T, NUM_DIMS, ThreadPoolDevice, VECTORIZABLE(T, true), TiledEvaluation::Off, ColMajor>(tp_device))); \
+ CALL_SUBTEST_PART(PART)((NAME<T, NUM_DIMS, ThreadPoolDevice, VECTORIZABLE(T, true), TiledEvaluation::On, ColMajor>(tp_device))); \
+ CALL_SUBTEST_PART(PART)((NAME<T, NUM_DIMS, ThreadPoolDevice, false, TiledEvaluation::Off, RowMajor>(tp_device))); \
+ CALL_SUBTEST_PART(PART)((NAME<T, NUM_DIMS, ThreadPoolDevice, false, TiledEvaluation::On, RowMajor>(tp_device))); \
+ CALL_SUBTEST_PART(PART)((NAME<T, NUM_DIMS, ThreadPoolDevice, VECTORIZABLE(T, true), TiledEvaluation::Off, RowMajor>(tp_device))); \
+ CALL_SUBTEST_PART(PART)((NAME<T, NUM_DIMS, ThreadPoolDevice, VECTORIZABLE(T, true), TiledEvaluation::On, RowMajor>(tp_device)))
+
+EIGEN_DECLARE_TEST(cxx11_tensor_executor) {
+ Eigen::DefaultDevice default_device;
+ // Default device is unused in ASYNC tests.
+ EIGEN_UNUSED_VARIABLE(default_device);
+
+ const auto num_threads = internal::random<int>(20, 24);
+ Eigen::ThreadPool tp(num_threads);
+ Eigen::ThreadPoolDevice tp_device(&tp, num_threads);
+
+ CALL_SUBTEST_COMBINATIONS(1, test_execute_unary_expr, float, 3);
+ CALL_SUBTEST_COMBINATIONS(1, test_execute_unary_expr, float, 4);
+ CALL_SUBTEST_COMBINATIONS(1, test_execute_unary_expr, float, 5);
+
+ CALL_SUBTEST_COMBINATIONS(2, test_execute_binary_expr, float, 3);
+ CALL_SUBTEST_COMBINATIONS(2, test_execute_binary_expr, float, 4);
+ CALL_SUBTEST_COMBINATIONS(2, test_execute_binary_expr, float, 5);
+
+ CALL_SUBTEST_COMBINATIONS(3, test_execute_broadcasting, float, 3);
+ CALL_SUBTEST_COMBINATIONS(3, test_execute_broadcasting, float, 4);
+ CALL_SUBTEST_COMBINATIONS(3, test_execute_broadcasting, float, 5);
+
+ CALL_SUBTEST_COMBINATIONS(4, test_execute_chipping_rvalue, float, 3);
+ CALL_SUBTEST_COMBINATIONS(4, test_execute_chipping_rvalue, float, 4);
+ CALL_SUBTEST_COMBINATIONS(4, test_execute_chipping_rvalue, float, 5);
+
+ CALL_SUBTEST_COMBINATIONS(5, test_execute_chipping_lvalue, float, 3);
+ CALL_SUBTEST_COMBINATIONS(5, test_execute_chipping_lvalue, float, 4);
+ CALL_SUBTEST_COMBINATIONS(5, test_execute_chipping_lvalue, float, 5);
+
+ CALL_SUBTEST_COMBINATIONS(6, test_execute_shuffle_rvalue, float, 3);
+ CALL_SUBTEST_COMBINATIONS(6, test_execute_shuffle_rvalue, float, 4);
+ CALL_SUBTEST_COMBINATIONS(6, test_execute_shuffle_rvalue, float, 5);
+
+ CALL_SUBTEST_COMBINATIONS(7, test_execute_shuffle_lvalue, float, 3);
+ CALL_SUBTEST_COMBINATIONS(7, test_execute_shuffle_lvalue, float, 4);
+ CALL_SUBTEST_COMBINATIONS(7, test_execute_shuffle_lvalue, float, 5);
+
+ CALL_SUBTEST_COMBINATIONS(9, test_execute_reshape, float, 2);
+ CALL_SUBTEST_COMBINATIONS(9, test_execute_reshape, float, 3);
+ CALL_SUBTEST_COMBINATIONS(9, test_execute_reshape, float, 4);
+ CALL_SUBTEST_COMBINATIONS(9, test_execute_reshape, float, 5);
+
+ CALL_SUBTEST_COMBINATIONS(10, test_execute_slice_rvalue, float, 2);
+ CALL_SUBTEST_COMBINATIONS(10, test_execute_slice_rvalue, float, 3);
+ CALL_SUBTEST_COMBINATIONS(10, test_execute_slice_rvalue, float, 4);
+ CALL_SUBTEST_COMBINATIONS(10, test_execute_slice_rvalue, float, 5);
+
+ CALL_SUBTEST_COMBINATIONS(11, test_execute_slice_lvalue, float, 2);
+ CALL_SUBTEST_COMBINATIONS(11, test_execute_slice_lvalue, float, 3);
+ CALL_SUBTEST_COMBINATIONS(11, test_execute_slice_lvalue, float, 4);
+ CALL_SUBTEST_COMBINATIONS(11, test_execute_slice_lvalue, float, 5);
+
+ CALL_SUBTEST_COMBINATIONS(12, test_execute_broadcasting_of_forced_eval, float, 2);
+ CALL_SUBTEST_COMBINATIONS(12, test_execute_broadcasting_of_forced_eval, float, 3);
+ CALL_SUBTEST_COMBINATIONS(12, test_execute_broadcasting_of_forced_eval, float, 4);
+ CALL_SUBTEST_COMBINATIONS(12, test_execute_broadcasting_of_forced_eval, float, 5);
+
+ CALL_SUBTEST_COMBINATIONS(13, test_execute_generator_op, float, 2);
+ CALL_SUBTEST_COMBINATIONS(13, test_execute_generator_op, float, 3);
+ CALL_SUBTEST_COMBINATIONS(13, test_execute_generator_op, float, 4);
+ CALL_SUBTEST_COMBINATIONS(13, test_execute_generator_op, float, 5);
+
+ CALL_SUBTEST_COMBINATIONS(14, test_execute_reverse_rvalue, float, 1);
+ CALL_SUBTEST_COMBINATIONS(14, test_execute_reverse_rvalue, float, 2);
+ CALL_SUBTEST_COMBINATIONS(14, test_execute_reverse_rvalue, float, 3);
+ CALL_SUBTEST_COMBINATIONS(14, test_execute_reverse_rvalue, float, 4);
+ CALL_SUBTEST_COMBINATIONS(14, test_execute_reverse_rvalue, float, 5);
+
+ CALL_ASYNC_SUBTEST_COMBINATIONS(15, test_async_execute_unary_expr, float, 3);
+ CALL_ASYNC_SUBTEST_COMBINATIONS(15, test_async_execute_unary_expr, float, 4);
+ CALL_ASYNC_SUBTEST_COMBINATIONS(15, test_async_execute_unary_expr, float, 5);
+
+ CALL_ASYNC_SUBTEST_COMBINATIONS(16, test_async_execute_binary_expr, float, 3);
+ CALL_ASYNC_SUBTEST_COMBINATIONS(16, test_async_execute_binary_expr, float, 4);
+ CALL_ASYNC_SUBTEST_COMBINATIONS(16, test_async_execute_binary_expr, float, 5);
+
+ // Force CMake to split this test.
+ // EIGEN_SUFFIXES;1;2;3;4;5;6;7;8;9;10;11;12;13;14;15;16
+}
diff --git a/unsupported/test/cxx11_tensor_expr.cpp b/unsupported/test/cxx11_tensor_expr.cpp
new file mode 100644
index 0000000..ddc8132
--- /dev/null
+++ b/unsupported/test/cxx11_tensor_expr.cpp
@@ -0,0 +1,464 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include <numeric>
+
+#include "main.h"
+
+#include <Eigen/CXX11/Tensor>
+
+using Eigen::Tensor;
+using Eigen::RowMajor;
+
+static void test_1d()
+{
+ Tensor<float, 1> vec1(6);
+ Tensor<float, 1, RowMajor> vec2(6);
+
+ vec1(0) = 4.0; vec2(0) = 0.0;
+ vec1(1) = 8.0; vec2(1) = 1.0;
+ vec1(2) = 15.0; vec2(2) = 2.0;
+ vec1(3) = 16.0; vec2(3) = 3.0;
+ vec1(4) = 23.0; vec2(4) = 4.0;
+ vec1(5) = 42.0; vec2(5) = 5.0;
+
+ float data3[6];
+ TensorMap<Tensor<float, 1>> vec3(data3, 6);
+ vec3 = vec1.sqrt();
+ float data4[6];
+ TensorMap<Tensor<float, 1, RowMajor>> vec4(data4, 6);
+ vec4 = vec2.square();
+ float data5[6];
+ TensorMap<Tensor<float, 1, RowMajor>> vec5(data5, 6);
+ vec5 = vec2.cube();
+
+ VERIFY_IS_APPROX(vec3(0), sqrtf(4.0));
+ VERIFY_IS_APPROX(vec3(1), sqrtf(8.0));
+ VERIFY_IS_APPROX(vec3(2), sqrtf(15.0));
+ VERIFY_IS_APPROX(vec3(3), sqrtf(16.0));
+ VERIFY_IS_APPROX(vec3(4), sqrtf(23.0));
+ VERIFY_IS_APPROX(vec3(5), sqrtf(42.0));
+
+ VERIFY_IS_APPROX(vec4(0), 0.0f);
+ VERIFY_IS_APPROX(vec4(1), 1.0f);
+ VERIFY_IS_APPROX(vec4(2), 2.0f * 2.0f);
+ VERIFY_IS_APPROX(vec4(3), 3.0f * 3.0f);
+ VERIFY_IS_APPROX(vec4(4), 4.0f * 4.0f);
+ VERIFY_IS_APPROX(vec4(5), 5.0f * 5.0f);
+
+ VERIFY_IS_APPROX(vec5(0), 0.0f);
+ VERIFY_IS_APPROX(vec5(1), 1.0f);
+ VERIFY_IS_APPROX(vec5(2), 2.0f * 2.0f * 2.0f);
+ VERIFY_IS_APPROX(vec5(3), 3.0f * 3.0f * 3.0f);
+ VERIFY_IS_APPROX(vec5(4), 4.0f * 4.0f * 4.0f);
+ VERIFY_IS_APPROX(vec5(5), 5.0f * 5.0f * 5.0f);
+
+ vec3 = vec1 + vec2;
+ VERIFY_IS_APPROX(vec3(0), 4.0f + 0.0f);
+ VERIFY_IS_APPROX(vec3(1), 8.0f + 1.0f);
+ VERIFY_IS_APPROX(vec3(2), 15.0f + 2.0f);
+ VERIFY_IS_APPROX(vec3(3), 16.0f + 3.0f);
+ VERIFY_IS_APPROX(vec3(4), 23.0f + 4.0f);
+ VERIFY_IS_APPROX(vec3(5), 42.0f + 5.0f);
+}
+
+static void test_2d()
+{
+ float data1[6];
+ TensorMap<Tensor<float, 2>> mat1(data1, 2, 3);
+ float data2[6];
+ TensorMap<Tensor<float, 2, RowMajor>> mat2(data2, 2, 3);
+
+ mat1(0,0) = 0.0;
+ mat1(0,1) = 1.0;
+ mat1(0,2) = 2.0;
+ mat1(1,0) = 3.0;
+ mat1(1,1) = 4.0;
+ mat1(1,2) = 5.0;
+
+ mat2(0,0) = -0.0;
+ mat2(0,1) = -1.0;
+ mat2(0,2) = -2.0;
+ mat2(1,0) = -3.0;
+ mat2(1,1) = -4.0;
+ mat2(1,2) = -5.0;
+
+ Tensor<float, 2> mat3(2,3);
+ Tensor<float, 2, RowMajor> mat4(2,3);
+ mat3 = mat1.abs();
+ mat4 = mat2.abs();
+
+ VERIFY_IS_APPROX(mat3(0,0), 0.0f);
+ VERIFY_IS_APPROX(mat3(0,1), 1.0f);
+ VERIFY_IS_APPROX(mat3(0,2), 2.0f);
+ VERIFY_IS_APPROX(mat3(1,0), 3.0f);
+ VERIFY_IS_APPROX(mat3(1,1), 4.0f);
+ VERIFY_IS_APPROX(mat3(1,2), 5.0f);
+
+ VERIFY_IS_APPROX(mat4(0,0), 0.0f);
+ VERIFY_IS_APPROX(mat4(0,1), 1.0f);
+ VERIFY_IS_APPROX(mat4(0,2), 2.0f);
+ VERIFY_IS_APPROX(mat4(1,0), 3.0f);
+ VERIFY_IS_APPROX(mat4(1,1), 4.0f);
+ VERIFY_IS_APPROX(mat4(1,2), 5.0f);
+}
+
+static void test_3d()
+{
+ Tensor<float, 3> mat1(2,3,7);
+ Tensor<float, 3, RowMajor> mat2(2,3,7);
+
+ float val = 1.0f;
+ for (int i = 0; i < 2; ++i) {
+ for (int j = 0; j < 3; ++j) {
+ for (int k = 0; k < 7; ++k) {
+ mat1(i,j,k) = val;
+ mat2(i,j,k) = val;
+ val += 1.0f;
+ }
+ }
+ }
+
+ Tensor<float, 3> mat3(2,3,7);
+ mat3 = mat1 + mat1;
+ Tensor<float, 3, RowMajor> mat4(2,3,7);
+ mat4 = mat2 * 3.14f;
+ Tensor<float, 3> mat5(2,3,7);
+ mat5 = (mat1 + mat1.constant(1)).inverse().log();
+ Tensor<float, 3, RowMajor> mat6(2,3,7);
+ mat6 = mat2.pow(0.5f) * 3.14f;
+ Tensor<float, 3> mat7(2,3,7);
+ mat7 = mat1.cwiseMax(mat5 * 2.0f).exp();
+ Tensor<float, 3, RowMajor> mat8(2,3,7);
+ mat8 = (-mat2).exp() * 3.14f;
+ Tensor<float, 3, RowMajor> mat9(2,3,7);
+ mat9 = mat2 + 3.14f;
+ Tensor<float, 3, RowMajor> mat10(2,3,7);
+ mat10 = mat2 - 3.14f;
+ Tensor<float, 3, RowMajor> mat11(2,3,7);
+ mat11 = mat2 / 3.14f;
+
+ val = 1.0f;
+ for (int i = 0; i < 2; ++i) {
+ for (int j = 0; j < 3; ++j) {
+ for (int k = 0; k < 7; ++k) {
+ VERIFY_IS_APPROX(mat3(i,j,k), val + val);
+ VERIFY_IS_APPROX(mat4(i,j,k), val * 3.14f);
+ VERIFY_IS_APPROX(mat5(i,j,k), logf(1.0f/(val + 1)));
+ VERIFY_IS_APPROX(mat6(i,j,k), sqrtf(val) * 3.14f);
+ VERIFY_IS_APPROX(mat7(i,j,k), expf((std::max)(val, mat5(i,j,k) * 2.0f)));
+ VERIFY_IS_APPROX(mat8(i,j,k), expf(-val) * 3.14f);
+ VERIFY_IS_APPROX(mat9(i,j,k), val + 3.14f);
+ VERIFY_IS_APPROX(mat10(i,j,k), val - 3.14f);
+ VERIFY_IS_APPROX(mat11(i,j,k), val / 3.14f);
+ val += 1.0f;
+ }
+ }
+ }
+}
+
+static void test_constants()
+{
+ Tensor<float, 3> mat1(2,3,7);
+ Tensor<float, 3> mat2(2,3,7);
+ Tensor<float, 3> mat3(2,3,7);
+
+ float val = 1.0f;
+ for (int i = 0; i < 2; ++i) {
+ for (int j = 0; j < 3; ++j) {
+ for (int k = 0; k < 7; ++k) {
+ mat1(i,j,k) = val;
+ val += 1.0f;
+ }
+ }
+ }
+ mat2 = mat1.constant(3.14f);
+ mat3 = mat1.cwiseMax(7.3f).exp();
+
+ val = 1.0f;
+ for (int i = 0; i < 2; ++i) {
+ for (int j = 0; j < 3; ++j) {
+ for (int k = 0; k < 7; ++k) {
+ VERIFY_IS_APPROX(mat2(i,j,k), 3.14f);
+ VERIFY_IS_APPROX(mat3(i,j,k), expf((std::max)(val, 7.3f)));
+ val += 1.0f;
+ }
+ }
+ }
+}
+
+static void test_boolean()
+{
+ const int kSize = 31;
+ Tensor<int, 1> vec(kSize);
+ std::iota(vec.data(), vec.data() + kSize, 0);
+
+ // Test ||.
+ Tensor<bool, 1> bool1 = vec < vec.constant(1) || vec > vec.constant(4);
+ for (int i = 0; i < kSize; ++i) {
+ bool expected = i < 1 || i > 4;
+ VERIFY_IS_EQUAL(bool1[i], expected);
+ }
+
+ // Test &&, including cast of operand vec.
+ Tensor<bool, 1> bool2 = vec.cast<bool>() && vec < vec.constant(4);
+ for (int i = 0; i < kSize; ++i) {
+ bool expected = bool(i) && i < 4;
+ VERIFY_IS_EQUAL(bool2[i], expected);
+ }
+
+ // Compilation tests:
+ // Test Tensor<bool> against results of cast or comparison; verifies that
+ // CoeffReturnType is set to match Op return type of bool for Unary and Binary
+ // Ops.
+ Tensor<bool, 1> bool3 = vec.cast<bool>() && bool2;
+ bool3 = vec < vec.constant(4) && bool2;
+}
+
+static void test_functors()
+{
+ Tensor<float, 3> mat1(2,3,7);
+ Tensor<float, 3> mat2(2,3,7);
+ Tensor<float, 3> mat3(2,3,7);
+
+ float val = 1.0f;
+ for (int i = 0; i < 2; ++i) {
+ for (int j = 0; j < 3; ++j) {
+ for (int k = 0; k < 7; ++k) {
+ mat1(i,j,k) = val;
+ val += 1.0f;
+ }
+ }
+ }
+ mat2 = mat1.inverse().unaryExpr(&asinf);
+ mat3 = mat1.unaryExpr(&tanhf);
+
+ val = 1.0f;
+ for (int i = 0; i < 2; ++i) {
+ for (int j = 0; j < 3; ++j) {
+ for (int k = 0; k < 7; ++k) {
+ VERIFY_IS_APPROX(mat2(i,j,k), asinf(1.0f / mat1(i,j,k)));
+ VERIFY_IS_APPROX(mat3(i,j,k), tanhf(mat1(i,j,k)));
+ val += 1.0f;
+ }
+ }
+ }
+}
+
+static void test_type_casting()
+{
+ Tensor<bool, 3> mat1(2,3,7);
+ Tensor<float, 3> mat2(2,3,7);
+ Tensor<double, 3> mat3(2,3,7);
+ mat1.setRandom();
+ mat2.setRandom();
+
+ mat3 = mat1.cast<double>();
+ for (int i = 0; i < 2; ++i) {
+ for (int j = 0; j < 3; ++j) {
+ for (int k = 0; k < 7; ++k) {
+ VERIFY_IS_APPROX(mat3(i,j,k), mat1(i,j,k) ? 1.0 : 0.0);
+ }
+ }
+ }
+
+ mat3 = mat2.cast<double>();
+ for (int i = 0; i < 2; ++i) {
+ for (int j = 0; j < 3; ++j) {
+ for (int k = 0; k < 7; ++k) {
+ VERIFY_IS_APPROX(mat3(i,j,k), static_cast<double>(mat2(i,j,k)));
+ }
+ }
+ }
+}
+
+static void test_select()
+{
+ Tensor<float, 3> selector(2,3,7);
+ Tensor<float, 3> mat1(2,3,7);
+ Tensor<float, 3> mat2(2,3,7);
+ Tensor<float, 3> result(2,3,7);
+
+ selector.setRandom();
+ mat1.setRandom();
+ mat2.setRandom();
+ result = (selector > selector.constant(0.5f)).select(mat1, mat2);
+
+ for (int i = 0; i < 2; ++i) {
+ for (int j = 0; j < 3; ++j) {
+ for (int k = 0; k < 7; ++k) {
+ VERIFY_IS_APPROX(result(i,j,k), (selector(i,j,k) > 0.5f) ? mat1(i,j,k) : mat2(i,j,k));
+ }
+ }
+ }
+}
+
+template <typename Scalar>
+void test_minmax_nan_propagation_templ() {
+ for (int size = 1; size < 17; ++size) {
+ const Scalar kNaN = std::numeric_limits<Scalar>::quiet_NaN();
+ const Scalar kInf = std::numeric_limits<Scalar>::infinity();
+ const Scalar kZero(0);
+ Tensor<Scalar, 1> vec_full_nan(size);
+ Tensor<Scalar, 1> vec_one_nan(size);
+ Tensor<Scalar, 1> vec_zero(size);
+ vec_full_nan.setConstant(kNaN);
+ vec_zero.setZero();
+ vec_one_nan.setZero();
+ vec_one_nan(size/2) = kNaN;
+
+ auto verify_all_nan = [&](const Tensor<Scalar, 1>& v) {
+ for (int i = 0; i < size; ++i) {
+ VERIFY((numext::isnan)(v(i)));
+ }
+ };
+
+ auto verify_all_zero = [&](const Tensor<Scalar, 1>& v) {
+ for (int i = 0; i < size; ++i) {
+ VERIFY_IS_EQUAL(v(i), Scalar(0));
+ }
+ };
+
+ // Test NaN propagating max.
+ // max(nan, nan) = nan
+ // max(nan, 0) = nan
+ // max(0, nan) = nan
+ // max(0, 0) = 0
+ verify_all_nan(vec_full_nan.template cwiseMax<PropagateNaN>(kNaN));
+ verify_all_nan(vec_full_nan.template cwiseMax<PropagateNaN>(vec_full_nan));
+ verify_all_nan(vec_full_nan.template cwiseMax<PropagateNaN>(kZero));
+ verify_all_nan(vec_full_nan.template cwiseMax<PropagateNaN>(vec_zero));
+ verify_all_nan(vec_zero.template cwiseMax<PropagateNaN>(kNaN));
+ verify_all_nan(vec_zero.template cwiseMax<PropagateNaN>(vec_full_nan));
+ verify_all_zero(vec_zero.template cwiseMax<PropagateNaN>(kZero));
+ verify_all_zero(vec_zero.template cwiseMax<PropagateNaN>(vec_zero));
+
+ // Test number propagating max.
+ // max(nan, nan) = nan
+ // max(nan, 0) = 0
+ // max(0, nan) = 0
+ // max(0, 0) = 0
+ verify_all_nan(vec_full_nan.template cwiseMax<PropagateNumbers>(kNaN));
+ verify_all_nan(vec_full_nan.template cwiseMax<PropagateNumbers>(vec_full_nan));
+ verify_all_zero(vec_full_nan.template cwiseMax<PropagateNumbers>(kZero));
+ verify_all_zero(vec_full_nan.template cwiseMax<PropagateNumbers>(vec_zero));
+ verify_all_zero(vec_zero.template cwiseMax<PropagateNumbers>(kNaN));
+ verify_all_zero(vec_zero.template cwiseMax<PropagateNumbers>(vec_full_nan));
+ verify_all_zero(vec_zero.template cwiseMax<PropagateNumbers>(kZero));
+ verify_all_zero(vec_zero.template cwiseMax<PropagateNumbers>(vec_zero));
+
+ // Test NaN propagating min.
+ // min(nan, nan) = nan
+ // min(nan, 0) = nan
+ // min(0, nan) = nan
+ // min(0, 0) = 0
+ verify_all_nan(vec_full_nan.template cwiseMin<PropagateNaN>(kNaN));
+ verify_all_nan(vec_full_nan.template cwiseMin<PropagateNaN>(vec_full_nan));
+ verify_all_nan(vec_full_nan.template cwiseMin<PropagateNaN>(kZero));
+ verify_all_nan(vec_full_nan.template cwiseMin<PropagateNaN>(vec_zero));
+ verify_all_nan(vec_zero.template cwiseMin<PropagateNaN>(kNaN));
+ verify_all_nan(vec_zero.template cwiseMin<PropagateNaN>(vec_full_nan));
+ verify_all_zero(vec_zero.template cwiseMin<PropagateNaN>(kZero));
+ verify_all_zero(vec_zero.template cwiseMin<PropagateNaN>(vec_zero));
+
+ // Test number propagating min.
+ // min(nan, nan) = nan
+ // min(nan, 0) = 0
+ // min(0, nan) = 0
+ // min(0, 0) = 0
+ verify_all_nan(vec_full_nan.template cwiseMin<PropagateNumbers>(kNaN));
+ verify_all_nan(vec_full_nan.template cwiseMin<PropagateNumbers>(vec_full_nan));
+ verify_all_zero(vec_full_nan.template cwiseMin<PropagateNumbers>(kZero));
+ verify_all_zero(vec_full_nan.template cwiseMin<PropagateNumbers>(vec_zero));
+ verify_all_zero(vec_zero.template cwiseMin<PropagateNumbers>(kNaN));
+ verify_all_zero(vec_zero.template cwiseMin<PropagateNumbers>(vec_full_nan));
+ verify_all_zero(vec_zero.template cwiseMin<PropagateNumbers>(kZero));
+ verify_all_zero(vec_zero.template cwiseMin<PropagateNumbers>(vec_zero));
+
+ // Test min and max reduction
+ Tensor<Scalar, 0> val;
+ val = vec_zero.minimum();
+ VERIFY_IS_EQUAL(val(), kZero);
+ val = vec_zero.template minimum<PropagateNaN>();
+ VERIFY_IS_EQUAL(val(), kZero);
+ val = vec_zero.template minimum<PropagateNumbers>();
+ VERIFY_IS_EQUAL(val(), kZero);
+ val = vec_zero.maximum();
+ VERIFY_IS_EQUAL(val(), kZero);
+ val = vec_zero.template maximum<PropagateNaN>();
+ VERIFY_IS_EQUAL(val(), kZero);
+ val = vec_zero.template maximum<PropagateNumbers>();
+ VERIFY_IS_EQUAL(val(), kZero);
+
+ // Test NaN propagation for tensor of all NaNs.
+ val = vec_full_nan.template minimum<PropagateNaN>();
+ VERIFY((numext::isnan)(val()));
+ val = vec_full_nan.template minimum<PropagateNumbers>();
+ VERIFY_IS_EQUAL(val(), kInf);
+ val = vec_full_nan.template maximum<PropagateNaN>();
+ VERIFY((numext::isnan)(val()));
+ val = vec_full_nan.template maximum<PropagateNumbers>();
+ VERIFY_IS_EQUAL(val(), -kInf);
+
+ // Test NaN propagation for tensor with a single NaN.
+ val = vec_one_nan.template minimum<PropagateNaN>();
+ VERIFY((numext::isnan)(val()));
+ val = vec_one_nan.template minimum<PropagateNumbers>();
+ VERIFY_IS_EQUAL(val(), (size == 1 ? kInf : kZero));
+ val = vec_one_nan.template maximum<PropagateNaN>();
+ VERIFY((numext::isnan)(val()));
+ val = vec_one_nan.template maximum<PropagateNumbers>();
+ VERIFY_IS_EQUAL(val(), (size == 1 ? -kInf : kZero));
+ }
+}
+
+static void test_clip()
+{
+ Tensor<float, 1> vec(6);
+ vec(0) = 4.0;
+ vec(1) = 8.0;
+ vec(2) = 15.0;
+ vec(3) = 16.0;
+ vec(4) = 23.0;
+ vec(5) = 42.0;
+
+ float kMin = 20;
+ float kMax = 30;
+
+ Tensor<float, 1> vec_clipped(6);
+ vec_clipped = vec.clip(kMin, kMax);
+ for (int i = 0; i < 6; ++i) {
+ VERIFY_IS_EQUAL(vec_clipped(i), numext::mini(numext::maxi(vec(i), kMin), kMax));
+ }
+}
+
+static void test_minmax_nan_propagation()
+{
+ test_minmax_nan_propagation_templ<float>();
+ test_minmax_nan_propagation_templ<double>();
+}
+
+EIGEN_DECLARE_TEST(cxx11_tensor_expr)
+{
+ CALL_SUBTEST(test_1d());
+ CALL_SUBTEST(test_2d());
+ CALL_SUBTEST(test_3d());
+ CALL_SUBTEST(test_constants());
+ CALL_SUBTEST(test_boolean());
+ CALL_SUBTEST(test_functors());
+ CALL_SUBTEST(test_type_casting());
+ CALL_SUBTEST(test_select());
+ CALL_SUBTEST(test_clip());
+
+// Nan propagation does currently not work like one would expect from std::max/std::min,
+// so we disable it for now
+#if !EIGEN_ARCH_ARM_OR_ARM64
+ CALL_SUBTEST(test_minmax_nan_propagation());
+#endif
+}
diff --git a/unsupported/test/cxx11_tensor_fft.cpp b/unsupported/test/cxx11_tensor_fft.cpp
new file mode 100644
index 0000000..ff8ebcf
--- /dev/null
+++ b/unsupported/test/cxx11_tensor_fft.cpp
@@ -0,0 +1,304 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2014 Jianwei Cui <thucjw@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "main.h"
+#include <Eigen/CXX11/Tensor>
+
+using Eigen::Tensor;
+
+template <int DataLayout>
+static void test_fft_2D_golden() {
+ Tensor<float, 2, DataLayout> input(2, 3);
+ input(0, 0) = 1;
+ input(0, 1) = 2;
+ input(0, 2) = 3;
+ input(1, 0) = 4;
+ input(1, 1) = 5;
+ input(1, 2) = 6;
+
+ array<ptrdiff_t, 2> fft;
+ fft[0] = 0;
+ fft[1] = 1;
+
+ Tensor<std::complex<float>, 2, DataLayout> output = input.template fft<Eigen::BothParts, Eigen::FFT_FORWARD>(fft);
+
+ std::complex<float> output_golden[6]; // in ColMajor order
+ output_golden[0] = std::complex<float>(21, 0);
+ output_golden[1] = std::complex<float>(-9, 0);
+ output_golden[2] = std::complex<float>(-3, 1.73205);
+ output_golden[3] = std::complex<float>( 0, 0);
+ output_golden[4] = std::complex<float>(-3, -1.73205);
+ output_golden[5] = std::complex<float>(0 ,0);
+
+ std::complex<float> c_offset = std::complex<float>(1.0, 1.0);
+
+ if (DataLayout == ColMajor) {
+ VERIFY_IS_APPROX(output(0) + c_offset, output_golden[0] + c_offset);
+ VERIFY_IS_APPROX(output(1) + c_offset, output_golden[1] + c_offset);
+ VERIFY_IS_APPROX(output(2) + c_offset, output_golden[2] + c_offset);
+ VERIFY_IS_APPROX(output(3) + c_offset, output_golden[3] + c_offset);
+ VERIFY_IS_APPROX(output(4) + c_offset, output_golden[4] + c_offset);
+ VERIFY_IS_APPROX(output(5) + c_offset, output_golden[5] + c_offset);
+ }
+ else {
+ VERIFY_IS_APPROX(output(0)+ c_offset, output_golden[0]+ c_offset);
+ VERIFY_IS_APPROX(output(1)+ c_offset, output_golden[2]+ c_offset);
+ VERIFY_IS_APPROX(output(2)+ c_offset, output_golden[4]+ c_offset);
+ VERIFY_IS_APPROX(output(3)+ c_offset, output_golden[1]+ c_offset);
+ VERIFY_IS_APPROX(output(4)+ c_offset, output_golden[3]+ c_offset);
+ VERIFY_IS_APPROX(output(5)+ c_offset, output_golden[5]+ c_offset);
+ }
+}
+
+static void test_fft_complex_input_golden() {
+ Tensor<std::complex<float>, 1, ColMajor> input(5);
+ input(0) = std::complex<float>(1, 1);
+ input(1) = std::complex<float>(2, 2);
+ input(2) = std::complex<float>(3, 3);
+ input(3) = std::complex<float>(4, 4);
+ input(4) = std::complex<float>(5, 5);
+
+ array<ptrdiff_t, 1> fft;
+ fft[0] = 0;
+
+ Tensor<std::complex<float>, 1, ColMajor> forward_output_both_parts = input.fft<BothParts, FFT_FORWARD>(fft);
+ Tensor<std::complex<float>, 1, ColMajor> reverse_output_both_parts = input.fft<BothParts, FFT_REVERSE>(fft);
+
+ Tensor<float, 1, ColMajor> forward_output_real_part = input.fft<RealPart, FFT_FORWARD>(fft);
+ Tensor<float, 1, ColMajor> reverse_output_real_part = input.fft<RealPart, FFT_REVERSE>(fft);
+
+ Tensor<float, 1, ColMajor> forward_output_imag_part = input.fft<ImagPart, FFT_FORWARD>(fft);
+ Tensor<float, 1, ColMajor> reverse_output_imag_part = input.fft<ImagPart, FFT_REVERSE>(fft);
+
+ VERIFY_IS_EQUAL(forward_output_both_parts.dimension(0), input.dimension(0));
+ VERIFY_IS_EQUAL(reverse_output_both_parts.dimension(0), input.dimension(0));
+
+ VERIFY_IS_EQUAL(forward_output_real_part.dimension(0), input.dimension(0));
+ VERIFY_IS_EQUAL(reverse_output_real_part.dimension(0), input.dimension(0));
+
+ VERIFY_IS_EQUAL(forward_output_imag_part.dimension(0), input.dimension(0));
+ VERIFY_IS_EQUAL(reverse_output_imag_part.dimension(0), input.dimension(0));
+
+ std::complex<float> forward_golden_result[5];
+ std::complex<float> reverse_golden_result[5];
+
+ forward_golden_result[0] = std::complex<float>(15.000000000000000,+15.000000000000000);
+ forward_golden_result[1] = std::complex<float>(-5.940954801177935, +0.940954801177934);
+ forward_golden_result[2] = std::complex<float>(-3.312299240582266, -1.687700759417735);
+ forward_golden_result[3] = std::complex<float>(-1.687700759417735, -3.312299240582266);
+ forward_golden_result[4] = std::complex<float>( 0.940954801177934, -5.940954801177935);
+
+ reverse_golden_result[0] = std::complex<float>( 3.000000000000000, + 3.000000000000000);
+ reverse_golden_result[1] = std::complex<float>( 0.188190960235587, - 1.188190960235587);
+ reverse_golden_result[2] = std::complex<float>(-0.337540151883547, - 0.662459848116453);
+ reverse_golden_result[3] = std::complex<float>(-0.662459848116453, - 0.337540151883547);
+ reverse_golden_result[4] = std::complex<float>(-1.188190960235587, + 0.188190960235587);
+
+ for(int i = 0; i < 5; ++i) {
+ VERIFY_IS_APPROX(forward_output_both_parts(i), forward_golden_result[i]);
+ VERIFY_IS_APPROX(forward_output_real_part(i), forward_golden_result[i].real());
+ VERIFY_IS_APPROX(forward_output_imag_part(i), forward_golden_result[i].imag());
+ }
+
+ for(int i = 0; i < 5; ++i) {
+ VERIFY_IS_APPROX(reverse_output_both_parts(i), reverse_golden_result[i]);
+ VERIFY_IS_APPROX(reverse_output_real_part(i), reverse_golden_result[i].real());
+ VERIFY_IS_APPROX(reverse_output_imag_part(i), reverse_golden_result[i].imag());
+ }
+}
+
+static void test_fft_real_input_golden() {
+ Tensor<float, 1, ColMajor> input(5);
+ input(0) = 1.0;
+ input(1) = 2.0;
+ input(2) = 3.0;
+ input(3) = 4.0;
+ input(4) = 5.0;
+
+ array<ptrdiff_t, 1> fft;
+ fft[0] = 0;
+
+ Tensor<std::complex<float>, 1, ColMajor> forward_output_both_parts = input.fft<BothParts, FFT_FORWARD>(fft);
+ Tensor<std::complex<float>, 1, ColMajor> reverse_output_both_parts = input.fft<BothParts, FFT_REVERSE>(fft);
+
+ Tensor<float, 1, ColMajor> forward_output_real_part = input.fft<RealPart, FFT_FORWARD>(fft);
+ Tensor<float, 1, ColMajor> reverse_output_real_part = input.fft<RealPart, FFT_REVERSE>(fft);
+
+ Tensor<float, 1, ColMajor> forward_output_imag_part = input.fft<ImagPart, FFT_FORWARD>(fft);
+ Tensor<float, 1, ColMajor> reverse_output_imag_part = input.fft<ImagPart, FFT_REVERSE>(fft);
+
+ VERIFY_IS_EQUAL(forward_output_both_parts.dimension(0), input.dimension(0));
+ VERIFY_IS_EQUAL(reverse_output_both_parts.dimension(0), input.dimension(0));
+
+ VERIFY_IS_EQUAL(forward_output_real_part.dimension(0), input.dimension(0));
+ VERIFY_IS_EQUAL(reverse_output_real_part.dimension(0), input.dimension(0));
+
+ VERIFY_IS_EQUAL(forward_output_imag_part.dimension(0), input.dimension(0));
+ VERIFY_IS_EQUAL(reverse_output_imag_part.dimension(0), input.dimension(0));
+
+ std::complex<float> forward_golden_result[5];
+ std::complex<float> reverse_golden_result[5];
+
+
+ forward_golden_result[0] = std::complex<float>( 15, 0);
+ forward_golden_result[1] = std::complex<float>(-2.5, +3.44095480117793);
+ forward_golden_result[2] = std::complex<float>(-2.5, +0.81229924058227);
+ forward_golden_result[3] = std::complex<float>(-2.5, -0.81229924058227);
+ forward_golden_result[4] = std::complex<float>(-2.5, -3.44095480117793);
+
+ reverse_golden_result[0] = std::complex<float>( 3.0, 0);
+ reverse_golden_result[1] = std::complex<float>(-0.5, -0.688190960235587);
+ reverse_golden_result[2] = std::complex<float>(-0.5, -0.162459848116453);
+ reverse_golden_result[3] = std::complex<float>(-0.5, +0.162459848116453);
+ reverse_golden_result[4] = std::complex<float>(-0.5, +0.688190960235587);
+
+ std::complex<float> c_offset(1.0, 1.0);
+ float r_offset = 1.0;
+
+ for(int i = 0; i < 5; ++i) {
+ VERIFY_IS_APPROX(forward_output_both_parts(i) + c_offset, forward_golden_result[i] + c_offset);
+ VERIFY_IS_APPROX(forward_output_real_part(i) + r_offset, forward_golden_result[i].real() + r_offset);
+ VERIFY_IS_APPROX(forward_output_imag_part(i) + r_offset, forward_golden_result[i].imag() + r_offset);
+ }
+
+ for(int i = 0; i < 5; ++i) {
+ VERIFY_IS_APPROX(reverse_output_both_parts(i) + c_offset, reverse_golden_result[i] + c_offset);
+ VERIFY_IS_APPROX(reverse_output_real_part(i) + r_offset, reverse_golden_result[i].real() + r_offset);
+ VERIFY_IS_APPROX(reverse_output_imag_part(i) + r_offset, reverse_golden_result[i].imag() + r_offset);
+ }
+}
+
+
+template <int DataLayout, typename RealScalar, bool isComplexInput, int FFTResultType, int FFTDirection, int TensorRank>
+static void test_fft_real_input_energy() {
+
+ Eigen::DSizes<ptrdiff_t, TensorRank> dimensions;
+ ptrdiff_t total_size = 1;
+ for (int i = 0; i < TensorRank; ++i) {
+ dimensions[i] = rand() % 20 + 1;
+ total_size *= dimensions[i];
+ }
+ const DSizes<ptrdiff_t, TensorRank> arr = dimensions;
+
+ typedef std::conditional_t<isComplexInput == true, std::complex<RealScalar>, RealScalar> InputScalar;
+
+ Tensor<InputScalar, TensorRank, DataLayout> input;
+ input.resize(arr);
+ input.setRandom();
+
+ array<ptrdiff_t, TensorRank> fft;
+ for (int i = 0; i < TensorRank; ++i) {
+ fft[i] = i;
+ }
+
+ typedef std::conditional_t<FFTResultType == Eigen::BothParts, std::complex<RealScalar>, RealScalar> OutputScalar;
+ Tensor<OutputScalar, TensorRank, DataLayout> output;
+ output = input.template fft<FFTResultType, FFTDirection>(fft);
+
+ for (int i = 0; i < TensorRank; ++i) {
+ VERIFY_IS_EQUAL(output.dimension(i), input.dimension(i));
+ }
+
+ RealScalar energy_original = 0.0;
+ RealScalar energy_after_fft = 0.0;
+
+ for (int i = 0; i < total_size; ++i) {
+ energy_original += numext::abs2(input(i));
+ }
+
+ for (int i = 0; i < total_size; ++i) {
+ energy_after_fft += numext::abs2(output(i));
+ }
+
+ if(FFTDirection == FFT_FORWARD) {
+ VERIFY_IS_APPROX(energy_original, energy_after_fft / total_size);
+ }
+ else {
+ VERIFY_IS_APPROX(energy_original, energy_after_fft * total_size);
+ }
+}
+
+template <typename RealScalar>
+static void test_fft_non_power_of_2_round_trip(int exponent) {
+ int n = (1 << exponent) + 1;
+
+ Eigen::DSizes<ptrdiff_t, 1> dimensions;
+ dimensions[0] = n;
+ const DSizes<ptrdiff_t, 1> arr = dimensions;
+ Tensor<RealScalar, 1, ColMajor, ptrdiff_t> input;
+
+ input.resize(arr);
+ input.setRandom();
+
+ array<int, 1> fft;
+ fft[0] = 0;
+
+ Tensor<std::complex<RealScalar>, 1, ColMajor> forward =
+ input.template fft<BothParts, FFT_FORWARD>(fft);
+
+ Tensor<RealScalar, 1, ColMajor, ptrdiff_t> output =
+ forward.template fft<RealPart, FFT_REVERSE>(fft);
+
+ for (int i = 0; i < n; ++i) {
+ RealScalar tol = test_precision<RealScalar>() *
+ (std::abs(input[i]) + std::abs(output[i]) + 1);
+ VERIFY_IS_APPROX_OR_LESS_THAN(std::abs(input[i] - output[i]), tol);
+ }
+}
+
+EIGEN_DECLARE_TEST(cxx11_tensor_fft) {
+ test_fft_complex_input_golden();
+ test_fft_real_input_golden();
+
+ test_fft_2D_golden<ColMajor>();
+ test_fft_2D_golden<RowMajor>();
+
+ test_fft_real_input_energy<ColMajor, float, true, Eigen::BothParts, FFT_FORWARD, 1>();
+ test_fft_real_input_energy<ColMajor, double, true, Eigen::BothParts, FFT_FORWARD, 1>();
+ test_fft_real_input_energy<ColMajor, float, false, Eigen::BothParts, FFT_FORWARD, 1>();
+ test_fft_real_input_energy<ColMajor, double, false, Eigen::BothParts, FFT_FORWARD, 1>();
+
+ test_fft_real_input_energy<ColMajor, float, true, Eigen::BothParts, FFT_FORWARD, 2>();
+ test_fft_real_input_energy<ColMajor, double, true, Eigen::BothParts, FFT_FORWARD, 2>();
+ test_fft_real_input_energy<ColMajor, float, false, Eigen::BothParts, FFT_FORWARD, 2>();
+ test_fft_real_input_energy<ColMajor, double, false, Eigen::BothParts, FFT_FORWARD, 2>();
+
+ test_fft_real_input_energy<ColMajor, float, true, Eigen::BothParts, FFT_FORWARD, 3>();
+ test_fft_real_input_energy<ColMajor, double, true, Eigen::BothParts, FFT_FORWARD, 3>();
+ test_fft_real_input_energy<ColMajor, float, false, Eigen::BothParts, FFT_FORWARD, 3>();
+ test_fft_real_input_energy<ColMajor, double, false, Eigen::BothParts, FFT_FORWARD, 3>();
+
+ test_fft_real_input_energy<ColMajor, float, true, Eigen::BothParts, FFT_FORWARD, 4>();
+ test_fft_real_input_energy<ColMajor, double, true, Eigen::BothParts, FFT_FORWARD, 4>();
+ test_fft_real_input_energy<ColMajor, float, false, Eigen::BothParts, FFT_FORWARD, 4>();
+ test_fft_real_input_energy<ColMajor, double, false, Eigen::BothParts, FFT_FORWARD, 4>();
+
+ test_fft_real_input_energy<RowMajor, float, true, Eigen::BothParts, FFT_FORWARD, 1>();
+ test_fft_real_input_energy<RowMajor, double, true, Eigen::BothParts, FFT_FORWARD, 1>();
+ test_fft_real_input_energy<RowMajor, float, false, Eigen::BothParts, FFT_FORWARD, 1>();
+ test_fft_real_input_energy<RowMajor, double, false, Eigen::BothParts, FFT_FORWARD, 1>();
+
+ test_fft_real_input_energy<RowMajor, float, true, Eigen::BothParts, FFT_FORWARD, 2>();
+ test_fft_real_input_energy<RowMajor, double, true, Eigen::BothParts, FFT_FORWARD, 2>();
+ test_fft_real_input_energy<RowMajor, float, false, Eigen::BothParts, FFT_FORWARD, 2>();
+ test_fft_real_input_energy<RowMajor, double, false, Eigen::BothParts, FFT_FORWARD, 2>();
+
+ test_fft_real_input_energy<RowMajor, float, true, Eigen::BothParts, FFT_FORWARD, 3>();
+ test_fft_real_input_energy<RowMajor, double, true, Eigen::BothParts, FFT_FORWARD, 3>();
+ test_fft_real_input_energy<RowMajor, float, false, Eigen::BothParts, FFT_FORWARD, 3>();
+ test_fft_real_input_energy<RowMajor, double, false, Eigen::BothParts, FFT_FORWARD, 3>();
+
+ test_fft_real_input_energy<RowMajor, float, true, Eigen::BothParts, FFT_FORWARD, 4>();
+ test_fft_real_input_energy<RowMajor, double, true, Eigen::BothParts, FFT_FORWARD, 4>();
+ test_fft_real_input_energy<RowMajor, float, false, Eigen::BothParts, FFT_FORWARD, 4>();
+ test_fft_real_input_energy<RowMajor, double, false, Eigen::BothParts, FFT_FORWARD, 4>();
+
+ test_fft_non_power_of_2_round_trip<float>(7);
+ test_fft_non_power_of_2_round_trip<double>(7);
+}
diff --git a/unsupported/test/cxx11_tensor_fixed_size.cpp b/unsupported/test/cxx11_tensor_fixed_size.cpp
new file mode 100644
index 0000000..456ce6b
--- /dev/null
+++ b/unsupported/test/cxx11_tensor_fixed_size.cpp
@@ -0,0 +1,261 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "main.h"
+
+#include <Eigen/CXX11/Tensor>
+
+using Eigen::Tensor;
+using Eigen::RowMajor;
+
+
+static void test_0d()
+{
+ TensorFixedSize<float, Sizes<> > scalar1;
+ TensorFixedSize<float, Sizes<>, RowMajor> scalar2;
+ VERIFY_IS_EQUAL(scalar1.rank(), 0);
+ VERIFY_IS_EQUAL(scalar1.size(), 1);
+ VERIFY_IS_EQUAL(internal::array_prod(scalar1.dimensions()), 1);
+
+ scalar1() = 7.0;
+ scalar2() = 13.0;
+
+ // Test against shallow copy.
+ TensorFixedSize<float, Sizes<> > copy = scalar1;
+ VERIFY_IS_NOT_EQUAL(scalar1.data(), copy.data());
+ VERIFY_IS_APPROX(scalar1(), copy());
+ copy = scalar1;
+ VERIFY_IS_NOT_EQUAL(scalar1.data(), copy.data());
+ VERIFY_IS_APPROX(scalar1(), copy());
+
+ TensorFixedSize<float, Sizes<> > scalar3 = scalar1.sqrt();
+ TensorFixedSize<float, Sizes<>, RowMajor> scalar4 = scalar2.sqrt();
+ VERIFY_IS_EQUAL(scalar3.rank(), 0);
+ VERIFY_IS_APPROX(scalar3(), sqrtf(7.0));
+ VERIFY_IS_APPROX(scalar4(), sqrtf(13.0));
+
+ scalar3 = scalar1 + scalar2;
+ VERIFY_IS_APPROX(scalar3(), 7.0f + 13.0f);
+}
+
+static void test_1d()
+{
+ TensorFixedSize<float, Sizes<6> > vec1;
+ TensorFixedSize<float, Sizes<6>, RowMajor> vec2;
+
+ VERIFY_IS_EQUAL((vec1.size()), 6);
+ // VERIFY_IS_EQUAL((vec1.dimensions()[0]), 6);
+ // VERIFY_IS_EQUAL((vec1.dimension(0)), 6);
+
+ vec1(0) = 4.0; vec2(0) = 0.0;
+ vec1(1) = 8.0; vec2(1) = 1.0;
+ vec1(2) = 15.0; vec2(2) = 2.0;
+ vec1(3) = 16.0; vec2(3) = 3.0;
+ vec1(4) = 23.0; vec2(4) = 4.0;
+ vec1(5) = 42.0; vec2(5) = 5.0;
+
+ // Test against shallow copy.
+ TensorFixedSize<float, Sizes<6> > copy = vec1;
+ VERIFY_IS_NOT_EQUAL(vec1.data(), copy.data());
+ for (int i = 0; i < 6; ++i) {
+ VERIFY_IS_APPROX(vec1(i), copy(i));
+ }
+ copy = vec1;
+ VERIFY_IS_NOT_EQUAL(vec1.data(), copy.data());
+ for (int i = 0; i < 6; ++i) {
+ VERIFY_IS_APPROX(vec1(i), copy(i));
+ }
+
+ TensorFixedSize<float, Sizes<6> > vec3 = vec1.sqrt();
+ TensorFixedSize<float, Sizes<6>, RowMajor> vec4 = vec2.sqrt();
+
+ VERIFY_IS_EQUAL((vec3.size()), 6);
+ VERIFY_IS_EQUAL(vec3.rank(), 1);
+ // VERIFY_IS_EQUAL((vec3.dimensions()[0]), 6);
+ // VERIFY_IS_EQUAL((vec3.dimension(0)), 6);
+
+ VERIFY_IS_APPROX(vec3(0), sqrtf(4.0));
+ VERIFY_IS_APPROX(vec3(1), sqrtf(8.0));
+ VERIFY_IS_APPROX(vec3(2), sqrtf(15.0));
+ VERIFY_IS_APPROX(vec3(3), sqrtf(16.0));
+ VERIFY_IS_APPROX(vec3(4), sqrtf(23.0));
+ VERIFY_IS_APPROX(vec3(5), sqrtf(42.0));
+
+ VERIFY_IS_APPROX(vec4(0), sqrtf(0.0));
+ VERIFY_IS_APPROX(vec4(1), sqrtf(1.0));
+ VERIFY_IS_APPROX(vec4(2), sqrtf(2.0));
+ VERIFY_IS_APPROX(vec4(3), sqrtf(3.0));
+ VERIFY_IS_APPROX(vec4(4), sqrtf(4.0));
+ VERIFY_IS_APPROX(vec4(5), sqrtf(5.0));
+
+ vec3 = vec1 + vec2;
+ VERIFY_IS_APPROX(vec3(0), 4.0f + 0.0f);
+ VERIFY_IS_APPROX(vec3(1), 8.0f + 1.0f);
+ VERIFY_IS_APPROX(vec3(2), 15.0f + 2.0f);
+ VERIFY_IS_APPROX(vec3(3), 16.0f + 3.0f);
+ VERIFY_IS_APPROX(vec3(4), 23.0f + 4.0f);
+ VERIFY_IS_APPROX(vec3(5), 42.0f + 5.0f);
+}
+
+static void test_tensor_map()
+{
+ TensorFixedSize<float, Sizes<6> > vec1;
+ TensorFixedSize<float, Sizes<6>, RowMajor> vec2;
+
+ vec1(0) = 4.0; vec2(0) = 0.0;
+ vec1(1) = 8.0; vec2(1) = 1.0;
+ vec1(2) = 15.0; vec2(2) = 2.0;
+ vec1(3) = 16.0; vec2(3) = 3.0;
+ vec1(4) = 23.0; vec2(4) = 4.0;
+ vec1(5) = 42.0; vec2(5) = 5.0;
+
+ float data3[6];
+ TensorMap<TensorFixedSize<float, Sizes<6> > > vec3(data3, 6);
+ vec3 = vec1.sqrt() + vec2;
+
+ VERIFY_IS_APPROX(vec3(0), sqrtf(4.0));
+ VERIFY_IS_APPROX(vec3(1), sqrtf(8.0) + 1.0f);
+ VERIFY_IS_APPROX(vec3(2), sqrtf(15.0) + 2.0f);
+ VERIFY_IS_APPROX(vec3(3), sqrtf(16.0) + 3.0f);
+ VERIFY_IS_APPROX(vec3(4), sqrtf(23.0) + 4.0f);
+ VERIFY_IS_APPROX(vec3(5), sqrtf(42.0) + 5.0f);
+}
+
+static void test_2d()
+{
+ float data1[6];
+ TensorMap<TensorFixedSize<float, Sizes<2, 3> > > mat1(data1,2,3);
+ float data2[6];
+ TensorMap<TensorFixedSize<float, Sizes<2, 3>, RowMajor> > mat2(data2,2,3);
+
+ VERIFY_IS_EQUAL((mat1.size()), 2*3);
+ VERIFY_IS_EQUAL(mat1.rank(), 2);
+ // VERIFY_IS_EQUAL((mat1.dimension(0)), 2);
+ // VERIFY_IS_EQUAL((mat1.dimension(1)), 3);
+
+ mat1(0,0) = 0.0;
+ mat1(0,1) = 1.0;
+ mat1(0,2) = 2.0;
+ mat1(1,0) = 3.0;
+ mat1(1,1) = 4.0;
+ mat1(1,2) = 5.0;
+
+ mat2(0,0) = -0.0;
+ mat2(0,1) = -1.0;
+ mat2(0,2) = -2.0;
+ mat2(1,0) = -3.0;
+ mat2(1,1) = -4.0;
+ mat2(1,2) = -5.0;
+
+ TensorFixedSize<float, Sizes<2, 3> > mat3;
+ TensorFixedSize<float, Sizes<2, 3>, RowMajor> mat4;
+ mat3 = mat1.abs();
+ mat4 = mat2.abs();
+
+ VERIFY_IS_EQUAL((mat3.size()), 2*3);
+ // VERIFY_IS_EQUAL((mat3.dimension(0)), 2);
+ // VERIFY_IS_EQUAL((mat3.dimension(1)), 3);
+
+ VERIFY_IS_APPROX(mat3(0,0), 0.0f);
+ VERIFY_IS_APPROX(mat3(0,1), 1.0f);
+ VERIFY_IS_APPROX(mat3(0,2), 2.0f);
+ VERIFY_IS_APPROX(mat3(1,0), 3.0f);
+ VERIFY_IS_APPROX(mat3(1,1), 4.0f);
+ VERIFY_IS_APPROX(mat3(1,2), 5.0f);
+
+ VERIFY_IS_APPROX(mat4(0,0), 0.0f);
+ VERIFY_IS_APPROX(mat4(0,1), 1.0f);
+ VERIFY_IS_APPROX(mat4(0,2), 2.0f);
+ VERIFY_IS_APPROX(mat4(1,0), 3.0f);
+ VERIFY_IS_APPROX(mat4(1,1), 4.0f);
+ VERIFY_IS_APPROX(mat4(1,2), 5.0f);
+}
+
+static void test_3d()
+{
+ TensorFixedSize<float, Sizes<2, 3, 7> > mat1;
+ TensorFixedSize<float, Sizes<2, 3, 7>, RowMajor> mat2;
+
+ VERIFY_IS_EQUAL((mat1.size()), 2*3*7);
+ VERIFY_IS_EQUAL(mat1.rank(), 3);
+ // VERIFY_IS_EQUAL((mat1.dimension(0)), 2);
+ // VERIFY_IS_EQUAL((mat1.dimension(1)), 3);
+ // VERIFY_IS_EQUAL((mat1.dimension(2)), 7);
+
+ float val = 0.0f;
+ for (int i = 0; i < 2; ++i) {
+ for (int j = 0; j < 3; ++j) {
+ for (int k = 0; k < 7; ++k) {
+ mat1(i,j,k) = val;
+ mat2(i,j,k) = val;
+ val += 1.0f;
+ }
+ }
+ }
+
+ TensorFixedSize<float, Sizes<2, 3, 7> > mat3;
+ mat3 = mat1.sqrt();
+ TensorFixedSize<float, Sizes<2, 3, 7>, RowMajor> mat4;
+ mat4 = mat2.sqrt();
+
+ VERIFY_IS_EQUAL((mat3.size()), 2*3*7);
+ // VERIFY_IS_EQUAL((mat3.dimension(0)), 2);
+ // VERIFY_IS_EQUAL((mat3.dimension(1)), 3);
+ // VERIFY_IS_EQUAL((mat3.dimension(2)), 7);
+
+
+ val = 0.0f;
+ for (int i = 0; i < 2; ++i) {
+ for (int j = 0; j < 3; ++j) {
+ for (int k = 0; k < 7; ++k) {
+ VERIFY_IS_APPROX(mat3(i,j,k), sqrtf(val));
+ VERIFY_IS_APPROX(mat4(i,j,k), sqrtf(val));
+ val += 1.0f;
+ }
+ }
+ }
+}
+
+
+static void test_array()
+{
+ TensorFixedSize<float, Sizes<2, 3, 7> > mat1;
+ float val = 0.0f;
+ for (int i = 0; i < 2; ++i) {
+ for (int j = 0; j < 3; ++j) {
+ for (int k = 0; k < 7; ++k) {
+ mat1(i,j,k) = val;
+ val += 1.0f;
+ }
+ }
+ }
+
+ TensorFixedSize<float, Sizes<2, 3, 7> > mat3;
+ mat3 = mat1.pow(3.5f);
+
+ val = 0.0f;
+ for (int i = 0; i < 2; ++i) {
+ for (int j = 0; j < 3; ++j) {
+ for (int k = 0; k < 7; ++k) {
+ VERIFY_IS_APPROX(mat3(i,j,k), powf(val, 3.5f));
+ val += 1.0f;
+ }
+ }
+ }
+}
+
+EIGEN_DECLARE_TEST(cxx11_tensor_fixed_size)
+{
+ CALL_SUBTEST(test_0d());
+ CALL_SUBTEST(test_1d());
+ CALL_SUBTEST(test_tensor_map());
+ CALL_SUBTEST(test_2d());
+ CALL_SUBTEST(test_3d());
+ CALL_SUBTEST(test_array());
+}
diff --git a/unsupported/test/cxx11_tensor_forced_eval.cpp b/unsupported/test/cxx11_tensor_forced_eval.cpp
new file mode 100644
index 0000000..a21a02b
--- /dev/null
+++ b/unsupported/test/cxx11_tensor_forced_eval.cpp
@@ -0,0 +1,79 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "main.h"
+
+#include <Eigen/Core>
+#include <Eigen/CXX11/Tensor>
+
+using Eigen::MatrixXf;
+using Eigen::Tensor;
+
+static void test_simple()
+{
+ MatrixXf m1(3,3);
+ MatrixXf m2(3,3);
+ m1.setRandom();
+ m2.setRandom();
+
+ TensorMap<Tensor<float, 2> > mat1(m1.data(), 3,3);
+ TensorMap<Tensor<float, 2> > mat2(m2.data(), 3,3);
+
+ Tensor<float, 2> mat3(3,3);
+ mat3 = mat1;
+
+ typedef Tensor<float, 1>::DimensionPair DimPair;
+ Eigen::array<DimPair, 1> dims;
+ dims[0] = DimPair(1, 0);
+
+ mat3 = mat3.contract(mat2, dims).eval();
+
+ VERIFY_IS_APPROX(mat3(0, 0), (m1*m2).eval()(0,0));
+ VERIFY_IS_APPROX(mat3(0, 1), (m1*m2).eval()(0,1));
+ VERIFY_IS_APPROX(mat3(0, 2), (m1*m2).eval()(0,2));
+ VERIFY_IS_APPROX(mat3(1, 0), (m1*m2).eval()(1,0));
+ VERIFY_IS_APPROX(mat3(1, 1), (m1*m2).eval()(1,1));
+ VERIFY_IS_APPROX(mat3(1, 2), (m1*m2).eval()(1,2));
+ VERIFY_IS_APPROX(mat3(2, 0), (m1*m2).eval()(2,0));
+ VERIFY_IS_APPROX(mat3(2, 1), (m1*m2).eval()(2,1));
+ VERIFY_IS_APPROX(mat3(2, 2), (m1*m2).eval()(2,2));
+}
+
+
+static void test_const()
+{
+ MatrixXf input(3,3);
+ input.setRandom();
+ MatrixXf output = input;
+ output.rowwise() -= input.colwise().maxCoeff();
+
+ Eigen::array<int, 1> depth_dim;
+ depth_dim[0] = 0;
+ Tensor<float, 2>::Dimensions dims2d;
+ dims2d[0] = 1;
+ dims2d[1] = 3;
+ Eigen::array<int, 2> bcast;
+ bcast[0] = 3;
+ bcast[1] = 1;
+ const TensorMap<const Tensor<float, 2> > input_tensor(input.data(), 3, 3);
+ Tensor<float, 2> output_tensor= (input_tensor - input_tensor.maximum(depth_dim).eval().reshape(dims2d).broadcast(bcast));
+
+ for (int i = 0; i < 3; ++i) {
+ for (int j = 0; j < 3; ++j) {
+ VERIFY_IS_APPROX(output(i, j), output_tensor(i, j));
+ }
+ }
+}
+
+
+EIGEN_DECLARE_TEST(cxx11_tensor_forced_eval)
+{
+ CALL_SUBTEST(test_simple());
+ CALL_SUBTEST(test_const());
+}
diff --git a/unsupported/test/cxx11_tensor_forced_eval_sycl.cpp b/unsupported/test/cxx11_tensor_forced_eval_sycl.cpp
new file mode 100644
index 0000000..a55a5ad
--- /dev/null
+++ b/unsupported/test/cxx11_tensor_forced_eval_sycl.cpp
@@ -0,0 +1,77 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2016
+// Mehdi Goli Codeplay Software Ltd.
+// Ralph Potter Codeplay Software Ltd.
+// Luke Iwanski Codeplay Software Ltd.
+// Contact: <eigen@codeplay.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#define EIGEN_TEST_NO_LONGDOUBLE
+#define EIGEN_TEST_NO_COMPLEX
+
+#define EIGEN_DEFAULT_DENSE_INDEX_TYPE int64_t
+#define EIGEN_USE_SYCL
+
+#include "main.h"
+#include <unsupported/Eigen/CXX11/Tensor>
+
+using Eigen::Tensor;
+template <typename DataType, int DataLayout, typename IndexType>
+void test_forced_eval_sycl(const Eigen::SyclDevice &sycl_device) {
+
+ IndexType sizeDim1 = 100;
+ IndexType sizeDim2 = 20;
+ IndexType sizeDim3 = 20;
+ Eigen::array<IndexType, 3> tensorRange = {{sizeDim1, sizeDim2, sizeDim3}};
+ Eigen::Tensor<DataType, 3, DataLayout, IndexType> in1(tensorRange);
+ Eigen::Tensor<DataType, 3, DataLayout, IndexType> in2(tensorRange);
+ Eigen::Tensor<DataType, 3, DataLayout, IndexType> out(tensorRange);
+
+ DataType * gpu_in1_data = static_cast<DataType*>(sycl_device.allocate(in1.dimensions().TotalSize()*sizeof(DataType)));
+ DataType * gpu_in2_data = static_cast<DataType*>(sycl_device.allocate(in2.dimensions().TotalSize()*sizeof(DataType)));
+ DataType * gpu_out_data = static_cast<DataType*>(sycl_device.allocate(out.dimensions().TotalSize()*sizeof(DataType)));
+
+ in1 = in1.random() + in1.constant(static_cast<DataType>(10.0f));
+ in2 = in2.random() + in2.constant(static_cast<DataType>(10.0f));
+
+ // creating TensorMap from tensor
+ Eigen::TensorMap<Eigen::Tensor<DataType, 3, DataLayout, IndexType>> gpu_in1(gpu_in1_data, tensorRange);
+ Eigen::TensorMap<Eigen::Tensor<DataType, 3, DataLayout, IndexType>> gpu_in2(gpu_in2_data, tensorRange);
+ Eigen::TensorMap<Eigen::Tensor<DataType, 3, DataLayout, IndexType>> gpu_out(gpu_out_data, tensorRange);
+ sycl_device.memcpyHostToDevice(gpu_in1_data, in1.data(),(in1.dimensions().TotalSize())*sizeof(DataType));
+ sycl_device.memcpyHostToDevice(gpu_in2_data, in2.data(),(in2.dimensions().TotalSize())*sizeof(DataType));
+ /// c=(a+b)*b
+ gpu_out.device(sycl_device) =(gpu_in1 + gpu_in2).eval() * gpu_in2;
+ sycl_device.memcpyDeviceToHost(out.data(), gpu_out_data,(out.dimensions().TotalSize())*sizeof(DataType));
+ for (IndexType i = 0; i < sizeDim1; ++i) {
+ for (IndexType j = 0; j < sizeDim2; ++j) {
+ for (IndexType k = 0; k < sizeDim3; ++k) {
+ VERIFY_IS_APPROX(out(i, j, k),
+ (in1(i, j, k) + in2(i, j, k)) * in2(i, j, k));
+ }
+ }
+ }
+ printf("(a+b)*b Test Passed\n");
+ sycl_device.deallocate(gpu_in1_data);
+ sycl_device.deallocate(gpu_in2_data);
+ sycl_device.deallocate(gpu_out_data);
+
+}
+
+template <typename DataType, typename Dev_selector> void tensorForced_evalperDevice(Dev_selector s){
+ QueueInterface queueInterface(s);
+ auto sycl_device = Eigen::SyclDevice(&queueInterface);
+ test_forced_eval_sycl<DataType, RowMajor, int64_t>(sycl_device);
+ test_forced_eval_sycl<DataType, ColMajor, int64_t>(sycl_device);
+}
+EIGEN_DECLARE_TEST(cxx11_tensor_forced_eval_sycl) {
+ for (const auto& device :Eigen::get_sycl_supported_devices()) {
+ CALL_SUBTEST(tensorForced_evalperDevice<float>(device));
+ CALL_SUBTEST(tensorForced_evalperDevice<half>(device));
+ }
+}
diff --git a/unsupported/test/cxx11_tensor_generator.cpp b/unsupported/test/cxx11_tensor_generator.cpp
new file mode 100644
index 0000000..6dcf676
--- /dev/null
+++ b/unsupported/test/cxx11_tensor_generator.cpp
@@ -0,0 +1,91 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2015 Benoit Steiner <benoit.steiner.goog@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "main.h"
+
+#include <Eigen/CXX11/Tensor>
+
+struct Generator1D {
+ Generator1D() { }
+
+ float operator()(const array<Eigen::DenseIndex, 1>& coordinates) const {
+ return coordinates[0];
+ }
+};
+
+template <int DataLayout>
+static void test_1D()
+{
+ Tensor<float, 1> vec(6);
+ Tensor<float, 1> result = vec.generate(Generator1D());
+
+ for (int i = 0; i < 6; ++i) {
+ VERIFY_IS_EQUAL(result(i), i);
+ }
+}
+
+
+struct Generator2D {
+ Generator2D() { }
+
+ float operator()(const array<Eigen::DenseIndex, 2>& coordinates) const {
+ return 3 * coordinates[0] + 11 * coordinates[1];
+ }
+};
+
+template <int DataLayout>
+static void test_2D()
+{
+ Tensor<float, 2> matrix(512, 512);
+ Tensor<float, 2> result = matrix.generate(Generator2D());
+
+ for (int i = 0; i < 512; ++i) {
+ for (int j = 0; j < 512; ++j) {
+ VERIFY_IS_EQUAL(result(i, j), 3*i + 11*j);
+ }
+ }
+}
+
+
+template <int DataLayout>
+static void test_gaussian()
+{
+ int rows = 32;
+ int cols = 48;
+ array<float, 2> means;
+ means[0] = rows / 2.0f;
+ means[1] = cols / 2.0f;
+ array<float, 2> std_devs;
+ std_devs[0] = 3.14f;
+ std_devs[1] = 2.7f;
+ internal::GaussianGenerator<float, Eigen::DenseIndex, 2> gaussian_gen(means, std_devs);
+
+ Tensor<float, 2> matrix(rows, cols);
+ Tensor<float, 2> result = matrix.generate(gaussian_gen);
+
+ for (int i = 0; i < rows; ++i) {
+ for (int j = 0; j < cols; ++j) {
+ float g_rows = powf(rows/2.0f - i, 2) / (3.14f * 3.14f) * 0.5f;
+ float g_cols = powf(cols/2.0f - j, 2) / (2.7f * 2.7f) * 0.5f;
+ float gaussian = expf(-g_rows - g_cols);
+ VERIFY_IS_EQUAL(result(i, j), gaussian);
+ }
+ }
+}
+
+
+EIGEN_DECLARE_TEST(cxx11_tensor_generator)
+{
+ CALL_SUBTEST(test_1D<ColMajor>());
+ CALL_SUBTEST(test_1D<RowMajor>());
+ CALL_SUBTEST(test_2D<ColMajor>());
+ CALL_SUBTEST(test_2D<RowMajor>());
+ CALL_SUBTEST(test_gaussian<ColMajor>());
+ CALL_SUBTEST(test_gaussian<RowMajor>());
+}
diff --git a/unsupported/test/cxx11_tensor_generator_sycl.cpp b/unsupported/test/cxx11_tensor_generator_sycl.cpp
new file mode 100644
index 0000000..fb6e3d9
--- /dev/null
+++ b/unsupported/test/cxx11_tensor_generator_sycl.cpp
@@ -0,0 +1,147 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2016
+// Mehdi Goli Codeplay Software Ltd.
+// Ralph Potter Codeplay Software Ltd.
+// Luke Iwanski Codeplay Software Ltd.
+// Contact: <eigen@codeplay.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#define EIGEN_TEST_NO_LONGDOUBLE
+#define EIGEN_TEST_NO_COMPLEX
+
+#define EIGEN_DEFAULT_DENSE_INDEX_TYPE int64_t
+#define EIGEN_USE_SYCL
+static const float error_threshold =1e-8f;
+
+#include "main.h"
+#include <unsupported/Eigen/CXX11/Tensor>
+
+using Eigen::Tensor;
+struct Generator1D {
+ Generator1D() { }
+
+ float operator()(const array<Eigen::DenseIndex, 1>& coordinates) const {
+ return coordinates[0];
+ }
+};
+
+template <typename DataType, int DataLayout, typename IndexType>
+static void test_1D_sycl(const Eigen::SyclDevice& sycl_device)
+{
+
+ IndexType sizeDim1 = 6;
+ array<IndexType, 1> tensorRange = {{sizeDim1}};
+ Tensor<DataType, 1, DataLayout,IndexType> vec(tensorRange);
+ Tensor<DataType, 1, DataLayout,IndexType> result(tensorRange);
+
+ const size_t tensorBuffSize =vec.size()*sizeof(DataType);
+ DataType* gpu_data_vec = static_cast<DataType*>(sycl_device.allocate(tensorBuffSize));
+ DataType* gpu_data_result = static_cast<DataType*>(sycl_device.allocate(tensorBuffSize));
+
+ TensorMap<Tensor<DataType, 1, DataLayout,IndexType>> gpu_vec(gpu_data_vec, tensorRange);
+ TensorMap<Tensor<DataType, 1, DataLayout,IndexType>> gpu_result(gpu_data_result, tensorRange);
+
+ sycl_device.memcpyHostToDevice(gpu_data_vec, vec.data(), tensorBuffSize);
+ gpu_result.device(sycl_device)=gpu_vec.generate(Generator1D());
+ sycl_device.memcpyDeviceToHost(result.data(), gpu_data_result, tensorBuffSize);
+
+ for (IndexType i = 0; i < 6; ++i) {
+ VERIFY_IS_EQUAL(result(i), i);
+ }
+}
+
+
+struct Generator2D {
+ Generator2D() { }
+
+ float operator()(const array<Eigen::DenseIndex, 2>& coordinates) const {
+ return 3 * coordinates[0] + 11 * coordinates[1];
+ }
+};
+
+template <typename DataType, int DataLayout, typename IndexType>
+static void test_2D_sycl(const Eigen::SyclDevice& sycl_device)
+{
+ IndexType sizeDim1 = 5;
+ IndexType sizeDim2 = 7;
+ array<IndexType, 2> tensorRange = {{sizeDim1, sizeDim2}};
+ Tensor<DataType, 2, DataLayout,IndexType> matrix(tensorRange);
+ Tensor<DataType, 2, DataLayout,IndexType> result(tensorRange);
+
+ const size_t tensorBuffSize =matrix.size()*sizeof(DataType);
+ DataType* gpu_data_matrix = static_cast<DataType*>(sycl_device.allocate(tensorBuffSize));
+ DataType* gpu_data_result = static_cast<DataType*>(sycl_device.allocate(tensorBuffSize));
+
+ TensorMap<Tensor<DataType, 2, DataLayout,IndexType>> gpu_matrix(gpu_data_matrix, tensorRange);
+ TensorMap<Tensor<DataType, 2, DataLayout,IndexType>> gpu_result(gpu_data_result, tensorRange);
+
+ sycl_device.memcpyHostToDevice(gpu_data_matrix, matrix.data(), tensorBuffSize);
+ gpu_result.device(sycl_device)=gpu_matrix.generate(Generator2D());
+ sycl_device.memcpyDeviceToHost(result.data(), gpu_data_result, tensorBuffSize);
+
+ for (IndexType i = 0; i < 5; ++i) {
+ for (IndexType j = 0; j < 5; ++j) {
+ VERIFY_IS_EQUAL(result(i, j), 3*i + 11*j);
+ }
+ }
+}
+
+template <typename DataType, int DataLayout, typename IndexType>
+static void test_gaussian_sycl(const Eigen::SyclDevice& sycl_device)
+{
+ IndexType rows = 32;
+ IndexType cols = 48;
+ array<DataType, 2> means;
+ means[0] = rows / 2.0f;
+ means[1] = cols / 2.0f;
+ array<DataType, 2> std_devs;
+ std_devs[0] = 3.14f;
+ std_devs[1] = 2.7f;
+ internal::GaussianGenerator<DataType, Eigen::DenseIndex, 2> gaussian_gen(means, std_devs);
+
+ array<IndexType, 2> tensorRange = {{rows, cols}};
+ Tensor<DataType, 2, DataLayout,IndexType> matrix(tensorRange);
+ Tensor<DataType, 2, DataLayout,IndexType> result(tensorRange);
+
+ const size_t tensorBuffSize =matrix.size()*sizeof(DataType);
+ DataType* gpu_data_matrix = static_cast<DataType*>(sycl_device.allocate(tensorBuffSize));
+ DataType* gpu_data_result = static_cast<DataType*>(sycl_device.allocate(tensorBuffSize));
+
+ TensorMap<Tensor<DataType, 2, DataLayout,IndexType>> gpu_matrix(gpu_data_matrix, tensorRange);
+ TensorMap<Tensor<DataType, 2, DataLayout,IndexType>> gpu_result(gpu_data_result, tensorRange);
+
+ sycl_device.memcpyHostToDevice(gpu_data_matrix, matrix.data(), tensorBuffSize);
+ gpu_result.device(sycl_device)=gpu_matrix.generate(gaussian_gen);
+ sycl_device.memcpyDeviceToHost(result.data(), gpu_data_result, tensorBuffSize);
+
+ for (IndexType i = 0; i < rows; ++i) {
+ for (IndexType j = 0; j < cols; ++j) {
+ DataType g_rows = powf(rows/2.0f - i, 2) / (3.14f * 3.14f) * 0.5f;
+ DataType g_cols = powf(cols/2.0f - j, 2) / (2.7f * 2.7f) * 0.5f;
+ DataType gaussian = expf(-g_rows - g_cols);
+ Eigen::internal::isApprox(result(i, j), gaussian, error_threshold);
+ }
+ }
+}
+
+template<typename DataType, typename dev_Selector> void sycl_generator_test_per_device(dev_Selector s){
+ QueueInterface queueInterface(s);
+ auto sycl_device = Eigen::SyclDevice(&queueInterface);
+ test_1D_sycl<DataType, RowMajor, int64_t>(sycl_device);
+ test_1D_sycl<DataType, ColMajor, int64_t>(sycl_device);
+ test_2D_sycl<DataType, RowMajor, int64_t>(sycl_device);
+ test_2D_sycl<DataType, ColMajor, int64_t>(sycl_device);
+ test_gaussian_sycl<DataType, RowMajor, int64_t>(sycl_device);
+ test_gaussian_sycl<DataType, ColMajor, int64_t>(sycl_device);
+}
+EIGEN_DECLARE_TEST(cxx11_tensor_generator_sycl)
+{
+ for (const auto& device :Eigen::get_sycl_supported_devices()) {
+ CALL_SUBTEST(sycl_generator_test_per_device<float>(device));
+ }
+}
diff --git a/unsupported/test/cxx11_tensor_gpu.cu b/unsupported/test/cxx11_tensor_gpu.cu
new file mode 100644
index 0000000..7b3fb5a
--- /dev/null
+++ b/unsupported/test/cxx11_tensor_gpu.cu
@@ -0,0 +1,1663 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#define EIGEN_TEST_NO_LONGDOUBLE
+#define EIGEN_TEST_NO_COMPLEX
+
+#define EIGEN_USE_GPU
+
+#include "main.h"
+#include <unsupported/Eigen/CXX11/Tensor>
+
+#include <unsupported/Eigen/CXX11/src/Tensor/TensorGpuHipCudaDefines.h>
+
+using Eigen::Tensor;
+
+void test_gpu_nullary() {
+ Tensor<float, 1, 0, int> in1(2);
+ Tensor<float, 1, 0, int> in2(2);
+ in1.setRandom();
+ in2.setRandom();
+
+ std::size_t tensor_bytes = in1.size() * sizeof(float);
+
+ float* d_in1;
+ float* d_in2;
+ gpuMalloc((void**)(&d_in1), tensor_bytes);
+ gpuMalloc((void**)(&d_in2), tensor_bytes);
+ gpuMemcpy(d_in1, in1.data(), tensor_bytes, gpuMemcpyHostToDevice);
+ gpuMemcpy(d_in2, in2.data(), tensor_bytes, gpuMemcpyHostToDevice);
+
+ Eigen::GpuStreamDevice stream;
+ Eigen::GpuDevice gpu_device(&stream);
+
+ Eigen::TensorMap<Eigen::Tensor<float, 1, 0, int>, Eigen::Aligned> gpu_in1(
+ d_in1, 2);
+ Eigen::TensorMap<Eigen::Tensor<float, 1, 0, int>, Eigen::Aligned> gpu_in2(
+ d_in2, 2);
+
+ gpu_in1.device(gpu_device) = gpu_in1.constant(3.14f);
+ gpu_in2.device(gpu_device) = gpu_in2.random();
+
+ Tensor<float, 1, 0, int> new1(2);
+ Tensor<float, 1, 0, int> new2(2);
+
+ assert(gpuMemcpyAsync(new1.data(), d_in1, tensor_bytes, gpuMemcpyDeviceToHost,
+ gpu_device.stream()) == gpuSuccess);
+ assert(gpuMemcpyAsync(new2.data(), d_in2, tensor_bytes, gpuMemcpyDeviceToHost,
+ gpu_device.stream()) == gpuSuccess);
+
+ assert(gpuStreamSynchronize(gpu_device.stream()) == gpuSuccess);
+
+ for (int i = 0; i < 2; ++i) {
+ VERIFY_IS_APPROX(new1(i), 3.14f);
+ VERIFY_IS_NOT_EQUAL(new2(i), in2(i));
+ }
+
+ gpuFree(d_in1);
+ gpuFree(d_in2);
+}
+
+// Tests that there are no indexing overflows when computing tensors with the
+// max representable size.
+template <typename IndexType,
+ IndexType N = (std::numeric_limits<IndexType>::max)()>
+void test_gpu_nullary_max_size()
+{
+ typedef int8_t DataType;
+ typedef Tensor<DataType, 1, 0, IndexType> TensorType;
+ typedef Eigen::array<IndexType, 1> ArrayType;
+
+ const IndexType n = N;
+ TensorType in1((ArrayType(n)));
+ in1.setZero();
+
+ std::size_t in1_bytes = in1.size() * sizeof(DataType);
+
+ DataType* d_in1;
+ gpuMalloc((void**)(&d_in1), in1_bytes);
+
+ gpuMemcpy(d_in1, in1.data(), in1_bytes, gpuMemcpyHostToDevice);
+
+ Eigen::GpuStreamDevice stream;
+ Eigen::GpuDevice gpu_device(&stream);
+
+ Eigen::TensorMap<TensorType> gpu_in1(d_in1, ArrayType(n));
+
+ gpu_in1.device(gpu_device) = gpu_in1.constant(123);
+
+ TensorType new1((ArrayType(n)));
+
+ assert(gpuMemcpyAsync(new1.data(), d_in1, in1_bytes, gpuMemcpyDeviceToHost,
+ gpu_device.stream()) == gpuSuccess);
+ assert(gpuStreamSynchronize(gpu_device.stream()) == gpuSuccess);
+
+ for (IndexType i = 0; i < n; ++i) {
+ VERIFY_IS_EQUAL(new1(ArrayType(i)), 123);
+ }
+
+ gpuFree(d_in1);
+}
+
+void test_gpu_elementwise_small() {
+ Tensor<float, 1> in1(Eigen::array<Eigen::DenseIndex, 1>(2));
+ Tensor<float, 1> in2(Eigen::array<Eigen::DenseIndex, 1>(2));
+ Tensor<float, 1> out(Eigen::array<Eigen::DenseIndex, 1>(2));
+ in1.setRandom();
+ in2.setRandom();
+
+ std::size_t in1_bytes = in1.size() * sizeof(float);
+ std::size_t in2_bytes = in2.size() * sizeof(float);
+ std::size_t out_bytes = out.size() * sizeof(float);
+
+ float* d_in1;
+ float* d_in2;
+ float* d_out;
+ gpuMalloc((void**)(&d_in1), in1_bytes);
+ gpuMalloc((void**)(&d_in2), in2_bytes);
+ gpuMalloc((void**)(&d_out), out_bytes);
+
+ gpuMemcpy(d_in1, in1.data(), in1_bytes, gpuMemcpyHostToDevice);
+ gpuMemcpy(d_in2, in2.data(), in2_bytes, gpuMemcpyHostToDevice);
+
+ Eigen::GpuStreamDevice stream;
+ Eigen::GpuDevice gpu_device(&stream);
+
+ Eigen::TensorMap<Eigen::Tensor<float, 1>, Eigen::Aligned> gpu_in1(
+ d_in1, Eigen::array<Eigen::DenseIndex, 1>(2));
+ Eigen::TensorMap<Eigen::Tensor<float, 1>, Eigen::Aligned> gpu_in2(
+ d_in2, Eigen::array<Eigen::DenseIndex, 1>(2));
+ Eigen::TensorMap<Eigen::Tensor<float, 1>, Eigen::Aligned> gpu_out(
+ d_out, Eigen::array<Eigen::DenseIndex, 1>(2));
+
+ gpu_out.device(gpu_device) = gpu_in1 + gpu_in2;
+
+ assert(gpuMemcpyAsync(out.data(), d_out, out_bytes, gpuMemcpyDeviceToHost,
+ gpu_device.stream()) == gpuSuccess);
+ assert(gpuStreamSynchronize(gpu_device.stream()) == gpuSuccess);
+
+ for (int i = 0; i < 2; ++i) {
+ VERIFY_IS_APPROX(
+ out(Eigen::array<Eigen::DenseIndex, 1>(i)),
+ in1(Eigen::array<Eigen::DenseIndex, 1>(i)) + in2(Eigen::array<Eigen::DenseIndex, 1>(i)));
+ }
+
+ gpuFree(d_in1);
+ gpuFree(d_in2);
+ gpuFree(d_out);
+}
+
+void test_gpu_elementwise()
+{
+ Tensor<float, 3> in1(Eigen::array<Eigen::DenseIndex, 3>(72,53,97));
+ Tensor<float, 3> in2(Eigen::array<Eigen::DenseIndex, 3>(72,53,97));
+ Tensor<float, 3> in3(Eigen::array<Eigen::DenseIndex, 3>(72,53,97));
+ Tensor<float, 3> out(Eigen::array<Eigen::DenseIndex, 3>(72,53,97));
+ in1.setRandom();
+ in2.setRandom();
+ in3.setRandom();
+
+ std::size_t in1_bytes = in1.size() * sizeof(float);
+ std::size_t in2_bytes = in2.size() * sizeof(float);
+ std::size_t in3_bytes = in3.size() * sizeof(float);
+ std::size_t out_bytes = out.size() * sizeof(float);
+
+ float* d_in1;
+ float* d_in2;
+ float* d_in3;
+ float* d_out;
+ gpuMalloc((void**)(&d_in1), in1_bytes);
+ gpuMalloc((void**)(&d_in2), in2_bytes);
+ gpuMalloc((void**)(&d_in3), in3_bytes);
+ gpuMalloc((void**)(&d_out), out_bytes);
+
+ gpuMemcpy(d_in1, in1.data(), in1_bytes, gpuMemcpyHostToDevice);
+ gpuMemcpy(d_in2, in2.data(), in2_bytes, gpuMemcpyHostToDevice);
+ gpuMemcpy(d_in3, in3.data(), in3_bytes, gpuMemcpyHostToDevice);
+
+ Eigen::GpuStreamDevice stream;
+ Eigen::GpuDevice gpu_device(&stream);
+
+ Eigen::TensorMap<Eigen::Tensor<float, 3> > gpu_in1(d_in1, Eigen::array<Eigen::DenseIndex, 3>(72,53,97));
+ Eigen::TensorMap<Eigen::Tensor<float, 3> > gpu_in2(d_in2, Eigen::array<Eigen::DenseIndex, 3>(72,53,97));
+ Eigen::TensorMap<Eigen::Tensor<float, 3> > gpu_in3(d_in3, Eigen::array<Eigen::DenseIndex, 3>(72,53,97));
+ Eigen::TensorMap<Eigen::Tensor<float, 3> > gpu_out(d_out, Eigen::array<Eigen::DenseIndex, 3>(72,53,97));
+
+ gpu_out.device(gpu_device) = gpu_in1 + gpu_in2 * gpu_in3;
+
+ assert(gpuMemcpyAsync(out.data(), d_out, out_bytes, gpuMemcpyDeviceToHost, gpu_device.stream()) == gpuSuccess);
+ assert(gpuStreamSynchronize(gpu_device.stream()) == gpuSuccess);
+
+ for (int i = 0; i < 72; ++i) {
+ for (int j = 0; j < 53; ++j) {
+ for (int k = 0; k < 97; ++k) {
+ VERIFY_IS_APPROX(out(Eigen::array<Eigen::DenseIndex, 3>(i,j,k)), in1(Eigen::array<Eigen::DenseIndex, 3>(i,j,k)) + in2(Eigen::array<Eigen::DenseIndex, 3>(i,j,k)) * in3(Eigen::array<Eigen::DenseIndex, 3>(i,j,k)));
+ }
+ }
+ }
+
+ gpuFree(d_in1);
+ gpuFree(d_in2);
+ gpuFree(d_in3);
+ gpuFree(d_out);
+}
+
+void test_gpu_props() {
+ Tensor<float, 1> in1(200);
+ Tensor<bool, 1> out(200);
+ in1.setRandom();
+
+ std::size_t in1_bytes = in1.size() * sizeof(float);
+ std::size_t out_bytes = out.size() * sizeof(bool);
+
+ float* d_in1;
+ bool* d_out;
+ gpuMalloc((void**)(&d_in1), in1_bytes);
+ gpuMalloc((void**)(&d_out), out_bytes);
+
+ gpuMemcpy(d_in1, in1.data(), in1_bytes, gpuMemcpyHostToDevice);
+
+ Eigen::GpuStreamDevice stream;
+ Eigen::GpuDevice gpu_device(&stream);
+
+ Eigen::TensorMap<Eigen::Tensor<float, 1>, Eigen::Aligned> gpu_in1(
+ d_in1, 200);
+ Eigen::TensorMap<Eigen::Tensor<bool, 1>, Eigen::Aligned> gpu_out(
+ d_out, 200);
+
+ gpu_out.device(gpu_device) = (gpu_in1.isnan)();
+
+ assert(gpuMemcpyAsync(out.data(), d_out, out_bytes, gpuMemcpyDeviceToHost,
+ gpu_device.stream()) == gpuSuccess);
+ assert(gpuStreamSynchronize(gpu_device.stream()) == gpuSuccess);
+
+ for (int i = 0; i < 200; ++i) {
+ VERIFY_IS_EQUAL(out(i), (std::isnan)(in1(i)));
+ }
+
+ gpuFree(d_in1);
+ gpuFree(d_out);
+}
+
+void test_gpu_reduction()
+{
+ Tensor<float, 4> in1(72,53,97,113);
+ Tensor<float, 2> out(72,97);
+ in1.setRandom();
+
+ std::size_t in1_bytes = in1.size() * sizeof(float);
+ std::size_t out_bytes = out.size() * sizeof(float);
+
+ float* d_in1;
+ float* d_out;
+ gpuMalloc((void**)(&d_in1), in1_bytes);
+ gpuMalloc((void**)(&d_out), out_bytes);
+
+ gpuMemcpy(d_in1, in1.data(), in1_bytes, gpuMemcpyHostToDevice);
+
+ Eigen::GpuStreamDevice stream;
+ Eigen::GpuDevice gpu_device(&stream);
+
+ Eigen::TensorMap<Eigen::Tensor<float, 4> > gpu_in1(d_in1, 72,53,97,113);
+ Eigen::TensorMap<Eigen::Tensor<float, 2> > gpu_out(d_out, 72,97);
+
+ array<Eigen::DenseIndex, 2> reduction_axis;
+ reduction_axis[0] = 1;
+ reduction_axis[1] = 3;
+
+ gpu_out.device(gpu_device) = gpu_in1.maximum(reduction_axis);
+
+ assert(gpuMemcpyAsync(out.data(), d_out, out_bytes, gpuMemcpyDeviceToHost, gpu_device.stream()) == gpuSuccess);
+ assert(gpuStreamSynchronize(gpu_device.stream()) == gpuSuccess);
+
+ for (int i = 0; i < 72; ++i) {
+ for (int j = 0; j < 97; ++j) {
+ float expected = 0;
+ for (int k = 0; k < 53; ++k) {
+ for (int l = 0; l < 113; ++l) {
+ expected =
+ std::max<float>(expected, in1(i, k, j, l));
+ }
+ }
+ VERIFY_IS_APPROX(out(i,j), expected);
+ }
+ }
+
+ gpuFree(d_in1);
+ gpuFree(d_out);
+}
+
+template<int DataLayout>
+void test_gpu_contraction()
+{
+ // with these dimensions, the output has 300 * 140 elements, which is
+ // more than 30 * 1024, which is the number of threads in blocks on
+ // a 15 SM GK110 GPU
+ Tensor<float, 4, DataLayout> t_left(6, 50, 3, 31);
+ Tensor<float, 5, DataLayout> t_right(Eigen::array<Eigen::DenseIndex, 5>(3, 31, 7, 20, 1));
+ Tensor<float, 5, DataLayout> t_result(Eigen::array<Eigen::DenseIndex, 5>(6, 50, 7, 20, 1));
+
+ t_left.setRandom();
+ t_right.setRandom();
+
+ std::size_t t_left_bytes = t_left.size() * sizeof(float);
+ std::size_t t_right_bytes = t_right.size() * sizeof(float);
+ std::size_t t_result_bytes = t_result.size() * sizeof(float);
+
+ float* d_t_left;
+ float* d_t_right;
+ float* d_t_result;
+
+ gpuMalloc((void**)(&d_t_left), t_left_bytes);
+ gpuMalloc((void**)(&d_t_right), t_right_bytes);
+ gpuMalloc((void**)(&d_t_result), t_result_bytes);
+
+ gpuMemcpy(d_t_left, t_left.data(), t_left_bytes, gpuMemcpyHostToDevice);
+ gpuMemcpy(d_t_right, t_right.data(), t_right_bytes, gpuMemcpyHostToDevice);
+
+ Eigen::GpuStreamDevice stream;
+ Eigen::GpuDevice gpu_device(&stream);
+
+ Eigen::TensorMap<Eigen::Tensor<float, 4, DataLayout> > gpu_t_left(d_t_left, 6, 50, 3, 31);
+ Eigen::TensorMap<Eigen::Tensor<float, 5, DataLayout> > gpu_t_right(d_t_right, 3, 31, 7, 20, 1);
+ Eigen::TensorMap<Eigen::Tensor<float, 5, DataLayout> > gpu_t_result(d_t_result, 6, 50, 7, 20, 1);
+
+ typedef Eigen::Map<Eigen::Matrix<float, Dynamic, Dynamic, DataLayout> > MapXf;
+ MapXf m_left(t_left.data(), 300, 93);
+ MapXf m_right(t_right.data(), 93, 140);
+ Eigen::Matrix<float, Dynamic, Dynamic, DataLayout> m_result(300, 140);
+
+ typedef Tensor<float, 1>::DimensionPair DimPair;
+ Eigen::array<DimPair, 2> dims;
+ dims[0] = DimPair(2, 0);
+ dims[1] = DimPair(3, 1);
+
+ m_result = m_left * m_right;
+ gpu_t_result.device(gpu_device) = gpu_t_left.contract(gpu_t_right, dims);
+
+ gpuMemcpy(t_result.data(), d_t_result, t_result_bytes, gpuMemcpyDeviceToHost);
+
+ for (DenseIndex i = 0; i < t_result.size(); i++) {
+ if (fabs(t_result.data()[i] - m_result.data()[i]) >= 1e-4f) {
+ std::cout << "mismatch detected at index " << i << ": " << t_result.data()[i] << " vs " << m_result.data()[i] << std::endl;
+ assert(false);
+ }
+ }
+
+ gpuFree(d_t_left);
+ gpuFree(d_t_right);
+ gpuFree(d_t_result);
+}
+
+template<int DataLayout>
+void test_gpu_convolution_1d()
+{
+ Tensor<float, 4, DataLayout> input(74,37,11,137);
+ Tensor<float, 1, DataLayout> kernel(4);
+ Tensor<float, 4, DataLayout> out(74,34,11,137);
+ input = input.constant(10.0f) + input.random();
+ kernel = kernel.constant(7.0f) + kernel.random();
+
+ std::size_t input_bytes = input.size() * sizeof(float);
+ std::size_t kernel_bytes = kernel.size() * sizeof(float);
+ std::size_t out_bytes = out.size() * sizeof(float);
+
+ float* d_input;
+ float* d_kernel;
+ float* d_out;
+ gpuMalloc((void**)(&d_input), input_bytes);
+ gpuMalloc((void**)(&d_kernel), kernel_bytes);
+ gpuMalloc((void**)(&d_out), out_bytes);
+
+ gpuMemcpy(d_input, input.data(), input_bytes, gpuMemcpyHostToDevice);
+ gpuMemcpy(d_kernel, kernel.data(), kernel_bytes, gpuMemcpyHostToDevice);
+
+ Eigen::GpuStreamDevice stream;
+ Eigen::GpuDevice gpu_device(&stream);
+
+ Eigen::TensorMap<Eigen::Tensor<float, 4, DataLayout> > gpu_input(d_input, 74,37,11,137);
+ Eigen::TensorMap<Eigen::Tensor<float, 1, DataLayout> > gpu_kernel(d_kernel, 4);
+ Eigen::TensorMap<Eigen::Tensor<float, 4, DataLayout> > gpu_out(d_out, 74,34,11,137);
+
+ Eigen::array<Eigen::DenseIndex, 1> dims(1);
+ gpu_out.device(gpu_device) = gpu_input.convolve(gpu_kernel, dims);
+
+ assert(gpuMemcpyAsync(out.data(), d_out, out_bytes, gpuMemcpyDeviceToHost, gpu_device.stream()) == gpuSuccess);
+ assert(gpuStreamSynchronize(gpu_device.stream()) == gpuSuccess);
+
+ for (int i = 0; i < 74; ++i) {
+ for (int j = 0; j < 34; ++j) {
+ for (int k = 0; k < 11; ++k) {
+ for (int l = 0; l < 137; ++l) {
+ const float result = out(i,j,k,l);
+ const float expected = input(i,j+0,k,l) * kernel(0) + input(i,j+1,k,l) * kernel(1) +
+ input(i,j+2,k,l) * kernel(2) + input(i,j+3,k,l) * kernel(3);
+ VERIFY_IS_APPROX(result, expected);
+ }
+ }
+ }
+ }
+
+ gpuFree(d_input);
+ gpuFree(d_kernel);
+ gpuFree(d_out);
+}
+
+void test_gpu_convolution_inner_dim_col_major_1d()
+{
+ Tensor<float, 4, ColMajor> input(74,9,11,7);
+ Tensor<float, 1, ColMajor> kernel(4);
+ Tensor<float, 4, ColMajor> out(71,9,11,7);
+ input = input.constant(10.0f) + input.random();
+ kernel = kernel.constant(7.0f) + kernel.random();
+
+ std::size_t input_bytes = input.size() * sizeof(float);
+ std::size_t kernel_bytes = kernel.size() * sizeof(float);
+ std::size_t out_bytes = out.size() * sizeof(float);
+
+ float* d_input;
+ float* d_kernel;
+ float* d_out;
+ gpuMalloc((void**)(&d_input), input_bytes);
+ gpuMalloc((void**)(&d_kernel), kernel_bytes);
+ gpuMalloc((void**)(&d_out), out_bytes);
+
+ gpuMemcpy(d_input, input.data(), input_bytes, gpuMemcpyHostToDevice);
+ gpuMemcpy(d_kernel, kernel.data(), kernel_bytes, gpuMemcpyHostToDevice);
+
+ Eigen::GpuStreamDevice stream;
+ Eigen::GpuDevice gpu_device(&stream);
+
+ Eigen::TensorMap<Eigen::Tensor<float, 4, ColMajor> > gpu_input(d_input,74,9,11,7);
+ Eigen::TensorMap<Eigen::Tensor<float, 1, ColMajor> > gpu_kernel(d_kernel,4);
+ Eigen::TensorMap<Eigen::Tensor<float, 4, ColMajor> > gpu_out(d_out,71,9,11,7);
+
+ Eigen::array<Eigen::DenseIndex, 1> dims(0);
+ gpu_out.device(gpu_device) = gpu_input.convolve(gpu_kernel, dims);
+
+ assert(gpuMemcpyAsync(out.data(), d_out, out_bytes, gpuMemcpyDeviceToHost, gpu_device.stream()) == gpuSuccess);
+ assert(gpuStreamSynchronize(gpu_device.stream()) == gpuSuccess);
+
+ for (int i = 0; i < 71; ++i) {
+ for (int j = 0; j < 9; ++j) {
+ for (int k = 0; k < 11; ++k) {
+ for (int l = 0; l < 7; ++l) {
+ const float result = out(i,j,k,l);
+ const float expected = input(i+0,j,k,l) * kernel(0) + input(i+1,j,k,l) * kernel(1) +
+ input(i+2,j,k,l) * kernel(2) + input(i+3,j,k,l) * kernel(3);
+ VERIFY_IS_APPROX(result, expected);
+ }
+ }
+ }
+ }
+
+ gpuFree(d_input);
+ gpuFree(d_kernel);
+ gpuFree(d_out);
+}
+
+void test_gpu_convolution_inner_dim_row_major_1d()
+{
+ Tensor<float, 4, RowMajor> input(7,9,11,74);
+ Tensor<float, 1, RowMajor> kernel(4);
+ Tensor<float, 4, RowMajor> out(7,9,11,71);
+ input = input.constant(10.0f) + input.random();
+ kernel = kernel.constant(7.0f) + kernel.random();
+
+ std::size_t input_bytes = input.size() * sizeof(float);
+ std::size_t kernel_bytes = kernel.size() * sizeof(float);
+ std::size_t out_bytes = out.size() * sizeof(float);
+
+ float* d_input;
+ float* d_kernel;
+ float* d_out;
+ gpuMalloc((void**)(&d_input), input_bytes);
+ gpuMalloc((void**)(&d_kernel), kernel_bytes);
+ gpuMalloc((void**)(&d_out), out_bytes);
+
+ gpuMemcpy(d_input, input.data(), input_bytes, gpuMemcpyHostToDevice);
+ gpuMemcpy(d_kernel, kernel.data(), kernel_bytes, gpuMemcpyHostToDevice);
+
+ Eigen::GpuStreamDevice stream;
+ Eigen::GpuDevice gpu_device(&stream);
+
+ Eigen::TensorMap<Eigen::Tensor<float, 4, RowMajor> > gpu_input(d_input, 7,9,11,74);
+ Eigen::TensorMap<Eigen::Tensor<float, 1, RowMajor> > gpu_kernel(d_kernel, 4);
+ Eigen::TensorMap<Eigen::Tensor<float, 4, RowMajor> > gpu_out(d_out, 7,9,11,71);
+
+ Eigen::array<Eigen::DenseIndex, 1> dims(3);
+ gpu_out.device(gpu_device) = gpu_input.convolve(gpu_kernel, dims);
+
+ assert(gpuMemcpyAsync(out.data(), d_out, out_bytes, gpuMemcpyDeviceToHost, gpu_device.stream()) == gpuSuccess);
+ assert(gpuStreamSynchronize(gpu_device.stream()) == gpuSuccess);
+
+ for (int i = 0; i < 7; ++i) {
+ for (int j = 0; j < 9; ++j) {
+ for (int k = 0; k < 11; ++k) {
+ for (int l = 0; l < 71; ++l) {
+ const float result = out(i,j,k,l);
+ const float expected = input(i,j,k,l+0) * kernel(0) + input(i,j,k,l+1) * kernel(1) +
+ input(i,j,k,l+2) * kernel(2) + input(i,j,k,l+3) * kernel(3);
+ VERIFY_IS_APPROX(result, expected);
+ }
+ }
+ }
+ }
+
+ gpuFree(d_input);
+ gpuFree(d_kernel);
+ gpuFree(d_out);
+}
+
+template<int DataLayout>
+void test_gpu_convolution_2d()
+{
+ Tensor<float, 4, DataLayout> input(74,37,11,137);
+ Tensor<float, 2, DataLayout> kernel(3,4);
+ Tensor<float, 4, DataLayout> out(74,35,8,137);
+ input = input.constant(10.0f) + input.random();
+ kernel = kernel.constant(7.0f) + kernel.random();
+
+ std::size_t input_bytes = input.size() * sizeof(float);
+ std::size_t kernel_bytes = kernel.size() * sizeof(float);
+ std::size_t out_bytes = out.size() * sizeof(float);
+
+ float* d_input;
+ float* d_kernel;
+ float* d_out;
+ gpuMalloc((void**)(&d_input), input_bytes);
+ gpuMalloc((void**)(&d_kernel), kernel_bytes);
+ gpuMalloc((void**)(&d_out), out_bytes);
+
+ gpuMemcpy(d_input, input.data(), input_bytes, gpuMemcpyHostToDevice);
+ gpuMemcpy(d_kernel, kernel.data(), kernel_bytes, gpuMemcpyHostToDevice);
+
+ Eigen::GpuStreamDevice stream;
+ Eigen::GpuDevice gpu_device(&stream);
+
+ Eigen::TensorMap<Eigen::Tensor<float, 4, DataLayout> > gpu_input(d_input,74,37,11,137);
+ Eigen::TensorMap<Eigen::Tensor<float, 2, DataLayout> > gpu_kernel(d_kernel,3,4);
+ Eigen::TensorMap<Eigen::Tensor<float, 4, DataLayout> > gpu_out(d_out,74,35,8,137);
+
+ Eigen::array<Eigen::DenseIndex, 2> dims(1,2);
+ gpu_out.device(gpu_device) = gpu_input.convolve(gpu_kernel, dims);
+
+ assert(gpuMemcpyAsync(out.data(), d_out, out_bytes, gpuMemcpyDeviceToHost, gpu_device.stream()) == gpuSuccess);
+ assert(gpuStreamSynchronize(gpu_device.stream()) == gpuSuccess);
+
+ for (int i = 0; i < 74; ++i) {
+ for (int j = 0; j < 35; ++j) {
+ for (int k = 0; k < 8; ++k) {
+ for (int l = 0; l < 137; ++l) {
+ const float result = out(i,j,k,l);
+ const float expected = input(i,j+0,k+0,l) * kernel(0,0) +
+ input(i,j+1,k+0,l) * kernel(1,0) +
+ input(i,j+2,k+0,l) * kernel(2,0) +
+ input(i,j+0,k+1,l) * kernel(0,1) +
+ input(i,j+1,k+1,l) * kernel(1,1) +
+ input(i,j+2,k+1,l) * kernel(2,1) +
+ input(i,j+0,k+2,l) * kernel(0,2) +
+ input(i,j+1,k+2,l) * kernel(1,2) +
+ input(i,j+2,k+2,l) * kernel(2,2) +
+ input(i,j+0,k+3,l) * kernel(0,3) +
+ input(i,j+1,k+3,l) * kernel(1,3) +
+ input(i,j+2,k+3,l) * kernel(2,3);
+ VERIFY_IS_APPROX(result, expected);
+ }
+ }
+ }
+ }
+
+ gpuFree(d_input);
+ gpuFree(d_kernel);
+ gpuFree(d_out);
+}
+
+template<int DataLayout>
+void test_gpu_convolution_3d()
+{
+ Tensor<float, 5, DataLayout> input(Eigen::array<Eigen::DenseIndex, 5>(74,37,11,137,17));
+ Tensor<float, 3, DataLayout> kernel(3,4,2);
+ Tensor<float, 5, DataLayout> out(Eigen::array<Eigen::DenseIndex, 5>(74,35,8,136,17));
+ input = input.constant(10.0f) + input.random();
+ kernel = kernel.constant(7.0f) + kernel.random();
+
+ std::size_t input_bytes = input.size() * sizeof(float);
+ std::size_t kernel_bytes = kernel.size() * sizeof(float);
+ std::size_t out_bytes = out.size() * sizeof(float);
+
+ float* d_input;
+ float* d_kernel;
+ float* d_out;
+ gpuMalloc((void**)(&d_input), input_bytes);
+ gpuMalloc((void**)(&d_kernel), kernel_bytes);
+ gpuMalloc((void**)(&d_out), out_bytes);
+
+ gpuMemcpy(d_input, input.data(), input_bytes, gpuMemcpyHostToDevice);
+ gpuMemcpy(d_kernel, kernel.data(), kernel_bytes, gpuMemcpyHostToDevice);
+
+ Eigen::GpuStreamDevice stream;
+ Eigen::GpuDevice gpu_device(&stream);
+
+ Eigen::TensorMap<Eigen::Tensor<float, 5, DataLayout> > gpu_input(d_input,74,37,11,137,17);
+ Eigen::TensorMap<Eigen::Tensor<float, 3, DataLayout> > gpu_kernel(d_kernel,3,4,2);
+ Eigen::TensorMap<Eigen::Tensor<float, 5, DataLayout> > gpu_out(d_out,74,35,8,136,17);
+
+ Eigen::array<Eigen::DenseIndex, 3> dims(1,2,3);
+ gpu_out.device(gpu_device) = gpu_input.convolve(gpu_kernel, dims);
+
+ assert(gpuMemcpyAsync(out.data(), d_out, out_bytes, gpuMemcpyDeviceToHost, gpu_device.stream()) == gpuSuccess);
+ assert(gpuStreamSynchronize(gpu_device.stream()) == gpuSuccess);
+
+ for (int i = 0; i < 74; ++i) {
+ for (int j = 0; j < 35; ++j) {
+ for (int k = 0; k < 8; ++k) {
+ for (int l = 0; l < 136; ++l) {
+ for (int m = 0; m < 17; ++m) {
+ const float result = out(i,j,k,l,m);
+ const float expected = input(i,j+0,k+0,l+0,m) * kernel(0,0,0) +
+ input(i,j+1,k+0,l+0,m) * kernel(1,0,0) +
+ input(i,j+2,k+0,l+0,m) * kernel(2,0,0) +
+ input(i,j+0,k+1,l+0,m) * kernel(0,1,0) +
+ input(i,j+1,k+1,l+0,m) * kernel(1,1,0) +
+ input(i,j+2,k+1,l+0,m) * kernel(2,1,0) +
+ input(i,j+0,k+2,l+0,m) * kernel(0,2,0) +
+ input(i,j+1,k+2,l+0,m) * kernel(1,2,0) +
+ input(i,j+2,k+2,l+0,m) * kernel(2,2,0) +
+ input(i,j+0,k+3,l+0,m) * kernel(0,3,0) +
+ input(i,j+1,k+3,l+0,m) * kernel(1,3,0) +
+ input(i,j+2,k+3,l+0,m) * kernel(2,3,0) +
+ input(i,j+0,k+0,l+1,m) * kernel(0,0,1) +
+ input(i,j+1,k+0,l+1,m) * kernel(1,0,1) +
+ input(i,j+2,k+0,l+1,m) * kernel(2,0,1) +
+ input(i,j+0,k+1,l+1,m) * kernel(0,1,1) +
+ input(i,j+1,k+1,l+1,m) * kernel(1,1,1) +
+ input(i,j+2,k+1,l+1,m) * kernel(2,1,1) +
+ input(i,j+0,k+2,l+1,m) * kernel(0,2,1) +
+ input(i,j+1,k+2,l+1,m) * kernel(1,2,1) +
+ input(i,j+2,k+2,l+1,m) * kernel(2,2,1) +
+ input(i,j+0,k+3,l+1,m) * kernel(0,3,1) +
+ input(i,j+1,k+3,l+1,m) * kernel(1,3,1) +
+ input(i,j+2,k+3,l+1,m) * kernel(2,3,1);
+ VERIFY_IS_APPROX(result, expected);
+ }
+ }
+ }
+ }
+ }
+
+ gpuFree(d_input);
+ gpuFree(d_kernel);
+ gpuFree(d_out);
+}
+
+
+template <typename Scalar>
+void test_gpu_lgamma(const Scalar stddev)
+{
+ Tensor<Scalar, 2> in(72,97);
+ in.setRandom();
+ in *= in.constant(stddev);
+ Tensor<Scalar, 2> out(72,97);
+ out.setZero();
+
+ std::size_t bytes = in.size() * sizeof(Scalar);
+
+ Scalar* d_in;
+ Scalar* d_out;
+ gpuMalloc((void**)(&d_in), bytes);
+ gpuMalloc((void**)(&d_out), bytes);
+
+ gpuMemcpy(d_in, in.data(), bytes, gpuMemcpyHostToDevice);
+
+ Eigen::GpuStreamDevice stream;
+ Eigen::GpuDevice gpu_device(&stream);
+
+ Eigen::TensorMap<Eigen::Tensor<Scalar, 2> > gpu_in(d_in, 72, 97);
+ Eigen::TensorMap<Eigen::Tensor<Scalar, 2> > gpu_out(d_out, 72, 97);
+
+ gpu_out.device(gpu_device) = gpu_in.lgamma();
+
+ assert(gpuMemcpyAsync(out.data(), d_out, bytes, gpuMemcpyDeviceToHost, gpu_device.stream()) == gpuSuccess);
+ assert(gpuStreamSynchronize(gpu_device.stream()) == gpuSuccess);
+
+ for (int i = 0; i < 72; ++i) {
+ for (int j = 0; j < 97; ++j) {
+ VERIFY_IS_APPROX(out(i,j), (std::lgamma)(in(i,j)));
+ }
+ }
+
+ gpuFree(d_in);
+ gpuFree(d_out);
+}
+
+template <typename Scalar>
+void test_gpu_digamma()
+{
+ Tensor<Scalar, 1> in(7);
+ Tensor<Scalar, 1> out(7);
+ Tensor<Scalar, 1> expected_out(7);
+ out.setZero();
+
+ in(0) = Scalar(1);
+ in(1) = Scalar(1.5);
+ in(2) = Scalar(4);
+ in(3) = Scalar(-10.5);
+ in(4) = Scalar(10000.5);
+ in(5) = Scalar(0);
+ in(6) = Scalar(-1);
+
+ expected_out(0) = Scalar(-0.5772156649015329);
+ expected_out(1) = Scalar(0.03648997397857645);
+ expected_out(2) = Scalar(1.2561176684318);
+ expected_out(3) = Scalar(2.398239129535781);
+ expected_out(4) = Scalar(9.210340372392849);
+ expected_out(5) = std::numeric_limits<Scalar>::quiet_NaN();
+ expected_out(6) = std::numeric_limits<Scalar>::quiet_NaN();
+
+ std::size_t bytes = in.size() * sizeof(Scalar);
+
+ Scalar* d_in;
+ Scalar* d_out;
+ gpuMalloc((void**)(&d_in), bytes);
+ gpuMalloc((void**)(&d_out), bytes);
+
+ gpuMemcpy(d_in, in.data(), bytes, gpuMemcpyHostToDevice);
+
+ Eigen::GpuStreamDevice stream;
+ Eigen::GpuDevice gpu_device(&stream);
+
+ Eigen::TensorMap<Eigen::Tensor<Scalar, 1> > gpu_in(d_in, 7);
+ Eigen::TensorMap<Eigen::Tensor<Scalar, 1> > gpu_out(d_out, 7);
+
+ gpu_out.device(gpu_device) = gpu_in.digamma();
+
+ assert(gpuMemcpyAsync(out.data(), d_out, bytes, gpuMemcpyDeviceToHost, gpu_device.stream()) == gpuSuccess);
+ assert(gpuStreamSynchronize(gpu_device.stream()) == gpuSuccess);
+
+ for (int i = 0; i < 7; ++i) {
+ VERIFY_IS_CWISE_APPROX(out(i), expected_out(i));
+ }
+
+ gpuFree(d_in);
+ gpuFree(d_out);
+}
+
+template <typename Scalar>
+void test_gpu_zeta()
+{
+ Tensor<Scalar, 1> in_x(6);
+ Tensor<Scalar, 1> in_q(6);
+ Tensor<Scalar, 1> out(6);
+ Tensor<Scalar, 1> expected_out(6);
+ out.setZero();
+
+ in_x(0) = Scalar(1);
+ in_x(1) = Scalar(1.5);
+ in_x(2) = Scalar(4);
+ in_x(3) = Scalar(-10.5);
+ in_x(4) = Scalar(10000.5);
+ in_x(5) = Scalar(3);
+
+ in_q(0) = Scalar(1.2345);
+ in_q(1) = Scalar(2);
+ in_q(2) = Scalar(1.5);
+ in_q(3) = Scalar(3);
+ in_q(4) = Scalar(1.0001);
+ in_q(5) = Scalar(-2.5);
+
+ expected_out(0) = std::numeric_limits<Scalar>::infinity();
+ expected_out(1) = Scalar(1.61237534869);
+ expected_out(2) = Scalar(0.234848505667);
+ expected_out(3) = std::numeric_limits<Scalar>::quiet_NaN();
+ expected_out(4) = Scalar(0.367879440865);
+ expected_out(5) = Scalar(0.054102025820864097);
+
+ std::size_t bytes = in_x.size() * sizeof(Scalar);
+
+ Scalar* d_in_x;
+ Scalar* d_in_q;
+ Scalar* d_out;
+ gpuMalloc((void**)(&d_in_x), bytes);
+ gpuMalloc((void**)(&d_in_q), bytes);
+ gpuMalloc((void**)(&d_out), bytes);
+
+ gpuMemcpy(d_in_x, in_x.data(), bytes, gpuMemcpyHostToDevice);
+ gpuMemcpy(d_in_q, in_q.data(), bytes, gpuMemcpyHostToDevice);
+
+ Eigen::GpuStreamDevice stream;
+ Eigen::GpuDevice gpu_device(&stream);
+
+ Eigen::TensorMap<Eigen::Tensor<Scalar, 1> > gpu_in_x(d_in_x, 6);
+ Eigen::TensorMap<Eigen::Tensor<Scalar, 1> > gpu_in_q(d_in_q, 6);
+ Eigen::TensorMap<Eigen::Tensor<Scalar, 1> > gpu_out(d_out, 6);
+
+ gpu_out.device(gpu_device) = gpu_in_x.zeta(gpu_in_q);
+
+ assert(gpuMemcpyAsync(out.data(), d_out, bytes, gpuMemcpyDeviceToHost, gpu_device.stream()) == gpuSuccess);
+ assert(gpuStreamSynchronize(gpu_device.stream()) == gpuSuccess);
+
+ for (int i = 0; i < 6; ++i) {
+ VERIFY_IS_CWISE_APPROX(out(i), expected_out(i));
+ }
+
+ gpuFree(d_in_x);
+ gpuFree(d_in_q);
+ gpuFree(d_out);
+}
+
+template <typename Scalar>
+void test_gpu_polygamma()
+{
+ Tensor<Scalar, 1> in_x(7);
+ Tensor<Scalar, 1> in_n(7);
+ Tensor<Scalar, 1> out(7);
+ Tensor<Scalar, 1> expected_out(7);
+ out.setZero();
+
+ in_n(0) = Scalar(1);
+ in_n(1) = Scalar(1);
+ in_n(2) = Scalar(1);
+ in_n(3) = Scalar(17);
+ in_n(4) = Scalar(31);
+ in_n(5) = Scalar(28);
+ in_n(6) = Scalar(8);
+
+ in_x(0) = Scalar(2);
+ in_x(1) = Scalar(3);
+ in_x(2) = Scalar(25.5);
+ in_x(3) = Scalar(4.7);
+ in_x(4) = Scalar(11.8);
+ in_x(5) = Scalar(17.7);
+ in_x(6) = Scalar(30.2);
+
+ expected_out(0) = Scalar(0.644934066848);
+ expected_out(1) = Scalar(0.394934066848);
+ expected_out(2) = Scalar(0.0399946696496);
+ expected_out(3) = Scalar(293.334565435);
+ expected_out(4) = Scalar(0.445487887616);
+ expected_out(5) = Scalar(-2.47810300902e-07);
+ expected_out(6) = Scalar(-8.29668781082e-09);
+
+ std::size_t bytes = in_x.size() * sizeof(Scalar);
+
+ Scalar* d_in_x;
+ Scalar* d_in_n;
+ Scalar* d_out;
+ gpuMalloc((void**)(&d_in_x), bytes);
+ gpuMalloc((void**)(&d_in_n), bytes);
+ gpuMalloc((void**)(&d_out), bytes);
+
+ gpuMemcpy(d_in_x, in_x.data(), bytes, gpuMemcpyHostToDevice);
+ gpuMemcpy(d_in_n, in_n.data(), bytes, gpuMemcpyHostToDevice);
+
+ Eigen::GpuStreamDevice stream;
+ Eigen::GpuDevice gpu_device(&stream);
+
+ Eigen::TensorMap<Eigen::Tensor<Scalar, 1> > gpu_in_x(d_in_x, 7);
+ Eigen::TensorMap<Eigen::Tensor<Scalar, 1> > gpu_in_n(d_in_n, 7);
+ Eigen::TensorMap<Eigen::Tensor<Scalar, 1> > gpu_out(d_out, 7);
+
+ gpu_out.device(gpu_device) = gpu_in_n.polygamma(gpu_in_x);
+
+ assert(gpuMemcpyAsync(out.data(), d_out, bytes, gpuMemcpyDeviceToHost, gpu_device.stream()) == gpuSuccess);
+ assert(gpuStreamSynchronize(gpu_device.stream()) == gpuSuccess);
+
+ for (int i = 0; i < 7; ++i) {
+ VERIFY_IS_APPROX(out(i), expected_out(i));
+ }
+
+ gpuFree(d_in_x);
+ gpuFree(d_in_n);
+ gpuFree(d_out);
+}
+
+template <typename Scalar>
+void test_gpu_igamma()
+{
+ Tensor<Scalar, 2> a(6, 6);
+ Tensor<Scalar, 2> x(6, 6);
+ Tensor<Scalar, 2> out(6, 6);
+ out.setZero();
+
+ Scalar a_s[] = {Scalar(0), Scalar(1), Scalar(1.5), Scalar(4), Scalar(0.0001), Scalar(1000.5)};
+ Scalar x_s[] = {Scalar(0), Scalar(1), Scalar(1.5), Scalar(4), Scalar(0.0001), Scalar(1000.5)};
+
+ for (int i = 0; i < 6; ++i) {
+ for (int j = 0; j < 6; ++j) {
+ a(i, j) = a_s[i];
+ x(i, j) = x_s[j];
+ }
+ }
+
+ Scalar nan = std::numeric_limits<Scalar>::quiet_NaN();
+ Scalar igamma_s[][6] = {{0.0, nan, nan, nan, nan, nan},
+ {0.0, 0.6321205588285578, 0.7768698398515702,
+ 0.9816843611112658, 9.999500016666262e-05, 1.0},
+ {0.0, 0.4275932955291202, 0.608374823728911,
+ 0.9539882943107686, 7.522076445089201e-07, 1.0},
+ {0.0, 0.01898815687615381, 0.06564245437845008,
+ 0.5665298796332909, 4.166333347221828e-18, 1.0},
+ {0.0, 0.9999780593618628, 0.9999899967080838,
+ 0.9999996219837988, 0.9991370418689945, 1.0},
+ {0.0, 0.0, 0.0, 0.0, 0.0, 0.5042041932513908}};
+
+
+
+ std::size_t bytes = a.size() * sizeof(Scalar);
+
+ Scalar* d_a;
+ Scalar* d_x;
+ Scalar* d_out;
+ assert(gpuMalloc((void**)(&d_a), bytes) == gpuSuccess);
+ assert(gpuMalloc((void**)(&d_x), bytes) == gpuSuccess);
+ assert(gpuMalloc((void**)(&d_out), bytes) == gpuSuccess);
+
+ gpuMemcpy(d_a, a.data(), bytes, gpuMemcpyHostToDevice);
+ gpuMemcpy(d_x, x.data(), bytes, gpuMemcpyHostToDevice);
+
+ Eigen::GpuStreamDevice stream;
+ Eigen::GpuDevice gpu_device(&stream);
+
+ Eigen::TensorMap<Eigen::Tensor<Scalar, 2> > gpu_a(d_a, 6, 6);
+ Eigen::TensorMap<Eigen::Tensor<Scalar, 2> > gpu_x(d_x, 6, 6);
+ Eigen::TensorMap<Eigen::Tensor<Scalar, 2> > gpu_out(d_out, 6, 6);
+
+ gpu_out.device(gpu_device) = gpu_a.igamma(gpu_x);
+
+ assert(gpuMemcpyAsync(out.data(), d_out, bytes, gpuMemcpyDeviceToHost, gpu_device.stream()) == gpuSuccess);
+ assert(gpuStreamSynchronize(gpu_device.stream()) == gpuSuccess);
+
+ for (int i = 0; i < 6; ++i) {
+ for (int j = 0; j < 6; ++j) {
+ if ((std::isnan)(igamma_s[i][j])) {
+ VERIFY((std::isnan)(out(i, j)));
+ } else {
+ VERIFY_IS_APPROX(out(i, j), igamma_s[i][j]);
+ }
+ }
+ }
+
+ gpuFree(d_a);
+ gpuFree(d_x);
+ gpuFree(d_out);
+}
+
+template <typename Scalar>
+void test_gpu_igammac()
+{
+ Tensor<Scalar, 2> a(6, 6);
+ Tensor<Scalar, 2> x(6, 6);
+ Tensor<Scalar, 2> out(6, 6);
+ out.setZero();
+
+ Scalar a_s[] = {Scalar(0), Scalar(1), Scalar(1.5), Scalar(4), Scalar(0.0001), Scalar(1000.5)};
+ Scalar x_s[] = {Scalar(0), Scalar(1), Scalar(1.5), Scalar(4), Scalar(0.0001), Scalar(1000.5)};
+
+ for (int i = 0; i < 6; ++i) {
+ for (int j = 0; j < 6; ++j) {
+ a(i, j) = a_s[i];
+ x(i, j) = x_s[j];
+ }
+ }
+
+ Scalar nan = std::numeric_limits<Scalar>::quiet_NaN();
+ Scalar igammac_s[][6] = {{nan, nan, nan, nan, nan, nan},
+ {1.0, 0.36787944117144233, 0.22313016014842982,
+ 0.018315638888734182, 0.9999000049998333, 0.0},
+ {1.0, 0.5724067044708798, 0.3916251762710878,
+ 0.04601170568923136, 0.9999992477923555, 0.0},
+ {1.0, 0.9810118431238462, 0.9343575456215499,
+ 0.4334701203667089, 1.0, 0.0},
+ {1.0, 2.1940638138146658e-05, 1.0003291916285e-05,
+ 3.7801620118431334e-07, 0.0008629581310054535,
+ 0.0},
+ {1.0, 1.0, 1.0, 1.0, 1.0, 0.49579580674813944}};
+
+ std::size_t bytes = a.size() * sizeof(Scalar);
+
+ Scalar* d_a;
+ Scalar* d_x;
+ Scalar* d_out;
+ gpuMalloc((void**)(&d_a), bytes);
+ gpuMalloc((void**)(&d_x), bytes);
+ gpuMalloc((void**)(&d_out), bytes);
+
+ gpuMemcpy(d_a, a.data(), bytes, gpuMemcpyHostToDevice);
+ gpuMemcpy(d_x, x.data(), bytes, gpuMemcpyHostToDevice);
+
+ Eigen::GpuStreamDevice stream;
+ Eigen::GpuDevice gpu_device(&stream);
+
+ Eigen::TensorMap<Eigen::Tensor<Scalar, 2> > gpu_a(d_a, 6, 6);
+ Eigen::TensorMap<Eigen::Tensor<Scalar, 2> > gpu_x(d_x, 6, 6);
+ Eigen::TensorMap<Eigen::Tensor<Scalar, 2> > gpu_out(d_out, 6, 6);
+
+ gpu_out.device(gpu_device) = gpu_a.igammac(gpu_x);
+
+ assert(gpuMemcpyAsync(out.data(), d_out, bytes, gpuMemcpyDeviceToHost, gpu_device.stream()) == gpuSuccess);
+ assert(gpuStreamSynchronize(gpu_device.stream()) == gpuSuccess);
+
+ for (int i = 0; i < 6; ++i) {
+ for (int j = 0; j < 6; ++j) {
+ if ((std::isnan)(igammac_s[i][j])) {
+ VERIFY((std::isnan)(out(i, j)));
+ } else {
+ VERIFY_IS_APPROX(out(i, j), igammac_s[i][j]);
+ }
+ }
+ }
+
+ gpuFree(d_a);
+ gpuFree(d_x);
+ gpuFree(d_out);
+}
+
+template <typename Scalar>
+void test_gpu_erf(const Scalar stddev)
+{
+ Tensor<Scalar, 2> in(72,97);
+ in.setRandom();
+ in *= in.constant(stddev);
+ Tensor<Scalar, 2> out(72,97);
+ out.setZero();
+
+ std::size_t bytes = in.size() * sizeof(Scalar);
+
+ Scalar* d_in;
+ Scalar* d_out;
+ assert(gpuMalloc((void**)(&d_in), bytes) == gpuSuccess);
+ assert(gpuMalloc((void**)(&d_out), bytes) == gpuSuccess);
+
+ gpuMemcpy(d_in, in.data(), bytes, gpuMemcpyHostToDevice);
+
+ Eigen::GpuStreamDevice stream;
+ Eigen::GpuDevice gpu_device(&stream);
+
+ Eigen::TensorMap<Eigen::Tensor<Scalar, 2> > gpu_in(d_in, 72, 97);
+ Eigen::TensorMap<Eigen::Tensor<Scalar, 2> > gpu_out(d_out, 72, 97);
+
+ gpu_out.device(gpu_device) = gpu_in.erf();
+
+ assert(gpuMemcpyAsync(out.data(), d_out, bytes, gpuMemcpyDeviceToHost, gpu_device.stream()) == gpuSuccess);
+ assert(gpuStreamSynchronize(gpu_device.stream()) == gpuSuccess);
+
+ for (int i = 0; i < 72; ++i) {
+ for (int j = 0; j < 97; ++j) {
+ VERIFY_IS_APPROX(out(i,j), (std::erf)(in(i,j)));
+ }
+ }
+
+ gpuFree(d_in);
+ gpuFree(d_out);
+}
+
+template <typename Scalar>
+void test_gpu_erfc(const Scalar stddev)
+{
+ Tensor<Scalar, 2> in(72,97);
+ in.setRandom();
+ in *= in.constant(stddev);
+ Tensor<Scalar, 2> out(72,97);
+ out.setZero();
+
+ std::size_t bytes = in.size() * sizeof(Scalar);
+
+ Scalar* d_in;
+ Scalar* d_out;
+ gpuMalloc((void**)(&d_in), bytes);
+ gpuMalloc((void**)(&d_out), bytes);
+
+ gpuMemcpy(d_in, in.data(), bytes, gpuMemcpyHostToDevice);
+
+ Eigen::GpuStreamDevice stream;
+ Eigen::GpuDevice gpu_device(&stream);
+
+ Eigen::TensorMap<Eigen::Tensor<Scalar, 2> > gpu_in(d_in, 72, 97);
+ Eigen::TensorMap<Eigen::Tensor<Scalar, 2> > gpu_out(d_out, 72, 97);
+
+ gpu_out.device(gpu_device) = gpu_in.erfc();
+
+ assert(gpuMemcpyAsync(out.data(), d_out, bytes, gpuMemcpyDeviceToHost, gpu_device.stream()) == gpuSuccess);
+ assert(gpuStreamSynchronize(gpu_device.stream()) == gpuSuccess);
+
+ for (int i = 0; i < 72; ++i) {
+ for (int j = 0; j < 97; ++j) {
+ VERIFY_IS_APPROX(out(i,j), (std::erfc)(in(i,j)));
+ }
+ }
+
+ gpuFree(d_in);
+ gpuFree(d_out);
+}
+
+template <typename Scalar>
+void test_gpu_ndtri()
+{
+ Tensor<Scalar, 1> in_x(8);
+ Tensor<Scalar, 1> out(8);
+ Tensor<Scalar, 1> expected_out(8);
+ out.setZero();
+
+ in_x(0) = Scalar(1);
+ in_x(1) = Scalar(0.);
+ in_x(2) = Scalar(0.5);
+ in_x(3) = Scalar(0.2);
+ in_x(4) = Scalar(0.8);
+ in_x(5) = Scalar(0.9);
+ in_x(6) = Scalar(0.1);
+ in_x(7) = Scalar(0.99);
+ in_x(8) = Scalar(0.01);
+
+ expected_out(0) = std::numeric_limits<Scalar>::infinity();
+ expected_out(1) = -std::numeric_limits<Scalar>::infinity();
+ expected_out(2) = Scalar(0.0);
+ expected_out(3) = Scalar(-0.8416212335729142);
+ expected_out(4) = Scalar(0.8416212335729142);
+ expected_out(5) = Scalar(1.2815515655446004);
+ expected_out(6) = Scalar(-1.2815515655446004);
+ expected_out(7) = Scalar(2.3263478740408408);
+ expected_out(8) = Scalar(-2.3263478740408408);
+
+ std::size_t bytes = in_x.size() * sizeof(Scalar);
+
+ Scalar* d_in_x;
+ Scalar* d_out;
+ gpuMalloc((void**)(&d_in_x), bytes);
+ gpuMalloc((void**)(&d_out), bytes);
+
+ gpuMemcpy(d_in_x, in_x.data(), bytes, gpuMemcpyHostToDevice);
+
+ Eigen::GpuStreamDevice stream;
+ Eigen::GpuDevice gpu_device(&stream);
+
+ Eigen::TensorMap<Eigen::Tensor<Scalar, 1> > gpu_in_x(d_in_x, 6);
+ Eigen::TensorMap<Eigen::Tensor<Scalar, 1> > gpu_out(d_out, 6);
+
+ gpu_out.device(gpu_device) = gpu_in_x.ndtri();
+
+ assert(gpuMemcpyAsync(out.data(), d_out, bytes, gpuMemcpyDeviceToHost, gpu_device.stream()) == gpuSuccess);
+ assert(gpuStreamSynchronize(gpu_device.stream()) == gpuSuccess);
+
+ for (int i = 0; i < 6; ++i) {
+ VERIFY_IS_CWISE_APPROX(out(i), expected_out(i));
+ }
+
+ gpuFree(d_in_x);
+ gpuFree(d_out);
+}
+
+template <typename Scalar>
+void test_gpu_betainc()
+{
+ Tensor<Scalar, 1> in_x(125);
+ Tensor<Scalar, 1> in_a(125);
+ Tensor<Scalar, 1> in_b(125);
+ Tensor<Scalar, 1> out(125);
+ Tensor<Scalar, 1> expected_out(125);
+ out.setZero();
+
+ Scalar nan = std::numeric_limits<Scalar>::quiet_NaN();
+
+ Array<Scalar, 1, Dynamic> x(125);
+ Array<Scalar, 1, Dynamic> a(125);
+ Array<Scalar, 1, Dynamic> b(125);
+ Array<Scalar, 1, Dynamic> v(125);
+
+ a << 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
+ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
+ 0.03062277660168379, 0.03062277660168379, 0.03062277660168379,
+ 0.03062277660168379, 0.03062277660168379, 0.03062277660168379,
+ 0.03062277660168379, 0.03062277660168379, 0.03062277660168379,
+ 0.03062277660168379, 0.03062277660168379, 0.03062277660168379,
+ 0.03062277660168379, 0.03062277660168379, 0.03062277660168379,
+ 0.03062277660168379, 0.03062277660168379, 0.03062277660168379,
+ 0.03062277660168379, 0.03062277660168379, 0.03062277660168379,
+ 0.03062277660168379, 0.03062277660168379, 0.03062277660168379,
+ 0.03062277660168379, 0.999, 0.999, 0.999, 0.999, 0.999, 0.999, 0.999,
+ 0.999, 0.999, 0.999, 0.999, 0.999, 0.999, 0.999, 0.999, 0.999, 0.999,
+ 0.999, 0.999, 0.999, 0.999, 0.999, 0.999, 0.999, 0.999, 31.62177660168379,
+ 31.62177660168379, 31.62177660168379, 31.62177660168379,
+ 31.62177660168379, 31.62177660168379, 31.62177660168379,
+ 31.62177660168379, 31.62177660168379, 31.62177660168379,
+ 31.62177660168379, 31.62177660168379, 31.62177660168379,
+ 31.62177660168379, 31.62177660168379, 31.62177660168379,
+ 31.62177660168379, 31.62177660168379, 31.62177660168379,
+ 31.62177660168379, 31.62177660168379, 31.62177660168379,
+ 31.62177660168379, 31.62177660168379, 31.62177660168379, 999.999, 999.999,
+ 999.999, 999.999, 999.999, 999.999, 999.999, 999.999, 999.999, 999.999,
+ 999.999, 999.999, 999.999, 999.999, 999.999, 999.999, 999.999, 999.999,
+ 999.999, 999.999, 999.999, 999.999, 999.999, 999.999, 999.999;
+
+ b << 0.0, 0.0, 0.0, 0.0, 0.0, 0.03062277660168379, 0.03062277660168379,
+ 0.03062277660168379, 0.03062277660168379, 0.03062277660168379, 0.999,
+ 0.999, 0.999, 0.999, 0.999, 31.62177660168379, 31.62177660168379,
+ 31.62177660168379, 31.62177660168379, 31.62177660168379, 999.999, 999.999,
+ 999.999, 999.999, 999.999, 0.0, 0.0, 0.0, 0.0, 0.0, 0.03062277660168379,
+ 0.03062277660168379, 0.03062277660168379, 0.03062277660168379,
+ 0.03062277660168379, 0.999, 0.999, 0.999, 0.999, 0.999, 31.62177660168379,
+ 31.62177660168379, 31.62177660168379, 31.62177660168379,
+ 31.62177660168379, 999.999, 999.999, 999.999, 999.999, 999.999, 0.0, 0.0,
+ 0.0, 0.0, 0.0, 0.03062277660168379, 0.03062277660168379,
+ 0.03062277660168379, 0.03062277660168379, 0.03062277660168379, 0.999,
+ 0.999, 0.999, 0.999, 0.999, 31.62177660168379, 31.62177660168379,
+ 31.62177660168379, 31.62177660168379, 31.62177660168379, 999.999, 999.999,
+ 999.999, 999.999, 999.999, 0.0, 0.0, 0.0, 0.0, 0.0, 0.03062277660168379,
+ 0.03062277660168379, 0.03062277660168379, 0.03062277660168379,
+ 0.03062277660168379, 0.999, 0.999, 0.999, 0.999, 0.999, 31.62177660168379,
+ 31.62177660168379, 31.62177660168379, 31.62177660168379,
+ 31.62177660168379, 999.999, 999.999, 999.999, 999.999, 999.999, 0.0, 0.0,
+ 0.0, 0.0, 0.0, 0.03062277660168379, 0.03062277660168379,
+ 0.03062277660168379, 0.03062277660168379, 0.03062277660168379, 0.999,
+ 0.999, 0.999, 0.999, 0.999, 31.62177660168379, 31.62177660168379,
+ 31.62177660168379, 31.62177660168379, 31.62177660168379, 999.999, 999.999,
+ 999.999, 999.999, 999.999;
+
+ x << -0.1, 0.2, 0.5, 0.8, 1.1, -0.1, 0.2, 0.5, 0.8, 1.1, -0.1, 0.2, 0.5, 0.8,
+ 1.1, -0.1, 0.2, 0.5, 0.8, 1.1, -0.1, 0.2, 0.5, 0.8, 1.1, -0.1, 0.2, 0.5,
+ 0.8, 1.1, -0.1, 0.2, 0.5, 0.8, 1.1, -0.1, 0.2, 0.5, 0.8, 1.1, -0.1, 0.2,
+ 0.5, 0.8, 1.1, -0.1, 0.2, 0.5, 0.8, 1.1, -0.1, 0.2, 0.5, 0.8, 1.1, -0.1,
+ 0.2, 0.5, 0.8, 1.1, -0.1, 0.2, 0.5, 0.8, 1.1, -0.1, 0.2, 0.5, 0.8, 1.1,
+ -0.1, 0.2, 0.5, 0.8, 1.1, -0.1, 0.2, 0.5, 0.8, 1.1, -0.1, 0.2, 0.5, 0.8,
+ 1.1, -0.1, 0.2, 0.5, 0.8, 1.1, -0.1, 0.2, 0.5, 0.8, 1.1, -0.1, 0.2, 0.5,
+ 0.8, 1.1, -0.1, 0.2, 0.5, 0.8, 1.1, -0.1, 0.2, 0.5, 0.8, 1.1, -0.1, 0.2,
+ 0.5, 0.8, 1.1, -0.1, 0.2, 0.5, 0.8, 1.1, -0.1, 0.2, 0.5, 0.8, 1.1;
+
+ v << nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,
+ nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,
+ nan, nan, 0.47972119876364683, 0.5, 0.5202788012363533, nan, nan,
+ 0.9518683957740043, 0.9789663010413743, 0.9931729188073435, nan, nan,
+ 0.999995949033062, 0.9999999999993698, 0.9999999999999999, nan, nan,
+ 0.9999999999999999, 0.9999999999999999, 0.9999999999999999, nan, nan, nan,
+ nan, nan, nan, nan, 0.006827081192655869, 0.0210336989586256,
+ 0.04813160422599567, nan, nan, 0.20014344256217678, 0.5000000000000001,
+ 0.7998565574378232, nan, nan, 0.9991401428435834, 0.999999999698403,
+ 0.9999999999999999, nan, nan, 0.9999999999999999, 0.9999999999999999,
+ 0.9999999999999999, nan, nan, nan, nan, nan, nan, nan,
+ 1.0646600232370887e-25, 6.301722877826246e-13, 4.050966937974938e-06, nan,
+ nan, 7.864342668429763e-23, 3.015969667594166e-10, 0.0008598571564165444,
+ nan, nan, 6.031987710123844e-08, 0.5000000000000007, 0.9999999396801229,
+ nan, nan, 0.9999999999999999, 0.9999999999999999, 0.9999999999999999, nan,
+ nan, nan, nan, nan, nan, nan, 0.0, 7.029920380986636e-306,
+ 2.2450728208591345e-101, nan, nan, 0.0, 9.275871147869727e-302,
+ 1.2232913026152827e-97, nan, nan, 0.0, 3.0891393081932924e-252,
+ 2.9303043666183996e-60, nan, nan, 2.248913486879199e-196,
+ 0.5000000000004947, 0.9999999999999999, nan;
+
+ for (int i = 0; i < 125; ++i) {
+ in_x(i) = x(i);
+ in_a(i) = a(i);
+ in_b(i) = b(i);
+ expected_out(i) = v(i);
+ }
+
+ std::size_t bytes = in_x.size() * sizeof(Scalar);
+
+ Scalar* d_in_x;
+ Scalar* d_in_a;
+ Scalar* d_in_b;
+ Scalar* d_out;
+ gpuMalloc((void**)(&d_in_x), bytes);
+ gpuMalloc((void**)(&d_in_a), bytes);
+ gpuMalloc((void**)(&d_in_b), bytes);
+ gpuMalloc((void**)(&d_out), bytes);
+
+ gpuMemcpy(d_in_x, in_x.data(), bytes, gpuMemcpyHostToDevice);
+ gpuMemcpy(d_in_a, in_a.data(), bytes, gpuMemcpyHostToDevice);
+ gpuMemcpy(d_in_b, in_b.data(), bytes, gpuMemcpyHostToDevice);
+
+ Eigen::GpuStreamDevice stream;
+ Eigen::GpuDevice gpu_device(&stream);
+
+ Eigen::TensorMap<Eigen::Tensor<Scalar, 1> > gpu_in_x(d_in_x, 125);
+ Eigen::TensorMap<Eigen::Tensor<Scalar, 1> > gpu_in_a(d_in_a, 125);
+ Eigen::TensorMap<Eigen::Tensor<Scalar, 1> > gpu_in_b(d_in_b, 125);
+ Eigen::TensorMap<Eigen::Tensor<Scalar, 1> > gpu_out(d_out, 125);
+
+ gpu_out.device(gpu_device) = betainc(gpu_in_a, gpu_in_b, gpu_in_x);
+
+ assert(gpuMemcpyAsync(out.data(), d_out, bytes, gpuMemcpyDeviceToHost, gpu_device.stream()) == gpuSuccess);
+ assert(gpuStreamSynchronize(gpu_device.stream()) == gpuSuccess);
+
+ for (int i = 0; i < 125; ++i) {
+ VERIFY_IS_CWISE_APPROX(out(i), expected_out(i));
+ }
+
+ gpuFree(d_in_x);
+ gpuFree(d_in_a);
+ gpuFree(d_in_b);
+ gpuFree(d_out);
+}
+
+template <typename Scalar>
+void test_gpu_i0e()
+{
+ Tensor<Scalar, 1> in_x(21);
+ Tensor<Scalar, 1> out(21);
+ Tensor<Scalar, 1> expected_out(21);
+ out.setZero();
+
+ Array<Scalar, 1, Dynamic> in_x_array(21);
+ Array<Scalar, 1, Dynamic> expected_out_array(21);
+
+ in_x_array << -20.0, -18.0, -16.0, -14.0, -12.0, -10.0, -8.0, -6.0, -4.0,
+ -2.0, 0.0, 2.0, 4.0, 6.0, 8.0, 10.0, 12.0, 14.0, 16.0, 18.0, 20.0;
+
+ expected_out_array << 0.0897803118848, 0.0947062952128, 0.100544127361,
+ 0.107615251671, 0.116426221213, 0.127833337163, 0.143431781857,
+ 0.16665743264, 0.207001921224, 0.308508322554, 1.0, 0.308508322554,
+ 0.207001921224, 0.16665743264, 0.143431781857, 0.127833337163,
+ 0.116426221213, 0.107615251671, 0.100544127361, 0.0947062952128,
+ 0.0897803118848;
+
+ for (int i = 0; i < 21; ++i) {
+ in_x(i) = in_x_array(i);
+ expected_out(i) = expected_out_array(i);
+ }
+
+ std::size_t bytes = in_x.size() * sizeof(Scalar);
+
+ Scalar* d_in;
+ Scalar* d_out;
+ gpuMalloc((void**)(&d_in), bytes);
+ gpuMalloc((void**)(&d_out), bytes);
+
+ gpuMemcpy(d_in, in_x.data(), bytes, gpuMemcpyHostToDevice);
+
+ Eigen::GpuStreamDevice stream;
+ Eigen::GpuDevice gpu_device(&stream);
+
+ Eigen::TensorMap<Eigen::Tensor<Scalar, 1> > gpu_in(d_in, 21);
+ Eigen::TensorMap<Eigen::Tensor<Scalar, 1> > gpu_out(d_out, 21);
+
+ gpu_out.device(gpu_device) = gpu_in.bessel_i0e();
+
+ assert(gpuMemcpyAsync(out.data(), d_out, bytes, gpuMemcpyDeviceToHost,
+ gpu_device.stream()) == gpuSuccess);
+ assert(gpuStreamSynchronize(gpu_device.stream()) == gpuSuccess);
+
+ for (int i = 0; i < 21; ++i) {
+ VERIFY_IS_APPROX(out(i), expected_out(i));
+ }
+
+ gpuFree(d_in);
+ gpuFree(d_out);
+}
+
+template <typename Scalar>
+void test_gpu_i1e()
+{
+ Tensor<Scalar, 1> in_x(21);
+ Tensor<Scalar, 1> out(21);
+ Tensor<Scalar, 1> expected_out(21);
+ out.setZero();
+
+ Array<Scalar, 1, Dynamic> in_x_array(21);
+ Array<Scalar, 1, Dynamic> expected_out_array(21);
+
+ in_x_array << -20.0, -18.0, -16.0, -14.0, -12.0, -10.0, -8.0, -6.0, -4.0,
+ -2.0, 0.0, 2.0, 4.0, 6.0, 8.0, 10.0, 12.0, 14.0, 16.0, 18.0, 20.0;
+
+ expected_out_array << -0.0875062221833, -0.092036796872, -0.0973496147565,
+ -0.103697667463, -0.11146429929, -0.121262681384, -0.134142493293,
+ -0.152051459309, -0.178750839502, -0.215269289249, 0.0, 0.215269289249,
+ 0.178750839502, 0.152051459309, 0.134142493293, 0.121262681384,
+ 0.11146429929, 0.103697667463, 0.0973496147565, 0.092036796872,
+ 0.0875062221833;
+
+ for (int i = 0; i < 21; ++i) {
+ in_x(i) = in_x_array(i);
+ expected_out(i) = expected_out_array(i);
+ }
+
+ std::size_t bytes = in_x.size() * sizeof(Scalar);
+
+ Scalar* d_in;
+ Scalar* d_out;
+ gpuMalloc((void**)(&d_in), bytes);
+ gpuMalloc((void**)(&d_out), bytes);
+
+ gpuMemcpy(d_in, in_x.data(), bytes, gpuMemcpyHostToDevice);
+
+ Eigen::GpuStreamDevice stream;
+ Eigen::GpuDevice gpu_device(&stream);
+
+ Eigen::TensorMap<Eigen::Tensor<Scalar, 1> > gpu_in(d_in, 21);
+ Eigen::TensorMap<Eigen::Tensor<Scalar, 1> > gpu_out(d_out, 21);
+
+ gpu_out.device(gpu_device) = gpu_in.bessel_i1e();
+
+ assert(gpuMemcpyAsync(out.data(), d_out, bytes, gpuMemcpyDeviceToHost,
+ gpu_device.stream()) == gpuSuccess);
+ assert(gpuStreamSynchronize(gpu_device.stream()) == gpuSuccess);
+
+ for (int i = 0; i < 21; ++i) {
+ VERIFY_IS_APPROX(out(i), expected_out(i));
+ }
+
+ gpuFree(d_in);
+ gpuFree(d_out);
+}
+
+template <typename Scalar>
+void test_gpu_igamma_der_a()
+{
+ Tensor<Scalar, 1> in_x(30);
+ Tensor<Scalar, 1> in_a(30);
+ Tensor<Scalar, 1> out(30);
+ Tensor<Scalar, 1> expected_out(30);
+ out.setZero();
+
+ Array<Scalar, 1, Dynamic> in_a_array(30);
+ Array<Scalar, 1, Dynamic> in_x_array(30);
+ Array<Scalar, 1, Dynamic> expected_out_array(30);
+
+ // See special_functions.cpp for the Python code that generates the test data.
+
+ in_a_array << 0.01, 0.01, 0.01, 0.01, 0.01, 0.1, 0.1, 0.1, 0.1, 0.1, 1.0, 1.0,
+ 1.0, 1.0, 1.0, 10.0, 10.0, 10.0, 10.0, 10.0, 100.0, 100.0, 100.0, 100.0,
+ 100.0, 1000.0, 1000.0, 1000.0, 1000.0, 1000.0;
+
+ in_x_array << 1.25668890405e-26, 1.17549435082e-38, 1.20938905072e-05,
+ 1.17549435082e-38, 1.17549435082e-38, 5.66572070696e-16, 0.0132865061065,
+ 0.0200034203853, 6.29263709118e-17, 1.37160367764e-06, 0.333412038288,
+ 1.18135687766, 0.580629033777, 0.170631439426, 0.786686768458,
+ 7.63873279537, 13.1944344379, 11.896042354, 10.5830172417, 10.5020942233,
+ 92.8918587747, 95.003720371, 86.3715926467, 96.0330217672, 82.6389930677,
+ 968.702906754, 969.463546828, 1001.79726022, 955.047416547, 1044.27458568;
+
+ expected_out_array << -32.7256441441, -36.4394150514, -9.66467612263,
+ -36.4394150514, -36.4394150514, -1.0891900302, -2.66351229645,
+ -2.48666868596, -0.929700494428, -3.56327722764, -0.455320135314,
+ -0.391437214323, -0.491352055991, -0.350454834292, -0.471773162921,
+ -0.104084440522, -0.0723646747909, -0.0992828975532, -0.121638215446,
+ -0.122619605294, -0.0317670267286, -0.0359974812869, -0.0154359225363,
+ -0.0375775365921, -0.00794899153653, -0.00777303219211, -0.00796085782042,
+ -0.0125850719397, -0.00455500206958, -0.00476436993148;
+
+ for (int i = 0; i < 30; ++i) {
+ in_x(i) = in_x_array(i);
+ in_a(i) = in_a_array(i);
+ expected_out(i) = expected_out_array(i);
+ }
+
+ std::size_t bytes = in_x.size() * sizeof(Scalar);
+
+ Scalar* d_a;
+ Scalar* d_x;
+ Scalar* d_out;
+ gpuMalloc((void**)(&d_a), bytes);
+ gpuMalloc((void**)(&d_x), bytes);
+ gpuMalloc((void**)(&d_out), bytes);
+
+ gpuMemcpy(d_a, in_a.data(), bytes, gpuMemcpyHostToDevice);
+ gpuMemcpy(d_x, in_x.data(), bytes, gpuMemcpyHostToDevice);
+
+ Eigen::GpuStreamDevice stream;
+ Eigen::GpuDevice gpu_device(&stream);
+
+ Eigen::TensorMap<Eigen::Tensor<Scalar, 1> > gpu_a(d_a, 30);
+ Eigen::TensorMap<Eigen::Tensor<Scalar, 1> > gpu_x(d_x, 30);
+ Eigen::TensorMap<Eigen::Tensor<Scalar, 1> > gpu_out(d_out, 30);
+
+ gpu_out.device(gpu_device) = gpu_a.igamma_der_a(gpu_x);
+
+ assert(gpuMemcpyAsync(out.data(), d_out, bytes, gpuMemcpyDeviceToHost,
+ gpu_device.stream()) == gpuSuccess);
+ assert(gpuStreamSynchronize(gpu_device.stream()) == gpuSuccess);
+
+ for (int i = 0; i < 30; ++i) {
+ VERIFY_IS_APPROX(out(i), expected_out(i));
+ }
+
+ gpuFree(d_a);
+ gpuFree(d_x);
+ gpuFree(d_out);
+}
+
+template <typename Scalar>
+void test_gpu_gamma_sample_der_alpha()
+{
+ Tensor<Scalar, 1> in_alpha(30);
+ Tensor<Scalar, 1> in_sample(30);
+ Tensor<Scalar, 1> out(30);
+ Tensor<Scalar, 1> expected_out(30);
+ out.setZero();
+
+ Array<Scalar, 1, Dynamic> in_alpha_array(30);
+ Array<Scalar, 1, Dynamic> in_sample_array(30);
+ Array<Scalar, 1, Dynamic> expected_out_array(30);
+
+ // See special_functions.cpp for the Python code that generates the test data.
+
+ in_alpha_array << 0.01, 0.01, 0.01, 0.01, 0.01, 0.1, 0.1, 0.1, 0.1, 0.1, 1.0,
+ 1.0, 1.0, 1.0, 1.0, 10.0, 10.0, 10.0, 10.0, 10.0, 100.0, 100.0, 100.0,
+ 100.0, 100.0, 1000.0, 1000.0, 1000.0, 1000.0, 1000.0;
+
+ in_sample_array << 1.25668890405e-26, 1.17549435082e-38, 1.20938905072e-05,
+ 1.17549435082e-38, 1.17549435082e-38, 5.66572070696e-16, 0.0132865061065,
+ 0.0200034203853, 6.29263709118e-17, 1.37160367764e-06, 0.333412038288,
+ 1.18135687766, 0.580629033777, 0.170631439426, 0.786686768458,
+ 7.63873279537, 13.1944344379, 11.896042354, 10.5830172417, 10.5020942233,
+ 92.8918587747, 95.003720371, 86.3715926467, 96.0330217672, 82.6389930677,
+ 968.702906754, 969.463546828, 1001.79726022, 955.047416547, 1044.27458568;
+
+ expected_out_array << 7.42424742367e-23, 1.02004297287e-34, 0.0130155240738,
+ 1.02004297287e-34, 1.02004297287e-34, 1.96505168277e-13, 0.525575786243,
+ 0.713903991771, 2.32077561808e-14, 0.000179348049886, 0.635500453302,
+ 1.27561284917, 0.878125852156, 0.41565819538, 1.03606488534,
+ 0.885964824887, 1.16424049334, 1.10764479598, 1.04590810812,
+ 1.04193666963, 0.965193152414, 0.976217589464, 0.93008035061,
+ 0.98153216096, 0.909196397698, 0.98434963993, 0.984738050206,
+ 1.00106492525, 0.97734200649, 1.02198794179;
+
+ for (int i = 0; i < 30; ++i) {
+ in_alpha(i) = in_alpha_array(i);
+ in_sample(i) = in_sample_array(i);
+ expected_out(i) = expected_out_array(i);
+ }
+
+ std::size_t bytes = in_alpha.size() * sizeof(Scalar);
+
+ Scalar* d_alpha;
+ Scalar* d_sample;
+ Scalar* d_out;
+ gpuMalloc((void**)(&d_alpha), bytes);
+ gpuMalloc((void**)(&d_sample), bytes);
+ gpuMalloc((void**)(&d_out), bytes);
+
+ gpuMemcpy(d_alpha, in_alpha.data(), bytes, gpuMemcpyHostToDevice);
+ gpuMemcpy(d_sample, in_sample.data(), bytes, gpuMemcpyHostToDevice);
+
+ Eigen::GpuStreamDevice stream;
+ Eigen::GpuDevice gpu_device(&stream);
+
+ Eigen::TensorMap<Eigen::Tensor<Scalar, 1> > gpu_alpha(d_alpha, 30);
+ Eigen::TensorMap<Eigen::Tensor<Scalar, 1> > gpu_sample(d_sample, 30);
+ Eigen::TensorMap<Eigen::Tensor<Scalar, 1> > gpu_out(d_out, 30);
+
+ gpu_out.device(gpu_device) = gpu_alpha.gamma_sample_der_alpha(gpu_sample);
+
+ assert(gpuMemcpyAsync(out.data(), d_out, bytes, gpuMemcpyDeviceToHost,
+ gpu_device.stream()) == gpuSuccess);
+ assert(gpuStreamSynchronize(gpu_device.stream()) == gpuSuccess);
+
+ for (int i = 0; i < 30; ++i) {
+ VERIFY_IS_APPROX(out(i), expected_out(i));
+ }
+
+ gpuFree(d_alpha);
+ gpuFree(d_sample);
+ gpuFree(d_out);
+}
+
+EIGEN_DECLARE_TEST(cxx11_tensor_gpu)
+{
+ CALL_SUBTEST_1(test_gpu_nullary());
+ CALL_SUBTEST_1(test_gpu_nullary_max_size<int16_t>());
+ CALL_SUBTEST_1(test_gpu_nullary_max_size<int32_t>());
+ CALL_SUBTEST_1((test_gpu_nullary_max_size<
+ int64_t, (std::numeric_limits<int32_t>::max)() + 100ll>()));
+ CALL_SUBTEST_1(test_gpu_elementwise_small());
+ CALL_SUBTEST_1(test_gpu_elementwise());
+ CALL_SUBTEST_1(test_gpu_props());
+ CALL_SUBTEST_1(test_gpu_reduction());
+ CALL_SUBTEST_2(test_gpu_contraction<ColMajor>());
+ CALL_SUBTEST_2(test_gpu_contraction<RowMajor>());
+ CALL_SUBTEST_3(test_gpu_convolution_1d<ColMajor>());
+ CALL_SUBTEST_3(test_gpu_convolution_1d<RowMajor>());
+ CALL_SUBTEST_3(test_gpu_convolution_inner_dim_col_major_1d());
+ CALL_SUBTEST_3(test_gpu_convolution_inner_dim_row_major_1d());
+ CALL_SUBTEST_3(test_gpu_convolution_2d<ColMajor>());
+ CALL_SUBTEST_3(test_gpu_convolution_2d<RowMajor>());
+#if !defined(EIGEN_USE_HIP)
+// disable these tests on HIP for now.
+// they hang..need to investigate and fix
+ CALL_SUBTEST_3(test_gpu_convolution_3d<ColMajor>());
+ CALL_SUBTEST_3(test_gpu_convolution_3d<RowMajor>());
+#endif
+
+ // std::erf, std::erfc, and so on where only added in c++11. We use them
+ // as a golden reference to validate the results produced by Eigen. Therefore
+ // we can only run these tests if we use a c++11 compiler.
+ CALL_SUBTEST_4(test_gpu_lgamma<float>(1.0f));
+ CALL_SUBTEST_4(test_gpu_lgamma<float>(100.0f));
+ CALL_SUBTEST_4(test_gpu_lgamma<float>(0.01f));
+ CALL_SUBTEST_4(test_gpu_lgamma<float>(0.001f));
+
+ CALL_SUBTEST_4(test_gpu_lgamma<double>(1.0));
+ CALL_SUBTEST_4(test_gpu_lgamma<double>(100.0));
+ CALL_SUBTEST_4(test_gpu_lgamma<double>(0.01));
+ CALL_SUBTEST_4(test_gpu_lgamma<double>(0.001));
+
+ CALL_SUBTEST_4(test_gpu_erf<float>(1.0f));
+ CALL_SUBTEST_4(test_gpu_erf<float>(100.0f));
+ CALL_SUBTEST_4(test_gpu_erf<float>(0.01f));
+ CALL_SUBTEST_4(test_gpu_erf<float>(0.001f));
+
+ CALL_SUBTEST_4(test_gpu_erfc<float>(1.0f));
+ // CALL_SUBTEST(test_gpu_erfc<float>(100.0f));
+ CALL_SUBTEST_4(test_gpu_erfc<float>(5.0f)); // GPU erfc lacks precision for large inputs
+ CALL_SUBTEST_4(test_gpu_erfc<float>(0.01f));
+ CALL_SUBTEST_4(test_gpu_erfc<float>(0.001f));
+
+ CALL_SUBTEST_4(test_gpu_erf<double>(1.0));
+ CALL_SUBTEST_4(test_gpu_erf<double>(100.0));
+ CALL_SUBTEST_4(test_gpu_erf<double>(0.01));
+ CALL_SUBTEST_4(test_gpu_erf<double>(0.001));
+
+ CALL_SUBTEST_4(test_gpu_erfc<double>(1.0));
+ // CALL_SUBTEST(test_gpu_erfc<double>(100.0));
+ CALL_SUBTEST_4(test_gpu_erfc<double>(5.0)); // GPU erfc lacks precision for large inputs
+ CALL_SUBTEST_4(test_gpu_erfc<double>(0.01));
+ CALL_SUBTEST_4(test_gpu_erfc<double>(0.001));
+
+#if !defined(EIGEN_USE_HIP)
+// disable these tests on HIP for now.
+
+ CALL_SUBTEST_5(test_gpu_ndtri<float>());
+ CALL_SUBTEST_5(test_gpu_ndtri<double>());
+
+ CALL_SUBTEST_5(test_gpu_digamma<float>());
+ CALL_SUBTEST_5(test_gpu_digamma<double>());
+
+ CALL_SUBTEST_5(test_gpu_polygamma<float>());
+ CALL_SUBTEST_5(test_gpu_polygamma<double>());
+
+ CALL_SUBTEST_5(test_gpu_zeta<float>());
+ CALL_SUBTEST_5(test_gpu_zeta<double>());
+#endif
+
+ CALL_SUBTEST_5(test_gpu_igamma<float>());
+ CALL_SUBTEST_5(test_gpu_igammac<float>());
+
+ CALL_SUBTEST_5(test_gpu_igamma<double>());
+ CALL_SUBTEST_5(test_gpu_igammac<double>());
+
+#if !defined(EIGEN_USE_HIP)
+// disable these tests on HIP for now.
+ CALL_SUBTEST_6(test_gpu_betainc<float>());
+ CALL_SUBTEST_6(test_gpu_betainc<double>());
+
+ CALL_SUBTEST_6(test_gpu_i0e<float>());
+ CALL_SUBTEST_6(test_gpu_i0e<double>());
+
+ CALL_SUBTEST_6(test_gpu_i1e<float>());
+ CALL_SUBTEST_6(test_gpu_i1e<double>());
+
+ CALL_SUBTEST_6(test_gpu_i1e<float>());
+ CALL_SUBTEST_6(test_gpu_i1e<double>());
+
+ CALL_SUBTEST_6(test_gpu_igamma_der_a<float>());
+ CALL_SUBTEST_6(test_gpu_igamma_der_a<double>());
+
+ CALL_SUBTEST_6(test_gpu_gamma_sample_der_alpha<float>());
+ CALL_SUBTEST_6(test_gpu_gamma_sample_der_alpha<double>());
+#endif
+}
diff --git a/unsupported/test/cxx11_tensor_ifft.cpp b/unsupported/test/cxx11_tensor_ifft.cpp
new file mode 100644
index 0000000..c20edd9
--- /dev/null
+++ b/unsupported/test/cxx11_tensor_ifft.cpp
@@ -0,0 +1,154 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2014 Jianwei Cui <thucjw@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "main.h"
+#include <complex>
+#include <cmath>
+#include <Eigen/CXX11/Tensor>
+
+using Eigen::Tensor;
+
+template <int DataLayout>
+static void test_1D_fft_ifft_invariant(int sequence_length) {
+ Tensor<double, 1, DataLayout> tensor(sequence_length);
+ tensor.setRandom();
+
+ array<int, 1> fft;
+ fft[0] = 0;
+
+ Tensor<std::complex<double>, 1, DataLayout> tensor_after_fft;
+ Tensor<std::complex<double>, 1, DataLayout> tensor_after_fft_ifft;
+
+ tensor_after_fft = tensor.template fft<Eigen::BothParts, Eigen::FFT_FORWARD>(fft);
+ tensor_after_fft_ifft = tensor_after_fft.template fft<Eigen::BothParts, Eigen::FFT_REVERSE>(fft);
+
+ VERIFY_IS_EQUAL(tensor_after_fft.dimension(0), sequence_length);
+ VERIFY_IS_EQUAL(tensor_after_fft_ifft.dimension(0), sequence_length);
+
+ for (int i = 0; i < sequence_length; ++i) {
+ VERIFY_IS_APPROX(static_cast<float>(tensor(i)), static_cast<float>(std::real(tensor_after_fft_ifft(i))));
+ }
+}
+
+template <int DataLayout>
+static void test_2D_fft_ifft_invariant(int dim0, int dim1) {
+ Tensor<double, 2, DataLayout> tensor(dim0, dim1);
+ tensor.setRandom();
+
+ array<int, 2> fft;
+ fft[0] = 0;
+ fft[1] = 1;
+
+ Tensor<std::complex<double>, 2, DataLayout> tensor_after_fft;
+ Tensor<std::complex<double>, 2, DataLayout> tensor_after_fft_ifft;
+
+ tensor_after_fft = tensor.template fft<Eigen::BothParts, Eigen::FFT_FORWARD>(fft);
+ tensor_after_fft_ifft = tensor_after_fft.template fft<Eigen::BothParts, Eigen::FFT_REVERSE>(fft);
+
+ VERIFY_IS_EQUAL(tensor_after_fft.dimension(0), dim0);
+ VERIFY_IS_EQUAL(tensor_after_fft.dimension(1), dim1);
+ VERIFY_IS_EQUAL(tensor_after_fft_ifft.dimension(0), dim0);
+ VERIFY_IS_EQUAL(tensor_after_fft_ifft.dimension(1), dim1);
+
+ for (int i = 0; i < dim0; ++i) {
+ for (int j = 0; j < dim1; ++j) {
+ //std::cout << "[" << i << "][" << j << "]" << " Original data: " << tensor(i,j) << " Transformed data:" << tensor_after_fft_ifft(i,j) << std::endl;
+ VERIFY_IS_APPROX(static_cast<float>(tensor(i,j)), static_cast<float>(std::real(tensor_after_fft_ifft(i,j))));
+ }
+ }
+}
+
+template <int DataLayout>
+static void test_3D_fft_ifft_invariant(int dim0, int dim1, int dim2) {
+ Tensor<double, 3, DataLayout> tensor(dim0, dim1, dim2);
+ tensor.setRandom();
+
+ array<int, 3> fft;
+ fft[0] = 0;
+ fft[1] = 1;
+ fft[2] = 2;
+
+ Tensor<std::complex<double>, 3, DataLayout> tensor_after_fft;
+ Tensor<std::complex<double>, 3, DataLayout> tensor_after_fft_ifft;
+
+ tensor_after_fft = tensor.template fft<Eigen::BothParts, Eigen::FFT_FORWARD>(fft);
+ tensor_after_fft_ifft = tensor_after_fft.template fft<Eigen::BothParts, Eigen::FFT_REVERSE>(fft);
+
+ VERIFY_IS_EQUAL(tensor_after_fft.dimension(0), dim0);
+ VERIFY_IS_EQUAL(tensor_after_fft.dimension(1), dim1);
+ VERIFY_IS_EQUAL(tensor_after_fft.dimension(2), dim2);
+ VERIFY_IS_EQUAL(tensor_after_fft_ifft.dimension(0), dim0);
+ VERIFY_IS_EQUAL(tensor_after_fft_ifft.dimension(1), dim1);
+ VERIFY_IS_EQUAL(tensor_after_fft_ifft.dimension(2), dim2);
+
+ for (int i = 0; i < dim0; ++i) {
+ for (int j = 0; j < dim1; ++j) {
+ for (int k = 0; k < dim2; ++k) {
+ VERIFY_IS_APPROX(static_cast<float>(tensor(i,j,k)), static_cast<float>(std::real(tensor_after_fft_ifft(i,j,k))));
+ }
+ }
+ }
+}
+
+template <int DataLayout>
+static void test_sub_fft_ifft_invariant(int dim0, int dim1, int dim2, int dim3) {
+ Tensor<double, 4, DataLayout> tensor(dim0, dim1, dim2, dim3);
+ tensor.setRandom();
+
+ array<int, 2> fft;
+ fft[0] = 2;
+ fft[1] = 0;
+
+ Tensor<std::complex<double>, 4, DataLayout> tensor_after_fft;
+ Tensor<double, 4, DataLayout> tensor_after_fft_ifft;
+
+ tensor_after_fft = tensor.template fft<Eigen::BothParts, Eigen::FFT_FORWARD>(fft);
+ tensor_after_fft_ifft = tensor_after_fft.template fft<Eigen::RealPart, Eigen::FFT_REVERSE>(fft);
+
+ VERIFY_IS_EQUAL(tensor_after_fft.dimension(0), dim0);
+ VERIFY_IS_EQUAL(tensor_after_fft.dimension(1), dim1);
+ VERIFY_IS_EQUAL(tensor_after_fft.dimension(2), dim2);
+ VERIFY_IS_EQUAL(tensor_after_fft.dimension(3), dim3);
+ VERIFY_IS_EQUAL(tensor_after_fft_ifft.dimension(0), dim0);
+ VERIFY_IS_EQUAL(tensor_after_fft_ifft.dimension(1), dim1);
+ VERIFY_IS_EQUAL(tensor_after_fft_ifft.dimension(2), dim2);
+ VERIFY_IS_EQUAL(tensor_after_fft_ifft.dimension(3), dim3);
+
+ for (int i = 0; i < dim0; ++i) {
+ for (int j = 0; j < dim1; ++j) {
+ for (int k = 0; k < dim2; ++k) {
+ for (int l = 0; l < dim3; ++l) {
+ VERIFY_IS_APPROX(static_cast<float>(tensor(i,j,k,l)), static_cast<float>(tensor_after_fft_ifft(i,j,k,l)));
+ }
+ }
+ }
+ }
+}
+
+EIGEN_DECLARE_TEST(cxx11_tensor_ifft) {
+ CALL_SUBTEST(test_1D_fft_ifft_invariant<ColMajor>(4));
+ CALL_SUBTEST(test_1D_fft_ifft_invariant<ColMajor>(16));
+ CALL_SUBTEST(test_1D_fft_ifft_invariant<ColMajor>(32));
+ CALL_SUBTEST(test_1D_fft_ifft_invariant<ColMajor>(1024*1024));
+
+ CALL_SUBTEST(test_2D_fft_ifft_invariant<ColMajor>(4,4));
+ CALL_SUBTEST(test_2D_fft_ifft_invariant<ColMajor>(8,16));
+ CALL_SUBTEST(test_2D_fft_ifft_invariant<ColMajor>(16,32));
+ CALL_SUBTEST(test_2D_fft_ifft_invariant<ColMajor>(1024,1024));
+
+ CALL_SUBTEST(test_3D_fft_ifft_invariant<ColMajor>(4,4,4));
+ CALL_SUBTEST(test_3D_fft_ifft_invariant<ColMajor>(8,16,32));
+ CALL_SUBTEST(test_3D_fft_ifft_invariant<ColMajor>(16,4,8));
+ CALL_SUBTEST(test_3D_fft_ifft_invariant<ColMajor>(256,256,256));
+
+ CALL_SUBTEST(test_sub_fft_ifft_invariant<ColMajor>(4,4,4,4));
+ CALL_SUBTEST(test_sub_fft_ifft_invariant<ColMajor>(8,16,32,64));
+ CALL_SUBTEST(test_sub_fft_ifft_invariant<ColMajor>(16,4,8,12));
+ CALL_SUBTEST(test_sub_fft_ifft_invariant<ColMajor>(64,64,64,64));
+}
diff --git a/unsupported/test/cxx11_tensor_image_op_sycl.cpp b/unsupported/test/cxx11_tensor_image_op_sycl.cpp
new file mode 100644
index 0000000..db1c020
--- /dev/null
+++ b/unsupported/test/cxx11_tensor_image_op_sycl.cpp
@@ -0,0 +1,103 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2016
+// Mehdi Goli Codeplay Software Ltd.
+// Ralph Potter Codeplay Software Ltd.
+// Luke Iwanski Codeplay Software Ltd.
+// Contact: <eigen@codeplay.com>
+// Benoit Steiner <benoit.steiner.goog@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#define EIGEN_TEST_NO_LONGDOUBLE
+#define EIGEN_TEST_NO_COMPLEX
+#define EIGEN_DEFAULT_DENSE_INDEX_TYPE int64_t
+#define EIGEN_USE_SYCL
+
+#include "main.h"
+#include <unsupported/Eigen/CXX11/Tensor>
+
+using Eigen::array;
+using Eigen::SyclDevice;
+using Eigen::Tensor;
+using Eigen::TensorMap;
+
+using Eigen::Tensor;
+using Eigen::RowMajor;
+template <typename DataType, int DataLayout, typename IndexType>
+static void test_image_op_sycl(const Eigen::SyclDevice &sycl_device)
+{
+ IndexType sizeDim1 = 245;
+ IndexType sizeDim2 = 343;
+ IndexType sizeDim3 = 577;
+
+ array<IndexType, 3> input_range ={{sizeDim1, sizeDim2, sizeDim3}};
+ array<IndexType, 3> slice_range ={{sizeDim1-1, sizeDim2, sizeDim3}};
+
+ Tensor<DataType, 3,DataLayout, IndexType> tensor1(input_range);
+ Tensor<DataType, 3,DataLayout, IndexType> tensor2(input_range);
+ Tensor<DataType, 3, DataLayout, IndexType> tensor3(slice_range);
+ Tensor<DataType, 3, DataLayout, IndexType> tensor3_cpu(slice_range);
+
+
+
+ typedef Eigen::DSizes<IndexType, 3> Index3;
+ Index3 strides1(1L,1L, 1L);
+ Index3 indicesStart1(1L, 0L, 0L);
+ Index3 indicesStop1(sizeDim1, sizeDim2, sizeDim3);
+
+ Index3 strides2(1L,1L, 1L);
+ Index3 indicesStart2(0L, 0L, 0L);
+ Index3 indicesStop2(sizeDim1-1, sizeDim2, sizeDim3);
+ Eigen::DSizes<IndexType, 3> sizes(sizeDim1-1,sizeDim2,sizeDim3);
+
+ tensor1.setRandom();
+ tensor2.setRandom();
+
+
+ DataType* gpu_data1 = static_cast<DataType*>(sycl_device.allocate(tensor1.size()*sizeof(DataType)));
+ DataType* gpu_data2 = static_cast<DataType*>(sycl_device.allocate(tensor2.size()*sizeof(DataType)));
+ DataType* gpu_data3 = static_cast<DataType*>(sycl_device.allocate(tensor3.size()*sizeof(DataType)));
+
+ TensorMap<Tensor<DataType, 3, DataLayout, IndexType>> gpu1(gpu_data1, input_range);
+ TensorMap<Tensor<DataType, 3, DataLayout, IndexType>> gpu2(gpu_data2, input_range);
+ TensorMap<Tensor<DataType, 3, DataLayout, IndexType>> gpu3(gpu_data3, slice_range);
+
+ sycl_device.memcpyHostToDevice(gpu_data1, tensor1.data(),(tensor1.size())*sizeof(DataType));
+ sycl_device.memcpyHostToDevice(gpu_data2, tensor2.data(),(tensor2.size())*sizeof(DataType));
+ gpu3.device(sycl_device)= gpu1.slice(indicesStart1, sizes) - gpu2.slice(indicesStart2, sizes);
+ sycl_device.memcpyDeviceToHost(tensor3.data(), gpu_data3,(tensor3.size())*sizeof(DataType));
+
+ tensor3_cpu = tensor1.stridedSlice(indicesStart1,indicesStop1,strides1) - tensor2.stridedSlice(indicesStart2,indicesStop2,strides2);
+
+
+ for (IndexType i = 0; i <slice_range[0] ; ++i) {
+ for (IndexType j = 0; j < slice_range[1]; ++j) {
+ for (IndexType k = 0; k < slice_range[2]; ++k) {
+ VERIFY_IS_EQUAL(tensor3_cpu(i,j,k), tensor3(i,j,k));
+ }
+ }
+ }
+ sycl_device.deallocate(gpu_data1);
+ sycl_device.deallocate(gpu_data2);
+ sycl_device.deallocate(gpu_data3);
+}
+
+
+template<typename DataType, typename dev_Selector> void sycl_computing_test_per_device(dev_Selector s){
+ QueueInterface queueInterface(s);
+ auto sycl_device = Eigen::SyclDevice(&queueInterface);
+ test_image_op_sycl<DataType, RowMajor, int64_t>(sycl_device);
+}
+
+EIGEN_DECLARE_TEST(cxx11_tensor_image_op_sycl) {
+ for (const auto& device :Eigen::get_sycl_supported_devices()) {
+ CALL_SUBTEST(sycl_computing_test_per_device<float>(device));
+#ifdef EIGEN_SYCL_DOUBLE_SUPPORT
+ CALL_SUBTEST(sycl_computing_test_per_device<double>(device));
+#endif
+ }
+}
diff --git a/unsupported/test/cxx11_tensor_image_patch.cpp b/unsupported/test/cxx11_tensor_image_patch.cpp
new file mode 100644
index 0000000..862f1f7
--- /dev/null
+++ b/unsupported/test/cxx11_tensor_image_patch.cpp
@@ -0,0 +1,809 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "main.h"
+
+#include <Eigen/CXX11/Tensor>
+
+using Eigen::Tensor;
+
+void test_simple_patch()
+{
+ Tensor<float, 4> tensor(2,3,5,7);
+ tensor.setRandom();
+ Tensor<float, 4, RowMajor> tensor_row_major = tensor.swap_layout();
+ VERIFY_IS_EQUAL(tensor.dimension(0), tensor_row_major.dimension(3));
+ VERIFY_IS_EQUAL(tensor.dimension(1), tensor_row_major.dimension(2));
+ VERIFY_IS_EQUAL(tensor.dimension(2), tensor_row_major.dimension(1));
+ VERIFY_IS_EQUAL(tensor.dimension(3), tensor_row_major.dimension(0));
+
+ // Single pixel patch: ColMajor
+ Tensor<float, 5> single_pixel_patch;
+ single_pixel_patch = tensor.extract_image_patches(1, 1);
+ VERIFY_IS_EQUAL(single_pixel_patch.dimension(0), 2);
+ VERIFY_IS_EQUAL(single_pixel_patch.dimension(1), 1);
+ VERIFY_IS_EQUAL(single_pixel_patch.dimension(2), 1);
+ VERIFY_IS_EQUAL(single_pixel_patch.dimension(3), 3*5);
+ VERIFY_IS_EQUAL(single_pixel_patch.dimension(4), 7);
+
+ // Single pixel patch: RowMajor
+ Tensor<float, 5, RowMajor> single_pixel_patch_row_major;
+ single_pixel_patch_row_major = tensor_row_major.extract_image_patches(1, 1);
+ VERIFY_IS_EQUAL(single_pixel_patch_row_major.dimension(0), 7);
+ VERIFY_IS_EQUAL(single_pixel_patch_row_major.dimension(1), 3*5);
+ VERIFY_IS_EQUAL(single_pixel_patch_row_major.dimension(2), 1);
+ VERIFY_IS_EQUAL(single_pixel_patch_row_major.dimension(3), 1);
+ VERIFY_IS_EQUAL(single_pixel_patch_row_major.dimension(4), 2);
+
+ for (int i = 0; i < tensor.size(); ++i) {
+ // ColMajor
+ if (tensor.data()[i] != single_pixel_patch.data()[i]) {
+ std::cout << "Mismatch detected at index " << i << " : "
+ << tensor.data()[i] << " vs " << single_pixel_patch.data()[i]
+ << std::endl;
+ }
+ VERIFY_IS_EQUAL(single_pixel_patch.data()[i], tensor.data()[i]);
+ // RowMajor
+ if (tensor_row_major.data()[i] != single_pixel_patch_row_major.data()[i]) {
+ std::cout << "Mismatch detected at index " << i << " : "
+ << tensor.data()[i] << " vs "
+ << single_pixel_patch_row_major.data()[i] << std::endl;
+ }
+ VERIFY_IS_EQUAL(single_pixel_patch_row_major.data()[i],
+ tensor_row_major.data()[i]);
+ VERIFY_IS_EQUAL(tensor.data()[i], tensor_row_major.data()[i]);
+ VERIFY_IS_EQUAL(single_pixel_patch.data()[i],
+ single_pixel_patch_row_major.data()[i]);
+ }
+
+ // Entire image patch: ColMajor
+ Tensor<float, 5> entire_image_patch;
+ entire_image_patch = tensor.extract_image_patches(3, 5);
+ VERIFY_IS_EQUAL(entire_image_patch.dimension(0), 2);
+ VERIFY_IS_EQUAL(entire_image_patch.dimension(1), 3);
+ VERIFY_IS_EQUAL(entire_image_patch.dimension(2), 5);
+ VERIFY_IS_EQUAL(entire_image_patch.dimension(3), 3*5);
+ VERIFY_IS_EQUAL(entire_image_patch.dimension(4), 7);
+
+ // Entire image patch: RowMajor
+ Tensor<float, 5, RowMajor> entire_image_patch_row_major;
+ entire_image_patch_row_major = tensor_row_major.extract_image_patches(3, 5);
+ VERIFY_IS_EQUAL(entire_image_patch_row_major.dimension(0), 7);
+ VERIFY_IS_EQUAL(entire_image_patch_row_major.dimension(1), 3*5);
+ VERIFY_IS_EQUAL(entire_image_patch_row_major.dimension(2), 5);
+ VERIFY_IS_EQUAL(entire_image_patch_row_major.dimension(3), 3);
+ VERIFY_IS_EQUAL(entire_image_patch_row_major.dimension(4), 2);
+
+ for (int i = 0; i < 3; ++i) {
+ for (int j = 0; j < 5; ++j) {
+ int patchId = i+3*j;
+ for (int r = 0; r < 3; ++r) {
+ for (int c = 0; c < 5; ++c) {
+ for (int d = 0; d < 2; ++d) {
+ for (int b = 0; b < 7; ++b) {
+ float expected = 0.0f;
+ float expected_row_major = 0.0f;
+ if (r-1+i >= 0 && c-2+j >= 0 && r-1+i < 3 && c-2+j < 5) {
+ expected = tensor(d, r-1+i, c-2+j, b);
+ expected_row_major = tensor_row_major(b, c-2+j, r-1+i, d);
+ }
+ // ColMajor
+ if (entire_image_patch(d, r, c, patchId, b) != expected) {
+ std::cout << "Mismatch detected at index i=" << i << " j=" << j << " r=" << r << " c=" << c << " d=" << d << " b=" << b << std::endl;
+ }
+ VERIFY_IS_EQUAL(entire_image_patch(d, r, c, patchId, b), expected);
+ // RowMajor
+ if (entire_image_patch_row_major(b, patchId, c, r, d) !=
+ expected_row_major) {
+ std::cout << "Mismatch detected at index i=" << i << " j=" << j
+ << " r=" << r << " c=" << c << " d=" << d << " b=" << b
+ << std::endl;
+ }
+ VERIFY_IS_EQUAL(entire_image_patch_row_major(b, patchId, c, r, d),
+ expected_row_major);
+ // Check that ColMajor and RowMajor agree.
+ VERIFY_IS_EQUAL(expected, expected_row_major);
+ }
+ }
+ }
+ }
+ }
+ }
+
+ // 2D patch: ColMajor
+ Tensor<float, 5> twod_patch;
+ twod_patch = tensor.extract_image_patches(2, 2);
+ VERIFY_IS_EQUAL(twod_patch.dimension(0), 2);
+ VERIFY_IS_EQUAL(twod_patch.dimension(1), 2);
+ VERIFY_IS_EQUAL(twod_patch.dimension(2), 2);
+ VERIFY_IS_EQUAL(twod_patch.dimension(3), 3*5);
+ VERIFY_IS_EQUAL(twod_patch.dimension(4), 7);
+
+ // 2D patch: RowMajor
+ Tensor<float, 5, RowMajor> twod_patch_row_major;
+ twod_patch_row_major = tensor_row_major.extract_image_patches(2, 2);
+ VERIFY_IS_EQUAL(twod_patch_row_major.dimension(0), 7);
+ VERIFY_IS_EQUAL(twod_patch_row_major.dimension(1), 3*5);
+ VERIFY_IS_EQUAL(twod_patch_row_major.dimension(2), 2);
+ VERIFY_IS_EQUAL(twod_patch_row_major.dimension(3), 2);
+ VERIFY_IS_EQUAL(twod_patch_row_major.dimension(4), 2);
+
+
+ // Based on the calculation described in TensorTraits.h, padding happens to be 0.
+ int row_padding = 0;
+ int col_padding = 0;
+ int stride = 1;
+
+ for (int i = 0; i < 3; ++i) {
+ for (int j = 0; j < 5; ++j) {
+ int patchId = i+3*j;
+ for (int r = 0; r < 2; ++r) {
+ for (int c = 0; c < 2; ++c) {
+ for (int d = 0; d < 2; ++d) {
+ for (int b = 0; b < 7; ++b) {
+ float expected = 0.0f;
+ float expected_row_major = 0.0f;
+ int row_offset = r*stride + i - row_padding;
+ int col_offset = c*stride + j - col_padding;
+ // ColMajor
+ if (row_offset >= 0 && col_offset >= 0 && row_offset < tensor.dimension(1) && col_offset < tensor.dimension(2)) {
+ expected = tensor(d, row_offset, col_offset, b);
+ }
+ if (twod_patch(d, r, c, patchId, b) != expected) {
+ std::cout << "Mismatch detected at index i=" << i << " j=" << j << " r=" << r << " c=" << c << " d=" << d << " b=" << b << std::endl;
+ }
+ VERIFY_IS_EQUAL(twod_patch(d, r, c, patchId, b), expected);
+
+ // RowMajor
+ if (row_offset >= 0 && col_offset >= 0 && row_offset < tensor_row_major.dimension(2) && col_offset < tensor_row_major.dimension(1)) {
+ expected_row_major = tensor_row_major(b, col_offset, row_offset, d);
+
+ }
+ if (twod_patch_row_major(b, patchId, c, r, d) != expected_row_major) {
+ std::cout << "Mismatch detected at index i=" << i << " j=" << j << " r=" << r << " c=" << c << " d=" << d << " b=" << b << std::endl;
+ }
+ VERIFY_IS_EQUAL(twod_patch_row_major(b, patchId, c, r, d), expected_row_major);
+ // Check that ColMajor and RowMajor agree.
+ VERIFY_IS_EQUAL(expected, expected_row_major);
+ }
+ }
+ }
+ }
+ }
+ }
+}
+
+// Verifies VALID padding (no padding) with incrementing values.
+void test_patch_padding_valid()
+{
+ int input_depth = 3;
+ int input_rows = 3;
+ int input_cols = 3;
+ int input_batches = 1;
+ int ksize = 2; // Corresponds to the Rows and Cols for tensor.extract_image_patches<>.
+ int stride = 2; // Only same stride is supported.
+ Tensor<float, 4> tensor(input_depth, input_rows, input_cols, input_batches);
+ // Initializes tensor with incrementing numbers.
+ for (int i = 0; i < tensor.size(); ++i) {
+ tensor.data()[i] = i + 1;
+ }
+ // ColMajor
+ Tensor<float, 5> result = tensor.extract_image_patches(ksize, ksize, stride, stride, 1, 1, PADDING_VALID);
+
+ VERIFY_IS_EQUAL(result.dimension(0), input_depth); // depth
+ VERIFY_IS_EQUAL(result.dimension(1), ksize); // kernel rows
+ VERIFY_IS_EQUAL(result.dimension(2), ksize); // kernel cols
+ VERIFY_IS_EQUAL(result.dimension(3), 1); // number of patches
+ VERIFY_IS_EQUAL(result.dimension(4), input_batches); // number of batches
+
+ // RowMajor
+ Tensor<float, 4, RowMajor> tensor_row_major = tensor.swap_layout();
+ VERIFY_IS_EQUAL(tensor.dimension(0), tensor_row_major.dimension(3));
+ VERIFY_IS_EQUAL(tensor.dimension(1), tensor_row_major.dimension(2));
+ VERIFY_IS_EQUAL(tensor.dimension(2), tensor_row_major.dimension(1));
+ VERIFY_IS_EQUAL(tensor.dimension(3), tensor_row_major.dimension(0));
+
+ Tensor<float, 5, RowMajor> result_row_major = tensor_row_major.extract_image_patches(ksize, ksize, stride, stride, 1, 1, PADDING_VALID);
+ VERIFY_IS_EQUAL(result.dimension(0), result_row_major.dimension(4));
+ VERIFY_IS_EQUAL(result.dimension(1), result_row_major.dimension(3));
+ VERIFY_IS_EQUAL(result.dimension(2), result_row_major.dimension(2));
+ VERIFY_IS_EQUAL(result.dimension(3), result_row_major.dimension(1));
+ VERIFY_IS_EQUAL(result.dimension(4), result_row_major.dimension(0));
+
+ // No padding is carried out.
+ int row_padding = 0;
+ int col_padding = 0;
+
+ for (int i = 0; (i+stride+ksize-1) < input_rows; i += stride) { // input rows
+ for (int j = 0; (j+stride+ksize-1) < input_cols; j += stride) { // input cols
+ int patchId = i+input_rows*j;
+ for (int r = 0; r < ksize; ++r) { // patch rows
+ for (int c = 0; c < ksize; ++c) { // patch cols
+ for (int d = 0; d < input_depth; ++d) { // depth
+ for (int b = 0; b < input_batches; ++b) { // batch
+ float expected = 0.0f;
+ float expected_row_major = 0.0f;
+ int row_offset = r + i - row_padding;
+ int col_offset = c + j - col_padding;
+ if (row_offset >= 0 && col_offset >= 0 && row_offset < input_rows && col_offset < input_cols) {
+ expected = tensor(d, row_offset, col_offset, b);
+ expected_row_major = tensor_row_major(b, col_offset, row_offset, d);
+ }
+ // ColMajor
+ if (result(d, r, c, patchId, b) != expected) {
+ std::cout << "Mismatch detected at index i=" << i << " j=" << j << " r=" << r << " c=" << c << " d=" << d << " b=" << b << std::endl;
+ }
+ VERIFY_IS_EQUAL(result(d, r, c, patchId, b), expected);
+ // RowMajor
+ if (result_row_major(b, patchId, c, r, d) != expected_row_major) {
+ std::cout << "Mismatch detected at index i=" << i << " j=" << j << " r=" << r << " c=" << c << " d=" << d << " b=" << b << std::endl;
+ }
+ VERIFY_IS_EQUAL(result_row_major(b, patchId, c, r, d), expected_row_major);
+ // Check that ColMajor and RowMajor agree.
+ VERIFY_IS_EQUAL(expected, expected_row_major);
+ }
+ }
+ }
+ }
+ }
+ }
+}
+
+// Verifies VALID padding (no padding) with the same value.
+void test_patch_padding_valid_same_value()
+{
+ int input_depth = 1;
+ int input_rows = 5;
+ int input_cols = 5;
+ int input_batches = 2;
+ int ksize = 3; // Corresponds to the Rows and Cols for tensor.extract_image_patches<>.
+ int stride = 2; // Only same stride is supported.
+ // ColMajor
+ Tensor<float, 4> tensor(input_depth, input_rows, input_cols, input_batches);
+ tensor = tensor.constant(11.0f);
+ Tensor<float, 5> result = tensor.extract_image_patches(ksize, ksize, stride, stride, 1, 1, PADDING_VALID);
+
+ VERIFY_IS_EQUAL(result.dimension(0), input_depth); // depth
+ VERIFY_IS_EQUAL(result.dimension(1), ksize); // kernel rows
+ VERIFY_IS_EQUAL(result.dimension(2), ksize); // kernel cols
+ VERIFY_IS_EQUAL(result.dimension(3), 4); // number of patches
+ VERIFY_IS_EQUAL(result.dimension(4), input_batches); // number of batches
+
+ // RowMajor
+ Tensor<float, 4, RowMajor> tensor_row_major = tensor.swap_layout();
+ VERIFY_IS_EQUAL(tensor.dimension(0), tensor_row_major.dimension(3));
+ VERIFY_IS_EQUAL(tensor.dimension(1), tensor_row_major.dimension(2));
+ VERIFY_IS_EQUAL(tensor.dimension(2), tensor_row_major.dimension(1));
+ VERIFY_IS_EQUAL(tensor.dimension(3), tensor_row_major.dimension(0));
+
+ Tensor<float, 5, RowMajor> result_row_major = tensor_row_major.extract_image_patches(ksize, ksize, stride, stride, 1, 1, PADDING_VALID);
+ VERIFY_IS_EQUAL(result.dimension(0), result_row_major.dimension(4));
+ VERIFY_IS_EQUAL(result.dimension(1), result_row_major.dimension(3));
+ VERIFY_IS_EQUAL(result.dimension(2), result_row_major.dimension(2));
+ VERIFY_IS_EQUAL(result.dimension(3), result_row_major.dimension(1));
+ VERIFY_IS_EQUAL(result.dimension(4), result_row_major.dimension(0));
+
+ // No padding is carried out.
+ int row_padding = 0;
+ int col_padding = 0;
+
+ for (int i = 0; (i+stride+ksize-1) <= input_rows; i += stride) { // input rows
+ for (int j = 0; (j+stride+ksize-1) <= input_cols; j += stride) { // input cols
+ int patchId = i+input_rows*j;
+ for (int r = 0; r < ksize; ++r) { // patch rows
+ for (int c = 0; c < ksize; ++c) { // patch cols
+ for (int d = 0; d < input_depth; ++d) { // depth
+ for (int b = 0; b < input_batches; ++b) { // batch
+ float expected = 0.0f;
+ float expected_row_major = 0.0f;
+ int row_offset = r + i - row_padding;
+ int col_offset = c + j - col_padding;
+ if (row_offset >= 0 && col_offset >= 0 && row_offset < input_rows && col_offset < input_cols) {
+ expected = tensor(d, row_offset, col_offset, b);
+ expected_row_major = tensor_row_major(b, col_offset, row_offset, d);
+ }
+ // ColMajor
+ if (result(d, r, c, patchId, b) != expected) {
+ std::cout << "Mismatch detected at index i=" << i << " j=" << j << " r=" << r << " c=" << c << " d=" << d << " b=" << b << std::endl;
+ }
+ VERIFY_IS_EQUAL(result(d, r, c, patchId, b), expected);
+ // RowMajor
+ if (result_row_major(b, patchId, c, r, d) != expected_row_major) {
+ std::cout << "Mismatch detected at index i=" << i << " j=" << j << " r=" << r << " c=" << c << " d=" << d << " b=" << b << std::endl;
+ }
+ VERIFY_IS_EQUAL(result_row_major(b, patchId, c, r, d), expected_row_major);
+ // Check that ColMajor and RowMajor agree.
+ VERIFY_IS_EQUAL(expected, expected_row_major);
+ }
+ }
+ }
+ }
+ }
+ }
+}
+
+// Verifies SAME padding.
+void test_patch_padding_same()
+{
+ int input_depth = 3;
+ int input_rows = 4;
+ int input_cols = 2;
+ int input_batches = 1;
+ int ksize = 2; // Corresponds to the Rows and Cols for tensor.extract_image_patches<>.
+ int stride = 2; // Only same stride is supported.
+ // ColMajor
+ Tensor<float, 4> tensor(input_depth, input_rows, input_cols, input_batches);
+ // Initializes tensor with incrementing numbers.
+ for (int i = 0; i < tensor.size(); ++i) {
+ tensor.data()[i] = i + 1;
+ }
+ Tensor<float, 5> result = tensor.extract_image_patches(ksize, ksize, stride, stride, PADDING_SAME);
+
+ VERIFY_IS_EQUAL(result.dimension(0), input_depth); // depth
+ VERIFY_IS_EQUAL(result.dimension(1), ksize); // kernel rows
+ VERIFY_IS_EQUAL(result.dimension(2), ksize); // kernel cols
+ VERIFY_IS_EQUAL(result.dimension(3), 2); // number of patches
+ VERIFY_IS_EQUAL(result.dimension(4), input_batches); // number of batches
+
+ // RowMajor
+ Tensor<float, 4, RowMajor> tensor_row_major = tensor.swap_layout();
+ VERIFY_IS_EQUAL(tensor.dimension(0), tensor_row_major.dimension(3));
+ VERIFY_IS_EQUAL(tensor.dimension(1), tensor_row_major.dimension(2));
+ VERIFY_IS_EQUAL(tensor.dimension(2), tensor_row_major.dimension(1));
+ VERIFY_IS_EQUAL(tensor.dimension(3), tensor_row_major.dimension(0));
+
+ Tensor<float, 5, RowMajor> result_row_major = tensor_row_major.extract_image_patches(ksize, ksize, stride, stride, PADDING_SAME);
+ VERIFY_IS_EQUAL(result.dimension(0), result_row_major.dimension(4));
+ VERIFY_IS_EQUAL(result.dimension(1), result_row_major.dimension(3));
+ VERIFY_IS_EQUAL(result.dimension(2), result_row_major.dimension(2));
+ VERIFY_IS_EQUAL(result.dimension(3), result_row_major.dimension(1));
+ VERIFY_IS_EQUAL(result.dimension(4), result_row_major.dimension(0));
+
+ // Based on the calculation described in TensorTraits.h, padding happens to be
+ // 0.
+ int row_padding = 0;
+ int col_padding = 0;
+
+ for (int i = 0; (i+stride+ksize-1) <= input_rows; i += stride) { // input rows
+ for (int j = 0; (j+stride+ksize-1) <= input_cols; j += stride) { // input cols
+ int patchId = i+input_rows*j;
+ for (int r = 0; r < ksize; ++r) { // patch rows
+ for (int c = 0; c < ksize; ++c) { // patch cols
+ for (int d = 0; d < input_depth; ++d) { // depth
+ for (int b = 0; b < input_batches; ++b) { // batch
+ float expected = 0.0f;
+ float expected_row_major = 0.0f;
+ int row_offset = r*stride + i - row_padding;
+ int col_offset = c*stride + j - col_padding;
+ if (row_offset >= 0 && col_offset >= 0 && row_offset < input_rows && col_offset < input_cols) {
+ expected = tensor(d, row_offset, col_offset, b);
+ expected_row_major = tensor_row_major(b, col_offset, row_offset, d);
+ }
+ // ColMajor
+ if (result(d, r, c, patchId, b) != expected) {
+ std::cout << "Mismatch detected at index i=" << i << " j=" << j << " r=" << r << " c=" << c << " d=" << d << " b=" << b << std::endl;
+ }
+ VERIFY_IS_EQUAL(result(d, r, c, patchId, b), expected);
+ // RowMajor
+ if (result_row_major(b, patchId, c, r, d) != expected_row_major) {
+ std::cout << "Mismatch detected at index i=" << i << " j=" << j << " r=" << r << " c=" << c << " d=" << d << " b=" << b << std::endl;
+ }
+ VERIFY_IS_EQUAL(result_row_major(b, patchId, c, r, d), expected_row_major);
+ // Check that ColMajor and RowMajor agree.
+ VERIFY_IS_EQUAL(expected, expected_row_major);
+ }
+ }
+ }
+ }
+ }
+ }
+}
+
+// Verifies that SAME padding, when computed as negative values, will be clipped
+// to zero.
+void test_patch_padding_same_negative_padding_clip_to_zero() {
+ int input_depth = 1;
+ int input_rows = 15;
+ int input_cols = 1;
+ int input_batches = 1;
+ int ksize = 1; // Corresponds to the Rows and Cols for
+ // tensor.extract_image_patches<>.
+ int row_stride = 5;
+ int col_stride = 1;
+ // ColMajor
+ Tensor<float, 4> tensor(input_depth, input_rows, input_cols, input_batches);
+ // Initializes tensor with incrementing numbers.
+ for (int i = 0; i < tensor.size(); ++i) {
+ tensor.data()[i] = i + 1;
+ }
+ Tensor<float, 5> result = tensor.extract_image_patches(
+ ksize, ksize, row_stride, col_stride, 1, 1, PADDING_SAME);
+ // row padding will be computed as -2 originally and then be clipped to 0.
+ VERIFY_IS_EQUAL(result.coeff(0), 1.0f);
+ VERIFY_IS_EQUAL(result.coeff(1), 6.0f);
+ VERIFY_IS_EQUAL(result.coeff(2), 11.0f);
+
+ VERIFY_IS_EQUAL(result.dimension(0), input_depth); // depth
+ VERIFY_IS_EQUAL(result.dimension(1), ksize); // kernel rows
+ VERIFY_IS_EQUAL(result.dimension(2), ksize); // kernel cols
+ VERIFY_IS_EQUAL(result.dimension(3), 3); // number of patches
+ VERIFY_IS_EQUAL(result.dimension(4), input_batches); // number of batches
+
+ // RowMajor
+ Tensor<float, 4, RowMajor> tensor_row_major = tensor.swap_layout();
+ VERIFY_IS_EQUAL(tensor.dimension(0), tensor_row_major.dimension(3));
+ VERIFY_IS_EQUAL(tensor.dimension(1), tensor_row_major.dimension(2));
+ VERIFY_IS_EQUAL(tensor.dimension(2), tensor_row_major.dimension(1));
+ VERIFY_IS_EQUAL(tensor.dimension(3), tensor_row_major.dimension(0));
+
+ Tensor<float, 5, RowMajor> result_row_major =
+ tensor_row_major.extract_image_patches(ksize, ksize, row_stride,
+ col_stride, 1, 1, PADDING_SAME);
+ VERIFY_IS_EQUAL(result_row_major.coeff(0), 1.0f);
+ VERIFY_IS_EQUAL(result_row_major.coeff(1), 6.0f);
+ VERIFY_IS_EQUAL(result_row_major.coeff(2), 11.0f);
+
+ VERIFY_IS_EQUAL(result.dimension(0), result_row_major.dimension(4));
+ VERIFY_IS_EQUAL(result.dimension(1), result_row_major.dimension(3));
+ VERIFY_IS_EQUAL(result.dimension(2), result_row_major.dimension(2));
+ VERIFY_IS_EQUAL(result.dimension(3), result_row_major.dimension(1));
+ VERIFY_IS_EQUAL(result.dimension(4), result_row_major.dimension(0));
+}
+
+void test_patch_no_extra_dim()
+{
+ Tensor<float, 3> tensor(2,3,5);
+ tensor.setRandom();
+ Tensor<float, 3, RowMajor> tensor_row_major = tensor.swap_layout();
+ VERIFY_IS_EQUAL(tensor.dimension(0), tensor_row_major.dimension(2));
+ VERIFY_IS_EQUAL(tensor.dimension(1), tensor_row_major.dimension(1));
+ VERIFY_IS_EQUAL(tensor.dimension(2), tensor_row_major.dimension(0));
+
+ // Single pixel patch: ColMajor
+ Tensor<float, 4> single_pixel_patch;
+ single_pixel_patch = tensor.extract_image_patches(1, 1);
+ VERIFY_IS_EQUAL(single_pixel_patch.dimension(0), 2);
+ VERIFY_IS_EQUAL(single_pixel_patch.dimension(1), 1);
+ VERIFY_IS_EQUAL(single_pixel_patch.dimension(2), 1);
+ VERIFY_IS_EQUAL(single_pixel_patch.dimension(3), 3*5);
+
+ // Single pixel patch: RowMajor
+ Tensor<float, 4, RowMajor> single_pixel_patch_row_major;
+ single_pixel_patch_row_major = tensor_row_major.extract_image_patches(1, 1);
+ VERIFY_IS_EQUAL(single_pixel_patch_row_major.dimension(0), 3*5);
+ VERIFY_IS_EQUAL(single_pixel_patch_row_major.dimension(1), 1);
+ VERIFY_IS_EQUAL(single_pixel_patch_row_major.dimension(2), 1);
+ VERIFY_IS_EQUAL(single_pixel_patch_row_major.dimension(3), 2);
+
+ for (int i = 0; i < tensor.size(); ++i) {
+ // ColMajor
+ if (tensor.data()[i] != single_pixel_patch.data()[i]) {
+ std::cout << "Mismatch detected at index " << i << " : " << tensor.data()[i] << " vs " << single_pixel_patch.data()[i] << std::endl;
+ }
+ VERIFY_IS_EQUAL(single_pixel_patch.data()[i], tensor.data()[i]);
+ // RowMajor
+ if (tensor_row_major.data()[i] != single_pixel_patch_row_major.data()[i]) {
+ std::cout << "Mismatch detected at index " << i << " : "
+ << tensor.data()[i] << " vs "
+ << single_pixel_patch_row_major.data()[i] << std::endl;
+ }
+ VERIFY_IS_EQUAL(single_pixel_patch_row_major.data()[i],
+ tensor_row_major.data()[i]);
+ VERIFY_IS_EQUAL(tensor.data()[i], tensor_row_major.data()[i]);
+ VERIFY_IS_EQUAL(single_pixel_patch.data()[i],
+ single_pixel_patch_row_major.data()[i]);
+ }
+
+ // Entire image patch: ColMajor
+ Tensor<float, 4> entire_image_patch;
+ entire_image_patch = tensor.extract_image_patches(3, 5);
+ VERIFY_IS_EQUAL(entire_image_patch.dimension(0), 2);
+ VERIFY_IS_EQUAL(entire_image_patch.dimension(1), 3);
+ VERIFY_IS_EQUAL(entire_image_patch.dimension(2), 5);
+ VERIFY_IS_EQUAL(entire_image_patch.dimension(3), 3*5);
+
+ // Entire image patch: RowMajor
+ Tensor<float, 4, RowMajor> entire_image_patch_row_major;
+ entire_image_patch_row_major = tensor_row_major.extract_image_patches(3, 5);
+ VERIFY_IS_EQUAL(entire_image_patch_row_major.dimension(0), 3*5);
+ VERIFY_IS_EQUAL(entire_image_patch_row_major.dimension(1), 5);
+ VERIFY_IS_EQUAL(entire_image_patch_row_major.dimension(2), 3);
+ VERIFY_IS_EQUAL(entire_image_patch_row_major.dimension(3), 2);
+
+ for (int i = 0; i < 3; ++i) {
+ for (int j = 0; j < 5; ++j) {
+ int patchId = i+3*j;
+ for (int r = 0; r < 3; ++r) {
+ for (int c = 0; c < 5; ++c) {
+ for (int d = 0; d < 2; ++d) {
+ float expected = 0.0f;
+ float expected_row_major = 0.0f;
+ if (r-1+i >= 0 && c-2+j >= 0 && r-1+i < 3 && c-2+j < 5) {
+ expected = tensor(d, r-1+i, c-2+j);
+ expected_row_major = tensor_row_major(c-2+j, r-1+i, d);
+ }
+ // ColMajor
+ if (entire_image_patch(d, r, c, patchId) != expected) {
+ std::cout << "Mismatch detected at index i=" << i << " j=" << j << " r=" << r << " c=" << c << " d=" << d << std::endl;
+ }
+ VERIFY_IS_EQUAL(entire_image_patch(d, r, c, patchId), expected);
+ // RowMajor
+ if (entire_image_patch_row_major(patchId, c, r, d) !=
+ expected_row_major) {
+ std::cout << "Mismatch detected at index i=" << i << " j=" << j << " r=" << r << " c=" << c << " d=" << d << std::endl;
+ }
+ VERIFY_IS_EQUAL(entire_image_patch_row_major(patchId, c, r, d),
+ expected_row_major);
+ // Check that ColMajor and RowMajor agree.
+ VERIFY_IS_EQUAL(expected, expected_row_major);
+ }
+ }
+ }
+ }
+ }
+
+ // 2D patch: ColMajor
+ Tensor<float, 4> twod_patch;
+ twod_patch = tensor.extract_image_patches(2, 2);
+ VERIFY_IS_EQUAL(twod_patch.dimension(0), 2);
+ VERIFY_IS_EQUAL(twod_patch.dimension(1), 2);
+ VERIFY_IS_EQUAL(twod_patch.dimension(2), 2);
+ VERIFY_IS_EQUAL(twod_patch.dimension(3), 3*5);
+
+ // 2D patch: RowMajor
+ Tensor<float, 4, RowMajor> twod_patch_row_major;
+ twod_patch_row_major = tensor_row_major.extract_image_patches(2, 2);
+ VERIFY_IS_EQUAL(twod_patch_row_major.dimension(0), 3*5);
+ VERIFY_IS_EQUAL(twod_patch_row_major.dimension(1), 2);
+ VERIFY_IS_EQUAL(twod_patch_row_major.dimension(2), 2);
+ VERIFY_IS_EQUAL(twod_patch_row_major.dimension(3), 2);
+
+ // Based on the calculation described in TensorTraits.h, padding happens to be 0.
+ int row_padding = 0;
+ int col_padding = 0;
+ int stride = 1;
+
+ for (int i = 0; i < 3; ++i) {
+ for (int j = 0; j < 5; ++j) {
+ int patchId = i+3*j;
+ for (int r = 0; r < 2; ++r) {
+ for (int c = 0; c < 2; ++c) {
+ for (int d = 0; d < 2; ++d) {
+ float expected = 0.0f;
+ float expected_row_major = 0.0f;
+ int row_offset = r*stride + i - row_padding;
+ int col_offset = c*stride + j - col_padding;
+ // ColMajor
+ if (row_offset >= 0 && col_offset >= 0 && row_offset < tensor.dimension(1) && col_offset < tensor.dimension(2)) {
+ expected = tensor(d, row_offset, col_offset);
+ }
+ if (twod_patch(d, r, c, patchId) != expected) {
+ std::cout << "Mismatch detected at index i=" << i << " j=" << j << " r=" << r << " c=" << c << " d=" << d << std::endl;
+ }
+ VERIFY_IS_EQUAL(twod_patch(d, r, c, patchId), expected);
+ // RowMajor
+ if (row_offset >= 0 && col_offset >= 0 && row_offset < tensor_row_major.dimension(1) && col_offset < tensor_row_major.dimension(0)) {
+ expected_row_major = tensor_row_major(col_offset, row_offset, d);
+ }
+ if (twod_patch_row_major(patchId, c, r, d) != expected_row_major) {
+ std::cout << "Mismatch detected at index i=" << i << " j=" << j << " r=" << r << " c=" << c << " d=" << d << std::endl;
+ }
+ VERIFY_IS_EQUAL(twod_patch_row_major(patchId, c, r, d), expected_row_major);
+ // Check that ColMajor and RowMajor agree.
+ VERIFY_IS_EQUAL(expected, expected_row_major);
+ }
+ }
+ }
+ }
+ }
+}
+
+void test_imagenet_patches()
+{
+ // Test the code on typical configurations used by the 'imagenet' benchmarks at
+ // https://github.com/soumith/convnet-benchmarks
+ // ColMajor
+ Tensor<float, 4> l_in(3, 128, 128, 16);
+ l_in.setRandom();
+ Tensor<float, 5> l_out = l_in.extract_image_patches(11, 11);
+ VERIFY_IS_EQUAL(l_out.dimension(0), 3);
+ VERIFY_IS_EQUAL(l_out.dimension(1), 11);
+ VERIFY_IS_EQUAL(l_out.dimension(2), 11);
+ VERIFY_IS_EQUAL(l_out.dimension(3), 128*128);
+ VERIFY_IS_EQUAL(l_out.dimension(4), 16);
+
+ // RowMajor
+ Tensor<float, 5, RowMajor> l_out_row_major = l_in.swap_layout().extract_image_patches(11, 11);
+ VERIFY_IS_EQUAL(l_out_row_major.dimension(0), 16);
+ VERIFY_IS_EQUAL(l_out_row_major.dimension(1), 128*128);
+ VERIFY_IS_EQUAL(l_out_row_major.dimension(2), 11);
+ VERIFY_IS_EQUAL(l_out_row_major.dimension(3), 11);
+ VERIFY_IS_EQUAL(l_out_row_major.dimension(4), 3);
+
+ for (int b = 0; b < 16; ++b) {
+ for (int i = 0; i < 128; ++i) {
+ for (int j = 0; j < 128; ++j) {
+ int patchId = i+128*j;
+ for (int c = 0; c < 11; ++c) {
+ for (int r = 0; r < 11; ++r) {
+ for (int d = 0; d < 3; ++d) {
+ float expected = 0.0f;
+ if (r-5+i >= 0 && c-5+j >= 0 && r-5+i < 128 && c-5+j < 128) {
+ expected = l_in(d, r-5+i, c-5+j, b);
+ }
+ // ColMajor
+ if (l_out(d, r, c, patchId, b) != expected) {
+ std::cout << "Mismatch detected at index i=" << i << " j=" << j << " r=" << r << " c=" << c << " d=" << d << " b=" << b << std::endl;
+ }
+ VERIFY_IS_EQUAL(l_out(d, r, c, patchId, b), expected);
+ // RowMajor
+ if (l_out_row_major(b, patchId, c, r, d) !=
+ expected) {
+ std::cout << "Mismatch detected at index i=" << i << " j=" << j
+ << " r=" << r << " c=" << c << " d=" << d << " b=" << b
+ << std::endl;
+ }
+ VERIFY_IS_EQUAL(l_out_row_major(b, patchId, c, r, d),
+ expected);
+ }
+ }
+ }
+ }
+ }
+ }
+
+ // ColMajor
+ l_in.resize(16, 64, 64, 32);
+ l_in.setRandom();
+ l_out = l_in.extract_image_patches(9, 9);
+ VERIFY_IS_EQUAL(l_out.dimension(0), 16);
+ VERIFY_IS_EQUAL(l_out.dimension(1), 9);
+ VERIFY_IS_EQUAL(l_out.dimension(2), 9);
+ VERIFY_IS_EQUAL(l_out.dimension(3), 64*64);
+ VERIFY_IS_EQUAL(l_out.dimension(4), 32);
+
+ // RowMajor
+ l_out_row_major = l_in.swap_layout().extract_image_patches(9, 9);
+ VERIFY_IS_EQUAL(l_out_row_major.dimension(0), 32);
+ VERIFY_IS_EQUAL(l_out_row_major.dimension(1), 64*64);
+ VERIFY_IS_EQUAL(l_out_row_major.dimension(2), 9);
+ VERIFY_IS_EQUAL(l_out_row_major.dimension(3), 9);
+ VERIFY_IS_EQUAL(l_out_row_major.dimension(4), 16);
+
+ for (int b = 0; b < 32; ++b) {
+ for (int i = 0; i < 64; ++i) {
+ for (int j = 0; j < 64; ++j) {
+ int patchId = i+64*j;
+ for (int c = 0; c < 9; ++c) {
+ for (int r = 0; r < 9; ++r) {
+ for (int d = 0; d < 16; ++d) {
+ float expected = 0.0f;
+ if (r-4+i >= 0 && c-4+j >= 0 && r-4+i < 64 && c-4+j < 64) {
+ expected = l_in(d, r-4+i, c-4+j, b);
+ }
+ // ColMajor
+ if (l_out(d, r, c, patchId, b) != expected) {
+ std::cout << "Mismatch detected at index i=" << i << " j=" << j << " r=" << r << " c=" << c << " d=" << d << " b=" << b << std::endl;
+ }
+ VERIFY_IS_EQUAL(l_out(d, r, c, patchId, b), expected);
+ // RowMajor
+ if (l_out_row_major(b, patchId, c, r, d) != expected) {
+ std::cout << "Mismatch detected at index i=" << i << " j=" << j << " r=" << r << " c=" << c << " d=" << d << " b=" << b << std::endl;
+ }
+ VERIFY_IS_EQUAL(l_out_row_major(b, patchId, c, r, d), expected);
+ }
+ }
+ }
+ }
+ }
+ }
+
+ // ColMajor
+ l_in.resize(32, 16, 16, 32);
+ l_in.setRandom();
+ l_out = l_in.extract_image_patches(7, 7);
+ VERIFY_IS_EQUAL(l_out.dimension(0), 32);
+ VERIFY_IS_EQUAL(l_out.dimension(1), 7);
+ VERIFY_IS_EQUAL(l_out.dimension(2), 7);
+ VERIFY_IS_EQUAL(l_out.dimension(3), 16*16);
+ VERIFY_IS_EQUAL(l_out.dimension(4), 32);
+
+ // RowMajor
+ l_out_row_major = l_in.swap_layout().extract_image_patches(7, 7);
+ VERIFY_IS_EQUAL(l_out_row_major.dimension(0), 32);
+ VERIFY_IS_EQUAL(l_out_row_major.dimension(1), 16*16);
+ VERIFY_IS_EQUAL(l_out_row_major.dimension(2), 7);
+ VERIFY_IS_EQUAL(l_out_row_major.dimension(3), 7);
+ VERIFY_IS_EQUAL(l_out_row_major.dimension(4), 32);
+
+ for (int b = 0; b < 32; ++b) {
+ for (int i = 0; i < 16; ++i) {
+ for (int j = 0; j < 16; ++j) {
+ int patchId = i+16*j;
+ for (int c = 0; c < 7; ++c) {
+ for (int r = 0; r < 7; ++r) {
+ for (int d = 0; d < 32; ++d) {
+ float expected = 0.0f;
+ if (r-3+i >= 0 && c-3+j >= 0 && r-3+i < 16 && c-3+j < 16) {
+ expected = l_in(d, r-3+i, c-3+j, b);
+ }
+ // ColMajor
+ if (l_out(d, r, c, patchId, b) != expected) {
+ std::cout << "Mismatch detected at index i=" << i << " j=" << j << " r=" << r << " c=" << c << " d=" << d << " b=" << b << std::endl;
+ }
+ VERIFY_IS_EQUAL(l_out(d, r, c, patchId, b), expected);
+ // RowMajor
+ if (l_out_row_major(b, patchId, c, r, d) != expected) {
+ std::cout << "Mismatch detected at index i=" << i << " j=" << j << " r=" << r << " c=" << c << " d=" << d << " b=" << b << std::endl;
+ }
+ VERIFY_IS_EQUAL(l_out_row_major(b, patchId, c, r, d), expected);
+ }
+ }
+ }
+ }
+ }
+ }
+
+ // ColMajor
+ l_in.resize(64, 13, 13, 32);
+ l_in.setRandom();
+ l_out = l_in.extract_image_patches(3, 3);
+ VERIFY_IS_EQUAL(l_out.dimension(0), 64);
+ VERIFY_IS_EQUAL(l_out.dimension(1), 3);
+ VERIFY_IS_EQUAL(l_out.dimension(2), 3);
+ VERIFY_IS_EQUAL(l_out.dimension(3), 13*13);
+ VERIFY_IS_EQUAL(l_out.dimension(4), 32);
+
+ // RowMajor
+ l_out_row_major = l_in.swap_layout().extract_image_patches(3, 3);
+ VERIFY_IS_EQUAL(l_out_row_major.dimension(0), 32);
+ VERIFY_IS_EQUAL(l_out_row_major.dimension(1), 13*13);
+ VERIFY_IS_EQUAL(l_out_row_major.dimension(2), 3);
+ VERIFY_IS_EQUAL(l_out_row_major.dimension(3), 3);
+ VERIFY_IS_EQUAL(l_out_row_major.dimension(4), 64);
+
+ for (int b = 0; b < 32; ++b) {
+ for (int i = 0; i < 13; ++i) {
+ for (int j = 0; j < 13; ++j) {
+ int patchId = i+13*j;
+ for (int c = 0; c < 3; ++c) {
+ for (int r = 0; r < 3; ++r) {
+ for (int d = 0; d < 64; ++d) {
+ float expected = 0.0f;
+ if (r-1+i >= 0 && c-1+j >= 0 && r-1+i < 13 && c-1+j < 13) {
+ expected = l_in(d, r-1+i, c-1+j, b);
+ }
+ // ColMajor
+ if (l_out(d, r, c, patchId, b) != expected) {
+ std::cout << "Mismatch detected at index i=" << i << " j=" << j << " r=" << r << " c=" << c << " d=" << d << " b=" << b << std::endl;
+ }
+ VERIFY_IS_EQUAL(l_out(d, r, c, patchId, b), expected);
+ // RowMajor
+ if (l_out_row_major(b, patchId, c, r, d) != expected) {
+ std::cout << "Mismatch detected at index i=" << i << " j=" << j << " r=" << r << " c=" << c << " d=" << d << " b=" << b << std::endl;
+ }
+ VERIFY_IS_EQUAL(l_out_row_major(b, patchId, c, r, d), expected);
+ }
+ }
+ }
+ }
+ }
+ }
+}
+
+EIGEN_DECLARE_TEST(cxx11_tensor_image_patch)
+{
+ CALL_SUBTEST_1(test_simple_patch());
+ CALL_SUBTEST_2(test_patch_no_extra_dim());
+ CALL_SUBTEST_3(test_patch_padding_valid());
+ CALL_SUBTEST_4(test_patch_padding_valid_same_value());
+ CALL_SUBTEST_5(test_patch_padding_same());
+ CALL_SUBTEST_6(test_imagenet_patches());
+ CALL_SUBTEST_7(test_patch_padding_same_negative_padding_clip_to_zero());
+}
diff --git a/unsupported/test/cxx11_tensor_image_patch_sycl.cpp b/unsupported/test/cxx11_tensor_image_patch_sycl.cpp
new file mode 100644
index 0000000..c1828a0
--- /dev/null
+++ b/unsupported/test/cxx11_tensor_image_patch_sycl.cpp
@@ -0,0 +1,1092 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2016
+// Mehdi Goli Codeplay Software Ltd.
+// Ralph Potter Codeplay Software Ltd.
+// Luke Iwanski Codeplay Software Ltd.
+// Contact: <eigen@codeplay.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#define EIGEN_TEST_NO_LONGDOUBLE
+#define EIGEN_TEST_NO_COMPLEX
+
+#define EIGEN_DEFAULT_DENSE_INDEX_TYPE int64_t
+#define EIGEN_USE_SYCL
+
+#include "main.h"
+#include <unsupported/Eigen/CXX11/Tensor>
+
+using Eigen::Tensor;
+static const int DataLayout = ColMajor;
+
+template <typename DataType, typename IndexType>
+static void test_simple_image_patch_sycl(const Eigen::SyclDevice& sycl_device)
+{
+ IndexType sizeDim1 = 2;
+ IndexType sizeDim2 = 3;
+ IndexType sizeDim3 = 5;
+ IndexType sizeDim4 = 7;
+ array<IndexType, 4> tensorColMajorRange = {{sizeDim1, sizeDim2, sizeDim3, sizeDim4}};
+ array<IndexType, 4> tensorRowMajorRange = {{sizeDim4, sizeDim3, sizeDim2, sizeDim1}};
+ Tensor<DataType, 4, DataLayout,IndexType> tensor_col_major(tensorColMajorRange);
+ Tensor<DataType, 4, RowMajor,IndexType> tensor_row_major(tensorRowMajorRange);
+ tensor_col_major.setRandom();
+
+ DataType* gpu_data_col_major = static_cast<DataType*>(sycl_device.allocate(tensor_col_major.size()*sizeof(DataType)));
+ DataType* gpu_data_row_major = static_cast<DataType*>(sycl_device.allocate(tensor_row_major.size()*sizeof(DataType)));
+ TensorMap<Tensor<DataType, 4, ColMajor, IndexType>> gpu_col_major(gpu_data_col_major, tensorColMajorRange);
+ TensorMap<Tensor<DataType, 4, RowMajor, IndexType>> gpu_row_major(gpu_data_row_major, tensorRowMajorRange);
+
+ sycl_device.memcpyHostToDevice(gpu_data_col_major, tensor_col_major.data(),(tensor_col_major.size())*sizeof(DataType));
+ gpu_row_major.device(sycl_device)=gpu_col_major.swap_layout();
+ sycl_device.memcpyDeviceToHost(tensor_row_major.data(), gpu_data_row_major, (tensor_col_major.size())*sizeof(DataType));
+
+ VERIFY_IS_EQUAL(tensor_col_major.dimension(0), tensor_row_major.dimension(3));
+ VERIFY_IS_EQUAL(tensor_col_major.dimension(1), tensor_row_major.dimension(2));
+ VERIFY_IS_EQUAL(tensor_col_major.dimension(2), tensor_row_major.dimension(1));
+ VERIFY_IS_EQUAL(tensor_col_major.dimension(3), tensor_row_major.dimension(0));
+
+ // Single pixel patch: ColMajor
+ array<IndexType, 5> patchColMajorTensorRange={{sizeDim1, 1, 1, sizeDim2*sizeDim3, sizeDim4}};
+ Tensor<DataType, 5, DataLayout,IndexType> single_patch_col_major(patchColMajorTensorRange);
+ size_t patchTensorBuffSize =single_patch_col_major.size()*sizeof(DataType);
+ DataType* gpu_data_single_patch_col_major = static_cast<DataType*>(sycl_device.allocate(patchTensorBuffSize));
+ TensorMap<Tensor<DataType, 5, DataLayout,IndexType>> gpu_single_patch_col_major(gpu_data_single_patch_col_major, patchColMajorTensorRange);
+ gpu_single_patch_col_major.device(sycl_device)=gpu_col_major.extract_image_patches(1, 1);
+ sycl_device.memcpyDeviceToHost(single_patch_col_major.data(), gpu_data_single_patch_col_major, patchTensorBuffSize);
+
+ VERIFY_IS_EQUAL(single_patch_col_major.dimension(0), 2);
+ VERIFY_IS_EQUAL(single_patch_col_major.dimension(1), 1);
+ VERIFY_IS_EQUAL(single_patch_col_major.dimension(2), 1);
+ VERIFY_IS_EQUAL(single_patch_col_major.dimension(3), 3*5);
+ VERIFY_IS_EQUAL(single_patch_col_major.dimension(4), 7);
+
+ // Single pixel patch: RowMajor
+ array<IndexType, 5> patchRowMajorTensorRange={{sizeDim4, sizeDim2*sizeDim3, 1, 1, sizeDim1}};
+ Tensor<DataType, 5, RowMajor,IndexType> single_patch_row_major(patchRowMajorTensorRange);
+ patchTensorBuffSize =single_patch_row_major.size()*sizeof(DataType);
+ DataType* gpu_data_single_patch_row_major = static_cast<DataType*>(sycl_device.allocate(patchTensorBuffSize));
+ TensorMap<Tensor<DataType, 5, RowMajor,IndexType>> gpu_single_patch_row_major(gpu_data_single_patch_row_major, patchRowMajorTensorRange);
+ gpu_single_patch_row_major.device(sycl_device)=gpu_row_major.extract_image_patches(1, 1);
+ sycl_device.memcpyDeviceToHost(single_patch_row_major.data(), gpu_data_single_patch_row_major, patchTensorBuffSize);
+
+ VERIFY_IS_EQUAL(single_patch_row_major.dimension(0), 7);
+ VERIFY_IS_EQUAL(single_patch_row_major.dimension(1), 3*5);
+ VERIFY_IS_EQUAL(single_patch_row_major.dimension(2), 1);
+ VERIFY_IS_EQUAL(single_patch_row_major.dimension(3), 1);
+ VERIFY_IS_EQUAL(single_patch_row_major.dimension(4), 2);
+
+ for (IndexType i = 0; i < tensor_col_major.size(); ++i) {
+ // ColMajor
+ if (tensor_col_major.data()[i] != single_patch_col_major.data()[i]) {
+ std::cout << "Mismatch detected at index colmajor " << i << " : "
+ << tensor_col_major.data()[i] << " vs " << single_patch_col_major.data()[i]
+ << std::endl;
+ }
+ VERIFY_IS_EQUAL(single_patch_col_major.data()[i], tensor_col_major.data()[i]);
+ // RowMajor
+ if (tensor_row_major.data()[i] != single_patch_row_major.data()[i]) {
+ std::cout << "Mismatch detected at index row major" << i << " : "
+ << tensor_row_major.data()[i] << " vs "
+ << single_patch_row_major.data()[i] << std::endl;
+ }
+ VERIFY_IS_EQUAL(single_patch_row_major.data()[i],
+ tensor_row_major.data()[i]);
+ VERIFY_IS_EQUAL(tensor_col_major.data()[i], tensor_row_major.data()[i]);
+ VERIFY_IS_EQUAL(single_patch_col_major.data()[i],
+ single_patch_row_major.data()[i]);
+ }
+
+
+ // Entire image patch: ColMajor
+ patchColMajorTensorRange={{sizeDim1, sizeDim2, sizeDim3, sizeDim2*sizeDim3, sizeDim4}};
+ Tensor<DataType, 5, DataLayout,IndexType> entire_image_patch_col_major(patchColMajorTensorRange);
+ patchTensorBuffSize =entire_image_patch_col_major.size()*sizeof(DataType);
+ DataType* gpu_data_entire_image_patch_col_major = static_cast<DataType*>(sycl_device.allocate(patchTensorBuffSize));
+ TensorMap<Tensor<DataType, 5, DataLayout,IndexType>> gpu_entire_image_patch_col_major(gpu_data_entire_image_patch_col_major, patchColMajorTensorRange);
+ gpu_entire_image_patch_col_major.device(sycl_device)=gpu_col_major.extract_image_patches(3, 5);
+ sycl_device.memcpyDeviceToHost(entire_image_patch_col_major.data(), gpu_data_entire_image_patch_col_major, patchTensorBuffSize);
+
+ VERIFY_IS_EQUAL(entire_image_patch_col_major.dimension(0), 2);
+ VERIFY_IS_EQUAL(entire_image_patch_col_major.dimension(1), 3);
+ VERIFY_IS_EQUAL(entire_image_patch_col_major.dimension(2), 5);
+ VERIFY_IS_EQUAL(entire_image_patch_col_major.dimension(3), 3*5);
+ VERIFY_IS_EQUAL(entire_image_patch_col_major.dimension(4), 7);
+
+ // Entire image patch: RowMajor
+ patchRowMajorTensorRange={{sizeDim4, sizeDim2*sizeDim3, sizeDim3, sizeDim2, sizeDim1}};
+ Tensor<DataType, 5, RowMajor,IndexType> entire_image_patch_row_major(patchRowMajorTensorRange);
+ patchTensorBuffSize =entire_image_patch_row_major.size()*sizeof(DataType);
+ DataType* gpu_data_entire_image_patch_row_major = static_cast<DataType*>(sycl_device.allocate(patchTensorBuffSize));
+ TensorMap<Tensor<DataType, 5, RowMajor,IndexType>> gpu_entire_image_patch_row_major(gpu_data_entire_image_patch_row_major, patchRowMajorTensorRange);
+ gpu_entire_image_patch_row_major.device(sycl_device)=gpu_row_major.extract_image_patches(3, 5);
+ sycl_device.memcpyDeviceToHost(entire_image_patch_row_major.data(), gpu_data_entire_image_patch_row_major, patchTensorBuffSize);
+
+ VERIFY_IS_EQUAL(entire_image_patch_row_major.dimension(0), 7);
+ VERIFY_IS_EQUAL(entire_image_patch_row_major.dimension(1), 3*5);
+ VERIFY_IS_EQUAL(entire_image_patch_row_major.dimension(2), 5);
+ VERIFY_IS_EQUAL(entire_image_patch_row_major.dimension(3), 3);
+ VERIFY_IS_EQUAL(entire_image_patch_row_major.dimension(4), 2);
+
+ for (IndexType i = 0; i < 3; ++i) {
+ for (IndexType j = 0; j < 5; ++j) {
+ IndexType patchId = i+3*j;
+ for (IndexType r = 0; r < 3; ++r) {
+ for (IndexType c = 0; c < 5; ++c) {
+ for (IndexType d = 0; d < 2; ++d) {
+ for (IndexType b = 0; b < 7; ++b) {
+ DataType expected_col_major = 0.0f;
+ DataType expected_row_major = 0.0f;
+ if (r-1+i >= 0 && c-2+j >= 0 && r-1+i < 3 && c-2+j < 5) {
+ expected_col_major = tensor_col_major(d, r-1+i, c-2+j, b);
+ expected_row_major = tensor_row_major(b, c-2+j, r-1+i, d);
+ }
+ // ColMajor
+ if (entire_image_patch_col_major(d, r, c, patchId, b) != expected_col_major) {
+ std::cout << "Mismatch detected at index i=" << i << " j=" << j << " r=" << r << " c=" << c << " d=" << d << " b=" << b << std::endl;
+ }
+ VERIFY_IS_EQUAL(entire_image_patch_col_major(d, r, c, patchId, b), expected_col_major);
+ // RowMajor
+ if (entire_image_patch_row_major(b, patchId, c, r, d) !=
+ expected_row_major) {
+ std::cout << "Mismatch detected at index i=" << i << " j=" << j
+ << " r=" << r << " c=" << c << " d=" << d << " b=" << b
+ << std::endl;
+ }
+ VERIFY_IS_EQUAL(entire_image_patch_row_major(b, patchId, c, r, d),
+ expected_row_major);
+ // Check that ColMajor and RowMajor agree.
+ VERIFY_IS_EQUAL(expected_col_major, expected_row_major);
+ }
+ }
+ }
+ }
+ }
+ }
+
+ // 2D patch: ColMajor
+ patchColMajorTensorRange={{sizeDim1, 2, 2, sizeDim2*sizeDim3, sizeDim4}};
+ Tensor<DataType, 5, DataLayout,IndexType> twod_patch_col_major(patchColMajorTensorRange);
+ patchTensorBuffSize =twod_patch_col_major.size()*sizeof(DataType);
+ DataType* gpu_data_twod_patch_col_major = static_cast<DataType*>(sycl_device.allocate(patchTensorBuffSize));
+ TensorMap<Tensor<DataType, 5, DataLayout,IndexType>> gpu_twod_patch_col_major(gpu_data_twod_patch_col_major, patchColMajorTensorRange);
+ gpu_twod_patch_col_major.device(sycl_device)=gpu_col_major.extract_image_patches(2, 2);
+ sycl_device.memcpyDeviceToHost(twod_patch_col_major.data(), gpu_data_twod_patch_col_major, patchTensorBuffSize);
+
+ VERIFY_IS_EQUAL(twod_patch_col_major.dimension(0), 2);
+ VERIFY_IS_EQUAL(twod_patch_col_major.dimension(1), 2);
+ VERIFY_IS_EQUAL(twod_patch_col_major.dimension(2), 2);
+ VERIFY_IS_EQUAL(twod_patch_col_major.dimension(3), 3*5);
+ VERIFY_IS_EQUAL(twod_patch_col_major.dimension(4), 7);
+
+ // 2D patch: RowMajor
+ patchRowMajorTensorRange={{sizeDim4, sizeDim2*sizeDim3, 2, 2, sizeDim1}};
+ Tensor<DataType, 5, RowMajor,IndexType> twod_patch_row_major(patchRowMajorTensorRange);
+ patchTensorBuffSize =twod_patch_row_major.size()*sizeof(DataType);
+ DataType* gpu_data_twod_patch_row_major = static_cast<DataType*>(sycl_device.allocate(patchTensorBuffSize));
+ TensorMap<Tensor<DataType, 5, RowMajor,IndexType>> gpu_twod_patch_row_major(gpu_data_twod_patch_row_major, patchRowMajorTensorRange);
+ gpu_twod_patch_row_major.device(sycl_device)=gpu_row_major.extract_image_patches(2, 2);
+ sycl_device.memcpyDeviceToHost(twod_patch_row_major.data(), gpu_data_twod_patch_row_major, patchTensorBuffSize);
+
+ VERIFY_IS_EQUAL(twod_patch_row_major.dimension(0), 7);
+ VERIFY_IS_EQUAL(twod_patch_row_major.dimension(1), 3*5);
+ VERIFY_IS_EQUAL(twod_patch_row_major.dimension(2), 2);
+ VERIFY_IS_EQUAL(twod_patch_row_major.dimension(3), 2);
+ VERIFY_IS_EQUAL(twod_patch_row_major.dimension(4), 2);
+
+
+ // Based on the calculation described in TensorTraits.h, padding happens to be 0.
+ IndexType row_padding = 0;
+ IndexType col_padding = 0;
+ IndexType stride = 1;
+
+ for (IndexType i = 0; i < 3; ++i) {
+ for (IndexType j = 0; j < 5; ++j) {
+ IndexType patchId = i+3*j;
+ for (IndexType r = 0; r < 2; ++r) {
+ for (IndexType c = 0; c < 2; ++c) {
+ for (IndexType d = 0; d < 2; ++d) {
+ for (IndexType b = 0; b < 7; ++b) {
+ DataType expected_col_major = 0.0f;
+ DataType expected_row_major = 0.0f;
+ IndexType row_offset = r*stride + i - row_padding;
+ IndexType col_offset = c*stride + j - col_padding;
+ // ColMajor
+ if (row_offset >= 0 && col_offset >= 0 && row_offset < tensor_col_major.dimension(1) && col_offset < tensor_col_major.dimension(2)) {
+ expected_col_major = tensor_col_major(d, row_offset, col_offset, b);
+ }
+ if (twod_patch_col_major(d, r, c, patchId, b) != expected_col_major) {
+ std::cout << "Mismatch detected at index i=" << i << " j=" << j << " r=" << r << " c=" << c << " d=" << d << " b=" << b << std::endl;
+ }
+ VERIFY_IS_EQUAL(twod_patch_col_major(d, r, c, patchId, b), expected_col_major);
+
+ // RowMajor
+ if (row_offset >= 0 && col_offset >= 0 && row_offset < tensor_row_major.dimension(2) && col_offset < tensor_row_major.dimension(1)) {
+ expected_row_major = tensor_row_major(b, col_offset, row_offset, d);
+
+ }
+ if (twod_patch_row_major(b, patchId, c, r, d) != expected_row_major) {
+ std::cout << "Mismatch detected at index i=" << i << " j=" << j << " r=" << r << " c=" << c << " d=" << d << " b=" << b << std::endl;
+ }
+ VERIFY_IS_EQUAL(twod_patch_row_major(b, patchId, c, r, d), expected_row_major);
+ // Check that ColMajor and RowMajor agree.
+ VERIFY_IS_EQUAL(expected_col_major, expected_row_major);
+ }
+ }
+ }
+ }
+ }
+ }
+
+ sycl_device.deallocate(gpu_data_col_major);
+ sycl_device.deallocate(gpu_data_row_major);
+ sycl_device.deallocate(gpu_data_single_patch_col_major);
+ sycl_device.deallocate(gpu_data_single_patch_row_major);
+ sycl_device.deallocate(gpu_data_entire_image_patch_col_major);
+ sycl_device.deallocate(gpu_data_entire_image_patch_row_major);
+ sycl_device.deallocate(gpu_data_twod_patch_col_major);
+ sycl_device.deallocate(gpu_data_twod_patch_row_major);
+
+}
+
+
+// Verifies VALID padding (no padding) with incrementing values.
+template <typename DataType, typename IndexType>
+static void test_patch_padding_valid_sycl(const Eigen::SyclDevice& sycl_device){
+ IndexType input_depth = 3;
+ IndexType input_rows = 3;
+ IndexType input_cols = 3;
+ IndexType input_batches = 1;
+ IndexType ksize = 2; // Corresponds to the Rows and Cols for tensor.extract_image_patches<>.
+ IndexType stride = 2; // Only same stride is supported.
+
+ array<IndexType, 4> tensorColMajorRange = {{input_depth, input_rows, input_cols, input_batches}};
+ array<IndexType, 4> tensorRowMajorRange = {{input_batches, input_cols, input_rows, input_depth}};
+ Tensor<DataType, 4, DataLayout,IndexType> tensor_col_major(tensorColMajorRange);
+ Tensor<DataType, 4, RowMajor,IndexType> tensor_row_major(tensorRowMajorRange);
+
+ DataType* gpu_data_col_major = static_cast<DataType*>(sycl_device.allocate(tensor_col_major.size()*sizeof(DataType)));
+ DataType* gpu_data_row_major = static_cast<DataType*>(sycl_device.allocate(tensor_row_major.size()*sizeof(DataType)));
+ TensorMap<Tensor<DataType, 4, ColMajor, IndexType>> gpu_col_major(gpu_data_col_major, tensorColMajorRange);
+ TensorMap<Tensor<DataType, 4, RowMajor, IndexType>> gpu_row_major(gpu_data_row_major, tensorRowMajorRange);
+
+ sycl_device.memcpyHostToDevice(gpu_data_col_major, tensor_col_major.data(),(tensor_col_major.size())*sizeof(DataType));
+ gpu_row_major.device(sycl_device)=gpu_col_major.swap_layout();
+ sycl_device.memcpyDeviceToHost(tensor_row_major.data(), gpu_data_row_major, (tensor_col_major.size())*sizeof(DataType));
+
+ VERIFY_IS_EQUAL(tensor_col_major.dimension(0), tensor_row_major.dimension(3));
+ VERIFY_IS_EQUAL(tensor_col_major.dimension(1), tensor_row_major.dimension(2));
+ VERIFY_IS_EQUAL(tensor_col_major.dimension(2), tensor_row_major.dimension(1));
+ VERIFY_IS_EQUAL(tensor_col_major.dimension(3), tensor_row_major.dimension(0));
+
+ // Initializes tensor with incrementing numbers.
+ for (IndexType i = 0; i < tensor_col_major.size(); ++i) {
+ tensor_col_major.data()[i] = i + 1;
+ }
+ // ColMajor
+ array<IndexType, 5> patchColMajorTensorRange={{input_depth, ksize, ksize, 1, input_batches}};
+ Tensor<DataType, 5, DataLayout,IndexType> result_col_major(patchColMajorTensorRange);
+ size_t patchTensorBuffSize =result_col_major.size()*sizeof(DataType);
+ DataType* gpu_data_result_col_major = static_cast<DataType*>(sycl_device.allocate(patchTensorBuffSize));
+ TensorMap<Tensor<DataType, 5, DataLayout,IndexType>> gpu_result_col_major(gpu_data_result_col_major, patchColMajorTensorRange);
+ gpu_result_col_major.device(sycl_device)=gpu_col_major.extract_image_patches(ksize, ksize, stride, stride, 1, 1, PADDING_VALID);
+ sycl_device.memcpyDeviceToHost(result_col_major.data(), gpu_data_result_col_major, patchTensorBuffSize);
+
+ VERIFY_IS_EQUAL(result_col_major.dimension(0), input_depth); // depth
+ VERIFY_IS_EQUAL(result_col_major.dimension(1), ksize); // kernel rows
+ VERIFY_IS_EQUAL(result_col_major.dimension(2), ksize); // kernel cols
+ VERIFY_IS_EQUAL(result_col_major.dimension(3), 1); // number of patches
+ VERIFY_IS_EQUAL(result_col_major.dimension(4), input_batches); // number of batches
+
+ // RowMajor
+ array<IndexType, 5> patchRowMajorTensorRange={{input_batches, 1, ksize, ksize, input_depth }};
+ Tensor<DataType, 5, RowMajor,IndexType> result_row_major(patchRowMajorTensorRange);
+ patchTensorBuffSize =result_row_major.size()*sizeof(DataType);
+ DataType* gpu_data_result_row_major = static_cast<DataType*>(sycl_device.allocate(patchTensorBuffSize));
+ TensorMap<Tensor<DataType, 5, RowMajor,IndexType>> gpu_result_row_major(gpu_data_result_row_major, patchRowMajorTensorRange);
+ gpu_result_row_major.device(sycl_device)=gpu_row_major.extract_image_patches(ksize, ksize, stride, stride, 1, 1, PADDING_VALID);
+ sycl_device.memcpyDeviceToHost(result_row_major.data(), gpu_data_result_row_major, patchTensorBuffSize);
+
+ VERIFY_IS_EQUAL(result_col_major.dimension(0), result_row_major.dimension(4));
+ VERIFY_IS_EQUAL(result_col_major.dimension(1), result_row_major.dimension(3));
+ VERIFY_IS_EQUAL(result_col_major.dimension(2), result_row_major.dimension(2));
+ VERIFY_IS_EQUAL(result_col_major.dimension(3), result_row_major.dimension(1));
+ VERIFY_IS_EQUAL(result_col_major.dimension(4), result_row_major.dimension(0));
+
+ // No padding is carried out.
+ IndexType row_padding = 0;
+ IndexType col_padding = 0;
+
+ for (IndexType i = 0; (i+stride+ksize-1) < input_rows; i += stride) { // input rows
+ for (IndexType j = 0; (j+stride+ksize-1) < input_cols; j += stride) { // input cols
+ IndexType patchId = i+input_rows*j;
+ for (IndexType r = 0; r < ksize; ++r) { // patch rows
+ for (IndexType c = 0; c < ksize; ++c) { // patch cols
+ for (IndexType d = 0; d < input_depth; ++d) { // depth
+ for (IndexType b = 0; b < input_batches; ++b) { // batch
+ DataType expected_col_major = 0.0f;
+ DataType expected_row_major = 0.0f;
+ IndexType row_offset = r + i - row_padding;
+ IndexType col_offset = c + j - col_padding;
+ if (row_offset >= 0 && col_offset >= 0 && row_offset < input_rows && col_offset < input_cols) {
+ expected_col_major = tensor_col_major(d, row_offset, col_offset, b);
+ expected_row_major = tensor_row_major(b, col_offset, row_offset, d);
+ }
+ // ColMajor
+ if (result_col_major(d, r, c, patchId, b) != expected_col_major) {
+ std::cout << "Mismatch detected at index i=" << i << " j=" << j << " r=" << r << " c=" << c << " d=" << d << " b=" << b << std::endl;
+ }
+ VERIFY_IS_EQUAL(result_col_major(d, r, c, patchId, b), expected_col_major);
+ // RowMajor
+ if (result_row_major(b, patchId, c, r, d) != expected_row_major) {
+ std::cout << "Mismatch detected at index i=" << i << " j=" << j << " r=" << r << " c=" << c << " d=" << d << " b=" << b << std::endl;
+ }
+ VERIFY_IS_EQUAL(result_row_major(b, patchId, c, r, d), expected_row_major);
+ // Check that ColMajor and RowMajor agree.
+ VERIFY_IS_EQUAL(expected_col_major, expected_row_major);
+ }
+ }
+ }
+ }
+ }
+ }
+ sycl_device.deallocate(gpu_data_col_major);
+ sycl_device.deallocate(gpu_data_row_major);
+ sycl_device.deallocate(gpu_data_result_col_major);
+ sycl_device.deallocate(gpu_data_result_row_major);
+}
+
+// Verifies VALID padding (no padding) with the same value.
+template <typename DataType, typename IndexType>
+static void test_patch_padding_valid_same_value_sycl(const Eigen::SyclDevice& sycl_device){
+ IndexType input_depth = 1;
+ IndexType input_rows = 5;
+ IndexType input_cols = 5;
+ IndexType input_batches = 2;
+ IndexType ksize = 3; // Corresponds to the Rows and Cols for tensor.extract_image_patches<>.
+ IndexType stride = 2; // Only same stride is supported.
+ // ColMajor
+
+ array<IndexType, 4> tensorColMajorRange = {{input_depth, input_rows, input_cols, input_batches}};
+ array<IndexType, 4> tensorRowMajorRange = {{input_batches, input_cols, input_rows, input_depth}};
+ Tensor<DataType, 4, DataLayout,IndexType> tensor_col_major(tensorColMajorRange);
+ Tensor<DataType, 4, RowMajor,IndexType> tensor_row_major(tensorRowMajorRange);
+
+ DataType* gpu_data_col_major = static_cast<DataType*>(sycl_device.allocate(tensor_col_major.size()*sizeof(DataType)));
+ DataType* gpu_data_row_major = static_cast<DataType*>(sycl_device.allocate(tensor_row_major.size()*sizeof(DataType)));
+ TensorMap<Tensor<DataType, 4, ColMajor, IndexType>> gpu_col_major(gpu_data_col_major, tensorColMajorRange);
+ TensorMap<Tensor<DataType, 4, RowMajor, IndexType>> gpu_row_major(gpu_data_row_major, tensorRowMajorRange);
+ gpu_col_major.device(sycl_device)=gpu_col_major.constant(11.0f);
+ gpu_row_major.device(sycl_device)=gpu_col_major.swap_layout();
+ sycl_device.memcpyDeviceToHost(tensor_col_major.data(), gpu_data_col_major, (tensor_col_major.size())*sizeof(DataType));
+ sycl_device.memcpyDeviceToHost(tensor_row_major.data(), gpu_data_row_major, (tensor_row_major.size())*sizeof(DataType));
+ VERIFY_IS_EQUAL(tensor_col_major.dimension(0), tensor_row_major.dimension(3));
+ VERIFY_IS_EQUAL(tensor_col_major.dimension(1), tensor_row_major.dimension(2));
+ VERIFY_IS_EQUAL(tensor_col_major.dimension(2), tensor_row_major.dimension(1));
+ VERIFY_IS_EQUAL(tensor_col_major.dimension(3), tensor_row_major.dimension(0));
+
+ array<IndexType, 5> patchColMajorTensorRange={{input_depth, ksize, ksize, 4, input_batches}};
+ Tensor<DataType, 5, DataLayout,IndexType> result_col_major(patchColMajorTensorRange);
+ size_t patchTensorBuffSize =result_col_major.size()*sizeof(DataType);
+ DataType* gpu_data_result_col_major = static_cast<DataType*>(sycl_device.allocate(patchTensorBuffSize));
+ TensorMap<Tensor<DataType, 5, DataLayout,IndexType>> gpu_result_col_major(gpu_data_result_col_major, patchColMajorTensorRange);
+ gpu_result_col_major.device(sycl_device)=gpu_col_major.extract_image_patches(ksize, ksize, stride, stride, 1, 1, PADDING_VALID);
+ sycl_device.memcpyDeviceToHost(result_col_major.data(), gpu_data_result_col_major, patchTensorBuffSize);
+
+ VERIFY_IS_EQUAL(result_col_major.dimension(0), input_depth); // depth
+ VERIFY_IS_EQUAL(result_col_major.dimension(1), ksize); // kernel rows
+ VERIFY_IS_EQUAL(result_col_major.dimension(2), ksize); // kernel cols
+ VERIFY_IS_EQUAL(result_col_major.dimension(3), 4); // number of patches
+ VERIFY_IS_EQUAL(result_col_major.dimension(4), input_batches); // number of batches
+
+ // RowMajor
+ array<IndexType, 5> patchRowMajorTensorRange={{input_batches, 4, ksize, ksize, input_depth }};
+ Tensor<DataType, 5, RowMajor,IndexType> result_row_major(patchRowMajorTensorRange);
+ patchTensorBuffSize =result_row_major.size()*sizeof(DataType);
+ DataType* gpu_data_result_row_major = static_cast<DataType*>(sycl_device.allocate(patchTensorBuffSize));
+ TensorMap<Tensor<DataType, 5, RowMajor,IndexType>> gpu_result_row_major(gpu_data_result_row_major, patchRowMajorTensorRange);
+ gpu_result_row_major.device(sycl_device)=gpu_row_major.extract_image_patches(ksize, ksize, stride, stride, 1, 1, PADDING_VALID);
+ sycl_device.memcpyDeviceToHost(result_row_major.data(), gpu_data_result_row_major, patchTensorBuffSize);
+
+ VERIFY_IS_EQUAL(result_col_major.dimension(0), result_row_major.dimension(4));
+ VERIFY_IS_EQUAL(result_col_major.dimension(1), result_row_major.dimension(3));
+ VERIFY_IS_EQUAL(result_col_major.dimension(2), result_row_major.dimension(2));
+ VERIFY_IS_EQUAL(result_col_major.dimension(3), result_row_major.dimension(1));
+ VERIFY_IS_EQUAL(result_col_major.dimension(4), result_row_major.dimension(0));
+
+ // No padding is carried out.
+ IndexType row_padding = 0;
+ IndexType col_padding = 0;
+
+ for (IndexType i = 0; (i+stride+ksize-1) <= input_rows; i += stride) { // input rows
+ for (IndexType j = 0; (j+stride+ksize-1) <= input_cols; j += stride) { // input cols
+ IndexType patchId = i+input_rows*j;
+ for (IndexType r = 0; r < ksize; ++r) { // patch rows
+ for (IndexType c = 0; c < ksize; ++c) { // patch cols
+ for (IndexType d = 0; d < input_depth; ++d) { // depth
+ for (IndexType b = 0; b < input_batches; ++b) { // batch
+ DataType expected_col_major = 0.0f;
+ DataType expected_row_major = 0.0f;
+ IndexType row_offset = r + i - row_padding;
+ IndexType col_offset = c + j - col_padding;
+ if (row_offset >= 0 && col_offset >= 0 && row_offset < input_rows && col_offset < input_cols) {
+ expected_col_major = tensor_col_major(d, row_offset, col_offset, b);
+ expected_row_major = tensor_row_major(b, col_offset, row_offset, d);
+ }
+ // ColMajor
+ if (result_col_major(d, r, c, patchId, b) != expected_col_major) {
+ std::cout << "Mismatch detected at index i=" << i << " j=" << j << " r=" << r << " c=" << c << " d=" << d << " b=" << b << std::endl;
+ }
+ VERIFY_IS_EQUAL(result_col_major(d, r, c, patchId, b), expected_col_major);
+ // RowMajor
+ if (result_row_major(b, patchId, c, r, d) != expected_row_major) {
+ std::cout << "Mismatch detected at index i=" << i << " j=" << j << " r=" << r << " c=" << c << " d=" << d << " b=" << b << std::endl;
+ }
+ VERIFY_IS_EQUAL(result_row_major(b, patchId, c, r, d), expected_row_major);
+ // Check that ColMajor and RowMajor agree.
+ VERIFY_IS_EQUAL(expected_col_major, expected_row_major);
+ }
+ }
+ }
+ }
+ }
+ }
+}
+
+// Verifies SAME padding.
+template <typename DataType, typename IndexType>
+static void test_patch_padding_same_sycl(const Eigen::SyclDevice& sycl_device){
+ IndexType input_depth = 3;
+ IndexType input_rows = 4;
+ IndexType input_cols = 2;
+ IndexType input_batches = 1;
+ IndexType ksize = 2; // Corresponds to the Rows and Cols for tensor.extract_image_patches<>.
+ IndexType stride = 2; // Only same stride is supported.
+
+ // ColMajor
+ array<IndexType, 4> tensorColMajorRange = {{input_depth, input_rows, input_cols, input_batches}};
+ array<IndexType, 4> tensorRowMajorRange = {{input_batches, input_cols, input_rows, input_depth}};
+ Tensor<DataType, 4, DataLayout,IndexType> tensor_col_major(tensorColMajorRange);
+ Tensor<DataType, 4, RowMajor,IndexType> tensor_row_major(tensorRowMajorRange);
+
+ DataType* gpu_data_col_major = static_cast<DataType*>(sycl_device.allocate(tensor_col_major.size()*sizeof(DataType)));
+ DataType* gpu_data_row_major = static_cast<DataType*>(sycl_device.allocate(tensor_row_major.size()*sizeof(DataType)));
+ TensorMap<Tensor<DataType, 4, ColMajor, IndexType>> gpu_col_major(gpu_data_col_major, tensorColMajorRange);
+ TensorMap<Tensor<DataType, 4, RowMajor, IndexType>> gpu_row_major(gpu_data_row_major, tensorRowMajorRange);
+
+ sycl_device.memcpyHostToDevice(gpu_data_col_major, tensor_col_major.data(),(tensor_col_major.size())*sizeof(DataType));
+ gpu_row_major.device(sycl_device)=gpu_col_major.swap_layout();
+ sycl_device.memcpyDeviceToHost(tensor_row_major.data(), gpu_data_row_major, (tensor_col_major.size())*sizeof(DataType));
+
+ VERIFY_IS_EQUAL(tensor_col_major.dimension(0), tensor_row_major.dimension(3));
+ VERIFY_IS_EQUAL(tensor_col_major.dimension(1), tensor_row_major.dimension(2));
+ VERIFY_IS_EQUAL(tensor_col_major.dimension(2), tensor_row_major.dimension(1));
+ VERIFY_IS_EQUAL(tensor_col_major.dimension(3), tensor_row_major.dimension(0));
+
+ // Initializes tensor with incrementing numbers.
+ for (IndexType i = 0; i < tensor_col_major.size(); ++i) {
+ tensor_col_major.data()[i] = i + 1;
+ }
+
+array<IndexType, 5> patchColMajorTensorRange={{input_depth, ksize, ksize, 2, input_batches}};
+Tensor<DataType, 5, DataLayout,IndexType> result_col_major(patchColMajorTensorRange);
+size_t patchTensorBuffSize =result_col_major.size()*sizeof(DataType);
+DataType* gpu_data_result_col_major = static_cast<DataType*>(sycl_device.allocate(patchTensorBuffSize));
+TensorMap<Tensor<DataType, 5, DataLayout,IndexType>> gpu_result_col_major(gpu_data_result_col_major, patchColMajorTensorRange);
+gpu_result_col_major.device(sycl_device)=gpu_col_major.extract_image_patches(ksize, ksize, stride, stride, PADDING_SAME);
+sycl_device.memcpyDeviceToHost(result_col_major.data(), gpu_data_result_col_major, patchTensorBuffSize);
+
+
+ VERIFY_IS_EQUAL(result_col_major.dimension(0), input_depth); // depth
+ VERIFY_IS_EQUAL(result_col_major.dimension(1), ksize); // kernel rows
+ VERIFY_IS_EQUAL(result_col_major.dimension(2), ksize); // kernel cols
+ VERIFY_IS_EQUAL(result_col_major.dimension(3), 2); // number of patches
+ VERIFY_IS_EQUAL(result_col_major.dimension(4), input_batches); // number of batches
+
+ // RowMajor
+
+ array<IndexType, 5> patchRowMajorTensorRange={{input_batches, 2, ksize, ksize, input_depth }};
+ Tensor<DataType, 5, RowMajor,IndexType> result_row_major(patchRowMajorTensorRange);
+ patchTensorBuffSize =result_row_major.size()*sizeof(DataType);
+ DataType* gpu_data_result_row_major = static_cast<DataType*>(sycl_device.allocate(patchTensorBuffSize));
+ TensorMap<Tensor<DataType, 5, RowMajor,IndexType>> gpu_result_row_major(gpu_data_result_row_major, patchRowMajorTensorRange);
+ gpu_result_row_major.device(sycl_device)=gpu_row_major.extract_image_patches(ksize, ksize, stride, stride, PADDING_SAME);
+ sycl_device.memcpyDeviceToHost(result_row_major.data(), gpu_data_result_row_major, patchTensorBuffSize);
+
+ VERIFY_IS_EQUAL(result_col_major.dimension(0), result_row_major.dimension(4));
+ VERIFY_IS_EQUAL(result_col_major.dimension(1), result_row_major.dimension(3));
+ VERIFY_IS_EQUAL(result_col_major.dimension(2), result_row_major.dimension(2));
+ VERIFY_IS_EQUAL(result_col_major.dimension(3), result_row_major.dimension(1));
+ VERIFY_IS_EQUAL(result_col_major.dimension(4), result_row_major.dimension(0));
+
+ // Based on the calculation described in TensorTraits.h, padding happens to be 0.
+ IndexType row_padding = 0;
+ IndexType col_padding = 0;
+
+ for (IndexType i = 0; (i+stride+ksize-1) <= input_rows; i += stride) { // input rows
+ for (IndexType j = 0; (j+stride+ksize-1) <= input_cols; j += stride) { // input cols
+ IndexType patchId = i+input_rows*j;
+ for (IndexType r = 0; r < ksize; ++r) { // patch rows
+ for (IndexType c = 0; c < ksize; ++c) { // patch cols
+ for (IndexType d = 0; d < input_depth; ++d) { // depth
+ for (IndexType b = 0; b < input_batches; ++b) { // batch
+ DataType expected_col_major = 0.0f;
+ DataType expected_row_major = 0.0f;
+ IndexType row_offset = r*stride + i - row_padding;
+ IndexType col_offset = c*stride + j - col_padding;
+ if (row_offset >= 0 && col_offset >= 0 && row_offset < input_rows && col_offset < input_cols) {
+ expected_col_major = tensor_col_major(d, row_offset, col_offset, b);
+ expected_row_major = tensor_row_major(b, col_offset, row_offset, d);
+ }
+ // ColMajor
+ if (result_col_major(d, r, c, patchId, b) != expected_col_major) {
+ std::cout << "Mismatch detected at index i=" << i << " j=" << j << " r=" << r << " c=" << c << " d=" << d << " b=" << b << std::endl;
+ }
+ VERIFY_IS_EQUAL(result_col_major(d, r, c, patchId, b), expected_col_major);
+ // RowMajor
+ if (result_row_major(b, patchId, c, r, d) != expected_row_major) {
+ std::cout << "Mismatch detected at index i=" << i << " j=" << j << " r=" << r << " c=" << c << " d=" << d << " b=" << b << std::endl;
+ }
+ VERIFY_IS_EQUAL(result_row_major(b, patchId, c, r, d), expected_row_major);
+ // Check that ColMajor and RowMajor agree.
+ VERIFY_IS_EQUAL(expected_col_major, expected_row_major);
+ }
+ }
+ }
+ }
+ }
+ }
+}
+
+
+template <typename DataType, typename IndexType>
+static void test_patch_no_extra_dim_sycl(const Eigen::SyclDevice& sycl_device){
+
+ IndexType sizeDim1 = 2;
+ IndexType sizeDim2 = 3;
+ IndexType sizeDim3 = 5;
+
+ // ColMajor
+ array<IndexType, 3> tensorColMajorRange = {{sizeDim1, sizeDim2, sizeDim3}};
+ array<IndexType, 3> tensorRowMajorRange = {{sizeDim3, sizeDim2, sizeDim1}};
+ Tensor<DataType, 3, DataLayout,IndexType> tensor_col_major(tensorColMajorRange);
+ tensor_col_major.setRandom();
+ Tensor<DataType, 3, RowMajor,IndexType> tensor_row_major(tensorRowMajorRange);
+
+ DataType* gpu_data_col_major = static_cast<DataType*>(sycl_device.allocate(tensor_col_major.size()*sizeof(DataType)));
+ DataType* gpu_data_row_major = static_cast<DataType*>(sycl_device.allocate(tensor_row_major.size()*sizeof(DataType)));
+ TensorMap<Tensor<DataType, 3, ColMajor, IndexType>> gpu_col_major(gpu_data_col_major, tensorColMajorRange);
+ TensorMap<Tensor<DataType, 3, RowMajor, IndexType>> gpu_row_major(gpu_data_row_major, tensorRowMajorRange);
+
+ sycl_device.memcpyHostToDevice(gpu_data_col_major, tensor_col_major.data(),(tensor_col_major.size())*sizeof(DataType));
+ gpu_row_major.device(sycl_device)=gpu_col_major.swap_layout();
+ sycl_device.memcpyDeviceToHost(tensor_row_major.data(), gpu_data_row_major, (tensor_row_major.size())*sizeof(DataType));
+
+ VERIFY_IS_EQUAL(tensor_col_major.dimension(0), tensor_row_major.dimension(2));
+ VERIFY_IS_EQUAL(tensor_col_major.dimension(1), tensor_row_major.dimension(1));
+ VERIFY_IS_EQUAL(tensor_col_major.dimension(2), tensor_row_major.dimension(0));
+
+
+ // Single pixel patch: ColMajor
+ array<IndexType, 4> patchColMajorTensorRange={{sizeDim1, 1, 1, sizeDim2*sizeDim3}};
+ Tensor<DataType, 4, DataLayout,IndexType> single_patch_col_major(patchColMajorTensorRange);
+ size_t patchTensorBuffSize =single_patch_col_major.size()*sizeof(DataType);
+ DataType* gpu_data_single_patch_col_major = static_cast<DataType*>(sycl_device.allocate(patchTensorBuffSize));
+ TensorMap<Tensor<DataType, 4, DataLayout,IndexType>> gpu_single_patch_col_major(gpu_data_single_patch_col_major, patchColMajorTensorRange);
+ gpu_single_patch_col_major.device(sycl_device)=gpu_col_major.extract_image_patches(1, 1);
+ sycl_device.memcpyDeviceToHost(single_patch_col_major.data(), gpu_data_single_patch_col_major, patchTensorBuffSize);
+
+ VERIFY_IS_EQUAL(single_patch_col_major.dimension(0), sizeDim1);
+ VERIFY_IS_EQUAL(single_patch_col_major.dimension(1), 1);
+ VERIFY_IS_EQUAL(single_patch_col_major.dimension(2), 1);
+ VERIFY_IS_EQUAL(single_patch_col_major.dimension(3), sizeDim2*sizeDim3);
+
+ // Single pixel patch: RowMajor
+ array<IndexType, 4> patchRowMajorTensorRange={{sizeDim2*sizeDim3, 1, 1, sizeDim1}};
+ Tensor<DataType, 4, RowMajor,IndexType> single_patch_row_major(patchRowMajorTensorRange);
+ patchTensorBuffSize =single_patch_row_major.size()*sizeof(DataType);
+ DataType* gpu_data_single_patch_row_major = static_cast<DataType*>(sycl_device.allocate(patchTensorBuffSize));
+ TensorMap<Tensor<DataType, 4, RowMajor,IndexType>> gpu_single_patch_row_major(gpu_data_single_patch_row_major, patchRowMajorTensorRange);
+ gpu_single_patch_row_major.device(sycl_device)=gpu_row_major.extract_image_patches(1, 1);
+ sycl_device.memcpyDeviceToHost(single_patch_row_major.data(), gpu_data_single_patch_row_major, patchTensorBuffSize);
+
+ VERIFY_IS_EQUAL(single_patch_row_major.dimension(0), sizeDim2*sizeDim3);
+ VERIFY_IS_EQUAL(single_patch_row_major.dimension(1), 1);
+ VERIFY_IS_EQUAL(single_patch_row_major.dimension(2), 1);
+ VERIFY_IS_EQUAL(single_patch_row_major.dimension(3), sizeDim1);
+
+ for (IndexType i = 0; i < tensor_col_major.size(); ++i) {
+ // ColMajor
+ if (tensor_col_major.data()[i] != single_patch_col_major.data()[i]) {
+ std::cout << "Mismatch detected at index " << i << " : " << tensor_col_major.data()[i] << " vs " << single_patch_col_major.data()[i] << std::endl;
+ }
+ VERIFY_IS_EQUAL(single_patch_col_major.data()[i], tensor_col_major.data()[i]);
+ // RowMajor
+ if (tensor_row_major.data()[i] != single_patch_row_major.data()[i]) {
+ std::cout << "Mismatch detected at index " << i << " : "
+ << tensor_col_major.data()[i] << " vs "
+ << single_patch_row_major.data()[i] << std::endl;
+ }
+ VERIFY_IS_EQUAL(single_patch_row_major.data()[i],
+ tensor_row_major.data()[i]);
+ VERIFY_IS_EQUAL(tensor_col_major.data()[i], tensor_row_major.data()[i]);
+ VERIFY_IS_EQUAL(single_patch_col_major.data()[i],
+ single_patch_row_major.data()[i]);
+ }
+
+ // Entire image patch: ColMajor
+ patchColMajorTensorRange={{sizeDim1, sizeDim2, sizeDim3, sizeDim2*sizeDim3}};
+ Tensor<DataType, 4, DataLayout,IndexType> entire_image_patch_col_major(patchColMajorTensorRange);
+ patchTensorBuffSize =entire_image_patch_col_major.size()*sizeof(DataType);
+ DataType* gpu_data_entire_image_patch_col_major = static_cast<DataType*>(sycl_device.allocate(patchTensorBuffSize));
+ TensorMap<Tensor<DataType, 4, DataLayout,IndexType>> gpu_entire_image_patch_col_major(gpu_data_entire_image_patch_col_major, patchColMajorTensorRange);
+ gpu_entire_image_patch_col_major.device(sycl_device)=gpu_col_major.extract_image_patches(3, 5);
+ sycl_device.memcpyDeviceToHost(entire_image_patch_col_major.data(), gpu_data_entire_image_patch_col_major, patchTensorBuffSize);
+
+ VERIFY_IS_EQUAL(entire_image_patch_col_major.dimension(0), 2);
+ VERIFY_IS_EQUAL(entire_image_patch_col_major.dimension(1), 3);
+ VERIFY_IS_EQUAL(entire_image_patch_col_major.dimension(2), 5);
+ VERIFY_IS_EQUAL(entire_image_patch_col_major.dimension(3), 3*5);
+
+ // Entire image patch: RowMajor
+patchRowMajorTensorRange={{sizeDim2*sizeDim3, sizeDim3, sizeDim2, sizeDim1}};
+Tensor<DataType, 4, RowMajor,IndexType> entire_image_patch_row_major(patchRowMajorTensorRange);
+patchTensorBuffSize =entire_image_patch_row_major.size()*sizeof(DataType);
+DataType* gpu_data_entire_image_patch_row_major = static_cast<DataType*>(sycl_device.allocate(patchTensorBuffSize));
+TensorMap<Tensor<DataType, 4, RowMajor,IndexType>> gpu_entire_image_patch_row_major(gpu_data_entire_image_patch_row_major, patchRowMajorTensorRange);
+gpu_entire_image_patch_row_major.device(sycl_device)=gpu_row_major.extract_image_patches(3, 5);
+sycl_device.memcpyDeviceToHost(entire_image_patch_row_major.data(), gpu_data_entire_image_patch_row_major, patchTensorBuffSize);
+ VERIFY_IS_EQUAL(entire_image_patch_row_major.dimension(0), 3*5);
+ VERIFY_IS_EQUAL(entire_image_patch_row_major.dimension(1), 5);
+ VERIFY_IS_EQUAL(entire_image_patch_row_major.dimension(2), 3);
+ VERIFY_IS_EQUAL(entire_image_patch_row_major.dimension(3), 2);
+
+ for (IndexType i = 0; i < 3; ++i) {
+ for (IndexType j = 0; j < 5; ++j) {
+ IndexType patchId = i+3*j;
+ for (IndexType r = 0; r < 3; ++r) {
+ for (IndexType c = 0; c < 5; ++c) {
+ for (IndexType d = 0; d < 2; ++d) {
+ DataType expected_col_major = 0.0f;
+ DataType expected_row_major = 0.0f;
+ if (r-1+i >= 0 && c-2+j >= 0 && r-1+i < 3 && c-2+j < 5) {
+ expected_col_major = tensor_col_major(d, r-1+i, c-2+j);
+ expected_row_major = tensor_row_major(c-2+j, r-1+i, d);
+ }
+ // ColMajor
+ if (entire_image_patch_col_major(d, r, c, patchId) != expected_col_major) {
+ std::cout << "Mismatch detected at index i=" << i << " j=" << j << " r=" << r << " c=" << c << " d=" << d << std::endl;
+ }
+ VERIFY_IS_EQUAL(entire_image_patch_col_major(d, r, c, patchId), expected_col_major);
+ // RowMajor
+ if (entire_image_patch_row_major(patchId, c, r, d) !=
+ expected_row_major) {
+ std::cout << "Mismatch detected at index i=" << i << " j=" << j << " r=" << r << " c=" << c << " d=" << d << std::endl;
+ }
+ VERIFY_IS_EQUAL(entire_image_patch_row_major(patchId, c, r, d),
+ expected_row_major);
+ // Check that ColMajor and RowMajor agree.
+ VERIFY_IS_EQUAL(expected_col_major, expected_row_major);
+ }
+ }
+ }
+ }
+ }
+
+ // 2D patch: ColMajor
+ patchColMajorTensorRange={{sizeDim1, 2, 2, sizeDim2*sizeDim3}};
+ Tensor<DataType, 4, DataLayout,IndexType> twod_patch_col_major(patchColMajorTensorRange);
+ patchTensorBuffSize =twod_patch_col_major.size()*sizeof(DataType);
+ DataType* gpu_data_twod_patch_col_major = static_cast<DataType*>(sycl_device.allocate(patchTensorBuffSize));
+ TensorMap<Tensor<DataType, 4, DataLayout,IndexType>> gpu_twod_patch_col_major(gpu_data_twod_patch_col_major, patchColMajorTensorRange);
+ gpu_twod_patch_col_major.device(sycl_device)=gpu_col_major.extract_image_patches(2, 2);
+ sycl_device.memcpyDeviceToHost(twod_patch_col_major.data(), gpu_data_twod_patch_col_major, patchTensorBuffSize);
+
+ VERIFY_IS_EQUAL(twod_patch_col_major.dimension(0), 2);
+ VERIFY_IS_EQUAL(twod_patch_col_major.dimension(1), 2);
+ VERIFY_IS_EQUAL(twod_patch_col_major.dimension(2), 2);
+ VERIFY_IS_EQUAL(twod_patch_col_major.dimension(3), 3*5);
+
+ // 2D patch: RowMajor
+ patchRowMajorTensorRange={{sizeDim2*sizeDim3, 2, 2, sizeDim1}};
+ Tensor<DataType, 4, RowMajor,IndexType> twod_patch_row_major(patchRowMajorTensorRange);
+ patchTensorBuffSize =twod_patch_row_major.size()*sizeof(DataType);
+ DataType* gpu_data_twod_patch_row_major = static_cast<DataType*>(sycl_device.allocate(patchTensorBuffSize));
+ TensorMap<Tensor<DataType, 4, RowMajor,IndexType>> gpu_twod_patch_row_major(gpu_data_twod_patch_row_major, patchRowMajorTensorRange);
+ gpu_twod_patch_row_major.device(sycl_device)=gpu_row_major.extract_image_patches(2, 2);
+ sycl_device.memcpyDeviceToHost(twod_patch_row_major.data(), gpu_data_twod_patch_row_major, patchTensorBuffSize);
+ VERIFY_IS_EQUAL(twod_patch_row_major.dimension(0), 3*5);
+ VERIFY_IS_EQUAL(twod_patch_row_major.dimension(1), 2);
+ VERIFY_IS_EQUAL(twod_patch_row_major.dimension(2), 2);
+ VERIFY_IS_EQUAL(twod_patch_row_major.dimension(3), 2);
+
+ // Based on the calculation described in TensorTraits.h, padding happens to be 0.
+ IndexType row_padding = 0;
+ IndexType col_padding = 0;
+ IndexType stride = 1;
+
+ for (IndexType i = 0; i < 3; ++i) {
+ for (IndexType j = 0; j < 5; ++j) {
+ IndexType patchId = i+3*j;
+ for (IndexType r = 0; r < 2; ++r) {
+ for (IndexType c = 0; c < 2; ++c) {
+ for (IndexType d = 0; d < 2; ++d) {
+ DataType expected_col_major = 0.0f;
+ DataType expected_row_major = 0.0f;
+ IndexType row_offset = r*stride + i - row_padding;
+ IndexType col_offset = c*stride + j - col_padding;
+ // ColMajor
+ if (row_offset >= 0 && col_offset >= 0 && row_offset < tensor_col_major.dimension(1) && col_offset < tensor_col_major.dimension(2)) {
+ expected_col_major = tensor_col_major(d, row_offset, col_offset);
+ }
+ if (twod_patch_col_major(d, r, c, patchId) != expected_col_major) {
+ std::cout << "Mismatch detected at index i=" << i << " j=" << j << " r=" << r << " c=" << c << " d=" << d << std::endl;
+ }
+ VERIFY_IS_EQUAL(twod_patch_col_major(d, r, c, patchId), expected_col_major);
+ // RowMajor
+ if (row_offset >= 0 && col_offset >= 0 && row_offset < tensor_row_major.dimension(1) && col_offset < tensor_row_major.dimension(0)) {
+ expected_row_major = tensor_row_major(col_offset, row_offset, d);
+ }
+ if (twod_patch_row_major(patchId, c, r, d) != expected_row_major) {
+ std::cout << "Mismatch detected at index i=" << i << " j=" << j << " r=" << r << " c=" << c << " d=" << d << std::endl;
+ }
+ VERIFY_IS_EQUAL(twod_patch_row_major(patchId, c, r, d), expected_row_major);
+ // Check that ColMajor and RowMajor agree.
+ VERIFY_IS_EQUAL(expected_col_major, expected_row_major);
+ }
+ }
+ }
+ }
+ }
+
+ sycl_device.deallocate(gpu_data_col_major);
+ sycl_device.deallocate(gpu_data_row_major);
+ sycl_device.deallocate(gpu_data_single_patch_col_major);
+ sycl_device.deallocate(gpu_data_single_patch_row_major);
+ sycl_device.deallocate(gpu_data_entire_image_patch_col_major);
+ sycl_device.deallocate(gpu_data_entire_image_patch_row_major);
+ sycl_device.deallocate(gpu_data_twod_patch_col_major);
+ sycl_device.deallocate(gpu_data_twod_patch_row_major);
+}
+
+template <typename DataType, typename IndexType>
+static void test_imagenet_patches_sycl(const Eigen::SyclDevice& sycl_device)
+{
+ // Test the code on typical configurations used by the 'imagenet' benchmarks at
+ // https://github.com/soumith/convnet-benchmarks
+ // ColMajor
+ IndexType sizeDim1 = 3;
+ IndexType sizeDim2 = 128;
+ IndexType sizeDim3 = 128;
+ IndexType sizeDim4 = 16;
+ array<IndexType, 4> tensorColMajorRange = {{sizeDim1, sizeDim2, sizeDim3, sizeDim4}};
+ Tensor<DataType, 4, DataLayout,IndexType> l_in_col_major(tensorColMajorRange);
+ l_in_col_major.setRandom();
+
+ DataType* gpu_data_l_in_col_major = static_cast<DataType*>(sycl_device.allocate(l_in_col_major.size()*sizeof(DataType)));
+ TensorMap<Tensor<DataType, 4, ColMajor, IndexType>> gpu_l_in_col_major(gpu_data_l_in_col_major, tensorColMajorRange);
+
+ sycl_device.memcpyHostToDevice(gpu_data_l_in_col_major, l_in_col_major.data(),(l_in_col_major.size())*sizeof(DataType));
+
+ array<IndexType, 5> patchTensorRange={{sizeDim1, 11, 11, sizeDim2*sizeDim3, sizeDim4}};
+ Tensor<DataType, 5, DataLayout,IndexType> l_out_col_major(patchTensorRange);
+ size_t patchTensorBuffSize =l_out_col_major.size()*sizeof(DataType);
+ DataType* gpu_data_l_out_col_major = static_cast<DataType*>(sycl_device.allocate(patchTensorBuffSize));
+ TensorMap<Tensor<DataType, 5, DataLayout,IndexType>> gpu_l_out_col_major(gpu_data_l_out_col_major, patchTensorRange);
+ gpu_l_out_col_major.device(sycl_device)=gpu_l_in_col_major.extract_image_patches(11, 11);
+ sycl_device.memcpyDeviceToHost(l_out_col_major.data(), gpu_data_l_out_col_major, patchTensorBuffSize);
+
+ VERIFY_IS_EQUAL(l_out_col_major.dimension(0), sizeDim1);
+ VERIFY_IS_EQUAL(l_out_col_major.dimension(1), 11);
+ VERIFY_IS_EQUAL(l_out_col_major.dimension(2), 11);
+ VERIFY_IS_EQUAL(l_out_col_major.dimension(3), sizeDim2*sizeDim3);
+ VERIFY_IS_EQUAL(l_out_col_major.dimension(4), sizeDim4);
+
+ // RowMajor
+ patchTensorRange={{sizeDim4, sizeDim2*sizeDim3, 11, 11, sizeDim1}};
+ Tensor<DataType, 5, RowMajor,IndexType> l_out_row_major(patchTensorRange);
+ patchTensorBuffSize =l_out_row_major.size()*sizeof(DataType);
+ DataType* gpu_data_l_out_row_major = static_cast<DataType*>(sycl_device.allocate(patchTensorBuffSize));
+ TensorMap<Tensor<DataType, 5, RowMajor,IndexType>> gpu_l_out_row_major(gpu_data_l_out_row_major, patchTensorRange);
+ gpu_l_out_row_major.device(sycl_device)=gpu_l_in_col_major.swap_layout().extract_image_patches(11, 11);
+ sycl_device.memcpyDeviceToHost(l_out_row_major.data(), gpu_data_l_out_row_major, patchTensorBuffSize);
+
+ VERIFY_IS_EQUAL(l_out_row_major.dimension(0), sizeDim4);
+ VERIFY_IS_EQUAL(l_out_row_major.dimension(1), sizeDim2*sizeDim3);
+ VERIFY_IS_EQUAL(l_out_row_major.dimension(2), 11);
+ VERIFY_IS_EQUAL(l_out_row_major.dimension(3), 11);
+ VERIFY_IS_EQUAL(l_out_row_major.dimension(4), sizeDim1);
+
+ for (IndexType b = 0; b < 16; ++b) {
+ for (IndexType i = 0; i < 128; ++i) {
+ for (IndexType j = 0; j < 128; ++j) {
+ IndexType patchId = i+128*j;
+ for (IndexType c = 0; c < 11; ++c) {
+ for (IndexType r = 0; r < 11; ++r) {
+ for (IndexType d = 0; d < 3; ++d) {
+ DataType expected = 0.0f;
+ if (r-5+i >= 0 && c-5+j >= 0 && r-5+i < 128 && c-5+j < 128) {
+ expected = l_in_col_major(d, r-5+i, c-5+j, b);
+ }
+ // ColMajor
+ if (l_out_col_major(d, r, c, patchId, b) != expected) {
+ std::cout << "Mismatch detected at index i=" << i << " j=" << j << " r=" << r << " c=" << c << " d=" << d << " b=" << b << std::endl;
+ }
+ VERIFY_IS_EQUAL(l_out_col_major(d, r, c, patchId, b), expected);
+ // RowMajor
+ if (l_out_row_major(b, patchId, c, r, d) !=
+ expected) {
+ std::cout << "Mismatch detected at index i=" << i << " j=" << j
+ << " r=" << r << " c=" << c << " d=" << d << " b=" << b
+ << std::endl;
+ }
+ VERIFY_IS_EQUAL(l_out_row_major(b, patchId, c, r, d),
+ expected);
+ }
+ }
+ }
+ }
+ }
+ }
+
+ // ColMajor
+ sycl_device.deallocate(gpu_data_l_in_col_major);
+ sycl_device.deallocate(gpu_data_l_out_col_major);
+ sizeDim1 = 16;
+ sizeDim2 = 64;
+ sizeDim3 = 64;
+ sizeDim4 = 32;
+ tensorColMajorRange = {{sizeDim1, sizeDim2, sizeDim3, sizeDim4}};
+ l_in_col_major.resize(tensorColMajorRange);
+ l_in_col_major.setRandom();
+ gpu_data_l_in_col_major = static_cast<DataType*>(sycl_device.allocate(l_in_col_major.size()*sizeof(DataType)));
+ TensorMap<Tensor<DataType, 4, ColMajor, IndexType>>gpu_l_in_col_major_resize1(gpu_data_l_in_col_major, tensorColMajorRange);
+
+ patchTensorRange={{sizeDim1, 9, 9, sizeDim2*sizeDim3, sizeDim4}};
+ l_out_col_major.resize(patchTensorRange);
+ patchTensorBuffSize =l_out_col_major.size()*sizeof(DataType);
+ gpu_data_l_out_col_major = static_cast<DataType*>(sycl_device.allocate(patchTensorBuffSize));
+ TensorMap<Tensor<DataType, 5, DataLayout,IndexType>>gpu_l_out_col_major_resize1(gpu_data_l_out_col_major, patchTensorRange);
+ sycl_device.memcpyHostToDevice(gpu_data_l_in_col_major, l_in_col_major.data(),(l_in_col_major.size())*sizeof(DataType));
+ gpu_l_out_col_major_resize1.device(sycl_device)=gpu_l_in_col_major_resize1.extract_image_patches(9, 9);
+ sycl_device.memcpyDeviceToHost(l_out_col_major.data(), gpu_data_l_out_col_major, patchTensorBuffSize);
+ VERIFY_IS_EQUAL(l_out_col_major.dimension(0), 16);
+ VERIFY_IS_EQUAL(l_out_col_major.dimension(1), 9);
+ VERIFY_IS_EQUAL(l_out_col_major.dimension(2), 9);
+ VERIFY_IS_EQUAL(l_out_col_major.dimension(3), 64*64);
+ VERIFY_IS_EQUAL(l_out_col_major.dimension(4), 32);
+
+// RowMajor
+ sycl_device.deallocate(gpu_data_l_out_row_major);
+ patchTensorRange={{sizeDim4, sizeDim2*sizeDim3, 9, 9 ,sizeDim1}};
+ l_out_row_major.resize(patchTensorRange);
+ patchTensorBuffSize =l_out_row_major.size()*sizeof(DataType);
+ gpu_data_l_out_row_major = static_cast<DataType*>(sycl_device.allocate(patchTensorBuffSize));
+ TensorMap<Tensor<DataType, 5, RowMajor,IndexType>>gpu_l_out_row_major_resize1(gpu_data_l_out_row_major, patchTensorRange);
+ gpu_l_out_row_major_resize1.device(sycl_device)=gpu_l_in_col_major_resize1.swap_layout().extract_image_patches(9, 9);
+ sycl_device.memcpyDeviceToHost(l_out_row_major.data(), gpu_data_l_out_row_major, patchTensorBuffSize);
+
+ VERIFY_IS_EQUAL(l_out_row_major.dimension(0), 32);
+ VERIFY_IS_EQUAL(l_out_row_major.dimension(1), 64*64);
+ VERIFY_IS_EQUAL(l_out_row_major.dimension(2), 9);
+ VERIFY_IS_EQUAL(l_out_row_major.dimension(3), 9);
+ VERIFY_IS_EQUAL(l_out_row_major.dimension(4), 16);
+
+ for (IndexType b = 0; b < 32; ++b) {
+ for (IndexType i = 0; i < 64; ++i) {
+ for (IndexType j = 0; j < 64; ++j) {
+ IndexType patchId = i+64*j;
+ for (IndexType c = 0; c < 9; ++c) {
+ for (IndexType r = 0; r < 9; ++r) {
+ for (IndexType d = 0; d < 16; ++d) {
+ DataType expected = 0.0f;
+ if (r-4+i >= 0 && c-4+j >= 0 && r-4+i < 64 && c-4+j < 64) {
+ expected = l_in_col_major(d, r-4+i, c-4+j, b);
+ }
+ // ColMajor
+ if (l_out_col_major(d, r, c, patchId, b) != expected) {
+ std::cout << "Mismatch detected at index i=" << i << " j=" << j << " r=" << r << " c=" << c << " d=" << d << " b=" << b << std::endl;
+ }
+ VERIFY_IS_EQUAL(l_out_col_major(d, r, c, patchId, b), expected);
+ // RowMajor
+ if (l_out_row_major(b, patchId, c, r, d) != expected) {
+ std::cout << "Mismatch detected at index i=" << i << " j=" << j << " r=" << r << " c=" << c << " d=" << d << " b=" << b << std::endl;
+ }
+ VERIFY_IS_EQUAL(l_out_row_major(b, patchId, c, r, d), expected);
+ }
+ }
+ }
+ }
+ }
+ }
+
+ // ColMajor
+
+ sycl_device.deallocate(gpu_data_l_in_col_major);
+ sycl_device.deallocate(gpu_data_l_out_col_major);
+ sizeDim1 = 32;
+ sizeDim2 = 16;
+ sizeDim3 = 16;
+ sizeDim4 = 32;
+ tensorColMajorRange = {{sizeDim1, sizeDim2, sizeDim3, sizeDim4}};
+ l_in_col_major.resize(tensorColMajorRange);
+ l_in_col_major.setRandom();
+ gpu_data_l_in_col_major = static_cast<DataType*>(sycl_device.allocate(l_in_col_major.size()*sizeof(DataType)));
+ TensorMap<Tensor<DataType, 4, ColMajor, IndexType>>gpu_l_in_col_major_resize2(gpu_data_l_in_col_major, tensorColMajorRange);
+
+ patchTensorRange={{sizeDim1, 7, 7, sizeDim2*sizeDim3, sizeDim4}};
+ l_out_col_major.resize(patchTensorRange);
+ patchTensorBuffSize =l_out_col_major.size()*sizeof(DataType);
+ gpu_data_l_out_col_major = static_cast<DataType*>(sycl_device.allocate(patchTensorBuffSize));
+ TensorMap<Tensor<DataType, 5, DataLayout,IndexType>>gpu_l_out_col_major_resize2(gpu_data_l_out_col_major, patchTensorRange);
+ sycl_device.memcpyHostToDevice(gpu_data_l_in_col_major, l_in_col_major.data(),(l_in_col_major.size())*sizeof(DataType));
+ gpu_l_out_col_major_resize2.device(sycl_device)=gpu_l_in_col_major_resize2.extract_image_patches(7, 7);
+ sycl_device.memcpyDeviceToHost(l_out_col_major.data(), gpu_data_l_out_col_major, patchTensorBuffSize);
+
+ VERIFY_IS_EQUAL(l_out_col_major.dimension(0), 32);
+ VERIFY_IS_EQUAL(l_out_col_major.dimension(1), 7);
+ VERIFY_IS_EQUAL(l_out_col_major.dimension(2), 7);
+ VERIFY_IS_EQUAL(l_out_col_major.dimension(3), 16*16);
+ VERIFY_IS_EQUAL(l_out_col_major.dimension(4), 32);
+
+ // RowMajor
+ sycl_device.deallocate(gpu_data_l_out_row_major);
+ patchTensorRange={{sizeDim4, sizeDim2*sizeDim3, 7, 7 ,sizeDim1}};
+ l_out_row_major.resize(patchTensorRange);
+ patchTensorBuffSize =l_out_row_major.size()*sizeof(DataType);
+ gpu_data_l_out_row_major = static_cast<DataType*>(sycl_device.allocate(patchTensorBuffSize));
+ TensorMap<Tensor<DataType, 5, RowMajor,IndexType>>gpu_l_out_row_major_resize2(gpu_data_l_out_row_major, patchTensorRange);
+ gpu_l_out_row_major_resize2.device(sycl_device)=gpu_l_in_col_major_resize2.swap_layout().extract_image_patches(7, 7);
+ sycl_device.memcpyDeviceToHost(l_out_row_major.data(), gpu_data_l_out_row_major, patchTensorBuffSize);
+
+ VERIFY_IS_EQUAL(l_out_row_major.dimension(0), 32);
+ VERIFY_IS_EQUAL(l_out_row_major.dimension(1), 16*16);
+ VERIFY_IS_EQUAL(l_out_row_major.dimension(2), 7);
+ VERIFY_IS_EQUAL(l_out_row_major.dimension(3), 7);
+ VERIFY_IS_EQUAL(l_out_row_major.dimension(4), 32);
+
+ for (IndexType b = 0; b < 32; ++b) {
+ for (IndexType i = 0; i < 16; ++i) {
+ for (IndexType j = 0; j < 16; ++j) {
+ IndexType patchId = i+16*j;
+ for (IndexType c = 0; c < 7; ++c) {
+ for (IndexType r = 0; r < 7; ++r) {
+ for (IndexType d = 0; d < 32; ++d) {
+ DataType expected = 0.0f;
+ if (r-3+i >= 0 && c-3+j >= 0 && r-3+i < 16 && c-3+j < 16) {
+ expected = l_in_col_major(d, r-3+i, c-3+j, b);
+ }
+ // ColMajor
+ if (l_out_col_major(d, r, c, patchId, b) != expected) {
+ std::cout << "Mismatch detected at index i=" << i << " j=" << j << " r=" << r << " c=" << c << " d=" << d << " b=" << b << std::endl;
+ }
+ VERIFY_IS_EQUAL(l_out_col_major(d, r, c, patchId, b), expected);
+ // RowMajor
+ if (l_out_row_major(b, patchId, c, r, d) != expected) {
+ std::cout << "Mismatch detected at index i=" << i << " j=" << j << " r=" << r << " c=" << c << " d=" << d << " b=" << b << std::endl;
+ }
+ VERIFY_IS_EQUAL(l_out_row_major(b, patchId, c, r, d), expected);
+ }
+ }
+ }
+ }
+ }
+ }
+
+ // ColMajor
+ sycl_device.deallocate(gpu_data_l_in_col_major);
+ sycl_device.deallocate(gpu_data_l_out_col_major);
+ sizeDim1 = 64;
+ sizeDim2 = 13;
+ sizeDim3 = 13;
+ sizeDim4 = 32;
+ tensorColMajorRange = {{sizeDim1, sizeDim2, sizeDim3, sizeDim4}};
+ l_in_col_major.resize(tensorColMajorRange);
+ l_in_col_major.setRandom();
+ gpu_data_l_in_col_major = static_cast<DataType*>(sycl_device.allocate(l_in_col_major.size()*sizeof(DataType)));
+ TensorMap<Tensor<DataType, 4, ColMajor, IndexType>>gpu_l_in_col_major_resize3(gpu_data_l_in_col_major, tensorColMajorRange);
+
+ patchTensorRange={{sizeDim1, 3, 3, sizeDim2*sizeDim3, sizeDim4}};
+ l_out_col_major.resize(patchTensorRange);
+ patchTensorBuffSize =l_out_col_major.size()*sizeof(DataType);
+ gpu_data_l_out_col_major = static_cast<DataType*>(sycl_device.allocate(patchTensorBuffSize));
+ TensorMap<Tensor<DataType, 5, DataLayout,IndexType>>gpu_l_out_col_major_resize3(gpu_data_l_out_col_major, patchTensorRange);
+ sycl_device.memcpyHostToDevice(gpu_data_l_in_col_major, l_in_col_major.data(),(l_in_col_major.size())*sizeof(DataType));
+ gpu_l_out_col_major_resize3.device(sycl_device)=gpu_l_in_col_major_resize3.extract_image_patches(3, 3);
+ sycl_device.memcpyDeviceToHost(l_out_col_major.data(), gpu_data_l_out_col_major, patchTensorBuffSize);
+
+ VERIFY_IS_EQUAL(l_out_col_major.dimension(0), 64);
+ VERIFY_IS_EQUAL(l_out_col_major.dimension(1), 3);
+ VERIFY_IS_EQUAL(l_out_col_major.dimension(2), 3);
+ VERIFY_IS_EQUAL(l_out_col_major.dimension(3), 13*13);
+ VERIFY_IS_EQUAL(l_out_col_major.dimension(4), 32);
+
+ // RowMajor
+ sycl_device.deallocate(gpu_data_l_out_row_major);
+ patchTensorRange={{sizeDim4, sizeDim2*sizeDim3, 3, 3 ,sizeDim1}};
+ l_out_row_major.resize(patchTensorRange);
+ patchTensorBuffSize =l_out_row_major.size()*sizeof(DataType);
+ gpu_data_l_out_row_major = static_cast<DataType*>(sycl_device.allocate(patchTensorBuffSize));
+ TensorMap<Tensor<DataType, 5, RowMajor,IndexType>>gpu_l_out_row_major_resize3(gpu_data_l_out_row_major, patchTensorRange);
+ gpu_l_out_row_major_resize3.device(sycl_device)=gpu_l_in_col_major_resize3.swap_layout().extract_image_patches(3, 3);
+ sycl_device.memcpyDeviceToHost(l_out_row_major.data(), gpu_data_l_out_row_major, patchTensorBuffSize);
+
+ VERIFY_IS_EQUAL(l_out_row_major.dimension(0), 32);
+ VERIFY_IS_EQUAL(l_out_row_major.dimension(1), 13*13);
+ VERIFY_IS_EQUAL(l_out_row_major.dimension(2), 3);
+ VERIFY_IS_EQUAL(l_out_row_major.dimension(3), 3);
+ VERIFY_IS_EQUAL(l_out_row_major.dimension(4), 64);
+
+ for (IndexType b = 0; b < 32; ++b) {
+ for (IndexType i = 0; i < 13; ++i) {
+ for (IndexType j = 0; j < 13; ++j) {
+ IndexType patchId = i+13*j;
+ for (IndexType c = 0; c < 3; ++c) {
+ for (IndexType r = 0; r < 3; ++r) {
+ for (IndexType d = 0; d < 64; ++d) {
+ DataType expected = 0.0f;
+ if (r-1+i >= 0 && c-1+j >= 0 && r-1+i < 13 && c-1+j < 13) {
+ expected = l_in_col_major(d, r-1+i, c-1+j, b);
+ }
+ // ColMajor
+ if (l_out_col_major(d, r, c, patchId, b) != expected) {
+ std::cout << "Mismatch detected at index i=" << i << " j=" << j << " r=" << r << " c=" << c << " d=" << d << " b=" << b << std::endl;
+ }
+ VERIFY_IS_EQUAL(l_out_col_major(d, r, c, patchId, b), expected);
+ // RowMajor
+ if (l_out_row_major(b, patchId, c, r, d) != expected) {
+ std::cout << "Mismatch detected at index i=" << i << " j=" << j << " r=" << r << " c=" << c << " d=" << d << " b=" << b << std::endl;
+ }
+ VERIFY_IS_EQUAL(l_out_row_major(b, patchId, c, r, d), expected);
+ }
+ }
+ }
+ }
+ }
+ }
+ sycl_device.deallocate(gpu_data_l_in_col_major);
+ sycl_device.deallocate(gpu_data_l_out_col_major);
+ sycl_device.deallocate(gpu_data_l_out_row_major);
+}
+
+
+template<typename DataType, typename dev_Selector> void sycl_tensor_image_patch_test_per_device(dev_Selector s){
+QueueInterface queueInterface(s);
+auto sycl_device = Eigen::SyclDevice(&queueInterface);
+test_simple_image_patch_sycl<DataType, int64_t>(sycl_device);
+test_patch_padding_valid_sycl<DataType, int64_t>(sycl_device);
+test_patch_padding_valid_same_value_sycl<DataType, int64_t>(sycl_device);
+test_patch_padding_same_sycl<DataType, int64_t>(sycl_device);
+test_patch_no_extra_dim_sycl<DataType, int64_t>(sycl_device);
+test_imagenet_patches_sycl<DataType, int64_t>(sycl_device);
+}
+EIGEN_DECLARE_TEST(cxx11_tensor_image_patch_sycl)
+{
+for (const auto& device :Eigen::get_sycl_supported_devices()) {
+ CALL_SUBTEST(sycl_tensor_image_patch_test_per_device<float>(device));
+}
+}
diff --git a/unsupported/test/cxx11_tensor_index_list.cpp b/unsupported/test/cxx11_tensor_index_list.cpp
new file mode 100644
index 0000000..9cbdaa7
--- /dev/null
+++ b/unsupported/test/cxx11_tensor_index_list.cpp
@@ -0,0 +1,381 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "main.h"
+
+#include <Eigen/CXX11/Tensor>
+
+static void test_static_index_list()
+{
+ Tensor<float, 4> tensor(2,3,5,7);
+ tensor.setRandom();
+
+ constexpr auto reduction_axis = make_index_list(0, 1, 2);
+ VERIFY_IS_EQUAL(internal::array_get<0>(reduction_axis), 0);
+ VERIFY_IS_EQUAL(internal::array_get<1>(reduction_axis), 1);
+ VERIFY_IS_EQUAL(internal::array_get<2>(reduction_axis), 2);
+ VERIFY_IS_EQUAL(static_cast<Index>(reduction_axis[0]), 0);
+ VERIFY_IS_EQUAL(static_cast<Index>(reduction_axis[1]), 1);
+ VERIFY_IS_EQUAL(static_cast<Index>(reduction_axis[2]), 2);
+
+ VERIFY_IS_EQUAL(reduction_axis.size(), std::size_t(3));
+
+ EIGEN_STATIC_ASSERT((internal::array_get<0>(reduction_axis) == 0), YOU_MADE_A_PROGRAMMING_MISTAKE);
+ EIGEN_STATIC_ASSERT((internal::array_get<1>(reduction_axis) == 1), YOU_MADE_A_PROGRAMMING_MISTAKE);
+ EIGEN_STATIC_ASSERT((internal::array_get<2>(reduction_axis) == 2), YOU_MADE_A_PROGRAMMING_MISTAKE);
+
+ Tensor<float, 1> result = tensor.sum(reduction_axis);
+ for (int i = 0; i < result.size(); ++i) {
+ float expected = 0.0f;
+ for (int j = 0; j < 2; ++j) {
+ for (int k = 0; k < 3; ++k) {
+ for (int l = 0; l < 5; ++l) {
+ expected += tensor(j,k,l,i);
+ }
+ }
+ }
+ VERIFY_IS_APPROX(result(i), expected);
+ }
+}
+
+
+static void test_type2index_list()
+{
+ Tensor<float, 5> tensor(2,3,5,7,11);
+ tensor.setRandom();
+ tensor += tensor.constant(10.0f);
+
+ typedef Eigen::IndexList<Eigen::type2index<0>> Dims0;
+ typedef Eigen::IndexList<Eigen::type2index<0>, Eigen::type2index<1>> Dims1;
+ typedef Eigen::IndexList<Eigen::type2index<0>, Eigen::type2index<1>, Eigen::type2index<2>> Dims2;
+ typedef Eigen::IndexList<Eigen::type2index<0>, Eigen::type2index<1>, Eigen::type2index<2>, Eigen::type2index<3>> Dims3;
+ typedef Eigen::IndexList<Eigen::type2index<0>, Eigen::type2index<1>, Eigen::type2index<2>, Eigen::type2index<3>, Eigen::type2index<4>> Dims4;
+
+#if 0
+ EIGEN_STATIC_ASSERT((internal::indices_statically_known_to_increase<Dims0>() == true), YOU_MADE_A_PROGRAMMING_MISTAKE);
+ EIGEN_STATIC_ASSERT((internal::indices_statically_known_to_increase<Dims1>() == true), YOU_MADE_A_PROGRAMMING_MISTAKE);
+ EIGEN_STATIC_ASSERT((internal::indices_statically_known_to_increase<Dims2>() == true), YOU_MADE_A_PROGRAMMING_MISTAKE);
+ EIGEN_STATIC_ASSERT((internal::indices_statically_known_to_increase<Dims3>() == true), YOU_MADE_A_PROGRAMMING_MISTAKE);
+ EIGEN_STATIC_ASSERT((internal::indices_statically_known_to_increase<Dims4>() == true), YOU_MADE_A_PROGRAMMING_MISTAKE);
+#endif
+
+ EIGEN_STATIC_ASSERT((internal::are_inner_most_dims<Dims0, 1, ColMajor>::value == true), YOU_MADE_A_PROGRAMMING_MISTAKE);
+ EIGEN_STATIC_ASSERT((internal::are_inner_most_dims<Dims1, 2, ColMajor>::value == true), YOU_MADE_A_PROGRAMMING_MISTAKE);
+ EIGEN_STATIC_ASSERT((internal::are_inner_most_dims<Dims2, 3, ColMajor>::value == true), YOU_MADE_A_PROGRAMMING_MISTAKE);
+ EIGEN_STATIC_ASSERT((internal::are_inner_most_dims<Dims3, 4, ColMajor>::value == true), YOU_MADE_A_PROGRAMMING_MISTAKE);
+ EIGEN_STATIC_ASSERT((internal::are_inner_most_dims<Dims4, 5, ColMajor>::value == true), YOU_MADE_A_PROGRAMMING_MISTAKE);
+
+ EIGEN_STATIC_ASSERT((internal::are_inner_most_dims<Dims0, 1, RowMajor>::value == true), YOU_MADE_A_PROGRAMMING_MISTAKE);
+ EIGEN_STATIC_ASSERT((internal::are_inner_most_dims<Dims1, 2, RowMajor>::value == true), YOU_MADE_A_PROGRAMMING_MISTAKE);
+ EIGEN_STATIC_ASSERT((internal::are_inner_most_dims<Dims2, 3, RowMajor>::value == true), YOU_MADE_A_PROGRAMMING_MISTAKE);
+ EIGEN_STATIC_ASSERT((internal::are_inner_most_dims<Dims3, 4, RowMajor>::value == true), YOU_MADE_A_PROGRAMMING_MISTAKE);
+ EIGEN_STATIC_ASSERT((internal::are_inner_most_dims<Dims4, 5, RowMajor>::value == true), YOU_MADE_A_PROGRAMMING_MISTAKE);
+
+ const Dims0 reduction_axis0;
+ Tensor<float, 4> result0 = tensor.sum(reduction_axis0);
+ for (int m = 0; m < 11; ++m) {
+ for (int l = 0; l < 7; ++l) {
+ for (int k = 0; k < 5; ++k) {
+ for (int j = 0; j < 3; ++j) {
+ float expected = 0.0f;
+ for (int i = 0; i < 2; ++i) {
+ expected += tensor(i,j,k,l,m);
+ }
+ VERIFY_IS_APPROX(result0(j,k,l,m), expected);
+ }
+ }
+ }
+ }
+
+ const Dims1 reduction_axis1;
+ Tensor<float, 3> result1 = tensor.sum(reduction_axis1);
+ for (int m = 0; m < 11; ++m) {
+ for (int l = 0; l < 7; ++l) {
+ for (int k = 0; k < 5; ++k) {
+ float expected = 0.0f;
+ for (int j = 0; j < 3; ++j) {
+ for (int i = 0; i < 2; ++i) {
+ expected += tensor(i,j,k,l,m);
+ }
+ }
+ VERIFY_IS_APPROX(result1(k,l,m), expected);
+ }
+ }
+ }
+
+ const Dims2 reduction_axis2;
+ Tensor<float, 2> result2 = tensor.sum(reduction_axis2);
+ for (int m = 0; m < 11; ++m) {
+ for (int l = 0; l < 7; ++l) {
+ float expected = 0.0f;
+ for (int k = 0; k < 5; ++k) {
+ for (int j = 0; j < 3; ++j) {
+ for (int i = 0; i < 2; ++i) {
+ expected += tensor(i,j,k,l,m);
+ }
+ }
+ }
+ VERIFY_IS_APPROX(result2(l,m), expected);
+ }
+ }
+
+ const Dims3 reduction_axis3;
+ Tensor<float, 1> result3 = tensor.sum(reduction_axis3);
+ for (int m = 0; m < 11; ++m) {
+ float expected = 0.0f;
+ for (int l = 0; l < 7; ++l) {
+ for (int k = 0; k < 5; ++k) {
+ for (int j = 0; j < 3; ++j) {
+ for (int i = 0; i < 2; ++i) {
+ expected += tensor(i,j,k,l,m);
+ }
+ }
+ }
+ }
+ VERIFY_IS_APPROX(result3(m), expected);
+ }
+
+ const Dims4 reduction_axis4;
+ Tensor<float, 0> result4 = tensor.sum(reduction_axis4);
+ float expected = 0.0f;
+ for (int m = 0; m < 11; ++m) {
+ for (int l = 0; l < 7; ++l) {
+ for (int k = 0; k < 5; ++k) {
+ for (int j = 0; j < 3; ++j) {
+ for (int i = 0; i < 2; ++i) {
+ expected += tensor(i,j,k,l,m);
+ }
+ }
+ }
+ }
+ }
+ VERIFY_IS_APPROX(result4(), expected);
+}
+
+
+static void test_type2indexpair_list()
+{
+ Tensor<float, 5> tensor(2,3,5,7,11);
+ tensor.setRandom();
+ tensor += tensor.constant(10.0f);
+
+ typedef Eigen::IndexPairList<Eigen::type2indexpair<0,10>> Dims0;
+ typedef Eigen::IndexPairList<Eigen::type2indexpair<0,10>, Eigen::type2indexpair<1,11>, Eigen::type2indexpair<2,12>> Dims2_a;
+ typedef Eigen::IndexPairList<Eigen::type2indexpair<0,10>, Eigen::IndexPair<Index>, Eigen::type2indexpair<2,12>> Dims2_b;
+ typedef Eigen::IndexPairList<Eigen::IndexPair<Index>, Eigen::type2indexpair<1,11>, Eigen::IndexPair<Index>> Dims2_c;
+
+ Dims2_a d2_a;
+
+ Dims2_b d2_b;
+ d2_b.set(1, Eigen::IndexPair<Index>(1,11));
+
+ Dims2_c d2_c;
+ d2_c.set(0, Eigen::IndexPair<Index>(Eigen::IndexPair<Index>(0,10)));
+ d2_c.set(1, Eigen::IndexPair<Index>(1,11)); // setting type2indexpair to correct value.
+ d2_c.set(2, Eigen::IndexPair<Index>(2,12));
+
+ VERIFY_IS_EQUAL(d2_a[0].first, 0);
+ VERIFY_IS_EQUAL(d2_a[0].second, 10);
+ VERIFY_IS_EQUAL(d2_a[1].first, 1);
+ VERIFY_IS_EQUAL(d2_a[1].second, 11);
+ VERIFY_IS_EQUAL(d2_a[2].first, 2);
+ VERIFY_IS_EQUAL(d2_a[2].second, 12);
+
+ VERIFY_IS_EQUAL(d2_b[0].first, 0);
+ VERIFY_IS_EQUAL(d2_b[0].second, 10);
+ VERIFY_IS_EQUAL(d2_b[1].first, 1);
+ VERIFY_IS_EQUAL(d2_b[1].second, 11);
+ VERIFY_IS_EQUAL(d2_b[2].first, 2);
+ VERIFY_IS_EQUAL(d2_b[2].second, 12);
+
+ VERIFY_IS_EQUAL(d2_c[0].first, 0);
+ VERIFY_IS_EQUAL(d2_c[0].second, 10);
+ VERIFY_IS_EQUAL(d2_c[1].first, 1);
+ VERIFY_IS_EQUAL(d2_c[1].second, 11);
+ VERIFY_IS_EQUAL(d2_c[2].first, 2);
+ VERIFY_IS_EQUAL(d2_c[2].second, 12);
+
+ EIGEN_STATIC_ASSERT((d2_a.value_known_statically(0) == true), YOU_MADE_A_PROGRAMMING_MISTAKE);
+ EIGEN_STATIC_ASSERT((d2_a.value_known_statically(1) == true), YOU_MADE_A_PROGRAMMING_MISTAKE);
+ EIGEN_STATIC_ASSERT((d2_a.value_known_statically(2) == true), YOU_MADE_A_PROGRAMMING_MISTAKE);
+
+ EIGEN_STATIC_ASSERT((d2_b.value_known_statically(0) == true), YOU_MADE_A_PROGRAMMING_MISTAKE);
+ EIGEN_STATIC_ASSERT((d2_b.value_known_statically(1) == false), YOU_MADE_A_PROGRAMMING_MISTAKE);
+ EIGEN_STATIC_ASSERT((d2_b.value_known_statically(2) == true), YOU_MADE_A_PROGRAMMING_MISTAKE);
+
+ EIGEN_STATIC_ASSERT((d2_c.value_known_statically(0) == false), YOU_MADE_A_PROGRAMMING_MISTAKE);
+ EIGEN_STATIC_ASSERT((d2_c.value_known_statically(1) == true), YOU_MADE_A_PROGRAMMING_MISTAKE);
+ EIGEN_STATIC_ASSERT((d2_c.value_known_statically(2) == false), YOU_MADE_A_PROGRAMMING_MISTAKE);
+
+ EIGEN_STATIC_ASSERT((Eigen::internal::index_pair_first_statically_eq<Dims0>(0, 0) == true), YOU_MADE_A_PROGRAMMING_MISTAKE);
+ EIGEN_STATIC_ASSERT((Eigen::internal::index_pair_first_statically_eq<Dims0>(0, 1) == false), YOU_MADE_A_PROGRAMMING_MISTAKE);
+
+ EIGEN_STATIC_ASSERT((Eigen::internal::index_pair_first_statically_eq<Dims2_a>(0, 0) == true), YOU_MADE_A_PROGRAMMING_MISTAKE);
+ EIGEN_STATIC_ASSERT((Eigen::internal::index_pair_first_statically_eq<Dims2_a>(0, 1) == false), YOU_MADE_A_PROGRAMMING_MISTAKE);
+ EIGEN_STATIC_ASSERT((Eigen::internal::index_pair_first_statically_eq<Dims2_a>(1, 1) == true), YOU_MADE_A_PROGRAMMING_MISTAKE);
+ EIGEN_STATIC_ASSERT((Eigen::internal::index_pair_first_statically_eq<Dims2_a>(1, 2) == false), YOU_MADE_A_PROGRAMMING_MISTAKE);
+ EIGEN_STATIC_ASSERT((Eigen::internal::index_pair_first_statically_eq<Dims2_a>(2, 2) == true), YOU_MADE_A_PROGRAMMING_MISTAKE);
+ EIGEN_STATIC_ASSERT((Eigen::internal::index_pair_first_statically_eq<Dims2_a>(2, 3) == false), YOU_MADE_A_PROGRAMMING_MISTAKE);
+
+ EIGEN_STATIC_ASSERT((Eigen::internal::index_pair_first_statically_eq<Dims2_b>(0, 0) == true), YOU_MADE_A_PROGRAMMING_MISTAKE);
+ EIGEN_STATIC_ASSERT((Eigen::internal::index_pair_first_statically_eq<Dims2_b>(0, 1) == false), YOU_MADE_A_PROGRAMMING_MISTAKE);
+ EIGEN_STATIC_ASSERT((Eigen::internal::index_pair_first_statically_eq<Dims2_b>(1, 1) == false), YOU_MADE_A_PROGRAMMING_MISTAKE);
+ EIGEN_STATIC_ASSERT((Eigen::internal::index_pair_first_statically_eq<Dims2_b>(1, 2) == false), YOU_MADE_A_PROGRAMMING_MISTAKE);
+ EIGEN_STATIC_ASSERT((Eigen::internal::index_pair_first_statically_eq<Dims2_b>(2, 2) == true), YOU_MADE_A_PROGRAMMING_MISTAKE);
+ EIGEN_STATIC_ASSERT((Eigen::internal::index_pair_first_statically_eq<Dims2_b>(2, 3) == false), YOU_MADE_A_PROGRAMMING_MISTAKE);
+
+ EIGEN_STATIC_ASSERT((Eigen::internal::index_pair_first_statically_eq<Dims2_c>(0, 0) == false), YOU_MADE_A_PROGRAMMING_MISTAKE);
+ EIGEN_STATIC_ASSERT((Eigen::internal::index_pair_first_statically_eq<Dims2_c>(0, 1) == false), YOU_MADE_A_PROGRAMMING_MISTAKE);
+ EIGEN_STATIC_ASSERT((Eigen::internal::index_pair_first_statically_eq<Dims2_c>(1, 1) == true), YOU_MADE_A_PROGRAMMING_MISTAKE);
+ EIGEN_STATIC_ASSERT((Eigen::internal::index_pair_first_statically_eq<Dims2_c>(1, 2) == false), YOU_MADE_A_PROGRAMMING_MISTAKE);
+ EIGEN_STATIC_ASSERT((Eigen::internal::index_pair_first_statically_eq<Dims2_c>(2, 2) == false), YOU_MADE_A_PROGRAMMING_MISTAKE);
+ EIGEN_STATIC_ASSERT((Eigen::internal::index_pair_first_statically_eq<Dims2_c>(2, 3) == false), YOU_MADE_A_PROGRAMMING_MISTAKE);
+
+ EIGEN_STATIC_ASSERT((Eigen::internal::index_pair_second_statically_eq<Dims0>(0, 10) == true), YOU_MADE_A_PROGRAMMING_MISTAKE);
+ EIGEN_STATIC_ASSERT((Eigen::internal::index_pair_second_statically_eq<Dims0>(0, 11) == false), YOU_MADE_A_PROGRAMMING_MISTAKE);
+
+ EIGEN_STATIC_ASSERT((Eigen::internal::index_pair_second_statically_eq<Dims2_a>(0, 10) == true), YOU_MADE_A_PROGRAMMING_MISTAKE);
+ EIGEN_STATIC_ASSERT((Eigen::internal::index_pair_second_statically_eq<Dims2_a>(0, 11) == false), YOU_MADE_A_PROGRAMMING_MISTAKE);
+ EIGEN_STATIC_ASSERT((Eigen::internal::index_pair_second_statically_eq<Dims2_a>(1, 11) == true), YOU_MADE_A_PROGRAMMING_MISTAKE);
+ EIGEN_STATIC_ASSERT((Eigen::internal::index_pair_second_statically_eq<Dims2_a>(1, 12) == false), YOU_MADE_A_PROGRAMMING_MISTAKE);
+ EIGEN_STATIC_ASSERT((Eigen::internal::index_pair_second_statically_eq<Dims2_a>(2, 12) == true), YOU_MADE_A_PROGRAMMING_MISTAKE);
+ EIGEN_STATIC_ASSERT((Eigen::internal::index_pair_second_statically_eq<Dims2_a>(2, 13) == false), YOU_MADE_A_PROGRAMMING_MISTAKE);
+
+ EIGEN_STATIC_ASSERT((Eigen::internal::index_pair_second_statically_eq<Dims2_b>(0, 10) == true), YOU_MADE_A_PROGRAMMING_MISTAKE);
+ EIGEN_STATIC_ASSERT((Eigen::internal::index_pair_second_statically_eq<Dims2_b>(0, 11) == false), YOU_MADE_A_PROGRAMMING_MISTAKE);
+ EIGEN_STATIC_ASSERT((Eigen::internal::index_pair_second_statically_eq<Dims2_b>(1, 11) == false), YOU_MADE_A_PROGRAMMING_MISTAKE);
+ EIGEN_STATIC_ASSERT((Eigen::internal::index_pair_second_statically_eq<Dims2_b>(1, 12) == false), YOU_MADE_A_PROGRAMMING_MISTAKE);
+ EIGEN_STATIC_ASSERT((Eigen::internal::index_pair_second_statically_eq<Dims2_b>(2, 12) == true), YOU_MADE_A_PROGRAMMING_MISTAKE);
+ EIGEN_STATIC_ASSERT((Eigen::internal::index_pair_second_statically_eq<Dims2_b>(2, 13) == false), YOU_MADE_A_PROGRAMMING_MISTAKE);
+
+ EIGEN_STATIC_ASSERT((Eigen::internal::index_pair_second_statically_eq<Dims2_c>(0, 10) == false), YOU_MADE_A_PROGRAMMING_MISTAKE);
+ EIGEN_STATIC_ASSERT((Eigen::internal::index_pair_second_statically_eq<Dims2_c>(0, 11) == false), YOU_MADE_A_PROGRAMMING_MISTAKE);
+ EIGEN_STATIC_ASSERT((Eigen::internal::index_pair_second_statically_eq<Dims2_c>(1, 11) == true), YOU_MADE_A_PROGRAMMING_MISTAKE);
+ EIGEN_STATIC_ASSERT((Eigen::internal::index_pair_second_statically_eq<Dims2_c>(1, 12) == false), YOU_MADE_A_PROGRAMMING_MISTAKE);
+ EIGEN_STATIC_ASSERT((Eigen::internal::index_pair_second_statically_eq<Dims2_c>(2, 12) == false), YOU_MADE_A_PROGRAMMING_MISTAKE);
+ EIGEN_STATIC_ASSERT((Eigen::internal::index_pair_second_statically_eq<Dims2_c>(2, 13) == false), YOU_MADE_A_PROGRAMMING_MISTAKE);
+}
+
+
+static void test_dynamic_index_list()
+{
+ Tensor<float, 4> tensor(2,3,5,7);
+ tensor.setRandom();
+
+ int dim1 = 2;
+ int dim2 = 1;
+ int dim3 = 0;
+
+ auto reduction_axis = make_index_list(dim1, dim2, dim3);
+
+ VERIFY_IS_EQUAL(internal::array_get<0>(reduction_axis), 2);
+ VERIFY_IS_EQUAL(internal::array_get<1>(reduction_axis), 1);
+ VERIFY_IS_EQUAL(internal::array_get<2>(reduction_axis), 0);
+ VERIFY_IS_EQUAL(static_cast<Index>(reduction_axis[0]), 2);
+ VERIFY_IS_EQUAL(static_cast<Index>(reduction_axis[1]), 1);
+ VERIFY_IS_EQUAL(static_cast<Index>(reduction_axis[2]), 0);
+
+ Tensor<float, 1> result = tensor.sum(reduction_axis);
+ for (int i = 0; i < result.size(); ++i) {
+ float expected = 0.0f;
+ for (int j = 0; j < 2; ++j) {
+ for (int k = 0; k < 3; ++k) {
+ for (int l = 0; l < 5; ++l) {
+ expected += tensor(j,k,l,i);
+ }
+ }
+ }
+ VERIFY_IS_APPROX(result(i), expected);
+ }
+}
+
+static void test_mixed_index_list()
+{
+ Tensor<float, 4> tensor(2,3,5,7);
+ tensor.setRandom();
+
+ int dim2 = 1;
+ int dim4 = 3;
+
+ auto reduction_axis = make_index_list(0, dim2, 2, dim4);
+
+ VERIFY_IS_EQUAL(internal::array_get<0>(reduction_axis), 0);
+ VERIFY_IS_EQUAL(internal::array_get<1>(reduction_axis), 1);
+ VERIFY_IS_EQUAL(internal::array_get<2>(reduction_axis), 2);
+ VERIFY_IS_EQUAL(internal::array_get<3>(reduction_axis), 3);
+ VERIFY_IS_EQUAL(static_cast<Index>(reduction_axis[0]), 0);
+ VERIFY_IS_EQUAL(static_cast<Index>(reduction_axis[1]), 1);
+ VERIFY_IS_EQUAL(static_cast<Index>(reduction_axis[2]), 2);
+ VERIFY_IS_EQUAL(static_cast<Index>(reduction_axis[3]), 3);
+
+ typedef IndexList<type2index<0>, int, type2index<2>, int> ReductionIndices;
+ ReductionIndices reduction_indices;
+ reduction_indices.set(1, 1);
+ reduction_indices.set(3, 3);
+ EIGEN_STATIC_ASSERT((internal::array_get<0>(reduction_indices) == 0), YOU_MADE_A_PROGRAMMING_MISTAKE);
+ EIGEN_STATIC_ASSERT((internal::array_get<2>(reduction_indices) == 2), YOU_MADE_A_PROGRAMMING_MISTAKE);
+ EIGEN_STATIC_ASSERT((internal::index_known_statically<ReductionIndices>(0) == true), YOU_MADE_A_PROGRAMMING_MISTAKE);
+ EIGEN_STATIC_ASSERT((internal::index_known_statically<ReductionIndices>(2) == true), YOU_MADE_A_PROGRAMMING_MISTAKE);
+ EIGEN_STATIC_ASSERT((internal::index_statically_eq<ReductionIndices>(0, 0) == true), YOU_MADE_A_PROGRAMMING_MISTAKE);
+ EIGEN_STATIC_ASSERT((internal::index_statically_eq<ReductionIndices>(2, 2) == true), YOU_MADE_A_PROGRAMMING_MISTAKE);
+#if 0
+ EIGEN_STATIC_ASSERT((internal::all_indices_known_statically<ReductionIndices>() == false), YOU_MADE_A_PROGRAMMING_MISTAKE);
+ EIGEN_STATIC_ASSERT((internal::indices_statically_known_to_increase<ReductionIndices>() == false), YOU_MADE_A_PROGRAMMING_MISTAKE);
+#endif
+
+ typedef IndexList<type2index<0>, type2index<1>, type2index<2>, type2index<3>> ReductionList;
+ ReductionList reduction_list;
+ EIGEN_STATIC_ASSERT((internal::index_statically_eq<ReductionList>(0, 0) == true), YOU_MADE_A_PROGRAMMING_MISTAKE);
+ EIGEN_STATIC_ASSERT((internal::index_statically_eq<ReductionList>(1, 1) == true), YOU_MADE_A_PROGRAMMING_MISTAKE);
+ EIGEN_STATIC_ASSERT((internal::index_statically_eq<ReductionList>(2, 2) == true), YOU_MADE_A_PROGRAMMING_MISTAKE);
+ EIGEN_STATIC_ASSERT((internal::index_statically_eq<ReductionList>(3, 3) == true), YOU_MADE_A_PROGRAMMING_MISTAKE);
+#if 0
+ EIGEN_STATIC_ASSERT((internal::all_indices_known_statically<ReductionList>() == true), YOU_MADE_A_PROGRAMMING_MISTAKE);
+ EIGEN_STATIC_ASSERT((internal::indices_statically_known_to_increase<ReductionList>() == true), YOU_MADE_A_PROGRAMMING_MISTAKE);
+#endif
+
+ Tensor<float, 0> result1 = tensor.sum(reduction_axis);
+ Tensor<float, 0> result2 = tensor.sum(reduction_indices);
+ Tensor<float, 0> result3 = tensor.sum(reduction_list);
+
+ float expected = 0.0f;
+ for (int i = 0; i < 2; ++i) {
+ for (int j = 0; j < 3; ++j) {
+ for (int k = 0; k < 5; ++k) {
+ for (int l = 0; l < 7; ++l) {
+ expected += tensor(i,j,k,l);
+ }
+ }
+ }
+ }
+ VERIFY_IS_APPROX(result1(), expected);
+ VERIFY_IS_APPROX(result2(), expected);
+ VERIFY_IS_APPROX(result3(), expected);
+}
+
+
+static void test_dim_check()
+{
+ Eigen::IndexList<Eigen::type2index<1>, int> dim1;
+ dim1.set(1, 2);
+ Eigen::IndexList<Eigen::type2index<1>, int> dim2;
+ dim2.set(1, 2);
+ VERIFY(dimensions_match(dim1, dim2));
+}
+
+
+EIGEN_DECLARE_TEST(cxx11_tensor_index_list)
+{
+ CALL_SUBTEST(test_static_index_list());
+ CALL_SUBTEST(test_type2index_list());
+ CALL_SUBTEST(test_type2indexpair_list());
+ CALL_SUBTEST(test_dynamic_index_list());
+ CALL_SUBTEST(test_mixed_index_list());
+ CALL_SUBTEST(test_dim_check());
+}
diff --git a/unsupported/test/cxx11_tensor_inflation.cpp b/unsupported/test/cxx11_tensor_inflation.cpp
new file mode 100644
index 0000000..75089e8
--- /dev/null
+++ b/unsupported/test/cxx11_tensor_inflation.cpp
@@ -0,0 +1,81 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2015 Ke Yang <yangke@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "main.h"
+
+#include <Eigen/CXX11/Tensor>
+
+using Eigen::Tensor;
+
+template<int DataLayout>
+static void test_simple_inflation()
+{
+ Tensor<float, 4, DataLayout> tensor(2,3,5,7);
+ tensor.setRandom();
+ array<ptrdiff_t, 4> strides;
+
+ strides[0] = 1;
+ strides[1] = 1;
+ strides[2] = 1;
+ strides[3] = 1;
+
+ Tensor<float, 4, DataLayout> no_stride;
+ no_stride = tensor.inflate(strides);
+
+ VERIFY_IS_EQUAL(no_stride.dimension(0), 2);
+ VERIFY_IS_EQUAL(no_stride.dimension(1), 3);
+ VERIFY_IS_EQUAL(no_stride.dimension(2), 5);
+ VERIFY_IS_EQUAL(no_stride.dimension(3), 7);
+
+ for (int i = 0; i < 2; ++i) {
+ for (int j = 0; j < 3; ++j) {
+ for (int k = 0; k < 5; ++k) {
+ for (int l = 0; l < 7; ++l) {
+ VERIFY_IS_EQUAL(tensor(i,j,k,l), no_stride(i,j,k,l));
+ }
+ }
+ }
+ }
+
+ strides[0] = 2;
+ strides[1] = 4;
+ strides[2] = 2;
+ strides[3] = 3;
+ Tensor<float, 4, DataLayout> inflated;
+ inflated = tensor.inflate(strides);
+
+ VERIFY_IS_EQUAL(inflated.dimension(0), 3);
+ VERIFY_IS_EQUAL(inflated.dimension(1), 9);
+ VERIFY_IS_EQUAL(inflated.dimension(2), 9);
+ VERIFY_IS_EQUAL(inflated.dimension(3), 19);
+
+ for (int i = 0; i < 3; ++i) {
+ for (int j = 0; j < 9; ++j) {
+ for (int k = 0; k < 9; ++k) {
+ for (int l = 0; l < 19; ++l) {
+ if (i % 2 == 0 &&
+ j % 4 == 0 &&
+ k % 2 == 0 &&
+ l % 3 == 0) {
+ VERIFY_IS_EQUAL(inflated(i,j,k,l),
+ tensor(i/2, j/4, k/2, l/3));
+ } else {
+ VERIFY_IS_EQUAL(0, inflated(i,j,k,l));
+ }
+ }
+ }
+ }
+ }
+}
+
+EIGEN_DECLARE_TEST(cxx11_tensor_inflation)
+{
+ CALL_SUBTEST(test_simple_inflation<ColMajor>());
+ CALL_SUBTEST(test_simple_inflation<RowMajor>());
+}
diff --git a/unsupported/test/cxx11_tensor_inflation_sycl.cpp b/unsupported/test/cxx11_tensor_inflation_sycl.cpp
new file mode 100644
index 0000000..521ae0c
--- /dev/null
+++ b/unsupported/test/cxx11_tensor_inflation_sycl.cpp
@@ -0,0 +1,136 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2016
+// Mehdi Goli Codeplay Software Ltd.
+// Ralph Potter Codeplay Software Ltd.
+// Luke Iwanski Codeplay Software Ltd.
+// Contact: <eigen@codeplay.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#define EIGEN_TEST_NO_LONGDOUBLE
+#define EIGEN_TEST_NO_COMPLEX
+
+#define EIGEN_DEFAULT_DENSE_INDEX_TYPE int64_t
+#define EIGEN_USE_SYCL
+
+#include "main.h"
+#include <unsupported/Eigen/CXX11/Tensor>
+
+using Eigen::Tensor;
+
+// Inflation Definition for each dimension the inflated val would be
+//((dim-1)*strid[dim] +1)
+
+// for 1 dimension vector of size 3 with value (4,4,4) with the inflated stride value of 3 would be changed to
+// tensor of size (2*3) +1 = 7 with the value of
+// (4, 0, 0, 4, 0, 0, 4).
+
+template <typename DataType, int DataLayout, typename IndexType>
+void test_simple_inflation_sycl(const Eigen::SyclDevice &sycl_device) {
+
+
+ IndexType sizeDim1 = 2;
+ IndexType sizeDim2 = 3;
+ IndexType sizeDim3 = 5;
+ IndexType sizeDim4 = 7;
+ array<IndexType, 4> tensorRange = {{sizeDim1, sizeDim2, sizeDim3, sizeDim4}};
+ Tensor<DataType, 4, DataLayout,IndexType> tensor(tensorRange);
+ Tensor<DataType, 4, DataLayout,IndexType> no_stride(tensorRange);
+ tensor.setRandom();
+
+ array<IndexType, 4> strides;
+ strides[0] = 1;
+ strides[1] = 1;
+ strides[2] = 1;
+ strides[3] = 1;
+
+
+ const size_t tensorBuffSize =tensor.size()*sizeof(DataType);
+ DataType* gpu_data_tensor = static_cast<DataType*>(sycl_device.allocate(tensorBuffSize));
+ DataType* gpu_data_no_stride = static_cast<DataType*>(sycl_device.allocate(tensorBuffSize));
+
+ TensorMap<Tensor<DataType, 4, DataLayout,IndexType>> gpu_tensor(gpu_data_tensor, tensorRange);
+ TensorMap<Tensor<DataType, 4, DataLayout,IndexType>> gpu_no_stride(gpu_data_no_stride, tensorRange);
+
+ sycl_device.memcpyHostToDevice(gpu_data_tensor, tensor.data(), tensorBuffSize);
+ gpu_no_stride.device(sycl_device)=gpu_tensor.inflate(strides);
+ sycl_device.memcpyDeviceToHost(no_stride.data(), gpu_data_no_stride, tensorBuffSize);
+
+ VERIFY_IS_EQUAL(no_stride.dimension(0), sizeDim1);
+ VERIFY_IS_EQUAL(no_stride.dimension(1), sizeDim2);
+ VERIFY_IS_EQUAL(no_stride.dimension(2), sizeDim3);
+ VERIFY_IS_EQUAL(no_stride.dimension(3), sizeDim4);
+
+ for (IndexType i = 0; i < 2; ++i) {
+ for (IndexType j = 0; j < 3; ++j) {
+ for (IndexType k = 0; k < 5; ++k) {
+ for (IndexType l = 0; l < 7; ++l) {
+ VERIFY_IS_EQUAL(tensor(i,j,k,l), no_stride(i,j,k,l));
+ }
+ }
+ }
+ }
+
+
+ strides[0] = 2;
+ strides[1] = 4;
+ strides[2] = 2;
+ strides[3] = 3;
+
+ IndexType inflatedSizeDim1 = 3;
+ IndexType inflatedSizeDim2 = 9;
+ IndexType inflatedSizeDim3 = 9;
+ IndexType inflatedSizeDim4 = 19;
+ array<IndexType, 4> inflatedTensorRange = {{inflatedSizeDim1, inflatedSizeDim2, inflatedSizeDim3, inflatedSizeDim4}};
+
+ Tensor<DataType, 4, DataLayout, IndexType> inflated(inflatedTensorRange);
+
+ const size_t inflatedTensorBuffSize =inflated.size()*sizeof(DataType);
+ DataType* gpu_data_inflated = static_cast<DataType*>(sycl_device.allocate(inflatedTensorBuffSize));
+ TensorMap<Tensor<DataType, 4, DataLayout, IndexType>> gpu_inflated(gpu_data_inflated, inflatedTensorRange);
+ gpu_inflated.device(sycl_device)=gpu_tensor.inflate(strides);
+ sycl_device.memcpyDeviceToHost(inflated.data(), gpu_data_inflated, inflatedTensorBuffSize);
+
+ VERIFY_IS_EQUAL(inflated.dimension(0), inflatedSizeDim1);
+ VERIFY_IS_EQUAL(inflated.dimension(1), inflatedSizeDim2);
+ VERIFY_IS_EQUAL(inflated.dimension(2), inflatedSizeDim3);
+ VERIFY_IS_EQUAL(inflated.dimension(3), inflatedSizeDim4);
+
+ for (IndexType i = 0; i < inflatedSizeDim1; ++i) {
+ for (IndexType j = 0; j < inflatedSizeDim2; ++j) {
+ for (IndexType k = 0; k < inflatedSizeDim3; ++k) {
+ for (IndexType l = 0; l < inflatedSizeDim4; ++l) {
+ if (i % strides[0] == 0 &&
+ j % strides[1] == 0 &&
+ k % strides[2] == 0 &&
+ l % strides[3] == 0) {
+ VERIFY_IS_EQUAL(inflated(i,j,k,l),
+ tensor(i/strides[0], j/strides[1], k/strides[2], l/strides[3]));
+ } else {
+ VERIFY_IS_EQUAL(0, inflated(i,j,k,l));
+ }
+ }
+ }
+ }
+ }
+ sycl_device.deallocate(gpu_data_tensor);
+ sycl_device.deallocate(gpu_data_no_stride);
+ sycl_device.deallocate(gpu_data_inflated);
+}
+
+template<typename DataType, typename dev_Selector> void sycl_inflation_test_per_device(dev_Selector s){
+ QueueInterface queueInterface(s);
+ auto sycl_device = Eigen::SyclDevice(&queueInterface);
+ test_simple_inflation_sycl<DataType, RowMajor, int64_t>(sycl_device);
+ test_simple_inflation_sycl<DataType, ColMajor, int64_t>(sycl_device);
+}
+EIGEN_DECLARE_TEST(cxx11_tensor_inflation_sycl)
+{
+ for (const auto& device :Eigen::get_sycl_supported_devices()) {
+ CALL_SUBTEST(sycl_inflation_test_per_device<float>(device));
+ }
+}
diff --git a/unsupported/test/cxx11_tensor_intdiv.cpp b/unsupported/test/cxx11_tensor_intdiv.cpp
new file mode 100644
index 0000000..d18a05e
--- /dev/null
+++ b/unsupported/test/cxx11_tensor_intdiv.cpp
@@ -0,0 +1,147 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2014-2015 Benoit Steiner <benoit.steiner.goog@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "main.h"
+
+#include <Eigen/CXX11/Tensor>
+
+
+void test_signed_32bit()
+{
+ // Divide by one
+ const Eigen::internal::TensorIntDivisor<int32_t, false> div_by_one(1);
+
+ for (int32_t j = 0; j < 25000; ++j) {
+ const int32_t fast_div = j / div_by_one;
+ const int32_t slow_div = j / 1;
+ VERIFY_IS_EQUAL(fast_div, slow_div);
+ }
+
+ // Standard divide by 2 or more
+ for (int32_t i = 2; i < 25000; ++i) {
+ const Eigen::internal::TensorIntDivisor<int32_t, false> div(i);
+
+ for (int32_t j = 0; j < 25000; ++j) {
+ const int32_t fast_div = j / div;
+ const int32_t slow_div = j / i;
+ VERIFY_IS_EQUAL(fast_div, slow_div);
+ }
+ }
+
+ // Optimized divide by 2 or more
+ for (int32_t i = 2; i < 25000; ++i) {
+ const Eigen::internal::TensorIntDivisor<int32_t, true> div(i);
+
+ for (int32_t j = 0; j < 25000; ++j) {
+ const int32_t fast_div = j / div;
+ const int32_t slow_div = j / i;
+ VERIFY_IS_EQUAL(fast_div, slow_div);
+ }
+ }
+}
+
+
+void test_unsigned_32bit()
+{
+ for (uint32_t i = 1; i < 25000; ++i) {
+ const Eigen::internal::TensorIntDivisor<uint32_t> div(i);
+
+ for (uint32_t j = 0; j < 25000; ++j) {
+ const uint32_t fast_div = j / div;
+ const uint32_t slow_div = j / i;
+ VERIFY_IS_EQUAL(fast_div, slow_div);
+ }
+ }
+}
+
+
+void test_signed_64bit()
+{
+ for (int64_t i = 1; i < 25000; ++i) {
+ const Eigen::internal::TensorIntDivisor<int64_t> div(i);
+
+ for (int64_t j = 0; j < 25000; ++j) {
+ const int64_t fast_div = j / div;
+ const int64_t slow_div = j / i;
+ VERIFY_IS_EQUAL(fast_div, slow_div);
+ }
+ }
+}
+
+
+void test_unsigned_64bit()
+{
+ for (uint64_t i = 1; i < 25000; ++i) {
+ const Eigen::internal::TensorIntDivisor<uint64_t> div(i);
+
+ for (uint64_t j = 0; j < 25000; ++j) {
+ const uint64_t fast_div = j / div;
+ const uint64_t slow_div = j / i;
+ VERIFY_IS_EQUAL(fast_div, slow_div);
+ }
+ }
+}
+
+void test_powers_32bit() {
+ for (int expon = 1; expon < 31; expon++) {
+ int32_t div = (1 << expon);
+ for (int num_expon = 0; num_expon < 32; num_expon++) {
+ int32_t start_num = (1 << num_expon) - 100;
+ int32_t end_num = (1 << num_expon) + 100;
+ if (start_num < 0)
+ start_num = 0;
+ for (int32_t num = start_num; num < end_num; num++) {
+ Eigen::internal::TensorIntDivisor<int32_t> divider =
+ Eigen::internal::TensorIntDivisor<int32_t>(div);
+ int32_t result = num/div;
+ int32_t result_op = divider.divide(num);
+ VERIFY_IS_EQUAL(result_op, result);
+ }
+ }
+ }
+}
+
+void test_powers_64bit() {
+ for (int expon = 0; expon < 63; expon++) {
+ int64_t div = (1ull << expon);
+ for (int num_expon = 0; num_expon < 63; num_expon++) {
+ int64_t start_num = (1ull << num_expon) - 10;
+ int64_t end_num = (1ull << num_expon) + 10;
+ if (start_num < 0)
+ start_num = 0;
+ for (int64_t num = start_num; num < end_num; num++) {
+ Eigen::internal::TensorIntDivisor<int64_t> divider(div);
+ int64_t result = num/div;
+ int64_t result_op = divider.divide(num);
+ VERIFY_IS_EQUAL(result_op, result);
+ }
+ }
+ }
+}
+
+void test_specific() {
+ // A particular combination that was previously failing
+ int64_t div = 209715200;
+ int64_t num = 3238002688ll;
+ Eigen::internal::TensorIntDivisor<int64_t> divider(div);
+ int64_t result = num/div;
+ int64_t result_op = divider.divide(num);
+ VERIFY_IS_EQUAL(result, result_op);
+}
+
+EIGEN_DECLARE_TEST(cxx11_tensor_intdiv)
+{
+ CALL_SUBTEST_1(test_signed_32bit());
+ CALL_SUBTEST_2(test_unsigned_32bit());
+ CALL_SUBTEST_3(test_signed_64bit());
+ CALL_SUBTEST_4(test_unsigned_64bit());
+ CALL_SUBTEST_5(test_powers_32bit());
+ CALL_SUBTEST_6(test_powers_64bit());
+ CALL_SUBTEST_7(test_specific());
+}
diff --git a/unsupported/test/cxx11_tensor_io.cpp b/unsupported/test/cxx11_tensor_io.cpp
new file mode 100644
index 0000000..c0ea2a1
--- /dev/null
+++ b/unsupported/test/cxx11_tensor_io.cpp
@@ -0,0 +1,142 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+#include "main.h"
+
+#include <sstream>
+#include <Eigen/CXX11/Tensor>
+
+template <typename Scalar, int rank, int Layout>
+struct test_tensor_ostream_impl {};
+
+template<typename Scalar, int Layout>
+struct test_tensor_ostream_impl<Scalar, 0, Layout> {
+ static void run() {
+ Eigen::Tensor<Scalar, 0> t;
+ t.setValues(1);
+ std::ostringstream os;
+ os << t.format(Eigen::TensorIOFormat::Plain());
+ VERIFY(os.str() == "1");
+ }
+};
+
+template<typename Scalar, int Layout>
+struct test_tensor_ostream_impl<Scalar, 1, Layout> {
+ static void run() {
+ Eigen::Tensor<Scalar, 1> t = {3};
+ t.setValues({1, 2, 3});
+ std::ostringstream os;
+ os << t.format(Eigen::TensorIOFormat::Plain());
+ VERIFY(os.str() == "1 2 3");
+ }
+};
+
+template<typename Scalar, int Layout>
+struct test_tensor_ostream_impl<Scalar, 2, Layout> {
+ static void run() {
+ Eigen::Tensor<Scalar, 2> t = {3, 2};
+ t.setValues({{1, 2}, {3, 4}, {5, 6}});
+ std::ostringstream os;
+ os << t.format(Eigen::TensorIOFormat::Plain());
+ VERIFY(os.str() == "1 2\n3 4\n5 6");
+ }
+};
+
+template<typename Scalar, int Layout>
+struct test_tensor_ostream_impl<Scalar, 3, Layout> {
+ static void run() {
+ Eigen::Tensor<Scalar, 3> t = {4, 3, 2};
+ t.setValues({{{1, 2}, {3, 4}, {5, 6}},
+ {{7, 8}, {9, 10}, {11, 12}},
+ {{13, 14}, {15, 16}, {17, 18}},
+ {{19, 20}, {21, 22}, {23, 24}}});
+ std::ostringstream os;
+ os << t.format(Eigen::TensorIOFormat::Plain());
+ VERIFY(os.str() == " 1 2\n 3 4\n 5 6\n\n 7 8\n 9 10\n11 12\n\n13 14\n15 16\n17 18\n\n19 20\n21 22\n23 24");
+ }
+};
+
+template<int Layout>
+struct test_tensor_ostream_impl<bool, 2, Layout> {
+ static void run() {
+ Eigen::Tensor<bool, 2> t = {3, 2};
+ t.setValues({{false, true}, {true, false}, {false, false}});
+ std::ostringstream os;
+ os << t.format(Eigen::TensorIOFormat::Plain());
+ VERIFY(os.str() == "0 1\n1 0\n0 0");
+ }
+};
+
+template<typename Scalar, int Layout>
+struct test_tensor_ostream_impl<std::complex<Scalar>, 2, Layout> {
+ static void run() {
+ Eigen::Tensor<std::complex<Scalar>, 2> t = {3, 2};
+ t.setValues({{std::complex<Scalar>(1, 2), std::complex<Scalar>(12, 3)},
+ {std::complex<Scalar>(-4, 2), std::complex<Scalar>(0, 5)},
+ {std::complex<Scalar>(-1, 4), std::complex<Scalar>(5, 27)}});
+ std::ostringstream os;
+ os << t.format(Eigen::TensorIOFormat::Plain());
+ VERIFY(os.str() == " (1,2) (12,3)\n(-4,2) (0,5)\n(-1,4) (5,27)");
+ }
+};
+
+template <typename Scalar, int rank, int Layout>
+void test_tensor_ostream() {
+ test_tensor_ostream_impl<Scalar, rank, Layout>::run();
+}
+
+void test_const_tensor_ostream() {
+ Eigen::Tensor<float, 0> t;
+ t.setValues(1);
+ const Eigen::TensorMap<Eigen::Tensor<const float, 0, Eigen::RowMajor>, Eigen::Unaligned> t_const(
+ t.data(), Eigen::DSizes<Eigen::DenseIndex, 0>{});
+ std::ostringstream os;
+ os << t_const.format(Eigen::TensorIOFormat::Plain());
+ VERIFY(os.str() == "1");
+}
+
+EIGEN_DECLARE_TEST(cxx11_tensor_io) {
+ CALL_SUBTEST((test_tensor_ostream<float, 0, Eigen::ColMajor>()));
+ CALL_SUBTEST((test_tensor_ostream<float, 1, Eigen::ColMajor>()));
+ CALL_SUBTEST((test_tensor_ostream<float, 2, Eigen::ColMajor>()));
+ CALL_SUBTEST((test_tensor_ostream<float, 3, Eigen::ColMajor>()));
+
+ CALL_SUBTEST((test_tensor_ostream<double, 0, Eigen::ColMajor>()));
+ CALL_SUBTEST((test_tensor_ostream<double, 1, Eigen::ColMajor>()));
+ CALL_SUBTEST((test_tensor_ostream<double, 2, Eigen::ColMajor>()));
+ CALL_SUBTEST((test_tensor_ostream<double, 3, Eigen::ColMajor>()));
+
+ CALL_SUBTEST((test_tensor_ostream<int, 0, Eigen::ColMajor>()));
+ CALL_SUBTEST((test_tensor_ostream<int, 1, Eigen::ColMajor>()));
+ CALL_SUBTEST((test_tensor_ostream<int, 2, Eigen::ColMajor>()));
+ CALL_SUBTEST((test_tensor_ostream<int, 3, Eigen::ColMajor>()));
+
+ CALL_SUBTEST((test_tensor_ostream<float, 0, Eigen::RowMajor>()));
+ CALL_SUBTEST((test_tensor_ostream<float, 1, Eigen::RowMajor>()));
+ CALL_SUBTEST((test_tensor_ostream<float, 2, Eigen::RowMajor>()));
+ CALL_SUBTEST((test_tensor_ostream<float, 3, Eigen::RowMajor>()));
+
+ CALL_SUBTEST((test_tensor_ostream<double, 0, Eigen::RowMajor>()));
+ CALL_SUBTEST((test_tensor_ostream<double, 1, Eigen::RowMajor>()));
+ CALL_SUBTEST((test_tensor_ostream<double, 2, Eigen::RowMajor>()));
+ CALL_SUBTEST((test_tensor_ostream<double, 3, Eigen::RowMajor>()));
+
+ CALL_SUBTEST((test_tensor_ostream<int, 0, Eigen::RowMajor>()));
+ CALL_SUBTEST((test_tensor_ostream<int, 1, Eigen::RowMajor>()));
+ CALL_SUBTEST((test_tensor_ostream<int, 2, Eigen::RowMajor>()));
+ CALL_SUBTEST((test_tensor_ostream<int, 3, Eigen::RowMajor>()));
+
+ CALL_SUBTEST((test_tensor_ostream<bool, 2, Eigen::ColMajor>()));
+ CALL_SUBTEST((test_tensor_ostream<bool, 2, Eigen::RowMajor>()));
+
+ CALL_SUBTEST((test_tensor_ostream<std::complex<double>, 2, Eigen::ColMajor>()));
+ CALL_SUBTEST((test_tensor_ostream<std::complex<float>, 2, Eigen::ColMajor>()));
+
+ // Test printing TensorMap with const elements.
+ CALL_SUBTEST((test_const_tensor_ostream()));
+}
diff --git a/unsupported/test/cxx11_tensor_layout_swap.cpp b/unsupported/test/cxx11_tensor_layout_swap.cpp
new file mode 100644
index 0000000..efb3333
--- /dev/null
+++ b/unsupported/test/cxx11_tensor_layout_swap.cpp
@@ -0,0 +1,61 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "main.h"
+
+#include <Eigen/CXX11/Tensor>
+
+using Eigen::Tensor;
+
+static void test_simple_swap()
+{
+ Tensor<float, 3, ColMajor> tensor(2,3,7);
+ tensor.setRandom();
+
+ Tensor<float, 3, RowMajor> tensor2 = tensor.swap_layout();
+ VERIFY_IS_EQUAL(tensor.dimension(0), tensor2.dimension(2));
+ VERIFY_IS_EQUAL(tensor.dimension(1), tensor2.dimension(1));
+ VERIFY_IS_EQUAL(tensor.dimension(2), tensor2.dimension(0));
+
+ for (int i = 0; i < 2; ++i) {
+ for (int j = 0; j < 3; ++j) {
+ for (int k = 0; k < 7; ++k) {
+ VERIFY_IS_EQUAL(tensor(i,j,k), tensor2(k,j,i));
+ }
+ }
+ }
+}
+
+
+static void test_swap_as_lvalue()
+{
+ Tensor<float, 3, ColMajor> tensor(2,3,7);
+ tensor.setRandom();
+
+ Tensor<float, 3, RowMajor> tensor2(7,3,2);
+ tensor2.swap_layout() = tensor;
+ VERIFY_IS_EQUAL(tensor.dimension(0), tensor2.dimension(2));
+ VERIFY_IS_EQUAL(tensor.dimension(1), tensor2.dimension(1));
+ VERIFY_IS_EQUAL(tensor.dimension(2), tensor2.dimension(0));
+
+ for (int i = 0; i < 2; ++i) {
+ for (int j = 0; j < 3; ++j) {
+ for (int k = 0; k < 7; ++k) {
+ VERIFY_IS_EQUAL(tensor(i,j,k), tensor2(k,j,i));
+ }
+ }
+ }
+}
+
+
+EIGEN_DECLARE_TEST(cxx11_tensor_layout_swap)
+{
+ CALL_SUBTEST(test_simple_swap());
+ CALL_SUBTEST(test_swap_as_lvalue());
+}
diff --git a/unsupported/test/cxx11_tensor_layout_swap_sycl.cpp b/unsupported/test/cxx11_tensor_layout_swap_sycl.cpp
new file mode 100644
index 0000000..9546b91
--- /dev/null
+++ b/unsupported/test/cxx11_tensor_layout_swap_sycl.cpp
@@ -0,0 +1,126 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2016
+// Mehdi Goli Codeplay Software Ltd.
+// Ralph Potter Codeplay Software Ltd.
+// Luke Iwanski Codeplay Software Ltd.
+// Contact: <eigen@codeplay.com>
+// Benoit Steiner <benoit.steiner.goog@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#define EIGEN_TEST_NO_LONGDOUBLE
+#define EIGEN_TEST_NO_COMPLEX
+
+#define EIGEN_DEFAULT_DENSE_INDEX_TYPE int64_t
+#define EIGEN_USE_SYCL
+
+#include "main.h"
+
+#include <Eigen/CXX11/Tensor>
+
+using Eigen::Tensor;
+
+template <typename DataType, typename IndexType>
+static void test_simple_swap_sycl(const Eigen::SyclDevice& sycl_device)
+{
+ IndexType sizeDim1 = 2;
+ IndexType sizeDim2 = 3;
+ IndexType sizeDim3 = 7;
+ array<IndexType, 3> tensorColRange = {{sizeDim1, sizeDim2, sizeDim3}};
+ array<IndexType, 3> tensorRowRange = {{sizeDim3, sizeDim2, sizeDim1}};
+
+
+ Tensor<DataType, 3, ColMajor, IndexType> tensor1(tensorColRange);
+ Tensor<DataType, 3, RowMajor, IndexType> tensor2(tensorRowRange);
+ tensor1.setRandom();
+
+ DataType* gpu_data1 = static_cast<DataType*>(sycl_device.allocate(tensor1.size()*sizeof(DataType)));
+ DataType* gpu_data2 = static_cast<DataType*>(sycl_device.allocate(tensor2.size()*sizeof(DataType)));
+ TensorMap<Tensor<DataType, 3, ColMajor, IndexType>> gpu1(gpu_data1, tensorColRange);
+ TensorMap<Tensor<DataType, 3, RowMajor, IndexType>> gpu2(gpu_data2, tensorRowRange);
+
+ sycl_device.memcpyHostToDevice(gpu_data1, tensor1.data(),(tensor1.size())*sizeof(DataType));
+ gpu2.device(sycl_device)=gpu1.swap_layout();
+ sycl_device.memcpyDeviceToHost(tensor2.data(), gpu_data2,(tensor2.size())*sizeof(DataType));
+
+
+// Tensor<float, 3, ColMajor> tensor(2,3,7);
+ //tensor.setRandom();
+
+// Tensor<float, 3, RowMajor> tensor2 = tensor.swap_layout();
+ VERIFY_IS_EQUAL(tensor1.dimension(0), tensor2.dimension(2));
+ VERIFY_IS_EQUAL(tensor1.dimension(1), tensor2.dimension(1));
+ VERIFY_IS_EQUAL(tensor1.dimension(2), tensor2.dimension(0));
+
+ for (IndexType i = 0; i < 2; ++i) {
+ for (IndexType j = 0; j < 3; ++j) {
+ for (IndexType k = 0; k < 7; ++k) {
+ VERIFY_IS_EQUAL(tensor1(i,j,k), tensor2(k,j,i));
+ }
+ }
+ }
+ sycl_device.deallocate(gpu_data1);
+ sycl_device.deallocate(gpu_data2);
+}
+
+template <typename DataType, typename IndexType>
+static void test_swap_as_lvalue_sycl(const Eigen::SyclDevice& sycl_device)
+{
+
+ IndexType sizeDim1 = 2;
+ IndexType sizeDim2 = 3;
+ IndexType sizeDim3 = 7;
+ array<IndexType, 3> tensorColRange = {{sizeDim1, sizeDim2, sizeDim3}};
+ array<IndexType, 3> tensorRowRange = {{sizeDim3, sizeDim2, sizeDim1}};
+
+ Tensor<DataType, 3, ColMajor, IndexType> tensor1(tensorColRange);
+ Tensor<DataType, 3, RowMajor, IndexType> tensor2(tensorRowRange);
+ tensor1.setRandom();
+
+ DataType* gpu_data1 = static_cast<DataType*>(sycl_device.allocate(tensor1.size()*sizeof(DataType)));
+ DataType* gpu_data2 = static_cast<DataType*>(sycl_device.allocate(tensor2.size()*sizeof(DataType)));
+ TensorMap<Tensor<DataType, 3, ColMajor, IndexType>> gpu1(gpu_data1, tensorColRange);
+ TensorMap<Tensor<DataType, 3, RowMajor, IndexType>> gpu2(gpu_data2, tensorRowRange);
+
+ sycl_device.memcpyHostToDevice(gpu_data1, tensor1.data(),(tensor1.size())*sizeof(DataType));
+ gpu2.swap_layout().device(sycl_device)=gpu1;
+ sycl_device.memcpyDeviceToHost(tensor2.data(), gpu_data2,(tensor2.size())*sizeof(DataType));
+
+
+// Tensor<float, 3, ColMajor> tensor(2,3,7);
+// tensor.setRandom();
+
+ //Tensor<float, 3, RowMajor> tensor2(7,3,2);
+// tensor2.swap_layout() = tensor;
+ VERIFY_IS_EQUAL(tensor1.dimension(0), tensor2.dimension(2));
+ VERIFY_IS_EQUAL(tensor1.dimension(1), tensor2.dimension(1));
+ VERIFY_IS_EQUAL(tensor1.dimension(2), tensor2.dimension(0));
+
+ for (IndexType i = 0; i < 2; ++i) {
+ for (IndexType j = 0; j < 3; ++j) {
+ for (IndexType k = 0; k < 7; ++k) {
+ VERIFY_IS_EQUAL(tensor1(i,j,k), tensor2(k,j,i));
+ }
+ }
+ }
+ sycl_device.deallocate(gpu_data1);
+ sycl_device.deallocate(gpu_data2);
+}
+
+
+template<typename DataType, typename dev_Selector> void sycl_tensor_layout_swap_test_per_device(dev_Selector s){
+ QueueInterface queueInterface(s);
+ auto sycl_device = Eigen::SyclDevice(&queueInterface);
+ test_simple_swap_sycl<DataType, int64_t>(sycl_device);
+ test_swap_as_lvalue_sycl<DataType, int64_t>(sycl_device);
+}
+EIGEN_DECLARE_TEST(cxx11_tensor_layout_swap_sycl)
+{
+ for (const auto& device :Eigen::get_sycl_supported_devices()) {
+ CALL_SUBTEST(sycl_tensor_layout_swap_test_per_device<float>(device));
+ }
+}
diff --git a/unsupported/test/cxx11_tensor_lvalue.cpp b/unsupported/test/cxx11_tensor_lvalue.cpp
new file mode 100644
index 0000000..6ba9a21
--- /dev/null
+++ b/unsupported/test/cxx11_tensor_lvalue.cpp
@@ -0,0 +1,42 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "main.h"
+
+#include <Eigen/CXX11/Tensor>
+
+using Eigen::Tensor;
+using Eigen::RowMajor;
+
+
+static void test_compound_assignment()
+{
+ Tensor<float, 3> mat1(2,3,7);
+ Tensor<float, 3> mat2(2,3,7);
+ Tensor<float, 3> mat3(2,3,7);
+
+ mat1.setRandom();
+ mat2.setRandom();
+ mat3 = mat1;
+ mat3 += mat2;
+
+ for (int i = 0; i < 2; ++i) {
+ for (int j = 0; j < 3; ++j) {
+ for (int k = 0; k < 7; ++k) {
+ VERIFY_IS_APPROX(mat3(i,j,k), mat1(i,j,k) + mat2(i,j,k));
+ }
+ }
+ }
+}
+
+
+EIGEN_DECLARE_TEST(cxx11_tensor_lvalue)
+{
+ CALL_SUBTEST(test_compound_assignment());
+}
diff --git a/unsupported/test/cxx11_tensor_map.cpp b/unsupported/test/cxx11_tensor_map.cpp
new file mode 100644
index 0000000..4d4f689
--- /dev/null
+++ b/unsupported/test/cxx11_tensor_map.cpp
@@ -0,0 +1,327 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "main.h"
+
+#include <Eigen/CXX11/Tensor>
+
+using Eigen::Tensor;
+using Eigen::RowMajor;
+
+static void test_0d()
+{
+ Tensor<int, 0> scalar1;
+ Tensor<int, 0, RowMajor> scalar2;
+
+ TensorMap<const Tensor<int, 0> > scalar3(scalar1.data());
+ TensorMap<const Tensor<int, 0, RowMajor> > scalar4(scalar2.data());
+
+ scalar1() = 7;
+ scalar2() = 13;
+
+ VERIFY_IS_EQUAL(scalar1.rank(), 0);
+ VERIFY_IS_EQUAL(scalar1.size(), 1);
+
+ VERIFY_IS_EQUAL(scalar3(), 7);
+ VERIFY_IS_EQUAL(scalar4(), 13);
+}
+
+static void test_1d()
+{
+ Tensor<int, 1> vec1(6);
+ Tensor<int, 1, RowMajor> vec2(6);
+
+ TensorMap<const Tensor<int, 1> > vec3(vec1.data(), 6);
+ TensorMap<const Tensor<int, 1, RowMajor> > vec4(vec2.data(), 6);
+
+ vec1(0) = 4; vec2(0) = 0;
+ vec1(1) = 8; vec2(1) = 1;
+ vec1(2) = 15; vec2(2) = 2;
+ vec1(3) = 16; vec2(3) = 3;
+ vec1(4) = 23; vec2(4) = 4;
+ vec1(5) = 42; vec2(5) = 5;
+
+ VERIFY_IS_EQUAL(vec1.rank(), 1);
+ VERIFY_IS_EQUAL(vec1.size(), 6);
+ VERIFY_IS_EQUAL(vec1.dimension(0), 6);
+
+ VERIFY_IS_EQUAL(vec3(0), 4);
+ VERIFY_IS_EQUAL(vec3(1), 8);
+ VERIFY_IS_EQUAL(vec3(2), 15);
+ VERIFY_IS_EQUAL(vec3(3), 16);
+ VERIFY_IS_EQUAL(vec3(4), 23);
+ VERIFY_IS_EQUAL(vec3(5), 42);
+
+ VERIFY_IS_EQUAL(vec4(0), 0);
+ VERIFY_IS_EQUAL(vec4(1), 1);
+ VERIFY_IS_EQUAL(vec4(2), 2);
+ VERIFY_IS_EQUAL(vec4(3), 3);
+ VERIFY_IS_EQUAL(vec4(4), 4);
+ VERIFY_IS_EQUAL(vec4(5), 5);
+}
+
+static void test_2d()
+{
+ Tensor<int, 2> mat1(2,3);
+ Tensor<int, 2, RowMajor> mat2(2,3);
+
+ mat1(0,0) = 0;
+ mat1(0,1) = 1;
+ mat1(0,2) = 2;
+ mat1(1,0) = 3;
+ mat1(1,1) = 4;
+ mat1(1,2) = 5;
+
+ mat2(0,0) = 0;
+ mat2(0,1) = 1;
+ mat2(0,2) = 2;
+ mat2(1,0) = 3;
+ mat2(1,1) = 4;
+ mat2(1,2) = 5;
+
+ TensorMap<const Tensor<int, 2> > mat3(mat1.data(), 2, 3);
+ TensorMap<const Tensor<int, 2, RowMajor> > mat4(mat2.data(), 2, 3);
+
+ VERIFY_IS_EQUAL(mat3.rank(), 2);
+ VERIFY_IS_EQUAL(mat3.size(), 6);
+ VERIFY_IS_EQUAL(mat3.dimension(0), 2);
+ VERIFY_IS_EQUAL(mat3.dimension(1), 3);
+
+ VERIFY_IS_EQUAL(mat4.rank(), 2);
+ VERIFY_IS_EQUAL(mat4.size(), 6);
+ VERIFY_IS_EQUAL(mat4.dimension(0), 2);
+ VERIFY_IS_EQUAL(mat4.dimension(1), 3);
+
+ VERIFY_IS_EQUAL(mat3(0,0), 0);
+ VERIFY_IS_EQUAL(mat3(0,1), 1);
+ VERIFY_IS_EQUAL(mat3(0,2), 2);
+ VERIFY_IS_EQUAL(mat3(1,0), 3);
+ VERIFY_IS_EQUAL(mat3(1,1), 4);
+ VERIFY_IS_EQUAL(mat3(1,2), 5);
+
+ VERIFY_IS_EQUAL(mat4(0,0), 0);
+ VERIFY_IS_EQUAL(mat4(0,1), 1);
+ VERIFY_IS_EQUAL(mat4(0,2), 2);
+ VERIFY_IS_EQUAL(mat4(1,0), 3);
+ VERIFY_IS_EQUAL(mat4(1,1), 4);
+ VERIFY_IS_EQUAL(mat4(1,2), 5);
+}
+
+static void test_3d()
+{
+ Tensor<int, 3> mat1(2,3,7);
+ Tensor<int, 3, RowMajor> mat2(2,3,7);
+
+ int val = 0;
+ for (int i = 0; i < 2; ++i) {
+ for (int j = 0; j < 3; ++j) {
+ for (int k = 0; k < 7; ++k) {
+ mat1(i,j,k) = val;
+ mat2(i,j,k) = val;
+ val++;
+ }
+ }
+ }
+
+ TensorMap<const Tensor<int, 3> > mat3(mat1.data(), 2, 3, 7);
+ TensorMap<const Tensor<int, 3, RowMajor> > mat4(mat2.data(), 2, 3, 7);
+
+ VERIFY_IS_EQUAL(mat3.rank(), 3);
+ VERIFY_IS_EQUAL(mat3.size(), 2*3*7);
+ VERIFY_IS_EQUAL(mat3.dimension(0), 2);
+ VERIFY_IS_EQUAL(mat3.dimension(1), 3);
+ VERIFY_IS_EQUAL(mat3.dimension(2), 7);
+
+ VERIFY_IS_EQUAL(mat4.rank(), 3);
+ VERIFY_IS_EQUAL(mat4.size(), 2*3*7);
+ VERIFY_IS_EQUAL(mat4.dimension(0), 2);
+ VERIFY_IS_EQUAL(mat4.dimension(1), 3);
+ VERIFY_IS_EQUAL(mat4.dimension(2), 7);
+
+ val = 0;
+ for (int i = 0; i < 2; ++i) {
+ for (int j = 0; j < 3; ++j) {
+ for (int k = 0; k < 7; ++k) {
+ VERIFY_IS_EQUAL(mat3(i,j,k), val);
+ VERIFY_IS_EQUAL(mat4(i,j,k), val);
+ val++;
+ }
+ }
+ }
+}
+
+
+static void test_from_tensor()
+{
+ Tensor<int, 3> mat1(2,3,7);
+ Tensor<int, 3, RowMajor> mat2(2,3,7);
+
+ int val = 0;
+ for (int i = 0; i < 2; ++i) {
+ for (int j = 0; j < 3; ++j) {
+ for (int k = 0; k < 7; ++k) {
+ mat1(i,j,k) = val;
+ mat2(i,j,k) = val;
+ val++;
+ }
+ }
+ }
+
+ TensorMap<Tensor<int, 3> > mat3(mat1);
+ TensorMap<Tensor<int, 3, RowMajor> > mat4(mat2);
+
+ VERIFY_IS_EQUAL(mat3.rank(), 3);
+ VERIFY_IS_EQUAL(mat3.size(), 2*3*7);
+ VERIFY_IS_EQUAL(mat3.dimension(0), 2);
+ VERIFY_IS_EQUAL(mat3.dimension(1), 3);
+ VERIFY_IS_EQUAL(mat3.dimension(2), 7);
+
+ VERIFY_IS_EQUAL(mat4.rank(), 3);
+ VERIFY_IS_EQUAL(mat4.size(), 2*3*7);
+ VERIFY_IS_EQUAL(mat4.dimension(0), 2);
+ VERIFY_IS_EQUAL(mat4.dimension(1), 3);
+ VERIFY_IS_EQUAL(mat4.dimension(2), 7);
+
+ val = 0;
+ for (int i = 0; i < 2; ++i) {
+ for (int j = 0; j < 3; ++j) {
+ for (int k = 0; k < 7; ++k) {
+ VERIFY_IS_EQUAL(mat3(i,j,k), val);
+ VERIFY_IS_EQUAL(mat4(i,j,k), val);
+ val++;
+ }
+ }
+ }
+
+ TensorFixedSize<int, Sizes<2,3,7> > mat5;
+
+ val = 0;
+ for (int i = 0; i < 2; ++i) {
+ for (int j = 0; j < 3; ++j) {
+ for (int k = 0; k < 7; ++k) {
+ array<ptrdiff_t, 3> coords;
+ coords[0] = i;
+ coords[1] = j;
+ coords[2] = k;
+ mat5(coords) = val;
+ val++;
+ }
+ }
+ }
+
+ TensorMap<TensorFixedSize<int, Sizes<2,3,7> > > mat6(mat5);
+
+ VERIFY_IS_EQUAL(mat6.rank(), 3);
+ VERIFY_IS_EQUAL(mat6.size(), 2*3*7);
+ VERIFY_IS_EQUAL(mat6.dimension(0), 2);
+ VERIFY_IS_EQUAL(mat6.dimension(1), 3);
+ VERIFY_IS_EQUAL(mat6.dimension(2), 7);
+
+ val = 0;
+ for (int i = 0; i < 2; ++i) {
+ for (int j = 0; j < 3; ++j) {
+ for (int k = 0; k < 7; ++k) {
+ VERIFY_IS_EQUAL(mat6(i,j,k), val);
+ val++;
+ }
+ }
+ }
+}
+
+
+static int f(const TensorMap<Tensor<int, 3> >& tensor) {
+ // Size<0> empty;
+ EIGEN_STATIC_ASSERT((internal::array_size<Sizes<> >::value == 0), YOU_MADE_A_PROGRAMMING_MISTAKE);
+ EIGEN_STATIC_ASSERT((internal::array_size<DSizes<int, 0> >::value == 0), YOU_MADE_A_PROGRAMMING_MISTAKE);
+ Tensor<int, 0> result = tensor.sum();
+ return result();
+}
+
+static void test_casting()
+{
+ Tensor<int, 3> tensor(2,3,7);
+
+ int val = 0;
+ for (int i = 0; i < 2; ++i) {
+ for (int j = 0; j < 3; ++j) {
+ for (int k = 0; k < 7; ++k) {
+ tensor(i,j,k) = val;
+ val++;
+ }
+ }
+ }
+
+ TensorMap<Tensor<int, 3> > map(tensor);
+ int sum1 = f(map);
+ int sum2 = f(tensor);
+
+ VERIFY_IS_EQUAL(sum1, sum2);
+ VERIFY_IS_EQUAL(sum1, 861);
+}
+
+template<typename T>
+static const T& add_const(T& value) {
+ return value;
+}
+
+static void test_0d_const_tensor()
+{
+ Tensor<int, 0> scalar1;
+ Tensor<int, 0, RowMajor> scalar2;
+
+ TensorMap<const Tensor<int, 0> > scalar3(add_const(scalar1).data());
+ TensorMap<const Tensor<int, 0, RowMajor> > scalar4(add_const(scalar2).data());
+
+ scalar1() = 7;
+ scalar2() = 13;
+
+ VERIFY_IS_EQUAL(scalar1.rank(), 0);
+ VERIFY_IS_EQUAL(scalar1.size(), 1);
+
+ VERIFY_IS_EQUAL(scalar3(), 7);
+ VERIFY_IS_EQUAL(scalar4(), 13);
+}
+
+static void test_0d_const_tensor_map()
+{
+ Tensor<int, 0> scalar1;
+ Tensor<int, 0, RowMajor> scalar2;
+
+ const TensorMap<Tensor<int, 0> > scalar3(scalar1.data());
+ const TensorMap<Tensor<int, 0, RowMajor> > scalar4(scalar2.data());
+
+ // Although TensorMap is constant, we still can write to the underlying
+ // storage, because we map over non-constant Tensor.
+ scalar3() = 7;
+ scalar4() = 13;
+
+ VERIFY_IS_EQUAL(scalar1(), 7);
+ VERIFY_IS_EQUAL(scalar2(), 13);
+
+ // Pointer to the underlying storage is also non-const.
+ scalar3.data()[0] = 8;
+ scalar4.data()[0] = 14;
+
+ VERIFY_IS_EQUAL(scalar1(), 8);
+ VERIFY_IS_EQUAL(scalar2(), 14);
+}
+
+EIGEN_DECLARE_TEST(cxx11_tensor_map)
+{
+ CALL_SUBTEST(test_0d());
+ CALL_SUBTEST(test_1d());
+ CALL_SUBTEST(test_2d());
+ CALL_SUBTEST(test_3d());
+
+ CALL_SUBTEST(test_from_tensor());
+ CALL_SUBTEST(test_casting());
+
+ CALL_SUBTEST(test_0d_const_tensor());
+ CALL_SUBTEST(test_0d_const_tensor_map());
+}
diff --git a/unsupported/test/cxx11_tensor_math.cpp b/unsupported/test/cxx11_tensor_math.cpp
new file mode 100644
index 0000000..82a1a26
--- /dev/null
+++ b/unsupported/test/cxx11_tensor_math.cpp
@@ -0,0 +1,46 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2015 Benoit Steiner <benoit.steiner.goog@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "main.h"
+
+#include <Eigen/CXX11/Tensor>
+
+using Eigen::Tensor;
+using Eigen::RowMajor;
+
+static void test_tanh()
+{
+ Tensor<float, 1> vec1(6);
+ vec1.setRandom();
+
+ Tensor<float, 1> vec2 = vec1.tanh();
+
+ for (int i = 0; i < 6; ++i) {
+ VERIFY_IS_APPROX(vec2(i), tanhf(vec1(i)));
+ }
+}
+
+static void test_sigmoid()
+{
+ Tensor<float, 1> vec1(6);
+ vec1.setRandom();
+
+ Tensor<float, 1> vec2 = vec1.sigmoid();
+
+ for (int i = 0; i < 6; ++i) {
+ VERIFY_IS_APPROX(vec2(i), 1.0f / (1.0f + std::exp(-vec1(i))));
+ }
+}
+
+
+EIGEN_DECLARE_TEST(cxx11_tensor_math)
+{
+ CALL_SUBTEST(test_tanh());
+ CALL_SUBTEST(test_sigmoid());
+}
diff --git a/unsupported/test/cxx11_tensor_math_sycl.cpp b/unsupported/test/cxx11_tensor_math_sycl.cpp
new file mode 100644
index 0000000..029653e
--- /dev/null
+++ b/unsupported/test/cxx11_tensor_math_sycl.cpp
@@ -0,0 +1,105 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2016
+// Mehdi Goli Codeplay Software Ltd.
+// Ralph Potter Codeplay Software Ltd.
+// Luke Iwanski Codeplay Software Ltd.
+// Contact: <eigen@codeplay.com>
+// Benoit Steiner <benoit.steiner.goog@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#define EIGEN_TEST_NO_LONGDOUBLE
+#define EIGEN_TEST_NO_COMPLEX
+#define EIGEN_DEFAULT_DENSE_INDEX_TYPE int64_t
+#define EIGEN_USE_SYCL
+
+#include "main.h"
+#include <unsupported/Eigen/CXX11/Tensor>
+
+using Eigen::array;
+using Eigen::SyclDevice;
+using Eigen::Tensor;
+using Eigen::TensorMap;
+
+using Eigen::Tensor;
+using Eigen::RowMajor;
+template <typename DataType, int DataLayout, typename IndexType>
+static void test_tanh_sycl(const Eigen::SyclDevice &sycl_device)
+{
+
+ IndexType sizeDim1 = 4;
+ IndexType sizeDim2 = 4;
+ IndexType sizeDim3 = 1;
+ array<IndexType, 3> tensorRange = {{sizeDim1, sizeDim2, sizeDim3}};
+ Tensor<DataType, 3, DataLayout, IndexType> in(tensorRange);
+ Tensor<DataType, 3, DataLayout, IndexType> out(tensorRange);
+ Tensor<DataType, 3, DataLayout, IndexType> out_cpu(tensorRange);
+
+ in = in.random();
+
+ DataType* gpu_data1 = static_cast<DataType*>(sycl_device.allocate(in.size()*sizeof(DataType)));
+ DataType* gpu_data2 = static_cast<DataType*>(sycl_device.allocate(out.size()*sizeof(DataType)));
+
+ TensorMap<Tensor<DataType, 3, DataLayout, IndexType>> gpu1(gpu_data1, tensorRange);
+ TensorMap<Tensor<DataType, 3, DataLayout, IndexType>> gpu2(gpu_data2, tensorRange);
+
+ sycl_device.memcpyHostToDevice(gpu_data1, in.data(),(in.size())*sizeof(DataType));
+ gpu2.device(sycl_device) = gpu1.tanh();
+ sycl_device.memcpyDeviceToHost(out.data(), gpu_data2,(out.size())*sizeof(DataType));
+
+ out_cpu=in.tanh();
+
+ for (int i = 0; i < in.size(); ++i) {
+ VERIFY_IS_APPROX(out(i), out_cpu(i));
+ }
+}
+template <typename DataType, int DataLayout, typename IndexType>
+static void test_sigmoid_sycl(const Eigen::SyclDevice &sycl_device)
+{
+
+ IndexType sizeDim1 = 4;
+ IndexType sizeDim2 = 4;
+ IndexType sizeDim3 = 1;
+ array<IndexType, 3> tensorRange = {{sizeDim1, sizeDim2, sizeDim3}};
+ Tensor<DataType, 3, DataLayout, IndexType> in(tensorRange);
+ Tensor<DataType, 3, DataLayout, IndexType> out(tensorRange);
+ Tensor<DataType, 3, DataLayout, IndexType> out_cpu(tensorRange);
+
+ in = in.random();
+
+ DataType* gpu_data1 = static_cast<DataType*>(sycl_device.allocate(in.size()*sizeof(DataType)));
+ DataType* gpu_data2 = static_cast<DataType*>(sycl_device.allocate(out.size()*sizeof(DataType)));
+
+ TensorMap<Tensor<DataType, 3, DataLayout, IndexType>> gpu1(gpu_data1, tensorRange);
+ TensorMap<Tensor<DataType, 3, DataLayout, IndexType>> gpu2(gpu_data2, tensorRange);
+
+ sycl_device.memcpyHostToDevice(gpu_data1, in.data(),(in.size())*sizeof(DataType));
+ gpu2.device(sycl_device) = gpu1.sigmoid();
+ sycl_device.memcpyDeviceToHost(out.data(), gpu_data2,(out.size())*sizeof(DataType));
+
+ out_cpu=in.sigmoid();
+
+ for (int i = 0; i < in.size(); ++i) {
+ VERIFY_IS_APPROX(out(i), out_cpu(i));
+ }
+}
+
+
+template<typename DataType, typename dev_Selector> void sycl_computing_test_per_device(dev_Selector s){
+ QueueInterface queueInterface(s);
+ auto sycl_device = Eigen::SyclDevice(&queueInterface);
+ test_tanh_sycl<DataType, RowMajor, int64_t>(sycl_device);
+ test_tanh_sycl<DataType, ColMajor, int64_t>(sycl_device);
+ test_sigmoid_sycl<DataType, RowMajor, int64_t>(sycl_device);
+ test_sigmoid_sycl<DataType, ColMajor, int64_t>(sycl_device);
+}
+
+EIGEN_DECLARE_TEST(cxx11_tensor_math_sycl) {
+ for (const auto& device :Eigen::get_sycl_supported_devices()) {
+ CALL_SUBTEST(sycl_computing_test_per_device<float>(device));
+ }
+}
diff --git a/unsupported/test/cxx11_tensor_mixed_indices.cpp b/unsupported/test/cxx11_tensor_mixed_indices.cpp
new file mode 100644
index 0000000..ee2616f
--- /dev/null
+++ b/unsupported/test/cxx11_tensor_mixed_indices.cpp
@@ -0,0 +1,53 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "main.h"
+
+#include <Eigen/CXX11/Tensor>
+
+
+static void test_simple()
+{
+ Tensor<float, 1, ColMajor> vec1(6);
+ Tensor<float, 1, ColMajor, int> vec2(6);
+
+ vec1(0) = 4.0; vec2(0) = 0.0;
+ vec1(1) = 8.0; vec2(1) = 1.0;
+ vec1(2) = 15.0; vec2(2) = 2.0;
+ vec1(3) = 16.0; vec2(3) = 3.0;
+ vec1(4) = 23.0; vec2(4) = 4.0;
+ vec1(5) = 42.0; vec2(5) = 5.0;
+
+ float data3[6];
+ TensorMap<Tensor<float, 1, ColMajor>> vec3(data3, 6);
+ vec3 = vec1.sqrt();
+ float data4[6];
+ TensorMap<Tensor<float, 1, ColMajor, int>> vec4(data4, 6);
+ vec4 = vec2.square();
+
+ VERIFY_IS_APPROX(vec3(0), sqrtf(4.0));
+ VERIFY_IS_APPROX(vec3(1), sqrtf(8.0));
+ VERIFY_IS_APPROX(vec3(2), sqrtf(15.0));
+ VERIFY_IS_APPROX(vec3(3), sqrtf(16.0));
+ VERIFY_IS_APPROX(vec3(4), sqrtf(23.0));
+ VERIFY_IS_APPROX(vec3(5), sqrtf(42.0));
+
+ VERIFY_IS_APPROX(vec4(0), 0.0f);
+ VERIFY_IS_APPROX(vec4(1), 1.0f);
+ VERIFY_IS_APPROX(vec4(2), 2.0f * 2.0f);
+ VERIFY_IS_APPROX(vec4(3), 3.0f * 3.0f);
+ VERIFY_IS_APPROX(vec4(4), 4.0f * 4.0f);
+ VERIFY_IS_APPROX(vec4(5), 5.0f * 5.0f);
+}
+
+
+EIGEN_DECLARE_TEST(cxx11_tensor_mixed_indices)
+{
+ CALL_SUBTEST(test_simple());
+}
diff --git a/unsupported/test/cxx11_tensor_morphing.cpp b/unsupported/test/cxx11_tensor_morphing.cpp
new file mode 100644
index 0000000..d039a7e
--- /dev/null
+++ b/unsupported/test/cxx11_tensor_morphing.cpp
@@ -0,0 +1,563 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "main.h"
+
+#include <Eigen/CXX11/Tensor>
+
+using Eigen::Tensor;
+
+template<typename>
+static void test_simple_reshape()
+{
+ Tensor<float, 5> tensor1(2,3,1,7,1);
+ tensor1.setRandom();
+
+ Tensor<float, 3> tensor2(2,3,7);
+ Tensor<float, 2> tensor3(6,7);
+ Tensor<float, 2> tensor4(2,21);
+
+ Tensor<float, 3>::Dimensions dim1(2,3,7);
+ tensor2 = tensor1.reshape(dim1);
+ Tensor<float, 2>::Dimensions dim2(6,7);
+ tensor3 = tensor1.reshape(dim2);
+ Tensor<float, 2>::Dimensions dim3(2,21);
+ tensor4 = tensor1.reshape(dim1).reshape(dim3);
+
+ for (int i = 0; i < 2; ++i) {
+ for (int j = 0; j < 3; ++j) {
+ for (int k = 0; k < 7; ++k) {
+ VERIFY_IS_EQUAL(tensor1(i,j,0,k,0), tensor2(i,j,k));
+ VERIFY_IS_EQUAL(tensor1(i,j,0,k,0), tensor3(i+2*j,k));
+ VERIFY_IS_EQUAL(tensor1(i,j,0,k,0), tensor4(i,j+3*k));
+ }
+ }
+ }
+}
+
+template <typename>
+static void test_static_reshape() {
+ using Eigen::type2index;
+
+ Tensor<float, 5> tensor(2, 3, 1, 7, 1);
+ tensor.setRandom();
+
+ // New dimensions: [2, 3, 7]
+ Eigen::IndexList<type2index<2>, type2index<3>, type2index<7>> dim;
+ Tensor<float, 3> reshaped = tensor.reshape(static_cast<Eigen::DSizes<ptrdiff_t,3>>(dim));
+
+ for (int i = 0; i < 2; ++i) {
+ for (int j = 0; j < 3; ++j) {
+ for (int k = 0; k < 7; ++k) {
+ VERIFY_IS_EQUAL(tensor(i, j, 0, k, 0), reshaped(i, j, k));
+ }
+ }
+ }
+}
+
+template <typename>
+static void test_reshape_in_expr() {
+ MatrixXf m1(2,3*5*7*11);
+ MatrixXf m2(3*5*7*11,13);
+ m1.setRandom();
+ m2.setRandom();
+ MatrixXf m3 = m1 * m2;
+
+ TensorMap<Tensor<float, 5>> tensor1(m1.data(), 2,3,5,7,11);
+ TensorMap<Tensor<float, 5>> tensor2(m2.data(), 3,5,7,11,13);
+ Tensor<float, 2>::Dimensions newDims1(2,3*5*7*11);
+ Tensor<float, 2>::Dimensions newDims2(3*5*7*11,13);
+ typedef Tensor<float, 1>::DimensionPair DimPair;
+ array<DimPair, 1> contract_along{{DimPair(1, 0)}};
+ Tensor<float, 2> tensor3(2,13);
+ tensor3 = tensor1.reshape(newDims1).contract(tensor2.reshape(newDims2), contract_along);
+
+ Map<MatrixXf> res(tensor3.data(), 2, 13);
+ for (int i = 0; i < 2; ++i) {
+ for (int j = 0; j < 13; ++j) {
+ VERIFY_IS_APPROX(res(i,j), m3(i,j));
+ }
+ }
+}
+
+template<typename>
+static void test_reshape_as_lvalue()
+{
+ Tensor<float, 3> tensor(2,3,7);
+ tensor.setRandom();
+
+ Tensor<float, 2> tensor2d(6,7);
+ Tensor<float, 3>::Dimensions dim(2,3,7);
+ tensor2d.reshape(dim) = tensor;
+
+ float scratch[2*3*1*7*1];
+ TensorMap<Tensor<float, 5>> tensor5d(scratch, 2,3,1,7,1);
+ tensor5d.reshape(dim).device(Eigen::DefaultDevice()) = tensor;
+
+ for (int i = 0; i < 2; ++i) {
+ for (int j = 0; j < 3; ++j) {
+ for (int k = 0; k < 7; ++k) {
+ VERIFY_IS_EQUAL(tensor2d(i+2*j,k), tensor(i,j,k));
+ VERIFY_IS_EQUAL(tensor5d(i,j,0,k,0), tensor(i,j,k));
+ }
+ }
+ }
+}
+
+template<typename T, int DataLayout>
+static void test_simple_slice()
+{
+ Tensor<T, 5, DataLayout> tensor(2,3,5,7,11);
+ tensor.setRandom();
+
+ Tensor<T, 5, DataLayout> slice1(1,1,1,1,1);
+ Eigen::DSizes<ptrdiff_t, 5> indices(1,2,3,4,5);
+ Eigen::DSizes<ptrdiff_t, 5> sizes(1,1,1,1,1);
+ slice1 = tensor.slice(indices, sizes);
+ VERIFY_IS_EQUAL(slice1(0,0,0,0,0), tensor(1,2,3,4,5));
+
+ Tensor<T, 5, DataLayout> slice2(1,1,2,2,3);
+ Eigen::DSizes<ptrdiff_t, 5> indices2(1,1,3,4,5);
+ Eigen::DSizes<ptrdiff_t, 5> sizes2(1,1,2,2,3);
+ slice2 = tensor.slice(indices2, sizes2);
+ for (int i = 0; i < 2; ++i) {
+ for (int j = 0; j < 2; ++j) {
+ for (int k = 0; k < 3; ++k) {
+ VERIFY_IS_EQUAL(slice2(0,0,i,j,k), tensor(1,1,3+i,4+j,5+k));
+ }
+ }
+ }
+}
+
+template<typename T>
+static void test_const_slice()
+{
+ const T b[1] = {42};
+ TensorMap<Tensor<const T, 1> > m(b, 1);
+ DSizes<DenseIndex, 1> offsets;
+ offsets[0] = 0;
+ TensorRef<Tensor<const T, 1> > slice_ref(m.slice(offsets, m.dimensions()));
+ VERIFY_IS_EQUAL(slice_ref(0), 42);
+}
+
+template<typename T, int DataLayout>
+static void test_slice_in_expr() {
+ typedef Matrix<T, Dynamic, Dynamic, DataLayout> Mtx;
+ Mtx m1(7,7);
+ Mtx m2(3,3);
+ m1.setRandom();
+ m2.setRandom();
+
+ Mtx m3 = m1.block(1, 2, 3, 3) * m2.block(0, 2, 3, 1);
+
+ TensorMap<Tensor<T, 2, DataLayout>> tensor1(m1.data(), 7, 7);
+ TensorMap<Tensor<T, 2, DataLayout>> tensor2(m2.data(), 3, 3);
+ Tensor<T, 2, DataLayout> tensor3(3,1);
+ typedef typename Tensor<T, 1>::DimensionPair DimPair;
+ array<DimPair, 1> contract_along{{DimPair(1, 0)}};
+
+ Eigen::DSizes<ptrdiff_t, 2> indices1(1,2);
+ Eigen::DSizes<ptrdiff_t, 2> sizes1(3,3);
+ Eigen::DSizes<ptrdiff_t, 2> indices2(0,2);
+ Eigen::DSizes<ptrdiff_t, 2> sizes2(3,1);
+ tensor3 = tensor1.slice(indices1, sizes1).contract(tensor2.slice(indices2, sizes2), contract_along);
+
+ Map<Mtx> res(tensor3.data(), 3, 1);
+ for (int i = 0; i < 3; ++i) {
+ for (int j = 0; j < 1; ++j) {
+ VERIFY_IS_APPROX(res(i,j), m3(i,j));
+ }
+ }
+
+ // Take an arbitrary slice of an arbitrarily sized tensor.
+ TensorMap<Tensor<const T, 2, DataLayout>> tensor4(m1.data(), 7, 7);
+ Tensor<T, 1, DataLayout> tensor6 = tensor4.reshape(DSizes<ptrdiff_t, 1>(7*7)).exp().slice(DSizes<ptrdiff_t, 1>(0), DSizes<ptrdiff_t, 1>(35));
+ for (int i = 0; i < 35; ++i) {
+ VERIFY_IS_APPROX(tensor6(i), expf(tensor4.data()[i]));
+ }
+}
+
+template<typename T, int DataLayout>
+static void test_slice_as_lvalue()
+{
+ Tensor<T, 3, DataLayout> tensor1(2,2,7);
+ tensor1.setRandom();
+ Tensor<T, 3, DataLayout> tensor2(2,2,7);
+ tensor2.setRandom();
+ Tensor<T, 3, DataLayout> tensor3(4,3,5);
+ tensor3.setRandom();
+ Tensor<T, 3, DataLayout> tensor4(4,3,2);
+ tensor4.setRandom();
+ Tensor<T, 3, DataLayout> tensor5(10,13,12);
+ tensor5.setRandom();
+
+ Tensor<T, 3, DataLayout> result(4,5,7);
+ Eigen::DSizes<ptrdiff_t, 3> sizes12(2,2,7);
+ Eigen::DSizes<ptrdiff_t, 3> first_slice(0,0,0);
+ result.slice(first_slice, sizes12) = tensor1;
+ Eigen::DSizes<ptrdiff_t, 3> second_slice(2,0,0);
+ result.slice(second_slice, sizes12).device(Eigen::DefaultDevice()) = tensor2;
+
+ Eigen::DSizes<ptrdiff_t, 3> sizes3(4,3,5);
+ Eigen::DSizes<ptrdiff_t, 3> third_slice(0,2,0);
+ result.slice(third_slice, sizes3) = tensor3;
+
+ Eigen::DSizes<ptrdiff_t, 3> sizes4(4,3,2);
+ Eigen::DSizes<ptrdiff_t, 3> fourth_slice(0,2,5);
+ result.slice(fourth_slice, sizes4) = tensor4;
+
+ for (int j = 0; j < 2; ++j) {
+ for (int k = 0; k < 7; ++k) {
+ for (int i = 0; i < 2; ++i) {
+ VERIFY_IS_EQUAL(result(i,j,k), tensor1(i,j,k));
+ VERIFY_IS_EQUAL(result(i+2,j,k), tensor2(i,j,k));
+ }
+ }
+ }
+ for (int i = 0; i < 4; ++i) {
+ for (int j = 2; j < 5; ++j) {
+ for (int k = 0; k < 5; ++k) {
+ VERIFY_IS_EQUAL(result(i,j,k), tensor3(i,j-2,k));
+ }
+ for (int k = 5; k < 7; ++k) {
+ VERIFY_IS_EQUAL(result(i,j,k), tensor4(i,j-2,k-5));
+ }
+ }
+ }
+
+ Eigen::DSizes<ptrdiff_t, 3> sizes5(4,5,7);
+ Eigen::DSizes<ptrdiff_t, 3> fifth_slice(0,0,0);
+ result.slice(fifth_slice, sizes5) = tensor5.slice(fifth_slice, sizes5);
+ for (int i = 0; i < 4; ++i) {
+ for (int j = 2; j < 5; ++j) {
+ for (int k = 0; k < 7; ++k) {
+ VERIFY_IS_EQUAL(result(i,j,k), tensor5(i,j,k));
+ }
+ }
+ }
+}
+
+template<typename T, int DataLayout>
+static void test_slice_raw_data()
+{
+ Tensor<T, 4, DataLayout> tensor(3,5,7,11);
+ tensor.setRandom();
+
+ Eigen::DSizes<ptrdiff_t, 4> offsets(1,2,3,4);
+ Eigen::DSizes<ptrdiff_t, 4> extents(1,1,1,1);
+ typedef TensorEvaluator<decltype(tensor.slice(offsets, extents)), DefaultDevice> SliceEvaluator;
+ auto slice1 = SliceEvaluator(tensor.slice(offsets, extents), DefaultDevice());
+ VERIFY_IS_EQUAL(slice1.dimensions().TotalSize(), 1);
+ VERIFY_IS_EQUAL(slice1.data()[0], tensor(1,2,3,4));
+
+ if (DataLayout == ColMajor) {
+ extents = Eigen::DSizes<ptrdiff_t, 4>(2,1,1,1);
+ auto slice2 = SliceEvaluator(tensor.slice(offsets, extents), DefaultDevice());
+ VERIFY_IS_EQUAL(slice2.dimensions().TotalSize(), 2);
+ VERIFY_IS_EQUAL(slice2.data()[0], tensor(1,2,3,4));
+ VERIFY_IS_EQUAL(slice2.data()[1], tensor(2,2,3,4));
+ } else {
+ extents = Eigen::DSizes<ptrdiff_t, 4>(1,1,1,2);
+ auto slice2 = SliceEvaluator(tensor.slice(offsets, extents), DefaultDevice());
+ VERIFY_IS_EQUAL(slice2.dimensions().TotalSize(), 2);
+ VERIFY_IS_EQUAL(slice2.data()[0], tensor(1,2,3,4));
+ VERIFY_IS_EQUAL(slice2.data()[1], tensor(1,2,3,5));
+ }
+
+ extents = Eigen::DSizes<ptrdiff_t, 4>(1,2,1,1);
+ auto slice3 = SliceEvaluator(tensor.slice(offsets, extents), DefaultDevice());
+ VERIFY_IS_EQUAL(slice3.dimensions().TotalSize(), 2);
+ VERIFY_IS_EQUAL(slice3.data(), static_cast<T*>(0));
+
+ if (DataLayout == ColMajor) {
+ offsets = Eigen::DSizes<ptrdiff_t, 4>(0,2,3,4);
+ extents = Eigen::DSizes<ptrdiff_t, 4>(3,2,1,1);
+ auto slice4 = SliceEvaluator(tensor.slice(offsets, extents), DefaultDevice());
+ VERIFY_IS_EQUAL(slice4.dimensions().TotalSize(), 6);
+ for (int i = 0; i < 3; ++i) {
+ for (int j = 0; j < 2; ++j) {
+ VERIFY_IS_EQUAL(slice4.data()[i+3*j], tensor(i,2+j,3,4));
+ }
+ }
+ } else {
+ offsets = Eigen::DSizes<ptrdiff_t, 4>(1,2,3,0);
+ extents = Eigen::DSizes<ptrdiff_t, 4>(1,1,2,11);
+ auto slice4 = SliceEvaluator(tensor.slice(offsets, extents), DefaultDevice());
+ VERIFY_IS_EQUAL(slice4.dimensions().TotalSize(), 22);
+ for (int l = 0; l < 11; ++l) {
+ for (int k = 0; k < 2; ++k) {
+ VERIFY_IS_EQUAL(slice4.data()[l+11*k], tensor(1,2,3+k,l));
+ }
+ }
+ }
+
+ if (DataLayout == ColMajor) {
+ offsets = Eigen::DSizes<ptrdiff_t, 4>(0,0,0,4);
+ extents = Eigen::DSizes<ptrdiff_t, 4>(3,5,7,2);
+ auto slice5 = SliceEvaluator(tensor.slice(offsets, extents), DefaultDevice());
+ VERIFY_IS_EQUAL(slice5.dimensions().TotalSize(), 210);
+ for (int i = 0; i < 3; ++i) {
+ for (int j = 0; j < 5; ++j) {
+ for (int k = 0; k < 7; ++k) {
+ for (int l = 0; l < 2; ++l) {
+ int slice_index = i + 3 * (j + 5 * (k + 7 * l));
+ VERIFY_IS_EQUAL(slice5.data()[slice_index], tensor(i,j,k,l+4));
+ }
+ }
+ }
+ }
+ } else {
+ offsets = Eigen::DSizes<ptrdiff_t, 4>(1,0,0,0);
+ extents = Eigen::DSizes<ptrdiff_t, 4>(2,5,7,11);
+ auto slice5 = SliceEvaluator(tensor.slice(offsets, extents), DefaultDevice());
+ VERIFY_IS_EQUAL(slice5.dimensions().TotalSize(), 770);
+ for (int l = 0; l < 11; ++l) {
+ for (int k = 0; k < 7; ++k) {
+ for (int j = 0; j < 5; ++j) {
+ for (int i = 0; i < 2; ++i) {
+ int slice_index = l + 11 * (k + 7 * (j + 5 * i));
+ VERIFY_IS_EQUAL(slice5.data()[slice_index], tensor(i+1,j,k,l));
+ }
+ }
+ }
+ }
+
+ }
+
+ offsets = Eigen::DSizes<ptrdiff_t, 4>(0,0,0,0);
+ extents = Eigen::DSizes<ptrdiff_t, 4>(3,5,7,11);
+ auto slice6 = SliceEvaluator(tensor.slice(offsets, extents), DefaultDevice());
+ VERIFY_IS_EQUAL(slice6.dimensions().TotalSize(), 3*5*7*11);
+ VERIFY_IS_EQUAL(slice6.data(), tensor.data());
+}
+
+
+template<typename T, int DataLayout>
+static void test_strided_slice()
+{
+ typedef Tensor<T, 5, DataLayout> Tensor5f;
+ typedef Eigen::DSizes<Eigen::DenseIndex, 5> Index5;
+ typedef Tensor<T, 2, DataLayout> Tensor2f;
+ typedef Eigen::DSizes<Eigen::DenseIndex, 2> Index2;
+ Tensor<T, 5, DataLayout> tensor(2,3,5,7,11);
+ Tensor<T, 2, DataLayout> tensor2(7,11);
+ tensor.setRandom();
+ tensor2.setRandom();
+
+ if (true) {
+ Tensor2f slice(2,3);
+ Index2 strides(-2,-1);
+ Index2 indicesStart(5,7);
+ Index2 indicesStop(0,4);
+ slice = tensor2.stridedSlice(indicesStart, indicesStop, strides);
+ for (int j = 0; j < 2; ++j) {
+ for (int k = 0; k < 3; ++k) {
+ VERIFY_IS_EQUAL(slice(j,k), tensor2(5-2*j,7-k));
+ }
+ }
+ }
+
+ if(true) {
+ Tensor2f slice(0,1);
+ Index2 strides(1,1);
+ Index2 indicesStart(5,4);
+ Index2 indicesStop(5,5);
+ slice = tensor2.stridedSlice(indicesStart, indicesStop, strides);
+ }
+
+ if(true) { // test clamped degenerate interavls
+ Tensor2f slice(7,11);
+ Index2 strides(1,-1);
+ Index2 indicesStart(-3,20); // should become 0,10
+ Index2 indicesStop(20,-11); // should become 11, -1
+ slice = tensor2.stridedSlice(indicesStart, indicesStop, strides);
+ for (int j = 0; j < 7; ++j) {
+ for (int k = 0; k < 11; ++k) {
+ VERIFY_IS_EQUAL(slice(j,k), tensor2(j,10-k));
+ }
+ }
+ }
+
+ if(true) {
+ Tensor5f slice1(1,1,1,1,1);
+ Eigen::DSizes<Eigen::DenseIndex, 5> indicesStart(1, 2, 3, 4, 5);
+ Eigen::DSizes<Eigen::DenseIndex, 5> indicesStop(2, 3, 4, 5, 6);
+ Eigen::DSizes<Eigen::DenseIndex, 5> strides(1, 1, 1, 1, 1);
+ slice1 = tensor.stridedSlice(indicesStart, indicesStop, strides);
+ VERIFY_IS_EQUAL(slice1(0,0,0,0,0), tensor(1,2,3,4,5));
+ }
+
+ if(true) {
+ Tensor5f slice(1,1,2,2,3);
+ Index5 start(1, 1, 3, 4, 5);
+ Index5 stop(2, 2, 5, 6, 8);
+ Index5 strides(1, 1, 1, 1, 1);
+ slice = tensor.stridedSlice(start, stop, strides);
+ for (int i = 0; i < 2; ++i) {
+ for (int j = 0; j < 2; ++j) {
+ for (int k = 0; k < 3; ++k) {
+ VERIFY_IS_EQUAL(slice(0,0,i,j,k), tensor(1,1,3+i,4+j,5+k));
+ }
+ }
+ }
+ }
+
+ if(true) {
+ Tensor5f slice(1,1,2,2,3);
+ Index5 strides3(1, 1, -2, 1, -1);
+ Index5 indices3Start(1, 1, 4, 4, 7);
+ Index5 indices3Stop(2, 2, 0, 6, 4);
+ slice = tensor.stridedSlice(indices3Start, indices3Stop, strides3);
+ for (int i = 0; i < 2; ++i) {
+ for (int j = 0; j < 2; ++j) {
+ for (int k = 0; k < 3; ++k) {
+ VERIFY_IS_EQUAL(slice(0,0,i,j,k), tensor(1,1,4-2*i,4+j,7-k));
+ }
+ }
+ }
+ }
+
+ if(false) { // tests degenerate interval
+ Tensor5f slice(1,1,2,2,3);
+ Index5 strides3(1, 1, 2, 1, 1);
+ Index5 indices3Start(1, 1, 4, 4, 7);
+ Index5 indices3Stop(2, 2, 0, 6, 4);
+ slice = tensor.stridedSlice(indices3Start, indices3Stop, strides3);
+ }
+}
+
+template<typename T, int DataLayout>
+static void test_strided_slice_write()
+{
+ typedef Tensor<T, 2, DataLayout> Tensor2f;
+ typedef Eigen::DSizes<Eigen::DenseIndex, 2> Index2;
+
+ Tensor<T, 2, DataLayout> tensor(7,11),tensor2(7,11);
+ tensor.setRandom();
+ tensor2=tensor;
+ Tensor2f slice(2,3);
+
+ slice.setRandom();
+
+ Index2 strides(1,1);
+ Index2 indicesStart(3,4);
+ Index2 indicesStop(5,7);
+ Index2 lengths(2,3);
+
+ tensor.slice(indicesStart,lengths)=slice;
+ tensor2.stridedSlice(indicesStart,indicesStop,strides)=slice;
+
+ for(int i=0;i<7;i++) for(int j=0;j<11;j++){
+ VERIFY_IS_EQUAL(tensor(i,j), tensor2(i,j));
+ }
+}
+
+template<typename T, int DataLayout>
+static void test_composition()
+{
+ Eigen::Tensor<T, 2, DataLayout> matrix(7, 11);
+ matrix.setRandom();
+
+ const DSizes<ptrdiff_t, 3> newDims(1, 1, 11);
+ Eigen::Tensor<T, 3, DataLayout> tensor =
+ matrix.slice(DSizes<ptrdiff_t, 2>(2, 0), DSizes<ptrdiff_t, 2>(1, 11)).reshape(newDims);
+
+ VERIFY_IS_EQUAL(tensor.dimensions().TotalSize(), 11);
+ VERIFY_IS_EQUAL(tensor.dimension(0), 1);
+ VERIFY_IS_EQUAL(tensor.dimension(1), 1);
+ VERIFY_IS_EQUAL(tensor.dimension(2), 11);
+ for (int i = 0; i < 11; ++i) {
+ VERIFY_IS_EQUAL(tensor(0,0,i), matrix(2,i));
+ }
+}
+
+template<typename T, int DataLayout>
+static void test_empty_slice()
+{
+ Tensor<T, 3, DataLayout> tensor(2,3,5);
+ tensor.setRandom();
+ Tensor<T, 3, DataLayout> copy = tensor;
+
+ // empty size in first dimension
+ Eigen::DSizes<ptrdiff_t, 3> indices1(1,2,3);
+ Eigen::DSizes<ptrdiff_t, 3> sizes1(0,1,2);
+ Tensor<T, 3, DataLayout> slice1(0,1,2);
+ slice1.setRandom();
+ tensor.slice(indices1, sizes1) = slice1;
+
+ // empty size in second dimension
+ Eigen::DSizes<ptrdiff_t, 3> indices2(1,2,3);
+ Eigen::DSizes<ptrdiff_t, 3> sizes2(1,0,2);
+ Tensor<T, 3, DataLayout> slice2(1,0,2);
+ slice2.setRandom();
+ tensor.slice(indices2, sizes2) = slice2;
+
+ // empty size in third dimension
+ Eigen::DSizes<ptrdiff_t, 3> indices3(1,2,3);
+ Eigen::DSizes<ptrdiff_t, 3> sizes3(1,1,0);
+ Tensor<T, 3, DataLayout> slice3(1,1,0);
+ slice3.setRandom();
+ tensor.slice(indices3, sizes3) = slice3;
+
+ // empty size in first and second dimension
+ Eigen::DSizes<ptrdiff_t, 3> indices4(1,2,3);
+ Eigen::DSizes<ptrdiff_t, 3> sizes4(0,0,2);
+ Tensor<T, 3, DataLayout> slice4(0,0,2);
+ slice4.setRandom();
+ tensor.slice(indices4, sizes4) = slice4;
+
+ // empty size in second and third dimension
+ Eigen::DSizes<ptrdiff_t, 3> indices5(1,2,3);
+ Eigen::DSizes<ptrdiff_t, 3> sizes5(1,0,0);
+ Tensor<T, 3, DataLayout> slice5(1,0,0);
+ slice5.setRandom();
+ tensor.slice(indices5, sizes5) = slice5;
+
+ // empty size in all dimensions
+ Eigen::DSizes<ptrdiff_t, 3> indices6(1,2,3);
+ Eigen::DSizes<ptrdiff_t, 3> sizes6(0,0,0);
+ Tensor<T, 3, DataLayout> slice6(0,0,0);
+ slice6.setRandom();
+ tensor.slice(indices6, sizes6) = slice6;
+
+ // none of these operations should change the tensor's components
+ // because all of the rvalue slices have at least one zero dimension
+ for (int i = 0; i < 2; ++i) {
+ for (int j = 0; j < 3; ++j) {
+ for (int k = 0; k < 5; ++k) {
+ VERIFY_IS_EQUAL(tensor(i,j,k), copy(i,j,k));
+ }
+ }
+ }
+}
+
+#define CALL_SUBTEST_PART(PART) \
+ CALL_SUBTEST_##PART
+
+#define CALL_SUBTESTS_TYPES_LAYOUTS(PART, NAME) \
+ CALL_SUBTEST_PART(PART)((NAME<float, ColMajor>())); \
+ CALL_SUBTEST_PART(PART)((NAME<float, RowMajor>())); \
+ CALL_SUBTEST_PART(PART)((NAME<bool, ColMajor>())); \
+ CALL_SUBTEST_PART(PART)((NAME<bool, RowMajor>()))
+
+EIGEN_DECLARE_TEST(cxx11_tensor_morphing)
+{
+ CALL_SUBTEST_1(test_simple_reshape<void>());
+ CALL_SUBTEST_1(test_static_reshape<void>());
+ CALL_SUBTEST_1(test_reshape_as_lvalue<void>());
+ CALL_SUBTEST_1(test_reshape_in_expr<void>());
+ CALL_SUBTEST_1(test_const_slice<float>());
+
+ CALL_SUBTESTS_TYPES_LAYOUTS(2, test_simple_slice);
+ CALL_SUBTESTS_TYPES_LAYOUTS(3, test_slice_as_lvalue);
+ CALL_SUBTESTS_TYPES_LAYOUTS(4, test_slice_raw_data);
+ CALL_SUBTESTS_TYPES_LAYOUTS(5, test_strided_slice_write);
+ CALL_SUBTESTS_TYPES_LAYOUTS(6, test_strided_slice);
+ CALL_SUBTESTS_TYPES_LAYOUTS(7, test_composition);
+}
diff --git a/unsupported/test/cxx11_tensor_morphing_sycl.cpp b/unsupported/test/cxx11_tensor_morphing_sycl.cpp
new file mode 100644
index 0000000..bf001b4
--- /dev/null
+++ b/unsupported/test/cxx11_tensor_morphing_sycl.cpp
@@ -0,0 +1,386 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2016
+// Mehdi Goli Codeplay Software Ltd.
+// Ralph Potter Codeplay Software Ltd.
+// Luke Iwanski Codeplay Software Ltd.
+// Contact: <eigen@codeplay.com>
+// Benoit Steiner <benoit.steiner.goog@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+
+#define EIGEN_TEST_NO_LONGDOUBLE
+#define EIGEN_TEST_NO_COMPLEX
+
+#define EIGEN_DEFAULT_DENSE_INDEX_TYPE int64_t
+#define EIGEN_USE_SYCL
+
+
+#include "main.h"
+#include <unsupported/Eigen/CXX11/Tensor>
+
+using Eigen::array;
+using Eigen::SyclDevice;
+using Eigen::Tensor;
+using Eigen::TensorMap;
+
+template <typename DataType, int DataLayout, typename IndexType>
+static void test_simple_reshape(const Eigen::SyclDevice& sycl_device)
+{
+ typename Tensor<DataType, 5 ,DataLayout, IndexType>::Dimensions dim1(2,3,1,7,1);
+ typename Tensor<DataType, 3 ,DataLayout, IndexType>::Dimensions dim2(2,3,7);
+ typename Tensor<DataType, 2 ,DataLayout, IndexType>::Dimensions dim3(6,7);
+ typename Tensor<DataType, 2 ,DataLayout, IndexType>::Dimensions dim4(2,21);
+
+ Tensor<DataType, 5, DataLayout, IndexType> tensor1(dim1);
+ Tensor<DataType, 3, DataLayout, IndexType> tensor2(dim2);
+ Tensor<DataType, 2, DataLayout, IndexType> tensor3(dim3);
+ Tensor<DataType, 2, DataLayout, IndexType> tensor4(dim4);
+
+ tensor1.setRandom();
+
+ DataType* gpu_data1 = static_cast<DataType*>(sycl_device.allocate(tensor1.size()*sizeof(DataType)));
+ DataType* gpu_data2 = static_cast<DataType*>(sycl_device.allocate(tensor2.size()*sizeof(DataType)));
+ DataType* gpu_data3 = static_cast<DataType*>(sycl_device.allocate(tensor3.size()*sizeof(DataType)));
+ DataType* gpu_data4 = static_cast<DataType*>(sycl_device.allocate(tensor4.size()*sizeof(DataType)));
+
+ TensorMap<Tensor<DataType, 5,DataLayout, IndexType>> gpu1(gpu_data1, dim1);
+ TensorMap<Tensor<DataType, 3,DataLayout, IndexType>> gpu2(gpu_data2, dim2);
+ TensorMap<Tensor<DataType, 2,DataLayout, IndexType>> gpu3(gpu_data3, dim3);
+ TensorMap<Tensor<DataType, 2,DataLayout, IndexType>> gpu4(gpu_data4, dim4);
+
+ sycl_device.memcpyHostToDevice(gpu_data1, tensor1.data(),(tensor1.size())*sizeof(DataType));
+
+ gpu2.device(sycl_device)=gpu1.reshape(dim2);
+ sycl_device.memcpyDeviceToHost(tensor2.data(), gpu_data2,(tensor1.size())*sizeof(DataType));
+
+ gpu3.device(sycl_device)=gpu1.reshape(dim3);
+ sycl_device.memcpyDeviceToHost(tensor3.data(), gpu_data3,(tensor3.size())*sizeof(DataType));
+
+ gpu4.device(sycl_device)=gpu1.reshape(dim2).reshape(dim4);
+ sycl_device.memcpyDeviceToHost(tensor4.data(), gpu_data4,(tensor4.size())*sizeof(DataType));
+ for (IndexType i = 0; i < 2; ++i){
+ for (IndexType j = 0; j < 3; ++j){
+ for (IndexType k = 0; k < 7; ++k){
+ VERIFY_IS_EQUAL(tensor1(i,j,0,k,0), tensor2(i,j,k)); ///ColMajor
+ if (static_cast<int>(DataLayout) == static_cast<int>(ColMajor)) {
+ VERIFY_IS_EQUAL(tensor1(i,j,0,k,0), tensor3(i+2*j,k)); ///ColMajor
+ VERIFY_IS_EQUAL(tensor1(i,j,0,k,0), tensor4(i,j+3*k)); ///ColMajor
+ }
+ else{
+ //VERIFY_IS_EQUAL(tensor1(i,j,0,k,0), tensor2(i,j,k)); /// RowMajor
+ VERIFY_IS_EQUAL(tensor1(i,j,0,k,0), tensor4(i,j*7 +k)); /// RowMajor
+ VERIFY_IS_EQUAL(tensor1(i,j,0,k,0), tensor3(i*3 +j,k)); /// RowMajor
+ }
+ }
+ }
+ }
+ sycl_device.deallocate(gpu_data1);
+ sycl_device.deallocate(gpu_data2);
+ sycl_device.deallocate(gpu_data3);
+ sycl_device.deallocate(gpu_data4);
+}
+
+
+template<typename DataType, int DataLayout, typename IndexType>
+static void test_reshape_as_lvalue(const Eigen::SyclDevice& sycl_device)
+{
+ typename Tensor<DataType, 3, DataLayout, IndexType>::Dimensions dim1(2,3,7);
+ typename Tensor<DataType, 2, DataLayout, IndexType>::Dimensions dim2(6,7);
+ typename Tensor<DataType, 5, DataLayout, IndexType>::Dimensions dim3(2,3,1,7,1);
+ Tensor<DataType, 3, DataLayout, IndexType> tensor(dim1);
+ Tensor<DataType, 2, DataLayout, IndexType> tensor2d(dim2);
+ Tensor<DataType, 5, DataLayout, IndexType> tensor5d(dim3);
+
+ tensor.setRandom();
+
+ DataType* gpu_data1 = static_cast<DataType*>(sycl_device.allocate(tensor.size()*sizeof(DataType)));
+ DataType* gpu_data2 = static_cast<DataType*>(sycl_device.allocate(tensor2d.size()*sizeof(DataType)));
+ DataType* gpu_data3 = static_cast<DataType*>(sycl_device.allocate(tensor5d.size()*sizeof(DataType)));
+
+ TensorMap< Tensor<DataType, 3, DataLayout, IndexType> > gpu1(gpu_data1, dim1);
+ TensorMap< Tensor<DataType, 2, DataLayout, IndexType> > gpu2(gpu_data2, dim2);
+ TensorMap< Tensor<DataType, 5, DataLayout, IndexType> > gpu3(gpu_data3, dim3);
+
+ sycl_device.memcpyHostToDevice(gpu_data1, tensor.data(),(tensor.size())*sizeof(DataType));
+
+ gpu2.reshape(dim1).device(sycl_device)=gpu1;
+ sycl_device.memcpyDeviceToHost(tensor2d.data(), gpu_data2,(tensor2d.size())*sizeof(DataType));
+
+ gpu3.reshape(dim1).device(sycl_device)=gpu1;
+ sycl_device.memcpyDeviceToHost(tensor5d.data(), gpu_data3,(tensor5d.size())*sizeof(DataType));
+
+
+ for (IndexType i = 0; i < 2; ++i){
+ for (IndexType j = 0; j < 3; ++j){
+ for (IndexType k = 0; k < 7; ++k){
+ VERIFY_IS_EQUAL(tensor5d(i,j,0,k,0), tensor(i,j,k));
+ if (static_cast<int>(DataLayout) == static_cast<int>(ColMajor)) {
+ VERIFY_IS_EQUAL(tensor2d(i+2*j,k), tensor(i,j,k)); ///ColMajor
+ }
+ else{
+ VERIFY_IS_EQUAL(tensor2d(i*3 +j,k),tensor(i,j,k)); /// RowMajor
+ }
+ }
+ }
+ }
+ sycl_device.deallocate(gpu_data1);
+ sycl_device.deallocate(gpu_data2);
+ sycl_device.deallocate(gpu_data3);
+}
+
+
+template <typename DataType, int DataLayout, typename IndexType>
+static void test_simple_slice(const Eigen::SyclDevice &sycl_device)
+{
+ IndexType sizeDim1 = 2;
+ IndexType sizeDim2 = 3;
+ IndexType sizeDim3 = 5;
+ IndexType sizeDim4 = 7;
+ IndexType sizeDim5 = 11;
+ array<IndexType, 5> tensorRange = {{sizeDim1, sizeDim2, sizeDim3, sizeDim4, sizeDim5}};
+ Tensor<DataType, 5,DataLayout, IndexType> tensor(tensorRange);
+ tensor.setRandom();
+ array<IndexType, 5> slice1_range ={{1, 1, 1, 1, 1}};
+ Tensor<DataType, 5,DataLayout, IndexType> slice1(slice1_range);
+
+ DataType* gpu_data1 = static_cast<DataType*>(sycl_device.allocate(tensor.size()*sizeof(DataType)));
+ DataType* gpu_data2 = static_cast<DataType*>(sycl_device.allocate(slice1.size()*sizeof(DataType)));
+ TensorMap<Tensor<DataType, 5,DataLayout, IndexType>> gpu1(gpu_data1, tensorRange);
+ TensorMap<Tensor<DataType, 5,DataLayout, IndexType>> gpu2(gpu_data2, slice1_range);
+ Eigen::DSizes<IndexType, 5> indices(1,2,3,4,5);
+ Eigen::DSizes<IndexType, 5> sizes(1,1,1,1,1);
+ sycl_device.memcpyHostToDevice(gpu_data1, tensor.data(),(tensor.size())*sizeof(DataType));
+ gpu2.device(sycl_device)=gpu1.slice(indices, sizes);
+ sycl_device.memcpyDeviceToHost(slice1.data(), gpu_data2,(slice1.size())*sizeof(DataType));
+ VERIFY_IS_EQUAL(slice1(0,0,0,0,0), tensor(1,2,3,4,5));
+
+
+ array<IndexType, 5> slice2_range ={{1,1,2,2,3}};
+ Tensor<DataType, 5,DataLayout, IndexType> slice2(slice2_range);
+ DataType* gpu_data3 = static_cast<DataType*>(sycl_device.allocate(slice2.size()*sizeof(DataType)));
+ TensorMap<Tensor<DataType, 5,DataLayout, IndexType>> gpu3(gpu_data3, slice2_range);
+ Eigen::DSizes<IndexType, 5> indices2(1,1,3,4,5);
+ Eigen::DSizes<IndexType, 5> sizes2(1,1,2,2,3);
+ gpu3.device(sycl_device)=gpu1.slice(indices2, sizes2);
+ sycl_device.memcpyDeviceToHost(slice2.data(), gpu_data3,(slice2.size())*sizeof(DataType));
+ for (IndexType i = 0; i < 2; ++i) {
+ for (IndexType j = 0; j < 2; ++j) {
+ for (IndexType k = 0; k < 3; ++k) {
+ VERIFY_IS_EQUAL(slice2(0,0,i,j,k), tensor(1,1,3+i,4+j,5+k));
+ }
+ }
+ }
+ sycl_device.deallocate(gpu_data1);
+ sycl_device.deallocate(gpu_data2);
+ sycl_device.deallocate(gpu_data3);
+}
+
+
+template <typename DataType, int DataLayout, typename IndexType>
+static void test_strided_slice_as_rhs_sycl(const Eigen::SyclDevice &sycl_device)
+{
+ IndexType sizeDim1 = 2;
+ IndexType sizeDim2 = 3;
+ IndexType sizeDim3 = 5;
+ IndexType sizeDim4 = 7;
+ IndexType sizeDim5 = 11;
+ typedef Eigen::DSizes<IndexType, 5> Index5;
+ Index5 strides(1L,1L,1L,1L,1L);
+ Index5 indicesStart(1L,2L,3L,4L,5L);
+ Index5 indicesStop(2L,3L,4L,5L,6L);
+ Index5 lengths(1L,1L,1L,1L,1L);
+
+ array<IndexType, 5> tensorRange = {{sizeDim1, sizeDim2, sizeDim3, sizeDim4, sizeDim5}};
+ Tensor<DataType, 5, DataLayout, IndexType> tensor(tensorRange);
+ tensor.setRandom();
+
+ array<IndexType, 5> slice1_range ={{1, 1, 1, 1, 1}};
+ Tensor<DataType, 5,DataLayout, IndexType> slice1(slice1_range);
+ Tensor<DataType, 5, DataLayout, IndexType> slice_stride1(slice1_range);
+
+ DataType* gpu_data1 = static_cast<DataType*>(sycl_device.allocate(tensor.size()*sizeof(DataType)));
+ DataType* gpu_data2 = static_cast<DataType*>(sycl_device.allocate(slice1.size()*sizeof(DataType)));
+ DataType* gpu_data_stride2 = static_cast<DataType*>(sycl_device.allocate(slice_stride1.size()*sizeof(DataType)));
+
+ TensorMap<Tensor<DataType, 5,DataLayout, IndexType>> gpu1(gpu_data1, tensorRange);
+ TensorMap<Tensor<DataType, 5,DataLayout, IndexType>> gpu2(gpu_data2, slice1_range);
+ TensorMap<Tensor<DataType, 5,DataLayout, IndexType>> gpu_stride2(gpu_data_stride2, slice1_range);
+
+ Eigen::DSizes<IndexType, 5> indices(1,2,3,4,5);
+ Eigen::DSizes<IndexType, 5> sizes(1,1,1,1,1);
+ sycl_device.memcpyHostToDevice(gpu_data1, tensor.data(),(tensor.size())*sizeof(DataType));
+ gpu2.device(sycl_device)=gpu1.slice(indices, sizes);
+ sycl_device.memcpyDeviceToHost(slice1.data(), gpu_data2,(slice1.size())*sizeof(DataType));
+
+ gpu_stride2.device(sycl_device)=gpu1.stridedSlice(indicesStart,indicesStop,strides);
+ sycl_device.memcpyDeviceToHost(slice_stride1.data(), gpu_data_stride2,(slice_stride1.size())*sizeof(DataType));
+
+ VERIFY_IS_EQUAL(slice1(0,0,0,0,0), tensor(1,2,3,4,5));
+ VERIFY_IS_EQUAL(slice_stride1(0,0,0,0,0), tensor(1,2,3,4,5));
+
+ array<IndexType, 5> slice2_range ={{1,1,2,2,3}};
+ Tensor<DataType, 5,DataLayout, IndexType> slice2(slice2_range);
+ Tensor<DataType, 5, DataLayout, IndexType> strideSlice2(slice2_range);
+
+ DataType* gpu_data3 = static_cast<DataType*>(sycl_device.allocate(slice2.size()*sizeof(DataType)));
+ DataType* gpu_data_stride3 = static_cast<DataType*>(sycl_device.allocate(strideSlice2.size()*sizeof(DataType)));
+ TensorMap<Tensor<DataType, 5,DataLayout, IndexType>> gpu3(gpu_data3, slice2_range);
+ TensorMap<Tensor<DataType, 5,DataLayout, IndexType>> gpu_stride3(gpu_data_stride3, slice2_range);
+ Eigen::DSizes<IndexType, 5> indices2(1,1,3,4,5);
+ Eigen::DSizes<IndexType, 5> sizes2(1,1,2,2,3);
+ Index5 strides2(1L,1L,1L,1L,1L);
+ Index5 indicesStart2(1L,1L,3L,4L,5L);
+ Index5 indicesStop2(2L,2L,5L,6L,8L);
+
+ gpu3.device(sycl_device)=gpu1.slice(indices2, sizes2);
+ sycl_device.memcpyDeviceToHost(slice2.data(), gpu_data3,(slice2.size())*sizeof(DataType));
+
+ gpu_stride3.device(sycl_device)=gpu1.stridedSlice(indicesStart2,indicesStop2,strides2);
+ sycl_device.memcpyDeviceToHost(strideSlice2.data(), gpu_data_stride3,(strideSlice2.size())*sizeof(DataType));
+
+ for (IndexType i = 0; i < 2; ++i) {
+ for (IndexType j = 0; j < 2; ++j) {
+ for (IndexType k = 0; k < 3; ++k) {
+ VERIFY_IS_EQUAL(slice2(0,0,i,j,k), tensor(1,1,3+i,4+j,5+k));
+ VERIFY_IS_EQUAL(strideSlice2(0,0,i,j,k), tensor(1,1,3+i,4+j,5+k));
+ }
+ }
+ }
+ sycl_device.deallocate(gpu_data1);
+ sycl_device.deallocate(gpu_data2);
+ sycl_device.deallocate(gpu_data3);
+}
+
+template<typename DataType, int DataLayout, typename IndexType>
+static void test_strided_slice_write_sycl(const Eigen::SyclDevice& sycl_device)
+{
+ typedef Tensor<DataType, 2, DataLayout, IndexType> Tensor2f;
+ typedef Eigen::DSizes<IndexType, 2> Index2;
+ IndexType sizeDim1 = 7L;
+ IndexType sizeDim2 = 11L;
+ array<IndexType, 2> tensorRange = {{sizeDim1, sizeDim2}};
+ Tensor<DataType, 2, DataLayout, IndexType> tensor(tensorRange),tensor2(tensorRange);
+ IndexType sliceDim1 = 2;
+ IndexType sliceDim2 = 3;
+ array<IndexType, 2> sliceRange = {{sliceDim1, sliceDim2}};
+ Tensor2f slice(sliceRange);
+ Index2 strides(1L,1L);
+ Index2 indicesStart(3L,4L);
+ Index2 indicesStop(5L,7L);
+ Index2 lengths(2L,3L);
+
+ DataType* gpu_data1 = static_cast<DataType*>(sycl_device.allocate(tensor.size()*sizeof(DataType)));
+ DataType* gpu_data2 = static_cast<DataType*>(sycl_device.allocate(tensor2.size()*sizeof(DataType)));
+ DataType* gpu_data3 = static_cast<DataType*>(sycl_device.allocate(slice.size()*sizeof(DataType)));
+ TensorMap<Tensor<DataType, 2,DataLayout,IndexType>> gpu1(gpu_data1, tensorRange);
+ TensorMap<Tensor<DataType, 2,DataLayout,IndexType>> gpu2(gpu_data2, tensorRange);
+ TensorMap<Tensor<DataType, 2,DataLayout,IndexType>> gpu3(gpu_data3, sliceRange);
+
+
+ tensor.setRandom();
+ sycl_device.memcpyHostToDevice(gpu_data1, tensor.data(),(tensor.size())*sizeof(DataType));
+ gpu2.device(sycl_device)=gpu1;
+
+ slice.setRandom();
+ sycl_device.memcpyHostToDevice(gpu_data3, slice.data(),(slice.size())*sizeof(DataType));
+
+
+ gpu1.slice(indicesStart,lengths).device(sycl_device)=gpu3;
+ gpu2.stridedSlice(indicesStart,indicesStop,strides).device(sycl_device)=gpu3;
+ sycl_device.memcpyDeviceToHost(tensor.data(), gpu_data1,(tensor.size())*sizeof(DataType));
+ sycl_device.memcpyDeviceToHost(tensor2.data(), gpu_data2,(tensor2.size())*sizeof(DataType));
+
+ for(IndexType i=0;i<sizeDim1;i++)
+ for(IndexType j=0;j<sizeDim2;j++){
+ VERIFY_IS_EQUAL(tensor(i,j), tensor2(i,j));
+ }
+ sycl_device.deallocate(gpu_data1);
+ sycl_device.deallocate(gpu_data2);
+ sycl_device.deallocate(gpu_data3);
+}
+
+template <typename OutIndex, typename DSizes>
+Eigen::array<OutIndex, DSizes::count> To32BitDims(const DSizes& in) {
+ Eigen::array<OutIndex, DSizes::count> out;
+ for (int i = 0; i < DSizes::count; ++i) {
+ out[i] = in[i];
+ }
+ return out;
+}
+
+template <class DataType, int DataLayout, typename IndexType, typename ConvertedIndexType>
+int run_eigen(const SyclDevice& sycl_device) {
+ using TensorI64 = Tensor<DataType, 5, DataLayout, IndexType>;
+ using TensorI32 = Tensor<DataType, 5, DataLayout, ConvertedIndexType>;
+ using TensorMI64 = TensorMap<TensorI64>;
+ using TensorMI32 = TensorMap<TensorI32>;
+ Eigen::array<IndexType, 5> tensor_range{{4, 1, 1, 1, 6}};
+ Eigen::array<IndexType, 5> slice_range{{4, 1, 1, 1, 3}};
+
+ TensorI64 out_tensor_gpu(tensor_range);
+ TensorI64 out_tensor_cpu(tensor_range);
+ out_tensor_cpu.setRandom();
+
+ TensorI64 sub_tensor(slice_range);
+ sub_tensor.setRandom();
+
+ DataType* out_gpu_data = static_cast<DataType*>(sycl_device.allocate(out_tensor_cpu.size() * sizeof(DataType)));
+ DataType* sub_gpu_data = static_cast<DataType*>(sycl_device.allocate(sub_tensor.size() * sizeof(DataType)));
+ TensorMI64 out_gpu(out_gpu_data, tensor_range);
+ TensorMI64 sub_gpu(sub_gpu_data, slice_range);
+
+ sycl_device.memcpyHostToDevice(out_gpu_data, out_tensor_cpu.data(), out_tensor_cpu.size() * sizeof(DataType));
+ sycl_device.memcpyHostToDevice(sub_gpu_data, sub_tensor.data(), sub_tensor.size() * sizeof(DataType));
+
+ Eigen::array<ConvertedIndexType, 5> slice_offset_32{{0, 0, 0, 0, 3}};
+ Eigen::array<ConvertedIndexType, 5> slice_range_32{{4, 1, 1, 1, 3}};
+ TensorMI32 out_cpu_32(out_tensor_cpu.data(), To32BitDims<ConvertedIndexType>(out_tensor_cpu.dimensions()));
+ TensorMI32 sub_cpu_32(sub_tensor.data(), To32BitDims<ConvertedIndexType>(sub_tensor.dimensions()));
+ TensorMI32 out_gpu_32(out_gpu.data(), To32BitDims<ConvertedIndexType>(out_gpu.dimensions()));
+ TensorMI32 sub_gpu_32(sub_gpu.data(), To32BitDims<ConvertedIndexType>(sub_gpu.dimensions()));
+
+ out_gpu_32.slice(slice_offset_32, slice_range_32).device(sycl_device) = sub_gpu_32;
+
+ out_cpu_32.slice(slice_offset_32, slice_range_32) = sub_cpu_32;
+
+ sycl_device.memcpyDeviceToHost(out_tensor_gpu.data(), out_gpu_data, out_tensor_cpu.size() * sizeof(DataType));
+ int has_err = 0;
+ for (IndexType i = 0; i < out_tensor_cpu.size(); ++i) {
+ auto exp = out_tensor_cpu(i);
+ auto val = out_tensor_gpu(i);
+ if (val != exp) {
+ std::cout << "#" << i << " got " << val << " but expected " << exp << std::endl;
+ has_err = 1;
+ }
+ }
+ sycl_device.deallocate(out_gpu_data);
+ sycl_device.deallocate(sub_gpu_data);
+ return has_err;
+}
+
+template<typename DataType, typename dev_Selector> void sycl_morphing_test_per_device(dev_Selector s){
+ QueueInterface queueInterface(s);
+ auto sycl_device = Eigen::SyclDevice(&queueInterface);
+ test_simple_slice<DataType, RowMajor, int64_t>(sycl_device);
+ test_simple_slice<DataType, ColMajor, int64_t>(sycl_device);
+ test_simple_reshape<DataType, RowMajor, int64_t>(sycl_device);
+ test_simple_reshape<DataType, ColMajor, int64_t>(sycl_device);
+ test_reshape_as_lvalue<DataType, RowMajor, int64_t>(sycl_device);
+ test_reshape_as_lvalue<DataType, ColMajor, int64_t>(sycl_device);
+ test_strided_slice_write_sycl<DataType, ColMajor, int64_t>(sycl_device);
+ test_strided_slice_write_sycl<DataType, RowMajor, int64_t>(sycl_device);
+ test_strided_slice_as_rhs_sycl<DataType, ColMajor, int64_t>(sycl_device);
+ test_strided_slice_as_rhs_sycl<DataType, RowMajor, int64_t>(sycl_device);
+ run_eigen<float, RowMajor, long, int>(sycl_device);
+}
+EIGEN_DECLARE_TEST(cxx11_tensor_morphing_sycl)
+{
+ for (const auto& device :Eigen::get_sycl_supported_devices()) {
+ CALL_SUBTEST(sycl_morphing_test_per_device<float>(device));
+ }
+}
diff --git a/unsupported/test/cxx11_tensor_move.cpp b/unsupported/test/cxx11_tensor_move.cpp
new file mode 100644
index 0000000..a298231
--- /dev/null
+++ b/unsupported/test/cxx11_tensor_move.cpp
@@ -0,0 +1,76 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2017 Viktor Csomor <viktor.csomor@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "main.h"
+
+#include <Eigen/CXX11/Tensor>
+#include <utility>
+
+using Eigen::Tensor;
+using Eigen::RowMajor;
+
+static void calc_indices(int i, int& x, int& y, int& z)
+{
+ x = i / 4;
+ y = (i % 4) / 2;
+ z = i % 2;
+}
+
+static void test_move()
+{
+ int x;
+ int y;
+ int z;
+
+ Tensor<int,3> tensor1(2, 2, 2);
+ Tensor<int,3,RowMajor> tensor2(2, 2, 2);
+
+ for (int i = 0; i < 8; i++)
+ {
+ calc_indices(i, x, y, z);
+ tensor1(x,y,z) = i;
+ tensor2(x,y,z) = 2 * i;
+ }
+
+ // Invokes the move constructor.
+ Tensor<int,3> moved_tensor1 = std::move(tensor1);
+ Tensor<int,3,RowMajor> moved_tensor2 = std::move(tensor2);
+
+ VERIFY_IS_EQUAL(tensor1.size(), 0);
+ VERIFY_IS_EQUAL(tensor2.size(), 0);
+
+ for (int i = 0; i < 8; i++)
+ {
+ calc_indices(i, x, y, z);
+ VERIFY_IS_EQUAL(moved_tensor1(x,y,z), i);
+ VERIFY_IS_EQUAL(moved_tensor2(x,y,z), 2 * i);
+ }
+
+ Tensor<int,3> moved_tensor3(2,2,2);
+ Tensor<int,3,RowMajor> moved_tensor4(2,2,2);
+
+ moved_tensor3.setZero();
+ moved_tensor4.setZero();
+
+ // Invokes the move assignment operator.
+ moved_tensor3 = std::move(moved_tensor1);
+ moved_tensor4 = std::move(moved_tensor2);
+
+ for (int i = 0; i < 8; i++)
+ {
+ calc_indices(i, x, y, z);
+ VERIFY_IS_EQUAL(moved_tensor3(x,y,z), i);
+ VERIFY_IS_EQUAL(moved_tensor4(x,y,z), 2 * i);
+ }
+}
+
+EIGEN_DECLARE_TEST(cxx11_tensor_move)
+{
+ CALL_SUBTEST(test_move());
+}
diff --git a/unsupported/test/cxx11_tensor_notification.cpp b/unsupported/test/cxx11_tensor_notification.cpp
new file mode 100644
index 0000000..8e81653
--- /dev/null
+++ b/unsupported/test/cxx11_tensor_notification.cpp
@@ -0,0 +1,64 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2015 Vijay Vasudevan <vrv@google.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#define EIGEN_USE_THREADS
+
+#include <atomic>
+
+#include <stdlib.h>
+#include "main.h"
+#include <Eigen/CXX11/Tensor>
+
+static void test_notification_single()
+{
+ ThreadPool thread_pool(1);
+
+ std::atomic<int> counter(0);
+ Eigen::Notification n;
+ auto func = [&n, &counter](){ n.Wait(); ++counter;};
+ thread_pool.Schedule(func);
+ std::this_thread::sleep_for(std::chrono::milliseconds(1000));
+
+ // The thread should be waiting for the notification.
+ VERIFY_IS_EQUAL(counter, 0);
+
+ // Unblock the thread
+ n.Notify();
+
+ std::this_thread::sleep_for(std::chrono::milliseconds(1000));
+
+ // Verify the counter has been incremented
+ VERIFY_IS_EQUAL(counter, 1);
+}
+
+// Like test_notification_single() but enqueues multiple threads to
+// validate that all threads get notified by Notify().
+static void test_notification_multiple()
+{
+ ThreadPool thread_pool(1);
+
+ std::atomic<int> counter(0);
+ Eigen::Notification n;
+ auto func = [&n, &counter](){ n.Wait(); ++counter;};
+ thread_pool.Schedule(func);
+ thread_pool.Schedule(func);
+ thread_pool.Schedule(func);
+ thread_pool.Schedule(func);
+ std::this_thread::sleep_for(std::chrono::milliseconds(1000));
+ VERIFY_IS_EQUAL(counter, 0);
+ n.Notify();
+ std::this_thread::sleep_for(std::chrono::milliseconds(1000));
+ VERIFY_IS_EQUAL(counter, 4);
+}
+
+EIGEN_DECLARE_TEST(cxx11_tensor_notification)
+{
+ CALL_SUBTEST(test_notification_single());
+ CALL_SUBTEST(test_notification_multiple());
+}
diff --git a/unsupported/test/cxx11_tensor_of_bfloat16_gpu.cu b/unsupported/test/cxx11_tensor_of_bfloat16_gpu.cu
new file mode 100644
index 0000000..10498e6
--- /dev/null
+++ b/unsupported/test/cxx11_tensor_of_bfloat16_gpu.cu
@@ -0,0 +1,487 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2021 Rohit Santhanam <rohit.santhanam@amd.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#define EIGEN_TEST_NO_LONGDOUBLE
+#define EIGEN_TEST_NO_COMPLEX
+
+#define EIGEN_DEFAULT_DENSE_INDEX_TYPE int
+#define EIGEN_USE_GPU
+
+#include "main.h"
+#include <unsupported/Eigen/CXX11/Tensor>
+
+
+using Eigen::Tensor;
+
+template<typename>
+void test_gpu_numext() {
+ Eigen::GpuStreamDevice stream;
+ Eigen::GpuDevice gpu_device(&stream);
+ int num_elem = 101;
+
+ float* d_float = (float*)gpu_device.allocate(num_elem * sizeof(float));
+ bool* d_res_bfloat16 = (bool*)gpu_device.allocate(num_elem * sizeof(bool));
+ bool* d_res_float = (bool*)gpu_device.allocate(num_elem * sizeof(bool));
+
+ Eigen::TensorMap<Eigen::Tensor<float, 1>, Eigen::Aligned> gpu_float(
+ d_float, num_elem);
+ Eigen::TensorMap<Eigen::Tensor<bool, 1>, Eigen::Aligned> gpu_res_bfloat16(
+ d_res_bfloat16, num_elem);
+ Eigen::TensorMap<Eigen::Tensor<bool, 1>, Eigen::Aligned> gpu_res_float(
+ d_res_float, num_elem);
+
+ gpu_float.device(gpu_device) = gpu_float.random() - gpu_float.constant(0.5f);
+ gpu_res_float.device(gpu_device) = gpu_float.unaryExpr(Eigen::internal::scalar_isnan_op<float>());
+ // Test bfloat16 specific isnan op.
+ gpu_res_bfloat16.device(gpu_device) = gpu_float.cast<Eigen::bfloat16>().unaryExpr(Eigen::internal::scalar_isnan_op<Eigen::bfloat16>());
+
+ Tensor<bool, 1> bfloat16_prec(num_elem);
+ Tensor<bool, 1> full_prec(num_elem);
+ gpu_device.memcpyDeviceToHost(bfloat16_prec.data(), d_res_bfloat16, num_elem*sizeof(bool));
+ gpu_device.memcpyDeviceToHost(full_prec.data(), d_res_float, num_elem*sizeof(bool));
+ gpu_device.synchronize();
+
+ for (int i = 0; i < num_elem; ++i) {
+ VERIFY_IS_EQUAL(full_prec(i), bfloat16_prec(i));
+ }
+
+ gpu_device.deallocate(d_float);
+ gpu_device.deallocate(d_res_bfloat16);
+ gpu_device.deallocate(d_res_float);
+}
+
+
+#ifdef EIGEN_HAS_GPU_BF16
+
+template<typename>
+void test_gpu_conversion() {
+ Eigen::GpuStreamDevice stream;
+ Eigen::GpuDevice gpu_device(&stream);
+ int num_elem = 101;
+
+ float* d_float = (float*)gpu_device.allocate(num_elem * sizeof(float));
+ Eigen::bfloat16* d_bfloat16 = (Eigen::bfloat16*)gpu_device.allocate(num_elem * sizeof(Eigen::bfloat16));
+ float* d_conv = (float*)gpu_device.allocate(num_elem * sizeof(float));
+
+ Eigen::TensorMap<Eigen::Tensor<float, 1>, Eigen::Aligned> gpu_float(
+ d_float, num_elem);
+ Eigen::TensorMap<Eigen::Tensor<Eigen::bfloat16, 1>, Eigen::Aligned> gpu_bfloat16(
+ d_bfloat16, num_elem);
+ Eigen::TensorMap<Eigen::Tensor<float, 1>, Eigen::Aligned> gpu_conv(
+ d_conv, num_elem);
+
+ gpu_float.device(gpu_device) = gpu_float.random();
+ gpu_bfloat16.device(gpu_device) = gpu_float.cast<Eigen::bfloat16>();
+ gpu_conv.device(gpu_device) = gpu_bfloat16.cast<float>();
+
+ Tensor<float, 1> initial(num_elem);
+ Tensor<float, 1> final(num_elem);
+ gpu_device.memcpyDeviceToHost(initial.data(), d_float, num_elem*sizeof(float));
+ gpu_device.memcpyDeviceToHost(final.data(), d_conv, num_elem*sizeof(float));
+
+ for (int i = 0; i < num_elem; ++i) {
+ VERIFY_IS_APPROX(static_cast<Eigen::bfloat16>(initial(i)), static_cast<Eigen::bfloat16>(final(i)));
+ }
+
+ gpu_device.deallocate(d_float);
+ gpu_device.deallocate(d_bfloat16);
+ gpu_device.deallocate(d_conv);
+}
+
+template<typename>
+void test_gpu_unary() {
+ Eigen::GpuStreamDevice stream;
+ Eigen::GpuDevice gpu_device(&stream);
+ int num_elem = 101;
+
+ float* d_float = (float*)gpu_device.allocate(num_elem * sizeof(float));
+ float* d_res_bfloat16 = (float*)gpu_device.allocate(num_elem * sizeof(float));
+ float* d_res_float = (float*)gpu_device.allocate(num_elem * sizeof(float));
+
+ Eigen::TensorMap<Eigen::Tensor<float, 1>, Eigen::Aligned> gpu_float(
+ d_float, num_elem);
+ Eigen::TensorMap<Eigen::Tensor<float, 1>, Eigen::Aligned> gpu_res_bfloat16(
+ d_res_bfloat16, num_elem);
+ Eigen::TensorMap<Eigen::Tensor<float, 1>, Eigen::Aligned> gpu_res_float(
+ d_res_float, num_elem);
+
+ gpu_float.device(gpu_device) = gpu_float.random() - gpu_float.constant(0.5f);
+ gpu_float.device(gpu_device) = gpu_float.cast<Eigen::bfloat16>().cast<float>();
+ gpu_res_float.device(gpu_device) = gpu_float.abs();
+ gpu_res_bfloat16.device(gpu_device) = gpu_float.cast<Eigen::bfloat16>().abs().cast<float>();
+
+ Tensor<float, 1> bfloat16_prec(num_elem);
+ Tensor<float, 1> full_prec(num_elem);
+ gpu_device.memcpyDeviceToHost(bfloat16_prec.data(), d_res_bfloat16, num_elem*sizeof(float));
+ gpu_device.memcpyDeviceToHost(full_prec.data(), d_res_float, num_elem*sizeof(float));
+ gpu_device.synchronize();
+
+ for (int i = 0; i < num_elem; ++i) {
+ VERIFY_IS_APPROX(full_prec(i), bfloat16_prec(i));
+ }
+
+ gpu_device.deallocate(d_float);
+ gpu_device.deallocate(d_res_bfloat16);
+ gpu_device.deallocate(d_res_float);
+}
+
+template<typename>
+void test_gpu_elementwise() {
+ Eigen::GpuStreamDevice stream;
+ Eigen::GpuDevice gpu_device(&stream);
+ int num_elem = 101;
+
+ float* d_float1 = (float*)gpu_device.allocate(num_elem * sizeof(float));
+ float* d_float2 = (float*)gpu_device.allocate(num_elem * sizeof(float));
+ float* d_res_bfloat16 = (float*)gpu_device.allocate(num_elem * sizeof(float));
+ float* d_res_float = (float*)gpu_device.allocate(num_elem * sizeof(float));
+
+ Eigen::TensorMap<Eigen::Tensor<float, 1>, Eigen::Aligned> gpu_float1(
+ d_float1, num_elem);
+ Eigen::TensorMap<Eigen::Tensor<float, 1>, Eigen::Aligned> gpu_float2(
+ d_float2, num_elem);
+ Eigen::TensorMap<Eigen::Tensor<float, 1>, Eigen::Aligned> gpu_res_bfloat16(
+ d_res_bfloat16, num_elem);
+ Eigen::TensorMap<Eigen::Tensor<float, 1>, Eigen::Aligned> gpu_res_float(
+ d_res_float, num_elem);
+
+ gpu_float1.device(gpu_device) = gpu_float1.random();
+ gpu_float1.device(gpu_device) = gpu_float1.cast<Eigen::bfloat16>().cast<float>();
+ gpu_float2.device(gpu_device) = gpu_float2.random();
+ gpu_float2.device(gpu_device) = gpu_float2.cast<Eigen::bfloat16>().cast<float>();
+ gpu_res_float.device(gpu_device) = (gpu_float1 + gpu_float2) * gpu_float1;
+ gpu_res_bfloat16.device(gpu_device) = ((gpu_float1.cast<Eigen::bfloat16>() + gpu_float2.cast<Eigen::bfloat16>()) * gpu_float1.cast<Eigen::bfloat16>()).cast<float>();
+
+ Tensor<float, 1> bfloat16_prec(num_elem);
+ Tensor<float, 1> full_prec(num_elem);
+ gpu_device.memcpyDeviceToHost(bfloat16_prec.data(), d_res_bfloat16, num_elem*sizeof(float));
+ gpu_device.memcpyDeviceToHost(full_prec.data(), d_res_float, num_elem*sizeof(float));
+ gpu_device.synchronize();
+
+ for (int i = 0; i < num_elem; ++i) {
+ VERIFY_IS_APPROX(static_cast<Eigen::bfloat16>(full_prec(i)), static_cast<Eigen::bfloat16>(bfloat16_prec(i)));
+ }
+
+ gpu_device.deallocate(d_float1);
+ gpu_device.deallocate(d_float2);
+ gpu_device.deallocate(d_res_bfloat16);
+ gpu_device.deallocate(d_res_float);
+}
+
+template<typename>
+void test_gpu_trancendental() {
+ Eigen::GpuStreamDevice stream;
+ Eigen::GpuDevice gpu_device(&stream);
+ int num_elem = 101;
+
+ float* d_float1 = (float*)gpu_device.allocate(num_elem * sizeof(float));
+ float* d_float2 = (float*)gpu_device.allocate(num_elem * sizeof(float));
+ float* d_float3 = (float*)gpu_device.allocate(num_elem * sizeof(float));
+ Eigen::bfloat16* d_res1_bfloat16 = (Eigen::bfloat16*)gpu_device.allocate(num_elem * sizeof(Eigen::bfloat16));
+ Eigen::bfloat16* d_res1_float = (Eigen::bfloat16*)gpu_device.allocate(num_elem * sizeof(Eigen::bfloat16));
+ Eigen::bfloat16* d_res2_bfloat16 = (Eigen::bfloat16*)gpu_device.allocate(num_elem * sizeof(Eigen::bfloat16));
+ Eigen::bfloat16* d_res2_float = (Eigen::bfloat16*)gpu_device.allocate(num_elem * sizeof(Eigen::bfloat16));
+ Eigen::bfloat16* d_res3_bfloat16 = (Eigen::bfloat16*)gpu_device.allocate(num_elem * sizeof(Eigen::bfloat16));
+ Eigen::bfloat16* d_res3_float = (Eigen::bfloat16*)gpu_device.allocate(num_elem * sizeof(Eigen::bfloat16));
+
+ Eigen::TensorMap<Eigen::Tensor<float, 1>, Eigen::Aligned> gpu_float1(d_float1, num_elem);
+ Eigen::TensorMap<Eigen::Tensor<float, 1>, Eigen::Aligned> gpu_float2(d_float2, num_elem);
+ Eigen::TensorMap<Eigen::Tensor<float, 1>, Eigen::Aligned> gpu_float3(d_float3, num_elem);
+ Eigen::TensorMap<Eigen::Tensor<Eigen::bfloat16, 1>, Eigen::Aligned> gpu_res1_bfloat16(d_res1_bfloat16, num_elem);
+ Eigen::TensorMap<Eigen::Tensor<Eigen::bfloat16, 1>, Eigen::Aligned> gpu_res1_float(d_res1_float, num_elem);
+ Eigen::TensorMap<Eigen::Tensor<Eigen::bfloat16, 1>, Eigen::Aligned> gpu_res2_bfloat16(d_res2_bfloat16, num_elem);
+ Eigen::TensorMap<Eigen::Tensor<Eigen::bfloat16, 1>, Eigen::Aligned> gpu_res2_float(d_res2_float, num_elem);
+ Eigen::TensorMap<Eigen::Tensor<Eigen::bfloat16, 1>, Eigen::Aligned> gpu_res3_bfloat16(d_res3_bfloat16, num_elem);
+ Eigen::TensorMap<Eigen::Tensor<Eigen::bfloat16, 1>, Eigen::Aligned> gpu_res3_float(d_res3_float, num_elem);
+ Eigen::TensorMap<Eigen::Tensor<Eigen::bfloat16, 1>, Eigen::Aligned> gpu_res4_bfloat16(d_res3_bfloat16, num_elem);
+ Eigen::TensorMap<Eigen::Tensor<Eigen::bfloat16, 1>, Eigen::Aligned> gpu_res4_float(d_res3_float, num_elem);
+
+ gpu_float1.device(gpu_device) = gpu_float1.random() - gpu_float1.constant(0.5f);
+ gpu_float1.device(gpu_device) = gpu_float1.cast<Eigen::bfloat16>().cast<float>();
+ gpu_float2.device(gpu_device) = gpu_float2.random() + gpu_float1.constant(0.5f);
+ gpu_float2.device(gpu_device) = gpu_float2.cast<Eigen::bfloat16>().cast<float>();
+ gpu_float3.device(gpu_device) = gpu_float3.random();
+ gpu_float3.device(gpu_device) = gpu_float3.cast<Eigen::bfloat16>().cast<float>();
+ gpu_res1_float.device(gpu_device) = gpu_float1.exp().cast<Eigen::bfloat16>();
+ gpu_res2_float.device(gpu_device) = gpu_float2.log().cast<Eigen::bfloat16>();
+ gpu_res3_float.device(gpu_device) = gpu_float3.log1p().cast<Eigen::bfloat16>();
+ gpu_res4_float.device(gpu_device) = gpu_float3.expm1().cast<Eigen::bfloat16>();
+
+ gpu_res1_bfloat16.device(gpu_device) = gpu_float1.cast<Eigen::bfloat16>();
+ gpu_res1_bfloat16.device(gpu_device) = gpu_res1_bfloat16.exp();
+
+ gpu_res2_bfloat16.device(gpu_device) = gpu_float2.cast<Eigen::bfloat16>();
+ gpu_res2_bfloat16.device(gpu_device) = gpu_res2_bfloat16.log();
+
+ gpu_res3_bfloat16.device(gpu_device) = gpu_float3.cast<Eigen::bfloat16>();
+ gpu_res3_bfloat16.device(gpu_device) = gpu_res3_bfloat16.log1p();
+
+ gpu_res3_bfloat16.device(gpu_device) = gpu_float3.cast<Eigen::bfloat16>();
+ gpu_res3_bfloat16.device(gpu_device) = gpu_res3_bfloat16.expm1();
+
+ Tensor<float, 1> input1(num_elem);
+ Tensor<Eigen::bfloat16, 1> bfloat16_prec1(num_elem);
+ Tensor<Eigen::bfloat16, 1> full_prec1(num_elem);
+ Tensor<float, 1> input2(num_elem);
+ Tensor<Eigen::bfloat16, 1> bfloat16_prec2(num_elem);
+ Tensor<Eigen::bfloat16, 1> full_prec2(num_elem);
+ Tensor<float, 1> input3(num_elem);
+ Tensor<Eigen::bfloat16, 1> bfloat16_prec3(num_elem);
+ Tensor<Eigen::bfloat16, 1> full_prec3(num_elem);
+ gpu_device.memcpyDeviceToHost(input1.data(), d_float1, num_elem*sizeof(float));
+ gpu_device.memcpyDeviceToHost(input2.data(), d_float2, num_elem*sizeof(float));
+ gpu_device.memcpyDeviceToHost(input3.data(), d_float3, num_elem*sizeof(float));
+ gpu_device.memcpyDeviceToHost(bfloat16_prec1.data(), d_res1_bfloat16, num_elem*sizeof(Eigen::bfloat16));
+ gpu_device.memcpyDeviceToHost(full_prec1.data(), d_res1_float, num_elem*sizeof(Eigen::bfloat16));
+ gpu_device.memcpyDeviceToHost(bfloat16_prec2.data(), d_res2_bfloat16, num_elem*sizeof(Eigen::bfloat16));
+ gpu_device.memcpyDeviceToHost(full_prec2.data(), d_res2_float, num_elem*sizeof(Eigen::bfloat16));
+ gpu_device.memcpyDeviceToHost(bfloat16_prec3.data(), d_res3_bfloat16, num_elem*sizeof(Eigen::bfloat16));
+ gpu_device.memcpyDeviceToHost(full_prec3.data(), d_res3_float, num_elem*sizeof(Eigen::bfloat16));
+ gpu_device.synchronize();
+
+ for (int i = 0; i < num_elem; ++i) {
+ VERIFY_IS_APPROX(full_prec1(i), bfloat16_prec1(i));
+ }
+ for (int i = 0; i < num_elem; ++i) {
+ if(std::abs(input2(i)-1.f)<0.05f) // log lacks accuracy nearby 1
+ VERIFY_IS_APPROX(full_prec2(i)+Eigen::bfloat16(0.1f), bfloat16_prec2(i)+Eigen::bfloat16(0.1f));
+ else
+ VERIFY_IS_APPROX(full_prec2(i), bfloat16_prec2(i));
+ }
+ for (int i = 0; i < num_elem; ++i) {
+ VERIFY_IS_APPROX(full_prec3(i), bfloat16_prec3(i));
+ }
+ gpu_device.deallocate(d_float1);
+ gpu_device.deallocate(d_float2);
+ gpu_device.deallocate(d_float3);
+ gpu_device.deallocate(d_res1_bfloat16);
+ gpu_device.deallocate(d_res1_float);
+ gpu_device.deallocate(d_res2_bfloat16);
+ gpu_device.deallocate(d_res2_float);
+ gpu_device.deallocate(d_res3_float);
+ gpu_device.deallocate(d_res3_bfloat16);
+}
+
+template<typename>
+void test_gpu_contractions() {
+ Eigen::GpuStreamDevice stream;
+ Eigen::GpuDevice gpu_device(&stream);
+ int rows = 23;
+ int cols = 23;
+ int num_elem = rows*cols;
+
+ float* d_float1 = (float*)gpu_device.allocate(num_elem * sizeof(float));
+ float* d_float2 = (float*)gpu_device.allocate(num_elem * sizeof(float));
+ Eigen::bfloat16* d_res_bfloat16 = (Eigen::bfloat16*)gpu_device.allocate(num_elem * sizeof(Eigen::bfloat16));
+ Eigen::bfloat16* d_res_float = (Eigen::bfloat16*)gpu_device.allocate(num_elem * sizeof(Eigen::bfloat16));
+
+ Eigen::TensorMap<Eigen::Tensor<float, 2>, Eigen::Aligned> gpu_float1(
+ d_float1, rows, cols);
+ Eigen::TensorMap<Eigen::Tensor<float, 2>, Eigen::Aligned> gpu_float2(
+ d_float2, rows, cols);
+ Eigen::TensorMap<Eigen::Tensor<Eigen::bfloat16, 2>, Eigen::Aligned> gpu_res_bfloat16(
+ d_res_bfloat16, rows, cols);
+ Eigen::TensorMap<Eigen::Tensor<Eigen::bfloat16, 2>, Eigen::Aligned> gpu_res_float(
+ d_res_float, rows, cols);
+
+ gpu_float1.device(gpu_device) = gpu_float1.random() - gpu_float1.constant(0.5f);
+ gpu_float2.device(gpu_device) = gpu_float2.random() - gpu_float2.constant(0.5f);
+
+ typedef Tensor<float, 2>::DimensionPair DimPair;
+ Eigen::array<DimPair, 1> dims(DimPair(1, 0));
+ gpu_res_float.device(gpu_device) = gpu_float1.contract(gpu_float2, dims).cast<Eigen::bfloat16>();
+ gpu_res_bfloat16.device(gpu_device) = gpu_float1.cast<Eigen::bfloat16>().contract(gpu_float2.cast<Eigen::bfloat16>(), dims);
+
+ Tensor<Eigen::bfloat16, 2> bfloat16_prec(rows, cols);
+ Tensor<Eigen::bfloat16, 2> full_prec(rows, cols);
+ gpu_device.memcpyDeviceToHost(bfloat16_prec.data(), d_res_bfloat16, num_elem*sizeof(Eigen::bfloat16));
+ gpu_device.memcpyDeviceToHost(full_prec.data(), d_res_float, num_elem*sizeof(Eigen::bfloat16));
+ gpu_device.synchronize();
+
+ for (int i = 0; i < rows; ++i) {
+ for (int j = 0; j < cols; ++j) {
+ if (numext::abs(full_prec(i, j) - bfloat16_prec(i, j)) > Eigen::bfloat16(1e-2f)) {
+ VERIFY_IS_APPROX(full_prec(i, j), bfloat16_prec(i, j));
+ }
+ }
+ }
+
+ gpu_device.deallocate(d_float1);
+ gpu_device.deallocate(d_float2);
+ gpu_device.deallocate(d_res_bfloat16);
+ gpu_device.deallocate(d_res_float);
+}
+
+template<typename>
+void test_gpu_reductions(int size1, int size2, int redux) {
+ Eigen::GpuStreamDevice stream;
+ Eigen::GpuDevice gpu_device(&stream);
+ int num_elem = size1*size2;
+ int result_size = (redux == 1 ? size1 : size2);
+
+ float* d_float = (float*)gpu_device.allocate(num_elem * sizeof(float));
+ Eigen::bfloat16* d_res_bfloat16 = (Eigen::bfloat16*)gpu_device.allocate(result_size * sizeof(Eigen::bfloat16));
+ Eigen::bfloat16* d_res_float = (Eigen::bfloat16*)gpu_device.allocate(result_size * sizeof(Eigen::bfloat16));
+
+ Eigen::TensorMap<Eigen::Tensor<float, 2>, Eigen::Aligned> gpu_float(
+ d_float, size1, size2);
+ Eigen::TensorMap<Eigen::Tensor<Eigen::bfloat16, 1>, Eigen::Aligned> gpu_res_bfloat16(
+ d_res_bfloat16, result_size);
+ Eigen::TensorMap<Eigen::Tensor<Eigen::bfloat16, 1>, Eigen::Aligned> gpu_res_float(
+ d_res_float, result_size);
+
+ gpu_float.device(gpu_device) = gpu_float.random() * 2.0f;
+
+ Eigen::array<int, 1> redux_dim = {redux};
+ gpu_res_float.device(gpu_device) = gpu_float.sum(redux_dim).cast<Eigen::bfloat16>();
+ gpu_res_bfloat16.device(gpu_device) = gpu_float.cast<Eigen::bfloat16>().sum(redux_dim);
+
+ Tensor<Eigen::bfloat16, 1> bfloat16_prec(result_size);
+ Tensor<Eigen::bfloat16, 1> full_prec(result_size);
+ gpu_device.memcpyDeviceToHost(bfloat16_prec.data(), d_res_bfloat16, result_size*sizeof(Eigen::bfloat16));
+ gpu_device.memcpyDeviceToHost(full_prec.data(), d_res_float, result_size*sizeof(Eigen::bfloat16));
+ gpu_device.synchronize();
+
+ for (int i = 0; i < result_size; ++i) {
+ VERIFY_IS_APPROX(full_prec(i), bfloat16_prec(i));
+ }
+
+ gpu_device.deallocate(d_float);
+ gpu_device.deallocate(d_res_bfloat16);
+ gpu_device.deallocate(d_res_float);
+}
+
+template<typename>
+void test_gpu_reductions() {
+ test_gpu_reductions<void>(13, 13, 0);
+ test_gpu_reductions<void>(13, 13, 1);
+
+ test_gpu_reductions<void>(35, 36, 0);
+ test_gpu_reductions<void>(35, 36, 1);
+
+ test_gpu_reductions<void>(36, 35, 0);
+ test_gpu_reductions<void>(36, 35, 1);
+}
+
+template<typename>
+void test_gpu_full_reductions() {
+ Eigen::GpuStreamDevice stream;
+ Eigen::GpuDevice gpu_device(&stream);
+ int size = 13;
+ int num_elem = size*size;
+
+ float* d_float = (float*)gpu_device.allocate(num_elem * sizeof(float));
+ Eigen::bfloat16* d_res_bfloat16 = (Eigen::bfloat16*)gpu_device.allocate(1 * sizeof(Eigen::bfloat16));
+ Eigen::bfloat16* d_res_float = (Eigen::bfloat16*)gpu_device.allocate(1 * sizeof(Eigen::bfloat16));
+
+ Eigen::TensorMap<Eigen::Tensor<float, 2>, Eigen::Aligned> gpu_float(
+ d_float, size, size);
+ Eigen::TensorMap<Eigen::Tensor<Eigen::bfloat16, 0>, Eigen::Aligned> gpu_res_bfloat16(
+ d_res_bfloat16);
+ Eigen::TensorMap<Eigen::Tensor<Eigen::bfloat16, 0>, Eigen::Aligned> gpu_res_float(
+ d_res_float);
+
+ gpu_float.device(gpu_device) = gpu_float.random();
+
+ gpu_res_float.device(gpu_device) = gpu_float.sum().cast<Eigen::bfloat16>();
+ gpu_res_bfloat16.device(gpu_device) = gpu_float.cast<Eigen::bfloat16>().sum();
+
+ Tensor<Eigen::bfloat16, 0> bfloat16_prec;
+ Tensor<Eigen::bfloat16, 0> full_prec;
+ gpu_device.memcpyDeviceToHost(bfloat16_prec.data(), d_res_bfloat16, sizeof(Eigen::bfloat16));
+ gpu_device.memcpyDeviceToHost(full_prec.data(), d_res_float, sizeof(Eigen::bfloat16));
+ gpu_device.synchronize();
+
+ VERIFY_IS_APPROX(full_prec(), bfloat16_prec());
+
+ gpu_res_float.device(gpu_device) = gpu_float.maximum().cast<Eigen::bfloat16>();
+ gpu_res_bfloat16.device(gpu_device) = gpu_float.cast<Eigen::bfloat16>().maximum();
+ gpu_device.memcpyDeviceToHost(bfloat16_prec.data(), d_res_bfloat16, sizeof(Eigen::bfloat16));
+ gpu_device.memcpyDeviceToHost(full_prec.data(), d_res_float, sizeof(Eigen::bfloat16));
+ gpu_device.synchronize();
+
+ VERIFY_IS_APPROX(full_prec(), bfloat16_prec());
+
+ gpu_device.deallocate(d_float);
+ gpu_device.deallocate(d_res_bfloat16);
+ gpu_device.deallocate(d_res_float);
+}
+
+template<typename>
+void test_gpu_forced_evals() {
+
+ Eigen::GpuStreamDevice stream;
+ Eigen::GpuDevice gpu_device(&stream);
+ int num_elem = 101;
+
+ float* d_float = (float*)gpu_device.allocate(num_elem * sizeof(float));
+ float* d_res_bfloat16_1 = (float*)gpu_device.allocate(num_elem * sizeof(float));
+ float* d_res_bfloat16_2 = (float*)gpu_device.allocate(num_elem * sizeof(float));
+ float* d_res_float = (float*)gpu_device.allocate(num_elem * sizeof(float));
+
+ Eigen::TensorMap<Eigen::Tensor<float, 1>, Eigen::Aligned> gpu_float(
+ d_float, num_elem);
+ Eigen::TensorMap<Eigen::Tensor<float, 1>, Eigen::Aligned> gpu_res_bfloat16_1(
+ d_res_bfloat16_1, num_elem);
+ Eigen::TensorMap<Eigen::Tensor<float, 1>, Eigen::Unaligned> gpu_res_bfloat16_2(
+ d_res_bfloat16_2, num_elem);
+ Eigen::TensorMap<Eigen::Tensor<float, 1>, Eigen::Aligned> gpu_res_float(
+ d_res_float, num_elem);
+
+ Eigen::array<int, 1> no_bcast;
+ no_bcast[0] = 1;
+
+ gpu_float.device(gpu_device) = gpu_float.random() - gpu_float.constant(0.5f);
+ gpu_float.device(gpu_device) = gpu_float.cast<Eigen::bfloat16>().cast<float>();
+ gpu_res_float.device(gpu_device) = gpu_float.abs();
+ gpu_res_bfloat16_1.device(gpu_device) = gpu_float.cast<Eigen::bfloat16>().abs().eval().cast<float>();
+ gpu_res_bfloat16_2.device(gpu_device) = gpu_float.cast<Eigen::bfloat16>().abs().broadcast(no_bcast).eval().cast<float>();
+
+ Tensor<float, 1> bfloat16_prec1(num_elem);
+ Tensor<float, 1> bfloat16_prec2(num_elem);
+ Tensor<float, 1> full_prec(num_elem);
+ gpu_device.memcpyDeviceToHost(bfloat16_prec1.data(), d_res_bfloat16_1, num_elem*sizeof(float));
+ gpu_device.memcpyDeviceToHost(bfloat16_prec2.data(), d_res_bfloat16_2, num_elem*sizeof(float));
+ gpu_device.memcpyDeviceToHost(full_prec.data(), d_res_float, num_elem*sizeof(float));
+ gpu_device.synchronize();
+
+ for (int i = 0; i < num_elem; ++i) {
+ VERIFY_IS_APPROX(full_prec(i), bfloat16_prec1(i));
+ VERIFY_IS_APPROX(full_prec(i), bfloat16_prec2(i));
+ }
+
+ gpu_device.deallocate(d_float);
+ gpu_device.deallocate(d_res_bfloat16_1);
+ gpu_device.deallocate(d_res_bfloat16_2);
+ gpu_device.deallocate(d_res_float);
+}
+
+#endif
+
+EIGEN_DECLARE_TEST(cxx11_tensor_of_bfloat16_gpu)
+{
+ CALL_SUBTEST_1(test_gpu_numext<void>());
+
+// The reduction unit tests have been excluded until a working
+// implementation to expand the accumulator data type to float32
+// is available.
+// TODO: add reduction unit tests
+#ifdef EIGEN_HAS_GPU_BF16
+ CALL_SUBTEST_2(test_gpu_conversion<void>());
+ CALL_SUBTEST_3(test_gpu_unary<void>());
+ CALL_SUBTEST_4(test_gpu_elementwise<void>());
+ CALL_SUBTEST_5(test_gpu_trancendental<void>());
+ CALL_SUBTEST_6(test_gpu_contractions<void>());
+ CALL_SUBTEST_7(test_gpu_reductions<void>());
+ CALL_SUBTEST_8(test_gpu_full_reductions<void>());
+ CALL_SUBTEST_9(test_gpu_forced_evals<void>());
+#else
+ std::cout << "bfloat16 floats are not supported by this version of gpu: skipping the test" << std::endl;
+#endif
+}
diff --git a/unsupported/test/cxx11_tensor_of_complex.cpp b/unsupported/test/cxx11_tensor_of_complex.cpp
new file mode 100644
index 0000000..b2f5994
--- /dev/null
+++ b/unsupported/test/cxx11_tensor_of_complex.cpp
@@ -0,0 +1,118 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "main.h"
+
+#include <Eigen/CXX11/Tensor>
+
+using Eigen::Tensor;
+using Eigen::TensorMap;
+
+
+
+static void test_additions()
+{
+ Tensor<std::complex<float>, 1> data1(3);
+ Tensor<std::complex<float>, 1> data2(3);
+ for (int i = 0; i < 3; ++i) {
+ data1(i) = std::complex<float>(i, -i);
+ data2(i) = std::complex<float>(i, 7 * i);
+ }
+
+ Tensor<std::complex<float>, 1> sum = data1 + data2;
+ for (int i = 0; i < 3; ++i) {
+ VERIFY_IS_EQUAL(sum(i), std::complex<float>(2*i, 6*i));
+ }
+}
+
+
+static void test_abs()
+{
+ Tensor<std::complex<float>, 1> data1(3);
+ Tensor<std::complex<double>, 1> data2(3);
+ data1.setRandom();
+ data2.setRandom();
+
+ Tensor<float, 1> abs1 = data1.abs();
+ Tensor<double, 1> abs2 = data2.abs();
+ for (int i = 0; i < 3; ++i) {
+ VERIFY_IS_APPROX(abs1(i), std::abs(data1(i)));
+ VERIFY_IS_APPROX(abs2(i), std::abs(data2(i)));
+ }
+}
+
+static void test_arg()
+{
+ Tensor<std::complex<float>, 1> data1(3);
+ Tensor<std::complex<double>, 1> data2(3);
+ data1.setRandom();
+ data2.setRandom();
+
+ Tensor<float, 1> arg1 = data1.arg();
+ Tensor<double, 1> arg2 = data2.arg();
+ for (int i = 0; i < 3; ++i) {
+ VERIFY_IS_APPROX(arg1(i), std::arg(data1(i)));
+ VERIFY_IS_APPROX(arg2(i), std::arg(data2(i)));
+ }
+}
+
+static void test_conjugate()
+{
+ Tensor<std::complex<float>, 1> data1(3);
+ Tensor<std::complex<double>, 1> data2(3);
+ Tensor<int, 1> data3(3);
+ data1.setRandom();
+ data2.setRandom();
+ data3.setRandom();
+
+ Tensor<std::complex<float>, 1> conj1 = data1.conjugate();
+ Tensor<std::complex<double>, 1> conj2 = data2.conjugate();
+ Tensor<int, 1> conj3 = data3.conjugate();
+ for (int i = 0; i < 3; ++i) {
+ VERIFY_IS_APPROX(conj1(i), std::conj(data1(i)));
+ VERIFY_IS_APPROX(conj2(i), std::conj(data2(i)));
+ VERIFY_IS_APPROX(conj3(i), data3(i));
+ }
+}
+
+static void test_contractions()
+{
+ Tensor<std::complex<float>, 4> t_left(30, 50, 8, 31);
+ Tensor<std::complex<float>, 5> t_right(8, 31, 7, 20, 10);
+ Tensor<std::complex<float>, 5> t_result(30, 50, 7, 20, 10);
+
+ t_left.setRandom();
+ t_right.setRandom();
+
+ typedef Map<Matrix<std::complex<float>, Dynamic, Dynamic>> MapXcf;
+ MapXcf m_left(t_left.data(), 1500, 248);
+ MapXcf m_right(t_right.data(), 248, 1400);
+ Matrix<std::complex<float>, Dynamic, Dynamic> m_result(1500, 1400);
+
+ // This contraction should be equivalent to a regular matrix multiplication
+ typedef Tensor<float, 1>::DimensionPair DimPair;
+ Eigen::array<DimPair, 2> dims;
+ dims[0] = DimPair(2, 0);
+ dims[1] = DimPair(3, 1);
+ t_result = t_left.contract(t_right, dims);
+ m_result = m_left * m_right;
+ for (int i = 0; i < t_result.dimensions().TotalSize(); i++) {
+ VERIFY_IS_APPROX(t_result.data()[i], m_result.data()[i]);
+ }
+}
+
+
+EIGEN_DECLARE_TEST(cxx11_tensor_of_complex)
+{
+ CALL_SUBTEST(test_additions());
+ CALL_SUBTEST(test_abs());
+ CALL_SUBTEST(test_arg());
+ CALL_SUBTEST(test_conjugate());
+ CALL_SUBTEST(test_contractions());
+}
diff --git a/unsupported/test/cxx11_tensor_of_const_values.cpp b/unsupported/test/cxx11_tensor_of_const_values.cpp
new file mode 100644
index 0000000..344d678
--- /dev/null
+++ b/unsupported/test/cxx11_tensor_of_const_values.cpp
@@ -0,0 +1,105 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "main.h"
+
+#include <Eigen/CXX11/Tensor>
+
+using Eigen::Tensor;
+using Eigen::RowMajor;
+
+static void test_assign()
+{
+ float data1[6];
+ TensorMap<Tensor<const float, 2>> mat1(data1, 2, 3);
+ float data2[6];
+ const TensorMap<Tensor<float, 2>> mat2(data2, 2, 3);
+
+ for (int i = 0; i < 6; ++i) {
+ data1[i] = i;
+ data2[i] = -i;
+ }
+
+ Tensor<float, 2> rslt1;
+ rslt1 = mat1;
+ Tensor<float, 2> rslt2;
+ rslt2 = mat2;
+
+ Tensor<float, 2> rslt3 = mat1;
+ Tensor<float, 2> rslt4 = mat2;
+
+ Tensor<float, 2> rslt5(mat1);
+ Tensor<float, 2> rslt6(mat2);
+
+ for (int i = 0; i < 2; ++i) {
+ for (int j = 0; j < 3; ++j) {
+ VERIFY_IS_APPROX(rslt1(i,j), static_cast<float>(i + 2*j));
+ VERIFY_IS_APPROX(rslt2(i,j), static_cast<float>(-i - 2*j));
+ VERIFY_IS_APPROX(rslt3(i,j), static_cast<float>(i + 2*j));
+ VERIFY_IS_APPROX(rslt4(i,j), static_cast<float>(-i - 2*j));
+ VERIFY_IS_APPROX(rslt5(i,j), static_cast<float>(i + 2*j));
+ VERIFY_IS_APPROX(rslt6(i,j), static_cast<float>(-i - 2*j));
+ }
+ }
+}
+
+
+static void test_plus()
+{
+ float data1[6];
+ TensorMap<Tensor<const float, 2>> mat1(data1, 2, 3);
+ float data2[6];
+ TensorMap<Tensor<float, 2>> mat2(data2, 2, 3);
+
+ for (int i = 0; i < 6; ++i) {
+ data1[i] = i;
+ data2[i] = -i;
+ }
+
+ Tensor<float, 2> sum1;
+ sum1 = mat1 + mat2;
+ Tensor<float, 2> sum2;
+ sum2 = mat2 + mat1;
+
+ for (int i = 0; i < 2; ++i) {
+ for (int j = 0; j < 3; ++j) {
+ VERIFY_IS_APPROX(sum1(i,j), 0.0f);
+ VERIFY_IS_APPROX(sum2(i,j), 0.0f);
+ }
+ }
+}
+
+
+static void test_plus_equal()
+{
+ float data1[6];
+ TensorMap<Tensor<const float, 2>> mat1(data1, 2, 3);
+ float data2[6];
+ TensorMap<Tensor<float, 2>> mat2(data2, 2, 3);
+
+ for (int i = 0; i < 6; ++i) {
+ data1[i] = i;
+ data2[i] = -i;
+ }
+ mat2 += mat1;
+
+ for (int i = 0; i < 2; ++i) {
+ for (int j = 0; j < 3; ++j) {
+ VERIFY_IS_APPROX(mat2(i,j), 0.0f);
+ }
+ }
+}
+
+
+EIGEN_DECLARE_TEST(cxx11_tensor_of_const_values)
+{
+ CALL_SUBTEST(test_assign());
+ CALL_SUBTEST(test_plus());
+ CALL_SUBTEST(test_plus_equal());
+}
diff --git a/unsupported/test/cxx11_tensor_of_float16_gpu.cu b/unsupported/test/cxx11_tensor_of_float16_gpu.cu
new file mode 100644
index 0000000..30bcc1d
--- /dev/null
+++ b/unsupported/test/cxx11_tensor_of_float16_gpu.cu
@@ -0,0 +1,488 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2016 Benoit Steiner <benoit.steiner.goog@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#define EIGEN_TEST_NO_LONGDOUBLE
+#define EIGEN_TEST_NO_COMPLEX
+
+#define EIGEN_DEFAULT_DENSE_INDEX_TYPE int
+#define EIGEN_USE_GPU
+
+#include "main.h"
+#include <unsupported/Eigen/CXX11/Tensor>
+
+
+using Eigen::Tensor;
+
+template<typename>
+void test_gpu_numext() {
+ Eigen::GpuStreamDevice stream;
+ Eigen::GpuDevice gpu_device(&stream);
+ int num_elem = 101;
+
+ float* d_float = (float*)gpu_device.allocate(num_elem * sizeof(float));
+ bool* d_res_half = (bool*)gpu_device.allocate(num_elem * sizeof(bool));
+ bool* d_res_float = (bool*)gpu_device.allocate(num_elem * sizeof(bool));
+
+ Eigen::TensorMap<Eigen::Tensor<float, 1>, Eigen::Aligned> gpu_float(
+ d_float, num_elem);
+ Eigen::TensorMap<Eigen::Tensor<bool, 1>, Eigen::Aligned> gpu_res_half(
+ d_res_half, num_elem);
+ Eigen::TensorMap<Eigen::Tensor<bool, 1>, Eigen::Aligned> gpu_res_float(
+ d_res_float, num_elem);
+
+ gpu_float.device(gpu_device) = gpu_float.random() - gpu_float.constant(0.5f);
+ gpu_res_float.device(gpu_device) = gpu_float.unaryExpr(Eigen::internal::scalar_isnan_op<float>());
+ gpu_res_half.device(gpu_device) = gpu_float.cast<Eigen::half>().unaryExpr(Eigen::internal::scalar_isnan_op<Eigen::half>());
+
+ Tensor<bool, 1> half_prec(num_elem);
+ Tensor<bool, 1> full_prec(num_elem);
+ gpu_device.memcpyDeviceToHost(half_prec.data(), d_res_half, num_elem*sizeof(bool));
+ gpu_device.memcpyDeviceToHost(full_prec.data(), d_res_float, num_elem*sizeof(bool));
+ gpu_device.synchronize();
+
+ for (int i = 0; i < num_elem; ++i) {
+ std::cout << "Checking numext " << i << std::endl;
+ VERIFY_IS_EQUAL(full_prec(i), half_prec(i));
+ }
+
+ gpu_device.deallocate(d_float);
+ gpu_device.deallocate(d_res_half);
+ gpu_device.deallocate(d_res_float);
+}
+
+
+#ifdef EIGEN_HAS_GPU_FP16
+
+template<typename>
+void test_gpu_conversion() {
+ Eigen::GpuStreamDevice stream;
+ Eigen::GpuDevice gpu_device(&stream);
+ int num_elem = 101;
+
+ float* d_float = (float*)gpu_device.allocate(num_elem * sizeof(float));
+ Eigen::half* d_half = (Eigen::half*)gpu_device.allocate(num_elem * sizeof(Eigen::half));
+ float* d_conv = (float*)gpu_device.allocate(num_elem * sizeof(float));
+
+ Eigen::TensorMap<Eigen::Tensor<float, 1>, Eigen::Aligned> gpu_float(
+ d_float, num_elem);
+ Eigen::TensorMap<Eigen::Tensor<Eigen::half, 1>, Eigen::Aligned> gpu_half(
+ d_half, num_elem);
+ Eigen::TensorMap<Eigen::Tensor<float, 1>, Eigen::Aligned> gpu_conv(
+ d_conv, num_elem);
+
+ gpu_float.device(gpu_device) = gpu_float.random();
+ gpu_half.device(gpu_device) = gpu_float.cast<Eigen::half>();
+ gpu_conv.device(gpu_device) = gpu_half.cast<float>();
+
+ Tensor<float, 1> initial(num_elem);
+ Tensor<float, 1> final(num_elem);
+ gpu_device.memcpyDeviceToHost(initial.data(), d_float, num_elem*sizeof(float));
+ gpu_device.memcpyDeviceToHost(final.data(), d_conv, num_elem*sizeof(float));
+
+ for (int i = 0; i < num_elem; ++i) {
+ VERIFY_IS_APPROX(initial(i), final(i));
+ }
+
+ gpu_device.deallocate(d_float);
+ gpu_device.deallocate(d_half);
+ gpu_device.deallocate(d_conv);
+}
+
+template<typename>
+void test_gpu_unary() {
+ Eigen::GpuStreamDevice stream;
+ Eigen::GpuDevice gpu_device(&stream);
+ int num_elem = 101;
+
+ float* d_float = (float*)gpu_device.allocate(num_elem * sizeof(float));
+ float* d_res_half = (float*)gpu_device.allocate(num_elem * sizeof(float));
+ float* d_res_float = (float*)gpu_device.allocate(num_elem * sizeof(float));
+
+ Eigen::TensorMap<Eigen::Tensor<float, 1>, Eigen::Aligned> gpu_float(
+ d_float, num_elem);
+ Eigen::TensorMap<Eigen::Tensor<float, 1>, Eigen::Aligned> gpu_res_half(
+ d_res_half, num_elem);
+ Eigen::TensorMap<Eigen::Tensor<float, 1>, Eigen::Aligned> gpu_res_float(
+ d_res_float, num_elem);
+
+ gpu_float.device(gpu_device) = gpu_float.random() - gpu_float.constant(0.5f);
+ gpu_res_float.device(gpu_device) = gpu_float.abs();
+ gpu_res_half.device(gpu_device) = gpu_float.cast<Eigen::half>().abs().cast<float>();
+
+ Tensor<float, 1> half_prec(num_elem);
+ Tensor<float, 1> full_prec(num_elem);
+ gpu_device.memcpyDeviceToHost(half_prec.data(), d_res_half, num_elem*sizeof(float));
+ gpu_device.memcpyDeviceToHost(full_prec.data(), d_res_float, num_elem*sizeof(float));
+ gpu_device.synchronize();
+
+ for (int i = 0; i < num_elem; ++i) {
+ std::cout << "Checking unary " << i << std::endl;
+ VERIFY_IS_APPROX(full_prec(i), half_prec(i));
+ }
+
+ gpu_device.deallocate(d_float);
+ gpu_device.deallocate(d_res_half);
+ gpu_device.deallocate(d_res_float);
+}
+
+template<typename>
+void test_gpu_elementwise() {
+ Eigen::GpuStreamDevice stream;
+ Eigen::GpuDevice gpu_device(&stream);
+ int num_elem = 101;
+
+ float* d_float1 = (float*)gpu_device.allocate(num_elem * sizeof(float));
+ float* d_float2 = (float*)gpu_device.allocate(num_elem * sizeof(float));
+ float* d_res_half = (float*)gpu_device.allocate(num_elem * sizeof(float));
+ float* d_res_float = (float*)gpu_device.allocate(num_elem * sizeof(float));
+
+ Eigen::TensorMap<Eigen::Tensor<float, 1>, Eigen::Aligned> gpu_float1(
+ d_float1, num_elem);
+ Eigen::TensorMap<Eigen::Tensor<float, 1>, Eigen::Aligned> gpu_float2(
+ d_float2, num_elem);
+ Eigen::TensorMap<Eigen::Tensor<float, 1>, Eigen::Aligned> gpu_res_half(
+ d_res_half, num_elem);
+ Eigen::TensorMap<Eigen::Tensor<float, 1>, Eigen::Aligned> gpu_res_float(
+ d_res_float, num_elem);
+
+ gpu_float1.device(gpu_device) = gpu_float1.random();
+ gpu_float2.device(gpu_device) = gpu_float2.random();
+ gpu_res_float.device(gpu_device) = (gpu_float1 + gpu_float2) * gpu_float1;
+ gpu_res_half.device(gpu_device) = ((gpu_float1.cast<Eigen::half>() + gpu_float2.cast<Eigen::half>()) * gpu_float1.cast<Eigen::half>()).cast<float>();
+
+ Tensor<float, 1> half_prec(num_elem);
+ Tensor<float, 1> full_prec(num_elem);
+ gpu_device.memcpyDeviceToHost(half_prec.data(), d_res_half, num_elem*sizeof(float));
+ gpu_device.memcpyDeviceToHost(full_prec.data(), d_res_float, num_elem*sizeof(float));
+ gpu_device.synchronize();
+
+ for (int i = 0; i < num_elem; ++i) {
+ std::cout << "Checking elemwise " << i << ": full prec = " << full_prec(i) << " vs half prec = " << half_prec(i) << std::endl;
+ VERIFY_IS_APPROX(static_cast<Eigen::half>(full_prec(i)), static_cast<Eigen::half>(half_prec(i)));
+ }
+
+ gpu_device.deallocate(d_float1);
+ gpu_device.deallocate(d_float2);
+ gpu_device.deallocate(d_res_half);
+ gpu_device.deallocate(d_res_float);
+}
+
+template<typename>
+void test_gpu_trancendental() {
+ Eigen::GpuStreamDevice stream;
+ Eigen::GpuDevice gpu_device(&stream);
+ int num_elem = 101;
+
+ float* d_float1 = (float*)gpu_device.allocate(num_elem * sizeof(float));
+ float* d_float2 = (float*)gpu_device.allocate(num_elem * sizeof(float));
+ float* d_float3 = (float*)gpu_device.allocate(num_elem * sizeof(float));
+ Eigen::half* d_res1_half = (Eigen::half*)gpu_device.allocate(num_elem * sizeof(Eigen::half));
+ Eigen::half* d_res1_float = (Eigen::half*)gpu_device.allocate(num_elem * sizeof(Eigen::half));
+ Eigen::half* d_res2_half = (Eigen::half*)gpu_device.allocate(num_elem * sizeof(Eigen::half));
+ Eigen::half* d_res2_float = (Eigen::half*)gpu_device.allocate(num_elem * sizeof(Eigen::half));
+ Eigen::half* d_res3_half = (Eigen::half*)gpu_device.allocate(num_elem * sizeof(Eigen::half));
+ Eigen::half* d_res3_float = (Eigen::half*)gpu_device.allocate(num_elem * sizeof(Eigen::half));
+
+ Eigen::TensorMap<Eigen::Tensor<float, 1>, Eigen::Aligned> gpu_float1(d_float1, num_elem);
+ Eigen::TensorMap<Eigen::Tensor<float, 1>, Eigen::Aligned> gpu_float2(d_float2, num_elem);
+ Eigen::TensorMap<Eigen::Tensor<float, 1>, Eigen::Aligned> gpu_float3(d_float3, num_elem);
+ Eigen::TensorMap<Eigen::Tensor<Eigen::half, 1>, Eigen::Aligned> gpu_res1_half(d_res1_half, num_elem);
+ Eigen::TensorMap<Eigen::Tensor<Eigen::half, 1>, Eigen::Aligned> gpu_res1_float(d_res1_float, num_elem);
+ Eigen::TensorMap<Eigen::Tensor<Eigen::half, 1>, Eigen::Aligned> gpu_res2_half(d_res2_half, num_elem);
+ Eigen::TensorMap<Eigen::Tensor<Eigen::half, 1>, Eigen::Aligned> gpu_res2_float(d_res2_float, num_elem);
+ Eigen::TensorMap<Eigen::Tensor<Eigen::half, 1>, Eigen::Aligned> gpu_res3_half(d_res3_half, num_elem);
+ Eigen::TensorMap<Eigen::Tensor<Eigen::half, 1>, Eigen::Aligned> gpu_res3_float(d_res3_float, num_elem);
+ Eigen::TensorMap<Eigen::Tensor<Eigen::half, 1>, Eigen::Aligned> gpu_res4_half(d_res3_half, num_elem);
+ Eigen::TensorMap<Eigen::Tensor<Eigen::half, 1>, Eigen::Aligned> gpu_res4_float(d_res3_float, num_elem);
+
+ gpu_float1.device(gpu_device) = gpu_float1.random() - gpu_float1.constant(0.5f);
+ gpu_float2.device(gpu_device) = gpu_float2.random() + gpu_float1.constant(0.5f);
+ gpu_float3.device(gpu_device) = gpu_float3.random();
+ gpu_res1_float.device(gpu_device) = gpu_float1.exp().cast<Eigen::half>();
+ gpu_res2_float.device(gpu_device) = gpu_float2.log().cast<Eigen::half>();
+ gpu_res3_float.device(gpu_device) = gpu_float3.log1p().cast<Eigen::half>();
+ gpu_res4_float.device(gpu_device) = gpu_float3.expm1().cast<Eigen::half>();
+
+ gpu_res1_half.device(gpu_device) = gpu_float1.cast<Eigen::half>();
+ gpu_res1_half.device(gpu_device) = gpu_res1_half.exp();
+
+ gpu_res2_half.device(gpu_device) = gpu_float2.cast<Eigen::half>();
+ gpu_res2_half.device(gpu_device) = gpu_res2_half.log();
+
+ gpu_res3_half.device(gpu_device) = gpu_float3.cast<Eigen::half>();
+ gpu_res3_half.device(gpu_device) = gpu_res3_half.log1p();
+
+ gpu_res3_half.device(gpu_device) = gpu_float3.cast<Eigen::half>();
+ gpu_res3_half.device(gpu_device) = gpu_res3_half.expm1();
+
+ Tensor<float, 1> input1(num_elem);
+ Tensor<Eigen::half, 1> half_prec1(num_elem);
+ Tensor<Eigen::half, 1> full_prec1(num_elem);
+ Tensor<float, 1> input2(num_elem);
+ Tensor<Eigen::half, 1> half_prec2(num_elem);
+ Tensor<Eigen::half, 1> full_prec2(num_elem);
+ Tensor<float, 1> input3(num_elem);
+ Tensor<Eigen::half, 1> half_prec3(num_elem);
+ Tensor<Eigen::half, 1> full_prec3(num_elem);
+ gpu_device.memcpyDeviceToHost(input1.data(), d_float1, num_elem*sizeof(float));
+ gpu_device.memcpyDeviceToHost(input2.data(), d_float2, num_elem*sizeof(float));
+ gpu_device.memcpyDeviceToHost(input3.data(), d_float3, num_elem*sizeof(float));
+ gpu_device.memcpyDeviceToHost(half_prec1.data(), d_res1_half, num_elem*sizeof(Eigen::half));
+ gpu_device.memcpyDeviceToHost(full_prec1.data(), d_res1_float, num_elem*sizeof(Eigen::half));
+ gpu_device.memcpyDeviceToHost(half_prec2.data(), d_res2_half, num_elem*sizeof(Eigen::half));
+ gpu_device.memcpyDeviceToHost(full_prec2.data(), d_res2_float, num_elem*sizeof(Eigen::half));
+ gpu_device.memcpyDeviceToHost(half_prec3.data(), d_res3_half, num_elem*sizeof(Eigen::half));
+ gpu_device.memcpyDeviceToHost(full_prec3.data(), d_res3_float, num_elem*sizeof(Eigen::half));
+ gpu_device.synchronize();
+
+ for (int i = 0; i < num_elem; ++i) {
+ std::cout << "Checking elemwise exp " << i << " input = " << input1(i) << " full = " << full_prec1(i) << " half = " << half_prec1(i) << std::endl;
+ VERIFY_IS_APPROX(full_prec1(i), half_prec1(i));
+ }
+ for (int i = 0; i < num_elem; ++i) {
+ std::cout << "Checking elemwise log " << i << " input = " << input2(i) << " full = " << full_prec2(i) << " half = " << half_prec2(i) << std::endl;
+ if(std::abs(input2(i)-1.f)<0.05f) // log lacks accuracy nearby 1
+ VERIFY_IS_APPROX(full_prec2(i)+Eigen::half(0.1f), half_prec2(i)+Eigen::half(0.1f));
+ else
+ VERIFY_IS_APPROX(full_prec2(i), half_prec2(i));
+ }
+ for (int i = 0; i < num_elem; ++i) {
+ std::cout << "Checking elemwise plog1 " << i << " input = " << input3(i) << " full = " << full_prec3(i) << " half = " << half_prec3(i) << std::endl;
+ VERIFY_IS_APPROX(full_prec3(i), half_prec3(i));
+ }
+ gpu_device.deallocate(d_float1);
+ gpu_device.deallocate(d_float2);
+ gpu_device.deallocate(d_float3);
+ gpu_device.deallocate(d_res1_half);
+ gpu_device.deallocate(d_res1_float);
+ gpu_device.deallocate(d_res2_half);
+ gpu_device.deallocate(d_res2_float);
+ gpu_device.deallocate(d_res3_float);
+ gpu_device.deallocate(d_res3_half);
+}
+
+template<typename>
+void test_gpu_contractions() {
+ Eigen::GpuStreamDevice stream;
+ Eigen::GpuDevice gpu_device(&stream);
+ int rows = 23;
+ int cols = 23;
+ int num_elem = rows*cols;
+
+ float* d_float1 = (float*)gpu_device.allocate(num_elem * sizeof(float));
+ float* d_float2 = (float*)gpu_device.allocate(num_elem * sizeof(float));
+ Eigen::half* d_res_half = (Eigen::half*)gpu_device.allocate(num_elem * sizeof(Eigen::half));
+ Eigen::half* d_res_float = (Eigen::half*)gpu_device.allocate(num_elem * sizeof(Eigen::half));
+
+ Eigen::TensorMap<Eigen::Tensor<float, 2>, Eigen::Aligned> gpu_float1(
+ d_float1, rows, cols);
+ Eigen::TensorMap<Eigen::Tensor<float, 2>, Eigen::Aligned> gpu_float2(
+ d_float2, rows, cols);
+ Eigen::TensorMap<Eigen::Tensor<Eigen::half, 2>, Eigen::Aligned> gpu_res_half(
+ d_res_half, rows, cols);
+ Eigen::TensorMap<Eigen::Tensor<Eigen::half, 2>, Eigen::Aligned> gpu_res_float(
+ d_res_float, rows, cols);
+
+ gpu_float1.device(gpu_device) = gpu_float1.random() - gpu_float1.constant(0.5f);
+ gpu_float2.device(gpu_device) = gpu_float2.random() - gpu_float2.constant(0.5f);
+
+ typedef Tensor<float, 2>::DimensionPair DimPair;
+ Eigen::array<DimPair, 1> dims(DimPair(1, 0));
+ gpu_res_float.device(gpu_device) = gpu_float1.contract(gpu_float2, dims).cast<Eigen::half>();
+ gpu_res_half.device(gpu_device) = gpu_float1.cast<Eigen::half>().contract(gpu_float2.cast<Eigen::half>(), dims);
+
+ Tensor<Eigen::half, 2> half_prec(rows, cols);
+ Tensor<Eigen::half, 2> full_prec(rows, cols);
+ gpu_device.memcpyDeviceToHost(half_prec.data(), d_res_half, num_elem*sizeof(Eigen::half));
+ gpu_device.memcpyDeviceToHost(full_prec.data(), d_res_float, num_elem*sizeof(Eigen::half));
+ gpu_device.synchronize();
+
+ for (int i = 0; i < rows; ++i) {
+ for (int j = 0; j < cols; ++j) {
+ std::cout << "Checking contract " << i << " " << j << full_prec(i, j) << " " << half_prec(i, j) << std::endl;
+ if (numext::abs(full_prec(i, j) - half_prec(i, j)) > Eigen::half(1e-2f)) {
+ VERIFY_IS_APPROX(full_prec(i, j), half_prec(i, j));
+ }
+ }
+ }
+
+ gpu_device.deallocate(d_float1);
+ gpu_device.deallocate(d_float2);
+ gpu_device.deallocate(d_res_half);
+ gpu_device.deallocate(d_res_float);
+}
+
+template<typename>
+void test_gpu_reductions(int size1, int size2, int redux) {
+
+ std::cout << "Reducing " << size1 << " by " << size2
+ << " tensor along dim " << redux << std::endl;
+
+ Eigen::GpuStreamDevice stream;
+ Eigen::GpuDevice gpu_device(&stream);
+ int num_elem = size1*size2;
+ int result_size = (redux == 1 ? size1 : size2);
+
+ float* d_float = (float*)gpu_device.allocate(num_elem * sizeof(float));
+ Eigen::half* d_res_half = (Eigen::half*)gpu_device.allocate(result_size * sizeof(Eigen::half));
+ Eigen::half* d_res_float = (Eigen::half*)gpu_device.allocate(result_size * sizeof(Eigen::half));
+
+ Eigen::TensorMap<Eigen::Tensor<float, 2>, Eigen::Aligned> gpu_float(
+ d_float, size1, size2);
+ Eigen::TensorMap<Eigen::Tensor<Eigen::half, 1>, Eigen::Aligned> gpu_res_half(
+ d_res_half, result_size);
+ Eigen::TensorMap<Eigen::Tensor<Eigen::half, 1>, Eigen::Aligned> gpu_res_float(
+ d_res_float, result_size);
+
+ gpu_float.device(gpu_device) = gpu_float.random() * 2.0f;
+
+ Eigen::array<int, 1> redux_dim = {redux};
+ gpu_res_float.device(gpu_device) = gpu_float.sum(redux_dim).cast<Eigen::half>();
+ gpu_res_half.device(gpu_device) = gpu_float.cast<Eigen::half>().sum(redux_dim);
+
+ Tensor<Eigen::half, 1> half_prec(result_size);
+ Tensor<Eigen::half, 1> full_prec(result_size);
+ gpu_device.memcpyDeviceToHost(half_prec.data(), d_res_half, result_size*sizeof(Eigen::half));
+ gpu_device.memcpyDeviceToHost(full_prec.data(), d_res_float, result_size*sizeof(Eigen::half));
+ gpu_device.synchronize();
+
+ for (int i = 0; i < result_size; ++i) {
+ std::cout << "EXPECTED " << full_prec(i) << " GOT " << half_prec(i) << std::endl;
+ VERIFY_IS_APPROX(full_prec(i), half_prec(i));
+ }
+
+ gpu_device.deallocate(d_float);
+ gpu_device.deallocate(d_res_half);
+ gpu_device.deallocate(d_res_float);
+}
+
+template<typename>
+void test_gpu_reductions() {
+ test_gpu_reductions<void>(13, 13, 0);
+ test_gpu_reductions<void>(13, 13, 1);
+
+ test_gpu_reductions<void>(35, 36, 0);
+ test_gpu_reductions<void>(35, 36, 1);
+
+ test_gpu_reductions<void>(36, 35, 0);
+ test_gpu_reductions<void>(36, 35, 1);
+}
+
+template<typename>
+void test_gpu_full_reductions() {
+ Eigen::GpuStreamDevice stream;
+ Eigen::GpuDevice gpu_device(&stream);
+ int size = 13;
+ int num_elem = size*size;
+
+ float* d_float = (float*)gpu_device.allocate(num_elem * sizeof(float));
+ Eigen::half* d_res_half = (Eigen::half*)gpu_device.allocate(1 * sizeof(Eigen::half));
+ Eigen::half* d_res_float = (Eigen::half*)gpu_device.allocate(1 * sizeof(Eigen::half));
+
+ Eigen::TensorMap<Eigen::Tensor<float, 2>, Eigen::Aligned> gpu_float(
+ d_float, size, size);
+ Eigen::TensorMap<Eigen::Tensor<Eigen::half, 0>, Eigen::Aligned> gpu_res_half(
+ d_res_half);
+ Eigen::TensorMap<Eigen::Tensor<Eigen::half, 0>, Eigen::Aligned> gpu_res_float(
+ d_res_float);
+
+ gpu_float.device(gpu_device) = gpu_float.random();
+
+ gpu_res_float.device(gpu_device) = gpu_float.sum().cast<Eigen::half>();
+ gpu_res_half.device(gpu_device) = gpu_float.cast<Eigen::half>().sum();
+
+ Tensor<Eigen::half, 0> half_prec;
+ Tensor<Eigen::half, 0> full_prec;
+ gpu_device.memcpyDeviceToHost(half_prec.data(), d_res_half, sizeof(Eigen::half));
+ gpu_device.memcpyDeviceToHost(full_prec.data(), d_res_float, sizeof(Eigen::half));
+ gpu_device.synchronize();
+
+ VERIFY_IS_APPROX(full_prec(), half_prec());
+
+ gpu_res_float.device(gpu_device) = gpu_float.maximum().cast<Eigen::half>();
+ gpu_res_half.device(gpu_device) = gpu_float.cast<Eigen::half>().maximum();
+ gpu_device.memcpyDeviceToHost(half_prec.data(), d_res_half, sizeof(Eigen::half));
+ gpu_device.memcpyDeviceToHost(full_prec.data(), d_res_float, sizeof(Eigen::half));
+ gpu_device.synchronize();
+
+ VERIFY_IS_APPROX(full_prec(), half_prec());
+
+ gpu_device.deallocate(d_float);
+ gpu_device.deallocate(d_res_half);
+ gpu_device.deallocate(d_res_float);
+}
+
+template<typename>
+void test_gpu_forced_evals() {
+
+ Eigen::GpuStreamDevice stream;
+ Eigen::GpuDevice gpu_device(&stream);
+ int num_elem = 101;
+
+ float* d_float = (float*)gpu_device.allocate(num_elem * sizeof(float));
+ float* d_res_half1 = (float*)gpu_device.allocate(num_elem * sizeof(float));
+ float* d_res_half2 = (float*)gpu_device.allocate(num_elem * sizeof(float));
+ float* d_res_float = (float*)gpu_device.allocate(num_elem * sizeof(float));
+
+ Eigen::TensorMap<Eigen::Tensor<float, 1>, Eigen::Aligned> gpu_float(
+ d_float, num_elem);
+ Eigen::TensorMap<Eigen::Tensor<float, 1>, Eigen::Aligned> gpu_res_half1(
+ d_res_half1, num_elem);
+ Eigen::TensorMap<Eigen::Tensor<float, 1>, Eigen::Unaligned> gpu_res_half2(
+ d_res_half2, num_elem);
+ Eigen::TensorMap<Eigen::Tensor<float, 1>, Eigen::Aligned> gpu_res_float(
+ d_res_float, num_elem);
+
+ Eigen::array<int, 1> no_bcast;
+ no_bcast[0] = 1;
+
+ gpu_float.device(gpu_device) = gpu_float.random() - gpu_float.constant(0.5f);
+ gpu_res_float.device(gpu_device) = gpu_float.abs();
+ gpu_res_half1.device(gpu_device) = gpu_float.cast<Eigen::half>().abs().eval().cast<float>();
+ gpu_res_half2.device(gpu_device) = gpu_float.cast<Eigen::half>().abs().broadcast(no_bcast).eval().cast<float>();
+
+ Tensor<float, 1> half_prec1(num_elem);
+ Tensor<float, 1> half_prec2(num_elem);
+ Tensor<float, 1> full_prec(num_elem);
+ gpu_device.memcpyDeviceToHost(half_prec1.data(), d_res_half1, num_elem*sizeof(float));
+ gpu_device.memcpyDeviceToHost(half_prec2.data(), d_res_half2, num_elem*sizeof(float));
+ gpu_device.memcpyDeviceToHost(full_prec.data(), d_res_float, num_elem*sizeof(float));
+ gpu_device.synchronize();
+
+ for (int i = 0; i < num_elem; ++i) {
+ std::cout << "Checking forced eval " << i << full_prec(i) << " vs " << half_prec1(i) << " vs " << half_prec2(i) << std::endl;
+ VERIFY_IS_APPROX(full_prec(i), half_prec1(i));
+ VERIFY_IS_APPROX(full_prec(i), half_prec2(i));
+ }
+
+ gpu_device.deallocate(d_float);
+ gpu_device.deallocate(d_res_half1);
+ gpu_device.deallocate(d_res_half2);
+ gpu_device.deallocate(d_res_float);
+}
+#endif
+
+
+EIGEN_DECLARE_TEST(cxx11_tensor_of_float16_gpu)
+{
+ CALL_SUBTEST_1(test_gpu_numext<void>());
+
+#ifdef EIGEN_HAS_GPU_FP16
+ CALL_SUBTEST_1(test_gpu_conversion<void>());
+ CALL_SUBTEST_1(test_gpu_unary<void>());
+ CALL_SUBTEST_1(test_gpu_elementwise<void>());
+ CALL_SUBTEST_1(test_gpu_trancendental<void>());
+ CALL_SUBTEST_2(test_gpu_contractions<void>());
+ CALL_SUBTEST_3(test_gpu_reductions<void>());
+ CALL_SUBTEST_4(test_gpu_full_reductions<void>());
+ CALL_SUBTEST_5(test_gpu_forced_evals<void>());
+#else
+ std::cout << "Half floats are not supported by this version of gpu: skipping the test" << std::endl;
+#endif
+}
diff --git a/unsupported/test/cxx11_tensor_of_strings.cpp b/unsupported/test/cxx11_tensor_of_strings.cpp
new file mode 100644
index 0000000..1596562
--- /dev/null
+++ b/unsupported/test/cxx11_tensor_of_strings.cpp
@@ -0,0 +1,152 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "main.h"
+
+#include <Eigen/CXX11/Tensor>
+
+using Eigen::Tensor;
+using Eigen::TensorMap;
+
+static void test_assign()
+{
+ std::string data1[6];
+ TensorMap<Tensor<std::string, 2>> mat1(data1, 2, 3);
+ std::string data2[6];
+ const TensorMap<Tensor<const std::string, 2>> mat2(data2, 2, 3);
+
+ for (int i = 0; i < 6; ++i) {
+ std::ostringstream s1;
+ s1 << "abc" << i*3;
+ data1[i] = s1.str();
+ std::ostringstream s2;
+ s2 << "def" << i*5;
+ data2[i] = s2.str();
+ }
+
+ Tensor<std::string, 2> rslt1;
+ rslt1 = mat1;
+ Tensor<std::string, 2> rslt2;
+ rslt2 = mat2;
+
+ Tensor<std::string, 2> rslt3 = mat1;
+ Tensor<std::string, 2> rslt4 = mat2;
+
+ Tensor<std::string, 2> rslt5(mat1);
+ Tensor<std::string, 2> rslt6(mat2);
+
+ for (int i = 0; i < 2; ++i) {
+ for (int j = 0; j < 3; ++j) {
+ VERIFY_IS_EQUAL(rslt1(i,j), data1[i+2*j]);
+ VERIFY_IS_EQUAL(rslt2(i,j), data2[i+2*j]);
+ VERIFY_IS_EQUAL(rslt3(i,j), data1[i+2*j]);
+ VERIFY_IS_EQUAL(rslt4(i,j), data2[i+2*j]);
+ VERIFY_IS_EQUAL(rslt5(i,j), data1[i+2*j]);
+ VERIFY_IS_EQUAL(rslt6(i,j), data2[i+2*j]);
+ }
+ }
+}
+
+
+static void test_concat()
+{
+ Tensor<std::string, 2> t1(2, 3);
+ Tensor<std::string, 2> t2(2, 3);
+
+ for (int i = 0; i < 2; ++i) {
+ for (int j = 0; j < 3; ++j) {
+ std::ostringstream s1;
+ s1 << "abc" << i + j*2;
+ t1(i, j) = s1.str();
+ std::ostringstream s2;
+ s2 << "def" << i*5 + j*32;
+ t2(i, j) = s2.str();
+ }
+ }
+
+ Tensor<std::string, 2> result = t1.concatenate(t2, 1);
+ VERIFY_IS_EQUAL(result.dimension(0), 2);
+ VERIFY_IS_EQUAL(result.dimension(1), 6);
+
+ for (int i = 0; i < 2; ++i) {
+ for (int j = 0; j < 3; ++j) {
+ VERIFY_IS_EQUAL(result(i, j), t1(i, j));
+ VERIFY_IS_EQUAL(result(i, j+3), t2(i, j));
+ }
+ }
+}
+
+
+static void test_slices()
+{
+ Tensor<std::string, 2> data(2, 6);
+ for (int i = 0; i < 2; ++i) {
+ for (int j = 0; j < 3; ++j) {
+ std::ostringstream s1;
+ s1 << "abc" << i + j*2;
+ data(i, j) = s1.str();
+ }
+ }
+
+ const Eigen::DSizes<ptrdiff_t, 2> half_size(2, 3);
+ const Eigen::DSizes<ptrdiff_t, 2> first_half(0, 0);
+ const Eigen::DSizes<ptrdiff_t, 2> second_half(0, 3);
+
+ Tensor<std::string, 2> t1 = data.slice(first_half, half_size);
+ Tensor<std::string, 2> t2 = data.slice(second_half, half_size);
+
+ for (int i = 0; i < 2; ++i) {
+ for (int j = 0; j < 3; ++j) {
+ VERIFY_IS_EQUAL(data(i, j), t1(i, j));
+ VERIFY_IS_EQUAL(data(i, j+3), t2(i, j));
+ }
+ }
+}
+
+
+static void test_additions()
+{
+ Tensor<std::string, 1> data1(3);
+ Tensor<std::string, 1> data2(3);
+ for (int i = 0; i < 3; ++i) {
+ data1(i) = "abc";
+ std::ostringstream s1;
+ s1 << i;
+ data2(i) = s1.str();
+ }
+
+ Tensor<std::string, 1> sum = data1 + data2;
+ for (int i = 0; i < 3; ++i) {
+ std::ostringstream concat;
+ concat << "abc" << i;
+ std::string expected = concat.str();
+ VERIFY_IS_EQUAL(sum(i), expected);
+ }
+}
+
+
+static void test_initialization()
+{
+ Tensor<std::string, 2> a(2, 3);
+ a.setConstant(std::string("foo"));
+ for (int i = 0; i < 2*3; ++i) {
+ VERIFY_IS_EQUAL(a(i), std::string("foo"));
+ }
+}
+
+
+EIGEN_DECLARE_TEST(cxx11_tensor_of_strings)
+{
+ // Beware: none of this is likely to ever work on a GPU.
+ CALL_SUBTEST(test_assign());
+ CALL_SUBTEST(test_concat());
+ CALL_SUBTEST(test_slices());
+ CALL_SUBTEST(test_additions());
+ CALL_SUBTEST(test_initialization());
+}
diff --git a/unsupported/test/cxx11_tensor_padding.cpp b/unsupported/test/cxx11_tensor_padding.cpp
new file mode 100644
index 0000000..b8a329d
--- /dev/null
+++ b/unsupported/test/cxx11_tensor_padding.cpp
@@ -0,0 +1,93 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "main.h"
+
+#include <Eigen/CXX11/Tensor>
+
+using Eigen::Tensor;
+
+template<int DataLayout>
+static void test_simple_padding()
+{
+ Tensor<float, 4, DataLayout> tensor(2,3,5,7);
+ tensor.setRandom();
+
+ array<std::pair<ptrdiff_t, ptrdiff_t>, 4> paddings;
+ paddings[0] = std::make_pair(0, 0);
+ paddings[1] = std::make_pair(2, 1);
+ paddings[2] = std::make_pair(3, 4);
+ paddings[3] = std::make_pair(0, 0);
+
+ Tensor<float, 4, DataLayout> padded;
+ padded = tensor.pad(paddings);
+
+ VERIFY_IS_EQUAL(padded.dimension(0), 2+0);
+ VERIFY_IS_EQUAL(padded.dimension(1), 3+3);
+ VERIFY_IS_EQUAL(padded.dimension(2), 5+7);
+ VERIFY_IS_EQUAL(padded.dimension(3), 7+0);
+
+ for (int i = 0; i < 2; ++i) {
+ for (int j = 0; j < 6; ++j) {
+ for (int k = 0; k < 12; ++k) {
+ for (int l = 0; l < 7; ++l) {
+ if (j >= 2 && j < 5 && k >= 3 && k < 8) {
+ VERIFY_IS_EQUAL(padded(i,j,k,l), tensor(i,j-2,k-3,l));
+ } else {
+ VERIFY_IS_EQUAL(padded(i,j,k,l), 0.0f);
+ }
+ }
+ }
+ }
+ }
+}
+
+template<int DataLayout>
+static void test_padded_expr()
+{
+ Tensor<float, 4, DataLayout> tensor(2,3,5,7);
+ tensor.setRandom();
+
+ array<std::pair<ptrdiff_t, ptrdiff_t>, 4> paddings;
+ paddings[0] = std::make_pair(0, 0);
+ paddings[1] = std::make_pair(2, 1);
+ paddings[2] = std::make_pair(3, 4);
+ paddings[3] = std::make_pair(0, 0);
+
+ Eigen::DSizes<ptrdiff_t, 2> reshape_dims;
+ reshape_dims[0] = 12;
+ reshape_dims[1] = 84;
+
+ Tensor<float, 2, DataLayout> result;
+ result = tensor.pad(paddings).reshape(reshape_dims);
+
+ for (int i = 0; i < 2; ++i) {
+ for (int j = 0; j < 6; ++j) {
+ for (int k = 0; k < 12; ++k) {
+ for (int l = 0; l < 7; ++l) {
+ const float result_value = DataLayout == ColMajor ?
+ result(i+2*j,k+12*l) : result(j+6*i,l+7*k);
+ if (j >= 2 && j < 5 && k >= 3 && k < 8) {
+ VERIFY_IS_EQUAL(result_value, tensor(i,j-2,k-3,l));
+ } else {
+ VERIFY_IS_EQUAL(result_value, 0.0f);
+ }
+ }
+ }
+ }
+ }
+}
+
+EIGEN_DECLARE_TEST(cxx11_tensor_padding)
+{
+ CALL_SUBTEST(test_simple_padding<ColMajor>());
+ CALL_SUBTEST(test_simple_padding<RowMajor>());
+ CALL_SUBTEST(test_padded_expr<ColMajor>());
+ CALL_SUBTEST(test_padded_expr<RowMajor>());
+}
diff --git a/unsupported/test/cxx11_tensor_padding_sycl.cpp b/unsupported/test/cxx11_tensor_padding_sycl.cpp
new file mode 100644
index 0000000..727a9ff
--- /dev/null
+++ b/unsupported/test/cxx11_tensor_padding_sycl.cpp
@@ -0,0 +1,157 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2016
+// Mehdi Goli Codeplay Software Ltd.
+// Ralph Potter Codeplay Software Ltd.
+// Luke Iwanski Codeplay Software Ltd.
+// Contact: <eigen@codeplay.com>
+// Benoit Steiner <benoit.steiner.goog@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+
+#define EIGEN_TEST_NO_LONGDOUBLE
+#define EIGEN_TEST_NO_COMPLEX
+
+#define EIGEN_DEFAULT_DENSE_INDEX_TYPE int64_t
+#define EIGEN_USE_SYCL
+
+
+#include "main.h"
+#include <unsupported/Eigen/CXX11/Tensor>
+
+using Eigen::array;
+using Eigen::SyclDevice;
+using Eigen::Tensor;
+using Eigen::TensorMap;
+
+
+template<typename DataType, int DataLayout, typename IndexType>
+static void test_simple_padding(const Eigen::SyclDevice& sycl_device)
+{
+
+ IndexType sizeDim1 = 2;
+ IndexType sizeDim2 = 3;
+ IndexType sizeDim3 = 5;
+ IndexType sizeDim4 = 7;
+ array<IndexType, 4> tensorRange = {{sizeDim1, sizeDim2, sizeDim3, sizeDim4}};
+
+ Tensor<DataType, 4, DataLayout, IndexType> tensor(tensorRange);
+ tensor.setRandom();
+
+ array<std::pair<IndexType, IndexType>, 4> paddings;
+ paddings[0] = std::make_pair(0, 0);
+ paddings[1] = std::make_pair(2, 1);
+ paddings[2] = std::make_pair(3, 4);
+ paddings[3] = std::make_pair(0, 0);
+
+ IndexType padedSizeDim1 = 2;
+ IndexType padedSizeDim2 = 6;
+ IndexType padedSizeDim3 = 12;
+ IndexType padedSizeDim4 = 7;
+ array<IndexType, 4> padedtensorRange = {{padedSizeDim1, padedSizeDim2, padedSizeDim3, padedSizeDim4}};
+
+ Tensor<DataType, 4, DataLayout, IndexType> padded(padedtensorRange);
+
+
+ DataType* gpu_data1 = static_cast<DataType*>(sycl_device.allocate(tensor.size()*sizeof(DataType)));
+ DataType* gpu_data2 = static_cast<DataType*>(sycl_device.allocate(padded.size()*sizeof(DataType)));
+ TensorMap<Tensor<DataType, 4,DataLayout,IndexType>> gpu1(gpu_data1, tensorRange);
+ TensorMap<Tensor<DataType, 4,DataLayout,IndexType>> gpu2(gpu_data2, padedtensorRange);
+
+ VERIFY_IS_EQUAL(padded.dimension(0), 2+0);
+ VERIFY_IS_EQUAL(padded.dimension(1), 3+3);
+ VERIFY_IS_EQUAL(padded.dimension(2), 5+7);
+ VERIFY_IS_EQUAL(padded.dimension(3), 7+0);
+ sycl_device.memcpyHostToDevice(gpu_data1, tensor.data(),(tensor.size())*sizeof(DataType));
+ gpu2.device(sycl_device)=gpu1.pad(paddings);
+ sycl_device.memcpyDeviceToHost(padded.data(), gpu_data2,(padded.size())*sizeof(DataType));
+ for (IndexType i = 0; i < padedSizeDim1; ++i) {
+ for (IndexType j = 0; j < padedSizeDim2; ++j) {
+ for (IndexType k = 0; k < padedSizeDim3; ++k) {
+ for (IndexType l = 0; l < padedSizeDim4; ++l) {
+ if (j >= 2 && j < 5 && k >= 3 && k < 8) {
+ VERIFY_IS_EQUAL(padded(i,j,k,l), tensor(i,j-2,k-3,l));
+ } else {
+ VERIFY_IS_EQUAL(padded(i,j,k,l), 0.0f);
+ }
+ }
+ }
+ }
+ }
+ sycl_device.deallocate(gpu_data1);
+ sycl_device.deallocate(gpu_data2);
+}
+
+template<typename DataType, int DataLayout, typename IndexType>
+static void test_padded_expr(const Eigen::SyclDevice& sycl_device)
+{
+ IndexType sizeDim1 = 2;
+ IndexType sizeDim2 = 3;
+ IndexType sizeDim3 = 5;
+ IndexType sizeDim4 = 7;
+ array<IndexType, 4> tensorRange = {{sizeDim1, sizeDim2, sizeDim3, sizeDim4}};
+
+ Tensor<DataType, 4, DataLayout, IndexType> tensor(tensorRange);
+ tensor.setRandom();
+
+ array<std::pair<IndexType, IndexType>, 4> paddings;
+ paddings[0] = std::make_pair(0, 0);
+ paddings[1] = std::make_pair(2, 1);
+ paddings[2] = std::make_pair(3, 4);
+ paddings[3] = std::make_pair(0, 0);
+
+ Eigen::DSizes<IndexType, 2> reshape_dims;
+ reshape_dims[0] = 12;
+ reshape_dims[1] = 84;
+
+
+ Tensor<DataType, 2, DataLayout, IndexType> result(reshape_dims);
+
+ DataType* gpu_data1 = static_cast<DataType*>(sycl_device.allocate(tensor.size()*sizeof(DataType)));
+ DataType* gpu_data2 = static_cast<DataType*>(sycl_device.allocate(result.size()*sizeof(DataType)));
+ TensorMap<Tensor<DataType, 4,DataLayout,IndexType>> gpu1(gpu_data1, tensorRange);
+ TensorMap<Tensor<DataType, 2,DataLayout,IndexType>> gpu2(gpu_data2, reshape_dims);
+
+
+ sycl_device.memcpyHostToDevice(gpu_data1, tensor.data(),(tensor.size())*sizeof(DataType));
+ gpu2.device(sycl_device)=gpu1.pad(paddings).reshape(reshape_dims);
+ sycl_device.memcpyDeviceToHost(result.data(), gpu_data2,(result.size())*sizeof(DataType));
+
+ for (IndexType i = 0; i < 2; ++i) {
+ for (IndexType j = 0; j < 6; ++j) {
+ for (IndexType k = 0; k < 12; ++k) {
+ for (IndexType l = 0; l < 7; ++l) {
+ const float result_value = DataLayout == ColMajor ?
+ result(i+2*j,k+12*l) : result(j+6*i,l+7*k);
+ if (j >= 2 && j < 5 && k >= 3 && k < 8) {
+ VERIFY_IS_EQUAL(result_value, tensor(i,j-2,k-3,l));
+ } else {
+ VERIFY_IS_EQUAL(result_value, 0.0f);
+ }
+ }
+ }
+ }
+ }
+ sycl_device.deallocate(gpu_data1);
+ sycl_device.deallocate(gpu_data2);
+}
+
+template<typename DataType, typename dev_Selector> void sycl_padding_test_per_device(dev_Selector s){
+ QueueInterface queueInterface(s);
+ auto sycl_device = Eigen::SyclDevice(&queueInterface);
+ test_simple_padding<DataType, RowMajor, int64_t>(sycl_device);
+ test_simple_padding<DataType, ColMajor, int64_t>(sycl_device);
+ test_padded_expr<DataType, RowMajor, int64_t>(sycl_device);
+ test_padded_expr<DataType, ColMajor, int64_t>(sycl_device);
+
+}
+EIGEN_DECLARE_TEST(cxx11_tensor_padding_sycl)
+{
+ for (const auto& device :Eigen::get_sycl_supported_devices()) {
+ CALL_SUBTEST(sycl_padding_test_per_device<float>(device));
+ }
+}
diff --git a/unsupported/test/cxx11_tensor_patch.cpp b/unsupported/test/cxx11_tensor_patch.cpp
new file mode 100644
index 0000000..498ab8c
--- /dev/null
+++ b/unsupported/test/cxx11_tensor_patch.cpp
@@ -0,0 +1,172 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "main.h"
+
+#include <Eigen/CXX11/Tensor>
+
+using Eigen::Tensor;
+
+template<int DataLayout>
+static void test_simple_patch()
+{
+ Tensor<float, 4, DataLayout> tensor(2,3,5,7);
+ tensor.setRandom();
+ array<ptrdiff_t, 4> patch_dims;
+
+ patch_dims[0] = 1;
+ patch_dims[1] = 1;
+ patch_dims[2] = 1;
+ patch_dims[3] = 1;
+
+ Tensor<float, 5, DataLayout> no_patch;
+ no_patch = tensor.extract_patches(patch_dims);
+
+ if (DataLayout == ColMajor) {
+ VERIFY_IS_EQUAL(no_patch.dimension(0), 1);
+ VERIFY_IS_EQUAL(no_patch.dimension(1), 1);
+ VERIFY_IS_EQUAL(no_patch.dimension(2), 1);
+ VERIFY_IS_EQUAL(no_patch.dimension(3), 1);
+ VERIFY_IS_EQUAL(no_patch.dimension(4), tensor.size());
+ } else {
+ VERIFY_IS_EQUAL(no_patch.dimension(0), tensor.size());
+ VERIFY_IS_EQUAL(no_patch.dimension(1), 1);
+ VERIFY_IS_EQUAL(no_patch.dimension(2), 1);
+ VERIFY_IS_EQUAL(no_patch.dimension(3), 1);
+ VERIFY_IS_EQUAL(no_patch.dimension(4), 1);
+ }
+
+ for (int i = 0; i < tensor.size(); ++i) {
+ VERIFY_IS_EQUAL(tensor.data()[i], no_patch.data()[i]);
+ }
+
+ patch_dims[0] = 2;
+ patch_dims[1] = 3;
+ patch_dims[2] = 5;
+ patch_dims[3] = 7;
+ Tensor<float, 5, DataLayout> single_patch;
+ single_patch = tensor.extract_patches(patch_dims);
+
+ if (DataLayout == ColMajor) {
+ VERIFY_IS_EQUAL(single_patch.dimension(0), 2);
+ VERIFY_IS_EQUAL(single_patch.dimension(1), 3);
+ VERIFY_IS_EQUAL(single_patch.dimension(2), 5);
+ VERIFY_IS_EQUAL(single_patch.dimension(3), 7);
+ VERIFY_IS_EQUAL(single_patch.dimension(4), 1);
+ } else {
+ VERIFY_IS_EQUAL(single_patch.dimension(0), 1);
+ VERIFY_IS_EQUAL(single_patch.dimension(1), 2);
+ VERIFY_IS_EQUAL(single_patch.dimension(2), 3);
+ VERIFY_IS_EQUAL(single_patch.dimension(3), 5);
+ VERIFY_IS_EQUAL(single_patch.dimension(4), 7);
+ }
+
+ for (int i = 0; i < tensor.size(); ++i) {
+ VERIFY_IS_EQUAL(tensor.data()[i], single_patch.data()[i]);
+ }
+
+ patch_dims[0] = 1;
+ patch_dims[1] = 2;
+ patch_dims[2] = 2;
+ patch_dims[3] = 1;
+ Tensor<float, 5, DataLayout> twod_patch;
+ twod_patch = tensor.extract_patches(patch_dims);
+
+ if (DataLayout == ColMajor) {
+ VERIFY_IS_EQUAL(twod_patch.dimension(0), 1);
+ VERIFY_IS_EQUAL(twod_patch.dimension(1), 2);
+ VERIFY_IS_EQUAL(twod_patch.dimension(2), 2);
+ VERIFY_IS_EQUAL(twod_patch.dimension(3), 1);
+ VERIFY_IS_EQUAL(twod_patch.dimension(4), 2*2*4*7);
+ } else {
+ VERIFY_IS_EQUAL(twod_patch.dimension(0), 2*2*4*7);
+ VERIFY_IS_EQUAL(twod_patch.dimension(1), 1);
+ VERIFY_IS_EQUAL(twod_patch.dimension(2), 2);
+ VERIFY_IS_EQUAL(twod_patch.dimension(3), 2);
+ VERIFY_IS_EQUAL(twod_patch.dimension(4), 1);
+ }
+
+ for (int i = 0; i < 2; ++i) {
+ for (int j = 0; j < 2; ++j) {
+ for (int k = 0; k < 4; ++k) {
+ for (int l = 0; l < 7; ++l) {
+ int patch_loc;
+ if (DataLayout == ColMajor) {
+ patch_loc = i + 2 * (j + 2 * (k + 4 * l));
+ } else {
+ patch_loc = l + 7 * (k + 4 * (j + 2 * i));
+ }
+ for (int x = 0; x < 2; ++x) {
+ for (int y = 0; y < 2; ++y) {
+ if (DataLayout == ColMajor) {
+ VERIFY_IS_EQUAL(tensor(i,j+x,k+y,l), twod_patch(0,x,y,0,patch_loc));
+ } else {
+ VERIFY_IS_EQUAL(tensor(i,j+x,k+y,l), twod_patch(patch_loc,0,x,y,0));
+ }
+ }
+ }
+ }
+ }
+ }
+ }
+
+ patch_dims[0] = 1;
+ patch_dims[1] = 2;
+ patch_dims[2] = 3;
+ patch_dims[3] = 5;
+ Tensor<float, 5, DataLayout> threed_patch;
+ threed_patch = tensor.extract_patches(patch_dims);
+
+ if (DataLayout == ColMajor) {
+ VERIFY_IS_EQUAL(threed_patch.dimension(0), 1);
+ VERIFY_IS_EQUAL(threed_patch.dimension(1), 2);
+ VERIFY_IS_EQUAL(threed_patch.dimension(2), 3);
+ VERIFY_IS_EQUAL(threed_patch.dimension(3), 5);
+ VERIFY_IS_EQUAL(threed_patch.dimension(4), 2*2*3*3);
+ } else {
+ VERIFY_IS_EQUAL(threed_patch.dimension(0), 2*2*3*3);
+ VERIFY_IS_EQUAL(threed_patch.dimension(1), 1);
+ VERIFY_IS_EQUAL(threed_patch.dimension(2), 2);
+ VERIFY_IS_EQUAL(threed_patch.dimension(3), 3);
+ VERIFY_IS_EQUAL(threed_patch.dimension(4), 5);
+ }
+
+ for (int i = 0; i < 2; ++i) {
+ for (int j = 0; j < 2; ++j) {
+ for (int k = 0; k < 3; ++k) {
+ for (int l = 0; l < 3; ++l) {
+ int patch_loc;
+ if (DataLayout == ColMajor) {
+ patch_loc = i + 2 * (j + 2 * (k + 3 * l));
+ } else {
+ patch_loc = l + 3 * (k + 3 * (j + 2 * i));
+ }
+ for (int x = 0; x < 2; ++x) {
+ for (int y = 0; y < 3; ++y) {
+ for (int z = 0; z < 5; ++z) {
+ if (DataLayout == ColMajor) {
+ VERIFY_IS_EQUAL(tensor(i,j+x,k+y,l+z), threed_patch(0,x,y,z,patch_loc));
+ } else {
+ VERIFY_IS_EQUAL(tensor(i,j+x,k+y,l+z), threed_patch(patch_loc,0,x,y,z));
+ }
+ }
+ }
+ }
+ }
+ }
+ }
+ }
+}
+
+EIGEN_DECLARE_TEST(cxx11_tensor_patch)
+{
+ CALL_SUBTEST(test_simple_patch<ColMajor>());
+ CALL_SUBTEST(test_simple_patch<RowMajor>());
+ // CALL_SUBTEST(test_expr_shuffling());
+}
diff --git a/unsupported/test/cxx11_tensor_patch_sycl.cpp b/unsupported/test/cxx11_tensor_patch_sycl.cpp
new file mode 100644
index 0000000..7f92bec
--- /dev/null
+++ b/unsupported/test/cxx11_tensor_patch_sycl.cpp
@@ -0,0 +1,249 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2016
+// Mehdi Goli Codeplay Software Ltd.
+// Ralph Potter Codeplay Software Ltd.
+// Luke Iwanski Codeplay Software Ltd.
+// Contact: <eigen@codeplay.com>
+// Benoit Steiner <benoit.steiner.goog@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#define EIGEN_TEST_NO_LONGDOUBLE
+#define EIGEN_TEST_NO_COMPLEX
+
+#define EIGEN_DEFAULT_DENSE_INDEX_TYPE int64_t
+#define EIGEN_USE_SYCL
+
+#include "main.h"
+
+#include <Eigen/CXX11/Tensor>
+
+using Eigen::Tensor;
+
+template <typename DataType, int DataLayout, typename IndexType>
+static void test_simple_patch_sycl(const Eigen::SyclDevice& sycl_device){
+
+ IndexType sizeDim1 = 2;
+ IndexType sizeDim2 = 3;
+ IndexType sizeDim3 = 5;
+ IndexType sizeDim4 = 7;
+ array<IndexType, 4> tensorRange = {{sizeDim1, sizeDim2, sizeDim3, sizeDim4}};
+ array<IndexType, 5> patchTensorRange;
+ if (DataLayout == ColMajor) {
+ patchTensorRange = {{1, 1, 1, 1, sizeDim1*sizeDim2*sizeDim3*sizeDim4}};
+ }else{
+ patchTensorRange = {{sizeDim1*sizeDim2*sizeDim3*sizeDim4,1, 1, 1, 1}};
+ }
+
+ Tensor<DataType, 4, DataLayout,IndexType> tensor(tensorRange);
+ Tensor<DataType, 5, DataLayout,IndexType> no_patch(patchTensorRange);
+
+ tensor.setRandom();
+
+ array<ptrdiff_t, 4> patch_dims;
+ patch_dims[0] = 1;
+ patch_dims[1] = 1;
+ patch_dims[2] = 1;
+ patch_dims[3] = 1;
+
+ const size_t tensorBuffSize =tensor.size()*sizeof(DataType);
+ size_t patchTensorBuffSize =no_patch.size()*sizeof(DataType);
+ DataType* gpu_data_tensor = static_cast<DataType*>(sycl_device.allocate(tensorBuffSize));
+ DataType* gpu_data_no_patch = static_cast<DataType*>(sycl_device.allocate(patchTensorBuffSize));
+
+ TensorMap<Tensor<DataType, 4, DataLayout,IndexType>> gpu_tensor(gpu_data_tensor, tensorRange);
+ TensorMap<Tensor<DataType, 5, DataLayout,IndexType>> gpu_no_patch(gpu_data_no_patch, patchTensorRange);
+
+ sycl_device.memcpyHostToDevice(gpu_data_tensor, tensor.data(), tensorBuffSize);
+ gpu_no_patch.device(sycl_device)=gpu_tensor.extract_patches(patch_dims);
+ sycl_device.memcpyDeviceToHost(no_patch.data(), gpu_data_no_patch, patchTensorBuffSize);
+
+ if (DataLayout == ColMajor) {
+ VERIFY_IS_EQUAL(no_patch.dimension(0), 1);
+ VERIFY_IS_EQUAL(no_patch.dimension(1), 1);
+ VERIFY_IS_EQUAL(no_patch.dimension(2), 1);
+ VERIFY_IS_EQUAL(no_patch.dimension(3), 1);
+ VERIFY_IS_EQUAL(no_patch.dimension(4), tensor.size());
+ } else {
+ VERIFY_IS_EQUAL(no_patch.dimension(0), tensor.size());
+ VERIFY_IS_EQUAL(no_patch.dimension(1), 1);
+ VERIFY_IS_EQUAL(no_patch.dimension(2), 1);
+ VERIFY_IS_EQUAL(no_patch.dimension(3), 1);
+ VERIFY_IS_EQUAL(no_patch.dimension(4), 1);
+ }
+
+ for (int i = 0; i < tensor.size(); ++i) {
+ VERIFY_IS_EQUAL(tensor.data()[i], no_patch.data()[i]);
+ }
+
+ patch_dims[0] = 2;
+ patch_dims[1] = 3;
+ patch_dims[2] = 5;
+ patch_dims[3] = 7;
+
+ if (DataLayout == ColMajor) {
+ patchTensorRange = {{sizeDim1,sizeDim2,sizeDim3,sizeDim4,1}};
+ }else{
+ patchTensorRange = {{1,sizeDim1,sizeDim2,sizeDim3,sizeDim4}};
+ }
+ Tensor<DataType, 5, DataLayout,IndexType> single_patch(patchTensorRange);
+ patchTensorBuffSize =single_patch.size()*sizeof(DataType);
+ DataType* gpu_data_single_patch = static_cast<DataType*>(sycl_device.allocate(patchTensorBuffSize));
+ TensorMap<Tensor<DataType, 5, DataLayout,IndexType>> gpu_single_patch(gpu_data_single_patch, patchTensorRange);
+
+ gpu_single_patch.device(sycl_device)=gpu_tensor.extract_patches(patch_dims);
+ sycl_device.memcpyDeviceToHost(single_patch.data(), gpu_data_single_patch, patchTensorBuffSize);
+
+ if (DataLayout == ColMajor) {
+ VERIFY_IS_EQUAL(single_patch.dimension(0), 2);
+ VERIFY_IS_EQUAL(single_patch.dimension(1), 3);
+ VERIFY_IS_EQUAL(single_patch.dimension(2), 5);
+ VERIFY_IS_EQUAL(single_patch.dimension(3), 7);
+ VERIFY_IS_EQUAL(single_patch.dimension(4), 1);
+ } else {
+ VERIFY_IS_EQUAL(single_patch.dimension(0), 1);
+ VERIFY_IS_EQUAL(single_patch.dimension(1), 2);
+ VERIFY_IS_EQUAL(single_patch.dimension(2), 3);
+ VERIFY_IS_EQUAL(single_patch.dimension(3), 5);
+ VERIFY_IS_EQUAL(single_patch.dimension(4), 7);
+ }
+
+ for (int i = 0; i < tensor.size(); ++i) {
+ VERIFY_IS_EQUAL(tensor.data()[i], single_patch.data()[i]);
+ }
+ patch_dims[0] = 1;
+ patch_dims[1] = 2;
+ patch_dims[2] = 2;
+ patch_dims[3] = 1;
+
+ if (DataLayout == ColMajor) {
+ patchTensorRange = {{1,2,2,1,2*2*4*7}};
+ }else{
+ patchTensorRange = {{2*2*4*7, 1, 2,2,1}};
+ }
+ Tensor<DataType, 5, DataLayout,IndexType> twod_patch(patchTensorRange);
+ patchTensorBuffSize =twod_patch.size()*sizeof(DataType);
+ DataType* gpu_data_twod_patch = static_cast<DataType*>(sycl_device.allocate(patchTensorBuffSize));
+ TensorMap<Tensor<DataType, 5, DataLayout,IndexType>> gpu_twod_patch(gpu_data_twod_patch, patchTensorRange);
+
+ gpu_twod_patch.device(sycl_device)=gpu_tensor.extract_patches(patch_dims);
+ sycl_device.memcpyDeviceToHost(twod_patch.data(), gpu_data_twod_patch, patchTensorBuffSize);
+
+ if (DataLayout == ColMajor) {
+ VERIFY_IS_EQUAL(twod_patch.dimension(0), 1);
+ VERIFY_IS_EQUAL(twod_patch.dimension(1), 2);
+ VERIFY_IS_EQUAL(twod_patch.dimension(2), 2);
+ VERIFY_IS_EQUAL(twod_patch.dimension(3), 1);
+ VERIFY_IS_EQUAL(twod_patch.dimension(4), 2*2*4*7);
+ } else {
+ VERIFY_IS_EQUAL(twod_patch.dimension(0), 2*2*4*7);
+ VERIFY_IS_EQUAL(twod_patch.dimension(1), 1);
+ VERIFY_IS_EQUAL(twod_patch.dimension(2), 2);
+ VERIFY_IS_EQUAL(twod_patch.dimension(3), 2);
+ VERIFY_IS_EQUAL(twod_patch.dimension(4), 1);
+ }
+
+ for (int i = 0; i < 2; ++i) {
+ for (int j = 0; j < 2; ++j) {
+ for (int k = 0; k < 4; ++k) {
+ for (int l = 0; l < 7; ++l) {
+ int patch_loc;
+ if (DataLayout == ColMajor) {
+ patch_loc = i + 2 * (j + 2 * (k + 4 * l));
+ } else {
+ patch_loc = l + 7 * (k + 4 * (j + 2 * i));
+ }
+ for (int x = 0; x < 2; ++x) {
+ for (int y = 0; y < 2; ++y) {
+ if (DataLayout == ColMajor) {
+ VERIFY_IS_EQUAL(tensor(i,j+x,k+y,l), twod_patch(0,x,y,0,patch_loc));
+ } else {
+ VERIFY_IS_EQUAL(tensor(i,j+x,k+y,l), twod_patch(patch_loc,0,x,y,0));
+ }
+ }
+ }
+ }
+ }
+ }
+ }
+
+ patch_dims[0] = 1;
+ patch_dims[1] = 2;
+ patch_dims[2] = 3;
+ patch_dims[3] = 5;
+
+ if (DataLayout == ColMajor) {
+ patchTensorRange = {{1,2,3,5,2*2*3*3}};
+ }else{
+ patchTensorRange = {{2*2*3*3, 1, 2,3,5}};
+ }
+ Tensor<DataType, 5, DataLayout,IndexType> threed_patch(patchTensorRange);
+ patchTensorBuffSize =threed_patch.size()*sizeof(DataType);
+ DataType* gpu_data_threed_patch = static_cast<DataType*>(sycl_device.allocate(patchTensorBuffSize));
+ TensorMap<Tensor<DataType, 5, DataLayout,IndexType>> gpu_threed_patch(gpu_data_threed_patch, patchTensorRange);
+
+ gpu_threed_patch.device(sycl_device)=gpu_tensor.extract_patches(patch_dims);
+ sycl_device.memcpyDeviceToHost(threed_patch.data(), gpu_data_threed_patch, patchTensorBuffSize);
+
+ if (DataLayout == ColMajor) {
+ VERIFY_IS_EQUAL(threed_patch.dimension(0), 1);
+ VERIFY_IS_EQUAL(threed_patch.dimension(1), 2);
+ VERIFY_IS_EQUAL(threed_patch.dimension(2), 3);
+ VERIFY_IS_EQUAL(threed_patch.dimension(3), 5);
+ VERIFY_IS_EQUAL(threed_patch.dimension(4), 2*2*3*3);
+ } else {
+ VERIFY_IS_EQUAL(threed_patch.dimension(0), 2*2*3*3);
+ VERIFY_IS_EQUAL(threed_patch.dimension(1), 1);
+ VERIFY_IS_EQUAL(threed_patch.dimension(2), 2);
+ VERIFY_IS_EQUAL(threed_patch.dimension(3), 3);
+ VERIFY_IS_EQUAL(threed_patch.dimension(4), 5);
+ }
+
+ for (int i = 0; i < 2; ++i) {
+ for (int j = 0; j < 2; ++j) {
+ for (int k = 0; k < 3; ++k) {
+ for (int l = 0; l < 3; ++l) {
+ int patch_loc;
+ if (DataLayout == ColMajor) {
+ patch_loc = i + 2 * (j + 2 * (k + 3 * l));
+ } else {
+ patch_loc = l + 3 * (k + 3 * (j + 2 * i));
+ }
+ for (int x = 0; x < 2; ++x) {
+ for (int y = 0; y < 3; ++y) {
+ for (int z = 0; z < 5; ++z) {
+ if (DataLayout == ColMajor) {
+ VERIFY_IS_EQUAL(tensor(i,j+x,k+y,l+z), threed_patch(0,x,y,z,patch_loc));
+ } else {
+ VERIFY_IS_EQUAL(tensor(i,j+x,k+y,l+z), threed_patch(patch_loc,0,x,y,z));
+ }
+ }
+ }
+ }
+ }
+ }
+ }
+ }
+ sycl_device.deallocate(gpu_data_tensor);
+ sycl_device.deallocate(gpu_data_no_patch);
+ sycl_device.deallocate(gpu_data_single_patch);
+ sycl_device.deallocate(gpu_data_twod_patch);
+ sycl_device.deallocate(gpu_data_threed_patch);
+}
+
+template<typename DataType, typename dev_Selector> void sycl_tensor_patch_test_per_device(dev_Selector s){
+ QueueInterface queueInterface(s);
+ auto sycl_device = Eigen::SyclDevice(&queueInterface);
+ test_simple_patch_sycl<DataType, RowMajor, int64_t>(sycl_device);
+ test_simple_patch_sycl<DataType, ColMajor, int64_t>(sycl_device);
+}
+EIGEN_DECLARE_TEST(cxx11_tensor_patch_sycl)
+{
+ for (const auto& device :Eigen::get_sycl_supported_devices()) {
+ CALL_SUBTEST(sycl_tensor_patch_test_per_device<float>(device));
+ }
+}
diff --git a/unsupported/test/cxx11_tensor_random.cpp b/unsupported/test/cxx11_tensor_random.cpp
new file mode 100644
index 0000000..b9d4c55
--- /dev/null
+++ b/unsupported/test/cxx11_tensor_random.cpp
@@ -0,0 +1,86 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "main.h"
+
+#include <Eigen/CXX11/Tensor>
+
+template<typename Scalar>
+static void test_default()
+{
+ Tensor<Scalar, 1> vec(6);
+ vec.setRandom();
+
+ // Fixme: we should check that the generated numbers follow a uniform
+ // distribution instead.
+ for (int i = 1; i < 6; ++i) {
+ VERIFY_IS_NOT_EQUAL(vec(i), vec(i-1));
+ }
+}
+
+template<typename Scalar>
+static void test_normal()
+{
+ Tensor<Scalar, 1> vec(6);
+ vec.template setRandom<Eigen::internal::NormalRandomGenerator<Scalar>>();
+
+ // Fixme: we should check that the generated numbers follow a gaussian
+ // distribution instead.
+ for (int i = 1; i < 6; ++i) {
+ VERIFY_IS_NOT_EQUAL(vec(i), vec(i-1));
+ }
+}
+
+
+struct MyGenerator {
+ MyGenerator() { }
+ MyGenerator(const MyGenerator&) { }
+
+ // Return a random value to be used. "element_location" is the
+ // location of the entry to set in the tensor, it can typically
+ // be ignored.
+ int operator()(Eigen::DenseIndex element_location, Eigen::DenseIndex /*unused*/ = 0) const {
+ return static_cast<int>(3 * element_location);
+ }
+
+ // Same as above but generates several numbers at a time.
+ internal::packet_traits<int>::type packetOp(
+ Eigen::DenseIndex packet_location, Eigen::DenseIndex /*unused*/ = 0) const {
+ const int packetSize = internal::packet_traits<int>::size;
+ EIGEN_ALIGN_MAX int values[packetSize];
+ for (int i = 0; i < packetSize; ++i) {
+ values[i] = static_cast<int>(3 * (packet_location + i));
+ }
+ return internal::pload<typename internal::packet_traits<int>::type>(values);
+ }
+};
+
+
+static void test_custom()
+{
+ Tensor<int, 1> vec(6);
+ vec.setRandom<MyGenerator>();
+
+ for (int i = 0; i < 6; ++i) {
+ VERIFY_IS_EQUAL(vec(i), 3*i);
+ }
+}
+
+EIGEN_DECLARE_TEST(cxx11_tensor_random)
+{
+ CALL_SUBTEST((test_default<float>()));
+ CALL_SUBTEST((test_normal<float>()));
+ CALL_SUBTEST((test_default<double>()));
+ CALL_SUBTEST((test_normal<double>()));
+ CALL_SUBTEST((test_default<Eigen::half>()));
+ CALL_SUBTEST((test_normal<Eigen::half>()));
+ CALL_SUBTEST((test_default<Eigen::bfloat16>()));
+ CALL_SUBTEST((test_normal<Eigen::bfloat16>()));
+ CALL_SUBTEST(test_custom());
+}
diff --git a/unsupported/test/cxx11_tensor_random_gpu.cu b/unsupported/test/cxx11_tensor_random_gpu.cu
new file mode 100644
index 0000000..090986e
--- /dev/null
+++ b/unsupported/test/cxx11_tensor_random_gpu.cu
@@ -0,0 +1,86 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#define EIGEN_TEST_NO_LONGDOUBLE
+#define EIGEN_TEST_NO_COMPLEX
+
+#define EIGEN_DEFAULT_DENSE_INDEX_TYPE int
+#define EIGEN_USE_GPU
+
+#include "main.h"
+#include <Eigen/CXX11/Tensor>
+
+#include <Eigen/CXX11/src/Tensor/TensorGpuHipCudaDefines.h>
+
+void test_gpu_random_uniform()
+{
+ Tensor<float, 2> out(72,97);
+ out.setZero();
+
+ std::size_t out_bytes = out.size() * sizeof(float);
+
+ float* d_out;
+ gpuMalloc((void**)(&d_out), out_bytes);
+
+ Eigen::GpuStreamDevice stream;
+ Eigen::GpuDevice gpu_device(&stream);
+
+ Eigen::TensorMap<Eigen::Tensor<float, 2> > gpu_out(d_out, 72,97);
+
+ gpu_out.device(gpu_device) = gpu_out.random();
+
+ assert(gpuMemcpyAsync(out.data(), d_out, out_bytes, gpuMemcpyDeviceToHost, gpu_device.stream()) == gpuSuccess);
+ assert(gpuStreamSynchronize(gpu_device.stream()) == gpuSuccess);
+
+ // For now we just check this code doesn't crash.
+ // TODO: come up with a valid test of randomness
+}
+
+
+void test_gpu_random_normal()
+{
+ Tensor<float, 2> out(72,97);
+ out.setZero();
+
+ std::size_t out_bytes = out.size() * sizeof(float);
+
+ float* d_out;
+ gpuMalloc((void**)(&d_out), out_bytes);
+
+ Eigen::GpuStreamDevice stream;
+ Eigen::GpuDevice gpu_device(&stream);
+
+ Eigen::TensorMap<Eigen::Tensor<float, 2> > gpu_out(d_out, 72,97);
+
+ Eigen::internal::NormalRandomGenerator<float> gen(true);
+ gpu_out.device(gpu_device) = gpu_out.random(gen);
+
+ assert(gpuMemcpyAsync(out.data(), d_out, out_bytes, gpuMemcpyDeviceToHost, gpu_device.stream()) == gpuSuccess);
+ assert(gpuStreamSynchronize(gpu_device.stream()) == gpuSuccess);
+}
+
+static void test_complex()
+{
+ Tensor<std::complex<float>, 1> vec(6);
+ vec.setRandom();
+
+ // Fixme: we should check that the generated numbers follow a uniform
+ // distribution instead.
+ for (int i = 1; i < 6; ++i) {
+ VERIFY_IS_NOT_EQUAL(vec(i), vec(i-1));
+ }
+}
+
+
+EIGEN_DECLARE_TEST(cxx11_tensor_random_gpu)
+{
+ CALL_SUBTEST(test_gpu_random_uniform());
+ CALL_SUBTEST(test_gpu_random_normal());
+ CALL_SUBTEST(test_complex());
+}
diff --git a/unsupported/test/cxx11_tensor_random_sycl.cpp b/unsupported/test/cxx11_tensor_random_sycl.cpp
new file mode 100644
index 0000000..14a7c48
--- /dev/null
+++ b/unsupported/test/cxx11_tensor_random_sycl.cpp
@@ -0,0 +1,86 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2016
+// Mehdi Goli Codeplay Software Ltd.
+// Ralph Potter Codeplay Software Ltd.
+// Luke Iwanski Codeplay Software Ltd.
+// Contact: <eigen@codeplay.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#define EIGEN_TEST_NO_LONGDOUBLE
+#define EIGEN_TEST_NO_COMPLEX
+#define EIGEN_DEFAULT_DENSE_INDEX_TYPE int64_t
+#define EIGEN_USE_SYCL
+
+#include "main.h"
+#include <unsupported/Eigen/CXX11/Tensor>
+
+template <typename DataType, int DataLayout, typename IndexType>
+static void test_sycl_random_uniform(const Eigen::SyclDevice& sycl_device)
+{
+ Tensor<DataType, 2,DataLayout, IndexType> out(72,97);
+ out.setZero();
+
+ std::size_t out_bytes = out.size() * sizeof(DataType);
+
+ IndexType sizeDim0 = 72;
+ IndexType sizeDim1 = 97;
+
+ array<IndexType, 2> tensorRange = {{sizeDim0, sizeDim1}};
+
+ DataType* d_out = static_cast<DataType*>(sycl_device.allocate(out_bytes));
+ TensorMap<Tensor<DataType, 2, DataLayout, IndexType>> gpu_out(d_out, tensorRange);
+
+ gpu_out.device(sycl_device)=gpu_out.random();
+ sycl_device.memcpyDeviceToHost(out.data(), d_out,out_bytes);
+
+ // For now we just check the code doesn't crash.
+ // TODO: come up with a valid test of randomness
+ sycl_device.deallocate(d_out);
+}
+
+template <typename DataType, int DataLayout, typename IndexType>
+void test_sycl_random_normal(const Eigen::SyclDevice& sycl_device)
+{
+ Tensor<DataType, 2,DataLayout,IndexType> out(72,97);
+ out.setZero();
+ std::size_t out_bytes = out.size() * sizeof(DataType);
+
+ IndexType sizeDim0 = 72;
+ IndexType sizeDim1 = 97;
+
+ array<IndexType, 2> tensorRange = {{sizeDim0, sizeDim1}};
+
+ DataType* d_out = static_cast<DataType*>(sycl_device.allocate(out_bytes));
+ TensorMap<Tensor<DataType, 2, DataLayout, IndexType>> gpu_out(d_out, tensorRange);
+ Eigen::internal::NormalRandomGenerator<DataType> gen(true);
+ gpu_out.device(sycl_device)=gpu_out.random(gen);
+ sycl_device.memcpyDeviceToHost(out.data(), d_out,out_bytes);
+
+ // For now we just check the code doesn't crash.
+ // TODO: come up with a valid test of randomness
+ sycl_device.deallocate(d_out);
+}
+
+template<typename DataType, typename dev_Selector> void sycl_random_test_per_device(dev_Selector s){
+ QueueInterface queueInterface(s);
+ auto sycl_device = Eigen::SyclDevice(&queueInterface);
+ test_sycl_random_uniform<DataType, RowMajor, int64_t>(sycl_device);
+ test_sycl_random_uniform<DataType, ColMajor, int64_t>(sycl_device);
+ test_sycl_random_normal<DataType, RowMajor, int64_t>(sycl_device);
+ test_sycl_random_normal<DataType, ColMajor, int64_t>(sycl_device);
+
+}
+EIGEN_DECLARE_TEST(cxx11_tensor_random_sycl)
+{
+ for (const auto& device :Eigen::get_sycl_supported_devices()) {
+ CALL_SUBTEST(sycl_random_test_per_device<float>(device));
+#ifdef EIGEN_SYCL_DOUBLE_SUPPORT
+ CALL_SUBTEST(sycl_random_test_per_device<double>(device));
+#endif
+ }
+}
diff --git a/unsupported/test/cxx11_tensor_reduction.cpp b/unsupported/test/cxx11_tensor_reduction.cpp
new file mode 100644
index 0000000..a090e4a
--- /dev/null
+++ b/unsupported/test/cxx11_tensor_reduction.cpp
@@ -0,0 +1,523 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "main.h"
+#include <limits>
+#include <numeric>
+#include <Eigen/CXX11/Tensor>
+
+using Eigen::Tensor;
+
+template <int DataLayout>
+static void test_trivial_reductions() {
+ {
+ Tensor<float, 0, DataLayout> tensor;
+ tensor.setRandom();
+ array<ptrdiff_t, 0> reduction_axis;
+
+ Tensor<float, 0, DataLayout> result = tensor.sum(reduction_axis);
+ VERIFY_IS_EQUAL(result(), tensor());
+ }
+
+ {
+ Tensor<float, 1, DataLayout> tensor(7);
+ tensor.setRandom();
+ array<ptrdiff_t, 0> reduction_axis;
+
+ Tensor<float, 1, DataLayout> result = tensor.sum(reduction_axis);
+ VERIFY_IS_EQUAL(result.dimension(0), 7);
+ for (int i = 0; i < 7; ++i) {
+ VERIFY_IS_EQUAL(result(i), tensor(i));
+ }
+ }
+
+ {
+ Tensor<float, 2, DataLayout> tensor(2, 3);
+ tensor.setRandom();
+ array<ptrdiff_t, 0> reduction_axis;
+
+ Tensor<float, 2, DataLayout> result = tensor.sum(reduction_axis);
+ VERIFY_IS_EQUAL(result.dimension(0), 2);
+ VERIFY_IS_EQUAL(result.dimension(1), 3);
+ for (int i = 0; i < 2; ++i) {
+ for (int j = 0; j < 3; ++j) {
+ VERIFY_IS_EQUAL(result(i, j), tensor(i, j));
+ }
+ }
+ }
+}
+
+template <typename Scalar,int DataLayout>
+static void test_simple_reductions() {
+ Tensor<Scalar, 4, DataLayout> tensor(2, 3, 5, 7);
+ tensor.setRandom();
+ // Add a little offset so that the product reductions won't be close to zero.
+ tensor += tensor.constant(Scalar(0.5f));
+ array<ptrdiff_t, 2> reduction_axis2;
+ reduction_axis2[0] = 1;
+ reduction_axis2[1] = 3;
+
+ Tensor<Scalar, 2, DataLayout> result = tensor.sum(reduction_axis2);
+ VERIFY_IS_EQUAL(result.dimension(0), 2);
+ VERIFY_IS_EQUAL(result.dimension(1), 5);
+ for (int i = 0; i < 2; ++i) {
+ for (int j = 0; j < 5; ++j) {
+ Scalar sum = Scalar(0.0f);
+ for (int k = 0; k < 3; ++k) {
+ for (int l = 0; l < 7; ++l) {
+ sum += tensor(i, k, j, l);
+ }
+ }
+ VERIFY_IS_APPROX(result(i, j), sum);
+ }
+ }
+
+ {
+ Tensor<Scalar, 0, DataLayout> sum1 = tensor.sum();
+ VERIFY_IS_EQUAL(sum1.rank(), 0);
+
+ array<ptrdiff_t, 4> reduction_axis4;
+ reduction_axis4[0] = 0;
+ reduction_axis4[1] = 1;
+ reduction_axis4[2] = 2;
+ reduction_axis4[3] = 3;
+ Tensor<Scalar, 0, DataLayout> sum2 = tensor.sum(reduction_axis4);
+ VERIFY_IS_EQUAL(sum2.rank(), 0);
+
+ VERIFY_IS_APPROX(sum1(), sum2());
+ }
+
+ reduction_axis2[0] = 0;
+ reduction_axis2[1] = 2;
+ result = tensor.prod(reduction_axis2);
+ VERIFY_IS_EQUAL(result.dimension(0), 3);
+ VERIFY_IS_EQUAL(result.dimension(1), 7);
+ for (int i = 0; i < 3; ++i) {
+ for (int j = 0; j < 7; ++j) {
+ Scalar prod = Scalar(1.0f);
+ for (int k = 0; k < 2; ++k) {
+ for (int l = 0; l < 5; ++l) {
+ prod *= tensor(k, i, l, j);
+ }
+ }
+ VERIFY_IS_APPROX(result(i, j), prod);
+ }
+ }
+
+ {
+ Tensor<Scalar, 0, DataLayout> prod1 = tensor.prod();
+ VERIFY_IS_EQUAL(prod1.rank(), 0);
+
+ array<ptrdiff_t, 4> reduction_axis4;
+ reduction_axis4[0] = 0;
+ reduction_axis4[1] = 1;
+ reduction_axis4[2] = 2;
+ reduction_axis4[3] = 3;
+ Tensor<Scalar, 0, DataLayout> prod2 = tensor.prod(reduction_axis4);
+ VERIFY_IS_EQUAL(prod2.rank(), 0);
+
+ VERIFY_IS_APPROX(prod1(), prod2());
+ }
+
+ reduction_axis2[0] = 0;
+ reduction_axis2[1] = 2;
+ result = tensor.maximum(reduction_axis2);
+ VERIFY_IS_EQUAL(result.dimension(0), 3);
+ VERIFY_IS_EQUAL(result.dimension(1), 7);
+ for (int i = 0; i < 3; ++i) {
+ for (int j = 0; j < 7; ++j) {
+ Scalar max_val = std::numeric_limits<Scalar>::lowest();
+ for (int k = 0; k < 2; ++k) {
+ for (int l = 0; l < 5; ++l) {
+ max_val = (std::max)(max_val, tensor(k, i, l, j));
+ }
+ }
+ VERIFY_IS_APPROX(result(i, j), max_val);
+ }
+ }
+
+ {
+ Tensor<Scalar, 0, DataLayout> max1 = tensor.maximum();
+ VERIFY_IS_EQUAL(max1.rank(), 0);
+
+ array<ptrdiff_t, 4> reduction_axis4;
+ reduction_axis4[0] = 0;
+ reduction_axis4[1] = 1;
+ reduction_axis4[2] = 2;
+ reduction_axis4[3] = 3;
+ Tensor<Scalar, 0, DataLayout> max2 = tensor.maximum(reduction_axis4);
+ VERIFY_IS_EQUAL(max2.rank(), 0);
+
+ VERIFY_IS_APPROX(max1(), max2());
+ }
+
+ reduction_axis2[0] = 0;
+ reduction_axis2[1] = 1;
+ result = tensor.minimum(reduction_axis2);
+ VERIFY_IS_EQUAL(result.dimension(0), 5);
+ VERIFY_IS_EQUAL(result.dimension(1), 7);
+ for (int i = 0; i < 5; ++i) {
+ for (int j = 0; j < 7; ++j) {
+ Scalar min_val = (std::numeric_limits<Scalar>::max)();
+ for (int k = 0; k < 2; ++k) {
+ for (int l = 0; l < 3; ++l) {
+ min_val = (std::min)(min_val, tensor(k, l, i, j));
+ }
+ }
+ VERIFY_IS_APPROX(result(i, j), min_val);
+ }
+ }
+
+ {
+ Tensor<Scalar, 0, DataLayout> min1 = tensor.minimum();
+ VERIFY_IS_EQUAL(min1.rank(), 0);
+
+ array<ptrdiff_t, 4> reduction_axis4;
+ reduction_axis4[0] = 0;
+ reduction_axis4[1] = 1;
+ reduction_axis4[2] = 2;
+ reduction_axis4[3] = 3;
+ Tensor<Scalar, 0, DataLayout> min2 = tensor.minimum(reduction_axis4);
+ VERIFY_IS_EQUAL(min2.rank(), 0);
+
+ VERIFY_IS_APPROX(min1(), min2());
+ }
+
+ reduction_axis2[0] = 0;
+ reduction_axis2[1] = 1;
+ result = tensor.mean(reduction_axis2);
+ VERIFY_IS_EQUAL(result.dimension(0), 5);
+ VERIFY_IS_EQUAL(result.dimension(1), 7);
+ for (int i = 0; i < 5; ++i) {
+ for (int j = 0; j < 7; ++j) {
+ Scalar sum = Scalar(0.0f);
+ int count = 0;
+ for (int k = 0; k < 2; ++k) {
+ for (int l = 0; l < 3; ++l) {
+ sum += tensor(k, l, i, j);
+ ++count;
+ }
+ }
+ VERIFY_IS_APPROX(result(i, j), sum / Scalar(count));
+ }
+ }
+
+ {
+ Tensor<Scalar, 0, DataLayout> mean1 = tensor.mean();
+ VERIFY_IS_EQUAL(mean1.rank(), 0);
+
+ array<ptrdiff_t, 4> reduction_axis4;
+ reduction_axis4[0] = 0;
+ reduction_axis4[1] = 1;
+ reduction_axis4[2] = 2;
+ reduction_axis4[3] = 3;
+ Tensor<Scalar, 0, DataLayout> mean2 = tensor.mean(reduction_axis4);
+ VERIFY_IS_EQUAL(mean2.rank(), 0);
+
+ VERIFY_IS_APPROX(mean1(), mean2());
+ }
+
+ {
+ Tensor<int, 1> ints(10);
+ std::iota(ints.data(), ints.data() + ints.dimension(0), 0);
+
+ TensorFixedSize<bool, Sizes<> > all_;
+ all_ = ints.all();
+ VERIFY(!all_());
+ all_ = (ints >= ints.constant(0)).all();
+ VERIFY(all_());
+
+ TensorFixedSize<bool, Sizes<> > any;
+ any = (ints > ints.constant(10)).any();
+ VERIFY(!any());
+ any = (ints < ints.constant(1)).any();
+ VERIFY(any());
+ }
+}
+
+
+template <int DataLayout>
+static void test_reductions_in_expr() {
+ Tensor<float, 4, DataLayout> tensor(2, 3, 5, 7);
+ tensor.setRandom();
+ array<ptrdiff_t, 2> reduction_axis2;
+ reduction_axis2[0] = 1;
+ reduction_axis2[1] = 3;
+
+ Tensor<float, 2, DataLayout> result(2, 5);
+ result = result.constant(1.0f) - tensor.sum(reduction_axis2);
+ VERIFY_IS_EQUAL(result.dimension(0), 2);
+ VERIFY_IS_EQUAL(result.dimension(1), 5);
+ for (int i = 0; i < 2; ++i) {
+ for (int j = 0; j < 5; ++j) {
+ float sum = 0.0f;
+ for (int k = 0; k < 3; ++k) {
+ for (int l = 0; l < 7; ++l) {
+ sum += tensor(i, k, j, l);
+ }
+ }
+ VERIFY_IS_APPROX(result(i, j), 1.0f - sum);
+ }
+ }
+}
+
+
+template <int DataLayout>
+static void test_full_reductions() {
+ Tensor<float, 2, DataLayout> tensor(2, 3);
+ tensor.setRandom();
+ array<ptrdiff_t, 2> reduction_axis;
+ reduction_axis[0] = 0;
+ reduction_axis[1] = 1;
+
+ Tensor<float, 0, DataLayout> result = tensor.sum(reduction_axis);
+ VERIFY_IS_EQUAL(result.rank(), 0);
+
+ float sum = 0.0f;
+ for (int i = 0; i < 2; ++i) {
+ for (int j = 0; j < 3; ++j) {
+ sum += tensor(i, j);
+ }
+ }
+ VERIFY_IS_APPROX(result(0), sum);
+
+ result = tensor.square().sum(reduction_axis).sqrt();
+ VERIFY_IS_EQUAL(result.rank(), 0);
+
+ sum = 0.0f;
+ for (int i = 0; i < 2; ++i) {
+ for (int j = 0; j < 3; ++j) {
+ sum += tensor(i, j) * tensor(i, j);
+ }
+ }
+ VERIFY_IS_APPROX(result(), sqrtf(sum));
+}
+
+struct UserReducer {
+ static const bool PacketAccess = false;
+ UserReducer(float offset) : offset_(offset) {}
+ void reduce(const float val, float* accum) { *accum += val * val; }
+ float initialize() const { return 0; }
+ float finalize(const float accum) const { return 1.0f / (accum + offset_); }
+
+ private:
+ const float offset_;
+};
+
+template <int DataLayout>
+static void test_user_defined_reductions() {
+ Tensor<float, 2, DataLayout> tensor(5, 7);
+ tensor.setRandom();
+ array<ptrdiff_t, 1> reduction_axis;
+ reduction_axis[0] = 1;
+
+ UserReducer reducer(10.0f);
+ Tensor<float, 1, DataLayout> result = tensor.reduce(reduction_axis, reducer);
+ VERIFY_IS_EQUAL(result.dimension(0), 5);
+ for (int i = 0; i < 5; ++i) {
+ float expected = 10.0f;
+ for (int j = 0; j < 7; ++j) {
+ expected += tensor(i, j) * tensor(i, j);
+ }
+ expected = 1.0f / expected;
+ VERIFY_IS_APPROX(result(i), expected);
+ }
+}
+
+template <int DataLayout>
+static void test_tensor_maps() {
+ int inputs[2 * 3 * 5 * 7];
+ TensorMap<Tensor<int, 4, DataLayout> > tensor_map(inputs, 2, 3, 5, 7);
+ TensorMap<Tensor<const int, 4, DataLayout> > tensor_map_const(inputs, 2, 3, 5,
+ 7);
+ const TensorMap<Tensor<const int, 4, DataLayout> > tensor_map_const_const(
+ inputs, 2, 3, 5, 7);
+
+ tensor_map.setRandom();
+ array<ptrdiff_t, 2> reduction_axis;
+ reduction_axis[0] = 1;
+ reduction_axis[1] = 3;
+
+ Tensor<int, 2, DataLayout> result = tensor_map.sum(reduction_axis);
+ Tensor<int, 2, DataLayout> result2 = tensor_map_const.sum(reduction_axis);
+ Tensor<int, 2, DataLayout> result3 =
+ tensor_map_const_const.sum(reduction_axis);
+
+ for (int i = 0; i < 2; ++i) {
+ for (int j = 0; j < 5; ++j) {
+ int sum = 0;
+ for (int k = 0; k < 3; ++k) {
+ for (int l = 0; l < 7; ++l) {
+ sum += tensor_map(i, k, j, l);
+ }
+ }
+ VERIFY_IS_EQUAL(result(i, j), sum);
+ VERIFY_IS_EQUAL(result2(i, j), sum);
+ VERIFY_IS_EQUAL(result3(i, j), sum);
+ }
+ }
+}
+
+template <int DataLayout>
+static void test_static_dims() {
+ Tensor<float, 4, DataLayout> in(72, 53, 97, 113);
+ Tensor<float, 2, DataLayout> out(72, 97);
+ in.setRandom();
+
+ Eigen::IndexList<Eigen::type2index<1>, Eigen::type2index<3> > reduction_axis;
+
+ out = in.maximum(reduction_axis);
+
+ for (int i = 0; i < 72; ++i) {
+ for (int j = 0; j < 97; ++j) {
+ float expected = -1e10f;
+ for (int k = 0; k < 53; ++k) {
+ for (int l = 0; l < 113; ++l) {
+ expected = (std::max)(expected, in(i, k, j, l));
+ }
+ }
+ VERIFY_IS_EQUAL(out(i, j), expected);
+ }
+ }
+}
+
+template <int DataLayout>
+static void test_innermost_last_dims() {
+ Tensor<float, 4, DataLayout> in(72, 53, 97, 113);
+ Tensor<float, 2, DataLayout> out(97, 113);
+ in.setRandom();
+
+// Reduce on the innermost dimensions.
+ // This triggers the use of packets for ColMajor.
+ Eigen::IndexList<Eigen::type2index<0>, Eigen::type2index<1> > reduction_axis;
+
+ out = in.maximum(reduction_axis);
+
+ for (int i = 0; i < 97; ++i) {
+ for (int j = 0; j < 113; ++j) {
+ float expected = -1e10f;
+ for (int k = 0; k < 53; ++k) {
+ for (int l = 0; l < 72; ++l) {
+ expected = (std::max)(expected, in(l, k, i, j));
+ }
+ }
+ VERIFY_IS_EQUAL(out(i, j), expected);
+ }
+ }
+}
+
+template <int DataLayout>
+static void test_innermost_first_dims() {
+ Tensor<float, 4, DataLayout> in(72, 53, 97, 113);
+ Tensor<float, 2, DataLayout> out(72, 53);
+ in.setRandom();
+
+// Reduce on the innermost dimensions.
+ // This triggers the use of packets for RowMajor.
+ Eigen::IndexList<Eigen::type2index<2>, Eigen::type2index<3>> reduction_axis;
+
+ out = in.maximum(reduction_axis);
+
+ for (int i = 0; i < 72; ++i) {
+ for (int j = 0; j < 53; ++j) {
+ float expected = -1e10f;
+ for (int k = 0; k < 97; ++k) {
+ for (int l = 0; l < 113; ++l) {
+ expected = (std::max)(expected, in(i, j, k, l));
+ }
+ }
+ VERIFY_IS_EQUAL(out(i, j), expected);
+ }
+ }
+}
+
+template <int DataLayout>
+static void test_reduce_middle_dims() {
+ Tensor<float, 4, DataLayout> in(72, 53, 97, 113);
+ Tensor<float, 2, DataLayout> out(72, 53);
+ in.setRandom();
+
+// Reduce on the innermost dimensions.
+ // This triggers the use of packets for RowMajor.
+ Eigen::IndexList<Eigen::type2index<1>, Eigen::type2index<2>> reduction_axis;
+
+ out = in.maximum(reduction_axis);
+
+ for (int i = 0; i < 72; ++i) {
+ for (int j = 0; j < 113; ++j) {
+ float expected = -1e10f;
+ for (int k = 0; k < 53; ++k) {
+ for (int l = 0; l < 97; ++l) {
+ expected = (std::max)(expected, in(i, k, l, j));
+ }
+ }
+ VERIFY_IS_EQUAL(out(i, j), expected);
+ }
+ }
+}
+
+template <typename ScalarType, int num_elements, int max_mean>
+void test_sum_accuracy() {
+ Tensor<double, 1> double_tensor(num_elements);
+ Tensor<ScalarType, 1> tensor(num_elements);
+ for (double prescribed_mean = 0; prescribed_mean <= max_mean; prescribed_mean = numext::maxi(1.0, prescribed_mean*3.99)) {
+ // FIXME: NormalRandomGenerator doesn't work in bfloat and half.
+ double_tensor.setRandom<Eigen::internal::NormalRandomGenerator<double>>();
+ double_tensor += double_tensor.constant(prescribed_mean);
+ tensor = double_tensor.cast<ScalarType>();
+
+ Tensor<ScalarType, 0> sum;
+ sum = tensor.sum();
+
+ // Compute the reference value in double precsion.
+ double expected_sum = 0.0;
+ double abs_sum = 0.0;
+ for (int i = 0; i < num_elements; ++i) {
+ expected_sum += static_cast<double>(tensor(i));
+ abs_sum += static_cast<double>(numext::abs(tensor(i)));
+ }
+ // Test against probabilistic forward error bound. In reality, the error is much smaller
+ // when we use tree summation.
+ double err = Eigen::numext::abs(static_cast<double>(sum()) - expected_sum);
+ double tol = numext::sqrt(num_elements) * NumTraits<ScalarType>::epsilon() * static_cast<ScalarType>(abs_sum);
+ VERIFY_LE(err, tol);
+ }
+}
+
+EIGEN_DECLARE_TEST(cxx11_tensor_reduction) {
+ CALL_SUBTEST(test_trivial_reductions<ColMajor>());
+ CALL_SUBTEST(test_trivial_reductions<RowMajor>());
+ CALL_SUBTEST(( test_simple_reductions<float,ColMajor>() ));
+ CALL_SUBTEST(( test_simple_reductions<float,RowMajor>() ));
+ CALL_SUBTEST(( test_simple_reductions<Eigen::half,ColMajor>() ));
+ CALL_SUBTEST(( test_simple_reductions<Eigen::bfloat16,ColMajor>() ));
+ CALL_SUBTEST(test_reductions_in_expr<ColMajor>());
+ CALL_SUBTEST(test_reductions_in_expr<RowMajor>());
+ CALL_SUBTEST(test_full_reductions<ColMajor>());
+ CALL_SUBTEST(test_full_reductions<RowMajor>());
+ CALL_SUBTEST(test_user_defined_reductions<ColMajor>());
+ CALL_SUBTEST(test_user_defined_reductions<RowMajor>());
+ CALL_SUBTEST(test_tensor_maps<ColMajor>());
+ CALL_SUBTEST(test_tensor_maps<RowMajor>());
+ CALL_SUBTEST(test_static_dims<ColMajor>());
+ CALL_SUBTEST(test_static_dims<RowMajor>());
+ CALL_SUBTEST(test_innermost_last_dims<ColMajor>());
+ CALL_SUBTEST(test_innermost_last_dims<RowMajor>());
+ CALL_SUBTEST(test_innermost_first_dims<ColMajor>());
+ CALL_SUBTEST(test_innermost_first_dims<RowMajor>());
+ CALL_SUBTEST(test_reduce_middle_dims<ColMajor>());
+ CALL_SUBTEST(test_reduce_middle_dims<RowMajor>());
+ CALL_SUBTEST((test_sum_accuracy<float,10*1024*1024,8*1024>()));
+ CALL_SUBTEST((test_sum_accuracy<Eigen::bfloat16,10*1024*1024,8*1024>()));
+ // The range of half is limited to 65519 when using round-to-even,
+ // so we are severely limited in the size and mean of the tensors
+ // we can reduce without overflow.
+ CALL_SUBTEST((test_sum_accuracy<Eigen::half,4*1024,16>()));
+ CALL_SUBTEST((test_sum_accuracy<Eigen::half,10*1024*1024,0>()));
+}
diff --git a/unsupported/test/cxx11_tensor_reduction_gpu.cu b/unsupported/test/cxx11_tensor_reduction_gpu.cu
new file mode 100644
index 0000000..122ac94
--- /dev/null
+++ b/unsupported/test/cxx11_tensor_reduction_gpu.cu
@@ -0,0 +1,154 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2015 Benoit Steiner <benoit.steiner.goog@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#define EIGEN_TEST_NO_LONGDOUBLE
+#define EIGEN_TEST_NO_COMPLEX
+
+#define EIGEN_USE_GPU
+
+#include "main.h"
+#include <unsupported/Eigen/CXX11/Tensor>
+
+
+template<typename Type, int DataLayout>
+static void test_full_reductions() {
+
+ Eigen::GpuStreamDevice stream;
+ Eigen::GpuDevice gpu_device(&stream);
+
+ const int num_rows = internal::random<int>(1024, 5*1024);
+ const int num_cols = internal::random<int>(1024, 5*1024);
+
+ Tensor<Type, 2, DataLayout> in(num_rows, num_cols);
+ in.setRandom();
+
+ Tensor<Type, 0, DataLayout> full_redux;
+ full_redux = in.sum();
+
+ std::size_t in_bytes = in.size() * sizeof(Type);
+ std::size_t out_bytes = full_redux.size() * sizeof(Type);
+ Type* gpu_in_ptr = static_cast<Type*>(gpu_device.allocate(in_bytes));
+ Type* gpu_out_ptr = static_cast<Type*>(gpu_device.allocate(out_bytes));
+ gpu_device.memcpyHostToDevice(gpu_in_ptr, in.data(), in_bytes);
+
+ TensorMap<Tensor<Type, 2, DataLayout> > in_gpu(gpu_in_ptr, num_rows, num_cols);
+ TensorMap<Tensor<Type, 0, DataLayout> > out_gpu(gpu_out_ptr);
+
+ out_gpu.device(gpu_device) = in_gpu.sum();
+
+ Tensor<Type, 0, DataLayout> full_redux_gpu;
+ gpu_device.memcpyDeviceToHost(full_redux_gpu.data(), gpu_out_ptr, out_bytes);
+ gpu_device.synchronize();
+
+ // Check that the CPU and GPU reductions return the same result.
+ VERIFY_IS_APPROX(full_redux(), full_redux_gpu());
+
+ gpu_device.deallocate(gpu_in_ptr);
+ gpu_device.deallocate(gpu_out_ptr);
+}
+
+template<typename Type, int DataLayout>
+static void test_first_dim_reductions() {
+ int dim_x = 33;
+ int dim_y = 1;
+ int dim_z = 128;
+
+ Tensor<Type, 3, DataLayout> in(dim_x, dim_y, dim_z);
+ in.setRandom();
+
+ Eigen::array<int, 1> red_axis;
+ red_axis[0] = 0;
+ Tensor<Type, 2, DataLayout> redux = in.sum(red_axis);
+
+ // Create device
+ Eigen::GpuStreamDevice stream;
+ Eigen::GpuDevice dev(&stream);
+
+ // Create data(T)
+ Type* in_data = (Type*)dev.allocate(dim_x*dim_y*dim_z*sizeof(Type));
+ Type* out_data = (Type*)dev.allocate(dim_z*dim_y*sizeof(Type));
+ Eigen::TensorMap<Eigen::Tensor<Type, 3, DataLayout> > gpu_in(in_data, dim_x, dim_y, dim_z);
+ Eigen::TensorMap<Eigen::Tensor<Type, 2, DataLayout> > gpu_out(out_data, dim_y, dim_z);
+
+ // Perform operation
+ dev.memcpyHostToDevice(in_data, in.data(), in.size()*sizeof(Type));
+ gpu_out.device(dev) = gpu_in.sum(red_axis);
+ gpu_out.device(dev) += gpu_in.sum(red_axis);
+ Tensor<Type, 2, DataLayout> redux_gpu(dim_y, dim_z);
+ dev.memcpyDeviceToHost(redux_gpu.data(), out_data, gpu_out.size()*sizeof(Type));
+ dev.synchronize();
+
+ // Check that the CPU and GPU reductions return the same result.
+ for (int i = 0; i < gpu_out.size(); ++i) {
+ VERIFY_IS_APPROX(2*redux(i), redux_gpu(i));
+ }
+
+ dev.deallocate(in_data);
+ dev.deallocate(out_data);
+}
+
+template<typename Type, int DataLayout>
+static void test_last_dim_reductions() {
+ int dim_x = 128;
+ int dim_y = 1;
+ int dim_z = 33;
+
+ Tensor<Type, 3, DataLayout> in(dim_x, dim_y, dim_z);
+ in.setRandom();
+
+ Eigen::array<int, 1> red_axis;
+ red_axis[0] = 2;
+ Tensor<Type, 2, DataLayout> redux = in.sum(red_axis);
+
+ // Create device
+ Eigen::GpuStreamDevice stream;
+ Eigen::GpuDevice dev(&stream);
+
+ // Create data
+ Type* in_data = (Type*)dev.allocate(dim_x*dim_y*dim_z*sizeof(Type));
+ Type* out_data = (Type*)dev.allocate(dim_x*dim_y*sizeof(Type));
+ Eigen::TensorMap<Eigen::Tensor<Type, 3, DataLayout> > gpu_in(in_data, dim_x, dim_y, dim_z);
+ Eigen::TensorMap<Eigen::Tensor<Type, 2, DataLayout> > gpu_out(out_data, dim_x, dim_y);
+
+ // Perform operation
+ dev.memcpyHostToDevice(in_data, in.data(), in.size()*sizeof(Type));
+ gpu_out.device(dev) = gpu_in.sum(red_axis);
+ gpu_out.device(dev) += gpu_in.sum(red_axis);
+ Tensor<Type, 2, DataLayout> redux_gpu(dim_x, dim_y);
+ dev.memcpyDeviceToHost(redux_gpu.data(), out_data, gpu_out.size()*sizeof(Type));
+ dev.synchronize();
+
+ // Check that the CPU and GPU reductions return the same result.
+ for (int i = 0; i < gpu_out.size(); ++i) {
+ VERIFY_IS_APPROX(2*redux(i), redux_gpu(i));
+ }
+
+ dev.deallocate(in_data);
+ dev.deallocate(out_data);
+}
+
+
+EIGEN_DECLARE_TEST(cxx11_tensor_reduction_gpu) {
+ CALL_SUBTEST_1((test_full_reductions<float, ColMajor>()));
+ CALL_SUBTEST_1((test_full_reductions<double, ColMajor>()));
+ CALL_SUBTEST_2((test_full_reductions<float, RowMajor>()));
+ CALL_SUBTEST_2((test_full_reductions<double, RowMajor>()));
+
+ CALL_SUBTEST_3((test_first_dim_reductions<float, ColMajor>()));
+ CALL_SUBTEST_3((test_first_dim_reductions<double, ColMajor>()));
+ CALL_SUBTEST_4((test_first_dim_reductions<float, RowMajor>()));
+// Outer reductions of doubles aren't supported just yet.
+// CALL_SUBTEST_4((test_first_dim_reductions<double, RowMajor>()))
+
+ CALL_SUBTEST_5((test_last_dim_reductions<float, ColMajor>()));
+// Outer reductions of doubles aren't supported just yet.
+// CALL_SUBTEST_5((test_last_dim_reductions<double, ColMajor>()));
+ CALL_SUBTEST_6((test_last_dim_reductions<float, RowMajor>()));
+ CALL_SUBTEST_6((test_last_dim_reductions<double, RowMajor>()));
+}
diff --git a/unsupported/test/cxx11_tensor_reduction_sycl.cpp b/unsupported/test/cxx11_tensor_reduction_sycl.cpp
new file mode 100644
index 0000000..3afa62a
--- /dev/null
+++ b/unsupported/test/cxx11_tensor_reduction_sycl.cpp
@@ -0,0 +1,1013 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2015
+// Mehdi Goli Codeplay Software Ltd.
+// Ralph Potter Codeplay Software Ltd.
+// Luke Iwanski Codeplay Software Ltd.
+// Contact: <eigen@codeplay.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#define EIGEN_TEST_NO_LONGDOUBLE
+#define EIGEN_TEST_NO_COMPLEX
+
+#define EIGEN_DEFAULT_DENSE_INDEX_TYPE int64_t
+#define EIGEN_USE_SYCL
+
+#include "main.h"
+
+#include <unsupported/Eigen/CXX11/Tensor>
+
+template <typename DataType, int DataLayout, typename IndexType>
+static void test_full_reductions_sum_sycl(
+ const Eigen::SyclDevice& sycl_device) {
+ const IndexType num_rows = 753;
+ const IndexType num_cols = 537;
+ array<IndexType, 2> tensorRange = {{num_rows, num_cols}};
+
+ array<IndexType, 2> outRange = {{1, 1}};
+
+ Tensor<DataType, 2, DataLayout, IndexType> in(tensorRange);
+ Tensor<DataType, 2, DataLayout, IndexType> full_redux(outRange);
+ Tensor<DataType, 2, DataLayout, IndexType> full_redux_gpu(outRange);
+
+ in.setRandom();
+ auto dim = DSizes<IndexType, 2>(1, 1);
+ full_redux = in.sum().reshape(dim);
+
+ DataType* gpu_in_data = static_cast<DataType*>(
+ sycl_device.allocate(in.dimensions().TotalSize() * sizeof(DataType)));
+ DataType* gpu_out_data = (DataType*)sycl_device.allocate(
+ sizeof(DataType) * (full_redux_gpu.dimensions().TotalSize()));
+
+ TensorMap<Tensor<DataType, 2, DataLayout, IndexType>> in_gpu(gpu_in_data,
+ tensorRange);
+ TensorMap<Tensor<DataType, 2, DataLayout, IndexType>> out_gpu(gpu_out_data,
+ outRange);
+ sycl_device.memcpyHostToDevice(
+ gpu_in_data, in.data(), (in.dimensions().TotalSize()) * sizeof(DataType));
+ out_gpu.device(sycl_device) = in_gpu.sum().reshape(dim);
+ sycl_device.memcpyDeviceToHost(
+ full_redux_gpu.data(), gpu_out_data,
+ (full_redux_gpu.dimensions().TotalSize()) * sizeof(DataType));
+ // Check that the CPU and GPU reductions return the same result.
+ std::cout << "SYCL FULL :" << full_redux_gpu(0, 0)
+ << ", CPU FULL: " << full_redux(0, 0) << "\n";
+ VERIFY_IS_APPROX(full_redux_gpu(0, 0), full_redux(0, 0));
+ sycl_device.deallocate(gpu_in_data);
+ sycl_device.deallocate(gpu_out_data);
+}
+
+template <typename DataType, int DataLayout, typename IndexType>
+static void test_full_reductions_sum_with_offset_sycl(
+ const Eigen::SyclDevice& sycl_device) {
+ using data_tensor = Tensor<DataType, 2, DataLayout, IndexType>;
+ using scalar_tensor = Tensor<DataType, 0, DataLayout, IndexType>;
+ const IndexType num_rows = 64;
+ const IndexType num_cols = 64;
+ array<IndexType, 2> tensor_range = {{num_rows, num_cols}};
+ const IndexType n_elems = internal::array_prod(tensor_range);
+
+ data_tensor in(tensor_range);
+ scalar_tensor full_redux;
+ scalar_tensor full_redux_gpu;
+
+ in.setRandom();
+ array<IndexType, 2> tensor_offset_range(tensor_range);
+ tensor_offset_range[0] -= 1;
+
+ const IndexType offset = 64;
+ TensorMap<data_tensor> in_offset(in.data() + offset, tensor_offset_range);
+ full_redux = in_offset.sum();
+
+ DataType* gpu_in_data =
+ static_cast<DataType*>(sycl_device.allocate(n_elems * sizeof(DataType)));
+ DataType* gpu_out_data =
+ static_cast<DataType*>(sycl_device.allocate(sizeof(DataType)));
+
+ TensorMap<data_tensor> in_gpu(gpu_in_data + offset, tensor_offset_range);
+ TensorMap<scalar_tensor> out_gpu(gpu_out_data);
+ sycl_device.memcpyHostToDevice(gpu_in_data, in.data(),
+ n_elems * sizeof(DataType));
+ out_gpu.device(sycl_device) = in_gpu.sum();
+ sycl_device.memcpyDeviceToHost(full_redux_gpu.data(), gpu_out_data,
+ sizeof(DataType));
+
+ // Check that the CPU and GPU reductions return the same result.
+ VERIFY_IS_APPROX(full_redux_gpu(), full_redux());
+
+ sycl_device.deallocate(gpu_in_data);
+ sycl_device.deallocate(gpu_out_data);
+}
+
+template <typename DataType, int DataLayout, typename IndexType>
+static void test_full_reductions_max_sycl(
+ const Eigen::SyclDevice& sycl_device) {
+ const IndexType num_rows = 4096;
+ const IndexType num_cols = 4096;
+ array<IndexType, 2> tensorRange = {{num_rows, num_cols}};
+
+ Tensor<DataType, 2, DataLayout, IndexType> in(tensorRange);
+ Tensor<DataType, 0, DataLayout, IndexType> full_redux;
+ Tensor<DataType, 0, DataLayout, IndexType> full_redux_gpu;
+
+ in.setRandom();
+
+ full_redux = in.maximum();
+
+ DataType* gpu_in_data = static_cast<DataType*>(
+ sycl_device.allocate(in.dimensions().TotalSize() * sizeof(DataType)));
+ DataType* gpu_out_data = (DataType*)sycl_device.allocate(sizeof(DataType));
+
+ TensorMap<Tensor<DataType, 2, DataLayout, IndexType>> in_gpu(gpu_in_data,
+ tensorRange);
+ TensorMap<Tensor<DataType, 0, DataLayout, IndexType>> out_gpu(gpu_out_data);
+ sycl_device.memcpyHostToDevice(
+ gpu_in_data, in.data(), (in.dimensions().TotalSize()) * sizeof(DataType));
+ out_gpu.device(sycl_device) = in_gpu.maximum();
+ sycl_device.memcpyDeviceToHost(full_redux_gpu.data(), gpu_out_data,
+ sizeof(DataType));
+ VERIFY_IS_APPROX(full_redux_gpu(), full_redux());
+ sycl_device.deallocate(gpu_in_data);
+ sycl_device.deallocate(gpu_out_data);
+}
+
+template <typename DataType, int DataLayout, typename IndexType>
+static void test_full_reductions_max_with_offset_sycl(
+ const Eigen::SyclDevice& sycl_device) {
+ using data_tensor = Tensor<DataType, 2, DataLayout, IndexType>;
+ using scalar_tensor = Tensor<DataType, 0, DataLayout, IndexType>;
+ const IndexType num_rows = 64;
+ const IndexType num_cols = 64;
+ array<IndexType, 2> tensor_range = {{num_rows, num_cols}};
+ const IndexType n_elems = internal::array_prod(tensor_range);
+
+ data_tensor in(tensor_range);
+ scalar_tensor full_redux;
+ scalar_tensor full_redux_gpu;
+
+ in.setRandom();
+ array<IndexType, 2> tensor_offset_range(tensor_range);
+ tensor_offset_range[0] -= 1;
+ // Set the initial value to be the max.
+ // As we don't include this in the reduction the result should not be 2.
+ in(0) = static_cast<DataType>(2);
+
+ const IndexType offset = 64;
+ TensorMap<data_tensor> in_offset(in.data() + offset, tensor_offset_range);
+ full_redux = in_offset.maximum();
+ VERIFY_IS_NOT_EQUAL(full_redux(), in(0));
+
+ DataType* gpu_in_data =
+ static_cast<DataType*>(sycl_device.allocate(n_elems * sizeof(DataType)));
+ DataType* gpu_out_data =
+ static_cast<DataType*>(sycl_device.allocate(sizeof(DataType)));
+
+ TensorMap<data_tensor> in_gpu(gpu_in_data + offset, tensor_offset_range);
+ TensorMap<scalar_tensor> out_gpu(gpu_out_data);
+ sycl_device.memcpyHostToDevice(gpu_in_data, in.data(),
+ n_elems * sizeof(DataType));
+ out_gpu.device(sycl_device) = in_gpu.maximum();
+ sycl_device.memcpyDeviceToHost(full_redux_gpu.data(), gpu_out_data,
+ sizeof(DataType));
+
+ // Check that the CPU and GPU reductions return the same result.
+ VERIFY_IS_APPROX(full_redux_gpu(), full_redux());
+
+ sycl_device.deallocate(gpu_in_data);
+ sycl_device.deallocate(gpu_out_data);
+}
+
+template <typename DataType, int DataLayout, typename IndexType>
+static void test_full_reductions_mean_sycl(
+ const Eigen::SyclDevice& sycl_device) {
+ const IndexType num_rows = 4096;
+ const IndexType num_cols = 4096;
+ array<IndexType, 2> tensorRange = {{num_rows, num_cols}};
+ array<IndexType, 1> argRange = {{num_cols}};
+ Eigen::array<IndexType, 1> red_axis;
+ red_axis[0] = 0;
+ // red_axis[1]=1;
+ Tensor<DataType, 2, DataLayout, IndexType> in(tensorRange);
+ Tensor<DataType, 2, DataLayout, IndexType> in_arg1(tensorRange);
+ Tensor<DataType, 2, DataLayout, IndexType> in_arg2(tensorRange);
+ Tensor<bool, 1, DataLayout, IndexType> out_arg_cpu(argRange);
+ Tensor<bool, 1, DataLayout, IndexType> out_arg_gpu(argRange);
+ Tensor<bool, 1, DataLayout, IndexType> out_arg_gpu_helper(argRange);
+ Tensor<DataType, 0, DataLayout, IndexType> full_redux;
+ Tensor<DataType, 0, DataLayout, IndexType> full_redux_gpu;
+
+ in.setRandom();
+ in_arg1.setRandom();
+ in_arg2.setRandom();
+
+ DataType* gpu_in_data = static_cast<DataType*>(
+ sycl_device.allocate(in.dimensions().TotalSize() * sizeof(DataType)));
+ DataType* gpu_in_arg1_data = static_cast<DataType*>(sycl_device.allocate(
+ in_arg1.dimensions().TotalSize() * sizeof(DataType)));
+ DataType* gpu_in_arg2_data = static_cast<DataType*>(sycl_device.allocate(
+ in_arg2.dimensions().TotalSize() * sizeof(DataType)));
+ bool* gpu_out_arg__gpu_helper_data = static_cast<bool*>(sycl_device.allocate(
+ out_arg_gpu.dimensions().TotalSize() * sizeof(DataType)));
+ bool* gpu_out_arg_data = static_cast<bool*>(sycl_device.allocate(
+ out_arg_gpu.dimensions().TotalSize() * sizeof(DataType)));
+
+ DataType* gpu_out_data = (DataType*)sycl_device.allocate(sizeof(DataType));
+
+ TensorMap<Tensor<DataType, 2, DataLayout, IndexType>> in_gpu(gpu_in_data,
+ tensorRange);
+ TensorMap<Tensor<DataType, 2, DataLayout, IndexType>> in_Arg1_gpu(
+ gpu_in_arg1_data, tensorRange);
+ TensorMap<Tensor<DataType, 2, DataLayout, IndexType>> in_Arg2_gpu(
+ gpu_in_arg2_data, tensorRange);
+ TensorMap<Tensor<bool, 1, DataLayout, IndexType>> out_Argout_gpu(
+ gpu_out_arg_data, argRange);
+ TensorMap<Tensor<bool, 1, DataLayout, IndexType>> out_Argout_gpu_helper(
+ gpu_out_arg__gpu_helper_data, argRange);
+ TensorMap<Tensor<DataType, 0, DataLayout, IndexType>> out_gpu(gpu_out_data);
+
+ // CPU VERSION
+ out_arg_cpu =
+ (in_arg1.argmax(1) == in_arg2.argmax(1))
+ .select(out_arg_cpu.constant(true), out_arg_cpu.constant(false));
+ full_redux = (out_arg_cpu.template cast<float>())
+ .reduce(red_axis, Eigen::internal::MeanReducer<DataType>());
+
+ // GPU VERSION
+ sycl_device.memcpyHostToDevice(
+ gpu_in_data, in.data(), (in.dimensions().TotalSize()) * sizeof(DataType));
+ sycl_device.memcpyHostToDevice(
+ gpu_in_arg1_data, in_arg1.data(),
+ (in_arg1.dimensions().TotalSize()) * sizeof(DataType));
+ sycl_device.memcpyHostToDevice(
+ gpu_in_arg2_data, in_arg2.data(),
+ (in_arg2.dimensions().TotalSize()) * sizeof(DataType));
+ out_Argout_gpu_helper.device(sycl_device) =
+ (in_Arg1_gpu.argmax(1) == in_Arg2_gpu.argmax(1));
+ out_Argout_gpu.device(sycl_device) =
+ (out_Argout_gpu_helper)
+ .select(out_Argout_gpu.constant(true),
+ out_Argout_gpu.constant(false));
+ out_gpu.device(sycl_device) =
+ (out_Argout_gpu.template cast<float>())
+ .reduce(red_axis, Eigen::internal::MeanReducer<DataType>());
+ sycl_device.memcpyDeviceToHost(full_redux_gpu.data(), gpu_out_data,
+ sizeof(DataType));
+ // Check that the CPU and GPU reductions return the same result.
+ std::cout << "SYCL : " << full_redux_gpu() << " , CPU : " << full_redux()
+ << '\n';
+ VERIFY_IS_EQUAL(full_redux_gpu(), full_redux());
+ sycl_device.deallocate(gpu_in_data);
+ sycl_device.deallocate(gpu_in_arg1_data);
+ sycl_device.deallocate(gpu_in_arg2_data);
+ sycl_device.deallocate(gpu_out_arg__gpu_helper_data);
+ sycl_device.deallocate(gpu_out_arg_data);
+ sycl_device.deallocate(gpu_out_data);
+}
+
+template <typename DataType, int DataLayout, typename IndexType>
+static void test_full_reductions_mean_with_offset_sycl(
+ const Eigen::SyclDevice& sycl_device) {
+ using data_tensor = Tensor<DataType, 2, DataLayout, IndexType>;
+ using scalar_tensor = Tensor<DataType, 0, DataLayout, IndexType>;
+ const IndexType num_rows = 64;
+ const IndexType num_cols = 64;
+ array<IndexType, 2> tensor_range = {{num_rows, num_cols}};
+ const IndexType n_elems = internal::array_prod(tensor_range);
+
+ data_tensor in(tensor_range);
+ scalar_tensor full_redux;
+ scalar_tensor full_redux_gpu;
+
+ in.setRandom();
+ array<IndexType, 2> tensor_offset_range(tensor_range);
+ tensor_offset_range[0] -= 1;
+
+ const IndexType offset = 64;
+ TensorMap<data_tensor> in_offset(in.data() + offset, tensor_offset_range);
+ full_redux = in_offset.mean();
+ VERIFY_IS_NOT_EQUAL(full_redux(), in(0));
+
+ DataType* gpu_in_data =
+ static_cast<DataType*>(sycl_device.allocate(n_elems * sizeof(DataType)));
+ DataType* gpu_out_data =
+ static_cast<DataType*>(sycl_device.allocate(sizeof(DataType)));
+
+ TensorMap<data_tensor> in_gpu(gpu_in_data + offset, tensor_offset_range);
+ TensorMap<scalar_tensor> out_gpu(gpu_out_data);
+ sycl_device.memcpyHostToDevice(gpu_in_data, in.data(),
+ n_elems * sizeof(DataType));
+ out_gpu.device(sycl_device) = in_gpu.mean();
+ sycl_device.memcpyDeviceToHost(full_redux_gpu.data(), gpu_out_data,
+ sizeof(DataType));
+
+ // Check that the CPU and GPU reductions return the same result.
+ VERIFY_IS_APPROX(full_redux_gpu(), full_redux());
+
+ sycl_device.deallocate(gpu_in_data);
+ sycl_device.deallocate(gpu_out_data);
+}
+
+template <typename DataType, int DataLayout, typename IndexType>
+static void test_full_reductions_mean_with_odd_offset_sycl(
+ const Eigen::SyclDevice& sycl_device) {
+ // This is a particular case which illustrates a possible problem when the
+ // number of local threads in a workgroup is even, but is not a power of two.
+ using data_tensor = Tensor<DataType, 1, DataLayout, IndexType>;
+ using scalar_tensor = Tensor<DataType, 0, DataLayout, IndexType>;
+ // 2177 = (17 * 128) + 1 gives rise to 18 local threads.
+ // 8708 = 4 * 2177 = 4 * (17 * 128) + 4 uses 18 vectorised local threads.
+ const IndexType n_elems = 8707;
+ array<IndexType, 1> tensor_range = {{n_elems}};
+
+ data_tensor in(tensor_range);
+ DataType full_redux;
+ DataType full_redux_gpu;
+ TensorMap<scalar_tensor> red_cpu(&full_redux);
+ TensorMap<scalar_tensor> red_gpu(&full_redux_gpu);
+
+ const DataType const_val = static_cast<DataType>(0.6391);
+ in = in.constant(const_val);
+
+ Eigen::IndexList<Eigen::type2index<0>> red_axis;
+ red_cpu = in.reduce(red_axis, Eigen::internal::MeanReducer<DataType>());
+ VERIFY_IS_APPROX(const_val, red_cpu());
+
+ DataType* gpu_in_data =
+ static_cast<DataType*>(sycl_device.allocate(n_elems * sizeof(DataType)));
+ DataType* gpu_out_data =
+ static_cast<DataType*>(sycl_device.allocate(sizeof(DataType)));
+
+ TensorMap<data_tensor> in_gpu(gpu_in_data, tensor_range);
+ TensorMap<scalar_tensor> out_gpu(gpu_out_data);
+ sycl_device.memcpyHostToDevice(gpu_in_data, in.data(),
+ n_elems * sizeof(DataType));
+ out_gpu.device(sycl_device) =
+ in_gpu.reduce(red_axis, Eigen::internal::MeanReducer<DataType>());
+ sycl_device.memcpyDeviceToHost(red_gpu.data(), gpu_out_data,
+ sizeof(DataType));
+
+ // Check that the CPU and GPU reductions return the same result.
+ VERIFY_IS_APPROX(full_redux_gpu, full_redux);
+
+ sycl_device.deallocate(gpu_in_data);
+ sycl_device.deallocate(gpu_out_data);
+}
+
+template <typename DataType, int DataLayout, typename IndexType>
+static void test_full_reductions_min_sycl(
+ const Eigen::SyclDevice& sycl_device) {
+ const IndexType num_rows = 876;
+ const IndexType num_cols = 953;
+ array<IndexType, 2> tensorRange = {{num_rows, num_cols}};
+
+ Tensor<DataType, 2, DataLayout, IndexType> in(tensorRange);
+ Tensor<DataType, 0, DataLayout, IndexType> full_redux;
+ Tensor<DataType, 0, DataLayout, IndexType> full_redux_gpu;
+
+ in.setRandom();
+
+ full_redux = in.minimum();
+
+ DataType* gpu_in_data = static_cast<DataType*>(
+ sycl_device.allocate(in.dimensions().TotalSize() * sizeof(DataType)));
+ DataType* gpu_out_data = (DataType*)sycl_device.allocate(sizeof(DataType));
+
+ TensorMap<Tensor<DataType, 2, DataLayout, IndexType>> in_gpu(gpu_in_data,
+ tensorRange);
+ TensorMap<Tensor<DataType, 0, DataLayout, IndexType>> out_gpu(gpu_out_data);
+
+ sycl_device.memcpyHostToDevice(
+ gpu_in_data, in.data(), (in.dimensions().TotalSize()) * sizeof(DataType));
+ out_gpu.device(sycl_device) = in_gpu.minimum();
+ sycl_device.memcpyDeviceToHost(full_redux_gpu.data(), gpu_out_data,
+ sizeof(DataType));
+ // Check that the CPU and GPU reductions return the same result.
+ VERIFY_IS_APPROX(full_redux_gpu(), full_redux());
+ sycl_device.deallocate(gpu_in_data);
+ sycl_device.deallocate(gpu_out_data);
+}
+
+template <typename DataType, int DataLayout, typename IndexType>
+static void test_full_reductions_min_with_offset_sycl(
+ const Eigen::SyclDevice& sycl_device) {
+ using data_tensor = Tensor<DataType, 2, DataLayout, IndexType>;
+ using scalar_tensor = Tensor<DataType, 0, DataLayout, IndexType>;
+ const IndexType num_rows = 64;
+ const IndexType num_cols = 64;
+ array<IndexType, 2> tensor_range = {{num_rows, num_cols}};
+ const IndexType n_elems = internal::array_prod(tensor_range);
+
+ data_tensor in(tensor_range);
+ scalar_tensor full_redux;
+ scalar_tensor full_redux_gpu;
+
+ in.setRandom();
+ array<IndexType, 2> tensor_offset_range(tensor_range);
+ tensor_offset_range[0] -= 1;
+ // Set the initial value to be the min.
+ // As we don't include this in the reduction the result should not be -2.
+ in(0) = static_cast<DataType>(-2);
+
+ const IndexType offset = 64;
+ TensorMap<data_tensor> in_offset(in.data() + offset, tensor_offset_range);
+ full_redux = in_offset.minimum();
+ VERIFY_IS_NOT_EQUAL(full_redux(), in(0));
+
+ DataType* gpu_in_data =
+ static_cast<DataType*>(sycl_device.allocate(n_elems * sizeof(DataType)));
+ DataType* gpu_out_data =
+ static_cast<DataType*>(sycl_device.allocate(sizeof(DataType)));
+
+ TensorMap<data_tensor> in_gpu(gpu_in_data + offset, tensor_offset_range);
+ TensorMap<scalar_tensor> out_gpu(gpu_out_data);
+ sycl_device.memcpyHostToDevice(gpu_in_data, in.data(),
+ n_elems * sizeof(DataType));
+ out_gpu.device(sycl_device) = in_gpu.minimum();
+ sycl_device.memcpyDeviceToHost(full_redux_gpu.data(), gpu_out_data,
+ sizeof(DataType));
+
+ // Check that the CPU and GPU reductions return the same result.
+ VERIFY_IS_APPROX(full_redux_gpu(), full_redux());
+
+ sycl_device.deallocate(gpu_in_data);
+ sycl_device.deallocate(gpu_out_data);
+}
+template <typename DataType, int DataLayout, typename IndexType>
+static void test_first_dim_reductions_max_sycl(
+ const Eigen::SyclDevice& sycl_device) {
+ IndexType dim_x = 145;
+ IndexType dim_y = 1;
+ IndexType dim_z = 67;
+
+ array<IndexType, 3> tensorRange = {{dim_x, dim_y, dim_z}};
+ Eigen::array<IndexType, 1> red_axis;
+ red_axis[0] = 0;
+ array<IndexType, 2> reduced_tensorRange = {{dim_y, dim_z}};
+
+ Tensor<DataType, 3, DataLayout, IndexType> in(tensorRange);
+ Tensor<DataType, 2, DataLayout, IndexType> redux(reduced_tensorRange);
+ Tensor<DataType, 2, DataLayout, IndexType> redux_gpu(reduced_tensorRange);
+
+ in.setRandom();
+
+ redux = in.maximum(red_axis);
+
+ DataType* gpu_in_data = static_cast<DataType*>(
+ sycl_device.allocate(in.dimensions().TotalSize() * sizeof(DataType)));
+ DataType* gpu_out_data = static_cast<DataType*>(sycl_device.allocate(
+ redux_gpu.dimensions().TotalSize() * sizeof(DataType)));
+
+ TensorMap<Tensor<DataType, 3, DataLayout, IndexType>> in_gpu(gpu_in_data,
+ tensorRange);
+ TensorMap<Tensor<DataType, 2, DataLayout, IndexType>> out_gpu(
+ gpu_out_data, reduced_tensorRange);
+
+ sycl_device.memcpyHostToDevice(
+ gpu_in_data, in.data(), (in.dimensions().TotalSize()) * sizeof(DataType));
+ out_gpu.device(sycl_device) = in_gpu.maximum(red_axis);
+ sycl_device.memcpyDeviceToHost(
+ redux_gpu.data(), gpu_out_data,
+ redux_gpu.dimensions().TotalSize() * sizeof(DataType));
+
+ // Check that the CPU and GPU reductions return the same result.
+ for (IndexType j = 0; j < reduced_tensorRange[0]; j++)
+ for (IndexType k = 0; k < reduced_tensorRange[1]; k++)
+ VERIFY_IS_APPROX(redux_gpu(j, k), redux(j, k));
+
+ sycl_device.deallocate(gpu_in_data);
+ sycl_device.deallocate(gpu_out_data);
+}
+
+template <typename DataType, int DataLayout, typename IndexType>
+static void test_first_dim_reductions_max_with_offset_sycl(
+ const Eigen::SyclDevice& sycl_device) {
+ using data_tensor = Tensor<DataType, 2, DataLayout, IndexType>;
+ using reduced_tensor = Tensor<DataType, 1, DataLayout, IndexType>;
+
+ const IndexType num_rows = 64;
+ const IndexType num_cols = 64;
+ array<IndexType, 2> tensor_range = {{num_rows, num_cols}};
+ array<IndexType, 1> reduced_range = {{num_cols}};
+ const IndexType n_elems = internal::array_prod(tensor_range);
+ const IndexType n_reduced = num_cols;
+
+ data_tensor in(tensor_range);
+ reduced_tensor redux;
+ reduced_tensor redux_gpu(reduced_range);
+
+ in.setRandom();
+ array<IndexType, 2> tensor_offset_range(tensor_range);
+ tensor_offset_range[0] -= 1;
+ // Set maximum value outside of the considered range.
+ for (IndexType i = 0; i < n_reduced; i++) {
+ in(i) = static_cast<DataType>(2);
+ }
+
+ Eigen::array<IndexType, 1> red_axis;
+ red_axis[0] = 0;
+
+ const IndexType offset = 64;
+ TensorMap<data_tensor> in_offset(in.data() + offset, tensor_offset_range);
+ redux = in_offset.maximum(red_axis);
+ for (IndexType i = 0; i < n_reduced; i++) {
+ VERIFY_IS_NOT_EQUAL(redux(i), in(i));
+ }
+
+ DataType* gpu_in_data =
+ static_cast<DataType*>(sycl_device.allocate(n_elems * sizeof(DataType)));
+ DataType* gpu_out_data = static_cast<DataType*>(
+ sycl_device.allocate(n_reduced * sizeof(DataType)));
+
+ TensorMap<data_tensor> in_gpu(gpu_in_data + offset, tensor_offset_range);
+ TensorMap<reduced_tensor> out_gpu(gpu_out_data, reduced_range);
+ sycl_device.memcpyHostToDevice(gpu_in_data, in.data(),
+ n_elems * sizeof(DataType));
+ out_gpu.device(sycl_device) = in_gpu.maximum(red_axis);
+ sycl_device.memcpyDeviceToHost(redux_gpu.data(), gpu_out_data,
+ n_reduced * sizeof(DataType));
+
+ // Check that the CPU and GPU reductions return the same result.
+ for (IndexType i = 0; i < n_reduced; i++) {
+ VERIFY_IS_APPROX(redux_gpu(i), redux(i));
+ }
+
+ sycl_device.deallocate(gpu_in_data);
+ sycl_device.deallocate(gpu_out_data);
+}
+
+template <typename DataType, int DataLayout, typename IndexType>
+static void test_last_dim_reductions_max_with_offset_sycl(
+ const Eigen::SyclDevice& sycl_device) {
+ using data_tensor = Tensor<DataType, 2, DataLayout, IndexType>;
+ using reduced_tensor = Tensor<DataType, 1, DataLayout, IndexType>;
+
+ const IndexType num_rows = 64;
+ const IndexType num_cols = 64;
+ array<IndexType, 2> tensor_range = {{num_rows, num_cols}};
+ array<IndexType, 1> full_reduced_range = {{num_rows}};
+ array<IndexType, 1> reduced_range = {{num_rows - 1}};
+ const IndexType n_elems = internal::array_prod(tensor_range);
+ const IndexType n_reduced = reduced_range[0];
+
+ data_tensor in(tensor_range);
+ reduced_tensor redux(full_reduced_range);
+ reduced_tensor redux_gpu(reduced_range);
+
+ in.setRandom();
+ redux.setZero();
+ array<IndexType, 2> tensor_offset_range(tensor_range);
+ tensor_offset_range[0] -= 1;
+ // Set maximum value outside of the considered range.
+ for (IndexType i = 0; i < n_reduced; i++) {
+ in(i) = static_cast<DataType>(2);
+ }
+
+ Eigen::array<IndexType, 1> red_axis;
+ red_axis[0] = 1;
+
+ const IndexType offset = 64;
+ // Introduce an offset in both the input and the output.
+ TensorMap<data_tensor> in_offset(in.data() + offset, tensor_offset_range);
+ TensorMap<reduced_tensor> red_offset(redux.data() + 1, reduced_range);
+ red_offset = in_offset.maximum(red_axis);
+
+ // Check that the first value hasn't been changed and that the reduced values
+ // are not equal to the previously set maximum in the input outside the range.
+ VERIFY_IS_EQUAL(redux(0), static_cast<DataType>(0));
+ for (IndexType i = 0; i < n_reduced; i++) {
+ VERIFY_IS_NOT_EQUAL(red_offset(i), in(i));
+ }
+
+ DataType* gpu_in_data =
+ static_cast<DataType*>(sycl_device.allocate(n_elems * sizeof(DataType)));
+ DataType* gpu_out_data = static_cast<DataType*>(
+ sycl_device.allocate((n_reduced + 1) * sizeof(DataType)));
+
+ TensorMap<data_tensor> in_gpu(gpu_in_data + offset, tensor_offset_range);
+ TensorMap<reduced_tensor> out_gpu(gpu_out_data + 1, reduced_range);
+ sycl_device.memcpyHostToDevice(gpu_in_data, in.data(),
+ n_elems * sizeof(DataType));
+ out_gpu.device(sycl_device) = in_gpu.maximum(red_axis);
+ sycl_device.memcpyDeviceToHost(redux_gpu.data(), out_gpu.data(),
+ n_reduced * sizeof(DataType));
+
+ // Check that the CPU and GPU reductions return the same result.
+ for (IndexType i = 0; i < n_reduced; i++) {
+ VERIFY_IS_APPROX(redux_gpu(i), red_offset(i));
+ }
+
+ sycl_device.deallocate(gpu_in_data);
+ sycl_device.deallocate(gpu_out_data);
+}
+
+template <typename DataType, int DataLayout, typename IndexType>
+static void test_first_dim_reductions_sum_sycl(
+ const Eigen::SyclDevice& sycl_device, IndexType dim_x, IndexType dim_y) {
+ array<IndexType, 2> tensorRange = {{dim_x, dim_y}};
+ Eigen::array<IndexType, 1> red_axis;
+ red_axis[0] = 0;
+ array<IndexType, 1> reduced_tensorRange = {{dim_y}};
+
+ Tensor<DataType, 2, DataLayout, IndexType> in(tensorRange);
+ Tensor<DataType, 1, DataLayout, IndexType> redux(reduced_tensorRange);
+ Tensor<DataType, 1, DataLayout, IndexType> redux_gpu(reduced_tensorRange);
+
+ in.setRandom();
+ redux = in.sum(red_axis);
+
+ DataType* gpu_in_data = static_cast<DataType*>(
+ sycl_device.allocate(in.dimensions().TotalSize() * sizeof(DataType)));
+ DataType* gpu_out_data = static_cast<DataType*>(sycl_device.allocate(
+ redux_gpu.dimensions().TotalSize() * sizeof(DataType)));
+
+ TensorMap<Tensor<DataType, 2, DataLayout, IndexType>> in_gpu(gpu_in_data,
+ tensorRange);
+ TensorMap<Tensor<DataType, 1, DataLayout, IndexType>> out_gpu(
+ gpu_out_data, reduced_tensorRange);
+
+ sycl_device.memcpyHostToDevice(
+ gpu_in_data, in.data(), (in.dimensions().TotalSize()) * sizeof(DataType));
+ out_gpu.device(sycl_device) = in_gpu.sum(red_axis);
+ sycl_device.memcpyDeviceToHost(
+ redux_gpu.data(), gpu_out_data,
+ redux_gpu.dimensions().TotalSize() * sizeof(DataType));
+
+ // Check that the CPU and GPU reductions return the same result.
+ for (IndexType i = 0; i < redux.size(); i++) {
+ VERIFY_IS_APPROX(redux_gpu.data()[i], redux.data()[i]);
+ }
+ sycl_device.deallocate(gpu_in_data);
+ sycl_device.deallocate(gpu_out_data);
+}
+
+template <typename DataType, int DataLayout, typename IndexType>
+static void test_first_dim_reductions_mean_sycl(
+ const Eigen::SyclDevice& sycl_device) {
+ IndexType dim_x = 145;
+ IndexType dim_y = 1;
+ IndexType dim_z = 67;
+
+ array<IndexType, 3> tensorRange = {{dim_x, dim_y, dim_z}};
+ Eigen::array<IndexType, 1> red_axis;
+ red_axis[0] = 0;
+ array<IndexType, 2> reduced_tensorRange = {{dim_y, dim_z}};
+
+ Tensor<DataType, 3, DataLayout, IndexType> in(tensorRange);
+ Tensor<DataType, 2, DataLayout, IndexType> redux(reduced_tensorRange);
+ Tensor<DataType, 2, DataLayout, IndexType> redux_gpu(reduced_tensorRange);
+
+ in.setRandom();
+
+ redux = in.mean(red_axis);
+
+ DataType* gpu_in_data = static_cast<DataType*>(
+ sycl_device.allocate(in.dimensions().TotalSize() * sizeof(DataType)));
+ DataType* gpu_out_data = static_cast<DataType*>(sycl_device.allocate(
+ redux_gpu.dimensions().TotalSize() * sizeof(DataType)));
+
+ TensorMap<Tensor<DataType, 3, DataLayout, IndexType>> in_gpu(gpu_in_data,
+ tensorRange);
+ TensorMap<Tensor<DataType, 2, DataLayout, IndexType>> out_gpu(
+ gpu_out_data, reduced_tensorRange);
+
+ sycl_device.memcpyHostToDevice(
+ gpu_in_data, in.data(), (in.dimensions().TotalSize()) * sizeof(DataType));
+ out_gpu.device(sycl_device) = in_gpu.mean(red_axis);
+ sycl_device.memcpyDeviceToHost(
+ redux_gpu.data(), gpu_out_data,
+ redux_gpu.dimensions().TotalSize() * sizeof(DataType));
+
+ // Check that the CPU and GPU reductions return the same result.
+ for (IndexType j = 0; j < reduced_tensorRange[0]; j++)
+ for (IndexType k = 0; k < reduced_tensorRange[1]; k++)
+ VERIFY_IS_APPROX(redux_gpu(j, k), redux(j, k));
+
+ sycl_device.deallocate(gpu_in_data);
+ sycl_device.deallocate(gpu_out_data);
+}
+
+template <typename DataType, int DataLayout, typename IndexType>
+static void test_last_dim_reductions_mean_sycl(
+ const Eigen::SyclDevice& sycl_device) {
+ IndexType dim_x = 64;
+ IndexType dim_y = 1;
+ IndexType dim_z = 32;
+
+ array<IndexType, 3> tensorRange = {{dim_x, dim_y, dim_z}};
+ Eigen::array<IndexType, 1> red_axis;
+ red_axis[0] = 2;
+ array<IndexType, 2> reduced_tensorRange = {{dim_x, dim_y}};
+
+ Tensor<DataType, 3, DataLayout, IndexType> in(tensorRange);
+ Tensor<DataType, 2, DataLayout, IndexType> redux(reduced_tensorRange);
+ Tensor<DataType, 2, DataLayout, IndexType> redux_gpu(reduced_tensorRange);
+
+ in.setRandom();
+
+ redux = in.mean(red_axis);
+
+ DataType* gpu_in_data = static_cast<DataType*>(
+ sycl_device.allocate(in.dimensions().TotalSize() * sizeof(DataType)));
+ DataType* gpu_out_data = static_cast<DataType*>(sycl_device.allocate(
+ redux_gpu.dimensions().TotalSize() * sizeof(DataType)));
+
+ TensorMap<Tensor<DataType, 3, DataLayout, IndexType>> in_gpu(gpu_in_data,
+ tensorRange);
+ TensorMap<Tensor<DataType, 2, DataLayout, IndexType>> out_gpu(
+ gpu_out_data, reduced_tensorRange);
+
+ sycl_device.memcpyHostToDevice(
+ gpu_in_data, in.data(), (in.dimensions().TotalSize()) * sizeof(DataType));
+ out_gpu.device(sycl_device) = in_gpu.mean(red_axis);
+ sycl_device.memcpyDeviceToHost(
+ redux_gpu.data(), gpu_out_data,
+ redux_gpu.dimensions().TotalSize() * sizeof(DataType));
+ // Check that the CPU and GPU reductions return the same result.
+ for (IndexType j = 0; j < reduced_tensorRange[0]; j++)
+ for (IndexType k = 0; k < reduced_tensorRange[1]; k++)
+ VERIFY_IS_APPROX(redux_gpu(j, k), redux(j, k));
+
+ sycl_device.deallocate(gpu_in_data);
+ sycl_device.deallocate(gpu_out_data);
+}
+
+template <typename DataType, int DataLayout, typename IndexType>
+static void test_last_dim_reductions_sum_sycl(
+ const Eigen::SyclDevice& sycl_device) {
+ IndexType dim_x = 64;
+ IndexType dim_y = 1;
+ IndexType dim_z = 32;
+
+ array<IndexType, 3> tensorRange = {{dim_x, dim_y, dim_z}};
+ Eigen::array<IndexType, 1> red_axis;
+ red_axis[0] = 2;
+ array<IndexType, 2> reduced_tensorRange = {{dim_x, dim_y}};
+
+ Tensor<DataType, 3, DataLayout, IndexType> in(tensorRange);
+ Tensor<DataType, 2, DataLayout, IndexType> redux(reduced_tensorRange);
+ Tensor<DataType, 2, DataLayout, IndexType> redux_gpu(reduced_tensorRange);
+
+ in.setRandom();
+
+ redux = in.sum(red_axis);
+
+ DataType* gpu_in_data = static_cast<DataType*>(
+ sycl_device.allocate(in.dimensions().TotalSize() * sizeof(DataType)));
+ DataType* gpu_out_data = static_cast<DataType*>(sycl_device.allocate(
+ redux_gpu.dimensions().TotalSize() * sizeof(DataType)));
+
+ TensorMap<Tensor<DataType, 3, DataLayout, IndexType>> in_gpu(gpu_in_data,
+ tensorRange);
+ TensorMap<Tensor<DataType, 2, DataLayout, IndexType>> out_gpu(
+ gpu_out_data, reduced_tensorRange);
+
+ sycl_device.memcpyHostToDevice(
+ gpu_in_data, in.data(), (in.dimensions().TotalSize()) * sizeof(DataType));
+ out_gpu.device(sycl_device) = in_gpu.sum(red_axis);
+ sycl_device.memcpyDeviceToHost(
+ redux_gpu.data(), gpu_out_data,
+ redux_gpu.dimensions().TotalSize() * sizeof(DataType));
+ // Check that the CPU and GPU reductions return the same result.
+ for (IndexType j = 0; j < reduced_tensorRange[0]; j++)
+ for (IndexType k = 0; k < reduced_tensorRange[1]; k++)
+ VERIFY_IS_APPROX(redux_gpu(j, k), redux(j, k));
+
+ sycl_device.deallocate(gpu_in_data);
+ sycl_device.deallocate(gpu_out_data);
+}
+
+template <typename DataType, int DataLayout, typename IndexType>
+static void test_last_reductions_sum_sycl(
+ const Eigen::SyclDevice& sycl_device) {
+ auto tensorRange = Sizes<64, 32>(64, 32);
+ // auto red_axis = Sizes<0,1>(0,1);
+ Eigen::IndexList<Eigen::type2index<1>> red_axis;
+ auto reduced_tensorRange = Sizes<64>(64);
+ TensorFixedSize<DataType, Sizes<64, 32>, DataLayout> in_fix;
+ TensorFixedSize<DataType, Sizes<64>, DataLayout> redux_fix;
+ TensorFixedSize<DataType, Sizes<64>, DataLayout> redux_gpu_fix;
+
+ in_fix.setRandom();
+
+ redux_fix = in_fix.sum(red_axis);
+
+ DataType* gpu_in_data = static_cast<DataType*>(
+ sycl_device.allocate(in_fix.dimensions().TotalSize() * sizeof(DataType)));
+ DataType* gpu_out_data = static_cast<DataType*>(sycl_device.allocate(
+ redux_gpu_fix.dimensions().TotalSize() * sizeof(DataType)));
+
+ TensorMap<TensorFixedSize<DataType, Sizes<64, 32>, DataLayout>> in_gpu_fix(
+ gpu_in_data, tensorRange);
+ TensorMap<TensorFixedSize<DataType, Sizes<64>, DataLayout>> out_gpu_fix(
+ gpu_out_data, reduced_tensorRange);
+
+ sycl_device.memcpyHostToDevice(
+ gpu_in_data, in_fix.data(),
+ (in_fix.dimensions().TotalSize()) * sizeof(DataType));
+ out_gpu_fix.device(sycl_device) = in_gpu_fix.sum(red_axis);
+ sycl_device.memcpyDeviceToHost(
+ redux_gpu_fix.data(), gpu_out_data,
+ redux_gpu_fix.dimensions().TotalSize() * sizeof(DataType));
+ // Check that the CPU and GPU reductions return the same result.
+ for (IndexType j = 0; j < reduced_tensorRange[0]; j++) {
+ VERIFY_IS_APPROX(redux_gpu_fix(j), redux_fix(j));
+ }
+
+ sycl_device.deallocate(gpu_in_data);
+ sycl_device.deallocate(gpu_out_data);
+}
+
+template <typename DataType, int DataLayout, typename IndexType>
+static void test_last_reductions_mean_sycl(
+ const Eigen::SyclDevice& sycl_device) {
+ auto tensorRange = Sizes<64, 32>(64, 32);
+ Eigen::IndexList<Eigen::type2index<1>> red_axis;
+ auto reduced_tensorRange = Sizes<64>(64);
+ TensorFixedSize<DataType, Sizes<64, 32>, DataLayout> in_fix;
+ TensorFixedSize<DataType, Sizes<64>, DataLayout> redux_fix;
+ TensorFixedSize<DataType, Sizes<64>, DataLayout> redux_gpu_fix;
+
+ in_fix.setRandom();
+ redux_fix = in_fix.mean(red_axis);
+
+ DataType* gpu_in_data = static_cast<DataType*>(
+ sycl_device.allocate(in_fix.dimensions().TotalSize() * sizeof(DataType)));
+ DataType* gpu_out_data = static_cast<DataType*>(sycl_device.allocate(
+ redux_gpu_fix.dimensions().TotalSize() * sizeof(DataType)));
+
+ TensorMap<TensorFixedSize<DataType, Sizes<64, 32>, DataLayout>> in_gpu_fix(
+ gpu_in_data, tensorRange);
+ TensorMap<TensorFixedSize<DataType, Sizes<64>, DataLayout>> out_gpu_fix(
+ gpu_out_data, reduced_tensorRange);
+
+ sycl_device.memcpyHostToDevice(
+ gpu_in_data, in_fix.data(),
+ (in_fix.dimensions().TotalSize()) * sizeof(DataType));
+ out_gpu_fix.device(sycl_device) = in_gpu_fix.mean(red_axis);
+ sycl_device.memcpyDeviceToHost(
+ redux_gpu_fix.data(), gpu_out_data,
+ redux_gpu_fix.dimensions().TotalSize() * sizeof(DataType));
+ sycl_device.synchronize();
+ // Check that the CPU and GPU reductions return the same result.
+ for (IndexType j = 0; j < reduced_tensorRange[0]; j++) {
+ VERIFY_IS_APPROX(redux_gpu_fix(j), redux_fix(j));
+ }
+
+ sycl_device.deallocate(gpu_in_data);
+ sycl_device.deallocate(gpu_out_data);
+}
+
+// SYCL supports a generic case of reduction where the accumulator is a
+// different type than the input data This is an example on how to get if a
+// Tensor contains nan and/or inf in one reduction
+template <typename InT, typename OutT>
+struct CustomReducer {
+ static const bool PacketAccess = false;
+ static const bool IsStateful = false;
+
+ static constexpr OutT InfBit = 1;
+ static constexpr OutT NanBit = 2;
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void reduce(const InT x,
+ OutT* accum) const {
+ if (Eigen::numext::isinf(x))
+ *accum |= InfBit;
+ else if (Eigen::numext::isnan(x))
+ *accum |= NanBit;
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void reduce(const OutT x,
+ OutT* accum) const {
+ *accum |= x;
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE OutT initialize() const {
+ return OutT(0);
+ }
+
+ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE OutT finalize(const OutT accum) const {
+ return accum;
+ }
+};
+
+template <typename DataType, typename AccumType, int DataLayout,
+ typename IndexType>
+static void test_full_reductions_custom_sycl(
+ const Eigen::SyclDevice& sycl_device) {
+ constexpr IndexType InSize = 64;
+ auto tensorRange = Sizes<InSize>(InSize);
+ Eigen::IndexList<Eigen::type2index<0>> dims;
+ auto reduced_tensorRange = Sizes<>();
+ TensorFixedSize<DataType, Sizes<InSize>, DataLayout> in_fix;
+ TensorFixedSize<AccumType, Sizes<>, DataLayout> redux_gpu_fix;
+
+ CustomReducer<DataType, AccumType> reducer;
+
+ in_fix.setRandom();
+
+ size_t in_size_bytes = in_fix.dimensions().TotalSize() * sizeof(DataType);
+ DataType* gpu_in_data =
+ static_cast<DataType*>(sycl_device.allocate(in_size_bytes));
+ AccumType* gpu_out_data =
+ static_cast<AccumType*>(sycl_device.allocate(sizeof(AccumType)));
+
+ TensorMap<TensorFixedSize<DataType, Sizes<InSize>, DataLayout>> in_gpu_fix(
+ gpu_in_data, tensorRange);
+ TensorMap<TensorFixedSize<AccumType, Sizes<>, DataLayout>> out_gpu_fix(
+ gpu_out_data, reduced_tensorRange);
+
+ sycl_device.memcpyHostToDevice(gpu_in_data, in_fix.data(), in_size_bytes);
+ out_gpu_fix.device(sycl_device) = in_gpu_fix.reduce(dims, reducer);
+ sycl_device.memcpyDeviceToHost(redux_gpu_fix.data(), gpu_out_data,
+ sizeof(AccumType));
+ VERIFY_IS_EQUAL(redux_gpu_fix(0), AccumType(0));
+
+ sycl_device.deallocate(gpu_in_data);
+ sycl_device.deallocate(gpu_out_data);
+}
+
+template <typename DataType, typename Dev>
+void sycl_reduction_test_full_per_device(const Dev& sycl_device) {
+ test_full_reductions_sum_sycl<DataType, RowMajor, int64_t>(sycl_device);
+ test_full_reductions_sum_sycl<DataType, ColMajor, int64_t>(sycl_device);
+ test_full_reductions_min_sycl<DataType, ColMajor, int64_t>(sycl_device);
+ test_full_reductions_min_sycl<DataType, RowMajor, int64_t>(sycl_device);
+ test_full_reductions_max_sycl<DataType, ColMajor, int64_t>(sycl_device);
+ test_full_reductions_max_sycl<DataType, RowMajor, int64_t>(sycl_device);
+
+ test_full_reductions_mean_sycl<DataType, ColMajor, int64_t>(sycl_device);
+ test_full_reductions_mean_sycl<DataType, RowMajor, int64_t>(sycl_device);
+ test_full_reductions_custom_sycl<DataType, int, RowMajor, int64_t>(
+ sycl_device);
+ test_full_reductions_custom_sycl<DataType, int, ColMajor, int64_t>(
+ sycl_device);
+ sycl_device.synchronize();
+}
+
+template <typename DataType, typename Dev>
+void sycl_reduction_full_offset_per_device(const Dev& sycl_device) {
+ test_full_reductions_sum_with_offset_sycl<DataType, RowMajor, int64_t>(
+ sycl_device);
+ test_full_reductions_sum_with_offset_sycl<DataType, ColMajor, int64_t>(
+ sycl_device);
+ test_full_reductions_min_with_offset_sycl<DataType, RowMajor, int64_t>(
+ sycl_device);
+ test_full_reductions_min_with_offset_sycl<DataType, ColMajor, int64_t>(
+ sycl_device);
+ test_full_reductions_max_with_offset_sycl<DataType, ColMajor, int64_t>(
+ sycl_device);
+ test_full_reductions_max_with_offset_sycl<DataType, RowMajor, int64_t>(
+ sycl_device);
+ test_full_reductions_mean_with_offset_sycl<DataType, RowMajor, int64_t>(
+ sycl_device);
+ test_full_reductions_mean_with_offset_sycl<DataType, ColMajor, int64_t>(
+ sycl_device);
+ test_full_reductions_mean_with_odd_offset_sycl<DataType, RowMajor, int64_t>(
+ sycl_device);
+ sycl_device.synchronize();
+}
+
+template <typename DataType, typename Dev>
+void sycl_reduction_test_first_dim_per_device(const Dev& sycl_device) {
+ test_first_dim_reductions_sum_sycl<DataType, ColMajor, int64_t>(sycl_device,
+ 4197, 4097);
+ test_first_dim_reductions_sum_sycl<DataType, RowMajor, int64_t>(sycl_device,
+ 4197, 4097);
+ test_first_dim_reductions_sum_sycl<DataType, RowMajor, int64_t>(sycl_device,
+ 129, 8);
+ test_first_dim_reductions_max_sycl<DataType, RowMajor, int64_t>(sycl_device);
+ test_first_dim_reductions_max_with_offset_sycl<DataType, RowMajor, int64_t>(
+ sycl_device);
+ sycl_device.synchronize();
+}
+
+template <typename DataType, typename Dev>
+void sycl_reduction_test_last_dim_per_device(const Dev& sycl_device) {
+ test_last_dim_reductions_sum_sycl<DataType, RowMajor, int64_t>(sycl_device);
+ test_last_dim_reductions_max_with_offset_sycl<DataType, RowMajor, int64_t>(
+ sycl_device);
+ test_last_reductions_sum_sycl<DataType, ColMajor, int64_t>(sycl_device);
+ test_last_reductions_sum_sycl<DataType, RowMajor, int64_t>(sycl_device);
+ test_last_reductions_mean_sycl<DataType, ColMajor, int64_t>(sycl_device);
+ test_last_reductions_mean_sycl<DataType, RowMajor, int64_t>(sycl_device);
+ sycl_device.synchronize();
+}
+
+EIGEN_DECLARE_TEST(cxx11_tensor_reduction_sycl) {
+ for (const auto& device : Eigen::get_sycl_supported_devices()) {
+ std::cout << "Running on "
+ << device.template get_info<cl::sycl::info::device::name>()
+ << std::endl;
+ QueueInterface queueInterface(device);
+ auto sycl_device = Eigen::SyclDevice(&queueInterface);
+ CALL_SUBTEST_1(sycl_reduction_test_full_per_device<float>(sycl_device));
+ CALL_SUBTEST_2(sycl_reduction_full_offset_per_device<float>(sycl_device));
+ CALL_SUBTEST_3(
+ sycl_reduction_test_first_dim_per_device<float>(sycl_device));
+ CALL_SUBTEST_4(sycl_reduction_test_last_dim_per_device<float>(sycl_device));
+ }
+}
diff --git a/unsupported/test/cxx11_tensor_ref.cpp b/unsupported/test/cxx11_tensor_ref.cpp
new file mode 100644
index 0000000..7dbd047
--- /dev/null
+++ b/unsupported/test/cxx11_tensor_ref.cpp
@@ -0,0 +1,248 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "main.h"
+
+#include <Eigen/CXX11/Tensor>
+
+using Eigen::Tensor;
+using Eigen::RowMajor;
+
+static void test_simple_lvalue_ref()
+{
+ Tensor<int, 1> input(6);
+ input.setRandom();
+
+ TensorRef<Tensor<int, 1>> ref3(input);
+ TensorRef<Tensor<int, 1>> ref4 = input;
+
+ VERIFY_IS_EQUAL(ref3.data(), input.data());
+ VERIFY_IS_EQUAL(ref4.data(), input.data());
+
+ for (int i = 0; i < 6; ++i) {
+ VERIFY_IS_EQUAL(ref3(i), input(i));
+ VERIFY_IS_EQUAL(ref4(i), input(i));
+ }
+
+ for (int i = 0; i < 6; ++i) {
+ ref3.coeffRef(i) = i;
+ }
+ for (int i = 0; i < 6; ++i) {
+ VERIFY_IS_EQUAL(input(i), i);
+ }
+ for (int i = 0; i < 6; ++i) {
+ ref4.coeffRef(i) = -i * 2;
+ }
+ for (int i = 0; i < 6; ++i) {
+ VERIFY_IS_EQUAL(input(i), -i*2);
+ }
+}
+
+
+static void test_simple_rvalue_ref()
+{
+ Tensor<int, 1> input1(6);
+ input1.setRandom();
+ Tensor<int, 1> input2(6);
+ input2.setRandom();
+
+ TensorRef<Tensor<int, 1>> ref3(input1 + input2);
+ TensorRef<Tensor<int, 1>> ref4 = input1 + input2;
+
+ VERIFY_IS_NOT_EQUAL(ref3.data(), input1.data());
+ VERIFY_IS_NOT_EQUAL(ref4.data(), input1.data());
+ VERIFY_IS_NOT_EQUAL(ref3.data(), input2.data());
+ VERIFY_IS_NOT_EQUAL(ref4.data(), input2.data());
+
+ for (int i = 0; i < 6; ++i) {
+ VERIFY_IS_EQUAL(ref3(i), input1(i) + input2(i));
+ VERIFY_IS_EQUAL(ref4(i), input1(i) + input2(i));
+ }
+}
+
+
+static void test_multiple_dims()
+{
+ Tensor<float, 3> input(3,5,7);
+ input.setRandom();
+
+ TensorRef<Tensor<float, 3>> ref(input);
+ VERIFY_IS_EQUAL(ref.data(), input.data());
+ VERIFY_IS_EQUAL(ref.dimension(0), 3);
+ VERIFY_IS_EQUAL(ref.dimension(1), 5);
+ VERIFY_IS_EQUAL(ref.dimension(2), 7);
+
+ for (int i = 0; i < 3; ++i) {
+ for (int j = 0; j < 5; ++j) {
+ for (int k = 0; k < 7; ++k) {
+ VERIFY_IS_EQUAL(ref(i,j,k), input(i,j,k));
+ }
+ }
+ }
+}
+
+
+static void test_slice()
+{
+ Tensor<float, 5> tensor(2,3,5,7,11);
+ tensor.setRandom();
+
+ Eigen::DSizes<ptrdiff_t, 5> indices(1,2,3,4,5);
+ Eigen::DSizes<ptrdiff_t, 5> sizes(1,1,1,1,1);
+ TensorRef<Tensor<float, 5>> slice = tensor.slice(indices, sizes);
+ VERIFY_IS_EQUAL(slice(0,0,0,0,0), tensor(1,2,3,4,5));
+
+ Eigen::DSizes<ptrdiff_t, 5> indices2(1,1,3,4,5);
+ Eigen::DSizes<ptrdiff_t, 5> sizes2(1,1,2,2,3);
+ slice = tensor.slice(indices2, sizes2);
+ for (int i = 0; i < 2; ++i) {
+ for (int j = 0; j < 2; ++j) {
+ for (int k = 0; k < 3; ++k) {
+ VERIFY_IS_EQUAL(slice(0,0,i,j,k), tensor(1,1,3+i,4+j,5+k));
+ }
+ }
+ }
+
+ Eigen::DSizes<ptrdiff_t, 5> indices3(0,0,0,0,0);
+ Eigen::DSizes<ptrdiff_t, 5> sizes3(2,3,1,1,1);
+ slice = tensor.slice(indices3, sizes3);
+ VERIFY_IS_EQUAL(slice.data(), tensor.data());
+}
+
+
+static void test_ref_of_ref()
+{
+ Tensor<float, 3> input(3,5,7);
+ input.setRandom();
+
+ TensorRef<Tensor<float, 3>> ref(input);
+ TensorRef<Tensor<float, 3>> ref_of_ref(ref);
+ TensorRef<Tensor<float, 3>> ref_of_ref2;
+ ref_of_ref2 = ref;
+
+ VERIFY_IS_EQUAL(ref_of_ref.data(), input.data());
+ VERIFY_IS_EQUAL(ref_of_ref.dimension(0), 3);
+ VERIFY_IS_EQUAL(ref_of_ref.dimension(1), 5);
+ VERIFY_IS_EQUAL(ref_of_ref.dimension(2), 7);
+
+ VERIFY_IS_EQUAL(ref_of_ref2.data(), input.data());
+ VERIFY_IS_EQUAL(ref_of_ref2.dimension(0), 3);
+ VERIFY_IS_EQUAL(ref_of_ref2.dimension(1), 5);
+ VERIFY_IS_EQUAL(ref_of_ref2.dimension(2), 7);
+
+ for (int i = 0; i < 3; ++i) {
+ for (int j = 0; j < 5; ++j) {
+ for (int k = 0; k < 7; ++k) {
+ VERIFY_IS_EQUAL(ref_of_ref(i,j,k), input(i,j,k));
+ VERIFY_IS_EQUAL(ref_of_ref2(i,j,k), input(i,j,k));
+ }
+ }
+ }
+}
+
+
+static void test_ref_in_expr()
+{
+ Tensor<float, 3> input(3,5,7);
+ input.setRandom();
+ TensorRef<Tensor<float, 3>> input_ref(input);
+
+ Tensor<float, 3> result(3,5,7);
+ result.setRandom();
+ TensorRef<Tensor<float, 3>> result_ref(result);
+
+ Tensor<float, 3> bias(3,5,7);
+ bias.setRandom();
+
+ result_ref = input_ref + bias;
+ for (int i = 0; i < 3; ++i) {
+ for (int j = 0; j < 5; ++j) {
+ for (int k = 0; k < 7; ++k) {
+ VERIFY_IS_EQUAL(result_ref(i,j,k), input(i,j,k) + bias(i,j,k));
+ VERIFY_IS_NOT_EQUAL(result(i,j,k), input(i,j,k) + bias(i,j,k));
+ }
+ }
+ }
+
+ result = result_ref;
+ for (int i = 0; i < 3; ++i) {
+ for (int j = 0; j < 5; ++j) {
+ for (int k = 0; k < 7; ++k) {
+ VERIFY_IS_EQUAL(result(i,j,k), input(i,j,k) + bias(i,j,k));
+ }
+ }
+ }
+}
+
+
+static void test_coeff_ref()
+{
+ Tensor<float, 5> tensor(2,3,5,7,11);
+ tensor.setRandom();
+ Tensor<float, 5> original = tensor;
+
+ TensorRef<Tensor<float, 4>> slice = tensor.chip(7, 4);
+ slice.coeffRef(0, 0, 0, 0) = 1.0f;
+ slice.coeffRef(1, 0, 0, 0) += 2.0f;
+
+ VERIFY_IS_EQUAL(tensor(0,0,0,0,7), 1.0f);
+ VERIFY_IS_EQUAL(tensor(1,0,0,0,7), original(1,0,0,0,7) + 2.0f);
+}
+
+
+static void test_nested_ops_with_ref()
+{
+ Tensor<float, 4> t(2, 3, 5, 7);
+ t.setRandom();
+ TensorMap<Tensor<const float, 4> > m(t.data(), 2, 3, 5, 7);
+ array<std::pair<ptrdiff_t, ptrdiff_t>, 4> paddings;
+ paddings[0] = std::make_pair(0, 0);
+ paddings[1] = std::make_pair(2, 1);
+ paddings[2] = std::make_pair(3, 4);
+ paddings[3] = std::make_pair(0, 0);
+ DSizes<Eigen::DenseIndex, 4> shuffle_dims(0, 1, 2, 3);
+ TensorRef<Tensor<const float, 4> > ref(m.pad(paddings));
+ array<std::pair<ptrdiff_t, ptrdiff_t>, 4> trivial;
+ trivial[0] = std::make_pair(0, 0);
+ trivial[1] = std::make_pair(0, 0);
+ trivial[2] = std::make_pair(0, 0);
+ trivial[3] = std::make_pair(0, 0);
+ Tensor<float, 4> padded = ref.shuffle(shuffle_dims).pad(trivial);
+ VERIFY_IS_EQUAL(padded.dimension(0), 2+0);
+ VERIFY_IS_EQUAL(padded.dimension(1), 3+3);
+ VERIFY_IS_EQUAL(padded.dimension(2), 5+7);
+ VERIFY_IS_EQUAL(padded.dimension(3), 7+0);
+
+ for (int i = 0; i < 2; ++i) {
+ for (int j = 0; j < 6; ++j) {
+ for (int k = 0; k < 12; ++k) {
+ for (int l = 0; l < 7; ++l) {
+ if (j >= 2 && j < 5 && k >= 3 && k < 8) {
+ VERIFY_IS_EQUAL(padded(i,j,k,l), t(i,j-2,k-3,l));
+ } else {
+ VERIFY_IS_EQUAL(padded(i,j,k,l), 0.0f);
+ }
+ }
+ }
+ }
+ }
+}
+
+
+EIGEN_DECLARE_TEST(cxx11_tensor_ref)
+{
+ CALL_SUBTEST(test_simple_lvalue_ref());
+ CALL_SUBTEST(test_simple_rvalue_ref());
+ CALL_SUBTEST(test_multiple_dims());
+ CALL_SUBTEST(test_slice());
+ CALL_SUBTEST(test_ref_of_ref());
+ CALL_SUBTEST(test_ref_in_expr());
+ CALL_SUBTEST(test_coeff_ref());
+ CALL_SUBTEST(test_nested_ops_with_ref());
+}
diff --git a/unsupported/test/cxx11_tensor_reverse.cpp b/unsupported/test/cxx11_tensor_reverse.cpp
new file mode 100644
index 0000000..5e44ec0
--- /dev/null
+++ b/unsupported/test/cxx11_tensor_reverse.cpp
@@ -0,0 +1,190 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2014 Navdeep Jaitly <ndjaitly@google.com and
+// Benoit Steiner <benoit.steiner.goog@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "main.h"
+
+#include <Eigen/CXX11/Tensor>
+
+using Eigen::Tensor;
+using Eigen::array;
+
+template <int DataLayout>
+static void test_simple_reverse()
+{
+ Tensor<float, 4, DataLayout> tensor(2,3,5,7);
+ tensor.setRandom();
+
+ array<bool, 4> dim_rev;
+ dim_rev[0] = false;
+ dim_rev[1] = true;
+ dim_rev[2] = true;
+ dim_rev[3] = false;
+
+ Tensor<float, 4, DataLayout> reversed_tensor;
+ reversed_tensor = tensor.reverse(dim_rev);
+
+ VERIFY_IS_EQUAL(reversed_tensor.dimension(0), 2);
+ VERIFY_IS_EQUAL(reversed_tensor.dimension(1), 3);
+ VERIFY_IS_EQUAL(reversed_tensor.dimension(2), 5);
+ VERIFY_IS_EQUAL(reversed_tensor.dimension(3), 7);
+
+ for (int i = 0; i < 2; ++i) {
+ for (int j = 0; j < 3; ++j) {
+ for (int k = 0; k < 5; ++k) {
+ for (int l = 0; l < 7; ++l) {
+ VERIFY_IS_EQUAL(tensor(i,j,k,l), reversed_tensor(i,2-j,4-k,l));
+ }
+ }
+ }
+ }
+
+ dim_rev[0] = true;
+ dim_rev[1] = false;
+ dim_rev[2] = false;
+ dim_rev[3] = false;
+
+ reversed_tensor = tensor.reverse(dim_rev);
+
+ VERIFY_IS_EQUAL(reversed_tensor.dimension(0), 2);
+ VERIFY_IS_EQUAL(reversed_tensor.dimension(1), 3);
+ VERIFY_IS_EQUAL(reversed_tensor.dimension(2), 5);
+ VERIFY_IS_EQUAL(reversed_tensor.dimension(3), 7);
+
+
+ for (int i = 0; i < 2; ++i) {
+ for (int j = 0; j < 3; ++j) {
+ for (int k = 0; k < 5; ++k) {
+ for (int l = 0; l < 7; ++l) {
+ VERIFY_IS_EQUAL(tensor(i,j,k,l), reversed_tensor(1-i,j,k,l));
+ }
+ }
+ }
+ }
+
+ dim_rev[0] = true;
+ dim_rev[1] = false;
+ dim_rev[2] = false;
+ dim_rev[3] = true;
+
+ reversed_tensor = tensor.reverse(dim_rev);
+
+ VERIFY_IS_EQUAL(reversed_tensor.dimension(0), 2);
+ VERIFY_IS_EQUAL(reversed_tensor.dimension(1), 3);
+ VERIFY_IS_EQUAL(reversed_tensor.dimension(2), 5);
+ VERIFY_IS_EQUAL(reversed_tensor.dimension(3), 7);
+
+
+ for (int i = 0; i < 2; ++i) {
+ for (int j = 0; j < 3; ++j) {
+ for (int k = 0; k < 5; ++k) {
+ for (int l = 0; l < 7; ++l) {
+ VERIFY_IS_EQUAL(tensor(i,j,k,l), reversed_tensor(1-i,j,k,6-l));
+ }
+ }
+ }
+ }
+}
+
+
+template <int DataLayout>
+static void test_expr_reverse(bool LValue)
+{
+ Tensor<float, 4, DataLayout> tensor(2,3,5,7);
+ tensor.setRandom();
+
+ array<bool, 4> dim_rev;
+ dim_rev[0] = false;
+ dim_rev[1] = true;
+ dim_rev[2] = false;
+ dim_rev[3] = true;
+
+ Tensor<float, 4, DataLayout> expected(2, 3, 5, 7);
+ if (LValue) {
+ expected.reverse(dim_rev) = tensor;
+ } else {
+ expected = tensor.reverse(dim_rev);
+ }
+
+ Tensor<float, 4, DataLayout> result(2,3,5,7);
+
+ array<ptrdiff_t, 4> src_slice_dim;
+ src_slice_dim[0] = 2;
+ src_slice_dim[1] = 3;
+ src_slice_dim[2] = 1;
+ src_slice_dim[3] = 7;
+ array<ptrdiff_t, 4> src_slice_start;
+ src_slice_start[0] = 0;
+ src_slice_start[1] = 0;
+ src_slice_start[2] = 0;
+ src_slice_start[3] = 0;
+ array<ptrdiff_t, 4> dst_slice_dim = src_slice_dim;
+ array<ptrdiff_t, 4> dst_slice_start = src_slice_start;
+
+ for (int i = 0; i < 5; ++i) {
+ if (LValue) {
+ result.slice(dst_slice_start, dst_slice_dim).reverse(dim_rev) =
+ tensor.slice(src_slice_start, src_slice_dim);
+ } else {
+ result.slice(dst_slice_start, dst_slice_dim) =
+ tensor.slice(src_slice_start, src_slice_dim).reverse(dim_rev);
+ }
+ src_slice_start[2] += 1;
+ dst_slice_start[2] += 1;
+ }
+
+ VERIFY_IS_EQUAL(result.dimension(0), 2);
+ VERIFY_IS_EQUAL(result.dimension(1), 3);
+ VERIFY_IS_EQUAL(result.dimension(2), 5);
+ VERIFY_IS_EQUAL(result.dimension(3), 7);
+
+ for (int i = 0; i < expected.dimension(0); ++i) {
+ for (int j = 0; j < expected.dimension(1); ++j) {
+ for (int k = 0; k < expected.dimension(2); ++k) {
+ for (int l = 0; l < expected.dimension(3); ++l) {
+ VERIFY_IS_EQUAL(result(i,j,k,l), expected(i,j,k,l));
+ }
+ }
+ }
+ }
+
+ dst_slice_start[2] = 0;
+ result.setRandom();
+ for (int i = 0; i < 5; ++i) {
+ if (LValue) {
+ result.slice(dst_slice_start, dst_slice_dim).reverse(dim_rev) =
+ tensor.slice(dst_slice_start, dst_slice_dim);
+ } else {
+ result.slice(dst_slice_start, dst_slice_dim) =
+ tensor.reverse(dim_rev).slice(dst_slice_start, dst_slice_dim);
+ }
+ dst_slice_start[2] += 1;
+ }
+
+ for (int i = 0; i < expected.dimension(0); ++i) {
+ for (int j = 0; j < expected.dimension(1); ++j) {
+ for (int k = 0; k < expected.dimension(2); ++k) {
+ for (int l = 0; l < expected.dimension(3); ++l) {
+ VERIFY_IS_EQUAL(result(i,j,k,l), expected(i,j,k,l));
+ }
+ }
+ }
+ }
+}
+
+
+EIGEN_DECLARE_TEST(cxx11_tensor_reverse)
+{
+ CALL_SUBTEST(test_simple_reverse<ColMajor>());
+ CALL_SUBTEST(test_simple_reverse<RowMajor>());
+ CALL_SUBTEST(test_expr_reverse<ColMajor>(true));
+ CALL_SUBTEST(test_expr_reverse<RowMajor>(true));
+ CALL_SUBTEST(test_expr_reverse<ColMajor>(false));
+ CALL_SUBTEST(test_expr_reverse<RowMajor>(false));
+}
diff --git a/unsupported/test/cxx11_tensor_reverse_sycl.cpp b/unsupported/test/cxx11_tensor_reverse_sycl.cpp
new file mode 100644
index 0000000..dd30c23
--- /dev/null
+++ b/unsupported/test/cxx11_tensor_reverse_sycl.cpp
@@ -0,0 +1,253 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2015
+// Mehdi Goli Codeplay Software Ltd.
+// Ralph Potter Codeplay Software Ltd.
+// Luke Iwanski Codeplay Software Ltd.
+// Contact: <eigen@codeplay.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#define EIGEN_TEST_NO_LONGDOUBLE
+#define EIGEN_TEST_NO_COMPLEX
+
+#define EIGEN_DEFAULT_DENSE_INDEX_TYPE int64_t
+#define EIGEN_USE_SYCL
+
+#include "main.h"
+#include <unsupported/Eigen/CXX11/Tensor>
+
+template <typename DataType, int DataLayout, typename IndexType>
+static void test_simple_reverse(const Eigen::SyclDevice& sycl_device) {
+ IndexType dim1 = 2;
+ IndexType dim2 = 3;
+ IndexType dim3 = 5;
+ IndexType dim4 = 7;
+
+ array<IndexType, 4> tensorRange = {{dim1, dim2, dim3, dim4}};
+ Tensor<DataType, 4, DataLayout, IndexType> tensor(tensorRange);
+ Tensor<DataType, 4, DataLayout, IndexType> reversed_tensor(tensorRange);
+ tensor.setRandom();
+
+ array<bool, 4> dim_rev;
+ dim_rev[0] = false;
+ dim_rev[1] = true;
+ dim_rev[2] = true;
+ dim_rev[3] = false;
+
+ DataType* gpu_in_data = static_cast<DataType*>(
+ sycl_device.allocate(tensor.dimensions().TotalSize() * sizeof(DataType)));
+ DataType* gpu_out_data = static_cast<DataType*>(sycl_device.allocate(
+ reversed_tensor.dimensions().TotalSize() * sizeof(DataType)));
+
+ TensorMap<Tensor<DataType, 4, DataLayout, IndexType> > in_gpu(gpu_in_data,
+ tensorRange);
+ TensorMap<Tensor<DataType, 4, DataLayout, IndexType> > out_gpu(gpu_out_data,
+ tensorRange);
+
+ sycl_device.memcpyHostToDevice(
+ gpu_in_data, tensor.data(),
+ (tensor.dimensions().TotalSize()) * sizeof(DataType));
+ out_gpu.device(sycl_device) = in_gpu.reverse(dim_rev);
+ sycl_device.memcpyDeviceToHost(
+ reversed_tensor.data(), gpu_out_data,
+ reversed_tensor.dimensions().TotalSize() * sizeof(DataType));
+ // Check that the CPU and GPU reductions return the same result.
+ for (IndexType i = 0; i < 2; ++i) {
+ for (IndexType j = 0; j < 3; ++j) {
+ for (IndexType k = 0; k < 5; ++k) {
+ for (IndexType l = 0; l < 7; ++l) {
+ VERIFY_IS_EQUAL(tensor(i, j, k, l),
+ reversed_tensor(i, 2 - j, 4 - k, l));
+ }
+ }
+ }
+ }
+ dim_rev[0] = true;
+ dim_rev[1] = false;
+ dim_rev[2] = false;
+ dim_rev[3] = false;
+
+ out_gpu.device(sycl_device) = in_gpu.reverse(dim_rev);
+ sycl_device.memcpyDeviceToHost(
+ reversed_tensor.data(), gpu_out_data,
+ reversed_tensor.dimensions().TotalSize() * sizeof(DataType));
+
+ for (IndexType i = 0; i < 2; ++i) {
+ for (IndexType j = 0; j < 3; ++j) {
+ for (IndexType k = 0; k < 5; ++k) {
+ for (IndexType l = 0; l < 7; ++l) {
+ VERIFY_IS_EQUAL(tensor(i, j, k, l), reversed_tensor(1 - i, j, k, l));
+ }
+ }
+ }
+ }
+
+ dim_rev[0] = true;
+ dim_rev[1] = false;
+ dim_rev[2] = false;
+ dim_rev[3] = true;
+ out_gpu.device(sycl_device) = in_gpu.reverse(dim_rev);
+ sycl_device.memcpyDeviceToHost(
+ reversed_tensor.data(), gpu_out_data,
+ reversed_tensor.dimensions().TotalSize() * sizeof(DataType));
+
+ for (IndexType i = 0; i < 2; ++i) {
+ for (IndexType j = 0; j < 3; ++j) {
+ for (IndexType k = 0; k < 5; ++k) {
+ for (IndexType l = 0; l < 7; ++l) {
+ VERIFY_IS_EQUAL(tensor(i, j, k, l),
+ reversed_tensor(1 - i, j, k, 6 - l));
+ }
+ }
+ }
+ }
+
+ sycl_device.deallocate(gpu_in_data);
+ sycl_device.deallocate(gpu_out_data);
+}
+
+template <typename DataType, int DataLayout, typename IndexType>
+static void test_expr_reverse(const Eigen::SyclDevice& sycl_device,
+ bool LValue) {
+ IndexType dim1 = 2;
+ IndexType dim2 = 3;
+ IndexType dim3 = 5;
+ IndexType dim4 = 7;
+
+ array<IndexType, 4> tensorRange = {{dim1, dim2, dim3, dim4}};
+ Tensor<DataType, 4, DataLayout, IndexType> tensor(tensorRange);
+ Tensor<DataType, 4, DataLayout, IndexType> expected(tensorRange);
+ Tensor<DataType, 4, DataLayout, IndexType> result(tensorRange);
+ tensor.setRandom();
+
+ array<bool, 4> dim_rev;
+ dim_rev[0] = false;
+ dim_rev[1] = true;
+ dim_rev[2] = false;
+ dim_rev[3] = true;
+
+ DataType* gpu_in_data = static_cast<DataType*>(
+ sycl_device.allocate(tensor.dimensions().TotalSize() * sizeof(DataType)));
+ DataType* gpu_out_data_expected = static_cast<DataType*>(sycl_device.allocate(
+ expected.dimensions().TotalSize() * sizeof(DataType)));
+ DataType* gpu_out_data_result = static_cast<DataType*>(
+ sycl_device.allocate(result.dimensions().TotalSize() * sizeof(DataType)));
+
+ TensorMap<Tensor<DataType, 4, DataLayout, IndexType> > in_gpu(gpu_in_data,
+ tensorRange);
+ TensorMap<Tensor<DataType, 4, DataLayout, IndexType> > out_gpu_expected(
+ gpu_out_data_expected, tensorRange);
+ TensorMap<Tensor<DataType, 4, DataLayout, IndexType> > out_gpu_result(
+ gpu_out_data_result, tensorRange);
+
+ sycl_device.memcpyHostToDevice(
+ gpu_in_data, tensor.data(),
+ (tensor.dimensions().TotalSize()) * sizeof(DataType));
+
+ if (LValue) {
+ out_gpu_expected.reverse(dim_rev).device(sycl_device) = in_gpu;
+ } else {
+ out_gpu_expected.device(sycl_device) = in_gpu.reverse(dim_rev);
+ }
+ sycl_device.memcpyDeviceToHost(
+ expected.data(), gpu_out_data_expected,
+ expected.dimensions().TotalSize() * sizeof(DataType));
+
+ array<IndexType, 4> src_slice_dim;
+ src_slice_dim[0] = 2;
+ src_slice_dim[1] = 3;
+ src_slice_dim[2] = 1;
+ src_slice_dim[3] = 7;
+ array<IndexType, 4> src_slice_start;
+ src_slice_start[0] = 0;
+ src_slice_start[1] = 0;
+ src_slice_start[2] = 0;
+ src_slice_start[3] = 0;
+ array<IndexType, 4> dst_slice_dim = src_slice_dim;
+ array<IndexType, 4> dst_slice_start = src_slice_start;
+
+ for (IndexType i = 0; i < 5; ++i) {
+ if (LValue) {
+ out_gpu_result.slice(dst_slice_start, dst_slice_dim)
+ .reverse(dim_rev)
+ .device(sycl_device) = in_gpu.slice(src_slice_start, src_slice_dim);
+ } else {
+ out_gpu_result.slice(dst_slice_start, dst_slice_dim).device(sycl_device) =
+ in_gpu.slice(src_slice_start, src_slice_dim).reverse(dim_rev);
+ }
+ src_slice_start[2] += 1;
+ dst_slice_start[2] += 1;
+ }
+ sycl_device.memcpyDeviceToHost(
+ result.data(), gpu_out_data_result,
+ result.dimensions().TotalSize() * sizeof(DataType));
+
+ for (IndexType i = 0; i < expected.dimension(0); ++i) {
+ for (IndexType j = 0; j < expected.dimension(1); ++j) {
+ for (IndexType k = 0; k < expected.dimension(2); ++k) {
+ for (IndexType l = 0; l < expected.dimension(3); ++l) {
+ VERIFY_IS_EQUAL(result(i, j, k, l), expected(i, j, k, l));
+ }
+ }
+ }
+ }
+
+ dst_slice_start[2] = 0;
+ result.setRandom();
+ sycl_device.memcpyHostToDevice(
+ gpu_out_data_result, result.data(),
+ (result.dimensions().TotalSize()) * sizeof(DataType));
+ for (IndexType i = 0; i < 5; ++i) {
+ if (LValue) {
+ out_gpu_result.slice(dst_slice_start, dst_slice_dim)
+ .reverse(dim_rev)
+ .device(sycl_device) = in_gpu.slice(dst_slice_start, dst_slice_dim);
+ } else {
+ out_gpu_result.slice(dst_slice_start, dst_slice_dim).device(sycl_device) =
+ in_gpu.reverse(dim_rev).slice(dst_slice_start, dst_slice_dim);
+ }
+ dst_slice_start[2] += 1;
+ }
+ sycl_device.memcpyDeviceToHost(
+ result.data(), gpu_out_data_result,
+ result.dimensions().TotalSize() * sizeof(DataType));
+
+ for (IndexType i = 0; i < expected.dimension(0); ++i) {
+ for (IndexType j = 0; j < expected.dimension(1); ++j) {
+ for (IndexType k = 0; k < expected.dimension(2); ++k) {
+ for (IndexType l = 0; l < expected.dimension(3); ++l) {
+ VERIFY_IS_EQUAL(result(i, j, k, l), expected(i, j, k, l));
+ }
+ }
+ }
+ }
+}
+
+template <typename DataType>
+void sycl_reverse_test_per_device(const cl::sycl::device& d) {
+ QueueInterface queueInterface(d);
+ auto sycl_device = Eigen::SyclDevice(&queueInterface);
+ test_simple_reverse<DataType, RowMajor, int64_t>(sycl_device);
+ test_simple_reverse<DataType, ColMajor, int64_t>(sycl_device);
+ test_expr_reverse<DataType, RowMajor, int64_t>(sycl_device, false);
+ test_expr_reverse<DataType, ColMajor, int64_t>(sycl_device, false);
+ test_expr_reverse<DataType, RowMajor, int64_t>(sycl_device, true);
+ test_expr_reverse<DataType, ColMajor, int64_t>(sycl_device, true);
+}
+EIGEN_DECLARE_TEST(cxx11_tensor_reverse_sycl) {
+ for (const auto& device : Eigen::get_sycl_supported_devices()) {
+ std::cout << "Running on "
+ << device.get_info<cl::sycl::info::device::name>() << std::endl;
+ CALL_SUBTEST_1(sycl_reverse_test_per_device<short>(device));
+ CALL_SUBTEST_2(sycl_reverse_test_per_device<int>(device));
+ CALL_SUBTEST_3(sycl_reverse_test_per_device<unsigned int>(device));
+#ifdef EIGEN_SYCL_DOUBLE_SUPPORT
+ CALL_SUBTEST_4(sycl_reverse_test_per_device<double>(device));
+#endif
+ CALL_SUBTEST_5(sycl_reverse_test_per_device<float>(device));
+ }
+}
diff --git a/unsupported/test/cxx11_tensor_roundings.cpp b/unsupported/test/cxx11_tensor_roundings.cpp
new file mode 100644
index 0000000..83b5923
--- /dev/null
+++ b/unsupported/test/cxx11_tensor_roundings.cpp
@@ -0,0 +1,62 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2016 Benoit Steiner <benoit.steiner.goog@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "main.h"
+
+#include <Eigen/CXX11/Tensor>
+
+
+static void test_float_rounding()
+{
+ Tensor<float, 2> ftensor(20,30);
+ ftensor = ftensor.random() * 100.f;
+
+ Tensor<float, 2> result = ftensor.round();
+
+ for (int i = 0; i < 20; ++i) {
+ for (int j = 0; j < 30; ++j) {
+ VERIFY_IS_EQUAL(result(i,j), numext::round(ftensor(i,j)));
+ }
+ }
+}
+
+static void test_float_flooring()
+{
+ Tensor<float, 2> ftensor(20,30);
+ ftensor = ftensor.random() * 100.f;
+
+ Tensor<float, 2> result = ftensor.floor();
+
+ for (int i = 0; i < 20; ++i) {
+ for (int j = 0; j < 30; ++j) {
+ VERIFY_IS_EQUAL(result(i,j), numext::floor(ftensor(i,j)));
+ }
+ }
+}
+
+static void test_float_ceiling()
+{
+ Tensor<float, 2> ftensor(20,30);
+ ftensor = ftensor.random() * 100.f;
+
+ Tensor<float, 2> result = ftensor.ceil();
+
+ for (int i = 0; i < 20; ++i) {
+ for (int j = 0; j < 30; ++j) {
+ VERIFY_IS_EQUAL(result(i,j), numext::ceil(ftensor(i,j)));
+ }
+ }
+}
+
+EIGEN_DECLARE_TEST(cxx11_tensor_roundings)
+{
+ CALL_SUBTEST(test_float_rounding());
+ CALL_SUBTEST(test_float_ceiling());
+ CALL_SUBTEST(test_float_flooring());
+}
diff --git a/unsupported/test/cxx11_tensor_scan.cpp b/unsupported/test/cxx11_tensor_scan.cpp
new file mode 100644
index 0000000..dccee9e
--- /dev/null
+++ b/unsupported/test/cxx11_tensor_scan.cpp
@@ -0,0 +1,110 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2016 Igor Babuschkin <igor@babuschk.in>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "main.h"
+#include <limits>
+#include <numeric>
+#include <Eigen/CXX11/Tensor>
+
+using Eigen::Tensor;
+
+template <int DataLayout, typename Type=float, bool Exclusive = false>
+static void test_1d_scan()
+{
+ int size = 50;
+ Tensor<Type, 1, DataLayout> tensor(size);
+ tensor.setRandom();
+ Tensor<Type, 1, DataLayout> result = tensor.cumsum(0, Exclusive);
+
+ VERIFY_IS_EQUAL(tensor.dimension(0), result.dimension(0));
+
+ float accum = 0;
+ for (int i = 0; i < size; i++) {
+ if (Exclusive) {
+ VERIFY_IS_EQUAL(result(i), accum);
+ accum += tensor(i);
+ } else {
+ accum += tensor(i);
+ VERIFY_IS_EQUAL(result(i), accum);
+ }
+ }
+
+ accum = 1;
+ result = tensor.cumprod(0, Exclusive);
+ for (int i = 0; i < size; i++) {
+ if (Exclusive) {
+ VERIFY_IS_EQUAL(result(i), accum);
+ accum *= tensor(i);
+ } else {
+ accum *= tensor(i);
+ VERIFY_IS_EQUAL(result(i), accum);
+ }
+ }
+}
+
+template <int DataLayout, typename Type=float>
+static void test_4d_scan()
+{
+ int size = 5;
+ Tensor<Type, 4, DataLayout> tensor(size, size, size, size);
+ tensor.setRandom();
+
+ Tensor<Type, 4, DataLayout> result(size, size, size, size);
+
+ result = tensor.cumsum(0);
+ float accum = 0;
+ for (int i = 0; i < size; i++) {
+ accum += tensor(i, 1, 2, 3);
+ VERIFY_IS_EQUAL(result(i, 1, 2, 3), accum);
+ }
+ result = tensor.cumsum(1);
+ accum = 0;
+ for (int i = 0; i < size; i++) {
+ accum += tensor(1, i, 2, 3);
+ VERIFY_IS_EQUAL(result(1, i, 2, 3), accum);
+ }
+ result = tensor.cumsum(2);
+ accum = 0;
+ for (int i = 0; i < size; i++) {
+ accum += tensor(1, 2, i, 3);
+ VERIFY_IS_EQUAL(result(1, 2, i, 3), accum);
+ }
+ result = tensor.cumsum(3);
+ accum = 0;
+ for (int i = 0; i < size; i++) {
+ accum += tensor(1, 2, 3, i);
+ VERIFY_IS_EQUAL(result(1, 2, 3, i), accum);
+ }
+}
+
+template <int DataLayout>
+static void test_tensor_maps() {
+ int inputs[20];
+ TensorMap<Tensor<int, 1, DataLayout> > tensor_map(inputs, 20);
+ tensor_map.setRandom();
+
+ Tensor<int, 1, DataLayout> result = tensor_map.cumsum(0);
+
+ int accum = 0;
+ for (int i = 0; i < 20; ++i) {
+ accum += tensor_map(i);
+ VERIFY_IS_EQUAL(result(i), accum);
+ }
+}
+
+EIGEN_DECLARE_TEST(cxx11_tensor_scan) {
+ CALL_SUBTEST((test_1d_scan<ColMajor, float, true>()));
+ CALL_SUBTEST((test_1d_scan<ColMajor, float, false>()));
+ CALL_SUBTEST((test_1d_scan<RowMajor, float, true>()));
+ CALL_SUBTEST((test_1d_scan<RowMajor, float, false>()));
+ CALL_SUBTEST(test_4d_scan<ColMajor>());
+ CALL_SUBTEST(test_4d_scan<RowMajor>());
+ CALL_SUBTEST(test_tensor_maps<ColMajor>());
+ CALL_SUBTEST(test_tensor_maps<RowMajor>());
+}
diff --git a/unsupported/test/cxx11_tensor_scan_gpu.cu b/unsupported/test/cxx11_tensor_scan_gpu.cu
new file mode 100644
index 0000000..770a144
--- /dev/null
+++ b/unsupported/test/cxx11_tensor_scan_gpu.cu
@@ -0,0 +1,78 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2016 Benoit Steiner <benoit.steiner.goog@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#define EIGEN_TEST_NO_LONGDOUBLE
+#define EIGEN_TEST_NO_COMPLEX
+
+#define EIGEN_DEFAULT_DENSE_INDEX_TYPE int
+#define EIGEN_USE_GPU
+
+#include "main.h"
+#include <unsupported/Eigen/CXX11/Tensor>
+
+#include <Eigen/CXX11/src/Tensor/TensorGpuHipCudaDefines.h>
+
+using Eigen::Tensor;
+typedef Tensor<float, 1>::DimensionPair DimPair;
+
+template<int DataLayout>
+void test_gpu_cumsum(int m_size, int k_size, int n_size)
+{
+ std::cout << "Testing for (" << m_size << "," << k_size << "," << n_size << ")" << std::endl;
+ Tensor<float, 3, DataLayout> t_input(m_size, k_size, n_size);
+ Tensor<float, 3, DataLayout> t_result(m_size, k_size, n_size);
+ Tensor<float, 3, DataLayout> t_result_gpu(m_size, k_size, n_size);
+
+ t_input.setRandom();
+
+ std::size_t t_input_bytes = t_input.size() * sizeof(float);
+ std::size_t t_result_bytes = t_result.size() * sizeof(float);
+
+ float* d_t_input;
+ float* d_t_result;
+
+ gpuMalloc((void**)(&d_t_input), t_input_bytes);
+ gpuMalloc((void**)(&d_t_result), t_result_bytes);
+
+ gpuMemcpy(d_t_input, t_input.data(), t_input_bytes, gpuMemcpyHostToDevice);
+
+ Eigen::GpuStreamDevice stream;
+ Eigen::GpuDevice gpu_device(&stream);
+
+ Eigen::TensorMap<Eigen::Tensor<float, 3, DataLayout> >
+ gpu_t_input(d_t_input, Eigen::array<int, 3>(m_size, k_size, n_size));
+ Eigen::TensorMap<Eigen::Tensor<float, 3, DataLayout> >
+ gpu_t_result(d_t_result, Eigen::array<int, 3>(m_size, k_size, n_size));
+
+ gpu_t_result.device(gpu_device) = gpu_t_input.cumsum(1);
+ t_result = t_input.cumsum(1);
+
+ gpuMemcpy(t_result_gpu.data(), d_t_result, t_result_bytes, gpuMemcpyDeviceToHost);
+ for (DenseIndex i = 0; i < t_result.size(); i++) {
+ if (fabs(t_result(i) - t_result_gpu(i)) < 1e-4f) {
+ continue;
+ }
+ if (Eigen::internal::isApprox(t_result(i), t_result_gpu(i), 1e-4f)) {
+ continue;
+ }
+ std::cout << "mismatch detected at index " << i << ": " << t_result(i)
+ << " vs " << t_result_gpu(i) << std::endl;
+ assert(false);
+ }
+
+ gpuFree((void*)d_t_input);
+ gpuFree((void*)d_t_result);
+}
+
+
+EIGEN_DECLARE_TEST(cxx11_tensor_scan_gpu)
+{
+ CALL_SUBTEST_1(test_gpu_cumsum<ColMajor>(128, 128, 128));
+ CALL_SUBTEST_2(test_gpu_cumsum<RowMajor>(128, 128, 128));
+}
diff --git a/unsupported/test/cxx11_tensor_scan_sycl.cpp b/unsupported/test/cxx11_tensor_scan_sycl.cpp
new file mode 100644
index 0000000..09c45fc
--- /dev/null
+++ b/unsupported/test/cxx11_tensor_scan_sycl.cpp
@@ -0,0 +1,141 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2016
+// Mehdi Goli Codeplay Software Ltd.
+// Ralph Potter Codeplay Software Ltd.
+// Luke Iwanski Codeplay Software Ltd.
+// Contact: <eigen@codeplay.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#define EIGEN_TEST_NO_LONGDOUBLE
+#define EIGEN_TEST_NO_COMPLEX
+#define EIGEN_DEFAULT_DENSE_INDEX_TYPE int64_t
+#define EIGEN_USE_SYCL
+
+#include "main.h"
+#include <unsupported/Eigen/CXX11/Tensor>
+
+using Eigen::Tensor;
+typedef Tensor<float, 1>::DimensionPair DimPair;
+
+template <typename DataType, int DataLayout, typename IndexType>
+void test_sycl_cumsum(const Eigen::SyclDevice& sycl_device, IndexType m_size,
+ IndexType k_size, IndexType n_size, int consume_dim,
+ bool exclusive) {
+ static const DataType error_threshold = 1e-4f;
+ std::cout << "Testing for (" << m_size << "," << k_size << "," << n_size
+ << " consume_dim : " << consume_dim << ")" << std::endl;
+ Tensor<DataType, 3, DataLayout, IndexType> t_input(m_size, k_size, n_size);
+ Tensor<DataType, 3, DataLayout, IndexType> t_result(m_size, k_size, n_size);
+ Tensor<DataType, 3, DataLayout, IndexType> t_result_gpu(m_size, k_size,
+ n_size);
+
+ t_input.setRandom();
+ std::size_t t_input_bytes = t_input.size() * sizeof(DataType);
+ std::size_t t_result_bytes = t_result.size() * sizeof(DataType);
+
+ DataType* gpu_data_in =
+ static_cast<DataType*>(sycl_device.allocate(t_input_bytes));
+ DataType* gpu_data_out =
+ static_cast<DataType*>(sycl_device.allocate(t_result_bytes));
+
+ array<IndexType, 3> tensorRange = {{m_size, k_size, n_size}};
+ TensorMap<Tensor<DataType, 3, DataLayout, IndexType>> gpu_t_input(
+ gpu_data_in, tensorRange);
+ TensorMap<Tensor<DataType, 3, DataLayout, IndexType>> gpu_t_result(
+ gpu_data_out, tensorRange);
+ sycl_device.memcpyHostToDevice(gpu_data_in, t_input.data(), t_input_bytes);
+ sycl_device.memcpyHostToDevice(gpu_data_out, t_input.data(), t_input_bytes);
+
+ gpu_t_result.device(sycl_device) = gpu_t_input.cumsum(consume_dim, exclusive);
+
+ t_result = t_input.cumsum(consume_dim, exclusive);
+
+ sycl_device.memcpyDeviceToHost(t_result_gpu.data(), gpu_data_out,
+ t_result_bytes);
+ sycl_device.synchronize();
+
+ for (IndexType i = 0; i < t_result.size(); i++) {
+ if (static_cast<DataType>(std::fabs(static_cast<DataType>(
+ t_result(i) - t_result_gpu(i)))) < error_threshold) {
+ continue;
+ }
+ if (Eigen::internal::isApprox(t_result(i), t_result_gpu(i),
+ error_threshold)) {
+ continue;
+ }
+ std::cout << "mismatch detected at index " << i << " CPU : " << t_result(i)
+ << " vs SYCL : " << t_result_gpu(i) << std::endl;
+ assert(false);
+ }
+ sycl_device.deallocate(gpu_data_in);
+ sycl_device.deallocate(gpu_data_out);
+}
+
+template <typename DataType, typename Dev>
+void sycl_scan_test_exclusive_dim0_per_device(const Dev& sycl_device) {
+ test_sycl_cumsum<DataType, ColMajor, int64_t>(sycl_device, 2049, 1023, 127, 0,
+ true);
+ test_sycl_cumsum<DataType, RowMajor, int64_t>(sycl_device, 2049, 1023, 127, 0,
+ true);
+}
+template <typename DataType, typename Dev>
+void sycl_scan_test_exclusive_dim1_per_device(const Dev& sycl_device) {
+ test_sycl_cumsum<DataType, ColMajor, int64_t>(sycl_device, 1023, 2049, 127, 1,
+ true);
+ test_sycl_cumsum<DataType, RowMajor, int64_t>(sycl_device, 1023, 2049, 127, 1,
+ true);
+}
+template <typename DataType, typename Dev>
+void sycl_scan_test_exclusive_dim2_per_device(const Dev& sycl_device) {
+ test_sycl_cumsum<DataType, ColMajor, int64_t>(sycl_device, 1023, 127, 2049, 2,
+ true);
+ test_sycl_cumsum<DataType, RowMajor, int64_t>(sycl_device, 1023, 127, 2049, 2,
+ true);
+}
+template <typename DataType, typename Dev>
+void sycl_scan_test_inclusive_dim0_per_device(const Dev& sycl_device) {
+ test_sycl_cumsum<DataType, ColMajor, int64_t>(sycl_device, 2049, 1023, 127, 0,
+ false);
+ test_sycl_cumsum<DataType, RowMajor, int64_t>(sycl_device, 2049, 1023, 127, 0,
+ false);
+}
+template <typename DataType, typename Dev>
+void sycl_scan_test_inclusive_dim1_per_device(const Dev& sycl_device) {
+ test_sycl_cumsum<DataType, ColMajor, int64_t>(sycl_device, 1023, 2049, 127, 1,
+ false);
+ test_sycl_cumsum<DataType, RowMajor, int64_t>(sycl_device, 1023, 2049, 127, 1,
+ false);
+}
+template <typename DataType, typename Dev>
+void sycl_scan_test_inclusive_dim2_per_device(const Dev& sycl_device) {
+ test_sycl_cumsum<DataType, ColMajor, int64_t>(sycl_device, 1023, 127, 2049, 2,
+ false);
+ test_sycl_cumsum<DataType, RowMajor, int64_t>(sycl_device, 1023, 127, 2049, 2,
+ false);
+}
+EIGEN_DECLARE_TEST(cxx11_tensor_scan_sycl) {
+ for (const auto& device : Eigen::get_sycl_supported_devices()) {
+ std::cout << "Running on "
+ << device.template get_info<cl::sycl::info::device::name>()
+ << std::endl;
+ QueueInterface queueInterface(device);
+ auto sycl_device = Eigen::SyclDevice(&queueInterface);
+ CALL_SUBTEST_1(
+ sycl_scan_test_exclusive_dim0_per_device<float>(sycl_device));
+ CALL_SUBTEST_2(
+ sycl_scan_test_exclusive_dim1_per_device<float>(sycl_device));
+ CALL_SUBTEST_3(
+ sycl_scan_test_exclusive_dim2_per_device<float>(sycl_device));
+ CALL_SUBTEST_4(
+ sycl_scan_test_inclusive_dim0_per_device<float>(sycl_device));
+ CALL_SUBTEST_5(
+ sycl_scan_test_inclusive_dim1_per_device<float>(sycl_device));
+ CALL_SUBTEST_6(
+ sycl_scan_test_inclusive_dim2_per_device<float>(sycl_device));
+ }
+}
diff --git a/unsupported/test/cxx11_tensor_shuffling.cpp b/unsupported/test/cxx11_tensor_shuffling.cpp
new file mode 100644
index 0000000..89a64c0
--- /dev/null
+++ b/unsupported/test/cxx11_tensor_shuffling.cpp
@@ -0,0 +1,283 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "main.h"
+
+#include <Eigen/CXX11/Tensor>
+
+using Eigen::Tensor;
+using Eigen::array;
+
+template <int DataLayout>
+static void test_simple_shuffling()
+{
+ Tensor<float, 4, DataLayout> tensor(2,3,5,7);
+ tensor.setRandom();
+ array<ptrdiff_t, 4> shuffles;
+ shuffles[0] = 0;
+ shuffles[1] = 1;
+ shuffles[2] = 2;
+ shuffles[3] = 3;
+
+ Tensor<float, 4, DataLayout> no_shuffle;
+ no_shuffle = tensor.shuffle(shuffles);
+
+ VERIFY_IS_EQUAL(no_shuffle.dimension(0), 2);
+ VERIFY_IS_EQUAL(no_shuffle.dimension(1), 3);
+ VERIFY_IS_EQUAL(no_shuffle.dimension(2), 5);
+ VERIFY_IS_EQUAL(no_shuffle.dimension(3), 7);
+
+ for (int i = 0; i < 2; ++i) {
+ for (int j = 0; j < 3; ++j) {
+ for (int k = 0; k < 5; ++k) {
+ for (int l = 0; l < 7; ++l) {
+ VERIFY_IS_EQUAL(tensor(i,j,k,l), no_shuffle(i,j,k,l));
+ }
+ }
+ }
+ }
+
+ shuffles[0] = 2;
+ shuffles[1] = 3;
+ shuffles[2] = 1;
+ shuffles[3] = 0;
+ Tensor<float, 4, DataLayout> shuffle;
+ shuffle = tensor.shuffle(shuffles);
+
+ VERIFY_IS_EQUAL(shuffle.dimension(0), 5);
+ VERIFY_IS_EQUAL(shuffle.dimension(1), 7);
+ VERIFY_IS_EQUAL(shuffle.dimension(2), 3);
+ VERIFY_IS_EQUAL(shuffle.dimension(3), 2);
+
+ for (int i = 0; i < 2; ++i) {
+ for (int j = 0; j < 3; ++j) {
+ for (int k = 0; k < 5; ++k) {
+ for (int l = 0; l < 7; ++l) {
+ VERIFY_IS_EQUAL(tensor(i,j,k,l), shuffle(k,l,j,i));
+ }
+ }
+ }
+ }
+}
+
+
+template <int DataLayout>
+static void test_expr_shuffling()
+{
+ Tensor<float, 4, DataLayout> tensor(2,3,5,7);
+ tensor.setRandom();
+
+ array<ptrdiff_t, 4> shuffles;
+ shuffles[0] = 2;
+ shuffles[1] = 3;
+ shuffles[2] = 1;
+ shuffles[3] = 0;
+ Tensor<float, 4, DataLayout> expected;
+ expected = tensor.shuffle(shuffles);
+
+ Tensor<float, 4, DataLayout> result(5, 7, 3, 2);
+
+ array<ptrdiff_t, 4> src_slice_dim{{2, 3, 1, 7}};
+ array<ptrdiff_t, 4> src_slice_start{{0, 0, 0, 0}};
+ array<ptrdiff_t, 4> dst_slice_dim{{1, 7, 3, 2}};
+ array<ptrdiff_t, 4> dst_slice_start{{0, 0, 0, 0}};
+
+ for (int i = 0; i < 5; ++i) {
+ result.slice(dst_slice_start, dst_slice_dim) =
+ tensor.slice(src_slice_start, src_slice_dim).shuffle(shuffles);
+ src_slice_start[2] += 1;
+ dst_slice_start[0] += 1;
+ }
+
+ VERIFY_IS_EQUAL(result.dimension(0), 5);
+ VERIFY_IS_EQUAL(result.dimension(1), 7);
+ VERIFY_IS_EQUAL(result.dimension(2), 3);
+ VERIFY_IS_EQUAL(result.dimension(3), 2);
+
+ for (int i = 0; i < expected.dimension(0); ++i) {
+ for (int j = 0; j < expected.dimension(1); ++j) {
+ for (int k = 0; k < expected.dimension(2); ++k) {
+ for (int l = 0; l < expected.dimension(3); ++l) {
+ VERIFY_IS_EQUAL(result(i,j,k,l), expected(i,j,k,l));
+ }
+ }
+ }
+ }
+
+ dst_slice_start[0] = 0;
+ result.setRandom();
+ for (int i = 0; i < 5; ++i) {
+ result.slice(dst_slice_start, dst_slice_dim) =
+ tensor.shuffle(shuffles).slice(dst_slice_start, dst_slice_dim);
+ dst_slice_start[0] += 1;
+ }
+
+ for (int i = 0; i < expected.dimension(0); ++i) {
+ for (int j = 0; j < expected.dimension(1); ++j) {
+ for (int k = 0; k < expected.dimension(2); ++k) {
+ for (int l = 0; l < expected.dimension(3); ++l) {
+ VERIFY_IS_EQUAL(result(i,j,k,l), expected(i,j,k,l));
+ }
+ }
+ }
+ }
+}
+
+
+template <int DataLayout>
+static void test_shuffling_as_value()
+{
+ Tensor<float, 4, DataLayout> tensor(2,3,5,7);
+ tensor.setRandom();
+ array<ptrdiff_t, 4> shuffles;
+ shuffles[2] = 0;
+ shuffles[3] = 1;
+ shuffles[1] = 2;
+ shuffles[0] = 3;
+ Tensor<float, 4, DataLayout> shuffle(5,7,3,2);
+ shuffle.shuffle(shuffles) = tensor;
+
+ VERIFY_IS_EQUAL(shuffle.dimension(0), 5);
+ VERIFY_IS_EQUAL(shuffle.dimension(1), 7);
+ VERIFY_IS_EQUAL(shuffle.dimension(2), 3);
+ VERIFY_IS_EQUAL(shuffle.dimension(3), 2);
+
+ for (int i = 0; i < 2; ++i) {
+ for (int j = 0; j < 3; ++j) {
+ for (int k = 0; k < 5; ++k) {
+ for (int l = 0; l < 7; ++l) {
+ VERIFY_IS_EQUAL(tensor(i,j,k,l), shuffle(k,l,j,i));
+ }
+ }
+ }
+ }
+
+ array<ptrdiff_t, 4> no_shuffle;
+ no_shuffle[0] = 0;
+ no_shuffle[1] = 1;
+ no_shuffle[2] = 2;
+ no_shuffle[3] = 3;
+ Tensor<float, 4, DataLayout> shuffle2(5,7,3,2);
+ shuffle2.shuffle(shuffles) = tensor.shuffle(no_shuffle);
+ for (int i = 0; i < 5; ++i) {
+ for (int j = 0; j < 7; ++j) {
+ for (int k = 0; k < 3; ++k) {
+ for (int l = 0; l < 2; ++l) {
+ VERIFY_IS_EQUAL(shuffle2(i,j,k,l), shuffle(i,j,k,l));
+ }
+ }
+ }
+ }
+}
+
+
+template <int DataLayout>
+static void test_shuffle_unshuffle()
+{
+ Tensor<float, 4, DataLayout> tensor(2,3,5,7);
+ tensor.setRandom();
+
+ // Choose a random permutation.
+ array<ptrdiff_t, 4> shuffles;
+ for (int i = 0; i < 4; ++i) {
+ shuffles[i] = i;
+ }
+ array<ptrdiff_t, 4> shuffles_inverse;
+ for (int i = 0; i < 4; ++i) {
+ const ptrdiff_t index = internal::random<ptrdiff_t>(i, 3);
+ shuffles_inverse[shuffles[index]] = i;
+ std::swap(shuffles[i], shuffles[index]);
+ }
+
+ Tensor<float, 4, DataLayout> shuffle;
+ shuffle = tensor.shuffle(shuffles).shuffle(shuffles_inverse);
+
+ VERIFY_IS_EQUAL(shuffle.dimension(0), 2);
+ VERIFY_IS_EQUAL(shuffle.dimension(1), 3);
+ VERIFY_IS_EQUAL(shuffle.dimension(2), 5);
+ VERIFY_IS_EQUAL(shuffle.dimension(3), 7);
+
+ for (int i = 0; i < 2; ++i) {
+ for (int j = 0; j < 3; ++j) {
+ for (int k = 0; k < 5; ++k) {
+ for (int l = 0; l < 7; ++l) {
+ VERIFY_IS_EQUAL(tensor(i,j,k,l), shuffle(i,j,k,l));
+ }
+ }
+ }
+ }
+}
+
+
+template <int DataLayout>
+static void test_empty_shuffling()
+{
+ Tensor<float, 4, DataLayout> tensor(2,3,0,7);
+ tensor.setRandom();
+ array<ptrdiff_t, 4> shuffles;
+ shuffles[0] = 0;
+ shuffles[1] = 1;
+ shuffles[2] = 2;
+ shuffles[3] = 3;
+
+ Tensor<float, 4, DataLayout> no_shuffle;
+ no_shuffle = tensor.shuffle(shuffles);
+
+ VERIFY_IS_EQUAL(no_shuffle.dimension(0), 2);
+ VERIFY_IS_EQUAL(no_shuffle.dimension(1), 3);
+ VERIFY_IS_EQUAL(no_shuffle.dimension(2), 0);
+ VERIFY_IS_EQUAL(no_shuffle.dimension(3), 7);
+
+ for (int i = 0; i < 2; ++i) {
+ for (int j = 0; j < 3; ++j) {
+ for (int k = 0; k < 0; ++k) {
+ for (int l = 0; l < 7; ++l) {
+ VERIFY_IS_EQUAL(tensor(i,j,k,l), no_shuffle(i,j,k,l));
+ }
+ }
+ }
+ }
+
+ shuffles[0] = 2;
+ shuffles[1] = 3;
+ shuffles[2] = 1;
+ shuffles[3] = 0;
+ Tensor<float, 4, DataLayout> shuffle;
+ shuffle = tensor.shuffle(shuffles);
+
+ VERIFY_IS_EQUAL(shuffle.dimension(0), 0);
+ VERIFY_IS_EQUAL(shuffle.dimension(1), 7);
+ VERIFY_IS_EQUAL(shuffle.dimension(2), 3);
+ VERIFY_IS_EQUAL(shuffle.dimension(3), 2);
+
+ for (int i = 0; i < 2; ++i) {
+ for (int j = 0; j < 3; ++j) {
+ for (int k = 0; k < 0; ++k) {
+ for (int l = 0; l < 7; ++l) {
+ VERIFY_IS_EQUAL(tensor(i,j,k,l), shuffle(k,l,j,i));
+ }
+ }
+ }
+ }
+}
+
+
+EIGEN_DECLARE_TEST(cxx11_tensor_shuffling)
+{
+ CALL_SUBTEST(test_simple_shuffling<ColMajor>());
+ CALL_SUBTEST(test_simple_shuffling<RowMajor>());
+ CALL_SUBTEST(test_expr_shuffling<ColMajor>());
+ CALL_SUBTEST(test_expr_shuffling<RowMajor>());
+ CALL_SUBTEST(test_shuffling_as_value<ColMajor>());
+ CALL_SUBTEST(test_shuffling_as_value<RowMajor>());
+ CALL_SUBTEST(test_shuffle_unshuffle<ColMajor>());
+ CALL_SUBTEST(test_shuffle_unshuffle<RowMajor>());
+ CALL_SUBTEST(test_empty_shuffling<ColMajor>());
+ CALL_SUBTEST(test_empty_shuffling<RowMajor>());
+}
diff --git a/unsupported/test/cxx11_tensor_shuffling_sycl.cpp b/unsupported/test/cxx11_tensor_shuffling_sycl.cpp
new file mode 100644
index 0000000..ca4e8b5
--- /dev/null
+++ b/unsupported/test/cxx11_tensor_shuffling_sycl.cpp
@@ -0,0 +1,117 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2016
+// Mehdi Goli Codeplay Software Ltd.
+// Ralph Potter Codeplay Software Ltd.
+// Luke Iwanski Codeplay Software Ltd.
+// Contact: <eigen@codeplay.com>
+// Benoit Steiner <benoit.steiner.goog@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#define EIGEN_TEST_NO_LONGDOUBLE
+#define EIGEN_TEST_NO_COMPLEX
+
+#define EIGEN_DEFAULT_DENSE_INDEX_TYPE int64_t
+#define EIGEN_USE_SYCL
+
+#include "main.h"
+#include <unsupported/Eigen/CXX11/Tensor>
+
+using Eigen::array;
+using Eigen::SyclDevice;
+using Eigen::Tensor;
+using Eigen::TensorMap;
+
+template <typename DataType, int DataLayout, typename IndexType>
+static void test_simple_shuffling_sycl(const Eigen::SyclDevice& sycl_device) {
+ IndexType sizeDim1 = 2;
+ IndexType sizeDim2 = 3;
+ IndexType sizeDim3 = 5;
+ IndexType sizeDim4 = 7;
+ array<IndexType, 4> tensorRange = {{sizeDim1, sizeDim2, sizeDim3, sizeDim4}};
+ Tensor<DataType, 4, DataLayout, IndexType> tensor(tensorRange);
+ Tensor<DataType, 4, DataLayout, IndexType> no_shuffle(tensorRange);
+ tensor.setRandom();
+
+ const size_t buffSize = tensor.size() * sizeof(DataType);
+ array<IndexType, 4> shuffles;
+ shuffles[0] = 0;
+ shuffles[1] = 1;
+ shuffles[2] = 2;
+ shuffles[3] = 3;
+ DataType* gpu_data1 = static_cast<DataType*>(sycl_device.allocate(buffSize));
+ DataType* gpu_data2 = static_cast<DataType*>(sycl_device.allocate(buffSize));
+
+ TensorMap<Tensor<DataType, 4, DataLayout, IndexType>> gpu1(gpu_data1,
+ tensorRange);
+ TensorMap<Tensor<DataType, 4, DataLayout, IndexType>> gpu2(gpu_data2,
+ tensorRange);
+
+ sycl_device.memcpyHostToDevice(gpu_data1, tensor.data(), buffSize);
+
+ gpu2.device(sycl_device) = gpu1.shuffle(shuffles);
+ sycl_device.memcpyDeviceToHost(no_shuffle.data(), gpu_data2, buffSize);
+ sycl_device.synchronize();
+
+ VERIFY_IS_EQUAL(no_shuffle.dimension(0), sizeDim1);
+ VERIFY_IS_EQUAL(no_shuffle.dimension(1), sizeDim2);
+ VERIFY_IS_EQUAL(no_shuffle.dimension(2), sizeDim3);
+ VERIFY_IS_EQUAL(no_shuffle.dimension(3), sizeDim4);
+
+ for (IndexType i = 0; i < sizeDim1; ++i) {
+ for (IndexType j = 0; j < sizeDim2; ++j) {
+ for (IndexType k = 0; k < sizeDim3; ++k) {
+ for (IndexType l = 0; l < sizeDim4; ++l) {
+ VERIFY_IS_EQUAL(tensor(i, j, k, l), no_shuffle(i, j, k, l));
+ }
+ }
+ }
+ }
+
+ shuffles[0] = 2;
+ shuffles[1] = 3;
+ shuffles[2] = 1;
+ shuffles[3] = 0;
+ array<IndexType, 4> tensorrangeShuffle = {
+ {sizeDim3, sizeDim4, sizeDim2, sizeDim1}};
+ Tensor<DataType, 4, DataLayout, IndexType> shuffle(tensorrangeShuffle);
+ DataType* gpu_data3 = static_cast<DataType*>(sycl_device.allocate(buffSize));
+ TensorMap<Tensor<DataType, 4, DataLayout, IndexType>> gpu3(
+ gpu_data3, tensorrangeShuffle);
+
+ gpu3.device(sycl_device) = gpu1.shuffle(shuffles);
+ sycl_device.memcpyDeviceToHost(shuffle.data(), gpu_data3, buffSize);
+ sycl_device.synchronize();
+
+ VERIFY_IS_EQUAL(shuffle.dimension(0), sizeDim3);
+ VERIFY_IS_EQUAL(shuffle.dimension(1), sizeDim4);
+ VERIFY_IS_EQUAL(shuffle.dimension(2), sizeDim2);
+ VERIFY_IS_EQUAL(shuffle.dimension(3), sizeDim1);
+
+ for (IndexType i = 0; i < sizeDim1; ++i) {
+ for (IndexType j = 0; j < sizeDim2; ++j) {
+ for (IndexType k = 0; k < sizeDim3; ++k) {
+ for (IndexType l = 0; l < sizeDim4; ++l) {
+ VERIFY_IS_EQUAL(tensor(i, j, k, l), shuffle(k, l, j, i));
+ }
+ }
+ }
+ }
+}
+
+template <typename DataType, typename dev_Selector>
+void sycl_shuffling_test_per_device(dev_Selector s) {
+ QueueInterface queueInterface(s);
+ auto sycl_device = Eigen::SyclDevice(&queueInterface);
+ test_simple_shuffling_sycl<DataType, RowMajor, int64_t>(sycl_device);
+ test_simple_shuffling_sycl<DataType, ColMajor, int64_t>(sycl_device);
+}
+EIGEN_DECLARE_TEST(cxx11_tensor_shuffling_sycl) {
+ for (const auto& device : Eigen::get_sycl_supported_devices()) {
+ CALL_SUBTEST(sycl_shuffling_test_per_device<float>(device));
+ }
+}
diff --git a/unsupported/test/cxx11_tensor_simple.cpp b/unsupported/test/cxx11_tensor_simple.cpp
new file mode 100644
index 0000000..6d70f54
--- /dev/null
+++ b/unsupported/test/cxx11_tensor_simple.cpp
@@ -0,0 +1,327 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2013 Christian Seiler <christian@iwakd.de>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "main.h"
+
+#include <Eigen/CXX11/Tensor>
+
+using Eigen::Tensor;
+using Eigen::RowMajor;
+
+static void test_0d()
+{
+ Tensor<int, 0> scalar1;
+ Tensor<int, 0, RowMajor> scalar2;
+ Tensor<int, 0> scalar3;
+ Tensor<int, 0, RowMajor> scalar4;
+
+ scalar3.resize();
+ scalar4.resize();
+
+ scalar1() = 7;
+ scalar2() = 13;
+ scalar3.setValues(17);
+ scalar4.setZero();
+
+ VERIFY_IS_EQUAL(scalar1.rank(), 0);
+ VERIFY_IS_EQUAL(scalar1.size(), 1);
+
+ VERIFY_IS_EQUAL(scalar1(), 7);
+ VERIFY_IS_EQUAL(scalar2(), 13);
+ VERIFY_IS_EQUAL(scalar3(), 17);
+ VERIFY_IS_EQUAL(scalar4(), 0);
+
+ Tensor<int, 0> scalar5(scalar1);
+
+ VERIFY_IS_EQUAL(scalar5(), 7);
+ VERIFY_IS_EQUAL(scalar5.data()[0], 7);
+}
+
+static void test_1d()
+{
+ Tensor<int, 1> vec1(6);
+ Tensor<int, 1, RowMajor> vec2(6);
+ Tensor<int, 1> vec3;
+ Tensor<int, 1, RowMajor> vec4;
+
+ vec3.resize(6);
+ vec4.resize(6);
+
+ vec1(0) = 4; vec2(0) = 0; vec3(0) = 5;
+ vec1(1) = 8; vec2(1) = 1; vec3(1) = 4;
+ vec1(2) = 15; vec2(2) = 2; vec3(2) = 3;
+ vec1(3) = 16; vec2(3) = 3; vec3(3) = 2;
+ vec1(4) = 23; vec2(4) = 4; vec3(4) = 1;
+ vec1(5) = 42; vec2(5) = 5; vec3(5) = 0;
+ vec4.setZero();
+
+ VERIFY_IS_EQUAL((vec1.rank()), 1);
+ VERIFY_IS_EQUAL((vec1.size()), 6);
+ VERIFY_IS_EQUAL((vec1.dimensions()[0]), 6);
+
+ VERIFY_IS_EQUAL((vec1[0]), 4);
+ VERIFY_IS_EQUAL((vec1[1]), 8);
+ VERIFY_IS_EQUAL((vec1[2]), 15);
+ VERIFY_IS_EQUAL((vec1[3]), 16);
+ VERIFY_IS_EQUAL((vec1[4]), 23);
+ VERIFY_IS_EQUAL((vec1[5]), 42);
+
+ VERIFY_IS_EQUAL((vec2[0]), 0);
+ VERIFY_IS_EQUAL((vec2[1]), 1);
+ VERIFY_IS_EQUAL((vec2[2]), 2);
+ VERIFY_IS_EQUAL((vec2[3]), 3);
+ VERIFY_IS_EQUAL((vec2[4]), 4);
+ VERIFY_IS_EQUAL((vec2[5]), 5);
+
+ VERIFY_IS_EQUAL((vec3[0]), 5);
+ VERIFY_IS_EQUAL((vec3[1]), 4);
+ VERIFY_IS_EQUAL((vec3[2]), 3);
+ VERIFY_IS_EQUAL((vec3[3]), 2);
+ VERIFY_IS_EQUAL((vec3[4]), 1);
+ VERIFY_IS_EQUAL((vec3[5]), 0);
+
+ VERIFY_IS_EQUAL((vec4[0]), 0);
+ VERIFY_IS_EQUAL((vec4[1]), 0);
+ VERIFY_IS_EQUAL((vec4[2]), 0);
+ VERIFY_IS_EQUAL((vec4[3]), 0);
+ VERIFY_IS_EQUAL((vec4[4]), 0);
+ VERIFY_IS_EQUAL((vec4[5]), 0);
+
+ Tensor<int, 1> vec5(vec1);
+
+ VERIFY_IS_EQUAL((vec5(0)), 4);
+ VERIFY_IS_EQUAL((vec5(1)), 8);
+ VERIFY_IS_EQUAL((vec5(2)), 15);
+ VERIFY_IS_EQUAL((vec5(3)), 16);
+ VERIFY_IS_EQUAL((vec5(4)), 23);
+ VERIFY_IS_EQUAL((vec5(5)), 42);
+
+ VERIFY_IS_EQUAL((vec5.data()[0]), 4);
+ VERIFY_IS_EQUAL((vec5.data()[1]), 8);
+ VERIFY_IS_EQUAL((vec5.data()[2]), 15);
+ VERIFY_IS_EQUAL((vec5.data()[3]), 16);
+ VERIFY_IS_EQUAL((vec5.data()[4]), 23);
+ VERIFY_IS_EQUAL((vec5.data()[5]), 42);
+}
+
+static void test_2d()
+{
+ Tensor<int, 2> mat1(2,3);
+ Tensor<int, 2, RowMajor> mat2(2,3);
+
+ mat1(0,0) = 0;
+ mat1(0,1) = 1;
+ mat1(0,2) = 2;
+ mat1(1,0) = 3;
+ mat1(1,1) = 4;
+ mat1(1,2) = 5;
+
+ mat2(0,0) = 0;
+ mat2(0,1) = 1;
+ mat2(0,2) = 2;
+ mat2(1,0) = 3;
+ mat2(1,1) = 4;
+ mat2(1,2) = 5;
+
+ VERIFY_IS_EQUAL((mat1.rank()), 2);
+ VERIFY_IS_EQUAL((mat1.size()), 6);
+ VERIFY_IS_EQUAL((mat1.dimensions()[0]), 2);
+ VERIFY_IS_EQUAL((mat1.dimensions()[1]), 3);
+
+ VERIFY_IS_EQUAL((mat2.rank()), 2);
+ VERIFY_IS_EQUAL((mat2.size()), 6);
+ VERIFY_IS_EQUAL((mat2.dimensions()[0]), 2);
+ VERIFY_IS_EQUAL((mat2.dimensions()[1]), 3);
+
+ VERIFY_IS_EQUAL((mat1.data()[0]), 0);
+ VERIFY_IS_EQUAL((mat1.data()[1]), 3);
+ VERIFY_IS_EQUAL((mat1.data()[2]), 1);
+ VERIFY_IS_EQUAL((mat1.data()[3]), 4);
+ VERIFY_IS_EQUAL((mat1.data()[4]), 2);
+ VERIFY_IS_EQUAL((mat1.data()[5]), 5);
+
+ VERIFY_IS_EQUAL((mat2.data()[0]), 0);
+ VERIFY_IS_EQUAL((mat2.data()[1]), 1);
+ VERIFY_IS_EQUAL((mat2.data()[2]), 2);
+ VERIFY_IS_EQUAL((mat2.data()[3]), 3);
+ VERIFY_IS_EQUAL((mat2.data()[4]), 4);
+ VERIFY_IS_EQUAL((mat2.data()[5]), 5);
+}
+
+static void test_3d()
+{
+ Tensor<int, 3> epsilon(3,3,3);
+ epsilon.setZero();
+ epsilon(0,1,2) = epsilon(2,0,1) = epsilon(1,2,0) = 1;
+ epsilon(2,1,0) = epsilon(0,2,1) = epsilon(1,0,2) = -1;
+
+ VERIFY_IS_EQUAL((epsilon.size()), 27);
+ VERIFY_IS_EQUAL((epsilon.dimensions()[0]), 3);
+ VERIFY_IS_EQUAL((epsilon.dimensions()[1]), 3);
+ VERIFY_IS_EQUAL((epsilon.dimensions()[2]), 3);
+
+ VERIFY_IS_EQUAL((epsilon(0,0,0)), 0);
+ VERIFY_IS_EQUAL((epsilon(0,0,1)), 0);
+ VERIFY_IS_EQUAL((epsilon(0,0,2)), 0);
+ VERIFY_IS_EQUAL((epsilon(0,1,0)), 0);
+ VERIFY_IS_EQUAL((epsilon(0,1,1)), 0);
+ VERIFY_IS_EQUAL((epsilon(0,2,0)), 0);
+ VERIFY_IS_EQUAL((epsilon(0,2,2)), 0);
+ VERIFY_IS_EQUAL((epsilon(1,0,0)), 0);
+ VERIFY_IS_EQUAL((epsilon(1,0,1)), 0);
+ VERIFY_IS_EQUAL((epsilon(1,1,0)), 0);
+ VERIFY_IS_EQUAL((epsilon(1,1,1)), 0);
+ VERIFY_IS_EQUAL((epsilon(1,1,2)), 0);
+ VERIFY_IS_EQUAL((epsilon(1,2,1)), 0);
+ VERIFY_IS_EQUAL((epsilon(1,2,2)), 0);
+ VERIFY_IS_EQUAL((epsilon(2,0,0)), 0);
+ VERIFY_IS_EQUAL((epsilon(2,0,2)), 0);
+ VERIFY_IS_EQUAL((epsilon(2,1,1)), 0);
+ VERIFY_IS_EQUAL((epsilon(2,1,2)), 0);
+ VERIFY_IS_EQUAL((epsilon(2,2,0)), 0);
+ VERIFY_IS_EQUAL((epsilon(2,2,1)), 0);
+ VERIFY_IS_EQUAL((epsilon(2,2,2)), 0);
+
+ VERIFY_IS_EQUAL((epsilon(0,1,2)), 1);
+ VERIFY_IS_EQUAL((epsilon(2,0,1)), 1);
+ VERIFY_IS_EQUAL((epsilon(1,2,0)), 1);
+ VERIFY_IS_EQUAL((epsilon(2,1,0)), -1);
+ VERIFY_IS_EQUAL((epsilon(0,2,1)), -1);
+ VERIFY_IS_EQUAL((epsilon(1,0,2)), -1);
+
+ array<Eigen::DenseIndex, 3> dims;
+ dims[0] = 2;
+ dims[1] = 3;
+ dims[2] = 4;
+ Tensor<int, 3> t1(dims);
+ Tensor<int, 3, RowMajor> t2(dims);
+
+ VERIFY_IS_EQUAL((t1.size()), 24);
+ VERIFY_IS_EQUAL((t1.dimensions()[0]), 2);
+ VERIFY_IS_EQUAL((t1.dimensions()[1]), 3);
+ VERIFY_IS_EQUAL((t1.dimensions()[2]), 4);
+
+ VERIFY_IS_EQUAL((t2.size()), 24);
+ VERIFY_IS_EQUAL((t2.dimensions()[0]), 2);
+ VERIFY_IS_EQUAL((t2.dimensions()[1]), 3);
+ VERIFY_IS_EQUAL((t2.dimensions()[2]), 4);
+
+ for (int i = 0; i < 2; i++) {
+ for (int j = 0; j < 3; j++) {
+ for (int k = 0; k < 4; k++) {
+ t1(i, j, k) = 100 * i + 10 * j + k;
+ t2(i, j, k) = 100 * i + 10 * j + k;
+ }
+ }
+ }
+
+ VERIFY_IS_EQUAL((t1.data()[0]), 0);
+ VERIFY_IS_EQUAL((t1.data()[1]), 100);
+ VERIFY_IS_EQUAL((t1.data()[2]), 10);
+ VERIFY_IS_EQUAL((t1.data()[3]), 110);
+ VERIFY_IS_EQUAL((t1.data()[4]), 20);
+ VERIFY_IS_EQUAL((t1.data()[5]), 120);
+ VERIFY_IS_EQUAL((t1.data()[6]), 1);
+ VERIFY_IS_EQUAL((t1.data()[7]), 101);
+ VERIFY_IS_EQUAL((t1.data()[8]), 11);
+ VERIFY_IS_EQUAL((t1.data()[9]), 111);
+ VERIFY_IS_EQUAL((t1.data()[10]), 21);
+ VERIFY_IS_EQUAL((t1.data()[11]), 121);
+ VERIFY_IS_EQUAL((t1.data()[12]), 2);
+ VERIFY_IS_EQUAL((t1.data()[13]), 102);
+ VERIFY_IS_EQUAL((t1.data()[14]), 12);
+ VERIFY_IS_EQUAL((t1.data()[15]), 112);
+ VERIFY_IS_EQUAL((t1.data()[16]), 22);
+ VERIFY_IS_EQUAL((t1.data()[17]), 122);
+ VERIFY_IS_EQUAL((t1.data()[18]), 3);
+ VERIFY_IS_EQUAL((t1.data()[19]), 103);
+ VERIFY_IS_EQUAL((t1.data()[20]), 13);
+ VERIFY_IS_EQUAL((t1.data()[21]), 113);
+ VERIFY_IS_EQUAL((t1.data()[22]), 23);
+ VERIFY_IS_EQUAL((t1.data()[23]), 123);
+
+ VERIFY_IS_EQUAL((t2.data()[0]), 0);
+ VERIFY_IS_EQUAL((t2.data()[1]), 1);
+ VERIFY_IS_EQUAL((t2.data()[2]), 2);
+ VERIFY_IS_EQUAL((t2.data()[3]), 3);
+ VERIFY_IS_EQUAL((t2.data()[4]), 10);
+ VERIFY_IS_EQUAL((t2.data()[5]), 11);
+ VERIFY_IS_EQUAL((t2.data()[6]), 12);
+ VERIFY_IS_EQUAL((t2.data()[7]), 13);
+ VERIFY_IS_EQUAL((t2.data()[8]), 20);
+ VERIFY_IS_EQUAL((t2.data()[9]), 21);
+ VERIFY_IS_EQUAL((t2.data()[10]), 22);
+ VERIFY_IS_EQUAL((t2.data()[11]), 23);
+ VERIFY_IS_EQUAL((t2.data()[12]), 100);
+ VERIFY_IS_EQUAL((t2.data()[13]), 101);
+ VERIFY_IS_EQUAL((t2.data()[14]), 102);
+ VERIFY_IS_EQUAL((t2.data()[15]), 103);
+ VERIFY_IS_EQUAL((t2.data()[16]), 110);
+ VERIFY_IS_EQUAL((t2.data()[17]), 111);
+ VERIFY_IS_EQUAL((t2.data()[18]), 112);
+ VERIFY_IS_EQUAL((t2.data()[19]), 113);
+ VERIFY_IS_EQUAL((t2.data()[20]), 120);
+ VERIFY_IS_EQUAL((t2.data()[21]), 121);
+ VERIFY_IS_EQUAL((t2.data()[22]), 122);
+ VERIFY_IS_EQUAL((t2.data()[23]), 123);
+}
+
+static void test_simple_assign()
+{
+ Tensor<int, 3> epsilon(3,3,3);
+ epsilon.setZero();
+ epsilon(0,1,2) = epsilon(2,0,1) = epsilon(1,2,0) = 1;
+ epsilon(2,1,0) = epsilon(0,2,1) = epsilon(1,0,2) = -1;
+
+ Tensor<int, 3> e2(3,3,3);
+ e2.setZero();
+ VERIFY_IS_EQUAL((e2(1,2,0)), 0);
+
+ e2 = epsilon;
+ VERIFY_IS_EQUAL((e2(1,2,0)), 1);
+ VERIFY_IS_EQUAL((e2(0,1,2)), 1);
+ VERIFY_IS_EQUAL((e2(2,0,1)), 1);
+ VERIFY_IS_EQUAL((e2(2,1,0)), -1);
+ VERIFY_IS_EQUAL((e2(0,2,1)), -1);
+ VERIFY_IS_EQUAL((e2(1,0,2)), -1);
+}
+
+static void test_resize()
+{
+ Tensor<int, 3> epsilon;
+ epsilon.resize(2,3,7);
+ VERIFY_IS_EQUAL(epsilon.dimension(0), 2);
+ VERIFY_IS_EQUAL(epsilon.dimension(1), 3);
+ VERIFY_IS_EQUAL(epsilon.dimension(2), 7);
+ VERIFY_IS_EQUAL(epsilon.size(), 2*3*7);
+
+ const int* old_data = epsilon.data();
+ epsilon.resize(3,2,7);
+ VERIFY_IS_EQUAL(epsilon.dimension(0), 3);
+ VERIFY_IS_EQUAL(epsilon.dimension(1), 2);
+ VERIFY_IS_EQUAL(epsilon.dimension(2), 7);
+ VERIFY_IS_EQUAL(epsilon.size(), 2*3*7);
+ VERIFY_IS_EQUAL(epsilon.data(), old_data);
+
+ epsilon.resize(3,5,7);
+ VERIFY_IS_EQUAL(epsilon.dimension(0), 3);
+ VERIFY_IS_EQUAL(epsilon.dimension(1), 5);
+ VERIFY_IS_EQUAL(epsilon.dimension(2), 7);
+ VERIFY_IS_EQUAL(epsilon.size(), 3*5*7);
+}
+
+EIGEN_DECLARE_TEST(cxx11_tensor_simple)
+{
+ CALL_SUBTEST(test_0d());
+ CALL_SUBTEST(test_1d());
+ CALL_SUBTEST(test_2d());
+ CALL_SUBTEST(test_3d());
+ CALL_SUBTEST(test_simple_assign());
+ CALL_SUBTEST(test_resize());
+}
diff --git a/unsupported/test/cxx11_tensor_striding.cpp b/unsupported/test/cxx11_tensor_striding.cpp
new file mode 100644
index 0000000..aefdfa9
--- /dev/null
+++ b/unsupported/test/cxx11_tensor_striding.cpp
@@ -0,0 +1,119 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "main.h"
+
+#include <Eigen/CXX11/Tensor>
+
+using Eigen::Tensor;
+
+template<int DataLayout>
+static void test_simple_striding()
+{
+ Tensor<float, 4, DataLayout> tensor(2,3,5,7);
+ tensor.setRandom();
+ array<ptrdiff_t, 4> strides;
+ strides[0] = 1;
+ strides[1] = 1;
+ strides[2] = 1;
+ strides[3] = 1;
+
+ Tensor<float, 4, DataLayout> no_stride;
+ no_stride = tensor.stride(strides);
+
+ VERIFY_IS_EQUAL(no_stride.dimension(0), 2);
+ VERIFY_IS_EQUAL(no_stride.dimension(1), 3);
+ VERIFY_IS_EQUAL(no_stride.dimension(2), 5);
+ VERIFY_IS_EQUAL(no_stride.dimension(3), 7);
+
+ for (int i = 0; i < 2; ++i) {
+ for (int j = 0; j < 3; ++j) {
+ for (int k = 0; k < 5; ++k) {
+ for (int l = 0; l < 7; ++l) {
+ VERIFY_IS_EQUAL(tensor(i,j,k,l), no_stride(i,j,k,l));
+ }
+ }
+ }
+ }
+
+ strides[0] = 2;
+ strides[1] = 4;
+ strides[2] = 2;
+ strides[3] = 3;
+ Tensor<float, 4, DataLayout> stride;
+ stride = tensor.stride(strides);
+
+ VERIFY_IS_EQUAL(stride.dimension(0), 1);
+ VERIFY_IS_EQUAL(stride.dimension(1), 1);
+ VERIFY_IS_EQUAL(stride.dimension(2), 3);
+ VERIFY_IS_EQUAL(stride.dimension(3), 3);
+
+ for (int i = 0; i < 1; ++i) {
+ for (int j = 0; j < 1; ++j) {
+ for (int k = 0; k < 3; ++k) {
+ for (int l = 0; l < 3; ++l) {
+ VERIFY_IS_EQUAL(tensor(2*i,4*j,2*k,3*l), stride(i,j,k,l));
+ }
+ }
+ }
+ }
+}
+
+
+template<int DataLayout>
+static void test_striding_as_lvalue()
+{
+ Tensor<float, 4, DataLayout> tensor(2,3,5,7);
+ tensor.setRandom();
+ array<ptrdiff_t, 4> strides;
+ strides[0] = 2;
+ strides[1] = 4;
+ strides[2] = 2;
+ strides[3] = 3;
+
+ Tensor<float, 4, DataLayout> result(3, 12, 10, 21);
+ result.stride(strides) = tensor;
+
+ for (int i = 0; i < 2; ++i) {
+ for (int j = 0; j < 3; ++j) {
+ for (int k = 0; k < 5; ++k) {
+ for (int l = 0; l < 7; ++l) {
+ VERIFY_IS_EQUAL(tensor(i,j,k,l), result(2*i,4*j,2*k,3*l));
+ }
+ }
+ }
+ }
+
+ array<ptrdiff_t, 4> no_strides;
+ no_strides[0] = 1;
+ no_strides[1] = 1;
+ no_strides[2] = 1;
+ no_strides[3] = 1;
+ Tensor<float, 4, DataLayout> result2(3, 12, 10, 21);
+ result2.stride(strides) = tensor.stride(no_strides);
+
+ for (int i = 0; i < 2; ++i) {
+ for (int j = 0; j < 3; ++j) {
+ for (int k = 0; k < 5; ++k) {
+ for (int l = 0; l < 7; ++l) {
+ VERIFY_IS_EQUAL(tensor(i,j,k,l), result2(2*i,4*j,2*k,3*l));
+ }
+ }
+ }
+ }
+}
+
+
+EIGEN_DECLARE_TEST(cxx11_tensor_striding)
+{
+ CALL_SUBTEST(test_simple_striding<ColMajor>());
+ CALL_SUBTEST(test_simple_striding<RowMajor>());
+ CALL_SUBTEST(test_striding_as_lvalue<ColMajor>());
+ CALL_SUBTEST(test_striding_as_lvalue<RowMajor>());
+}
diff --git a/unsupported/test/cxx11_tensor_striding_sycl.cpp b/unsupported/test/cxx11_tensor_striding_sycl.cpp
new file mode 100644
index 0000000..d3b1fa7
--- /dev/null
+++ b/unsupported/test/cxx11_tensor_striding_sycl.cpp
@@ -0,0 +1,203 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2016
+// Mehdi Goli Codeplay Software Ltd.
+// Ralph Potter Codeplay Software Ltd.
+// Luke Iwanski Codeplay Software Ltd.
+// Contact: <eigen@codeplay.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#define EIGEN_TEST_NO_LONGDOUBLE
+#define EIGEN_TEST_NO_COMPLEX
+
+#define EIGEN_DEFAULT_DENSE_INDEX_TYPE int64_t
+#define EIGEN_USE_SYCL
+
+#include <iostream>
+#include <chrono>
+#include <ctime>
+
+#include "main.h"
+#include <unsupported/Eigen/CXX11/Tensor>
+
+using Eigen::array;
+using Eigen::SyclDevice;
+using Eigen::Tensor;
+using Eigen::TensorMap;
+
+
+template <typename DataType, int DataLayout, typename IndexType>
+static void test_simple_striding(const Eigen::SyclDevice& sycl_device)
+{
+
+ Eigen::array<IndexType, 4> tensor_dims = {{2,3,5,7}};
+ Eigen::array<IndexType, 4> stride_dims = {{1,1,3,3}};
+
+
+ Tensor<DataType, 4, DataLayout, IndexType> tensor(tensor_dims);
+ Tensor<DataType, 4, DataLayout,IndexType> no_stride(tensor_dims);
+ Tensor<DataType, 4, DataLayout,IndexType> stride(stride_dims);
+
+
+ std::size_t tensor_bytes = tensor.size() * sizeof(DataType);
+ std::size_t no_stride_bytes = no_stride.size() * sizeof(DataType);
+ std::size_t stride_bytes = stride.size() * sizeof(DataType);
+ DataType * d_tensor = static_cast<DataType*>(sycl_device.allocate(tensor_bytes));
+ DataType * d_no_stride = static_cast<DataType*>(sycl_device.allocate(no_stride_bytes));
+ DataType * d_stride = static_cast<DataType*>(sycl_device.allocate(stride_bytes));
+
+ Eigen::TensorMap<Eigen::Tensor<DataType, 4, DataLayout, IndexType> > gpu_tensor(d_tensor, tensor_dims);
+ Eigen::TensorMap<Eigen::Tensor<DataType, 4, DataLayout, IndexType> > gpu_no_stride(d_no_stride, tensor_dims);
+ Eigen::TensorMap<Eigen::Tensor<DataType, 4, DataLayout, IndexType> > gpu_stride(d_stride, stride_dims);
+
+
+ tensor.setRandom();
+ array<IndexType, 4> strides;
+ strides[0] = 1;
+ strides[1] = 1;
+ strides[2] = 1;
+ strides[3] = 1;
+ sycl_device.memcpyHostToDevice(d_tensor, tensor.data(), tensor_bytes);
+ gpu_no_stride.device(sycl_device)=gpu_tensor.stride(strides);
+ sycl_device.memcpyDeviceToHost(no_stride.data(), d_no_stride, no_stride_bytes);
+
+ //no_stride = tensor.stride(strides);
+
+ VERIFY_IS_EQUAL(no_stride.dimension(0), 2);
+ VERIFY_IS_EQUAL(no_stride.dimension(1), 3);
+ VERIFY_IS_EQUAL(no_stride.dimension(2), 5);
+ VERIFY_IS_EQUAL(no_stride.dimension(3), 7);
+
+ for (IndexType i = 0; i < 2; ++i) {
+ for (IndexType j = 0; j < 3; ++j) {
+ for (IndexType k = 0; k < 5; ++k) {
+ for (IndexType l = 0; l < 7; ++l) {
+ VERIFY_IS_EQUAL(tensor(i,j,k,l), no_stride(i,j,k,l));
+ }
+ }
+ }
+ }
+
+ strides[0] = 2;
+ strides[1] = 4;
+ strides[2] = 2;
+ strides[3] = 3;
+//Tensor<float, 4, DataLayout> stride;
+// stride = tensor.stride(strides);
+
+ gpu_stride.device(sycl_device)=gpu_tensor.stride(strides);
+ sycl_device.memcpyDeviceToHost(stride.data(), d_stride, stride_bytes);
+
+ VERIFY_IS_EQUAL(stride.dimension(0), 1);
+ VERIFY_IS_EQUAL(stride.dimension(1), 1);
+ VERIFY_IS_EQUAL(stride.dimension(2), 3);
+ VERIFY_IS_EQUAL(stride.dimension(3), 3);
+
+ for (IndexType i = 0; i < 1; ++i) {
+ for (IndexType j = 0; j < 1; ++j) {
+ for (IndexType k = 0; k < 3; ++k) {
+ for (IndexType l = 0; l < 3; ++l) {
+ VERIFY_IS_EQUAL(tensor(2*i,4*j,2*k,3*l), stride(i,j,k,l));
+ }
+ }
+ }
+ }
+
+ sycl_device.deallocate(d_tensor);
+ sycl_device.deallocate(d_no_stride);
+ sycl_device.deallocate(d_stride);
+}
+
+template <typename DataType, int DataLayout, typename IndexType>
+static void test_striding_as_lvalue(const Eigen::SyclDevice& sycl_device)
+{
+
+ Eigen::array<IndexType, 4> tensor_dims = {{2,3,5,7}};
+ Eigen::array<IndexType, 4> stride_dims = {{3,12,10,21}};
+
+
+ Tensor<DataType, 4, DataLayout, IndexType> tensor(tensor_dims);
+ Tensor<DataType, 4, DataLayout,IndexType> no_stride(stride_dims);
+ Tensor<DataType, 4, DataLayout,IndexType> stride(stride_dims);
+
+
+ std::size_t tensor_bytes = tensor.size() * sizeof(DataType);
+ std::size_t no_stride_bytes = no_stride.size() * sizeof(DataType);
+ std::size_t stride_bytes = stride.size() * sizeof(DataType);
+
+ DataType * d_tensor = static_cast<DataType*>(sycl_device.allocate(tensor_bytes));
+ DataType * d_no_stride = static_cast<DataType*>(sycl_device.allocate(no_stride_bytes));
+ DataType * d_stride = static_cast<DataType*>(sycl_device.allocate(stride_bytes));
+
+ Eigen::TensorMap<Eigen::Tensor<DataType, 4, DataLayout, IndexType> > gpu_tensor(d_tensor, tensor_dims);
+ Eigen::TensorMap<Eigen::Tensor<DataType, 4, DataLayout, IndexType> > gpu_no_stride(d_no_stride, stride_dims);
+ Eigen::TensorMap<Eigen::Tensor<DataType, 4, DataLayout, IndexType> > gpu_stride(d_stride, stride_dims);
+
+ //Tensor<float, 4, DataLayout> tensor(2,3,5,7);
+ tensor.setRandom();
+ array<IndexType, 4> strides;
+ strides[0] = 2;
+ strides[1] = 4;
+ strides[2] = 2;
+ strides[3] = 3;
+
+// Tensor<float, 4, DataLayout> result(3, 12, 10, 21);
+// result.stride(strides) = tensor;
+ sycl_device.memcpyHostToDevice(d_tensor, tensor.data(), tensor_bytes);
+ gpu_stride.stride(strides).device(sycl_device)=gpu_tensor;
+ sycl_device.memcpyDeviceToHost(stride.data(), d_stride, stride_bytes);
+
+ for (IndexType i = 0; i < 2; ++i) {
+ for (IndexType j = 0; j < 3; ++j) {
+ for (IndexType k = 0; k < 5; ++k) {
+ for (IndexType l = 0; l < 7; ++l) {
+ VERIFY_IS_EQUAL(tensor(i,j,k,l), stride(2*i,4*j,2*k,3*l));
+ }
+ }
+ }
+ }
+
+ array<IndexType, 4> no_strides;
+ no_strides[0] = 1;
+ no_strides[1] = 1;
+ no_strides[2] = 1;
+ no_strides[3] = 1;
+// Tensor<float, 4, DataLayout> result2(3, 12, 10, 21);
+// result2.stride(strides) = tensor.stride(no_strides);
+
+ gpu_no_stride.stride(strides).device(sycl_device)=gpu_tensor.stride(no_strides);
+ sycl_device.memcpyDeviceToHost(no_stride.data(), d_no_stride, no_stride_bytes);
+
+ for (IndexType i = 0; i < 2; ++i) {
+ for (IndexType j = 0; j < 3; ++j) {
+ for (IndexType k = 0; k < 5; ++k) {
+ for (IndexType l = 0; l < 7; ++l) {
+ VERIFY_IS_EQUAL(tensor(i,j,k,l), no_stride(2*i,4*j,2*k,3*l));
+ }
+ }
+ }
+ }
+ sycl_device.deallocate(d_tensor);
+ sycl_device.deallocate(d_no_stride);
+ sycl_device.deallocate(d_stride);
+}
+
+
+template <typename Dev_selector> void tensorStridingPerDevice(Dev_selector& s){
+ QueueInterface queueInterface(s);
+ auto sycl_device=Eigen::SyclDevice(&queueInterface);
+ test_simple_striding<float, ColMajor, int64_t>(sycl_device);
+ test_simple_striding<float, RowMajor, int64_t>(sycl_device);
+ test_striding_as_lvalue<float, ColMajor, int64_t>(sycl_device);
+ test_striding_as_lvalue<float, RowMajor, int64_t>(sycl_device);
+}
+
+EIGEN_DECLARE_TEST(cxx11_tensor_striding_sycl) {
+ for (const auto& device :Eigen::get_sycl_supported_devices()) {
+ CALL_SUBTEST(tensorStridingPerDevice(device));
+ }
+}
diff --git a/unsupported/test/cxx11_tensor_sugar.cpp b/unsupported/test/cxx11_tensor_sugar.cpp
new file mode 100644
index 0000000..2ca5c47
--- /dev/null
+++ b/unsupported/test/cxx11_tensor_sugar.cpp
@@ -0,0 +1,81 @@
+#include "main.h"
+
+#include <Eigen/CXX11/Tensor>
+
+using Eigen::Tensor;
+using Eigen::RowMajor;
+
+static void test_comparison_sugar() {
+ // we already trust comparisons between tensors, we're simply checking that
+ // the sugared versions are doing the same thing
+ Tensor<int, 3> t(6, 7, 5);
+
+ t.setRandom();
+ // make sure we have at least one value == 0
+ t(0,0,0) = 0;
+
+ Tensor<bool,0> b;
+
+#define TEST_TENSOR_EQUAL(e1, e2) \
+ b = ((e1) == (e2)).all(); \
+ VERIFY(b())
+
+#define TEST_OP(op) TEST_TENSOR_EQUAL(t op 0, t op t.constant(0))
+
+ TEST_OP(==);
+ TEST_OP(!=);
+ TEST_OP(<=);
+ TEST_OP(>=);
+ TEST_OP(<);
+ TEST_OP(>);
+#undef TEST_OP
+#undef TEST_TENSOR_EQUAL
+}
+
+
+static void test_scalar_sugar_add_mul() {
+ Tensor<float, 3> A(6, 7, 5);
+ Tensor<float, 3> B(6, 7, 5);
+ A.setRandom();
+ B.setRandom();
+
+ const float alpha = 0.43f;
+ const float beta = 0.21f;
+ const float gamma = 0.14f;
+
+ Tensor<float, 3> R = A.constant(gamma) + A * A.constant(alpha) + B * B.constant(beta);
+ Tensor<float, 3> S = A * alpha + B * beta + gamma;
+ Tensor<float, 3> T = gamma + alpha * A + beta * B;
+
+ for (int i = 0; i < 6*7*5; ++i) {
+ VERIFY_IS_APPROX(R(i), S(i));
+ VERIFY_IS_APPROX(R(i), T(i));
+ }
+}
+
+static void test_scalar_sugar_sub_div() {
+ Tensor<float, 3> A(6, 7, 5);
+ Tensor<float, 3> B(6, 7, 5);
+ A.setRandom();
+ B.setRandom();
+
+ const float alpha = 0.43f;
+ const float beta = 0.21f;
+ const float gamma = 0.14f;
+ const float delta = 0.32f;
+
+ Tensor<float, 3> R = A.constant(gamma) - A / A.constant(alpha)
+ - B.constant(beta) / B - A.constant(delta);
+ Tensor<float, 3> S = gamma - A / alpha - beta / B - delta;
+
+ for (int i = 0; i < 6*7*5; ++i) {
+ VERIFY_IS_APPROX(R(i), S(i));
+ }
+}
+
+EIGEN_DECLARE_TEST(cxx11_tensor_sugar)
+{
+ CALL_SUBTEST(test_comparison_sugar());
+ CALL_SUBTEST(test_scalar_sugar_add_mul());
+ CALL_SUBTEST(test_scalar_sugar_sub_div());
+}
diff --git a/unsupported/test/cxx11_tensor_sycl.cpp b/unsupported/test/cxx11_tensor_sycl.cpp
new file mode 100644
index 0000000..e6c5e23
--- /dev/null
+++ b/unsupported/test/cxx11_tensor_sycl.cpp
@@ -0,0 +1,361 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2016
+// Mehdi Goli Codeplay Software Ltd.
+// Ralph Potter Codeplay Software Ltd.
+// Luke Iwanski Codeplay Software Ltd.
+// Contact: <eigen@codeplay.com>
+// Benoit Steiner <benoit.steiner.goog@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+
+#define EIGEN_TEST_NO_LONGDOUBLE
+#define EIGEN_TEST_NO_COMPLEX
+
+#define EIGEN_DEFAULT_DENSE_INDEX_TYPE int64_t
+#define EIGEN_USE_SYCL
+
+#include "main.h"
+#include <unsupported/Eigen/CXX11/Tensor>
+
+using Eigen::array;
+using Eigen::SyclDevice;
+using Eigen::Tensor;
+using Eigen::TensorMap;
+
+template <typename DataType, int DataLayout, typename IndexType>
+void test_sycl_mem_transfers(const Eigen::SyclDevice &sycl_device) {
+ IndexType sizeDim1 = 5;
+ IndexType sizeDim2 = 5;
+ IndexType sizeDim3 = 1;
+ array<IndexType, 3> tensorRange = {{sizeDim1, sizeDim2, sizeDim3}};
+ Tensor<DataType, 3, DataLayout, IndexType> in1(tensorRange);
+ Tensor<DataType, 3, DataLayout, IndexType> out1(tensorRange);
+ Tensor<DataType, 3, DataLayout, IndexType> out2(tensorRange);
+ Tensor<DataType, 3, DataLayout, IndexType> out3(tensorRange);
+
+ in1 = in1.random();
+
+ DataType* gpu_data1 = static_cast<DataType*>(sycl_device.allocate(in1.size()*sizeof(DataType)));
+ DataType* gpu_data2 = static_cast<DataType*>(sycl_device.allocate(out1.size()*sizeof(DataType)));
+
+ TensorMap<Tensor<DataType, 3, DataLayout, IndexType>> gpu1(gpu_data1, tensorRange);
+ TensorMap<Tensor<DataType, 3, DataLayout, IndexType>> gpu2(gpu_data2, tensorRange);
+
+ sycl_device.memcpyHostToDevice(gpu_data1, in1.data(),(in1.size())*sizeof(DataType));
+ sycl_device.memcpyHostToDevice(gpu_data2, in1.data(),(in1.size())*sizeof(DataType));
+ gpu1.device(sycl_device) = gpu1 * 3.14f;
+ gpu2.device(sycl_device) = gpu2 * 2.7f;
+ sycl_device.memcpyDeviceToHost(out1.data(), gpu_data1,(out1.size())*sizeof(DataType));
+ sycl_device.memcpyDeviceToHost(out2.data(), gpu_data1,(out2.size())*sizeof(DataType));
+ sycl_device.memcpyDeviceToHost(out3.data(), gpu_data2,(out3.size())*sizeof(DataType));
+ sycl_device.synchronize();
+
+ for (IndexType i = 0; i < in1.size(); ++i) {
+ // std::cout << "SYCL DATA : " << out1(i) << " vs CPU DATA : " << in1(i) * 3.14f << "\n";
+ VERIFY_IS_APPROX(out1(i), in1(i) * 3.14f);
+ VERIFY_IS_APPROX(out2(i), in1(i) * 3.14f);
+ VERIFY_IS_APPROX(out3(i), in1(i) * 2.7f);
+ }
+
+ sycl_device.deallocate(gpu_data1);
+ sycl_device.deallocate(gpu_data2);
+}
+
+template <typename DataType, int DataLayout, typename IndexType>
+void test_sycl_mem_sync(const Eigen::SyclDevice &sycl_device) {
+ IndexType size = 20;
+ array<IndexType, 1> tensorRange = {{size}};
+ Tensor<DataType, 1, DataLayout, IndexType> in1(tensorRange);
+ Tensor<DataType, 1, DataLayout, IndexType> in2(tensorRange);
+ Tensor<DataType, 1, DataLayout, IndexType> out(tensorRange);
+
+ in1 = in1.random();
+ in2 = in1;
+
+ DataType* gpu_data = static_cast<DataType*>(sycl_device.allocate(in1.size()*sizeof(DataType)));
+
+ TensorMap<Tensor<DataType, 1, DataLayout, IndexType>> gpu1(gpu_data, tensorRange);
+ sycl_device.memcpyHostToDevice(gpu_data, in1.data(),(in1.size())*sizeof(DataType));
+ sycl_device.synchronize();
+ in1.setZero();
+
+ sycl_device.memcpyDeviceToHost(out.data(), gpu_data, out.size()*sizeof(DataType));
+ sycl_device.synchronize();
+
+ for (IndexType i = 0; i < in1.size(); ++i) {
+ VERIFY_IS_APPROX(out(i), in2(i));
+ }
+
+ sycl_device.deallocate(gpu_data);
+}
+
+template <typename DataType, int DataLayout, typename IndexType>
+void test_sycl_mem_sync_offsets(const Eigen::SyclDevice &sycl_device) {
+ using tensor_type = Tensor<DataType, 1, DataLayout, IndexType>;
+ IndexType full_size = 32;
+ IndexType half_size = full_size / 2;
+ array<IndexType, 1> tensorRange = {{full_size}};
+ tensor_type in1(tensorRange);
+ tensor_type out(tensorRange);
+
+ DataType* gpu_data = static_cast<DataType*>(sycl_device.allocate(full_size * sizeof(DataType)));
+ TensorMap<tensor_type> gpu1(gpu_data, tensorRange);
+
+ in1 = in1.random();
+ // Copy all data to device, then permute on copy back to host
+ sycl_device.memcpyHostToDevice(gpu_data, in1.data(), full_size * sizeof(DataType));
+ sycl_device.memcpyDeviceToHost(out.data(), gpu_data + half_size, half_size * sizeof(DataType));
+ sycl_device.memcpyDeviceToHost(out.data() + half_size, gpu_data, half_size * sizeof(DataType));
+
+ for (IndexType i = 0; i < half_size; ++i) {
+ VERIFY_IS_APPROX(out(i), in1(i + half_size));
+ VERIFY_IS_APPROX(out(i + half_size), in1(i));
+ }
+
+ in1 = in1.random();
+ out.setZero();
+ // Permute copies to device, then copy all back to host
+ sycl_device.memcpyHostToDevice(gpu_data + half_size, in1.data(), half_size * sizeof(DataType));
+ sycl_device.memcpyHostToDevice(gpu_data, in1.data() + half_size, half_size * sizeof(DataType));
+ sycl_device.memcpyDeviceToHost(out.data(), gpu_data, full_size * sizeof(DataType));
+
+ for (IndexType i = 0; i < half_size; ++i) {
+ VERIFY_IS_APPROX(out(i), in1(i + half_size));
+ VERIFY_IS_APPROX(out(i + half_size), in1(i));
+ }
+
+ in1 = in1.random();
+ out.setZero();
+ DataType* gpu_data_out = static_cast<DataType*>(sycl_device.allocate(full_size * sizeof(DataType)));
+ TensorMap<tensor_type> gpu2(gpu_data_out, tensorRange);
+ // Copy all to device, permute copies on device, then copy all back to host
+ sycl_device.memcpyHostToDevice(gpu_data, in1.data(), full_size * sizeof(DataType));
+ sycl_device.memcpy(gpu_data_out + half_size, gpu_data, half_size * sizeof(DataType));
+ sycl_device.memcpy(gpu_data_out, gpu_data + half_size, half_size * sizeof(DataType));
+ sycl_device.memcpyDeviceToHost(out.data(), gpu_data_out, full_size * sizeof(DataType));
+
+ for (IndexType i = 0; i < half_size; ++i) {
+ VERIFY_IS_APPROX(out(i), in1(i + half_size));
+ VERIFY_IS_APPROX(out(i + half_size), in1(i));
+ }
+
+ sycl_device.deallocate(gpu_data_out);
+ sycl_device.deallocate(gpu_data);
+}
+
+template <typename DataType, int DataLayout, typename IndexType>
+void test_sycl_memset_offsets(const Eigen::SyclDevice &sycl_device) {
+ using tensor_type = Tensor<DataType, 1, DataLayout, IndexType>;
+ IndexType full_size = 32;
+ IndexType half_size = full_size / 2;
+ array<IndexType, 1> tensorRange = {{full_size}};
+ tensor_type cpu_out(tensorRange);
+ tensor_type out(tensorRange);
+
+ cpu_out.setZero();
+
+ std::memset(cpu_out.data(), 0, half_size * sizeof(DataType));
+ std::memset(cpu_out.data() + half_size, 1, half_size * sizeof(DataType));
+
+ DataType* gpu_data = static_cast<DataType*>(sycl_device.allocate(full_size * sizeof(DataType)));
+ TensorMap<tensor_type> gpu1(gpu_data, tensorRange);
+
+ sycl_device.memset(gpu_data, 0, half_size * sizeof(DataType));
+ sycl_device.memset(gpu_data + half_size, 1, half_size * sizeof(DataType));
+ sycl_device.memcpyDeviceToHost(out.data(), gpu_data, full_size * sizeof(DataType));
+
+ for (IndexType i = 0; i < full_size; ++i) {
+ VERIFY_IS_APPROX(out(i), cpu_out(i));
+ }
+
+ sycl_device.deallocate(gpu_data);
+}
+
+template <typename DataType, int DataLayout, typename IndexType>
+void test_sycl_computations(const Eigen::SyclDevice &sycl_device) {
+
+ IndexType sizeDim1 = 100;
+ IndexType sizeDim2 = 10;
+ IndexType sizeDim3 = 20;
+ array<IndexType, 3> tensorRange = {{sizeDim1, sizeDim2, sizeDim3}};
+ Tensor<DataType, 3,DataLayout, IndexType> in1(tensorRange);
+ Tensor<DataType, 3,DataLayout, IndexType> in2(tensorRange);
+ Tensor<DataType, 3,DataLayout, IndexType> in3(tensorRange);
+ Tensor<DataType, 3,DataLayout, IndexType> out(tensorRange);
+
+ in2 = in2.random();
+ in3 = in3.random();
+
+ DataType * gpu_in1_data = static_cast<DataType*>(sycl_device.allocate(in1.size()*sizeof(DataType)));
+ DataType * gpu_in2_data = static_cast<DataType*>(sycl_device.allocate(in2.size()*sizeof(DataType)));
+ DataType * gpu_in3_data = static_cast<DataType*>(sycl_device.allocate(in3.size()*sizeof(DataType)));
+ DataType * gpu_out_data = static_cast<DataType*>(sycl_device.allocate(out.size()*sizeof(DataType)));
+
+ TensorMap<Tensor<DataType, 3, DataLayout, IndexType>> gpu_in1(gpu_in1_data, tensorRange);
+ TensorMap<Tensor<DataType, 3, DataLayout, IndexType>> gpu_in2(gpu_in2_data, tensorRange);
+ TensorMap<Tensor<DataType, 3, DataLayout, IndexType>> gpu_in3(gpu_in3_data, tensorRange);
+ TensorMap<Tensor<DataType, 3, DataLayout, IndexType>> gpu_out(gpu_out_data, tensorRange);
+
+ /// a=1.2f
+ gpu_in1.device(sycl_device) = gpu_in1.constant(1.2f);
+ sycl_device.memcpyDeviceToHost(in1.data(), gpu_in1_data ,(in1.size())*sizeof(DataType));
+ sycl_device.synchronize();
+
+ for (IndexType i = 0; i < sizeDim1; ++i) {
+ for (IndexType j = 0; j < sizeDim2; ++j) {
+ for (IndexType k = 0; k < sizeDim3; ++k) {
+ VERIFY_IS_APPROX(in1(i,j,k), 1.2f);
+ }
+ }
+ }
+ printf("a=1.2f Test passed\n");
+
+ /// a=b*1.2f
+ gpu_out.device(sycl_device) = gpu_in1 * 1.2f;
+ sycl_device.memcpyDeviceToHost(out.data(), gpu_out_data ,(out.size())*sizeof(DataType));
+ sycl_device.synchronize();
+
+ for (IndexType i = 0; i < sizeDim1; ++i) {
+ for (IndexType j = 0; j < sizeDim2; ++j) {
+ for (IndexType k = 0; k < sizeDim3; ++k) {
+ VERIFY_IS_APPROX(out(i,j,k),
+ in1(i,j,k) * 1.2f);
+ }
+ }
+ }
+ printf("a=b*1.2f Test Passed\n");
+
+ /// c=a*b
+ sycl_device.memcpyHostToDevice(gpu_in2_data, in2.data(),(in2.size())*sizeof(DataType));
+ gpu_out.device(sycl_device) = gpu_in1 * gpu_in2;
+ sycl_device.memcpyDeviceToHost(out.data(), gpu_out_data,(out.size())*sizeof(DataType));
+ sycl_device.synchronize();
+
+ for (IndexType i = 0; i < sizeDim1; ++i) {
+ for (IndexType j = 0; j < sizeDim2; ++j) {
+ for (IndexType k = 0; k < sizeDim3; ++k) {
+ VERIFY_IS_APPROX(out(i,j,k),
+ in1(i,j,k) *
+ in2(i,j,k));
+ }
+ }
+ }
+ printf("c=a*b Test Passed\n");
+
+ /// c=a+b
+ gpu_out.device(sycl_device) = gpu_in1 + gpu_in2;
+ sycl_device.memcpyDeviceToHost(out.data(), gpu_out_data,(out.size())*sizeof(DataType));
+ sycl_device.synchronize();
+ for (IndexType i = 0; i < sizeDim1; ++i) {
+ for (IndexType j = 0; j < sizeDim2; ++j) {
+ for (IndexType k = 0; k < sizeDim3; ++k) {
+ VERIFY_IS_APPROX(out(i,j,k),
+ in1(i,j,k) +
+ in2(i,j,k));
+ }
+ }
+ }
+ printf("c=a+b Test Passed\n");
+
+ /// c=a*a
+ gpu_out.device(sycl_device) = gpu_in1 * gpu_in1;
+ sycl_device.memcpyDeviceToHost(out.data(), gpu_out_data,(out.size())*sizeof(DataType));
+ sycl_device.synchronize();
+ for (IndexType i = 0; i < sizeDim1; ++i) {
+ for (IndexType j = 0; j < sizeDim2; ++j) {
+ for (IndexType k = 0; k < sizeDim3; ++k) {
+ VERIFY_IS_APPROX(out(i,j,k),
+ in1(i,j,k) *
+ in1(i,j,k));
+ }
+ }
+ }
+ printf("c= a*a Test Passed\n");
+
+ //a*3.14f + b*2.7f
+ gpu_out.device(sycl_device) = gpu_in1 * gpu_in1.constant(3.14f) + gpu_in2 * gpu_in2.constant(2.7f);
+ sycl_device.memcpyDeviceToHost(out.data(),gpu_out_data,(out.size())*sizeof(DataType));
+ sycl_device.synchronize();
+ for (IndexType i = 0; i < sizeDim1; ++i) {
+ for (IndexType j = 0; j < sizeDim2; ++j) {
+ for (IndexType k = 0; k < sizeDim3; ++k) {
+ VERIFY_IS_APPROX(out(i,j,k),
+ in1(i,j,k) * 3.14f
+ + in2(i,j,k) * 2.7f);
+ }
+ }
+ }
+ printf("a*3.14f + b*2.7f Test Passed\n");
+
+ ///d= (a>0.5? b:c)
+ sycl_device.memcpyHostToDevice(gpu_in3_data, in3.data(),(in3.size())*sizeof(DataType));
+ gpu_out.device(sycl_device) =(gpu_in1 > gpu_in1.constant(0.5f)).select(gpu_in2, gpu_in3);
+ sycl_device.memcpyDeviceToHost(out.data(), gpu_out_data,(out.size())*sizeof(DataType));
+ sycl_device.synchronize();
+ for (IndexType i = 0; i < sizeDim1; ++i) {
+ for (IndexType j = 0; j < sizeDim2; ++j) {
+ for (IndexType k = 0; k < sizeDim3; ++k) {
+ VERIFY_IS_APPROX(out(i, j, k), (in1(i, j, k) > 0.5f)
+ ? in2(i, j, k)
+ : in3(i, j, k));
+ }
+ }
+ }
+ printf("d= (a>0.5? b:c) Test Passed\n");
+ sycl_device.deallocate(gpu_in1_data);
+ sycl_device.deallocate(gpu_in2_data);
+ sycl_device.deallocate(gpu_in3_data);
+ sycl_device.deallocate(gpu_out_data);
+}
+template<typename Scalar1, typename Scalar2, int DataLayout, typename IndexType>
+static void test_sycl_cast(const Eigen::SyclDevice& sycl_device){
+ IndexType size = 20;
+ array<IndexType, 1> tensorRange = {{size}};
+ Tensor<Scalar1, 1, DataLayout, IndexType> in(tensorRange);
+ Tensor<Scalar2, 1, DataLayout, IndexType> out(tensorRange);
+ Tensor<Scalar2, 1, DataLayout, IndexType> out_host(tensorRange);
+
+ in = in.random();
+
+ Scalar1* gpu_in_data = static_cast<Scalar1*>(sycl_device.allocate(in.size()*sizeof(Scalar1)));
+ Scalar2 * gpu_out_data = static_cast<Scalar2*>(sycl_device.allocate(out.size()*sizeof(Scalar2)));
+
+ TensorMap<Tensor<Scalar1, 1, DataLayout, IndexType>> gpu_in(gpu_in_data, tensorRange);
+ TensorMap<Tensor<Scalar2, 1, DataLayout, IndexType>> gpu_out(gpu_out_data, tensorRange);
+ sycl_device.memcpyHostToDevice(gpu_in_data, in.data(),(in.size())*sizeof(Scalar1));
+ gpu_out.device(sycl_device) = gpu_in. template cast<Scalar2>();
+ sycl_device.memcpyDeviceToHost(out.data(), gpu_out_data, out.size()*sizeof(Scalar2));
+ out_host = in. template cast<Scalar2>();
+ for(IndexType i=0; i< size; i++)
+ {
+ VERIFY_IS_APPROX(out(i), out_host(i));
+ }
+ printf("cast Test Passed\n");
+ sycl_device.deallocate(gpu_in_data);
+ sycl_device.deallocate(gpu_out_data);
+}
+template<typename DataType, typename dev_Selector> void sycl_computing_test_per_device(dev_Selector s){
+ QueueInterface queueInterface(s);
+ auto sycl_device = Eigen::SyclDevice(&queueInterface);
+ test_sycl_mem_transfers<DataType, RowMajor, int64_t>(sycl_device);
+ test_sycl_computations<DataType, RowMajor, int64_t>(sycl_device);
+ test_sycl_mem_sync<DataType, RowMajor, int64_t>(sycl_device);
+ test_sycl_mem_sync_offsets<DataType, RowMajor, int64_t>(sycl_device);
+ test_sycl_memset_offsets<DataType, RowMajor, int64_t>(sycl_device);
+ test_sycl_mem_transfers<DataType, ColMajor, int64_t>(sycl_device);
+ test_sycl_computations<DataType, ColMajor, int64_t>(sycl_device);
+ test_sycl_mem_sync<DataType, ColMajor, int64_t>(sycl_device);
+ test_sycl_cast<DataType, int, RowMajor, int64_t>(sycl_device);
+ test_sycl_cast<DataType, int, ColMajor, int64_t>(sycl_device);
+}
+
+EIGEN_DECLARE_TEST(cxx11_tensor_sycl) {
+ for (const auto& device :Eigen::get_sycl_supported_devices()) {
+ CALL_SUBTEST(sycl_computing_test_per_device<float>(device));
+ }
+}
diff --git a/unsupported/test/cxx11_tensor_symmetry.cpp b/unsupported/test/cxx11_tensor_symmetry.cpp
new file mode 100644
index 0000000..fed269a
--- /dev/null
+++ b/unsupported/test/cxx11_tensor_symmetry.cpp
@@ -0,0 +1,818 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2013 Christian Seiler <christian@iwakd.de>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "main.h"
+
+#include <Eigen/CXX11/Tensor>
+#include <Eigen/CXX11/TensorSymmetry>
+
+#include <map>
+#include <set>
+
+using Eigen::Tensor;
+using Eigen::SGroup;
+using Eigen::DynamicSGroup;
+using Eigen::StaticSGroup;
+using Eigen::Symmetry;
+using Eigen::AntiSymmetry;
+using Eigen::Hermiticity;
+using Eigen::AntiHermiticity;
+
+using Eigen::NegationFlag;
+using Eigen::ConjugationFlag;
+using Eigen::GlobalZeroFlag;
+using Eigen::GlobalRealFlag;
+using Eigen::GlobalImagFlag;
+
+// helper function to determine if the compiler intantiated a static
+// or dynamic symmetry group
+template<typename... Sym>
+bool isDynGroup(StaticSGroup<Sym...> const& dummy)
+{
+ (void)dummy;
+ return false;
+}
+
+bool isDynGroup(DynamicSGroup const& dummy)
+{
+ (void)dummy;
+ return true;
+}
+
+// helper class for checking that the symmetry groups are correct
+struct checkIdx {
+ template<typename ArrType>
+ static inline int doCheck_(ArrType e, int flags, int dummy, std::set<uint64_t>& found, std::map<uint64_t, int> const& expected)
+ {
+ // use decimal representation of value
+ uint64_t value = e[0];
+ for (std::size_t i = 1; i < e.size(); i++)
+ value = value * 10 + e[i];
+
+ // we want to make sure that we find each element
+ auto it = expected.find(value);
+ VERIFY((it != expected.end()));
+ VERIFY_IS_EQUAL(it->second, flags);
+
+ // we want to make sure we only have each element once;
+ // set::insert returns true for the second part of the pair
+ // if the element was really inserted and not already there
+ auto p = found.insert(value);
+ VERIFY((p.second));
+
+ return dummy;
+ }
+
+ static inline int run(std::vector<int> e, int flags, int dummy, std::set<uint64_t>& found, std::map<uint64_t, int> const& expected)
+ {
+ return doCheck_(e, flags, dummy, found, expected);
+ }
+
+ template<std::size_t N>
+ static inline int run(std::array<int, N> e, int flags, int dummy, std::set<uint64_t>& found, std::map<uint64_t, int> const& expected)
+ {
+ return doCheck_(e, flags, dummy, found, expected);
+ }
+};
+
+static void test_symgroups_static()
+{
+ std::array<int, 7> identity{{0,1,2,3,4,5,6}};
+
+ // Simple static symmetry group
+ StaticSGroup<
+ AntiSymmetry<0,1>,
+ Hermiticity<0,2>
+ > group;
+
+ std::set<uint64_t> found;
+ std::map<uint64_t, int> expected;
+ expected[ 123456] = 0;
+ expected[1023456] = NegationFlag;
+ expected[2103456] = ConjugationFlag;
+ expected[1203456] = ConjugationFlag | NegationFlag;
+ expected[2013456] = ConjugationFlag | NegationFlag;
+ expected[ 213456] = ConjugationFlag;
+
+ VERIFY_IS_EQUAL(group.size(), 6u);
+ VERIFY_IS_EQUAL(group.globalFlags(), GlobalImagFlag);
+ group.apply<checkIdx, int>(identity, 0, found, expected);
+ VERIFY_IS_EQUAL(found.size(), 6u);
+}
+
+static void test_symgroups_dynamic()
+{
+ std::vector<int> identity;
+ for (int i = 0; i <= 6; i++)
+ identity.push_back(i);
+
+ // Simple dynamic symmetry group
+ DynamicSGroup group;
+ group.add(0,1,NegationFlag);
+ group.add(0,2,ConjugationFlag);
+
+ VERIFY_IS_EQUAL(group.size(), 6u);
+ VERIFY_IS_EQUAL(group.globalFlags(), GlobalImagFlag);
+
+ std::set<uint64_t> found;
+ std::map<uint64_t, int> expected;
+ expected[ 123456] = 0;
+ expected[1023456] = NegationFlag;
+ expected[2103456] = ConjugationFlag;
+ expected[1203456] = ConjugationFlag | NegationFlag;
+ expected[2013456] = ConjugationFlag | NegationFlag;
+ expected[ 213456] = ConjugationFlag;
+
+ VERIFY_IS_EQUAL(group.size(), 6u);
+ VERIFY_IS_EQUAL(group.globalFlags(), GlobalImagFlag);
+ group.apply<checkIdx, int>(identity, 0, found, expected);
+ VERIFY_IS_EQUAL(found.size(), 6u);
+}
+
+static void test_symgroups_selection()
+{
+ std::array<int, 7> identity7{{0,1,2,3,4,5,6}};
+ std::array<int, 10> identity10{{0,1,2,3,4,5,6,7,8,9}};
+
+ {
+ // Do the same test as in test_symgroups_static but
+ // require selection via SGroup
+ SGroup<
+ AntiSymmetry<0,1>,
+ Hermiticity<0,2>
+ > group;
+
+ std::set<uint64_t> found;
+ std::map<uint64_t, int> expected;
+ expected[ 123456] = 0;
+ expected[1023456] = NegationFlag;
+ expected[2103456] = ConjugationFlag;
+ expected[1203456] = ConjugationFlag | NegationFlag;
+ expected[2013456] = ConjugationFlag | NegationFlag;
+ expected[ 213456] = ConjugationFlag;
+
+ VERIFY(!isDynGroup(group));
+ VERIFY_IS_EQUAL(group.size(), 6u);
+ VERIFY_IS_EQUAL(group.globalFlags(), GlobalImagFlag);
+ group.apply<checkIdx, int>(identity7, 0, found, expected);
+ VERIFY_IS_EQUAL(found.size(), 6u);
+ }
+
+ {
+ // simple factorizing group: 5 generators, 2^5 = 32 elements
+ // selection should make this dynamic, although static group
+ // can still be reasonably generated
+ SGroup<
+ Symmetry<0,1>,
+ Symmetry<2,3>,
+ Symmetry<4,5>,
+ Symmetry<6,7>,
+ Symmetry<8,9>
+ > group;
+
+ std::set<uint64_t> found;
+ std::map<uint64_t, int> expected;
+ expected[ 123456789] = 0; expected[ 123456798] = 0; expected[ 123457689] = 0; expected[ 123457698] = 0;
+ expected[ 123546789] = 0; expected[ 123546798] = 0; expected[ 123547689] = 0; expected[ 123547698] = 0;
+ expected[ 132456789] = 0; expected[ 132456798] = 0; expected[ 132457689] = 0; expected[ 132457698] = 0;
+ expected[ 132546789] = 0; expected[ 132546798] = 0; expected[ 132547689] = 0; expected[ 132547698] = 0;
+ expected[1023456789] = 0; expected[1023456798] = 0; expected[1023457689] = 0; expected[1023457698] = 0;
+ expected[1023546789] = 0; expected[1023546798] = 0; expected[1023547689] = 0; expected[1023547698] = 0;
+ expected[1032456789] = 0; expected[1032456798] = 0; expected[1032457689] = 0; expected[1032457698] = 0;
+ expected[1032546789] = 0; expected[1032546798] = 0; expected[1032547689] = 0; expected[1032547698] = 0;
+
+ VERIFY(isDynGroup(group));
+ VERIFY_IS_EQUAL(group.size(), 32u);
+ VERIFY_IS_EQUAL(group.globalFlags(), 0);
+ group.apply<checkIdx, int>(identity10, 0, found, expected);
+ VERIFY_IS_EQUAL(found.size(), 32u);
+
+ // no verify that we could also generate a static group
+ // with these generators
+ found.clear();
+ StaticSGroup<
+ Symmetry<0,1>,
+ Symmetry<2,3>,
+ Symmetry<4,5>,
+ Symmetry<6,7>,
+ Symmetry<8,9>
+ > group_static;
+ VERIFY_IS_EQUAL(group_static.size(), 32u);
+ VERIFY_IS_EQUAL(group_static.globalFlags(), 0);
+ group_static.apply<checkIdx, int>(identity10, 0, found, expected);
+ VERIFY_IS_EQUAL(found.size(), 32u);
+ }
+
+ {
+ // try to create a HUGE group
+ SGroup<
+ Symmetry<0,1>,
+ Symmetry<1,2>,
+ Symmetry<2,3>,
+ Symmetry<3,4>,
+ Symmetry<4,5>,
+ Symmetry<5,6>
+ > group;
+
+ std::set<uint64_t> found;
+ uint64_t pre_expected[5040] = {
+ 123456, 1023456, 213456, 2013456, 1203456, 2103456, 132456, 1032456, 312456, 3012456, 1302456, 3102456,
+ 231456, 2031456, 321456, 3021456, 2301456, 3201456, 1230456, 2130456, 1320456, 3120456, 2310456, 3210456,
+ 124356, 1024356, 214356, 2014356, 1204356, 2104356, 142356, 1042356, 412356, 4012356, 1402356, 4102356,
+ 241356, 2041356, 421356, 4021356, 2401356, 4201356, 1240356, 2140356, 1420356, 4120356, 2410356, 4210356,
+ 134256, 1034256, 314256, 3014256, 1304256, 3104256, 143256, 1043256, 413256, 4013256, 1403256, 4103256,
+ 341256, 3041256, 431256, 4031256, 3401256, 4301256, 1340256, 3140256, 1430256, 4130256, 3410256, 4310256,
+ 234156, 2034156, 324156, 3024156, 2304156, 3204156, 243156, 2043156, 423156, 4023156, 2403156, 4203156,
+ 342156, 3042156, 432156, 4032156, 3402156, 4302156, 2340156, 3240156, 2430156, 4230156, 3420156, 4320156,
+ 1234056, 2134056, 1324056, 3124056, 2314056, 3214056, 1243056, 2143056, 1423056, 4123056, 2413056, 4213056,
+ 1342056, 3142056, 1432056, 4132056, 3412056, 4312056, 2341056, 3241056, 2431056, 4231056, 3421056, 4321056,
+ 123546, 1023546, 213546, 2013546, 1203546, 2103546, 132546, 1032546, 312546, 3012546, 1302546, 3102546,
+ 231546, 2031546, 321546, 3021546, 2301546, 3201546, 1230546, 2130546, 1320546, 3120546, 2310546, 3210546,
+ 125346, 1025346, 215346, 2015346, 1205346, 2105346, 152346, 1052346, 512346, 5012346, 1502346, 5102346,
+ 251346, 2051346, 521346, 5021346, 2501346, 5201346, 1250346, 2150346, 1520346, 5120346, 2510346, 5210346,
+ 135246, 1035246, 315246, 3015246, 1305246, 3105246, 153246, 1053246, 513246, 5013246, 1503246, 5103246,
+ 351246, 3051246, 531246, 5031246, 3501246, 5301246, 1350246, 3150246, 1530246, 5130246, 3510246, 5310246,
+ 235146, 2035146, 325146, 3025146, 2305146, 3205146, 253146, 2053146, 523146, 5023146, 2503146, 5203146,
+ 352146, 3052146, 532146, 5032146, 3502146, 5302146, 2350146, 3250146, 2530146, 5230146, 3520146, 5320146,
+ 1235046, 2135046, 1325046, 3125046, 2315046, 3215046, 1253046, 2153046, 1523046, 5123046, 2513046, 5213046,
+ 1352046, 3152046, 1532046, 5132046, 3512046, 5312046, 2351046, 3251046, 2531046, 5231046, 3521046, 5321046,
+ 124536, 1024536, 214536, 2014536, 1204536, 2104536, 142536, 1042536, 412536, 4012536, 1402536, 4102536,
+ 241536, 2041536, 421536, 4021536, 2401536, 4201536, 1240536, 2140536, 1420536, 4120536, 2410536, 4210536,
+ 125436, 1025436, 215436, 2015436, 1205436, 2105436, 152436, 1052436, 512436, 5012436, 1502436, 5102436,
+ 251436, 2051436, 521436, 5021436, 2501436, 5201436, 1250436, 2150436, 1520436, 5120436, 2510436, 5210436,
+ 145236, 1045236, 415236, 4015236, 1405236, 4105236, 154236, 1054236, 514236, 5014236, 1504236, 5104236,
+ 451236, 4051236, 541236, 5041236, 4501236, 5401236, 1450236, 4150236, 1540236, 5140236, 4510236, 5410236,
+ 245136, 2045136, 425136, 4025136, 2405136, 4205136, 254136, 2054136, 524136, 5024136, 2504136, 5204136,
+ 452136, 4052136, 542136, 5042136, 4502136, 5402136, 2450136, 4250136, 2540136, 5240136, 4520136, 5420136,
+ 1245036, 2145036, 1425036, 4125036, 2415036, 4215036, 1254036, 2154036, 1524036, 5124036, 2514036, 5214036,
+ 1452036, 4152036, 1542036, 5142036, 4512036, 5412036, 2451036, 4251036, 2541036, 5241036, 4521036, 5421036,
+ 134526, 1034526, 314526, 3014526, 1304526, 3104526, 143526, 1043526, 413526, 4013526, 1403526, 4103526,
+ 341526, 3041526, 431526, 4031526, 3401526, 4301526, 1340526, 3140526, 1430526, 4130526, 3410526, 4310526,
+ 135426, 1035426, 315426, 3015426, 1305426, 3105426, 153426, 1053426, 513426, 5013426, 1503426, 5103426,
+ 351426, 3051426, 531426, 5031426, 3501426, 5301426, 1350426, 3150426, 1530426, 5130426, 3510426, 5310426,
+ 145326, 1045326, 415326, 4015326, 1405326, 4105326, 154326, 1054326, 514326, 5014326, 1504326, 5104326,
+ 451326, 4051326, 541326, 5041326, 4501326, 5401326, 1450326, 4150326, 1540326, 5140326, 4510326, 5410326,
+ 345126, 3045126, 435126, 4035126, 3405126, 4305126, 354126, 3054126, 534126, 5034126, 3504126, 5304126,
+ 453126, 4053126, 543126, 5043126, 4503126, 5403126, 3450126, 4350126, 3540126, 5340126, 4530126, 5430126,
+ 1345026, 3145026, 1435026, 4135026, 3415026, 4315026, 1354026, 3154026, 1534026, 5134026, 3514026, 5314026,
+ 1453026, 4153026, 1543026, 5143026, 4513026, 5413026, 3451026, 4351026, 3541026, 5341026, 4531026, 5431026,
+ 234516, 2034516, 324516, 3024516, 2304516, 3204516, 243516, 2043516, 423516, 4023516, 2403516, 4203516,
+ 342516, 3042516, 432516, 4032516, 3402516, 4302516, 2340516, 3240516, 2430516, 4230516, 3420516, 4320516,
+ 235416, 2035416, 325416, 3025416, 2305416, 3205416, 253416, 2053416, 523416, 5023416, 2503416, 5203416,
+ 352416, 3052416, 532416, 5032416, 3502416, 5302416, 2350416, 3250416, 2530416, 5230416, 3520416, 5320416,
+ 245316, 2045316, 425316, 4025316, 2405316, 4205316, 254316, 2054316, 524316, 5024316, 2504316, 5204316,
+ 452316, 4052316, 542316, 5042316, 4502316, 5402316, 2450316, 4250316, 2540316, 5240316, 4520316, 5420316,
+ 345216, 3045216, 435216, 4035216, 3405216, 4305216, 354216, 3054216, 534216, 5034216, 3504216, 5304216,
+ 453216, 4053216, 543216, 5043216, 4503216, 5403216, 3450216, 4350216, 3540216, 5340216, 4530216, 5430216,
+ 2345016, 3245016, 2435016, 4235016, 3425016, 4325016, 2354016, 3254016, 2534016, 5234016, 3524016, 5324016,
+ 2453016, 4253016, 2543016, 5243016, 4523016, 5423016, 3452016, 4352016, 3542016, 5342016, 4532016, 5432016,
+ 1234506, 2134506, 1324506, 3124506, 2314506, 3214506, 1243506, 2143506, 1423506, 4123506, 2413506, 4213506,
+ 1342506, 3142506, 1432506, 4132506, 3412506, 4312506, 2341506, 3241506, 2431506, 4231506, 3421506, 4321506,
+ 1235406, 2135406, 1325406, 3125406, 2315406, 3215406, 1253406, 2153406, 1523406, 5123406, 2513406, 5213406,
+ 1352406, 3152406, 1532406, 5132406, 3512406, 5312406, 2351406, 3251406, 2531406, 5231406, 3521406, 5321406,
+ 1245306, 2145306, 1425306, 4125306, 2415306, 4215306, 1254306, 2154306, 1524306, 5124306, 2514306, 5214306,
+ 1452306, 4152306, 1542306, 5142306, 4512306, 5412306, 2451306, 4251306, 2541306, 5241306, 4521306, 5421306,
+ 1345206, 3145206, 1435206, 4135206, 3415206, 4315206, 1354206, 3154206, 1534206, 5134206, 3514206, 5314206,
+ 1453206, 4153206, 1543206, 5143206, 4513206, 5413206, 3451206, 4351206, 3541206, 5341206, 4531206, 5431206,
+ 2345106, 3245106, 2435106, 4235106, 3425106, 4325106, 2354106, 3254106, 2534106, 5234106, 3524106, 5324106,
+ 2453106, 4253106, 2543106, 5243106, 4523106, 5423106, 3452106, 4352106, 3542106, 5342106, 4532106, 5432106,
+ 123465, 1023465, 213465, 2013465, 1203465, 2103465, 132465, 1032465, 312465, 3012465, 1302465, 3102465,
+ 231465, 2031465, 321465, 3021465, 2301465, 3201465, 1230465, 2130465, 1320465, 3120465, 2310465, 3210465,
+ 124365, 1024365, 214365, 2014365, 1204365, 2104365, 142365, 1042365, 412365, 4012365, 1402365, 4102365,
+ 241365, 2041365, 421365, 4021365, 2401365, 4201365, 1240365, 2140365, 1420365, 4120365, 2410365, 4210365,
+ 134265, 1034265, 314265, 3014265, 1304265, 3104265, 143265, 1043265, 413265, 4013265, 1403265, 4103265,
+ 341265, 3041265, 431265, 4031265, 3401265, 4301265, 1340265, 3140265, 1430265, 4130265, 3410265, 4310265,
+ 234165, 2034165, 324165, 3024165, 2304165, 3204165, 243165, 2043165, 423165, 4023165, 2403165, 4203165,
+ 342165, 3042165, 432165, 4032165, 3402165, 4302165, 2340165, 3240165, 2430165, 4230165, 3420165, 4320165,
+ 1234065, 2134065, 1324065, 3124065, 2314065, 3214065, 1243065, 2143065, 1423065, 4123065, 2413065, 4213065,
+ 1342065, 3142065, 1432065, 4132065, 3412065, 4312065, 2341065, 3241065, 2431065, 4231065, 3421065, 4321065,
+ 123645, 1023645, 213645, 2013645, 1203645, 2103645, 132645, 1032645, 312645, 3012645, 1302645, 3102645,
+ 231645, 2031645, 321645, 3021645, 2301645, 3201645, 1230645, 2130645, 1320645, 3120645, 2310645, 3210645,
+ 126345, 1026345, 216345, 2016345, 1206345, 2106345, 162345, 1062345, 612345, 6012345, 1602345, 6102345,
+ 261345, 2061345, 621345, 6021345, 2601345, 6201345, 1260345, 2160345, 1620345, 6120345, 2610345, 6210345,
+ 136245, 1036245, 316245, 3016245, 1306245, 3106245, 163245, 1063245, 613245, 6013245, 1603245, 6103245,
+ 361245, 3061245, 631245, 6031245, 3601245, 6301245, 1360245, 3160245, 1630245, 6130245, 3610245, 6310245,
+ 236145, 2036145, 326145, 3026145, 2306145, 3206145, 263145, 2063145, 623145, 6023145, 2603145, 6203145,
+ 362145, 3062145, 632145, 6032145, 3602145, 6302145, 2360145, 3260145, 2630145, 6230145, 3620145, 6320145,
+ 1236045, 2136045, 1326045, 3126045, 2316045, 3216045, 1263045, 2163045, 1623045, 6123045, 2613045, 6213045,
+ 1362045, 3162045, 1632045, 6132045, 3612045, 6312045, 2361045, 3261045, 2631045, 6231045, 3621045, 6321045,
+ 124635, 1024635, 214635, 2014635, 1204635, 2104635, 142635, 1042635, 412635, 4012635, 1402635, 4102635,
+ 241635, 2041635, 421635, 4021635, 2401635, 4201635, 1240635, 2140635, 1420635, 4120635, 2410635, 4210635,
+ 126435, 1026435, 216435, 2016435, 1206435, 2106435, 162435, 1062435, 612435, 6012435, 1602435, 6102435,
+ 261435, 2061435, 621435, 6021435, 2601435, 6201435, 1260435, 2160435, 1620435, 6120435, 2610435, 6210435,
+ 146235, 1046235, 416235, 4016235, 1406235, 4106235, 164235, 1064235, 614235, 6014235, 1604235, 6104235,
+ 461235, 4061235, 641235, 6041235, 4601235, 6401235, 1460235, 4160235, 1640235, 6140235, 4610235, 6410235,
+ 246135, 2046135, 426135, 4026135, 2406135, 4206135, 264135, 2064135, 624135, 6024135, 2604135, 6204135,
+ 462135, 4062135, 642135, 6042135, 4602135, 6402135, 2460135, 4260135, 2640135, 6240135, 4620135, 6420135,
+ 1246035, 2146035, 1426035, 4126035, 2416035, 4216035, 1264035, 2164035, 1624035, 6124035, 2614035, 6214035,
+ 1462035, 4162035, 1642035, 6142035, 4612035, 6412035, 2461035, 4261035, 2641035, 6241035, 4621035, 6421035,
+ 134625, 1034625, 314625, 3014625, 1304625, 3104625, 143625, 1043625, 413625, 4013625, 1403625, 4103625,
+ 341625, 3041625, 431625, 4031625, 3401625, 4301625, 1340625, 3140625, 1430625, 4130625, 3410625, 4310625,
+ 136425, 1036425, 316425, 3016425, 1306425, 3106425, 163425, 1063425, 613425, 6013425, 1603425, 6103425,
+ 361425, 3061425, 631425, 6031425, 3601425, 6301425, 1360425, 3160425, 1630425, 6130425, 3610425, 6310425,
+ 146325, 1046325, 416325, 4016325, 1406325, 4106325, 164325, 1064325, 614325, 6014325, 1604325, 6104325,
+ 461325, 4061325, 641325, 6041325, 4601325, 6401325, 1460325, 4160325, 1640325, 6140325, 4610325, 6410325,
+ 346125, 3046125, 436125, 4036125, 3406125, 4306125, 364125, 3064125, 634125, 6034125, 3604125, 6304125,
+ 463125, 4063125, 643125, 6043125, 4603125, 6403125, 3460125, 4360125, 3640125, 6340125, 4630125, 6430125,
+ 1346025, 3146025, 1436025, 4136025, 3416025, 4316025, 1364025, 3164025, 1634025, 6134025, 3614025, 6314025,
+ 1463025, 4163025, 1643025, 6143025, 4613025, 6413025, 3461025, 4361025, 3641025, 6341025, 4631025, 6431025,
+ 234615, 2034615, 324615, 3024615, 2304615, 3204615, 243615, 2043615, 423615, 4023615, 2403615, 4203615,
+ 342615, 3042615, 432615, 4032615, 3402615, 4302615, 2340615, 3240615, 2430615, 4230615, 3420615, 4320615,
+ 236415, 2036415, 326415, 3026415, 2306415, 3206415, 263415, 2063415, 623415, 6023415, 2603415, 6203415,
+ 362415, 3062415, 632415, 6032415, 3602415, 6302415, 2360415, 3260415, 2630415, 6230415, 3620415, 6320415,
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+ 563142, 5063142, 653142, 6053142, 5603142, 6503142, 3560142, 5360142, 3650142, 6350142, 5630142, 6530142,
+ 1356042, 3156042, 1536042, 5136042, 3516042, 5316042, 1365042, 3165042, 1635042, 6135042, 3615042, 6315042,
+ 1563042, 5163042, 1653042, 6153042, 5613042, 6513042, 3561042, 5361042, 3651042, 6351042, 5631042, 6531042,
+ 145632, 1045632, 415632, 4015632, 1405632, 4105632, 154632, 1054632, 514632, 5014632, 1504632, 5104632,
+ 451632, 4051632, 541632, 5041632, 4501632, 5401632, 1450632, 4150632, 1540632, 5140632, 4510632, 5410632,
+ 146532, 1046532, 416532, 4016532, 1406532, 4106532, 164532, 1064532, 614532, 6014532, 1604532, 6104532,
+ 461532, 4061532, 641532, 6041532, 4601532, 6401532, 1460532, 4160532, 1640532, 6140532, 4610532, 6410532,
+ 156432, 1056432, 516432, 5016432, 1506432, 5106432, 165432, 1065432, 615432, 6015432, 1605432, 6105432,
+ 561432, 5061432, 651432, 6051432, 5601432, 6501432, 1560432, 5160432, 1650432, 6150432, 5610432, 6510432,
+ 456132, 4056132, 546132, 5046132, 4506132, 5406132, 465132, 4065132, 645132, 6045132, 4605132, 6405132,
+ 564132, 5064132, 654132, 6054132, 5604132, 6504132, 4560132, 5460132, 4650132, 6450132, 5640132, 6540132,
+ 1456032, 4156032, 1546032, 5146032, 4516032, 5416032, 1465032, 4165032, 1645032, 6145032, 4615032, 6415032,
+ 1564032, 5164032, 1654032, 6154032, 5614032, 6514032, 4561032, 5461032, 4651032, 6451032, 5641032, 6541032,
+ 345612, 3045612, 435612, 4035612, 3405612, 4305612, 354612, 3054612, 534612, 5034612, 3504612, 5304612,
+ 453612, 4053612, 543612, 5043612, 4503612, 5403612, 3450612, 4350612, 3540612, 5340612, 4530612, 5430612,
+ 346512, 3046512, 436512, 4036512, 3406512, 4306512, 364512, 3064512, 634512, 6034512, 3604512, 6304512,
+ 463512, 4063512, 643512, 6043512, 4603512, 6403512, 3460512, 4360512, 3640512, 6340512, 4630512, 6430512,
+ 356412, 3056412, 536412, 5036412, 3506412, 5306412, 365412, 3065412, 635412, 6035412, 3605412, 6305412,
+ 563412, 5063412, 653412, 6053412, 5603412, 6503412, 3560412, 5360412, 3650412, 6350412, 5630412, 6530412,
+ 456312, 4056312, 546312, 5046312, 4506312, 5406312, 465312, 4065312, 645312, 6045312, 4605312, 6405312,
+ 564312, 5064312, 654312, 6054312, 5604312, 6504312, 4560312, 5460312, 4650312, 6450312, 5640312, 6540312,
+ 3456012, 4356012, 3546012, 5346012, 4536012, 5436012, 3465012, 4365012, 3645012, 6345012, 4635012, 6435012,
+ 3564012, 5364012, 3654012, 6354012, 5634012, 6534012, 4563012, 5463012, 4653012, 6453012, 5643012, 6543012,
+ 1345602, 3145602, 1435602, 4135602, 3415602, 4315602, 1354602, 3154602, 1534602, 5134602, 3514602, 5314602,
+ 1453602, 4153602, 1543602, 5143602, 4513602, 5413602, 3451602, 4351602, 3541602, 5341602, 4531602, 5431602,
+ 1346502, 3146502, 1436502, 4136502, 3416502, 4316502, 1364502, 3164502, 1634502, 6134502, 3614502, 6314502,
+ 1463502, 4163502, 1643502, 6143502, 4613502, 6413502, 3461502, 4361502, 3641502, 6341502, 4631502, 6431502,
+ 1356402, 3156402, 1536402, 5136402, 3516402, 5316402, 1365402, 3165402, 1635402, 6135402, 3615402, 6315402,
+ 1563402, 5163402, 1653402, 6153402, 5613402, 6513402, 3561402, 5361402, 3651402, 6351402, 5631402, 6531402,
+ 1456302, 4156302, 1546302, 5146302, 4516302, 5416302, 1465302, 4165302, 1645302, 6145302, 4615302, 6415302,
+ 1564302, 5164302, 1654302, 6154302, 5614302, 6514302, 4561302, 5461302, 4651302, 6451302, 5641302, 6541302,
+ 3456102, 4356102, 3546102, 5346102, 4536102, 5436102, 3465102, 4365102, 3645102, 6345102, 4635102, 6435102,
+ 3564102, 5364102, 3654102, 6354102, 5634102, 6534102, 4563102, 5463102, 4653102, 6453102, 5643102, 6543102,
+ 234561, 2034561, 324561, 3024561, 2304561, 3204561, 243561, 2043561, 423561, 4023561, 2403561, 4203561,
+ 342561, 3042561, 432561, 4032561, 3402561, 4302561, 2340561, 3240561, 2430561, 4230561, 3420561, 4320561,
+ 235461, 2035461, 325461, 3025461, 2305461, 3205461, 253461, 2053461, 523461, 5023461, 2503461, 5203461,
+ 352461, 3052461, 532461, 5032461, 3502461, 5302461, 2350461, 3250461, 2530461, 5230461, 3520461, 5320461,
+ 245361, 2045361, 425361, 4025361, 2405361, 4205361, 254361, 2054361, 524361, 5024361, 2504361, 5204361,
+ 452361, 4052361, 542361, 5042361, 4502361, 5402361, 2450361, 4250361, 2540361, 5240361, 4520361, 5420361,
+ 345261, 3045261, 435261, 4035261, 3405261, 4305261, 354261, 3054261, 534261, 5034261, 3504261, 5304261,
+ 453261, 4053261, 543261, 5043261, 4503261, 5403261, 3450261, 4350261, 3540261, 5340261, 4530261, 5430261,
+ 2345061, 3245061, 2435061, 4235061, 3425061, 4325061, 2354061, 3254061, 2534061, 5234061, 3524061, 5324061,
+ 2453061, 4253061, 2543061, 5243061, 4523061, 5423061, 3452061, 4352061, 3542061, 5342061, 4532061, 5432061,
+ 234651, 2034651, 324651, 3024651, 2304651, 3204651, 243651, 2043651, 423651, 4023651, 2403651, 4203651,
+ 342651, 3042651, 432651, 4032651, 3402651, 4302651, 2340651, 3240651, 2430651, 4230651, 3420651, 4320651,
+ 236451, 2036451, 326451, 3026451, 2306451, 3206451, 263451, 2063451, 623451, 6023451, 2603451, 6203451,
+ 362451, 3062451, 632451, 6032451, 3602451, 6302451, 2360451, 3260451, 2630451, 6230451, 3620451, 6320451,
+ 246351, 2046351, 426351, 4026351, 2406351, 4206351, 264351, 2064351, 624351, 6024351, 2604351, 6204351,
+ 462351, 4062351, 642351, 6042351, 4602351, 6402351, 2460351, 4260351, 2640351, 6240351, 4620351, 6420351,
+ 346251, 3046251, 436251, 4036251, 3406251, 4306251, 364251, 3064251, 634251, 6034251, 3604251, 6304251,
+ 463251, 4063251, 643251, 6043251, 4603251, 6403251, 3460251, 4360251, 3640251, 6340251, 4630251, 6430251,
+ 2346051, 3246051, 2436051, 4236051, 3426051, 4326051, 2364051, 3264051, 2634051, 6234051, 3624051, 6324051,
+ 2463051, 4263051, 2643051, 6243051, 4623051, 6423051, 3462051, 4362051, 3642051, 6342051, 4632051, 6432051,
+ 235641, 2035641, 325641, 3025641, 2305641, 3205641, 253641, 2053641, 523641, 5023641, 2503641, 5203641,
+ 352641, 3052641, 532641, 5032641, 3502641, 5302641, 2350641, 3250641, 2530641, 5230641, 3520641, 5320641,
+ 236541, 2036541, 326541, 3026541, 2306541, 3206541, 263541, 2063541, 623541, 6023541, 2603541, 6203541,
+ 362541, 3062541, 632541, 6032541, 3602541, 6302541, 2360541, 3260541, 2630541, 6230541, 3620541, 6320541,
+ 256341, 2056341, 526341, 5026341, 2506341, 5206341, 265341, 2065341, 625341, 6025341, 2605341, 6205341,
+ 562341, 5062341, 652341, 6052341, 5602341, 6502341, 2560341, 5260341, 2650341, 6250341, 5620341, 6520341,
+ 356241, 3056241, 536241, 5036241, 3506241, 5306241, 365241, 3065241, 635241, 6035241, 3605241, 6305241,
+ 563241, 5063241, 653241, 6053241, 5603241, 6503241, 3560241, 5360241, 3650241, 6350241, 5630241, 6530241,
+ 2356041, 3256041, 2536041, 5236041, 3526041, 5326041, 2365041, 3265041, 2635041, 6235041, 3625041, 6325041,
+ 2563041, 5263041, 2653041, 6253041, 5623041, 6523041, 3562041, 5362041, 3652041, 6352041, 5632041, 6532041,
+ 245631, 2045631, 425631, 4025631, 2405631, 4205631, 254631, 2054631, 524631, 5024631, 2504631, 5204631,
+ 452631, 4052631, 542631, 5042631, 4502631, 5402631, 2450631, 4250631, 2540631, 5240631, 4520631, 5420631,
+ 246531, 2046531, 426531, 4026531, 2406531, 4206531, 264531, 2064531, 624531, 6024531, 2604531, 6204531,
+ 462531, 4062531, 642531, 6042531, 4602531, 6402531, 2460531, 4260531, 2640531, 6240531, 4620531, 6420531,
+ 256431, 2056431, 526431, 5026431, 2506431, 5206431, 265431, 2065431, 625431, 6025431, 2605431, 6205431,
+ 562431, 5062431, 652431, 6052431, 5602431, 6502431, 2560431, 5260431, 2650431, 6250431, 5620431, 6520431,
+ 456231, 4056231, 546231, 5046231, 4506231, 5406231, 465231, 4065231, 645231, 6045231, 4605231, 6405231,
+ 564231, 5064231, 654231, 6054231, 5604231, 6504231, 4560231, 5460231, 4650231, 6450231, 5640231, 6540231,
+ 2456031, 4256031, 2546031, 5246031, 4526031, 5426031, 2465031, 4265031, 2645031, 6245031, 4625031, 6425031,
+ 2564031, 5264031, 2654031, 6254031, 5624031, 6524031, 4562031, 5462031, 4652031, 6452031, 5642031, 6542031,
+ 345621, 3045621, 435621, 4035621, 3405621, 4305621, 354621, 3054621, 534621, 5034621, 3504621, 5304621,
+ 453621, 4053621, 543621, 5043621, 4503621, 5403621, 3450621, 4350621, 3540621, 5340621, 4530621, 5430621,
+ 346521, 3046521, 436521, 4036521, 3406521, 4306521, 364521, 3064521, 634521, 6034521, 3604521, 6304521,
+ 463521, 4063521, 643521, 6043521, 4603521, 6403521, 3460521, 4360521, 3640521, 6340521, 4630521, 6430521,
+ 356421, 3056421, 536421, 5036421, 3506421, 5306421, 365421, 3065421, 635421, 6035421, 3605421, 6305421,
+ 563421, 5063421, 653421, 6053421, 5603421, 6503421, 3560421, 5360421, 3650421, 6350421, 5630421, 6530421,
+ 456321, 4056321, 546321, 5046321, 4506321, 5406321, 465321, 4065321, 645321, 6045321, 4605321, 6405321,
+ 564321, 5064321, 654321, 6054321, 5604321, 6504321, 4560321, 5460321, 4650321, 6450321, 5640321, 6540321,
+ 3456021, 4356021, 3546021, 5346021, 4536021, 5436021, 3465021, 4365021, 3645021, 6345021, 4635021, 6435021,
+ 3564021, 5364021, 3654021, 6354021, 5634021, 6534021, 4563021, 5463021, 4653021, 6453021, 5643021, 6543021,
+ 2345601, 3245601, 2435601, 4235601, 3425601, 4325601, 2354601, 3254601, 2534601, 5234601, 3524601, 5324601,
+ 2453601, 4253601, 2543601, 5243601, 4523601, 5423601, 3452601, 4352601, 3542601, 5342601, 4532601, 5432601,
+ 2346501, 3246501, 2436501, 4236501, 3426501, 4326501, 2364501, 3264501, 2634501, 6234501, 3624501, 6324501,
+ 2463501, 4263501, 2643501, 6243501, 4623501, 6423501, 3462501, 4362501, 3642501, 6342501, 4632501, 6432501,
+ 2356401, 3256401, 2536401, 5236401, 3526401, 5326401, 2365401, 3265401, 2635401, 6235401, 3625401, 6325401,
+ 2563401, 5263401, 2653401, 6253401, 5623401, 6523401, 3562401, 5362401, 3652401, 6352401, 5632401, 6532401,
+ 2456301, 4256301, 2546301, 5246301, 4526301, 5426301, 2465301, 4265301, 2645301, 6245301, 4625301, 6425301,
+ 2564301, 5264301, 2654301, 6254301, 5624301, 6524301, 4562301, 5462301, 4652301, 6452301, 5642301, 6542301,
+ 3456201, 4356201, 3546201, 5346201, 4536201, 5436201, 3465201, 4365201, 3645201, 6345201, 4635201, 6435201,
+ 3564201, 5364201, 3654201, 6354201, 5634201, 6534201, 4563201, 5463201, 4653201, 6453201, 5643201, 6543201,
+ 1234560, 2134560, 1324560, 3124560, 2314560, 3214560, 1243560, 2143560, 1423560, 4123560, 2413560, 4213560,
+ 1342560, 3142560, 1432560, 4132560, 3412560, 4312560, 2341560, 3241560, 2431560, 4231560, 3421560, 4321560,
+ 1235460, 2135460, 1325460, 3125460, 2315460, 3215460, 1253460, 2153460, 1523460, 5123460, 2513460, 5213460,
+ 1352460, 3152460, 1532460, 5132460, 3512460, 5312460, 2351460, 3251460, 2531460, 5231460, 3521460, 5321460,
+ 1245360, 2145360, 1425360, 4125360, 2415360, 4215360, 1254360, 2154360, 1524360, 5124360, 2514360, 5214360,
+ 1452360, 4152360, 1542360, 5142360, 4512360, 5412360, 2451360, 4251360, 2541360, 5241360, 4521360, 5421360,
+ 1345260, 3145260, 1435260, 4135260, 3415260, 4315260, 1354260, 3154260, 1534260, 5134260, 3514260, 5314260,
+ 1453260, 4153260, 1543260, 5143260, 4513260, 5413260, 3451260, 4351260, 3541260, 5341260, 4531260, 5431260,
+ 2345160, 3245160, 2435160, 4235160, 3425160, 4325160, 2354160, 3254160, 2534160, 5234160, 3524160, 5324160,
+ 2453160, 4253160, 2543160, 5243160, 4523160, 5423160, 3452160, 4352160, 3542160, 5342160, 4532160, 5432160,
+ 1234650, 2134650, 1324650, 3124650, 2314650, 3214650, 1243650, 2143650, 1423650, 4123650, 2413650, 4213650,
+ 1342650, 3142650, 1432650, 4132650, 3412650, 4312650, 2341650, 3241650, 2431650, 4231650, 3421650, 4321650,
+ 1236450, 2136450, 1326450, 3126450, 2316450, 3216450, 1263450, 2163450, 1623450, 6123450, 2613450, 6213450,
+ 1362450, 3162450, 1632450, 6132450, 3612450, 6312450, 2361450, 3261450, 2631450, 6231450, 3621450, 6321450,
+ 1246350, 2146350, 1426350, 4126350, 2416350, 4216350, 1264350, 2164350, 1624350, 6124350, 2614350, 6214350,
+ 1462350, 4162350, 1642350, 6142350, 4612350, 6412350, 2461350, 4261350, 2641350, 6241350, 4621350, 6421350,
+ 1346250, 3146250, 1436250, 4136250, 3416250, 4316250, 1364250, 3164250, 1634250, 6134250, 3614250, 6314250,
+ 1463250, 4163250, 1643250, 6143250, 4613250, 6413250, 3461250, 4361250, 3641250, 6341250, 4631250, 6431250,
+ 2346150, 3246150, 2436150, 4236150, 3426150, 4326150, 2364150, 3264150, 2634150, 6234150, 3624150, 6324150,
+ 2463150, 4263150, 2643150, 6243150, 4623150, 6423150, 3462150, 4362150, 3642150, 6342150, 4632150, 6432150,
+ 1235640, 2135640, 1325640, 3125640, 2315640, 3215640, 1253640, 2153640, 1523640, 5123640, 2513640, 5213640,
+ 1352640, 3152640, 1532640, 5132640, 3512640, 5312640, 2351640, 3251640, 2531640, 5231640, 3521640, 5321640,
+ 1236540, 2136540, 1326540, 3126540, 2316540, 3216540, 1263540, 2163540, 1623540, 6123540, 2613540, 6213540,
+ 1362540, 3162540, 1632540, 6132540, 3612540, 6312540, 2361540, 3261540, 2631540, 6231540, 3621540, 6321540,
+ 1256340, 2156340, 1526340, 5126340, 2516340, 5216340, 1265340, 2165340, 1625340, 6125340, 2615340, 6215340,
+ 1562340, 5162340, 1652340, 6152340, 5612340, 6512340, 2561340, 5261340, 2651340, 6251340, 5621340, 6521340,
+ 1356240, 3156240, 1536240, 5136240, 3516240, 5316240, 1365240, 3165240, 1635240, 6135240, 3615240, 6315240,
+ 1563240, 5163240, 1653240, 6153240, 5613240, 6513240, 3561240, 5361240, 3651240, 6351240, 5631240, 6531240,
+ 2356140, 3256140, 2536140, 5236140, 3526140, 5326140, 2365140, 3265140, 2635140, 6235140, 3625140, 6325140,
+ 2563140, 5263140, 2653140, 6253140, 5623140, 6523140, 3562140, 5362140, 3652140, 6352140, 5632140, 6532140,
+ 1245630, 2145630, 1425630, 4125630, 2415630, 4215630, 1254630, 2154630, 1524630, 5124630, 2514630, 5214630,
+ 1452630, 4152630, 1542630, 5142630, 4512630, 5412630, 2451630, 4251630, 2541630, 5241630, 4521630, 5421630,
+ 1246530, 2146530, 1426530, 4126530, 2416530, 4216530, 1264530, 2164530, 1624530, 6124530, 2614530, 6214530,
+ 1462530, 4162530, 1642530, 6142530, 4612530, 6412530, 2461530, 4261530, 2641530, 6241530, 4621530, 6421530,
+ 1256430, 2156430, 1526430, 5126430, 2516430, 5216430, 1265430, 2165430, 1625430, 6125430, 2615430, 6215430,
+ 1562430, 5162430, 1652430, 6152430, 5612430, 6512430, 2561430, 5261430, 2651430, 6251430, 5621430, 6521430,
+ 1456230, 4156230, 1546230, 5146230, 4516230, 5416230, 1465230, 4165230, 1645230, 6145230, 4615230, 6415230,
+ 1564230, 5164230, 1654230, 6154230, 5614230, 6514230, 4561230, 5461230, 4651230, 6451230, 5641230, 6541230,
+ 2456130, 4256130, 2546130, 5246130, 4526130, 5426130, 2465130, 4265130, 2645130, 6245130, 4625130, 6425130,
+ 2564130, 5264130, 2654130, 6254130, 5624130, 6524130, 4562130, 5462130, 4652130, 6452130, 5642130, 6542130,
+ 1345620, 3145620, 1435620, 4135620, 3415620, 4315620, 1354620, 3154620, 1534620, 5134620, 3514620, 5314620,
+ 1453620, 4153620, 1543620, 5143620, 4513620, 5413620, 3451620, 4351620, 3541620, 5341620, 4531620, 5431620,
+ 1346520, 3146520, 1436520, 4136520, 3416520, 4316520, 1364520, 3164520, 1634520, 6134520, 3614520, 6314520,
+ 1463520, 4163520, 1643520, 6143520, 4613520, 6413520, 3461520, 4361520, 3641520, 6341520, 4631520, 6431520,
+ 1356420, 3156420, 1536420, 5136420, 3516420, 5316420, 1365420, 3165420, 1635420, 6135420, 3615420, 6315420,
+ 1563420, 5163420, 1653420, 6153420, 5613420, 6513420, 3561420, 5361420, 3651420, 6351420, 5631420, 6531420,
+ 1456320, 4156320, 1546320, 5146320, 4516320, 5416320, 1465320, 4165320, 1645320, 6145320, 4615320, 6415320,
+ 1564320, 5164320, 1654320, 6154320, 5614320, 6514320, 4561320, 5461320, 4651320, 6451320, 5641320, 6541320,
+ 3456120, 4356120, 3546120, 5346120, 4536120, 5436120, 3465120, 4365120, 3645120, 6345120, 4635120, 6435120,
+ 3564120, 5364120, 3654120, 6354120, 5634120, 6534120, 4563120, 5463120, 4653120, 6453120, 5643120, 6543120,
+ 2345610, 3245610, 2435610, 4235610, 3425610, 4325610, 2354610, 3254610, 2534610, 5234610, 3524610, 5324610,
+ 2453610, 4253610, 2543610, 5243610, 4523610, 5423610, 3452610, 4352610, 3542610, 5342610, 4532610, 5432610,
+ 2346510, 3246510, 2436510, 4236510, 3426510, 4326510, 2364510, 3264510, 2634510, 6234510, 3624510, 6324510,
+ 2463510, 4263510, 2643510, 6243510, 4623510, 6423510, 3462510, 4362510, 3642510, 6342510, 4632510, 6432510,
+ 2356410, 3256410, 2536410, 5236410, 3526410, 5326410, 2365410, 3265410, 2635410, 6235410, 3625410, 6325410,
+ 2563410, 5263410, 2653410, 6253410, 5623410, 6523410, 3562410, 5362410, 3652410, 6352410, 5632410, 6532410,
+ 2456310, 4256310, 2546310, 5246310, 4526310, 5426310, 2465310, 4265310, 2645310, 6245310, 4625310, 6425310,
+ 2564310, 5264310, 2654310, 6254310, 5624310, 6524310, 4562310, 5462310, 4652310, 6452310, 5642310, 6542310,
+ 3456210, 4356210, 3546210, 5346210, 4536210, 5436210, 3465210, 4365210, 3645210, 6345210, 4635210, 6435210,
+ 3564210, 5364210, 3654210, 6354210, 5634210, 6534210, 4563210, 5463210, 4653210, 6453210, 5643210, 6543210
+ };
+ std::map<uint64_t, int> expected;
+ for (std::size_t i = 0; i < 5040; i++)
+ expected[pre_expected[i]] = 0; // flags are 0, everything is symmetric here
+
+ VERIFY(isDynGroup(group));
+ VERIFY_IS_EQUAL(group.size(), 5040u);
+ VERIFY_IS_EQUAL(group.globalFlags(), 0);
+ group.apply<checkIdx, int>(identity7, 0, found, expected);
+ VERIFY_IS_EQUAL(found.size(), 5040u);
+ }
+}
+
+static void test_tensor_epsilon()
+{
+ SGroup<AntiSymmetry<0,1>, AntiSymmetry<1,2>> sym;
+ Tensor<int, 3> epsilon(3,3,3);
+
+ epsilon.setZero();
+ sym(epsilon, 0, 1, 2) = 1;
+
+ for (int i = 0; i < 3; i++) {
+ for (int j = 0; j < 3; j++) {
+ for (int k = 0; k < 3; k++) {
+ VERIFY_IS_EQUAL((epsilon(i,j,k)), (- (j - i) * (k - j) * (i - k) / 2) );
+ }
+ }
+ }
+}
+
+static void test_tensor_sym()
+{
+ SGroup<Symmetry<0,1>, Symmetry<2,3>> sym;
+ Tensor<int, 4> t(10,10,10,10);
+
+ t.setZero();
+
+ for (int l = 0; l < 10; l++) {
+ for (int k = l; k < 10; k++) {
+ for (int j = 0; j < 10; j++) {
+ for (int i = j; i < 10; i++) {
+ sym(t, i, j, k, l) = (i + j) * (k + l);
+ }
+ }
+ }
+ }
+
+ for (int l = 0; l < 10; l++) {
+ for (int k = 0; k < 10; k++) {
+ for (int j = 0; j < 10; j++) {
+ for (int i = 0; i < 10; i++) {
+ VERIFY_IS_EQUAL((t(i, j, k, l)), ((i + j) * (k + l)));
+ }
+ }
+ }
+ }
+
+}
+
+static void test_tensor_asym()
+{
+ SGroup<AntiSymmetry<0,1>, AntiSymmetry<2,3>> sym;
+ Tensor<int, 4> t(10,10,10,10);
+
+ t.setZero();
+
+ for (int l = 0; l < 10; l++) {
+ for (int k = l + 1; k < 10; k++) {
+ for (int j = 0; j < 10; j++) {
+ for (int i = j + 1; i < 10; i++) {
+ sym(t, i, j, k, l) = ((i * j) + (k * l));
+ }
+ }
+ }
+ }
+
+ for (int l = 0; l < 10; l++) {
+ for (int k = 0; k < 10; k++) {
+ for (int j = 0; j < 10; j++) {
+ for (int i = 0; i < 10; i++) {
+ if (i < j && k < l)
+ VERIFY_IS_EQUAL((t(i, j, k, l)), (((i * j) + (k * l))));
+ else if (i > j && k > l)
+ VERIFY_IS_EQUAL((t(i, j, k, l)), (((i * j) + (k * l))));
+ else if (i < j && k > l)
+ VERIFY_IS_EQUAL((t(i, j, k, l)), (- ((i * j) + (k * l))));
+ else if (i > j && k < l)
+ VERIFY_IS_EQUAL((t(i, j, k, l)), (- ((i * j) + (k * l))));
+ else
+ VERIFY_IS_EQUAL((t(i, j, k, l)), 0);
+ }
+ }
+ }
+ }
+}
+
+static void test_tensor_dynsym()
+{
+ DynamicSGroup sym;
+ sym.addSymmetry(0,1);
+ sym.addSymmetry(2,3);
+ Tensor<int, 4> t(10,10,10,10);
+
+ t.setZero();
+
+ for (int l = 0; l < 10; l++) {
+ for (int k = l; k < 10; k++) {
+ for (int j = 0; j < 10; j++) {
+ for (int i = j; i < 10; i++) {
+ sym(t, i, j, k, l) = (i + j) * (k + l);
+ }
+ }
+ }
+ }
+
+ for (int l = 0; l < 10; l++) {
+ for (int k = 0; k < 10; k++) {
+ for (int j = 0; j < 10; j++) {
+ for (int i = 0; i < 10; i++) {
+ VERIFY_IS_EQUAL((t(i, j, k, l)), ((i + j) * (k + l)));
+ }
+ }
+ }
+ }
+}
+
+static void test_tensor_randacc()
+{
+ SGroup<Symmetry<0,1>, Symmetry<2,3>> sym;
+ Tensor<int, 4> t(10,10,10,10);
+
+ t.setZero();
+
+ // set elements 1 million times, that way we access the
+ // entire matrix
+ for (int n = 0; n < 1000000; n++) {
+ int i = rand() % 10;
+ int j = rand() % 10;
+ int k = rand() % 10;
+ int l = rand() % 10;
+ // only access those indices in a given order
+ if (i < j)
+ std::swap(i, j);
+ if (k < l)
+ std::swap(k, l);
+ sym(t, i, j, k, l) = (i + j) * (k + l);
+ }
+
+ for (int l = 0; l < 10; l++) {
+ for (int k = 0; k < 10; k++) {
+ for (int j = 0; j < 10; j++) {
+ for (int i = 0; i < 10; i++) {
+ VERIFY_IS_EQUAL((t(i, j, k, l)), ((i + j) * (k + l)));
+ }
+ }
+ }
+ }
+}
+
+EIGEN_DECLARE_TEST(cxx11_tensor_symmetry)
+{
+ CALL_SUBTEST(test_symgroups_static());
+ CALL_SUBTEST(test_symgroups_dynamic());
+ CALL_SUBTEST(test_symgroups_selection());
+ CALL_SUBTEST(test_tensor_epsilon());
+ CALL_SUBTEST(test_tensor_sym());
+ CALL_SUBTEST(test_tensor_asym());
+ CALL_SUBTEST(test_tensor_dynsym());
+ CALL_SUBTEST(test_tensor_randacc());
+}
+
+/*
+ * kate: space-indent on; indent-width 2; mixedindent off; indent-mode cstyle;
+ */
diff --git a/unsupported/test/cxx11_tensor_thread_local.cpp b/unsupported/test/cxx11_tensor_thread_local.cpp
new file mode 100644
index 0000000..7e866f6
--- /dev/null
+++ b/unsupported/test/cxx11_tensor_thread_local.cpp
@@ -0,0 +1,149 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#define EIGEN_USE_THREADS
+
+#include <iostream>
+#include <unordered_set>
+
+#include "main.h"
+#include <Eigen/CXX11/ThreadPool>
+
+struct Counter {
+ Counter() = default;
+
+ void inc() {
+ // Check that mutation happens only in a thread that created this counter.
+ VERIFY_IS_EQUAL(std::this_thread::get_id(), created_by);
+ counter_value++;
+ }
+ int value() { return counter_value; }
+
+ std::thread::id created_by;
+ int counter_value = 0;
+};
+
+struct InitCounter {
+ void operator()(Counter& counter) {
+ counter.created_by = std::this_thread::get_id();
+ }
+};
+
+void test_simple_thread_local() {
+ int num_threads = internal::random<int>(4, 32);
+ Eigen::ThreadPool thread_pool(num_threads);
+ Eigen::ThreadLocal<Counter, InitCounter> counter(num_threads, InitCounter());
+
+ int num_tasks = 3 * num_threads;
+ Eigen::Barrier barrier(num_tasks);
+
+ for (int i = 0; i < num_tasks; ++i) {
+ thread_pool.Schedule([&counter, &barrier]() {
+ Counter& local = counter.local();
+ local.inc();
+
+ std::this_thread::sleep_for(std::chrono::milliseconds(100));
+ barrier.Notify();
+ });
+ }
+
+ barrier.Wait();
+
+ counter.ForEach(
+ [](std::thread::id, Counter& cnt) { VERIFY_IS_EQUAL(cnt.value(), 3); });
+}
+
+void test_zero_sized_thread_local() {
+ Eigen::ThreadLocal<Counter, InitCounter> counter(0, InitCounter());
+
+ Counter& local = counter.local();
+ local.inc();
+
+ int total = 0;
+ counter.ForEach([&total](std::thread::id, Counter& cnt) {
+ total += cnt.value();
+ VERIFY_IS_EQUAL(cnt.value(), 1);
+ });
+
+ VERIFY_IS_EQUAL(total, 1);
+}
+
+// All thread local values fits into the lock-free storage.
+void test_large_number_of_tasks_no_spill() {
+ int num_threads = internal::random<int>(4, 32);
+ Eigen::ThreadPool thread_pool(num_threads);
+ Eigen::ThreadLocal<Counter, InitCounter> counter(num_threads, InitCounter());
+
+ int num_tasks = 10000;
+ Eigen::Barrier barrier(num_tasks);
+
+ for (int i = 0; i < num_tasks; ++i) {
+ thread_pool.Schedule([&counter, &barrier]() {
+ Counter& local = counter.local();
+ local.inc();
+ barrier.Notify();
+ });
+ }
+
+ barrier.Wait();
+
+ int total = 0;
+ std::unordered_set<std::thread::id> unique_threads;
+
+ counter.ForEach([&](std::thread::id id, Counter& cnt) {
+ total += cnt.value();
+ unique_threads.insert(id);
+ });
+
+ VERIFY_IS_EQUAL(total, num_tasks);
+ // Not all threads in a pool might be woken up to execute submitted tasks.
+ // Also thread_pool.Schedule() might use current thread if queue is full.
+ VERIFY_IS_EQUAL(
+ unique_threads.size() <= (static_cast<size_t>(num_threads + 1)), true);
+}
+
+// Lock free thread local storage is too small to fit all the unique threads,
+// and it spills to a map guarded by a mutex.
+void test_large_number_of_tasks_with_spill() {
+ int num_threads = internal::random<int>(4, 32);
+ Eigen::ThreadPool thread_pool(num_threads);
+ Eigen::ThreadLocal<Counter, InitCounter> counter(1, InitCounter());
+
+ int num_tasks = 10000;
+ Eigen::Barrier barrier(num_tasks);
+
+ for (int i = 0; i < num_tasks; ++i) {
+ thread_pool.Schedule([&counter, &barrier]() {
+ Counter& local = counter.local();
+ local.inc();
+ barrier.Notify();
+ });
+ }
+
+ barrier.Wait();
+
+ int total = 0;
+ std::unordered_set<std::thread::id> unique_threads;
+
+ counter.ForEach([&](std::thread::id id, Counter& cnt) {
+ total += cnt.value();
+ unique_threads.insert(id);
+ });
+
+ VERIFY_IS_EQUAL(total, num_tasks);
+ // Not all threads in a pool might be woken up to execute submitted tasks.
+ // Also thread_pool.Schedule() might use current thread if queue is full.
+ VERIFY_IS_EQUAL(
+ unique_threads.size() <= (static_cast<size_t>(num_threads + 1)), true);
+}
+
+EIGEN_DECLARE_TEST(cxx11_tensor_thread_local) {
+ CALL_SUBTEST(test_simple_thread_local());
+ CALL_SUBTEST(test_zero_sized_thread_local());
+ CALL_SUBTEST(test_large_number_of_tasks_no_spill());
+ CALL_SUBTEST(test_large_number_of_tasks_with_spill());
+}
diff --git a/unsupported/test/cxx11_tensor_thread_pool.cpp b/unsupported/test/cxx11_tensor_thread_pool.cpp
new file mode 100644
index 0000000..b772a1d
--- /dev/null
+++ b/unsupported/test/cxx11_tensor_thread_pool.cpp
@@ -0,0 +1,721 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#define EIGEN_USE_THREADS
+
+
+#include "main.h"
+#include <iostream>
+#include <Eigen/CXX11/Tensor>
+
+using Eigen::Tensor;
+
+class TestAllocator : public Allocator {
+ public:
+ ~TestAllocator() EIGEN_OVERRIDE {}
+ EIGEN_DEVICE_FUNC void* allocate(size_t num_bytes) const EIGEN_OVERRIDE {
+ const_cast<TestAllocator*>(this)->alloc_count_++;
+ return internal::aligned_malloc(num_bytes);
+ }
+ EIGEN_DEVICE_FUNC void deallocate(void* buffer) const EIGEN_OVERRIDE {
+ const_cast<TestAllocator*>(this)->dealloc_count_++;
+ internal::aligned_free(buffer);
+ }
+
+ int alloc_count() const { return alloc_count_; }
+ int dealloc_count() const { return dealloc_count_; }
+
+ private:
+ int alloc_count_ = 0;
+ int dealloc_count_ = 0;
+};
+
+void test_multithread_elementwise()
+{
+ Tensor<float, 3> in1(200, 30, 70);
+ Tensor<float, 3> in2(200, 30, 70);
+ Tensor<double, 3> out(200, 30, 70);
+
+ in1.setRandom();
+ in2.setRandom();
+
+ Eigen::ThreadPool tp(internal::random<int>(3, 11));
+ Eigen::ThreadPoolDevice thread_pool_device(&tp, internal::random<int>(3, 11));
+ out.device(thread_pool_device) = (in1 + in2 * 3.14f).cast<double>();
+
+ for (int i = 0; i < 200; ++i) {
+ for (int j = 0; j < 30; ++j) {
+ for (int k = 0; k < 70; ++k) {
+ VERIFY_IS_APPROX(out(i, j, k), static_cast<double>(in1(i, j, k) + in2(i, j, k) * 3.14f));
+ }
+ }
+ }
+}
+
+void test_async_multithread_elementwise()
+{
+ Tensor<float, 3> in1(200, 30, 70);
+ Tensor<float, 3> in2(200, 30, 70);
+ Tensor<double, 3> out(200, 30, 70);
+
+ in1.setRandom();
+ in2.setRandom();
+
+ Eigen::ThreadPool tp(internal::random<int>(3, 11));
+ Eigen::ThreadPoolDevice thread_pool_device(&tp, internal::random<int>(3, 11));
+
+ Eigen::Barrier b(1);
+ out.device(thread_pool_device, [&b]() { b.Notify(); }) = (in1 + in2 * 3.14f).cast<double>();
+ b.Wait();
+
+ for (int i = 0; i < 200; ++i) {
+ for (int j = 0; j < 30; ++j) {
+ for (int k = 0; k < 70; ++k) {
+ VERIFY_IS_APPROX(out(i, j, k), static_cast<double>(in1(i, j, k) + in2(i, j, k) * 3.14f));
+ }
+ }
+ }
+}
+
+void test_multithread_compound_assignment()
+{
+ Tensor<float, 3> in1(2,3,7);
+ Tensor<float, 3> in2(2,3,7);
+ Tensor<float, 3> out(2,3,7);
+
+ in1.setRandom();
+ in2.setRandom();
+
+ Eigen::ThreadPool tp(internal::random<int>(3, 11));
+ Eigen::ThreadPoolDevice thread_pool_device(&tp, internal::random<int>(3, 11));
+ out.device(thread_pool_device) = in1;
+ out.device(thread_pool_device) += in2 * 3.14f;
+
+ for (int i = 0; i < 2; ++i) {
+ for (int j = 0; j < 3; ++j) {
+ for (int k = 0; k < 7; ++k) {
+ VERIFY_IS_APPROX(out(i,j,k), in1(i,j,k) + in2(i,j,k) * 3.14f);
+ }
+ }
+ }
+}
+
+template<int DataLayout>
+void test_multithread_contraction()
+{
+ Tensor<float, 4, DataLayout> t_left(30, 50, 37, 31);
+ Tensor<float, 5, DataLayout> t_right(37, 31, 70, 2, 10);
+ Tensor<float, 5, DataLayout> t_result(30, 50, 70, 2, 10);
+
+ t_left.setRandom();
+ t_right.setRandom();
+
+ // this contraction should be equivalent to a single matrix multiplication
+ typedef Tensor<float, 1>::DimensionPair DimPair;
+ Eigen::array<DimPair, 2> dims({{DimPair(2, 0), DimPair(3, 1)}});
+
+ typedef Map<Matrix<float, Dynamic, Dynamic, DataLayout>> MapXf;
+ MapXf m_left(t_left.data(), 1500, 1147);
+ MapXf m_right(t_right.data(), 1147, 1400);
+ Matrix<float, Dynamic, Dynamic, DataLayout> m_result(1500, 1400);
+
+ Eigen::ThreadPool tp(4);
+ Eigen::ThreadPoolDevice thread_pool_device(&tp, 4);
+
+ // compute results by separate methods
+ t_result.device(thread_pool_device) = t_left.contract(t_right, dims);
+ m_result = m_left * m_right;
+
+ for (ptrdiff_t i = 0; i < t_result.size(); i++) {
+ VERIFY(&t_result.data()[i] != &m_result.data()[i]);
+ if (fabsf(t_result(i) - m_result(i)) < 1e-4f) {
+ continue;
+ }
+ if (Eigen::internal::isApprox(t_result(i), m_result(i), 1e-4f)) {
+ continue;
+ }
+ std::cout << "mismatch detected at index " << i << ": " << t_result(i)
+ << " vs " << m_result(i) << std::endl;
+ assert(false);
+ }
+}
+
+template<int DataLayout>
+void test_contraction_corner_cases()
+{
+ Tensor<float, 2, DataLayout> t_left(32, 500);
+ Tensor<float, 2, DataLayout> t_right(32, 28*28);
+ Tensor<float, 2, DataLayout> t_result(500, 28*28);
+
+ t_left = (t_left.constant(-0.5f) + t_left.random()) * 2.0f;
+ t_right = (t_right.constant(-0.6f) + t_right.random()) * 2.0f;
+ t_result = t_result.constant(NAN);
+
+ // this contraction should be equivalent to a single matrix multiplication
+ typedef Tensor<float, 1>::DimensionPair DimPair;
+ Eigen::array<DimPair, 1> dims{{DimPair(0, 0)}};
+
+ typedef Map<Matrix<float, Dynamic, Dynamic, DataLayout>> MapXf;
+ MapXf m_left(t_left.data(), 32, 500);
+ MapXf m_right(t_right.data(), 32, 28*28);
+ Matrix<float, Dynamic, Dynamic, DataLayout> m_result(500, 28*28);
+
+ Eigen::ThreadPool tp(12);
+ Eigen::ThreadPoolDevice thread_pool_device(&tp, 12);
+
+ // compute results by separate methods
+ t_result.device(thread_pool_device) = t_left.contract(t_right, dims);
+ m_result = m_left.transpose() * m_right;
+
+ for (ptrdiff_t i = 0; i < t_result.size(); i++) {
+ assert(!(numext::isnan)(t_result.data()[i]));
+ if (fabsf(t_result.data()[i] - m_result.data()[i]) >= 1e-4f) {
+ std::cout << "mismatch detected at index " << i << " : " << t_result.data()[i] << " vs " << m_result.data()[i] << std::endl;
+ assert(false);
+ }
+ }
+
+ t_left.resize(32, 1);
+ t_left = (t_left.constant(-0.5f) + t_left.random()) * 2.0f;
+ t_result.resize (1, 28*28);
+ t_result = t_result.constant(NAN);
+ t_result.device(thread_pool_device) = t_left.contract(t_right, dims);
+ new(&m_left) MapXf(t_left.data(), 32, 1);
+ m_result = m_left.transpose() * m_right;
+ for (ptrdiff_t i = 0; i < t_result.size(); i++) {
+ assert(!(numext::isnan)(t_result.data()[i]));
+ if (fabsf(t_result.data()[i] - m_result.data()[i]) >= 1e-4f) {
+ std::cout << "mismatch detected: " << t_result.data()[i] << " vs " << m_result.data()[i] << std::endl;
+ assert(false);
+ }
+ }
+
+ t_left.resize(32, 500);
+ t_right.resize(32, 4);
+ t_left = (t_left.constant(-0.5f) + t_left.random()) * 2.0f;
+ t_right = (t_right.constant(-0.6f) + t_right.random()) * 2.0f;
+ t_result.resize (500, 4);
+ t_result = t_result.constant(NAN);
+ t_result.device(thread_pool_device) = t_left.contract(t_right, dims);
+ new(&m_left) MapXf(t_left.data(), 32, 500);
+ new(&m_right) MapXf(t_right.data(), 32, 4);
+ m_result = m_left.transpose() * m_right;
+ for (ptrdiff_t i = 0; i < t_result.size(); i++) {
+ assert(!(numext::isnan)(t_result.data()[i]));
+ if (fabsf(t_result.data()[i] - m_result.data()[i]) >= 1e-4f) {
+ std::cout << "mismatch detected: " << t_result.data()[i] << " vs " << m_result.data()[i] << std::endl;
+ assert(false);
+ }
+ }
+
+ t_left.resize(32, 1);
+ t_right.resize(32, 4);
+ t_left = (t_left.constant(-0.5f) + t_left.random()) * 2.0f;
+ t_right = (t_right.constant(-0.6f) + t_right.random()) * 2.0f;
+ t_result.resize (1, 4);
+ t_result = t_result.constant(NAN);
+ t_result.device(thread_pool_device) = t_left.contract(t_right, dims);
+ new(&m_left) MapXf(t_left.data(), 32, 1);
+ new(&m_right) MapXf(t_right.data(), 32, 4);
+ m_result = m_left.transpose() * m_right;
+ for (ptrdiff_t i = 0; i < t_result.size(); i++) {
+ assert(!(numext::isnan)(t_result.data()[i]));
+ if (fabsf(t_result.data()[i] - m_result.data()[i]) >= 1e-4f) {
+ std::cout << "mismatch detected: " << t_result.data()[i] << " vs " << m_result.data()[i] << std::endl;
+ assert(false);
+ }
+ }
+}
+
+template<int DataLayout>
+void test_multithread_contraction_agrees_with_singlethread() {
+ int contract_size = internal::random<int>(1, 5000);
+
+ Tensor<float, 3, DataLayout> left(internal::random<int>(1, 80),
+ contract_size,
+ internal::random<int>(1, 100));
+
+ Tensor<float, 4, DataLayout> right(internal::random<int>(1, 25),
+ internal::random<int>(1, 37),
+ contract_size,
+ internal::random<int>(1, 51));
+
+ left.setRandom();
+ right.setRandom();
+
+ // add constants to shift values away from 0 for more precision
+ left += left.constant(1.5f);
+ right += right.constant(1.5f);
+
+ typedef Tensor<float, 1>::DimensionPair DimPair;
+ Eigen::array<DimPair, 1> dims({{DimPair(1, 2)}});
+
+ Eigen::ThreadPool tp(internal::random<int>(2, 11));
+ Eigen::ThreadPoolDevice thread_pool_device(&tp, internal::random<int>(2, 11));
+
+ Tensor<float, 5, DataLayout> st_result;
+ st_result = left.contract(right, dims);
+
+ Tensor<float, 5, DataLayout> tp_result(st_result.dimensions());
+ tp_result.device(thread_pool_device) = left.contract(right, dims);
+
+ VERIFY(dimensions_match(st_result.dimensions(), tp_result.dimensions()));
+ for (ptrdiff_t i = 0; i < st_result.size(); i++) {
+ // if both of the values are very small, then do nothing (because the test will fail
+ // due to numerical precision issues when values are small)
+ if (numext::abs(st_result.data()[i] - tp_result.data()[i]) >= 1e-4f) {
+ VERIFY_IS_APPROX(st_result.data()[i], tp_result.data()[i]);
+ }
+ }
+}
+
+// Apply Sqrt to all output elements.
+struct SqrtOutputKernel {
+ template <typename Index, typename Scalar>
+ EIGEN_ALWAYS_INLINE void operator()(
+ const internal::blas_data_mapper<Scalar, Index, ColMajor>& output_mapper,
+ const TensorContractionParams&, Index, Index, Index num_rows,
+ Index num_cols) const {
+ for (int i = 0; i < num_rows; ++i) {
+ for (int j = 0; j < num_cols; ++j) {
+ output_mapper(i, j) = std::sqrt(output_mapper(i, j));
+ }
+ }
+ }
+};
+
+template <int DataLayout>
+static void test_multithread_contraction_with_output_kernel() {
+ typedef Tensor<float, 1>::DimensionPair DimPair;
+
+ const int num_threads = internal::random<int>(2, 11);
+ ThreadPool threads(num_threads);
+ Eigen::ThreadPoolDevice device(&threads, num_threads);
+
+ Tensor<float, 4, DataLayout> t_left(30, 50, 8, 31);
+ Tensor<float, 5, DataLayout> t_right(8, 31, 7, 20, 10);
+ Tensor<float, 5, DataLayout> t_result(30, 50, 7, 20, 10);
+
+ t_left.setRandom();
+ t_right.setRandom();
+ // Put trash in mat4 to verify contraction clears output memory.
+ t_result.setRandom();
+
+ // Add a little offset so that the results won't be close to zero.
+ t_left += t_left.constant(1.0f);
+ t_right += t_right.constant(1.0f);
+
+ typedef Map<Eigen::Matrix<float, Dynamic, Dynamic, DataLayout>> MapXf;
+ MapXf m_left(t_left.data(), 1500, 248);
+ MapXf m_right(t_right.data(), 248, 1400);
+ Eigen::Matrix<float, Dynamic, Dynamic, DataLayout> m_result(1500, 1400);
+
+ // this contraction should be equivalent to a single matrix multiplication
+ Eigen::array<DimPair, 2> dims({{DimPair(2, 0), DimPair(3, 1)}});
+
+ // compute results by separate methods
+ t_result.device(device) = t_left.contract(t_right, dims, SqrtOutputKernel());
+
+ m_result = m_left * m_right;
+
+ for (Index i = 0; i < t_result.dimensions().TotalSize(); i++) {
+ VERIFY(&t_result.data()[i] != &m_result.data()[i]);
+ VERIFY_IS_APPROX(t_result.data()[i], std::sqrt(m_result.data()[i]));
+ }
+}
+
+template<int DataLayout>
+void test_async_multithread_contraction_agrees_with_singlethread()
+{
+ int contract_size = internal::random<int>(100, 500);
+
+ Tensor<float, 3, DataLayout> left(internal::random<int>(10, 40),
+ contract_size,
+ internal::random<int>(10, 40));
+
+ Tensor<float, 4, DataLayout> right(
+ internal::random<int>(1, 20), internal::random<int>(1, 20), contract_size,
+ internal::random<int>(1, 20));
+
+ left.setRandom();
+ right.setRandom();
+
+ // add constants to shift values away from 0 for more precision
+ left += left.constant(1.5f);
+ right += right.constant(1.5f);
+
+ typedef Tensor<float, 1>::DimensionPair DimPair;
+ Eigen::array<DimPair, 1> dims({{DimPair(1, 2)}});
+
+ Eigen::ThreadPool tp(internal::random<int>(2, 11));
+ Eigen::ThreadPoolDevice thread_pool_device(&tp, internal::random<int>(8, 32));
+
+ Tensor<float, 5, DataLayout> st_result;
+ st_result = left.contract(right, dims);
+
+ Tensor<float, 5, DataLayout> tp_result(st_result.dimensions());
+
+ Eigen::Barrier barrier(1);
+ tp_result.device(thread_pool_device, [&barrier]() { barrier.Notify(); }) =
+ left.contract(right, dims);
+ barrier.Wait();
+
+ VERIFY(dimensions_match(st_result.dimensions(), tp_result.dimensions()));
+ for (ptrdiff_t i = 0; i < st_result.size(); i++) {
+ // if both of the values are very small, then do nothing (because the test
+ // will fail due to numerical precision issues when values are small)
+ if (numext::abs(st_result.data()[i] - tp_result.data()[i]) >= 1e-4f) {
+ VERIFY_IS_APPROX(st_result.data()[i], tp_result.data()[i]);
+ }
+ }
+}
+
+// We are triggering 'evalShardedByInnerDim' optimization.
+template <int DataLayout>
+static void test_sharded_by_inner_dim_contraction()
+{
+ typedef Tensor<float, 1>::DimensionPair DimPair;
+
+ const int num_threads = internal::random<int>(4, 16);
+ ThreadPool threads(num_threads);
+ Eigen::ThreadPoolDevice device(&threads, num_threads);
+
+ Tensor<float, 2, DataLayout> t_left(2, 10000);
+ Tensor<float, 2, DataLayout> t_right(10000, 10);
+ Tensor<float, 2, DataLayout> t_result(2, 10);
+
+ t_left.setRandom();
+ t_right.setRandom();
+ // Put trash in t_result to verify contraction clears output memory.
+ t_result.setRandom();
+
+ // Add a little offset so that the results won't be close to zero.
+ t_left += t_left.constant(1.0f);
+ t_right += t_right.constant(1.0f);
+
+ typedef Map<Eigen::Matrix<float, Dynamic, Dynamic, DataLayout>> MapXf;
+ MapXf m_left(t_left.data(), 2, 10000);
+ MapXf m_right(t_right.data(), 10000, 10);
+ Eigen::Matrix<float, Dynamic, Dynamic, DataLayout> m_result(2, 10);
+
+ // this contraction should be equivalent to a single matrix multiplication
+ Eigen::array<DimPair, 1> dims({{DimPair(1, 0)}});
+
+ // compute results by separate methods
+ t_result.device(device) = t_left.contract(t_right, dims);
+ m_result = m_left * m_right;
+
+ for (Index i = 0; i < t_result.dimensions().TotalSize(); i++) {
+ VERIFY_IS_APPROX(t_result.data()[i], m_result.data()[i]);
+ }
+}
+
+// We are triggering 'evalShardedByInnerDim' optimization with output kernel.
+template <int DataLayout>
+static void test_sharded_by_inner_dim_contraction_with_output_kernel()
+{
+ typedef Tensor<float, 1>::DimensionPair DimPair;
+
+ const int num_threads = internal::random<int>(4, 16);
+ ThreadPool threads(num_threads);
+ Eigen::ThreadPoolDevice device(&threads, num_threads);
+
+ Tensor<float, 2, DataLayout> t_left(2, 10000);
+ Tensor<float, 2, DataLayout> t_right(10000, 10);
+ Tensor<float, 2, DataLayout> t_result(2, 10);
+
+ t_left.setRandom();
+ t_right.setRandom();
+ // Put trash in t_result to verify contraction clears output memory.
+ t_result.setRandom();
+
+ // Add a little offset so that the results won't be close to zero.
+ t_left += t_left.constant(1.0f);
+ t_right += t_right.constant(1.0f);
+
+ typedef Map<Eigen::Matrix<float, Dynamic, Dynamic, DataLayout>> MapXf;
+ MapXf m_left(t_left.data(), 2, 10000);
+ MapXf m_right(t_right.data(), 10000, 10);
+ Eigen::Matrix<float, Dynamic, Dynamic, DataLayout> m_result(2, 10);
+
+ // this contraction should be equivalent to a single matrix multiplication
+ Eigen::array<DimPair, 1> dims({{DimPair(1, 0)}});
+
+ // compute results by separate methods
+ t_result.device(device) = t_left.contract(t_right, dims, SqrtOutputKernel());
+ m_result = m_left * m_right;
+
+ for (Index i = 0; i < t_result.dimensions().TotalSize(); i++) {
+ VERIFY_IS_APPROX(t_result.data()[i], std::sqrt(m_result.data()[i]));
+ }
+}
+
+// We are triggering 'evalShardedByInnerDim' optimization.
+template <int DataLayout>
+static void test_async_sharded_by_inner_dim_contraction()
+{
+ typedef Tensor<float, 1>::DimensionPair DimPair;
+
+ const int num_threads = internal::random<int>(4, 16);
+ ThreadPool threads(num_threads);
+ Eigen::ThreadPoolDevice device(&threads, num_threads);
+
+ Tensor<float, 2, DataLayout> t_left(2, 10000);
+ Tensor<float, 2, DataLayout> t_right(10000, 10);
+ Tensor<float, 2, DataLayout> t_result(2, 10);
+
+ t_left.setRandom();
+ t_right.setRandom();
+ // Put trash in t_result to verify contraction clears output memory.
+ t_result.setRandom();
+
+ // Add a little offset so that the results won't be close to zero.
+ t_left += t_left.constant(1.0f);
+ t_right += t_right.constant(1.0f);
+
+ typedef Map<Eigen::Matrix<float, Dynamic, Dynamic, DataLayout>> MapXf;
+ MapXf m_left(t_left.data(), 2, 10000);
+ MapXf m_right(t_right.data(), 10000, 10);
+ Eigen::Matrix<float, Dynamic, Dynamic, DataLayout> m_result(2, 10);
+
+ // this contraction should be equivalent to a single matrix multiplication
+ Eigen::array<DimPair, 1> dims({{DimPair(1, 0)}});
+
+ // compute results by separate methods
+ Eigen::Barrier barrier(1);
+ t_result.device(device, [&barrier]() { barrier.Notify(); }) =
+ t_left.contract(t_right, dims);
+ barrier.Wait();
+
+ m_result = m_left * m_right;
+
+ for (Index i = 0; i < t_result.dimensions().TotalSize(); i++) {
+ VERIFY_IS_APPROX(t_result.data()[i], m_result.data()[i]);
+ }
+}
+
+// We are triggering 'evalShardedByInnerDim' optimization with output kernel.
+template <int DataLayout>
+static void test_async_sharded_by_inner_dim_contraction_with_output_kernel()
+{
+ typedef Tensor<float, 1>::DimensionPair DimPair;
+
+ const int num_threads = internal::random<int>(4, 16);
+ ThreadPool threads(num_threads);
+ Eigen::ThreadPoolDevice device(&threads, num_threads);
+
+ Tensor<float, 2, DataLayout> t_left(2, 10000);
+ Tensor<float, 2, DataLayout> t_right(10000, 10);
+ Tensor<float, 2, DataLayout> t_result(2, 10);
+
+ t_left.setRandom();
+ t_right.setRandom();
+ // Put trash in t_result to verify contraction clears output memory.
+ t_result.setRandom();
+
+ // Add a little offset so that the results won't be close to zero.
+ t_left += t_left.constant(1.0f);
+ t_right += t_right.constant(1.0f);
+
+ typedef Map<Eigen::Matrix<float, Dynamic, Dynamic, DataLayout>> MapXf;
+ MapXf m_left(t_left.data(), 2, 10000);
+ MapXf m_right(t_right.data(), 10000, 10);
+ Eigen::Matrix<float, Dynamic, Dynamic, DataLayout> m_result(2, 10);
+
+ // this contraction should be equivalent to a single matrix multiplication
+ Eigen::array<DimPair, 1> dims({{DimPair(1, 0)}});
+
+ // compute results by separate methods
+ Eigen::Barrier barrier(1);
+ t_result.device(device, [&barrier]() { barrier.Notify(); }) =
+ t_left.contract(t_right, dims, SqrtOutputKernel());
+ barrier.Wait();
+ m_result = m_left * m_right;
+
+ for (Index i = 0; i < t_result.dimensions().TotalSize(); i++) {
+ VERIFY_IS_APPROX(t_result.data()[i], std::sqrt(m_result.data()[i]));
+ }
+}
+
+template<int DataLayout>
+void test_full_contraction() {
+ int contract_size1 = internal::random<int>(1, 500);
+ int contract_size2 = internal::random<int>(1, 500);
+
+ Tensor<float, 2, DataLayout> left(contract_size1,
+ contract_size2);
+ Tensor<float, 2, DataLayout> right(contract_size1,
+ contract_size2);
+ left.setRandom();
+ right.setRandom();
+
+ // add constants to shift values away from 0 for more precision
+ left += left.constant(1.5f);
+ right += right.constant(1.5f);
+
+ typedef Tensor<float, 2>::DimensionPair DimPair;
+ Eigen::array<DimPair, 2> dims({{DimPair(0, 0), DimPair(1, 1)}});
+
+ Eigen::ThreadPool tp(internal::random<int>(2, 11));
+ Eigen::ThreadPoolDevice thread_pool_device(&tp, internal::random<int>(2, 11));
+
+ Tensor<float, 0, DataLayout> st_result;
+ st_result = left.contract(right, dims);
+
+ Tensor<float, 0, DataLayout> tp_result;
+ tp_result.device(thread_pool_device) = left.contract(right, dims);
+
+ VERIFY(dimensions_match(st_result.dimensions(), tp_result.dimensions()));
+ // if both of the values are very small, then do nothing (because the test will fail
+ // due to numerical precision issues when values are small)
+ if (numext::abs(st_result() - tp_result()) >= 1e-4f) {
+ VERIFY_IS_APPROX(st_result(), tp_result());
+ }
+}
+
+template<int DataLayout>
+void test_multithreaded_reductions() {
+ const int num_threads = internal::random<int>(3, 11);
+ ThreadPool thread_pool(num_threads);
+ Eigen::ThreadPoolDevice thread_pool_device(&thread_pool, num_threads);
+
+ const int num_rows = internal::random<int>(13, 732);
+ const int num_cols = internal::random<int>(13, 732);
+ Tensor<float, 2, DataLayout> t1(num_rows, num_cols);
+ t1.setRandom();
+
+ Tensor<float, 0, DataLayout> full_redux;
+ full_redux = t1.sum();
+
+ Tensor<float, 0, DataLayout> full_redux_tp;
+ full_redux_tp.device(thread_pool_device) = t1.sum();
+
+ // Check that the single threaded and the multi threaded reductions return
+ // the same result.
+ VERIFY_IS_APPROX(full_redux(), full_redux_tp());
+}
+
+
+void test_memcpy() {
+
+ for (int i = 0; i < 5; ++i) {
+ const int num_threads = internal::random<int>(3, 11);
+ Eigen::ThreadPool tp(num_threads);
+ Eigen::ThreadPoolDevice thread_pool_device(&tp, num_threads);
+
+ const int size = internal::random<int>(13, 7632);
+ Tensor<float, 1> t1(size);
+ t1.setRandom();
+ std::vector<float> result(size);
+ thread_pool_device.memcpy(&result[0], t1.data(), size*sizeof(float));
+ for (int j = 0; j < size; j++) {
+ VERIFY_IS_EQUAL(t1(j), result[j]);
+ }
+ }
+}
+
+
+void test_multithread_random()
+{
+ Eigen::ThreadPool tp(2);
+ Eigen::ThreadPoolDevice device(&tp, 2);
+ Tensor<float, 1> t(1 << 20);
+ t.device(device) = t.random<Eigen::internal::NormalRandomGenerator<float>>();
+}
+
+template<int DataLayout>
+void test_multithread_shuffle(Allocator* allocator)
+{
+ Tensor<float, 4, DataLayout> tensor(17,5,7,11);
+ tensor.setRandom();
+
+ const int num_threads = internal::random<int>(2, 11);
+ ThreadPool threads(num_threads);
+ Eigen::ThreadPoolDevice device(&threads, num_threads, allocator);
+
+ Tensor<float, 4, DataLayout> shuffle(7,5,11,17);
+ array<ptrdiff_t, 4> shuffles = {{2,1,3,0}};
+ shuffle.device(device) = tensor.shuffle(shuffles);
+
+ for (int i = 0; i < 17; ++i) {
+ for (int j = 0; j < 5; ++j) {
+ for (int k = 0; k < 7; ++k) {
+ for (int l = 0; l < 11; ++l) {
+ VERIFY_IS_EQUAL(tensor(i,j,k,l), shuffle(k,j,l,i));
+ }
+ }
+ }
+ }
+}
+
+void test_threadpool_allocate(TestAllocator* allocator)
+{
+ const int num_threads = internal::random<int>(2, 11);
+ const int num_allocs = internal::random<int>(2, 11);
+ ThreadPool threads(num_threads);
+ Eigen::ThreadPoolDevice device(&threads, num_threads, allocator);
+
+ for (int a = 0; a < num_allocs; ++a) {
+ void* ptr = device.allocate(512);
+ device.deallocate(ptr);
+ }
+ VERIFY(allocator != NULL);
+ VERIFY_IS_EQUAL(allocator->alloc_count(), num_allocs);
+ VERIFY_IS_EQUAL(allocator->dealloc_count(), num_allocs);
+}
+
+EIGEN_DECLARE_TEST(cxx11_tensor_thread_pool)
+{
+ CALL_SUBTEST_1(test_multithread_elementwise());
+ CALL_SUBTEST_1(test_async_multithread_elementwise());
+ CALL_SUBTEST_1(test_multithread_compound_assignment());
+
+ CALL_SUBTEST_2(test_multithread_contraction<ColMajor>());
+ CALL_SUBTEST_2(test_multithread_contraction<RowMajor>());
+
+ CALL_SUBTEST_3(test_multithread_contraction_agrees_with_singlethread<ColMajor>());
+ CALL_SUBTEST_3(test_multithread_contraction_agrees_with_singlethread<RowMajor>());
+ CALL_SUBTEST_3(test_multithread_contraction_with_output_kernel<ColMajor>());
+ CALL_SUBTEST_3(test_multithread_contraction_with_output_kernel<RowMajor>());
+
+ CALL_SUBTEST_4(test_async_multithread_contraction_agrees_with_singlethread<ColMajor>());
+ CALL_SUBTEST_4(test_async_multithread_contraction_agrees_with_singlethread<RowMajor>());
+
+ // Test EvalShardedByInnerDimContext parallelization strategy.
+ CALL_SUBTEST_5(test_sharded_by_inner_dim_contraction<ColMajor>());
+ CALL_SUBTEST_5(test_sharded_by_inner_dim_contraction<RowMajor>());
+ CALL_SUBTEST_5(test_sharded_by_inner_dim_contraction_with_output_kernel<ColMajor>());
+ CALL_SUBTEST_5(test_sharded_by_inner_dim_contraction_with_output_kernel<RowMajor>());
+
+ CALL_SUBTEST_6(test_async_sharded_by_inner_dim_contraction<ColMajor>());
+ CALL_SUBTEST_6(test_async_sharded_by_inner_dim_contraction<RowMajor>());
+ CALL_SUBTEST_6(test_async_sharded_by_inner_dim_contraction_with_output_kernel<ColMajor>());
+ CALL_SUBTEST_6(test_async_sharded_by_inner_dim_contraction_with_output_kernel<RowMajor>());
+
+ // Exercise various cases that have been problematic in the past.
+ CALL_SUBTEST_7(test_contraction_corner_cases<ColMajor>());
+ CALL_SUBTEST_7(test_contraction_corner_cases<RowMajor>());
+
+ CALL_SUBTEST_8(test_full_contraction<ColMajor>());
+ CALL_SUBTEST_8(test_full_contraction<RowMajor>());
+
+ CALL_SUBTEST_9(test_multithreaded_reductions<ColMajor>());
+ CALL_SUBTEST_9(test_multithreaded_reductions<RowMajor>());
+
+ CALL_SUBTEST_10(test_memcpy());
+ CALL_SUBTEST_10(test_multithread_random());
+
+ TestAllocator test_allocator;
+ CALL_SUBTEST_11(test_multithread_shuffle<ColMajor>(NULL));
+ CALL_SUBTEST_11(test_multithread_shuffle<RowMajor>(&test_allocator));
+ CALL_SUBTEST_11(test_threadpool_allocate(&test_allocator));
+
+ // Force CMake to split this test.
+ // EIGEN_SUFFIXES;1;2;3;4;5;6;7;8;9;10;11
+}
diff --git a/unsupported/test/cxx11_tensor_trace.cpp b/unsupported/test/cxx11_tensor_trace.cpp
new file mode 100644
index 0000000..0097228
--- /dev/null
+++ b/unsupported/test/cxx11_tensor_trace.cpp
@@ -0,0 +1,172 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2017 Gagan Goel <gagan.nith@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "main.h"
+
+#include <Eigen/CXX11/Tensor>
+
+using Eigen::Tensor;
+using Eigen::array;
+
+template <int DataLayout>
+static void test_0D_trace() {
+ Tensor<float, 0, DataLayout> tensor;
+ tensor.setRandom();
+ array<ptrdiff_t, 0> dims;
+ Tensor<float, 0, DataLayout> result = tensor.trace(dims);
+ VERIFY_IS_EQUAL(result(), tensor());
+}
+
+
+template <int DataLayout>
+static void test_all_dimensions_trace() {
+ Tensor<float, 3, DataLayout> tensor1(5, 5, 5);
+ tensor1.setRandom();
+ Tensor<float, 0, DataLayout> result1 = tensor1.trace();
+ VERIFY_IS_EQUAL(result1.rank(), 0);
+ float sum = 0.0f;
+ for (int i = 0; i < 5; ++i) {
+ sum += tensor1(i, i, i);
+ }
+ VERIFY_IS_EQUAL(result1(), sum);
+
+ Tensor<float, 5, DataLayout> tensor2(7, 7, 7, 7, 7);
+ tensor2.setRandom();
+ array<ptrdiff_t, 5> dims = { { 2, 1, 0, 3, 4 } };
+ Tensor<float, 0, DataLayout> result2 = tensor2.trace(dims);
+ VERIFY_IS_EQUAL(result2.rank(), 0);
+ sum = 0.0f;
+ for (int i = 0; i < 7; ++i) {
+ sum += tensor2(i, i, i, i, i);
+ }
+ VERIFY_IS_EQUAL(result2(), sum);
+}
+
+
+template <int DataLayout>
+static void test_simple_trace() {
+ Tensor<float, 3, DataLayout> tensor1(3, 5, 3);
+ tensor1.setRandom();
+ array<ptrdiff_t, 2> dims1 = { { 0, 2 } };
+ Tensor<float, 1, DataLayout> result1 = tensor1.trace(dims1);
+ VERIFY_IS_EQUAL(result1.rank(), 1);
+ VERIFY_IS_EQUAL(result1.dimension(0), 5);
+ float sum = 0.0f;
+ for (int i = 0; i < 5; ++i) {
+ sum = 0.0f;
+ for (int j = 0; j < 3; ++j) {
+ sum += tensor1(j, i, j);
+ }
+ VERIFY_IS_EQUAL(result1(i), sum);
+ }
+
+ Tensor<float, 4, DataLayout> tensor2(5, 5, 7, 7);
+ tensor2.setRandom();
+ array<ptrdiff_t, 2> dims2 = { { 2, 3 } };
+ Tensor<float, 2, DataLayout> result2 = tensor2.trace(dims2);
+ VERIFY_IS_EQUAL(result2.rank(), 2);
+ VERIFY_IS_EQUAL(result2.dimension(0), 5);
+ VERIFY_IS_EQUAL(result2.dimension(1), 5);
+ for (int i = 0; i < 5; ++i) {
+ for (int j = 0; j < 5; ++j) {
+ sum = 0.0f;
+ for (int k = 0; k < 7; ++k) {
+ sum += tensor2(i, j, k, k);
+ }
+ VERIFY_IS_EQUAL(result2(i, j), sum);
+ }
+ }
+
+ array<ptrdiff_t, 2> dims3 = { { 1, 0 } };
+ Tensor<float, 2, DataLayout> result3 = tensor2.trace(dims3);
+ VERIFY_IS_EQUAL(result3.rank(), 2);
+ VERIFY_IS_EQUAL(result3.dimension(0), 7);
+ VERIFY_IS_EQUAL(result3.dimension(1), 7);
+ for (int i = 0; i < 7; ++i) {
+ for (int j = 0; j < 7; ++j) {
+ sum = 0.0f;
+ for (int k = 0; k < 5; ++k) {
+ sum += tensor2(k, k, i, j);
+ }
+ VERIFY_IS_EQUAL(result3(i, j), sum);
+ }
+ }
+
+ Tensor<float, 5, DataLayout> tensor3(3, 7, 3, 7, 3);
+ tensor3.setRandom();
+ array<ptrdiff_t, 3> dims4 = { { 0, 2, 4 } };
+ Tensor<float, 2, DataLayout> result4 = tensor3.trace(dims4);
+ VERIFY_IS_EQUAL(result4.rank(), 2);
+ VERIFY_IS_EQUAL(result4.dimension(0), 7);
+ VERIFY_IS_EQUAL(result4.dimension(1), 7);
+ for (int i = 0; i < 7; ++i) {
+ for (int j = 0; j < 7; ++j) {
+ sum = 0.0f;
+ for (int k = 0; k < 3; ++k) {
+ sum += tensor3(k, i, k, j, k);
+ }
+ VERIFY_IS_EQUAL(result4(i, j), sum);
+ }
+ }
+
+ Tensor<float, 5, DataLayout> tensor4(3, 7, 4, 7, 5);
+ tensor4.setRandom();
+ array<ptrdiff_t, 2> dims5 = { { 1, 3 } };
+ Tensor<float, 3, DataLayout> result5 = tensor4.trace(dims5);
+ VERIFY_IS_EQUAL(result5.rank(), 3);
+ VERIFY_IS_EQUAL(result5.dimension(0), 3);
+ VERIFY_IS_EQUAL(result5.dimension(1), 4);
+ VERIFY_IS_EQUAL(result5.dimension(2), 5);
+ for (int i = 0; i < 3; ++i) {
+ for (int j = 0; j < 4; ++j) {
+ for (int k = 0; k < 5; ++k) {
+ sum = 0.0f;
+ for (int l = 0; l < 7; ++l) {
+ sum += tensor4(i, l, j, l, k);
+ }
+ VERIFY_IS_EQUAL(result5(i, j, k), sum);
+ }
+ }
+ }
+}
+
+
+template<int DataLayout>
+static void test_trace_in_expr() {
+ Tensor<float, 4, DataLayout> tensor(2, 3, 5, 3);
+ tensor.setRandom();
+ array<ptrdiff_t, 2> dims = { { 1, 3 } };
+ Tensor<float, 2, DataLayout> result(2, 5);
+ result = result.constant(1.0f) - tensor.trace(dims);
+ VERIFY_IS_EQUAL(result.rank(), 2);
+ VERIFY_IS_EQUAL(result.dimension(0), 2);
+ VERIFY_IS_EQUAL(result.dimension(1), 5);
+ float sum = 0.0f;
+ for (int i = 0; i < 2; ++i) {
+ for (int j = 0; j < 5; ++j) {
+ sum = 0.0f;
+ for (int k = 0; k < 3; ++k) {
+ sum += tensor(i, k, j, k);
+ }
+ VERIFY_IS_EQUAL(result(i, j), 1.0f - sum);
+ }
+ }
+}
+
+
+EIGEN_DECLARE_TEST(cxx11_tensor_trace) {
+ CALL_SUBTEST(test_0D_trace<ColMajor>());
+ CALL_SUBTEST(test_0D_trace<RowMajor>());
+ CALL_SUBTEST(test_all_dimensions_trace<ColMajor>());
+ CALL_SUBTEST(test_all_dimensions_trace<RowMajor>());
+ CALL_SUBTEST(test_simple_trace<ColMajor>());
+ CALL_SUBTEST(test_simple_trace<RowMajor>());
+ CALL_SUBTEST(test_trace_in_expr<ColMajor>());
+ CALL_SUBTEST(test_trace_in_expr<RowMajor>());
+}
diff --git a/unsupported/test/cxx11_tensor_uint128.cpp b/unsupported/test/cxx11_tensor_uint128.cpp
new file mode 100644
index 0000000..46fceaa
--- /dev/null
+++ b/unsupported/test/cxx11_tensor_uint128.cpp
@@ -0,0 +1,160 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2015 Benoit Steiner <benoit.steiner.goog@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "main.h"
+
+#include <Eigen/CXX11/Tensor>
+
+
+#if EIGEN_COMP_MSVC || !defined(__SIZEOF_INT128__)
+#define EIGEN_NO_INT128
+#else
+typedef __uint128_t uint128_t;
+#endif
+
+// Only run the test on compilers that support 128bit integers natively
+#ifndef EIGEN_NO_INT128
+
+using Eigen::internal::TensorUInt128;
+using Eigen::internal::static_val;
+
+void VERIFY_EQUAL(TensorUInt128<uint64_t, uint64_t> actual, uint128_t expected) {
+ bool matchl = actual.lower() == static_cast<uint64_t>(expected);
+ bool matchh = actual.upper() == static_cast<uint64_t>(expected >> 64);
+ if (!matchl || !matchh) {
+ const char* testname = g_test_stack.back().c_str();
+ std::cerr << "Test " << testname << " failed in " << __FILE__
+ << " (" << __LINE__ << ")"
+ << std::endl;
+ abort();
+ }
+}
+
+
+void test_add() {
+ uint64_t incr = internal::random<uint64_t>(1, 9999999999);
+ for (uint64_t i1 = 0; i1 < 100; ++i1) {
+ for (uint64_t i2 = 1; i2 < 100 * incr; i2 += incr) {
+ TensorUInt128<uint64_t, uint64_t> i(i1, i2);
+ uint128_t a = (static_cast<uint128_t>(i1) << 64) + static_cast<uint128_t>(i2);
+ for (uint64_t j1 = 0; j1 < 100; ++j1) {
+ for (uint64_t j2 = 1; j2 < 100 * incr; j2 += incr) {
+ TensorUInt128<uint64_t, uint64_t> j(j1, j2);
+ uint128_t b = (static_cast<uint128_t>(j1) << 64) + static_cast<uint128_t>(j2);
+ TensorUInt128<uint64_t, uint64_t> actual = i + j;
+ uint128_t expected = a + b;
+ VERIFY_EQUAL(actual, expected);
+ }
+ }
+ }
+ }
+}
+
+void test_sub() {
+ uint64_t incr = internal::random<uint64_t>(1, 9999999999);
+ for (uint64_t i1 = 0; i1 < 100; ++i1) {
+ for (uint64_t i2 = 1; i2 < 100 * incr; i2 += incr) {
+ TensorUInt128<uint64_t, uint64_t> i(i1, i2);
+ uint128_t a = (static_cast<uint128_t>(i1) << 64) + static_cast<uint128_t>(i2);
+ for (uint64_t j1 = 0; j1 < 100; ++j1) {
+ for (uint64_t j2 = 1; j2 < 100 * incr; j2 += incr) {
+ TensorUInt128<uint64_t, uint64_t> j(j1, j2);
+ uint128_t b = (static_cast<uint128_t>(j1) << 64) + static_cast<uint128_t>(j2);
+ TensorUInt128<uint64_t, uint64_t> actual = i - j;
+ uint128_t expected = a - b;
+ VERIFY_EQUAL(actual, expected);
+ }
+ }
+ }
+ }
+}
+
+void test_mul() {
+ uint64_t incr = internal::random<uint64_t>(1, 9999999999);
+ for (uint64_t i1 = 0; i1 < 100; ++i1) {
+ for (uint64_t i2 = 1; i2 < 100 * incr; i2 += incr) {
+ TensorUInt128<uint64_t, uint64_t> i(i1, i2);
+ uint128_t a = (static_cast<uint128_t>(i1) << 64) + static_cast<uint128_t>(i2);
+ for (uint64_t j1 = 0; j1 < 100; ++j1) {
+ for (uint64_t j2 = 1; j2 < 100 * incr; j2 += incr) {
+ TensorUInt128<uint64_t, uint64_t> j(j1, j2);
+ uint128_t b = (static_cast<uint128_t>(j1) << 64) + static_cast<uint128_t>(j2);
+ TensorUInt128<uint64_t, uint64_t> actual = i * j;
+ uint128_t expected = a * b;
+ VERIFY_EQUAL(actual, expected);
+ }
+ }
+ }
+ }
+}
+
+void test_div() {
+ uint64_t incr = internal::random<uint64_t>(1, 9999999999);
+ for (uint64_t i1 = 0; i1 < 100; ++i1) {
+ for (uint64_t i2 = 1; i2 < 100 * incr; i2 += incr) {
+ TensorUInt128<uint64_t, uint64_t> i(i1, i2);
+ uint128_t a = (static_cast<uint128_t>(i1) << 64) + static_cast<uint128_t>(i2);
+ for (uint64_t j1 = 0; j1 < 100; ++j1) {
+ for (uint64_t j2 = 1; j2 < 100 * incr; j2 += incr) {
+ TensorUInt128<uint64_t, uint64_t> j(j1, j2);
+ uint128_t b = (static_cast<uint128_t>(j1) << 64) + static_cast<uint128_t>(j2);
+ TensorUInt128<uint64_t, uint64_t> actual = i / j;
+ uint128_t expected = a / b;
+ VERIFY_EQUAL(actual, expected);
+ }
+ }
+ }
+ }
+}
+
+void test_misc1() {
+ uint64_t incr = internal::random<uint64_t>(1, 9999999999);
+ for (uint64_t i2 = 1; i2 < 100 * incr; i2 += incr) {
+ TensorUInt128<static_val<0>, uint64_t> i(0, i2);
+ uint128_t a = static_cast<uint128_t>(i2);
+ for (uint64_t j2 = 1; j2 < 100 * incr; j2 += incr) {
+ TensorUInt128<static_val<0>, uint64_t> j(0, j2);
+ uint128_t b = static_cast<uint128_t>(j2);
+ uint64_t actual = (i * j).upper();
+ uint64_t expected = (a * b) >> 64;
+ VERIFY_IS_EQUAL(actual, expected);
+ }
+ }
+}
+
+void test_misc2() {
+ int64_t incr = internal::random<int64_t>(1, 100);
+ for (int64_t log_div = 0; log_div < 63; ++log_div) {
+ for (int64_t divider = 1; divider <= 1000000 * incr; divider += incr) {
+ uint64_t expected = (static_cast<uint128_t>(1) << (64+log_div)) / static_cast<uint128_t>(divider) - (static_cast<uint128_t>(1) << 64) + 1;
+ uint64_t shift = 1ULL << log_div;
+
+ TensorUInt128<uint64_t, uint64_t> result = (TensorUInt128<uint64_t, static_val<0> >(shift, 0) / TensorUInt128<static_val<0>, uint64_t>(divider) - TensorUInt128<static_val<1>, static_val<0> >(1, 0) + TensorUInt128<static_val<0>, static_val<1> >(1));
+ uint64_t actual = static_cast<uint64_t>(result);
+ VERIFY_IS_EQUAL(actual, expected);
+ }
+ }
+}
+#endif
+
+
+EIGEN_DECLARE_TEST(cxx11_tensor_uint128)
+{
+#ifdef EIGEN_NO_INT128
+ // Skip the test on compilers that don't support 128bit integers natively
+ return;
+#else
+ CALL_SUBTEST_1(test_add());
+ CALL_SUBTEST_2(test_sub());
+ CALL_SUBTEST_3(test_mul());
+ CALL_SUBTEST_4(test_div());
+ CALL_SUBTEST_5(test_misc1());
+ CALL_SUBTEST_6(test_misc2());
+#endif
+}
diff --git a/unsupported/test/cxx11_tensor_volume_patch.cpp b/unsupported/test/cxx11_tensor_volume_patch.cpp
new file mode 100644
index 0000000..862212e
--- /dev/null
+++ b/unsupported/test/cxx11_tensor_volume_patch.cpp
@@ -0,0 +1,112 @@
+#include "main.h"
+
+#include <Eigen/CXX11/Tensor>
+
+using Eigen::Tensor;
+
+static void test_single_voxel_patch()
+{
+ Tensor<float, 5> tensor(4,2,3,5,7);
+ tensor.setRandom();
+ Tensor<float, 5, RowMajor> tensor_row_major = tensor.swap_layout();
+
+ Tensor<float, 6> single_voxel_patch;
+ single_voxel_patch = tensor.extract_volume_patches(1, 1, 1);
+ VERIFY_IS_EQUAL(single_voxel_patch.dimension(0), 4);
+ VERIFY_IS_EQUAL(single_voxel_patch.dimension(1), 1);
+ VERIFY_IS_EQUAL(single_voxel_patch.dimension(2), 1);
+ VERIFY_IS_EQUAL(single_voxel_patch.dimension(3), 1);
+ VERIFY_IS_EQUAL(single_voxel_patch.dimension(4), 2 * 3 * 5);
+ VERIFY_IS_EQUAL(single_voxel_patch.dimension(5), 7);
+
+ Tensor<float, 6, RowMajor> single_voxel_patch_row_major;
+ single_voxel_patch_row_major = tensor_row_major.extract_volume_patches(1, 1, 1);
+ VERIFY_IS_EQUAL(single_voxel_patch_row_major.dimension(0), 7);
+ VERIFY_IS_EQUAL(single_voxel_patch_row_major.dimension(1), 2 * 3 * 5);
+ VERIFY_IS_EQUAL(single_voxel_patch_row_major.dimension(2), 1);
+ VERIFY_IS_EQUAL(single_voxel_patch_row_major.dimension(3), 1);
+ VERIFY_IS_EQUAL(single_voxel_patch_row_major.dimension(4), 1);
+ VERIFY_IS_EQUAL(single_voxel_patch_row_major.dimension(5), 4);
+
+ for (int i = 0; i < tensor.size(); ++i) {
+ VERIFY_IS_EQUAL(tensor.data()[i], single_voxel_patch.data()[i]);
+ VERIFY_IS_EQUAL(tensor_row_major.data()[i], single_voxel_patch_row_major.data()[i]);
+ VERIFY_IS_EQUAL(tensor.data()[i], tensor_row_major.data()[i]);
+ }
+}
+
+
+static void test_entire_volume_patch()
+{
+ const int depth = 4;
+ const int patch_z = 2;
+ const int patch_y = 3;
+ const int patch_x = 5;
+ const int batch = 7;
+
+ Tensor<float, 5> tensor(depth, patch_z, patch_y, patch_x, batch);
+ tensor.setRandom();
+ Tensor<float, 5, RowMajor> tensor_row_major = tensor.swap_layout();
+
+ Tensor<float, 6> entire_volume_patch;
+ entire_volume_patch = tensor.extract_volume_patches(patch_z, patch_y, patch_x);
+ VERIFY_IS_EQUAL(entire_volume_patch.dimension(0), depth);
+ VERIFY_IS_EQUAL(entire_volume_patch.dimension(1), patch_z);
+ VERIFY_IS_EQUAL(entire_volume_patch.dimension(2), patch_y);
+ VERIFY_IS_EQUAL(entire_volume_patch.dimension(3), patch_x);
+ VERIFY_IS_EQUAL(entire_volume_patch.dimension(4), patch_z * patch_y * patch_x);
+ VERIFY_IS_EQUAL(entire_volume_patch.dimension(5), batch);
+
+ Tensor<float, 6, RowMajor> entire_volume_patch_row_major;
+ entire_volume_patch_row_major = tensor_row_major.extract_volume_patches(patch_z, patch_y, patch_x);
+ VERIFY_IS_EQUAL(entire_volume_patch_row_major.dimension(0), batch);
+ VERIFY_IS_EQUAL(entire_volume_patch_row_major.dimension(1), patch_z * patch_y * patch_x);
+ VERIFY_IS_EQUAL(entire_volume_patch_row_major.dimension(2), patch_x);
+ VERIFY_IS_EQUAL(entire_volume_patch_row_major.dimension(3), patch_y);
+ VERIFY_IS_EQUAL(entire_volume_patch_row_major.dimension(4), patch_z);
+ VERIFY_IS_EQUAL(entire_volume_patch_row_major.dimension(5), depth);
+
+ const int dz = patch_z - 1;
+ const int dy = patch_y - 1;
+ const int dx = patch_x - 1;
+
+ const int forward_pad_z = dz / 2;
+ const int forward_pad_y = dy / 2;
+ const int forward_pad_x = dx / 2;
+
+ for (int pz = 0; pz < patch_z; pz++) {
+ for (int py = 0; py < patch_y; py++) {
+ for (int px = 0; px < patch_x; px++) {
+ const int patchId = pz + patch_z * (py + px * patch_y);
+ for (int z = 0; z < patch_z; z++) {
+ for (int y = 0; y < patch_y; y++) {
+ for (int x = 0; x < patch_x; x++) {
+ for (int b = 0; b < batch; b++) {
+ for (int d = 0; d < depth; d++) {
+ float expected = 0.0f;
+ float expected_row_major = 0.0f;
+ const int eff_z = z - forward_pad_z + pz;
+ const int eff_y = y - forward_pad_y + py;
+ const int eff_x = x - forward_pad_x + px;
+ if (eff_z >= 0 && eff_y >= 0 && eff_x >= 0 &&
+ eff_z < patch_z && eff_y < patch_y && eff_x < patch_x) {
+ expected = tensor(d, eff_z, eff_y, eff_x, b);
+ expected_row_major = tensor_row_major(b, eff_x, eff_y, eff_z, d);
+ }
+ VERIFY_IS_EQUAL(entire_volume_patch(d, z, y, x, patchId, b), expected);
+ VERIFY_IS_EQUAL(entire_volume_patch_row_major(b, patchId, x, y, z, d), expected_row_major);
+ }
+ }
+ }
+ }
+ }
+ }
+ }
+ }
+}
+
+EIGEN_DECLARE_TEST(cxx11_tensor_volume_patch)
+{
+ CALL_SUBTEST(test_single_voxel_patch());
+ CALL_SUBTEST(test_entire_volume_patch());
+}
diff --git a/unsupported/test/cxx11_tensor_volume_patch_sycl.cpp b/unsupported/test/cxx11_tensor_volume_patch_sycl.cpp
new file mode 100644
index 0000000..8d99a48
--- /dev/null
+++ b/unsupported/test/cxx11_tensor_volume_patch_sycl.cpp
@@ -0,0 +1,222 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2016
+// Mehdi Goli Codeplay Software Ltd.
+// Ralph Potter Codeplay Software Ltd.
+// Luke Iwanski Codeplay Software Ltd.
+// Contact: <eigen@codeplay.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#define EIGEN_TEST_NO_LONGDOUBLE
+#define EIGEN_TEST_NO_COMPLEX
+
+#define EIGEN_DEFAULT_DENSE_INDEX_TYPE int64_t
+#define EIGEN_USE_SYCL
+
+#include "main.h"
+#include <unsupported/Eigen/CXX11/Tensor>
+
+using Eigen::Tensor;
+static const int DataLayout = ColMajor;
+
+template <typename DataType, typename IndexType>
+static void test_single_voxel_patch_sycl(const Eigen::SyclDevice& sycl_device)
+{
+
+IndexType sizeDim0 = 4;
+IndexType sizeDim1 = 2;
+IndexType sizeDim2 = 3;
+IndexType sizeDim3 = 5;
+IndexType sizeDim4 = 7;
+array<IndexType, 5> tensorColMajorRange = {{sizeDim0, sizeDim1, sizeDim2, sizeDim3, sizeDim4}};
+array<IndexType, 5> tensorRowMajorRange = {{sizeDim4, sizeDim3, sizeDim2, sizeDim1, sizeDim0}};
+Tensor<DataType, 5, DataLayout,IndexType> tensor_col_major(tensorColMajorRange);
+Tensor<DataType, 5, RowMajor,IndexType> tensor_row_major(tensorRowMajorRange);
+tensor_col_major.setRandom();
+
+
+ DataType* gpu_data_col_major = static_cast<DataType*>(sycl_device.allocate(tensor_col_major.size()*sizeof(DataType)));
+ DataType* gpu_data_row_major = static_cast<DataType*>(sycl_device.allocate(tensor_row_major.size()*sizeof(DataType)));
+ TensorMap<Tensor<DataType, 5, ColMajor, IndexType>> gpu_col_major(gpu_data_col_major, tensorColMajorRange);
+ TensorMap<Tensor<DataType, 5, RowMajor, IndexType>> gpu_row_major(gpu_data_row_major, tensorRowMajorRange);
+
+ sycl_device.memcpyHostToDevice(gpu_data_col_major, tensor_col_major.data(),(tensor_col_major.size())*sizeof(DataType));
+ gpu_row_major.device(sycl_device)=gpu_col_major.swap_layout();
+
+
+ // single volume patch: ColMajor
+ array<IndexType, 6> patchColMajorTensorRange={{sizeDim0,1, 1, 1, sizeDim1*sizeDim2*sizeDim3, sizeDim4}};
+ Tensor<DataType, 6, DataLayout,IndexType> single_voxel_patch_col_major(patchColMajorTensorRange);
+ size_t patchTensorBuffSize =single_voxel_patch_col_major.size()*sizeof(DataType);
+ DataType* gpu_data_single_voxel_patch_col_major = static_cast<DataType*>(sycl_device.allocate(patchTensorBuffSize));
+ TensorMap<Tensor<DataType, 6, DataLayout,IndexType>> gpu_single_voxel_patch_col_major(gpu_data_single_voxel_patch_col_major, patchColMajorTensorRange);
+ gpu_single_voxel_patch_col_major.device(sycl_device)=gpu_col_major.extract_volume_patches(1, 1, 1);
+ sycl_device.memcpyDeviceToHost(single_voxel_patch_col_major.data(), gpu_data_single_voxel_patch_col_major, patchTensorBuffSize);
+
+
+ VERIFY_IS_EQUAL(single_voxel_patch_col_major.dimension(0), 4);
+ VERIFY_IS_EQUAL(single_voxel_patch_col_major.dimension(1), 1);
+ VERIFY_IS_EQUAL(single_voxel_patch_col_major.dimension(2), 1);
+ VERIFY_IS_EQUAL(single_voxel_patch_col_major.dimension(3), 1);
+ VERIFY_IS_EQUAL(single_voxel_patch_col_major.dimension(4), 2 * 3 * 5);
+ VERIFY_IS_EQUAL(single_voxel_patch_col_major.dimension(5), 7);
+
+ array<IndexType, 6> patchRowMajorTensorRange={{sizeDim4, sizeDim1*sizeDim2*sizeDim3, 1, 1, 1, sizeDim0}};
+ Tensor<DataType, 6, RowMajor,IndexType> single_voxel_patch_row_major(patchRowMajorTensorRange);
+ patchTensorBuffSize =single_voxel_patch_row_major.size()*sizeof(DataType);
+ DataType* gpu_data_single_voxel_patch_row_major = static_cast<DataType*>(sycl_device.allocate(patchTensorBuffSize));
+ TensorMap<Tensor<DataType, 6, RowMajor,IndexType>> gpu_single_voxel_patch_row_major(gpu_data_single_voxel_patch_row_major, patchRowMajorTensorRange);
+ gpu_single_voxel_patch_row_major.device(sycl_device)=gpu_row_major.extract_volume_patches(1, 1, 1);
+ sycl_device.memcpyDeviceToHost(single_voxel_patch_row_major.data(), gpu_data_single_voxel_patch_row_major, patchTensorBuffSize);
+
+ VERIFY_IS_EQUAL(single_voxel_patch_row_major.dimension(0), 7);
+ VERIFY_IS_EQUAL(single_voxel_patch_row_major.dimension(1), 2 * 3 * 5);
+ VERIFY_IS_EQUAL(single_voxel_patch_row_major.dimension(2), 1);
+ VERIFY_IS_EQUAL(single_voxel_patch_row_major.dimension(3), 1);
+ VERIFY_IS_EQUAL(single_voxel_patch_row_major.dimension(4), 1);
+ VERIFY_IS_EQUAL(single_voxel_patch_row_major.dimension(5), 4);
+
+ sycl_device.memcpyDeviceToHost(tensor_row_major.data(), gpu_data_row_major, (tensor_col_major.size())*sizeof(DataType));
+ for (IndexType i = 0; i < tensor_col_major.size(); ++i) {
+ VERIFY_IS_EQUAL(tensor_col_major.data()[i], single_voxel_patch_col_major.data()[i]);
+ VERIFY_IS_EQUAL(tensor_row_major.data()[i], single_voxel_patch_row_major.data()[i]);
+ VERIFY_IS_EQUAL(tensor_col_major.data()[i], tensor_row_major.data()[i]);
+ }
+
+
+ sycl_device.deallocate(gpu_data_col_major);
+ sycl_device.deallocate(gpu_data_row_major);
+ sycl_device.deallocate(gpu_data_single_voxel_patch_col_major);
+ sycl_device.deallocate(gpu_data_single_voxel_patch_row_major);
+}
+
+template <typename DataType, typename IndexType>
+static void test_entire_volume_patch_sycl(const Eigen::SyclDevice& sycl_device)
+{
+ const int depth = 4;
+ const int patch_z = 2;
+ const int patch_y = 3;
+ const int patch_x = 5;
+ const int batch = 7;
+
+ array<IndexType, 5> tensorColMajorRange = {{depth, patch_z, patch_y, patch_x, batch}};
+ array<IndexType, 5> tensorRowMajorRange = {{batch, patch_x, patch_y, patch_z, depth}};
+ Tensor<DataType, 5, DataLayout,IndexType> tensor_col_major(tensorColMajorRange);
+ Tensor<DataType, 5, RowMajor,IndexType> tensor_row_major(tensorRowMajorRange);
+ tensor_col_major.setRandom();
+
+
+ DataType* gpu_data_col_major = static_cast<DataType*>(sycl_device.allocate(tensor_col_major.size()*sizeof(DataType)));
+ DataType* gpu_data_row_major = static_cast<DataType*>(sycl_device.allocate(tensor_row_major.size()*sizeof(DataType)));
+ TensorMap<Tensor<DataType, 5, ColMajor, IndexType>> gpu_col_major(gpu_data_col_major, tensorColMajorRange);
+ TensorMap<Tensor<DataType, 5, RowMajor, IndexType>> gpu_row_major(gpu_data_row_major, tensorRowMajorRange);
+
+ sycl_device.memcpyHostToDevice(gpu_data_col_major, tensor_col_major.data(),(tensor_col_major.size())*sizeof(DataType));
+ gpu_row_major.device(sycl_device)=gpu_col_major.swap_layout();
+ sycl_device.memcpyDeviceToHost(tensor_row_major.data(), gpu_data_row_major, (tensor_col_major.size())*sizeof(DataType));
+
+
+ // single volume patch: ColMajor
+ array<IndexType, 6> patchColMajorTensorRange={{depth,patch_z, patch_y, patch_x, patch_z*patch_y*patch_x, batch}};
+ Tensor<DataType, 6, DataLayout,IndexType> entire_volume_patch_col_major(patchColMajorTensorRange);
+ size_t patchTensorBuffSize =entire_volume_patch_col_major.size()*sizeof(DataType);
+ DataType* gpu_data_entire_volume_patch_col_major = static_cast<DataType*>(sycl_device.allocate(patchTensorBuffSize));
+ TensorMap<Tensor<DataType, 6, DataLayout,IndexType>> gpu_entire_volume_patch_col_major(gpu_data_entire_volume_patch_col_major, patchColMajorTensorRange);
+ gpu_entire_volume_patch_col_major.device(sycl_device)=gpu_col_major.extract_volume_patches(patch_z, patch_y, patch_x);
+ sycl_device.memcpyDeviceToHost(entire_volume_patch_col_major.data(), gpu_data_entire_volume_patch_col_major, patchTensorBuffSize);
+
+
+// Tensor<float, 5> tensor(depth, patch_z, patch_y, patch_x, batch);
+// tensor.setRandom();
+// Tensor<float, 5, RowMajor> tensor_row_major = tensor.swap_layout();
+
+ //Tensor<float, 6> entire_volume_patch;
+ //entire_volume_patch = tensor.extract_volume_patches(patch_z, patch_y, patch_x);
+ VERIFY_IS_EQUAL(entire_volume_patch_col_major.dimension(0), depth);
+ VERIFY_IS_EQUAL(entire_volume_patch_col_major.dimension(1), patch_z);
+ VERIFY_IS_EQUAL(entire_volume_patch_col_major.dimension(2), patch_y);
+ VERIFY_IS_EQUAL(entire_volume_patch_col_major.dimension(3), patch_x);
+ VERIFY_IS_EQUAL(entire_volume_patch_col_major.dimension(4), patch_z * patch_y * patch_x);
+ VERIFY_IS_EQUAL(entire_volume_patch_col_major.dimension(5), batch);
+
+// Tensor<float, 6, RowMajor> entire_volume_patch_row_major;
+ //entire_volume_patch_row_major = tensor_row_major.extract_volume_patches(patch_z, patch_y, patch_x);
+
+ array<IndexType, 6> patchRowMajorTensorRange={{batch,patch_z*patch_y*patch_x, patch_x, patch_y, patch_z, depth}};
+ Tensor<DataType, 6, RowMajor,IndexType> entire_volume_patch_row_major(patchRowMajorTensorRange);
+ patchTensorBuffSize =entire_volume_patch_row_major.size()*sizeof(DataType);
+ DataType* gpu_data_entire_volume_patch_row_major = static_cast<DataType*>(sycl_device.allocate(patchTensorBuffSize));
+ TensorMap<Tensor<DataType, 6, RowMajor,IndexType>> gpu_entire_volume_patch_row_major(gpu_data_entire_volume_patch_row_major, patchRowMajorTensorRange);
+ gpu_entire_volume_patch_row_major.device(sycl_device)=gpu_row_major.extract_volume_patches(patch_z, patch_y, patch_x);
+ sycl_device.memcpyDeviceToHost(entire_volume_patch_row_major.data(), gpu_data_entire_volume_patch_row_major, patchTensorBuffSize);
+
+
+ VERIFY_IS_EQUAL(entire_volume_patch_row_major.dimension(0), batch);
+ VERIFY_IS_EQUAL(entire_volume_patch_row_major.dimension(1), patch_z * patch_y * patch_x);
+ VERIFY_IS_EQUAL(entire_volume_patch_row_major.dimension(2), patch_x);
+ VERIFY_IS_EQUAL(entire_volume_patch_row_major.dimension(3), patch_y);
+ VERIFY_IS_EQUAL(entire_volume_patch_row_major.dimension(4), patch_z);
+ VERIFY_IS_EQUAL(entire_volume_patch_row_major.dimension(5), depth);
+
+ const int dz = patch_z - 1;
+ const int dy = patch_y - 1;
+ const int dx = patch_x - 1;
+
+ const int forward_pad_z = dz / 2;
+ const int forward_pad_y = dy / 2;
+ const int forward_pad_x = dx / 2;
+
+ for (int pz = 0; pz < patch_z; pz++) {
+ for (int py = 0; py < patch_y; py++) {
+ for (int px = 0; px < patch_x; px++) {
+ const int patchId = pz + patch_z * (py + px * patch_y);
+ for (int z = 0; z < patch_z; z++) {
+ for (int y = 0; y < patch_y; y++) {
+ for (int x = 0; x < patch_x; x++) {
+ for (int b = 0; b < batch; b++) {
+ for (int d = 0; d < depth; d++) {
+ float expected = 0.0f;
+ float expected_row_major = 0.0f;
+ const int eff_z = z - forward_pad_z + pz;
+ const int eff_y = y - forward_pad_y + py;
+ const int eff_x = x - forward_pad_x + px;
+ if (eff_z >= 0 && eff_y >= 0 && eff_x >= 0 &&
+ eff_z < patch_z && eff_y < patch_y && eff_x < patch_x) {
+ expected = tensor_col_major(d, eff_z, eff_y, eff_x, b);
+ expected_row_major = tensor_row_major(b, eff_x, eff_y, eff_z, d);
+ }
+ VERIFY_IS_EQUAL(entire_volume_patch_col_major(d, z, y, x, patchId, b), expected);
+ VERIFY_IS_EQUAL(entire_volume_patch_row_major(b, patchId, x, y, z, d), expected_row_major);
+ }
+ }
+ }
+ }
+ }
+ }
+ }
+ }
+ sycl_device.deallocate(gpu_data_col_major);
+ sycl_device.deallocate(gpu_data_row_major);
+ sycl_device.deallocate(gpu_data_entire_volume_patch_col_major);
+ sycl_device.deallocate(gpu_data_entire_volume_patch_row_major);
+}
+
+
+
+template<typename DataType, typename dev_Selector> void sycl_tensor_volume_patch_test_per_device(dev_Selector s){
+QueueInterface queueInterface(s);
+auto sycl_device = Eigen::SyclDevice(&queueInterface);
+std::cout << "Running on " << s.template get_info<cl::sycl::info::device::name>() << std::endl;
+test_single_voxel_patch_sycl<DataType, int64_t>(sycl_device);
+test_entire_volume_patch_sycl<DataType, int64_t>(sycl_device);
+}
+EIGEN_DECLARE_TEST(cxx11_tensor_volume_patch_sycl)
+{
+for (const auto& device :Eigen::get_sycl_supported_devices()) {
+ CALL_SUBTEST(sycl_tensor_volume_patch_test_per_device<float>(device));
+}
+}
diff --git a/unsupported/test/dgmres.cpp b/unsupported/test/dgmres.cpp
new file mode 100644
index 0000000..5f63161
--- /dev/null
+++ b/unsupported/test/dgmres.cpp
@@ -0,0 +1,31 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2011 Gael Guennebaud <g.gael@free.fr>
+// Copyright (C) 2012 desire Nuentsa <desire.nuentsa_wakam@inria.fr
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "../../test/sparse_solver.h"
+#include <unsupported/Eigen/IterativeSolvers>
+
+template<typename T> void test_dgmres_T()
+{
+ DGMRES<SparseMatrix<T>, DiagonalPreconditioner<T> > dgmres_colmajor_diag;
+ DGMRES<SparseMatrix<T>, IdentityPreconditioner > dgmres_colmajor_I;
+ DGMRES<SparseMatrix<T>, IncompleteLUT<T> > dgmres_colmajor_ilut;
+ //GMRES<SparseMatrix<T>, SSORPreconditioner<T> > dgmres_colmajor_ssor;
+
+ CALL_SUBTEST( check_sparse_square_solving(dgmres_colmajor_diag) );
+// CALL_SUBTEST( check_sparse_square_solving(dgmres_colmajor_I) );
+ CALL_SUBTEST( check_sparse_square_solving(dgmres_colmajor_ilut) );
+ //CALL_SUBTEST( check_sparse_square_solving(dgmres_colmajor_ssor) );
+}
+
+EIGEN_DECLARE_TEST(dgmres)
+{
+ CALL_SUBTEST_1(test_dgmres_T<double>());
+ CALL_SUBTEST_2(test_dgmres_T<std::complex<double> >());
+}
diff --git a/unsupported/test/fft_test_shared.h b/unsupported/test/fft_test_shared.h
new file mode 100644
index 0000000..0e040ad
--- /dev/null
+++ b/unsupported/test/fft_test_shared.h
@@ -0,0 +1,277 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009 Mark Borgerding mark a borgerding net
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "main.h"
+#include <unsupported/Eigen/FFT>
+
+template <typename T>
+inline std::complex<T> RandomCpx() {
+ return std::complex<T>((T)(rand() / (T)RAND_MAX - .5), (T)(rand() / (T)RAND_MAX - .5));
+}
+
+using namespace std;
+using namespace Eigen;
+
+template <typename T>
+inline complex<long double> promote(complex<T> x) {
+ return complex<long double>((long double)x.real(), (long double)x.imag());
+}
+
+inline complex<long double> promote(float x) { return complex<long double>((long double)x); }
+inline complex<long double> promote(double x) { return complex<long double>((long double)x); }
+inline complex<long double> promote(long double x) { return complex<long double>((long double)x); }
+
+template <typename VT1, typename VT2>
+long double fft_rmse(const VT1& fftbuf, const VT2& timebuf) {
+ long double totalpower = 0;
+ long double difpower = 0;
+ long double pi = acos((long double)-1);
+ for (size_t k0 = 0; k0 < (size_t)fftbuf.size(); ++k0) {
+ complex<long double> acc = 0;
+ long double phinc = (long double)(-2.) * k0 * pi / timebuf.size();
+ for (size_t k1 = 0; k1 < (size_t)timebuf.size(); ++k1) {
+ acc += promote(timebuf[k1]) * exp(complex<long double>(0, k1 * phinc));
+ }
+ totalpower += numext::abs2(acc);
+ complex<long double> x = promote(fftbuf[k0]);
+ complex<long double> dif = acc - x;
+ difpower += numext::abs2(dif);
+ // cerr << k0 << "\t" << acc << "\t" << x << "\t" << sqrt(numext::abs2(dif)) << endl;
+ }
+ // cerr << "rmse:" << sqrt(difpower/totalpower) << endl;
+ return sqrt(difpower / totalpower);
+}
+
+template <typename VT1, typename VT2>
+long double dif_rmse(const VT1 buf1, const VT2 buf2) {
+ long double totalpower = 0;
+ long double difpower = 0;
+ size_t n = (min)(buf1.size(), buf2.size());
+ for (size_t k = 0; k < n; ++k) {
+ totalpower += (long double)((numext::abs2(buf1[k]) + numext::abs2(buf2[k])) / 2);
+ difpower += (long double)(numext::abs2(buf1[k] - buf2[k]));
+ }
+ return sqrt(difpower / totalpower);
+}
+
+enum { StdVectorContainer, EigenVectorContainer };
+
+template <int Container, typename Scalar>
+struct VectorType;
+
+template <typename Scalar>
+struct VectorType<StdVectorContainer, Scalar> {
+ typedef vector<Scalar> type;
+};
+
+template <typename Scalar>
+struct VectorType<EigenVectorContainer, Scalar> {
+ typedef Matrix<Scalar, Dynamic, 1> type;
+};
+
+template <int Container, typename T>
+void test_scalar_generic(int nfft) {
+ typedef typename FFT<T>::Complex Complex;
+ typedef typename FFT<T>::Scalar Scalar;
+ typedef typename VectorType<Container, Scalar>::type ScalarVector;
+ typedef typename VectorType<Container, Complex>::type ComplexVector;
+
+ FFT<T> fft;
+ ScalarVector tbuf(nfft);
+ ComplexVector freqBuf;
+ for (int k = 0; k < nfft; ++k) tbuf[k] = (T)(rand() / (double)RAND_MAX - .5);
+
+ // make sure it DOESN'T give the right full spectrum answer
+ // if we've asked for half-spectrum
+ fft.SetFlag(fft.HalfSpectrum);
+ fft.fwd(freqBuf, tbuf);
+ VERIFY((size_t)freqBuf.size() == (size_t)((nfft >> 1) + 1));
+ VERIFY(T(fft_rmse(freqBuf, tbuf)) < test_precision<T>()); // gross check
+
+ fft.ClearFlag(fft.HalfSpectrum);
+ fft.fwd(freqBuf, tbuf);
+ VERIFY((size_t)freqBuf.size() == (size_t)nfft);
+ VERIFY(T(fft_rmse(freqBuf, tbuf)) < test_precision<T>()); // gross check
+
+ if (nfft & 1) return; // odd FFTs get the wrong size inverse FFT
+
+ ScalarVector tbuf2;
+ fft.inv(tbuf2, freqBuf);
+ VERIFY(T(dif_rmse(tbuf, tbuf2)) < test_precision<T>()); // gross check
+
+ // verify that the Unscaled flag takes effect
+ ScalarVector tbuf3;
+ fft.SetFlag(fft.Unscaled);
+
+ fft.inv(tbuf3, freqBuf);
+
+ for (int k = 0; k < nfft; ++k) tbuf3[k] *= T(1. / nfft);
+
+ // for (size_t i=0;i<(size_t) tbuf.size();++i)
+ // cout << "freqBuf=" << freqBuf[i] << " in2=" << tbuf3[i] << " - in=" << tbuf[i] << " => " << (tbuf3[i] -
+ // tbuf[i] ) << endl;
+
+ VERIFY(T(dif_rmse(tbuf, tbuf3)) < test_precision<T>()); // gross check
+
+ // verify that ClearFlag works
+ fft.ClearFlag(fft.Unscaled);
+ fft.inv(tbuf2, freqBuf);
+ VERIFY(T(dif_rmse(tbuf, tbuf2)) < test_precision<T>()); // gross check
+}
+
+template <typename T>
+void test_scalar(int nfft) {
+ test_scalar_generic<StdVectorContainer, T>(nfft);
+ // test_scalar_generic<EigenVectorContainer,T>(nfft);
+}
+
+template <int Container, typename T>
+void test_complex_generic(int nfft) {
+ typedef typename FFT<T>::Complex Complex;
+ typedef typename VectorType<Container, Complex>::type ComplexVector;
+
+ FFT<T> fft;
+
+ ComplexVector inbuf(nfft);
+ ComplexVector outbuf;
+ ComplexVector buf3;
+ for (int k = 0; k < nfft; ++k)
+ inbuf[k] = Complex((T)(rand() / (double)RAND_MAX - .5), (T)(rand() / (double)RAND_MAX - .5));
+ fft.fwd(outbuf, inbuf);
+
+ VERIFY(T(fft_rmse(outbuf, inbuf)) < test_precision<T>()); // gross check
+ fft.inv(buf3, outbuf);
+
+ VERIFY(T(dif_rmse(inbuf, buf3)) < test_precision<T>()); // gross check
+
+ // verify that the Unscaled flag takes effect
+ ComplexVector buf4;
+ fft.SetFlag(fft.Unscaled);
+ fft.inv(buf4, outbuf);
+ for (int k = 0; k < nfft; ++k) buf4[k] *= T(1. / nfft);
+ VERIFY(T(dif_rmse(inbuf, buf4)) < test_precision<T>()); // gross check
+
+ // verify that ClearFlag works
+ fft.ClearFlag(fft.Unscaled);
+ fft.inv(buf3, outbuf);
+ VERIFY(T(dif_rmse(inbuf, buf3)) < test_precision<T>()); // gross check
+}
+
+template <typename T>
+void test_complex(int nfft) {
+ test_complex_generic<StdVectorContainer, T>(nfft);
+ test_complex_generic<EigenVectorContainer, T>(nfft);
+}
+
+template <typename T, int nrows, int ncols>
+void test_complex2d() {
+ typedef typename Eigen::FFT<T>::Complex Complex;
+ FFT<T> fft;
+ Eigen::Matrix<Complex, nrows, ncols> src, src2, dst, dst2;
+
+ src = Eigen::Matrix<Complex, nrows, ncols>::Random();
+ // src = Eigen::Matrix<Complex,nrows,ncols>::Identity();
+
+ for (int k = 0; k < ncols; k++) {
+ Eigen::Matrix<Complex, nrows, 1> tmpOut;
+ fft.fwd(tmpOut, src.col(k));
+ dst2.col(k) = tmpOut;
+ }
+
+ for (int k = 0; k < nrows; k++) {
+ Eigen::Matrix<Complex, 1, ncols> tmpOut;
+ fft.fwd(tmpOut, dst2.row(k));
+ dst2.row(k) = tmpOut;
+ }
+
+ fft.fwd2(dst.data(), src.data(), ncols, nrows);
+ fft.inv2(src2.data(), dst.data(), ncols, nrows);
+ VERIFY((src - src2).norm() < test_precision<T>());
+ VERIFY((dst - dst2).norm() < test_precision<T>());
+}
+
+inline void test_return_by_value(int len) {
+ VectorXf in;
+ VectorXf in1;
+ in.setRandom(len);
+ VectorXcf out1, out2;
+ FFT<float> fft;
+
+ fft.SetFlag(fft.HalfSpectrum);
+
+ fft.fwd(out1, in);
+ out2 = fft.fwd(in);
+ VERIFY((out1 - out2).norm() < test_precision<float>());
+ in1 = fft.inv(out1);
+ VERIFY((in1 - in).norm() < test_precision<float>());
+}
+
+EIGEN_DECLARE_TEST(FFTW) {
+ CALL_SUBTEST(test_return_by_value(32));
+ CALL_SUBTEST(test_complex<float>(32));
+ CALL_SUBTEST(test_complex<double>(32));
+ CALL_SUBTEST(test_complex<float>(256));
+ CALL_SUBTEST(test_complex<double>(256));
+ CALL_SUBTEST(test_complex<float>(3 * 8));
+ CALL_SUBTEST(test_complex<double>(3 * 8));
+ CALL_SUBTEST(test_complex<float>(5 * 32));
+ CALL_SUBTEST(test_complex<double>(5 * 32));
+ CALL_SUBTEST(test_complex<float>(2 * 3 * 4));
+ CALL_SUBTEST(test_complex<double>(2 * 3 * 4));
+ CALL_SUBTEST(test_complex<float>(2 * 3 * 4 * 5));
+ CALL_SUBTEST(test_complex<double>(2 * 3 * 4 * 5));
+ CALL_SUBTEST(test_complex<float>(2 * 3 * 4 * 5 * 7));
+ CALL_SUBTEST(test_complex<double>(2 * 3 * 4 * 5 * 7));
+
+ CALL_SUBTEST(test_scalar<float>(32));
+ CALL_SUBTEST(test_scalar<double>(32));
+ CALL_SUBTEST(test_scalar<float>(45));
+ CALL_SUBTEST(test_scalar<double>(45));
+ CALL_SUBTEST(test_scalar<float>(50));
+ CALL_SUBTEST(test_scalar<double>(50));
+ CALL_SUBTEST(test_scalar<float>(256));
+ CALL_SUBTEST(test_scalar<double>(256));
+ CALL_SUBTEST(test_scalar<float>(2 * 3 * 4 * 5 * 7));
+ CALL_SUBTEST(test_scalar<double>(2 * 3 * 4 * 5 * 7));
+
+#if defined EIGEN_HAS_FFTWL || defined EIGEN_POCKETFFT_DEFAULT
+ CALL_SUBTEST(test_complex<long double>(32));
+ CALL_SUBTEST(test_complex<long double>(256));
+ CALL_SUBTEST(test_complex<long double>(3 * 8));
+ CALL_SUBTEST(test_complex<long double>(5 * 32));
+ CALL_SUBTEST(test_complex<long double>(2 * 3 * 4));
+ CALL_SUBTEST(test_complex<long double>(2 * 3 * 4 * 5));
+ CALL_SUBTEST(test_complex<long double>(2 * 3 * 4 * 5 * 7));
+
+ CALL_SUBTEST(test_scalar<long double>(32));
+ CALL_SUBTEST(test_scalar<long double>(45));
+ CALL_SUBTEST(test_scalar<long double>(50));
+ CALL_SUBTEST(test_scalar<long double>(256));
+ CALL_SUBTEST(test_scalar<long double>(2 * 3 * 4 * 5 * 7));
+
+ CALL_SUBTEST((test_complex2d<long double, 2 * 3 * 4, 2 * 3 * 4>()));
+ CALL_SUBTEST((test_complex2d<long double, 3 * 4 * 5, 3 * 4 * 5>()));
+ CALL_SUBTEST((test_complex2d<long double, 24, 60>()));
+ CALL_SUBTEST((test_complex2d<long double, 60, 24>()));
+// fail to build since Eigen limit the stack allocation size,too big here.
+// CALL_SUBTEST( ( test_complex2d<long double, 256, 256> () ) );
+#endif
+#if defined EIGEN_FFTW_DEFAULT || defined EIGEN_POCKETFFT_DEFAULT || defined EIGEN_MKL_DEFAULT
+ CALL_SUBTEST((test_complex2d<float, 24, 24>()));
+ CALL_SUBTEST((test_complex2d<float, 60, 60>()));
+ CALL_SUBTEST((test_complex2d<float, 24, 60>()));
+ CALL_SUBTEST((test_complex2d<float, 60, 24>()));
+#endif
+#if defined EIGEN_FFTW_DEFAULT || defined EIGEN_POCKETFFT_DEFAULT || defined EIGEN_MKL_DEFAULT
+ CALL_SUBTEST((test_complex2d<double, 24, 24>()));
+ CALL_SUBTEST((test_complex2d<double, 60, 60>()));
+ CALL_SUBTEST((test_complex2d<double, 24, 60>()));
+ CALL_SUBTEST((test_complex2d<double, 60, 24>()));
+#endif
+}
diff --git a/unsupported/test/forward_adolc.cpp b/unsupported/test/forward_adolc.cpp
new file mode 100644
index 0000000..27d09dd
--- /dev/null
+++ b/unsupported/test/forward_adolc.cpp
@@ -0,0 +1,141 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "main.h"
+#include <Eigen/Dense>
+
+#define NUMBER_DIRECTIONS 16
+#include <unsupported/Eigen/AdolcForward>
+
+template<typename Vector>
+EIGEN_DONT_INLINE typename Vector::Scalar foo(const Vector& p)
+{
+ typedef typename Vector::Scalar Scalar;
+ return (p-Vector(Scalar(-1),Scalar(1.))).norm() + (p.array().sqrt().abs() * p.array().sin()).sum() + p.dot(p);
+}
+
+template<typename Scalar_, int NX=Dynamic, int NY=Dynamic>
+struct TestFunc1
+{
+ typedef Scalar_ Scalar;
+ enum {
+ InputsAtCompileTime = NX,
+ ValuesAtCompileTime = NY
+ };
+ typedef Matrix<Scalar,InputsAtCompileTime,1> InputType;
+ typedef Matrix<Scalar,ValuesAtCompileTime,1> ValueType;
+ typedef Matrix<Scalar,ValuesAtCompileTime,InputsAtCompileTime> JacobianType;
+
+ int m_inputs, m_values;
+
+ TestFunc1() : m_inputs(InputsAtCompileTime), m_values(ValuesAtCompileTime) {}
+ TestFunc1(int inputs_, int values_) : m_inputs(inputs_), m_values(values_) {}
+
+ int inputs() const { return m_inputs; }
+ int values() const { return m_values; }
+
+ template<typename T>
+ void operator() (const Matrix<T,InputsAtCompileTime,1>& x, Matrix<T,ValuesAtCompileTime,1>* _v) const
+ {
+ Matrix<T,ValuesAtCompileTime,1>& v = *_v;
+
+ v[0] = 2 * x[0] * x[0] + x[0] * x[1];
+ v[1] = 3 * x[1] * x[0] + 0.5 * x[1] * x[1];
+ if(inputs()>2)
+ {
+ v[0] += 0.5 * x[2];
+ v[1] += x[2];
+ }
+ if(values()>2)
+ {
+ v[2] = 3 * x[1] * x[0] * x[0];
+ }
+ if (inputs()>2 && values()>2)
+ v[2] *= x[2];
+ }
+
+ void operator() (const InputType& x, ValueType* v, JacobianType* _j) const
+ {
+ (*this)(x, v);
+
+ if(_j)
+ {
+ JacobianType& j = *_j;
+
+ j(0,0) = 4 * x[0] + x[1];
+ j(1,0) = 3 * x[1];
+
+ j(0,1) = x[0];
+ j(1,1) = 3 * x[0] + 2 * 0.5 * x[1];
+
+ if (inputs()>2)
+ {
+ j(0,2) = 0.5;
+ j(1,2) = 1;
+ }
+ if(values()>2)
+ {
+ j(2,0) = 3 * x[1] * 2 * x[0];
+ j(2,1) = 3 * x[0] * x[0];
+ }
+ if (inputs()>2 && values()>2)
+ {
+ j(2,0) *= x[2];
+ j(2,1) *= x[2];
+
+ j(2,2) = 3 * x[1] * x[0] * x[0];
+ j(2,2) = 3 * x[1] * x[0] * x[0];
+ }
+ }
+ }
+};
+
+template<typename Func> void adolc_forward_jacobian(const Func& f)
+{
+ typename Func::InputType x = Func::InputType::Random(f.inputs());
+ typename Func::ValueType y(f.values()), yref(f.values());
+ typename Func::JacobianType j(f.values(),f.inputs()), jref(f.values(),f.inputs());
+
+ jref.setZero();
+ yref.setZero();
+ f(x,&yref,&jref);
+// std::cerr << y.transpose() << "\n\n";;
+// std::cerr << j << "\n\n";;
+
+ j.setZero();
+ y.setZero();
+ AdolcForwardJacobian<Func> autoj(f);
+ autoj(x, &y, &j);
+// std::cerr << y.transpose() << "\n\n";;
+// std::cerr << j << "\n\n";;
+
+ VERIFY_IS_APPROX(y, yref);
+ VERIFY_IS_APPROX(j, jref);
+}
+
+EIGEN_DECLARE_TEST(forward_adolc)
+{
+ adtl::setNumDir(NUMBER_DIRECTIONS);
+
+ for(int i = 0; i < g_repeat; i++) {
+ CALL_SUBTEST(( adolc_forward_jacobian(TestFunc1<double,2,2>()) ));
+ CALL_SUBTEST(( adolc_forward_jacobian(TestFunc1<double,2,3>()) ));
+ CALL_SUBTEST(( adolc_forward_jacobian(TestFunc1<double,3,2>()) ));
+ CALL_SUBTEST(( adolc_forward_jacobian(TestFunc1<double,3,3>()) ));
+ CALL_SUBTEST(( adolc_forward_jacobian(TestFunc1<double>(3,3)) ));
+ }
+
+ {
+ // simple instantiation tests
+ Matrix<adtl::adouble,2,1> x;
+ foo(x);
+ Matrix<adtl::adouble,Dynamic,Dynamic> A(4,4);;
+ A.selfadjointView<Lower>().eigenvalues();
+ }
+}
diff --git a/unsupported/test/gmres.cpp b/unsupported/test/gmres.cpp
new file mode 100644
index 0000000..8d2254b
--- /dev/null
+++ b/unsupported/test/gmres.cpp
@@ -0,0 +1,31 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2011 Gael Guennebaud <g.gael@free.fr>
+// Copyright (C) 2012 Kolja Brix <brix@igpm.rwth-aaachen.de>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "../../test/sparse_solver.h"
+#include <Eigen/IterativeSolvers>
+
+template<typename T> void test_gmres_T()
+{
+ GMRES<SparseMatrix<T>, DiagonalPreconditioner<T> > gmres_colmajor_diag;
+ GMRES<SparseMatrix<T>, IdentityPreconditioner > gmres_colmajor_I;
+ GMRES<SparseMatrix<T>, IncompleteLUT<T> > gmres_colmajor_ilut;
+ //GMRES<SparseMatrix<T>, SSORPreconditioner<T> > gmres_colmajor_ssor;
+
+ CALL_SUBTEST( check_sparse_square_solving(gmres_colmajor_diag) );
+// CALL_SUBTEST( check_sparse_square_solving(gmres_colmajor_I) );
+ CALL_SUBTEST( check_sparse_square_solving(gmres_colmajor_ilut) );
+ //CALL_SUBTEST( check_sparse_square_solving(gmres_colmajor_ssor) );
+}
+
+EIGEN_DECLARE_TEST(gmres)
+{
+ CALL_SUBTEST_1(test_gmres_T<double>());
+ CALL_SUBTEST_2(test_gmres_T<std::complex<double> >());
+}
diff --git a/unsupported/test/idrs.cpp b/unsupported/test/idrs.cpp
new file mode 100644
index 0000000..f88c016
--- /dev/null
+++ b/unsupported/test/idrs.cpp
@@ -0,0 +1,27 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2011 Gael Guennebaud <g.gael@free.fr>
+// Copyright (C) 2012 Kolja Brix <brix@igpm.rwth-aaachen.de>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "../../test/sparse_solver.h"
+#include <Eigen/IterativeSolvers>
+
+template<typename T> void test_idrs_T()
+{
+ IDRS<SparseMatrix<T>, DiagonalPreconditioner<T> > idrs_colmajor_diag;
+ IDRS<SparseMatrix<T>, IncompleteLUT<T> > idrs_colmajor_ilut;
+
+ CALL_SUBTEST( check_sparse_square_solving(idrs_colmajor_diag) );
+ CALL_SUBTEST( check_sparse_square_solving(idrs_colmajor_ilut) );
+}
+
+EIGEN_DECLARE_TEST(idrs)
+{
+ CALL_SUBTEST_1(test_idrs_T<double>());
+ CALL_SUBTEST_2(test_idrs_T<std::complex<double> >());
+}
diff --git a/unsupported/test/idrstabl.cpp b/unsupported/test/idrstabl.cpp
new file mode 100644
index 0000000..7e40dd6
--- /dev/null
+++ b/unsupported/test/idrstabl.cpp
@@ -0,0 +1,28 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2011 Gael Guennebaud <g.gael@free.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "../../test/sparse_solver.h"
+#include <unsupported/Eigen/IterativeSolvers>
+
+template <typename T>
+void test_idrstabl_T() {
+ IDRSTABL<SparseMatrix<T>, DiagonalPreconditioner<T> > idrstabl_colmajor_diag;
+ IDRSTABL<SparseMatrix<T>, IncompleteLUT<T> > idrstabl_colmajor_ilut;
+
+ idrstabl_colmajor_diag.setTolerance(NumTraits<T>::epsilon() * 4);
+ idrstabl_colmajor_ilut.setTolerance(NumTraits<T>::epsilon() * 4);
+
+ CALL_SUBTEST(check_sparse_square_solving(idrstabl_colmajor_diag));
+ CALL_SUBTEST(check_sparse_square_solving(idrstabl_colmajor_ilut));
+}
+
+EIGEN_DECLARE_TEST(idrstabl) {
+ CALL_SUBTEST_1((test_idrstabl_T<double>()));
+ CALL_SUBTEST_2((test_idrstabl_T<std::complex<double> >()));
+}
diff --git a/unsupported/test/kronecker_product.cpp b/unsupported/test/kronecker_product.cpp
new file mode 100644
index 0000000..3bac01d
--- /dev/null
+++ b/unsupported/test/kronecker_product.cpp
@@ -0,0 +1,252 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2011 Kolja Brix <brix@igpm.rwth-aachen.de>
+// Copyright (C) 2011 Andreas Platen <andiplaten@gmx.de>
+// Copyright (C) 2012 Chen-Pang He <jdh8@ms63.hinet.net>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+
+#ifdef EIGEN_TEST_PART_1
+
+#include "sparse.h"
+#include <Eigen/SparseExtra>
+#include <Eigen/KroneckerProduct>
+
+template<typename MatrixType>
+void check_dimension(const MatrixType& ab, const int rows, const int cols)
+{
+ VERIFY_IS_EQUAL(ab.rows(), rows);
+ VERIFY_IS_EQUAL(ab.cols(), cols);
+}
+
+
+template<typename MatrixType>
+void check_kronecker_product(const MatrixType& ab)
+{
+ VERIFY_IS_EQUAL(ab.rows(), 6);
+ VERIFY_IS_EQUAL(ab.cols(), 6);
+ VERIFY_IS_EQUAL(ab.size(), 36);
+ VERIFY_IS_APPROX(ab.coeff(0,0), -0.4017367630386106);
+ VERIFY_IS_APPROX(ab.coeff(0,1), 0.1056863433932735);
+ VERIFY_IS_APPROX(ab.coeff(0,2), -0.7255206194554212);
+ VERIFY_IS_APPROX(ab.coeff(0,3), 0.1908653336744706);
+ VERIFY_IS_APPROX(ab.coeff(0,4), 0.350864567234111);
+ VERIFY_IS_APPROX(ab.coeff(0,5), -0.0923032108308013);
+ VERIFY_IS_APPROX(ab.coeff(1,0), 0.415417514804677);
+ VERIFY_IS_APPROX(ab.coeff(1,1), -0.2369227701722048);
+ VERIFY_IS_APPROX(ab.coeff(1,2), 0.7502275131458511);
+ VERIFY_IS_APPROX(ab.coeff(1,3), -0.4278731019742696);
+ VERIFY_IS_APPROX(ab.coeff(1,4), -0.3628129162264507);
+ VERIFY_IS_APPROX(ab.coeff(1,5), 0.2069210808481275);
+ VERIFY_IS_APPROX(ab.coeff(2,0), 0.05465890160863986);
+ VERIFY_IS_APPROX(ab.coeff(2,1), -0.2634092511419858);
+ VERIFY_IS_APPROX(ab.coeff(2,2), 0.09871180285793758);
+ VERIFY_IS_APPROX(ab.coeff(2,3), -0.4757066334017702);
+ VERIFY_IS_APPROX(ab.coeff(2,4), -0.04773740823058334);
+ VERIFY_IS_APPROX(ab.coeff(2,5), 0.2300535609645254);
+ VERIFY_IS_APPROX(ab.coeff(3,0), -0.8172945853260133);
+ VERIFY_IS_APPROX(ab.coeff(3,1), 0.2150086428359221);
+ VERIFY_IS_APPROX(ab.coeff(3,2), 0.5825113847292743);
+ VERIFY_IS_APPROX(ab.coeff(3,3), -0.1532433770097174);
+ VERIFY_IS_APPROX(ab.coeff(3,4), -0.329383387282399);
+ VERIFY_IS_APPROX(ab.coeff(3,5), 0.08665207912033064);
+ VERIFY_IS_APPROX(ab.coeff(4,0), 0.8451267514863225);
+ VERIFY_IS_APPROX(ab.coeff(4,1), -0.481996458918977);
+ VERIFY_IS_APPROX(ab.coeff(4,2), -0.6023482390791535);
+ VERIFY_IS_APPROX(ab.coeff(4,3), 0.3435339347164565);
+ VERIFY_IS_APPROX(ab.coeff(4,4), 0.3406002157428891);
+ VERIFY_IS_APPROX(ab.coeff(4,5), -0.1942526344200915);
+ VERIFY_IS_APPROX(ab.coeff(5,0), 0.1111982482925399);
+ VERIFY_IS_APPROX(ab.coeff(5,1), -0.5358806424754169);
+ VERIFY_IS_APPROX(ab.coeff(5,2), -0.07925446559335647);
+ VERIFY_IS_APPROX(ab.coeff(5,3), 0.3819388757769038);
+ VERIFY_IS_APPROX(ab.coeff(5,4), 0.04481475387219876);
+ VERIFY_IS_APPROX(ab.coeff(5,5), -0.2159688616158057);
+}
+
+
+template<typename MatrixType>
+void check_sparse_kronecker_product(const MatrixType& ab)
+{
+ VERIFY_IS_EQUAL(ab.rows(), 12);
+ VERIFY_IS_EQUAL(ab.cols(), 10);
+ VERIFY_IS_EQUAL(ab.nonZeros(), 3*2);
+ VERIFY_IS_APPROX(ab.coeff(3,0), -0.04);
+ VERIFY_IS_APPROX(ab.coeff(5,1), 0.05);
+ VERIFY_IS_APPROX(ab.coeff(0,6), -0.08);
+ VERIFY_IS_APPROX(ab.coeff(2,7), 0.10);
+ VERIFY_IS_APPROX(ab.coeff(6,8), 0.12);
+ VERIFY_IS_APPROX(ab.coeff(8,9), -0.15);
+}
+
+
+EIGEN_DECLARE_TEST(kronecker_product)
+{
+ // DM = dense matrix; SM = sparse matrix
+
+ Matrix<double, 2, 3> DM_a;
+ SparseMatrix<double> SM_a(2,3);
+ SM_a.insert(0,0) = DM_a.coeffRef(0,0) = -0.4461540300782201;
+ SM_a.insert(0,1) = DM_a.coeffRef(0,1) = -0.8057364375283049;
+ SM_a.insert(0,2) = DM_a.coeffRef(0,2) = 0.3896572459516341;
+ SM_a.insert(1,0) = DM_a.coeffRef(1,0) = -0.9076572187376921;
+ SM_a.insert(1,1) = DM_a.coeffRef(1,1) = 0.6469156566545853;
+ SM_a.insert(1,2) = DM_a.coeffRef(1,2) = -0.3658010398782789;
+
+ MatrixXd DM_b(3,2);
+ SparseMatrix<double> SM_b(3,2);
+ SM_b.insert(0,0) = DM_b.coeffRef(0,0) = 0.9004440976767099;
+ SM_b.insert(0,1) = DM_b.coeffRef(0,1) = -0.2368830858139832;
+ SM_b.insert(1,0) = DM_b.coeffRef(1,0) = -0.9311078389941825;
+ SM_b.insert(1,1) = DM_b.coeffRef(1,1) = 0.5310335762980047;
+ SM_b.insert(2,0) = DM_b.coeffRef(2,0) = -0.1225112806872035;
+ SM_b.insert(2,1) = DM_b.coeffRef(2,1) = 0.5903998022741264;
+
+ SparseMatrix<double,RowMajor> SM_row_a(SM_a), SM_row_b(SM_b);
+
+ // test DM_fixedSize = kroneckerProduct(DM_block,DM)
+ Matrix<double, 6, 6> DM_fix_ab = kroneckerProduct(DM_a.topLeftCorner<2,3>(),DM_b);
+
+ CALL_SUBTEST(check_kronecker_product(DM_fix_ab));
+ CALL_SUBTEST(check_kronecker_product(kroneckerProduct(DM_a.topLeftCorner<2,3>(),DM_b)));
+
+ for(int i=0;i<DM_fix_ab.rows();++i)
+ for(int j=0;j<DM_fix_ab.cols();++j)
+ VERIFY_IS_APPROX(kroneckerProduct(DM_a,DM_b).coeff(i,j), DM_fix_ab(i,j));
+
+ // test DM_block = kroneckerProduct(DM,DM)
+ MatrixXd DM_block_ab(10,15);
+ DM_block_ab.block<6,6>(2,5) = kroneckerProduct(DM_a,DM_b);
+ CALL_SUBTEST(check_kronecker_product(DM_block_ab.block<6,6>(2,5)));
+
+ // test DM = kroneckerProduct(DM,DM)
+ MatrixXd DM_ab = kroneckerProduct(DM_a,DM_b);
+ CALL_SUBTEST(check_kronecker_product(DM_ab));
+ CALL_SUBTEST(check_kronecker_product(kroneckerProduct(DM_a,DM_b)));
+
+ // test SM = kroneckerProduct(SM,DM)
+ SparseMatrix<double> SM_ab = kroneckerProduct(SM_a,DM_b);
+ CALL_SUBTEST(check_kronecker_product(SM_ab));
+ SparseMatrix<double,RowMajor> SM_ab2 = kroneckerProduct(SM_a,DM_b);
+ CALL_SUBTEST(check_kronecker_product(SM_ab2));
+ CALL_SUBTEST(check_kronecker_product(kroneckerProduct(SM_a,DM_b)));
+
+ // test SM = kroneckerProduct(DM,SM)
+ SM_ab.setZero();
+ SM_ab.insert(0,0)=37.0;
+ SM_ab = kroneckerProduct(DM_a,SM_b);
+ CALL_SUBTEST(check_kronecker_product(SM_ab));
+ SM_ab2.setZero();
+ SM_ab2.insert(0,0)=37.0;
+ SM_ab2 = kroneckerProduct(DM_a,SM_b);
+ CALL_SUBTEST(check_kronecker_product(SM_ab2));
+ CALL_SUBTEST(check_kronecker_product(kroneckerProduct(DM_a,SM_b)));
+
+ // test SM = kroneckerProduct(SM,SM)
+ SM_ab.resize(2,33);
+ SM_ab.insert(0,0)=37.0;
+ SM_ab = kroneckerProduct(SM_a,SM_b);
+ CALL_SUBTEST(check_kronecker_product(SM_ab));
+ SM_ab2.resize(5,11);
+ SM_ab2.insert(0,0)=37.0;
+ SM_ab2 = kroneckerProduct(SM_a,SM_b);
+ CALL_SUBTEST(check_kronecker_product(SM_ab2));
+ CALL_SUBTEST(check_kronecker_product(kroneckerProduct(SM_a,SM_b)));
+
+ // test SM = kroneckerProduct(SM,SM) with sparse pattern
+ SM_a.resize(4,5);
+ SM_b.resize(3,2);
+ SM_a.resizeNonZeros(0);
+ SM_b.resizeNonZeros(0);
+ SM_a.insert(1,0) = -0.1;
+ SM_a.insert(0,3) = -0.2;
+ SM_a.insert(2,4) = 0.3;
+ SM_a.finalize();
+
+ SM_b.insert(0,0) = 0.4;
+ SM_b.insert(2,1) = -0.5;
+ SM_b.finalize();
+ SM_ab.resize(1,1);
+ SM_ab.insert(0,0)=37.0;
+ SM_ab = kroneckerProduct(SM_a,SM_b);
+ CALL_SUBTEST(check_sparse_kronecker_product(SM_ab));
+
+ // test dimension of result of DM = kroneckerProduct(DM,DM)
+ MatrixXd DM_a2(2,1);
+ MatrixXd DM_b2(5,4);
+ MatrixXd DM_ab2 = kroneckerProduct(DM_a2,DM_b2);
+ CALL_SUBTEST(check_dimension(DM_ab2,2*5,1*4));
+ DM_a2.resize(10,9);
+ DM_b2.resize(4,8);
+ DM_ab2 = kroneckerProduct(DM_a2,DM_b2);
+ CALL_SUBTEST(check_dimension(DM_ab2,10*4,9*8));
+
+ for(int i = 0; i < g_repeat; i++)
+ {
+ double density = Eigen::internal::random<double>(0.01,0.5);
+ int ra = Eigen::internal::random<int>(1,50);
+ int ca = Eigen::internal::random<int>(1,50);
+ int rb = Eigen::internal::random<int>(1,50);
+ int cb = Eigen::internal::random<int>(1,50);
+ SparseMatrix<float,ColMajor> sA(ra,ca), sB(rb,cb), sC;
+ SparseMatrix<float,RowMajor> sC2;
+ MatrixXf dA(ra,ca), dB(rb,cb), dC;
+ initSparse(density, dA, sA);
+ initSparse(density, dB, sB);
+
+ sC = kroneckerProduct(sA,sB);
+ dC = kroneckerProduct(dA,dB);
+ VERIFY_IS_APPROX(MatrixXf(sC),dC);
+
+ sC = kroneckerProduct(sA.transpose(),sB);
+ dC = kroneckerProduct(dA.transpose(),dB);
+ VERIFY_IS_APPROX(MatrixXf(sC),dC);
+
+ sC = kroneckerProduct(sA.transpose(),sB.transpose());
+ dC = kroneckerProduct(dA.transpose(),dB.transpose());
+ VERIFY_IS_APPROX(MatrixXf(sC),dC);
+
+ sC = kroneckerProduct(sA,sB.transpose());
+ dC = kroneckerProduct(dA,dB.transpose());
+ VERIFY_IS_APPROX(MatrixXf(sC),dC);
+
+ sC2 = kroneckerProduct(sA,sB);
+ dC = kroneckerProduct(dA,dB);
+ VERIFY_IS_APPROX(MatrixXf(sC2),dC);
+
+ sC2 = kroneckerProduct(dA,sB);
+ dC = kroneckerProduct(dA,dB);
+ VERIFY_IS_APPROX(MatrixXf(sC2),dC);
+
+ sC2 = kroneckerProduct(sA,dB);
+ dC = kroneckerProduct(dA,dB);
+ VERIFY_IS_APPROX(MatrixXf(sC2),dC);
+
+ sC2 = kroneckerProduct(2*sA,sB);
+ dC = kroneckerProduct(2*dA,dB);
+ VERIFY_IS_APPROX(MatrixXf(sC2),dC);
+ }
+}
+
+#endif
+
+#ifdef EIGEN_TEST_PART_2
+
+// simply check that for a dense kronecker product, sparse module is not needed
+#include "main.h"
+#include <Eigen/KroneckerProduct>
+
+EIGEN_DECLARE_TEST(kronecker_product)
+{
+ MatrixXd a(2,2), b(3,3), c;
+ a.setRandom();
+ b.setRandom();
+ c = kroneckerProduct(a,b);
+ VERIFY_IS_APPROX(c.block(3,3,3,3), a(1,1)*b);
+}
+
+#endif
diff --git a/unsupported/test/levenberg_marquardt.cpp b/unsupported/test/levenberg_marquardt.cpp
new file mode 100644
index 0000000..d0748d1
--- /dev/null
+++ b/unsupported/test/levenberg_marquardt.cpp
@@ -0,0 +1,1508 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009 Thomas Capricelli <orzel@freehackers.org>
+// Copyright (C) 2012 desire Nuentsa <desire.nuentsa_wakam@inria.fr
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+
+// FIXME: These tests all check for hard-coded values. Ideally, parameters and start estimates should be randomized.
+
+
+#include <stdio.h>
+
+#include "main.h"
+#include <unsupported/Eigen/LevenbergMarquardt>
+
+// This disables some useless Warnings on MSVC.
+// It is intended to be done for this test only.
+#include <Eigen/src/Core/util/DisableStupidWarnings.h>
+
+using std::sqrt;
+
+// tolerance for chekcing number of iterations
+#define LM_EVAL_COUNT_TOL 2
+
+struct lmder_functor : DenseFunctor<double>
+{
+ lmder_functor(void): DenseFunctor<double>(3,15) {}
+ int operator()(const VectorXd &x, VectorXd &fvec) const
+ {
+ double tmp1, tmp2, tmp3;
+ static const double y[15] = {1.4e-1, 1.8e-1, 2.2e-1, 2.5e-1, 2.9e-1, 3.2e-1, 3.5e-1,
+ 3.9e-1, 3.7e-1, 5.8e-1, 7.3e-1, 9.6e-1, 1.34, 2.1, 4.39};
+
+ for (int i = 0; i < values(); i++)
+ {
+ tmp1 = i+1;
+ tmp2 = 16 - i - 1;
+ tmp3 = (i>=8)? tmp2 : tmp1;
+ fvec[i] = y[i] - (x[0] + tmp1/(x[1]*tmp2 + x[2]*tmp3));
+ }
+ return 0;
+ }
+
+ int df(const VectorXd &x, MatrixXd &fjac) const
+ {
+ double tmp1, tmp2, tmp3, tmp4;
+ for (int i = 0; i < values(); i++)
+ {
+ tmp1 = i+1;
+ tmp2 = 16 - i - 1;
+ tmp3 = (i>=8)? tmp2 : tmp1;
+ tmp4 = (x[1]*tmp2 + x[2]*tmp3); tmp4 = tmp4*tmp4;
+ fjac(i,0) = -1;
+ fjac(i,1) = tmp1*tmp2/tmp4;
+ fjac(i,2) = tmp1*tmp3/tmp4;
+ }
+ return 0;
+ }
+};
+
+void testLmder1()
+{
+ int n=3, info;
+
+ VectorXd x;
+
+ /* the following starting values provide a rough fit. */
+ x.setConstant(n, 1.);
+
+ // do the computation
+ lmder_functor functor;
+ LevenbergMarquardt<lmder_functor> lm(functor);
+ info = lm.lmder1(x);
+ EIGEN_UNUSED_VARIABLE(info)
+ // check return value
+ // VERIFY_IS_EQUAL(info, 1);
+ // VERIFY_IS_EQUAL(lm.nfev(), 6);
+ // VERIFY_IS_EQUAL(lm.njev(), 5);
+
+ // check norm
+ VERIFY_IS_APPROX(lm.fvec().blueNorm(), 0.09063596);
+
+ // check x
+ VectorXd x_ref(n);
+ x_ref << 0.08241058, 1.133037, 2.343695;
+ VERIFY_IS_APPROX(x, x_ref);
+}
+
+void testLmder()
+{
+ const int m=15, n=3;
+ int info;
+ double fnorm, covfac;
+ VectorXd x;
+
+ /* the following starting values provide a rough fit. */
+ x.setConstant(n, 1.);
+
+ // do the computation
+ lmder_functor functor;
+ LevenbergMarquardt<lmder_functor> lm(functor);
+ info = lm.minimize(x);
+ EIGEN_UNUSED_VARIABLE(info)
+
+ // check return values
+ // VERIFY_IS_EQUAL(info, 1);
+ // VERIFY_IS_EQUAL(lm.nfev(), 6);
+ // VERIFY_IS_EQUAL(lm.njev(), 5);
+
+ // check norm
+ fnorm = lm.fvec().blueNorm();
+ VERIFY_IS_APPROX(fnorm, 0.09063596);
+
+ // check x
+ VectorXd x_ref(n);
+ x_ref << 0.08241058, 1.133037, 2.343695;
+ VERIFY_IS_APPROX(x, x_ref);
+
+ // check covariance
+ covfac = fnorm*fnorm/(m-n);
+ internal::covar(lm.matrixR(), lm.permutation().indices()); // TODO : move this as a function of lm
+
+ MatrixXd cov_ref(n,n);
+ cov_ref <<
+ 0.0001531202, 0.002869941, -0.002656662,
+ 0.002869941, 0.09480935, -0.09098995,
+ -0.002656662, -0.09098995, 0.08778727;
+
+// std::cout << fjac*covfac << std::endl;
+
+ MatrixXd cov;
+ cov = covfac*lm.matrixR().topLeftCorner<n,n>();
+ VERIFY_IS_APPROX( cov, cov_ref);
+ // TODO: why isn't this allowed ? :
+ // VERIFY_IS_APPROX( covfac*fjac.topLeftCorner<n,n>() , cov_ref);
+}
+
+struct lmdif_functor : DenseFunctor<double>
+{
+ lmdif_functor(void) : DenseFunctor<double>(3,15) {}
+ int operator()(const VectorXd &x, VectorXd &fvec) const
+ {
+ int i;
+ double tmp1,tmp2,tmp3;
+ static const double y[15]={1.4e-1,1.8e-1,2.2e-1,2.5e-1,2.9e-1,3.2e-1,3.5e-1,3.9e-1,
+ 3.7e-1,5.8e-1,7.3e-1,9.6e-1,1.34e0,2.1e0,4.39e0};
+
+ assert(x.size()==3);
+ assert(fvec.size()==15);
+ for (i=0; i<15; i++)
+ {
+ tmp1 = i+1;
+ tmp2 = 15 - i;
+ tmp3 = tmp1;
+
+ if (i >= 8) tmp3 = tmp2;
+ fvec[i] = y[i] - (x[0] + tmp1/(x[1]*tmp2 + x[2]*tmp3));
+ }
+ return 0;
+ }
+};
+
+void testLmdif1()
+{
+ const int n=3;
+ int info;
+
+ VectorXd x(n), fvec(15);
+
+ /* the following starting values provide a rough fit. */
+ x.setConstant(n, 1.);
+
+ // do the computation
+ lmdif_functor functor;
+ DenseIndex nfev;
+ info = LevenbergMarquardt<lmdif_functor>::lmdif1(functor, x, &nfev);
+ EIGEN_UNUSED_VARIABLE(info)
+
+ // check return value
+ // VERIFY_IS_EQUAL(info, 1);
+// VERIFY_IS_EQUAL(nfev, 26);
+
+ // check norm
+ functor(x, fvec);
+ VERIFY_IS_APPROX(fvec.blueNorm(), 0.09063596);
+
+ // check x
+ VectorXd x_ref(n);
+ x_ref << 0.0824106, 1.1330366, 2.3436947;
+ VERIFY_IS_APPROX(x, x_ref);
+
+}
+
+void testLmdif()
+{
+ const int m=15, n=3;
+ int info;
+ double fnorm, covfac;
+ VectorXd x(n);
+
+ /* the following starting values provide a rough fit. */
+ x.setConstant(n, 1.);
+
+ // do the computation
+ lmdif_functor functor;
+ NumericalDiff<lmdif_functor> numDiff(functor);
+ LevenbergMarquardt<NumericalDiff<lmdif_functor> > lm(numDiff);
+ info = lm.minimize(x);
+ EIGEN_UNUSED_VARIABLE(info)
+
+ // check return values
+ // VERIFY_IS_EQUAL(info, 1);
+// VERIFY_IS_EQUAL(lm.nfev(), 26);
+
+ // check norm
+ fnorm = lm.fvec().blueNorm();
+ VERIFY_IS_APPROX(fnorm, 0.09063596);
+
+ // check x
+ VectorXd x_ref(n);
+ x_ref << 0.08241058, 1.133037, 2.343695;
+ VERIFY_IS_APPROX(x, x_ref);
+
+ // check covariance
+ covfac = fnorm*fnorm/(m-n);
+ internal::covar(lm.matrixR(), lm.permutation().indices()); // TODO : move this as a function of lm
+
+ MatrixXd cov_ref(n,n);
+ cov_ref <<
+ 0.0001531202, 0.002869942, -0.002656662,
+ 0.002869942, 0.09480937, -0.09098997,
+ -0.002656662, -0.09098997, 0.08778729;
+
+// std::cout << fjac*covfac << std::endl;
+
+ MatrixXd cov;
+ cov = covfac*lm.matrixR().topLeftCorner<n,n>();
+ VERIFY_IS_APPROX( cov, cov_ref);
+ // TODO: why isn't this allowed ? :
+ // VERIFY_IS_APPROX( covfac*fjac.topLeftCorner<n,n>() , cov_ref);
+}
+
+struct chwirut2_functor : DenseFunctor<double>
+{
+ chwirut2_functor(void) : DenseFunctor<double>(3,54) {}
+ static const double m_x[54];
+ static const double m_y[54];
+ int operator()(const VectorXd &b, VectorXd &fvec)
+ {
+ int i;
+
+ assert(b.size()==3);
+ assert(fvec.size()==54);
+ for(i=0; i<54; i++) {
+ double x = m_x[i];
+ fvec[i] = exp(-b[0]*x)/(b[1]+b[2]*x) - m_y[i];
+ }
+ return 0;
+ }
+ int df(const VectorXd &b, MatrixXd &fjac)
+ {
+ assert(b.size()==3);
+ assert(fjac.rows()==54);
+ assert(fjac.cols()==3);
+ for(int i=0; i<54; i++) {
+ double x = m_x[i];
+ double factor = 1./(b[1]+b[2]*x);
+ double e = exp(-b[0]*x);
+ fjac(i,0) = -x*e*factor;
+ fjac(i,1) = -e*factor*factor;
+ fjac(i,2) = -x*e*factor*factor;
+ }
+ return 0;
+ }
+};
+const double chwirut2_functor::m_x[54] = { 0.500E0, 1.000E0, 1.750E0, 3.750E0, 5.750E0, 0.875E0, 2.250E0, 3.250E0, 5.250E0, 0.750E0, 1.750E0, 2.750E0, 4.750E0, 0.625E0, 1.250E0, 2.250E0, 4.250E0, .500E0, 3.000E0, .750E0, 3.000E0, 1.500E0, 6.000E0, 3.000E0, 6.000E0, 1.500E0, 3.000E0, .500E0, 2.000E0, 4.000E0, .750E0, 2.000E0, 5.000E0, .750E0, 2.250E0, 3.750E0, 5.750E0, 3.000E0, .750E0, 2.500E0, 4.000E0, .750E0, 2.500E0, 4.000E0, .750E0, 2.500E0, 4.000E0, .500E0, 6.000E0, 3.000E0, .500E0, 2.750E0, .500E0, 1.750E0};
+const double chwirut2_functor::m_y[54] = { 92.9000E0 ,57.1000E0 ,31.0500E0 ,11.5875E0 ,8.0250E0 ,63.6000E0 ,21.4000E0 ,14.2500E0 ,8.4750E0 ,63.8000E0 ,26.8000E0 ,16.4625E0 ,7.1250E0 ,67.3000E0 ,41.0000E0 ,21.1500E0 ,8.1750E0 ,81.5000E0 ,13.1200E0 ,59.9000E0 ,14.6200E0 ,32.9000E0 ,5.4400E0 ,12.5600E0 ,5.4400E0 ,32.0000E0 ,13.9500E0 ,75.8000E0 ,20.0000E0 ,10.4200E0 ,59.5000E0 ,21.6700E0 ,8.5500E0 ,62.0000E0 ,20.2000E0 ,7.7600E0 ,3.7500E0 ,11.8100E0 ,54.7000E0 ,23.7000E0 ,11.5500E0 ,61.3000E0 ,17.7000E0 ,8.7400E0 ,59.2000E0 ,16.3000E0 ,8.6200E0 ,81.0000E0 ,4.8700E0 ,14.6200E0 ,81.7000E0 ,17.1700E0 ,81.3000E0 ,28.9000E0 };
+
+// http://www.itl.nist.gov/div898/strd/nls/data/chwirut2.shtml
+void testNistChwirut2(void)
+{
+ const int n=3;
+ LevenbergMarquardtSpace::Status info;
+
+ VectorXd x(n);
+
+ /*
+ * First try
+ */
+ x<< 0.1, 0.01, 0.02;
+ // do the computation
+ chwirut2_functor functor;
+ LevenbergMarquardt<chwirut2_functor> lm(functor);
+ info = lm.minimize(x);
+ EIGEN_UNUSED_VARIABLE(info)
+
+ // check return value
+ // VERIFY_IS_EQUAL(info, 1);
+// VERIFY_IS_EQUAL(lm.nfev(), 10);
+ // VERIFY_IS_EQUAL(lm.njev(), 8);
+ // check norm^2
+ VERIFY_IS_APPROX(lm.fvec().squaredNorm(), 5.1304802941E+02);
+ // check x
+ VERIFY_IS_APPROX(x[0], 1.6657666537E-01);
+ VERIFY_IS_APPROX(x[1], 5.1653291286E-03);
+ VERIFY_IS_APPROX(x[2], 1.2150007096E-02);
+
+ /*
+ * Second try
+ */
+ x<< 0.15, 0.008, 0.010;
+ // do the computation
+ lm.resetParameters();
+ lm.setFtol(1.E6*NumTraits<double>::epsilon());
+ lm.setXtol(1.E6*NumTraits<double>::epsilon());
+ info = lm.minimize(x);
+ EIGEN_UNUSED_VARIABLE(info)
+
+ // check return value
+ // VERIFY_IS_EQUAL(info, 1);
+// VERIFY_IS_EQUAL(lm.nfev(), 7);
+ // VERIFY_IS_EQUAL(lm.njev(), 6);
+ // check norm^2
+ VERIFY_IS_APPROX(lm.fvec().squaredNorm(), 5.1304802941E+02);
+ // check x
+ VERIFY_IS_APPROX(x[0], 1.6657666537E-01);
+ VERIFY_IS_APPROX(x[1], 5.1653291286E-03);
+ VERIFY_IS_APPROX(x[2], 1.2150007096E-02);
+}
+
+
+struct misra1a_functor : DenseFunctor<double>
+{
+ misra1a_functor(void) : DenseFunctor<double>(2,14) {}
+ static const double m_x[14];
+ static const double m_y[14];
+ int operator()(const VectorXd &b, VectorXd &fvec)
+ {
+ assert(b.size()==2);
+ assert(fvec.size()==14);
+ for(int i=0; i<14; i++) {
+ fvec[i] = b[0]*(1.-exp(-b[1]*m_x[i])) - m_y[i] ;
+ }
+ return 0;
+ }
+ int df(const VectorXd &b, MatrixXd &fjac)
+ {
+ assert(b.size()==2);
+ assert(fjac.rows()==14);
+ assert(fjac.cols()==2);
+ for(int i=0; i<14; i++) {
+ fjac(i,0) = (1.-exp(-b[1]*m_x[i]));
+ fjac(i,1) = (b[0]*m_x[i]*exp(-b[1]*m_x[i]));
+ }
+ return 0;
+ }
+};
+const double misra1a_functor::m_x[14] = { 77.6E0, 114.9E0, 141.1E0, 190.8E0, 239.9E0, 289.0E0, 332.8E0, 378.4E0, 434.8E0, 477.3E0, 536.8E0, 593.1E0, 689.1E0, 760.0E0};
+const double misra1a_functor::m_y[14] = { 10.07E0, 14.73E0, 17.94E0, 23.93E0, 29.61E0, 35.18E0, 40.02E0, 44.82E0, 50.76E0, 55.05E0, 61.01E0, 66.40E0, 75.47E0, 81.78E0};
+
+// http://www.itl.nist.gov/div898/strd/nls/data/misra1a.shtml
+void testNistMisra1a(void)
+{
+ const int n=2;
+ int info;
+
+ VectorXd x(n);
+
+ /*
+ * First try
+ */
+ x<< 500., 0.0001;
+ // do the computation
+ misra1a_functor functor;
+ LevenbergMarquardt<misra1a_functor> lm(functor);
+ info = lm.minimize(x);
+ EIGEN_UNUSED_VARIABLE(info)
+
+ // check return value
+ // VERIFY_IS_EQUAL(info, 1);
+ // VERIFY_IS_EQUAL(lm.nfev(), 19);
+ // VERIFY_IS_EQUAL(lm.njev(), 15);
+ // check norm^2
+ VERIFY_IS_APPROX(lm.fvec().squaredNorm(), 1.2455138894E-01);
+ // check x
+ VERIFY_IS_APPROX(x[0], 2.3894212918E+02);
+ VERIFY_IS_APPROX(x[1], 5.5015643181E-04);
+
+ /*
+ * Second try
+ */
+ x<< 250., 0.0005;
+ // do the computation
+ info = lm.minimize(x);
+ EIGEN_UNUSED_VARIABLE(info)
+
+ // check return value
+ // VERIFY_IS_EQUAL(info, 1);
+ // VERIFY_IS_EQUAL(lm.nfev(), 5);
+ // VERIFY_IS_EQUAL(lm.njev(), 4);
+ // check norm^2
+ VERIFY_IS_APPROX(lm.fvec().squaredNorm(), 1.2455138894E-01);
+ // check x
+ VERIFY_IS_APPROX(x[0], 2.3894212918E+02);
+ VERIFY_IS_APPROX(x[1], 5.5015643181E-04);
+}
+
+struct hahn1_functor : DenseFunctor<double>
+{
+ hahn1_functor(void) : DenseFunctor<double>(7,236) {}
+ static const double m_x[236];
+ int operator()(const VectorXd &b, VectorXd &fvec)
+ {
+ static const double m_y[236] = { .591E0 , 1.547E0 , 2.902E0 , 2.894E0 , 4.703E0 , 6.307E0 , 7.03E0 , 7.898E0 , 9.470E0 , 9.484E0 , 10.072E0 , 10.163E0 , 11.615E0 , 12.005E0 , 12.478E0 , 12.982E0 , 12.970E0 , 13.926E0 , 14.452E0 , 14.404E0 , 15.190E0 , 15.550E0 , 15.528E0 , 15.499E0 , 16.131E0 , 16.438E0 , 16.387E0 , 16.549E0 , 16.872E0 , 16.830E0 , 16.926E0 , 16.907E0 , 16.966E0 , 17.060E0 , 17.122E0 , 17.311E0 , 17.355E0 , 17.668E0 , 17.767E0 , 17.803E0 , 17.765E0 , 17.768E0 , 17.736E0 , 17.858E0 , 17.877E0 , 17.912E0 , 18.046E0 , 18.085E0 , 18.291E0 , 18.357E0 , 18.426E0 , 18.584E0 , 18.610E0 , 18.870E0 , 18.795E0 , 19.111E0 , .367E0 , .796E0 , 0.892E0 , 1.903E0 , 2.150E0 , 3.697E0 , 5.870E0 , 6.421E0 , 7.422E0 , 9.944E0 , 11.023E0 , 11.87E0 , 12.786E0 , 14.067E0 , 13.974E0 , 14.462E0 , 14.464E0 , 15.381E0 , 15.483E0 , 15.59E0 , 16.075E0 , 16.347E0 , 16.181E0 , 16.915E0 , 17.003E0 , 16.978E0 , 17.756E0 , 17.808E0 , 17.868E0 , 18.481E0 , 18.486E0 , 19.090E0 , 16.062E0 , 16.337E0 , 16.345E0 ,
+ 16.388E0 , 17.159E0 , 17.116E0 , 17.164E0 , 17.123E0 , 17.979E0 , 17.974E0 , 18.007E0 , 17.993E0 , 18.523E0 , 18.669E0 , 18.617E0 , 19.371E0 , 19.330E0 , 0.080E0 , 0.248E0 , 1.089E0 , 1.418E0 , 2.278E0 , 3.624E0 , 4.574E0 , 5.556E0 , 7.267E0 , 7.695E0 , 9.136E0 , 9.959E0 , 9.957E0 , 11.600E0 , 13.138E0 , 13.564E0 , 13.871E0 , 13.994E0 , 14.947E0 , 15.473E0 , 15.379E0 , 15.455E0 , 15.908E0 , 16.114E0 , 17.071E0 , 17.135E0 , 17.282E0 , 17.368E0 , 17.483E0 , 17.764E0 , 18.185E0 , 18.271E0 , 18.236E0 , 18.237E0 , 18.523E0 , 18.627E0 , 18.665E0 , 19.086E0 , 0.214E0 , 0.943E0 , 1.429E0 , 2.241E0 , 2.951E0 , 3.782E0 , 4.757E0 , 5.602E0 , 7.169E0 , 8.920E0 , 10.055E0 , 12.035E0 , 12.861E0 , 13.436E0 , 14.167E0 , 14.755E0 , 15.168E0 , 15.651E0 , 15.746E0 , 16.216E0 , 16.445E0 , 16.965E0 , 17.121E0 , 17.206E0 , 17.250E0 , 17.339E0 , 17.793E0 , 18.123E0 , 18.49E0 , 18.566E0 , 18.645E0 , 18.706E0 , 18.924E0 , 19.1E0 , 0.375E0 , 0.471E0 , 1.504E0 , 2.204E0 , 2.813E0 , 4.765E0 , 9.835E0 , 10.040E0 , 11.946E0 ,
+12.596E0 ,
+13.303E0 , 13.922E0 , 14.440E0 , 14.951E0 , 15.627E0 , 15.639E0 , 15.814E0 , 16.315E0 , 16.334E0 , 16.430E0 , 16.423E0 , 17.024E0 , 17.009E0 , 17.165E0 , 17.134E0 , 17.349E0 , 17.576E0 , 17.848E0 , 18.090E0 , 18.276E0 , 18.404E0 , 18.519E0 , 19.133E0 , 19.074E0 , 19.239E0 , 19.280E0 , 19.101E0 , 19.398E0 , 19.252E0 , 19.89E0 , 20.007E0 , 19.929E0 , 19.268E0 , 19.324E0 , 20.049E0 , 20.107E0 , 20.062E0 , 20.065E0 , 19.286E0 , 19.972E0 , 20.088E0 , 20.743E0 , 20.83E0 , 20.935E0 , 21.035E0 , 20.93E0 , 21.074E0 , 21.085E0 , 20.935E0 };
+
+ // int called=0; printf("call hahn1_functor with iflag=%d, called=%d\n", iflag, called); if (iflag==1) called++;
+
+ assert(b.size()==7);
+ assert(fvec.size()==236);
+ for(int i=0; i<236; i++) {
+ double x=m_x[i], xx=x*x, xxx=xx*x;
+ fvec[i] = (b[0]+b[1]*x+b[2]*xx+b[3]*xxx) / (1.+b[4]*x+b[5]*xx+b[6]*xxx) - m_y[i];
+ }
+ return 0;
+ }
+
+ int df(const VectorXd &b, MatrixXd &fjac)
+ {
+ assert(b.size()==7);
+ assert(fjac.rows()==236);
+ assert(fjac.cols()==7);
+ for(int i=0; i<236; i++) {
+ double x=m_x[i], xx=x*x, xxx=xx*x;
+ double fact = 1./(1.+b[4]*x+b[5]*xx+b[6]*xxx);
+ fjac(i,0) = 1.*fact;
+ fjac(i,1) = x*fact;
+ fjac(i,2) = xx*fact;
+ fjac(i,3) = xxx*fact;
+ fact = - (b[0]+b[1]*x+b[2]*xx+b[3]*xxx) * fact * fact;
+ fjac(i,4) = x*fact;
+ fjac(i,5) = xx*fact;
+ fjac(i,6) = xxx*fact;
+ }
+ return 0;
+ }
+};
+const double hahn1_functor::m_x[236] = { 24.41E0 , 34.82E0 , 44.09E0 , 45.07E0 , 54.98E0 , 65.51E0 , 70.53E0 , 75.70E0 , 89.57E0 , 91.14E0 , 96.40E0 , 97.19E0 , 114.26E0 , 120.25E0 , 127.08E0 , 133.55E0 , 133.61E0 , 158.67E0 , 172.74E0 , 171.31E0 , 202.14E0 , 220.55E0 , 221.05E0 , 221.39E0 , 250.99E0 , 268.99E0 , 271.80E0 , 271.97E0 , 321.31E0 , 321.69E0 , 330.14E0 , 333.03E0 , 333.47E0 , 340.77E0 , 345.65E0 , 373.11E0 , 373.79E0 , 411.82E0 , 419.51E0 , 421.59E0 , 422.02E0 , 422.47E0 , 422.61E0 , 441.75E0 , 447.41E0 , 448.7E0 , 472.89E0 , 476.69E0 , 522.47E0 , 522.62E0 , 524.43E0 , 546.75E0 , 549.53E0 , 575.29E0 , 576.00E0 , 625.55E0 , 20.15E0 , 28.78E0 , 29.57E0 , 37.41E0 , 39.12E0 , 50.24E0 , 61.38E0 , 66.25E0 , 73.42E0 , 95.52E0 , 107.32E0 , 122.04E0 , 134.03E0 , 163.19E0 , 163.48E0 , 175.70E0 , 179.86E0 , 211.27E0 , 217.78E0 , 219.14E0 , 262.52E0 , 268.01E0 , 268.62E0 , 336.25E0 , 337.23E0 , 339.33E0 , 427.38E0 , 428.58E0 , 432.68E0 , 528.99E0 , 531.08E0 , 628.34E0 , 253.24E0 , 273.13E0 , 273.66E0 ,
+282.10E0 , 346.62E0 , 347.19E0 , 348.78E0 , 351.18E0 , 450.10E0 , 450.35E0 , 451.92E0 , 455.56E0 , 552.22E0 , 553.56E0 , 555.74E0 , 652.59E0 , 656.20E0 , 14.13E0 , 20.41E0 , 31.30E0 , 33.84E0 , 39.70E0 , 48.83E0 , 54.50E0 , 60.41E0 , 72.77E0 , 75.25E0 , 86.84E0 , 94.88E0 , 96.40E0 , 117.37E0 , 139.08E0 , 147.73E0 , 158.63E0 , 161.84E0 , 192.11E0 , 206.76E0 , 209.07E0 , 213.32E0 , 226.44E0 , 237.12E0 , 330.90E0 , 358.72E0 , 370.77E0 , 372.72E0 , 396.24E0 , 416.59E0 , 484.02E0 , 495.47E0 , 514.78E0 , 515.65E0 , 519.47E0 , 544.47E0 , 560.11E0 , 620.77E0 , 18.97E0 , 28.93E0 , 33.91E0 , 40.03E0 , 44.66E0 , 49.87E0 , 55.16E0 , 60.90E0 , 72.08E0 , 85.15E0 , 97.06E0 , 119.63E0 , 133.27E0 , 143.84E0 , 161.91E0 , 180.67E0 , 198.44E0 , 226.86E0 , 229.65E0 , 258.27E0 , 273.77E0 , 339.15E0 , 350.13E0 , 362.75E0 , 371.03E0 , 393.32E0 , 448.53E0 , 473.78E0 , 511.12E0 , 524.70E0 , 548.75E0 , 551.64E0 , 574.02E0 , 623.86E0 , 21.46E0 , 24.33E0 , 33.43E0 , 39.22E0 , 44.18E0 , 55.02E0 , 94.33E0 , 96.44E0 , 118.82E0 , 128.48E0 ,
+141.94E0 , 156.92E0 , 171.65E0 , 190.00E0 , 223.26E0 , 223.88E0 , 231.50E0 , 265.05E0 , 269.44E0 , 271.78E0 , 273.46E0 , 334.61E0 , 339.79E0 , 349.52E0 , 358.18E0 , 377.98E0 , 394.77E0 , 429.66E0 , 468.22E0 , 487.27E0 , 519.54E0 , 523.03E0 , 612.99E0 , 638.59E0 , 641.36E0 , 622.05E0 , 631.50E0 , 663.97E0 , 646.9E0 , 748.29E0 , 749.21E0 , 750.14E0 , 647.04E0 , 646.89E0 , 746.9E0 , 748.43E0 , 747.35E0 , 749.27E0 , 647.61E0 , 747.78E0 , 750.51E0 , 851.37E0 , 845.97E0 , 847.54E0 , 849.93E0 , 851.61E0 , 849.75E0 , 850.98E0 , 848.23E0};
+
+// http://www.itl.nist.gov/div898/strd/nls/data/hahn1.shtml
+void testNistHahn1(void)
+{
+ const int n=7;
+ int info;
+
+ VectorXd x(n);
+
+ /*
+ * First try
+ */
+ x<< 10., -1., .05, -.00001, -.05, .001, -.000001;
+ // do the computation
+ hahn1_functor functor;
+ LevenbergMarquardt<hahn1_functor> lm(functor);
+ info = lm.minimize(x);
+ EIGEN_UNUSED_VARIABLE(info)
+
+ // check return value
+ // VERIFY_IS_EQUAL(info, 1);
+ // VERIFY_IS_EQUAL(lm.nfev(), 11);
+ // VERIFY_IS_EQUAL(lm.njev(), 10);
+ // check norm^2
+ VERIFY_IS_APPROX(lm.fvec().squaredNorm(), 1.5324382854E+00);
+ // check x
+ VERIFY_IS_APPROX(x[0], 1.0776351733E+00);
+ VERIFY_IS_APPROX(x[1],-1.2269296921E-01);
+ VERIFY_IS_APPROX(x[2], 4.0863750610E-03);
+ VERIFY_IS_APPROX(x[3],-1.426264e-06); // shoulde be : -1.4262662514E-06
+ VERIFY_IS_APPROX(x[4],-5.7609940901E-03);
+ VERIFY_IS_APPROX(x[5], 2.4053735503E-04);
+ VERIFY_IS_APPROX(x[6],-1.2314450199E-07);
+
+ /*
+ * Second try
+ */
+ x<< .1, -.1, .005, -.000001, -.005, .0001, -.0000001;
+ // do the computation
+ info = lm.minimize(x);
+ EIGEN_UNUSED_VARIABLE(info)
+
+ // check return value
+ // VERIFY_IS_EQUAL(info, 1);
+// VERIFY_IS_EQUAL(lm.nfev(), 11);
+ // VERIFY_IS_EQUAL(lm.njev(), 10);
+ // check norm^2
+ VERIFY_IS_APPROX(lm.fvec().squaredNorm(), 1.5324382854E+00);
+ // check x
+ VERIFY_IS_APPROX(x[0], 1.077640); // should be : 1.0776351733E+00
+ VERIFY_IS_APPROX(x[1], -0.1226933); // should be : -1.2269296921E-01
+ VERIFY_IS_APPROX(x[2], 0.004086383); // should be : 4.0863750610E-03
+ VERIFY_IS_APPROX(x[3], -1.426277e-06); // shoulde be : -1.4262662514E-06
+ VERIFY_IS_APPROX(x[4],-5.7609940901E-03);
+ VERIFY_IS_APPROX(x[5], 0.00024053772); // should be : 2.4053735503E-04
+ VERIFY_IS_APPROX(x[6], -1.231450e-07); // should be : -1.2314450199E-07
+
+}
+
+struct misra1d_functor : DenseFunctor<double>
+{
+ misra1d_functor(void) : DenseFunctor<double>(2,14) {}
+ static const double x[14];
+ static const double y[14];
+ int operator()(const VectorXd &b, VectorXd &fvec)
+ {
+ assert(b.size()==2);
+ assert(fvec.size()==14);
+ for(int i=0; i<14; i++) {
+ fvec[i] = b[0]*b[1]*x[i]/(1.+b[1]*x[i]) - y[i];
+ }
+ return 0;
+ }
+ int df(const VectorXd &b, MatrixXd &fjac)
+ {
+ assert(b.size()==2);
+ assert(fjac.rows()==14);
+ assert(fjac.cols()==2);
+ for(int i=0; i<14; i++) {
+ double den = 1.+b[1]*x[i];
+ fjac(i,0) = b[1]*x[i] / den;
+ fjac(i,1) = b[0]*x[i]*(den-b[1]*x[i])/den/den;
+ }
+ return 0;
+ }
+};
+const double misra1d_functor::x[14] = { 77.6E0, 114.9E0, 141.1E0, 190.8E0, 239.9E0, 289.0E0, 332.8E0, 378.4E0, 434.8E0, 477.3E0, 536.8E0, 593.1E0, 689.1E0, 760.0E0};
+const double misra1d_functor::y[14] = { 10.07E0, 14.73E0, 17.94E0, 23.93E0, 29.61E0, 35.18E0, 40.02E0, 44.82E0, 50.76E0, 55.05E0, 61.01E0, 66.40E0, 75.47E0, 81.78E0};
+
+// http://www.itl.nist.gov/div898/strd/nls/data/misra1d.shtml
+void testNistMisra1d(void)
+{
+ const int n=2;
+ int info;
+
+ VectorXd x(n);
+
+ /*
+ * First try
+ */
+ x<< 500., 0.0001;
+ // do the computation
+ misra1d_functor functor;
+ LevenbergMarquardt<misra1d_functor> lm(functor);
+ info = lm.minimize(x);
+ EIGEN_UNUSED_VARIABLE(info)
+
+ // check return value
+ // VERIFY_IS_EQUAL(info, 1);
+ // VERIFY_IS_EQUAL(lm.nfev(), 9);
+ // VERIFY_IS_EQUAL(lm.njev(), 7);
+ // check norm^2
+ VERIFY_IS_APPROX(lm.fvec().squaredNorm(), 5.6419295283E-02);
+ // check x
+ VERIFY_IS_APPROX(x[0], 4.3736970754E+02);
+ VERIFY_IS_APPROX(x[1], 3.0227324449E-04);
+
+ /*
+ * Second try
+ */
+ x<< 450., 0.0003;
+ // do the computation
+ info = lm.minimize(x);
+ EIGEN_UNUSED_VARIABLE(info)
+
+ // check return value
+ // VERIFY_IS_EQUAL(info, 1);
+ // VERIFY_IS_EQUAL(lm.nfev(), 4);
+ // VERIFY_IS_EQUAL(lm.njev(), 3);
+ // check norm^2
+ VERIFY_IS_APPROX(lm.fvec().squaredNorm(), 5.6419295283E-02);
+ // check x
+ VERIFY_IS_APPROX(x[0], 4.3736970754E+02);
+ VERIFY_IS_APPROX(x[1], 3.0227324449E-04);
+}
+
+
+struct lanczos1_functor : DenseFunctor<double>
+{
+ lanczos1_functor(void) : DenseFunctor<double>(6,24) {}
+ static const double x[24];
+ static const double y[24];
+ int operator()(const VectorXd &b, VectorXd &fvec)
+ {
+ assert(b.size()==6);
+ assert(fvec.size()==24);
+ for(int i=0; i<24; i++)
+ fvec[i] = b[0]*exp(-b[1]*x[i]) + b[2]*exp(-b[3]*x[i]) + b[4]*exp(-b[5]*x[i]) - y[i];
+ return 0;
+ }
+ int df(const VectorXd &b, MatrixXd &fjac)
+ {
+ assert(b.size()==6);
+ assert(fjac.rows()==24);
+ assert(fjac.cols()==6);
+ for(int i=0; i<24; i++) {
+ fjac(i,0) = exp(-b[1]*x[i]);
+ fjac(i,1) = -b[0]*x[i]*exp(-b[1]*x[i]);
+ fjac(i,2) = exp(-b[3]*x[i]);
+ fjac(i,3) = -b[2]*x[i]*exp(-b[3]*x[i]);
+ fjac(i,4) = exp(-b[5]*x[i]);
+ fjac(i,5) = -b[4]*x[i]*exp(-b[5]*x[i]);
+ }
+ return 0;
+ }
+};
+const double lanczos1_functor::x[24] = { 0.000000000000E+00, 5.000000000000E-02, 1.000000000000E-01, 1.500000000000E-01, 2.000000000000E-01, 2.500000000000E-01, 3.000000000000E-01, 3.500000000000E-01, 4.000000000000E-01, 4.500000000000E-01, 5.000000000000E-01, 5.500000000000E-01, 6.000000000000E-01, 6.500000000000E-01, 7.000000000000E-01, 7.500000000000E-01, 8.000000000000E-01, 8.500000000000E-01, 9.000000000000E-01, 9.500000000000E-01, 1.000000000000E+00, 1.050000000000E+00, 1.100000000000E+00, 1.150000000000E+00 };
+const double lanczos1_functor::y[24] = { 2.513400000000E+00 ,2.044333373291E+00 ,1.668404436564E+00 ,1.366418021208E+00 ,1.123232487372E+00 ,9.268897180037E-01 ,7.679338563728E-01 ,6.388775523106E-01 ,5.337835317402E-01 ,4.479363617347E-01 ,3.775847884350E-01 ,3.197393199326E-01 ,2.720130773746E-01 ,2.324965529032E-01 ,1.996589546065E-01 ,1.722704126914E-01 ,1.493405660168E-01 ,1.300700206922E-01 ,1.138119324644E-01 ,1.000415587559E-01 ,8.833209084540E-02 ,7.833544019350E-02 ,6.976693743449E-02 ,6.239312536719E-02 };
+
+// http://www.itl.nist.gov/div898/strd/nls/data/lanczos1.shtml
+void testNistLanczos1(void)
+{
+ const int n=6;
+ LevenbergMarquardtSpace::Status info;
+
+ VectorXd x(n);
+
+ /*
+ * First try
+ */
+ x<< 1.2, 0.3, 5.6, 5.5, 6.5, 7.6;
+ // do the computation
+ lanczos1_functor functor;
+ LevenbergMarquardt<lanczos1_functor> lm(functor);
+ info = lm.minimize(x);
+ EIGEN_UNUSED_VARIABLE(info)
+
+ // check return value
+ // VERIFY_IS_EQUAL(info, LevenbergMarquardtSpace::RelativeErrorTooSmall);
+ // VERIFY_IS_EQUAL(lm.nfev(), 79);
+ // VERIFY_IS_EQUAL(lm.njev(), 72);
+ // check norm^2
+ VERIFY(lm.fvec().squaredNorm() <= 1.4307867721E-25);
+ // check x
+ VERIFY_IS_APPROX(x[0], 9.5100000027E-02);
+ VERIFY_IS_APPROX(x[1], 1.0000000001E+00);
+ VERIFY_IS_APPROX(x[2], 8.6070000013E-01);
+ VERIFY_IS_APPROX(x[3], 3.0000000002E+00);
+ VERIFY_IS_APPROX(x[4], 1.5575999998E+00);
+ VERIFY_IS_APPROX(x[5], 5.0000000001E+00);
+
+ /*
+ * Second try
+ */
+ x<< 0.5, 0.7, 3.6, 4.2, 4., 6.3;
+ // do the computation
+ info = lm.minimize(x);
+ EIGEN_UNUSED_VARIABLE(info)
+
+ // check return value
+ // VERIFY_IS_EQUAL(info, LevenbergMarquardtSpace::RelativeErrorTooSmall);
+ // VERIFY_IS_EQUAL(lm.nfev(), 9);
+ // VERIFY_IS_EQUAL(lm.njev(), 8);
+ // check norm^2
+ VERIFY(lm.fvec().squaredNorm() <= 1.4307867721E-25);
+ // check x
+ VERIFY_IS_APPROX(x[0], 9.5100000027E-02);
+ VERIFY_IS_APPROX(x[1], 1.0000000001E+00);
+ VERIFY_IS_APPROX(x[2], 8.6070000013E-01);
+ VERIFY_IS_APPROX(x[3], 3.0000000002E+00);
+ VERIFY_IS_APPROX(x[4], 1.5575999998E+00);
+ VERIFY_IS_APPROX(x[5], 5.0000000001E+00);
+
+}
+
+struct rat42_functor : DenseFunctor<double>
+{
+ rat42_functor(void) : DenseFunctor<double>(3,9) {}
+ static const double x[9];
+ static const double y[9];
+ int operator()(const VectorXd &b, VectorXd &fvec)
+ {
+ assert(b.size()==3);
+ assert(fvec.size()==9);
+ for(int i=0; i<9; i++) {
+ fvec[i] = b[0] / (1.+exp(b[1]-b[2]*x[i])) - y[i];
+ }
+ return 0;
+ }
+
+ int df(const VectorXd &b, MatrixXd &fjac)
+ {
+ assert(b.size()==3);
+ assert(fjac.rows()==9);
+ assert(fjac.cols()==3);
+ for(int i=0; i<9; i++) {
+ double e = exp(b[1]-b[2]*x[i]);
+ fjac(i,0) = 1./(1.+e);
+ fjac(i,1) = -b[0]*e/(1.+e)/(1.+e);
+ fjac(i,2) = +b[0]*e*x[i]/(1.+e)/(1.+e);
+ }
+ return 0;
+ }
+};
+const double rat42_functor::x[9] = { 9.000E0, 14.000E0, 21.000E0, 28.000E0, 42.000E0, 57.000E0, 63.000E0, 70.000E0, 79.000E0 };
+const double rat42_functor::y[9] = { 8.930E0 ,10.800E0 ,18.590E0 ,22.330E0 ,39.350E0 ,56.110E0 ,61.730E0 ,64.620E0 ,67.080E0 };
+
+// http://www.itl.nist.gov/div898/strd/nls/data/ratkowsky2.shtml
+void testNistRat42(void)
+{
+ const int n=3;
+ LevenbergMarquardtSpace::Status info;
+
+ VectorXd x(n);
+
+ /*
+ * First try
+ */
+ x<< 100., 1., 0.1;
+ // do the computation
+ rat42_functor functor;
+ LevenbergMarquardt<rat42_functor> lm(functor);
+ info = lm.minimize(x);
+ EIGEN_UNUSED_VARIABLE(info)
+
+ // check return value
+ // VERIFY_IS_EQUAL(info, LevenbergMarquardtSpace::RelativeReductionTooSmall);
+ // VERIFY_IS_EQUAL(lm.nfev(), 10);
+ // VERIFY_IS_EQUAL(lm.njev(), 8);
+ // check norm^2
+ VERIFY_IS_APPROX(lm.fvec().squaredNorm(), 8.0565229338E+00);
+ // check x
+ VERIFY_IS_APPROX(x[0], 7.2462237576E+01);
+ VERIFY_IS_APPROX(x[1], 2.6180768402E+00);
+ VERIFY_IS_APPROX(x[2], 6.7359200066E-02);
+
+ /*
+ * Second try
+ */
+ x<< 75., 2.5, 0.07;
+ // do the computation
+ info = lm.minimize(x);
+ EIGEN_UNUSED_VARIABLE(info)
+
+ // check return value
+ // VERIFY_IS_EQUAL(info, LevenbergMarquardtSpace::RelativeReductionTooSmall);
+ // VERIFY_IS_EQUAL(lm.nfev(), 6);
+ // VERIFY_IS_EQUAL(lm.njev(), 5);
+ // check norm^2
+ VERIFY_IS_APPROX(lm.fvec().squaredNorm(), 8.0565229338E+00);
+ // check x
+ VERIFY_IS_APPROX(x[0], 7.2462237576E+01);
+ VERIFY_IS_APPROX(x[1], 2.6180768402E+00);
+ VERIFY_IS_APPROX(x[2], 6.7359200066E-02);
+}
+
+struct MGH10_functor : DenseFunctor<double>
+{
+ MGH10_functor(void) : DenseFunctor<double>(3,16) {}
+ static const double x[16];
+ static const double y[16];
+ int operator()(const VectorXd &b, VectorXd &fvec)
+ {
+ assert(b.size()==3);
+ assert(fvec.size()==16);
+ for(int i=0; i<16; i++)
+ fvec[i] = b[0] * exp(b[1]/(x[i]+b[2])) - y[i];
+ return 0;
+ }
+ int df(const VectorXd &b, MatrixXd &fjac)
+ {
+ assert(b.size()==3);
+ assert(fjac.rows()==16);
+ assert(fjac.cols()==3);
+ for(int i=0; i<16; i++) {
+ double factor = 1./(x[i]+b[2]);
+ double e = exp(b[1]*factor);
+ fjac(i,0) = e;
+ fjac(i,1) = b[0]*factor*e;
+ fjac(i,2) = -b[1]*b[0]*factor*factor*e;
+ }
+ return 0;
+ }
+};
+const double MGH10_functor::x[16] = { 5.000000E+01, 5.500000E+01, 6.000000E+01, 6.500000E+01, 7.000000E+01, 7.500000E+01, 8.000000E+01, 8.500000E+01, 9.000000E+01, 9.500000E+01, 1.000000E+02, 1.050000E+02, 1.100000E+02, 1.150000E+02, 1.200000E+02, 1.250000E+02 };
+const double MGH10_functor::y[16] = { 3.478000E+04, 2.861000E+04, 2.365000E+04, 1.963000E+04, 1.637000E+04, 1.372000E+04, 1.154000E+04, 9.744000E+03, 8.261000E+03, 7.030000E+03, 6.005000E+03, 5.147000E+03, 4.427000E+03, 3.820000E+03, 3.307000E+03, 2.872000E+03 };
+
+// http://www.itl.nist.gov/div898/strd/nls/data/mgh10.shtml
+void testNistMGH10(void)
+{
+ const int n=3;
+ LevenbergMarquardtSpace::Status info;
+
+ VectorXd x(n);
+
+ /*
+ * First try
+ */
+ x << 2., 400000., 25000.;
+ // do the computation
+ MGH10_functor functor;
+ LevenbergMarquardt<MGH10_functor> lm(functor);
+ info = lm.minimize(x);
+ EIGEN_UNUSED_VARIABLE(info)
+ // ++g_test_level;
+ // VERIFY_IS_EQUAL(info, LevenbergMarquardtSpace::RelativeReductionTooSmall);
+ // --g_test_level;
+ // was: VERIFY_IS_EQUAL(info, 1);
+
+ // check norm^2
+ VERIFY_IS_APPROX(lm.fvec().squaredNorm(), 8.7945855171E+01);
+ // check x
+ VERIFY_IS_APPROX(x[0], 5.6096364710E-03);
+ VERIFY_IS_APPROX(x[1], 6.1813463463E+03);
+ VERIFY_IS_APPROX(x[2], 3.4522363462E+02);
+
+ // check return value
+
+ // ++g_test_level;
+ // VERIFY_IS_EQUAL(lm.nfev(), 284 );
+ // VERIFY_IS_EQUAL(lm.njev(), 249 );
+ // --g_test_level;
+ VERIFY(lm.nfev() < 284 * LM_EVAL_COUNT_TOL);
+ VERIFY(lm.njev() < 249 * LM_EVAL_COUNT_TOL);
+
+ /*
+ * Second try
+ */
+ x<< 0.02, 4000., 250.;
+ // do the computation
+ info = lm.minimize(x);
+ EIGEN_UNUSED_VARIABLE(info)
+ // ++g_test_level;
+ // VERIFY_IS_EQUAL(info, LevenbergMarquardtSpace::RelativeReductionTooSmall);
+ // // was: VERIFY_IS_EQUAL(info, 1);
+ // --g_test_level;
+
+ // check norm^2
+ VERIFY_IS_APPROX(lm.fvec().squaredNorm(), 8.7945855171E+01);
+ // check x
+ VERIFY_IS_APPROX(x[0], 5.6096364710E-03);
+ VERIFY_IS_APPROX(x[1], 6.1813463463E+03);
+ VERIFY_IS_APPROX(x[2], 3.4522363462E+02);
+
+ // check return value
+ // ++g_test_level;
+ // VERIFY_IS_EQUAL(lm.nfev(), 126);
+ // VERIFY_IS_EQUAL(lm.njev(), 116);
+ // --g_test_level;
+ VERIFY(lm.nfev() < 126 * LM_EVAL_COUNT_TOL);
+ VERIFY(lm.njev() < 116 * LM_EVAL_COUNT_TOL);
+}
+
+
+struct BoxBOD_functor : DenseFunctor<double>
+{
+ BoxBOD_functor(void) : DenseFunctor<double>(2,6) {}
+ static const double x[6];
+ int operator()(const VectorXd &b, VectorXd &fvec)
+ {
+ static const double y[6] = { 109., 149., 149., 191., 213., 224. };
+ assert(b.size()==2);
+ assert(fvec.size()==6);
+ for(int i=0; i<6; i++)
+ fvec[i] = b[0]*(1.-exp(-b[1]*x[i])) - y[i];
+ return 0;
+ }
+ int df(const VectorXd &b, MatrixXd &fjac)
+ {
+ assert(b.size()==2);
+ assert(fjac.rows()==6);
+ assert(fjac.cols()==2);
+ for(int i=0; i<6; i++) {
+ double e = exp(-b[1]*x[i]);
+ fjac(i,0) = 1.-e;
+ fjac(i,1) = b[0]*x[i]*e;
+ }
+ return 0;
+ }
+};
+const double BoxBOD_functor::x[6] = { 1., 2., 3., 5., 7., 10. };
+
+// http://www.itl.nist.gov/div898/strd/nls/data/boxbod.shtml
+void testNistBoxBOD(void)
+{
+ const int n=2;
+ int info;
+
+ VectorXd x(n);
+
+ /*
+ * First try
+ */
+ x<< 1., 1.;
+ // do the computation
+ BoxBOD_functor functor;
+ LevenbergMarquardt<BoxBOD_functor> lm(functor);
+ lm.setFtol(1.E6*NumTraits<double>::epsilon());
+ lm.setXtol(1.E6*NumTraits<double>::epsilon());
+ lm.setFactor(10);
+ info = lm.minimize(x);
+ EIGEN_UNUSED_VARIABLE(info)
+
+ // check norm^2
+ VERIFY_IS_APPROX(lm.fvec().squaredNorm(), 1.1680088766E+03);
+ // check x
+ VERIFY_IS_APPROX(x[0], 2.1380940889E+02);
+ VERIFY_IS_APPROX(x[1], 5.4723748542E-01);
+
+ // check return value
+ // VERIFY_IS_EQUAL(info, 1);
+ // VERIFY(lm.nfev() < 31); // 31
+ // VERIFY(lm.njev() < 25); // 25
+
+ /*
+ * Second try
+ */
+ x<< 100., 0.75;
+ // do the computation
+ lm.resetParameters();
+ lm.setFtol(NumTraits<double>::epsilon());
+ lm.setXtol( NumTraits<double>::epsilon());
+ info = lm.minimize(x);
+ EIGEN_UNUSED_VARIABLE(info)
+
+ // check return value
+ // VERIFY_IS_EQUAL(info, 1);
+ // ++g_test_level;
+ // VERIFY_IS_EQUAL(lm.nfev(), 16 );
+ // VERIFY_IS_EQUAL(lm.njev(), 15 );
+ // --g_test_level;
+ VERIFY(lm.nfev() < 16 * LM_EVAL_COUNT_TOL);
+ VERIFY(lm.njev() < 15 * LM_EVAL_COUNT_TOL);
+ // check norm^2
+ VERIFY_IS_APPROX(lm.fvec().squaredNorm(), 1.1680088766E+03);
+ // check x
+ VERIFY_IS_APPROX(x[0], 2.1380940889E+02);
+ VERIFY_IS_APPROX(x[1], 5.4723748542E-01);
+}
+
+struct MGH17_functor : DenseFunctor<double>
+{
+ MGH17_functor(void) : DenseFunctor<double>(5,33) {}
+ static const double x[33];
+ static const double y[33];
+ int operator()(const VectorXd &b, VectorXd &fvec)
+ {
+ assert(b.size()==5);
+ assert(fvec.size()==33);
+ for(int i=0; i<33; i++)
+ fvec[i] = b[0] + b[1]*exp(-b[3]*x[i]) + b[2]*exp(-b[4]*x[i]) - y[i];
+ return 0;
+ }
+ int df(const VectorXd &b, MatrixXd &fjac)
+ {
+ assert(b.size()==5);
+ assert(fjac.rows()==33);
+ assert(fjac.cols()==5);
+ for(int i=0; i<33; i++) {
+ fjac(i,0) = 1.;
+ fjac(i,1) = exp(-b[3]*x[i]);
+ fjac(i,2) = exp(-b[4]*x[i]);
+ fjac(i,3) = -x[i]*b[1]*exp(-b[3]*x[i]);
+ fjac(i,4) = -x[i]*b[2]*exp(-b[4]*x[i]);
+ }
+ return 0;
+ }
+};
+const double MGH17_functor::x[33] = { 0.000000E+00, 1.000000E+01, 2.000000E+01, 3.000000E+01, 4.000000E+01, 5.000000E+01, 6.000000E+01, 7.000000E+01, 8.000000E+01, 9.000000E+01, 1.000000E+02, 1.100000E+02, 1.200000E+02, 1.300000E+02, 1.400000E+02, 1.500000E+02, 1.600000E+02, 1.700000E+02, 1.800000E+02, 1.900000E+02, 2.000000E+02, 2.100000E+02, 2.200000E+02, 2.300000E+02, 2.400000E+02, 2.500000E+02, 2.600000E+02, 2.700000E+02, 2.800000E+02, 2.900000E+02, 3.000000E+02, 3.100000E+02, 3.200000E+02 };
+const double MGH17_functor::y[33] = { 8.440000E-01, 9.080000E-01, 9.320000E-01, 9.360000E-01, 9.250000E-01, 9.080000E-01, 8.810000E-01, 8.500000E-01, 8.180000E-01, 7.840000E-01, 7.510000E-01, 7.180000E-01, 6.850000E-01, 6.580000E-01, 6.280000E-01, 6.030000E-01, 5.800000E-01, 5.580000E-01, 5.380000E-01, 5.220000E-01, 5.060000E-01, 4.900000E-01, 4.780000E-01, 4.670000E-01, 4.570000E-01, 4.480000E-01, 4.380000E-01, 4.310000E-01, 4.240000E-01, 4.200000E-01, 4.140000E-01, 4.110000E-01, 4.060000E-01 };
+
+// http://www.itl.nist.gov/div898/strd/nls/data/mgh17.shtml
+void testNistMGH17(void)
+{
+ const int n=5;
+ int info;
+
+ VectorXd x(n);
+
+ /*
+ * First try
+ */
+ x<< 50., 150., -100., 1., 2.;
+ // do the computation
+ MGH17_functor functor;
+ LevenbergMarquardt<MGH17_functor> lm(functor);
+ lm.setFtol(NumTraits<double>::epsilon());
+ lm.setXtol(NumTraits<double>::epsilon());
+ lm.setMaxfev(1000);
+ info = lm.minimize(x);
+ EIGEN_UNUSED_VARIABLE(info)
+
+ // check norm^2
+ VERIFY_IS_APPROX(lm.fvec().squaredNorm(), 5.4648946975E-05);
+ // check x
+ VERIFY_IS_APPROX(x[0], 3.7541005211E-01);
+ VERIFY_IS_APPROX(x[1], 1.9358469127E+00);
+ VERIFY_IS_APPROX(x[2], -1.4646871366E+00);
+ VERIFY_IS_APPROX(x[3], 1.2867534640E-02);
+ VERIFY_IS_APPROX(x[4], 2.2122699662E-02);
+
+ // check return value
+// VERIFY_IS_EQUAL(info, 2); //FIXME Use (lm.info() == Success)
+ // VERIFY(lm.nfev() < 700 ); // 602
+ // VERIFY(lm.njev() < 600 ); // 545
+
+ /*
+ * Second try
+ */
+ x<< 0.5 ,1.5 ,-1 ,0.01 ,0.02;
+ // do the computation
+ lm.resetParameters();
+ info = lm.minimize(x);
+ EIGEN_UNUSED_VARIABLE(info)
+
+ // check return value
+ // VERIFY_IS_EQUAL(info, 1);
+ // VERIFY_IS_EQUAL(lm.nfev(), 18);
+ // VERIFY_IS_EQUAL(lm.njev(), 15);
+ // check norm^2
+ VERIFY_IS_APPROX(lm.fvec().squaredNorm(), 5.4648946975E-05);
+ // check x
+ VERIFY_IS_APPROX(x[0], 3.7541005211E-01);
+ VERIFY_IS_APPROX(x[1], 1.9358469127E+00);
+ VERIFY_IS_APPROX(x[2], -1.4646871366E+00);
+ VERIFY_IS_APPROX(x[3], 1.2867534640E-02);
+ VERIFY_IS_APPROX(x[4], 2.2122699662E-02);
+}
+
+struct MGH09_functor : DenseFunctor<double>
+{
+ MGH09_functor(void) : DenseFunctor<double>(4,11) {}
+ static const double _x[11];
+ static const double y[11];
+ int operator()(const VectorXd &b, VectorXd &fvec)
+ {
+ assert(b.size()==4);
+ assert(fvec.size()==11);
+ for(int i=0; i<11; i++) {
+ double x = _x[i], xx=x*x;
+ fvec[i] = b[0]*(xx+x*b[1])/(xx+x*b[2]+b[3]) - y[i];
+ }
+ return 0;
+ }
+ int df(const VectorXd &b, MatrixXd &fjac)
+ {
+ assert(b.size()==4);
+ assert(fjac.rows()==11);
+ assert(fjac.cols()==4);
+ for(int i=0; i<11; i++) {
+ double x = _x[i], xx=x*x;
+ double factor = 1./(xx+x*b[2]+b[3]);
+ fjac(i,0) = (xx+x*b[1]) * factor;
+ fjac(i,1) = b[0]*x* factor;
+ fjac(i,2) = - b[0]*(xx+x*b[1]) * x * factor * factor;
+ fjac(i,3) = - b[0]*(xx+x*b[1]) * factor * factor;
+ }
+ return 0;
+ }
+};
+const double MGH09_functor::_x[11] = { 4., 2., 1., 5.E-1 , 2.5E-01, 1.670000E-01, 1.250000E-01, 1.E-01, 8.330000E-02, 7.140000E-02, 6.250000E-02 };
+const double MGH09_functor::y[11] = { 1.957000E-01, 1.947000E-01, 1.735000E-01, 1.600000E-01, 8.440000E-02, 6.270000E-02, 4.560000E-02, 3.420000E-02, 3.230000E-02, 2.350000E-02, 2.460000E-02 };
+
+// http://www.itl.nist.gov/div898/strd/nls/data/mgh09.shtml
+void testNistMGH09(void)
+{
+ const int n=4;
+ int info;
+
+ VectorXd x(n);
+
+ /*
+ * First try
+ */
+ x<< 25., 39, 41.5, 39.;
+ // do the computation
+ MGH09_functor functor;
+ LevenbergMarquardt<MGH09_functor> lm(functor);
+ lm.setMaxfev(1000);
+ info = lm.minimize(x);
+ EIGEN_UNUSED_VARIABLE(info)
+
+ // check norm^2
+ VERIFY_IS_APPROX(lm.fvec().squaredNorm(), 3.0750560385E-04);
+ // check x
+ VERIFY_IS_APPROX(x[0], 0.1928077089); // should be 1.9280693458E-01
+ VERIFY_IS_APPROX(x[1], 0.19126423573); // should be 1.9128232873E-01
+ VERIFY_IS_APPROX(x[2], 0.12305309914); // should be 1.2305650693E-01
+ VERIFY_IS_APPROX(x[3], 0.13605395375); // should be 1.3606233068E-01
+ // check return value
+ // VERIFY_IS_EQUAL(info, 1);
+ // VERIFY(lm.nfev() < 510 ); // 490
+ // VERIFY(lm.njev() < 400 ); // 376
+
+ /*
+ * Second try
+ */
+ x<< 0.25, 0.39, 0.415, 0.39;
+ // do the computation
+ lm.resetParameters();
+ info = lm.minimize(x);
+ EIGEN_UNUSED_VARIABLE(info)
+
+ // check return value
+ // VERIFY_IS_EQUAL(info, 1);
+ // VERIFY_IS_EQUAL(lm.nfev(), 18);
+ // VERIFY_IS_EQUAL(lm.njev(), 16);
+ // check norm^2
+ VERIFY_IS_APPROX(lm.fvec().squaredNorm(), 3.0750560385E-04);
+ // check x
+ VERIFY_IS_APPROX(x[0], 0.19280781); // should be 1.9280693458E-01
+ VERIFY_IS_APPROX(x[1], 0.19126265); // should be 1.9128232873E-01
+ VERIFY_IS_APPROX(x[2], 0.12305280); // should be 1.2305650693E-01
+ VERIFY_IS_APPROX(x[3], 0.13605322); // should be 1.3606233068E-01
+}
+
+
+
+struct Bennett5_functor : DenseFunctor<double>
+{
+ Bennett5_functor(void) : DenseFunctor<double>(3,154) {}
+ static const double x[154];
+ static const double y[154];
+ int operator()(const VectorXd &b, VectorXd &fvec)
+ {
+ assert(b.size()==3);
+ assert(fvec.size()==154);
+ for(int i=0; i<154; i++)
+ fvec[i] = b[0]* pow(b[1]+x[i],-1./b[2]) - y[i];
+ return 0;
+ }
+ int df(const VectorXd &b, MatrixXd &fjac)
+ {
+ assert(b.size()==3);
+ assert(fjac.rows()==154);
+ assert(fjac.cols()==3);
+ for(int i=0; i<154; i++) {
+ double e = pow(b[1]+x[i],-1./b[2]);
+ fjac(i,0) = e;
+ fjac(i,1) = - b[0]*e/b[2]/(b[1]+x[i]);
+ fjac(i,2) = b[0]*e*log(b[1]+x[i])/b[2]/b[2];
+ }
+ return 0;
+ }
+};
+const double Bennett5_functor::x[154] = { 7.447168E0, 8.102586E0, 8.452547E0, 8.711278E0, 8.916774E0, 9.087155E0, 9.232590E0, 9.359535E0, 9.472166E0, 9.573384E0, 9.665293E0, 9.749461E0, 9.827092E0, 9.899128E0, 9.966321E0, 10.029280E0, 10.088510E0, 10.144430E0, 10.197380E0, 10.247670E0, 10.295560E0, 10.341250E0, 10.384950E0, 10.426820E0, 10.467000E0, 10.505640E0, 10.542830E0, 10.578690E0, 10.613310E0, 10.646780E0, 10.679150E0, 10.710520E0, 10.740920E0, 10.770440E0, 10.799100E0, 10.826970E0, 10.854080E0, 10.880470E0, 10.906190E0, 10.931260E0, 10.955720E0, 10.979590E0, 11.002910E0, 11.025700E0, 11.047980E0, 11.069770E0, 11.091100E0, 11.111980E0, 11.132440E0, 11.152480E0, 11.172130E0, 11.191410E0, 11.210310E0, 11.228870E0, 11.247090E0, 11.264980E0, 11.282560E0, 11.299840E0, 11.316820E0, 11.333520E0, 11.349940E0, 11.366100E0, 11.382000E0, 11.397660E0, 11.413070E0, 11.428240E0, 11.443200E0, 11.457930E0, 11.472440E0, 11.486750E0, 11.500860E0, 11.514770E0, 11.528490E0, 11.542020E0, 11.555380E0, 11.568550E0,
+11.581560E0, 11.594420E0, 11.607121E0, 11.619640E0, 11.632000E0, 11.644210E0, 11.656280E0, 11.668200E0, 11.679980E0, 11.691620E0, 11.703130E0, 11.714510E0, 11.725760E0, 11.736880E0, 11.747890E0, 11.758780E0, 11.769550E0, 11.780200E0, 11.790730E0, 11.801160E0, 11.811480E0, 11.821700E0, 11.831810E0, 11.841820E0, 11.851730E0, 11.861550E0, 11.871270E0, 11.880890E0, 11.890420E0, 11.899870E0, 11.909220E0, 11.918490E0, 11.927680E0, 11.936780E0, 11.945790E0, 11.954730E0, 11.963590E0, 11.972370E0, 11.981070E0, 11.989700E0, 11.998260E0, 12.006740E0, 12.015150E0, 12.023490E0, 12.031760E0, 12.039970E0, 12.048100E0, 12.056170E0, 12.064180E0, 12.072120E0, 12.080010E0, 12.087820E0, 12.095580E0, 12.103280E0, 12.110920E0, 12.118500E0, 12.126030E0, 12.133500E0, 12.140910E0, 12.148270E0, 12.155570E0, 12.162830E0, 12.170030E0, 12.177170E0, 12.184270E0, 12.191320E0, 12.198320E0, 12.205270E0, 12.212170E0, 12.219030E0, 12.225840E0, 12.232600E0, 12.239320E0, 12.245990E0, 12.252620E0, 12.259200E0, 12.265750E0, 12.272240E0 };
+const double Bennett5_functor::y[154] = { -34.834702E0 ,-34.393200E0 ,-34.152901E0 ,-33.979099E0 ,-33.845901E0 ,-33.732899E0 ,-33.640301E0 ,-33.559200E0 ,-33.486801E0 ,-33.423100E0 ,-33.365101E0 ,-33.313000E0 ,-33.260899E0 ,-33.217400E0 ,-33.176899E0 ,-33.139198E0 ,-33.101601E0 ,-33.066799E0 ,-33.035000E0 ,-33.003101E0 ,-32.971298E0 ,-32.942299E0 ,-32.916302E0 ,-32.890202E0 ,-32.864101E0 ,-32.841000E0 ,-32.817799E0 ,-32.797501E0 ,-32.774300E0 ,-32.757000E0 ,-32.733799E0 ,-32.716400E0 ,-32.699100E0 ,-32.678799E0 ,-32.661400E0 ,-32.644001E0 ,-32.626701E0 ,-32.612202E0 ,-32.597698E0 ,-32.583199E0 ,-32.568699E0 ,-32.554298E0 ,-32.539799E0 ,-32.525299E0 ,-32.510799E0 ,-32.499199E0 ,-32.487598E0 ,-32.473202E0 ,-32.461601E0 ,-32.435501E0 ,-32.435501E0 ,-32.426800E0 ,-32.412300E0 ,-32.400799E0 ,-32.392101E0 ,-32.380501E0 ,-32.366001E0 ,-32.357300E0 ,-32.348598E0 ,-32.339901E0 ,-32.328400E0 ,-32.319698E0 ,-32.311001E0 ,-32.299400E0 ,-32.290699E0 ,-32.282001E0 ,-32.273300E0 ,-32.264599E0 ,-32.256001E0 ,-32.247299E0
+,-32.238602E0 ,-32.229900E0 ,-32.224098E0 ,-32.215401E0 ,-32.203800E0 ,-32.198002E0 ,-32.189400E0 ,-32.183601E0 ,-32.174900E0 ,-32.169102E0 ,-32.163300E0 ,-32.154598E0 ,-32.145901E0 ,-32.140099E0 ,-32.131401E0 ,-32.125599E0 ,-32.119801E0 ,-32.111198E0 ,-32.105400E0 ,-32.096699E0 ,-32.090900E0 ,-32.088001E0 ,-32.079300E0 ,-32.073502E0 ,-32.067699E0 ,-32.061901E0 ,-32.056099E0 ,-32.050301E0 ,-32.044498E0 ,-32.038799E0 ,-32.033001E0 ,-32.027199E0 ,-32.024300E0 ,-32.018501E0 ,-32.012699E0 ,-32.004002E0 ,-32.001099E0 ,-31.995300E0 ,-31.989500E0 ,-31.983700E0 ,-31.977900E0 ,-31.972099E0 ,-31.969299E0 ,-31.963501E0 ,-31.957701E0 ,-31.951900E0 ,-31.946100E0 ,-31.940300E0 ,-31.937401E0 ,-31.931601E0 ,-31.925800E0 ,-31.922899E0 ,-31.917101E0 ,-31.911301E0 ,-31.908400E0 ,-31.902599E0 ,-31.896900E0 ,-31.893999E0 ,-31.888201E0 ,-31.885300E0 ,-31.882401E0 ,-31.876600E0 ,-31.873699E0 ,-31.867901E0 ,-31.862101E0 ,-31.859200E0 ,-31.856300E0 ,-31.850500E0 ,-31.844700E0 ,-31.841801E0 ,-31.838900E0 ,-31.833099E0 ,-31.830200E0 ,
+-31.827299E0 ,-31.821600E0 ,-31.818701E0 ,-31.812901E0 ,-31.809999E0 ,-31.807100E0 ,-31.801300E0 ,-31.798401E0 ,-31.795500E0 ,-31.789700E0 ,-31.786800E0 };
+
+// http://www.itl.nist.gov/div898/strd/nls/data/bennett5.shtml
+void testNistBennett5(void)
+{
+ const int n=3;
+ int info;
+
+ VectorXd x(n);
+
+ /*
+ * First try
+ */
+ x<< -2000., 50., 0.8;
+ // do the computation
+ Bennett5_functor functor;
+ LevenbergMarquardt<Bennett5_functor> lm(functor);
+ lm.setMaxfev(1000);
+ info = lm.minimize(x);
+ EIGEN_UNUSED_VARIABLE(info)
+
+ // check return value
+ // VERIFY_IS_EQUAL(info, 1);
+ // VERIFY_IS_EQUAL(lm.nfev(), 758);
+ // VERIFY_IS_EQUAL(lm.njev(), 744);
+ // check norm^2
+ VERIFY_IS_APPROX(lm.fvec().squaredNorm(), 5.2404744073E-04);
+ // check x
+ VERIFY_IS_APPROX(x[0], -2.5235058043E+03);
+ VERIFY_IS_APPROX(x[1], 4.6736564644E+01);
+ VERIFY_IS_APPROX(x[2], 9.3218483193E-01);
+ /*
+ * Second try
+ */
+ x<< -1500., 45., 0.85;
+ // do the computation
+ lm.resetParameters();
+ info = lm.minimize(x);
+ EIGEN_UNUSED_VARIABLE(info)
+
+ // check return value
+ // VERIFY_IS_EQUAL(info, 1);
+ // VERIFY_IS_EQUAL(lm.nfev(), 203);
+ // VERIFY_IS_EQUAL(lm.njev(), 192);
+ // check norm^2
+ VERIFY_IS_APPROX(lm.fvec().squaredNorm(), 5.2404744073E-04);
+ // check x
+ VERIFY_IS_APPROX(x[0], -2523.3007865); // should be -2.5235058043E+03
+ VERIFY_IS_APPROX(x[1], 46.735705771); // should be 4.6736564644E+01);
+ VERIFY_IS_APPROX(x[2], 0.93219881891); // should be 9.3218483193E-01);
+}
+
+struct thurber_functor : DenseFunctor<double>
+{
+ thurber_functor(void) : DenseFunctor<double>(7,37) {}
+ static const double _x[37];
+ static const double _y[37];
+ int operator()(const VectorXd &b, VectorXd &fvec)
+ {
+ // int called=0; printf("call hahn1_functor with iflag=%d, called=%d\n", iflag, called); if (iflag==1) called++;
+ assert(b.size()==7);
+ assert(fvec.size()==37);
+ for(int i=0; i<37; i++) {
+ double x=_x[i], xx=x*x, xxx=xx*x;
+ fvec[i] = (b[0]+b[1]*x+b[2]*xx+b[3]*xxx) / (1.+b[4]*x+b[5]*xx+b[6]*xxx) - _y[i];
+ }
+ return 0;
+ }
+ int df(const VectorXd &b, MatrixXd &fjac)
+ {
+ assert(b.size()==7);
+ assert(fjac.rows()==37);
+ assert(fjac.cols()==7);
+ for(int i=0; i<37; i++) {
+ double x=_x[i], xx=x*x, xxx=xx*x;
+ double fact = 1./(1.+b[4]*x+b[5]*xx+b[6]*xxx);
+ fjac(i,0) = 1.*fact;
+ fjac(i,1) = x*fact;
+ fjac(i,2) = xx*fact;
+ fjac(i,3) = xxx*fact;
+ fact = - (b[0]+b[1]*x+b[2]*xx+b[3]*xxx) * fact * fact;
+ fjac(i,4) = x*fact;
+ fjac(i,5) = xx*fact;
+ fjac(i,6) = xxx*fact;
+ }
+ return 0;
+ }
+};
+const double thurber_functor::_x[37] = { -3.067E0, -2.981E0, -2.921E0, -2.912E0, -2.840E0, -2.797E0, -2.702E0, -2.699E0, -2.633E0, -2.481E0, -2.363E0, -2.322E0, -1.501E0, -1.460E0, -1.274E0, -1.212E0, -1.100E0, -1.046E0, -0.915E0, -0.714E0, -0.566E0, -0.545E0, -0.400E0, -0.309E0, -0.109E0, -0.103E0, 0.010E0, 0.119E0, 0.377E0, 0.790E0, 0.963E0, 1.006E0, 1.115E0, 1.572E0, 1.841E0, 2.047E0, 2.200E0 };
+const double thurber_functor::_y[37] = { 80.574E0, 84.248E0, 87.264E0, 87.195E0, 89.076E0, 89.608E0, 89.868E0, 90.101E0, 92.405E0, 95.854E0, 100.696E0, 101.060E0, 401.672E0, 390.724E0, 567.534E0, 635.316E0, 733.054E0, 759.087E0, 894.206E0, 990.785E0, 1090.109E0, 1080.914E0, 1122.643E0, 1178.351E0, 1260.531E0, 1273.514E0, 1288.339E0, 1327.543E0, 1353.863E0, 1414.509E0, 1425.208E0, 1421.384E0, 1442.962E0, 1464.350E0, 1468.705E0, 1447.894E0, 1457.628E0};
+
+// http://www.itl.nist.gov/div898/strd/nls/data/thurber.shtml
+void testNistThurber(void)
+{
+ const int n=7;
+ int info;
+
+ VectorXd x(n);
+
+ /*
+ * First try
+ */
+ x<< 1000 ,1000 ,400 ,40 ,0.7,0.3,0.0 ;
+ // do the computation
+ thurber_functor functor;
+ LevenbergMarquardt<thurber_functor> lm(functor);
+ lm.setFtol(1.E4*NumTraits<double>::epsilon());
+ lm.setXtol(1.E4*NumTraits<double>::epsilon());
+ info = lm.minimize(x);
+ EIGEN_UNUSED_VARIABLE(info)
+
+ // check return value
+ // VERIFY_IS_EQUAL(info, 1);
+ // VERIFY_IS_EQUAL(lm.nfev(), 39);
+ // VERIFY_IS_EQUAL(lm.njev(), 36);
+ // check norm^2
+ VERIFY_IS_APPROX(lm.fvec().squaredNorm(), 5.6427082397E+03);
+ // check x
+ VERIFY_IS_APPROX(x[0], 1.2881396800E+03);
+ VERIFY_IS_APPROX(x[1], 1.4910792535E+03);
+ VERIFY_IS_APPROX(x[2], 5.8323836877E+02);
+ VERIFY_IS_APPROX(x[3], 7.5416644291E+01);
+ VERIFY_IS_APPROX(x[4], 9.6629502864E-01);
+ VERIFY_IS_APPROX(x[5], 3.9797285797E-01);
+ VERIFY_IS_APPROX(x[6], 4.9727297349E-02);
+
+ /*
+ * Second try
+ */
+ x<< 1300 ,1500 ,500 ,75 ,1 ,0.4 ,0.05 ;
+ // do the computation
+ lm.resetParameters();
+ lm.setFtol(1.E4*NumTraits<double>::epsilon());
+ lm.setXtol(1.E4*NumTraits<double>::epsilon());
+ info = lm.minimize(x);
+ EIGEN_UNUSED_VARIABLE(info)
+
+ // check return value
+ // VERIFY_IS_EQUAL(info, 1);
+ // VERIFY_IS_EQUAL(lm.nfev(), 29);
+ // VERIFY_IS_EQUAL(lm.njev(), 28);
+ // check norm^2
+ VERIFY_IS_APPROX(lm.fvec().squaredNorm(), 5.6427082397E+03);
+ // check x
+ VERIFY_IS_APPROX(x[0], 1.2881396800E+03);
+ VERIFY_IS_APPROX(x[1], 1.4910792535E+03);
+ VERIFY_IS_APPROX(x[2], 5.8323836877E+02);
+ VERIFY_IS_APPROX(x[3], 7.5416644291E+01);
+ VERIFY_IS_APPROX(x[4], 9.6629502864E-01);
+ VERIFY_IS_APPROX(x[5], 3.9797285797E-01);
+ VERIFY_IS_APPROX(x[6], 4.9727297349E-02);
+}
+
+struct rat43_functor : DenseFunctor<double>
+{
+ rat43_functor(void) : DenseFunctor<double>(4,15) {}
+ static const double x[15];
+ static const double y[15];
+ int operator()(const VectorXd &b, VectorXd &fvec)
+ {
+ assert(b.size()==4);
+ assert(fvec.size()==15);
+ for(int i=0; i<15; i++)
+ fvec[i] = b[0] * pow(1.+exp(b[1]-b[2]*x[i]),-1./b[3]) - y[i];
+ return 0;
+ }
+ int df(const VectorXd &b, MatrixXd &fjac)
+ {
+ assert(b.size()==4);
+ assert(fjac.rows()==15);
+ assert(fjac.cols()==4);
+ for(int i=0; i<15; i++) {
+ double e = exp(b[1]-b[2]*x[i]);
+ double power = -1./b[3];
+ fjac(i,0) = pow(1.+e, power);
+ fjac(i,1) = power*b[0]*e*pow(1.+e, power-1.);
+ fjac(i,2) = -power*b[0]*e*x[i]*pow(1.+e, power-1.);
+ fjac(i,3) = b[0]*power*power*log(1.+e)*pow(1.+e, power);
+ }
+ return 0;
+ }
+};
+const double rat43_functor::x[15] = { 1., 2., 3., 4., 5., 6., 7., 8., 9., 10., 11., 12., 13., 14., 15. };
+const double rat43_functor::y[15] = { 16.08, 33.83, 65.80, 97.20, 191.55, 326.20, 386.87, 520.53, 590.03, 651.92, 724.93, 699.56, 689.96, 637.56, 717.41 };
+
+// http://www.itl.nist.gov/div898/strd/nls/data/ratkowsky3.shtml
+void testNistRat43(void)
+{
+ const int n=4;
+ int info;
+
+ VectorXd x(n);
+
+ /*
+ * First try
+ */
+ x<< 100., 10., 1., 1.;
+ // do the computation
+ rat43_functor functor;
+ LevenbergMarquardt<rat43_functor> lm(functor);
+ lm.setFtol(1.E6*NumTraits<double>::epsilon());
+ lm.setXtol(1.E6*NumTraits<double>::epsilon());
+ info = lm.minimize(x);
+ EIGEN_UNUSED_VARIABLE(info)
+
+ // check return value
+ // VERIFY_IS_EQUAL(info, 1);
+ // VERIFY_IS_EQUAL(lm.nfev(), 27);
+ // VERIFY_IS_EQUAL(lm.njev(), 20);
+ // check norm^2
+ VERIFY_IS_APPROX(lm.fvec().squaredNorm(), 8.7864049080E+03);
+ // check x
+ VERIFY_IS_APPROX(x[0], 6.9964151270E+02);
+ VERIFY_IS_APPROX(x[1], 5.2771253025E+00);
+ VERIFY_IS_APPROX(x[2], 7.5962938329E-01);
+ VERIFY_IS_APPROX(x[3], 1.2792483859E+00);
+
+ /*
+ * Second try
+ */
+ x<< 700., 5., 0.75, 1.3;
+ // do the computation
+ lm.resetParameters();
+ lm.setFtol(1.E5*NumTraits<double>::epsilon());
+ lm.setXtol(1.E5*NumTraits<double>::epsilon());
+ info = lm.minimize(x);
+ EIGEN_UNUSED_VARIABLE(info)
+
+ // check return value
+ // VERIFY_IS_EQUAL(info, 1);
+ // VERIFY_IS_EQUAL(lm.nfev(), 9);
+ // VERIFY_IS_EQUAL(lm.njev(), 8);
+ // check norm^2
+ VERIFY_IS_APPROX(lm.fvec().squaredNorm(), 8.7864049080E+03);
+ // check x
+ VERIFY_IS_APPROX(x[0], 6.9964151270E+02);
+ VERIFY_IS_APPROX(x[1], 5.2771253025E+00);
+ VERIFY_IS_APPROX(x[2], 7.5962938329E-01);
+ VERIFY_IS_APPROX(x[3], 1.2792483859E+00);
+}
+
+
+
+struct eckerle4_functor : DenseFunctor<double>
+{
+ eckerle4_functor(void) : DenseFunctor<double>(3,35) {}
+ static const double x[35];
+ static const double y[35];
+ int operator()(const VectorXd &b, VectorXd &fvec)
+ {
+ assert(b.size()==3);
+ assert(fvec.size()==35);
+ for(int i=0; i<35; i++)
+ fvec[i] = b[0]/b[1] * exp(-0.5*(x[i]-b[2])*(x[i]-b[2])/(b[1]*b[1])) - y[i];
+ return 0;
+ }
+ int df(const VectorXd &b, MatrixXd &fjac)
+ {
+ assert(b.size()==3);
+ assert(fjac.rows()==35);
+ assert(fjac.cols()==3);
+ for(int i=0; i<35; i++) {
+ double b12 = b[1]*b[1];
+ double e = exp(-0.5*(x[i]-b[2])*(x[i]-b[2])/b12);
+ fjac(i,0) = e / b[1];
+ fjac(i,1) = ((x[i]-b[2])*(x[i]-b[2])/b12-1.) * b[0]*e/b12;
+ fjac(i,2) = (x[i]-b[2])*e*b[0]/b[1]/b12;
+ }
+ return 0;
+ }
+};
+const double eckerle4_functor::x[35] = { 400.0, 405.0, 410.0, 415.0, 420.0, 425.0, 430.0, 435.0, 436.5, 438.0, 439.5, 441.0, 442.5, 444.0, 445.5, 447.0, 448.5, 450.0, 451.5, 453.0, 454.5, 456.0, 457.5, 459.0, 460.5, 462.0, 463.5, 465.0, 470.0, 475.0, 480.0, 485.0, 490.0, 495.0, 500.0};
+const double eckerle4_functor::y[35] = { 0.0001575, 0.0001699, 0.0002350, 0.0003102, 0.0004917, 0.0008710, 0.0017418, 0.0046400, 0.0065895, 0.0097302, 0.0149002, 0.0237310, 0.0401683, 0.0712559, 0.1264458, 0.2073413, 0.2902366, 0.3445623, 0.3698049, 0.3668534, 0.3106727, 0.2078154, 0.1164354, 0.0616764, 0.0337200, 0.0194023, 0.0117831, 0.0074357, 0.0022732, 0.0008800, 0.0004579, 0.0002345, 0.0001586, 0.0001143, 0.0000710 };
+
+// http://www.itl.nist.gov/div898/strd/nls/data/eckerle4.shtml
+void testNistEckerle4(void)
+{
+ const int n=3;
+ int info;
+
+ VectorXd x(n);
+
+ /*
+ * First try
+ */
+ x<< 1., 10., 500.;
+ // do the computation
+ eckerle4_functor functor;
+ LevenbergMarquardt<eckerle4_functor> lm(functor);
+ info = lm.minimize(x);
+ EIGEN_UNUSED_VARIABLE(info)
+
+ // check return value
+ // VERIFY_IS_EQUAL(info, 1);
+ // VERIFY_IS_EQUAL(lm.nfev(), 18);
+ // VERIFY_IS_EQUAL(lm.njev(), 15);
+ // check norm^2
+ VERIFY_IS_APPROX(lm.fvec().squaredNorm(), 1.4635887487E-03);
+ // check x
+ VERIFY_IS_APPROX(x[0], 1.5543827178);
+ VERIFY_IS_APPROX(x[1], 4.0888321754);
+ VERIFY_IS_APPROX(x[2], 4.5154121844E+02);
+
+ /*
+ * Second try
+ */
+ x<< 1.5, 5., 450.;
+ // do the computation
+ info = lm.minimize(x);
+ EIGEN_UNUSED_VARIABLE(info)
+
+ // check return value
+ // VERIFY_IS_EQUAL(info, 1);
+ // VERIFY_IS_EQUAL(lm.nfev(), 7);
+ // VERIFY_IS_EQUAL(lm.njev(), 6);
+ // check norm^2
+ VERIFY_IS_APPROX(lm.fvec().squaredNorm(), 1.4635887487E-03);
+ // check x
+ VERIFY_IS_APPROX(x[0], 1.5543827178);
+ VERIFY_IS_APPROX(x[1], 4.0888321754);
+ VERIFY_IS_APPROX(x[2], 4.5154121844E+02);
+}
+
+EIGEN_DECLARE_TEST(levenberg_marquardt)
+{
+ // Tests using the examples provided by (c)minpack
+ CALL_SUBTEST(testLmder1());
+ CALL_SUBTEST(testLmder());
+ CALL_SUBTEST(testLmdif1());
+// CALL_SUBTEST(testLmstr1());
+// CALL_SUBTEST(testLmstr());
+ CALL_SUBTEST(testLmdif());
+
+ // NIST tests, level of difficulty = "Lower"
+ CALL_SUBTEST(testNistMisra1a());
+ CALL_SUBTEST(testNistChwirut2());
+
+ // NIST tests, level of difficulty = "Average"
+ CALL_SUBTEST(testNistHahn1());
+ CALL_SUBTEST(testNistMisra1d());
+ CALL_SUBTEST(testNistMGH17());
+ CALL_SUBTEST(testNistLanczos1());
+
+// // NIST tests, level of difficulty = "Higher"
+ CALL_SUBTEST(testNistRat42());
+ CALL_SUBTEST(testNistMGH10());
+ CALL_SUBTEST(testNistBoxBOD());
+// CALL_SUBTEST(testNistMGH09());
+ CALL_SUBTEST(testNistBennett5());
+ CALL_SUBTEST(testNistThurber());
+ CALL_SUBTEST(testNistRat43());
+ CALL_SUBTEST(testNistEckerle4());
+}
diff --git a/unsupported/test/matrix_exponential.cpp b/unsupported/test/matrix_exponential.cpp
new file mode 100644
index 0000000..b032cbf
--- /dev/null
+++ b/unsupported/test/matrix_exponential.cpp
@@ -0,0 +1,141 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009 Jitse Niesen <jitse@maths.leeds.ac.uk>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "matrix_functions.h"
+
+double binom(int n, int k)
+{
+ double res = 1;
+ for (int i=0; i<k; i++)
+ res = res * (n-k+i+1) / (i+1);
+ return res;
+}
+
+template <typename T>
+T expfn(T x, int)
+{
+ return std::exp(x);
+}
+
+template <typename T>
+void test2dRotation(double tol)
+{
+ Matrix<T,2,2> A, B, C;
+ T angle;
+
+ A << 0, 1, -1, 0;
+ for (int i=0; i<=20; i++)
+ {
+ angle = static_cast<T>(pow(10, i / 5. - 2));
+ B << std::cos(angle), std::sin(angle), -std::sin(angle), std::cos(angle);
+
+ C = (angle*A).matrixFunction(expfn);
+ std::cout << "test2dRotation: i = " << i << " error funm = " << relerr(C, B);
+ VERIFY(C.isApprox(B, static_cast<T>(tol)));
+
+ C = (angle*A).exp();
+ std::cout << " error expm = " << relerr(C, B) << "\n";
+ VERIFY(C.isApprox(B, static_cast<T>(tol)));
+ }
+}
+
+template <typename T>
+void test2dHyperbolicRotation(double tol)
+{
+ Matrix<std::complex<T>,2,2> A, B, C;
+ std::complex<T> imagUnit(0,1);
+ T angle, ch, sh;
+
+ for (int i=0; i<=20; i++)
+ {
+ angle = static_cast<T>((i-10) / 2.0);
+ ch = std::cosh(angle);
+ sh = std::sinh(angle);
+ A << 0, angle*imagUnit, -angle*imagUnit, 0;
+ B << ch, sh*imagUnit, -sh*imagUnit, ch;
+
+ C = A.matrixFunction(expfn);
+ std::cout << "test2dHyperbolicRotation: i = " << i << " error funm = " << relerr(C, B);
+ VERIFY(C.isApprox(B, static_cast<T>(tol)));
+
+ C = A.exp();
+ std::cout << " error expm = " << relerr(C, B) << "\n";
+ VERIFY(C.isApprox(B, static_cast<T>(tol)));
+ }
+}
+
+template <typename T>
+void testPascal(double tol)
+{
+ for (int size=1; size<20; size++)
+ {
+ Matrix<T,Dynamic,Dynamic> A(size,size), B(size,size), C(size,size);
+ A.setZero();
+ for (int i=0; i<size-1; i++)
+ A(i+1,i) = static_cast<T>(i+1);
+ B.setZero();
+ for (int i=0; i<size; i++)
+ for (int j=0; j<=i; j++)
+ B(i,j) = static_cast<T>(binom(i,j));
+
+ C = A.matrixFunction(expfn);
+ std::cout << "testPascal: size = " << size << " error funm = " << relerr(C, B);
+ VERIFY(C.isApprox(B, static_cast<T>(tol)));
+
+ C = A.exp();
+ std::cout << " error expm = " << relerr(C, B) << "\n";
+ VERIFY(C.isApprox(B, static_cast<T>(tol)));
+ }
+}
+
+template<typename MatrixType>
+void randomTest(const MatrixType& m, double tol)
+{
+ /* this test covers the following files:
+ Inverse.h
+ */
+ typename MatrixType::Index rows = m.rows();
+ typename MatrixType::Index cols = m.cols();
+ MatrixType m1(rows, cols), m2(rows, cols), identity = MatrixType::Identity(rows, cols);
+
+ typedef typename NumTraits<typename internal::traits<MatrixType>::Scalar>::Real RealScalar;
+
+ for(int i = 0; i < g_repeat; i++) {
+ m1 = MatrixType::Random(rows, cols);
+
+ m2 = m1.matrixFunction(expfn) * (-m1).matrixFunction(expfn);
+ std::cout << "randomTest: error funm = " << relerr(identity, m2);
+ VERIFY(identity.isApprox(m2, static_cast<RealScalar>(tol)));
+
+ m2 = m1.exp() * (-m1).exp();
+ std::cout << " error expm = " << relerr(identity, m2) << "\n";
+ VERIFY(identity.isApprox(m2, static_cast<RealScalar>(tol)));
+ }
+}
+
+EIGEN_DECLARE_TEST(matrix_exponential)
+{
+ CALL_SUBTEST_2(test2dRotation<double>(1e-13));
+ CALL_SUBTEST_1(test2dRotation<float>(2e-5)); // was 1e-5, relaxed for clang 2.8 / linux / x86-64
+ CALL_SUBTEST_8(test2dRotation<long double>(1e-13));
+ CALL_SUBTEST_2(test2dHyperbolicRotation<double>(1e-14));
+ CALL_SUBTEST_1(test2dHyperbolicRotation<float>(1e-5));
+ CALL_SUBTEST_8(test2dHyperbolicRotation<long double>(1e-14));
+ CALL_SUBTEST_6(testPascal<float>(1e-6));
+ CALL_SUBTEST_5(testPascal<double>(1e-15));
+ CALL_SUBTEST_2(randomTest(Matrix2d(), 1e-13));
+ CALL_SUBTEST_7(randomTest(Matrix<double,3,3,RowMajor>(), 1e-13));
+ CALL_SUBTEST_3(randomTest(Matrix4cd(), 1e-13));
+ CALL_SUBTEST_4(randomTest(MatrixXd(8,8), 1e-13));
+ CALL_SUBTEST_1(randomTest(Matrix2f(), 1e-4));
+ CALL_SUBTEST_5(randomTest(Matrix3cf(), 1e-4));
+ CALL_SUBTEST_1(randomTest(Matrix4f(), 1e-4));
+ CALL_SUBTEST_6(randomTest(MatrixXf(8,8), 1e-4));
+ CALL_SUBTEST_9(randomTest(Matrix<long double,Dynamic,Dynamic>(7,7), 1e-13));
+}
diff --git a/unsupported/test/matrix_function.cpp b/unsupported/test/matrix_function.cpp
new file mode 100644
index 0000000..6d75373
--- /dev/null
+++ b/unsupported/test/matrix_function.cpp
@@ -0,0 +1,227 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2010 Jitse Niesen <jitse@maths.leeds.ac.uk>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "main.h"
+#include <unsupported/Eigen/MatrixFunctions>
+
+// Variant of VERIFY_IS_APPROX which uses absolute error instead of
+// relative error.
+#define VERIFY_IS_APPROX_ABS(a, b) VERIFY(test_isApprox_abs(a, b))
+
+template<typename Type1, typename Type2>
+inline bool test_isApprox_abs(const Type1& a, const Type2& b)
+{
+ return ((a-b).array().abs() < test_precision<typename Type1::RealScalar>()).all();
+}
+
+
+// Returns a matrix with eigenvalues clustered around 0, 1 and 2.
+template<typename MatrixType>
+MatrixType randomMatrixWithRealEivals(const Index size)
+{
+ typedef typename MatrixType::Scalar Scalar;
+ typedef typename MatrixType::RealScalar RealScalar;
+ MatrixType diag = MatrixType::Zero(size, size);
+ for (Index i = 0; i < size; ++i) {
+ diag(i, i) = Scalar(RealScalar(internal::random<int>(0,2)))
+ + internal::random<Scalar>() * Scalar(RealScalar(0.01));
+ }
+ MatrixType A = MatrixType::Random(size, size);
+ HouseholderQR<MatrixType> QRofA(A);
+ return QRofA.householderQ().inverse() * diag * QRofA.householderQ();
+}
+
+template <typename MatrixType, int IsComplex = NumTraits<typename internal::traits<MatrixType>::Scalar>::IsComplex>
+struct randomMatrixWithImagEivals
+{
+ // Returns a matrix with eigenvalues clustered around 0 and +/- i.
+ static MatrixType run(const Index size);
+};
+
+// Partial specialization for real matrices
+template<typename MatrixType>
+struct randomMatrixWithImagEivals<MatrixType, 0>
+{
+ static MatrixType run(const Index size)
+ {
+ typedef typename MatrixType::Scalar Scalar;
+ MatrixType diag = MatrixType::Zero(size, size);
+ Index i = 0;
+ while (i < size) {
+ Index randomInt = internal::random<Index>(-1, 1);
+ if (randomInt == 0 || i == size-1) {
+ diag(i, i) = internal::random<Scalar>() * Scalar(0.01);
+ ++i;
+ } else {
+ Scalar alpha = Scalar(randomInt) + internal::random<Scalar>() * Scalar(0.01);
+ diag(i, i+1) = alpha;
+ diag(i+1, i) = -alpha;
+ i += 2;
+ }
+ }
+ MatrixType A = MatrixType::Random(size, size);
+ HouseholderQR<MatrixType> QRofA(A);
+ return QRofA.householderQ().inverse() * diag * QRofA.householderQ();
+ }
+};
+
+// Partial specialization for complex matrices
+template<typename MatrixType>
+struct randomMatrixWithImagEivals<MatrixType, 1>
+{
+ static MatrixType run(const Index size)
+ {
+ typedef typename MatrixType::Scalar Scalar;
+ typedef typename MatrixType::RealScalar RealScalar;
+ const Scalar imagUnit(0, 1);
+ MatrixType diag = MatrixType::Zero(size, size);
+ for (Index i = 0; i < size; ++i) {
+ diag(i, i) = Scalar(RealScalar(internal::random<Index>(-1, 1))) * imagUnit
+ + internal::random<Scalar>() * Scalar(RealScalar(0.01));
+ }
+ MatrixType A = MatrixType::Random(size, size);
+ HouseholderQR<MatrixType> QRofA(A);
+ return QRofA.householderQ().inverse() * diag * QRofA.householderQ();
+ }
+};
+
+
+template<typename MatrixType>
+void testMatrixExponential(const MatrixType& A)
+{
+ typedef typename internal::traits<MatrixType>::Scalar Scalar;
+ typedef typename NumTraits<Scalar>::Real RealScalar;
+ typedef std::complex<RealScalar> ComplexScalar;
+
+ VERIFY_IS_APPROX(A.exp(), A.matrixFunction(internal::stem_function_exp<ComplexScalar>));
+}
+
+template<typename MatrixType>
+void testMatrixLogarithm(const MatrixType& A)
+{
+ typedef typename internal::traits<MatrixType>::Scalar Scalar;
+ typedef typename NumTraits<Scalar>::Real RealScalar;
+
+ MatrixType scaledA;
+ RealScalar maxImagPartOfSpectrum = A.eigenvalues().imag().cwiseAbs().maxCoeff();
+ if (maxImagPartOfSpectrum >= RealScalar(0.9L * EIGEN_PI))
+ scaledA = A * RealScalar(0.9L * EIGEN_PI) / maxImagPartOfSpectrum;
+ else
+ scaledA = A;
+
+ // identity X.exp().log() = X only holds if Im(lambda) < pi for all eigenvalues of X
+ MatrixType expA = scaledA.exp();
+ MatrixType logExpA = expA.log();
+ VERIFY_IS_APPROX(logExpA, scaledA);
+}
+
+template<typename MatrixType>
+void testHyperbolicFunctions(const MatrixType& A)
+{
+ // Need to use absolute error because of possible cancellation when
+ // adding/subtracting expA and expmA.
+ VERIFY_IS_APPROX_ABS(A.sinh(), (A.exp() - (-A).exp()) / 2);
+ VERIFY_IS_APPROX_ABS(A.cosh(), (A.exp() + (-A).exp()) / 2);
+}
+
+template<typename MatrixType>
+void testGonioFunctions(const MatrixType& A)
+{
+ typedef typename MatrixType::Scalar Scalar;
+ typedef typename NumTraits<Scalar>::Real RealScalar;
+ typedef std::complex<RealScalar> ComplexScalar;
+ typedef Matrix<ComplexScalar, MatrixType::RowsAtCompileTime,
+ MatrixType::ColsAtCompileTime, MatrixType::Options> ComplexMatrix;
+
+ ComplexScalar imagUnit(0,1);
+ ComplexScalar two(2,0);
+
+ ComplexMatrix Ac = A.template cast<ComplexScalar>();
+
+ ComplexMatrix exp_iA = (imagUnit * Ac).exp();
+ ComplexMatrix exp_miA = (-imagUnit * Ac).exp();
+
+ ComplexMatrix sinAc = A.sin().template cast<ComplexScalar>();
+ VERIFY_IS_APPROX_ABS(sinAc, (exp_iA - exp_miA) / (two*imagUnit));
+
+ ComplexMatrix cosAc = A.cos().template cast<ComplexScalar>();
+ VERIFY_IS_APPROX_ABS(cosAc, (exp_iA + exp_miA) / 2);
+}
+
+template<typename MatrixType>
+void testMatrix(const MatrixType& A)
+{
+ testMatrixExponential(A);
+ testMatrixLogarithm(A);
+ testHyperbolicFunctions(A);
+ testGonioFunctions(A);
+}
+
+template<typename MatrixType>
+void testMatrixType(const MatrixType& m)
+{
+ // Matrices with clustered eigenvalue lead to different code paths
+ // in MatrixFunction.h and are thus useful for testing.
+
+ const Index size = m.rows();
+ for (int i = 0; i < g_repeat; i++) {
+ testMatrix(MatrixType::Random(size, size).eval());
+ testMatrix(randomMatrixWithRealEivals<MatrixType>(size));
+ testMatrix(randomMatrixWithImagEivals<MatrixType>::run(size));
+ }
+}
+
+template<typename MatrixType>
+void testMapRef(const MatrixType& A)
+{
+ // Test if passing Ref and Map objects is possible
+ // (Regression test for Bug #1796)
+ Index size = A.rows();
+ MatrixType X; X.setRandom(size, size);
+ MatrixType Y(size,size);
+ Ref< MatrixType> R(Y);
+ Ref<const MatrixType> Rc(X);
+ Map< MatrixType> M(Y.data(), size, size);
+ Map<const MatrixType> Mc(X.data(), size, size);
+
+ X = X*X; // make sure sqrt is possible
+ Y = X.sqrt();
+ R = Rc.sqrt();
+ M = Mc.sqrt();
+ Y = X.exp();
+ R = Rc.exp();
+ M = Mc.exp();
+ X = Y; // make sure log is possible
+ Y = X.log();
+ R = Rc.log();
+ M = Mc.log();
+
+ Y = X.cos() + Rc.cos() + Mc.cos();
+ Y = X.sin() + Rc.sin() + Mc.sin();
+
+ Y = X.cosh() + Rc.cosh() + Mc.cosh();
+ Y = X.sinh() + Rc.sinh() + Mc.sinh();
+}
+
+
+EIGEN_DECLARE_TEST(matrix_function)
+{
+ CALL_SUBTEST_1(testMatrixType(Matrix<float,1,1>()));
+ CALL_SUBTEST_2(testMatrixType(Matrix3cf()));
+ CALL_SUBTEST_3(testMatrixType(MatrixXf(8,8)));
+ CALL_SUBTEST_4(testMatrixType(Matrix2d()));
+ CALL_SUBTEST_5(testMatrixType(Matrix<double,5,5,RowMajor>()));
+ CALL_SUBTEST_6(testMatrixType(Matrix4cd()));
+ CALL_SUBTEST_7(testMatrixType(MatrixXd(13,13)));
+
+ CALL_SUBTEST_1(testMapRef(Matrix<float,1,1>()));
+ CALL_SUBTEST_2(testMapRef(Matrix3cf()));
+ CALL_SUBTEST_3(testMapRef(MatrixXf(8,8)));
+ CALL_SUBTEST_7(testMapRef(MatrixXd(13,13)));
+}
diff --git a/unsupported/test/matrix_functions.h b/unsupported/test/matrix_functions.h
new file mode 100644
index 0000000..4e26364
--- /dev/null
+++ b/unsupported/test/matrix_functions.h
@@ -0,0 +1,67 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009-2011 Jitse Niesen <jitse@maths.leeds.ac.uk>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "main.h"
+#include <unsupported/Eigen/MatrixFunctions>
+
+// For complex matrices, any matrix is fine.
+template<typename MatrixType, int IsComplex = NumTraits<typename internal::traits<MatrixType>::Scalar>::IsComplex>
+struct processTriangularMatrix
+{
+ static void run(MatrixType&, MatrixType&, const MatrixType&)
+ { }
+};
+
+// For real matrices, make sure none of the eigenvalues are negative.
+template<typename MatrixType>
+struct processTriangularMatrix<MatrixType,0>
+{
+ static void run(MatrixType& m, MatrixType& T, const MatrixType& U)
+ {
+ const Index size = m.cols();
+
+ for (Index i=0; i < size; ++i) {
+ if (i == size - 1 || T.coeff(i+1,i) == 0)
+ T.coeffRef(i,i) = std::abs(T.coeff(i,i));
+ else
+ ++i;
+ }
+ m = U * T * U.transpose();
+ }
+};
+
+template <typename MatrixType, int IsComplex = NumTraits<typename internal::traits<MatrixType>::Scalar>::IsComplex>
+struct generateTestMatrix;
+
+template <typename MatrixType>
+struct generateTestMatrix<MatrixType,0>
+{
+ static void run(MatrixType& result, typename MatrixType::Index size)
+ {
+ result = MatrixType::Random(size, size);
+ RealSchur<MatrixType> schur(result);
+ MatrixType T = schur.matrixT();
+ processTriangularMatrix<MatrixType>::run(result, T, schur.matrixU());
+ }
+};
+
+template <typename MatrixType>
+struct generateTestMatrix<MatrixType,1>
+{
+ static void run(MatrixType& result, typename MatrixType::Index size)
+ {
+ result = MatrixType::Random(size, size);
+ }
+};
+
+template <typename Derived, typename OtherDerived>
+typename Derived::RealScalar relerr(const MatrixBase<Derived>& A, const MatrixBase<OtherDerived>& B)
+{
+ return std::sqrt((A - B).cwiseAbs2().sum() / (std::min)(A.cwiseAbs2().sum(), B.cwiseAbs2().sum()));
+}
diff --git a/unsupported/test/matrix_power.cpp b/unsupported/test/matrix_power.cpp
new file mode 100644
index 0000000..b13eb5a
--- /dev/null
+++ b/unsupported/test/matrix_power.cpp
@@ -0,0 +1,204 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2012, 2013 Chen-Pang He <jdh8@ms63.hinet.net>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "matrix_functions.h"
+
+template<typename T>
+void test2dRotation(const T& tol)
+{
+ Matrix<T,2,2> A, B, C;
+ T angle, c, s;
+
+ A << 0, 1, -1, 0;
+ MatrixPower<Matrix<T,2,2> > Apow(A);
+
+ for (int i=0; i<=20; ++i) {
+ angle = std::pow(T(10), T(i-10) / T(5.));
+ c = std::cos(angle);
+ s = std::sin(angle);
+ B << c, s, -s, c;
+
+ C = Apow(std::ldexp(angle,1) / T(EIGEN_PI));
+ std::cout << "test2dRotation: i = " << i << " error powerm = " << relerr(C,B) << '\n';
+ VERIFY(C.isApprox(B, tol));
+ }
+}
+
+template<typename T>
+void test2dHyperbolicRotation(const T& tol)
+{
+ Matrix<std::complex<T>,2,2> A, B, C;
+ T angle, ch = std::cosh((T)1);
+ std::complex<T> ish(0, std::sinh((T)1));
+
+ A << ch, ish, -ish, ch;
+ MatrixPower<Matrix<std::complex<T>,2,2> > Apow(A);
+
+ for (int i=0; i<=20; ++i) {
+ angle = std::ldexp(static_cast<T>(i-10), -1);
+ ch = std::cosh(angle);
+ ish = std::complex<T>(0, std::sinh(angle));
+ B << ch, ish, -ish, ch;
+
+ C = Apow(angle);
+ std::cout << "test2dHyperbolicRotation: i = " << i << " error powerm = " << relerr(C,B) << '\n';
+ VERIFY(C.isApprox(B, tol));
+ }
+}
+
+template<typename T>
+void test3dRotation(const T& tol)
+{
+ Matrix<T,3,1> v;
+ T angle;
+
+ for (int i=0; i<=20; ++i) {
+ v = Matrix<T,3,1>::Random();
+ v.normalize();
+ angle = std::pow(T(10), T(i-10) / T(5.));
+ VERIFY(AngleAxis<T>(angle, v).matrix().isApprox(AngleAxis<T>(1,v).matrix().pow(angle), tol));
+ }
+}
+
+template<typename MatrixType>
+void testGeneral(const MatrixType& m, const typename MatrixType::RealScalar& tol)
+{
+ typedef typename MatrixType::RealScalar RealScalar;
+ MatrixType m1, m2, m3, m4, m5;
+ RealScalar x, y;
+
+ for (int i=0; i < g_repeat; ++i) {
+ generateTestMatrix<MatrixType>::run(m1, m.rows());
+ MatrixPower<MatrixType> mpow(m1);
+
+ x = internal::random<RealScalar>();
+ y = internal::random<RealScalar>();
+ m2 = mpow(x);
+ m3 = mpow(y);
+
+ m4 = mpow(x+y);
+ m5.noalias() = m2 * m3;
+ VERIFY(m4.isApprox(m5, tol));
+
+ m4 = mpow(x*y);
+ m5 = m2.pow(y);
+ VERIFY(m4.isApprox(m5, tol));
+
+ m4 = (std::abs(x) * m1).pow(y);
+ m5 = std::pow(std::abs(x), y) * m3;
+ VERIFY(m4.isApprox(m5, tol));
+ }
+}
+
+template<typename MatrixType>
+void testSingular(const MatrixType& m_const, const typename MatrixType::RealScalar& tol)
+{
+ // we need to pass by reference in order to prevent errors with
+ // MSVC for aligned data types ...
+ MatrixType& m = const_cast<MatrixType&>(m_const);
+
+ const int IsComplex = NumTraits<typename internal::traits<MatrixType>::Scalar>::IsComplex;
+ typedef std::conditional_t<IsComplex, TriangularView<MatrixType,Upper>, const MatrixType&> TriangularType;
+ std::conditional_t< IsComplex, ComplexSchur<MatrixType>, RealSchur<MatrixType> > schur;
+ MatrixType T;
+
+ for (int i=0; i < g_repeat; ++i) {
+ m.setRandom();
+ m.col(0).fill(0);
+
+ schur.compute(m);
+ T = schur.matrixT();
+ const MatrixType& U = schur.matrixU();
+ processTriangularMatrix<MatrixType>::run(m, T, U);
+ MatrixPower<MatrixType> mpow(m);
+
+ T = T.sqrt();
+ VERIFY(mpow(0.5L).isApprox(U * (TriangularType(T) * U.adjoint()), tol));
+
+ T = T.sqrt();
+ VERIFY(mpow(0.25L).isApprox(U * (TriangularType(T) * U.adjoint()), tol));
+
+ T = T.sqrt();
+ VERIFY(mpow(0.125L).isApprox(U * (TriangularType(T) * U.adjoint()), tol));
+ }
+}
+
+template<typename MatrixType>
+void testLogThenExp(const MatrixType& m_const, const typename MatrixType::RealScalar& tol)
+{
+ // we need to pass by reference in order to prevent errors with
+ // MSVC for aligned data types ...
+ MatrixType& m = const_cast<MatrixType&>(m_const);
+
+ typedef typename MatrixType::Scalar Scalar;
+ Scalar x;
+
+ for (int i=0; i < g_repeat; ++i) {
+ generateTestMatrix<MatrixType>::run(m, m.rows());
+ x = internal::random<Scalar>();
+ VERIFY(m.pow(x).isApprox((x * m.log()).exp(), tol));
+ }
+}
+
+typedef Matrix<double,3,3,RowMajor> Matrix3dRowMajor;
+typedef Matrix<long double,3,3> Matrix3e;
+typedef Matrix<long double,Dynamic,Dynamic> MatrixXe;
+
+EIGEN_DECLARE_TEST(matrix_power)
+{
+ CALL_SUBTEST_2(test2dRotation<double>(1e-13));
+ CALL_SUBTEST_1(test2dRotation<float>(2e-5f)); // was 1e-5, relaxed for clang 2.8 / linux / x86-64
+ CALL_SUBTEST_9(test2dRotation<long double>(1e-13L));
+ CALL_SUBTEST_2(test2dHyperbolicRotation<double>(1e-14));
+ CALL_SUBTEST_1(test2dHyperbolicRotation<float>(1e-5f));
+ CALL_SUBTEST_9(test2dHyperbolicRotation<long double>(1e-14L));
+
+ CALL_SUBTEST_10(test3dRotation<double>(1e-13));
+ CALL_SUBTEST_11(test3dRotation<float>(1e-5f));
+ CALL_SUBTEST_12(test3dRotation<long double>(1e-13L));
+
+ CALL_SUBTEST_2(testGeneral(Matrix2d(), 1e-13));
+ CALL_SUBTEST_7(testGeneral(Matrix3dRowMajor(), 1e-13));
+ CALL_SUBTEST_3(testGeneral(Matrix4cd(), 1e-13));
+ CALL_SUBTEST_4(testGeneral(MatrixXd(8,8), 2e-12));
+ CALL_SUBTEST_1(testGeneral(Matrix2f(), 1e-4f));
+ CALL_SUBTEST_5(testGeneral(Matrix3cf(), 1e-4f));
+ CALL_SUBTEST_8(testGeneral(Matrix4f(), 1e-4f));
+ CALL_SUBTEST_6(testGeneral(MatrixXf(2,2), 1e-3f)); // see bug 614
+ CALL_SUBTEST_9(testGeneral(MatrixXe(7,7), 1e-12L));
+ CALL_SUBTEST_10(testGeneral(Matrix3d(), 1e-13));
+ CALL_SUBTEST_11(testGeneral(Matrix3f(), 1e-4f));
+ CALL_SUBTEST_12(testGeneral(Matrix3e(), 1e-13L));
+
+ CALL_SUBTEST_2(testSingular(Matrix2d(), 1e-13));
+ CALL_SUBTEST_7(testSingular(Matrix3dRowMajor(), 1e-13));
+ CALL_SUBTEST_3(testSingular(Matrix4cd(), 1e-13));
+ CALL_SUBTEST_4(testSingular(MatrixXd(8,8), 2e-12));
+ CALL_SUBTEST_1(testSingular(Matrix2f(), 1e-4f));
+ CALL_SUBTEST_5(testSingular(Matrix3cf(), 1e-4f));
+ CALL_SUBTEST_8(testSingular(Matrix4f(), 1e-4f));
+ CALL_SUBTEST_6(testSingular(MatrixXf(2,2), 1e-3f));
+ CALL_SUBTEST_9(testSingular(MatrixXe(7,7), 1e-12L));
+ CALL_SUBTEST_10(testSingular(Matrix3d(), 1e-13));
+ CALL_SUBTEST_11(testSingular(Matrix3f(), 1e-4f));
+ CALL_SUBTEST_12(testSingular(Matrix3e(), 1e-13L));
+
+ CALL_SUBTEST_2(testLogThenExp(Matrix2d(), 1e-13));
+ CALL_SUBTEST_7(testLogThenExp(Matrix3dRowMajor(), 1e-13));
+ CALL_SUBTEST_3(testLogThenExp(Matrix4cd(), 1e-13));
+ CALL_SUBTEST_4(testLogThenExp(MatrixXd(8,8), 2e-12));
+ CALL_SUBTEST_1(testLogThenExp(Matrix2f(), 1e-4f));
+ CALL_SUBTEST_5(testLogThenExp(Matrix3cf(), 1e-4f));
+ CALL_SUBTEST_8(testLogThenExp(Matrix4f(), 1e-4f));
+ CALL_SUBTEST_6(testLogThenExp(MatrixXf(2,2), 1e-3f));
+ CALL_SUBTEST_9(testLogThenExp(MatrixXe(7,7), 1e-12L));
+ CALL_SUBTEST_10(testLogThenExp(Matrix3d(), 1e-13));
+ CALL_SUBTEST_11(testLogThenExp(Matrix3f(), 1e-4f));
+ CALL_SUBTEST_12(testLogThenExp(Matrix3e(), 1e-13L));
+}
diff --git a/unsupported/test/matrix_square_root.cpp b/unsupported/test/matrix_square_root.cpp
new file mode 100644
index 0000000..034f292
--- /dev/null
+++ b/unsupported/test/matrix_square_root.cpp
@@ -0,0 +1,31 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2011 Jitse Niesen <jitse@maths.leeds.ac.uk>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "matrix_functions.h"
+
+template<typename MatrixType>
+void testMatrixSqrt(const MatrixType& m)
+{
+ MatrixType A;
+ generateTestMatrix<MatrixType>::run(A, m.rows());
+ MatrixType sqrtA = A.sqrt();
+ VERIFY_IS_APPROX(sqrtA * sqrtA, A);
+}
+
+EIGEN_DECLARE_TEST(matrix_square_root)
+{
+ for (int i = 0; i < g_repeat; i++) {
+ CALL_SUBTEST_1(testMatrixSqrt(Matrix3cf()));
+ CALL_SUBTEST_2(testMatrixSqrt(MatrixXcd(12,12)));
+ CALL_SUBTEST_3(testMatrixSqrt(Matrix4f()));
+ CALL_SUBTEST_4(testMatrixSqrt(Matrix<double,Dynamic,Dynamic,RowMajor>(9, 9)));
+ CALL_SUBTEST_5(testMatrixSqrt(Matrix<float,1,1>()));
+ CALL_SUBTEST_5(testMatrixSqrt(Matrix<std::complex<float>,1,1>()));
+ }
+}
diff --git a/unsupported/test/minres.cpp b/unsupported/test/minres.cpp
new file mode 100644
index 0000000..2eb40fe
--- /dev/null
+++ b/unsupported/test/minres.cpp
@@ -0,0 +1,44 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2012 Giacomo Po <gpo@ucla.edu>
+// Copyright (C) 2011 Gael Guennebaud <g.gael@free.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+#include <cmath>
+
+#include "../../test/sparse_solver.h"
+#include <Eigen/IterativeSolvers>
+
+template<typename T> void test_minres_T()
+{
+ // Identity preconditioner
+ MINRES<SparseMatrix<T>, Lower, IdentityPreconditioner > minres_colmajor_lower_I;
+ MINRES<SparseMatrix<T>, Upper, IdentityPreconditioner > minres_colmajor_upper_I;
+
+ // Diagonal preconditioner
+ MINRES<SparseMatrix<T>, Lower, DiagonalPreconditioner<T> > minres_colmajor_lower_diag;
+ MINRES<SparseMatrix<T>, Upper, DiagonalPreconditioner<T> > minres_colmajor_upper_diag;
+ MINRES<SparseMatrix<T>, Lower|Upper, DiagonalPreconditioner<T> > minres_colmajor_uplo_diag;
+
+ // call tests for SPD matrix
+ CALL_SUBTEST( check_sparse_spd_solving(minres_colmajor_lower_I) );
+ CALL_SUBTEST( check_sparse_spd_solving(minres_colmajor_upper_I) );
+
+ CALL_SUBTEST( check_sparse_spd_solving(minres_colmajor_lower_diag) );
+ CALL_SUBTEST( check_sparse_spd_solving(minres_colmajor_upper_diag) );
+ CALL_SUBTEST( check_sparse_spd_solving(minres_colmajor_uplo_diag) );
+
+ // TO DO: symmetric semi-definite matrix
+ // TO DO: symmetric indefinite matrix
+
+}
+
+EIGEN_DECLARE_TEST(minres)
+{
+ CALL_SUBTEST_1(test_minres_T<double>());
+// CALL_SUBTEST_2(test_minres_T<std::compex<double> >());
+
+}
diff --git a/unsupported/test/mklfft.cpp b/unsupported/test/mklfft.cpp
new file mode 100644
index 0000000..631dd20
--- /dev/null
+++ b/unsupported/test/mklfft.cpp
@@ -0,0 +1,2 @@
+#define EIGEN_MKL_DEFAULT 1
+#include "fft_test_shared.h"
diff --git a/unsupported/test/mpreal_support.cpp b/unsupported/test/mpreal_support.cpp
new file mode 100644
index 0000000..10beb07
--- /dev/null
+++ b/unsupported/test/mpreal_support.cpp
@@ -0,0 +1,66 @@
+#include <mpreal.h> // Must be included before main.h.
+#include "main.h"
+#include <Eigen/MPRealSupport>
+#include <Eigen/LU>
+#include <Eigen/Eigenvalues>
+#include <sstream>
+
+using namespace mpfr;
+using namespace Eigen;
+
+EIGEN_DECLARE_TEST(mpreal_support)
+{
+ // set precision to 256 bits (double has only 53 bits)
+ mpreal::set_default_prec(256);
+ typedef Matrix<mpreal,Eigen::Dynamic,Eigen::Dynamic> MatrixXmp;
+ typedef Matrix<std::complex<mpreal>,Eigen::Dynamic,Eigen::Dynamic> MatrixXcmp;
+
+ std::cerr << "epsilon = " << NumTraits<mpreal>::epsilon() << "\n";
+ std::cerr << "dummy_precision = " << NumTraits<mpreal>::dummy_precision() << "\n";
+ std::cerr << "highest = " << NumTraits<mpreal>::highest() << "\n";
+ std::cerr << "lowest = " << NumTraits<mpreal>::lowest() << "\n";
+ std::cerr << "digits10 = " << NumTraits<mpreal>::digits10() << "\n";
+
+ for(int i = 0; i < g_repeat; i++) {
+ int s = Eigen::internal::random<int>(1,100);
+ MatrixXmp A = MatrixXmp::Random(s,s);
+ MatrixXmp B = MatrixXmp::Random(s,s);
+ MatrixXmp S = A.adjoint() * A;
+ MatrixXmp X;
+ MatrixXcmp Ac = MatrixXcmp::Random(s,s);
+ MatrixXcmp Bc = MatrixXcmp::Random(s,s);
+ MatrixXcmp Sc = Ac.adjoint() * Ac;
+ MatrixXcmp Xc;
+
+ // Basic stuffs
+ VERIFY_IS_APPROX(A.real(), A);
+ VERIFY(Eigen::internal::isApprox(A.array().abs2().sum(), A.squaredNorm()));
+ VERIFY_IS_APPROX(A.array().exp(), exp(A.array()));
+ VERIFY_IS_APPROX(A.array().abs2().sqrt(), A.array().abs());
+ VERIFY_IS_APPROX(A.array().sin(), sin(A.array()));
+ VERIFY_IS_APPROX(A.array().cos(), cos(A.array()));
+
+ // Cholesky
+ X = S.selfadjointView<Lower>().llt().solve(B);
+ VERIFY_IS_APPROX((S.selfadjointView<Lower>()*X).eval(),B);
+
+ Xc = Sc.selfadjointView<Lower>().llt().solve(Bc);
+ VERIFY_IS_APPROX((Sc.selfadjointView<Lower>()*Xc).eval(),Bc);
+
+ // partial LU
+ X = A.lu().solve(B);
+ VERIFY_IS_APPROX((A*X).eval(),B);
+
+ // symmetric eigenvalues
+ SelfAdjointEigenSolver<MatrixXmp> eig(S);
+ VERIFY_IS_EQUAL(eig.info(), Success);
+ VERIFY( (S.selfadjointView<Lower>() * eig.eigenvectors()).isApprox(eig.eigenvectors() * eig.eigenvalues().asDiagonal(), NumTraits<mpreal>::dummy_precision()*1e3) );
+ }
+
+ {
+ MatrixXmp A(8,3); A.setRandom();
+ // test output (interesting things happen in this code)
+ std::stringstream stream;
+ stream << A;
+ }
+}
diff --git a/unsupported/test/openglsupport.cpp b/unsupported/test/openglsupport.cpp
new file mode 100644
index 0000000..1c44381
--- /dev/null
+++ b/unsupported/test/openglsupport.cpp
@@ -0,0 +1,600 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2010 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include <main.h>
+#include <iostream>
+#include <string>
+
+#if defined(__APPLE_CC__)
+ // Prevent deprecation warnings caused by GLEW on MacOS.
+ #define GL_SILENCE_DEPRECATION 1
+#endif
+#include <GL/glew.h>
+#include <Eigen/OpenGLSupport>
+#if defined(__APPLE_CC__)
+ #include <GLUT/glut.h>
+#else
+ #include <GL/freeglut.h>
+#endif
+
+using namespace Eigen;
+
+#define VERIFY_MATRIX(CODE,REF) { \
+ glMatrixMode(GL_MODELVIEW); \
+ glLoadIdentity(); \
+ CODE; \
+ Matrix<float,4,4,ColMajor> m; m.setZero(); \
+ glGet(GL_MODELVIEW_MATRIX, m); \
+ if(!(REF).cast<float>().isApprox(m)) { \
+ std::cerr << "Expected:\n" << ((REF).cast<float>()) << "\n" << "got\n" << m << "\n\n"; \
+ } \
+ VERIFY_IS_APPROX((REF).cast<float>(), m); \
+ }
+
+#define VERIFY_UNIFORM(SUFFIX,NAME,TYPE) { \
+ TYPE value; value.setRandom(); \
+ TYPE data; \
+ int loc = glGetUniformLocation(prg_id, #NAME); \
+ VERIFY((loc!=-1) && "uniform not found"); \
+ glUniform(loc,value); \
+ EIGEN_CAT(glGetUniform,SUFFIX)(prg_id,loc,data.data()); \
+ if(!value.isApprox(data)) { \
+ std::cerr << "Expected:\n" << value << "\n" << "got\n" << data << "\n\n"; \
+ } \
+ VERIFY_IS_APPROX(value, data); \
+ }
+
+#define VERIFY_UNIFORMi(NAME,TYPE) { \
+ TYPE value = TYPE::Random().eval().cast<float>().cast<TYPE::Scalar>(); \
+ TYPE data; \
+ int loc = glGetUniformLocation(prg_id, #NAME); \
+ VERIFY((loc!=-1) && "uniform not found"); \
+ glUniform(loc,value); \
+ glGetUniformiv(prg_id,loc,(GLint*)data.data()); \
+ if(!value.isApprox(data)) { \
+ std::cerr << "Expected:\n" << value << "\n" << "got\n" << data << "\n\n"; \
+ } \
+ VERIFY_IS_APPROX(value, data); \
+ }
+
+void printProgramInfoLog(GLuint objectID)
+{
+ int infologLength, charsWritten;
+ GLchar *infoLog;
+ glGetProgramiv(objectID, GL_INFO_LOG_LENGTH, &infologLength);
+ if(infologLength > 0)
+ {
+ infoLog = new GLchar[infologLength];
+ glGetProgramInfoLog(objectID, infologLength, &charsWritten, infoLog);
+ if (charsWritten > 0)
+ std::cerr << "Program info : \n" << infoLog << std::endl;
+ delete[] infoLog;
+ }
+}
+
+void printShaderInfoLog(GLuint objectID)
+{
+ int infologLength, charsWritten;
+ GLchar *infoLog;
+ glGetShaderiv(objectID, GL_INFO_LOG_LENGTH, &infologLength);
+ if(infologLength > 0)
+ {
+ infoLog = new GLchar[infologLength];
+ glGetShaderInfoLog(objectID, infologLength, &charsWritten, infoLog);
+ if (charsWritten > 0)
+ std::cerr << "Shader info : \n" << infoLog << std::endl;
+ delete[] infoLog;
+ }
+}
+
+GLint createProgram(const char* vtx, const char* frg, bool print_errors = true)
+{
+ GLint prg_id = glCreateProgram();
+ GLint vtx_id = glCreateShader(GL_VERTEX_SHADER);
+ GLint frg_id = glCreateShader(GL_FRAGMENT_SHADER);
+ GLint ok;
+
+ glShaderSource(vtx_id, 1, &vtx, 0);
+ glCompileShader(vtx_id);
+ glGetShaderiv(vtx_id, GL_COMPILE_STATUS, &ok);
+ if(!ok)
+ {
+ if (print_errors)
+ {
+ std::cerr << "vtx compilation failed\n";
+ std::cerr << "Source:\n" << vtx << "\n";
+ printShaderInfoLog(vtx_id);
+ }
+ glDeleteShader(vtx_id);
+ return GL_ZERO;
+ }
+
+ glShaderSource(frg_id, 1, &frg, 0);
+ glCompileShader(frg_id);
+ glGetShaderiv(frg_id, GL_COMPILE_STATUS, &ok);
+ if(!ok)
+ {
+ if (print_errors)
+ {
+ std::cerr << "frg compilation failed.\n";
+ std::cerr << "Source:\n" << frg << "\n";
+ printShaderInfoLog(frg_id);
+ }
+ glDeleteShader(vtx_id);
+ glDeleteShader(frg_id);
+ return GL_ZERO;
+ }
+
+ glAttachShader(prg_id, vtx_id);
+ glAttachShader(prg_id, frg_id);
+ glLinkProgram(prg_id);
+
+ // Delete shaders once linked.
+ glDeleteShader(vtx_id);
+ glDeleteShader(frg_id);
+ glGetProgramiv(prg_id, GL_LINK_STATUS, &ok);
+ if(!ok)
+ {
+ if (print_errors)
+ {
+ std::cerr << "linking failed.\n";
+ printProgramInfoLog(prg_id);
+ }
+ glDeleteProgram(prg_id);
+ return GL_ZERO;
+ }
+
+ glUseProgram(prg_id);
+ return prg_id;
+}
+
+GLint createProgram(const std::string& vtx, const std::string& frg, bool print_errors = true)
+{
+ return createProgram(vtx.c_str(), frg.c_str(), print_errors);
+}
+
+std::string getGlslVersionString(int gl_major_version, int gl_minor_version)
+{
+ switch (gl_major_version)
+ {
+ case 2:
+ switch (gl_minor_version)
+ {
+ case 0:
+ return "#version 110";
+ case 1:
+ return "#version 120";
+ }
+ break;
+ case 3:
+ switch (gl_minor_version)
+ {
+ case 0:
+ return "#version 130";
+ case 1:
+ return "#version 140";
+ case 2:
+ return "#version 150";
+ case 3:
+ return "#version 330";
+ }
+ break;
+ case 4:
+ switch (gl_minor_version)
+ {
+ case 0:
+ return "#version 400";
+ case 1:
+ return "#version 410";
+ case 2:
+ return "#version 420";
+ case 3:
+ return "#version 430";
+ case 4:
+ return "#version 440";
+ case 5:
+ return "#version 450";
+ case 6:
+ return "#version 460";
+ }
+ break;
+ }
+ return "";
+}
+
+void find_and_replace(
+ std::string& str,
+ const std::string& find,
+ const std::string& replace)
+{
+ size_t loc = 0;
+ size_t flen = find.length();
+ size_t rlen = replace.length();
+ while ( (loc = str.find(find, loc)) != std::string::npos) {
+ str.replace(loc, flen, replace);
+ loc += rlen;
+ }
+}
+
+// Finds and replaces a set of substrings in a string.
+std::string format(
+ const std::string& str,
+ const std::vector<std::string>& find,
+ const std::vector<std::string>& replace)
+{
+ std::string out = str;
+ for (std::size_t i=0; i<find.size(); ++i) {
+ find_and_replace(out, find[i], replace[i]);
+ }
+ return out;
+}
+
+// GLUT display function that runs test. Must be run within the display loop
+// in order to properly destroy resources.
+void openglsupport_test_loop()
+{
+ // Get context info.
+ const GLubyte* gl_version_string = glGetString(GL_VERSION);
+ std::cerr << "GL version: " << gl_version_string << std::endl;
+ std::cerr << "GLSL version: " << glGetString(GL_SHADING_LANGUAGE_VERSION) << std::endl;
+ // Parse version from string since GL_MAJOR_VERSION is only supported in GL 3.0+.
+ // Version string guaranteed to be <major>.<minor><vender extension>.
+ GLint gl_major_version = gl_version_string[0] - '0';
+ GLint gl_minor_version = gl_version_string[2] - '0';
+ bool legacy_gl = gl_major_version < 3 || (gl_major_version == 3 && gl_minor_version < 2);
+
+ // Fixed-function pipeline removed in OpenGL 3.2.
+ if (legacy_gl)
+ {
+ // Draw a basic triangle.
+ Vector3f v3f;
+ Matrix3f rot;
+ glBegin(GL_POINTS);
+ {
+ glVertex(v3f);
+ glVertex(2*v3f+v3f);
+ glVertex(rot*v3f);
+ }
+ glEnd();
+
+ // 4x4 matrices
+ Matrix4f mf44; mf44.setRandom();
+ VERIFY_MATRIX(glLoadMatrix(mf44), mf44);
+ VERIFY_MATRIX(glMultMatrix(mf44), mf44);
+ Matrix4d md44; md44.setRandom();
+ VERIFY_MATRIX(glLoadMatrix(md44), md44);
+ VERIFY_MATRIX(glMultMatrix(md44), md44);
+
+ // Quaternion
+ Quaterniond qd(AngleAxisd(internal::random<double>(), Vector3d::Random()));
+ VERIFY_MATRIX(glRotate(qd), Projective3d(qd).matrix());
+
+ Quaternionf qf(AngleAxisf(internal::random<double>(), Vector3f::Random()));
+ VERIFY_MATRIX(glRotate(qf), Projective3f(qf).matrix());
+
+ // 3D Transform
+ Transform<float,3,AffineCompact> acf3; acf3.matrix().setRandom();
+ VERIFY_MATRIX(glLoadMatrix(acf3), Projective3f(acf3).matrix());
+ VERIFY_MATRIX(glMultMatrix(acf3), Projective3f(acf3).matrix());
+
+ Transform<float,3,Affine> af3(acf3);
+ VERIFY_MATRIX(glLoadMatrix(af3), Projective3f(af3).matrix());
+ VERIFY_MATRIX(glMultMatrix(af3), Projective3f(af3).matrix());
+
+ Transform<float,3,Projective> pf3; pf3.matrix().setRandom();
+ VERIFY_MATRIX(glLoadMatrix(pf3), Projective3f(pf3).matrix());
+ VERIFY_MATRIX(glMultMatrix(pf3), Projective3f(pf3).matrix());
+
+ Transform<double,3,AffineCompact> acd3; acd3.matrix().setRandom();
+ VERIFY_MATRIX(glLoadMatrix(acd3), Projective3d(acd3).matrix());
+ VERIFY_MATRIX(glMultMatrix(acd3), Projective3d(acd3).matrix());
+
+ Transform<double,3,Affine> ad3(acd3);
+ VERIFY_MATRIX(glLoadMatrix(ad3), Projective3d(ad3).matrix());
+ VERIFY_MATRIX(glMultMatrix(ad3), Projective3d(ad3).matrix());
+
+ Transform<double,3,Projective> pd3; pd3.matrix().setRandom();
+ VERIFY_MATRIX(glLoadMatrix(pd3), Projective3d(pd3).matrix());
+ VERIFY_MATRIX(glMultMatrix(pd3), Projective3d(pd3).matrix());
+
+ // translations (2D and 3D)
+ {
+ Vector2f vf2; vf2.setRandom(); Vector3f vf23; vf23 << vf2, 0;
+ VERIFY_MATRIX(glTranslate(vf2), Projective3f(Translation3f(vf23)).matrix());
+ Vector2d vd2; vd2.setRandom(); Vector3d vd23; vd23 << vd2, 0;
+ VERIFY_MATRIX(glTranslate(vd2), Projective3d(Translation3d(vd23)).matrix());
+
+ Vector3f vf3; vf3.setRandom();
+ VERIFY_MATRIX(glTranslate(vf3), Projective3f(Translation3f(vf3)).matrix());
+ Vector3d vd3; vd3.setRandom();
+ VERIFY_MATRIX(glTranslate(vd3), Projective3d(Translation3d(vd3)).matrix());
+
+ Translation<float,3> tf3; tf3.vector().setRandom();
+ VERIFY_MATRIX(glTranslate(tf3), Projective3f(tf3).matrix());
+
+ Translation<double,3> td3; td3.vector().setRandom();
+ VERIFY_MATRIX(glTranslate(td3), Projective3d(td3).matrix());
+ }
+
+ // scaling (2D and 3D)
+ {
+ Vector2f vf2; vf2.setRandom(); Vector3f vf23; vf23 << vf2, 1;
+ VERIFY_MATRIX(glScale(vf2), Projective3f(Scaling(vf23)).matrix());
+ Vector2d vd2; vd2.setRandom(); Vector3d vd23; vd23 << vd2, 1;
+ VERIFY_MATRIX(glScale(vd2), Projective3d(Scaling(vd23)).matrix());
+
+ Vector3f vf3; vf3.setRandom();
+ VERIFY_MATRIX(glScale(vf3), Projective3f(Scaling(vf3)).matrix());
+ Vector3d vd3; vd3.setRandom();
+ VERIFY_MATRIX(glScale(vd3), Projective3d(Scaling(vd3)).matrix());
+
+ UniformScaling<float> usf(internal::random<float>());
+ VERIFY_MATRIX(glScale(usf), Projective3f(usf).matrix());
+
+ UniformScaling<double> usd(internal::random<double>());
+ VERIFY_MATRIX(glScale(usd), Projective3d(usd).matrix());
+ }
+ } else {
+ std::cerr << "Warning: fixed-function pipeline was not tested.\n";
+ }
+
+ // Dynamic shader substitution variables.
+ // Modern shaders require a version string, and newer runtimes fail to
+ // compile old GLSL versions. Thus, we dynamically set the GLSL version
+ // string based on runtime. Also, pre OpenGL 3.0, the output gl_FragColor was
+ // built-in. This was deprecated in OpenGL 3.0, requiring us to explicitly
+ // define the output variable.
+ std::vector<std::string> glsl_vars;
+ glsl_vars.push_back("${GLSL_VERSION}");
+ glsl_vars.push_back("${FRAG_OUTPUT_DECLARATION}");
+ glsl_vars.push_back("${FRAG_OUTPUT_VARIABLE}");
+
+ std::vector<std::string> glsl_vals;
+ glsl_vals.push_back(getGlslVersionString(gl_major_version, gl_minor_version));
+ if (gl_major_version >= 3) {
+ glsl_vals.push_back("out vec4 fragColor;");
+ glsl_vals.push_back("fragColor");
+ } else {
+ glsl_vals.push_back("");
+ glsl_vals.push_back("gl_FragColor");
+ }
+
+ // uniform
+ {
+ // vertex shader.
+ std::string vtx = format(
+ "${GLSL_VERSION}\n"
+ "void main(void) {\n"
+ " gl_Position = vec4(0,0,0,1);\n"
+ "}\n",
+ glsl_vars, glsl_vals);
+
+#ifdef GL_VERSION_2_0
+ if(GLEW_VERSION_2_0 && GL_VERSION_2_0)
+ {
+ std::string frg = format(
+ "${GLSL_VERSION}\n"
+ "uniform vec2 v2f;\n"
+ "uniform vec3 v3f;\n"
+ "uniform vec4 v4f;\n"
+ "uniform ivec2 v2i;\n"
+ "uniform ivec3 v3i;\n"
+ "uniform ivec4 v4i;\n"
+ "uniform mat2 m2f;\n"
+ "uniform mat3 m3f;\n"
+ "uniform mat4 m4f;\n"
+ "${FRAG_OUTPUT_DECLARATION}\n"
+ "void main(void) { \n"
+ " ${FRAG_OUTPUT_VARIABLE} = vec4(v2f[0]+v3f[0]+v4f[0])+vec4(v2i[0]+v3i[0]+v4i[0])+vec4(m2f[0][0]+m3f[0][0]+m4f[0][0]);\n"
+ "}\n",
+ glsl_vars, glsl_vals);
+
+ GLint prg_id = createProgram(vtx, frg);
+ VERIFY(prg_id > 0 && "Failed to create program.");
+ VERIFY_UNIFORM(fv, v2f, Vector2f);
+ VERIFY_UNIFORM(fv, v3f, Vector3f);
+ VERIFY_UNIFORM(fv, v4f, Vector4f);
+ VERIFY_UNIFORMi(v2i, Vector2i);
+ VERIFY_UNIFORMi(v3i, Vector3i);
+ VERIFY_UNIFORMi(v4i, Vector4i);
+ VERIFY_UNIFORM(fv, m2f, Matrix2f);
+ VERIFY_UNIFORM(fv, m3f, Matrix3f);
+ VERIFY_UNIFORM(fv, m4f, Matrix4f);
+ glDeleteProgram(prg_id);
+ }
+ else
+#endif
+ std::cerr << "Warning: opengl 2.0 was not tested.\n";
+
+#ifdef GL_VERSION_2_1
+ if(GLEW_VERSION_2_1 && GL_VERSION_2_1 &&
+ (gl_major_version > 2 || (gl_major_version == 2 && gl_minor_version >= 1)))
+ {
+ std::string frg = format(
+ "${GLSL_VERSION}\n"
+ "uniform mat2x3 m23f;\n"
+ "uniform mat3x2 m32f;\n"
+ "uniform mat2x4 m24f;\n"
+ "uniform mat4x2 m42f;\n"
+ "uniform mat3x4 m34f;\n"
+ "uniform mat4x3 m43f;\n"
+ "${FRAG_OUTPUT_DECLARATION}\n"
+ "void main(void) {\n"
+ " ${FRAG_OUTPUT_VARIABLE} = vec4(m23f[0][0]+m32f[0][0]+m24f[0][0]+m42f[0][0]+m34f[0][0]+m43f[0][0]);\n"
+ "}\n",
+ glsl_vars, glsl_vals);
+
+ GLint prg_id = createProgram(vtx, frg);
+ VERIFY(prg_id > 0 && "Failed to create program.");
+ typedef Matrix<float,2,3> Matrix23f;
+ typedef Matrix<float,3,2> Matrix32f;
+ typedef Matrix<float,2,4> Matrix24f;
+ typedef Matrix<float,4,2> Matrix42f;
+ typedef Matrix<float,3,4> Matrix34f;
+ typedef Matrix<float,4,3> Matrix43f;
+
+ VERIFY_UNIFORM(fv, m23f, Matrix23f);
+ VERIFY_UNIFORM(fv, m32f, Matrix32f);
+ VERIFY_UNIFORM(fv, m24f, Matrix24f);
+ VERIFY_UNIFORM(fv, m42f, Matrix42f);
+ VERIFY_UNIFORM(fv, m34f, Matrix34f);
+ VERIFY_UNIFORM(fv, m43f, Matrix43f);
+ glDeleteProgram(prg_id);
+ }
+ else
+#endif
+ std::cerr << "Warning: opengl 2.1 was not tested.\n";
+
+#ifdef GL_VERSION_3_0
+ if(GLEW_VERSION_3_0 && GL_VERSION_3_0 && gl_major_version >= 3)
+ {
+ std::string frg = format(
+ "${GLSL_VERSION}\n"
+ "uniform uvec2 v2ui;\n"
+ "uniform uvec3 v3ui;\n"
+ "uniform uvec4 v4ui;\n"
+ "${FRAG_OUTPUT_DECLARATION}\n"
+ "void main(void) {\n"
+ " ${FRAG_OUTPUT_VARIABLE} = vec4(v2ui[0]+v3ui[0]+v4ui[0]);\n"
+ "}\n",
+ glsl_vars, glsl_vals);
+
+ GLint prg_id = createProgram(vtx, frg);
+ VERIFY(prg_id > 0 && "Failed to create program.");
+ typedef Matrix<unsigned int,2,1> Vector2ui;
+ typedef Matrix<unsigned int,3,1> Vector3ui;
+ typedef Matrix<unsigned int,4,1> Vector4ui;
+
+ VERIFY_UNIFORMi(v2ui, Vector2ui);
+ VERIFY_UNIFORMi(v3ui, Vector3ui);
+ VERIFY_UNIFORMi(v4ui, Vector4ui);
+ glDeleteProgram(prg_id);
+ }
+ else
+#endif
+ std::cerr << "Warning: opengl 3.0 was not tested.\n";
+
+ // dvecn supported if >= 4.1 or ARB_vertex_attrib_64bit
+ bool has_fp64_native = (gl_major_version == 4 && gl_minor_version >= 1);
+ bool has_fp64_extension = false;
+#ifdef GLEW_ARB_gpu_shader_fp64
+ if(GLEW_ARB_gpu_shader_fp64)
+ {
+ // Check that extension can actually be compiled.
+ if (has_fp64_extension)
+ {
+ std::string frg = format(
+ "${GLSL_VERSION}\n"
+ "#extension GL_ARB_gpu_shader_fp64 : enable\n"
+ "uniform dvec2 dv2;\n"
+ "${FRAG_OUTPUT_DECLARATION}\n"
+ "void main(void) {\n"
+ " ${FRAG_OUTPUT_VARIABLE} = vec4(dv2.x, dv2.y, dv2.x, dv2.y);\n"
+ "}\n",
+ glsl_vars, glsl_vals);
+ GLint prg_id = createProgram(vtx, frg, /*print_errors=*/false);
+ if (prg_id)
+ {
+ has_fp64_extension = true;
+ glDeleteProgram(prg_id);
+ }
+ }
+ }
+#endif
+
+ if( has_fp64_native || has_fp64_extension )
+ {
+ std::vector<std::string> glsl_vars_with_extension = glsl_vars;
+ glsl_vars_with_extension.push_back("${GLSL_EXTENSIONS}");
+ std::vector<std::string> glsl_vals_with_extension = glsl_vals;
+ if (has_fp64_extension)
+ {
+ glsl_vals_with_extension.push_back("#extension GL_ARB_gpu_shader_fp64 : enable");
+ }
+ else
+ {
+ glsl_vals_with_extension.push_back("");
+ }
+
+ std::string frg = format(
+ "${GLSL_VERSION}\n"
+ "${GLSL_EXTENSIONS}\n"
+ "uniform dvec2 v2d;\n"
+ "uniform dvec3 v3d;\n"
+ "uniform dvec4 v4d;\n"
+ "${FRAG_OUTPUT_DECLARATION}\n"
+ "void main(void) {\n"
+ " ${FRAG_OUTPUT_VARIABLE} = vec4(v2d[0]+v3d[0]+v4d[0]);\n"
+ "}\n",
+ glsl_vars_with_extension, glsl_vals_with_extension);
+
+ GLint prg_id = createProgram(vtx,frg);
+ VERIFY(prg_id > 0 && "Failed to create program.");
+ VERIFY_UNIFORM(dv, v2d, Vector2d);
+ VERIFY_UNIFORM(dv, v3d, Vector3d);
+ VERIFY_UNIFORM(dv, v4d, Vector4d);
+ glDeleteProgram(prg_id);
+ }
+ else
+ std::cerr << "Warning: dvec (fp64) was not tested.\n";
+ }
+
+ // Exit loop - Leaving main loop is supported by freeglut, otherwise we
+ // are forced to exit.
+#ifdef FREEGLUT
+ glutLeaveMainLoop();
+ // Trigger another display loop iteration. Otherwise, it just hangs.
+ glutPostRedisplay();
+#else
+ exit(0);
+#endif
+}
+
+EIGEN_DECLARE_TEST(openglsupport)
+{
+ int argc = 0;
+ glutInit(&argc, 0);
+
+ GLint glut_display_mode = GLUT_DOUBLE | GLUT_RGB | GLUT_DEPTH;
+
+#ifndef EIGEN_LEGACY_OPENGL
+ // Initialize 3.2+ OpenGL context.
+#if defined(__APPLE_CC__)
+ glut_display_mode |= GLUT_3_2_CORE_PROFILE;
+#elif defined(FREEGLUT)
+ glutInitContextVersion(3, 2);
+ glutInitContextFlags(GLUT_FORWARD_COMPATIBLE);
+ glutInitContextProfile(GLUT_CORE_PROFILE);
+#endif
+#endif
+
+ glutInitDisplayMode(glut_display_mode);
+ glutInitWindowPosition(0, 0);
+ glutInitWindowSize(10, 10);
+
+ int window = glutCreateWindow("Eigen");
+ if(window <= 0)
+ {
+ std::cerr << "Error: Unable to create GLUT Window.\n";
+ exit(1);
+ }
+
+ glewExperimental = GL_TRUE;
+ if(glewInit() != GLEW_OK)
+ {
+ std::cerr << "Warning: Failed to initialize GLEW.\n";
+ exit(1);
+ }
+
+ // Run test in display, otherwise GLUT fails to clean up and leads to memory
+ // access errors on exit.
+ glutDisplayFunc(openglsupport_test_loop);
+ glutMainLoop();
+ glutDestroyWindow(window);
+}
diff --git a/unsupported/test/pocketfft.cpp b/unsupported/test/pocketfft.cpp
new file mode 100644
index 0000000..5e8a0b6
--- /dev/null
+++ b/unsupported/test/pocketfft.cpp
@@ -0,0 +1,2 @@
+#define EIGEN_POCKETFFT_DEFAULT 1
+#include "fft_test_shared.h"
diff --git a/unsupported/test/polynomialsolver.cpp b/unsupported/test/polynomialsolver.cpp
new file mode 100644
index 0000000..fed9f89
--- /dev/null
+++ b/unsupported/test/polynomialsolver.cpp
@@ -0,0 +1,232 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2010 Manuel Yguel <manuel.yguel@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "main.h"
+#include <unsupported/Eigen/Polynomials>
+#include <iostream>
+#include <algorithm>
+
+using namespace std;
+
+namespace Eigen {
+namespace internal {
+template<int Size>
+struct increment_if_fixed_size
+{
+ enum {
+ ret = (Size == Dynamic) ? Dynamic : Size+1
+ };
+};
+}
+}
+
+template<typename PolynomialType>
+PolynomialType polyder(const PolynomialType& p)
+{
+ typedef typename PolynomialType::Scalar Scalar;
+ PolynomialType res(p.size());
+ for(Index i=1; i<p.size(); ++i)
+ res[i-1] = p[i]*Scalar(i);
+ res[p.size()-1] = 0.;
+ return res;
+}
+
+template<int Deg, typename POLYNOMIAL, typename SOLVER>
+bool aux_evalSolver( const POLYNOMIAL& pols, SOLVER& psolve )
+{
+ typedef typename POLYNOMIAL::Scalar Scalar;
+ typedef typename POLYNOMIAL::RealScalar RealScalar;
+
+ typedef typename SOLVER::RootsType RootsType;
+ typedef Matrix<RealScalar,Deg,1> EvalRootsType;
+
+ const Index deg = pols.size()-1;
+
+ // Test template constructor from coefficient vector
+ SOLVER solve_constr (pols);
+
+ psolve.compute( pols );
+ const RootsType& roots( psolve.roots() );
+ EvalRootsType evr( deg );
+ POLYNOMIAL pols_der = polyder(pols);
+ EvalRootsType der( deg );
+ for( int i=0; i<roots.size(); ++i ){
+ evr[i] = std::abs( poly_eval( pols, roots[i] ) );
+ der[i] = numext::maxi(RealScalar(1.), std::abs( poly_eval( pols_der, roots[i] ) ));
+ }
+
+ // we need to divide by the magnitude of the derivative because
+ // with a high derivative is very small error in the value of the root
+ // yiels a very large error in the polynomial evaluation.
+ bool evalToZero = (evr.cwiseQuotient(der)).isZero( test_precision<Scalar>() );
+ if( !evalToZero )
+ {
+ cerr << "WRONG root: " << endl;
+ cerr << "Polynomial: " << pols.transpose() << endl;
+ cerr << "Roots found: " << roots.transpose() << endl;
+ cerr << "Abs value of the polynomial at the roots: " << evr.transpose() << endl;
+ cerr << endl;
+ }
+
+ std::vector<RealScalar> rootModuli( roots.size() );
+ Map< EvalRootsType > aux( &rootModuli[0], roots.size() );
+ aux = roots.array().abs();
+ std::sort( rootModuli.begin(), rootModuli.end() );
+ bool distinctModuli=true;
+ for( size_t i=1; i<rootModuli.size() && distinctModuli; ++i )
+ {
+ if( internal::isApprox( rootModuli[i], rootModuli[i-1] ) ){
+ distinctModuli = false; }
+ }
+ VERIFY( evalToZero || !distinctModuli );
+
+ return distinctModuli;
+}
+
+
+
+
+
+
+
+template<int Deg, typename POLYNOMIAL>
+void evalSolver( const POLYNOMIAL& pols )
+{
+ typedef typename POLYNOMIAL::Scalar Scalar;
+
+ typedef PolynomialSolver<Scalar, Deg > PolynomialSolverType;
+
+ PolynomialSolverType psolve;
+ aux_evalSolver<Deg, POLYNOMIAL, PolynomialSolverType>( pols, psolve );
+}
+
+
+
+
+template< int Deg, typename POLYNOMIAL, typename ROOTS, typename REAL_ROOTS >
+void evalSolverSugarFunction( const POLYNOMIAL& pols, const ROOTS& roots, const REAL_ROOTS& real_roots )
+{
+ using std::sqrt;
+ typedef typename POLYNOMIAL::Scalar Scalar;
+ typedef typename POLYNOMIAL::RealScalar RealScalar;
+
+ typedef PolynomialSolver<Scalar, Deg > PolynomialSolverType;
+
+ PolynomialSolverType psolve;
+ if( aux_evalSolver<Deg, POLYNOMIAL, PolynomialSolverType>( pols, psolve ) )
+ {
+ //It is supposed that
+ // 1) the roots found are correct
+ // 2) the roots have distinct moduli
+
+ //Test realRoots
+ std::vector< RealScalar > calc_realRoots;
+ psolve.realRoots( calc_realRoots, test_precision<RealScalar>());
+ VERIFY_IS_EQUAL( calc_realRoots.size() , (size_t)real_roots.size() );
+
+ const RealScalar psPrec = sqrt( test_precision<RealScalar>() );
+
+ for( size_t i=0; i<calc_realRoots.size(); ++i )
+ {
+ bool found = false;
+ for( size_t j=0; j<calc_realRoots.size()&& !found; ++j )
+ {
+ if( internal::isApprox( calc_realRoots[i], real_roots[j], psPrec ) ){
+ found = true; }
+ }
+ VERIFY( found );
+ }
+
+ //Test greatestRoot
+ VERIFY( internal::isApprox( roots.array().abs().maxCoeff(),
+ abs( psolve.greatestRoot() ), psPrec ) );
+
+ //Test smallestRoot
+ VERIFY( internal::isApprox( roots.array().abs().minCoeff(),
+ abs( psolve.smallestRoot() ), psPrec ) );
+
+ bool hasRealRoot;
+ //Test absGreatestRealRoot
+ RealScalar r = psolve.absGreatestRealRoot( hasRealRoot );
+ VERIFY( hasRealRoot == (real_roots.size() > 0 ) );
+ if( hasRealRoot ){
+ VERIFY( internal::isApprox( real_roots.array().abs().maxCoeff(), abs(r), psPrec ) ); }
+
+ //Test absSmallestRealRoot
+ r = psolve.absSmallestRealRoot( hasRealRoot );
+ VERIFY( hasRealRoot == (real_roots.size() > 0 ) );
+ if( hasRealRoot ){
+ VERIFY( internal::isApprox( real_roots.array().abs().minCoeff(), abs( r ), psPrec ) ); }
+
+ //Test greatestRealRoot
+ r = psolve.greatestRealRoot( hasRealRoot );
+ VERIFY( hasRealRoot == (real_roots.size() > 0 ) );
+ if( hasRealRoot ){
+ VERIFY( internal::isApprox( real_roots.array().maxCoeff(), r, psPrec ) ); }
+
+ //Test smallestRealRoot
+ r = psolve.smallestRealRoot( hasRealRoot );
+ VERIFY( hasRealRoot == (real_roots.size() > 0 ) );
+ if( hasRealRoot ){
+ VERIFY( internal::isApprox( real_roots.array().minCoeff(), r, psPrec ) ); }
+ }
+}
+
+
+template<typename Scalar_, int Deg_>
+void polynomialsolver(int deg)
+{
+ typedef typename NumTraits<Scalar_>::Real RealScalar;
+ typedef internal::increment_if_fixed_size<Deg_> Dim;
+ typedef Matrix<Scalar_,Dim::ret,1> PolynomialType;
+ typedef Matrix<Scalar_,Deg_,1> EvalRootsType;
+ typedef Matrix<RealScalar,Deg_,1> RealRootsType;
+
+ cout << "Standard cases" << endl;
+ PolynomialType pols = PolynomialType::Random(deg+1);
+ evalSolver<Deg_,PolynomialType>( pols );
+
+ cout << "Hard cases" << endl;
+ Scalar_ multipleRoot = internal::random<Scalar_>();
+ EvalRootsType allRoots = EvalRootsType::Constant(deg,multipleRoot);
+ roots_to_monicPolynomial( allRoots, pols );
+ evalSolver<Deg_,PolynomialType>( pols );
+
+ cout << "Test sugar" << endl;
+ RealRootsType realRoots = RealRootsType::Random(deg);
+ roots_to_monicPolynomial( realRoots, pols );
+ evalSolverSugarFunction<Deg_>(
+ pols,
+ realRoots.template cast <std::complex<RealScalar> >().eval(),
+ realRoots );
+}
+
+EIGEN_DECLARE_TEST(polynomialsolver)
+{
+ for(int i = 0; i < g_repeat; i++)
+ {
+ CALL_SUBTEST_1( (polynomialsolver<float,1>(1)) );
+ CALL_SUBTEST_2( (polynomialsolver<double,2>(2)) );
+ CALL_SUBTEST_3( (polynomialsolver<double,3>(3)) );
+ CALL_SUBTEST_4( (polynomialsolver<float,4>(4)) );
+ CALL_SUBTEST_5( (polynomialsolver<double,5>(5)) );
+ CALL_SUBTEST_6( (polynomialsolver<float,6>(6)) );
+ CALL_SUBTEST_7( (polynomialsolver<float,7>(7)) );
+ CALL_SUBTEST_8( (polynomialsolver<double,8>(8)) );
+
+ CALL_SUBTEST_9( (polynomialsolver<float,Dynamic>(
+ internal::random<int>(9,13)
+ )) );
+ CALL_SUBTEST_10((polynomialsolver<double,Dynamic>(
+ internal::random<int>(9,13)
+ )) );
+ CALL_SUBTEST_11((polynomialsolver<float,Dynamic>(1)) );
+ CALL_SUBTEST_12((polynomialsolver<std::complex<double>,Dynamic>(internal::random<int>(2,13))) );
+ }
+}
diff --git a/unsupported/test/polynomialutils.cpp b/unsupported/test/polynomialutils.cpp
new file mode 100644
index 0000000..15a0f27
--- /dev/null
+++ b/unsupported/test/polynomialutils.cpp
@@ -0,0 +1,113 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2010 Manuel Yguel <manuel.yguel@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "main.h"
+#include <unsupported/Eigen/Polynomials>
+#include <iostream>
+
+using namespace std;
+
+namespace Eigen {
+namespace internal {
+template<int Size>
+struct increment_if_fixed_size
+{
+ enum {
+ ret = (Size == Dynamic) ? Dynamic : Size+1
+ };
+};
+}
+}
+
+template<typename Scalar_, int Deg_>
+void realRoots_to_monicPolynomial_test(int deg)
+{
+ typedef internal::increment_if_fixed_size<Deg_> Dim;
+ typedef Matrix<Scalar_,Dim::ret,1> PolynomialType;
+ typedef Matrix<Scalar_,Deg_,1> EvalRootsType;
+
+ PolynomialType pols(deg+1);
+ EvalRootsType roots = EvalRootsType::Random(deg);
+ roots_to_monicPolynomial( roots, pols );
+
+ EvalRootsType evr( deg );
+ for( int i=0; i<roots.size(); ++i ){
+ evr[i] = std::abs( poly_eval( pols, roots[i] ) ); }
+
+ bool evalToZero = evr.isZero( test_precision<Scalar_>() );
+ if( !evalToZero ){
+ cerr << evr.transpose() << endl; }
+ VERIFY( evalToZero );
+}
+
+template<typename Scalar_> void realRoots_to_monicPolynomial_scalar()
+{
+ CALL_SUBTEST_2( (realRoots_to_monicPolynomial_test<Scalar_,2>(2)) );
+ CALL_SUBTEST_3( (realRoots_to_monicPolynomial_test<Scalar_,3>(3)) );
+ CALL_SUBTEST_4( (realRoots_to_monicPolynomial_test<Scalar_,4>(4)) );
+ CALL_SUBTEST_5( (realRoots_to_monicPolynomial_test<Scalar_,5>(5)) );
+ CALL_SUBTEST_6( (realRoots_to_monicPolynomial_test<Scalar_,6>(6)) );
+ CALL_SUBTEST_7( (realRoots_to_monicPolynomial_test<Scalar_,7>(7)) );
+ CALL_SUBTEST_8( (realRoots_to_monicPolynomial_test<Scalar_,17>(17)) );
+
+ CALL_SUBTEST_9( (realRoots_to_monicPolynomial_test<Scalar_,Dynamic>(
+ internal::random<int>(18,26) )) );
+}
+
+
+
+
+template<typename Scalar_, int Deg_>
+void CauchyBounds(int deg)
+{
+ typedef internal::increment_if_fixed_size<Deg_> Dim;
+ typedef Matrix<Scalar_,Dim::ret,1> PolynomialType;
+ typedef Matrix<Scalar_,Deg_,1> EvalRootsType;
+
+ PolynomialType pols(deg+1);
+ EvalRootsType roots = EvalRootsType::Random(deg);
+ roots_to_monicPolynomial( roots, pols );
+ Scalar_ M = cauchy_max_bound( pols );
+ Scalar_ m = cauchy_min_bound( pols );
+ Scalar_ Max = roots.array().abs().maxCoeff();
+ Scalar_ min = roots.array().abs().minCoeff();
+ bool eval = (M >= Max) && (m <= min);
+ if( !eval )
+ {
+ cerr << "Roots: " << roots << endl;
+ cerr << "Bounds: (" << m << ", " << M << ")" << endl;
+ cerr << "Min,Max: (" << min << ", " << Max << ")" << endl;
+ }
+ VERIFY( eval );
+}
+
+template<typename Scalar_> void CauchyBounds_scalar()
+{
+ CALL_SUBTEST_2( (CauchyBounds<Scalar_,2>(2)) );
+ CALL_SUBTEST_3( (CauchyBounds<Scalar_,3>(3)) );
+ CALL_SUBTEST_4( (CauchyBounds<Scalar_,4>(4)) );
+ CALL_SUBTEST_5( (CauchyBounds<Scalar_,5>(5)) );
+ CALL_SUBTEST_6( (CauchyBounds<Scalar_,6>(6)) );
+ CALL_SUBTEST_7( (CauchyBounds<Scalar_,7>(7)) );
+ CALL_SUBTEST_8( (CauchyBounds<Scalar_,17>(17)) );
+
+ CALL_SUBTEST_9( (CauchyBounds<Scalar_,Dynamic>(
+ internal::random<int>(18,26) )) );
+}
+
+EIGEN_DECLARE_TEST(polynomialutils)
+{
+ for(int i = 0; i < g_repeat; i++)
+ {
+ realRoots_to_monicPolynomial_scalar<double>();
+ realRoots_to_monicPolynomial_scalar<float>();
+ CauchyBounds_scalar<double>();
+ CauchyBounds_scalar<float>();
+ }
+}
diff --git a/unsupported/test/sparse_extra.cpp b/unsupported/test/sparse_extra.cpp
new file mode 100644
index 0000000..4a1f938
--- /dev/null
+++ b/unsupported/test/sparse_extra.cpp
@@ -0,0 +1,249 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2010 Gael Guennebaud <g.gael@free.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "sparse_product.cpp"
+
+#ifdef min
+#undef min
+#endif
+
+#ifdef max
+#undef max
+#endif
+
+#include <Eigen/SparseExtra>
+
+template<typename SetterType,typename DenseType, typename Scalar, int Options>
+bool test_random_setter(SparseMatrix<Scalar,Options>& sm, const DenseType& ref, const std::vector<Vector2i>& nonzeroCoords)
+{
+ {
+ sm.setZero();
+ SetterType w(sm);
+ std::vector<Vector2i> remaining = nonzeroCoords;
+ while(!remaining.empty())
+ {
+ int i = internal::random<int>(0,static_cast<int>(remaining.size())-1);
+ w(remaining[i].x(),remaining[i].y()) = ref.coeff(remaining[i].x(),remaining[i].y());
+ remaining[i] = remaining.back();
+ remaining.pop_back();
+ }
+ }
+ return sm.isApprox(ref);
+}
+
+template<typename SparseMatrixType> void sparse_extra(const SparseMatrixType& ref)
+{
+ const Index rows = ref.rows();
+ const Index cols = ref.cols();
+ typedef typename SparseMatrixType::Scalar Scalar;
+ enum { Flags = SparseMatrixType::Flags };
+
+ double density = (std::max)(8./(rows*cols), 0.01);
+ typedef Matrix<Scalar,Dynamic,Dynamic> DenseMatrix;
+ typedef Matrix<Scalar,Dynamic,1> DenseVector;
+ Scalar eps = 1e-6;
+
+ SparseMatrixType m(rows, cols);
+ DenseMatrix refMat = DenseMatrix::Zero(rows, cols);
+ DenseVector vec1 = DenseVector::Random(rows);
+
+ std::vector<Vector2i> zeroCoords;
+ std::vector<Vector2i> nonzeroCoords;
+ initSparse<Scalar>(density, refMat, m, 0, &zeroCoords, &nonzeroCoords);
+
+ if (zeroCoords.size()==0 || nonzeroCoords.size()==0)
+ return;
+
+ // test coeff and coeffRef
+ for (int i=0; i<(int)zeroCoords.size(); ++i)
+ {
+ VERIFY_IS_MUCH_SMALLER_THAN( m.coeff(zeroCoords[i].x(),zeroCoords[i].y()), eps );
+ if(internal::is_same<SparseMatrixType,SparseMatrix<Scalar,Flags> >::value)
+ VERIFY_RAISES_ASSERT( m.coeffRef(zeroCoords[0].x(),zeroCoords[0].y()) = 5 );
+ }
+ VERIFY_IS_APPROX(m, refMat);
+
+ m.coeffRef(nonzeroCoords[0].x(), nonzeroCoords[0].y()) = Scalar(5);
+ refMat.coeffRef(nonzeroCoords[0].x(), nonzeroCoords[0].y()) = Scalar(5);
+
+ VERIFY_IS_APPROX(m, refMat);
+
+ // random setter
+// {
+// m.setZero();
+// VERIFY_IS_NOT_APPROX(m, refMat);
+// SparseSetter<SparseMatrixType, RandomAccessPattern> w(m);
+// std::vector<Vector2i> remaining = nonzeroCoords;
+// while(!remaining.empty())
+// {
+// int i = internal::random<int>(0,remaining.size()-1);
+// w->coeffRef(remaining[i].x(),remaining[i].y()) = refMat.coeff(remaining[i].x(),remaining[i].y());
+// remaining[i] = remaining.back();
+// remaining.pop_back();
+// }
+// }
+// VERIFY_IS_APPROX(m, refMat);
+
+ VERIFY(( test_random_setter<RandomSetter<SparseMatrixType, StdMapTraits> >(m,refMat,nonzeroCoords) ));
+ VERIFY(( test_random_setter<RandomSetter<SparseMatrixType, StdUnorderedMapTraits> >(m,refMat,nonzeroCoords) ));
+ #ifdef EIGEN_GOOGLEHASH_SUPPORT
+ VERIFY(( test_random_setter<RandomSetter<SparseMatrixType, GoogleDenseHashMapTraits> >(m,refMat,nonzeroCoords) ));
+ VERIFY(( test_random_setter<RandomSetter<SparseMatrixType, GoogleSparseHashMapTraits> >(m,refMat,nonzeroCoords) ));
+ #endif
+
+
+ // test RandomSetter
+ /*{
+ SparseMatrixType m1(rows,cols), m2(rows,cols);
+ DenseMatrix refM1 = DenseMatrix::Zero(rows, rows);
+ initSparse<Scalar>(density, refM1, m1);
+ {
+ Eigen::RandomSetter<SparseMatrixType > setter(m2);
+ for (int j=0; j<m1.outerSize(); ++j)
+ for (typename SparseMatrixType::InnerIterator i(m1,j); i; ++i)
+ setter(i.index(), j) = i.value();
+ }
+ VERIFY_IS_APPROX(m1, m2);
+ }*/
+
+
+}
+
+
+template<typename SparseMatrixType>
+void check_marketio()
+{
+ typedef Matrix<typename SparseMatrixType::Scalar, Dynamic, Dynamic> DenseMatrix;
+ Index rows = internal::random<Index>(1,100);
+ Index cols = internal::random<Index>(1,100);
+ SparseMatrixType m1, m2;
+ m1 = DenseMatrix::Random(rows, cols).sparseView();
+ saveMarket(m1, "sparse_extra.mtx");
+ loadMarket(m2, "sparse_extra.mtx");
+ VERIFY_IS_EQUAL(DenseMatrix(m1),DenseMatrix(m2));
+}
+
+template<typename VectorType>
+void check_marketio_vector()
+{
+ Index size = internal::random<Index>(1,100);
+ VectorType v1, v2;
+ v1 = VectorType::Random(size);
+ saveMarketVector(v1, "vector_extra.mtx");
+ loadMarketVector(v2, "vector_extra.mtx");
+ VERIFY_IS_EQUAL(v1,v2);
+}
+
+template<typename DenseMatrixType>
+void check_marketio_dense()
+{
+ Index rows=DenseMatrixType::MaxRowsAtCompileTime;
+ if (DenseMatrixType::MaxRowsAtCompileTime==Dynamic){
+ rows=internal::random<Index>(1,100);
+ }else if(DenseMatrixType::RowsAtCompileTime==Dynamic){
+ rows=internal::random<Index>(1,DenseMatrixType::MaxRowsAtCompileTime);
+ }
+
+ Index cols =DenseMatrixType::MaxColsAtCompileTime;
+ if (DenseMatrixType::MaxColsAtCompileTime==Dynamic){
+ cols=internal::random<Index>(1,100);
+ }else if(DenseMatrixType::ColsAtCompileTime==Dynamic){
+ cols=internal::random<Index>(1,DenseMatrixType::MaxColsAtCompileTime);
+ }
+
+ DenseMatrixType m1, m2;
+ m1= DenseMatrixType::Random(rows,cols);
+ saveMarketDense(m1, "dense_extra.mtx");
+ loadMarketDense(m2, "dense_extra.mtx");
+ VERIFY_IS_EQUAL(m1,m2);
+}
+
+template <typename Scalar>
+void check_sparse_inverse() {
+ typedef SparseMatrix<Scalar> MatrixType;
+
+ Matrix<Scalar, -1, -1> A;
+ A.resize(1000, 1000);
+ A.fill(0);
+ A.setIdentity();
+ A.col(0).array() += 1;
+ A.row(0).array() += 2;
+ A.col(2).array() += 3;
+ A.row(7).array() += 3;
+ A.col(9).array() += 3;
+ A.block(3, 4, 4, 2).array() += 9;
+ A.middleRows(10, 50).array() += 3;
+ A.middleCols(50, 50).array() += 40;
+ A.block(500, 300, 40, 20).array() += 10;
+ A.transposeInPlace();
+
+ Eigen::SparseLU<MatrixType> slu;
+ slu.compute(A.sparseView());
+ Matrix<Scalar, -1, -1> Id(A.rows(), A.cols());
+ Id.setIdentity();
+ Matrix<Scalar, -1, -1> inv = slu.solve(Id);
+
+ const MatrixType sparseInv = Eigen::SparseInverse<Scalar>().compute(A.sparseView()).inverse();
+
+ Scalar sumdiff = 0; // Check the diff only of the non-zero elements
+ for (Eigen::Index j = 0; j < A.cols(); j++) {
+ for (typename MatrixType::InnerIterator iter(sparseInv, j); iter; ++iter) {
+ const Scalar diff = std::abs(inv(iter.row(), iter.col()) - iter.value());
+ VERIFY_IS_APPROX_OR_LESS_THAN(diff, 1e-11);
+
+ if (iter.value() != 0) {
+ sumdiff += diff;
+ }
+ }
+ }
+
+ VERIFY_IS_APPROX_OR_LESS_THAN(sumdiff, 1e-10);
+}
+
+EIGEN_DECLARE_TEST(sparse_extra)
+{
+ for(int i = 0; i < g_repeat; i++) {
+ int s = Eigen::internal::random<int>(1,50);
+ CALL_SUBTEST_1( sparse_extra(SparseMatrix<double>(8, 8)) );
+ CALL_SUBTEST_2( sparse_extra(SparseMatrix<std::complex<double> >(s, s)) );
+ CALL_SUBTEST_1( sparse_extra(SparseMatrix<double>(s, s)) );
+
+ CALL_SUBTEST_3( (check_marketio<SparseMatrix<float,ColMajor,int> >()) );
+ CALL_SUBTEST_3( (check_marketio<SparseMatrix<double,ColMajor,int> >()) );
+ CALL_SUBTEST_3( (check_marketio<SparseMatrix<std::complex<float>,ColMajor,int> >()) );
+ CALL_SUBTEST_3( (check_marketio<SparseMatrix<std::complex<double>,ColMajor,int> >()) );
+ CALL_SUBTEST_3( (check_marketio<SparseMatrix<float,ColMajor,long int> >()) );
+ CALL_SUBTEST_3( (check_marketio<SparseMatrix<double,ColMajor,long int> >()) );
+ CALL_SUBTEST_3( (check_marketio<SparseMatrix<std::complex<float>,ColMajor,long int> >()) );
+ CALL_SUBTEST_3( (check_marketio<SparseMatrix<std::complex<double>,ColMajor,long int> >()) );
+
+ CALL_SUBTEST_4( (check_marketio_dense<Matrix<float,Dynamic,Dynamic> >()) );
+ CALL_SUBTEST_4( (check_marketio_dense<Matrix<float,Dynamic,Dynamic,RowMajor> >()) );
+ CALL_SUBTEST_4( (check_marketio_dense<Matrix<double,Dynamic,Dynamic> >()) );
+ CALL_SUBTEST_4( (check_marketio_dense<Matrix<std::complex<float>,Dynamic,Dynamic> >()) );
+ CALL_SUBTEST_4( (check_marketio_dense<Matrix<std::complex<double>,Dynamic,Dynamic> >()) );
+ CALL_SUBTEST_4( (check_marketio_dense<Matrix<float,Dynamic,3> >()) );
+ CALL_SUBTEST_4( (check_marketio_dense<Matrix<double,3,Dynamic> >()) );
+ CALL_SUBTEST_4( (check_marketio_dense<Matrix<double,3,4> >()) );
+ CALL_SUBTEST_4( (check_marketio_dense<Matrix<double,Dynamic,Dynamic,ColMajor,5,5> >()) );
+
+ CALL_SUBTEST_5( (check_marketio_vector<Matrix<float,1,Dynamic> >()) );
+ CALL_SUBTEST_5( (check_marketio_vector<Matrix<double,1,Dynamic> >()) );
+ CALL_SUBTEST_5( (check_marketio_vector<Matrix<std::complex<float>,1,Dynamic> >()) );
+ CALL_SUBTEST_5( (check_marketio_vector<Matrix<std::complex<double>,1,Dynamic> >()) );
+ CALL_SUBTEST_5( (check_marketio_vector<Matrix<float,Dynamic,1> >()) );
+ CALL_SUBTEST_5( (check_marketio_vector<Matrix<double,Dynamic,1> >()) );
+ CALL_SUBTEST_5( (check_marketio_vector<Matrix<std::complex<float>,Dynamic,1> >()) );
+ CALL_SUBTEST_5( (check_marketio_vector<Matrix<std::complex<double>,Dynamic,1> >()) );
+
+ CALL_SUBTEST_6((check_sparse_inverse<double>()));
+
+ TEST_SET_BUT_UNUSED_VARIABLE(s);
+ }
+}
diff --git a/unsupported/test/special_functions.cpp b/unsupported/test/special_functions.cpp
new file mode 100644
index 0000000..756f031
--- /dev/null
+++ b/unsupported/test/special_functions.cpp
@@ -0,0 +1,497 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2016 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include <limits.h>
+#include "main.h"
+#include "../Eigen/SpecialFunctions"
+
+// Hack to allow "implicit" conversions from double to Scalar via comma-initialization.
+template<typename Derived>
+Eigen::CommaInitializer<Derived> operator<<(Eigen::DenseBase<Derived>& dense, double v) {
+ return (dense << static_cast<typename Derived::Scalar>(v));
+}
+
+template<typename XprType>
+Eigen::CommaInitializer<XprType>& operator,(Eigen::CommaInitializer<XprType>& ci, double v) {
+ return (ci, static_cast<typename XprType::Scalar>(v));
+}
+
+template<typename X, typename Y>
+void verify_component_wise(const X& x, const Y& y)
+{
+ for(Index i=0; i<x.size(); ++i)
+ {
+ if((numext::isfinite)(y(i)))
+ VERIFY_IS_APPROX( x(i), y(i) );
+ else if((numext::isnan)(y(i)))
+ VERIFY((numext::isnan)(x(i)));
+ else
+ VERIFY_IS_EQUAL( x(i), y(i) );
+ }
+}
+
+template<typename ArrayType> void array_special_functions()
+{
+ using std::abs;
+ using std::sqrt;
+ typedef typename ArrayType::Scalar Scalar;
+ typedef typename NumTraits<Scalar>::Real RealScalar;
+
+ Scalar plusinf = std::numeric_limits<Scalar>::infinity();
+ Scalar nan = std::numeric_limits<Scalar>::quiet_NaN();
+
+ Index rows = internal::random<Index>(1,30);
+ Index cols = 1;
+
+ // API
+ {
+ ArrayType m1 = ArrayType::Random(rows,cols);
+#if EIGEN_HAS_C99_MATH
+ VERIFY_IS_APPROX(m1.lgamma(), lgamma(m1));
+ VERIFY_IS_APPROX(m1.digamma(), digamma(m1));
+ VERIFY_IS_APPROX(m1.erf(), erf(m1));
+ VERIFY_IS_APPROX(m1.erfc(), erfc(m1));
+#endif // EIGEN_HAS_C99_MATH
+ }
+
+
+#if EIGEN_HAS_C99_MATH
+ // check special functions (comparing against numpy implementation)
+ if (!NumTraits<Scalar>::IsComplex)
+ {
+
+ {
+ ArrayType m1 = ArrayType::Random(rows,cols);
+ ArrayType m2 = ArrayType::Random(rows,cols);
+
+ // Test various propreties of igamma & igammac. These are normalized
+ // gamma integrals where
+ // igammac(a, x) = Gamma(a, x) / Gamma(a)
+ // igamma(a, x) = gamma(a, x) / Gamma(a)
+ // where Gamma and gamma are considered the standard unnormalized
+ // upper and lower incomplete gamma functions, respectively.
+ ArrayType a = m1.abs() + Scalar(2);
+ ArrayType x = m2.abs() + Scalar(2);
+ ArrayType zero = ArrayType::Zero(rows, cols);
+ ArrayType one = ArrayType::Constant(rows, cols, Scalar(1.0));
+ ArrayType a_m1 = a - one;
+ ArrayType Gamma_a_x = Eigen::igammac(a, x) * a.lgamma().exp();
+ ArrayType Gamma_a_m1_x = Eigen::igammac(a_m1, x) * a_m1.lgamma().exp();
+ ArrayType gamma_a_x = Eigen::igamma(a, x) * a.lgamma().exp();
+ ArrayType gamma_a_m1_x = Eigen::igamma(a_m1, x) * a_m1.lgamma().exp();
+
+
+ // Gamma(a, 0) == Gamma(a)
+ VERIFY_IS_APPROX(Eigen::igammac(a, zero), one);
+
+ // Gamma(a, x) + gamma(a, x) == Gamma(a)
+ VERIFY_IS_APPROX(Gamma_a_x + gamma_a_x, a.lgamma().exp());
+
+ // Gamma(a, x) == (a - 1) * Gamma(a-1, x) + x^(a-1) * exp(-x)
+ VERIFY_IS_APPROX(Gamma_a_x, (a - Scalar(1)) * Gamma_a_m1_x + x.pow(a-Scalar(1)) * (-x).exp());
+
+ // gamma(a, x) == (a - 1) * gamma(a-1, x) - x^(a-1) * exp(-x)
+ VERIFY_IS_APPROX(gamma_a_x, (a - Scalar(1)) * gamma_a_m1_x - x.pow(a-Scalar(1)) * (-x).exp());
+ }
+ {
+ // Verify for large a and x that values are between 0 and 1.
+ ArrayType m1 = ArrayType::Random(rows,cols);
+ ArrayType m2 = ArrayType::Random(rows,cols);
+ int max_exponent = std::numeric_limits<Scalar>::max_exponent10;
+ ArrayType a = m1.abs() * Scalar(pow(10., max_exponent - 1));
+ ArrayType x = m2.abs() * Scalar(pow(10., max_exponent - 1));
+ for (int i = 0; i < a.size(); ++i) {
+ Scalar igam = numext::igamma(a(i), x(i));
+ VERIFY(0 <= igam);
+ VERIFY(igam <= 1);
+ }
+ }
+
+ {
+ // Check exact values of igamma and igammac against a third party calculation.
+ Scalar a_s[] = {Scalar(0), Scalar(1), Scalar(1.5), Scalar(4), Scalar(0.0001), Scalar(1000.5)};
+ Scalar x_s[] = {Scalar(0), Scalar(1), Scalar(1.5), Scalar(4), Scalar(0.0001), Scalar(1000.5)};
+
+ // location i*6+j corresponds to a_s[i], x_s[j].
+ Scalar igamma_s[][6] = {
+ {Scalar(0.0), nan, nan, nan, nan, nan},
+ {Scalar(0.0), Scalar(0.6321205588285578), Scalar(0.7768698398515702),
+ Scalar(0.9816843611112658), Scalar(9.999500016666262e-05),
+ Scalar(1.0)},
+ {Scalar(0.0), Scalar(0.4275932955291202), Scalar(0.608374823728911),
+ Scalar(0.9539882943107686), Scalar(7.522076445089201e-07),
+ Scalar(1.0)},
+ {Scalar(0.0), Scalar(0.01898815687615381),
+ Scalar(0.06564245437845008), Scalar(0.5665298796332909),
+ Scalar(4.166333347221828e-18), Scalar(1.0)},
+ {Scalar(0.0), Scalar(0.9999780593618628), Scalar(0.9999899967080838),
+ Scalar(0.9999996219837988), Scalar(0.9991370418689945), Scalar(1.0)},
+ {Scalar(0.0), Scalar(0.0), Scalar(0.0), Scalar(0.0), Scalar(0.0),
+ Scalar(0.5042041932513908)}};
+ Scalar igammac_s[][6] = {
+ {nan, nan, nan, nan, nan, nan},
+ {Scalar(1.0), Scalar(0.36787944117144233),
+ Scalar(0.22313016014842982), Scalar(0.018315638888734182),
+ Scalar(0.9999000049998333), Scalar(0.0)},
+ {Scalar(1.0), Scalar(0.5724067044708798), Scalar(0.3916251762710878),
+ Scalar(0.04601170568923136), Scalar(0.9999992477923555),
+ Scalar(0.0)},
+ {Scalar(1.0), Scalar(0.9810118431238462), Scalar(0.9343575456215499),
+ Scalar(0.4334701203667089), Scalar(1.0), Scalar(0.0)},
+ {Scalar(1.0), Scalar(2.1940638138146658e-05),
+ Scalar(1.0003291916285e-05), Scalar(3.7801620118431334e-07),
+ Scalar(0.0008629581310054535), Scalar(0.0)},
+ {Scalar(1.0), Scalar(1.0), Scalar(1.0), Scalar(1.0), Scalar(1.0),
+ Scalar(0.49579580674813944)}};
+
+ for (int i = 0; i < 6; ++i) {
+ for (int j = 0; j < 6; ++j) {
+ if ((std::isnan)(igamma_s[i][j])) {
+ VERIFY((std::isnan)(numext::igamma(a_s[i], x_s[j])));
+ } else {
+ VERIFY_IS_APPROX(numext::igamma(a_s[i], x_s[j]), igamma_s[i][j]);
+ }
+
+ if ((std::isnan)(igammac_s[i][j])) {
+ VERIFY((std::isnan)(numext::igammac(a_s[i], x_s[j])));
+ } else {
+ VERIFY_IS_APPROX(numext::igammac(a_s[i], x_s[j]), igammac_s[i][j]);
+ }
+ }
+ }
+ }
+ }
+#endif // EIGEN_HAS_C99_MATH
+
+ // Check the ndtri function against scipy.special.ndtri
+ {
+ ArrayType x(7), res(7), ref(7);
+ x << 0.5, 0.2, 0.8, 0.9, 0.1, 0.99, 0.01;
+ ref << 0., -0.8416212335729142, 0.8416212335729142, 1.2815515655446004, -1.2815515655446004, 2.3263478740408408, -2.3263478740408408;
+ CALL_SUBTEST( verify_component_wise(ref, ref); );
+ CALL_SUBTEST( res = x.ndtri(); verify_component_wise(res, ref); );
+ CALL_SUBTEST( res = ndtri(x); verify_component_wise(res, ref); );
+
+ // ndtri(normal_cdf(x)) ~= x
+ CALL_SUBTEST(
+ ArrayType m1 = ArrayType::Random(32);
+ using std::sqrt;
+
+ ArrayType cdf_val = (m1 / Scalar(sqrt(2.))).erf();
+ cdf_val = (cdf_val + Scalar(1)) / Scalar(2);
+ verify_component_wise(cdf_val.ndtri(), m1););
+
+ }
+
+ // Check the zeta function against scipy.special.zeta
+ {
+ ArrayType x(11), q(11), res(11), ref(11);
+ x << 1.5, 4, 10.5, 10000.5, 3, 1, 0.9, 2, 3, 4, 2000;
+ q << 2, 1.5, 3, 1.0001, -2.5, 1.2345, 1.2345, -1, -2, -3, 2000;
+ ref << 1.61237534869, 0.234848505667, 1.03086757337e-5, 0.367879440865, 0.054102025820864097, plusinf, nan, plusinf, nan, plusinf, 0;
+ CALL_SUBTEST( verify_component_wise(ref, ref); );
+ CALL_SUBTEST( res = x.zeta(q); verify_component_wise(res, ref); );
+ CALL_SUBTEST( res = zeta(x,q); verify_component_wise(res, ref); );
+ }
+
+ // digamma
+ {
+ ArrayType x(9), res(9), ref(9);
+ x << 1, 1.5, 4, -10.5, 10000.5, 0, -1, -2, -3;
+ ref << -0.5772156649015329, 0.03648997397857645, 1.2561176684318, 2.398239129535781, 9.210340372392849, nan, nan, nan, nan;
+ CALL_SUBTEST( verify_component_wise(ref, ref); );
+
+ CALL_SUBTEST( res = x.digamma(); verify_component_wise(res, ref); );
+ CALL_SUBTEST( res = digamma(x); verify_component_wise(res, ref); );
+ }
+
+#if EIGEN_HAS_C99_MATH
+ {
+ ArrayType n(16), x(16), res(16), ref(16);
+ n << 1, 1, 1, 1.5, 17, 31, 28, 8, 42, 147, 170, -1, 0, 1, 2, 3;
+ x << 2, 3, 25.5, 1.5, 4.7, 11.8, 17.7, 30.2, 15.8, 54.1, 64, -1, -2, -3, -4, -5;
+ ref << 0.644934066848, 0.394934066848, 0.0399946696496, nan, 293.334565435, 0.445487887616, -2.47810300902e-07, -8.29668781082e-09, -0.434562276666, 0.567742190178, -0.0108615497927, nan, nan, plusinf, nan, plusinf;
+ CALL_SUBTEST( verify_component_wise(ref, ref); );
+
+ if(sizeof(RealScalar)>=8) { // double
+ // Reason for commented line: http://eigen.tuxfamily.org/bz/show_bug.cgi?id=1232
+ // CALL_SUBTEST( res = x.polygamma(n); verify_component_wise(res, ref); );
+ CALL_SUBTEST( res = polygamma(n,x); verify_component_wise(res, ref); );
+ }
+ else {
+ // CALL_SUBTEST( res = x.polygamma(n); verify_component_wise(res.head(8), ref.head(8)); );
+ CALL_SUBTEST( res = polygamma(n,x); verify_component_wise(res.head(8), ref.head(8)); );
+ }
+ }
+#endif
+
+#if EIGEN_HAS_C99_MATH
+ {
+ // Inputs and ground truth generated with scipy via:
+ // a = np.logspace(-3, 3, 5) - 1e-3
+ // b = np.logspace(-3, 3, 5) - 1e-3
+ // x = np.linspace(-0.1, 1.1, 5)
+ // (full_a, full_b, full_x) = np.vectorize(lambda a, b, x: (a, b, x))(*np.ix_(a, b, x))
+ // full_a = full_a.flatten().tolist() # same for full_b, full_x
+ // v = scipy.special.betainc(full_a, full_b, full_x).flatten().tolist()
+ //
+ // Note in Eigen, we call betainc with arguments in the order (x, a, b).
+ ArrayType a(125);
+ ArrayType b(125);
+ ArrayType x(125);
+ ArrayType v(125);
+ ArrayType res(125);
+
+ a << 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
+ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
+ 0.03062277660168379, 0.03062277660168379, 0.03062277660168379,
+ 0.03062277660168379, 0.03062277660168379, 0.03062277660168379,
+ 0.03062277660168379, 0.03062277660168379, 0.03062277660168379,
+ 0.03062277660168379, 0.03062277660168379, 0.03062277660168379,
+ 0.03062277660168379, 0.03062277660168379, 0.03062277660168379,
+ 0.03062277660168379, 0.03062277660168379, 0.03062277660168379,
+ 0.03062277660168379, 0.03062277660168379, 0.03062277660168379,
+ 0.03062277660168379, 0.03062277660168379, 0.03062277660168379,
+ 0.03062277660168379, 0.999, 0.999, 0.999, 0.999, 0.999, 0.999, 0.999,
+ 0.999, 0.999, 0.999, 0.999, 0.999, 0.999, 0.999, 0.999, 0.999, 0.999,
+ 0.999, 0.999, 0.999, 0.999, 0.999, 0.999, 0.999, 0.999,
+ 31.62177660168379, 31.62177660168379, 31.62177660168379,
+ 31.62177660168379, 31.62177660168379, 31.62177660168379,
+ 31.62177660168379, 31.62177660168379, 31.62177660168379,
+ 31.62177660168379, 31.62177660168379, 31.62177660168379,
+ 31.62177660168379, 31.62177660168379, 31.62177660168379,
+ 31.62177660168379, 31.62177660168379, 31.62177660168379,
+ 31.62177660168379, 31.62177660168379, 31.62177660168379,
+ 31.62177660168379, 31.62177660168379, 31.62177660168379,
+ 31.62177660168379, 999.999, 999.999, 999.999, 999.999, 999.999, 999.999,
+ 999.999, 999.999, 999.999, 999.999, 999.999, 999.999, 999.999, 999.999,
+ 999.999, 999.999, 999.999, 999.999, 999.999, 999.999, 999.999, 999.999,
+ 999.999, 999.999, 999.999;
+
+ b << 0.0, 0.0, 0.0, 0.0, 0.0, 0.03062277660168379, 0.03062277660168379,
+ 0.03062277660168379, 0.03062277660168379, 0.03062277660168379, 0.999,
+ 0.999, 0.999, 0.999, 0.999, 31.62177660168379, 31.62177660168379,
+ 31.62177660168379, 31.62177660168379, 31.62177660168379, 999.999,
+ 999.999, 999.999, 999.999, 999.999, 0.0, 0.0, 0.0, 0.0, 0.0,
+ 0.03062277660168379, 0.03062277660168379, 0.03062277660168379,
+ 0.03062277660168379, 0.03062277660168379, 0.999, 0.999, 0.999, 0.999,
+ 0.999, 31.62177660168379, 31.62177660168379, 31.62177660168379,
+ 31.62177660168379, 31.62177660168379, 999.999, 999.999, 999.999,
+ 999.999, 999.999, 0.0, 0.0, 0.0, 0.0, 0.0, 0.03062277660168379,
+ 0.03062277660168379, 0.03062277660168379, 0.03062277660168379,
+ 0.03062277660168379, 0.999, 0.999, 0.999, 0.999, 0.999,
+ 31.62177660168379, 31.62177660168379, 31.62177660168379,
+ 31.62177660168379, 31.62177660168379, 999.999, 999.999, 999.999,
+ 999.999, 999.999, 0.0, 0.0, 0.0, 0.0, 0.0, 0.03062277660168379,
+ 0.03062277660168379, 0.03062277660168379, 0.03062277660168379,
+ 0.03062277660168379, 0.999, 0.999, 0.999, 0.999, 0.999,
+ 31.62177660168379, 31.62177660168379, 31.62177660168379,
+ 31.62177660168379, 31.62177660168379, 999.999, 999.999, 999.999,
+ 999.999, 999.999, 0.0, 0.0, 0.0, 0.0, 0.0, 0.03062277660168379,
+ 0.03062277660168379, 0.03062277660168379, 0.03062277660168379,
+ 0.03062277660168379, 0.999, 0.999, 0.999, 0.999, 0.999,
+ 31.62177660168379, 31.62177660168379, 31.62177660168379,
+ 31.62177660168379, 31.62177660168379, 999.999, 999.999, 999.999,
+ 999.999, 999.999;
+
+ x << -0.1, 0.2, 0.5, 0.8, 1.1, -0.1, 0.2, 0.5, 0.8, 1.1, -0.1, 0.2, 0.5,
+ 0.8, 1.1, -0.1, 0.2, 0.5, 0.8, 1.1, -0.1, 0.2, 0.5, 0.8, 1.1, -0.1, 0.2,
+ 0.5, 0.8, 1.1, -0.1, 0.2, 0.5, 0.8, 1.1, -0.1, 0.2, 0.5, 0.8, 1.1, -0.1,
+ 0.2, 0.5, 0.8, 1.1, -0.1, 0.2, 0.5, 0.8, 1.1, -0.1, 0.2, 0.5, 0.8, 1.1,
+ -0.1, 0.2, 0.5, 0.8, 1.1, -0.1, 0.2, 0.5, 0.8, 1.1, -0.1, 0.2, 0.5, 0.8,
+ 1.1, -0.1, 0.2, 0.5, 0.8, 1.1, -0.1, 0.2, 0.5, 0.8, 1.1, -0.1, 0.2, 0.5,
+ 0.8, 1.1, -0.1, 0.2, 0.5, 0.8, 1.1, -0.1, 0.2, 0.5, 0.8, 1.1, -0.1, 0.2,
+ 0.5, 0.8, 1.1, -0.1, 0.2, 0.5, 0.8, 1.1, -0.1, 0.2, 0.5, 0.8, 1.1, -0.1,
+ 0.2, 0.5, 0.8, 1.1, -0.1, 0.2, 0.5, 0.8, 1.1, -0.1, 0.2, 0.5,
+ 0.8, 1.1;
+
+ v << nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,
+ nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,
+ nan, nan, nan, 0.47972119876364683, 0.5, 0.5202788012363533, nan, nan,
+ 0.9518683957740043, 0.9789663010413743, 0.9931729188073435, nan, nan,
+ 0.999995949033062, 0.9999999999993698, 0.9999999999999999, nan, nan,
+ 0.9999999999999999, 0.9999999999999999, 0.9999999999999999, nan, nan,
+ nan, nan, nan, nan, nan, 0.006827081192655869, 0.0210336989586256,
+ 0.04813160422599567, nan, nan, 0.20014344256217678, 0.5000000000000001,
+ 0.7998565574378232, nan, nan, 0.9991401428435834, 0.999999999698403,
+ 0.9999999999999999, nan, nan, 0.9999999999999999, 0.9999999999999999,
+ 0.9999999999999999, nan, nan, nan, nan, nan, nan, nan,
+ 1.0646600232370887e-25, 6.301722877826246e-13, 4.050966937974938e-06,
+ nan, nan, 7.864342668429763e-23, 3.015969667594166e-10,
+ 0.0008598571564165444, nan, nan, 6.031987710123844e-08,
+ 0.5000000000000007, 0.9999999396801229, nan, nan, 0.9999999999999999,
+ 0.9999999999999999, 0.9999999999999999, nan, nan, nan, nan, nan, nan,
+ nan, 0.0, 7.029920380986636e-306, 2.2450728208591345e-101, nan, nan,
+ 0.0, 9.275871147869727e-302, 1.2232913026152827e-97, nan, nan, 0.0,
+ 3.0891393081932924e-252, 2.9303043666183996e-60, nan, nan,
+ 2.248913486879199e-196, 0.5000000000004947, 0.9999999999999999, nan;
+
+ CALL_SUBTEST(res = betainc(a, b, x);
+ verify_component_wise(res, v););
+ }
+
+ // Test various properties of betainc
+ {
+ ArrayType m1 = ArrayType::Random(32);
+ ArrayType m2 = ArrayType::Random(32);
+ ArrayType m3 = ArrayType::Random(32);
+ ArrayType one = ArrayType::Constant(32, Scalar(1.0));
+ const Scalar eps = std::numeric_limits<Scalar>::epsilon();
+ ArrayType a = (m1 * Scalar(4)).exp();
+ ArrayType b = (m2 * Scalar(4)).exp();
+ ArrayType x = m3.abs();
+
+ // betainc(a, 1, x) == x**a
+ CALL_SUBTEST(
+ ArrayType test = betainc(a, one, x);
+ ArrayType expected = x.pow(a);
+ verify_component_wise(test, expected););
+
+ // betainc(1, b, x) == 1 - (1 - x)**b
+ CALL_SUBTEST(
+ ArrayType test = betainc(one, b, x);
+ ArrayType expected = one - (one - x).pow(b);
+ verify_component_wise(test, expected););
+
+ // betainc(a, b, x) == 1 - betainc(b, a, 1-x)
+ CALL_SUBTEST(
+ ArrayType test = betainc(a, b, x) + betainc(b, a, one - x);
+ ArrayType expected = one;
+ verify_component_wise(test, expected););
+
+ // betainc(a+1, b, x) = betainc(a, b, x) - x**a * (1 - x)**b / (a * beta(a, b))
+ CALL_SUBTEST(
+ ArrayType num = x.pow(a) * (one - x).pow(b);
+ ArrayType denom = a * (a.lgamma() + b.lgamma() - (a + b).lgamma()).exp();
+ // Add eps to rhs and lhs so that component-wise test doesn't result in
+ // nans when both outputs are zeros.
+ ArrayType expected = betainc(a, b, x) - num / denom + eps;
+ ArrayType test = betainc(a + one, b, x) + eps;
+ if (sizeof(Scalar) >= 8) { // double
+ verify_component_wise(test, expected);
+ } else {
+ // Reason for limited test: http://eigen.tuxfamily.org/bz/show_bug.cgi?id=1232
+ verify_component_wise(test.head(8), expected.head(8));
+ });
+
+ // betainc(a, b+1, x) = betainc(a, b, x) + x**a * (1 - x)**b / (b * beta(a, b))
+ CALL_SUBTEST(
+ // Add eps to rhs and lhs so that component-wise test doesn't result in
+ // nans when both outputs are zeros.
+ ArrayType num = x.pow(a) * (one - x).pow(b);
+ ArrayType denom = b * (a.lgamma() + b.lgamma() - (a + b).lgamma()).exp();
+ ArrayType expected = betainc(a, b, x) + num / denom + eps;
+ ArrayType test = betainc(a, b + one, x) + eps;
+ verify_component_wise(test, expected););
+ }
+#endif // EIGEN_HAS_C99_MATH
+
+ /* Code to generate the data for the following two test cases.
+ N = 5
+ np.random.seed(3)
+
+ a = np.logspace(-2, 3, 6)
+ a = np.ravel(np.tile(np.reshape(a, [-1, 1]), [1, N]))
+ x = np.random.gamma(a, 1.0)
+ x = np.maximum(x, np.finfo(np.float32).tiny)
+
+ def igamma(a, x):
+ return mpmath.gammainc(a, 0, x, regularized=True)
+
+ def igamma_der_a(a, x):
+ res = mpmath.diff(lambda a_prime: igamma(a_prime, x), a)
+ return np.float64(res)
+
+ def gamma_sample_der_alpha(a, x):
+ igamma_x = igamma(a, x)
+ def igammainv_of_igamma(a_prime):
+ return mpmath.findroot(lambda x_prime: igamma(a_prime, x_prime) -
+ igamma_x, x, solver='newton')
+ return np.float64(mpmath.diff(igammainv_of_igamma, a))
+
+ v_igamma_der_a = np.vectorize(igamma_der_a)(a, x)
+ v_gamma_sample_der_alpha = np.vectorize(gamma_sample_der_alpha)(a, x)
+ */
+
+#if EIGEN_HAS_C99_MATH
+ // Test igamma_der_a
+ {
+ ArrayType a(30);
+ ArrayType x(30);
+ ArrayType res(30);
+ ArrayType v(30);
+
+ a << 0.01, 0.01, 0.01, 0.01, 0.01, 0.1, 0.1, 0.1, 0.1, 0.1, 1.0, 1.0, 1.0,
+ 1.0, 1.0, 10.0, 10.0, 10.0, 10.0, 10.0, 100.0, 100.0, 100.0, 100.0,
+ 100.0, 1000.0, 1000.0, 1000.0, 1000.0, 1000.0;
+
+ x << 1.25668890405e-26, 1.17549435082e-38, 1.20938905072e-05,
+ 1.17549435082e-38, 1.17549435082e-38, 5.66572070696e-16,
+ 0.0132865061065, 0.0200034203853, 6.29263709118e-17, 1.37160367764e-06,
+ 0.333412038288, 1.18135687766, 0.580629033777, 0.170631439426,
+ 0.786686768458, 7.63873279537, 13.1944344379, 11.896042354,
+ 10.5830172417, 10.5020942233, 92.8918587747, 95.003720371,
+ 86.3715926467, 96.0330217672, 82.6389930677, 968.702906754,
+ 969.463546828, 1001.79726022, 955.047416547, 1044.27458568;
+
+ v << -32.7256441441, -36.4394150514, -9.66467612263, -36.4394150514,
+ -36.4394150514, -1.0891900302, -2.66351229645, -2.48666868596,
+ -0.929700494428, -3.56327722764, -0.455320135314, -0.391437214323,
+ -0.491352055991, -0.350454834292, -0.471773162921, -0.104084440522,
+ -0.0723646747909, -0.0992828975532, -0.121638215446, -0.122619605294,
+ -0.0317670267286, -0.0359974812869, -0.0154359225363, -0.0375775365921,
+ -0.00794899153653, -0.00777303219211, -0.00796085782042,
+ -0.0125850719397, -0.00455500206958, -0.00476436993148;
+
+ CALL_SUBTEST(res = igamma_der_a(a, x); verify_component_wise(res, v););
+ }
+
+ // Test gamma_sample_der_alpha
+ {
+ ArrayType alpha(30);
+ ArrayType sample(30);
+ ArrayType res(30);
+ ArrayType v(30);
+
+ alpha << 0.01, 0.01, 0.01, 0.01, 0.01, 0.1, 0.1, 0.1, 0.1, 0.1, 1.0, 1.0,
+ 1.0, 1.0, 1.0, 10.0, 10.0, 10.0, 10.0, 10.0, 100.0, 100.0, 100.0, 100.0,
+ 100.0, 1000.0, 1000.0, 1000.0, 1000.0, 1000.0;
+
+ sample << 1.25668890405e-26, 1.17549435082e-38, 1.20938905072e-05,
+ 1.17549435082e-38, 1.17549435082e-38, 5.66572070696e-16,
+ 0.0132865061065, 0.0200034203853, 6.29263709118e-17, 1.37160367764e-06,
+ 0.333412038288, 1.18135687766, 0.580629033777, 0.170631439426,
+ 0.786686768458, 7.63873279537, 13.1944344379, 11.896042354,
+ 10.5830172417, 10.5020942233, 92.8918587747, 95.003720371,
+ 86.3715926467, 96.0330217672, 82.6389930677, 968.702906754,
+ 969.463546828, 1001.79726022, 955.047416547, 1044.27458568;
+
+ v << 7.42424742367e-23, 1.02004297287e-34, 0.0130155240738,
+ 1.02004297287e-34, 1.02004297287e-34, 1.96505168277e-13, 0.525575786243,
+ 0.713903991771, 2.32077561808e-14, 0.000179348049886, 0.635500453302,
+ 1.27561284917, 0.878125852156, 0.41565819538, 1.03606488534,
+ 0.885964824887, 1.16424049334, 1.10764479598, 1.04590810812,
+ 1.04193666963, 0.965193152414, 0.976217589464, 0.93008035061,
+ 0.98153216096, 0.909196397698, 0.98434963993, 0.984738050206,
+ 1.00106492525, 0.97734200649, 1.02198794179;
+
+ CALL_SUBTEST(res = gamma_sample_der_alpha(alpha, sample);
+ verify_component_wise(res, v););
+ }
+#endif // EIGEN_HAS_C99_MATH
+}
+
+EIGEN_DECLARE_TEST(special_functions)
+{
+ CALL_SUBTEST_1(array_special_functions<ArrayXf>());
+ CALL_SUBTEST_2(array_special_functions<ArrayXd>());
+ // TODO(cantonios): half/bfloat16 don't have enough precision to reproduce results above.
+ // CALL_SUBTEST_3(array_special_functions<ArrayX<Eigen::half>>());
+ // CALL_SUBTEST_4(array_special_functions<ArrayX<Eigen::bfloat16>>());
+}
diff --git a/unsupported/test/special_packetmath.cpp b/unsupported/test/special_packetmath.cpp
new file mode 100644
index 0000000..faf10ef
--- /dev/null
+++ b/unsupported/test/special_packetmath.cpp
@@ -0,0 +1,149 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include <limits>
+#include "packetmath_test_shared.h"
+#include "../Eigen/SpecialFunctions"
+
+template<typename Scalar,typename Packet> void packetmath_real()
+{
+ using std::abs;
+ typedef internal::packet_traits<Scalar> PacketTraits;
+ const int PacketSize = internal::unpacket_traits<Packet>::size;
+
+ const int size = PacketSize*4;
+ EIGEN_ALIGN_MAX Scalar data1[PacketSize*4];
+ EIGEN_ALIGN_MAX Scalar data2[PacketSize*4];
+ EIGEN_ALIGN_MAX Scalar ref[PacketSize*4];
+
+#if EIGEN_HAS_C99_MATH
+ {
+ data1[0] = std::numeric_limits<Scalar>::quiet_NaN();
+ test::packet_helper<internal::packet_traits<Scalar>::HasLGamma,Packet> h;
+ h.store(data2, internal::plgamma(h.load(data1)));
+ VERIFY((numext::isnan)(data2[0]));
+ }
+ if (internal::packet_traits<Scalar>::HasErf) {
+ data1[0] = std::numeric_limits<Scalar>::quiet_NaN();
+ test::packet_helper<internal::packet_traits<Scalar>::HasErf,Packet> h;
+ h.store(data2, internal::perf(h.load(data1)));
+ VERIFY((numext::isnan)(data2[0]));
+ }
+ {
+ data1[0] = std::numeric_limits<Scalar>::quiet_NaN();
+ test::packet_helper<internal::packet_traits<Scalar>::HasErfc,Packet> h;
+ h.store(data2, internal::perfc(h.load(data1)));
+ VERIFY((numext::isnan)(data2[0]));
+ }
+ {
+ for (int i=0; i<size; ++i) {
+ data1[i] = internal::random<Scalar>(Scalar(0),Scalar(1));
+ }
+ CHECK_CWISE1_IF(internal::packet_traits<Scalar>::HasNdtri, numext::ndtri, internal::pndtri);
+ }
+#endif // EIGEN_HAS_C99_MATH
+
+ // For bessel_i*e and bessel_j*, the valid range is negative reals.
+ {
+ const int max_exponent = numext::mini(std::numeric_limits<Scalar>::max_exponent10-1, 6);
+ for (int i=0; i<size; ++i)
+ {
+ data1[i] = internal::random<Scalar>(Scalar(-1),Scalar(1)) * Scalar(std::pow(Scalar(10), internal::random<Scalar>(Scalar(-max_exponent),Scalar(max_exponent))));
+ data2[i] = internal::random<Scalar>(Scalar(-1),Scalar(1)) * Scalar(std::pow(Scalar(10), internal::random<Scalar>(Scalar(-max_exponent),Scalar(max_exponent))));
+ }
+
+ CHECK_CWISE1_IF(PacketTraits::HasBessel, numext::bessel_i0e, internal::pbessel_i0e);
+ CHECK_CWISE1_IF(PacketTraits::HasBessel, numext::bessel_i1e, internal::pbessel_i1e);
+ CHECK_CWISE1_IF(PacketTraits::HasBessel, numext::bessel_j0, internal::pbessel_j0);
+ CHECK_CWISE1_IF(PacketTraits::HasBessel, numext::bessel_j1, internal::pbessel_j1);
+ }
+
+ // Use a smaller data range for the bessel_i* as these can become very large.
+ // Following #1693, we also restrict this range further to avoid inf's due to
+ // differences in pexp and exp.
+ for (int i=0; i<size; ++i) {
+ data1[i] = internal::random<Scalar>(Scalar(0.01),Scalar(1)) *
+ Scalar(std::pow(Scalar(9), internal::random<Scalar>(Scalar(-1),Scalar(2))));
+ data2[i] = internal::random<Scalar>(Scalar(0.01),Scalar(1)) *
+ Scalar(std::pow(Scalar(9), internal::random<Scalar>(Scalar(-1),Scalar(2))));
+ }
+ CHECK_CWISE1_IF(PacketTraits::HasBessel, numext::bessel_i0, internal::pbessel_i0);
+ CHECK_CWISE1_IF(PacketTraits::HasBessel, numext::bessel_i1, internal::pbessel_i1);
+
+
+ // y_i, and k_i are valid for x > 0.
+ {
+ const int max_exponent = numext::mini(std::numeric_limits<Scalar>::max_exponent10-1, 5);
+ for (int i=0; i<size; ++i)
+ {
+ data1[i] = internal::random<Scalar>(Scalar(0.01),Scalar(1)) * Scalar(std::pow(Scalar(10), internal::random<Scalar>(Scalar(-2),Scalar(max_exponent))));
+ data2[i] = internal::random<Scalar>(Scalar(0.01),Scalar(1)) * Scalar(std::pow(Scalar(10), internal::random<Scalar>(Scalar(-2),Scalar(max_exponent))));
+ }
+ }
+
+ // TODO(srvasude): Re-enable this test once properly investigated why the
+ // scalar and vector paths differ.
+ // CHECK_CWISE1_IF(PacketTraits::HasBessel, numext::bessel_y0, internal::pbessel_y0);
+ CHECK_CWISE1_IF(PacketTraits::HasBessel, numext::bessel_y1, internal::pbessel_y1);
+ CHECK_CWISE1_IF(PacketTraits::HasBessel, numext::bessel_k0e, internal::pbessel_k0e);
+ CHECK_CWISE1_IF(PacketTraits::HasBessel, numext::bessel_k1e, internal::pbessel_k1e);
+
+ // Following #1693, we restrict the range for exp to avoid zeroing out too
+ // fast.
+ for (int i=0; i<size; ++i) {
+ data1[i] = internal::random<Scalar>(Scalar(0.01),Scalar(1)) *
+ Scalar(std::pow(Scalar(9), internal::random<Scalar>(Scalar(-1),Scalar(2))));
+ data2[i] = internal::random<Scalar>(Scalar(0.01),Scalar(1)) *
+ Scalar(std::pow(Scalar(9), internal::random<Scalar>(Scalar(-1),Scalar(2))));
+ }
+ CHECK_CWISE1_IF(PacketTraits::HasBessel, numext::bessel_k0, internal::pbessel_k0);
+ CHECK_CWISE1_IF(PacketTraits::HasBessel, numext::bessel_k1, internal::pbessel_k1);
+
+
+ for (int i=0; i<size; ++i) {
+ data1[i] = internal::random<Scalar>(Scalar(0.01),Scalar(1)) *
+ Scalar(std::pow(Scalar(10), internal::random<Scalar>(Scalar(-1),Scalar(2))));
+ data2[i] = internal::random<Scalar>(Scalar(0.01),Scalar(1)) *
+ Scalar(std::pow(Scalar(10), internal::random<Scalar>(Scalar(-1),Scalar(2))));
+ }
+
+#if EIGEN_HAS_C99_MATH
+ CHECK_CWISE1_IF(internal::packet_traits<Scalar>::HasLGamma, std::lgamma, internal::plgamma);
+ CHECK_CWISE1_IF(internal::packet_traits<Scalar>::HasErf, std::erf, internal::perf);
+ CHECK_CWISE1_IF(internal::packet_traits<Scalar>::HasErfc, std::erfc, internal::perfc);
+#endif
+
+}
+
+namespace Eigen {
+namespace test {
+
+template<typename Scalar,typename PacketType, bool IsComplex, bool IsInteger>
+struct runall {
+ static void run() {
+ packetmath_real<Scalar,PacketType>();
+ }
+};
+
+}
+}
+
+EIGEN_DECLARE_TEST(special_packetmath)
+{
+ g_first_pass = true;
+ for(int i = 0; i < g_repeat; i++) {
+
+ CALL_SUBTEST_1( test::runner<float>::run() );
+ CALL_SUBTEST_2( test::runner<double>::run() );
+ CALL_SUBTEST_3( test::runner<Eigen::half>::run() );
+ CALL_SUBTEST_4( test::runner<Eigen::bfloat16>::run() );
+ g_first_pass = false;
+ }
+}
diff --git a/unsupported/test/splines.cpp b/unsupported/test/splines.cpp
new file mode 100644
index 0000000..88ec87b
--- /dev/null
+++ b/unsupported/test/splines.cpp
@@ -0,0 +1,281 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2010-2011 Hauke Heibel <heibel@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "main.h"
+
+#include <unsupported/Eigen/Splines>
+
+namespace Eigen {
+
+ // lets do some explicit instantiations and thus
+ // force the compilation of all spline functions...
+ template class Spline<double, 2, Dynamic>;
+ template class Spline<double, 3, Dynamic>;
+
+ template class Spline<double, 2, 2>;
+ template class Spline<double, 2, 3>;
+ template class Spline<double, 2, 4>;
+ template class Spline<double, 2, 5>;
+
+ template class Spline<float, 2, Dynamic>;
+ template class Spline<float, 3, Dynamic>;
+
+ template class Spline<float, 3, 2>;
+ template class Spline<float, 3, 3>;
+ template class Spline<float, 3, 4>;
+ template class Spline<float, 3, 5>;
+
+}
+
+Spline<double, 2, Dynamic> closed_spline2d()
+{
+ RowVectorXd knots(12);
+ knots << 0,
+ 0,
+ 0,
+ 0,
+ 0.867193179093898,
+ 1.660330955342408,
+ 2.605084834823134,
+ 3.484154586374428,
+ 4.252699478956276,
+ 4.252699478956276,
+ 4.252699478956276,
+ 4.252699478956276;
+
+ MatrixXd ctrls(8,2);
+ ctrls << -0.370967741935484, 0.236842105263158,
+ -0.231401860693277, 0.442245185027632,
+ 0.344361228532831, 0.773369994120753,
+ 0.828990216203802, 0.106550882647595,
+ 0.407270163678382, -1.043452922172848,
+ -0.488467813584053, -0.390098582530090,
+ -0.494657189446427, 0.054804824897884,
+ -0.370967741935484, 0.236842105263158;
+ ctrls.transposeInPlace();
+
+ return Spline<double, 2, Dynamic>(knots, ctrls);
+}
+
+/* create a reference spline */
+Spline<double, 3, Dynamic> spline3d()
+{
+ RowVectorXd knots(11);
+ knots << 0,
+ 0,
+ 0,
+ 0.118997681558377,
+ 0.162611735194631,
+ 0.498364051982143,
+ 0.655098003973841,
+ 0.679702676853675,
+ 1.000000000000000,
+ 1.000000000000000,
+ 1.000000000000000;
+
+ MatrixXd ctrls(8,3);
+ ctrls << 0.959743958516081, 0.340385726666133, 0.585267750979777,
+ 0.223811939491137, 0.751267059305653, 0.255095115459269,
+ 0.505957051665142, 0.699076722656686, 0.890903252535799,
+ 0.959291425205444, 0.547215529963803, 0.138624442828679,
+ 0.149294005559057, 0.257508254123736, 0.840717255983663,
+ 0.254282178971531, 0.814284826068816, 0.243524968724989,
+ 0.929263623187228, 0.349983765984809, 0.196595250431208,
+ 0.251083857976031, 0.616044676146639, 0.473288848902729;
+ ctrls.transposeInPlace();
+
+ return Spline<double, 3, Dynamic>(knots, ctrls);
+}
+
+/* compares evaluations against known results */
+void eval_spline3d()
+{
+ Spline3d spline = spline3d();
+
+ RowVectorXd u(10);
+ u << 0.351659507062997,
+ 0.830828627896291,
+ 0.585264091152724,
+ 0.549723608291140,
+ 0.917193663829810,
+ 0.285839018820374,
+ 0.757200229110721,
+ 0.753729094278495,
+ 0.380445846975357,
+ 0.567821640725221;
+
+ MatrixXd pts(10,3);
+ pts << 0.707620811535916, 0.510258911240815, 0.417485437023409,
+ 0.603422256426978, 0.529498282727551, 0.270351549348981,
+ 0.228364197569334, 0.423745615677815, 0.637687289287490,
+ 0.275556796335168, 0.350856706427970, 0.684295784598905,
+ 0.514519311047655, 0.525077224890754, 0.351628308305896,
+ 0.724152914315666, 0.574461155457304, 0.469860285484058,
+ 0.529365063753288, 0.613328702656816, 0.237837040141739,
+ 0.522469395136878, 0.619099658652895, 0.237139665242069,
+ 0.677357023849552, 0.480655768435853, 0.422227610314397,
+ 0.247046593173758, 0.380604672404750, 0.670065791405019;
+ pts.transposeInPlace();
+
+ for (int i=0; i<u.size(); ++i)
+ {
+ Vector3d pt = spline(u(i));
+ VERIFY( (pt - pts.col(i)).norm() < 1e-14 );
+ }
+}
+
+/* compares evaluations on corner cases */
+void eval_spline3d_onbrks()
+{
+ Spline3d spline = spline3d();
+
+ RowVectorXd u = spline.knots();
+
+ MatrixXd pts(11,3);
+ pts << 0.959743958516081, 0.340385726666133, 0.585267750979777,
+ 0.959743958516081, 0.340385726666133, 0.585267750979777,
+ 0.959743958516081, 0.340385726666133, 0.585267750979777,
+ 0.430282980289940, 0.713074680056118, 0.720373307943349,
+ 0.558074875553060, 0.681617921034459, 0.804417124839942,
+ 0.407076008291750, 0.349707710518163, 0.617275937419545,
+ 0.240037008286602, 0.738739390398014, 0.324554153129411,
+ 0.302434111480572, 0.781162443963899, 0.240177089094644,
+ 0.251083857976031, 0.616044676146639, 0.473288848902729,
+ 0.251083857976031, 0.616044676146639, 0.473288848902729,
+ 0.251083857976031, 0.616044676146639, 0.473288848902729;
+ pts.transposeInPlace();
+
+ for (int i=0; i<u.size(); ++i)
+ {
+ Vector3d pt = spline(u(i));
+ VERIFY( (pt - pts.col(i)).norm() < 1e-14 );
+ }
+}
+
+void eval_closed_spline2d()
+{
+ Spline2d spline = closed_spline2d();
+
+ RowVectorXd u(12);
+ u << 0,
+ 0.332457030395796,
+ 0.356467130532952,
+ 0.453562180176215,
+ 0.648017921874804,
+ 0.973770235555003,
+ 1.882577647219307,
+ 2.289408593930498,
+ 3.511951429883045,
+ 3.884149321369450,
+ 4.236261590369414,
+ 4.252699478956276;
+
+ MatrixXd pts(12,2);
+ pts << -0.370967741935484, 0.236842105263158,
+ -0.152576775123250, 0.448975001279334,
+ -0.133417538277668, 0.461615613865667,
+ -0.053199060826740, 0.507630360006299,
+ 0.114249591147281, 0.570414135097409,
+ 0.377810316891987, 0.560497102875315,
+ 0.665052120135908, -0.157557441109611,
+ 0.516006487053228, -0.559763292174825,
+ -0.379486035348887, -0.331959640488223,
+ -0.462034726249078, -0.039105670080824,
+ -0.378730600917982, 0.225127015099919,
+ -0.370967741935484, 0.236842105263158;
+ pts.transposeInPlace();
+
+ for (int i=0; i<u.size(); ++i)
+ {
+ Vector2d pt = spline(u(i));
+ VERIFY( (pt - pts.col(i)).norm() < 1e-14 );
+ }
+}
+
+void check_global_interpolation2d()
+{
+ typedef Spline2d::PointType PointType;
+ typedef Spline2d::KnotVectorType KnotVectorType;
+ typedef Spline2d::ControlPointVectorType ControlPointVectorType;
+
+ ControlPointVectorType points = ControlPointVectorType::Random(2,100);
+
+ KnotVectorType chord_lengths; // knot parameters
+ Eigen::ChordLengths(points, chord_lengths);
+
+ // interpolation without knot parameters
+ {
+ const Spline2d spline = SplineFitting<Spline2d>::Interpolate(points,3);
+
+ for (Eigen::DenseIndex i=0; i<points.cols(); ++i)
+ {
+ PointType pt = spline( chord_lengths(i) );
+ PointType ref = points.col(i);
+ VERIFY( (pt - ref).matrix().norm() < 1e-14 );
+ }
+ }
+
+ // interpolation with given knot parameters
+ {
+ const Spline2d spline = SplineFitting<Spline2d>::Interpolate(points,3,chord_lengths);
+
+ for (Eigen::DenseIndex i=0; i<points.cols(); ++i)
+ {
+ PointType pt = spline( chord_lengths(i) );
+ PointType ref = points.col(i);
+ VERIFY( (pt - ref).matrix().norm() < 1e-14 );
+ }
+ }
+}
+
+void check_global_interpolation_with_derivatives2d()
+{
+ typedef Spline2d::PointType PointType;
+ typedef Spline2d::KnotVectorType KnotVectorType;
+
+ const Eigen::DenseIndex numPoints = 100;
+ const unsigned int dimension = 2;
+ const unsigned int degree = 3;
+
+ ArrayXXd points = ArrayXXd::Random(dimension, numPoints);
+
+ KnotVectorType knots;
+ Eigen::ChordLengths(points, knots);
+
+ ArrayXXd derivatives = ArrayXXd::Random(dimension, numPoints);
+ VectorXd derivativeIndices(numPoints);
+
+ for (Eigen::DenseIndex i = 0; i < numPoints; ++i)
+ derivativeIndices(i) = static_cast<double>(i);
+
+ const Spline2d spline = SplineFitting<Spline2d>::InterpolateWithDerivatives(
+ points, derivatives, derivativeIndices, degree);
+
+ for (Eigen::DenseIndex i = 0; i < points.cols(); ++i)
+ {
+ PointType point = spline(knots(i));
+ PointType referencePoint = points.col(i);
+ VERIFY_IS_APPROX(point, referencePoint);
+ PointType derivative = spline.derivatives(knots(i), 1).col(1);
+ PointType referenceDerivative = derivatives.col(i);
+ VERIFY_IS_APPROX(derivative, referenceDerivative);
+ }
+}
+
+EIGEN_DECLARE_TEST(splines)
+{
+ for (int i = 0; i < g_repeat; ++i)
+ {
+ CALL_SUBTEST( eval_spline3d() );
+ CALL_SUBTEST( eval_spline3d_onbrks() );
+ CALL_SUBTEST( eval_closed_spline2d() );
+ CALL_SUBTEST( check_global_interpolation2d() );
+ CALL_SUBTEST( check_global_interpolation_with_derivatives2d() );
+ }
+}
